LMFDB - Embedded newform 189.2.v.a.43.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(22,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 0]))

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

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

chi := DirichletCharacter("189.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.v (of order $9$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			43.7
Character	$\chi$	$=$	189.43
Dual form			189.2.v.a.22.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.969537 + 0.813538i) q^{2} +(-0.430185 - 1.67778i) q^{3} +(-0.0691389 - 0.392106i) q^{4} +(-0.855069 - 0.311220i) q^{5} +(0.947857 - 1.97664i) q^{6} +(0.173648 - 0.984808i) q^{7} +(1.51760 - 2.62856i) q^{8} +(-2.62988 + 1.44351i) q^{9} +O(q^{10})$	\(q+(0.969537 + 0.813538i) q^{2} +(-0.430185 - 1.67778i) q^{3} +(-0.0691389 - 0.392106i) q^{4} +(-0.855069 - 0.311220i) q^{5} +(0.947857 - 1.97664i) q^{6} +(0.173648 - 0.984808i) q^{7} +(1.51760 - 2.62856i) q^{8} +(-2.62988 + 1.44351i) q^{9} +(-0.575832 - 0.997370i) q^{10} +(5.60170 - 2.03885i) q^{11} +(-0.628125 + 0.284678i) q^{12} +(-2.54437 + 2.13498i) q^{13} +(0.969537 - 0.813538i) q^{14} +(-0.154320 + 1.56850i) q^{15} +(2.86152 - 1.04151i) q^{16} +(0.518461 + 0.898001i) q^{17} +(-3.72412 - 0.739974i) q^{18} +(-1.02967 + 1.78343i) q^{19} +(-0.0629126 + 0.356795i) q^{20} +(-1.72699 + 0.132306i) q^{21} +(7.08973 + 2.58045i) q^{22} +(0.554384 + 3.14407i) q^{23} +(-5.06299 - 1.41543i) q^{24} +(-3.19594 - 2.68171i) q^{25} -4.20376 q^{26} +(3.55322 + 3.79139i) q^{27} -0.398155 q^{28} +(5.59972 + 4.69872i) q^{29} +(-1.42565 + 1.39517i) q^{30} +(1.21241 + 6.87590i) q^{31} +(-2.08266 - 0.758027i) q^{32} +(-5.83050 - 8.52132i) q^{33} +(-0.227891 + 1.29243i) q^{34} +(-0.454973 + 0.788036i) q^{35} +(0.747836 + 0.931390i) q^{36} +(1.93726 + 3.35543i) q^{37} +(-2.44919 + 0.891432i) q^{38} +(4.67658 + 3.35046i) q^{39} +(-2.11571 + 1.77529i) q^{40} +(4.36990 - 3.66678i) q^{41} +(-1.78202 - 1.27670i) q^{42} +(-4.17077 + 1.51804i) q^{43} +(-1.18674 - 2.05550i) q^{44} +(2.69798 - 0.415829i) q^{45} +(-2.02032 + 3.49930i) q^{46} +(1.09019 - 6.18276i) q^{47} +(-2.97840 - 4.35295i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(-0.916906 - 5.20003i) q^{50} +(1.28361 - 1.25617i) q^{51} +(1.01306 + 0.850054i) q^{52} +1.64075 q^{53} +(0.360545 + 6.56657i) q^{54} -5.42437 q^{55} +(-2.32510 - 1.95099i) q^{56} +(3.43515 + 0.960346i) q^{57} +(1.60654 + 9.11117i) q^{58} +(-9.01389 - 3.28079i) q^{59} +(0.625687 - 0.0479343i) q^{60} +(2.19228 - 12.4331i) q^{61} +(-4.41833 + 7.65277i) q^{62} +(0.964905 + 2.84059i) q^{63} +(-4.44770 - 7.70364i) q^{64} +(2.84006 - 1.03370i) q^{65} +(1.27953 - 13.0051i) q^{66} +(-7.72379 + 6.48103i) q^{67} +(0.316266 - 0.265378i) q^{68} +(5.03657 - 2.28267i) q^{69} +(-1.08221 + 0.393892i) q^{70} +(-2.11115 - 3.65661i) q^{71} +(-0.196759 + 9.10348i) q^{72} +(2.29380 - 3.97297i) q^{73} +(-0.851527 + 4.82925i) q^{74} +(-3.12447 + 6.51571i) q^{75} +(0.770485 + 0.280434i) q^{76} +(-1.03515 - 5.87064i) q^{77} +(1.80839 + 7.05297i) q^{78} +(11.0138 + 9.24166i) q^{79} -2.77093 q^{80} +(4.83256 - 7.59252i) q^{81} +7.21984 q^{82} +(13.1807 + 11.0599i) q^{83} +(0.171280 + 0.668016i) q^{84} +(-0.163844 - 0.929208i) q^{85} +(-5.27869 - 1.92129i) q^{86} +(5.47450 - 11.4164i) q^{87} +(3.14189 - 17.8186i) q^{88} +(-0.379514 + 0.657337i) q^{89} +(2.95408 + 1.79175i) q^{90} +(1.66072 + 2.87646i) q^{91} +(1.19448 - 0.434755i) q^{92} +(11.0147 - 4.99205i) q^{93} +(6.08689 - 5.10751i) q^{94} +(1.43548 - 1.20451i) q^{95} +(-0.375872 + 3.82034i) q^{96} +(-9.76000 + 3.55235i) q^{97} +(-0.632820 - 1.09608i) q^{98} +(-11.7887 + 13.4480i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 3 q^{3} - 3 q^{5} - 27 q^{8} - 9 q^{9}+O(q^{10}) $ 54 * q - 3 * q^3 - 3 * q^5 - 27 * q^8 - 9 * q^9	$ 54 q - 3 q^{3} - 3 q^{5} - 27 q^{8} - 9 q^{9} - 6 q^{11} + 24 q^{12} - 9 q^{13} - 9 q^{15} - 30 q^{17} - 27 q^{18} - 12 q^{20} - 3 q^{21} - 9 q^{22} - 12 q^{23} + 36 q^{24} + 27 q^{25} + 18 q^{26} + 63 q^{27} + 54 q^{28} + 6 q^{29} - 72 q^{30} - 9 q^{31} - 9 q^{32} - 36 q^{33} - 9 q^{34} - 12 q^{35} + 54 q^{38} + 12 q^{39} - 45 q^{40} - 15 q^{41} - 18 q^{42} - 9 q^{43} - 42 q^{44} - 9 q^{45} - 45 q^{47} - 93 q^{48} + 18 q^{50} + 72 q^{51} - 63 q^{52} + 132 q^{53} + 54 q^{54} - 9 q^{56} + 3 q^{57} - 27 q^{58} - 9 q^{60} - 36 q^{62} - 9 q^{63} - 27 q^{64} + 66 q^{65} + 153 q^{66} + 45 q^{67} + 87 q^{68} - 72 q^{71} - 45 q^{72} - 72 q^{74} - 39 q^{75} + 54 q^{76} + 3 q^{77} - 54 q^{78} - 36 q^{79} + 42 q^{80} + 27 q^{81} + 24 q^{83} - 12 q^{84} + 18 q^{85} - 90 q^{86} - 99 q^{87} + 54 q^{88} - 42 q^{89} - 9 q^{90} + 87 q^{92} + 93 q^{93} - 90 q^{94} + 12 q^{95} + 108 q^{96} - 18 q^{97} - 9 q^{98} - 117 q^{99}+O(q^{100}) $ 54 * q - 3 * q^3 - 3 * q^5 - 27 * q^8 - 9 * q^9 - 6 * q^11 + 24 * q^12 - 9 * q^13 - 9 * q^15 - 30 * q^17 - 27 * q^18 - 12 * q^20 - 3 * q^21 - 9 * q^22 - 12 * q^23 + 36 * q^24 + 27 * q^25 + 18 * q^26 + 63 * q^27 + 54 * q^28 + 6 * q^29 - 72 * q^30 - 9 * q^31 - 9 * q^32 - 36 * q^33 - 9 * q^34 - 12 * q^35 + 54 * q^38 + 12 * q^39 - 45 * q^40 - 15 * q^41 - 18 * q^42 - 9 * q^43 - 42 * q^44 - 9 * q^45 - 45 * q^47 - 93 * q^48 + 18 * q^50 + 72 * q^51 - 63 * q^52 + 132 * q^53 + 54 * q^54 - 9 * q^56 + 3 * q^57 - 27 * q^58 - 9 * q^60 - 36 * q^62 - 9 * q^63 - 27 * q^64 + 66 * q^65 + 153 * q^66 + 45 * q^67 + 87 * q^68 - 72 * q^71 - 45 * q^72 - 72 * q^74 - 39 * q^75 + 54 * q^76 + 3 * q^77 - 54 * q^78 - 36 * q^79 + 42 * q^80 + 27 * q^81 + 24 * q^83 - 12 * q^84 + 18 * q^85 - 90 * q^86 - 99 * q^87 + 54 * q^88 - 42 * q^89 - 9 * q^90 + 87 * q^92 + 93 * q^93 - 90 * q^94 + 12 * q^95 + 108 * q^96 - 18 * q^97 - 9 * q^98 - 117 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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 $

$2$	0.969537	+	0.813538i	0.685566	+	0.575258i	0.917627	−	0.397443i	$-0.130102\pi$
$2$	0.969537	+	0.813538i	0.685566	+	0.575258i	−0.232061	+	0.972701i	$0.574547\pi$
$3$	−0.430185	−	1.67778i	−0.248367	−	0.968666i
$3$	−0.430185	−	1.67778i	−0.248367	−	0.968666i
$4$	−0.0691389	−	0.392106i	−0.0345694	−	0.196053i
$5$	−0.855069	−	0.311220i	−0.382398	−	0.139182i	0.143666	−	0.989626i	$-0.454111\pi$
$5$	−0.855069	−	0.311220i	−0.382398	−	0.139182i	−0.526065	+	0.850445i	$0.676333\pi$
$6$	0.947857	−	1.97664i	0.386961	−	0.806960i
$7$	0.173648	−	0.984808i	0.0656328	−	0.372222i
$7$	0.173648	−	0.984808i	0.0656328	−	0.372222i
$8$	1.51760	−	2.62856i	0.536553	−	0.929337i
$9$	−2.62988	+	1.44351i	−0.876627	+	0.481170i
$10$	−0.575832	−	0.997370i	−0.182094	−	0.315396i
$11$	5.60170	−	2.03885i	1.68898	−	0.614737i	0.694479	−	0.719513i	$-0.255635\pi$
$11$	5.60170	−	2.03885i	1.68898	−	0.614737i	0.994496	+	0.104776i	$0.0334126\pi$
$12$	−0.628125	+	0.284678i	−0.181324	+	0.0821794i
$13$	−2.54437	+	2.13498i	−0.705683	+	0.592138i	−0.923384	−	0.383877i	$-0.874589\pi$
$13$	−2.54437	+	2.13498i	−0.705683	+	0.592138i	0.217701	+	0.976015i	$0.430144\pi$
$14$	0.969537	−	0.813538i	0.259120	−	0.217427i
$15$	−0.154320	+	1.56850i	−0.0398453	+	0.404984i
$16$	2.86152	−	1.04151i	0.715379	−	0.260377i
$17$	0.518461	+	0.898001i	0.125745	+	0.217797i	0.922024	−	0.387133i	$-0.126534\pi$
$17$	0.518461	+	0.898001i	0.125745	+	0.217797i	−0.796279	+	0.604930i	$0.793201\pi$
$18$	−3.72412	−	0.739974i	−0.877783	−	0.174414i
$19$	−1.02967	+	1.78343i	−0.236222	+	0.409148i	−0.959627	−	0.281276i	$-0.909242\pi$
$19$	−1.02967	+	1.78343i	−0.236222	+	0.409148i	0.723405	+	0.690424i	$0.242576\pi$
$20$	−0.0629126	+	0.356795i	−0.0140677	+	0.0797818i
$21$	−1.72699	+	0.132306i	−0.376860	+	0.0288715i
$22$	7.08973	+	2.58045i	1.51154	+	0.550154i
$23$	0.554384	+	3.14407i	0.115597	+	0.655584i	0.986453	+	0.164045i	$0.0524543\pi$
$23$	0.554384	+	3.14407i	0.115597	+	0.655584i	−0.870856	+	0.491539i	$0.836435\pi$
$24$	−5.06299	−	1.41543i	−1.03348	−	0.288924i
$25$	−3.19594	−	2.68171i	−0.639187	−	0.536342i
$26$	−4.20376			−0.824424
$27$	3.55322	+	3.79139i	0.683818	+	0.729652i
$28$	−0.398155			−0.0752442
$29$	5.59972	+	4.69872i	1.03984	+	0.872531i	0.991989	−	0.126323i	$-0.0403177\pi$
$29$	5.59972	+	4.69872i	1.03984	+	0.872531i	0.0478528	+	0.998854i	$0.484762\pi$
$30$	−1.42565	+	1.39517i	−0.260287	+	0.254722i
$31$	1.21241	+	6.87590i	0.217755	+	1.23495i	0.876062	+	0.482198i	$0.160162\pi$
$31$	1.21241	+	6.87590i	0.217755	+	1.23495i	−0.658308	+	0.752749i	$0.728727\pi$
$32$	−2.08266	−	0.758027i	−0.368166	−	0.134001i
$33$	−5.83050	−	8.52132i	−1.01496	−	1.48337i
$34$	−0.227891	+	1.29243i	−0.0390829	+	0.221650i
$35$	−0.454973	+	0.788036i	−0.0769044	+	0.133202i
$36$	0.747836	+	0.931390i	0.124639	+	0.155232i
$37$	1.93726	+	3.35543i	0.318483	+	0.551630i	0.980172	−	0.198149i	$-0.0634931\pi$
$37$	1.93726	+	3.35543i	0.318483	+	0.551630i	−0.661688	+	0.749779i	$0.730160\pi$
$38$	−2.44919	+	0.891432i	−0.397311	+	0.144609i
$39$	4.67658	+	3.35046i	0.748852	+	0.536503i
$40$	−2.11571	+	1.77529i	−0.334524	+	0.280699i
$41$	4.36990	−	3.66678i	0.682463	−	0.572654i	−0.234262	−	0.972174i	$-0.575267\pi$
$41$	4.36990	−	3.66678i	0.682463	−	0.572654i	0.916725	+	0.399519i	$0.130823\pi$
$42$	−1.78202	−	1.27670i	−0.274971	−	0.196999i
$43$	−4.17077	+	1.51804i	−0.636036	+	0.231498i	−0.639856	−	0.768494i	$-0.721006\pi$
$43$	−4.17077	+	1.51804i	−0.636036	+	0.231498i	0.00382025	+	0.999993i	$0.498784\pi$
$44$	−1.18674	−	2.05550i	−0.178908	−	0.309878i
$45$	2.69798	−	0.415829i	0.402191	−	0.0619881i
$46$	−2.02032	+	3.49930i	−0.297881	+	0.515944i
$47$	1.09019	−	6.18276i	0.159020	−	0.901849i	−0.795997	−	0.605300i	$-0.793053\pi$
$47$	1.09019	−	6.18276i	0.159020	−	0.901849i	0.955018	−	0.296549i	$-0.0958357\pi$
$48$	−2.97840	−	4.35295i	−0.429895	−	0.628294i
$49$	−0.939693	−	0.342020i	−0.134242	−	0.0488600i
