LMFDB - Embedded newform 450.2.l.b.379.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(19,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("450.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.l (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			379.1
Root			$-0.951057 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	450.379
Dual form			450.2.l.b.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(0.809017 + 0.587785i) q^{4} +(2.22982 + 0.166977i) q^{5} -5.07768i q^{7} +(-0.587785 - 0.809017i) q^{8} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(0.809017 + 0.587785i) q^{4} +(2.22982 + 0.166977i) q^{5} -5.07768i q^{7} +(-0.587785 - 0.809017i) q^{8} +(-2.06909 - 0.847859i) q^{10} +(0.361243 - 1.11179i) q^{11} +(-3.27398 + 1.06378i) q^{13} +(-1.56909 + 4.82916i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-1.86655 - 2.56909i) q^{17} +(0.857960 - 0.623345i) q^{19} +(1.70582 + 1.44575i) q^{20} +(-0.687124 + 0.945746i) q^{22} +(0.484587 + 0.157452i) q^{23} +(4.94424 + 0.744661i) q^{25} +3.44246 q^{26} +(2.98459 - 4.10793i) q^{28} +(-2.22982 - 1.62006i) q^{29} +(2.09310 - 1.52072i) q^{31} -1.00000i q^{32} +(0.981305 + 3.02015i) q^{34} +(0.847859 - 11.3223i) q^{35} +(2.41602 - 0.785011i) q^{37} +(-1.00859 + 0.327712i) q^{38} +(-1.17557 - 1.90211i) q^{40} +(2.58653 + 7.96053i) q^{41} -7.18504i q^{43} +(0.945746 - 0.687124i) q^{44} +(-0.412215 - 0.299492i) q^{46} +(2.52307 - 3.47271i) q^{47} -18.7829 q^{49} +(-4.47214 - 2.23607i) q^{50} +(-3.27398 - 1.06378i) q^{52} +(2.96261 - 4.07768i) q^{53} +(0.991152 - 2.41878i) q^{55} +(-4.10793 + 2.98459i) q^{56} +(1.62006 + 2.22982i) q^{58} +(-1.45309 - 4.47214i) q^{59} +(0.486616 - 1.49765i) q^{61} +(-2.46058 + 0.799492i) q^{62} +(-0.309017 + 0.951057i) q^{64} +(-7.47802 + 1.82536i) q^{65} +(3.29032 + 4.52874i) q^{67} -3.17557i q^{68} +(-4.30516 + 10.5062i) q^{70} +(10.1228 + 7.35462i) q^{71} +(10.1785 + 3.30719i) q^{73} -2.54035 q^{74} +1.06050 q^{76} +(-5.64532 - 1.83428i) q^{77} +(10.2935 + 7.47870i) q^{79} +(0.530249 + 2.17229i) q^{80} -8.37019i q^{82} +(1.88815 + 2.59882i) q^{83} +(-3.73311 - 6.04029i) q^{85} +(-2.22030 + 6.83338i) q^{86} +(-1.11179 + 0.361243i) q^{88} +(-3.61803 + 11.1352i) q^{89} +(5.40154 + 16.6242i) q^{91} +(0.299492 + 0.412215i) q^{92} +(-3.47271 + 2.52307i) q^{94} +(2.01719 - 1.24669i) q^{95} +(-5.30017 + 7.29506i) q^{97} +(17.8636 + 5.80423i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} + 10 q^{5}+O(q^{10}) $ 8 * q + 2 * q^4 + 10 * q^5	$ 8 q + 2 q^{4} + 10 q^{5} + 4 q^{11} + 4 q^{14} - 2 q^{16} - 10 q^{17} + 10 q^{19} + 20 q^{22} - 10 q^{23} + 10 q^{25} + 28 q^{26} + 10 q^{28} - 10 q^{29} + 6 q^{31} - 4 q^{34} - 10 q^{35} - 10 q^{37} + 14 q^{41} + 6 q^{44} - 8 q^{46} + 30 q^{47} - 16 q^{49} - 10 q^{55} - 4 q^{56} - 14 q^{61} + 2 q^{64} - 50 q^{65} + 10 q^{67} + 34 q^{71} - 36 q^{74} - 40 q^{77} - 50 q^{83} - 20 q^{85} - 22 q^{86} - 10 q^{88} - 20 q^{89} - 4 q^{91} + 10 q^{92} - 24 q^{94} - 20 q^{97} + 40 q^{98}+O(q^{100}) $ 8 * q + 2 * q^4 + 10 * q^5 + 4 * q^11 + 4 * q^14 - 2 * q^16 - 10 * q^17 + 10 * q^19 + 20 * q^22 - 10 * q^23 + 10 * q^25 + 28 * q^26 + 10 * q^28 - 10 * q^29 + 6 * q^31 - 4 * q^34 - 10 * q^35 - 10 * q^37 + 14 * q^41 + 6 * q^44 - 8 * q^46 + 30 * q^47 - 16 * q^49 - 10 * q^55 - 4 * q^56 - 14 * q^61 + 2 * q^64 - 50 * q^65 + 10 * q^67 + 34 * q^71 - 36 * q^74 - 40 * q^77 - 50 * q^83 - 20 * q^85 - 22 * q^86 - 10 * q^88 - 20 * q^89 - 4 * q^91 + 10 * q^92 - 24 * q^94 - 20 * q^97 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$		0			0
$3$		0			0
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	2.22982	+	0.166977i	0.997208	+	0.0746746i
$5$	2.22982	+	0.166977i	0.997208	+	0.0746746i
$6$		0			0
$7$		−	5.07768i		−	1.91918i	−0.281395	−	0.959592i	$-0.590797\pi$
$7$		−	5.07768i		−	1.91918i	0.281395	−	0.959592i	$-0.409203\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$		0			0
$10$	−2.06909	−	0.847859i	−0.654304	−	0.268116i
$11$	0.361243	−	1.11179i	0.108919	−	0.335218i	−0.881711	−	0.471789i	$-0.843608\pi$
$11$	0.361243	−	1.11179i	0.108919	−	0.335218i	0.990630	+	0.136572i	$0.0436084\pi$
$12$		0			0
$13$	−3.27398	+	1.06378i	−0.908038	+	0.295039i	−0.725551	−	0.688169i	$-0.758415\pi$
$13$	−3.27398	+	1.06378i	−0.908038	+	0.295039i	−0.182487	+	0.983208i	$0.558415\pi$
$14$	−1.56909	+	4.82916i	−0.419357	+	1.29065i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−1.86655	−	2.56909i	−0.452706	−	0.623096i	0.520270	−	0.854002i	$-0.325831\pi$
$17$	−1.86655	−	2.56909i	−0.452706	−	0.623096i	−0.972976	+	0.230906i	$0.925831\pi$
$18$		0			0
$19$	0.857960	−	0.623345i	0.196830	−	0.143005i	−0.485005	−	0.874511i	$-0.661182\pi$
$19$	0.857960	−	0.623345i	0.196830	−	0.143005i	0.681835	+	0.731506i	$0.261182\pi$
$20$	1.70582	+	1.44575i	0.381433	+	0.323279i
$21$		0			0
$22$	−0.687124	+	0.945746i	−0.146495	+	0.201634i
$23$	0.484587	+	0.157452i	0.101043	+	0.0328310i	0.359102	−	0.933298i	$-0.383083\pi$
$23$	0.484587	+	0.157452i	0.101043	+	0.0328310i	−0.258059	+	0.966129i	$0.583083\pi$
$24$		0			0
$25$	4.94424	+	0.744661i	0.988847	+	0.148932i
$26$	3.44246			0.675123
$27$		0			0
$28$	2.98459	−	4.10793i	0.564034	−	0.776326i
$29$	−2.22982	−	1.62006i	−0.414068	−	0.300838i	0.361179	−	0.932497i	$-0.382374\pi$
$29$	−2.22982	−	1.62006i	−0.414068	−	0.300838i	−0.775247	+	0.631659i	$0.782374\pi$
$30$		0			0
$31$	2.09310	−	1.52072i	0.375931	−	0.273130i	−0.383735	−	0.923443i	$-0.625362\pi$
$31$	2.09310	−	1.52072i	0.375931	−	0.273130i	0.759666	+	0.650313i	$0.225362\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	0.981305	+	3.02015i	0.168292	+	0.517951i
$35$	0.847859	−	11.3223i	0.143314	−	1.91383i
$36$		0			0
$37$	2.41602	−	0.785011i	0.397191	−	0.129055i	−0.103609	−	0.994618i	$-0.533039\pi$
$37$	2.41602	−	0.785011i	0.397191	−	0.129055i	0.500800	+	0.865563i	$0.333039\pi$
$38$	−1.00859	+	0.327712i	−0.163615	+	0.0531619i
$39$		0			0
$40$	−1.17557	−	1.90211i	−0.185874	−	0.300750i
$41$	2.58653	+	7.96053i	0.403948	+	1.24323i	0.921770	+	0.387737i	$0.126743\pi$
$41$	2.58653	+	7.96053i	0.403948	+	1.24323i	−0.517822	+	0.855489i	$0.673257\pi$
$42$		0			0
$43$		−	7.18504i		−	1.09571i	−0.836574	−	0.547854i	$-0.815445\pi$
$43$		−	7.18504i		−	1.09571i	0.836574	−	0.547854i	$-0.184555\pi$
$44$	0.945746	−	0.687124i	0.142577	−	0.103588i
$45$		0			0
$46$	−0.412215	−	0.299492i	−0.0607777	−	0.0441576i
$47$	2.52307	−	3.47271i	0.368028	−	0.506547i	−0.584336	−	0.811512i	$-0.698645\pi$
$47$	2.52307	−	3.47271i	0.368028	−	0.506547i	0.952364	+	0.304965i	$0.0986448\pi$
$48$		0			0
$49$	−18.7829			−2.68327
$50$	−4.47214	−	2.23607i	−0.632456	−	0.316228i
$51$		0			0
$52$	−3.27398	−	1.06378i	−0.454019	−	0.147520i
$53$	2.96261	−	4.07768i	0.406946	−	0.560113i	−0.555524	−	0.831500i	$-0.687482\pi$
$53$	2.96261	−	4.07768i	0.406946	−	0.560113i	0.962470	+	0.271387i	$0.0874824\pi$
$54$		0			0
$55$	0.991152	−	2.41878i	0.133647	−	0.326148i
$56$	−4.10793	+	2.98459i	−0.548946	+	0.398832i
$57$		0			0
$58$	1.62006	+	2.22982i	0.212725	+	0.292790i
$59$	−1.45309	−	4.47214i	−0.189176	−	0.582223i	0.810820	−	0.585296i	$-0.199022\pi$
$59$	−1.45309	−	4.47214i	−0.189176	−	0.582223i	−0.999995	+	0.00307347i	$0.999022\pi$
$60$		0			0
$61$	0.486616	−	1.49765i	0.0623048	−	0.191754i	−0.915059	−	0.403320i	$-0.867856\pi$
$61$	0.486616	−	1.49765i	0.0623048	−	0.191754i	0.977364	+	0.211566i	$0.0678562\pi$
$62$	−2.46058	+	0.799492i	−0.312494	+	0.101536i
$63$		0			0
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	−7.47802	+	1.82536i	−0.927535	+	0.226408i
$66$		0			0
$67$	3.29032	+	4.52874i	0.401977	+	0.553274i	0.961239	−	0.275717i	$-0.0889154\pi$
$67$	3.29032	+	4.52874i	0.401977	+	0.553274i	−0.559262	+	0.828991i	$0.688915\pi$
