LMFDB - Embedded newform 616.2.bs.a.41.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [616,2,Mod(41,616)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(616, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 5, 3]))

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

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

chi := DirichletCharacter("616.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 616 = 2^{3} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	616.bs (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.91878476451$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			41.19
Character	$\chi$	$=$	616.41
Dual form			616.2.bs.a.601.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.74058 - 0.565549i) q^{3} +(2.00195 - 2.75545i) q^{5} +(2.13612 - 1.56108i) q^{7} +(0.282723 - 0.205410i) q^{9} +(1.95412 + 2.67981i) q^{11} +(-3.12180 + 2.26812i) q^{13} +(1.92622 - 5.92829i) q^{15} +(5.18566 + 3.76761i) q^{17} +(-1.35921 - 4.18322i) q^{19} +(2.83523 - 3.92527i) q^{21} -8.95339 q^{23} +(-2.03962 - 6.27729i) q^{25} +(-2.85128 + 3.92445i) q^{27} +(-2.95805 - 0.961130i) q^{29} +(-0.176454 - 0.242868i) q^{31} +(4.91687 + 3.55928i) q^{33} +(-0.0250589 - 9.01120i) q^{35} +(0.331607 - 1.02058i) q^{37} +(-4.15102 + 5.71338i) q^{39} +(0.131310 + 0.404129i) q^{41} +9.11292i q^{43} -1.19025i q^{45} +(-2.54609 + 0.827275i) q^{47} +(2.12606 - 6.66932i) q^{49} +(11.1568 + 3.62507i) q^{51} +(10.0478 - 7.30017i) q^{53} +(11.2962 - 0.0196264i) q^{55} +(-4.73163 - 6.51254i) q^{57} +(-3.66163 - 1.18974i) q^{59} +(8.45547 + 6.14326i) q^{61} +(0.283270 - 0.880135i) q^{63} +13.1427i q^{65} -1.32838 q^{67} +(-15.5841 + 5.06358i) q^{69} +(-12.9080 - 9.37823i) q^{71} +(-2.20202 + 6.77713i) q^{73} +(-7.10023 - 9.77263i) q^{75} +(8.35765 + 2.67388i) q^{77} +(4.31766 + 5.94275i) q^{79} +(-3.06739 + 9.44044i) q^{81} +(-0.928477 - 0.674578i) q^{83} +(20.7629 - 6.74628i) q^{85} -5.69230 q^{87} -3.59000i q^{89} +(-3.12784 + 9.71838i) q^{91} +(-0.444485 - 0.322937i) q^{93} +(-14.2478 - 4.62938i) q^{95} +(-1.20391 - 1.65704i) q^{97} +(1.10294 + 0.356248i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{9} + 4 q^{11} + 12 q^{15} - 24 q^{23} + 36 q^{25} + 20 q^{29} - 30 q^{35} + 16 q^{37} - 60 q^{39} - 30 q^{49} + 60 q^{51} - 80 q^{57} + 40 q^{63} + 64 q^{67} - 24 q^{71} + 50 q^{77} - 8 q^{81}+ \cdots - 84 q^{99}+O(q^{100}) $ 96 * q + 24 * q^9 + 4 * q^11 + 12 * q^15 - 24 * q^23 + 36 * q^25 + 20 * q^29 - 30 * q^35 + 16 * q^37 - 60 * q^39 - 30 * q^49 + 60 * q^51 - 80 * q^57 + 40 * q^63 + 64 * q^67 - 24 * q^71 + 50 * q^77 - 8 * q^81 - 60 * q^85 + 18 * q^91 + 20 * q^93 - 84 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/616\mathbb{Z}\right)^\times$.

$n$	$57$	$309$	$353$	$463$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$	$-1$	$1$

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
$3$	1.74058	−	0.565549i	1.00492	−	0.326520i	0.240093	−	0.970750i	$-0.422822\pi$
$3$	1.74058	−	0.565549i	1.00492	−	0.326520i	0.764832	+	0.644230i	$0.222822\pi$
$4$		0			0
$5$	2.00195	−	2.75545i	0.895301	−	1.23228i	−0.0766420	−	0.997059i	$-0.524420\pi$
$5$	2.00195	−	2.75545i	0.895301	−	1.23228i	0.971943	−	0.235217i	$-0.0755801\pi$
$6$		0			0
$7$	2.13612	−	1.56108i	0.807379	−	0.590033i
$7$	2.13612	−	1.56108i	0.807379	−	0.590033i
$8$		0			0
$9$	0.282723	−	0.205410i	0.0942410	−	0.0684701i
$10$		0			0
$11$	1.95412	+	2.67981i	0.589190	+	0.807995i
$11$	1.95412	+	2.67981i	0.589190	+	0.807995i
$12$		0			0
$13$	−3.12180	+	2.26812i	−0.865833	+	0.629064i	−0.929465	−	0.368909i	$-0.879731\pi$
$13$	−3.12180	+	2.26812i	−0.865833	+	0.629064i	0.0636328	+	0.997973i	$0.479731\pi$
$14$		0			0
$15$	1.92622	−	5.92829i	0.497347	−	1.53068i
$16$		0			0
$17$	5.18566	+	3.76761i	1.25771	+	0.913779i	0.998643	−	0.0520811i	$-0.0165854\pi$
$17$	5.18566	+	3.76761i	1.25771	+	0.913779i	0.259066	+	0.965860i	$0.416585\pi$
$18$		0			0
$19$	−1.35921	−	4.18322i	−0.311825	−	0.959697i	−0.977042	−	0.213048i	$-0.931661\pi$
$19$	−1.35921	−	4.18322i	−0.311825	−	0.959697i	0.665217	−	0.746650i	$-0.268339\pi$
$20$		0			0
$21$	2.83523	−	3.92527i	0.618698	−	0.856564i
$22$		0			0
$23$	−8.95339			−1.86691			−0.933455	−	0.358694i	$-0.883222\pi$
$23$	−8.95339			−1.86691			−0.933455	+	0.358694i	$0.883222\pi$
$24$		0			0
$25$	−2.03962	−	6.27729i	−0.407923	−	1.25546i
$26$		0			0
$27$	−2.85128	+	3.92445i	−0.548729	+	0.755261i
$28$		0			0
$29$	−2.95805	−	0.961130i	−0.549297	−	0.178477i	0.0212028	−	0.999775i	$-0.493250\pi$
$29$	−2.95805	−	0.961130i	−0.549297	−	0.178477i	−0.570500	+	0.821298i	$0.693250\pi$
$30$		0			0
$31$	−0.176454	−	0.242868i	−0.0316920	−	0.0436203i	0.792877	−	0.609382i	$-0.208582\pi$
$31$	−0.176454	−	0.242868i	−0.0316920	−	0.0436203i	−0.824569	+	0.565761i	$0.808582\pi$
$32$		0			0
$33$	4.91687	+	3.55928i	0.855918	+	0.619591i
$34$		0			0
$35$	−0.0250589	−	9.01120i	−0.00423572	−	1.52317i
$36$		0			0
$37$	0.331607	−	1.02058i	0.0545158	−	0.167783i	−0.920091	−	0.391704i	$-0.871886\pi$
$37$	0.331607	−	1.02058i	0.0545158	−	0.167783i	0.974607	+	0.223921i	$0.0718858\pi$
$38$		0			0
$39$	−4.15102	+	5.71338i	−0.664694	+	0.914873i
$40$		0			0
$41$	0.131310	+	0.404129i	0.0205071	+	0.0631144i	0.960786	−	0.277290i	$-0.0894362\pi$
$41$	0.131310	+	0.404129i	0.0205071	+	0.0631144i	−0.940279	+	0.340404i	$0.889436\pi$
$42$		0			0
$43$			9.11292i			1.38971i	0.719151	+	0.694854i	$0.244531\pi$
$43$			9.11292i			1.38971i	−0.719151	+	0.694854i	$0.755469\pi$
$44$		0			0
$45$		−	1.19025i		−	0.177432i
$46$		0			0
$47$	−2.54609	+	0.827275i	−0.371385	+	0.120670i	−0.488762	−	0.872417i	$-0.662551\pi$
$47$	−2.54609	+	0.827275i	−0.371385	+	0.120670i	0.117377	+	0.993087i	$0.462551\pi$
$48$		0			0
$49$	2.12606	−	6.66932i	0.303723	−	0.952760i
$50$		0			0
$51$	11.1568	+	3.62507i	1.56227	+	0.507612i
$52$		0			0
$53$	10.0478	−	7.30017i	1.38017	−	1.00275i	0.383310	−	0.923620i	$-0.374784\pi$
$53$	10.0478	−	7.30017i	1.38017	−	1.00275i	0.996864	−	0.0791352i	$-0.0252159\pi$
$54$		0			0
$55$	11.2962	−	0.0196264i	1.52317	−	0.00264643i
$56$		0			0
$57$	−4.73163	−	6.51254i	−0.626720	−	0.862607i
$58$		0			0
$59$	−3.66163	−	1.18974i	−0.476703	−	0.154890i	0.0608034	−	0.998150i	$-0.480634\pi$
$59$	−3.66163	−	1.18974i	−0.476703	−	0.154890i	−0.537507	+	0.843259i	$0.680634\pi$
$60$		0			0
$61$	8.45547	+	6.14326i	1.08261	+	0.786564i	0.978137	−	0.207964i	$-0.0666837\pi$
$61$	8.45547	+	6.14326i	1.08261	+	0.786564i	0.104475	+	0.994527i	$0.466684\pi$
$62$		0			0
$63$	0.283270	−	0.880135i	0.0356886	−	0.110887i
$64$		0			0
$65$			13.1427i			1.63015i
$66$		0			0
$67$	−1.32838			−0.162287			−0.0811435	−	0.996702i	$-0.525857\pi$
$67$	−1.32838			−0.162287			−0.0811435	+	0.996702i	$0.525857\pi$
$68$		0			0
