LMFDB - Embedded newform 324.2.l.a.35.13

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			35.13
Character	$\chi$	$=$	324.35
Dual form			324.2.l.a.287.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06666 + 0.928568i) q^{2} +(0.275524 + 1.98093i) q^{4} +(-0.605021 + 1.66228i) q^{5} +(0.748045 + 0.131901i) q^{7} +(-1.54554 + 2.36882i) q^{8} +O(q^{10})$	\(q+(1.06666 + 0.928568i) q^{2} +(0.275524 + 1.98093i) q^{4} +(-0.605021 + 1.66228i) q^{5} +(0.748045 + 0.131901i) q^{7} +(-1.54554 + 2.36882i) q^{8} +(-2.18889 + 1.21129i) q^{10} +(3.01780 - 1.09839i) q^{11} +(-1.07167 + 0.899234i) q^{13} +(0.675431 + 0.835303i) q^{14} +(-3.84817 + 1.09159i) q^{16} +(-5.55887 + 3.20941i) q^{17} +(2.51793 + 1.45373i) q^{19} +(-3.45956 - 0.740506i) q^{20} +(4.23889 + 1.63062i) q^{22} +(-1.06877 - 6.06131i) q^{23} +(1.43309 + 1.20251i) q^{25} +(-1.97810 - 0.0359374i) q^{26} +(-0.0551813 + 1.51817i) q^{28} +(4.87432 - 5.80899i) q^{29} +(9.30557 - 1.64082i) q^{31} +(-5.11830 - 2.40894i) q^{32} +(-8.90957 - 1.73843i) q^{34} +(-0.671839 + 1.16366i) q^{35} +(1.62042 + 2.80666i) q^{37} +(1.33589 + 3.88870i) q^{38} +(-3.00257 - 4.00231i) q^{40} +(4.14810 + 4.94351i) q^{41} +(-2.50294 - 6.87676i) q^{43} +(3.00731 + 5.67542i) q^{44} +(4.48832 - 7.45778i) q^{46} +(0.737485 - 4.18249i) q^{47} +(-6.03567 - 2.19681i) q^{49} +(0.412011 + 2.61338i) q^{50} +(-2.07659 - 1.87513i) q^{52} -9.63986i q^{53} +5.68099i q^{55} +(-1.46858 + 1.56813i) q^{56} +(10.5933 - 1.67008i) q^{58} +(0.397395 + 0.144640i) q^{59} +(1.38430 - 7.85077i) q^{61} +(11.4495 + 6.89065i) q^{62} +(-3.22263 - 7.32220i) q^{64} +(-0.846401 - 2.32547i) q^{65} +(-3.65540 - 4.35634i) q^{67} +(-7.88923 - 10.1275i) q^{68} +(-1.79716 + 0.617380i) q^{70} +(1.88825 + 3.27054i) q^{71} +(-5.59853 + 9.69694i) q^{73} +(-0.877730 + 4.49842i) q^{74} +(-2.18598 + 5.38838i) q^{76} +(2.40233 - 0.423595i) q^{77} +(-6.53113 + 7.78350i) q^{79} +(0.513698 - 7.05719i) q^{80} +(-0.165777 + 9.12484i) q^{82} +(3.80396 + 3.19190i) q^{83} +(-1.97172 - 11.1822i) q^{85} +(3.71576 - 9.65931i) q^{86} +(-2.06224 + 8.84623i) q^{88} +(0.509288 + 0.294037i) q^{89} +(-0.920264 + 0.531314i) q^{91} +(11.7126 - 3.78720i) q^{92} +(4.67037 - 3.77648i) q^{94} +(-3.93991 + 3.30598i) q^{95} +(15.8811 - 5.78024i) q^{97} +(-4.39813 - 7.94778i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.06666	+	0.928568i	0.754242	+	0.656596i
$2$	1.06666	+	0.928568i	0.754242	+	0.656596i
$3$		0			0
$3$		0			0
$4$	0.275524	+	1.98093i	0.137762	+	0.990465i
$5$	−0.605021	+	1.66228i	−0.270574	+	0.743395i	0.727768	+	0.685824i	$0.240558\pi$
$5$	−0.605021	+	1.66228i	−0.270574	+	0.743395i	−0.998341	+	0.0575715i	$0.981664\pi$
$6$		0			0
$7$	0.748045	+	0.131901i	0.282734	+	0.0498537i	0.313217	−	0.949682i	$-0.398593\pi$
$7$	0.748045	+	0.131901i	0.282734	+	0.0498537i	−0.0304825	+	0.999535i	$0.509704\pi$
$8$	−1.54554	+	2.36882i	−0.546430	+	0.837505i
$9$		0			0
$10$	−2.18889	+	1.21129i	−0.692189	+	0.383042i
$11$	3.01780	−	1.09839i	0.909901	−	0.331177i	0.155688	−	0.987806i	$-0.450241\pi$
$11$	3.01780	−	1.09839i	0.909901	−	0.331177i	0.754213	+	0.656629i	$0.228018\pi$
$12$		0			0
$13$	−1.07167	+	0.899234i	−0.297227	+	0.249403i	−0.779189	−	0.626789i	$-0.784369\pi$
$13$	−1.07167	+	0.899234i	−0.297227	+	0.249403i	0.481962	+	0.876192i	$0.339924\pi$
$14$	0.675431	+	0.835303i	0.180516	+	0.223244i
$15$		0			0
$16$	−3.84817	+	1.09159i	−0.962043	+	0.272897i
$17$	−5.55887	+	3.20941i	−1.34822	+	0.778397i	−0.987998	−	0.154469i	$-0.950633\pi$
$17$	−5.55887	+	3.20941i	−1.34822	+	0.778397i	−0.360225	+	0.932865i	$0.617300\pi$
$18$		0			0
$19$	2.51793	+	1.45373i	0.577653	+	0.333508i	0.760200	−	0.649689i	$-0.225101\pi$
$19$	2.51793	+	1.45373i	0.577653	+	0.333508i	−0.182547	+	0.983197i	$0.558434\pi$
$20$	−3.45956	−	0.740506i	−0.773582	−	0.165582i
$21$		0			0
$22$	4.23889	+	1.63062i	0.903735	+	0.347650i
$23$	−1.06877	−	6.06131i	−0.222854	−	1.26387i	−0.866744	−	0.498752i	$-0.833792\pi$
$23$	−1.06877	−	6.06131i	−0.222854	−	1.26387i	0.643890	−	0.765118i	$-0.277319\pi$
$24$		0			0
$25$	1.43309	+	1.20251i	0.286618	+	0.240501i
$26$	−1.97810	−	0.0359374i	−0.387938	−	0.00704791i
$27$		0			0
$28$	−0.0551813	+	1.51817i	−0.0104283	+	0.286907i
$29$	4.87432	−	5.80899i	0.905138	−	1.07870i	−0.0914207	−	0.995812i	$-0.529141\pi$
$29$	4.87432	−	5.80899i	0.905138	−	1.07870i	0.996559	−	0.0828892i	$-0.0264148\pi$
$30$		0			0
$31$	9.30557	−	1.64082i	1.67133	−	0.294701i	0.743787	−	0.668417i	$-0.233028\pi$
$31$	9.30557	−	1.64082i	1.67133	−	0.294701i	0.927543	+	0.373716i	$0.121916\pi$
$32$	−5.11830	−	2.40894i	−0.904797	−	0.425844i
$33$		0			0
$34$	−8.90957	−	1.73843i	−1.52798	−	0.298139i
$35$	−0.671839	+	1.16366i	−0.113562	+	0.196694i
$36$		0			0
$37$	1.62042	+	2.80666i	0.266396	+	0.461411i	0.967928	−	0.251226i	$-0.0808338\pi$
$37$	1.62042	+	2.80666i	0.266396	+	0.461411i	−0.701532	+	0.712638i	$0.747500\pi$
$38$	1.33589	+	3.88870i	0.216710	+	0.630831i
$39$		0			0
$40$	−3.00257	−	4.00231i	−0.474747	−	0.632820i
$41$	4.14810	+	4.94351i	0.647824	+	0.772047i	0.985584	−	0.169185i	$-0.0541136\pi$
$41$	4.14810	+	4.94351i	0.647824	+	0.772047i	−0.337760	+	0.941232i	$0.609669\pi$
$42$		0			0
$43$	−2.50294	−	6.87676i	−0.381694	−	1.04870i	−0.970643	−	0.240526i	$-0.922680\pi$
$43$	−2.50294	−	6.87676i	−0.381694	−	1.04870i	0.588949	−	0.808171i	$-0.299542\pi$
$44$	3.00731	+	5.67542i	0.453369	+	0.855602i
$45$		0			0
$46$	4.48832	−	7.45778i	0.661767	−	1.09959i
$47$	0.737485	−	4.18249i	0.107573	−	0.610079i	−0.882588	−	0.470147i	$-0.844201\pi$
$47$	0.737485	−	4.18249i	0.107573	−	0.610079i	0.990161	−	0.139931i	$-0.0446881\pi$
$48$		0			0
$49$	−6.03567	−	2.19681i	−0.862239	−	0.313829i
$50$	0.412011	+	2.61338i	0.0582672	+	0.369588i
$51$		0			0
$52$	−2.07659	−	1.87513i	−0.287971	−	0.260034i
$53$		−	9.63986i		−	1.32414i	−0.749444	−	0.662068i	$-0.769679\pi$
$53$		−	9.63986i		−	1.32414i	0.749444	−	0.662068i	$-0.230321\pi$
$54$		0			0
$55$			5.68099i			0.766024i
$56$	−1.46858	+	1.56813i	−0.196247	+	0.209550i
$57$		0			0
$58$	10.5933	−	1.67008i	1.39096	−	0.219292i
$59$	0.397395	+	0.144640i	0.0517364	+	0.0188305i	0.367759	−	0.929921i	$-0.380125\pi$
$59$	0.397395	+	0.144640i	0.0517364	+	0.0188305i	−0.316022	+	0.948752i	$0.602347\pi$
$60$		0			0
$61$	1.38430	−	7.85077i	0.177242	−	1.00519i	−0.758283	−	0.651926i	$-0.773961\pi$
$61$	1.38430	−	7.85077i	0.177242	−	1.00519i	0.935524	−	0.353262i	$-0.114928\pi$
$62$	11.4495	+	6.89065i	1.45409	+	0.875114i
$63$		0			0
$64$	−3.22263	−	7.32220i	−0.402828	−	0.915276i
$65$	−0.846401	−	2.32547i	−0.104983	−	0.288439i
$66$		0			0
$67$	−3.65540	−	4.35634i	−0.446579	−	0.532212i	0.495050	−	0.868864i	$-0.335150\pi$
$67$	−3.65540	−	4.35634i	−0.446579	−	0.532212i	−0.941629	+	0.336653i	$0.890705\pi$
$68$	−7.88923	−	10.1275i	−0.956709	−	1.22813i
$69$		0			0
$70$	−1.79716	+	0.617380i	−0.214802	+	0.0737911i
$71$	1.88825	+	3.27054i	0.224094	+	0.388142i	0.956047	−	0.293213i	$-0.0947245\pi$
$71$	1.88825	+	3.27054i	0.224094	+	0.388142i	−0.731953	+	0.681355i	$0.761391\pi$
$72$		0			0
$73$	−5.59853	+	9.69694i	−0.655258	+	1.13494i	0.326571	+	0.945173i	$0.394107\pi$
$73$	−5.59853	+	9.69694i	−0.655258	+	1.13494i	−0.981829	+	0.189768i	$0.939226\pi$
$74$	−0.877730	+	4.49842i	−0.102034	+	0.522931i
$75$		0			0
$76$	−2.18598	+	5.38838i	−0.250750	+	0.618090i
$77$	2.40233	−	0.423595i	0.273771	−	0.0482732i
$78$		0			0
$79$	−6.53113	+	7.78350i	−0.734810	+	0.875712i	−0.995980	−	0.0895809i	$-0.971447\pi$
$79$	−6.53113	+	7.78350i	−0.734810	+	0.875712i	0.261170	+	0.965293i	$0.415892\pi$
$80$	0.513698	−	7.05719i	0.0574331	−	0.789017i
$81$		0			0
$82$	−0.165777	+	9.12484i	−0.0183070	+	1.00767i
$83$	3.80396	+	3.19190i	0.417538	+	0.350356i	0.827226	−	0.561870i	$-0.189918\pi$
