LMFDB - Embedded newform 729.2.g.b.28.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			28.7
Character	$\chi$	$=$	729.28
Dual form			729.2.g.b.703.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29056 - 0.848814i) q^{2} +(0.152898 - 0.354458i) q^{4} +(-0.349244 + 0.370177i) q^{5} +(-3.96148 - 0.463031i) q^{7} +(0.432916 + 2.45519i) q^{8} +O(q^{10})$	\(q+(1.29056 - 0.848814i) q^{2} +(0.152898 - 0.354458i) q^{4} +(-0.349244 + 0.370177i) q^{5} +(-3.96148 - 0.463031i) q^{7} +(0.432916 + 2.45519i) q^{8} +(-0.136509 + 0.774179i) q^{10} +(-1.09805 + 3.66773i) q^{11} +(-0.181020 + 3.10799i) q^{13} +(-5.50556 + 2.76500i) q^{14} +(3.17252 + 3.36268i) q^{16} +(1.41129 - 0.513668i) q^{17} +(6.30242 + 2.29389i) q^{19} +(0.0778134 + 0.180392i) q^{20} +(1.69613 + 5.66546i) q^{22} +(-1.17843 + 0.137739i) q^{23} +(0.275664 + 4.73298i) q^{25} +(2.40449 + 4.16470i) q^{26} +(-0.769829 + 1.33338i) q^{28} +(-6.17988 - 3.10365i) q^{29} +(-0.0276800 - 0.0371807i) q^{31} +(2.09689 + 0.496972i) q^{32} +(1.38535 - 1.86084i) q^{34} +(1.55493 - 1.30474i) q^{35} +(-2.33905 - 1.96269i) q^{37} +(10.0807 - 2.38918i) q^{38} +(-1.06005 - 0.697205i) q^{40} +(-4.96389 - 3.26480i) q^{41} +(0.231769 - 0.0549304i) q^{43} +(1.13217 + 0.950001i) q^{44} +(-1.40392 + 1.17803i) q^{46} +(2.82910 - 3.80014i) q^{47} +(8.66765 + 2.05427i) q^{49} +(4.37318 + 5.87420i) q^{50} +(1.07397 + 0.539370i) q^{52} +(-6.81173 + 11.7983i) q^{53} +(-0.974224 - 1.68741i) q^{55} +(-0.578162 - 9.92665i) q^{56} +(-10.6099 + 1.24012i) q^{58} +(-0.400604 - 1.33811i) q^{59} +(-0.124364 - 0.288308i) q^{61} +(-0.0672822 - 0.0244887i) q^{62} +(-5.56048 + 2.02385i) q^{64} +(-1.08729 - 1.15246i) q^{65} +(4.90826 - 2.46502i) q^{67} +(0.0337102 - 0.578782i) q^{68} +(0.899246 - 3.00369i) q^{70} +(2.03991 - 11.5689i) q^{71} +(2.70207 + 15.3242i) q^{73} +(-4.68464 - 0.547556i) q^{74} +(1.77672 - 1.88321i) q^{76} +(6.04817 - 14.0212i) q^{77} +(11.6941 - 7.69136i) q^{79} -2.35277 q^{80} -9.17740 q^{82} +(0.587346 - 0.386304i) q^{83} +(-0.302737 + 0.701823i) q^{85} +(0.252487 - 0.267620i) q^{86} +(-9.48034 - 1.10809i) q^{88} +(-2.00921 - 11.3948i) q^{89} +(2.15620 - 12.2284i) q^{91} +(-0.131358 + 0.438765i) q^{92} +(0.425507 - 7.30568i) q^{94} +(-3.05023 + 1.53188i) q^{95} +(8.92799 + 9.46312i) q^{97} +(12.9298 - 4.70606i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{22}{27}\right)$

Coefficient data

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

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

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

$2$	1.29056	−	0.848814i	0.912563	−	0.600202i	−0.00404373	−	0.999992i	$-0.501287\pi$
$2$	1.29056	−	0.848814i	0.912563	−	0.600202i	0.916607	+	0.399790i	$0.130917\pi$
$3$		0			0
$3$		0			0
$4$	0.152898	−	0.354458i	0.0764491	−	0.177229i
$5$	−0.349244	+	0.370177i	−0.156187	+	0.165548i	−0.800742	−	0.599010i	$-0.795561\pi$
$5$	−0.349244	+	0.370177i	−0.156187	+	0.165548i	0.644555	+	0.764558i	$0.277043\pi$
$6$		0			0
$7$	−3.96148	−	0.463031i	−1.49730	−	0.175009i	−0.672358	−	0.740226i	$-0.734718\pi$
$7$	−3.96148	−	0.463031i	−1.49730	−	0.175009i	−0.824942	+	0.565217i	$0.808793\pi$
$8$	0.432916	+	2.45519i	0.153059	+	0.868041i
$9$		0			0
$10$	−0.136509	+	0.774179i	−0.0431678	+	0.244817i
$11$	−1.09805	+	3.66773i	−0.331074	+	1.10586i	0.616775	+	0.787140i	$0.288439\pi$
$11$	−1.09805	+	3.66773i	−0.331074	+	1.10586i	−0.947848	+	0.318723i	$0.896746\pi$
$12$		0			0
$13$	−0.181020	+	3.10799i	−0.0502059	+	0.862002i	0.875373	+	0.483448i	$0.160616\pi$
$13$	−0.181020	+	3.10799i	−0.0502059	+	0.862002i	−0.925579	+	0.378554i	$0.876421\pi$
$14$	−5.50556	+	2.76500i	−1.47142	+	0.738976i
$15$		0			0
$16$	3.17252	+	3.36268i	0.793131	+	0.840669i
$17$	1.41129	−	0.513668i	0.342288	−	0.124583i	−0.165156	−	0.986268i	$-0.552813\pi$
$17$	1.41129	−	0.513668i	0.342288	−	0.124583i	0.507444	+	0.861685i	$0.330590\pi$
$18$		0			0
$19$	6.30242	+	2.29389i	1.44587	+	0.526255i	0.941436	−	0.337192i	$-0.109477\pi$
$19$	6.30242	+	2.29389i	1.44587	+	0.526255i	0.504439	+	0.863447i	$0.331699\pi$
$20$	0.0778134	+	0.180392i	0.0173996	+	0.0403368i
$21$		0			0
$22$	1.69613	+	5.66546i	0.361616	+	1.20788i
$23$	−1.17843	+	0.137739i	−0.245720	+	0.0287206i	−0.238062	−	0.971250i	$-0.576512\pi$
$23$	−1.17843	+	0.137739i	−0.245720	+	0.0287206i	−0.00765887	+	0.999971i	$0.502438\pi$
$24$		0			0
$25$	0.275664	+	4.73298i	0.0551329	+	0.946595i
$26$	2.40449	+	4.16470i	0.471559	+	0.816765i
$27$		0			0
$28$	−0.769829	+	1.33338i	−0.145484	+	0.251986i
$29$	−6.17988	−	3.10365i	−1.14757	−	0.576333i	−0.229722	−	0.973256i	$-0.573782\pi$
$29$	−6.17988	−	3.10365i	−1.14757	−	0.576333i	−0.917852	+	0.396923i	$0.870078\pi$
$30$		0			0
$31$	−0.0276800	−	0.0371807i	−0.00497148	−	0.00667785i	0.799631	−	0.600492i	$-0.205029\pi$
$31$	−0.0276800	−	0.0371807i	−0.00497148	−	0.00667785i	−0.804602	+	0.593814i	$0.797621\pi$
$32$	2.09689	+	0.496972i	0.370681	+	0.0878530i
$33$		0			0
$34$	1.38535	−	1.86084i	0.237585	−	0.319132i
$35$	1.55493	−	1.30474i	0.262831	−	0.220541i
$36$		0			0
$37$	−2.33905	−	1.96269i	−0.384537	−	0.322665i	0.429943	−	0.902856i	$-0.358533\pi$
$37$	−2.33905	−	1.96269i	−0.384537	−	0.322665i	−0.814481	+	0.580191i	$0.802978\pi$
$38$	10.0807	−	2.38918i	1.63531	−	0.387576i
$39$		0			0
$40$	−1.06005	−	0.697205i	−0.167608	−	0.110238i
$41$	−4.96389	−	3.26480i	−0.775229	−	0.509876i	0.0991780	−	0.995070i	$-0.468379\pi$
$41$	−4.96389	−	3.26480i	−0.775229	−	0.509876i	−0.874407	+	0.485194i	$0.838749\pi$
$42$		0			0
$43$	0.231769	−	0.0549304i	0.0353445	−	0.00837680i	−0.212906	−	0.977073i	$-0.568293\pi$
$43$	0.231769	−	0.0549304i	0.0353445	−	0.00837680i	0.248250	+	0.968696i	$0.420145\pi$
$44$	1.13217	+	0.950001i	0.170681	+	0.143218i
$45$		0			0
$46$	−1.40392	+	1.17803i	−0.206997	+	0.173691i
$47$	2.82910	−	3.80014i	0.412666	−	0.554307i	−0.546387	−	0.837533i	$-0.683997\pi$
$47$	2.82910	−	3.80014i	0.412666	−	0.554307i	0.959053	+	0.283226i	$0.0914046\pi$
$48$		0			0
$49$	8.66765	+	2.05427i	1.23824	+	0.293467i
$50$	4.37318	+	5.87420i	0.618461	+	0.830737i
$51$		0			0
$52$	1.07397	+	0.539370i	0.148933	+	0.0747972i
$53$	−6.81173	+	11.7983i	−0.935663	+	1.62062i	−0.162216	+	0.986755i	$0.551864\pi$
