LMFDB - Embedded newform 405.2.m.c.377.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(53,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("405.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.m (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.162447943996702457856.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} - 15x^{8} - 16x^{4} + 256 $ x^16 - x^12 - 15x^8 - 16x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			377.3
Root			$-0.140577 - 1.40721i$ of defining polynomial
Character	$\chi$	$=$	405.377
Dual form			405.2.m.c.188.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.441283 + 0.118242i) q^{2} +(-1.55130 - 0.895644i) q^{4} +(1.00781 + 1.99607i) q^{5} +(0.655657 - 2.44694i) q^{7} +(-1.22474 - 1.22474i) q^{8} +O(q^{10})$	\(q+(0.441283 + 0.118242i) q^{2} +(-1.55130 - 0.895644i) q^{4} +(1.00781 + 1.99607i) q^{5} +(0.655657 - 2.44694i) q^{7} +(-1.22474 - 1.22474i) q^{8} +(0.208712 + 1.00000i) q^{10} +(4.80217 - 2.77253i) q^{11} +(0.655657 + 2.44694i) q^{13} +(0.578661 - 1.00227i) q^{14} +(1.39564 + 2.41733i) q^{16} +(1.87083 - 1.87083i) q^{17} -3.00000i q^{19} +(0.224351 - 3.99915i) q^{20} +(2.44694 - 0.655657i) q^{22} +(5.90166 - 1.58135i) q^{23} +(-2.96863 + 4.02334i) q^{25} +1.15732i q^{26} +(-3.20871 + 3.20871i) q^{28} +(2.19387 + 3.79990i) q^{29} +(0.500000 - 0.866025i) q^{31} +(1.22662 + 4.57781i) q^{32} +(1.04678 - 0.604356i) q^{34} +(5.54506 - 1.15732i) q^{35} +(-5.00000 - 5.00000i) q^{37} +(0.354725 - 1.32385i) q^{38} +(1.21037 - 3.67900i) q^{40} +(-4.80217 - 2.77253i) q^{41} +(-4.38318 - 1.17447i) q^{43} -9.93280 q^{44} +2.79129 q^{46} +(-0.882567 - 0.236483i) q^{47} +(0.504525 + 0.291288i) q^{49} +(-1.78573 + 1.42442i) q^{50} +(1.17447 - 4.38318i) q^{52} +(0.0674228 + 0.0674228i) q^{53} +(10.3739 + 6.79129i) q^{55} +(-3.79990 + 2.19387i) q^{56} +(0.518813 + 1.93624i) q^{58} +(-2.19387 + 3.79990i) q^{59} +(0.500000 + 0.866025i) q^{61} +(0.323042 - 0.323042i) q^{62} -3.41742i q^{64} +(-4.22350 + 3.77480i) q^{65} +(-11.7240 + 3.14144i) q^{67} +(-4.57781 + 1.22662i) q^{68} +(2.58379 + 0.144950i) q^{70} +5.54506i q^{71} +(-10.3739 + 10.3739i) q^{73} +(-1.61521 - 2.79763i) q^{74} +(-2.68693 + 4.65390i) q^{76} +(-3.63566 - 13.5685i) q^{77} +(9.16478 - 5.29129i) q^{79} +(-3.41862 + 5.22202i) q^{80} +(-1.79129 - 1.79129i) q^{82} +(-3.18737 + 11.8954i) q^{83} +(5.61976 + 1.84887i) q^{85} +(-1.79535 - 1.03655i) q^{86} +(-9.27707 - 2.48578i) q^{88} +16.6352 q^{89} +6.41742 q^{91} +(-10.5716 - 2.83265i) q^{92} +(-0.361500 - 0.208712i) q^{94} +(5.98822 - 3.02344i) q^{95} +(-1.31131 + 4.89389i) q^{97} +(0.188196 + 0.188196i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{7}+O(q^{10}) $ 16 * q + 4 * q^7	$ 16 q + 4 q^{7} + 40 q^{10} + 4 q^{13} + 4 q^{16} - 4 q^{22} + 16 q^{25} - 88 q^{28} + 8 q^{31} - 80 q^{37} + 12 q^{40} - 44 q^{43} + 8 q^{46} - 44 q^{52} + 56 q^{55} - 48 q^{58} + 8 q^{61} - 32 q^{67} + 48 q^{70} - 56 q^{73} + 12 q^{76} + 8 q^{82} + 28 q^{85} - 36 q^{88} + 176 q^{91} - 8 q^{97}+O(q^{100}) $ 16 * q + 4 * q^7 + 40 * q^10 + 4 * q^13 + 4 * q^16 - 4 * q^22 + 16 * q^25 - 88 * q^28 + 8 * q^31 - 80 * q^37 + 12 * q^40 - 44 * q^43 + 8 * q^46 - 44 * q^52 + 56 * q^55 - 48 * q^58 + 8 * q^61 - 32 * q^67 + 48 * q^70 - 56 * q^73 + 12 * q^76 + 8 * q^82 + 28 * q^85 - 36 * q^88 + 176 * q^91 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.441283	+	0.118242i	0.312035	+	0.0836094i	0.411438	−	0.911438i	$-0.365027\pi$
$2$	0.441283	+	0.118242i	0.312035	+	0.0836094i	−0.0994033	+	0.995047i	$0.531693\pi$
$3$		0			0
$3$		0			0
$4$	−1.55130	−	0.895644i	−0.775650	−	0.447822i
$5$	1.00781	+	1.99607i	0.450708	+	0.892672i
$5$	1.00781	+	1.99607i	0.450708	+	0.892672i
$6$		0			0
$7$	0.655657	−	2.44694i	0.247815	−	0.924858i	−0.724133	−	0.689661i	$-0.757760\pi$
$7$	0.655657	−	2.44694i	0.247815	−	0.924858i	0.971948	−	0.235197i	$-0.0755737\pi$
$8$	−1.22474	−	1.22474i	−0.433013	−	0.433013i
$9$		0			0
$10$	0.208712	+	1.00000i	0.0660006	+	0.316228i
$11$	4.80217	−	2.77253i	1.44791	−	0.835950i	0.449551	−	0.893255i	$-0.351584\pi$
$11$	4.80217	−	2.77253i	1.44791	−	0.835950i	0.998357	+	0.0573051i	$0.0182508\pi$
$12$		0			0
$13$	0.655657	+	2.44694i	0.181846	+	0.678660i	0.995284	+	0.0970075i	$0.0309271\pi$
$13$	0.655657	+	2.44694i	0.181846	+	0.678660i	−0.813437	+	0.581653i	$0.802406\pi$
$14$	0.578661	−	1.00227i	0.154654	−	0.267868i
$15$		0			0
$16$	1.39564	+	2.41733i	0.348911	+	0.604332i
$17$	1.87083	−	1.87083i	0.453743	−	0.453743i	−0.442852	−	0.896595i	$-0.646033\pi$
$17$	1.87083	−	1.87083i	0.453743	−	0.453743i	0.896595	+	0.442852i	$0.146033\pi$
$18$		0			0
$19$		−	3.00000i		−	0.688247i	−0.938924	−	0.344124i	$-0.888176\pi$
$19$		−	3.00000i		−	0.688247i	0.938924	−	0.344124i	$-0.111824\pi$
$20$	0.224351	−	3.99915i	0.0501665	−	0.894238i
$21$		0			0
$22$	2.44694	−	0.655657i	0.521690	−	0.139787i
$23$	5.90166	−	1.58135i	1.23058	−	0.329733i	0.415776	−	0.909467i	$-0.363510\pi$
$23$	5.90166	−	1.58135i	1.23058	−	0.329733i	0.814806	+	0.579734i	$0.196843\pi$
$24$		0			0
$25$	−2.96863	+	4.02334i	−0.593725	+	0.804668i
$26$			1.15732i			0.226970i
$27$		0			0
$28$	−3.20871	+	3.20871i	−0.606390	+	0.606390i
$29$	2.19387	+	3.79990i	0.407392	+	0.705623i	0.994597	−	0.103815i	$-0.0331051\pi$
$29$	2.19387	+	3.79990i	0.407392	+	0.705623i	−0.587205	+	0.809438i	$0.699772\pi$
$30$		0			0
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	−0.817625	−	0.575751i	$-0.804710\pi$
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	0.907428	+	0.420208i	$0.138043\pi$
$32$	1.22662	+	4.57781i	0.216838	+	0.809251i
$33$		0			0
$34$	1.04678	−	0.604356i	0.179521	−	0.103646i
$35$	5.54506	−	1.15732i	0.937287	−	0.195623i
$36$		0			0
$37$	−5.00000	−	5.00000i	−0.821995	−	0.821995i	0.164399	−	0.986394i	$-0.447432\pi$
$37$	−5.00000	−	5.00000i	−0.821995	−	0.821995i	−0.986394	+	0.164399i	$0.947432\pi$
$38$	0.354725	−	1.32385i	0.0575439	−	0.214757i
$39$		0			0
$40$	1.21037	−	3.67900i	0.191376	−	0.581700i
$41$	−4.80217	−	2.77253i	−0.749972	−	0.432997i	0.0757116	−	0.997130i	$-0.475877\pi$
$41$	−4.80217	−	2.77253i	−0.749972	−	0.432997i	−0.825684	+	0.564133i	$0.809210\pi$
$42$		0			0
$43$	−4.38318	−	1.17447i	−0.668429	−	0.179105i	−0.0913820	−	0.995816i	$-0.529128\pi$
$43$	−4.38318	−	1.17447i	−0.668429	−	0.179105i	−0.577047	+	0.816711i	$0.695795\pi$
$44$	−9.93280			−1.49743
$45$		0			0
$46$	2.79129			0.411553
$47$	−0.882567	−	0.236483i	−0.128736	−	0.0344946i	0.193876	−	0.981026i	$-0.437894\pi$
$47$	−0.882567	−	0.236483i	−0.128736	−	0.0344946i	−0.322612	+	0.946531i	$0.604561\pi$
$48$		0			0
$49$	0.504525	+	0.291288i	0.0720751	+	0.0416125i
$50$	−1.78573	+	1.42442i	−0.252541	+	0.201443i
$51$		0			0
$52$	1.17447	−	4.38318i	0.162870	−	0.607838i
$53$	0.0674228	+	0.0674228i	0.00926123	+	0.00926123i	0.711722	−	0.702461i	$-0.247915\pi$
$53$	0.0674228	+	0.0674228i	0.00926123	+	0.00926123i	−0.702461	+	0.711722i	$0.747915\pi$
$54$		0			0
$55$	10.3739	+	6.79129i	1.39881	+	0.915737i
$56$	−3.79990	+	2.19387i	−0.507782	+	0.293168i
$57$		0			0
$58$	0.518813	+	1.93624i	0.0681235	+	0.254240i
$59$	−2.19387	+	3.79990i	−0.285618	+	0.494704i	−0.972759	−	0.231820i	$-0.925532\pi$
$59$	−2.19387	+	3.79990i	−0.285618	+	0.494704i	0.687141	+	0.726524i	$0.258865\pi$
$60$		0			0
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$	0.323042	−	0.323042i	0.0410264	−	0.0410264i
$63$		0			0
$64$		−	3.41742i		−	0.427178i
$65$	−4.22350	+	3.77480i	−0.523861	+	0.468207i
$66$		0			0
$67$	−11.7240	+	3.14144i	−1.43232	+	0.383788i	−0.889836	−	0.456280i	$-0.849181\pi$
$67$	−11.7240	+	3.14144i	−1.43232	+	0.383788i	−0.542480	+	0.840068i	$0.682515\pi$
$68$	−4.57781	+	1.22662i	−0.555142	+	0.148750i
$69$		0			0
$70$	2.58379	+	0.144950i	0.308822	+	0.0173248i
