LMFDB - Embedded newform 630.2.bv.c.397.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(73,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.73"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bv (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,12,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			397.1
Root			$-0.587308 - 2.01725i$ of defining polynomial
Character	$\chi$	$=$	630.397
Dual form			630.2.bv.c.73.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(1.38266 + 1.75735i) q^{5} +(2.58583 + 0.559876i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.79038 - 1.33961i) q^{10} +(1.83557 + 3.17930i) q^{11} +(-0.830578 - 0.830578i) q^{13} +(-2.64263 + 0.128464i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.761471 + 0.204036i) q^{17} +(-1.09461 + 1.89593i) q^{19} +(2.07609 + 0.830578i) q^{20} +(-2.59589 - 2.59589i) q^{22} +(-1.21791 - 4.54529i) q^{23} +(-1.17653 + 4.85961i) q^{25} +(1.01725 + 0.587308i) q^{26} +(2.51934 - 0.808050i) q^{28} -2.62236i q^{29} +(0.0359651 - 0.0207644i) q^{31} +(-0.258819 + 0.965926i) q^{32} -0.788333 q^{34} +(2.59142 + 5.31832i) q^{35} +(-0.248174 + 0.0664979i) q^{37} +(0.566614 - 2.11463i) q^{38} +(-2.22032 - 0.264946i) q^{40} +8.98026i q^{41} +(-0.474569 + 0.474569i) q^{43} +(3.17930 + 1.83557i) q^{44} +(2.35282 + 4.07520i) q^{46} +(-1.65648 - 6.18205i) q^{47} +(6.37308 + 2.89549i) q^{49} +(-0.121320 - 4.99853i) q^{50} +(-1.13459 - 0.304013i) q^{52} +(7.64413 + 2.04824i) q^{53} +(-3.04917 + 7.62161i) q^{55} +(-2.22435 + 1.43257i) q^{56} +(0.678717 + 2.53301i) q^{58} +(5.35616 + 9.27713i) q^{59} +(1.72539 + 0.996157i) q^{61} +(-0.0293654 + 0.0293654i) q^{62} -1.00000i q^{64} +(0.311210 - 2.60802i) q^{65} +(-1.71399 + 6.39671i) q^{67} +(0.761471 - 0.204036i) q^{68} +(-3.87960 - 4.46639i) q^{70} -8.11777 q^{71} +(2.55331 - 9.52910i) q^{73} +(0.222506 - 0.128464i) q^{74} +2.18923i q^{76} +(2.96647 + 9.24884i) q^{77} +(11.6145 + 6.70563i) q^{79} +(2.21323 - 0.318742i) q^{80} +(-2.32426 - 8.67427i) q^{82} +(-9.73033 - 9.73033i) q^{83} +(0.694291 + 1.62028i) q^{85} +(0.335571 - 0.581226i) q^{86} +(-3.54605 - 0.950161i) q^{88} +(0.715130 - 1.23864i) q^{89} +(-1.68272 - 2.61276i) q^{91} +(-3.32739 - 3.32739i) q^{92} +(3.20007 + 5.54268i) q^{94} +(-4.84527 + 0.697798i) q^{95} +(3.16693 - 3.16693i) q^{97} +(-6.90533 - 1.14736i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5} + 8 q^{7} - 12 q^{10} + 12 q^{11} + 8 q^{16} + 36 q^{17} - 8 q^{22} + 4 q^{23} + 12 q^{25} - 12 q^{26} + 4 q^{28} + 24 q^{31} - 8 q^{35} + 4 q^{37} - 24 q^{38} - 8 q^{43} - 8 q^{46} - 12 q^{47}+ \cdots - 40 q^{98}+O(q^{100}) $ 16 * q + 12 * q^5 + 8 * q^7 - 12 * q^10 + 12 * q^11 + 8 * q^16 + 36 * q^17 - 8 * q^22 + 4 * q^23 + 12 * q^25 - 12 * q^26 + 4 * q^28 + 24 * q^31 - 8 * q^35 + 4 * q^37 - 24 * q^38 - 8 * q^43 - 8 * q^46 - 12 * q^47 + 32 * q^50 + 28 * q^53 + 4 * q^56 - 32 * q^58 - 12 * q^61 + 8 * q^65 + 32 * q^67 + 36 * q^68 - 12 * q^70 - 16 * q^71 - 12 * q^73 - 16 * q^77 + 12 * q^80 - 48 * q^82 + 24 * q^85 - 12 * q^86 - 4 * q^88 - 16 * q^91 - 8 * q^92 - 20 * q^95 - 40 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	1.38266	+	1.75735i	0.618342	+	0.785909i
$5$	1.38266	+	1.75735i	0.618342	+	0.785909i
$6$		0			0
$7$	2.58583	+	0.559876i	0.977353	+	0.211613i
$7$	2.58583	+	0.559876i	0.977353	+	0.211613i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−1.79038	−	1.33961i	−0.566167	−	0.423621i
$11$	1.83557	+	3.17930i	0.553445	+	0.958596i	0.998023	+	0.0628551i	$0.0200206\pi$
$11$	1.83557	+	3.17930i	0.553445	+	0.958596i	−0.444577	+	0.895741i	$0.646646\pi$
$12$		0			0
$13$	−0.830578	−	0.830578i	−0.230361	−	0.230361i	0.582482	−	0.812843i	$-0.302082\pi$
$13$	−0.830578	−	0.830578i	−0.230361	−	0.230361i	−0.812843	+	0.582482i	$0.802082\pi$
$14$	−2.64263	+	0.128464i	−0.706273	+	0.0343335i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.761471	+	0.204036i	0.184684	+	0.0494859i	0.349976	−	0.936759i	$-0.386190\pi$
$17$	0.761471	+	0.204036i	0.184684	+	0.0494859i	−0.165292	+	0.986245i	$0.552857\pi$
$18$		0			0
$19$	−1.09461	+	1.89593i	−0.251122	+	0.434955i	−0.963835	−	0.266500i	$-0.914133\pi$
$19$	−1.09461	+	1.89593i	−0.251122	+	0.434955i	0.712713	+	0.701455i	$0.247466\pi$
$20$	2.07609	+	0.830578i	0.464227	+	0.185723i
$21$		0			0
$22$	−2.59589	−	2.59589i	−0.553445	−	0.553445i
$23$	−1.21791	−	4.54529i	−0.253951	−	0.947759i	−0.968671	−	0.248348i	$-0.920112\pi$
$23$	−1.21791	−	4.54529i	−0.253951	−	0.947759i	0.714719	−	0.699411i	$-0.246554\pi$
$24$		0			0
$25$	−1.17653	+	4.85961i	−0.235306	+	0.971921i
$26$	1.01725	+	0.587308i	0.199498	+	0.115180i
$27$		0			0
$28$	2.51934	−	0.808050i	0.476110	−	0.152707i
$29$		−	2.62236i		−	0.486960i	−0.969906	−	0.243480i	$-0.921711\pi$
$29$		−	2.62236i		−	0.486960i	0.969906	−	0.243480i	$-0.0782891\pi$
$30$		0			0
$31$	0.0359651	−	0.0207644i	0.00645952	−	0.00372940i	−0.496767	−	0.867884i	$-0.665480\pi$
$31$	0.0359651	−	0.0207644i	0.00645952	−	0.00372940i	0.503226	+	0.864155i	$0.332146\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$		0			0
$34$	−0.788333			−0.135198
$35$	2.59142	+	5.31832i	0.438030	+	0.898960i
$36$		0			0
$37$	−0.248174	+	0.0664979i	−0.0407995	+	0.0109322i	−0.279161	−	0.960244i	$-0.590056\pi$
$37$	−0.248174	+	0.0664979i	−0.0407995	+	0.0109322i	0.238362	+	0.971176i	$0.423390\pi$
$38$	0.566614	−	2.11463i	0.0919169	−	0.343038i
$39$		0			0
$40$	−2.22032	−	0.264946i	−0.351063	−	0.0418916i
$41$			8.98026i			1.40248i	0.712925	+	0.701241i	$0.247370\pi$
$41$			8.98026i			1.40248i	−0.712925	+	0.701241i	$0.752630\pi$
$42$		0			0
$43$	−0.474569	+	0.474569i	−0.0723711	+	0.0723711i	−0.742366	−	0.669995i	$-0.766296\pi$
$43$	−0.474569	+	0.474569i	−0.0723711	+	0.0723711i	0.669995	+	0.742366i	$0.266296\pi$
$44$	3.17930	+	1.83557i	0.479298	+	0.276723i
$45$		0			0
$46$	2.35282	+	4.07520i	0.346904	+	0.600855i
$47$	−1.65648	−	6.18205i	−0.241622	−	0.901745i	−0.975051	−	0.221980i	$-0.928748\pi$
$47$	−1.65648	−	6.18205i	−0.241622	−	0.901745i	0.733429	−	0.679766i	$-0.237919\pi$
$48$		0			0
$49$	6.37308	+	2.89549i	0.910440	+	0.413642i
$50$	−0.121320	−	4.99853i	−0.0171573	−	0.706899i
$51$		0			0
$52$	−1.13459	−	0.304013i	−0.157339	−	0.0421590i
$53$	7.64413	+	2.04824i	1.05000	+	0.281347i	0.742252	−	0.670120i	$-0.233758\pi$
$53$	7.64413	+	2.04824i	1.05000	+	0.281347i	0.307749	+	0.951468i	$0.400424\pi$
$54$		0			0
$55$	−3.04917	+	7.62161i	−0.411150	+	1.02770i
$56$	−2.22435	+	1.43257i	−0.297242	+	0.191435i
$57$		0			0
$58$	0.678717	+	2.53301i	0.0891199	+	0.332600i
$59$	5.35616	+	9.27713i	0.697312	+	1.20778i	0.969395	+	0.245506i	$0.0789541\pi$
$59$	5.35616	+	9.27713i	0.697312	+	1.20778i	−0.272083	+	0.962274i	$0.587713\pi$
$60$		0			0
$61$	1.72539	+	0.996157i	0.220914	+	0.127545i	0.606373	−	0.795180i	$-0.292624\pi$
$61$	1.72539	+	0.996157i	0.220914	+	0.127545i	−0.385459	+	0.922725i	$0.625957\pi$
$62$	−0.0293654	+	0.0293654i	−0.00372940	+	0.00372940i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	0.311210	−	2.60802i	0.0386008	−	0.323485i
$66$		0			0
$67$	−1.71399	+	6.39671i	−0.209398	+	0.781482i	0.778666	+	0.627438i	$0.215897\pi$
$67$	−1.71399	+	6.39671i	−0.209398	+	0.781482i	−0.988064	+	0.154044i	$0.950770\pi$
$68$	0.761471	−	0.204036i	0.0923420	−	0.0247430i
$69$		0			0
$70$	−3.87960	−	4.46639i	−0.463701	−	0.533836i
$71$	−8.11777			−0.963402			−0.481701	−	0.876336i	$-0.659981\pi$
$71$	−8.11777			−0.963402			−0.481701	+	0.876336i	$0.659981\pi$
$72$		0			0
$73$	2.55331	−	9.52910i	0.298843	−	1.11530i	−0.639274	−	0.768979i	$-0.720765\pi$
$73$	2.55331	−	9.52910i	0.298843	−	1.11530i	0.938117	−	0.346318i	$-0.112568\pi$
$74$	0.222506	−	0.128464i	0.0258658	−	0.0149336i
$75$		0			0
$76$			2.18923i			0.251122i
$77$	2.96647	+	9.24884i	0.338060	+	1.05400i
$78$		0			0
