LMFDB - Embedded newform 405.2.k.a.226.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(46,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("405.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.k (of order $9$, degree $6$, 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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			226.3
Character	$\chi$	$=$	405.226
Dual form			405.2.k.a.181.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.282715 + 0.102900i) q^{2} +(-1.46275 - 1.22739i) q^{4} +(0.173648 - 0.984808i) q^{5} +(-3.28585 + 2.75715i) q^{7} +(-0.588102 - 1.01862i) q^{8} +O(q^{10})$	\(q+(0.282715 + 0.102900i) q^{2} +(-1.46275 - 1.22739i) q^{4} +(0.173648 - 0.984808i) q^{5} +(-3.28585 + 2.75715i) q^{7} +(-0.588102 - 1.01862i) q^{8} +(0.150430 - 0.260552i) q^{10} +(-0.307813 - 1.74570i) q^{11} +(-3.80087 + 1.38340i) q^{13} +(-1.21267 + 0.441375i) q^{14} +(0.601708 + 3.41245i) q^{16} +(-1.95214 + 3.38121i) q^{17} +(-0.556845 - 0.964484i) q^{19} +(-1.46275 + 1.22739i) q^{20} +(0.0926084 - 0.525208i) q^{22} +(-6.60755 - 5.54440i) q^{23} +(-0.939693 - 0.342020i) q^{25} -1.21692 q^{26} +8.19048 q^{28} +(0.562260 + 0.204646i) q^{29} +(1.24781 + 1.04704i) q^{31} +(-0.589520 + 3.34334i) q^{32} +(-0.899826 + 0.755043i) q^{34} +(2.14468 + 3.71470i) q^{35} +(-2.60857 + 4.51818i) q^{37} +(-0.0581832 - 0.329973i) q^{38} +(-1.10527 + 0.402285i) q^{40} +(0.711333 - 0.258904i) q^{41} +(-1.25194 - 7.10010i) q^{43} +(-1.69240 + 2.93132i) q^{44} +(-1.29754 - 2.24740i) q^{46} +(9.00022 - 7.55208i) q^{47} +(1.97936 - 11.2255i) q^{49} +(-0.230471 - 0.193388i) q^{50} +(7.25771 + 2.64159i) q^{52} -3.97724 q^{53} -1.77263 q^{55} +(4.74091 + 1.72555i) q^{56} +(0.137901 + 0.115713i) q^{58} +(2.39974 - 13.6096i) q^{59} +(-6.49619 + 5.45095i) q^{61} +(0.245035 + 0.424413i) q^{62} +(2.95440 - 5.11717i) q^{64} +(0.702373 + 3.98336i) q^{65} +(-7.36217 + 2.67961i) q^{67} +(7.00557 - 2.54982i) q^{68} +(0.224092 + 1.27089i) q^{70} +(-2.59176 + 4.48907i) q^{71} +(2.18764 + 3.78911i) q^{73} +(-1.20240 + 1.00894i) q^{74} +(-0.369276 + 2.09427i) q^{76} +(5.82458 + 4.88740i) q^{77} +(12.1133 + 4.40888i) q^{79} +3.46510 q^{80} +0.227746 q^{82} +(7.43037 + 2.70443i) q^{83} +(2.99086 + 2.50963i) q^{85} +(0.376657 - 2.13613i) q^{86} +(-1.59718 + 1.34019i) q^{88} +(-1.62783 - 2.81949i) q^{89} +(8.67483 - 15.0252i) q^{91} +(2.86005 + 16.2201i) q^{92} +(3.32160 - 1.20896i) q^{94} +(-1.04653 + 0.380904i) q^{95} +(-0.345856 - 1.96145i) q^{97} +(1.71470 - 2.96995i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 9 q^{8}+O(q^{10}) $ 30 * q + 9 * q^8	$ 30 q + 9 q^{8} + 3 q^{10} + 6 q^{11} + 3 q^{13} + 9 q^{14} + 12 q^{16} + 12 q^{17} + 24 q^{19} - 51 q^{22} - 18 q^{23} + 18 q^{26} - 60 q^{28} - 18 q^{29} + 12 q^{31} - 36 q^{32} - 69 q^{34} + 12 q^{35} + 24 q^{37} + 24 q^{38} + 9 q^{40} + 75 q^{41} + 6 q^{43} - 12 q^{44} + 30 q^{46} - 45 q^{47} - 36 q^{49} + 30 q^{52} - 36 q^{53} - 30 q^{56} + 27 q^{58} + 27 q^{59} - 12 q^{61} - 36 q^{62} + 27 q^{64} - 6 q^{65} - 30 q^{67} - 69 q^{68} + 27 q^{70} - 12 q^{71} + 21 q^{73} - 30 q^{76} + 36 q^{77} + 54 q^{79} - 6 q^{80} - 48 q^{82} + 87 q^{83} + 27 q^{85} - 18 q^{86} - 18 q^{88} - 9 q^{89} + 51 q^{91} - 24 q^{92} + 15 q^{94} - 21 q^{95} - 75 q^{97} + 15 q^{98}+O(q^{100}) $ 30 * q + 9 * q^8 + 3 * q^10 + 6 * q^11 + 3 * q^13 + 9 * q^14 + 12 * q^16 + 12 * q^17 + 24 * q^19 - 51 * q^22 - 18 * q^23 + 18 * q^26 - 60 * q^28 - 18 * q^29 + 12 * q^31 - 36 * q^32 - 69 * q^34 + 12 * q^35 + 24 * q^37 + 24 * q^38 + 9 * q^40 + 75 * q^41 + 6 * q^43 - 12 * q^44 + 30 * q^46 - 45 * q^47 - 36 * q^49 + 30 * q^52 - 36 * q^53 - 30 * q^56 + 27 * q^58 + 27 * q^59 - 12 * q^61 - 36 * q^62 + 27 * q^64 - 6 * q^65 - 30 * q^67 - 69 * q^68 + 27 * q^70 - 12 * q^71 + 21 * q^73 - 30 * q^76 + 36 * q^77 + 54 * q^79 - 6 * q^80 - 48 * q^82 + 87 * q^83 + 27 * q^85 - 18 * q^86 - 18 * q^88 - 9 * q^89 + 51 * q^91 - 24 * q^92 + 15 * q^94 - 21 * q^95 - 75 * q^97 + 15 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	0.282715	+	0.102900i	0.199910	+	0.0727612i	0.440035	−	0.897981i	$-0.354966\pi$
$2$	0.282715	+	0.102900i	0.199910	+	0.0727612i	−0.240125	+	0.970742i	$0.577188\pi$
$3$		0			0
$3$		0			0
$4$	−1.46275	−	1.22739i	−0.731375	−	0.613696i
$5$	0.173648	−	0.984808i	0.0776578	−	0.440419i
$5$	0.173648	−	0.984808i	0.0776578	−	0.440419i
$6$		0			0
$7$	−3.28585	+	2.75715i	−1.24193	+	1.04211i	−0.244563	+	0.969633i	$0.578645\pi$
$7$	−3.28585	+	2.75715i	−1.24193	+	1.04211i	−0.997370	+	0.0724727i	$0.976911\pi$
$8$	−0.588102	−	1.01862i	−0.207925	−	0.360137i
$9$		0			0
$10$	0.150430	−	0.260552i	0.0475700	−	0.0823936i
$11$	−0.307813	−	1.74570i	−0.0928092	−	0.526347i	−0.995397	−	0.0958407i	$-0.969446\pi$
$11$	−0.307813	−	1.74570i	−0.0928092	−	0.526347i	0.902587	−	0.430506i	$-0.141665\pi$
$12$		0			0
$13$	−3.80087	+	1.38340i	−1.05417	+	0.383687i	−0.810236	−	0.586104i	$-0.800661\pi$
$13$	−3.80087	+	1.38340i	−1.05417	+	0.383687i	−0.243937	+	0.969791i	$0.578439\pi$
$14$	−1.21267	+	0.441375i	−0.324099	+	0.117963i
$15$		0			0
$16$	0.601708	+	3.41245i	0.150427	+	0.853113i
$17$	−1.95214	+	3.38121i	−0.473464	+	0.820064i	−0.999539	−	0.0303747i	$-0.990330\pi$
$17$	−1.95214	+	3.38121i	−0.473464	+	0.820064i	0.526075	+	0.850438i	$0.323663\pi$
$18$		0			0
$19$	−0.556845	−	0.964484i	−0.127749	−	0.221268i	0.795055	−	0.606537i	$-0.207442\pi$
$19$	−0.556845	−	0.964484i	−0.127749	−	0.221268i	−0.922804	+	0.385269i	$0.874109\pi$
$20$	−1.46275	+	1.22739i	−0.327081	+	0.274453i
$21$		0			0
$22$	0.0926084	−	0.525208i	0.0197442	−	0.111975i
$23$	−6.60755	−	5.54440i	−1.37777	−	1.15609i	−0.970029	−	0.242989i	$-0.921872\pi$
$23$	−6.60755	−	5.54440i	−1.37777	−	1.15609i	−0.407741	−	0.913098i	$-0.633683\pi$
$24$		0			0
$25$	−0.939693	−	0.342020i	−0.187939	−	0.0684040i
$26$	−1.21692			−0.238657
$27$		0			0
$28$	8.19048			1.54786
$29$	0.562260	+	0.204646i	0.104409	+	0.0380018i	0.393696	−	0.919240i	$-0.371196\pi$
$29$	0.562260	+	0.204646i	0.104409	+	0.0380018i	−0.289287	+	0.957242i	$0.593418\pi$
$30$		0			0
$31$	1.24781	+	1.04704i	0.224114	+	0.188054i	0.747930	−	0.663777i	$-0.231048\pi$
$31$	1.24781	+	1.04704i	0.224114	+	0.188054i	−0.523816	+	0.851831i	$0.675492\pi$
$32$	−0.589520	+	3.34334i	−0.104213	+	0.591024i
$33$		0			0
$34$	−0.899826	+	0.755043i	−0.154319	+	0.129489i
$35$	2.14468	+	3.71470i	0.362518	+	0.627899i
$36$		0			0
$37$	−2.60857	+	4.51818i	−0.428847	+	0.742785i	−0.996771	−	0.0802963i	$-0.974413\pi$
$37$	−2.60857	+	4.51818i	−0.428847	+	0.742785i	0.567924	+	0.823081i	$0.307747\pi$
$38$	−0.0581832	−	0.329973i	−0.00943856	−	0.0535287i
$39$		0			0
$40$	−1.10527	+	0.402285i	−0.174758	+	0.0636069i
$41$	0.711333	−	0.258904i	0.111092	−	0.0404340i	−0.285876	−	0.958267i	$-0.592285\pi$
$41$	0.711333	−	0.258904i	0.111092	−	0.0404340i	0.396968	+	0.917833i	$0.370062\pi$
$42$		0			0
$43$	−1.25194	−	7.10010i	−0.190919	−	1.08276i	−0.918112	−	0.396322i	$-0.870286\pi$
$43$	−1.25194	−	7.10010i	−0.190919	−	1.08276i	0.727193	−	0.686434i	$-0.240825\pi$
$44$	−1.69240	+	2.93132i	−0.255139	+	0.441914i
$45$		0			0
$46$	−1.29754	−	2.24740i	−0.191311	−	0.331361i
$47$	9.00022	−	7.55208i	1.31282	−	1.10158i	0.325041	−	0.945700i	$-0.394622\pi$
$47$	9.00022	−	7.55208i	1.31282	−	1.10158i	0.987775	−	0.155884i	$-0.0498225\pi$
$48$		0			0
$49$	1.97936	−	11.2255i	0.282766	−	1.60365i
$50$	−0.230471	−	0.193388i	−0.0325936	−	0.0273493i
$51$		0			0
$52$	7.25771	+	2.64159i	1.00646	+	0.366323i
$53$	−3.97724			−0.546316			−0.273158	−	0.961969i	$-0.588068\pi$
$53$	−3.97724			−0.546316			−0.273158	+	0.961969i	$0.588068\pi$
$54$		0			0
$55$	−1.77263			−0.239021
$56$	4.74091	+	1.72555i	0.633531	+	0.230586i
$57$		0			0
$58$	0.137901	+	0.115713i	0.0181073	+	0.0151939i
$59$	2.39974	−	13.6096i	0.312419	−	1.77182i	−0.273919	−	0.961753i	$-0.588320\pi$
$59$	2.39974	−	13.6096i	0.312419	−	1.77182i	0.586339	−	0.810066i	$-0.300569\pi$
$60$		0			0
