LMFDB - Embedded newform 324.2.l.a.35.10

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			35.10
Character	$\chi$	$=$	324.35
Dual form			324.2.l.a.287.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.419899 + 1.35044i) q^{2} +(-1.64737 + 1.13410i) q^{4} +(0.847966 - 2.32977i) q^{5} +(4.59553 + 0.810316i) q^{7} +(-2.22326 - 1.74846i) q^{8} +O(q^{10})$	\(q+(0.419899 + 1.35044i) q^{2} +(-1.64737 + 1.13410i) q^{4} +(0.847966 - 2.32977i) q^{5} +(4.59553 + 0.810316i) q^{7} +(-2.22326 - 1.74846i) q^{8} +(3.50227 + 0.166858i) q^{10} +(2.23250 - 0.812562i) q^{11} +(-1.53462 + 1.28770i) q^{13} +(0.835378 + 6.54624i) q^{14} +(1.42765 - 3.73655i) q^{16} +(-1.59381 + 0.920188i) q^{17} +(1.56341 + 0.902634i) q^{19} +(1.24527 + 4.79966i) q^{20} +(2.03474 + 2.67365i) q^{22} +(0.496152 + 2.81382i) q^{23} +(-0.878547 - 0.737189i) q^{25} +(-2.38335 - 1.53171i) q^{26} +(-8.48951 + 3.87689i) q^{28} +(-4.19826 + 5.00329i) q^{29} +(0.704699 - 0.124257i) q^{31} +(5.64545 + 0.358978i) q^{32} +(-1.91190 - 1.76596i) q^{34} +(5.78470 - 10.0194i) q^{35} +(-5.60913 - 9.71530i) q^{37} +(-0.562478 + 2.49030i) q^{38} +(-5.95876 + 3.69703i) q^{40} +(-4.52704 - 5.39511i) q^{41} +(-0.206872 - 0.568377i) q^{43} +(-2.75622 + 3.87045i) q^{44} +(-3.59156 + 1.85154i) q^{46} +(-0.587034 + 3.32923i) q^{47} +(13.8845 + 5.05353i) q^{49} +(0.626627 - 1.49597i) q^{50} +(1.06771 - 3.86173i) q^{52} -5.16402i q^{53} -5.89022i q^{55} +(-8.80024 - 9.83667i) q^{56} +(-8.51948 - 3.56861i) q^{58} +(-7.69223 - 2.79974i) q^{59} +(1.01407 - 5.75108i) q^{61} +(0.463705 + 0.899477i) q^{62} +(1.88574 + 7.77457i) q^{64} +(1.69874 + 4.66724i) q^{65} +(0.427623 + 0.509621i) q^{67} +(1.58202 - 3.32343i) q^{68} +(15.9596 + 3.60475i) q^{70} +(0.933575 + 1.61700i) q^{71} +(0.519326 - 0.899498i) q^{73} +(10.7647 - 11.6542i) q^{74} +(-3.59918 + 0.286084i) q^{76} +(10.9179 - 1.92513i) q^{77} +(-8.75072 + 10.4287i) q^{79} +(-7.49470 - 6.49456i) q^{80} +(5.38487 - 8.37889i) q^{82} +(2.22145 + 1.86402i) q^{83} +(0.792326 + 4.49350i) q^{85} +(0.680692 - 0.518029i) q^{86} +(-6.38415 - 2.09691i) q^{88} +(9.13625 + 5.27482i) q^{89} +(-8.09585 + 4.67414i) q^{91} +(-4.00849 - 4.07271i) q^{92} +(-4.74242 + 0.605190i) q^{94} +(3.42864 - 2.87697i) q^{95} +(-14.6120 + 5.31834i) q^{97} +(-0.994407 + 20.8721i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.419899	+	1.35044i	0.296914	+	0.954904i
$2$	0.419899	+	1.35044i	0.296914	+	0.954904i
$3$		0			0
$3$		0			0
$4$	−1.64737	+	1.13410i	−0.823685	+	0.567048i
$5$	0.847966	−	2.32977i	0.379222	−	1.04190i	−0.592458	−	0.805602i	$-0.701842\pi$
$5$	0.847966	−	2.32977i	0.379222	−	1.04190i	0.971680	−	0.236302i	$-0.0759355\pi$
$6$		0			0
$7$	4.59553	+	0.810316i	1.73695	+	0.306271i	0.950347	−	0.311191i	$-0.100728\pi$
$7$	4.59553	+	0.810316i	1.73695	+	0.306271i	0.786601	+	0.617462i	$0.211839\pi$
$8$	−2.22326	−	1.74846i	−0.786040	−	0.618176i
$9$		0			0
$10$	3.50227	+	0.166858i	1.10751	+	0.0527652i
$11$	2.23250	−	0.812562i	0.673123	−	0.244997i	0.0172309	−	0.999852i	$-0.494515\pi$
$11$	2.23250	−	0.812562i	0.673123	−	0.244997i	0.655892	+	0.754855i	$0.272293\pi$
$12$		0			0
$13$	−1.53462	+	1.28770i	−0.425628	+	0.357144i	−0.830299	−	0.557318i	$-0.811830\pi$
$13$	−1.53462	+	1.28770i	−0.425628	+	0.357144i	0.404671	+	0.914462i	$0.367386\pi$
$14$	0.835378	+	6.54624i	0.223264	+	1.74956i
$15$		0			0
$16$	1.42765	−	3.73655i	0.356912	−	0.934138i
$17$	−1.59381	+	0.920188i	−0.386556	+	0.223178i	−0.680667	−	0.732593i	$-0.738310\pi$
$17$	−1.59381	+	0.920188i	−0.386556	+	0.223178i	0.294111	+	0.955771i	$0.404977\pi$
$18$		0			0
$19$	1.56341	+	0.902634i	0.358670	+	0.207078i	0.668497	−	0.743715i	$-0.266938\pi$
$19$	1.56341	+	0.902634i	0.358670	+	0.207078i	−0.309827	+	0.950793i	$0.600271\pi$
$20$	1.24527	+	4.79966i	0.278450	+	1.07324i
$21$		0			0
$22$	2.03474	+	2.67365i	0.433808	+	0.570025i
$23$	0.496152	+	2.81382i	0.103455	+	0.586722i	0.991826	+	0.127596i	$0.0407261\pi$
$23$	0.496152	+	2.81382i	0.103455	+	0.586722i	−0.888371	+	0.459126i	$0.848163\pi$
$24$		0			0
$25$	−0.878547	−	0.737189i	−0.175709	−	0.147438i
$26$	−2.38335	−	1.53171i	−0.467413	−	0.300393i
$27$		0			0
$28$	−8.48951	+	3.87689i	−1.60437	+	0.732663i
$29$	−4.19826	+	5.00329i	−0.779597	+	0.929088i	−0.998915	−	0.0465658i	$-0.985172\pi$
$29$	−4.19826	+	5.00329i	−0.779597	+	0.929088i	0.219318	+	0.975653i	$0.429617\pi$
$30$		0			0
$31$	0.704699	−	0.124257i	0.126568	−	0.0223173i	−0.110005	−	0.993931i	$-0.535087\pi$
$31$	0.704699	−	0.124257i	0.126568	−	0.0223173i	0.236573	+	0.971614i	$0.423976\pi$
$32$	5.64545	+	0.358978i	0.997984	+	0.0634590i
$33$		0			0
$34$	−1.91190	−	1.76596i	−0.327888	−	0.302860i
$35$	5.78470	−	10.0194i	0.977793	−	1.69359i
$36$		0			0
$37$	−5.60913	−	9.71530i	−0.922136	−	1.59719i	−0.796104	−	0.605160i	$-0.793109\pi$
$37$	−5.60913	−	9.71530i	−0.922136	−	1.59719i	−0.126032	−	0.992026i	$-0.540224\pi$
$38$	−0.562478	+	2.49030i	−0.0912459	+	0.403980i
$39$		0			0
$40$	−5.95876	+	3.69703i	−0.942163	+	0.584552i
$41$	−4.52704	−	5.39511i	−0.707005	−	0.842575i	0.286295	−	0.958141i	$-0.407576\pi$
$41$	−4.52704	−	5.39511i	−0.707005	−	0.842575i	−0.993300	+	0.115566i	$0.963132\pi$
$42$		0			0
$43$	−0.206872	−	0.568377i	−0.0315477	−	0.0866766i	0.922919	−	0.384995i	$-0.125797\pi$
$43$	−0.206872	−	0.568377i	−0.0315477	−	0.0866766i	−0.954467	+	0.298318i	$0.903574\pi$
$44$	−2.75622	+	3.87045i	−0.415516	+	0.583493i
$45$		0			0
$46$	−3.59156	+	1.85154i	−0.529546	+	0.272995i
$47$	−0.587034	+	3.32923i	−0.0856277	+	0.485619i	0.911592	+	0.411097i	$0.134854\pi$
$47$	−0.587034	+	3.32923i	−0.0856277	+	0.485619i	−0.997219	+	0.0745219i	$0.976257\pi$
$48$		0			0
$49$	13.8845	+	5.05353i	1.98349	+	0.721933i
$50$	0.626627	−	1.49597i	0.0886184	−	0.211562i
$51$		0			0
$52$	1.06771	−	3.86173i	0.148065	−	0.535525i
$53$		−	5.16402i		−	0.709333i	−0.934993	−	0.354667i	$-0.884594\pi$
$53$		−	5.16402i		−	0.709333i	0.934993	−	0.354667i	$-0.115406\pi$
$54$		0			0
$55$		−	5.89022i		−	0.794237i
$56$	−8.80024	−	9.83667i	−1.17598	−	1.31448i
$57$		0			0
$58$	−8.51948	−	3.56861i	−1.11866	−	0.468582i
$59$	−7.69223	−	2.79974i	−1.00144	−	0.364496i	−0.211302	−	0.977421i	$-0.567770\pi$
$59$	−7.69223	−	2.79974i	−1.00144	−	0.364496i	−0.790141	+	0.612925i	$0.789993\pi$
$60$		0			0
$61$	1.01407	−	5.75108i	0.129838	−	0.736350i	−0.848478	−	0.529231i	$-0.822480\pi$
$61$	1.01407	−	5.75108i	0.129838	−	0.736350i	0.978316	−	0.207118i	$-0.0664086\pi$
$62$	0.463705	+	0.899477i	0.0588906	+	0.114234i
$63$		0			0
$64$	1.88574	+	7.77457i	0.235718	+	0.971822i
$65$	1.69874	+	4.66724i	0.210702	+	0.578900i
$66$		0			0
$67$	0.427623	+	0.509621i	0.0522424	+	0.0622601i	0.791533	−	0.611127i	$-0.209283\pi$
$67$	0.427623	+	0.509621i	0.0522424	+	0.0622601i	−0.739290	+	0.673387i	$0.764839\pi$
$68$	1.58202	−	3.32343i	0.191848	−	0.403025i
$69$		0			0
$70$	15.9596	+	3.60475i	1.90753	+	0.430850i
$71$	0.933575	+	1.61700i	0.110795	+	0.191902i	0.916091	−	0.400970i	$-0.131327\pi$
$71$	0.933575	+	1.61700i	0.110795	+	0.191902i	−0.805296	+	0.592873i	$0.797994\pi$
$72$		0			0
$73$	0.519326	−	0.899498i	0.0607825	−	0.105278i	−0.834033	−	0.551715i	$-0.813974\pi$
$73$	0.519326	−	0.899498i	0.0607825	−	0.105278i	0.894815	+	0.446436i	$0.147307\pi$
$74$	10.7647	−	11.6542i	1.25137	−	1.35478i
$75$		0			0
$76$	−3.59918	+	0.286084i	−0.412855	+	0.0328161i
$77$	10.9179	−	1.92513i	1.24421	−	0.219389i
$78$		0			0
$79$	−8.75072	+	10.4287i	−0.984533	+	1.17332i	0.000332592		1.00000i	$0.499894\pi$
$79$	−8.75072	+	10.4287i	−0.984533	+	1.17332i	−0.984865	+	0.173321i	$0.944550\pi$
$80$	−7.49470	−	6.49456i	−0.837933	−	0.726114i
$81$		0			0
$82$	5.38487	−	8.37889i	0.594659	−	0.925294i
$83$	2.22145	+	1.86402i	0.243836	+	0.204602i	0.756513	−	0.653979i	$-0.226902\pi$