$79$	11.6145	+	6.70563i	1.30673	+	0.754443i	0.981550	−	0.191208i	$-0.0612405\pi$
$79$	11.6145	+	6.70563i	1.30673	+	0.754443i	0.325184	+	0.945651i	$0.394574\pi$
$80$	2.21323	−	0.318742i	0.247447	−	0.0356364i
$81$		0			0
$82$	−2.32426	−	8.67427i	−0.256672	−	0.957912i
$83$	−9.73033	−	9.73033i	−1.06804	−	1.06804i	−0.997509	−	0.0705331i	$-0.977530\pi$
$83$	−9.73033	−	9.73033i	−1.06804	−	1.06804i	−0.0705331	−	0.997509i	$-0.522470\pi$
$84$		0			0
$85$	0.694291	+	1.62028i	0.0753065	+	0.175744i
$86$	0.335571	−	0.581226i	0.0361855	−	0.0626752i
$87$		0			0
$88$	−3.54605	−	0.950161i	−0.378010	−	0.101288i
$89$	0.715130	−	1.23864i	0.0758036	−	0.131296i	−0.825632	−	0.564209i	$-0.809181\pi$
$89$	0.715130	−	1.23864i	0.0758036	−	0.131296i	0.901435	+	0.432914i	$0.142514\pi$
$90$		0			0
$91$	−1.68272	−	2.61276i	−0.176397	−	0.273892i
$92$	−3.32739	−	3.32739i	−0.346904	−	0.346904i
$93$		0			0
$94$	3.20007	+	5.54268i	0.330062	+	0.571684i
$95$	−4.84527	+	0.697798i	−0.497114	+	0.0715926i
$96$		0			0
$97$	3.16693	−	3.16693i	0.321553	−	0.321553i	−0.527810	−	0.849363i	$-0.676987\pi$
$97$	3.16693	−	3.16693i	0.321553	−	0.321553i	0.849363	+	0.527810i	$0.176987\pi$
$98$	−6.90533	−	1.14736i	−0.697544	−	0.115901i
$99$		0			0
$100$	1.41090	+	4.79681i	0.141090	+	0.479681i
$101$	0.0622734	−	0.0359536i	0.00619644	−	0.00357751i	−0.496899	−	0.867809i	$-0.665528\pi$
$101$	0.0622734	−	0.0359536i	0.00619644	−	0.00357751i	0.503095	+	0.864231i	$0.332195\pi$
$102$		0			0
$103$	−16.0148	+	4.29116i	−1.57799	+	0.422820i	−0.938302	−	0.345817i	$-0.887602\pi$
$103$	−16.0148	+	4.29116i	−1.57799	+	0.422820i	−0.639685	+	0.768638i	$0.720935\pi$
$104$	1.17462			0.115180
$105$		0			0
$106$	−7.91378			−0.768654
$107$	4.41372	−	1.18265i	0.426690	−	0.114331i	−0.0390819	−	0.999236i	$-0.512443\pi$
$107$	4.41372	−	1.18265i	0.426690	−	0.114331i	0.465772	+	0.884905i	$0.345777\pi$
$108$		0			0
$109$	15.6773	−	9.05131i	1.50162	−	0.866958i	0.501617	−	0.865090i	$-0.332739\pi$
$109$	15.6773	−	9.05131i	1.50162	−	0.866958i	0.999998	−	0.00186842i	$-0.000594737\pi$
$110$	0.972654	−	8.15110i	0.0927390	−	0.777176i
$111$		0			0
$112$	1.77778	−	1.95946i	0.167985	−	0.185152i
$113$	−1.52064	+	1.52064i	−0.143049	+	0.143049i	−0.775005	−	0.631955i	$-0.782253\pi$
$113$	−1.52064	+	1.52064i	−0.143049	+	0.143049i	0.631955	+	0.775005i	$0.282253\pi$
$114$		0			0
$115$	6.30371	−	8.42486i	0.587824	−	0.785622i
$116$	−1.31118	−	2.27103i	−0.121740	−	0.210860i
$117$		0			0
$118$	−7.57475	−	7.57475i	−0.697312	−	0.697312i
$119$	1.85480	+	0.953932i	0.170030	+	0.0874468i
$120$		0			0
$121$	−1.23864	+	2.14539i	−0.112604	+	0.195035i
$122$	−1.92443	−	0.515649i	−0.174229	−	0.0466846i
$123$		0			0
$124$	0.0207644	−	0.0359651i	0.00186470	−	0.00322976i
$125$	−10.1667	+	4.65160i	−0.909341	+	0.416051i
$126$		0			0
$127$	−13.2527	−	13.2527i	−1.17599	−	1.17599i	−0.980757	−	0.195234i	$-0.937453\pi$
$127$	−13.2527	−	13.2527i	−1.17599	−	1.17599i	−0.195234	−	0.980757i	$-0.562547\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$		0			0
$130$	0.374399	+	2.59970i	0.0328370	+	0.228009i
$131$	−12.2929	−	7.09731i	−1.07404	−	0.620095i	−0.144755	−	0.989468i	$-0.546239\pi$
$131$	−12.2929	−	7.09731i	−1.07404	−	0.620095i	−0.929281	+	0.369372i	$0.879573\pi$
$132$		0			0
$133$	−3.89197	+	4.28970i	−0.337477	+	0.371964i
$134$		−	6.62236i		−	0.572085i
$135$		0			0
$136$	−0.682717	+	0.394167i	−0.0585425	+	0.0337995i
$137$	4.90887	−	18.3201i	0.419393	−	1.56519i	−0.356479	−	0.934303i	$-0.616023\pi$
$137$	4.90887	−	18.3201i	0.419393	−	1.56519i	0.775871	−	0.630891i	$-0.217311\pi$
$138$		0			0
$139$	−8.23706			−0.698658			−0.349329	−	0.937000i	$-0.613591\pi$
$139$	−8.23706			−0.698658			−0.349329	+	0.937000i	$0.613591\pi$
$140$	4.90340	+	3.31009i	0.414413	+	0.279754i
$141$		0			0
$142$	7.84116	−	2.10103i	0.658016	−	0.176315i
$143$	1.11607	−	4.16524i	0.0933308	−	0.348315i
$144$		0			0
$145$	4.60840	−	3.62582i	0.382706	−	0.301108i
$146$			9.86525i			0.816454i
$147$		0			0
$148$	−0.181676	+	0.181676i	−0.0149336	+	0.0149336i
$149$	4.19317	+	2.42093i	0.343518	+	0.198330i	0.661826	−	0.749657i	$-0.269782\pi$
$149$	4.19317	+	2.42093i	0.343518	+	0.198330i	−0.318309	+	0.947987i	$0.603115\pi$
$150$		0			0
$151$	−5.02292	−	8.69995i	−0.408759	−	0.707992i	0.585992	−	0.810317i	$-0.300705\pi$
$151$	−5.02292	−	8.69995i	−0.408759	−	0.707992i	−0.994751	+	0.102325i	$0.967372\pi$
$152$	−0.566614	−	2.11463i	−0.0459584	−	0.171519i
$153$		0			0
$154$	−5.25916	−	8.16592i	−0.423795	−	0.658028i
$155$	0.0862176	+	0.0344930i	0.00692516	+	0.00277054i
$156$		0			0
$157$	23.6523	+	6.33762i	1.88766	+	0.505797i	0.998872	+	0.0474774i	$0.0151182\pi$
$157$	23.6523	+	6.33762i	1.88766	+	0.505797i	0.888788	+	0.458320i	$0.151548\pi$
$158$	−12.9543	−	3.47109i	−1.03059	−	0.276145i
$159$		0			0
$160$	−2.05532	+	0.880708i	−0.162488	+	0.0696261i
$161$	−0.604505	−	12.4353i	−0.0476417	−	0.980035i
$162$		0			0
$163$	−5.68510	−	21.2171i	−0.445291	−	1.66185i	−0.715166	−	0.698954i	$-0.753649\pi$
$163$	−5.68510	−	21.2171i	−0.445291	−	1.66185i	0.269875	−	0.962895i	$-0.413018\pi$
$164$	4.49013	+	7.77713i	0.350620	+	0.607292i
$165$		0			0
$166$	11.9172	+	6.88038i	0.924952	+	0.534021i
$167$	−3.14616	+	3.14616i	−0.243457	+	0.243457i	−0.818279	−	0.574821i	$-0.805072\pi$
$167$	−3.14616	+	3.14616i	−0.243457	+	0.243457i	0.574821	+	0.818279i	$0.305072\pi$
$168$		0			0
$169$		−	11.6203i		−	0.893868i
$170$	−1.08999	−	1.38537i	−0.0835987	−	0.106253i
$171$		0			0
$172$	−0.173704	+	0.648273i	−0.0132448	+	0.0494304i
$173$	5.04844	−	1.35273i	0.383826	−	0.102846i	−0.0617463	−	0.998092i	$-0.519667\pi$
$173$	5.04844	−	1.35273i	0.383826	−	0.102846i	0.445572	+	0.895246i	$0.353000\pi$
$174$		0			0
$175$	−5.76309	+	11.9074i	−0.435648	+	0.900117i
$176$	3.67114			0.276723
$177$		0			0
$178$	−0.370178	+	1.38152i	−0.0277460	+	0.103550i
$179$	10.8847	−	6.28428i	0.813560	−	0.469709i	−0.0346308	−	0.999400i	$-0.511026\pi$
$179$	10.8847	−	6.28428i	0.813560	−	0.469709i	0.848191	+	0.529691i	$0.177692\pi$
$180$		0			0
$181$			11.6742i			0.867740i	0.900976	+	0.433870i	$0.142852\pi$
$181$			11.6742i			0.867740i	−0.900976	+	0.433870i	$0.857148\pi$
$182$	2.30161	+	2.08821i	0.170607	+	0.154789i
$183$		0			0
$184$	4.07520	+	2.35282i	0.300428	+	0.173452i
$185$	−0.459998	−	0.344183i	−0.0338197	−	0.0253048i
$186$		0			0
$187$	0.749044	+	2.79547i	0.0547755	+	0.204425i
$188$	−4.52558	−	4.52558i	−0.330062	−	0.330062i
$189$		0			0
$190$	4.49957	−	1.92807i	0.326433	−	0.139877i
$191$	7.75170	−	13.4263i	0.560894	−	0.971496i	−0.436525	−	0.899692i	$-0.643791\pi$
$191$	7.75170	−	13.4263i	0.560894	−	0.971496i	0.997419	−	0.0718040i	$-0.0228756\pi$
$192$		0			0
$193$	−8.69132	−	2.32883i	−0.625615	−	0.167633i	−0.0679359	−	0.997690i	$-0.521641\pi$
$193$	−8.69132	−	2.32883i	−0.625615	−	0.167633i	−0.557679	+	0.830057i	$0.688308\pi$
$194$	−2.23936	+	3.87868i	−0.160776	+	0.278473i
$195$		0			0
$196$	6.96699	−	0.678966i	0.497642	−	0.0484976i
$197$	−12.1951	−	12.1951i	−0.868865	−	0.868865i	0.123482	−	0.992347i	$-0.460594\pi$
$197$	−12.1951	−	12.1951i	−0.868865	−	0.868865i	−0.992347	+	0.123482i	$0.960594\pi$
$198$		0			0
$199$	−4.36557	−	7.56140i	−0.309467	−	0.536013i	0.668779	−	0.743462i	$-0.266817\pi$
$199$	−4.36557	−	7.56140i	−0.309467	−	0.536013i	−0.978246	+	0.207448i	$0.933484\pi$
$200$	−2.60433	−	4.26819i	−0.184154	−	0.301807i
$201$		0			0
$202$	−0.0508460	+	0.0508460i	−0.00357751	+	0.00357751i
$203$	1.46820	−	6.78099i	0.103047	−	0.475932i
$204$		0			0
$205$	−15.7814	+	12.4166i	−1.10222	+	0.867213i
$206$	14.3585	−	8.28988i	1.00040	−	0.577583i
$207$		0			0
$208$	−1.13459	+	0.304013i	−0.0786697	+	0.0210795i
$209$	−8.03696			−0.555928
$210$		0			0
$211$	−11.1745			−0.769288			−0.384644	−	0.923065i	$-0.625676\pi$
$211$	−11.1745			−0.769288			−0.384644	+	0.923065i	$0.625676\pi$
