LMFDB - Embedded newform 1120.2.bw.h.289.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1120,2,Mod(289,1120)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1120, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1120.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.bw (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,0,-8,0,0,0,40,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$8.94324502638$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.15
Character	$\chi$	$=$	1120.289
Dual form			1120.2.bw.h.1089.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.04145 - 1.17863i) q^{3} +(2.20846 - 0.350280i) q^{5} +(-0.745750 - 2.53848i) q^{7} +(1.27835 - 2.21416i) q^{9} +(0.300162 + 0.519896i) q^{11} +3.96891i q^{13} +(4.09561 - 3.31804i) q^{15} +(2.53473 - 1.46343i) q^{17} +(1.65804 - 2.87180i) q^{19} +(-4.51434 - 4.30320i) q^{21} +(-0.370565 - 0.213946i) q^{23} +(4.75461 - 1.54716i) q^{25} +1.04500i q^{27} +2.15375 q^{29} +(-0.664524 - 1.15099i) q^{31} +(1.22553 + 0.707561i) q^{33} +(-2.53614 - 5.34490i) q^{35} +(-5.33077 - 3.07772i) q^{37} +(4.67789 + 8.10234i) q^{39} +5.99880 q^{41} -7.79270i q^{43} +(2.04760 - 5.33766i) q^{45} +(-9.37449 - 5.41236i) q^{47} +(-5.88771 + 3.78614i) q^{49} +(3.44968 - 5.97502i) q^{51} +(-10.5518 + 6.09206i) q^{53} +(0.845006 + 1.04303i) q^{55} -7.81686i q^{57} +(3.98454 + 6.90142i) q^{59} +(-3.54639 + 6.14253i) q^{61} +(-6.57391 - 1.59384i) q^{63} +(1.39023 + 8.76519i) q^{65} +(10.7315 - 6.19584i) q^{67} -1.00865 q^{69} +6.86218 q^{71} +(-14.0159 + 8.09206i) q^{73} +(7.88276 - 8.76238i) q^{75} +(1.09590 - 1.14967i) q^{77} +(-6.76969 + 11.7254i) q^{79} +(5.06670 + 8.77579i) q^{81} +5.18749i q^{83} +(5.08524 - 4.11978i) q^{85} +(4.39677 - 2.53848i) q^{87} +(-0.395273 + 0.684632i) q^{89} +(10.0750 - 2.95982i) q^{91} +(-2.71318 - 1.56646i) q^{93} +(2.65577 - 6.92305i) q^{95} +2.80588i q^{97} +1.53484 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{5} + 40 q^{9} - 4 q^{21} + 24 q^{25} + 24 q^{29} - 40 q^{41} - 8 q^{45} - 52 q^{49} - 44 q^{61} + 16 q^{65} - 56 q^{69} - 4 q^{81} - 72 q^{85} - 76 q^{89}+O(q^{100}) $ 40 * q - 8 * q^5 + 40 * q^9 - 4 * q^21 + 24 * q^25 + 24 * q^29 - 40 * q^41 - 8 * q^45 - 52 * q^49 - 44 * q^61 + 16 * q^65 - 56 * q^69 - 4 * q^81 - 72 * q^85 - 76 * q^89

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.04145	−	1.17863i	1.17863	−	0.680483i	0.222934	−	0.974834i	$-0.428437\pi$
$3$	2.04145	−	1.17863i	1.17863	−	0.680483i	0.955698	+	0.294350i	$0.0951032\pi$
$4$		0			0
$5$	2.20846	−	0.350280i	0.987654	−	0.156650i
$5$	2.20846	−	0.350280i	0.987654	−	0.156650i
$6$		0			0
$7$	−0.745750	−	2.53848i	−0.281867	−	0.959453i
$7$	−0.745750	−	2.53848i	−0.281867	−	0.959453i
$8$		0			0
$9$	1.27835	−	2.21416i	0.426115	−	0.738053i
$10$		0			0
$11$	0.300162	+	0.519896i	0.0905023	+	0.156755i	0.907723	−	0.419571i	$-0.137819\pi$
$11$	0.300162	+	0.519896i	0.0905023	+	0.156755i	−0.817220	+	0.576325i	$0.804486\pi$
$12$		0			0
$13$			3.96891i			1.10078i	0.834908	+	0.550389i	$0.185521\pi$
$13$			3.96891i			1.10078i	−0.834908	+	0.550389i	$0.814479\pi$
$14$		0			0
$15$	4.09561	−	3.31804i	1.05748	−	0.856715i
$16$		0			0
$17$	2.53473	−	1.46343i	0.614762	−	0.354933i	−0.160065	−	0.987106i	$-0.551170\pi$
$17$	2.53473	−	1.46343i	0.614762	−	0.354933i	0.774827	+	0.632174i	$0.217837\pi$
$18$		0			0
$19$	1.65804	−	2.87180i	0.380380	−	0.658837i	−0.610737	−	0.791834i	$-0.709127\pi$
$19$	1.65804	−	2.87180i	0.380380	−	0.658837i	0.991116	+	0.132997i	$0.0424599\pi$
$20$		0			0
$21$	−4.51434	−	4.30320i	−0.985110	−	0.939036i
$22$		0			0
$23$	−0.370565	−	0.213946i	−0.0772681	−	0.0446108i	0.460868	−	0.887469i	$-0.347538\pi$
$23$	−0.370565	−	0.213946i	−0.0772681	−	0.0446108i	−0.538136	+	0.842858i	$0.680871\pi$
$24$		0			0
$25$	4.75461	−	1.54716i	0.950921	−	0.309432i
$26$		0			0
$27$			1.04500i			0.201110i
$28$		0			0
$29$	2.15375			0.399941			0.199970	−	0.979802i	$-0.435915\pi$
$29$	2.15375			0.399941			0.199970	+	0.979802i	$0.435915\pi$
$30$		0			0
$31$	−0.664524	−	1.15099i	−0.119352	−	0.206724i	0.800159	−	0.599788i	$-0.204748\pi$
$31$	−0.664524	−	1.15099i	−0.119352	−	0.206724i	−0.919511	+	0.393064i	$0.871415\pi$
$32$		0			0
$33$	1.22553	+	0.707561i	0.213338	+	0.123171i
$34$		0			0
$35$	−2.53614	−	5.34490i	−0.428686	−	0.903454i
$36$		0			0
$37$	−5.33077	−	3.07772i	−0.876373	−	0.505974i	−0.00691230	−	0.999976i	$-0.502200\pi$
$37$	−5.33077	−	3.07772i	−0.876373	−	0.505974i	−0.869461	+	0.494002i	$0.835534\pi$
$38$		0			0
$39$	4.67789	+	8.10234i	0.749061	+	1.29741i
$40$		0			0
$41$	5.99880			0.936854			0.468427	−	0.883502i	$-0.344821\pi$
$41$	5.99880			0.936854			0.468427	+	0.883502i	$0.344821\pi$
$42$		0			0
$43$		−	7.79270i		−	1.18838i	−0.804326	−	0.594188i	$-0.797474\pi$
$43$		−	7.79270i		−	1.18838i	0.804326	−	0.594188i	$-0.202526\pi$
$44$		0			0
$45$	2.04760	−	5.33766i	0.305238	−	0.795692i
$46$		0			0
$47$	−9.37449	−	5.41236i	−1.36741	−	0.789474i	−0.376813	−	0.926289i	$-0.622980\pi$
$47$	−9.37449	−	5.41236i	−1.36741	−	0.789474i	−0.990597	+	0.136815i	$0.956313\pi$
$48$		0			0
$49$	−5.88771	+	3.78614i	−0.841102	+	0.540877i
$50$		0			0
$51$	3.44968	−	5.97502i	0.483052	−	0.836670i
$52$		0			0
$53$	−10.5518	+	6.09206i	−1.44940	+	0.836809i	−0.998445	−	0.0557402i	$-0.982248\pi$
$53$	−10.5518	+	6.09206i	−1.44940	+	0.836809i	−0.450950	+	0.892549i	$0.648915\pi$
$54$		0			0
$55$	0.845006	+	1.04303i	0.113941	+	0.140642i
$56$		0			0
$57$		−	7.81686i		−	1.03537i
$58$		0			0
$59$	3.98454	+	6.90142i	0.518742	+	0.898488i	0.999763	+	0.0217787i	$0.00693291\pi$
$59$	3.98454	+	6.90142i	0.518742	+	0.898488i	−0.481021	+	0.876709i	$0.659734\pi$
$60$		0			0
$61$	−3.54639	+	6.14253i	−0.454069	+	0.786470i	−0.998634	−	0.0522484i	$-0.983361\pi$
$61$	−3.54639	+	6.14253i	−0.454069	+	0.786470i	0.544566	+	0.838718i	$0.316695\pi$
$62$		0			0
$63$	−6.57391	−	1.59384i	−0.828235	−	0.200805i
$64$		0			0
$65$	1.39023	+	8.76519i	0.172437	+	1.08719i
$66$		0			0
$67$	10.7315	−	6.19584i	1.31106	−	0.756942i	0.328790	−	0.944403i	$-0.393359\pi$
$67$	10.7315	−	6.19584i	1.31106	−	0.756942i	0.982272	+	0.187461i	$0.0600259\pi$
$68$		0			0
$69$	−1.00865			−0.121428
$70$		0			0
$71$	6.86218			0.814391			0.407195	−	0.913341i	$-0.366507\pi$
$71$	6.86218			0.814391			0.407195	+	0.913341i	$0.366507\pi$
$72$		0			0
$73$	−14.0159	+	8.09206i	−1.64043	+	0.947104i	−0.659753	+	0.751483i	$0.729339\pi$
$73$	−14.0159	+	8.09206i	−1.64043	+	0.947104i	−0.980679	+	0.195621i	$0.937328\pi$
$74$		0			0
$75$	7.88276	−	8.76238i	0.910223	−	1.01179i
$76$		0			0
