LMFDB - Embedded newform 324.2.l.a.35.14

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			35.14
Character	$\chi$	$=$	324.35
Dual form			324.2.l.a.287.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.27725 - 0.607153i) q^{2} +(1.26273 - 1.55097i) q^{4} +(-1.29726 + 3.56419i) q^{5} +(2.58045 + 0.455003i) q^{7} +(0.671144 - 2.74765i) q^{8} +O(q^{10})$	\(q+(1.27725 - 0.607153i) q^{2} +(1.26273 - 1.55097i) q^{4} +(-1.29726 + 3.56419i) q^{5} +(2.58045 + 0.455003i) q^{7} +(0.671144 - 2.74765i) q^{8} +(0.507086 + 5.33999i) q^{10} +(3.39295 - 1.23493i) q^{11} +(-0.819980 + 0.688045i) q^{13} +(3.57213 - 0.985577i) q^{14} +(-0.811025 - 3.91692i) q^{16} +(-0.980503 + 0.566093i) q^{17} +(-0.0627092 - 0.0362052i) q^{19} +(3.88987 + 6.51262i) q^{20} +(3.58385 - 3.63736i) q^{22} +(-0.0731435 - 0.414817i) q^{23} +(-7.19034 - 6.03341i) q^{25} +(-0.629570 + 1.37666i) q^{26} +(3.96411 - 3.42766i) q^{28} +(0.192281 - 0.229152i) q^{29} +(-6.88084 + 1.21328i) q^{31} +(-3.41405 - 4.51046i) q^{32} +(-0.908641 + 1.31836i) q^{34} +(-4.96923 + 8.60696i) q^{35} +(0.377668 + 0.654141i) q^{37} +(-0.102077 - 0.00816893i) q^{38} +(8.92249 + 5.95649i) q^{40} +(-6.36586 - 7.58654i) q^{41} +(-3.18308 - 8.74545i) q^{43} +(2.36904 - 6.82177i) q^{44} +(-0.345280 - 0.485416i) q^{46} +(0.0443203 - 0.251353i) q^{47} +(-0.126150 - 0.0459147i) q^{49} +(-12.8471 - 3.34053i) q^{50} +(0.0317246 + 2.14058i) q^{52} +12.0634i q^{53} +13.6952i q^{55} +(2.98204 - 6.78480i) q^{56} +(0.106461 - 0.409428i) q^{58} +(11.7359 + 4.27153i) q^{59} +(-1.13416 + 6.43213i) q^{61} +(-8.05190 + 5.72738i) q^{62} +(-7.09913 - 3.68813i) q^{64} +(-1.38860 - 3.81514i) q^{65} +(4.37678 + 5.21604i) q^{67} +(-0.360115 + 2.23555i) q^{68} +(-1.12120 + 14.0103i) q^{70} +(-6.35108 - 11.0004i) q^{71} +(-0.578249 + 1.00156i) q^{73} +(0.879540 + 0.606198i) q^{74} +(-0.135338 + 0.0515428i) q^{76} +(9.31725 - 1.64288i) q^{77} +(5.09561 - 6.07271i) q^{79} +(15.0127 + 2.19061i) q^{80} +(-12.7370 - 5.82484i) q^{82} +(-3.00034 - 2.51758i) q^{83} +(-0.745699 - 4.22907i) q^{85} +(-9.37542 - 9.23750i) q^{86} +(-1.11601 - 10.1515i) q^{88} +(-2.07380 - 1.19731i) q^{89} +(-2.42898 + 1.40237i) q^{91} +(-0.735730 - 0.410359i) q^{92} +(-0.0960018 - 0.347950i) q^{94} +(0.210392 - 0.176540i) q^{95} +(1.81485 - 0.660552i) q^{97} +(-0.189002 + 0.0179476i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	1.27725	−	0.607153i	0.903151	−	0.429322i
$2$	1.27725	−	0.607153i	0.903151	−	0.429322i
$3$		0			0
$3$		0			0
$4$	1.26273	−	1.55097i	0.631365	−	0.775486i
$5$	−1.29726	+	3.56419i	−0.580152	+	1.59395i	0.207769	+	0.978178i	$0.433380\pi$
$5$	−1.29726	+	3.56419i	−0.580152	+	1.59395i	−0.787921	+	0.615776i	$0.788843\pi$
$6$		0			0
$7$	2.58045	+	0.455003i	0.975319	+	0.171975i	0.638523	−	0.769603i	$-0.279546\pi$
$7$	2.58045	+	0.455003i	0.975319	+	0.171975i	0.336796	+	0.941578i	$0.390657\pi$
$8$	0.671144	−	2.74765i	0.237285	−	0.971440i
$9$		0			0
$10$	0.507086	+	5.33999i	0.160355	+	1.68865i
$11$	3.39295	−	1.23493i	1.02301	−	0.372347i	0.224597	−	0.974452i	$-0.427893\pi$
$11$	3.39295	−	1.23493i	1.02301	−	0.372347i	0.798417	+	0.602105i	$0.205671\pi$
$12$		0			0
$13$	−0.819980	+	0.688045i	−0.227421	+	0.190829i	−0.749377	−	0.662143i	$-0.769647\pi$
$13$	−0.819980	+	0.688045i	−0.227421	+	0.190829i	0.521956	+	0.852973i	$0.325203\pi$
$14$	3.57213	−	0.985577i	0.954693	−	0.263406i
$15$		0			0
$16$	−0.811025	−	3.91692i	−0.202756	−	0.979229i
$17$	−0.980503	+	0.566093i	−0.237807	+	0.137298i	−0.614168	−	0.789175i	$-0.710508\pi$
$17$	−0.980503	+	0.566093i	−0.237807	+	0.137298i	0.376361	+	0.926473i	$0.377175\pi$
$18$		0			0
$19$	−0.0627092	−	0.0362052i	−0.0143865	−	0.00830603i	0.492790	−	0.870149i	$-0.335977\pi$
$19$	−0.0627092	−	0.0362052i	−0.0143865	−	0.00830603i	−0.507176	+	0.861843i	$0.669311\pi$
$20$	3.88987	+	6.51262i	0.869801	+	1.45627i
$21$		0			0
$22$	3.58385	−	3.63736i	0.764080	−	0.775488i
$23$	−0.0731435	−	0.414817i	−0.0152515	−	0.0864954i	0.976232	−	0.216728i	$-0.0695386\pi$
$23$	−0.0731435	−	0.414817i	−0.0152515	−	0.0864954i	−0.991483	+	0.130233i	$0.958427\pi$
$24$		0			0
$25$	−7.19034	−	6.03341i	−1.43807	−	1.20668i
$26$	−0.629570	+	1.37666i	−0.123469	+	0.269985i
$27$		0			0
$28$	3.96411	−	3.42766i	0.749146	−	0.647767i
$29$	0.192281	−	0.229152i	0.0357057	−	0.0425524i	−0.747896	−	0.663816i	$-0.768936\pi$
$29$	0.192281	−	0.229152i	0.0357057	−	0.0425524i	0.783602	+	0.621263i	$0.213380\pi$
$30$		0			0
$31$	−6.88084	+	1.21328i	−1.23583	+	0.217911i	−0.753130	−	0.657872i	$-0.771457\pi$
$31$	−6.88084	+	1.21328i	−1.23583	+	0.217911i	−0.482705	+	0.875783i	$0.660346\pi$
$32$	−3.41405	−	4.51046i	−0.603524	−	0.797345i
$33$		0			0
$34$	−0.908641	+	1.31836i	−0.155831	+	0.226096i
$35$	−4.96923	+	8.60696i	−0.839953	+	1.45484i
$36$		0			0
$37$	0.377668	+	0.654141i	0.0620883	+	0.107540i	0.895399	−	0.445265i	$-0.146891\pi$
$37$	0.377668	+	0.654141i	0.0620883	+	0.107540i	−0.833310	+	0.552805i	$0.813557\pi$
$38$	−0.102077	−	0.00816893i	−0.0165591	−	0.00132518i
$39$		0			0
$40$	8.92249	+	5.95649i	1.41077	+	0.941804i
$41$	−6.36586	−	7.58654i	−0.994180	−	1.18482i	−0.982761	−	0.184883i	$-0.940809\pi$
$41$	−6.36586	−	7.58654i	−0.994180	−	1.18482i	−0.0114196	−	0.999935i	$-0.503635\pi$
$42$		0			0
$43$	−3.18308	−	8.74545i	−0.485416	−	1.33367i	−0.904791	−	0.425856i	$-0.859973\pi$
$43$	−3.18308	−	8.74545i	−0.485416	−	1.33367i	0.419375	−	0.907813i	$-0.362249\pi$
$44$	2.36904	−	6.82177i	0.357146	−	1.02842i
$45$		0			0
$46$	−0.345280	−	0.485416i	−0.0509088	−	0.0715706i
$47$	0.0443203	−	0.251353i	0.00646479	−	0.0366636i	−0.981405	−	0.191950i	$-0.938519\pi$
$47$	0.0443203	−	0.251353i	0.00646479	−	0.0366636i	0.987870	+	0.155286i	$0.0496300\pi$
$48$		0			0
$49$	−0.126150	−	0.0459147i	−0.0180214	−	0.00655925i
$50$	−12.8471	−	3.34053i	−1.81685	−	0.472423i
$51$		0			0
$52$	0.0317246	+	2.14058i	0.00439941	+	0.296845i
$53$			12.0634i			1.65703i	0.559967	+	0.828515i	$0.310814\pi$
$53$			12.0634i			1.65703i	−0.559967	+	0.828515i	$0.689186\pi$
$54$		0			0
$55$			13.6952i			1.84666i
$56$	2.98204	−	6.78480i	0.398492	−	0.906657i
$57$		0			0
$58$	0.106461	−	0.409428i	0.0139790	−	0.0537605i
$59$	11.7359	+	4.27153i	1.52789	+	0.556106i	0.963104	−	0.269131i	$-0.0867365\pi$
$59$	11.7359	+	4.27153i	1.52789	+	0.556106i	0.564786	+	0.825237i	$0.308959\pi$
$60$		0			0
$61$	−1.13416	+	6.43213i	−0.145214	+	0.823550i	0.821981	+	0.569515i	$0.192869\pi$
$61$	−1.13416	+	6.43213i	−0.145214	+	0.823550i	−0.967195	+	0.254035i	$0.918242\pi$
$62$	−8.05190	+	5.72738i	−1.02259	+	0.727378i
$63$		0			0
$64$	−7.09913	−	3.68813i	−0.887392	−	0.461016i
$65$	−1.38860	−	3.81514i	−0.172234	−	0.473209i
$66$		0			0
$67$	4.37678	+	5.21604i	0.534709	+	0.637241i	0.963993	−	0.265928i	$-0.0856785\pi$
$67$	4.37678	+	5.21604i	0.534709	+	0.637241i	−0.429284	+	0.903170i	$0.641234\pi$
$68$	−0.360115	+	2.23555i	−0.0436704	+	0.271101i
$69$		0			0
$70$	−1.12120	+	14.0103i	−0.134009	+	1.67455i
$71$	−6.35108	−	11.0004i	−0.753734	−	1.30551i	−0.946001	−	0.324163i	$-0.894917\pi$
$71$	−6.35108	−	11.0004i	−0.753734	−	1.30551i	0.192267	−	0.981343i	$-0.438416\pi$
$72$		0			0
$73$	−0.578249	+	1.00156i	−0.0676789	+	0.117223i	−0.897879	−	0.440242i	$-0.854893\pi$
$73$	−0.578249	+	1.00156i	−0.0676789	+	0.117223i	0.830200	+	0.557465i	$0.188226\pi$
$74$	0.879540	+	0.606198i	0.102244	+	0.0704691i
$75$		0			0
$76$	−0.135338	+	0.0515428i	−0.0155243	+	0.00591236i
$77$	9.31725	−	1.64288i	1.06180	−	0.187224i
$78$		0			0
$79$	5.09561	−	6.07271i	0.573301	−	0.683233i	−0.399004	−	0.916949i	$-0.630644\pi$
$79$	5.09561	−	6.07271i	0.573301	−	0.683233i	0.972305	+	0.233716i	$0.0750886\pi$
$80$	15.0127	+	2.19061i	1.67848	+	0.244917i
$81$		0			0
$82$	−12.7370	−	5.82484i	−1.40656	−	0.643246i