$83$	2.22145	+	1.86402i	0.243836	+	0.204602i	−0.512677	+	0.858582i	$0.671346\pi$
$84$		0			0
$85$	0.792326	+	4.49350i	0.0859398	+	0.487389i
$86$	0.680692	−	0.518029i	0.0734009	−	0.0558605i
$87$		0			0
$88$	−6.38415	−	2.09691i	−0.680552	−	0.223531i
$89$	9.13625	+	5.27482i	0.968441	+	0.559130i	0.898761	−	0.438440i	$-0.144469\pi$
$89$	9.13625	+	5.27482i	0.968441	+	0.559130i	0.0696802	+	0.997569i	$0.477802\pi$
$90$		0			0
$91$	−8.09585	+	4.67414i	−0.848676	+	0.489983i
$92$	−4.00849	−	4.07271i	−0.417914	−	0.424610i
$93$		0			0
$94$	−4.74242	+	0.605190i	−0.489143	+	0.0624206i
$95$	3.42864	−	2.87697i	0.351771	−	0.295171i
$96$		0			0
$97$	−14.6120	+	5.31834i	−1.48362	+	0.539995i	−0.951763	−	0.306836i	$-0.900730\pi$
$97$	−14.6120	+	5.31834i	−1.48362	+	0.539995i	−0.531862	+	0.846831i	$0.678508\pi$
$98$	−0.994407	+	20.8721i	−0.100450	+	2.10840i
$99$		0			0
$100$	2.28333	+	0.218064i	0.228333	+	0.0218064i
$101$	−7.77944	−	1.37173i	−0.774083	−	0.136492i	−0.227366	−	0.973809i	$-0.573011\pi$
$101$	−7.77944	−	1.37173i	−0.774083	−	0.136492i	−0.546717	+	0.837318i	$0.684123\pi$
$102$		0			0
$103$	3.66967	−	10.0823i	0.361584	−	0.993443i	−0.616886	−	0.787053i	$-0.711606\pi$
$103$	3.66967	−	10.0823i	0.361584	−	0.993443i	0.978470	−	0.206391i	$-0.0661718\pi$
$104$	5.66336	−	0.179658i	0.555338	−	0.0176169i
$105$		0			0
$106$	6.97370	−	2.16837i	0.677346	−	0.210611i
$107$	−12.7270			−1.23037			−0.615184	−	0.788384i	$-0.710918\pi$
$107$	−12.7270			−1.23037			−0.615184	+	0.788384i	$0.710918\pi$
$108$		0			0
$109$	−3.14870			−0.301591			−0.150795	−	0.988565i	$-0.548183\pi$
$109$	−3.14870			−0.301591			−0.150795	+	0.988565i	$0.548183\pi$
$110$	7.95438	−	2.47330i	0.758420	−	0.235820i
$111$		0			0
$112$	9.58860	−	16.0146i	0.906038	−	1.51324i
$113$	0.811474	−	2.22951i	0.0763371	−	0.209734i	−0.895654	−	0.444751i	$-0.853292\pi$
$113$	0.811474	−	2.22951i	0.0763371	−	0.209734i	0.971991	+	0.235017i	$0.0755144\pi$
$114$		0			0
$115$	6.97626	+	1.23010i	0.650540	+	0.114708i
$116$	1.24187	−	13.0035i	0.115305	−	1.20734i
$117$		0			0
$118$	0.550919	−	11.5635i	0.0507162	−	1.06451i
$119$	−8.07006	+	2.93726i	−0.739781	+	0.269258i
$120$		0			0
$121$	−4.10271	+	3.44258i	−0.372974	+	0.312962i
$122$	8.19228	−	1.04543i	0.741695	−	0.0946491i
$123$		0			0
$124$	−1.01998	+	1.00389i	−0.0915968	+	0.0901524i
$125$	8.27317	−	4.77652i	0.739975	−	0.427225i
$126$		0			0
$127$	−15.4897	−	8.94299i	−1.37449	−	0.793562i	−0.383000	−	0.923748i	$-0.625109\pi$
$127$	−15.4897	−	8.94299i	−1.37449	−	0.793562i	−0.991490	+	0.130186i	$0.958442\pi$
$128$	−9.70726	+	5.81112i	−0.858009	+	0.513635i
$129$		0			0
$130$	−5.58952	+	4.25381i	−0.490234	+	0.373084i
$131$	0.587315	+	3.33083i	0.0513140	+	0.291016i	0.999656	−	0.0262343i	$-0.00835158\pi$
$131$	0.587315	+	3.33083i	0.0513140	+	0.291016i	−0.948342	+	0.317250i	$0.897240\pi$
$132$		0			0
$133$	6.45327	+	5.41494i	0.559570	+	0.469535i
$134$	−0.508653	+	0.791468i	−0.0439410	+	0.0683724i
$135$		0			0
$136$	5.15237	+	0.740910i	0.441812	+	0.0635325i
$137$	−4.18635	+	4.98910i	−0.357664	+	0.426247i	−0.914633	−	0.404286i	$-0.867520\pi$
$137$	−4.18635	+	4.98910i	−0.357664	+	0.426247i	0.556968	+	0.830534i	$0.311964\pi$
$138$		0			0
$139$	3.77403	−	0.665463i	0.320109	−	0.0564438i	−0.0112850	−	0.999936i	$-0.503592\pi$
$139$	3.77403	−	0.665463i	0.320109	−	0.0564438i	0.331394	+	0.943492i	$0.392481\pi$
$140$	1.83343	+	23.0661i	0.154953	+	1.94944i
$141$		0			0
$142$	−1.79165	+	1.93971i	−0.150352	+	0.162777i
$143$	−2.37970	+	4.12176i	−0.199001	+	0.344679i
$144$		0			0
$145$	8.09652	+	14.0236i	0.672379	+	1.16460i
$146$	1.43278	+	0.323619i	0.118578	+	0.0267829i
$147$		0			0
$148$	20.2584	+	9.64339i	1.66523	+	0.792682i
$149$	−1.86523	−	2.22289i	−0.152805	−	0.182106i	0.684211	−	0.729284i	$-0.260147\pi$
$149$	−1.86523	−	2.22289i	−0.152805	−	0.182106i	−0.837016	+	0.547178i	$0.815702\pi$
$150$		0			0
$151$	−0.547815	−	1.50511i	−0.0445806	−	0.122484i	0.915405	−	0.402535i	$-0.131871\pi$
$151$	−0.547815	−	1.50511i	−0.0445806	−	0.122484i	−0.959985	+	0.280051i	$0.909649\pi$
$152$	−1.89763	−	4.74035i	−0.153918	−	0.384493i
$153$		0			0
$154$	7.18420	+	13.9356i	0.578919	+	1.12297i
$155$	0.308070	−	1.74715i	0.0247448	−	0.140335i
$156$		0			0
$157$	−7.36520	−	2.68071i	−0.587807	−	0.213944i	0.0309578	−	0.999521i	$-0.490144\pi$
$157$	−7.36520	−	2.68071i	−0.587807	−	0.213944i	−0.618765	+	0.785577i	$0.712366\pi$
$158$	−17.7577	−	7.43831i	−1.41273	−	0.591760i
$159$		0			0
$160$	5.62349	−	12.8482i	0.444576	−	1.01574i
$161$			13.3330i			1.05079i
$162$		0			0
$163$			12.5843i			0.985676i	0.870121	+	0.492838i	$0.164040\pi$
$163$			12.5843i			0.985676i	−0.870121	+	0.492838i	$0.835960\pi$
$164$	13.5763	+	3.75365i	1.06013	+	0.293110i
$165$		0			0
$166$	−1.58446	+	3.78263i	−0.122978	+	0.293589i
$167$	7.12937	+	2.59488i	0.551687	+	0.200798i	0.602796	−	0.797895i	$-0.294053\pi$
$167$	7.12937	+	2.59488i	0.551687	+	0.200798i	−0.0511090	+	0.998693i	$0.516276\pi$
$168$		0			0
$169$	−1.56053	+	8.85023i	−0.120041	+	0.680787i
$170$	−5.73550	+	2.95681i	−0.439893	+	0.226777i
$171$		0			0
$172$	0.985389	+	0.701713i	0.0751352	+	0.0535051i
$173$	0.820320	+	2.25381i	0.0623678	+	0.171354i	0.966963	−	0.254919i	$-0.0820487\pi$
$173$	0.820320	+	2.25381i	0.0623678	+	0.171354i	−0.904595	+	0.426273i	$0.859826\pi$
$174$		0			0
$175$	−3.44004	−	4.09968i	−0.260042	−	0.309906i
$176$	0.151043	−	9.50189i	0.0113853	−	0.716232i
$177$		0			0
$178$	−3.28701	+	14.5528i	−0.246372	+	1.09078i
$179$	12.3836	+	21.4490i	0.925593	+	1.60317i	0.790605	+	0.612326i	$0.209766\pi$
$179$	12.3836	+	21.4490i	0.925593	+	1.60317i	0.134988	+	0.990847i	$0.456901\pi$
$180$		0			0
$181$	10.8787	−	18.8424i	0.808605	−	1.40054i	−0.105225	−	0.994448i	$-0.533556\pi$
$181$	10.8787	−	18.8424i	0.808605	−	1.40054i	0.913830	−	0.406096i	$-0.133110\pi$
$182$	−9.71158	−	8.97028i	−0.719871	−	0.664921i
$183$		0			0
$184$	3.81679	−	7.12335i	0.281377	−	0.525140i
$185$	−27.3908	+	4.82973i	−2.01381	+	0.355089i
$186$		0			0
$187$	−2.81047	+	3.34939i	−0.205522	+	0.244931i
$188$	−2.80861	−	6.15023i	−0.204839	−	0.448552i
$189$		0			0
$190$	5.32486	+	3.42213i	0.386306	+	0.248268i
$191$	7.21505	+	6.05415i	0.522063	+	0.438063i	0.865350	−	0.501168i	$-0.167096\pi$
$191$	7.21505	+	6.05415i	0.522063	+	0.438063i	−0.343287	+	0.939230i	$0.611540\pi$
$192$		0			0
$193$	−0.963275	−	5.46301i	−0.0693381	−	0.393236i	−0.999650	−	0.0264657i	$-0.991575\pi$
$193$	−0.963275	−	5.46301i	−0.0693381	−	0.393236i	0.930312	−	0.366770i	$-0.119536\pi$
$194$	−13.3177	−	17.4995i	−0.956152	−	1.25639i
$195$		0			0
$196$	−28.6040	+	7.42129i	−2.04314	+	0.530092i
$197$	13.5445	+	7.81992i	0.965006	+	0.557146i	0.897710	−	0.440587i	$-0.145230\pi$
$197$	13.5445	+	7.81992i	0.965006	+	0.557146i	0.0672958	+	0.997733i	$0.478563\pi$
$198$		0			0
$199$	13.9609	−	8.06033i	0.989662	−	0.571382i	0.0844887	−	0.996424i	$-0.473074\pi$
$199$	13.9609	−	8.06033i	0.989662	−	0.571382i	0.905173	+	0.425043i	$0.139741\pi$
$200$	0.664288	+	3.17507i	0.0469723	+	0.224511i
$201$		0			0
$202$	−1.41415	−	11.0816i	−0.0994993	−	0.779702i
$203$	−23.3475	+	19.5909i	−1.63867	+	1.37501i
$204$		0			0
$205$	−16.4081	+	5.97207i	−1.14599	+	0.417108i
$206$	15.1565	+	0.722099i	1.05600	+	0.0503110i
$207$		0			0
$208$	2.62066	+	7.57258i	0.181710	+	0.525064i
$209$	4.22375	+	0.744760i	0.292163	+	0.0515162i
$210$		0			0
$211$	−3.29026	+	9.03991i	−0.226511	+	0.622333i	−0.999933	−	0.0115578i	$-0.996321\pi$
$211$	−3.29026	+	9.03991i	−0.226511	+	0.622333i	0.773423	+	0.633891i	$0.218543\pi$
$212$	5.85650	+	8.50706i	0.402226	+	0.584267i
$213$		0			0
$214$	−5.34407	−	17.1871i	−0.365313	−	1.17488i
$215$	−1.49961			−0.102272
$216$		0			0
$217$	3.33915			0.226677
