LMFDB - Embedded newform 324.2.l.a.71.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(35,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("324.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.l (of order $18$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			71.2
Character	$\chi$	$=$	324.71
Dual form			324.2.l.a.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24669 + 0.667664i) q^{2} +(1.10845 - 1.66473i) q^{4} +(2.12601 - 2.53368i) q^{5} +(-1.10219 + 3.02825i) q^{7} +(-0.270407 + 2.81547i) q^{8} +O(q^{10})$	\(q+(-1.24669 + 0.667664i) q^{2} +(1.10845 - 1.66473i) q^{4} +(2.12601 - 2.53368i) q^{5} +(-1.10219 + 3.02825i) q^{7} +(-0.270407 + 2.81547i) q^{8} +(-0.958821 + 4.57817i) q^{10} +(2.39850 - 2.01258i) q^{11} +(0.431530 - 2.44733i) q^{13} +(-0.647764 - 4.51117i) q^{14} +(-1.54268 - 3.69055i) q^{16} +(-1.16511 - 0.672678i) q^{17} +(5.00336 - 2.88869i) q^{19} +(-1.86133 - 6.34771i) q^{20} +(-1.64645 + 4.11044i) q^{22} +(-2.02346 + 0.736479i) q^{23} +(-1.03138 - 5.84925i) q^{25} +(1.09601 + 3.33916i) q^{26} +(3.81950 + 5.19152i) q^{28} +(7.98578 - 1.40811i) q^{29} +(1.43357 + 3.93870i) q^{31} +(4.38728 + 3.57097i) q^{32} +(1.90165 + 0.0607148i) q^{34} +(5.32935 + 9.23070i) q^{35} +(0.857888 - 1.48590i) q^{37} +(-4.30894 + 6.94185i) q^{38} +(6.55862 + 6.67085i) q^{40} +(-0.757721 - 0.133607i) q^{41} +(-0.738845 - 0.880521i) q^{43} +(-0.691791 - 6.22370i) q^{44} +(2.03090 - 2.26915i) q^{46} +(-2.75778 - 1.00375i) q^{47} +(-2.59316 - 2.17592i) q^{49} +(5.19114 + 6.60356i) q^{50} +(-3.59582 - 3.43112i) q^{52} +2.35375i q^{53} -10.3558i q^{55} +(-8.22791 - 3.92205i) q^{56} +(-9.01562 + 7.08729i) q^{58} +(-3.53187 - 2.96359i) q^{59} +(1.07303 + 0.390550i) q^{61} +(-4.41694 - 3.95318i) q^{62} +(-7.85376 - 1.52265i) q^{64} +(-5.28331 - 6.29641i) q^{65} +(-14.0125 - 2.47079i) q^{67} +(-2.41130 + 1.19397i) q^{68} +(-12.8070 - 7.94957i) q^{70} +(-4.55132 + 7.88312i) q^{71} +(6.23943 + 10.8070i) q^{73} +(-0.0774314 + 2.42524i) q^{74} +(0.737075 - 11.5312i) q^{76} +(3.45098 + 9.48149i) q^{77} +(9.28580 - 1.63734i) q^{79} +(-12.6304 - 3.93750i) q^{80} +(1.03384 - 0.339337i) q^{82} +(-0.863010 - 4.89437i) q^{83} +(-4.18140 + 1.52190i) q^{85} +(1.50900 + 0.604433i) q^{86} +(5.01778 + 7.29711i) q^{88} +(-5.96340 + 3.44297i) q^{89} +(6.93549 + 4.00421i) q^{91} +(-1.01686 + 4.18487i) q^{92} +(4.10826 - 0.589910i) q^{94} +(3.31817 - 18.8183i) q^{95} +(-5.19235 + 4.35690i) q^{97} +(4.68563 + 0.981328i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−1.24669	+	0.667664i	−0.881540	+	0.472110i
$2$	−1.24669	+	0.667664i	−0.881540	+	0.472110i
$3$		0			0
$3$		0			0
$4$	1.10845	−	1.66473i	0.554225	−	0.832367i
$5$	2.12601	−	2.53368i	0.950782	−	1.13310i	−0.0402123	−	0.999191i	$-0.512803\pi$
$5$	2.12601	−	2.53368i	0.950782	−	1.13310i	0.990994	−	0.133906i	$-0.0427521\pi$
$6$		0			0
$7$	−1.10219	+	3.02825i	−0.416590	+	1.14457i	0.537032	+	0.843562i	$0.319546\pi$
$7$	−1.10219	+	3.02825i	−0.416590	+	1.14457i	−0.953621	+	0.301009i	$0.902677\pi$
$8$	−0.270407	+	2.81547i	−0.0956034	+	0.995420i
$9$		0			0
$10$	−0.958821	+	4.57817i	−0.303206	+	1.44774i
$11$	2.39850	−	2.01258i	0.723174	−	0.606815i	−0.205087	−	0.978744i	$-0.565748\pi$
$11$	2.39850	−	2.01258i	0.723174	−	0.606815i	0.928261	+	0.371929i	$0.121303\pi$
$12$		0			0
$13$	0.431530	−	2.44733i	0.119685	−	0.678767i	−0.864639	−	0.502394i	$-0.832453\pi$
$13$	0.431530	−	2.44733i	0.119685	−	0.678767i	0.984324	−	0.176372i	$-0.0564363\pi$
$14$	−0.647764	−	4.51117i	−0.173122	−	1.20566i
$15$		0			0
$16$	−1.54268	−	3.69055i	−0.385669	−	0.922637i
$17$	−1.16511	−	0.672678i	−0.282581	−	0.163148i	0.352010	−	0.935996i	$-0.385498\pi$
$17$	−1.16511	−	0.672678i	−0.282581	−	0.163148i	−0.634591	+	0.772848i	$0.718832\pi$
$18$		0			0
$19$	5.00336	−	2.88869i	1.14785	−	0.662711i	0.199486	−	0.979901i	$-0.436073\pi$
$19$	5.00336	−	2.88869i	1.14785	−	0.662711i	0.948362	+	0.317190i	$0.102739\pi$
$20$	−1.86133	−	6.34771i	−0.416206	−	1.41939i
$21$		0			0
$22$	−1.64645	+	4.11044i	−0.351024	+	0.876349i
$23$	−2.02346	+	0.736479i	−0.421920	+	0.153566i	−0.544250	−	0.838923i	$-0.683186\pi$
$23$	−2.02346	+	0.736479i	−0.421920	+	0.153566i	0.122330	+	0.992490i	$0.460963\pi$
$24$		0			0
$25$	−1.03138	−	5.84925i	−0.206276	−	1.16985i
$26$	1.09601	+	3.33916i	0.214945	+	0.654864i
$27$		0			0
$28$	3.81950	+	5.19152i	0.721818	+	0.981105i
$29$	7.98578	−	1.40811i	1.48292	−	0.261479i	0.627177	−	0.778877i	$-0.284210\pi$
$29$	7.98578	−	1.40811i	1.48292	−	0.261479i	0.855745	+	0.517397i	$0.173099\pi$
$30$		0			0
$31$	1.43357	+	3.93870i	0.257477	+	0.707412i	0.999321	+	0.0368398i	$0.0117291\pi$
$31$	1.43357	+	3.93870i	0.257477	+	0.707412i	−0.741844	+	0.670572i	$0.766049\pi$
$32$	4.38728	+	3.57097i	0.775568	+	0.631264i
$33$		0			0
$34$	1.90165	+	0.0607148i	0.326131	+	0.0104125i
$35$	5.32935	+	9.23070i	0.900824	+	1.56027i
$36$		0			0
$37$	0.857888	−	1.48590i	0.141036	−	0.244281i	−0.786851	−	0.617143i	$-0.788290\pi$
$37$	0.857888	−	1.48590i	0.141036	−	0.244281i	0.927887	+	0.372862i	$0.121623\pi$
$38$	−4.30894	+	6.94185i	−0.699002	+	1.12612i
$39$		0			0
$40$	6.55862	+	6.67085i	1.03701	+	1.05475i
$41$	−0.757721	−	0.133607i	−0.118336	−	0.0208659i	0.114166	−	0.993462i	$-0.463580\pi$
$41$	−0.757721	−	0.133607i	−0.118336	−	0.0208659i	−0.232503	+	0.972596i	$0.574691\pi$
$42$		0			0
$43$	−0.738845	−	0.880521i	−0.112673	−	0.134278i	0.706760	−	0.707453i	$-0.250156\pi$
$43$	−0.738845	−	0.880521i	−0.112673	−	0.134278i	−0.819433	+	0.573175i	$0.805712\pi$
$44$	−0.691791	−	6.22370i	−0.104291	−	0.938258i
$45$		0			0
$46$	2.03090	−	2.26915i	0.299439	−	0.334568i
$47$	−2.75778	−	1.00375i	−0.402264	−	0.146412i	0.132962	−	0.991121i	$-0.457551\pi$
$47$	−2.75778	−	1.00375i	−0.402264	−	0.146412i	−0.535226	+	0.844709i	$0.679774\pi$
$48$		0			0
$49$	−2.59316	−	2.17592i	−0.370451	−	0.310845i
$50$	5.19114	+	6.60356i	0.734137	+	0.933884i
$51$		0			0
$52$	−3.59582	−	3.43112i	−0.498650	−	0.475811i
$53$			2.35375i			0.323312i	0.986847	+	0.161656i	$0.0516835\pi$
$53$			2.35375i			0.323312i	−0.986847	+	0.161656i	$0.948317\pi$
$54$		0			0
$55$		−	10.3558i		−	1.39638i
$56$	−8.22791	−	3.92205i	−1.09950	−	0.524106i
$57$		0			0
$58$	−9.01562	+	7.08729i	−1.18381	+	0.930606i
$59$	−3.53187	−	2.96359i	−0.459810	−	0.385827i	0.383251	−	0.923644i	$-0.374804\pi$
$59$	−3.53187	−	2.96359i	−0.459810	−	0.385827i	−0.843061	+	0.537818i	$0.819249\pi$
$60$		0			0
$61$	1.07303	+	0.390550i	0.137387	+	0.0500048i	0.409799	−	0.912176i	$-0.365599\pi$
$61$	1.07303	+	0.390550i	0.137387	+	0.0500048i	−0.272412	+	0.962181i	$0.587821\pi$
$62$	−4.41694	−	3.95318i	−0.560952	−	0.502055i
$63$		0			0
$64$	−7.85376	−	1.52265i	−0.981720	−	0.190331i
$65$	−5.28331	−	6.29641i	−0.655314	−	0.780973i
$66$		0			0
$67$	−14.0125	−	2.47079i	−1.71190	−	0.301855i	−0.770076	−	0.637952i	$-0.779782\pi$
$67$	−14.0125	−	2.47079i	−1.71190	−	0.301855i	−0.941827	+	0.336097i	$0.890893\pi$
$68$	−2.41130	+	1.19397i	−0.292413	+	0.144790i
$69$		0			0
$70$	−12.8070	−	7.94957i	−1.53073	−	0.950156i
$71$	−4.55132	+	7.88312i	−0.540143	+	0.935554i	0.458753	+	0.888564i	$0.348296\pi$
$71$	−4.55132	+	7.88312i	−0.540143	+	0.935554i	−0.998895	+	0.0469904i	$0.985037\pi$
$72$		0			0
$73$	6.23943	+	10.8070i	0.730270	+	1.26486i	0.956768	+	0.290853i	$0.0939389\pi$
$73$	6.23943	+	10.8070i	0.730270	+	1.26486i	−0.226498	+	0.974012i	$0.572728\pi$
$74$	−0.0774314	+	2.42524i	−0.00900122	+	0.281928i
$75$		0			0
$76$	0.737075	−	11.5312i	0.0845483	−	1.32272i
$77$	3.45098	+	9.48149i	0.393276	+	1.08052i
$78$		0			0
$79$	9.28580	−	1.63734i	1.04473	−	0.184215i	0.375160	−	0.926960i	$-0.377588\pi$
$79$	9.28580	−	1.63734i	1.04473	−	0.184215i	0.669574	+	0.742745i	$0.266477\pi$
$80$	−12.6304	−	3.93750i	−1.41212	−	0.440226i