$83$	−3.00034	−	2.51758i	−0.329330	−	0.276340i	0.463097	−	0.886308i	$-0.346738\pi$
$83$	−3.00034	−	2.51758i	−0.329330	−	0.276340i	−0.792427	+	0.609967i	$0.791183\pi$
$84$		0			0
$85$	−0.745699	−	4.22907i	−0.0808824	−	0.458707i
$86$	−9.37542	−	9.23750i	−1.01098	−	0.996105i
$87$		0			0
$88$	−1.11601	−	10.1515i	−0.118967	−	1.08215i
$89$	−2.07380	−	1.19731i	−0.219823	−	0.126915i	0.386046	−	0.922480i	$-0.373841\pi$
$89$	−2.07380	−	1.19731i	−0.219823	−	0.126915i	−0.605868	+	0.795565i	$0.707174\pi$
$90$		0			0
$91$	−2.42898	+	1.40237i	−0.254626	+	0.147009i
$92$	−0.735730	−	0.410359i	−0.0767052	−	0.0427829i
$93$		0			0
$94$	−0.0960018	−	0.347950i	−0.00990183	−	0.0358883i
$95$	0.210392	−	0.176540i	0.0215858	−	0.0181126i
$96$		0			0
$97$	1.81485	−	0.660552i	0.184270	−	0.0670689i	−0.248237	−	0.968699i	$-0.579851\pi$
$97$	1.81485	−	0.660552i	0.184270	−	0.0670689i	0.432507	+	0.901630i	$0.357629\pi$
$98$	−0.189002	+	0.0179476i	−0.0190921	+	0.00181299i
$99$		0			0
$100$	−18.4371	+	3.53344i	−1.84371	+	0.353344i
$101$	−4.42993	−	0.781117i	−0.440795	−	0.0777241i	−0.0511538	−	0.998691i	$-0.516290\pi$
$101$	−4.42993	−	0.781117i	−0.440795	−	0.0777241i	−0.389641	+	0.920967i	$0.627401\pi$
$102$		0			0
$103$	2.17204	−	5.96763i	0.214017	−	0.588008i	−0.785507	−	0.618853i	$-0.787598\pi$
$103$	2.17204	−	5.96763i	0.214017	−	0.588008i	0.999524	+	0.0308451i	$0.00981984\pi$
$104$	1.34018	+	2.71479i	0.131415	+	0.266207i
$105$		0			0
$106$	7.32430	+	15.4079i	0.711399	+	1.49655i
$107$	−9.90677			−0.957724			−0.478862	−	0.877890i	$-0.658951\pi$
$107$	−9.90677			−0.957724			−0.478862	+	0.877890i	$0.658951\pi$
$108$		0			0
$109$	7.94635			0.761122			0.380561	−	0.924756i	$-0.375731\pi$
$109$	7.94635			0.761122			0.380561	+	0.924756i	$0.375731\pi$
$110$	8.31506	+	17.4921i	0.792810	+	1.66781i
$111$		0			0
$112$	−0.310602	−	10.4764i	−0.0293491	−	0.989930i
$113$	3.44642	−	9.46897i	0.324212	−	0.890766i	−0.665334	−	0.746546i	$-0.731711\pi$
$113$	3.44642	−	9.46897i	0.324212	−	0.890766i	0.989546	−	0.144219i	$-0.0460671\pi$
$114$		0			0
$115$	1.57337	+	0.277428i	0.146718	+	0.0258703i
$116$	−0.112609	−	0.587579i	−0.0104554	−	0.0545554i
$117$		0			0
$118$	17.5832	−	1.66970i	1.61866	−	0.153709i
$119$	−2.78771	+	1.01464i	−0.255549	+	0.0930123i
$120$		0			0
$121$	1.56059	−	1.30949i	0.141872	−	0.119045i
$122$	2.45669	+	8.90404i	0.222418	+	0.806134i
$123$		0			0
$124$	−6.80688	+	12.2040i	−0.611276	+	1.09595i
$125$	14.4081	−	8.31852i	1.28870	−	0.744031i
$126$		0			0
$127$	11.0681	+	6.39020i	0.982139	+	0.567038i	0.902915	−	0.429819i	$-0.141423\pi$
$127$	11.0681	+	6.39020i	0.982139	+	0.567038i	0.0792237	+	0.996857i	$0.474756\pi$
$128$	−11.3066	−	0.400402i	−0.999374	−	0.0353909i
$129$		0			0
$130$	−4.08995	−	4.02979i	−0.358713	−	0.353436i
$131$	1.12042	+	6.35420i	0.0978913	+	0.555169i	0.993823	+	0.110977i	$0.0353981\pi$
$131$	1.12042	+	6.35420i	0.0978913	+	0.555169i	−0.895932	+	0.444192i	$0.853491\pi$
$132$		0			0
$133$	−0.145344	−	0.121958i	−0.0126030	−	0.0105751i
$134$	8.75717	+	4.00481i	0.756505	+	0.345963i
$135$		0			0
$136$	0.897367	+	3.07401i	0.0769486	+	0.263594i
$137$	−1.38785	+	1.65398i	−0.118572	+	0.141309i	−0.822065	−	0.569393i	$-0.807178\pi$
$137$	−1.38785	+	1.65398i	−0.118572	+	0.141309i	0.703493	+	0.710702i	$0.251623\pi$
$138$		0			0
$139$	−6.90717	+	1.21792i	−0.585859	+	0.103303i	−0.458718	−	0.888582i	$-0.651691\pi$
$139$	−6.90717	+	1.21792i	−0.585859	+	0.103303i	−0.127141	+	0.991885i	$0.540580\pi$
$140$	7.07435	+	18.5754i	0.597892	+	1.56991i
$141$		0			0
$142$	−14.7908	−	10.1942i	−1.24122	−	0.855475i
$143$	−1.93246	+	3.34713i	−0.161601	+	0.279901i
$144$		0			0
$145$	0.567302	+	0.982595i	0.0471118	+	0.0816001i
$146$	−0.130470	+	1.63032i	−0.0107977	+	0.134926i
$147$		0			0
$148$	1.49145	+	0.240250i	0.122596	+	0.0197485i
$149$	7.49826	+	8.93608i	0.614282	+	0.732072i	0.980076	−	0.198623i	$-0.0636470\pi$
$149$	7.49826	+	8.93608i	0.614282	+	0.732072i	−0.365794	+	0.930696i	$0.619203\pi$
$150$		0			0
$151$	−0.154723	−	0.425097i	−0.0125911	−	0.0345939i	0.933238	−	0.359259i	$-0.116971\pi$
$151$	−0.154723	−	0.425097i	−0.0125911	−	0.0345939i	−0.945829	+	0.324665i	$0.894748\pi$
$152$	−0.141566	+	0.148004i	−0.0114825	+	0.0120047i
$153$		0			0
$154$	10.9030	−	7.75537i	0.878586	−	0.624946i
$155$	4.60188	−	26.0985i	0.369632	−	2.09629i
$156$		0			0
$157$	17.2816	+	6.28998i	1.37922	+	0.501995i	0.921942	−	0.387328i	$-0.126602\pi$
$157$	17.2816	+	6.28998i	1.37922	+	0.501995i	0.457279	+	0.889323i	$0.348824\pi$
$158$	2.82130	−	10.8502i	0.224450	−	0.863193i
$159$		0			0
$160$	20.5050	−	6.31708i	1.62107	−	0.499409i
$161$		−	1.10370i		−	0.0869834i
$162$		0			0
$163$		−	22.5880i		−	1.76923i	−0.466320	−	0.884616i	$-0.654421\pi$
$163$		−	22.5880i		−	1.76923i	0.466320	−	0.884616i	$-0.345579\pi$
$164$	−19.8049	+	0.293519i	−1.54650	+	0.0229200i
$165$		0			0
$166$	−5.36073	−	1.39391i	−0.416074	−	0.108189i
$167$	−4.32888	−	1.57558i	−0.334979	−	0.121922i	0.169054	−	0.985607i	$-0.445929\pi$
$167$	−4.32888	−	1.57558i	−0.334979	−	0.121922i	−0.504033	+	0.863684i	$0.668151\pi$
$168$		0			0
$169$	−2.05847	+	11.6741i	−0.158343	+	0.898010i
$170$	−3.52013	−	4.94882i	−0.269982	−	0.379557i
$171$		0			0
$172$	−17.5833	−	6.10627i	−1.34072	−	0.465599i
$173$	2.55462	+	7.01876i	0.194224	+	0.533626i	0.998130	−	0.0611306i	$-0.0194706\pi$
$173$	2.55462	+	7.01876i	0.194224	+	0.533626i	−0.803906	+	0.594757i	$0.797248\pi$
$174$		0			0
$175$	−15.8091	−	18.8406i	−1.19506	−	1.42421i
$176$	−7.58891	−	12.2884i	−0.572036	−	0.926270i
$177$		0			0
$178$	−3.37571	−	0.270148i	−0.253020	−	0.0202484i
$179$	5.08749	+	8.81180i	0.380257	+	0.658625i	0.991099	−	0.133128i	$-0.0425022\pi$
$179$	5.08749	+	8.81180i	0.380257	+	0.658625i	−0.610842	+	0.791753i	$0.709169\pi$
$180$		0			0
$181$	8.40432	−	14.5567i	0.624688	−	1.08199i	−0.363913	−	0.931433i	$-0.618559\pi$
$181$	8.40432	−	14.5567i	0.624688	−	1.08199i	0.988601	−	0.150559i	$-0.0481073\pi$
$182$	−2.25096	+	3.26594i	−0.166852	+	0.242088i
$183$		0			0
$184$	−1.18886	−	0.0774295i	−0.0876440	−	0.00570818i
$185$	−2.82142	+	0.497492i	−0.207435	+	0.0365763i
$186$		0			0
$187$	−2.62771	+	3.13159i	−0.192157	+	0.229004i
$188$	−0.333877	−	0.386131i	−0.0243505	−	0.0281615i
$189$		0			0
$190$	0.161536	−	0.353226i	0.0117191	−	0.0256257i
$191$	0.0529445	+	0.0444257i	0.00383093	+	0.00321453i	0.644701	−	0.764435i	$-0.276982\pi$
$191$	0.0529445	+	0.0444257i	0.00383093	+	0.00321453i	−0.640870	+	0.767649i	$0.721426\pi$
$192$		0			0
$193$	4.64409	+	26.3379i	0.334289	+	1.89585i	0.434144	+	0.900843i	$0.357051\pi$
$193$	4.64409	+	26.3379i	0.334289	+	1.89585i	−0.0998555	+	0.995002i	$0.531838\pi$
$194$	1.91696	−	1.94558i	0.137630	−	0.139685i
$195$		0			0
$196$	−0.230505	+	0.137677i	−0.0164647	+	0.00983405i
$197$	−3.87890	−	2.23948i	−0.276360	−	0.159557i	0.355414	−	0.934709i	$-0.384340\pi$
$197$	−3.87890	−	2.23948i	−0.276360	−	0.159557i	−0.631774	+	0.775152i	$0.717673\pi$
$198$		0			0
$199$	8.51533	−	4.91633i	0.603636	−	0.348509i	−0.166835	−	0.985985i	$-0.553355\pi$
$199$	8.51533	−	4.91633i	0.603636	−	0.348509i	0.770470	+	0.637476i	$0.220021\pi$
$200$	−21.4034	+	15.7072i	−1.51345	+	1.11067i
$201$		0			0
$202$	−6.13239	+	1.69197i	−0.431473	+	0.119046i
$203$	0.600437	−	0.503826i	0.0421424	−	0.0353617i
$204$		0			0
$205$	35.2980	−	12.8474i	2.46532	−	0.897303i
$206$	−0.849030	−	8.94091i	−0.0591547	−	0.622943i
$207$		0			0
$208$	3.36004	+	2.65377i	0.232977	+	0.184006i
$209$	−0.257480	−	0.0454007i	−0.0178103	−	0.00314043i
$210$		0			0
$211$	−4.53594	+	12.4624i	−0.312267	+	0.857947i	0.679931	+	0.733276i	$0.262010\pi$
$211$	−4.53594	+	12.4624i	−0.312267	+	0.857947i	−0.992198	+	0.124671i	$0.960212\pi$
$212$	18.7099	+	15.2328i	1.28500	+	1.04619i
$213$		0			0
$214$	−12.6534	+	6.01493i	−0.864970	+	0.411172i
$215$	35.2997			2.40742
$216$		0			0
