LMFDB - Embedded newform 369.2.u.a.289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [369,2,Mod(46,369)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(369, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 11]))

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

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

chi := DirichletCharacter("369.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 369 = 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	369.u (of order $20$, degree $8$, 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:	$2.94647983459$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 41)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			289.2
Character	$\chi$	$=$	369.289
Dual form			369.2.u.a.226.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40718 - 0.457221i) q^{2} +(0.153075 - 0.111216i) q^{4} +(0.455161 + 0.626475i) q^{5} +(2.12336 + 4.16732i) q^{7} +(-1.57482 + 2.16755i) q^{8} +O(q^{10})$	\(q+(1.40718 - 0.457221i) q^{2} +(0.153075 - 0.111216i) q^{4} +(0.455161 + 0.626475i) q^{5} +(2.12336 + 4.16732i) q^{7} +(-1.57482 + 2.16755i) q^{8} +(0.926931 + 0.673455i) q^{10} +(0.538340 - 0.0852647i) q^{11} +(-0.808560 - 0.411982i) q^{13} +(4.89333 + 4.89333i) q^{14} +(-1.34194 + 4.13008i) q^{16} +(-0.937351 - 5.91820i) q^{17} +(3.90401 - 1.98919i) q^{19} +(0.139348 + 0.0452768i) q^{20} +(0.718557 - 0.366123i) q^{22} +(0.323498 + 0.995624i) q^{23} +(1.35979 - 4.18499i) q^{25} +(-1.32616 - 0.210043i) q^{26} +(0.788504 + 0.401763i) q^{28} +(-0.193017 + 1.21866i) q^{29} +(1.22986 + 0.893547i) q^{31} +1.06686i q^{32} +(-4.02495 - 7.89940i) q^{34} +(-1.64425 + 3.22703i) q^{35} +(5.87120 - 4.26568i) q^{37} +(4.58415 - 4.58415i) q^{38} -2.07471 q^{40} +(-6.21116 + 1.55612i) q^{41} +(-5.91654 + 1.92240i) q^{43} +(0.0729237 - 0.0729237i) q^{44} +(0.910440 + 1.25311i) q^{46} +(1.80254 - 3.53768i) q^{47} +(-8.74342 + 12.0343i) q^{49} -6.51076i q^{50} +(-0.169589 + 0.0268603i) q^{52} +(-0.837443 + 5.28741i) q^{53} +(0.298447 + 0.298447i) q^{55} +(-12.3768 - 1.96029i) q^{56} +(0.285587 + 1.80313i) q^{58} +(-2.74251 - 8.44059i) q^{59} +(1.31994 + 0.428873i) q^{61} +(2.13919 + 0.695064i) q^{62} +(-2.19610 - 6.75890i) q^{64} +(-0.109928 - 0.694060i) q^{65} +(-5.56618 - 0.881596i) q^{67} +(-0.801681 - 0.801681i) q^{68} +(-0.838297 + 5.29280i) q^{70} +(1.07629 - 0.170468i) q^{71} -5.61291i q^{73} +(6.31149 - 8.68702i) q^{74} +(0.376378 - 0.738683i) q^{76} +(1.49841 + 2.06239i) q^{77} +(8.62379 - 8.62379i) q^{79} +(-3.19819 + 1.03915i) q^{80} +(-8.02874 + 5.02962i) q^{82} +13.1576 q^{83} +(3.28096 - 3.28096i) q^{85} +(-7.44668 + 5.41033i) q^{86} +(-0.662972 + 1.30116i) q^{88} +(0.885629 + 1.73814i) q^{89} -4.24431i q^{91} +(0.160248 + 0.116427i) q^{92} +(0.918996 - 5.80231i) q^{94} +(3.02313 + 1.54036i) q^{95} +(-1.91879 - 0.303907i) q^{97} +(-6.80125 + 20.9321i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8}+O(q^{10}) $ 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8	$ 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8} + 6 q^{10} + 16 q^{11} - 14 q^{14} - 20 q^{16} - 8 q^{17} + 16 q^{19} - 20 q^{20} + 6 q^{22} - 12 q^{23} - 8 q^{25} + 28 q^{26} + 18 q^{28} - 40 q^{29} - 12 q^{31} - 16 q^{34} + 36 q^{35} - 46 q^{38} - 44 q^{40} + 4 q^{41} + 48 q^{44} + 70 q^{46} + 12 q^{47} - 30 q^{49} + 20 q^{52} + 26 q^{53} + 20 q^{55} - 106 q^{56} - 20 q^{58} - 6 q^{59} + 30 q^{61} + 10 q^{62} + 70 q^{64} - 68 q^{65} - 22 q^{67} + 20 q^{68} - 20 q^{70} - 4 q^{71} - 10 q^{74} - 128 q^{76} + 20 q^{77} - 2 q^{79} + 70 q^{80} - 90 q^{82} - 80 q^{83} - 56 q^{85} + 46 q^{86} + 10 q^{88} + 72 q^{89} - 18 q^{94} + 40 q^{95} - 22 q^{97} - 6 q^{98}+O(q^{100}) $ 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8 + 6 * q^10 + 16 * q^11 - 14 * q^14 - 20 * q^16 - 8 * q^17 + 16 * q^19 - 20 * q^20 + 6 * q^22 - 12 * q^23 - 8 * q^25 + 28 * q^26 + 18 * q^28 - 40 * q^29 - 12 * q^31 - 16 * q^34 + 36 * q^35 - 46 * q^38 - 44 * q^40 + 4 * q^41 + 48 * q^44 + 70 * q^46 + 12 * q^47 - 30 * q^49 + 20 * q^52 + 26 * q^53 + 20 * q^55 - 106 * q^56 - 20 * q^58 - 6 * q^59 + 30 * q^61 + 10 * q^62 + 70 * q^64 - 68 * q^65 - 22 * q^67 + 20 * q^68 - 20 * q^70 - 4 * q^71 - 10 * q^74 - 128 * q^76 + 20 * q^77 - 2 * q^79 + 70 * q^80 - 90 * q^82 - 80 * q^83 - 56 * q^85 + 46 * q^86 + 10 * q^88 + 72 * q^89 - 18 * q^94 + 40 * q^95 - 22 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/369\mathbb{Z}\right)^\times$.

$n$	$83$	$334$
$\chi(n)$	$1$	$e\left(\frac{13}{20}\right)$

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 $

$2$	1.40718	−	0.457221i	0.995028	−	0.323304i	0.234151	−	0.972200i	$-0.424769\pi$
$2$	1.40718	−	0.457221i	0.995028	−	0.323304i	0.760877	+	0.648896i	$0.224769\pi$
$3$		0			0
$3$		0			0
$4$	0.153075	−	0.111216i	0.0765376	−	0.0556078i
$5$	0.455161	+	0.626475i	0.203554	+	0.280168i	0.898574	−	0.438823i	$-0.144604\pi$
$5$	0.455161	+	0.626475i	0.203554	+	0.280168i	−0.695020	+	0.718991i	$0.744604\pi$
$6$		0			0
$7$	2.12336	+	4.16732i	0.802553	+	1.57510i	0.818000	+	0.575218i	$0.195083\pi$
$7$	2.12336	+	4.16732i	0.802553	+	1.57510i	−0.0154469	+	0.999881i	$0.504917\pi$
$8$	−1.57482	+	2.16755i	−0.556782	+	0.766345i
$9$		0			0
$10$	0.926931	+	0.673455i	0.293121	+	0.212965i
$11$	0.538340	−	0.0852647i	0.162316	−	0.0257083i	−0.0747477	−	0.997202i	$-0.523815\pi$
$11$	0.538340	−	0.0852647i	0.162316	−	0.0257083i	0.237063	+	0.971494i	$0.423815\pi$
$12$		0			0
$13$	−0.808560	−	0.411982i	−0.224254	−	0.114263i	0.338254	−	0.941055i	$-0.390164\pi$
$13$	−0.808560	−	0.411982i	−0.224254	−	0.114263i	−0.562508	+	0.826792i	$0.690164\pi$
$14$	4.89333	+	4.89333i	1.30780	+	1.30780i
$15$		0			0
$16$	−1.34194	+	4.13008i	−0.335486	+	1.03252i
$17$	−0.937351	−	5.91820i	−0.227341	−	1.43537i	−0.792238	−	0.610212i	$-0.791084\pi$
$17$	−0.937351	−	5.91820i	−0.227341	−	1.43537i	0.564897	−	0.825161i	$-0.308916\pi$
$18$		0			0
$19$	3.90401	−	1.98919i	0.895641	−	0.456352i	0.0553374	−	0.998468i	$-0.482377\pi$
$19$	3.90401	−	1.98919i	0.895641	−	0.456352i	0.840304	+	0.542116i	$0.182377\pi$
$20$	0.139348	+	0.0452768i	0.0311591	+	0.0101242i
$21$		0			0
$22$	0.718557	−	0.366123i	0.153197	−	0.0780577i
$23$	0.323498	+	0.995624i	0.0674539	+	0.207602i	0.979102	−	0.203370i	$-0.0651894\pi$
$23$	0.323498	+	0.995624i	0.0674539	+	0.207602i	−0.911648	+	0.410972i	$0.865189\pi$
$24$		0			0
$25$	1.35979	−	4.18499i	0.271957	−	0.836998i
$26$	−1.32616	−	0.210043i	−0.260081	−	0.0411927i
$27$		0			0
$28$	0.788504	+	0.401763i	0.149013	+	0.0759260i
$29$	−0.193017	+	1.21866i	−0.0358423	+	0.226299i	−0.999107	−	0.0422549i	$-0.986546\pi$
$29$	−0.193017	+	1.21866i	−0.0358423	+	0.226299i	0.963265	+	0.268554i	$0.0865458\pi$
$30$		0			0
$31$	1.22986	+	0.893547i	0.220890	+	0.160486i	0.692727	−	0.721200i	$-0.256409\pi$
$31$	1.22986	+	0.893547i	0.220890	+	0.160486i	−0.471837	+	0.881686i	$0.656409\pi$
$32$			1.06686i			0.188595i
$33$		0			0
$34$	−4.02495	−	7.89940i	−0.690273	−	1.35474i
$35$	−1.64425	+	3.22703i	−0.277929	+	0.545467i
$36$		0			0
$37$	5.87120	−	4.26568i	0.965220	−	0.701273i	0.0108626	−	0.999941i	$-0.496542\pi$
$37$	5.87120	−	4.26568i	0.965220	−	0.701273i	0.954357	+	0.298668i	$0.0965423\pi$
$38$	4.58415	−	4.58415i	0.743647	−	0.743647i
$39$		0			0
$40$	−2.07471			−0.328041
$41$	−6.21116	+	1.55612i	−0.970020	+	0.243025i
$41$	−6.21116	+	1.55612i	−0.970020	+	0.243025i
$42$		0			0
$43$	−5.91654	+	1.92240i	−0.902263	+	0.293163i	−0.723171	−	0.690669i	$-0.757316\pi$
$43$	−5.91654	+	1.92240i	−0.902263	+	0.293163i	−0.179092	+	0.983832i	$0.557316\pi$
$44$	0.0729237	−	0.0729237i	0.0109937	−	0.0109937i
$45$		0			0
$46$	0.910440	+	1.25311i	0.134237	+	0.184761i
$47$	1.80254	−	3.53768i	0.262927	−	0.516023i	−0.721369	−	0.692551i	$-0.756487\pi$
$47$	1.80254	−	3.53768i	0.262927	−	0.516023i	0.984296	+	0.176528i	$0.0564867\pi$
$48$		0			0
$49$	−8.74342	+	12.0343i	−1.24906	+	1.71918i
$50$		−	6.51076i		−	0.920761i
$51$		0			0
$52$	−0.169589	+	0.0268603i	−0.0235178	+	0.00372485i
$53$	−0.837443	+	5.28741i	−0.115032	+	0.726281i	0.860992	+	0.508618i	$0.169843\pi$