$53$	−6.81173	+	11.7983i	−0.935663	+	1.62062i	−0.773447	+	0.633860i	$0.781469\pi$
$54$		0			0
$55$	−0.974224	−	1.68741i	−0.131364	−	0.227530i
$56$	−0.578162	−	9.92665i	−0.0772601	−	1.32650i
$57$		0			0
$58$	−10.6099	+	1.24012i	−1.39315	+	0.162836i
$59$	−0.400604	−	1.33811i	−0.0521543	−	0.174207i	0.927944	−	0.372719i	$-0.121574\pi$
$59$	−0.400604	−	1.33811i	−0.0521543	−	0.174207i	−0.980099	+	0.198512i	$0.936389\pi$
$60$		0			0
$61$	−0.124364	−	0.288308i	−0.0159232	−	0.0369141i	0.910069	−	0.414457i	$-0.136028\pi$
$61$	−0.124364	−	0.288308i	−0.0159232	−	0.0369141i	−0.925992	+	0.377543i	$0.876769\pi$
$62$	−0.0672822	−	0.0244887i	−0.00854485	−	0.00311007i
$63$		0			0
$64$	−5.56048	+	2.02385i	−0.695060	+	0.252981i
$65$	−1.08729	−	1.15246i	−0.134861	−	0.142945i
$66$		0			0
$67$	4.90826	−	2.46502i	0.599639	−	0.301150i	−0.122966	−	0.992411i	$-0.539241\pi$
$67$	4.90826	−	2.46502i	0.599639	−	0.301150i	0.722605	+	0.691261i	$0.242944\pi$
$68$	0.0337102	−	0.578782i	0.00408797	−	0.0701877i
$69$		0			0
$70$	0.899246	−	3.00369i	0.107480	−	0.359010i
$71$	2.03991	−	11.5689i	0.242093	−	1.37298i	−0.585054	−	0.810994i	$-0.698927\pi$
$71$	2.03991	−	11.5689i	0.242093	−	1.37298i	0.827147	−	0.561985i	$-0.189962\pi$
$72$		0			0
$73$	2.70207	+	15.3242i	0.316253	+	1.79356i	0.565106	+	0.825019i	$0.308835\pi$
$73$	2.70207	+	15.3242i	0.316253	+	1.79356i	−0.248853	+	0.968541i	$0.580053\pi$
$74$	−4.68464	−	0.547556i	−0.544579	−	0.0636521i
$75$		0			0
$76$	1.77672	−	1.88321i	0.203804	−	0.216019i
$77$	6.04817	−	14.0212i	0.689253	−	1.59787i
$78$		0			0
$79$	11.6941	−	7.69136i	1.31569	−	0.865346i	0.319093	−	0.947723i	$-0.396622\pi$
$79$	11.6941	−	7.69136i	1.31569	−	0.865346i	0.996601	+	0.0823774i	$0.0262513\pi$
$80$	−2.35277			−0.263048
$81$		0			0
$82$	−9.17740			−1.01347
$83$	0.587346	−	0.386304i	0.0644696	−	0.0424023i	−0.516865	−	0.856067i	$-0.672901\pi$
$83$	0.587346	−	0.386304i	0.0644696	−	0.0424023i	0.581335	+	0.813665i	$0.302531\pi$
$84$		0			0
$85$	−0.302737	+	0.701823i	−0.0328364	+	0.0761234i
$86$	0.252487	−	0.267620i	0.0272263	−	0.0288582i
$87$		0			0
$88$	−9.48034	−	1.10809i	−1.01061	−	0.118123i
$89$	−2.00921	−	11.3948i	−0.212976	−	1.20785i	−0.884384	−	0.466760i	$-0.845421\pi$
$89$	−2.00921	−	11.3948i	−0.212976	−	1.20785i	0.671408	−	0.741088i	$-0.265690\pi$
$90$		0			0
$91$	2.15620	−	12.2284i	0.226032	−	1.28189i
$92$	−0.131358	+	0.438765i	−0.0136950	+	0.0457444i
$93$		0			0
$94$	0.425507	−	7.30568i	0.0438877	−	0.753523i
$95$	−3.05023	+	1.53188i	−0.312947	+	0.157168i
$96$		0			0
$97$	8.92799	+	9.46312i	0.906500	+	0.960834i	0.999393	−	0.0348418i	$-0.0110927\pi$
$97$	8.92799	+	9.46312i	0.906500	+	0.960834i	−0.0928924	+	0.995676i	$0.529611\pi$
$98$	12.9298	−	4.70606i	1.30611	−	0.475384i
$99$		0			0
$100$	1.71979	+	0.625952i	0.171979	+	0.0625952i
$101$	4.89713	+	11.3528i	0.487283	+	1.12965i	0.967585	+	0.252545i	$0.0812677\pi$
$101$	4.89713	+	11.3528i	0.487283	+	1.12965i	−0.480302	+	0.877103i	$0.659473\pi$
$102$		0			0
$103$	0.599460	+	2.00234i	0.0590666	+	0.197296i	0.982430	−	0.186631i	$-0.0597567\pi$
$103$	0.599460	+	2.00234i	0.0590666	+	0.197296i	−0.923364	+	0.383927i	$0.874572\pi$
$104$	−7.70907	+	0.901062i	−0.755937	+	0.0883564i
$105$		0			0
$106$	1.22359	+	21.0082i	0.118846	+	2.04050i
$107$	−0.831363	−	1.43996i	−0.0803709	−	0.139207i	0.823038	−	0.567986i	$-0.192277\pi$
$107$	−0.831363	−	1.43996i	−0.0803709	−	0.139207i	−0.903409	+	0.428779i	$0.858944\pi$
$108$		0			0
$109$	−2.14981	+	3.72357i	−0.205914	+	0.356654i	−0.950424	−	0.310958i	$-0.899350\pi$
$109$	−2.14981	+	3.72357i	−0.205914	+	0.356654i	0.744510	+	0.667612i	$0.232683\pi$
$110$	−2.68959	−	1.35076i	−0.256442	−	0.128790i
$111$		0			0
$112$	−11.0109	−	14.7902i	−1.04043	−	1.39754i
$113$	13.8508	+	3.28270i	1.30297	+	0.308810i	0.822784	−	0.568354i	$-0.192420\pi$
$113$	13.8508	+	3.28270i	1.30297	+	0.308810i	0.480189	+	0.877165i	$0.340568\pi$
$114$		0			0
$115$	0.360573	−	0.484334i	0.0336236	−	0.0451644i
$116$	−2.04501	+	1.71596i	−0.189874	+	0.159323i
$117$		0			0
$118$	−1.65281	−	1.38687i	−0.152154	−	0.127672i
$119$	−5.82865	+	1.38142i	−0.534312	+	0.126634i
$120$		0			0
$121$	−3.05618	−	2.01008i	−0.277834	−	0.182735i
$122$	−0.405219	−	0.266517i	−0.0366868	−	0.0241293i
$123$		0			0
$124$	−0.0174112	+	0.00412654i	−0.00156357	+	0.000370574i
$125$	−3.79760	−	3.18657i	−0.339668	−	0.285015i
$126$		0			0
$127$	14.1754	−	11.8946i	1.25787	−	1.05548i	0.261961	−	0.965078i	$-0.415631\pi$
$127$	14.1754	−	11.8946i	1.25787	−	1.05548i	0.995906	−	0.0903976i	$-0.0288138\pi$
$128$	−8.03198	+	10.7888i	−0.709933	+	0.953606i
$129$		0			0
$130$	−2.38143	−	0.564410i	−0.208865	−	0.0495020i
$131$	3.31614	+	4.45435i	0.289732	+	0.389178i	0.923029	−	0.384731i	$-0.125706\pi$
$131$	3.31614	+	4.45435i	0.289732	+	0.389178i	−0.633296	+	0.773909i	$0.718299\pi$
$132$		0			0
$133$	−23.9048	−	12.0054i	−2.07281	−	1.04100i
$134$	4.24205	−	7.34745i	0.366458	−	0.634723i
$135$		0			0
$136$	1.87212	+	3.24261i	0.160533	+	0.278052i
$137$	0.173481	+	2.97856i	0.0148215	+	0.254475i	0.997577	+	0.0695670i	$0.0221618\pi$
$137$	0.173481	+	2.97856i	0.0148215	+	0.254475i	−0.982756	+	0.184908i	$0.940801\pi$
$138$		0			0
$139$	5.85385	−	0.684217i	0.496517	−	0.0580345i	0.135851	−	0.990729i	$-0.456623\pi$
$139$	5.85385	−	0.684217i	0.496517	−	0.0580345i	0.360667	+	0.932695i	$0.382549\pi$
$140$	−0.224730	−	0.750649i	−0.0189931	−	0.0634415i
$141$		0			0
$142$	−7.18724	−	16.6619i	−0.603140	−	1.39824i
$143$	−11.2005	−	4.07665i	−0.936633	−	0.340907i
$144$		0			0
$145$	3.30719	−	1.20372i	0.274647	−	0.0999633i
$146$	16.4946	+	17.4832i	1.36510	+	1.44692i
$147$		0			0
$148$	−1.05333	+	0.529002i	−0.0865831	+	0.0434837i
$149$	0.316650	−	5.43668i	0.0259410	−	0.445390i	−0.960182	−	0.279375i	$-0.909873\pi$
$149$	0.316650	−	5.43668i	0.0259410	−	0.445390i	0.986123	−	0.166015i	$-0.0530901\pi$
$150$		0			0
$151$	4.27673	−	14.2853i	0.348035	−	1.16252i	−0.587482	−	0.809237i	$-0.699881\pi$
$151$	4.27673	−	14.2853i	0.348035	−	1.16252i	0.935517	−	0.353281i	$-0.114934\pi$
$152$	−2.90352	+	16.4667i	−0.235507	+	1.33563i
$153$		0			0
$154$	−4.09590	−	23.2290i	−0.330057	−	1.87185i
$155$	0.0234305	+	0.00273864i	0.00188199	+	0.000219973i
$156$		0			0