$50$	−0.916906	−	5.20003i	−0.129670	−	0.735396i
$51$	1.28361	−	1.25617i	0.179742	−	0.175899i
$52$	1.01306	+	0.850054i	0.140486	+	0.117881i
$53$	1.64075			0.225374			0.112687	−	0.993631i	$-0.464054\pi$
$53$	1.64075			0.225374			0.112687	+	0.993631i	$0.464054\pi$
$54$	0.360545	+	6.56657i	0.0490640	+	0.893597i
$55$	−5.42437			−0.731421
$56$	−2.32510	−	1.95099i	−0.310704	−	0.260712i
$57$	3.43515	+	0.960346i	0.454997	+	0.127201i
$58$	1.60654	+	9.11117i	0.210950	+	1.19636i
$59$	−9.01389	−	3.28079i	−1.17351	−	0.427122i	−0.319604	−	0.947551i	$-0.603550\pi$
$59$	−9.01389	−	3.28079i	−1.17351	−	0.427122i	−0.853905	+	0.520429i	$0.825772\pi$
$60$	0.625687	−	0.0479343i	0.0807759	−	0.00618829i
$61$	2.19228	−	12.4331i	0.280693	−	1.59189i	−0.439583	−	0.898202i	$-0.644874\pi$
$61$	2.19228	−	12.4331i	0.280693	−	1.59189i	0.720276	−	0.693687i	$-0.244015\pi$
$62$	−4.41833	+	7.65277i	−0.561128	+	0.971903i
$63$	0.964905	+	2.84059i	0.121567	+	0.357881i
$64$	−4.44770	−	7.70364i	−0.555962	−	0.962954i
$65$	2.84006	−	1.03370i	0.352267	−	0.128215i
$66$	1.27953	−	13.0051i	0.157500	−	1.60081i
$67$	−7.72379	+	6.48103i	−0.943612	+	0.791784i	−0.978210	−	0.207617i	$-0.933429\pi$
$67$	−7.72379	+	6.48103i	−0.943612	+	0.791784i	0.0345986	+	0.999401i	$0.488985\pi$
$68$	0.316266	−	0.265378i	0.0383529	−	0.0321819i
$69$	5.03657	−	2.28267i	0.606331	−	0.274801i
$70$	−1.08221	+	0.393892i	−0.129349	+	0.0470791i
$71$	−2.11115	−	3.65661i	−0.250547	−	0.433960i	0.713130	−	0.701032i	$-0.247277\pi$
$71$	−2.11115	−	3.65661i	−0.250547	−	0.433960i	−0.963676	+	0.267072i	$0.913944\pi$
$72$	−0.196759	+	9.10348i	−0.0231883	+	1.07286i
$73$	2.29380	−	3.97297i	0.268469	−	0.465001i	−0.699998	−	0.714145i	$-0.746816\pi$
$73$	2.29380	−	3.97297i	0.268469	−	0.465001i	0.968467	+	0.249144i	$0.0801491\pi$
$74$	−0.851527	+	4.82925i	−0.0989880	+	0.561389i
$75$	−3.12447	+	6.51571i	−0.360783	+	0.752369i
$76$	0.770485	+	0.280434i	0.0883807	+	0.0321680i
$77$	−1.03515	−	5.87064i	−0.117966	−	0.669021i
$78$	1.80839	+	7.05297i	0.204760	+	0.798592i
$79$	11.0138	+	9.24166i	1.23915	+	1.03977i	0.997590	+	0.0693810i	$0.0221024\pi$
$79$	11.0138	+	9.24166i	1.23915	+	1.03977i	0.241557	+	0.970387i	$0.422342\pi$
$80$	−2.77093			−0.309800
$81$	4.83256	−	7.59252i	0.536951	−	0.843613i
$82$	7.21984			0.797298
$83$	13.1807	+	11.0599i	1.44677	+	1.21399i	0.934894	+	0.354927i	$0.115494\pi$
$83$	13.1807	+	11.0599i	1.44677	+	1.21399i	0.511878	+	0.859058i	$0.328950\pi$
$84$	0.171280	+	0.668016i	0.0186882	+	0.0728865i
$85$	−0.163844	−	0.929208i	−0.0177714	−	0.100787i
$86$	−5.27869	−	1.92129i	−0.569216	−	0.207178i
$87$	5.47450	−	11.4164i	0.586928	−	1.22397i
$88$	3.14189	−	17.8186i	0.334927	−	1.89947i
$89$	−0.379514	+	0.657337i	−0.0402284	+	0.0696776i	−0.885439	−	0.464756i	$-0.846142\pi$
$89$	−0.379514	+	0.657337i	−0.0402284	+	0.0696776i	0.845210	+	0.534434i	$0.179475\pi$
$90$	2.95408	+	1.79175i	0.311388	+	0.188867i
$91$	1.66072	+	2.87646i	0.174091	+	0.301535i
$92$	1.19448	−	0.434755i	0.124533	−	0.0453263i
$93$	11.0147	−	4.99205i	1.14217	−	0.517652i
$94$	6.08689	−	5.10751i	0.627815	−	0.526799i
$95$	1.43548	−	1.20451i	0.147277	−	0.123580i
$96$	−0.375872	+	3.82034i	−0.0383623	+	0.389911i
$97$	−9.76000	+	3.55235i	−0.990978	+	0.360686i	−0.786099	−	0.618101i	$-0.787902\pi$
$97$	−9.76000	+	3.55235i	−0.990978	+	0.360686i	−0.204879	+	0.978787i	$0.565680\pi$
$98$	−0.632820	−	1.09608i	−0.0639245	−	0.110720i
$99$	−11.7887	+	13.4480i	−1.18481	+	1.35158i
$100$	−0.830551	+	1.43856i	−0.0830551	+	0.143856i
$101$	−2.50505	+	14.2068i	−0.249262	+	1.41363i	0.561122	+	0.827733i	$0.310370\pi$
$101$	−2.50505	+	14.2068i	−0.249262	+	1.41363i	−0.810384	+	0.585899i	$0.800741\pi$
$102$	2.26645	−	0.173634i	0.224412	−	0.0171924i
$103$	2.58428	+	0.940602i	0.254637	+	0.0926803i	0.466185	−	0.884687i	$-0.345628\pi$
$103$	2.58428	+	0.940602i	0.254637	+	0.0926803i	−0.211548	+	0.977368i	$0.567850\pi$
$104$	1.75059	+	9.92810i	0.171660	+	0.973530i
$105$	1.51787	+	0.424343i	0.148129	+	0.0414116i
$106$	1.59077	+	1.33481i	0.154509	+	0.129648i
$107$	−4.35433			−0.420949			−0.210475	−	0.977599i	$-0.567501\pi$
$107$	−4.35433			−0.420949			−0.210475	+	0.977599i	$0.567501\pi$
$108$	1.24096	−	1.65537i	0.119411	−	0.159288i
$109$	−16.1963			−1.55132			−0.775660	−	0.631151i	$-0.782583\pi$
$109$	−16.1963			−1.55132			−0.775660	+	0.631151i	$0.782583\pi$
$110$	−5.25912	−	4.41293i	−0.501438	−	0.420756i
$111$	4.79629	−	4.69375i	0.455244	−	0.445511i
$112$	−0.528787	−	2.99890i	−0.0499657	−	0.283369i
$113$	−5.39706	−	1.96437i	−0.507713	−	0.184792i	0.0754469	−	0.997150i	$-0.475962\pi$
$113$	−5.39706	−	1.96437i	−0.507713	−	0.184792i	−0.583160	+	0.812357i	$0.698184\pi$
$114$	2.54923	+	3.72572i	0.238757	+	0.348945i
$115$	0.504459	−	2.86093i	0.0470411	−	0.266783i
$116$	1.45524	−	2.52055i	0.135116	−	0.234027i
$117$	3.60954	−	9.28759i	0.333702	−	0.858638i
$118$	−6.07025	−	10.5140i	−0.558812	−	0.967891i
$119$	0.974388	−	0.354648i	0.0893220	−	0.0325105i
$120$	3.88870	+	2.78599i	0.354988	+	0.254325i
$121$	18.7956	−	15.7714i	1.70869	−	1.43376i
$122$	12.2403	−	10.2708i	1.10818	−	0.929874i
$123$	−8.03190	−	5.75433i	−0.724212	−	0.518850i
$124$	2.61226	−	0.950784i	0.234588	−	0.0853829i
$125$	4.17301	+	7.22786i	0.373245	+	0.646480i
$126$	−1.37542	+	3.53904i	−0.122532	+	0.315283i
$127$	−1.26783	+	2.19594i	−0.112501	+	0.194858i	−0.916778	−	0.399397i	$-0.869220\pi$
$127$	−1.26783	+	2.19594i	−0.112501	+	0.194858i	0.804277	+	0.594255i	$0.202553\pi$
$128$	1.18527	−	6.72202i	0.104764	−	0.594149i
$129$	4.34113	+	6.34459i	0.382215	+	0.558610i
$130$	3.59450	+	1.30829i	0.315258	+	0.114745i
$131$	0.397749	+	2.25575i	0.0347515	+	0.197085i	0.997241	−	0.0742340i	$-0.0236512\pi$
$131$	0.397749	+	2.25575i	0.0347515	+	0.197085i	−0.962489	+	0.271319i	$0.912540\pi$
$132$	−2.93815	+	2.87533i	−0.255733	+	0.250265i
$133$	1.57754	+	1.32371i	0.136790	+	0.114780i
$134$	−12.7611			−1.10239
$135$	−1.85830	−	4.34773i	−0.159937	−	0.374193i
$136$	3.14727			0.269876
$137$	−8.44087	−	7.08273i	−0.721152	−	0.605118i	0.206552	−	0.978436i	$-0.433776\pi$
$137$	−8.44087	−	7.08273i	−0.721152	−	0.605118i	−0.927704	+	0.373317i	$0.878220\pi$
$138$	6.74017	+	1.88431i	0.573761	+	0.160403i
$139$	−3.71019	−	21.0415i	−0.314694	−	1.78472i	−0.573928	−	0.818906i	$-0.694581\pi$
$139$	−3.71019	−	21.0415i	−0.314694	−	1.78472i	0.259233	−	0.965815i	$-0.416530\pi$
$140$	0.340450	+	0.123914i	0.0287733	+	0.0104726i
$141$	−10.8423	+	0.830635i	−0.913086	+	0.0699521i
$142$	0.927958	−	5.26271i	0.0778725	−	0.441637i
$143$	−9.89990	+	17.1471i	−0.827871	+	1.43392i
$144$	−6.02203	+	6.86967i	−0.501836	+	0.572472i
$145$	−3.32581	−	5.76047i	−0.276194	−	0.478381i
$146$	5.45608	−	1.98585i	0.451549	−	0.164350i
$147$	−0.169593	+	1.72373i	−0.0139878	+	0.142171i
$148$	1.18175	−	0.991602i	0.0971389	−	0.0815092i
$149$	−6.07567	+	5.09809i	−0.497738	+	0.417652i	−0.856790	−	0.515666i	$-0.827545\pi$
$149$	−6.07567	+	5.09809i	−0.497738	+	0.417652i	0.359052	+	0.933318i	$0.383100\pi$
$150$	−8.33006	+	3.77534i	−0.680147	+	0.308255i
$151$	4.36436	−	1.58850i	0.355166	−	0.129270i	−0.158274	−	0.987395i	$-0.550593\pi$
$151$	4.36436	−	1.58850i	0.355166	−	0.129270i	0.513440	+	0.858125i	$0.328371\pi$
$152$	3.12524	+	5.41308i	0.253491	+	0.439059i
$153$	−2.65976	−	1.61323i	−0.215029	−	0.130422i
$154$	3.77237	−	6.53393i	0.303986	−	0.526519i
$155$	1.10322	−	6.25669i	0.0886130	−	0.502549i
$156$	0.990402	−	2.06536i	0.0792957	−	0.165361i
$157$	−20.5332	−	7.47348i	−1.63873	−	0.596449i	−0.651913	−	0.758294i	$-0.726033\pi$
$157$	−20.5332	−	7.47348i	−1.63873	−	0.596449i	−0.986816	+	0.161845i	$0.948255\pi$
$158$	3.15982	+	17.9203i	0.251382	+	1.42566i
$159$	−0.705825	−	2.75281i	−0.0559755	−	0.218312i
$160$	1.54491	+	1.29633i	0.122136	+	0.102484i
$161$	3.19257			0.251610
$162$	10.8621	−	3.42975i	0.853411	−	0.269467i
$163$	−13.0830			−1.02474			−0.512369	−	0.858765i	$-0.671232\pi$
$163$	−13.0830			−1.02474			−0.512369	+	0.858765i	$0.671232\pi$
$164$	−1.73990	−	1.45995i	−0.135863	−	0.114003i
$165$	2.33348	+	9.10089i	0.181661	+	0.708503i
$166$	3.78151	+	21.4460i	0.293502	+	1.66453i
$167$	−3.36251	−	1.22386i	−0.260199	−	0.0947047i	0.208627	−	0.977995i	$-0.433101\pi$
$167$	−3.36251	−	1.22386i	−0.260199	−	0.0947047i	−0.468826	+	0.883291i	$0.655323\pi$
$168$	−2.27311	+	4.74029i	−0.175374	+	0.365721i
$169$	−0.341739	+	1.93810i	−0.0262876	+	0.149085i
$170$	0.597093	−	1.03419i	0.0457949	−	0.0793191i
$171$	0.133498	−	6.17655i	0.0102088	−	0.472333i
$172$	0.883593	+	1.53043i	0.0673733	+	0.116694i
$173$	−4.02819	+	1.46614i	−0.306258	+	0.111469i	−0.490577	−	0.871398i	$-0.663214\pi$
$173$	−4.02819	+	1.46614i	−0.306258	+	0.111469i	0.184320	+	0.982866i	$0.440992\pi$
$174$	14.5954	−	6.61491i	1.10648	−	0.501475i
$175$	−3.19594	+	2.68171i	−0.241590	+	0.202718i
$176$	13.9059	−	11.6684i	1.04819	−	0.879540i
$177$	−1.62680	+	16.5347i	−0.122278	+	1.24282i
$178$	−0.902721	+	0.328564i	−0.0676618	+	0.0246269i
$179$	8.76305	+	15.1780i	0.654981	+	1.13446i	0.981899	+	0.189408i	$0.0606568\pi$
$179$	8.76305	+	15.1780i	0.654981	+	1.13446i	−0.326917	+	0.945053i	$0.606010\pi$
$180$	−0.349584	−	1.02914i	−0.0260565	−	0.0767079i
$181$	−0.687118	+	1.19012i	−0.0510731	+	0.0884611i	−0.890432	−	0.455117i	$-0.849597\pi$
$181$	−0.687118	+	1.19012i	−0.0510731	+	0.0884611i	0.839359	+	0.543578i	$0.182931\pi$
$182$	−0.729974	+	4.13989i	−0.0541093	+	0.306869i
$183$	−21.8030	+	1.67034i	−1.61172	+	0.123475i
$184$	9.10572	+	3.31421i	0.671282	+	0.244327i
$185$	−0.612214	−	3.47204i	−0.0450109	−	0.255269i
$186$	14.7404	+	4.12087i	1.08082	+	0.302157i
$187$	4.73515	+	3.97326i	0.346269	+	0.290554i
$188$	−2.49967			−0.182307
$189$	4.35080	−	2.84087i	0.316474	−	0.206643i
$190$	2.37166			0.172058
$191$	5.23350	+	4.39143i	0.378683	+	0.317753i	0.812185	−	0.583400i	$-0.198278\pi$