$68$		−	3.17557i		−	0.385094i
$69$		0			0
$70$	−4.30516	+	10.5062i	−0.514565	+	1.25573i
$71$	10.1228	+	7.35462i	1.20135	+	0.872833i	0.994417	−	0.105522i	$-0.0336513\pi$
$71$	10.1228	+	7.35462i	1.20135	+	0.872833i	0.206935	+	0.978355i	$0.433651\pi$
$72$		0			0
$73$	10.1785	+	3.30719i	1.19130	+	0.387077i	0.836553	−	0.547885i	$-0.184567\pi$
$73$	10.1785	+	3.30719i	1.19130	+	0.387077i	0.354747	+	0.934962i	$0.384567\pi$
$74$	−2.54035			−0.295310
$75$		0			0
$76$	1.06050			0.121647
$77$	−5.64532	−	1.83428i	−0.643344	−	0.209035i
$78$		0			0
$79$	10.2935	+	7.47870i	1.15811	+	0.841420i	0.989538	−	0.144269i	$-0.0460831\pi$
$79$	10.2935	+	7.47870i	1.15811	+	0.841420i	0.168576	+	0.985689i	$0.446083\pi$
$80$	0.530249	+	2.17229i	0.0592836	+	0.242869i
$81$		0			0
$82$		−	8.37019i		−	0.924333i
$83$	1.88815	+	2.59882i	0.207252	+	0.285257i	0.899971	−	0.435950i	$-0.143587\pi$
$83$	1.88815	+	2.59882i	0.207252	+	0.285257i	−0.692719	+	0.721207i	$0.743587\pi$
$84$		0			0
$85$	−3.73311	−	6.04029i	−0.404912	−	0.655162i
$86$	−2.22030	+	6.83338i	−0.239421	+	0.736862i
$87$		0			0
$88$	−1.11179	+	0.361243i	−0.118517	+	0.0385086i
$89$	−3.61803	+	11.1352i	−0.383511	+	1.18032i	0.554044	+	0.832487i	$0.313084\pi$
$89$	−3.61803	+	11.1352i	−0.383511	+	1.18032i	−0.937555	+	0.347838i	$0.886916\pi$
$90$		0			0
$91$	5.40154	+	16.6242i	0.566235	+	1.74269i
$92$	0.299492	+	0.412215i	0.0312242	+	0.0429764i
$93$		0			0
$94$	−3.47271	+	2.52307i	−0.358183	+	0.260235i
$95$	2.01719	−	1.24669i	0.206959	−	0.127908i
$96$		0			0
$97$	−5.30017	+	7.29506i	−0.538151	+	0.740701i	−0.988345	−	0.152230i	$-0.951355\pi$
$97$	−5.30017	+	7.29506i	−0.538151	+	0.740701i	0.450195	+	0.892931i	$0.351355\pi$
$98$	17.8636	+	5.80423i	1.80449	+	0.586315i
$99$		0			0
$100$	3.56227	+	3.50859i	0.356227	+	0.350859i
$101$	−6.45193			−0.641991			−0.320996	−	0.947081i	$-0.604017\pi$
$101$	−6.45193			−0.641991			−0.320996	+	0.947081i	$0.604017\pi$
$102$		0			0
$103$	−4.18146	+	5.75528i	−0.412011	+	0.567085i	−0.963708	−	0.266960i	$-0.913981\pi$
$103$	−4.18146	+	5.75528i	−0.412011	+	0.567085i	0.551696	+	0.834045i	$0.313981\pi$
$104$	2.78501	+	2.02343i	0.273093	+	0.198414i
$105$		0			0
$106$	−4.07768	+	2.96261i	−0.396060	+	0.287754i
$107$			4.36582i			0.422060i	0.977480	+	0.211030i	$0.0676817\pi$
$107$			4.36582i			0.422060i	−0.977480	+	0.211030i	$0.932318\pi$
$108$		0			0
$109$	−3.15890	−	9.72211i	−0.302568	−	0.931209i	−0.980573	−	0.196152i	$-0.937155\pi$
$109$	−3.15890	−	9.72211i	−0.302568	−	0.931209i	0.678005	−	0.735057i	$-0.262845\pi$
$110$	−1.69009	+	1.99411i	−0.161143	+	0.190131i
$111$		0			0
$112$	4.82916	−	1.56909i	0.456313	−	0.148265i
$113$	8.35233	−	2.71384i	0.785721	−	0.255296i	0.111440	−	0.993771i	$-0.464454\pi$
$113$	8.35233	−	2.71384i	0.785721	−	0.255296i	0.674281	+	0.738475i	$0.264454\pi$
$114$		0			0
$115$	1.05425	+	0.432006i	0.0983097	+	0.0402847i
$116$	−0.851717	−	2.62132i	−0.0790800	−	0.243383i
$117$		0			0
$118$			4.70228i			0.432880i
$119$	−13.0450	+	9.47777i	−1.19584	+	0.868826i
$120$		0			0
$121$	7.79360	+	5.66239i	0.708509	+	0.514762i
$122$	−0.925599	+	1.27398i	−0.0837998	+	0.115340i
$123$		0			0
$124$	2.58721			0.232338
$125$	10.9004	+	2.48604i	0.974965	+	0.222358i
$126$		0			0
$127$	−10.3464	−	3.36176i	−0.918098	−	0.298308i	−0.188412	−	0.982090i	$-0.560334\pi$
$127$	−10.3464	−	3.36176i	−0.918098	−	0.298308i	−0.729686	+	0.683782i	$0.760334\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$		0			0
$130$	7.67609	+	0.574814i	0.673238	+	0.0504145i
$131$	11.9053	−	8.64973i	1.04017	−	0.755731i	0.0698547	−	0.997557i	$-0.477746\pi$
$131$	11.9053	−	8.64973i	1.04017	−	0.755731i	0.970320	+	0.241826i	$0.0777464\pi$
$132$		0			0
$133$	−3.16515	−	4.35645i	−0.274453	−	0.377752i
$134$	−1.72982	−	5.32385i	−0.149434	−	0.459911i
$135$		0			0
$136$	−0.981305	+	3.02015i	−0.0841462	+	0.258975i
$137$	−16.5824	+	5.38795i	−1.41673	+	0.460324i	−0.914562	−	0.404445i	$-0.867465\pi$
$137$	−16.5824	+	5.38795i	−1.41673	+	0.460324i	−0.502169	+	0.864769i	$0.667465\pi$
$138$		0			0
$139$	−2.23993	+	6.89378i	−0.189988	+	0.584723i	−0.999999	−	0.00169219i	$-0.999461\pi$
$139$	−2.23993	+	6.89378i	−0.189988	+	0.584723i	0.810010	+	0.586415i	$0.199461\pi$
$140$	7.34104	−	8.66161i	0.620431	−	0.732040i
$141$		0			0
$142$	−7.35462	−	10.1228i	−0.617186	−	0.849484i
$143$			4.02426i			0.336526i
$144$		0			0
$145$	−4.70160	−	3.98479i	−0.390447	−	0.330918i
$146$	−8.65833	−	6.29064i	−0.716568	−	0.520617i
$147$		0			0
$148$	2.41602	+	0.785011i	0.198595	+	0.0645275i
$149$	−11.9057			−0.975350			−0.487675	−	0.873025i	$-0.662155\pi$
$149$	−11.9057			−0.975350			−0.487675	+	0.873025i	$0.662155\pi$
$150$		0			0
$151$	−8.21471			−0.668504			−0.334252	−	0.942484i	$-0.608484\pi$
$151$	−8.21471			−0.668504			−0.334252	+	0.942484i	$0.608484\pi$
$152$	−1.00859	−	0.327712i	−0.0818077	−	0.0265809i
$153$		0			0
$154$	4.80220	+	3.48900i	0.386972	+	0.281152i
$155$	4.92116	−	3.04145i	0.395277	−	0.244295i
$156$		0			0
$157$			21.2722i			1.69771i	0.528629	+	0.848853i	$0.322706\pi$
$157$			21.2722i			1.69771i	−0.528629	+	0.848853i	$0.677294\pi$
$158$	−7.47870	−	10.2935i	−0.594973	−	0.818911i
$159$		0			0
$160$	0.166977	−	2.22982i	0.0132007	−	0.176283i
$161$	0.799492	−	2.46058i	0.0630088	−	0.193921i
$162$		0			0
$163$	−7.31698	+	2.37743i	−0.573110	+	0.186215i	−0.581212	−	0.813752i	$-0.697421\pi$
$163$	−7.31698	+	2.37743i	−0.573110	+	0.186215i	0.00810167	+	0.999967i	$0.497421\pi$
$164$	−2.58653	+	7.96053i	−0.201974	+	0.621613i
$165$		0			0
$166$	−0.992661	−	3.05510i	−0.0770454	−	0.237121i
$167$	−1.26580	−	1.74222i	−0.0979503	−	0.134817i	0.757229	−	0.653150i	$-0.226553\pi$
$167$	−1.26580	−	1.74222i	−0.0979503	−	0.134817i	−0.855179	+	0.518333i	$0.826553\pi$
$168$		0			0
$169$	−0.929921	+	0.675627i	−0.0715324	+	0.0519713i
$170$	1.68384	+	6.89825i	0.129145	+	0.529072i
$171$		0			0
$172$	4.22326	−	5.81282i	0.322021	−	0.443223i
$173$	−1.91460	−	0.622091i	−0.145564	−	0.0472967i	0.235329	−	0.971916i	$-0.424383\pi$
$173$	−1.91460	−	0.622091i	−0.145564	−	0.0472967i	−0.380893	+	0.924619i	$0.624383\pi$
$174$		0			0
$175$	3.78115	−	25.1053i	0.285828	−	1.89778i
$176$	1.16901			0.0881171
$177$		0			0
$178$	6.88191	−	9.47214i	0.515821	−	0.709967i
$179$	15.3200	+	11.1306i	1.14507	+	0.831942i	0.987818	−	0.155616i	$-0.0497363\pi$
$179$	15.3200	+	11.1306i	1.14507	+	0.831942i	0.157253	+	0.987558i	$0.449736\pi$
$180$		0			0
$181$	14.9988	−	10.8973i	1.11486	−	0.809990i	0.131434	−	0.991325i	$-0.458042\pi$
$181$	14.9988	−	10.8973i	1.11486	−	0.809990i	0.983421	+	0.181335i	$0.0580418\pi$
$182$		−	17.4797i		−	1.29568i
$183$		0			0
$184$	−0.157452	−	0.484587i	−0.0116075	−	0.0357243i
$185$	5.51837	−	1.34702i	0.405719	−	0.0990347i
$186$		0			0
$187$	−3.53057	+	1.14715i	−0.258181	+	0.0838880i
$188$	4.08242	−	1.32646i	0.297741	−	0.0967419i
$189$		0			0
$190$	−2.30371	+	0.562327i	−0.167128	+	0.0407955i
$191$	3.39327	+	10.4434i	0.245528	+	0.755658i	0.995549	+	0.0942437i	$0.0300433\pi$
$191$	3.39327	+	10.4434i	0.245528	+	0.755658i	−0.750021	+	0.661414i	$0.769957\pi$
$192$		0			0
$193$			6.00000i			0.431889i	0.976406	+	0.215945i	$0.0692831\pi$
$193$			6.00000i			0.431889i	−0.976406	+	0.215945i	$0.930717\pi$
$194$	7.29506	−	5.30017i	0.523755	−	0.380530i
$195$		0			0
$196$	−15.1957	−	11.0403i	−1.08540	−	0.788592i
$197$	1.93700	−	2.66605i	0.138005	−	0.189948i	−0.734420	−	0.678695i	$-0.762546\pi$
$197$	1.93700	−	2.66605i	0.138005	−	0.189948i	0.872426	+	0.488747i	$0.162546\pi$
$198$		0			0
$199$	12.0117			0.851484			0.425742	−	0.904845i	$-0.360013\pi$
$199$	12.0117			0.851484			0.425742	+	0.904845i	$0.360013\pi$
$200$	−2.30371	−	4.43767i	−0.162897	−	0.313791i
$201$		0			0
$202$	6.13615	+	1.99376i	0.431738	+	0.140280i
