LMFDB - Embedded newform 1638.2.cm.a.341.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(269,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 4]))

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

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

chi := DirichletCharacter("1638.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.cm (of order $6$, degree $2$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.1
Character	$\chi$	$=$	1638.341
Dual form			1638.2.cm.a.269.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(-1.84803 + 3.20089i) q^{5} +(2.64526 + 0.0512262i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.84803 + 3.20089i) q^{5} +(2.64526 + 0.0512262i) q^{7} -1.00000i q^{8} +(-3.20089 - 1.84803i) q^{10} +(3.50241 + 2.02212i) q^{11} +(3.08929 - 1.85912i) q^{13} +(-0.0512262 + 2.64526i) q^{14} +1.00000 q^{16} +6.36324 q^{17} +(-3.07700 + 1.77650i) q^{19} +(1.84803 - 3.20089i) q^{20} +(-2.02212 + 3.50241i) q^{22} +4.48039i q^{23} +(-4.33045 - 7.50056i) q^{25} +(1.85912 + 3.08929i) q^{26} +(-2.64526 - 0.0512262i) q^{28} +(5.32687 - 3.07547i) q^{29} +(6.99170 - 4.03666i) q^{31} +1.00000i q^{32} +6.36324i q^{34} +(-5.05249 + 8.37250i) q^{35} +4.25094 q^{37} +(-1.77650 - 3.07700i) q^{38} +(3.20089 + 1.84803i) q^{40} +(-0.744907 - 1.29022i) q^{41} +(-1.09865 + 1.90293i) q^{43} +(-3.50241 - 2.02212i) q^{44} -4.48039 q^{46} +(-1.69012 + 2.92738i) q^{47} +(6.99475 + 0.271013i) q^{49} +(7.50056 - 4.33045i) q^{50} +(-3.08929 + 1.85912i) q^{52} +(-6.29149 + 3.63239i) q^{53} +(-12.9451 + 7.47387i) q^{55} +(0.0512262 - 2.64526i) q^{56} +(3.07547 + 5.32687i) q^{58} +3.93668 q^{59} +(-13.3021 + 7.67998i) q^{61} +(4.03666 + 6.99170i) q^{62} -1.00000 q^{64} +(0.241722 + 13.3242i) q^{65} +(7.73256 - 13.3932i) q^{67} -6.36324 q^{68} +(-8.37250 - 5.05249i) q^{70} +(-8.16754 - 4.71553i) q^{71} +(-8.73924 + 5.04560i) q^{73} +4.25094i q^{74} +(3.07700 - 1.77650i) q^{76} +(9.16117 + 5.52843i) q^{77} +(0.583429 - 1.01053i) q^{79} +(-1.84803 + 3.20089i) q^{80} +(1.29022 - 0.744907i) q^{82} -6.64988 q^{83} +(-11.7595 + 20.3680i) q^{85} +(-1.90293 - 1.09865i) q^{86} +(2.02212 - 3.50241i) q^{88} -5.37260 q^{89} +(8.26718 - 4.75959i) q^{91} -4.48039i q^{92} +(-2.92738 - 1.69012i) q^{94} -13.1322i q^{95} +(-8.55751 - 4.94068i) q^{97} +(-0.271013 + 6.99475i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 72 q^{4} - 4 q^{7}+O(q^{10}) $ 72 * q - 72 * q^4 - 4 * q^7	$ 72 q - 72 q^{4} - 4 q^{7} + 4 q^{13} + 72 q^{16} - 36 q^{19} - 28 q^{25} + 4 q^{28} - 40 q^{37} + 12 q^{43} - 16 q^{46} + 4 q^{49} - 4 q^{52} + 48 q^{55} + 16 q^{58} - 60 q^{61} - 72 q^{64} + 64 q^{67} + 108 q^{73} + 36 q^{76} + 64 q^{79} + 48 q^{82} - 64 q^{85} + 16 q^{91} - 24 q^{94} - 108 q^{97}+O(q^{100}) $ 72 * q - 72 * q^4 - 4 * q^7 + 4 * q^13 + 72 * q^16 - 36 * q^19 - 28 * q^25 + 4 * q^28 - 40 * q^37 + 12 * q^43 - 16 * q^46 + 4 * q^49 - 4 * q^52 + 48 * q^55 + 16 * q^58 - 60 * q^61 - 72 * q^64 + 64 * q^67 + 108 * q^73 + 36 * q^76 + 64 * q^79 + 48 * q^82 - 64 * q^85 + 16 * q^91 - 24 * q^94 - 108 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−1.84803	+	3.20089i	−0.826466	+	1.43148i	0.0743285	+	0.997234i	$0.476319\pi$
$5$	−1.84803	+	3.20089i	−0.826466	+	1.43148i	−0.900794	+	0.434246i	$0.857015\pi$
$6$		0			0
$7$	2.64526	+	0.0512262i	0.999813	+	0.0193617i
$7$	2.64526	+	0.0512262i	0.999813	+	0.0193617i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−3.20089	−	1.84803i	−1.01221	−	0.584399i
$11$	3.50241	+	2.02212i	1.05602	+	0.609691i	0.924327	−	0.381600i	$-0.124627\pi$
$11$	3.50241	+	2.02212i	1.05602	+	0.609691i	0.131688	+	0.991291i	$0.457960\pi$
$12$		0			0
$13$	3.08929	−	1.85912i	0.856814	−	0.515626i
$13$	3.08929	−	1.85912i	0.856814	−	0.515626i
$14$	−0.0512262	+	2.64526i	−0.0136908	+	0.706974i
$15$		0			0
$16$	1.00000			0.250000
$17$	6.36324			1.54331			0.771656	−	0.636040i	$-0.219429\pi$
$17$	6.36324			1.54331			0.771656	+	0.636040i	$0.219429\pi$
$18$		0			0
$19$	−3.07700	+	1.77650i	−0.705911	+	0.407558i	−0.809545	−	0.587058i	$-0.800286\pi$
$19$	−3.07700	+	1.77650i	−0.705911	+	0.407558i	0.103634	+	0.994615i	$0.466953\pi$
$20$	1.84803	−	3.20089i	0.413233	−	0.715740i
$21$		0			0
$22$	−2.02212	+	3.50241i	−0.431116	+	0.746716i
$23$			4.48039i			0.934225i	0.884198	+	0.467113i	$0.154706\pi$
$23$			4.48039i			0.934225i	−0.884198	+	0.467113i	$0.845294\pi$
$24$		0			0
$25$	−4.33045	−	7.50056i	−0.866091	−	1.50011i
$26$	1.85912	+	3.08929i	0.364603	+	0.605859i
$27$		0			0
$28$	−2.64526	−	0.0512262i	−0.499906	−	0.00968085i
$29$	5.32687	−	3.07547i	0.989175	−	0.571100i	0.0841472	−	0.996453i	$-0.473183\pi$
$29$	5.32687	−	3.07547i	0.989175	−	0.571100i	0.905027	+	0.425353i	$0.139850\pi$
$30$		0			0
$31$	6.99170	−	4.03666i	1.25575	−	0.725006i	0.283502	−	0.958972i	$-0.408504\pi$
$31$	6.99170	−	4.03666i	1.25575	−	0.725006i	0.972245	+	0.233966i	$0.0751705\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$			6.36324i			1.09129i
$35$	−5.05249	+	8.37250i	−0.854027	+	1.41521i
$36$		0			0
$37$	4.25094			0.698850			0.349425	−	0.936964i	$-0.386377\pi$
$37$	4.25094			0.698850			0.349425	+	0.936964i	$0.386377\pi$
$38$	−1.77650	−	3.07700i	−0.288187	−	0.499155i
$39$		0			0
$40$	3.20089	+	1.84803i	0.506105	+	0.292200i
$41$	−0.744907	−	1.29022i	−0.116335	−	0.201498i	0.801978	−	0.597354i	$-0.203781\pi$
$41$	−0.744907	−	1.29022i	−0.116335	−	0.201498i	−0.918313	+	0.395856i	$0.870448\pi$
$42$		0			0
$43$	−1.09865	+	1.90293i	−0.167543	+	0.290193i	−0.937556	−	0.347836i	$-0.886917\pi$
$43$	−1.09865	+	1.90293i	−0.167543	+	0.290193i	0.770012	+	0.638029i	$0.220250\pi$
$44$	−3.50241	−	2.02212i	−0.528008	−	0.304845i
$45$		0			0
$46$	−4.48039			−0.660597
$47$	−1.69012	+	2.92738i	−0.246530	+	0.427002i	−0.962561	−	0.271067i	$-0.912624\pi$
$47$	−1.69012	+	2.92738i	−0.246530	+	0.427002i	0.716031	+	0.698068i	$0.245957\pi$
$48$		0			0
$49$	6.99475	+	0.271013i	0.999250	+	0.0387161i
$50$	7.50056	−	4.33045i	1.06074	−	0.612419i
$51$		0			0
$52$	−3.08929	+	1.85912i	−0.428407	+	0.257813i
$53$	−6.29149	+	3.63239i	−0.864202	+	0.498947i	−0.865417	−	0.501052i	$-0.832947\pi$
$53$	−6.29149	+	3.63239i	−0.864202	+	0.498947i	0.00121501	+	0.999999i	$0.499613\pi$
$54$		0			0
$55$	−12.9451	+	7.47387i	−1.74552	+	1.00778i
$56$	0.0512262	−	2.64526i	0.00684539	−	0.353487i
$57$		0			0
$58$	3.07547	+	5.32687i	0.403829	+	0.699452i
$59$	3.93668			0.512513			0.256256	−	0.966609i	$-0.417511\pi$
$59$	3.93668			0.512513			0.256256	+	0.966609i	$0.417511\pi$
$60$		0			0
$61$	−13.3021	+	7.67998i	−1.70316	+	0.983320i	−0.760640	+	0.649174i	$0.775115\pi$
$61$	−13.3021	+	7.67998i	−1.70316	+	0.983320i	−0.942521	+	0.334146i	$0.891552\pi$
$62$	4.03666	+	6.99170i	0.512656	+	0.887947i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.241722	+	13.3242i	0.0299820	+	1.65266i
$66$		0			0
$67$	7.73256	−	13.3932i	0.944683	−	1.63624i	0.188299	−	0.982112i	$-0.439703\pi$
$67$	7.73256	−	13.3932i	0.944683	−	1.63624i	0.756384	−	0.654127i	$-0.226964\pi$
$68$	−6.36324			−0.771656
$69$		0			0
$70$	−8.37250	−	5.05249i	−1.00070	−	0.603888i
$71$	−8.16754	−	4.71553i	−0.969309	−	0.559631i	−0.0702833	−	0.997527i	$-0.522390\pi$
$71$	−8.16754	−	4.71553i	−0.969309	−	0.559631i	−0.899025	+	0.437896i	$0.855724\pi$
$72$		0			0
$73$	−8.73924	+	5.04560i	−1.02285	+	0.590543i	−0.914928	−	0.403616i	$-0.867753\pi$
