LMFDB - Embedded newform 450.3.k.a.149.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [450,3,Mod(149,450)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("450.149"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(450, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	450.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-8,0,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$12.2616118962$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.4
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	450.149
Dual form			450.3.k.a.299.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 1.22474i) q^{2} +(1.73205 + 2.44949i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.77526 + 3.85337i) q^{6} +(-7.22999 + 4.17423i) q^{7} -2.82843 q^{8} +(-3.00000 + 8.48528i) q^{9} +(0.825765 - 0.476756i) q^{11} +(-5.97469 + 0.550510i) q^{12} +(-8.39780 - 4.84847i) q^{13} +(-10.2247 - 5.90326i) q^{14} +(-2.00000 - 3.46410i) q^{16} -18.8776 q^{17} +(-12.5136 + 2.32577i) q^{18} +24.6969 q^{19} +(-22.7474 - 10.4798i) q^{21} +(1.16781 + 0.674235i) q^{22} +(0.476756 - 0.825765i) q^{23} +(-4.89898 - 6.92820i) q^{24} -13.7135i q^{26} +(-25.9808 + 7.34847i) q^{27} -16.6969i q^{28} +(-11.8485 + 6.84072i) q^{29} +(-1.52270 + 2.63740i) q^{31} +(2.82843 - 4.89898i) q^{32} +(2.59808 + 1.19694i) q^{33} +(-13.3485 - 23.1202i) q^{34} +(-11.6969 - 13.6814i) q^{36} +46.6969i q^{37} +(17.4634 + 30.2474i) q^{38} +(-2.66913 - 28.9681i) q^{39} +(-9.45459 - 5.45861i) q^{41} +(-3.24980 - 35.2702i) q^{42} +(-39.0105 + 22.5227i) q^{43} +1.90702i q^{44} +1.34847 q^{46} +(22.6435 + 39.2196i) q^{47} +(5.02118 - 10.8990i) q^{48} +(10.3485 - 17.9241i) q^{49} +(-32.6969 - 46.2405i) q^{51} +(16.7956 - 9.69694i) q^{52} +94.3879 q^{53} +(-27.3712 - 26.6237i) q^{54} +(20.4495 - 11.8065i) q^{56} +(42.7764 + 60.4949i) q^{57} +(-16.7563 - 9.67423i) q^{58} +(16.2650 + 9.39063i) q^{59} +(-6.54541 - 11.3370i) q^{61} -4.30686 q^{62} +(-13.7296 - 73.8712i) q^{63} +8.00000 q^{64} +(0.371173 + 4.02834i) q^{66} +(-64.9912 - 37.5227i) q^{67} +(18.8776 - 32.6969i) q^{68} +(2.84847 - 0.262459i) q^{69} -18.0204i q^{71} +(8.48528 - 24.0000i) q^{72} +7.90918i q^{73} +(-57.1918 + 33.0197i) q^{74} +(-24.6969 + 42.7764i) q^{76} +(-3.98018 + 6.89388i) q^{77} +(33.5912 - 23.7526i) q^{78} +(-21.8712 - 37.8820i) q^{79} +(-63.0000 - 50.9117i) q^{81} -15.4393i q^{82} +(65.1662 + 112.871i) q^{83} +(40.8990 - 28.9199i) q^{84} +(-55.1691 - 31.8519i) q^{86} +(-37.2784 - 17.1742i) q^{87} +(-2.33562 + 1.34847i) q^{88} +145.300i q^{89} +80.9546 q^{91} +(0.953512 + 1.65153i) q^{92} +(-9.09769 + 0.838264i) q^{93} +(-32.0227 + 55.4650i) q^{94} +(16.8990 - 1.55708i) q^{96} +(-95.1576 + 54.9393i) q^{97} +29.2699 q^{98} +(1.56811 + 8.43712i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 24 q^{6} - 24 q^{9} + 36 q^{11} - 72 q^{14} - 16 q^{16} + 80 q^{19} - 84 q^{21} - 36 q^{29} + 76 q^{31} - 48 q^{34} + 24 q^{36} + 204 q^{39} - 252 q^{41} - 48 q^{46} + 24 q^{49} - 144 q^{51}+ \cdots - 252 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 24 * q^6 - 24 * q^9 + 36 * q^11 - 72 * q^14 - 16 * q^16 + 80 * q^19 - 84 * q^21 - 36 * q^29 + 76 * q^31 - 48 * q^34 + 24 * q^36 + 204 * q^39 - 252 * q^41 - 48 * q^46 + 24 * q^49 - 144 * q^51 - 72 * q^54 + 144 * q^56 - 252 * q^59 + 124 * q^61 + 64 * q^64 - 144 * q^66 - 36 * q^69 - 144 * q^74 - 80 * q^76 - 28 * q^79 - 504 * q^81 + 288 * q^84 - 216 * q^86 + 824 * q^91 - 168 * q^94 + 96 * q^96 - 252 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$3$	1.73205	+	2.44949i	0.577350	+	0.816497i
$3$	1.73205	+	2.44949i	0.577350	+	0.816497i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.77526	+	3.85337i	−0.295876	+	0.642229i
$7$	−7.22999	+	4.17423i	−1.03286	+	0.596319i	−0.917801	−	0.397040i	$-0.870037\pi$
$7$	−7.22999	+	4.17423i	−1.03286	+	0.596319i	−0.115054	+	0.993359i	$0.536704\pi$
$8$	−2.82843			−0.353553
$9$	−3.00000	+	8.48528i	−0.333333	+	0.942809i
$10$		0			0
$11$	0.825765	−	0.476756i	0.0750696	−	0.0433414i	−0.461995	−	0.886882i	$-0.652866\pi$
$11$	0.825765	−	0.476756i	0.0750696	−	0.0433414i	0.537065	+	0.843541i	$0.319533\pi$
$12$	−5.97469	+	0.550510i	−0.497891	+	0.0458759i
$13$	−8.39780	−	4.84847i	−0.645984	−	0.372959i	0.140932	−	0.990019i	$-0.454990\pi$
$13$	−8.39780	−	4.84847i	−0.645984	−	0.372959i	−0.786916	+	0.617060i	$0.788324\pi$
$14$	−10.2247	−	5.90326i	−0.730339	−	0.421661i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−18.8776			−1.11045			−0.555223	−	0.831701i	$-0.687367\pi$
$17$	−18.8776			−1.11045			−0.555223	+	0.831701i	$0.687367\pi$
$18$	−12.5136	+	2.32577i	−0.695201	+	0.129209i
$19$	24.6969			1.29984			0.649919	−	0.760003i	$-0.274803\pi$
$19$	24.6969			1.29984			0.649919	+	0.760003i	$0.274803\pi$
$20$		0			0
$21$	−22.7474	−	10.4798i	−1.08321	−	0.499038i
$22$	1.16781	+	0.674235i	0.0530822	+	0.0306470i
$23$	0.476756	−	0.825765i	0.0207285	−	0.0359028i	−0.855475	−	0.517844i	$-0.826735\pi$
$23$	0.476756	−	0.825765i	0.0207285	−	0.0359028i	0.876204	+	0.481941i	$0.160068\pi$
$24$	−4.89898	−	6.92820i	−0.204124	−	0.288675i
$25$		0			0
$26$		−	13.7135i		−	0.527444i
$27$	−25.9808	+	7.34847i	−0.962250	+	0.272166i
$28$		−	16.6969i		−	0.596319i
$29$	−11.8485	+	6.84072i	−0.408568	+	0.235887i	−0.690174	−	0.723643i	$-0.742466\pi$
$29$	−11.8485	+	6.84072i	−0.408568	+	0.235887i	0.281606	+	0.959530i	$0.409133\pi$
$30$		0			0
$31$	−1.52270	+	2.63740i	−0.0491195	+	0.0850774i	−0.889540	−	0.456858i	$-0.848975\pi$
$31$	−1.52270	+	2.63740i	−0.0491195	+	0.0850774i	0.840420	+	0.541935i	$0.182308\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$	2.59808	+	1.19694i	0.0787296	+	0.0362709i
$34$	−13.3485	−	23.1202i	−0.392602	−	0.680007i
$35$		0			0
$36$	−11.6969	−	13.6814i	−0.324915	−	0.380040i
$37$			46.6969i			1.26208i	0.775751	+	0.631040i	$0.217372\pi$
$37$			46.6969i			1.26208i	−0.775751	+	0.631040i	$0.782628\pi$
$38$	17.4634	+	30.2474i	0.459562	+	0.795985i
$39$	−2.66913	−	28.9681i	−0.0684393	−	0.742772i
$40$		0			0
$41$	−9.45459	−	5.45861i	−0.230600	−	0.133137i	0.380249	−	0.924884i	$-0.375838\pi$
$41$	−9.45459	−	5.45861i	−0.230600	−	0.133137i	−0.610849	+	0.791747i	$0.709172\pi$
$42$	−3.24980	−	35.2702i	−0.0773763	−	0.839766i
$43$	−39.0105	+	22.5227i	−0.907220	+	0.523784i	−0.879536	−	0.475833i	$-0.842147\pi$
$43$	−39.0105	+	22.5227i	−0.907220	+	0.523784i	−0.0276845	+	0.999617i	$0.508813\pi$
$44$			1.90702i			0.0433414i
$45$		0			0
$46$	1.34847			0.0293145
$47$	22.6435	+	39.2196i	0.481776	+	0.834460i	0.999781	−	0.0209170i	$-0.00665856\pi$
$47$	22.6435	+	39.2196i	0.481776	+	0.834460i	−0.518005	+	0.855377i	$0.673325\pi$
$48$	5.02118	−	10.8990i	0.104608	−	0.227062i
$49$	10.3485	−	17.9241i	0.211193	−	0.365797i
$50$		0			0
$51$	−32.6969	−	46.2405i	−0.641116	−	0.906676i
$52$	16.7956	−	9.69694i	0.322992	−	0.186480i
$53$	94.3879			1.78090			0.890452	−	0.455077i	$-0.150388\pi$
$53$	94.3879			1.78090			0.890452	+	0.455077i	$0.150388\pi$
$54$	−27.3712	−	26.6237i	−0.506874	−	0.493031i
$55$		0			0
$56$	20.4495	−	11.8065i	0.365169	−	0.210831i
$57$	42.7764	+	60.4949i	0.750462	+	1.06131i
$58$	−16.7563	−	9.67423i	−0.288901	−	0.166797i
$59$	16.2650	+	9.39063i	0.275679	+	0.159163i	0.631466	−	0.775404i	$-0.282454\pi$
$59$	16.2650	+	9.39063i	0.275679	+	0.159163i	−0.355787	+	0.934567i	$0.615787\pi$
$60$		0			0
$61$	−6.54541	−	11.3370i	−0.107302	−	0.185852i	0.807375	−	0.590039i	$-0.200888\pi$
$61$	−6.54541	−	11.3370i	−0.107302	−	0.185852i	−0.914676	+	0.404187i	$0.867554\pi$
$62$	−4.30686			−0.0694654
$63$	−13.7296	−	73.8712i	−0.217930	−	1.17256i
$64$	8.00000			0.125000
$65$		0			0
$66$	0.371173	+	4.02834i	0.00562383	+	0.0610355i
$67$	−64.9912	−	37.5227i	−0.970018	−	0.560040i	−0.0707765	−	0.997492i	$-0.522548\pi$
$67$	−64.9912	−	37.5227i	−0.970018	−	0.560040i	−0.899242	+	0.437452i	$0.855881\pi$
$68$	18.8776	−	32.6969i	0.277612	−	0.480837i
$69$	2.84847	−	0.262459i	0.0412822	−	0.00380375i
$70$		0			0
$71$		−	18.0204i		−	0.253808i	−0.991915	−	0.126904i	$-0.959496\pi$
$71$		−	18.0204i		−	0.253808i	0.991915	−	0.126904i	$-0.0405041\pi$
$72$	8.48528	−	24.0000i	0.117851	−	0.333333i
$73$			7.90918i			0.108345i	0.998532	+	0.0541725i	$0.0172521\pi$