$218$	−1.32214	−	4.25212i	−0.0895464	−	0.287990i
$219$		0			0
$220$	6.68008	+	9.70337i	0.450371	+	0.654201i
$221$	1.26097	−	3.46450i	0.0848222	−	0.233047i
$222$		0			0
$223$	10.1708	+	1.79339i	0.681088	+	0.120094i	0.503480	−	0.864007i	$-0.332053\pi$
$223$	10.1708	+	1.79339i	0.681088	+	0.120094i	0.177608	+	0.984101i	$0.443164\pi$
$224$	25.6530	+	6.22430i	1.71401	+	0.415878i
$225$		0			0
$226$	3.35155	+	0.159678i	0.222942	+	0.0106216i
$227$	12.4052	−	4.51512i	0.823362	−	0.299679i	0.104230	−	0.994553i	$-0.466762\pi$
$227$	12.4052	−	4.51512i	0.823362	−	0.299679i	0.719131	+	0.694874i	$0.244540\pi$
$228$		0			0
$229$	13.0462	−	10.9471i	0.862117	−	0.723402i	−0.100306	−	0.994957i	$-0.531982\pi$
$229$	13.0462	−	10.9471i	0.862117	−	0.723402i	0.962423	+	0.271555i	$0.0875377\pi$
$230$	1.26815	+	9.93754i	0.0836193	+	0.655262i
$231$		0			0
$232$	18.0819	−	3.78309i	1.18713	−	0.248372i
$233$	−15.8755	+	9.16572i	−1.04004	+	0.600467i	−0.919844	−	0.392284i	$-0.871685\pi$
$233$	−15.8755	+	9.16572i	−1.04004	+	0.600467i	−0.120194	+	0.992750i	$0.538352\pi$
$234$		0			0
$235$	7.25856	+	4.19073i	0.473496	+	0.273373i
$236$	15.8471	−	4.11152i	1.03156	−	0.267637i
$237$		0			0
$238$	−7.35521	−	9.66477i	−0.476767	−	0.626474i
$239$	−3.60534	−	20.4469i	−0.233210	−	1.32260i	−0.846350	−	0.532627i	$-0.821205\pi$
$239$	−3.60534	−	20.4469i	−0.233210	−	1.32260i	0.613140	−	0.789974i	$-0.289906\pi$
$240$		0			0
$241$	10.8109	+	9.07140i	0.696390	+	0.584340i	0.920744	−	0.390167i	$-0.127583\pi$
$241$	10.8109	+	9.07140i	0.696390	+	0.584340i	−0.224354	+	0.974508i	$0.572027\pi$
$242$	−6.37172	−	4.09492i	−0.409590	−	0.263231i
$243$		0			0
$244$	4.85173	+	10.6242i	0.310600	+	0.680145i
$245$	23.5471	−	28.0623i	1.50437	−	1.79284i
$246$		0			0
$247$	−3.56156	+	0.628000i	−0.226617	+	0.0399587i
$248$	−1.78399	−	0.955885i	−0.113283	−	0.0606988i
$249$		0			0
$250$	9.92429	+	9.16675i	0.627667	+	0.579756i
$251$	12.3464	−	21.3846i	0.779297	−	1.34978i	−0.153050	−	0.988218i	$-0.548910\pi$
$251$	12.3464	−	21.3846i	0.779297	−	1.34978i	0.932347	−	0.361564i	$-0.117757\pi$
$252$		0			0
$253$	3.39406	+	5.87868i	0.213383	+	0.369590i
$254$	5.57284	−	24.6731i	0.349671	−	1.54813i
$255$		0			0
$256$	−11.9236	−	10.6690i	−0.745227	−	0.666811i
$257$	13.4321	+	16.0077i	0.837868	+	0.998533i	0.999931	+	0.0117523i	$0.00374095\pi$
$257$	13.4321	+	16.0077i	0.837868	+	0.998533i	−0.162062	+	0.986780i	$0.551815\pi$
$258$		0			0
$259$	−17.9045	−	49.1922i	−1.11253	−	3.05665i
$260$	−8.09155	−	5.76214i	−0.501816	−	0.357352i
$261$		0			0
$262$	−4.25147	+	2.19175i	−0.262657	+	0.135407i
$263$	−0.464688	+	2.63538i	−0.0286539	+	0.162504i	−0.995777	−	0.0918040i	$-0.970737\pi$
$263$	−0.464688	+	2.63538i	−0.0286539	+	0.162504i	0.967123	+	0.254308i	$0.0818478\pi$
$264$		0			0
$265$	−12.0310	−	4.37892i	−0.739057	−	0.268995i
$266$	−4.60282	+	10.9885i	−0.282217	+	0.673747i
$267$		0			0
$268$	−1.28241	−	0.354568i	−0.0783358	−	0.0216587i
$269$		−	18.9582i		−	1.15590i	−0.816071	−	0.577952i	$-0.803852\pi$
$269$		−	18.9582i		−	1.15590i	0.816071	−	0.577952i	$-0.196148\pi$
$270$		0			0
$271$			7.16436i			0.435204i	0.976038	+	0.217602i	$0.0698234\pi$
$271$			7.16436i			0.435204i	−0.976038	+	0.217602i	$0.930177\pi$
$272$	1.16292	+	7.26907i	0.0705126	+	0.440752i
$273$		0			0
$274$	−8.49532	−	3.55849i	−0.513221	−	0.214976i
$275$	−2.56036	−	0.931896i	−0.154396	−	0.0561955i
$276$		0			0
$277$	2.95763	−	16.7735i	0.177707	−	1.00782i	−0.757266	−	0.653106i	$-0.773466\pi$
$277$	2.95763	−	16.7735i	0.177707	−	1.00782i	0.934973	−	0.354719i	$-0.115423\pi$
$278$	2.48338	+	4.81717i	0.148943	+	0.288914i
$279$		0			0
$280$	−30.3794	+	12.1614i	−1.81552	+	0.726780i
$281$	−8.47273	−	23.2786i	−0.505441	−	1.38869i	−0.885894	−	0.463887i	$-0.846454\pi$
$281$	−8.47273	−	23.2786i	−0.505441	−	1.38869i	0.380453	−	0.924800i	$-0.375768\pi$
$282$		0			0
$283$	4.75165	+	5.66279i	0.282456	+	0.336618i	0.888554	−	0.458772i	$-0.151710\pi$
$283$	4.75165	+	5.66279i	0.282456	+	0.336618i	−0.606098	+	0.795390i	$0.707266\pi$
$284$	−3.37177	−	1.60503i	−0.200078	−	0.0952410i
$285$		0			0
$286$	−6.56542	−	1.48291i	−0.388222	−	0.0876866i
$287$	−16.4324	−	28.4618i	−0.969974	−	1.68004i
$288$		0			0
$289$	−6.80651	+	11.7892i	−0.400383	+	0.693483i
$290$	−15.5383	+	16.8223i	−0.912438	+	0.987842i
$291$		0			0
$292$	0.164597	+	2.07077i	0.00963231	+	0.121183i
$293$	−2.00549	+	0.353621i	−0.117162	+	0.0206588i	−0.231922	−	0.972734i	$-0.574501\pi$
$293$	−2.00549	+	0.353621i	−0.117162	+	0.0206588i	0.114760	+	0.993393i	$0.463390\pi$
$294$		0			0
$295$	−13.0455	+	15.5470i	−0.759538	+	0.905183i
$296$	−4.51632	+	31.4070i	−0.262506	+	1.82549i
$297$		0			0
$298$	2.21867	−	3.45226i	0.128524	−	0.199984i
$299$	−4.38476	−	3.67925i	−0.253577	−	0.212777i
$300$		0			0
$301$	−0.490123	−	2.77962i	−0.0282502	−	0.160215i
$302$	1.80253	−	1.37179i	0.103724	−	0.0789374i
$303$		0			0
$304$	5.60474	−	4.55311i	0.321454	−	0.261139i
$305$	−12.5388	−	7.23926i	−0.717968	−	0.414519i
$306$		0			0
$307$	−7.15348	+	4.13006i	−0.408271	+	0.235715i	−0.690046	−	0.723765i	$-0.742410\pi$
$307$	−7.15348	+	4.13006i	−0.408271	+	0.235715i	0.281776	+	0.959480i	$0.409077\pi$
$308$	−15.8026	+	15.5534i	−0.900436	+	0.886237i
$309$		0			0
$310$	2.48878	−	0.317598i	0.141353	−	0.0180384i
$311$	17.7965	−	14.9330i	1.00915	−	0.846775i	0.0209220	−	0.999781i	$-0.493340\pi$
$311$	17.7965	−	14.9330i	1.00915	−	0.846775i	0.988225	+	0.153006i	$0.0488954\pi$
$312$		0			0
$313$	12.2324	−	4.45222i	0.691414	−	0.251654i	0.0276735	−	0.999617i	$-0.491190\pi$
$313$	12.2324	−	4.45222i	0.691414	−	0.251654i	0.663741	+	0.747963i	$0.268968\pi$
$314$	0.527496	−	11.0719i	0.0297683	−	0.624822i
$315$		0			0
$316$	2.58851	−	27.1041i	0.145615	−	1.52472i
$317$	5.90446	+	1.04112i	0.331628	+	0.0584749i	0.336983	−	0.941511i	$-0.390594\pi$
$317$	5.90446	+	1.04112i	0.331628	+	0.0584749i	−0.00535522	+	0.999986i	$0.501705\pi$
$318$		0			0
$319$	−5.30711	+	14.5812i	−0.297141	+	0.816389i
$320$	19.7120	+	2.19923i	1.10193	+	0.122941i
$321$		0			0
$322$	−18.0054	+	5.59853i	−1.00340	+	0.311994i
$323$	−3.32237			−0.184862
$324$		0			0
$325$	2.29752			0.127443
$326$	−16.9943	+	5.28412i	−0.941226	+	0.292661i
$327$		0			0
$328$	0.631604	+	19.9101i	0.0348745	+	1.09935i
$329$	−5.39547	+	14.8239i	−0.297462	+	0.817269i
$330$		0			0
$331$	20.0853	+	3.54158i	1.10399	+	0.194663i	0.695800	−	0.718236i	$-0.255050\pi$
$331$	20.0853	+	3.54158i	1.10399	+	0.194663i	0.408187	+	0.912898i	$0.366161\pi$
$332$	−5.77352	−	0.551386i	−0.316863	−	0.0302613i
$333$		0			0
$334$	−0.510606	+	10.7174i	−0.0279391	+	0.586428i
$335$	1.54991	−	0.564120i	0.0846805	−	0.0308212i
$336$		0			0
$337$	−0.423775	+	0.355590i	−0.0230845	+	0.0193702i	−0.654257	−	0.756272i	$-0.727018\pi$
$337$	−0.423775	+	0.355590i	−0.0230845	+	0.0193702i	0.631172	+	0.775643i	$0.282574\pi$
$338$	−12.6070	+	1.60880i	−0.685728	+	0.0875072i
$339$		0			0
$340$	−6.40132	−	6.50388i	−0.347160	−	0.352723i
$341$	1.47227	−	0.850016i	0.0797279	−	0.0460309i
$342$		0			0
$343$	31.4228	+	18.1420i	1.69667	+	0.979574i
$344$	−0.533856	+	1.62536i	−0.0287836	+	0.0876333i
$345$		0			0
$346$	−2.69918	+	2.05416i	−0.145109	+	0.110433i
$347$	−1.00594	−	5.70495i	−0.0540015	−	0.306258i	0.945829	−	0.324665i	$-0.105252\pi$
$347$	−1.00594	−	5.70495i	−0.0540015	−	0.306258i	−0.999831	+	0.0184072i	$0.994140\pi$
$348$		0			0
$349$	−8.36132	−	7.01598i	−0.447571	−	0.375557i	0.390962	−	0.920407i	$-0.372142\pi$
$349$	−8.36132	−	7.01598i	−0.447571	−	0.375557i	−0.838534	+	0.544850i	$0.816587\pi$
$350$	4.09189	−	6.36701i	0.218721	−	0.340331i
$351$		0			0
$352$	12.8951	−	3.78586i	0.687313	−	0.201787i
$353$	−20.7168	+	24.6893i	−1.10264	+	1.31408i	−0.157465	+	0.987525i	$0.550332\pi$
$353$	−20.7168	+	24.6893i	−1.10264	+	1.31408i	−0.945178	+	0.326554i	$0.894112\pi$