$73$	−8.73924	+	5.04560i	−1.02285	+	0.590543i	−0.107922	+	0.994159i	$0.534420\pi$
$74$			4.25094i			0.494161i
$75$		0			0
$76$	3.07700	−	1.77650i	0.352956	−	0.203779i
$77$	9.16117	+	5.52843i	1.04401	+	0.630023i
$78$		0			0
$79$	0.583429	−	1.01053i	0.0656409	−	0.113693i	−0.831337	−	0.555768i	$-0.812424\pi$
$79$	0.583429	−	1.01053i	0.0656409	−	0.113693i	0.896978	+	0.442075i	$0.145757\pi$
$80$	−1.84803	+	3.20089i	−0.206616	+	0.357870i
$81$		0			0
$82$	1.29022	−	0.744907i	0.142481	−	0.0822612i
$83$	−6.64988			−0.729920			−0.364960	−	0.931023i	$-0.618917\pi$
$83$	−6.64988			−0.729920			−0.364960	+	0.931023i	$0.618917\pi$
$84$		0			0
$85$	−11.7595	+	20.3680i	−1.27549	+	2.20922i
$86$	−1.90293	−	1.09865i	−0.205198	−	0.118471i
$87$		0			0
$88$	2.02212	−	3.50241i	0.215558	−	0.373358i
$89$	−5.37260			−0.569494			−0.284747	−	0.958603i	$-0.591910\pi$
$89$	−5.37260			−0.569494			−0.284747	+	0.958603i	$0.591910\pi$
$90$		0			0
$91$	8.26718	−	4.75959i	0.866636	−	0.498940i
$92$		−	4.48039i		−	0.467113i
$93$		0			0
$94$	−2.92738	−	1.69012i	−0.301936	−	0.174323i
$95$		−	13.1322i		−	1.34733i
$96$		0			0
$97$	−8.55751	−	4.94068i	−0.868883	−	0.501650i	−0.00190628	−	0.999998i	$-0.500607\pi$
$97$	−8.55751	−	4.94068i	−0.868883	−	0.501650i	−0.866977	+	0.498348i	$0.833940\pi$
$98$	−0.271013	+	6.99475i	−0.0273764	+	0.706577i
$99$		0			0
$100$	4.33045	+	7.50056i	0.433045	+	0.750056i
$101$	−1.55296	+	2.68980i	−0.154525	+	0.267645i	−0.932886	−	0.360172i	$-0.882718\pi$
$101$	−1.55296	+	2.68980i	−0.154525	+	0.267645i	0.778361	+	0.627817i	$0.216051\pi$
$102$		0			0
$103$	−6.75515	−	3.90009i	−0.665605	−	0.384287i	0.128804	−	0.991670i	$-0.458886\pi$
$103$	−6.75515	−	3.90009i	−0.665605	−	0.384287i	−0.794409	+	0.607383i	$0.792219\pi$
$104$	−1.85912	−	3.08929i	−0.182301	−	0.302929i
$105$		0			0
$106$	−3.63239	−	6.29149i	−0.352809	−	0.611083i
$107$			0.0972344i			0.00940000i	0.999989	+	0.00470000i	$0.00149606\pi$
$107$			0.0972344i			0.00940000i	−0.999989	+	0.00470000i	$0.998504\pi$
$108$		0			0
$109$	5.57485	+	9.65593i	0.533974	+	0.924870i	0.999212	+	0.0396847i	$0.0126354\pi$
$109$	5.57485	+	9.65593i	0.533974	+	0.924870i	−0.465238	+	0.885186i	$0.654031\pi$
$110$	−7.47387	−	12.9451i	−0.712606	−	1.23427i
$111$		0			0
$112$	2.64526	+	0.0512262i	0.249953	+	0.00484043i
$113$	13.4242	+	7.75047i	1.26284	+	0.729103i	0.973624	−	0.228159i	$-0.0732707\pi$
$113$	13.4242	+	7.75047i	1.26284	+	0.729103i	0.289220	+	0.957263i	$0.406604\pi$
$114$		0			0
$115$	−14.3412	−	8.27990i	−1.33732	−	0.772105i
$116$	−5.32687	+	3.07547i	−0.494587	+	0.285550i
$117$		0			0
$118$			3.93668i			0.362401i
$119$	16.8324	+	0.325965i	1.54302	+	0.0298811i
$120$		0			0
$121$	2.67790	+	4.63826i	0.243446	+	0.421660i
$122$	−7.67998	−	13.3021i	−0.695313	−	1.20432i
$123$		0			0
$124$	−6.99170	+	4.03666i	−0.627873	+	0.362503i
$125$	13.5310			1.21025
$126$		0			0
$127$	−0.0206135	−	0.0357036i	−0.00182915	−	0.00316818i	0.865109	−	0.501583i	$-0.167249\pi$
$127$	−0.0206135	−	0.0357036i	−0.00182915	−	0.00316818i	−0.866939	+	0.498415i	$0.833916\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−13.3242	+	0.241722i	−1.16861	+	0.0212005i
$131$	−10.3017	+	17.8430i	−0.900063	+	1.55895i	−0.0726514	+	0.997357i	$0.523146\pi$
$131$	−10.3017	+	17.8430i	−0.900063	+	1.55895i	−0.827411	+	0.561597i	$0.810187\pi$
$132$		0			0
$133$	−8.23044	+	4.54168i	−0.713670	+	0.393814i
$134$	13.3932	+	7.73256i	1.15700	+	0.667992i
$135$		0			0
$136$		−	6.36324i		−	0.545643i
$137$		−	11.7210i		−	1.00139i	−0.865624	−	0.500695i	$-0.833078\pi$
$137$		−	11.7210i		−	1.00139i	0.865624	−	0.500695i	$-0.166922\pi$
$138$		0			0
$139$	18.5921	+	10.7341i	1.57696	+	0.910457i	0.995281	+	0.0970374i	$0.0309367\pi$
$139$	18.5921	+	10.7341i	1.57696	+	0.910457i	0.581677	+	0.813420i	$0.302397\pi$
$140$	5.05249	−	8.37250i	0.427013	−	0.707605i
$141$		0			0
$142$	4.71553	−	8.16754i	0.395719	−	0.685405i
$143$	14.5793	−	0.264492i	1.21918	−	0.0221180i
$144$		0			0
$145$			22.7343i			1.88798i
$146$	−5.04560	−	8.73924i	−0.417577	−	0.723265i
$147$		0			0
$148$	−4.25094			−0.349425
$149$	5.31891	−	3.07087i	0.435742	−	0.251576i	−0.266048	−	0.963960i	$-0.585718\pi$
$149$	5.31891	−	3.07087i	0.435742	−	0.251576i	0.701790	+	0.712384i	$0.252385\pi$
$150$		0			0
$151$	3.86299	+	6.69089i	0.314366	+	0.544497i	0.979302	−	0.202402i	$-0.0648749\pi$
$151$	3.86299	+	6.69089i	0.314366	+	0.544497i	−0.664937	+	0.746900i	$0.731542\pi$
$152$	1.77650	+	3.07700i	0.144093	+	0.249577i
$153$		0			0
$154$	−5.52843	+	9.16117i	−0.445493	+	0.738228i
$155$			29.8395i			2.39677i
$156$		0			0
$157$	−11.4780	+	6.62684i	−0.916046	+	0.528880i	−0.882372	−	0.470553i	$-0.844054\pi$
$157$	−11.4780	+	6.62684i	−0.916046	+	0.528880i	−0.0336747	+	0.999433i	$0.510721\pi$
$158$	1.01053	+	0.583429i	0.0803934	+	0.0464151i
$159$		0			0
$160$	−3.20089	−	1.84803i	−0.253052	−	0.146100i
$161$	−0.229513	+	11.8518i	−0.0180882	+	0.934050i
$162$		0			0
$163$	−9.67041	−	16.7496i	−0.757445	−	1.31193i	−0.944150	−	0.329517i	$-0.893114\pi$
$163$	−9.67041	−	16.7496i	−0.757445	−	1.31193i	0.186705	−	0.982416i	$-0.440219\pi$
$164$	0.744907	+	1.29022i	0.0581675	+	0.100749i
$165$		0			0
$166$		−	6.64988i		−	0.516131i
$167$	−4.08666	−	7.07831i	−0.316236	−	0.547736i	0.663464	−	0.748208i	$-0.269086\pi$
$167$	−4.08666	−	7.07831i	−0.316236	−	0.547736i	−0.979699	+	0.200472i	$0.935752\pi$
$168$		0			0
$169$	6.08737	−	11.4867i	0.468259	−	0.883591i
$170$	−20.3680	−	11.7595i	−1.56216	−	0.901911i
$171$		0			0
$172$	1.09865	−	1.90293i	0.0837716	−	0.145097i
$173$	−1.87775	−	3.25236i	−0.142763	−	0.247272i	0.785773	−	0.618515i	$-0.212265\pi$
$173$	−1.87775	−	3.25236i	−0.142763	−	0.247272i	−0.928536	+	0.371242i	$0.878932\pi$
$174$		0			0
$175$	−11.0709	−	20.0627i	−0.836883	−	1.51660i
$176$	3.50241	+	2.02212i	0.264004	+	0.152423i
$177$		0			0
$178$		−	5.37260i		−	0.402693i
$179$	6.31551	+	3.64626i	0.472043	+	0.272534i	0.717095	−	0.696976i	$-0.245471\pi$
$179$	6.31551	+	3.64626i	0.472043	+	0.272534i	−0.245051	+	0.969510i	$0.578805\pi$
$180$		0			0
$181$		−	15.5459i		−	1.15552i	−0.816208	−	0.577758i	$-0.803928\pi$
$181$		−	15.5459i		−	1.15552i	0.816208	−	0.577758i	$-0.196072\pi$
$182$	4.75959	+	8.26718i	0.352804	+	0.612804i
$183$		0			0
$184$	4.48039			0.330298
$185$	−7.85587	+	13.6068i	−0.577575	+	1.00039i
$186$		0			0
$187$	22.2867	+	12.8672i	1.62976	+	0.940943i
$188$	1.69012	−	2.92738i	0.123265	−	0.213501i
$189$		0			0
$190$	13.1322			0.952706
$191$	−8.84918	+	5.10907i	−0.640304	+	0.369680i	−0.784732	−	0.619836i	$-0.787199\pi$
$191$	−8.84918	+	5.10907i	−0.640304	+	0.369680i	0.144428	+	0.989515i	$0.453866\pi$
$192$		0			0
$193$	4.35362	−	7.54070i	0.313381	−	0.542791i	−0.665711	−	0.746209i	$-0.731872\pi$
$193$	4.35362	−	7.54070i	0.313381	−	0.542791i	0.979092	+	0.203418i	$0.0652051\pi$
$194$	4.94068	−	8.55751i	0.354720	−	0.614393i
$195$		0			0
$196$	−6.99475	−	0.271013i	−0.499625	−	0.0193581i
$197$	11.4983	−	6.63856i	0.819222	−	0.472978i	−0.0309260	−	0.999522i	$-0.509846\pi$
$197$	11.4983	−	6.63856i	0.819222	−	0.472978i	0.850148	+	0.526544i	$0.176512\pi$
$198$		0			0
$199$		−	0.909155i		−	0.0644483i	−0.999481	−	0.0322241i	$-0.989741\pi$
$199$		−	0.909155i		−	0.0644483i	0.999481	−	0.0322241i	$-0.0102590\pi$
$200$	−7.50056	+	4.33045i	−0.530370	+	0.306209i