$203$	−8.22616	+	11.3223i	−0.577364	+	0.794673i
$204$		0			0
$205$	4.43828	+	18.1825i	0.309983	+	1.26992i
$206$	5.75528	−	4.18146i	0.400990	−	0.291336i
$207$		0			0
$208$	−2.02343	−	2.78501i	−0.140300	−	0.193106i
$209$	−0.383097	−	1.17905i	−0.0264994	−	0.0815567i
$210$		0			0
$211$	5.56681	−	17.1329i	0.383235	−	1.17948i	−0.554518	−	0.832172i	$-0.687097\pi$
$211$	5.56681	−	17.1329i	0.383235	−	1.17948i	0.937753	−	0.347304i	$-0.112903\pi$
$212$	4.79360	−	1.55754i	0.329226	−	0.106972i
$213$		0			0
$214$	1.34911	−	4.15214i	0.0922234	−	0.283835i
$215$	1.19974	−	16.0214i	0.0818216	−	1.09265i
$216$		0			0
$217$	−7.72175	−	10.6281i	−0.524187	−	0.721481i
$218$			10.2224i			0.692350i
$219$		0			0
$220$	2.22358	−	1.37425i	0.149914	−	0.0926518i
$221$	8.84400	+	6.42554i	0.594912	+	0.432229i
$222$		0			0
$223$	3.54978	+	1.15339i	0.237711	+	0.0772370i	0.425450	−	0.904982i	$-0.360116\pi$
$223$	3.54978	+	1.15339i	0.237711	+	0.0772370i	−0.187739	+	0.982219i	$0.560116\pi$
$224$	−5.07768			−0.339267
$225$		0			0
$226$	−8.78216			−0.584180
$227$	−13.2663	−	4.31047i	−0.880513	−	0.286096i	−0.166342	−	0.986068i	$-0.553196\pi$
$227$	−13.2663	−	4.31047i	−0.880513	−	0.286096i	−0.714170	+	0.699972i	$0.753196\pi$
$228$		0			0
$229$	−15.9898	−	11.6173i	−1.05663	−	0.767690i	−0.0831719	−	0.996535i	$-0.526505\pi$
$229$	−15.9898	−	11.6173i	−1.05663	−	0.767690i	−0.973463	+	0.228845i	$0.926505\pi$
$230$	−0.869158	−	0.736644i	−0.0573106	−	0.0485729i
$231$		0			0
$232$			2.75621i			0.180954i
$233$	−4.36833	−	6.01249i	−0.286179	−	0.393891i	0.641590	−	0.767048i	$-0.278275\pi$
$233$	−4.36833	−	6.01249i	−0.286179	−	0.393891i	−0.927768	+	0.373157i	$0.878275\pi$
$234$		0			0
$235$	6.20588	−	7.32224i	0.404827	−	0.477650i
$236$	1.45309	−	4.47214i	0.0945878	−	0.291111i
$237$		0			0
$238$	15.3354	−	4.98276i	0.994043	−	0.322984i
$239$	7.44901	−	22.9257i	0.481836	−	1.48294i	−0.354675	−	0.934990i	$-0.615409\pi$
$239$	7.44901	−	22.9257i	0.481836	−	1.48294i	0.836511	−	0.547950i	$-0.184591\pi$
$240$		0			0
$241$	4.67371	+	14.3842i	0.301060	+	0.926567i	0.981118	+	0.193409i	$0.0619544\pi$
$241$	4.67371	+	14.3842i	0.301060	+	0.926567i	−0.680058	+	0.733158i	$0.738046\pi$
$242$	−5.66239	−	7.79360i	−0.363992	−	0.500992i
$243$		0			0
$244$	1.27398	−	0.925599i	0.0815580	−	0.0592554i
$245$	−41.8825	−	3.13632i	−2.67578	−	0.200372i
$246$		0			0
$247$	−2.14584	+	2.95350i	−0.136537	+	0.187927i
$248$	−2.46058	−	0.799492i	−0.156247	−	0.0507678i
$249$		0			0
$250$	−9.59871	−	5.73279i	−0.607076	−	0.362573i
$251$	−29.3777			−1.85430			−0.927151	−	0.374687i	$-0.877750\pi$
$251$	−29.3777			−1.85430			−0.927151	+	0.374687i	$0.877750\pi$
$252$		0			0
$253$	0.350107	−	0.481882i	0.0220111	−	0.0302956i
$254$	8.80121	+	6.39445i	0.552237	+	0.401224i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$			11.7657i			0.733923i	0.930236	+	0.366962i	$0.119602\pi$
$257$			11.7657i			0.733923i	−0.930236	+	0.366962i	$0.880398\pi$
$258$		0			0
$259$	−3.98604	−	12.2678i	−0.247680	−	0.762282i
$260$	−7.12277	−	2.91872i	−0.441735	−	0.181012i
$261$		0			0
$262$	−13.9956	+	4.54743i	−0.864649	+	0.280941i
$263$	15.7646	−	5.12221i	0.972084	−	0.315849i	0.220427	−	0.975403i	$-0.429255\pi$
$263$	15.7646	−	5.12221i	0.972084	−	0.315849i	0.751657	+	0.659554i	$0.229255\pi$
$264$		0			0
$265$	7.28698	−	8.59783i	0.447636	−	0.528161i
$266$	1.66402	+	5.12132i	0.102027	+	0.314008i
$267$		0			0
$268$			5.59783i			0.341942i
$269$	14.2556	−	10.3573i	0.869182	−	0.631497i	−0.0611856	−	0.998126i	$-0.519488\pi$
$269$	14.2556	−	10.3573i	0.869182	−	0.631497i	0.930367	+	0.366629i	$0.119488\pi$
$270$		0			0
$271$	−1.43649	−	1.04367i	−0.0872603	−	0.0633983i	0.543300	−	0.839539i	$-0.317175\pi$
$271$	−1.43649	−	1.04367i	−0.0872603	−	0.0633983i	−0.630560	+	0.776141i	$0.717175\pi$
$272$	1.86655	−	2.56909i	0.113176	−	0.155774i
$273$		0			0
$274$	17.4358			1.05333
$275$	2.61398	−	5.22795i	0.157629	−	0.315257i
$276$		0			0
$277$	20.1945	+	6.56159i	1.21337	+	0.394248i	0.844663	−	0.535298i	$-0.179801\pi$
$277$	20.1945	+	6.56159i	1.21337	+	0.394248i	0.368707	+	0.929546i	$0.379801\pi$
$278$	4.26059	−	5.86420i	0.255533	−	0.351712i
$279$		0			0
$280$	−9.65833	+	5.96917i	−0.577195	+	0.356726i
$281$	−6.68031	+	4.85353i	−0.398514	+	0.289537i	−0.768935	−	0.639327i	$-0.779213\pi$
$281$	−6.68031	+	4.85353i	−0.398514	+	0.289537i	0.370422	+	0.928864i	$0.379213\pi$
$282$		0			0
$283$	−11.5242	−	15.8617i	−0.685043	−	0.942881i	0.314938	−	0.949112i	$-0.398016\pi$
$283$	−11.5242	−	15.8617i	−0.685043	−	0.942881i	−0.999981	+	0.00623177i	$0.998016\pi$
$284$	3.86655	+	11.9000i	0.229438	+	0.706137i
$285$		0			0
$286$	1.24356	−	3.82730i	0.0735335	−	0.226313i
$287$	40.4210	−	13.1336i	2.38598	−	0.775251i
$288$		0			0
$289$	2.13708	−	6.57727i	0.125711	−	0.386898i
$290$	3.24013	+	5.24263i	0.190267	+	0.307858i
$291$		0			0
$292$	6.29064	+	8.65833i	0.368132	+	0.506690i
$293$			18.9958i			1.10975i	0.831934	+	0.554874i	$0.187234\pi$
$293$			18.9958i			1.10975i	−0.831934	+	0.554874i	$0.812766\pi$
$294$		0			0
$295$	−2.49338	−	10.2147i	−0.145170	−	0.594724i
$296$	−2.05519	−	1.49318i	−0.119455	−	0.0867894i
$297$		0			0
$298$	11.3230	+	3.67905i	0.655921	+	0.213122i
$299$	−1.75402			−0.101438
$300$		0			0
$301$	−36.4834			−2.10287
$302$	7.81266	+	2.53849i	0.449568	+	0.146073i
$303$		0			0
$304$	0.857960	+	0.623345i	0.0492074	+	0.0357513i
$305$	1.33514	−	3.25824i	0.0764500	−	0.186566i
$306$		0			0
$307$		−	6.81955i		−	0.389212i	−0.980881	−	0.194606i	$-0.937657\pi$
$307$		−	6.81955i		−	0.389212i	0.980881	−	0.194606i	$-0.0623428\pi$
$308$	−3.48900	−	4.80220i	−0.198804	−	0.273631i
$309$		0			0
$310$	−5.62016	+	1.37186i	−0.319204	+	0.0779167i
$311$	−1.00953	+	3.10700i	−0.0572449	+	0.176182i	−0.975591	−	0.219598i	$-0.929526\pi$
$311$	−1.00953	+	3.10700i	−0.0572449	+	0.176182i	0.918346	+	0.395779i	$0.129526\pi$
$312$		0			0
$313$	8.40502	−	2.73096i	0.475080	−	0.154363i	−0.0616834	−	0.998096i	$-0.519647\pi$
$313$	8.40502	−	2.73096i	0.475080	−	0.154363i	0.536763	+	0.843733i	$0.319647\pi$
$314$	6.57347	−	20.2311i	0.370962	−	1.14170i
$315$		0			0
$316$	3.93179	+	12.1008i	0.221180	+	0.680723i
$317$	20.6412	+	28.4101i	1.15932	+	1.59567i	0.713703	+	0.700448i	$0.247016\pi$
$317$	20.6412	+	28.4101i	1.15932	+	1.59567i	0.445619	+	0.895223i	$0.352984\pi$
$318$		0			0
$319$	−2.60668	+	1.89386i	−0.145946	+	0.106036i
$320$	−0.847859	+	2.06909i	−0.0473967	+	0.115666i
$321$		0			0
$322$	−1.52072	+	2.09310i	−0.0847466	+	0.116644i
$323$	−3.20286	−	1.04067i	−0.178212	−	0.0579045i
$324$		0			0
$325$	−16.9795	+	2.82158i	−0.941852	+	0.156513i
$326$	7.69353			0.426105
$327$		0			0
$328$	4.91988	−	6.77163i	0.271655	−	0.373901i
$329$	−17.6333	−	12.8114i	−0.972157	−	0.706314i
$330$		0			0
$331$	9.15911	−	6.65448i	0.503430	−	0.365764i	−0.306895	−	0.951743i	$-0.599290\pi$
$331$	9.15911	−	6.65448i	0.503430	−	0.365764i	0.810326	+	0.585980i	$0.199290\pi$
$332$			3.21232i			0.176299i
$333$		0			0
$334$	0.665469	+	2.04810i	0.0364128	+	0.112067i
$335$	6.58064	+	10.6477i	0.359539	+	0.581746i
$336$		0			0
$337$	8.98823	−	2.92045i	0.489620	−	0.159087i	−0.0537940	−	0.998552i	$-0.517131\pi$
$337$	8.98823	−	2.92045i	0.489620	−	0.159087i	0.543414	+	0.839465i	$0.317131\pi$
$338$	1.09319	−	0.355198i	0.0594616	−	0.0193202i
$339$		0			0
$340$	0.530249	−	7.08097i	0.0287568	−	0.384019i
$341$	−0.934610	−	2.87644i	−0.0506120	−	0.155768i
$342$		0			0
$343$			59.8297i			3.23050i
$344$	−5.81282	+	4.22326i	−0.313406	+	0.227703i
$345$		0			0
$346$	1.62866	+	1.18329i	0.0875571	+	0.0636139i
$347$	−19.5214	+	26.8689i	−1.04796	+	1.44240i	−0.157401	+	0.987535i	$0.550312\pi$
$347$	−19.5214	+	26.8689i	−1.04796	+	1.44240i	−0.890562	+	0.454862i	$0.849688\pi$
$348$		0			0