$53$	−0.837443	+	5.28741i	−0.115032	+	0.726281i	−0.976024	+	0.217663i	$0.930157\pi$
$54$		0			0
$55$	0.298447	+	0.298447i	0.0402426	+	0.0402426i
$56$	−12.3768	−	1.96029i	−1.65392	−	0.261955i
$57$		0			0
$58$	0.285587	+	1.80313i	0.0374994	+	0.236762i
$59$	−2.74251	−	8.44059i	−0.357045	−	1.09887i	−0.954814	−	0.297203i	$-0.903946\pi$
$59$	−2.74251	−	8.44059i	−0.357045	−	1.09887i	0.597769	−	0.801668i	$-0.296054\pi$
$60$		0			0
$61$	1.31994	+	0.428873i	0.169001	+	0.0549116i	0.392295	−	0.919839i	$-0.371681\pi$
$61$	1.31994	+	0.428873i	0.169001	+	0.0549116i	−0.223295	+	0.974751i	$0.571681\pi$
$62$	2.13919	+	0.695064i	0.271677	+	0.0882732i
$63$		0			0
$64$	−2.19610	−	6.75890i	−0.274512	−	0.844862i
$65$	−0.109928	−	0.694060i	−0.0136349	−	0.0860875i
$66$		0			0
$67$	−5.56618	−	0.881596i	−0.680017	−	0.107704i	−0.193135	−	0.981172i	$-0.561866\pi$
$67$	−5.56618	−	0.881596i	−0.680017	−	0.107704i	−0.486881	+	0.873468i	$0.661866\pi$
$68$	−0.801681	−	0.801681i	−0.0972181	−	0.0972181i
$69$		0			0
$70$	−0.838297	+	5.29280i	−0.100196	+	0.632611i
$71$	1.07629	−	0.170468i	0.127732	−	0.0202308i	−0.0922409	−	0.995737i	$-0.529403\pi$
$71$	1.07629	−	0.170468i	0.127732	−	0.0202308i	0.219973	+	0.975506i	$0.429403\pi$
$72$		0			0
$73$		−	5.61291i		−	0.656941i	−0.944514	−	0.328471i	$-0.893467\pi$
$73$		−	5.61291i		−	0.656941i	0.944514	−	0.328471i	$-0.106533\pi$
$74$	6.31149	−	8.68702i	0.733696	−	1.00985i
$75$		0			0
$76$	0.376378	−	0.738683i	0.0431735	−	0.0847327i
$77$	1.49841	+	2.06239i	0.170760	+	0.235031i
$78$		0			0
$79$	8.62379	−	8.62379i	0.970252	−	0.970252i	−0.0293183	−	0.999570i	$-0.509334\pi$
$79$	8.62379	−	8.62379i	0.970252	−	0.970252i	0.999570	+	0.0293183i	$0.00933364\pi$
$80$	−3.19819	+	1.03915i	−0.357568	+	0.116181i
$81$		0			0
$82$	−8.02874	+	5.02962i	−0.886626	+	0.555428i
$83$	13.1576			1.44423			0.722116	−	0.691772i	$-0.243170\pi$
$83$	13.1576			1.44423			0.722116	+	0.691772i	$0.243170\pi$
$84$		0			0
$85$	3.28096	−	3.28096i	0.355870	−	0.355870i
$86$	−7.44668	+	5.41033i	−0.802996	+	0.583411i
$87$		0			0
$88$	−0.662972	+	1.30116i	−0.0706730	+	0.138704i
$89$	0.885629	+	1.73814i	0.0938764	+	0.184243i	0.933170	−	0.359436i	$-0.117031\pi$
$89$	0.885629	+	1.73814i	0.0938764	+	0.184243i	−0.839293	+	0.543679i	$0.817031\pi$
$90$		0			0
$91$		−	4.24431i		−	0.444925i
$92$	0.160248	+	0.116427i	0.0167070	+	0.0121384i
$93$		0			0
$94$	0.918996	−	5.80231i	0.0947872	−	0.598463i
$95$	3.02313	+	1.54036i	0.310167	+	0.158038i
$96$		0			0
$97$	−1.91879	−	0.303907i	−0.194824	−	0.0308571i	0.0582598	−	0.998301i	$-0.481445\pi$
$97$	−1.91879	−	0.303907i	−0.194824	−	0.0308571i	−0.253084	+	0.967444i	$0.581445\pi$
$98$	−6.80125	+	20.9321i	−0.687030	+	2.11446i
$99$		0			0
$100$	−0.257287	−	0.791847i	−0.0257287	−	0.0791847i
$101$	−7.49597	+	3.81939i	−0.745877	+	0.380043i	−0.785248	−	0.619181i	$-0.787465\pi$
$101$	−7.49597	+	3.81939i	−0.745877	+	0.380043i	0.0393710	+	0.999225i	$0.487465\pi$
$102$		0			0
$103$	4.08634	+	1.32773i	0.402639	+	0.130825i	0.503334	−	0.864092i	$-0.332107\pi$
$103$	4.08634	+	1.32773i	0.402639	+	0.130825i	−0.100695	+	0.994917i	$0.532107\pi$
$104$	2.16632	−	1.10380i	0.212426	−	0.108236i
$105$		0			0
$106$	1.23908	+	7.82324i	0.120350	+	0.759860i
$107$	−3.82695	+	11.7782i	−0.369966	+	1.13864i	0.576847	+	0.816852i	$0.304283\pi$
$107$	−3.82695	+	11.7782i	−0.369966	+	1.13864i	−0.946813	+	0.321785i	$0.895717\pi$
$108$		0			0
$109$	1.22345	+	1.22345i	0.117185	+	0.117185i	0.763268	−	0.646082i	$-0.223594\pi$
$109$	1.22345	+	1.22345i	0.117185	+	0.117185i	−0.646082	+	0.763268i	$0.723594\pi$
$110$	0.556426	+	0.283513i	0.0530531	+	0.0270319i
$111$		0			0
$112$	−20.0608	+	3.17732i	−1.89557	+	0.300228i
$113$	−0.944802	−	0.686439i	−0.0888795	−	0.0645747i	0.542458	−	0.840083i	$-0.317494\pi$
$113$	−0.944802	−	0.686439i	−0.0888795	−	0.0645747i	−0.631338	+	0.775508i	$0.717494\pi$
$114$		0			0
$115$	−0.476490	+	0.655832i	−0.0444329	+	0.0611566i
$116$	0.105988	+	0.208013i	0.00984073	+	0.0193135i
$117$		0			0
$118$	−7.71843	−	10.6235i	−0.710539	−	0.977973i
$119$	22.6727	−	16.4727i	2.07840	−	1.51005i
$120$		0			0
$121$	−10.1791	+	3.30738i	−0.925371	+	0.300671i
$122$	2.05348			0.185913
$123$		0			0
$124$	0.287638			0.0258306
$125$	6.92304	−	2.24943i	0.619215	−	0.201195i
$126$		0			0
$127$	8.08534	−	5.87434i	0.717458	−	0.521264i	−0.168113	−	0.985768i	$-0.553767\pi$
$127$	8.08534	−	5.87434i	0.717458	−	0.521264i	0.885571	+	0.464504i	$0.153767\pi$
$128$	−7.43478	−	10.2331i	−0.657148	−	0.904487i
$129$		0			0
$130$	−0.472028	−	0.926407i	−0.0413996	−	0.0812513i
$131$	0.478992	−	0.659276i	0.0418497	−	0.0576012i	−0.787579	−	0.616213i	$-0.788666\pi$
$131$	0.478992	−	0.659276i	0.0418497	−	0.0576012i	0.829429	+	0.558612i	$0.188666\pi$
$132$		0			0
$133$	16.5792	+	12.0455i	1.43760	+	1.04448i
$134$	−8.23570	+	1.30441i	−0.711456	+	0.112684i
$135$		0			0
$136$	14.3042	+	7.28833i	1.22657	+	0.624969i
$137$	3.04334	+	3.04334i	0.260010	+	0.260010i	0.825058	−	0.565048i	$-0.191142\pi$
$137$	3.04334	+	3.04334i	0.260010	+	0.260010i	−0.565048	+	0.825058i	$0.691142\pi$
$138$		0			0
$139$	1.55254	−	4.77824i	0.131685	−	0.405285i	−0.863375	−	0.504563i	$-0.831653\pi$
$139$	1.55254	−	4.77824i	0.131685	−	0.405285i	0.995060	+	0.0992785i	$0.0316535\pi$
$140$	0.107202	+	0.676844i	0.00906019	+	0.0572038i
$141$		0			0
$142$	1.43660	−	0.731983i	0.120557	−	0.0614266i
$143$	−0.470407	−	0.152845i	−0.0393374	−	0.0127815i
$144$		0			0
$145$	−0.851313	+	0.433765i	−0.0706977	+	0.0360223i
$146$	−2.56634	−	7.89838i	−0.212392	−	0.653675i
$147$		0			0
$148$	0.424325	−	1.30594i	0.0348793	−	0.107347i
$149$	−7.82798	−	1.23983i	−0.641293	−	0.101571i	−0.172685	−	0.984977i	$-0.555244\pi$
$149$	−7.82798	−	1.23983i	−0.641293	−	0.101571i	−0.468608	+	0.883406i	$0.655244\pi$
$150$		0			0
$151$	−18.4200	−	9.38545i	−1.49900	−	0.763777i	−0.504002	−	0.863702i	$-0.668140\pi$
$151$	−18.4200	−	9.38545i	−1.49900	−	0.763777i	−0.994995	+	0.0999253i	$0.968140\pi$
$152$	−1.83643	+	11.5948i	−0.148954	+	0.940459i
$153$		0			0
$154$	3.05151	+	2.21705i	0.245897	+	0.178655i
$155$			1.17718i			0.0945537i
$156$		0			0
$157$	5.47977	+	10.7546i	0.437333	+	0.858314i	0.999510	+	0.0312976i	$0.00996395\pi$
$157$	5.47977	+	10.7546i	0.437333	+	0.858314i	−0.562177	+	0.827017i	$0.690036\pi$
$158$	8.19226	−	16.0782i	0.651741	−	1.27911i
$159$		0			0
$160$	−0.668358	+	0.485591i	−0.0528384	+	0.0383893i
$161$	−3.46218	+	3.46218i	−0.272858	+	0.272858i
$162$		0			0
$163$	−2.00089			−0.156722			−0.0783609	−	0.996925i	$-0.524969\pi$
$163$	−2.00089			−0.156722			−0.0783609	+	0.996925i	$0.524969\pi$
$164$	−0.777709	+	0.928981i	−0.0607289	+	0.0725413i
$165$		0			0
$166$	18.5151	−	6.01592i	1.43705	−	0.466926i
$167$	−13.5221	+	13.5221i	−1.04638	+	1.04638i	−0.0475043	+	0.998871i	$0.515127\pi$
$167$	−13.5221	+	13.5221i	−1.04638	+	1.04638i	−0.998871	+	0.0475043i	$0.984873\pi$
$168$		0			0
$169$	−7.15717	−	9.85100i	−0.550551	−	0.757769i
$170$	3.11678	−	6.11702i	0.239046	−	0.469154i
$171$		0			0
$172$	−0.691874	+	0.952283i	−0.0527549	+	0.0726109i
$173$		−	6.00388i		−	0.456467i	−0.973606	−	0.228233i	$-0.926705\pi$
$173$		−	6.00388i		−	0.456467i	0.973606	−	0.228233i	$-0.0732949\pi$
$174$		0			0
$175$	20.3275	−	3.21956i	1.53661	−	0.243376i
$176$	−0.370272	+	2.33781i	−0.0279103	+	0.176219i
$177$		0			0
$178$	2.04096	+	2.04096i	0.152976	+	0.152976i
$179$	9.04156	+	1.43204i	0.675798	+	0.107036i	0.484894	−	0.874573i	$-0.338858\pi$
$179$	9.04156	+	1.43204i	0.675798	+	0.107036i	0.190904	+	0.981609i	$0.438858\pi$
$180$		0			0
$181$	2.98065	+	18.8191i	0.221550	+	1.39881i	0.808169	+	0.588950i	$0.200459\pi$
$181$	2.98065	+	18.8191i	0.221550	+	1.39881i	−0.586619	+	0.809863i	$0.699541\pi$
$182$	−1.94059	−	5.97252i	−0.143846	−	0.442712i
$183$		0			0
$184$	−2.66751	−	0.866728i	−0.196652	−	0.0638960i
$185$	5.34468	+	1.73659i	0.392949	+	0.127677i
$186$		0			0
$187$	−1.00923	−	3.10608i	−0.0738019	−	0.227139i
$188$	−0.117521	−	0.742000i	−0.00857112	−	0.0541159i
$189$		0			0
$190$	4.95838	+	0.785330i	0.359719	+	0.0569738i