$157$	−5.75380	+	6.09867i	−0.459203	+	0.486727i	−0.915055	−	0.403329i	$-0.867853\pi$
$157$	−5.75380	+	6.09867i	−0.459203	+	0.486727i	0.455852	+	0.890056i	$0.349335\pi$
$158$	8.56345	−	19.8523i	0.681272	−	1.57937i
$159$		0			0
$160$	−0.916293	+	0.602656i	−0.0724394	+	0.0476441i
$161$	4.73212			0.372944
$162$		0			0
$163$	3.04537			0.238531			0.119266	−	0.992862i	$-0.461946\pi$
$163$	3.04537			0.238531			0.119266	+	0.992862i	$0.461946\pi$
$164$	−1.91620	+	1.26031i	−0.149630	+	0.0984134i
$165$		0			0
$166$	0.430105	−	0.997096i	0.0333826	−	0.0773896i
$167$	−14.4823	+	15.3503i	−1.12067	+	1.18785i	−0.140422	+	0.990092i	$0.544846\pi$
$167$	−14.4823	+	15.3503i	−1.12067	+	1.18785i	−0.980252	+	0.197753i	$0.936635\pi$
$168$		0			0
$169$	3.28526	+	0.383992i	0.252712	+	0.0295378i
$170$	0.205018	+	1.16271i	0.0157241	+	0.0891760i
$171$		0			0
$172$	0.0159666	−	0.0905513i	0.00121744	−	0.00690447i
$173$	0.486058	−	1.62355i	0.0369543	−	0.123436i	−0.937522	−	0.347925i	$-0.886886\pi$
$173$	0.486058	−	1.62355i	0.0369543	−	0.123436i	0.974477	+	0.224489i	$0.0720714\pi$
$174$		0			0
$175$	1.09947	−	18.8773i	0.0831125	−	1.42699i
$176$	−15.8170	+	7.94358i	−1.19225	+	0.598770i
$177$		0			0
$178$	−12.2651	−	13.0002i	−0.919307	−	0.974409i
$179$	−11.3362	+	4.12604i	−0.847308	+	0.308395i	−0.728942	−	0.684575i	$-0.759988\pi$
$179$	−11.3362	+	4.12604i	−0.847308	+	0.308395i	−0.118366	+	0.992970i	$0.537765\pi$
$180$		0			0
$181$	−7.09567	−	2.58261i	−0.527417	−	0.191964i	0.0645678	−	0.997913i	$-0.479433\pi$
$181$	−7.09567	−	2.58261i	−0.527417	−	0.191964i	−0.591985	+	0.805949i	$0.701655\pi$
$182$	−7.59697	−	17.6117i	−0.563125	−	1.30547i
$183$		0			0
$184$	−0.848339	−	2.83365i	−0.0625404	−	0.208899i
$185$	1.54344	−	0.180403i	0.113476	−	0.0132635i
$186$		0			0
$187$	0.334333	+	5.74027i	0.0244488	+	0.419770i
$188$	−0.914425	−	1.58383i	−0.0666913	−	0.115513i
$189$		0			0
$190$	−2.63622	+	4.56607i	−0.191251	+	0.331257i
$191$	11.5732	+	5.81226i	0.837404	+	0.420560i	0.815190	−	0.579193i	$-0.196632\pi$
$191$	11.5732	+	5.81226i	0.837404	+	0.420560i	0.0222137	+	0.999753i	$0.492929\pi$
$192$		0			0
$193$	10.7961	+	14.5016i	0.777118	+	1.04385i	0.997653	+	0.0684715i	$0.0218122\pi$
$193$	10.7961	+	14.5016i	0.777118	+	1.04385i	−0.220535	+	0.975379i	$0.570780\pi$
$194$	19.5545	+	4.63451i	1.40393	+	0.332738i
$195$		0			0
$196$	2.05342	−	2.75822i	0.146673	−	0.197016i
$197$	−7.47510	+	6.27235i	−0.532579	+	0.446886i	−0.868991	−	0.494828i	$-0.835231\pi$
$197$	−7.47510	+	6.27235i	−0.532579	+	0.446886i	0.336412	+	0.941715i	$0.390786\pi$
$198$		0			0
$199$	−6.35460	−	5.33214i	−0.450465	−	0.377985i	0.389143	−	0.921177i	$-0.372771\pi$
$199$	−6.35460	−	5.33214i	−0.450465	−	0.377985i	−0.839609	+	0.543192i	$0.817216\pi$
$200$	−11.5010	+	2.72579i	−0.813245	+	0.192743i
$201$		0			0
$202$	15.9565	+	10.4947i	1.12269	+	0.738407i
$203$	23.0444	+	15.1565i	1.61740	+	1.06378i
$204$		0			0
$205$	2.94216	−	0.697305i	0.205490	−	0.0487019i
$206$	2.47325	+	2.07530i	0.172320	+	0.144593i
$207$		0			0
$208$	−11.0255	+	9.25146i	−0.764478	+	0.641473i
$209$	−15.3337	+	20.5968i	−1.06066	+	1.42471i
$210$		0			0
$211$	−11.0335	−	2.61499i	−0.759577	−	0.180023i	−0.167464	−	0.985878i	$-0.553558\pi$
$211$	−11.0335	−	2.61499i	−0.759577	−	0.180023i	−0.592113	+	0.805855i	$0.701706\pi$
$212$	3.14049	+	4.21840i	0.215689	+	0.289721i
$213$		0			0
$214$	−2.29519	−	1.15269i	−0.156896	−	0.0787960i
$215$	−0.0606102	+	0.104980i	−0.00413358	+	0.00715957i
$216$		0			0
$217$	0.0924381	+	0.160108i	0.00627511	+	0.0108688i
$218$	0.386170	+	6.63028i	0.0261547	+	0.449059i
$219$		0			0
$220$	−0.747071	+	0.0873201i	−0.0503676	+	0.00588712i
$221$	1.34100	+	4.47926i	0.0902057	+	0.301308i
$222$		0			0
$223$	7.49598	+	17.3776i	0.501968	+	1.16369i	0.961319	+	0.275438i	$0.0888227\pi$
$223$	7.49598	+	17.3776i	0.501968	+	1.16369i	−0.459351	+	0.888255i	$0.651918\pi$
$224$	−8.07667	−	2.93967i	−0.539646	−	0.196415i
$225$		0			0
$226$	20.6617	−	7.52023i	1.37439	−	0.500239i
$227$	−7.61638	−	8.07290i	−0.505517	−	0.535817i	0.423479	−	0.905906i	$-0.360809\pi$
$227$	−7.61638	−	8.07290i	−0.505517	−	0.535817i	−0.928996	+	0.370089i	$0.879327\pi$
$228$		0			0
$229$	2.72124	−	1.36666i	0.179825	−	0.0903113i	−0.356609	−	0.934254i	$-0.616067\pi$
$229$	2.72124	−	1.36666i	0.179825	−	0.0903113i	0.536434	+	0.843942i	$0.319771\pi$
$230$	0.0542316	−	0.931121i	0.00357593	−	0.0613963i
$231$		0			0
$232$	4.94468	−	16.5164i	0.324634	−	1.08435i
$233$	2.47370	−	14.0290i	0.162057	−	0.919073i	−0.789989	−	0.613121i	$-0.789914\pi$
$233$	2.47370	−	14.0290i	0.162057	−	0.919073i	0.952047	−	0.305953i	$-0.0989750\pi$
$234$		0			0
$235$	0.418679	+	2.37444i	0.0273116	+	0.154892i
$236$	−0.535556	−	0.0625975i	−0.0348617	−	0.00407475i
$237$		0			0
$238$	−6.34966	+	6.73024i	−0.411587	+	0.436257i
$239$	3.14737	−	7.29642i	0.203586	−	0.471966i	−0.785581	−	0.618759i	$-0.787636\pi$
$239$	3.14737	−	7.29642i	0.203586	−	0.471966i	0.989167	+	0.146793i	$0.0468950\pi$
$240$		0			0
$241$	−3.02761	+	1.99129i	−0.195026	+	0.128270i	−0.643266	−	0.765643i	$-0.722421\pi$
$241$	−3.02761	+	1.99129i	−0.195026	+	0.128270i	0.448241	+	0.893913i	$0.352051\pi$
$242$	−5.65036			−0.363219
$243$		0			0
$244$	−0.121208			−0.00775955
$245$	−3.78757	+	2.49112i	−0.241979	+	0.159152i
$246$		0			0
$247$	−8.27026	+	19.1726i	−0.526224	+	1.21993i
$248$	0.0793026	−	0.0840558i	0.00503572	−	0.00533755i
$249$		0			0
$250$	−7.60584	−	0.888995i	−0.481035	−	0.0562250i
$251$	0.441351	+	2.50303i	0.0278578	+	0.157990i	0.995563	−	0.0940939i	$-0.0299954\pi$
$251$	0.441351	+	2.50303i	0.0278578	+	0.157990i	−0.967706	+	0.252083i	$0.918884\pi$
$252$		0			0
$253$	0.788785	−	4.47342i	0.0495905	−	0.281242i
$254$	8.19794	−	27.3830i	0.514384	−	1.71816i
$255$		0			0
$256$	−0.519916	+	8.92662i	−0.0324948	+	0.557914i
$257$	25.0214	−	12.5662i	1.56079	−	0.783860i	0.561739	−	0.827314i	$-0.310133\pi$
$257$	25.0214	−	12.5662i	1.56079	−	0.783860i	0.999055	+	0.0434541i	$0.0138362\pi$
$258$		0			0
$259$	8.35731	+	8.85823i	0.519298	+	0.550424i
$260$	−0.574742	+	0.209189i	−0.0356440	+	0.0129733i
$261$		0			0
$262$	8.06059	+	2.93381i	0.497985	+	0.181252i
$263$	0.974610	+	2.25940i	0.0600970	+	0.139321i	0.945618	−	0.325278i	$-0.105458\pi$
