LMFDB - Embedded newform 110.2.k.a.13.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,2,Mod(7,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 14]))

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

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

chi := DirichletCharacter("110.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	110.k (of order $20$, degree $8$, 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:	$0.878354422234$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.6
Character	$\chi$	$=$	110.13
Dual form			110.2.k.a.17.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.891007 - 0.453990i) q^{2} +(1.61854 + 0.256351i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-2.22860 - 0.182641i) q^{5} +(1.55851 - 0.506390i) q^{6} +(0.119289 + 0.753160i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-0.299227 - 0.0972249i) q^{9} +O(q^{10})$	\(q+(0.891007 - 0.453990i) q^{2} +(1.61854 + 0.256351i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-2.22860 - 0.182641i) q^{5} +(1.55851 - 0.506390i) q^{6} +(0.119289 + 0.753160i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-0.299227 - 0.0972249i) q^{9} +(-2.06861 + 0.849027i) q^{10} +(-1.49880 + 2.95865i) q^{11} +(1.15874 - 1.15874i) q^{12} +(-0.387452 - 0.760418i) q^{13} +(0.448214 + 0.616914i) q^{14} +(-3.56024 - 0.866914i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-0.657479 + 1.29037i) q^{17} +(-0.310753 + 0.0492184i) q^{18} +(4.09783 - 2.97724i) q^{19} +(-1.45770 + 1.69562i) q^{20} +1.24960i q^{21} +(0.00776159 + 3.31662i) q^{22} +(-1.65567 - 1.65567i) q^{23} +(0.506390 - 1.55851i) q^{24} +(4.93328 + 0.814066i) q^{25} +(-0.690445 - 0.501638i) q^{26} +(-4.83969 - 2.46595i) q^{27} +(0.679435 + 0.346189i) q^{28} +(0.552936 + 0.401731i) q^{29} +(-3.56577 + 0.843891i) q^{30} +(-1.08804 + 3.34864i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.18431 + 4.40446i) q^{33} +1.44822i q^{34} +(-0.128289 - 1.70028i) q^{35} +(-0.254538 + 0.184933i) q^{36} +(-8.01741 + 1.26983i) q^{37} +(2.29955 - 4.51312i) q^{38} +(-0.432172 - 1.33009i) q^{39} +(-0.529022 + 2.17259i) q^{40} +(7.30492 + 10.0544i) q^{41} +(0.567304 + 1.11340i) q^{42} +(7.61267 - 7.61267i) q^{43} +(1.51263 + 2.95160i) q^{44} +(0.649100 + 0.271326i) q^{45} +(-2.22687 - 0.723555i) q^{46} +(1.98553 - 12.5361i) q^{47} +(-0.256351 - 1.61854i) q^{48} +(6.10438 - 1.98343i) q^{49} +(4.76517 - 1.51433i) q^{50} +(-1.39494 + 1.91997i) q^{51} +(-0.842930 - 0.133507i) q^{52} +(-7.31784 + 3.72862i) q^{53} -5.43171 q^{54} +(3.88058 - 6.31990i) q^{55} +0.762548 q^{56} +(7.39570 - 3.76830i) q^{57} +(0.675052 + 0.106918i) q^{58} +(-0.254349 + 0.350081i) q^{59} +(-2.79401 + 2.37074i) q^{60} +(12.0627 - 3.91939i) q^{61} +(0.550800 + 3.47761i) q^{62} +(0.0375314 - 0.236964i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(0.724592 + 1.76543i) q^{65} +(-0.837655 + 5.37005i) q^{66} +(-3.82631 + 3.82631i) q^{67} +(0.657479 + 1.29037i) q^{68} +(-2.25533 - 3.10420i) q^{69} +(-0.886215 - 1.45671i) q^{70} +(-2.45595 - 7.55864i) q^{71} +(-0.142837 + 0.280334i) q^{72} +(1.13052 - 0.179057i) q^{73} +(-6.56708 + 4.77126i) q^{74} +(7.77601 + 2.58225i) q^{75} -5.06519i q^{76} +(-2.40712 - 0.775899i) q^{77} +(-0.988915 - 0.988915i) q^{78} +(-3.11720 + 9.59376i) q^{79} +(0.514972 + 2.17596i) q^{80} +(-6.43745 - 4.67708i) q^{81} +(11.0733 + 5.64213i) q^{82} +(-0.212826 - 0.108440i) q^{83} +(1.01094 + 0.734494i) q^{84} +(1.70093 - 2.75564i) q^{85} +(3.32686 - 10.2390i) q^{86} +(0.791962 + 0.791962i) q^{87} +(2.68776 + 1.94318i) q^{88} +11.2102i q^{89} +(0.701532 - 0.0529317i) q^{90} +(0.526498 - 0.382523i) q^{91} +(-2.31265 + 0.366287i) q^{92} +(-2.61945 + 5.14097i) q^{93} +(-3.92217 - 12.0712i) q^{94} +(-9.67617 + 5.88665i) q^{95} +(-0.963210 - 1.32575i) q^{96} +(6.45889 + 12.6763i) q^{97} +(4.53858 - 4.53858i) q^{98} +(0.736135 - 0.739589i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7}+O(q^{10}) $ 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7	$ 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7} + 12 q^{11} - 16 q^{12} - 16 q^{15} + 12 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{25} + 8 q^{26} + 8 q^{27} - 20 q^{28} + 16 q^{31} - 104 q^{33} - 4 q^{36} + 20 q^{37} - 36 q^{38} - 20 q^{41} - 20 q^{42} + 16 q^{45} + 40 q^{46} + 40 q^{47} + 4 q^{48} + 40 q^{50} + 40 q^{51} + 40 q^{52} + 96 q^{55} - 8 q^{56} + 48 q^{58} + 20 q^{60} + 80 q^{61} + 40 q^{62} + 100 q^{63} + 24 q^{66} + 20 q^{68} - 56 q^{70} - 56 q^{71} - 20 q^{73} - 76 q^{75} - 96 q^{77} + 16 q^{78} - 12 q^{80} - 68 q^{81} - 80 q^{85} - 56 q^{86} - 4 q^{88} - 80 q^{90} - 68 q^{91} - 12 q^{92} + 76 q^{93} + 20 q^{95} + 72 q^{97}+O(q^{100}) $ 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7 + 12 * q^11 - 16 * q^12 - 16 * q^15 + 12 * q^16 - 20 * q^17 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^25 + 8 * q^26 + 8 * q^27 - 20 * q^28 + 16 * q^31 - 104 * q^33 - 4 * q^36 + 20 * q^37 - 36 * q^38 - 20 * q^41 - 20 * q^42 + 16 * q^45 + 40 * q^46 + 40 * q^47 + 4 * q^48 + 40 * q^50 + 40 * q^51 + 40 * q^52 + 96 * q^55 - 8 * q^56 + 48 * q^58 + 20 * q^60 + 80 * q^61 + 40 * q^62 + 100 * q^63 + 24 * q^66 + 20 * q^68 - 56 * q^70 - 56 * q^71 - 20 * q^73 - 76 * q^75 - 96 * q^77 + 16 * q^78 - 12 * q^80 - 68 * q^81 - 80 * q^85 - 56 * q^86 - 4 * q^88 - 80 * q^90 - 68 * q^91 - 12 * q^92 + 76 * q^93 + 20 * q^95 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.891007	−	0.453990i	0.630037	−	0.321020i
$2$	0.891007	−	0.453990i	0.630037	−	0.321020i
$3$	1.61854	+	0.256351i	0.934462	+	0.148004i	0.605055	−	0.796184i	$-0.293151\pi$
$3$	1.61854	+	0.256351i	0.934462	+	0.148004i	0.329407	+	0.944188i	$0.393151\pi$
$4$	0.587785	−	0.809017i	0.293893	−	0.404508i
$5$	−2.22860	−	0.182641i	−0.996659	−	0.0816796i
$5$	−2.22860	−	0.182641i	−0.996659	−	0.0816796i
$6$	1.55851	−	0.506390i	0.636258	−	0.206733i
$7$	0.119289	+	0.753160i	0.0450869	+	0.284668i	0.999922	−	0.0124678i	$-0.00396873\pi$
$7$	0.119289	+	0.753160i	0.0450869	+	0.284668i	−0.954835	+	0.297135i	$0.903969\pi$
$8$	0.156434	−	0.987688i	0.0553079	−	0.349201i
$9$	−0.299227	−	0.0972249i	−0.0997424	−	0.0324083i
$10$	−2.06861	+	0.849027i	−0.654152	+	0.268486i
$11$	−1.49880	+	2.95865i	−0.451904	+	0.892067i
$11$	−1.49880	+	2.95865i	−0.451904	+	0.892067i
$12$	1.15874	−	1.15874i	0.334500	−	0.334500i
$13$	−0.387452	−	0.760418i	−0.107460	−	0.210902i	0.831014	−	0.556251i	$-0.187761\pi$
$13$	−0.387452	−	0.760418i	−0.107460	−	0.210902i	−0.938474	+	0.345349i	$0.887761\pi$
$14$	0.448214	+	0.616914i	0.119790	+	0.164877i
$15$	−3.56024	−	0.866914i	−0.919251	−	0.223836i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	−0.657479	+	1.29037i	−0.159462	+	0.312962i	−0.956889	−	0.290453i	$-0.906194\pi$
$17$	−0.657479	+	1.29037i	−0.159462	+	0.312962i	0.797427	+	0.603415i	$0.206194\pi$
$18$	−0.310753	+	0.0492184i	−0.0732451	+	0.0116009i
$19$	4.09783	−	2.97724i	0.940106	−	0.683027i	−0.00834049	−	0.999965i	$-0.502655\pi$
$19$	4.09783	−	2.97724i	0.940106	−	0.683027i	0.948446	+	0.316939i	$0.102655\pi$
$20$	−1.45770	+	1.69562i	−0.325951	+	0.379152i
$21$			1.24960i			0.272684i
$22$	0.00776159	+	3.31662i	0.00165478	+	0.707105i
$23$	−1.65567	−	1.65567i	−0.345231	−	0.345231i	0.513098	−	0.858330i	$-0.328498\pi$
$23$	−1.65567	−	1.65567i	−0.345231	−	0.345231i	−0.858330	+	0.513098i	$0.828498\pi$
$24$	0.506390	−	1.55851i	0.103366	−	0.318129i
$25$	4.93328	+	0.814066i	0.986657	+	0.162813i
$26$	−0.690445	−	0.501638i	−0.135407	−	0.0983793i
$27$	−4.83969	−	2.46595i	−0.931399	−	0.474572i
$28$	0.679435	+	0.346189i	0.128401	+	0.0654237i
$29$	0.552936	+	0.401731i	0.102678	+	0.0745996i	0.637939	−	0.770087i	$-0.279787\pi$
$29$	0.552936	+	0.401731i	0.102678	+	0.0745996i	−0.535262	+	0.844686i	$0.679787\pi$
$30$	−3.56577	+	0.843891i	−0.651018	+	0.154073i
$31$	−1.08804	+	3.34864i	−0.195417	+	0.601433i	0.804554	+	0.593879i	$0.202404\pi$
$31$	−1.08804	+	3.34864i	−0.195417	+	0.601433i	−0.999971	+	0.00755335i	$0.997596\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−3.18431	+	4.40446i	−0.554317	+	0.766719i
$34$			1.44822i			0.248368i
$35$	−0.128289	−	1.70028i	−0.0216847	−	0.287399i
$36$	−0.254538	+	0.184933i	−0.0424230	+	0.0308221i
$37$	−8.01741	+	1.26983i	−1.31805	+	0.208759i	−0.775546	−	0.631291i	$-0.782525\pi$
$37$	−8.01741	+	1.26983i	−1.31805	+	0.208759i	−0.542509	+	0.840050i	$0.682525\pi$
$38$	2.29955	−	4.51312i	0.373036	−	0.732124i
$39$	−0.432172	−	1.33009i	−0.0692029	−	0.212985i
$40$	−0.529022	+	2.17259i	−0.0836457	+	0.343516i
$41$	7.30492	+	10.0544i	1.14084	+	1.57023i	0.765624	+	0.643288i	$0.222430\pi$
$41$	7.30492	+	10.0544i	1.14084	+	1.57023i	0.375212	+	0.926939i	$0.377570\pi$
$42$	0.567304	+	1.11340i	0.0875370	+	0.171801i
$43$	7.61267	−	7.61267i	1.16092	−	1.16092i	0.176647	−	0.984274i	$-0.443475\pi$
$43$	7.61267	−	7.61267i	1.16092	−	1.16092i	0.984274	−	0.176647i	$-0.0565249\pi$
$44$	1.51263	+	2.95160i	0.228037	+	0.444971i
$45$	0.649100	+	0.271326i	0.0967621	+	0.0404469i
$46$	−2.22687	−	0.723555i	−0.328335	−	0.106682i
$47$	1.98553	−	12.5361i	0.289619	−	1.82858i	−0.228821	−	0.973468i	$-0.573487\pi$
$47$	1.98553	−	12.5361i	0.289619	−	1.82858i	0.518440	−	0.855114i	$-0.326513\pi$
$48$	−0.256351	−	1.61854i	−0.0370011	−	0.233616i
$49$	6.10438	−	1.98343i	0.872054	−	0.283347i
$50$	4.76517	−	1.51433i	0.673896	−	0.214158i
$51$	−1.39494	+	1.91997i	−0.195331	+	0.268850i
$52$	−0.842930	−	0.133507i	−0.116893	−	0.0185141i
$53$	−7.31784	+	3.72862i	−1.00518	+	0.512166i	−0.877463	−	0.479644i	$-0.840766\pi$
$53$	−7.31784	+	3.72862i	−1.00518	+	0.512166i	−0.127719	+	0.991810i	$0.540766\pi$
$54$	−5.43171			−0.739163
$55$	3.88058	−	6.31990i	0.523258	−	0.852174i
$56$	0.762548			0.101900
$57$	7.39570	−	3.76830i	0.979584	−	0.499123i
$58$	0.675052	+	0.106918i	0.0886386	+	0.0140390i