$191$	−7.96614	−	7.96614i	−0.576410	−	0.576410i	0.357503	−	0.933912i	$-0.383628\pi$
$191$	−7.96614	−	7.96614i	−0.576410	−	0.576410i	−0.933912	+	0.357503i	$0.883628\pi$
$192$		0			0
$193$	−1.82911	+	11.5486i	−0.131663	+	0.831285i	0.830143	+	0.557551i	$0.188259\pi$
$193$	−1.82911	+	11.5486i	−0.131663	+	0.831285i	−0.961805	+	0.273734i	$0.911741\pi$
$194$	−2.83904	+	0.449660i	−0.203831	+	0.0322837i
$195$		0			0
$196$			2.81456i			0.201040i
$197$	5.94003	−	8.17575i	0.423210	−	0.582498i	−0.543168	−	0.839624i	$-0.682775\pi$
$197$	5.94003	−	8.17575i	0.423210	−	0.582498i	0.966378	+	0.257126i	$0.0827754\pi$
$198$		0			0
$199$	3.82058	−	7.49832i	0.270834	−	0.531542i	−0.715029	−	0.699095i	$-0.753587\pi$
$199$	3.82058	−	7.49832i	0.270834	−	0.531542i	0.985863	+	0.167553i	$0.0535866\pi$
$200$	6.92976	+	9.53800i	0.490008	+	0.674438i
$201$		0			0
$202$	−8.80189	+	8.80189i	−0.619299	+	0.619299i
$203$	−5.48839	+	1.78328i	−0.385209	+	0.125162i
$204$		0			0
$205$	−3.80195	−	3.18285i	−0.265539	−	0.222300i
$206$	6.35728			0.442933
$207$		0			0
$208$	2.78656	−	2.78656i	0.193213	−	0.193213i
$209$	1.93208	−	1.40374i	0.133645	−	0.0970984i
$210$		0			0
$211$	−5.89458	+	11.5688i	−0.405800	+	0.796427i	−0.999969	−	0.00791335i	$-0.997481\pi$
$211$	−5.89458	+	11.5688i	−0.405800	+	0.796427i	0.594169	+	0.804340i	$0.297481\pi$
$212$	0.459850	+	0.902507i	0.0315827	+	0.0619845i
$213$		0			0
$214$			18.3238i			1.25259i
$215$	−3.89731	−	2.83156i	−0.265794	−	0.193111i
$216$		0			0
$217$	−1.11226	+	7.02254i	−0.0755052	+	0.476721i
$218$	2.28100	+	1.16223i	0.154489	+	0.0787160i
$219$		0			0
$220$	0.0788768	+	0.0124929i	0.00531788	+	0.000842269i
$221$	−1.68029	+	5.17139i	−0.113028	+	0.347865i
$222$		0			0
$223$	−5.40722	−	16.6417i	−0.362094	−	1.11441i	−0.951781	−	0.306779i	$-0.900749\pi$
$223$	−5.40722	−	16.6417i	−0.362094	−	1.11441i	0.589686	−	0.807632i	$-0.299251\pi$
$224$	−4.44593	+	2.26531i	−0.297056	+	0.151358i
$225$		0			0
$226$	−1.64336	−	0.533961i	−0.109315	−	0.0355185i
$227$	24.2713	−	12.3668i	1.61094	−	0.820816i	0.611377	−	0.791339i	$-0.290616\pi$
$227$	24.2713	−	12.3668i	1.61094	−	0.820816i	0.999565	−	0.0294771i	$-0.00938422\pi$
$228$		0			0
$229$	3.54084	+	22.3560i	0.233985	+	1.47733i	0.772665	+	0.634815i	$0.218923\pi$
$229$	3.54084	+	22.3560i	0.233985	+	1.47733i	−0.538679	+	0.842511i	$0.681077\pi$
$230$	−0.370647	+	1.14074i	−0.0244398	+	0.0752179i
$231$		0			0
$232$	−2.33754	−	2.33754i	−0.153467	−	0.153467i
$233$	−21.5716	−	10.9913i	−1.41320	−	0.720062i	−0.430041	−	0.902809i	$-0.641501\pi$
$233$	−21.5716	−	10.9913i	−1.41320	−	0.720062i	−0.983160	+	0.182747i	$0.941501\pi$
$234$		0			0
$235$	3.03671	−	0.480967i	0.198093	−	0.0313748i
$236$	−1.35854	−	0.987034i	−0.0884332	−	0.0642504i
$237$		0			0
$238$	24.3729	−	33.5465i	1.57986	−	2.17450i
$239$	10.1154	+	19.8526i	0.654312	+	1.28416i	0.944915	+	0.327316i	$0.106144\pi$
$239$	10.1154	+	19.8526i	0.654312	+	1.28416i	−0.290603	+	0.956844i	$0.593856\pi$
$240$		0			0
$241$	−7.10275	−	9.77610i	−0.457528	−	0.629734i	0.516466	−	0.856308i	$-0.327247\pi$
$241$	−7.10275	−	9.77610i	−0.457528	−	0.629734i	−0.973994	+	0.226574i	$0.927247\pi$
$242$	−12.8116	+	9.30818i	−0.823562	+	0.598353i
$243$		0			0
$244$	0.249747	−	0.0811477i	0.0159884	−	0.00519495i
$245$	−11.5188			−0.735911
$246$		0			0
$247$	−3.97613			−0.252995
$248$	−3.87361	+	1.25861i	−0.245975	+	0.0799221i
$249$		0			0
$250$	8.71348	−	6.33072i	0.551089	−	0.400390i
$251$	−4.67048	−	6.42836i	−0.294798	−	0.405755i	0.635767	−	0.771881i	$-0.280684\pi$
$251$	−4.67048	−	6.42836i	−0.294798	−	0.405755i	−0.930565	+	0.366126i	$0.880684\pi$
$252$		0			0
$253$	0.259043	+	0.508401i	0.0162859	+	0.0319629i
$254$	8.69167	−	11.9631i	0.545364	−	0.750629i
$255$		0			0
$256$	−3.64196	−	2.64604i	−0.227622	−	0.165377i
$257$	23.2164	−	3.67711i	1.44820	−	0.229372i	0.617709	−	0.786407i	$-0.288061\pi$
$257$	23.2164	−	3.67711i	1.44820	−	0.229372i	0.830489	+	0.557035i	$0.188061\pi$
$258$		0			0
$259$	30.2431	+	15.4096i	1.87921	+	0.957508i
$260$	−0.0940176	−	0.0940176i	−0.00583072	−	0.00583072i
$261$		0			0
$262$	0.372594	−	1.14673i	0.0230189	−	0.0708450i
$263$	3.34437	+	21.1155i	0.206222	+	1.30204i	0.845878	+	0.533376i	$0.179077\pi$
$263$	3.34437	+	21.1155i	0.206222	+	1.30204i	−0.639656	+	0.768661i	$0.720923\pi$
$264$		0			0
$265$	−3.69360	+	1.88198i	−0.226896	+	0.115609i
$266$	28.8374	+	9.36984i	1.76813	+	0.574502i
$267$		0			0
$268$	−0.950090	+	0.484095i	−0.0580360	+	0.0295708i
$269$	8.35420	+	25.7116i	0.509364	+	1.56766i	0.793308	+	0.608821i	$0.208357\pi$
$269$	8.35420	+	25.7116i	0.509364	+	1.56766i	−0.283943	+	0.958841i	$0.591643\pi$
$270$		0			0
$271$	−3.68892	+	11.3533i	−0.224086	+	0.689666i	0.774297	+	0.632822i	$0.218104\pi$
$271$	−3.68892	+	11.3533i	−0.224086	+	0.689666i	−0.998383	+	0.0568438i	$0.981896\pi$
$272$	25.7005	+	4.07056i	1.55832	+	0.246814i
$273$		0			0
$274$	5.67401	+	2.89105i	0.342780	+	0.174655i
$275$	0.375195	−	2.36889i	0.0226251	−	0.142849i
$276$		0			0
$277$	−11.8657	−	8.62092i	−0.712940	−	0.517981i	0.171181	−	0.985240i	$-0.445242\pi$
$277$	−11.8657	−	8.62092i	−0.712940	−	0.517981i	−0.884121	+	0.467259i	$0.845242\pi$
$278$		−	7.43371i		−	0.445844i
$279$		0			0
$280$	−4.40535	−	8.64598i	−0.263270	−	0.516696i
$281$	−4.85610	+	9.53063i	−0.289691	+	0.568550i	−0.989286	−	0.145989i	$-0.953364\pi$
$281$	−4.85610	+	9.53063i	−0.289691	+	0.568550i	0.699596	+	0.714539i	$0.253364\pi$
$282$		0			0
$283$	15.4306	−	11.2110i	0.917254	−	0.666424i	−0.0255849	−	0.999673i	$-0.508145\pi$
$283$	15.4306	−	11.2110i	0.917254	−	0.666424i	0.942839	+	0.333249i	$0.108145\pi$
$284$	0.145795	−	0.145795i	0.00865133	−	0.00865133i
$285$		0			0
$286$	−0.731832			−0.0432742
$287$	−19.6734	−	22.5797i	−1.16128	−	1.33284i
$288$		0			0
$289$	−17.9785	+	5.84156i	−1.05756	+	0.343621i
$290$	−0.999625	+	0.999625i	−0.0587000	+	0.0587000i
$291$		0			0
$292$	−0.624243	−	0.859197i	−0.0365311	−	0.0502807i
$293$	−11.7759	+	23.1115i	−0.687957	+	1.35019i	0.237519	+	0.971383i	$0.423666\pi$
$293$	−11.7759	+	23.1115i	−0.687957	+	1.35019i	−0.925475	+	0.378808i	$0.876334\pi$
$294$		0			0
$295$	4.03953	−	5.55994i	0.235191	−	0.323712i
$296$			19.4438i			1.13015i
$297$		0			0
$298$	−11.5823	+	1.83445i	−0.670943	+	0.106267i
$299$	0.148612	−	0.938296i	0.00859443	−	0.0542631i
$300$		0			0
$301$	−20.5742	−	20.5742i	−1.18587	−	1.18587i
$302$	−30.2115	−	4.78503i	−1.73848	−	0.275348i
$303$		0			0
$304$	2.97656	+	18.7933i	0.170717	+	1.07787i
$305$	0.332105	+	1.02211i	0.0190163	+	0.0585260i
$306$		0			0
$307$	−8.23334	−	2.67517i	−0.469901	−	0.152680i	0.0644882	−	0.997918i	$-0.479459\pi$
$307$	−8.23334	−	2.67517i	−0.469901	−	0.152680i	−0.534390	+	0.845238i	$0.679459\pi$
$308$	0.458739	+	0.149053i	0.0261391	+	0.00849311i
$309$		0			0
$310$	0.538233	+	1.65651i	0.0305696	+	0.0940836i
$311$	−1.26384	−	7.97957i	−0.0716658	−	0.452480i	−0.997261	−	0.0739647i	$-0.976435\pi$
$311$	−1.26384	−	7.97957i	−0.0716658	−	0.452480i	0.925595	−	0.378515i	$-0.123565\pi$
$312$		0			0
$313$	−3.40878	−	0.539898i	−0.192676	−	0.0305168i	0.0593507	−	0.998237i	$-0.481097\pi$
$313$	−3.40878	−	0.539898i	−0.192676	−	0.0305168i	−0.252026	+	0.967720i	$0.581097\pi$
$314$	12.6283	+	12.6283i	0.712655	+	0.712655i
$315$		0			0
$316$	0.360988	−	2.27919i	0.0203071	−	0.128214i
$317$	−27.5726	+	4.36707i	−1.54863	+	0.245279i	−0.871431	−	0.490519i	$-0.836807\pi$
$317$	−27.5726	+	4.36707i	−1.54863	+	0.245279i	−0.677201	+	0.735798i	$0.736807\pi$
$318$		0			0
$319$			0.672510i			0.0376534i
$320$	3.23470	−	4.45218i	0.180825	−	0.248885i
$321$		0			0
$322$	−3.28894	+	6.45490i	−0.183285	+	0.359718i
$323$	−15.4319	−	21.2401i	−0.858652	−	1.18183i
$324$		0			0
$325$	−2.82361	+	2.82361i	−0.156625	+	0.156625i
$326$	−2.81562	+	0.914849i	−0.155943	+	0.0506688i
$327$		0			0
$328$	6.40847	−	15.9136i	0.353848	−	0.878682i
$329$	18.5701			1.02380
$330$		0			0
$331$	−15.9651	+	15.9651i	−0.877522	+	0.877522i	−0.993278	−	0.115756i	$-0.963071\pi$
$331$	−15.9651	+	15.9651i	−0.877522	+	0.877522i	0.115756	+	0.993278i	$0.463071\pi$