$201$		0			0
$202$	−2.68980	−	1.55296i	−0.189254	−	0.109266i
$203$	14.2485	−	7.86253i	1.00005	−	0.551841i
$204$		0			0
$205$	5.50645			0.384587
$206$	3.90009	−	6.75515i	0.271732	−	0.470654i
$207$		0			0
$208$	3.08929	−	1.85912i	0.214203	−	0.128907i
$209$	−14.3692			−0.993937
$210$		0			0
$211$	6.29538	+	10.9039i	0.433392	+	0.750656i	0.997163	−	0.0752746i	$-0.0239833\pi$
$211$	6.29538	+	10.9039i	0.433392	+	0.750656i	−0.563771	+	0.825931i	$0.690650\pi$
$212$	6.29149	−	3.63239i	0.432101	−	0.249474i
$213$		0			0
$214$	−0.0972344			−0.00664681
$215$	−4.06070	−	7.03334i	−0.276937	−	0.479670i
$216$		0			0
$217$	18.7016	−	10.3198i	1.26955	−	0.700556i
$218$	−9.65593	+	5.57485i	−0.653982	+	0.377577i
$219$		0			0
$220$	12.9451	−	7.47387i	0.872760	−	0.503888i
$221$	19.6579	−	11.8300i	1.32233	−	0.795772i
$222$		0			0
$223$	24.9890	−	14.4274i	1.67339	−	0.966130i	0.707666	−	0.706547i	$-0.249748\pi$
$223$	24.9890	−	14.4274i	1.67339	−	0.966130i	0.965721	−	0.259583i	$-0.0835850\pi$
$224$	−0.0512262	+	2.64526i	−0.00342270	+	0.176744i
$225$		0			0
$226$	−7.75047	+	13.4242i	−0.515554	+	0.892965i
$227$	1.36548			0.0906304			0.0453152	−	0.998973i	$-0.485571\pi$
$227$	1.36548			0.0906304			0.0453152	+	0.998973i	$0.485571\pi$
$228$		0			0
$229$	9.27104	+	5.35264i	0.612648	+	0.353712i	0.774001	−	0.633184i	$-0.218253\pi$
$229$	9.27104	+	5.35264i	0.612648	+	0.353712i	−0.161353	+	0.986897i	$0.551586\pi$
$230$	8.27990	−	14.3412i	0.545961	−	0.945632i
$231$		0			0
$232$	−3.07547	−	5.32687i	−0.201914	−	0.349726i
$233$	−17.2730	−	9.97258i	−1.13159	−	0.653325i	−0.187258	−	0.982311i	$-0.559960\pi$
$233$	−17.2730	−	9.97258i	−1.13159	−	0.653325i	−0.944335	+	0.328986i	$0.893293\pi$
$234$		0			0
$235$	−6.24680	−	10.8198i	−0.407496	−	0.705804i
$236$	−3.93668			−0.256256
$237$		0			0
$238$	−0.325965	+	16.8324i	−0.0211292	+	1.09108i
$239$		−	24.5831i		−	1.59015i	−0.606511	−	0.795075i	$-0.707431\pi$
$239$		−	24.5831i		−	1.59015i	0.606511	−	0.795075i	$-0.292569\pi$
$240$		0			0
$241$		−	15.8405i		−	1.02038i	−0.860063	−	0.510188i	$-0.829576\pi$
$241$		−	15.8405i		−	1.02038i	0.860063	−	0.510188i	$-0.170424\pi$
$242$	−4.63826	+	2.67790i	−0.298159	+	0.172142i
$243$		0			0
$244$	13.3021	−	7.67998i	0.851580	−	0.491660i
$245$	−13.7940	+	21.8886i	−0.881267	+	1.39841i
$246$		0			0
$247$	−6.20299	+	11.2086i	−0.394687	+	0.713187i
$248$	−4.03666	−	6.99170i	−0.256328	−	0.443973i
$249$		0			0
$250$			13.5310i			0.855772i
$251$	3.88881	−	6.73561i	0.245459	−	0.425148i	−0.716801	−	0.697277i	$-0.754395\pi$
$251$	3.88881	−	6.73561i	0.245459	−	0.425148i	0.962261	+	0.272129i	$0.0877279\pi$
$252$		0			0
$253$	−9.05986	+	15.6921i	−0.569588	+	0.986556i
$254$	0.0357036	−	0.0206135i	0.00224024	−	0.00129340i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−5.36870			−0.334890			−0.167445	−	0.985881i	$-0.553552\pi$
$257$	−5.36870			−0.334890			−0.167445	+	0.985881i	$0.553552\pi$
$258$		0			0
$259$	11.2448	+	0.217760i	0.698719	+	0.0135309i
$260$	−0.241722	−	13.3242i	−0.0149910	−	0.826330i
$261$		0			0
$262$	−17.8430	−	10.3017i	−1.10235	−	0.636440i
$263$	−19.1007	−	11.0278i	−1.17780	−	0.680004i	−0.222296	−	0.974979i	$-0.571355\pi$
$263$	−19.1007	−	11.0278i	−1.17780	−	0.680004i	−0.955505	+	0.294975i	$0.904689\pi$
$264$		0			0
$265$		−	26.8511i		−	1.64945i
$266$	−4.54168	−	8.23044i	−0.278468	−	0.504641i
$267$		0			0
$268$	−7.73256	+	13.3932i	−0.472342	+	0.818120i
$269$	−20.5379			−1.25222			−0.626108	−	0.779736i	$-0.715353\pi$
$269$	−20.5379			−1.25222			−0.626108	+	0.779736i	$0.715353\pi$
$270$		0			0
$271$			16.7429i			1.01706i	0.861044	+	0.508530i	$0.169811\pi$
$271$			16.7429i			1.01706i	−0.861044	+	0.508530i	$0.830189\pi$
$272$	6.36324			0.385828
$273$		0			0
$274$	11.7210			0.708089
$275$		−	35.0267i		−	2.11219i
$276$		0			0
$277$	14.4982			0.871112			0.435556	−	0.900162i	$-0.356552\pi$
$277$	14.4982			0.871112			0.435556	+	0.900162i	$0.356552\pi$
$278$	−10.7341	+	18.5921i	−0.643790	+	1.11508i
$279$		0			0
$280$	8.37250	+	5.05249i	0.500352	+	0.301944i
$281$		−	7.69457i		−	0.459019i	−0.973306	−	0.229510i	$-0.926288\pi$
$281$		−	7.69457i		−	0.459019i	0.973306	−	0.229510i	$-0.0737123\pi$
$282$		0			0
$283$	−2.81255	−	1.62383i	−0.167189	−	0.0965264i	0.414071	−	0.910245i	$-0.364107\pi$
$283$	−2.81255	−	1.62383i	−0.167189	−	0.0965264i	−0.581260	+	0.813718i	$0.697440\pi$
$284$	8.16754	+	4.71553i	0.484654	+	0.279815i
$285$		0			0
$286$	0.264492	+	14.5793i	0.0156398	+	0.862091i
$287$	−1.90438	−	3.45111i	−0.112412	−	0.203713i
$288$		0			0
$289$	23.4908			1.38181
$290$	−22.7343			−1.33500
$291$		0			0
$292$	8.73924	−	5.04560i	0.511425	−	0.295272i
$293$	−6.82413	+	11.8197i	−0.398670	+	0.690516i	−0.993562	−	0.113289i	$-0.963861\pi$
$293$	−6.82413	+	11.8197i	−0.398670	+	0.690516i	0.594892	+	0.803805i	$0.297195\pi$
$294$		0			0
$295$	−7.27512	+	12.6009i	−0.423574	+	0.733652i
$296$		−	4.25094i		−	0.247081i
$297$		0			0
$298$	3.07087	+	5.31891i	0.177891	+	0.308116i
$299$	8.32956	+	13.8412i	0.481711	+	0.800457i
$300$		0			0
$301$	−3.00370	+	4.97744i	−0.173131	+	0.286895i
$302$	−6.69089	+	3.86299i	−0.385018	+	0.222290i
$303$		0			0
$304$	−3.07700	+	1.77650i	−0.176478	+	0.101889i
$305$		−	56.7714i		−	3.25072i
$306$		0			0
$307$		−	11.6540i		−	0.665131i	−0.943080	−	0.332565i	$-0.892086\pi$
$307$		−	11.6540i		−	0.665131i	0.943080	−	0.332565i	$-0.107914\pi$
$308$	−9.16117	−	5.52843i	−0.522006	−	0.315011i
$309$		0			0
$310$	−29.8395			−1.69477
$311$	1.82467	+	3.16043i	0.103468	+	0.179211i	0.913111	−	0.407711i	$-0.133673\pi$
$311$	1.82467	+	3.16043i	0.103468	+	0.179211i	−0.809643	+	0.586922i	$0.800339\pi$
$312$		0			0
$313$	−16.9578	−	9.79057i	−0.958510	−	0.553396i	−0.0627955	−	0.998026i	$-0.520002\pi$
$313$	−16.9578	−	9.79057i	−0.958510	−	0.553396i	−0.895714	+	0.444631i	$0.853335\pi$
$314$	−6.62684	−	11.4780i	−0.373974	−	0.647743i
$315$		0			0
$316$	−0.583429	+	1.01053i	−0.0328205	+	0.0568467i
$317$	−7.92662	−	4.57644i	−0.445203	−	0.257038i	0.260599	−	0.965447i	$-0.416080\pi$
$317$	−7.92662	−	4.57644i	−0.445203	−	0.257038i	−0.705802	+	0.708409i	$0.749413\pi$
$318$		0			0
$319$	24.8758			1.39278
$320$	1.84803	−	3.20089i	0.103308	−	0.178935i
$321$		0			0
$322$	−11.8518	−	0.229513i	−0.660473	−	0.0127903i
$323$	−19.5797	+	11.3043i	−1.08944	+	0.628989i
$324$		0			0
$325$	−27.3224	−	15.1206i	−1.51558	−	0.838738i
$326$	16.7496	−	9.67041i	0.927677	−	0.535594i
$327$		0			0
$328$	−1.29022	+	0.744907i	−0.0712403	+	0.0411306i
$329$	−4.62076	+	7.65708i	−0.254751	+	0.422148i
$330$		0			0
$331$	−4.61064	−	7.98587i	−0.253424	−	0.438943i	0.711042	−	0.703149i	$-0.248223\pi$
$331$	−4.61064	−	7.98587i	−0.253424	−	0.438943i	−0.964466	+	0.264206i	$0.914890\pi$
$332$	6.64988			0.364960
$333$		0			0
$334$	7.07831	−	4.08666i	0.387308	−	0.223612i
$335$	28.5801	+	49.5021i	1.56150	+	2.70459i
$336$		0			0
$337$	−3.21877			−0.175337			−0.0876687	−	0.996150i	$-0.527942\pi$
$337$	−3.21877			−0.175337			−0.0876687	+	0.996150i	$0.527942\pi$
$338$	11.4867	+	6.08737i	0.624793	+	0.331109i
$339$		0			0
$340$	11.7595	−	20.3680i	0.637747	−	1.10461i
$341$	32.6504			1.76812
$342$		0			0
$343$	18.4890	+	1.07521i	0.998313	+	0.0580561i
$344$	1.90293	+	1.09865i	0.102599	+	0.0592355i
$345$		0			0
$346$	3.25236	−	1.87775i	0.174848	−	0.100948i