$191$	5.23350	+	4.39143i	0.378683	+	0.317753i	−0.433502	+	0.901152i	$0.642722\pi$
$192$	−11.0117	+	10.7762i	−0.794698	+	0.777708i
$193$	−0.457288	−	2.59341i	−0.0329163	−	0.186678i	0.963916	−	0.266205i	$-0.0857699\pi$
$193$	−0.457288	−	2.59341i	−0.0329163	−	0.186678i	−0.996833	+	0.0795276i	$0.974659\pi$
$194$	−12.3526	−	4.49600i	−0.886868	−	0.322794i
$195$	−2.95607	−	4.32032i	−0.211689	−	0.309384i
$196$	−0.0691389	+	0.392106i	−0.00493849	+	0.0280076i
$197$	−0.219915	+	0.380905i	−0.0156683	+	0.0271383i	−0.873753	−	0.486369i	$-0.838321\pi$
$197$	−0.219915	+	0.380905i	−0.0156683	+	0.0271383i	0.858085	+	0.513508i	$0.171654\pi$
$198$	−22.3701	+	3.44781i	−1.58977	+	0.245025i
$199$	10.7197	+	18.5671i	0.759899	+	1.31618i	0.942902	+	0.333071i	$0.108085\pi$
$199$	10.7197	+	18.5671i	0.759899	+	1.31618i	−0.183003	+	0.983112i	$0.558582\pi$
$200$	−11.8992	+	4.33095i	−0.841400	+	0.306245i
$201$	14.1964	+	10.1708i	1.00134	+	0.717391i
$202$	−13.9865	+	11.7361i	−0.984089	+	0.825748i
$203$	5.59972	−	4.69872i	0.393023	−	0.329786i
$204$	−0.581299	−	0.416462i	−0.0406991	−	0.0291582i
$205$	−4.87773	+	1.77535i	−0.340676	+	0.123996i
$206$	1.74034	+	3.01436i	0.121255	+	0.210020i
$207$	−5.99646	−	7.46828i	−0.416783	−	0.519081i
$208$	−5.05717	+	8.75928i	−0.350652	+	0.607347i
$209$	−2.13172	+	12.0896i	−0.147454	+	0.836255i
$210$	1.12641	+	1.64626i	0.0777299	+	0.113603i
$211$	−9.87861	−	3.59552i	−0.680071	−	0.247526i	−0.0211932	−	0.999775i	$-0.506747\pi$
$211$	−9.87861	−	3.59552i	−0.680071	−	0.247526i	−0.658878	+	0.752250i	$0.728969\pi$
$212$	−0.113439	−	0.643347i	−0.00779106	−	0.0441853i
$213$	−5.22680	+	5.11505i	−0.358135	+	0.350478i
$214$	−4.22168	−	3.54241i	−0.288588	−	0.242154i
$215$	4.03874			0.275440
$216$	15.3583	−	3.58606i	1.04500	−	0.244000i
$217$	6.98197			0.473967
$218$	−15.7029	−	13.1763i	−1.06353	−	0.892409i
$219$	−7.65253	−	2.13937i	−0.517110	−	0.144565i
$220$	0.375035	+	2.12693i	0.0252848	+	0.143397i
$221$	−3.23638	−	1.17794i	−0.217702	−	0.0792371i
$222$	8.46872	−	0.648795i	0.568383	−	0.0435442i
$223$	−2.24722	+	12.7446i	−0.150485	+	0.853441i	0.812314	+	0.583221i	$0.198208\pi$
$223$	−2.24722	+	12.7446i	−0.150485	+	0.853441i	−0.962798	+	0.270220i	$0.912903\pi$
$224$	−1.10816	+	1.91939i	−0.0740421	+	0.128245i
$225$	12.2760	+	2.43922i	0.818401	+	0.162614i
$226$	−3.63456	−	6.29524i	−0.241767	−	0.418753i
$227$	−5.72511	+	2.08377i	−0.379989	+	0.138305i	−0.524951	−	0.851133i	$-0.675916\pi$
$227$	−5.72511	+	2.08377i	−0.379989	+	0.138305i	0.144962	+	0.989437i	$0.453694\pi$
$228$	0.139055	−	1.41334i	0.00920913	−	0.0936009i
$229$	15.3246	−	12.8589i	1.01268	−	0.849738i	0.0239882	−	0.999712i	$-0.492364\pi$
$229$	15.3246	−	12.8589i	1.01268	−	0.849738i	0.988690	+	0.149974i	$0.0479191\pi$
$230$	2.81657	−	2.36338i	0.185719	−	0.155837i
$231$	−9.40432	+	4.26221i	−0.618759	+	0.280433i
$232$	20.8490	−	7.58842i	1.36881	−	0.498204i
$233$	−13.5795	−	23.5205i	−0.889625	−	1.54088i	−0.840319	−	0.542092i	$-0.817632\pi$
$233$	−13.5795	−	23.5205i	−0.889625	−	1.54088i	−0.0493064	−	0.998784i	$-0.515701\pi$
$234$	11.0554	−	6.06816i	0.722713	−	0.396688i
$235$	−2.85638	+	4.94740i	−0.186330	+	0.322733i
$236$	−0.663206	+	3.76123i	−0.0431711	+	0.244835i
$237$	10.7675	−	22.4543i	0.699424	−	1.45856i
$238$	1.23322	+	0.448857i	0.0799381	+	0.0290951i
$239$	1.97250	+	11.1866i	0.127591	+	0.723602i	0.979735	+	0.200296i	$0.0641904\pi$
$239$	1.97250	+	11.1866i	0.127591	+	0.723602i	−0.852145	+	0.523306i	$0.824698\pi$
$240$	1.19201	+	4.64901i	0.0769440	+	0.300092i
$241$	−5.06797	−	4.25253i	−0.326457	−	0.273930i	0.464798	−	0.885417i	$-0.346127\pi$
$241$	−5.06797	−	4.25253i	−0.326457	−	0.273930i	−0.791254	+	0.611487i	$0.790572\pi$
$242$	31.0536			1.99620
$243$	−14.8175	−	4.84179i	−0.950540	−	0.310601i
$244$	−5.02665			−0.321798
$245$	0.697058	+	0.584902i	0.0445334	+	0.0373680i
$246$	−3.10586	−	12.1133i	−0.198023	−	0.772315i
$247$	−1.18775	−	6.73605i	−0.0755745	−	0.428604i
$248$	19.9137	+	7.24798i	1.26452	+	0.460247i
$249$	12.8860	−	26.8721i	0.816616	−	1.70295i
$250$	−1.83426	+	10.4026i	−0.116008	+	0.657917i
$251$	8.13620	−	14.0923i	0.513552	−	0.889499i	−0.486324	−	0.873778i	$-0.661663\pi$
$251$	8.13620	−	14.0923i	0.513552	−	0.889499i	0.999876	−	0.0157201i	$-0.00500406\pi$
$252$	1.04710	−	0.574740i	0.0659611	−	0.0362052i
$253$	9.51578	+	16.4818i	0.598252	+	1.03620i
$254$	−3.01568	+	1.09762i	−0.189221	+	0.0688707i
$255$	−1.48852	+	0.674625i	−0.0932148	+	0.0422467i
$256$	−7.01074	+	5.88271i	−0.438172	+	0.367670i
$257$	10.2219	−	8.57718i	0.637624	−	0.535030i	−0.265664	−	0.964066i	$-0.585591\pi$
$257$	10.2219	−	8.57718i	0.637624	−	0.535030i	0.903287	+	0.429036i	$0.141147\pi$
$258$	−0.952682	+	9.68298i	−0.0593114	+	0.602836i
$259$	3.64086	−	1.32516i	0.226232	−	0.0823417i
$260$	−0.601679	−	1.04214i	−0.0373145	−	0.0646306i
$261$	−21.5093	−	4.27384i	−1.33139	−	0.264544i
$262$	−1.44950	+	2.51061i	−0.0895505	+	0.155106i
$263$	3.92210	−	22.2433i	0.241847	−	1.37158i	−0.585855	−	0.810416i	$-0.699241\pi$
$263$	3.92210	−	22.2433i	0.241847	−	1.37158i	0.827702	−	0.561167i	$-0.189648\pi$
$264$	−31.2472	+	2.39387i	−1.92313	+	0.147332i
$265$	−1.40295	−	0.510633i	−0.0861827	−	0.0313679i
$266$	0.452592	+	2.56678i	0.0277502	+	0.157379i
$267$	1.26613	+	0.353964i	0.0774857	+	0.0216622i
$268$	3.07527	+	2.58045i	0.187852	+	0.157626i
$269$	1.28401			0.0782877			0.0391439	−	0.999234i	$-0.487537\pi$
$269$	1.28401			0.0782877			0.0391439	+	0.999234i	$0.487537\pi$
$270$	1.73535	−	5.72708i	0.105610	−	0.348539i
$271$	13.7466			0.835049			0.417525	−	0.908666i	$-0.362898\pi$
$271$	13.7466			0.835049			0.417525	+	0.908666i	$0.362898\pi$
$272$	2.41886	+	2.02966i	0.146665	+	0.123066i
$273$	4.11164	−	4.02373i	0.248848	−	0.243527i
$274$	−2.42166	−	13.7339i	−0.146298	−	0.829697i
$275$	−23.3703	−	8.50608i	−1.40928	−	0.512936i
$276$	−1.24327	−	1.81705i	−0.0748360	−	0.109373i
$277$	−1.61921	+	9.18301i	−0.0972891	+	0.551754i	0.896733	+	0.442572i	$0.145934\pi$
$277$	−1.61921	+	9.18301i	−0.0972891	+	0.551754i	−0.994022	+	0.109181i	$0.965177\pi$
$278$	13.5209	−	23.4189i	0.810931	−	1.40457i
$279$	−13.1139	−	16.3327i	−0.785109	−	0.977812i
$280$	1.38093	+	2.39185i	0.0825266	+	0.142940i
$281$	9.29228	−	3.38211i	0.554331	−	0.201760i	−0.0496387	−	0.998767i	$-0.515807\pi$
$281$	9.29228	−	3.38211i	0.554331	−	0.201760i	0.603970	+	0.797007i	$0.293585\pi$
$282$	−11.1878	−	8.01528i	−0.666221	−	0.477303i
$283$	−12.8295	+	10.7652i	−0.762635	+	0.639927i	−0.938811	−	0.344432i	$-0.888072\pi$
$283$	−12.8295	+	10.7652i	−0.762635	+	0.639927i	0.176176	+	0.984359i	$0.443627\pi$
$284$	−1.28782	+	1.08061i	−0.0764179	+	0.0641222i
$285$	−2.63841	−	1.89025i	−0.156286	−	0.111969i
$286$	−23.5482	+	8.57083i	−1.39243	+	0.506804i
$287$	−2.85225	−	4.94024i	−0.168363	−	0.291613i
$288$	6.57137	−	1.01282i	0.387222	−	0.0596810i
$289$	7.96240	−	13.7913i	0.468376	−	0.811251i
$290$	1.46187	−	8.29066i	0.0858438	−	0.486845i
$291$	10.1587	+	14.8470i	0.595511	+	0.870344i
$292$	−1.71642	−	0.624725i	−0.100446	−	0.0365593i
$293$	2.69578	+	15.2885i	0.157489	+	0.893167i	0.956475	+	0.291816i	$0.0942594\pi$
$293$	2.69578	+	15.2885i	0.157489	+	0.893167i	−0.798985	+	0.601351i	$0.794629\pi$
$294$	−1.56674	+	1.53325i	−0.0913744	+	0.0894208i
$295$	6.68645	+	5.61060i	0.389300	+	0.326662i
$296$	11.7599			0.683533
$297$	27.6341	+	13.9937i	1.60350	+	0.811997i
$298$	−10.0381			−0.581490
$299$	−8.12310	−	6.81609i	−0.469771	−	0.394185i
$300$	2.77087	+	0.774636i	0.159976	+	0.0447236i
$301$	0.770727	+	4.37101i	0.0444240	+	0.251941i
$302$	5.52370	+	2.01046i	0.317853	+	0.115689i
$303$	24.9135	−	1.90864i	1.43125	−	0.109649i
$304$	−1.08895	+	6.17573i	−0.0624555	+	0.354202i
$305$	−5.74396	+	9.94883i	−0.328898	+	0.569669i
$306$	−1.26631	−	3.72791i	−0.0723902	−	0.213110i
$307$	−1.74046	−	3.01457i	−0.0993335	−	0.172051i	0.812075	−	0.583552i	$-0.198338\pi$
$307$	−1.74046	−	3.01457i	−0.0993335	−	0.172051i	−0.911409	+	0.411502i	$0.865004\pi$
$308$	−2.23034	+	0.811778i	−0.127086	+	0.0462554i
$309$	0.466403	−	4.74049i	0.0265328	−	0.269677i
$310$	6.15967	−	5.16858i	0.349846	−	0.293555i
$311$	10.6115	−	8.90413i	0.601725	−	0.504907i	−0.290275	−	0.956943i	$-0.593747\pi$
$311$	10.6115	−	8.90413i	0.601725	−	0.504907i	0.891999	+	0.452036i	$0.149302\pi$
$312$	15.9041	−	7.20802i	0.900391	−	0.408074i
$313$	−9.67485	+	3.52136i	−0.546855	+	0.199039i	−0.600649	−	0.799513i	$-0.705091\pi$
$313$	−9.67485	+	3.52136i	−0.546855	+	0.199039i	0.0537937	+	0.998552i	$0.482869\pi$
$314$	−13.8277	−	23.9504i	−0.780345	−	1.35160i
$315$	0.0589879	−	2.72920i	0.00332359	−	0.153773i
$316$	2.86223	−	4.95753i	0.161013	−	0.278883i
$317$	4.94275	−	28.0317i	0.277613	−	1.57442i	−0.452926	−	0.891548i	$-0.649620\pi$
$317$	4.94275	−	28.0317i	0.277613	−	1.57442i	0.730539	−	0.682871i	$-0.239269\pi$
$318$	1.55519	−	3.24317i	0.0872110	−	0.181868i
$319$	40.9479	+	14.9038i	2.29264	+	0.834454i
$320$	1.40556	+	7.97135i	0.0785734	+	0.445612i
$321$	1.87317	+	7.30560i	0.104550	+	0.407759i
$322$	3.09532	+	2.59728i	0.172495	+	0.144741i
$323$	−2.13537			−0.118815
$324$	−3.31119	−	1.36994i	−0.183955	−	0.0761077i
$325$	13.8571			0.768652
$326$	−12.6844	−	10.6435i	−0.702526	−	0.589489i
$327$	6.96738	+	27.1737i	0.385297	+	1.50271i
$328$	−3.00659	−	17.0512i	−0.166011	−	0.941497i
$329$	−5.89952	−	2.14725i	−0.325251	−	0.118382i
$330$	−5.14152	+	10.7220i	−0.283031	+	0.590228i
$331$	−4.67529	+	26.5149i	−0.256977	+	1.45739i	0.533969	+	0.845504i	$0.320700\pi$
$331$	−4.67529	+	26.5149i	−0.256977	+	1.45739i	−0.790946	+	0.611886i	$0.790411\pi$
$332$	3.42537	−	5.93291i	0.187991	−	0.325611i
$333$	−9.93836	−	6.02794i	−0.544619	−	0.330329i
$334$	−2.26443	−	3.92210i	−0.123904	−	0.214608i
$335$	8.62140	−	3.13793i	0.471037	−	0.171444i
$336$	−4.80401	+	2.17727i	−0.262080	+	0.118780i