$212$	7.64413	−	2.04824i	0.525001	−	0.140674i
$213$		0			0
$214$	−3.95723	+	2.28471i	−0.270511	+	0.156179i
$215$	−1.49015	−	0.177816i	−0.101627	−	0.0121270i
$216$		0			0
$217$	0.104625	−	0.0335574i	0.00710242	−	0.00227803i
$218$	−12.8005	+	12.8005i	−0.866958	+	0.866958i
$219$		0			0
$220$	1.17015	+	8.12509i	0.0788913	+	0.547794i
$221$	−0.462994	−	0.801929i	−0.0311443	−	0.0539436i
$222$		0			0
$223$	−0.746804	−	0.746804i	−0.0500097	−	0.0500097i	0.681660	−	0.731669i	$-0.261258\pi$
$223$	−0.746804	−	0.746804i	−0.0500097	−	0.0500097i	−0.731669	+	0.681660i	$0.761258\pi$
$224$	−1.21006	+	2.35282i	−0.0808507	+	0.157204i
$225$		0			0
$226$	1.07525	−	1.86239i	0.0715247	−	0.123884i
$227$	3.01404	+	0.807609i	0.200049	+	0.0536029i	0.357452	−	0.933932i	$-0.383646\pi$
$227$	3.01404	+	0.807609i	0.200049	+	0.0536029i	−0.157403	+	0.987534i	$0.550312\pi$
$228$		0			0
$229$	−4.21091	+	7.29350i	−0.278264	+	0.481968i	−0.970954	−	0.239268i	$-0.923093\pi$
$229$	−4.21091	+	7.29350i	−0.278264	+	0.481968i	0.692689	+	0.721236i	$0.256426\pi$
$230$	−3.90840	+	9.76931i	−0.257712	+	0.644169i
$231$		0			0
$232$	1.85429	+	1.85429i	0.121740	+	0.121740i
$233$	5.90027	+	22.0201i	0.386540	+	1.44259i	0.835725	+	0.549148i	$0.185048\pi$
$233$	5.90027	+	22.0201i	0.386540	+	1.44259i	−0.449186	+	0.893439i	$0.648286\pi$
$234$		0			0
$235$	8.57367	−	11.4587i	0.559285	−	0.747480i
$236$	9.27713	+	5.35616i	0.603890	+	0.348656i
$237$		0			0
$238$	−2.03850	−	0.441369i	−0.132136	−	0.0286097i
$239$		−	23.9971i		−	1.55224i	−0.630585	−	0.776120i	$-0.717185\pi$
$239$		−	23.9971i		−	1.55224i	0.630585	−	0.776120i	$-0.282815\pi$
$240$		0			0
$241$	−21.4666	+	12.3937i	−1.38278	+	0.798350i	−0.992488	−	0.122340i	$-0.960960\pi$
$241$	−21.4666	+	12.3937i	−1.38278	+	0.798350i	−0.390295	+	0.920690i	$0.627627\pi$
$242$	0.641168	−	2.39287i	0.0412158	−	0.153820i
$243$		0			0
$244$	1.99231			0.127545
$245$	3.72338	+	15.2032i	0.237878	+	0.971295i
$246$		0			0
$247$	2.48388	−	0.665553i	0.158045	−	0.0423481i
$248$	−0.0107485	+	0.0401138i	−0.000682528	+	0.00254723i
$249$		0			0
$250$	8.61640	−	7.12444i	0.544949	−	0.450589i
$251$			11.1158i			0.701623i	0.936446	+	0.350811i	$0.114094\pi$
$251$			11.1158i			0.701623i	−0.936446	+	0.350811i	$0.885906\pi$
$252$		0			0
$253$	12.2153	−	12.2153i	0.767970	−	0.767970i
$254$	16.2312	+	9.37110i	1.01844	+	0.587995i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.54637	+	24.4314i	0.408351	+	1.52399i	0.797790	+	0.602935i	$0.206002\pi$
$257$	6.54637	+	24.4314i	0.408351	+	1.52399i	−0.389439	+	0.921052i	$0.627331\pi$
$258$		0			0
$259$	−0.678966	+	0.0330060i	−0.0421889	+	0.00205090i
$260$	−1.03449	−	2.41421i	−0.0641565	−	0.149723i
$261$		0			0
$262$	13.7110	+	3.67384i	0.847066	+	0.226971i
$263$	10.9595	+	2.93659i	0.675792	+	0.181078i	0.580363	−	0.814358i	$-0.302911\pi$
$263$	10.9595	+	2.93659i	0.675792	+	0.181078i	0.0954297	+	0.995436i	$0.469577\pi$
$264$		0			0
$265$	6.96973	+	16.2654i	0.428147	+	0.999174i
$266$	2.64910	−	5.15085i	0.162427	−	0.315819i
$267$		0			0
$268$	1.71399	+	6.39671i	0.104699	+	0.390741i
$269$	−4.03346	−	6.98616i	−0.245924	−	0.425954i	0.716467	−	0.697621i	$-0.245758\pi$
$269$	−4.03346	−	6.98616i	−0.245924	−	0.425954i	−0.962391	+	0.271668i	$0.912425\pi$
$270$		0			0
$271$	7.27419	+	4.19976i	0.441876	+	0.255117i	0.704393	−	0.709810i	$-0.251219\pi$
$271$	7.27419	+	4.19976i	0.441876	+	0.255117i	−0.262517	+	0.964927i	$0.584553\pi$
$272$	0.557436	−	0.557436i	0.0337995	−	0.0337995i
$273$		0			0
$274$			18.9664i			1.14580i
$275$	−17.6098	+	5.17962i	−1.06191	+	0.312343i
$276$		0			0
$277$	1.47009	−	5.48646i	0.0883293	−	0.329650i	−0.907594	−	0.419848i	$-0.862083\pi$
$277$	1.47009	−	5.48646i	0.0883293	−	0.329650i	0.995924	+	0.0901983i	$0.0287501\pi$
$278$	7.95639	−	2.13191i	0.477193	−	0.127863i
$279$		0			0
$280$	−5.59303	−	1.92821i	−0.334248	−	0.115233i
$281$	−7.27627			−0.434066			−0.217033	−	0.976164i	$-0.569638\pi$
$281$	−7.27627			−0.434066			−0.217033	+	0.976164i	$0.569638\pi$
$282$		0			0
$283$	−1.99550	+	7.44729i	−0.118620	+	0.442696i	−0.999532	−	0.0305840i	$-0.990263\pi$
$283$	−1.99550	+	7.44729i	−0.118620	+	0.442696i	0.880912	+	0.473280i	$0.156930\pi$
$284$	−7.03019	+	4.05888i	−0.417165	+	0.240850i
$285$		0			0
$286$			4.31218i			0.254984i
$287$	−5.02784	+	23.2215i	−0.296784	+	1.37072i
$288$		0			0
$289$	−14.1842	−	8.18927i	−0.834366	−	0.481721i
$290$	−3.51294	+	4.69502i	−0.206287	+	0.275701i
$291$		0			0
$292$	−2.55331	−	9.52910i	−0.149421	−	0.557648i
$293$	3.35198	+	3.35198i	0.195824	+	0.195824i	0.798207	−	0.602383i	$-0.205782\pi$
$293$	3.35198	+	3.35198i	0.195824	+	0.195824i	−0.602383	+	0.798207i	$0.705782\pi$
$294$		0			0
$295$	−8.89741	+	22.2397i	−0.518027	+	1.29485i
$296$	0.128464	−	0.222506i	0.00746682	−	0.0129329i
$297$		0			0
$298$	−4.67687	−	1.25316i	−0.270924	−	0.0725938i
$299$	−2.76365	+	4.78679i	−0.159826	+	0.276827i
$300$		0			0
$301$	−1.49286	+	0.961456i	−0.0860468	+	0.0554174i
$302$	7.10348	+	7.10348i	0.408759	+	0.408759i
$303$		0			0
$304$	1.09461	+	1.89593i	0.0627804	+	0.108739i
$305$	0.635034	+	4.40946i	0.0363619	+	0.252485i
$306$		0			0
$307$	1.06546	−	1.06546i	0.0608089	−	0.0608089i	−0.676048	−	0.736857i	$-0.736309\pi$
$307$	1.06546	−	1.06546i	0.0608089	−	0.0608089i	0.736857	+	0.676048i	$0.236309\pi$
$308$	7.19345	+	6.52650i	0.409885	+	0.371882i
$309$		0			0
$310$	−0.0922072	−	0.0110029i	−0.00523702	−	0.000624923i
$311$	−11.9584	+	6.90417i	−0.678097	+	0.391500i	−0.799138	−	0.601148i	$-0.794710\pi$
$311$	−11.9584	+	6.90417i	−0.678097	+	0.391500i	0.121040	+	0.992648i	$0.461377\pi$
$312$		0			0
$313$	22.5515	−	6.04266i	1.27469	−	0.341551i	0.442863	−	0.896590i	$-0.353963\pi$
$313$	22.5515	−	6.04266i	1.27469	−	0.341551i	0.831825	+	0.555038i	$0.187296\pi$
$314$	−24.4867			−1.38186
$315$		0			0
$316$	13.4113			0.754443
$317$	12.7394	−	3.41352i	0.715518	−	0.191722i	0.117347	−	0.993091i	$-0.462561\pi$
$317$	12.7394	−	3.41352i	0.715518	−	0.191722i	0.598171	+	0.801369i	$0.295894\pi$
$318$		0			0
$319$	8.33728	−	4.81353i	0.466798	−	0.269506i
$320$	1.75735	−	1.38266i	0.0982386	−	0.0772928i
$321$		0			0
$322$	3.80239	+	11.8551i	0.211899	+	0.660658i
$323$	−1.22035	+	1.22035i	−0.0679023	+	0.0679023i
$324$		0			0
$325$	5.01348	−	3.05909i	0.278098	−	0.169688i
$326$	10.9828	+	19.0227i	0.608279	+	1.05357i
$327$		0			0
$328$	−6.35000	−	6.35000i	−0.350620	−	0.350620i
$329$	−0.822187	−	16.9132i	−0.0453286	−	0.932454i
$330$		0			0
$331$	9.54799	−	16.5376i	0.524805	−	0.908989i	−0.474778	−	0.880106i	$-0.657472\pi$
$331$	9.54799	−	16.5376i	0.524805	−	0.908989i	0.999583	−	0.0288830i	$-0.00919501\pi$
$332$	−13.2919	−	3.56155i	−0.729487	−	0.195465i
$333$		0			0
$334$	2.22467	−	3.85325i	0.121729	−	0.210840i
$335$	−13.6111	+	5.83237i	−0.743653	+	0.318656i
$336$		0			0
$337$	0.488226	+	0.488226i	0.0265953	+	0.0265953i	0.720279	−	0.693684i	$-0.244014\pi$
$337$	0.488226	+	0.488226i	0.0265953	+	0.0265953i	−0.693684	+	0.720279i	$0.744014\pi$
$338$	3.00755	+	11.2243i	0.163589	+	0.610523i
$339$		0			0
$340$	1.41141	+	1.05606i	0.0765447	+	0.0572728i
$341$	0.132033	+	0.0762292i	0.00714998	+	0.00412804i
$342$		0			0
$343$	14.8586	+	11.0554i	0.802289	+	0.596936i
$344$		−	0.671142i		−	0.0361855i
$345$		0			0
$346$	−4.52631	+	2.61327i	−0.243336	+	0.140490i
$347$	−0.986094	+	3.68015i	−0.0529363	+	0.197561i	−0.987330	−	0.158682i	$-0.949276\pi$
$347$	−0.986094	+	3.68015i	−0.0529363	+	0.197561i	0.934393	+	0.356243i	$0.115942\pi$
$348$		0			0
$349$	7.91303			0.423575			0.211787	−	0.977316i	$-0.432072\pi$
$349$	7.91303			0.423575			0.211787	+	0.977316i	$0.432072\pi$
$350$	2.48484	−	12.9933i	0.132820	−	0.694520i
$351$		0			0
$352$	−3.54605	+	0.950161i	−0.189005	+	0.0506438i
$353$	6.67203	−	24.9004i	0.355116	−	1.32531i	−0.525222	−	0.850965i	$-0.676018\pi$