$217$	−18.3077			−1.24281
$218$	10.1495	−	4.82465i	0.687408	−	0.326766i
$219$		0			0
$220$	21.2408	+	17.2933i	1.43206	+	1.16591i
$221$	0.414495	−	1.13881i	0.0278819	−	0.0766050i
$222$		0			0
$223$	17.4629	+	3.07919i	1.16940	+	0.206198i	0.724432	−	0.689346i	$-0.242102\pi$
$223$	17.4629	+	3.07919i	1.16940	+	0.206198i	0.444973	+	0.895544i	$0.353213\pi$
$224$	−6.75751	−	13.1924i	−0.451505	−	0.881456i
$225$		0			0
$226$	−1.34717	−	14.1867i	−0.0896127	−	0.943688i
$227$	5.66395	−	2.06151i	0.375929	−	0.136827i	−0.147143	−	0.989115i	$-0.547008\pi$
$227$	5.66395	−	2.06151i	0.375929	−	0.136827i	0.523073	+	0.852288i	$0.324786\pi$
$228$		0			0
$229$	−13.4367	+	11.2747i	−0.887922	+	0.745055i	−0.967792	−	0.251751i	$-0.918994\pi$
$229$	−13.4367	+	11.2747i	−0.887922	+	0.745055i	0.0798705	+	0.996805i	$0.474549\pi$
$230$	2.17803	−	0.600934i	0.143615	−	0.0396244i
$231$		0			0
$232$	−0.500580	−	0.682114i	−0.0328647	−	0.0447830i
$233$	0.818415	−	0.472512i	0.0536162	−	0.0309553i	−0.472952	−	0.881088i	$-0.656812\pi$
$233$	0.818415	−	0.472512i	0.0536162	−	0.0309553i	0.526568	+	0.850133i	$0.323478\pi$
$234$		0			0
$235$	0.838375	+	0.484036i	0.0546896	+	0.0315750i
$236$	21.4444	−	12.8083i	1.39591	−	0.833750i
$237$		0			0
$238$	−2.94456	+	2.98852i	−0.190867	+	0.193717i
$239$	1.94169	+	11.0119i	0.125598	+	0.712300i	0.980951	+	0.194255i	$0.0622288\pi$
$239$	1.94169	+	11.0119i	0.125598	+	0.712300i	−0.855353	+	0.518045i	$0.826660\pi$
$240$		0			0
$241$	−14.8130	−	12.4295i	−0.954187	−	0.800658i	0.0258110	−	0.999667i	$-0.491783\pi$
$241$	−14.8130	−	12.4295i	−0.954187	−	0.800658i	−0.979998	+	0.199009i	$0.936228\pi$
$242$	1.19820	−	2.62006i	0.0770233	−	0.168424i
$243$		0			0
$244$	8.54392	+	9.88109i	0.546968	+	0.632572i
$245$	0.327298	−	0.390058i	0.0209103	−	0.0249199i
$246$		0			0
$247$	0.0763310	−	0.0134592i	0.00485683	−	0.000856389i
$248$	−1.28437	+	19.7204i	−0.0815577	+	1.25225i
$249$		0			0
$250$	13.3521	−	19.3727i	0.844462	−	1.22524i
$251$	−3.70756	+	6.42169i	−0.234019	+	0.405333i	−0.958987	−	0.283449i	$-0.908521\pi$
$251$	−3.70756	+	6.42169i	−0.234019	+	0.405333i	0.724968	+	0.688783i	$0.241855\pi$
$252$		0			0
$253$	−0.760445	−	1.31713i	−0.0478088	−	0.0828072i
$254$	18.0166	+	1.44181i	1.13046	+	0.0904674i
$255$		0			0
$256$	−14.6845	+	6.35344i	−0.917780	+	0.397090i
$257$	14.5395	+	17.3275i	0.906949	+	1.08086i	0.996392	+	0.0848673i	$0.0270466\pi$
$257$	14.5395	+	17.3275i	0.906949	+	1.08086i	−0.0894438	+	0.995992i	$0.528509\pi$
$258$		0			0
$259$	0.676919	+	1.85982i	0.0420617	+	0.115564i
$260$	−7.67059	−	2.66381i	−0.475710	−	0.165203i
$261$		0			0
$262$	5.28903	+	7.43563i	0.326757	+	0.459375i
$263$	−4.29886	+	24.3800i	−0.265079	+	1.50334i	0.503731	+	0.863860i	$0.331960\pi$
$263$	−4.29886	+	24.3800i	−0.265079	+	1.50334i	−0.768810	+	0.639477i	$0.779151\pi$
$264$		0			0
$265$	−42.9961	−	15.6493i	−2.64123	−	0.961328i
$266$	−0.259689	−	0.0675250i	−0.0159225	−	0.00414022i
$267$		0			0
$268$	13.6166	−	0.201806i	0.831768	−	0.0123273i
$269$		−	11.8242i		−	0.720932i	−0.932772	−	0.360466i	$-0.882618\pi$
$269$		−	11.8242i		−	0.720932i	0.932772	−	0.360466i	$-0.117382\pi$
$270$		0			0
$271$			5.20136i			0.315960i	0.987442	+	0.157980i	$0.0504982\pi$
$271$			5.20136i			0.315960i	−0.987442	+	0.157980i	$0.949502\pi$
$272$	3.01255	+	3.38143i	0.182663	+	0.205029i
$273$		0			0
$274$	−0.768414	+	2.95518i	−0.0464216	+	0.178529i
$275$	−31.8474	−	11.5915i	−1.92047	−	0.698994i
$276$		0			0
$277$	−1.28253	+	7.27359i	−0.0770598	+	0.437028i	0.921729	+	0.387834i	$0.126776\pi$
$277$	−1.28253	+	7.27359i	−0.0770598	+	0.437028i	−0.998789	+	0.0491944i	$0.984335\pi$
$278$	−8.08271	+	5.74930i	−0.484769	+	0.344820i
$279$		0			0
$280$	20.3138	+	19.4302i	1.21398	+	1.16118i
$281$	−4.19816	−	11.5344i	−0.250441	−	0.688082i	−0.999668	−	0.0257683i	$-0.991797\pi$
$281$	−4.19816	−	11.5344i	−0.250441	−	0.688082i	0.749226	−	0.662314i	$-0.230425\pi$
$282$		0			0
$283$	7.15737	+	8.52982i	0.425461	+	0.507045i	0.935607	−	0.353043i	$-0.114853\pi$
$283$	7.15737	+	8.52982i	0.425461	+	0.507045i	−0.510146	+	0.860088i	$0.670409\pi$
$284$	−25.0810	−	4.04018i	−1.48828	−	0.239741i
$285$		0			0
$286$	−0.436020	+	5.44842i	−0.0257824	+	0.322172i
$287$	−12.9749	−	22.4732i	−0.765883	−	1.32655i
$288$		0			0
$289$	−7.85908	+	13.6123i	−0.462299	+	0.800725i
$290$	1.32117	+	0.910580i	0.0775818	+	0.0534711i
$291$		0			0
$292$	0.823213	+	2.16154i	0.0481749	+	0.126495i
$293$	−22.9154	+	4.04060i	−1.33873	+	0.236055i	−0.796737	−	0.604327i	$-0.793442\pi$
$293$	−22.9154	+	4.04060i	−1.33873	+	0.236055i	−0.541995	+	0.840381i	$0.682331\pi$
$294$		0			0
$295$	−30.4491	+	36.2878i	−1.77282	+	2.11276i
$296$	2.05082	−	0.598677i	0.119201	−	0.0347974i
$297$		0			0
$298$	15.0027	+	6.86101i	0.869084	+	0.397448i
$299$	0.345389	+	0.289816i	0.0199744	+	0.0167605i
$300$		0			0
$301$	−4.23458	−	24.0155i	−0.244077	−	1.38423i
$302$	−0.455718	−	0.449014i	−0.0262236	−	0.0258379i
$303$		0			0
$304$	−0.0909539	+	0.274990i	−0.00521656	+	0.0157718i
$305$	−21.4540	−	12.3865i	−1.22845	−	0.709249i
$306$		0			0
$307$	−12.7201	+	7.34397i	−0.725976	+	0.419142i	−0.816948	−	0.576711i	$-0.804336\pi$
$307$	−12.7201	+	7.34397i	−0.725976	+	0.419142i	0.0909723	+	0.995853i	$0.471003\pi$
$308$	9.21711	−	16.5253i	0.525194	−	0.941617i
$309$		0			0
$310$	−9.96807	−	36.1284i	−0.566148	−	2.05195i
$311$	−1.78694	+	1.49942i	−0.101328	+	0.0850244i	−0.692044	−	0.721855i	$-0.743290\pi$
$311$	−1.78694	+	1.49942i	−0.101328	+	0.0850244i	0.590716	+	0.806879i	$0.298845\pi$
$312$		0			0
$313$	6.61824	−	2.40884i	0.374085	−	0.136156i	−0.148134	−	0.988967i	$-0.547327\pi$
$313$	6.61824	−	2.40884i	0.374085	−	0.136156i	0.522219	+	0.852811i	$0.325104\pi$
$314$	25.8919	−	2.45870i	1.46116	−	0.138752i
$315$		0			0
$316$	−2.98422	−	15.5713i	−0.167876	−	0.875956i
$317$	1.88259	+	0.331952i	0.105737	+	0.0186443i	0.226266	−	0.974065i	$-0.427348\pi$
$317$	1.88259	+	0.331952i	0.105737	+	0.0186443i	−0.120529	+	0.992710i	$0.538459\pi$
$318$		0			0
$319$	0.369414	−	1.01496i	0.0206832	−	0.0568266i
$320$	22.3546	−	20.5182i	1.24966	−	1.14700i
$321$		0			0
$322$	−0.670113	−	1.40969i	−0.0373439	−	0.0785592i
$323$	0.0819820			0.00456160
$324$		0			0
$325$	10.0472			0.557318
$326$	−13.7144	−	28.8506i	−0.759570	−	1.59788i
$327$		0			0
$328$	−25.1175	+	12.3995i	−1.38688	+	0.684647i
$329$	0.228733	−	0.628439i	0.0126105	−	0.0346469i
$330$		0			0
$331$	5.64140	+	0.994732i	0.310080	+	0.0546754i	0.326523	−	0.945189i	$-0.394123\pi$
$331$	5.64140	+	0.994732i	0.310080	+	0.0546754i	−0.0164430	+	0.999865i	$0.505234\pi$
$332$	−7.69331	+	1.47441i	−0.422225	+	0.0809188i
$333$		0			0
$334$	−6.48568	+	0.615880i	−0.354880	+	0.0336995i
$335$	−24.2688	+	8.83311i	−1.32595	+	0.482605i
$336$		0			0
$337$	15.9033	−	13.3444i	0.866306	−	0.726917i	−0.0970109	−	0.995283i	$-0.530928\pi$
$337$	15.9033	−	13.3444i	0.866306	−	0.726917i	0.963317	+	0.268366i	$0.0864837\pi$
$338$	4.45882	+	16.1606i	0.242528	+	0.879020i
$339$		0			0
$340$	−7.50078	−	4.18361i	−0.406787	−	0.226888i
$341$	−21.8481	+	12.6140i	−1.18314	+	0.683085i
$342$		0			0
$343$	−16.1891	−	9.34678i	−0.874129	−	0.504679i
$344$	−26.1657	+	2.87654i	−1.41076	+	0.155093i
$345$		0			0
$346$	7.52434	+	7.41365i	0.404511	+	0.398561i
$347$	−2.69361	−	15.2762i	−0.144601	−	0.820071i	−0.967687	−	0.252155i	$-0.918861\pi$
$347$	−2.69361	−	15.2762i	−0.144601	−	0.820071i	0.823086	−	0.567917i	$-0.192250\pi$
$348$		0			0
$349$	−23.0588	−	19.3486i	−1.23431	−	1.03571i	−0.997947	−	0.0640413i	$-0.979601\pi$
$349$	−23.0588	−	19.3486i	−1.23431	−	1.03571i	−0.236360	−	0.971666i	$-0.575954\pi$
$350$	−31.6313	−	14.4655i	−1.69076	−	0.773215i
$351$		0			0
$352$	−17.1538	−	11.0877i	−0.914303	−	0.590975i
$353$	−7.20122	+	8.58208i	−0.383282	+	0.456778i	−0.922847	−	0.385166i	$-0.874144\pi$