$71$			5.54506i			0.658078i	0.944316	+	0.329039i	$0.106725\pi$
$71$			5.54506i			0.658078i	−0.944316	+	0.329039i	$0.893275\pi$
$72$		0			0
$73$	−10.3739	+	10.3739i	−1.21417	+	1.21417i	−0.244526	+	0.969643i	$0.578632\pi$
$73$	−10.3739	+	10.3739i	−1.21417	+	1.21417i	−0.969643	+	0.244526i	$0.921368\pi$
$74$	−1.61521	−	2.79763i	−0.187764	−	0.325217i
$75$		0			0
$76$	−2.68693	+	4.65390i	−0.308212	+	0.533839i
$77$	−3.63566	−	13.5685i	−0.414322	−	1.54627i
$78$		0			0
$79$	9.16478	−	5.29129i	1.03112	−	0.595316i	0.113813	−	0.993502i	$-0.463693\pi$
$79$	9.16478	−	5.29129i	1.03112	−	0.595316i	0.917305	+	0.398186i	$0.130360\pi$
$80$	−3.41862	+	5.22202i	−0.382213	+	0.583840i
$81$		0			0
$82$	−1.79129	−	1.79129i	−0.197815	−	0.197815i
$83$	−3.18737	+	11.8954i	−0.349859	+	1.30569i	0.536972	+	0.843600i	$0.319568\pi$
$83$	−3.18737	+	11.8954i	−0.349859	+	1.30569i	−0.886831	+	0.462093i	$0.847099\pi$
$84$		0			0
$85$	5.61976	+	1.84887i	0.609548	+	0.200538i
$86$	−1.79535	−	1.03655i	−0.193598	−	0.111774i
$87$		0			0
$88$	−9.27707	−	2.48578i	−0.988939	−	0.264985i
$89$	16.6352			1.76333			0.881663	−	0.471879i	$-0.156424\pi$
$89$	16.6352			1.76333			0.881663	+	0.471879i	$0.156424\pi$
$90$		0			0
$91$	6.41742			0.672729
$92$	−10.5716	−	2.83265i	−1.10216	−	0.295324i
$93$		0			0
$94$	−0.361500	−	0.208712i	−0.0372859	−	0.0215270i
$95$	5.98822	−	3.02344i	0.614379	−	0.310198i
$96$		0			0
$97$	−1.31131	+	4.89389i	−0.133144	+	0.496899i	−0.999999	−	0.00166135i	$-0.999471\pi$
$97$	−1.31131	+	4.89389i	−0.133144	+	0.496899i	0.866855	+	0.498561i	$0.166138\pi$
$98$	0.188196	+	0.188196i	0.0190107	+	0.0190107i
$99$		0			0
$100$	8.20871	−	3.58258i	0.820871	−	0.358258i
$101$	−9.60433	+	5.54506i	−0.955667	+	0.551754i	−0.894837	−	0.446394i	$-0.852708\pi$
$101$	−9.60433	+	5.54506i	−0.955667	+	0.551754i	−0.0608300	+	0.998148i	$0.519375\pi$
$102$		0			0
$103$	−1.31131	−	4.89389i	−0.129208	−	0.482209i	0.870747	−	0.491731i	$-0.163636\pi$
$103$	−1.31131	−	4.89389i	−0.129208	−	0.482209i	−0.999955	+	0.00952189i	$0.996969\pi$
$104$	2.19387	−	3.79990i	0.215127	−	0.372610i
$105$		0			0
$106$	0.0217804	+	0.0377247i	0.00211550	+	0.00366415i
$107$	−3.74166	+	3.74166i	−0.361720	+	0.361720i	−0.864446	−	0.502726i	$-0.832330\pi$
$107$	−3.74166	+	3.74166i	−0.361720	+	0.361720i	0.502726	+	0.864446i	$0.332330\pi$
$108$		0			0
$109$		−	13.7477i		−	1.31679i	−0.752671	−	0.658397i	$-0.771235\pi$
$109$		−	13.7477i		−	1.31679i	0.752671	−	0.658397i	$-0.228765\pi$
$110$	3.77480	+	4.22350i	0.359913	+	0.402695i
$111$		0			0
$112$	6.83013	−	1.83013i	0.645386	−	0.172931i
$113$	−11.8033	+	3.16269i	−1.11036	+	0.297521i	−0.766978	−	0.641673i	$-0.778240\pi$
$113$	−11.8033	+	3.16269i	−1.11036	+	0.297521i	−0.343386	+	0.939194i	$0.611574\pi$
$114$		0			0
$115$	9.10426	+	10.1865i	0.848976	+	0.949892i
$116$		−	7.85971i		−	0.729756i
$117$		0			0
$118$	−1.41742	+	1.41742i	−0.130484	+	0.130484i
$119$	−3.35119	−	5.80444i	−0.307203	−	0.532092i
$120$		0			0
$121$	9.87386	−	17.1020i	0.897624	−	1.55473i
$122$	0.118242	+	0.441283i	0.0107051	+	0.0399519i
$123$		0			0
$124$	−1.55130	+	0.895644i	−0.139311	+	0.0804312i
$125$	−11.0227	−	1.87083i	−0.985901	−	0.167332i
$126$		0			0
$127$	−5.00000	−	5.00000i	−0.443678	−	0.443678i	0.449568	−	0.893246i	$-0.351578\pi$
$127$	−5.00000	−	5.00000i	−0.443678	−	0.443678i	−0.893246	+	0.449568i	$0.851578\pi$
$128$	2.85732	−	10.6637i	0.252554	−	0.942545i
$129$		0			0
$130$	−2.31010	+	1.16636i	−0.202609	+	0.102297i
$131$	6.59752	+	3.80908i	0.576428	+	0.332801i	0.759713	−	0.650259i	$-0.225340\pi$
$131$	6.59752	+	3.80908i	0.576428	+	0.332801i	−0.183285	+	0.983060i	$0.558673\pi$
$132$		0			0
$133$	−7.34083	−	1.96697i	−0.636531	−	0.170558i
$134$	−5.54506			−0.479021
$135$		0			0
$136$	−4.58258			−0.392953
$137$	14.1747	+	3.79811i	1.21103	+	0.324494i	0.807165	−	0.590325i	$-0.201001\pi$
$137$	14.1747	+	3.79811i	1.21103	+	0.324494i	0.403863	+	0.914819i	$0.367667\pi$
$138$		0			0
$139$	−2.74110	−	1.58258i	−0.232497	−	0.134232i	0.379226	−	0.925304i	$-0.376190\pi$
$139$	−2.74110	−	1.58258i	−0.232497	−	0.134232i	−0.611724	+	0.791072i	$0.709524\pi$
$140$	−9.63861	−	3.17105i	−0.814611	−	0.268002i
$141$		0			0
$142$	−0.655657	+	2.44694i	−0.0550215	+	0.205343i
$143$	9.93280	+	9.93280i	0.830623	+	0.830623i
$144$		0			0
$145$	−5.37386	+	8.20871i	−0.446275	+	0.681696i
$146$	−5.80444	+	3.35119i	−0.480379	+	0.277347i
$147$		0			0
$148$	3.27828	+	12.2347i	0.269473	+	1.00569i
$149$	−3.92985	+	6.80671i	−0.321946	+	0.557627i	−0.980890	−	0.194565i	$-0.937670\pi$
$149$	−3.92985	+	6.80671i	−0.321946	+	0.557627i	0.658943	+	0.752193i	$0.271004\pi$
$150$		0			0
$151$	−1.00000	−	1.73205i	−0.0813788	−	0.140952i	0.822464	−	0.568818i	$-0.192599\pi$
$151$	−1.00000	−	1.73205i	−0.0813788	−	0.140952i	−0.903842	+	0.427865i	$0.859266\pi$
$152$	−3.67423	+	3.67423i	−0.298020	+	0.298020i
$153$		0			0
$154$		−	6.41742i		−	0.517131i
$155$	2.23256	+	0.125246i	0.179323	+	0.0100600i
$156$		0			0
$157$	−4.38318	+	1.17447i	−0.349816	+	0.0937329i	−0.429448	−	0.903091i	$-0.641292\pi$
$157$	−4.38318	+	1.17447i	−0.349816	+	0.0937329i	0.0796324	+	0.996824i	$0.474625\pi$
$158$	4.66992	−	1.25130i	0.371519	−	0.0995481i
$159$		0			0
$160$	−7.90145	+	7.06201i	−0.624665	+	0.558301i
$161$		−	15.4779i		−	1.21983i
$162$		0			0
$163$	−5.00000	+	5.00000i	−0.391630	+	0.391630i	−0.875268	−	0.483638i	$-0.839315\pi$
$163$	−5.00000	+	5.00000i	−0.391630	+	0.391630i	0.483638	+	0.875268i	$0.339315\pi$
$164$	4.96640	+	8.60206i	0.387811	+	0.671708i
$165$		0			0
$166$	−2.81307	+	4.87238i	−0.218336	+	0.378170i
$167$	3.89682	+	14.5431i	0.301545	+	1.12538i	0.935879	+	0.352322i	$0.114608\pi$
$167$	3.89682	+	14.5431i	0.301545	+	1.12538i	−0.634334	+	0.773059i	$0.718726\pi$
$168$		0			0
$169$	5.70068	−	3.29129i	0.438514	−	0.253176i
$170$	2.26129	+	1.48036i	0.173433	+	0.113539i
$171$		0			0
$172$	5.74773	+	5.74773i	0.438260	+	0.438260i
$173$	2.90153	−	10.8287i	0.220599	−	0.823288i	−0.763521	−	0.645783i	$-0.776531\pi$
$173$	2.90153	−	10.8287i	0.220599	−	0.823288i	0.984120	−	0.177504i	$-0.0568024\pi$
$174$		0			0
$175$	7.89849	+	9.90200i	0.597069	+	0.748521i
$176$	13.4042	+	7.73893i	1.01038	+	0.583344i
$177$		0			0
$178$	7.34083	+	1.96697i	0.550219	+	0.147431i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$	9.74773			0.724543			0.362271	−	0.932073i	$-0.382001\pi$
$181$	9.74773			0.724543			0.362271	+	0.932073i	$0.382001\pi$
$182$	2.83190	+	0.758806i	0.209915	+	0.0562465i
$183$		0			0
$184$	−9.16478	−	5.29129i	−0.675637	−	0.390079i
$185$	4.94131	−	15.0194i	0.363292	−	1.10425i
$186$		0			0
$187$	3.79710	−	14.1710i	0.277671	−	1.03628i
$188$	1.15732	+	1.15732i	0.0844064	+	0.0844064i
$189$		0			0
$190$	3.00000	−	0.626136i	0.217643	−	0.0454247i
$191$	16.2019	−	9.35414i	1.17232	−	0.676842i	0.218098	−	0.975927i	$-0.430015\pi$
$191$	16.2019	−	9.35414i	1.17232	−	0.676842i	0.954227	+	0.299085i	$0.0966813\pi$
$192$		0			0
$193$	0.655657	+	2.44694i	0.0471952	+	0.176135i	0.985500	−	0.169674i	$-0.0542713\pi$
$193$	0.655657	+	2.44694i	0.0471952	+	0.176135i	−0.938305	+	0.345809i	$0.887605\pi$
$194$	−1.15732	+	2.00454i	−0.0830909	+	0.143918i
$195$		0			0
$196$	−0.521780	−	0.903750i	−0.0372700	−	0.0645536i
$197$	1.87083	−	1.87083i	0.133291	−	0.133291i	−0.637314	−	0.770605i	$-0.719954\pi$
$197$	1.87083	−	1.87083i	0.133291	−	0.133291i	0.770605	+	0.637314i	$0.219954\pi$
$198$		0			0
$199$			16.7477i			1.18721i	0.804755	+	0.593607i	$0.202297\pi$
$199$			16.7477i			1.18721i	−0.804755	+	0.593607i	$0.797703\pi$
$200$	8.56337	−	1.29175i	0.605522	−	0.0913407i
$201$		0			0
$202$	−4.89389	+	1.31131i	−0.344333	+	0.0922637i
$203$	10.7366	−	2.87685i	0.753559	−	0.201915i
$204$		0			0
$205$	0.694496	−	12.3797i	0.0485057	−	0.864634i