$69$	−15.5841	+	5.06358i	−1.87610	+	0.609583i
$70$		0			0
$71$	−12.9080	−	9.37823i	−1.53190	−	1.11299i	−0.955170	−	0.296056i	$-0.904328\pi$
$71$	−12.9080	−	9.37823i	−1.53190	−	1.11299i	−0.576730	−	0.816935i	$-0.695672\pi$
$72$		0			0
$73$	−2.20202	+	6.77713i	−0.257727	+	0.793203i	0.735553	+	0.677468i	$0.236923\pi$
$73$	−2.20202	+	6.77713i	−0.257727	+	0.793203i	−0.993280	+	0.115736i	$0.963077\pi$
$74$		0			0
$75$	−7.10023	−	9.77263i	−0.819864	−	1.12845i
$76$		0			0
$77$	8.35765	+	2.67388i	0.952443	+	0.304717i
$78$		0			0
$79$	4.31766	+	5.94275i	0.485774	+	0.668611i	0.979602	−	0.200949i	$-0.0644025\pi$
$79$	4.31766	+	5.94275i	0.485774	+	0.668611i	−0.493827	+	0.869560i	$0.664403\pi$
$80$		0			0
$81$	−3.06739	+	9.44044i	−0.340821	+	1.04894i
$82$		0			0
$83$	−0.928477	−	0.674578i	−0.101914	−	0.0740446i	0.535661	−	0.844433i	$-0.320062\pi$
$83$	−0.928477	−	0.674578i	−0.101914	−	0.0740446i	−0.637575	+	0.770388i	$0.720062\pi$
$84$		0			0
$85$	20.7629	−	6.74628i	2.25205	−	0.731737i
$86$		0			0
$87$	−5.69230			−0.610278
$88$		0			0
$89$		−	3.59000i		−	0.380539i	−0.981732	−	0.190270i	$-0.939064\pi$
$89$		−	3.59000i		−	0.380539i	0.981732	−	0.190270i	$-0.0609362\pi$
$90$		0			0
$91$	−3.12784	+	9.71838i	−0.327887	+	1.01876i
$92$		0			0
$93$	−0.444485	−	0.322937i	−0.0460910	−	0.0334870i
$94$		0			0
$95$	−14.2478	−	4.62938i	−1.46179	−	0.474964i
$96$		0			0
$97$	−1.20391	−	1.65704i	−0.122238	−	0.168247i	0.743512	−	0.668722i	$-0.233158\pi$
$97$	−1.20391	−	1.65704i	−0.122238	−	0.168247i	−0.865751	+	0.500476i	$0.833158\pi$
$98$		0			0
$99$	1.10294	+	0.356248i	0.110849	+	0.0358043i
$100$		0			0
$101$	11.7244	−	8.51826i	1.16662	−	0.847599i	0.176020	−	0.984387i	$-0.443678\pi$
$101$	11.7244	−	8.51826i	1.16662	−	0.847599i	0.990600	+	0.136788i	$0.0436778\pi$
$102$		0			0
$103$	−7.31257	−	2.37600i	−0.720529	−	0.234114i	−0.0742764	−	0.997238i	$-0.523665\pi$
$103$	−7.31257	−	2.37600i	−0.720529	−	0.234114i	−0.646252	+	0.763124i	$0.723665\pi$
$104$		0			0
$105$	−5.13989	−	15.6705i	−0.501602	−	1.52929i
$106$		0			0
$107$	4.00359	−	1.30085i	0.387042	−	0.125758i	−0.109031	−	0.994038i	$-0.534775\pi$
$107$	4.00359	−	1.30085i	0.387042	−	0.125758i	0.496073	+	0.868281i	$0.334775\pi$
$108$		0			0
$109$			10.7133i			1.02615i	0.858344	+	0.513075i	$0.171494\pi$
$109$			10.7133i			1.02615i	−0.858344	+	0.513075i	$0.828506\pi$
$110$		0			0
$111$		−	1.96394i		−	0.186409i
$112$		0			0
$113$	−1.38832	−	4.27282i	−0.130603	−	0.401953i	0.864278	−	0.503015i	$-0.167776\pi$
$113$	−1.38832	−	4.27282i	−0.130603	−	0.401953i	−0.994880	+	0.101062i	$0.967776\pi$
$114$		0			0
$115$	−17.9243	+	24.6706i	−1.67145	+	2.30055i
$116$		0			0
$117$	−0.416710	+	1.28250i	−0.0385248	+	0.118567i
$118$		0			0
$119$	16.9588	−	0.0471599i	1.55461	−	0.00432314i
$120$		0			0
$121$	−3.36281	+	10.4734i	−0.305710	+	0.952125i
$122$		0			0
$123$	0.457109	+	0.629157i	0.0412162	+	0.0567292i
$124$		0			0
$125$	−5.18385	−	1.68434i	−0.463658	−	0.150652i
$126$		0			0
$127$	5.83622	−	8.03287i	0.517881	−	0.712802i	−0.467343	−	0.884076i	$-0.654789\pi$
$127$	5.83622	−	8.03287i	0.517881	−	0.712802i	0.985223	+	0.171275i	$0.0547885\pi$
$128$		0			0
$129$	5.15380	+	15.8618i	0.453767	+	1.39655i
$130$		0			0
$131$	−3.37722			−0.295069			−0.147534	−	0.989057i	$-0.547134\pi$
$131$	−3.37722			−0.295069			−0.147534	+	0.989057i	$0.547134\pi$
$132$		0			0
$133$	−9.43379	−	6.81405i	−0.818014	−	0.590853i
$134$		0			0
$135$	5.10551	+	15.7131i	0.439412	+	1.35237i
$136$		0			0
$137$	9.37496	+	6.81131i	0.800957	+	0.581930i	0.911195	−	0.411976i	$-0.135161\pi$
$137$	9.37496	+	6.81131i	0.800957	+	0.581930i	−0.110238	+	0.993905i	$0.535161\pi$
$138$		0			0
$139$	2.43146	−	7.48327i	0.206234	−	0.634722i	−0.793427	−	0.608666i	$-0.791705\pi$
$139$	2.43146	−	7.48327i	0.206234	−	0.634722i	0.999660	−	0.0260565i	$-0.00829498\pi$
$140$		0			0
$141$	−3.96381	+	2.87988i	−0.333813	+	0.242529i
$142$		0			0
$143$	−12.1785	−	3.93367i	−1.01842	−	0.328950i
$144$		0			0
$145$	−8.57023	+	6.22664i	−0.711719	+	0.517094i
$146$		0			0
$147$	−0.0712510	−	12.8109i	−0.00587668	−	1.05662i
$148$		0			0
$149$	−14.0868	+	19.3888i	−1.15404	+	1.58839i	−0.422879	+	0.906186i	$0.638980\pi$
$149$	−14.0868	+	19.3888i	−1.15404	+	1.58839i	−0.731158	+	0.682209i	$0.761020\pi$
$150$		0			0
$151$	−6.30442	+	2.04843i	−0.513047	+	0.166699i	−0.554087	−	0.832458i	$-0.686933\pi$
$151$	−6.30442	+	2.04843i	−0.513047	+	0.166699i	0.0410407	+	0.999157i	$0.486933\pi$
$152$		0			0
$153$	2.24001			0.181094
$154$		0			0
$155$	−1.02246			−0.0821261
$156$		0			0
$157$	4.24211	−	1.37835i	0.338557	−	0.110004i	−0.134804	−	0.990872i	$-0.543040\pi$
$157$	4.24211	−	1.37835i	0.338557	−	0.110004i	0.473361	+	0.880868i	$0.343040\pi$
$158$		0			0
$159$	13.3604	−	18.3891i	1.05955	−	1.45835i
$160$		0			0
$161$	−19.1256	+	13.9770i	−1.50731	+	1.10154i
$162$		0			0
$163$	−17.4850	+	12.7036i	−1.36953	+	0.995023i	−0.371758	+	0.928330i	$0.621245\pi$
$163$	−17.4850	+	12.7036i	−1.36953	+	0.995023i	−0.997774	+	0.0666930i	$0.978755\pi$
$164$		0			0
$165$	19.6508	−	6.42269i	1.52981	−	0.500006i
$166$		0			0
$167$	14.9260	−	10.8444i	1.15501	−	0.839163i	0.165870	−	0.986148i	$-0.446957\pi$
$167$	14.9260	−	10.8444i	1.15501	−	0.839163i	0.989139	+	0.146984i	$0.0469567\pi$
$168$		0			0
$169$	0.584055	−	1.79754i	0.0449273	−	0.138272i
$170$		0			0
$171$	−1.24356	−	0.903497i	−0.0950972	−	0.0690922i
$172$		0			0
$173$	−6.28216	−	19.3345i	−0.477624	−	1.46997i	−0.842386	−	0.538874i	$-0.818850\pi$
$173$	−6.28216	−	19.3345i	−0.477624	−	1.46997i	0.364762	−	0.931101i	$-0.381150\pi$
$174$		0			0
$175$	−14.1562	−	10.2251i	−1.07011	−	0.772943i
$176$		0			0
$177$	−7.04621			−0.529626
$178$		0			0
$179$	5.85667	+	18.0250i	0.437748	+	1.34725i	0.890244	+	0.455484i	$0.150534\pi$
$179$	5.85667	+	18.0250i	0.437748	+	1.34725i	−0.452496	+	0.891766i	$0.649466\pi$
$180$		0			0
$181$	−7.50624	+	10.3315i	−0.557935	+	0.767931i	−0.991062	−	0.133402i	$-0.957410\pi$
$181$	−7.50624	+	10.3315i	−0.557935	+	0.767931i	0.433128	+	0.901333i	$0.357410\pi$
$182$		0			0
$183$	18.1917	+	5.91085i	1.34477	+	0.436943i
$184$		0			0
$185$	−2.14830	−	2.95688i	−0.157946	−	0.217394i
$186$		0			0
$187$	0.0369363	+	21.2590i	0.00270105	+	1.55461i
$188$		0			0
$189$	0.0356901	+	12.8342i	0.00259607	+	0.933550i
$190$		0			0
$191$	3.28372	−	10.1063i	0.237602	−	0.731263i	−0.759164	−	0.650899i	$-0.774392\pi$
$191$	3.28372	−	10.1063i	0.237602	−	0.731263i	0.996766	−	0.0803633i	$-0.0256080\pi$
$192$		0			0
$193$	6.40859	−	8.82066i	0.461300	−	0.634925i	−0.513478	−	0.858103i	$-0.671643\pi$
$193$	6.40859	−	8.82066i	0.461300	−	0.634925i	0.974778	+	0.223178i	$0.0716431\pi$
$194$		0			0
$195$	7.43282	+	22.8759i	0.532275	+	1.63817i
$196$		0			0
$197$			2.87020i			0.204493i	0.994759	+	0.102247i	$0.0326031\pi$
