LMFDB - Embedded newform 880.2.bo.h.401.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(81,880)] 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("880.81"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bo (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,5,0,2,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			401.1
Root			$-0.386111 - 0.280526i$ of defining polynomial
Character	$\chi$	$=$	880.401
Dual form			880.2.bo.h.801.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.261370 + 0.189896i) q^{3} +(-0.309017 + 0.951057i) q^{5} +(2.17239 - 1.57833i) q^{7} +(-0.894797 - 2.75390i) q^{9} +(2.79042 - 1.79264i) q^{11} +(-1.44244 - 4.43939i) q^{13} +(-0.261370 + 0.189896i) q^{15} +(-1.42961 + 4.39990i) q^{17} +(-3.51149 - 2.55125i) q^{19} +0.867517 q^{21} -2.77222 q^{23} +(-0.809017 - 0.587785i) q^{25} +(0.588587 - 1.81148i) q^{27} +(2.43790 - 1.77124i) q^{29} +(-0.737407 - 2.26951i) q^{31} +(1.06975 + 0.0613500i) q^{33} +(0.829779 + 2.55380i) q^{35} +(8.61029 - 6.25574i) q^{37} +(0.466012 - 1.43424i) q^{39} +(1.78826 + 1.29924i) q^{41} +7.06719 q^{43} +2.89563 q^{45} +(3.52905 + 2.56401i) q^{47} +(0.0650188 - 0.200107i) q^{49} +(-1.20918 + 0.878523i) q^{51} +(-1.95733 - 6.02403i) q^{53} +(0.842610 + 3.20780i) q^{55} +(-0.433326 - 1.33364i) q^{57} +(9.50375 - 6.90488i) q^{59} +(-1.23070 + 3.78770i) q^{61} +(-6.29042 - 4.57026i) q^{63} +4.66785 q^{65} -7.31984 q^{67} +(-0.724576 - 0.526435i) q^{69} +(-0.369495 + 1.13719i) q^{71} +(-0.826577 + 0.600544i) q^{73} +(-0.0998345 - 0.307259i) q^{75} +(3.23251 - 8.29852i) q^{77} +(-1.08222 - 3.33073i) q^{79} +(-6.53000 + 4.74432i) q^{81} +(-3.43498 + 10.5718i) q^{83} +(-3.74278 - 2.71929i) q^{85} +0.973547 q^{87} +2.76978 q^{89} +(-10.1404 - 7.36742i) q^{91} +(0.238235 - 0.733212i) q^{93} +(3.51149 - 2.55125i) q^{95} +(5.72738 + 17.6271i) q^{97} +(-7.43361 - 6.08051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{3} + 2 q^{5} + q^{7} - 5 q^{9} - 3 q^{11} - 2 q^{13} - 5 q^{15} - 13 q^{17} - 15 q^{19} - 20 q^{21} - 10 q^{23} - 2 q^{25} - 10 q^{27} - 9 q^{29} + 10 q^{31} + 5 q^{33} + 4 q^{35} + 24 q^{37}+ \cdots + 20 q^{99}+O(q^{100}) $ 8 * q + 5 * q^3 + 2 * q^5 + q^7 - 5 * q^9 - 3 * q^11 - 2 * q^13 - 5 * q^15 - 13 * q^17 - 15 * q^19 - 20 * q^21 - 10 * q^23 - 2 * q^25 - 10 * q^27 - 9 * q^29 + 10 * q^31 + 5 * q^33 + 4 * q^35 + 24 * q^37 - 21 * q^39 + 8 * q^41 + 38 * q^43 + q^49 - q^51 + 13 * q^53 - 7 * q^55 - 45 * q^57 + 27 * q^59 + 6 * q^61 - 25 * q^63 + 2 * q^65 + 38 * q^67 - q^69 + 20 * q^71 + 13 * q^73 - 5 * q^75 + 34 * q^77 - 37 * q^79 + 8 * q^81 - 27 * q^83 - 12 * q^85 - 38 * q^87 - 16 * q^89 - 44 * q^91 - 35 * q^93 + 15 * q^95 + 24 * q^97 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$1$

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
$3$	0.261370	+	0.189896i	0.150902	+	0.109637i	0.660674	−	0.750673i	$-0.270270\pi$
$3$	0.261370	+	0.189896i	0.150902	+	0.109637i	−0.509772	+	0.860309i	$0.670270\pi$
$4$		0			0
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$		0			0
$7$	2.17239	−	1.57833i	0.821086	−	0.596554i	−0.0959376	−	0.995387i	$-0.530585\pi$
$7$	2.17239	−	1.57833i	0.821086	−	0.596554i	0.917023	+	0.398834i	$0.130585\pi$
$8$		0			0
$9$	−0.894797	−	2.75390i	−0.298266	−	0.917968i
$10$		0			0
$11$	2.79042	−	1.79264i	0.841344	−	0.540500i
$11$	2.79042	−	1.79264i	0.841344	−	0.540500i
$12$		0			0
$13$	−1.44244	−	4.43939i	−0.400062	−	1.23126i	−0.924949	−	0.380092i	$-0.875892\pi$
$13$	−1.44244	−	4.43939i	−0.400062	−	1.23126i	0.524886	−	0.851172i	$-0.324108\pi$
$14$		0			0
$15$	−0.261370	+	0.189896i	−0.0674854	+	0.0490310i
$16$		0			0
$17$	−1.42961	+	4.39990i	−0.346732	+	1.06713i	0.613918	+	0.789370i	$0.289593\pi$
$17$	−1.42961	+	4.39990i	−0.346732	+	1.06713i	−0.960650	+	0.277762i	$0.910407\pi$
$18$		0			0
$19$	−3.51149	−	2.55125i	−0.805592	−	0.585297i	0.106958	−	0.994264i	$-0.465889\pi$
$19$	−3.51149	−	2.55125i	−0.805592	−	0.585297i	−0.912549	+	0.408967i	$0.865889\pi$
$20$		0			0
$21$	0.867517			0.189308
$22$		0			0
$23$	−2.77222			−0.578048			−0.289024	−	0.957322i	$-0.593331\pi$
$23$	−2.77222			−0.578048			−0.289024	+	0.957322i	$0.593331\pi$
$24$		0			0
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$		0			0
$27$	0.588587	−	1.81148i	0.113274	−	0.348620i
$28$		0			0
$29$	2.43790	−	1.77124i	0.452707	−	0.328911i	−0.337956	−	0.941162i	$-0.609736\pi$
$29$	2.43790	−	1.77124i	0.452707	−	0.328911i	0.790664	+	0.612251i	$0.209736\pi$
$30$		0			0
$31$	−0.737407	−	2.26951i	−0.132442	−	0.407615i	0.862741	−	0.505646i	$-0.168746\pi$
$31$	−0.737407	−	2.26951i	−0.132442	−	0.407615i	−0.995183	+	0.0980305i	$0.968746\pi$
$32$		0			0
$33$	1.06975	+	0.0613500i	0.186219	+	0.0106797i
$34$		0			0
$35$	0.829779	+	2.55380i	0.140258	+	0.431670i
$36$		0			0
$37$	8.61029	−	6.25574i	1.41552	−	1.02844i	0.423033	−	0.906114i	$-0.360965\pi$
$37$	8.61029	−	6.25574i	1.41552	−	1.02844i	0.992490	−	0.122324i	$-0.0390346\pi$
$38$		0			0
$39$	0.466012	−	1.43424i	0.0746217	−	0.229662i
$40$		0			0
$41$	1.78826	+	1.29924i	0.279279	+	0.202908i	0.718603	−	0.695421i	$-0.244782\pi$
$41$	1.78826	+	1.29924i	0.279279	+	0.202908i	−0.439324	+	0.898329i	$0.644782\pi$
$42$		0			0
$43$	7.06719			1.07774			0.538868	−	0.842390i	$-0.318852\pi$
$43$	7.06719			1.07774			0.538868	+	0.842390i	$0.318852\pi$
$44$		0			0
$45$	2.89563			0.431654
$46$		0			0
$47$	3.52905	+	2.56401i	0.514765	+	0.373999i	0.814628	−	0.579983i	$-0.196941\pi$
$47$	3.52905	+	2.56401i	0.514765	+	0.373999i	−0.299863	+	0.953982i	$0.596941\pi$
$48$		0			0
$49$	0.0650188	−	0.200107i	0.00928840	−	0.0285868i
$50$		0			0
$51$	−1.20918	+	0.878523i	−0.169319	+	0.123018i
$52$		0			0
$53$	−1.95733	−	6.02403i	−0.268859	−	0.827464i	−0.990779	−	0.135487i	$-0.956740\pi$
$53$	−1.95733	−	6.02403i	−0.268859	−	0.827464i	0.721920	−	0.691977i	$-0.243260\pi$
$54$		0			0
$55$	0.842610	+	3.20780i	0.113617	+	0.432540i
$56$		0			0
$57$	−0.433326	−	1.33364i	−0.0573954	−	0.176645i
$58$		0			0
$59$	9.50375	−	6.90488i	1.23728	−	0.898939i	0.239869	−	0.970805i	$-0.422896\pi$
$59$	9.50375	−	6.90488i	1.23728	−	0.898939i	0.997414	+	0.0718667i	$0.0228956\pi$
$60$		0			0
$61$	−1.23070	+	3.78770i	−0.157575	+	0.484966i	−0.998413	−	0.0563214i	$-0.982063\pi$
$61$	−1.23070	+	3.78770i	−0.157575	+	0.484966i	0.840838	+	0.541287i	$0.182063\pi$
$62$		0			0
$63$	−6.29042	−	4.57026i	−0.792519	−	0.575799i
$64$		0			0
$65$	4.66785			0.578975
$66$		0			0
$67$	−7.31984			−0.894260			−0.447130	−	0.894469i	$-0.647554\pi$
$67$	−7.31984			−0.894260			−0.447130	+	0.894469i	$0.647554\pi$
$68$		0			0
$69$	−0.724576	−	0.526435i	−0.0872287	−	0.0633754i
$70$		0			0
$71$	−0.369495	+	1.13719i	−0.0438510	+	0.134960i	−0.970585	−	0.240758i	$-0.922604\pi$
$71$	−0.369495	+	1.13719i	−0.0438510	+	0.134960i	0.926734	+	0.375718i	$0.122604\pi$
$72$		0			0
$73$	−0.826577	+	0.600544i	−0.0967436	+	0.0702883i	−0.635105	−	0.772425i	$-0.719043\pi$