$353$	6.67203	−	24.9004i	0.355116	−	1.32531i	0.880338	−	0.474347i	$-0.157316\pi$
$354$		0			0
$355$	−11.2241	−	14.2657i	−0.595712	−	0.757146i
$356$		−	1.43026i		−	0.0758036i
$357$		0			0
$358$	−8.88731	+	8.88731i	−0.469709	+	0.469709i
$359$	8.99497	+	5.19325i	0.474737	+	0.274089i	0.718220	−	0.695816i	$-0.244957\pi$
$359$	8.99497	+	5.19325i	0.474737	+	0.274089i	−0.243484	+	0.969905i	$0.578290\pi$
$360$		0			0
$361$	7.10364	+	12.3039i	0.373876	+	0.647572i
$362$	−3.02152	−	11.2765i	−0.158807	−	0.592677i
$363$		0			0
$364$	−2.76365	−	1.42136i	−0.144855	−	0.0744994i
$365$	20.2763	−	8.68840i	1.06131	−	0.454772i
$366$		0			0
$367$	−8.39004	−	2.24811i	−0.437957	−	0.117350i	0.0331020	−	0.999452i	$-0.489461\pi$
$367$	−8.39004	−	2.24811i	−0.437957	−	0.117350i	−0.471059	+	0.882102i	$0.656128\pi$
$368$	−4.54529	−	1.21791i	−0.236940	−	0.0634878i
$369$		0			0
$370$	0.533405	+	0.213399i	0.0277304	+	0.0110941i
$371$	18.6197	+	9.57617i	0.966686	+	0.497170i
$372$		0			0
$373$	3.44476	+	12.8560i	0.178363	+	0.665660i	0.995954	+	0.0898611i	$0.0286423\pi$
$373$	3.44476	+	12.8560i	0.178363	+	0.665660i	−0.817591	+	0.575799i	$0.804691\pi$
$374$	−1.44704	−	2.50635i	−0.0748247	−	0.129600i
$375$		0			0
$376$	5.54268	+	3.20007i	0.285842	+	0.165031i
$377$	−2.17808	+	2.17808i	−0.112177	+	0.112177i
$378$		0			0
$379$		−	25.3453i		−	1.30190i	−0.759121	−	0.650949i	$-0.774371\pi$
$379$		−	25.3453i		−	1.30190i	0.759121	−	0.650949i	$-0.225629\pi$
$380$	−3.84723	+	3.02695i	−0.197359	+	0.155279i
$381$		0			0
$382$	−4.01258	+	14.9751i	−0.205301	+	0.766195i
$383$	−17.7739	+	4.76251i	−0.908205	+	0.243353i	−0.682537	−	0.730851i	$-0.739123\pi$
$383$	−17.7739	+	4.76251i	−0.908205	+	0.243353i	−0.225668	+	0.974204i	$0.572457\pi$
$384$		0			0
$385$	−12.1518	+	18.0011i	−0.619314	+	0.917419i
$386$	8.99792			0.457982
$387$		0			0
$388$	1.15918	−	4.32611i	0.0588483	−	0.219625i
$389$	−19.3621	+	11.1787i	−0.981699	+	0.566784i	−0.902783	−	0.430097i	$-0.858479\pi$
$389$	−19.3621	+	11.1787i	−0.981699	+	0.566784i	−0.0789164	+	0.996881i	$0.525146\pi$
$390$		0			0
$391$		−	3.70961i		−	0.187603i
$392$	−6.55387	+	2.45902i	−0.331020	+	0.124199i
$393$		0			0
$394$	14.9359	+	8.62324i	0.752459	+	0.434432i
$395$	4.27473	+	29.6823i	0.215085	+	1.49348i
$396$		0			0
$397$	−4.08518	−	15.2461i	−0.205029	−	0.765181i	−0.989441	−	0.144939i	$-0.953701\pi$
$397$	−4.08518	−	15.2461i	−0.205029	−	0.765181i	0.784411	−	0.620241i	$-0.212965\pi$
$398$	6.17385	+	6.17385i	0.309467	+	0.309467i
$399$		0			0
$400$	3.62028	+	3.44871i	0.181014	+	0.172435i
$401$	6.98528	−	12.0989i	0.348828	−	0.604188i	−0.637213	−	0.770687i	$-0.719913\pi$
$401$	6.98528	−	12.0989i	0.348828	−	0.604188i	0.986042	+	0.166499i	$0.0532463\pi$
$402$		0			0
$403$	−0.0471183	−	0.0126253i	−0.00234713	−	0.000628911i
$404$	0.0359536	−	0.0622734i	0.00178876	−	0.00309822i
$405$		0			0
$406$	0.336879	+	6.92993i	0.0167190	+	0.343927i
$407$	−0.666957	−	0.666957i	−0.0330598	−	0.0330598i
$408$		0			0
$409$	0.156681	+	0.271379i	0.00774737	+	0.0134188i	0.869873	−	0.493276i	$-0.164201\pi$
$409$	0.156681	+	0.271379i	0.00774737	+	0.0134188i	−0.862126	+	0.506694i	$0.830867\pi$
$410$	12.0300	−	16.0781i	0.594121	−	0.794038i
$411$		0			0
$412$	−11.7237	+	11.7237i	−0.577583	+	0.577583i
$413$	8.65608	+	26.9879i	0.425938	+	1.32799i
$414$		0			0
$415$	3.64586	−	30.5532i	0.178968	−	1.49980i
$416$	1.01725	−	0.587308i	0.0498746	−	0.0287951i
$417$		0			0
$418$	7.76311	−	2.08012i	0.379706	−	0.101742i
$419$	31.6254			1.54500			0.772501	−	0.635014i	$-0.219006\pi$
$419$	31.6254			1.54500			0.772501	+	0.635014i	$0.219006\pi$
$420$		0			0
$421$	24.2137			1.18011			0.590053	−	0.807365i	$-0.299107\pi$
$421$	24.2137			1.18011			0.590053	+	0.807365i	$0.299107\pi$
$422$	10.7938	−	2.89219i	0.525433	−	0.140789i
$423$		0			0
$424$	−6.85354	+	3.95689i	−0.332837	+	0.192164i
$425$	−1.88743	+	3.46040i	−0.0915536	+	0.167854i
$426$		0			0
$427$	3.90386	+	3.54190i	0.188921	+	0.171405i
$428$	3.23107	−	3.23107i	0.156179	−	0.156179i
$429$		0			0
$430$	1.48539	−	0.213921i	0.0716320	−	0.0103162i
$431$	0.779037	+	1.34933i	0.0375249	+	0.0649950i	0.884178	−	0.467150i	$-0.154719\pi$
$431$	0.779037	+	1.34933i	0.0375249	+	0.0649950i	−0.846653	+	0.532145i	$0.821386\pi$
$432$		0			0
$433$	−6.28166	−	6.28166i	−0.301877	−	0.301877i	0.539871	−	0.841748i	$-0.318473\pi$
$433$	−6.28166	−	6.28166i	−0.301877	−	0.301877i	−0.841748	+	0.539871i	$0.818473\pi$
$434$	−0.0923749	+	0.0594930i	−0.00443414	+	0.00285575i
$435$		0			0
$436$	9.05131	−	15.6773i	0.433479	−	0.750808i
$437$	9.95068	+	2.66628i	0.476006	+	0.127545i
$438$		0			0
$439$	−11.9571	+	20.7103i	−0.570681	+	0.988449i	0.425815	+	0.904810i	$0.359988\pi$
$439$	−11.9571	+	20.7103i	−0.570681	+	0.988449i	−0.996496	+	0.0836389i	$0.973346\pi$
$440$	−3.23320	−	7.54538i	−0.154137	−	0.359712i
$441$		0			0
$442$	0.654772	+	0.654772i	0.0311443	+	0.0311443i
$443$	−3.32895	−	12.4238i	−0.158163	−	0.590272i	−0.998814	−	0.0486946i	$-0.984494\pi$
$443$	−3.32895	−	12.4238i	−0.158163	−	0.590272i	0.840651	−	0.541578i	$-0.182173\pi$
$444$		0			0
$445$	3.16550	−	0.455884i	0.150059	−	0.0216110i
$446$	0.914645	+	0.528070i	0.0433097	+	0.0250049i
$447$		0			0
$448$	0.559876	−	2.58583i	0.0264517	−	0.122169i
$449$		−	17.8932i		−	0.844435i	−0.906495	−	0.422217i	$-0.861252\pi$
$449$		−	17.8932i		−	0.844435i	0.906495	−	0.422217i	$-0.138748\pi$
$450$		0			0
$451$	−28.5510	+	16.4839i	−1.34441	+	0.776197i
$452$	−0.556592	+	2.07723i	−0.0261799	+	0.0977046i
$453$		0			0
$454$	−3.12036			−0.146446
$455$	2.26490	−	6.56966i	0.106180	−	0.307990i
$456$		0			0
$457$	−33.0454	+	8.85449i	−1.54580	+	0.414196i	−0.928134	−	0.372246i	$-0.878588\pi$
$457$	−33.0454	+	8.85449i	−1.54580	+	0.414196i	−0.617665	+	0.786442i	$0.711921\pi$
$458$	2.17973	−	8.13485i	0.101852	−	0.380116i
$459$		0			0
$460$	1.24674	−	10.4480i	0.0581295	−	0.487140i
$461$		−	23.3471i		−	1.08738i	−0.839286	−	0.543690i	$-0.817027\pi$
$461$		−	23.3471i		−	1.08738i	0.839286	−	0.543690i	$-0.182973\pi$
$462$		0			0
$463$	3.98510	−	3.98510i	0.185203	−	0.185203i	−0.608415	−	0.793619i	$-0.708195\pi$
$463$	3.98510	−	3.98510i	0.185203	−	0.185203i	0.793619	+	0.608415i	$0.208195\pi$
$464$	−2.27103	−	1.31118i	−0.105430	−	0.0608700i
$465$		0			0
$466$	−11.3985	−	19.7427i	−0.528023	−	0.914563i
$467$	1.26454	+	4.71932i	0.0585159	+	0.218384i	0.988992	−	0.147968i	$-0.0472732\pi$
$467$	1.26454	+	4.71932i	0.0585159	+	0.218384i	−0.930476	+	0.366352i	$0.880607\pi$
$468$		0			0
$469$	−8.01347	+	15.5812i	−0.370028	+	0.719473i
$470$	−5.31581	+	13.2872i	−0.245200	+	0.612895i
$471$		0			0
$472$	−10.3473	−	2.77255i	−0.476273	−	0.127617i
$473$	−2.37990	−	0.637693i	−0.109428	−	0.0293212i
$474$		0			0
$475$	−7.92561	−	7.55000i	−0.363652	−	0.346418i
$476$	2.08327	−	0.101272i	0.0954867	−	0.00464182i
$477$		0			0
$478$	6.21090	+	23.1794i	0.284080	+	1.06020i
$479$	−8.55572	−	14.8189i	−0.390921	−	0.677094i	0.601651	−	0.798759i	$-0.294510\pi$
$479$	−8.55572	−	14.8189i	−0.390921	−	0.677094i	−0.992571	+	0.121665i	$0.961177\pi$
$480$		0			0
$481$	0.261359	+	0.150896i	0.0119170	+	0.00688026i
$482$	17.5274	−	17.5274i	0.798350	−	0.798350i
$483$		0			0
$484$			2.47728i			0.112604i
$485$	9.94416	+	1.18662i	0.451541	+	0.0538815i
$486$		0			0
$487$	0.0337240	−	0.125860i	0.00152818	−	0.00570325i	−0.965158	−	0.261670i	$-0.915727\pi$
$487$	0.0337240	−	0.125860i	0.00152818	−	0.00570325i	0.966686	+	0.255966i	$0.0823936\pi$
$488$	−1.92443	+	0.515649i	−0.0871147	+	0.0233423i
$489$		0			0
$490$	−7.53138	−	13.7215i	−0.340233	−	0.619872i
$491$	−26.9895			−1.21802			−0.609011	−	0.793162i	$-0.708433\pi$
$491$	−26.9895			−1.21802			−0.609011	+	0.793162i	$0.708433\pi$
$492$		0			0
$493$	0.535055	−	1.99685i	0.0240977	−	0.0899337i