$61$	−6.49619	+	5.45095i	−0.831752	+	0.697923i	−0.955693	−	0.294366i	$-0.904891\pi$
$61$	−6.49619	+	5.45095i	−0.831752	+	0.697923i	0.123940	+	0.992290i	$0.460447\pi$
$62$	0.245035	+	0.424413i	0.0311195	+	0.0539006i
$63$		0			0
$64$	2.95440	−	5.11717i	0.369300	−	0.639647i
$65$	0.702373	+	3.98336i	0.0871187	+	0.494074i
$66$		0			0
$67$	−7.36217	+	2.67961i	−0.899432	+	0.327367i	−0.750025	−	0.661409i	$-0.769959\pi$
$67$	−7.36217	+	2.67961i	−0.899432	+	0.327367i	−0.149407	+	0.988776i	$0.547736\pi$
$68$	7.00557	−	2.54982i	0.849550	−	0.309211i
$69$		0			0
$70$	0.224092	+	1.27089i	0.0267841	+	0.151900i
$71$	−2.59176	+	4.48907i	−0.307586	+	0.532754i	−0.977834	−	0.209383i	$-0.932854\pi$
$71$	−2.59176	+	4.48907i	−0.307586	+	0.532754i	0.670248	+	0.742137i	$0.266188\pi$
$72$		0			0
$73$	2.18764	+	3.78911i	0.256044	+	0.443481i	0.965179	−	0.261592i	$-0.0842474\pi$
$73$	2.18764	+	3.78911i	0.256044	+	0.443481i	−0.709135	+	0.705073i	$0.750914\pi$
$74$	−1.20240	+	1.00894i	−0.139777	+	0.117286i
$75$		0			0
$76$	−0.369276	+	2.09427i	−0.0423588	+	0.240229i
$77$	5.82458	+	4.88740i	0.663772	+	0.556971i
$78$		0			0
$79$	12.1133	+	4.40888i	1.36285	+	0.496038i	0.916935	−	0.399036i	$-0.130655\pi$
$79$	12.1133	+	4.40888i	1.36285	+	0.496038i	0.445917	+	0.895074i	$0.352877\pi$
$80$	3.46510			0.387410
$81$		0			0
$82$	0.227746			0.0251503
$83$	7.43037	+	2.70443i	0.815589	+	0.296850i	0.715930	−	0.698172i	$-0.246003\pi$
$83$	7.43037	+	2.70443i	0.815589	+	0.296850i	0.0996585	+	0.995022i	$0.468225\pi$
$84$		0			0
$85$	2.99086	+	2.50963i	0.324404	+	0.272207i
$86$	0.376657	−	2.13613i	0.0406160	−	0.230345i
$87$		0			0
$88$	−1.59718	+	1.34019i	−0.170260	+	0.142865i
$89$	−1.62783	−	2.81949i	−0.172550	−	0.298865i	0.766761	−	0.641933i	$-0.221867\pi$
$89$	−1.62783	−	2.81949i	−0.172550	−	0.298865i	−0.939311	+	0.343068i	$0.888534\pi$
$90$		0			0
$91$	8.67483	−	15.0252i	0.909369	−	1.57507i
$92$	2.86005	+	16.2201i	0.298180	+	1.69106i
$93$		0			0
$94$	3.32160	−	1.20896i	0.342597	−	0.124695i
$95$	−1.04653	+	0.380904i	−0.107371	+	0.0390800i
$96$		0			0
$97$	−0.345856	−	1.96145i	−0.0351164	−	0.199155i	0.962202	−	0.272336i	$-0.0877961\pi$
$97$	−0.345856	−	1.96145i	−0.0351164	−	0.199155i	−0.997319	+	0.0731807i	$0.976685\pi$
$98$	1.71470	−	2.96995i	0.173211	−	0.300010i
$99$		0			0
$100$	0.954742	+	1.65366i	0.0954742	+	0.165366i
$101$	−7.02258	+	5.89264i	−0.698773	+	0.586340i	−0.921424	−	0.388558i	$-0.872973\pi$
$101$	−7.02258	+	5.89264i	−0.698773	+	0.586340i	0.222652	+	0.974898i	$0.428529\pi$
$102$		0			0
$103$	0.314812	−	1.78539i	0.0310193	−	0.175919i	−0.965362	−	0.260914i	$-0.915976\pi$
$103$	0.314812	−	1.78539i	0.0310193	−	0.175919i	0.996381	+	0.0849945i	$0.0270873\pi$
$104$	3.64447	+	3.05807i	0.357369	+	0.299869i
$105$		0			0
$106$	−1.12442	−	0.409257i	−0.109214	−	0.0397506i
$107$	−3.71297			−0.358946			−0.179473	−	0.983763i	$-0.557439\pi$
$107$	−3.71297			−0.358946			−0.179473	+	0.983763i	$0.557439\pi$
$108$		0			0
$109$	−3.24138			−0.310468			−0.155234	−	0.987878i	$-0.549613\pi$
$109$	−3.24138			−0.310468			−0.155234	+	0.987878i	$0.549613\pi$
$110$	−0.501148	−	0.182403i	−0.0477826	−	0.0173914i
$111$		0			0
$112$	−11.3858	−	9.55380i	−1.07585	−	0.902749i
$113$	−2.13575	+	12.1124i	−0.200914	+	1.13944i	0.702827	+	0.711361i	$0.251921\pi$
$113$	−2.13575	+	12.1124i	−0.200914	+	1.13944i	−0.903741	+	0.428080i	$0.859190\pi$
$114$		0			0
$115$	−6.60755	+	5.54440i	−0.616157	+	0.517018i
$116$	−0.571265	−	0.989460i	−0.0530406	−	0.0918690i
$117$		0			0
$118$	2.07887	−	3.60070i	0.191375	−	0.331472i
$119$	−2.90807	−	16.4925i	−0.266583	−	1.51186i
$120$		0			0
$121$	7.38391	−	2.68752i	0.671265	−	0.244320i
$122$	−2.39747	+	0.872609i	−0.217057	+	0.0790023i
$123$		0			0
$124$	−0.540109	−	3.06311i	−0.0485033	−	0.275076i
$125$	−0.500000	+	0.866025i	−0.0447214	+	0.0774597i
$126$		0			0
$127$	5.50593	+	9.53655i	0.488572	+	0.846232i	0.999914	−	0.0131457i	$-0.00418454\pi$
$127$	5.50593	+	9.53655i	0.488572	+	0.846232i	−0.511341	+	0.859378i	$0.670851\pi$
$128$	6.56312	−	5.50711i	0.580103	−	0.486764i
$129$		0			0
$130$	−0.211315	+	1.19843i	−0.0185336	+	0.105109i
$131$	−13.4406	−	11.2780i	−1.17431	−	0.985361i	−1.00000		0.000669520i	$-0.999787\pi$
$131$	−13.4406	−	11.2780i	−1.17431	−	0.985361i	−0.174307	−	0.984691i	$-0.555769\pi$
$132$		0			0
$133$	4.48894	+	1.63384i	0.389240	+	0.141672i
$134$	−2.35713			−0.203625
$135$		0			0
$136$	4.59223			0.393781
$137$	0.335210	+	0.122007i	0.0286389	+	0.0104237i	0.356300	−	0.934372i	$-0.384038\pi$
$137$	0.335210	+	0.122007i	0.0286389	+	0.0104237i	−0.327661	+	0.944795i	$0.606260\pi$
$138$		0			0
$139$	−1.14234	−	0.958535i	−0.0968918	−	0.0813019i	0.593055	−	0.805162i	$-0.297922\pi$
$139$	−1.14234	−	0.958535i	−0.0968918	−	0.0813019i	−0.689947	+	0.723860i	$0.742366\pi$
$140$	1.42226	−	8.06605i	0.120203	−	0.681706i
$141$		0			0
$142$	−1.19465	+	1.00243i	−0.100253	+	0.0841224i
$143$	3.58496	+	6.20934i	0.299790	+	0.519251i
$144$		0			0
$145$	0.299172	−	0.518182i	0.0248449	−	0.0430326i
$146$	0.228581	+	1.29635i	0.0189175	+	0.107286i
$147$		0			0
$148$	9.36127	−	3.40722i	0.769492	−	0.280072i
$149$	−17.0077	+	6.19029i	−1.39332	+	0.507128i	−0.926190	−	0.377058i	$-0.876936\pi$
$149$	−17.0077	+	6.19029i	−1.39332	+	0.507128i	−0.467134	+	0.884186i	$0.654714\pi$
$150$		0			0
$151$	−3.68305	−	20.8876i	−0.299723	−	1.69981i	−0.647361	−	0.762183i	$-0.724127\pi$
$151$	−3.68305	−	20.8876i	−0.299723	−	1.69981i	0.347638	−	0.937629i	$-0.386984\pi$
$152$	−0.654963	+	1.13443i	−0.0531245	+	0.0920144i
$153$		0			0
$154$	1.14378	+	1.98109i	0.0921687	+	0.159641i
$155$	1.24781	−	1.04704i	0.100227	−	0.0841002i
$156$		0			0
$157$	−0.950859	+	5.39259i	−0.0758868	+	0.430375i	0.923067	+	0.384640i	$0.125674\pi$
$157$	−0.950859	+	5.39259i	−0.0758868	+	0.430375i	−0.998954	+	0.0457357i	$0.985437\pi$
$158$	2.97094	+	2.49291i	0.236355	+	0.198326i
$159$		0			0
$160$	3.19017	+	1.16113i	0.252205	+	0.0917953i
$161$	36.9982			2.91586
$162$		0			0
$163$	−17.9869			−1.40884			−0.704420	−	0.709783i	$-0.748793\pi$
$163$	−17.9869			−1.40884			−0.704420	+	0.709783i	$0.748793\pi$
$164$	−1.35828	−	0.494373i	−0.106064	−	0.0386040i
$165$		0			0
$166$	1.82239	+	1.52917i	0.141445	+	0.118686i
$167$	−3.46215	+	19.6348i	−0.267909	+	1.51939i	0.492711	+	0.870193i	$0.336006\pi$
$167$	−3.46215	+	19.6348i	−0.267909	+	1.51939i	−0.760620	+	0.649197i	$0.775105\pi$
$168$		0			0
$169$	2.57425	−	2.16006i	0.198019	−	0.166158i
$170$	0.587320	+	1.01727i	0.0450454	+	0.0780208i
$171$		0			0
$172$	−6.88334	+	11.9223i	−0.524850	+	0.909066i
$173$	−1.17486	−	6.66294i	−0.0893226	−	0.506574i	−0.996340	−	0.0854803i	$-0.972758\pi$
$173$	−1.17486	−	6.66294i	−0.0893226	−	0.506574i	0.907017	−	0.421094i	$-0.138354\pi$
$174$		0			0
$175$	4.03069	−	1.46705i	0.304691	−	0.110899i
$176$	5.77189	−	2.10080i	0.435073	−	0.158354i
$177$		0			0
$178$	−0.170088	−	0.964615i	−0.0127486	−	0.0723009i
$179$	4.71985	−	8.17503i	0.352778	−	0.611030i	−0.633957	−	0.773369i	$-0.718570\pi$
$179$	4.71985	−	8.17503i	0.352778	−	0.611030i	0.986735	+	0.162338i	$0.0519036\pi$
$180$		0			0
$181$	−0.566202	−	0.980691i	−0.0420855	−	0.0728942i	0.844215	−	0.536004i	$-0.180067\pi$
$181$	−0.566202	−	0.980691i	−0.0420855	−	0.0728942i	−0.886301	+	0.463110i	$0.846734\pi$
$182$	3.99860	−	3.35522i	0.296396	−	0.248706i
$183$		0			0
$184$	−1.76173	+	9.99127i	−0.129876	+	0.736566i
$185$	3.99657	+	3.35352i	0.293833	+	0.246556i
$186$		0			0
$187$	6.50346	+	2.36707i	0.475580	+	0.173097i
$188$	−22.4344			−1.63620
$189$		0			0
$190$	−0.335064			−0.0243081
$191$	−22.1994	−	8.07991i	−1.60629	−	0.584642i	−0.625588	−	0.780153i	$-0.715141\pi$
$191$	−22.1994	−	8.07991i	−1.60629	−	0.584642i	−0.980701	+	0.195512i	$0.937363\pi$
$192$		0			0
$193$	−2.08055	−	1.74579i	−0.149761	−	0.125665i	0.564829	−	0.825208i	$-0.308942\pi$
$193$	−2.08055	−	1.74579i	−0.149761	−	0.125665i	−0.714590	+	0.699544i	$0.753387\pi$
$194$	0.104054	−	0.590120i	0.00747064	−	0.0423681i
$195$		0			0