$197$			2.87020i			0.204493i	−0.994759	+	0.102247i	$0.967397\pi$
$198$		0			0
$199$		−	14.6219i		−	1.03652i	−0.855224	−	0.518259i	$-0.826580\pi$
$199$		−	14.6219i		−	1.03652i	0.855224	−	0.518259i	$-0.173420\pi$
$200$		0			0
$201$	−2.31215	+	0.751262i	−0.163086	+	0.0529899i
$202$		0			0
$203$	−7.81917	+	2.56466i	−0.548798	+	0.180004i
$204$		0			0
$205$	1.37643	+	0.447231i	0.0961343	+	0.0312359i
$206$		0			0
$207$	−2.53133	+	1.83912i	−0.175939	+	0.127828i
$208$		0			0
$209$	8.55420	−	11.8170i	0.591706	−	0.817397i
$210$		0			0
$211$	−6.28539	−	8.65110i	−0.432704	−	0.595566i	0.535867	−	0.844302i	$-0.319985\pi$
$211$	−6.28539	−	8.65110i	−0.432704	−	0.595566i	−0.968571	+	0.248736i	$0.919985\pi$
$212$		0			0
$213$	−27.7713	−	9.02344i	−1.90286	−	0.618276i
$214$		0			0
$215$	25.1102	+	18.2436i	1.71250	+	1.24421i
$216$		0			0
$217$	−0.756063	−	0.243337i	−0.0513249	−	0.0165188i
$218$		0			0
$219$			13.0415i			0.881263i
$220$		0			0
$221$	−24.7340			−1.66379
$222$		0			0
$223$	16.7185	−	5.43215i	1.11955	−	0.363764i	0.309954	−	0.950751i	$-0.399686\pi$
$223$	16.7185	−	5.43215i	1.11955	−	0.363764i	0.809596	+	0.586988i	$0.199686\pi$
$224$		0			0
$225$	−1.86607	−	1.35578i	−0.124404	−	0.0903851i
$226$		0			0
$227$	−3.20035	+	9.84966i	−0.212415	+	0.653745i	0.786912	+	0.617065i	$0.211678\pi$
$227$	−3.20035	+	9.84966i	−0.212415	+	0.653745i	−0.999327	+	0.0366803i	$0.988322\pi$
$228$		0			0
$229$	8.25603	+	11.3634i	0.545574	+	0.750918i	0.989403	−	0.145194i	$-0.0463805\pi$
$229$	8.25603	+	11.3634i	0.545574	+	0.750918i	−0.443830	+	0.896111i	$0.646381\pi$
$230$		0			0
$231$	16.0594	−	0.0725614i	1.05663	−	0.00477419i
$232$		0			0
$233$	−3.84035	−	5.28579i	−0.251590	−	0.346283i	0.664478	−	0.747308i	$-0.268654\pi$
$233$	−3.84035	−	5.28579i	−0.251590	−	0.346283i	−0.916067	+	0.401025i	$0.868654\pi$
$234$		0			0
$235$	−2.81764	+	8.67180i	−0.183802	+	0.565686i
$236$		0			0
$237$	10.8761	+	7.90198i	0.706481	+	0.513289i
$238$		0			0
$239$	−10.7878	+	3.50518i	−0.697807	+	0.226731i	−0.636375	−	0.771380i	$-0.719567\pi$
$239$	−10.7878	+	3.50518i	−0.697807	+	0.226731i	−0.0614325	+	0.998111i	$0.519567\pi$
$240$		0			0
$241$	−12.4668			−0.803060			−0.401530	−	0.915846i	$-0.631521\pi$
$241$	−12.4668			−0.803060			−0.401530	+	0.915846i	$0.631521\pi$
$242$		0			0
$243$			3.61394i			0.231834i
$244$		0			0
$245$	−14.1207	−	19.2099i	−0.902140	−	1.22728i
$246$		0			0
$247$	13.7313	+	9.97635i	0.873699	+	0.634780i
$248$		0			0
$249$	−1.99760	−	0.649058i	−0.126592	−	0.0411324i
$250$		0			0
$251$	−9.05092	−	12.4575i	−0.571289	−	0.786312i	0.421417	−	0.906867i	$-0.361533\pi$
$251$	−9.05092	−	12.4575i	−0.571289	−	0.786312i	−0.992707	+	0.120555i	$0.961533\pi$
$252$		0			0
$253$	−17.4960	−	23.9934i	−1.09997	−	1.50845i
$254$		0			0
$255$	32.3242	−	23.4849i	2.02422	−	1.47068i
$256$		0			0
$257$	−6.68910	−	2.17342i	−0.417255	−	0.135574i	0.0928629	−	0.995679i	$-0.470398\pi$
$257$	−6.68910	−	2.17342i	−0.417255	−	0.135574i	−0.510118	+	0.860105i	$0.670398\pi$
$258$		0			0
$259$	−0.884855	−	2.69775i	−0.0549822	−	0.167630i
$260$		0			0
$261$	−1.03374	+	0.335881i	−0.0639866	+	0.0207905i
$262$		0			0
$263$			3.48330i			0.214789i	0.994216	+	0.107395i	$0.0342509\pi$
$263$			3.48330i			0.214789i	−0.994216	+	0.107395i	$0.965749\pi$
$264$		0			0
$265$		−	42.3009i		−	2.59852i
$266$		0			0
$267$	−2.03032	−	6.24868i	−0.124254	−	0.382413i
$268$		0			0
$269$	17.1132	−	23.5542i	1.04341	−	1.43613i	0.149020	−	0.988834i	$-0.452388\pi$
$269$	17.1132	−	23.5542i	1.04341	−	1.43613i	0.894387	−	0.447293i	$-0.147612\pi$
$270$		0			0
$271$	−3.81905	+	11.7538i	−0.231991	+	0.713993i	0.765516	+	0.643417i	$0.222484\pi$
$271$	−3.81905	+	11.7538i	−0.231991	+	0.713993i	−0.997506	+	0.0705764i	$0.977516\pi$
$272$		0			0
$273$	0.0519591	+	18.6846i	0.00314471	+	1.13084i
$274$		0			0
$275$	12.8363	−	17.7324i	0.774059	−	1.06930i
$276$		0			0
$277$	−3.09097	−	4.25436i	−0.185719	−	0.255620i	0.705998	−	0.708214i	$-0.250499\pi$
$277$	−3.09097	−	4.25436i	−0.185719	−	0.255620i	−0.891717	+	0.452594i	$0.850499\pi$
$278$		0			0
$279$	−0.0997750	−	0.0324189i	−0.00597337	−	0.00194087i
$280$		0			0
$281$	18.2340	−	25.0969i	1.08775	−	1.49716i	0.237054	−	0.971496i	$-0.423818\pi$
$281$	18.2340	−	25.0969i	1.08775	−	1.49716i	0.850694	−	0.525661i	$-0.176182\pi$
$282$		0			0
$283$	4.23133	+	13.0227i	0.251526	+	0.774118i	0.994494	+	0.104791i	$0.0334174\pi$
$283$	4.23133	+	13.0227i	0.251526	+	0.774118i	−0.742968	+	0.669327i	$0.766583\pi$
$284$		0			0
$285$	−27.4175			−1.62407
$286$		0			0
$287$	0.911371	+	0.658286i	0.0537965	+	0.0388574i
$288$		0			0
$289$	7.44297	+	22.9071i	0.437822	+	1.34748i
$290$		0			0
$291$	−3.03263	−	2.20334i	−0.177776	−	0.129162i
$292$		0			0
$293$	−2.30824	+	7.10403i	−0.134849	+	0.415022i	−0.995566	−	0.0940607i	$-0.970015\pi$
$293$	−2.30824	+	7.10403i	−0.134849	+	0.415022i	0.860718	+	0.509083i	$0.170015\pi$
$294$		0			0
$295$	−10.6087	+	7.70765i	−0.617660	+	0.448757i
$296$		0			0
$297$	−16.0886	+	0.0279529i	−0.933553	+	0.00162199i
$298$		0			0
$299$	27.9507	−	20.3074i	1.61643	−	1.17441i
$300$		0			0
$301$	14.2260	+	19.4663i	0.819973	+	1.12202i
$302$		0			0
$303$	15.5897	−	21.4574i	0.895607	−	1.23270i
$304$		0			0
$305$	33.8549	−	11.0001i	1.93853	−	0.629865i
$306$		0			0
$307$	5.04115			0.287714			0.143857	−	0.989599i	$-0.454050\pi$
$307$	5.04115			0.287714			0.143857	+	0.989599i	$0.454050\pi$
$308$		0			0
$309$	−14.0719			−0.800520
$310$		0			0
$311$	26.1908	−	8.50992i	1.48515	−	0.482553i	0.549500	−	0.835494i	$-0.314818\pi$
$311$	26.1908	−	8.50992i	1.48515	−	0.482553i	0.935646	+	0.352940i	$0.114818\pi$
$312$		0			0
$313$	3.57851	−	4.92539i	0.202269	−	0.278400i	−0.695817	−	0.718219i	$-0.744958\pi$
$313$	3.57851	−	4.92539i	0.202269	−	0.278400i	0.898086	+	0.439819i	$0.144958\pi$
$314$		0			0
$315$	−1.85808	−	2.54253i	−0.104691	−	0.143255i
$316$		0			0
$317$	−0.0366660	+	0.0266394i	−0.00205937	+	0.00149622i	−0.588814	−	0.808268i	$-0.700405\pi$
$317$	−0.0366660	+	0.0266394i	−0.00205937	+	0.00149622i	0.586755	+	0.809764i	$0.300405\pi$
$318$		0			0
$319$	−3.20475	−	9.80520i	−0.179431	−	0.548986i
$320$		0			0
$321$	6.23288	−	4.52845i	0.347886	−	0.252754i
$322$		0			0
$323$	8.71232	−	26.8138i	0.484767	−	1.49196i
$324$		0			0
$325$	20.6050	+	14.9704i	1.14296	+	0.830407i
$326$		0			0
$327$	6.05891	+	18.6474i	0.335058	+	1.03120i
$328$		0			0
$329$	−4.14733	+	5.74181i	−0.228649	+	0.316556i
$330$		0			0
$331$	16.6993			0.917878			0.458939	−	0.888468i	$-0.348230\pi$
$331$	16.6993			0.917878			0.458939	+	0.888468i	$0.348230\pi$
$332$		0			0
$333$	−0.115885	−	0.356657i	−0.00635046	−	0.0195447i
$334$		0			0
$335$	−2.65935	+	3.66028i	−0.145296	+	0.199982i
$336$		0			0
$337$	9.24849	+	3.00502i	0.503797	+	0.163694i	0.549880	−	0.835244i	$-0.314674\pi$