$494$	−2.22698	+	1.28575i	−0.100197	+	0.0578486i
$495$		0			0
$496$		−	0.0415289i		−	0.00186470i
$497$	−20.9912	−	4.54495i	−0.941584	−	0.203869i
$498$		0			0
$499$	0.0833977	+	0.0481497i	0.00373339	+	0.00215548i	0.501866	−	0.864946i	$-0.332647\pi$
$499$	0.0833977	+	0.0481497i	0.00373339	+	0.00215548i	−0.498132	+	0.867101i	$0.665981\pi$
$500$	−6.47886	+	9.11177i	−0.289743	+	0.407491i
$501$		0			0
$502$	−2.87698	−	10.7370i	−0.128406	−	0.479217i
$503$	−13.6334	−	13.6334i	−0.607883	−	0.607883i	0.334509	−	0.942392i	$-0.391429\pi$
$503$	−13.6334	−	13.6334i	−0.607883	−	0.607883i	−0.942392	+	0.334509i	$0.891429\pi$
$504$		0			0
$505$	0.149286	+	0.0597245i	0.00664312	+	0.00265771i
$506$	−8.63753	+	14.9606i	−0.383985	+	0.665081i
$507$		0			0
$508$	−18.1036	−	4.85084i	−0.803217	−	0.215221i
$509$	−6.16366	+	10.6758i	−0.273199	+	0.473195i	−0.969679	−	0.244381i	$-0.921415\pi$
$509$	−6.16366	+	10.6758i	−0.273199	+	0.473195i	0.696480	+	0.717576i	$0.254749\pi$
$510$		0			0
$511$	11.9376	−	23.2111i	0.528087	−	1.02680i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−12.6466	−	21.9046i	−0.557818	−	0.966169i
$515$	−29.6840	−	22.2104i	−1.30803	−	0.978706i
$516$		0			0
$517$	16.6140	−	16.6140i	0.730684	−	0.730684i
$518$	0.647288	−	0.207611i	0.0284402	−	0.00912189i
$519$		0			0
$520$	1.62409	+	2.06420i	0.0712210	+	0.0905214i
$521$	−14.1415	+	8.16461i	−0.619551	+	0.357698i	−0.776694	−	0.629878i	$-0.783105\pi$
$521$	−14.1415	+	8.16461i	−0.619551	+	0.357698i	0.157143	+	0.987576i	$0.449772\pi$
$522$		0			0
$523$	−26.4703	+	7.09270i	−1.15747	+	0.310142i	−0.785953	−	0.618286i	$-0.787827\pi$
$523$	−26.4703	+	7.09270i	−1.15747	+	0.310142i	−0.371512	+	0.928428i	$0.621161\pi$
$524$	−14.1946			−0.620095
$525$		0			0
$526$	−11.3461			−0.494714
$527$	0.0316231	−	0.00847337i	0.00137752	−	0.000369106i
$528$		0			0
$529$	0.742186	−	0.428501i	0.0322689	−	0.0186305i
$530$	−10.9420	−	13.9073i	−0.475292	−	0.604092i
$531$		0			0
$532$	−1.22570	+	5.66098i	−0.0531407	+	0.245435i
$533$	7.45881	−	7.45881i	0.323077	−	0.323077i
$534$		0			0
$535$	8.18098	+	6.12123i	0.353695	+	0.264644i
$536$	−3.31118	−	5.73513i	−0.143021	−	0.247720i
$537$		0			0
$538$	5.70417	+	5.70417i	0.245924	+	0.245924i
$539$	2.49258	+	25.5768i	0.107363	+	1.10167i
$540$		0			0
$541$	20.5773	−	35.6410i	0.884689	−	1.53233i	0.0386200	−	0.999254i	$-0.487704\pi$
$541$	20.5773	−	35.6410i	0.884689	−	1.53233i	0.846069	−	0.533073i	$-0.178963\pi$
$542$	−8.11330	−	2.17395i	−0.348496	−	0.0933793i
$543$		0			0
$544$	−0.394167	+	0.682717i	−0.0168998	+	0.0292712i
$545$	37.5826	+	15.0356i	1.60986	+	0.644056i
$546$		0			0
$547$	8.06541	+	8.06541i	0.344852	+	0.344852i	0.858188	−	0.513336i	$-0.171590\pi$
$547$	8.06541	+	8.06541i	0.344852	+	0.344852i	−0.513336	+	0.858188i	$0.671590\pi$
$548$	−4.90887	−	18.3201i	−0.209696	−	0.782597i
$549$		0			0
$550$	15.6691	−	9.56087i	0.668134	−	0.407677i
$551$	4.97180	+	2.87047i	0.211806	+	0.122286i
$552$		0			0
$553$	26.2788	+	23.8423i	1.11749	+	1.01388i
$554$			5.68000i			0.241320i
$555$		0			0
$556$	−7.13350	+	4.11853i	−0.302528	+	0.174665i
$557$	6.64049	−	24.7826i	0.281367	−	1.05007i	−0.670087	−	0.742282i	$-0.733743\pi$
$557$	6.64049	−	24.7826i	0.281367	−	1.05007i	0.951454	−	0.307792i	$-0.0995901\pi$
$558$		0			0
$559$	0.788333			0.0333429
$560$	5.90151	+	0.414924i	0.249384	+	0.0175337i
$561$		0			0
$562$	7.02834	−	1.88324i	0.296473	−	0.0794396i
$563$	3.31584	−	12.3749i	0.139746	−	0.521539i	−0.860187	−	0.509978i	$-0.829653\pi$
$563$	3.31584	−	12.3749i	0.139746	−	0.521539i	0.999933	−	0.0115606i	$-0.00367993\pi$
$564$		0			0
$565$	−4.77480	−	0.569768i	−0.200877	−	0.0239703i
$566$		−	7.71000i		−	0.324076i
$567$		0			0
$568$	5.74013	−	5.74013i	0.240850	−	0.240850i
$569$	−29.8291	−	17.2218i	−1.25050	−	0.721977i	−0.279292	−	0.960206i	$-0.590100\pi$
$569$	−29.8291	−	17.2218i	−1.25050	−	0.721977i	−0.971209	+	0.238229i	$0.923433\pi$
$570$		0			0
$571$	4.11985	+	7.13579i	0.172410	+	0.298623i	0.939262	−	0.343201i	$-0.111511\pi$
$571$	4.11985	+	7.13579i	0.172410	+	0.298623i	−0.766852	+	0.641824i	$0.778178\pi$
$572$	−1.11607	−	4.16524i	−0.0466654	−	0.174158i
$573$		0			0
$574$	−1.15364	−	23.7315i	−0.0481520	−	0.990534i
$575$	23.5212	−	0.570889i	0.980904	−	0.0238077i
$576$		0			0
$577$	−3.39649	−	0.910086i	−0.141398	−	0.0378874i	0.187426	−	0.982279i	$-0.439985\pi$
$577$	−3.39649	−	0.910086i	−0.141398	−	0.0378874i	−0.328824	+	0.944391i	$0.606652\pi$
$578$	15.8204	+	4.23908i	0.658044	+	0.176322i
$579$		0			0
$580$	2.17808	−	5.44425i	0.0904397	−	0.226060i
$581$	−19.7132	−	30.6088i	−0.817843	−	1.26987i
$582$		0			0
$583$	7.51937	+	28.0627i	0.311421	+	1.16224i
$584$	4.93262	+	8.54355i	0.204113	+	0.353535i
$585$		0			0
$586$	−4.10531	−	2.37020i	−0.169589	−	0.0979122i
$587$	−5.37485	+	5.37485i	−0.221844	+	0.221844i	−0.809275	−	0.587431i	$-0.800139\pi$
$587$	−5.37485	+	5.37485i	−0.221844	+	0.221844i	0.587431	+	0.809275i	$0.300139\pi$
$588$		0			0
$589$			0.0909162i			0.00374613i
$590$	2.83818	−	23.7847i	0.116846	−	0.979201i
$591$		0			0
$592$	−0.0664979	+	0.248174i	−0.00273305	+	0.0101999i
$593$	−0.709668	+	0.190155i	−0.0291426	+	0.00780872i	−0.273361	−	0.961912i	$-0.588135\pi$
$593$	−0.709668	+	0.190155i	−0.0291426	+	0.00780872i	0.244218	+	0.969720i	$0.421469\pi$
$594$		0			0
$595$	0.888166	+	4.57849i	0.0364113	+	0.187700i
$596$	4.84185			0.198330
$597$		0			0
$598$	1.43057	−	5.33897i	0.0585005	−	0.218327i
$599$	7.23778	−	4.17873i	0.295727	−	0.170738i	−0.344794	−	0.938678i	$-0.612051\pi$
$599$	7.23778	−	4.17873i	0.295727	−	0.170738i	0.640522	+	0.767940i	$0.278718\pi$
$600$		0			0
$601$		−	39.9236i		−	1.62852i	−0.580501	−	0.814259i	$-0.697143\pi$
$601$		−	39.9236i		−	1.62852i	0.580501	−	0.814259i	$-0.302857\pi$
$602$	1.19315	−	1.31508i	0.0486290	−	0.0535985i
$603$		0			0
$604$	−8.69995	−	5.02292i	−0.353996	−	0.204380i
$605$	−5.48280	+	0.789613i	−0.222908	+	0.0321024i
$606$		0			0
$607$	8.91623	+	33.2758i	0.361899	+	1.35062i	0.871577	+	0.490259i	$0.163098\pi$
$607$	8.91623	+	33.2758i	0.361899	+	1.35062i	−0.509678	+	0.860365i	$0.670235\pi$
$608$	−1.54802	−	1.54802i	−0.0627804	−	0.0627804i
$609$		0			0
$610$	−1.75465	−	4.09485i	−0.0710436	−	0.165796i
$611$	−3.75885	+	6.51051i	−0.152067	+	0.263387i
$612$		0			0
$613$	31.6042	+	8.46832i	1.27648	+	0.342032i	0.832510	−	0.554009i	$-0.186903\pi$
$613$	31.6042	+	8.46832i	1.27648	+	0.342032i	0.443971	+	0.896041i	$0.353569\pi$
$614$	−0.753393	+	1.30491i	−0.0304044	+	0.0526620i
$615$		0			0
$616$	−8.63753	−	4.44231i	−0.348016	−	0.178986i
$617$	15.5005	+	15.5005i	0.624025	+	0.624025i	0.946558	−	0.322533i	$-0.104534\pi$
$617$	15.5005	+	15.5005i	0.624025	+	0.624025i	−0.322533	+	0.946558i	$0.604534\pi$
$618$		0			0
$619$	−4.31138	−	7.46752i	−0.173289	−	0.300145i	0.766279	−	0.642508i	$-0.222106\pi$
$619$	−4.31138	−	7.46752i	−0.173289	−	0.300145i	−0.939568	+	0.342363i	$0.888773\pi$
$620$	0.0919131	−	0.0132370i	0.00369132	−	0.000531611i
$621$		0			0
$622$	9.76397	−	9.76397i	0.391500	−	0.391500i
$623$	2.54269	−	2.80254i	0.101871	−	0.112281i
$624$		0			0
$625$	−22.2316	−	11.4349i	−0.889263	−	0.457397i
$626$	−20.2191	+	11.6735i	−0.808119	+	0.466568i
$627$		0			0
$628$	23.6523	−	6.33762i	0.943830	−	0.252898i
$629$	−0.202545			−0.00807600
$630$		0			0
$631$	−4.13675			−0.164682			−0.0823408	−	0.996604i	$-0.526240\pi$
$631$	−4.13675			−0.164682			−0.0823408	+	0.996604i	$0.526240\pi$
$632$	−12.9543	+	3.47109i	−0.515294	+	0.138073i
$633$		0			0
$634$	−11.4219	+	6.59442i	−0.453620	+	0.261898i
$635$	4.96567	−	41.6136i	0.197057	−	1.65139i
$636$		0			0
$637$	−2.88840	−	7.69827i	−0.114443	−	0.305017i
$638$	−6.80736	+	6.80736i	−0.269506	+	0.269506i
$639$		0			0
$640$	−1.33961	+	1.79038i	−0.0529527	+	0.0707709i
$641$	5.42807	+	9.40169i	0.214396	+	0.371345i	0.953086	−	0.302701i	$-0.0978884\pi$