$206$		−	2.31464i		−	0.161269i
$207$		0			0
$208$	−5.00000	+	5.00000i	−0.346688	+	0.346688i
$209$	−8.31759	−	14.4065i	−0.575340	−	0.996518i
$210$		0			0
$211$	−4.87386	+	8.44178i	−0.335531	+	0.581156i	−0.983587	−	0.180437i	$-0.942249\pi$
$211$	−4.87386	+	8.44178i	−0.335531	+	0.581156i	0.648056	+	0.761593i	$0.275582\pi$
$212$	−0.0442062	−	0.164980i	−0.00303609	−	0.0113309i
$213$		0			0
$214$	−2.09355	+	1.20871i	−0.143112	+	0.0826259i
$215$	−2.07310	−	9.93280i	−0.141384	−	0.677412i
$216$		0			0
$217$	−1.79129	−	1.79129i	−0.121601	−	0.121601i
$218$	1.62555	−	6.06664i	0.110096	−	0.410885i
$219$		0			0
$220$	−10.0104	−	19.8266i	−0.674901	−	1.33671i
$221$	5.80444	+	3.35119i	0.390449	+	0.225426i
$222$		0			0
$223$	−11.7240	−	3.14144i	−0.785098	−	0.210366i	−0.156067	−	0.987746i	$-0.549882\pi$
$223$	−11.7240	−	3.14144i	−0.785098	−	0.210366i	−0.629031	+	0.777380i	$0.716548\pi$
$224$	12.0059			0.802178
$225$		0			0
$226$	−5.58258			−0.371347
$227$	9.43193	+	2.52728i	0.626019	+	0.167741i	0.557863	−	0.829933i	$-0.311622\pi$
$227$	9.43193	+	2.52728i	0.626019	+	0.167741i	0.0681566	+	0.997675i	$0.478288\pi$
$228$		0			0
$229$	5.05313	+	2.91742i	0.333920	+	0.192789i	0.657580	−	0.753385i	$-0.271580\pi$
$229$	5.05313	+	2.91742i	0.333920	+	0.192789i	−0.323660	+	0.946173i	$0.604913\pi$
$230$	2.81310	+	5.57162i	0.185490	+	0.367382i
$231$		0			0
$232$	1.96697	−	7.34083i	0.129138	−	0.481949i
$233$	−16.7700	−	16.7700i	−1.09864	−	1.09864i	−0.994570	−	0.104072i	$-0.966813\pi$
$233$	−16.7700	−	16.7700i	−1.09864	−	1.09864i	−0.104072	−	0.994570i	$-0.533187\pi$
$234$		0			0
$235$	−0.417424	−	2.00000i	−0.0272298	−	0.130466i
$236$	6.80671	−	3.92985i	0.443079	−	0.255812i
$237$		0			0
$238$	−0.792500	−	2.95765i	−0.0513702	−	0.191716i
$239$	6.12372	−	10.6066i	0.396111	−	0.686084i	−0.597131	−	0.802143i	$-0.703693\pi$
$239$	6.12372	−	10.6066i	0.396111	−	0.686084i	0.993242	+	0.116059i	$0.0370263\pi$
$240$		0			0
$241$	5.87386	+	10.1738i	0.378369	+	0.655354i	0.990825	−	0.135150i	$-0.0431518\pi$
$241$	5.87386	+	10.1738i	0.378369	+	0.655354i	−0.612456	+	0.790504i	$0.709818\pi$
$242$	6.37934	−	6.37934i	0.410080	−	0.410080i
$243$		0			0
$244$		−	1.79129i		−	0.114675i
$245$	−0.0729652	+	1.30063i	−0.00466157	+	0.0830944i
$246$		0			0
$247$	7.34083	−	1.96697i	0.467086	−	0.125155i
$248$	−1.67303	+	0.448288i	−0.106238	+	0.0284663i
$249$		0			0
$250$	−4.64293	−	2.12891i	−0.293644	−	0.134644i
$251$			22.1803i			1.40001i	0.714140	+	0.700003i	$0.246818\pi$
$251$			22.1803i			1.40001i	−0.714140	+	0.700003i	$0.753182\pi$
$252$		0			0
$253$	23.9564	−	23.9564i	1.50613	−	1.50613i
$254$	−1.61521	−	2.79763i	−0.101347	−	0.175539i
$255$		0			0
$256$	−0.895644	+	1.55130i	−0.0559777	+	0.0969563i
$257$	−0.921254	−	3.43817i	−0.0574662	−	0.214467i	0.931222	−	0.364453i	$-0.118744\pi$
$257$	−0.921254	−	3.43817i	−0.0574662	−	0.214467i	−0.988688	+	0.149986i	$0.952077\pi$
$258$		0			0
$259$	−15.5130	+	8.95644i	−0.963931	+	0.556526i
$260$	9.93280	−	2.07310i	0.616006	−	0.128568i
$261$		0			0
$262$	2.46099	+	2.46099i	0.152040	+	0.152040i
$263$	0.285840	−	1.06677i	0.0176256	−	0.0657798i	−0.956553	−	0.291559i	$-0.905826\pi$
$263$	0.285840	−	1.06677i	0.0176256	−	0.0657798i	0.974179	+	0.225779i	$0.0724927\pi$
$264$		0			0
$265$	−0.0666313	+	0.202530i	−0.00409313	+	0.0124413i
$266$	−3.00681	−	1.73598i	−0.184359	−	0.106440i
$267$		0			0
$268$	21.0011	+	5.62722i	1.28285	+	0.343737i
$269$	−3.47197			−0.211690			−0.105845	−	0.994383i	$-0.533755\pi$
$269$	−3.47197			−0.211690			−0.105845	+	0.994383i	$0.533755\pi$
$270$		0			0
$271$	−1.00000			−0.0607457			−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	−1.00000			−0.0607457			−0.0303728	+	0.999539i	$0.509669\pi$
$272$	7.13341	+	1.91139i	0.432527	+	0.115895i
$273$		0			0
$274$	5.80598	+	3.35208i	0.350752	+	0.202507i
$275$	−3.10100	+	27.5514i	−0.186998	+	1.66141i
$276$		0			0
$277$	−4.83472	+	18.0434i	−0.290490	+	1.08413i	0.654243	+	0.756285i	$0.272987\pi$
$277$	−4.83472	+	18.0434i	−0.290490	+	1.08413i	−0.944733	+	0.327840i	$0.893679\pi$
$278$	−1.02248	−	1.02248i	−0.0613241	−	0.0613241i
$279$		0			0
$280$	−8.20871	−	5.37386i	−0.490564	−	0.321150i
$281$	1.79535	−	1.03655i	0.107102	−	0.0618353i	−0.445492	−	0.895286i	$-0.646971\pi$
$281$	1.79535	−	1.03655i	0.107102	−	0.0618353i	0.552594	+	0.833450i	$0.313638\pi$
$282$		0			0
$283$	−4.83472	−	18.0434i	−0.287395	−	1.07257i	−0.947072	−	0.321022i	$-0.895974\pi$
$283$	−4.83472	−	18.0434i	−0.287395	−	1.07257i	0.659677	−	0.751549i	$-0.270693\pi$
$284$	4.96640	−	8.60206i	0.294702	−	0.510438i
$285$		0			0
$286$	3.20871	+	5.55765i	0.189735	+	0.328631i
$287$	−9.93280	+	9.93280i	−0.586315	+	0.586315i
$288$		0			0
$289$			10.0000i			0.588235i
$290$	−3.34201	+	2.98695i	−0.196249	+	0.175400i
$291$		0			0
$292$	25.3843	−	6.80169i	1.48550	−	0.398039i
$293$	−16.8224	+	4.50756i	−0.982777	+	0.263334i	−0.714214	−	0.699928i	$-0.753215\pi$
$293$	−16.8224	+	4.50756i	−0.982777	+	0.263334i	−0.268563	+	0.963262i	$0.586549\pi$
$294$		0			0
$295$	−9.79589	−	0.549546i	−0.570338	−	0.0319958i
$296$			12.2474i			0.711868i
$297$		0			0
$298$	−2.53901	+	2.53901i	−0.147081	+	0.147081i
$299$	7.73893	+	13.4042i	0.447554	+	0.775186i
$300$		0			0
$301$	−5.74773	+	9.95536i	−0.331293	+	0.573817i
$302$	−0.236483	−	0.882567i	−0.0136081	−	0.0507860i
$303$		0			0
$304$	7.25198	−	4.18693i	0.415929	−	0.240137i
$305$	−1.22474	+	1.87083i	−0.0701287	+	0.107123i
$306$		0			0
$307$	−15.7477	−	15.7477i	−0.898770	−	0.898770i	0.0965572	−	0.995327i	$-0.469217\pi$
$307$	−15.7477	−	15.7477i	−0.898770	−	0.898770i	−0.995327	+	0.0965572i	$0.969217\pi$
$308$	−6.51251	+	24.3050i	−0.371085	+	1.38491i
$309$		0			0
$310$	0.970381	+	0.319250i	0.0551140	+	0.0181322i
$311$	−7.80898	−	4.50851i	−0.442806	−	0.255654i	0.261981	−	0.965073i	$-0.415624\pi$
$311$	−7.80898	−	4.50851i	−0.442806	−	0.255654i	−0.704787	+	0.709419i	$0.748958\pi$
$312$		0			0
$313$	23.4480	+	6.28288i	1.32536	+	0.355129i	0.850984	−	0.525192i	$-0.176007\pi$
$313$	23.4480	+	6.28288i	1.32536	+	0.355129i	0.474377	+	0.880322i	$0.342673\pi$
$314$	−2.07310			−0.116992
$315$		0			0
$316$	−18.9564			−1.06638
$317$	−31.2735	−	8.37970i	−1.75649	−	0.470651i	−0.770500	−	0.637440i	$-0.779993\pi$
$317$	−31.2735	−	8.37970i	−1.75649	−	0.470651i	−0.985993	+	0.166789i	$0.946660\pi$
$318$		0			0
$319$	21.0707	+	12.1652i	1.17973	+	0.681118i
$320$	6.82143	−	3.44412i	0.381330	−	0.192532i
$321$		0			0
$322$	1.83013	−	6.83013i	0.101989	−	0.380628i
$323$	−5.61249	−	5.61249i	−0.312287	−	0.312287i
$324$		0			0
$325$	−11.7913	−	4.62614i	−0.654063	−	0.256612i
$326$	−2.79763	+	1.61521i	−0.154946	+	0.0894582i
$327$		0			0
$328$	2.48578	+	9.27707i	0.137254	+	0.512241i
$329$	−1.15732	+	2.00454i	−0.0638052	+	0.110514i
$330$		0			0
$331$	−6.37386	−	11.0399i	−0.350339	−	0.606805i	0.635970	−	0.771714i	$-0.280600\pi$
$331$	−6.37386	−	11.0399i	−0.350339	−	0.606805i	−0.986309	+	0.164909i	$0.947267\pi$
$332$	15.5986	−	15.5986i	0.856087	−	0.856087i
$333$		0			0
$334$			6.87841i			0.376370i
$335$	−18.0862	−	20.2360i	−0.988153	−	1.10561i
$336$		0			0
$337$	−24.8736	+	6.66485i	−1.35495	+	0.363058i	−0.861959	−	0.506977i	$-0.830763\pi$
$337$	−24.8736	+	6.66485i	−1.35495	+	0.363058i	−0.492990	+	0.870035i	$0.664096\pi$
$338$	2.90478	−	0.778334i	0.157999	−	0.0423358i
$339$		0			0
$340$	−7.06201	−	7.90145i	−0.382991	−	0.428516i
$341$		−	5.54506i		−	0.300282i
$342$		0			0
$343$	13.5826	−	13.5826i	0.733390	−	0.733390i
$344$	3.92985	+	6.80671i	0.211884	+	0.366993i
$345$		0			0
$346$	2.56080	−	4.43543i	0.137669	−	0.238450i
$347$	3.11334	+	11.6191i	0.167133	+	0.623747i	0.997759	+	0.0669166i	$0.0213162\pi$
$347$	3.11334	+	11.6191i	0.167133	+	0.623747i	−0.830626	+	0.556831i	$0.812017\pi$
$348$		0			0