$337$	9.24849	+	3.00502i	0.503797	+	0.163694i	−0.0460822	+	0.998938i	$0.514674\pi$
$338$		0			0
$339$	−4.83298	−	6.65203i	−0.262491	−	0.361289i
$340$		0			0
$341$	0.306028	−	0.947456i	0.0165724	−	0.0513076i
$342$		0			0
$343$	−5.86982	−	17.5655i	−0.316940	−	0.948445i
$344$		0			0
$345$	−17.2462	+	53.0783i	−0.928503	+	2.85764i
$346$		0			0
$347$	−4.83159	+	6.65011i	−0.259373	+	0.356997i	−0.918766	−	0.394802i	$-0.870813\pi$
$347$	−4.83159	+	6.65011i	−0.259373	+	0.356997i	0.659393	+	0.751798i	$0.270813\pi$
$348$		0			0
$349$	1.58539	+	4.87934i	0.0848642	+	0.261185i	0.984480	−	0.175497i	$-0.0561533\pi$
$349$	1.58539	+	4.87934i	0.0848642	+	0.261185i	−0.899616	+	0.436682i	$0.856153\pi$
$350$		0			0
$351$		−	18.7184i		−	0.999116i
$352$		0			0
$353$		−	26.8998i		−	1.43173i	−0.698238	−	0.715866i	$-0.746032\pi$
$353$		−	26.8998i		−	1.43173i	0.698238	−	0.715866i	$-0.253968\pi$
$354$		0			0
$355$	−51.6825	+	16.7927i	−2.74302	+	0.891262i
$356$		0			0
$357$	29.4914	−	9.67309i	1.56085	−	0.511954i
$358$		0			0
$359$	−24.9077	−	8.09300i	−1.31458	−	0.427132i	−0.433949	−	0.900938i	$-0.642880\pi$
$359$	−24.9077	−	8.09300i	−1.31458	−	0.427132i	−0.880630	+	0.473805i	$0.842880\pi$
$360$		0			0
$361$	−0.280584	+	0.203856i	−0.0147676	+	0.0107293i
$362$		0			0
$363$	0.0699551	+	20.1316i	0.00367169	+	1.05663i
$364$		0			0
$365$	14.2657	+	19.6351i	0.746702	+	1.02775i
$366$		0			0
$367$	11.9245	+	3.87449i	0.622452	+	0.202247i	0.603228	−	0.797568i	$-0.293881\pi$
$367$	11.9245	+	3.87449i	0.622452	+	0.202247i	0.0192232	+	0.999815i	$0.493881\pi$
$368$		0			0
$369$	0.120136	+	0.0872843i	0.00625405	+	0.00454384i
$370$		0			0
$371$	10.0672	−	31.2795i	0.522666	−	1.62395i
$372$		0			0
$373$		−	5.31859i		−	0.275386i	−0.990475	−	0.137693i	$-0.956031\pi$
$373$		−	5.31859i		−	0.275386i	0.990475	−	0.137693i	$-0.0439688\pi$
$374$		0			0
$375$	−9.97549			−0.515132
$376$		0			0
$377$	11.4144	−	3.70877i	0.587873	−	0.191011i
$378$		0			0
$379$	8.36679	+	6.07883i	0.429773	+	0.312248i	0.781558	−	0.623832i	$-0.214425\pi$
$379$	8.36679	+	6.07883i	0.429773	+	0.312248i	−0.351785	+	0.936081i	$0.614425\pi$
$380$		0			0
$381$	5.61543	−	17.2825i	0.287687	−	0.885410i
$382$		0			0
$383$	0.495500	+	0.681997i	0.0253188	+	0.0348484i	0.821489	−	0.570225i	$-0.193144\pi$
$383$	0.495500	+	0.681997i	0.0253188	+	0.0348484i	−0.796170	+	0.605073i	$0.793144\pi$
$384$		0			0
$385$	24.0994	−	17.6761i	1.22822	−	0.900859i
$386$		0			0
$387$	1.87189	+	2.57643i	0.0951534	+	0.130967i
$388$		0			0
$389$	0.705746	−	2.17206i	0.0357827	−	0.110128i	−0.931570	−	0.363563i	$-0.881560\pi$
$389$	0.705746	−	2.17206i	0.0357827	−	0.110128i	0.967353	+	0.253435i	$0.0815603\pi$
$390$		0			0
$391$	−46.4293	−	33.7328i	−2.34803	−	1.70594i
$392$		0			0
$393$	−5.87832	+	1.90998i	−0.296522	+	0.0963458i
$394$		0			0
$395$	25.0187			1.25883
$396$		0			0
$397$			23.8577i			1.19738i	0.800979	+	0.598692i	$0.204313\pi$
$397$			23.8577i			1.19738i	−0.800979	+	0.598692i	$0.795687\pi$
$398$		0			0
$399$	−20.2740	−	6.52513i	−1.01497	−	0.326665i
$400$		0			0
$401$	−12.0439	−	8.75039i	−0.601443	−	0.436974i	0.244948	−	0.969536i	$-0.421229\pi$
$401$	−12.0439	−	8.75039i	−0.601443	−	0.436974i	−0.846391	+	0.532563i	$0.821229\pi$
$402$		0			0
$403$	1.10171	+	0.357966i	0.0548799	+	0.0178316i
$404$		0			0
$405$	19.8719	+	27.3514i	0.987444	+	1.35910i
$406$		0			0
$407$	3.38297	−	1.10570i	0.167688	−	0.0548073i
$408$		0			0
$409$	12.8887	−	9.36422i	0.637307	−	0.463031i	−0.221617	−	0.975134i	$-0.571133\pi$
$409$	12.8887	−	9.36422i	0.637307	−	0.463031i	0.858924	+	0.512103i	$0.171133\pi$
$410$		0			0
$411$	20.1700	+	6.55363i	0.994913	+	0.323267i
$412$		0			0
$413$	−9.67897	+	3.17467i	−0.476271	+	0.156215i
$414$		0			0
$415$	−3.71754	+	1.20790i	−0.182487	+	0.0592935i
$416$		0			0
$417$		−	14.4003i		−	0.705187i
$418$		0			0
$419$		−	11.9321i		−	0.582921i	−0.956583	−	0.291461i	$-0.905859\pi$
$419$		−	11.9321i		−	0.582921i	0.956583	−	0.291461i	$-0.0941412\pi$
$420$		0			0
$421$	10.2174	+	31.4459i	0.497965	+	1.53258i	0.812284	+	0.583262i	$0.198224\pi$
$421$	10.2174	+	31.4459i	0.497965	+	1.53258i	−0.314319	+	0.949317i	$0.601776\pi$
$422$		0			0
$423$	−0.549907	+	0.756883i	−0.0267374	+	0.0368009i
$424$		0			0
$425$	13.0736	−	40.2364i	0.634163	−	1.95175i
$426$		0			0
$427$	27.6521	−	0.0768964i	1.33818	−	0.00372128i
$428$		0			0
$429$	−23.4224	+	0.0406951i	−1.13084	+	0.00196478i
$430$		0			0
$431$	−5.08495	−	6.99883i	−0.244933	−	0.337122i	0.668796	−	0.743446i	$-0.266810\pi$
$431$	−5.08495	−	6.99883i	−0.244933	−	0.337122i	−0.913729	+	0.406325i	$0.866810\pi$
$432$		0			0
$433$	15.6779	+	5.09405i	0.753430	+	0.244804i	0.660457	−	0.750864i	$-0.270363\pi$
$433$	15.6779	+	5.09405i	0.753430	+	0.244804i	0.0929737	+	0.995669i	$0.470363\pi$
$434$		0			0
$435$	−11.3957	+	15.6849i	−0.546383	+	0.752031i
$436$		0			0
$437$	12.1696	+	37.4540i	0.582149	+	1.79167i
$438$		0			0
$439$	−10.1008			−0.482086			−0.241043	−	0.970514i	$-0.577489\pi$
$439$	−10.1008			−0.482086			−0.241043	+	0.970514i	$0.577489\pi$
$440$		0			0
$441$	−0.768862	−	2.32228i	−0.0366125	−	0.110585i
$442$		0			0
$443$	−1.23368	−	3.79689i	−0.0586141	−	0.180396i	0.917463	−	0.397822i	$-0.130234\pi$
$443$	−1.23368	−	3.79689i	−0.0586141	−	0.180396i	−0.976077	+	0.217426i	$0.930234\pi$
$444$		0			0
$445$	−9.89207	−	7.18701i	−0.468929	−	0.340697i
$446$		0			0
$447$	−13.5539	+	41.7146i	−0.641077	+	1.97303i
$448$		0			0
$449$	−3.36424	+	2.44426i	−0.158768	+	0.115352i	−0.664333	−	0.747437i	$-0.731284\pi$
$449$	−3.36424	+	2.44426i	−0.158768	+	0.115352i	0.505565	+	0.862789i	$0.331284\pi$
$450$		0			0
$451$	−0.826396	+	1.14160i	−0.0389135	+	0.0537560i
$452$		0			0
$453$	−9.81487	+	7.13092i	−0.461143	+	0.335040i
$454$		0			0
$455$	20.5167	+	28.0744i	0.961840	+	1.31615i
$456$		0			0
$457$	8.43325	−	11.6074i	0.394491	−	0.542970i	−0.564860	−	0.825187i	$-0.691070\pi$
$457$	8.43325	−	11.6074i	0.394491	−	0.542970i	0.959351	+	0.282217i	$0.0910697\pi$
$458$		0			0
$459$	−29.5716	+	9.60839i	−1.38028	+	0.448481i
$460$		0			0
$461$	−38.8150			−1.80780			−0.903898	−	0.427747i	$-0.859307\pi$
$461$	−38.8150			−1.80780			−0.903898	+	0.427747i	$0.859307\pi$
$462$		0			0
$463$	−18.9223			−0.879394			−0.439697	−	0.898146i	$-0.644914\pi$
$463$	−18.9223			−0.879394			−0.439697	+	0.898146i	$0.644914\pi$
$464$		0			0
$465$	−1.77968	+	0.578252i	−0.0825306	+	0.0268158i
$466$		0			0
$467$	18.7492	−	25.8061i	0.867611	−	1.19416i	−0.112090	−	0.993698i	$-0.535754\pi$
$467$	18.7492	−	25.8061i	0.867611	−	1.19416i	0.979701	−	0.200466i	$-0.0642456\pi$
$468$		0			0
$469$	−2.83758	+	2.07370i	−0.131027	+	0.0957547i
$470$		0			0
$471$	6.60421	−	4.79824i	0.304306	−	0.221091i
$472$		0			0
$473$	−24.4209	+	17.8078i	−1.12288	+	0.818802i