$332$	2.01410	−	1.46333i	0.110538	−	0.0803106i
$333$		0			0
$334$	−12.8455	+	25.2107i	−0.702875	+	1.37947i
$335$	−1.98121	−	3.88834i	−0.108245	−	0.212442i
$336$		0			0
$337$		−	24.7909i		−	1.35045i	−0.737614	−	0.675223i	$-0.764048\pi$
$337$		−	24.7909i		−	1.35045i	0.737614	−	0.675223i	$-0.235952\pi$
$338$	−14.5755	−	10.5897i	−0.792804	−	0.576006i
$339$		0			0
$340$	0.137339	−	0.867127i	0.00744827	−	0.0470265i
$341$	0.738271	+	0.376168i	0.0399796	+	0.0203706i
$342$		0			0
$343$	−36.3795	−	5.76195i	−1.96431	−	0.311116i
$344$	5.15057	−	15.8518i	0.277700	−	0.854673i
$345$		0			0
$346$	−2.74510	−	8.44855i	−0.147578	−	0.454197i
$347$	3.20315	−	1.63209i	0.171954	−	0.0876149i	−0.365895	−	0.930656i	$-0.619237\pi$
$347$	3.20315	−	1.63209i	0.171954	−	0.0876149i	0.537849	+	0.843041i	$0.319237\pi$
$348$		0			0
$349$	−0.272833	−	0.0886489i	−0.0146044	−	0.00474526i	0.301706	−	0.953401i	$-0.402444\pi$
$349$	−0.272833	−	0.0886489i	−0.0146044	−	0.00474526i	−0.316310	+	0.948656i	$0.602444\pi$
$350$	27.1324	−	13.8247i	1.45029	−	0.738959i
$351$		0			0
$352$	0.0909651	+	0.574331i	0.00484846	+	0.0306119i
$353$	7.26560	−	22.3612i	0.386709	−	1.19017i	−0.548524	−	0.836135i	$-0.684810\pi$
$353$	7.26560	−	22.3612i	0.386709	−	1.19017i	0.935233	−	0.354033i	$-0.115190\pi$
$354$		0			0
$355$	0.596679	+	0.596679i	0.0316685	+	0.0316685i
$356$	0.328876	+	0.167571i	0.0174304	+	0.00888124i
$357$		0			0
$358$	13.3779	−	2.11885i	0.707043	−	0.111985i
$359$	−27.7932	−	20.1929i	−1.46687	−	1.06574i	−0.981506	−	0.191430i	$-0.938687\pi$
$359$	−27.7932	−	20.1929i	−1.46687	−	1.06574i	−0.485363	−	0.874313i	$-0.661313\pi$
$360$		0			0
$361$	0.116485	−	0.160328i	0.00613080	−	0.00843832i
$362$	12.7988	+	25.1191i	0.672691	+	1.32023i
$363$		0			0
$364$	−0.472033	−	0.649698i	−0.0247413	−	0.0340534i
$365$	3.51635	−	2.55477i	0.184054	−	0.133723i
$366$		0			0
$367$	24.8067	−	8.06019i	1.29490	−	0.420738i	0.421096	−	0.907016i	$-0.361646\pi$
$367$	24.8067	−	8.06019i	1.29490	−	0.420738i	0.873804	+	0.486278i	$0.161646\pi$
$368$	−4.54612			−0.236983
$369$		0			0
$370$	8.31494			0.432273
$371$	−23.8125	+	7.73715i	−1.23628	+	0.401693i
$372$		0			0
$373$	8.17007	−	5.93590i	0.423030	−	0.307349i	−0.355826	−	0.934552i	$-0.615800\pi$
$373$	8.17007	−	5.93590i	0.423030	−	0.307349i	0.778856	+	0.627203i	$0.215800\pi$
$374$	−2.84033	−	3.90938i	−0.146870	−	0.202149i
$375$		0			0
$376$	4.82943	+	9.47828i	0.249059	+	0.488805i
$377$	0.658131	−	0.905839i	0.0338955	−	0.0466531i
$378$		0			0
$379$	10.7064	+	7.77867i	0.549952	+	0.399563i	0.827768	−	0.561071i	$-0.189611\pi$
$379$	10.7064	+	7.77867i	0.549952	+	0.399563i	−0.277816	+	0.960634i	$0.589611\pi$
$380$	0.634078	−	0.100428i	0.0325275	−	0.00515185i
$381$		0			0
$382$	−14.8521	−	7.56752i	−0.759899	−	0.387188i
$383$	−4.86397	−	4.86397i	−0.248537	−	0.248537i	0.571833	−	0.820370i	$-0.306233\pi$
$383$	−4.86397	−	4.86397i	−0.248537	−	0.248537i	−0.820370	+	0.571833i	$0.806233\pi$
$384$		0			0
$385$	−0.610016	+	1.87743i	−0.0310893	+	0.0956829i
$386$	2.70636	+	17.0873i	0.137750	+	0.869718i
$387$		0			0
$388$	−0.327519	+	0.166879i	−0.0166272	+	0.00847201i
$389$	−29.0233	−	9.43023i	−1.47154	−	0.478132i	−0.539965	−	0.841687i	$-0.681563\pi$
$389$	−29.0233	−	9.43023i	−1.47154	−	0.478132i	−0.931572	+	0.363556i	$0.881563\pi$
$390$		0			0
$391$	5.58907	−	2.84777i	0.282651	−	0.144018i
$392$	−12.3156	−	37.9036i	−0.622033	−	1.91442i
$393$		0			0
$394$	4.62058	−	14.2207i	0.232781	−	0.716427i
$395$	9.32779	+	1.47738i	0.469332	+	0.0743349i
$396$		0			0
$397$	−21.4147	−	10.9114i	−1.07477	−	0.547625i	−0.175263	−	0.984522i	$-0.556078\pi$
$397$	−21.4147	−	10.9114i	−1.07477	−	0.547625i	−0.899512	+	0.436896i	$0.856078\pi$
$398$	1.94787	−	12.2983i	0.0976377	−	0.616460i
$399$		0			0
$400$	15.4596	+	11.2320i	0.772979	+	0.561602i
$401$			4.76630i			0.238018i	0.992893	+	0.119009i	$0.0379717\pi$
$401$			4.76630i			0.238018i	−0.992893	+	0.119009i	$0.962028\pi$
$402$		0			0
$403$	−0.626291	−	1.22917i	−0.0311978	−	0.0612291i
$404$	−0.722671	+	1.41832i	−0.0359542	+	0.0705642i
$405$		0			0
$406$	−6.90780	+	5.01881i	−0.342828	+	0.249079i
$407$	2.79699	−	2.79699i	0.138642	−	0.138642i
$408$		0			0
$409$	−37.1120			−1.83507			−0.917534	−	0.397657i	$-0.869824\pi$
$409$	−37.1120			−1.83507			−0.917534	+	0.397657i	$0.869824\pi$
$410$	−6.80529	−	2.74052i	−0.336089	−	0.135344i
$411$		0			0
$412$	0.773181	−	0.251222i	0.0380919	−	0.0123768i
$413$	29.3513	−	29.3513i	1.44428	−	1.44428i
$414$		0			0
$415$	5.98881	+	8.24289i	0.293979	+	0.404628i
$416$	0.439525	−	0.862616i	0.0215495	−	0.0422933i
$417$		0			0
$418$	2.07696	−	2.85870i	0.101588	−	0.139823i
$419$			11.2273i			0.548491i	0.961660	+	0.274246i	$0.0884281\pi$
$419$			11.2273i			0.548491i	−0.961660	+	0.274246i	$0.911572\pi$
$420$		0			0
$421$	−16.7385	+	2.65113i	−0.815787	+	0.129208i	−0.550365	−	0.834924i	$-0.685511\pi$
$421$	−16.7385	+	2.65113i	−0.815787	+	0.129208i	−0.265422	+	0.964132i	$0.585511\pi$
$422$	−3.00526	+	18.9745i	−0.146294	+	0.923664i
$423$		0			0
$424$	−10.1419	−	10.1419i	−0.492534	−	0.492534i
$425$	−26.0422	−	4.12468i	−1.26323	−	0.200076i
$426$		0			0
$427$	1.01544	+	6.41125i	0.0491407	+	0.310262i
$428$	0.724103	+	2.22856i	0.0350008	+	0.107722i
$429$		0			0
$430$	−6.77887	−	2.20259i	−0.326906	−	0.106218i
$431$	19.3545	+	6.28864i	0.932271	+	0.302913i	0.735491	−	0.677534i	$-0.236952\pi$
$431$	19.3545	+	6.28864i	0.932271	+	0.302913i	0.196780	+	0.980448i	$0.436952\pi$
$432$		0			0
$433$	6.55082	+	20.1613i	0.314812	+	0.968893i	0.975832	+	0.218524i	$0.0701241\pi$
$433$	6.55082	+	20.1613i	0.314812	+	0.968893i	−0.661019	+	0.750369i	$0.729876\pi$
$434$	1.64570	+	10.3905i	0.0789961	+	0.498762i
$435$		0			0
$436$	0.323346	+	0.0512130i	0.0154855	+	0.00245266i
$437$	3.24343	+	3.24343i	0.155154	+	0.155154i
$438$		0			0
$439$	3.23308	−	20.4129i	0.154306	−	0.974252i	−0.782054	−	0.623211i	$-0.785828\pi$
$439$	3.23308	−	20.4129i	0.154306	−	0.974252i	0.936360	−	0.351041i	$-0.114172\pi$
$440$	−1.11690	+	0.176900i	−0.0532461	+	0.00843335i
$441$		0			0
$442$			8.04534i			0.382678i
$443$	−12.7566	+	17.5580i	−0.606086	+	0.834206i	−0.996248	−	0.0865400i	$-0.972419\pi$
$443$	−12.7566	+	17.5580i	−0.606086	+	0.834206i	0.390162	+	0.920746i	$0.372419\pi$
$444$		0			0
$445$	−0.685800	+	1.34596i	−0.0325100	+	0.0638045i
$446$	−15.2179	−	20.9456i	−0.720588	−	0.991804i
$447$		0			0
$448$	23.5034	−	23.5034i	1.11043	−	1.11043i
$449$	5.28118	−	1.71596i	0.249234	−	0.0809812i	−0.181736	−	0.983347i	$-0.558171\pi$
$449$	5.28118	−	1.71596i	0.249234	−	0.0809812i	0.430970	+	0.902366i	$0.358171\pi$
$450$		0			0
$451$	−3.21103	+	1.36731i	−0.151202	+	0.0643843i
$452$	−0.220968			−0.0103935
$453$		0			0
$454$	28.4997	−	28.4997i	1.33756	−	1.33756i
$455$	2.65895	−	1.93184i	0.124654	−	0.0905662i
$456$		0			0
$457$	−17.5772	+	34.4973i	−0.822229	+	1.61371i	−0.0331277	+	0.999451i	$0.510547\pi$
$457$	−17.5772	+	34.4973i	−0.822229	+	1.61371i	−0.789101	+	0.614264i	$0.789453\pi$
$458$	15.2042	+	29.8400i	0.710447	+	1.39433i
$459$		0			0
$460$			0.153385i			0.00715160i
$461$	4.11822	+	2.99206i	0.191805	+	0.139354i	0.679543	−	0.733636i	$-0.262178\pi$
$461$	4.11822	+	2.99206i	0.191805	+	0.139354i	−0.487738	+	0.872990i	$0.662178\pi$
$462$		0			0
$463$	−0.451109	+	2.84819i	−0.0209648	+	0.132367i	−0.995951	−	0.0898996i	$-0.971345\pi$
$463$	−0.451109	+	2.84819i	−0.0209648	+	0.132367i	0.974986	+	0.222266i	$0.0713454\pi$
$464$	−4.77414	−	2.43255i	−0.221634	−	0.112928i
$465$		0			0
$466$	−35.3806	−	5.60373i	−1.63897	−	0.259588i
$467$	−11.3892	+	35.0524i	−0.527030	+	1.62203i	0.233235	+	0.972420i	$0.425069\pi$
$467$	−11.3892	+	35.0524i	−0.527030	+	1.62203i	−0.760266	+	0.649612i	$0.774931\pi$
$468$		0			0
$469$	−8.14508	−	25.0680i	−0.376105	−	1.15753i
$470$	4.05329	−	2.06525i	0.186964	−	0.0952631i
$471$		0			0
$472$	22.6144	+	7.34785i	1.04091	+	0.338212i
$473$	−3.02119	+	1.53938i	−0.138915	+	0.0707806i
$474$		0			0
$475$	−3.01613	−	19.0431i	−0.138390	−	0.873758i
$476$	1.63861	−	5.04312i	0.0751055	−	0.231151i
$477$		0			0