$59$	−0.254349	+	0.350081i	−0.0331134	+	0.0455767i	−0.825253	−	0.564764i	$-0.808967\pi$
$59$	−0.254349	+	0.350081i	−0.0331134	+	0.0455767i	0.792139	+	0.610340i	$0.208967\pi$
$60$	−2.79401	+	2.37074i	−0.360705	+	0.306061i
$61$	12.0627	−	3.91939i	1.54446	−	0.501827i	0.591860	−	0.806040i	$-0.298394\pi$
$61$	12.0627	−	3.91939i	1.54446	−	0.501827i	0.952604	+	0.304214i	$0.0983937\pi$
$62$	0.550800	+	3.47761i	0.0699517	+	0.441657i
$63$	0.0375314	−	0.236964i	0.00472851	−	0.0298546i
$64$	−0.951057	−	0.309017i	−0.118882	−	0.0386271i
$65$	0.724592	+	1.76543i	0.0898745	+	0.218975i
$66$	−0.837655	+	5.37005i	−0.103108	+	0.661008i
$67$	−3.82631	+	3.82631i	−0.467458	+	0.467458i	−0.901090	−	0.433632i	$-0.857232\pi$
$67$	−3.82631	+	3.82631i	−0.467458	+	0.467458i	0.433632	+	0.901090i	$0.357232\pi$
$68$	0.657479	+	1.29037i	0.0797310	+	0.156481i
$69$	−2.25533	−	3.10420i	−0.271510	−	0.373701i
$70$	−0.886215	−	1.45671i	−0.105923	−	0.174111i
$71$	−2.45595	−	7.55864i	−0.291468	−	0.897045i	−0.984385	−	0.176028i	$-0.943675\pi$
$71$	−2.45595	−	7.55864i	−0.291468	−	0.897045i	0.692918	−	0.721017i	$-0.256325\pi$
$72$	−0.142837	+	0.280334i	−0.0168335	+	0.0330377i
$73$	1.13052	−	0.179057i	0.132318	−	0.0209571i	−0.0899243	−	0.995949i	$-0.528663\pi$
$73$	1.13052	−	0.179057i	0.132318	−	0.0209571i	0.222242	+	0.974992i	$0.428663\pi$
$74$	−6.56708	+	4.77126i	−0.763407	+	0.554648i
$75$	7.77601	+	2.58225i	0.897896	+	0.298172i
$76$		−	5.06519i		−	0.581017i
$77$	−2.40712	−	0.775899i	−0.274317	−	0.0884219i
$78$	−0.988915	−	0.988915i	−0.111973	−	0.111973i
$79$	−3.11720	+	9.59376i	−0.350713	+	1.07938i	0.607741	+	0.794135i	$0.292076\pi$
$79$	−3.11720	+	9.59376i	−0.350713	+	1.07938i	−0.958454	+	0.285247i	$0.907924\pi$
$80$	0.514972	+	2.17596i	0.0575756	+	0.243280i
$81$	−6.43745	−	4.67708i	−0.715273	−	0.519676i
$82$	11.0733	+	5.64213i	1.22284	+	0.623070i
$83$	−0.212826	−	0.108440i	−0.0233607	−	0.0119029i	0.442271	−	0.896881i	$-0.354173\pi$
$83$	−0.212826	−	0.108440i	−0.0233607	−	0.0119029i	−0.465632	+	0.884979i	$0.654173\pi$
$84$	1.01094	+	0.734494i	0.110303	+	0.0801398i
$85$	1.70093	−	2.75564i	0.184492	−	0.298891i
$86$	3.32686	−	10.2390i	0.358744	−	1.10410i
$87$	0.791962	+	0.791962i	0.0849073	+	0.0849073i
$88$	2.68776	+	1.94318i	0.286516	+	0.207144i
$89$			11.2102i			1.18828i	0.804361	+	0.594141i	$0.202508\pi$
$89$			11.2102i			1.18828i	−0.804361	+	0.594141i	$0.797492\pi$
$90$	0.701532	−	0.0529317i	0.0739479	−	0.00557949i
$91$	0.526498	−	0.382523i	0.0551919	−	0.0400993i
$92$	−2.31265	+	0.366287i	−0.241110	+	0.0381881i
$93$	−2.61945	+	5.14097i	−0.271625	+	0.533093i
$94$	−3.92217	−	12.0712i	−0.404540	−	1.24505i
$95$	−9.67617	+	5.88665i	−0.992754	+	0.603957i
$96$	−0.963210	−	1.32575i	−0.0983072	−	0.135308i
$97$	6.45889	+	12.6763i	0.655800	+	1.28708i	0.944137	+	0.329552i	$0.106898\pi$
$97$	6.45889	+	12.6763i	0.655800	+	1.28708i	−0.288337	+	0.957529i	$0.593102\pi$
$98$	4.53858	−	4.53858i	0.458466	−	0.458466i
$99$	0.736135	−	0.739589i	0.0739844	−	0.0743315i
$100$	3.55831	−	3.51261i	0.355831	−	0.351261i
$101$	−8.91281	−	2.89595i	−0.886858	−	0.288158i	−0.170056	−	0.985434i	$-0.554395\pi$
$101$	−8.91281	−	2.89595i	−0.886858	−	0.288158i	−0.716802	+	0.697277i	$0.754395\pi$
$102$	−0.371253	+	2.34400i	−0.0367595	+	0.232090i
$103$	0.0154640	+	0.0976359i	0.00152371	+	0.00962035i	0.988438	−	0.151622i	$-0.0484498\pi$
$103$	0.0154640	+	0.0976359i	0.00152371	+	0.00962035i	−0.986915	+	0.161243i	$0.948450\pi$
$104$	−0.811667	+	0.263727i	−0.0795905	+	0.0258605i
$105$	0.228227	−	2.78484i	0.0222727	−	0.271773i
$106$	−4.82748	+	6.64446i	−0.468886	+	0.645367i
$107$	−6.44826	−	1.02130i	−0.623377	−	0.0987332i	−0.163248	−	0.986585i	$-0.552197\pi$
$107$	−6.44826	−	1.02130i	−0.623377	−	0.0987332i	−0.460129	+	0.887852i	$0.652197\pi$
$108$	−4.83969	+	2.46595i	−0.465700	+	0.237286i
$109$	−11.8125			−1.13143			−0.565716	−	0.824600i	$-0.691400\pi$
$109$	−11.8125			−1.13143			−0.565716	+	0.824600i	$0.691400\pi$
$110$	0.588453	−	7.39282i	0.0561068	−	0.704877i
$111$	−13.3020			−1.26257
$112$	0.679435	−	0.346189i	0.0642006	−	0.0327118i
$113$	−11.3861	−	1.80338i	−1.07111	−	0.169647i	−0.404115	−	0.914708i	$-0.632420\pi$
$113$	−11.3861	−	1.80338i	−1.07111	−	0.169647i	−0.666997	+	0.745061i	$0.732420\pi$
$114$	4.87884	−	6.71515i	0.456946	−	0.628932i
$115$	3.38743	+	3.99222i	0.315880	+	0.372276i
$116$	0.650015	−	0.211203i	0.0603524	−	0.0196097i
$117$	0.0420048	+	0.265208i	0.00388335	+	0.0245185i
$118$	−0.0676930	+	0.427397i	−0.00623165	+	0.0393451i
$119$	−1.05029	−	0.341259i	−0.0962797	−	0.0312832i
$120$	−1.41319	+	3.38080i	−0.129006	+	0.308623i
$121$	−6.50722	−	8.86883i	−0.591565	−	0.806257i
$122$	8.96853	−	8.96853i	0.811973	−	0.811973i
$123$	9.24583	+	18.1460i	0.833668	+	1.63617i
$124$	2.06957	+	2.84852i	0.185853	+	0.255805i
$125$	−10.8456	−	2.71525i	−0.970062	−	0.242859i
$126$	−0.0741386	−	0.228175i	−0.00660479	−	0.0203275i
$127$	−2.94658	+	5.78299i	−0.261467	+	0.513157i	−0.983998	−	0.178181i	$-0.942979\pi$
$127$	−2.94658	+	5.78299i	−0.261467	+	0.513157i	0.722531	+	0.691339i	$0.242979\pi$
$128$	−0.987688	+	0.156434i	−0.0873001	+	0.0138270i
$129$	14.2729	−	10.3699i	1.25666	−	0.913015i
$130$	1.44710	+	1.24405i	0.126919	+	0.109111i
$131$			1.56355i			0.136608i	0.997665	+	0.0683040i	$0.0217588\pi$
$131$			1.56355i			0.136608i	−0.997665	+	0.0683040i	$0.978241\pi$
$132$	1.69160	+	5.16504i	0.147235	+	0.449559i
$133$	2.73116	+	2.73116i	0.236822	+	0.236822i
$134$	−1.67216	+	5.14637i	−0.144452	+	0.444579i
$135$	10.3353	+	6.37953i	0.889524	+	0.549062i
$136$	1.17164	+	0.851243i	0.100467	+	0.0729935i
$137$	1.50396	+	0.766306i	0.128492	+	0.0654700i	0.517055	−	0.855952i	$-0.327028\pi$
$137$	1.50396	+	0.766306i	0.128492	+	0.0654700i	−0.388563	+	0.921422i	$0.627028\pi$
$138$	−3.41879	−	1.74196i	−0.291027	−	0.148286i
$139$	−7.01947	−	5.09995i	−0.595384	−	0.432572i	0.248854	−	0.968541i	$-0.419946\pi$
$139$	−7.01947	−	5.09995i	−0.595384	−	0.432572i	−0.844237	+	0.535969i	$0.819946\pi$
$140$	−1.45096	−	0.895609i	−0.122628	−	0.0756928i
$141$	6.42730	−	19.7812i	0.541276	−	1.66588i
$142$	−5.61982	−	5.61982i	−0.471605	−	0.471605i
$143$	2.83052	−	0.00662403i	0.236700	−	0.000553929i
$144$			0.314626i			0.0262189i
$145$	−1.15890	−	0.996286i	−0.0962413	−	0.0827370i
$146$	0.926013	−	0.672788i	0.0766374	−	0.0556803i
$147$	10.3886	−	1.64539i	0.856838	−	0.135710i
$148$	−3.68520	+	7.23261i	−0.302922	+	0.594517i
$149$	4.55529	+	14.0197i	0.373184	+	1.14854i	0.944696	+	0.327948i	$0.106357\pi$
$149$	4.55529	+	14.0197i	0.373184	+	1.14854i	−0.571512	+	0.820594i	$0.693643\pi$
$150$	8.10079	−	1.22944i	0.661427	−	0.100383i
$151$	6.72937	+	9.26219i	0.547629	+	0.753746i	0.989688	−	0.143240i	$-0.0457519\pi$
$151$	6.72937	+	9.26219i	0.547629	+	0.753746i	−0.442059	+	0.896986i	$0.645752\pi$
$152$	−2.29955	−	4.51312i	−0.186518	−	0.366062i
$153$	0.322192	−	0.322192i	0.0260477	−	0.0260477i
$154$	−2.49701	+	0.401481i	−0.201215	+	0.0323522i
$155$	3.03639	−	7.26404i	0.243889	−	0.583461i
$156$	−1.33009	−	0.432172i	−0.106492	−	0.0346014i
$157$	0.128944	−	0.814122i	0.0102909	−	0.0649740i	−0.982008	−	0.188837i	$-0.939528\pi$
$157$	0.128944	−	0.814122i	0.0102909	−	0.0649740i	0.992299	+	0.123863i	$0.0395283\pi$
$158$	1.57803	+	9.96328i	0.125541	+	0.792636i
$159$	−12.8000	+	4.15898i	−1.01511	+	0.329828i
$160$	1.44671	+	1.70500i	0.114372	+	0.134792i
$161$	1.04948	−	1.44449i	0.0827108	−	0.113842i
$162$	−7.85917	−	1.24477i	−0.617474	−	0.0977983i
$163$	−7.96301	+	4.05736i	−0.623711	+	0.317797i	−0.737131	−	0.675750i	$-0.763820\pi$
$163$	−7.96301	+	4.05736i	−0.623711	+	0.317797i	0.113419	+	0.993547i	$0.463820\pi$
$164$	12.4279			0.970454
$165$	7.90097	−	9.23419i	0.615090	−	0.718880i
$166$	−0.238860			−0.0185391
$167$	18.8224	−	9.59049i	1.45652	−	0.742134i	0.466695	−	0.884418i	$-0.345445\pi$
$167$	18.8224	−	9.59049i	1.45652	−	0.742134i	0.989826	+	0.142284i	$0.0454447\pi$
$168$	1.23421	+	0.195480i	0.0952214	+	0.0150816i
$169$	7.21309	−	9.92797i	0.554853	−	0.763690i
$170$	0.264505	−	3.22750i	0.0202866	−	0.247538i
$171$	−1.51564	+	0.492462i	−0.115904	+	0.0376595i
$172$	−1.68416	−	10.6334i	−0.128416	−	0.810788i
$173$	−0.384613	+	2.42835i	−0.0292416	+	0.184624i	−0.997986	−	0.0634376i	$-0.979794\pi$
$173$	−0.384613	+	2.42835i	−0.0292416	+	0.184624i	0.968744	+	0.248062i	$0.0797936\pi$
$174$	1.06519	+	0.346100i	0.0807516	+	0.0262378i
$175$	−0.0246365	+	3.81266i	−0.00186234	+	0.288210i
$176$	3.27700	+	0.511167i	0.247013	+	0.0385307i
$177$	−0.501417	+	0.501417i	−0.0376888	+	0.0376888i
$178$	5.08934	+	9.98839i	0.381462	+	0.748661i
$179$	−9.35481	−	12.8758i	−0.699211	−	0.962382i	−0.999962	−	0.00867926i	$-0.997237\pi$
$179$	−9.35481	−	12.8758i	−0.699211	−	0.962382i	0.300751	−	0.953703i	$-0.402763\pi$
$180$	0.601039	−	0.365651i	0.0447988	−	0.0272540i
$181$	−1.59094	−	4.89640i	−0.118253	−	0.363947i	0.874358	−	0.485281i	$-0.161283\pi$
$181$	−1.59094	−	4.89640i	−0.118253	−	0.363947i	−0.992612	+	0.121334i	$0.961283\pi$
$182$	0.295451	−	0.579855i	0.0219003	−	0.0429817i
$183$	20.5286	−	3.25141i	1.51752	−	0.240351i
$184$	−1.89429	+	1.37628i	−0.139649	+	0.101461i
$185$	18.0995	−	1.36564i	1.33070	−	0.100404i
$186$			5.76984i			0.423065i
$187$	−2.83234	−	3.87926i	−0.207121	−	0.283679i
$188$	−8.97488	−	8.97488i	−0.654560	−	0.654560i
$189$	1.27993	−	3.93922i	0.0931012	−	0.286536i
$190$	−5.94905	+	9.63793i	−0.431589	+	0.699209i
$191$	21.7592	+	15.8090i	1.57444	+	1.14390i	0.922744	+	0.385413i	$0.125941\pi$
$191$	21.7592	+	15.8090i	1.57444	+	1.14390i	0.651693	+	0.758482i	$0.274059\pi$
$192$	−1.46010	−	0.743959i	−0.105374	−	0.0536906i
$193$	−8.62943	−	4.39692i	−0.621160	−	0.316497i	0.114937	−	0.993373i	$-0.463333\pi$
$193$	−8.62943	−	4.39692i	−0.621160	−	0.316497i	−0.736097	+	0.676876i	$0.763333\pi$
$194$	11.5098	+	8.36237i	0.826357	+	0.600383i
$195$	0.720208	+	3.04316i	0.0515752	+	0.217925i
$196$	1.98343	−	6.10438i	0.141674	−	0.436027i
