LMFDB - Embedded newform 368.2.m.b.289.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [368,2,Mod(49,368)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("368.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(368, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 0, 16])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.m (of order $11$, degree $10$, not minimal)

Newform invariants

comment:select newform

sage:traces = [10,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 46)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			289.1
Root			$-0.841254 + 0.540641i$ of defining polynomial
Character	$\chi$	$=$	368.289
Dual form			368.2.m.b.177.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.71616 + 1.74557i) q^{3} +(0.985691 - 2.15836i) q^{5} +(-0.381761 - 0.112095i) q^{7} +(3.08427 + 6.75361i) q^{9} +(-2.10260 + 2.42653i) q^{11} +(-0.149167 + 0.0437995i) q^{13} +(6.44487 - 4.14187i) q^{15} +(-0.467137 - 3.24901i) q^{17} +(0.404992 - 2.81678i) q^{19} +(-0.841254 - 0.970858i) q^{21} +(-1.27778 - 4.62248i) q^{23} +(-0.412635 - 0.476206i) q^{25} +(-2.03305 + 14.1402i) q^{27} +(-0.0538974 - 0.374864i) q^{29} +(-2.31086 + 1.48510i) q^{31} +(-9.94668 + 2.92061i) q^{33} +(-0.618239 + 0.713486i) q^{35} +(2.66750 + 5.84100i) q^{37} +(-0.481618 - 0.141416i) q^{39} +(-1.66324 + 3.64198i) q^{41} +(-6.25061 - 4.01702i) q^{43} +17.6169 q^{45} -2.97017 q^{47} +(-5.75560 - 3.69890i) q^{49} +(4.40255 - 9.64025i) q^{51} +(-12.5046 - 3.67168i) q^{53} +(3.16481 + 6.92998i) q^{55} +(6.01691 - 6.94388i) q^{57} +(8.29589 - 2.43589i) q^{59} +(9.37463 - 6.02471i) q^{61} +(-0.420407 - 2.92399i) q^{63} +(-0.0524978 + 0.365130i) q^{65} +(5.50581 + 6.35404i) q^{67} +(4.59821 - 14.7858i) q^{69} +(0.233571 + 0.269556i) q^{71} +(-0.802078 + 5.57857i) q^{73} +(-0.289532 - 2.01374i) q^{75} +(1.07469 - 0.690662i) q^{77} +(-7.23307 + 2.12382i) q^{79} +(-15.6186 + 18.0249i) q^{81} +(-5.56234 - 12.1798i) q^{83} +(-7.47299 - 2.19427i) q^{85} +(0.507959 - 1.11227i) q^{87} +(1.81771 + 1.16817i) q^{89} +0.0618559 q^{91} -8.86900 q^{93} +(-5.68043 - 3.65059i) q^{95} +(-1.09254 + 2.39234i) q^{97} +(-22.8728 - 6.71606i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{3} - 6 q^{5} - 3 q^{7} + 9 q^{9} + 12 q^{11} - 14 q^{13} + 13 q^{15} + 15 q^{17} - 2 q^{19} + q^{21} + q^{23} + 13 q^{25} - 26 q^{27} - 8 q^{29} + 21 q^{31} - 15 q^{33} - 7 q^{35} + 28 q^{37}+ \cdots - 20 q^{99}+O(q^{100}) $ 10 * q + 4 * q^3 - 6 * q^5 - 3 * q^7 + 9 * q^9 + 12 * q^11 - 14 * q^13 + 13 * q^15 + 15 * q^17 - 2 * q^19 + q^21 + q^23 + 13 * q^25 - 26 * q^27 - 8 * q^29 + 21 * q^31 - 15 * q^33 - 7 * q^35 + 28 * q^37 + 12 * q^39 - 31 * q^41 - 11 * q^43 + 10 * q^45 - 18 * q^47 - 24 * q^49 + 17 * q^51 - 21 * q^53 - 5 * q^55 + 19 * q^57 + 5 * q^59 + 37 * q^61 - 17 * q^63 + 37 * q^65 + 13 * q^67 - 15 * q^69 - 49 * q^71 - 8 * q^73 - 8 * q^75 - 8 * q^77 - 8 * q^79 - 11 * q^81 + 7 * q^83 - 42 * q^85 + 21 * q^87 - 13 * q^89 + 24 * q^91 - 40 * q^93 + 10 * q^95 - 32 * q^97 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$e\left(\frac{7}{11}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	2.71616	+	1.74557i	1.56818	+	1.00781i	0.979982	+	0.199087i	$0.0637975\pi$
$3$	2.71616	+	1.74557i	1.56818	+	1.00781i	0.588195	+	0.808719i	$0.299839\pi$
$4$		0			0
$5$	0.985691	−	2.15836i	0.440814	−	0.965249i	−0.550634	−	0.834747i	$-0.685614\pi$
$5$	0.985691	−	2.15836i	0.440814	−	0.965249i	0.991448	−	0.130502i	$-0.0416588\pi$
$6$		0			0
$7$	−0.381761	−	0.112095i	−0.144292	−	0.0423679i	0.208789	−	0.977961i	$-0.433048\pi$
$7$	−0.381761	−	0.112095i	−0.144292	−	0.0423679i	−0.353081	+	0.935593i	$0.614866\pi$
$8$		0			0
$9$	3.08427	+	6.75361i	1.02809	+	2.25120i
$10$		0			0
$11$	−2.10260	+	2.42653i	−0.633957	+	0.731626i	−0.978294	−	0.207220i	$-0.933558\pi$
$11$	−2.10260	+	2.42653i	−0.633957	+	0.731626i	0.344337	+	0.938846i	$0.388104\pi$
$12$		0			0
$13$	−0.149167	+	0.0437995i	−0.0413716	+	0.0121478i	−0.302353	−	0.953196i	$-0.597772\pi$
$13$	−0.149167	+	0.0437995i	−0.0413716	+	0.0121478i	0.260981	+	0.965344i	$0.415954\pi$
$14$		0			0
$15$	6.44487	−	4.14187i	1.66406	−	1.06943i
$16$		0			0
$17$	−0.467137	−	3.24901i	−0.113297	−	0.788000i	−0.964674	−	0.263446i	$-0.915141\pi$
$17$	−0.467137	−	3.24901i	−0.113297	−	0.788000i	0.851377	−	0.524554i	$-0.175768\pi$
$18$		0			0
$19$	0.404992	−	2.81678i	0.0929114	−	0.646213i	−0.889145	−	0.457626i	$-0.848700\pi$
$19$	0.404992	−	2.81678i	0.0929114	−	0.646213i	0.982056	−	0.188588i	$-0.0603909\pi$
$20$		0			0
$21$	−0.841254	−	0.970858i	−0.183577	−	0.211859i
$22$		0			0
$23$	−1.27778	−	4.62248i	−0.266435	−	0.963853i
$23$	−1.27778	−	4.62248i	−0.266435	−	0.963853i
$24$		0			0
$25$	−0.412635	−	0.476206i	−0.0825271	−	0.0952413i
$26$		0			0
$27$	−2.03305	+	14.1402i	−0.391261	+	2.72128i
$28$		0			0
$29$	−0.0538974	−	0.374864i	−0.0100085	−	0.0696106i	0.984205	−	0.177032i	$-0.0566496\pi$
$29$	−0.0538974	−	0.374864i	−0.0100085	−	0.0696106i	−0.994214	+	0.107422i	$0.965741\pi$
$30$		0			0
$31$	−2.31086	+	1.48510i	−0.415042	+	0.266731i	−0.731454	−	0.681891i	$-0.761158\pi$
$31$	−2.31086	+	1.48510i	−0.415042	+	0.266731i	0.316412	+	0.948622i	$0.397522\pi$
$32$		0			0
$33$	−9.94668	+	2.92061i	−1.73149	+	0.508413i
$34$		0			0
$35$	−0.618239	+	0.713486i	−0.104502	+	0.120601i
$36$		0			0
$37$	2.66750	+	5.84100i	0.438534	+	0.960255i	0.991865	+	0.127294i	$0.0406290\pi$
$37$	2.66750	+	5.84100i	0.438534	+	0.960255i	−0.553331	+	0.832961i	$0.686644\pi$
$38$		0			0
$39$	−0.481618	−	0.141416i	−0.0771206	−	0.0226446i
$40$		0			0
$41$	−1.66324	+	3.64198i	−0.259754	+	0.568782i	−0.993909	−	0.110200i	$-0.964851\pi$
$41$	−1.66324	+	3.64198i	−0.259754	+	0.568782i	0.734156	+	0.678981i	$0.237578\pi$
$42$		0			0
$43$	−6.25061	−	4.01702i	−0.953209	−	0.612590i	−0.0310980	−	0.999516i	$-0.509900\pi$
$43$	−6.25061	−	4.01702i	−0.953209	−	0.612590i	−0.922111	+	0.386926i	$0.873537\pi$
$44$		0			0
$45$	17.6169			2.62617
$46$		0			0
$47$	−2.97017			−0.433244			−0.216622	−	0.976256i	$-0.569504\pi$
$47$	−2.97017			−0.433244			−0.216622	+	0.976256i	$0.569504\pi$
$48$		0			0
$49$	−5.75560	−	3.69890i	−0.822228	−	0.528414i
$50$		0			0
$51$	4.40255	−	9.64025i	0.616481	−	1.34990i
$52$		0			0
$53$	−12.5046	−	3.67168i	−1.71764	−	0.504344i	−0.733191	−	0.680023i	$-0.761970\pi$
$53$	−12.5046	−	3.67168i	−1.71764	−	0.504344i	−0.984447	+	0.175679i	$0.943788\pi$
$54$		0			0
$55$	3.16481	+	6.92998i	0.426743	+	0.934438i
$56$		0			0
$57$	6.01691	−	6.94388i	0.796959	−	0.919740i
$58$		0			0
$59$	8.29589	−	2.43589i	1.08003	−	0.317126i	0.307141	−	0.951664i	$-0.400628\pi$
$59$	8.29589	−	2.43589i	1.08003	−	0.317126i	0.772892	+	0.634538i	$0.218810\pi$
$60$		0			0
$61$	9.37463	−	6.02471i	1.20030	−	0.771385i	0.221291	−	0.975208i	$-0.428973\pi$
$61$	9.37463	−	6.02471i	1.20030	−	0.771385i	0.979008	+	0.203823i	$0.0653367\pi$
$62$		0			0
$63$	−0.420407	−	2.92399i	−0.0529663	−	0.368389i
$64$		0			0
$65$	−0.0524978	+	0.365130i	−0.00651155	+	0.0452888i
$66$		0			0