$474$		0			0
$475$	−23.4871	+	17.0643i	−1.07766	+	0.782966i
$476$		0			0
$477$	1.34122	−	4.12785i	0.0614102	−	0.189001i
$478$		0			0
$479$	−17.3848	−	12.6308i	−0.794332	−	0.577116i	0.114914	−	0.993375i	$-0.463341\pi$
$479$	−17.3848	−	12.6308i	−0.794332	−	0.577116i	−0.909246	+	0.416260i	$0.863341\pi$
$480$		0			0
$481$	1.27959	+	3.93818i	0.0583444	+	0.179566i
$482$		0			0
$483$	−25.3849	+	35.1444i	−1.15505	+	1.59913i
$484$		0			0
$485$	−6.97606			−0.316766
$486$		0			0
$487$	−2.06634	−	6.35956i	−0.0936350	−	0.288179i	0.893261	−	0.449539i	$-0.148412\pi$
$487$	−2.06634	−	6.35956i	−0.0936350	−	0.288179i	−0.986896	+	0.161360i	$0.948412\pi$
$488$		0			0
$489$	−23.2495	+	32.0003i	−1.05138	+	1.44710i
$490$		0			0
$491$	13.9756	+	4.54096i	0.630712	+	0.204931i	0.606891	−	0.794785i	$-0.292417\pi$
$491$	13.9756	+	4.54096i	0.630712	+	0.204931i	0.0238217	+	0.999716i	$0.492417\pi$
$492$		0			0
$493$	−11.7183	−	16.1289i	−0.527766	−	0.726408i
$494$		0			0
$495$	3.18965	−	2.32590i	0.143364	−	0.104541i
$496$		0			0
$497$	−42.2133	+	0.117389i	−1.89353	+	0.00526563i
$498$		0			0
$499$	−5.98148	+	18.4091i	−0.267768	+	0.824104i	0.723275	+	0.690560i	$0.242636\pi$
$499$	−5.98148	+	18.4091i	−0.267768	+	0.824104i	−0.991043	+	0.133544i	$0.957364\pi$
$500$		0			0
$501$	19.8469	−	27.3169i	0.886694	−	1.22043i
$502$		0			0
$503$	0.293100	+	0.902069i	0.0130687	+	0.0402213i	0.957378	−	0.288837i	$-0.0932687\pi$
$503$	0.293100	+	0.902069i	0.0130687	+	0.0402213i	−0.944310	+	0.329059i	$0.893269\pi$
$504$		0			0
$505$		−	49.3592i		−	2.19645i
$506$		0			0
$507$		−	3.45907i		−	0.153623i
$508$		0			0
$509$	−37.7006	+	12.2497i	−1.67105	+	0.542957i	−0.983142	−	0.182841i	$-0.941471\pi$
$509$	−37.7006	+	12.2497i	−1.67105	+	0.542957i	−0.687908	+	0.725798i	$0.741471\pi$
$510$		0			0
$511$	5.87585	+	17.9143i	0.259932	+	0.792484i
$512$		0			0
$513$	20.2924	+	6.59339i	0.895929	+	0.291105i
$514$		0			0
$515$	−21.1864	+	15.3928i	−0.933583	+	0.678288i
$516$		0			0
$517$	−7.19232	−	5.20645i	−0.316318	−	0.228980i
$518$		0			0
$519$	−21.8692	−	30.1004i	−0.959952	−	1.32126i
$520$		0			0
$521$	−36.9475	−	12.0050i	−1.61870	−	0.525948i	−0.647066	−	0.762434i	$-0.724004\pi$
$521$	−36.9475	−	12.0050i	−1.61870	−	0.525948i	−0.971635	+	0.236486i	$0.924004\pi$
$522$		0			0
$523$	7.31919	+	5.31770i	0.320046	+	0.232527i	0.736195	−	0.676769i	$-0.236621\pi$
$523$	7.31919	+	5.31770i	0.320046	+	0.232527i	−0.416149	+	0.909296i	$0.636621\pi$
$524$		0			0
$525$	−30.4228	−	9.79153i	−1.32776	−	0.427337i
$526$		0			0
$527$		−	1.92424i		−	0.0838211i
$528$		0			0
$529$	57.1632			2.48536
$530$		0			0
$531$	−1.27961	+	0.415770i	−0.0555303	+	0.0180429i
$532$		0			0
$533$	−1.32654	−	0.963786i	−0.0574587	−	0.0417462i
$534$		0			0
$535$	4.43059	−	13.6359i	0.191551	−	0.589533i
$536$		0			0
$537$	20.3880	+	28.0617i	0.879808	+	1.21095i
$538$		0			0
$539$	22.0271	−	7.33523i	0.948776	−	0.315951i
$540$		0			0
$541$	−13.1552	−	18.1066i	−0.565587	−	0.778464i	0.426436	−	0.904518i	$-0.359769\pi$
$541$	−13.1552	−	18.1066i	−0.565587	−	0.778464i	−0.992023	+	0.126053i	$0.959769\pi$
$542$		0			0
$543$	−7.22227	+	22.2279i	−0.309937	+	0.953889i
$544$		0			0
$545$	29.5201	+	21.4476i	1.26450	+	0.918713i
$546$		0			0
$547$	12.6499	−	4.11021i	0.540872	−	0.175740i	−0.0258247	−	0.999666i	$-0.508221\pi$
$547$	12.6499	−	4.11021i	0.540872	−	0.175740i	0.566697	+	0.823927i	$0.308221\pi$
$548$		0			0
$549$	3.65244			0.155882
$550$		0			0
$551$			13.6806i			0.582812i
$552$		0			0
$553$	18.5002	+	5.95424i	0.786707	+	0.253200i
$554$		0			0
$555$	−5.41155	−	3.93172i	−0.229708	−	0.166892i
$556$		0			0
$557$	36.9227	+	11.9969i	1.56446	+	0.508325i	0.957996	−	0.286782i	$-0.0925855\pi$
$557$	36.9227	+	11.9969i	1.56446	+	0.508325i	0.606469	+	0.795107i	$0.292585\pi$
$558$		0			0
$559$	−20.6692	−	28.4488i	−0.874215	−	1.20325i
$560$		0			0
$561$	12.0873	+	36.9821i	0.510325	+	1.56138i
$562$		0			0
$563$	−14.6910	+	10.6737i	−0.619153	+	0.449841i	−0.852626	−	0.522522i	$-0.824991\pi$
$563$	−14.6910	+	10.6737i	−0.619153	+	0.449841i	0.233472	+	0.972363i	$0.424991\pi$
$564$		0			0
$565$	−14.5529	−	4.72853i	−0.612246	−	0.198931i
$566$		0			0
$567$	8.18497	+	24.9544i	0.343736	+	1.04799i
$568$		0			0
$569$	12.3540	−	4.01405i	0.517906	−	0.168278i	−0.0383889	−	0.999263i	$-0.512223\pi$
$569$	12.3540	−	4.01405i	0.517906	−	0.168278i	0.556295	+	0.830985i	$0.312223\pi$
$570$		0			0
$571$			34.4792i			1.44291i	0.692462	+	0.721454i	$0.256526\pi$
$571$			34.4792i			1.44291i	−0.692462	+	0.721454i	$0.743474\pi$
$572$		0			0
$573$		−	19.4478i		−	0.812445i
$574$		0			0
$575$	18.2615	+	56.2030i	0.761556	+	2.34383i
$576$		0			0
$577$	−6.05240	+	8.33041i	−0.251965	+	0.346799i	−0.916198	−	0.400726i	$-0.868758\pi$
$577$	−6.05240	+	8.33041i	−0.251965	+	0.346799i	0.664234	+	0.747525i	$0.268758\pi$
$578$		0			0
$579$	6.16614	−	18.9774i	0.256256	−	0.788675i
$580$		0			0
$581$	−3.03641	+	0.00844383i	−0.125972	+	0.000350309i
$582$		0			0
$583$	39.1978	+	12.6609i	1.62341	+	0.524360i
$584$		0			0
$585$	2.69964	+	3.71573i	0.111616	+	0.153627i
$586$		0			0
$587$	−29.5852	−	9.61282i	−1.22111	−	0.396764i	−0.373626	−	0.927580i	$-0.621886\pi$
$587$	−29.5852	−	9.61282i	−1.22111	−	0.396764i	−0.847487	+	0.530816i	$0.821886\pi$
$588$		0			0
$589$	−0.776132	+	1.06825i	−0.0319799	+	0.0440166i
$590$		0			0
$591$	1.62324	+	4.99581i	0.0667711	+	0.205500i
$592$		0			0
$593$	−16.1102			−0.661567			−0.330783	−	0.943707i	$-0.607313\pi$
$593$	−16.1102			−0.661567			−0.330783	+	0.943707i	$0.607313\pi$
$594$		0			0
$595$	33.8207	−	46.8235i	1.38651	−	1.91958i
$596$		0			0
$597$	−8.26939	−	25.4506i	−0.338444	−	1.04162i
$598$		0			0
$599$	18.3095	+	13.3027i	0.748108	+	0.543532i	0.895240	−	0.445585i	$-0.147004\pi$
$599$	18.3095	+	13.3027i	0.748108	+	0.543532i	−0.147132	+	0.989117i	$0.547004\pi$
$600$		0			0
$601$	3.11936	−	9.60039i	0.127241	−	0.391608i	−0.867062	−	0.498201i	$-0.833994\pi$
$601$	3.11936	−	9.60039i	0.127241	−	0.391608i	0.994303	+	0.106593i	$0.0339942\pi$
$602$		0			0
$603$	−0.375563	+	0.272862i	−0.0152941	+	0.0111118i
$604$		0			0
$605$	22.1267	+	30.2333i	0.899577	+	1.22916i
$606$		0			0
$607$	−5.45860	+	3.96591i	−0.221558	+	0.160971i	−0.693028	−	0.720911i	$-0.743724\pi$
$607$	−5.45860	+	3.96591i	−0.221558	+	0.160971i	0.471470	+	0.881882i	$0.343724\pi$
$608$		0			0
$609$	−12.1595	+	8.88613i	−0.492726	+	0.360084i
$610$		0			0
$611$	6.07203	−	8.35744i	0.245648	−	0.338106i
$612$		0			0
$613$	−11.5257	+	3.74493i	−0.465519	+	0.151256i	−0.532379	−	0.846506i	$-0.678702\pi$
$613$	−11.5257	+	3.74493i	−0.465519	+	0.151256i	0.0668601	+	0.997762i	$0.478702\pi$
$614$		0			0
$615$	2.64872			0.106807
$616$		0			0
$617$	−40.8433			−1.64429			−0.822144	−	0.569279i	$-0.807222\pi$