$73$	−0.826577	+	0.600544i	−0.0967436	+	0.0702883i	0.538362	+	0.842714i	$0.319043\pi$
$74$		0			0
$75$	−0.0998345	−	0.307259i	−0.0115279	−	0.0354792i
$76$		0			0
$77$	3.23251	−	8.29852i	0.368378	−	0.945704i
$78$		0			0
$79$	−1.08222	−	3.33073i	−0.121759	−	0.374736i	0.871538	−	0.490329i	$-0.163123\pi$
$79$	−1.08222	−	3.33073i	−0.121759	−	0.374736i	−0.993297	+	0.115593i	$0.963123\pi$
$80$		0			0
$81$	−6.53000	+	4.74432i	−0.725555	+	0.527147i
$82$		0			0
$83$	−3.43498	+	10.5718i	−0.377038	+	1.16040i	0.565055	+	0.825053i	$0.308855\pi$
$83$	−3.43498	+	10.5718i	−0.377038	+	1.16040i	−0.942093	+	0.335351i	$0.891145\pi$
$84$		0			0
$85$	−3.74278	−	2.71929i	−0.405961	−	0.294948i
$86$		0			0
$87$	0.973547			0.104375
$88$		0			0
$89$	2.76978			0.293596			0.146798	−	0.989167i	$-0.453103\pi$
$89$	2.76978			0.293596			0.146798	+	0.989167i	$0.453103\pi$
$90$		0			0
$91$	−10.1404	−	7.36742i	−1.06300	−	0.772315i
$92$		0			0
$93$	0.238235	−	0.733212i	0.0247038	−	0.0760305i
$94$		0			0
$95$	3.51149	−	2.55125i	0.360271	−	0.261753i
$96$		0			0
$97$	5.72738	+	17.6271i	0.581528	+	1.78976i	0.612789	+	0.790247i	$0.290048\pi$
$97$	5.72738	+	17.6271i	0.581528	+	1.78976i	−0.0312615	+	0.999511i	$0.509952\pi$
$98$		0			0
$99$	−7.43361	−	6.08051i	−0.747106	−	0.611114i
$100$		0			0
$101$	−2.19852	−	6.76634i	−0.218761	−	0.673276i	−0.998865	−	0.0476270i	$-0.984834\pi$
$101$	−2.19852	−	6.76634i	−0.218761	−	0.673276i	0.780104	−	0.625649i	$-0.215166\pi$
$102$		0			0
$103$	6.09056	−	4.42505i	0.600121	−	0.436014i	−0.245801	−	0.969320i	$-0.579051\pi$
$103$	6.09056	−	4.42505i	0.600121	−	0.436014i	0.845922	+	0.533307i	$0.179051\pi$
$104$		0			0
$105$	−0.268077	+	0.825058i	−0.0261617	+	0.0805174i
$106$		0			0
$107$	14.5859	+	10.5973i	1.41008	+	1.02448i	0.993312	+	0.115465i	$0.0368358\pi$
$107$	14.5859	+	10.5973i	1.41008	+	1.02448i	0.416764	+	0.909015i	$0.363164\pi$
$108$		0			0
$109$	−16.3653			−1.56751			−0.783756	−	0.621068i	$-0.786699\pi$
$109$	−16.3653			−1.56751			−0.783756	+	0.621068i	$0.786699\pi$
$110$		0			0
$111$	3.43842			0.326360
$112$		0			0
$113$	1.66154	+	1.20718i	0.156304	+	0.113562i	0.663188	−	0.748453i	$-0.269203\pi$
$113$	1.66154	+	1.20718i	0.156304	+	0.113562i	−0.506884	+	0.862014i	$0.669203\pi$
$114$		0			0
$115$	0.856664	−	2.63654i	0.0798843	−	0.245859i
$116$		0			0
$117$	−10.9349	+	7.94470i	−1.01094	+	0.734488i
$118$		0			0
$119$	3.83883	+	11.8147i	0.351905	+	1.08305i
$120$		0			0
$121$	4.57291	−	10.0044i	0.415720	−	0.909493i
$122$		0			0
$123$	0.220675	+	0.679167i	0.0198976	+	0.0612384i
$124$		0			0
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$		0			0
$127$	0.0235677	−	0.0725340i	0.00209130	−	0.00643635i	−0.950005	−	0.312233i	$-0.898923\pi$
$127$	0.0235677	−	0.0725340i	0.00209130	−	0.00643635i	0.952097	+	0.305797i	$0.0989229\pi$
$128$		0			0
$129$	1.84715	+	1.34203i	0.162633	+	0.118159i
$130$		0			0
$131$	11.4831			1.00328			0.501642	−	0.865075i	$-0.332730\pi$
$131$	11.4831			1.00328			0.501642	+	0.865075i	$0.332730\pi$
$132$		0			0
$133$	−11.6550			−1.01062
$134$		0			0
$135$	1.54094	+	1.11956i	0.132623	+	0.0963562i
$136$		0			0
$137$	−5.66406	+	17.4322i	−0.483914	+	1.48933i	0.349635	+	0.936886i	$0.386306\pi$
$137$	−5.66406	+	17.4322i	−0.483914	+	1.48933i	−0.833548	+	0.552447i	$0.813694\pi$
$138$		0			0
$139$	−18.7590	+	13.6292i	−1.59111	+	1.15601i	−0.688785	+	0.724966i	$0.741855\pi$
$139$	−18.7590	+	13.6292i	−1.59111	+	1.15601i	−0.902330	+	0.431046i	$0.858145\pi$
$140$		0			0
$141$	0.435493	+	1.34031i	0.0366751	+	0.112874i
$142$		0			0
$143$	−11.9832	−	9.80199i	−1.00209	−	0.819683i
$144$		0			0
$145$	0.931196	+	2.86593i	0.0773317	+	0.238002i
$146$		0			0
$147$	0.0549936	−	0.0399552i	0.00453580	−	0.00329545i
$148$		0			0
$149$	4.53161	−	13.9469i	0.371244	−	1.14257i	−0.574733	−	0.818341i	$-0.694894\pi$
$149$	4.53161	−	13.9469i	0.371244	−	1.14257i	0.945978	−	0.324232i	$-0.105106\pi$
$150$		0			0
$151$	−6.08301	−	4.41957i	−0.495028	−	0.359659i	0.312086	−	0.950054i	$-0.398972\pi$
$151$	−6.08301	−	4.41957i	−0.495028	−	0.359659i	−0.807115	+	0.590394i	$0.798972\pi$
$152$		0			0
$153$	13.3961			1.08301
$154$		0			0
$155$	2.38630			0.191672
$156$		0			0
$157$	10.8262	+	7.86568i	0.864023	+	0.627750i	0.928977	−	0.370139i	$-0.120690\pi$
$157$	10.8262	+	7.86568i	0.864023	+	0.627750i	−0.0649531	+	0.997888i	$0.520690\pi$
$158$		0			0
$159$	0.632355	−	1.94619i	0.0501491	−	0.154343i
$160$		0			0
$161$	−6.02234	+	4.37549i	−0.474627	+	0.344837i
$162$		0			0
$163$	0.238558	+	0.734206i	0.0186853	+	0.0575075i	0.959964	−	0.280122i	$-0.0903749\pi$
$163$	0.238558	+	0.734206i	0.0186853	+	0.0575075i	−0.941279	+	0.337629i	$0.890375\pi$
$164$		0			0
$165$	−0.388918	+	0.998432i	−0.0302772	+	0.0777279i
$166$		0			0
$167$	2.62118	+	8.06716i	0.202833	+	0.624256i	0.999795	+	0.0202268i	$0.00643884\pi$
$167$	2.62118	+	8.06716i	0.202833	+	0.624256i	−0.796962	+	0.604029i	$0.793561\pi$
$168$		0			0
$169$	−7.11029	+	5.16593i	−0.546946	+	0.397379i
$170$		0			0
$171$	−3.88382	+	11.9532i	−0.297003	+	0.914081i
$172$		0			0
$173$	−4.10876	−	2.98519i	−0.312384	−	0.226960i	0.420535	−	0.907276i	$-0.361842\pi$
$173$	−4.10876	−	2.98519i	−0.312384	−	0.226960i	−0.732919	+	0.680316i	$0.761842\pi$
$174$		0			0
$175$	−2.68522			−0.202984
$176$		0			0
$177$	3.79521			0.285265
$178$		0			0
$179$	−9.15568	−	6.65199i	−0.684328	−	0.497193i	0.190463	−	0.981694i	$-0.439001\pi$
$179$	−9.15568	−	6.65199i	−0.684328	−	0.497193i	−0.874791	+	0.484501i	$0.839001\pi$
$180$		0			0
$181$	2.28674	−	7.03787i	0.169972	−	0.523121i	−0.829396	−	0.558661i	$-0.811315\pi$
$181$	2.28674	−	7.03787i	0.169972	−	0.523121i	0.999368	+	0.0355402i	$0.0113152\pi$
$182$		0			0
$183$	−1.04094	+	0.756287i	−0.0769485	+	0.0559063i
$184$		0			0
$185$	3.28884	+	10.1220i	0.241800	+	0.744185i
$186$		0			0
$187$	3.89819	+	14.8403i	0.285064	+	1.08523i
$188$		0			0
$189$	−1.58048	−	4.86423i	−0.114963	−	0.353821i
$190$		0			0
$191$	−4.17135	+	3.03067i	−0.301829	+	0.219291i	−0.728382	−	0.685171i	$-0.759728\pi$
$191$	−4.17135	+	3.03067i	−0.301829	+	0.219291i	0.426554	+	0.904462i	$0.359728\pi$
$192$		0			0
$193$	−1.24605	+	3.83494i	−0.0896925	+	0.276045i	−0.985834	−	0.167723i	$-0.946359\pi$
$193$	−1.24605	+	3.83494i	−0.0896925	+	0.276045i	0.896142	+	0.443768i	$0.146359\pi$
$194$		0			0
$195$	1.22004	+	0.886408i	0.0873686	+	0.0634770i
$196$		0			0
$197$	11.4176			0.813469			0.406734	−	0.913547i	$-0.366667\pi$
$197$	11.4176			0.813469			0.406734	+	0.913547i	$0.366667\pi$
$198$		0			0
$199$	7.16644			0.508015			0.254008	−	0.967202i	$-0.418251\pi$
$199$	7.16644			0.508015			0.254008	+	0.967202i	$0.418251\pi$
$200$		0			0
$201$	−1.91319	−	1.39001i	−0.134946	−	0.0980438i
$202$		0			0
$203$	2.50047	−	7.69565i	0.175498	−	0.540128i
$204$		0			0
$205$	−1.78826	+	1.29924i	−0.124897	+	0.0907431i
$206$		0			0
$207$	2.48058	+	7.63443i	0.172412	+	0.530630i
$208$		0			0
$209$	−14.3720	−	0.824235i	−0.994132	−	0.0570135i
$210$		0			0