$81$		0			0
$82$	1.03384	−	0.339337i	0.114169	−	0.0374735i
$83$	−0.863010	−	4.89437i	−0.0947277	−	0.537227i	−0.994830	−	0.101550i	$-0.967620\pi$
$83$	−0.863010	−	4.89437i	−0.0947277	−	0.537227i	0.900103	−	0.435678i	$-0.143491\pi$
$84$		0			0
$85$	−4.18140	+	1.52190i	−0.453536	+	0.165074i
$86$	1.50900	+	0.604433i	0.162720	+	0.0651777i
$87$		0			0
$88$	5.01778	+	7.29711i	0.534898	+	0.777875i
$89$	−5.96340	+	3.44297i	−0.632119	+	0.364954i	−0.781572	−	0.623815i	$-0.785582\pi$
$89$	−5.96340	+	3.44297i	−0.632119	+	0.364954i	0.149454	+	0.988769i	$0.452249\pi$
$90$		0			0
$91$	6.93549	+	4.00421i	0.727037	+	0.419755i
$92$	−1.01686	+	4.18487i	−0.106015	+	0.436303i
$93$		0			0
$94$	4.10826	−	0.589910i	0.423735	−	0.0608446i
$95$	3.31817	−	18.8183i	0.340438	−	1.93072i
$96$		0			0
$97$	−5.19235	+	4.35690i	−0.527204	+	0.442376i	−0.867135	−	0.498074i	$-0.834041\pi$
$97$	−5.19235	+	4.35690i	−0.527204	+	0.442376i	0.339931	+	0.940450i	$0.389596\pi$
$98$	4.68563	+	0.981328i	0.473320	+	0.0991291i
$99$		0			0
$100$	−10.8807	−	4.76663i	−1.08807	−	0.476663i
$101$	−4.03614	+	11.0892i	−0.401611	+	1.10342i	0.559879	+	0.828575i	$0.310848\pi$
$101$	−4.03614	+	11.0892i	−0.401611	+	1.10342i	−0.961489	+	0.274842i	$0.911375\pi$
$102$		0			0
$103$	−7.36980	+	8.78299i	−0.726168	+	0.865414i	−0.995215	−	0.0977135i	$-0.968847\pi$
$103$	−7.36980	+	8.78299i	−0.726168	+	0.865414i	0.269046	+	0.963127i	$0.413292\pi$
$104$	6.77369	+	1.87673i	0.664215	+	0.184029i
$105$		0			0
$106$	−1.57151	−	2.93438i	−0.152639	−	0.285012i
$107$	4.97436			0.480889			0.240445	−	0.970663i	$-0.422707\pi$
$107$	4.97436			0.480889			0.240445	+	0.970663i	$0.422707\pi$
$108$		0			0
$109$	−14.8006			−1.41764			−0.708818	−	0.705391i	$-0.750771\pi$
$109$	−14.8006			−1.41764			−0.708818	+	0.705391i	$0.750771\pi$
$110$	6.91419	+	12.9104i	0.659242	+	1.23096i
$111$		0			0
$112$	12.8762	−	0.603910i	1.21669	−	0.0570641i
$113$	6.53179	−	7.78429i	0.614459	−	0.732284i	−0.365648	−	0.930753i	$-0.619152\pi$
$113$	6.53179	−	7.78429i	0.614459	−	0.732284i	0.980107	+	0.198469i	$0.0635969\pi$
$114$		0			0
$115$	−2.43589	+	6.69257i	−0.227148	+	0.624085i
$116$	6.50772	−	14.8550i	0.604226	−	1.37925i
$117$		0			0
$118$	6.38181	+	1.33656i	0.587493	+	0.123041i
$119$	3.32122	−	2.78683i	0.304456	−	0.255469i
$120$		0			0
$121$	−0.207813	+	1.17857i	−0.0188921	+	0.107142i
$122$	−1.59848	+	0.229528i	−0.144720	+	0.0207805i
$123$		0			0
$124$	8.14593	+	1.97934i	0.731526	+	0.177750i
$125$	−2.69102	−	1.55366i	−0.240692	−	0.138963i
$126$		0			0
$127$	−5.89940	+	3.40602i	−0.523487	+	0.302235i	−0.738360	−	0.674407i	$-0.764399\pi$
$127$	−5.89940	+	3.40602i	−0.523487	+	0.302235i	0.214873	+	0.976642i	$0.431066\pi$
$128$	10.8078	−	3.34541i	0.955282	−	0.295695i
$129$		0			0
$130$	10.7905	+	4.32217i	0.946391	+	0.379079i
$131$	−19.4933	+	7.09499i	−1.70314	+	0.619892i	−0.996177	−	0.0873587i	$-0.972157\pi$
$131$	−19.4933	+	7.09499i	−1.70314	+	0.619892i	−0.706963	+	0.707251i	$0.749935\pi$
$132$		0			0
$133$	3.23301	+	18.3353i	0.280337	+	1.58987i
$134$	19.1189	−	6.27536i	1.65162	−	0.542109i
$135$		0			0
$136$	2.20896	−	3.09845i	0.189417	−	0.265690i
$137$	−10.5875	+	1.86687i	−0.904555	+	0.159497i	−0.606530	−	0.795061i	$-0.707439\pi$
$137$	−10.5875	+	1.86687i	−0.904555	+	0.159497i	−0.298025	+	0.954558i	$0.596328\pi$
$138$		0			0
$139$	−4.19427	−	11.5237i	−0.355753	−	0.977425i	−0.980487	−	0.196586i	$-0.937014\pi$
$139$	−4.19427	−	11.5237i	−0.355753	−	0.977425i	0.624733	−	0.780838i	$-0.285208\pi$
$140$	21.2740	+	1.35983i	1.79798	+	0.114927i
$141$		0			0
$142$	0.410794	−	12.8665i	0.0344731	−	1.07973i
$143$	−3.89041	−	6.73839i	−0.325333	−	0.563493i
$144$		0			0
$145$	13.4102	−	23.2271i	1.11365	−	1.92891i
$146$	−14.9940	−	9.30710i	−1.24092	−	0.770261i
$147$		0			0
$148$	−1.52271	−	3.07521i	−0.125166	−	0.252780i
$149$	−15.8663	−	2.79766i	−1.29982	−	0.229193i	−0.519444	−	0.854504i	$-0.673861\pi$
$149$	−15.8663	−	2.79766i	−1.29982	−	0.229193i	−0.780376	+	0.625311i	$0.784972\pi$
$150$		0			0
$151$	7.56244	+	9.01257i	0.615423	+	0.733432i	0.980276	−	0.197633i	$-0.0633254\pi$
$151$	7.56244	+	9.01257i	0.615423	+	0.733432i	−0.364853	+	0.931065i	$0.618881\pi$
$152$	6.78008	+	14.8679i	0.549937	+	1.20595i
$153$		0			0
$154$	−10.6327	−	9.51635i	−0.856811	−	0.766849i
$155$	13.0272	+	4.74152i	1.04637	+	0.380848i
$156$		0			0
$157$	2.23343	+	1.87407i	0.178247	+	0.149567i	0.727546	−	0.686059i	$-0.240661\pi$
$157$	2.23343	+	1.87407i	0.178247	+	0.149567i	−0.549299	+	0.835626i	$0.685105\pi$
$158$	−10.4833	+	8.24104i	−0.834006	+	0.655622i
$159$		0			0
$160$	18.3751	−	3.52405i	1.45268	−	0.278601i
$161$		−	6.93928i		−	0.546892i
$162$		0			0
$163$		−	5.87169i		−	0.459906i	−0.973202	−	0.229953i	$-0.926143\pi$
$163$		−	5.87169i		−	0.459906i	0.973202	−	0.229953i	$-0.0738573\pi$
$164$	−1.06232	+	1.11331i	−0.0829529	+	0.0869347i
$165$		0			0
$166$	4.34370	+	5.52555i	0.337136	+	0.428866i
$167$	11.4565	+	9.61313i	0.886529	+	0.743886i	0.967511	−	0.252829i	$-0.0813610\pi$
$167$	11.4565	+	9.61313i	0.886529	+	0.743886i	−0.0809815	+	0.996716i	$0.525805\pi$
$168$		0			0
$169$	6.41281	+	2.33407i	0.493293	+	0.179544i
$170$	4.19677	−	4.68911i	0.321878	−	0.359638i
$171$		0			0
$172$	−2.28481	+	0.253966i	−0.174215	+	0.0193647i
$173$	11.9103	+	14.1942i	0.905525	+	1.07916i	0.996524	+	0.0833113i	$0.0265496\pi$
$173$	11.9103	+	14.1942i	0.905525	+	1.07916i	−0.0909989	+	0.995851i	$0.529006\pi$
$174$		0			0
$175$	18.8498	+	3.32372i	1.42491	+	0.251250i
$176$	−11.1276	−	5.74702i	−0.838776	−	0.433198i
$177$		0			0
$178$	5.13573	−	8.27384i	0.384940	−	0.620151i
$179$	2.24925	−	3.89581i	0.168117	−	0.291186i	−0.769641	−	0.638477i	$-0.779565\pi$
$179$	2.24925	−	3.89581i	0.168117	−	0.291186i	0.937758	+	0.347290i	$0.112898\pi$
$180$		0			0
$181$	11.1009	+	19.2272i	0.825120	+	1.42915i	0.901827	+	0.432096i	$0.142226\pi$
$181$	11.1009	+	19.2272i	0.825120	+	1.42915i	−0.0767073	+	0.997054i	$0.524441\pi$
$182$	−11.3198	−	0.361413i	−0.839082	−	0.0267897i
$183$		0			0
$184$	−1.52638	−	5.89614i	−0.112526	−	0.434669i
$185$	−1.94093	−	5.33267i	−0.142700	−	0.392066i
$186$		0			0
$187$	−4.14834	+	0.731464i	−0.303356	+	0.0534899i
$188$	−4.72785	+	3.47837i	−0.344814	+	0.253686i
$189$		0			0
$190$	8.42758	+	25.6759i	0.611401	+	1.86273i
$191$	0.0574829	+	0.326002i	0.00415932	+	0.0235887i	0.986817	−	0.161841i	$-0.0517433\pi$
$191$	0.0574829	+	0.326002i	0.00415932	+	0.0235887i	−0.982657	+	0.185430i	$0.940632\pi$
$192$		0			0
$193$	13.1159	−	4.77380i	0.944103	−	0.343625i	0.176318	−	0.984333i	$-0.443581\pi$
$193$	13.1159	−	4.77380i	0.944103	−	0.343625i	0.767785	+	0.640708i	$0.221359\pi$
$194$	3.56429	−	8.89843i	0.255901	−	0.638870i
$195$		0			0
$196$	−6.49671	+	1.90502i	−0.464051	+	0.136073i
$197$	6.02393	−	3.47792i	0.429187	−	0.247791i	−0.269813	−	0.962913i	$-0.586962\pi$
$197$	6.02393	−	3.47792i	0.429187	−	0.247791i	0.699000	+	0.715121i	$0.253629\pi$
$198$		0			0
$199$	−11.9269	−	6.88598i	−0.845473	−	0.488134i	0.0136479	−	0.999907i	$-0.495656\pi$
$199$	−11.9269	−	6.88598i	−0.845473	−	0.488134i	−0.859121	+	0.511773i	$0.828989\pi$
$200$	16.7473	−	1.32214i	1.18421	−	0.0934896i
$201$		0			0
$202$	−2.37206	−	16.5195i	−0.166897	−	1.16231i
$203$	−4.53777	+	25.7349i	−0.318489	+	1.80624i
$204$		0			0
$205$	−1.94944	+	1.63578i	−0.136155	+	0.114248i
$206$	3.32375	−	15.8702i	0.231576	−	1.10573i
$207$		0			0
$208$	−9.69769	+	2.18285i	−0.672414	+	0.151353i
$209$	6.18682	−	16.9981i	0.427951	−	1.17579i
$210$		0			0
$211$	1.91739	−	2.28505i	0.131998	−	0.157310i	−0.695997	−	0.718045i	$-0.745037\pi$
$211$	1.91739	−	2.28505i	0.131998	−	0.157310i	0.827995	+	0.560736i	$0.189482\pi$
$212$	3.91836	+	2.60901i	0.269114	+	0.179188i
$213$		0			0
$214$	−6.20146	+	3.32120i	−0.423923	+	0.227032i