$83$	3.80396	+	3.19190i	0.417538	+	0.350356i	−0.409687	+	0.912226i	$0.634362\pi$
$84$		0			0
$85$	−1.97172	−	11.1822i	−0.213863	−	1.21288i
$86$	3.71576	−	9.65931i	0.400680	−	1.04159i
$87$		0			0
$88$	−2.06224	+	8.84623i	−0.219835	+	0.943012i
$89$	0.509288	+	0.294037i	0.0539844	+	0.0311679i	0.526749	−	0.850021i	$-0.323411\pi$
$89$	0.509288	+	0.294037i	0.0539844	+	0.0311679i	−0.472765	+	0.881189i	$0.656744\pi$
$90$		0			0
$91$	−0.920264	+	0.531314i	−0.0964698	+	0.0556969i
$92$	11.7126	−	3.78720i	1.22112	−	0.394843i
$93$		0			0
$94$	4.67037	−	3.77648i	0.481712	−	0.389515i
$95$	−3.93991	+	3.30598i	−0.404226	+	0.339186i
$96$		0			0
$97$	15.8811	−	5.78024i	1.61248	−	0.586895i	0.630552	−	0.776147i	$-0.282829\pi$
$97$	15.8811	−	5.78024i	1.61248	−	0.586895i	0.981928	+	0.189252i	$0.0606065\pi$
$98$	−4.39813	−	7.94778i	−0.444278	−	0.802847i
$99$		0			0
$100$	−1.98723	+	3.17017i	−0.198723	+	0.317017i
$101$	5.39858	+	0.951915i	0.537178	+	0.0947191i	0.435654	−	0.900114i	$-0.356517\pi$
$101$	5.39858	+	0.951915i	0.537178	+	0.0947191i	0.101524	+	0.994833i	$0.467628\pi$
$102$		0			0
$103$	−2.06594	+	5.67611i	−0.203563	+	0.559284i	−0.998900	−	0.0468827i	$-0.985071\pi$
$103$	−2.06594	+	5.67611i	−0.203563	+	0.559284i	0.795338	+	0.606167i	$0.207294\pi$
$104$	−0.473825	−	3.92838i	−0.0464624	−	0.385210i
$105$		0			0
$106$	8.95126	−	10.2824i	0.869423	−	0.998719i
$107$	−4.28762			−0.414500			−0.207250	−	0.978288i	$-0.566451\pi$
$107$	−4.28762			−0.414500			−0.207250	+	0.978288i	$0.566451\pi$
$108$		0			0
$109$	−4.75148			−0.455109			−0.227554	−	0.973765i	$-0.573073\pi$
$109$	−4.75148			−0.455109			−0.227554	+	0.973765i	$0.573073\pi$
$110$	−5.27518	+	6.05968i	−0.502969	+	0.577768i
$111$		0			0
$112$	−3.02259	+	0.308982i	−0.285608	+	0.0291960i
$113$	−3.11256	+	8.55169i	−0.292805	+	0.804475i	0.702848	+	0.711340i	$0.251911\pi$
$113$	−3.11256	+	8.55169i	−0.292805	+	0.804475i	−0.995653	+	0.0931357i	$0.970311\pi$
$114$		0			0
$115$	10.7222	+	1.89062i	0.999854	+	0.176301i
$116$	12.8502	+	8.05517i	1.19311	+	0.747904i
$117$		0			0
$118$	0.289577	+	0.523290i	0.0266577	+	0.0481727i
$119$	−4.58161	+	1.66757i	−0.419995	+	0.152866i
$120$		0			0
$121$	−0.525827	+	0.441221i	−0.0478025	+	0.0401110i
$122$	8.76655	−	7.08868i	0.793686	−	0.641779i
$123$		0			0
$124$	5.81427	+	17.9816i	0.522137	+	1.61480i
$125$	−10.5258	+	6.07707i	−0.941456	+	0.543550i
$126$		0			0
$127$	−7.58333	−	4.37824i	−0.672911	−	0.388506i	0.124267	−	0.992249i	$-0.460342\pi$
$127$	−7.58333	−	4.37824i	−0.672911	−	0.388506i	−0.797179	+	0.603743i	$0.793675\pi$
$128$	3.36172	−	10.8027i	0.297137	−	0.954835i
$129$		0			0
$130$	1.25653	−	3.26642i	0.110205	−	0.286484i
$131$	1.28295	+	7.27595i	0.112092	+	0.635703i	0.988149	+	0.153496i	$0.0490533\pi$
$131$	1.28295	+	7.27595i	0.112092	+	0.635703i	−0.876058	+	0.482206i	$0.839836\pi$
$132$		0			0
$133$	1.69178	+	1.41957i	0.146696	+	0.123092i
$134$	0.146086	−	8.04102i	0.0126199	−	0.694639i
$135$		0			0
$136$	0.988912	−	18.1282i	0.0847985	−	1.55448i
$137$	−3.47834	+	4.14532i	−0.297174	+	0.354158i	−0.893884	−	0.448299i	$-0.852030\pi$
$137$	−3.47834	+	4.14532i	−0.297174	+	0.354158i	0.596709	+	0.802457i	$0.296474\pi$
$138$		0			0
$139$	−14.3790	+	2.53541i	−1.21961	+	0.215050i	−0.746158	−	0.665769i	$-0.768104\pi$
$139$	−14.3790	+	2.53541i	−1.21961	+	0.215050i	−0.473453	+	0.880819i	$0.656993\pi$
$140$	−2.49024	−	1.01025i	−0.210463	−	0.0853818i
$141$		0			0
$142$	−1.02280	+	5.24192i	−0.0858316	+	0.439892i
$143$	−2.24636	+	3.89082i	−0.187850	+	0.325366i
$144$		0			0
$145$	6.70711	+	11.6171i	0.556995	+	0.964744i
$146$	−14.9760	+	5.14471i	−1.23942	+	0.425780i
$147$		0			0
$148$	−5.11333	+	3.98325i	−0.420313	+	0.327421i
$149$	0.667920	+	0.795997i	0.0547182	+	0.0652106i	0.792709	−	0.609600i	$-0.208670\pi$
$149$	0.667920	+	0.795997i	0.0547182	+	0.0652106i	−0.737991	+	0.674810i	$0.764225\pi$
$150$		0			0
$151$	−5.18707	−	14.2513i	−0.422117	−	1.15976i	−0.950493	−	0.310747i	$-0.899421\pi$
$151$	−5.18707	−	14.2513i	−0.422117	−	1.15976i	0.528375	−	0.849011i	$-0.322801\pi$
$152$	−7.33518	+	3.71774i	−0.594962	+	0.301548i
$153$		0			0
$154$	2.95580	+	1.77889i	0.238185	+	0.143347i
$155$	−2.90256	+	16.4612i	−0.233139	+	1.32220i
$156$		0			0
$157$	−7.35933	−	2.67858i	−0.587338	−	0.213774i	0.0312200	−	0.999513i	$-0.490061\pi$
$157$	−7.35933	−	2.67858i	−0.587338	−	0.213774i	−0.618558	+	0.785739i	$0.712283\pi$
$158$	−14.1940	+	2.23774i	−1.12921	+	0.178025i
$159$		0			0
$160$	7.10101	−	7.05061i	0.561384	−	0.557400i
$161$		−	4.67510i		−	0.368450i
$162$		0			0
$163$		−	14.8714i		−	1.16482i	−0.812897	−	0.582408i	$-0.802111\pi$
$163$		−	14.8714i		−	1.16482i	0.812897	−	0.582408i	$-0.197889\pi$
$164$	−8.64985	+	9.57916i	−0.675440	+	0.748006i
$165$		0			0
$166$	1.09363	+	6.93690i	0.0848823	+	0.538408i
$167$	0.956267	+	0.348053i	0.0739981	+	0.0269331i	0.378754	−	0.925497i	$-0.376353\pi$
$167$	0.956267	+	0.348053i	0.0739981	+	0.0269331i	−0.304756	+	0.952431i	$0.598575\pi$
$168$		0			0
$169$	−1.91758	+	10.8751i	−0.147506	+	0.836550i
$170$	8.28025	−	13.7584i	0.635066	−	1.05522i
$171$		0			0
$172$	12.9328	−	6.85286i	0.986114	−	0.522526i
$173$	−2.67234	−	7.34218i	−0.203174	−	0.558216i	0.795698	−	0.605693i	$-0.207104\pi$
$173$	−2.67234	−	7.34218i	−0.203174	−	0.558216i	−0.998872	+	0.0474772i	$0.984882\pi$
$174$		0			0
$175$	0.913405	+	1.08855i	0.0690469	+	0.0822869i
$176$	−10.4140	+	7.52099i	−0.784987	+	0.566916i
$177$		0			0
$178$	0.270203	+	0.786546i	0.0202526	+	0.0589541i
$179$	−3.90388	−	6.76172i	−0.291790	−	0.505395i	0.682443	−	0.730939i	$-0.260917\pi$
$179$	−3.90388	−	6.76172i	−0.291790	−	0.505395i	−0.974233	+	0.225544i	$0.927584\pi$
$180$		0			0
$181$	1.45395	−	2.51831i	0.108071	−	0.187184i	−0.806918	−	0.590664i	$-0.798866\pi$
$181$	1.45395	−	2.51831i	0.108071	−	0.187184i	0.914989	+	0.403479i	$0.132199\pi$
$182$	−1.47497	−	0.287796i	−0.109332	−	0.0213328i
$183$		0			0
$184$	16.0100	+	6.83625i	1.18027	+	0.503975i
$185$	−5.64585	+	0.995515i	−0.415091	+	0.0731917i
$186$		0			0
$187$	−13.2504	+	15.7912i	−0.968963	+	1.15476i
$188$	8.48841	+	0.308531i	0.619081	+	0.0225019i
$189$		0			0
$190$	−7.27236	−	0.132122i	−0.527593	−	0.00958512i
$191$	−12.1323	−	10.1802i	−0.877859	−	0.736611i	0.0878785	−	0.996131i	$-0.471991\pi$
$191$	−12.1323	−	10.1802i	−0.877859	−	0.736611i	−0.965738	+	0.259520i	$0.916436\pi$
$192$		0			0
$193$	2.21465	+	12.5599i	0.159414	+	0.904083i	0.954638	+	0.297767i	$0.0962420\pi$
$193$	2.21465	+	12.5599i	0.159414	+	0.904083i	−0.795224	+	0.606315i	$0.792647\pi$
$194$	22.3071	+	8.58111i	1.60155	+	0.616088i
$195$		0			0
$196$	2.68875	−	12.5615i	0.192053	−	0.897252i
$197$	6.84336	+	3.95102i	0.487570	+	0.281498i	0.723566	−	0.690256i	$-0.242502\pi$
$197$	6.84336	+	3.95102i	0.487570	+	0.281498i	−0.235996	+	0.971754i	$0.575835\pi$
$198$		0			0
$199$	−3.36883	+	1.94499i	−0.238810	+	0.137877i	−0.614630	−	0.788816i	$-0.710694\pi$
$199$	−3.36883	+	1.94499i	−0.238810	+	0.137877i	0.375820	+	0.926693i	$0.377361\pi$
$200$	−5.06341	+	1.53622i	−0.358037	+	0.108627i
$201$		0			0
$202$	4.87452	+	6.02831i	0.342970	+	0.424151i
$203$	4.41242	−	3.70246i	0.309691	−	0.259862i
$204$		0			0
$205$	−10.7272	+	3.90438i	−0.749220	+	0.272694i
$206$	−7.47430	+	4.13612i	−0.520759	+	0.288177i
$207$		0			0
$208$	3.14236	−	4.63023i	0.217883	−	0.321048i
$209$	9.19538	+	1.62139i	0.636057	+	0.112154i
$210$		0			0
$211$	−1.32215	+	3.63257i	−0.0910203	+	0.250076i	−0.976847	−	0.213941i	$-0.931370\pi$
$211$	−1.32215	+	3.63257i	−0.0910203	+	0.250076i	0.885826	+	0.464017i	$0.153592\pi$
$212$	19.0959	−	2.65602i	1.31151	−	0.182416i
$213$		0			0
$214$	−4.57343	−	3.98134i	−0.312633	−	0.272159i
$215$	12.9455			0.882872
$216$		0			0
$217$	7.17741			0.487235
$218$	−5.06821	−	4.41207i	−0.343262	−	0.298823i
