LMFDB - Embedded newform 1148.2.n.e.141.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(57,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("1148.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.n (of order $5$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.2
Character	$\chi$	$=$	1148.141
Dual form			1148.2.n.e.57.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.842614 q^{3} +(2.54946 - 1.85229i) q^{5} +(-0.309017 + 0.951057i) q^{7} -2.29000 q^{9} +O(q^{10})$	\(q-0.842614 q^{3} +(2.54946 - 1.85229i) q^{5} +(-0.309017 + 0.951057i) q^{7} -2.29000 q^{9} +(0.696228 + 0.505840i) q^{11} +(-1.28490 - 3.95451i) q^{13} +(-2.14821 + 1.56077i) q^{15} +(-3.99341 - 2.90138i) q^{17} +(0.379578 - 1.16822i) q^{19} +(0.260382 - 0.801374i) q^{21} +(-0.845549 - 2.60233i) q^{23} +(1.52368 - 4.68942i) q^{25} +4.45743 q^{27} +(2.90253 - 2.10881i) q^{29} +(-1.65846 - 1.20494i) q^{31} +(-0.586652 - 0.426228i) q^{33} +(0.973808 + 2.99707i) q^{35} +(-3.03640 + 2.20607i) q^{37} +(1.08267 + 3.33212i) q^{39} +(-6.18314 - 1.66398i) q^{41} +(1.12146 + 3.45150i) q^{43} +(-5.83827 + 4.24175i) q^{45} +(0.0692958 + 0.213271i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(3.36491 + 2.44475i) q^{51} +(1.91460 - 1.39104i) q^{53} +2.71197 q^{55} +(-0.319838 + 0.984359i) q^{57} +(-4.28890 - 13.1999i) q^{59} +(2.89170 - 8.89974i) q^{61} +(0.707649 - 2.17792i) q^{63} +(-10.6007 - 7.70186i) q^{65} +(-2.73418 + 1.98649i) q^{67} +(0.712471 + 2.19276i) q^{69} +(2.37728 + 1.72720i) q^{71} -13.1715 q^{73} +(-1.28388 + 3.95137i) q^{75} +(-0.696228 + 0.505840i) q^{77} +2.33755 q^{79} +3.11411 q^{81} +13.2998 q^{83} -15.5553 q^{85} +(-2.44572 + 1.77692i) q^{87} +(1.36527 - 4.20187i) q^{89} +4.15802 q^{91} +(1.39744 + 1.01530i) q^{93} +(-1.19617 - 3.68142i) q^{95} +(2.78964 - 2.02679i) q^{97} +(-1.59436 - 1.15837i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9}+O(q^{10}) $ 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9	$ 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9} - 8 q^{11} + 10 q^{15} + 8 q^{17} - 28 q^{19} + 3 q^{21} - 23 q^{23} + 17 q^{25} + 12 q^{27} - 31 q^{29} + 2 q^{31} + 12 q^{33} + 13 q^{35} + 7 q^{37} - 16 q^{39} - q^{41} - 2 q^{43} + 71 q^{45} + 15 q^{47} - 6 q^{49} + 2 q^{51} + 28 q^{53} - 16 q^{55} - 15 q^{57} + 17 q^{59} + 35 q^{61} - q^{63} + 62 q^{65} - 10 q^{67} - 9 q^{69} - 25 q^{71} - 74 q^{73} + 17 q^{75} + 8 q^{77} + 64 q^{81} + 96 q^{83} - 94 q^{85} - q^{87} - 33 q^{89} - 15 q^{93} - 29 q^{95} - 34 q^{97} - 3 q^{99}+O(q^{100}) $ 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9 - 8 * q^11 + 10 * q^15 + 8 * q^17 - 28 * q^19 + 3 * q^21 - 23 * q^23 + 17 * q^25 + 12 * q^27 - 31 * q^29 + 2 * q^31 + 12 * q^33 + 13 * q^35 + 7 * q^37 - 16 * q^39 - q^41 - 2 * q^43 + 71 * q^45 + 15 * q^47 - 6 * q^49 + 2 * q^51 + 28 * q^53 - 16 * q^55 - 15 * q^57 + 17 * q^59 + 35 * q^61 - q^63 + 62 * q^65 - 10 * q^67 - 9 * q^69 - 25 * q^71 - 74 * q^73 + 17 * q^75 + 8 * q^77 + 64 * q^81 + 96 * q^83 - 94 * q^85 - q^87 - 33 * q^89 - 15 * q^93 - 29 * q^95 - 34 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.842614			−0.486484			−0.243242	−	0.969966i	$-0.578211\pi$