$354$		0			0
$355$	4.55887	−	0.803852i	0.241960	−	0.0426640i
$356$	−21.0329	+	1.67182i	−1.11474	+	0.0886063i
$357$		0			0
$358$	−23.7657	+	25.7297i	−1.25606	+	1.35986i
$359$	−12.4329	+	21.5345i	−0.656185	+	1.13655i	0.325410	+	0.945573i	$0.394498\pi$
$359$	−12.4329	+	21.5345i	−0.656185	+	1.13655i	−0.981595	+	0.190973i	$0.938836\pi$
$360$		0			0
$361$	−7.87050	−	13.6321i	−0.414237	−	0.717480i
$362$	30.0135	+	6.77906i	1.57747	+	0.356299i
$363$		0			0
$364$	8.03593	−	16.8815i	0.421197	−	0.884832i
$365$	−1.65525	−	1.97265i	−0.0866398	−	0.103253i
$366$		0			0
$367$	5.44785	+	14.9678i	0.284375	+	0.781315i	0.996827	+	0.0795941i	$0.0253624\pi$
$367$	5.44785	+	14.9678i	0.284375	+	0.781315i	−0.712452	+	0.701721i	$0.752415\pi$
$368$	11.2223	+	2.16325i	0.585003	+	0.112767i
$369$		0			0
$370$	−18.0236	−	34.9615i	−0.937003	−	1.81756i
$371$	4.18449	−	23.7314i	0.217248	−	1.23208i
$372$		0			0
$373$	−32.2490	−	11.7377i	−1.66979	−	0.607754i	−0.677936	−	0.735121i	$-0.737125\pi$
$373$	−32.2490	−	11.7377i	−1.66979	−	0.607754i	−0.991856	+	0.127367i	$0.959347\pi$
$374$	−5.70326	−	2.38896i	−0.294908	−	0.123530i
$375$		0			0
$376$	7.12617	−	6.37533i	0.367504	−	0.328783i
$377$		−	13.0843i		−	0.673874i
$378$		0			0
$379$		−	20.3118i		−	1.04335i	−0.853145	−	0.521673i	$-0.825308\pi$
$379$		−	20.3118i		−	1.04335i	0.853145	−	0.521673i	$-0.174692\pi$
$380$	−2.38548	+	8.62785i	−0.122372	+	0.442599i
$381$		0			0
$382$	−5.14616	+	12.2856i	−0.263300	+	0.628587i
$383$	23.4300	+	8.52782i	1.19722	+	0.435751i	0.862252	−	0.506480i	$-0.169053\pi$
$383$	23.4300	+	8.52782i	1.19722	+	0.435751i	0.334964	+	0.942231i	$0.391276\pi$
$384$		0			0
$385$	4.77294	−	27.0687i	0.243252	−	1.37955i
$386$	6.97298	−	3.59476i	0.354915	−	0.182968i
$387$		0			0
$388$	18.0399	−	25.3327i	0.915836	−	1.28607i
$389$	2.43782	+	6.69786i	0.123602	+	0.339595i	0.986026	−	0.166593i	$-0.0532765\pi$
$389$	2.43782	+	6.69786i	0.123602	+	0.339595i	−0.862423	+	0.506188i	$0.831054\pi$
$390$		0			0
$391$	−3.38002	−	4.02815i	−0.170935	−	0.203712i
$392$	−22.0328	−	35.5118i	−1.11282	−	1.79362i
$393$		0			0
$394$	−4.87300	+	21.5746i	−0.245498	+	1.08691i
$395$	16.8761	+	29.2303i	0.849131	+	1.47074i
$396$		0			0
$397$	−18.3887	+	31.8501i	−0.922901	+	1.59851i	−0.127997	+	0.991775i	$0.540855\pi$
$397$	−18.3887	+	31.8501i	−0.922901	+	1.59851i	−0.794903	+	0.606736i	$0.792478\pi$
$398$	16.7472	+	15.4688i	0.839459	+	0.775381i
$399$		0			0
$400$	−4.00880	+	2.23029i	−0.200440	+	0.111514i
$401$	36.2027	−	6.38352i	1.80788	−	0.318778i	0.835027	−	0.550209i	$-0.185452\pi$
$401$	36.2027	−	6.38352i	1.80788	−	0.318778i	0.972851	+	0.231431i	$0.0743408\pi$
$402$		0			0
$403$	−0.921440	+	1.09813i	−0.0459002	+	0.0547017i
$404$	14.3713	−	6.56290i	0.714998	−	0.326516i
$405$		0			0
$406$	−36.2598	−	23.3032i	−1.79955	−	1.15652i
$407$	−20.4167	−	17.1316i	−1.01202	−	0.849182i
$408$		0			0
$409$	1.78158	+	10.1038i	0.0880934	+	0.499602i	0.996646	+	0.0818323i	$0.0260772\pi$
$409$	1.78158	+	10.1038i	0.0880934	+	0.499602i	−0.908553	+	0.417770i	$0.862812\pi$
$410$	−14.9547	−	19.6505i	−0.738559	−	0.970470i
$411$		0			0
$412$	5.38905	+	20.7711i	0.265499	+	1.02332i
$413$	−33.0812	−	19.0994i	−1.62782	−	0.939822i
$414$		0			0
$415$	6.22644	−	3.59484i	0.305644	−	0.176464i
$416$	−9.12589	+	6.71876i	−0.447434	+	0.329414i
$417$		0			0
$418$	0.767795	+	6.01664i	0.0375541	+	0.294283i
$419$	24.0344	−	20.1673i	1.17416	−	0.985237i	0.174160	−	0.984717i	$-0.444279\pi$
$419$	24.0344	−	20.1673i	1.17416	−	0.985237i	1.00000		0.000519235i	$-0.000165278\pi$
$420$		0			0
$421$	19.3207	−	7.03216i	0.941634	−	0.342727i	0.174823	−	0.984600i	$-0.444065\pi$
$421$	19.3207	−	7.03216i	0.941634	−	0.342727i	0.766811	+	0.641873i	$0.221842\pi$
$422$	−13.5894	−	0.647440i	−0.661523	−	0.0315169i
$423$		0			0
$424$	−9.02911	+	11.4810i	−0.438493	+	0.557564i
$425$	2.07859	+	0.366512i	0.100827	+	0.0177784i
$426$		0			0
$427$	9.32038	−	25.6075i	0.451045	−	1.23924i
$428$	20.9661	−	14.4337i	1.01344	−	0.697678i
$429$		0			0
$430$	−0.629683	−	2.02513i	−0.0303660	−	0.0976602i
$431$	11.1277			0.536001			0.268000	−	0.963419i	$-0.413637\pi$
$431$	11.1277			0.536001			0.268000	+	0.963419i	$0.413637\pi$
$432$		0			0
$433$	3.88415			0.186660			0.0933301	−	0.995635i	$-0.470249\pi$
$433$	3.88415			0.186660			0.0933301	+	0.995635i	$0.470249\pi$
$434$	1.40211	+	4.50932i	0.0673034	+	0.216454i
$435$		0			0
$436$	5.18707	−	3.57093i	0.248416	−	0.171016i
$437$	−1.76416	+	4.84699i	−0.0843912	+	0.231863i
$438$		0			0
$439$	13.3089	+	2.34672i	0.635199	+	0.112003i	0.481970	−	0.876188i	$-0.339921\pi$
$439$	13.3089	+	2.34672i	0.635199	+	0.112003i	0.153230	+	0.988191i	$0.451033\pi$
$440$	−10.2988	+	13.0955i	−0.490978	+	0.624302i
$441$		0			0
$442$	5.20807	+	0.248128i	0.247723	+	0.0118022i
$443$	−7.47039	+	2.71900i	−0.354929	+	0.129184i	−0.513330	−	0.858191i	$-0.671588\pi$
$443$	−7.47039	+	2.71900i	−0.354929	+	0.129184i	0.158401	+	0.987375i	$0.449366\pi$
$444$		0			0
$445$	20.0363	−	16.8125i	0.949813	−	0.796988i
$446$	1.84886	+	14.4881i	0.0875458	+	0.686031i
$447$		0			0
$448$	2.36613	+	37.2563i	0.111789	+	1.76020i
$449$	9.00315	−	5.19797i	0.424885	−	0.245307i	−0.272280	−	0.962218i	$-0.587778\pi$
$449$	9.00315	−	5.19797i	0.424885	−	0.245307i	0.697165	+	0.716911i	$0.254444\pi$
$450$		0			0
$451$	−14.4905	−	8.36607i	−0.682329	−	0.393943i
$452$	1.19168	+	4.59311i	0.0560519	+	0.216042i
$453$		0			0
$454$	11.3063	+	14.8566i	0.530632	+	0.697253i
$455$	4.02466	+	22.8250i	0.188679	+	1.07005i
$456$		0			0
$457$	28.6354	+	24.0279i	1.33951	+	1.12398i	0.981753	+	0.190163i	$0.0609016\pi$
$457$	28.6354	+	24.0279i	1.33951	+	1.12398i	0.357753	+	0.933816i	$0.383543\pi$
$458$	20.2614	+	13.0214i	0.946754	+	0.608451i
$459$		0			0
$460$	−12.8875	+	5.88532i	−0.600884	+	0.274405i
$461$	8.60771	−	10.2583i	0.400901	−	0.477775i	−0.527393	−	0.849621i	$-0.676831\pi$
$461$	8.60771	−	10.2583i	0.400901	−	0.477775i	0.928294	+	0.371846i	$0.121275\pi$
$462$		0			0
$463$	−14.2689	+	2.51599i	−0.663131	+	0.116928i	−0.495076	−	0.868850i	$-0.664860\pi$
$463$	−14.2689	+	2.51599i	−0.663131	+	0.116928i	−0.168055	+	0.985778i	$0.553749\pi$
$464$	12.7014	+	22.8300i	0.589648	+	1.05985i
$465$		0			0
$466$	−19.0439	−	17.5902i	−0.882190	−	0.814851i
$467$	−19.0970	+	33.0769i	−0.883702	+	1.53062i	−0.0365086	+	0.999333i	$0.511624\pi$
$467$	−19.0970	+	33.0769i	−0.883702	+	1.53062i	−0.847194	+	0.531284i	$0.821710\pi$
$468$		0			0
$469$	1.55220	+	2.68849i	0.0716739	+	0.124143i
$470$	−2.61146	+	11.5619i	−0.120458	+	0.533312i
$471$		0			0
$472$	12.2066	+	19.6741i	0.561852	+	0.905576i
$473$	−0.923682	−	1.10080i	−0.0424710	−	0.0506149i
$474$		0			0
$475$	−0.708116	−	1.94553i	−0.0324906	−	0.0892672i
$476$	9.96323	−	13.9910i	0.456664	−	0.641276i
$477$		0			0
$478$	26.0984	−	13.4544i	1.19371	−	0.615392i
$479$	−5.21540	+	29.5780i	−0.238298	+	1.35145i	0.597259	+	0.802049i	$0.296257\pi$
$479$	−5.21540	+	29.5780i	−0.238298	+	1.35145i	−0.835556	+	0.549405i	$0.814855\pi$
$480$		0			0
$481$	21.1183	+	7.68644i	0.962912	+	0.350471i
$482$	−7.71089	+	18.4085i	−0.351221	+	0.838484i
$483$		0			0
$484$	2.85446	−	10.3241i	0.129748	−	0.469276i
$485$			38.5524i			1.75057i
$486$		0			0
$487$		−	14.9474i		−	0.677331i	−0.940907	−	0.338666i	$-0.890024\pi$
$487$		−	14.9474i		−	0.677331i	0.940907	−	0.338666i	$-0.109976\pi$
$488$	−12.3101	+	11.0131i	−0.557252	+	0.498538i
$489$		0			0
$490$	47.7839	+	20.0155i	2.15866	+	0.904210i
$491$	7.42871	+	2.70383i	0.335253	+	0.122022i	0.504161	−	0.863610i	$-0.331802\pi$
$491$	7.42871	+	2.70383i	0.335253	+	0.122022i	−0.168908	+	0.985632i	$0.554024\pi$
$492$		0			0
$493$	2.08727	−	11.8375i	0.0940059	−	0.533134i
$494$	−2.34357	−	4.54598i	−0.105442	−	0.204533i