$337$	3.56596	−	2.99220i	0.194250	−	0.162995i	−0.540475	−	0.841360i	$-0.681755\pi$
$337$	3.56596	−	2.99220i	0.194250	−	0.162995i	0.734725	+	0.678365i	$0.237311\pi$
$338$	−1.90805	+	1.60104i	−0.103784	+	0.0870852i
$339$	−0.974045	+	9.90012i	−0.0529029	+	0.537701i
$340$	−0.353020	+	0.128489i	−0.0191452	+	0.00696828i
$341$	20.8105	+	36.0448i	1.12695	+	1.95193i
$342$	5.15429	−	5.87979i	0.278712	−	0.317943i
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$	−2.33931	+	13.2669i	−0.126127	+	0.715303i
$345$	−5.01702	+	0.384357i	−0.270107	+	0.0206931i
$346$	−5.09824	−	1.85561i	−0.274083	−	0.0997581i
$347$	1.36919	+	7.76507i	0.0735020	+	0.416851i	0.999250	+	0.0387107i	$0.0123251\pi$
$347$	1.36919	+	7.76507i	0.0735020	+	0.416851i	−0.925748	+	0.378140i	$0.876564\pi$
$348$	−4.85494	−	1.35727i	−0.260252	−	0.0727572i
$349$	8.63445	+	7.24516i	0.462191	+	0.387825i	0.843937	−	0.536443i	$-0.180232\pi$
$349$	8.63445	+	7.24516i	0.462191	+	0.387825i	−0.381745	+	0.924268i	$0.624677\pi$
$350$	−5.28025			−0.282241
$351$	−17.1353	−	2.06063i	−0.914614	−	0.109988i
$352$	−13.2119			−0.704199
$353$	14.1108	+	11.8404i	0.751043	+	0.630200i	0.935779	−	0.352588i	$-0.114698\pi$
$353$	14.1108	+	11.8404i	0.751043	+	0.630200i	−0.184735	+	0.982788i	$0.559143\pi$
$354$	−15.0288	+	14.7075i	−0.798772	+	0.781694i
$355$	0.667165	+	3.78368i	0.0354095	+	0.200817i
$356$	0.283985	+	0.103362i	0.0150512	+	0.00547818i
$357$	−1.01419	−	1.48224i	−0.0536765	−	0.0784486i
$358$	−3.85182	+	21.8447i	−0.203575	+	1.15453i
$359$	9.58093	−	16.5947i	0.505662	−	0.875832i	−0.494316	−	0.869282i	$-0.664582\pi$
$359$	9.58093	−	16.5947i	0.505662	−	0.875832i	0.999979	−	0.00655044i	$-0.00208508\pi$
$360$	3.00142	−	7.72286i	0.158189	−	0.407031i
$361$	7.37958	+	12.7818i	0.388399	+	0.672726i
$362$	−1.63440	+	0.594871i	−0.0859019	+	0.0312657i
$363$	−34.5465	−	24.7503i	−1.81322	−	1.29905i
$364$	1.01306	−	0.850054i	0.0530985	−	0.0445550i
$365$	−3.19782	+	2.68329i	−0.167382	+	0.140450i
$366$	−22.4977	−	16.1181i	−1.17597	−	0.842507i
$367$	−5.88643	+	2.14249i	−0.307269	+	0.111837i	−0.491053	−	0.871130i	$-0.663388\pi$
$367$	−5.88643	+	2.14249i	−0.307269	+	0.111837i	0.183783	+	0.982967i	$0.441166\pi$
$368$	4.86095	+	8.41942i	0.253395	+	0.438892i
$369$	−6.19929	+	15.9512i	−0.322722	+	0.830385i
$370$	2.23107	−	3.86433i	0.115988	−	0.200897i
$371$	0.284913	−	1.61582i	0.0147919	−	0.0838893i
$372$	−2.71896	−	3.97378i	−0.140971	−	0.206031i
$373$	−18.0622	−	6.57411i	−0.935227	−	0.340395i	−0.170948	−	0.985280i	$-0.554683\pi$
$373$	−18.0622	−	6.57411i	−0.935227	−	0.340395i	−0.764279	+	0.644885i	$0.776905\pi$
$374$	1.35850	+	7.70445i	0.0702465	+	0.398388i
$375$	10.3316	−	10.1107i	0.533521	−	0.522114i
$376$	−14.5973	−	12.2486i	−0.752798	−	0.631673i
$377$	−24.2795			−1.25046
$378$	6.52942	+	0.785205i	0.335837	+	0.0403866i
$379$	30.6727			1.57555			0.787775	−	0.615963i	$-0.211233\pi$
$379$	30.6727			1.57555			0.787775	+	0.615963i	$0.211233\pi$
$380$	−0.571541	−	0.479580i	−0.0293195	−	0.0246019i
$381$	4.22970	+	1.18247i	0.216694	+	0.0605799i
$382$	1.50148	+	8.51530i	0.0768223	+	0.435681i
$383$	3.67776	+	1.33860i	0.187925	+	0.0683991i	0.434268	−	0.900783i	$-0.357007\pi$
$383$	3.67776	+	1.33860i	0.187925	+	0.0683991i	−0.246344	+	0.969183i	$0.579229\pi$
$384$	−11.7880	+	0.903083i	−0.601551	+	0.0460853i
$385$	−0.941931	+	5.34196i	−0.0480053	+	0.272251i
$386$	1.66648	−	2.88643i	0.0848216	−	0.146915i
$387$	8.77733	−	10.0128i	0.446177	−	0.508979i
$388$	2.06769	+	3.58135i	0.104971	+	0.181815i
$389$	−25.3344	+	9.22096i	−1.28450	+	0.467521i	−0.891919	−	0.452194i	$-0.850641\pi$
$389$	−25.3344	+	9.22096i	−1.28450	+	0.467521i	−0.392585	+	0.919716i	$0.628419\pi$
$390$	0.648724	−	6.59358i	0.0328494	−	0.333879i
$391$	−2.53595	+	2.12792i	−0.128249	+	0.107613i
$392$	−2.32510	+	1.95099i	−0.117435	+	0.0985399i
$393$	3.61354	−	1.63772i	0.182279	−	0.0826121i
$394$	−0.523096	+	0.190392i	−0.0263532	+	0.00959179i
$395$	−6.54135	−	11.3300i	−0.329131	−	0.570072i
$396$	6.08811	+	3.69264i	0.305939	+	0.185562i
$397$	−1.99273	+	3.45151i	−0.100012	+	0.173226i	−0.911689	−	0.410880i	$-0.865222\pi$
$397$	−1.99273	+	3.45151i	−0.100012	+	0.173226i	0.811677	+	0.584106i	$0.198555\pi$
$398$	−4.71187	+	26.7223i	−0.236184	+	1.33947i
$399$	1.54226	−	3.21620i	0.0772098	−	0.161012i
$400$	−11.9382	−	4.34517i	−0.596912	−	0.217258i
$401$	5.30540	+	30.0884i	0.264939	+	1.50254i	0.769209	+	0.638997i	$0.220650\pi$
$401$	5.30540	+	30.0884i	0.264939	+	1.50254i	−0.504270	+	0.863546i	$0.668238\pi$
$402$	5.48961	+	21.4102i	0.273797	+	1.06785i
$403$	−17.7647	−	14.9064i	−0.884925	−	0.742540i
$404$	5.74378			0.285764
$405$	−6.49511	+	4.98814i	−0.322745	+	0.247863i
$406$	9.25172			0.459155
$407$	17.6932	+	14.8463i	0.877018	+	0.735905i
$408$	−1.35391	−	5.28042i	−0.0670283	−	0.261420i
$409$	−5.57941	−	31.6424i	−0.275884	−	1.56462i	−0.736140	−	0.676830i	$-0.763353\pi$
$409$	−5.57941	−	31.6424i	−0.275884	−	1.56462i	0.460256	−	0.887786i	$-0.347758\pi$
$410$	−6.17346	−	2.24695i	−0.304885	−	0.110969i
$411$	−8.25212	+	17.2088i	−0.407047	+	0.848847i
$412$	0.190141	−	1.07835i	0.00936759	−	0.0531263i
$413$	−4.79619	+	8.30724i	−0.236005	+	0.408773i
$414$	0.261938	−	12.1191i	0.0128736	−	0.595622i
$415$	−7.82835	−	13.5591i	−0.384279	−	0.665590i
$416$	6.91745	−	2.51774i	0.339156	−	0.123443i
$417$	−33.7070	+	15.2766i	−1.65064	+	0.748100i
$418$	−11.9021	+	9.98707i	−0.582152	+	0.488483i
$419$	−3.87959	+	3.25537i	−0.189531	+	0.159035i	−0.732615	−	0.680643i	$-0.761701\pi$
$419$	−3.87959	+	3.25537i	−0.189531	+	0.159035i	0.543085	+	0.839678i	$0.317256\pi$
$420$	0.0614433	−	0.624505i	0.00299813	−	0.0304727i
$421$	−10.0867	+	3.67125i	−0.491594	+	0.178926i	−0.575909	−	0.817514i	$-0.695352\pi$
$421$	−10.0867	+	3.67125i	−0.491594	+	0.178926i	0.0843153	+	0.996439i	$0.473130\pi$
$422$	−6.65258	−	11.5226i	−0.323843	−	0.560912i
$423$	6.05781	+	17.8336i	0.294541	+	0.867101i
$424$	2.49000	−	4.31281i	0.120925	−	0.209448i
$425$	0.751209	−	4.26032i	0.0364390	−	0.206656i
$426$	−9.22886	+	0.707030i	−0.447140	+	0.0342557i
$427$	−11.8635	−	4.31795i	−0.574114	−	0.208960i
$428$	0.301054	+	1.70736i	0.0145520	+	0.0825283i
$429$	33.0279	+	9.23341i	1.59460	+	0.445793i
$430$	3.91570	+	3.28566i	0.188832	+	0.158449i
$431$	34.2002			1.64736			0.823682	−	0.567052i	$-0.191916\pi$
$431$	34.2002			1.64736			0.823682	+	0.567052i	$0.191916\pi$
$432$	14.1164	+	7.14841i	0.679174	+	0.343928i
$433$	36.4825			1.75324			0.876619	−	0.481185i	$-0.159793\pi$
$433$	36.4825			1.75324			0.876619	+	0.481185i	$0.159793\pi$
$434$	6.76927	+	5.68010i	0.324936	+	0.272653i
$435$	−8.23409	+	8.05804i	−0.394794	+	0.386354i
$436$	1.11979	+	6.35065i	0.0536283	+	0.304141i
$437$	−6.17807	−	2.24863i	−0.295537	−	0.107567i
$438$	−5.67894	−	8.29982i	−0.271350	−	0.396581i
$439$	6.89969	−	39.1301i	0.329304	−	1.86758i	−0.148215	−	0.988955i	$-0.547353\pi$
$439$	6.89969	−	39.1301i	0.329304	−	1.86758i	0.477519	−	0.878622i	$-0.341536\pi$
$440$	−8.23202	+	14.2583i	−0.392446	+	0.679737i
$441$	2.96499	−	0.456982i	0.141190	−	0.0217610i
$442$	−2.17948	−	3.77498i	−0.103667	−	0.179557i
$443$	4.39345	−	1.59909i	0.208739	−	0.0759749i	−0.235534	−	0.971866i	$-0.575684\pi$
$443$	4.39345	−	1.59909i	0.208739	−	0.0759749i	0.444274	+	0.895891i	$0.353462\pi$
$444$	−2.17206	−	1.55613i	−0.103081	−	0.0738509i
$445$	0.529087	−	0.443956i	0.0250811	−	0.0210455i
$446$	−12.5470	+	10.5282i	−0.594116	+	0.498523i
$447$	11.1671	+	8.00051i	0.528187	+	0.378411i
$448$	−8.35893	+	3.04240i	−0.394923	+	0.143740i
$449$	−11.7994	−	20.4371i	−0.556848	−	0.964488i	−0.997757	−	0.0669369i	$-0.978677\pi$
$449$	−11.7994	−	20.4371i	−0.556848	−	0.964488i	0.440910	−	0.897552i	$-0.354656\pi$
$450$	9.91765	+	12.3519i	0.467522	+	0.582275i
$451$	17.0028	−	29.4497i	0.800631	−	1.38673i
$452$	−0.397095	+	2.25204i	−0.0186778	+	0.105927i
$453$	−4.54262	−	6.63908i	−0.213431	−	0.311931i
$454$	−7.24592	−	2.63730i	−0.340068	−	0.123775i
$455$	−0.524823	−	2.97642i	−0.0246041	−	0.139537i
$456$	7.73752	−	7.57209i	0.362343	−	0.354596i
$457$	−14.0954	−	11.8274i	−0.659353	−	0.553263i	0.250540	−	0.968106i	$-0.419392\pi$
$457$	−14.0954	−	11.8274i	−0.659353	−	0.553263i	−0.909893	+	0.414843i	$0.863836\pi$
$458$	25.3189			1.18308
$459$	−1.56246	+	5.15648i	−0.0729294	+	0.240684i
$460$	−1.15667			−0.0539299
$461$	0.430417	+	0.361163i	0.0200465	+	0.0168210i	0.652756	−	0.757568i	$-0.273613\pi$
$461$	0.430417	+	0.361163i	0.0200465	+	0.0168210i	−0.632709	+	0.774389i	$0.718057\pi$
$462$	−12.5853	−	3.51840i	−0.585521	−	0.163691i
$463$	4.26861	+	24.2085i	0.198379	+	1.12506i	0.907524	+	0.420001i	$0.137970\pi$
$463$	4.26861	+	24.2085i	0.198379	+	1.12506i	−0.709144	+	0.705063i	$0.750919\pi$
$464$	20.9174	+	7.61333i	0.971068	+	0.353440i
$465$	−10.9719	+	0.840567i	−0.508811	+	0.0389804i
$466$	5.96892	−	33.8514i	0.276505	−	1.56814i
$467$	7.39203	−	12.8034i	0.342062	−	0.592470i	−0.642753	−	0.766073i	$-0.722208\pi$
$467$	7.39203	−	12.8034i	0.342062	−	0.592470i	0.984816	+	0.173604i	$0.0555412\pi$
$468$	−3.89128	−	0.773189i	−0.179874	−	0.0357407i
$469$	5.04135	+	8.73187i	0.232788	+	0.403200i
$470$	−6.79427	+	2.47291i	−0.313396	+	0.114067i
$471$	−3.70577	+	37.6652i	−0.170753	+	1.73552i
$472$	−22.3032	+	18.7146i	−1.02659	+	0.861411i
$473$	−20.2683	+	17.0071i	−0.931939	+	0.781989i
$474$	28.7069	−	13.0105i	1.31855	−	0.597592i
$475$	8.07340	−	2.93848i	0.370433	−	0.134827i
$476$	−0.206428	−	0.357543i	−0.00946160	−	0.0163880i
$477$	−4.31498	+	2.36843i	−0.197569	+	0.108443i
$478$	−7.18832	+	12.4505i	−0.328786	+	0.569474i
$479$	1.66574	−	9.44691i	0.0761098	−	0.431640i	−0.922813	−	0.385247i	$-0.874116\pi$
$479$	1.66574	−	9.44691i	0.0761098	−	0.431640i	0.998923	−	0.0463931i	$-0.0147727\pi$
$480$	1.51036	−	3.14967i	0.0689382	−	0.143762i
$481$	−12.0929	−	4.40146i	−0.551389	−	0.200689i
$482$	−1.45399	−	8.24597i	−0.0662273	−	0.375594i