$197$	5.96449	+	5.96449i	0.424952	+	0.424952i	0.886905	−	0.461952i	$-0.152851\pi$
$197$	5.96449	+	5.96449i	0.424952	+	0.424952i	−0.461952	+	0.886905i	$0.652851\pi$
$198$	0.320135	−	0.993177i	0.0227510	−	0.0705820i
$199$			0.826885i			0.0586163i	0.999570	+	0.0293082i	$0.00933042\pi$
$199$			0.826885i			0.0586163i	−0.999570	+	0.0293082i	$0.990670\pi$
$200$	1.57578	−	4.74520i	0.111424	−	0.335536i
$201$	−7.17389	+	5.21214i	−0.506007	+	0.367636i
$202$	−9.25610	+	1.46602i	−0.651257	+	0.103149i
$203$	−0.236609	+	0.464371i	−0.0166067	+	0.0325924i
$204$	0.733364	+	2.25706i	0.0513458	+	0.158026i
$205$	−14.4434	−	23.7413i	−1.00877	−	1.65816i
$206$	0.0581043	+	0.0799737i	0.00404832	+	0.00557203i
$207$	0.334450	+	0.656395i	0.0232459	+	0.0456226i
$208$	−0.603471	+	0.603471i	−0.0418432	+	0.0418432i
$209$	2.66682	+	16.5863i	0.184468	+	1.14730i
$210$	−1.06094	−	2.58493i	−0.0732119	−	0.178377i
$211$	−13.8523	−	4.50087i	−0.953629	−	0.309853i	−0.209440	−	0.977822i	$-0.567164\pi$
$211$	−13.8523	−	4.50087i	−0.953629	−	0.309853i	−0.744190	+	0.667969i	$0.767164\pi$
$212$	−1.28480	+	8.11188i	−0.0882402	+	0.557126i
$213$	−2.03738	−	12.8635i	−0.139599	−	0.881393i
$214$	−6.20910	+	2.01746i	−0.424446	+	0.137911i
$215$	−18.3559	+	15.5752i	−1.25187	+	1.06222i
$216$	−3.19268	+	4.39435i	−0.217234	+	0.298998i
$217$	−2.65185	−	0.420011i	−0.180019	−	0.0285122i
$218$	−10.5250	+	5.36276i	−0.712844	+	0.363212i
$219$	1.87569			0.126748
$220$	−2.83195	−	6.85420i	−0.190930	−	0.462110i
$221$	1.23597			0.0831401
$222$	−11.8522	+	6.03898i	−0.795465	+	0.405310i
$223$	−1.32935	−	0.210549i	−0.0890201	−	0.0140994i	0.111766	−	0.993735i	$-0.464349\pi$
$223$	−1.32935	−	0.210549i	−0.0890201	−	0.0140994i	−0.200786	+	0.979635i	$0.564349\pi$
$224$	0.448214	−	0.616914i	0.0299476	−	0.0412193i
$225$	−1.39703	−	0.723229i	−0.0931351	−	0.0482152i
$226$	−10.9638	+	3.56235i	−0.729300	+	0.236964i
$227$	−0.321020	−	2.02684i	−0.0213068	−	0.134526i	0.974742	−	0.223334i	$-0.0716941\pi$
$227$	−0.321020	−	2.02684i	−0.0213068	−	0.134526i	−0.996049	+	0.0888083i	$0.971694\pi$
$228$	1.29847	−	8.19819i	0.0859930	−	0.542939i
$229$	−17.0466	−	5.53877i	−1.12647	−	0.366012i	−0.314237	−	0.949345i	$-0.601749\pi$
$229$	−17.0466	−	5.53877i	−1.12647	−	0.366012i	−0.812234	+	0.583332i	$0.801749\pi$
$230$	4.83065	+	2.01923i	0.318524	+	0.133144i
$231$	−3.69712	−	1.87289i	−0.243252	−	0.123227i
$232$	0.483284	−	0.483284i	0.0317291	−	0.0317291i
$233$	−11.1608	−	21.9042i	−0.731166	−	1.43499i	−0.893873	−	0.448320i	$-0.852023\pi$
$233$	−11.1608	−	21.9042i	−0.731166	−	1.43499i	0.162707	−	0.986674i	$-0.447977\pi$
$234$	0.157828	+	0.217232i	0.0103176	+	0.0142009i
$235$	−6.71455	+	27.5753i	−0.438009	+	1.79882i
$236$	0.133719	+	0.411545i	0.00870438	+	0.0267893i
$237$	−7.50467	+	14.7287i	−0.487481	+	0.956735i
$238$	−1.09074	+	0.172757i	−0.0707023	+	0.0111981i
$239$	−2.40071	+	1.74422i	−0.155289	+	0.112824i	−0.662717	−	0.748870i	$-0.730597\pi$
$239$	−2.40071	+	1.74422i	−0.155289	+	0.112824i	0.507427	+	0.861695i	$0.330597\pi$
$240$	0.275692	+	3.65388i	0.0177958	+	0.235857i
$241$			21.2858i			1.37114i	0.728007	+	0.685570i	$0.240447\pi$
$241$			21.2858i			1.37114i	−0.728007	+	0.685570i	$0.759553\pi$
$242$	−9.82434	−	4.94797i	−0.631532	−	0.318067i
$243$	2.30213	+	2.30213i	0.147682	+	0.147682i
$244$	3.91939	−	12.0627i	0.250913	−	0.772232i
$245$	−13.9664	+	3.30536i	−0.892284	+	0.211172i
$246$	16.4762	+	11.9707i	1.05048	+	0.763221i
$247$	−3.85166	−	1.96252i	−0.245075	−	0.124872i
$248$	3.13720	+	1.59848i	0.199212	+	0.101504i
$249$	−0.316667	−	0.230072i	−0.0200680	−	0.0145802i
$250$	−10.8962	+	2.50451i	−0.689137	+	0.158399i
$251$	4.10394	−	12.6306i	0.259038	−	0.797238i	−0.733969	−	0.679183i	$-0.762334\pi$
$251$	4.10394	−	12.6306i	0.259038	−	0.797238i	0.993007	−	0.118055i	$-0.0376658\pi$
$252$	−0.169647	−	0.169647i	−0.0106868	−	0.0106868i
$253$	7.38007	−	2.41704i	0.463981	−	0.151958i
$254$			6.49040i			0.407244i
$255$	3.45943	−	4.02407i	0.216638	−	0.251997i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	18.2813	−	2.89548i	1.14036	−	0.180615i	0.442444	−	0.896796i	$-0.354112\pi$
$257$	18.2813	−	2.89548i	1.14036	−	0.180615i	0.697914	+	0.716181i	$0.254112\pi$
$258$	8.00942	−	15.7194i	0.498645	−	0.978645i
$259$	−1.91277	−	5.88692i	−0.118854	−	0.365795i
$260$	1.85417	+	0.451487i	0.114991	+	0.0280000i
$261$	−0.126395	−	0.173968i	−0.00782367	−	0.0107684i
$262$	0.709837	+	1.39313i	0.0438539	+	0.0860681i
$263$	17.4405	−	17.4405i	1.07543	−	1.07543i	0.0785172	−	0.996913i	$-0.474981\pi$
$263$	17.4405	−	17.4405i	1.07543	−	1.07543i	0.996913	−	0.0785172i	$-0.0250185\pi$
$264$	3.85210	+	3.83411i	0.237080	+	0.235973i
$265$	16.9895	−	6.97306i	1.04366	−	0.428352i
$266$	3.67341	+	1.19356i	0.225231	+	0.0731820i
$267$	−2.87375	+	18.1442i	−0.175871	+	1.11040i
$268$	0.846501	+	5.34459i	0.0517083	+	0.326473i
$269$	19.3677	−	6.29294i	1.18087	−	0.383687i	0.348179	−	0.937428i	$-0.386800\pi$
$269$	19.3677	−	6.29294i	1.18087	−	0.383687i	0.832689	+	0.553741i	$0.186800\pi$
$270$	12.1051	+	0.992054i	0.736693	+	0.0603745i
$271$	4.38344	−	6.03328i	0.266275	−	0.366496i	−0.654853	−	0.755756i	$-0.727269\pi$
$271$	4.38344	−	6.03328i	0.266275	−	0.366496i	0.921128	+	0.389261i	$0.127269\pi$
$272$	1.43039	+	0.226552i	0.0867302	+	0.0137367i
$273$	0.950215	−	0.484159i	0.0575096	−	0.0293026i
$274$	1.68793			0.101972
$275$	−9.80253	+	13.3757i	−0.591115	+	0.806588i
$276$	−3.83700			−0.230960
$277$	−14.5902	+	7.43406i	−0.876638	+	0.446669i	−0.833577	−	0.552403i	$-0.813711\pi$
$277$	−14.5902	+	7.43406i	−0.876638	+	0.446669i	−0.0430609	+	0.999072i	$0.513711\pi$
$278$	−8.56972	−	1.35731i	−0.513978	−	0.0814061i
$279$	0.651141	−	0.896219i	0.0389828	−	0.0536552i
$280$	−1.69941	−	0.139273i	−0.101559	−	0.00832312i
$281$	3.98244	−	1.29397i	0.237572	−	0.0771919i	−0.187811	−	0.982205i	$-0.560139\pi$
$281$	3.98244	−	1.29397i	0.237572	−	0.0771919i	0.425383	+	0.905013i	$0.360139\pi$
$282$	−3.25371	−	20.5431i	−0.193755	−	1.22332i
$283$	4.32395	−	27.3003i	0.257032	−	1.62284i	−0.434626	−	0.900611i	$-0.643119\pi$
$283$	4.32395	−	27.3003i	0.257032	−	1.62284i	0.691658	−	0.722225i	$-0.256881\pi$
$284$	−7.55864	−	2.45595i	−0.448523	−	0.145734i
$285$	−17.1703	+	7.04725i	−1.01708	+	0.417443i
$286$	2.51901	−	1.29093i	0.148952	−	0.0763345i
$287$	−6.70114	+	6.70114i	−0.395556	+	0.395556i
$288$	0.142837	+	0.280334i	0.00841677	+	0.0165188i
$289$	8.75956	+	12.0565i	0.515268	+	0.709206i
$290$	−1.48489	−	0.361568i	−0.0871958	−	0.0212320i
$291$	7.20436	+	22.1727i	0.422327	+	1.29979i
$292$	0.519644	−	1.01986i	0.0304099	−	0.0596827i
$293$	18.4662	−	2.92476i	1.07881	−	0.170866i	0.408357	−	0.912822i	$-0.366102\pi$
$293$	18.4662	−	2.92476i	1.07881	−	0.170866i	0.670448	+	0.741956i	$0.266102\pi$
$294$	8.50932	−	6.18238i	0.496274	−	0.360564i
$295$	0.630780	−	0.733735i	0.0367255	−	0.0427197i
$296$			8.11735i			0.471812i
$297$	14.5496	−	10.6230i	0.844253	−	0.616409i
$298$	10.4236	+	10.4236i	0.603824	+	0.603824i
$299$	−0.617509	+	1.90050i	−0.0357115	+	0.109909i
$300$	6.65971	−	4.77312i	0.384498	−	0.275576i
$301$	6.64166	+	4.82545i	0.382819	+	0.278134i
$302$	10.2009	+	5.19760i	0.586994	+	0.299088i
$303$	−13.6833	−	6.97200i	−0.786086	−	0.400531i
$304$	−4.09783	−	2.97724i	−0.235026	−	0.170757i
$305$	−27.5986	+	6.53161i	−1.58029	+	0.373999i
$306$	0.140803	−	0.433347i	0.00804918	−	0.0247728i
$307$	−7.13262	−	7.13262i	−0.407080	−	0.407080i	0.473639	−	0.880719i	$-0.342940\pi$
$307$	−7.13262	−	7.13262i	−0.407080	−	0.407080i	−0.880719	+	0.473639i	$0.842940\pi$
$308$	−2.04259	+	1.49134i	−0.116387	+	0.0849771i
$309$			0.161991i			0.00921537i
$310$	−0.592356	−	7.85080i	−0.0336436	−	0.445895i
$311$	18.5344	−	13.4660i	1.05099	−	0.763589i	0.0785899	−	0.996907i	$-0.474958\pi$
$311$	18.5344	−	13.4660i	1.05099	−	0.763589i	0.972401	+	0.233318i	$0.0749582\pi$
$312$	−1.38132	+	0.218779i	−0.0782018	+	0.0123859i
$313$	−6.57514	+	12.9044i	−0.371649	+	0.729402i	−0.998773	−	0.0495173i	$-0.984232\pi$
$313$	−6.57514	+	12.9044i	−0.371649	+	0.729402i	0.627125	+	0.778919i	$0.284232\pi$
$314$	−0.254714	−	0.783928i	−0.0143743	−	0.0442396i
$315$	−0.126922	+	0.521242i	−0.00715122	+	0.0293686i
$316$	5.92927	+	8.16094i	0.333547	+	0.459089i
$317$	1.01556	+	1.99314i	0.0570393	+	0.111946i	0.917766	−	0.397121i	$-0.129991\pi$
$317$	1.01556	+	1.99314i	0.0570393	+	0.111946i	−0.860727	+	0.509067i	$0.829991\pi$
$318$	−9.51676	+	9.51676i	−0.533673	+	0.533673i
$319$	−2.01732	+	1.03383i	−0.112948	+	0.0578834i
$320$	2.06308	+	0.862376i	0.115330	+	0.0482083i
$321$	−10.1749	−	3.30603i	−0.567909	−	0.184525i
$322$	0.279311	−	1.76350i	0.0155654	−	0.0982762i
$323$	1.14753	+	7.24520i	0.0638501	+	0.403134i
$324$	−7.56768	+	2.45889i	−0.420427	+	0.136605i
$325$	−1.29238	−	4.06677i	−0.0716885	−	0.225584i
$326$	−5.25310	+	7.23027i	−0.290942	+	0.400447i
$327$	−19.1190	−	3.02815i	−1.05728	−	0.167457i
$328$	11.0733	−	5.64213i	0.611421	−	0.311535i
$329$	9.67856			0.533596
$330$	2.84759	−	11.8147i	0.156754	−	0.650377i
$331$	1.96672			0.108101			0.0540503	−	0.998538i	$-0.482787\pi$
$331$	1.96672			0.108101			0.0540503	+	0.998538i	$0.482787\pi$
$332$	−0.212826	+	0.108440i	−0.0116803	+	0.00595143i
$333$	2.52249	+	0.399523i	0.138232	+	0.0218937i
$334$	12.4169	−	17.0904i	0.679422	−	0.935144i
$335$	9.22613	−	7.82845i	0.504078	−	0.427714i
$336$	1.18844	−	0.386146i	0.0648345	−	0.0210660i
$337$	0.0634205	+	0.400422i	0.00345474	+	0.0218123i	0.989355	−	0.145519i	$-0.0464851\pi$
$337$	0.0634205	+	0.400422i	0.00345474	+	0.0218123i	−0.985901	+	0.167331i	$0.946485\pi$
$338$	1.91971	−	12.1206i	0.104418	−	0.659272i
$339$	−17.9665	−	5.83766i	−0.975805	−	0.317058i
$340$	−1.22958	−	2.99581i	−0.0666833	−	0.162470i
$341$	−8.27669	−	8.23804i	−0.448208	−	0.446115i
$342$	−1.12687	+	1.12687i	−0.0609344	+	0.0609344i
$343$	4.64535	+	9.11701i	0.250825	+	0.492272i
$344$	−6.32806	−	8.70983i	−0.341186	−	0.469602i