$3$	−0.842614			−0.486484			−0.243242	+	0.969966i	$0.578211\pi$
$4$		0			0
$5$	2.54946	−	1.85229i	1.14015	−	0.828371i	0.153014	−	0.988224i	$-0.451102\pi$
$5$	2.54946	−	1.85229i	1.14015	−	0.828371i	0.987141	+	0.159854i	$0.0511022\pi$
$6$		0			0
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$		0			0
$9$	−2.29000			−0.763334
$10$		0			0
$11$	0.696228	+	0.505840i	0.209921	+	0.152516i	0.687778	−	0.725921i	$-0.258586\pi$
$11$	0.696228	+	0.505840i	0.209921	+	0.152516i	−0.477857	+	0.878438i	$0.658586\pi$
$12$		0			0
$13$	−1.28490	−	3.95451i	−0.356366	−	1.09678i	−0.955213	−	0.295919i	$-0.904374\pi$
$13$	−1.28490	−	3.95451i	−0.356366	−	1.09678i	0.598846	−	0.800864i	$-0.295626\pi$
$14$		0			0
$15$	−2.14821	+	1.56077i	−0.554666	+	0.402989i
$16$		0			0
$17$	−3.99341	−	2.90138i	−0.968545	−	0.703689i	−0.0134254	−	0.999910i	$-0.504274\pi$
$17$	−3.99341	−	2.90138i	−0.968545	−	0.703689i	−0.955119	+	0.296221i	$0.904274\pi$
$18$		0			0
$19$	0.379578	−	1.16822i	0.0870811	−	0.268008i	−0.898028	−	0.439938i	$-0.855000\pi$
$19$	0.379578	−	1.16822i	0.0870811	−	0.268008i	0.985109	+	0.171930i	$0.0550003\pi$
$20$		0			0
$21$	0.260382	−	0.801374i	0.0568200	−	0.174874i
$22$		0			0
$23$	−0.845549	−	2.60233i	−0.176309	−	0.542624i	0.823382	−	0.567488i	$-0.192085\pi$
$23$	−0.845549	−	2.60233i	−0.176309	−	0.542624i	−0.999691	+	0.0248643i	$0.992085\pi$
$24$		0			0
$25$	1.52368	−	4.68942i	0.304737	−	0.937884i
$26$		0			0
$27$	4.45743			0.857833
$28$		0			0
$29$	2.90253	−	2.10881i	0.538987	−	0.391597i	−0.284722	−	0.958610i	$-0.591901\pi$
$29$	2.90253	−	2.10881i	0.538987	−	0.391597i	0.823709	+	0.567013i	$0.191901\pi$
$30$		0			0
$31$	−1.65846	−	1.20494i	−0.297868	−	0.216414i	0.428805	−	0.903397i	$-0.358935\pi$
$31$	−1.65846	−	1.20494i	−0.297868	−	0.216414i	−0.726673	+	0.686983i	$0.758935\pi$
$32$		0			0
$33$	−0.586652	−	0.426228i	−0.102123	−	0.0741967i
$34$		0			0
$35$	0.973808	+	2.99707i	0.164604	+	0.506598i
$36$		0			0
$37$	−3.03640	+	2.20607i	−0.499180	+	0.362676i	−0.808704	−	0.588216i	$-0.799830\pi$
$37$	−3.03640	+	2.20607i	−0.499180	+	0.362676i	0.309523	+	0.950892i	$0.399830\pi$
$38$		0			0
$39$	1.08267	+	3.33212i	0.173366	+	0.533567i
$40$		0			0
$41$	−6.18314	−	1.66398i	−0.965644	−	0.259870i
$41$	−6.18314	−	1.66398i	−0.965644	−	0.259870i
$42$		0			0
$43$	1.12146	+	3.45150i	0.171021	+	0.526348i	0.999429	−	0.0337762i	$-0.0107533\pi$
$43$	1.12146	+	3.45150i	0.171021	+	0.526348i	−0.828409	+	0.560124i	$0.810753\pi$
$44$		0			0
$45$	−5.83827	+	4.24175i	−0.870318	+	0.632323i
$46$		0			0
$47$	0.0692958	+	0.213271i	0.0101078	+	0.0311087i	0.955983	−	0.293421i	$-0.0947939\pi$
$47$	0.0692958	+	0.213271i	0.0101078	+	0.0311087i	−0.945875	+	0.324530i	$0.894794\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$		0			0
$51$	3.36491	+	2.44475i	0.471181	+	0.342333i
$52$		0			0
$53$	1.91460	−	1.39104i	0.262990	−	0.191074i	−0.448474	−	0.893796i	$-0.648032\pi$
$53$	1.91460	−	1.39104i	0.262990	−	0.191074i	0.711464	+	0.702722i	$0.248032\pi$
$54$		0			0
$55$	2.71197			0.365682
$56$		0			0
$57$	−0.319838	+	0.984359i	−0.0423635	+	0.130382i