$349$	−16.8160	+	9.70871i	−0.900139	+	0.519695i	−0.877245	−	0.480042i	$-0.840621\pi$
$349$	−16.8160	+	9.70871i	−0.900139	+	0.519695i	−0.0228937	+	0.999738i	$0.507288\pi$
$350$	2.31464	+	5.30352i	0.123723	+	0.283485i
$351$		0			0
$352$	18.5826	+	18.5826i	0.990455	+	0.990455i
$353$	−4.53223	+	16.9145i	−0.241226	+	0.900270i	0.734016	+	0.679132i	$0.237644\pi$
$353$	−4.53223	+	16.9145i	−0.241226	+	0.900270i	−0.975243	+	0.221138i	$0.929023\pi$
$354$		0			0
$355$	−11.0684	+	5.58839i	−0.587448	+	0.296601i
$356$	−25.8062	−	14.8992i	−1.36772	−	0.789656i
$357$		0			0
$358$		0			0
$359$	−29.7984			−1.57270			−0.786350	−	0.617781i	$-0.788032\pi$
$359$	−29.7984			−1.57270			−0.786350	+	0.617781i	$0.788032\pi$
$360$		0			0
$361$	10.0000			0.526316
$362$	4.30151	+	1.15259i	0.226082	+	0.0605786i
$363$		0			0
$364$	−9.95536	−	5.74773i	−0.521802	−	0.301263i
$365$	−31.1619	−	10.2521i	−1.63109	−	0.536619i
$366$		0			0
$367$	−3.27828	+	12.2347i	−0.171125	+	0.638647i	0.826054	+	0.563591i	$0.190580\pi$
$367$	−3.27828	+	12.2347i	−0.171125	+	0.638647i	−0.997179	+	0.0750567i	$0.976086\pi$
$368$	12.0593	+	12.0593i	0.628632	+	0.628632i
$369$		0			0
$370$	3.95644	−	6.04356i	0.205685	−	0.314190i
$371$	0.209186	−	0.120774i	0.0108604	−	0.00627025i
$372$		0			0
$373$	−1.31131	−	4.89389i	−0.0678973	−	0.253396i	0.923632	−	0.383281i	$-0.125206\pi$
$373$	−1.31131	−	4.89389i	−0.0678973	−	0.253396i	−0.991529	+	0.129885i	$0.958539\pi$
$374$	3.35119	−	5.80444i	0.173286	−	0.300140i
$375$		0			0
$376$	0.791288	+	1.37055i	0.0408076	+	0.0706808i
$377$	−7.85971	+	7.85971i	−0.404796	+	0.404796i
$378$		0			0
$379$			7.74773i			0.397974i	0.980002	+	0.198987i	$0.0637652\pi$
$379$			7.74773i			0.397974i	−0.980002	+	0.198987i	$0.936235\pi$
$380$	−11.9975	−	0.673054i	−0.615457	−	0.0345269i
$381$		0			0
$382$	8.25566	−	2.21210i	0.422396	−	0.113181i
$383$	28.6258	−	7.67025i	1.46271	−	0.391931i	0.562284	−	0.826944i	$-0.309923\pi$
$383$	28.6258	−	7.67025i	1.46271	−	0.391931i	0.900424	+	0.435013i	$0.143256\pi$
$384$		0			0
$385$	23.4196	−	20.9315i	1.19357	−	1.06677i
$386$			1.15732i			0.0589061i
$387$		0			0
$388$	6.41742	−	6.41742i	0.325795	−	0.325795i
$389$	3.92985	+	6.80671i	0.199251	+	0.345114i	0.948286	−	0.317417i	$-0.102816\pi$
$389$	3.92985	+	6.80671i	0.199251	+	0.345114i	−0.749034	+	0.662531i	$0.769482\pi$
$390$		0			0
$391$	8.08258	−	13.9994i	0.408753	−	0.707982i
$392$	−0.261162	−	0.974668i	−0.0131906	−	0.0492282i
$393$		0			0
$394$	1.04678	−	0.604356i	0.0527358	−	0.0304470i
$395$	19.7982	+	12.9610i	0.996155	+	0.652136i
$396$		0			0
$397$	26.1216	+	26.1216i	1.31101	+	1.31101i	0.920675	+	0.390330i	$0.127639\pi$
$397$	26.1216	+	26.1216i	1.31101	+	1.31101i	0.390330	+	0.920675i	$0.372361\pi$
$398$	−1.98028	+	7.39049i	−0.0992623	+	0.370452i
$399$		0			0
$400$	−13.8689	−	1.56099i	−0.693443	−	0.0780496i
$401$	−16.2019	−	9.35414i	−0.809082	−	0.467124i	0.0375551	−	0.999295i	$-0.488043\pi$
$401$	−16.2019	−	9.35414i	−0.809082	−	0.467124i	−0.846637	+	0.532171i	$0.821376\pi$
$402$		0			0
$403$	2.44694	+	0.655657i	0.121891	+	0.0326606i
$404$	19.8656			0.988351
$405$		0			0
$406$	5.07803			0.252018
$407$	−37.8735	−	10.1482i	−1.87732	−	0.503026i
$408$		0			0
$409$	−20.9276	−	12.0826i	−1.03480	−	0.597445i	−0.116447	−	0.993197i	$-0.537151\pi$
$409$	−20.9276	−	12.0826i	−1.03480	−	0.597445i	−0.918357	+	0.395752i	$0.870484\pi$
$410$	1.77026	−	5.38083i	0.0874270	−	0.265740i
$411$		0			0
$412$	−2.34894	+	8.76636i	−0.115724	+	0.431888i
$413$	7.85971	+	7.85971i	0.386751	+	0.386751i
$414$		0			0
$415$	−26.9564	+	5.62614i	−1.32324	+	0.276176i
$416$	−10.3974	+	6.00295i	−0.509775	+	0.294319i
$417$		0			0
$418$	−1.96697	−	7.34083i	−0.0962077	−	0.359052i
$419$	−0.457887	+	0.793084i	−0.0223693	+	0.0387447i	−0.876993	−	0.480503i	$-0.840454\pi$
$419$	−0.457887	+	0.793084i	−0.0223693	+	0.0387447i	0.854624	+	0.519247i	$0.173788\pi$
$420$		0			0
$421$	−19.8739	−	34.4225i	−0.968593	−	1.67765i	−0.699636	−	0.714500i	$-0.746654\pi$
$421$	−19.8739	−	34.4225i	−0.968593	−	1.67765i	−0.268957	−	0.963152i	$-0.586679\pi$
$422$	−3.14892	+	3.14892i	−0.153287	+	0.153287i
$423$		0			0
$424$		−	0.165151i		−	0.00802046i
$425$	1.97318	+	13.0808i	0.0957135	+	0.634511i
$426$		0			0
$427$	2.44694	−	0.655657i	0.118416	−	0.0317295i
$428$	9.15563	−	2.45324i	0.442554	−	0.118582i
$429$		0			0
$430$	0.259647	−	4.62831i	0.0125213	−	0.223197i
$431$			9.01703i			0.434335i	0.976134	+	0.217168i	$0.0696818\pi$
$431$			9.01703i			0.434335i	−0.976134	+	0.217168i	$0.930318\pi$
$432$		0			0
$433$	4.62614	−	4.62614i	0.222318	−	0.222318i	−0.587156	−	0.809474i	$-0.699752\pi$
$433$	4.62614	−	4.62614i	0.222318	−	0.222318i	0.809474	+	0.587156i	$0.199752\pi$
$434$	−0.578661	−	1.00227i	−0.0277766	−	0.0481105i
$435$		0			0
$436$	−12.3131	+	21.3269i	−0.589689	+	1.02137i
$437$	−4.74404	−	17.7050i	−0.226938	−	0.846945i
$438$		0			0
$439$	9.16478	−	5.29129i	0.437411	−	0.252539i	−0.265088	−	0.964224i	$-0.585401\pi$
$439$	9.16478	−	5.29129i	0.437411	−	0.252539i	0.702499	+	0.711685i	$0.252068\pi$
$440$	−4.38774	−	21.0229i	−0.209177	−	1.00223i
$441$		0			0
$442$	2.16515	+	2.16515i	0.102986	+	0.102986i
$443$	2.90153	−	10.8287i	0.137856	−	0.514485i	−0.862114	−	0.506715i	$-0.830860\pi$
$443$	2.90153	−	10.8287i	0.137856	−	0.514485i	0.999970	−	0.00777070i	$-0.00247352\pi$
$444$		0			0
$445$	16.7652	+	33.2051i	0.794745	+	1.57407i
$446$	−4.80217	−	2.77253i	−0.227389	−	0.131283i
$447$		0			0
$448$	−8.36225	−	2.24066i	−0.395079	−	0.105861i
$449$	−13.1632			−0.621211			−0.310605	−	0.950539i	$-0.600532\pi$
$449$	−13.1632			−0.621211			−0.310605	+	0.950539i	$0.600532\pi$
$450$		0			0
$451$	−30.7477			−1.44785
$452$	21.1432	+	5.66529i	0.994491	+	0.266473i
$453$		0			0
$454$	3.86333	+	2.23049i	0.181315	+	0.104682i
$455$	6.46756	+	12.8097i	0.303204	+	0.600526i
$456$		0			0
$457$	−1.31131	+	4.89389i	−0.0613407	+	0.228926i	−0.989790	−	0.142532i	$-0.954476\pi$
$457$	−1.31131	+	4.89389i	−0.0613407	+	0.228926i	0.928450	+	0.371459i	$0.121142\pi$
$458$	1.88490	+	1.88490i	0.0880756	+	0.0880756i
$459$		0			0
$460$	−5.00000	−	23.9564i	−0.233126	−	1.11697i
$461$	−12.6111	+	7.28105i	−0.587359	+	0.339112i	−0.764053	−	0.645154i	$-0.776793\pi$
$461$	−12.6111	+	7.28105i	−0.587359	+	0.339112i	0.176693	+	0.984266i	$0.443460\pi$
$462$		0			0
$463$	−2.86775	−	10.7026i	−0.133276	−	0.497392i	0.866723	−	0.498789i	$-0.166222\pi$
$463$	−2.86775	−	10.7026i	−0.133276	−	0.497392i	−0.999999	+	0.00139730i	$0.999555\pi$
$464$	−6.12372	+	10.6066i	−0.284287	+	0.492399i
$465$		0			0
$466$	−5.41742	−	9.38325i	−0.250957	−	0.434671i
$467$	5.34279	−	5.34279i	0.247235	−	0.247235i	−0.572600	−	0.819835i	$-0.694065\pi$
$467$	5.34279	−	5.34279i	0.247235	−	0.247235i	0.819835	+	0.572600i	$0.194065\pi$
$468$		0			0
$469$			30.7477i			1.41980i
$470$	0.0522807	−	0.931924i	0.00241153	−	0.0429864i
$471$		0			0
$472$	7.34083	−	1.96697i	0.337889	−	0.0905372i
$473$	−24.3050	+	6.51251i	−1.11755	+	0.299446i
$474$		0			0
$475$	12.0700	+	8.90588i	0.553810	+	0.408630i
$476$			12.0059i			0.550290i
$477$		0			0
$478$	3.95644	−	3.95644i	0.180963	−	0.180963i
$479$	3.92985	+	6.80671i	0.179560	+	0.311006i	0.941730	−	0.336370i	$-0.109199\pi$
$479$	3.92985	+	6.80671i	0.179560	+	0.311006i	−0.762170	+	0.647377i	$0.775866\pi$
$480$		0			0
$481$	8.95644	−	15.5130i	0.408378	−	0.707332i
$482$	1.38907	+	5.18408i	0.0632704	+	0.236128i
$483$		0			0
$484$	−30.6347	+	17.6869i	−1.39248	+	0.803951i
$485$	−11.0901	+	2.31464i	−0.503577	+	0.105103i
$486$		0			0
$487$	0.373864	+	0.373864i	0.0169414	+	0.0169414i	0.715527	−	0.698585i	$-0.246187\pi$
$487$	0.373864	+	0.373864i	0.0169414	+	0.0169414i	−0.698585	+	0.715527i	$0.746187\pi$
$488$	0.448288	−	1.67303i	0.0202930	−	0.0757346i
$489$		0			0