$495$		0			0
$496$	0.541769	−	2.81054i	0.0243262	−	0.126197i
$497$	2.97999	+	8.18746i	0.133671	+	0.367258i
$498$		0			0
$499$	14.1617	+	16.8772i	0.633963	+	0.755528i	0.983404	−	0.181431i	$-0.0580728\pi$
$499$	14.1617	+	16.8772i	0.633963	+	0.755528i	−0.349440	+	0.936959i	$0.613628\pi$
$500$	−8.21193	+	17.2513i	−0.367249	+	0.771500i
$501$		0			0
$502$	34.0628	+	7.69367i	1.52030	+	0.343386i
$503$	−15.3597	−	26.6038i	−0.684855	−	1.18620i	−0.973482	−	0.228762i	$-0.926532\pi$
$503$	−15.3597	−	26.6038i	−0.684855	−	1.18620i	0.288628	−	0.957441i	$-0.406801\pi$
$504$		0			0
$505$	−9.79250	+	16.9611i	−0.435761	+	0.754759i
$506$	−6.51364	+	7.05192i	−0.289567	+	0.313496i
$507$		0			0
$508$	35.6595	−	2.83442i	1.58213	−	0.125757i
$509$	−17.3155	+	3.05319i	−0.767496	+	0.135330i	−0.543670	−	0.839299i	$-0.682966\pi$
$509$	−17.3155	+	3.05319i	−0.767496	+	0.135330i	−0.223826	+	0.974629i	$0.571855\pi$
$510$		0			0
$511$	3.11546	−	3.71286i	0.137820	−	0.164247i
$512$	9.40107	−	20.5820i	0.415473	−	0.909606i
$513$		0			0
$514$	−15.9773	+	24.8608i	−0.704729	+	1.09656i
$515$	−20.3778	−	17.0990i	−0.897952	−	0.753471i
$516$		0			0
$517$	1.39466	+	7.90950i	0.0613370	+	0.347859i
$518$	58.9129	−	44.8347i	2.58849	−	1.96992i
$519$		0			0
$520$	4.38378	−	13.3467i	0.192241	−	0.585289i
$521$	−22.6652	−	13.0858i	−0.992980	−	0.573297i	−0.0868161	−	0.996224i	$-0.527669\pi$
$521$	−22.6652	−	13.0858i	−0.992980	−	0.573297i	−0.906164	+	0.422927i	$0.861003\pi$
$522$		0			0
$523$	−7.08428	+	4.09011i	−0.309774	+	0.178848i	−0.646825	−	0.762638i	$-0.723904\pi$
$523$	−7.08428	+	4.09011i	−0.309774	+	0.178848i	0.337051	+	0.941486i	$0.390570\pi$
$524$	−4.74501	−	4.82104i	−0.207287	−	0.210608i
$525$		0			0
$526$	−3.75404	+	0.479060i	−0.163684	+	0.0208880i
$527$	−1.00882	+	0.846499i	−0.0439448	+	0.0368741i
$528$		0			0
$529$	13.9415	−	5.07430i	0.606153	−	0.220622i
$530$	0.861660	−	18.0858i	0.0374281	−	0.785597i
$531$		0			0
$532$	−16.7720	−	1.60177i	−0.727158	−	0.0694455i
$533$	13.8946	+	2.44999i	0.601841	+	0.106121i
$534$		0			0
$535$	−10.7921	+	29.6510i	−0.466583	+	1.28192i
$536$	−0.0596611	−	1.88070i	−0.00257697	−	0.0812339i
$537$		0			0
$538$	25.6019	−	7.96055i	1.10378	−	0.343204i
$539$	35.1033			1.51201
$540$		0			0
$541$	−7.80321			−0.335486			−0.167743	−	0.985831i	$-0.553648\pi$
$541$	−7.80321			−0.335486			−0.167743	+	0.985831i	$0.553648\pi$
$542$	−9.67503	+	3.00831i	−0.415578	+	0.129218i
$543$		0			0
$544$	−9.32812	+	4.62273i	−0.399940	+	0.198198i
$545$	−2.66999	+	7.33574i	−0.114370	+	0.314228i
$546$		0			0
$547$	−39.6028	−	6.98304i	−1.69329	−	0.298573i	−0.757950	−	0.652313i	$-0.773799\pi$
$547$	−39.6028	−	6.98304i	−1.69329	−	0.298573i	−0.935344	+	0.353740i	$0.884910\pi$
$548$	1.23835	−	12.9666i	0.0528995	−	0.553906i
$549$		0			0
$550$	0.183374	−	3.84892i	0.00781908	−	0.164118i
$551$	−11.0797	+	4.03269i	−0.472012	+	0.171798i
$552$		0			0
$553$	−48.6648	+	40.8346i	−2.06944	+	1.73646i
$554$	23.8936	−	3.04910i	1.01514	−	0.129544i
$555$		0			0
$556$	−5.46252	+	5.37638i	−0.231662	+	0.228009i
$557$	−27.5205	+	15.8890i	−1.16608	+	0.673238i	−0.952754	−	0.303742i	$-0.901764\pi$
$557$	−27.5205	+	15.8890i	−1.16608	+	0.673238i	−0.213329	+	0.976980i	$0.568431\pi$
$558$		0			0
$559$	1.04937	+	0.605854i	0.0443836	+	0.0256249i
$560$	−29.1795	−	35.9190i	−1.23306	−	1.51786i
$561$		0			0
$562$	27.8787	−	21.2166i	1.17599	−	0.894968i
$563$	4.72244	+	26.7823i	0.199027	+	1.12874i	0.906566	+	0.422064i	$0.138694\pi$
$563$	4.72244	+	26.7823i	0.199027	+	1.12874i	−0.707539	+	0.706675i	$0.750195\pi$
$564$		0			0
$565$	−4.50613	−	3.78109i	−0.189574	−	0.159072i
$566$	−5.65204	+	8.79461i	−0.237573	+	0.369665i
$567$		0			0
$568$	0.751688	−	5.22733i	0.0315401	−	0.219334i
$569$	10.7609	−	12.8243i	0.451121	−	0.537625i	−0.491771	−	0.870725i	$-0.663650\pi$
$569$	10.7609	−	12.8243i	0.451121	−	0.537625i	0.942892	+	0.333100i	$0.108095\pi$
$570$		0			0
$571$	16.5413	−	2.91668i	0.692233	−	0.122059i	0.183546	−	0.983011i	$-0.441242\pi$
$571$	16.5413	−	2.91668i	0.692233	−	0.122059i	0.508687	+	0.860952i	$0.330131\pi$
$572$	−0.754231	−	9.48887i	−0.0315360	−	0.396750i
$573$		0			0
$574$	31.5359	−	34.1420i	1.31628	−	1.42506i
$575$	1.63842	−	2.83783i	0.0683269	−	0.118346i
$576$		0			0
$577$	−1.22069	−	2.11429i	−0.0508179	−	0.0880192i	0.839497	−	0.543364i	$-0.182849\pi$
$577$	−1.22069	−	2.11429i	−0.0508179	−	0.0880192i	−0.890315	+	0.455344i	$0.849516\pi$
$578$	−18.7787	−	4.24149i	−0.781089	−	0.176423i
$579$		0			0
$580$	−29.2421	−	13.9198i	−1.21421	−	0.577988i
$581$	8.69830	+	10.3662i	0.360866	+	0.430064i
$582$		0			0
$583$	−4.19609	−	11.5287i	−0.173784	−	0.477468i
$584$	−2.72734	+	1.09179i	−0.112858	+	0.0451787i
$585$		0			0
$586$	−1.31965	−	2.55980i	−0.0545141	−	0.105744i
$587$	2.47253	−	14.0224i	0.102052	−	0.578766i	−0.890305	−	0.455365i	$-0.849509\pi$
$587$	2.47253	−	14.0224i	0.102052	−	0.578766i	0.992357	−	0.123401i	$-0.0393802\pi$
$588$		0			0
$589$	1.21389	+	0.441820i	0.0500175	+	0.0182049i
$590$	−26.4731	−	11.0890i	−1.08988	−	0.456525i
$591$		0			0
$592$	−44.3096	+	7.08876i	−1.82111	+	0.291346i
$593$		−	14.5479i		−	0.597412i	−0.954345	−	0.298706i	$-0.903445\pi$
$593$		−	14.5479i		−	0.597412i	0.954345	−	0.298706i	$-0.0965549\pi$
$594$		0			0
$595$			21.2921i			0.872890i
$596$	5.59369	+	1.54657i	0.229126	+	0.0633501i
$597$		0			0
$598$	3.12745	−	7.46627i	0.127891	−	0.305318i
$599$	−27.4921	−	10.0063i	−1.12330	−	0.408846i	−0.287442	−	0.957798i	$-0.592805\pi$
$599$	−27.4921	−	10.0063i	−1.12330	−	0.408846i	−0.835854	+	0.548952i	$0.815027\pi$
$600$		0			0
$601$	−1.13737	+	6.45037i	−0.0463945	+	0.263116i	−0.999178	−	0.0405338i	$-0.987094\pi$
$601$	−1.13737	+	6.45037i	−0.0463945	+	0.263116i	0.952784	+	0.303650i	$0.0982053\pi$
$602$	3.54791	−	1.82904i	0.144602	−	0.0745462i
$603$		0			0
$604$	2.60939	+	1.85820i	0.106175	+	0.0756089i
$605$	4.54146	+	12.4776i	0.184636	+	0.507285i
$606$		0			0
$607$	−21.3252	−	25.4144i	−0.865565	−	1.03154i	−0.999179	−	0.0405067i	$-0.987103\pi$
$607$	−21.3252	−	25.4144i	−0.865565	−	1.03154i	0.133614	−	0.991033i	$-0.457342\pi$
$608$	8.50212	+	5.65701i	0.344806	+	0.229422i
$609$		0			0
$610$	4.51116	−	19.9726i	0.182652	−	0.808667i
$611$	−3.38618	−	5.86504i	−0.136990	−	0.237274i
$612$		0			0
$613$	4.11508	−	7.12752i	0.166206	−	0.287878i	−0.770877	−	0.636984i	$-0.780182\pi$
$613$	4.11508	−	7.12752i	0.166206	−	0.287878i	0.937083	+	0.349107i	$0.113515\pi$
$614$	−8.58114	−	7.92613i	−0.346307	−	0.319872i
$615$		0			0
$616$	−27.6394	−	14.8096i	−1.11362	−	0.596695i
$617$	18.2737	−	3.22215i	0.735673	−	0.129719i	0.206756	−	0.978392i	$-0.433709\pi$
$617$	18.2737	−	3.22215i	0.735673	−	0.129719i	0.528917	+	0.848673i	$0.322598\pi$
$618$		0			0
$619$	8.14884	−	9.71141i	0.327530	−	0.390335i	−0.577001	−	0.816744i	$-0.695777\pi$
$619$	8.14884	−	9.71141i	0.327530	−	0.390335i	0.904530	+	0.426409i	$0.140222\pi$
$620$	1.47393	+	3.22758i	0.0591946	+	0.129623i
$621$		0			0
$622$	27.6389	+	17.7627i	1.10822	+	0.712220i
$623$	37.7117	+	31.6438i	1.51089	+	1.26778i
$624$		0			0
$625$	−5.10856	−	28.9721i	−0.204342	−	1.15888i
$626$	11.1488	+	14.6496i	0.445596	+	0.585515i
$627$		0			0
$628$	15.1734	−	3.93672i	0.605484	−	0.157092i
$629$	17.8798	+	10.3229i	0.712915	+	0.411602i
$630$		0			0
$631$	26.9805	−	15.5772i	1.07408	−	0.620119i	0.144785	−	0.989463i	$-0.453751\pi$
$631$	26.9805	−	15.5772i	1.07408	−	0.620119i	0.929293	+	0.369344i	$0.120418\pi$
$632$	37.6893	−	7.88536i	1.49920	−	0.313663i
$633$		0			0
$634$	1.07332	+	8.41078i	0.0426269	+	0.334035i
$635$	−33.9698	+	28.5041i	−1.34805	+	1.13115i
$636$		0			0
$637$	−27.8148	+	10.1238i	−1.10206	+	0.401118i
$638$	−21.9194	−	1.04431i	−0.867798	−	0.0413444i
$639$		0			0
$640$	5.30713	+	27.5433i	0.209783	+	1.08874i