$345$	4.45927	+	7.32992i	0.240079	+	0.394630i
$346$	0.759756	+	2.33829i	0.0408447	+	0.125707i
$347$	4.85384	−	9.52619i	0.260568	−	0.511393i	−0.723245	−	0.690591i	$-0.757350\pi$
$347$	4.85384	−	9.52619i	0.260568	−	0.511393i	0.983813	+	0.179198i	$0.0573504\pi$
$348$	1.10621	−	0.175207i	0.0592993	−	0.00939209i
$349$	6.50852	−	4.72872i	0.348393	−	0.253123i	−0.399801	−	0.916602i	$-0.630921\pi$
$349$	6.50852	−	4.72872i	0.348393	−	0.253123i	0.748195	+	0.663479i	$0.230921\pi$
$350$	1.70896	+	3.40829i	0.0913477	+	0.182181i
$351$			4.63563i			0.247432i
$352$	3.15189	−	1.03227i	0.167996	−	0.0550203i
$353$	17.8934	+	17.8934i	0.952372	+	0.952372i	0.998916	−	0.0465446i	$-0.0148210\pi$
$353$	17.8934	+	17.8934i	0.952372	+	0.952372i	−0.0465446	+	0.998916i	$0.514821\pi$
$354$	−0.219127	+	0.674404i	−0.0116465	+	0.0358442i
$355$	4.09280	+	17.2937i	0.217223	+	0.917855i
$356$	9.06926	+	6.58921i	0.480670	+	0.349227i
$357$	−1.61245	−	0.821582i	−0.0853397	−	0.0434828i
$358$	−14.1807	−	7.22542i	−0.749473	−	0.381875i
$359$	13.1469	+	9.55175i	0.693864	+	0.504122i	0.877928	−	0.478792i	$-0.158925\pi$
$359$	13.1469	+	9.55175i	0.693864	+	0.504122i	−0.184064	+	0.982914i	$0.558925\pi$
$360$	0.369527	−	0.598663i	0.0194758	−	0.0315523i
$361$	2.05687	−	6.33038i	0.108256	−	0.333178i
$362$	−3.64046	−	3.64046i	−0.191338	−	0.191338i
$363$	−8.25863	−	16.0226i	−0.433466	−	0.840971i
$364$		−	0.650787i		−	0.0341105i
$365$	−2.55218	+	0.192566i	−0.133587	+	0.0100794i
$366$	16.8150	−	12.2168i	0.878933	−	0.638582i
$367$	8.46611	−	1.34090i	0.441927	−	0.0699944i	0.0684942	−	0.997652i	$-0.478181\pi$
$367$	8.46611	−	1.34090i	0.441927	−	0.0699944i	0.373433	+	0.927657i	$0.378181\pi$
$368$	−1.06301	+	2.08627i	−0.0554131	+	0.108754i
$369$	−1.20830	−	3.71876i	−0.0629015	−	0.193591i
$370$	15.5068	−	9.43380i	0.806160	−	0.490440i
$371$	−3.68118	−	5.06672i	−0.191118	−	0.263051i
$372$	2.61945	+	5.14097i	0.135812	+	0.266547i
$373$	−23.2440	+	23.2440i	−1.20353	+	1.20353i	−0.230446	+	0.973085i	$0.574018\pi$
$373$	−23.2440	+	23.2440i	−1.20353	+	1.20353i	−0.973085	+	0.230446i	$0.925982\pi$
$374$	−4.28478	−	2.17059i	−0.221561	−	0.112238i
$375$	−16.8580	−	7.17501i	−0.870542	−	0.370516i
$376$	−12.0712	−	3.92217i	−0.622524	−	0.202270i
$377$	0.0912475	−	0.576114i	0.00469949	−	0.0296714i
$378$	−0.647942	−	4.09095i	−0.0333266	−	0.210416i
$379$	12.1822	−	3.95823i	0.625757	−	0.203321i	0.0210622	−	0.999778i	$-0.493295\pi$
$379$	12.1822	−	3.95823i	0.625757	−	0.203321i	0.604695	+	0.796457i	$0.293295\pi$
$380$	−0.925112	+	11.2883i	−0.0474572	+	0.579076i
$381$	−6.25162	+	8.60462i	−0.320280	+	0.440828i
$382$	26.5647	+	4.20743i	1.35917	+	0.215271i
$383$	−19.8586	+	10.1184i	−1.01473	+	0.517028i	−0.880562	−	0.473931i	$-0.842835\pi$
$383$	−19.8586	+	10.1184i	−1.01473	+	0.517028i	−0.134163	+	0.990959i	$0.542835\pi$
$384$	−1.63871			−0.0836251
$385$	5.22280	+	2.16881i	0.266178	+	0.110533i
$386$	−9.68504			−0.492955
$387$	−3.01806	+	1.53778i	−0.153417	+	0.0781696i
$388$	14.0518	+	2.22558i	0.713370	+	0.112987i
$389$	−8.06422	+	11.0995i	−0.408872	+	0.562765i	−0.962943	−	0.269705i	$-0.913074\pi$
$389$	−8.06422	+	11.0995i	−0.408872	+	0.562765i	0.554071	+	0.832470i	$0.313074\pi$
$390$	2.02328	+	2.38451i	0.102453	+	0.120744i
$391$	3.22501	−	1.04787i	0.163096	−	0.0529930i
$392$	−1.00408	−	6.33950i	−0.0507136	−	0.320193i
$393$	−0.400817	+	2.53066i	−0.0202186	+	0.127655i
$394$	8.02222	+	2.60658i	0.404154	+	0.131318i
$395$	8.69920	−	20.8113i	0.437704	−	1.04713i
$396$	−0.165650	−	1.03027i	−0.00832425	−	0.0517728i
$397$	−0.807418	+	0.807418i	−0.0405232	+	0.0405232i	−0.727078	−	0.686555i	$-0.759122\pi$
$397$	−0.807418	+	0.807418i	−0.0405232	+	0.0405232i	0.686555	+	0.727078i	$0.259122\pi$
$398$	0.375398	+	0.736760i	0.0188170	+	0.0369304i
$399$	3.72035	+	5.12062i	0.186251	+	0.256352i
$400$	−0.750246	−	4.94339i	−0.0375123	−	0.247170i
$401$	4.25930	+	13.1088i	0.212700	+	0.654622i	0.999309	+	0.0371709i	$0.0118346\pi$
$401$	4.25930	+	13.1088i	0.212700	+	0.654622i	−0.786609	+	0.617451i	$0.788165\pi$
$402$	−4.02572	+	7.90093i	−0.200785	+	0.394062i
$403$	2.96793	−	0.470073i	0.147843	−	0.0234160i
$404$	−7.58169	+	5.50842i	−0.377203	+	0.274054i
$405$	13.4923	+	11.5991i	0.670436	+	0.576363i
$406$			0.521176i			0.0258655i
$407$	8.25948	−	25.6239i	0.409407	−	1.27013i
$408$	1.67812	+	1.67812i	0.0830792	+	0.0830792i
$409$	−6.24805	+	19.2295i	−0.308946	+	0.950839i	0.669229	+	0.743056i	$0.266625\pi$
$409$	−6.24805	+	19.2295i	−0.308946	+	0.950839i	−0.978175	+	0.207782i	$0.933375\pi$
$410$	−23.6475	−	14.5965i	−1.16786	−	0.720869i
$411$	2.23777	+	1.62584i	0.110381	+	0.0801966i
$412$	0.0880786	+	0.0448783i	0.00433932	+	0.00221099i
$413$	−0.294008	−	0.149805i	−0.0144672	−	0.00737140i
$414$	0.595994	+	0.433015i	0.0292915	+	0.0212815i
$415$	0.454497	+	0.280540i	0.0223104	+	0.0137712i
$416$	−0.263727	+	0.811667i	−0.0129303	+	0.0397953i
$417$	−10.0539	−	10.0539i	−0.492341	−	0.492341i
$418$	9.90618	+	13.5678i	0.484527	+	0.663623i
$419$		−	19.4960i		−	0.952442i	−0.879326	−	0.476221i	$-0.842006\pi$
$419$		−	19.4960i		−	0.952442i	0.879326	−	0.476221i	$-0.157994\pi$
$420$	−2.11884	−	1.82153i	−0.103389	−	0.0888816i
$421$	−2.31295	+	1.68045i	−0.112726	+	0.0819003i	−0.642720	−	0.766101i	$-0.722194\pi$
$421$	−2.31295	+	1.68045i	−0.112726	+	0.0819003i	0.529994	+	0.848001i	$0.322194\pi$
$422$	−14.3858	+	2.27849i	−0.700290	+	0.110915i
$423$	−1.81295	+	3.55811i	−0.0881485	+	0.173001i
$424$	2.53796	+	7.81103i	0.123254	+	0.379337i
$425$	−4.29398	+	5.83055i	−0.208289	+	0.282823i
$426$	−7.65523	−	10.5365i	−0.370897	−	0.510496i
$427$	4.39087	+	8.61756i	0.212489	+	0.417033i
$428$	−4.61644	+	4.61644i	−0.223144	+	0.223144i
$429$	4.58300	+	0.714886i	0.221269	+	0.0345150i
$430$	−9.28429	+	22.2110i	−0.447728	+	1.07111i
$431$	−15.3238	−	4.97899i	−0.738120	−	0.239830i	−0.0842582	−	0.996444i	$-0.526852\pi$
$431$	−15.3238	−	4.97899i	−0.738120	−	0.239830i	−0.653861	+	0.756614i	$0.726852\pi$
$432$	−0.849707	+	5.36484i	−0.0408816	+	0.258116i
$433$	−3.82063	−	24.1225i	−0.183608	−	1.15925i	−0.891529	−	0.452963i	$-0.850367\pi$
$433$	−3.82063	−	24.1225i	−0.183608	−	1.15925i	0.707922	−	0.706291i	$-0.249633\pi$
$434$	−2.55349	+	0.829681i	−0.122572	+	0.0398259i
$435$	−1.62032	−	1.90961i	−0.0776884	−	0.0915587i
$436$	−6.94322	+	9.55652i	−0.332520	+	0.457674i
$437$	−11.7140	−	1.85531i	−0.560356	−	0.0887517i
$438$	1.67125	−	0.851547i	0.0798556	−	0.0406885i
$439$	13.2566			0.632702			0.316351	−	0.948642i	$-0.397542\pi$
$439$	13.2566			0.632702			0.316351	+	0.948642i	$0.397542\pi$
$440$	−5.63503	−	4.82146i	−0.268640	−	0.229854i
$441$	−2.01944			−0.0961636
$442$	1.10125	−	0.561117i	0.0523813	−	0.0266896i
$443$	−2.15069	−	0.340637i	−0.102183	−	0.0161841i	0.105134	−	0.994458i	$-0.466473\pi$
$443$	−2.15069	−	0.340637i	−0.102183	−	0.0161841i	−0.207316	+	0.978274i	$0.566473\pi$
$444$	−7.81872	+	10.7615i	−0.371060	+	0.510720i
$445$	2.04745	−	24.9831i	0.0970583	−	1.18431i
$446$	−1.28005	+	0.415913i	−0.0606121	+	0.0196941i
$447$	3.77893	+	23.8592i	0.178737	+	1.12850i
$448$	0.119289	−	0.753160i	0.00563586	−	0.0355834i
$449$	4.58948	+	1.49121i	0.216591	+	0.0703747i	0.415303	−	0.909683i	$-0.363676\pi$
$449$	4.58948	+	1.49121i	0.216591	+	0.0703747i	−0.198712	+	0.980058i	$0.563676\pi$
$450$	−1.57310	−	0.0101650i	−0.0741566	−	0.000479182i
$451$	−40.6959	+	6.54326i	−1.91630	+	0.308110i
$452$	−8.15153	+	8.15153i	−0.383416	+	0.383416i
$453$	8.51736	+	16.7163i	0.400181	+	0.785399i
$454$	−1.20620	−	1.66019i	−0.0566096	−	0.0779164i
$455$	−1.24321	+	0.756329i	−0.0582828	+	0.0354573i
$456$	−2.56496	−	7.89413i	−0.120115	−	0.369677i
$457$	9.29594	−	18.2443i	0.434846	−	0.853433i	−0.564757	−	0.825257i	$-0.691030\pi$
$457$	9.29594	−	18.2443i	0.434846	−	0.853433i	0.999603	−	0.0281758i	$-0.00896981\pi$
$458$	−17.7032	+	2.80391i	−0.827215	+	0.131018i
$459$	6.36399	−	4.62371i	0.297046	−	0.215816i
$460$	5.22085	−	0.393922i	0.243424	−	0.0183667i
$461$			0.616244i			0.0287013i	0.999897	+	0.0143507i	$0.00456812\pi$
$461$			0.616244i			0.0287013i	−0.999897	+	0.0143507i	$0.995432\pi$
$462$	−4.14443	+	0.00969884i	−0.192816	+	0.000451231i
$463$	−13.5983	−	13.5983i	−0.631968	−	0.631968i	0.316593	−	0.948561i	$-0.397461\pi$
$463$	−13.5983	−	13.5983i	−0.631968	−	0.631968i	−0.948561	+	0.316593i	$0.897461\pi$
$464$	0.211203	−	0.650015i	0.00980484	−	0.0301762i
$465$	6.77666	−	10.9787i	0.314260	−	0.509126i
$466$	−19.8886	−	14.4499i	−0.921323	−	0.669380i
$467$	−1.38491	−	0.705649i	−0.0640862	−	0.0326535i	0.421654	−	0.906757i	$-0.361450\pi$
$467$	−1.38491	−	0.705649i	−0.0640862	−	0.0326535i	−0.485740	+	0.874103i	$0.661450\pi$
$468$	0.239248	+	0.121903i	0.0110592	+	0.00563495i
$469$	−3.33825	−	2.42538i	−0.154146	−	0.111994i
$470$	6.53623	+	27.6181i	0.301494	+	1.27393i
$471$	0.417402	−	1.28463i	0.0192329	−	0.0591927i
$472$	0.305982	+	0.305982i	0.0140840	+	0.0140840i
$473$	11.1134	+	33.9331i	0.510994	+	1.56024i
$474$			16.5305i			0.759269i
$475$	22.6394	−	11.3517i	1.03877	−	0.520851i
$476$	−0.893428	+	0.649114i	−0.0409502	+	0.0297521i
$477$	2.55221	−	0.404231i	0.116858	−	0.0185084i
$478$	−1.34719	+	2.64401i	−0.0616191	+	0.120934i
$479$	−7.47583	−	23.0082i	−0.341579	−	1.05127i	−0.963390	−	0.268105i	$-0.913603\pi$
$479$	−7.47583	−	23.0082i	−0.341579	−	1.05127i	0.621810	−	0.783168i	$-0.286397\pi$
$480$	1.90447	+	3.13047i	0.0869268	+	0.142886i
$481$	4.07197	+	5.60459i	0.185666	+	0.255547i
$482$	9.66356	+	18.9658i	0.440163	+	0.863869i
$483$	2.06892	−	2.06892i	0.0941391	−	0.0941391i
$484$	−10.9999	+	0.0514844i	−0.499995	+	0.00234020i
$485$	−12.0790	−	29.4300i	−0.548481	−	1.33635i
$486$	3.09636	+	1.00607i	0.140454	+	0.0456362i
$487$	−2.93550	+	18.5340i	−0.133020	+	0.839857i	0.827463	+	0.561520i	$0.189783\pi$
$487$	−2.93550	+	18.5340i	−0.133020	+	0.839857i	−0.960483	+	0.278337i	$0.910217\pi$
$488$	−1.98412	−	12.5273i	−0.0898171	−	0.567083i