$641$	5.42807	+	9.40169i	0.214396	+	0.371345i	−0.738690	+	0.674046i	$0.764555\pi$
$642$		0			0
$643$	8.06230	+	8.06230i	0.317946	+	0.317946i	0.847978	−	0.530032i	$-0.177820\pi$
$643$	8.06230	+	8.06230i	0.317946	+	0.317946i	−0.530032	+	0.847978i	$0.677820\pi$
$644$	−6.74114	−	10.4670i	−0.265638	−	0.412457i
$645$		0			0
$646$	0.862920	−	1.49462i	0.0339511	−	0.0588051i
$647$	10.0715	+	2.69865i	0.395951	+	0.106095i	0.451300	−	0.892372i	$-0.350960\pi$
$647$	10.0715	+	2.69865i	0.395951	+	0.106095i	−0.0553490	+	0.998467i	$0.517627\pi$
$648$		0			0
$649$	−19.6632	+	34.0577i	−0.771848	+	1.33688i
$650$	−4.05090	+	4.25243i	−0.158889	+	0.166794i
$651$		0			0
$652$	−15.5320	−	15.5320i	−0.608279	−	0.608279i
$653$	1.72009	+	6.41946i	0.0673123	+	0.251213i	0.991380	−	0.131015i	$-0.0418236\pi$
$653$	1.72009	+	6.41946i	0.0673123	+	0.251213i	−0.924068	+	0.382228i	$0.875157\pi$
$654$		0			0
$655$	−4.52442	−	31.4160i	−0.176784	−	1.22753i
$656$	7.77713	+	4.49013i	0.303646	+	0.175310i
$657$		0			0
$658$	5.17163	+	16.1241i	0.201611	+	0.628582i
$659$			22.0345i			0.858343i	0.903223	+	0.429172i	$0.141194\pi$
$659$			22.0345i			0.858343i	−0.903223	+	0.429172i	$0.858806\pi$
$660$		0			0
$661$	−9.94278	+	5.74047i	−0.386729	+	0.223278i	−0.680742	−	0.732523i	$-0.738343\pi$
$661$	−9.94278	+	5.74047i	−0.386729	+	0.223278i	0.294013	+	0.955802i	$0.405009\pi$
$662$	−4.94240	+	18.4453i	−0.192092	+	0.716897i
$663$		0			0
$664$	13.7608			0.534021
$665$	−12.9197	−	0.908362i	−0.501006	−	0.0352248i
$666$		0			0
$667$	−11.9194	+	3.19379i	−0.461521	+	0.123664i
$668$	−1.15158	+	4.29774i	−0.0445558	+	0.166285i
$669$		0			0
$670$	11.6378	−	9.15644i	0.449607	−	0.353744i
$671$			7.31407i			0.282356i
$672$		0			0
$673$	−15.2073	+	15.2073i	−0.586198	+	0.586198i	−0.936600	−	0.350402i	$-0.886045\pi$
$673$	−15.2073	+	15.2073i	−0.586198	+	0.586198i	0.350402	+	0.936600i	$0.386045\pi$
$674$	−0.597952	−	0.345228i	−0.0230322	−	0.0132977i
$675$		0			0
$676$	−5.81014	−	10.0635i	−0.223467	−	0.387056i
$677$	1.48523	+	5.54296i	0.0570821	+	0.213033i	0.988576	−	0.150724i	$-0.0481604\pi$
$677$	1.48523	+	5.54296i	0.0570821	+	0.213033i	−0.931494	+	0.363757i	$0.881494\pi$
$678$		0			0
$679$	9.96224	−	6.41606i	0.382316	−	0.246226i
$680$	−1.63665	−	0.654772i	−0.0627626	−	0.0251094i
$681$		0			0
$682$	−0.147264	−	0.0394591i	−0.00563901	−	0.00151097i
$683$	18.7685	+	5.02900i	0.718157	+	0.192430i	0.599349	−	0.800488i	$-0.295426\pi$
$683$	18.7685	+	5.02900i	0.718157	+	0.192430i	0.118808	+	0.992917i	$0.462093\pi$
$684$		0			0
$685$	38.9821	−	16.7039i	1.48943	−	0.638222i
$686$	−17.2137	−	6.83301i	−0.657220	−	0.260886i
$687$		0			0
$688$	0.173704	+	0.648273i	0.00662241	+	0.0247152i
$689$	−4.64782	−	8.05027i	−0.177068	−	0.306691i
$690$		0			0
$691$	19.0914	+	11.0224i	0.726270	+	0.419312i	0.817056	−	0.576558i	$-0.195605\pi$
$691$	19.0914	+	11.0224i	0.726270	+	0.419312i	−0.0907861	+	0.995870i	$0.528938\pi$
$692$	3.69572	−	3.69572i	0.140490	−	0.140490i
$693$		0			0
$694$		−	3.80998i		−	0.144625i
$695$	−11.3890	−	14.4754i	−0.432010	−	0.549082i
$696$		0			0
$697$	−1.83229	+	6.83821i	−0.0694031	+	0.259016i
$698$	−7.64340	+	2.04804i	−0.289307	+	0.0775196i
$699$		0			0
$700$	0.962736	+	13.1937i	0.0363880	+	0.498674i
$701$	18.0270			0.680870			0.340435	−	0.940268i	$-0.389426\pi$
$701$	18.0270			0.680870			0.340435	+	0.940268i	$0.389426\pi$
$702$		0			0
$703$	0.145579	−	0.543308i	0.00549062	−	0.0204913i
$704$	3.17930	−	1.83557i	0.119824	−	0.0691807i
$705$		0			0
$706$			25.7787i			0.970196i
$707$	0.181158	−	0.0581046i	0.00681316	−	0.00218525i
$708$		0			0
$709$	37.0614	+	21.3974i	1.39187	+	0.803597i	0.993522	−	0.113637i	$-0.0362500\pi$
$709$	37.0614	+	21.3974i	1.39187	+	0.803597i	0.398349	+	0.917234i	$0.369583\pi$
$710$	14.5339	+	10.8746i	0.545446	+	0.408117i
$711$		0			0
$712$	0.370178	+	1.38152i	0.0138730	+	0.0517748i
$713$	−0.138183	−	0.138183i	−0.00517498	−	0.00517498i
$714$		0			0
$715$	8.86292	−	3.79777i	0.331454	−	0.142029i
$716$	6.28428	−	10.8847i	0.234854	−	0.406780i
$717$		0			0
$718$	−10.0326	−	2.68822i	−0.374413	−	0.100324i
$719$	−2.72691	+	4.72315i	−0.101697	+	0.176144i	−0.912384	−	0.409336i	$-0.865760\pi$
$719$	−2.72691	+	4.72315i	−0.101697	+	0.176144i	0.810687	+	0.585480i	$0.199094\pi$
$720$		0			0
$721$	−43.8142	+	2.12990i	−1.63172	+	0.0793217i
$722$	−10.0461	−	10.0461i	−0.373876	−	0.373876i
$723$		0			0
$724$	5.83712	+	10.1102i	0.216935	+	0.375742i
$725$	12.7436	+	3.08528i	0.473287	+	0.114584i
$726$		0			0
$727$	−16.6781	+	16.6781i	−0.618555	+	0.618555i	−0.945161	−	0.326606i	$-0.894095\pi$
$727$	−16.6781	+	16.6781i	−0.618555	+	0.618555i	0.326606	+	0.945161i	$0.394095\pi$
$728$	3.03736	+	0.657639i	0.112572	+	0.0243737i
$729$		0			0
$730$	−17.3366	+	13.6402i	−0.641658	+	0.504848i
$731$	−0.458200	+	0.264542i	−0.0169471	+	0.00978443i
$732$		0			0
$733$	−32.8405	+	8.79960i	−1.21299	+	0.325021i	−0.807936	−	0.589271i	$-0.799415\pi$
$733$	−32.8405	+	8.79960i	−1.21299	+	0.325021i	−0.405057	+	0.914291i	$0.632748\pi$
$734$	8.68601			0.320607
$735$		0			0
$736$	4.70563			0.173452
$737$	−23.4832	+	6.29231i	−0.865016	+	0.231780i
$738$		0			0
$739$	−25.0733	+	14.4761i	−0.922335	+	0.532510i	−0.884379	−	0.466769i	$-0.845418\pi$
$739$	−25.0733	+	14.4761i	−0.922335	+	0.532510i	−0.0379557	+	0.999279i	$0.512085\pi$
$740$	−0.570462	−	0.0680721i	−0.0209706	−	0.00250238i
$741$		0			0
$742$	−20.4637	−	4.43074i	−0.751247	−	0.162658i
$743$	−34.0351	+	34.0351i	−1.24863	+	1.24863i	−0.292300	+	0.956327i	$0.594421\pi$
$743$	−34.0351	+	34.0351i	−1.24863	+	1.24863i	−0.956327	+	0.292300i	$0.905579\pi$
$744$		0			0
$745$	1.54330	+	10.7162i	0.0565422	+	0.392609i
$746$	−6.65477	−	11.5264i	−0.243649	−	0.422012i
$747$		0			0
$748$	2.04643	+	2.04643i	0.0748247	+	0.0748247i
$749$	12.0753	−	0.587006i	0.441221	−	0.0214487i
$750$		0			0
$751$	9.30569	−	16.1179i	0.339569	−	0.588151i	−0.644782	−	0.764366i	$-0.723052\pi$
$751$	9.30569	−	16.1179i	0.339569	−	0.588151i	0.984352	+	0.176215i	$0.0563853\pi$
$752$	−6.18205	−	1.65648i	−0.225436	−	0.0604055i
$753$		0			0
$754$	1.54013	−	2.66759i	0.0560883	−	0.0971478i
$755$	8.34385	−	20.8560i	0.303664	−	0.759029i
$756$		0			0
$757$	29.7422	+	29.7422i	1.08100	+	1.08100i	0.996416	+	0.0845825i	$0.0269557\pi$
$757$	29.7422	+	29.7422i	1.08100	+	1.08100i	0.0845825	+	0.996416i	$0.473044\pi$
$758$	6.55984	+	24.4816i	0.238264	+	0.889213i
$759$		0			0
$760$	2.93271	−	3.91954i	0.106380	−	0.142177i
$761$	−17.6474	−	10.1887i	−0.639718	−	0.369341i	0.144788	−	0.989463i	$-0.453750\pi$
$761$	−17.6474	−	10.1887i	−0.639718	−	0.369341i	−0.784506	+	0.620122i	$0.787083\pi$
$762$		0			0
$763$	45.6066	−	14.6278i	1.65107	−	0.529563i
$764$		−	15.5034i		−	0.560894i
$765$		0			0
$766$	15.9357	−	9.20046i	0.575779	−	0.332426i
$767$	3.25668	−	12.1541i	0.117592	−	0.438859i
$768$		0			0
$769$	−40.9728			−1.47752			−0.738759	−	0.673970i	$-0.764588\pi$
$769$	−40.9728			−1.47752			−0.738759	+	0.673970i	$0.764588\pi$
$770$	7.07873	−	20.5328i	0.255100	−	0.739951i
$771$		0			0
$772$	−8.69132	+	2.32883i	−0.312808	+	0.0838165i
$773$	−6.39265	+	23.8577i	−0.229928	+	0.858101i	0.750443	+	0.660936i	$0.229840\pi$
$773$	−6.39265	+	23.8577i	−0.229928	+	0.858101i	−0.980370	+	0.197166i	$0.936826\pi$
$774$		0			0
$775$	0.0585931	+	0.199206i	0.00210473	+	0.00715569i
$776$			4.47871i			0.160776i
$777$		0			0
$778$	15.8091	−	15.8091i	0.566784	−	0.566784i
$779$	−17.0259	−	9.82991i	−0.610017	−	0.352193i
$780$		0			0
$781$	−14.9007	−	25.8088i	−0.533190	−	0.923513i
$782$	0.960117	+	3.58321i	0.0343337	+	0.128135i
$783$		0			0
$784$	5.69411	−	4.07150i	0.203361	−	0.145411i
$785$	21.5656	+	50.3280i	0.769710	+	1.79628i
$786$		0			0
$787$	7.92843	+	2.12442i	0.282618	+	0.0757273i	0.397343	−	0.917670i	$-0.369932\pi$