$77$	1.09590	−	1.14967i	0.124889	−	0.131017i
$78$		0			0
$79$	−6.76969	+	11.7254i	−0.761650	+	1.31922i	0.180350	+	0.983602i	$0.442277\pi$
$79$	−6.76969	+	11.7254i	−0.761650	+	1.31922i	−0.942000	+	0.335613i	$0.891056\pi$
$80$		0			0
$81$	5.06670	+	8.77579i	0.562967	+	0.975087i
$82$		0			0
$83$			5.18749i			0.569401i	0.958617	+	0.284700i	$0.0918941\pi$
$83$			5.18749i			0.569401i	−0.958617	+	0.284700i	$0.908106\pi$
$84$		0			0
$85$	5.08524	−	4.11978i	0.551572	−	0.446853i
$86$		0			0
$87$	4.39677	−	2.53848i	0.471383	−	0.272153i
$88$		0			0
$89$	−0.395273	+	0.684632i	−0.0418988	+	0.0725709i	−0.886214	−	0.463275i	$-0.846674\pi$
$89$	−0.395273	+	0.684632i	−0.0418988	+	0.0725709i	0.844316	+	0.535846i	$0.180007\pi$
$90$		0			0
$91$	10.0750	−	2.95982i	1.05615	−	0.310273i
$92$		0			0
$93$	−2.71318	−	1.56646i	−0.281344	−	0.162434i
$94$		0			0
$95$	2.65577	−	6.92305i	0.272477	−	0.710290i
$96$		0			0
$97$			2.80588i			0.284894i	0.989802	+	0.142447i	$0.0454971\pi$
$97$			2.80588i			0.284894i	−0.989802	+	0.142447i	$0.954503\pi$
$98$		0			0
$99$	1.53484			0.154258
$100$		0			0
$101$	−0.175266	−	0.303570i	−0.0174396	−	0.0302063i	0.857174	−	0.515027i	$-0.172218\pi$
$101$	−0.175266	−	0.303570i	−0.0174396	−	0.0302063i	−0.874614	+	0.484821i	$0.838885\pi$
$102$		0			0
$103$	−11.9705	−	6.91118i	−1.17949	−	0.680978i	−0.223593	−	0.974683i	$-0.571779\pi$
$103$	−11.9705	−	6.91118i	−1.17949	−	0.680978i	−0.955896	+	0.293704i	$0.905112\pi$
$104$		0			0
$105$	−11.4771	−	7.92218i	−1.12005	−	0.773126i
$106$		0			0
$107$	0.904995	+	0.522499i	0.0874892	+	0.0505119i	0.543106	−	0.839664i	$-0.317248\pi$
$107$	0.904995	+	0.522499i	0.0874892	+	0.0505119i	−0.455617	+	0.890176i	$0.650581\pi$
$108$		0			0
$109$	8.45410	+	14.6429i	0.809756	+	1.40254i	0.913033	+	0.407886i	$0.133734\pi$
$109$	8.45410	+	14.6429i	0.809756	+	1.40254i	−0.103277	+	0.994653i	$0.532933\pi$
$110$		0			0
$111$	−14.5100			−1.37723
$112$		0			0
$113$			5.75946i			0.541804i	0.962607	+	0.270902i	$0.0873220\pi$
$113$			5.75946i			0.541804i	−0.962607	+	0.270902i	$0.912678\pi$
$114$		0			0
$115$	−0.893319	−	0.342689i	−0.0833025	−	0.0319560i
$116$		0			0
$117$	8.78780	+	5.07364i	0.812433	+	0.469058i
$118$		0			0
$119$	−5.60514	−	5.34299i	−0.513823	−	0.489791i
$120$		0			0
$121$	5.31981	−	9.21417i	0.483619	−	0.837652i
$122$		0			0
$123$	12.2462	−	7.07037i	1.10421	−	0.637514i
$124$		0			0
$125$	9.95843	−	5.08229i	0.890709	−	0.454574i
$126$		0			0
$127$		−	3.47167i		−	0.308061i	−0.988066	−	0.154030i	$-0.950775\pi$
$127$		−	3.47167i		−	0.308061i	0.988066	−	0.154030i	$-0.0492253\pi$
$128$		0			0
$129$	−9.18472	−	15.9084i	−0.808670	−	1.40066i
$130$		0			0
$131$	7.80881	−	13.5253i	0.682259	−	1.18171i	−0.292031	−	0.956409i	$-0.594331\pi$
$131$	7.80881	−	13.5253i	0.682259	−	1.18171i	0.974290	−	0.225299i	$-0.0723358\pi$
$132$		0			0
$133$	−8.52649	−	2.06724i	−0.739340	−	0.179252i
$134$		0			0
$135$	0.366042	+	2.30784i	0.0315039	+	0.198627i
$136$		0			0
$137$	−7.70689	+	4.44958i	−0.658444	+	0.380153i	−0.791684	−	0.610931i	$-0.790795\pi$
$137$	−7.70689	+	4.44958i	−0.658444	+	0.380153i	0.133240	+	0.991084i	$0.457462\pi$
$138$		0			0
$139$	−13.7244			−1.16408			−0.582042	−	0.813159i	$-0.697746\pi$
$139$	−13.7244			−1.16408			−0.582042	+	0.813159i	$0.697746\pi$
$140$		0			0
$141$	−25.5167			−2.14890
$142$		0			0
$143$	−2.06342	+	1.19132i	−0.172552	+	0.0996229i
$144$		0			0
$145$	4.75647	−	0.754416i	0.395003	−	0.0626508i
$146$		0			0
$147$	−7.55701	+	14.6687i	−0.623292	+	1.20985i
$148$		0			0
$149$	2.79268	−	4.83707i	0.228786	−	0.396268i	−0.728663	−	0.684873i	$-0.759858\pi$
$149$	2.79268	−	4.83707i	0.228786	−	0.396268i	0.957448	+	0.288604i	$0.0931912\pi$
$150$		0			0
$151$	10.1680	+	17.6115i	0.827461	+	1.43320i	0.900024	+	0.435841i	$0.143549\pi$
$151$	10.1680	+	17.6115i	0.827461	+	1.43320i	−0.0725624	+	0.997364i	$0.523118\pi$
$152$		0			0
$153$		−	7.48305i		−	0.604969i
$154$		0			0
$155$	−1.87074	−	2.30915i	−0.150262	−	0.185475i
$156$		0			0
$157$	19.2419	−	11.1093i	1.53567	−	0.886619i	0.536584	−	0.843847i	$-0.319715\pi$
$157$	19.2419	−	11.1093i	1.53567	−	0.886619i	0.999085	−	0.0427714i	$-0.0136187\pi$
$158$		0			0
$159$	−14.3606	+	24.8733i	−1.13887	+	1.97258i
$160$		0			0
$161$	−0.266747	+	1.10022i	−0.0210226	+	0.0867095i
$162$		0			0
$163$	11.3580	+	6.55753i	0.889625	+	0.513625i	0.873820	−	0.486250i	$-0.161635\pi$
$163$	11.3580	+	6.55753i	0.889625	+	0.513625i	0.0158054	+	0.999875i	$0.494969\pi$
$164$		0			0
$165$	2.95438	+	1.13334i	0.229999	+	0.0882305i
$166$		0			0
$167$			11.4865i			0.888854i	0.895815	+	0.444427i	$0.146593\pi$
$167$			11.4865i			0.888854i	−0.895815	+	0.444427i	$0.853407\pi$
$168$		0			0
$169$	−2.75227			−0.211713
$170$		0			0
$171$	−4.23909	−	7.34231i	−0.324171	−	0.561481i
$172$		0			0
$173$	12.3137	+	7.10930i	0.936191	+	0.540510i	0.888764	−	0.458365i	$-0.151565\pi$
$173$	12.3137	+	7.10930i	0.936191	+	0.540510i	0.0474266	+	0.998875i	$0.484898\pi$
$174$		0			0
$175$	−7.47318	−	10.9157i	−0.564919	−	0.825146i
$176$		0			0
$177$	16.2685	+	9.39260i	1.22281	+	0.705991i
$178$		0			0
$179$	0.835558	+	1.44723i	0.0624525	+	0.108171i	0.895561	−	0.444938i	$-0.146774\pi$
$179$	0.835558	+	1.44723i	0.0624525	+	0.108171i	−0.833109	+	0.553109i	$0.813441\pi$
$180$		0			0
$181$	5.84964			0.434800			0.217400	−	0.976083i	$-0.430242\pi$
$181$	5.84964			0.434800			0.217400	+	0.976083i	$0.430242\pi$
$182$		0			0
$183$			16.7195i			1.23594i
$184$		0			0
$185$	−12.8509	−	4.92977i	−0.944815	−	0.362444i
$186$		0			0
$187$	1.52166	+	0.878530i	0.111275	+	0.0642444i
$188$		0			0
$189$	2.65270	−	0.779308i	0.192956	−	0.0566863i
$190$		0			0
$191$	10.8089	−	18.7216i	0.782106	−	1.35465i	−0.148607	−	0.988896i	$-0.547479\pi$
$191$	10.8089	−	18.7216i	0.782106	−	1.35465i	0.930713	−	0.365750i	$-0.119188\pi$
$192$		0			0
$193$	−14.6201	+	8.44092i	−1.05238	+	0.607591i	−0.923314	−	0.384045i	$-0.874531\pi$
$193$	−14.6201	+	8.44092i	−1.05238	+	0.607591i	−0.129064	+	0.991636i	$0.541197\pi$
$194$		0			0
$195$	13.1690	+	16.2551i	0.943053	+	1.16405i
$196$		0			0
$197$		−	7.42088i		−	0.528716i	−0.964425	−	0.264358i	$-0.914840\pi$
$197$		−	7.42088i		−	0.528716i	0.964425	−	0.264358i	$-0.0851600\pi$
$198$		0			0
$199$	7.30115	+	12.6460i	0.517565	+	0.896448i	0.999792	+	0.0204022i	$0.00649466\pi$
$199$	7.30115	+	12.6460i	0.517565	+	0.896448i	−0.482227	+	0.876046i	$0.660172\pi$
$200$		0			0
$201$	14.6052	−	25.2970i	1.03017	−	1.78431i
$202$		0			0
$203$	−1.60616	−	5.46724i	−0.112730	−	0.383725i
$204$		0			0
$205$	13.2481	−	2.10126i	0.925288	−	0.146758i