$490$	−0.185987	+	0.565321i	−0.00840205	+	0.0255386i
$491$	12.6111	+	7.28105i	0.569133	+	0.328589i	0.756803	−	0.653643i	$-0.226760\pi$
$491$	12.6111	+	7.28105i	0.569133	+	0.328589i	−0.187670	+	0.982232i	$0.560094\pi$
$492$		0			0
$493$	11.2133	+	3.00460i	0.505022	+	0.135320i
$494$	3.47197			0.156211
$495$		0			0
$496$	2.79129			0.125333
$497$	13.5685	+	3.63566i	0.608629	+	0.163082i
$498$		0			0
$499$	23.6687	+	13.6652i	1.05956	+	0.611736i	0.925310	−	0.379212i	$-0.123805\pi$
$499$	23.6687	+	13.6652i	1.05956	+	0.611736i	0.134248	+	0.990948i	$0.457138\pi$
$500$	15.4239	+	12.7746i	0.689779	+	0.571299i
$501$		0			0
$502$	−2.62263	+	9.78778i	−0.117054	+	0.436850i
$503$	−16.5678	−	16.5678i	−0.738720	−	0.738720i	0.233610	−	0.972330i	$-0.424946\pi$
$503$	−16.5678	−	16.5678i	−0.738720	−	0.738720i	−0.972330	+	0.233610i	$0.924946\pi$
$504$		0			0
$505$	−20.7477	−	13.5826i	−0.923262	−	0.604417i
$506$	13.4042	−	7.73893i	0.595891	−	0.344038i
$507$		0			0
$508$	3.27828	+	12.2347i	0.145450	+	0.542828i
$509$	−8.77548	+	15.1996i	−0.388966	+	0.673710i	−0.992311	−	0.123771i	$-0.960501\pi$
$509$	−8.77548	+	15.1996i	−0.388966	+	0.673710i	0.603344	+	0.797481i	$0.293834\pi$
$510$		0			0
$511$	18.5826	+	32.1860i	0.822045	+	1.42382i
$512$	−16.1914	+	16.1914i	−0.715564	+	0.715564i
$513$		0			0
$514$		−	1.62614i		−	0.0717258i
$515$	8.44701	−	7.54960i	0.372220	−	0.332675i
$516$		0			0
$517$	−4.89389	+	1.31131i	−0.215233	+	0.0576715i
$518$	−7.90466	+	2.11805i	−0.347311	+	0.0930616i
$519$		0			0
$520$	9.79589	+	0.549546i	0.429578	+	0.0240992i
$521$		−	27.7253i		−	1.21467i	−0.794447	−	0.607334i	$-0.792239\pi$
$521$		−	27.7253i		−	1.21467i	0.794447	−	0.607334i	$-0.207761\pi$
$522$		0			0
$523$	15.3739	−	15.3739i	0.672252	−	0.672252i	−0.285983	−	0.958235i	$-0.592320\pi$
$523$	15.3739	−	15.3739i	0.672252	−	0.672252i	0.958235	+	0.285983i	$0.0923200\pi$
$524$	−6.82316	−	11.8181i	−0.298071	−	0.516274i
$525$		0			0
$526$	0.252273	−	0.436950i	0.0109996	−	0.0190519i
$527$	−0.684771	−	2.55560i	−0.0298291	−	0.111324i
$528$		0			0
$529$	12.4104	−	7.16515i	0.539583	−	0.311528i
$530$	−0.0533508	+	0.0814947i	−0.00231741	+	0.00353990i
$531$		0			0
$532$	9.62614	+	9.62614i	0.417346	+	0.417346i
$533$	3.63566	−	13.5685i	0.157478	−	0.587715i
$534$		0			0
$535$	−11.2395	−	3.69774i	−0.485927	−	0.159867i
$536$	18.2064	+	10.5115i	0.786396	+	0.454026i
$537$		0			0
$538$	−1.53212	−	0.410531i	−0.0660544	−	0.0176992i
$539$	3.23042			0.139144
$540$		0			0
$541$	−19.4955			−0.838175			−0.419088	−	0.907946i	$-0.637650\pi$
$541$	−19.4955			−0.838175			−0.419088	+	0.907946i	$0.637650\pi$
$542$	−0.441283	−	0.118242i	−0.0189547	−	0.00507891i
$543$		0			0
$544$	10.8591	+	6.26951i	0.465580	+	0.268803i
$545$	27.4415	−	13.8551i	1.17546	−	0.593489i
$546$		0			0
$547$	−8.76867	+	32.7251i	−0.374921	+	1.39922i	0.478539	+	0.878066i	$0.341167\pi$
$547$	−8.76867	+	32.7251i	−0.374921	+	1.39922i	−0.853460	+	0.521158i	$0.825500\pi$
$548$	−18.5875	−	18.5875i	−0.794019	−	0.794019i
$549$		0			0
$550$	−4.62614	+	11.7913i	−0.197259	+	0.502782i
$551$	11.3997	−	6.58161i	0.485643	−	0.280386i
$552$		0			0
$553$	−6.93854	−	25.8950i	−0.295057	−	1.10117i
$554$	−4.26697	+	7.39060i	−0.181286	+	0.313997i
$555$		0			0
$556$	2.83485	+	4.91010i	0.120224	+	0.208235i
$557$	26.0568	−	26.0568i	1.10406	−	1.10406i	0.110145	−	0.993916i	$-0.464869\pi$
$557$	26.0568	−	26.0568i	1.10406	−	1.10406i	0.993916	−	0.110145i	$-0.0351314\pi$
$558$		0			0
$559$		−	11.4955i		−	0.486206i
$560$	10.5366	+	11.7890i	0.445251	+	0.498177i
$561$		0			0
$562$	0.914823	−	0.245126i	0.0385895	−	0.0103400i
$563$	−11.8033	+	3.16269i	−0.497451	+	0.133292i	−0.498817	−	0.866707i	$-0.666232\pi$
$563$	−11.8033	+	3.16269i	−0.497451	+	0.133292i	0.00136574	+	0.999999i	$0.499565\pi$
$564$		0			0
$565$	−18.2085	−	20.3729i	−0.766038	−	0.857095i
$566$		−	8.53394i		−	0.358708i
$567$		0			0
$568$	6.79129	−	6.79129i	0.284956	−	0.284956i
$569$	−14.4413	−	25.0131i	−0.605412	−	1.04860i	−0.991986	−	0.126346i	$-0.959675\pi$
$569$	−14.4413	−	25.0131i	−0.605412	−	1.04860i	0.386575	−	0.922258i	$-0.373658\pi$
$570$		0			0
$571$	11.2477	−	19.4816i	0.470703	−	0.815281i	−0.528736	−	0.848786i	$-0.677334\pi$
$571$	11.2477	−	19.4816i	0.470703	−	0.815281i	0.999439	+	0.0335054i	$0.0106671\pi$
$572$	−6.51251	−	24.3050i	−0.272302	−	1.01624i
$573$		0			0
$574$	−5.55765	+	3.20871i	−0.231972	+	0.133929i
$575$	−11.1575	+	28.4388i	−0.465302	+	1.18598i
$576$		0			0
$577$	−10.3739	−	10.3739i	−0.431870	−	0.431870i	0.457394	−	0.889264i	$-0.348783\pi$
$577$	−10.3739	−	10.3739i	−0.431870	−	0.431870i	−0.889264	+	0.457394i	$0.848783\pi$
$578$	−1.18242	+	4.41283i	−0.0491820	+	0.183550i
$579$		0			0
$580$	15.6886	−	7.92111i	0.651432	−	0.328906i
$581$	27.0176	+	15.5986i	1.12088	+	0.647141i
$582$		0			0
$583$	0.510707	+	0.136844i	0.0211513	+	0.00566748i
$584$	25.4107			1.05150
$585$		0			0
$586$	−7.95644			−0.328677
$587$	36.8988	+	9.88701i	1.52298	+	0.408081i	0.920721	−	0.390222i	$-0.127602\pi$
$587$	36.8988	+	9.88701i	1.52298	+	0.408081i	0.602256	+	0.798303i	$0.294268\pi$
$588$		0			0
$589$	−2.59808	−	1.50000i	−0.107052	−	0.0618064i
$590$	−4.25778	−	1.40079i	−0.175290	−	0.0576695i
$591$		0			0
$592$	5.10841	−	19.0649i	0.209954	−	0.783561i
$593$	29.8658	+	29.8658i	1.22644	+	1.22644i	0.965300	+	0.261143i	$0.0840993\pi$
$593$	29.8658	+	29.8658i	1.22644	+	1.22644i	0.261143	+	0.965300i	$0.415901\pi$
$594$		0			0
$595$	8.20871	−	12.5390i	0.336524	−	0.514049i
$596$	12.1928	−	7.03950i	0.499435	−	0.288349i
$597$		0			0
$598$	1.83013	+	6.83013i	0.0748395	+	0.279305i
$599$	14.4413	−	25.0131i	0.590056	−	1.02201i	−0.404168	−	0.914685i	$-0.632439\pi$
$599$	14.4413	−	25.0131i	0.590056	−	1.02201i	0.994224	−	0.107323i	$-0.0342278\pi$
$600$		0			0
$601$	−19.8739	−	34.4225i	−0.810672	−	1.40412i	−0.912394	−	0.409312i	$-0.865769\pi$
$601$	−19.8739	−	34.4225i	−0.810672	−	1.40412i	0.101723	−	0.994813i	$-0.467565\pi$
$602$	−3.71351	+	3.71351i	−0.151352	+	0.151352i
$603$		0			0
$604$			3.58258i			0.145773i
$605$	44.0879	+	2.47332i	1.79243	+	0.100555i
$606$		0			0
$607$	−19.0649	+	5.10841i	−0.773818	+	0.207344i	−0.624058	−	0.781378i	$-0.714517\pi$
$607$	−19.0649	+	5.10841i	−0.773818	+	0.207344i	−0.149761	+	0.988722i	$0.547850\pi$
$608$	13.7334	−	3.67986i	0.556965	−	0.149238i
$609$		0			0
$610$	−0.761669	+	0.680750i	−0.0308391	+	0.0275628i
$611$		−	2.31464i		−	0.0936405i
$612$		0			0
$613$	10.0000	−	10.0000i	0.403896	−	0.403896i	−0.475707	−	0.879604i	$-0.657808\pi$
$613$	10.0000	−	10.0000i	0.403896	−	0.403896i	0.879604	+	0.475707i	$0.157808\pi$
$614$	−5.08718	−	8.81125i	−0.205302	−	0.355593i
$615$		0			0
$616$	−12.1652	+	21.0707i	−0.490148	+	0.848961i
$617$	5.16765	+	19.2859i	0.208042	+	0.776422i	0.988501	+	0.151215i	$0.0483187\pi$
$617$	5.16765	+	19.2859i	0.208042	+	0.776422i	−0.780459	+	0.625207i	$0.785015\pi$
$618$		0			0
$619$	16.9590	−	9.79129i	0.681640	−	0.393545i	−0.118833	−	0.992914i	$-0.537915\pi$
$619$	16.9590	−	9.79129i	0.681640	−	0.393545i	0.800473	+	0.599369i	$0.204582\pi$
$620$	−3.35119	−	2.19387i	−0.134587	−	0.0881080i
$621$		0			0
$622$	−2.91288	−	2.91288i	−0.116796	−	0.116796i
$623$	10.9070	−	40.7054i	0.436979	−	1.63083i
$624$		0			0
$625$	−7.37451	−	23.8876i	−0.294980	−	0.955503i
$626$	9.60433	+	5.54506i	0.383866	+	0.221625i
$627$		0			0
$628$	7.85154	+	2.10381i	0.313311	+	0.0839513i
$629$	−18.7083			−0.745948
$630$		0			0
$631$	39.7477			1.58233			0.791166	−	0.611601i	$-0.209474\pi$
$631$	39.7477			1.58233			0.791166	+	0.611601i	$0.209474\pi$
$632$	−17.7050	−	4.74404i	−0.704267	−	0.188708i
$633$		0			0
$634$	−12.8096	−	7.39564i	−0.508735	−	0.293719i
$635$	4.94131	−	15.0194i	0.196090	−	0.596028i
$636$		0			0
$637$	−0.381970	+	1.42553i	−0.0151342	+	0.0564816i