$67$	5.50581	+	6.35404i	0.672642	+	0.776270i	0.984787	−	0.173764i	$-0.0555931\pi$
$67$	5.50581	+	6.35404i	0.672642	+	0.776270i	−0.312145	+	0.950034i	$0.601048\pi$
$68$		0			0
$69$	4.59821	−	14.7858i	0.553560	−	1.78001i
$70$		0			0
$71$	0.233571	+	0.269556i	0.0277198	+	0.0319904i	0.769440	−	0.638719i	$-0.220535\pi$
$71$	0.233571	+	0.269556i	0.0277198	+	0.0319904i	−0.741720	+	0.670709i	$0.765990\pi$
$72$		0			0
$73$	−0.802078	+	5.57857i	−0.0938761	+	0.652923i	0.887497	+	0.460813i	$0.152442\pi$
$73$	−0.802078	+	5.57857i	−0.0938761	+	0.652923i	−0.981373	+	0.192110i	$0.938467\pi$
$74$		0			0
$75$	−0.289532	−	2.01374i	−0.0334323	−	0.232526i
$76$		0			0
$77$	1.07469	−	0.690662i	0.122472	−	0.0787082i
$78$		0			0
$79$	−7.23307	+	2.12382i	−0.813784	+	0.238949i	−0.662037	−	0.749471i	$-0.730308\pi$
$79$	−7.23307	+	2.12382i	−0.813784	+	0.238949i	−0.151747	+	0.988419i	$0.548490\pi$
$80$		0			0
$81$	−15.6186	+	18.0249i	−1.73540	+	2.00276i
$82$		0			0
$83$	−5.56234	−	12.1798i	−0.610547	−	1.33691i	−0.922199	−	0.386715i	$-0.873610\pi$
$83$	−5.56234	−	12.1798i	−0.610547	−	1.33691i	0.311653	−	0.950196i	$-0.399117\pi$
$84$		0			0
$85$	−7.47299	−	2.19427i	−0.810559	−	0.238002i
$86$		0			0
$87$	0.507959	−	1.11227i	0.0544589	−	0.119248i
$88$		0			0
$89$	1.81771	+	1.16817i	0.192677	+	0.123826i	0.633422	−	0.773806i	$-0.281650\pi$
$89$	1.81771	+	1.16817i	0.192677	+	0.123826i	−0.440746	+	0.897632i	$0.645286\pi$
$90$		0			0
$91$	0.0618559			0.00648426
$92$		0			0
$93$	−8.86900			−0.919672
$94$		0			0
$95$	−5.68043	−	3.65059i	−0.582800	−	0.374543i
$96$		0			0
$97$	−1.09254	+	2.39234i	−0.110931	+	0.242905i	−0.956953	−	0.290243i	$-0.906264\pi$
$97$	−1.09254	+	2.39234i	−0.110931	+	0.242905i	0.846022	+	0.533148i	$0.178991\pi$
$98$		0			0
$99$	−22.8728	−	6.71606i	−2.29880	−	0.674990i
$100$		0			0
$101$	−3.62945	−	7.94740i	−0.361144	−	0.790795i	−0.999774	−	0.0212810i	$-0.993226\pi$
$101$	−3.62945	−	7.94740i	−0.361144	−	0.790795i	0.638629	−	0.769514i	$-0.279502\pi$
$102$		0			0
$103$	2.80497	−	3.23711i	0.276382	−	0.318962i	−0.600540	−	0.799595i	$-0.705048\pi$
$103$	2.80497	−	3.23711i	0.276382	−	0.318962i	0.876922	+	0.480633i	$0.159593\pi$
$104$		0			0
$105$	−2.92468	+	0.858763i	−0.285419	+	0.0838067i
$106$		0			0
$107$	15.1529	−	9.73821i	1.46489	−	0.941428i	0.466511	−	0.884515i	$-0.345511\pi$
$107$	15.1529	−	9.73821i	1.46489	−	0.941428i	0.998379	−	0.0569126i	$-0.0181256\pi$
$108$		0			0
$109$	1.35720	+	9.43952i	0.129996	+	0.904142i	0.945554	+	0.325466i	$0.105521\pi$
$109$	1.35720	+	9.43952i	0.129996	+	0.904142i	−0.815558	+	0.578676i	$0.803570\pi$
$110$		0			0
$111$	−2.95053	+	20.5214i	−0.280052	+	1.94781i
$112$		0			0
$113$	4.11470	+	4.74861i	0.387078	+	0.446712i	0.915529	−	0.402252i	$-0.131772\pi$
$113$	4.11470	+	4.74861i	0.387078	+	0.446712i	−0.528451	+	0.848964i	$0.677227\pi$
$114$		0			0
$115$	−11.2365	−	1.79843i	−1.04781	−	0.167704i
$116$		0			0
$117$	−0.755877	−	0.872329i	−0.0698809	−	0.0806468i
$118$		0			0
$119$	−0.185863	+	1.29271i	−0.0170380	+	0.118502i
$120$		0			0
$121$	0.0983447	+	0.684003i	0.00894043	+	0.0621821i
$122$		0			0
$123$	−10.8750	+	6.98891i	−0.980561	+	0.630169i
$124$		0			0
$125$	9.94880	−	2.92123i	0.889848	−	0.261283i
$126$		0			0
$127$	−5.80796	+	6.70274i	−0.515373	+	0.594772i	−0.952466	−	0.304644i	$-0.901462\pi$
$127$	−5.80796	+	6.70274i	−0.515373	+	0.594772i	0.437093	+	0.899416i	$0.356008\pi$
$128$		0			0
$129$	−9.96566	−	21.8218i	−0.877428	−	1.92130i
$130$		0			0
$131$	4.99107	+	1.46551i	0.436072	+	0.128042i	0.492398	−	0.870370i	$-0.336120\pi$
$131$	4.99107	+	1.46551i	0.436072	+	0.128042i	−0.0563262	+	0.998412i	$0.517939\pi$
$132$		0			0
$133$	−0.470357	+	1.02994i	−0.0407851	+	0.0893069i
$134$		0			0
$135$	28.5157	+	18.3259i	2.45424	+	1.57724i
$136$		0			0
$137$	−0.501086			−0.0428107			−0.0214053	−	0.999771i	$-0.506814\pi$
$137$	−0.501086			−0.0428107			−0.0214053	+	0.999771i	$0.506814\pi$
$138$		0			0
$139$	15.7509			1.33598			0.667989	−	0.744171i	$-0.267155\pi$
$139$	15.7509			1.33598			0.667989	+	0.744171i	$0.267155\pi$
$140$		0			0
$141$	−8.06747	−	5.18465i	−0.679404	−	0.436626i
$142$		0			0
$143$	0.207359	−	0.454052i	0.0173402	−	0.0379697i
$144$		0			0
$145$	−0.862219	−	0.253170i	−0.0716034	−	0.0210247i
$146$		0			0
$147$	−9.17645	−	20.0936i	−0.756860	−	1.65729i
$148$		0			0
$149$	2.53429	−	2.92473i	0.207617	−	0.239603i	−0.642385	−	0.766382i	$-0.722055\pi$
$149$	2.53429	−	2.92473i	0.207617	−	0.239603i	0.850002	+	0.526779i	$0.176600\pi$
$150$		0			0
$151$	−15.2097	+	4.46596i	−1.23774	+	0.363435i	−0.834167	−	0.551511i	$-0.814051\pi$
$151$	−15.2097	+	4.46596i	−1.23774	+	0.363435i	−0.403577	+	0.914946i	$0.632233\pi$
$152$		0			0
$153$	20.5018	−	13.1757i	1.65747	−	1.06519i
$154$		0			0
$155$	0.927587	+	6.45151i	0.0745056	+	0.518198i
$156$		0			0
$157$	−2.97025	+	20.6585i	−0.237051	+	1.64873i	0.429352	+	0.903137i	$0.358742\pi$
$157$	−2.97025	+	20.6585i	−0.237051	+	1.64873i	−0.666403	+	0.745592i	$0.732167\pi$
$158$		0			0
$159$	−27.5553	−	31.8005i	−2.18528	−	2.52195i
$160$		0			0
$161$	−0.0303516	+	1.90791i	−0.00239204	+	0.150364i
$162$		0			0
$163$	15.5752	+	17.9747i	1.21994	+	1.40789i	0.884964	+	0.465659i	$0.154183\pi$
$163$	15.5752	+	17.9747i	1.21994	+	1.40789i	0.334976	+	0.942227i	$0.391272\pi$
$164$		0			0
$165$	−3.50062	+	24.3473i	−0.272523	+	1.89544i
$166$		0			0
$167$	0.795161	+	5.53047i	0.0615314	+	0.427960i	0.997181	+	0.0750306i	$0.0239054\pi$
$167$	0.795161	+	5.53047i	0.0615314	+	0.427960i	−0.935650	+	0.352930i	$0.885185\pi$
$168$		0			0
$169$	−10.9160	+	7.01526i	−0.839689	+	0.539636i
$170$		0			0
$171$	20.2725	−	5.95255i	1.55028	−	0.455203i
$172$		0			0
$173$	14.9062	−	17.2026i	1.13329	−	1.30789i	0.187817	−	0.982204i	$-0.439859\pi$
$173$	14.9062	−	17.2026i	1.13329	−	1.30789i	0.945478	−	0.325687i	$-0.105596\pi$
$174$		0			0
$175$	0.104147	+	0.228051i	0.00787281	+	0.0172391i
$176$		0			0
$177$	26.7850	+	7.86478i	2.01328	+	0.591153i
$178$		0			0
$179$	−1.03536	+	2.26712i	−0.0773864	+	0.169453i	−0.944371	−	0.328883i	$-0.893328\pi$
$179$	−1.03536	+	2.26712i	−0.0773864	+	0.169453i	0.866984	+	0.498335i	$0.166055\pi$
$180$		0			0
$181$	8.49697	+	5.46067i	0.631575	+	0.405888i	0.816892	−	0.576790i	$-0.195695\pi$
$181$	8.49697	+	5.46067i	0.631575	+	0.405888i	−0.185318	+	0.982679i	$0.559331\pi$
$182$		0			0
$183$	35.9796			2.65969
$184$		0			0
$185$	15.2363			1.12020
$186$		0			0
$187$	8.86601	+	5.69784i	0.648347	+	0.416667i
$188$		0			0
$189$	2.36118	−	5.17027i	0.171751	−	0.376082i
$190$		0			0
$191$	2.46643	+	0.724209i	0.178465	+	0.0524019i	0.369744	−	0.929134i	$-0.379445\pi$
$191$	2.46643	+	0.724209i	0.178465	+	0.0524019i	−0.191279	+	0.981536i	$0.561264\pi$
$192$		0			0
$193$	−9.38297	−	20.5458i	−0.675401	−	1.47892i	−0.867444	−	0.497535i	$-0.834239\pi$
$193$	−9.38297	−	20.5458i	−0.675401	−	1.47892i	0.192043	−	0.981387i	$-0.438489\pi$
$194$		0			0
$195$	−0.779953	+	0.900113i	−0.0558536	+	0.0644585i
$196$		0			0
$197$	−0.491527	+	0.144325i	−0.0350198	+	0.0102828i	−0.299196	−	0.954192i	$-0.596718\pi$