$478$	23.3113	+	23.3113i	1.06623	+	1.06623i
$479$	28.4248	+	14.4832i	1.29876	+	0.661752i	0.960232	−	0.279203i	$-0.0900704\pi$
$479$	28.4248	+	14.4832i	1.29876	+	0.661752i	0.338530	+	0.940956i	$0.390070\pi$
$480$		0			0
$481$	−6.50460	+	1.03023i	−0.296584	+	0.0469743i
$482$	−14.4647	−	10.5092i	−0.658849	−	0.478682i
$483$		0			0
$484$	−1.19033	+	1.63835i	−0.0541060	+	0.0744705i
$485$	−0.682969	−	1.34040i	−0.0310120	−	0.0608645i
$486$		0			0
$487$	10.5402	+	14.5073i	0.477621	+	0.657389i	0.978046	−	0.208391i	$-0.0668227\pi$
$487$	10.5402	+	14.5073i	0.477621	+	0.657389i	−0.500424	+	0.865780i	$0.666823\pi$
$488$	−3.00826	+	2.18563i	−0.136178	+	0.0989389i
$489$		0			0
$490$	−16.2091	+	5.26665i	−0.732252	+	0.237923i
$491$	−25.0172			−1.12901			−0.564505	−	0.825430i	$-0.690933\pi$
$491$	−25.0172			−1.12901			−0.564505	+	0.825430i	$0.690933\pi$
$492$		0			0
$493$	7.39319			0.332973
$494$	−5.59514	+	1.81797i	−0.251737	+	0.0817944i
$495$		0			0
$496$	−5.34082	+	3.88033i	−0.239810	+	0.174232i
$497$	2.99575	+	4.12329i	0.134378	+	0.184955i
$498$		0			0
$499$	11.7228	+	23.0074i	0.524786	+	1.02995i	0.989506	+	0.144493i	$0.0461551\pi$
$499$	11.7228	+	23.0074i	0.524786	+	1.02995i	−0.464720	+	0.885458i	$0.653845\pi$
$500$	0.809573	−	1.11428i	0.0362052	−	0.0498322i
$501$		0			0
$502$	−9.51139	−	6.91043i	−0.424514	−	0.308428i
$503$	18.1861	−	2.88039i	0.810878	−	0.128430i	0.262792	−	0.964853i	$-0.415357\pi$
$503$	18.1861	−	2.88039i	0.810878	−	0.128430i	0.548086	+	0.836422i	$0.315357\pi$
$504$		0			0
$505$	−5.80462	−	2.95760i	−0.258302	−	0.131612i
$506$	0.596973	+	0.596973i	0.0265387	+	0.0265387i
$507$		0			0
$508$	0.584346	−	1.79843i	0.0259262	−	0.0797925i
$509$	2.90230	+	18.3244i	0.128642	+	0.812214i	0.964657	+	0.263508i	$0.0848794\pi$
$509$	2.90230	+	18.3244i	0.128642	+	0.812214i	−0.836015	+	0.548706i	$0.815121\pi$
$510$		0			0
$511$	23.3908	−	11.9182i	1.03475	−	0.527230i
$512$	17.7247	+	5.75912i	0.783330	+	0.254519i
$513$		0			0
$514$	30.9884	−	15.7894i	1.36684	−	0.696440i
$515$	1.02815	+	3.16432i	0.0453057	+	0.139436i
$516$		0			0
$517$	0.668738	−	2.05816i	0.0294111	−	0.0905180i
$518$	49.6031	+	7.85636i	2.17944	+	0.345189i
$519$		0			0
$520$	1.67753	+	0.854743i	0.0735644	+	0.0374829i
$521$	1.28799	−	8.13203i	0.0564277	−	0.356271i	−0.943278	−	0.332005i	$-0.892275\pi$
$521$	1.28799	−	8.13203i	0.0564277	−	0.356271i	0.999706	−	0.0242662i	$-0.00772493\pi$
$522$		0			0
$523$	−27.7382	−	20.1530i	−1.21291	−	0.881229i	−0.217416	−	0.976079i	$-0.569763\pi$
$523$	−27.7382	−	20.1530i	−1.21291	−	0.881229i	−0.995492	+	0.0948499i	$0.969763\pi$
$524$		−	0.154190i		−	0.00673583i
$525$		0			0
$526$	14.3606	+	28.1842i	0.626151	+	1.22889i
$527$	4.13537	−	8.11613i	0.180140	−	0.353544i
$528$		0			0
$529$	17.7208	−	12.8749i	0.770468	−	0.559778i
$530$	−4.33708	+	4.33708i	−0.188391	+	0.188391i
$531$		0			0
$532$	3.87751			0.168111
$533$	5.66318	+	1.30067i	0.245300	+	0.0563381i
$534$		0			0
$535$	−9.12060	+	2.96346i	−0.394318	+	0.128122i
$536$	10.6766	−	10.6766i	0.461160	−	0.461160i
$537$		0			0
$538$	23.5117	+	32.3611i	1.01366	+	1.39519i
$539$	−3.68083	+	7.22404i	−0.158545	+	0.311162i
$540$		0			0
$541$	0.490706	−	0.675399i	0.0210971	−	0.0290377i	−0.798338	−	0.602209i	$-0.794287\pi$
$541$	0.490706	−	0.675399i	0.0210971	−	0.0290377i	0.819435	+	0.573172i	$0.194287\pi$
$542$			17.6629i			0.758685i
$543$		0			0
$544$	6.31386	−	1.00002i	0.270705	−	0.0428754i
$545$	−0.209594	+	1.32332i	−0.00897802	+	0.0566850i
$546$		0			0
$547$	22.5832	+	22.5832i	0.965590	+	0.965590i	0.999427	−	0.0338377i	$-0.0107729\pi$
$547$	22.5832	+	22.5832i	0.965590	+	0.965590i	−0.0338377	+	0.999427i	$0.510773\pi$
$548$	0.804327	+	0.127393i	0.0343591	+	0.00544195i
$549$		0			0
$550$	−0.555138	−	3.50500i	−0.0236712	−	0.149454i
$551$	1.67061	+	5.14160i	0.0711703	+	0.219040i
$552$		0			0
$553$	54.2494	+	17.6267i	2.30692	+	0.749564i
$554$	−20.6388	−	6.70597i	−0.876860	−	0.284909i
$555$		0			0
$556$	−0.293759	−	0.904097i	−0.0124581	−	0.0383422i
$557$	−4.35403	−	27.4903i	−0.184486	−	1.16480i	−0.889951	−	0.456055i	$-0.849262\pi$
$557$	−4.35403	−	27.4903i	−0.184486	−	1.16480i	0.705465	−	0.708744i	$-0.250738\pi$
$558$		0			0
$559$	5.57586	+	0.883130i	0.235834	+	0.0373524i
$560$	−11.1214	−	11.1214i	−0.469964	−	0.469964i
$561$		0			0
$562$	−2.47581	+	15.6316i	−0.104436	+	0.659381i
$563$	29.1631	−	4.61898i	1.22908	−	0.194667i	0.492073	−	0.870554i	$-0.336239\pi$
$563$	29.1631	−	4.61898i	1.22908	−	0.194667i	0.737005	+	0.675887i	$0.236239\pi$
$564$		0			0
$565$		−	0.904334i		−	0.0380456i
$566$	16.5878	−	22.8311i	0.697236	−	0.959662i
$567$		0			0
$568$	−1.32547	+	2.60137i	−0.0556153	+	0.109151i
$569$	16.9189	+	23.2869i	0.709278	+	0.976237i	0.999812	+	0.0193726i	$0.00616686\pi$
$569$	16.9189	+	23.2869i	0.709278	+	0.976237i	−0.290535	+	0.956864i	$0.593833\pi$
$570$		0			0
$571$	−19.3493	+	19.3493i	−0.809742	+	0.809742i	−0.984595	−	0.174853i	$-0.944055\pi$
$571$	−19.3493	+	19.3493i	−0.809742	+	0.809742i	0.174853	+	0.984595i	$0.444055\pi$
$572$	−0.0890064	+	0.0289199i	−0.00372154	+	0.00120920i
$573$		0			0
$574$	−38.0079	−	22.7786i	−1.58642	−	0.950762i
$575$	4.60656			0.192107
$576$		0			0
$577$	6.40224	−	6.40224i	0.266529	−	0.266529i	−0.561171	−	0.827700i	$-0.689649\pi$
$577$	6.40224	−	6.40224i	0.266529	−	0.266529i	0.827700	+	0.561171i	$0.189649\pi$
$578$	−22.6281	+	16.4403i	−0.941205	+	0.683826i
$579$		0			0
$580$	−0.0820733	+	0.161078i	−0.00340791	+	0.00668840i
$581$	27.9382	+	54.8318i	1.15907	+	2.27481i
$582$		0			0
$583$			2.91783i			0.120844i
$584$	12.1663	+	8.83931i	0.503444	+	0.365773i
$585$		0			0
$586$	−6.00377	+	37.9063i	−0.248014	+	1.56590i
$587$	4.62167	+	2.35486i	0.190757	+	0.0971955i	0.546760	−	0.837289i	$-0.315861\pi$
$587$	4.62167	+	2.35486i	0.190757	+	0.0971955i	−0.356003	+	0.934485i	$0.615861\pi$
$588$		0			0
$589$	6.57883	+	1.04198i	0.271076	+	0.0429342i
$590$	3.14223	−	9.67080i	0.129364	−	0.398141i
$591$		0			0
$592$	9.73876	+	29.9728i	0.400261	+	1.23188i
$593$	20.8824	−	10.6401i	0.857538	−	0.436937i	0.0308006	−	0.999526i	$-0.490194\pi$
$593$	20.8824	−	10.6401i	0.857538	−	0.436937i	0.826737	+	0.562588i	$0.190194\pi$
$594$		0			0
$595$	20.6394	+	6.70616i	0.846134	+	0.274926i
$596$	−1.33616	+	0.680807i	−0.0547312	+	0.0278869i
$597$		0			0
$598$	−0.219885	−	1.38830i	−0.00899178	−	0.0567719i
$599$	9.48601	−	29.1949i	0.387588	−	1.19287i	−0.546998	−	0.837134i	$-0.684229\pi$
$599$	9.48601	−	29.1949i	0.387588	−	1.19287i	0.934586	−	0.355739i	$-0.115771\pi$
$600$		0			0
$601$	5.21941	+	5.21941i	0.212904	+	0.212904i	0.805500	−	0.592596i	$-0.201897\pi$
$601$	5.21941	+	5.21941i	0.212904	+	0.212904i	−0.592596	+	0.805500i	$0.701897\pi$
$602$	−38.3585	−	19.5446i	−1.56338	−	0.796580i
$603$		0			0
$604$	−3.86345	+	0.611910i	−0.157202	+	0.0248983i
$605$	−6.70511	−	4.87155i	−0.272601	−	0.198057i
$606$		0			0
$607$	18.4399	−	25.3803i	0.748452	−	1.03016i	−0.249636	−	0.968340i	$-0.580311\pi$
$607$	18.4399	−	25.3803i	0.748452	−	1.03016i	0.998088	−	0.0618155i	$-0.0196890\pi$
$608$	2.12218	+	4.16502i	0.0860658	+	0.168914i
$609$		0			0
$610$	0.934663	+	1.28645i	0.0378434	+	0.0520870i
$611$	−2.91492	+	2.11781i	−0.117925	+	0.0856774i
$612$		0			0
$613$	16.7669	−	5.44789i	0.677208	−	0.220038i	0.0498354	−	0.998757i	$-0.484130\pi$
$613$	16.7669	−	5.44789i	0.677208	−	0.220038i	0.627373	+	0.778719i	$0.284130\pi$
$614$	−12.8089			−0.516927
$615$		0			0
$616$	−6.83006			−0.275191
$617$	7.65218	−	2.48634i	0.308065	−	0.100096i	−0.150905	−	0.988548i	$-0.548219\pi$
$617$	7.65218	−	2.48634i	0.308065	−	0.100096i	0.458970	+	0.888452i	$0.348219\pi$
$618$		0			0
$619$	−5.14200	+	3.73588i	−0.206675	+	0.150158i	−0.686308	−	0.727311i	$-0.740770\pi$
$619$	−5.14200	+	3.73588i	−0.206675	+	0.150158i	0.479633	+	0.877469i	$0.340770\pi$
$620$	0.130921	+	0.180198i	0.00525792	+	0.00723691i
$621$		0			0
$622$	−5.42688	−	10.6509i	−0.217598	−	0.427060i
$623$	−5.36290	+	7.38140i	−0.214860	+	0.295729i
$624$		0			0
$625$	−13.2395	−	9.61907i	−0.529581	−	0.384763i
$626$	−5.04362	+	0.798832i	−0.201584	+	0.0319277i