$215$	−3.80176			−0.259278
$216$		0			0
$217$	−13.5074			−0.916945
$218$	18.4516	−	9.88180i	1.24970	−	0.669280i
$219$		0			0
$220$	−17.2396	−	11.4789i	−1.16230	−	0.773906i
$221$	−2.14905	+	2.56113i	−0.144560	+	0.172280i
$222$		0			0
$223$	−0.347617	+	0.955070i	−0.0232782	+	0.0639562i	−0.950787	−	0.309844i	$-0.899723\pi$
$223$	−0.347617	+	0.955070i	−0.0232782	+	0.0639562i	0.927509	+	0.373800i	$0.121945\pi$
$224$	−15.6494	+	9.34988i	−1.04562	+	0.624715i
$225$		0			0
$226$	−2.94581	+	14.0656i	−0.195952	+	0.935630i
$227$	13.4856	−	11.3158i	0.895073	−	0.751056i	−0.0741477	−	0.997247i	$-0.523624\pi$
$227$	13.4856	−	11.3158i	0.895073	−	0.751056i	0.969221	+	0.246191i	$0.0791792\pi$
$228$		0			0
$229$	−1.90332	+	10.7943i	−0.125775	+	0.713307i	0.855069	+	0.518514i	$0.173515\pi$
$229$	−1.90332	+	10.7943i	−0.125775	+	0.713307i	−0.980844	+	0.194793i	$0.937597\pi$
$230$	−1.43159	−	9.96989i	−0.0943961	−	0.657395i
$231$		0			0
$232$	1.80508	+	22.8645i	0.118509	+	1.50113i
$233$	5.10213	+	2.94572i	0.334252	+	0.192980i	0.657727	−	0.753256i	$-0.271518\pi$
$233$	5.10213	+	2.94572i	0.334252	+	0.192980i	−0.323476	+	0.946237i	$0.604851\pi$
$234$		0			0
$235$	−8.40627	+	4.85336i	−0.548365	+	0.316599i
$236$	−8.84849	+	2.59463i	−0.575988	+	0.168896i
$237$		0			0
$238$	−2.27985	+	5.69176i	−0.147781	+	0.368942i
$239$	1.13809	−	0.414231i	0.0736169	−	0.0267943i	−0.304949	−	0.952369i	$-0.598639\pi$
$239$	1.13809	−	0.414231i	0.0736169	−	0.0267943i	0.378566	+	0.925574i	$0.376417\pi$
$240$		0			0
$241$	−4.18206	−	23.7176i	−0.269390	−	1.52779i	−0.756236	−	0.654299i	$-0.772964\pi$
$241$	−4.18206	−	23.7176i	−0.269390	−	1.52779i	0.486846	−	0.873488i	$-0.338147\pi$
$242$	−0.527808	−	1.60805i	−0.0339288	−	0.103369i
$243$		0			0
$244$	1.83956	−	1.35340i	0.117766	−	0.0866424i
$245$	−11.0262	+	1.94421i	−0.704436	+	0.124211i
$246$		0			0
$247$	−4.91047	−	13.4914i	−0.312446	−	0.858437i
$248$	−11.4770	+	2.97112i	−0.728787	+	0.188667i
$249$		0			0
$250$	4.39217	+	0.140231i	0.277785	+	0.00886896i
$251$	−9.35066	−	16.1958i	−0.590208	−	1.02227i	−0.994204	−	0.107510i	$-0.965712\pi$
$251$	−9.35066	−	16.1958i	−0.590208	−	1.02227i	0.403996	−	0.914761i	$-0.367621\pi$
$252$		0			0
$253$	−3.37104	+	5.83881i	−0.211935	+	0.367083i
$254$	5.08062	−	8.18505i	0.318786	−	0.513576i
$255$		0			0
$256$	−11.2403	+	11.3866i	−0.702519	+	0.711665i
$257$	−12.8978	−	2.27423i	−0.804541	−	0.141862i	−0.243770	−	0.969833i	$-0.578384\pi$
$257$	−12.8978	−	2.27423i	−0.804541	−	0.141862i	−0.560771	+	0.827971i	$0.689495\pi$
$258$		0			0
$259$	3.55413	+	4.23565i	0.220843	+	0.263191i
$260$	−16.3381	+	1.81605i	−1.01325	+	0.112627i
$261$		0			0
$262$	19.5650	−	21.8602i	1.20873	−	1.35053i
$263$	−0.704065	−	0.256259i	−0.0434145	−	0.0158016i	0.320222	−	0.947343i	$-0.396243\pi$
$263$	−0.704065	−	0.256259i	−0.0434145	−	0.0158016i	−0.363636	+	0.931541i	$0.618465\pi$
$264$		0			0
$265$	5.96365	+	5.00409i	0.366344	+	0.307399i
$266$	−16.2724	−	20.6998i	−0.997722	−	1.26919i
$267$		0			0
$268$	−19.6454	+	20.5884i	−1.20003	+	1.25764i
$269$			12.1479i			0.740673i	0.928898	+	0.370337i	$0.120758\pi$
$269$			12.1479i			0.740673i	−0.928898	+	0.370337i	$0.879242\pi$
$270$		0			0
$271$			3.15453i			0.191624i	0.995399	+	0.0958120i	$0.0305448\pi$
$271$			3.15453i			0.191624i	−0.995399	+	0.0958120i	$0.969455\pi$
$272$	−0.685161	+	5.33763i	−0.0415440	+	0.323641i
$273$		0			0
$274$	11.9529	−	9.39631i	0.722101	−	0.567652i
$275$	−14.2458	−	11.9537i	−0.859055	−	0.720833i
$276$		0			0
$277$	−31.1453	−	11.3360i	−1.87134	−	0.681113i	−0.967280	−	0.253712i	$-0.918348\pi$
$277$	−31.1453	−	11.3360i	−1.87134	−	0.681113i	−0.904062	−	0.427401i	$-0.859429\pi$
$278$	12.9229	+	11.5660i	0.775062	+	0.693684i
$279$		0			0
$280$	−27.4299	+	12.5086i	−1.63925	+	0.747531i
$281$	12.2090	+	14.5502i	0.728330	+	0.867990i	0.995412	−	0.0956839i	$-0.0305038\pi$
$281$	12.2090	+	14.5502i	0.728330	+	0.867990i	−0.267082	+	0.963674i	$0.586059\pi$
$282$		0			0
$283$	−5.92754	−	1.04519i	−0.352356	−	0.0621298i	−0.00533091	−	0.999986i	$-0.501697\pi$
$283$	−5.92754	−	1.04519i	−0.352356	−	0.0621298i	−0.347025	+	0.937856i	$0.612808\pi$
$284$	8.07838	+	16.3148i	0.479364	+	0.968104i
$285$		0			0
$286$	9.34910	+	5.80317i	0.552824	+	0.343149i
$287$	1.23975	−	2.14731i	0.0731801	−	0.126752i
$288$		0			0
$289$	−7.59501	−	13.1549i	−0.446765	−	0.773820i
$290$	−1.21038	+	37.9104i	−0.0710759	+	2.22617i
$291$		0			0
$292$	24.9069	+	1.59205i	1.45756	+	0.0931674i
$293$	1.87431	+	5.14962i	0.109498	+	0.300844i	0.982324	−	0.187188i	$-0.0599373\pi$
$293$	1.87431	+	5.14962i	0.109498	+	0.300844i	−0.872826	+	0.488032i	$0.837715\pi$
$294$		0			0
$295$	−15.0176	+	2.64801i	−0.874358	+	0.154173i
$296$	3.95154	+	2.81716i	0.229679	+	0.163744i
$297$		0			0
$298$	21.6482	−	7.10556i	1.25405	−	0.411614i
$299$	0.929222	+	5.26988i	0.0537383	+	0.304765i
$300$		0			0
$301$	3.48079	−	1.26690i	0.200629	−	0.0730231i
$302$	−15.4453	−	6.18667i	−0.888780	−	0.356003i
$303$		0			0
$304$	−18.3794	−	14.0088i	−1.05413	−	0.803461i
$305$	3.27080	−	1.88840i	0.187285	−	0.108129i
$306$		0			0
$307$	27.0184	+	15.5991i	1.54202	+	0.890287i	0.998711	+	0.0507556i	$0.0161630\pi$
$307$	27.0184	+	15.5991i	1.54202	+	0.890287i	0.543311	+	0.839531i	$0.317170\pi$
$308$	19.6094	+	4.76480i	1.11735	+	0.271500i
$309$		0			0
$310$	−19.4066	+	2.78662i	−1.10222	+	0.158269i
$311$	1.72377	−	9.77599i	0.0977461	−	0.554346i	−0.896125	−	0.443802i	$-0.853630\pi$
$311$	1.72377	−	9.77599i	0.0977461	−	0.554346i	0.993871	−	0.110544i	$-0.0352594\pi$
$312$		0			0
$313$	7.70712	−	6.46704i	0.435632	−	0.365539i	−0.398440	−	0.917195i	$-0.630448\pi$
$313$	7.70712	−	6.46704i	0.435632	−	0.365539i	0.834072	+	0.551656i	$0.186004\pi$
$314$	−4.03564	−	0.845197i	−0.227744	−	0.0476972i
$315$		0			0
$316$	7.56712	−	17.2733i	0.425684	−	0.971699i
$317$	3.97784	−	10.9290i	0.223418	−	0.613835i	−0.776449	−	0.630181i	$-0.782981\pi$
$317$	3.97784	−	10.9290i	0.223418	−	0.613835i	0.999866	+	0.0163452i	$0.00520308\pi$
$318$		0			0
$319$	16.3199	−	19.4493i	0.913741	−	1.08895i
$320$	−20.5551	+	16.6618i	−1.14906	+	0.931421i
$321$		0			0
$322$	4.63311	+	8.65110i	0.258193	+	0.482107i
$323$	−7.77263			−0.432481
$324$		0			0
$325$	−14.7601			−0.818742
$326$	3.92032	+	7.32016i	0.217126	+	0.405426i
$327$		0			0
$328$	0.581059	−	2.09721i	0.0320836	−	0.115799i
$329$	6.07922	−	7.24493i	0.335158	−	0.399426i
$330$		0			0
$331$	12.1348	−	33.3401i	0.666990	−	1.83254i	0.124996	−	0.992157i	$-0.460108\pi$
$331$	12.1348	−	33.3401i	0.666990	−	1.83254i	0.541994	−	0.840382i	$-0.317670\pi$
$332$	−9.10443	−	3.98849i	−0.499671	−	0.218897i
$333$		0			0
$334$	−20.7010	−	4.33548i	−1.13271	−	0.237227i
$335$	−36.0510	+	30.2504i	−1.96968	+	1.65276i
$336$		0			0
$337$	5.38292	−	30.5280i	0.293226	−	1.66297i	−0.381099	−	0.924534i	$-0.624454\pi$
$337$	5.38292	−	30.5280i	0.293226	−	1.66297i	0.674325	−	0.738434i	$-0.264435\pi$
$338$	−9.55313	+	1.37175i	−0.519622	+	0.0746132i
$339$		0			0
$340$	−2.10131	+	8.64787i	−0.113959	+	0.468997i
$341$	11.3654	+	6.56179i	0.615469	+	0.355341i
$342$		0			0
$343$	−10.0886	+	5.82464i	−0.544732	+	0.314501i
$344$	2.67887	−	1.84210i	0.144435	−	0.0993193i
$345$		0			0
$346$	−24.3254	−	9.74357i	−1.30774	−	0.523818i
$347$	24.4947	−	8.91533i	1.31494	−	0.478600i	0.413108	−	0.910682i	$-0.364443\pi$
$347$	24.4947	−	8.91533i	1.31494	−	0.478600i	0.901834	+	0.432082i	$0.142221\pi$
$348$		0			0
$349$	4.05398	+	22.9913i	0.217005	+	1.23069i	0.877394	+	0.479771i	$0.159280\pi$
$349$	4.05398	+	22.9913i	0.217005	+	1.23069i	−0.660389	+	0.750924i	$0.729609\pi$
$350$	−25.7188	+	8.44166i	−1.37473	+	0.451226i
$351$		0			0
$352$	17.7097	−	0.264784i	0.943931	−	0.0141131i
$353$	8.13236	−	1.43395i	0.432842	−	0.0763217i	0.0470178	−	0.998894i	$-0.485028\pi$