$483$	−1.37340	−	5.35643i	−0.0624917	−	0.243726i
$484$	−7.48356	−	6.27945i	−0.340162	−	0.285430i
$485$	9.45103			0.429149
$486$	−10.4271	−	16.7489i	−0.472983	−	0.759743i
$487$	−10.5107			−0.476284			−0.238142	−	0.971230i	$-0.576538\pi$
$487$	−10.5107			−0.476284			−0.238142	+	0.971230i	$0.576538\pi$
$488$	−29.3540	−	24.6310i	−1.32879	−	1.11499i
$489$	5.62810	+	21.9504i	0.254511	+	0.992629i
$490$	0.199984	+	1.13417i	0.00903437	+	0.0512364i
$491$	−30.4235	−	11.0732i	−1.37299	−	0.499728i	−0.452945	−	0.891538i	$-0.649627\pi$
$491$	−30.4235	−	11.0732i	−1.37299	−	0.499728i	−0.920046	+	0.391810i	$0.871849\pi$
$492$	−1.70099	+	3.54721i	−0.0766865	+	0.159920i
$493$	−1.31622	+	7.46466i	−0.0592796	+	0.336191i
$494$	4.32846	−	7.49712i	0.194747	−	0.337311i
$495$	14.2654	−	7.83012i	0.641184	−	0.351938i
$496$	10.6306	+	18.4128i	0.477329	+	0.826758i
$497$	−3.96765	+	1.44411i	−0.177974	+	0.0647771i
$498$	34.3549	−	15.5703i	1.53948	−	0.697721i
$499$	8.50526	−	7.13676i	0.380748	−	0.319485i	−0.432248	−	0.901755i	$-0.642280\pi$
$499$	8.50526	−	7.13676i	0.380748	−	0.319485i	0.812996	+	0.582269i	$0.197835\pi$
$500$	2.54557	−	2.13599i	0.113841	−	0.0955243i
$501$	−0.606856	+	6.16804i	−0.0271123	+	0.275568i
$502$	19.3530	−	7.04390i	0.863765	−	0.314385i
$503$	8.24287	+	14.2771i	0.367531	+	0.636583i	0.989179	−	0.146714i	$-0.0468697\pi$
$503$	8.24287	+	14.2771i	0.367531	+	0.636583i	−0.621648	+	0.783297i	$0.713536\pi$
$504$	8.93101	+	1.77457i	0.397819	+	0.0790457i
$505$	6.56343	−	11.3682i	0.292069	−	0.505878i
$506$	−4.18268	+	23.7212i	−0.185943	+	1.05454i
$507$	3.39871	−	0.260378i	0.150942	−	0.0115638i
$508$	0.948697	+	0.345297i	0.0420916	+	0.0153201i
$509$	−0.0998034	−	0.566013i	−0.00442371	−	0.0250881i	0.982516	−	0.186178i	$-0.0596102\pi$
$509$	−0.0998034	−	0.566013i	−0.00442371	−	0.0250881i	−0.986940	+	0.161090i	$0.948499\pi$
$510$	−1.99201	−	0.556895i	−0.0882077	−	0.0246597i
$511$	−3.51430	−	2.94885i	−0.155464	−	0.130449i
$512$	−25.2344			−1.11521
$513$	−10.4203	+	2.43308i	−0.460068	+	0.107423i
$514$	16.8884			0.744913
$515$	−1.91701	−	1.60856i	−0.0844734	−	0.0708816i
$516$	2.18761	−	2.14084i	0.0963042	−	0.0942452i
$517$	−6.49883	−	36.8567i	−0.285818	−	1.62096i
$518$	4.60801	+	1.67718i	0.202465	+	0.0736911i
$519$	4.19273	+	6.12770i	0.184040	+	0.268976i
$520$	1.59294	−	9.03403i	0.0698552	−	0.396168i
$521$	−0.717246	+	1.24231i	−0.0314231	+	0.0544264i	−0.881309	−	0.472540i	$-0.843337\pi$
$521$	−0.717246	+	1.24231i	−0.0314231	+	0.0544264i	0.849886	+	0.526966i	$0.176671\pi$
$522$	−17.3771	−	21.6422i	−0.760574	−	0.947255i
$523$	8.90816	+	15.4294i	0.389527	+	0.674680i	0.992386	−	0.123167i	$-0.0393052\pi$
$523$	8.90816	+	15.4294i	0.389527	+	0.674680i	−0.602859	+	0.797848i	$0.705972\pi$
$524$	0.856992	−	0.311919i	0.0374378	−	0.0136263i
$525$	5.87416	+	4.20845i	0.256369	+	0.183672i
$526$	21.8984	−	18.3750i	0.954816	−	0.801186i
$527$	−5.54598	+	4.65363i	−0.241586	+	0.202715i
$528$	−25.5591	−	18.3114i	−1.11232	−	0.796902i
$529$	12.0351	−	4.38042i	0.523265	−	0.190453i
$530$	−0.944795	−	1.63643i	−0.0410393	−	0.0710821i
$531$	28.4413	−	4.38354i	1.23425	−	0.190230i
$532$	0.409967	−	0.710083i	0.0177743	−	0.0307860i
$533$	−3.29014	+	18.6593i	−0.142512	+	0.808225i
$534$	0.939594	+	1.37322i	0.0406602	+	0.0594252i
$535$	3.72325	+	1.35515i	0.160970	+	0.0585884i
$536$	5.31416	+	30.1381i	0.229537	+	1.30177i
$537$	21.6957	−	21.2318i	0.936238	−	0.916221i
$538$	1.24490	+	1.04459i	0.0536714	+	0.0450357i
$539$	−5.96120			−0.256767
$540$	−1.57629	+	1.02925i	−0.0678327	+	0.0442917i
$541$	2.90252			0.124789			0.0623946	−	0.998052i	$-0.480126\pi$
$541$	2.90252			0.124789			0.0623946	+	0.998052i	$0.480126\pi$
$542$	13.3279	+	11.1834i	0.572481	+	0.480369i
$543$	2.29235	+	0.640859i	0.0983741	+	0.0275019i
$544$	−0.399070	−	2.26324i	−0.0171100	−	0.0970356i
$545$	13.8489	+	5.04059i	0.593222	+	0.215915i
$546$	7.25984	−	0.556182i	0.310693	−	0.0238024i
$547$	−5.04161	+	28.5924i	−0.215564	+	1.22252i	0.664362	+	0.747411i	$0.268703\pi$
$547$	−5.04161	+	28.5924i	−0.215564	+	1.22252i	−0.879925	+	0.475112i	$0.842408\pi$
$548$	−2.19359	+	3.79941i	−0.0937055	+	0.162303i
$549$	12.1818	+	35.8620i	0.519906	+	1.53055i
$550$	−15.7383	−	27.2596i	−0.671084	−	1.16235i
$551$	−14.1457	+	5.14862i	−0.602627	+	0.219338i
$552$	1.64337	−	16.7031i	0.0699465	−	0.710931i
$553$	11.0138	−	9.24166i	0.468354	−	0.392995i
$554$	−9.04061	+	7.58598i	−0.384099	+	0.322297i
$555$	−5.56195	+	2.52078i	−0.236091	+	0.107001i
$556$	−7.99400	+	2.90958i	−0.339021	+	0.123394i
$557$	−16.6830	−	28.8958i	−0.706882	−	1.22436i	−0.966008	−	0.258513i	$-0.916768\pi$
$557$	−16.6830	−	28.8958i	−0.706882	−	1.22436i	0.259125	−	0.965844i	$-0.416566\pi$
$558$	0.572843	−	26.5038i	0.0242504	−	1.12199i
$559$	7.37102	−	12.7670i	0.311761	−	0.539986i
$560$	−0.481167	+	2.72883i	−0.0203330	+	0.115314i
$561$	4.62927	−	9.65377i	0.195448	−	0.407583i
$562$	11.7607	+	4.28054i	0.496095	+	0.180564i
$563$	−4.36987	−	24.7827i	−0.184168	−	1.04447i	−0.927020	−	0.375012i	$-0.877639\pi$
$563$	−4.36987	−	24.7827i	−0.184168	−	1.04447i	0.742852	−	0.669456i	$-0.233473\pi$
$564$	1.07532	+	4.19390i	0.0452792	+	0.176595i
$565$	4.00351	+	3.35934i	0.168429	+	0.141329i
$566$	−21.1966			−0.890960
$567$	−6.63800	−	6.07757i	−0.278770	−	0.255234i
$568$	−12.8155			−0.537726
$569$	−23.6612	−	19.8541i	−0.991927	−	0.832326i	−0.00608162	−	0.999982i	$-0.501936\pi$
$569$	−23.6612	−	19.8541i	−0.991927	−	0.832326i	−0.985846	+	0.167656i	$0.946380\pi$
$570$	−1.02025	−	3.97912i	−0.0427336	−	0.166667i
$571$	6.41747	+	36.3953i	0.268563	+	1.52309i	0.758695	+	0.651446i	$0.225837\pi$
$571$	6.41747	+	36.3953i	0.268563	+	1.52309i	−0.490132	+	0.871648i	$0.663051\pi$
$572$	7.40796	+	2.69628i	0.309743	+	0.112737i
$573$	5.11647	−	10.6698i	0.213744	−	0.445736i
$574$	1.25371	−	7.11015i	0.0523289	−	0.296772i
$575$	6.65971	−	11.5349i	0.277729	−	0.481041i
$576$	22.8172	+	13.8394i	0.950716	+	0.576640i
$577$	−18.9831	−	32.8798i	−0.790278	−	1.36880i	−0.925794	−	0.378027i	$-0.876603\pi$
$577$	−18.9831	−	32.8798i	−0.790278	−	1.36880i	0.135516	−	0.990775i	$-0.456731\pi$
$578$	18.9396	−	6.89344i	0.787782	−	0.286729i
$579$	−4.15445	+	1.88287i	−0.172653	+	0.0782495i
$580$	−2.02877	+	1.70234i	−0.0842403	+	0.0706860i
$581$	13.1807	−	11.0599i	0.546828	−	0.458843i
$582$	−2.22937	+	22.6591i	−0.0924103	+	0.939251i
$583$	9.19097	−	3.34524i	0.380651	−	0.138546i
$584$	−6.96214	−	12.0588i	−0.288095	−	0.498996i
$585$	−5.97688	+	6.81817i	−0.247114	+	0.281896i
$586$	−9.82415	+	17.0159i	−0.405832	+	0.702922i
$587$	6.44293	−	36.5397i	0.265928	−	1.50815i	−0.500451	−	0.865765i	$-0.666833\pi$
$587$	6.44293	−	36.5397i	0.265928	−	1.50815i	0.766379	−	0.642388i	$-0.222056\pi$
$588$	0.687610	−	0.0526782i	0.0283565	−	0.00217241i
$589$	−13.5111	−	4.91763i	−0.556714	−	0.202627i
$590$	1.91832	+	10.8794i	0.0789762	+	0.447896i
$591$	0.733678	+	0.205110i	0.0301795	+	0.00843710i
$592$	9.03821	+	7.58396i	0.371468	+	0.311699i
$593$	−26.3991			−1.08408			−0.542041	−	0.840352i	$-0.682348\pi$
$593$	−26.3991			−1.08408			−0.542041	+	0.840352i	$0.682348\pi$
$594$	15.4079	+	36.0488i	0.632195	+	1.47910i
$595$	−0.943542			−0.0386815
$596$	2.41906	+	2.02983i	0.0990884	+	0.0831451i
$597$	26.5400	−	25.9725i	1.08621	−	1.06299i
$598$	−2.33050	−	13.2169i	−0.0953011	−	0.540479i
$599$	−2.34587	−	0.853828i	−0.0958498	−	0.0348865i	0.293650	−	0.955913i	$-0.405130\pi$
$599$	−2.34587	−	0.853828i	−0.0958498	−	0.0348865i	−0.389500	+	0.921026i	$0.627352\pi$
$600$	12.3852	+	18.1011i	0.505625	+	0.738975i
$601$	−6.87743	+	39.0039i	−0.280536	+	1.59100i	0.440270	+	0.897865i	$0.354883\pi$
$601$	−6.87743	+	39.0039i	−0.280536	+	1.59100i	−0.720807	+	0.693136i	$0.756229\pi$
$602$	−2.80873	+	4.86487i	−0.114475	+	0.198277i
$603$	10.9572	−	28.1937i	0.446213	−	1.14814i
$604$	−0.924606	−	1.60146i	−0.0376217	−	0.0651626i
$605$	−20.9799	+	7.63606i	−0.852954	+	0.310450i
$606$	25.7074	+	18.4176i	1.04429	+	0.748164i
$607$	−5.54784	+	4.65519i	−0.225180	+	0.188948i	−0.748397	−	0.663251i	$-0.769176\pi$
$607$	−5.54784	+	4.65519i	−0.225180	+	0.188948i	0.523217	+	0.852199i	$0.324732\pi$
$608$	3.49634	−	2.93377i	0.141795	−	0.118980i
$609$	−10.2923	−	7.37377i	−0.417066	−	0.298800i
$610$	−13.6627	+	4.97283i	−0.553188	+	0.201344i
$611$	10.4263	+	18.0588i	0.421801	+	0.730581i
$612$	−0.448666	+	1.15445i	−0.0181362	+	0.0466657i
$613$	−8.97274	+	15.5412i	−0.362405	+	0.627705i	−0.988356	−	0.152158i	$-0.951378\pi$
$613$	−8.97274	+	15.5412i	−0.362405	+	0.627705i	0.625951	+	0.779863i	$0.284711\pi$
$614$	0.765025	−	4.33867i	0.0308739	−	0.175095i
$615$	5.07697	+	7.42003i	0.204723	+	0.299205i
$616$	−17.0023	−	6.18832i	−0.685041	−	0.249335i
$617$	0.248854	+	1.41132i	0.0100185	+	0.0568177i	0.989407	−	0.145167i	$-0.0463720\pi$
$617$	0.248854	+	1.41132i	0.0100185	+	0.0568177i	−0.979389	+	0.201985i	$0.935261\pi$
$618$	4.30876	−	4.21664i	0.173324	−	0.169618i
$619$	−31.7747	−	26.6621i	−1.27713	−	1.07164i	−0.993633	−	0.112669i	$-0.964060\pi$
$619$	−31.7747	−	26.6621i	−1.27713	−	1.07164i	−0.283500	−	0.958972i	$-0.591496\pi$
$620$	−2.52956			−0.101590
$621$	−9.95053	+	13.2735i	−0.399301	+	0.532646i
$622$	17.5321			0.702974
$623$	0.581449	+	0.487893i	0.0232953	+	0.0195470i
$624$	16.8716	+	4.71671i	0.675406	+	0.188819i
$625$	2.30354	+	13.0640i	0.0921417	+	0.522562i
$626$	−12.2449	−	4.45677i	−0.489404	−	0.178128i
$627$	21.2007	−	1.62420i	0.846674	−	0.0648643i
$628$	−1.51075	+	8.56791i	−0.0602856	+	0.341897i
$629$	−2.00879	+	3.47932i	−0.0800956	+	0.138730i
$630$	2.27750	−	2.59807i	0.0907377	−	0.103510i
$631$	−11.2346	−	19.4589i	−0.447243	−	0.774647i	0.550963	−	0.834530i	$-0.314261\pi$
$631$	−11.2346	−	19.4589i	−0.447243	−	0.774647i	−0.998205	+	0.0598827i	$0.980927\pi$
$632$	41.0068	−	14.9252i	1.63116	−	0.593694i