$617$	−40.8433			−1.64429			−0.822144	+	0.569279i	$0.807222\pi$
$618$		0			0
$619$	−20.5276	+	6.66981i	−0.825073	+	0.268082i	−0.690968	−	0.722885i	$-0.742816\pi$
$619$	−20.5276	+	6.66981i	−0.825073	+	0.268082i	−0.134104	+	0.990967i	$0.542816\pi$
$620$		0			0
$621$	25.5286	−	35.1371i	1.02443	−	1.41000i
$622$		0			0
$623$	−5.60427	−	7.66868i	−0.224531	−	0.307239i
$624$		0			0
$625$	11.6800	−	8.48600i	0.467199	−	0.339440i
$626$		0			0
$627$	8.20620	−	25.4062i	0.327724	−	1.01463i
$628$		0			0
$629$	5.56475	−	4.04303i	0.221881	−	0.161206i
$630$		0			0
$631$	−8.14269	+	25.0606i	−0.324155	+	0.997648i	0.647665	+	0.761925i	$0.275746\pi$
$631$	−8.14269	+	25.0606i	−0.324155	+	0.997648i	−0.971820	+	0.235723i	$0.924254\pi$
$632$		0			0
$633$	−15.8328	−	11.5032i	−0.629299	−	0.457213i
$634$		0			0
$635$	−10.4503	−	32.1629i	−0.414709	−	1.27634i
$636$		0			0
$637$	8.48971	+	25.6425i	0.336374	+	1.01599i
$638$		0			0
$639$	−5.57578			−0.220574
$640$		0			0
$641$	−0.281105	−	0.865152i	−0.0111030	−	0.0341715i	0.945352	−	0.326053i	$-0.105719\pi$
$641$	−0.281105	−	0.865152i	−0.0111030	−	0.0341715i	−0.956455	+	0.291881i	$0.905719\pi$
$642$		0			0
$643$	12.2102	−	16.8059i	0.481523	−	0.662760i	−0.497274	−	0.867594i	$-0.665666\pi$
$643$	12.2102	−	16.8059i	0.481523	−	0.662760i	0.978797	+	0.204834i	$0.0656655\pi$
$644$		0			0
$645$	54.0240	+	17.5535i	2.12719	+	0.691167i
$646$		0			0
$647$	−14.4142	−	19.8394i	−0.566680	−	0.779967i	0.425477	−	0.904969i	$-0.360106\pi$
$647$	−14.4142	−	19.8394i	−0.566680	−	0.779967i	−0.992157	+	0.125002i	$0.960106\pi$
$648$		0			0
$649$	−3.96700	−	12.1374i	−0.155718	−	0.476434i
$650$		0			0
$651$	−1.45361	+	0.00404227i	−0.0569713	+	0.000158429i
$652$		0			0
$653$	14.1720	−	43.6168i	0.554592	−	1.70686i	−0.142428	−	0.989805i	$-0.545491\pi$
$653$	14.1720	−	43.6168i	0.554592	−	1.70686i	0.697020	−	0.717052i	$-0.254509\pi$
$654$		0			0
$655$	−6.76103	+	9.30577i	−0.264175	+	0.363606i
$656$		0			0
$657$	0.769530	+	2.36837i	0.0300222	+	0.0923989i
$658$		0			0
$659$			3.41699i			0.133107i	0.997783	+	0.0665535i	$0.0212003\pi$
$659$			3.41699i			0.133107i	−0.997783	+	0.0665535i	$0.978800\pi$
$660$		0			0
$661$		−	3.03335i		−	0.117983i	−0.998258	−	0.0589917i	$-0.981211\pi$
$661$		−	3.03335i		−	0.117983i	0.998258	−	0.0589917i	$-0.0187886\pi$
$662$		0			0
$663$	−43.0515	+	13.9883i	−1.67198	+	0.543260i
$664$		0			0
$665$	−37.6618	+	12.3530i	−1.46046	+	0.479027i
$666$		0			0
$667$	26.4846	+	8.60537i	1.02549	+	0.333201i
$668$		0			0
$669$	26.0277	−	18.9102i	1.00629	−	0.731111i
$670$		0			0
$671$	0.0602263	+	34.6638i	0.00232501	+	1.33818i
$672$		0			0
$673$	6.12312	+	8.42776i	0.236029	+	0.324866i	0.910557	−	0.413383i	$-0.135653\pi$
$673$	6.12312	+	8.42776i	0.236029	+	0.324866i	−0.674528	+	0.738249i	$0.735653\pi$
$674$		0			0
$675$	30.4504	+	9.89395i	1.17204	+	0.380818i
$676$		0			0
$677$	35.7156	+	25.9489i	1.37266	+	0.997298i	0.997524	+	0.0703294i	$0.0224050\pi$
$677$	35.7156	+	25.9489i	1.37266	+	0.997298i	0.375139	+	0.926969i	$0.377595\pi$
$678$		0			0
$679$	−5.15847	−	1.66024i	−0.197964	−	0.0637142i
$680$		0			0
$681$			18.9541i			0.726322i
$682$		0			0
$683$	12.7927			0.489499			0.244749	−	0.969586i	$-0.421294\pi$
$683$	12.7927			0.489499			0.244749	+	0.969586i	$0.421294\pi$
$684$		0			0
$685$	37.5365	−	12.1963i	1.43420	−	0.465998i
$686$		0			0
$687$	20.7969	+	15.1098i	0.793450	+	0.576475i
$688$		0			0
$689$	−14.8096	+	45.5794i	−0.564202	+	1.73644i
$690$		0			0
$691$	−12.6032	−	17.3469i	−0.479450	−	0.659906i	0.498949	−	0.866631i	$-0.333719\pi$
$691$	−12.6032	−	17.3469i	−0.479450	−	0.659906i	−0.978399	+	0.206725i	$0.933719\pi$
$692$		0			0
$693$	2.91214	−	0.960781i	0.110623	−	0.0364970i
$694$		0			0
$695$	−15.7521	−	21.6809i	−0.597512	−	0.822404i
$696$		0			0
$697$	−0.841672	+	2.59040i	−0.0318806	+	0.0981184i
$698$		0			0
$699$	−9.67381	−	7.02843i	−0.365897	−	0.265840i
$700$		0			0
$701$	−30.1589	+	9.79922i	−1.13909	+	0.370111i	−0.817022	−	0.576607i	$-0.804377\pi$
$701$	−30.1589	+	9.79922i	−1.13909	+	0.370111i	−0.322064	+	0.946718i	$0.604377\pi$
$702$		0			0
$703$	−4.72004			−0.178020
$704$		0			0
$705$			16.6875i			0.628486i
$706$		0			0
$707$	11.7471	−	36.4988i	0.441794	−	1.37268i
$708$		0			0
$709$	−2.31499	−	1.68194i	−0.0869412	−	0.0631665i	0.543466	−	0.839431i	$-0.317112\pi$
$709$	−2.31499	−	1.68194i	−0.0869412	−	0.0631665i	−0.630407	+	0.776265i	$0.717112\pi$
$710$		0			0
$711$	2.44140	+	0.793259i	0.0915597	+	0.0297496i
$712$		0			0
$713$	1.57986	+	2.17449i	0.0591661	+	0.0814352i
$714$		0			0
$715$	−35.2199	+	25.6824i	−1.31715	+	0.960466i
$716$		0			0
$717$	−16.7948	+	12.2021i	−0.627211	+	0.455696i
$718$		0			0
$719$	−1.17630	−	0.382203i	−0.0438686	−	0.0142538i	0.287001	−	0.957930i	$-0.407342\pi$
$719$	−1.17630	−	0.382203i	−0.0438686	−	0.0142538i	−0.330869	+	0.943677i	$0.607342\pi$
$720$		0			0
$721$	−19.3297	+	6.34008i	−0.719875	+	0.236117i
$722$		0			0
$723$	−21.6995	+	7.05061i	−0.807014	+	0.262215i
$724$		0			0
$725$			20.5289i			0.762424i
$726$		0			0
$727$		−	10.5201i		−	0.390170i	−0.980786	−	0.195085i	$-0.937502\pi$
$727$		−	10.5201i		−	0.390170i	0.980786	−	0.195085i	$-0.0624982\pi$
$728$		0			0
$729$	−7.15830	−	22.0310i	−0.265122	−	0.815962i
$730$		0			0
$731$	−34.3339	+	47.2566i	−1.26989	+	1.74785i
$732$		0			0
$733$	9.82660	−	30.2432i	0.362954	−	1.11706i	−0.588299	−	0.808644i	$-0.700202\pi$
$733$	9.82660	−	30.2432i	0.362954	−	1.11706i	0.951252	−	0.308413i	$-0.0997980\pi$
$734$		0			0
$735$	−35.4424	−	25.4505i	−1.30731	−	0.938754i
$736$		0			0
$737$	−2.59581	−	3.55980i	−0.0956179	−	0.131127i
$738$		0			0
$739$	−23.8766	−	32.8634i	−0.878316	−	1.20890i	−0.976884	−	0.213768i	$-0.931426\pi$
$739$	−23.8766	−	32.8634i	−0.878316	−	1.20890i	0.0985683	−	0.995130i	$-0.468574\pi$
$740$		0			0
$741$	29.5425	+	9.59893i	1.08527	+	0.352626i
$742$		0			0
$743$	−13.1338	+	18.0771i	−0.481832	+	0.663185i	−0.978856	−	0.204552i	$-0.934426\pi$
$743$	−13.1338	+	18.0771i	−0.481832	+	0.663185i	0.497024	+	0.867737i	$0.334426\pi$
$744$		0			0
$745$	25.2239	+	77.6311i	0.924131	+	2.84418i
$746$		0			0
$747$	−0.401067			−0.0146743
$748$		0			0
$749$	6.52145	−	9.02870i	0.238289	−	0.329901i
$750$		0			0
$751$	−9.01810	−	27.7549i	−0.329075	−	1.01279i	−0.969567	−	0.244825i	$-0.921270\pi$
$751$	−9.01810	−	27.7549i	−0.329075	−	1.01279i	0.640492	−	0.767965i	$-0.278730\pi$
$752$		0			0
$753$	−22.7992	−	16.5646i	−0.830849	−	0.603647i
$754$		0			0
$755$	−6.97681	+	21.4724i	−0.253912	+	0.781461i
$756$		0			0
$757$	14.7917	−	10.7468i	0.537613	−	0.390599i	−0.285585	−	0.958353i	$-0.592188\pi$
$757$	14.7917	−	10.7468i	0.537613	−	0.390599i	0.823198	+	0.567755i	$0.192188\pi$
$758$		0			0
$759$	−44.0227	−	31.8676i	−1.59792	−	1.15672i
$760$		0			0