$489$	−13.9285	+	4.52565i	−0.629870	+	0.204657i
$490$	−10.9436	+	9.28573i	−0.494381	+	0.419487i
$491$	14.9190	−	20.5343i	0.673285	−	0.926698i	−0.326544	−	0.945182i	$-0.605884\pi$
$491$	14.9190	−	20.5343i	0.673285	−	0.926698i	0.999829	+	0.0184843i	$0.00588406\pi$
$492$	20.1150	+	3.18590i	0.906852	+	0.143631i
$493$	−0.881928	+	0.449365i	−0.0397200	+	0.0202384i
$494$	−4.32282			−0.194493
$495$	−1.77563	+	1.51380i	−0.0798085	+	0.0680401i
$496$	3.52096			0.158096
$497$	5.39989	−	2.75138i	0.242218	−	0.123416i
$498$	−0.386603	−	0.0612320i	−0.0173241	−	0.00274387i
$499$	−5.36524	+	7.38462i	−0.240181	+	0.330581i	−0.912042	−	0.410096i	$-0.865495\pi$
$499$	−5.36524	+	7.38462i	−0.240181	+	0.330581i	0.671861	+	0.740677i	$0.265495\pi$
$500$	−8.57157	+	7.17831i	−0.383332	+	0.321024i
$501$	32.9232	−	10.6974i	1.47090	−	0.477925i
$502$	−2.07755	−	13.1171i	−0.0927255	−	0.585446i
$503$	−3.51517	+	22.1939i	−0.156734	+	0.989577i	0.776451	+	0.630178i	$0.217018\pi$
$503$	−3.51517	+	22.1939i	−0.156734	+	0.989577i	−0.933184	+	0.359399i	$0.882982\pi$
$504$	−0.228175	−	0.0741386i	−0.0101637	−	0.00330240i
$505$	19.3341	+	8.08174i	0.860358	+	0.359633i
$506$	5.47838	−	5.50408i	0.243544	−	0.244686i
$507$	14.2197	−	14.2197i	0.631519	−	0.631519i
$508$	2.94658	+	5.78299i	0.130733	+	0.256579i
$509$	−16.8593	−	23.2049i	−0.747276	−	1.02854i	−0.998167	−	0.0605220i	$-0.980723\pi$
$509$	−16.8593	−	23.2049i	−0.747276	−	1.02854i	0.250891	−	0.968015i	$-0.419277\pi$
$510$	1.25548	−	5.15602i	0.0555937	−	0.228312i
$511$	0.269717	+	0.830104i	0.0119316	+	0.0367217i
$512$	−0.453990	+	0.891007i	−0.0200637	+	0.0393773i
$513$	−27.1739	+	4.30393i	−1.19976	+	0.190023i
$514$	14.9743	−	10.8794i	0.660486	−	0.479871i
$515$	−0.0166307	−	0.220415i	−0.000732837	−	0.00971266i
$516$		−	17.6423i		−	0.776657i
$517$	34.1141	+	24.6636i	1.50034	+	1.08470i
$518$	−4.37690	−	4.37690i	−0.192310	−	0.192310i
$519$	−1.24502	+	3.83178i	−0.0546503	+	0.168196i
$520$	1.85705	−	0.439497i	0.0814368	−	0.0192732i
$521$	−27.5311	−	20.0025i	−1.20616	−	0.876325i	−0.211282	−	0.977425i	$-0.567764\pi$
$521$	−27.5311	−	20.0025i	−1.20616	−	0.876325i	−0.994876	+	0.101100i	$0.967764\pi$
$522$	−0.191599	−	0.0976245i	−0.00838605	−	0.00427291i
$523$	25.4321	+	12.9583i	1.11207	+	0.566628i	0.910775	−	0.412903i	$-0.135485\pi$
$523$	25.4321	+	12.9583i	1.11207	+	0.566628i	0.201295	+	0.979531i	$0.435485\pi$
$524$	1.26494	+	0.919032i	0.0552591	+	0.0401481i
$525$	−1.01725	+	6.16461i	−0.0443966	+	0.269046i
$526$	7.62180	−	23.4575i	0.332326	−	1.02279i
$527$	−3.60563	−	3.60563i	−0.157064	−	0.157064i
$528$	5.17290	+	1.66740i	0.225122	+	0.0725644i
$529$		−	17.5175i		−	0.761630i
$530$	11.9721	−	13.9261i	0.520033	−	0.604912i
$531$	0.110145	−	0.0800249i	0.00477988	−	0.00347278i
$532$	3.81490	−	0.604220i	0.165397	−	0.0261963i
$533$	4.81521	−	9.45038i	0.208570	−	0.409341i
$534$	5.67674	+	17.4712i	0.245657	+	0.756053i
$535$	14.1840	+	3.45379i	0.613229	+	0.149320i
$536$	3.18063	+	4.37777i	0.137382	+	0.189091i
$537$	−11.8404	−	23.2380i	−0.510950	−	1.00280i
$538$	14.3998	−	14.3998i	0.620819	−	0.620819i
$539$	−3.28094	+	21.0335i	−0.141320	+	0.905976i
$540$	11.2361	−	4.61167i	0.483525	−	0.198455i
$541$	29.0892	+	9.45165i	1.25064	+	0.406358i	0.858151	−	0.513398i	$-0.171613\pi$
$541$	29.0892	+	9.45165i	1.25064	+	0.406358i	0.392491	+	0.919756i	$0.371613\pi$
$542$	1.16662	−	7.36573i	0.0501105	−	0.316385i
$543$	−1.31979	−	8.33284i	−0.0566377	−	0.357596i
$544$	1.37734	−	0.447525i	0.0590530	−	0.0191875i
$545$	26.3253	+	2.15745i	1.12765	+	0.0924149i
$546$	0.626844	−	0.862777i	0.0268265	−	0.0369235i
$547$	−0.121591	−	0.0192582i	−0.00519887	−	0.000823420i	0.153834	−	0.988097i	$-0.450838\pi$
$547$	−0.121591	−	0.0192582i	−0.00519887	−	0.000823420i	−0.159033	+	0.987273i	$0.550838\pi$
$548$	1.50396	−	0.766306i	0.0642460	−	0.0327350i
$549$	−3.99054			−0.170312
$550$	−2.66166	+	16.3681i	−0.113493	+	0.697939i
$551$	3.46189			0.147481
$552$	−3.41879	+	1.74196i	−0.145513	+	0.0741428i
$553$	−7.59748	−	1.20332i	−0.323078	−	0.0511705i
$554$	−9.62494	+	13.2476i	−0.408924	+	0.562836i
$555$	29.6448	+	2.42949i	1.25835	+	0.103126i
$556$	−8.25188	+	2.68120i	−0.349958	+	0.113708i
$557$	5.63365	+	35.5695i	0.238705	+	1.50713i	0.757844	+	0.652436i	$0.226253\pi$
$557$	5.63365	+	35.5695i	0.238705	+	1.50713i	−0.519138	+	0.854690i	$0.673747\pi$
$558$	0.173296	−	1.09415i	0.00733621	−	0.0463190i
$559$	−8.73836	−	2.83926i	−0.369593	−	0.120088i
$560$	−1.57741	+	0.647424i	−0.0666579	+	0.0273587i
$561$	−3.58979	−	7.00479i	−0.151561	−	0.295743i
$562$	2.96093	−	2.96093i	0.124899	−	0.124899i
$563$	5.38016	+	10.5592i	0.226747	+	0.445015i	0.976150	−	0.217099i	$-0.0696594\pi$
$563$	5.38016	+	10.5592i	0.226747	+	0.445015i	−0.749403	+	0.662114i	$0.769659\pi$
$564$	−12.2254	−	16.8269i	−0.514784	−	0.708539i
$565$	25.0456	+	6.09856i	1.05368	+	0.256569i
$566$	−8.54143	−	26.2878i	−0.359023	−	1.10496i
$567$	2.75467	−	5.40635i	0.115685	−	0.227046i
$568$	−7.84977	+	1.24328i	−0.329369	+	0.0521669i
$569$	−28.8735	+	20.9778i	−1.21044	+	0.879435i	−0.995270	−	0.0971424i	$-0.969030\pi$
$569$	−28.8735	+	20.9778i	−1.21044	+	0.879435i	−0.215168	+	0.976577i	$0.569030\pi$
$570$	−12.0994	+	14.0743i	−0.506790	+	0.589507i
$571$		−	31.2536i		−	1.30792i	−0.756528	−	0.653961i	$-0.773106\pi$
$571$		−	31.2536i		−	1.30792i	0.756528	−	0.653961i	$-0.226894\pi$
$572$	1.65838	−	2.29384i	0.0693404	−	0.0959101i
$573$	31.1653	+	31.1653i	1.30195	+	1.30195i
$574$	−2.92851	+	9.01301i	−0.122233	+	0.376196i
$575$	−6.82007	−	9.51573i	−0.284417	−	0.396833i
$576$	0.254538	+	0.184933i	0.0106057	+	0.00770553i
$577$	−41.1550	−	20.9695i	−1.71330	−	0.872972i	−0.981502	−	0.191454i	$-0.938680\pi$
$577$	−41.1550	−	20.9695i	−1.71330	−	0.872972i	−0.731801	−	0.681518i	$-0.761320\pi$
$578$	13.2784	+	6.76566i	0.552307	+	0.281415i
$579$	−12.8399	−	9.32873i	−0.533608	−	0.387689i
$580$	−1.48720	+	0.351966i	−0.0617524	+	0.0146146i
$581$	0.0562850	−	0.173227i	0.00233510	−	0.00718668i
$582$	16.4854	+	16.4854i	0.683340	+	0.683340i
$583$	−0.0637459	−	27.2394i	−0.00264009	−	1.12814i
$584$		−	1.14461i		−	0.0473645i
$585$	−0.0451739	−	0.598713i	−0.00186771	−	0.0247537i
$586$	15.1257	−	10.9894i	0.624836	−	0.453970i
$587$	−30.4725	+	4.82637i	−1.25773	+	0.199205i	−0.749494	−	0.662011i	$-0.769703\pi$
$587$	−30.4725	+	4.82637i	−1.25773	+	0.199205i	−0.508239	+	0.861216i	$0.669703\pi$
$588$	4.77512	−	9.37170i	0.196923	−	0.386482i
$589$	5.51112	+	16.9615i	0.227082	+	0.698885i
$590$	0.228921	−	0.940131i	0.00942451	−	0.0387046i
$591$	8.12474	+	11.1827i	0.334207	+	0.459997i
$592$	3.68520	+	7.23261i	0.151461	+	0.297259i
$593$	−3.14365	+	3.14365i	−0.129094	+	0.129094i	−0.768702	−	0.639607i	$-0.779097\pi$
$593$	−3.14365	+	3.14365i	−0.129094	+	0.129094i	0.639607	+	0.768702i	$0.279097\pi$
$594$	8.14103	−	16.0705i	0.334031	−	0.659382i
$595$	2.27834	+	0.952355i	0.0934028	+	0.0390427i
$596$	14.0197	+	4.55529i	0.574271	+	0.186592i
$597$	−0.211973	+	1.33834i	−0.00867547	+	0.0547747i
$598$	0.312603	+	1.97370i	0.0127833	+	0.0807105i
$599$	−8.63991	+	2.80728i	−0.353017	+	0.114702i	−0.480157	−	0.877183i	$-0.659420\pi$
$599$	−8.63991	+	2.80728i	−0.353017	+	0.114702i	0.127140	+	0.991885i	$0.459420\pi$
$600$	3.76689	−	7.27632i	0.153783	−	0.297055i
$601$	−17.5277	+	24.1249i	−0.714971	+	0.984074i	0.284705	+	0.958615i	$0.408105\pi$
$601$	−17.5277	+	24.1249i	−0.714971	+	0.984074i	−0.999676	+	0.0254583i	$0.991895\pi$
$602$	8.10847	+	1.28426i	0.330476	+	0.0523423i
$603$	1.51695	−	0.772923i	0.0617749	−	0.0314759i
$604$	11.4487			0.465841
$605$	12.8822	+	20.9535i	0.523734	+	0.851882i
$606$	−15.3572			−0.623842
$607$	18.4276	−	9.38932i	0.747952	−	0.381101i	−0.0380895	−	0.999274i	$-0.512127\pi$
$607$	18.4276	−	9.38932i	0.747952	−	0.381101i	0.786041	+	0.618174i	$0.212127\pi$
$608$	−5.00283	−	0.792370i	−0.202892	−	0.0321349i
$609$	−0.502002	+	0.690946i	−0.0203421	+	0.0279985i
$610$	−21.6253	+	18.3492i	−0.875581	+	0.742938i
$611$	−10.3020	+	3.34732i	−0.416774	+	0.135418i
$612$	−0.0712791	−	0.450039i	−0.00288129	−	0.0181917i
$613$	1.97249	−	12.4538i	0.0796682	−	0.503005i	−0.915297	−	0.402780i	$-0.868044\pi$
$613$	1.97249	−	12.4538i	0.0796682	−	0.503005i	0.994965	−	0.100225i	$-0.0319562\pi$
$614$	−9.59336	−	3.11707i	−0.387156	−	0.125795i
$615$	−17.2910	−	42.1287i	−0.697241	−	1.69879i
$616$	−1.14290	+	2.25611i	−0.0460489	+	0.0909013i
$617$	6.47501	−	6.47501i	0.260674	−	0.260674i	−0.564654	−	0.825328i	$-0.690990\pi$
$617$	6.47501	−	6.47501i	0.260674	−	0.260674i	0.825328	+	0.564654i	$0.190990\pi$
$618$	0.0735426	+	0.144335i	0.00295832	+	0.00580602i
$619$	23.3769	+	32.1756i	0.939598	+	1.29325i	0.955996	+	0.293380i	$0.0947800\pi$
$619$	23.3769	+	32.1756i	0.939598	+	1.29325i	−0.0163985	+	0.999866i	$0.505220\pi$
$620$	−4.09198	−	6.72619i	−0.164338	−	0.270130i
$621$	3.93015	+	12.0957i	0.157711	+	0.485385i
$622$	10.4008	−	20.4128i	0.417035	−	0.818478i
$623$	−8.44309	+	1.33725i	−0.338265	+	0.0535759i
$624$	−1.13144	+	0.822040i	−0.0452939	+	0.0329079i
$625$	23.6746	+	8.03204i	0.946984	+	0.321282i
$626$			14.4830i			0.578857i
$627$	0.0644241	+	27.5292i	0.00257285	+	1.09941i
$628$	−0.582847	−	0.582847i	−0.0232581	−	0.0232581i
$629$	3.63272	−	11.1804i	0.144846	−	0.445790i
$630$	0.123551	+	0.522051i	0.00492238	+	0.0207990i
$631$	−21.6416	−	15.7235i	−0.861537	−	0.625943i	0.0667657	−	0.997769i	$-0.478732\pi$
$631$	−21.6416	−	15.7235i	−0.861537	−	0.625943i	−0.928303	+	0.371825i	$0.878732\pi$
$632$	8.98801	+	4.57962i	0.357524	+	0.182167i
$633$	−21.2666	−	10.8359i	−0.845271	−	0.430687i
$634$	1.80973	+	1.31485i	0.0718737	+	0.0522193i
$635$	7.62295	−	12.3498i	0.302508	−	0.490086i
$636$	−4.15898	+	12.8000i	−0.164914	+	0.507554i
$637$	−3.87339	−	3.87339i	−0.153469	−	0.153469i
$638$	−1.32810	+	1.83699i	−0.0525799	+	0.0727273i
$639$			2.50053i			0.0989194i
$640$	2.22973	−	0.168237i	0.0881378	−	0.00665015i