$353$	−7.20122	+	8.58208i	−0.383282	+	0.456778i	0.539565	+	0.841944i	$0.318589\pi$
$354$		0			0
$355$	47.4464	−	8.36609i	2.51820	−	0.444026i
$356$	−4.47565	+	1.70453i	−0.237209	+	0.0903398i
$357$		0			0
$358$	11.8481	+	8.16597i	0.626192	+	0.431585i
$359$	9.95142	−	17.2364i	0.525216	−	0.909701i	−0.474353	−	0.880335i	$-0.657318\pi$
$359$	9.95142	−	17.2364i	0.525216	−	0.909701i	0.999569	−	0.0293659i	$-0.00934879\pi$
$360$		0			0
$361$	−9.49738	−	16.4499i	−0.499862	−	0.865786i
$362$	1.89626	−	23.6953i	0.0996651	−	1.24539i
$363$		0			0
$364$	−0.892107	+	5.53810i	−0.0467591	+	0.290275i
$365$	−2.81960	−	3.36027i	−0.147585	−	0.175884i
$366$		0			0
$367$	−5.14389	−	14.1327i	−0.268509	−	0.737722i	−0.998525	−	0.0542921i	$-0.982710\pi$
$367$	−5.14389	−	14.1327i	−0.268509	−	0.737722i	0.730016	−	0.683430i	$-0.239512\pi$
$368$	−1.56548	+	0.622924i	−0.0816065	+	0.0324722i
$369$		0			0
$370$	−3.30160	+	2.34845i	−0.171642	+	0.122090i
$371$	−5.48886	+	31.1289i	−0.284968	+	1.61613i
$372$		0			0
$373$	25.1757	+	9.16321i	1.30355	+	0.474453i	0.898151	−	0.439688i	$-0.144911\pi$
$373$	25.1757	+	9.16321i	1.30355	+	0.474453i	0.405398	+	0.914140i	$0.367133\pi$
$374$	−1.45489	+	5.59524i	−0.0752306	+	0.289323i
$375$		0			0
$376$	−0.660885	−	0.290471i	−0.0340825	−	0.0149799i
$377$			0.320198i			0.0164910i
$378$		0			0
$379$			17.1769i			0.882321i	0.897428	+	0.441160i	$0.145433\pi$
$379$			17.1769i			0.882321i	−0.897428	+	0.441160i	$0.854567\pi$
$380$	−0.00813997	−	0.549234i	−0.000417572	−	0.0281751i
$381$		0			0
$382$	0.0945966	+	0.0245973i	0.00483998	+	0.00125851i
$383$	33.8259	+	12.3116i	1.72842	+	0.629095i	0.998516	−	0.0544509i	$-0.0173408\pi$
$383$	33.8259	+	12.3116i	1.72842	+	0.629095i	0.729908	+	0.683546i	$0.239563\pi$
$384$		0			0
$385$	−6.23134	+	35.3397i	−0.317579	+	1.80108i
$386$	21.9228	+	30.8204i	1.11584	+	1.56872i
$387$		0			0
$388$	1.26717	−	3.64888i	0.0643308	−	0.185244i
$389$	11.0897	+	30.4688i	0.562271	+	1.54483i	0.816298	+	0.577631i	$0.196023\pi$
$389$	11.0897	+	30.4688i	0.562271	+	1.54483i	−0.254027	+	0.967197i	$0.581755\pi$
$390$		0			0
$391$	0.306543	+	0.365323i	0.0155025	+	0.0184752i
$392$	−0.210822	+	0.315800i	−0.0106481	+	0.0159503i
$393$		0			0
$394$	−6.31403	−	0.505292i	−0.318096	−	0.0254563i
$395$	15.0340	+	26.0396i	0.756441	+	1.31019i
$396$		0			0
$397$	−9.13398	+	15.8205i	−0.458421	+	0.794009i	−0.998878	−	0.0473630i	$-0.984918\pi$
$397$	−9.13398	+	15.8205i	−0.458421	+	0.794009i	0.540456	+	0.841372i	$0.318252\pi$
$398$	7.89123	−	11.4495i	0.395552	−	0.573911i
$399$		0			0
$400$	−17.8008	+	33.0572i	−0.890042	+	1.65286i
$401$	−18.1056	+	3.19251i	−0.904152	+	0.159426i	−0.606347	−	0.795200i	$-0.707366\pi$
$401$	−18.1056	+	3.19251i	−0.904152	+	0.159426i	−0.297805	+	0.954627i	$0.596255\pi$
$402$		0			0
$403$	4.80736	−	5.72919i	0.239472	−	0.285391i
$404$	−6.80530	+	5.88436i	−0.338576	+	0.292758i
$405$		0			0
$406$	0.461007	−	1.00807i	0.0228794	−	0.0500296i
$407$	2.08923	+	1.75307i	0.103559	+	0.0868967i
$408$		0			0
$409$	−2.54225	−	14.4178i	−0.125706	−	0.712914i	−0.980886	−	0.194583i	$-0.937665\pi$
$409$	−2.54225	−	14.4178i	−0.125706	−	0.712914i	0.855180	−	0.518331i	$-0.173447\pi$
$410$	37.2840	−	37.8407i	1.84133	−	1.86882i
$411$		0			0
$412$	−6.51292	−	10.9043i	−0.320869	−	0.537215i
$413$	28.3405	+	16.3624i	1.39454	+	0.805140i
$414$		0			0
$415$	12.8654	−	7.42781i	0.631535	−	0.364617i
$416$	5.90285	+	1.34947i	0.289411	+	0.0661631i
$417$		0			0
$418$	−0.356432	+	0.0983420i	−0.0174336	+	0.00481006i
$419$	5.75834	−	4.83182i	0.281313	−	0.236050i	−0.491203	−	0.871045i	$-0.663443\pi$
$419$	5.75834	−	4.83182i	0.281313	−	0.236050i	0.772516	+	0.634996i	$0.218998\pi$
$420$		0			0
$421$	−16.2535	+	5.91580i	−0.792149	+	0.288319i	−0.706229	−	0.707984i	$-0.749605\pi$
$421$	−16.2535	+	5.91580i	−0.792149	+	0.288319i	−0.0859197	+	0.996302i	$0.527383\pi$
$422$	1.77306	+	18.6716i	0.0863111	+	0.908920i
$423$		0			0
$424$	33.1458	+	8.09624i	1.60970	+	0.393188i
$425$	10.4656	+	1.84537i	0.507657	+	0.0895137i
$426$		0			0
$427$	−5.85328	+	16.0818i	−0.283260	+	0.778251i
$428$	−12.5096	+	15.3651i	−0.604673	+	0.742701i
$429$		0			0
$430$	45.0865	−	21.4323i	2.17427	−	1.03356i
$431$	−22.9632			−1.10610			−0.553050	−	0.833148i	$-0.686536\pi$
$431$	−22.9632			−1.10610			−0.553050	+	0.833148i	$0.686536\pi$
$432$		0			0
$433$	−2.94287			−0.141425			−0.0707126	−	0.997497i	$-0.522527\pi$
$433$	−2.94287			−0.141425			−0.0707126	+	0.997497i	$0.522527\pi$
$434$	−23.3835	+	11.1156i	−1.12244	+	0.533565i
$435$		0			0
$436$	10.0341	−	12.3246i	0.480546	−	0.590239i
$437$	−0.0104318	+	0.0286610i	−0.000499019	+	0.00137104i
$438$		0			0
$439$	−35.9702	−	6.34252i	−1.71676	−	0.302712i	−0.773264	−	0.634084i	$-0.781377\pi$
$439$	−35.9702	−	6.34252i	−1.71676	−	0.302712i	−0.943500	+	0.331372i	$0.892489\pi$
$440$	37.6295	+	9.19142i	1.79392	+	0.438184i
$441$		0			0
$442$	−0.162022	−	1.70621i	−0.00770660	−	0.0811562i
$443$	25.7106	−	9.35788i	1.22155	−	0.444606i	0.350852	−	0.936431i	$-0.385892\pi$
$443$	25.7106	−	9.35788i	1.22155	−	0.444606i	0.870694	+	0.491825i	$0.163670\pi$
$444$		0			0
$445$	6.95770	−	5.83820i	0.329827	−	0.276757i
$446$	24.1741	−	6.66979i	1.14467	−	0.315824i
$447$		0			0
$448$	−16.6409	−	12.7472i	−0.786206	−	0.602247i
$449$	10.4394	−	6.02718i	0.492665	−	0.284440i	−0.233014	−	0.972473i	$-0.574859\pi$
$449$	10.4394	−	6.02718i	0.492665	−	0.284440i	0.725679	+	0.688033i	$0.241526\pi$
$450$		0			0
$451$	−30.9679	−	17.8794i	−1.45822	−	0.841906i
$452$	−10.3342	−	17.3021i	−0.486080	−	0.813820i
$453$		0			0
$454$	5.98262	−	6.07194i	0.280778	−	0.284970i
$455$	−1.84730	−	10.4766i	−0.0866030	−	0.491150i
$456$		0			0
$457$	12.1847	+	10.2241i	0.569974	+	0.478265i	0.881637	−	0.471927i	$-0.156442\pi$
$457$	12.1847	+	10.2241i	0.569974	+	0.478265i	−0.311663	+	0.950193i	$0.600886\pi$
$458$	−10.3165	+	22.5588i	−0.482059	+	1.05410i
$459$		0			0
$460$	2.41703	−	2.08994i	0.112695	−	0.0974440i
$461$	9.40166	−	11.2045i	0.437879	−	0.521844i	−0.501299	−	0.865274i	$-0.667144\pi$
$461$	9.40166	−	11.2045i	0.437879	−	0.521844i	0.939178	+	0.343430i	$0.111589\pi$
$462$		0			0
$463$	19.4128	−	3.42301i	0.902191	−	0.159081i	0.296735	−	0.954960i	$-0.404102\pi$
$463$	19.4128	−	3.42301i	0.902191	−	0.159081i	0.605456	+	0.795879i	$0.292991\pi$
$464$	−1.05351	−	0.567301i	−0.0489081	−	0.0263363i
$465$		0			0
$466$	0.758433	−	1.10042i	0.0351337	−	0.0509759i
$467$	18.2329	−	31.5803i	0.843718	−	1.46136i	−0.0430124	−	0.999075i	$-0.513696\pi$
$467$	18.2329	−	31.5803i	0.843718	−	1.46136i	0.886730	−	0.462287i	$-0.152971\pi$
$468$		0			0
$469$	8.92075	+	15.4512i	0.411922	+	0.713470i
$470$	1.36470	+	0.109213i	0.0629488	+	0.00503760i
$471$		0			0
$472$	19.6132	−	29.3794i	0.902769	−	1.35230i
$473$	−21.6001	−	25.7420i	−0.993175	−	1.18362i
$474$		0			0
$475$	0.232460	+	0.638678i	0.0106660	+	0.0293045i
$476$	−1.94644	+	5.60489i	−0.0892151	+	0.256900i
$477$		0			0
$478$	9.16592	+	12.8860i	0.419240	+	0.589392i
$479$	−1.10609	+	6.27294i	−0.0505384	+	0.286618i	−0.999594	−	0.0284909i	$-0.990930\pi$
$479$	−1.10609	+	6.27294i	−0.0505384	+	0.286618i	0.949056	+	0.315109i	$0.102041\pi$
$480$		0			0
$481$	−0.759759	−	0.276530i	−0.0346420	−	0.0126087i
$482$	−26.4665	−	6.88189i	−1.20552	−	0.313462i
$483$		0			0
$484$	−0.0603785	−	4.07397i	−0.00274448	−	0.185180i
$485$			7.32538i			0.332628i
$486$		0			0
$487$		−	31.5578i		−	1.43002i	−0.699115	−	0.715009i	$-0.746423\pi$
$487$		−	31.5578i		−	1.43002i	0.699115	−	0.715009i	$-0.253577\pi$
$488$	16.9120	+	7.43315i	0.765572	+	0.336483i
$489$		0			0
$490$	0.181216	−	0.696921i	0.00818648	−	0.0314837i
$491$	−25.0585	−	9.12054i	−1.13087	−	0.411604i	−0.292264	−	0.956338i	$-0.594409\pi$
$491$	−25.0585	−	9.12054i	−1.13087	−	0.411604i	−0.838609	+	0.544734i	$0.816631\pi$
$492$		0			0