$58$		0			0
$59$	−4.28890	−	13.1999i	−0.558368	−	1.71848i	−0.686879	−	0.726771i	$-0.741020\pi$
$59$	−4.28890	−	13.1999i	−0.558368	−	1.71848i	0.128512	−	0.991708i	$-0.458980\pi$
$60$		0			0
$61$	2.89170	−	8.89974i	0.370244	−	1.13949i	−0.576387	−	0.817177i	$-0.695538\pi$
$61$	2.89170	−	8.89974i	0.370244	−	1.13949i	0.946632	−	0.322318i	$-0.104462\pi$
$62$		0			0
$63$	0.707649	−	2.17792i	0.0891554	−	0.274392i
$64$		0			0
$65$	−10.6007	−	7.70186i	−1.31486	−	0.955299i
$66$		0			0
$67$	−2.73418	+	1.98649i	−0.334033	+	0.242689i	−0.742140	−	0.670245i	$-0.766189\pi$
$67$	−2.73418	+	1.98649i	−0.334033	+	0.242689i	0.408107	+	0.912934i	$0.366189\pi$
$68$		0			0
$69$	0.712471	+	2.19276i	0.0857715	+	0.263977i
$70$		0			0
$71$	2.37728	+	1.72720i	0.282132	+	0.204981i	0.719847	−	0.694133i	$-0.244212\pi$
$71$	2.37728	+	1.72720i	0.282132	+	0.204981i	−0.437715	+	0.899114i	$0.644212\pi$
$72$		0			0
$73$	−13.1715			−1.54161			−0.770804	−	0.637072i	$-0.780145\pi$
$73$	−13.1715			−1.54161			−0.770804	+	0.637072i	$0.780145\pi$
$74$		0			0
$75$	−1.28388	+	3.95137i	−0.148250	+	0.456265i
$76$		0			0
$77$	−0.696228	+	0.505840i	−0.0793426	+	0.0576458i
$78$		0			0
$79$	2.33755			0.262995			0.131498	−	0.991316i	$-0.458021\pi$
$79$	2.33755			0.262995			0.131498	+	0.991316i	$0.458021\pi$
$80$		0			0
$81$	3.11411			0.346012
$82$		0			0
$83$	13.2998			1.45984			0.729920	−	0.683532i	$-0.239557\pi$
$83$	13.2998			1.45984			0.729920	+	0.683532i	$0.239557\pi$
$84$		0			0
$85$	−15.5553			−1.68721
$86$		0			0
$87$	−2.44572	+	1.77692i	−0.262208	+	0.190506i
$88$		0			0
$89$	1.36527	−	4.20187i	0.144719	−	0.445398i	−0.852256	−	0.523125i	$-0.824766\pi$
$89$	1.36527	−	4.20187i	0.144719	−	0.445398i	0.996975	+	0.0777269i	$0.0247662\pi$
$90$		0			0
$91$	4.15802			0.435878
$92$		0			0
$93$	1.39744	+	1.01530i	0.144908	+	0.105282i
$94$		0			0
$95$	−1.19617	−	3.68142i	−0.122724	−	0.377706i
$96$		0			0
$97$	2.78964	−	2.02679i	0.283245	−	0.205790i	−0.437086	−	0.899420i	$-0.643990\pi$
$97$	2.78964	−	2.02679i	0.283245	−	0.205790i	0.720332	+	0.693630i	$0.243990\pi$
$98$		0			0
$99$	−1.59436	−	1.15837i	−0.160240	−	0.116421i
$100$		0			0
$101$	1.74743	−	5.37802i	0.173875	−	0.535133i	−0.825705	−	0.564102i	$-0.809222\pi$
$101$	1.74743	−	5.37802i	0.173875	−	0.535133i	0.999580	+	0.0289689i	$0.00922238\pi$
$102$		0			0
$103$	0.853888	−	2.62800i	0.0841361	−	0.258944i	−0.900134	−	0.435612i	$-0.856532\pi$
$103$	0.853888	−	2.62800i	0.0841361	−	0.258944i	0.984271	+	0.176668i	$0.0565319\pi$
$104$		0			0
$105$	−0.820545	−	2.52538i	−0.0800769	−	0.246451i
$106$		0			0
$107$	−0.147621	+	0.454331i	−0.0142711	+	0.0439219i	−0.957938	−	0.286974i	$-0.907351\pi$
$107$	−0.147621	+	0.454331i	−0.0142711	+	0.0439219i	0.943667	+	0.330896i	$0.107351\pi$
$108$		0			0
$109$	−4.08928			−0.391682			−0.195841	−	0.980636i	$-0.562744\pi$
$109$	−4.08928			−0.391682			−0.195841	+	0.980636i	$0.562744\pi$
$110$		0			0
$111$	2.55851	−	1.85887i	0.242843	−	0.176436i
$112$		0			0
$113$	−7.31961	−	5.31801i	−0.688571	−	0.500276i	0.187619	−	0.982242i	$-0.439923\pi$
$113$	−7.31961	−	5.31801i	−0.688571	−	0.500276i	−0.876190	+	0.481966i	$0.839923\pi$