$353$	8.13236	−	1.43395i	0.432842	−	0.0763217i	0.385824	+	0.922572i	$0.373917\pi$
$354$		0			0
$355$	10.2972	+	28.2912i	0.546517	+	1.50154i
$356$	−0.878504	+	13.7438i	−0.0465606	+	0.728421i
$357$		0			0
$358$	−0.203013	+	6.35859i	−0.0107296	+	0.336062i
$359$	15.4150	+	26.6995i	0.813571	+	1.40915i	0.910350	+	0.413840i	$0.135813\pi$
$359$	15.4150	+	26.6995i	0.813571	+	1.40915i	−0.0967792	+	0.995306i	$0.530854\pi$
$360$		0			0
$361$	7.18904	−	12.4518i	0.378371	−	0.655357i
$362$	−26.6766	−	16.5587i	−1.40209	−	0.870306i
$363$		0			0
$364$	14.3536	−	7.10728i	0.752332	−	0.372523i
$365$	40.6466	+	7.16710i	2.12754	+	0.375143i
$366$		0			0
$367$	−7.90487	−	9.42065i	−0.412631	−	0.491754i	0.519197	−	0.854654i	$-0.326231\pi$
$367$	−7.90487	−	9.42065i	−0.412631	−	0.491754i	−0.931828	+	0.362900i	$0.881787\pi$
$368$	5.83955	+	6.33153i	0.304408	+	0.330054i
$369$		0			0
$370$	5.98016	+	5.35227i	0.310894	+	0.278251i
$371$	−7.12773	−	2.59428i	−0.370053	−	0.134688i
$372$		0			0
$373$	−8.36649	−	7.02032i	−0.433200	−	0.363498i	0.399957	−	0.916534i	$-0.369025\pi$
$373$	−8.36649	−	7.02032i	−0.433200	−	0.363498i	−0.833158	+	0.553035i	$0.813469\pi$
$374$	4.68330	−	3.68160i	0.242168	−	0.190371i
$375$		0			0
$376$	3.57176	−	7.49304i	0.184199	−	0.386424i
$377$		−	20.1515i		−	1.03785i
$378$		0			0
$379$			33.4481i			1.71811i	0.511880	+	0.859057i	$0.328949\pi$
$379$			33.4481i			1.71811i	−0.511880	+	0.859057i	$0.671051\pi$
$380$	−27.6494	−	26.3830i	−1.41839	−	1.35342i
$381$		0			0
$382$	−0.289323	−	0.368043i	−0.0148030	−	0.0188307i
$383$	24.5248	+	20.5787i	1.25316	+	1.05152i	0.996376	+	0.0850541i	$0.0271063\pi$
$383$	24.5248	+	20.5787i	1.25316	+	1.05152i	0.256781	+	0.966470i	$0.417338\pi$
$384$		0			0
$385$	31.3599	+	11.4141i	1.59825	+	0.581715i
$386$	−13.1641	+	14.7084i	−0.670036	+	0.748640i
$387$		0			0
$388$	1.49761	+	13.4733i	0.0760299	+	0.684003i
$389$	−19.4388	−	23.1663i	−0.985588	−	1.17458i	−0.984643	−	0.174579i	$-0.944144\pi$
$389$	−19.4388	−	23.1663i	−0.985588	−	1.17458i	−0.000945326	−	1.00000i	$-0.500301\pi$
$390$		0			0
$391$	2.85297	+	0.503056i	0.144281	+	0.0254406i
$392$	6.82744	−	6.71258i	0.344838	−	0.339036i
$393$		0			0
$394$	−5.18787	+	8.35783i	−0.261361	+	0.421062i
$395$	15.5932	−	27.0083i	0.784581	−	1.35893i
$396$		0			0
$397$	1.26408	+	2.18945i	0.0634424	+	0.109885i	0.896002	−	0.444050i	$-0.146459\pi$
$397$	1.26408	+	2.18945i	0.0634424	+	0.109885i	−0.832560	+	0.553935i	$0.813125\pi$
$398$	19.4666	+	0.621516i	0.975771	+	0.0311538i
$399$		0			0
$400$	−19.9958	+	12.8298i	−0.999792	+	0.641492i
$401$	−0.174473	−	0.479359i	−0.00871274	−	0.0239381i	0.935260	−	0.353961i	$-0.115166\pi$
$401$	−0.174473	−	0.479359i	−0.00871274	−	0.0239381i	−0.943973	+	0.330023i	$0.892943\pi$
$402$		0			0
$403$	10.2579	−	1.80875i	0.510984	−	0.0901002i
$404$	13.9867	+	19.0109i	0.695864	+	0.945828i
$405$		0			0
$406$	−11.5251	−	35.1131i	−0.571982	−	1.74263i
$407$	−0.932858	−	5.29050i	−0.0462401	−	0.262240i
$408$		0			0
$409$	−24.4824	+	8.91086i	−1.21058	+	0.440614i	−0.866904	−	0.498476i	$-0.833893\pi$
$409$	−24.4824	+	8.91086i	−1.21058	+	0.440614i	−0.343672	+	0.939090i	$0.611671\pi$
$410$	1.33819	−	3.34087i	0.0660887	−	0.164994i
$411$		0			0
$412$	6.45228	+	22.0043i	0.317881	+	1.08407i
$413$	12.8673	−	7.42893i	0.633158	−	0.365554i
$414$		0			0
$415$	−14.2356	−	8.21891i	−0.698796	−	0.403450i
$416$	10.6326	−	9.19612i	0.521304	−	0.450877i
$417$		0			0
$418$	3.63603	+	25.3221i	0.177844	+	1.23854i
$419$	0.510419	−	2.89473i	0.0249356	−	0.141417i	−0.969798	−	0.243908i	$-0.921570\pi$
$419$	0.510419	−	2.89473i	0.0249356	−	0.141417i	0.994734	+	0.102492i	$0.0326815\pi$
$420$		0			0
$421$	28.4621	−	23.8826i	1.38716	−	1.16396i	0.420684	−	0.907207i	$-0.361790\pi$
$421$	28.4621	−	23.8826i	1.38716	−	1.16396i	0.966476	−	0.256758i	$-0.0826542\pi$
$422$	−0.864732	+	4.12891i	−0.0420945	+	0.200992i
$423$		0			0
$424$	−6.62691	−	0.636470i	−0.321831	−	0.0309097i
$425$	−2.73299	+	7.50882i	−0.132569	+	0.364231i
$426$		0			0
$427$	−2.36536	+	2.81893i	−0.114468	+	0.136418i
$428$	5.51383	−	8.28098i	0.266521	−	0.400276i
$429$		0			0
$430$	4.73959	−	2.53829i	0.228564	−	0.122407i
$431$	4.47060			0.215341			0.107671	−	0.994187i	$-0.465661\pi$
$431$	4.47060			0.215341			0.107671	+	0.994187i	$0.465661\pi$
$432$		0			0
$433$	−12.4529			−0.598448			−0.299224	−	0.954183i	$-0.596728\pi$
$433$	−12.4529			−0.598448			−0.299224	+	0.954183i	$0.596728\pi$
$434$	16.8395	−	9.01843i	0.808324	−	0.432899i
$435$		0			0
$436$	−16.4057	+	24.6390i	−0.785690	+	1.17999i
$437$	−7.99663	+	9.53001i	−0.382530	+	0.455882i
$438$		0			0
$439$	2.78433	−	7.64989i	0.132889	−	0.365109i	−0.855345	−	0.518059i	$-0.826655\pi$
$439$	2.78433	−	7.64989i	0.132889	−	0.365109i	0.988234	+	0.152949i	$0.0488771\pi$
$440$	29.1564	+	2.80028i	1.38998	+	0.133498i
$441$		0			0
$442$	0.969209	−	4.62777i	0.0461006	−	0.220120i
$443$	−24.2213	+	20.3241i	−1.15079	+	0.965626i	−0.999738	−	0.0229004i	$-0.992710\pi$
$443$	−24.2213	+	20.3241i	−1.15079	+	0.965626i	−0.151050	+	0.988526i	$0.548266\pi$
$444$		0			0
$445$	−3.95486	+	22.4291i	−0.187479	+	1.06324i
$446$	−0.204296	−	1.42276i	−0.00967372	−	0.0673698i
$447$		0			0
$448$	13.2673	−	22.1049i	0.626822	−	1.04436i
$449$	−14.0496	−	8.11155i	−0.663042	−	0.382808i	0.130393	−	0.991462i	$-0.458376\pi$
$449$	−14.0496	−	8.11155i	−0.663042	−	0.382808i	−0.793435	+	0.608655i	$0.791709\pi$
$450$		0			0
$451$	−2.08629	+	1.20452i	−0.0982394	+	0.0567185i
$452$	−5.71860	−	19.5022i	−0.268980	−	0.917306i
$453$		0			0
$454$	−9.25721	+	23.1111i	−0.434462	+	1.08466i
$455$	24.8903	−	9.05934i	1.16688	−	0.424708i
$456$		0			0
$457$	0.612177	+	3.47183i	0.0286364	+	0.162405i	0.995772	−	0.0918543i	$-0.0292794\pi$
$457$	0.612177	+	3.47183i	0.0286364	+	0.162405i	−0.967136	+	0.254259i	$0.918168\pi$
$458$	−4.83411	−	14.7279i	−0.225883	−	0.688188i
$459$		0			0
$460$	8.44127	+	11.4735i	0.393576	+	0.534954i
$461$	2.72997	−	0.481368i	0.127147	−	0.0224195i	−0.109712	−	0.993963i	$-0.534993\pi$
$461$	2.72997	−	0.481368i	0.127147	−	0.0224195i	0.236860	+	0.971544i	$0.423882\pi$
$462$		0			0
$463$	8.26603	+	22.7107i	0.384155	+	1.05546i	0.969589	+	0.244737i	$0.0787017\pi$
$463$	8.26603	+	22.7107i	0.384155	+	1.05546i	−0.585435	+	0.810720i	$0.699076\pi$
$464$	−17.5162	−	27.2997i	−0.813167	−	1.26736i
$465$		0			0
$466$	−8.32750	−	0.265875i	−0.385764	−	0.0123164i
$467$	−17.5430	−	30.3853i	−0.811793	−	1.40607i	−0.911608	−	0.411060i	$-0.865159\pi$
$467$	−17.5430	−	30.3853i	−0.811793	−	1.40607i	0.0998155	−	0.995006i	$-0.468175\pi$
$468$		0			0
$469$	22.9267	−	39.7102i	1.05866	−	1.83365i
$470$	7.23956	−	11.6632i	0.333936	−	0.537982i
$471$		0			0
$472$	9.29894	−	9.14250i	0.428019	−	0.420818i
$473$	−3.54423	−	0.624944i	−0.162964	−	0.0287350i
$474$		0			0
$475$	−22.0570	−	26.2865i	−1.01204	−	1.20611i
$476$	−0.957928	−	8.61801i	−0.0439066	−	0.395006i
$477$		0			0
$478$	−1.14227	+	1.27628i	−0.0522463	+	0.0583755i
$479$	−25.9687	−	9.45185i	−1.18654	−	0.431866i	−0.328034	−	0.944666i	$-0.606386\pi$
$479$	−25.9687	−	9.45185i	−1.18654	−	0.431866i	−0.858508	+	0.512800i	$0.828608\pi$
$480$		0			0
$481$	−3.26629	−	2.74074i	−0.148930	−	0.124967i
$482$	21.0491	+	26.7762i	0.958760	+	1.21962i
$483$		0			0
$484$	1.73165	+	1.65234i	0.0787113	+	0.0751061i
$485$			22.4186i			1.01798i
$486$		0			0
$487$		−	23.0253i		−	1.04338i	−0.853136	−	0.521688i	$-0.825302\pi$
$487$		−	23.0253i		−	1.04338i	0.853136	−	0.521688i	$-0.174698\pi$
$488$	−1.38974	+	2.91547i	−0.0629104	+	0.131977i
$489$		0			0
$490$	12.4481	−	9.78559i	0.562347	−	0.442068i
$491$	10.9997	+	9.22988i	0.496412	+	0.416539i	0.856317	−	0.516450i	$-0.172747\pi$
$491$	10.9997	+	9.22988i	0.496412	+	0.416539i	−0.359906	+	0.932989i	$0.617191\pi$