$219$		0			0
$220$	−11.2536	+	1.56525i	−0.758720	+	0.105529i
$221$	3.07123	−	8.43814i	0.206593	−	0.567611i
$222$		0			0
$223$	23.0164	+	4.05841i	1.54129	+	0.271771i	0.878760	−	0.477264i	$-0.158371\pi$
$223$	23.0164	+	4.05841i	1.54129	+	0.271771i	0.662531	+	0.749035i	$0.269482\pi$
$224$	−3.51098	−	2.47710i	−0.234587	−	0.165508i
$225$		0			0
$226$	−11.2609	+	6.23152i	−0.749062	+	0.414514i
$227$	−9.97504	+	3.63062i	−0.662067	+	0.240973i	−0.651128	−	0.758968i	$-0.725704\pi$
$227$	−9.97504	+	3.63062i	−0.662067	+	0.240973i	−0.0109383	+	0.999940i	$0.503482\pi$
$228$		0			0
$229$	−5.32931	+	4.47182i	−0.352171	+	0.295506i	−0.801661	−	0.597779i	$-0.796050\pi$
$229$	−5.32931	+	4.47182i	−0.352171	+	0.295506i	0.449490	+	0.893285i	$0.351606\pi$
$230$	9.68141	+	11.9730i	0.638373	+	0.789474i
$231$		0			0
$232$	6.22701	+	20.5244i	0.408823	+	1.34749i
$233$	−13.9988	+	8.08221i	−0.917091	+	0.529483i	−0.882706	−	0.469926i	$-0.844281\pi$
$233$	−13.9988	+	8.08221i	−0.917091	+	0.529483i	−0.0343854	+	0.999409i	$0.510947\pi$
$234$		0			0
$235$	6.50628	+	3.75640i	0.424423	+	0.245041i
$236$	−0.177030	+	0.827064i	−0.0115237	+	0.0538373i
$237$		0			0
$238$	−6.43546	−	2.47560i	−0.417149	−	0.160470i
$239$	3.92960	+	22.2858i	0.254184	+	1.44155i	0.798157	+	0.602449i	$0.205808\pi$
$239$	3.92960	+	22.2858i	0.254184	+	1.44155i	−0.543973	+	0.839103i	$0.683081\pi$
$240$		0			0
$241$	−0.165024	−	0.138471i	−0.0106301	−	0.00891972i	0.637457	−	0.770486i	$-0.279986\pi$
$241$	−0.165024	−	0.138471i	−0.0106301	−	0.00891972i	−0.648087	+	0.761566i	$0.724431\pi$
$242$	−0.970582	−	0.0176332i	−0.0623914	−	0.00113350i
$243$		0			0
$244$	15.9332	+	0.579130i	1.02002	+	0.0370750i
$245$	7.30342	−	8.70388i	0.466599	−	0.556071i
$246$		0			0
$247$	−4.00562	+	0.706299i	−0.254872	+	0.0449407i
$248$	−10.4953	+	24.5792i	−0.666452	+	1.56078i
$249$		0			0
$250$	−16.8704	−	3.29175i	−1.06698	−	0.208188i
$251$	11.9282	−	20.6602i	0.752899	−	1.30406i	−0.193513	−	0.981098i	$-0.561988\pi$
$251$	11.9282	−	20.6602i	0.752899	−	1.30406i	0.946412	−	0.322961i	$-0.104678\pi$
$252$		0			0
$253$	−9.88302	−	17.1179i	−0.621340	−	1.07619i
$254$	−4.02334	−	11.7117i	−0.252447	−	0.734859i
$255$		0			0
$256$	13.6169	−	8.40124i	0.851054	−	0.525078i
$257$	0.876576	+	1.04466i	0.0546793	+	0.0651642i	0.792691	−	0.609624i	$-0.208679\pi$
$257$	0.876576	+	1.04466i	0.0546793	+	0.0651642i	−0.738012	+	0.674788i	$0.764235\pi$
$258$		0			0
$259$	0.841951	+	2.31324i	0.0523163	+	0.143738i
$260$	4.37338	−	2.31738i	0.271226	−	0.143718i
$261$		0			0
$262$	−5.38774	+	8.95226i	−0.332856	+	0.553073i
$263$	2.98147	−	16.9087i	0.183845	−	1.04264i	−0.743585	−	0.668641i	$-0.766876\pi$
$263$	2.98147	−	16.9087i	0.183845	−	1.04264i	0.927430	−	0.373996i	$-0.122013\pi$
$264$		0			0
$265$	16.0242	+	5.83232i	0.984357	+	0.358277i
$266$	0.486384	+	3.08513i	0.0298221	+	0.189161i
$267$		0			0
$268$	7.62246	−	8.44138i	0.465616	−	0.515639i
$269$		−	8.79633i		−	0.536322i	−0.963374	−	0.268161i	$-0.913584\pi$
$269$		−	8.79633i		−	0.536322i	0.963374	−	0.268161i	$-0.0864159\pi$
$270$		0			0
$271$			3.18958i			0.193753i	0.995296	+	0.0968765i	$0.0308852\pi$
$271$			3.18958i			0.193753i	−0.995296	+	0.0968765i	$0.969115\pi$
$272$	17.8881	−	18.4184i	1.08463	−	1.11678i
$273$		0			0
$274$	−7.55941	+	1.19177i	−0.456680	+	0.0719976i
$275$	5.64560	+	2.05483i	0.340442	+	0.123911i
$276$		0			0
$277$	2.42778	−	13.7686i	0.145871	−	0.827276i	−0.820793	−	0.571226i	$-0.806468\pi$
$277$	2.42778	−	13.7686i	0.145871	−	0.827276i	0.966664	−	0.256049i	$-0.0824210\pi$
$278$	−17.6918	−	10.6475i	−1.06108	−	0.638593i
$279$		0			0
$280$	−1.71815	−	3.38995i	−0.102679	−	0.202588i
$281$	1.60512	+	4.41002i	0.0957532	+	0.263080i	0.978317	−	0.207113i	$-0.0664067\pi$
$281$	1.60512	+	4.41002i	0.0957532	+	0.263080i	−0.882564	+	0.470192i	$0.844184\pi$
$282$		0			0
$283$	2.77680	+	3.30926i	0.165063	+	0.196715i	0.842236	−	0.539110i	$-0.181239\pi$
$283$	2.77680	+	3.30926i	0.165063	+	0.196715i	−0.677172	+	0.735825i	$0.736795\pi$
$284$	−5.95846	+	4.64160i	−0.353569	+	0.275428i
$285$		0			0
$286$	−6.00899	+	2.06427i	−0.355319	+	0.122063i
$287$	2.45091	+	4.24511i	0.144673	+	0.250581i
$288$		0			0
$289$	12.1007	−	20.9590i	0.711803	−	1.23288i
$290$	−3.63302	+	18.6194i	−0.213338	+	1.09337i
$291$		0			0
$292$	−20.7515	−	8.41856i	−1.21439	−	0.492659i
$293$	11.2158	−	1.97765i	0.655235	−	0.115536i	0.163860	−	0.986484i	$-0.447605\pi$
$293$	11.2158	−	1.97765i	0.655235	−	0.115536i	0.491375	+	0.870948i	$0.336494\pi$
$294$		0			0
$295$	−0.480865	+	0.573073i	−0.0279970	+	0.0333656i
$296$	−9.15289	−	0.499299i	−0.532001	−	0.0290212i
$297$		0			0
$298$	−0.0266931	+	1.46927i	−0.00154629	+	0.0851123i
$299$	6.59590	+	5.53462i	0.381451	+	0.320075i
$300$		0			0
$301$	−0.965261	−	5.47427i	−0.0556367	−	0.315531i
$302$	7.70051	−	20.0179i	0.443114	−	1.15190i
$303$		0			0
$304$	−11.2763	−	2.84565i	−0.646741	−	0.163209i
$305$	12.2127	+	7.05099i	0.699295	+	0.403738i
$306$		0			0
$307$	18.5894	−	10.7326i	1.06095	−	0.612541i	0.135257	−	0.990811i	$-0.456814\pi$
$307$	18.5894	−	10.7326i	1.06095	−	0.612541i	0.925696	+	0.378269i	$0.123481\pi$
$308$	1.50101	+	4.64214i	0.0855282	+	0.264510i
$309$		0			0
$310$	−18.3814	+	14.8633i	−1.04399	+	0.844179i
$311$	8.69917	−	7.29947i	0.493285	−	0.413915i	−0.361917	−	0.932210i	$-0.617878\pi$
$311$	8.69917	−	7.29947i	0.493285	−	0.413915i	0.855202	+	0.518295i	$0.173433\pi$
$312$		0			0
$313$	−24.1218	+	8.77962i	−1.36345	+	0.496254i	−0.917118	−	0.398616i	$-0.869491\pi$
$313$	−24.1218	+	8.77962i	−1.36345	+	0.496254i	−0.446328	+	0.894870i	$0.647268\pi$
$314$	−5.36266	−	9.69076i	−0.302632	−	0.546881i
$315$		0			0
$316$	−17.2181	−	10.7932i	−0.968591	−	0.607163i
$317$	−24.5290	−	4.32513i	−1.37769	−	0.242923i	−0.564743	−	0.825267i	$-0.691025\pi$
$317$	−24.5290	−	4.32513i	−1.37769	−	0.242923i	−0.812943	+	0.582343i	$0.802136\pi$
$318$		0			0
$319$	8.32919	−	22.8843i	0.466345	−	1.28127i
$320$	14.1213	−	0.926826i	0.789406	−	0.0518111i
$321$		0			0
$322$	4.34115	−	4.98674i	0.241923	−	0.277900i
$323$	−18.6625			−1.03841
$324$		0			0
$325$	−2.61713			−0.145172
$326$	13.8091	−	15.8627i	0.764814	−	0.878553i
$327$		0			0
$328$	−18.1213	+	2.18572i	−1.00058	+	0.120686i
$329$	1.10334	−	3.03141i	0.0608294	−	0.167127i
$330$		0			0
$331$	31.0724	+	5.47891i	1.70790	+	0.301148i	0.940442	−	0.339955i	$-0.110412\pi$
$331$	31.0724	+	5.47891i	1.70790	+	0.301148i	0.767454	+	0.641103i	$0.221523\pi$
$332$	−5.27485	+	8.41482i	−0.289495	+	0.461823i
$333$		0			0
$334$	0.696820	+	1.25921i	0.0381283	+	0.0689010i
$335$	9.45307	−	3.44064i	0.516476	−	0.187982i
$336$		0			0
$337$	15.8413	−	13.2924i	0.862929	−	0.724083i	−0.0996680	−	0.995021i	$-0.531778\pi$
$337$	15.8413	−	13.2924i	0.862929	−	0.724083i	0.962597	+	0.270937i	$0.0873336\pi$
$338$	−12.1437	+	9.81947i	−0.660531	+	0.534109i
$339$		0			0
$340$	21.6078	−	6.98679i	1.17185	−	0.378912i
$341$	26.2801	−	15.1728i	1.42315	−	0.821655i
$342$		0			0
$343$	−8.82994	−	5.09797i	−0.476772	−	0.275264i
$344$	20.1582	+	4.69929i	1.08686	+	0.253368i
$345$		0			0
$346$	3.96724	−	10.3131i	0.213280	−	0.554433i
$347$	−4.96431	−	28.1540i	−0.266498	−	1.51139i	−0.764734	−	0.644346i	$-0.777130\pi$
$347$	−4.96431	−	28.1540i	−0.266498	−	1.51139i	0.498236	−	0.867041i	$-0.333981\pi$
$348$		0			0
$349$	−11.0490	−	9.27121i	−0.591439	−	0.496276i	0.297242	−	0.954802i	$-0.403933\pi$
$349$	−11.0490	−	9.27121i	−0.591439	−	0.496276i	−0.888681	+	0.458526i	$0.848378\pi$
$350$	−0.0365038	+	2.00927i	−0.00195121	+	0.107400i
$351$		0			0
$352$	−18.0920	−	1.64780i	−0.964305	−	0.0878278i
$353$	−16.3175	+	19.4465i	−0.868496	+	1.03503i	0.130554	+	0.991441i	$0.458324\pi$
$353$	−16.3175	+	19.4465i	−0.868496	+	1.03503i	−0.999049	+	0.0435915i	$0.986120\pi$
$354$		0			0