$263$	0.974610	+	2.25940i	0.0600970	+	0.139321i	−0.885521	+	0.464599i	$0.846199\pi$
$264$		0			0
$265$	−1.98849	−	6.64202i	−0.122152	−	0.408016i
$266$	−41.0410	+	4.79700i	−2.51638	+	0.294123i
$267$		0			0
$268$	−0.123282	−	2.11667i	−0.00753064	−	0.129296i
$269$	5.65271	+	9.79078i	0.344652	+	0.596954i	0.985290	−	0.170888i	$-0.0546637\pi$
$269$	5.65271	+	9.79078i	0.344652	+	0.596954i	−0.640639	+	0.767842i	$0.721330\pi$
$270$		0			0
$271$	2.14084	−	3.70804i	0.130047	−	0.225248i	−0.793648	−	0.608378i	$-0.791821\pi$
$271$	2.14084	−	3.70804i	0.130047	−	0.225248i	0.923694	+	0.383130i	$0.125154\pi$
$272$	6.20465	+	3.11609i	0.376212	+	0.188941i
$273$		0			0
$274$	2.75213	+	3.69675i	0.166262	+	0.223329i
$275$	−17.6620	−	4.18597i	−1.06506	−	0.252423i
$276$		0			0
$277$	11.2400	−	15.0980i	0.675349	−	0.907151i	−0.323893	−	0.946094i	$-0.604992\pi$
$277$	11.2400	−	15.0980i	0.675349	−	0.907151i	0.999241	+	0.0389429i	$0.0123990\pi$
$278$	6.97397	−	5.85185i	0.418271	−	0.350971i
$279$		0			0
$280$	3.87654	+	3.25280i	0.231668	+	0.194392i
$281$	13.2369	−	3.13720i	0.789647	−	0.187150i	0.184046	−	0.982918i	$-0.441081\pi$
$281$	13.2369	−	3.13720i	0.789647	−	0.187150i	0.605602	+	0.795768i	$0.292932\pi$
$282$		0			0
$283$	−13.9445	−	9.17147i	−0.828917	−	0.545187i	0.0626713	−	0.998034i	$-0.480038\pi$
$283$	−13.9445	−	9.17147i	−0.828917	−	0.545187i	−0.891588	+	0.452847i	$0.850408\pi$
$284$	−3.78880	−	2.49193i	−0.224824	−	0.147869i
$285$		0			0
$286$	−17.9152	+	4.24599i	−1.05935	+	0.251071i
$287$	18.1527	+	15.2319i	1.07152	+	0.899110i
$288$		0			0
$289$	−11.2949	+	9.47752i	−0.664404	+	0.557501i
$290$	3.24639	−	4.36066i	0.190634	−	0.256067i
$291$		0			0
$292$	5.84492	+	1.38527i	0.342048	+	0.0810669i
$293$	15.1735	+	20.3815i	0.886444	+	1.19070i	0.980771	+	0.195160i	$0.0625225\pi$
$293$	15.1735	+	20.3815i	0.886444	+	1.19070i	−0.0943276	+	0.995541i	$0.530070\pi$
$294$		0			0
$295$	0.635248	+	0.319033i	0.0369855	+	0.0185748i
$296$	3.80617	−	6.59249i	0.221229	−	0.383181i
$297$		0			0
$298$	−4.20607	−	7.28513i	−0.243651	−	0.422016i
$299$	−0.214772	−	3.68749i	−0.0124206	−	0.213253i
$300$		0			0
$301$	−0.943585	+	0.110289i	−0.0543874	+	0.00635697i
$302$	−6.60616	−	22.0661i	−0.380142	−	1.26976i
$303$		0			0
$304$	12.2809	+	28.4704i	0.704361	+	1.63289i
$305$	0.150158	+	0.0546532i	0.00859805	+	0.00312943i
$306$		0			0
$307$	−9.43080	+	3.43253i	−0.538244	+	0.195905i	−0.596816	−	0.802378i	$-0.703568\pi$
$307$	−9.43080	+	3.43253i	−0.538244	+	0.195905i	0.0585714	+	0.998283i	$0.481345\pi$
$308$	−4.04518	−	4.28764i	−0.230496	−	0.244311i
$309$		0			0
$310$	0.0325631	−	0.0163538i	0.00184946	−	0.000928834i
$311$	1.56707	−	26.9055i	0.0888602	−	1.52567i	−0.599543	−	0.800342i	$-0.704651\pi$
$311$	1.56707	−	26.9055i	0.0888602	−	1.52567i	0.688403	−	0.725328i	$-0.258312\pi$
$312$		0			0
$313$	−3.73743	+	12.4839i	−0.211252	+	0.705631i	0.785028	+	0.619460i	$0.212648\pi$
$313$	−3.73743	+	12.4839i	−0.211252	+	0.705631i	−0.996280	+	0.0861711i	$0.972537\pi$
$314$	−2.24898	+	12.7546i	−0.126917	+	0.719784i
$315$		0			0
$316$	−0.938250	−	5.32108i	−0.0527807	−	0.299334i
$317$	9.42954	+	1.10216i	0.529616	+	0.0619032i	0.376699	−	0.926336i	$-0.377059\pi$
$317$	9.42954	+	1.10216i	0.529616	+	0.0619032i	0.152917	+	0.988239i	$0.451133\pi$
$318$		0			0
$319$	18.1691	−	19.2582i	1.01728	−	1.07825i
$320$	1.19278	−	2.76518i	0.0666785	−	0.154578i
$321$		0			0
$322$	6.10709	−	4.01669i	0.340335	−	0.223842i
$323$	10.0729			0.560468
$324$		0			0
$325$	−14.7599			−0.818735
$326$	3.93023	−	2.58495i	0.217675	−	0.143167i
$327$		0			0
$328$	5.86675	−	13.6007i	0.323937	−	0.750971i
$329$	−12.9670	+	13.7442i	−0.714894	+	0.757744i
$330$		0			0
$331$	23.3551	+	2.72982i	1.28371	+	0.150045i	0.730452	−	0.682964i	$-0.239309\pi$
$331$	23.3551	+	2.72982i	1.28371	+	0.150045i	0.553261	+	0.833008i	$0.313383\pi$
$332$	−0.0471242	−	0.267255i	−0.00258628	−	0.0146675i
$333$		0			0
$334$	−5.66068	+	32.1033i	−0.309739	+	1.75661i
$335$	−0.801686	+	2.67782i	−0.0438008	+	0.146305i
$336$		0			0
$337$	0.180721	−	3.10287i	0.00984453	−	0.169024i	−0.989802	−	0.142448i	$-0.954503\pi$
$337$	0.180721	−	3.10287i	0.00984453	−	0.169024i	0.999647	−	0.0265759i	$-0.00846036\pi$
$338$	4.56576	−	2.29301i	0.248344	−	0.124723i
$339$		0			0
$340$	0.202479	+	0.214615i	0.0109810	+	0.0116391i
$341$	0.166763	−	0.0606967i	0.00903071	−	0.00328691i
$342$		0			0
$343$	−7.15012	−	2.60243i	−0.386070	−	0.140518i
$344$	0.235201	+	0.545258i	0.0126812	+	0.0293983i
$345$		0			0
$346$	−0.750803	−	2.50786i	−0.0403634	−	0.134823i
$347$	−22.1439	+	2.58826i	−1.18875	+	0.138945i	−0.687386	−	0.726292i	$-0.741242\pi$
$347$	−22.1439	+	2.58826i	−1.18875	+	0.138945i	−0.501363	+	0.865237i	$0.667168\pi$
$348$		0			0
$349$	−0.175177	−	3.00767i	−0.00937701	−	0.160997i	−0.999746	−	0.0225430i	$-0.992824\pi$
$349$	−0.175177	−	3.00767i	−0.00937701	−	0.160997i	0.990369	−	0.138454i	$-0.0442133\pi$
$350$	−14.6043	−	25.2955i	−0.780635	−	1.35210i
$351$		0			0
$352$	−4.12524	+	7.14512i	−0.219876	+	0.380836i
$353$	−1.93406	−	0.971320i	−0.102939	−	0.0516981i	0.396584	−	0.917998i	$-0.370195\pi$
$353$	−1.93406	−	0.971320i	−0.102939	−	0.0516981i	−0.499524	+	0.866300i	$0.666492\pi$
$354$		0			0
$355$	3.57013	+	4.79551i	0.189483	+	0.254519i
$356$	−4.34619	−	1.03007i	−0.230348	−	0.0545934i
$357$		0			0
$358$	−11.1278	+	14.9472i	−0.588123	+	0.789986i
$359$	0.496794	−	0.416860i	0.0262198	−	0.0220010i	−0.629584	−	0.776933i	$-0.716774\pi$
$359$	0.496794	−	0.416860i	0.0262198	−	0.0220010i	0.655803	+	0.754932i	$0.272330\pi$
$360$		0			0
$361$	19.9037	+	16.7012i	1.04756	+	0.879011i
$362$	−11.3495	+	2.68989i	−0.596518	+	0.141377i
$363$		0			0
$364$	−4.00479	−	2.63399i	−0.209908	−	0.138059i
$365$	−6.61635	−	4.35164i	−0.346315	−	0.227775i
$366$		0			0
$367$	−9.21403	+	2.18376i	−0.480968	+	0.113992i	−0.463946	−	0.885864i	$-0.653567\pi$
$367$	−9.21403	+	2.18376i	−0.480968	+	0.113992i	−0.0170223	+	0.999855i	$0.505419\pi$
$368$	−4.20178	−	3.52571i	−0.219033	−	0.183790i
$369$		0			0
$370$	1.83878	−	1.54292i	0.0955935	−	0.0802124i
$371$	32.4475	−	43.5846i	1.68459	−	2.26280i
$372$		0			0
$373$	−4.75011	−	1.12580i	−0.245951	−	0.0582915i	0.105791	−	0.994388i	$-0.466263\pi$