$349$	23.0407			1.23334			0.616670	−	0.787222i	$-0.288481\pi$
$349$	23.0407			1.23334			0.616670	+	0.787222i	$0.288481\pi$
$350$	−11.3540	+	22.7081i	−0.606899	+	1.21380i
$351$		0			0
$352$	−1.11179	−	0.361243i	−0.0592586	−	0.0192543i
$353$	−0.440711	+	0.606587i	−0.0234567	+	0.0322854i	−0.820584	−	0.571526i	$-0.806352\pi$
$353$	−0.440711	+	0.606587i	−0.0234567	+	0.0322854i	0.797128	+	0.603811i	$0.206352\pi$
$354$		0			0
$355$	21.3439	+	18.0898i	1.13282	+	0.960106i
$356$	−9.47214	+	6.88191i	−0.502022	+	0.364740i
$357$		0			0
$358$	−11.1306	−	15.3200i	−0.588272	−	0.809687i
$359$	0.270894	+	0.833725i	0.0142972	+	0.0440023i	0.957951	−	0.286933i	$-0.0926358\pi$
$359$	0.270894	+	0.833725i	0.0142972	+	0.0440023i	−0.943653	+	0.330935i	$0.892636\pi$
$360$		0			0
$361$	−5.52379	+	17.0005i	−0.290726	+	0.894761i
$362$	−17.6322	+	5.72905i	−0.926728	+	0.301112i
$363$		0			0
$364$	−5.40154	+	16.6242i	−0.283117	+	0.871346i
$365$	22.1440	+	9.07402i	1.15907	+	0.474956i
$366$		0			0
$367$	12.8731	+	17.7182i	0.671968	+	0.924885i	0.999803	−	0.0198500i	$-0.00631888\pi$
$367$	12.8731	+	17.7182i	0.671968	+	0.924885i	−0.327835	+	0.944735i	$0.606319\pi$
$368$			0.509525i			0.0265609i
$369$		0			0
$370$	−5.66454	−	0.424181i	−0.294485	−	0.0220521i
$371$	−20.7052	−	15.0432i	−1.07496	−	0.781004i
$372$		0			0
$373$	−17.9210	−	5.82290i	−0.927916	−	0.301498i	−0.194206	−	0.980961i	$-0.562213\pi$
$373$	−17.9210	−	5.82290i	−0.927916	−	0.301498i	−0.733710	+	0.679462i	$0.762213\pi$
$374$	3.71226			0.191956
$375$		0			0
$376$	−4.29251			−0.221369
$377$	9.02379	+	2.93201i	0.464749	+	0.151006i
$378$		0			0
$379$	−10.2636	−	7.45691i	−0.527203	−	0.383036i	0.292107	−	0.956386i	$-0.405644\pi$
$379$	−10.2636	−	7.45691i	−0.527203	−	0.383036i	−0.819311	+	0.573350i	$0.805644\pi$
$380$	2.36472	+	0.177079i	0.121308	+	0.00908397i
$381$		0			0
$382$		−	10.9808i		−	0.561828i
$383$	−19.4651	−	26.7914i	−0.994620	−	1.36898i	−0.928569	−	0.371161i	$-0.878960\pi$
$383$	−19.4651	−	26.7914i	−0.994620	−	1.36898i	−0.0660513	−	0.997816i	$-0.521040\pi$
$384$		0			0
$385$	−12.2818	−	5.03276i	−0.625938	−	0.256493i
$386$	1.85410	−	5.70634i	0.0943713	−	0.290445i
$387$		0			0
$388$	−8.57585	+	2.78646i	−0.435373	+	0.141461i
$389$	−1.37278	+	4.22497i	−0.0696025	+	0.214214i	−0.979807	−	0.199944i	$-0.935924\pi$
$389$	−1.37278	+	4.22497i	−0.0696025	+	0.214214i	0.910205	+	0.414158i	$0.135924\pi$
$390$		0			0
$391$	−0.500000	−	1.53884i	−0.0252861	−	0.0778226i
$392$	11.0403	+	15.1957i	0.557619	+	0.767497i
$393$		0			0
$394$	−2.66605	+	1.93700i	−0.134313	+	0.0975844i
$395$	21.7040	+	18.3950i	1.09205	+	0.925552i
$396$		0			0
$397$	9.08246	−	12.5009i	0.455836	−	0.627404i	−0.517803	−	0.855500i	$-0.673250\pi$
$397$	9.08246	−	12.5009i	0.455836	−	0.627404i	0.973639	+	0.228096i	$0.0732500\pi$
$398$	−11.4238	−	3.71181i	−0.572622	−	0.186056i
$399$		0			0
$400$	0.819639	+	4.93236i	0.0409819	+	0.246618i
$401$	8.41989			0.420469			0.210235	−	0.977651i	$-0.432577\pi$
$401$	8.41989			0.420469			0.210235	+	0.977651i	$0.432577\pi$
$402$		0			0
$403$	−5.23503	+	7.20541i	−0.260776	+	0.358927i
$404$	−5.21972	−	3.79235i	−0.259691	−	0.188677i
$405$		0			0
$406$	11.3223	−	8.22616i	0.561919	−	0.408258i
$407$		−	2.96968i		−	0.147202i
$408$		0			0
$409$	6.21590	+	19.1306i	0.307356	+	0.945946i	0.978787	+	0.204879i	$0.0656800\pi$
$409$	6.21590	+	19.1306i	0.307356	+	0.945946i	−0.671431	+	0.741067i	$0.734320\pi$
$410$	1.39763	−	18.6641i	0.0690242	−	0.921752i
$411$		0			0
$412$	−6.76574	+	2.19832i	−0.333324	+	0.108304i
$413$	−22.7081	+	7.37831i	−1.11739	+	0.363063i
$414$		0			0
$415$	3.77631	+	6.11019i	0.185372	+	0.299937i
$416$	1.06378	+	3.27398i	0.0521561	+	0.160520i
$417$		0			0
$418$			1.23973i			0.0606371i
$419$	12.7033	−	9.22950i	0.620598	−	0.450891i	−0.232532	−	0.972589i	$-0.574701\pi$
$419$	12.7033	−	9.22950i	0.620598	−	0.450891i	0.853130	+	0.521698i	$0.174701\pi$
$420$		0			0
$421$	5.22733	+	3.79788i	0.254764	+	0.185097i	0.707836	−	0.706377i	$-0.249672\pi$
$421$	5.22733	+	3.79788i	0.254764	+	0.185097i	−0.453071	+	0.891474i	$0.649672\pi$
$422$	−10.5887	+	14.5741i	−0.515450	+	0.709456i
$423$		0			0
$424$	−5.04029			−0.244778
$425$	−7.31558	−	14.0921i	−0.354858	−	0.683569i
$426$		0			0
$427$	−7.60459	−	2.47088i	−0.368012	−	0.119574i
$428$	−2.56616	+	3.53202i	−0.124040	+	0.170727i
$429$		0			0
$430$	−6.09190	+	14.8665i	−0.293777	+	0.716926i
$431$	30.0966	−	21.8665i	1.44970	−	1.05327i	0.463803	−	0.885938i	$-0.346485\pi$
$431$	30.0966	−	21.8665i	1.44970	−	1.05327i	0.985901	−	0.167333i	$-0.0535154\pi$
$432$		0			0
$433$	−12.5676	−	17.2979i	−0.603962	−	0.831282i	0.392102	−	0.919922i	$-0.371748\pi$
$433$	−12.5676	−	17.2979i	−0.603962	−	0.831282i	−0.996064	+	0.0886399i	$0.971748\pi$
$434$	4.05957	+	12.4941i	0.194865	+	0.599734i
$435$		0			0
$436$	3.15890	−	9.72211i	0.151284	−	0.465605i
$437$	0.513904	−	0.166977i	0.0245834	−	0.00798762i
$438$		0			0
$439$	1.94539	−	5.98729i	0.0928484	−	0.285758i	−0.893839	−	0.448389i	$-0.851998\pi$
$439$	1.94539	−	5.98729i	0.0928484	−	0.285758i	0.986687	+	0.162631i	$0.0519980\pi$
$440$	−2.53942	+	0.619864i	−0.121062	+	0.0295509i
$441$		0			0
$442$	−6.42554	−	8.84400i	−0.305632	−	0.420666i
$443$			10.5123i			0.499455i	0.968316	+	0.249728i	$0.0803411\pi$
$443$			10.5123i			0.499455i	−0.968316	+	0.249728i	$0.919659\pi$
$444$		0			0
$445$	−9.92690	+	24.2253i	−0.470580	+	1.14839i
$446$	−3.01963	−	2.19389i	−0.142983	−	0.103884i
$447$		0			0
$448$	4.82916	+	1.56909i	0.228157	+	0.0741326i
$449$	2.81363			0.132783			0.0663916	−	0.997794i	$-0.478851\pi$
$449$	2.81363			0.132783			0.0663916	+	0.997794i	$0.478851\pi$
$450$		0			0
$451$	9.78480			0.460748
$452$	8.35233	+	2.71384i	0.392860	+	0.127648i
$453$		0			0
$454$	11.2850	+	8.19900i	0.529629	+	0.384798i
$455$	9.26861	+	37.9710i	0.434519	+	1.78011i
$456$		0			0
$457$			5.01719i			0.234694i	0.993091	+	0.117347i	$0.0374390\pi$
$457$			5.01719i			0.234694i	−0.993091	+	0.117347i	$0.962561\pi$
$458$	11.6173	+	15.9898i	0.542839	+	0.747154i
$459$		0			0
$460$	0.598983	+	0.969175i	0.0279277	+	0.0451880i
$461$	6.34748	−	19.5355i	0.295632	−	0.909861i	−0.687377	−	0.726301i	$-0.741238\pi$
$461$	6.34748	−	19.5355i	0.295632	−	0.909861i	0.983009	−	0.183560i	$-0.0587621\pi$
$462$		0			0
$463$	7.37312	−	2.39567i	0.342658	−	0.111336i	−0.132633	−	0.991165i	$-0.542343\pi$
$463$	7.37312	−	2.39567i	0.342658	−	0.111336i	0.475290	+	0.879829i	$0.342343\pi$
$464$	0.851717	−	2.62132i	0.0395400	−	0.121692i
$465$		0			0
$466$	2.29657	+	7.06810i	0.106386	+	0.327423i
$467$	−17.3394	−	23.8656i	−0.802370	−	1.10437i	−0.992456	−	0.122601i	$-0.960877\pi$
$467$	−17.3394	−	23.8656i	−0.802370	−	1.10437i	0.190086	−	0.981768i	$-0.439123\pi$
$468$		0			0
$469$	22.9955	−	16.7072i	1.06183	−	0.771468i
$470$	−8.16484	+	5.04615i	−0.376616	+	0.232761i
$471$		0			0
$472$	−2.76393	+	3.80423i	−0.127220	+	0.175104i
$473$	−7.98826	−	2.59554i	−0.367301	−	0.119343i
$474$		0			0
$475$	4.70614	−	2.44307i	0.215933	−	0.112096i
$476$	−16.1245			−0.739067
$477$		0			0
$478$	−14.1689	+	19.5018i	−0.648068	+	0.891989i
$479$	12.2532	+	8.90247i	0.559863	+	0.406764i	0.831409	−	0.555661i	$-0.187535\pi$
$479$	12.2532	+	8.90247i	0.559863	+	0.406764i	−0.271546	+	0.962425i	$0.587535\pi$
$480$		0			0
$481$	−7.07491	+	5.14022i	−0.322588	+	0.234374i
$482$		−	15.1244i		−	0.688899i
$483$		0			0
$484$	2.97689	+	9.16193i	0.135313	+	0.416451i
$485$	−13.0366	+	15.3817i	−0.591960	+	0.698447i
$486$		0			0
$487$	−10.1520	+	3.29858i	−0.460030	+	0.149473i	−0.529858	−	0.848086i	$-0.677755\pi$
$487$	−10.1520	+	3.29858i	−0.460030	+	0.149473i	0.0698280	+	0.997559i	$0.477755\pi$
$488$	−1.49765	+	0.486616i	−0.0677954	+	0.0220281i
$489$		0			0
$490$	38.8635	+	15.9252i	1.75567	+	0.719428i