$114$		0			0
$115$	−6.97597	−	5.06834i	−0.650513	−	0.472625i
$116$		0			0
$117$	2.94242	+	9.05583i	0.272027	+	0.837212i
$118$		0			0
$119$	3.99341	−	2.90138i	0.366076	−	0.265969i
$120$		0			0
$121$	−3.17033	−	9.75726i	−0.288212	−	0.887024i
$122$		0			0
$123$	5.21000	+	1.40209i	0.469770	+	0.126423i
$124$		0			0
$125$	0.0674387	+	0.207555i	0.00603190	+	0.0185643i
$126$		0			0
$127$	7.30159	−	5.30492i	0.647911	−	0.470735i	−0.214648	−	0.976692i	$-0.568860\pi$
$127$	7.30159	−	5.30492i	0.647911	−	0.470735i	0.862559	+	0.505956i	$0.168860\pi$
$128$		0			0
$129$	−0.944957	−	2.90828i	−0.0831989	−	0.256060i
$130$		0			0
$131$	9.30829	+	6.76287i	0.813269	+	0.590874i	0.914776	−	0.403960i	$-0.132367\pi$
$131$	9.30829	+	6.76287i	0.813269	+	0.590874i	−0.101508	+	0.994835i	$0.532367\pi$
$132$		0			0
$133$	0.993747	+	0.722000i	0.0861688	+	0.0626053i
$134$		0			0
$135$	11.3641	−	8.25647i	0.978062	−	0.710604i
$136$		0			0
$137$	−11.8316			−1.01084			−0.505421	−	0.862873i	$-0.668663\pi$
$137$	−11.8316			−1.01084			−0.505421	+	0.862873i	$0.668663\pi$
$138$		0			0
$139$	−1.58617	+	4.88172i	−0.134537	+	0.414062i	−0.995518	−	0.0945753i	$-0.969851\pi$
$139$	−1.58617	+	4.88172i	−0.134537	+	0.414062i	0.860981	+	0.508638i	$0.169851\pi$
$140$		0			0
$141$	−0.0583896	−	0.179705i	−0.00491729	−	0.0151339i
$142$		0			0
$143$	1.10576	−	3.40319i	0.0924687	−	0.284589i
$144$		0			0
$145$	3.49376	−	10.7527i	0.290141	−	0.892962i
$146$		0			0
$147$	0.681689	+	0.495276i	0.0562248	+	0.0408497i
$148$		0			0
$149$	9.68328	−	7.03532i	0.793286	−	0.576356i	−0.115651	−	0.993290i	$-0.536895\pi$
$149$	9.68328	−	7.03532i	0.793286	−	0.576356i	0.908937	+	0.416934i	$0.136895\pi$
$150$		0			0
$151$	0.619918	+	1.90791i	0.0504482	+	0.155264i	0.973107	−	0.230354i	$-0.0739884\pi$
$151$	0.619918	+	1.90791i	0.0504482	+	0.155264i	−0.922659	+	0.385618i	$0.873988\pi$
$152$		0			0
$153$	9.14492	+	6.64417i	0.739323	+	0.537150i
$154$		0			0
$155$	−6.46008			−0.518886
$156$		0			0
$157$	−5.53707	+	17.0414i	−0.441907	+	1.36005i	0.443934	+	0.896059i	$0.353582\pi$
$157$	−5.53707	+	17.0414i	−0.441907	+	1.36005i	−0.885841	+	0.463989i	$0.846418\pi$
$158$		0			0
$159$	−1.61327	+	1.17211i	−0.127940	+	0.0929542i
$160$		0			0
$161$	2.73625			0.215647
$162$		0			0
$163$	−11.5121			−0.901694			−0.450847	−	0.892601i	$-0.648878\pi$
$163$	−11.5121			−0.901694			−0.450847	+	0.892601i	$0.648878\pi$
$164$		0			0
$165$	−2.28515			−0.177898
$166$		0			0
$167$	−12.5245			−0.969175			−0.484587	−	0.874743i	$-0.661030\pi$
$167$	−12.5245			−0.969175			−0.484587	+	0.874743i	$0.661030\pi$
$168$		0			0
$169$	−3.46995	+	2.52107i	−0.266919	+	0.193928i
$170$		0			0
$171$	−0.869233	+	2.67523i	−0.0664719	+	0.204580i
$172$		0			0
$173$	23.4675			1.78420			0.892102	−	0.451835i	$-0.149230\pi$
$173$	23.4675			1.78420			0.892102	+	0.451835i	$0.149230\pi$
$174$		0			0
$175$	3.98906	+	2.89822i	0.301544	+	0.219085i
$176$		0			0
$177$	3.61389	+	11.1224i	0.271637	+	0.836012i
$178$		0			0
$179$	−15.6229	+	11.3507i	−1.16771	+	0.848390i	−0.990733	−	0.135825i	$-0.956632\pi$
$179$	−15.6229	+	11.3507i	−1.16771	+	0.848390i	−0.176976	+	0.984215i	$0.556632\pi$