$641$	−10.9993	+	7.99147i	−0.434447	+	0.315644i	−0.783425	−	0.621487i	$-0.786529\pi$
$641$	−10.9993	+	7.99147i	−0.434447	+	0.315644i	0.348978	+	0.937131i	$0.386529\pi$
$642$	−10.5668	+	1.67362i	−0.417040	+	0.0660526i
$643$	−8.38228	+	16.4511i	−0.330565	+	0.648770i	−0.995142	−	0.0984497i	$-0.968612\pi$
$643$	−8.38228	+	16.4511i	−0.330565	+	0.648770i	0.664577	+	0.747220i	$0.268612\pi$
$644$	−0.551745	−	1.69810i	−0.0217418	−	0.0669144i
$645$	−33.7025	+	20.5034i	−1.32703	+	0.807321i
$646$	4.31171	+	5.93456i	0.169642	+	0.233492i
$647$	−8.17393	−	16.0422i	−0.321350	−	0.630686i	0.672662	−	0.739950i	$-0.265151\pi$
$647$	−8.17393	−	16.0422i	−0.321350	−	0.630686i	−0.994013	+	0.109264i	$0.965151\pi$
$648$	−5.62654	+	5.62654i	−0.221031	+	0.221031i
$649$	−0.654551	−	1.27723i	−0.0256934	−	0.0501357i
$650$	−2.99780	−	3.03679i	−0.117583	−	0.119113i
$651$	−4.18444	−	1.35961i	−0.164001	−	0.0532872i
$652$	−1.39807	+	8.82707i	−0.0547527	+	0.345695i
$653$	−4.15411	−	26.2280i	−0.162563	−	1.02638i	−0.925179	−	0.379531i	$-0.876086\pi$
$653$	−4.15411	−	26.2280i	−0.162563	−	1.02638i	0.762616	−	0.646851i	$-0.223914\pi$
$654$	−18.4099	+	5.98173i	−0.719883	+	0.233904i
$655$	0.285568	−	3.48452i	0.0111581	−	0.136152i
$656$	7.30492	−	10.0544i	0.285209	−	0.392557i
$657$	−0.355692	−	0.0563361i	−0.0138769	−	0.00219788i
$658$	8.62366	−	4.39397i	0.336185	−	0.171295i
$659$	36.6251			1.42671			0.713356	−	0.700802i	$-0.247174\pi$
$659$	36.6251			1.42671			0.713356	+	0.700802i	$0.247174\pi$
$660$	−2.82654	−	11.8197i	−0.110023	−	0.460083i
$661$	7.39959			0.287811			0.143905	−	0.989591i	$-0.454034\pi$
$661$	7.39959			0.287811			0.143905	+	0.989591i	$0.454034\pi$
$662$	1.75236	−	0.892871i	0.0681073	−	0.0347024i
$663$	2.00046	+	0.316841i	0.0776912	+	0.0123051i
$664$	−0.140398	+	0.193242i	−0.00544851	+	0.00749923i
$665$	−5.58784	−	6.58549i	−0.216687	−	0.255374i
$666$	2.42893	−	0.789208i	0.0941193	−	0.0305812i
$667$	−0.250345	−	1.58062i	−0.00969339	−	0.0612017i
$668$	3.30466	−	20.8648i	0.127861	−	0.807283i
$669$	−2.09763	−	0.681562i	−0.0810991	−	0.0263507i
$670$	4.66650	−	11.1638i	0.180283	−	0.431294i
$671$	−6.48335	+	41.5635i	−0.250287	+	1.60454i
$672$	0.883597	−	0.883597i	0.0340855	−	0.0340855i
$673$	−13.8527	−	27.1875i	−0.533983	−	1.04800i	−0.987627	−	0.156818i	$-0.949876\pi$
$673$	−13.8527	−	27.1875i	−0.533983	−	1.04800i	0.453644	−	0.891183i	$-0.350124\pi$
$674$	0.238296	+	0.327986i	0.00917881	+	0.0126335i
$675$	−21.8681	−	16.1050i	−0.841705	−	0.619884i
$676$	−3.79215	−	11.6710i	−0.145852	−	0.448886i
$677$	−13.5878	+	26.6676i	−0.522223	+	1.02492i	0.467776	+	0.883847i	$0.345055\pi$
$677$	−13.5878	+	26.6676i	−0.522223	+	1.02492i	−0.989999	+	0.141074i	$0.954945\pi$
$678$	−18.6585	+	2.95521i	−0.716575	+	0.113494i
$679$	−8.77679	+	6.37671i	−0.336822	+	0.244716i
$680$	−2.45563	−	2.11107i	−0.0941692	−	0.0809557i
$681$		−	3.36280i		−	0.128863i
$682$	−11.1146	−	3.58261i	−0.425599	−	0.137185i
$683$	−13.9351	−	13.9351i	−0.533214	−	0.533214i	0.388314	−	0.921527i	$-0.373058\pi$
$683$	−13.9351	−	13.9351i	−0.533214	−	0.533214i	−0.921527	+	0.388314i	$0.873058\pi$
$684$	−0.492462	+	1.51564i	−0.0188298	+	0.0579521i
$685$	−3.21176	−	1.98247i	−0.122715	−	0.0757464i
$686$	8.27807	+	6.01437i	0.316058	+	0.229630i
$687$	−26.1706	−	13.3346i	−0.998472	−	0.508747i
$688$	−9.59252	−	4.88763i	−0.365711	−	0.186339i
$689$	5.67063	+	4.11995i	0.216034	+	0.156958i
$690$	7.30095	+	4.50654i	0.277942	+	0.171561i
$691$	−9.06481	+	27.8986i	−0.344841	+	1.06131i	0.616827	+	0.787099i	$0.288418\pi$
$691$	−9.06481	+	27.8986i	−0.344841	+	1.06131i	−0.961669	+	0.274214i	$0.911582\pi$
$692$	1.73851	+	1.73851i	0.0660882	+	0.0660882i
$693$	0.644841	+	0.466203i	0.0244955	+	0.0177096i
$694$		−	10.6915i		−	0.405844i
$695$	14.7121	+	12.6478i	0.558062	+	0.479757i
$696$	0.906102	−	0.658322i	0.0343457	−	0.0249536i
$697$	−17.7767	+	2.81556i	−0.673341	+	0.106647i
$698$	3.65234	−	7.16813i	0.138243	−	0.271318i
$699$	−12.4489	−	38.3139i	−0.470862	−	1.44916i
$700$	3.07003	+	2.26096i	0.116036	+	0.0854561i
$701$	4.36586	+	6.00910i	0.164896	+	0.226960i	0.883467	−	0.468494i	$-0.155203\pi$
$701$	4.36586	+	6.00910i	0.164896	+	0.226960i	−0.718570	+	0.695454i	$0.755203\pi$
$702$	2.10453	+	4.13037i	0.0794304	+	0.155891i
$703$	−29.0734	+	29.0734i	−1.09652	+	1.09652i
$704$	2.33971	−	2.35069i	0.0881813	−	0.0885950i
$705$	−17.9367	+	42.9104i	−0.675535	+	1.61610i
$706$	24.0666	+	7.81972i	0.905759	+	0.294299i
$707$	1.11791	−	7.05822i	0.0420434	−	0.265452i
$708$	0.110929	+	0.700380i	0.00416898	+	0.0263219i
$709$	25.9291	−	8.42488i	0.973788	−	0.316403i	0.221444	−	0.975173i	$-0.428923\pi$
$709$	25.9291	−	8.42488i	0.973788	−	0.316403i	0.752344	+	0.658770i	$0.228923\pi$
$710$	11.4979	+	13.5507i	0.431508	+	0.508549i
$711$	1.86550	−	2.56765i	0.0699619	−	0.0962942i
$712$	11.0722	+	1.75367i	0.414949	+	0.0657214i
$713$	7.34567	−	3.74281i	0.275098	−	0.140169i
$714$	−1.80969			−0.0677260
$715$	−6.30930	−	0.502207i	−0.235955	−	0.0187815i
$716$	−15.9154			−0.594785
$717$	−4.33277	+	2.20766i	−0.161810	+	0.0824464i
$718$	16.0503	+	2.54212i	0.598993	+	0.0948712i
$719$	1.00656	−	1.38541i	0.0375383	−	0.0516670i	−0.789835	−	0.613319i	$-0.789834\pi$
$719$	1.00656	−	1.38541i	0.0375383	−	0.0516670i	0.827374	+	0.561652i	$0.189834\pi$
$720$	0.0574637	−	0.701175i	0.00214154	−	0.0261312i
$721$	−0.0716907	+	0.0232937i	−0.00266990	+	0.000867504i
$722$	−1.04125	−	6.57421i	−0.0387514	−	0.244667i
$723$	−5.45664	+	34.4519i	−0.202935	+	1.28128i
$724$	−4.89640	−	1.59094i	−0.181973	−	0.0591267i
$725$	2.40075	+	2.43198i	0.0891618	+	0.0903215i
$726$	−14.6326	−	10.5269i	−0.543068	−	0.390691i
$727$	−13.9556	+	13.9556i	−0.517583	+	0.517583i	−0.916839	−	0.399256i	$-0.869268\pi$
$727$	−13.9556	+	13.9556i	−0.517583	+	0.517583i	0.399256	+	0.916839i	$0.369268\pi$
$728$	−0.295451	−	0.579855i	−0.0109501	−	0.0214909i
$729$	17.1672	+	23.6286i	0.635822	+	0.875133i
$730$	−2.18659	+	1.33024i	−0.0809292	+	0.0492345i
$731$	4.81803	+	14.8284i	0.178201	+	0.548447i
$732$	9.43595	−	18.5191i	0.348763	−	0.684485i
$733$	5.82783	−	0.923038i	0.215256	−	0.0340932i	−0.0478750	−	0.998853i	$-0.515245\pi$
$733$	5.82783	−	0.923038i	0.215256	−	0.0340932i	0.263131	+	0.964760i	$0.415245\pi$
$734$	6.93460	−	5.03828i	0.255961	−	0.185966i
$735$	−23.4525	+	1.76953i	−0.865059	+	0.0652702i
$736$			2.34147i			0.0863079i
$737$	−5.58585	−	17.0556i	−0.205757	−	0.628250i
$738$	−2.76488	−	2.76488i	−0.101777	−	0.101777i
$739$	−10.0720	+	30.9985i	−0.370505	+	1.14030i	0.575956	+	0.817480i	$0.304630\pi$
$739$	−10.0720	+	30.9985i	−0.370505	+	1.14030i	−0.946461	+	0.322817i	$0.895370\pi$
$740$	9.53380	−	15.4455i	0.350469	−	0.567788i
$741$	−5.73096	−	4.16379i	−0.210532	−	0.152961i
$742$	−5.58020	−	2.84325i	−0.204856	−	0.104379i
$743$	37.9296	+	19.3261i	1.39150	+	0.709007i	0.979362	−	0.202113i	$-0.0647809\pi$
$743$	37.9296	+	19.3261i	1.39150	+	0.709007i	0.412142	+	0.911120i	$0.364781\pi$
$744$	4.66790	+	3.39143i	0.171134	+	0.124336i
$745$	−7.59132	−	32.0763i	−0.278125	−	1.17519i
$746$	−10.1580	+	31.2632i	−0.371911	+	1.14463i
$747$	0.0531402	+	0.0531402i	0.00194430	+	0.00194430i
$748$	−4.80319	+	0.0112405i	−0.175622	+	0.000410993i
$749$		−	4.97840i		−	0.181907i
$750$	−18.2779	+	1.26038i	−0.667416	+	0.0460225i
$751$	22.4102	−	16.2819i	0.817758	−	0.594136i	−0.0983111	−	0.995156i	$-0.531344\pi$
$751$	22.4102	−	16.2819i	0.817758	−	0.594136i	0.916070	+	0.401019i	$0.131344\pi$
$752$	−12.5361	+	1.98553i	−0.457146	+	0.0724047i
$753$	9.88024	−	19.3911i	0.360056	−	0.706650i
$754$	−0.180248	−	0.554747i	−0.00656425	−	0.0202027i
$755$	−13.3054	−	21.8707i	−0.484233	−	0.795958i
$756$	−2.43457	−	3.35090i	−0.0885445	−	0.121871i
$757$	−7.26251	−	14.2535i	−0.263960	−	0.518051i	0.720544	−	0.693409i	$-0.243892\pi$
$757$	−7.26251	−	14.2535i	−0.263960	−	0.518051i	−0.984505	+	0.175357i	$0.943892\pi$
$758$	9.05740	−	9.05740i	0.328980	−	0.328980i
$759$	12.5645	−	2.02018i	0.456063	−	0.0733277i
$760$	4.30048	+	10.4779i	0.155995	+	0.380074i
$761$	6.47967	+	2.10537i	0.234888	+	0.0763197i	0.424096	−	0.905617i	$-0.360592\pi$
$761$	6.47967	+	2.10537i	0.234888	+	0.0763197i	−0.189208	+	0.981937i	$0.560592\pi$
$762$	−1.66382	+	10.5049i	−0.0602738	+	0.380554i
$763$	−1.40910	−	8.89670i	−0.0510128	−	0.322082i
$764$	25.5794	−	8.31126i	0.925431	−	0.300691i
$765$	−0.776882	+	0.659191i	−0.0280882	+	0.0238331i
$766$	−13.1004	+	18.0312i	−0.473338	+	0.651494i
$767$	0.364756	+	0.0577717i	0.0131706	+	0.00208602i
$768$	−1.46010	+	0.743959i	−0.0526869	+	0.0268453i
$769$	−48.7563			−1.75820			−0.879098	−	0.476640i	$-0.841854\pi$
$769$	−48.7563			−1.75820			−0.879098	+	0.476640i	$0.841854\pi$
$770$	5.63817	−	0.438681i	0.203185	−	0.0158090i
$771$	30.3312			1.09235
$772$	−8.62943	+	4.39692i	−0.310580	+	0.158248i
$773$	25.8396	+	4.09258i	0.929384	+	0.147200i	0.602731	−	0.797944i	$-0.294079\pi$
$773$	25.8396	+	4.09258i	0.929384	+	0.147200i	0.326653	+	0.945144i	$0.394079\pi$
$774$	−1.99097	+	2.74034i	−0.0715641	+	0.0984995i
$775$	−8.09361	+	15.6340i	−0.290731	+	0.561591i
$776$	13.5306	−	4.39636i	0.485720	−	0.157820i
$777$	−1.58678	−	10.0185i	−0.0569254	−	0.359413i
$778$	−2.14623	+	13.5508i	−0.0769461	+	0.485818i
$779$	59.8686	+	19.4525i	2.14501	+	0.696957i
$780$	2.88530	+	1.20607i	0.103310	+	0.0431841i
$781$	26.0443	+	4.06256i	0.931939	+	0.145370i
$782$	2.39778	−	2.39778i	0.0857444	−	0.0857444i
$783$	−1.68539	−	3.30777i	−0.0602310	−	0.118210i
$784$	−3.77271	−	5.19269i	−0.134740	−	0.185453i
$785$	−0.436057	+	1.79080i	−0.0155635	+	0.0639164i
$786$	0.791765	+	2.43680i	0.0282413	+	0.0869179i
$787$	10.5858	−	20.7757i	0.377341	−	0.740574i	−0.621749	−	0.783217i	$-0.713578\pi$
$787$	10.5858	−	20.7757i	0.377341	−	0.740574i	0.999090	+	0.0426425i	$0.0135776\pi$
$788$	8.33122	−	1.31953i	0.296787	−	0.0470065i
$789$	32.6990	−	23.7572i	1.16412	−	0.845780i