$197$	−0.491527	+	0.144325i	−0.0350198	+	0.0102828i	0.264176	+	0.964475i	$0.414900\pi$
$198$		0			0
$199$	1.10660	−	0.711170i	0.0784449	−	0.0504135i	−0.500830	−	0.865545i	$-0.666972\pi$
$199$	1.10660	−	0.711170i	0.0784449	−	0.0504135i	0.579275	+	0.815132i	$0.303336\pi$
$200$		0			0
$201$	3.86324	+	26.8694i	0.272492	+	1.89522i
$202$		0			0
$203$	−0.0214445	+	0.149150i	−0.00150511	+	0.0104683i
$204$		0			0
$205$	6.22127	+	7.17973i	0.434513	+	0.501454i
$206$		0			0
$207$	27.2774	−	22.8866i	1.89591	−	1.59073i
$208$		0			0
$209$	5.98346	+	6.90528i	0.413884	+	0.477648i
$210$		0			0
$211$	−0.998177	+	6.94248i	−0.0687174	+	0.477940i	0.926183	+	0.377075i	$0.123070\pi$
$211$	−0.998177	+	6.94248i	−0.0687174	+	0.477940i	−0.994900	+	0.100865i	$0.967839\pi$
$212$		0			0
$213$	0.163889	+	1.13987i	0.0112295	+	0.0781028i
$214$		0			0
$215$	−14.8314	+	9.53153i	−1.01149	+	0.650045i
$216$		0			0
$217$	1.04867	−	0.307916i	0.0711880	−	0.0209027i
$218$		0			0
$219$	−11.9164	+	13.7522i	−0.805234	+	0.929289i
$220$		0			0
$221$	0.211986	+	0.464186i	0.0142598	+	0.0312245i
$222$		0			0
$223$	12.3773	+	3.63430i	0.828846	+	0.243371i	0.668521	−	0.743693i	$-0.266928\pi$
$223$	12.3773	+	3.63430i	0.828846	+	0.243371i	0.160325	+	0.987064i	$0.448746\pi$
$224$		0			0
$225$	1.94343	−	4.25553i	0.129562	−	0.283702i
$226$		0			0
$227$	0.648126	+	0.416525i	0.0430176	+	0.0276457i	0.561973	−	0.827156i	$-0.310043\pi$
$227$	0.648126	+	0.416525i	0.0430176	+	0.0276457i	−0.518955	+	0.854801i	$0.673679\pi$
$228$		0			0
$229$	−19.2701			−1.27341			−0.636703	−	0.771109i	$-0.719702\pi$
$229$	−19.2701			−1.27341			−0.636703	+	0.771109i	$0.719702\pi$
$230$		0			0
$231$	4.12463			0.271381
$232$		0			0
$233$	7.12327	+	4.57785i	0.466661	+	0.299905i	0.752760	−	0.658295i	$-0.228722\pi$
$233$	7.12327	+	4.57785i	0.466661	+	0.299905i	−0.286099	+	0.958200i	$0.592359\pi$
$234$		0			0
$235$	−2.92767	+	6.41071i	−0.190980	+	0.418189i
$236$		0			0
$237$	−23.3535	−	6.85720i	−1.51697	−	0.445423i
$238$		0			0
$239$	−3.30114	−	7.22848i	−0.213533	−	0.467572i	0.772310	−	0.635246i	$-0.219101\pi$
$239$	−3.30114	−	7.22848i	−0.213533	−	0.467572i	−0.985842	+	0.167675i	$0.946374\pi$
$240$		0			0
$241$	−8.80435	+	10.1608i	−0.567138	+	0.654512i	−0.964789	−	0.263025i	$-0.915280\pi$
$241$	−8.80435	+	10.1608i	−0.567138	+	0.654512i	0.397651	+	0.917537i	$0.369825\pi$
$242$		0			0
$243$	−32.7657	+	9.62087i	−2.10192	+	0.617179i
$244$		0			0
$245$	−13.6568	+	8.77669i	−0.872501	+	0.560722i
$246$		0			0
$247$	0.0629619	+	0.437910i	0.00400617	+	0.0278635i
$248$		0			0
$249$	6.15254	−	42.7919i	0.389902	−	2.71182i
$250$		0			0
$251$	9.85898	+	11.3779i	0.622293	+	0.718165i	0.976141	−	0.217138i	$-0.0696723\pi$
$251$	9.85898	+	11.3779i	0.622293	+	0.718165i	−0.353848	+	0.935303i	$0.615127\pi$
$252$		0			0
$253$	13.9032	+	6.61865i	0.874088	+	0.416111i
$254$		0			0
$255$	−16.4676	−	19.0046i	−1.03124	−	1.19011i
$256$		0			0
$257$	0.669316	−	4.65520i	0.0417508	−	0.290383i	−0.958239	−	0.285967i	$-0.907685\pi$
$257$	0.669316	−	4.65520i	0.0417508	−	0.290383i	0.999990	−	0.00441617i	$-0.00140572\pi$
$258$		0			0
$259$	−0.363598	−	2.52888i	−0.0225929	−	0.157137i
$260$		0			0
$261$	2.36545	−	1.52019i	0.146418	−	0.0940971i
$262$		0			0
$263$	−19.8270	+	5.82172i	−1.22258	+	0.358983i	−0.828446	−	0.560069i	$-0.810775\pi$
$263$	−19.8270	+	5.82172i	−1.22258	+	0.358983i	−0.394137	+	0.919052i	$0.628956\pi$
$264$		0			0
$265$	−20.2505	+	23.3703i	−1.24398	+	1.43563i
$266$		0			0
$267$	2.89806	+	6.34588i	0.177359	+	0.388361i
$268$		0			0
$269$	−16.0994	−	4.72721i	−0.981598	−	0.288223i	−0.248714	−	0.968577i	$-0.580008\pi$
$269$	−16.0994	−	4.72721i	−0.981598	−	0.288223i	−0.732884	+	0.680354i	$0.761826\pi$
$270$		0			0
$271$	−4.26445	+	9.33785i	−0.259047	+	0.567234i	−0.993810	−	0.111090i	$-0.964566\pi$
$271$	−4.26445	+	9.33785i	−0.259047	+	0.567234i	0.734763	+	0.678324i	$0.237293\pi$
$272$		0			0
$273$	0.168011	+	0.107974i	0.0101685	+	0.00653488i
$274$		0			0
$275$	2.02314			0.122000
$276$		0			0
$277$	25.2836			1.51914			0.759572	−	0.650423i	$-0.225408\pi$
$277$	25.2836			1.51914			0.759572	+	0.650423i	$0.225408\pi$
$278$		0			0
$279$	−17.1571	−	11.0262i	−1.02717	−	0.660120i
$280$		0			0
$281$	−5.58559	+	12.2307i	−0.333208	+	0.729624i	−0.999876	−	0.0157304i	$-0.994993\pi$
$281$	−5.58559	+	12.2307i	−0.333208	+	0.729624i	0.666668	+	0.745355i	$0.267720\pi$
$282$		0			0
$283$	−4.21075	−	1.23639i	−0.250303	−	0.0734957i	0.154174	−	0.988044i	$-0.450728\pi$
$283$	−4.21075	−	1.23639i	−0.250303	−	0.0734957i	−0.404477	+	0.914548i	$0.632547\pi$
$284$		0			0
$285$	−9.05660	−	19.8312i	−0.536467	−	1.17470i
$286$		0			0
$287$	1.04321	−	1.20392i	0.0615785	−	0.0710654i
$288$		0			0
$289$	5.97355	−	1.75399i	0.351385	−	0.103176i
$290$		0			0
$291$	−7.14352	+	4.59086i	−0.418760	+	0.269121i
$292$		0			0
$293$	0.783862	+	5.45188i	0.0457937	+	0.318502i	0.999823	+	0.0187902i	$0.00598145\pi$
$293$	0.783862	+	5.45188i	0.0457937	+	0.318502i	−0.954030	+	0.299712i	$0.903109\pi$
$294$		0			0
$295$	2.91964	−	20.3066i	0.169988	−	1.18229i
$296$		0			0
$297$	−30.0369	−	34.6644i	−1.74291	−	2.01143i
$298$		0			0
$299$	0.393065	+	0.633557i	0.0227315	+	0.0366395i
$300$		0			0
$301$	1.93595	+	2.23420i	0.111586	+	0.128777i
$302$		0			0
$303$	4.01456	−	27.9219i	0.230630	−	1.60407i
$304$		0			0
$305$	−3.76301	−	26.1723i	−0.215470	−	1.49862i
$306$		0			0
$307$	21.4631	−	13.7935i	1.22497	−	0.787238i	0.241867	−	0.970309i	$-0.422240\pi$
$307$	21.4631	−	13.7935i	1.22497	−	0.787238i	0.983100	+	0.183071i	$0.0586039\pi$
$308$		0			0
$309$	13.2694	−	3.89624i	0.754868	−	0.221649i
$310$		0			0
$311$	6.58523	−	7.59976i	0.373414	−	0.430943i	−0.537675	−	0.843152i	$-0.680697\pi$
$311$	6.58523	−	7.59976i	0.373414	−	0.430943i	0.911089	+	0.412209i	$0.135243\pi$
$312$		0			0
$313$	−1.46099	−	3.19913i	−0.0825803	−	0.180826i	0.863837	−	0.503771i	$-0.168054\pi$
$313$	−1.46099	−	3.19913i	−0.0825803	−	0.180826i	−0.946418	+	0.322945i	$0.895327\pi$
$314$		0			0
$315$	−6.72543	−	1.97476i	−0.378935	−	0.111265i
$316$		0			0
$317$	−14.5188	+	31.7918i	−0.815459	+	1.78561i	−0.233566	+	0.972341i	$0.575039\pi$
$317$	−14.5188	+	31.7918i	−0.815459	+	1.78561i	−0.581893	+	0.813265i	$0.697688\pi$
$318$		0			0
$319$	1.02294	+	0.657406i	0.0572739	+	0.0368077i
$320$		0			0
$321$	58.1566			3.24598
$322$		0			0
$323$	−9.34092			−0.519743
$324$		0			0
$325$	0.0824093	+	0.0529613i	0.00457125	+	0.00293776i
$326$		0			0
$327$	−12.7910	+	28.0084i	−0.707343	+	1.54887i
$328$		0			0
$329$	1.13390	+	0.332942i	0.0625137	+	0.0183557i
$330$		0			0
$331$	−0.978864	−	2.14341i	−0.0538033	−	0.117813i	0.880821	−	0.473449i	$-0.156991\pi$
$331$	−0.978864	−	2.14341i	−0.0538033	−	0.117813i	−0.934624	+	0.355637i	$0.884264\pi$
$332$		0			0
$333$	−31.2206	+	36.0305i	−1.71088	+	1.97446i
$334$		0			0
$335$	19.1414	−	5.62041i	1.04580	−	0.307076i
$336$		0			0
$337$	14.9883	−	9.63237i	0.816462	−	0.524708i	−0.0644874	−	0.997919i	$-0.520541\pi$
$337$	14.9883	−	9.63237i	0.816462	−	0.524708i	0.880950	+	0.473210i	$0.156905\pi$