$73$			7.90918i			0.108345i	−0.998532	+	0.0541725i	$0.982748\pi$
$74$	−57.1918	+	33.0197i	−0.772863	+	0.446212i
$75$		0			0
$76$	−24.6969	+	42.7764i	−0.324960	+	0.562847i
$77$	−3.98018	+	6.89388i	−0.0516907	+	0.0895309i
$78$	33.5912	−	23.7526i	0.430656	−	0.304520i
$79$	−21.8712	−	37.8820i	−0.276850	−	0.479519i	0.693750	−	0.720216i	$-0.255957\pi$
$79$	−21.8712	−	37.8820i	−0.276850	−	0.479519i	−0.970600	+	0.240697i	$0.922624\pi$
$80$		0			0
$81$	−63.0000	−	50.9117i	−0.777778	−	0.628539i
$82$		−	15.4393i		−	0.188284i
$83$	65.1662	+	112.871i	0.785135	+	1.35989i	0.928918	+	0.370284i	$0.120740\pi$
$83$	65.1662	+	112.871i	0.785135	+	1.35989i	−0.143783	+	0.989609i	$0.545927\pi$
$84$	40.8990	−	28.9199i	0.486893	−	0.344285i
$85$		0			0
$86$	−55.1691	−	31.8519i	−0.641502	−	0.370371i
$87$	−37.2784	−	17.1742i	−0.428488	−	0.197405i
$88$	−2.33562	+	1.34847i	−0.0265411	+	0.0153235i
$89$			145.300i			1.63258i	0.577642	+	0.816290i	$0.303973\pi$
$89$			145.300i			1.63258i	−0.577642	+	0.816290i	$0.696027\pi$
$90$		0			0
$91$	80.9546			0.889611
$92$	0.953512	+	1.65153i	0.0103643	+	0.0179514i
$93$	−9.09769	+	0.838264i	−0.0978246	+	0.00901359i
$94$	−32.0227	+	55.4650i	−0.340667	+	0.590053i
$95$		0			0
$96$	16.8990	−	1.55708i	0.176031	−	0.0162196i
$97$	−95.1576	+	54.9393i	−0.981007	+	0.566384i	−0.902574	−	0.430535i	$-0.858325\pi$
$97$	−95.1576	+	54.9393i	−0.981007	+	0.566384i	−0.0784327	+	0.996919i	$0.524992\pi$
$98$	29.2699			0.298672
$99$	1.56811	+	8.43712i	0.0158395	+	0.0852234i
$100$		0			0
$101$	127.772	−	73.7695i	1.26507	−	0.730391i	0.291022	−	0.956716i	$-0.406005\pi$
$101$	127.772	−	73.7695i	1.26507	−	0.730391i	0.974052	+	0.226326i	$0.0726714\pi$
$102$	33.5125	−	72.7423i	0.328554	−	0.713160i
$103$	−89.3186	−	51.5681i	−0.867171	−	0.500661i	−0.000763745	−	1.00000i	$-0.500243\pi$
$103$	−89.3186	−	51.5681i	−0.867171	−	0.500661i	−0.866407	+	0.499338i	$0.833576\pi$
$104$	23.7526	+	13.7135i	0.228390	+	0.131861i
$105$		0			0
$106$	66.7423	+	115.601i	0.629645	+	1.09058i
$107$	36.0408			0.336830			0.168415	−	0.985716i	$-0.446135\pi$
$107$	36.0408			0.336830			0.168415	+	0.985716i	$0.446135\pi$
$108$	13.2528	−	52.3485i	0.122711	−	0.484708i
$109$	148.272			1.36030			0.680149	−	0.733074i	$-0.261915\pi$
$109$	148.272			1.36030			0.680149	+	0.733074i	$0.261915\pi$
$110$		0			0
$111$	−114.384	+	80.8815i	−1.03048	+	0.728662i
$112$	28.9199	+	16.6969i	0.258214	+	0.149080i
$113$	−85.5439	+	148.166i	−0.757025	+	1.31121i	0.187336	+	0.982296i	$0.440015\pi$
$113$	−85.5439	+	148.166i	−0.757025	+	1.31121i	−0.944361	+	0.328910i	$0.893319\pi$
$114$	−43.8434	+	95.1665i	−0.384591	+	0.834794i
$115$		0			0
$116$		−	27.3629i		−	0.235887i
$117$	66.3340	−	56.7122i	0.566957	−	0.484720i
$118$			26.5607i			0.225091i
$119$	136.485	−	78.7995i	1.14693	−	0.662180i
$120$		0			0
$121$	−60.0454	+	104.002i	−0.496243	+	0.859518i
$122$	9.25660	−	16.0329i	0.0758738	−	0.131417i
$123$	−3.00502	−	32.6135i	−0.0244311	−	0.265151i
$124$	−3.04541	−	5.27480i	−0.0245597	−	0.0425387i
$125$		0			0
$126$	80.7650	−	69.0501i	0.640992	−	0.548016i
$127$		−	78.0908i		−	0.614888i	−0.951566	−	0.307444i	$-0.900526\pi$
$127$		−	78.0908i		−	0.614888i	0.951566	−	0.307444i	$-0.0994737\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$	−122.737	−	56.5453i	−0.951452	−	0.438335i
$130$		0			0
$131$	202.704	+	117.031i	1.54736	+	0.893369i	0.998342	+	0.0575598i	$0.0183320\pi$
$131$	202.704	+	117.031i	1.54736	+	0.893369i	0.549019	+	0.835810i	$0.315001\pi$
$132$	−4.67123	+	3.30306i	−0.0353881	+	0.0250232i
$133$	−178.559	+	103.091i	−1.34255	+	0.775119i
$134$		−	106.130i		−	0.792017i
$135$		0			0
$136$	53.3939			0.392602
$137$	74.9156	+	129.758i	0.546829	+	0.947136i	0.998489	+	0.0549460i	$0.0174987\pi$
$137$	74.9156	+	129.758i	0.546829	+	0.947136i	−0.451660	+	0.892190i	$0.649168\pi$
$138$	2.33562	+	3.30306i	0.0169248	+	0.0239352i
$139$	−42.2650	+	73.2052i	−0.304065	+	0.526656i	−0.977053	−	0.212998i	$-0.931677\pi$
$139$	−42.2650	+	73.2052i	−0.304065	+	0.526656i	0.672988	+	0.739654i	$0.265011\pi$
$140$		0			0
$141$	−56.8485	+	123.395i	−0.403181	+	0.875144i
$142$	22.0704	−	12.7423i	0.155425	−	0.0897348i
$143$	−9.24614			−0.0646584
$144$	35.3939	−	6.57826i	0.245791	−	0.0456823i
$145$		0			0
$146$	−9.68673	+	5.59264i	−0.0663475	+	0.0383057i
$147$	61.8289	−	5.69694i	0.420605	−	0.0387547i
$148$	−80.8815	−	46.6969i	−0.546496	−	0.315520i
$149$	−100.030	−	57.7524i	−0.671343	−	0.387600i	0.125242	−	0.992126i	$-0.460029\pi$
$149$	−100.030	−	57.7524i	−0.671343	−	0.387600i	−0.796585	+	0.604526i	$0.793362\pi$
$150$		0			0
$151$	32.3865	+	56.0950i	0.214480	+	0.371490i	0.953112	−	0.302619i	$-0.0978610\pi$
$151$	32.3865	+	56.0950i	0.214480	+	0.371490i	−0.738632	+	0.674109i	$0.764528\pi$
$152$	−69.8535			−0.459562
$153$	56.6328	−	160.182i	0.370149	−	1.04694i
$154$	−11.2577			−0.0731016
$155$		0			0
$156$	52.8434	+	24.3450i	0.338740	+	0.156058i
$157$	18.0292	+	10.4092i	0.114836	+	0.0663005i	0.556318	−	0.830970i	$-0.312214\pi$
$157$	18.0292	+	10.4092i	0.114836	+	0.0663005i	−0.441482	+	0.897270i	$0.645547\pi$
$158$	30.9305	−	53.5732i	0.195763	−	0.339071i
$159$	163.485	+	231.202i	1.02821	+	1.45410i
$160$		0			0
$161$			7.96036i			0.0494433i
$162$	17.8061	−	113.159i	0.109914	−	0.698512i
$163$		−	133.060i		−	0.816320i	−0.912910	−	0.408160i	$-0.866171\pi$
$163$		−	133.060i		−	0.816320i	0.912910	−	0.408160i	$-0.133829\pi$
$164$	18.9092	−	10.9172i	0.115300	−	0.0665684i
$165$		0			0
$166$	−92.1589	+	159.624i	−0.555174	+	0.961590i
$167$	147.255	−	255.053i	0.881765	−	1.52726i	0.0323885	−	0.999475i	$-0.489689\pi$
$167$	147.255	−	255.053i	0.881765	−	1.52726i	0.849377	−	0.527787i	$-0.176978\pi$
$168$	64.3395	+	29.6413i	0.382973	+	0.176436i
$169$	−37.4847	−	64.9254i	−0.221803	−	0.384174i
$170$		0			0
$171$	−74.0908	+	209.560i	−0.433280	+	1.22550i
$172$		−	90.0908i		−	0.523784i
$173$	34.6322	+	59.9847i	0.200186	+	0.346732i	0.948588	−	0.316513i	$-0.102512\pi$
$173$	34.6322	+	59.9847i	0.200186	+	0.346732i	−0.748402	+	0.663245i	$0.769179\pi$
$174$	−5.32577	−	57.8006i	−0.0306078	−	0.332187i
$175$		0			0
$176$	−3.30306	−	1.90702i	−0.0187674	−	0.0108354i
$177$	5.16964	+	56.1061i	0.0292070	+	0.316984i
$178$	−177.955	+	102.742i	−0.999747	+	0.577204i
$179$			47.4829i			0.265268i	0.991165	+	0.132634i	$0.0423435\pi$
$179$			47.4829i			0.265268i	−0.991165	+	0.132634i	$0.957657\pi$
$180$		0			0
$181$	242.879			1.34187			0.670935	−	0.741516i	$-0.265893\pi$
$181$	242.879			1.34187			0.670935	+	0.741516i	$0.265893\pi$
$182$	57.2435	+	99.1487i	0.314525	+	0.544773i
$183$	16.4328	−	35.6691i	0.0897969	−	0.194913i
$184$	−1.34847	+	2.33562i	−0.00732864	+	0.0126936i
$185$		0			0
$186$	−7.45969	−	10.5496i	−0.0401059	−	0.0567183i
$187$	−15.5885	+	9.00000i	−0.0833607	+	0.0481283i
$188$	−90.5739			−0.481776
$189$	157.166	−	161.579i	0.831568	−	0.854916i
$190$		0			0
$191$	6.52270	−	3.76588i	0.0341503	−	0.0197167i	−0.482828	−	0.875715i	$-0.660390\pi$
$191$	6.52270	−	3.76588i	0.0341503	−	0.0197167i	0.516978	+	0.855999i	$0.327057\pi$
$192$	13.8564	+	19.5959i	0.0721688	+	0.102062i
$193$	299.172	+	172.727i	1.55011	+	0.894959i	0.998131	+	0.0611031i	$0.0194618\pi$
$193$	299.172	+	172.727i	1.55011	+	0.894959i	0.551983	+	0.833856i	$0.313871\pi$
$194$	−134.573	−	77.6959i	−0.693676	−	0.400494i
$195$		0			0
$196$	20.6969	+	35.8481i	0.105597	+	0.182899i
$197$	77.2247			0.392004			0.196002	−	0.980604i	$-0.437204\pi$
$197$	77.2247			0.392004			0.196002	+	0.980604i	$0.437204\pi$
$198$	−9.22450	+	7.88648i	−0.0465884	+	0.0398307i
$199$	−153.485			−0.771280			−0.385640	−	0.922649i	$-0.626019\pi$
$199$	−153.485			−0.771280			−0.385640	+	0.922649i	$0.626019\pi$
$200$		0			0
$201$	−20.6566	−	224.187i	−0.102769	−	1.11536i
$202$	180.698	+	104.326i	0.894542	+	0.516464i
$203$	57.1095	−	98.9166i	0.281328	−	0.487274i
$204$	112.788	−	10.3923i	0.552881	−	0.0509427i
$205$		0			0
$206$		−	145.857i		−	0.708042i
$207$	5.57658	+	6.52270i	0.0269400	+	0.0315106i
$208$			38.7878i			0.186480i
$209$	20.3939	−	11.7744i	0.0975784	−	0.0563369i
$210$		0			0
$211$	25.7804	−	44.6529i	0.122182	−	0.211625i	−0.798446	−	0.602066i	$-0.794344\pi$
$211$	25.7804	−	44.6529i	0.122182	−	0.211625i	0.920628	+	0.390441i	$0.127678\pi$