$790$	−1.69709	−	22.4923i	−0.0603796	−	0.800242i
$791$		−	8.79065i		−	0.312560i
$792$	−0.615326	−	0.842769i	−0.0218647	−	0.0299465i
$793$	−7.65408	−	7.65408i	−0.271804	−	0.271804i
$794$	−0.352855	+	1.08598i	−0.0125223	+	0.0385398i
$795$	29.2857	−	6.93087i	1.03866	−	0.245813i
$796$	0.668964	+	0.486031i	0.0237108	+	0.0172269i
$797$	31.4855	+	16.0427i	1.11527	+	0.568261i	0.911724	−	0.410804i	$-0.134752\pi$
$797$	31.4855	+	16.0427i	1.11527	+	0.568261i	0.203551	+	0.979064i	$0.434752\pi$
$798$	5.63957	+	2.87351i	0.199639	+	0.101721i
$799$	14.8709	+	10.8043i	0.526093	+	0.382229i
$800$	−2.91273	−	4.06399i	−0.102980	−	0.143684i
$801$	1.08991	−	3.35441i	0.0385102	−	0.118522i
$802$	9.74633	+	9.74633i	0.344155	+	0.344155i
$803$	−1.16466	+	3.61319i	−0.0410998	+	0.127507i
$804$			8.86742i			0.312730i
$805$	−2.60269	+	3.02750i	−0.0917329	+	0.106705i
$806$	2.43103	−	1.76625i	0.0856295	−	0.0622135i
$807$	32.9605	−	5.22043i	1.16026	−	0.183768i
$808$	−4.25456	+	8.35005i	−0.149675	+	0.293754i
$809$	−11.3255	−	34.8562i	−0.398182	−	1.22548i	−0.926455	−	0.376405i	$-0.877160\pi$
$809$	−11.3255	−	34.8562i	−0.398182	−	1.22548i	0.528273	−	0.849075i	$-0.322840\pi$
$810$	17.2876	+	4.20950i	0.607423	+	0.147907i
$811$	14.6687	+	20.1898i	0.515089	+	0.708960i	0.984767	−	0.173878i	$-0.0556299\pi$
$811$	14.6687	+	20.1898i	0.515089	+	0.708960i	−0.469678	+	0.882838i	$0.655630\pi$
$812$	0.236609	+	0.464371i	0.00830334	+	0.0162962i
$813$	8.64138	−	8.64138i	0.303067	−	0.303067i
$814$	−4.27378	−	26.5808i	−0.149796	−	0.931657i
$815$	18.4874	−	7.58784i	0.647585	−	0.265790i
$816$	2.25706	+	0.733364i	0.0790130	+	0.0256729i
$817$	8.53061	−	53.8602i	0.298448	−	1.88433i
$818$	3.16297	+	19.9702i	0.110591	+	0.698241i
$819$	−0.194733	+	0.0632726i	−0.00680453	+	0.00221093i
$820$	−27.6967	−	2.26984i	−0.967211	−	0.0792662i
$821$	7.96168	−	10.9583i	0.277865	−	0.382448i	−0.647160	−	0.762354i	$-0.724044\pi$
$821$	7.96168	−	10.9583i	0.277865	−	0.382448i	0.925025	+	0.379906i	$0.124044\pi$
$822$	2.73198	+	0.432704i	0.0952888	+	0.0150923i
$823$	−7.67193	+	3.90905i	−0.267427	+	0.136261i	−0.582563	−	0.812786i	$-0.697950\pi$
$823$	−7.67193	+	3.90905i	−0.267427	+	0.136261i	0.315136	+	0.949047i	$0.397950\pi$
$824$	0.0988529			0.00344371
$825$	−19.2946	+	19.1362i	−0.671753	+	0.666238i
$826$	−0.329973			−0.0114812
$827$	−8.89722	+	4.53336i	−0.309387	+	0.157640i	−0.601789	−	0.798655i	$-0.705545\pi$
$827$	−8.89722	+	4.53336i	−0.309387	+	0.157640i	0.292403	+	0.956295i	$0.405545\pi$
$828$	0.727619	+	0.115244i	0.0252865	+	0.00400499i
$829$	12.4310	−	17.1098i	0.431746	−	0.594247i	−0.536607	−	0.843832i	$-0.680294\pi$
$829$	12.4310	−	17.1098i	0.431746	−	0.594247i	0.968353	+	0.249585i	$0.0802942\pi$
$830$	0.532322	+	0.0436256i	0.0184772	+	0.00151427i
$831$	−25.5204	+	8.29209i	−0.885294	+	0.287649i
$832$	0.133507	+	0.842930i	0.00462852	+	0.0292233i
$833$	−1.45413	+	9.18100i	−0.0503825	+	0.318103i
$834$	−13.5225	−	4.39371i	−0.468244	−	0.152142i
$835$	−43.6991	+	17.9356i	−1.51227	+	0.620687i
$836$	14.9861	+	7.59169i	0.518306	+	0.262564i
$837$	13.5233	−	13.5233i	0.467434	−	0.467434i
$838$	−8.85100	−	17.3711i	−0.305753	−	0.600073i
$839$	−23.3328	−	32.1148i	−0.805537	−	1.10873i	−0.991997	−	0.126264i	$-0.959701\pi$
$839$	−23.3328	−	32.1148i	−0.805537	−	1.10873i	0.186460	−	0.982463i	$-0.440299\pi$
$840$	−2.71486	−	0.661063i	−0.0936714	−	0.0228088i
$841$	−8.81714	−	27.1364i	−0.304039	−	0.935737i
$842$	−1.29794	+	2.54735i	−0.0447300	+	0.0877875i
$843$	6.77743	−	1.07344i	0.233427	−	0.0369712i
$844$	−11.7834	+	8.56117i	−0.405603	+	0.294688i
$845$	−17.8883	+	20.8080i	−0.615377	+	0.715818i
$846$			3.99336i			0.137295i
$847$	5.90340	−	5.95893i	0.202843	−	0.204751i
$848$	5.80747	+	5.80747i	0.199429	+	0.199429i
$849$	13.9969	−	43.0781i	0.480373	−	1.47844i
$850$	−1.17895	+	7.14449i	−0.0404376	+	0.245054i
$851$	15.3766	+	11.1718i	0.527104	+	0.382964i
$852$	−11.6043	−	5.91271i	−0.397558	−	0.202566i
$853$	32.4298	+	16.5238i	1.11037	+	0.565764i	0.910272	−	0.414012i	$-0.135873\pi$
$853$	32.4298	+	16.5238i	1.11037	+	0.565764i	0.200102	+	0.979775i	$0.435873\pi$
$854$	7.82458	+	5.68489i	0.267752	+	0.194533i
$855$	3.46770	−	0.820681i	0.118593	−	0.0280667i
$856$	−2.01746	+	6.20910i	−0.0689554	+	0.212223i
$857$	10.3508	+	10.3508i	0.353576	+	0.353576i	0.861438	−	0.507862i	$-0.169564\pi$
$857$	10.3508	+	10.3508i	0.353576	+	0.353576i	−0.507862	+	0.861438i	$0.669564\pi$
$858$	4.40804	−	1.44367i	0.150488	−	0.0492861i
$859$			21.8229i			0.744588i	0.928115	+	0.372294i	$0.121429\pi$
$859$			21.8229i			0.744588i	−0.928115	+	0.372294i	$0.878571\pi$
$860$	1.81123	+	24.0051i	0.0617624	+	0.818568i
$861$	−12.5639	+	9.12819i	−0.428176	+	0.311088i
$862$	−15.9140	+	2.52053i	−0.542032	+	0.0858495i
$863$	2.72232	−	5.34286i	0.0926690	−	0.181873i	−0.840019	−	0.542556i	$-0.817456\pi$
$863$	2.72232	−	5.34286i	0.0926690	−	0.181873i	0.932688	+	0.360683i	$0.117456\pi$
$864$	1.67849	+	5.16587i	0.0571035	+	0.175746i
$865$	1.30066	−	5.34157i	0.0442239	−	0.181619i
$866$	−14.3556	−	19.7588i	−0.487823	−	0.671431i
$867$	11.0870	+	21.7594i	0.376533	+	0.738988i
$868$	−1.89851	+	1.89851i	−0.0644397	+	0.0644397i
$869$	−23.7125	−	23.6018i	−0.804392	−	0.800636i
$870$	−2.31066	−	0.965864i	−0.0783387	−	0.0327459i
$871$	4.39211	+	1.42708i	0.148821	+	0.0483548i
$872$	−1.84788	+	11.6671i	−0.0625772	+	0.395097i
$873$	−0.700226	−	4.42105i	−0.0236991	−	0.149630i
$874$	−11.2795	+	3.66494i	−0.381536	+	0.123969i
$875$	0.751253	−	8.49238i	0.0253970	−	0.287095i
$876$	1.10250	−	1.51747i	0.0372502	−	0.0512705i
$877$	−28.0379	−	4.44076i	−0.946771	−	0.149954i	−0.336090	−	0.941830i	$-0.609105\pi$
$877$	−28.0379	−	4.44076i	−0.946771	−	0.149954i	−0.610682	+	0.791876i	$0.709105\pi$
$878$	11.8117	−	6.01836i	0.398625	−	0.203110i
$879$	30.6379			1.03339
$880$	−7.20974	−	1.73770i	−0.243040	−	0.0585778i
$881$	−9.63291			−0.324541			−0.162270	−	0.986746i	$-0.551882\pi$
$881$	−9.63291			−0.324541			−0.162270	+	0.986746i	$0.551882\pi$
$882$	−1.79933	+	0.916804i	−0.0605866	+	0.0308704i
$883$	−49.2384	−	7.79859i	−1.65700	−	0.262443i	−0.743339	−	0.668915i	$-0.766759\pi$
$883$	−49.2384	−	7.79859i	−1.65700	−	0.262443i	−0.913663	+	0.406471i	$0.866759\pi$
$884$	0.726483	−	0.999918i	0.0244343	−	0.0336309i
$885$	1.20903	−	1.02588i	0.0406412	−	0.0344844i
$886$	−2.07093	+	0.672885i	−0.0695742	+	0.0226060i
$887$	5.23210	+	33.0342i	0.175677	+	1.10918i	0.905126	+	0.425144i	$0.139777\pi$
$887$	5.23210	+	33.0342i	0.175677	+	1.10918i	−0.729449	+	0.684035i	$0.760223\pi$
$888$	−2.08089	+	13.1382i	−0.0698301	+	0.440890i
$889$	−4.70701	−	1.52940i	−0.157868	−	0.0512944i
$890$	−9.51779	−	23.1896i	−0.319037	−	0.777317i
$891$	23.4863	−	12.0362i	0.786820	−	0.403227i
$892$	−0.951712	+	0.951712i	−0.0318657	+	0.0318657i
$893$	−29.1868	−	57.2823i	−0.976698	−	1.91688i
$894$	14.1989	+	19.5431i	0.474882	+	0.653619i
$895$	18.4965	+	30.4035i	0.618268	+	1.01628i
$896$	−0.235640	−	0.725226i	−0.00787219	−	0.0242281i
$897$	−1.48665	+	2.91772i	−0.0496380	+	0.0974200i
$898$	4.76625	−	0.754900i	0.159052	−	0.0251913i
$899$	−1.94687	+	1.41448i	−0.0649316	+	0.0471756i
$900$	−1.40626	+	0.705115i	−0.0468752	+	0.0235038i
$901$		−	11.8942i		−	0.396255i
$902$	−33.2897	+	24.3056i	−1.10843	+	0.809289i
$903$	9.51275	+	9.51275i	0.316565	+	0.316565i
$904$	−3.56235	+	10.9638i	−0.118482	+	0.364650i
$905$	2.65127	+	11.2027i	0.0881313	+	0.372389i
$906$	15.1781	+	11.0275i	0.504257	+	0.366364i
$907$	37.7962	+	19.2581i	1.25500	+	0.639456i	0.949808	−	0.312833i	$-0.101278\pi$
$907$	37.7962	+	19.2581i	1.25500	+	0.639456i	0.305196	+	0.952290i	$0.401278\pi$
$908$	−1.82844	−	0.931635i	−0.0606788	−	0.0309174i
$909$	2.38540	+	1.73309i	0.0791187	+	0.0574831i
$910$	−0.764346	+	1.23830i	−0.0253378	+	0.0410493i
$911$	−4.93516	+	15.1889i	−0.163509	+	0.503229i	−0.998923	−	0.0463915i	$-0.985228\pi$
$911$	−4.93516	+	15.1889i	−0.163509	+	0.503229i	0.835414	+	0.549621i	$0.185228\pi$
$912$	−5.86926	−	5.86926i	−0.194351	−	0.194351i
$913$	0.639819	−	0.467147i	0.0211749	−	0.0154603i
$914$		−	20.4761i		−	0.677288i
$915$	−46.3437	+	3.49671i	−1.53208	+	0.115598i
$916$	−14.5007	+	10.5354i	−0.479116	+	0.348098i
$917$	−1.17760	+	0.186514i	−0.0388879	+	0.00615923i
$918$	3.57124	−	7.00895i	0.117868	−	0.231330i
$919$	7.78224	+	23.9513i	0.256713	+	0.790080i	0.993487	+	0.113942i	$0.0363478\pi$
$919$	7.78224	+	23.9513i	0.256713	+	0.790080i	−0.736775	+	0.676138i	$0.763652\pi$
$920$	4.47298	−	2.72121i	0.147470	−	0.0897155i
$921$	−9.71595	−	13.3729i	−0.320151	−	0.440651i
$922$	0.279769	+	0.549077i	0.00921369	+	0.0180829i
$923$	−4.79616	+	4.79616i	−0.157868	+	0.157868i
$924$	−3.68831	+	1.89017i	−0.121336	+	0.0621821i
$925$	−40.5859	−	0.262256i	−1.33446	−	0.00862293i
$926$	−18.2897	−	5.94269i	−0.601037	−	0.195289i
$927$	0.00486538	−	0.0307188i	0.000159800	−	0.00100894i
$928$	−0.106918	−	0.675052i	−0.00350974	−	0.0221597i
$929$	8.61430	−	2.79896i	0.282626	−	0.0918308i	−0.164274	−	0.986415i	$-0.552528\pi$
$929$	8.61430	−	2.79896i	0.282626	−	0.0918308i	0.446900	+	0.894584i	$0.352528\pi$
$930$	1.05381	−	12.8586i	0.0345558	−	0.421652i
$931$	19.1095	−	26.3020i	0.626289	−	0.862012i
$932$	−24.2810	−	3.84574i	−0.795352	−	0.125971i
$933$	33.4507	−	17.0440i	1.09513	−	0.557994i
$934$	−1.55432			−0.0508591
$935$	5.60363	+	9.16260i	0.183258	+	0.299649i
$936$	0.268514			0.00877665
$937$	−19.8149	+	10.0962i	−0.647326	+	0.329829i	−0.746641	−	0.665227i	$-0.768335\pi$
$937$	−19.8149	+	10.0962i	−0.647326	+	0.329829i	0.0993152	+	0.995056i	$0.468335\pi$
$938$	−4.07551	−	0.645497i	−0.133070	−	0.0210762i
$939$	−13.9502	+	19.2007i	−0.455246	+	0.626593i
$940$	18.3622	+	21.6406i	0.598909	+	0.705837i
$941$	−20.9430	+	6.80478i	−0.682721	+	0.221829i	−0.629786	−	0.776769i	$-0.716857\pi$
$941$	−20.9430	+	6.80478i	−0.682721	+	0.221829i	−0.0529346	+	0.998598i	$0.516857\pi$
$942$	−0.211302	−	1.33411i	−0.00688461	−	0.0434677i