$196$	−16.6734	+	13.9907i	−1.19096	+	0.999333i
$197$	−7.13716	−	12.3619i	−0.508501	−	0.880750i	−0.999952	−	0.00984437i	$-0.996866\pi$
$197$	−7.13716	−	12.3619i	−0.508501	−	0.880750i	0.491450	−	0.870906i	$-0.336467\pi$
$198$		0			0
$199$	−10.6351	+	18.4206i	−0.753905	+	1.30580i	0.192012	+	0.981393i	$0.438499\pi$
$199$	−10.6351	+	18.4206i	−0.753905	+	1.30580i	−0.945917	+	0.324409i	$0.894835\pi$
$200$	0.204246	+	1.15833i	0.0144423	+	0.0819066i
$201$		0			0
$202$	−2.59174	+	0.943316i	−0.182354	+	0.0663715i
$203$	−2.41174	+	0.877802i	−0.169271	+	0.0616096i
$204$		0			0
$205$	−0.131449	−	0.745484i	−0.00918080	−	0.0520669i
$206$	0.272718	−	0.472361i	0.0190012	−	0.0329110i
$207$		0			0
$208$	−7.00782	−	12.1379i	−0.485905	−	0.841612i
$209$	−1.51229	+	1.26896i	−0.104607	+	0.0877760i
$210$		0			0
$211$	−3.49805	+	19.8384i	−0.240815	+	1.36573i	0.589198	+	0.807989i	$0.299444\pi$
$211$	−3.49805	+	19.8384i	−0.240815	+	1.36573i	−0.830013	+	0.557743i	$0.811667\pi$
$212$	5.81770	+	4.88163i	0.399562	+	0.335272i
$213$		0			0
$214$	−1.04971	−	0.382064i	−0.0717568	−	0.0261173i
$215$	−7.20963			−0.491693
$216$		0			0
$217$	−6.98697			−0.474306
$218$	−0.916386	−	0.333537i	−0.0620655	−	0.0225900i
$219$		0			0
$220$	2.59291	+	2.17571i	0.174814	+	0.146686i
$221$	2.74226	−	15.5522i	0.184465	−	1.04615i
$222$		0			0
$223$	−4.43003	+	3.71723i	−0.296657	+	0.248924i	−0.778951	−	0.627085i	$-0.784248\pi$
$223$	−4.43003	+	3.71723i	−0.296657	+	0.248924i	0.482294	+	0.876009i	$0.339804\pi$
$224$	−7.28102	−	12.6111i	−0.486483	−	0.842614i
$225$		0			0
$226$	−1.85017	+	3.20460i	−0.123072	+	0.213167i
$227$	−2.65839	−	15.0765i	−0.176443	−	1.00066i	−0.936465	−	0.350762i	$-0.885923\pi$
$227$	−2.65839	−	15.0765i	−0.176443	−	1.00066i	0.760021	−	0.649898i	$-0.225188\pi$
$228$		0			0
$229$	−2.31831	+	0.843797i	−0.153198	+	0.0557596i	−0.417481	−	0.908686i	$-0.637087\pi$
$229$	−2.31831	+	0.843797i	−0.153198	+	0.0557596i	0.264283	+	0.964445i	$0.414865\pi$
$230$	−2.43857	+	0.887567i	−0.160795	+	0.0585245i
$231$		0			0
$232$	−0.122209	−	0.693083i	−0.00802343	−	0.0455031i
$233$	4.21427	−	7.29932i	0.276086	−	0.478195i	−0.694323	−	0.719664i	$-0.744296\pi$
$233$	4.21427	−	7.29932i	0.276086	−	0.478195i	0.970408	+	0.241469i	$0.0776293\pi$
$234$		0			0
$235$	−5.87447	−	10.1749i	−0.383208	−	0.663736i
$236$	−20.2145	+	16.9620i	−1.31585	+	1.10413i
$237$		0			0
$238$	0.874920	−	4.96192i	0.0567126	−	0.321633i
$239$	11.6818	+	9.80219i	0.755633	+	0.634051i	0.936986	−	0.349367i	$-0.113603\pi$
$239$	11.6818	+	9.80219i	0.755633	+	0.634051i	−0.181353	+	0.983418i	$0.558048\pi$
$240$		0			0
$241$	0.611555	+	0.222588i	0.0393937	+	0.0143381i	0.361642	−	0.932317i	$-0.382216\pi$
$241$	0.611555	+	0.222588i	0.0393937	+	0.0143381i	−0.322248	+	0.946655i	$0.604439\pi$
$242$	2.36409			0.151969
$243$		0			0
$244$	16.1928			1.03664
$245$	−10.7113	−	3.89858i	−0.684318	−	0.249071i
$246$		0			0
$247$	3.45077	+	2.89554i	0.219567	+	0.184239i
$248$	0.332696	−	1.88682i	0.0211262	−	0.119813i
$249$		0			0
$250$	−0.230471	+	0.193388i	−0.0145763	+	0.0122310i
$251$	3.07930	+	5.33350i	0.194364	+	0.336648i	0.946692	−	0.322141i	$-0.104403\pi$
$251$	3.07930	+	5.33350i	0.194364	+	0.336648i	−0.752328	+	0.658789i	$0.771069\pi$
$252$		0			0
$253$	−7.64494	+	13.2414i	−0.480633	+	0.832481i
$254$	0.575299	+	3.26268i	0.0360975	+	0.204719i
$255$		0			0
$256$	−8.68274	+	3.16026i	−0.542672	+	0.197516i
$257$	6.58933	−	2.39832i	0.411031	−	0.149603i	−0.128225	−	0.991745i	$-0.540928\pi$
$257$	6.58933	−	2.39832i	0.411031	−	0.149603i	0.539256	+	0.842142i	$0.318706\pi$
$258$		0			0
$259$	−3.88595	−	22.0383i	−0.241461	−	1.36939i
$260$	3.86175	−	6.68874i	0.239495	−	0.414818i
$261$		0			0
$262$	−2.63935	−	4.57148i	−0.163059	−	0.282427i
$263$	−14.9017	+	12.5040i	−0.918880	+	0.771032i	−0.973788	−	0.227459i	$-0.926958\pi$
$263$	−14.9017	+	12.5040i	−0.918880	+	0.771032i	0.0549074	+	0.998491i	$0.482514\pi$
$264$		0			0
$265$	−0.690640	+	3.91682i	−0.0424257	+	0.240608i
$266$	1.10097	+	0.923822i	0.0675047	+	0.0566432i
$267$		0			0
$268$	14.0579	+	5.11667i	0.858726	+	0.312551i
$269$	−10.1856			−0.621026			−0.310513	−	0.950569i	$-0.600501\pi$
$269$	−10.1856			−0.621026			−0.310513	+	0.950569i	$0.600501\pi$
$270$		0			0
$271$	−6.87083			−0.417373			−0.208687	−	0.977983i	$-0.566919\pi$
$271$	−6.87083			−0.417373			−0.208687	+	0.977983i	$0.566919\pi$
$272$	−12.7128	−	4.62710i	−0.770829	−	0.280559i
$273$		0			0
$274$	0.0822145	+	0.0689862i	0.00496676	+	0.00416761i
$275$	−0.307813	+	1.74570i	−0.0185618	+	0.105269i
$276$		0			0
$277$	20.3488	−	17.0747i	1.22264	−	1.02592i	0.223959	−	0.974599i	$-0.428102\pi$
$277$	20.3488	−	17.0747i	1.22264	−	1.02592i	0.998682	−	0.0513192i	$-0.0163426\pi$
$278$	−0.224323	−	0.388539i	−0.0134540	−	0.0233030i
$279$		0			0
$280$	2.52259	−	4.36925i	0.150753	−	0.261112i
$281$	4.15446	+	23.5611i	0.247834	+	1.40554i	0.813817	+	0.581121i	$0.197386\pi$
$281$	4.15446	+	23.5611i	0.247834	+	1.40554i	−0.565983	+	0.824417i	$0.691503\pi$
$282$		0			0
$283$	12.6874	−	4.61782i	0.754186	−	0.274501i	0.0638197	−	0.997961i	$-0.479672\pi$
$283$	12.6874	−	4.61782i	0.754186	−	0.274501i	0.690366	+	0.723460i	$0.257450\pi$
$284$	9.30095	−	3.38527i	0.551910	−	0.200879i
$285$		0			0
$286$	0.374583	+	2.12437i	0.0221496	+	0.125616i
$287$	−1.62349	+	2.81197i	−0.0958318	+	0.165985i
$288$		0			0
$289$	0.878281	+	1.52123i	0.0516636	+	0.0894840i
$290$	0.137901	−	0.115713i	0.00809784	−	0.00679490i
$291$		0			0
$292$	1.45075	−	8.22761i	0.0848987	−	0.481484i
$293$	4.22408	+	3.54442i	0.246773	+	0.207067i	0.757781	−	0.652508i	$-0.226283\pi$
$293$	4.22408	+	3.54442i	0.246773	+	0.207067i	−0.511008	+	0.859576i	$0.670728\pi$
$294$		0			0
$295$	−12.9861	−	4.72656i	−0.756082	−	0.275191i
$296$	6.13643			0.356673
$297$		0			0
$298$	−5.44531			−0.315438
$299$	32.7846	+	11.9326i	1.89598	+	0.690082i
$300$		0			0
$301$	23.6898	+	19.8781i	1.36545	+	1.14575i
$302$	1.10808	−	6.28424i	0.0637628	−	0.361617i
$303$		0			0
$304$	2.95620	−	2.48055i	0.169550	−	0.142269i
$305$	4.24009	+	7.34405i	0.242787	+	0.420519i
$306$		0			0
$307$	−2.38360	+	4.12852i	−0.136039	+	0.235627i	−0.925994	−	0.377538i	$-0.876771\pi$
$307$	−2.38360	+	4.12852i	−0.136039	+	0.235627i	0.789955	+	0.613165i	$0.210104\pi$
$308$	−2.52114	−	14.2981i	−0.143655	−	0.814709i
$309$		0			0
$310$	0.460516	−	0.167614i	0.0261555	−	0.00951983i
$311$	10.2196	−	3.71963i	0.579500	−	0.210921i	−0.0356051	−	0.999366i	$-0.511336\pi$
$311$	10.2196	−	3.71963i	0.579500	−	0.210921i	0.615105	+	0.788445i	$0.289114\pi$
$312$		0			0
$313$	−2.15639	−	12.2295i	−0.121887	−	0.691253i	−0.983108	−	0.183024i	$-0.941411\pi$
$313$	−2.15639	−	12.2295i	−0.121887	−	0.691253i	0.861222	−	0.508229i	$-0.169700\pi$
$314$	−0.823719	+	1.42672i	−0.0464851	+	0.0805146i
$315$		0			0
$316$	−12.3073	−	21.3169i	−0.692339	−	1.19917i
$317$	8.45181	−	7.09191i	0.474701	−	0.398321i	−0.373805	−	0.927507i	$-0.621947\pi$
$317$	8.45181	−	7.09191i	0.474701	−	0.398321i	0.848506	+	0.529186i	$0.177503\pi$
$318$		0			0
$319$	0.184178	−	1.04453i	0.0103120	−	0.0584823i
$320$	−4.52641	−	3.79811i	−0.253034	−	0.212321i
$321$		0			0
$322$	10.4599	+	3.80710i	0.582909	+	0.212162i
$323$	4.34816			0.241938
$324$		0			0
$325$	4.04481			0.224365
$326$	−5.08516	−	1.85085i	−0.281641	−	0.102509i
$327$		0			0
$328$	−0.682061	−	0.572317i	−0.0376605	−	0.0316009i
$329$	−8.75110	+	49.6300i	−0.482464	+	2.73619i
$330$		0			0
$331$	1.55201	−	1.30229i	0.0853061	−	0.0715803i	−0.599137	−	0.800646i	$-0.704490\pi$
$331$	1.55201	−	1.30229i	0.0853061	−	0.0715803i	0.684443	+	0.729066i	$0.260045\pi$
$332$	−7.54937	−	13.0759i	−0.414325	−	0.717633i
$333$		0			0
$334$	−2.99923	+	5.19481i	−0.164110	+	0.284247i
$335$	1.36047	+	7.71563i	0.0743306	+	0.421550i
$336$		0			0
$337$	14.4525	−	5.26029i	0.787280	−	0.286546i	0.0830749	−	0.996543i	$-0.473526\pi$
$337$	14.4525	−	5.26029i	0.787280	−	0.286546i	0.704205	+	0.709997i	$0.251304\pi$
$338$	0.950049	−	0.345790i	0.0516759	−	0.0188085i