$211$	−1.07649	−	3.31309i	−0.0741086	−	0.228083i	0.907140	−	0.420829i	$-0.138261\pi$
$211$	−1.07649	−	3.31309i	−0.0741086	−	0.228083i	−0.981249	+	0.192746i	$0.938261\pi$
$212$		0			0
$213$	−0.312523	+	0.227061i	−0.0214137	+	0.0155580i
$214$		0			0
$215$	−2.18388	+	6.72129i	−0.148939	+	0.458388i
$216$		0			0
$217$	−5.18397	−	3.76638i	−0.351911	−	0.255678i
$218$		0			0
$219$	−0.330084			−0.0223050
$220$		0			0
$221$	21.5950			1.45264
$222$		0			0
$223$	8.53103	+	6.19816i	0.571280	+	0.415059i	0.835570	−	0.549384i	$-0.185138\pi$
$223$	8.53103	+	6.19816i	0.571280	+	0.415059i	−0.264290	+	0.964443i	$0.585138\pi$
$224$		0			0
$225$	−0.894797	+	2.75390i	−0.0596532	+	0.183594i
$226$		0			0
$227$	0.174762	−	0.126972i	0.0115994	−	0.00842743i	−0.581970	−	0.813210i	$-0.697718\pi$
$227$	0.174762	−	0.126972i	0.0115994	−	0.00842743i	0.593570	+	0.804782i	$0.297718\pi$
$228$		0			0
$229$	−0.0233956	−	0.0720042i	−0.00154602	−	0.00475817i	0.950281	−	0.311395i	$-0.100796\pi$
$229$	−0.0233956	−	0.0720042i	−0.00154602	−	0.00475817i	−0.951827	+	0.306637i	$0.900796\pi$
$230$		0			0
$231$	2.42074	−	1.55514i	0.159273	−	0.102321i
$232$		0			0
$233$	4.67235	+	14.3800i	0.306096	+	0.942067i	0.979266	+	0.202579i	$0.0649323\pi$
$233$	4.67235	+	14.3800i	0.306096	+	0.942067i	−0.673170	+	0.739488i	$0.735068\pi$
$234$		0			0
$235$	−3.52905	+	2.56401i	−0.230210	+	0.167257i
$236$		0			0
$237$	0.349634	−	1.07606i	0.0227111	−	0.0698977i
$238$		0			0
$239$	−18.7406	−	13.6158i	−1.21223	−	0.880734i	−0.216796	−	0.976217i	$-0.569561\pi$
$239$	−18.7406	−	13.6158i	−1.21223	−	0.880734i	−0.995431	+	0.0954825i	$0.969561\pi$
$240$		0			0
$241$	−21.3349			−1.37430			−0.687151	−	0.726515i	$-0.741139\pi$
$241$	−21.3349			−1.37430			−0.687151	+	0.726515i	$0.741139\pi$
$242$		0			0
$243$	−8.32179			−0.533843
$244$		0			0
$245$	0.170221	+	0.123673i	0.0108750	+	0.00790119i
$246$		0			0
$247$	−6.26085	+	19.2689i	−0.398368	+	1.22605i
$248$		0			0
$249$	−2.90535	+	2.11086i	−0.184119	+	0.133770i
$250$		0			0
$251$	1.92266	+	5.91734i	0.121357	+	0.373499i	0.993220	−	0.116251i	$-0.0370878\pi$
$251$	1.92266	+	5.91734i	0.121357	+	0.373499i	−0.871863	+	0.489751i	$0.837088\pi$
$252$		0			0
$253$	−7.73567	+	4.96959i	−0.486338	+	0.312435i
$254$		0			0
$255$	−0.461867	−	1.42148i	−0.0289232	−	0.0890165i
$256$		0			0
$257$	11.5611	−	8.39964i	0.721163	−	0.523955i	−0.165593	−	0.986194i	$-0.552954\pi$
$257$	11.5611	−	8.39964i	0.721163	−	0.523955i	0.886755	+	0.462239i	$0.152954\pi$
$258$		0			0
$259$	8.83126	−	27.1798i	0.548748	−	1.68887i
$260$		0			0
$261$	−7.05926	−	5.12885i	−0.436957	−	0.317468i
$262$		0			0
$263$	−4.13132			−0.254748			−0.127374	−	0.991855i	$-0.540655\pi$
$263$	−4.13132			−0.254748			−0.127374	+	0.991855i	$0.540655\pi$
$264$		0			0
$265$	6.33404			0.389097
$266$		0			0
$267$	0.723937	+	0.525971i	0.0443042	+	0.0321889i
$268$		0			0
$269$	−0.520367	+	1.60152i	−0.0317273	+	0.0976466i	−0.965666	−	0.259786i	$-0.916348\pi$
$269$	−0.520367	+	1.60152i	−0.0317273	+	0.0976466i	0.933939	+	0.357433i	$0.116348\pi$
$270$		0			0
$271$	−14.9110	+	10.8335i	−0.905778	+	0.658086i	−0.939943	−	0.341330i	$-0.889123\pi$
$271$	−14.9110	+	10.8335i	−0.905778	+	0.658086i	0.0341657	+	0.999416i	$0.489123\pi$
$272$		0			0
$273$	−1.25134	−	3.85124i	−0.0757348	−	0.233088i
$274$		0			0
$275$	−3.31118	−	0.189896i	−0.199672	−	0.0114512i
$276$		0			0
$277$	−1.05914	−	3.25969i	−0.0636375	−	0.195856i	0.914183	−	0.405303i	$-0.132834\pi$
$277$	−1.05914	−	3.25969i	−0.0636375	−	0.195856i	−0.977820	+	0.209446i	$0.932834\pi$
$278$		0			0
$279$	−5.59017	+	4.06150i	−0.334675	+	0.243155i
$280$		0			0
$281$	−7.05230	+	21.7048i	−0.420705	+	1.29480i	0.486342	+	0.873769i	$0.338331\pi$
$281$	−7.05230	+	21.7048i	−0.420705	+	1.29480i	−0.907047	+	0.421029i	$0.861669\pi$
$282$		0			0
$283$	−23.5416	−	17.1040i	−1.39941	−	1.01673i	−0.994758	−	0.102255i	$-0.967394\pi$
$283$	−23.5416	−	17.1040i	−1.39941	−	1.01673i	−0.404647	−	0.914473i	$-0.632606\pi$
$284$		0			0
$285$	1.40227			0.0830634
$286$		0			0
$287$	5.93542			0.350357
$288$		0			0
$289$	−3.56201	−	2.58795i	−0.209530	−	0.152232i
$290$		0			0
$291$	−1.85035	+	5.69480i	−0.108470	+	0.333835i
$292$		0			0
$293$	−17.1621	+	12.4690i	−1.00262	+	0.728448i	−0.962649	−	0.270753i	$-0.912727\pi$
$293$	−17.1621	+	12.4690i	−1.00262	+	0.728448i	−0.0399740	+	0.999201i	$0.512727\pi$
$294$		0			0
$295$	3.63011	+	11.1723i	0.211353	+	0.650478i
$296$		0			0
$297$	−1.60492	−	6.10992i	−0.0931271	−	0.354534i
$298$		0			0
$299$	3.99878	+	12.3070i	0.231255	+	0.711731i
$300$		0			0
$301$	15.3527	−	11.1544i	0.884913	−	0.642927i
$302$		0			0
$303$	0.710278	−	2.18601i	0.0408044	−	0.125583i
$304$		0			0
$305$	−3.22201	−	2.34093i	−0.184492	−	0.134041i
$306$		0			0
$307$	6.87520			0.392388			0.196194	−	0.980565i	$-0.437142\pi$
$307$	6.87520			0.392388			0.196194	+	0.980565i	$0.437142\pi$
$308$		0			0
$309$	2.43219			0.138363
$310$		0			0
$311$	20.3530	+	14.7873i	1.15411	+	0.838511i	0.989022	−	0.147768i	$-0.0472087\pi$
$311$	20.3530	+	14.7873i	1.15411	+	0.838511i	0.165089	+	0.986279i	$0.447209\pi$
$312$		0			0
$313$	−3.57821	+	11.0126i	−0.202252	+	0.622469i	0.797563	+	0.603236i	$0.206122\pi$
$313$	−3.57821	+	11.0126i	−0.202252	+	0.622469i	−0.999815	+	0.0192328i	$0.993878\pi$
$314$		0			0
$315$	6.29042	−	4.57026i	0.354425	−	0.257505i
$316$		0			0
$317$	6.40940	+	19.7261i	0.359988	+	1.10793i	0.953061	+	0.302780i	$0.0979146\pi$
$317$	6.40940	+	19.7261i	0.359988	+	1.10793i	−0.593073	+	0.805149i	$0.702085\pi$
$318$		0			0
$319$	3.62759	−	9.31278i	0.203106	−	0.521416i
$320$		0			0
$321$	1.79994	+	5.53963i	0.100463	+	0.309192i
$322$		0			0
$323$	16.2453	−	11.8029i	0.903913	−	0.656731i
$324$		0			0
$325$	−1.44244	+	4.43939i	−0.0800124	+	0.246253i
$326$		0			0
$327$	−4.27740	−	3.10771i	−0.236541	−	0.171857i
$328$		0			0
$329$	11.7133			0.645777
$330$		0			0
$331$	32.1415			1.76665			0.883327	−	0.468757i	$-0.155298\pi$
$331$	32.1415			1.76665			0.883327	+	0.468757i	$0.155298\pi$
$332$		0			0
$333$	−24.9322	−	18.1143i	−1.36627	−	0.992657i
$334$		0			0
$335$	2.26195	−	6.96158i	0.123584	−	0.380352i
$336$		0			0
$337$	14.5594	−	10.5780i	0.793100	−	0.576221i	−0.115782	−	0.993275i	$-0.536937\pi$
$337$	14.5594	−	10.5780i	0.793100	−	0.576221i	0.908882	+	0.417054i	$0.136937\pi$
$338$		0			0
$339$	0.205037	+	0.631039i	0.0111361	+	0.0342734i
$340$		0			0
$341$	−6.12608	−	5.01098i	−0.331746	−	0.271360i
$342$		0			0
$343$	5.63386	+	17.3392i	0.304200	+	0.936231i
$344$		0			0
$345$	0.724576	−	0.526435i	0.0390099	−	0.0283423i
$346$		0			0
$347$	2.48753	−	7.65583i	0.133538	−	0.410986i	−0.861822	−	0.507211i	$-0.830677\pi$
$347$	2.48753	−	7.65583i	0.133538	−	0.410986i	0.995360	+	0.0962243i	$0.0306766\pi$
$348$		0			0
$349$	−15.5569	−	11.3027i	−0.832741	−	0.605022i	0.0875926	−	0.996156i	$-0.472083\pi$
$349$	−15.5569	−	11.3027i	−0.832741	−	0.605022i	−0.920333	+	0.391135i	$0.872083\pi$
$350$		0			0
$351$	−8.89088			−0.474560