$943$	4.55217	−	28.7413i	0.148239	−	0.935944i
$944$	0.411545	+	0.133719i	0.0133947	+	0.00435219i
$945$	−3.57191	+	8.54517i	−0.116194	+	0.277974i
$946$	25.3074	+	25.1892i	0.822814	+	0.818972i
$947$	−2.70333	+	2.70333i	−0.0878464	+	0.0878464i	−0.749664	−	0.661818i	$-0.769785\pi$
$947$	−2.70333	+	2.70333i	−0.0878464	+	0.0878464i	0.661818	+	0.749664i	$0.269785\pi$
$948$	7.50467	+	14.7287i	0.243740	+	0.478367i
$949$	−0.574182	−	0.790294i	−0.0186387	−	0.0256540i
$950$	15.0183	−	20.3925i	0.487258	−	0.661620i
$951$	1.13277	+	3.48631i	0.0367326	+	0.113051i
$952$	−0.501359	+	0.983972i	−0.0162491	+	0.0318907i
$953$	36.6765	−	5.80899i	1.18807	−	0.188172i	0.469056	−	0.883168i	$-0.344594\pi$
$953$	36.6765	−	5.80899i	1.18807	−	0.188172i	0.719013	+	0.694997i	$0.244594\pi$
$954$	2.09052	−	1.51885i	0.0676831	−	0.0491746i
$955$	−45.6050	−	39.2059i	−1.47574	−	1.26867i
$956$			2.96744i			0.0959740i
$957$	−3.53013	+	1.15615i	−0.114113	+	0.0373730i
$958$	−17.1065	−	17.1065i	−0.552687	−	0.552687i
$959$	−0.397745	+	1.22413i	−0.0128439	+	0.0395294i
$960$	3.11810	+	1.92466i	0.100636	+	0.0621181i
$961$	15.0500	+	10.9345i	0.485484	+	0.352725i
$962$	6.17258	+	3.14509i	0.199012	+	0.101402i
$963$	1.83020	+	0.932533i	0.0589773	+	0.0300505i
$964$	17.2206	+	12.5115i	0.554638	+	0.402968i
$965$	18.4285	+	11.3750i	0.593233	+	0.366175i
$966$	0.904151	−	2.78269i	0.0290906	−	0.0895316i
$967$	16.6994	+	16.6994i	0.537017	+	0.537017i	0.922652	−	0.385634i	$-0.126017\pi$
$967$	16.6994	+	16.6994i	0.537017	+	0.537017i	−0.385634	+	0.922652i	$0.626017\pi$
$968$	−9.77759	+	5.03971i	−0.314264	+	0.161983i
$969$			12.0208i			0.386163i
$970$	−24.1234	−	20.7385i	−0.774557	−	0.665874i
$971$	−21.9153	+	15.9224i	−0.703294	+	0.510973i	−0.881003	−	0.473110i	$-0.843131\pi$
$971$	−21.9153	+	15.9224i	−0.703294	+	0.510973i	0.177709	+	0.984083i	$0.443131\pi$
$972$	3.21562	−	0.509304i	0.103141	−	0.0163359i
$973$	3.00373	−	5.89515i	0.0962951	−	0.188990i
$974$	5.79872	+	17.8466i	0.185803	+	0.571843i
$975$	−1.04925	−	6.91352i	−0.0336028	−	0.221410i
$976$	−7.45513	−	10.2611i	−0.238633	−	0.328450i
$977$	−18.3451	−	36.0042i	−0.586911	−	1.15188i	−0.973299	−	0.229541i	$-0.926278\pi$
$977$	−18.3451	−	36.0042i	−0.586911	−	1.15188i	0.386388	−	0.922336i	$-0.373722\pi$
$978$	−10.3558	+	10.3558i	−0.331142	+	0.331142i
$979$	−33.1671	−	16.8018i	−1.06003	−	0.536989i
$980$	−5.53518	+	13.2419i	−0.176815	+	0.422998i
$981$	3.53462	+	1.14847i	0.112852	+	0.0366678i
$982$	3.97058	−	25.0692i	0.126706	−	0.799992i
$983$	3.76279	+	23.7573i	0.120014	+	0.757740i	0.972140	+	0.234402i	$0.0753133\pi$
$983$	3.76279	+	23.7573i	0.120014	+	0.757740i	−0.852125	+	0.523338i	$0.824687\pi$
$984$	19.3689	−	6.29334i	0.617459	−	0.200624i
$985$	−12.2031	−	14.3818i	−0.388823	−	0.458242i
$986$	−0.581796	+	0.800773i	−0.0185282	+	0.0255018i
$987$	15.6651	+	2.48111i	0.498625	+	0.0789745i
$988$	−3.85166	+	1.96252i	−0.122538	+	0.0624361i
$989$	−25.2082			−0.801573
$990$	−0.894847	+	2.15492i	−0.0284401	+	0.0684879i
$991$	−4.81752			−0.153034			−0.0765169	−	0.997068i	$-0.524380\pi$
$991$	−4.81752			−0.153034			−0.0765169	+	0.997068i	$0.524380\pi$
$992$	3.13720	−	1.59848i	0.0996062	−	0.0507519i
$993$	3.18320	+	0.504170i	0.101016	+	0.0159993i
$994$	3.56224	−	4.90300i	0.112987	−	0.155514i
$995$	0.151023	−	1.84279i	0.00478776	−	0.0584205i
$996$	−0.372265	+	0.120956i	−0.0117957	+	0.00383264i
$997$	5.75364	+	36.3270i	0.182219	+	1.15049i	0.893993	+	0.448080i	$0.147892\pi$
$997$	5.75364	+	36.3270i	0.182219	+	1.15049i	−0.711774	+	0.702409i	$0.752108\pi$
$998$	−1.42792	+	9.01551i	−0.0451999	+	0.285381i
$999$	41.9332	+	13.6249i	1.32671	+	0.431073i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.2.k.a.13.6	✓	48
3.2	odd	2		990.2.bh.c.343.3		48
4.3	odd	2		880.2.cm.c.673.2		48
5.2	odd	4	inner	110.2.k.a.57.6	yes	48
5.3	odd	4		550.2.bh.b.57.1		48
5.4	even	2		550.2.bh.b.343.1		48
11.6	odd	10	inner	110.2.k.a.83.6	yes	48
15.2	even	4		990.2.bh.c.937.1		48
20.7	even	4		880.2.cm.c.497.2		48
33.17	even	10		990.2.bh.c.523.1		48
44.39	even	10		880.2.cm.c.193.2		48
55.17	even	20	inner	110.2.k.a.17.6	yes	48
55.28	even	20		550.2.bh.b.457.1		48
55.39	odd	10		550.2.bh.b.193.1		48
165.17	odd	20		990.2.bh.c.127.3		48
220.127	odd	20		880.2.cm.c.17.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.k.a.13.6	✓	48	1.1	even	1	trivial
110.2.k.a.17.6	yes	48	55.17	even	20	inner
110.2.k.a.57.6	yes	48	5.2	odd	4	inner
110.2.k.a.83.6	yes	48	11.6	odd	10	inner
550.2.bh.b.57.1		48	5.3	odd	4
550.2.bh.b.193.1		48	55.39	odd	10
550.2.bh.b.343.1		48	5.4	even	2
550.2.bh.b.457.1		48	55.28	even	20
880.2.cm.c.17.2		48	220.127	odd	20
880.2.cm.c.193.2		48	44.39	even	10
880.2.cm.c.497.2		48	20.7	even	4
880.2.cm.c.673.2		48	4.3	odd	2
990.2.bh.c.127.3		48	165.17	odd	20
990.2.bh.c.343.3		48	3.2	odd	2
990.2.bh.c.523.1		48	33.17	even	10
990.2.bh.c.937.1		48	15.2	even	4

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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	110.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.891007 - 0.453990i) q^{2} +(1.61854 + 0.256351i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-2.22860 - 0.182641i) q^{5} +(1.55851 - 0.506390i) q^{6} +(0.119289 + 0.753160i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-0.299227 - 0.0972249i) q^{9} +O(q^{10})\)	\(q+(0.891007 - 0.453990i) q^{2} +(1.61854 + 0.256351i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-2.22860 - 0.182641i) q^{5} +(1.55851 - 0.506390i) q^{6} +(0.119289 + 0.753160i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-0.299227 - 0.0972249i) q^{9} +(-2.06861 + 0.849027i) q^{10} +(-1.49880 + 2.95865i) q^{11} +(1.15874 - 1.15874i) q^{12} +(-0.387452 - 0.760418i) q^{13} +(0.448214 + 0.616914i) q^{14} +(-3.56024 - 0.866914i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-0.657479 + 1.29037i) q^{17} +(-0.310753 + 0.0492184i) q^{18} +(4.09783 - 2.97724i) q^{19} +(-1.45770 + 1.69562i) q^{20} +1.24960i q^{21} +(0.00776159 + 3.31662i) q^{22} +(-1.65567 - 1.65567i) q^{23} +(0.506390 - 1.55851i) q^{24} +(4.93328 + 0.814066i) q^{25} +(-0.690445 - 0.501638i) q^{26} +(-4.83969 - 2.46595i) q^{27} +(0.679435 + 0.346189i) q^{28} +(0.552936 + 0.401731i) q^{29} +(-3.56577 + 0.843891i) q^{30} +(-1.08804 + 3.34864i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.18431 + 4.40446i) q^{33} +1.44822i q^{34} +(-0.128289 - 1.70028i) q^{35} +(-0.254538 + 0.184933i) q^{36} +(-8.01741 + 1.26983i) q^{37} +(2.29955 - 4.51312i) q^{38} +(-0.432172 - 1.33009i) q^{39} +(-0.529022 + 2.17259i) q^{40} +(7.30492 + 10.0544i) q^{41} +(0.567304 + 1.11340i) q^{42} +(7.61267 - 7.61267i) q^{43} +(1.51263 + 2.95160i) q^{44} +(0.649100 + 0.271326i) q^{45} +(-2.22687 - 0.723555i) q^{46} +(1.98553 - 12.5361i) q^{47} +(-0.256351 - 1.61854i) q^{48} +(6.10438 - 1.98343i) q^{49} +(4.76517 - 1.51433i) q^{50} +(-1.39494 + 1.91997i) q^{51} +(-0.842930 - 0.133507i) q^{52} +(-7.31784 + 3.72862i) q^{53} -5.43171 q^{54} +(3.88058 - 6.31990i) q^{55} +0.762548 q^{56} +(7.39570 - 3.76830i) q^{57} +(0.675052 + 0.106918i) q^{58} +(-0.254349 + 0.350081i) q^{59} +(-2.79401 + 2.37074i) q^{60} +(12.0627 - 3.91939i) q^{61} +(0.550800 + 3.47761i) q^{62} +(0.0375314 - 0.236964i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(0.724592 + 1.76543i) q^{65} +(-0.837655 + 5.37005i) q^{66} +(-3.82631 + 3.82631i) q^{67} +(0.657479 + 1.29037i) q^{68} +(-2.25533 - 3.10420i) q^{69} +(-0.886215 - 1.45671i) q^{70} +(-2.45595 - 7.55864i) q^{71} +(-0.142837 + 0.280334i) q^{72} +(1.13052 - 0.179057i) q^{73} +(-6.56708 + 4.77126i) q^{74} +(7.77601 + 2.58225i) q^{75} -5.06519i q^{76} +(-2.40712 - 0.775899i) q^{77} +(-0.988915 - 0.988915i) q^{78} +(-3.11720 + 9.59376i) q^{79} +(0.514972 + 2.17596i) q^{80} +(-6.43745 - 4.67708i) q^{81} +(11.0733 + 5.64213i) q^{82} +(-0.212826 - 0.108440i) q^{83} +(1.01094 + 0.734494i) q^{84} +(1.70093 - 2.75564i) q^{85} +(3.32686 - 10.2390i) q^{86} +(0.791962 + 0.791962i) q^{87} +(2.68776 + 1.94318i) q^{88} +11.2102i q^{89} +(0.701532 - 0.0529317i) q^{90} +(0.526498 - 0.382523i) q^{91} +(-2.31265 + 0.366287i) q^{92} +(-2.61945 + 5.14097i) q^{93} +(-3.92217 - 12.0712i) q^{94} +(-9.67617 + 5.88665i) q^{95} +(-0.963210 - 1.32575i) q^{96} +(6.45889 + 12.6763i) q^{97} +(4.53858 - 4.53858i) q^{98} +(0.736135 - 0.739589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7}+O(q^{10}) \) 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7	\( 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7} + 12 q^{11} - 16 q^{12} - 16 q^{15} + 12 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{25} + 8 q^{26} + 8 q^{27} - 20 q^{28} + 16 q^{31} - 104 q^{33} - 4 q^{36} + 20 q^{37} - 36 q^{38} - 20 q^{41} - 20 q^{42} + 16 q^{45} + 40 q^{46} + 40 q^{47} + 4 q^{48} + 40 q^{50} + 40 q^{51} + 40 q^{52} + 96 q^{55} - 8 q^{56} + 48 q^{58} + 20 q^{60} + 80 q^{61} + 40 q^{62} + 100 q^{63} + 24 q^{66} + 20 q^{68} - 56 q^{70} - 56 q^{71} - 20 q^{73} - 76 q^{75} - 96 q^{77} + 16 q^{78} - 12 q^{80} - 68 q^{81} - 80 q^{85} - 56 q^{86} - 4 q^{88} - 80 q^{90} - 68 q^{91} - 12 q^{92} + 76 q^{93} + 20 q^{95} + 72 q^{97}+O(q^{100}) \) 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7 + 12 * q^11 - 16 * q^12 - 16 * q^15 + 12 * q^16 - 20 * q^17 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^25 + 8 * q^26 + 8 * q^27 - 20 * q^28 + 16 * q^31 - 104 * q^33 - 4 * q^36 + 20 * q^37 - 36 * q^38 - 20 * q^41 - 20 * q^42 + 16 * q^45 + 40 * q^46 + 40 * q^47 + 4 * q^48 + 40 * q^50 + 40 * q^51 + 40 * q^52 + 96 * q^55 - 8 * q^56 + 48 * q^58 + 20 * q^60 + 80 * q^61 + 40 * q^62 + 100 * q^63 + 24 * q^66 + 20 * q^68 - 56 * q^70 - 56 * q^71 - 20 * q^73 - 76 * q^75 - 96 * q^77 + 16 * q^78 - 12 * q^80 - 68 * q^81 - 80 * q^85 - 56 * q^86 - 4 * q^88 - 80 * q^90 - 68 * q^91 - 12 * q^92 + 76 * q^93 + 20 * q^95 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more