$355$	−6.57900	+	1.16005i	−0.349177	+	0.0615693i
$356$	−0.442147	+	1.08988i	−0.0234337	+	0.0577634i
$357$		0			0
$358$	2.11460	−	10.8375i	0.111760	−	0.572778i
$359$	−2.61678	+	4.53239i	−0.138108	+	0.239211i	−0.926781	−	0.375603i	$-0.877436\pi$
$359$	−2.61678	+	4.53239i	−0.138108	+	0.239211i	0.788672	+	0.614814i	$0.210769\pi$
$360$		0			0
$361$	−5.27335	−	9.13371i	−0.277545	−	0.480721i
$362$	3.88929	−	1.33609i	0.204416	−	0.0702233i
$363$		0			0
$364$	−1.30605	−	1.67659i	−0.0684557	−	0.0878771i
$365$	−12.7318	−	15.1732i	−0.666414	−	0.794201i
$366$		0			0
$367$	−11.0968	−	30.4882i	−0.579247	−	1.59147i	−0.789452	−	0.613812i	$-0.789635\pi$
$367$	−11.0968	−	30.4882i	−0.579247	−	1.59147i	0.210205	−	0.977657i	$-0.432587\pi$
$368$	10.7293	+	22.1583i	0.559302	+	1.15508i
$369$		0			0
$370$	−6.94660	−	4.18067i	−0.361136	−	0.217343i
$371$	1.27150	−	7.21105i	0.0660131	−	0.374379i
$372$		0			0
$373$	13.8536	+	5.04230i	0.717312	+	0.261080i	0.674784	−	0.738015i	$-0.264237\pi$
$373$	13.8536	+	5.04230i	0.717312	+	0.261080i	0.0425278	+	0.999095i	$0.486459\pi$
$374$	−28.7968	+	4.53994i	−1.48905	+	0.234755i
$375$		0			0
$376$	8.76775	+	8.21116i	0.452162	+	0.423458i
$377$			10.6084i			0.546363i
$378$		0			0
$379$			2.17390i			0.111666i	0.998440	+	0.0558329i	$0.0177814\pi$
$379$			2.17390i			0.111666i	−0.998440	+	0.0558329i	$0.982219\pi$
$380$	−7.63445	−	6.89381i	−0.391639	−	0.353645i
$381$		0			0
$382$	−3.48801	−	22.1244i	−0.178462	−	1.13198i
$383$	−25.4781	−	9.27327i	−1.30187	−	0.473842i	−0.404265	−	0.914642i	$-0.632473\pi$
$383$	−25.4781	−	9.27327i	−1.30187	−	0.473842i	−0.897605	+	0.440800i	$0.854695\pi$
$384$		0			0
$385$	−0.749325	+	4.24963i	−0.0381891	+	0.216581i
$386$	−9.30046	+	15.4536i	−0.473381	+	0.786568i
$387$		0			0
$388$	15.8259	+	29.8667i	0.803438	+	1.51625i
$389$	9.29522	+	25.5384i	0.471286	+	1.29485i	0.916719	+	0.399533i	$0.130828\pi$
$389$	9.29522	+	25.5384i	0.471286	+	1.29485i	−0.445432	+	0.895316i	$0.646950\pi$
$390$		0			0
$391$	25.3944	+	30.2639i	1.28425	+	1.53051i
$392$	14.5322	−	10.9022i	0.733987	−	0.550644i
$393$		0			0
$394$	3.63075	+	10.5689i	0.182915	+	0.532454i
$395$	−8.98690	−	15.5658i	−0.452180	−	0.783199i
$396$		0			0
$397$	−4.91342	+	8.51029i	−0.246597	+	0.427119i	−0.962579	−	0.271000i	$-0.912646\pi$
$397$	−4.91342	+	8.51029i	−0.246597	+	0.427119i	0.715982	+	0.698119i	$0.245979\pi$
$398$	−5.39945	−	1.05354i	−0.270650	−	0.0528091i
$399$		0			0
$400$	−6.82742	−	3.06310i	−0.341371	−	0.153155i
$401$	−8.92802	+	1.57425i	−0.445844	+	0.0786143i	−0.392063	−	0.919938i	$-0.628238\pi$
$401$	−8.92802	+	1.57425i	−0.445844	+	0.0786143i	−0.0537811	+	0.998553i	$0.517127\pi$
$402$		0			0
$403$	−8.49698	+	10.1263i	−0.423265	+	0.504427i
$404$	−0.398238	+	10.9565i	−0.0198131	+	0.545105i
$405$		0			0
$406$	8.14453	+	0.147967i	0.404206	+	0.00734348i
$407$	7.97292	+	6.69007i	0.395203	+	0.331615i
$408$		0			0
$409$	4.97696	+	28.2258i	0.246095	+	1.39567i	0.817936	+	0.575309i	$0.195118\pi$
$409$	4.97696	+	28.2258i	0.246095	+	1.39567i	−0.571841	+	0.820364i	$0.693771\pi$
$410$	−15.0678	−	5.79629i	−0.744143	−	0.286258i
$411$		0			0
$412$	−11.8132	−	2.52857i	−0.581995	−	0.124574i
$413$	0.278191	+	0.160614i	0.0136889	+	0.00790329i
$414$		0			0
$415$	−7.60731	+	4.39208i	−0.373428	+	0.215599i
$416$	7.65131	−	2.02098i	0.375136	−	0.0990867i
$417$		0			0
$418$	8.30276	+	10.2680i	0.406101	+	0.502224i
$419$	12.8762	−	10.8044i	0.629046	−	0.527832i	−0.271587	−	0.962414i	$-0.587548\pi$
$419$	12.8762	−	10.8044i	0.629046	−	0.527832i	0.900632	+	0.434582i	$0.143104\pi$
$420$		0			0
$421$	9.49415	−	3.45559i	0.462716	−	0.168415i	−0.100134	−	0.994974i	$-0.531927\pi$
$421$	9.49415	−	3.45559i	0.462716	−	0.168415i	0.562850	+	0.826559i	$0.309705\pi$
$422$	−4.78336	+	2.64701i	−0.232850	+	0.128854i
$423$		0			0
$424$	22.8351	+	14.8988i	1.10897	+	0.723548i
$425$	−11.8257	−	2.08519i	−0.573630	−	0.101146i
$426$		0			0
$427$	2.07104	−	5.69014i	0.100225	−	0.275365i
$428$	−1.18134	−	8.49347i	−0.0571023	−	0.410547i
$429$		0			0
$430$	13.8084	+	12.0207i	0.665900	+	0.579691i
$431$	27.3550			1.31764			0.658822	−	0.752299i	$-0.271055\pi$
$431$	27.3550			1.31764			0.658822	+	0.752299i	$0.271055\pi$
$432$		0			0
$433$	−8.86214			−0.425887			−0.212944	−	0.977065i	$-0.568305\pi$
$433$	−8.86214			−0.425887			−0.212944	+	0.977065i	$0.568305\pi$
$434$	7.65586	+	6.66472i	0.367493	+	0.319917i
$435$		0			0
$436$	−1.30915	−	9.41235i	−0.0626968	−	0.450770i
$437$	6.12040	−	16.8157i	0.292779	−	0.804402i
$438$		0			0
$439$	−24.2876	−	4.28256i	−1.15918	−	0.204395i	−0.439202	−	0.898388i	$-0.644739\pi$
$439$	−24.2876	−	4.28256i	−1.15918	−	0.204395i	−0.719982	+	0.693993i	$0.755850\pi$
$440$	−13.4572	−	8.78018i	−0.641549	−	0.418579i
$441$		0			0
$442$	11.1113	−	6.14877i	0.528513	−	0.292467i
$443$	11.7116	−	4.26266i	0.556433	−	0.202525i	−0.0484697	−	0.998825i	$-0.515434\pi$
$443$	11.7116	−	4.26266i	0.556433	−	0.202525i	0.604902	+	0.796300i	$0.293212\pi$
$444$		0			0
$445$	−0.796903	+	0.668681i	−0.0377768	+	0.0316985i
$446$	20.7821	+	25.7012i	0.984062	+	1.21699i
$447$		0			0
$448$	−1.44487	−	5.90241i	−0.0682636	−	0.278862i
$449$	30.7560	−	17.7570i	1.45146	−	0.838003i	0.452899	−	0.891562i	$-0.350390\pi$
$449$	30.7560	−	17.7570i	1.45146	−	0.838003i	0.998565	+	0.0535589i	$0.0170565\pi$
$450$		0			0
$451$	17.9480	+	10.3623i	0.845140	+	0.487942i
$452$	−17.7979	−	3.80957i	−0.837143	−	0.179187i
$453$		0			0
$454$	−14.0112	−	5.38987i	−0.657580	−	0.252959i
$455$	−0.326416	−	1.85119i	−0.0153026	−	0.0867853i
$456$		0			0
$457$	12.8012	+	10.7415i	0.598816	+	0.502467i	0.891065	−	0.453876i	$-0.149959\pi$
$457$	12.8012	+	10.7415i	0.598816	+	0.502467i	−0.292249	+	0.956342i	$0.594403\pi$
$458$	−9.83695	−	0.178714i	−0.459651	−	0.00835077i
$459$		0			0
$460$	−0.790951	+	21.7609i	−0.0368783	+	1.01461i
$461$	−4.70721	+	5.60984i	−0.219237	+	0.261276i	−0.864441	−	0.502734i	$-0.832328\pi$
$461$	−4.70721	+	5.60984i	−0.219237	+	0.261276i	0.645205	+	0.764010i	$0.276772\pi$
$462$		0			0
$463$	14.7017	−	2.59231i	0.683246	−	0.120475i	0.178758	−	0.983893i	$-0.442792\pi$
$463$	14.7017	−	2.59231i	0.683246	−	0.120475i	0.504489	+	0.863418i	$0.331681\pi$
$464$	−12.4162	+	27.6747i	−0.576407	+	1.28477i
$465$		0			0
$466$	−22.4368	−	4.37786i	−1.03937	−	0.202801i
$467$	−15.8668	+	27.4821i	−0.734227	+	1.27172i	0.220834	+	0.975311i	$0.429122\pi$
$467$	−15.8668	+	27.4821i	−0.734227	+	1.27172i	−0.955062	+	0.296408i	$0.904211\pi$
$468$		0			0
$469$	−2.15980	−	3.74089i	−0.0997305	−	0.172738i
$470$	3.45191	+	10.0483i	0.159225	+	0.463495i
$471$		0			0
$472$	−0.956815	+	0.717811i	−0.0440410	+	0.0330399i
$473$	−15.1067	−	18.0035i	−0.694608	−	0.827802i
$474$		0			0
$475$	1.86031	+	5.11115i	0.0853567	+	0.234516i
$476$	−4.56568	−	8.61639i	−0.209268	−	0.394931i
$477$		0			0
$478$	−16.5024	+	27.4203i	−0.754801	+	1.25418i
$479$	−2.34547	+	13.3018i	−0.107167	+	0.607775i	0.883165	+	0.469062i	$0.155408\pi$
$479$	−2.34547	+	13.3018i	−0.107167	+	0.607775i	−0.990333	+	0.138713i	$0.955703\pi$
$480$		0			0
$481$	−4.26039	−	1.55066i	−0.194257	−	0.0707038i
$482$	−0.0474440	−	0.300937i	−0.00216102	−	0.0137073i
$483$		0			0
$484$	−1.01891	−	0.920060i	−0.0463139	−	0.0418209i
$485$			29.8960i			1.35751i
$486$		0			0
$487$			21.1864i			0.960045i	0.877256	+	0.480023i	$0.159372\pi$
$487$			21.1864i			0.960045i	−0.877256	+	0.480023i	$0.840628\pi$
$488$	16.4576	+	15.4128i	0.745000	+	0.697706i
$489$		0			0
$490$	15.8724	−	2.50235i	0.717042	−	0.113045i
$491$	18.5924	+	6.76707i	0.839062	+	0.305394i	0.725573	−	0.688145i	$-0.241575\pi$
$491$	18.5924	+	6.76707i	0.839062	+	0.305394i	0.113490	+	0.993539i	$0.463797\pi$
$492$		0			0
$493$	−8.45225	+	47.9351i	−0.380670	+	2.15889i
$494$	−4.92848	−	2.96611i	−0.221743	−	0.133452i