$787$	7.92843	+	2.12442i	0.282618	+	0.0757273i	−0.114725	+	0.993397i	$0.536599\pi$
$788$	−16.6588	−	4.46372i	−0.593446	−	0.159013i
$789$		0			0
$790$	−11.8114	−	27.5645i	−0.420231	−	0.980701i
$791$	−4.78348	+	3.08075i	−0.170081	+	0.109539i
$792$		0			0
$793$	−0.605689	−	2.26046i	−0.0215086	−	0.0802713i
$794$	7.89197	+	13.6693i	0.280076	+	0.485105i
$795$		0			0
$796$	−7.56140	−	4.36557i	−0.268007	−	0.154734i
$797$	11.7928	−	11.7928i	0.417722	−	0.417722i	−0.466696	−	0.884418i	$-0.654556\pi$
$797$	11.7928	−	11.7928i	0.417722	−	0.417722i	0.884418	+	0.466696i	$0.154556\pi$
$798$		0			0
$799$		−	5.04544i		−	0.178495i
$800$	−4.38951	−	2.39420i	−0.155193	−	0.0846477i
$801$		0			0
$802$	−3.61585	+	13.4945i	−0.127680	+	0.476508i
$803$	34.9827	−	9.37358i	1.23451	−	0.330786i
$804$		0			0
$805$	21.0172	−	18.2560i	0.740760	−	0.643439i
$806$	0.0487805			0.00171822
$807$		0			0
$808$	−0.0186109	+	0.0694570i	−0.000654730	+	0.00244349i
$809$	−28.8498	+	16.6564i	−1.01430	+	0.585609i	−0.912449	−	0.409191i	$-0.865811\pi$
$809$	−28.8498	+	16.6564i	−1.01430	+	0.585609i	−0.101855	+	0.994799i	$0.532478\pi$
$810$		0			0
$811$			55.2368i			1.93963i	0.243850	+	0.969813i	$0.421590\pi$
$811$			55.2368i			1.93963i	−0.243850	+	0.969813i	$0.578410\pi$
$812$	−2.11900	−	6.60661i	−0.0743623	−	0.231847i
$813$		0			0
$814$	0.816852	+	0.471610i	0.0286307	+	0.0165299i
$815$	29.4252	−	39.3266i	1.03072	−	1.37755i
$816$		0			0
$817$	−0.380278	−	1.41922i	−0.0133042	−	0.0496521i
$818$	−0.221580	−	0.221580i	−0.00774737	−	0.00774737i
$819$		0			0
$820$	−7.45881	+	18.6438i	−0.260473	+	0.651070i
$821$	9.31457	−	16.1333i	0.325081	−	0.563056i	−0.656448	−	0.754371i	$-0.727942\pi$
$821$	9.31457	−	16.1333i	0.325081	−	0.563056i	0.981529	+	0.191315i	$0.0612752\pi$
$822$		0			0
$823$	16.3139	+	4.37130i	0.568668	+	0.152374i	0.531685	−	0.846942i	$-0.321559\pi$
$823$	16.3139	+	4.37130i	0.568668	+	0.152374i	0.0369821	+	0.999316i	$0.488226\pi$
$824$	8.28988	−	14.3585i	0.288792	−	0.500202i
$825$		0			0
$826$	−15.3461	−	23.8280i	−0.533960	−	0.829081i
$827$	5.62716	+	5.62716i	0.195675	+	0.195675i	0.798143	−	0.602468i	$-0.205816\pi$
$827$	5.62716	+	5.62716i	0.195675	+	0.195675i	−0.602468	+	0.798143i	$0.705816\pi$
$828$		0			0
$829$	−3.29757	−	5.71155i	−0.114529	−	0.198370i	0.803062	−	0.595895i	$-0.203203\pi$
$829$	−3.29757	−	5.71155i	−0.114529	−	0.198370i	−0.917591	+	0.397525i	$0.869869\pi$
$830$	4.38613	+	30.4558i	0.152245	+	1.05714i
$831$		0			0
$832$	−0.830578	+	0.830578i	−0.0287951	+	0.0287951i
$833$	4.26213	+	3.50517i	0.147674	+	0.121447i
$834$		0			0
$835$	−9.87896	−	1.17884i	−0.341875	−	0.0407953i
$836$	−6.96021	+	4.01848i	−0.240724	+	0.138982i
$837$		0			0
$838$	−30.5478	+	8.18525i	−1.05526	+	0.282755i
$839$	46.0930			1.59131			0.795654	−	0.605752i	$-0.207128\pi$
$839$	46.0930			1.59131			0.795654	+	0.605752i	$0.207128\pi$
$840$		0			0
$841$	22.1232			0.762870
$842$	−23.3887	+	6.26698i	−0.806027	+	0.215974i
$843$		0			0
$844$	−9.67744	+	5.58727i	−0.333111	+	0.192322i
$845$	20.4208	−	16.0668i	0.702499	−	0.552716i
$846$		0			0
$847$	−4.40407	+	4.85413i	−0.151326	+	0.166790i
$848$	5.59589	−	5.59589i	0.192164	−	0.192164i
$849$		0			0
$850$	0.927496	−	3.83099i	0.0318128	−	0.131402i
$851$	0.604505	+	1.04703i	0.0207222	+	0.0358918i
$852$		0			0
$853$	−14.9594	−	14.9594i	−0.512200	−	0.512200i	0.403000	−	0.915200i	$-0.367968\pi$
$853$	−14.9594	−	14.9594i	−0.512200	−	0.512200i	−0.915200	+	0.403000i	$0.867968\pi$
$854$	−4.68755	−	2.41082i	−0.160405	−	0.0824967i
$855$		0			0
$856$	−2.28471	+	3.95723i	−0.0780897	+	0.135255i
$857$	−11.6491	−	3.12136i	−0.397924	−	0.106623i	0.0543068	−	0.998524i	$-0.482705\pi$
$857$	−11.6491	−	3.12136i	−0.397924	−	0.106623i	−0.452231	+	0.891901i	$0.649372\pi$
$858$		0			0
$859$	2.90061	−	5.02401i	0.0989677	−	0.171417i	−0.812290	−	0.583254i	$-0.801779\pi$
$859$	2.90061	−	5.02401i	0.0989677	−	0.171417i	0.911258	+	0.411837i	$0.135113\pi$
$860$	−1.37941	+	0.591080i	−0.0470376	+	0.0201557i
$861$		0			0
$862$	−1.10172	−	1.10172i	−0.0375249	−	0.0375249i
$863$	0.778623	+	2.90586i	0.0265046	+	0.0989167i	0.977911	−	0.209021i	$-0.0670278\pi$
$863$	0.778623	+	2.90586i	0.0265046	+	0.0989167i	−0.951406	+	0.307938i	$0.900361\pi$
$864$		0			0
$865$	9.35746	+	7.00150i	0.318163	+	0.238058i
$866$	7.69343	+	4.44180i	0.261433	+	0.150939i
$867$		0			0
$868$	0.0738294	−	0.0813742i	0.00250593	−	0.00276202i
$869$			49.2347i			1.67017i
$870$		0			0
$871$	6.73657	−	3.88936i	0.228260	−	0.131786i
$872$	−4.68530	+	17.4858i	−0.158664	+	0.592143i
$873$		0			0
$874$	−10.3017			−0.348460
$875$	−28.8938	+	6.33614i	−0.976790	+	0.214201i
$876$		0			0
$877$	−33.8582	+	9.07228i	−1.14331	+	0.306349i	−0.780282	−	0.625428i	$-0.784924\pi$
$877$	−33.8582	+	9.07228i	−1.14331	+	0.306349i	−0.363030	+	0.931778i	$0.618258\pi$
$878$	6.18945	−	23.0994i	0.208884	−	0.779565i
$879$		0			0
$880$	5.07592	+	6.45147i	0.171109	+	0.217479i
$881$			23.7116i			0.798864i	0.916763	+	0.399432i	$0.130793\pi$
$881$			23.7116i			0.798864i	−0.916763	+	0.399432i	$0.869207\pi$
$882$		0			0
$883$	−7.95370	+	7.95370i	−0.267663	+	0.267663i	−0.828158	−	0.560495i	$-0.810611\pi$
$883$	−7.95370	+	7.95370i	−0.267663	+	0.267663i	0.560495	+	0.828158i	$0.310611\pi$
$884$	−0.801929	−	0.462994i	−0.0269718	−	0.0155722i
$885$		0			0
$886$	6.43103	+	11.1389i	0.216055	+	0.374218i
$887$	5.27738	+	19.6954i	0.177197	+	0.661308i	0.996167	+	0.0874718i	$0.0278788\pi$
$887$	5.27738	+	19.6954i	0.177197	+	0.661308i	−0.818970	+	0.573836i	$0.805455\pi$
$888$		0			0
$889$	−26.8495	−	41.6893i	−0.900503	−	1.39821i
$890$	−2.93964	+	1.25964i	−0.0985371	+	0.0422233i
$891$		0			0
$892$	−1.02015	−	0.273349i	−0.0341573	−	0.00915241i
$893$	13.5339	+	3.62640i	0.452895	+	0.121353i
$894$		0			0
$895$	26.0934	+	10.4392i	0.872207	+	0.348943i
$896$	0.128464	+	2.64263i	0.00429168	+	0.0882841i
$897$		0			0
$898$	4.63111	+	17.2836i	0.154542	+	0.576760i
$899$	−0.0544519	−	0.0943134i	−0.00181607	−	0.00314553i
$900$		0			0
$901$	5.40287	+	3.11935i	0.179996	+	0.103921i
$902$	23.3118	−	23.3118i	0.776197	−	0.776197i
$903$		0			0
$904$		−	2.15051i		−	0.0715247i
$905$	−20.5157	+	16.1415i	−0.681964	+	0.536560i
$906$		0			0
$907$	−1.68614	+	6.29276i	−0.0559874	+	0.208948i	−0.988253	−	0.152827i	$-0.951162\pi$
$907$	−1.68614	+	6.29276i	−0.0559874	+	0.208948i	0.932266	+	0.361775i	$0.117829\pi$
$908$	3.01404	−	0.807609i	0.100024	−	0.0268014i
$909$		0			0
$910$	−0.487376	+	6.93200i	−0.0161563	+	0.229794i
$911$	24.2528			0.803531			0.401765	−	0.915743i	$-0.368397\pi$
$911$	24.2528			0.803531			0.401765	+	0.915743i	$0.368397\pi$
$912$		0			0
$913$	13.0749	−	48.7964i	0.432718	−	1.61492i
$914$	29.6277	−	17.1056i	0.979997	−	0.565802i
$915$		0			0
$916$			8.42181i			0.278264i
$917$	−27.8138	−	25.2350i	−0.918493	−	0.833333i
$918$		0			0
$919$	31.2542	+	18.0446i	1.03098	+	0.595236i	0.917265	−	0.398277i	$-0.130392\pi$
$919$	31.2542	+	18.0446i	1.03098	+	0.595236i	0.113714	+	0.993513i	$0.463725\pi$
$920$	1.49988	+	10.4147i	0.0494497	+	0.343361i
$921$		0			0
$922$	6.04266	+	22.5515i	0.199004	+	0.742695i
$923$	6.74244	+	6.74244i	0.221930	+	0.221930i
$924$		0			0
$925$	−0.0311706	−	1.28426i	−0.00102488	−	0.0422263i
$926$	−2.81789	+	4.88073i	−0.0926017	+	0.160391i
$927$		0			0
$928$	2.53301	+	0.678717i	0.0831500	+	0.0222800i
$929$	−21.2041	+	36.7266i	−0.695685	+	1.20496i	0.274264	+	0.961654i	$0.411566\pi$
$929$	−21.2041	+	36.7266i	−0.695685	+	1.20496i	−0.969949	+	0.243307i	$0.921768\pi$
$930$		0			0
$931$	−12.4657	+	8.91344i	−0.408547	+	0.292126i
$932$	16.1198	+	16.1198i	0.528023	+	0.528023i
$933$		0			0
$934$	−2.44290	−	4.23123i	−0.0799342	−	0.138450i
$935$	−3.87694	+	5.18150i	−0.126789	+	0.169453i
$936$		0			0
$937$	−4.06709	+	4.06709i	−0.132866	+	0.132866i	−0.770412	−	0.637546i	$-0.779950\pi$