$206$		0			0
$207$	−0.947420	+	0.546993i	−0.0658502	+	0.0380186i
$208$		0			0
$209$	1.99072			0.137701
$210$		0			0
$211$	−12.7079			−0.874851			−0.437426	−	0.899255i	$-0.644110\pi$
$211$	−12.7079			−0.874851			−0.437426	+	0.899255i	$0.644110\pi$
$212$		0			0
$213$	14.0088	−	8.08798i	0.959867	−	0.554179i
$214$		0			0
$215$	−2.72963	−	17.2099i	−0.186159	−	1.17370i
$216$		0			0
$217$	−2.42619	+	2.54523i	−0.164700	+	0.172781i
$218$		0			0
$219$	−19.0751	+	33.0391i	−1.28898	+	2.23257i
$220$		0			0
$221$	5.80821	+	10.0601i	0.390702	+	0.676716i
$222$		0			0
$223$			22.6819i			1.51889i	0.650570	+	0.759446i	$0.274530\pi$
$223$			22.6819i			1.51889i	−0.650570	+	0.759446i	$0.725470\pi$
$224$		0			0
$225$	2.65237	−	12.5053i	0.176824	−	0.833684i
$226$		0			0
$227$	−16.7168	+	9.65145i	−1.10953	+	0.640589i	−0.938708	−	0.344712i	$-0.887977\pi$
$227$	−16.7168	+	9.65145i	−1.10953	+	0.640589i	−0.170825	+	0.985301i	$0.554643\pi$
$228$		0			0
$229$	11.2526	−	19.4901i	0.743595	−	1.28794i	−0.207254	−	0.978287i	$-0.566453\pi$
$229$	11.2526	−	19.4901i	0.743595	−	1.28794i	0.950848	−	0.309657i	$-0.100214\pi$
$230$		0			0
$231$	0.882185	−	3.63865i	0.0580435	−	0.239405i
$232$		0			0
$233$	4.44817	+	2.56815i	0.291409	+	0.168245i	0.638577	−	0.769558i	$-0.279523\pi$
$233$	4.44817	+	2.56815i	0.291409	+	0.168245i	−0.347168	+	0.937803i	$0.612857\pi$
$234$		0			0
$235$	−22.5990	−	8.66930i	−1.47420	−	0.565523i
$236$		0			0
$237$			31.9159i			2.07316i
$238$		0			0
$239$	−6.99311			−0.452347			−0.226173	−	0.974087i	$-0.572622\pi$
$239$	−6.99311			−0.452347			−0.226173	+	0.974087i	$0.572622\pi$
$240$		0			0
$241$	6.11633	+	10.5938i	0.393987	+	0.682406i	0.992971	−	0.118355i	$-0.0377621\pi$
$241$	6.11633	+	10.5938i	0.393987	+	0.682406i	−0.598984	+	0.800761i	$0.704429\pi$
$242$		0			0
$243$	17.9719	+	10.3761i	1.15290	+	0.665624i
$244$		0			0
$245$	−11.6766	+	10.4239i	−0.745989	+	0.665958i
$246$		0			0
$247$	11.3979	+	6.58061i	0.725234	+	0.418714i
$248$		0			0
$249$	6.11414	+	10.5900i	0.387468	+	0.671114i
$250$		0			0
$251$	−31.6584			−1.99826			−0.999129	−	0.0417342i	$-0.986712\pi$
$251$	−31.6584			−1.99826			−0.999129	+	0.0417342i	$0.986712\pi$
$252$		0			0
$253$		−	0.256874i		−	0.0161495i
$254$		0			0
$255$	5.52555	−	14.4040i	0.346023	−	0.902011i
$256$		0			0
$257$	−2.95465	−	1.70587i	−0.184306	−	0.106409i	0.405008	−	0.914313i	$-0.367269\pi$
$257$	−2.95465	−	1.70587i	−0.184306	−	0.106409i	−0.589314	+	0.807904i	$0.700602\pi$
$258$		0			0
$259$	−3.83730	+	15.8272i	−0.238438	+	0.983457i
$260$		0			0
$261$	2.75323	−	4.76874i	0.170421	−	0.295178i
$262$		0			0
$263$	−19.5818	+	11.3056i	−1.20746	+	0.697130i	−0.962205	−	0.272327i	$-0.912207\pi$
$263$	−19.5818	+	11.3056i	−1.20746	+	0.697130i	−0.245260	+	0.969457i	$0.578873\pi$
$264$		0			0
$265$	−21.1692	+	17.1502i	−1.30042	+	1.05353i
$266$		0			0
$267$			1.86352i			0.114046i
$268$		0			0
$269$	1.31780	+	2.28249i	0.0803475	+	0.139166i	0.903399	−	0.428800i	$-0.141064\pi$
$269$	1.31780	+	2.28249i	0.0803475	+	0.139166i	−0.823052	+	0.567966i	$0.807730\pi$
$270$		0			0
$271$	−8.92122	+	15.4520i	−0.541925	+	0.938642i	0.456868	+	0.889534i	$0.348971\pi$
$271$	−8.92122	+	15.4520i	−0.541925	+	0.938642i	−0.998793	+	0.0491078i	$0.984362\pi$
$272$		0			0
$273$	17.0790	−	17.9170i	1.03367	−	1.08439i
$274$		0			0
$275$	2.23152	+	2.00750i	0.134565	+	0.121057i
$276$		0			0
$277$	−6.18316	+	3.56985i	−0.371510	+	0.214491i	−0.674118	−	0.738624i	$-0.735476\pi$
$277$	−6.18316	+	3.56985i	−0.371510	+	0.214491i	0.302608	+	0.953115i	$0.402143\pi$
$278$		0			0
$279$	−3.39796			−0.203431
$280$		0			0
$281$	−4.14630			−0.247347			−0.123674	−	0.992323i	$-0.539468\pi$
$281$	−4.14630			−0.247347			−0.123674	+	0.992323i	$0.539468\pi$
$282$		0			0
$283$	10.3250	−	5.96114i	0.613758	−	0.354353i	−0.160677	−	0.987007i	$-0.551368\pi$
$283$	10.3250	−	5.96114i	0.613758	−	0.354353i	0.774435	+	0.632654i	$0.218034\pi$
$284$		0			0
$285$	−2.73809	−	17.2632i	−0.162191	−	1.02259i
$286$		0			0
$287$	−4.47360	−	15.2278i	−0.264069	−	0.898868i
$288$		0			0
$289$	−4.21677	+	7.30367i	−0.248045	+	0.429627i
$290$		0			0
$291$	3.30710	+	5.72807i	0.193866	+	0.335786i
$292$		0			0
$293$		−	22.8244i		−	1.33342i	−0.745318	−	0.666709i	$-0.767702\pi$
$293$		−	22.8244i		−	1.33342i	0.745318	−	0.666709i	$-0.232298\pi$
$294$		0			0
$295$	11.2171	+	13.8458i	0.653086	+	0.806134i
$296$		0			0
$297$	−0.543290	+	0.313669i	−0.0315249	+	0.0182009i
$298$		0			0
$299$	0.849132	−	1.47074i	0.0491066	−	0.0850551i
$300$		0			0
$301$	−19.7816	+	5.81141i	−1.14019	+	0.334964i
$302$		0			0
$303$	−0.715593	−	0.413148i	−0.0411098	−	0.0237347i
$304$		0			0
$305$	−5.68046	+	14.8078i	−0.325262	+	0.847890i
$306$		0			0
$307$			3.37016i			0.192345i	0.995365	+	0.0961725i	$0.0306600\pi$
$307$			3.37016i			0.192345i	−0.995365	+	0.0961725i	$0.969340\pi$
$308$		0			0
$309$	−32.5829			−1.85358
$310$		0			0
$311$	−15.0725	−	26.1064i	−0.854685	−	1.48036i	−0.876937	−	0.480605i	$-0.840417\pi$
$311$	−15.0725	−	26.1064i	−0.854685	−	1.48036i	0.0222522	−	0.999752i	$-0.492916\pi$
$312$		0			0
$313$	15.7181	+	9.07482i	0.888437	+	0.512939i	0.873431	−	0.486948i	$-0.161890\pi$
$313$	15.7181	+	9.07482i	0.888437	+	0.512939i	0.0150060	+	0.999887i	$0.495223\pi$
$314$		0			0
$315$	−15.0765	−	1.21722i	−0.849466	−	0.0685824i
$316$		0			0
$317$	−28.5143	−	16.4627i	−1.60152	−	0.924638i	−0.991184	−	0.132496i	$-0.957701\pi$
$317$	−28.5143	−	16.4627i	−1.60152	−	0.924638i	−0.610336	−	0.792142i	$-0.708966\pi$
$318$		0			0
$319$	0.646473	+	1.11972i	0.0361956	+	0.0626926i
$320$		0			0
$321$	2.46334			0.137490
$322$		0			0
$323$		−	9.70565i		−	0.540037i
$324$		0			0
$325$	6.14055	+	18.8706i	0.340616	+	1.04675i
$326$		0			0
$327$	34.5173	+	19.9285i	1.90881	+	1.10205i
$328$		0			0
$329$	−6.74812	+	27.8332i	−0.372036	+	1.53449i
$330$		0			0
$331$	10.3469	−	17.9213i	0.568715	−	0.985043i	−0.427978	−	0.903789i	$-0.640774\pi$
$331$	10.3469	−	17.9213i	0.568715	−	0.985043i	0.996693	−	0.0812542i	$-0.0258926\pi$
$332$		0			0
$333$	−13.6291	+	7.86878i	−0.746872	+	0.431206i
$334$		0			0
$335$	21.5298	−	17.4423i	1.17630	−	0.952975i
$336$		0			0
$337$		−	26.6719i		−	1.45291i	−0.687212	−	0.726457i	$-0.741166\pi$
$337$		−	26.6719i		−	1.45291i	0.687212	−	0.726457i	$-0.258834\pi$
$338$		0			0
$339$	6.78828	+	11.7576i	0.368689	+	0.638588i
$340$		0			0
$341$	0.398930	−	0.690967i	0.0216033	−	0.0374179i
$342$		0			0
$343$	14.0018	+	12.1223i	0.756025	+	0.654543i
$344$		0			0
$345$	−2.22757	+	0.353311i	−0.119928	+	0.0190216i
$346$		0			0