$638$	7.85971	+	7.85971i	0.311169	+	0.311169i
$639$		0			0
$640$	24.1652	−	5.04356i	0.955211	−	0.199364i
$641$	−32.4037	+	18.7083i	−1.27987	+	0.738933i	−0.976824	−	0.214043i	$-0.931337\pi$
$641$	−32.4037	+	18.7083i	−1.27987	+	0.738933i	−0.303045	+	0.952976i	$0.598003\pi$
$642$		0			0
$643$	0.655657	+	2.44694i	0.0258566	+	0.0964981i	0.977648	−	0.210247i	$-0.0674268\pi$
$643$	0.655657	+	2.44694i	0.0258566	+	0.0964981i	−0.951792	+	0.306745i	$0.900760\pi$
$644$	−13.8627	+	24.0108i	−0.546265	+	0.946159i
$645$		0			0
$646$	−1.81307	−	3.14033i	−0.0713342	−	0.123554i
$647$	18.5060	−	18.5060i	0.727547	−	0.727547i	−0.242584	−	0.970130i	$-0.577995\pi$
$647$	18.5060	−	18.5060i	0.727547	−	0.727547i	0.970130	+	0.242584i	$0.0779949\pi$
$648$		0			0
$649$			24.3303i			0.955048i
$650$	−4.65630	−	3.43566i	−0.182635	−	0.134758i
$651$		0			0
$652$	12.2347	−	3.27828i	0.479149	−	0.128388i
$653$	23.8830	−	6.39942i	0.934613	−	0.250429i	0.240792	−	0.970577i	$-0.422593\pi$
$653$	23.8830	−	6.39942i	0.934613	−	0.250429i	0.693820	+	0.720148i	$0.255926\pi$
$654$		0			0
$655$	−0.954143	+	17.0080i	−0.0372814	+	0.664557i
$656$		−	15.4779i		−	0.604309i
$657$		0			0
$658$	−0.747727	+	0.747727i	−0.0291494	+	0.0291494i
$659$	18.8291	+	32.6129i	0.733476	+	1.27042i	0.955389	+	0.295351i	$0.0954367\pi$
$659$	18.8291	+	32.6129i	0.733476	+	1.27042i	−0.221913	+	0.975067i	$0.571230\pi$
$660$		0			0
$661$	−11.7477	+	20.3477i	−0.456934	+	0.791432i	−0.998797	−	0.0490343i	$-0.984386\pi$
$661$	−11.7477	+	20.3477i	−0.456934	+	0.791432i	0.541863	+	0.840467i	$0.317719\pi$
$662$	−1.50731	−	5.62536i	−0.0585833	−	0.218636i
$663$		0			0
$664$	18.4726	−	10.6652i	0.716875	−	0.413888i
$665$	−3.47197	−	16.6352i	−0.134637	−	0.645085i
$666$		0			0
$667$	18.9564	+	18.9564i	0.733996	+	0.733996i
$668$	6.98033	−	26.0509i	0.270077	−	1.00794i
$669$		0			0
$670$	−5.58839	−	11.0684i	−0.215898	−	0.427608i
$671$	4.80217	+	2.77253i	0.185386	+	0.107032i
$672$		0			0
$673$	30.7889	+	8.24985i	1.18682	+	0.318008i	0.797630	−	0.603147i	$-0.206087\pi$
$673$	30.7889	+	8.24985i	1.18682	+	0.318008i	0.389194	+	0.921156i	$0.372754\pi$
$674$	−11.7644			−0.453146
$675$		0			0
$676$	−11.7913			−0.453511
$677$	17.0987	+	4.58159i	0.657158	+	0.176085i	0.571963	−	0.820279i	$-0.306182\pi$
$677$	17.0987	+	4.58159i	0.657158	+	0.176085i	0.0851947	+	0.996364i	$0.472849\pi$
$678$		0			0
$679$	11.1153	+	6.41742i	0.426566	+	0.246278i
$680$	−4.61838	−	9.14716i	−0.177107	−	0.350778i
$681$		0			0
$682$	0.655657	−	2.44694i	0.0251064	−	0.0936984i
$683$	0.0674228	+	0.0674228i	0.00257986	+	0.00257986i	0.708396	−	0.705816i	$-0.249419\pi$
$683$	0.0674228	+	0.0674228i	0.00257986	+	0.00257986i	−0.705816	+	0.708396i	$0.749419\pi$
$684$		0			0
$685$	6.70417	+	32.1216i	0.256153	+	1.22730i
$686$	7.59979	−	4.38774i	0.290161	−	0.167525i
$687$		0			0
$688$	−3.27828	−	12.2347i	−0.124983	−	0.466444i
$689$	−0.120774	+	0.209186i	−0.00460111	+	0.00796935i
$690$		0			0
$691$	5.87386	+	10.1738i	0.223452	+	0.387031i	0.955854	−	0.293842i	$-0.0949340\pi$
$691$	5.87386	+	10.1738i	0.223452	+	0.387031i	−0.732402	+	0.680873i	$0.761601\pi$
$692$	−14.1998	+	14.1998i	−0.539794	+	0.539794i
$693$		0			0
$694$			5.49545i			0.208605i
$695$	0.396422	−	7.06638i	0.0150371	−	0.268043i
$696$		0			0
$697$	−14.1710	+	3.79710i	−0.536763	+	0.143825i
$698$	−8.56859	+	2.29595i	−0.324326	+	0.0869028i
$699$		0			0
$700$	−3.38427	−	22.4352i	−0.127913	−	0.847971i
$701$		−	47.8325i		−	1.80661i	−0.429001	−	0.903304i	$-0.641134\pi$
$701$		−	47.8325i		−	1.80661i	0.429001	−	0.903304i	$-0.358866\pi$
$702$		0			0
$703$	−15.0000	+	15.0000i	−0.565736	+	0.565736i
$704$	−9.47492	−	16.4110i	−0.357099	−	0.618514i
$705$		0			0
$706$	−4.00000	+	6.92820i	−0.150542	+	0.260746i
$707$	7.27132	+	27.1369i	0.273466	+	1.02059i
$708$		0			0
$709$	−36.9452	+	21.3303i	−1.38750	+	0.801076i	−0.993034	−	0.117832i	$-0.962406\pi$
$709$	−36.9452	+	21.3303i	−1.38750	+	0.801076i	−0.394471	+	0.918908i	$0.629072\pi$
$710$	−5.54506	+	1.15732i	−0.208103	+	0.0434335i
$711$		0			0
$712$	−20.3739	−	20.3739i	−0.763543	−	0.763543i
$713$	1.58135	−	5.90166i	0.0592219	−	0.221019i
$714$		0			0
$715$	−9.81621	+	29.8370i	−0.367105	+	1.11584i
$716$		0			0
$717$		0			0
$718$	−13.1495	−	3.52341i	−0.490737	−	0.131493i
$719$	29.7984			1.11129			0.555647	−	0.831419i	$-0.312471\pi$
$719$	29.7984			1.11129			0.555647	+	0.831419i	$0.312471\pi$
$720$		0			0
$721$	−12.8348			−0.477995
$722$	4.41283	+	1.18242i	0.164229	+	0.0440049i
$723$		0			0
$724$	−15.1217	−	8.73049i	−0.561992	−	0.324466i
$725$	−21.8010	−	2.45379i	−0.809671	−	0.0911314i
$726$		0			0
$727$	13.6034	−	50.7685i	0.504522	−	1.88290i	0.0361968	−	0.999345i	$-0.488476\pi$
$727$	13.6034	−	50.7685i	0.504522	−	1.88290i	0.468325	−	0.883556i	$-0.344858\pi$
$728$	−7.85971	−	7.85971i	−0.291300	−	0.291300i
$729$		0			0
$730$	−12.5390	−	8.20871i	−0.464090	−	0.303818i
$731$	−10.3974	+	6.00295i	−0.384562	+	0.222027i
$732$		0			0
$733$	9.66945	+	36.0869i	0.357149	+	1.33290i	0.877758	+	0.479104i	$0.159038\pi$
$733$	9.66945	+	36.0869i	0.357149	+	1.33290i	−0.520609	+	0.853795i	$0.674295\pi$
$734$	−2.89331	+	5.01135i	−0.106794	+	0.184972i
$735$		0			0
$736$	14.4782	+	25.0770i	0.533674	+	0.924351i
$737$	−47.5909	+	47.5909i	−1.75303	+	1.75303i
$738$		0			0
$739$		−	24.4955i		−	0.901080i	−0.892756	−	0.450540i	$-0.851231\pi$
$739$		−	24.4955i		−	0.901080i	0.892756	−	0.450540i	$-0.148769\pi$
$740$	−21.1175	+	18.8740i	−0.776296	+	0.693822i
$741$		0			0
$742$	0.106591	−	0.0285609i	0.00391307	−	0.00104850i
$743$	−16.5461	+	4.43352i	−0.607018	+	0.162650i	−0.549219	−	0.835678i	$-0.685075\pi$
$743$	−16.5461	+	4.43352i	−0.607018	+	0.162650i	−0.0577989	+	0.998328i	$0.518408\pi$
$744$		0			0
$745$	−17.5472	−	0.984396i	−0.642881	−	0.0360655i
$746$		−	2.31464i		−	0.0847451i
$747$		0			0
$748$	−18.5826	+	18.5826i	−0.679446	+	0.679446i
$749$	6.70239	+	11.6089i	0.244900	+	0.424179i
$750$		0			0
$751$	−4.87386	+	8.44178i	−0.177850	+	0.308045i	−0.941144	−	0.338006i	$-0.890247\pi$
$751$	−4.87386	+	8.44178i	−0.177850	+	0.308045i	0.763294	+	0.646051i	$0.223581\pi$
$752$	−0.660092	−	2.46350i	−0.0240711	−	0.0898345i
$753$		0			0
$754$	−4.39770	+	2.53901i	−0.160155	+	0.0924655i
$755$	2.44949	−	3.74166i	0.0891461	−	0.136173i
$756$		0			0
$757$	−5.00000	−	5.00000i	−0.181728	−	0.181728i	0.610380	−	0.792108i	$-0.291017\pi$
$757$	−5.00000	−	5.00000i	−0.181728	−	0.181728i	−0.792108	+	0.610380i	$0.791017\pi$
$758$	−0.916103	+	3.41894i	−0.0332744	+	0.124182i
$759$		0			0
$760$	−11.0370	−	3.63111i	−0.400354	−	0.131714i
$761$	−7.80898	−	4.50851i	−0.283075	−	0.163434i	0.351740	−	0.936098i	$-0.385590\pi$
$761$	−7.80898	−	4.50851i	−0.283075	−	0.163434i	−0.634815	+	0.772664i	$0.718924\pi$
$762$		0			0
$763$	−33.6399	−	9.01379i	−1.21785	−	0.326321i
$764$	−33.5119			−1.21242
$765$		0			0
$766$	13.5390			0.489184
$767$	−10.7366	−	2.87685i	−0.387675	−	0.103877i
$768$		0			0
$769$	23.6687	+	13.6652i	0.853516	+	0.492778i	0.861836	−	0.507187i	$-0.169315\pi$
$769$	23.6687	+	13.6652i	0.853516	+	0.492778i	−0.00831931	+	0.999965i	$0.502648\pi$
$770$	12.8097	−	6.46756i	0.461628	−	0.233075i
$771$		0			0
$772$	1.17447	−	4.38318i	0.0422701	−	0.157754i
$773$	36.8098	+	36.8098i	1.32396	+	1.32396i	0.910545	+	0.413411i	$0.135663\pi$
$773$	36.8098	+	36.8098i	1.32396	+	1.32396i	0.413411	+	0.910545i	$0.364337\pi$
$774$		0			0
$775$	2.00000	+	4.58258i	0.0718421	+	0.164611i
$776$	7.59979	−	4.38774i	0.272817	−	0.157511i
$777$		0			0
$778$	0.929344	+	3.46836i	0.0333186	+	0.124347i
$779$	−8.31759	+	14.4065i	−0.298009	+	0.516166i
$780$		0			0
$781$	15.3739	+	26.6283i	0.550120	+	0.952836i
$782$	5.22202	−	5.22202i	0.186739	−	0.186739i
$783$		0			0
$784$			1.62614i			0.0580763i