$937$	−4.06709	+	4.06709i	−0.132866	+	0.132866i	0.637546	+	0.770412i	$0.279950\pi$
$938$	3.70770	−	17.1243i	0.121061	−	0.559129i
$939$		0			0
$940$	1.69569	−	14.2103i	0.0553073	−	0.463489i
$941$	17.4071	−	10.0500i	0.567455	−	0.327621i	−0.188677	−	0.982039i	$-0.560420\pi$
$941$	17.4071	−	10.0500i	0.567455	−	0.327621i	0.756132	+	0.654419i	$0.227087\pi$
$942$		0			0
$943$	40.8179	−	10.9371i	1.32921	−	0.356162i
$944$	10.7123			0.348656
$945$		0			0
$946$	2.46386			0.0801069
$947$	−56.9449	+	15.2583i	−1.85046	+	0.495830i	−0.999565	−	0.0295030i	$-0.990608\pi$
$947$	−56.9449	+	15.2583i	−1.85046	+	0.495830i	−0.850897	+	0.525333i	$0.823941\pi$
$948$		0			0
$949$	−10.0354	+	5.79393i	−0.325762	+	0.188079i
$950$	9.60964	+	5.24144i	0.311778	+	0.170055i
$951$		0			0
$952$	−1.98608	+	0.637013i	−0.0643691	+	0.0206457i
$953$	31.1044	−	31.1044i	1.00757	−	1.00757i	0.00759828	−	0.999971i	$-0.497581\pi$
$953$	31.1044	−	31.1044i	1.00757	−	1.00757i	0.999971	−	0.00759828i	$-0.00241863\pi$
$954$		0			0
$955$	34.3127	−	4.94158i	1.11033	−	0.159906i
$956$	−11.9985	−	20.7821i	−0.388060	−	0.672140i
$957$		0			0
$958$	12.0996	+	12.0996i	0.390921	+	0.390921i
$959$	22.9505	−	44.6245i	0.741111	−	1.44100i
$960$		0			0
$961$	−15.4991	+	26.8453i	−0.499972	+	0.865977i
$962$	−0.291508	−	0.0781094i	−0.00939861	−	0.00251835i
$963$		0			0
$964$	−12.3937	+	21.4666i	−0.399175	+	0.691391i
$965$	−7.92454	−	18.4936i	−0.255100	−	0.595331i
$966$		0			0
$967$	−21.5036	−	21.5036i	−0.691510	−	0.691510i	0.271054	−	0.962564i	$-0.412628\pi$
$967$	−21.5036	−	21.5036i	−0.691510	−	0.691510i	−0.962564	+	0.271054i	$0.912628\pi$
$968$	−0.641168	−	2.39287i	−0.0206079	−	0.0769098i
$969$		0			0
$970$	−9.91244	+	1.42755i	−0.318269	+	0.0458360i
$971$	45.3034	+	26.1559i	1.45385	+	0.839384i	0.998697	−	0.0510273i	$-0.0162496\pi$
$971$	45.3034	+	26.1559i	1.45385	+	0.839384i	0.455158	+	0.890411i	$0.349583\pi$
$972$		0			0
$973$	−21.2997	−	4.61174i	−0.682836	−	0.147845i
$974$			0.130300i			0.00417507i
$975$		0			0
$976$	1.72539	−	0.996157i	0.0552285	−	0.0318862i
$977$	−14.6477	+	54.6658i	−0.468620	+	1.74891i	0.175979	+	0.984394i	$0.443691\pi$
$977$	−14.6477	+	54.6658i	−0.468620	+	1.74891i	−0.644599	+	0.764520i	$0.722976\pi$
$978$		0			0
$979$	5.25068			0.167813
$980$	10.8261	+	11.3046i	0.345828	+	0.361113i
$981$		0			0
$982$	26.0699	−	6.98541i	0.831924	−	0.222913i
$983$	−4.00621	+	14.9514i	−0.127778	+	0.476875i	−0.999923	−	0.0123723i	$-0.996062\pi$
$983$	−4.00621	+	14.9514i	−0.127778	+	0.476875i	0.872145	+	0.489247i	$0.162728\pi$
$984$		0			0
$985$	4.56939	−	38.2926i	0.145593	−	1.22010i
$986$			2.06729i			0.0658361i
$987$		0			0
$988$	1.81832	−	1.81832i	0.0578486	−	0.0578486i
$989$	2.73504	+	1.57907i	0.0869691	+	0.0502116i
$990$		0			0
$991$	26.8648	+	46.5311i	0.853388	+	1.47811i	0.878133	+	0.478417i	$0.158789\pi$
$991$	26.8648	+	46.5311i	0.853388	+	1.47811i	−0.0247453	+	0.999694i	$0.507877\pi$
$992$	0.0107485	+	0.0401138i	0.000341264	+	0.00127362i
$993$		0			0
$994$	21.4523	−	1.04284i	0.680424	−	0.0330769i
$995$	7.25190	−	18.1266i	0.229901	−	0.574653i
$996$		0			0
$997$	37.2167	+	9.97217i	1.17866	+	0.315822i	0.794396	−	0.607400i	$-0.207787\pi$
$997$	37.2167	+	9.97217i	1.17866	+	0.315822i	0.384267	+	0.923222i	$0.374454\pi$
$998$	−0.0930180	−	0.0249241i	−0.00294443	−	0.000788959i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bv.c.397.1		16
3.2	odd	2		70.2.k.a.47.3	yes	16
5.3	odd	4	inner	630.2.bv.c.523.4		16
7.3	odd	6	inner	630.2.bv.c.577.4		16
12.11	even	2		560.2.ci.c.257.4		16
15.2	even	4		350.2.o.c.243.4		16
15.8	even	4		70.2.k.a.33.1	yes	16
15.14	odd	2		350.2.o.c.257.2		16
21.2	odd	6		490.2.g.c.97.1		16
21.5	even	6		490.2.g.c.97.4		16
21.11	odd	6		490.2.l.c.227.2		16
21.17	even	6		70.2.k.a.17.1	yes	16
21.20	even	2		490.2.l.c.117.4		16
35.3	even	12	inner	630.2.bv.c.73.1		16
60.23	odd	4		560.2.ci.c.33.4		16
84.59	odd	6		560.2.ci.c.17.4		16
105.17	odd	12		350.2.o.c.143.2		16
105.23	even	12		490.2.g.c.293.4		16
105.38	odd	12		70.2.k.a.3.3	✓	16
105.53	even	12		490.2.l.c.423.4		16
105.59	even	6		350.2.o.c.157.4		16
105.68	odd	12		490.2.g.c.293.1		16
105.83	odd	4		490.2.l.c.313.2		16
420.143	even	12		560.2.ci.c.353.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.3	✓	16	105.38	odd	12
70.2.k.a.17.1	yes	16	21.17	even	6
70.2.k.a.33.1	yes	16	15.8	even	4
70.2.k.a.47.3	yes	16	3.2	odd	2
350.2.o.c.143.2		16	105.17	odd	12
350.2.o.c.157.4		16	105.59	even	6
350.2.o.c.243.4		16	15.2	even	4
350.2.o.c.257.2		16	15.14	odd	2
490.2.g.c.97.1		16	21.2	odd	6
490.2.g.c.97.4		16	21.5	even	6
490.2.g.c.293.1		16	105.68	odd	12
490.2.g.c.293.4		16	105.23	even	12
490.2.l.c.117.4		16	21.20	even	2
490.2.l.c.227.2		16	21.11	odd	6
490.2.l.c.313.2		16	105.83	odd	4
490.2.l.c.423.4		16	105.53	even	12
560.2.ci.c.17.4		16	84.59	odd	6
560.2.ci.c.33.4		16	60.23	odd	4
560.2.ci.c.257.4		16	12.11	even	2
560.2.ci.c.353.4		16	420.143	even	12
630.2.bv.c.73.1		16	35.3	even	12	inner
630.2.bv.c.397.1		16	1.1	even	1	trivial
630.2.bv.c.523.4		16	5.3	odd	4	inner
630.2.bv.c.577.4		16	7.3	odd	6	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(1.38266 + 1.75735i) q^{5} +(2.58583 + 0.559876i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.79038 - 1.33961i) q^{10} +(1.83557 + 3.17930i) q^{11} +(-0.830578 - 0.830578i) q^{13} +(-2.64263 + 0.128464i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.761471 + 0.204036i) q^{17} +(-1.09461 + 1.89593i) q^{19} +(2.07609 + 0.830578i) q^{20} +(-2.59589 - 2.59589i) q^{22} +(-1.21791 - 4.54529i) q^{23} +(-1.17653 + 4.85961i) q^{25} +(1.01725 + 0.587308i) q^{26} +(2.51934 - 0.808050i) q^{28} -2.62236i q^{29} +(0.0359651 - 0.0207644i) q^{31} +(-0.258819 + 0.965926i) q^{32} -0.788333 q^{34} +(2.59142 + 5.31832i) q^{35} +(-0.248174 + 0.0664979i) q^{37} +(0.566614 - 2.11463i) q^{38} +(-2.22032 - 0.264946i) q^{40} +8.98026i q^{41} +(-0.474569 + 0.474569i) q^{43} +(3.17930 + 1.83557i) q^{44} +(2.35282 + 4.07520i) q^{46} +(-1.65648 - 6.18205i) q^{47} +(6.37308 + 2.89549i) q^{49} +(-0.121320 - 4.99853i) q^{50} +(-1.13459 - 0.304013i) q^{52} +(7.64413 + 2.04824i) q^{53} +(-3.04917 + 7.62161i) q^{55} +(-2.22435 + 1.43257i) q^{56} +(0.678717 + 2.53301i) q^{58} +(5.35616 + 9.27713i) q^{59} +(1.72539 + 0.996157i) q^{61} +(-0.0293654 + 0.0293654i) q^{62} -1.00000i q^{64} +(0.311210 - 2.60802i) q^{65} +(-1.71399 + 6.39671i) q^{67} +(0.761471 - 0.204036i) q^{68} +(-3.87960 - 4.46639i) q^{70} -8.11777 q^{71} +(2.55331 - 9.52910i) q^{73} +(0.222506 - 0.128464i) q^{74} +2.18923i q^{76} +(2.96647 + 9.24884i) q^{77} +(11.6145 + 6.70563i) q^{79} +(2.21323 - 0.318742i) q^{80} +(-2.32426 - 8.67427i) q^{82} +(-9.73033 - 9.73033i) q^{83} +(0.694291 + 1.62028i) q^{85} +(0.335571 - 0.581226i) q^{86} +(-3.54605 - 0.950161i) q^{88} +(0.715130 - 1.23864i) q^{89} +(-1.68272 - 2.61276i) q^{91} +(-3.32739 - 3.32739i) q^{92} +(3.20007 + 5.54268i) q^{94} +(-4.84527 + 0.697798i) q^{95} +(3.16693 - 3.16693i) q^{97} +(-6.90533 - 1.14736i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} + 8 q^{7} - 12 q^{10} + 12 q^{11} + 8 q^{16} + 36 q^{17} - 8 q^{22} + 4 q^{23} + 12 q^{25} - 12 q^{26} + 4 q^{28} + 24 q^{31} - 8 q^{35} + 4 q^{37} - 24 q^{38} - 8 q^{43} - 8 q^{46} - 12 q^{47}+ \cdots - 40 q^{98}+O(q^{100}) \) 16 * q + 12 * q^5 + 8 * q^7 - 12 * q^10 + 12 * q^11 + 8 * q^16 + 36 * q^17 - 8 * q^22 + 4 * q^23 + 12 * q^25 - 12 * q^26 + 4 * q^28 + 24 * q^31 - 8 * q^35 + 4 * q^37 - 24 * q^38 - 8 * q^43 - 8 * q^46 - 12 * q^47 + 32 * q^50 + 28 * q^53 + 4 * q^56 - 32 * q^58 - 12 * q^61 + 8 * q^65 + 32 * q^67 + 36 * q^68 - 12 * q^70 - 16 * q^71 - 12 * q^73 - 16 * q^77 + 12 * q^80 - 48 * q^82 + 24 * q^85 - 12 * q^86 - 4 * q^88 - 16 * q^91 - 8 * q^92 - 20 * q^95 - 40 * q^98

Introduction

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