$627$		0			0
$628$	2.03490	+	1.03683i	0.0812014	+	0.0413742i
$629$	−30.7485	−	30.7485i	−1.22602	−	1.22602i
$630$		0			0
$631$	1.29270	−	3.97853i	0.0514616	−	0.158383i	−0.922023	−	0.387135i	$-0.873465\pi$
$631$	1.29270	−	3.97853i	0.0514616	−	0.158383i	0.973485	+	0.228753i	$0.0734647\pi$
$632$	5.11160	+	32.2734i	0.203329	+	1.28377i
$633$		0			0
$634$	−36.8030	+	18.7520i	−1.46163	+	0.744739i
$635$	7.36026	+	2.39149i	0.292083	+	0.0949035i
$636$		0			0
$637$	12.0275	−	6.12831i	0.476546	−	0.242812i
$638$	0.307486	+	0.946344i	0.0121735	+	0.0374661i
$639$		0			0
$640$	3.02676	−	9.31541i	0.119643	−	0.368224i
$641$	−19.3732	−	3.06842i	−0.765196	−	0.121195i	−0.238377	−	0.971173i	$-0.576615\pi$
$641$	−19.3732	−	3.06842i	−0.765196	−	0.121195i	−0.526819	+	0.849978i	$0.676615\pi$
$642$		0			0
$643$	−9.90543	−	5.04707i	−0.390632	−	0.199037i	0.247633	−	0.968854i	$-0.420347\pi$
$643$	−9.90543	−	5.04707i	−0.390632	−	0.199037i	−0.638265	+	0.769817i	$0.720347\pi$
$644$	−0.144925	+	0.915023i	−0.00571086	+	0.0360569i
$645$		0			0
$646$	−31.4269	−	22.8330i	−1.23647	−	0.898351i
$647$		−	10.4368i		−	0.410313i	−0.978729	−	0.205157i	$-0.934230\pi$
$647$		−	10.4368i		−	0.410313i	0.978729	−	0.205157i	$-0.0657704\pi$
$648$		0			0
$649$	−2.19609	−	4.31007i	−0.0862040	−	0.169185i
$650$	−2.68231	+	5.26434i	−0.105209	+	0.206484i
$651$		0			0
$652$	−0.306287	+	0.222530i	−0.0119951	+	0.00871496i
$653$	−19.0837	+	19.0837i	−0.746802	+	0.746802i	−0.973877	−	0.227075i	$-0.927084\pi$
$653$	−19.0837	+	19.0837i	−0.746802	+	0.746802i	0.227075	+	0.973877i	$0.427084\pi$
$654$		0			0
$655$	0.631038			0.0246567
$656$	1.90812	−	27.7408i	0.0744995	−	1.08310i
$657$		0			0
$658$	26.1314	−	8.49062i	1.01871	−	0.330999i
$659$	10.8584	−	10.8584i	0.422984	−	0.422984i	−0.463246	−	0.886230i	$-0.653315\pi$
$659$	10.8584	−	10.8584i	0.422984	−	0.422984i	0.886230	+	0.463246i	$0.153315\pi$
$660$		0			0
$661$	0.199484	+	0.274566i	0.00775902	+	0.0106794i	0.812879	−	0.582433i	$-0.197899\pi$
$661$	0.199484	+	0.274566i	0.00775902	+	0.0106794i	−0.805120	+	0.593112i	$0.797899\pi$
$662$	−15.1662	+	29.7654i	−0.589452	+	1.15686i
$663$		0			0
$664$	−20.7208	+	28.5197i	−0.804123	+	1.10678i
$665$			15.8691i			0.615377i
$666$		0			0
$667$	−1.27577	+	0.202062i	−0.0493979	+	0.00782385i
$668$	−0.566031	+	3.57378i	−0.0219004	+	0.138274i
$669$		0			0
$670$	−4.56575	−	4.56575i	−0.176390	−	0.176390i
$671$	0.747142	+	0.118336i	0.0288431	+	0.00456830i
$672$		0			0
$673$	1.95952	+	12.3719i	0.0755340	+	0.476903i	0.996239	+	0.0866442i	$0.0276143\pi$
$673$	1.95952	+	12.3719i	0.0755340	+	0.476903i	−0.920705	+	0.390258i	$0.872386\pi$
$674$	−11.3349	−	34.8853i	−0.436604	−	1.34373i
$675$		0			0
$676$	−2.19117	−	0.711954i	−0.0842757	−	0.0273828i
$677$	27.8174	+	9.03841i	1.06911	+	0.347374i	0.790140	−	0.612926i	$-0.210008\pi$
$677$	27.8174	+	9.03841i	1.06911	+	0.347374i	0.278968	+	0.960300i	$0.410008\pi$
$678$		0			0
$679$	−2.80780	−	8.64153i	−0.107754	−	0.331631i
$680$	1.94473	+	12.2785i	0.0745770	+	0.470861i
$681$		0			0
$682$	1.21087	+	0.191784i	0.0463668	+	0.00734377i
$683$	−16.7263	−	16.7263i	−0.640013	−	0.640013i	0.310545	−	0.950559i	$-0.399488\pi$
$683$	−16.7263	−	16.7263i	−0.640013	−	0.640013i	−0.950559	+	0.310545i	$0.899488\pi$
$684$		0			0
$685$	−0.521367	+	3.29178i	−0.0199204	+	0.125773i
$686$	−53.8271	+	8.52538i	−2.05513	+	0.325500i
$687$		0			0
$688$		−	27.0155i		−	1.02996i
$689$	2.85544	−	3.93017i	0.108783	−	0.149728i
$690$		0			0
$691$	−7.58691	+	14.8902i	−0.288620	+	0.566448i	−0.989104	−	0.147220i	$-0.952967\pi$
$691$	−7.58691	+	14.8902i	−0.288620	+	0.566448i	0.700484	+	0.713668i	$0.252967\pi$
$692$	−0.667725	−	0.919045i	−0.0253831	−	0.0349369i
$693$		0			0
$694$	3.76119	−	3.76119i	0.142773	−	0.142773i
$695$	3.70010	−	1.20224i	0.140353	−	0.0456034i
$696$		0			0
$697$	15.0315	+	35.3002i	0.569358	+	1.33709i
$698$	−0.424458			−0.0160660
$699$		0			0
$700$	2.75357	−	2.75357i	0.104075	−	0.104075i
$701$	29.0200	−	21.0843i	1.09607	−	0.796342i	0.115656	−	0.993289i	$-0.463103\pi$
$701$	29.0200	−	21.0843i	1.09607	−	0.796342i	0.980414	+	0.196948i	$0.0631029\pi$
$702$		0			0
$703$	14.4360	−	28.3322i	0.544463	−	1.06857i
$704$	−1.75854	−	3.45133i	−0.0662776	−	0.130077i
$705$		0			0
$706$		−	34.7883i		−	1.30927i
$707$	−31.8332	−	23.1282i	−1.19721	−	0.869825i
$708$		0			0
$709$	2.89893	−	18.3031i	0.108872	−	0.687389i	−0.871524	−	0.490352i	$-0.836868\pi$
$709$	2.89893	−	18.3031i	0.108872	−	0.687389i	0.980396	−	0.197037i	$-0.0631319\pi$
$710$	1.11245	+	0.566822i	0.0417495	+	0.0212725i
$711$		0			0
$712$	−5.16222	−	0.817615i	−0.193462	−	0.0306414i
$713$	−0.491779	+	1.51354i	−0.0184173	+	0.0566825i
$714$		0			0
$715$	−0.118358	−	0.364267i	−0.00442632	−	0.0136228i
$716$	1.54330	−	0.786353i	0.0576760	−	0.0293874i
$717$		0			0
$718$	−48.3427	−	15.7075i	−1.80413	−	0.586199i
$719$	26.6096	−	13.5583i	0.992371	−	0.505638i	0.119104	−	0.992882i	$-0.461998\pi$
$719$	26.6096	−	13.5583i	0.992371	−	0.505638i	0.873266	+	0.487244i	$0.161998\pi$
$720$		0			0
$721$	3.14366	+	19.8483i	0.117076	+	0.739190i
$722$	0.0906104	−	0.278870i	0.00337217	−	0.0103785i
$723$		0			0
$724$	2.54924	+	2.54924i	0.0947418	+	0.0947418i
$725$	4.83761	+	2.46489i	0.179664	+	0.0915436i
$726$		0			0
$727$	5.04235	−	0.798630i	0.187010	−	0.0296195i	−0.0622267	−	0.998062i	$-0.519820\pi$
$727$	5.04235	−	0.798630i	0.187010	−	0.0296195i	0.249237	+	0.968443i	$0.419820\pi$
$728$	9.19976	+	6.68401i	0.340966	+	0.247726i
$729$		0			0
$730$	3.78004	−	5.20278i	0.139906	−	0.192564i
$731$	16.9230	+	33.2133i	0.625920	+	1.22844i
$732$		0			0
$733$	−11.5449	−	15.8902i	−0.426421	−	0.586918i	0.540706	−	0.841212i	$-0.318157\pi$
$733$	−11.5449	−	15.8902i	−0.426421	−	0.586918i	−0.967127	+	0.254293i	$0.918157\pi$
$734$	31.2223	−	22.6843i	1.15243	−	0.837293i
$735$		0			0
$736$	−1.06219	+	0.345125i	−0.0391527	+	0.0127215i
$737$	−3.07166			−0.113146
$738$		0			0
$739$	21.4364			0.788552			0.394276	−	0.918992i	$-0.370995\pi$
$739$	21.4364			0.788552			0.394276	+	0.918992i	$0.370995\pi$
$740$	1.01127	−	0.328583i	0.0371752	−	0.0120789i
$741$		0			0
$742$	−29.9709	+	21.7752i	−1.10027	+	0.799391i
$743$	−15.6932	−	21.5998i	−0.575727	−	0.792420i	0.417492	−	0.908681i	$-0.362909\pi$
$743$	−15.6932	−	21.5998i	−0.575727	−	0.792420i	−0.993219	+	0.116261i	$0.962909\pi$
$744$		0			0
$745$	−2.78627	−	5.46835i	−0.102081	−	0.200345i
$746$	8.78275	−	12.0884i	0.321559	−	0.442588i
$747$		0			0
$748$	−0.499932	−	0.363222i	−0.0182793	−	0.0132807i
$749$	−57.2093	+	9.06107i	−2.09038	+	0.331084i
$750$		0			0
$751$	−16.3078	−	8.30926i	−0.595082	−	0.303209i	0.130388	−	0.991463i	$-0.458378\pi$
$751$	−16.3078	−	8.30926i	−0.595082	−	0.303209i	−0.725470	+	0.688254i	$0.758378\pi$
$752$	12.1920	+	12.1920i	0.444596	+	0.444596i
$753$		0			0
$754$	0.511941	−	1.57559i	0.0186438	−	0.0573797i
$755$	−2.50430	−	15.8115i	−0.0911409	−	0.575441i
$756$		0			0
$757$	15.9241	−	8.11374i	0.578772	−	0.294899i	−0.139993	−	0.990153i	$-0.544708\pi$
$757$	15.9241	−	8.11374i	0.578772	−	0.294899i	0.718765	+	0.695254i	$0.244708\pi$
$758$	18.6224	+	6.05080i	0.676398	+	0.219775i
$759$		0			0
$760$	−8.09969	+	4.12700i	−0.293807	+	0.149702i
$761$	−2.00583	−	6.17330i	−0.0727111	−	0.223782i	0.908096	−	0.418762i	$-0.137536\pi$
$761$	−2.00583	−	6.17330i	−0.0727111	−	0.223782i	−0.980807	+	0.194980i	$0.937536\pi$
$762$		0			0
$763$	−2.50068	+	7.69632i	−0.0905309	+	0.278625i
$764$	−2.10538	−	0.333459i	−0.0761699	−	0.0120641i
$765$		0			0
$766$	−9.06839	−	4.62058i	−0.327654	−	0.166948i
$767$	−1.25988	+	7.95458i	−0.0454917	+	0.287223i
$768$		0			0
$769$	12.0454	+	8.75147i	0.434367	+	0.315586i	0.783393	−	0.621527i	$-0.213487\pi$
$769$	12.0454	+	8.75147i	0.434367	+	0.315586i	−0.349026	+	0.937113i	$0.613487\pi$
$770$			2.92080i			0.105258i
$771$		0			0
$772$	1.00439	+	1.97123i	0.0361488	+	0.0709460i
$773$	15.0844	−	29.6048i	0.542548	−	1.06481i	−0.443175	−	0.896435i	$-0.646148\pi$
$773$	15.0844	−	29.6048i	0.542548	−	1.06481i	0.985723	−	0.168375i	$-0.0538520\pi$
$774$		0			0
$775$	5.41183	−	3.93192i	0.194399	−	0.141239i