$493$	−0.0588108	+	0.333533i	−0.00264871	+	0.0150216i
$494$	0.0893219	−	0.0635354i	0.00401878	−	0.00285859i
$495$		0			0
$496$	10.3328	+	25.9677i	0.463958	+	1.16598i
$497$	−11.3834	−	31.2757i	−0.510617	−	1.40291i
$498$		0			0
$499$	14.4331	+	17.2006i	0.646112	+	0.770007i	0.985322	−	0.170704i	$-0.0546042\pi$
$499$	14.4331	+	17.2006i	0.646112	+	0.770007i	−0.339210	+	0.940711i	$0.610160\pi$
$500$	5.29175	−	32.8506i	0.236654	−	1.46912i
$501$		0			0
$502$	−0.836533	+	10.4532i	−0.0373363	+	0.466547i
$503$	13.0818	+	22.6583i	0.583287	+	1.01028i	0.995087	+	0.0990084i	$0.0315671\pi$
$503$	13.0818	+	22.6583i	0.583287	+	1.01028i	−0.411799	+	0.911274i	$0.635100\pi$
$504$		0			0
$505$	8.53082	−	14.7758i	0.379617	−	0.657515i
$506$	−1.77098	−	1.22060i	−0.0787295	−	0.0542621i
$507$		0			0
$508$	23.8871	−	9.09728i	1.05982	−	0.403627i
$509$	28.8191	−	5.08158i	1.27738	−	0.225237i	0.506515	−	0.862231i	$-0.330934\pi$
$509$	28.8191	−	5.08158i	1.27738	−	0.225237i	0.770869	+	0.636994i	$0.219822\pi$
$510$		0			0
$511$	−1.94785	+	2.32136i	−0.0861680	+	0.102691i
$512$	−14.8982	+	17.0306i	−0.658415	+	0.752655i
$513$		0			0
$514$	29.0910	+	13.3038i	1.28315	+	0.586806i
$515$	18.4521	+	15.4831i	0.813095	+	0.682268i
$516$		0			0
$517$	−0.160028	−	0.907563i	−0.00703801	−	0.0399146i
$518$	1.99379	+	1.96446i	0.0876020	+	0.0863133i
$519$		0			0
$520$	−11.4146	+	1.25487i	−0.500563	+	0.0550296i
$521$	12.2522	+	7.07379i	0.536777	+	0.309909i	0.743772	−	0.668434i	$-0.233035\pi$
$521$	12.2522	+	7.07379i	0.536777	+	0.309909i	−0.206995	+	0.978342i	$0.566368\pi$
$522$		0			0
$523$	−7.35440	+	4.24607i	−0.321586	+	0.185668i	−0.652099	−	0.758134i	$-0.726111\pi$
$523$	−7.35440	+	4.24607i	−0.321586	+	0.185668i	0.330513	+	0.943801i	$0.392778\pi$
$524$	11.2700	+	6.28591i	0.492331	+	0.274601i
$525$		0			0
$526$	9.31170	+	33.7494i	0.406010	+	1.47155i
$527$	6.05985	−	5.08482i	0.263971	−	0.221498i
$528$		0			0
$529$	21.4462	−	7.80578i	0.932444	−	0.339382i
$530$	−64.4182	+	6.11716i	−2.79815	+	0.265712i
$531$		0			0
$532$	−0.372685	+	0.0714245i	−0.0161579	+	0.00309664i
$533$	10.4398	+	1.84081i	0.452196	+	0.0797343i
$534$		0			0
$535$	12.8516	−	35.3096i	0.555625	−	1.52657i
$536$	17.2693	−	8.52513i	0.745920	−	0.368230i
$537$		0			0
$538$	−7.17907	−	15.1024i	−0.309512	−	0.651110i
$539$	−0.484722			−0.0208785
$540$		0			0
$541$	−26.2456			−1.12839			−0.564194	−	0.825642i	$-0.690813\pi$
$541$	−26.2456			−1.12839			−0.564194	+	0.825642i	$0.690813\pi$
$542$	3.15802	+	6.64343i	0.135649	+	0.285360i
$543$		0			0
$544$	5.90083	+	2.48985i	0.252996	+	0.106751i
$545$	−10.3085	+	28.3223i	−0.441566	+	1.21319i
$546$		0			0
$547$	29.4440	+	5.19178i	1.25894	+	0.221984i	0.763014	−	0.646382i	$-0.223719\pi$
$547$	29.4440	+	5.19178i	1.25894	+	0.221984i	0.495923	+	0.868367i	$0.334830\pi$
$548$	0.812789	+	4.24104i	0.0347206	+	0.181168i
$549$		0			0
$550$	−47.7149	+	4.53101i	−2.03457	+	0.193203i
$551$	−0.0203543	+	0.00740834i	−0.000867121	+	0.000315606i
$552$		0			0
$553$	15.9121	−	13.3518i	0.676650	−	0.567777i
$554$	2.77807	+	10.0689i	0.118029	+	0.427786i
$555$		0			0
$556$	−6.83293	+	12.2507i	−0.289781	+	0.519547i
$557$	−12.1389	+	7.00840i	−0.514342	+	0.296955i	−0.734617	−	0.678482i	$-0.762638\pi$
$557$	−12.1389	+	7.00840i	−0.514342	+	0.296955i	0.220275	+	0.975438i	$0.429305\pi$
$558$		0			0
$559$	8.62733	+	4.98099i	0.364897	+	0.210673i
$560$	37.7429	+	12.4836i	1.59493	+	0.527528i
$561$		0			0
$562$	−12.3652	−	12.1833i	−0.521595	−	0.513922i
$563$	−8.08075	−	45.8282i	−0.340563	−	1.93143i	−0.363263	−	0.931687i	$-0.618337\pi$
$563$	−8.08075	−	45.8282i	−0.340563	−	1.93143i	0.0226998	−	0.999742i	$-0.492774\pi$
$564$		0			0
$565$	29.2783	+	24.5674i	1.23175	+	1.03356i
$566$	14.3206	+	6.54908i	0.601942	+	0.275279i
$567$		0			0
$568$	−34.4877	+	10.0677i	−1.44707	+	0.422430i
$569$	8.80061	−	10.4882i	0.368941	−	0.439686i	−0.549350	−	0.835592i	$-0.685125\pi$
$569$	8.80061	−	10.4882i	0.368941	−	0.439686i	0.918291	+	0.395906i	$0.129569\pi$
$570$		0			0
$571$	−41.0075	+	7.23074i	−1.71611	+	0.302597i	−0.943276	−	0.332009i	$-0.892274\pi$
$571$	−41.0075	+	7.23074i	−1.71611	+	0.302597i	−0.772836	+	0.634606i	$0.781163\pi$
$572$	2.75112	+	7.22371i	0.115030	+	0.302039i
$573$		0			0
$574$	−30.2168	−	20.8261i	−1.26123	−	0.869264i
$575$	−1.97684	+	3.42398i	−0.0824398	+	0.142790i
$576$		0			0
$577$	11.9468	+	20.6925i	0.497352	+	0.861439i	0.999995	−	0.00305510i	$-0.000972470\pi$
$577$	11.9468	+	20.6925i	0.497352	+	0.861439i	−0.502643	+	0.864494i	$0.667639\pi$
$578$	−1.77323	+	22.1580i	−0.0737568	+	0.921651i
$579$		0			0
$580$	2.24033	+	0.360884i	0.0930245	+	0.0149849i
$581$	−6.59671	−	7.86166i	−0.273678	−	0.326157i
$582$		0			0
$583$	14.8975	+	40.9304i	0.616990	+	1.69516i
$584$	2.36384	+	2.26101i	0.0978162	+	0.0935614i
$585$		0			0
$586$	−26.8154	+	19.0740i	−1.10773	+	0.787940i
$587$	2.47759	−	14.0511i	0.102261	−	0.579952i	−0.890018	−	0.455926i	$-0.849308\pi$
$587$	2.47759	−	14.0511i	0.102261	−	0.579952i	0.992279	−	0.124026i	$-0.0395807\pi$
$588$		0			0
$589$	0.475418	+	0.173038i	0.0195893	+	0.00712991i
$590$	−16.8588	+	64.8359i	−0.694067	+	2.66925i
$591$		0			0
$592$	2.25592	−	2.00982i	0.0927176	−	0.0826031i
$593$		−	15.2762i		−	0.627320i	−0.949535	−	0.313660i	$-0.898445\pi$
$593$		−	15.2762i		−	0.627320i	0.949535	−	0.313660i	$-0.101555\pi$
$594$		0			0
$595$		−	11.2522i		−	0.461295i
$596$	23.3279	−	0.345733i	0.955548	−	0.0141618i
$597$		0			0
$598$	0.617110	+	0.160463i	0.0252355	+	0.00656182i
$599$	−14.3465	−	5.22168i	−0.586180	−	0.213352i	0.0318684	−	0.999492i	$-0.489854\pi$
$599$	−14.3465	−	5.22168i	−0.586180	−	0.213352i	−0.618048	+	0.786140i	$0.712076\pi$
$600$		0			0
$601$	7.19286	−	40.7927i	0.293403	−	1.66397i	−0.380220	−	0.924896i	$-0.624152\pi$
$601$	7.19286	−	40.7927i	0.293403	−	1.66397i	0.673623	−	0.739075i	$-0.264737\pi$
$602$	−19.9897	−	28.1028i	−0.814720	−	1.14538i
$603$		0			0
$604$	−0.854686	−	0.296812i	−0.0347767	−	0.0120771i
$605$	2.64278	+	7.26099i	0.107444	+	0.295201i
$606$		0			0
$607$	8.26489	+	9.84971i	0.335461	+	0.399787i	0.907235	−	0.420624i	$-0.138189\pi$
$607$	8.26489	+	9.84971i	0.335461	+	0.399787i	−0.571774	+	0.820411i	$0.693744\pi$
$608$	0.0507902	+	0.406453i	0.00205982	+	0.0164839i
$609$		0			0
$610$	−34.9226	−	2.79475i	−1.41398	−	0.113156i
$611$	0.136600	+	0.236599i	0.00552626	+	0.00957177i
$612$		0			0
$613$	−15.8003	+	27.3670i	−0.638170	+	1.10534i	0.347664	+	0.937619i	$0.386975\pi$
$613$	−15.8003	+	27.3670i	−0.638170	+	1.10534i	−0.985834	+	0.167723i	$0.946358\pi$
$614$	−11.7879	+	17.1031i	−0.475719	+	0.690227i
$615$		0			0
$616$	1.73915	−	26.7031i	0.0700724	−	1.07590i
$617$	32.9384	−	5.80793i	1.32605	−	0.233819i	0.534628	−	0.845088i	$-0.320452\pi$
$617$	32.9384	−	5.80793i	1.32605	−	0.233819i	0.791423	+	0.611269i	$0.209341\pi$
$618$		0			0
$619$	21.1853	−	25.2477i	0.851511	−	1.01479i	−0.148155	−	0.988964i	$-0.547334\pi$
$619$	21.1853	−	25.2477i	0.851511	−	1.01479i	0.999666	−	0.0258272i	$-0.00822196\pi$
$620$	−34.6672	−	40.0928i	−1.39227	−	1.61017i
$621$		0			0
$622$	−1.37199	+	3.00008i	−0.0550118	+	0.120292i
$623$	−4.80656	−	4.03319i	−0.192571	−	0.161586i
$624$		0			0
$625$	2.80815	+	15.9258i	0.112326	+	0.637032i
$626$	6.99061	−	7.09498i	0.279401	−	0.283572i
$627$		0			0
$628$	31.5776	−	18.8607i	1.26008	−	0.752624i
$629$	−0.740610	−	0.427591i	−0.0295300	−	0.0170492i
$630$		0			0
$631$	10.5759	−	6.10598i	0.421018	−	0.243075i	−0.274495	−	0.961589i	$-0.588511\pi$
$631$	10.5759	−	6.10598i	0.421018	−	0.243075i	0.695513	+	0.718514i	$0.255177\pi$
$632$	−13.2658	−	18.0766i	−0.527684	−	0.719048i
$633$		0			0
$634$	2.60608	−	0.719037i	0.103501	−	0.0285566i
$635$	−37.1341	+	31.1592i	−1.47362	+	1.23652i
$636$		0			0
$637$	0.135032	−	0.0491475i	0.00535015	−	0.00194729i