$347$			24.9848i			1.34125i	0.741795	+	0.670627i	$0.233975\pi$
$347$			24.9848i			1.34125i	−0.741795	+	0.670627i	$0.766025\pi$
$348$		0			0
$349$	−26.7370	+	15.4366i	−1.43120	+	0.826302i	−0.997212	−	0.0746175i	$-0.976226\pi$
$349$	−26.7370	+	15.4366i	−1.43120	+	0.826302i	−0.433985	+	0.900920i	$0.642893\pi$
$350$	20.0627	−	11.0709i	1.07240	−	0.591766i
$351$		0			0
$352$	−2.02212	+	3.50241i	−0.107779	+	0.186679i
$353$	−14.7041	+	25.4683i	−0.782621	+	1.35554i	0.147789	+	0.989019i	$0.452784\pi$
$353$	−14.7041	+	25.4683i	−0.782621	+	1.35554i	−0.930410	+	0.366521i	$0.880549\pi$
$354$		0			0
$355$	30.1878	−	17.4289i	1.60220	−	0.925031i
$356$	5.37260			0.284747
$357$		0			0
$358$	−3.64626	+	6.31551i	−0.192711	+	0.333785i
$359$	0.329648	+	0.190322i	0.0173982	+	0.0100448i	0.508674	−	0.860959i	$-0.330136\pi$
$359$	0.329648	+	0.190322i	0.0173982	+	0.0100448i	−0.491276	+	0.871004i	$0.663469\pi$
$360$		0			0
$361$	−3.18807	+	5.52190i	−0.167793	+	0.290626i
$362$	15.5459			0.817073
$363$		0			0
$364$	−8.26718	+	4.75959i	−0.433318	+	0.249470i
$365$		−	37.2978i		−	1.95225i
$366$		0			0
$367$	25.8423	+	14.9200i	1.34895	+	0.778820i	0.988102	−	0.153803i	$-0.0491521\pi$
$367$	25.8423	+	14.9200i	1.34895	+	0.778820i	0.360853	+	0.932623i	$0.382485\pi$
$368$			4.48039i			0.233556i
$369$		0			0
$370$	−13.6068	−	7.85587i	−0.707382	−	0.408407i
$371$	−16.8287	+	9.28631i	−0.873701	+	0.482121i
$372$		0			0
$373$	3.05968	+	5.29953i	0.158424	+	0.274399i	0.934301	−	0.356486i	$-0.116025\pi$
$373$	3.05968	+	5.29953i	0.158424	+	0.274399i	−0.775876	+	0.630885i	$0.782692\pi$
$374$	−12.8672	+	22.2867i	−0.665347	+	1.15242i
$375$		0			0
$376$	2.92738	+	1.69012i	0.150968	+	0.0871613i
$377$	10.7386	−	19.4043i	0.553064	−	0.999371i
$378$		0			0
$379$	−4.12904	−	7.15170i	−0.212094	−	0.367358i	0.740275	−	0.672304i	$-0.234695\pi$
$379$	−4.12904	−	7.15170i	−0.212094	−	0.367358i	−0.952370	+	0.304946i	$0.901362\pi$
$380$			13.1322i			0.673665i
$381$		0			0
$382$	−5.10907	−	8.84918i	−0.261403	−	0.452763i
$383$	5.73341	+	9.93055i	0.292963	+	0.507427i	0.974509	−	0.224348i	$-0.0720253\pi$
$383$	5.73341	+	9.93055i	0.292963	+	0.507427i	−0.681546	+	0.731776i	$0.738692\pi$
$384$		0			0
$385$	−34.6260	+	19.1072i	−1.76471	+	0.973792i
$386$	7.54070	+	4.35362i	0.383811	+	0.221594i
$387$		0			0
$388$	8.55751	+	4.94068i	0.434442	+	0.250825i
$389$	−13.4375	+	7.75815i	−0.681309	+	0.393354i	−0.800348	−	0.599536i	$-0.795352\pi$
$389$	−13.4375	+	7.75815i	−0.681309	+	0.393354i	0.119039	+	0.992890i	$0.462019\pi$
$390$		0			0
$391$			28.5098i			1.44180i
$392$	0.271013	−	6.99475i	0.0136882	−	0.353288i
$393$		0			0
$394$	6.63856	+	11.4983i	0.334446	+	0.579277i
$395$	2.15639	+	3.73498i	0.108500	+	0.187927i
$396$		0			0
$397$	14.3607	−	8.29117i	0.720744	−	0.416122i	−0.0942823	−	0.995546i	$-0.530056\pi$
$397$	14.3607	−	8.29117i	0.720744	−	0.416122i	0.815027	+	0.579424i	$0.196722\pi$
$398$	0.909155			0.0455718
$399$		0			0
$400$	−4.33045	−	7.50056i	−0.216523	−	0.375028i
$401$		−	35.3789i		−	1.76674i	−0.468677	−	0.883370i	$-0.655269\pi$
$401$		−	35.3789i		−	1.76674i	0.468677	−	0.883370i	$-0.344731\pi$
$402$		0			0
$403$	14.0947	−	25.4688i	0.702109	−	1.26869i
$404$	1.55296	−	2.68980i	0.0772625	−	0.133823i
$405$		0			0
$406$	7.86253	+	14.2485i	0.390211	+	0.707140i
$407$	14.8885	+	8.59589i	0.737996	+	0.426082i
$408$		0			0
$409$		−	10.0312i		−	0.496009i	−0.968759	−	0.248005i	$-0.920225\pi$
$409$		−	10.0312i		−	0.496009i	0.968759	−	0.248005i	$-0.0797748\pi$
$410$			5.50645i			0.271944i
$411$		0			0
$412$	6.75515	+	3.90009i	0.332802	+	0.192144i
$413$	10.4135	+	0.201661i	0.512416	+	0.00992311i
$414$		0			0
$415$	12.2892	−	21.2855i	0.603253	−	1.04487i
$416$	1.85912	+	3.08929i	0.0911507	+	0.151465i
$417$		0			0
$418$		−	14.3692i		−	0.702820i
$419$	−7.54013	−	13.0599i	−0.368360	−	0.638018i	0.620950	−	0.783851i	$-0.286747\pi$
$419$	−7.54013	−	13.0599i	−0.368360	−	0.638018i	−0.989309	+	0.145833i	$0.953414\pi$
$420$		0			0
$421$	11.3259			0.551993			0.275996	−	0.961159i	$-0.410992\pi$
$421$	11.3259			0.551993			0.275996	+	0.961159i	$0.410992\pi$
$422$	−10.9039	+	6.29538i	−0.530794	+	0.306454i
$423$		0			0
$424$	3.63239	+	6.29149i	0.176405	+	0.305542i
$425$	−27.5557	−	47.7279i	−1.33665	−	2.31514i
$426$		0			0
$427$	−35.5809	+	19.6341i	−1.72188	+	0.950160i
$428$		−	0.0972344i		−	0.00470000i
$429$		0			0
$430$	7.03334	−	4.06070i	0.339178	−	0.195824i
$431$	−10.2597	−	5.92342i	−0.494190	−	0.285321i	0.232121	−	0.972687i	$-0.425434\pi$
$431$	−10.2597	−	5.92342i	−0.494190	−	0.285321i	−0.726311	+	0.687366i	$0.758767\pi$
$432$		0			0
$433$	16.6820	+	9.63135i	0.801685	+	0.462853i	0.844060	−	0.536249i	$-0.180159\pi$
$433$	16.6820	+	9.63135i	0.801685	+	0.462853i	−0.0423751	+	0.999102i	$0.513492\pi$
$434$	10.3198	+	18.7016i	0.495368	+	0.897706i
$435$		0			0
$436$	−5.57485	−	9.65593i	−0.266987	−	0.462435i
$437$	−7.95942	−	13.7861i	−0.380751	−	0.659480i
$438$		0			0
$439$		−	16.1358i		−	0.770121i	−0.922891	−	0.385060i	$-0.874181\pi$
$439$		−	16.1358i		−	0.770121i	0.922891	−	0.385060i	$-0.125819\pi$
$440$	7.47387	+	12.9451i	0.356303	+	0.617135i
$441$		0			0
$442$	11.8300	+	19.6579i	0.562696	+	0.935029i
$443$	26.1064	+	15.0726i	1.24035	+	0.716119i	0.969166	−	0.246408i	$-0.0792503\pi$
$443$	26.1064	+	15.0726i	1.24035	+	0.716119i	0.271188	+	0.962527i	$0.412584\pi$
$444$		0			0
$445$	9.92874	−	17.1971i	0.470667	−	0.815219i
$446$	14.4274	+	24.9890i	0.683157	+	1.18326i
$447$		0			0
$448$	−2.64526	−	0.0512262i	−0.124977	−	0.00242021i
$449$	−34.6859	−	20.0259i	−1.63693	−	0.945081i	−0.981882	−	0.189493i	$-0.939316\pi$
$449$	−34.6859	−	20.0259i	−1.63693	−	0.945081i	−0.655047	−	0.755588i	$-0.727351\pi$
$450$		0			0
$451$		−	6.02515i		−	0.283713i
$452$	−13.4242	−	7.75047i	−0.631422	−	0.364552i
$453$		0			0
$454$			1.36548i			0.0640854i
$455$	−0.0431292	+	35.2582i	−0.00202193	+	1.65293i
$456$		0			0
$457$	−5.95064			−0.278359			−0.139180	−	0.990267i	$-0.544447\pi$
$457$	−5.95064			−0.278359			−0.139180	+	0.990267i	$0.544447\pi$
$458$	−5.35264	+	9.27104i	−0.250112	+	0.433207i
$459$		0			0
$460$	14.3412	+	8.27990i	0.668662	+	0.386052i
$461$	−20.9173	+	36.2299i	−0.974217	+	1.68739i	−0.291722	+	0.956503i	$0.594228\pi$
$461$	−20.9173	+	36.2299i	−0.974217	+	1.68739i	−0.682495	+	0.730890i	$0.739105\pi$
$462$		0			0
$463$	29.2953			1.36147			0.680734	−	0.732531i	$-0.261661\pi$
$463$	29.2953			1.36147			0.680734	+	0.732531i	$0.261661\pi$
$464$	5.32687	−	3.07547i	0.247294	−	0.142775i
$465$		0			0
$466$	9.97258	−	17.2730i	0.461971	−	0.800157i
$467$	−7.42845	+	12.8665i	−0.343748	+	0.595388i	−0.985125	−	0.171837i	$-0.945030\pi$
$467$	−7.42845	+	12.8665i	−0.343748	+	0.595388i	0.641378	+	0.767225i	$0.278363\pi$
$468$		0			0
$469$	21.1407	−	35.0323i	0.976186	−	1.61764i
$470$	10.8198	−	6.24680i	0.499079	−	0.288143i
$471$		0			0
$472$		−	3.93668i		−	0.181201i
$473$	−7.69587	+	4.44321i	−0.353857	+	0.204299i
$474$		0			0
$475$	26.6496	+	15.3861i	1.22277	+	0.705964i
$476$	−16.8324	−	0.325965i	−0.771511	−	0.0149406i
$477$		0			0
$478$	24.5831			1.12441
$479$	−15.8747	+	27.4958i	−0.725334	+	1.25632i	0.233502	+	0.972356i	$0.424981\pi$
$479$	−15.8747	+	27.4958i	−0.725334	+	1.25632i	−0.958836	+	0.283959i	$0.908352\pi$
$480$		0			0
$481$	13.1324	−	7.90299i	0.598784	−	0.360345i
$482$	15.8405			0.721514
$483$		0			0