$338$		0			0
$339$	2.88714	+	20.0805i	0.156808	+	1.09062i
$340$		0			0
$341$	1.25517	−	8.72992i	0.0679714	−	0.472752i
$342$		0			0
$343$	3.60651	+	4.16214i	0.194733	+	0.224734i
$344$		0			0
$345$	−27.3808	−	24.4989i	−1.47413	−	1.31897i
$346$		0			0
$347$	−15.1382	−	17.4704i	−0.812660	−	0.937859i	0.186344	−	0.982485i	$-0.440336\pi$
$347$	−15.1382	−	17.4704i	−0.812660	−	0.937859i	−0.999004	+	0.0446251i	$0.985791\pi$
$348$		0			0
$349$	−1.41310	+	9.82834i	−0.0756416	+	0.526099i	0.916407	+	0.400247i	$0.131076\pi$
$349$	−1.41310	+	9.82834i	−0.0756416	+	0.526099i	−0.992049	+	0.125852i	$0.959833\pi$
$350$		0			0
$351$	−0.316068	−	2.19830i	−0.0168705	−	0.117337i
$352$		0			0
$353$	−8.23891	+	5.29483i	−0.438513	+	0.281815i	−0.741212	−	0.671271i	$-0.765749\pi$
$353$	−8.23891	+	5.29483i	−0.438513	+	0.281815i	0.302699	+	0.953086i	$0.402112\pi$
$354$		0			0
$355$	0.812028	−	0.238433i	0.0430980	−	0.0126547i
$356$		0			0
$357$	−2.76135	+	3.18676i	−0.146146	+	0.168661i
$358$		0			0
$359$	11.1748	+	24.4694i	0.589783	+	1.29144i	0.935573	+	0.353133i	$0.114884\pi$
$359$	11.1748	+	24.4694i	0.589783	+	1.29144i	−0.345790	+	0.938312i	$0.612389\pi$
$360$		0			0
$361$	10.4601	+	3.07138i	0.550534	+	0.161651i
$362$		0			0
$363$	−0.926855	+	2.02953i	−0.0486473	+	0.106523i
$364$		0			0
$365$	11.2500	+	7.22992i	0.588851	+	0.378431i
$366$		0			0
$367$	−20.9617			−1.09419			−0.547097	−	0.837069i	$-0.684267\pi$
$367$	−20.9617			−1.09419			−0.547097	+	0.837069i	$0.684267\pi$
$368$		0			0
$369$	−29.7264			−1.54749
$370$		0			0
$371$	4.36218	+	2.80341i	0.226473	+	0.145546i
$372$		0			0
$373$	11.3868	−	24.9337i	0.589588	−	1.29102i	−0.346103	−	0.938196i	$-0.612495\pi$
$373$	11.3868	−	24.9337i	0.589588	−	1.29102i	0.935691	−	0.352820i	$-0.114777\pi$
$374$		0			0
$375$	32.1218	+	9.43180i	1.65876	+	0.487056i
$376$		0			0
$377$	0.0244586	+	0.0535569i	0.00125968	+	0.00275832i
$378$		0			0
$379$	−2.66138	+	3.07140i	−0.136706	+	0.157767i	−0.819975	−	0.572400i	$-0.806012\pi$
$379$	−2.66138	+	3.07140i	−0.136706	+	0.157767i	0.683268	+	0.730167i	$0.260558\pi$
$380$		0			0
$381$	−27.4755	+	8.06752i	−1.40761	+	0.413312i
$382$		0			0
$383$	14.6836	−	9.43657i	0.750297	−	0.482186i	−0.108759	−	0.994068i	$-0.534688\pi$
$383$	14.6836	−	9.43657i	0.750297	−	0.482186i	0.859056	+	0.511882i	$0.171051\pi$
$384$		0			0
$385$	−0.431385	−	3.00035i	−0.0219854	−	0.152912i
$386$		0			0
$387$	7.85083	−	54.6037i	0.399080	−	2.77566i
$388$		0			0
$389$	−7.20827	−	8.31878i	−0.365474	−	0.421779i	0.542992	−	0.839738i	$-0.317291\pi$
$389$	−7.20827	−	8.31878i	−0.365474	−	0.421779i	−0.908466	+	0.417959i	$0.862746\pi$
$390$		0			0
$391$	−14.4216	+	6.31084i	−0.729330	+	0.319153i
$392$		0			0
$393$	10.9984	+	12.6928i	0.554796	+	0.640268i
$394$		0			0
$395$	−2.54560	+	17.7050i	−0.128083	+	0.890836i
$396$		0			0
$397$	−3.19923	−	22.2511i	−0.160565	−	1.11675i	−0.897572	−	0.440868i	$-0.854671\pi$
$397$	−3.19923	−	22.2511i	−0.160565	−	1.11675i	0.737007	−	0.675885i	$-0.236238\pi$
$398$		0			0
$399$	−3.07539	+	1.97643i	−0.153962	+	0.0989455i
$400$		0			0
$401$	0.621311	−	0.182433i	0.0310268	−	0.00911029i	−0.266182	−	0.963923i	$-0.585762\pi$
$401$	0.621311	−	0.182433i	0.0310268	−	0.00911029i	0.297209	+	0.954812i	$0.403944\pi$
$402$		0			0
$403$	0.279658	−	0.322742i	0.0139307	−	0.0160769i
$404$		0			0
$405$	23.5090	+	51.4776i	1.16817	+	2.55794i
$406$		0			0
$407$	−19.7820	−	5.80853i	−0.980559	−	0.287918i
$408$		0			0
$409$	9.93727	−	21.7596i	0.491367	−	1.07594i	−0.487813	−	0.872948i	$-0.662205\pi$
$409$	9.93727	−	21.7596i	0.491367	−	1.07594i	0.979180	−	0.202995i	$-0.0650674\pi$
$410$		0			0
$411$	−1.36103	−	0.874681i	−0.0671347	−	0.0431449i
$412$		0			0
$413$	−3.44009			−0.169276
$414$		0			0
$415$	−31.7712			−1.55959
$416$		0			0
$417$	42.7821	+	27.4944i	2.09505	+	1.34641i
$418$		0			0
$419$	13.5866	−	29.7505i	0.663748	−	1.45340i	−0.215240	−	0.976561i	$-0.569053\pi$
$419$	13.5866	−	29.7505i	0.663748	−	1.45340i	0.878988	−	0.476844i	$-0.158219\pi$
$420$		0			0
$421$	26.8578	+	7.88616i	1.30897	+	0.384348i	0.860500	−	0.509451i	$-0.170151\pi$
$421$	26.8578	+	7.88616i	1.30897	+	0.384348i	0.448468	+	0.893799i	$0.351970\pi$
$422$		0			0
$423$	−9.16082	−	20.0594i	−0.445414	−	0.975321i
$424$		0			0
$425$	−1.35444	+	1.56311i	−0.0657001	+	0.0758219i
$426$		0			0
$427$	−4.25420	+	1.24915i	−0.205875	+	0.0604505i
$428$		0			0
$429$	1.35580	−	0.871319i	0.0654586	−	0.0420677i
$430$		0			0
$431$	0.854386	+	5.94238i	0.0411543	+	0.286235i	0.999997	+	0.00229793i	$0.000731455\pi$
$431$	0.854386	+	5.94238i	0.0411543	+	0.286235i	−0.958843	+	0.283937i	$0.908359\pi$
$432$		0			0
$433$	−1.51859	+	10.5621i	−0.0729790	+	0.507580i	0.920243	+	0.391347i	$0.127991\pi$
$433$	−1.51859	+	10.5621i	−0.0729790	+	0.507580i	−0.993222	+	0.116233i	$0.962918\pi$
$434$		0			0
$435$	−1.90000	−	2.19272i	−0.0910980	−	0.105133i
$436$		0			0
$437$	−13.5380	+	1.72715i	−0.647609	+	0.0826208i
$438$		0			0
$439$	21.5079	+	24.8215i	1.02652	+	1.18466i	0.982620	+	0.185628i	$0.0594320\pi$
$439$	21.5079	+	24.8215i	1.02652	+	1.18466i	0.0438973	+	0.999036i	$0.486023\pi$
$440$		0			0
$441$	7.22910	−	50.2795i	0.344243	−	2.39426i
$442$		0			0
$443$	−0.0587614	−	0.408695i	−0.00279184	−	0.0194177i	0.988378	−	0.152017i	$-0.0485768\pi$
$443$	−0.0587614	−	0.408695i	−0.00279184	−	0.0194177i	−0.991170	+	0.132599i	$0.957668\pi$
$444$		0			0
$445$	4.31303	−	2.77182i	0.204457	−	0.131397i
$446$		0			0
$447$	11.9889	−	3.52025i	0.567054	−	0.166502i
$448$		0			0
$449$	6.17485	−	7.12616i	0.291409	−	0.336304i	−0.591101	−	0.806598i	$-0.701306\pi$
$449$	6.17485	−	7.12616i	0.291409	−	0.336304i	0.882510	+	0.470293i	$0.155852\pi$
$450$		0			0
$451$	−5.34025	−	11.6935i	−0.251462	−	0.550626i
$452$		0			0
$453$	−49.1075	−	14.4193i	−2.30727	−	0.677477i
$454$		0			0
$455$	0.0609708	−	0.133507i	0.00285836	−	0.00625893i
$456$		0			0
$457$	−26.1069	−	16.7779i	−1.22123	−	0.784837i	−0.238728	−	0.971087i	$-0.576730\pi$
$457$	−26.1069	−	16.7779i	−1.22123	−	0.784837i	−0.982502	+	0.186250i	$0.940367\pi$
$458$		0			0
$459$	46.8912			2.18870
$460$		0			0
$461$	−33.0117			−1.53751			−0.768753	−	0.639546i	$-0.779122\pi$
$461$	−33.0117			−1.53751			−0.768753	+	0.639546i	$0.779122\pi$
$462$		0			0
$463$	14.8651	+	9.55319i	0.690838	+	0.443975i	0.838384	−	0.545081i	$-0.183501\pi$
$463$	14.8651	+	9.55319i	0.690838	+	0.443975i	−0.147546	+	0.989055i	$0.547137\pi$
$464$		0			0
$465$	−8.74209	+	19.1425i	−0.405405	+	0.887712i
$466$		0			0
$467$	−10.6555	−	3.12873i	−0.493076	−	0.144780i	0.0257355	−	0.999669i	$-0.491807\pi$
$467$	−10.6555	−	3.12873i	−0.493076	−	0.144780i	−0.518812	+	0.854889i	$0.673625\pi$
$468$		0			0
$469$	−1.38964	−	3.04290i	−0.0641678	−	0.140508i
$470$		0			0
$471$	−44.1286	+	50.9271i	−2.03334	+	2.34660i
$472$		0			0
$473$	22.8899	−	6.72109i	1.05248	−	0.309036i
$474$		0			0
$475$	−1.50848	+	0.969442i	−0.0692139	+	0.0444811i
$476$		0			0
$477$	−13.7705	−	95.7756i	−0.630506	−	4.38526i
$478$		0			0
$479$	−1.46637	+	10.1988i	−0.0670002	+	0.465997i	0.928507	+	0.371314i	$0.121093\pi$