$776$	3.68048	−	3.68048i	0.132122	−	0.132122i
$777$		0			0
$778$	−45.1527			−1.61880
$779$	−21.1530	+	18.4303i	−0.757885	+	0.660334i
$780$		0			0
$781$	0.564876	−	0.183539i	0.0202129	−	0.00656755i
$782$	6.56277	−	6.56277i	0.234684	−	0.234684i
$783$		0			0
$784$	−37.9694	−	52.2604i	−1.35605	−	1.86644i
$785$	−4.24334	+	8.32803i	−0.151451	+	0.297240i
$786$		0			0
$787$	30.3707	−	41.8017i	1.08260	−	1.49007i	0.225974	−	0.974133i	$-0.427444\pi$
$787$	30.3707	−	41.8017i	1.08260	−	1.49007i	0.856626	−	0.515937i	$-0.172556\pi$
$788$		−	1.91213i		−	0.0681168i
$789$		0			0
$790$	13.8014	−	2.18592i	0.491031	−	0.0777717i
$791$	0.854459	−	5.39484i	0.0303811	−	0.191819i
$792$		0			0
$793$	−0.890559	−	0.890559i	−0.0316247	−	0.0316247i
$794$	−35.1233	−	5.56299i	−1.24648	−	0.197423i
$795$		0			0
$796$	−0.249093	−	1.57271i	−0.00882888	−	0.0557434i
$797$	−4.43551	−	13.6511i	−0.157114	−	0.483547i	0.841255	−	0.540639i	$-0.181817\pi$
$797$	−4.43551	−	13.6511i	−0.157114	−	0.483547i	−0.998369	+	0.0570915i	$0.981817\pi$
$798$		0			0
$799$	−22.6263	−	7.35172i	−0.800460	−	0.260085i
$800$	4.46478	+	1.45070i	0.157854	+	0.0512898i
$801$		0			0
$802$	2.17925	+	6.70706i	0.0769521	+	0.236834i
$803$	−0.478583	−	3.02165i	−0.0168888	−	0.106632i
$804$		0			0
$805$	−3.74482	−	0.593121i	−0.131987	−	0.0209048i
$806$	−1.44331	−	1.44331i	−0.0508383	−	0.0508383i
$807$		0			0
$808$	3.52607	−	22.2627i	0.124047	−	0.783200i
$809$	−43.6281	+	6.91001i	−1.53388	+	0.242943i	−0.865513	−	0.500887i	$-0.833007\pi$
$809$	−43.6281	+	6.91001i	−1.53388	+	0.242943i	−0.668369	+	0.743830i	$0.733007\pi$
$810$		0			0
$811$			27.7113i			0.973074i	0.873660	+	0.486537i	$0.161740\pi$
$811$			27.7113i			0.973074i	−0.873660	+	0.486537i	$0.838260\pi$
$812$	−0.641806	+	0.883371i	−0.0225230	+	0.0310002i
$813$		0			0
$814$	2.65703	−	5.21472i	0.0931289	−	0.182776i
$815$	−0.910726	−	1.25351i	−0.0319014	−	0.0439084i
$816$		0			0
$817$	−19.2742	+	19.2742i	−0.674319	+	0.674319i
$818$	−52.2233	+	16.9684i	−1.82594	+	0.593285i
$819$		0			0
$820$	−0.935966	−	0.0643793i	−0.0326853	−	0.00224822i
$821$	−11.1582			−0.389424			−0.194712	−	0.980860i	$-0.562377\pi$
$821$	−11.1582			−0.389424			−0.194712	+	0.980860i	$0.562377\pi$
$822$		0			0
$823$	−28.5619	+	28.5619i	−0.995606	+	0.995606i	−0.999990	−	0.00438414i	$-0.998604\pi$
$823$	−28.5619	+	28.5619i	−0.995606	+	0.995606i	0.00438414	+	0.999990i	$0.498604\pi$
$824$	−9.31316	+	6.76641i	−0.324439	+	0.235719i
$825$		0			0
$826$	27.8826	−	54.7226i	0.970159	−	1.90404i
$827$	0.960885	+	1.88584i	0.0334133	+	0.0655772i	0.907110	−	0.420894i	$-0.138284\pi$
$827$	0.960885	+	1.88584i	0.0334133	+	0.0655772i	−0.873696	+	0.486472i	$0.838284\pi$
$828$		0			0
$829$			22.5376i			0.782765i	0.920228	+	0.391382i	$0.128003\pi$
$829$			22.5376i			0.782765i	−0.920228	+	0.391382i	$0.871997\pi$
$830$	12.1962	+	8.86103i	0.423335	+	0.307571i
$831$		0			0
$832$	−1.00887	+	6.36972i	−0.0349761	+	0.220830i
$833$	79.4169	+	40.4650i	2.75163	+	1.40203i
$834$		0			0
$835$	−14.6260	−	2.31654i	−0.506155	−	0.0801670i
$836$	0.139636	−	0.429754i	0.00482940	−	0.0148634i
$837$		0			0
$838$	5.13337	+	15.7989i	0.177329	+	0.545764i
$839$	−27.0427	+	13.7790i	−0.933619	+	0.475703i	−0.853506	−	0.521083i	$-0.825528\pi$
$839$	−27.0427	+	13.7790i	−0.933619	+	0.475703i	−0.0801132	+	0.996786i	$0.525528\pi$
$840$		0			0
$841$	26.1328	+	8.49105i	0.901130	+	0.292795i
$842$	−22.3420	+	11.3838i	−0.769957	+	0.392313i
$843$		0			0
$844$	0.384314	+	2.42646i	0.0132286	+	0.0835222i
$845$	2.91374	−	8.96757i	0.100236	−	0.308494i
$846$		0			0
$847$	−35.3967	−	35.3967i	−1.21625	−	1.21625i
$848$	−20.7136	−	10.5541i	−0.711308	−	0.362430i
$849$		0			0
$850$	−38.5320	+	6.10287i	−1.32164	+	0.209327i
$851$	6.14633	+	4.46557i	0.210694	+	0.153078i
$852$		0			0
$853$	−10.9647	+	15.0916i	−0.375423	+	0.516726i	−0.954365	−	0.298643i	$-0.903466\pi$
$853$	−10.9647	+	15.0916i	−0.375423	+	0.516726i	0.578942	+	0.815369i	$0.303466\pi$
$854$	4.36027	+	8.55751i	0.149205	+	0.292832i
$855$		0			0
$856$	−19.5030	−	26.8436i	−0.666599	−	0.917494i
$857$	38.9323	−	28.2860i	1.32990	−	0.966232i	0.330152	−	0.943928i	$-0.392900\pi$
$857$	38.9323	−	28.2860i	1.32990	−	0.966232i	0.999751	−	0.0223039i	$-0.00710014\pi$
$858$		0			0
$859$	−17.0896	+	5.55276i	−0.583091	+	0.189458i	−0.585685	−	0.810539i	$-0.699174\pi$
$859$	−17.0896	+	5.55276i	−0.583091	+	0.189458i	0.00259400	+	0.999997i	$0.499174\pi$
$860$	−0.911495			−0.0310817
$861$		0			0
$862$	30.1105			1.02557
$863$	32.1502	−	10.4462i	1.09441	−	0.355594i	0.294459	−	0.955664i	$-0.404861\pi$
$863$	32.1502	−	10.4462i	1.09441	−	0.355594i	0.799947	+	0.600070i	$0.204861\pi$
$864$		0			0
$865$	3.76128	−	2.73273i	0.127887	−	0.0929156i
$866$	18.4364	+	25.3755i	0.626494	+	0.862295i
$867$		0			0
$868$	0.610757	+	1.19868i	0.0207304	+	0.0406858i
$869$	3.90722	−	5.37783i	0.132544	−	0.182430i
$870$		0			0
$871$	4.13738	+	3.00598i	0.140190	+	0.101854i
$872$	−4.57859	+	0.725178i	−0.155051	+	0.0245576i
$873$		0			0
$874$	6.04705	+	3.08113i	0.204545	+	0.104221i
$875$	24.0742	+	24.0742i	0.813855	+	0.813855i
$876$		0			0
$877$	−8.35976	+	25.7287i	−0.282289	+	0.868796i	0.704909	+	0.709298i	$0.250988\pi$
$877$	−8.35976	+	25.7287i	−0.282289	+	0.868796i	−0.987198	+	0.159499i	$0.949012\pi$
$878$	−4.78366	−	30.2028i	−0.161441	−	1.01930i
$879$		0			0
$880$	−1.63311	+	0.832111i	−0.0550521	+	0.0280505i
$881$	15.9073	+	5.16859i	0.535930	+	0.174134i	0.564462	−	0.825459i	$-0.309084\pi$
$881$	15.9073	+	5.16859i	0.535930	+	0.174134i	−0.0285328	+	0.999593i	$0.509084\pi$
$882$		0			0
$883$	22.7575	−	11.5955i	0.765852	−	0.390221i	−0.0269999	−	0.999635i	$-0.508595\pi$
$883$	22.7575	−	11.5955i	0.765852	−	0.390221i	0.792852	+	0.609414i	$0.208595\pi$
$884$	0.317929	+	0.978485i	0.0106931	+	0.0329100i
$885$		0			0
$886$	−9.92302	+	30.5399i	−0.333370	+	1.02601i
$887$	−39.5201	−	6.25936i	−1.32695	−	0.210169i	−0.547594	−	0.836744i	$-0.684456\pi$
$887$	−39.5201	−	6.25936i	−1.32695	−	0.210169i	−0.779361	+	0.626576i	$0.784456\pi$
$888$		0			0
$889$	41.6483	+	21.2209i	1.39684	+	0.711726i
$890$	−0.349645	+	2.20757i	−0.0117201	+	0.0739979i
$891$		0			0
$892$	−2.67853	−	1.94607i	−0.0896838	−	0.0651591i
$893$		−	17.3967i		−	0.582159i
$894$		0			0
$895$	3.21822	+	6.31612i	0.107573	+	0.211125i
$896$	26.8579	−	52.7116i	0.897260	−	1.76097i
$897$		0			0
$898$	6.64701	−	4.82933i	0.221814	−	0.161157i
$899$	−1.32631	+	1.32631i	−0.0442350	+	0.0442350i
$900$		0			0
$901$	32.0769			1.06864
$902$	−3.89334	+	3.39221i	−0.129634	+	0.112948i
$903$		0			0
$904$	2.97578	−	0.966890i	0.0989730	−	0.0321583i
$905$	−10.4330	+	10.4330i	−0.346805	+	0.346805i
$906$		0			0
$907$	−14.3108	−	19.6971i	−0.475182	−	0.654032i	0.502388	−	0.864642i	$-0.332455\pi$
$907$	−14.3108	−	19.6971i	−0.475182	−	0.654032i	−0.977570	+	0.210610i	$0.932455\pi$
$908$	2.33995	−	4.59240i	0.0776539	−	0.152404i
$909$		0			0
$910$	2.85835	−	3.93418i	0.0947534	−	0.130417i
$911$			24.0894i			0.798118i	0.916925	+	0.399059i	$0.130663\pi$
$911$			24.0894i			0.798118i	−0.916925	+	0.399059i	$0.869337\pi$
$912$		0			0
$913$	7.08325	−	1.12188i	0.234421	−	0.0371287i
$914$	−8.96149	+	56.5806i	−0.296420	+	1.87152i
$915$		0			0
$916$	3.02835	+	3.02835i	0.100059	+	0.100059i
$917$	3.76449	+	0.596236i	0.124314	+	0.0196894i
$918$		0			0
$919$	1.12618	+	7.11039i	0.0371491	+	0.234550i	0.999276	−	0.0380527i	$-0.0121155\pi$
$919$	1.12618	+	7.11039i	0.0371491	+	0.234550i	−0.962127	+	0.272603i	$0.912115\pi$
$920$	−0.671164	−	2.06563i	−0.0221276	−	0.0681018i
$921$		0			0
$922$	7.16312	+	2.32744i	0.235905	+	0.0766501i
$923$	−0.940476	−	0.305579i	−0.0309561	−	0.0100583i
$924$		0			0
$925$	−9.86824	−	30.3713i	−0.324466	−	0.998603i
$926$	0.667460	+	4.21418i	0.0219341	+	0.138486i
$927$		0			0
$928$	−1.30013	−	0.205921i	−0.0426790	−	0.00675969i
$929$	−4.87523	−	4.87523i	−0.159951	−	0.159951i	0.622594	−	0.782545i	$-0.286079\pi$
$929$	−4.87523	−	4.87523i	−0.159951	−	0.159951i	−0.782545	+	0.622594i	$0.786079\pi$
$930$		0			0
$931$	−10.1959	+	64.3743i	−0.334157	+	2.10978i