$484$	−2.67790	−	4.63826i	−0.121723	−	0.210830i
$485$	31.6291	−	18.2611i	1.43620	−	0.829193i
$486$		0			0
$487$	37.5229			1.70033			0.850163	−	0.526520i	$-0.176503\pi$
$487$	37.5229			1.70033			0.850163	+	0.526520i	$0.176503\pi$
$488$	7.67998	+	13.3021i	0.347656	+	0.602158i
$489$		0			0
$490$	−21.8886	−	13.7940i	−0.988825	−	0.623150i
$491$	31.6466	−	18.2712i	1.42819	−	0.824567i	0.431214	−	0.902250i	$-0.358086\pi$
$491$	31.6466	−	18.2712i	1.42819	−	0.824567i	0.996978	+	0.0776831i	$0.0247522\pi$
$492$		0			0
$493$	33.8961	−	19.5699i	1.52661	−	0.881386i
$494$	−11.2086	−	6.20299i	−0.504300	−	0.279086i
$495$		0			0
$496$	6.99170	−	4.03666i	0.313937	−	0.181251i
$497$	−21.3637	−	12.8922i	−0.958292	−	0.578293i
$498$		0			0
$499$	−4.54301	+	7.86873i	−0.203373	+	0.352253i	−0.949613	−	0.313424i	$-0.898524\pi$
$499$	−4.54301	+	7.86873i	−0.203373	+	0.352253i	0.746240	+	0.665677i	$0.231857\pi$
$500$	−13.5310			−0.605123
$501$		0			0
$502$	6.73561	+	3.88881i	0.300625	+	0.173566i
$503$	−3.05811	+	5.29680i	−0.136354	+	0.236173i	−0.926114	−	0.377244i	$-0.876872\pi$
$503$	−3.05811	+	5.29680i	−0.136354	+	0.236173i	0.789760	+	0.613416i	$0.210205\pi$
$504$		0			0
$505$	−5.73983	−	9.94168i	−0.255419	−	0.442399i
$506$	−15.6921	−	9.05986i	−0.697601	−	0.402760i
$507$		0			0
$508$	0.0206135	+	0.0357036i	0.000914575	+	0.00158409i
$509$	38.6933			1.71505			0.857526	−	0.514441i	$-0.172001\pi$
$509$	38.6933			1.71505			0.857526	+	0.514441i	$0.172001\pi$
$510$		0			0
$511$	−23.3760	+	12.8992i	−1.03409	+	0.570628i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$		−	5.36870i		−	0.236803i
$515$	24.9675	−	14.4150i	1.10020	−	0.635200i
$516$		0			0
$517$	−11.8390	+	6.83524i	−0.520678	+	0.300614i
$518$	−0.217760	+	11.2448i	−0.00956780	+	0.494069i
$519$		0			0
$520$	13.3242	−	0.241722i	0.584303	−	0.0106002i
$521$	−0.680956	−	1.17945i	−0.0298332	−	0.0516726i	0.850723	−	0.525614i	$-0.176164\pi$
$521$	−0.680956	−	1.17945i	−0.0298332	−	0.0516726i	−0.880557	+	0.473941i	$0.842831\pi$
$522$		0			0
$523$		−	28.4238i		−	1.24288i	−0.783460	−	0.621442i	$-0.786547\pi$
$523$		−	28.4238i		−	1.24288i	0.783460	−	0.621442i	$-0.213453\pi$
$524$	10.3017	−	17.8430i	0.450031	−	0.779477i
$525$		0			0
$526$	11.0278	−	19.1007i	0.480835	−	0.832831i
$527$	44.4899	−	25.6862i	1.93801	−	1.11891i
$528$		0			0
$529$	2.92614			0.127223
$530$	26.8511			1.16634
$531$		0			0
$532$	8.23044	−	4.54168i	0.356835	−	0.196907i
$533$	−4.69989	−	2.60098i	−0.203575	−	0.112661i
$534$		0			0
$535$	−0.311236	−	0.179692i	−0.0134559	−	0.00776878i
$536$	−13.3932	−	7.73256i	−0.578498	−	0.333996i
$537$		0			0
$538$		−	20.5379i		−	0.885451i
$539$	23.9504	+	15.0934i	1.03162	+	0.650118i
$540$		0			0
$541$	−2.38086	+	4.12376i	−0.102361	+	0.177294i	−0.912657	−	0.408726i	$-0.865973\pi$
$541$	−2.38086	+	4.12376i	−0.102361	+	0.177294i	0.810296	+	0.586021i	$0.199306\pi$
$542$	−16.7429			−0.719170
$543$		0			0
$544$			6.36324i			0.272822i
$545$	−41.2101			−1.76524
$546$		0			0
$547$	−0.785744			−0.0335960			−0.0167980	−	0.999859i	$-0.505347\pi$
$547$	−0.785744			−0.0335960			−0.0167980	+	0.999859i	$0.505347\pi$
$548$			11.7210i			0.500695i
$549$		0			0
$550$	35.0267			1.49354
$551$	−10.9272	+	18.9264i	−0.465513	+	0.806292i
$552$		0			0
$553$	1.59508	−	2.64322i	0.0678299	−	0.112401i
$554$			14.4982i			0.615969i
$555$		0			0
$556$	−18.5921	−	10.7341i	−0.788479	−	0.455229i
$557$	29.1337	+	16.8203i	1.23443	+	0.712701i	0.967951	−	0.251139i	$-0.0808051\pi$
$557$	29.1337	+	16.8203i	1.23443	+	0.712701i	0.266483	+	0.963840i	$0.414138\pi$
$558$		0			0
$559$	0.143704	+	7.92121i	0.00607803	+	0.335031i
$560$	−5.05249	+	8.37250i	−0.213507	+	0.353803i
$561$		0			0
$562$	7.69457			0.324576
$563$	−3.00653			−0.126710			−0.0633550	−	0.997991i	$-0.520180\pi$
$563$	−3.00653			−0.126710			−0.0633550	+	0.997991i	$0.520180\pi$
$564$		0			0
$565$	−49.6168	+	28.6463i	−2.08739	+	1.20516i
$566$	1.62383	−	2.81255i	0.0682545	−	0.118220i
$567$		0			0
$568$	−4.71553	+	8.16754i	−0.197859	+	0.342702i
$569$		−	43.5063i		−	1.82388i	−0.410323	−	0.911940i	$-0.634584\pi$
$569$		−	43.5063i		−	1.82388i	0.410323	−	0.911940i	$-0.365416\pi$
$570$		0			0
$571$	−9.41467	−	16.3067i	−0.393992	−	0.682413i	0.598980	−	0.800764i	$-0.295573\pi$
$571$	−9.41467	−	16.3067i	−0.393992	−	0.682413i	−0.992972	+	0.118350i	$0.962239\pi$
$572$	−14.5793	+	0.264492i	−0.609590	+	0.0110590i
$573$		0			0
$574$	3.45111	−	1.90438i	0.144047	−	0.0794871i
$575$	33.6054	−	19.4021i	1.40144	−	0.809124i
$576$		0			0
$577$	−18.8057	+	10.8575i	−0.782893	+	0.452004i	−0.837455	−	0.546507i	$-0.815957\pi$
$577$	−18.8057	+	10.8575i	−0.782893	+	0.452004i	0.0545614	+	0.998510i	$0.482624\pi$
$578$			23.4908i			0.977089i
$579$		0			0
$580$		−	22.7343i		−	0.943989i
$581$	−17.5906	−	0.340649i	−0.729783	−	0.0141325i
$582$		0			0
$583$	−29.3805			−1.21681
$584$	5.04560	+	8.73924i	0.208789	+	0.361632i
$585$		0			0
$586$	−11.8197	−	6.82413i	−0.488269	−	0.281902i
$587$	2.06029	+	3.56852i	0.0850372	+	0.147289i	0.905407	−	0.424545i	$-0.139566\pi$
$587$	2.06029	+	3.56852i	0.0850372	+	0.147289i	−0.820370	+	0.571833i	$0.806232\pi$
$588$		0			0
$589$	−14.3423	+	24.8416i	−0.590964	+	1.02358i
$590$	−12.6009	−	7.27512i	−0.518770	−	0.299512i
$591$		0			0
$592$	4.25094			0.174712
$593$	12.8003	−	22.1708i	0.525646	−	0.910446i	−0.473908	−	0.880574i	$-0.657157\pi$
$593$	12.8003	−	22.1708i	0.525646	−	0.910446i	0.999554	−	0.0298711i	$-0.00950968\pi$
$594$		0			0
$595$	−32.1502	+	53.2762i	−1.31803	+	2.18411i
$596$	−5.31891	+	3.07087i	−0.217871	+	0.125788i
$597$		0			0
$598$	−13.8412	+	8.32956i	−0.566008	+	0.340621i
$599$	7.75883	−	4.47956i	0.317017	−	0.183030i	−0.333045	−	0.942911i	$-0.608076\pi$
$599$	7.75883	−	4.47956i	0.317017	−	0.183030i	0.650062	+	0.759881i	$0.274743\pi$
$600$		0			0
$601$	4.74428	−	2.73911i	0.193523	−	0.111731i	−0.400108	−	0.916468i	$-0.631027\pi$
$601$	4.74428	−	2.73911i	0.193523	−	0.111731i	0.593631	+	0.804737i	$0.297694\pi$
$602$	−4.97744	−	3.00370i	−0.202866	−	0.122422i
$603$		0			0
$604$	−3.86299	−	6.69089i	−0.157183	−	0.272249i
$605$	−19.7954			−0.804798
$606$		0			0
$607$	−18.3240	+	10.5794i	−0.743750	+	0.429404i	−0.823431	−	0.567416i	$-0.807943\pi$
$607$	−18.3240	+	10.5794i	−0.743750	+	0.429404i	0.0796812	+	0.996820i	$0.474610\pi$
$608$	−1.77650	−	3.07700i	−0.0720467	−	0.124789i
$609$		0			0
$610$	56.7714			2.29861
$611$	0.221068	+	12.1856i	0.00894344	+	0.492978i
$612$		0			0
$613$	−21.4740	+	37.1941i	−0.867327	+	1.50225i	−0.00260968	+	0.999997i	$0.500831\pi$
$613$	−21.4740	+	37.1941i	−0.867327	+	1.50225i	−0.864718	+	0.502258i	$0.832503\pi$
$614$	11.6540			0.470318
$615$		0			0
$616$	5.52843	−	9.16117i	0.222747	−	0.369114i
$617$	−22.5953	−	13.0454i	−0.909654	−	0.525189i	−0.0293341	−	0.999570i	$-0.509339\pi$
$617$	−22.5953	−	13.0454i	−0.909654	−	0.525189i	−0.880320	+	0.474381i	$0.842672\pi$
$618$		0			0
$619$	−23.2233	+	13.4080i	−0.933422	+	0.538911i	−0.887892	−	0.460052i	$-0.847831\pi$
$619$	−23.2233	+	13.4080i	−0.933422	+	0.538911i	−0.0455298	+	0.998963i	$0.514498\pi$
$620$		−	29.8395i		−	1.19838i
$621$		0			0
$622$	−3.16043	+	1.82467i	−0.126722	+	0.0731627i
$623$	−14.2119	−	0.275218i	−0.569387	−	0.0110264i
$624$		0			0
$625$	−3.35338	+	5.80822i	−0.134135	+	0.232329i
$626$	9.79057	−	16.9578i	0.391310	−	0.677769i
$627$		0			0