$373$	−4.75011	−	1.12580i	−0.245951	−	0.0582915i	−0.351742	+	0.936097i	$0.614411\pi$
$374$	5.30390	+	7.12437i	0.274258	+	0.368392i
$375$		0			0
$376$	10.5548	+	5.30083i	0.544323	+	0.273369i
$377$	10.7648	−	18.6452i	0.554415	−	0.960275i
$378$		0			0
$379$	13.0190	+	22.5495i	0.668739	+	1.15829i	0.978257	+	0.207396i	$0.0664989\pi$
$379$	13.0190	+	22.5495i	0.668739	+	1.15829i	−0.309518	+	0.950894i	$0.600168\pi$
$380$	0.0766134	+	1.31540i	0.00393018	+	0.0674787i
$381$		0			0
$382$	19.8694	−	2.32240i	1.01661	−	0.118824i
$383$	−2.30331	−	7.69359i	−0.117694	−	0.393124i	0.878760	−	0.477263i	$-0.158371\pi$
$383$	−2.30331	−	7.69359i	−0.117694	−	0.393124i	−0.996454	+	0.0841390i	$0.973186\pi$
$384$		0			0
$385$	3.07805	+	7.13573i	0.156872	+	0.363670i
$386$	26.2422	+	9.55136i	1.33569	+	0.486152i
$387$		0			0
$388$	4.71935	−	1.71770i	0.239589	−	0.0872032i
$389$	−15.6093	−	16.5449i	−0.791422	−	0.838858i	0.198555	−	0.980090i	$-0.436375\pi$
$389$	−15.6093	−	16.5449i	−0.791422	−	0.838858i	−0.989977	+	0.141231i	$0.954894\pi$
$390$		0			0
$391$	−1.59236	+	0.799714i	−0.0805291	+	0.0404433i
$392$	−1.29126	+	22.1700i	−0.0652184	+	1.11976i
$393$		0			0
$394$	−4.32300	+	14.4398i	−0.217789	+	0.727467i
$395$	−1.23695	+	7.01507i	−0.0622375	+	0.352967i
$396$		0			0
$397$	4.29294	+	24.3465i	0.215456	+	1.22191i	0.880113	+	0.474765i	$0.157467\pi$
$397$	4.29294	+	24.3465i	0.215456	+	1.22191i	−0.664656	+	0.747149i	$0.731422\pi$
$398$	−12.7270	−	1.48757i	−0.637946	−	0.0745652i
$399$		0			0
$400$	−15.0409	+	15.9424i	−0.752046	+	0.797122i
$401$	6.72403	−	15.5880i	0.335782	−	0.778430i	−0.663754	−	0.747951i	$-0.731038\pi$
$401$	6.72403	−	15.5880i	0.335782	−	0.778430i	0.999535	−	0.0304785i	$-0.00970310\pi$
$402$		0			0
$403$	0.120568	−	0.0792988i	0.00600592	−	0.00395015i
$404$	4.77286			0.237459
$405$		0			0
$406$	42.6052			2.11446
$407$	9.76702	−	6.42387i	0.484133	−	0.318419i
$408$		0			0
$409$	4.47516	−	10.3746i	0.221282	−	0.512990i	−0.771023	−	0.636808i	$-0.780255\pi$
$409$	4.47516	−	10.3746i	0.221282	−	0.512990i	0.992305	+	0.123818i	$0.0395138\pi$
$410$	3.20515	−	3.39726i	0.158291	−	0.167779i
$411$		0			0
$412$	0.801401	+	0.0936703i	0.0394822	+	0.00461481i
$413$	0.967401	+	5.48640i	0.0476027	+	0.269968i
$414$		0			0
$415$	−0.0621265	+	0.352337i	−0.00304967	+	0.0172955i
$416$	−1.92416	+	6.42715i	−0.0943398	+	0.315117i
$417$		0			0
$418$	−2.30625	+	39.5969i	−0.112803	+	1.93675i
$419$	−28.9814	+	14.5550i	−1.41584	+	0.711059i	−0.981814	−	0.189843i	$-0.939202\pi$
$419$	−28.9814	+	14.5550i	−1.41584	+	0.711059i	−0.434021	+	0.900903i	$0.642906\pi$
$420$		0			0
$421$	0.455943	+	0.483271i	0.0222213	+	0.0235532i	0.738389	−	0.674375i	$-0.235587\pi$
$421$	0.455943	+	0.483271i	0.0222213	+	0.0235532i	−0.716168	+	0.697928i	$0.754105\pi$
$422$	−16.4590	+	5.99059i	−0.801212	+	0.291617i
$423$		0			0
$424$	−31.9159	−	11.6164i	−1.54997	−	0.564144i
$425$	2.82022	+	6.53801i	0.136801	+	0.317140i
$426$		0			0
$427$	0.359170	+	1.19971i	0.0173815	+	0.0580581i
$428$	−0.637521	+	0.0745155i	−0.0308157	+	0.00360184i
$429$		0			0
$430$	0.0108874	+	0.186930i	0.000525037	+	0.00901454i
$431$	15.1861	+	26.3031i	0.731488	+	1.26698i	0.956247	+	0.292561i	$0.0945073\pi$
$431$	15.1861	+	26.3031i	0.731488	+	1.26698i	−0.224759	+	0.974414i	$0.572159\pi$
$432$		0			0
$433$	5.68299	−	9.84323i	0.273107	−	0.473035i	−0.696549	−	0.717510i	$-0.745282\pi$
$433$	5.68299	−	9.84323i	0.273107	−	0.473035i	0.969656	+	0.244474i	$0.0786153\pi$
$434$	0.255198	+	0.128165i	0.0122499	+	0.00615214i
$435$		0			0
$436$	0.991149	+	1.33134i	0.0474674	+	0.0637598i
$437$	−7.74294	−	1.83511i	−0.370395	−	0.0877853i
$438$		0			0
$439$	−4.28247	+	5.75236i	−0.204391	+	0.274545i	−0.892485	−	0.451076i	$-0.851040\pi$
$439$	−4.28247	+	5.75236i	−0.204391	+	0.274545i	0.688094	+	0.725621i	$0.258448\pi$
$440$	3.72114	−	3.12241i	0.177399	−	0.148855i
$441$		0			0
$442$	5.53271	+	4.64249i	0.263164	+	0.220821i
$443$	1.69953	−	0.402796i	0.0807471	−	0.0191374i	−0.190044	−	0.981776i	$-0.560863\pi$
$443$	1.69953	−	0.402796i	0.0807471	−	0.0191374i	0.270791	+	0.962638i	$0.412715\pi$
$444$		0			0
$445$	4.91981	+	3.23581i	0.233221	+	0.153392i
$446$	24.4244	+	16.0642i	1.15653	+	0.760661i
$447$		0			0
$448$	22.9649	−	5.44277i	1.08499	−	0.257147i
$449$	−25.6694	−	21.5392i	−1.21142	−	1.01650i	−0.999229	−	0.0392691i	$-0.987497\pi$
$449$	−25.6694	−	21.5392i	−1.21142	−	1.01650i	−0.212187	−	0.977229i	$-0.568059\pi$
$450$		0			0
$451$	17.4250	−	14.6213i	0.820510	−	0.688490i
$452$	3.28134	−	4.40761i	0.154341	−	0.207316i
$453$		0			0
$454$	−16.6818	−	3.95366i	−0.782915	−	0.185554i
$455$	3.77365	+	5.06889i	0.176911	+	0.237633i
$456$		0			0
$457$	10.2116	+	5.12846i	0.477679	+	0.239899i	0.671312	−	0.741175i	$-0.265731\pi$
$457$	10.2116	+	5.12846i	0.477679	+	0.239899i	−0.193634	+	0.981074i	$0.562027\pi$
$458$	2.35188	−	4.07358i	0.109896	−	0.190346i
$459$		0			0
$460$	−0.116545	−	0.201862i	−0.00543394	−	0.00941186i
$461$	0.967981	+	16.6196i	0.0450834	+	0.774051i	0.942776	+	0.333428i	$0.108205\pi$
$461$	0.967981	+	16.6196i	0.0450834	+	0.774051i	−0.897692	+	0.440623i	$0.854758\pi$
$462$		0			0
$463$	4.54546	−	0.531288i	0.211245	−	0.0246910i	−0.00981201	−	0.999952i	$-0.503123\pi$
$463$	4.54546	−	0.531288i	0.211245	−	0.0246910i	0.221057	+	0.975261i	$0.429049\pi$
$464$	−9.16922	−	30.6273i	−0.425670	−	1.42184i
$465$		0			0
$466$	−8.71560	−	20.2050i	−0.403742	−	0.935980i
$467$	31.8531	+	11.5936i	1.47398	+	0.536486i	0.949179	−	0.314736i	$-0.101916\pi$
$467$	31.8531	+	11.5936i	1.47398	+	0.536486i	0.524805	+	0.851222i	$0.324138\pi$
$468$		0			0
$469$	−20.5854	+	7.49246i	−0.950544	+	0.345970i
$470$	2.55579	+	2.70898i	0.117890	+	0.124956i
$471$		0			0
$472$	3.11189	−	1.56285i	0.143236	−	0.0719360i
$473$	−0.0530238	+	0.910384i	−0.00243804	+	0.0418595i
$474$		0			0
$475$	−9.11959	+	30.4616i	−0.418436	+	1.39767i
$476$	−0.401537	+	2.27723i	−0.0184044	+	0.104377i
$477$		0			0
$478$	−2.13144	−	12.0880i	−0.0974898	−	0.552892i
$479$	8.62453	+	1.00806i	0.394065	+	0.0460596i	0.310818	−	0.950469i	$-0.399397\pi$
$479$	8.62453	+	1.00806i	0.394065	+	0.0460596i	0.0832467	+	0.996529i	$0.473471\pi$
$480$		0			0
$481$	6.52345	−	6.91445i	0.297444	−	0.315272i