$492$		0			0
$493$	−10.2515	−	3.73126i	−0.461706	−	0.168047i
$494$	15.1295	+	13.5410i	0.680710	+	0.609238i
$495$		0			0
$496$	12.3244	−	11.3668i	0.553384	−	0.510385i
$497$	−18.8556	−	22.4713i	−0.845790	−	1.00797i
$498$		0			0
$499$	13.0653	+	2.30376i	0.584881	+	0.103130i	0.458256	−	0.888820i	$-0.348474\pi$
$499$	13.0653	+	2.30376i	0.584881	+	0.103130i	0.126625	+	0.991951i	$0.459585\pi$
$500$	−5.56929	+	2.75767i	−0.249066	+	0.123327i
$501$		0			0
$502$	22.4707	+	13.9480i	1.00292	+	0.622530i
$503$	−7.87140	+	13.6337i	−0.350969	+	0.607895i	−0.986419	−	0.164246i	$-0.947481\pi$
$503$	−7.87140	+	13.6337i	−0.350969	+	0.607895i	0.635451	+	0.772141i	$0.280814\pi$
$504$		0			0
$505$	19.5156	+	33.8021i	0.868434	+	1.50417i
$506$	0.304264	−	9.52988i	0.0135262	−	0.423655i
$507$		0			0
$508$	−0.869076	+	13.5963i	−0.0385590	+	0.603239i
$509$	−0.744660	−	2.04594i	−0.0330065	−	0.0906845i	0.922095	−	0.386964i	$-0.126476\pi$
$509$	−0.744660	−	2.04594i	−0.0330065	−	0.0906845i	−0.955101	+	0.296279i	$0.904254\pi$
$510$		0			0
$511$	−39.6034	+	6.98314i	−1.75195	+	0.308916i
$512$	6.41068	−	21.7003i	0.283315	−	0.959027i
$513$		0			0
$514$	17.5979	−	5.77613i	0.776210	−	0.254774i
$515$	6.58502	+	37.3455i	0.290171	+	1.64564i
$516$		0			0
$517$	−8.63466	+	3.14276i	−0.379752	+	0.138218i
$518$	−7.25888	−	2.90756i	−0.318937	−	0.127751i
$519$		0			0
$520$	19.1560	−	13.1724i	0.840046	−	0.577649i
$521$	−12.2960	+	7.09911i	−0.538698	+	0.311018i	−0.744551	−	0.667565i	$-0.767337\pi$
$521$	−12.2960	+	7.09911i	−0.538698	+	0.311018i	0.205853	+	0.978583i	$0.434003\pi$
$522$		0			0
$523$	5.03668	+	2.90793i	0.220239	+	0.127155i	0.606061	−	0.795418i	$-0.292749\pi$
$523$	5.03668	+	2.90793i	0.220239	+	0.127155i	−0.385822	+	0.922573i	$0.626082\pi$
$524$	−9.79612	+	40.3156i	−0.427945	+	1.76120i
$525$		0			0
$526$	1.04884	−	0.150604i	0.0457317	−	0.00656667i
$527$	0.979209	−	5.55337i	0.0426550	−	0.241908i
$528$		0			0
$529$	−14.0670	+	11.8036i	−0.611610	+	0.513202i
$530$	−10.7758	−	2.25682i	−0.468073	−	0.0980301i
$531$		0			0
$532$	34.1070	+	14.9417i	1.47873	+	0.647804i
$533$	−0.653959	+	1.79674i	−0.0283261	+	0.0778253i
$534$		0			0
$535$	10.5755	−	12.6034i	0.457221	−	0.544894i
$536$	10.7455	−	38.7838i	0.464136	−	1.67520i
$537$		0			0
$538$	−8.11074	−	15.1447i	−0.349679	−	0.652933i
$539$	−10.5989			−0.456526
$540$		0			0
$541$	11.7222			0.503978			0.251989	−	0.967730i	$-0.418915\pi$
$541$	11.7222			0.503978			0.251989	+	0.967730i	$0.418915\pi$
$542$	−2.10616	−	3.93270i	−0.0904675	−	0.168924i
$543$		0			0
$544$	−2.70956	−	7.11181i	−0.116172	−	0.304916i
$545$	−31.4662	+	37.4999i	−1.34786	+	1.60632i
$546$		0			0
$547$	0.577207	−	1.58586i	0.0246796	−	0.0678066i	−0.926741	−	0.375701i	$-0.877402\pi$
$547$	0.577207	−	1.58586i	0.0246796	−	0.0678066i	0.951421	+	0.307894i	$0.0996243\pi$
$548$	−8.62792	+	19.6948i	−0.368567	+	0.841319i
$549$		0			0
$550$	25.7411	+	5.39104i	1.09760	+	0.229875i
$551$	35.8881	−	30.1137i	1.52889	−	1.28289i
$552$		0			0
$553$	−5.27648	+	29.9244i	−0.224379	+	1.27251i
$554$	46.3971	−	6.66221i	1.97122	−	0.283050i
$555$		0			0
$556$	−23.8330	−	5.79107i	−1.01074	−	0.245596i
$557$	−20.7520	−	11.9812i	−0.879289	−	0.507658i	−0.00886525	−	0.999961i	$-0.502822\pi$
$557$	−20.7520	−	11.9812i	−0.879289	−	0.507658i	−0.870424	+	0.492303i	$0.836155\pi$
$558$		0			0
$559$	−2.47376	+	1.42822i	−0.104629	+	0.0604075i
$560$	25.8449	−	33.9082i	1.09215	−	1.43288i
$561$		0			0
$562$	−24.9354	−	9.98795i	−1.05184	−	0.421316i
$563$	4.17331	−	1.51896i	0.175884	−	0.0640165i	−0.252577	−	0.967577i	$-0.581278\pi$
$563$	4.17331	−	1.51896i	0.175884	−	0.0640165i	0.428461	+	0.903560i	$0.359056\pi$
$564$		0			0
$565$	−5.83624	−	33.0990i	−0.245533	−	1.39248i
$566$	8.08761	−	2.65459i	0.339948	−	0.111581i
$567$		0			0
$568$	−20.9640	−	14.9458i	−0.879630	−	0.627111i
$569$	4.09535	−	0.722121i	0.171686	−	0.0302729i	−0.0871441	−	0.996196i	$-0.527774\pi$
$569$	4.09535	−	0.722121i	0.171686	−	0.0302729i	0.258830	+	0.965923i	$0.416663\pi$
$570$		0			0
$571$	1.32069	+	3.62857i	0.0552692	+	0.151851i	0.964255	−	0.264976i	$-0.0853642\pi$
$571$	1.32069	+	3.62857i	0.0552692	+	0.151851i	−0.908986	+	0.416827i	$0.863142\pi$
$572$	−15.5300	−	0.992674i	−0.649340	−	0.0415058i
$573$		0			0
$574$	−0.111898	+	3.50476i	−0.00467052	+	0.146286i
$575$	6.39480	+	11.0761i	0.266682	+	0.461906i
$576$		0			0
$577$	−19.9191	+	34.5009i	−0.829243	+	1.43629i	0.0693894	+	0.997590i	$0.477895\pi$
$577$	−19.9191	+	34.5009i	−0.829243	+	1.43629i	−0.898633	+	0.438702i	$0.855438\pi$
$578$	18.2517	+	11.3292i	0.759169	+	0.471231i
$579$		0			0
$580$	−23.8024	−	48.0704i	−0.988342	−	1.99602i
$581$	15.7726	+	2.78113i	0.654357	+	0.115381i
$582$		0			0
$583$	4.73710	+	5.64545i	0.196190	+	0.233811i
$584$	−32.1140	+	14.6446i	−1.32889	+	0.605999i
$585$		0			0
$586$	−5.77488	−	5.16855i	−0.238558	−	0.213511i
$587$	12.9776	+	4.72345i	0.535642	+	0.194958i	0.595656	−	0.803240i	$-0.296892\pi$
$587$	12.9776	+	4.72345i	0.535642	+	0.194958i	−0.0600138	+	0.998198i	$0.519114\pi$
$588$		0			0
$589$	18.5504	+	15.5656i	0.764354	+	0.641369i
$590$	16.9542	−	13.3279i	0.697995	−	0.548702i
$591$		0			0
$592$	−6.80725	−	0.873807i	−0.279776	−	0.0359133i
$593$		−	28.4223i		−	1.16716i	−0.812054	−	0.583582i	$-0.801651\pi$
$593$		−	28.4223i		−	1.16716i	0.812054	−	0.583582i	$-0.198349\pi$
$594$		0			0
$595$		−	14.3398i		−	0.587873i
$596$	−22.2444	+	23.3121i	−0.911166	+	0.954902i
$597$		0			0
$598$	−4.67695	−	5.94947i	−0.191255	−	0.243292i
$599$	−21.1989	−	17.7880i	−0.866163	−	0.726797i	0.0971235	−	0.995272i	$-0.469036\pi$
$599$	−21.1989	−	17.7880i	−0.866163	−	0.726797i	−0.963287	+	0.268475i	$0.913480\pi$
$600$		0			0
$601$	4.29687	+	1.56393i	0.175273	+	0.0637942i	0.428166	−	0.903700i	$-0.359160\pi$
$601$	4.29687	+	1.56393i	0.175273	+	0.0637942i	−0.252893	+	0.967494i	$0.581382\pi$
$602$	−3.49358	+	3.90343i	−0.142388	+	0.159092i
$603$		0			0
$604$	23.3861	−	2.59947i	0.951567	−	0.105771i
$605$	2.54430	+	3.03218i	0.103440	+	0.123276i
$606$		0			0
$607$	30.1218	+	5.31129i	1.22261	+	0.215578i	0.747447	−	0.664322i	$-0.231279\pi$
$607$	30.1218	+	5.31129i	1.22261	+	0.215578i	0.475159	+	0.879900i	$0.342391\pi$
$608$	32.2665	+	5.19334i	1.30858	+	0.210618i
$609$		0			0
$610$	−2.81684	+	4.53803i	−0.114051	+	0.183739i
$611$	−3.64657	+	6.31605i	−0.147525	+	0.255520i
$612$		0			0
$613$	8.14531	+	14.1081i	0.328986	+	0.569820i	0.982311	−	0.187257i	$-0.0599598\pi$
$613$	8.14531	+	14.1081i	0.328986	+	0.569820i	−0.653325	+	0.757078i	$0.726626\pi$
$614$	−44.0984	−	1.40795i	−1.77967	−	0.0568201i
$615$		0			0
$616$	−27.6280	+	7.15228i	−1.11317	+	0.288173i
$617$	−1.54040	−	4.23222i	−0.0620143	−	0.170383i	0.904816	−	0.425803i	$-0.140008\pi$
$617$	−1.54040	−	4.23222i	−0.0620143	−	0.170383i	−0.966830	+	0.255420i	$0.917786\pi$
$618$		0			0
$619$	10.0452	−	1.77124i	0.403751	−	0.0711922i	0.0319149	−	0.999491i	$-0.489839\pi$
$619$	10.0452	−	1.77124i	0.403751	−	0.0711922i	0.371836	+	0.928298i	$0.378728\pi$
$620$	22.3334	−	16.4311i	0.896930	−	0.659889i
$621$		0			0
$622$	4.37807	+	13.3385i	0.175545	+	0.534825i
$623$	−3.85336	−	21.8535i	−0.154381	−	0.875541i
$624$		0			0
$625$	18.2488	−	6.64202i	0.729952	−	0.265681i
$626$	−5.29055	+	13.2081i	−0.211453	+	0.527903i
$627$		0			0
$628$	5.59548	−	1.64075i	0.223284	−	0.0654732i
$629$	−1.99907	+	1.15416i	−0.0797082	+	0.0460196i
$630$		0			0
$631$	22.3687	+	12.9146i	0.890484	+	0.514121i	0.874101	−	0.485745i	$-0.161452\pi$
$631$	22.3687	+	12.9146i	0.890484	+	0.514121i	0.0163832	+	0.999866i	$0.494785\pi$
$632$	2.09893	+	26.5867i	0.0834910	+	1.05756i
$633$		0			0
$634$	2.33780	+	16.2809i	0.0928458	+	0.646598i
$635$	−3.91242	+	22.1884i	−0.155260	+	0.880521i
$636$		0			0
$637$	−6.44421	+	5.40733i	−0.255329	+	0.214246i