$212$	−94.3879	+	163.485i	−0.445226	+	0.771154i
$213$	44.1408	−	31.2122i	0.207234	−	0.146536i
$214$	25.4847	+	44.1408i	0.119087	+	0.206265i
$215$		0			0
$216$	73.4847	−	20.7846i	0.340207	−	0.0962250i
$217$		−	25.4245i		−	0.117164i
$218$	104.844	+	181.596i	0.480938	+	0.833009i
$219$	−19.3735	+	13.6991i	−0.0884633	+	0.0625530i
$220$		0			0
$221$	158.530	+	91.5274i	0.717331	+	0.414151i
$222$	−179.941	−	82.8990i	−0.810543	−	0.373419i
$223$	−271.263	+	156.614i	−1.21642	+	0.702303i	−0.964151	−	0.265353i	$-0.914511\pi$
$223$	−271.263	+	156.614i	−1.21642	+	0.702303i	−0.252273	+	0.967656i	$0.581178\pi$
$224$			47.2261i			0.210831i
$225$		0			0
$226$	−241.955			−1.07060
$227$	−38.1356	−	66.0528i	−0.167998	−	0.290982i	0.769718	−	0.638384i	$-0.220397\pi$
$227$	−38.1356	−	66.0528i	−0.167998	−	0.290982i	−0.937716	+	0.347403i	$0.887064\pi$
$228$	−147.557	+	13.5959i	−0.647178	+	0.0596312i
$229$	−60.7724	+	105.261i	−0.265382	+	0.459655i	−0.967664	−	0.252244i	$-0.918831\pi$
$229$	−60.7724	+	105.261i	−0.265382	+	0.459655i	0.702282	+	0.711899i	$0.252165\pi$
$230$		0			0
$231$	−23.7804	+	2.19113i	−0.102945	+	0.00948541i
$232$	33.5125	−	19.3485i	0.144451	−	0.0833986i
$233$	151.021			0.648157			0.324079	−	0.946030i	$-0.394946\pi$
$233$	151.021			0.648157			0.324079	+	0.946030i	$0.394946\pi$
$234$	116.363	+	41.1406i	0.497279	+	0.175815i
$235$		0			0
$236$	−32.5301	+	18.7813i	−0.137839	+	0.0795816i
$237$	54.9095	−	119.187i	0.231686	−	0.502898i
$238$	193.019	+	111.439i	0.811002	+	0.468232i
$239$	75.9620	+	43.8567i	0.317833	+	0.183501i	0.650426	−	0.759570i	$-0.274590\pi$
$239$	75.9620	+	43.8567i	0.317833	+	0.183501i	−0.332593	+	0.943070i	$0.607924\pi$
$240$		0			0
$241$	−100.894	−	174.753i	−0.418647	−	0.725118i	0.577157	−	0.816633i	$-0.304162\pi$
$241$	−100.894	−	174.753i	−0.418647	−	0.725118i	−0.995804	+	0.0915158i	$0.970829\pi$
$242$	−169.834			−0.701794
$243$	15.5885	−	242.499i	0.0641500	−	0.997940i
$244$	26.1816			0.107302
$245$		0			0
$246$	37.8184	−	26.7416i	0.153733	−	0.108706i
$247$	−207.400	−	119.742i	−0.839675	−	0.484787i
$248$	4.30686	−	7.45969i	0.0173664	−	0.0300794i
$249$	−163.606	+	355.123i	−0.657051	+	1.42619i
$250$		0			0
$251$		−	52.6261i		−	0.209666i	−0.994490	−	0.104833i	$-0.966569\pi$
$251$		−	52.6261i		−	0.209666i	0.994490	−	0.104833i	$-0.0334307\pi$
$252$	141.678	+	50.0908i	0.562215	+	0.198773i
$253$		−	0.909185i		−	0.00359362i
$254$	95.6413	−	55.2185i	0.376541	−	0.217396i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	40.3532	−	69.8939i	0.157017	−	0.271961i	−0.776775	−	0.629778i	$-0.783146\pi$
$257$	40.3532	−	69.8939i	0.157017	−	0.271961i	0.933791	+	0.357818i	$0.116479\pi$
$258$	−17.5348	−	190.305i	−0.0679644	−	0.737618i
$259$	−194.924	−	337.618i	−0.752602	−	1.30355i
$260$		0			0
$261$	−22.5000	−	121.060i	−0.0862069	−	0.463830i
$262$			331.015i			1.26342i
$263$	−231.872	−	401.614i	−0.881641	−	1.52705i	−0.849515	−	0.527564i	$-0.823106\pi$
$263$	−231.872	−	401.614i	−0.881641	−	1.52705i	−0.0321259	−	0.999484i	$-0.510228\pi$
$264$	−7.34847	−	3.38545i	−0.0278351	−	0.0128237i
$265$		0			0
$266$	−252.520	−	145.792i	−0.949323	−	0.548092i
$267$	−355.910	+	251.666i	−1.33300	+	0.942570i
$268$	129.982	−	75.0454i	0.485009	−	0.280020i
$269$		−	43.4762i		−	0.161622i	−0.996729	−	0.0808109i	$-0.974249\pi$
$269$		−	43.4762i		−	0.161622i	0.996729	−	0.0808109i	$-0.0257510\pi$
$270$		0			0
$271$	−342.636			−1.26434			−0.632169	−	0.774830i	$-0.717835\pi$
$271$	−342.636			−1.26434			−0.632169	+	0.774830i	$0.717835\pi$
$272$	37.7552	+	65.3939i	0.138806	+	0.240419i
$273$	140.217	+	198.297i	0.513617	+	0.726364i
$274$	−105.947	+	183.505i	−0.386667	+	0.669726i
$275$		0			0
$276$	−2.39388	+	5.19615i	−0.00867347	+	0.0188266i
$277$	−42.4352	+	24.5000i	−0.153196	+	0.0884477i	−0.574638	−	0.818407i	$-0.694857\pi$
$277$	−42.4352	+	24.5000i	−0.153196	+	0.0884477i	0.421442	+	0.906855i	$0.361524\pi$
$278$	−119.544			−0.430013
$279$	−17.8110	−	20.8328i	−0.0638386	−	0.0746694i
$280$		0			0
$281$	−17.8791	+	10.3225i	−0.0636266	+	0.0367349i	−0.531476	−	0.847073i	$-0.678362\pi$
$281$	−17.8791	+	10.3225i	−0.0636266	+	0.0367349i	0.467849	+	0.883808i	$0.345029\pi$
$282$	−191.326	+	17.6288i	−0.678460	+	0.0625136i
$283$	46.2533	+	26.7043i	0.163439	+	0.0943616i	0.579489	−	0.814980i	$-0.303252\pi$
$283$	46.2533	+	26.7043i	0.163439	+	0.0943616i	−0.416049	+	0.909342i	$0.636586\pi$
$284$	31.2122	+	18.0204i	0.109902	+	0.0634521i
$285$		0			0
$286$	−6.53801	−	11.3242i	−0.0228602	−	0.0395950i
$287$	91.1421			0.317568
$288$	33.0839	+	38.6969i	0.114875	+	0.134364i
$289$	67.3633			0.233091
$290$		0			0
$291$	−299.391	−	137.930i	−1.02884	−	0.473986i
$292$	−13.6991	−	7.90918i	−0.0469148	−	0.0270862i
$293$	−7.46196	+	12.9245i	−0.0254674	+	0.0441109i	−0.878478	−	0.477782i	$-0.841441\pi$
$293$	−7.46196	+	12.9245i	−0.0254674	+	0.0441109i	0.853011	+	0.521893i	$0.174774\pi$
$294$	50.6969	+	71.6963i	0.172439	+	0.243865i
$295$		0			0
$296$		−	132.079i		−	0.446212i
$297$	−17.9506	+	18.4546i	−0.0604397	+	0.0621367i
$298$		−	163.348i		−	0.548149i
$299$	−8.00740	+	4.62307i	−0.0267806	+	0.0154618i
$300$		0			0
$301$	188.030	−	325.678i	0.624685	−	1.08199i
$302$	−45.8014	+	79.3304i	−0.151660	+	0.262683i
$303$	402.006	+	185.205i	1.32675	+	0.611237i
$304$	−49.3939	−	85.5527i	−0.162480	−	0.281423i
$305$		0			0
$306$	236.227	−	43.9048i	0.771984	−	0.143480i
$307$			65.9092i			0.214688i	0.994222	+	0.107344i	$0.0342346\pi$
$307$			65.9092i			0.214688i	−0.994222	+	0.107344i	$0.965765\pi$
$308$	−7.96036	−	13.7878i	−0.0258453	−	0.0447654i
$309$	−28.3888	−	308.104i	−0.0918731	−	0.997099i
$310$		0			0
$311$	−216.659	−	125.088i	−0.696652	−	0.402213i	0.109447	−	0.993993i	$-0.465092\pi$
$311$	−216.659	−	125.088i	−0.696652	−	0.402213i	−0.806099	+	0.591780i	$0.798425\pi$
$312$	7.54945	+	81.9342i	0.0241969	+	0.262610i
$313$	369.268	−	213.197i	1.17977	−	0.681140i	0.223808	−	0.974633i	$-0.428151\pi$
$313$	369.268	−	213.197i	1.17977	−	0.681140i	0.955961	+	0.293493i	$0.0948177\pi$
$314$			29.4416i			0.0937631i
$315$		0			0
$316$	87.4847			0.276850
$317$	−231.990	−	401.818i	−0.731829	−	1.26756i	−0.956101	−	0.293038i	$-0.905334\pi$
$317$	−231.990	−	401.818i	−0.731829	−	1.26756i	0.224272	−	0.974527i	$-0.427999\pi$
$318$	−167.563	+	363.712i	−0.526927	+	1.14375i
$319$	−6.52270	+	11.2977i	−0.0204473	+	0.0354158i
$320$		0			0
$321$	62.4245	+	88.2816i	0.194469	+	0.275020i
$322$	−9.74941	+	5.62883i	−0.0302777	+	0.0174808i
$323$	−466.219			−1.44340
$324$	151.182	−	58.2075i	0.466610	−	0.179653i
$325$		0			0
$326$	162.965	−	94.0878i	0.499892	−	0.288613i
$327$	256.815	+	363.192i	0.785368	+	1.11068i
$328$	26.7416	+	15.4393i	0.0815293	+	0.0470710i
$329$	−327.424	−	189.038i	−0.995210	−	0.574585i
$330$		0			0
$331$	−236.401	−	409.459i	−0.714203	−	1.23704i	−0.963266	−	0.268549i	$-0.913456\pi$
$331$	−236.401	−	409.459i	−0.714203	−	1.23704i	0.249063	−	0.968487i	$-0.419877\pi$
$332$	−260.665			−0.785135
$333$	−396.237	−	140.091i	−1.18990	−	0.420693i
$334$	416.499			1.24700
$335$		0			0
$336$	9.19184	+	99.7591i	0.0273567	+	0.296902i
$337$	−264.663	−	152.803i	−0.785349	−	0.453422i	0.0529735	−	0.998596i	$-0.483130\pi$
$337$	−264.663	−	152.803i	−0.785349	−	0.453422i	−0.838323	+	0.545174i	$0.816463\pi$
$338$	53.0114	−	91.8184i	0.156838	−	0.271652i
$339$	−511.098	+	47.0928i	−1.50766	+	0.138917i
$340$		0			0
$341$			2.90383i			0.00851564i
$342$	−309.048	+	57.4393i	−0.903650	+	0.167951i
$343$		−	236.287i		−	0.688884i
$344$	110.338	−	63.7038i	0.320751	−	0.185186i
$345$		0			0
$346$	−48.9773	+	84.8312i	−0.141553	+	0.245177i
$347$	−66.8373	+	115.766i	−0.192615	+	0.333618i	−0.946116	−	0.323828i	$-0.895030\pi$
$347$	−66.8373	+	115.766i	−0.192615	+	0.333618i	0.753501	+	0.657446i	$0.228363\pi$
$348$	67.0251	−	47.3939i	0.192601	−	0.136189i
$349$	−49.3786	−	85.5262i	−0.141486	−	0.245061i	0.786570	−	0.617500i	$-0.211855\pi$
$349$	−49.3786	−	85.5262i	−0.141486	−	0.245061i	−0.928056	+	0.372440i	$0.878521\pi$
$350$		0			0
$351$	253.810	+	64.2560i	0.723105	+	0.183065i
$352$		−	5.39388i		−	0.0153235i
$353$	163.058	+	282.424i	0.461919	+	0.800068i	0.999057	−	0.0434270i	$-0.0138276\pi$