$347$	−5.73774	+	3.31269i	−0.308018	+	0.177834i	−0.646039	−	0.763304i	$-0.723576\pi$
$347$	−5.73774	+	3.31269i	−0.308018	+	0.177834i	0.338021	+	0.941139i	$0.390242\pi$
$348$		0			0
$349$	11.9911			0.641870			0.320935	−	0.947101i	$-0.396003\pi$
$349$	11.9911			0.641870			0.320935	+	0.947101i	$0.396003\pi$
$350$		0			0
$351$	−4.14751			−0.221378
$352$		0			0
$353$	15.3192	−	8.84456i	0.815360	−	0.470748i	−0.0334536	−	0.999440i	$-0.510651\pi$
$353$	15.3192	−	8.84456i	0.815360	−	0.470748i	0.848814	+	0.528692i	$0.177317\pi$
$354$		0			0
$355$	15.1549	−	2.40369i	0.804336	−	0.127574i
$356$		0			0
$357$	−17.7400	−	4.30105i	−0.938902	−	0.227636i
$358$		0			0
$359$	−5.46524	+	9.46607i	−0.288444	+	0.499600i	−0.973439	−	0.228948i	$-0.926471\pi$
$359$	−5.46524	+	9.46607i	−0.288444	+	0.499600i	0.684994	+	0.728548i	$0.259805\pi$
$360$		0			0
$361$	4.00183	+	6.93136i	0.210622	+	0.364809i
$362$		0			0
$363$		−	25.0804i		−	1.31638i
$364$		0			0
$365$	−28.1190	+	22.7805i	−1.47182	+	1.19239i
$366$		0			0
$367$	17.8709	−	10.3178i	0.932853	−	0.538583i	0.0451400	−	0.998981i	$-0.485627\pi$
$367$	17.8709	−	10.3178i	0.932853	−	0.538583i	0.887713	+	0.460398i	$0.152293\pi$
$368$		0			0
$369$	7.66853	−	13.2823i	0.399208	−	0.691448i
$370$		0			0
$371$	23.3335	+	22.2422i	1.21142	+	1.15476i
$372$		0			0
$373$	−4.04850	−	2.33740i	−0.209623	−	0.121026i	0.391513	−	0.920173i	$-0.371952\pi$
$373$	−4.04850	−	2.33740i	−0.209623	−	0.121026i	−0.601136	+	0.799147i	$0.705285\pi$
$374$		0			0
$375$	14.3395	−	22.1126i	0.740488	−	1.14189i
$376$		0			0
$377$			8.54804i			0.440246i
$378$		0			0
$379$	−23.7176			−1.21829			−0.609146	−	0.793058i	$-0.708488\pi$
$379$	−23.7176			−1.21829			−0.609146	+	0.793058i	$0.708488\pi$
$380$		0			0
$381$	−4.09182	−	7.08723i	−0.209630	−	0.363090i
$382$		0			0
$383$	−16.8311	−	9.71744i	−0.860029	−	0.496538i	0.00399321	−	0.999992i	$-0.498729\pi$
$383$	−16.8311	−	9.71744i	−0.860029	−	0.496538i	−0.864022	+	0.503454i	$0.832062\pi$
$384$		0			0
$385$	2.01754	−	2.92287i	0.102823	−	0.148963i
$386$		0			0
$387$	−17.2543	−	9.96176i	−0.877084	−	0.506385i
$388$		0			0
$389$	−0.899913	−	1.55869i	−0.0456274	−	0.0790290i	0.842310	−	0.538994i	$-0.181195\pi$
$389$	−0.899913	−	1.55869i	−0.0456274	−	0.0790290i	−0.887937	+	0.459965i	$0.847862\pi$
$390$		0			0
$391$	−1.25237			−0.0633353
$392$		0			0
$393$		−	36.8149i		−	1.85706i
$394$		0			0
$395$	−10.8434	+	28.2665i	−0.545591	+	1.42224i
$396$		0			0
$397$	−9.88285	−	5.70587i	−0.496006	−	0.286369i	0.231057	−	0.972940i	$-0.425782\pi$
$397$	−9.88285	−	5.70587i	−0.496006	−	0.286369i	−0.727063	+	0.686571i	$0.759115\pi$
$398$		0			0
$399$	−19.8429	+	5.82943i	−0.993388	+	0.291836i
$400$		0			0
$401$	−12.3560	+	21.4013i	−0.617030	+	1.06873i	0.372994	+	0.927834i	$0.378331\pi$
$401$	−12.3560	+	21.4013i	−0.617030	+	1.06873i	−0.990025	+	0.140894i	$0.955002\pi$
$402$		0			0
$403$	4.56818	−	2.63744i	0.227557	−	0.131380i
$404$		0			0
$405$	14.2636	+	17.6062i	0.708764	+	0.874860i
$406$		0			0
$407$		−	3.69526i		−	0.183167i
$408$		0			0
$409$	8.26947	+	14.3231i	0.408899	+	0.708234i	0.994767	−	0.102173i	$-0.0325795\pi$
$409$	8.26947	+	14.3231i	0.408899	+	0.708234i	−0.585868	+	0.810407i	$0.699246\pi$
$410$		0			0
$411$	−10.4888	+	18.1672i	−0.517376	+	0.896121i
$412$		0			0
$413$	14.5476	−	15.2614i	0.715841	−	0.750963i
$414$		0			0
$415$	1.81708	+	11.4564i	0.0891967	+	0.562371i
$416$		0			0
$417$	−28.0176	+	16.1760i	−1.37203	+	0.792140i
$418$		0			0
$419$	30.1276			1.47183			0.735915	−	0.677073i	$-0.236752\pi$
$419$	30.1276			1.47183			0.735915	+	0.677073i	$0.236752\pi$
$420$		0			0
$421$	−6.67555			−0.325347			−0.162673	−	0.986680i	$-0.552012\pi$
$421$	−6.67555			−0.325347			−0.162673	+	0.986680i	$0.552012\pi$
$422$		0			0
$423$	−23.9677	+	13.8377i	−1.16535	+	0.672814i
$424$		0			0
$425$	9.78748	−	10.8796i	0.474762	−	0.527740i
$426$		0			0
$427$	18.2374	+	4.42163i	0.882568	+	0.213978i
$428$		0			0
$429$	−2.80825	+	4.86403i	−0.135584	+	0.234838i
$430$		0			0
$431$	−9.97972	−	17.2854i	−0.480706	−	0.832608i	0.519049	−	0.854745i	$-0.326286\pi$
$431$	−9.97972	−	17.2854i	−0.480706	−	0.832608i	−0.999755	+	0.0221371i	$0.992953\pi$
$432$		0			0
$433$		−	2.49880i		−	0.120085i	−0.998196	−	0.0600423i	$-0.980876\pi$
$433$		−	2.49880i		−	0.120085i	0.998196	−	0.0600423i	$-0.0191235\pi$
$434$		0			0
$435$	8.82092	−	7.14623i	0.422931	−	0.342635i
$436$		0			0
$437$	−1.22882	+	0.709460i	−0.0587825	+	0.0339381i
$438$		0			0
$439$	4.20723	−	7.28714i	0.200800	−	0.347796i	−0.747986	−	0.663714i	$-0.768979\pi$
$439$	4.20723	−	7.28714i	0.200800	−	0.347796i	0.948786	+	0.315918i	$0.102312\pi$
$440$		0			0
$441$	0.856581	+	17.8763i	0.0407896	+	0.851253i
$442$		0			0
$443$	−26.2626	−	15.1627i	−1.24778	−	0.720404i	−0.277110	−	0.960838i	$-0.589377\pi$
$443$	−26.2626	−	15.1627i	−1.24778	−	0.720404i	−0.970665	+	0.240434i	$0.922710\pi$
$444$		0			0
$445$	−0.633131	+	1.65044i	−0.0300133	+	0.0782384i
$446$		0			0
$447$		−	13.1662i		−	0.622739i
$448$		0			0
$449$	−0.159010			−0.00750417			−0.00375208	−	0.999993i	$-0.501194\pi$
$449$	−0.159010			−0.00750417			−0.00375208	+	0.999993i	$0.501194\pi$
$450$		0			0
$451$	1.80061	+	3.11875i	0.0847875	+	0.146856i
$452$		0			0
$453$	41.5150	+	23.9687i	1.95054	+	1.12615i
$454$		0			0
$455$	21.2135	−	10.0657i	0.994502	−	0.471888i
$456$		0			0
$457$	6.72158	+	3.88071i	0.314422	+	0.181532i	0.648904	−	0.760871i	$-0.275228\pi$
$457$	6.72158	+	3.88071i	0.314422	+	0.181532i	−0.334481	+	0.942402i	$0.608561\pi$
$458$		0			0
$459$	1.52928	+	2.64878i	0.0713805	+	0.123635i
$460$		0			0
$461$	7.83640			0.364977			0.182489	−	0.983208i	$-0.441585\pi$
$461$	7.83640			0.364977			0.182489	+	0.983208i	$0.441585\pi$
$462$		0			0
$463$			16.6461i			0.773609i	0.922162	+	0.386805i	$0.126421\pi$
$463$			16.6461i			0.773609i	−0.922162	+	0.386805i	$0.873579\pi$
$464$		0			0
$465$	−6.54066	−	2.50909i	−0.303316	−	0.116356i
$466$		0			0
$467$	−33.2628	−	19.2043i	−1.53922	−	0.888669i	−0.998885	−	0.0472189i	$-0.984964\pi$
$467$	−33.2628	−	19.2043i	−1.53922	−	0.888669i	−0.540335	−	0.841450i	$-0.681703\pi$
$468$		0			0
$469$	−23.7310	−	22.6211i	−1.09580	−	1.04455i
$470$		0			0
$471$	26.1875	−	45.3582i	1.20666	−	2.08999i
$472$		0			0
$473$	4.05139	−	2.33907i	0.186283	−	0.107551i
$474$		0			0
$475$	3.44017	−	16.2196i	0.157846	−	0.744204i
$476$		0			0
$477$			31.1510i			1.42631i
$478$		0			0
$479$	−2.13348	−	3.69529i	−0.0974810	−	0.168842i	0.813160	−	0.582040i	$-0.197745\pi$
$479$	−2.13348	−	3.69529i	−0.0974810	−	0.168842i	−0.910641	+	0.413198i	$0.864412\pi$
$480$		0			0