$495$		0			0
$496$	−34.0184	+	16.4720i	−1.52747	+	0.739616i
$497$	0.981109	+	2.69557i	0.0440087	+	0.120913i
$498$		0			0
$499$	−18.9238	−	22.5525i	−0.847146	−	1.00959i	−0.999773	−	0.0213055i	$-0.993218\pi$
$499$	−18.9238	−	22.5525i	−0.847146	−	1.00959i	0.152627	−	0.988284i	$-0.451227\pi$
$500$	−14.9384	−	19.1765i	−0.668064	−	0.857599i
$501$		0			0
$502$	31.9077	−	10.9613i	1.42411	−	0.489225i
$503$	15.3565	+	26.5983i	0.684714	+	1.18596i	0.973527	+	0.228574i	$0.0734063\pi$
$503$	15.3565	+	26.5983i	0.684714	+	1.18596i	−0.288812	+	0.957386i	$0.593260\pi$
$504$		0			0
$505$	−4.84861	+	8.39803i	−0.215760	+	0.373707i
$506$	5.35331	−	27.4360i	0.237984	−	1.21968i
$507$		0			0
$508$	6.58359	−	16.2284i	0.292100	−	0.720017i
$509$	−13.2428	+	2.33506i	−0.586977	+	0.103500i	−0.459246	−	0.888309i	$-0.651880\pi$
$509$	−13.2428	+	2.33506i	−0.586977	+	0.103500i	−0.127731	+	0.991809i	$0.540769\pi$
$510$		0			0
$511$	−5.46698	+	6.51530i	−0.241845	+	0.288220i
$512$	22.3257	+	3.68292i	0.986665	+	0.162763i
$513$		0			0
$514$	−0.0350319	+	1.92826i	−0.00154519	+	0.0850518i
$515$	−8.18537	−	6.86834i	−0.360690	−	0.302655i
$516$		0			0
$517$	−2.36842	−	13.4320i	−0.104163	−	0.590737i
$518$	−1.24993	+	3.24925i	−0.0549186	+	0.142764i
$519$		0			0
$520$	6.81676	+	1.58912i	0.298935	+	0.0696877i
$521$	−9.44955	−	5.45570i	−0.413992	−	0.239018i	0.278511	−	0.960433i	$-0.410159\pi$
$521$	−9.44955	−	5.45570i	−0.413992	−	0.239018i	−0.692504	+	0.721414i	$0.743492\pi$
$522$		0			0
$523$	−16.1086	+	9.30028i	−0.704378	+	0.406673i	−0.808976	−	0.587842i	$-0.799978\pi$
$523$	−16.1086	+	9.30028i	−0.704378	+	0.406673i	0.104598	+	0.994515i	$0.466644\pi$
$524$	−14.0597	+	4.54613i	−0.614199	+	0.198599i
$525$		0			0
$526$	18.8811	−	15.2674i	0.823256	−	0.665689i
$527$	−46.4624	+	38.9865i	−2.02393	+	1.69828i
$528$		0			0
$529$	−13.9843	+	5.08986i	−0.608012	+	0.221298i
$530$	11.6766	+	21.1006i	0.507200	+	0.916553i
$531$		0			0
$532$	−2.34595	+	3.74242i	−0.101710	+	0.162255i
$533$	−8.89075	−	1.56768i	−0.385101	−	0.0679037i
$534$		0			0
$535$	2.59410	−	7.12723i	0.112153	−	0.308137i
$536$	15.9690	−	1.92611i	0.689754	−	0.0831953i
$537$		0			0
$538$	8.16799	−	9.38269i	0.352147	−	0.404516i
$539$	−20.6274			−0.888486
$540$		0			0
$541$	16.5311			0.710730			0.355365	−	0.934728i	$-0.384357\pi$
$541$	16.5311			0.710730			0.355365	+	0.934728i	$0.384357\pi$
$542$	−2.96174	+	3.40219i	−0.127218	+	0.146137i
$543$		0			0
$544$	36.1832	−	3.03580i	1.55134	−	0.130159i
$545$	2.87475	−	7.89830i	0.123141	−	0.338326i
$546$		0			0
$547$	−9.59158	−	1.69125i	−0.410106	−	0.0723128i	−0.0352109	−	0.999380i	$-0.511210\pi$
$547$	−9.59158	−	1.69125i	−0.410106	−	0.0723128i	−0.374895	+	0.927067i	$0.622321\pi$
$548$	−9.16995	−	5.74821i	−0.391721	−	0.245551i
$549$		0			0
$550$	4.11388	+	7.43412i	0.175417	+	0.316992i
$551$	20.7179	−	7.54069i	0.882612	−	0.321244i
$552$		0			0
$553$	−5.91223	+	4.96095i	−0.251413	+	0.210961i
$554$	15.3747	−	12.4321i	0.653208	−	0.528188i
$555$		0			0
$556$	−8.98423	−	27.7853i	−0.381016	−	1.17836i
$557$	16.9093	−	9.76261i	0.716471	−	0.413655i	−0.0969812	−	0.995286i	$-0.530919\pi$
$557$	16.9093	−	9.76261i	0.716471	−	0.413655i	0.813453	+	0.581631i	$0.197585\pi$
$558$		0			0
$559$	8.86613	+	5.11886i	0.374997	+	0.216505i
$560$	1.31512	−	5.21134i	0.0555738	−	0.220219i
$561$		0			0
$562$	−2.38289	+	6.19445i	−0.100516	+	0.261297i
$563$	−0.00844444	−	0.0478908i	−0.000355891	−	0.00201836i	0.984629	−	0.174657i	$-0.0558817\pi$
$563$	−0.00844444	−	0.0478908i	−0.000355891	−	0.00201836i	−0.984985	+	0.172639i	$0.944771\pi$
$564$		0			0
$565$	−12.3322	−	10.3479i	−0.518818	−	0.435340i
$566$	−0.110973	+	6.10829i	−0.00466456	+	0.256751i
$567$		0			0
$568$	−10.6657	−	0.581823i	−0.447522	−	0.0244128i
$569$	−14.3594	+	17.1129i	−0.601978	+	0.717409i	−0.977860	−	0.209258i	$-0.932895\pi$
$569$	−14.3594	+	17.1129i	−0.601978	+	0.717409i	0.375883	+	0.926667i	$0.377340\pi$
$570$		0			0
$571$	7.54185	−	1.32983i	0.315617	−	0.0556518i	−0.0135958	−	0.999908i	$-0.504328\pi$
$571$	7.54185	−	1.32983i	0.315617	−	0.0556518i	0.329213	+	0.944256i	$0.393217\pi$
$572$	−8.32636	−	3.37788i	−0.348143	−	0.141236i
$573$		0			0
$574$	−1.32758	+	6.80392i	−0.0554121	+	0.283990i
$575$	5.75711	−	9.97161i	0.240088	−	0.415845i
$576$		0			0
$577$	−0.594755	−	1.03015i	−0.0247600	−	0.0428855i	0.853380	−	0.521289i	$-0.174549\pi$
$577$	−0.594755	−	1.03015i	−0.0247600	−	0.0428855i	−0.878140	+	0.478404i	$0.841215\pi$
$578$	32.3691	−	11.1198i	1.34638	−	0.462522i
$579$		0			0
$580$	−21.1646	+	16.4871i	−0.878813	+	0.684590i
$581$	2.42452	+	2.88943i	0.100586	+	0.119874i
$582$		0			0
$583$	−10.5883	−	29.0912i	−0.438524	−	1.20483i
$584$	−14.3176	−	28.2489i	−0.592465	−	1.16895i
$585$		0			0
$586$	13.7998	+	8.30517i	0.570066	+	0.343083i
$587$	−2.07929	+	11.7922i	−0.0858214	+	0.486717i	0.911355	+	0.411621i	$0.135037\pi$
$587$	−2.07929	+	11.7922i	−0.0858214	+	0.486717i	−0.997176	+	0.0750959i	$0.976074\pi$
$588$		0			0
$589$	25.8161	+	9.39629i	1.06373	+	0.387168i
$590$	−1.04506	+	0.164758i	−0.0430243	+	0.00678296i
$591$		0			0
$592$	−9.29938	−	9.03166i	−0.382202	−	0.371199i
$593$			33.8346i			1.38942i	0.719290	+	0.694710i	$0.244467\pi$
$593$			33.8346i			1.38942i	−0.719290	+	0.694710i	$0.755533\pi$
$594$		0			0
$595$		−	8.62484i		−	0.353584i
$596$	−1.39279	+	1.54242i	−0.0570507	+	0.0631800i
$597$		0			0
$598$	1.89631	+	12.0283i	0.0775460	+	0.491874i
$599$	−4.43045	−	1.61255i	−0.181023	−	0.0658871i	0.249918	−	0.968267i	$-0.419596\pi$
$599$	−4.43045	−	1.61255i	−0.181023	−	0.0658871i	−0.430942	+	0.902380i	$0.641818\pi$
$600$		0			0
$601$	2.90395	−	16.4691i	0.118455	−	0.671790i	−0.866527	−	0.499131i	$-0.833653\pi$
$601$	2.90395	−	16.4691i	0.118455	−	0.671790i	0.984982	−	0.172660i	$-0.0552361\pi$
$602$	4.05362	−	6.73549i	0.165213	−	0.274518i
$603$		0			0
$604$	26.8018	−	14.2018i	1.09055	−	0.577863i
$605$	−0.415298	−	1.14102i	−0.0168843	−	0.0463891i
$606$		0			0
$607$	−16.3490	−	19.4839i	−0.663584	−	0.790828i	0.324311	−	0.945950i	$-0.394867\pi$
$607$	−16.3490	−	19.4839i	−0.663584	−	0.790828i	−0.987895	+	0.155122i	$0.950423\pi$
$608$	−9.38560	−	13.5062i	−0.380636	−	0.547747i
$609$		0			0
$610$	6.47944	+	18.8613i	0.262345	+	0.763671i
$611$	2.97070	+	5.14540i	0.120182	+	0.208161i
$612$		0			0
$613$	23.0173	−	39.8671i	0.929658	−	1.61022i	0.145765	−	0.989319i	$-0.453436\pi$
$613$	23.0173	−	39.8671i	0.929658	−	1.61022i	0.783893	−	0.620896i	$-0.213231\pi$
$614$	29.7945	+	5.81349i	1.20241	+	0.234613i
$615$		0			0
$616$	−2.70947	+	6.34537i	−0.109168	+	0.255662i
$617$	0.162348	−	0.0286264i	0.00653590	−	0.00115246i	−0.170379	−	0.985379i	$-0.554499\pi$
$617$	0.162348	−	0.0286264i	0.00653590	−	0.00115246i	0.176915	+	0.984226i	$0.443388\pi$
$618$		0			0
$619$	−8.86726	+	10.5676i	−0.356405	+	0.424747i	−0.914220	−	0.405218i	$-0.867195\pi$
$619$	−8.86726	+	10.5676i	−0.356405	+	0.424747i	0.557815	+	0.829965i	$0.311640\pi$
$620$	−33.4083	−	1.21430i	−1.34171	−	0.0487675i
$621$		0			0
$622$	16.0571	+	0.291720i	0.643831	+	0.0116969i
$623$	0.342186	+	0.287129i	0.0137094	+	0.0115036i
$624$		0			0
$625$	−2.10920	−	11.9619i	−0.0843681	−	0.478475i
$626$	−33.8822	−	13.0339i	−1.35421	−	0.520938i
$627$		0			0
$628$	3.27840	−	15.3163i	0.130822	−	0.611188i
$629$	−18.0154	−	10.4012i	−0.718322	−	0.414724i
$630$		0			0
$631$	−28.8999	+	16.6854i	−1.15049	+	0.664234i	−0.949006	−	0.315259i	$-0.897909\pi$
$631$	−28.8999	+	16.6854i	−1.15049	+	0.664234i	−0.201481	+	0.979492i	$0.564575\pi$
$632$	−8.34361	−	27.5008i	−0.331891	−	1.09392i
$633$		0			0
$634$	−22.1479	−	27.3903i	−0.879606	−	1.08781i
$635$	11.8659	−	9.95671i	0.470885	−	0.395120i
$636$		0			0
$637$	8.44367	−	3.07324i	0.334550	−	0.121766i
$638$	30.1340	−	16.6755i	1.19302	−	0.660189i
$639$		0			0