$638$	−0.144400	−	1.52064i	−0.00571686	−	0.0602028i
$639$		0			0
$640$	16.0947	−	39.7795i	0.636200	−	1.57242i
$641$	2.91455	+	0.513915i	0.115118	+	0.0202984i	0.230910	−	0.972975i	$-0.425830\pi$
$641$	2.91455	+	0.513915i	0.115118	+	0.0202984i	−0.115792	+	0.993273i	$0.536941\pi$
$642$		0			0
$643$	1.28689	−	3.53570i	0.0507499	−	0.139434i	−0.911728	−	0.410795i	$-0.865251\pi$
$643$	1.28689	−	3.53570i	0.0507499	−	0.139434i	0.962478	+	0.271360i	$0.0874735\pi$
$644$	−1.71180	−	1.39367i	−0.0674544	−	0.0549183i
$645$		0			0
$646$	0.104711	−	0.0497756i	0.00411982	−	0.00195840i
$647$	−17.3248			−0.681109			−0.340555	−	0.940225i	$-0.610615\pi$
$647$	−17.3248			−0.681109			−0.340555	+	0.940225i	$0.610615\pi$
$648$		0			0
$649$	45.0946			1.77012
$650$	12.8328	−	6.10019i	0.503343	−	0.239269i
$651$		0			0
$652$	−35.0334	−	28.5226i	−1.37201	−	1.11703i
$653$	−7.83529	+	21.5273i	−0.306619	+	0.842428i	0.686691	+	0.726949i	$0.259062\pi$
$653$	−7.83529	+	21.5273i	−0.306619	+	0.842428i	−0.993310	+	0.115479i	$0.963160\pi$
$654$		0			0
$655$	−24.1010	−	4.24967i	−0.941706	−	0.166048i
$656$	−24.5530	+	31.0874i	−0.958632	+	1.21376i
$657$		0			0
$658$	−0.0894096	−	0.941549i	−0.00348555	−	0.0367054i
$659$	−29.5497	+	10.7552i	−1.15109	+	0.418963i	−0.845907	−	0.533331i	$-0.820940\pi$
$659$	−29.5497	+	10.7552i	−1.15109	+	0.418963i	−0.305184	+	0.952293i	$0.598718\pi$
$660$		0			0
$661$	−11.3401	+	9.51547i	−0.441079	+	0.370109i	−0.836113	−	0.548557i	$-0.815177\pi$
$661$	−11.3401	+	9.51547i	−0.441079	+	0.370109i	0.395034	+	0.918666i	$0.370733\pi$
$662$	7.80943	−	2.15468i	0.303522	−	0.0837439i
$663$		0			0
$664$	−8.93108	+	6.55421i	−0.346593	+	0.254353i
$665$	0.623232	−	0.359823i	0.0241679	−	0.0139534i
$666$		0			0
$667$	−0.109120	−	0.0630006i	−0.00422515	−	0.00243939i
$668$	−7.90989	+	4.72443i	−0.306043	+	0.182794i
$669$		0			0
$670$	−25.6342	+	26.0170i	−0.990336	+	1.00512i
$671$	4.09511	+	23.2245i	0.158090	+	0.896574i
$672$		0			0
$673$	−6.38737	−	5.35964i	−0.246215	−	0.206599i	0.511325	−	0.859387i	$-0.329155\pi$
$673$	−6.38737	−	5.35964i	−0.246215	−	0.206599i	−0.757540	+	0.652788i	$0.773599\pi$
$674$	12.2103	−	26.6999i	0.470324	−	1.02844i
$675$		0			0
$676$	15.5070	+	17.9339i	0.596422	+	0.689765i
$677$	26.9751	−	32.1477i	1.03674	−	1.23553i	0.0653922	−	0.997860i	$-0.479170\pi$
$677$	26.9751	−	32.1477i	1.03674	−	1.23553i	0.971345	−	0.237675i	$-0.0763854\pi$
$678$		0			0
$679$	4.98369	−	0.878759i	0.191256	−	0.0337237i
$680$	−12.1205	−	0.789394i	−0.464798	−	0.0302719i
$681$		0			0
$682$	−20.2468	+	29.3763i	−0.775290	+	1.12488i
$683$	−8.40955	+	14.5658i	−0.321782	+	0.557344i	−0.980856	−	0.194735i	$-0.937615\pi$
$683$	−8.40955	+	14.5658i	−0.321782	+	0.557344i	0.659073	+	0.752079i	$0.270949\pi$
$684$		0			0
$685$	−4.09468	−	7.09220i	−0.156450	−	0.270979i
$686$	−26.3524	−	2.10890i	−1.00614	−	0.0805184i
$687$		0			0
$688$	−31.6736	+	19.5607i	−1.20755	+	0.745743i
$689$	−8.30013	−	9.89171i	−0.316210	−	0.376844i
$690$		0			0
$691$	−11.0161	−	30.2664i	−0.419071	−	1.15139i	−0.952232	−	0.305374i	$-0.901218\pi$
$691$	−11.0161	−	30.2664i	−0.419071	−	1.15139i	0.533161	−	0.846014i	$-0.321004\pi$
$692$	14.1117	+	4.90065i	0.536446	+	0.186295i
$693$		0			0
$694$	−12.7154	−	17.8761i	−0.482671	−	0.678568i
$695$	4.61949	−	26.1984i	0.175227	−	0.993763i
$696$		0			0
$697$	10.5364	+	3.83495i	0.399096	+	0.145259i
$698$	−41.1993	−	10.7128i	−1.55942	−	0.405485i
$699$		0			0
$700$	−49.1838	+	0.728932i	−1.85897	+	0.0275510i
$701$		−	22.5259i		−	0.850790i	−0.905008	−	0.425395i	$-0.860135\pi$
$701$		−	22.5259i		−	0.850790i	0.905008	−	0.425395i	$-0.139865\pi$
$702$		0			0
$703$		−	0.0546942i		−	0.00206283i
$704$	−28.6416	−	3.74670i	−1.07947	−	0.141209i
$705$		0			0
$706$	−3.98711	+	15.3337i	−0.150057	+	0.577091i
$707$	−11.0758	−	4.03127i	−0.416549	−	0.151611i
$708$		0			0
$709$	−1.33870	+	7.59217i	−0.0502761	+	0.285130i	−0.999572	−	0.0292540i	$-0.990687\pi$
$709$	−1.33870	+	7.59217i	−0.0502761	+	0.285130i	0.949296	+	0.314384i	$0.101798\pi$
$710$	55.5214	−	39.4928i	2.08368	−	1.48214i
$711$		0			0
$712$	−4.68161	+	4.89451i	−0.175451	+	0.183430i
$713$	1.00658	+	2.76555i	0.0376966	+	0.103571i
$714$		0			0
$715$	−9.42288	−	11.2298i	−0.352396	−	0.419969i
$716$	20.0910	+	3.23636i	0.750835	+	0.120949i
$717$		0			0
$718$	2.24533	−	28.0572i	0.0837949	−	1.04708i
$719$	−9.44892	−	16.3660i	−0.352385	−	0.610349i	0.634282	−	0.773102i	$-0.281296\pi$
$719$	−9.44892	−	16.3660i	−0.352385	−	0.610349i	−0.986667	+	0.162753i	$0.947963\pi$
$720$		0			0
$721$	8.32013	−	14.4109i	0.309858	−	0.536690i
$722$	−22.1182	−	15.2443i	−0.823152	−	0.567334i
$723$		0			0
$724$	−11.9647	−	31.4161i	−0.444663	−	1.16757i
$725$	−2.76513	+	0.487568i	−0.102695	+	0.0181078i
$726$		0			0
$727$	−14.0555	+	16.7507i	−0.521289	+	0.621248i	−0.960885	−	0.276947i	$-0.910677\pi$
$727$	−14.0555	+	16.7507i	−0.521289	+	0.621248i	0.439596	+	0.898196i	$0.355122\pi$
$728$	2.22303	+	7.61517i	0.0823910	+	0.282237i
$729$		0			0
$730$	−5.64153	−	2.57997i	−0.208802	−	0.0954890i
$731$	8.07177	+	6.77302i	0.298545	+	0.250509i
$732$		0			0
$733$	−3.02175	−	17.1372i	−0.111611	−	0.632977i	−0.988373	−	0.152052i	$-0.951412\pi$
$733$	−3.02175	−	17.1372i	−0.111611	−	0.632977i	0.876762	−	0.480925i	$-0.159699\pi$
$734$	−15.1507	−	14.9279i	−0.559224	−	0.550998i
$735$		0			0
$736$	−1.62130	+	1.74612i	−0.0597620	+	0.0643628i
$737$	21.2917	+	12.2928i	0.784289	+	0.452810i
$738$		0			0
$739$	−24.7291	+	14.2773i	−0.909674	+	0.525201i	−0.880326	−	0.474369i	$-0.842676\pi$
$739$	−24.7291	+	14.2773i	−0.909674	+	0.525201i	−0.0293479	+	0.999569i	$0.509343\pi$
$740$	−2.79109	+	5.00413i	−0.102603	+	0.183956i
$741$		0			0
$742$	11.8894	+	43.0919i	0.436472	+	1.58195i
$743$	24.1483	−	20.2629i	0.885917	−	0.743373i	−0.0814700	−	0.996676i	$-0.525961\pi$
$743$	24.1483	−	20.2629i	0.885917	−	0.743373i	0.967387	+	0.253303i	$0.0815170\pi$
$744$		0			0
$745$	−41.5771	+	15.1328i	−1.52327	+	0.554424i
$746$	37.7191	−	3.58181i	1.38099	−	0.131139i
$747$		0			0
$748$	1.53891	+	8.02986i	0.0562681	+	0.293601i
$749$	−25.5639	−	4.50761i	−0.934086	−	0.164705i
$750$		0			0
$751$	−9.89995	+	27.1999i	−0.361254	+	0.992538i	0.617332	+	0.786703i	$0.288213\pi$
$751$	−9.89995	+	27.1999i	−0.361254	+	0.992538i	−0.978587	+	0.205836i	$0.934009\pi$
$752$	−1.02047	+	0.0302547i	−0.0372129	+	0.00110327i
$753$		0			0
$754$	0.194409	+	0.408972i	0.00707996	+	0.0148939i
$755$	1.71584			0.0624458
$756$		0			0
$757$	8.58739			0.312114			0.156057	−	0.987748i	$-0.450122\pi$
$757$	8.58739			0.312114			0.156057	+	0.987748i	$0.450122\pi$
$758$	10.4290	+	21.9392i	0.378800	+	0.796869i
$759$		0			0
$760$	−0.343866	−	0.696567i	−0.0124733	−	0.0252671i
$761$	4.64163	−	12.7528i	0.168259	−	0.462287i	−0.826691	−	0.562655i	$-0.809780\pi$
$761$	4.64163	−	12.7528i	0.168259	−	0.462287i	0.994950	+	0.100368i	$0.0320020\pi$
$762$		0			0
$763$	20.5052	+	3.61561i	0.742336	+	0.130894i
$764$	0.135758	−	0.0260178i	0.00491154	−	0.000941289i
$765$		0			0
$766$	50.6792	−	4.81250i	1.83111	−	0.173883i
$767$	−12.5622	+	4.57228i	−0.453596	+	0.165096i
$768$		0			0
$769$	−22.9731	+	19.2767i	−0.828432	+	0.695137i	−0.954930	−	0.296830i	$-0.904071\pi$
$769$	−22.9731	+	19.2767i	−0.828432	+	0.695137i	0.126499	+	0.991967i	$0.459626\pi$
$770$	13.4976	+	48.9210i	0.486421	+	1.76299i
$771$		0			0
$772$	46.7136	+	26.0548i	1.68126	+	0.937734i
$773$	4.59241	−	2.65143i	0.165177	−	0.0953652i	−0.415132	−	0.909761i	$-0.636265\pi$
$773$	4.59241	−	2.65143i	0.165177	−	0.0953652i	0.580310	+	0.814396i	$0.302931\pi$
$774$		0			0
$775$	56.7958	+	32.7911i	2.04016	+	1.17789i
$776$	−0.596938	−	5.42990i	−0.0214288	−	0.194922i
$777$		0			0
$778$	32.6635	+	32.1830i	1.17104	+	1.15382i
$779$	0.124526	+	0.706222i	0.00446161	+	0.0253030i
$780$		0			0
$781$	−35.1337	−	29.4806i	−1.25718	−	1.05490i