$180$		0			0
$181$	18.0158	+	13.0892i	1.33910	+	0.972915i	0.999476	+	0.0323550i	$0.0103007\pi$
$181$	18.0158	+	13.0892i	1.33910	+	0.972915i	0.339627	+	0.940560i	$0.389699\pi$
$182$		0			0
$183$	−2.43659	+	7.49904i	−0.180118	+	0.554345i
$184$		0			0
$185$	−3.65489	+	11.2486i	−0.268713	+	0.827013i
$186$		0			0
$187$	−1.31269	−	4.04005i	−0.0959936	−	0.295438i
$188$		0			0
$189$	−1.37742	+	4.23927i	−0.100193	+	0.308361i
$190$		0			0
$191$	19.7863			1.43169			0.715845	−	0.698259i	$-0.246042\pi$
$191$	19.7863			1.43169			0.715845	+	0.698259i	$0.246042\pi$
$192$		0			0
$193$	−0.0691065	+	0.0502088i	−0.00497439	+	0.00361411i	−0.590270	−	0.807206i	$-0.700979\pi$
$193$	−0.0691065	+	0.0502088i	−0.00497439	+	0.00361411i	0.585295	+	0.810820i	$0.300979\pi$
$194$		0			0
$195$	8.93231	+	6.48970i	0.639656	+	0.464737i
$196$		0			0
$197$	−5.90157	−	4.28774i	−0.420470	−	0.305489i	0.357357	−	0.933968i	$-0.383678\pi$
$197$	−5.90157	−	4.28774i	−0.420470	−	0.305489i	−0.777827	+	0.628479i	$0.783678\pi$
$198$		0			0
$199$	5.29942	+	16.3099i	0.375666	+	1.15618i	0.943028	+	0.332713i	$0.107964\pi$
$199$	5.29942	+	16.3099i	0.375666	+	1.15618i	−0.567362	+	0.823469i	$0.692036\pi$
$200$		0			0
$201$	2.30386	−	1.67385i	0.162501	−	0.118064i
$202$		0			0
$203$	1.10867	+	3.41213i	0.0778133	+	0.239485i
$204$		0			0
$205$	−18.8459	+	7.21072i	−1.31625	+	0.503618i
$206$		0			0
$207$	1.93631	+	5.95934i	0.134583	+	0.414203i
$208$		0			0
$209$	0.855205	−	0.621343i	0.0591557	−	0.0429792i
$210$		0			0
$211$	0.840584	+	2.58705i	0.0578682	+	0.178100i	0.975812	−	0.218609i	$-0.0701521\pi$
$211$	0.840584	+	2.58705i	0.0578682	+	0.178100i	−0.917944	+	0.396709i	$0.870152\pi$
$212$		0			0
$213$	−2.00313	−	1.45536i	−0.137252	−	0.0997198i
$214$		0			0
$215$	9.25230	+	6.72219i	0.631002	+	0.458449i
$216$		0			0
$217$	1.65846	−	1.20494i	0.112583	−	0.0817967i
$218$		0			0
$219$	11.0985			0.749967
$220$		0			0
$221$	−6.34242	+	19.5200i	−0.426637	+	1.31305i
$222$		0			0
$223$	−1.34339	−	4.13454i	−0.0899604	−	0.276870i	0.895947	−	0.444161i	$-0.146498\pi$
$223$	−1.34339	−	4.13454i	−0.0899604	−	0.276870i	−0.985908	+	0.167291i	$0.946498\pi$
$224$		0			0
$225$	−3.48924	+	10.7388i	−0.232616	+	0.715918i
$226$		0			0
$227$	−6.09727	+	18.7655i	−0.404690	+	1.24551i	0.516463	+	0.856309i	$0.327248\pi$
$227$	−6.09727	+	18.7655i	−0.404690	+	1.24551i	−0.921154	+	0.389199i	$0.872752\pi$
$228$		0			0
$229$	2.71677	+	1.97385i	0.179529	+	0.130436i	0.673921	−	0.738804i	$-0.264609\pi$
$229$	2.71677	+	1.97385i	0.179529	+	0.130436i	−0.494391	+	0.869239i	$0.664609\pi$
$230$		0			0
$231$	0.586652	−	0.426228i	0.0385989	−	0.0280437i
$232$		0			0
$233$	5.73261	+	17.6432i	0.375556	+	1.15584i	0.943103	+	0.332501i	$0.107893\pi$
$233$	5.73261	+	17.6432i	0.375556	+	1.15584i	−0.567547	+	0.823341i	$0.692107\pi$
$234$		0			0
$235$	0.571707	+	0.415369i	0.0372940	+	0.0270957i
$236$		0			0
$237$	−1.96965			−0.127943
$238$		0			0
$239$	−4.56711	+	14.0561i	−0.295422	+	0.909215i	0.687658	+	0.726035i	$0.258639\pi$
$239$	−4.56711	+	14.0561i	−0.295422	+	0.909215i	−0.983079	+	0.183180i	$0.941361\pi$
$240$		0			0