$640$	15.9233	+	12.1240i	0.629423	+	0.479243i
$641$	44.1736	+	7.78900i	1.74475	+	0.307647i	0.952949	−	0.303129i	$-0.0980313\pi$
$641$	44.1736	+	7.78900i	1.74475	+	0.307647i	0.791803	+	0.610776i	$0.209142\pi$
$642$		0			0
$643$	−9.50479	+	26.1142i	−0.374832	+	1.02984i	0.598636	+	0.801021i	$0.295710\pi$
$643$	−9.50479	+	26.1142i	−0.374832	+	1.02984i	−0.973468	+	0.228822i	$0.926513\pi$
$644$	9.26106	−	1.28810i	0.364937	−	0.0507584i
$645$		0			0
$646$	−19.9065	−	17.3294i	−0.783210	−	0.681814i
$647$	−29.6395			−1.16525			−0.582624	−	0.812742i	$-0.697974\pi$
$647$	−29.6395			−1.16525			−0.582624	+	0.812742i	$0.697974\pi$
$648$		0			0
$649$	1.35813			0.0533113
$650$	−2.79158	−	2.43018i	−0.109495	−	0.0953195i
$651$		0			0
$652$	29.4591	−	4.09742i	1.15371	−	0.160467i
$653$	−3.24289	+	8.90976i	−0.126904	+	0.348666i	−0.986832	−	0.161750i	$-0.948286\pi$
$653$	−3.24289	+	8.90976i	−0.126904	+	0.348666i	0.859928	+	0.510416i	$0.170508\pi$
$654$		0			0
$655$	−12.8709	−	2.26949i	−0.502907	−	0.0886762i
$656$	−21.3589	−	14.4955i	−0.833924	−	0.565953i
$657$		0			0
$658$	3.99177	−	2.20896i	0.155615	−	0.0861141i
$659$	−39.0039	+	14.1963i	−1.51938	+	0.553008i	−0.960993	−	0.276573i	$-0.910801\pi$
$659$	−39.0039	+	14.1963i	−1.51938	+	0.553008i	−0.558385	+	0.829582i	$0.688579\pi$
$660$		0			0
$661$	−1.13289	+	0.950604i	−0.0440642	+	0.0369742i	−0.664554	−	0.747240i	$-0.731378\pi$
$661$	−1.13289	+	0.950604i	−0.0440642	+	0.0369742i	0.620490	+	0.784215i	$0.286934\pi$
$662$	28.0562	+	34.6970i	1.09043	+	1.34854i
$663$		0			0
$664$	−13.4402	+	4.07769i	−0.521581	+	0.158245i
$665$	−3.38329	+	1.95334i	−0.131198	+	0.0757474i
$666$		0			0
$667$	−40.4196	−	23.3363i	−1.56505	−	0.903584i
$668$	−0.425993	+	1.99019i	−0.0164822	+	0.0770030i
$669$		0			0
$670$	13.2781	+	5.10783i	0.512977	+	0.197333i
$671$	−4.44566	−	25.2126i	−0.171623	−	0.973320i
$672$		0			0
$673$	−6.61457	−	5.55028i	−0.254973	−	0.213948i	0.506337	−	0.862335i	$-0.330999\pi$
$673$	−6.61457	−	5.55028i	−0.254973	−	0.213948i	−0.761310	+	0.648388i	$0.775444\pi$
$674$	29.2401	+	0.531224i	1.12629	+	0.0204620i
$675$		0			0
$676$	−22.0712	−	0.802230i	−0.848894	−	0.0308550i
$677$	16.1671	−	19.2672i	0.621353	−	0.740499i	−0.359950	−	0.932972i	$-0.617206\pi$
$677$	16.1671	−	19.2672i	0.621353	−	0.740499i	0.981302	+	0.192472i	$0.0616506\pi$
$678$		0			0
$679$	12.6422	−	2.22916i	0.485163	−	0.0855473i
$680$	29.5359	+	12.6118i	1.13265	+	0.483641i
$681$		0			0
$682$	42.1209	+	8.21862i	1.61289	+	0.314707i
$683$	−10.1910	+	17.6513i	−0.389948	+	0.675409i	−0.992442	−	0.122714i	$-0.960840\pi$
$683$	−10.1910	+	17.6513i	−0.389948	+	0.675409i	0.602494	+	0.798123i	$0.294174\pi$
$684$		0			0
$685$	−4.78622	−	8.28998i	−0.182872	−	0.316744i
$686$	−4.68473	−	13.6370i	−0.178864	−	0.520663i
$687$		0			0
$688$	17.1383	+	23.7308i	0.653393	+	0.904728i
$689$	8.66849	+	10.3307i	0.330243	+	0.393569i
$690$		0			0
$691$	10.6380	+	29.2276i	0.404688	+	1.11187i	0.959944	+	0.280192i	$0.0903980\pi$
$691$	10.6380	+	29.2276i	0.404688	+	1.11187i	−0.555256	+	0.831679i	$0.687380\pi$
$692$	13.8081	−	7.31666i	0.524904	−	0.278138i
$693$		0			0
$694$	20.8477	−	34.6405i	0.791367	−	1.31493i
$695$	4.48504	−	25.4360i	0.170127	−	0.964841i
$696$		0			0
$697$	−38.9245	−	14.1674i	−1.47437	−	0.536627i
$698$	−3.17657	−	20.1490i	−0.120235	−	0.762649i
$699$		0			0
$700$	−1.90468	+	2.10931i	−0.0719903	+	0.0797246i
$701$		−	6.46847i		−	0.244311i	−0.992511	−	0.122155i	$-0.961019\pi$
$701$		−	6.46847i		−	0.244311i	0.992511	−	0.122155i	$-0.0389806\pi$
$702$		0			0
$703$			9.42262i			0.355381i
$704$	−17.7679	−	18.5573i	−0.669652	−	0.699403i
$705$		0			0
$706$	−35.4627	+	5.59084i	−1.33465	+	0.210414i
$707$	3.91282	+	1.42415i	0.147157	+	0.0535607i
$708$		0			0
$709$	3.74684	−	21.2494i	0.140715	−	0.798036i	−0.829993	−	0.557774i	$-0.811655\pi$
$709$	3.74684	−	21.2494i	0.140715	−	0.798036i	0.970708	−	0.240262i	$-0.0772334\pi$
$710$	−8.09474	−	4.87166i	−0.303790	−	0.182830i
$711$		0			0
$712$	−1.48365	+	0.751965i	−0.0556019	+	0.0281811i
$713$	−19.8911	−	54.6503i	−0.744927	−	2.04667i
$714$		0			0
$715$	−5.10854	−	6.08812i	−0.191048	−	0.227683i
$716$	12.3189	−	9.59634i	0.460378	−	0.358632i
$717$		0			0
$718$	−6.99985	+	2.40466i	−0.261232	+	0.0897413i
$719$	−4.48435	−	7.76713i	−0.167238	−	0.289665i	0.770210	−	0.637791i	$-0.220152\pi$
$719$	−4.48435	−	7.76713i	−0.167238	−	0.289665i	−0.937448	+	0.348126i	$0.886818\pi$
$720$		0			0
$721$	−2.29410	+	3.97349i	−0.0854366	+	0.147980i
$722$	2.85640	−	14.6392i	0.106304	−	0.544815i
$723$		0			0
$724$	5.38919	+	2.18631i	0.200288	+	0.0812536i
$725$	13.9707	−	2.46341i	0.518858	−	0.0914886i
$726$		0			0
$727$	25.5804	−	30.4856i	0.948726	−	1.13065i	−0.0425829	−	0.999093i	$-0.513559\pi$
$727$	25.5804	−	30.4856i	0.948726	−	1.13065i	0.991309	−	0.131555i	$-0.0419969\pi$
$728$	0.163713	−	3.00111i	0.00606762	−	0.111228i
$729$		0			0
$730$	0.508821	−	28.0070i	0.0188323	−	1.03658i
$731$	35.9839	+	30.1940i	1.33091	+	1.11677i
$732$		0			0
$733$	5.60310	+	31.7768i	0.206955	+	1.17370i	0.894333	+	0.447402i	$0.147651\pi$
$733$	5.60310	+	31.7768i	0.206955	+	1.17370i	−0.687378	+	0.726300i	$0.741238\pi$
$734$	16.4738	−	42.8246i	0.608060	−	1.58068i
$735$		0			0
$736$	−9.13100	+	33.5982i	−0.336573	+	1.23845i
$737$	−15.8162	−	9.13151i	−0.582599	−	0.336364i
$738$		0			0
$739$	45.5964	−	26.3251i	1.67729	−	0.968384i	0.713912	−	0.700235i	$-0.246922\pi$
$739$	45.5964	−	26.3251i	1.67729	−	0.968384i	0.963378	−	0.268148i	$-0.0864118\pi$
$740$	−3.52761	−	10.9097i	−0.129678	−	0.401050i
$741$		0			0
$742$	8.05221	−	6.51106i	0.295606	−	0.239028i
$743$	−5.64333	+	4.73531i	−0.207034	+	0.173722i	−0.740409	−	0.672157i	$-0.765368\pi$
$743$	−5.64333	+	4.73531i	−0.207034	+	0.173722i	0.533375	+	0.845879i	$0.320923\pi$
$744$		0			0
$745$	−1.72728	+	0.628678i	−0.0632825	+	0.0230330i
$746$	10.0950	+	18.2424i	0.369603	+	0.667902i
$747$		0			0
$748$	−34.9320	−	21.8972i	−1.27724	−	0.800641i
$749$	−3.20733	−	0.565539i	−0.117193	−	0.0206643i
$750$		0			0
$751$	−14.4395	+	39.6722i	−0.526905	+	1.44766i	0.335792	+	0.941936i	$0.390996\pi$
$751$	−14.4395	+	39.6722i	−0.526905	+	1.44766i	−0.862696	+	0.505722i	$0.831226\pi$
$752$	1.72759	+	16.9000i	0.0629986	+	0.616278i
$753$		0			0
$754$	−9.85066	+	11.3156i	−0.358740	+	0.412090i
$755$	26.8280			0.976373
$756$		0			0
$757$	−18.7376			−0.681028			−0.340514	−	0.940239i	$-0.610601\pi$
$757$	−18.7376			−0.681028			−0.340514	+	0.940239i	$0.610601\pi$
$758$	−2.01861	+	2.31881i	−0.0733194	+	0.0842231i
$759$		0			0
$760$	−1.74199	−	14.4425i	−0.0631886	−	0.523883i
$761$	−2.99398	+	8.22589i	−0.108532	+	0.298188i	−0.982055	−	0.188594i	$-0.939607\pi$
$761$	−2.99398	+	8.22589i	−0.108532	+	0.298188i	0.873524	+	0.486782i	$0.161829\pi$
$762$		0			0
$763$	−3.55432	−	0.626722i	−0.128675	−	0.0226889i
$764$	16.8235	−	26.8380i	0.608652	−	0.970966i
$765$		0			0
$766$	−18.5656	−	33.5496i	−0.670802	−	1.21219i
$767$	−0.555940	+	0.202346i	−0.0200738	+	0.00730627i
$768$		0			0
$769$	18.0034	−	15.1066i	0.649219	−	0.544759i	−0.257615	−	0.966248i	$-0.582937\pi$
$769$	18.0034	−	15.1066i	0.649219	−	0.544759i	0.906834	+	0.421489i	$0.138492\pi$
$770$	−4.74535	+	3.83711i	−0.171010	+	0.138280i
$771$		0			0
$772$	−24.2701	+	7.84764i	−0.873501	+	0.282443i
$773$	−13.5604	+	7.82910i	−0.487733	+	0.281593i	−0.723634	−	0.690184i	$-0.757529\pi$
$773$	−13.5604	+	7.82910i	−0.487733	+	0.281593i	0.235900	+	0.971777i	$0.424196\pi$
$774$		0			0
$775$	15.3088	+	8.83855i	0.549909	+	0.317490i
$776$	−10.8525	+	46.5530i	−0.389581	+	1.67116i
$777$		0			0
$778$	−13.7993	+	35.8720i	−0.494729	+	1.28607i
$779$	3.25811	+	18.4776i	0.116734	+	0.662030i
$780$		0			0
$781$	9.29069	+	7.79581i	0.332447	+	0.278956i
$782$	−1.01487	+	55.8617i	−0.0362919	+	1.99761i