$482$	−2.21708	+	5.13976i	−0.100985	+	0.234110i
$483$		0			0
$484$	−1.17977	+	0.775949i	−0.0536261	+	0.0352704i
$485$	−6.62108			−0.300648
$486$		0			0
$487$	−21.3432			−0.967154			−0.483577	−	0.875302i	$-0.660663\pi$
$487$	−21.3432			−0.967154			−0.483577	+	0.875302i	$0.660663\pi$
$488$	0.654012	−	0.430150i	0.0296057	−	0.0194720i
$489$		0			0
$490$	−2.77358	+	6.42989i	−0.125298	+	0.290473i
$491$	2.89262	−	3.06600i	0.130542	−	0.138366i	−0.658805	−	0.752314i	$-0.728938\pi$
$491$	2.89262	−	3.06600i	0.130542	−	0.138366i	0.789347	+	0.613947i	$0.210419\pi$
$492$		0			0
$493$	−10.3158	−	1.20575i	−0.464602	−	0.0543042i
$494$	5.60073	+	31.7633i	0.251989	+	1.42910i
$495$		0			0
$496$	0.0372113	−	0.211036i	0.00167084	−	0.00947578i
$497$	−13.4379	+	44.8856i	−0.602770	+	2.01339i
$498$		0			0
$499$	−1.76905	+	30.3734i	−0.0791936	+	1.35970i	0.691445	+	0.722429i	$0.256975\pi$
$499$	−1.76905	+	30.3734i	−0.0791936	+	1.35970i	−0.770638	+	0.637273i	$0.780062\pi$
$500$	−1.71015	+	0.858870i	−0.0764803	+	0.0384098i
$501$		0			0
$502$	2.69419	+	2.85568i	0.120248	+	0.127455i
$503$	11.9111	−	4.33528i	0.531089	−	0.193301i	−0.0625356	−	0.998043i	$-0.519919\pi$
$503$	11.9111	−	4.33528i	0.531089	−	0.193301i	0.593624	+	0.804742i	$0.297696\pi$
$504$		0			0
$505$	−5.91285	−	2.15210i	−0.263118	−	0.0957673i
$506$	−2.77913	−	6.44275i	−0.123547	−	0.286415i
$507$		0			0
$508$	−2.04874	−	6.84326i	−0.0908981	−	0.303621i
$509$	−3.48848	+	0.407744i	−0.154624	+	0.0180730i	−0.193053	−	0.981188i	$-0.561839\pi$
$509$	−3.48848	+	0.407744i	−0.154624	+	0.0180730i	0.0384287	+	0.999261i	$0.487765\pi$
$510$		0			0
$511$	−3.60862	−	61.9577i	−0.159636	−	2.74085i
$512$	−6.54427	−	11.3350i	−0.289219	−	0.500941i
$513$		0			0
$514$	21.6252	−	37.4560i	0.953849	−	1.65211i
$515$	−0.950578	−	0.477398i	−0.0418875	−	0.0210367i
$516$		0			0
$517$	10.8314	+	14.5491i	0.476364	+	0.639869i
$518$	18.3046	+	4.33827i	0.804258	+	0.190613i
$519$		0			0
$520$	2.35880	−	3.16841i	0.103440	−	0.138944i
$521$	−6.50992	+	5.46247i	−0.285205	+	0.239315i	−0.774154	−	0.632997i	$-0.781825\pi$
$521$	−6.50992	+	5.46247i	−0.285205	+	0.239315i	0.488950	+	0.872312i	$0.337380\pi$
$522$		0			0
$523$	−9.72249	−	8.15814i	−0.425135	−	0.356730i	0.404978	−	0.914327i	$-0.367279\pi$
$523$	−9.72249	−	8.15814i	−0.425135	−	0.356730i	−0.830112	+	0.557596i	$0.811724\pi$
$524$	2.08591	−	0.494370i	0.0911234	−	0.0215966i
$525$		0			0
$526$	3.17560	+	2.08863i	0.138463	+	0.0910685i
$527$	−0.0581631	−	0.0382545i	−0.00253362	−	0.00166639i
$528$		0			0
$529$	−21.0103	+	4.97953i	−0.913491	+	0.216501i
$530$	−8.20411	−	6.88406i	−0.356364	−	0.299025i
$531$		0			0
$532$	−7.91043	+	6.63763i	−0.342960	+	0.287778i
$533$	11.0455	−	14.8367i	0.478435	−	0.642650i
$534$		0			0
$535$	0.823391	+	0.195147i	0.0355983	+	0.00843695i
$536$	8.17695	+	10.9836i	0.353191	+	0.474417i
$537$		0			0
$538$	15.6057	+	7.83748i	0.672810	+	0.337898i
$539$	−17.0520	+	29.5349i	−0.734481	+	1.27216i
$540$		0			0
$541$	−6.14520	−	10.6438i	−0.264203	−	0.457612i	0.703152	−	0.711040i	$-0.251775\pi$
$541$	−6.14520	−	10.6438i	−0.264203	−	0.457612i	−0.967354	+	0.253427i	$0.918442\pi$
$542$	−0.384559	−	6.60262i	−0.0165182	−	0.283607i
$543$		0			0
$544$	3.21460	−	0.375733i	0.137825	−	0.0161094i
$545$	−0.627575	−	2.09625i	−0.0268824	−	0.0897933i
$546$		0			0
$547$	−10.6521	−	24.6944i	−0.455452	−	1.05586i	−0.979000	−	0.203861i	$-0.934651\pi$
$547$	−10.6521	−	24.6944i	−0.455452	−	1.05586i	0.523548	−	0.851996i	$-0.324608\pi$
$548$	1.08230	+	0.393924i	0.0462335	+	0.0168276i
$549$		0			0
$550$	−26.3469	+	9.58950i	−1.12344	+	0.408898i
$551$	−31.8287	−	33.7365i	−1.35595	−	1.43722i
$552$		0			0
$553$	−49.8875	+	25.0545i	−2.12143	+	1.06542i
$554$	1.69055	−	29.0256i	0.0718245	−	1.23318i
$555$		0			0
$556$	0.652517	−	2.17956i	0.0276729	−	0.0924339i
$557$	−3.81879	+	21.6574i	−0.161807	+	0.917654i	0.790488	+	0.612477i	$0.209827\pi$
$557$	−3.81879	+	21.6574i	−0.161807	+	0.917654i	−0.952296	+	0.305177i	$0.901284\pi$
$558$		0			0
$559$	0.128768	+	0.730281i	0.00544631	+	0.0308876i
$560$	9.32047	+	1.08941i	0.393862	+	0.0460358i
$561$		0			0
$562$	14.4201	−	15.2844i	0.608275	−	0.644734i
$563$	−18.7536	+	43.4757i	−0.790370	+	1.83228i	−0.333505	+	0.942748i	$0.608232\pi$
$563$	−18.7536	+	43.4757i	−0.790370	+	1.83228i	−0.456865	+	0.889536i	$0.651028\pi$
$564$		0			0
$565$	−6.05249	+	3.98079i	−0.254630	+	0.167473i
$566$	−25.7811			−1.08366
$567$		0			0
$568$	29.2870			1.22886
$569$	−14.4816	+	9.52469i	−0.607099	+	0.399296i	−0.815508	−	0.578746i	$-0.803542\pi$
$569$	−14.4816	+	9.52469i	−0.607099	+	0.399296i	0.208408	+	0.978042i	$0.433172\pi$
$570$		0			0
$571$	14.1217	−	32.7377i	0.590973	−	1.37003i	−0.315967	−	0.948770i	$-0.602329\pi$
$571$	14.1217	−	32.7377i	0.590973	−	1.37003i	0.906940	−	0.421260i	$-0.138412\pi$
$572$	−3.15754	+	3.34680i	−0.132023	+	0.139937i
$573$		0			0
$574$	36.3561	+	4.24942i	1.51747	+	0.177367i
$575$	−0.976768	−	5.53953i	−0.0407341	−	0.231014i
$576$		0			0
$577$	−0.228884	+	1.29807i	−0.00952858	+	0.0540393i	−0.989201	−	0.146563i	$-0.953179\pi$
$577$	−0.228884	+	1.29807i	−0.00952858	+	0.0540393i	0.979673	+	0.200602i	$0.0642899\pi$
$578$	−6.53204	+	21.8185i	−0.271697	+	0.907532i
$579$		0			0
$580$	0.0789958	−	1.35630i	0.00328012	−	0.0563175i
$581$	−2.50563	+	1.25838i	−0.103951	+	0.0522063i
$582$		0			0
$583$	−35.7933	−	37.9386i	−1.48241	−	1.57126i
$584$	−36.4540	+	13.2682i	−1.50848	+	0.549041i
$585$		0			0
$586$	36.8824	+	13.4241i	1.52360	+	0.554544i
$587$	−1.99538	−	4.62581i	−0.0823582	−	0.190928i	0.872061	−	0.489397i	$-0.162783\pi$
$587$	−1.99538	−	4.62581i	−0.0823582	−	0.190928i	−0.954419	+	0.298469i	$0.903524\pi$
$588$		0			0
$589$	−0.0891625	−	0.297824i	−0.00367388	−	0.0122716i
$590$	1.09062	−	0.127476i	0.0449003	−	0.00524809i
$591$		0			0
$592$	−0.820774	−	14.0922i	−0.0337336	−	0.579184i
$593$	−13.0012	−	22.5187i	−0.533895	−	0.924732i	−0.999216	−	0.0395907i	$-0.987395\pi$
$593$	−13.0012	−	22.5187i	−0.533895	−	0.924732i	0.465321	−	0.885142i	$-0.345939\pi$
$594$		0			0
$595$	1.52425	−	2.64009i	0.0624883	−	0.108233i
$596$	−1.87866	−	0.943497i	−0.0769528	−	0.0386472i
$597$		0			0
$598$	−3.40717	−	4.57663i	−0.139330	−	0.187152i