$353$	163.058	+	282.424i	0.461919	+	0.800068i	−0.537137	+	0.843495i	$0.680494\pi$
$354$	−65.0602	+	46.0045i	−0.183786	+	0.129956i
$355$		0			0
$356$	−251.666	−	145.300i	−0.706928	−	0.408145i
$357$	429.417	+	197.833i	1.20285	+	0.554155i
$358$	−58.1545	+	33.5755i	−0.162443	+	0.0937863i
$359$		−	418.736i		−	1.16639i	−0.812331	−	0.583197i	$-0.801801\pi$
$359$		−	418.736i		−	1.16639i	0.812331	−	0.583197i	$-0.198199\pi$
$360$		0			0
$361$	248.939			0.689581
$362$	171.741	+	297.464i	0.474423	+	0.821725i
$363$	−358.753	+	33.0556i	−0.988300	+	0.0910623i
$364$	−80.9546	+	140.217i	−0.222403	+	0.385213i
$365$		0			0
$366$	55.3054	−	5.09586i	0.151108	−	0.0139231i
$367$	162.143	−	93.6135i	0.441808	−	0.255078i	−0.262557	−	0.964917i	$-0.584566\pi$
$367$	162.143	−	93.6135i	0.441808	−	0.255078i	0.704364	+	0.709839i	$0.251232\pi$
$368$	−3.81405			−0.0103643
$369$	74.6816	−	63.8490i	0.202389	−	0.173033i
$370$		0			0
$371$	−682.423	+	393.997i	−1.83942	+	1.06199i
$372$	7.64577	−	16.5959i	0.0205531	−	0.0446127i
$373$	390.603	+	225.515i	1.04719	+	0.604597i	0.921862	−	0.387518i	$-0.126667\pi$
$373$	390.603	+	225.515i	1.04719	+	0.604597i	0.125331	+	0.992115i	$0.460001\pi$
$374$	−22.0454	−	12.7279i	−0.0589449	−	0.0340319i
$375$		0			0
$376$	−64.0454	−	110.930i	−0.170334	−	0.295026i
$377$	132.668			0.351905
$378$	309.027	+	78.2350i	0.817531	+	0.206971i
$379$	489.666			1.29200			0.645998	−	0.763339i	$-0.276442\pi$
$379$	489.666			1.29200			0.645998	+	0.763339i	$0.276442\pi$
$380$		0			0
$381$	191.283	−	135.257i	0.502054	−	0.355006i
$382$	9.22450	+	5.32577i	0.0241479	+	0.0139418i
$383$	51.5281	−	89.2492i	0.134538	−	0.233027i	−0.790883	−	0.611968i	$-0.790378\pi$
$383$	51.5281	−	89.2492i	0.134538	−	0.233027i	0.925421	+	0.378941i	$0.123712\pi$
$384$	−14.2020	+	30.8270i	−0.0369845	+	0.0802786i
$385$		0			0
$386$			488.546i			1.26566i
$387$	−74.0801	−	398.583i	−0.191421	−	1.02993i
$388$		−	219.757i		−	0.566384i
$389$	−29.6816	+	17.1367i	−0.0763024	+	0.0440532i	−0.537666	−	0.843158i	$-0.680694\pi$
$389$	−29.6816	+	17.1367i	−0.0763024	+	0.0440532i	0.461363	+	0.887211i	$0.347360\pi$
$390$		0			0
$391$	−9.00000	+	15.5885i	−0.0230179	+	0.0398682i
$392$	−29.2699	+	50.6969i	−0.0746681	+	0.129329i
$393$	64.4270	+	699.227i	0.163936	+	1.77920i
$394$	54.6061	+	94.5806i	0.138594	+	0.240052i
$395$		0			0
$396$	−16.1816	−	5.72107i	−0.0408627	−	0.0144471i
$397$			8.27245i			0.0208374i	0.999946	+	0.0104187i	$0.00331643\pi$
$397$			8.27245i			0.0208374i	−0.999946	+	0.0104187i	$0.996684\pi$
$398$	−108.530	−	187.980i	−0.272689	−	0.472311i
$399$	−561.792	−	258.819i	−1.40800	−	0.648669i
$400$		0			0
$401$	358.636	+	207.059i	0.894355	+	0.516356i	0.875364	−	0.483464i	$-0.160622\pi$
$401$	358.636	+	207.059i	0.894355	+	0.516356i	0.0189903	+	0.999820i	$0.493955\pi$
$402$	259.965	−	183.823i	0.646679	−	0.457271i
$403$	25.5747	−	14.7656i	0.0634608	−	0.0366391i
$404$			295.078i			0.730391i
$405$		0			0
$406$	161.530			0.397857
$407$	22.2630	+	38.5607i	0.0547003	+	0.0947438i
$408$	92.4809	+	130.788i	0.226669	+	0.320558i
$409$	−163.106	+	282.508i	−0.398792	+	0.690729i	−0.993577	−	0.113156i	$-0.963904\pi$
$409$	−163.106	+	282.508i	−0.398792	+	0.690729i	0.594785	+	0.803885i	$0.297237\pi$
$410$		0			0
$411$	−188.082	+	408.252i	−0.457621	+	0.993314i
$412$	178.637	−	103.136i	0.433585	−	0.250331i
$413$	−156.795			−0.379648
$414$	−4.04541	+	11.4421i	−0.00977152	+	0.0276380i
$415$		0			0
$416$	−47.5051	+	27.4271i	−0.114195	+	0.0659305i
$417$	−252.521	+	23.2673i	−0.605565	+	0.0557970i
$418$	28.8413	+	16.6515i	0.0689983	+	0.0398362i
$419$	468.325	+	270.388i	1.11772	+	0.645317i	0.940818	−	0.338912i	$-0.110059\pi$
$419$	468.325	+	270.388i	1.11772	+	0.645317i	0.176903	+	0.984228i	$0.443392\pi$
$420$		0			0
$421$	−141.848	−	245.689i	−0.336932	−	0.583584i	0.646922	−	0.762556i	$-0.276056\pi$
$421$	−141.848	−	245.689i	−0.336932	−	0.583584i	−0.983854	+	0.178973i	$0.942723\pi$
$422$	72.9179			0.172791
$423$	−400.720	+	74.4773i	−0.947329	+	0.176069i
$424$	−266.969			−0.629645
$425$		0			0
$426$	69.4393	+	31.9908i	0.163003	+	0.0750958i
$427$	94.6464	+	54.6441i	0.221654	+	0.127972i
$428$	−36.0408	+	62.4245i	−0.0842075	+	0.145852i
$429$	−16.0148	−	22.6483i	−0.0373305	−	0.0527933i
$430$		0			0
$431$			257.429i			0.597282i	0.954365	+	0.298641i	$0.0965334\pi$
$431$			257.429i			0.597282i	−0.954365	+	0.298641i	$0.903467\pi$
$432$	77.4174	+	75.3031i	0.179207	+	0.174313i
$433$		−	476.272i		−	1.09994i	−0.835186	−	0.549968i	$-0.814640\pi$
$433$		−	476.272i		−	1.09994i	0.835186	−	0.549968i	$-0.185360\pi$
$434$	31.1385	−	17.9778i	0.0717477	−	0.0414236i
$435$		0			0
$436$	−148.272	+	256.815i	−0.340074	+	0.589026i
$437$	11.7744	−	20.3939i	0.0269437	−	0.0466679i
$438$	−30.4770	−	14.0408i	−0.0695822	−	0.0320567i
$439$	−278.931	−	483.123i	−0.635379	−	1.10051i	−0.986435	−	0.164154i	$-0.947511\pi$
$439$	−278.931	−	483.123i	−0.635379	−	1.10051i	0.351056	−	0.936355i	$-0.385823\pi$
$440$		0			0
$441$	121.045	+	141.582i	0.274479	+	0.321047i
$442$			258.879i			0.585698i
$443$	−415.923	−	720.400i	−0.938879	−	1.62619i	−0.767567	−	0.640969i	$-0.778533\pi$
$443$	−415.923	−	720.400i	−0.938879	−	1.62619i	−0.171312	−	0.985217i	$-0.554801\pi$
$444$	−25.7071	−	279.000i	−0.0578990	−	0.628378i
$445$		0			0
$446$	−383.623	−	221.485i	−0.860142	−	0.496603i
$447$	−31.7933	−	345.053i	−0.0711259	−	0.771930i
$448$	−57.8399	+	33.3939i	−0.129107	+	0.0745399i
$449$			729.927i			1.62567i	0.582492	+	0.812836i	$0.302078\pi$
$449$			729.927i			1.62567i	−0.582492	+	0.812836i	$0.697922\pi$
$450$		0			0
$451$	−10.4097			−0.0230814
$452$	−171.088	−	296.333i	−0.378513	−	0.655603i
$453$	−81.3092	+	176.490i	−0.179490	+	0.389602i
$454$	53.9319	−	93.4128i	0.118793	−	0.205755i
$455$		0			0
$456$	−120.990	−	171.105i	−0.265328	−	0.375231i
$457$	614.563	−	354.818i	1.34478	−	0.776407i	0.357272	−	0.934000i	$-0.383707\pi$
$457$	614.563	−	354.818i	1.34478	−	0.776407i	0.987504	+	0.157594i	$0.0503737\pi$
$458$	−171.890			−0.375307
$459$	490.454	−	138.721i	1.06853	−	0.302225i
$460$		0			0
$461$	−7.96990	+	4.60142i	−0.0172883	+	0.00998140i	−0.508619	−	0.860992i	$-0.669844\pi$
$461$	−7.96990	+	4.60142i	−0.0172883	+	0.00998140i	0.491331	+	0.870973i	$0.336511\pi$
$462$	−19.4988	−	27.5755i	−0.0422053	−	0.0596872i
$463$	−47.8024	−	27.5987i	−0.103245	−	0.0596085i	0.447488	−	0.894290i	$-0.352319\pi$
$463$	−47.8024	−	27.5987i	−0.103245	−	0.0596085i	−0.550733	+	0.834681i	$0.685652\pi$
$464$	47.3939	+	27.3629i	0.102142	+	0.0589717i
$465$		0			0
$466$	106.788	+	184.962i	0.229158	+	0.396914i
$467$	−625.811			−1.34007			−0.670033	−	0.742331i	$-0.733720\pi$
$467$	−625.811			−1.34007			−0.670033	+	0.742331i	$0.733720\pi$
$468$	31.8945	+	171.606i	0.0681506	+	0.366680i
$469$	626.514			1.33585
$470$		0			0
$471$	5.73036	+	62.1917i	0.0121664	+	0.132042i
$472$	−46.0045	−	26.5607i	−0.0974672	−	0.0562727i
$473$	−21.4757	+	37.1969i	−0.0454031	+	0.0786405i
$474$	184.800	−	17.0276i	0.389874	−	0.0359231i
$475$		0			0
$476$			315.198i			0.662180i
$477$	−283.164	+	800.908i	−0.593635	+	1.67905i
$478$			124.045i			0.259509i
$479$	−267.856	+	154.647i	−0.559199	+	0.322854i	−0.752824	−	0.658222i	$-0.771309\pi$
$479$	−267.856	+	154.647i	−0.559199	+	0.322854i	0.193625	+	0.981076i	$0.437976\pi$
$480$		0			0
$481$	226.409	−	392.151i	0.470704	−	0.815283i
$482$	142.685	−	247.139i	0.296028	−	0.512736i
$483$	−19.4988	+	13.7878i	−0.0403702	+	0.0285461i
$484$	−120.091	−	208.003i	−0.248122	−	0.429759i
$485$		0			0
$486$	308.023	−	152.381i	0.633792	−	0.313541i
$487$		−	28.3337i		−	0.0581800i	−0.999577	−	0.0290900i	$-0.990739\pi$
$487$		−	28.3337i		−	0.0581800i	0.999577	−	0.0290900i	$-0.00926095\pi$
$488$	18.5132	+	32.0658i	0.0379369	+	0.0657086i
$489$	325.930	−	230.467i	0.666523	−	0.471303i
$490$		0			0
$491$	822.461	+	474.848i	1.67507	+	0.967105i	0.964727	+	0.263254i	$0.0847956\pi$
$491$	822.461	+	474.848i	1.67507	+	0.967105i	0.710348	+	0.703851i	$0.248538\pi$
$492$	59.4933	+	27.4087i	0.120921	+	0.0557087i
$493$	223.670	−	129.136i	0.453693	−	0.261940i
$494$		−	338.682i		−	0.685592i
$495$		0			0
$496$	12.1816			0.0245597
$497$	75.2214	+	130.287i	0.151351	+	0.262147i
$498$	−550.621	+	50.7344i	−1.10566	+	0.101876i