$479$	−1.46637	+	10.1988i	−0.0670002	+	0.465997i	−0.995508	+	0.0946826i	$0.969816\pi$
$480$		0			0
$481$	−0.653736	−	0.754452i	−0.0298078	−	0.0344001i
$482$		0			0
$483$	−3.41283	+	5.12921i	−0.155289	+	0.233387i
$484$		0			0
$485$	4.08662	+	4.71621i	0.185564	+	0.214152i
$486$		0			0
$487$	−1.60654	+	11.1737i	−0.0727994	+	0.506331i	0.920498	+	0.390747i	$0.127783\pi$
$487$	−1.60654	+	11.1737i	−0.0727994	+	0.506331i	−0.993298	+	0.115584i	$0.963126\pi$
$488$		0			0
$489$	10.9285	+	76.0097i	0.494206	+	3.43728i
$490$		0			0
$491$	7.70415	−	4.95115i	0.347683	−	0.223442i	−0.355130	−	0.934817i	$-0.615563\pi$
$491$	7.70415	−	4.95115i	0.347683	−	0.223442i	0.702813	+	0.711375i	$0.251927\pi$
$492$		0			0
$493$	−1.19276	+	0.350226i	−0.0537192	+	0.0157734i
$494$		0			0
$495$	−37.0412	+	42.7478i	−1.66488	+	1.92137i
$496$		0			0
$497$	−0.0589525	−	0.129088i	−0.00264438	−	0.00579039i
$498$		0			0
$499$	−29.9602	−	8.79710i	−1.34120	−	0.393812i	−0.469103	−	0.883143i	$-0.655423\pi$
$499$	−29.9602	−	8.79710i	−1.34120	−	0.393812i	−0.872098	+	0.489331i	$0.837241\pi$
$500$		0			0
$501$	−7.49404	+	16.4097i	−0.334809	+	0.733129i
$502$		0			0
$503$	−14.3084	−	9.19543i	−0.637979	−	0.410004i	0.181277	−	0.983432i	$-0.441977\pi$
$503$	−14.3084	−	9.19543i	−0.637979	−	0.410004i	−0.819256	+	0.573428i	$0.805613\pi$
$504$		0			0
$505$	−20.7309			−0.922512
$506$		0			0
$507$	−41.8952			−1.86063
$508$		0			0
$509$	15.4467	+	9.92700i	0.684663	+	0.440007i	0.836185	−	0.548447i	$-0.184781\pi$
$509$	15.4467	+	9.92700i	0.684663	+	0.440007i	−0.151522	+	0.988454i	$0.548417\pi$
$510$		0			0
$511$	0.931532	−	2.03977i	0.0412085	−	0.0902341i
$512$		0			0
$513$	39.0064	+	11.4533i	1.72217	+	0.505676i
$514$		0			0
$515$	−4.22202	−	9.24494i	−0.186045	−	0.407381i
$516$		0			0
$517$	6.24508	−	7.20721i	0.274658	−	0.316973i
$518$		0			0
$519$	70.5159	−	20.7053i	3.09531	−	0.908864i
$520$		0			0
$521$	−22.1100	+	14.2092i	−0.968655	+	0.622517i	−0.926380	−	0.376589i	$-0.877097\pi$
$521$	−22.1100	+	14.2092i	−0.968655	+	0.622517i	−0.0422744	+	0.999106i	$0.513460\pi$
$522$		0			0
$523$	−4.87720	−	33.9217i	−0.213265	−	1.48329i	−0.762153	−	0.647397i	$-0.775858\pi$
$523$	−4.87720	−	33.9217i	−0.213265	−	1.48329i	0.548888	−	0.835896i	$-0.315051\pi$
$524$		0			0
$525$	−0.115198	+	0.801221i	−0.00502766	+	0.0349681i
$526$		0			0
$527$	5.90457	+	6.81424i	0.257207	+	0.296833i
$528$		0			0
$529$	−19.7346	+	11.8130i	−0.858025	+	0.513608i
$530$		0			0
$531$	42.0378	+	48.5142i	1.82429	+	2.10534i
$532$		0			0
$533$	0.0885838	−	0.616114i	0.00383699	−	0.0266868i
$534$		0			0
$535$	−6.08245	−	42.3044i	−0.262967	−	1.82898i
$536$		0			0
$537$	−6.76963	+	4.35057i	−0.292131	+	0.187741i
$538$		0			0
$539$	21.0772	−	6.18882i	0.907859	−	0.266572i
$540$		0			0
$541$	−5.25176	+	6.06086i	−0.225791	+	0.260577i	−0.857330	−	0.514768i	$-0.827878\pi$
$541$	−5.25176	+	6.06086i	−0.225791	+	0.260577i	0.631539	+	0.775344i	$0.282424\pi$
$542$		0			0
$543$	13.5472	+	29.6641i	0.581364	+	1.27301i
$544$		0			0
$545$	21.7117	+	6.37512i	0.930026	+	0.273080i
$546$		0			0
$547$	−5.85916	+	12.8298i	−0.250520	+	0.548562i	−0.992555	−	0.121799i	$-0.961134\pi$
$547$	−5.85916	+	12.8298i	−0.250520	+	0.548562i	0.742035	+	0.670361i	$0.233861\pi$
$548$		0			0
$549$	69.6024	+	44.7308i	2.97056	+	1.90906i
$550$		0			0
$551$	−1.07774			−0.0459132
$552$		0			0
$553$	2.99937			0.127546
$554$		0			0
$555$	41.3843	+	26.5961i	1.75667	+	1.12894i
$556$		0			0
$557$	−2.71856	+	5.95281i	−0.115189	+	0.252229i	−0.958442	−	0.285289i	$-0.907910\pi$
$557$	−2.71856	+	5.95281i	−0.115189	+	0.252229i	0.843253	+	0.537517i	$0.180638\pi$
$558$		0			0
$559$	1.10833	+	0.325435i	0.0468774	+	0.0137644i
$560$		0			0
$561$	14.1355	+	30.9525i	0.596803	+	1.30682i
$562$		0			0
$563$	−11.8897	+	13.7215i	−0.501093	+	0.578292i	−0.948796	−	0.315890i	$-0.897697\pi$
$563$	−11.8897	+	13.7215i	−0.501093	+	0.578292i	0.447703	+	0.894183i	$0.352242\pi$
$564$		0			0
$565$	14.3050	−	4.20034i	0.601818	−	0.176710i
$566$		0			0
$567$	7.98308	−	5.13041i	0.335258	−	0.215457i
$568$		0			0
$569$	0.552105	+	3.83998i	0.0231455	+	0.160980i	0.998116	−	0.0613534i	$-0.0195417\pi$
$569$	0.552105	+	3.83998i	0.0231455	+	0.160980i	−0.974971	+	0.222334i	$0.928633\pi$
$570$		0			0
$571$	4.70574	−	32.7291i	0.196929	−	1.36967i	−0.616200	−	0.787589i	$-0.711329\pi$
$571$	4.70574	−	32.7291i	0.196929	−	1.36967i	0.813130	−	0.582083i	$-0.197762\pi$
$572$		0			0
$573$	5.43506	+	6.27240i	0.227053	+	0.262033i
$574$		0			0
$575$	−1.67400	+	2.51588i	−0.0698105	+	0.104920i
$576$		0			0
$577$	−13.0284	−	15.0356i	−0.542380	−	0.625940i	0.416711	−	0.909039i	$-0.363183\pi$
$577$	−13.0284	−	15.0356i	−0.542380	−	0.625940i	−0.959091	+	0.283099i	$0.908637\pi$
$578$		0			0
$579$	10.3786	−	72.1844i	0.431318	−	2.99988i
$580$		0			0
$581$	0.758185	+	5.27329i	0.0314548	+	0.218773i
$582$		0			0
$583$	35.2016	−	22.6227i	1.45790	−	0.936936i
$584$		0			0
$585$	−2.62786	+	0.771610i	−0.108649	+	0.0319022i
$586$		0			0
$587$	−1.81135	+	2.09041i	−0.0747623	+	0.0862803i	−0.791898	−	0.610653i	$-0.790907\pi$
$587$	−1.81135	+	2.09041i	−0.0747623	+	0.0862803i	0.717136	+	0.696933i	$0.245453\pi$
$588$		0			0
$589$	3.24731	+	7.11062i	0.133803	+	0.292988i
$590$		0			0
$591$	−1.58700	−	0.465984i	−0.0652803	−	0.0191680i
$592$		0			0
$593$	17.7134	−	38.7869i	0.727401	−	1.59279i	−0.0758313	−	0.997121i	$-0.524161\pi$
$593$	17.7134	−	38.7869i	0.727401	−	1.59279i	0.803232	−	0.595666i	$-0.203112\pi$
$594$		0			0
$595$	2.60692	+	1.67537i	0.106873	+	0.0686834i
$596$		0			0
$597$	4.24711			0.173823
$598$		0			0
$599$	20.1889			0.824895			0.412448	−	0.910981i	$-0.364674\pi$
$599$	20.1889			0.824895			0.412448	+	0.910981i	$0.364674\pi$
$600$		0			0
$601$	−12.5371	−	8.05708i	−0.511397	−	0.328655i	0.259363	−	0.965780i	$-0.416487\pi$
$601$	−12.5371	−	8.05708i	−0.511397	−	0.328655i	−0.770761	+	0.637125i	$0.780124\pi$
$602$		0			0
$603$	−25.9313	+	56.7817i	−1.05601	+	2.31233i
$604$		0			0
$605$	1.57326	+	0.461952i	0.0639622	+	0.0187810i
$606$		0			0
$607$	−12.7592	−	27.9387i	−0.517879	−	1.13400i	−0.970236	−	0.242161i	$-0.922144\pi$
$607$	−12.7592	−	27.9387i	−0.517879	−	1.13400i	0.452357	−	0.891837i	$-0.350583\pi$
$608$		0			0
$609$	−0.318599	+	0.367683i	−0.0129103	+	0.0148993i
$610$		0			0
$611$	0.443053	−	0.130092i	0.0179240	−	0.00526296i
$612$		0			0
$613$	15.9162	−	10.2287i	0.642850	−	0.413135i	−0.178197	−	0.983995i	$-0.557026\pi$
$613$	15.9162	−	10.2287i	0.642850	−	0.413135i	0.821047	+	0.570860i	$0.193390\pi$
$614$		0			0
$615$	4.36525	+	30.3610i	0.176024	+	1.22427i
$616$		0			0
$617$	3.03989	−	21.1429i	0.122381	−	0.851181i	−0.832464	−	0.554079i	$-0.813071\pi$
$617$	3.03989	−	21.1429i	0.122381	−	0.851181i	0.954846	−	0.297103i	$-0.0960203\pi$
$618$		0			0
$619$	5.27356	+	6.08601i	0.211962	+	0.244618i	0.851768	−	0.523919i	$-0.175531\pi$
$619$	5.27356	+	6.08601i	0.211962	+	0.244618i	−0.639806	+	0.768537i	$0.720985\pi$
$620$		0			0
$621$	67.9604	−	8.67027i	2.72716	−	0.347926i
$622$		0			0