$782$	0.613339	+	0.280491i	0.0219329	+	0.0100303i
$783$		0			0
$784$	−0.0775336	+	0.531356i	−0.00276906	+	0.0189770i
$785$	−44.8374	+	53.4351i	−1.60032	+	1.90718i
$786$		0			0
$787$	−21.5184	+	3.79428i	−0.767048	+	0.135251i	−0.543463	−	0.839433i	$-0.682887\pi$
$787$	−21.5184	+	3.79428i	−0.767048	+	0.135251i	−0.223585	+	0.974684i	$0.571776\pi$
$788$	−8.37138	+	3.18820i	−0.298218	+	0.113575i
$789$		0			0
$790$	35.0121	+	24.1311i	1.24568	+	0.858547i
$791$	13.2017	−	22.8661i	0.469400	−	0.813024i
$792$		0			0
$793$	−3.49561	−	6.05457i	−0.124133	−	0.215004i
$794$	−2.06089	+	25.7525i	−0.0731382	+	0.913921i
$795$		0			0
$796$	3.12748	−	19.4150i	0.110851	−	0.688147i
$797$	−1.65407	−	1.97124i	−0.0585902	−	0.0698251i	0.735953	−	0.677032i	$-0.236734\pi$
$797$	−1.65407	−	1.97124i	−0.0585902	−	0.0698251i	−0.794544	+	0.607207i	$0.792290\pi$
$798$		0			0
$799$	0.0988332	+	0.271542i	0.00349647	+	0.00960646i
$800$	−2.66529	+	53.0301i	−0.0942324	+	1.87490i
$801$		0			0
$802$	−21.1871	+	15.0705i	−0.748141	+	0.532159i
$803$	−0.725116	+	4.11234i	−0.0255888	+	0.145121i
$804$		0			0
$805$	3.93378	+	1.43178i	0.138648	+	0.0504636i
$806$	2.66170	−	10.2364i	0.0937544	−	0.360562i
$807$		0			0
$808$	−5.11936	+	11.6477i	−0.180098	+	0.409763i
$809$		−	41.7773i		−	1.46881i	−0.678710	−	0.734407i	$-0.737461\pi$
$809$		−	41.7773i		−	1.46881i	0.678710	−	0.734407i	$-0.262539\pi$
$810$		0			0
$811$			49.5187i			1.73884i	0.494077	+	0.869418i	$0.335506\pi$
$811$			49.5187i			1.73884i	−0.494077	+	0.869418i	$0.664494\pi$
$812$	−0.0232306	−	1.56746i	−0.000815234	−	0.0550069i
$813$		0			0
$814$	3.73286	+	0.970629i	0.130837	+	0.0340205i
$815$	80.5081	+	29.3025i	2.82007	+	1.02642i
$816$		0			0
$817$	−0.117022	+	0.663664i	−0.00409408	+	0.0232187i
$818$	−12.0009	−	16.8716i	−0.419601	−	0.589901i
$819$		0			0
$820$	24.6459	−	70.9690i	0.860671	−	2.47835i
$821$	−4.28022	−	11.7598i	−0.149381	−	0.410420i	0.842322	−	0.538975i	$-0.181188\pi$
$821$	−4.28022	−	11.7598i	−0.149381	−	0.410420i	−0.991702	+	0.128555i	$0.958966\pi$
$822$		0			0
$823$	3.52799	+	4.20450i	0.122978	+	0.146560i	0.824020	−	0.566560i	$-0.191726\pi$
$823$	3.52799	+	4.20450i	0.122978	+	0.146560i	−0.701042	+	0.713120i	$0.747282\pi$
$824$	−14.9392	−	9.97313i	−0.520431	−	0.347431i
$825$		0			0
$826$	46.1323	+	3.69182i	1.60515	+	0.128455i
$827$	10.0525	+	17.4114i	0.349559	+	0.605454i	0.986171	−	0.165730i	$-0.0529980\pi$
$827$	10.0525	+	17.4114i	0.349559	+	0.605454i	−0.636612	+	0.771184i	$0.719665\pi$
$828$		0			0
$829$	23.9459	−	41.4755i	0.831675	−	1.44050i	−0.0650348	−	0.997883i	$-0.520716\pi$
$829$	23.9459	−	41.4755i	0.831675	−	1.44050i	0.896709	−	0.442620i	$-0.145951\pi$
$830$	11.9224	−	17.2984i	0.413834	−	0.600436i
$831$		0			0
$832$	8.35874	−	1.86033i	0.289787	−	0.0644952i
$833$	0.149682	−	0.0263930i	0.00518618	−	0.000914463i
$834$		0			0
$835$	11.2314	−	13.3850i	0.388677	−	0.463207i
$836$	−0.395543	+	0.342016i	−0.0136802	+	0.0118289i
$837$		0			0
$838$	4.42118	−	9.66763i	0.152727	−	0.333963i
$839$	−34.1645	−	28.6674i	−1.17949	−	0.989708i	−0.999982	−	0.00595149i	$-0.998106\pi$
$839$	−34.1645	−	28.6674i	−1.17949	−	0.989708i	−0.179506	−	0.983757i	$-0.557450\pi$
$840$		0			0
$841$	5.02026	+	28.4713i	0.173112	+	0.981769i
$842$	−17.1680	+	17.4243i	−0.591649	+	0.600482i
$843$		0			0
$844$	13.6012	+	22.7718i	0.468171	+	0.783837i
$845$	−38.9385	−	22.4811i	−1.33952	−	0.773375i
$846$		0			0
$847$	4.62285	−	2.66900i	0.158843	−	0.0917081i
$848$	47.2512	−	9.78369i	1.62261	−	0.335973i
$849$		0			0
$850$	14.4876	−	3.99724i	0.496922	−	0.137104i
$851$	0.243725	−	0.204510i	0.00835479	−	0.00701050i
$852$		0			0
$853$	4.65044	−	1.69262i	0.159228	−	0.0579542i	−0.261176	−	0.965291i	$-0.584110\pi$
$853$	4.65044	−	1.69262i	0.159228	−	0.0579542i	0.420404	+	0.907337i	$0.361888\pi$
$854$	2.28799	+	24.0942i	0.0782935	+	0.824488i
$855$		0			0
$856$	−6.64887	+	27.2203i	−0.227254	+	0.930371i
$857$	54.3261	+	9.57915i	1.85574	+	0.327218i	0.986060	−	0.166393i	$-0.0532119\pi$
$857$	54.3261	+	9.57915i	1.85574	+	0.327218i	0.869683	+	0.493610i	$0.164323\pi$
$858$		0			0
$859$	16.3765	−	44.9941i	0.558759	−	1.53518i	−0.262681	−	0.964883i	$-0.584607\pi$
$859$	16.3765	−	44.9941i	0.558759	−	1.53518i	0.821440	−	0.570295i	$-0.193171\pi$
$860$	44.5740	−	54.7489i	1.51996	−	1.86692i
$861$		0			0
$862$	−29.3297	+	13.9422i	−0.998975	+	0.474873i
$863$	−29.9620			−1.01992			−0.509959	−	0.860199i	$-0.670339\pi$
$863$	−29.9620			−1.01992			−0.509959	+	0.860199i	$0.670339\pi$
$864$		0			0
$865$	−28.3302			−0.963255
$866$	−3.75878	+	1.78677i	−0.127728	+	0.0607170i
$867$		0			0
$868$	−23.1177	+	28.3947i	−0.784666	+	0.963780i
$869$	9.78977	−	26.8972i	0.332095	−	0.912424i
$870$		0			0
$871$	−7.17774	−	1.26563i	−0.243208	−	0.0428842i
$872$	5.33314	−	21.8338i	0.180603	−	0.739384i
$873$		0			0
$874$	0.00407768	+	0.0429409i	0.000137929	+	0.00145250i
$875$	40.9643	−	14.9098i	1.38485	−	0.504043i
$876$		0			0
$877$	−22.6770	+	19.0283i	−0.765749	+	0.642540i	−0.939617	−	0.342229i	$-0.888818\pi$
$877$	−22.6770	+	19.0283i	−0.765749	+	0.642540i	0.173867	+	0.984769i	$0.444374\pi$
$878$	−49.7938	+	13.7385i	−1.68046	+	0.463650i
$879$		0			0
$880$	53.6428	−	11.1071i	1.80830	−	0.374421i
$881$	−41.2789	+	23.8324i	−1.39072	+	0.802934i	−0.993395	−	0.114743i	$-0.963395\pi$
$881$	−41.2789	+	23.8324i	−1.39072	+	0.802934i	−0.397327	+	0.917677i	$0.630062\pi$
$882$		0			0
$883$	−27.0065	−	15.5922i	−0.908842	−	0.524720i	−0.0287839	−	0.999586i	$-0.509163\pi$
$883$	−27.0065	−	15.5922i	−0.908842	−	0.524720i	−0.880059	+	0.474865i	$0.842497\pi$
$884$	−1.24287	−	2.08089i	−0.0418024	−	0.0699877i
$885$		0			0
$886$	27.1571	−	27.5626i	0.912362	−	0.925984i
$887$	9.61775	+	54.5450i	0.322932	+	1.83144i	0.523824	+	0.851827i	$0.324505\pi$
$887$	9.61775	+	54.5450i	0.322932	+	1.83144i	−0.200891	+	0.979614i	$0.564384\pi$
$888$		0			0
$889$	25.6532	+	21.5256i	0.860382	+	0.721946i
$890$	5.34203	−	11.6812i	0.179065	−	0.391556i
$891$		0			0
$892$	26.8267	−	23.1963i	0.898225	−	0.776671i
$893$	−0.0118796	+	0.0141575i	−0.000397535	+	0.000473763i
$894$		0			0
$895$	−38.0067	+	6.70161i	−1.27042	+	0.224010i
$896$	−28.9940	−	6.17776i	−0.968621	−	0.206385i
$897$		0			0
$898$	9.67427	−	14.0365i	0.322835	−	0.468405i
$899$	−1.04503	+	1.81005i	−0.0348537	+	0.0603684i
$900$		0			0
$901$	−6.82899	−	11.8282i	−0.227507	−	0.394053i
$902$	−50.4093	−	4.03410i	−1.67845	−	0.134321i
$903$		0			0
$904$	−23.7043	−	15.8246i	−0.788395	−	0.526318i
$905$	40.9803	+	48.8384i	1.36223	+	1.62344i
$906$		0			0
$907$	−7.14714	−	19.6366i	−0.237317	−	0.652022i	−0.999986	−	0.00523411i	$-0.998334\pi$
$907$	−7.14714	−	19.6366i	−0.237317	−	0.652022i	0.762670	−	0.646788i	$-0.223888\pi$
$908$	3.95469	−	11.3877i	0.131241	−	0.377916i
$909$		0			0
$910$	−8.72036	−	12.2596i	−0.289077	−	0.406402i
$911$	0.180967	−	1.02631i	0.00599569	−	0.0340033i	−0.981663	−	0.190624i	$-0.938949\pi$
$911$	0.180967	−	1.02631i	0.00599569	−	0.0340033i	0.987659	+	0.156621i	$0.0500600\pi$
$912$		0			0
$913$	−13.2891	−	4.83682i	−0.439804	−	0.160075i
$914$	21.7705	+	5.66082i	0.720103	+	0.187243i
$915$		0			0
$916$	0.519859	+	35.0769i	0.0171766	+	1.15897i
$917$			16.9065i			0.558302i
$918$		0			0
$919$		−	18.6355i		−	0.614729i	−0.951592	−	0.307365i	$-0.900553\pi$
$919$		−	18.6355i		−	0.614729i	0.951592	−	0.307365i	$-0.0994471\pi$
$920$	1.81823	−	4.13688i	0.0599454	−	0.136389i
$921$		0			0
$922$	5.20544	−	20.0191i	0.171432	−	0.659295i
$923$	12.7765	+	4.65027i	0.420544	+	0.153065i
$924$		0			0
$925$	1.23114	−	6.98213i	0.0404796	−	0.229571i
$926$	22.7167	−	16.1586i	0.746518	−	0.531004i
$927$		0			0
$928$	−1.69004	−	0.0849413i	−0.0554782	−	0.00278833i
$929$	14.3578	+	39.4478i	0.471065	+	1.29424i	0.916897	+	0.399123i	$0.130685\pi$