$499$	−280.113	+	485.170i	−0.561349	+	0.972284i	0.436030	+	0.899932i	$0.356384\pi$
$499$	−280.113	+	485.170i	−0.561349	+	0.972284i	−0.997379	+	0.0723525i	$0.976949\pi$
$500$		0			0
$501$	879.802	−	81.0653i	1.75609	−	0.161807i
$502$	64.4535	−	37.2122i	0.128393	−	0.0741280i
$503$	897.832			1.78495			0.892477	−	0.451094i	$-0.148966\pi$
$503$	897.832			1.78495			0.892477	+	0.451094i	$0.148966\pi$
$504$	38.8332	+	208.939i	0.0770499	+	0.414562i
$505$		0			0
$506$	1.11352	−	0.642891i	0.00220063	−	0.00127053i
$507$	94.1087	−	204.272i	0.185619	−	0.402904i
$508$	135.257	+	78.0908i	0.266254	+	0.153722i
$509$	170.454	+	98.4114i	0.334879	+	0.193343i	0.658005	−	0.753013i	$-0.271400\pi$
$509$	170.454	+	98.4114i	0.334879	+	0.193343i	−0.323126	+	0.946356i	$0.604734\pi$
$510$		0			0
$511$	−33.0148	−	57.1833i	−0.0646082	−	0.111905i
$512$	−22.6274			−0.0441942
$513$	−641.645	+	181.485i	−1.25077	+	0.353771i
$514$	114.136			0.222055
$515$		0			0
$516$	220.677	−	156.042i	0.427668	−	0.302407i
$517$	37.3964	+	21.5908i	0.0723334	+	0.0417617i
$518$	275.664	−	477.464i	0.532170	−	0.921746i
$519$	−86.9472	+	188.728i	−0.167528	+	0.363637i
$520$		0			0
$521$			375.837i			0.721377i	0.932686	+	0.360688i	$0.117458\pi$
$521$			375.837i			0.721377i	−0.932686	+	0.360688i	$0.882542\pi$
$522$	132.357	−	113.159i	0.253558	−	0.216780i
$523$		−	91.1827i		−	0.174345i	−0.996193	−	0.0871727i	$-0.972217\pi$
$523$		−	91.1827i		−	0.174345i	0.996193	−	0.0871727i	$-0.0277832\pi$
$524$	−405.409	+	234.063i	−0.773681	+	0.446685i
$525$		0			0
$526$	327.916	−	567.967i	0.623415	−	1.07979i
$527$	28.7450	−	49.7878i	0.0545445	−	0.0944739i
$528$	−1.04984	−	11.3939i	−0.00198833	−	0.0215793i
$529$	264.045	+	457.340i	0.499141	+	0.864537i
$530$		0			0
$531$	−128.477	+	109.842i	−0.241953	+	0.206858i
$532$		−	412.363i		−	0.775119i
$533$	52.9318	+	91.6806i	0.0993092	+	0.172009i
$534$	−559.893	−	257.944i	−1.04849	−	0.483041i
$535$		0			0
$536$	183.823	+	106.130i	0.342953	+	0.198004i
$537$	−116.309	+	82.2429i	−0.216590	+	0.153152i
$538$	53.2473	−	30.7423i	0.0989727	−	0.0571419i
$539$		−	19.7348i		−	0.0366137i
$540$		0			0
$541$	−38.8490			−0.0718096			−0.0359048	−	0.999355i	$-0.511431\pi$
$541$	−38.8490			−0.0718096			−0.0359048	+	0.999355i	$0.511431\pi$
$542$	−242.280	−	419.641i	−0.447011	−	0.774246i
$543$	420.678	+	594.929i	0.774729	+	1.09563i
$544$	−53.3939	+	92.4809i	−0.0981505	+	0.170002i
$545$		0			0
$546$	−143.715	+	311.948i	−0.263214	+	0.571333i
$547$	−403.606	+	233.022i	−0.737854	+	0.426000i	−0.821289	−	0.570513i	$-0.806744\pi$
$547$	−403.606	+	233.022i	−0.737854	+	0.426000i	0.0834344	+	0.996513i	$0.473411\pi$
$548$	−299.662			−0.546829
$549$	115.834	−	21.5287i	0.210990	−	0.0392144i
$550$		0			0
$551$	−292.621	+	168.945i	−0.531072	+	0.306615i
$552$	−8.05669	+	0.742346i	−0.0145954	+	0.00134483i
$553$	316.257	+	182.591i	0.571893	+	0.330182i
$554$	−60.0125	−	34.6482i	−0.108326	−	0.0625419i
$555$		0			0
$556$	−84.5301	−	146.410i	−0.152033	−	0.263328i
$557$	695.042			1.24783			0.623916	−	0.781492i	$-0.285541\pi$
$557$	695.042			1.24783			0.623916	+	0.781492i	$0.285541\pi$
$558$	12.9206	−	36.5449i	0.0231551	−	0.0654926i
$559$	436.803			0.781400
$560$		0			0
$561$	−49.0454	−	22.5953i	−0.0874250	−	0.0402768i
$562$	−25.2848	−	14.5982i	−0.0449908	−	0.0259755i
$563$	−273.537	+	473.780i	−0.485857	+	0.841528i	−0.999868	−	0.0162552i	$-0.994826\pi$
$563$	−273.537	+	473.780i	−0.485857	+	0.841528i	0.514011	+	0.857783i	$0.328159\pi$
$564$	−156.879	−	221.860i	−0.278153	−	0.393368i
$565$		0			0
$566$			75.5313i			0.133447i
$567$	668.006	+	105.114i	1.17814	+	0.185386i
$568$			50.9694i			0.0897348i
$569$	−215.954	+	124.681i	−0.379533	+	0.219123i	−0.677615	−	0.735417i	$-0.736986\pi$
$569$	−215.954	+	124.681i	−0.379533	+	0.219123i	0.298082	+	0.954540i	$0.403653\pi$
$570$		0			0
$571$	−36.9166	+	63.9414i	−0.0646525	+	0.111981i	−0.896540	−	0.442963i	$-0.853927\pi$
$571$	−36.9166	+	63.9414i	−0.0646525	+	0.111981i	0.831887	+	0.554945i	$0.187261\pi$
$572$	9.24614	−	16.0148i	0.0161646	−	0.0279979i
$573$	20.5222	+	9.45459i	0.0358153	+	0.0165002i
$574$	64.4472	+	111.626i	0.112277	+	0.194470i
$575$		0			0
$576$	−24.0000	+	67.8823i	−0.0416667	+	0.117851i
$577$		−	43.9092i		−	0.0760991i	−0.999276	−	0.0380496i	$-0.987886\pi$
$577$		−	43.9092i		−	0.0760991i	0.999276	−	0.0380496i	$-0.0121145\pi$
$578$	47.6330	+	82.5028i	0.0824101	+	0.142738i
$579$	95.0880	+	1031.99i	0.164228	+	1.78237i
$580$		0			0
$581$	−942.302	−	544.038i	−1.62186	−	0.936382i
$582$	−42.7724	−	464.209i	−0.0734921	−	0.797610i
$583$	77.9423	−	45.0000i	0.133692	−	0.0771870i
$584$		−	22.3706i		−	0.0383057i
$585$		0			0
$586$	−21.1056			−0.0360164
$587$	−220.194	−	381.386i	−0.375117	−	0.649721i	0.615228	−	0.788349i	$-0.289064\pi$
$587$	−220.194	−	381.386i	−0.375117	−	0.649721i	−0.990345	+	0.138628i	$0.955731\pi$
$588$	−51.9615	+	112.788i	−0.0883699	+	0.191816i
$589$	−37.6061	+	65.1357i	−0.0638474	+	0.110587i
$590$		0			0
$591$	133.757	+	189.161i	0.226323	+	0.320070i
$592$	161.763	−	93.3939i	0.273248	−	0.157760i
$593$	347.232			0.585551			0.292776	−	0.956181i	$-0.405421\pi$
$593$	347.232			0.585551			0.292776	+	0.956181i	$0.405421\pi$
$594$	−35.2951	−	8.93552i	−0.0594194	−	0.0150430i
$595$		0			0
$596$	200.060	−	115.505i	0.335671	−	0.193800i
$597$	−265.843	−	375.959i	−0.445299	−	0.629747i
$598$	−11.3242	−	6.53801i	−0.0189367	−	0.0109331i
$599$	684.083	+	394.956i	1.14204	+	0.659359i	0.946936	−	0.321423i	$-0.104161\pi$
$599$	684.083	+	394.956i	1.14204	+	0.659359i	0.195107	+	0.980782i	$0.437495\pi$
$600$		0			0
$601$	353.455	+	612.201i	0.588111	+	1.01864i	0.994480	+	0.104929i	$0.0334614\pi$
$601$	353.455	+	612.201i	0.588111	+	1.01864i	−0.406369	+	0.913709i	$0.633205\pi$
$602$	531.829			0.883438
$603$	513.364	−	438.901i	0.851351	−	0.727862i
$604$	−129.546			−0.214480
$605$		0			0
$606$	57.4324	+	623.314i	0.0947729	+	1.02857i
$607$	1033.39	+	596.628i	1.70246	+	0.982913i	0.943263	+	0.332048i	$0.107739\pi$
$607$	1033.39	+	596.628i	1.70246	+	0.982913i	0.759193	+	0.650866i	$0.225594\pi$
$608$	69.8535	−	120.990i	0.114891	−	0.198996i
$609$	341.212	−	31.4394i	0.560282	−	0.0516246i
$610$		0			0
$611$		−	439.145i		−	0.718731i
$612$	220.810	+	258.272i	0.360801	+	0.422014i
$613$		−	629.181i		−	1.02640i	−0.858270	−	0.513198i	$-0.828461\pi$
$613$		−	629.181i		−	1.02640i	0.858270	−	0.513198i	$-0.171539\pi$
$614$	−80.7219	+	46.6048i	−0.131469	+	0.0759036i
$615$		0			0
$616$	11.2577	−	19.4988i	0.0182754	−	0.0316539i
$617$	−96.3648	+	166.909i	−0.156183	+	0.270516i	−0.933489	−	0.358606i	$-0.883252\pi$
$617$	−96.3648	+	166.909i	−0.156183	+	0.270516i	0.777306	+	0.629122i	$0.216586\pi$
$618$	357.274	−	252.631i	0.578114	−	0.408788i
$619$	−76.4773	−	132.463i	−0.123550	−	0.213994i	0.797615	−	0.603166i	$-0.206095\pi$
$619$	−76.4773	−	132.463i	−0.123550	−	0.213994i	−0.921165	+	0.389172i	$0.872761\pi$
$620$		0			0
$621$	−6.31837	+	24.9574i	−0.0101745	+	0.0401891i
$622$		−	353.803i		−	0.568814i
$623$	−606.515	−	1050.51i	−0.973539	−	1.68622i
$624$	−95.0102	+	67.1824i	−0.152260	+	0.107664i
$625$		0			0
$626$	522.224	+	301.506i	0.834223	+	0.481639i
$627$	64.1645	+	29.5607i	0.102336	+	0.0471463i
$628$	−36.0585	+	20.8184i	−0.0574180	+	0.0331503i
$629$		−	881.525i		−	1.40147i
$630$		0			0
$631$	44.8786			0.0711229			0.0355615	−	0.999367i	$-0.488678\pi$
$631$	44.8786			0.0711229			0.0355615	+	0.999367i	$0.488678\pi$
$632$	61.8610	+	107.146i	0.0978814	+	0.169535i
$633$	154.030	−	14.1924i	0.243333	−	0.0224208i
$634$	328.083	−	568.256i	0.517481	−	0.896303i
$635$		0			0
$636$	−563.939	+	51.9615i	−0.886696	+	0.0817005i
$637$	−173.809	+	100.348i	−0.272855	+	0.157533i
$638$	−18.4490			−0.0289169
$639$	152.908	+	54.0612i	0.239293	+	0.0846028i
$640$		0			0
$641$	−209.106	+	120.727i	−0.326219	+	0.188342i	−0.654161	−	0.756355i	$-0.726978\pi$
$641$	−209.106	+	120.727i	−0.326219	+	0.188342i	0.327942	+	0.944698i	$0.393645\pi$
$642$	−63.9816	+	138.879i	−0.0996598	+	0.216322i
$643$	685.380	+	395.704i	1.06591	+	0.615403i	0.927061	−	0.374910i	$-0.122326\pi$
$643$	685.380	+	395.704i	1.06591	+	0.615403i	0.138849	+	0.990314i	$0.455660\pi$
$644$	−13.7878	−	7.96036i	−0.0214096	−	0.0123608i