$623$	−0.562983	−	0.649717i	−0.0225554	−	0.0260304i
$624$		0			0
$625$	3.94974	−	27.4710i	0.157989	−	1.09884i
$626$		0			0
$627$	4.19838	+	29.2004i	0.167667	+	1.16615i
$628$		0			0
$629$	17.7314	−	11.3953i	0.706996	−	0.454359i
$630$		0			0
$631$	25.9629	−	7.62339i	1.03357	−	0.303483i	0.279406	−	0.960173i	$-0.409862\pi$
$631$	25.9629	−	7.62339i	1.03357	−	0.303483i	0.754160	+	0.656690i	$0.228044\pi$
$632$		0			0
$633$	−14.8298	+	17.1145i	−0.589431	+	0.680240i
$634$		0			0
$635$	8.74209	+	19.1425i	0.346919	+	0.759647i
$636$		0			0
$637$	1.02056	+	0.299663i	0.0404360	+	0.0118731i
$638$		0			0
$639$	−1.10008	+	2.40883i	−0.0435184	+	0.0952920i
$640$		0			0
$641$	−33.4278	−	21.4827i	−1.32032	−	0.848517i	−0.325051	−	0.945697i	$-0.605381\pi$
$641$	−33.4278	−	21.4827i	−1.32032	−	0.848517i	−0.995267	+	0.0971801i	$0.969018\pi$
$642$		0			0
$643$	1.75237			0.0691066			0.0345533	−	0.999403i	$-0.488999\pi$
$643$	1.75237			0.0691066			0.0345533	+	0.999403i	$0.488999\pi$
$644$		0			0
$645$	−56.9223			−2.24131
$646$		0			0
$647$	−7.48969	−	4.81333i	−0.294450	−	0.189232i	0.385072	−	0.922886i	$-0.374177\pi$
$647$	−7.48969	−	4.81333i	−0.294450	−	0.189232i	−0.679522	+	0.733655i	$0.737813\pi$
$648$		0			0
$649$	−11.5322	+	25.2519i	−0.452677	+	0.991224i
$650$		0			0
$651$	3.38583	+	0.994170i	0.132701	+	0.0389646i
$652$		0			0
$653$	−9.55387	−	20.9200i	−0.373872	−	0.818665i	−0.999264	−	0.0383544i	$-0.987788\pi$
$653$	−9.55387	−	20.9200i	−0.373872	−	0.818665i	0.625393	−	0.780310i	$-0.284939\pi$
$654$		0			0
$655$	8.08275	−	9.32799i	0.315819	−	0.364475i
$656$		0			0
$657$	−40.1493	+	11.7889i	−1.56637	+	0.459929i
$658$		0			0
$659$	−27.8796	+	17.9171i	−1.08604	+	0.697953i	−0.955944	−	0.293549i	$-0.905163\pi$
$659$	−27.8796	+	17.9171i	−1.08604	+	0.697953i	−0.130092	+	0.991502i	$0.541527\pi$
$660$		0			0
$661$	3.05748	+	21.2652i	0.118922	+	0.827121i	0.958746	+	0.284263i	$0.0917489\pi$
$661$	3.05748	+	21.2652i	0.118922	+	0.827121i	−0.839824	+	0.542858i	$0.817342\pi$
$662$		0			0
$663$	−0.234479	+	1.63084i	−0.00910643	+	0.0633366i
$664$		0			0
$665$	1.75935	+	2.03040i	0.0682247	+	0.0787355i
$666$		0			0
$667$	−1.66393	+	0.728133i	−0.0644278	+	0.0281934i
$668$		0			0
$669$	27.2748	+	31.4768i	1.05451	+	1.21696i
$670$		0			0
$671$	−5.09196	+	35.4154i	−0.196573	+	1.36719i
$672$		0			0
$673$	−3.63513	−	25.2829i	−0.140124	−	0.974583i	−0.931627	−	0.363417i	$-0.881610\pi$
$673$	−3.63513	−	25.2829i	−0.140124	−	0.974583i	0.791503	−	0.611166i	$-0.209299\pi$
$674$		0			0
$675$	7.57255	−	4.86658i	0.291468	−	0.187315i
$676$		0			0
$677$	46.2052	−	13.5671i	1.77581	−	0.521425i	0.781123	−	0.624377i	$-0.214647\pi$
$677$	46.2052	−	13.5671i	1.77581	−	0.521425i	0.994686	+	0.102952i	$0.0328288\pi$
$678$		0			0
$679$	0.685259	−	0.790831i	0.0262978	−	0.0303493i
$680$		0			0
$681$	1.03334	+	2.26270i	0.0395977	+	0.0867068i
$682$		0			0
$683$	−4.51551	−	1.32587i	−0.172781	−	0.0507331i	0.194198	−	0.980962i	$-0.437790\pi$
$683$	−4.51551	−	1.32587i	−0.172781	−	0.0507331i	−0.366979	+	0.930229i	$0.619608\pi$
$684$		0			0
$685$	−0.493916	+	1.08153i	−0.0188716	+	0.0413230i
$686$		0			0
$687$	−52.3408	−	33.6374i	−1.99693	−	1.28335i
$688$		0			0
$689$	2.02610			0.0771881
$690$		0			0
$691$	7.93027			0.301682			0.150841	−	0.988558i	$-0.451802\pi$
$691$	7.93027			0.301682			0.150841	+	0.988558i	$0.451802\pi$
$692$		0			0
$693$	7.97910	+	5.12786i	0.303101	+	0.194791i
$694$		0			0
$695$	15.5256	−	33.9962i	0.588918	−	1.28955i
$696$		0			0
$697$	12.6098	+	3.70256i	0.477629	+	0.140245i
$698$		0			0
$699$	11.3570	+	24.8683i	0.429561	+	0.940607i
$700$		0			0
$701$	−21.4018	+	24.6990i	−0.808335	+	0.932868i	−0.998807	−	0.0488247i	$-0.984452\pi$
$701$	−21.4018	+	24.6990i	−0.808335	+	0.932868i	0.190473	+	0.981692i	$0.438998\pi$
$702$		0			0
$703$	17.5331	−	5.14819i	0.661274	−	0.194168i
$704$		0			0
$705$	−19.1424	+	12.3021i	−0.720944	+	0.463322i
$706$		0			0
$707$	0.494719	+	3.44085i	0.0186058	+	0.129406i
$708$		0			0
$709$	7.03916	−	48.9584i	0.264361	−	1.83867i	−0.234655	−	0.972079i	$-0.575396\pi$
$709$	7.03916	−	48.9584i	0.264361	−	1.83867i	0.499016	−	0.866593i	$-0.333695\pi$
$710$		0			0
$711$	−36.6522	−	42.2989i	−1.37456	−	1.58633i
$712$		0			0
$713$	9.81758	+	8.78425i	0.367671	+	0.328973i
$714$		0			0
$715$	−0.775617	−	0.895109i	−0.0290064	−	0.0334752i
$716$		0			0
$717$	3.65141	−	25.3961i	0.136364	−	0.948435i
$718$		0			0
$719$	−4.00200	−	27.8345i	−0.149249	−	1.03805i	−0.917452	−	0.397846i	$-0.869758\pi$
$719$	−4.00200	−	27.8345i	−0.149249	−	1.03805i	0.768203	−	0.640207i	$-0.221151\pi$
$720$		0			0
$721$	−1.43369	+	0.921379i	−0.0533935	+	0.0343139i
$722$		0			0
$723$	−41.6503	+	12.2296i	−1.54899	+	0.454825i
$724$		0			0
$725$	−0.156273	+	0.180349i	−0.00580383	+	0.00669798i
$726$		0			0
$727$	−6.50239	−	14.2382i	−0.241160	−	0.528067i	0.749889	−	0.661564i	$-0.230107\pi$
$727$	−6.50239	−	14.2382i	−0.241160	−	0.528067i	−0.991049	+	0.133496i	$0.957380\pi$
$728$		0			0
$729$	−37.1381	−	10.9047i	−1.37549	−	0.403879i
$730$		0			0
$731$	−10.1314	+	22.1848i	−0.374725	+	0.820533i
$732$		0			0
$733$	−8.51386	−	5.47152i	−0.314466	−	0.202095i	0.373881	−	0.927477i	$-0.378027\pi$
$733$	−8.51386	−	5.47152i	−0.314466	−	0.202095i	−0.688347	+	0.725382i	$0.741663\pi$
$734$		0			0
$735$	−52.4144			−1.93334
$736$		0			0
$737$	−26.9948			−0.994366
$738$		0			0
$739$	−10.7530	−	6.91052i	−0.395554	−	0.254207i	0.327710	−	0.944778i	$-0.393723\pi$
$739$	−10.7530	−	6.91052i	−0.395554	−	0.254207i	−0.723265	+	0.690571i	$0.757359\pi$
$740$		0			0
$741$	−0.593388	+	1.29934i	−0.0217987	+	0.0477324i
$742$		0			0
$743$	−34.6951	−	10.1874i	−1.27284	−	0.373739i	−0.425581	−	0.904921i	$-0.639930\pi$
$743$	−34.6951	−	10.1874i	−1.27284	−	0.373739i	−0.847258	+	0.531181i	$0.821748\pi$
$744$		0			0
$745$	−3.81459	−	8.35280i	−0.139756	−	0.306023i
$746$		0			0
$747$	65.1021	−	75.1318i	2.38196	−	2.74893i
$748$		0			0
$749$	−6.87640	+	2.01909i	−0.251258	+	0.0737761i
$750$		0			0
$751$	−14.8497	+	9.54330i	−0.541872	+	0.348240i	−0.782771	−	0.622310i	$-0.786194\pi$
$751$	−14.8497	+	9.54330i	−0.541872	+	0.348240i	0.240899	+	0.970550i	$0.422558\pi$
$752$		0			0
$753$	6.91770	+	48.1137i	0.252095	+	1.75336i
$754$		0			0
$755$	−5.35287	+	37.2300i	−0.194811	+	1.35494i
$756$		0			0
$757$	−32.4005	−	37.3921i	−1.17762	−	1.35904i	−0.919579	−	0.392905i	$-0.871470\pi$
$757$	−32.4005	−	37.3921i	−1.17762	−	1.35904i	−0.258036	−	0.966135i	$-0.583075\pi$
$758$		0			0
$759$	26.2101	+	42.2464i	0.951365	+	1.53345i
$760$		0			0
$761$	15.2253	+	17.5710i	0.551918	+	0.636947i	0.961329	−	0.275403i	$-0.0888112\pi$
$761$	15.2253	+	17.5710i	0.551918	+	0.636947i	−0.409411	+	0.912350i	$0.634266\pi$
$762$		0			0
$763$	0.539999	−	3.75577i	0.0195493	−	0.135968i
$764$		0			0
$765$	−8.22949	−	57.2373i	−0.297538	−	2.06942i
$766$		0			0
$767$	−1.13079	+	0.726712i	−0.0408303	+	0.0262400i
$768$		0			0
$769$	−40.5167	+	11.8968i	−1.46107	+	0.429009i	−0.913186	−	0.407544i	$-0.866385\pi$
$769$	−40.5167	+	11.8968i	−1.46107	+	0.429009i	−0.547886	+	0.836553i	$0.684567\pi$