$241$	16.2712	−	11.8217i	1.04812	−	0.761503i	0.0762648	−	0.997088i	$-0.475701\pi$
$241$	16.2712	−	11.8217i	1.04812	−	0.761503i	0.971854	+	0.235585i	$0.0757006\pi$
$242$		0			0
$243$	−15.9963			−1.02616
$244$		0			0
$245$	−3.15131			−0.201330
$246$		0			0
$247$	−5.10745			−0.324979
$248$		0			0
$249$	−11.2066			−0.710189
$250$		0			0
$251$	18.4311	−	13.3910i	1.16336	−	0.845230i	0.173161	−	0.984894i	$-0.444602\pi$
$251$	18.4311	−	13.3910i	1.16336	−	0.845230i	0.990199	+	0.139663i	$0.0446020\pi$
$252$		0			0
$253$	0.727667	−	2.23953i	0.0457480	−	0.140798i
$254$		0			0
$255$	13.1071			0.820798
$256$		0			0
$257$	19.1559	+	13.9176i	1.19491	+	0.868156i	0.993775	−	0.111406i	$-0.0355355\pi$
$257$	19.1559	+	13.9176i	1.19491	+	0.868156i	0.201140	+	0.979563i	$0.435536\pi$
$258$		0			0
$259$	−1.15980	−	3.56950i	−0.0720665	−	0.221798i
$260$		0			0
$261$	−6.64681	+	4.82919i	−0.411427	+	0.298919i
$262$		0			0
$263$	9.08677	+	6.60193i	0.560314	+	0.407092i	0.831574	−	0.555414i	$-0.187440\pi$
$263$	9.08677	+	6.60193i	0.560314	+	0.407092i	−0.271260	+	0.962506i	$0.587440\pi$
$264$		0			0
$265$	2.30459	−	7.09279i	0.141570	−	0.435707i
$266$		0			0
$267$	−1.15040	+	3.54056i	−0.0704032	+	0.216679i
$268$		0			0
$269$	−0.254916	−	0.784550i	−0.0155425	−	0.0478349i	0.942984	−	0.332837i	$-0.108006\pi$
$269$	−0.254916	−	0.784550i	−0.0155425	−	0.0478349i	−0.958527	+	0.285002i	$0.908006\pi$
$270$		0			0
$271$	0.901889	−	2.77573i	0.0547859	−	0.168614i	−0.919920	−	0.392107i	$-0.871746\pi$
$271$	0.901889	−	2.77573i	0.0547859	−	0.168614i	0.974705	+	0.223494i	$0.0717462\pi$
$272$		0			0
$273$	−3.50360			−0.212048
$274$		0			0
$275$	3.43293	−	2.49417i	0.207013	−	0.150404i
$276$		0			0
$277$	−18.0214	−	13.0933i	−1.08280	−	0.786701i	−0.104632	−	0.994511i	$-0.533366\pi$
$277$	−18.0214	−	13.0933i	−1.08280	−	0.786701i	−0.978169	+	0.207810i	$0.933366\pi$
$278$		0			0
$279$	3.79787	+	2.75931i	0.227373	+	0.165196i
$280$		0			0
$281$	7.98185	+	24.5656i	0.476157	+	1.46546i	0.844391	+	0.535728i	$0.179963\pi$
$281$	7.98185	+	24.5656i	0.476157	+	1.46546i	−0.368233	+	0.929733i	$0.620037\pi$
$282$		0			0
$283$	9.65844	−	7.01727i	0.574135	−	0.417133i	−0.262470	−	0.964940i	$-0.584537\pi$
$283$	9.65844	−	7.01727i	0.574135	−	0.417133i	0.836605	+	0.547807i	$0.184537\pi$
$284$		0			0
$285$	1.00791	+	3.10202i	0.0597033	+	0.183748i
$286$		0			0
$287$	3.49323	−	5.36631i	0.206199	−	0.316763i
$288$		0			0
$289$	2.27603	+	7.00489i	0.133884	+	0.412052i
$290$		0			0
$291$	−2.35059	+	1.70781i	−0.137794	+	0.100113i
$292$		0			0
$293$	−1.00631	−	3.09711i	−0.0587893	−	0.180935i	0.917349	−	0.398083i	$-0.130324\pi$
$293$	−1.00631	−	3.09711i	−0.0587893	−	0.180935i	−0.976139	+	0.217148i	$0.930324\pi$
$294$		0			0
$295$	−35.3845	−	25.7083i	−2.06016	−	1.49680i
$296$		0			0
$297$	3.10339	+	2.25474i	0.180077	+	0.130834i
$298$		0			0
$299$	−9.20450	+	6.68746i	−0.532310	+	0.386746i
$300$		0			0
$301$	−3.62912			−0.209179
$302$		0			0
$303$	−1.47241	+	4.53160i	−0.0845875	+	0.260334i
$304$		0			0
$305$	−9.11264	−	28.0458i	−0.521788	−	1.60590i
$306$		0			0
$307$	7.37737	−	22.7052i	0.421049	−	1.29586i	−0.485678	−	0.874138i	$-0.661427\pi$