$645$		0			0
$646$	−329.666	−	570.999i	−0.510319	−	0.883899i
$647$	294.028			0.454448			0.227224	−	0.973842i	$-0.427035\pi$
$647$	294.028			0.454448			0.227224	+	0.973842i	$0.427035\pi$
$648$	178.191	+	144.000i	0.274986	+	0.222222i
$649$	17.9082			0.0275935
$650$		0			0
$651$	62.2770	−	44.0365i	0.0956636	−	0.0676444i
$652$	230.467	+	133.060i	0.353477	+	0.204080i
$653$	−384.156	+	665.379i	−0.588295	+	1.01896i	0.406161	+	0.913802i	$0.366867\pi$
$653$	−384.156	+	665.379i	−0.588295	+	1.01896i	−0.994456	+	0.105155i	$0.966466\pi$
$654$	−263.221	+	571.349i	−0.402479	+	0.873622i
$655$		0			0
$656$			43.6689i			0.0665684i
$657$	−67.1117	−	23.7276i	−0.102149	−	0.0361150i
$658$		−	534.681i		−	0.812585i
$659$	373.204	−	215.469i	0.566318	−	0.326964i	−0.189359	−	0.981908i	$-0.560641\pi$
$659$	373.204	−	215.469i	0.566318	−	0.326964i	0.755678	+	0.654944i	$0.227308\pi$
$660$		0			0
$661$	−506.136	+	876.653i	−0.765712	+	1.32625i	0.174157	+	0.984718i	$0.444280\pi$
$661$	−506.136	+	876.653i	−0.765712	+	1.32625i	−0.939869	+	0.341534i	$0.889053\pi$
$662$	334.322	−	579.062i	0.505018	−	0.874717i
$663$	50.3868	+	546.848i	0.0759981	+	0.824808i
$664$	−184.318	−	319.248i	−0.277587	−	0.480795i
$665$		0			0
$666$	−108.606	−	584.348i	−0.163072	−	0.877399i
$667$			13.0454i			0.0195583i
$668$	294.510	+	510.106i	0.440883	+	0.763631i
$669$	−853.464	−	393.192i	−1.27573	−	0.587731i
$670$		0			0
$671$	−10.8099	−	6.24112i	−0.0161102	−	0.00930123i
$672$	−115.680	+	81.7980i	−0.172143	+	0.121723i
$673$	−487.755	+	281.606i	−0.724748	+	0.418433i	−0.816498	−	0.577349i	$-0.804087\pi$
$673$	−487.755	+	281.606i	−0.724748	+	0.418433i	0.0917499	+	0.995782i	$0.470754\pi$
$674$		−	432.192i		−	0.641235i
$675$		0			0
$676$	149.939			0.221803
$677$	−175.068	−	303.227i	−0.258594	−	0.447897i	0.707272	−	0.706942i	$-0.249926\pi$
$677$	−175.068	−	303.227i	−0.258594	−	0.447897i	−0.965865	+	0.259044i	$0.916592\pi$
$678$	−419.078	−	592.665i	−0.618109	−	0.874138i
$679$	458.659	−	794.421i	0.675492	−	1.16999i
$680$		0			0
$681$	95.7429	−	207.820i	0.140592	−	0.305168i
$682$	−3.55645	+	2.05332i	−0.00521474	+	0.00301073i
$683$	−502.818			−0.736190			−0.368095	−	0.929788i	$-0.619990\pi$
$683$	−502.818			−0.736190			−0.368095	+	0.929788i	$0.619990\pi$
$684$	−288.879	−	337.890i	−0.422337	−	0.493991i
$685$		0			0
$686$	289.392	−	167.080i	0.421854	−	0.243557i
$687$	−363.097	+	33.4559i	−0.528525	+	0.0486985i
$688$	156.042	+	90.0908i	0.226805	+	0.130946i
$689$	−792.650	−	457.637i	−1.15044	−	0.664205i
$690$		0			0
$691$	−188.159	−	325.902i	−0.272300	−	0.471638i	0.697150	−	0.716925i	$-0.254451\pi$
$691$	−188.159	−	325.902i	−0.272300	−	0.471638i	−0.969450	+	0.245287i	$0.921118\pi$
$692$	−138.529			−0.200186
$693$	−46.5559	−	54.4546i	−0.0671803	−	0.0785781i
$694$	−189.044			−0.272398
$695$		0			0
$696$	105.439	+	48.5761i	0.151493	+	0.0697932i
$697$	178.480	+	103.045i	0.256069	+	0.147841i
$698$	69.8318	−	120.952i	0.100046	−	0.173284i
$699$	261.576	+	369.924i	0.374214	+	0.529218i
$700$		0			0
$701$		−	489.681i		−	0.698546i	−0.937021	−	0.349273i	$-0.886429\pi$
$701$		−	489.681i		−	0.698546i	0.937021	−	0.349273i	$-0.113571\pi$
$702$	100.774	+	356.288i	0.143552	+	0.507533i
$703$			1153.27i			1.64050i
$704$	6.60612	−	3.81405i	0.00938370	−	0.00541768i
$705$		0			0
$706$	−230.598	+	399.408i	−0.326626	+	0.565733i
$707$	−615.862	+	1066.70i	−0.871092	+	1.50878i
$708$	−102.348	−	47.1520i	−0.144560	−	0.0665989i
$709$	237.014	+	410.521i	0.334294	+	0.579014i	0.983349	−	0.181728i	$-0.0581689\pi$
$709$	237.014	+	410.521i	0.334294	+	0.579014i	−0.649055	+	0.760741i	$0.724836\pi$
$710$		0			0
$711$	387.053	−	71.9371i	0.544378	−	0.101177i
$712$		−	410.969i		−	0.577204i
$713$	1.45192	+	2.51479i	0.00203635	+	0.00352706i
$714$	61.3485	+	665.815i	0.0859222	+	0.932514i
$715$		0			0
$716$	−82.2429	−	47.4829i	−0.114864	−	0.0663170i
$717$	24.1435	+	262.030i	0.0336730	+	0.365453i
$718$	512.844	−	296.091i	0.714268	−	0.412383i
$719$		−	108.122i		−	0.150379i	−0.997169	−	0.0751894i	$-0.976044\pi$
$719$		−	108.122i		−	0.150379i	0.997169	−	0.0751894i	$-0.0239561\pi$
$720$		0			0
$721$	861.030			1.19422
$722$	176.026	+	304.886i	0.243804	+	0.422280i
$723$	253.303	−	549.820i	0.350350	−	0.760470i
$724$	−242.879	+	420.678i	−0.335468	+	0.581047i
$725$		0			0
$726$	−294.161	−	416.007i	−0.405181	−	0.573012i
$727$	−385.027	+	222.296i	−0.529611	+	0.305771i	−0.740858	−	0.671662i	$-0.765581\pi$
$727$	−385.027	+	222.296i	−0.529611	+	0.305771i	0.211247	+	0.977433i	$0.432248\pi$
$728$	−228.974			−0.314525
$729$	621.000	−	381.838i	0.851852	−	0.523783i
$730$		0			0
$731$	736.423	−	425.174i	1.00742	−	0.581634i
$732$	45.3479	+	64.1316i	0.0619507	+	0.0876115i
$733$	−620.388	−	358.181i	−0.846368	−	0.488651i	0.0130556	−	0.999915i	$-0.495844\pi$
$733$	−620.388	−	358.181i	−0.846368	−	0.488651i	−0.859424	+	0.511264i	$0.829177\pi$
$734$	229.305	+	132.390i	0.312405	+	0.180367i
$735$		0			0
$736$	−2.69694	−	4.67123i	−0.00366432	−	0.00634679i
$737$	−71.5567			−0.0970918
$738$	131.007	+	46.3179i	0.177516	+	0.0627613i
$739$	−933.362			−1.26301			−0.631504	−	0.775373i	$-0.717562\pi$
$739$	−933.362			−1.26301			−0.631504	+	0.775373i	$0.717562\pi$
$740$		0			0
$741$	−65.9194	−	715.424i	−0.0889600	−	0.965484i
$742$	−965.093	−	557.196i	−1.30066	−	0.750939i
$743$	−7.95550	+	13.7793i	−0.0107073	+	0.0185455i	−0.871329	−	0.490699i	$-0.836742\pi$
$743$	−7.95550	+	13.7793i	−0.0107073	+	0.0185455i	0.860622	+	0.509244i	$0.170075\pi$
$744$	25.7321	−	2.37097i	0.0345862	−	0.00318679i
$745$		0			0
$746$			637.852i			0.855030i
$747$	−1153.24	+	214.340i	−1.54383	+	0.286934i
$748$		−	36.0000i		−	0.0481283i
$749$	−260.574	+	150.443i	−0.347896	+	0.200858i
$750$		0			0
$751$	−404.916	+	701.334i	−0.539169	+	0.933867i	0.459781	+	0.888033i	$0.347928\pi$
$751$	−404.916	+	701.334i	−0.539169	+	0.933867i	−0.998949	+	0.0458347i	$0.985405\pi$
$752$	90.5739	−	156.879i	0.120444	−	0.208615i
$753$	128.907	−	91.1510i	0.171191	−	0.121050i
$754$	93.8105	+	162.484i	0.124417	+	0.215497i
$755$		0			0
$756$	122.697	+	433.799i	0.162298	+	0.573808i
$757$			689.637i			0.911013i	0.890232	+	0.455506i	$0.150542\pi$
$757$			689.637i			0.911013i	−0.890232	+	0.455506i	$0.849458\pi$
$758$	346.246	+	599.716i	0.456789	+	0.791182i
$759$	2.22704	−	1.57475i	0.00293417	−	0.00207477i
$760$		0			0
$761$	−825.393	−	476.541i	−1.08462	−	0.626204i	−0.152479	−	0.988307i	$-0.548726\pi$
$761$	−825.393	−	476.541i	−1.08462	−	0.626204i	−0.932138	+	0.362103i	$0.882059\pi$
$762$	300.913	+	138.631i	0.394899	+	0.181931i
$763$	−1072.01	+	618.924i	−1.40499	+	0.811172i
$764$			15.0635i			0.0197167i
$765$		0			0
$766$	145.743			0.190266
$767$	−91.0604	−	157.721i	−0.118723	−	0.205634i
$768$	−47.7975	+	4.40408i	−0.0622364	+	0.00573448i
$769$	−328.348	+	568.715i	−0.426980	+	0.739552i	−0.996603	−	0.0823545i	$-0.973756\pi$
$769$	−328.348	+	568.715i	−0.426980	+	0.739552i	0.569623	+	0.821906i	$0.307089\pi$
$770$		0			0
$771$	241.098	−	22.2149i	0.312708	−	0.0288131i
$772$	−598.344	+	345.454i	−0.775057	+	0.447479i
$773$	278.021			0.359665			0.179832	−	0.983697i	$-0.442445\pi$
$773$	278.021			0.359665			0.179832	+	0.983697i	$0.442445\pi$
$774$	435.780	−	372.570i	0.563023	−	0.481356i
$775$		0			0
$776$	269.146	−	155.392i	0.346838	−	0.200247i
$777$	489.374	−	1062.24i	0.629825	−	1.36710i
$778$	−41.9762	−	24.2350i	−0.0539539	−	0.0311503i
$779$	−233.499	−	134.811i	−0.299743	−	0.173056i
$780$		0			0
$781$	−8.59133	−	14.8806i	−0.0110004	−	0.0190533i
$782$	−25.4558			−0.0325522
$783$	257.563	−	264.795i	0.328944	−	0.338180i
$784$	−82.7878			−0.105597
$785$		0			0
$786$	−810.817	+	573.334i	−1.03157	+	0.729433i
$787$	−711.833	−	410.977i	−0.904489	−	0.522207i	−0.0258350	−	0.999666i	$-0.508224\pi$
$787$	−711.833	−	410.977i	−0.904489	−	0.522207i	−0.878654	+	0.477459i	$0.841558\pi$
$788$	−77.2247	+	133.757i	−0.0980009	+	0.169743i
$789$	582.135	−	1263.58i	0.737813	−	1.60150i
$790$		0			0
$791$		−	1428.32i		−	1.80572i
$792$	−4.43529	−	23.8638i	−0.00560011	−	0.0301310i
$793$			126.941i			0.160077i
$794$	−10.1316	+	5.84950i	−0.0127602	+	0.00736713i
$795$		0			0
$796$	153.485	−	265.843i	0.192820	−	0.333974i