$932$	−4.52447	+	0.716606i	−0.148204	+	0.0234732i
$933$		0			0
$934$			54.5325i			1.78436i
$935$	1.48652	−	2.04602i	0.0486144	−	0.0669120i
$936$		0			0
$937$	26.3251	−	51.6659i	0.860003	−	1.68785i	0.144200	−	0.989549i	$-0.453939\pi$
$937$	26.3251	−	51.6659i	0.860003	−	1.68785i	0.715803	−	0.698303i	$-0.246061\pi$
$938$	−22.9232	−	31.5511i	−0.748469	−	1.03018i
$939$		0			0
$940$	0.411353	−	0.411353i	0.0134169	−	0.0134169i
$941$	−38.7521	+	12.5913i	−1.26328	+	0.410466i	−0.862663	−	0.505779i	$-0.831205\pi$
$941$	−38.7521	+	12.5913i	−1.26328	+	0.410466i	−0.400620	+	0.916244i	$0.631205\pi$
$942$		0			0
$943$	−3.55861	−	5.68057i	−0.115884	−	0.184985i
$944$	38.5406			1.25439
$945$		0			0
$946$	−3.54753	+	3.54753i	−0.115340	+	0.115340i
$947$	22.6790	−	16.4773i	0.736970	−	0.535440i	−0.154791	−	0.987947i	$-0.549470\pi$
$947$	22.6790	−	16.4773i	0.736970	−	0.535440i	0.891761	+	0.452507i	$0.149470\pi$
$948$		0			0
$949$	−2.31242	+	4.53837i	−0.0750642	+	0.147322i
$950$	−12.9512	−	25.4181i	−0.420191	−	0.824671i
$951$		0			0
$952$			75.0857i			2.43354i
$953$	31.1757	+	22.6505i	1.00988	+	0.733721i	0.964184	−	0.265235i	$-0.0854494\pi$
$953$	31.1757	+	22.6505i	1.00988	+	0.733721i	0.0456960	+	0.998955i	$0.485449\pi$
$954$		0			0
$955$	1.36471	−	8.61646i	0.0441611	−	0.278822i
$956$	3.75634	+	1.91395i	0.121489	+	0.0619016i
$957$		0			0
$958$	46.6208	+	7.38402i	1.50625	+	0.238567i
$959$	−6.22048	+	19.1447i	−0.200870	+	0.618213i
$960$		0			0
$961$	−8.86539	−	27.2849i	−0.285980	−	0.880157i
$962$	−8.68211	+	4.42376i	−0.279922	+	0.142628i
$963$		0			0
$964$	−2.17451	−	0.706541i	−0.0700362	−	0.0227561i
$965$	−8.06743	+	4.11056i	−0.259700	+	0.132324i
$966$		0			0
$967$	−6.60601	−	41.7087i	−0.212435	−	1.34126i	−0.831326	−	0.555785i	$-0.812418\pi$
$967$	−6.60601	−	41.7087i	−0.212435	−	1.34126i	0.618891	−	0.785477i	$-0.287582\pi$
$968$	8.86128	−	27.2722i	0.284812	−	0.876562i
$969$		0			0
$970$	−1.57392	−	1.57392i	−0.0505356	−	0.0505356i
$971$	1.85832	+	0.946862i	0.0596364	+	0.0303863i	0.483554	−	0.875314i	$-0.339346\pi$
$971$	1.85832	+	0.946862i	0.0596364	+	0.0303863i	−0.423918	+	0.905701i	$0.639346\pi$
$972$		0			0
$973$	23.2091	−	3.67595i	0.744048	−	0.117846i
$974$	21.4650	+	15.5952i	0.687783	+	0.499703i
$975$		0			0
$976$	−3.54256	+	4.87592i	−0.113395	+	0.156074i
$977$	−13.5363	−	26.5664i	−0.433063	−	0.849935i	−0.999663	−	0.0259417i	$-0.991742\pi$
$977$	−13.5363	−	26.5664i	−0.433063	−	0.849935i	0.566600	−	0.823993i	$-0.308258\pi$
$978$		0			0
$979$	0.624971	+	0.860199i	0.0199742	+	0.0274921i
$980$	−1.76325	+	1.28107i	−0.0563249	+	0.0409224i
$981$		0			0
$982$	−35.2037	+	11.4384i	−1.12340	+	0.365013i
$983$	36.2484			1.15615			0.578073	−	0.815985i	$-0.303805\pi$
$983$	36.2484			1.15615			0.578073	+	0.815985i	$0.303805\pi$
$984$		0			0
$985$	7.82557			0.249343
$986$	10.4036	−	3.38032i	0.331317	−	0.107651i
$987$		0			0
$988$	−0.608647	+	0.442208i	−0.0193637	+	0.0140685i
$989$	−3.82797	−	5.26875i	−0.121722	−	0.167537i
$990$		0			0
$991$	6.13732	+	12.0452i	0.194959	+	0.382628i	0.967704	−	0.252088i	$-0.0811172\pi$
$991$	6.13732	+	12.0452i	0.194959	+	0.382628i	−0.772746	+	0.634716i	$0.781117\pi$
$992$	−0.953285	+	1.31208i	−0.0302668	+	0.0416587i
$993$		0			0
$994$	6.10081	+	4.43250i	0.193506	+	0.140590i
$995$	6.43648	−	1.01944i	0.204050	−	0.0323184i
$996$		0			0
$997$	24.8214	+	12.6471i	0.786101	+	0.400538i	0.800481	−	0.599358i	$-0.204577\pi$
$997$	24.8214	+	12.6471i	0.786101	+	0.400538i	−0.0143801	+	0.999897i	$0.504577\pi$
$998$	27.0156	+	27.0156i	0.855164	+	0.855164i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	369.2.u.a.289.2		24
3.2	odd	2		41.2.g.a.2.2	✓	24
12.11	even	2		656.2.bs.d.289.3		24
41.21	even	20	inner	369.2.u.a.226.2		24
123.29	even	40		1681.2.a.m.1.18		24
123.53	even	40		1681.2.a.m.1.17		24
123.62	odd	20		41.2.g.a.21.2	yes	24
492.431	even	20		656.2.bs.d.513.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.2.2	✓	24	3.2	odd	2
41.2.g.a.21.2	yes	24	123.62	odd	20
369.2.u.a.226.2		24	41.21	even	20	inner
369.2.u.a.289.2		24	1.1	even	1	trivial
656.2.bs.d.289.3		24	12.11	even	2
656.2.bs.d.513.3		24	492.431	even	20
1681.2.a.m.1.17		24	123.53	even	40
1681.2.a.m.1.18		24	123.29	even	40

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:	\( N \)	\(=\)	\( 369 = 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	369.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40718 - 0.457221i) q^{2} +(0.153075 - 0.111216i) q^{4} +(0.455161 + 0.626475i) q^{5} +(2.12336 + 4.16732i) q^{7} +(-1.57482 + 2.16755i) q^{8} +O(q^{10})\)	\(q+(1.40718 - 0.457221i) q^{2} +(0.153075 - 0.111216i) q^{4} +(0.455161 + 0.626475i) q^{5} +(2.12336 + 4.16732i) q^{7} +(-1.57482 + 2.16755i) q^{8} +(0.926931 + 0.673455i) q^{10} +(0.538340 - 0.0852647i) q^{11} +(-0.808560 - 0.411982i) q^{13} +(4.89333 + 4.89333i) q^{14} +(-1.34194 + 4.13008i) q^{16} +(-0.937351 - 5.91820i) q^{17} +(3.90401 - 1.98919i) q^{19} +(0.139348 + 0.0452768i) q^{20} +(0.718557 - 0.366123i) q^{22} +(0.323498 + 0.995624i) q^{23} +(1.35979 - 4.18499i) q^{25} +(-1.32616 - 0.210043i) q^{26} +(0.788504 + 0.401763i) q^{28} +(-0.193017 + 1.21866i) q^{29} +(1.22986 + 0.893547i) q^{31} +1.06686i q^{32} +(-4.02495 - 7.89940i) q^{34} +(-1.64425 + 3.22703i) q^{35} +(5.87120 - 4.26568i) q^{37} +(4.58415 - 4.58415i) q^{38} -2.07471 q^{40} +(-6.21116 + 1.55612i) q^{41} +(-5.91654 + 1.92240i) q^{43} +(0.0729237 - 0.0729237i) q^{44} +(0.910440 + 1.25311i) q^{46} +(1.80254 - 3.53768i) q^{47} +(-8.74342 + 12.0343i) q^{49} -6.51076i q^{50} +(-0.169589 + 0.0268603i) q^{52} +(-0.837443 + 5.28741i) q^{53} +(0.298447 + 0.298447i) q^{55} +(-12.3768 - 1.96029i) q^{56} +(0.285587 + 1.80313i) q^{58} +(-2.74251 - 8.44059i) q^{59} +(1.31994 + 0.428873i) q^{61} +(2.13919 + 0.695064i) q^{62} +(-2.19610 - 6.75890i) q^{64} +(-0.109928 - 0.694060i) q^{65} +(-5.56618 - 0.881596i) q^{67} +(-0.801681 - 0.801681i) q^{68} +(-0.838297 + 5.29280i) q^{70} +(1.07629 - 0.170468i) q^{71} -5.61291i q^{73} +(6.31149 - 8.68702i) q^{74} +(0.376378 - 0.738683i) q^{76} +(1.49841 + 2.06239i) q^{77} +(8.62379 - 8.62379i) q^{79} +(-3.19819 + 1.03915i) q^{80} +(-8.02874 + 5.02962i) q^{82} +13.1576 q^{83} +(3.28096 - 3.28096i) q^{85} +(-7.44668 + 5.41033i) q^{86} +(-0.662972 + 1.30116i) q^{88} +(0.885629 + 1.73814i) q^{89} -4.24431i q^{91} +(0.160248 + 0.116427i) q^{92} +(0.918996 - 5.80231i) q^{94} +(3.02313 + 1.54036i) q^{95} +(-1.91879 - 0.303907i) q^{97} +(-6.80125 + 20.9321i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8}+O(q^{10}) \) 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8	\( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8} + 6 q^{10} + 16 q^{11} - 14 q^{14} - 20 q^{16} - 8 q^{17} + 16 q^{19} - 20 q^{20} + 6 q^{22} - 12 q^{23} - 8 q^{25} + 28 q^{26} + 18 q^{28} - 40 q^{29} - 12 q^{31} - 16 q^{34} + 36 q^{35} - 46 q^{38} - 44 q^{40} + 4 q^{41} + 48 q^{44} + 70 q^{46} + 12 q^{47} - 30 q^{49} + 20 q^{52} + 26 q^{53} + 20 q^{55} - 106 q^{56} - 20 q^{58} - 6 q^{59} + 30 q^{61} + 10 q^{62} + 70 q^{64} - 68 q^{65} - 22 q^{67} + 20 q^{68} - 20 q^{70} - 4 q^{71} - 10 q^{74} - 128 q^{76} + 20 q^{77} - 2 q^{79} + 70 q^{80} - 90 q^{82} - 80 q^{83} - 56 q^{85} + 46 q^{86} + 10 q^{88} + 72 q^{89} - 18 q^{94} + 40 q^{95} - 22 q^{97} - 6 q^{98}+O(q^{100}) \) 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8 + 6 * q^10 + 16 * q^11 - 14 * q^14 - 20 * q^16 - 8 * q^17 + 16 * q^19 - 20 * q^20 + 6 * q^22 - 12 * q^23 - 8 * q^25 + 28 * q^26 + 18 * q^28 - 40 * q^29 - 12 * q^31 - 16 * q^34 + 36 * q^35 - 46 * q^38 - 44 * q^40 + 4 * q^41 + 48 * q^44 + 70 * q^46 + 12 * q^47 - 30 * q^49 + 20 * q^52 + 26 * q^53 + 20 * q^55 - 106 * q^56 - 20 * q^58 - 6 * q^59 + 30 * q^61 + 10 * q^62 + 70 * q^64 - 68 * q^65 - 22 * q^67 + 20 * q^68 - 20 * q^70 - 4 * q^71 - 10 * q^74 - 128 * q^76 + 20 * q^77 - 2 * q^79 + 70 * q^80 - 90 * q^82 - 80 * q^83 - 56 * q^85 + 46 * q^86 + 10 * q^88 + 72 * q^89 - 18 * q^94 + 40 * q^95 - 22 * q^97 - 6 * q^98

Introduction

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