$339$		0			0
$340$	−1.29458	−	7.34191i	−0.0702083	−	0.398171i
$341$	1.44372	−	2.50059i	0.0781818	−	0.135415i
$342$		0			0
$343$	9.43380	+	16.3398i	0.509377	+	0.882267i
$344$	−6.49605	+	5.45084i	−0.350244	+	0.293889i
$345$		0			0
$346$	0.353466	−	2.00461i	0.0190024	−	0.107768i
$347$	−0.887983	−	0.745107i	−0.0476695	−	0.0399994i	0.618642	−	0.785673i	$-0.287683\pi$
$347$	−0.887983	−	0.745107i	−0.0476695	−	0.0399994i	−0.666311	+	0.745674i	$0.732128\pi$
$348$		0			0
$349$	4.85238	+	1.76612i	0.259742	+	0.0945383i	0.468609	−	0.883406i	$-0.344755\pi$
$349$	4.85238	+	1.76612i	0.259742	+	0.0945383i	−0.208867	+	0.977944i	$0.566978\pi$
$350$	1.29050			0.0689799
$351$		0			0
$352$	6.01791			0.320756
$353$	−11.4102	−	4.15296i	−0.607301	−	0.221040i	0.0200207	−	0.999800i	$-0.493627\pi$
$353$	−11.4102	−	4.15296i	−0.607301	−	0.221040i	−0.627322	+	0.778760i	$0.715849\pi$
$354$		0			0
$355$	3.97081	+	3.33191i	0.210749	+	0.176839i
$356$	−1.07951	+	6.12219i	−0.0572138	+	0.324475i
$357$		0			0
$358$	2.17558	−	1.82553i	0.114983	−	0.0964823i
$359$	4.44707	+	7.70256i	0.234708	+	0.406525i	0.959188	−	0.282770i	$-0.0912534\pi$
$359$	4.44707	+	7.70256i	0.234708	+	0.406525i	−0.724480	+	0.689296i	$0.757920\pi$
$360$		0			0
$361$	8.87985	−	15.3803i	0.467360	−	0.809492i
$362$	−0.0591609	−	0.335518i	−0.00310943	−	0.0176344i
$363$		0			0
$364$	−31.1310	+	11.3308i	−1.63171	+	0.593893i
$365$	4.11142	−	1.49643i	0.215202	−	0.0783270i
$366$		0			0
$367$	−4.79749	−	27.2079i	−0.250427	−	1.42024i	−0.807544	−	0.589807i	$-0.799204\pi$
$367$	−4.79749	−	27.2079i	−0.250427	−	1.42024i	0.557117	−	0.830434i	$-0.311907\pi$
$368$	14.9442	−	25.8841i	0.779019	−	1.34930i
$369$		0			0
$370$	0.784813	+	1.35934i	0.0408005	+	0.0706685i
$371$	13.0686	−	10.9659i	0.678488	−	0.569319i
$372$		0			0
$373$	−5.35646	+	30.3780i	−0.277347	+	1.57291i	0.454060	+	0.890971i	$0.349975\pi$
$373$	−5.35646	+	30.3780i	−0.277347	+	1.57291i	−0.731407	+	0.681942i	$0.761136\pi$
$374$	1.59505	+	1.33841i	0.0824783	+	0.0692075i
$375$		0			0
$376$	−12.9858	−	4.72643i	−0.669689	−	0.243747i
$377$	−2.42019			−0.124646
$378$		0			0
$379$	−21.0219			−1.07982			−0.539911	−	0.841722i	$-0.681542\pi$
$379$	−21.0219			−1.07982			−0.539911	+	0.841722i	$0.681542\pi$
$380$	1.99833	+	0.727331i	0.102512	+	0.0373113i
$381$		0			0
$382$	−5.44467	−	4.56862i	−0.278574	−	0.233751i
$383$	3.73782	−	21.1982i	0.190994	−	1.08318i	−0.727016	−	0.686621i	$-0.759093\pi$
$383$	3.73782	−	21.1982i	0.190994	−	1.08318i	0.918009	−	0.396559i	$-0.129796\pi$
$384$		0			0
$385$	5.82458	−	4.88740i	0.296848	−	0.249085i
$386$	−0.408561	−	0.707648i	−0.0207952	−	0.0360184i
$387$		0			0
$388$	−1.90157	+	3.29361i	−0.0965374	+	0.167208i
$389$	−2.32909	−	13.2089i	−0.118089	−	0.669718i	−0.985174	−	0.171558i	$-0.945120\pi$
$389$	−2.32909	−	13.2089i	−0.118089	−	0.669718i	0.867085	−	0.498161i	$-0.165991\pi$
$390$		0			0
$391$	31.6456	−	11.5181i	1.60039	−	0.582494i
$392$	−12.5986	+	4.58552i	−0.636327	+	0.231604i
$393$		0			0
$394$	−0.745742	−	4.22931i	−0.0375699	−	0.213070i
$395$	6.44535	−	11.1637i	0.324301	−	0.561706i
$396$		0			0
$397$	8.50299	+	14.7276i	0.426753	+	0.739158i	0.996582	−	0.0826052i	$-0.0263241\pi$
$397$	8.50299	+	14.7276i	0.426753	+	0.739158i	−0.569829	+	0.821763i	$0.692991\pi$
$398$	−4.90219	+	4.11343i	−0.245725	+	0.206187i
$399$		0			0
$400$	0.601708	−	3.41245i	0.0300854	−	0.170623i
$401$	−4.77991	−	4.01082i	−0.238697	−	0.200291i	0.515590	−	0.856836i	$-0.327573\pi$
$401$	−4.77991	−	4.01082i	−0.238697	−	0.200291i	−0.754287	+	0.656545i	$0.772017\pi$
$402$		0			0
$403$	−6.19126	−	2.25343i	−0.308409	−	0.112252i
$404$	17.5049			0.870899
$405$		0			0
$406$	−0.772161			−0.0383217
$407$	8.69033	+	3.16302i	0.430764	+	0.156785i
$408$		0			0
$409$	7.35423	+	6.17093i	0.363643	+	0.305133i	0.806241	−	0.591587i	$-0.201499\pi$
$409$	7.35423	+	6.17093i	0.363643	+	0.305133i	−0.442598	+	0.896720i	$0.645943\pi$
$410$	0.0395476	−	0.224286i	0.00195312	−	0.0110767i
$411$		0			0
$412$	−2.65186	+	2.22517i	−0.130648	+	0.109626i
$413$	29.6386	+	51.3355i	1.45842	+	2.52606i
$414$		0			0
$415$	3.95362	−	6.84787i	0.194075	−	0.336149i
$416$	−2.38449	−	13.5231i	−0.116909	−	0.663027i
$417$		0			0
$418$	−0.558124	+	0.203140i	−0.0272987	+	0.00993592i
$419$	14.1004	−	5.13212i	0.688849	−	0.250721i	0.0262069	−	0.999657i	$-0.491657\pi$
$419$	14.1004	−	5.13212i	0.688849	−	0.250721i	0.662642	+	0.748936i	$0.269435\pi$
$420$		0			0
$421$	6.43175	+	36.4763i	0.313464	+	1.77774i	0.580705	+	0.814114i	$0.302777\pi$
$421$	6.43175	+	36.4763i	0.313464	+	1.77774i	−0.267240	+	0.963630i	$0.586112\pi$
$422$	−3.03032	+	5.24867i	−0.147514	+	0.255501i
$423$		0			0
$424$	2.33902	+	4.05130i	0.113593	+	0.196749i
$425$	2.99086	−	2.50963i	0.145078	−	0.121735i
$426$		0			0
$427$	6.31639	−	35.8220i	0.305671	−	1.73355i
$428$	5.43114	+	4.55727i	0.262524	+	0.220284i
$429$		0			0
$430$	−2.03827	−	0.741870i	−0.0982942	−	0.0357762i
$431$	14.3326			0.690378			0.345189	−	0.938533i	$-0.387815\pi$
$431$	14.3326			0.690378			0.345189	+	0.938533i	$0.387815\pi$
$432$		0			0
$433$	14.4669			0.695233			0.347616	−	0.937637i	$-0.386991\pi$
$433$	14.4669			0.695233			0.347616	+	0.937637i	$0.386991\pi$
$434$	−1.97532	−	0.718958i	−0.0948185	−	0.0345111i
$435$		0			0
$436$	4.74132	+	3.97844i	0.227068	+	0.190533i
$437$	−1.66810	+	9.46025i	−0.0797959	+	0.452545i
$438$		0			0
$439$	−11.4536	+	9.61070i	−0.546650	+	0.458694i	−0.873805	−	0.486277i	$-0.838355\pi$
$439$	−11.4536	+	9.61070i	−0.546650	+	0.458694i	0.327155	+	0.944971i	$0.393910\pi$
$440$	1.04248	+	1.80564i	0.0496985	+	0.0860803i
$441$		0			0
$442$	2.37559	−	4.11465i	0.112995	−	0.195714i
$443$	6.01661	+	34.1219i	0.285858	+	1.62118i	0.702206	+	0.711974i	$0.252199\pi$
$443$	6.01661	+	34.1219i	0.285858	+	1.62118i	−0.416348	+	0.909205i	$0.636690\pi$
$444$		0			0
$445$	−3.05932	+	1.11350i	−0.145026	+	0.0527851i
$446$	−1.63494	+	0.595069i	−0.0774166	+	0.0281773i
$447$		0			0
$448$	4.40112	+	24.9600i	0.207933	+	1.17925i
$449$	−12.7777	+	22.1315i	−0.603015	+	1.04445i	0.389347	+	0.921091i	$0.372701\pi$
$449$	−12.7777	+	22.1315i	−0.603015	+	1.04445i	−0.992362	+	0.123361i	$0.960633\pi$
$450$		0			0
$451$	−0.670925	−	1.16208i	−0.0315926	−	0.0547201i
$452$	17.9908	−	15.0960i	0.846214	−	0.710058i
$453$		0			0
$454$	0.799800	−	4.53589i	0.0375365	−	0.212880i
$455$	−13.2906	−	11.1521i	−0.623074	−	0.522821i
$456$		0			0
$457$	18.0578	+	6.57250i	0.844707	+	0.307448i	0.727881	−	0.685704i	$-0.240506\pi$
$457$	18.0578	+	6.57250i	0.844707	+	0.307448i	0.116827	+	0.993152i	$0.462728\pi$
$458$	−0.742248			−0.0346830
$459$		0			0
$460$	16.4703			0.767934
$461$	−10.5314	−	3.83312i	−0.490497	−	0.178526i	0.0849181	−	0.996388i	$-0.472937\pi$
$461$	−10.5314	−	3.83312i	−0.490497	−	0.178526i	−0.575415	+	0.817862i	$0.695159\pi$
$462$		0			0
$463$	−9.75323	−	8.18393i	−0.453271	−	0.380340i	0.387377	−	0.921921i	$-0.373381\pi$
$463$	−9.75323	−	8.18393i	−0.453271	−	0.380340i	−0.840648	+	0.541582i	$0.817826\pi$
$464$	−0.360029	+	2.04182i	−0.0167139	+	0.0947893i
$465$		0			0
$466$	1.94254	−	1.62998i	0.0899862	−	0.0755074i
$467$	−16.4688	−	28.5249i	−0.762087	−	1.31997i	−0.941773	−	0.336249i	$-0.890842\pi$
$467$	−16.4688	−	28.5249i	−0.762087	−	1.31997i	0.179687	−	0.983724i	$-0.442492\pi$
$468$		0			0
$469$	16.8029	−	29.1034i	0.775884	−	1.34387i
$470$	−0.613808	−	3.48108i	−0.0283128	−	0.160570i
$471$		0			0
$472$	−15.2743	+	5.55940i	−0.703058	+	0.255892i
$473$	−12.0093	+	4.37101i	−0.552186	+	0.200979i
$474$		0			0
$475$	0.193390	+	1.09677i	0.00887335	+	0.0503233i
$476$	−15.9890	+	27.6937i	−0.732854	+	1.26934i
$477$		0			0
$478$	2.29398	+	3.97328i	0.104924	+	0.181734i
$479$	16.9755	−	14.2441i	0.775628	−	0.650829i	−0.166515	−	0.986039i	$-0.553252\pi$
$479$	16.9755	−	14.2441i	0.775628	−	0.650829i	0.942144	+	0.335209i	$0.108807\pi$
$480$		0			0
$481$	3.66438	−	20.7818i	0.167082	−	0.947566i
$482$	0.149992	+	0.125858i	0.00683193	+	0.00573267i
$483$		0			0