$307$	7.37737	−	22.7052i	0.421049	−	1.29586i	0.906727	−	0.421718i	$-0.138573\pi$
$308$		0			0
$309$	−0.719498	+	2.21439i	−0.0409308	+	0.125972i
$310$		0			0
$311$	7.67575	+	5.57676i	0.435252	+	0.316229i	0.783745	−	0.621082i	$-0.213307\pi$
$311$	7.67575	+	5.57676i	0.435252	+	0.316229i	−0.348494	+	0.937311i	$0.613307\pi$
$312$		0			0
$313$	27.5092	−	19.9866i	1.55491	−	1.12971i	0.614884	−	0.788618i	$-0.289203\pi$
$313$	27.5092	−	19.9866i	1.55491	−	1.12971i	0.940030	−	0.341093i	$-0.110797\pi$
$314$		0			0
$315$	−2.23002	−	6.86330i	−0.125647	−	0.386703i
$316$		0			0
$317$	13.6110	+	9.88898i	0.764471	+	0.555421i	0.900278	−	0.435315i	$-0.143363\pi$
$317$	13.6110	+	9.88898i	0.764471	+	0.555421i	−0.135807	+	0.990735i	$0.543363\pi$
$318$		0			0
$319$	3.08755			0.172870
$320$		0			0
$321$	0.124388	−	0.382826i	0.00694265	−	0.0213673i
$322$		0			0
$323$	−4.90527	+	3.56388i	−0.272936	+	0.198300i
$324$		0			0
$325$	−20.5021			−1.13725
$326$		0			0
$327$	3.44569			0.190547
$328$		0			0
$329$	−0.224246			−0.0123631
$330$		0			0
$331$	−1.77427			−0.0975228			−0.0487614	−	0.998810i	$-0.515527\pi$
$331$	−1.77427			−0.0975228			−0.0487614	+	0.998810i	$0.515527\pi$
$332$		0			0
$333$	6.95335	−	5.05190i	0.381041	−	0.276843i
$334$		0			0
$335$	−3.29111	+	10.1290i	−0.179812	+	0.553406i
$336$		0			0
$337$	−17.7317			−0.965908			−0.482954	−	0.875646i	$-0.660436\pi$
$337$	−17.7317			−0.965908			−0.482954	+	0.875646i	$0.660436\pi$
$338$		0			0
$339$	6.16761	+	4.48103i	0.334979	+	0.243376i
$340$		0			0
$341$	−0.545159	−	1.67783i	−0.0295220	−	0.0908594i
$342$		0			0
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$		0			0
$345$	5.87806	+	4.27066i	0.316464	+	0.229924i
$346$		0			0
$347$	2.73783	−	8.42618i	0.146974	−	0.452341i	−0.850285	−	0.526322i	$-0.823571\pi$
$347$	2.73783	−	8.42618i	0.146974	−	0.452341i	0.997260	+	0.0739814i	$0.0235705\pi$
$348$		0			0
$349$	7.45672	−	22.9494i	0.399149	−	1.22845i	−0.526534	−	0.850154i	$-0.676509\pi$
$349$	7.45672	−	22.9494i	0.399149	−	1.22845i	0.925683	−	0.378300i	$-0.123491\pi$
$350$		0			0
$351$	−5.72734	−	17.6269i	−0.305703	−	0.940857i
$352$		0			0
$353$	1.90978	−	5.87769i	0.101647	−	0.312838i	−0.887282	−	0.461228i	$-0.847409\pi$
$353$	1.90978	−	5.87769i	0.101647	−	0.312838i	0.988929	+	0.148390i	$0.0474091\pi$
$354$		0			0
$355$	9.26007			0.491474
$356$		0			0
$357$	−3.36491	+	2.44475i	−0.178090	+	0.129390i
$358$		0			0
$359$	24.2062	+	17.5869i	1.27756	+	0.928199i	0.999476	−	0.0323595i	$-0.0103021\pi$
$359$	24.2062	+	17.5869i	1.27756	+	0.928199i	0.278079	+	0.960558i	$0.410302\pi$
$360$		0			0
$361$	14.1507	+	10.2811i	0.744772	+	0.541108i
$362$		0			0
$363$	2.67136	+	8.22161i	0.140210	+	0.431523i
$364$		0			0
$365$	−33.5803	+	24.3975i	−1.75767	+	1.27702i
$366$		0			0
$367$	0.510549	+	1.57131i	0.0266504	+	0.0820216i	0.963497	−	0.267719i	$-0.0862698\pi$
$367$	0.510549	+	1.57131i	0.0266504	+	0.0820216i	−0.936847	+	0.349740i	$0.886270\pi$
$368$		0			0
$369$	14.1594	+	3.81052i	0.737108	+	0.198368i
$370$		0			0
$371$	0.731311	+	2.25074i	0.0379678	+	0.116853i
$372$		0			0