$770$		0			0
$771$	9.94395	−	11.4759i	0.358123	−	0.413296i
$772$		0			0
$773$	5.46707	+	11.9712i	0.196637	+	0.430574i	0.982107	−	0.188325i	$-0.0603060\pi$
$773$	5.46707	+	11.9712i	0.196637	+	0.430574i	−0.785470	+	0.618900i	$0.787579\pi$
$774$		0			0
$775$	1.66075	+	0.487641i	0.0596560	+	0.0175166i
$776$		0			0
$777$	3.42674	−	7.50352i	0.122934	−	0.269187i
$778$		0			0
$779$	9.58505	+	6.15994i	0.343420	+	0.220703i
$780$		0			0
$781$	−1.14519			−0.0409782
$782$		0			0
$783$	5.41023			0.193346
$784$		0			0
$785$	41.6608	+	26.7738i	1.48694	+	0.955597i
$786$		0			0
$787$	−15.6368	+	34.2398i	−0.557391	+	1.22052i	0.395853	+	0.918314i	$0.370449\pi$
$787$	−15.6368	+	34.2398i	−0.557391	+	1.22052i	−0.953244	+	0.302202i	$0.902278\pi$
$788$		0			0
$789$	−64.0155	−	18.7966i	−2.27901	−	0.669178i
$790$		0			0
$791$	−1.03853	−	2.27407i	−0.0369260	−	0.0808566i
$792$		0			0
$793$	−1.13451	+	1.30929i	−0.0402876	+	0.0464944i
$794$		0			0
$795$	−95.7981	+	28.1289i	−3.39761	+	0.997628i
$796$		0			0
$797$	5.36489	−	3.44780i	0.190034	−	0.122127i	−0.442164	−	0.896934i	$-0.645789\pi$
$797$	5.36489	−	3.44780i	0.190034	−	0.122127i	0.632198	+	0.774807i	$0.282153\pi$
$798$		0			0
$799$	1.38748	+	9.65012i	0.0490854	+	0.341397i
$800$		0			0
$801$	−2.28306	+	15.8790i	−0.0806680	+	0.561058i
$802$		0			0
$803$	−11.8501	−	13.6758i	−0.418182	−	0.482607i
$804$		0			0
$805$	4.08805	+	1.94612i	0.144085	+	0.0685917i
$806$		0			0
$807$	−35.4769	−	40.9425i	−1.24885	−	1.44125i
$808$		0			0
$809$	−3.74186	+	26.0252i	−0.131557	+	0.914998i	0.811969	+	0.583700i	$0.198396\pi$
$809$	−3.74186	+	26.0252i	−0.131557	+	0.914998i	−0.943526	+	0.331298i	$0.892514\pi$
$810$		0			0
$811$	−1.80260	−	12.5374i	−0.0632978	−	0.440246i	−0.996684	−	0.0813719i	$-0.974070\pi$
$811$	−1.80260	−	12.5374i	−0.0632978	−	0.440246i	0.933386	−	0.358874i	$-0.116839\pi$
$812$		0			0
$813$	−27.8828	+	17.9192i	−0.977894	+	0.628454i
$814$		0			0
$815$	54.1482	−	15.8993i	1.89673	−	0.556929i
$816$		0			0
$817$	−13.8465	+	15.9797i	−0.484428	+	0.559059i
$818$		0			0
$819$	0.190780	+	0.417751i	0.00666641	+	0.0145974i
$820$		0			0
$821$	−47.5748	−	13.9692i	−1.66037	−	0.487529i	−0.688933	−	0.724825i	$-0.741921\pi$
$821$	−47.5748	−	13.9692i	−1.66037	−	0.487529i	−0.971437	+	0.237296i	$0.923739\pi$
$822$		0			0
$823$	12.4380	−	27.2354i	0.433561	−	0.949365i	−0.559175	−	0.829050i	$-0.688882\pi$
$823$	12.4380	−	27.2354i	0.433561	−	0.949365i	0.992736	−	0.120316i	$-0.0383907\pi$
$824$		0			0
$825$	5.49516	+	3.53153i	0.191317	+	0.122952i
$826$		0			0
$827$	−19.8427			−0.689998			−0.344999	−	0.938603i	$-0.612121\pi$
$827$	−19.8427			−0.689998			−0.344999	+	0.938603i	$0.612121\pi$
$828$		0			0
$829$	38.9517			1.35285			0.676425	−	0.736512i	$-0.263528\pi$
$829$	38.9517			1.35285			0.676425	+	0.736512i	$0.263528\pi$
$830$		0			0
$831$	68.6744	+	44.1343i	2.38229	+	1.53100i
$832$		0			0
$833$	−9.32910	+	20.4279i	−0.323234	+	0.707784i
$834$		0			0
$835$	12.7205	+	3.73508i	0.440212	+	0.129258i
$836$		0			0
$837$	−16.3014	−	35.6952i	−0.563460	−	1.23381i
$838$		0			0
$839$	−30.6040	+	35.3190i	−1.05657	+	1.21935i	−0.0816792	+	0.996659i	$0.526028\pi$
$839$	−30.6040	+	35.3190i	−1.05657	+	1.21935i	−0.974890	+	0.222687i	$0.928517\pi$
$840$		0			0
$841$	27.6877	−	8.12984i	0.954748	−	0.280339i
$842$		0			0
$843$	−36.5210	+	23.4706i	−1.25785	+	0.808371i
$844$		0			0
$845$	4.38171	+	30.4755i	0.150735	+	1.04839i
$846$		0			0
$847$	0.0391291	−	0.272149i	0.00134449	−	0.00935116i
$848$		0			0
$849$	−9.27888	−	10.7084i	−0.318450	−	0.367511i
$850$		0			0
$851$	23.5914	−	19.7939i	0.808704	−	0.678527i
$852$		0			0
$853$	−11.6361	−	13.4288i	−0.398414	−	0.459794i	0.520727	−	0.853723i	$-0.325661\pi$
$853$	−11.6361	−	13.4288i	−0.398414	−	0.459794i	−0.919141	+	0.393929i	$0.871115\pi$
$854$		0			0
$855$	7.13468	−	49.6228i	0.244001	−	1.69706i
$856$		0			0
$857$	3.35722	+	23.3500i	0.114680	+	0.797620i	0.963264	+	0.268558i	$0.0865470\pi$
$857$	3.35722	+	23.3500i	0.114680	+	0.797620i	−0.848583	+	0.529062i	$0.822544\pi$
$858$		0			0
$859$	−19.5067	+	12.5362i	−0.665561	+	0.427730i	−0.829323	−	0.558770i	$-0.811274\pi$
$859$	−19.5067	+	12.5362i	−0.665561	+	0.427730i	0.163762	+	0.986500i	$0.447637\pi$
$860$		0			0
$861$	4.93505	−	1.44906i	0.168186	−	0.0493839i
$862$		0			0
$863$	23.0756	−	26.6307i	0.785502	−	0.906518i	−0.211992	−	0.977272i	$-0.567995\pi$
$863$	23.0756	−	26.6307i	0.785502	−	0.906518i	0.997494	+	0.0707535i	$0.0225404\pi$
$864$		0			0
$865$	−22.4366	−	49.1294i	−0.762868	−	1.67045i
$866$		0			0
$867$	19.2868	+	5.66313i	0.655015	+	0.192330i
$868$		0			0
$869$	10.0547	−	22.0168i	0.341083	−	0.746869i
$870$		0			0
$871$	−1.09959	−	0.706665i	−0.0372582	−	0.0239444i
$872$		0			0
$873$	−19.5266			−0.660876
$874$		0			0
$875$	−4.12551			−0.139468
$876$		0			0
$877$	27.9357	+	17.9532i	0.943323	+	0.606237i	0.919335	−	0.393475i	$-0.128727\pi$
$877$	27.9357	+	17.9532i	0.943323	+	0.606237i	0.0239879	+	0.999712i	$0.492364\pi$
$878$		0			0
$879$	−7.38754	+	16.1765i	−0.249176	+	0.545619i
$880$		0			0
$881$	−11.9769	−	3.51674i	−0.403512	−	0.118482i	0.0736776	−	0.997282i	$-0.476526\pi$
$881$	−11.9769	−	3.51674i	−0.403512	−	0.118482i	−0.477190	+	0.878800i	$0.658345\pi$
$882$		0			0
$883$	8.57642	+	18.7797i	0.288620	+	0.631989i	0.997292	−	0.0735494i	$-0.0234327\pi$
$883$	8.57642	+	18.7797i	0.288620	+	0.631989i	−0.708672	+	0.705538i	$0.750705\pi$
$884$		0			0
$885$	43.3768	−	50.0595i	1.45809	−	1.68273i
$886$		0			0
$887$	22.0294	−	6.46840i	0.739674	−	0.217188i	0.109874	−	0.993946i	$-0.464955\pi$
$887$	22.0294	−	6.46840i	0.739674	−	0.217188i	0.629799	+	0.776758i	$0.283137\pi$
$888$		0			0
$889$	2.96859	−	1.90780i	0.0995634	−	0.0639855i
$890$		0			0
$891$	−10.8981	−	75.7981i	−0.365101	−	2.53933i
$892$		0			0
$893$	−1.20289	+	8.36632i	−0.0402533	+	0.279968i
$894$		0			0
$895$	3.87272	+	4.46936i	0.129451	+	0.149394i
$896$		0			0
$897$	−0.0382907	+	2.40697i	−0.00127849	+	0.0803662i
$898$		0			0
$899$	0.681259	+	0.786215i	0.0227213	+	0.0262217i
$900$		0			0
$901$	−6.08796	+	42.3427i	−0.202819	+	1.41064i
$902$		0			0
$903$	1.35839	+	9.44779i	0.0452043	+	0.314403i
$904$		0			0
$905$	20.1615	−	12.9570i	0.670191	−	0.430705i
$906$		0			0
$907$	24.1820	−	7.10046i	0.802949	−	0.235767i	0.145590	−	0.989345i	$-0.453492\pi$
$907$	24.1820	−	7.10046i	0.802949	−	0.235767i	0.657359	+	0.753578i	$0.271674\pi$
$908$		0			0
$909$	42.4794	−	49.0238i	1.40895	−	1.62602i
$910$		0			0
$911$	−12.0923	−	26.4784i	−0.400636	−	0.877270i	−0.997205	−	0.0747088i	$-0.976197\pi$
$911$	−12.0923	−	26.4784i	−0.400636	−	0.877270i	0.596570	−	0.802561i	$-0.296530\pi$
$912$		0			0
$913$	41.2501	+	12.1121i	1.36518	+	0.400853i
$914$		0			0
$915$	35.4647	−	77.6569i	1.17243	−	2.56726i
$916$		0			0
$917$	−1.74112	−	1.11895i	−0.0574967	−	0.0369509i
$918$		0			0
$919$	−22.9832			−0.758147			−0.379074	−	0.925367i	$-0.623757\pi$
$919$	−22.9832			−0.758147			−0.379074	+	0.925367i	$0.623757\pi$
$920$		0			0
$921$	82.3750			2.71435
$922$		0			0