$929$	14.3578	+	39.4478i	0.471065	+	1.29424i	−0.445833	+	0.895116i	$0.647092\pi$
$930$		0			0
$931$	0.00624839	+	0.00744654i	0.000204783	+	0.000244051i
$932$	0.300584	−	1.86599i	0.00984597	−	0.0611227i
$933$		0			0
$934$	4.11387	−	51.4061i	0.134610	−	1.68206i
$935$	−7.75274	−	13.4281i	−0.253542	−	0.439147i
$936$		0			0
$937$	−2.35834	+	4.08476i	−0.0770435	+	0.133443i	−0.901973	−	0.431792i	$-0.857881\pi$
$937$	−2.35834	+	4.08476i	−0.0770435	+	0.133443i	0.824930	+	0.565235i	$0.191215\pi$
$938$	20.7753	+	14.3188i	0.678336	+	0.467524i
$939$		0			0
$940$	1.80937	−	0.689089i	0.0590151	−	0.0224756i
$941$	−22.7195	+	4.00605i	−0.740633	+	0.130594i	−0.531220	−	0.847234i	$-0.678266\pi$
$941$	−22.7195	+	4.00605i	−0.740633	+	0.130594i	−0.209413	+	0.977827i	$0.567155\pi$
$942$		0			0
$943$	−2.68141	+	3.19557i	−0.0873186	+	0.104062i
$944$	7.21310	−	49.4330i	0.234766	−	1.60891i
$945$		0			0
$946$	−43.2181	−	19.7644i	−1.40514	−	0.642596i
$947$	24.2924	+	20.3838i	0.789397	+	0.662383i	0.945596	−	0.325343i	$-0.105480\pi$
$947$	24.2924	+	20.3838i	0.789397	+	0.662383i	−0.156199	+	0.987726i	$0.549924\pi$
$948$		0			0
$949$	−0.214963	−	1.21912i	−0.00697800	−	0.0395742i
$950$	0.684684	+	0.674612i	0.0222141	+	0.0218873i
$951$		0			0
$952$	0.916930	+	8.34062i	0.0297179	+	0.270321i
$953$	38.9248	+	22.4732i	1.26090	+	0.727980i	0.973248	−	0.229756i	$-0.0737927\pi$
$953$	38.9248	+	22.4732i	1.26090	+	0.727980i	0.287650	+	0.957736i	$0.407126\pi$
$954$		0			0
$955$	−0.227025	+	0.131073i	−0.00734634	+	0.00424141i
$956$	19.5310	+	10.8935i	0.631676	+	0.352322i
$957$		0			0
$958$	2.39588	+	8.68367i	0.0774075	+	0.280557i
$959$	−4.33384	+	3.63653i	−0.139947	+	0.117430i
$960$		0			0
$961$	16.7434	−	6.09410i	0.540110	−	0.196584i
$962$	−1.13830	+	0.108093i	−0.0367002	+	0.00348505i
$963$		0			0
$964$	−37.9826	+	7.27931i	−1.22334	+	0.234451i
$965$	−99.8979	−	17.6147i	−3.21583	−	0.567037i
$966$		0			0
$967$	10.8906	−	29.9216i	0.350217	−	0.962215i	−0.632083	−	0.774901i	$-0.717800\pi$
$967$	10.8906	−	29.9216i	0.350217	−	0.962215i	0.982300	−	0.187314i	$-0.0599781\pi$
$968$	−2.55064	−	5.16681i	−0.0819807	−	0.166068i
$969$		0			0
$970$	4.44763	+	9.35634i	0.142805	+	0.300414i
$971$	11.0287			0.353929			0.176964	−	0.984217i	$-0.443372\pi$
$971$	11.0287			0.353929			0.176964	+	0.984217i	$0.443372\pi$
$972$		0			0
$973$	−18.3778			−0.589164
$974$	−19.1604	−	40.3071i	−0.613938	−	1.29152i
$975$		0			0
$976$	26.1140	−	0.774218i	0.835887	−	0.0247821i
$977$	−2.46836	+	6.78175i	−0.0789697	+	0.216968i	−0.972894	−	0.231250i	$-0.925719\pi$
$977$	−2.46836	+	6.78175i	−0.0789697	+	0.216968i	0.893925	+	0.448217i	$0.147941\pi$
$978$		0			0
$979$	−8.51492	−	1.50141i	−0.272138	−	0.0479853i
$980$	−0.191680	−	1.00017i	−0.00612301	−	0.0319492i
$981$		0			0
$982$	−37.5435	+	3.56513i	−1.19806	+	0.113768i
$983$	−16.9790	+	6.17984i	−0.541545	+	0.197106i	−0.598286	−	0.801283i	$-0.704151\pi$
$983$	−16.9790	+	6.17984i	−0.541545	+	0.197106i	0.0567408	+	0.998389i	$0.481929\pi$
$984$		0			0
$985$	13.0139	−	10.9199i	0.414657	−	0.347938i
$986$	0.127389	+	0.461712i	0.00405691	+	0.0147039i
$987$		0			0
$988$	0.0755106	−	0.135383i	0.00240231	−	0.00430709i
$989$	−3.39494	+	1.96007i	−0.107953	+	0.0623266i
$990$		0			0
$991$	14.8777	+	8.58966i	0.472607	+	0.272860i	0.717330	−	0.696733i	$-0.245364\pi$
$991$	14.8777	+	8.58966i	0.472607	+	0.272860i	−0.244724	+	0.969593i	$0.578697\pi$
$992$	28.9640	+	26.8936i	0.919607	+	0.853871i
$993$		0			0
$994$	−33.5286	−	33.0354i	−1.06346	−	1.04782i
$995$	6.47614	+	36.7280i	0.205307	+	1.16436i
$996$		0			0
$997$	37.0763	+	31.1107i	1.17422	+	0.985286i	1.00000		0.000579452i	$0.000184445\pi$
$997$	37.0763	+	31.1107i	1.17422	+	0.985286i	0.174219	+	0.984707i	$0.444260\pi$
$998$	28.8780	+	13.2064i	0.914118	+	0.418042i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.l.a.35.14		96
3.2	odd	2		108.2.l.a.11.3	✓	96
4.3	odd	2	inner	324.2.l.a.35.9		96
9.2	odd	6		972.2.l.d.755.13		96
9.4	even	3		972.2.l.b.431.7		96
9.5	odd	6		972.2.l.c.431.10		96
9.7	even	3		972.2.l.a.755.4		96
12.11	even	2		108.2.l.a.11.8	yes	96
27.4	even	9		972.2.l.d.215.15		96
27.5	odd	18	inner	324.2.l.a.287.9		96
27.13	even	9		972.2.l.c.539.4		96
27.14	odd	18		972.2.l.b.539.13		96
27.22	even	9		108.2.l.a.59.8	yes	96
27.23	odd	18		972.2.l.a.215.2		96
36.7	odd	6		972.2.l.a.755.2		96
36.11	even	6		972.2.l.d.755.15		96
36.23	even	6		972.2.l.c.431.4		96
36.31	odd	6		972.2.l.b.431.13		96
108.23	even	18		972.2.l.a.215.4		96
108.31	odd	18		972.2.l.d.215.13		96
108.59	even	18	inner	324.2.l.a.287.14		96
108.67	odd	18		972.2.l.c.539.10		96
108.95	even	18		972.2.l.b.539.7		96
108.103	odd	18		108.2.l.a.59.3	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.11.3	✓	96	3.2	odd	2
108.2.l.a.11.8	yes	96	12.11	even	2
108.2.l.a.59.3	yes	96	108.103	odd	18
108.2.l.a.59.8	yes	96	27.22	even	9
324.2.l.a.35.9		96	4.3	odd	2	inner
324.2.l.a.35.14		96	1.1	even	1	trivial
324.2.l.a.287.9		96	27.5	odd	18	inner
324.2.l.a.287.14		96	108.59	even	18	inner
972.2.l.a.215.2		96	27.23	odd	18
972.2.l.a.215.4		96	108.23	even	18
972.2.l.a.755.2		96	36.7	odd	6
972.2.l.a.755.4		96	9.7	even	3
972.2.l.b.431.7		96	9.4	even	3
972.2.l.b.431.13		96	36.31	odd	6
972.2.l.b.539.7		96	108.95	even	18
972.2.l.b.539.13		96	27.14	odd	18
972.2.l.c.431.4		96	36.23	even	6
972.2.l.c.431.10		96	9.5	odd	6
972.2.l.c.539.4		96	27.13	even	9
972.2.l.c.539.10		96	108.67	odd	18
972.2.l.d.215.13		96	108.31	odd	18
972.2.l.d.215.15		96	27.4	even	9
972.2.l.d.755.13		96	9.2	odd	6
972.2.l.d.755.15		96	36.11	even	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)

\(f(q)\)	\(=\)	\(q+(1.27725 - 0.607153i) q^{2} +(1.26273 - 1.55097i) q^{4} +(-1.29726 + 3.56419i) q^{5} +(2.58045 + 0.455003i) q^{7} +(0.671144 - 2.74765i) q^{8} +O(q^{10})\)	\(q+(1.27725 - 0.607153i) q^{2} +(1.26273 - 1.55097i) q^{4} +(-1.29726 + 3.56419i) q^{5} +(2.58045 + 0.455003i) q^{7} +(0.671144 - 2.74765i) q^{8} +(0.507086 + 5.33999i) q^{10} +(3.39295 - 1.23493i) q^{11} +(-0.819980 + 0.688045i) q^{13} +(3.57213 - 0.985577i) q^{14} +(-0.811025 - 3.91692i) q^{16} +(-0.980503 + 0.566093i) q^{17} +(-0.0627092 - 0.0362052i) q^{19} +(3.88987 + 6.51262i) q^{20} +(3.58385 - 3.63736i) q^{22} +(-0.0731435 - 0.414817i) q^{23} +(-7.19034 - 6.03341i) q^{25} +(-0.629570 + 1.37666i) q^{26} +(3.96411 - 3.42766i) q^{28} +(0.192281 - 0.229152i) q^{29} +(-6.88084 + 1.21328i) q^{31} +(-3.41405 - 4.51046i) q^{32} +(-0.908641 + 1.31836i) q^{34} +(-4.96923 + 8.60696i) q^{35} +(0.377668 + 0.654141i) q^{37} +(-0.102077 - 0.00816893i) q^{38} +(8.92249 + 5.95649i) q^{40} +(-6.36586 - 7.58654i) q^{41} +(-3.18308 - 8.74545i) q^{43} +(2.36904 - 6.82177i) q^{44} +(-0.345280 - 0.485416i) q^{46} +(0.0443203 - 0.251353i) q^{47} +(-0.126150 - 0.0459147i) q^{49} +(-12.8471 - 3.34053i) q^{50} +(0.0317246 + 2.14058i) q^{52} +12.0634i q^{53} +13.6952i q^{55} +(2.98204 - 6.78480i) q^{56} +(0.106461 - 0.409428i) q^{58} +(11.7359 + 4.27153i) q^{59} +(-1.13416 + 6.43213i) q^{61} +(-8.05190 + 5.72738i) q^{62} +(-7.09913 - 3.68813i) q^{64} +(-1.38860 - 3.81514i) q^{65} +(4.37678 + 5.21604i) q^{67} +(-0.360115 + 2.23555i) q^{68} +(-1.12120 + 14.0103i) q^{70} +(-6.35108 - 11.0004i) q^{71} +(-0.578249 + 1.00156i) q^{73} +(0.879540 + 0.606198i) q^{74} +(-0.135338 + 0.0515428i) q^{76} +(9.31725 - 1.64288i) q^{77} +(5.09561 - 6.07271i) q^{79} +(15.0127 + 2.19061i) q^{80} +(-12.7370 - 5.82484i) q^{82} +(-3.00034 - 2.51758i) q^{83} +(-0.745699 - 4.22907i) q^{85} +(-9.37542 - 9.23750i) q^{86} +(-1.11601 - 10.1515i) q^{88} +(-2.07380 - 1.19731i) q^{89} +(-2.42898 + 1.40237i) q^{91} +(-0.735730 - 0.410359i) q^{92} +(-0.0960018 - 0.347950i) q^{94} +(0.210392 - 0.176540i) q^{95} +(1.81485 - 0.660552i) q^{97} +(-0.189002 + 0.0179476i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more