$352$		0			0
$353$	14.8497			0.790371			0.395186	−	0.918601i	$-0.370680\pi$
$353$	14.8497			0.790371			0.395186	+	0.918601i	$0.370680\pi$
$354$		0			0
$355$	−0.967351	−	0.702822i	−0.0513417	−	0.0373019i
$356$		0			0
$357$	−1.24021	+	3.81698i	−0.0656391	+	0.202016i
$358$		0			0
$359$	8.27079	−	6.00908i	0.436516	−	0.317147i	−0.347733	−	0.937594i	$-0.613048\pi$
$359$	8.27079	−	6.00908i	0.436516	−	0.317147i	0.784249	+	0.620446i	$0.213048\pi$
$360$		0			0
$361$	−0.0496143	−	0.152697i	−0.00261128	−	0.00803670i
$362$		0			0
$363$	3.09503	−	1.74648i	0.162447	−	0.0916662i
$364$		0			0
$365$	−0.315724	−	0.971700i	−0.0165258	−	0.0508611i
$366$		0			0
$367$	11.4422	−	8.31327i	0.597280	−	0.433949i	−0.247632	−	0.968854i	$-0.579653\pi$
$367$	11.4422	−	8.31327i	0.597280	−	0.433949i	0.844912	+	0.534905i	$0.179653\pi$
$368$		0			0
$369$	1.97786	−	6.08724i	0.102964	−	0.316889i
$370$		0			0
$371$	−13.7600	−	9.99722i	−0.714383	−	0.519030i
$372$		0			0
$373$	12.4600			0.645154			0.322577	−	0.946543i	$-0.395451\pi$
$373$	12.4600			0.645154			0.322577	+	0.946543i	$0.395451\pi$
$374$		0			0
$375$	0.323071			0.0166833
$376$		0			0
$377$	−11.3798	−	8.26788i	−0.586088	−	0.425818i
$378$		0			0
$379$	−5.04840	+	15.5374i	−0.259319	+	0.798102i	0.733629	+	0.679550i	$0.237825\pi$
$379$	−5.04840	+	15.5374i	−0.259319	+	0.798102i	−0.992948	+	0.118552i	$0.962175\pi$
$380$		0			0
$381$	0.0199338	−	0.0144828i	0.00102124	−	0.000741975i
$382$		0			0
$383$	0.251122	+	0.772874i	0.0128317	+	0.0394920i	0.957267	−	0.289204i	$-0.0933907\pi$
$383$	0.251122	+	0.772874i	0.0128317	+	0.0394920i	−0.944436	+	0.328696i	$0.893391\pi$
$384$		0			0
$385$	6.89346	+	5.63868i	0.351323	+	0.287374i
$386$		0			0
$387$	−6.32370	−	19.4623i	−0.321452	−	0.989327i
$388$		0			0
$389$	24.5894	−	17.8652i	1.24673	−	0.905802i	0.248702	−	0.968580i	$-0.419996\pi$
$389$	24.5894	−	17.8652i	1.24673	−	0.905802i	0.998028	+	0.0627780i	$0.0199960\pi$
$390$		0			0
$391$	3.96321	−	12.1975i	0.200428	−	0.616854i
$392$		0			0
$393$	3.00134	+	2.18060i	0.151398	+	0.109997i
$394$		0			0
$395$	3.50213			0.176211
$396$		0			0
$397$	−14.8996			−0.747789			−0.373894	−	0.927471i	$-0.621978\pi$
$397$	−14.8996			−0.747789			−0.373894	+	0.927471i	$0.621978\pi$
$398$		0			0
$399$	−3.04628	−	2.21325i	−0.152505	−	0.110801i
$400$		0			0
$401$	3.76049	−	11.5736i	0.187790	−	0.577957i	−0.812196	−	0.583385i	$-0.801728\pi$
$401$	3.76049	−	11.5736i	0.187790	−	0.577957i	0.999985	+	0.00542792i	$0.00172777\pi$
$402$		0			0
$403$	−9.01155	+	6.54727i	−0.448897	+	0.326143i
$404$		0			0
$405$	−2.49424	−	7.67647i	−0.123940	−	0.381447i
$406$		0			0
$407$	12.8121	−	32.8913i	0.635071	−	1.63036i
$408$		0			0
$409$	−0.0809957	−	0.249279i	−0.00400498	−	0.0123261i	0.949034	−	0.315174i	$-0.102063\pi$
$409$	−0.0809957	−	0.249279i	−0.00400498	−	0.0123261i	−0.953039	+	0.302847i	$0.902063\pi$
$410$		0			0
$411$	−4.79073	+	3.48067i	−0.236309	+	0.171689i
$412$		0			0
$413$	9.74764	−	30.0002i	0.479650	−	1.47621i
$414$		0			0
$415$	−8.99290	−	6.53372i	−0.441444	−	0.320728i
$416$		0			0
$417$	−7.49116			−0.366844
$418$		0			0
$419$	1.26916			0.0620023			0.0310012	−	0.999519i	$-0.490130\pi$
$419$	1.26916			0.0620023			0.0310012	+	0.999519i	$0.490130\pi$
$420$		0			0
$421$	23.9999	+	17.4369i	1.16968	+	0.849824i	0.990971	−	0.134078i	$-0.0428071\pi$
$421$	23.9999	+	17.4369i	1.16968	+	0.849824i	0.178712	+	0.983902i	$0.442807\pi$
$422$		0			0
$423$	3.90324	−	12.0129i	0.189782	−	0.584089i
$424$		0			0
$425$	3.74278	−	2.71929i	0.181551	−	0.131905i
$426$		0			0
$427$	3.30470	+	10.1708i	0.159926	+	0.492200i
$428$		0			0
$429$	−1.27070	−	4.83752i	−0.0613497	−	0.233558i
$430$		0			0
$431$	−9.68919	−	29.8203i	−0.466712	−	1.43639i	−0.856817	−	0.515621i	$-0.827561\pi$
$431$	−9.68919	−	29.8203i	−0.466712	−	1.43639i	0.390105	−	0.920771i	$-0.372439\pi$
$432$		0			0
$433$	21.0607	−	15.3015i	1.01212	−	0.735345i	0.0474634	−	0.998873i	$-0.484886\pi$
$433$	21.0607	−	15.3015i	1.01212	−	0.735345i	0.964652	+	0.263528i	$0.0848863\pi$
$434$		0			0
$435$	−0.300843	+	0.925898i	−0.0144243	+	0.0443934i
$436$		0			0
$437$	9.73464	+	7.07263i	0.465671	+	0.338330i
$438$		0			0
$439$	−14.4191			−0.688185			−0.344093	−	0.938936i	$-0.611813\pi$
$439$	−14.4191			−0.688185			−0.344093	+	0.938936i	$0.611813\pi$
$440$		0			0
$441$	−0.609255			−0.0290121
$442$		0			0
$443$	−0.267467	−	0.194326i	−0.0127078	−	0.00923273i	0.581413	−	0.813608i	$-0.302500\pi$
$443$	−0.267467	−	0.194326i	−0.0127078	−	0.00923273i	−0.594121	+	0.804376i	$0.702500\pi$
$444$		0			0
$445$	−0.855908	+	2.63421i	−0.0405739	+	0.124874i
$446$		0			0
$447$	3.83289	−	2.78476i	0.181289	−	0.131715i
$448$		0			0
$449$	2.62920	+	8.09185i	0.124080	+	0.381878i	0.993732	−	0.111786i	$-0.0356571\pi$
$449$	2.62920	+	8.09185i	0.124080	+	0.381878i	−0.869653	+	0.493664i	$0.835657\pi$
$450$		0			0
$451$	7.31906	+	0.419748i	0.344641	+	0.0197652i
$452$		0			0
$453$	−0.750657	−	2.31028i	−0.0352689	−	0.108547i
$454$		0			0
$455$	10.1404	−	7.36742i	0.475388	−	0.345390i
$456$		0			0
$457$	0.351807	−	1.08275i	0.0164569	−	0.0506490i	−0.942491	−	0.334232i	$-0.891523\pi$
$457$	0.351807	−	1.08275i	0.0164569	−	0.0506490i	0.958948	+	0.283583i	$0.0915231\pi$
$458$		0			0
$459$	7.12889	+	5.17944i	0.332748	+	0.241756i
$460$		0			0
$461$	14.5073			0.675670			0.337835	−	0.941205i	$-0.390305\pi$
$461$	14.5073			0.675670			0.337835	+	0.941205i	$0.390305\pi$
$462$		0			0
$463$	4.89739			0.227601			0.113801	−	0.993504i	$-0.463698\pi$
$463$	4.89739			0.227601			0.113801	+	0.993504i	$0.463698\pi$
$464$		0			0
$465$	0.623707	+	0.453150i	0.0289237	+	0.0210143i
$466$		0			0
$467$	−10.0193	+	30.8361i	−0.463637	+	1.42693i	0.397053	+	0.917796i	$0.370033\pi$
$467$	−10.0193	+	30.8361i	−0.463637	+	1.42693i	−0.860689	+	0.509131i	$0.829967\pi$
$468$		0			0
$469$	−15.9015	+	11.5531i	−0.734264	+	0.533474i
$470$		0			0
$471$	1.33597	+	4.11171i	0.0615585	+	0.189457i
$472$		0			0
$473$	19.7204	−	12.6689i	0.906747	−	0.582516i
$474$		0			0
$475$	1.34127	+	4.12801i	0.0615417	+	0.189406i
$476$		0			0
$477$	−14.8382	+	10.7806i	−0.679394	+	0.493609i
$478$		0			0
$479$	−5.48054	+	16.8674i	−0.250412	+	0.770690i	0.744287	+	0.667860i	$0.232790\pi$
$479$	−5.48054	+	16.8674i	−0.250412	+	0.770690i	−0.994699	+	0.102830i	$0.967210\pi$
$480$		0			0
$481$	−40.1915	−	29.2009i	−1.83258	−	1.33144i
$482$		0			0
$483$	−2.40495			−0.109429
$484$		0			0
$485$	−18.5342			−0.841595
$486$		0			0
$487$	−14.9347	−	10.8507i	−0.676754	−	0.491691i	0.195525	−	0.980699i	$-0.437359\pi$
$487$	−14.9347	−	10.8507i	−0.676754	−	0.491691i	−0.872279	+	0.489008i	$0.837359\pi$
$488$		0			0
$489$	−0.0770712	+	0.237201i	−0.00348528	+	0.0107266i
$490$		0			0
$491$	−9.25018	+	6.72065i	−0.417455	+	0.303299i	−0.776613	−	0.629978i	$-0.783064\pi$
$491$	−9.25018	+	6.72065i	−0.417455	+	0.303299i	0.359158	+	0.933277i	$0.383064\pi$
$492$		0			0
$493$	4.30802	+	13.2587i	0.194023	+	0.597142i
$494$		0			0