$761$	13.9804	−	10.1573i	0.506788	−	0.368203i	−0.304816	−	0.952411i	$-0.598595\pi$
$761$	13.9804	−	10.1573i	0.506788	−	0.368203i	0.811604	+	0.584208i	$0.198595\pi$
$762$		0			0
$763$	16.7244	+	22.8850i	0.605462	+	0.828493i
$764$		0			0
$765$	4.48440	−	6.17224i	0.162134	−	0.223158i
$766$		0			0
$767$	14.1294	−	4.59090i	0.510181	−	0.165768i
$768$		0			0
$769$	−4.28390			−0.154481			−0.0772407	−	0.997012i	$-0.524611\pi$
$769$	−4.28390			−0.154481			−0.0772407	+	0.997012i	$0.524611\pi$
$770$		0			0
$771$	−12.8721			−0.463577
$772$		0			0
$773$	−3.68810	+	1.19834i	−0.132652	+	0.0431012i	−0.374591	−	0.927190i	$-0.622217\pi$
$773$	−3.68810	+	1.19834i	−0.132652	+	0.0431012i	0.241939	+	0.970292i	$0.422217\pi$
$774$		0			0
$775$	−1.16465	+	1.60301i	−0.0418356	+	0.0575817i
$776$		0			0
$777$	−3.06587	−	4.19523i	−0.109988	−	0.150503i
$778$		0			0
$779$	1.51209	−	1.09859i	0.0541761	−	0.0393612i
$780$		0			0
$781$	−0.0919408	−	52.9173i	−0.00328990	−	1.89353i
$782$		0			0
$783$	12.2061	−	8.86829i	0.436212	−	0.316927i
$784$		0			0
$785$	4.69454	−	14.4483i	0.167555	−	0.515683i
$786$		0			0
$787$	40.6129	+	29.5070i	1.44770	+	1.05181i	0.986363	+	0.164585i	$0.0526284\pi$
$787$	40.6129	+	29.5070i	1.44770	+	1.05181i	0.461332	+	0.887227i	$0.347372\pi$
$788$		0			0
$789$	1.96998	+	6.06296i	0.0701330	+	0.215847i
$790$		0			0
$791$	−9.63585	−	6.96000i	−0.342612	−	0.247469i
$792$		0			0
$793$	−40.3300			−1.43216
$794$		0			0
$795$	−23.9232	−	73.6281i	−0.848469	−	2.61132i
$796$		0			0
$797$	13.6428	−	18.7777i	0.483254	−	0.665141i	−0.495873	−	0.868395i	$-0.665152\pi$
$797$	13.6428	−	18.7777i	0.483254	−	0.665141i	0.979126	+	0.203254i	$0.0651517\pi$
$798$		0			0
$799$	−16.3200	−	5.30270i	−0.577361	−	0.187596i
$800$		0			0
$801$	−0.737422	−	1.01497i	−0.0260555	−	0.0358624i
$802$		0			0
$803$	−22.4645	+	7.34233i	−0.792754	+	0.259105i
$804$		0			0
$805$	0.224362	+	80.6808i	0.00790771	+	2.84362i
$806$		0			0
$807$	16.4657	−	50.6764i	0.579622	−	1.78389i
$808$		0			0
$809$	−30.8117	+	42.4087i	−1.08328	+	1.49101i	−0.227425	+	0.973796i	$0.573031\pi$
$809$	−30.8117	+	42.4087i	−1.08328	+	1.49101i	−0.855856	+	0.517213i	$0.826969\pi$
$810$		0			0
$811$	−5.05077	−	15.5447i	−0.177356	−	0.545847i	0.822377	−	0.568943i	$-0.192648\pi$
$811$	−5.05077	−	15.5447i	−0.177356	−	0.545847i	−0.999733	+	0.0230963i	$0.992648\pi$
$812$		0			0
$813$			22.6183i			0.793259i
$814$		0			0
$815$			73.6111i			2.57849i
$816$		0			0
$817$	38.1214	−	12.3864i	1.33370	−	0.433345i
$818$		0			0
$819$	1.11194	+	3.39010i	0.0388544	+	0.118460i
$820$		0			0
$821$	−21.9198	−	7.12218i	−0.765007	−	0.248566i	−0.0995807	−	0.995029i	$-0.531750\pi$
$821$	−21.9198	−	7.12218i	−0.765007	−	0.248566i	−0.665426	+	0.746464i	$0.731750\pi$
$822$		0			0
$823$	−6.41986	+	4.66430i	−0.223782	+	0.162587i	−0.694028	−	0.719948i	$-0.744165\pi$
$823$	−6.41986	+	4.66430i	−0.223782	+	0.162587i	0.470245	+	0.882536i	$0.344165\pi$
$824$		0			0
$825$	12.3141	−	38.1242i	0.428723	−	1.32731i
$826$		0			0
$827$	7.07734	+	9.74113i	0.246103	+	0.338732i	0.914142	−	0.405395i	$-0.132866\pi$
$827$	7.07734	+	9.74113i	0.246103	+	0.338732i	−0.668038	+	0.744127i	$0.732866\pi$
$828$		0			0
$829$	−50.8525	−	16.5230i	−1.76618	−	0.573866i	−0.768369	−	0.640008i	$-0.778931\pi$
$829$	−50.8525	−	16.5230i	−1.76618	−	0.573866i	−0.997810	+	0.0661413i	$0.978931\pi$
$830$		0			0
$831$	−7.78613	−	5.65696i	−0.270098	−	0.196238i
$832$		0			0
$833$	36.1524	−	26.5747i	1.25261	−	0.920759i
$834$		0			0
$835$		−	62.8379i		−	2.17459i
$836$		0			0
$837$	1.45624			0.0503350
$838$		0			0
$839$	9.35230	−	3.03875i	0.322877	−	0.104909i	−0.143094	−	0.989709i	$-0.545705\pi$
$839$	9.35230	−	3.03875i	0.322877	−	0.104909i	0.465971	+	0.884800i	$0.345705\pi$
$840$		0			0
$841$	−15.6352	−	11.3596i	−0.539144	−	0.391711i
$842$		0			0
$843$	17.5442	−	53.9954i	0.604254	−	1.85970i
$844$		0			0
$845$	−3.78378	−	5.20792i	−0.130166	−	0.179158i
$846$		0			0
$847$	9.16638	+	27.6220i	0.314960	+	0.949105i
$848$		0			0
$849$	14.7299	+	20.2740i	0.505530	+	0.695802i
$850$		0			0
$851$	−2.96901	+	9.13766i	−0.101776	+	0.313235i
$852$		0			0
$853$	−9.55822	−	6.94445i	−0.327267	−	0.237774i	0.412003	−	0.911182i	$-0.364829\pi$
$853$	−9.55822	−	6.94445i	−0.327267	−	0.237774i	−0.739270	+	0.673409i	$0.764829\pi$
$854$		0			0
$855$	−4.97909	+	1.61780i	−0.170281	+	0.0553277i
$856$		0			0
$857$	43.0370			1.47011			0.735057	−	0.678005i	$-0.237155\pi$
$857$	43.0370			1.47011			0.735057	+	0.678005i	$0.237155\pi$
$858$		0			0
$859$			4.02650i			0.137383i	0.997638	+	0.0686913i	$0.0218823\pi$
$859$			4.02650i			0.137383i	−0.997638	+	0.0686913i	$0.978118\pi$
$860$		0			0
$861$	1.95861	+	0.630374i	0.0667492	+	0.0214831i
$862$		0			0
$863$	−4.12740	−	2.99873i	−0.140498	−	0.102078i	0.515316	−	0.857000i	$-0.327675\pi$
$863$	−4.12740	−	2.99873i	−0.140498	−	0.102078i	−0.655814	+	0.754922i	$0.727675\pi$
$864$		0			0
$865$	−65.8519	−	21.3966i	−2.23903	−	0.727505i
$866$		0			0
$867$	25.9102	+	35.6623i	0.879956	+	1.21116i
$868$		0			0
$869$	−7.48823	+	23.1834i	−0.254021	+	0.786442i
$870$		0			0
$871$	4.14693	−	3.01292i	0.140513	−	0.102089i
$872$		0			0
$873$	−0.680745	−	0.221187i	−0.0230397	−	0.00748606i
$874$		0			0
$875$	−13.7027	+	4.49446i	−0.463237	+	0.151940i
$876$		0			0
$877$	−6.04823	+	1.96519i	−0.204234	+	0.0663597i	−0.409348	−	0.912379i	$-0.634244\pi$
$877$	−6.04823	+	1.96519i	−0.204234	+	0.0663597i	0.205114	+	0.978738i	$0.434244\pi$
$878$		0			0
$879$			13.6706i			0.461096i
$880$		0			0
$881$			9.57826i			0.322700i	0.986897	+	0.161350i	$0.0515848\pi$
$881$			9.57826i			0.322700i	−0.986897	+	0.161350i	$0.948415\pi$
$882$		0			0
$883$	16.8872	+	51.9735i	0.568300	+	1.74905i	0.657936	+	0.753073i	$0.271430\pi$
$883$	16.8872	+	51.9735i	0.568300	+	1.74905i	−0.0896363	+	0.995975i	$0.528570\pi$
$884$		0			0
$885$	−14.1062	+	19.4155i	−0.474174	+	0.652645i
$886$		0			0
$887$	6.54781	−	20.1521i	0.219854	−	0.676641i	−0.778919	−	0.627124i	$-0.784232\pi$
$887$	6.54781	−	20.1521i	0.219854	−	0.676641i	0.998773	−	0.0495169i	$-0.0157682\pi$
$888$		0			0
$889$	−0.0730532	−	26.2700i	−0.00245012	−	0.881068i
$890$		0			0
$891$	−31.2927	+	10.2278i	−1.04834	+	0.342643i
$892$		0			0
$893$	6.92135	+	9.52643i	0.231614	+	0.318790i
$894$		0			0
$895$	61.3918	+	19.9474i	2.05210	+	0.666768i
$896$		0			0
$897$	37.1657	−	51.1541i	1.24093	−	1.70799i
$898$		0			0
$899$	0.288532	+	0.888010i	0.00962308	+	0.0296168i
$900$		0			0
$901$	79.6088			2.65215
$902$		0			0
$903$	35.7707	+	25.8372i	1.19037	+	0.859809i
$904$		0			0
$905$	13.4407	+	41.3662i	0.446784	+	1.37506i
$906$		0			0
$907$	−7.61281	−	5.53103i	−0.252779	−	0.183655i	0.454178	−	0.890911i	$-0.349933\pi$
$907$	−7.61281	−	5.53103i	−0.252779	−	0.183655i	−0.706958	+	0.707256i	$0.749933\pi$
$908$		0			0