$599$	17.4587	+	4.13779i	0.713344	+	0.169066i	0.571236	−	0.820786i	$-0.306464\pi$
$599$	17.4587	+	4.13779i	0.713344	+	0.169066i	0.142108	+	0.989851i	$0.454612\pi$
$600$		0			0
$601$	−20.4833	+	27.5138i	−0.835531	+	1.12231i	0.155389	+	0.987853i	$0.450337\pi$
$601$	−20.4833	+	27.5138i	−0.835531	+	1.12231i	−0.990919	+	0.134459i	$0.957070\pi$
$602$	−1.12414	+	0.943264i	−0.0458164	+	0.0384446i
$603$		0			0
$604$	−4.40962	−	3.70011i	−0.179425	−	0.150555i
$605$	1.81144	−	0.429319i	0.0736455	−	0.0174543i
$606$		0			0
$607$	1.64151	+	1.07964i	0.0666267	+	0.0438211i	0.582385	−	0.812913i	$-0.302120\pi$
$607$	1.64151	+	1.07964i	0.0666267	+	0.0438211i	−0.515759	+	0.856734i	$0.672490\pi$
$608$	12.0755	+	7.94216i	0.489725	+	0.322097i
$609$		0			0
$610$	0.240179	−	0.0569234i	0.00972456	−	0.00230476i
$611$	11.2987	+	9.48071i	0.457095	+	0.383549i
$612$		0			0
$613$	−1.60067	+	1.34312i	−0.0646505	+	0.0542482i	−0.674540	−	0.738238i	$-0.735658\pi$
$613$	−1.60067	+	1.34312i	−0.0646505	+	0.0542482i	0.609890	+	0.792486i	$0.291214\pi$
$614$	−9.25743	+	12.4349i	−0.373599	+	0.501831i
$615$		0			0
$616$	37.0431	+	8.77938i	1.49251	+	0.353731i
$617$	24.8220	+	33.3418i	0.999298	+	1.34229i	0.938928	+	0.344113i	$0.111820\pi$
$617$	24.8220	+	33.3418i	0.999298	+	1.34229i	0.0603694	+	0.998176i	$0.480772\pi$
$618$		0			0
$619$	−6.28378	−	3.15583i	−0.252567	−	0.126844i	0.318012	−	0.948087i	$-0.396985\pi$
$619$	−6.28378	−	3.15583i	−0.252567	−	0.126844i	−0.570579	+	0.821243i	$0.693281\pi$
$620$	0.00455322	−	0.00788641i	0.000182862	−	0.000316726i
$621$		0			0
$622$	−20.8154	−	36.0533i	−0.834620	−	1.44561i
$623$	2.68331	+	46.0707i	0.107505	+	1.84578i
$624$		0			0
$625$	−21.0388	+	2.45908i	−0.841553	+	0.0983634i
$626$	5.77312	+	19.2836i	0.230740	+	0.770727i
$627$		0			0
$628$	1.28198	+	2.97195i	0.0511564	+	0.118594i
$629$	−4.30925	−	1.56844i	−0.171821	−	0.0625378i
$630$		0			0
$631$	6.32771	−	2.30310i	0.251902	−	0.0916848i	−0.212983	−	0.977056i	$-0.568318\pi$
$631$	6.32771	−	2.30310i	0.251902	−	0.0916848i	0.464885	+	0.885371i	$0.346096\pi$
$632$	23.9463	+	25.3816i	0.952534	+	1.00963i
$633$		0			0
$634$	13.1049	−	6.58153i	0.520463	−	0.261386i
$635$	−0.547578	+	9.40155i	−0.0217300	+	0.373089i
$636$		0			0
$637$	−7.95367	+	26.5671i	−0.315136	+	1.05263i
$638$	7.10175	−	40.2760i	0.281161	−	1.59454i
$639$		0			0
$640$	−1.18865	−	6.74119i	−0.0469857	−	0.266469i
$641$	12.9949	+	1.51889i	0.513270	+	0.0599926i	0.368786	−	0.929515i	$-0.379774\pi$
$641$	12.9949	+	1.51889i	0.513270	+	0.0599926i	0.144484	+	0.989507i	$0.453848\pi$
$642$		0			0
$643$	1.79987	−	1.90775i	0.0709800	−	0.0752344i	−0.690910	−	0.722941i	$-0.742790\pi$
$643$	1.79987	−	1.90775i	0.0709800	−	0.0752344i	0.761890	+	0.647706i	$0.224272\pi$
$644$	0.723533	−	1.67734i	0.0285112	−	0.0660964i
$645$		0			0
$646$	12.9996	−	8.54998i	0.511463	−	0.336394i
$647$	−2.94663			−0.115844			−0.0579219	−	0.998321i	$-0.518447\pi$
$647$	−2.94663			−0.115844			−0.0579219	+	0.998321i	$0.518447\pi$
$648$		0			0
$649$	5.34772			0.209916
$650$	−19.0486	+	12.5285i	−0.747147	+	0.491406i
$651$		0			0
$652$	0.465631	−	1.07945i	0.0182355	−	0.0422747i
$653$	24.1758	−	25.6248i	0.946071	−	1.00278i	−0.0539200	−	0.998545i	$-0.517172\pi$
$653$	24.1758	−	25.6248i	0.946071	−	1.00278i	0.999991	−	0.00423147i	$-0.00134692\pi$
$654$		0			0
$655$	−2.80704	−	0.328096i	−0.109680	−	0.0128198i
$656$	−4.76957	−	27.0496i	−0.186221	−	1.05611i
$657$		0			0
$658$	−5.06840	+	28.7443i	−0.197587	+	1.12057i
$659$	4.81941	−	16.0979i	0.187738	−	0.627087i	−0.811357	−	0.584550i	$-0.801271\pi$
$659$	4.81941	−	16.0979i	0.187738	−	0.627087i	0.999095	−	0.0425366i	$-0.0135439\pi$
$660$		0			0
$661$	0.169220	−	2.90540i	0.00658190	−	0.113007i	−0.993417	−	0.114555i	$-0.963456\pi$
$661$	0.169220	−	2.90540i	0.00658190	−	0.113007i	0.999999	+	0.00154821i	$0.000492812\pi$
$662$	32.4583	−	16.3012i	1.26153	−	0.633562i
$663$		0			0
$664$	1.20272	+	1.27481i	0.0466746	+	0.0494722i
$665$	12.7928	−	4.65618i	0.496082	−	0.180559i
$666$		0			0
$667$	7.71007	+	2.80623i	0.298535	+	0.108658i
$668$	3.22673	+	7.48041i	0.124846	+	0.289426i
$669$		0			0
$670$	1.23835	+	4.13637i	0.0478415	+	0.159802i
$671$	1.19399	−	0.139558i	0.0460936	−	0.00538757i
$672$		0			0
$673$	−0.176906	−	3.03736i	−0.00681923	−	0.117082i	−1.00000		0.000496017i	$-0.999842\pi$
$673$	−0.176906	−	3.03736i	−0.00681923	−	0.117082i	0.993181	−	0.116586i	$-0.0371949\pi$
$674$	−2.40053	−	4.15783i	−0.0924648	−	0.160154i
$675$		0			0
$676$	0.638419	−	1.10577i	0.0245546	−	0.0425298i
$677$	−33.4519	−	16.8002i	−1.28566	−	0.645684i	−0.331072	−	0.943605i	$-0.607410\pi$
$677$	−33.4519	−	16.8002i	−1.28566	−	0.645684i	−0.954590	+	0.297921i	$0.903707\pi$
$678$		0			0
$679$	−30.9864	−	41.6219i	−1.18915	−	1.59730i
$680$	−1.85417	−	0.439446i	−0.0711042	−	0.0168520i
$681$		0			0
$682$	0.163697	−	0.219883i	0.00626829	−	0.00841977i
$683$	23.8512	−	20.0135i	0.912641	−	0.765797i	−0.0599783	−	0.998200i	$-0.519103\pi$
$683$	23.8512	−	20.0135i	0.912641	−	0.765797i	0.972620	+	0.232403i	$0.0746587\pi$
$684$		0			0
$685$	−1.16318	−	0.976025i	−0.0444429	−	0.0372920i
$686$	−11.4366	+	2.71053i	−0.436653	+	0.103489i
$687$		0			0
$688$	0.920007	+	0.605098i	0.0350749	+	0.0230691i
$689$	−35.4358	−	23.3065i	−1.35000	−	0.887907i
$690$		0			0
$691$	10.4258	−	2.47095i	0.396615	−	0.0939995i	−0.0274683	−	0.999623i	$-0.508745\pi$
$691$	10.4258	−	2.47095i	0.396615	−	0.0939995i	0.424083	+	0.905623i	$0.360596\pi$
$692$	−0.501162	−	0.420525i	−0.0190513	−	0.0159859i
$693$		0			0
$694$	−26.3811	+	22.1364i	−1.00141	+	0.840286i
$695$	−1.79114	+	2.40592i	−0.0679419	+	0.0912618i
$696$		0			0
$697$	−8.68251	−	2.05779i	−0.328874	−	0.0779445i
$698$	−2.77903	−	3.73289i	−0.105188	−	0.141292i
$699$		0			0
$700$	−6.52308	−	3.27602i	−0.246549	−	0.123822i
$701$	10.3580	−	17.9406i	0.391216	−	0.677607i	−0.601394	−	0.798953i	$-0.705388\pi$
$701$	10.3580	−	17.9406i	0.391216	−	0.677607i	0.992610	+	0.121346i	$0.0387210\pi$
$702$		0			0
$703$	−10.2395	−	17.7353i	−0.386188	−	0.668898i
$704$	−1.31727	−	22.6166i	−0.0496464	−	0.852396i
$705$		0			0
$706$	−3.32048	+	0.388109i	−0.124968	+	0.0146067i
$707$	−14.1432	−	47.2416i	−0.531910	−	1.77670i
$708$		0			0
$709$	−7.20452	−	16.7019i	−0.270571	−	0.627255i	0.727708	−	0.685887i	$-0.240585\pi$