$481$	12.2152	−	21.1574i	0.556966	−	0.964693i
$482$		0			0
$483$	0.752203	+	2.56044i	0.0342264	+	0.116504i
$484$		0			0
$485$	0.982846	+	6.19669i	0.0446288	+	0.281377i
$486$		0			0
$487$	−30.8177	+	17.7926i	−1.39648	+	0.806259i	−0.994022	−	0.109179i	$-0.965178\pi$
$487$	−30.8177	+	17.7926i	−1.39648	+	0.806259i	−0.402460	+	0.915438i	$0.631845\pi$
$488$		0			0
$489$	30.9157			1.39805
$490$		0			0
$491$	−5.06047			−0.228376			−0.114188	−	0.993459i	$-0.536427\pi$
$491$	−5.06047			−0.228376			−0.114188	+	0.993459i	$0.536427\pi$
$492$		0			0
$493$	5.45916	−	3.15185i	0.245868	−	0.141952i
$494$		0			0
$495$	3.38964	−	0.537625i	0.152353	−	0.0241645i
$496$		0			0
$497$	−5.11747	−	17.4195i	−0.229550	−	0.781370i
$498$		0			0
$499$	−3.33860	+	5.78263i	−0.149456	+	0.258866i	−0.931027	−	0.364951i	$-0.881086\pi$
$499$	−3.33860	+	5.78263i	−0.149456	+	0.258866i	0.781570	+	0.623817i	$0.214419\pi$
$500$		0			0
$501$	13.5384	+	23.4492i	0.604850	+	1.04763i
$502$		0			0
$503$		−	25.4412i		−	1.13437i	−0.823591	−	0.567184i	$-0.808033\pi$
$503$		−	25.4412i		−	1.13437i	0.823591	−	0.567184i	$-0.191967\pi$
$504$		0			0
$505$	−0.493403	−	0.609030i	−0.0219561	−	0.0271015i
$506$		0			0
$507$	−5.61862	+	3.24391i	−0.249532	+	0.144067i
$508$		0			0
$509$	11.9190	−	20.6443i	0.528299	−	0.915041i	−0.471156	−	0.882050i	$-0.656163\pi$
$509$	11.9190	−	20.6443i	0.528299	−	0.915041i	0.999456	−	0.0329916i	$-0.0105035\pi$
$510$		0			0
$511$	30.9938	+	29.5443i	1.37109	+	1.30696i
$512$		0			0
$513$	3.00103	+	1.73265i	0.132499	+	0.0764982i
$514$		0			0
$515$	−28.8573	−	11.0700i	−1.27160	−	0.487804i
$516$		0			0
$517$		−	6.49834i		−	0.285797i
$518$		0			0
$519$	33.5170			1.47123
$520$		0			0
$521$	−22.0372	−	38.1695i	−0.965467	−	1.67224i	−0.708354	−	0.705857i	$-0.750562\pi$
$521$	−22.0372	−	38.1695i	−0.965467	−	1.67224i	−0.257113	−	0.966381i	$-0.582771\pi$
$522$		0			0
$523$	11.0357	+	6.37148i	0.482558	+	0.278605i	0.721482	−	0.692433i	$-0.243461\pi$
$523$	11.0357	+	6.37148i	0.482558	+	0.278605i	−0.238924	+	0.971038i	$0.576795\pi$
$524$		0			0
$525$	−28.1217	−	13.4756i	−1.22733	−	0.588125i
$526$		0			0
$527$	−3.36877	−	1.94496i	−0.146746	−	0.0847239i
$528$		0			0
$529$	−11.4085	−	19.7600i	−0.496020	−	0.859131i
$530$		0			0
$531$	20.3744			0.884176
$532$		0			0
$533$			23.8087i			1.03127i
$534$		0			0
$535$	2.18167	+	0.836917i	0.0943217	+	0.0361831i
$536$		0			0
$537$	3.41150	+	1.96963i	0.147217	+	0.0849958i
$538$		0			0
$539$	−3.73567	−	1.92454i	−0.160907	−	0.0828959i
$540$		0			0
$541$	17.8879	−	30.9827i	0.769060	−	1.33205i	−0.169012	−	0.985614i	$-0.554058\pi$
$541$	17.8879	−	30.9827i	0.769060	−	1.33205i	0.938073	−	0.346438i	$-0.112609\pi$
$542$		0			0
$543$	11.9418	−	6.89457i	0.512470	−	0.295874i
$544$		0			0
$545$	23.7997	+	29.3771i	1.01947	+	1.25837i
$546$		0			0
$547$			29.0663i			1.24279i	0.783498	+	0.621394i	$0.213433\pi$
$547$			29.0663i			1.24279i	−0.783498	+	0.621394i	$0.786567\pi$
$548$		0			0
$549$	9.06702	+	15.7045i	0.386971	+	0.670253i
$550$		0			0
$551$	3.57099	−	6.18514i	0.152129	−	0.263496i
$552$		0			0
$553$	34.8133	+	8.44043i	1.48041	+	0.358924i
$554$		0			0
$555$	−32.0448	+	5.08257i	−1.36023	+	0.215743i
$556$		0			0
$557$	20.0615	−	11.5825i	0.850032	−	0.490766i	−0.0106300	−	0.999944i	$-0.503384\pi$
$557$	20.0615	−	11.5825i	0.850032	−	0.490766i	0.860661	+	0.509178i	$0.170050\pi$
$558$		0			0
$559$	30.9286			1.30814
$560$		0			0
$561$	4.14185			0.174869
$562$		0			0
$563$	22.3258	−	12.8898i	0.940921	−	0.543241i	0.0506723	−	0.998715i	$-0.483864\pi$
$563$	22.3258	−	12.8898i	0.940921	−	0.543241i	0.890249	+	0.455474i	$0.150530\pi$
$564$		0			0
$565$	2.01743	+	12.7195i	0.0848737	+	0.535115i
$566$		0			0
$567$	18.4986	−	19.4062i	0.776869	−	0.814986i
$568$		0			0
$569$	0.0565598	−	0.0979645i	0.00237111	−	0.00410689i	−0.864837	−	0.502052i	$-0.832579\pi$
$569$	0.0565598	−	0.0979645i	0.00237111	−	0.00410689i	0.867209	+	0.497945i	$0.165912\pi$
$570$		0			0
$571$	13.1255	+	22.7341i	0.549287	+	0.951393i	0.998324	+	0.0578795i	$0.0184339\pi$
$571$	13.1255	+	22.7341i	0.549287	+	0.951393i	−0.449037	+	0.893513i	$0.648233\pi$
$572$		0			0
$573$		−	50.9589i		−	2.12884i
$574$		0			0
$575$	−2.09290	−	0.443904i	−0.0872799	−	0.0185121i
$576$		0			0
$577$	−4.54477	+	2.62393i	−0.189201	+	0.109236i	−0.591609	−	0.806225i	$-0.701507\pi$
$577$	−4.54477	+	2.62393i	−0.189201	+	0.109236i	0.402407	+	0.915461i	$0.368174\pi$
$578$		0			0
$579$	−19.8975	+	34.4634i	−0.826911	+	1.43225i
$580$		0			0
$581$	13.1683	−	3.86857i	0.546314	−	0.160495i
$582$		0			0
$583$	−6.33448	−	3.65721i	−0.262347	−	0.151466i
$584$		0			0
$585$	21.1847	+	8.12675i	0.875881	+	0.336000i
$586$		0			0
$587$		−	45.2908i		−	1.86935i	−0.355500	−	0.934676i	$-0.615689\pi$
$587$		−	45.2908i		−	1.86935i	0.355500	−	0.934676i	$-0.384311\pi$
$588$		0			0
$589$	−4.40722			−0.181596
$590$		0			0
$591$	−8.74648	−	15.1493i	−0.359782	−	0.623161i
$592$		0			0
$593$	4.13011	+	2.38452i	0.169603	+	0.0979206i	0.582399	−	0.812903i	$-0.302114\pi$
$593$	4.13011	+	2.38452i	0.169603	+	0.0979206i	−0.412795	+	0.910824i	$0.635448\pi$
$594$		0			0
$595$	−14.2503	−	9.83642i	−0.584205	−	0.403254i
$596$		0			0
$597$	29.8099	+	17.2107i	1.22004	+	0.704388i
$598$		0			0
$599$	−7.44105	−	12.8883i	−0.304033	−	0.526601i	0.673012	−	0.739631i	$-0.265000\pi$
$599$	−7.44105	−	12.8883i	−0.304033	−	0.526601i	−0.977046	+	0.213030i	$0.931667\pi$
$600$		0			0
$601$	−21.5026			−0.877109			−0.438555	−	0.898705i	$-0.644509\pi$
$601$	−21.5026			−0.877109			−0.438555	+	0.898705i	$0.644509\pi$
$602$		0			0
$603$		−	31.6817i		−	1.29018i
$604$		0			0
$605$	8.52104	−	22.2126i	0.346430	−	0.903070i
$606$		0			0
$607$	2.15820	+	1.24604i	0.0875986	+	0.0505751i	0.543159	−	0.839630i	$-0.317228\pi$
$607$	2.15820	+	1.24604i	0.0875986	+	0.0505751i	−0.455561	+	0.890205i	$0.650561\pi$
$608$		0			0
$609$	−9.72275	−	9.26802i	−0.393986	−	0.375559i
$610$		0			0
$611$	21.4812	−	37.2065i	0.869036	−	1.50521i
$612$		0			0
$613$	−13.0206	+	7.51744i	−0.525896	+	0.303626i	−0.739344	−	0.673328i	$-0.764864\pi$
$613$	−13.0206	+	7.51744i	−0.525896	+	0.303626i	0.213447	+	0.976955i	$0.431531\pi$
$614$		0			0
$615$	24.5687	−	19.9043i	0.990707	−	0.802617i
$616$		0			0
$617$		−	19.5231i		−	0.785970i	−0.919545	−	0.392985i	$-0.871442\pi$
$617$		−	19.5231i		−	0.785970i	0.919545	−	0.392985i	$-0.128558\pi$
$618$		0			0
$619$	1.65750	+	2.87087i	0.0666205	+	0.115390i	0.897412	−	0.441194i	$-0.145445\pi$
$619$	1.65750	+	2.87087i	0.0666205	+	0.115390i	−0.830791	+	0.556584i	$0.812112\pi$
$620$		0			0
$621$	0.223573	−	0.387240i	0.00897167	−	0.0155394i