$491$	−8.27596	−	25.4708i	−0.373489	−	1.14948i	−0.944492	−	0.328533i	$-0.893446\pi$
$491$	−8.27596	−	25.4708i	−0.373489	−	1.14948i	0.571003	−	0.820948i	$-0.306554\pi$
$492$		0			0
$493$			8.75256i			0.394195i
$494$	2.95350	−	2.14584i	0.132884	−	0.0965460i
$495$		0			0
$496$	2.09310	+	1.52072i	0.0939828	+	0.0682825i
$497$	37.3444	−	51.4002i	1.67513	−	2.30561i
$498$		0			0
$499$	−16.5186			−0.739474			−0.369737	−	0.929136i	$-0.620552\pi$
$499$	−16.5186			−0.739474			−0.369737	+	0.929136i	$0.620552\pi$
$500$	7.35738	+	8.41837i	0.329032	+	0.376481i
$501$		0			0
$502$	27.9398	+	9.07820i	1.24702	+	0.405180i
$503$	−11.6554	+	16.0423i	−0.519690	+	0.715292i	−0.985516	−	0.169584i	$-0.945757\pi$
$503$	−11.6554	+	16.0423i	−0.519690	+	0.715292i	0.465825	+	0.884877i	$0.345757\pi$
$504$		0			0
$505$	−14.3867	−	1.07733i	−0.640199	−	0.0479404i
$506$	−0.481882	+	0.350107i	−0.0214222	+	0.0155642i
$507$		0			0
$508$	−6.39445	−	8.80121i	−0.283708	−	0.390490i
$509$	−2.29160	−	7.05281i	−0.101573	−	0.312610i	0.887338	−	0.461120i	$-0.152552\pi$
$509$	−2.29160	−	7.05281i	−0.101573	−	0.312610i	−0.988911	+	0.148510i	$0.952552\pi$
$510$		0			0
$511$	16.7928	−	51.6831i	0.742872	−	2.28632i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$		0			0
$514$	3.63580	−	11.1898i	0.160368	−	0.493562i
$515$	−10.2849	+	12.1351i	−0.453208	+	0.534735i
$516$		0			0
$517$	−2.94949	−	4.05962i	−0.129718	−	0.178542i
$518$			12.8991i			0.566754i
$519$		0			0
$520$	5.87222	+	4.97693i	0.257514	+	0.218253i
$521$	3.93758	+	2.86082i	0.172509	+	0.125335i	0.670689	−	0.741738i	$-0.265998\pi$
$521$	3.93758	+	2.86082i	0.172509	+	0.125335i	−0.498181	+	0.867073i	$0.665998\pi$
$522$		0			0
$523$	2.28344	+	0.741933i	0.0998477	+	0.0324425i	0.358515	−	0.933524i	$-0.383283\pi$
$523$	2.28344	+	0.741933i	0.0998477	+	0.0324425i	−0.258667	+	0.965967i	$0.583283\pi$
$524$	14.7158			0.642863
$525$		0			0
$526$	−16.5758			−0.722741
$527$	−7.81375	−	2.53884i	−0.340372	−	0.110594i
$528$		0			0
$529$	−18.3974	−	13.3665i	−0.799885	−	0.581151i
$530$	−9.58721	+	5.92522i	−0.416442	+	0.257375i
$531$		0			0
$532$		−	5.38487i		−	0.233464i
$533$	−16.9365	−	23.3111i	−0.733601	−	1.00971i
$534$		0			0
$535$	−0.728994	+	9.73501i	−0.0315171	+	0.420881i
$536$	1.72982	−	5.32385i	0.0747171	−	0.229955i
$537$		0			0
$538$	−16.7585	+	5.44517i	−0.722511	+	0.234758i
$539$	−6.78518	+	20.8826i	−0.292258	+	0.899478i
$540$		0			0
$541$	5.48173	+	16.8710i	0.235678	+	0.725342i	0.997031	+	0.0770042i	$0.0245355\pi$
$541$	5.48173	+	16.8710i	0.235678	+	0.725342i	−0.761353	+	0.648338i	$0.775465\pi$
$542$	1.04367	+	1.43649i	0.0448294	+	0.0617023i
$543$		0			0
$544$	−2.56909	+	1.86655i	−0.110149	+	0.0800278i
$545$	−5.42043	−	22.2061i	−0.232186	−	0.951203i
$546$		0			0
$547$	−9.12513	+	12.5597i	−0.390162	+	0.537013i	−0.958241	−	0.285962i	$-0.907687\pi$
$547$	−9.12513	+	12.5597i	−0.390162	+	0.537013i	0.568079	+	0.822974i	$0.307687\pi$
$548$	−16.5824	−	5.38795i	−0.708366	−	0.230162i
$549$		0			0
$550$	−4.10157	+	4.16432i	−0.174891	+	0.177567i
$551$	−2.92296			−0.124522
$552$		0			0
$553$	37.9745	−	52.2674i	1.61484	−	2.22264i
$554$	−17.1785	−	12.4809i	−0.729843	−	0.530262i
$555$		0			0
$556$	−5.86420	+	4.26059i	−0.248698	+	0.180689i
$557$			27.6087i			1.16982i	0.811100	+	0.584908i	$0.198869\pi$
$557$			27.6087i			1.16982i	−0.811100	+	0.584908i	$0.801131\pi$
$558$		0			0
$559$	7.64330	+	23.5237i	0.323277	+	0.994945i
$560$	11.0302	−	2.69244i	0.466111	−	0.113776i
$561$		0			0
$562$	7.85317	−	2.55165i	0.331266	−	0.107635i
$563$	−24.6828	+	8.01993i	−1.04026	+	0.338000i	−0.778837	−	0.627226i	$-0.784190\pi$
$563$	−24.6828	+	8.01993i	−1.04026	+	0.338000i	−0.261419	+	0.965226i	$0.584190\pi$
$564$		0			0
$565$	19.0774	−	4.65673i	0.802591	−	0.195910i
$566$	6.05863	+	18.6466i	0.254663	+	0.783773i
$567$		0			0
$568$		−	12.5124i		−	0.525010i
$569$	22.5641	−	16.3938i	0.945935	−	0.687262i	−0.00390663	−	0.999992i	$-0.501244\pi$
$569$	22.5641	−	16.3938i	0.945935	−	0.687262i	0.949842	+	0.312730i	$0.101244\pi$
$570$		0			0
$571$	−31.2970	−	22.7386i	−1.30974	−	0.951580i	−1.00000		0.000758017i	$-0.999759\pi$
$571$	−31.2970	−	22.7386i	−1.30974	−	0.951580i	−0.309738	−	0.950822i	$-0.600241\pi$
$572$	−2.36540	+	3.25570i	−0.0989024	+	0.136127i
$573$		0			0
$574$	−42.5012			−1.77397
$575$	2.27867	+	1.13933i	0.0950270	+	0.0475135i
$576$		0			0
$577$	−8.09721	−	2.63094i	−0.337091	−	0.109528i	0.135580	−	0.990766i	$-0.456710\pi$
$577$	−8.09721	−	2.63094i	−0.337091	−	0.109528i	−0.472671	+	0.881239i	$0.656710\pi$
$578$	−4.06498	+	5.59496i	−0.169081	+	0.232720i
$579$		0			0
$580$	−1.46148	−	5.98729i	−0.0606846	−	0.248609i
$581$	13.1960	−	9.58744i	0.547462	−	0.397754i
$582$		0			0
$583$	−3.46331	−	4.76684i	−0.143436	−	0.197422i
$584$	−3.30719	−	10.1785i	−0.136852	−	0.421188i
$585$		0			0
$586$	5.87003	−	18.0661i	0.242489	−	0.746304i
$587$	−6.40851	+	2.08225i	−0.264507	+	0.0859437i	−0.438268	−	0.898844i	$-0.644408\pi$
$587$	−6.40851	+	2.08225i	−0.264507	+	0.0859437i	0.173761	+	0.984788i	$0.444408\pi$
$588$		0			0
$589$	0.847859	−	2.60944i	0.0349354	−	0.107520i
$590$	−0.785175	+	10.4853i	−0.0323252	+	0.431672i
$591$		0			0
$592$	1.49318	+	2.05519i	0.0613693	+	0.0844677i
$593$		−	16.3070i		−	0.669648i	−0.942281	−	0.334824i	$-0.891323\pi$
$593$		−	16.3070i		−	0.669648i	0.942281	−	0.334824i	$-0.108677\pi$
$594$		0			0
$595$	−30.6707	+	18.9555i	−1.25738	+	0.777101i
$596$	−9.63188	−	6.99797i	−0.394537	−	0.286648i
$597$		0			0
$598$	1.66817	+	0.542023i	0.0682167	+	0.0221650i
$599$	20.3249			0.830452			0.415226	−	0.909718i	$-0.363702\pi$
$599$	20.3249			0.830452			0.415226	+	0.909718i	$0.363702\pi$
$600$		0			0
$601$	−0.340091			−0.0138726			−0.00693631	−	0.999976i	$-0.502208\pi$
$601$	−0.340091			−0.0138726			−0.00693631	+	0.999976i	$0.502208\pi$
$602$	34.6977	+	11.2740i	1.41417	+	0.459493i
$603$		0			0
$604$	−6.64584	−	4.82849i	−0.270415	−	0.196468i
$605$	16.4329	+	13.9275i	0.668092	+	0.566233i
$606$		0			0
$607$			15.1440i			0.614676i	0.951600	+	0.307338i	$0.0994381\pi$
$607$			15.1440i			0.614676i	−0.951600	+	0.307338i	$0.900562\pi$
$608$	−0.623345	−	0.857960i	−0.0252800	−	0.0347949i
$609$		0			0
$610$	−2.27665	+	2.68619i	−0.0921788	+	0.108761i
$611$	−4.56628	+	14.0536i	−0.184732	+	0.568547i
$612$		0			0
$613$	−38.5516	+	12.5262i	−1.55708	+	0.505927i	−0.956027	−	0.293279i	$-0.905254\pi$
$613$	−38.5516	+	12.5262i	−1.55708	+	0.505927i	−0.601057	+	0.799206i	$0.705254\pi$
$614$	−2.10736	+	6.48577i	−0.0850460	+	0.261745i
$615$		0			0
$616$	1.83428	+	5.64532i	0.0739051	+	0.227456i
$617$	−3.90251	−	5.37134i	−0.157109	−	0.216242i	0.723205	−	0.690633i	$-0.242668\pi$
$617$	−3.90251	−	5.37134i	−0.157109	−	0.216242i	−0.880314	+	0.474391i	$0.842668\pi$
$618$		0			0
$619$	−21.0590	+	15.3003i	−0.846434	+	0.614970i	−0.924160	−	0.382005i	$-0.875234\pi$
$619$	−21.0590	+	15.3003i	−0.846434	+	0.614970i	0.0777268	+	0.996975i	$0.475234\pi$
$620$	5.76902	+	0.432006i	0.231690	+	0.0173498i
$621$		0			0
$622$	1.92023	−	2.64297i	0.0769943	−	0.105974i
$623$	56.5408	+	18.3712i	2.26526	+	0.736028i
$624$		0			0
$625$	23.8910	+	7.36356i	0.955638	+	0.294542i
$626$	−8.83756			−0.353220
$627$		0			0
$628$	−12.5035	+	17.2096i	−0.498943	+	0.686736i
$629$	−6.52639	−	4.74170i	−0.260224	−	0.189064i
$630$		0			0
$631$	40.5824	−	29.4848i	1.61556	−	1.17377i	0.775286	−	0.631610i	$-0.217606\pi$
$631$	40.5824	−	29.4848i	1.61556	−	1.17377i	0.840274	−	0.542163i	$-0.182394\pi$
$632$		−	12.7235i		−	0.506115i
$633$		0			0
$634$	−10.8517	−	33.3981i	−0.430976	−	1.32641i
$635$	−22.5094	−	9.22376i	−0.893259	−	0.366034i
$636$		0			0
$637$	61.4947	−	19.9808i	2.43651	−	0.791670i
$638$	3.06433	−	0.995663i	0.121318	−	0.0394187i
$639$		0			0
$640$	1.44575	−	1.70582i	0.0571481	−	0.0674284i