$797$	−661.257	+	1145.33i	−0.829683	+	1.43705i	0.0686043	+	0.997644i	$0.478145\pi$
$797$	−661.257	+	1145.33i	−0.829683	+	1.43705i	−0.898287	+	0.439409i	$0.855188\pi$
$798$	−80.2602	−	871.065i	−0.100577	−	1.09156i
$799$	−427.454	−	740.372i	−0.534986	−	0.926624i
$800$		0			0
$801$	−1232.91	−	435.899i	−1.53921	−	0.544193i
$802$			585.650i			0.730238i
$803$	3.77075	+	6.53113i	0.00469583	+	0.00813341i
$804$	408.959	+	188.408i	0.508656	+	0.234339i
$805$		0			0
$806$	36.1681	+	20.8817i	0.0448736	+	0.0259078i
$807$	106.495	−	75.3031i	0.131964	−	0.0933123i
$808$	−361.395	+	208.652i	−0.447271	+	0.258232i
$809$			235.681i			0.291324i	0.989334	+	0.145662i	$0.0465311\pi$
$809$			235.681i			0.291324i	−0.989334	+	0.145662i	$0.953469\pi$
$810$		0			0
$811$	−587.362			−0.724244			−0.362122	−	0.932131i	$-0.617948\pi$
$811$	−587.362			−0.724244			−0.362122	+	0.932131i	$0.617948\pi$
$812$	114.219	+	197.833i	0.140664	+	0.243637i
$813$	−593.462	−	839.283i	−0.729966	−	1.03233i
$814$	−31.4847	+	54.5331i	−0.0386790	+	0.0669940i
$815$		0			0
$816$	−94.7878	+	205.746i	−0.116161	+	0.252140i
$817$	−963.439	+	556.242i	−1.17924	+	0.680835i
$818$	−461.334			−0.563978
$819$	−242.864	+	686.922i	−0.296537	+	0.838733i
$820$		0			0
$821$	−817.453	+	471.956i	−0.995679	+	0.574856i	−0.906967	−	0.421202i	$-0.861608\pi$
$821$	−817.453	+	471.956i	−0.995679	+	0.574856i	−0.0887121	+	0.996057i	$0.528275\pi$
$822$	−632.999	+	58.3247i	−0.770071	+	0.0709547i
$823$	−1399.27	−	807.871i	−1.70021	−	0.981617i	−0.945535	−	0.325520i	$-0.894461\pi$
$823$	−1399.27	−	807.871i	−1.70021	−	0.981617i	−0.754676	−	0.656097i	$-0.772206\pi$
$824$	252.631	+	145.857i	0.306591	+	0.177010i
$825$		0			0
$826$	−110.871	−	192.034i	−0.134226	−	0.232486i
$827$	582.354			0.704177			0.352088	−	0.935967i	$-0.385472\pi$
$827$	582.354			0.704177			0.352088	+	0.935967i	$0.385472\pi$
$828$	−16.8742	+	3.13622i	−0.0203795	+	0.00378771i
$829$	−877.121			−1.05805			−0.529024	−	0.848607i	$-0.677442\pi$
$829$	−877.121			−1.05805			−0.529024	+	0.848607i	$0.677442\pi$
$830$		0			0
$831$	−133.512	−	61.5095i	−0.160665	−	0.0740186i
$832$	−67.1824	−	38.7878i	−0.0807480	−	0.0466199i
$833$	−195.354	+	338.363i	−0.234519	+	0.406198i
$834$	−207.056	−	292.821i	−0.248268	−	0.351104i
$835$		0			0
$836$			47.0976i			0.0563369i
$837$	20.1802	−	79.7112i	0.0241101	−	0.0952344i
$838$			764.772i			0.912616i
$839$	984.778	−	568.562i	1.17375	−	0.677666i	0.219191	−	0.975682i	$-0.429658\pi$
$839$	984.778	−	568.562i	1.17375	−	0.677666i	0.954561	+	0.298016i	$0.0963247\pi$
$840$		0			0
$841$	−326.909	+	566.223i	−0.388715	+	0.673274i
$842$	200.604	−	347.456i	0.238247	−	0.412656i
$843$	−56.2523	−	25.9155i	−0.0667287	−	0.0307421i
$844$	51.5607	+	89.3058i	0.0610909	+	0.105813i
$845$		0			0
$846$	−374.568	−	438.117i	−0.442751	−	0.517868i
$847$		−	1002.57i		−	1.18368i
$848$	−188.776	−	326.969i	−0.222613	−	0.385577i
$849$	14.7010	+	159.550i	0.0173157	+	0.187927i
$850$		0			0
$851$	38.5607	+	22.2630i	0.0453122	+	0.0261610i
$852$	9.92041	+	107.666i	0.0116437	+	0.126369i
$853$	276.970	−	159.909i	0.324701	−	0.187466i	−0.328785	−	0.944405i	$-0.606639\pi$
$853$	276.970	−	159.909i	0.324701	−	0.187466i	0.653486	+	0.756939i	$0.273306\pi$
$854$			154.557i			0.180980i
$855$		0			0
$856$	−101.939			−0.119087
$857$	398.984	+	691.061i	0.465559	+	0.806372i	0.999227	−	0.0393225i	$-0.0125200\pi$
$857$	398.984	+	691.061i	0.465559	+	0.806372i	−0.533668	+	0.845694i	$0.679187\pi$
$858$	16.4143	−	35.6288i	0.0191308	−	0.0415254i
$859$	−233.901	+	405.128i	−0.272294	+	0.471627i	−0.969449	−	0.245293i	$-0.921116\pi$
$859$	−233.901	+	405.128i	−0.272294	+	0.471627i	0.697155	+	0.716921i	$0.254449\pi$
$860$		0			0
$861$	157.863	+	223.252i	0.183348	+	0.259293i
$862$	−315.284	+	182.030i	−0.365759	+	0.211171i
$863$	1304.85			1.51199			0.755994	−	0.654578i	$-0.227154\pi$
$863$	1304.85			1.51199			0.755994	+	0.654578i	$0.227154\pi$
$864$	−37.4847	+	148.064i	−0.0433851	+	0.171370i
$865$		0			0
$866$	583.312	−	336.775i	0.673571	−	0.388886i
$867$	116.677	+	165.006i	0.134575	+	0.190318i
$868$	44.0365	+	25.4245i	0.0507333	+	0.0292909i
$869$	−36.1209	−	20.8544i	−0.0415661	−	0.0239982i
$870$		0			0
$871$	363.855	+	630.216i	0.417744	+	0.723554i
$872$	−419.378			−0.480938
$873$	−180.702	−	972.257i	−0.206990	−	1.11370i
$874$	33.3031			0.0381042
$875$		0			0
$876$	−4.35409	−	47.2549i	−0.00497042	−	0.0539440i
$877$	323.682	+	186.878i	0.369079	+	0.213088i	0.673056	−	0.739592i	$-0.264981\pi$
$877$	323.682	+	186.878i	0.369079	+	0.213088i	−0.303977	+	0.952679i	$0.598315\pi$
$878$	394.469	−	683.240i	0.449281	−	0.778177i
$879$	−44.5829	+	4.10789i	−0.0507200	+	0.00467336i
$880$		0			0
$881$		−	229.979i		−	0.261043i	−0.991445	−	0.130522i	$-0.958335\pi$
$881$		−	229.979i		−	0.261043i	0.991445	−	0.130522i	$-0.0416652\pi$
$882$	−87.8097	+	248.363i	−0.0995575	+	0.281591i
$883$			1381.79i			1.56488i	0.622728	+	0.782439i	$0.286024\pi$
$883$			1381.79i			1.56488i	−0.622728	+	0.782439i	$0.713976\pi$
$884$	−317.060	+	183.055i	−0.358665	+	0.207076i
$885$		0			0
$886$	588.204	−	1018.80i	0.663888	−	1.14989i
$887$	−438.090	+	758.794i	−0.493901	+	0.855461i	−0.999975	−	0.00702852i	$-0.997763\pi$
$887$	−438.090	+	758.794i	−0.493901	+	0.855461i	0.506075	+	0.862490i	$0.331096\pi$
$888$	323.526	−	228.767i	0.364331	−	0.257621i
$889$	325.969	+	564.596i	0.366670	+	0.635091i
$890$		0			0
$891$	−76.2957	−	12.0055i	−0.0856293	−	0.0134742i
$892$		−	626.454i		−	0.702303i
$893$	559.224	+	968.605i	0.626231	+	1.08466i
$894$	400.120	−	282.928i	0.447562	−	0.316474i
$895$		0			0
$896$	−81.7980	−	47.2261i	−0.0912924	−	0.0527077i
$897$	−25.1934	−	11.6066i	−0.0280863	−	0.0129394i
$898$	−893.974	+	516.136i	−0.995517	+	0.574762i
$899$		−	41.6655i		−	0.0463465i
$900$		0			0
$901$	−1781.82			−1.97760
$902$	−7.36077	−	12.7492i	−0.00816050	−	0.0141344i
$903$	1123.42	−	103.512i	1.24410	−	0.114632i
$904$	241.955	−	419.078i	0.267649	−	0.463581i
$905$		0			0
$906$	−273.649	+	25.2141i	−0.302041	+	0.0278302i
$907$	1021.97	−	590.037i	1.12676	−	0.650537i	0.183644	−	0.982993i	$-0.441211\pi$
$907$	1021.97	−	590.037i	1.12676	−	0.650537i	0.943119	+	0.332456i	$0.107877\pi$
$908$	152.542			0.167998
$909$	242.637	+	1305.49i	0.266928	+	1.43619i
$910$		0			0
$911$	1100.13	−	635.158i	1.20760	−	0.697210i	0.245368	−	0.969430i	$-0.421091\pi$
$911$	1100.13	−	635.158i	1.20760	−	0.697210i	0.962235	+	0.272220i	$0.0877578\pi$
$912$	124.008	−	269.171i	0.135973	−	0.295144i
$913$	107.624	+	62.1367i	0.117880	+	0.0680578i
$914$	869.123	+	501.788i	0.950900	+	0.549002i
$915$		0			0
$916$	−121.545	−	210.522i	−0.132691	−	0.229827i
$917$	−1954.07			−2.13093
$918$	516.702	+	502.590i	0.562856	+	0.547484i
$919$	−1316.63			−1.43268			−0.716340	−	0.697751i	$-0.754184\pi$
$919$	−1316.63			−1.43268			−0.716340	+	0.697751i	$0.754184\pi$
$920$		0			0
$921$	−161.444	+	114.158i	−0.175292	+	0.123950i
$922$	−11.2711	−	6.50740i	−0.0122247	−	0.00705791i
$923$	−87.3713	+	151.332i	−0.0946602	+	0.163956i
$924$	19.9852	−	43.3799i	0.0216290	−	0.0469480i
$925$		0			0
$926$		−	78.0610i		−	0.0842991i
$927$	705.526	−	603.189i	0.761085	−	0.650689i
$928$			77.3939i			0.0833986i
$929$	−543.424	+	313.746i	−0.584956	+	0.337724i	−0.763100	−	0.646280i	$-0.776324\pi$
$929$	−543.424	+	313.746i	−0.584956	+	0.337724i	0.178145	+	0.984004i	$0.442991\pi$
$930$		0			0
$931$	255.576	−	442.670i	0.274517	−	0.475478i
$932$	−151.021	+	261.576i	−0.162039	+	0.280660i
$933$	−68.8623	−	747.363i	−0.0738074	−	0.801032i
$934$	−442.515	−	766.459i	−0.473785	−	0.820620i
$935$		0			0
$936$	−187.621	+	160.406i	−0.200450	+	0.171374i
$937$			469.789i			0.501375i	0.968068	+	0.250688i	$0.0806567\pi$
$937$			469.789i			0.501375i	−0.968068	+	0.250688i	$0.919343\pi$
$938$	443.012	+	767.320i	0.472295	+	0.818039i
$939$	1161.81	+	535.250i	1.23729	+	0.570021i
$940$		0			0
$941$	805.984	+	465.335i	0.856518	+	0.494511i	0.862845	−	0.505469i	$-0.168680\pi$
$941$	805.984	+	465.335i	0.856518	+	0.494511i	−0.00632656	+	0.999980i	$0.502014\pi$
$942$	−72.1169	+	50.9944i	−0.0765573	+	0.0541342i
$943$	−9.01506	+	5.20485i	−0.00955998	+	0.00551946i
$944$		−	75.1250i		−	0.0795816i
$945$		0			0
$946$	−60.7423			−0.0642097