$633$	−1.78286	+	18.1209i	−0.0708623	+	0.720239i
$634$	27.5971	−	23.1567i	1.09602	−	0.919669i
$635$	1.76750	−	1.48311i	0.0701410	−	0.0588553i
$636$	−1.03059	+	0.467084i	−0.0408657	+	0.0185211i
$637$	3.12114	−	1.13600i	0.123664	−	0.0450100i
$638$	27.5757	+	47.7625i	1.09173	+	1.89094i
$639$	10.8304	+	6.56900i	0.428445	+	0.259866i
$640$	−3.10552	+	5.37891i	−0.122756	+	0.212620i
$641$	3.90028	−	22.1196i	0.154052	−	0.873672i	−0.805596	−	0.592466i	$-0.798154\pi$
$641$	3.90028	−	22.1196i	0.154052	−	0.873672i	0.959647	−	0.281206i	$-0.0907344\pi$
$642$	−4.12728	+	8.60694i	−0.162891	+	0.339689i
$643$	28.7088	+	10.4492i	1.13217	+	0.412075i	0.839078	−	0.544011i	$-0.183095\pi$
$643$	28.7088	+	10.4492i	1.13217	+	0.412075i	0.293088	+	0.956085i	$0.405317\pi$
$644$	−0.220731	−	1.25183i	−0.00869802	−	0.0493289i
$645$	−1.73740	−	6.77611i	−0.0684101	−	0.266809i
$646$	−2.07032	−	1.73720i	−0.0814555	−	0.0683493i
$647$	−36.1118			−1.41970			−0.709851	−	0.704352i	$-0.751238\pi$
$647$	−36.1118			−1.41970			−0.709851	+	0.704352i	$0.751238\pi$
$648$	−12.6235	−	24.2251i	−0.495898	−	0.951652i
$649$	−57.1821			−2.24459
$650$	13.4349	+	11.2733i	0.526962	+	0.442173i
$651$	−3.00354	−	11.7142i	−0.117718	−	0.459116i
$652$	0.904543	+	5.12992i	0.0354246	+	0.200903i
$653$	12.9734	+	4.72193i	0.507688	+	0.184783i	0.583149	−	0.812365i	$-0.301820\pi$
$653$	12.9734	+	4.72193i	0.507688	+	0.184783i	−0.0754605	+	0.997149i	$0.524043\pi$
$654$	−15.3517	+	32.0141i	−0.600300	+	1.25185i
$655$	0.361930	−	2.05260i	0.0141418	−	0.0802019i
$656$	8.68556	−	15.0438i	0.339114	−	0.587363i
$657$	−0.297394	+	13.7596i	−0.0116025	+	0.536812i
$658$	−3.97294	−	6.88133i	−0.154881	−	0.268262i
$659$	−0.168341	+	0.0612712i	−0.00655764	+	0.00238679i	−0.345297	−	0.938494i	$-0.612222\pi$
$659$	−0.168341	+	0.0612712i	−0.00655764	+	0.00238679i	0.338739	+	0.940880i	$0.390000\pi$
$660$	3.40718	−	1.54420i	0.132624	−	0.0601078i
$661$	−2.00117	+	1.67918i	−0.0778365	+	0.0653126i	−0.680876	−	0.732399i	$-0.738401\pi$
$661$	−2.00117	+	1.67918i	−0.0778365	+	0.0653126i	0.603039	+	0.797711i	$0.293956\pi$
$662$	−26.1037	+	21.9036i	−1.01455	+	0.851309i
$663$	−0.584091	+	5.93666i	−0.0226842	+	0.230561i
$664$	49.0748	−	17.8618i	1.90447	−	0.693171i
$665$	−0.936940	−	1.62283i	−0.0363330	−	0.0629305i
$666$	−4.73165	−	13.9295i	−0.183348	−	0.539759i
$667$	−11.6687	+	20.2108i	−0.451815	+	0.782566i
$668$	−0.247401	+	1.40308i	−0.00957221	+	0.0542867i
$669$	22.3493	−	1.71220i	0.864075	−	0.0661974i
$670$	10.9116	+	3.97149i	0.421551	+	0.153432i
$671$	−13.0686	−	74.1159i	−0.504509	−	2.86121i
$672$	3.69703	+	1.03356i	0.142616	+	0.0398703i
$673$	−18.6504	−	15.6496i	−0.718921	−	0.603247i	0.208165	−	0.978094i	$-0.433251\pi$
$673$	−18.6504	−	15.6496i	−0.718921	−	0.603247i	−0.927087	+	0.374847i	$0.877695\pi$
$674$	5.89160			0.226936
$675$	−1.18848	−	21.6457i	−0.0457448	−	0.833145i
$676$	0.783568			0.0301372
$677$	23.0383	+	19.3315i	0.885435	+	0.742968i	0.967289	−	0.253676i	$-0.0816397\pi$
$677$	23.0383	+	19.3315i	0.885435	+	0.742968i	−0.0818541	+	0.996644i	$0.526084\pi$
$678$	−8.99849	+	8.80610i	−0.345585	+	0.338196i
$679$	1.80357	+	10.2286i	0.0692149	+	0.392537i
$680$	−2.69113	−	0.979491i	−0.103200	−	0.0375618i
$681$	5.95895	+	8.70905i	0.228348	+	0.333732i
$682$	−9.14728	+	51.8768i	−0.350268	+	1.98647i
$683$	−0.986904	+	1.70937i	−0.0377628	+	0.0654071i	−0.884289	−	0.466940i	$-0.845356\pi$
$683$	−0.986904	+	1.70937i	−0.0377628	+	0.0654071i	0.846526	+	0.532347i	$0.178690\pi$
$684$	−2.43109	+	0.374695i	−0.0929552	+	0.0143268i
$685$	5.01324	+	8.68319i	0.191546	+	0.331767i
$686$	−1.18931	+	0.432874i	−0.0454082	+	0.0165272i
$687$	−28.1667	−	20.1796i	−1.07463	−	0.769900i
$688$	−10.3537	+	8.68777i	−0.394730	+	0.331218i
$689$	−4.17468	+	3.50297i	−0.159043	+	0.133453i
$690$	−5.17688	−	3.70889i	−0.197080	−	0.141195i
$691$	24.9545	−	9.08268i	0.949313	−	0.345522i	0.179476	−	0.983762i	$-0.442560\pi$
$691$	24.9545	−	9.08268i	0.949313	−	0.345522i	0.769837	+	0.638241i	$0.220338\pi$
$692$	0.853387	+	1.47811i	0.0324409	+	0.0561893i
$693$	11.1966	+	13.9448i	0.425325	+	0.529720i
$694$	−4.98969	+	8.64240i	−0.189406	+	0.328061i
$695$	−3.37607	+	19.1467i	−0.128062	+	0.726274i
$696$	−21.7006	−	31.7156i	−0.822560	−	1.20218i
$697$	5.55839	+	2.02309i	0.210539	+	0.0766299i
$698$	2.47720	+	14.0489i	0.0937634	+	0.531759i
$699$	−33.6204	+	32.9016i	−1.27164	+	1.24445i
$700$	1.27248	+	1.06774i	0.0480952	+	0.0403566i
$701$	6.58398			0.248673			0.124337	−	0.992240i	$-0.460320\pi$
$701$	6.58398			0.248673			0.124337	+	0.992240i	$0.460320\pi$
$702$	−14.9369	−	15.9381i	−0.563756	−	0.601543i
$703$	−7.97892			−0.300931
$704$	−40.6212	−	34.0852i	−1.53097	−	1.28464i
$705$	9.52942	+	2.66408i	0.358899	+	0.100335i
$706$	4.04836	+	22.9594i	0.152362	+	0.864087i
$707$	13.5560	+	4.93398i	0.509826	+	0.185561i
$708$	6.59581	−	0.505310i	0.247886	−	0.0189907i
$709$	1.99560	−	11.3176i	0.0749462	−	0.425041i	−0.924130	−	0.382077i	$-0.875209\pi$
$709$	1.99560	−	11.3176i	0.0749462	−	0.425041i	0.999077	−	0.0429637i	$-0.0136800\pi$
$710$	−2.43133	+	4.21118i	−0.0912461	+	0.158043i
$711$	−42.3054	−	8.40598i	−1.58657	−	0.315249i
$712$	1.15190	+	1.99515i	0.0431693	+	0.0747714i
$713$	−20.9462	+	7.62378i	−0.784440	+	0.285513i
$714$	0.222569	−	2.26217i	0.00832942	−	0.0846596i
$715$	13.8016	−	11.5809i	0.516151	−	0.433102i
$716$	5.34554	−	4.48544i	0.199772	−	0.167629i
$717$	17.9201	−	8.12173i	0.669239	−	0.303312i
$718$	22.7894	−	8.29468i	0.850494	−	0.309555i
$719$	22.7233	+	39.3580i	0.847438	+	1.46781i	0.883487	+	0.468455i	$0.155189\pi$
$719$	22.7233	+	39.3580i	0.847438	+	1.46781i	−0.0360492	+	0.999350i	$0.511477\pi$
$720$	7.28722	−	3.99986i	0.271579	−	0.149066i
$721$	1.37507	−	2.38169i	0.0512102	−	0.0886987i
$722$	−3.24371	+	18.3960i	−0.120718	+	0.684628i
$723$	−4.95465	+	10.3323i	−0.184265	+	0.384263i
$724$	0.514161	+	0.187139i	0.0191086	+	0.00695498i
$725$	−5.29574	−	30.0336i	−0.196679	−	1.11542i
$726$	−13.3588	−	52.1011i	−0.495791	−	1.93365i
$727$	19.7408	+	16.5645i	0.732146	+	0.614344i	0.930716	−	0.365743i	$-0.119185\pi$
$727$	19.7408	+	16.5645i	0.732146	+	0.614344i	−0.198570	+	0.980087i	$0.563630\pi$
$728$	10.0813			0.373636
$729$	−1.74921	+	26.9433i	−0.0647854	+	0.997899i
$730$	−5.28336			−0.195546
$731$	−3.52558	−	2.95831i	−0.130398	−	0.109417i
$732$	2.16239	+	8.43360i	0.0799241	+	0.311715i
$733$	−2.27159	−	12.8828i	−0.0839030	−	0.475837i	−0.997588	−	0.0694142i	$-0.977887\pi$
$733$	−2.27159	−	12.8828i	−0.0839030	−	0.475837i	0.913685	−	0.406423i	$-0.133224\pi$
$734$	−7.45010	−	2.71162i	−0.274988	−	0.100088i
$735$	0.681471	−	1.42113i	0.0251365	−	0.0524190i
$736$	1.22869	−	6.96827i	0.0452903	−	0.256854i
$737$	−30.0525	+	52.0524i	−1.10700	+	1.91738i
$738$	−18.9873	+	10.4219i	−0.698933	+	0.383635i
$739$	10.4383	+	18.0797i	0.383981	+	0.665074i	0.991627	−	0.129133i	$-0.0412196\pi$
$739$	10.4383	+	18.0797i	0.383981	+	0.665074i	−0.607646	+	0.794208i	$0.707886\pi$
$740$	−1.31908	+	0.480106i	−0.0484903	+	0.0176490i
$741$	−10.7906	+	4.89052i	−0.396404	+	0.179658i
$742$	1.59077	−	1.33481i	0.0583988	−	0.0490024i
$743$	13.2930	−	11.1541i	0.487672	−	0.409205i	−0.365519	−	0.930804i	$-0.619109\pi$
$743$	13.2930	−	11.1541i	0.487672	−	0.409205i	0.853191	+	0.521599i	$0.174664\pi$
$744$	3.59396	−	36.5287i	0.131761	−	1.33921i
$745$	6.78174	−	2.46835i	0.248464	−	0.0904334i
$746$	−12.1637	−	21.0682i	−0.445345	−	0.771360i
$747$	−50.6288	−	10.0598i	−1.85241	−	0.368070i
$748$	1.23056	−	2.13139i	0.0449936	−	0.0779313i
$749$	−0.756122	+	4.28818i	−0.0276281	+	0.156687i
$750$	18.2423	−	1.39755i	0.666114	−	0.0510315i
$751$	−5.99632	−	2.18248i	−0.218809	−	0.0796399i	0.230290	−	0.973122i	$-0.426033\pi$
$751$	−5.99632	−	2.18248i	−0.218809	−	0.0796399i	−0.449099	+	0.893482i	$0.648255\pi$
$752$	−3.31980	−	18.8275i	−0.121061	−	0.686569i
$753$	−27.1438	−	7.58844i	−0.989176	−	0.276538i
$754$	−23.5399	−	19.7523i	−0.857271	−	0.719336i
$755$	−4.22620			−0.153807
$756$	−1.41473	−	1.50956i	−0.0514534	−	0.0549021i
$757$	−8.80999			−0.320205			−0.160102	−	0.987100i	$-0.551182\pi$
$757$	−8.80999			−0.320205			−0.160102	+	0.987100i	$0.551182\pi$
$758$	29.7383	+	24.9534i	1.08014	+	0.906348i
$759$	23.5593	−	23.0556i	0.855149	−	0.836865i
$760$	−0.987642	−	5.60119i	−0.0358255	−	0.203177i
$761$	−6.43543	−	2.34231i	−0.233284	−	0.0849085i	0.222733	−	0.974880i	$-0.428502\pi$
$761$	−6.43543	−	2.34231i	−0.233284	−	0.0849085i	−0.456017	+	0.889971i	$0.650724\pi$
$762$	3.13886	+	4.58747i	0.113709	+	0.166186i
$763$	−2.81245	+	15.9502i	−0.101818	+	0.577436i
$764$	1.36007	−	2.35571i	0.0492055	−	0.0852264i
$765$	1.77221	+	2.20720i	0.0640744	+	0.0798014i
$766$	2.47673	+	4.28982i	0.0894878	+	0.154997i
$767$	29.9391	−	10.8970i	1.08104	−	0.393466i
$768$	12.8858	+	9.23182i	0.464976	+	0.333125i
$769$	−15.2071	+	12.7603i	−0.548383	+	0.460148i	−0.874393	−	0.485219i	$-0.838740\pi$
$769$	−15.2071	+	12.7603i	−0.548383	+	0.460148i	0.326010	+	0.945366i	$0.394296\pi$
$770$	−5.25912	+	4.41293i	−0.189526	+	0.159031i
$771$	−18.7879	−	13.4603i	−0.676630	−	0.484760i
$772$	−0.985275	+	0.358611i	−0.0354608	+	0.0129067i
$773$	−7.25448	−	12.5651i	−0.260926	−	0.451936i	0.705563	−	0.708648i	$-0.250694\pi$
$773$	−7.25448	−	12.5651i	−0.260926	−	0.451936i	−0.966488	+	0.256711i	$0.917361\pi$
$774$	16.6557	−	2.56708i	0.598678	−	0.0922718i
$775$	14.5644	−	25.2263i	0.523168	−	0.906154i
$776$	−5.47421	+	31.0458i	−0.196513	+	1.11448i
$777$	−3.78957	−	5.53849i	−0.135950	−	0.198692i
$778$	−32.0642	−	11.6704i	−1.14956	−	0.418405i
$779$	2.03992	+	11.5690i	0.0730878	+	0.414502i
$780$	−1.48964	+	1.45779i	−0.0533378	+	0.0521974i
$781$	−19.2813	−	16.1789i	−0.689938	−	0.578927i
$782$	−4.18984			−0.149828
$783$	2.08239	+	37.9263i	0.0744185	+	1.35538i
$784$	−3.04516			−0.108756
$785$	15.2314	+	12.7807i	0.543633	+	0.456162i