$641$	31.4814	+	5.55103i	1.24344	+	0.219252i	0.756390	−	0.654121i	$-0.226961\pi$
$641$	31.4814	+	5.55103i	1.24344	+	0.219252i	0.487052	+	0.873373i	$0.338072\pi$
$642$		0			0
$643$	−10.2506	+	28.1633i	−0.404244	+	1.11065i	0.555925	+	0.831233i	$0.312364\pi$
$643$	−10.2506	+	28.1633i	−0.404244	+	1.11065i	−0.960169	+	0.279420i	$0.909858\pi$
$644$	−15.1209	−	21.9644i	−0.595849	−	0.865520i
$645$		0			0
$646$	−1.39506	−	4.48666i	−0.0548880	−	0.176525i
$647$	−1.60615			−0.0631443			−0.0315721	−	0.999501i	$-0.510051\pi$
$647$	−1.60615			−0.0631443			−0.0315721	+	0.999501i	$0.510051\pi$
$648$		0			0
$649$	−19.4478			−0.763394
$650$	0.964726	+	3.10266i	0.0378397	+	0.121696i
$651$		0			0
$652$	−14.2718	−	20.7309i	−0.558926	−	0.811886i
$653$	5.67960	−	15.6046i	0.222260	−	0.610654i	−0.777576	−	0.628790i	$-0.783551\pi$
$653$	5.67960	−	15.6046i	0.222260	−	0.610654i	0.999836	+	0.0181352i	$0.00577293\pi$
$654$		0			0
$655$	8.25808	+	1.45612i	0.322670	+	0.0568954i
$656$	−26.6221	+	9.21318i	−1.03942	+	0.359714i
$657$		0			0
$658$	−22.2843	−	1.06169i	−0.868734	−	0.0413890i
$659$	−22.5548	+	8.20928i	−0.878611	+	0.319788i	−0.741649	−	0.670788i	$-0.765956\pi$
$659$	−22.5548	+	8.20928i	−0.878611	+	0.319788i	−0.136962	+	0.990576i	$0.543734\pi$
$660$		0			0
$661$	0.722514	−	0.606261i	0.0281025	−	0.0235808i	−0.628628	−	0.777706i	$-0.716383\pi$
$661$	0.722514	−	0.606261i	0.0281025	−	0.0235808i	0.656731	+	0.754125i	$0.271939\pi$
$662$	3.65111	+	28.6110i	0.141904	+	1.11200i
$663$		0			0
$664$	−1.67968	−	8.02831i	−0.0651844	−	0.311559i
$665$	18.0877	−	10.4429i	0.701411	−	0.404960i
$666$		0			0
$667$	−16.1613	−	9.33075i	−0.625769	−	0.361288i
$668$	−14.6875	+	3.81067i	−0.568278	+	0.147439i
$669$		0			0
$670$	1.41262	+	1.85618i	0.0545741	+	0.0717106i
$671$	−2.40920	−	13.6632i	−0.0930061	−	0.527464i
$672$		0			0
$673$	−4.60299	−	3.86237i	−0.177432	−	0.148883i	0.549746	−	0.835332i	$-0.314724\pi$
$673$	−4.60299	−	3.86237i	−0.177432	−	0.148883i	−0.727179	+	0.686448i	$0.759169\pi$
$674$	−0.658145	−	0.422971i	−0.0253508	−	0.0162922i
$675$		0			0
$676$	−7.46624	−	16.3494i	−0.287163	−	0.628823i
$677$	2.76557	−	3.29588i	0.106290	−	0.126671i	−0.710277	−	0.703922i	$-0.751430\pi$
$677$	2.76557	−	3.29588i	0.106290	−	0.126671i	0.816567	+	0.577251i	$0.195875\pi$
$678$		0			0
$679$	−71.4595	+	12.6002i	−2.74236	+	0.483553i
$680$	6.09518	−	11.3756i	0.233740	−	0.436233i
$681$		0			0
$682$	1.76610	+	1.63129i	0.0676274	+	0.0624653i
$683$	−7.98799	+	13.8356i	−0.305652	+	0.529405i	−0.977406	−	0.211369i	$-0.932208\pi$
$683$	−7.98799	+	13.8356i	−0.305652	+	0.529405i	0.671754	+	0.740774i	$0.265541\pi$
$684$		0			0
$685$	8.07356	+	13.9838i	0.308475	+	0.534294i
$686$	−11.3052	+	50.0524i	−0.431634	+	1.91101i
$687$		0			0
$688$	−2.41911	−	0.0384544i	−0.0922277	−	0.00146606i
$689$	6.64972	+	7.92483i	0.253334	+	0.301912i
$690$		0			0
$691$	6.40655	+	17.6018i	0.243717	+	0.669606i	0.999884	+	0.0152277i	$0.00484732\pi$
$691$	6.40655	+	17.6018i	0.243717	+	0.669606i	−0.756167	+	0.654378i	$0.772930\pi$
$692$	−3.90741	−	2.78253i	−0.148537	−	0.105776i
$693$		0			0
$694$	7.28180	−	3.75396i	0.276413	−	0.142498i
$695$	1.64987	−	9.35690i	0.0625833	−	0.354927i
$696$		0			0
$697$	12.1798	+	4.43307i	0.461342	+	0.167915i
$698$	5.96374	−	14.2375i	0.225731	−	0.538896i
$699$		0			0
$700$	10.3164	+	2.85235i	0.389925	+	0.107809i
$701$		−	2.57851i		−	0.0973888i	−0.998814	−	0.0486944i	$-0.984494\pi$
$701$		−	2.57851i		−	0.0973888i	0.998814	−	0.0486944i	$-0.0155060\pi$
$702$		0			0
$703$		−	20.2520i		−	0.763818i
$704$	10.5272	+	15.8244i	0.396760	+	0.596405i
$705$		0			0
$706$	−42.0404	−	17.6097i	−1.58221	−	0.662751i
$707$	−34.6391	−	12.6076i	−1.30274	−	0.474158i
$708$		0			0
$709$	−5.73026	+	32.4979i	−0.215204	+	1.22048i	0.665347	+	0.746534i	$0.268284\pi$
$709$	−5.73026	+	32.4979i	−0.215204	+	1.22048i	−0.880552	+	0.473950i	$0.842828\pi$
$710$	2.99982	+	5.81894i	0.112581	+	0.218381i
$711$		0			0
$712$	−11.0894	−	27.7017i	−0.415593	−	1.03816i
$713$	0.699276	+	1.92124i	0.0261881	+	0.0719512i
$714$		0			0
$715$	7.58484	+	9.03926i	0.283657	+	0.338049i
$716$	−44.7256	−	21.2902i	−1.67147	−	0.795654i
$717$		0			0
$718$	−34.3016	−	7.74760i	−1.28012	−	0.289138i
$719$	−18.8429	−	32.6368i	−0.702721	−	1.21715i	−0.967508	−	0.252842i	$-0.918635\pi$
$719$	−18.8429	−	32.6368i	−0.702721	−	1.21715i	0.264787	−	0.964307i	$-0.414698\pi$
$720$		0			0
$721$	25.0340	−	43.3602i	0.932315	−	1.61482i
$722$	15.1045	−	16.3527i	0.562132	−	0.608586i
$723$		0			0
$724$	3.44793	+	43.3778i	0.128141	+	1.61213i
$725$	7.37674	−	1.30072i	0.273965	−	0.0483074i
$726$		0			0
$727$	−5.29383	+	6.30894i	−0.196337	+	0.233986i	−0.855227	−	0.518254i	$-0.826582\pi$
$727$	−5.29383	+	6.30894i	−0.196337	+	0.233986i	0.658889	+	0.752240i	$0.271027\pi$
$728$	26.1717	+	3.76349i	0.969989	+	0.139484i
$729$		0			0
$730$	1.96891	−	3.06363i	0.0728725	−	0.113390i
$731$	0.852729	+	0.715525i	0.0315393	+	0.0264646i
$732$		0			0
$733$	0.159851	+	0.906562i	0.00590425	+	0.0334846i	0.987618	−	0.156881i	$-0.0501438\pi$
$733$	0.159851	+	0.906562i	0.00590425	+	0.0334846i	−0.981713	+	0.190365i	$0.939033\pi$
$734$	−17.9256	+	13.6420i	−0.661646	+	0.503534i
$735$		0			0
$736$	1.79090	+	16.0634i	0.0660136	+	0.592104i
$737$	1.36876	+	0.790257i	0.0504191	+	0.0291095i
$738$		0			0
$739$	−21.9417	+	12.6681i	−0.807139	+	0.466002i	−0.845961	−	0.533244i	$-0.820973\pi$
$739$	−21.9417	+	12.6681i	−0.807139	+	0.466002i	0.0388223	+	0.999246i	$0.487639\pi$
$740$	39.6453	−	39.0201i	1.45739	−	1.43441i
$741$		0			0
$742$	33.8049	−	4.31391i	1.24102	−	0.158369i
$743$	16.8393	−	14.1298i	0.617773	−	0.518373i	−0.279330	−	0.960195i	$-0.590112\pi$
$743$	16.8393	−	14.1298i	0.617773	−	0.518373i	0.897103	+	0.441822i	$0.145668\pi$
$744$		0			0
$745$	−6.76046	+	2.46061i	−0.247684	+	0.0901497i
$746$	2.30968	−	48.4790i	0.0845634	−	1.77494i
$747$		0			0
$748$	0.831352	−	8.70502i	0.0303973	−	0.318287i
$749$	−58.4875	−	10.3129i	−2.13709	−	0.376826i
$750$		0			0
$751$	14.1809	−	38.9618i	0.517470	−	1.42174i	−0.355828	−	0.934551i	$-0.615801\pi$
$751$	14.1809	−	38.9618i	0.517470	−	1.42174i	0.873298	−	0.487186i	$-0.161977\pi$
$752$	11.6018	+	6.94646i	0.423073	+	0.253311i
$753$		0			0
$754$	17.6695	−	5.49407i	0.643485	−	0.200082i
$755$	−3.97108			−0.144523
$756$		0			0
$757$	2.67068			0.0970675			0.0485338	−	0.998822i	$-0.484545\pi$
$757$	2.67068			0.0970675			0.0485338	+	0.998822i	$0.484545\pi$
$758$	27.4298	−	8.52890i	0.996296	−	0.309784i
$759$		0			0
$760$	−12.6530	+	0.401390i	−0.458974	+	0.0145599i
$761$	0.975731	−	2.68080i	0.0353702	−	0.0971789i	−0.920750	−	0.390152i	$-0.872422\pi$
$761$	0.975731	−	2.68080i	0.0353702	−	0.0971789i	0.956121	+	0.292973i	$0.0946447\pi$
$762$		0			0
$763$	−14.4699	−	2.55144i	−0.523847	−	0.0923684i
$764$	−18.7518	−	1.79085i	−0.678418	−	0.0647907i
$765$		0			0
$766$	−1.67806	+	35.2216i	−0.0606307	+	1.27261i
$767$	15.4099	−	5.60875i	0.556419	−	0.202520i
$768$		0			0
$769$	16.8767	−	14.1612i	0.608590	−	0.510667i	−0.285604	−	0.958348i	$-0.592194\pi$
$769$	16.8767	−	14.1612i	0.608590	−	0.510667i	0.894194	+	0.447680i	$0.147750\pi$
$770$	38.5588	−	4.92056i	1.38956	−	0.177325i
$771$		0			0
$772$	7.78245	+	7.90714i	0.280096	+	0.284584i
$773$	25.5618	−	14.7581i	0.919396	−	0.530813i	0.0359534	−	0.999353i	$-0.488553\pi$
$773$	25.5618	−	14.7581i	0.919396	−	0.530813i	0.883442	+	0.468540i	$0.155220\pi$
$774$		0			0
$775$	−0.710712	−	0.410330i	−0.0255295	−	0.0147395i
$776$	41.7852	+	13.7246i	1.50000	+	0.492683i
$777$		0			0
$778$	−8.02141	+	6.10456i	−0.287581	+	0.218859i
$779$	−2.20779	−	12.5210i	−0.0791024	−	0.448612i
$780$		0			0
$781$	3.39811	+	2.85135i	0.121594	+	0.102029i
$782$	4.02050	−	6.25592i	0.143773	−	0.223711i
$783$		0			0