$785$	−6.76176	−	7.56551i	−0.241337	−	0.270025i
$786$		0			0
$787$	51.2792	−	13.7402i	1.82791	−	0.489786i	0.830201	−	0.557465i	$-0.188226\pi$
$787$	51.2792	−	13.7402i	1.82791	−	0.489786i	0.997707	+	0.0676784i	$0.0215592\pi$
$788$	−4.57781	+	1.22662i	−0.163078	+	0.0436966i
$789$		0			0
$790$	7.20409	+	8.06042i	0.256310	+	0.286777i
$791$			30.9557i			1.10066i
$792$		0			0
$793$	−1.79129	+	1.79129i	−0.0636105	+	0.0636105i
$794$	8.43837	+	14.6157i	0.299466	+	0.518691i
$795$		0			0
$796$	15.0000	−	25.9808i	0.531661	−	0.920864i
$797$	−0.921254	−	3.43817i	−0.0326325	−	0.121786i	0.947688	−	0.319197i	$-0.103413\pi$
$797$	−0.921254	−	3.43817i	−0.0326325	−	0.121786i	−0.980321	+	0.197411i	$0.936747\pi$
$798$		0			0
$799$	−2.09355	+	1.20871i	−0.0740645	+	0.0427612i
$800$	−22.0595	−	8.65471i	−0.779920	−	0.305990i
$801$		0			0
$802$	−6.04356	−	6.04356i	−0.213406	−	0.213406i
$803$	−21.0551	+	78.5789i	−0.743020	+	2.77299i
$804$		0			0
$805$	30.8950	−	15.5988i	1.08890	−	0.549785i
$806$	1.00227	+	0.578661i	0.0353035	+	0.0203825i
$807$		0			0
$808$	18.5541	+	4.97157i	0.652732	+	0.174899i
$809$	42.9616			1.51045			0.755225	−	0.655465i	$-0.227527\pi$
$809$	42.9616			1.51045			0.755225	+	0.655465i	$0.227527\pi$
$810$		0			0
$811$	23.4955			0.825037			0.412518	−	0.910949i	$-0.364649\pi$
$811$	23.4955			0.825037			0.412518	+	0.910949i	$0.364649\pi$
$812$	−19.2323	−	5.15327i	−0.674920	−	0.180844i
$813$		0			0
$814$	−15.5130	−	8.95644i	−0.543731	−	0.313923i
$815$	−15.0194	−	4.94131i	−0.526108	−	0.173087i
$816$		0			0
$817$	−3.52341	+	13.1495i	−0.123269	+	0.460044i
$818$	−7.80636	−	7.80636i	−0.272943	−	0.272943i
$819$		0			0
$820$	−12.1652	+	18.5826i	−0.424826	+	0.648932i
$821$	−6.59752	+	3.80908i	−0.230255	+	0.132938i	−0.610690	−	0.791870i	$-0.709108\pi$
$821$	−6.59752	+	3.80908i	−0.230255	+	0.132938i	0.380435	+	0.924808i	$0.375774\pi$
$822$		0			0
$823$	−8.76867	−	32.7251i	−0.305656	−	1.14073i	−0.932379	−	0.361483i	$-0.882271\pi$
$823$	−8.76867	−	32.7251i	−0.305656	−	1.14073i	0.626722	−	0.779243i	$-0.284396\pi$
$824$	−4.38774	+	7.59979i	−0.152854	+	0.264751i
$825$		0			0
$826$	2.53901	+	4.39770i	0.0883436	+	0.153016i
$827$	31.6692	−	31.6692i	1.10125	−	1.10125i	0.106987	−	0.994260i	$-0.465880\pi$
$827$	31.6692	−	31.6692i	1.10125	−	1.10125i	0.994260	−	0.106987i	$-0.0341203\pi$
$828$		0			0
$829$		−	34.7477i		−	1.20684i	−0.797424	−	0.603419i	$-0.793805\pi$
$829$		−	34.7477i		−	1.20684i	0.797424	−	0.603419i	$-0.206195\pi$
$830$	−12.5607	−	0.704650i	−0.435987	−	0.0244588i
$831$		0			0
$832$	8.36225	−	2.24066i	0.289909	−	0.0776808i
$833$	1.48883	−	0.398931i	0.0515849	−	0.0138221i
$834$		0			0
$835$	−25.1019	+	22.4351i	−0.868687	+	0.776399i
$836$			29.7984i			1.03060i
$837$		0			0
$838$	−0.295834	+	0.295834i	−0.0102194	+	0.0102194i
$839$	−17.5510	−	30.3992i	−0.605927	−	1.04950i	−0.991904	−	0.126988i	$-0.959469\pi$
$839$	−17.5510	−	30.3992i	−0.605927	−	1.04950i	0.385978	−	0.922508i	$-0.373864\pi$
$840$		0			0
$841$	4.87386	−	8.44178i	0.168064	−	0.291096i
$842$	−4.69983	−	17.5400i	−0.161967	−	0.604469i
$843$		0			0
$844$	15.1217	−	8.73049i	0.520509	−	0.300516i
$845$	12.3149	+	8.06198i	0.423644	+	0.277340i
$846$		0			0
$847$	−35.3739	−	35.3739i	−1.21546	−	1.21546i
$848$	−0.0688847	+	0.257081i	−0.00236551	+	0.00882820i
$849$		0			0
$850$	−0.675957	+	6.00564i	−0.0231851	+	0.205992i
$851$	−37.4151	−	21.6016i	−1.28257	−	0.740493i
$852$		0			0
$853$	−5.91530	−	1.58500i	−0.202536	−	0.0542694i	0.156125	−	0.987737i	$-0.450100\pi$
$853$	−5.91530	−	1.58500i	−0.202536	−	0.0542694i	−0.358661	+	0.933468i	$0.616767\pi$
$854$	1.15732			0.0396027
$855$		0			0
$856$	9.16515			0.313258
$857$	−8.54937	−	2.29080i	−0.292041	−	0.0782521i	0.109824	−	0.993951i	$-0.464971\pi$
$857$	−8.54937	−	2.29080i	−0.292041	−	0.0782521i	−0.401865	+	0.915699i	$0.631638\pi$
$858$		0			0
$859$	−39.5432	−	22.8303i	−1.34920	−	0.778960i	−0.361062	−	0.932542i	$-0.617586\pi$
$859$	−39.5432	−	22.8303i	−1.34920	−	0.778960i	−0.988136	+	0.153582i	$0.950919\pi$
$860$	−5.68026	+	17.2655i	−0.193695	+	0.588749i
$861$		0			0
$862$	−1.06619	+	3.97907i	−0.0363145	+	0.135528i
$863$	−26.2590	−	26.2590i	−0.893868	−	0.893868i	0.101017	−	0.994885i	$-0.467790\pi$
$863$	−26.2590	−	26.2590i	−0.893868	−	0.893868i	−0.994885	+	0.101017i	$0.967790\pi$
$864$		0			0
$865$	24.5390	−	5.12159i	0.834352	−	0.174139i
$866$	2.58844	−	1.49444i	0.0879587	−	0.0507830i
$867$		0			0
$868$	1.17447	+	4.38318i	0.0398641	+	0.148775i
$869$	29.3405	−	50.8193i	0.995309	−	1.72393i
$870$		0			0
$871$	−15.3739	−	26.6283i	−0.520923	−	0.902266i
$872$	−16.8375	+	16.8375i	−0.570188	+	0.570188i
$873$		0			0
$874$		−	8.37386i		−	0.283250i
$875$	−11.8049	+	25.7453i	−0.399079	+	0.870351i
$876$		0			0
$877$	−4.38318	+	1.17447i	−0.148010	+	0.0396590i	−0.332063	−	0.943257i	$-0.607745\pi$
$877$	−4.38318	+	1.17447i	−0.148010	+	0.0396590i	0.184054	+	0.982916i	$0.441078\pi$
$878$	4.66992	−	1.25130i	0.157602	−	0.0422293i
$879$		0			0
$880$	−1.93854	+	34.5552i	−0.0653481	+	1.16486i
$881$			35.3435i			1.19075i	0.803447	+	0.595376i	$0.202997\pi$
$881$			35.3435i			1.19075i	−0.803447	+	0.595376i	$0.797003\pi$
$882$		0			0
$883$	−25.3739	+	25.3739i	−0.853898	+	0.853898i	−0.990611	−	0.136712i	$-0.956346\pi$
$883$	−25.3739	+	25.3739i	−0.853898	+	0.853898i	0.136712	+	0.990611i	$0.456346\pi$
$884$	−6.00295	−	10.3974i	−0.201901	−	0.349703i
$885$		0			0
$886$	2.56080	−	4.43543i	0.0860316	−	0.149011i
$887$	−13.0991	−	48.8864i	−0.439823	−	1.64144i	−0.729253	−	0.684244i	$-0.760132\pi$
$887$	−13.0991	−	48.8864i	−0.439823	−	1.64144i	0.289430	−	0.957199i	$-0.406534\pi$
$888$		0			0
$889$	−15.5130	+	8.95644i	−0.520290	+	0.300389i
$890$	3.47197	+	16.6352i	0.116381	+	0.557613i
$891$		0			0
$892$	15.3739	+	15.3739i	0.514755	+	0.514755i
$893$	−0.709449	+	2.64770i	−0.0237408	+	0.0886019i
$894$		0			0
$895$		0			0
$896$	−24.2200	−	13.9834i	−0.809134	−	0.467154i
$897$		0			0
$898$	−5.80871	−	1.55644i	−0.193839	−	0.0519391i
$899$	4.38774			0.146339
$900$		0			0
$901$	0.252273			0.00840443
$902$	−13.5685	−	3.63566i	−0.451780	−	0.121054i
$903$		0			0
$904$	18.3296	+	10.5826i	0.609632	+	0.351971i
$905$	9.82388	+	19.4572i	0.326557	+	0.646779i
$906$		0			0
$907$	6.55657	−	24.4694i	0.217707	−	0.812495i	−0.767489	−	0.641063i	$-0.778494\pi$
$907$	6.55657	−	24.4694i	0.217707	−	0.812495i	0.985196	−	0.171432i	$-0.0548394\pi$
$908$	−12.3682	−	12.3682i	−0.410454	−	0.410454i
$909$		0			0
$910$	1.33939	+	6.41742i	0.0444005	+	0.212736i
$911$	−21.0040	+	12.1267i	−0.695894	+	0.401775i	−0.805816	−	0.592166i	$-0.798273\pi$
$911$	−21.0040	+	12.1267i	−0.695894	+	0.401775i	0.109922	+	0.993940i	$0.464940\pi$
$912$		0			0
$913$	17.6742	+	65.9609i	0.584930	+	2.18299i
$914$	−1.15732	+	2.00454i	−0.0382808	+	0.0663043i
$915$		0			0
$916$	−5.22595	−	9.05161i	−0.172670	−	0.299073i
$917$	13.6463	−	13.6463i	0.450641	−	0.450641i
$918$		0			0
$919$		−	24.0000i		−	0.791687i	−0.918318	−	0.395843i	$-0.870452\pi$
$919$		−	24.0000i		−	0.791687i	0.918318	−	0.395843i	$-0.129548\pi$
$920$	1.32542	−	23.6262i	0.0436979	−	0.778933i
$921$		0			0
$922$	−6.42601	+	1.72184i	−0.211629	+	0.0567059i
$923$	−13.5685	+	3.63566i	−0.446611	+	0.119669i
$924$		0			0
$925$	34.9598	−	5.27356i	1.14947	−	0.173394i
$926$		−	5.06197i		−	0.166347i
$927$		0			0
$928$	−14.7042	+	14.7042i	−0.482688	+	0.482688i
$929$	0.457887	+	0.793084i	0.0150228	+	0.0260203i	0.873439	−	0.486933i	$-0.161885\pi$
$929$	0.457887	+	0.793084i	0.0150228	+	0.0260203i	−0.858416	+	0.512954i	$0.828551\pi$
$930$		0			0
$931$	0.873864	−	1.51358i	0.0286397	−	0.0496055i
$932$	10.9954	+	41.0353i	0.360166	+	1.34416i
$933$		0			0
$934$	2.98943	−	1.72595i	0.0978171	−	0.0564747i
$935$	32.1131	−	6.70239i	1.05021	−	0.219191i
$936$		0			0