$484$	−14.0995	−	5.13178i	−0.640885	−	0.233263i
$485$	−1.99171			−0.0904388
$486$		0			0
$487$	−15.7072			−0.711761			−0.355881	−	0.934531i	$-0.615819\pi$
$487$	−15.7072			−0.711761			−0.355881	+	0.934531i	$0.615819\pi$
$488$	9.37289	+	3.41145i	0.424291	+	0.154429i
$489$		0			0
$490$	−2.62707	−	2.20437i	−0.118679	−	0.0995835i
$491$	4.61638	−	26.1808i	0.208334	−	1.18152i	−0.683772	−	0.729696i	$-0.739662\pi$
$491$	4.61638	−	26.1808i	0.208334	−	1.18152i	0.892106	−	0.451826i	$-0.149227\pi$
$492$		0			0
$493$	−1.78956	+	1.50162i	−0.0805978	+	0.0676296i
$494$	0.677634	+	1.17370i	0.0304882	+	0.0528071i
$495$		0			0
$496$	−2.82215	+	4.88811i	−0.126718	+	0.219483i
$497$	−3.86090	−	21.8963i	−0.173185	−	0.982182i
$498$		0			0
$499$	1.98733	−	0.723329i	0.0889652	−	0.0323807i	−0.297154	−	0.954830i	$-0.596038\pi$
$499$	1.98733	−	0.723329i	0.0889652	−	0.0323807i	0.386119	+	0.922449i	$0.373815\pi$
$500$	1.79433	−	0.653082i	0.0802448	−	0.0292067i
$501$		0			0
$502$	0.321747	+	1.82472i	0.0143603	+	0.0814412i
$503$	4.80026	−	8.31430i	0.214033	−	0.370716i	−0.738940	−	0.673771i	$-0.764673\pi$
$503$	4.80026	−	8.31430i	0.214033	−	0.370716i	0.952973	+	0.303055i	$0.0980066\pi$
$504$		0			0
$505$	4.58366	+	7.93914i	0.203970	+	0.353287i
$506$	−3.52388	+	2.95688i	−0.156655	+	0.131450i
$507$		0			0
$508$	3.65129	−	20.7075i	0.162000	−	0.918748i
$509$	3.02405	+	2.53748i	0.134039	+	0.112472i	0.707342	−	0.706871i	$-0.249894\pi$
$509$	3.02405	+	2.53748i	0.134039	+	0.112472i	−0.573304	+	0.819343i	$0.694338\pi$
$510$		0			0
$511$	−17.6354	−	6.41876i	−0.780144	−	0.283949i
$512$	−19.9150			−0.880128
$513$		0			0
$514$	2.10969			0.0930544
$515$	−1.70359	−	0.620058i	−0.0750694	−	0.0273230i
$516$		0			0
$517$	−15.9540	−	13.3870i	−0.701657	−	0.588760i
$518$	1.16912	−	6.63042i	0.0513683	−	0.291324i
$519$		0			0
$520$	3.64447	−	3.05807i	0.159820	−	0.134105i
$521$	−12.6619	−	21.9311i	−0.554729	−	0.960818i	−0.997925	−	0.0643933i	$-0.979489\pi$
$521$	−12.6619	−	21.9311i	−0.554729	−	0.960818i	0.443196	−	0.896425i	$-0.353845\pi$
$522$		0			0
$523$	7.76052	−	13.4416i	0.339344	−	0.587761i	−0.644966	−	0.764211i	$-0.723128\pi$
$523$	7.76052	−	13.4416i	0.339344	−	0.587761i	0.984309	+	0.176451i	$0.0564617\pi$
$524$	5.81768	+	32.9937i	0.254146	+	1.44134i
$525$		0			0
$526$	−5.49961	+	2.00169i	−0.239794	+	0.0872780i
$527$	−5.97617	+	2.17515i	−0.260326	+	0.0947509i
$528$		0			0
$529$	8.92553	+	50.6192i	0.388066	+	2.20083i
$530$	−0.598294	+	1.03628i	−0.0259882	+	0.0450129i
$531$		0			0
$532$	−4.56083	−	7.89959i	−0.197737	−	0.342491i
$533$	−2.34552	+	1.96812i	−0.101596	+	0.0852488i
$534$		0			0
$535$	−0.644750	+	3.65656i	−0.0278750	+	0.158087i
$536$	7.05922	+	5.92338i	0.304912	+	0.255851i
$537$		0			0
$538$	−2.87962	−	1.04810i	−0.124149	−	0.0451866i
$539$	−20.2056			−0.870317
$540$		0			0
$541$	11.7630			0.505730			0.252865	−	0.967502i	$-0.418627\pi$
$541$	11.7630			0.505730			0.252865	+	0.967502i	$0.418627\pi$
$542$	−1.94249	−	0.707008i	−0.0834370	−	0.0303686i
$543$		0			0
$544$	−10.1537	−	8.51996i	−0.435336	−	0.365290i
$545$	−0.562859	+	3.19213i	−0.0241102	+	0.136736i
$546$		0			0
$547$	13.8145	−	11.5917i	0.590665	−	0.495627i	−0.297765	−	0.954639i	$-0.596241\pi$
$547$	13.8145	−	11.5917i	0.590665	−	0.495627i	0.888430	+	0.459012i	$0.151797\pi$
$548$	−0.340579	−	0.589900i	−0.0145488	−	0.0251993i
$549$		0			0
$550$	−0.266655	+	0.461860i	−0.0113702	+	0.0196938i
$551$	−0.115714	−	0.656247i	−0.00492958	−	0.0279571i
$552$		0			0
$553$	−51.9584	+	18.9113i	−2.20950	+	0.804191i
$554$	7.50989	−	2.73338i	0.319065	−	0.116130i
$555$		0			0
$556$	0.494455	+	2.80419i	0.0209696	+	0.118924i
$557$	4.95446	−	8.58137i	0.209927	−	0.363604i	−0.741764	−	0.670661i	$-0.766011\pi$
$557$	4.95446	−	8.58137i	0.209927	−	0.363604i	0.951691	+	0.307056i	$0.0993440\pi$
$558$		0			0
$559$	14.5808	+	25.2547i	0.616701	+	1.06816i
$560$	−11.3858	+	9.55380i	−0.481137	+	0.403722i
$561$		0			0
$562$	−1.24991	+	7.08857i	−0.0527241	+	0.299013i
$563$	0.891731	+	0.748251i	0.0375820	+	0.0315350i	0.661385	−	0.750046i	$-0.269969\pi$
$563$	0.891731	+	0.748251i	0.0375820	+	0.0315350i	−0.623803	+	0.781581i	$0.714413\pi$
$564$		0			0
$565$	11.5575	+	4.20660i	0.486229	+	0.176973i
$566$	4.06208			0.170742
$567$		0			0
$568$	6.09688			0.255820
$569$	−4.81240	−	1.75157i	−0.201746	−	0.0734296i	0.239171	−	0.970978i	$-0.423124\pi$
$569$	−4.81240	−	1.75157i	−0.201746	−	0.0734296i	−0.440917	+	0.897548i	$0.645347\pi$
$570$		0			0
$571$	−11.3635	−	9.53515i	−0.475550	−	0.399033i	0.373264	−	0.927725i	$-0.378238\pi$
$571$	−11.3635	−	9.53515i	−0.475550	−	0.399033i	−0.848814	+	0.528691i	$0.822683\pi$
$572$	2.37739	−	13.4829i	0.0994038	−	0.563747i
$573$		0			0
$574$	−0.748337	+	0.627930i	−0.0312350	+	0.0262093i
$575$	4.31277	+	7.46994i	0.179855	+	0.311518i
$576$		0			0
$577$	15.7817	−	27.3347i	0.657001	−	1.13796i	−0.324387	−	0.945924i	$-0.605158\pi$
$577$	15.7817	−	27.3347i	0.657001	−	1.13796i	0.981388	−	0.192035i	$-0.0615086\pi$
$578$	0.0917692	+	0.520449i	0.00381710	+	0.0216478i
$579$		0			0
$580$	−1.07363	+	0.390768i	−0.0445799	+	0.0162258i
$581$	−31.8716	+	11.6003i	−1.32226	+	0.481262i
$582$		0			0
$583$	1.22425	+	6.94305i	0.0507031	+	0.287552i
$584$	2.57311	−	4.45676i	0.106476	−	0.184422i
$585$		0			0
$586$	0.829490	+	1.43672i	0.0342659	+	0.0593503i
$587$	−13.0278	+	10.9316i	−0.537713	+	0.451195i	−0.870755	−	0.491717i	$-0.836369\pi$
$587$	−13.0278	+	10.9316i	−0.537713	+	0.451195i	0.333042	+	0.942912i	$0.391925\pi$
$588$		0			0
$589$	0.315014	−	1.78653i	0.0129799	−	0.0736129i
$590$	−3.18501	−	2.67254i	−0.131125	−	0.110027i
$591$		0			0
$592$	−16.9877	−	6.18301i	−0.698190	−	0.254120i
$593$	−42.7865			−1.75703			−0.878517	−	0.477712i	$-0.841466\pi$
$593$	−42.7865			−1.75703			−0.878517	+	0.477712i	$0.841466\pi$
$594$		0			0
$595$	−16.7469			−0.686557
$596$	32.4759	+	11.8203i	1.33026	+	0.484177i
$597$		0			0
$598$	8.04084	+	6.74706i	0.328814	+	0.275908i
$599$	0.336622	−	1.90908i	0.0137540	−	0.0780029i	−0.977158	−	0.212513i	$-0.931835\pi$
$599$	0.336622	−	1.90908i	0.0137540	−	0.0780029i	0.990912	+	0.134511i	$0.0429462\pi$
$600$		0			0
$601$	−15.1011	+	12.6713i	−0.615986	+	0.516874i	−0.896539	−	0.442965i	$-0.853927\pi$
$601$	−15.1011	+	12.6713i	−0.615986	+	0.516874i	0.280553	+	0.959839i	$0.409482\pi$
$602$	4.65200	+	8.05750i	0.189601	+	0.328399i
$603$		0			0
$604$	−20.2499	+	35.0739i	−0.823959	+	1.42714i
$605$	−1.36449	−	7.73842i	−0.0554745	−	0.314611i
$606$		0			0
$607$	10.8522	−	3.94987i	0.440477	−	0.160320i	−0.112255	−	0.993679i	$-0.535807\pi$
$607$	10.8522	−	3.94987i	0.440477	−	0.160320i	0.552732	+	0.833359i	$0.313585\pi$
$608$	3.55287	−	1.29314i	0.144088	−	0.0524436i
$609$		0			0
$610$	0.443035	+	2.51258i	0.0179380	+	0.101731i
$611$	−23.7611	+	41.1554i	−0.961271	+	1.66497i
$612$		0			0
$613$	−5.95138	−	10.3081i	−0.240374	−	0.416340i	0.720447	−	0.693510i	$-0.243937\pi$
$613$	−5.95138	−	10.3081i	−0.240374	−	0.416340i	−0.960821	+	0.277170i	$0.910603\pi$
$614$	−1.09870	+	0.921923i	−0.0443401	+	0.0372058i
$615$		0			0
$616$	1.55297	−	8.80733i	0.0625710	−	0.354858i
$617$	−22.1687	−	18.6018i	−0.892480	−	0.748879i	0.0762262	−	0.997091i	$-0.475713\pi$
$617$	−22.1687	−	18.6018i	−0.892480	−	0.748879i	−0.968706	+	0.248211i	$0.920157\pi$
$618$		0			0
$619$	5.52194	+	2.00982i	0.221946	+	0.0807816i	0.450600	−	0.892726i	$-0.351210\pi$
$619$	5.52194	+	2.00982i	0.221946	+	0.0807816i	−0.228654	+	0.973508i	$0.573432\pi$
$620$	−3.11037			−0.124915
$621$		0			0
$622$	3.27198			0.131194
$623$	13.1226	+	4.77622i	0.525744	+	0.191355i
$624$		0			0
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	0.648770	−	3.67936i	0.0259301	−	0.147057i
$627$		0			0
$628$	8.00969	−	6.72093i	0.319621	−	0.268194i
$629$	−10.1846	−	17.6403i	−0.406087	−	0.703364i
$630$		0			0
$631$	−10.1424	+	17.5671i	−0.403761	+	0.699335i	−0.994176	−	0.107765i	$-0.965631\pi$
$631$	−10.1424	+	17.5671i	−0.403761	+	0.699335i	0.590415	+	0.807100i	$0.298964\pi$