$641$	3.87785	+	11.9348i	0.153166	+	0.471396i	0.997970	−	0.0636787i	$-0.0202833\pi$
$641$	3.87785	+	11.9348i	0.153166	+	0.471396i	−0.844804	+	0.535075i	$0.820283\pi$
$642$		0			0
$643$		−	38.9701i		−	1.53683i	−0.639951	−	0.768415i	$-0.721046\pi$
$643$		−	38.9701i		−	1.53683i	0.639951	−	0.768415i	$-0.278954\pi$
$644$	2.09310	−	1.52072i	0.0824795	−	0.0599249i
$645$		0			0
$646$	2.72451	+	1.97948i	0.107195	+	0.0778814i
$647$	−9.02843	+	12.4266i	−0.354944	+	0.488539i	−0.948731	−	0.316083i	$-0.897632\pi$
$647$	−9.02843	+	12.4266i	−0.354944	+	0.488539i	0.593787	+	0.804622i	$0.297632\pi$
$648$		0			0
$649$	−5.49700			−0.215776
$650$	17.0204	+	2.56347i	0.667593	+	0.100548i
$651$		0			0
$652$	−7.31698	−	2.37743i	−0.286555	−	0.0931073i
$653$	13.2339	−	18.2149i	0.517882	−	0.712803i	−0.467342	−	0.884077i	$-0.654788\pi$
$653$	13.2339	−	18.2149i	0.517882	−	0.712803i	0.985224	+	0.171274i	$0.0547882\pi$
$654$		0			0
$655$	27.9911	−	17.2995i	1.09370	−	0.675946i
$656$	−6.77163	+	4.91988i	−0.264388	+	0.192089i
$657$		0			0
$658$	12.8114	+	17.6333i	0.499439	+	0.687419i
$659$	−15.0771	−	46.4024i	−0.587319	−	1.80758i	−0.589753	−	0.807583i	$-0.700775\pi$
$659$	−15.0771	−	46.4024i	−0.587319	−	1.80758i	0.00243474	−	0.999997i	$-0.499225\pi$
$660$		0			0
$661$	−6.31188	+	19.4260i	−0.245504	+	0.755583i	0.750049	+	0.661382i	$0.230030\pi$
$661$	−6.31188	+	19.4260i	−0.245504	+	0.755583i	−0.995553	+	0.0942010i	$0.969970\pi$
$662$	−10.7672	+	3.49847i	−0.418478	+	0.135972i
$663$		0			0
$664$	0.992661	−	3.05510i	0.0385227	−	0.118561i
$665$	−6.33030	−	10.2426i	−0.245478	−	0.397192i
$666$		0			0
$667$	−0.825463	−	1.13615i	−0.0319621	−	0.0439920i
$668$		−	2.15350i		−	0.0833215i
$669$		0			0
$670$	−2.96824	−	12.1601i	−0.114673	−	0.469786i
$671$	−1.48929	−	1.08203i	−0.0574933	−	0.0417713i
$672$		0			0
$673$	13.3629	+	4.34187i	0.515103	+	0.167367i	0.555022	−	0.831836i	$-0.312710\pi$
$673$	13.3629	+	4.34187i	0.515103	+	0.167367i	−0.0399190	+	0.999203i	$0.512710\pi$
$674$	−9.45078			−0.364030
$675$		0			0
$676$	−1.14945			−0.0442094
$677$	41.2458	+	13.4016i	1.58520	+	0.515064i	0.963390	−	0.268102i	$-0.0863965\pi$
$677$	41.2458	+	13.4016i	1.58520	+	0.515064i	0.621813	+	0.783166i	$0.286397\pi$
$678$		0			0
$679$	37.0420	+	26.9126i	1.42154	+	1.03281i
$680$	−2.69244	+	6.57054i	−0.103250	+	0.251969i
$681$		0			0
$682$			3.02446i			0.115813i
$683$	−9.84941	−	13.5565i	−0.376877	−	0.518727i	0.577877	−	0.816124i	$-0.303881\pi$
$683$	−9.84941	−	13.5565i	−0.376877	−	0.518727i	−0.954754	+	0.297397i	$0.903881\pi$
$684$		0			0
$685$	−37.8756	+	9.24530i	−1.44715	+	0.353245i
$686$	18.4884	−	56.9014i	0.705890	−	2.17251i
$687$		0			0
$688$	6.83338	−	2.22030i	0.260520	−	0.0846481i
$689$	−5.36176	+	16.5018i	−0.204267	+	0.628669i
$690$		0			0
$691$	5.93564	+	18.2680i	0.225803	+	0.694949i	0.998209	+	0.0598204i	$0.0190528\pi$
$691$	5.93564	+	18.2680i	0.225803	+	0.694949i	−0.772407	+	0.635128i	$0.780947\pi$
$692$	−1.18329	−	1.62866i	−0.0449818	−	0.0619122i
$693$		0			0
$694$	26.8689	−	19.5214i	1.01993	−	0.741022i
$695$	−6.14575	+	14.9979i	−0.233122	+	0.568903i
$696$		0			0
$697$	15.6234	−	21.5038i	0.591779	−	0.814514i
$698$	−21.9130	−	7.11997i	−0.829419	−	0.269495i
$699$		0			0
$700$	17.8155	−	18.0881i	0.673364	−	0.683665i
$701$	−16.8695			−0.637152			−0.318576	−	0.947897i	$-0.603205\pi$
$701$	−16.8695			−0.637152			−0.318576	+	0.947897i	$0.603205\pi$
$702$		0			0
$703$	1.58351	−	2.17952i	0.0597234	−	0.0822022i
$704$	0.945746	+	0.687124i	0.0356441	+	0.0258970i
$705$		0			0
$706$	0.606587	−	0.440711i	0.0228292	−	0.0165864i
$707$			32.7609i			1.23210i
$708$		0			0
$709$	−1.77558	−	5.46468i	−0.0666834	−	0.205231i	0.912163	−	0.409828i	$-0.134411\pi$
$709$	−1.77558	−	5.46468i	−0.0666834	−	0.205231i	−0.978846	+	0.204598i	$0.934411\pi$
$710$	−14.7092	−	23.8001i	−0.552028	−	0.893200i
$711$		0			0
$712$	11.1352	−	3.61803i	0.417308	−	0.135592i
$713$	1.25373	−	0.407361i	0.0469525	−	0.0152558i
$714$		0			0
$715$	−0.671961	+	8.97340i	−0.0251299	+	0.335586i
$716$	5.85172	+	18.0097i	0.218689	+	0.673055i
$717$		0			0
$718$		−	0.876630i		−	0.0327156i
$719$	−30.2426	+	21.9725i	−1.12786	+	0.819436i	−0.985381	−	0.170362i	$-0.945506\pi$
$719$	−30.2426	+	21.9725i	−1.12786	+	0.819436i	−0.142475	+	0.989798i	$0.545506\pi$
$720$		0			0
$721$	29.2235	+	21.2321i	1.08834	+	0.790725i
$722$	10.5069	−	14.4615i	0.391025	−	0.538200i
$723$		0			0
$724$	18.5396			0.689019
$725$	−9.81838	−	9.67044i	−0.364646	−	0.359151i
$726$		0			0
$727$	−38.8740	−	12.6309i	−1.44176	−	0.468455i	−0.519311	−	0.854585i	$-0.673812\pi$
$727$	−38.8740	−	12.6309i	−1.44176	−	0.468455i	−0.922444	+	0.386130i	$0.873812\pi$
$728$	10.2743	−	14.1414i	0.380792	−	0.524115i
$729$		0			0
$730$	−18.2562	−	15.4728i	−0.675691	−	0.572673i
$731$	−18.4590	+	13.4113i	−0.682731	+	0.496033i
$732$		0			0
$733$	−6.61430	−	9.10381i	−0.244305	−	0.336257i	0.669202	−	0.743081i	$-0.266636\pi$
$733$	−6.61430	−	9.10381i	−0.244305	−	0.336257i	−0.913507	+	0.406824i	$0.866636\pi$
$734$	−6.76777	−	20.8291i	−0.249803	−	0.768814i
$735$		0			0
$736$	0.157452	−	0.484587i	0.00580376	−	0.0178621i
$737$	6.22362	−	2.02218i	0.229250	−	0.0744878i
$738$		0			0
$739$	9.74404	−	29.9891i	0.358440	−	1.10317i	−0.595547	−	0.803320i	$-0.703065\pi$
$739$	9.74404	−	29.9891i	0.358440	−	1.10317i	0.953988	−	0.299846i	$-0.0969353\pi$
$740$	5.25621	+	2.15386i	0.193222	+	0.0791774i
$741$		0			0
$742$	15.0432	+	20.7052i	0.552253	+	0.760111i
$743$		−	12.1762i		−	0.446700i	−0.974738	−	0.223350i	$-0.928301\pi$
$743$		−	12.1762i		−	0.446700i	0.974738	−	0.223350i	$-0.0716993\pi$
$744$		0			0
$745$	−26.5475	−	1.98798i	−0.972626	−	0.0728338i
$746$	15.2445	+	11.0758i	0.558143	+	0.405514i
$747$		0			0
$748$	−3.53057	−	1.14715i	−0.129090	−	0.0419440i
$749$	22.1683			0.810010
$750$		0			0
$751$	−50.0011			−1.82457			−0.912284	−	0.409559i	$-0.865683\pi$
$751$	−50.0011			−1.82457			−0.912284	+	0.409559i	$0.865683\pi$
$752$	4.08242	+	1.32646i	0.148870	+	0.0483709i
$753$		0			0
$754$	−7.67609	−	5.57701i	−0.279547	−	0.203103i
$755$	−18.3174	−	1.37167i	−0.666637	−	0.0499202i
$756$		0			0
$757$		−	14.6954i		−	0.534113i	−0.963681	−	0.267057i	$-0.913949\pi$
$757$		−	14.6954i		−	0.534113i	0.963681	−	0.267057i	$-0.0860510\pi$
$758$	7.45691	+	10.2636i	0.270847	+	0.372789i
$759$		0			0
$760$	−2.19427	−	0.899152i	−0.0795944	−	0.0326157i
$761$	−10.7342	+	33.0365i	−0.389115	+	1.19757i	0.544337	+	0.838867i	$0.316781\pi$
$761$	−10.7342	+	33.0365i	−0.389115	+	1.19757i	−0.933451	+	0.358705i	$0.883219\pi$
$762$		0			0
$763$	−49.3658	+	16.0399i	−1.78716	+	0.580684i
$764$	−3.39327	+	10.4434i	−0.122764	+	0.377829i
$765$		0			0
$766$	10.2334	+	31.4952i	0.369748	+	1.13797i
$767$	9.51474	+	13.0959i	0.343557	+	0.472866i
$768$		0			0
$769$	11.1092	−	8.07132i	0.400609	−	0.291059i	−0.369180	−	0.929358i	$-0.620361\pi$
$769$	11.1092	−	8.07132i	0.400609	−	0.291059i	0.769789	+	0.638299i	$0.220361\pi$
$770$	10.1255	+	8.58172i	0.364897	+	0.309264i
$771$		0			0
$772$	−3.52671	+	4.85410i	−0.126929	+	0.174703i
$773$	22.4558	+	7.29633i	0.807679	+	0.262431i	0.683614	−	0.729843i	$-0.260407\pi$
$773$	22.4558	+	7.29633i	0.807679	+	0.262431i	0.124065	+	0.992274i	$0.460407\pi$
$774$		0			0
$775$	11.4812	−	5.96017i	0.412416	−	0.214096i
$776$	9.01719			0.323698
$777$		0			0
$778$	2.61117	−	3.59397i	0.0936151	−	0.128850i
$779$	7.18129	+	5.21752i	0.257297	+	0.186937i
$780$		0			0
$781$	11.8336	−	8.59760i	0.423439	−	0.307646i
$782$			1.61803i			0.0578608i
$783$		0			0
$784$	−5.80423	−	17.8636i	−0.207294	−	0.637985i
$785$	−3.55198	+	47.4333i	−0.126775	+	1.69297i
$786$		0			0
$787$	−43.8852	+	14.2592i	−1.56434	+	0.508285i	−0.957963	−	0.286893i	$-0.907378\pi$