$937$	−0.747727	−	0.747727i	−0.0244272	−	0.0244272i	0.694788	−	0.719215i	$-0.255498\pi$
$937$	−0.747727	−	0.747727i	−0.0244272	−	0.0244272i	−0.719215	+	0.694788i	$0.755498\pi$
$938$	−3.63566	+	13.5685i	−0.118708	+	0.443026i
$939$		0			0
$940$	−1.14374	+	3.47647i	−0.0373046	+	0.113390i
$941$	12.6111	+	7.28105i	0.411111	+	0.237355i	0.691267	−	0.722599i	$-0.257053\pi$
$941$	12.6111	+	7.28105i	0.411111	+	0.237355i	−0.280156	+	0.959955i	$0.590386\pi$
$942$		0			0
$943$	−32.7251	−	8.76867i	−1.06568	−	0.285547i
$944$	−12.2474			−0.398621
$945$		0			0
$946$	−11.4955			−0.373749
$947$	−13.2922	−	3.56162i	−0.431937	−	0.115737i	0.0362982	−	0.999341i	$-0.488443\pi$
$947$	−13.2922	−	3.56162i	−0.431937	−	0.115737i	−0.468235	+	0.883604i	$0.655110\pi$
$948$		0			0
$949$	−32.1860	−	18.5826i	−1.04480	−	0.603216i
$950$	4.27325	+	5.35720i	0.138643	+	0.173810i
$951$		0			0
$952$	−3.00460	+	11.2133i	−0.0973796	+	0.363425i
$953$	−20.2420	−	20.2420i	−0.655703	−	0.655703i	0.298658	−	0.954360i	$-0.403461\pi$
$953$	−20.2420	−	20.2420i	−0.655703	−	0.655703i	−0.954360	+	0.298658i	$0.903461\pi$
$954$		0			0
$955$	35.0000	+	22.9129i	1.13257	+	0.741443i
$956$	−18.9995	+	10.9694i	−0.614487	+	0.354774i
$957$		0			0
$958$	0.929344	+	3.46836i	0.0300257	+	0.112058i
$959$	18.5875	−	32.1945i	0.600222	−	1.03962i
$960$		0			0
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$	5.78661	−	5.78661i	0.186568	−	0.186568i
$963$		0			0
$964$		−	21.0436i		−	0.677767i
$965$	−4.22350	+	3.77480i	−0.135959	+	0.121515i
$966$		0			0
$967$	−26.4057	+	7.07538i	−0.849150	+	0.227529i	−0.657050	−	0.753847i	$-0.728196\pi$
$967$	−26.4057	+	7.07538i	−0.849150	+	0.227529i	−0.192099	+	0.981376i	$0.561530\pi$
$968$	−33.0386	+	8.85266i	−1.06190	+	0.284535i
$969$		0			0
$970$	−5.16758	−	0.289900i	−0.165921	−	0.00930811i
$971$			18.7083i			0.600377i	0.953880	+	0.300189i	$0.0970497\pi$
$971$			18.7083i			0.600377i	−0.953880	+	0.300189i	$0.902950\pi$
$972$		0			0
$973$	−5.66970	+	5.66970i	−0.181762	+	0.181762i
$974$	0.120774	+	0.209186i	0.00386984	+	0.00670275i
$975$		0			0
$976$	−1.39564	+	2.41733i	−0.0446735	+	0.0773767i
$977$	0.571680	+	2.13354i	0.0182897	+	0.0682580i	0.974468	−	0.224528i	$-0.0720842\pi$
$977$	0.571680	+	2.13354i	0.0182897	+	0.0682580i	−0.956178	+	0.292786i	$0.905418\pi$
$978$		0			0
$979$	79.8849	−	46.1216i	2.55313	−	1.47405i
$980$	1.27810	−	1.95232i	0.0408273	−	0.0623647i
$981$		0			0
$982$	4.70417	+	4.70417i	0.150116	+	0.150116i
$983$	−4.45820	+	16.6382i	−0.142194	+	0.530677i	0.857670	+	0.514201i	$0.171911\pi$
$983$	−4.45820	+	16.6382i	−0.142194	+	0.530677i	−0.999864	+	0.0164761i	$0.994755\pi$
$984$		0			0
$985$	5.61976	+	1.84887i	0.179060	+	0.0589098i
$986$	4.59298	+	2.65176i	0.146270	+	0.0844492i
$987$		0			0
$988$	−13.1495	−	3.52341i	−0.418343	−	0.112095i
$989$	−27.7253			−0.881614
$990$		0			0
$991$	18.2523			0.579803			0.289901	−	0.957057i	$-0.406378\pi$
$991$	18.2523			0.579803			0.289901	+	0.957057i	$0.406378\pi$
$992$	4.57781	+	1.22662i	0.145346	+	0.0389453i
$993$		0			0
$994$	5.55765	+	3.20871i	0.176278	+	0.101774i
$995$	−33.4297	+	16.8786i	−1.05979	+	0.535087i
$996$		0			0
$997$	6.14604	−	22.9373i	0.194647	−	0.726432i	−0.797711	−	0.603040i	$-0.793956\pi$
$997$	6.14604	−	22.9373i	0.194647	−	0.726432i	0.992358	−	0.123392i	$-0.0393774\pi$
$998$	8.82883	+	8.82883i	0.279472	+	0.279472i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.m.c.377.3		16
3.2	odd	2	inner	405.2.m.c.377.2		16
5.3	odd	4	inner	405.2.m.c.53.3		16
9.2	odd	6	inner	405.2.m.c.107.3		16
9.4	even	3		135.2.f.a.107.2	yes	8
9.5	odd	6		135.2.f.a.107.3	yes	8
9.7	even	3	inner	405.2.m.c.107.2		16
15.8	even	4	inner	405.2.m.c.53.2		16
36.23	even	6		2160.2.w.d.1457.2		8
36.31	odd	6		2160.2.w.d.1457.3		8
45.4	even	6		675.2.f.i.107.3		8
45.13	odd	12		135.2.f.a.53.3	yes	8
45.14	odd	6		675.2.f.i.107.2		8
45.22	odd	12		675.2.f.i.593.2		8
45.23	even	12		135.2.f.a.53.2	✓	8
45.32	even	12		675.2.f.i.593.3		8
45.38	even	12	inner	405.2.m.c.188.3		16
45.43	odd	12	inner	405.2.m.c.188.2		16
180.23	odd	12		2160.2.w.d.593.4		8
180.103	even	12		2160.2.w.d.593.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.f.a.53.2	✓	8	45.23	even	12
135.2.f.a.53.3	yes	8	45.13	odd	12
135.2.f.a.107.2	yes	8	9.4	even	3
135.2.f.a.107.3	yes	8	9.5	odd	6
405.2.m.c.53.2		16	15.8	even	4	inner
405.2.m.c.53.3		16	5.3	odd	4	inner
405.2.m.c.107.2		16	9.7	even	3	inner
405.2.m.c.107.3		16	9.2	odd	6	inner
405.2.m.c.188.2		16	45.43	odd	12	inner
405.2.m.c.188.3		16	45.38	even	12	inner
405.2.m.c.377.2		16	3.2	odd	2	inner
405.2.m.c.377.3		16	1.1	even	1	trivial
675.2.f.i.107.2		8	45.14	odd	6
675.2.f.i.107.3		8	45.4	even	6
675.2.f.i.593.2		8	45.22	odd	12
675.2.f.i.593.3		8	45.32	even	12
2160.2.w.d.593.1		8	180.103	even	12
2160.2.w.d.593.4		8	180.23	odd	12
2160.2.w.d.1457.2		8	36.23	even	6
2160.2.w.d.1457.3		8	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.m (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.441283 + 0.118242i) q^{2} +(-1.55130 - 0.895644i) q^{4} +(1.00781 + 1.99607i) q^{5} +(0.655657 - 2.44694i) q^{7} +(-1.22474 - 1.22474i) q^{8} +O(q^{10})\)	\(q+(0.441283 + 0.118242i) q^{2} +(-1.55130 - 0.895644i) q^{4} +(1.00781 + 1.99607i) q^{5} +(0.655657 - 2.44694i) q^{7} +(-1.22474 - 1.22474i) q^{8} +(0.208712 + 1.00000i) q^{10} +(4.80217 - 2.77253i) q^{11} +(0.655657 + 2.44694i) q^{13} +(0.578661 - 1.00227i) q^{14} +(1.39564 + 2.41733i) q^{16} +(1.87083 - 1.87083i) q^{17} -3.00000i q^{19} +(0.224351 - 3.99915i) q^{20} +(2.44694 - 0.655657i) q^{22} +(5.90166 - 1.58135i) q^{23} +(-2.96863 + 4.02334i) q^{25} +1.15732i q^{26} +(-3.20871 + 3.20871i) q^{28} +(2.19387 + 3.79990i) q^{29} +(0.500000 - 0.866025i) q^{31} +(1.22662 + 4.57781i) q^{32} +(1.04678 - 0.604356i) q^{34} +(5.54506 - 1.15732i) q^{35} +(-5.00000 - 5.00000i) q^{37} +(0.354725 - 1.32385i) q^{38} +(1.21037 - 3.67900i) q^{40} +(-4.80217 - 2.77253i) q^{41} +(-4.38318 - 1.17447i) q^{43} -9.93280 q^{44} +2.79129 q^{46} +(-0.882567 - 0.236483i) q^{47} +(0.504525 + 0.291288i) q^{49} +(-1.78573 + 1.42442i) q^{50} +(1.17447 - 4.38318i) q^{52} +(0.0674228 + 0.0674228i) q^{53} +(10.3739 + 6.79129i) q^{55} +(-3.79990 + 2.19387i) q^{56} +(0.518813 + 1.93624i) q^{58} +(-2.19387 + 3.79990i) q^{59} +(0.500000 + 0.866025i) q^{61} +(0.323042 - 0.323042i) q^{62} -3.41742i q^{64} +(-4.22350 + 3.77480i) q^{65} +(-11.7240 + 3.14144i) q^{67} +(-4.57781 + 1.22662i) q^{68} +(2.58379 + 0.144950i) q^{70} +5.54506i q^{71} +(-10.3739 + 10.3739i) q^{73} +(-1.61521 - 2.79763i) q^{74} +(-2.68693 + 4.65390i) q^{76} +(-3.63566 - 13.5685i) q^{77} +(9.16478 - 5.29129i) q^{79} +(-3.41862 + 5.22202i) q^{80} +(-1.79129 - 1.79129i) q^{82} +(-3.18737 + 11.8954i) q^{83} +(5.61976 + 1.84887i) q^{85} +(-1.79535 - 1.03655i) q^{86} +(-9.27707 - 2.48578i) q^{88} +16.6352 q^{89} +6.41742 q^{91} +(-10.5716 - 2.83265i) q^{92} +(-0.361500 - 0.208712i) q^{94} +(5.98822 - 3.02344i) q^{95} +(-1.31131 + 4.89389i) q^{97} +(0.188196 + 0.188196i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{7}+O(q^{10}) \) 16 * q + 4 * q^7	\( 16 q + 4 q^{7} + 40 q^{10} + 4 q^{13} + 4 q^{16} - 4 q^{22} + 16 q^{25} - 88 q^{28} + 8 q^{31} - 80 q^{37} + 12 q^{40} - 44 q^{43} + 8 q^{46} - 44 q^{52} + 56 q^{55} - 48 q^{58} + 8 q^{61} - 32 q^{67} + 48 q^{70} - 56 q^{73} + 12 q^{76} + 8 q^{82} + 28 q^{85} - 36 q^{88} + 176 q^{91} - 8 q^{97}+O(q^{100}) \) 16 * q + 4 * q^7 + 40 * q^10 + 4 * q^13 + 4 * q^16 - 4 * q^22 + 16 * q^25 - 88 * q^28 + 8 * q^31 - 80 * q^37 + 12 * q^40 - 44 * q^43 + 8 * q^46 - 44 * q^52 + 56 * q^55 - 48 * q^58 + 8 * q^61 - 32 * q^67 + 48 * q^70 - 56 * q^73 + 12 * q^76 + 8 * q^82 + 28 * q^85 - 36 * q^88 + 176 * q^91 - 8 * q^97

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