$786$	4.83580	+	1.35192i	0.172487	+	0.0482213i
$787$	−3.22782	−	18.3059i	−0.115059	−	0.652534i	−0.986721	−	0.162426i	$-0.948068\pi$
$787$	−3.22782	−	18.3059i	−0.115059	−	0.652534i	0.871661	−	0.490109i	$-0.163043\pi$
$788$	0.164560	+	0.0598948i	0.00586220	+	0.00213367i
$789$	−39.0066	+	2.98832i	−1.38867	+	0.106387i
$790$	2.87527	−	16.3064i	0.102297	−	0.580157i
$791$	−2.87172	+	4.97396i	−0.102106	+	0.176854i
$792$	17.4584	+	51.3961i	0.620359	+	1.82628i
$793$	20.9664	+	36.3148i	0.744538	+	1.28958i
$794$	−4.73996	+	1.72520i	−0.168215	+	0.0612252i
$795$	−0.253201	+	2.57351i	−0.00898010	+	0.0912730i
$796$	6.53911	−	5.48696i	0.231773	−	0.194480i
$797$	39.5992	−	33.2276i	1.40267	−	1.17698i	0.442777	−	0.896632i	$-0.353993\pi$
$797$	39.5992	−	33.2276i	1.40267	−	1.17698i	0.959897	−	0.280352i	$-0.0904511\pi$
$798$	4.11179	−	1.86354i	0.145556	−	0.0659685i
$799$	6.11735	−	2.22653i	0.216416	−	0.0787691i
$800$	4.62325	+	8.00770i	0.163456	+	0.283115i
$801$	0.0492045	−	2.27655i	0.00173856	−	0.0804380i
$802$	−19.3343	+	33.4880i	−0.682717	+	1.18250i
$803$	4.74886	−	26.9321i	0.167583	−	0.950413i
$804$	3.00650	−	6.26969i	0.106031	−	0.221115i
$805$	−2.72987	−	0.993591i	−0.0962153	−	0.0350195i
$806$	−5.09666	−	28.9046i	−0.179522	−	1.01812i
$807$	−0.552363	−	2.15429i	−0.0194441	−	0.0758347i
$808$	33.5419	+	28.1450i	1.18000	+	0.990136i
$809$	28.1422			0.989426			0.494713	−	0.869057i	$-0.335273\pi$
$809$	28.1422			0.989426			0.494713	+	0.869057i	$0.335273\pi$
$810$	−10.3553	−	0.447840i	−0.363848	−	0.0157355i
$811$	−35.1405			−1.23395			−0.616975	−	0.786983i	$-0.711642\pi$
$811$	−35.1405			−1.23395			−0.616975	+	0.786983i	$0.711642\pi$
$812$	−2.22956	−	1.87082i	−0.0782421	−	0.0656529i
$813$	−5.91360	−	23.0638i	−0.207399	−	0.808884i
$814$	5.07612	+	28.7881i	0.177918	+	1.00902i
$815$	11.1869	+	4.07168i	0.391858	+	0.142625i
$816$	2.36477	−	4.93144i	0.0827835	−	0.172635i
$817$	1.58718	−	9.00136i	0.0555285	−	0.314918i
$818$	20.3328	−	35.2175i	0.710921	−	1.23135i
$819$	−8.51970	−	5.16747i	−0.297702	−	0.180566i
$820$	1.03337	+	1.78984i	0.0360867	+	0.0625041i
$821$	−31.0839	+	11.3136i	−1.08484	+	0.394848i	−0.821705	−	0.569913i	$-0.806977\pi$
$821$	−31.0839	+	11.3136i	−1.08484	+	0.394848i	−0.263130	+	0.964760i	$0.584755\pi$
$822$	−22.0007	+	9.97114i	−0.767364	+	0.347783i
$823$	−26.7460	+	22.4426i	−0.932307	+	0.782298i	−0.976230	−	0.216737i	$-0.930459\pi$
$823$	−26.7460	+	22.4426i	−0.932307	+	0.782298i	0.0439233	+	0.999035i	$0.486014\pi$
$824$	6.39434	−	5.36549i	0.222757	−	0.186916i
$825$	−4.21780	+	42.8693i	−0.146845	+	1.49252i
$826$	−11.4083	+	4.15230i	−0.396947	+	0.144477i
$827$	14.4136	+	24.9651i	0.501211	+	0.868122i	0.999999	+	0.00139856i	$0.000445175\pi$
$827$	14.4136	+	24.9651i	0.501211	+	0.868122i	−0.498788	+	0.866724i	$0.666221\pi$
$828$	−2.51377	+	2.86760i	−0.0873595	+	0.0996559i
$829$	−9.96084	+	17.2527i	−0.345954	+	0.599210i	−0.985527	−	0.169520i	$-0.945778\pi$
$829$	−9.96084	+	17.2527i	−0.345954	+	0.599210i	0.639572	+	0.768731i	$0.279111\pi$
$830$	3.44097	−	19.5147i	0.119438	−	0.677365i
$831$	16.1036	−	1.23371i	0.558628	−	0.0427969i
$832$	27.7637	+	10.1052i	0.962535	+	0.350334i
$833$	−0.180060	−	1.02117i	−0.00623870	−	0.0353814i
$834$	−45.1083	−	12.6107i	−1.56197	−	0.436671i
$835$	2.49429	+	2.09296i	0.0863186	+	0.0724299i
$836$	4.88779			0.169048
$837$	−21.7612	+	29.0283i	−0.752178	+	1.00336i
$838$	−6.40977			−0.221422
$839$	−23.8944	−	20.0498i	−0.824926	−	0.692195i	0.129194	−	0.991619i	$-0.458761\pi$
$839$	−23.8944	−	20.0498i	−0.824926	−	0.692195i	−0.954120	+	0.299425i	$0.903205\pi$
$840$	3.41893	−	3.34584i	0.117964	−	0.115442i
$841$	4.24307	+	24.0636i	0.146313	+	0.829781i
$842$	−12.7661	−	4.64648i	−0.439949	−	0.160128i
$843$	−9.67183	−	14.1355i	−0.333116	−	0.486851i
$844$	−0.726829	+	4.12205i	−0.0250185	+	0.141887i
$845$	0.895386	−	1.55085i	0.0308022	−	0.0533510i
$846$	−8.63507	+	22.2186i	−0.296880	+	0.763892i
$847$	−12.2680	−	21.2487i	−0.421532	−	0.730115i
$848$	4.69503	−	1.70885i	0.161228	−	0.0586822i
$849$	23.5807	+	16.8940i	0.809289	+	0.579802i
$850$	4.19425	−	3.51940i	0.143862	−	0.120714i
$851$	−9.47573	+	7.95108i	−0.324824	+	0.272559i
$852$	2.36702	+	1.69581i	0.0810927	+	0.0580975i
$853$	−26.4813	+	9.63840i	−0.906702	+	0.330012i	−0.752935	−	0.658095i	$-0.771363\pi$
$853$	−26.4813	+	9.63840i	−0.906702	+	0.330012i	−0.153766	+	0.988107i	$0.549140\pi$
$854$	−7.98926	−	13.8378i	−0.273387	−	0.473520i
$855$	−2.03641	+	5.23983i	−0.0696439	+	0.179198i
$856$	−6.60813	+	11.4456i	−0.225861	+	0.391203i
$857$	−2.15884	+	12.2434i	−0.0737446	+	0.418226i	0.925478	+	0.378801i	$0.123664\pi$
$857$	−2.15884	+	12.2434i	−0.0737446	+	0.418226i	−0.999223	+	0.0394249i	$0.987447\pi$
$858$	24.5100	+	35.8216i	0.836758	+	1.22293i
$859$	10.2489	+	3.73030i	0.349689	+	0.127276i	0.510892	−	0.859645i	$-0.329315\pi$
$859$	10.2489	+	3.73030i	0.349689	+	0.127276i	−0.161203	+	0.986921i	$0.551537\pi$
$860$	−0.279234	−	1.58361i	−0.00952179	−	0.0540008i
$861$	−7.06163	+	6.91065i	−0.240660	+	0.235514i
$862$	33.1583	+	27.8231i	1.12938	+	0.947660i
$863$	57.0196			1.94097			0.970485	−	0.241162i	$-0.0775287\pi$
$863$	57.0196			1.94097			0.970485	+	0.241162i	$0.0775287\pi$
$864$	−4.52619	−	10.5896i	−0.153984	−	0.360266i
$865$	3.90067			0.132627
$866$	35.3711	+	29.6799i	1.20196	+	1.00856i
$867$	−26.5640	−	7.42634i	−0.902161	−	0.252212i
$868$	−0.482725	−	2.73767i	−0.0163848	−	0.0929226i
$869$	80.5382	+	29.3135i	2.73207	+	0.994393i
$870$	−14.5388	+	1.11383i	−0.492911	+	0.0377622i
$871$	5.81533	−	32.9804i	0.197045	−	1.11750i
$872$	−24.5794	+	42.5728i	−0.832365	+	1.44170i
$873$	20.5398	−	23.4309i	0.695167	−	0.793016i
$874$	−4.16052	−	7.20623i	−0.140732	−	0.243754i
$875$	7.84269	−	2.85451i	0.265131	−	0.0964999i
$876$	−0.309774	+	3.14852i	−0.0104663	+	0.106378i
$877$	0.573736	−	0.481422i	0.0193737	−	0.0162565i	−0.633049	−	0.774111i	$-0.718197\pi$
$877$	0.573736	−	0.481422i	0.0193737	−	0.0162565i	0.652423	+	0.757855i	$0.273753\pi$
$878$	38.5233	−	32.3249i	1.30010	−	1.09091i
$879$	24.4911	−	11.0998i	0.826065	−	0.374388i
$880$	−15.5219	+	5.64952i	−0.523244	+	0.190445i
$881$	−5.83958	−	10.1145i	−0.196741	−	0.340765i	0.750729	−	0.660610i	$-0.229702\pi$
$881$	−5.83958	−	10.1145i	−0.196741	−	0.340765i	−0.947470	+	0.319845i	$0.896369\pi$
$882$	3.24644	+	1.96907i	0.109313	+	0.0663021i
$883$	9.48480	−	16.4282i	0.319189	−	0.552852i	−0.661130	−	0.750271i	$-0.729923\pi$
$883$	9.48480	−	16.4282i	0.319189	−	0.552852i	0.980319	+	0.197420i	$0.0632562\pi$
$884$	−0.238120	+	1.35044i	−0.00800884	+	0.0454204i
$885$	6.53693	−	13.6320i	0.219737	−	0.458234i
$886$	5.56053	+	2.02387i	0.186810	+	0.0679931i
$887$	−1.26699	−	7.18544i	−0.0425412	−	0.241263i	0.956121	−	0.292972i	$-0.0946443\pi$
$887$	−1.26699	−	7.18544i	−0.0425412	−	0.241263i	−0.998662	+	0.0517088i	$0.983533\pi$
$888$	−5.05895	−	19.7306i	−0.169767	−	0.662115i
$889$	1.94242	+	1.62988i	0.0651467	+	0.0546646i
$890$	0.874144			0.0293014
$891$	11.5905	−	52.3839i	0.388298	−	1.75493i
$892$	5.15260			0.172522
$893$	9.90402	+	8.31046i	0.331425	+	0.278099i
$894$	4.31822	+	16.8417i	0.144423	+	0.563269i
$895$	−2.76931	−	15.7055i	−0.0925677	−	0.524977i
$896$	−6.41408	−	2.33453i	−0.214279	−	0.0779913i
$897$	−7.94146	+	16.5609i	−0.265158	+	0.552954i
$898$	5.18645	−	29.4138i	0.173074	−	0.981552i
$899$	−25.5188	+	44.1999i	−0.851100	+	1.47415i
$900$	0.107682	−	4.98214i	0.00358941	−	0.166071i
$901$	0.850664	+	1.47339i	0.0283397	+	0.0490858i
$902$	40.4433	−	14.7202i	1.34662	−	0.490128i
$903$	7.00203	−	3.17345i	0.233013	−	0.105606i
$904$	−13.3541	+	11.2054i	−0.444149	+	0.372685i
$905$	0.957922	−	0.803792i	0.0318424	−	0.0267190i
$906$	0.996901	−	10.1324i	0.0331198	−	0.336627i
$907$	43.6409	−	15.8840i	1.44907	−	0.527419i	0.506740	−	0.862099i	$-0.330850\pi$
$907$	43.6409	−	15.8840i	1.44907	−	0.527419i	0.942332	+	0.334680i	$0.108628\pi$
$908$	1.21289	+	2.10078i	0.0402510	+	0.0697168i
$909$	−13.9197	−	40.9783i	−0.461688	−	1.35917i
$910$	1.91259	−	3.31271i	0.0634019	−	0.109815i
$911$	6.79331	−	38.5268i	0.225072	−	1.27645i	−0.637474	−	0.770472i	$-0.720021\pi$
$911$	6.79331	−	38.5268i	0.225072	−	1.27645i	0.862547	−	0.505978i	$-0.168868\pi$
$912$	10.8300	−	0.829691i	0.358616	−	0.0274738i
$913$	96.3839	+	35.0809i	3.18984	+	1.16101i
$914$	−4.04392	−	22.9342i	−0.133761	−	0.758596i
$915$	19.1629	+	5.35726i	0.633506	+	0.177106i
$916$	−6.10157	−	5.11982i	−0.201601	−	0.169164i
$917$	2.29054			0.0756404
$918$	−5.70986	+	3.72828i	−0.188453	+	0.123052i
$919$	1.47738			0.0487343			0.0243671	−	0.999703i	$-0.492243\pi$
$919$	1.47738			0.0487343			0.0243671	+	0.999703i	$0.492243\pi$
$920$	−6.75457	−	5.66775i	−0.222691	−	0.186860i
$921$	−4.30906	+	4.21694i	−0.141989	+	0.138953i
$922$	0.123486	+	0.700321i	0.00406678	+	0.0230639i
$923$	13.1783	+	4.79653i	0.433771	+	0.157880i
$924$	2.32144	+	3.39281i	0.0763699	+	0.111615i
$925$	2.80693	−	15.9189i	0.0922914	−	0.523411i
$926$	−15.5560	+	26.9437i	−0.511200	+	0.885425i
$927$	−8.15413	+	1.25676i	−0.267817	+	0.0412775i
$928$	−8.10056	−	14.0306i	−0.265914	−	0.460577i
$929$	−6.64956	+	2.42024i	−0.218165	+	0.0794055i	−0.448790	−	0.893637i	$-0.648145\pi$
$929$	−6.64956	+	2.42024i	−0.218165	+	0.0794055i	0.230625	+	0.973043i	$0.425923\pi$
$930$	−11.3215	−	8.11112i	−0.371247	−	0.265974i
$931$	1.57754	−	1.32371i	0.0517018	−	0.0433829i
$932$	−8.28364	+	6.95080i	−0.271340	+	0.227681i
$933$	−19.5041	−	13.9734i	−0.638535	−	0.457468i
$934$	17.5829	−	6.39964i	0.575329	−	0.209403i
$935$	−2.81232	−	4.87109i	−0.0919728	−	0.159302i
$936$	−18.9352	−	23.5827i	−0.618915	−	0.770826i
$937$	10.6738	−	18.4875i	0.348696	−	0.603960i	−0.637322	−	0.770598i	$-0.719958\pi$
$937$	10.6738	−	18.4875i	0.348696	−	0.603960i	0.986018	+	0.166638i	$0.0532911\pi$
$938$	−2.21594	+	12.5672i	−0.0723529	+	0.410333i