$784$	38.7049	−	44.6653i	1.38232	−	1.59519i
$785$	−12.4909	+	14.8860i	−0.445818	+	0.531306i
$786$		0			0
$787$	37.3662	−	6.58868i	1.33196	−	0.234861i	0.538060	−	0.842906i	$-0.319157\pi$
$787$	37.3662	−	6.58868i	1.33196	−	0.234861i	0.793902	+	0.608045i	$0.208046\pi$
$788$	−31.1813	+	2.47848i	−1.11079	+	0.0882920i
$789$		0			0
$790$	−32.3875	+	35.0640i	−1.15229	+	1.24752i
$791$	5.53576	−	9.58822i	0.196829	−	0.340918i
$792$		0			0
$793$	5.84945	+	10.1315i	0.207720	+	0.359782i
$794$	−50.7330	−	11.4589i	−1.80045	−	0.406662i
$795$		0			0
$796$	−13.8576	+	29.1113i	−0.491168	+	1.03182i
$797$	−16.1467	−	19.2429i	−0.571947	−	0.681619i	0.400083	−	0.916479i	$-0.368981\pi$
$797$	−16.1467	−	19.2429i	−0.571947	−	0.681619i	−0.972029	+	0.234860i	$0.924537\pi$
$798$		0			0
$799$	−2.12790	−	5.84636i	−0.0752797	−	0.206829i
$800$	−4.69516	−	4.47714i	−0.165999	−	0.158291i
$801$		0			0
$802$	23.8221	+	46.2091i	0.841186	+	1.63170i
$803$	0.428494	−	2.43011i	0.0151212	−	0.0857567i
$804$		0			0
$805$	31.0629	+	11.3060i	1.09482	+	0.398483i
$806$	−1.86987	−	0.783245i	−0.0658633	−	0.0275886i
$807$		0			0
$808$	14.8973	+	16.6518i	0.524085	+	0.585807i
$809$			17.5875i			0.618343i	0.951006	+	0.309171i	$0.100052\pi$
$809$			17.5875i			0.618343i	−0.951006	+	0.309171i	$0.899948\pi$
$810$		0			0
$811$			51.1104i			1.79473i	0.441292	+	0.897364i	$0.354520\pi$
$811$			51.1104i			1.79473i	−0.441292	+	0.897364i	$0.645480\pi$
$812$	16.2440	−	58.7517i	0.570052	−	2.06178i
$813$		0			0
$814$	14.5622	−	34.7650i	0.510406	−	1.21851i
$815$	29.3184	+	10.6710i	1.02698	+	0.373790i
$816$		0			0
$817$	0.189610	−	1.07533i	0.00663363	−	0.0376212i
$818$	−12.8965	+	6.64851i	−0.450916	+	0.232460i
$819$		0			0
$820$	20.2573	−	28.4466i	0.707417	−	0.993399i
$821$	3.57660	+	9.82664i	0.124824	+	0.342952i	0.986327	−	0.164801i	$-0.0526983\pi$
$821$	3.57660	+	9.82664i	0.124824	+	0.342952i	−0.861502	+	0.507753i	$0.830476\pi$
$822$		0			0
$823$	−14.7797	−	17.6137i	−0.515187	−	0.613976i	0.444249	−	0.895904i	$-0.353471\pi$
$823$	−14.7797	−	17.6137i	−0.515187	−	0.613976i	−0.959436	+	0.281927i	$0.909026\pi$
$824$	−25.7873	+	15.9994i	−0.898342	+	0.557364i
$825$		0			0
$826$	11.9019	−	52.6940i	0.414118	−	1.83346i
$827$	1.77573	+	3.07566i	0.0617483	+	0.106951i	0.895247	−	0.445570i	$-0.146999\pi$
$827$	1.77573	+	3.07566i	0.0617483	+	0.106951i	−0.833499	+	0.552521i	$0.813666\pi$
$828$		0			0
$829$	−1.40521	+	2.43389i	−0.0488049	+	0.0845326i	−0.889396	−	0.457138i	$-0.848875\pi$
$829$	−1.40521	+	2.43389i	−0.0488049	+	0.0845326i	0.840591	+	0.541670i	$0.182208\pi$
$830$	7.46908	+	6.89895i	0.259256	+	0.239466i
$831$		0			0
$832$	−12.9052	−	9.50276i	−0.447408	−	0.329449i
$833$	−26.7794	+	4.72193i	−0.927852	+	0.163605i
$834$		0			0
$835$	12.0909	−	14.4094i	0.418423	−	0.498658i
$836$	−7.80270	+	3.56324i	−0.269862	+	0.123237i
$837$		0			0
$838$	37.3267	+	23.9888i	1.28943	+	0.828680i
$839$	9.47819	+	7.95315i	0.327223	+	0.274573i	0.791567	−	0.611082i	$-0.209265\pi$
$839$	9.47819	+	7.95315i	0.327223	+	0.274573i	−0.464344	+	0.885655i	$0.653710\pi$
$840$		0			0
$841$	−2.37174	−	13.4508i	−0.0817840	−	0.463820i
$842$	17.6093	+	23.1386i	0.606855	+	0.797410i
$843$		0			0
$844$	−4.83186	−	18.6235i	−0.166320	−	0.641049i
$845$	19.2957	+	11.1404i	0.663792	+	0.383241i
$846$		0			0
$847$	−21.6437	+	12.4960i	−0.743687	+	0.429368i
$848$	−19.2956	−	7.37242i	−0.662615	−	0.253170i
$849$		0			0
$850$	0.377848	+	2.96091i	0.0129601	+	0.101558i
$851$	24.5541	−	20.6034i	0.841704	−	0.706274i
$852$		0			0
$853$	31.6292	−	11.5121i	1.08296	−	0.394167i	0.261954	−	0.965080i	$-0.415633\pi$
$853$	31.6292	−	11.5121i	1.08296	−	0.394167i	0.821010	+	0.570913i	$0.193411\pi$
$854$	38.4950	+	1.83402i	1.31727	+	0.0627587i
$855$		0			0
$856$	28.2955	+	22.2528i	0.967119	+	0.760583i
$857$	−25.5052	−	4.49725i	−0.871239	−	0.153623i	−0.279884	−	0.960034i	$-0.590296\pi$
$857$	−25.5052	−	4.49725i	−0.871239	−	0.153623i	−0.591356	+	0.806411i	$0.701407\pi$
$858$		0			0
$859$	9.04957	−	24.8635i	0.308767	−	0.848331i	−0.684130	−	0.729360i	$-0.739818\pi$
$859$	9.04957	−	24.8635i	0.308767	−	0.848331i	0.992898	−	0.118971i	$-0.0379597\pi$
$860$	2.47040	−	1.70070i	0.0842401	−	0.0579933i
$861$		0			0
$862$	4.67250	+	15.0272i	0.159146	+	0.511829i
$863$	−13.2516			−0.451090			−0.225545	−	0.974233i	$-0.572416\pi$
$863$	−13.2516			−0.451090			−0.225545	+	0.974233i	$0.572416\pi$
$864$		0			0
$865$	5.94646			0.202186
$866$	1.63095	+	5.24530i	0.0554220	+	0.178243i
$867$		0			0
$868$	−5.50082	+	3.78692i	−0.186710	+	0.128537i
$869$	−11.0620	+	30.3925i	−0.375252	+	1.03100i
$870$		0			0
$871$	−1.31248	−	0.231425i	−0.0444717	−	0.00784155i
$872$	7.00037	+	5.50539i	0.237062	+	0.186436i
$873$		0			0
$874$	−7.28633	−	0.347142i	−0.246464	−	0.0117423i
$875$	41.8901	−	15.2468i	1.41614	−	0.515434i
$876$		0			0
$877$	−23.4391	+	19.6678i	−0.791483	+	0.664133i	−0.946112	−	0.323840i	$-0.895026\pi$
$877$	−23.4391	+	19.6678i	−0.791483	+	0.664133i	0.154629	+	0.987973i	$0.450582\pi$
$878$	2.41930	+	18.9582i	0.0816474	+	0.639810i
$879$		0			0
$880$	−22.0091	−	8.40917i	−0.741927	−	0.283473i
$881$	18.5204	−	10.6927i	0.623967	−	0.360248i	−0.154445	−	0.988001i	$-0.549359\pi$
$881$	18.5204	−	10.6927i	0.623967	−	0.360248i	0.778412	+	0.627754i	$0.216026\pi$
$882$		0			0
$883$	−0.600783	−	0.346862i	−0.0202180	−	0.0116728i	0.489857	−	0.871803i	$-0.337049\pi$
$883$	−0.600783	−	0.346862i	−0.0202180	−	0.0116728i	−0.510075	+	0.860130i	$0.670382\pi$
$884$	1.85178	+	7.13737i	0.0622822	+	0.240056i
$885$		0			0
$886$	−6.80865	−	8.94659i	−0.228741	−	0.300567i
$887$	4.88382	+	27.6975i	0.163983	+	0.929992i	0.950107	+	0.311924i	$0.100973\pi$
$887$	4.88382	+	27.6975i	0.163983	+	0.929992i	−0.786125	+	0.618068i	$0.787916\pi$
$888$		0			0
$889$	−63.9368	−	53.6494i	−2.14437	−	1.79934i
$890$	31.1175	+	19.9983i	1.04306	+	0.670344i
$891$		0			0
$892$	−18.7890	+	8.58031i	−0.629101	+	0.287290i
$893$	−3.92285	+	4.67507i	−0.131273	+	0.156445i
$894$		0			0
$895$	60.4720	−	10.6629i	2.02136	−	0.356420i
$896$	−49.3189	+	18.8392i	−1.64763	+	0.629375i
$897$		0			0
$898$	10.8000	+	9.97558i	0.360399	+	0.332889i
$899$	−2.33681	+	4.04748i	−0.0779371	+	0.134991i
$900$		0			0
$901$	4.75188	+	8.23049i	0.158308	+	0.274197i
$902$	5.21333	−	23.0814i	0.173585	−	0.768526i
$903$		0			0
$904$	−5.70233	+	3.53793i	−0.189657	+	0.117670i
$905$	−34.6737	−	41.3225i	−1.15259	−	1.37361i
$906$		0			0
$907$	5.84900	+	16.0700i	0.194213	+	0.533596i	0.998129	−	0.0611474i	$-0.0194760\pi$
$907$	5.84900	+	16.0700i	0.194213	+	0.533596i	−0.803916	+	0.594743i	$0.797254\pi$
$908$	−15.3153	+	21.5068i	−0.508258	+	0.713727i
$909$		0			0
$910$	−29.1338	+	15.0192i	−0.965775	+	0.497883i
$911$	−7.12328	+	40.3981i	−0.236005	+	1.33845i	0.604482	+	0.796619i	$0.293380\pi$
$911$	−7.12328	+	40.3981i	−0.236005	+	1.33845i	−0.840487	+	0.541832i	$0.817731\pi$
$912$		0			0
$913$	6.47400	+	2.35634i	0.214258	+	0.0779836i
$914$	−20.4243	+	48.7596i	−0.675575	+	1.61282i
$915$		0			0
$916$	−9.07688	+	32.8295i	−0.299909	+	1.08472i
$917$			15.7829i			0.521196i
$918$		0			0
$919$			11.9455i			0.394044i	0.980399	+	0.197022i	$0.0631271\pi$
$919$			11.9455i			0.394044i	−0.980399	+	0.197022i	$0.936873\pi$
$920$	−13.3592	−	14.9326i	−0.440441	−	0.492313i
$921$		0			0
$922$	17.4675	+	7.31675i	0.575263	+	0.240964i
$923$	−3.51489	−	1.27932i	−0.115694	−	0.0421092i
$924$		0			0
$925$	−2.23412	+	12.6703i	−0.0734575	+	0.416598i
$926$	−9.38918	−	18.2128i	−0.308548	−	0.598509i
$927$		0			0
$928$	−25.4971	+	26.7388i	−0.836985	+	0.877743i
$929$	−18.9806	−	52.1487i	−0.622733	−	1.71094i	−0.700197	−	0.713950i	$-0.746905\pi$
$929$	−18.9806	−	52.1487i	−0.622733	−	1.71094i	0.0774640	−	0.996995i	$-0.475318\pi$
$930$		0			0