$632$	−2.63287	−	14.9317i	−0.104730	−	0.593953i
$633$		0			0
$634$	3.11921	−	1.13530i	0.123880	−	0.0450885i
$635$	10.3478	−	3.76628i	0.410638	−	0.149460i
$636$		0			0
$637$	8.00613	+	45.4050i	0.317214	+	1.79901i
$638$	0.159552	−	0.276352i	0.00631671	−	0.0109409i
$639$		0			0
$640$	−4.28377	−	7.41971i	−0.169331	−	0.293290i
$641$	−7.37134	+	6.18529i	−0.291151	+	0.244304i	−0.776650	−	0.629933i	$-0.783082\pi$
$641$	−7.37134	+	6.18529i	−0.291151	+	0.244304i	0.485499	+	0.874237i	$0.338638\pi$
$642$		0			0
$643$	−1.13466	+	6.43500i	−0.0447468	+	0.253772i	−0.998973	−	0.0453151i	$-0.985571\pi$
$643$	−1.13466	+	6.43500i	−0.0447468	+	0.253772i	0.954226	+	0.299087i	$0.0966819\pi$
$644$	−54.1190	−	45.4113i	−2.13259	−	1.78945i
$645$		0			0
$646$	1.22929	+	0.447425i	0.0483658	+	0.0176037i
$647$	4.88147			0.191910			0.0959551	−	0.995386i	$-0.469409\pi$
$647$	4.88147			0.191910			0.0959551	+	0.995386i	$0.469409\pi$
$648$		0			0
$649$	−24.4969			−0.961587
$650$	1.14353	+	0.416210i	0.0448528	+	0.0163251i
$651$		0			0
$652$	26.3103	+	22.0769i	1.03039	+	0.864600i
$653$	−1.09046	+	6.18430i	−0.0426730	+	0.242010i	−0.998682	−	0.0513272i	$-0.983655\pi$
$653$	−1.09046	+	6.18430i	−0.0426730	+	0.242010i	0.956009	+	0.293338i	$0.0947660\pi$
$654$		0			0
$655$	−13.4406	+	11.2780i	−0.525166	+	0.440667i
$656$	1.31151	+	2.27161i	0.0512059	+	0.0886913i
$657$		0			0
$658$	−7.58098	+	13.1306i	−0.295537	+	0.511886i
$659$	−1.25353	−	7.10913i	−0.0488307	−	0.276933i	0.950609	−	0.310389i	$-0.100459\pi$
$659$	−1.25353	−	7.10913i	−0.0488307	−	0.276933i	−0.999440	+	0.0334569i	$0.989348\pi$
$660$		0			0
$661$	−41.0593	+	14.9444i	−1.59702	+	0.581268i	−0.978815	−	0.204748i	$-0.934363\pi$
$661$	−41.0593	+	14.9444i	−1.59702	+	0.581268i	−0.618206	+	0.786016i	$0.712140\pi$
$662$	0.572781	−	0.208475i	0.0222618	−	0.00810263i
$663$		0			0
$664$	−1.61502	−	9.15922i	−0.0626748	−	0.355447i
$665$	2.38851	−	4.13703i	0.0926226	−	0.160427i
$666$		0			0
$667$	−2.58053	−	4.46960i	−0.0999183	−	0.173064i
$668$	29.1639	−	24.4714i	1.12839	−	0.946828i
$669$		0			0
$670$	−0.409311	+	2.32132i	−0.0158131	+	0.0896803i
$671$	11.5153	+	9.66250i	0.444544	+	0.373017i
$672$		0			0
$673$	−33.3471	−	12.1373i	−1.28543	−	0.467860i	−0.393209	−	0.919449i	$-0.628635\pi$
$673$	−33.3471	−	12.1373i	−1.28543	−	0.467860i	−0.892226	+	0.451589i	$0.850857\pi$
$674$	4.62723			0.178234
$675$		0			0
$676$	−6.41672			−0.246797
$677$	13.4876	+	4.90907i	0.518369	+	0.188671i	0.587937	−	0.808906i	$-0.299940\pi$
$677$	13.4876	+	4.90907i	0.518369	+	0.188671i	−0.0695687	+	0.997577i	$0.522162\pi$
$678$		0			0
$679$	6.54445	+	5.49144i	0.251153	+	0.210742i
$680$	0.797433	−	4.52247i	0.0305802	−	0.173429i
$681$		0			0
$682$	0.665472	−	0.558397i	0.0254822	−	0.0213821i
$683$	7.28683	+	12.6212i	0.278823	+	0.482935i	0.971092	−	0.238704i	$-0.0767225\pi$
$683$	7.28683	+	12.6212i	0.278823	+	0.482935i	−0.692270	+	0.721639i	$0.743389\pi$
$684$		0			0
$685$	0.178362	−	0.308931i	0.00681485	−	0.0118037i
$686$	0.985712	+	5.59025i	0.0376346	+	0.213437i
$687$		0			0
$688$	23.4755	−	8.54437i	0.894994	−	0.325751i
$689$	15.1170	−	5.50213i	0.575911	−	0.209614i
$690$		0			0
$691$	−4.75235	−	26.9519i	−0.180788	−	1.02530i	−0.931249	−	0.364384i	$-0.881280\pi$
$691$	−4.75235	−	26.9519i	−0.180788	−	1.02530i	0.750461	−	0.660915i	$-0.229832\pi$
$692$	−6.45952	+	11.1882i	−0.245554	+	0.425312i
$693$		0			0
$694$	−0.174375	−	0.302026i	−0.00661918	−	0.0114648i
$695$	−1.14234	+	0.958535i	−0.0433313	+	0.0363593i
$696$		0			0
$697$	−0.513214	+	2.91058i	−0.0194394	+	0.110246i
$698$	1.19011	+	0.998618i	0.0450462	+	0.0377983i
$699$		0			0
$700$	−7.69653	−	2.80131i	−0.290902	−	0.105880i
$701$	30.5667			1.15449			0.577243	−	0.816572i	$-0.304128\pi$
$701$	30.5667			1.15449			0.577243	+	0.816572i	$0.304128\pi$
$702$		0			0
$703$	5.81029			0.219139
$704$	−9.84243	−	3.58235i	−0.370951	−	0.135015i
$705$		0			0
$706$	−2.79848	−	2.34821i	−0.105322	−	0.0883759i
$707$	6.82820	−	38.7246i	0.256801	−	1.45639i
$708$		0			0
$709$	11.3456	−	9.52012i	0.426094	−	0.357536i	−0.404381	−	0.914590i	$-0.632513\pi$
$709$	11.3456	−	9.52012i	0.426094	−	0.357536i	0.830476	+	0.557055i	$0.188069\pi$
$710$	0.779756	+	1.35058i	0.0292637	+	0.0506862i
$711$		0			0
$712$	−1.91466	+	3.31629i	−0.0717549	+	0.124283i
$713$	−2.43979	−	13.8367i	−0.0913708	−	0.518190i
$714$		0			0
$715$	6.73753	−	2.45226i	0.251969	−	0.0917093i
$716$	−16.9379	+	6.16490i	−0.633000	+	0.230393i
$717$		0			0
$718$	0.464662	+	2.63523i	0.0173410	+	0.0983460i
$719$	2.62426	−	4.54535i	0.0978684	−	0.169513i	−0.812934	−	0.582356i	$-0.802131\pi$
$719$	2.62426	−	4.54535i	0.0978684	−	0.169513i	0.910802	+	0.412843i	$0.135464\pi$
$720$		0			0
$721$	3.88816	+	6.73449i	0.144803	+	0.250805i
$722$	4.09310	−	3.43452i	0.152329	−	0.127820i
$723$		0			0
$724$	−0.375481	+	2.12946i	−0.0139546	+	0.0791407i
$725$	−0.458359	−	0.384609i	−0.0170230	−	0.0142840i
$726$		0			0
$727$	−44.6043	−	16.2347i	−1.65428	−	0.602110i	−0.664834	−	0.746991i	$-0.731498\pi$
$727$	−44.6043	−	16.2347i	−1.65428	−	0.602110i	−0.989449	+	0.144881i	$0.953720\pi$
$728$	−20.4067			−0.756324
$729$		0			0
$730$	1.31634			0.0487200
$731$	26.4509	+	9.62734i	0.978322	+	0.356080i
$732$		0			0
$733$	−29.7170	−	24.9355i	−1.09762	−	0.921014i	−0.100358	−	0.994951i	$-0.531999\pi$
$733$	−29.7170	−	24.9355i	−1.09762	−	0.921014i	−0.997263	+	0.0739377i	$0.976443\pi$
$734$	1.44337	−	8.18574i	0.0532757	−	0.302141i
$735$		0			0
$736$	22.4321	−	18.8227i	0.826857	−	0.693815i
$737$	6.94396	+	12.0273i	0.255784	+	0.443031i
$738$		0			0
$739$	7.71235	−	13.3582i	0.283704	−	0.491389i	−0.688590	−	0.725150i	$-0.741770\pi$
$739$	7.71235	−	13.3582i	0.283704	−	0.491389i	0.972294	+	0.233762i	$0.0751035\pi$
$740$	−1.72989	−	9.81071i	−0.0635921	−	0.360649i
$741$		0			0
$742$	4.82307	−	1.75546i	0.177061	−	0.0644448i
$743$	−38.6448	+	14.0656i	−1.41774	+	0.516015i	−0.933391	−	0.358860i	$-0.883166\pi$
$743$	−38.6448	+	14.0656i	−1.41774	+	0.516015i	−0.484349	+	0.874875i	$0.660943\pi$
$744$		0			0
$745$	3.14289	+	17.8242i	0.115147	+	0.653029i
$746$	−4.64024	+	8.03714i	−0.169891	+	0.294260i
$747$		0			0
$748$	−6.60761	−	11.4447i	−0.241598	−	0.418460i
$749$	12.2002	−	10.2372i	0.445787	−	0.374060i
$750$		0			0
$751$	−8.93875	+	50.6942i	−0.326180	+	1.84986i	0.175074	+	0.984555i	$0.443984\pi$
$751$	−8.93875	+	50.6942i	−0.326180	+	1.84986i	−0.501253	+	0.865301i	$0.667128\pi$
$752$	31.1866	+	26.1687i	1.13726	+	0.954273i
$753$		0			0
$754$	−0.684223	−	0.249037i	−0.0249179	−	0.00906939i
$755$	−21.2099			−0.771906
$756$		0			0
$757$	36.7855			1.33699			0.668497	−	0.743715i	$-0.266938\pi$
$757$	36.7855			1.33699			0.668497	+	0.743715i	$0.266938\pi$
$758$	−5.94321	−	2.16315i	−0.215867	−	0.0785691i
$759$		0			0
$760$	1.00346	+	0.842004i	0.0363994	+	0.0305427i
$761$	4.11655	−	23.3461i	0.149225	−	0.846295i	−0.814653	−	0.579949i	$-0.803072\pi$
$761$	4.11655	−	23.3461i	0.149225	−	0.846295i	0.963877	−	0.266346i	$-0.0858164\pi$
$762$		0			0
$763$	10.6507	−	8.93697i	0.385580	−	0.323540i
$764$	22.5549	+	39.0662i	0.816007	+	1.41337i
$765$		0			0
$766$	3.23803	−	5.60844i	0.116995	−	0.202641i
$767$	9.70648	+	55.0482i	0.350481	+	1.98767i
$768$		0			0
$769$	10.3649	−	3.77252i	0.373768	−	0.136040i	−0.148304	−	0.988942i	$-0.547381\pi$
$769$	10.3649	−	3.77252i	0.373768	−	0.136040i	0.522072	+	0.852901i	$0.325159\pi$
$770$	2.14961	−	0.782394i	0.0774665	−	0.0281955i
$771$		0			0
$772$	0.900555	+	5.10730i	0.0324117	+	0.183816i
$773$	22.1299	−	38.3301i	0.795958	−	1.37864i	−0.126272	−	0.991996i	$-0.540301\pi$
$773$	22.1299	−	38.3301i	0.795958	−	1.37864i	0.922229	−	0.386644i	$-0.126366\pi$
$774$		0			0
$775$	−0.814452	−	1.41067i	−0.0292560	−	0.0506728i
$776$	−1.79458	+	1.50583i	−0.0644216	+	0.0540561i
$777$		0			0
$778$	0.700727	−	3.97402i	0.0251223	−	0.142475i
$779$	−0.645811	−	0.541900i	−0.0231386	−	0.0194156i
$780$		0			0
$781$	8.63433	+	3.14264i	0.308960	+	0.112452i