$939$	10.0700	+	14.7174i	0.328623	+	0.480285i
$940$	2.13739	+	0.777947i	0.0697141	+	0.0253738i
$941$	−2.37364	−	13.4616i	−0.0773784	−	0.438835i	−0.998743	−	0.0501340i	$-0.984035\pi$
$941$	−2.37364	−	13.4616i	−0.0773784	−	0.438835i	0.921364	−	0.388701i	$-0.127076\pi$
$942$	−34.2349	+	33.5030i	−1.11543	+	1.09159i
$943$	13.9512	+	11.7065i	0.454314	+	0.381215i
$944$	−29.2104			−0.950716
$945$	−4.60437	+	1.07509i	−0.149780	+	0.0349727i
$946$	−33.4868			−1.08875
$947$	−12.6097	−	10.5808i	−0.409760	−	0.343829i	0.414492	−	0.910053i	$-0.363959\pi$
$947$	−12.6097	−	10.5808i	−0.409760	−	0.343829i	−0.824251	+	0.566224i	$0.808404\pi$
$948$	−9.54892	−	2.66954i	−0.310135	−	0.0867025i
$949$	2.64595	+	15.0060i	0.0858913	+	0.487114i
$950$	10.2180	+	3.71906i	0.331516	+	0.120662i
$951$	−49.1573	+	3.76598i	−1.59404	+	0.122120i
$952$	0.546517	−	3.09945i	0.0177127	−	0.100454i
$953$	3.09623	−	5.36283i	0.100297	−	0.173719i	−0.811510	−	0.584338i	$-0.801354\pi$
$953$	3.09623	−	5.36283i	0.100297	−	0.173719i	0.911807	+	0.410619i	$0.134687\pi$
$954$	−6.11034	−	1.21411i	−0.197829	−	0.0393083i
$955$	−3.10830	−	5.38374i	−0.100582	−	0.174214i
$956$	4.24996	−	1.54686i	0.137454	−	0.0500290i
$957$	7.39016	−	75.1130i	0.238890	−	2.42806i
$958$	9.30042	−	7.80398i	0.300483	−	0.252135i
$959$	−8.44087	+	7.08273i	−0.272570	+	0.228713i
$960$	12.7695	−	5.78738i	0.412134	−	0.186787i
$961$	−16.6776	+	6.07013i	−0.537986	+	0.195811i
$962$	−8.14376	−	14.1054i	−0.262565	−	0.454777i
$963$	11.4514	−	6.28552i	0.369015	−	0.202548i
$964$	−1.31705	+	2.28120i	−0.0424193	+	0.0734724i
$965$	−0.416107	+	2.35986i	−0.0133950	+	0.0759666i
$966$	3.02610	−	6.31056i	0.0973632	−	0.203039i
$967$	−38.5993	−	14.0490i	−1.24127	−	0.451785i	−0.363826	−	0.931467i	$-0.618530\pi$
$967$	−38.5993	−	14.0490i	−1.24127	−	0.451785i	−0.877442	+	0.479682i	$0.840752\pi$
$968$	−12.9318	−	73.3401i	−0.415645	−	2.35724i
$969$	0.918602	+	3.58267i	0.0295097	+	0.115092i
$970$	9.16312	+	7.68877i	0.294210	+	0.246872i
$971$	−53.7396			−1.72459			−0.862293	−	0.506409i	$-0.830973\pi$
$971$	−53.7396			−1.72459			−0.862293	+	0.506409i	$0.830973\pi$
$972$	−0.874032	+	6.14477i	−0.0280346	+	0.197094i
$973$	−21.3661			−0.684967
$974$	−10.1905	−	8.55082i	−0.326524	−	0.273986i
$975$	−5.96110	−	23.2491i	−0.190908	−	0.744567i
$976$	−6.67586	−	37.8607i	−0.213689	−	1.21189i
$977$	7.57063	+	2.75548i	0.242206	+	0.0881557i	0.460271	−	0.887779i	$-0.347752\pi$
$977$	7.57063	+	2.75548i	0.242206	+	0.0881557i	−0.218065	+	0.975934i	$0.569975\pi$
$978$	−12.4008	+	25.8603i	−0.396534	+	0.826922i
$979$	−0.785709	+	4.45597i	−0.0251114	+	0.142414i
$980$	0.181150	−	0.313760i	0.00578661	−	0.0100227i
$981$	42.5942	−	23.3794i	1.35993	−	0.746448i
$982$	−20.4882	−	35.4865i	−0.653804	−	1.13242i
$983$	46.0911	−	16.7758i	1.47008	−	0.535065i	0.521957	−	0.852972i	$-0.325202\pi$
$983$	46.0911	−	16.7758i	1.47008	−	0.535065i	0.948122	+	0.317907i	$0.102980\pi$
$984$	−27.3148	+	12.3796i	−0.870765	+	0.394647i
$985$	0.306588	−	0.257258i	0.00976870	−	0.00819691i
$986$	−7.34891	+	6.16646i	−0.234037	+	0.196380i
$987$	−1.06473	+	10.8218i	−0.0338907	+	0.344462i
$988$	−2.55912	+	0.931445i	−0.0814166	+	0.0296332i
$989$	−7.08502	−	12.2716i	−0.225291	−	0.390215i
$990$	20.2010	+	4.01389i	0.642029	+	0.127570i
$991$	−5.30155	+	9.18255i	−0.168409	+	0.291693i	−0.937861	−	0.347012i	$-0.887196\pi$
$991$	−5.30155	+	9.18255i	−0.168409	+	0.291693i	0.769451	+	0.638705i	$0.220530\pi$
$992$	2.68708	−	15.2392i	0.0853149	−	0.483845i
$993$	46.4974	−	3.56220i	1.47555	−	0.113043i
$994$	−5.02162	−	1.82772i	−0.159276	−	0.0579718i
$995$	−3.38765	−	19.2123i	−0.107396	−	0.609071i
$996$	−11.4277	−	3.19476i	−0.362099	−	0.101230i
$997$	44.1468	+	37.0436i	1.39814	+	1.17318i	0.961916	+	0.273346i	$0.0881305\pi$
$997$	44.1468	+	37.0436i	1.39814	+	1.17318i	0.436228	+	0.899836i	$0.356314\pi$
$998$	14.0522			0.444814
$999$	−5.83822	+	19.2675i	−0.184713	+	0.609597i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.v.a.43.7	yes	54
3.2	odd	2		567.2.v.b.127.3		54
27.5	odd	18		567.2.v.b.442.3		54
27.7	even	9		5103.2.a.i.1.18		27
27.20	odd	18		5103.2.a.f.1.10		27
27.22	even	9	inner	189.2.v.a.22.7	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.v.a.22.7	✓	54	27.22	even	9	inner
189.2.v.a.43.7	yes	54	1.1	even	1	trivial
567.2.v.b.127.3		54	3.2	odd	2
567.2.v.b.442.3		54	27.5	odd	18
5103.2.a.f.1.10		27	27.20	odd	18
5103.2.a.i.1.18		27	27.7	even	9

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.969537 + 0.813538i) q^{2} +(-0.430185 - 1.67778i) q^{3} +(-0.0691389 - 0.392106i) q^{4} +(-0.855069 - 0.311220i) q^{5} +(0.947857 - 1.97664i) q^{6} +(0.173648 - 0.984808i) q^{7} +(1.51760 - 2.62856i) q^{8} +(-2.62988 + 1.44351i) q^{9} +O(q^{10})\)	\(q+(0.969537 + 0.813538i) q^{2} +(-0.430185 - 1.67778i) q^{3} +(-0.0691389 - 0.392106i) q^{4} +(-0.855069 - 0.311220i) q^{5} +(0.947857 - 1.97664i) q^{6} +(0.173648 - 0.984808i) q^{7} +(1.51760 - 2.62856i) q^{8} +(-2.62988 + 1.44351i) q^{9} +(-0.575832 - 0.997370i) q^{10} +(5.60170 - 2.03885i) q^{11} +(-0.628125 + 0.284678i) q^{12} +(-2.54437 + 2.13498i) q^{13} +(0.969537 - 0.813538i) q^{14} +(-0.154320 + 1.56850i) q^{15} +(2.86152 - 1.04151i) q^{16} +(0.518461 + 0.898001i) q^{17} +(-3.72412 - 0.739974i) q^{18} +(-1.02967 + 1.78343i) q^{19} +(-0.0629126 + 0.356795i) q^{20} +(-1.72699 + 0.132306i) q^{21} +(7.08973 + 2.58045i) q^{22} +(0.554384 + 3.14407i) q^{23} +(-5.06299 - 1.41543i) q^{24} +(-3.19594 - 2.68171i) q^{25} -4.20376 q^{26} +(3.55322 + 3.79139i) q^{27} -0.398155 q^{28} +(5.59972 + 4.69872i) q^{29} +(-1.42565 + 1.39517i) q^{30} +(1.21241 + 6.87590i) q^{31} +(-2.08266 - 0.758027i) q^{32} +(-5.83050 - 8.52132i) q^{33} +(-0.227891 + 1.29243i) q^{34} +(-0.454973 + 0.788036i) q^{35} +(0.747836 + 0.931390i) q^{36} +(1.93726 + 3.35543i) q^{37} +(-2.44919 + 0.891432i) q^{38} +(4.67658 + 3.35046i) q^{39} +(-2.11571 + 1.77529i) q^{40} +(4.36990 - 3.66678i) q^{41} +(-1.78202 - 1.27670i) q^{42} +(-4.17077 + 1.51804i) q^{43} +(-1.18674 - 2.05550i) q^{44} +(2.69798 - 0.415829i) q^{45} +(-2.02032 + 3.49930i) q^{46} +(1.09019 - 6.18276i) q^{47} +(-2.97840 - 4.35295i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(-0.916906 - 5.20003i) q^{50} +(1.28361 - 1.25617i) q^{51} +(1.01306 + 0.850054i) q^{52} +1.64075 q^{53} +(0.360545 + 6.56657i) q^{54} -5.42437 q^{55} +(-2.32510 - 1.95099i) q^{56} +(3.43515 + 0.960346i) q^{57} +(1.60654 + 9.11117i) q^{58} +(-9.01389 - 3.28079i) q^{59} +(0.625687 - 0.0479343i) q^{60} +(2.19228 - 12.4331i) q^{61} +(-4.41833 + 7.65277i) q^{62} +(0.964905 + 2.84059i) q^{63} +(-4.44770 - 7.70364i) q^{64} +(2.84006 - 1.03370i) q^{65} +(1.27953 - 13.0051i) q^{66} +(-7.72379 + 6.48103i) q^{67} +(0.316266 - 0.265378i) q^{68} +(5.03657 - 2.28267i) q^{69} +(-1.08221 + 0.393892i) q^{70} +(-2.11115 - 3.65661i) q^{71} +(-0.196759 + 9.10348i) q^{72} +(2.29380 - 3.97297i) q^{73} +(-0.851527 + 4.82925i) q^{74} +(-3.12447 + 6.51571i) q^{75} +(0.770485 + 0.280434i) q^{76} +(-1.03515 - 5.87064i) q^{77} +(1.80839 + 7.05297i) q^{78} +(11.0138 + 9.24166i) q^{79} -2.77093 q^{80} +(4.83256 - 7.59252i) q^{81} +7.21984 q^{82} +(13.1807 + 11.0599i) q^{83} +(0.171280 + 0.668016i) q^{84} +(-0.163844 - 0.929208i) q^{85} +(-5.27869 - 1.92129i) q^{86} +(5.47450 - 11.4164i) q^{87} +(3.14189 - 17.8186i) q^{88} +(-0.379514 + 0.657337i) q^{89} +(2.95408 + 1.79175i) q^{90} +(1.66072 + 2.87646i) q^{91} +(1.19448 - 0.434755i) q^{92} +(11.0147 - 4.99205i) q^{93} +(6.08689 - 5.10751i) q^{94} +(1.43548 - 1.20451i) q^{95} +(-0.375872 + 3.82034i) q^{96} +(-9.76000 + 3.55235i) q^{97} +(-0.632820 - 1.09608i) q^{98} +(-11.7887 + 13.4480i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 3 q^{3} - 3 q^{5} - 27 q^{8} - 9 q^{9}+O(q^{10}) \) 54 * q - 3 * q^3 - 3 * q^5 - 27 * q^8 - 9 * q^9	\( 54 q - 3 q^{3} - 3 q^{5} - 27 q^{8} - 9 q^{9} - 6 q^{11} + 24 q^{12} - 9 q^{13} - 9 q^{15} - 30 q^{17} - 27 q^{18} - 12 q^{20} - 3 q^{21} - 9 q^{22} - 12 q^{23} + 36 q^{24} + 27 q^{25} + 18 q^{26} + 63 q^{27} + 54 q^{28} + 6 q^{29} - 72 q^{30} - 9 q^{31} - 9 q^{32} - 36 q^{33} - 9 q^{34} - 12 q^{35} + 54 q^{38} + 12 q^{39} - 45 q^{40} - 15 q^{41} - 18 q^{42} - 9 q^{43} - 42 q^{44} - 9 q^{45} - 45 q^{47} - 93 q^{48} + 18 q^{50} + 72 q^{51} - 63 q^{52} + 132 q^{53} + 54 q^{54} - 9 q^{56} + 3 q^{57} - 27 q^{58} - 9 q^{60} - 36 q^{62} - 9 q^{63} - 27 q^{64} + 66 q^{65} + 153 q^{66} + 45 q^{67} + 87 q^{68} - 72 q^{71} - 45 q^{72} - 72 q^{74} - 39 q^{75} + 54 q^{76} + 3 q^{77} - 54 q^{78} - 36 q^{79} + 42 q^{80} + 27 q^{81} + 24 q^{83} - 12 q^{84} + 18 q^{85} - 90 q^{86} - 99 q^{87} + 54 q^{88} - 42 q^{89} - 9 q^{90} + 87 q^{92} + 93 q^{93} - 90 q^{94} + 12 q^{95} + 108 q^{96} - 18 q^{97} - 9 q^{98} - 117 q^{99}+O(q^{100}) \) 54 * q - 3 * q^3 - 3 * q^5 - 27 * q^8 - 9 * q^9 - 6 * q^11 + 24 * q^12 - 9 * q^13 - 9 * q^15 - 30 * q^17 - 27 * q^18 - 12 * q^20 - 3 * q^21 - 9 * q^22 - 12 * q^23 + 36 * q^24 + 27 * q^25 + 18 * q^26 + 63 * q^27 + 54 * q^28 + 6 * q^29 - 72 * q^30 - 9 * q^31 - 9 * q^32 - 36 * q^33 - 9 * q^34 - 12 * q^35 + 54 * q^38 + 12 * q^39 - 45 * q^40 - 15 * q^41 - 18 * q^42 - 9 * q^43 - 42 * q^44 - 9 * q^45 - 45 * q^47 - 93 * q^48 + 18 * q^50 + 72 * q^51 - 63 * q^52 + 132 * q^53 + 54 * q^54 - 9 * q^56 + 3 * q^57 - 27 * q^58 - 9 * q^60 - 36 * q^62 - 9 * q^63 - 27 * q^64 + 66 * q^65 + 153 * q^66 + 45 * q^67 + 87 * q^68 - 72 * q^71 - 45 * q^72 - 72 * q^74 - 39 * q^75 + 54 * q^76 + 3 * q^77 - 54 * q^78 - 36 * q^79 + 42 * q^80 + 27 * q^81 + 24 * q^83 - 12 * q^84 + 18 * q^85 - 90 * q^86 - 99 * q^87 + 54 * q^88 - 42 * q^89 - 9 * q^90 + 87 * q^92 + 93 * q^93 - 90 * q^94 + 12 * q^95 + 108 * q^96 - 18 * q^97 - 9 * q^98 - 117 * q^99

Introduction

L-functions

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