$909$	1.56501	−	4.81662i	0.0519082	−	0.159757i
$910$		0			0
$911$	41.2238	−	29.9508i	1.36580	−	0.992315i	0.367752	−	0.929924i	$-0.380128\pi$
$911$	41.2238	−	29.9508i	1.36580	−	0.992315i	0.998052	−	0.0623907i	$-0.0198725\pi$
$912$		0			0
$913$	−0.00661333	−	3.80636i	−0.000218869	−	0.125972i
$914$		0			0
$915$	52.7061	−	38.2932i	1.74241	−	1.26593i
$916$		0			0
$917$	−7.21416	+	5.27211i	−0.238233	+	0.174100i
$918$		0			0
$919$	−14.0763	+	19.3743i	−0.464333	+	0.639100i	−0.975400	−	0.220441i	$-0.929250\pi$
$919$	−14.0763	+	19.3743i	−0.464333	+	0.639100i	0.511067	+	0.859541i	$0.329250\pi$
$920$		0			0
$921$	8.77452	−	2.85102i	0.289130	−	0.0939442i
$922$		0			0
$923$	61.5673			2.02651
$924$		0			0
$925$	−7.08284			−0.232882
$926$		0			0
$927$	−2.55549	+	0.830328i	−0.0839332	+	0.0272715i
$928$		0			0
$929$	5.51443	−	7.58996i	0.180922	−	0.249018i	−0.708917	−	0.705292i	$-0.750816\pi$
$929$	5.51443	−	7.58996i	0.180922	−	0.249018i	0.889840	+	0.456273i	$0.150816\pi$
$930$		0			0
$931$	−30.7890	+	0.171241i	−1.00907	+	0.00561220i
$932$		0			0
$933$	40.7745	−	29.6244i	1.33490	−	0.969859i
$934$		0			0
$935$	58.6521	+	42.4577i	1.91813	+	1.38852i
$936$		0			0
$937$	−10.0139	+	7.27549i	−0.327138	+	0.237680i	−0.739215	−	0.673469i	$-0.764803\pi$
$937$	−10.0139	+	7.27549i	−0.327138	+	0.237680i	0.412077	+	0.911149i	$0.364803\pi$
$938$		0			0
$939$	3.44313	−	10.5969i	0.112362	−	0.345815i
$940$		0			0
$941$	−13.9610	−	10.1432i	−0.455115	−	0.330660i	0.336497	−	0.941685i	$-0.390758\pi$
$941$	−13.9610	−	10.1432i	−0.455115	−	0.330660i	−0.791612	+	0.611024i	$0.790758\pi$
$942$		0			0
$943$	−1.17567	−	3.61833i	−0.0382849	−	0.117829i
$944$		0			0
$945$	35.4355	+	25.5951i	1.15272	+	0.832609i
$946$		0			0
$947$	22.3782			0.727195			0.363598	−	0.931556i	$-0.381548\pi$
$947$	22.3782			0.727195			0.363598	+	0.931556i	$0.381548\pi$
$948$		0			0
$949$	−8.49709	−	26.1513i	−0.275827	−	0.848909i
$950$		0			0
$951$	−0.0487542	+	0.0671044i	−0.00158096	+	0.00217601i
$952$		0			0
$953$	37.6110	+	12.2206i	1.21834	+	0.395863i	0.846477	−	0.532425i	$-0.178719\pi$
$953$	37.6110	+	12.2206i	1.21834	+	0.395863i	0.371863	+	0.928288i	$0.378719\pi$
$954$		0			0
$955$	−21.2734	−	29.2804i	−0.688392	−	0.947491i
$956$		0			0
$957$	−11.1234	−	15.2543i	−0.359570	−	0.493101i
$958$		0			0
$959$	30.6591	−	0.0852586i	0.990034	−	0.00275314i
$960$		0			0
$961$	9.55168	−	29.3970i	0.308119	−	0.948292i
$962$		0			0
$963$	0.864700	−	1.19016i	0.0278646	−	0.0383523i
$964$		0			0
$965$	−11.4752	−	35.3171i	−0.369401	−	1.13690i
$966$		0			0
$967$		−	30.8881i		−	0.993293i	−0.867953	−	0.496647i	$-0.834565\pi$
$967$		−	30.8881i		−	0.993293i	0.867953	−	0.496647i	$-0.165435\pi$
$968$		0			0
$969$		−	51.5988i		−	1.65759i
$970$		0			0
$971$	7.58840	−	2.46562i	0.243523	−	0.0791256i	−0.184712	−	0.982793i	$-0.559135\pi$
$971$	7.58840	−	2.46562i	0.243523	−	0.0791256i	0.428236	+	0.903667i	$0.359135\pi$
$972$		0			0
$973$	−6.48807	−	19.7809i	−0.207998	−	0.634146i
$974$		0			0
$975$	44.3311	+	14.4040i	1.41973	+	0.461298i
$976$		0			0
$977$	37.1630	−	27.0005i	1.18895	−	0.863823i	0.195798	−	0.980644i	$-0.437270\pi$
$977$	37.1630	−	27.0005i	1.18895	−	0.863823i	0.993153	+	0.116821i	$0.0372703\pi$
$978$		0			0
$979$	9.62053	−	7.01530i	0.307473	−	0.224210i
$980$		0			0
$981$	2.20063	+	3.02890i	0.0702606	+	0.0967054i
$982$		0			0
$983$	−16.4568	−	5.34714i	−0.524890	−	0.170547i	0.0345731	−	0.999402i	$-0.488993\pi$
$983$	−16.4568	−	5.34714i	−0.524890	−	0.170547i	−0.559464	+	0.828855i	$0.688993\pi$
$984$		0			0
$985$	7.90870	+	5.74601i	0.251992	+	0.183083i
$986$		0			0
$987$	−3.97148	+	12.3396i	−0.126413	+	0.392774i
$988$		0			0
$989$		−	81.5915i		−	2.59446i
$990$		0			0
$991$	−1.30584			−0.0414815			−0.0207407	−	0.999785i	$-0.506602\pi$
$991$	−1.30584			−0.0414815			−0.0207407	+	0.999785i	$0.506602\pi$
$992$		0			0
$993$	29.0665	−	9.44428i	0.922398	−	0.299705i
$994$		0			0
$995$	−40.2899	−	29.2723i	−1.27728	−	0.927995i
$996$		0			0
$997$	2.78145	−	8.56043i	0.0880895	−	0.271112i	−0.897302	−	0.441418i	$-0.854476\pi$
$997$	2.78145	−	8.56043i	0.0880895	−	0.271112i	0.985391	+	0.170306i	$0.0544757\pi$
$998$		0			0
$999$	3.05972	+	4.21134i	0.0968051	+	0.133241i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	616.2.bs.a.41.19	yes	96
7.6	odd	2	inner	616.2.bs.a.41.6	✓	96
11.7	odd	10	inner	616.2.bs.a.601.6	yes	96
77.62	even	10	inner	616.2.bs.a.601.19	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.bs.a.41.6	✓	96	7.6	odd	2	inner
616.2.bs.a.41.19	yes	96	1.1	even	1	trivial
616.2.bs.a.601.6	yes	96	11.7	odd	10	inner
616.2.bs.a.601.19	yes	96	77.62	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	616.bs (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.74058 - 0.565549i) q^{3} +(2.00195 - 2.75545i) q^{5} +(2.13612 - 1.56108i) q^{7} +(0.282723 - 0.205410i) q^{9} +(1.95412 + 2.67981i) q^{11} +(-3.12180 + 2.26812i) q^{13} +(1.92622 - 5.92829i) q^{15} +(5.18566 + 3.76761i) q^{17} +(-1.35921 - 4.18322i) q^{19} +(2.83523 - 3.92527i) q^{21} -8.95339 q^{23} +(-2.03962 - 6.27729i) q^{25} +(-2.85128 + 3.92445i) q^{27} +(-2.95805 - 0.961130i) q^{29} +(-0.176454 - 0.242868i) q^{31} +(4.91687 + 3.55928i) q^{33} +(-0.0250589 - 9.01120i) q^{35} +(0.331607 - 1.02058i) q^{37} +(-4.15102 + 5.71338i) q^{39} +(0.131310 + 0.404129i) q^{41} +9.11292i q^{43} -1.19025i q^{45} +(-2.54609 + 0.827275i) q^{47} +(2.12606 - 6.66932i) q^{49} +(11.1568 + 3.62507i) q^{51} +(10.0478 - 7.30017i) q^{53} +(11.2962 - 0.0196264i) q^{55} +(-4.73163 - 6.51254i) q^{57} +(-3.66163 - 1.18974i) q^{59} +(8.45547 + 6.14326i) q^{61} +(0.283270 - 0.880135i) q^{63} +13.1427i q^{65} -1.32838 q^{67} +(-15.5841 + 5.06358i) q^{69} +(-12.9080 - 9.37823i) q^{71} +(-2.20202 + 6.77713i) q^{73} +(-7.10023 - 9.77263i) q^{75} +(8.35765 + 2.67388i) q^{77} +(4.31766 + 5.94275i) q^{79} +(-3.06739 + 9.44044i) q^{81} +(-0.928477 - 0.674578i) q^{83} +(20.7629 - 6.74628i) q^{85} -5.69230 q^{87} -3.59000i q^{89} +(-3.12784 + 9.71838i) q^{91} +(-0.444485 - 0.322937i) q^{93} +(-14.2478 - 4.62938i) q^{95} +(-1.20391 - 1.65704i) q^{97} +(1.10294 + 0.356248i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{9} + 4 q^{11} + 12 q^{15} - 24 q^{23} + 36 q^{25} + 20 q^{29} - 30 q^{35} + 16 q^{37} - 60 q^{39} - 30 q^{49} + 60 q^{51} - 80 q^{57} + 40 q^{63} + 64 q^{67} - 24 q^{71} + 50 q^{77} - 8 q^{81}+ \cdots - 84 q^{99}+O(q^{100}) \) 96 * q + 24 * q^9 + 4 * q^11 + 12 * q^15 - 24 * q^23 + 36 * q^25 + 20 * q^29 - 30 * q^35 + 16 * q^37 - 60 * q^39 - 30 * q^49 + 60 * q^51 - 80 * q^57 + 40 * q^63 + 64 * q^67 - 24 * q^71 + 50 * q^77 - 8 * q^81 - 60 * q^85 + 18 * q^91 + 20 * q^93 - 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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