$622$		0			0
$623$	2.03270	+	0.492825i	0.0814383	+	0.0197446i
$624$		0			0
$625$	20.2126	−	14.7123i	0.808503	−	0.588492i
$626$		0			0
$627$	4.06395	−	2.34633i	0.162299	−	0.0937032i
$628$		0			0
$629$	−18.0161			−0.718347
$630$		0			0
$631$	9.52923			0.379352			0.189676	−	0.981847i	$-0.439256\pi$
$631$	9.52923			0.379352			0.189676	+	0.981847i	$0.439256\pi$
$632$		0			0
$633$	−25.9426	+	14.9780i	−1.03113	+	0.595322i
$634$		0			0
$635$	−1.21606	−	7.66704i	−0.0482577	−	0.304257i
$636$		0			0
$637$	−15.0269	−	23.3678i	−0.595386	−	0.925867i
$638$		0			0
$639$	8.77223	−	15.1939i	0.347024	−	0.601063i
$640$		0			0
$641$	−11.3355	−	19.6337i	−0.447726	−	0.775485i	0.550511	−	0.834828i	$-0.314433\pi$
$641$	−11.3355	−	19.6337i	−0.447726	−	0.775485i	−0.998238	+	0.0593429i	$0.981099\pi$
$642$		0			0
$643$		−	27.2239i		−	1.07361i	−0.843707	−	0.536804i	$-0.819632\pi$
$643$		−	27.2239i		−	1.07361i	0.843707	−	0.536804i	$-0.180368\pi$
$644$		0			0
$645$	−25.8565	−	31.9159i	−1.01810	−	1.25669i
$646$		0			0
$647$	20.0105	−	11.5531i	0.786693	−	0.454197i	−0.0521041	−	0.998642i	$-0.516593\pi$
$647$	20.0105	−	11.5531i	0.786693	−	0.454197i	0.838797	+	0.544444i	$0.183259\pi$
$648$		0			0
$649$	−2.39201	+	4.14309i	−0.0938947	+	0.162630i
$650$		0			0
$651$	−1.95306	+	8.05554i	−0.0765463	+	0.315721i
$652$		0			0
$653$	−8.52235	−	4.92038i	−0.333505	−	0.192549i	0.323891	−	0.946094i	$-0.395009\pi$
$653$	−8.52235	−	4.92038i	−0.333505	−	0.192549i	−0.657396	+	0.753545i	$0.728342\pi$
$654$		0			0
$655$	12.5078	−	32.6053i	0.488721	−	1.27399i
$656$		0			0
$657$			41.3778i			1.61430i
$658$		0			0
$659$	7.00099			0.272720			0.136360	−	0.990659i	$-0.456460\pi$
$659$	7.00099			0.272720			0.136360	+	0.990659i	$0.456460\pi$
$660$		0			0
$661$	0.0752886	+	0.130404i	0.00292839	+	0.00507212i	0.867486	−	0.497462i	$-0.165735\pi$
$661$	0.0752886	+	0.130404i	0.00292839	+	0.00507212i	−0.864557	+	0.502534i	$0.832401\pi$
$662$		0			0
$663$	23.7143	+	13.6915i	0.920988	+	0.531733i
$664$		0			0
$665$	−19.5545	−	1.57875i	−0.758292	−	0.0612214i
$666$		0			0
$667$	−0.798103	−	0.460785i	−0.0309027	−	0.0178417i
$668$		0			0
$669$	26.7336	+	46.3040i	1.03358	+	1.79022i
$670$		0			0
$671$	−4.25797			−0.164377
$672$		0			0
$673$		−	11.6610i		−	0.449499i	−0.974417	−	0.224749i	$-0.927844\pi$
$673$		−	11.6610i		−	0.449499i	0.974417	−	0.224749i	$-0.0721564\pi$
$674$		0			0
$675$	1.61678	+	4.96856i	0.0622299	+	0.191240i
$676$		0			0
$677$	33.7522	+	19.4868i	1.29720	+	0.748940i	0.979920	−	0.199391i	$-0.0638964\pi$
$677$	33.7522	+	19.4868i	1.29720	+	0.748940i	0.317282	+	0.948331i	$0.397230\pi$
$678$		0			0
$679$	7.12267	−	2.09249i	0.273343	−	0.0803024i
$680$		0			0
$681$	−22.7510	+	39.4059i	−0.871821	+	1.51004i
$682$		0			0
$683$	−16.8500	+	9.72834i	−0.644747	+	0.372245i	−0.786441	−	0.617666i	$-0.788078\pi$
$683$	−16.8500	+	9.72834i	−0.644747	+	0.372245i	0.141694	+	0.989911i	$0.454745\pi$
$684$		0			0
$685$	−15.4618	+	12.5263i	−0.590764	+	0.478605i
$686$		0			0
$687$		−	53.0508i		−	2.02402i
$688$		0			0
$689$	−24.1789	−	41.8790i	−0.921141	−	1.59546i
$690$		0			0
$691$	−11.9076	+	20.6245i	−0.452985	+	0.784594i	−0.998570	−	0.0534621i	$-0.982974\pi$
$691$	−11.9076	+	20.6245i	−0.452985	+	0.784594i	0.545584	+	0.838056i	$0.316308\pi$
$692$		0			0
$693$	−1.14461	−	3.89616i	−0.0434801	−	0.148003i
$694$		0			0
$695$	−30.3097	+	4.80737i	−1.14971	+	0.182354i
$696$		0			0
$697$	15.2053	−	8.77879i	0.575942	−	0.332520i
$698$		0			0
$699$	12.1076			0.457952
$700$		0			0
$701$	43.2250			1.63258			0.816292	−	0.577639i	$-0.196026\pi$
$701$	43.2250			1.63258			0.816292	+	0.577639i	$0.196026\pi$
$702$		0			0
$703$	−17.6772	+	10.2060i	−0.666709	+	0.384925i
$704$		0			0
$705$	−56.3527	+	8.93801i	−2.12237	+	0.336625i
$706$		0			0
$707$	−0.639899	+	0.671295i	−0.0240659	+	0.0252467i
$708$		0			0
$709$	6.27709	−	10.8722i	0.235741	−	0.408316i	−0.723747	−	0.690066i	$-0.757582\pi$
$709$	6.27709	−	10.8722i	0.235741	−	0.408316i	0.959488	+	0.281750i	$0.0909149\pi$
$710$		0			0
$711$	17.3080	+	29.9783i	0.649101	+	1.12428i
$712$		0			0
$713$			0.568688i			0.0212975i
$714$		0			0
$715$	−4.13969	+	3.35375i	−0.154816	+	0.125423i
$716$		0			0
$717$	−14.2761	+	8.24230i	−0.533150	+	0.307814i
$718$		0			0
$719$	15.9721	−	27.6645i	0.595659	−	1.03171i	−0.397794	−	0.917475i	$-0.630224\pi$
$719$	15.9721	−	27.6645i	0.595659	−	1.03171i	0.993453	−	0.114237i	$-0.0364425\pi$
$720$		0			0
$721$	−8.61684	+	35.5408i	−0.320908	+	1.32361i
$722$		0			0
$723$	24.9723	+	14.4178i	0.928731	+	0.536203i
$724$		0			0
$725$	10.2402	−	3.33220i	0.380312	−	0.123755i
$726$		0			0
$727$		−	4.97260i		−	0.184424i	−0.995739	−	0.0922118i	$-0.970606\pi$
$727$		−	4.97260i		−	0.184424i	0.995739	−	0.0922118i	$-0.0293937\pi$
$728$		0			0
$729$	18.5180			0.685851
$730$		0			0
$731$	−11.4040	−	19.7524i	−0.421793	−	0.730568i
$732$		0			0
$733$	−12.0552	−	6.96010i	−0.445271	−	0.257077i	0.260560	−	0.965458i	$-0.416093\pi$
$733$	−12.0552	−	6.96010i	−0.445271	−	0.257077i	−0.705831	+	0.708380i	$0.749426\pi$
$734$		0			0
$735$	−11.5512	+	35.0422i	−0.426073	+	1.29255i
$736$		0			0
$737$	6.44238	+	3.71951i	0.237308	+	0.137010i
$738$		0			0
$739$	−19.1401	−	33.1516i	−0.704080	−	1.21950i	−0.967022	−	0.254691i	$-0.918026\pi$
$739$	−19.1401	−	33.1516i	−0.704080	−	1.21950i	0.262942	−	0.964812i	$-0.415307\pi$
$740$		0			0
$741$	31.0244			1.13971
$742$		0			0
$743$			18.0800i			0.663292i	0.943404	+	0.331646i	$0.107604\pi$
$743$			18.0800i			0.663292i	−0.943404	+	0.331646i	$0.892396\pi$
$744$		0			0
$745$	4.47321	−	11.6607i	0.163886	−	0.427215i
$746$		0			0
$747$	11.4859	+	6.63140i	0.420248	+	0.242630i
$748$		0			0
$749$	0.651451	−	2.68696i	0.0238035	−	0.0981794i
$750$		0			0
$751$	2.46210	−	4.26448i	0.0898433	−	0.155613i	−0.817601	−	0.575785i	$-0.804697\pi$
$751$	2.46210	−	4.26448i	0.0898433	−	0.155613i	0.907445	+	0.420171i	$0.138030\pi$
$752$		0			0
$753$	−64.6289	+	37.3135i	−2.35521	+	1.35978i
$754$		0			0
$755$	28.6246	+	35.3327i	1.04176	+	1.28589i
$756$		0			0
$757$		−	8.13716i		−	0.295750i	−0.989006	−	0.147875i	$-0.952757\pi$
$757$		−	8.13716i		−	0.295750i	0.989006	−	0.147875i	$-0.0472434\pi$
$758$		0			0
$759$	−0.302759	−	0.524395i	−0.0109895	−	0.0190343i
$760$		0			0
$761$	3.64812	−	6.31874i	0.132244	−	0.229054i	−0.792297	−	0.610136i	$-0.791115\pi$
$761$	3.64812	−	6.31874i	0.132244	−	0.229054i	0.924541	+	0.381082i	$0.124448\pi$
$762$		0			0
$763$	30.8661	−	32.3805i	1.11743	−	1.17225i
$764$		0			0
$765$	−2.62117	−	16.5260i	−0.0947684	−	0.597500i
$766$		0			0