$495$	8.08002	−	5.19080i	0.363170	−	0.233309i
$496$		0			0
$497$	0.992176	+	3.05360i	0.0445052	+	0.136973i
$498$		0			0
$499$	8.80335	−	6.39601i	0.394092	−	0.286325i	−0.373038	−	0.927816i	$-0.621684\pi$
$499$	8.80335	−	6.39601i	0.394092	−	0.286325i	0.767130	+	0.641491i	$0.221684\pi$
$500$		0			0
$501$	−0.846827	+	2.60627i	−0.0378335	+	0.116439i
$502$		0			0
$503$	36.1830	+	26.2885i	1.61332	+	1.17215i	0.851490	+	0.524371i	$0.175699\pi$
$503$	36.1830	+	26.2885i	1.61332	+	1.17215i	0.761831	+	0.647776i	$0.224301\pi$
$504$		0			0
$505$	7.11455			0.316594
$506$		0			0
$507$	−2.83941			−0.126103
$508$		0			0
$509$	11.1720	+	8.11693i	0.495190	+	0.359777i	0.807177	−	0.590310i	$-0.200994\pi$
$509$	11.1720	+	8.11693i	0.495190	+	0.359777i	−0.311987	+	0.950086i	$0.600994\pi$
$510$		0			0
$511$	−0.847790	+	2.60923i	−0.0375040	+	0.115425i
$512$		0			0
$513$	−6.68836	+	4.85938i	−0.295298	+	0.214547i
$514$		0			0
$515$	2.32639	+	7.15989i	0.102513	+	0.315502i
$516$		0			0
$517$	14.4439	+	0.828356i	0.635241	+	0.0364311i
$518$		0			0
$519$	−0.507030	−	1.56048i	−0.0222562	−	0.0684974i
$520$		0			0
$521$	2.95269	−	2.14525i	0.129360	−	0.0939852i	−0.521224	−	0.853420i	$-0.674524\pi$
$521$	2.95269	−	2.14525i	0.129360	−	0.0939852i	0.650584	+	0.759435i	$0.274524\pi$
$522$		0			0
$523$	1.54109	−	4.74299i	0.0673872	−	0.207396i	−0.911693	−	0.410873i	$-0.865224\pi$
$523$	1.54109	−	4.74299i	0.0673872	−	0.207396i	0.979080	+	0.203476i	$0.0652240\pi$
$524$		0			0
$525$	−0.701836	−	0.509914i	−0.0306306	−	0.0222545i
$526$		0			0
$527$	11.0398			0.480901
$528$		0			0
$529$	−15.3148			−0.665860
$530$		0			0
$531$	−27.5193	−	19.9939i	−1.19424	−	0.867663i
$532$		0			0
$533$	3.18839	−	9.81284i	0.138104	−	0.425041i
$534$		0			0
$535$	−14.5859	+	10.5973i	−0.630605	+	0.458161i
$536$		0			0
$537$	−1.12983	−	3.47726i	−0.0487558	−	0.150055i
$538$		0			0
$539$	−0.177290	−	0.674939i	−0.00763640	−	0.0290717i
$540$		0			0
$541$	0.0765109	+	0.235476i	0.00328946	+	0.0101239i	0.952688	−	0.303951i	$-0.0983058\pi$
$541$	0.0765109	+	0.235476i	0.00328946	+	0.0101239i	−0.949398	+	0.314075i	$0.898306\pi$
$542$		0			0
$543$	1.93415	−	1.40524i	0.0830025	−	0.0603048i
$544$		0			0
$545$	5.05716	−	15.5643i	0.216625	−	0.666703i
$546$		0			0
$547$	−20.4779	−	14.8780i	−0.875570	−	0.636139i	0.0565056	−	0.998402i	$-0.482004\pi$
$547$	−20.4779	−	14.8780i	−0.875570	−	0.636139i	−0.932076	+	0.362263i	$0.882004\pi$
$548$		0			0
$549$	11.5322			0.492182
$550$		0			0
$551$	−13.0796			−0.557208
$552$		0			0
$553$	−7.60799	−	5.52753i	−0.323525	−	0.235054i
$554$		0			0
$555$	−1.06253	+	3.27013i	−0.0451018	+	0.138809i
$556$		0			0
$557$	31.2824	−	22.7280i	1.32548	−	0.963015i	0.325630	−	0.945497i	$-0.394424\pi$
$557$	31.2824	−	22.7280i	1.32548	−	0.963015i	0.999847	−	0.0175177i	$-0.00557635\pi$
$558$		0			0
$559$	−10.1940	−	31.3740i	−0.431161	−	1.32698i
$560$		0			0
$561$	−1.79926	+	4.61907i	−0.0759648	+	0.195017i
$562$		0			0
$563$	−4.30653	−	13.2541i	−0.181498	−	0.558595i	0.818372	−	0.574689i	$-0.194877\pi$
$563$	−4.30653	−	13.2541i	−0.181498	−	0.558595i	−0.999870	+	0.0160940i	$0.994877\pi$
$564$		0			0
$565$	−1.66154	+	1.20718i	−0.0699013	+	0.0507863i
$566$		0			0
$567$	−6.69757	+	20.6130i	−0.281272	+	0.865665i
$568$		0			0
$569$	−22.5817	−	16.4065i	−0.946672	−	0.687798i	0.00334520	−	0.999994i	$-0.498935\pi$
$569$	−22.5817	−	16.4065i	−0.946672	−	0.687798i	−0.950017	+	0.312197i	$0.898935\pi$
$570$		0			0
$571$	31.4113			1.31452			0.657261	−	0.753663i	$-0.271715\pi$
$571$	31.4113			1.31452			0.657261	+	0.753663i	$0.271715\pi$
$572$		0			0
$573$	−1.66578			−0.0695889
$574$		0			0
$575$	2.24278	+	1.62947i	0.0935302	+	0.0679537i
$576$		0			0
$577$	6.40744	−	19.7201i	0.266745	−	0.820958i	−0.724541	−	0.689232i	$-0.757948\pi$
$577$	6.40744	−	19.7201i	0.266745	−	0.820958i	0.991286	−	0.131726i	$-0.0420519\pi$
$578$		0			0
$579$	−1.05392	+	0.765719i	−0.0437995	+	0.0318222i
$580$		0			0
$581$	9.22368	+	28.3876i	0.382663	+	1.17771i
$582$		0			0
$583$	−16.2607	−	13.3008i	−0.673448	−	0.550864i
$584$		0			0
$585$	−4.17678	−	12.8548i	−0.172689	−	0.531481i
$586$		0			0
$587$	12.3267	−	8.95591i	0.508779	−	0.369650i	−0.303581	−	0.952806i	$-0.598182\pi$
$587$	12.3267	−	8.95591i	0.508779	−	0.369650i	0.812360	+	0.583156i	$0.198182\pi$
$588$		0			0
$589$	−3.20067	+	9.85066i	−0.131881	+	0.405889i
$590$		0			0
$591$	2.98421	+	2.16816i	0.122754	+	0.0891860i
$592$		0			0
$593$	27.5413			1.13098			0.565492	−	0.824754i	$-0.308686\pi$
$593$	27.5413			1.13098			0.565492	+	0.824754i	$0.308686\pi$
$594$		0			0
$595$	−12.4227			−0.509281
$596$		0			0
$597$	1.87309	+	1.36088i	0.0766605	+	0.0556971i
$598$		0			0
$599$	8.26097	−	25.4247i	0.337534	−	1.03882i	−0.627926	−	0.778273i	$-0.716096\pi$
$599$	8.26097	−	25.4247i	0.337534	−	1.03882i	0.965460	−	0.260551i	$-0.0839041\pi$
$600$		0			0
$601$	−1.94714	+	1.41468i	−0.0794255	+	0.0577060i	−0.626789	−	0.779189i	$-0.715631\pi$
$601$	−1.94714	+	1.41468i	−0.0794255	+	0.0577060i	0.547364	+	0.836895i	$0.315631\pi$
$602$		0			0
$603$	6.54977	+	20.1581i	0.266727	+	0.820902i
$604$		0			0
$605$	8.10166	+	7.44064i	0.329379	+	0.302505i
$606$		0			0
$607$	−3.18067	−	9.78909i	−0.129099	−	0.397327i	0.865526	−	0.500864i	$-0.166984\pi$
$607$	−3.18067	−	9.78909i	−0.129099	−	0.397327i	−0.994626	+	0.103536i	$0.966984\pi$
$608$		0			0
$609$	2.11492	−	1.53658i	0.0857010	−	0.0622654i
$610$		0			0
$611$	6.29216	−	19.3653i	0.254553	−	0.783435i
$612$		0			0
$613$	−22.5519	−	16.3849i	−0.910861	−	0.661779i	0.0303715	−	0.999539i	$-0.490331\pi$
$613$	−22.5519	−	16.3849i	−0.910861	−	0.661779i	−0.941232	+	0.337759i	$0.890331\pi$
$614$		0			0
$615$	−0.714118			−0.0287960
$616$		0			0
$617$	−28.7216			−1.15629			−0.578143	−	0.815935i	$-0.696222\pi$
$617$	−28.7216			−1.15629			−0.578143	+	0.815935i	$0.696222\pi$
$618$		0			0
$619$	18.3621	+	13.3408i	0.738035	+	0.536214i	0.892095	−	0.451848i	$-0.149235\pi$
$619$	18.3621	+	13.3408i	0.738035	+	0.536214i	−0.154060	+	0.988061i	$0.549235\pi$
$620$		0			0
$621$	−1.63169	+	5.02183i	−0.0654776	+	0.201519i
$622$		0			0
$623$	6.01703	−	4.37163i	0.241067	−	0.175146i
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$		0			0
$627$	−3.59989	−	2.94462i	−0.143766	−	0.117597i
$628$		0			0
$629$	15.2152	+	46.8277i	0.606671	+	1.86714i
$630$		0			0
$631$	23.0864	−	16.7733i	0.919056	−	0.667733i	−0.0242327	−	0.999706i	$-0.507714\pi$
$631$	23.0864	−	16.7733i	0.919056	−	0.667733i	0.943289	+	0.331973i	$0.107714\pi$
$632$		0			0
$633$	0.347783	−	1.07037i	0.0138231	−	0.0425432i
$634$		0			0
$635$	0.0617011	+	0.0448285i	0.00244853	+	0.00177896i
$636$		0			0
$637$	−0.982140			−0.0389138
$638$		0			0
$639$	3.46233			0.136968
$640$		0			0
$641$	−1.92040	−	1.39526i	−0.0758514	−	0.0551093i	0.549213	−	0.835682i	$-0.314927\pi$
$641$	−1.92040	−	1.39526i	−0.0758514	−	0.0551093i	−0.625065	+	0.780573i	$0.714927\pi$
$642$		0			0
$643$	−3.51053	+	10.8043i	−0.138442	+	0.426080i	−0.996109	−	0.0881244i	$-0.971913\pi$