$923$	−0.0466477	−	0.0299786i	−0.00153543	−	0.000986759i
$924$		0			0
$925$	1.68082	−	3.68048i	0.0552650	−	0.121014i
$926$		0			0
$927$	30.5135	+	8.95957i	1.00219	+	0.294271i
$928$		0			0
$929$	−7.30034	−	15.9855i	−0.239516	−	0.524467i	0.751255	−	0.660012i	$-0.229449\pi$
$929$	−7.30034	−	15.9855i	−0.239516	−	0.524467i	−0.990771	+	0.135545i	$0.956722\pi$
$930$		0			0
$931$	−12.7499	+	14.7142i	−0.417863	+	0.482239i
$932$		0			0
$933$	31.1525	−	9.14719i	1.01989	−	0.299466i
$934$		0			0
$935$	21.0371	−	13.5198i	0.687988	−	0.442143i
$936$		0			0
$937$	−2.69350	−	18.7337i	−0.0879930	−	0.612004i	−0.985330	−	0.170659i	$-0.945410\pi$
$937$	−2.69350	−	18.7337i	−0.0879930	−	0.612004i	0.897337	−	0.441346i	$-0.145499\pi$
$938$		0			0
$939$	1.61601	−	11.2396i	0.0527367	−	0.366791i
$940$		0			0
$941$	26.6714	+	30.7804i	0.869463	+	1.00341i	0.999928	+	0.0119609i	$0.00380737\pi$
$941$	26.6714	+	30.7804i	0.869463	+	1.00341i	−0.130465	+	0.991453i	$0.541647\pi$
$942$		0			0
$943$	18.9602	+	3.03463i	0.617429	+	0.0988212i
$944$		0			0
$945$	−8.83191	−	10.1926i	−0.287302	−	0.331564i
$946$		0			0
$947$	−2.24956	+	15.6460i	−0.0731009	+	0.508428i	0.920069	+	0.391755i	$0.128132\pi$
$947$	−2.24956	+	15.6460i	−0.0731009	+	0.508428i	−0.993170	+	0.116673i	$0.962777\pi$
$948$		0			0
$949$	−0.124695	−	0.867272i	−0.00404777	−	0.0281528i
$950$		0			0
$951$	−94.9304	+	61.0080i	−3.07833	+	1.97832i
$952$		0			0
$953$	15.5810	−	4.57498i	0.504717	−	0.148198i	−0.0194551	−	0.999811i	$-0.506193\pi$
$953$	15.5810	−	4.57498i	0.504717	−	0.148198i	0.524172	+	0.851613i	$0.324375\pi$
$954$		0			0
$955$	3.99424	−	4.60960i	0.129251	−	0.149163i
$956$		0			0
$957$	1.63093	+	3.57124i	0.0527205	+	0.115442i
$958$		0			0
$959$	0.191295	+	0.0561693i	0.00617724	+	0.00181380i
$960$		0			0
$961$	−9.74333	+	21.3349i	−0.314301	+	0.688223i
$962$		0			0
$963$	112.504	+	72.3018i	3.62538	+	2.32989i
$964$		0			0
$965$	−53.5941			−1.72525
$966$		0			0
$967$	22.9012			0.736453			0.368226	−	0.929736i	$-0.379965\pi$
$967$	22.9012			0.736453			0.368226	+	0.929736i	$0.379965\pi$
$968$		0			0
$969$	−25.3714	−	16.3052i	−0.815048	−	0.523800i
$970$		0			0
$971$	−11.1988	+	24.5220i	−0.359388	+	0.786949i	0.640433	+	0.768014i	$0.278755\pi$
$971$	−11.1988	+	24.5220i	−0.359388	+	0.786949i	−0.999821	+	0.0189350i	$0.993972\pi$
$972$		0			0
$973$	−6.01309	−	1.76560i	−0.192771	−	0.0566026i
$974$		0			0
$975$	0.131389	+	0.287703i	0.00420783	+	0.00921386i
$976$		0			0
$977$	−18.1607	+	20.9585i	−0.581012	+	0.670523i	−0.967822	−	0.251636i	$-0.919031\pi$
$977$	−18.1607	+	20.9585i	−0.581012	+	0.670523i	0.386810	+	0.922159i	$0.373577\pi$
$978$		0			0
$979$	−6.65651	+	1.95453i	−0.212743	+	0.0624670i
$980$		0			0
$981$	−59.5649	+	38.2800i	−1.90176	+	1.22219i
$982$		0			0
$983$	6.36764	+	44.2879i	0.203096	+	1.41256i	0.795026	+	0.606575i	$0.207457\pi$
$983$	6.36764	+	44.2879i	0.203096	+	1.41256i	−0.591930	+	0.805989i	$0.701634\pi$
$984$		0			0
$985$	−0.172987	+	1.20315i	−0.00551183	+	0.0383356i
$986$		0			0
$987$	2.49867	+	2.88362i	0.0795335	+	0.0917866i
$988$		0			0
$989$	−10.5817	+	34.0261i	−0.336479	+	1.08197i
$990$		0			0
$991$	1.42071	+	1.63959i	0.0451305	+	0.0520833i	0.777866	−	0.628430i	$-0.216302\pi$
$991$	1.42071	+	1.63959i	0.0451305	+	0.0520833i	−0.732736	+	0.680514i	$0.761757\pi$
$992$		0			0
$993$	1.08273	−	7.53054i	0.0343593	−	0.238974i
$994$		0			0
$995$	−0.444195	−	3.08944i	−0.0140819	−	0.0979419i
$996$		0			0
$997$	9.17431	−	5.89597i	0.290553	−	0.186727i	−0.387242	−	0.921978i	$-0.626572\pi$
$997$	9.17431	−	5.89597i	0.290553	−	0.186727i	0.677795	+	0.735251i	$0.262936\pi$
$998$		0			0
$999$	−88.0159	+	25.8438i	−2.78470	+	0.817662i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.m.b.289.1		10
4.3	odd	2		46.2.c.a.13.1	✓	10
12.11	even	2		414.2.i.f.289.1		10
23.4	even	11		8464.2.a.bx.1.5		5
23.16	even	11	inner	368.2.m.b.177.1		10
23.19	odd	22		8464.2.a.bw.1.5		5
92.19	even	22		1058.2.a.l.1.1		5
92.27	odd	22		1058.2.a.m.1.1		5
92.39	odd	22		46.2.c.a.39.1	yes	10
276.119	even	22		9522.2.a.bp.1.3		5
276.131	even	22		414.2.i.f.361.1		10
276.203	odd	22		9522.2.a.bu.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.2.c.a.13.1	✓	10	4.3	odd	2
46.2.c.a.39.1	yes	10	92.39	odd	22
368.2.m.b.177.1		10	23.16	even	11	inner
368.2.m.b.289.1		10	1.1	even	1	trivial
414.2.i.f.289.1		10	12.11	even	2
414.2.i.f.361.1		10	276.131	even	22
1058.2.a.l.1.1		5	92.19	even	22
1058.2.a.m.1.1		5	92.27	odd	22
8464.2.a.bw.1.5		5	23.19	odd	22
8464.2.a.bx.1.5		5	23.4	even	11
9522.2.a.bp.1.3		5	276.119	even	22
9522.2.a.bu.1.3		5	276.203	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.m (of order \(11\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.71616 + 1.74557i) q^{3} +(0.985691 - 2.15836i) q^{5} +(-0.381761 - 0.112095i) q^{7} +(3.08427 + 6.75361i) q^{9} +(-2.10260 + 2.42653i) q^{11} +(-0.149167 + 0.0437995i) q^{13} +(6.44487 - 4.14187i) q^{15} +(-0.467137 - 3.24901i) q^{17} +(0.404992 - 2.81678i) q^{19} +(-0.841254 - 0.970858i) q^{21} +(-1.27778 - 4.62248i) q^{23} +(-0.412635 - 0.476206i) q^{25} +(-2.03305 + 14.1402i) q^{27} +(-0.0538974 - 0.374864i) q^{29} +(-2.31086 + 1.48510i) q^{31} +(-9.94668 + 2.92061i) q^{33} +(-0.618239 + 0.713486i) q^{35} +(2.66750 + 5.84100i) q^{37} +(-0.481618 - 0.141416i) q^{39} +(-1.66324 + 3.64198i) q^{41} +(-6.25061 - 4.01702i) q^{43} +17.6169 q^{45} -2.97017 q^{47} +(-5.75560 - 3.69890i) q^{49} +(4.40255 - 9.64025i) q^{51} +(-12.5046 - 3.67168i) q^{53} +(3.16481 + 6.92998i) q^{55} +(6.01691 - 6.94388i) q^{57} +(8.29589 - 2.43589i) q^{59} +(9.37463 - 6.02471i) q^{61} +(-0.420407 - 2.92399i) q^{63} +(-0.0524978 + 0.365130i) q^{65} +(5.50581 + 6.35404i) q^{67} +(4.59821 - 14.7858i) q^{69} +(0.233571 + 0.269556i) q^{71} +(-0.802078 + 5.57857i) q^{73} +(-0.289532 - 2.01374i) q^{75} +(1.07469 - 0.690662i) q^{77} +(-7.23307 + 2.12382i) q^{79} +(-15.6186 + 18.0249i) q^{81} +(-5.56234 - 12.1798i) q^{83} +(-7.47299 - 2.19427i) q^{85} +(0.507959 - 1.11227i) q^{87} +(1.81771 + 1.16817i) q^{89} +0.0618559 q^{91} -8.86900 q^{93} +(-5.68043 - 3.65059i) q^{95} +(-1.09254 + 2.39234i) q^{97} +(-22.8728 - 6.71606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{3} - 6 q^{5} - 3 q^{7} + 9 q^{9} + 12 q^{11} - 14 q^{13} + 13 q^{15} + 15 q^{17} - 2 q^{19} + q^{21} + q^{23} + 13 q^{25} - 26 q^{27} - 8 q^{29} + 21 q^{31} - 15 q^{33} - 7 q^{35} + 28 q^{37}+ \cdots - 20 q^{99}+O(q^{100}) \) 10 * q + 4 * q^3 - 6 * q^5 - 3 * q^7 + 9 * q^9 + 12 * q^11 - 14 * q^13 + 13 * q^15 + 15 * q^17 - 2 * q^19 + q^21 + q^23 + 13 * q^25 - 26 * q^27 - 8 * q^29 + 21 * q^31 - 15 * q^33 - 7 * q^35 + 28 * q^37 + 12 * q^39 - 31 * q^41 - 11 * q^43 + 10 * q^45 - 18 * q^47 - 24 * q^49 + 17 * q^51 - 21 * q^53 - 5 * q^55 + 19 * q^57 + 5 * q^59 + 37 * q^61 - 17 * q^63 + 37 * q^65 + 13 * q^67 - 15 * q^69 - 49 * q^71 - 8 * q^73 - 8 * q^75 - 8 * q^77 - 8 * q^79 - 11 * q^81 + 7 * q^83 - 42 * q^85 + 21 * q^87 - 13 * q^89 + 24 * q^91 - 40 * q^93 + 10 * q^95 - 32 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more