$783$		0			0
$784$	25.6243	+	1.86521i	0.915155	+	0.0666148i
$785$	8.90510	−	10.6127i	0.317837	−	0.378783i
$786$		0			0
$787$	−15.9427	+	2.81113i	−0.568296	+	0.100206i	−0.450411	−	0.892821i	$-0.648723\pi$
$787$	−15.9427	+	2.81113i	−0.568296	+	0.100206i	−0.117885	+	0.993027i	$0.537612\pi$
$788$	−5.94118	+	14.6448i	−0.211646	+	0.521701i
$789$		0			0
$790$	4.86791	−	24.9483i	0.173192	−	0.887621i
$791$	−3.45631	+	5.98650i	−0.122892	+	0.212856i
$792$		0			0
$793$	5.57617	+	9.65821i	0.198016	+	0.342973i
$794$	−13.1433	+	4.51514i	−0.466439	+	0.160236i
$795$		0			0
$796$	−4.78109	−	6.13752i	−0.169461	−	0.217539i
$797$	19.0625	+	22.7178i	0.675229	+	0.804707i	0.989486	−	0.144631i	$-0.0461996\pi$
$797$	19.0625	+	22.7178i	0.675229	+	0.804707i	−0.314256	+	0.949338i	$0.601755\pi$
$798$		0			0
$799$	9.32375	+	25.6168i	0.329850	+	0.906257i
$800$	−4.43823	−	9.60701i	−0.156915	−	0.339659i
$801$		0			0
$802$	−10.9850	−	6.61108i	−0.387892	−	0.233445i
$803$	−6.24423	+	35.4128i	−0.220354	+	1.24969i
$804$		0			0
$805$	7.77135	+	2.82854i	0.273904	+	0.0996929i
$806$	−18.4663	+	2.91130i	−0.650449	+	0.102546i
$807$		0			0
$808$	−10.5986	+	11.3170i	−0.372858	+	0.398132i
$809$		−	28.2066i		−	0.991690i	−0.868411	−	0.495845i	$-0.834858\pi$
$809$		−	28.2066i		−	0.991690i	0.868411	−	0.495845i	$-0.165142\pi$
$810$		0			0
$811$		−	28.0396i		−	0.984605i	−0.870424	−	0.492302i	$-0.836155\pi$
$811$		−	28.0396i		−	0.984605i	0.870424	−	0.492302i	$-0.163845\pi$
$812$	8.55004	+	7.72058i	0.300048	+	0.270939i
$813$		0			0
$814$	2.29220	+	14.5394i	0.0803416	+	0.509606i
$815$	24.7204	+	8.99750i	0.865918	+	0.315169i
$816$		0			0
$817$	3.69472	−	20.9538i	0.129262	−	0.733081i
$818$	−20.9008	+	34.7287i	−0.730779	+	1.21426i
$819$		0			0
$820$	−10.6899	−	20.1741i	−0.373308	−	0.704510i
$821$	10.1420	+	27.8650i	0.353960	+	0.972496i	0.981085	+	0.193578i	$0.0620092\pi$
$821$	10.1420	+	27.8650i	0.353960	+	0.972496i	−0.627125	+	0.778918i	$0.715769\pi$
$822$		0			0
$823$	7.87250	+	9.38208i	0.274418	+	0.327039i	0.885598	−	0.464453i	$-0.153749\pi$
$823$	7.87250	+	9.38208i	0.274418	+	0.327039i	−0.611180	+	0.791492i	$0.709305\pi$
$824$	−10.2527	−	13.6665i	−0.357170	−	0.476094i
$825$		0			0
$826$	0.147595	+	0.429640i	0.00513547	+	0.0149491i
$827$	−5.15219	−	8.92386i	−0.179159	−	0.310313i	0.762434	−	0.647067i	$-0.224004\pi$
$827$	−5.15219	−	8.92386i	−0.179159	−	0.310313i	−0.941593	+	0.336754i	$0.890671\pi$
$828$		0			0
$829$	−20.0735	+	34.7684i	−0.697183	+	1.20756i	0.272256	+	0.962225i	$0.412230\pi$
$829$	−20.0735	+	34.7684i	−0.697183	+	1.20756i	−0.969439	+	0.245332i	$0.921103\pi$
$830$	−12.1928	−	2.37905i	−0.423217	−	0.0825779i
$831$		0			0
$832$	10.0380	+	4.94906i	0.348003	+	0.171578i
$833$	40.6020	−	7.15922i	1.40677	−	0.248052i
$834$		0			0
$835$	−1.15712	+	1.37901i	−0.0400439	+	0.0477225i
$836$	−0.678318	+	18.6621i	−0.0234601	+	0.645443i
$837$		0			0
$838$	23.7672	+	0.431795i	0.821025	+	0.0149161i
$839$	−37.1850	−	31.2019i	−1.28377	−	1.07721i	−0.992713	−	0.120502i	$-0.961549\pi$
$839$	−37.1850	−	31.2019i	−1.28377	−	1.07721i	−0.291055	−	0.956706i	$-0.594006\pi$
$840$		0			0
$841$	−4.94954	−	28.0703i	−0.170674	−	0.967940i
$842$	13.3358	+	5.13002i	0.459581	+	0.176792i
$843$		0			0
$844$	−7.56015	−	1.61822i	−0.260231	−	0.0557014i
$845$	−16.9174	−	9.76726i	−0.581976	−	0.336004i
$846$		0			0
$847$	−0.451540	+	0.260697i	−0.0155151	+	0.00895764i
$848$	10.5228	+	37.0958i	0.361353	+	1.27388i
$849$		0			0
$850$	−10.6777	−	13.2051i	−0.366244	−	0.452932i
$851$	15.2801	−	12.8216i	0.523797	−	0.439518i
$852$		0			0
$853$	−10.1083	+	3.67913i	−0.346102	+	0.125971i	−0.509222	−	0.860635i	$-0.670067\pi$
$853$	−10.1083	+	3.67913i	−0.346102	+	0.125971i	0.163119	+	0.986606i	$0.447844\pi$
$854$	7.49278	−	4.14634i	0.256398	−	0.141885i
$855$		0			0
$856$	6.62667	−	10.1566i	0.226495	−	0.347145i
$857$	3.33877	+	0.588716i	0.114050	+	0.0201102i	0.230382	−	0.973100i	$-0.426002\pi$
$857$	3.33877	+	0.588716i	0.114050	+	0.0201102i	−0.116332	+	0.993210i	$0.537114\pi$
$858$		0			0
$859$	6.70377	−	18.4184i	0.228730	−	0.628429i	−0.771237	−	0.636548i	$-0.780362\pi$
$859$	6.70377	−	18.4184i	0.228730	−	0.628429i	0.999967	+	0.00811819i	$0.00258413\pi$
$860$	3.56679	+	25.6440i	0.121626	+	0.874455i
$861$		0			0
$862$	29.1785	+	25.4010i	0.993823	+	0.865161i
$863$	48.0692			1.63629			0.818147	−	0.575009i	$-0.195001\pi$
$863$	48.0692			1.63629			0.818147	+	0.575009i	$0.195001\pi$
$864$		0			0
$865$	13.8216			0.469949
$866$	−9.45288	−	8.22909i	−0.321222	−	0.279636i
$867$		0			0
$868$	1.97755	+	14.2180i	0.0671225	+	0.482589i
$869$	−11.1603	+	30.6628i	−0.378588	+	1.04016i
$870$		0			0
$871$	7.83474	+	1.38148i	0.265470	+	0.0468095i
$872$	7.34359	−	11.2554i	0.248685	−	0.381156i
$873$		0			0
$874$	22.1429	−	12.2534i	0.748994	−	0.414477i
$875$	−8.67534	+	3.15756i	−0.293280	+	0.106745i
$876$		0			0
$877$	−36.3911	+	30.5358i	−1.22884	+	1.03112i	−0.230527	+	0.973066i	$0.574045\pi$
$877$	−36.3911	+	30.5358i	−1.22884	+	1.03112i	−0.998313	+	0.0580531i	$0.981511\pi$
$878$	−21.9299	−	27.1207i	−0.740100	−	0.915279i
$879$		0			0
$880$	−6.20130	−	21.8614i	−0.209046	−	0.736948i
$881$	9.71356	−	5.60813i	0.327258	−	0.188943i	−0.327365	−	0.944898i	$-0.606161\pi$
$881$	9.71356	−	5.60813i	0.327258	−	0.188943i	0.654623	+	0.755955i	$0.272827\pi$
$882$		0			0
$883$	−7.49573	−	4.32766i	−0.252251	−	0.145637i	0.368543	−	0.929611i	$-0.379857\pi$
$883$	−7.49573	−	4.32766i	−0.252251	−	0.145637i	−0.620795	+	0.783973i	$0.713190\pi$
$884$	17.5616	+	3.75898i	0.590659	+	0.126428i
$885$		0			0
$886$	16.4504	+	6.32817i	0.552662	+	0.212599i
$887$	5.65003	+	32.0429i	0.189710	+	1.07590i	0.919754	+	0.392496i	$0.128388\pi$
$887$	5.65003	+	32.0429i	0.189710	+	1.07590i	−0.730044	+	0.683400i	$0.760500\pi$
$888$		0			0
$889$	−5.09518	−	4.27536i	−0.170887	−	0.143391i
$890$	−1.47094	−	0.0267235i	−0.0493060	−	0.000895774i
$891$		0			0
$892$	−1.69786	+	46.7120i	−0.0568484	+	1.56404i
$893$	7.93714	−	9.45911i	0.265606	−	0.316537i
$894$		0			0
$895$	13.6018	−	2.39837i	0.454659	−	0.0801686i
$896$	3.93960	−	7.63751i	0.131613	−	0.255151i
$897$		0			0
$898$	49.2947	+	9.61836i	1.64498	+	0.320969i
$899$	35.8268	−	62.0538i	1.19489	−	2.06961i
$900$		0			0
$901$	30.9383	+	53.5867i	1.03070	+	1.78523i
$902$	9.52234	+	27.7190i	0.317059	+	0.922943i
$903$		0			0
$904$	−15.4468	−	20.5901i	−0.513754	−	0.684815i
$905$	3.30647	+	3.94050i	0.109911	+	0.130987i
$906$		0			0
$907$	13.7943	+	37.8996i	0.458033	+	1.25843i	0.926947	+	0.375191i	$0.122423\pi$
$907$	13.7943	+	37.8996i	0.458033	+	1.25843i	−0.468915	+	0.883243i	$0.655355\pi$
$908$	−9.94037	−	18.7595i	−0.329883	−	0.622557i
$909$		0			0
$910$	1.37079	−	2.27769i	0.0454411	−	0.0755048i
$911$	8.02183	−	45.4941i	0.265775	−	1.50729i	−0.501044	−	0.865422i	$-0.667051\pi$
$911$	8.02183	−	45.4941i	0.265775	−	1.50729i	0.766819	−	0.641863i	$-0.221838\pi$
$912$		0			0
$913$	14.9855	+	5.45429i	0.495949	+	0.180511i
$914$	3.68034	+	23.3443i	0.121735	+	0.772162i
$915$		0			0
$916$	−10.3267	−	9.32490i	−0.341205	−	0.308103i
$917$			5.61196i			0.185323i
$918$		0			0
$919$			1.23662i			0.0407922i	0.999792	+	0.0203961i	$0.00649274\pi$
$919$			1.23662i			0.0407922i	−0.999792	+	0.0203961i	$0.993507\pi$
$920$	−21.0502	+	22.4770i	−0.694003	+	0.741046i
$921$		0			0
$922$	−10.2301	+	1.61282i	−0.336911	+	0.0531154i
$923$	−4.96455	−	1.80695i	−0.163410	−	0.0594765i
$924$		0			0
$925$	−1.05281	+	5.97076i	−0.0346160	+	0.196317i
$926$	18.0888	+	10.8864i	0.594436	+	0.357750i
$927$		0			0
$928$	−38.9417	+	17.9902i	−1.27832	+	0.590558i
$929$	−8.79850	−	24.1737i	−0.288669	−	0.793112i	−0.996253	−	0.0864831i	$-0.972437\pi$
$929$	−8.79850	−	24.1737i	−0.288669	−	0.793112i	0.707584	−	0.706629i	$-0.249785\pi$
$930$		0			0