$787$	−43.8852	+	14.2592i	−1.56434	+	0.508285i	−0.606377	+	0.795177i	$0.707378\pi$
$788$	3.13412	−	1.01834i	0.111649	−	0.0362768i
$789$		0			0
$790$	−14.9574	−	24.2016i	−0.532160	−	0.861054i
$791$	−13.7800	−	42.4105i	−0.489960	−	1.50794i
$792$		0			0
$793$			5.42092i			0.192503i
$794$	−12.5009	+	9.08246i	−0.443641	+	0.322324i
$795$		0			0
$796$	9.71764	+	7.06028i	0.344433	+	0.250245i
$797$	15.2351	−	20.9693i	0.539655	−	0.742772i	−0.448908	−	0.893578i	$-0.648187\pi$
$797$	15.2351	−	20.9693i	0.539655	−	0.742772i	0.988563	+	0.150806i	$0.0481870\pi$
$798$		0			0
$799$	−13.6312			−0.482236
$800$	0.744661	−	4.94424i	0.0263277	−	0.174805i
$801$		0			0
$802$	−8.00779	−	2.60189i	−0.282765	−	0.0918758i
$803$	7.35380	−	10.1216i	0.259510	−	0.357185i
$804$		0			0
$805$	2.19359	−	5.35317i	0.0773138	−	0.188674i
$806$	7.20541	−	5.23503i	0.253800	−	0.184396i
$807$		0			0
$808$	3.79235	+	5.21972i	0.133414	+	0.183629i
$809$	1.22362	+	3.76590i	0.0430201	+	0.132402i	0.970260	−	0.242066i	$-0.0778252\pi$
$809$	1.22362	+	3.76590i	0.0430201	+	0.132402i	−0.927240	+	0.374469i	$0.877825\pi$
$810$		0			0
$811$	−10.8386	+	33.3578i	−0.380595	+	1.17135i	0.559031	+	0.829147i	$0.311173\pi$
$811$	−10.8386	+	33.3578i	−0.380595	+	1.17135i	−0.939626	+	0.342203i	$0.888827\pi$
$812$	−13.3102	+	4.32475i	−0.467097	+	0.151769i
$813$		0			0
$814$	−0.917683	+	2.82434i	−0.0321648	+	0.0989930i
$815$	−16.7126	+	4.07948i	−0.585415	+	0.142898i
$816$		0			0
$817$	−4.47876	−	6.16448i	−0.156692	−	0.215668i
$818$		−	20.1151i		−	0.703307i
$819$		0			0
$820$	−7.09674	+	17.3187i	−0.247829	+	0.604795i
$821$	−18.4835	−	13.4290i	−0.645078	−	0.468677i	0.216513	−	0.976280i	$-0.430532\pi$
$821$	−18.4835	−	13.4290i	−0.645078	−	0.468677i	−0.861591	+	0.507603i	$0.830532\pi$
$822$		0			0
$823$	27.7815	+	9.02677i	0.968403	+	0.314653i	0.750171	−	0.661244i	$-0.229971\pi$
$823$	27.7815	+	9.02677i	0.968403	+	0.314653i	0.218232	+	0.975897i	$0.429971\pi$
$824$	7.11392			0.247825
$825$		0			0
$826$	23.8767			0.830777
$827$	−53.0917	−	17.2505i	−1.84618	−	0.599860i	−0.997477	−	0.0709875i	$-0.977385\pi$
$827$	−53.0917	−	17.2505i	−1.84618	−	0.599860i	−0.848701	−	0.528872i	$-0.822615\pi$
$828$		0			0
$829$	10.9038	+	7.92207i	0.378704	+	0.275145i	0.760811	−	0.648973i	$-0.224801\pi$
$829$	10.9038	+	7.92207i	0.378704	+	0.275145i	−0.382107	+	0.924118i	$0.624801\pi$
$830$	−1.70333	−	6.97808i	−0.0591234	−	0.242213i
$831$		0			0
$832$		−	3.44246i		−	0.119346i
$833$	35.0592	+	48.2549i	1.21473	+	1.67193i
$834$		0			0
$835$	−2.53159	−	4.09620i	−0.0876094	−	0.141755i
$836$	0.383097	−	1.17905i	0.0132497	−	0.0407783i
$837$		0			0
$838$	−14.9337	+	4.85224i	−0.515874	+	0.167618i
$839$	4.10958	−	12.6480i	0.141879	−	0.436657i	−0.854718	−	0.519093i	$-0.826270\pi$
$839$	4.10958	−	12.6480i	0.141879	−	0.436657i	0.996596	+	0.0824356i	$0.0262699\pi$
$840$		0			0
$841$	−6.61398	−	20.3557i	−0.228068	−	0.701922i
$842$	−3.79788	−	5.22733i	−0.130883	−	0.180146i
$843$		0			0
$844$	14.5741	−	10.5887i	0.501661	−	0.364478i
$845$	−2.18637	+	1.35125i	−0.0752136	+	0.0464845i
$846$		0			0
$847$	28.7518	−	39.5735i	0.987924	−	1.35976i
$848$	4.79360	+	1.55754i	0.164613	+	0.0534860i
$849$		0			0
$850$	2.60282	+	15.6631i	0.0892760	+	0.537239i
$851$	1.29437			0.0443705
$852$		0			0
$853$	18.2147	−	25.0704i	0.623660	−	0.858394i	−0.373953	−	0.927448i	$-0.621998\pi$
$853$	18.2147	−	25.0704i	0.623660	−	0.858394i	0.997613	+	0.0690536i	$0.0219979\pi$
$854$	6.46885	+	4.69990i	0.221360	+	0.160827i
$855$		0			0
$856$	3.53202	−	2.56616i	0.120722	−	0.0877097i
$857$			11.8287i			0.404061i	0.979379	+	0.202030i	$0.0647540\pi$
$857$			11.8287i			0.404061i	−0.979379	+	0.202030i	$0.935246\pi$
$858$		0			0
$859$	9.00696	+	27.7206i	0.307313	+	0.945813i	0.978804	+	0.204800i	$0.0656544\pi$
$859$	9.00696	+	27.7206i	0.307313	+	0.945813i	−0.671490	+	0.741013i	$0.734346\pi$
$860$	10.3877	−	12.2564i	0.354219	−	0.417939i
$861$		0			0
$862$	−35.3807	+	11.4959i	−1.20507	+	0.391551i
$863$	−44.7468	+	14.5391i	−1.52320	+	0.494918i	−0.946683	−	0.322167i	$-0.895589\pi$
$863$	−44.7468	+	14.5391i	−1.52320	+	0.494918i	−0.576517	+	0.817085i	$0.695589\pi$
$864$		0			0
$865$	−4.16535	−	1.70685i	−0.141626	−	0.0580346i
$866$	6.60719	+	20.3348i	0.224522	+	0.691006i
$867$		0			0
$868$		−	13.1370i		−	0.445900i
$869$	12.0332	−	8.74265i	0.408199	−	0.296574i
$870$		0			0
$871$	−15.5900	−	11.3268i	−0.528248	−	0.383794i
$872$	−6.00859	+	8.27012i	−0.203477	+	0.280062i
$873$		0			0
$874$	−0.540350			−0.0182776
$875$	12.6233	−	55.3490i	0.426746	−	1.87114i
$876$		0			0
$877$	28.4723	+	9.25123i	0.961443	+	0.312392i	0.747357	−	0.664423i	$-0.231323\pi$
$877$	28.4723	+	9.25123i	0.961443	+	0.312392i	0.214086	+	0.976815i	$0.431323\pi$
$878$	−3.70035	+	5.09310i	−0.124881	+	0.171884i
$879$		0			0
$880$	2.60668	+	0.195198i	0.0878711	+	0.00658011i
$881$	−4.65241	+	3.38017i	−0.156744	+	0.113881i	−0.663393	−	0.748272i	$-0.730884\pi$
$881$	−4.65241	+	3.38017i	−0.156744	+	0.113881i	0.506649	+	0.862152i	$0.330884\pi$
$882$		0			0
$883$	22.3458	+	30.7564i	0.751996	+	1.03503i	0.997838	+	0.0657241i	$0.0209357\pi$
$883$	22.3458	+	30.7564i	0.751996	+	1.03503i	−0.245841	+	0.969310i	$0.579064\pi$
$884$	3.37811	+	10.3967i	0.113618	+	0.349680i
$885$		0			0
$886$	3.24848	−	9.99781i	0.109135	−	0.335883i
$887$	20.8764	−	6.78316i	0.700962	−	0.227756i	0.0632121	−	0.998000i	$-0.479866\pi$
$887$	20.8764	−	6.78316i	0.700962	−	0.227756i	0.637749	+	0.770244i	$0.279866\pi$
$888$		0			0
$889$	−17.0700	+	52.5360i	−0.572508	+	1.76200i
$890$	16.9271	−	19.9721i	0.567397	−	0.669466i
$891$		0			0
$892$	2.19389	+	3.01963i	0.0734568	+	0.101105i
$893$		−	4.55219i		−	0.152333i
$894$		0			0
$895$	32.3023	+	27.3774i	1.07975	+	0.915127i
$896$	−4.10793	−	2.98459i	−0.137236	−	0.0997081i
$897$		0			0
$898$	−2.67592	−	0.869458i	−0.0892965	−	0.0290142i
$899$	−7.13090			−0.237829
$900$		0			0
$901$	−16.0058			−0.533231
$902$	−9.30590	−	3.02367i	−0.309853	−	0.100677i
$903$		0			0
$904$	−7.10491	−	5.16202i	−0.236306	−	0.171686i
$905$	35.2644	−	21.7946i	1.17223	−	0.724477i
$906$		0			0
$907$		−	1.11102i		−	0.0368907i	−0.999830	−	0.0184453i	$-0.994128\pi$
$907$		−	1.11102i		−	0.0368907i	0.999830	−	0.0184453i	$-0.00587167\pi$
$908$	−8.19900	−	11.2850i	−0.272093	−	0.374504i
$909$		0			0
$910$	2.91872	−	38.9768i	0.0967547	−	1.29207i
$911$	−5.21069	+	16.0369i	−0.172638	+	0.531325i	−0.999518	−	0.0310539i	$-0.990114\pi$
$911$	−5.21069	+	16.0369i	−0.172638	+	0.531325i	0.826880	+	0.562379i	$0.190114\pi$
$912$		0			0
$913$	3.57142	−	1.16043i	0.118197	−	0.0384045i
$914$	1.55040	−	4.77163i	0.0512825	−	0.157831i
$915$		0			0
$916$	−6.10755	−	18.7971i	−0.201799	−	0.621074i
$917$	−43.9206	−	60.4515i	−1.45039	−	1.99629i
$918$		0			0
$919$	12.8551	−	9.33974i	0.424049	−	0.308090i	−0.355216	−	0.934784i	$-0.615593\pi$
$919$	12.8551	−	9.33974i	0.424049	−	0.308090i	0.779265	+	0.626695i	$0.215593\pi$
$920$	−0.270175	−	1.10684i	−0.00890741	−	0.0364913i
$921$		0			0
$922$	−12.0736	+	16.6179i	−0.397624	+	0.547282i
$923$	−40.9654	−	13.3105i	−1.34839	−	0.438119i
$924$		0			0
$925$	12.5299	−	2.08217i	0.411981	−	0.0684613i
$926$	−7.75256			−0.254765
$927$		0			0
$928$	−1.62006	+	2.22982i	−0.0531812	+	0.0731976i
$929$	24.5450	+	17.8330i	0.805296	+	0.585082i	0.912463	−	0.409159i	$-0.134178\pi$
$929$	24.5450	+	17.8330i	0.805296	+	0.585082i	−0.107167	+	0.994241i	$0.534178\pi$
$930$		0			0
$931$	−16.1150	+	11.7082i	−0.528146	+	0.383721i
$932$		−	7.43184i		−	0.243438i
$933$		0			0
$934$	9.11585	+	28.0557i	0.298280	+	0.918010i
$935$	−8.06410	+	1.96842i	−0.263724	+	0.0643743i
$936$		0			0
$937$	−11.6456	+	3.78389i	−0.380445	+	0.123614i	−0.492996	−	0.870032i	$-0.664098\pi$
$937$	−11.6456	+	3.78389i	−0.380445	+	0.123614i	0.112550	+	0.993646i	$0.464098\pi$