$638$	−7.36021	+	35.1435i	−0.291394	+	1.39134i
$639$		0			0
$640$	14.5013	−	34.4959i	0.573214	−	1.36357i
$641$	−8.84603	+	24.3043i	−0.349397	+	0.959960i	0.633164	+	0.774018i	$0.281756\pi$
$641$	−8.84603	+	24.3043i	−0.349397	+	0.959960i	−0.982561	+	0.185942i	$0.940466\pi$
$642$		0			0
$643$	−26.9098	+	32.0698i	−1.06122	+	1.26471i	−0.0982307	+	0.995164i	$0.531318\pi$
$643$	−26.9098	+	32.0698i	−1.06122	+	1.26471i	−0.962987	+	0.269547i	$0.913126\pi$
$644$	−11.5521	−	7.69185i	−0.455215	−	0.303101i
$645$		0			0
$646$	9.69003	−	5.18950i	0.381249	−	0.204178i
$647$	−1.81053			−0.0711791			−0.0355896	−	0.999366i	$-0.511331\pi$
$647$	−1.81053			−0.0711791			−0.0355896	+	0.999366i	$0.511331\pi$
$648$		0			0
$649$	−14.4356			−0.566648
$650$	18.4012	−	9.85478i	0.721754	−	0.386536i
$651$		0			0
$652$	−9.77480	−	6.50848i	−0.382811	−	0.254892i
$653$	−0.805175	+	0.959570i	−0.0315089	+	0.0375509i	−0.781569	−	0.623819i	$-0.785580\pi$
$653$	−0.805175	+	0.959570i	−0.0315089	+	0.0375509i	0.750060	+	0.661370i	$0.230025\pi$
$654$		0			0
$655$	−23.4666	+	64.4739i	−0.916916	+	2.51921i
$656$	0.675836	+	3.00252i	0.0263870	+	0.117229i
$657$		0			0
$658$	−2.74170	+	13.0910i	−0.106883	+	0.510341i
$659$	4.93871	−	4.14407i	0.192385	−	0.161430i	−0.541507	−	0.840696i	$-0.682146\pi$
$659$	4.93871	−	4.14407i	0.192385	−	0.161430i	0.733892	+	0.679266i	$0.237702\pi$
$660$		0			0
$661$	4.41939	−	25.0636i	0.171894	−	0.974862i	−0.769773	−	0.638317i	$-0.779631\pi$
$661$	4.41939	−	25.0636i	0.171894	−	0.974862i	0.941668	−	0.336544i	$-0.109258\pi$
$662$	7.13170	+	49.6667i	0.277181	+	1.93035i
$663$		0			0
$664$	14.0133	−	1.10631i	0.543823	−	0.0429330i
$665$	53.3293	+	30.7897i	2.06802	+	1.19397i
$666$		0			0
$667$	−15.1219	+	8.73061i	−0.585521	+	0.338051i
$668$	28.7022	−	8.41631i	1.11052	−	0.325637i
$669$		0			0
$670$	24.7472	−	61.7827i	0.956068	−	2.38687i
$671$	3.35966	−	1.22282i	0.129698	−	0.0472063i
$672$		0			0
$673$	−0.177054	−	1.00413i	−0.00682494	−	0.0387062i	0.981205	−	0.192968i	$-0.0618113\pi$
$673$	−0.177054	−	1.00413i	−0.00682494	−	0.0387062i	−0.988030	+	0.154262i	$0.950700\pi$
$674$	13.6717	+	41.6529i	0.526613	+	1.60441i
$675$		0			0
$676$	10.9939	−	8.08842i	0.422842	−	0.311093i
$677$	13.0857	−	2.30736i	0.502923	−	0.0886789i	0.0835696	−	0.996502i	$-0.473368\pi$
$677$	13.0857	−	2.30736i	0.502923	−	0.0886789i	0.419353	+	0.907823i	$0.362257\pi$
$678$		0			0
$679$	−7.47081	−	20.5259i	−0.286704	−	0.787711i
$680$	−3.15420	−	12.1841i	−0.120958	−	0.467241i
$681$		0			0
$682$	−18.5501	−	0.592256i	−0.710320	−	0.0226787i
$683$	−19.4988	−	33.7729i	−0.746100	−	1.29228i	−0.949679	−	0.313225i	$-0.898591\pi$
$683$	−19.4988	−	33.7729i	−0.746100	−	1.29228i	0.203579	−	0.979059i	$-0.434743\pi$
$684$		0			0
$685$	−17.7792	+	30.7945i	−0.679308	+	1.17660i
$686$	8.68838	−	13.9973i	0.331724	−	0.534418i
$687$		0			0
$688$	−2.10981	+	4.08510i	−0.0804357	+	0.155743i
$689$	5.76039	+	1.01571i	0.219453	+	0.0386955i
$690$		0			0
$691$	−11.4631	−	13.6612i	−0.436077	−	0.519697i	0.502588	−	0.864526i	$-0.332381\pi$
$691$	−11.4631	−	13.6612i	−0.436077	−	0.519697i	−0.938665	+	0.344829i	$0.887937\pi$
$692$	36.8315	−	4.09398i	1.40012	−	0.155630i
$693$		0			0
$694$	−24.5847	+	27.4688i	−0.933223	+	1.04270i
$695$	−38.1144	−	13.8725i	−1.44576	−	0.526214i
$696$		0			0
$697$	0.792957	+	0.665370i	0.0300354	+	0.0252027i
$698$	−20.4045	−	25.9562i	−0.772321	−	0.982456i
$699$		0			0
$700$	26.4271	−	27.6956i	0.998852	−	1.04680i
$701$			38.4308i			1.45151i	0.687952	+	0.725756i	$0.258510\pi$
$701$			38.4308i			1.45151i	−0.687952	+	0.725756i	$0.741490\pi$
$702$		0			0
$703$		−	9.91268i		−	0.373864i
$704$	−21.9017	+	12.1542i	−0.825450	+	0.458080i
$705$		0			0
$706$	−9.18110	+	7.21737i	−0.345535	+	0.271629i
$707$	−29.1323	−	24.4449i	−1.09563	−	0.919344i
$708$		0			0
$709$	17.9465	+	6.53199i	0.673995	+	0.245314i	0.656267	−	0.754529i	$-0.272135\pi$
$709$	17.9465	+	6.53199i	0.673995	+	0.245314i	0.0177278	+	0.999843i	$0.494357\pi$
$710$	−31.7263	−	28.3952i	−1.19067	−	1.06565i
$711$		0			0
$712$	−8.08103	−	17.7208i	−0.302850	−	0.664114i
$713$	−5.80154	−	6.91401i	−0.217269	−	0.258932i
$714$		0			0
$715$	−25.3440	−	4.46883i	−0.947813	−	0.167125i
$716$	−3.99231	−	8.06271i	−0.149199	−	0.301317i
$717$		0			0
$718$	−37.0439	−	22.9939i	−1.38247	−	0.858124i
$719$	1.55128	−	2.68689i	0.0578529	−	0.100204i	−0.835648	−	0.549265i	$-0.814908\pi$
$719$	1.55128	−	2.68689i	0.0578529	−	0.100204i	0.893501	+	0.449060i	$0.148241\pi$
$720$		0			0
$721$	−18.4741	−	31.9982i	−0.688013	−	1.19167i
$722$	−0.648870	+	20.3233i	−0.0241485	+	0.756356i
$723$		0			0
$724$	44.3130	+	2.83248i	1.64688	+	0.105268i
$725$	−16.4727	−	45.2585i	−0.611782	−	1.68086i
$726$		0			0
$727$	23.8610	−	4.20733i	0.884954	−	0.156041i	0.287343	−	0.957828i	$-0.407228\pi$
$727$	23.8610	−	4.20733i	0.884954	−	0.156041i	0.597611	+	0.801786i	$0.296117\pi$
$728$	−13.1491	+	18.4439i	−0.487339	+	0.683577i
$729$		0			0
$730$	−55.4588	+	18.2032i	−2.05262	+	0.673729i
$731$	0.268530	+	1.52291i	0.00993196	+	0.0563269i
$732$		0			0
$733$	−16.2983	+	5.93209i	−0.601991	+	0.219107i	−0.624995	−	0.780629i	$-0.714899\pi$
$733$	−16.2983	+	5.93209i	−0.601991	+	0.219107i	0.0230044	+	0.999735i	$0.492677\pi$
$734$	16.1447	+	6.46680i	0.595912	+	0.238694i
$735$		0			0
$736$	−11.5074	−	3.99457i	−0.424169	−	0.147242i
$737$	−38.5817	+	22.2751i	−1.42117	+	0.820515i
$738$		0			0
$739$	−31.8859	−	18.4094i	−1.17294	−	0.677199i	−0.218572	−	0.975821i	$-0.570140\pi$
$739$	−31.8859	−	18.4094i	−1.17294	−	0.677199i	−0.954372	+	0.298622i	$0.903473\pi$
$740$	−11.0289	−	2.67986i	−0.405430	−	0.0985137i
$741$		0			0
$742$	10.6181	−	1.52467i	0.389804	−	0.0559725i
$743$	−4.95314	+	28.0906i	−0.181713	+	1.03055i	0.748393	+	0.663255i	$0.230826\pi$
$743$	−4.95314	+	28.0906i	−0.181713	+	1.03055i	−0.930106	+	0.367291i	$0.880285\pi$
$744$		0			0
$745$	−40.8204	+	34.2524i	−1.49554	+	1.25491i
$746$	15.1176	+	3.16613i	0.553494	+	0.115920i
$747$		0			0
$748$	−3.38053	+	7.71667i	−0.123605	+	0.282149i
$749$	−5.48270	+	15.0636i	−0.200334	+	0.550412i
$750$		0			0
$751$	19.3010	−	23.0020i	0.704302	−	0.839355i	−0.288704	−	0.957418i	$-0.593224\pi$
$751$	19.3010	−	23.0020i	0.704302	−	0.839355i	0.993006	+	0.118064i	$0.0376688\pi$
$752$	0.549972	+	11.7262i	0.0200554	+	0.427611i
$753$		0			0
$754$	13.4544	+	25.1225i	0.489980	+	0.914909i
$755$	38.9128			1.41618
$756$		0			0
$757$	1.80445			0.0655839			0.0327920	−	0.999462i	$-0.489560\pi$
$757$	1.80445			0.0655839			0.0327920	+	0.999462i	$0.489560\pi$
$758$	−22.3321	−	41.6993i	−0.811138	−	1.51459i
$759$		0			0
$760$	52.0851	+	14.4308i	1.88933	+	0.523461i
$761$	−6.56742	+	7.82675i	−0.238069	+	0.283719i	−0.871829	−	0.489810i	$-0.837066\pi$
$761$	−6.56742	+	7.82675i	−0.238069	+	0.283719i	0.633760	+	0.773530i	$0.281511\pi$
$762$		0			0
$763$	16.3131	−	44.8198i	0.590573	−	1.62259i
$764$	0.606423	+	0.265663i	0.0219396	+	0.00961136i
$765$		0			0
$766$	−44.3143	−	9.28090i	−1.60114	−	0.335333i
$767$	−8.77698	+	7.36476i	−0.316918	+	0.265926i
$768$		0			0
$769$	−1.00744	+	5.71347i	−0.0363292	+	0.206033i	−0.997569	−	0.0696791i	$-0.977802\pi$
$769$	−1.00744	+	5.71347i	−0.0363292	+	0.206033i	0.961240	+	0.275712i	$0.0889136\pi$
$770$	−46.7167	+	6.70812i	−1.68355	+	0.241744i
$771$		0			0
$772$	6.59122	−	27.1260i	0.237223	−	0.976286i
$773$	−35.5486	−	20.5240i	−1.27859	−	0.738196i	−0.302004	−	0.953307i	$-0.597656\pi$
$773$	−35.5486	−	20.5240i	−1.27859	−	0.738196i	−0.976590	+	0.215110i	$0.930989\pi$
$774$		0			0
$775$	21.5599	−	12.4476i	0.774454	−	0.447131i
$776$	−10.8627	−	15.7971i	−0.389948	−	0.567082i
$777$		0			0
$778$	39.7014	+	15.9025i	1.42337	+	0.570132i
$779$	−4.17710	+	1.52034i	−0.149660	+	0.0544718i
$780$		0			0
$781$	4.94906	+	28.0675i	0.177091	+	1.00433i