$628$	11.4780	−	6.62684i	0.458023	−	0.264440i
$629$	27.0497			1.07854
$630$		0			0
$631$	−1.72214	+	2.98284i	−0.0685575	+	0.118745i	−0.898267	−	0.439451i	$-0.855173\pi$
$631$	−1.72214	+	2.98284i	−0.0685575	+	0.118745i	0.829709	+	0.558196i	$0.188506\pi$
$632$	−1.01053	−	0.583429i	−0.0401967	−	0.0232076i
$633$		0			0
$634$	4.57644	−	7.92662i	0.181754	−	0.314806i
$635$	0.152377			0.00604692
$636$		0			0
$637$	22.1126	−	12.1668i	0.876134	−	0.482067i
$638$			24.8758i			0.984843i
$639$		0			0
$640$	3.20089	+	1.84803i	0.126526	+	0.0730499i
$641$		−	1.01769i		−	0.0401964i	−0.999798	−	0.0200982i	$-0.993602\pi$
$641$		−	1.01769i		−	0.0401964i	0.999798	−	0.0200982i	$-0.00639788\pi$
$642$		0			0
$643$	0.268683	+	0.155124i	0.0105958	+	0.00611751i	0.505289	−	0.862950i	$-0.331386\pi$
$643$	0.268683	+	0.155124i	0.0105958	+	0.00611751i	−0.494693	+	0.869068i	$0.664719\pi$
$644$	0.229513	−	11.8518i	0.00904409	−	0.467025i
$645$		0			0
$646$	−11.3043	−	19.5797i	−0.444762	−	0.770351i
$647$	9.94178	−	17.2197i	0.390852	−	0.676975i	−0.601711	−	0.798714i	$-0.705514\pi$
$647$	9.94178	−	17.2197i	0.390852	−	0.676975i	0.992562	+	0.121739i	$0.0388472\pi$
$648$		0			0
$649$	13.7879	+	7.96043i	0.541221	+	0.312474i
$650$	15.1206	−	27.3224i	0.593077	−	1.07167i
$651$		0			0
$652$	9.67041	+	16.7496i	0.378722	+	0.655966i
$653$			37.4640i			1.46608i	0.680185	+	0.733041i	$0.261899\pi$
$653$			37.4640i			1.46608i	−0.680185	+	0.733041i	$0.738101\pi$
$654$		0			0
$655$	−38.0757	−	65.9491i	−1.48774	−	2.57684i
$656$	−0.744907	−	1.29022i	−0.0290837	−	0.0503745i
$657$		0			0
$658$	−7.65708	−	4.62076i	−0.298504	−	0.180136i
$659$	2.96855	+	1.71389i	0.115638	+	0.0667637i	0.556703	−	0.830711i	$-0.312066\pi$
$659$	2.96855	+	1.71389i	0.115638	+	0.0667637i	−0.441065	+	0.897475i	$0.645399\pi$
$660$		0			0
$661$	−41.2567	−	23.8196i	−1.60470	−	0.926474i	−0.990529	−	0.137302i	$-0.956157\pi$
$661$	−41.2567	−	23.8196i	−1.60470	−	0.926474i	−0.614172	−	0.789173i	$-0.710510\pi$
$662$	7.98587	−	4.61064i	0.310379	−	0.179198i
$663$		0			0
$664$			6.64988i			0.258066i
$665$	0.672711	−	34.7379i	0.0260866	−	1.34708i
$666$		0			0
$667$	13.7793	+	23.8664i	0.533536	+	0.924112i
$668$	4.08666	+	7.07831i	0.158118	+	0.273868i
$669$		0			0
$670$	−49.5021	+	28.5801i	−1.91243	+	1.10414i
$671$	−62.1192			−2.39809
$672$		0			0
$673$	10.0653	+	17.4336i	0.387989	+	0.672017i	0.992179	−	0.124823i	$-0.0398364\pi$
$673$	10.0653	+	17.4336i	0.387989	+	0.672017i	−0.604190	+	0.796841i	$0.706503\pi$
$674$		−	3.21877i		−	0.123982i
$675$		0			0
$676$	−6.08737	+	11.4867i	−0.234130	+	0.441796i
$677$	3.52495	−	6.10539i	0.135475	−	0.234649i	−0.790304	−	0.612715i	$-0.790077\pi$
$677$	3.52495	−	6.10539i	0.135475	−	0.234649i	0.925779	+	0.378066i	$0.123411\pi$
$678$		0			0
$679$	−22.3837	−	13.5077i	−0.859008	−	0.518379i
$680$	20.3680	+	11.7595i	0.781078	+	0.450955i
$681$		0			0
$682$			32.6504i			1.25025i
$683$			15.9052i			0.608597i	0.952577	+	0.304299i	$0.0984221\pi$
$683$			15.9052i			0.608597i	−0.952577	+	0.304299i	$0.901578\pi$
$684$		0			0
$685$	37.5175	+	21.6607i	1.43347	+	0.827614i
$686$	−1.07521	+	18.4890i	−0.0410518	+	0.705914i
$687$		0			0
$688$	−1.09865	+	1.90293i	−0.0418858	+	0.0725484i
$689$	−12.6832	+	22.9181i	−0.483190	+	0.873110i
$690$		0			0
$691$		−	20.8355i		−	0.792622i	−0.918116	−	0.396311i	$-0.870290\pi$
$691$		−	20.8355i		−	0.792622i	0.918116	−	0.396311i	$-0.129710\pi$
$692$	1.87775	+	3.25236i	0.0713813	+	0.123636i
$693$		0			0
$694$	−24.9848			−0.948410
$695$	−68.7175	+	39.6741i	−2.60660	+	1.50492i
$696$		0			0
$697$	−4.74002	−	8.20996i	−0.179541	−	0.310974i
$698$	−15.4366	−	26.7370i	−0.584284	−	1.01201i
$699$		0			0
$700$	11.0709	+	20.0627i	0.418442	+	0.758300i
$701$			15.1847i			0.573518i	0.958003	+	0.286759i	$0.0925778\pi$
$701$			15.1847i			0.573518i	−0.958003	+	0.286759i	$0.907422\pi$
$702$		0			0
$703$	−13.0801	+	7.55181i	−0.493326	+	0.284822i
$704$	−3.50241	−	2.02212i	−0.132002	−	0.0762113i
$705$		0			0
$706$	−25.4683	−	14.7041i	−0.958511	−	0.553397i
$707$	−4.24576	+	7.03566i	−0.159678	+	0.264603i
$708$		0			0
$709$	−12.6446	−	21.9010i	−0.474877	−	0.822511i	0.524709	−	0.851282i	$-0.324174\pi$
$709$	−12.6446	−	21.9010i	−0.474877	−	0.822511i	−0.999586	+	0.0287706i	$0.990841\pi$
$710$	17.4289	+	30.1878i	0.654096	+	1.13293i
$711$		0			0
$712$			5.37260i			0.201347i
$713$	18.0858	+	31.3255i	0.677318	+	1.17315i
$714$		0			0
$715$	−26.0964	+	47.1554i	−0.975950	+	1.76351i
$716$	−6.31551	−	3.64626i	−0.236022	−	0.136267i
$717$		0			0
$718$	−0.190322	+	0.329648i	−0.00710277	+	0.0123024i
$719$	−12.8401	−	22.2397i	−0.478854	−	0.829400i	0.520852	−	0.853647i	$-0.325614\pi$
$719$	−12.8401	−	22.2397i	−0.478854	−	0.829400i	−0.999706	+	0.0242474i	$0.992281\pi$
$720$		0			0
$721$	−17.6693	−	10.6628i	−0.658040	−	0.397102i
$722$	−5.52190	−	3.18807i	−0.205504	−	0.118648i
$723$		0			0
$724$			15.5459i			0.577758i
$725$	−46.1355	−	26.6363i	−1.71343	−	0.989249i
$726$		0			0
$727$			46.0966i			1.70963i	0.518935	+	0.854814i	$0.326329\pi$
$727$			46.0966i			1.70963i	−0.518935	+	0.854814i	$0.673671\pi$
$728$	−4.75959	−	8.26718i	−0.176402	−	0.306402i
$729$		0			0
$730$	37.2978			1.38045
$731$	−6.99100	+	12.1088i	−0.258572	+	0.447859i
$732$		0			0
$733$	15.0262	+	8.67537i	0.555005	+	0.320432i	0.751138	−	0.660145i	$-0.229505\pi$
$733$	15.0262	+	8.67537i	0.555005	+	0.320432i	−0.196133	+	0.980577i	$0.562839\pi$
$734$	−14.9200	+	25.8423i	−0.550709	+	0.953855i
$735$		0			0
$736$	−4.48039			−0.165149
$737$	54.1652	−	31.2723i	1.99520	−	1.15193i
$738$		0			0
$739$	−9.31410	+	16.1325i	−0.342625	+	0.593443i	−0.984919	−	0.173015i	$-0.944649\pi$
$739$	−9.31410	+	16.1325i	−0.342625	+	0.593443i	0.642295	+	0.766458i	$0.277983\pi$
$740$	7.85587	−	13.6068i	0.288788	−	0.500195i
$741$		0			0
$742$	−9.28631	−	16.8287i	−0.340911	−	0.617800i
$743$	−3.25374	+	1.87855i	−0.119368	+	0.0689171i	−0.558495	−	0.829508i	$-0.688621\pi$
$743$	−3.25374	+	1.87855i	−0.119368	+	0.0689171i	0.439127	+	0.898425i	$0.355288\pi$
$744$		0			0
$745$			22.7003i			0.831675i
$746$	−5.29953	+	3.05968i	−0.194030	+	0.112023i
$747$		0			0
$748$	−22.2867	−	12.8672i	−0.814881	−	0.470472i
$749$	−0.00498095	+	0.257210i	−0.000182000	+	0.00939824i
$750$		0			0
$751$	−18.5705			−0.677648			−0.338824	−	0.940850i	$-0.610029\pi$
$751$	−18.5705			−0.677648			−0.338824	+	0.940850i	$0.610029\pi$
$752$	−1.69012	+	2.92738i	−0.0616324	+	0.106750i
$753$		0			0
$754$	19.4043	+	10.7386i	0.706662	+	0.391075i
$755$	−28.5557			−1.03925
$756$		0			0
$757$	25.2343	+	43.7070i	0.917155	+	1.58856i	0.803716	+	0.595013i	$0.202853\pi$
$757$	25.2343	+	43.7070i	0.917155	+	1.58856i	0.113439	+	0.993545i	$0.463813\pi$
$758$	7.15170	−	4.12904i	0.259761	−	0.149973i
$759$		0			0
$760$	−13.1322			−0.476353
$761$	19.3692	+	33.5484i	0.702133	+	1.21613i	0.967716	+	0.252042i	$0.0811020\pi$
$761$	19.3692	+	33.5484i	0.702133	+	1.21613i	−0.265584	+	0.964088i	$0.585565\pi$
$762$		0			0
$763$	14.2523	+	25.8280i	0.515967	+	0.935036i
$764$	8.84918	−	5.10907i	0.320152	−	0.184840i
$765$		0			0
$766$	−9.93055	+	5.73341i	−0.358805	+	0.207156i
$767$	12.1615	−	7.31875i	0.439128	−	0.264265i
$768$		0			0
$769$	−9.73863	+	5.62260i	−0.351184	+	0.202756i	−0.665207	−	0.746659i	$-0.731657\pi$
$769$	−9.73863	+	5.62260i	−0.351184	+	0.202756i	0.314023	+	0.949415i	$0.398323\pi$