$931$	−12.0039	−	14.3056i	−0.393410	−	0.468848i
$932$	−19.8673	−	25.5038i	−0.650775	−	0.835404i
$933$		0			0
$934$	−42.4434	+	14.5806i	−1.38879	+	0.477093i
$935$	−18.2326	−	31.5798i	−0.596271	−	1.03277i
$936$		0			0
$937$	−13.9758	+	24.2068i	−0.456569	+	0.790801i	−0.998777	−	0.0494437i	$-0.984255\pi$
$937$	−13.9758	+	24.2068i	−0.456569	+	0.790801i	0.542208	+	0.840244i	$0.317588\pi$
$938$	1.16989	−	5.99578i	0.0381984	−	0.195769i
$939$		0			0
$940$	−5.64854	+	13.9235i	−0.184235	+	0.454134i
$941$	−48.5322	+	8.55753i	−1.58210	+	0.278968i	−0.894483	−	0.447103i	$-0.852456\pi$
$941$	−48.5322	+	8.55753i	−1.58210	+	0.278968i	−0.687621	+	0.726070i	$0.741345\pi$
$942$		0			0
$943$	25.5308	−	30.4264i	0.831397	−	0.990820i
$944$	−1.68713	−	0.122808i	−0.0549115	−	0.00399705i
$945$		0			0
$946$	0.603733	−	33.2312i	0.0196291	−	1.08044i
$947$	−21.6693	−	18.1827i	−0.704158	−	0.590858i	0.218796	−	0.975771i	$-0.429787\pi$
$947$	−21.6693	−	18.1827i	−0.704158	−	0.590858i	−0.922953	+	0.384912i	$0.874232\pi$
$948$		0			0
$949$	−2.72007	−	15.4263i	−0.0882971	−	0.500758i
$950$	−2.76173	+	7.17927i	−0.0896025	+	0.232926i
$951$		0			0
$952$	3.13087	−	13.4303i	0.101472	−	0.435278i
$953$	−18.2626	−	10.5439i	−0.591583	−	0.341551i	0.174140	−	0.984721i	$-0.444285\pi$
$953$	−18.2626	−	10.5439i	−0.591583	−	0.341551i	−0.765723	+	0.643170i	$0.777619\pi$
$954$		0			0
$955$	24.2626	−	14.0080i	0.785119	−	0.453289i
$956$	−43.0640	+	13.9245i	−1.39279	+	0.450352i
$957$		0			0
$958$	−14.8534	+	12.0106i	−0.479893	+	0.388044i
$959$	−3.14872	+	2.64209i	−0.101678	+	0.0853176i
$960$		0			0
$961$	54.7709	−	19.9350i	1.76680	−	0.643064i
$962$	−3.10450	−	5.61009i	−0.100093	−	0.180876i
$963$		0			0
$964$	0.228834	−	0.365052i	0.00737024	−	0.0117575i
$965$	−22.2180	−	3.91764i	−0.715224	−	0.126113i
$966$		0			0
$967$	−3.43633	+	9.44123i	−0.110505	+	0.303610i	−0.982602	−	0.185723i	$-0.940537\pi$
$967$	−3.43633	+	9.44123i	−0.110505	+	0.303610i	0.872097	+	0.489333i	$0.162760\pi$
$968$	−0.232489	−	1.92751i	−0.00747247	−	0.0619527i
$969$		0			0
$970$	−27.7605	+	31.8889i	−0.891335	+	1.02389i
$971$	−38.1342			−1.22378			−0.611892	−	0.790942i	$-0.709591\pi$
$971$	−38.1342			−1.22378			−0.611892	+	0.790942i	$0.709591\pi$
$972$		0			0
$973$	−11.0906			−0.355547
$974$	−19.6730	+	22.5986i	−0.630362	+	0.724107i
$975$		0			0
$976$	3.24278	+	31.7222i	0.103799	+	1.01540i
$977$	2.05993	−	5.65962i	0.0659031	−	0.181067i	−0.902370	−	0.430963i	$-0.858174\pi$
$977$	2.05993	−	5.65962i	0.0659031	−	0.181067i	0.968273	+	0.249895i	$0.0803962\pi$
$978$		0			0
$979$	1.85990	+	0.327950i	0.0594425	+	0.0104813i
$980$	19.2541	+	12.0694i	0.615048	+	0.385544i
$981$		0			0
$982$	13.5481	+	24.4824i	0.432336	+	0.781266i
$983$	2.09396	−	0.762140i	0.0667870	−	0.0243085i	−0.308411	−	0.951253i	$-0.599797\pi$
$983$	2.09396	−	0.762140i	0.0667870	−	0.0243085i	0.375198	+	0.926945i	$0.377575\pi$
$984$		0			0
$985$	−10.7081	+	8.98515i	−0.341188	+	0.286291i
$986$	−53.5266	+	43.2819i	−1.70463	+	1.37838i
$987$		0			0
$988$	−2.50278	−	7.74026i	−0.0796239	−	0.246250i
$989$	−39.0071	+	22.5208i	−1.24035	+	0.716119i
$990$		0			0
$991$	29.4685	+	17.0137i	0.936098	+	0.540457i	0.888735	−	0.458421i	$-0.151585\pi$
$991$	29.4685	+	17.0137i	0.936098	+	0.540457i	0.0473631	+	0.998878i	$0.484918\pi$
$992$	−51.5814	−	14.0183i	−1.63771	−	0.445081i
$993$		0			0
$994$	−1.45651	+	3.78628i	−0.0461978	+	0.120094i
$995$	−1.19492	−	6.77670i	−0.0378814	−	0.214836i
$996$		0			0
$997$	36.1230	+	30.3108i	1.14403	+	0.959953i	0.999563	−	0.0295568i	$-0.00940960\pi$
$997$	36.1230	+	30.3108i	1.14403	+	0.959953i	0.144465	+	0.989510i	$0.453854\pi$
$998$	0.756281	−	41.6279i	0.0239396	−	1.31771i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.l.a.35.13		96
3.2	odd	2		108.2.l.a.11.4	✓	96
4.3	odd	2	inner	324.2.l.a.35.4		96
9.2	odd	6		972.2.l.d.755.7		96
9.4	even	3		972.2.l.b.431.2		96
9.5	odd	6		972.2.l.c.431.15		96
9.7	even	3		972.2.l.a.755.10		96
12.11	even	2		108.2.l.a.11.13	yes	96
27.4	even	9		972.2.l.d.215.8		96
27.5	odd	18	inner	324.2.l.a.287.4		96
27.13	even	9		972.2.l.c.539.3		96
27.14	odd	18		972.2.l.b.539.14		96
27.22	even	9		108.2.l.a.59.13	yes	96
27.23	odd	18		972.2.l.a.215.9		96
36.7	odd	6		972.2.l.a.755.9		96
36.11	even	6		972.2.l.d.755.8		96
36.23	even	6		972.2.l.c.431.3		96
36.31	odd	6		972.2.l.b.431.14		96
108.23	even	18		972.2.l.a.215.10		96
108.31	odd	18		972.2.l.d.215.7		96
108.59	even	18	inner	324.2.l.a.287.13		96
108.67	odd	18		972.2.l.c.539.15		96
108.95	even	18		972.2.l.b.539.2		96
108.103	odd	18		108.2.l.a.59.4	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.11.4	✓	96	3.2	odd	2
108.2.l.a.11.13	yes	96	12.11	even	2
108.2.l.a.59.4	yes	96	108.103	odd	18
108.2.l.a.59.13	yes	96	27.22	even	9
324.2.l.a.35.4		96	4.3	odd	2	inner
324.2.l.a.35.13		96	1.1	even	1	trivial
324.2.l.a.287.4		96	27.5	odd	18	inner
324.2.l.a.287.13		96	108.59	even	18	inner
972.2.l.a.215.9		96	27.23	odd	18
972.2.l.a.215.10		96	108.23	even	18
972.2.l.a.755.9		96	36.7	odd	6
972.2.l.a.755.10		96	9.7	even	3
972.2.l.b.431.2		96	9.4	even	3
972.2.l.b.431.14		96	36.31	odd	6
972.2.l.b.539.2		96	108.95	even	18
972.2.l.b.539.14		96	27.14	odd	18
972.2.l.c.431.3		96	36.23	even	6
972.2.l.c.431.15		96	9.5	odd	6
972.2.l.c.539.3		96	27.13	even	9
972.2.l.c.539.15		96	108.67	odd	18
972.2.l.d.215.7		96	108.31	odd	18
972.2.l.d.215.8		96	27.4	even	9
972.2.l.d.755.7		96	9.2	odd	6
972.2.l.d.755.8		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)

\(f(q)\)	\(=\)	\(q+(1.06666 + 0.928568i) q^{2} +(0.275524 + 1.98093i) q^{4} +(-0.605021 + 1.66228i) q^{5} +(0.748045 + 0.131901i) q^{7} +(-1.54554 + 2.36882i) q^{8} +O(q^{10})\)	\(q+(1.06666 + 0.928568i) q^{2} +(0.275524 + 1.98093i) q^{4} +(-0.605021 + 1.66228i) q^{5} +(0.748045 + 0.131901i) q^{7} +(-1.54554 + 2.36882i) q^{8} +(-2.18889 + 1.21129i) q^{10} +(3.01780 - 1.09839i) q^{11} +(-1.07167 + 0.899234i) q^{13} +(0.675431 + 0.835303i) q^{14} +(-3.84817 + 1.09159i) q^{16} +(-5.55887 + 3.20941i) q^{17} +(2.51793 + 1.45373i) q^{19} +(-3.45956 - 0.740506i) q^{20} +(4.23889 + 1.63062i) q^{22} +(-1.06877 - 6.06131i) q^{23} +(1.43309 + 1.20251i) q^{25} +(-1.97810 - 0.0359374i) q^{26} +(-0.0551813 + 1.51817i) q^{28} +(4.87432 - 5.80899i) q^{29} +(9.30557 - 1.64082i) q^{31} +(-5.11830 - 2.40894i) q^{32} +(-8.90957 - 1.73843i) q^{34} +(-0.671839 + 1.16366i) q^{35} +(1.62042 + 2.80666i) q^{37} +(1.33589 + 3.88870i) q^{38} +(-3.00257 - 4.00231i) q^{40} +(4.14810 + 4.94351i) q^{41} +(-2.50294 - 6.87676i) q^{43} +(3.00731 + 5.67542i) q^{44} +(4.48832 - 7.45778i) q^{46} +(0.737485 - 4.18249i) q^{47} +(-6.03567 - 2.19681i) q^{49} +(0.412011 + 2.61338i) q^{50} +(-2.07659 - 1.87513i) q^{52} -9.63986i q^{53} +5.68099i q^{55} +(-1.46858 + 1.56813i) q^{56} +(10.5933 - 1.67008i) q^{58} +(0.397395 + 0.144640i) q^{59} +(1.38430 - 7.85077i) q^{61} +(11.4495 + 6.89065i) q^{62} +(-3.22263 - 7.32220i) q^{64} +(-0.846401 - 2.32547i) q^{65} +(-3.65540 - 4.35634i) q^{67} +(-7.88923 - 10.1275i) q^{68} +(-1.79716 + 0.617380i) q^{70} +(1.88825 + 3.27054i) q^{71} +(-5.59853 + 9.69694i) q^{73} +(-0.877730 + 4.49842i) q^{74} +(-2.18598 + 5.38838i) q^{76} +(2.40233 - 0.423595i) q^{77} +(-6.53113 + 7.78350i) q^{79} +(0.513698 - 7.05719i) q^{80} +(-0.165777 + 9.12484i) q^{82} +(3.80396 + 3.19190i) q^{83} +(-1.97172 - 11.1822i) q^{85} +(3.71576 - 9.65931i) q^{86} +(-2.06224 + 8.84623i) q^{88} +(0.509288 + 0.294037i) q^{89} +(-0.920264 + 0.531314i) q^{91} +(11.7126 - 3.78720i) q^{92} +(4.67037 - 3.77648i) q^{94} +(-3.93991 + 3.30598i) q^{95} +(15.8811 - 5.78024i) q^{97} +(-4.39813 - 7.94778i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) 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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