$643$	−3.51053	+	10.8043i	−0.138442	+	0.426080i	0.857668	+	0.514204i	$0.171913\pi$
$644$		0			0
$645$	−1.84715	+	1.34203i	−0.0727315	+	0.0528425i
$646$		0			0
$647$	14.9632	+	46.0520i	0.588264	+	1.81049i	0.585746	+	0.810495i	$0.300802\pi$
$647$	14.9632	+	46.0520i	0.588264	+	1.81049i	0.00251822	+	0.999997i	$0.499198\pi$
$648$		0			0
$649$	14.1415	−	36.3043i	0.555104	−	1.42507i
$650$		0			0
$651$	−0.639713	−	1.96883i	−0.0250723	−	0.0771647i
$652$		0			0
$653$	−24.0722	+	17.4894i	−0.942016	+	0.684415i	−0.948905	−	0.315562i	$-0.897807\pi$
$653$	−24.0722	+	17.4894i	−0.942016	+	0.684415i	0.00688905	+	0.999976i	$0.497807\pi$
$654$		0			0
$655$	−3.54847	+	10.9211i	−0.138650	+	0.426722i
$656$		0			0
$657$	2.39346	+	1.73895i	0.0933777	+	0.0678429i
$658$		0			0
$659$	28.4931			1.10993			0.554966	−	0.831873i	$-0.312731\pi$
$659$	28.4931			1.10993			0.554966	+	0.831873i	$0.312731\pi$
$660$		0			0
$661$	−1.02875			−0.0400139			−0.0200070	−	0.999800i	$-0.506369\pi$
$661$	−1.02875			−0.0400139			−0.0200070	+	0.999800i	$0.506369\pi$
$662$		0			0
$663$	5.64428	+	4.10081i	0.219206	+	0.159262i
$664$		0			0
$665$	3.60161	−	11.0846i	0.139664	−	0.429843i
$666$		0			0
$667$	−6.75841	+	4.91027i	−0.261687	+	0.190127i
$668$		0			0
$669$	1.05275	+	3.24002i	0.0407016	+	0.125267i
$670$		0			0
$671$	3.35580	+	12.7755i	0.129549	+	0.493192i
$672$		0			0
$673$	4.02863	+	12.3988i	0.155292	+	0.477940i	0.998190	−	0.0601327i	$-0.0191524\pi$
$673$	4.02863	+	12.3988i	0.155292	+	0.477940i	−0.842898	+	0.538073i	$0.819152\pi$
$674$		0			0
$675$	−1.54094	+	1.11956i	−0.0593108	+	0.0430918i
$676$		0			0
$677$	−11.4665	+	35.2903i	−0.440694	+	1.35632i	0.446444	+	0.894812i	$0.352690\pi$
$677$	−11.4665	+	35.2903i	−0.440694	+	1.35632i	−0.887138	+	0.461505i	$0.847310\pi$
$678$		0			0
$679$	40.2635	+	29.2531i	1.54517	+	1.12263i
$680$		0			0
$681$	0.0697890			0.00267432
$682$		0			0
$683$	32.8992			1.25885			0.629426	−	0.777061i	$-0.283290\pi$
$683$	32.8992			1.25885			0.629426	+	0.777061i	$0.283290\pi$
$684$		0			0
$685$	−14.8287	−	10.7737i	−0.566576	−	0.411641i
$686$		0			0
$687$	0.00755844	−	0.0232625i	0.000288372	−	0.000887519i
$688$		0			0
$689$	−23.9197	+	17.3787i	−0.911267	+	0.662074i
$690$		0			0
$691$	−11.3409	−	34.9036i	−0.431427	−	1.32780i	−0.896704	−	0.442631i	$-0.854045\pi$
$691$	−11.3409	−	34.9036i	−0.431427	−	1.32780i	0.465277	−	0.885165i	$-0.345955\pi$
$692$		0			0
$693$	−25.7457	−	1.47652i	−0.978000	−	0.0560883i
$694$		0			0
$695$	−7.16529	−	22.0525i	−0.271795	−	0.836498i
$696$		0			0
$697$	−8.27305	+	6.01072i	−0.313364	+	0.227672i
$698$		0			0
$699$	−1.50950	+	4.64577i	−0.0570946	+	0.175719i
$700$		0			0
$701$	29.3266	+	21.3070i	1.10765	+	0.804755i	0.982292	−	0.187356i	$-0.0599919\pi$
$701$	29.3266	+	21.3070i	1.10765	+	0.804755i	0.125359	+	0.992111i	$0.459992\pi$
$702$		0			0
$703$	−46.1949			−1.74227
$704$		0			0
$705$	−1.40928			−0.0530767
$706$		0			0
$707$	−15.4556	−	11.2291i	−0.581267	−	0.422315i
$708$		0			0
$709$	−5.74811	+	17.6909i	−0.215875	+	0.664394i	0.783216	+	0.621750i	$0.213578\pi$
$709$	−5.74811	+	17.6909i	−0.215875	+	0.664394i	−0.999090	+	0.0426440i	$0.986422\pi$
$710$		0			0
$711$	−8.20413	+	5.96065i	−0.307679	+	0.223542i
$712$		0			0
$713$	2.04426	+	6.29158i	0.0765580	+	0.235621i
$714$		0			0
$715$	13.0253	−	8.36775i	0.487117	−	0.312936i
$716$		0			0
$717$	−2.31263	−	7.11754i	−0.0863667	−	0.265809i
$718$		0			0
$719$	−30.2799	+	21.9996i	−1.12925	+	0.820447i	−0.985585	−	0.169179i	$-0.945888\pi$
$719$	−30.2799	+	21.9996i	−1.12925	+	0.820447i	−0.143664	+	0.989627i	$0.545888\pi$
$720$		0			0
$721$	6.24687	−	19.2259i	0.232645	−	0.716009i
$722$		0			0
$723$	−5.57630	−	4.05142i	−0.207385	−	0.150674i
$724$		0			0
$725$	−3.01341			−0.111915
$726$		0			0
$727$	−14.6011			−0.541526			−0.270763	−	0.962646i	$-0.587276\pi$
$727$	−14.6011			−0.541526			−0.270763	+	0.962646i	$0.587276\pi$
$728$		0			0
$729$	17.4149	+	12.6527i	0.644997	+	0.468618i
$730$		0			0
$731$	−10.1033	+	31.0949i	−0.373686	+	1.15009i
$732$		0			0
$733$	−33.8468	+	24.5911i	−1.25016	+	0.908293i	−0.998231	−	0.0594528i	$-0.981064\pi$
$733$	−33.8468	+	24.5911i	−1.25016	+	0.908293i	−0.251927	+	0.967746i	$0.581064\pi$
$734$		0			0
$735$	0.0210057	+	0.0646489i	0.000774807	+	0.00238461i
$736$		0			0
$737$	−20.4254	+	13.1218i	−0.752381	+	0.483348i
$738$		0			0
$739$	3.68654	+	11.3460i	0.135612	+	0.417370i	0.995685	−	0.0928012i	$-0.0295821\pi$
$739$	3.68654	+	11.3460i	0.135612	+	0.417370i	−0.860073	+	0.510171i	$0.829582\pi$
$740$		0			0
$741$	−5.29549	+	3.84740i	−0.194535	+	0.141338i
$742$		0			0
$743$	−14.4250	+	44.3956i	−0.529202	+	1.62872i	0.226652	+	0.973976i	$0.427222\pi$
$743$	−14.4250	+	44.3956i	−0.529202	+	1.62872i	−0.755854	+	0.654740i	$0.772778\pi$
$744$		0			0
$745$	11.8639	+	8.61964i	0.434660	+	0.315799i
$746$		0			0
$747$	32.1873			1.17767
$748$		0			0
$749$	48.4124			1.76895
$750$		0			0
$751$	11.6530	+	8.46642i	0.425225	+	0.308944i	0.779737	−	0.626108i	$-0.215353\pi$
$751$	11.6530	+	8.46642i	0.425225	+	0.308944i	−0.354512	+	0.935052i	$0.615353\pi$
$752$		0			0
$753$	−0.621156	+	1.91172i	−0.0226362	+	0.0696670i
$754$		0			0
$755$	6.08301	−	4.41957i	0.221383	−	0.160845i
$756$		0			0
$757$	−4.96330	−	15.2755i	−0.180394	−	0.555196i	0.819444	−	0.573159i	$-0.194282\pi$
$757$	−4.96330	−	15.2755i	−0.180394	−	0.555196i	−0.999839	+	0.0179624i	$0.994282\pi$
$758$		0			0
$759$	−2.96558	−	0.170076i	−0.107644	−	0.00617337i
$760$		0			0
$761$	−12.0158	−	36.9809i	−0.435573	−	1.34056i	−0.892498	−	0.451051i	$-0.851049\pi$
$761$	−12.0158	−	36.9809i	−0.435573	−	1.34056i	0.456925	−	0.889505i	$-0.348951\pi$
$762$		0			0
$763$	−35.5518	+	25.8299i	−1.28706	+	0.935106i
$764$		0			0
$765$	−4.13962	+	12.7405i	−0.149668	+	0.460632i
$766$		0			0
$767$	−44.3621	−	32.2309i	−1.60182	−	1.16379i
$768$		0			0
$769$	43.0017			1.55068			0.775341	−	0.631543i	$-0.217578\pi$
$769$	43.0017			1.55068			0.775341	+	0.631543i	$0.217578\pi$
$770$		0			0
$771$	4.61679			0.166270
$772$		0			0
$773$	6.35452	+	4.61683i	0.228556	+	0.166056i	0.696170	−	0.717877i	$-0.254886\pi$
$773$	6.35452	+	4.61683i	0.228556	+	0.166056i	−0.467613	+	0.883933i	$0.654886\pi$
$774$		0			0
$775$	−0.737407	+	2.26951i	−0.0264885	+	0.0815231i
$776$		0			0
$777$	7.46957	−	5.42696i	0.267969	−	0.194691i
$778$		0			0
$779$	−2.96475	−	9.12457i	−0.106223	−	0.326922i
$780$		0			0
$781$	1.00752	+	3.83561i	0.0360519	+	0.137249i
$782$		0			0
$783$	−1.77366	−	5.45875i	−0.0633853	−	0.195080i
$784$		0			0
$785$	−10.8262	+	7.86568i	−0.386403	+	0.280738i
$786$		0			0
$787$	3.53048	−	10.8657i	0.125848	−	0.387321i	−0.868206	−	0.496203i	$-0.834727\pi$
$787$	3.53048	−	10.8657i	0.125848	−	0.387321i	0.994055	+	0.108882i	$0.0347271\pi$
$788$		0			0
$789$	−1.07980	−	0.784522i	−0.0384420	−	0.0279297i
$790$		0			0
$791$	5.51483			0.196085
$792$		0			0
$793$	18.5903			0.660161
$794$		0			0