$770$	−19.1072	−	34.6260i	−0.688575	−	1.24784i
$771$		0			0
$772$	−4.35362	+	7.54070i	−0.156690	+	0.271396i
$773$	−45.7439			−1.64529			−0.822647	−	0.568552i	$-0.807504\pi$
$773$	−45.7439			−1.64529			−0.822647	+	0.568552i	$0.807504\pi$
$774$		0			0
$775$	−60.5545	−	34.9611i	−2.17518	−	1.25584i
$776$	−4.94068	+	8.55751i	−0.177360	+	0.307197i
$777$		0			0
$778$	−7.75815	−	13.4375i	−0.278143	−	0.481758i
$779$	4.58415	+	2.64666i	0.164244	+	0.0948264i
$780$		0			0
$781$	−19.0707	−	33.0314i	−0.682403	−	1.18196i
$782$	−28.5098			−1.01951
$783$		0			0
$784$	6.99475	+	0.271013i	0.249813	+	0.00967904i
$785$		−	48.9865i		−	1.74840i
$786$		0			0
$787$		−	11.5424i		−	0.411444i	−0.978611	−	0.205722i	$-0.934046\pi$
$787$		−	11.5424i		−	0.411444i	0.978611	−	0.205722i	$-0.0659542\pi$
$788$	−11.4983	+	6.63856i	−0.409611	+	0.236489i
$789$		0			0
$790$	−3.73498	+	2.15639i	−0.132885	+	0.0767210i
$791$	35.1134	+	21.1897i	1.24849	+	0.753417i
$792$		0			0
$793$	−26.8160	+	48.4558i	−0.952266	+	1.72072i
$794$	8.29117	+	14.3607i	0.294243	+	0.509643i
$795$		0			0
$796$			0.909155i			0.0322241i
$797$	8.92933	−	15.4660i	0.316293	−	0.547836i	−0.663419	−	0.748249i	$-0.730895\pi$
$797$	8.92933	−	15.4660i	0.316293	−	0.547836i	0.979712	+	0.200413i	$0.0642284\pi$
$798$		0			0
$799$	−10.7546	+	18.6276i	−0.380472	+	0.658997i
$800$	7.50056	−	4.33045i	0.265185	−	0.153105i
$801$		0			0
$802$	35.3789			1.24927
$803$	−40.8112			−1.44019
$804$		0			0
$805$	−37.5120	−	22.6371i	−1.32212	−	0.797853i
$806$	25.4688	+	14.0947i	0.897100	+	0.496466i
$807$		0			0
$808$	2.68980	+	1.55296i	0.0946268	+	0.0546328i
$809$	−38.2037	−	22.0569i	−1.34317	−	0.775480i	−0.355899	−	0.934524i	$-0.615825\pi$
$809$	−38.2037	−	22.0569i	−1.34317	−	0.775480i	−0.987271	+	0.159044i	$0.949159\pi$
$810$		0			0
$811$		−	38.7342i		−	1.36014i	−0.733146	−	0.680071i	$-0.761949\pi$
$811$		−	38.7342i		−	1.36014i	0.733146	−	0.680071i	$-0.238051\pi$
$812$	−14.2485	+	7.86253i	−0.500023	+	0.275921i
$813$		0			0
$814$	−8.59589	+	14.8885i	−0.301286	+	0.521842i
$815$	71.4849			2.50401
$816$		0			0
$817$		−	7.80706i		−	0.273134i
$818$	10.0312			0.350731
$819$		0			0
$820$	−5.50645			−0.192294
$821$		−	21.3301i		−	0.744427i	−0.928147	−	0.372213i	$-0.878599\pi$
$821$		−	21.3301i		−	0.744427i	0.928147	−	0.372213i	$-0.121401\pi$
$822$		0			0
$823$	37.6102			1.31101			0.655504	−	0.755192i	$-0.272456\pi$
$823$	37.6102			1.31101			0.655504	+	0.755192i	$0.272456\pi$
$824$	−3.90009	+	6.75515i	−0.135866	+	0.235327i
$825$		0			0
$826$	−0.201661	+	10.4135i	−0.00701670	+	0.362333i
$827$			28.8741i			1.00405i	0.864853	+	0.502026i	$0.167412\pi$
$827$			28.8741i			1.00405i	−0.864853	+	0.502026i	$0.832588\pi$
$828$		0			0
$829$	−8.90189	−	5.13951i	−0.309176	−	0.178503i	0.337382	−	0.941368i	$-0.390459\pi$
$829$	−8.90189	−	5.13951i	−0.309176	−	0.178503i	−0.646558	+	0.762865i	$0.723792\pi$
$830$	21.2855	+	12.2892i	0.738831	+	0.426565i
$831$		0			0
$832$	−3.08929	+	1.85912i	−0.107102	+	0.0644533i
$833$	44.5093	+	1.72452i	1.54216	+	0.0597511i
$834$		0			0
$835$	30.2092			1.04543
$836$	14.3692			0.496969
$837$		0			0
$838$	13.0599	−	7.54013i	0.451147	−	0.260470i
$839$	14.9614	−	25.9140i	0.516526	−	0.894650i	−0.483290	−	0.875461i	$-0.660558\pi$
$839$	14.9614	−	25.9140i	0.516526	−	0.894650i	0.999816	−	0.0191893i	$-0.00610852\pi$
$840$		0			0
$841$	4.41702	−	7.65050i	0.152311	−	0.263810i
$842$			11.3259i			0.390318i
$843$		0			0
$844$	−6.29538	−	10.9039i	−0.216696	−	0.375328i
$845$	25.5179	+	40.7128i	0.877843	+	1.40056i
$846$		0			0
$847$	6.84613	+	12.4066i	0.235236	+	0.426295i
$848$	−6.29149	+	3.63239i	−0.216051	+	0.124737i
$849$		0			0
$850$	47.7279	−	27.5557i	1.63705	−	0.945153i
$851$			19.0458i			0.652883i
$852$		0			0
$853$		−	31.3848i		−	1.07460i	−0.843392	−	0.537298i	$-0.819445\pi$
$853$		−	31.3848i		−	1.07460i	0.843392	−	0.537298i	$-0.180555\pi$
$854$	−19.6341	−	35.5809i	−0.671865	−	1.21755i
$855$		0			0
$856$	0.0972344			0.00332340
$857$	−11.3646	−	19.6840i	−0.388207	−	0.672394i	0.604002	−	0.796983i	$-0.293572\pi$
$857$	−11.3646	−	19.6840i	−0.388207	−	0.672394i	−0.992208	+	0.124589i	$0.960239\pi$
$858$		0			0
$859$	33.2633	+	19.2046i	1.13493	+	0.655251i	0.945170	−	0.326580i	$-0.105896\pi$
$859$	33.2633	+	19.2046i	1.13493	+	0.655251i	0.189758	+	0.981831i	$0.439229\pi$
$860$	4.06070	+	7.03334i	0.138469	+	0.239835i
$861$		0			0
$862$	5.92342	−	10.2597i	0.201752	−	0.349445i
$863$	−35.3241	−	20.3944i	−1.20245	−	0.694233i	−0.241348	−	0.970439i	$-0.577589\pi$
$863$	−35.3241	−	20.3944i	−1.20245	−	0.694233i	−0.961098	+	0.276206i	$0.910923\pi$
$864$		0			0
$865$	13.8806			0.471954
$866$	−9.63135	+	16.6820i	−0.327286	+	0.566877i
$867$		0			0
$868$	−18.7016	+	10.3198i	−0.634774	+	0.350278i
$869$	4.08681	−	2.35952i	0.138636	−	0.0800413i
$870$		0			0
$871$	−1.01142	−	55.7511i	−0.0342706	−	1.88906i
$872$	9.65593	−	5.57485i	0.326991	−	0.188788i
$873$		0			0
$874$	13.7861	−	7.95942i	0.466323	−	0.269232i
$875$	35.7928	+	0.693140i	1.21002	+	0.0234324i
$876$		0			0
$877$	14.2500	+	24.6817i	0.481189	+	0.833443i	0.999767	−	0.0215871i	$-0.00687191\pi$
$877$	14.2500	+	24.6817i	0.481189	+	0.833443i	−0.518578	+	0.855030i	$0.673539\pi$
$878$	16.1358			0.544558
$879$		0			0
$880$	−12.9451	+	7.47387i	−0.436380	+	0.251944i
$881$	−27.3954	−	47.4502i	−0.922973	−	1.59864i	−0.794789	−	0.606886i	$-0.792418\pi$
$881$	−27.3954	−	47.4502i	−0.922973	−	1.59864i	−0.128185	−	0.991750i	$-0.540915\pi$
$882$		0			0
$883$	−5.16459			−0.173802			−0.0869011	−	0.996217i	$-0.527696\pi$
$883$	−5.16459			−0.173802			−0.0869011	+	0.996217i	$0.527696\pi$
$884$	−19.6579	+	11.8300i	−0.661165	+	0.397886i
$885$		0			0
$886$	−15.0726	+	26.1064i	−0.506372	+	0.877063i
$887$	29.3444			0.985289			0.492644	−	0.870231i	$-0.336030\pi$
$887$	29.3444			0.985289			0.492644	+	0.870231i	$0.336030\pi$
$888$		0			0
$889$	−0.0526989	−	0.0955010i	−0.00176747	−	0.00320300i
$890$	17.1971	+	9.92874i	0.576447	+	0.332812i
$891$		0			0
$892$	−24.9890	+	14.4274i	−0.836693	+	0.483065i
$893$		−	12.0100i		−	0.401900i
$894$		0			0
$895$	−23.3425	+	13.4768i	−0.780255	+	0.450481i
$896$	0.0512262	−	2.64526i	0.00171135	−	0.0883718i
$897$		0			0
$898$	20.0259	−	34.6859i	0.668273	−	1.15748i
$899$	24.8292	−	43.0055i	0.828102	−	1.43431i
$900$		0			0
$901$	−40.0342	+	23.1138i	−1.33373	+	0.770032i
$902$	6.02515			0.200616
$903$		0			0
$904$	7.75047	−	13.4242i	0.257777	−	0.446483i
$905$	49.7606	+	28.7293i	1.65410	+	0.954994i
$906$		0			0
$907$	−26.7644	+	46.3573i	−0.888698	+	1.53927i	−0.0472821	+	0.998882i	$0.515056\pi$
$907$	−26.7644	+	46.3573i	−0.888698	+	1.53927i	−0.841416	+	0.540388i	$0.818277\pi$
$908$	−1.36548			−0.0453152
$909$		0			0
$910$	−35.2582	−	0.0431292i	−1.16880	−	0.00142972i
$911$		−	22.9778i		−	0.761290i	−0.924721	−	0.380645i	$-0.875702\pi$
$911$		−	22.9778i		−	0.761290i	0.924721	−	0.380645i	$-0.124298\pi$
$912$		0			0
$913$	−23.2906	−	13.4468i	−0.770806	−	0.445025i
$914$		−	5.95064i		−	0.196830i
$915$		0			0
$916$	−9.27104	−	5.35264i	−0.306324	−	0.176856i
$917$	−28.1646	+	46.6717i	−0.930078	+	1.54124i
$918$		0			0
$919$	−9.18158	−	15.9030i	−0.302872	−	0.524591i	0.673913	−	0.738811i	$-0.264612\pi$
$919$	−9.18158	−	15.9030i	−0.302872	−	0.524591i	−0.976785	+	0.214220i	$0.931279\pi$
$920$	−8.27990	+	14.3412i	−0.272980	+	0.472816i