$767$	−27.3911	+	15.8143i	−0.989036	+	0.571020i
$768$		0			0
$769$	−7.83640			−0.282588			−0.141294	−	0.989968i	$-0.545126\pi$
$769$	−7.83640			−0.282588			−0.141294	+	0.989968i	$0.545126\pi$
$770$		0			0
$771$	−8.04235			−0.289638
$772$		0			0
$773$	4.77210	−	2.75517i	0.171641	−	0.0990967i	−0.411719	−	0.911311i	$-0.635071\pi$
$773$	4.77210	−	2.75517i	0.171641	−	0.0990967i	0.583359	+	0.812214i	$0.301738\pi$
$774$		0			0
$775$	−4.94032	−	4.44437i	−0.177461	−	0.159647i
$776$		0			0
$777$	10.8208	+	36.8333i	0.388195	+	1.32139i
$778$		0			0
$779$	9.94623	−	17.2274i	0.356361	−	0.617235i
$780$		0			0
$781$	2.05977	+	3.56762i	0.0737042	+	0.127659i
$782$		0			0
$783$			2.25066i			0.0804321i
$784$		0			0
$785$	38.6036	−	31.2745i	1.37782	−	1.11624i
$786$		0			0
$787$	−13.7324	+	7.92842i	−0.489508	+	0.282618i	−0.724371	−	0.689411i	$-0.757869\pi$
$787$	−13.7324	+	7.92842i	−0.489508	+	0.282618i	0.234862	+	0.972029i	$0.424536\pi$
$788$		0			0
$789$	−26.6502	+	46.1594i	−0.948771	+	1.64332i
$790$		0			0
$791$	14.6202	−	4.29512i	0.519836	−	0.152717i
$792$		0			0
$793$	−24.3792	−	14.0753i	−0.865729	−	0.499829i
$794$		0			0
$795$	−23.0022	+	59.9619i	−0.815804	+	2.12663i
$796$		0			0
$797$		−	43.6533i		−	1.54628i	−0.634237	−	0.773139i	$-0.718686\pi$
$797$		−	43.6533i		−	1.54628i	0.634237	−	0.773139i	$-0.281314\pi$
$798$		0			0
$799$	−31.6824			−1.12084
$800$		0			0
$801$	1.01059	+	1.75039i	0.0357074	+	0.0618471i
$802$		0			0
$803$	−8.41406	−	4.85786i	−0.296926	−	0.171430i
$804$		0			0
$805$	−0.203715	+	2.52323i	−0.00718002	+	0.0889322i
$806$		0			0
$807$	5.38043	+	3.10639i	0.189400	+	0.109350i
$808$		0			0
$809$	19.3307	+	33.4817i	0.679631	+	1.17716i	0.975092	+	0.221800i	$0.0711934\pi$
$809$	19.3307	+	33.4817i	0.679631	+	1.17716i	−0.295461	+	0.955355i	$0.595473\pi$
$810$		0			0
$811$	−37.9019			−1.33092			−0.665458	−	0.746435i	$-0.731764\pi$
$811$	−37.9019			−1.33092			−0.665458	+	0.746435i	$0.731764\pi$
$812$		0			0
$813$			42.0593i			1.47508i
$814$		0			0
$815$	27.3806	+	10.5036i	0.959102	+	0.367924i
$816$		0			0
$817$	−22.3791	−	12.9206i	−0.782946	−	0.452034i
$818$		0			0
$819$	6.32580	−	26.0913i	0.221041	−	0.911703i
$820$		0			0
$821$	−4.32225	+	7.48636i	−0.150848	+	0.261276i	−0.931539	−	0.363641i	$-0.881534\pi$
$821$	−4.32225	+	7.48636i	−0.150848	+	0.261276i	0.780692	+	0.624916i	$0.214867\pi$
$822$		0			0
$823$	−29.5340	+	17.0515i	−1.02949	+	0.594377i	−0.916839	−	0.399257i	$-0.869268\pi$
$823$	−29.5340	+	17.0515i	−1.02949	+	0.594377i	−0.112653	+	0.993634i	$0.535935\pi$
$824$		0			0
$825$	6.92163	+	1.46808i	0.240980	+	0.0511120i
$826$		0			0
$827$			32.6226i			1.13440i	0.823581	+	0.567199i	$0.191973\pi$
$827$			32.6226i			1.13440i	−0.823581	+	0.567199i	$0.808027\pi$
$828$		0			0
$829$	17.7385	+	30.7240i	0.616083	+	1.06709i	0.990193	+	0.139703i	$0.0446149\pi$
$829$	17.7385	+	30.7240i	0.616083	+	1.06709i	−0.374110	+	0.927384i	$0.622052\pi$
$830$		0			0
$831$	−8.41507	+	14.5753i	−0.291916	+	0.505613i
$832$		0			0
$833$	−9.38301	+	18.2131i	−0.325102	+	0.631045i
$834$		0			0
$835$	4.02350	+	25.3675i	0.139239	+	0.877880i
$836$		0			0
$837$	1.20278	−	0.694426i	0.0415742	−	0.0240029i
$838$		0			0
$839$	10.2512			0.353909			0.176955	−	0.984219i	$-0.443375\pi$
$839$	10.2512			0.353909			0.176955	+	0.984219i	$0.443375\pi$
$840$		0			0
$841$	−24.3614			−0.840047
$842$		0			0
$843$	−8.46446	+	4.88696i	−0.291532	+	0.168316i
$844$		0			0
$845$	−6.07828	+	0.964066i	−0.209099	+	0.0331649i
$846$		0			0
$847$	−27.3572	−	6.63272i	−0.940004	−	0.227903i
$848$		0			0
$849$	14.0520	−	24.3388i	0.482263	−	0.835304i
$850$		0			0
$851$	1.31693	+	2.28099i	0.0451438	+	0.0781914i
$852$		0			0
$853$		−	1.86650i		−	0.0639078i	−0.999489	−	0.0319539i	$-0.989827\pi$
$853$		−	1.86650i		−	0.0639078i	0.999489	−	0.0319539i	$-0.0101730\pi$
$854$		0			0
$855$	−11.9337	−	14.7304i	−0.408125	−	0.503767i
$856$		0			0
$857$	5.85835	−	3.38232i	0.200117	−	0.115538i	−0.396593	−	0.917995i	$-0.629808\pi$
$857$	5.85835	−	3.38232i	0.200117	−	0.115538i	0.596710	+	0.802457i	$0.296474\pi$
$858$		0			0
$859$	18.7612	−	32.4954i	0.640124	−	1.10873i	−0.345281	−	0.938499i	$-0.612216\pi$
$859$	18.7612	−	32.4954i	0.640124	−	1.10873i	0.985405	−	0.170228i	$-0.0544504\pi$
$860$		0			0
$861$	−27.0806	−	25.8140i	−0.922904	−	0.879740i
$862$		0			0
$863$	−22.6478	−	13.0757i	−0.770939	−	0.445102i	0.0622704	−	0.998059i	$-0.480166\pi$
$863$	−22.6478	−	13.0757i	−0.770939	−	0.445102i	−0.833210	+	0.552957i	$0.813499\pi$
$864$		0			0
$865$	29.6845	+	11.3874i	1.00930	+	0.387183i
$866$		0			0
$867$			19.8801i			0.675163i
$868$		0			0
$869$	−8.12802			−0.275724
$870$		0			0
$871$	24.5907	+	42.5924i	0.833225	+	1.44319i
$872$		0			0
$873$	6.21267	+	3.58689i	0.210267	+	0.121398i
$874$		0			0
$875$	−20.3278	−	21.4891i	−0.687204	−	0.726464i
$876$		0			0
$877$	26.0834	+	15.0593i	0.880775	+	0.508516i	0.870914	−	0.491436i	$-0.163528\pi$
$877$	26.0834	+	15.0593i	0.880775	+	0.508516i	0.00986116	+	0.999951i	$0.496861\pi$
$878$		0			0
$879$	−26.9016	−	46.5950i	−0.907369	−	1.57161i
$880$		0			0
$881$	−48.3437			−1.62874			−0.814370	−	0.580347i	$-0.802917\pi$
$881$	−48.3437			−1.62874			−0.814370	+	0.580347i	$0.802917\pi$
$882$		0			0
$883$		−	3.28707i		−	0.110619i	−0.998469	−	0.0553093i	$-0.982386\pi$
$883$		−	3.28707i		−	0.110619i	0.998469	−	0.0553093i	$-0.0176145\pi$
$884$		0			0
$885$	39.2183	+	15.0447i	1.31831	+	0.505721i
$886$		0			0
$887$	45.8502	+	26.4716i	1.53950	+	0.888830i	0.998868	+	0.0475704i	$0.0151478\pi$
$887$	45.8502	+	26.4716i	1.53950	+	0.888830i	0.540631	+	0.841260i	$0.318185\pi$
$888$		0			0
$889$	−8.81274	+	2.58900i	−0.295570	+	0.0868321i
$890$		0			0
$891$	−3.04166	+	5.26832i	−0.101900	+	0.176495i
$892$		0			0
$893$	−31.0865	+	17.9478i	−1.04027	+	0.600600i
$894$		0			0
$895$	2.35223	+	2.90347i	0.0786265	+	0.0970523i
$896$		0			0
$897$		−	4.00326i		−	0.133665i
$898$		0			0
$899$	−1.43122	−	2.47894i	−0.0477337	−	0.0826773i
$900$		0			0
$901$	−17.8306	+	30.8834i	−0.594022	+	1.02888i
$902$		0			0
$903$	−33.5336	+	35.1789i	−1.11593	+	1.17068i
$904$		0			0
$905$	12.9187	−	2.04902i	0.429433	−	0.0681116i
$906$		0			0
$907$	45.3678	−	26.1931i	1.50641	−	0.869727i	0.506439	−	0.862276i	$-0.330961\pi$
$907$	45.3678	−	26.1931i	1.50641	−	0.869727i	0.999972	−	0.00745157i	$-0.00237193\pi$
$908$		0			0
$909$	−0.896202			−0.0297251
$910$		0			0
$911$	−50.1269			−1.66078			−0.830390	−	0.557183i	$-0.811882\pi$
$911$	−50.1269			−1.66078			−0.830390	+	0.557183i	$0.811882\pi$
$912$		0			0
$913$	−2.69695	+	1.55709i	−0.0892562	+	0.0515321i