$795$	1.65553	+	1.20281i	0.0587155	+	0.0426593i
$796$		0			0
$797$	−1.32414	+	4.07529i	−0.0469035	+	0.144354i	−0.971766	−	0.235949i	$-0.924180\pi$
$797$	−1.32414	+	4.07529i	−0.0469035	+	0.144354i	0.924862	+	0.380303i	$0.124180\pi$
$798$		0			0
$799$	−16.3265	+	11.8619i	−0.577592	+	0.419645i
$800$		0			0
$801$	−2.47839	−	7.62770i	−0.0875696	−	0.269511i
$802$		0			0
$803$	−1.22994	+	3.15752i	−0.0434038	+	0.111427i
$804$		0			0
$805$	−2.30033	−	7.07969i	−0.0810760	−	0.249526i
$806$		0			0
$807$	−0.440132	+	0.319774i	−0.0154934	+	0.0112566i
$808$		0			0
$809$	−6.13350	+	18.8770i	−0.215642	+	0.663679i	0.783465	+	0.621436i	$0.213450\pi$
$809$	−6.13350	+	18.8770i	−0.215642	+	0.663679i	−0.999107	+	0.0422430i	$0.986550\pi$
$810$		0			0
$811$	−2.53899	−	1.84468i	−0.0891559	−	0.0647756i	0.542314	−	0.840176i	$-0.317548\pi$
$811$	−2.53899	−	1.84468i	−0.0891559	−	0.0647756i	−0.631470	+	0.775400i	$0.717548\pi$
$812$		0			0
$813$	−5.95452			−0.208834
$814$		0			0
$815$	−0.771990			−0.0270416
$816$		0			0
$817$	−24.8164	−	18.0301i	−0.868215	−	0.630795i
$818$		0			0
$819$	−11.2156	+	34.5180i	−0.391904	+	1.20616i
$820$		0			0
$821$	−19.0118	+	13.8129i	−0.663516	+	0.482073i	−0.867849	−	0.496829i	$-0.834498\pi$
$821$	−19.0118	+	13.8129i	−0.663516	+	0.482073i	0.204332	+	0.978902i	$0.434498\pi$
$822$		0			0
$823$	3.91103	+	12.0369i	0.136330	+	0.419580i	0.995795	−	0.0916150i	$-0.0292029\pi$
$823$	3.91103	+	12.0369i	0.136330	+	0.419580i	−0.859465	+	0.511195i	$0.829203\pi$
$824$		0			0
$825$	−0.829384	−	0.678415i	−0.0288754	−	0.0236194i
$826$		0			0
$827$	−9.33959	−	28.7443i	−0.324770	−	0.999538i	−0.971545	−	0.236857i	$-0.923883\pi$
$827$	−9.33959	−	28.7443i	−0.324770	−	0.999538i	0.646775	−	0.762681i	$-0.276117\pi$
$828$		0			0
$829$	−1.61937	+	1.17654i	−0.0562432	+	0.0408630i	−0.615552	−	0.788097i	$-0.711067\pi$
$829$	−1.61937	+	1.17654i	−0.0562432	+	0.0408630i	0.559308	+	0.828960i	$0.311067\pi$
$830$		0			0
$831$	0.342177	−	1.05311i	0.0118700	−	0.0365321i
$832$		0			0
$833$	0.787500	+	0.572152i	0.0272852	+	0.0198239i
$834$		0			0
$835$	−8.48232			−0.293543
$836$		0			0
$837$	−4.54520			−0.157105
$838$		0			0
$839$	28.6185	+	20.7925i	0.988019	+	0.717838i	0.959486	−	0.281755i	$-0.0909166\pi$
$839$	28.6185	+	20.7925i	0.988019	+	0.717838i	0.0285326	+	0.999593i	$0.490917\pi$
$840$		0			0
$841$	−6.15541	+	18.9444i	−0.212256	+	0.653255i
$842$		0			0
$843$	−5.96492	+	4.33377i	−0.205443	+	0.149263i
$844$		0			0
$845$	−2.71589	−	8.35865i	−0.0934295	−	0.287546i
$846$		0			0
$847$	−5.85616	−	28.9511i	−0.201220	−	0.994771i
$848$		0			0
$849$	−2.90509	−	8.94095i	−0.0997024	−	0.306853i
$850$		0			0
$851$	−23.8696	+	17.3423i	−0.818241	+	0.594487i
$852$		0			0
$853$	−5.62515	+	17.3124i	−0.192602	+	0.592767i	0.807395	+	0.590012i	$0.200877\pi$
$853$	−5.62515	+	17.3124i	−0.192602	+	0.592767i	−0.999996	+	0.00275489i	$0.999123\pi$
$854$		0			0
$855$	−10.1680	−	7.38746i	−0.347737	−	0.252646i
$856$		0			0
$857$	−29.2837			−1.00031			−0.500156	−	0.865935i	$-0.666724\pi$
$857$	−29.2837			−1.00031			−0.500156	+	0.865935i	$0.666724\pi$
$858$		0			0
$859$	−8.44030			−0.287979			−0.143990	−	0.989579i	$-0.545993\pi$
$859$	−8.44030			−0.287979			−0.143990	+	0.989579i	$0.545993\pi$
$860$		0			0
$861$	1.55134	+	1.12712i	0.0528696	+	0.0384120i
$862$		0			0
$863$	5.97907	−	18.4017i	0.203530	−	0.626400i	−0.796241	−	0.604980i	$-0.793181\pi$
$863$	5.97907	−	18.4017i	0.203530	−	0.626400i	0.999771	−	0.0214204i	$-0.00681885\pi$
$864$		0			0
$865$	4.10876	−	2.98519i	0.139702	−	0.101500i
$866$		0			0
$867$	−0.439559	−	1.35282i	−0.0149282	−	0.0459443i
$868$		0			0
$869$	−8.99063	−	7.35411i	−0.304986	−	0.249471i
$870$		0			0
$871$	10.5585	+	32.4956i	0.357760	+	1.10107i
$872$		0			0
$873$	43.4184	−	31.5453i	1.46949	−	1.06765i
$874$		0			0
$875$	0.829779	−	2.55380i	0.0280516	−	0.0863341i
$876$		0			0
$877$	−14.1691	−	10.2945i	−0.478456	−	0.347619i	0.322271	−	0.946647i	$-0.395554\pi$
$877$	−14.1691	−	10.2945i	−0.478456	−	0.347619i	−0.800728	+	0.599028i	$0.795554\pi$
$878$		0			0
$879$	−6.85349			−0.231163
$880$		0			0
$881$	−20.0575			−0.675754			−0.337877	−	0.941190i	$-0.609709\pi$
$881$	−20.0575			−0.675754			−0.337877	+	0.941190i	$0.609709\pi$
$882$		0			0
$883$	21.7609	+	15.8102i	0.732313	+	0.532057i	0.890294	−	0.455386i	$-0.150499\pi$
$883$	21.7609	+	15.8102i	0.732313	+	0.532057i	−0.157981	+	0.987442i	$0.550499\pi$
$884$		0			0
$885$	−1.17278	+	3.60946i	−0.0394227	+	0.121331i
$886$		0			0
$887$	5.50591	−	4.00028i	0.184870	−	0.134316i	−0.491501	−	0.870877i	$-0.663552\pi$
$887$	5.50591	−	4.00028i	0.184870	−	0.134316i	0.676371	+	0.736561i	$0.263552\pi$
$888$		0			0
$889$	−0.0632845	−	0.194770i	−0.00212249	−	0.00653237i
$890$		0			0
$891$	−9.71661	+	24.9446i	−0.325519	+	0.835674i
$892$		0			0
$893$	−5.85082	−	18.0070i	−0.195790	−	0.602581i
$894$		0			0
$895$	9.15568	−	6.65199i	0.306041	−	0.222352i
$896$		0			0
$897$	−1.29189	+	3.97603i	−0.0431349	+	0.132756i
$898$		0			0
$899$	−5.81757	−	4.22671i	−0.194027	−	0.140969i
$900$		0			0
$901$	29.3033			0.976235
$902$		0			0
$903$	6.13090			0.204024
$904$		0			0
$905$	5.98677	+	4.34965i	0.199007	+	0.144587i
$906$		0			0
$907$	6.59174	−	20.2873i	0.218875	−	0.673629i	−0.779981	−	0.625804i	$-0.784771\pi$
$907$	6.59174	−	20.2873i	0.218875	−	0.673629i	0.998856	−	0.0478248i	$-0.0152289\pi$
$908$		0			0
$909$	−16.6666	+	12.1090i	−0.552797	+	0.401631i
$910$		0			0
$911$	8.52542	+	26.2385i	0.282460	+	0.869322i	0.987149	+	0.159805i	$0.0510866\pi$
$911$	8.52542	+	26.2385i	0.282460	+	0.869322i	−0.704689	+	0.709516i	$0.748913\pi$
$912$		0			0
$913$	9.36631	+	35.6574i	0.309980	+	1.18009i
$914$		0			0
$915$	−0.397604	−	1.22370i	−0.0131444	−	0.0404542i
$916$		0			0
$917$	24.9458	−	18.1242i	0.823782	−	0.598512i
$918$		0			0
$919$	1.85685	−	5.71479i	0.0612518	−	0.188514i	−0.915748	−	0.401752i	$-0.868401\pi$
$919$	1.85685	−	5.71479i	0.0612518	−	0.188514i	0.977000	+	0.213239i	$0.0684012\pi$
$920$		0			0
$921$	1.79697	+	1.30558i	0.0592122	+	0.0430202i
$922$		0			0
$923$	5.58140			0.183714
$924$		0			0
$925$	−10.6429			−0.349937
$926$		0			0
$927$	−17.6360	−	12.8133i	−0.579242	−	0.420844i
$928$		0			0
$929$	2.96576	−	9.12766i	0.0973034	−	0.299469i	−0.890544	−	0.454898i	$-0.849676\pi$
$929$	2.96576	−	9.12766i	0.0973034	−	0.299469i	0.987847	+	0.155429i	$0.0496759\pi$
$930$		0			0
$931$	−0.738836	+	0.536796i	−0.0242144	+	0.0175928i
$932$		0			0
$933$	2.51160	+	7.72992i	0.0822261	+	0.253066i
$934$		0			0
$935$	−15.3186	−	0.878523i	−0.500972	−	0.0287308i
$936$		0			0
$937$	−11.9255	−	36.7029i	−0.389589	−	1.19903i	−0.933096	−	0.359628i	$-0.882904\pi$
$937$	−11.9255	−	36.7029i	−0.389589	−	1.19903i	0.543507	−	0.839405i	$-0.317096\pi$
$938$		0			0
$939$	−3.02649	+	2.19887i	−0.0987658	+	0.0717575i
$940$		0			0
$941$	−9.01854	+	27.7562i	−0.293996	+	0.904826i	0.689561	+	0.724228i	$0.257804\pi$
$941$	−9.01854	+	27.7562i	−0.293996	+	0.904826i	−0.983557	+	0.180599i	$0.942196\pi$