$782$	10.1319			0.362316
$783$		0			0
$784$	39.4976			1.41063
$785$	5.14555	+	1.87283i	0.183652	+	0.0668440i
$786$		0			0
$787$	−31.5179	−	26.4467i	−1.12349	−	0.942722i	−0.124717	−	0.992192i	$-0.539802\pi$
$787$	−31.5179	−	26.4467i	−1.12349	−	0.942722i	−0.998776	+	0.0494704i	$0.984247\pi$
$788$	−4.73305	+	26.8425i	−0.168608	+	0.956224i
$789$		0			0
$790$	2.97094	−	2.49291i	0.105701	−	0.0886939i
$791$	−26.3781	−	45.6882i	−0.937896	−	1.62448i
$792$		0			0
$793$	17.1503	−	29.7053i	0.609026	−	1.05486i
$794$	0.888454	+	5.03867i	0.0315301	+	0.178816i
$795$		0			0
$796$	38.1659	−	13.8912i	1.35275	−	0.492362i
$797$	21.9590	−	7.99243i	0.777828	−	0.283106i	0.0775615	−	0.996988i	$-0.475287\pi$
$797$	21.9590	−	7.99243i	0.777828	−	0.283106i	0.700267	+	0.713881i	$0.253064\pi$
$798$		0			0
$799$	7.96546	+	45.1743i	0.281798	+	1.59815i
$800$	1.69746	−	2.94008i	0.0600141	−	0.103948i
$801$		0			0
$802$	−0.938639	−	1.62577i	−0.0331445	−	0.0574080i
$803$	5.94124	−	4.98529i	0.209662	−	0.175927i
$804$		0			0
$805$	6.42466	−	36.4361i	0.226440	−	1.28420i
$806$	−1.51848	−	1.27416i	−0.0534863	−	0.0448803i
$807$		0			0
$808$	10.1324	+	3.68788i	0.356455	+	0.129739i
$809$	16.4420			0.578070			0.289035	−	0.957319i	$-0.406666\pi$
$809$	16.4420			0.578070			0.289035	+	0.957319i	$0.406666\pi$
$810$		0			0
$811$	49.2346			1.72886			0.864430	−	0.502753i	$-0.167679\pi$
$811$	49.2346			1.72886			0.864430	+	0.502753i	$0.167679\pi$
$812$	4.60518	+	1.67615i	0.161610	+	0.0588213i
$813$		0			0
$814$	2.13141	+	1.78847i	0.0747059	+	0.0626857i
$815$	−3.12339	+	17.7136i	−0.109407	+	0.620481i
$816$		0			0
$817$	−6.15080	+	5.16113i	−0.215189	+	0.180565i
$818$	1.44416	+	2.50136i	0.0504940	+	0.0874582i
$819$		0			0
$820$	−0.722725	+	1.25180i	−0.0252386	+	0.0437146i
$821$	0.479682	+	2.72041i	0.0167410	+	0.0949431i	0.992033	−	0.125975i	$-0.0402058\pi$
$821$	0.479682	+	2.72041i	0.0167410	+	0.0949431i	−0.975292	+	0.220918i	$0.929095\pi$
$822$		0			0
$823$	31.0031	−	11.2842i	1.08070	−	0.393343i	0.260533	−	0.965465i	$-0.416102\pi$
$823$	31.0031	−	11.2842i	1.08070	−	0.393343i	0.820169	+	0.572122i	$0.193880\pi$
$824$	−2.00377	+	0.729314i	−0.0698048	+	0.0254069i
$825$		0			0
$826$	3.09685	+	17.5631i	0.107753	+	0.611099i
$827$	−27.3913	+	47.4431i	−0.952489	+	1.64976i	−0.212475	+	0.977166i	$0.568153\pi$
$827$	−27.3913	+	47.4431i	−0.952489	+	1.64976i	−0.740013	+	0.672592i	$0.765181\pi$
$828$		0			0
$829$	−25.5346	−	44.2272i	−0.886852	−	1.53607i	−0.843576	−	0.537010i	$-0.819554\pi$
$829$	−25.5346	−	44.2272i	−0.886852	−	1.53607i	−0.0432768	−	0.999063i	$-0.513780\pi$
$830$	1.82239	−	1.52917i	0.0632561	−	0.0530782i
$831$		0			0
$832$	−4.15018	+	23.5369i	−0.143882	+	0.815994i
$833$	34.0918	+	28.6064i	1.18121	+	0.991154i
$834$		0			0
$835$	18.7354	+	6.81911i	0.648364	+	0.235985i
$836$	3.76962			0.130375
$837$		0			0
$838$	4.51449			0.155950
$839$	−38.7316	−	14.0971i	−1.33716	−	0.486688i	−0.428245	−	0.903663i	$-0.640868\pi$
$839$	−38.7316	−	14.0971i	−1.33716	−	0.486688i	−0.908918	+	0.416975i	$0.863090\pi$
$840$		0			0
$841$	−21.9410	−	18.4107i	−0.756587	−	0.634852i
$842$	−1.93505	+	10.9742i	−0.0666862	+	0.378196i
$843$		0			0
$844$	29.4663	−	24.7251i	1.01427	−	0.851074i
$845$	−1.68022	−	2.91023i	−0.0578015	−	0.100115i
$846$		0			0
$847$	−16.8525	+	29.1894i	−0.579059	+	1.00296i
$848$	−2.39313	−	13.5721i	−0.0821806	−	0.466069i
$849$		0			0
$850$	1.10380	−	0.401750i	0.0378600	−	0.0137799i
$851$	42.2869	−	15.3912i	1.44958	−	0.527602i
$852$		0			0
$853$	3.58449	+	20.3286i	0.122730	+	0.696039i	0.982630	+	0.185576i	$0.0594150\pi$
$853$	3.58449	+	20.3286i	0.122730	+	0.696039i	−0.859900	+	0.510463i	$0.829474\pi$
$854$	5.47182	−	9.47746i	0.187242	−	0.324312i
$855$		0			0
$856$	2.18360	+	3.78211i	0.0746339	+	0.129270i
$857$	−28.2977	+	23.7446i	−0.966630	+	0.811099i	−0.982019	−	0.188783i	$-0.939546\pi$
$857$	−28.2977	+	23.7446i	−0.966630	+	0.811099i	0.0153887	+	0.999882i	$0.495101\pi$
$858$		0			0
$859$	4.11514	−	23.3381i	0.140407	−	0.796286i	−0.830535	−	0.556967i	$-0.811965\pi$
$859$	4.11514	−	23.3381i	0.140407	−	0.796286i	0.970941	−	0.239318i	$-0.0769240\pi$
$860$	10.5459	+	8.84905i	0.359612	+	0.301750i
$861$		0			0
$862$	4.05205	+	1.47482i	0.138013	+	0.0502327i
$863$	−36.6147			−1.24638			−0.623189	−	0.782072i	$-0.714163\pi$
$863$	−36.6147			−1.24638			−0.623189	+	0.782072i	$0.714163\pi$
$864$		0			0
$865$	−6.76573			−0.230042
$866$	4.09000	+	1.48864i	0.138984	+	0.0505859i
$867$		0			0
$868$	10.2202	+	8.57576i	0.346896	+	0.291080i
$869$	3.96793	−	22.5032i	0.134603	−	0.763370i
$870$		0			0
$871$	24.2757	−	20.3697i	0.822550	−	0.690202i
$872$	1.90626	+	3.30174i	0.0645541	+	0.111811i
$873$		0			0
$874$	−1.44505	+	2.50291i	−0.0488797	+	0.0846621i
$875$	−0.744841	−	4.22420i	−0.0251802	−	0.142804i
$876$		0			0
$877$	−22.7520	+	8.28105i	−0.768280	+	0.279631i	−0.696277	−	0.717773i	$-0.745161\pi$
$877$	−22.7520	+	8.28105i	−0.768280	+	0.279631i	−0.0720034	+	0.997404i	$0.522939\pi$
$878$	−4.22704	+	1.53852i	−0.142656	+	0.0519224i
$879$		0			0
$880$	−1.06660	−	6.04900i	−0.0359552	−	0.203912i
$881$	13.4734	−	23.3367i	0.453931	−	0.786232i	−0.544695	−	0.838634i	$-0.683354\pi$
$881$	13.4734	−	23.3367i	0.453931	−	0.786232i	0.998626	+	0.0524023i	$0.0166878\pi$
$882$		0			0
$883$	−0.494590	−	0.856656i	−0.0166443	−	0.0288288i	0.857583	−	0.514345i	$-0.171965\pi$
$883$	−0.494590	−	0.856656i	−0.0166443	−	0.0288288i	−0.874228	+	0.485516i	$0.838632\pi$
$884$	−23.0998	+	19.3831i	−0.776932	+	0.651923i
$885$		0			0
$886$	−1.81015	+	10.2659i	−0.0608132	+	0.344889i
$887$	−19.0122	−	15.9532i	−0.638368	−	0.535655i	0.265148	−	0.964208i	$-0.414579\pi$
$887$	−19.0122	−	15.9532i	−0.638368	−	0.535655i	−0.903517	+	0.428553i	$0.859024\pi$
$888$		0			0
$889$	−44.3854	−	16.1550i	−1.48864	−	0.541820i
$890$	−0.979495			−0.0328328
$891$		0			0
$892$	11.0425			0.369731
$893$	−12.2956	−	4.47523i	−0.411456	−	0.149758i
$894$		0			0
$895$	−7.23124	−	6.06773i	−0.241714	−	0.202822i
$896$	−6.38146	+	36.1910i	−0.213190	+	1.20906i
$897$		0			0
$898$	−5.88977	+	4.94210i	−0.196544	+	0.164920i
$899$	0.487323	+	0.844068i	0.0162531	+	0.0281512i
$900$		0			0
$901$	7.76414	−	13.4479i	0.258661	−	0.448014i
$902$	−0.0701031	−	0.397575i	−0.00233418	−	0.0132378i
$903$		0			0
$904$	13.5940	−	4.94782i	0.452130	−	0.164562i
$905$	−1.06411	+	0.387305i	−0.0353723	+	0.0128745i
$906$		0			0
$907$	0.569479	+	3.22968i	0.0189092	+	0.107240i	0.992802	−	0.119771i	$-0.0382160\pi$
$907$	0.569479	+	3.22968i	0.0189092	+	0.107240i	−0.973892	+	0.227010i	$0.927105\pi$
$908$	−14.6162	+	25.3160i	−0.485055	+	0.840140i
$909$		0			0
$910$	−2.60990	−	4.52048i	−0.0865174	−	0.149853i
$911$	30.1923	−	25.3344i	1.00032	−	0.839365i	0.0132884	−	0.999912i	$-0.495770\pi$
$911$	30.1923	−	25.3344i	1.00032	−	0.839365i	0.987028	+	0.160546i	$0.0513256\pi$
$912$		0			0
$913$	2.43395	−	13.8036i	0.0805521	−	0.456833i
$914$	4.42890	+	3.71629i	0.146495	+	0.122924i
$915$		0			0
$916$	4.42678	+	1.61122i	0.146265	+	0.0532361i
$917$	75.2587			2.48526
$918$		0			0
$919$	−9.02247			−0.297624			−0.148812	−	0.988866i	$-0.547545\pi$
$919$	−9.02247			−0.297624			−0.148812	+	0.988866i	$0.547545\pi$
$920$	9.53356	+	3.46993i	0.314312	+	0.114400i
$921$		0			0
$922$	−2.58296	−	2.16736i	−0.0850653	−	0.0713782i
$923$	3.64077	−	20.6478i	0.119837	−	0.679632i
$924$		0			0
$925$	3.99657	−	3.35352i	0.131406	−	0.110263i
$926$	−1.91526	−	3.31733i	−0.0629393	−	0.109014i
$927$		0			0
$928$	−1.01566	+	1.75918i	−0.0333408	+	0.0577480i
$929$	4.32579	+	24.5328i	0.141925	+	0.804894i	0.969785	+	0.243960i	$0.0784467\pi$
$929$	4.32579	+	24.5328i	0.141925	+	0.804894i	−0.827861	+	0.560934i	$0.810442\pi$
$930$		0			0
$931$	−11.9290	+	4.34181i	−0.390958	+	0.142297i
$932$	−15.1235	+	5.50452i	−0.495388	+	0.180307i
$933$		0			0
$934$	−1.72078	−	9.75904i	−0.0563057	−	0.319326i
$935$	3.46042	−	5.99362i	0.113168	−	0.196012i
$936$		0			0
$937$	12.7014	+	21.9995i	0.414938	+	0.718694i	0.995422	−	0.0955779i	$-0.0304699\pi$