$931$	17.1456	+	20.4333i	0.561924	+	0.669675i
$932$	15.7580	−	33.1037i	0.516170	−	1.08435i
$933$		0			0
$934$	−52.6872	−	11.9003i	−1.72398	−	0.389390i
$935$	5.42011	+	9.38791i	0.177257	+	0.307017i
$936$		0			0
$937$	18.9064	−	32.7469i	0.617646	−	1.06979i	−0.372269	−	0.928125i	$-0.621420\pi$
$937$	18.9064	−	32.7469i	0.617646	−	1.06979i	0.989914	−	0.141669i	$-0.0452467\pi$
$938$	−2.97887	+	3.22505i	−0.0972636	+	0.105301i
$939$		0			0
$940$	−16.7102	+	1.32823i	−0.545027	+	0.0433219i
$941$	−0.275896	+	0.0486479i	−0.00899395	+	0.00158588i	−0.178143	−	0.984005i	$-0.557009\pi$
$941$	−0.275896	+	0.0486479i	−0.00899395	+	0.00158588i	0.169149	+	0.985590i	$0.445898\pi$
$942$		0			0
$943$	12.9348	−	15.4151i	0.421214	−	0.501984i
$944$	−21.4432	+	24.7454i	−0.697917	+	0.805393i
$945$		0			0
$946$	1.09871	−	1.70960i	0.0357222	−	0.0555840i
$947$	2.57807	+	2.16325i	0.0837759	+	0.0702963i	0.683714	−	0.729750i	$-0.260364\pi$
$947$	2.57807	+	2.16325i	0.0837759	+	0.0702963i	−0.599938	+	0.800047i	$0.704808\pi$
$948$		0			0
$949$	0.361316	+	2.04913i	0.0117288	+	0.0665175i
$950$	2.32999	−	1.77320i	0.0755947	−	0.0575301i
$951$		0			0
$952$	23.0775	+	7.57993i	0.747947	+	0.245667i
$953$	43.7288	+	25.2468i	1.41651	+	0.817825i	0.995991	−	0.0894568i	$-0.0285131\pi$
$953$	43.7288	+	25.2468i	1.41651	+	0.817825i	0.420523	+	0.907282i	$0.361846\pi$
$954$		0			0
$955$	20.2229	−	11.6757i	0.654397	−	0.377816i
$956$	29.1281	+	29.5948i	0.942070	+	0.957165i
$957$		0			0
$958$	−42.1332	+	5.37670i	−1.36126	+	0.173713i
$959$	−23.2813	+	19.5353i	−0.751791	+	0.630828i
$960$		0			0
$961$	−28.6493	+	10.4275i	−0.924171	+	0.336371i
$962$	−1.51250	+	31.7465i	−0.0487648	+	1.02355i
$963$		0			0
$964$	−28.0973	−	2.68337i	−0.904954	−	0.0864255i
$965$	−13.5444	−	2.38824i	−0.436008	−	0.0768800i
$966$		0			0
$967$	9.74534	−	26.7751i	0.313389	−	0.861029i	−0.678578	−	0.734529i	$-0.737403\pi$
$967$	9.74534	−	26.7751i	0.313389	−	0.861029i	0.991967	−	0.126500i	$-0.0403745\pi$
$968$	15.1406	−	0.480303i	0.486638	−	0.0154375i
$969$		0			0
$970$	−52.0626	+	16.1881i	−1.67163	+	0.519769i
$971$	47.1658			1.51362			0.756811	−	0.653633i	$-0.226756\pi$
$971$	47.1658			1.51362			0.756811	+	0.653633i	$0.226756\pi$
$972$		0			0
$973$	17.8829			0.573300
$974$	20.1855	−	6.27640i	0.646787	−	0.201109i
$975$		0			0
$976$	−20.0415	−	11.9996i	−0.641511	−	0.384099i
$977$	9.95994	−	27.3647i	0.318647	−	0.875475i	−0.672186	−	0.740382i	$-0.734645\pi$
$977$	9.95994	−	27.3647i	0.318647	−	0.875475i	0.990833	−	0.135093i	$-0.0431332\pi$
$978$		0			0
$979$	24.6828	+	4.35224i	0.788864	+	0.139098i
$980$	−6.96536	+	72.9337i	−0.222500	+	2.32978i
$981$		0			0
$982$	−0.532045	+	11.1673i	−0.0169782	+	0.356364i
$983$	−17.1941	+	6.25816i	−0.548408	+	0.199604i	−0.601339	−	0.798994i	$-0.705366\pi$
$983$	−17.1941	+	6.25816i	−0.548408	+	0.199604i	0.0529309	+	0.998598i	$0.483144\pi$
$984$		0			0
$985$	29.7039	−	24.9245i	0.946444	−	0.794161i
$986$	16.8623	−	2.15183i	0.537004	−	0.0685281i
$987$		0			0
$988$	5.15500	−	5.07370i	0.164002	−	0.161416i
$989$	1.49667	−	0.864102i	0.0475913	−	0.0274768i
$990$		0			0
$991$	13.9725	+	8.06700i	0.443850	+	0.256257i	0.705229	−	0.708979i	$-0.250844\pi$
$991$	13.9725	+	8.06700i	0.443850	+	0.256257i	−0.261379	+	0.965236i	$0.584177\pi$
$992$	4.02295	−	0.448518i	0.127729	−	0.0142405i
$993$		0			0
$994$	−9.80537	+	7.46220i	−0.311007	+	0.236687i
$995$	−6.94032	−	39.3605i	−0.220023	−	1.24781i
$996$		0			0
$997$	5.43694	+	4.56213i	0.172190	+	0.144484i	0.724810	−	0.688949i	$-0.241928\pi$
$997$	5.43694	+	4.56213i	0.172190	+	0.144484i	−0.552620	+	0.833433i	$0.686372\pi$
$998$	−16.8452	+	26.2112i	−0.533225	+	0.829701i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.l.a.35.10		96
3.2	odd	2		108.2.l.a.11.7	✓	96
4.3	odd	2	inner	324.2.l.a.35.1		96
9.2	odd	6		972.2.l.d.755.5		96
9.4	even	3		972.2.l.b.431.1		96
9.5	odd	6		972.2.l.c.431.16		96
9.7	even	3		972.2.l.a.755.12		96
12.11	even	2		108.2.l.a.11.16	yes	96
27.4	even	9		972.2.l.d.215.6		96
27.5	odd	18	inner	324.2.l.a.287.1		96
27.13	even	9		972.2.l.c.539.5		96
27.14	odd	18		972.2.l.b.539.12		96
27.22	even	9		108.2.l.a.59.16	yes	96
27.23	odd	18		972.2.l.a.215.11		96
36.7	odd	6		972.2.l.a.755.11		96
36.11	even	6		972.2.l.d.755.6		96
36.23	even	6		972.2.l.c.431.5		96
36.31	odd	6		972.2.l.b.431.12		96
108.23	even	18		972.2.l.a.215.12		96
108.31	odd	18		972.2.l.d.215.5		96
108.59	even	18	inner	324.2.l.a.287.10		96
108.67	odd	18		972.2.l.c.539.16		96
108.95	even	18		972.2.l.b.539.1		96
108.103	odd	18		108.2.l.a.59.7	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.11.7	✓	96	3.2	odd	2
108.2.l.a.11.16	yes	96	12.11	even	2
108.2.l.a.59.7	yes	96	108.103	odd	18
108.2.l.a.59.16	yes	96	27.22	even	9
324.2.l.a.35.1		96	4.3	odd	2	inner
324.2.l.a.35.10		96	1.1	even	1	trivial
324.2.l.a.287.1		96	27.5	odd	18	inner
324.2.l.a.287.10		96	108.59	even	18	inner
972.2.l.a.215.11		96	27.23	odd	18
972.2.l.a.215.12		96	108.23	even	18
972.2.l.a.755.11		96	36.7	odd	6
972.2.l.a.755.12		96	9.7	even	3
972.2.l.b.431.1		96	9.4	even	3
972.2.l.b.431.12		96	36.31	odd	6
972.2.l.b.539.1		96	108.95	even	18
972.2.l.b.539.12		96	27.14	odd	18
972.2.l.c.431.5		96	36.23	even	6
972.2.l.c.431.16		96	9.5	odd	6
972.2.l.c.539.5		96	27.13	even	9
972.2.l.c.539.16		96	108.67	odd	18
972.2.l.d.215.5		96	108.31	odd	18
972.2.l.d.215.6		96	27.4	even	9
972.2.l.d.755.5		96	9.2	odd	6
972.2.l.d.755.6		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)

\(f(q)\)	\(=\)	\(q+(0.419899 + 1.35044i) q^{2} +(-1.64737 + 1.13410i) q^{4} +(0.847966 - 2.32977i) q^{5} +(4.59553 + 0.810316i) q^{7} +(-2.22326 - 1.74846i) q^{8} +O(q^{10})\)	\(q+(0.419899 + 1.35044i) q^{2} +(-1.64737 + 1.13410i) q^{4} +(0.847966 - 2.32977i) q^{5} +(4.59553 + 0.810316i) q^{7} +(-2.22326 - 1.74846i) q^{8} +(3.50227 + 0.166858i) q^{10} +(2.23250 - 0.812562i) q^{11} +(-1.53462 + 1.28770i) q^{13} +(0.835378 + 6.54624i) q^{14} +(1.42765 - 3.73655i) q^{16} +(-1.59381 + 0.920188i) q^{17} +(1.56341 + 0.902634i) q^{19} +(1.24527 + 4.79966i) q^{20} +(2.03474 + 2.67365i) q^{22} +(0.496152 + 2.81382i) q^{23} +(-0.878547 - 0.737189i) q^{25} +(-2.38335 - 1.53171i) q^{26} +(-8.48951 + 3.87689i) q^{28} +(-4.19826 + 5.00329i) q^{29} +(0.704699 - 0.124257i) q^{31} +(5.64545 + 0.358978i) q^{32} +(-1.91190 - 1.76596i) q^{34} +(5.78470 - 10.0194i) q^{35} +(-5.60913 - 9.71530i) q^{37} +(-0.562478 + 2.49030i) q^{38} +(-5.95876 + 3.69703i) q^{40} +(-4.52704 - 5.39511i) q^{41} +(-0.206872 - 0.568377i) q^{43} +(-2.75622 + 3.87045i) q^{44} +(-3.59156 + 1.85154i) q^{46} +(-0.587034 + 3.32923i) q^{47} +(13.8845 + 5.05353i) q^{49} +(0.626627 - 1.49597i) q^{50} +(1.06771 - 3.86173i) q^{52} -5.16402i q^{53} -5.89022i q^{55} +(-8.80024 - 9.83667i) q^{56} +(-8.51948 - 3.56861i) q^{58} +(-7.69223 - 2.79974i) q^{59} +(1.01407 - 5.75108i) q^{61} +(0.463705 + 0.899477i) q^{62} +(1.88574 + 7.77457i) q^{64} +(1.69874 + 4.66724i) q^{65} +(0.427623 + 0.509621i) q^{67} +(1.58202 - 3.32343i) q^{68} +(15.9596 + 3.60475i) q^{70} +(0.933575 + 1.61700i) q^{71} +(0.519326 - 0.899498i) q^{73} +(10.7647 - 11.6542i) q^{74} +(-3.59918 + 0.286084i) q^{76} +(10.9179 - 1.92513i) q^{77} +(-8.75072 + 10.4287i) q^{79} +(-7.49470 - 6.49456i) q^{80} +(5.38487 - 8.37889i) q^{82} +(2.22145 + 1.86402i) q^{83} +(0.792326 + 4.49350i) q^{85} +(0.680692 - 0.518029i) q^{86} +(-6.38415 - 2.09691i) q^{88} +(9.13625 + 5.27482i) q^{89} +(-8.09585 + 4.67414i) q^{91} +(-4.00849 - 4.07271i) q^{92} +(-4.74242 + 0.605190i) q^{94} +(3.42864 - 2.87697i) q^{95} +(-14.6120 + 5.31834i) q^{97} +(-0.994407 + 20.8721i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) 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

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