$782$	−3.89263	+	1.27767i	−0.139200	+	0.0456895i
$783$		0			0
$784$	−4.02993	+	12.9269i	−0.143926	+	0.461675i
$785$	9.49661	−	1.67451i	0.338948	−	0.0597657i
$786$		0			0
$787$	−15.0125	−	41.2465i	−0.535138	−	1.47028i	−0.852882	−	0.522103i	$-0.825148\pi$
$787$	−15.0125	−	41.2465i	−0.535138	−	1.47028i	0.317745	−	0.948176i	$-0.397075\pi$
$788$	0.887422	−	13.8833i	0.0316131	−	0.494574i
$789$		0			0
$790$	−1.40742	+	44.0819i	−0.0500737	+	1.56836i
$791$	16.3735	+	28.3597i	0.582174	+	1.00835i
$792$		0			0
$793$	1.41885	−	2.45751i	0.0503847	−	0.0872689i
$794$	−3.03773	−	1.88558i	−0.107805	−	0.0669166i
$795$		0			0
$796$	−24.6837	+	12.2223i	−0.874889	+	0.433207i
$797$	−33.4033	−	5.88991i	−1.18321	−	0.208631i	−0.452780	−	0.891622i	$-0.649568\pi$
$797$	−33.4033	−	5.88991i	−1.18321	−	0.208631i	−0.730427	+	0.682991i	$0.760679\pi$
$798$		0			0
$799$	2.53793	+	3.02459i	0.0897855	+	0.107002i
$800$	16.3625	−	29.3453i	0.578502	−	1.03751i
$801$		0			0
$802$	0.537563	+	0.481121i	0.0189820	+	0.0169890i
$803$	36.7152	+	13.3632i	1.29565	+	0.471578i
$804$		0			0
$805$	−17.5819	−	14.7530i	−0.619682	−	0.519975i
$806$	−11.5808	+	9.10379i	−0.407915	+	0.320667i
$807$		0			0
$808$	−30.1299	−	14.3622i	−1.05997	−	0.505261i
$809$			12.0465i			0.423532i	0.977320	+	0.211766i	$0.0679215\pi$
$809$			12.0465i			0.423532i	−0.977320	+	0.211766i	$0.932079\pi$
$810$		0			0
$811$			39.0359i			1.37073i	0.728198	+	0.685367i	$0.240358\pi$
$811$			39.0359i			1.37073i	−0.728198	+	0.685367i	$0.759642\pi$
$812$	37.8119	+	36.0801i	1.32694	+	1.26616i
$813$		0			0
$814$	4.69526	+	5.97276i	0.164569	+	0.209345i
$815$	−14.8770	−	12.4833i	−0.521119	−	0.437271i
$816$		0			0
$817$	−6.24026	−	2.27127i	−0.218319	−	0.0794616i
$818$	24.5724	−	27.4550i	0.859153	−	0.959943i
$819$		0			0
$820$	0.562271	+	5.05848i	0.0196354	+	0.176650i
$821$	13.3419	+	15.9003i	0.465636	+	0.554923i	0.946848	−	0.321681i	$-0.104248\pi$
$821$	13.3419	+	15.9003i	0.465636	+	0.554923i	−0.481212	+	0.876604i	$0.659803\pi$
$822$		0			0
$823$	−29.9085	−	5.27368i	−1.04255	−	0.183829i	−0.373945	−	0.927451i	$-0.621995\pi$
$823$	−29.9085	−	5.27368i	−1.04255	−	0.183829i	−0.668601	+	0.743622i	$0.733106\pi$
$824$	−22.7354	−	23.1245i	−0.792026	−	0.805579i
$825$		0			0
$826$	−11.0814	+	17.8526i	−0.385573	+	0.621170i
$827$	−13.2989	+	23.0343i	−0.462447	+	0.800981i	−0.999082	−	0.0428331i	$-0.986362\pi$
$827$	−13.2989	+	23.0343i	−0.462447	+	0.800981i	0.536636	+	0.843814i	$0.319695\pi$
$828$		0			0
$829$	−19.0593	−	33.0116i	−0.661956	−	1.14654i	−0.980101	−	0.198499i	$-0.936393\pi$
$829$	−19.0593	−	33.0116i	−0.661956	−	1.14654i	0.318146	−	0.948042i	$-0.396940\pi$
$830$	23.2347	+	0.741824i	0.806490	+	0.0257491i
$831$		0			0
$832$	−7.11555	+	18.5637i	−0.246687	+	0.643579i
$833$	1.55763	+	4.27955i	0.0539686	+	0.148278i
$834$		0			0
$835$	48.7133	−	8.58946i	1.68579	−	0.297251i
$836$	−21.4396	−	29.1410i	−0.741504	−	1.00786i
$837$		0			0
$838$	1.29637	+	3.94960i	0.0447825	+	0.136437i
$839$	−4.56919	−	25.9131i	−0.157746	−	0.894621i	−0.956232	−	0.292608i	$-0.905477\pi$
$839$	−4.56919	−	25.9131i	−0.157746	−	0.894621i	0.798486	−	0.602013i	$-0.205634\pi$
$840$		0			0
$841$	34.5388	−	12.5711i	1.19099	−	0.433487i
$842$	−19.5378	+	48.7772i	−0.673317	+	1.68097i
$843$		0			0
$844$	−1.67868	−	5.72481i	−0.0577824	−	0.197056i
$845$	19.5475	−	11.2858i	0.672455	−	0.388242i
$846$		0			0
$847$	−3.33994	−	1.92832i	−0.114762	−	0.0662577i
$848$	8.68662	−	3.63107i	0.298300	−	0.124691i
$849$		0			0
$850$	−1.60619	−	11.1859i	−0.0550919	−	0.383672i
$851$	−0.641563	+	3.63848i	−0.0219925	+	0.124726i
$852$		0			0
$853$	19.0710	−	16.0025i	0.652979	−	0.547915i	−0.254994	−	0.966943i	$-0.582074\pi$
$853$	19.0710	−	16.0025i	0.652979	−	0.547915i	0.907973	+	0.419028i	$0.137629\pi$
$854$	1.06677	−	5.09359i	0.0365040	−	0.174299i
$855$		0			0
$856$	−1.34510	+	14.0052i	−0.0459746	+	0.478687i
$857$	−1.27702	+	3.50859i	−0.0436222	+	0.119851i	−0.959591	−	0.281398i	$-0.909202\pi$
$857$	−1.27702	+	3.50859i	−0.0436222	+	0.119851i	0.915969	+	0.401250i	$0.131424\pi$
$858$		0			0
$859$	−25.9095	+	30.8778i	−0.884021	+	1.05354i	0.114173	+	0.993461i	$0.463578\pi$
$859$	−25.9095	+	30.8778i	−0.884021	+	1.05354i	−0.998194	+	0.0600745i	$0.980866\pi$
$860$	−4.21406	+	6.32891i	−0.143698	+	0.215814i
$861$		0			0
$862$	−5.57343	+	2.98485i	−0.189832	+	0.101665i
$863$	16.2955			0.554704			0.277352	−	0.960768i	$-0.410543\pi$
$863$	16.2955			0.554704			0.277352	+	0.960768i	$0.410543\pi$
$864$		0			0
$865$	61.2850			2.08375
$866$	15.5248	−	8.31434i	0.527555	−	0.282533i
$867$		0			0
$868$	−14.9723	+	22.4863i	−0.508194	+	0.763235i
$869$	18.9767	−	22.6155i	0.643740	−	0.767180i
$870$		0			0
$871$	−12.0937	+	33.2270i	−0.409778	+	1.12586i
$872$	4.00218	−	41.6706i	0.135531	−	1.41114i
$873$		0			0
$874$	3.60644	−	17.2200i	0.121990	−	0.582474i
$875$	7.67089	−	6.43664i	0.259323	−	0.217598i
$876$		0			0
$877$	1.39295	−	7.89983i	0.0470367	−	0.266758i	−0.952215	−	0.305427i	$-0.901201\pi$
$877$	1.39295	−	7.89983i	0.0470367	−	0.266758i	0.999252	+	0.0386690i	$0.0123118\pi$
$878$	1.63637	+	11.3960i	0.0552247	+	0.384597i
$879$		0			0
$880$	−38.2186	+	15.9756i	−1.28835	+	0.538538i
$881$	−7.83455	−	4.52328i	−0.263953	−	0.152393i	0.362184	−	0.932107i	$-0.382031\pi$
$881$	−7.83455	−	4.52328i	−0.263953	−	0.152393i	−0.626136	+	0.779714i	$0.715365\pi$
$882$		0			0
$883$	46.5963	−	26.9024i	1.56809	−	0.905337i	0.571697	−	0.820464i	$-0.306285\pi$
$883$	46.5963	−	26.9024i	1.56809	−	0.905337i	0.996392	−	0.0848723i	$-0.0270482\pi$
$884$	1.88149	+	6.41648i	0.0632815	+	0.215809i
$885$		0			0
$886$	16.6267	−	41.5094i	0.558584	−	1.39454i
$887$	−12.3726	+	4.50327i	−0.415433	+	0.151205i	−0.541276	−	0.840845i	$-0.682059\pi$
$887$	−12.3726	+	4.50327i	−0.415433	+	0.151205i	0.125843	+	0.992050i	$0.459836\pi$
$888$		0			0
$889$	−3.81200	−	21.6189i	−0.127850	−	0.725076i
$890$	−10.0447	−	30.6026i	−0.336698	−	1.02580i
$891$		0			0
$892$	1.20462	+	1.63734i	0.0403337	+	0.0548221i
$893$	−16.6977	+	2.94426i	−0.558767	+	0.0985257i
$894$		0			0
$895$	−5.08882	−	13.9814i	−0.170100	−	0.467347i
$896$	−1.78153	+	36.4160i	−0.0595169	+	1.21657i
$897$		0			0
$898$	22.9312	+	0.732134i	0.765225	+	0.0244316i
$899$	16.9943	+	29.4350i	0.566792	+	0.981712i
$900$		0			0
$901$	1.58331	−	2.74238i	0.0527478	−	0.0913619i
$902$	1.79673	−	2.89459i	0.0598246	−	0.0963794i
$903$		0			0
$904$	20.1502	+	20.4950i	0.670186	+	0.681654i
$905$	72.3163	+	12.7513i	2.40388	+	0.423868i
$906$		0			0
$907$	14.6657	+	17.4779i	0.486968	+	0.580345i	0.952444	−	0.304715i	$-0.0985613\pi$
$907$	14.6657	+	17.4779i	0.486968	+	0.580345i	−0.465476	+	0.885061i	$0.654117\pi$
$908$	−3.88962	−	34.9930i	−0.129082	−	1.16128i
$909$		0			0
$910$	−24.9818	+	27.9125i	−0.828139	+	0.925291i
$911$	22.5574	+	8.21023i	0.747361	+	0.272017i	0.687495	−	0.726189i	$-0.258710\pi$
$911$	22.5574	+	8.21023i	0.747361	+	0.272017i	0.0598662	+	0.998206i	$0.480933\pi$
$912$		0			0
$913$	−11.9202	−	10.0023i	−0.394502	−	0.331027i
$914$	−3.08120	−	3.91955i	−0.101917	−	0.129647i
$915$		0			0
$916$	15.8599	+	15.1335i	0.524025	+	0.500024i
$917$		−	66.8507i		−	2.20760i
$918$		0			0
$919$			26.4967i			0.874046i	0.899450	+	0.437023i	$0.143967\pi$
$919$			26.4967i			0.874046i	−0.899450	+	0.437023i	$0.856033\pi$
$920$	−18.1840	−	8.66791i	−0.599510	−	0.285773i
$921$		0			0
$922$	−3.08203	+	2.42282i	−0.101501	+	0.0797912i
$923$	17.3285	+	14.5404i	0.570376	+	0.478602i
$924$		0			0
$925$	−9.57623	−	3.48546i	−0.314865	−	0.114601i
$926$	−25.4683	−	22.7942i	−0.836939	−	0.749064i
$927$		0			0
$928$	40.0641	+	22.3392i	1.31517	+	0.733320i
$929$	20.9431	+	24.9590i	0.687121	+	0.818879i	0.991004	−	0.133830i	$-0.0427276\pi$
$929$	20.9431	+	24.9590i	0.687121	+	0.818879i	−0.303883	+	0.952709i	$0.598283\pi$