$914$		0			0
$915$	5.85653	+	36.9245i	0.193611	+	1.22069i
$916$		0			0
$917$	−40.1570	−	9.73601i	−1.32610	−	0.321511i
$918$		0			0
$919$	−13.3285	+	23.0856i	−0.439667	+	0.761525i	−0.997664	−	0.0683181i	$-0.978237\pi$
$919$	−13.3285	+	23.0856i	−0.439667	+	0.761525i	0.557997	+	0.829843i	$0.311570\pi$
$920$		0			0
$921$	3.97217	+	6.88001i	0.130888	+	0.226704i
$922$		0			0
$923$			27.2354i			0.896464i
$924$		0			0
$925$	−30.1074	−	6.38579i	−0.989927	−	0.209964i
$926$		0			0
$927$	−30.6049	+	17.6697i	−1.00520	+	0.580350i
$928$		0			0
$929$	−7.04900	+	12.2092i	−0.231270	+	0.400572i	−0.958182	−	0.286159i	$-0.907621\pi$
$929$	−7.04900	+	12.2092i	−0.231270	+	0.400572i	0.726912	+	0.686731i	$0.240955\pi$
$930$		0			0
$931$	1.11100	+	23.1859i	0.0364116	+	0.759888i
$932$		0			0
$933$	−61.5396	−	35.5299i	−2.01472	−	1.16320i
$934$		0			0
$935$	3.66825	+	1.40719i	0.119965	+	0.0460201i
$936$		0			0
$937$		−	13.1880i		−	0.430835i	−0.976522	−	0.215417i	$-0.930889\pi$
$937$		−	13.1880i		−	0.430835i	0.976522	−	0.215417i	$-0.0691112\pi$
$938$		0			0
$939$	42.7835			1.39619
$940$		0			0
$941$	−2.51245	−	4.35169i	−0.0819034	−	0.141861i	0.822164	−	0.569251i	$-0.192767\pi$
$941$	−2.51245	−	4.35169i	−0.0819034	−	0.141861i	−0.904068	+	0.427390i	$0.859433\pi$
$942$		0			0
$943$	−2.22294	−	1.28342i	−0.0723890	−	0.0417938i
$944$		0			0
$945$	5.58541	−	2.65026i	0.181694	−	0.0862130i
$946$		0			0
$947$	−13.5831	−	7.84218i	−0.441390	−	0.254837i	0.262797	−	0.964851i	$-0.415355\pi$
$947$	−13.5831	−	7.84218i	−0.441390	−	0.254837i	−0.704187	+	0.710015i	$0.748688\pi$
$948$		0			0
$949$	−32.1167	−	55.6277i	−1.04255	−	1.80575i
$950$		0			0
$951$	−77.6139			−2.51680
$952$		0			0
$953$			25.4887i			0.825659i	0.910808	+	0.412830i	$0.135460\pi$
$953$			25.4887i			0.825659i	−0.910808	+	0.412830i	$0.864540\pi$
$954$		0			0
$955$	17.3133	−	45.1321i	0.560244	−	1.46044i
$956$		0			0
$957$	2.63949	+	1.52391i	0.0853225	+	0.0492610i
$958$		0			0
$959$	17.0426	+	16.2455i	0.550333	+	0.524594i
$960$		0			0
$961$	14.6168	−	25.3171i	0.471510	−	0.816680i
$962$		0			0
$963$	2.31379	−	1.33587i	0.0745609	−	0.0430477i
$964$		0			0
$965$	−29.3313	+	23.7626i	−0.944207	+	0.764945i
$966$		0			0
$967$			11.9730i			0.385027i	0.981294	+	0.192514i	$0.0616639\pi$
$967$			11.9730i			0.385027i	−0.981294	+	0.192514i	$0.938336\pi$
$968$		0			0
$969$	−11.4394	−	19.8136i	−0.367486	−	0.636505i
$970$		0			0
$971$	−3.02372	+	5.23725i	−0.0970360	+	0.168071i	−0.910456	−	0.413605i	$-0.864270\pi$
$971$	−3.02372	+	5.23725i	−0.0970360	+	0.168071i	0.813421	+	0.581676i	$0.197603\pi$
$972$		0			0
$973$	10.2349	+	34.8389i	0.328117	+	1.11688i
$974$		0			0
$975$	34.7771	+	31.2860i	1.11376	+	1.00195i
$976$		0			0
$977$	45.7143	−	26.3932i	1.46253	−	0.844392i	0.463402	−	0.886148i	$-0.346629\pi$
$977$	45.7143	−	26.3932i	1.46253	−	0.844392i	0.999128	+	0.0417564i	$0.0132953\pi$
$978$		0			0
$979$	−0.474583			−0.0151678
$980$		0			0
$981$	43.2290			1.38020
$982$		0			0
$983$	2.43961	−	1.40851i	0.0778114	−	0.0449244i	−0.460589	−	0.887613i	$-0.652362\pi$
$983$	2.43961	−	1.40851i	0.0778114	−	0.0449244i	0.538401	+	0.842689i	$0.319029\pi$
$984$		0			0
$985$	−2.59939	−	16.3887i	−0.0828234	−	0.522188i
$986$		0			0
$987$	19.0291	+	64.7736i	0.605703	+	2.06177i
$988$		0			0
$989$	−1.66722	+	2.88770i	−0.0530144	+	0.0918236i
$990$		0			0
$991$	12.8466	+	22.2509i	0.408085	+	0.706823i	0.994675	−	0.103060i	$-0.0328635\pi$
$991$	12.8466	+	22.2509i	0.408085	+	0.706823i	−0.586590	+	0.809884i	$0.699530\pi$
$992$		0			0
$993$		−	48.7806i		−	1.54800i
$994$		0			0
$995$	20.5539	+	25.3707i	0.651604	+	0.804304i
$996$		0			0
$997$	18.8558	−	10.8864i	0.597169	−	0.344776i	−0.170758	−	0.985313i	$-0.554622\pi$
$997$	18.8558	−	10.8864i	0.597169	−	0.344776i	0.767927	+	0.640537i	$0.221288\pi$
$998$		0			0
$999$	3.21621	−	5.57064i	0.101756	−	0.176247i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bw.h.289.15	yes	40
4.3	odd	2	inner	1120.2.bw.h.289.6	yes	40
5.4	even	2	inner	1120.2.bw.h.289.5	✓	40
7.4	even	3	inner	1120.2.bw.h.1089.5	yes	40
20.19	odd	2	inner	1120.2.bw.h.289.16	yes	40
28.11	odd	6	inner	1120.2.bw.h.1089.16	yes	40
35.4	even	6	inner	1120.2.bw.h.1089.15	yes	40
140.39	odd	6	inner	1120.2.bw.h.1089.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1120.2.bw.h.289.5	✓	40	5.4	even	2	inner
1120.2.bw.h.289.6	yes	40	4.3	odd	2	inner
1120.2.bw.h.289.15	yes	40	1.1	even	1	trivial
1120.2.bw.h.289.16	yes	40	20.19	odd	2	inner
1120.2.bw.h.1089.5	yes	40	7.4	even	3	inner
1120.2.bw.h.1089.6	yes	40	140.39	odd	6	inner
1120.2.bw.h.1089.15	yes	40	35.4	even	6	inner
1120.2.bw.h.1089.16	yes	40	28.11	odd	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bw (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.04145 - 1.17863i) q^{3} +(2.20846 - 0.350280i) q^{5} +(-0.745750 - 2.53848i) q^{7} +(1.27835 - 2.21416i) q^{9} +(0.300162 + 0.519896i) q^{11} +3.96891i q^{13} +(4.09561 - 3.31804i) q^{15} +(2.53473 - 1.46343i) q^{17} +(1.65804 - 2.87180i) q^{19} +(-4.51434 - 4.30320i) q^{21} +(-0.370565 - 0.213946i) q^{23} +(4.75461 - 1.54716i) q^{25} +1.04500i q^{27} +2.15375 q^{29} +(-0.664524 - 1.15099i) q^{31} +(1.22553 + 0.707561i) q^{33} +(-2.53614 - 5.34490i) q^{35} +(-5.33077 - 3.07772i) q^{37} +(4.67789 + 8.10234i) q^{39} +5.99880 q^{41} -7.79270i q^{43} +(2.04760 - 5.33766i) q^{45} +(-9.37449 - 5.41236i) q^{47} +(-5.88771 + 3.78614i) q^{49} +(3.44968 - 5.97502i) q^{51} +(-10.5518 + 6.09206i) q^{53} +(0.845006 + 1.04303i) q^{55} -7.81686i q^{57} +(3.98454 + 6.90142i) q^{59} +(-3.54639 + 6.14253i) q^{61} +(-6.57391 - 1.59384i) q^{63} +(1.39023 + 8.76519i) q^{65} +(10.7315 - 6.19584i) q^{67} -1.00865 q^{69} +6.86218 q^{71} +(-14.0159 + 8.09206i) q^{73} +(7.88276 - 8.76238i) q^{75} +(1.09590 - 1.14967i) q^{77} +(-6.76969 + 11.7254i) q^{79} +(5.06670 + 8.77579i) q^{81} +5.18749i q^{83} +(5.08524 - 4.11978i) q^{85} +(4.39677 - 2.53848i) q^{87} +(-0.395273 + 0.684632i) q^{89} +(10.0750 - 2.95982i) q^{91} +(-2.71318 - 1.56646i) q^{93} +(2.65577 - 6.92305i) q^{95} +2.80588i q^{97} +1.53484 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{5} + 40 q^{9} - 4 q^{21} + 24 q^{25} + 24 q^{29} - 40 q^{41} - 8 q^{45} - 52 q^{49} - 44 q^{61} + 16 q^{65} - 56 q^{69} - 4 q^{81} - 72 q^{85} - 76 q^{89}+O(q^{100}) \) 40 * q - 8 * q^5 + 40 * q^9 - 4 * q^21 + 24 * q^25 + 24 * q^29 - 40 * q^41 - 8 * q^45 - 52 * q^49 - 44 * q^61 + 16 * q^65 - 56 * q^69 - 4 * q^81 - 72 * q^85 - 76 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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