$942$		0			0
$943$	−4.95744	−	3.60179i	−0.161437	−	0.117291i
$944$		0			0
$945$	5.11455			0.166376
$946$		0			0
$947$	−46.7623			−1.51957			−0.759785	−	0.650174i	$-0.774696\pi$
$947$	−46.7623			−1.51957			−0.759785	+	0.650174i	$0.774696\pi$
$948$		0			0
$949$	3.85834	+	2.80325i	0.125247	+	0.0909972i
$950$		0			0
$951$	−2.07069	+	6.37293i	−0.0671468	+	0.206657i
$952$		0			0
$953$	4.97738	−	3.61628i	0.161233	−	0.117143i	−0.504243	−	0.863562i	$-0.668228\pi$
$953$	4.97738	−	3.61628i	0.161233	−	0.117143i	0.665476	+	0.746419i	$0.268228\pi$
$954$		0			0
$955$	−1.59332	−	4.90372i	−0.0515585	−	0.158681i
$956$		0			0
$957$	2.71661	−	1.74522i	0.0878155	−	0.0564148i
$958$		0			0
$959$	15.2093	+	46.8093i	0.491132	+	1.51155i
$960$		0			0
$961$	20.4726	−	14.8742i	0.660408	−	0.479814i
$962$		0			0
$963$	16.1325	−	49.6507i	0.519862	−	1.59997i
$964$		0			0
$965$	−3.26220	−	2.37013i	−0.105014	−	0.0762970i
$966$		0			0
$967$	−3.39625			−0.109216			−0.0546080	−	0.998508i	$-0.517391\pi$
$967$	−3.39625			−0.109216			−0.0546080	+	0.998508i	$0.517391\pi$
$968$		0			0
$969$	6.48736			0.208404
$970$		0			0
$971$	−7.60072	−	5.52224i	−0.243919	−	0.177217i	0.459109	−	0.888380i	$-0.348169\pi$
$971$	−7.60072	−	5.52224i	−0.243919	−	0.177217i	−0.703027	+	0.711163i	$0.748169\pi$
$972$		0			0
$973$	−19.2404	+	59.2158i	−0.616818	+	1.89837i
$974$		0			0
$975$	−1.22004	+	0.886408i	−0.0390724	+	0.0283878i
$976$		0			0
$977$	−5.11585	−	15.7450i	−0.163671	−	0.503726i	0.835265	−	0.549847i	$-0.185314\pi$
$977$	−5.11585	−	15.7450i	−0.163671	−	0.503726i	−0.998936	+	0.0461210i	$0.985314\pi$
$978$		0			0
$979$	7.72885	−	4.96520i	0.247015	−	0.158689i
$980$		0			0
$981$	14.6436	+	45.0685i	0.467535	+	1.43893i
$982$		0			0
$983$	41.1126	−	29.8701i	1.31129	−	0.952707i	0.311291	−	0.950315i	$-0.399238\pi$
$983$	41.1126	−	29.8701i	1.31129	−	0.952707i	0.999997	−	0.00239240i	$-0.000761525\pi$
$984$		0			0
$985$	−3.52822	+	10.8588i	−0.112419	+	0.345989i
$986$		0			0
$987$	3.06151	+	2.22432i	0.0974490	+	0.0708009i
$988$		0			0
$989$	−19.5918			−0.622983
$990$		0			0
$991$	−11.3642			−0.360996			−0.180498	−	0.983575i	$-0.557771\pi$
$991$	−11.3642			−0.360996			−0.180498	+	0.983575i	$0.557771\pi$
$992$		0			0
$993$	8.40081	+	6.10355i	0.266592	+	0.193690i
$994$		0			0
$995$	−2.21455	+	6.81569i	−0.0702060	+	0.216072i
$996$		0			0
$997$	23.5945	−	17.1424i	0.747246	−	0.542906i	−0.147726	−	0.989028i	$-0.547195\pi$
$997$	23.5945	−	17.1424i	0.747246	−	0.542906i	0.894972	+	0.446122i	$0.147195\pi$
$998$		0			0
$999$	−6.26427	−	19.2794i	−0.198193	−	0.609975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bo.h.401.1		8
4.3	odd	2		55.2.g.b.16.2	✓	8
11.3	even	5		9680.2.a.cn.1.3		4
11.8	odd	10		9680.2.a.cm.1.3		4
11.9	even	5	inner	880.2.bo.h.801.1		8
12.11	even	2		495.2.n.e.181.1		8
20.3	even	4		275.2.z.a.49.3		16
20.7	even	4		275.2.z.a.49.2		16
20.19	odd	2		275.2.h.a.126.1		8
44.3	odd	10		605.2.a.j.1.3		4
44.7	even	10		605.2.g.e.366.2		8
44.15	odd	10		605.2.g.m.366.1		8
44.19	even	10		605.2.a.k.1.2		4
44.27	odd	10		605.2.g.m.81.1		8
44.31	odd	10		55.2.g.b.31.2	yes	8
44.35	even	10		605.2.g.k.251.1		8
44.39	even	10		605.2.g.e.81.2		8
44.43	even	2		605.2.g.k.511.1		8
132.47	even	10		5445.2.a.bp.1.2		4
132.107	odd	10		5445.2.a.bi.1.3		4
132.119	even	10		495.2.n.e.361.1		8
220.19	even	10		3025.2.a.w.1.3		4
220.119	odd	10		275.2.h.a.251.1		8
220.163	even	20		275.2.z.a.174.2		16
220.179	odd	10		3025.2.a.bd.1.2		4
220.207	even	20		275.2.z.a.174.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.16.2	✓	8	4.3	odd	2
55.2.g.b.31.2	yes	8	44.31	odd	10
275.2.h.a.126.1		8	20.19	odd	2
275.2.h.a.251.1		8	220.119	odd	10
275.2.z.a.49.2		16	20.7	even	4
275.2.z.a.49.3		16	20.3	even	4
275.2.z.a.174.2		16	220.163	even	20
275.2.z.a.174.3		16	220.207	even	20
495.2.n.e.181.1		8	12.11	even	2
495.2.n.e.361.1		8	132.119	even	10
605.2.a.j.1.3		4	44.3	odd	10
605.2.a.k.1.2		4	44.19	even	10
605.2.g.e.81.2		8	44.39	even	10
605.2.g.e.366.2		8	44.7	even	10
605.2.g.k.251.1		8	44.35	even	10
605.2.g.k.511.1		8	44.43	even	2
605.2.g.m.81.1		8	44.27	odd	10
605.2.g.m.366.1		8	44.15	odd	10
880.2.bo.h.401.1		8	1.1	even	1	trivial
880.2.bo.h.801.1		8	11.9	even	5	inner
3025.2.a.w.1.3		4	220.19	even	10
3025.2.a.bd.1.2		4	220.179	odd	10
5445.2.a.bi.1.3		4	132.107	odd	10
5445.2.a.bp.1.2		4	132.47	even	10
9680.2.a.cm.1.3		4	11.8	odd	10
9680.2.a.cn.1.3		4	11.3	even	5

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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bo (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.261370 + 0.189896i) q^{3} +(-0.309017 + 0.951057i) q^{5} +(2.17239 - 1.57833i) q^{7} +(-0.894797 - 2.75390i) q^{9} +(2.79042 - 1.79264i) q^{11} +(-1.44244 - 4.43939i) q^{13} +(-0.261370 + 0.189896i) q^{15} +(-1.42961 + 4.39990i) q^{17} +(-3.51149 - 2.55125i) q^{19} +0.867517 q^{21} -2.77222 q^{23} +(-0.809017 - 0.587785i) q^{25} +(0.588587 - 1.81148i) q^{27} +(2.43790 - 1.77124i) q^{29} +(-0.737407 - 2.26951i) q^{31} +(1.06975 + 0.0613500i) q^{33} +(0.829779 + 2.55380i) q^{35} +(8.61029 - 6.25574i) q^{37} +(0.466012 - 1.43424i) q^{39} +(1.78826 + 1.29924i) q^{41} +7.06719 q^{43} +2.89563 q^{45} +(3.52905 + 2.56401i) q^{47} +(0.0650188 - 0.200107i) q^{49} +(-1.20918 + 0.878523i) q^{51} +(-1.95733 - 6.02403i) q^{53} +(0.842610 + 3.20780i) q^{55} +(-0.433326 - 1.33364i) q^{57} +(9.50375 - 6.90488i) q^{59} +(-1.23070 + 3.78770i) q^{61} +(-6.29042 - 4.57026i) q^{63} +4.66785 q^{65} -7.31984 q^{67} +(-0.724576 - 0.526435i) q^{69} +(-0.369495 + 1.13719i) q^{71} +(-0.826577 + 0.600544i) q^{73} +(-0.0998345 - 0.307259i) q^{75} +(3.23251 - 8.29852i) q^{77} +(-1.08222 - 3.33073i) q^{79} +(-6.53000 + 4.74432i) q^{81} +(-3.43498 + 10.5718i) q^{83} +(-3.74278 - 2.71929i) q^{85} +0.973547 q^{87} +2.76978 q^{89} +(-10.1404 - 7.36742i) q^{91} +(0.238235 - 0.733212i) q^{93} +(3.51149 - 2.55125i) q^{95} +(5.72738 + 17.6271i) q^{97} +(-7.43361 - 6.08051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{3} + 2 q^{5} + q^{7} - 5 q^{9} - 3 q^{11} - 2 q^{13} - 5 q^{15} - 13 q^{17} - 15 q^{19} - 20 q^{21} - 10 q^{23} - 2 q^{25} - 10 q^{27} - 9 q^{29} + 10 q^{31} + 5 q^{33} + 4 q^{35} + 24 q^{37}+ \cdots + 20 q^{99}+O(q^{100}) \) 8 * q + 5 * q^3 + 2 * q^5 + q^7 - 5 * q^9 - 3 * q^11 - 2 * q^13 - 5 * q^15 - 13 * q^17 - 15 * q^19 - 20 * q^21 - 10 * q^23 - 2 * q^25 - 10 * q^27 - 9 * q^29 + 10 * q^31 + 5 * q^33 + 4 * q^35 + 24 * q^37 - 21 * q^39 + 8 * q^41 + 38 * q^43 + q^49 - q^51 + 13 * q^53 - 7 * q^55 - 45 * q^57 + 27 * q^59 + 6 * q^61 - 25 * q^63 + 2 * q^65 + 38 * q^67 - q^69 + 20 * q^71 + 13 * q^73 - 5 * q^75 + 34 * q^77 - 37 * q^79 + 8 * q^81 - 27 * q^83 - 12 * q^85 - 38 * q^87 - 16 * q^89 - 44 * q^91 - 35 * q^93 + 15 * q^95 + 24 * q^97 + 20 * q^99

Introduction

L-functions

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Database

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