$937$	12.7014	+	21.9995i	0.414938	+	0.718694i	−0.580484	+	0.814272i	$0.697137\pi$
$938$	7.74516	−	6.49896i	0.252888	−	0.212199i
$939$		0			0
$940$	−3.89570	+	22.0936i	−0.127064	+	0.720614i
$941$	−18.5701	−	15.5822i	−0.605368	−	0.507964i	0.287798	−	0.957691i	$-0.407077\pi$
$941$	−18.5701	−	15.5822i	−0.605368	−	0.507964i	−0.893166	+	0.449727i	$0.851521\pi$
$942$		0			0
$943$	−6.13563	−	2.23319i	−0.199804	−	0.0727226i
$944$	47.8861			1.55856
$945$		0			0
$946$	−3.84497			−0.125011
$947$	10.2582	+	3.73369i	0.333348	+	0.121329i	0.503271	−	0.864129i	$-0.332130\pi$
$947$	10.2582	+	3.73369i	0.333348	+	0.121329i	−0.169923	+	0.985457i	$0.554352\pi$
$948$		0			0
$949$	−13.5568	−	11.3755i	−0.440073	−	0.369265i
$950$	−0.0581832	+	0.329973i	−0.00188771	+	0.0107057i
$951$		0			0
$952$	−15.0894	+	12.6615i	−0.489050	+	0.410361i
$953$	−7.28673	−	12.6210i	−0.236040	−	0.408834i	0.723534	−	0.690289i	$-0.242516\pi$
$953$	−7.28673	−	12.6210i	−0.236040	−	0.408834i	−0.959575	+	0.281455i	$0.909183\pi$
$954$		0			0
$955$	−11.8120	+	20.4590i	−0.382228	+	0.662039i
$956$	−5.05641	−	28.6763i	−0.163536	−	0.927458i
$957$		0			0
$958$	6.26493	−	2.28025i	0.202411	−	0.0736715i
$959$	−1.43784	+	0.523331i	−0.0464303	+	0.0168992i
$960$		0			0
$961$	−4.92235	−	27.9160i	−0.158785	−	0.900517i
$962$	3.17442	−	5.49825i	0.102347	−	0.177271i
$963$		0			0
$964$	−0.621349	−	1.07621i	−0.0200123	−	0.0346623i
$965$	−2.08055	+	1.74579i	−0.0669752	+	0.0561989i
$966$		0			0
$967$	−8.32112	+	47.1914i	−0.267589	+	1.51757i	0.493971	+	0.869478i	$0.335545\pi$
$967$	−8.32112	+	47.1914i	−0.267589	+	1.51757i	−0.761560	+	0.648095i	$0.775566\pi$
$968$	−7.08006	−	5.94088i	−0.227562	−	0.190947i
$969$		0			0
$970$	−0.563086	−	0.204946i	−0.0180796	−	0.00658043i
$971$	−10.0839			−0.323608			−0.161804	−	0.986823i	$-0.551731\pi$
$971$	−10.0839			−0.323608			−0.161804	+	0.986823i	$0.551731\pi$
$972$		0			0
$973$	6.39638			0.205058
$974$	−4.44066	−	1.61627i	−0.142288	−	0.0517886i
$975$		0			0
$976$	−22.5099	−	18.8881i	−0.720526	−	0.604593i
$977$	−5.59597	+	31.7363i	−0.179031	+	1.01534i	0.754356	+	0.656465i	$0.227949\pi$
$977$	−5.59597	+	31.7363i	−0.179031	+	1.01534i	−0.933387	+	0.358870i	$0.883162\pi$
$978$		0			0
$979$	−4.42090	+	3.70957i	−0.141293	+	0.118558i
$980$	10.8828	+	18.8496i	0.347638	+	0.602128i
$981$		0			0
$982$	3.99912	−	6.92667i	0.127617	−	0.221039i
$983$	−0.439376	−	2.49182i	−0.0140139	−	0.0794768i	0.976999	−	0.213245i	$-0.0684033\pi$
$983$	−0.439376	−	2.49182i	−0.0140139	−	0.0794768i	−0.991013	+	0.133768i	$0.957292\pi$
$984$		0			0
$985$	−13.4135	+	4.88210i	−0.427388	+	0.155557i
$986$	−0.660453	+	0.240385i	−0.0210331	+	0.00765542i
$987$		0			0
$988$	−1.49365	−	8.47090i	−0.0475193	−	0.269495i
$989$	−31.0935	+	53.8556i	−0.988716	+	1.71251i
$990$		0			0
$991$	25.3489	+	43.9056i	0.805234	+	1.39471i	0.916133	+	0.400875i	$0.131294\pi$
$991$	25.3489	+	43.9056i	0.805234	+	1.39471i	−0.110899	+	0.993832i	$0.535373\pi$
$992$	−4.23621	+	3.55461i	−0.134500	+	0.112859i
$993$		0			0
$994$	1.16159	−	6.58769i	0.0368433	−	0.208949i
$995$	16.2940	+	13.6723i	0.516554	+	0.433440i
$996$		0			0
$997$	−13.1297	−	4.77883i	−0.415822	−	0.151347i	0.125632	−	0.992077i	$-0.459904\pi$
$997$	−13.1297	−	4.77883i	−0.415822	−	0.151347i	−0.541455	+	0.840730i	$0.682126\pi$
$998$	0.636279			0.0201411
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.k.a.226.3		30
3.2	odd	2		135.2.k.a.31.3	✓	30
15.2	even	4		675.2.u.c.274.6		60
15.8	even	4		675.2.u.c.274.5		60
15.14	odd	2		675.2.l.d.301.3		30
27.7	even	9	inner	405.2.k.a.181.3		30
27.13	even	9		3645.2.a.g.1.7		15
27.14	odd	18		3645.2.a.h.1.9		15
27.20	odd	18		135.2.k.a.61.3	yes	30
135.47	even	36		675.2.u.c.574.5		60
135.74	odd	18		675.2.l.d.601.3		30
135.128	even	36		675.2.u.c.574.6		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.k.a.31.3	✓	30	3.2	odd	2
135.2.k.a.61.3	yes	30	27.20	odd	18
405.2.k.a.181.3		30	27.7	even	9	inner
405.2.k.a.226.3		30	1.1	even	1	trivial
675.2.l.d.301.3		30	15.14	odd	2
675.2.l.d.601.3		30	135.74	odd	18
675.2.u.c.274.5		60	15.8	even	4
675.2.u.c.274.6		60	15.2	even	4
675.2.u.c.574.5		60	135.47	even	36
675.2.u.c.574.6		60	135.128	even	36
3645.2.a.g.1.7		15	27.13	even	9
3645.2.a.h.1.9		15	27.14	odd	18

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.k (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.282715 + 0.102900i) q^{2} +(-1.46275 - 1.22739i) q^{4} +(0.173648 - 0.984808i) q^{5} +(-3.28585 + 2.75715i) q^{7} +(-0.588102 - 1.01862i) q^{8} +O(q^{10})\)	\(q+(0.282715 + 0.102900i) q^{2} +(-1.46275 - 1.22739i) q^{4} +(0.173648 - 0.984808i) q^{5} +(-3.28585 + 2.75715i) q^{7} +(-0.588102 - 1.01862i) q^{8} +(0.150430 - 0.260552i) q^{10} +(-0.307813 - 1.74570i) q^{11} +(-3.80087 + 1.38340i) q^{13} +(-1.21267 + 0.441375i) q^{14} +(0.601708 + 3.41245i) q^{16} +(-1.95214 + 3.38121i) q^{17} +(-0.556845 - 0.964484i) q^{19} +(-1.46275 + 1.22739i) q^{20} +(0.0926084 - 0.525208i) q^{22} +(-6.60755 - 5.54440i) q^{23} +(-0.939693 - 0.342020i) q^{25} -1.21692 q^{26} +8.19048 q^{28} +(0.562260 + 0.204646i) q^{29} +(1.24781 + 1.04704i) q^{31} +(-0.589520 + 3.34334i) q^{32} +(-0.899826 + 0.755043i) q^{34} +(2.14468 + 3.71470i) q^{35} +(-2.60857 + 4.51818i) q^{37} +(-0.0581832 - 0.329973i) q^{38} +(-1.10527 + 0.402285i) q^{40} +(0.711333 - 0.258904i) q^{41} +(-1.25194 - 7.10010i) q^{43} +(-1.69240 + 2.93132i) q^{44} +(-1.29754 - 2.24740i) q^{46} +(9.00022 - 7.55208i) q^{47} +(1.97936 - 11.2255i) q^{49} +(-0.230471 - 0.193388i) q^{50} +(7.25771 + 2.64159i) q^{52} -3.97724 q^{53} -1.77263 q^{55} +(4.74091 + 1.72555i) q^{56} +(0.137901 + 0.115713i) q^{58} +(2.39974 - 13.6096i) q^{59} +(-6.49619 + 5.45095i) q^{61} +(0.245035 + 0.424413i) q^{62} +(2.95440 - 5.11717i) q^{64} +(0.702373 + 3.98336i) q^{65} +(-7.36217 + 2.67961i) q^{67} +(7.00557 - 2.54982i) q^{68} +(0.224092 + 1.27089i) q^{70} +(-2.59176 + 4.48907i) q^{71} +(2.18764 + 3.78911i) q^{73} +(-1.20240 + 1.00894i) q^{74} +(-0.369276 + 2.09427i) q^{76} +(5.82458 + 4.88740i) q^{77} +(12.1133 + 4.40888i) q^{79} +3.46510 q^{80} +0.227746 q^{82} +(7.43037 + 2.70443i) q^{83} +(2.99086 + 2.50963i) q^{85} +(0.376657 - 2.13613i) q^{86} +(-1.59718 + 1.34019i) q^{88} +(-1.62783 - 2.81949i) q^{89} +(8.67483 - 15.0252i) q^{91} +(2.86005 + 16.2201i) q^{92} +(3.32160 - 1.20896i) q^{94} +(-1.04653 + 0.380904i) q^{95} +(-0.345856 - 1.96145i) q^{97} +(1.71470 - 2.96995i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 9 q^{8}+O(q^{10}) \) 30 * q + 9 * q^8	\( 30 q + 9 q^{8} + 3 q^{10} + 6 q^{11} + 3 q^{13} + 9 q^{14} + 12 q^{16} + 12 q^{17} + 24 q^{19} - 51 q^{22} - 18 q^{23} + 18 q^{26} - 60 q^{28} - 18 q^{29} + 12 q^{31} - 36 q^{32} - 69 q^{34} + 12 q^{35} + 24 q^{37} + 24 q^{38} + 9 q^{40} + 75 q^{41} + 6 q^{43} - 12 q^{44} + 30 q^{46} - 45 q^{47} - 36 q^{49} + 30 q^{52} - 36 q^{53} - 30 q^{56} + 27 q^{58} + 27 q^{59} - 12 q^{61} - 36 q^{62} + 27 q^{64} - 6 q^{65} - 30 q^{67} - 69 q^{68} + 27 q^{70} - 12 q^{71} + 21 q^{73} - 30 q^{76} + 36 q^{77} + 54 q^{79} - 6 q^{80} - 48 q^{82} + 87 q^{83} + 27 q^{85} - 18 q^{86} - 18 q^{88} - 9 q^{89} + 51 q^{91} - 24 q^{92} + 15 q^{94} - 21 q^{95} - 75 q^{97} + 15 q^{98}+O(q^{100}) \) 30 * q + 9 * q^8 + 3 * q^10 + 6 * q^11 + 3 * q^13 + 9 * q^14 + 12 * q^16 + 12 * q^17 + 24 * q^19 - 51 * q^22 - 18 * q^23 + 18 * q^26 - 60 * q^28 - 18 * q^29 + 12 * q^31 - 36 * q^32 - 69 * q^34 + 12 * q^35 + 24 * q^37 + 24 * q^38 + 9 * q^40 + 75 * q^41 + 6 * q^43 - 12 * q^44 + 30 * q^46 - 45 * q^47 - 36 * q^49 + 30 * q^52 - 36 * q^53 - 30 * q^56 + 27 * q^58 + 27 * q^59 - 12 * q^61 - 36 * q^62 + 27 * q^64 - 6 * q^65 - 30 * q^67 - 69 * q^68 + 27 * q^70 - 12 * q^71 + 21 * q^73 - 30 * q^76 + 36 * q^77 + 54 * q^79 - 6 * q^80 - 48 * q^82 + 87 * q^83 + 27 * q^85 - 18 * q^86 - 18 * q^88 - 9 * q^89 + 51 * q^91 - 24 * q^92 + 15 * q^94 - 21 * q^95 - 75 * q^97 + 15 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more