$930$		0			0
$931$	−19.2600	−	3.39606i	−0.631222	−	0.111301i
$932$	10.5593	−	5.22851i	0.345881	−	0.171265i
$933$		0			0
$934$	42.1578	+	26.1682i	1.37944	+	0.856248i
$935$	−6.96612	+	12.0657i	−0.227816	+	0.394590i
$936$		0			0
$937$	−6.56312	−	11.3677i	−0.214408	−	0.371365i	0.738681	−	0.674055i	$-0.235449\pi$
$937$	−6.56312	−	11.3677i	−0.214408	−	0.371365i	−0.953089	+	0.302690i	$0.902115\pi$
$938$	−2.06932	+	64.8134i	−0.0675658	+	2.11623i
$939$		0			0
$940$	−1.23838	+	19.3739i	−0.0403915	+	0.631907i
$941$	1.90221	+	5.22629i	0.0620104	+	0.170372i	0.966829	−	0.255426i	$-0.0822156\pi$
$941$	1.90221	+	5.22629i	0.0620104	+	0.170372i	−0.904818	+	0.425798i	$0.859993\pi$
$942$		0			0
$943$	1.63162	−	0.287698i	0.0531327	−	0.00936874i
$944$	−5.48875	+	17.6064i	−0.178643	+	0.573039i
$945$		0			0
$946$	4.83580	−	1.58725i	0.157225	−	0.0516059i
$947$	2.90983	+	16.5025i	0.0945568	+	0.536258i	0.994882	+	0.101041i	$0.0322173\pi$
$947$	2.90983	+	16.5025i	0.0945568	+	0.536258i	−0.900325	+	0.435217i	$0.856672\pi$
$948$		0			0
$949$	29.1408	−	10.6064i	0.945950	−	0.344298i
$950$	45.0487	+	18.0444i	1.46157	+	0.585436i
$951$		0			0
$952$	6.94817	+	10.1044i	0.225191	+	0.327485i
$953$	38.9306	−	22.4766i	1.26109	−	0.728089i	0.287802	−	0.957690i	$-0.407075\pi$
$953$	38.9306	−	22.4766i	1.26109	−	0.728089i	0.973285	+	0.229601i	$0.0737421\pi$
$954$		0			0
$955$	0.948195	+	0.547441i	0.0306829	+	0.0177148i
$956$	0.571932	−	2.35377i	0.0184976	−	0.0761263i
$957$		0			0
$958$	38.6855	−	5.55490i	1.24987	−	0.179471i
$959$	6.01616	−	34.1194i	0.194272	−	1.10177i
$960$		0			0
$961$	10.2891	−	8.63360i	0.331907	−	0.278503i
$962$	5.90193	+	1.23606i	0.190286	+	0.0398522i
$963$		0			0
$964$	−44.1191	−	19.3278i	−1.42098	−	0.622506i
$965$	15.7893	−	43.3807i	0.508275	−	1.39647i
$966$		0			0
$967$	4.17482	−	4.97536i	0.134253	−	0.159997i	−0.694729	−	0.719271i	$-0.744476\pi$
$967$	4.17482	−	4.97536i	0.134253	−	0.159997i	0.828983	+	0.559275i	$0.188920\pi$
$968$	−3.26202	−	0.903784i	−0.104845	−	0.0290487i
$969$		0			0
$970$	−14.9681	−	27.9490i	−0.480596	−	0.897387i
$971$	−54.3130			−1.74299			−0.871493	−	0.490407i	$-0.836848\pi$
$971$	−54.3130			−1.74299			−0.871493	+	0.490407i	$0.836848\pi$
$972$		0			0
$973$	39.5194			1.26693
$974$	15.3732	+	28.7053i	0.492588	+	0.919778i
$975$		0			0
$976$	−0.213989	−	4.56255i	−0.00684961	−	0.146044i
$977$	36.8474	−	43.9131i	1.17885	−	1.40490i	0.283837	−	0.958873i	$-0.408393\pi$
$977$	36.8474	−	43.9131i	1.17885	−	1.40490i	0.895017	−	0.446031i	$-0.147163\pi$
$978$		0			0
$979$	−7.37394	+	20.2597i	−0.235672	+	0.647504i
$980$	−8.98537	+	20.5107i	−0.287027	+	0.655190i
$981$		0			0
$982$	−19.8757	−	4.16263i	−0.634259	−	0.132835i
$983$	26.6456	−	22.3583i	0.849862	−	0.713119i	−0.109897	−	0.993943i	$-0.535052\pi$
$983$	26.6456	−	22.3583i	0.849862	−	0.713119i	0.959759	+	0.280824i	$0.0906077\pi$
$984$		0			0
$985$	3.99501	−	22.6568i	0.127292	−	0.721907i
$986$	15.2717	−	2.19288i	0.486349	−	0.0698355i
$987$		0			0
$988$	−27.9026	−	6.77993i	−0.887700	−	0.215698i
$989$	2.14351	+	1.23755i	0.0681596	+	0.0393520i
$990$		0			0
$991$	−4.09615	+	2.36491i	−0.130118	+	0.0751239i	−0.563646	−	0.826016i	$-0.690602\pi$
$991$	−4.09615	+	2.36491i	−0.130118	+	0.0751239i	0.433528	+	0.901140i	$0.357269\pi$
$992$	−7.77551	+	22.3994i	−0.246873	+	0.711182i
$993$		0			0
$994$	38.5103	+	15.4254i	1.22147	+	0.489263i
$995$	−42.8035	+	15.5792i	−1.35696	+	0.493894i
$996$		0			0
$997$	−0.561268	−	3.18311i	−0.0177755	−	0.100810i	0.974629	−	0.223826i	$-0.0718546\pi$
$997$	−0.561268	−	3.18311i	−0.0177755	−	0.100810i	−0.992405	+	0.123016i	$0.960744\pi$
$998$	−17.8264	+	5.85114i	−0.564285	+	0.185215i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.l.a.71.2		96
3.2	odd	2		108.2.l.a.95.15	yes	96
4.3	odd	2	inner	324.2.l.a.71.1		96
9.2	odd	6		972.2.l.c.863.4		96
9.4	even	3		972.2.l.a.539.9		96
9.5	odd	6		972.2.l.d.539.8		96
9.7	even	3		972.2.l.b.863.13		96
12.11	even	2		108.2.l.a.95.16	yes	96
27.2	odd	18	inner	324.2.l.a.251.1		96
27.7	even	9		972.2.l.c.107.6		96
27.11	odd	18		972.2.l.a.431.12		96
27.16	even	9		972.2.l.d.431.5		96
27.20	odd	18		972.2.l.b.107.11		96
27.25	even	9		108.2.l.a.83.16	yes	96
36.7	odd	6		972.2.l.b.863.11		96
36.11	even	6		972.2.l.c.863.6		96
36.23	even	6		972.2.l.d.539.5		96
36.31	odd	6		972.2.l.a.539.12		96
108.7	odd	18		972.2.l.c.107.4		96
108.11	even	18		972.2.l.a.431.9		96
108.43	odd	18		972.2.l.d.431.8		96
108.47	even	18		972.2.l.b.107.13		96
108.79	odd	18		108.2.l.a.83.15	✓	96
108.83	even	18	inner	324.2.l.a.251.2		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.83.15	✓	96	108.79	odd	18
108.2.l.a.83.16	yes	96	27.25	even	9
108.2.l.a.95.15	yes	96	3.2	odd	2
108.2.l.a.95.16	yes	96	12.11	even	2
324.2.l.a.71.1		96	4.3	odd	2	inner
324.2.l.a.71.2		96	1.1	even	1	trivial
324.2.l.a.251.1		96	27.2	odd	18	inner
324.2.l.a.251.2		96	108.83	even	18	inner
972.2.l.a.431.9		96	108.11	even	18
972.2.l.a.431.12		96	27.11	odd	18
972.2.l.a.539.9		96	9.4	even	3
972.2.l.a.539.12		96	36.31	odd	6
972.2.l.b.107.11		96	27.20	odd	18
972.2.l.b.107.13		96	108.47	even	18
972.2.l.b.863.11		96	36.7	odd	6
972.2.l.b.863.13		96	9.7	even	3
972.2.l.c.107.4		96	108.7	odd	18
972.2.l.c.107.6		96	27.7	even	9
972.2.l.c.863.4		96	9.2	odd	6
972.2.l.c.863.6		96	36.11	even	6
972.2.l.d.431.5		96	27.16	even	9
972.2.l.d.431.8		96	108.43	odd	18
972.2.l.d.539.5		96	36.23	even	6
972.2.l.d.539.8		96	9.5	odd	6

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.24669 + 0.667664i) q^{2} +(1.10845 - 1.66473i) q^{4} +(2.12601 - 2.53368i) q^{5} +(-1.10219 + 3.02825i) q^{7} +(-0.270407 + 2.81547i) q^{8} +O(q^{10})\)	\(q+(-1.24669 + 0.667664i) q^{2} +(1.10845 - 1.66473i) q^{4} +(2.12601 - 2.53368i) q^{5} +(-1.10219 + 3.02825i) q^{7} +(-0.270407 + 2.81547i) q^{8} +(-0.958821 + 4.57817i) q^{10} +(2.39850 - 2.01258i) q^{11} +(0.431530 - 2.44733i) q^{13} +(-0.647764 - 4.51117i) q^{14} +(-1.54268 - 3.69055i) q^{16} +(-1.16511 - 0.672678i) q^{17} +(5.00336 - 2.88869i) q^{19} +(-1.86133 - 6.34771i) q^{20} +(-1.64645 + 4.11044i) q^{22} +(-2.02346 + 0.736479i) q^{23} +(-1.03138 - 5.84925i) q^{25} +(1.09601 + 3.33916i) q^{26} +(3.81950 + 5.19152i) q^{28} +(7.98578 - 1.40811i) q^{29} +(1.43357 + 3.93870i) q^{31} +(4.38728 + 3.57097i) q^{32} +(1.90165 + 0.0607148i) q^{34} +(5.32935 + 9.23070i) q^{35} +(0.857888 - 1.48590i) q^{37} +(-4.30894 + 6.94185i) q^{38} +(6.55862 + 6.67085i) q^{40} +(-0.757721 - 0.133607i) q^{41} +(-0.738845 - 0.880521i) q^{43} +(-0.691791 - 6.22370i) q^{44} +(2.03090 - 2.26915i) q^{46} +(-2.75778 - 1.00375i) q^{47} +(-2.59316 - 2.17592i) q^{49} +(5.19114 + 6.60356i) q^{50} +(-3.59582 - 3.43112i) q^{52} +2.35375i q^{53} -10.3558i q^{55} +(-8.22791 - 3.92205i) q^{56} +(-9.01562 + 7.08729i) q^{58} +(-3.53187 - 2.96359i) q^{59} +(1.07303 + 0.390550i) q^{61} +(-4.41694 - 3.95318i) q^{62} +(-7.85376 - 1.52265i) q^{64} +(-5.28331 - 6.29641i) q^{65} +(-14.0125 - 2.47079i) q^{67} +(-2.41130 + 1.19397i) q^{68} +(-12.8070 - 7.94957i) q^{70} +(-4.55132 + 7.88312i) q^{71} +(6.23943 + 10.8070i) q^{73} +(-0.0774314 + 2.42524i) q^{74} +(0.737075 - 11.5312i) q^{76} +(3.45098 + 9.48149i) q^{77} +(9.28580 - 1.63734i) q^{79} +(-12.6304 - 3.93750i) q^{80} +(1.03384 - 0.339337i) q^{82} +(-0.863010 - 4.89437i) q^{83} +(-4.18140 + 1.52190i) q^{85} +(1.50900 + 0.604433i) q^{86} +(5.01778 + 7.29711i) q^{88} +(-5.96340 + 3.44297i) q^{89} +(6.93549 + 4.00421i) q^{91} +(-1.01686 + 4.18487i) q^{92} +(4.10826 - 0.589910i) q^{94} +(3.31817 - 18.8183i) q^{95} +(-5.19235 + 4.35690i) q^{97} +(4.68563 + 0.981328i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Introduction

L-functions

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