$921$		0			0
$922$	−36.2299	−	20.9173i	−1.19317	−	0.688875i
$923$	−33.9986	+	0.616791i	−1.11908	+	0.0203019i
$924$		0			0
$925$	−18.4085	−	31.8844i	−0.605267	−	1.04835i
$926$			29.2953i			0.962703i
$927$		0			0
$928$	3.07547	+	5.32687i	0.100957	+	0.174863i
$929$	9.24733	+	16.0168i	0.303395	+	0.525495i	0.976903	−	0.213685i	$-0.0685465\pi$
$929$	9.24733	+	16.0168i	0.303395	+	0.525495i	−0.673508	+	0.739180i	$0.735213\pi$
$930$		0			0
$931$	−22.0043	+	11.5923i	−0.721161	+	0.379922i
$932$	17.2730	+	9.97258i	0.565796	+	0.326663i
$933$		0			0
$934$	−12.8665	−	7.42845i	−0.421003	−	0.243066i
$935$	−82.3729	+	47.5580i	−2.69388	+	1.55531i
$936$		0			0
$937$		−	59.7536i		−	1.95207i	−0.217623	−	0.976033i	$-0.569830\pi$
$937$		−	59.7536i		−	1.95207i	0.217623	−	0.976033i	$-0.430170\pi$
$938$	35.0323	+	21.1407i	1.14385	+	0.690268i
$939$		0			0
$940$	6.24680	+	10.8198i	0.203748	+	0.352902i
$941$	2.20778	+	3.82399i	0.0719716	+	0.124659i	0.899765	−	0.436374i	$-0.143738\pi$
$941$	2.20778	+	3.82399i	0.0719716	+	0.124659i	−0.827794	+	0.561033i	$0.810404\pi$
$942$		0			0
$943$	5.78067	−	3.33747i	0.188244	−	0.108683i
$944$	3.93668			0.128128
$945$		0			0
$946$	−4.44321	−	7.69587i	−0.144461	−	0.250214i
$947$		−	38.3306i		−	1.24558i	−0.782390	−	0.622789i	$-0.786000\pi$
$947$		−	38.3306i		−	1.24558i	0.782390	−	0.622789i	$-0.214000\pi$
$948$		0			0
$949$	−17.6176	+	31.8346i	−0.571893	+	1.03339i
$950$	−15.3861	+	26.6496i	−0.499192	+	0.864626i
$951$		0			0
$952$	0.325965	−	16.8324i	0.0105646	−	0.545541i
$953$	−1.55399	−	0.897194i	−0.0503385	−	0.0290630i	0.474620	−	0.880191i	$-0.342586\pi$
$953$	−1.55399	−	0.897194i	−0.0503385	−	0.0290630i	−0.524958	+	0.851128i	$0.675919\pi$
$954$		0			0
$955$		−	37.7670i		−	1.22211i
$956$			24.5831i			0.795075i
$957$		0			0
$958$	−27.4958	−	15.8747i	−0.888349	−	0.512889i
$959$	0.600421	−	31.0049i	0.0193886	−	1.00120i
$960$		0			0
$961$	17.0893	−	29.5995i	0.551266	−	0.954821i
$962$	7.90299	+	13.1324i	0.254803	+	0.423404i
$963$		0			0
$964$			15.8405i			0.510188i
$965$	16.0913	+	27.8709i	0.517997	+	0.897197i
$966$		0			0
$967$	5.46465			0.175731			0.0878656	−	0.996132i	$-0.471995\pi$
$967$	5.46465			0.175731			0.0878656	+	0.996132i	$0.471995\pi$
$968$	4.63826	−	2.67790i	0.149079	−	0.0860710i
$969$		0			0
$970$	18.2611	+	31.6291i	0.586328	+	1.01555i
$971$	12.9355	+	22.4050i	0.415121	+	0.719011i	0.995441	−	0.0953777i	$-0.0304059\pi$
$971$	12.9355	+	22.4050i	0.415121	+	0.719011i	−0.580320	+	0.814388i	$0.697073\pi$
$972$		0			0
$973$	48.6309	+	29.3469i	1.55903	+	0.940819i
$974$			37.5229i			1.20231i
$975$		0			0
$976$	−13.3021	+	7.67998i	−0.425790	+	0.245830i
$977$	−1.88033	−	1.08561i	−0.0601570	−	0.0347316i	0.469620	−	0.882869i	$-0.344391\pi$
$977$	−1.88033	−	1.08561i	−0.0601570	−	0.0347316i	−0.529777	+	0.848137i	$0.677724\pi$
$978$		0			0
$979$	−18.8170	−	10.8640i	−0.601394	−	0.347215i
$980$	13.7940	−	21.8886i	0.440634	−	0.699205i
$981$		0			0
$982$	18.2712	+	31.6466i	0.583057	+	1.00988i
$983$	15.9801	+	27.6783i	0.509685	+	0.882800i	0.999937	+	0.0112194i	$0.00357134\pi$
$983$	15.9801	+	27.6783i	0.509685	+	0.882800i	−0.490252	+	0.871581i	$0.663095\pi$
$984$		0			0
$985$			49.0731i			1.56360i
$986$	19.5699	+	33.8961i	0.623234	+	1.07947i
$987$		0			0
$988$	6.20299	−	11.2086i	0.197343	−	0.356594i
$989$	−8.52584	−	4.92240i	−0.271106	−	0.156523i
$990$		0			0
$991$	10.6147	−	18.3851i	0.337186	−	0.584023i	−0.646716	−	0.762731i	$-0.723858\pi$
$991$	10.6147	−	18.3851i	0.337186	−	0.584023i	0.983902	+	0.178707i	$0.0571915\pi$
$992$	4.03666	+	6.99170i	0.128164	+	0.221987i
$993$		0			0
$994$	12.8922	−	21.3637i	0.408915	−	0.677615i
$995$	2.91010	+	1.68015i	0.0922565	+	0.0532643i
$996$		0			0
$997$			12.9962i			0.411592i	0.978595	+	0.205796i	$0.0659784\pi$
$997$			12.9962i			0.411592i	−0.978595	+	0.205796i	$0.934022\pi$
$998$	−7.86873	−	4.54301i	−0.249080	−	0.143807i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.cm.a.341.1	yes	72
3.2	odd	2	inner	1638.2.cm.a.341.36	yes	72
7.3	odd	6		1638.2.bq.a.1277.18	yes	72
13.9	even	3		1638.2.bq.a.971.19	yes	72
21.17	even	6		1638.2.bq.a.1277.19	yes	72
39.35	odd	6		1638.2.bq.a.971.18	✓	72
91.87	odd	6	inner	1638.2.cm.a.269.36	yes	72
273.269	even	6	inner	1638.2.cm.a.269.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.bq.a.971.18	✓	72	39.35	odd	6
1638.2.bq.a.971.19	yes	72	13.9	even	3
1638.2.bq.a.1277.18	yes	72	7.3	odd	6
1638.2.bq.a.1277.19	yes	72	21.17	even	6
1638.2.cm.a.269.1	yes	72	273.269	even	6	inner
1638.2.cm.a.269.36	yes	72	91.87	odd	6	inner
1638.2.cm.a.341.1	yes	72	1.1	even	1	trivial
1638.2.cm.a.341.36	yes	72	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.cm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.84803 + 3.20089i) q^{5} +(2.64526 + 0.0512262i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.84803 + 3.20089i) q^{5} +(2.64526 + 0.0512262i) q^{7} -1.00000i q^{8} +(-3.20089 - 1.84803i) q^{10} +(3.50241 + 2.02212i) q^{11} +(3.08929 - 1.85912i) q^{13} +(-0.0512262 + 2.64526i) q^{14} +1.00000 q^{16} +6.36324 q^{17} +(-3.07700 + 1.77650i) q^{19} +(1.84803 - 3.20089i) q^{20} +(-2.02212 + 3.50241i) q^{22} +4.48039i q^{23} +(-4.33045 - 7.50056i) q^{25} +(1.85912 + 3.08929i) q^{26} +(-2.64526 - 0.0512262i) q^{28} +(5.32687 - 3.07547i) q^{29} +(6.99170 - 4.03666i) q^{31} +1.00000i q^{32} +6.36324i q^{34} +(-5.05249 + 8.37250i) q^{35} +4.25094 q^{37} +(-1.77650 - 3.07700i) q^{38} +(3.20089 + 1.84803i) q^{40} +(-0.744907 - 1.29022i) q^{41} +(-1.09865 + 1.90293i) q^{43} +(-3.50241 - 2.02212i) q^{44} -4.48039 q^{46} +(-1.69012 + 2.92738i) q^{47} +(6.99475 + 0.271013i) q^{49} +(7.50056 - 4.33045i) q^{50} +(-3.08929 + 1.85912i) q^{52} +(-6.29149 + 3.63239i) q^{53} +(-12.9451 + 7.47387i) q^{55} +(0.0512262 - 2.64526i) q^{56} +(3.07547 + 5.32687i) q^{58} +3.93668 q^{59} +(-13.3021 + 7.67998i) q^{61} +(4.03666 + 6.99170i) q^{62} -1.00000 q^{64} +(0.241722 + 13.3242i) q^{65} +(7.73256 - 13.3932i) q^{67} -6.36324 q^{68} +(-8.37250 - 5.05249i) q^{70} +(-8.16754 - 4.71553i) q^{71} +(-8.73924 + 5.04560i) q^{73} +4.25094i q^{74} +(3.07700 - 1.77650i) q^{76} +(9.16117 + 5.52843i) q^{77} +(0.583429 - 1.01053i) q^{79} +(-1.84803 + 3.20089i) q^{80} +(1.29022 - 0.744907i) q^{82} -6.64988 q^{83} +(-11.7595 + 20.3680i) q^{85} +(-1.90293 - 1.09865i) q^{86} +(2.02212 - 3.50241i) q^{88} -5.37260 q^{89} +(8.26718 - 4.75959i) q^{91} -4.48039i q^{92} +(-2.92738 - 1.69012i) q^{94} -13.1322i q^{95} +(-8.55751 - 4.94068i) q^{97} +(-0.271013 + 6.99475i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 72 q^{4} - 4 q^{7}+O(q^{10}) \) 72 * q - 72 * q^4 - 4 * q^7	\( 72 q - 72 q^{4} - 4 q^{7} + 4 q^{13} + 72 q^{16} - 36 q^{19} - 28 q^{25} + 4 q^{28} - 40 q^{37} + 12 q^{43} - 16 q^{46} + 4 q^{49} - 4 q^{52} + 48 q^{55} + 16 q^{58} - 60 q^{61} - 72 q^{64} + 64 q^{67} + 108 q^{73} + 36 q^{76} + 64 q^{79} + 48 q^{82} - 64 q^{85} + 16 q^{91} - 24 q^{94} - 108 q^{97}+O(q^{100}) \) 72 * q - 72 * q^4 - 4 * q^7 + 4 * q^13 + 72 * q^16 - 36 * q^19 - 28 * q^25 + 4 * q^28 - 40 * q^37 + 12 * q^43 - 16 * q^46 + 4 * q^49 - 4 * q^52 + 48 * q^55 + 16 * q^58 - 60 * q^61 - 72 * q^64 + 64 * q^67 + 108 * q^73 + 36 * q^76 + 64 * q^79 + 48 * q^82 - 64 * q^85 + 16 * q^91 - 24 * q^94 - 108 * q^97

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