$938$	−27.0328	+	8.78350i	−0.882654	+	0.286792i
$939$		0			0
$940$	9.32457	−	2.27610i	0.304134	−	0.0742381i
$941$	14.6477	+	45.0810i	0.477502	+	1.46960i	0.842554	+	0.538612i	$0.181051\pi$
$941$	14.6477	+	45.0810i	0.477502	+	1.46960i	−0.365052	+	0.930987i	$0.618949\pi$
$942$		0			0
$943$			4.26483i			0.138882i
$944$	3.80423	−	2.76393i	0.123817	−	0.0899583i
$945$		0			0
$946$	6.79522	+	4.93702i	0.220932	+	0.160516i
$947$	14.3102	−	19.6963i	0.465020	−	0.640045i	−0.510521	−	0.859866i	$-0.670547\pi$
$947$	14.3102	−	19.6963i	0.465020	−	0.640045i	0.975540	+	0.219821i	$0.0705473\pi$
$948$		0			0
$949$	−36.8422			−1.19595
$950$	−5.23076	+	0.869225i	−0.169708	+	0.0282014i
$951$		0			0
$952$	15.3354	+	4.98276i	0.497022	+	0.161492i
$953$	18.6971	−	25.7344i	0.605659	−	0.833619i	−0.390552	−	0.920581i	$-0.627716\pi$
$953$	18.6971	−	25.7344i	0.605659	−	0.833619i	0.996212	+	0.0869621i	$0.0277159\pi$
$954$		0			0
$955$	5.82257	+	23.8535i	0.188414	+	0.771882i
$956$	19.5018	−	14.1689i	0.630732	−	0.458253i
$957$		0			0
$958$	−8.90247	−	12.2532i	−0.287626	−	0.395883i
$959$	27.3583	+	84.2003i	0.883446	+	2.71897i
$960$		0			0
$961$	−7.51108	+	23.1167i	−0.242293	+	0.745700i
$962$	8.31705	−	2.70237i	0.268152	−	0.0871280i
$963$		0			0
$964$	−4.67371	+	14.3842i	−0.150530	+	0.463283i
$965$	−1.00186	+	13.3789i	−0.0322512	+	0.430684i
$966$		0			0
$967$	−0.815288	−	1.12215i	−0.0262179	−	0.0360858i	0.795707	−	0.605682i	$-0.207100\pi$
$967$	−0.815288	−	1.12215i	−0.0262179	−	0.0360858i	−0.821925	+	0.569596i	$0.807100\pi$
$968$		−	9.63342i		−	0.309630i
$969$		0			0
$970$	17.1517	−	10.6003i	0.550708	−	0.340356i
$971$	30.6312	+	22.2549i	0.983003	+	0.714194i	0.958378	−	0.285503i	$-0.0921607\pi$
$971$	30.6312	+	22.2549i	0.983003	+	0.714194i	0.0246253	+	0.999697i	$0.492161\pi$
$972$		0			0
$973$	35.0045	+	11.3736i	1.12219	+	0.364622i
$974$	10.6744			0.342031
$975$		0			0
$976$	1.57472			0.0504056
$977$	−40.7355	−	13.2358i	−1.30325	−	0.423450i	−0.426536	−	0.904471i	$-0.640266\pi$
$977$	−40.7355	−	13.2358i	−1.30325	−	0.423450i	−0.876709	+	0.481021i	$0.840266\pi$
$978$		0			0
$979$	11.0730	+	8.04499i	0.353894	+	0.257119i
$980$	−32.0402	−	27.1553i	−1.02349	−	0.867443i
$981$		0			0
$982$			26.7816i			0.854635i
$983$	26.5028	+	36.4780i	0.845309	+	1.16347i	0.984877	+	0.173255i	$0.0554286\pi$
$983$	26.5028	+	36.4780i	0.845309	+	1.16347i	−0.139568	+	0.990212i	$0.544571\pi$
$984$		0			0
$985$	4.76433	−	5.62138i	0.151804	−	0.179112i
$986$	2.70469	−	8.32417i	0.0861348	−	0.265096i
$987$		0			0
$988$	−3.47204	+	1.12814i	−0.110460	+	0.0358908i
$989$	1.13130	−	3.48178i	0.0359732	−	0.110714i
$990$		0			0
$991$	−9.19755	−	28.3071i	−0.292170	−	0.899206i	−0.984157	−	0.177297i	$-0.943265\pi$
$991$	−9.19755	−	28.3071i	−0.292170	−	0.899206i	0.691988	−	0.721909i	$-0.256735\pi$
$992$	−1.52072	−	2.09310i	−0.0482830	−	0.0664559i
$993$		0			0
$994$	−51.4002	+	37.3444i	−1.63032	+	1.18449i
$995$	26.7839	+	2.00568i	0.849107	+	0.0635842i
$996$		0			0
$997$	−22.7215	+	31.2734i	−0.719596	+	0.990438i	0.279942	+	0.960017i	$0.409685\pi$
$997$	−22.7215	+	31.2734i	−0.719596	+	0.990438i	−0.999537	+	0.0304213i	$0.990315\pi$
$998$	15.7101	+	5.10453i	0.497295	+	0.161581i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.l.b.379.1		8
3.2	odd	2		50.2.e.a.29.2	yes	8
12.11	even	2		400.2.y.a.129.1		8
15.2	even	4		250.2.d.c.101.2		8
15.8	even	4		250.2.d.b.101.1		8
15.14	odd	2		250.2.e.a.149.1		8
25.19	even	10	inner	450.2.l.b.19.1		8
75.8	even	20		250.2.d.b.151.1		8
75.17	even	20		250.2.d.c.151.2		8
75.38	even	20		1250.2.a.i.1.4		4
75.41	odd	10		1250.2.b.c.1249.5		8
75.44	odd	10		50.2.e.a.19.2	✓	8
75.56	odd	10		250.2.e.a.99.1		8
75.59	odd	10		1250.2.b.c.1249.4		8
75.62	even	20		1250.2.a.h.1.1		4
300.119	even	10		400.2.y.a.369.1		8
300.263	odd	20		10000.2.a.bb.1.1		4
300.287	odd	20		10000.2.a.o.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.e.a.19.2	✓	8	75.44	odd	10
50.2.e.a.29.2	yes	8	3.2	odd	2
250.2.d.b.101.1		8	15.8	even	4
250.2.d.b.151.1		8	75.8	even	20
250.2.d.c.101.2		8	15.2	even	4
250.2.d.c.151.2		8	75.17	even	20
250.2.e.a.99.1		8	75.56	odd	10
250.2.e.a.149.1		8	15.14	odd	2
400.2.y.a.129.1		8	12.11	even	2
400.2.y.a.369.1		8	300.119	even	10
450.2.l.b.19.1		8	25.19	even	10	inner
450.2.l.b.379.1		8	1.1	even	1	trivial
1250.2.a.h.1.1		4	75.62	even	20
1250.2.a.i.1.4		4	75.38	even	20
1250.2.b.c.1249.4		8	75.59	odd	10
1250.2.b.c.1249.5		8	75.41	odd	10
10000.2.a.o.1.4		4	300.287	odd	20
10000.2.a.bb.1.1		4	300.263	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.809017 + 0.587785i) q^{4} +(2.22982 + 0.166977i) q^{5} -5.07768i q^{7} +(-0.587785 - 0.809017i) q^{8} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.809017 + 0.587785i) q^{4} +(2.22982 + 0.166977i) q^{5} -5.07768i q^{7} +(-0.587785 - 0.809017i) q^{8} +(-2.06909 - 0.847859i) q^{10} +(0.361243 - 1.11179i) q^{11} +(-3.27398 + 1.06378i) q^{13} +(-1.56909 + 4.82916i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-1.86655 - 2.56909i) q^{17} +(0.857960 - 0.623345i) q^{19} +(1.70582 + 1.44575i) q^{20} +(-0.687124 + 0.945746i) q^{22} +(0.484587 + 0.157452i) q^{23} +(4.94424 + 0.744661i) q^{25} +3.44246 q^{26} +(2.98459 - 4.10793i) q^{28} +(-2.22982 - 1.62006i) q^{29} +(2.09310 - 1.52072i) q^{31} -1.00000i q^{32} +(0.981305 + 3.02015i) q^{34} +(0.847859 - 11.3223i) q^{35} +(2.41602 - 0.785011i) q^{37} +(-1.00859 + 0.327712i) q^{38} +(-1.17557 - 1.90211i) q^{40} +(2.58653 + 7.96053i) q^{41} -7.18504i q^{43} +(0.945746 - 0.687124i) q^{44} +(-0.412215 - 0.299492i) q^{46} +(2.52307 - 3.47271i) q^{47} -18.7829 q^{49} +(-4.47214 - 2.23607i) q^{50} +(-3.27398 - 1.06378i) q^{52} +(2.96261 - 4.07768i) q^{53} +(0.991152 - 2.41878i) q^{55} +(-4.10793 + 2.98459i) q^{56} +(1.62006 + 2.22982i) q^{58} +(-1.45309 - 4.47214i) q^{59} +(0.486616 - 1.49765i) q^{61} +(-2.46058 + 0.799492i) q^{62} +(-0.309017 + 0.951057i) q^{64} +(-7.47802 + 1.82536i) q^{65} +(3.29032 + 4.52874i) q^{67} -3.17557i q^{68} +(-4.30516 + 10.5062i) q^{70} +(10.1228 + 7.35462i) q^{71} +(10.1785 + 3.30719i) q^{73} -2.54035 q^{74} +1.06050 q^{76} +(-5.64532 - 1.83428i) q^{77} +(10.2935 + 7.47870i) q^{79} +(0.530249 + 2.17229i) q^{80} -8.37019i q^{82} +(1.88815 + 2.59882i) q^{83} +(-3.73311 - 6.04029i) q^{85} +(-2.22030 + 6.83338i) q^{86} +(-1.11179 + 0.361243i) q^{88} +(-3.61803 + 11.1352i) q^{89} +(5.40154 + 16.6242i) q^{91} +(0.299492 + 0.412215i) q^{92} +(-3.47271 + 2.52307i) q^{94} +(2.01719 - 1.24669i) q^{95} +(-5.30017 + 7.29506i) q^{97} +(17.8636 + 5.80423i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} + 10 q^{5}+O(q^{10}) \) 8 * q + 2 * q^4 + 10 * q^5	\( 8 q + 2 q^{4} + 10 q^{5} + 4 q^{11} + 4 q^{14} - 2 q^{16} - 10 q^{17} + 10 q^{19} + 20 q^{22} - 10 q^{23} + 10 q^{25} + 28 q^{26} + 10 q^{28} - 10 q^{29} + 6 q^{31} - 4 q^{34} - 10 q^{35} - 10 q^{37} + 14 q^{41} + 6 q^{44} - 8 q^{46} + 30 q^{47} - 16 q^{49} - 10 q^{55} - 4 q^{56} - 14 q^{61} + 2 q^{64} - 50 q^{65} + 10 q^{67} + 34 q^{71} - 36 q^{74} - 40 q^{77} - 50 q^{83} - 20 q^{85} - 22 q^{86} - 10 q^{88} - 20 q^{89} - 4 q^{91} + 10 q^{92} - 24 q^{94} - 20 q^{97} + 40 q^{98}+O(q^{100}) \) 8 * q + 2 * q^4 + 10 * q^5 + 4 * q^11 + 4 * q^14 - 2 * q^16 - 10 * q^17 + 10 * q^19 + 20 * q^22 - 10 * q^23 + 10 * q^25 + 28 * q^26 + 10 * q^28 - 10 * q^29 + 6 * q^31 - 4 * q^34 - 10 * q^35 - 10 * q^37 + 14 * q^41 + 6 * q^44 - 8 * q^46 + 30 * q^47 - 16 * q^49 - 10 * q^55 - 4 * q^56 - 14 * q^61 + 2 * q^64 - 50 * q^65 + 10 * q^67 + 34 * q^71 - 36 * q^74 - 40 * q^77 - 50 * q^83 - 20 * q^85 - 22 * q^86 - 10 * q^88 - 20 * q^89 - 4 * q^91 + 10 * q^92 - 24 * q^94 - 20 * q^97 + 40 * q^98

Introduction

L-functions

Modular forms

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