$709$	−7.20452	−	16.7019i	−0.270571	−	0.627255i	−0.998280	+	0.0586319i	$0.981326\pi$
$710$	8.67796	+	3.15852i	0.325678	+	0.118537i
$711$		0			0
$712$	27.1066	−	9.86600i	1.01586	−	0.369744i
$713$	0.0377403	+	0.0400024i	0.00141339	+	0.00149810i
$714$		0			0
$715$	5.42080	−	2.72243i	0.202726	−	0.101813i
$716$	−0.270778	+	4.64907i	−0.0101194	+	0.173744i
$717$		0			0
$718$	0.287306	−	0.959668i	0.0107222	−	0.0358145i
$719$	5.53156	−	31.3710i	0.206292	−	1.16994i	−0.689101	−	0.724666i	$-0.741994\pi$
$719$	5.53156	−	31.3710i	0.206292	−	1.16994i	0.895393	−	0.445277i	$-0.146895\pi$
$720$		0			0
$721$	−1.44761	−	8.20980i	−0.0539118	−	0.305749i
$722$	39.8631	+	4.65933i	1.48355	+	0.173402i
$723$		0			0
$724$	−2.00034	+	2.12024i	−0.0743421	+	0.0787981i
$725$	12.9859	−	30.1048i	0.482285	−	1.11806i
$726$		0			0
$727$	−7.91945	+	5.20870i	−0.293716	+	0.193180i	−0.687811	−	0.725890i	$-0.741428\pi$
$727$	−7.91945	+	5.20870i	−0.293716	+	0.193180i	0.394095	+	0.919070i	$0.371058\pi$
$728$	30.9566			1.14733
$729$		0			0
$730$	−12.2325			−0.452746
$731$	0.298878	−	0.196575i	0.0110544	−	0.00727060i
$732$		0			0
$733$	−16.6921	+	38.6967i	−0.616538	+	1.42930i	0.268271	+	0.963343i	$0.413548\pi$
$733$	−16.6921	+	38.6967i	−0.616538	+	1.42930i	−0.884809	+	0.465953i	$0.845712\pi$
$734$	−10.0376	+	10.6393i	−0.370496	+	0.392703i
$735$		0			0
$736$	−2.53950	−	0.296824i	−0.0936070	−	0.0109411i
$737$	3.65153	+	20.7089i	0.134506	+	0.762821i
$738$		0			0
$739$	8.32565	−	47.2171i	0.306264	−	1.73691i	−0.311232	−	0.950334i	$-0.600742\pi$
$739$	8.32565	−	47.2171i	0.306264	−	1.73691i	0.617496	−	0.786574i	$-0.288147\pi$
$740$	0.172045	−	0.574669i	0.00632449	−	0.0211253i
$741$		0			0
$742$	4.88024	−	83.7904i	0.179159	−	3.07604i
$743$	9.21372	−	4.62730i	0.338019	−	0.169759i	−0.271690	−	0.962385i	$-0.587583\pi$
$743$	9.21372	−	4.62730i	0.338019	−	0.169759i	0.609709	+	0.792625i	$0.291286\pi$
$744$		0			0
$745$	1.90195	+	2.01594i	0.0696819	+	0.0738585i
$746$	−7.08589	+	2.57905i	−0.259433	+	0.0944258i
$747$		0			0
$748$	2.08580	+	0.759170i	0.0762645	+	0.0277580i
$749$	2.62669	+	6.08934i	0.0959770	+	0.222500i
$750$		0			0
$751$	−7.18583	−	24.0023i	−0.262215	−	0.875858i	−0.983141	−	0.182847i	$-0.941469\pi$
$751$	−7.18583	−	24.0023i	−0.262215	−	0.875858i	0.720927	−	0.693011i	$-0.243716\pi$
$752$	21.7540	−	2.54268i	0.793287	−	0.0927220i
$753$		0			0
$754$	−1.93368	−	33.2000i	−0.0704205	−	1.20907i
$755$	3.79446	+	6.57219i	0.138094	+	0.239187i
$756$		0			0
$757$	3.05875	−	5.29791i	0.111172	−	0.192556i	−0.805071	−	0.593178i	$-0.797873\pi$
$757$	3.05875	−	5.29791i	0.111172	−	0.192556i	0.916243	+	0.400623i	$0.131206\pi$
$758$	35.9421	+	18.0508i	1.30547	+	0.655634i
$759$		0			0
$760$	−5.08156	−	6.82572i	−0.184328	−	0.247595i
$761$	−43.6455	−	10.3442i	−1.58215	−	0.374976i	−0.656790	−	0.754073i	$-0.728086\pi$
$761$	−43.6455	−	10.3442i	−1.58215	−	0.374976i	−0.925357	+	0.379097i	$0.876234\pi$
$762$		0			0
$763$	10.2406	−	13.7555i	0.370733	−	0.497981i
$764$	3.82972	−	3.21351i	0.138554	−	0.116261i
$765$		0			0
$766$	−9.50299	−	7.97396i	−0.343357	−	0.288111i
$767$	4.23136	−	1.00285i	0.152785	−	0.0362108i
$768$		0			0
$769$	−31.6906	−	20.8432i	−1.14279	−	0.751626i	−0.170490	−	0.985359i	$-0.554535\pi$
$769$	−31.6906	−	20.8432i	−1.14279	−	0.751626i	−0.972301	+	0.233734i	$0.924906\pi$
$770$	10.0293	+	6.59639i	0.361431	+	0.237717i
$771$		0			0
$772$	6.79092	−	1.60948i	0.244411	−	0.0579264i
$773$	−11.7711	−	9.87712i	−0.423377	−	0.355255i	0.406069	−	0.913842i	$-0.366899\pi$
$773$	−11.7711	−	9.87712i	−0.423377	−	0.355255i	−0.829446	+	0.558587i	$0.811344\pi$
$774$		0			0
$775$	0.168345	−	0.141258i	0.00604713	−	0.00507415i
$776$	−19.3687	+	26.0167i	−0.695295	+	0.933944i
$777$		0			0
$778$	−34.1882	−	8.10276i	−1.22571	−	0.290498i
$779$	−23.7954	−	31.9628i	−0.852559	−	1.14518i
$780$		0			0
$781$	40.1918	+	20.1851i	1.43818	+	0.722279i
$782$	−1.37623	+	2.38370i	−0.0492138	+	0.0852408i

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.29056 - 0.848814i) q^{2} +(0.152898 - 0.354458i) q^{4} +(-0.349244 + 0.370177i) q^{5} +(-3.96148 - 0.463031i) q^{7} +(0.432916 + 2.45519i) q^{8} +O(q^{10})\)	\(q+(1.29056 - 0.848814i) q^{2} +(0.152898 - 0.354458i) q^{4} +(-0.349244 + 0.370177i) q^{5} +(-3.96148 - 0.463031i) q^{7} +(0.432916 + 2.45519i) q^{8} +(-0.136509 + 0.774179i) q^{10} +(-1.09805 + 3.66773i) q^{11} +(-0.181020 + 3.10799i) q^{13} +(-5.50556 + 2.76500i) q^{14} +(3.17252 + 3.36268i) q^{16} +(1.41129 - 0.513668i) q^{17} +(6.30242 + 2.29389i) q^{19} +(0.0778134 + 0.180392i) q^{20} +(1.69613 + 5.66546i) q^{22} +(-1.17843 + 0.137739i) q^{23} +(0.275664 + 4.73298i) q^{25} +(2.40449 + 4.16470i) q^{26} +(-0.769829 + 1.33338i) q^{28} +(-6.17988 - 3.10365i) q^{29} +(-0.0276800 - 0.0371807i) q^{31} +(2.09689 + 0.496972i) q^{32} +(1.38535 - 1.86084i) q^{34} +(1.55493 - 1.30474i) q^{35} +(-2.33905 - 1.96269i) q^{37} +(10.0807 - 2.38918i) q^{38} +(-1.06005 - 0.697205i) q^{40} +(-4.96389 - 3.26480i) q^{41} +(0.231769 - 0.0549304i) q^{43} +(1.13217 + 0.950001i) q^{44} +(-1.40392 + 1.17803i) q^{46} +(2.82910 - 3.80014i) q^{47} +(8.66765 + 2.05427i) q^{49} +(4.37318 + 5.87420i) q^{50} +(1.07397 + 0.539370i) q^{52} +(-6.81173 + 11.7983i) q^{53} +(-0.974224 - 1.68741i) q^{55} +(-0.578162 - 9.92665i) q^{56} +(-10.6099 + 1.24012i) q^{58} +(-0.400604 - 1.33811i) q^{59} +(-0.124364 - 0.288308i) q^{61} +(-0.0672822 - 0.0244887i) q^{62} +(-5.56048 + 2.02385i) q^{64} +(-1.08729 - 1.15246i) q^{65} +(4.90826 - 2.46502i) q^{67} +(0.0337102 - 0.578782i) q^{68} +(0.899246 - 3.00369i) q^{70} +(2.03991 - 11.5689i) q^{71} +(2.70207 + 15.3242i) q^{73} +(-4.68464 - 0.547556i) q^{74} +(1.77672 - 1.88321i) q^{76} +(6.04817 - 14.0212i) q^{77} +(11.6941 - 7.69136i) q^{79} -2.35277 q^{80} -9.17740 q^{82} +(0.587346 - 0.386304i) q^{83} +(-0.302737 + 0.701823i) q^{85} +(0.252487 - 0.267620i) q^{86} +(-9.48034 - 1.10809i) q^{88} +(-2.00921 - 11.3948i) q^{89} +(2.15620 - 12.2284i) q^{91} +(-0.131358 + 0.438765i) q^{92} +(0.425507 - 7.30568i) q^{94} +(-3.05023 + 1.53188i) q^{95} +(8.92799 + 9.46312i) q^{97} +(12.9298 - 4.70606i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more