$947$	−1.81556	−	3.14465i	−0.00191717	−	0.00332064i	0.865065	−	0.501659i	$-0.167277\pi$
$947$	−1.81556	−	3.14465i	−0.00191717	−	0.00332064i	−0.866982	+	0.498339i	$0.833944\pi$
$948$	151.528	+	214.293i	0.159840	+	0.226047i
$949$	38.3474	−	66.4197i	0.0404083	−	0.0699892i
$950$		0			0
$951$	582.431	−	1264.23i	0.612440	−	1.32936i
$952$	−386.037	+	222.879i	−0.405501	+	0.234116i
$953$	719.641			0.755132			0.377566	−	0.925983i	$-0.376761\pi$
$953$	719.641			0.755132			0.377566	+	0.925983i	$0.376761\pi$
$954$	−1181.14	+	219.524i	−1.23809	+	0.230109i
$955$		0			0
$956$	−151.924	+	87.7133i	−0.158916	+	0.0917504i
$957$	−38.9711	+	3.59082i	−0.0407222	+	0.00375216i
$958$	−378.806	−	218.704i	−0.395413	−	0.228292i
$959$	−1083.28	−	625.431i	−1.12959	−	0.652170i
$960$		0			0
$961$	475.863	+	824.218i	0.495175	+	0.857667i
$962$	640.380			0.665676
$963$	−108.122	+	305.816i	−0.112277	+	0.317566i
$964$	403.576			0.418647
$965$		0			0
$966$	−30.6742	−	14.1317i	−0.0317539	−	0.0146291i
$967$	−29.2491	−	16.8870i	−0.0302473	−	0.0174633i	0.484800	−	0.874625i	$-0.338892\pi$
$967$	−29.2491	−	16.8870i	−0.0302473	−	0.0174633i	−0.515047	+	0.857162i	$0.672226\pi$
$968$	169.834	−	294.161i	0.175448	−	0.303886i
$969$	−807.514	−	1142.00i	−0.833348	−	1.17853i
$970$		0			0
$971$		−	970.472i		−	0.999456i	−0.866182	−	0.499728i	$-0.833433\pi$
$971$		−	970.472i		−	0.999456i	0.866182	−	0.499728i	$-0.166567\pi$
$972$	404.433	+	269.499i	0.416083	+	0.277263i
$973$		−	705.697i		−	0.725279i
$974$	34.7015	−	20.0349i	0.0356278	−	0.0205697i
$975$		0			0
$976$	−26.1816	+	45.3479i	−0.0268254	+	0.0464630i
$977$	785.151	−	1359.92i	0.803635	−	1.39194i	−0.113574	−	0.993529i	$-0.536230\pi$
$977$	785.151	−	1359.92i	0.803635	−	1.39194i	0.917209	−	0.398406i	$-0.130437\pi$
$978$	512.730	+	236.216i	0.524264	+	0.241529i
$979$	69.2724	+	119.983i	0.0707584	+	0.122557i
$980$		0			0
$981$	−444.817	+	1258.13i	−0.453433	+	1.28250i
$982$			1343.07i			1.36769i
$983$	387.939	+	671.930i	0.394648	+	0.683551i	0.993056	−	0.117641i	$-0.0375331\pi$
$983$	387.939	+	671.930i	0.394648	+	0.683551i	−0.598408	+	0.801192i	$0.704200\pi$
$984$	8.49948	+	92.2450i	0.00863769	+	0.0937449i
$985$		0			0
$986$	316.318	+	182.626i	0.320809	+	0.185219i
$987$	−104.068	−	1129.45i	−0.105438	−	1.14432i
$988$	414.800	−	239.485i	0.419838	−	0.242393i
$989$			42.9513i			0.0434290i
$990$		0			0
$991$	870.454			0.878359			0.439180	−	0.898399i	$-0.355269\pi$
$991$	870.454			0.878359			0.439180	+	0.898399i	$0.355269\pi$
$992$	8.61371	+	14.9194i	0.00868318	+	0.0150397i
$993$	593.507	−	1288.27i	0.597690	−	1.29735i
$994$	−106.379	+	184.254i	−0.107021	+	0.185366i
$995$		0			0
$996$	−451.485	−	638.496i	−0.453298	−	0.641060i
$997$	1078.20	−	622.499i	1.08144	−	0.624372i	0.150159	−	0.988662i	$-0.452022\pi$
$997$	1078.20	−	622.499i	1.08144	−	0.624372i	0.931286	+	0.364290i	$0.118688\pi$
$998$	−792.279			−0.793867
$999$	−343.151	−	1213.22i	−0.343495	−	1.21444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.3.k.a.149.4		8
3.2	odd	2		1350.3.k.a.449.1		8
5.2	odd	4		450.3.i.b.401.1		4
5.3	odd	4		18.3.d.a.5.2	✓	4
5.4	even	2	inner	450.3.k.a.149.1		8
9.2	odd	6	inner	450.3.k.a.299.1		8
9.7	even	3		1350.3.k.a.899.4		8
15.2	even	4		1350.3.i.b.1151.2		4
15.8	even	4		54.3.d.a.17.1		4
15.14	odd	2		1350.3.k.a.449.4		8
20.3	even	4		144.3.q.c.113.2		4
40.3	even	4		576.3.q.e.257.1		4
40.13	odd	4		576.3.q.f.257.2		4
45.2	even	12		450.3.i.b.101.1		4
45.7	odd	12		1350.3.i.b.251.2		4
45.13	odd	12		162.3.b.a.161.4		4
45.23	even	12		162.3.b.a.161.1		4
45.29	odd	6	inner	450.3.k.a.299.4		8
45.34	even	6		1350.3.k.a.899.1		8
45.38	even	12		18.3.d.a.11.2	yes	4
45.43	odd	12		54.3.d.a.35.1		4
60.23	odd	4		432.3.q.d.17.1		4
120.53	even	4		1728.3.q.d.449.2		4
120.83	odd	4		1728.3.q.c.449.1		4
180.23	odd	12		1296.3.e.g.161.2		4
180.43	even	12		432.3.q.d.305.1		4
180.83	odd	12		144.3.q.c.65.2		4
180.103	even	12		1296.3.e.g.161.4		4
360.43	even	12		1728.3.q.c.1601.1		4
360.83	odd	12		576.3.q.e.65.1		4
360.133	odd	12		1728.3.q.d.1601.2		4
360.173	even	12		576.3.q.f.65.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.3.d.a.5.2	✓	4	5.3	odd	4
18.3.d.a.11.2	yes	4	45.38	even	12
54.3.d.a.17.1		4	15.8	even	4
54.3.d.a.35.1		4	45.43	odd	12
144.3.q.c.65.2		4	180.83	odd	12
144.3.q.c.113.2		4	20.3	even	4
162.3.b.a.161.1		4	45.23	even	12
162.3.b.a.161.4		4	45.13	odd	12
432.3.q.d.17.1		4	60.23	odd	4
432.3.q.d.305.1		4	180.43	even	12
450.3.i.b.101.1		4	45.2	even	12
450.3.i.b.401.1		4	5.2	odd	4
450.3.k.a.149.1		8	5.4	even	2	inner
450.3.k.a.149.4		8	1.1	even	1	trivial
450.3.k.a.299.1		8	9.2	odd	6	inner
450.3.k.a.299.4		8	45.29	odd	6	inner
576.3.q.e.65.1		4	360.83	odd	12
576.3.q.e.257.1		4	40.3	even	4
576.3.q.f.65.2		4	360.173	even	12
576.3.q.f.257.2		4	40.13	odd	4
1296.3.e.g.161.2		4	180.23	odd	12
1296.3.e.g.161.4		4	180.103	even	12
1350.3.i.b.251.2		4	45.7	odd	12
1350.3.i.b.1151.2		4	15.2	even	4
1350.3.k.a.449.1		8	3.2	odd	2
1350.3.k.a.449.4		8	15.14	odd	2
1350.3.k.a.899.1		8	45.34	even	6
1350.3.k.a.899.4		8	9.7	even	3
1728.3.q.c.449.1		4	120.83	odd	4
1728.3.q.c.1601.1		4	360.43	even	12
1728.3.q.d.449.2		4	120.53	even	4
1728.3.q.d.1601.2		4	360.133	odd	12

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	450.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(1.73205 + 2.44949i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.77526 + 3.85337i) q^{6} +(-7.22999 + 4.17423i) q^{7} -2.82843 q^{8} +(-3.00000 + 8.48528i) q^{9} +(0.825765 - 0.476756i) q^{11} +(-5.97469 + 0.550510i) q^{12} +(-8.39780 - 4.84847i) q^{13} +(-10.2247 - 5.90326i) q^{14} +(-2.00000 - 3.46410i) q^{16} -18.8776 q^{17} +(-12.5136 + 2.32577i) q^{18} +24.6969 q^{19} +(-22.7474 - 10.4798i) q^{21} +(1.16781 + 0.674235i) q^{22} +(0.476756 - 0.825765i) q^{23} +(-4.89898 - 6.92820i) q^{24} -13.7135i q^{26} +(-25.9808 + 7.34847i) q^{27} -16.6969i q^{28} +(-11.8485 + 6.84072i) q^{29} +(-1.52270 + 2.63740i) q^{31} +(2.82843 - 4.89898i) q^{32} +(2.59808 + 1.19694i) q^{33} +(-13.3485 - 23.1202i) q^{34} +(-11.6969 - 13.6814i) q^{36} +46.6969i q^{37} +(17.4634 + 30.2474i) q^{38} +(-2.66913 - 28.9681i) q^{39} +(-9.45459 - 5.45861i) q^{41} +(-3.24980 - 35.2702i) q^{42} +(-39.0105 + 22.5227i) q^{43} +1.90702i q^{44} +1.34847 q^{46} +(22.6435 + 39.2196i) q^{47} +(5.02118 - 10.8990i) q^{48} +(10.3485 - 17.9241i) q^{49} +(-32.6969 - 46.2405i) q^{51} +(16.7956 - 9.69694i) q^{52} +94.3879 q^{53} +(-27.3712 - 26.6237i) q^{54} +(20.4495 - 11.8065i) q^{56} +(42.7764 + 60.4949i) q^{57} +(-16.7563 - 9.67423i) q^{58} +(16.2650 + 9.39063i) q^{59} +(-6.54541 - 11.3370i) q^{61} -4.30686 q^{62} +(-13.7296 - 73.8712i) q^{63} +8.00000 q^{64} +(0.371173 + 4.02834i) q^{66} +(-64.9912 - 37.5227i) q^{67} +(18.8776 - 32.6969i) q^{68} +(2.84847 - 0.262459i) q^{69} -18.0204i q^{71} +(8.48528 - 24.0000i) q^{72} +7.90918i q^{73} +(-57.1918 + 33.0197i) q^{74} +(-24.6969 + 42.7764i) q^{76} +(-3.98018 + 6.89388i) q^{77} +(33.5912 - 23.7526i) q^{78} +(-21.8712 - 37.8820i) q^{79} +(-63.0000 - 50.9117i) q^{81} -15.4393i q^{82} +(65.1662 + 112.871i) q^{83} +(40.8990 - 28.9199i) q^{84} +(-55.1691 - 31.8519i) q^{86} +(-37.2784 - 17.1742i) q^{87} +(-2.33562 + 1.34847i) q^{88} +145.300i q^{89} +80.9546 q^{91} +(0.953512 + 1.65153i) q^{92} +(-9.09769 + 0.838264i) q^{93} +(-32.0227 + 55.4650i) q^{94} +(16.8990 - 1.55708i) q^{96} +(-95.1576 + 54.9393i) q^{97} +29.2699 q^{98} +(1.56811 + 8.43712i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 24 q^{6} - 24 q^{9} + 36 q^{11} - 72 q^{14} - 16 q^{16} + 80 q^{19} - 84 q^{21} - 36 q^{29} + 76 q^{31} - 48 q^{34} + 24 q^{36} + 204 q^{39} - 252 q^{41} - 48 q^{46} + 24 q^{49} - 144 q^{51}+ \cdots - 252 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 24 * q^6 - 24 * q^9 + 36 * q^11 - 72 * q^14 - 16 * q^16 + 80 * q^19 - 84 * q^21 - 36 * q^29 + 76 * q^31 - 48 * q^34 + 24 * q^36 + 204 * q^39 - 252 * q^41 - 48 * q^46 + 24 * q^49 - 144 * q^51 - 72 * q^54 + 144 * q^56 - 252 * q^59 + 124 * q^61 + 64 * q^64 - 144 * q^66 - 36 * q^69 - 144 * q^74 - 80 * q^76 - 28 * q^79 - 504 * q^81 + 288 * q^84 - 216 * q^86 + 824 * q^91 - 168 * q^94 + 96 * q^96 - 252 * q^99

Introduction

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