$373$	5.08330	−	3.69323i	0.263203	−	0.191228i	−0.448355	−	0.893856i	$-0.647990\pi$
$373$	5.08330	−	3.69323i	0.263203	−	0.191228i	0.711558	+	0.702627i	$0.247990\pi$
$374$		0			0
$375$	−0.0568248	−	0.174889i	−0.00293442	−	0.00903122i
$376$		0			0
$377$	−12.0688	−	8.76848i	−0.621574	−	0.451600i
$378$		0			0
$379$	−6.30855	−	4.58343i	−0.324048	−	0.235435i	0.413853	−	0.910344i	$-0.364183\pi$
$379$	−6.30855	−	4.58343i	−0.324048	−	0.235435i	−0.737901	+	0.674909i	$0.764183\pi$
$380$		0			0
$381$	−6.15243	+	4.47000i	−0.315198	+	0.229005i
$382$		0			0
$383$	−8.54614			−0.436687			−0.218344	−	0.975872i	$-0.570065\pi$
$383$	−8.54614			−0.436687			−0.218344	+	0.975872i	$0.570065\pi$
$384$		0			0
$385$	−0.838045	+	2.57924i	−0.0427107	+	0.131450i
$386$		0			0
$387$	−2.56814	−	7.90393i	−0.130546	−	0.401779i
$388$		0			0
$389$	4.66717	−	14.3641i	0.236635	−	0.728288i	−0.760265	−	0.649613i	$-0.774931\pi$
$389$	4.66717	−	14.3641i	0.236635	−	0.728288i	0.996900	−	0.0786752i	$-0.0250690\pi$
$390$		0			0
$391$	−4.17374	+	12.8454i	−0.211075	+	0.649622i
$392$		0			0
$393$	−7.84329	−	5.69849i	−0.395642	−	0.287451i
$394$		0			0
$395$	5.95950	−	4.32983i	0.299855	−	0.217857i
$396$		0			0
$397$	−4.77241	−	14.6880i	−0.239520	−	0.737168i	−0.996490	−	0.0837174i	$-0.973321\pi$
$397$	−4.77241	−	14.6880i	−0.239520	−	0.737168i	0.756969	−	0.653451i	$-0.226679\pi$
$398$		0			0
$399$	−0.837346	−	0.608367i	−0.0419197	−	0.0304565i
$400$		0			0
$401$	3.85244			0.192382			0.0961908	−	0.995363i	$-0.469334\pi$
$401$	3.85244			0.192382			0.0961908	+	0.995363i	$0.469334\pi$
$402$		0			0
$403$	−2.63400	+	8.10661i	−0.131209	+	0.403819i
$404$		0			0
$405$	7.93930	−	5.76824i	0.394507	−	0.286626i
$406$		0			0
$407$	−3.22994			−0.160102
$408$		0			0
$409$	6.25030			0.309057			0.154529	−	0.987988i	$-0.450614\pi$
$409$	6.25030			0.309057			0.154529	+	0.987988i	$0.450614\pi$
$410$		0			0
$411$	9.96949			0.491758
$412$		0			0
$413$	13.8792			0.682950
$414$		0			0
$415$	33.9073	−	24.6351i	1.66444	−	1.20929i
$416$		0			0
$417$	1.33653	−	4.11341i	0.0654500	−	0.201434i
$418$		0			0
$419$	−24.8624			−1.21461			−0.607303	−	0.794471i	$-0.707748\pi$
$419$	−24.8624			−1.21461			−0.607303	+	0.794471i	$0.707748\pi$
$420$		0			0
$421$	−23.4838	−	17.0620i	−1.14453	−	0.831551i	−0.156787	−	0.987632i	$-0.550114\pi$
$421$	−23.4838	−	17.0620i	−1.14453	−	0.831551i	−0.987744	+	0.156081i	$0.950114\pi$
$422$		0			0
$423$	−0.158687	−	0.488390i	−0.00771565	−	0.0237463i
$424$		0			0
$425$	−19.6905	+	14.3060i	−0.955130	+	0.693943i
$426$		0			0
$427$	7.57057	+	5.50034i	0.366365	+	0.266180i
$428$		0			0
$429$	−0.931733	+	2.86758i	−0.0449845	+	0.138448i
$430$		0			0
$431$	−8.08845	+	24.8937i	−0.389607	+	1.19909i	0.543475	+	0.839425i	$0.317108\pi$
$431$	−8.08845	+	24.8937i	−0.389607	+	1.19909i	−0.933083	+	0.359662i	$0.882892\pi$
$432$		0			0
$433$	1.70932	+	5.26075i	0.0821447	+	0.252815i	0.983691	−	0.179868i	$-0.0575669\pi$
$433$	1.70932	+	5.26075i	0.0821447	+	0.252815i	−0.901546	+	0.432683i	$0.857567\pi$
$434$		0			0
$435$	−2.94389	+	9.06037i	−0.141149	+	0.434411i
$436$		0			0
$437$	−3.36105			−0.160781
$438$		0			0
$439$	10.8042	−	7.84970i	0.515656	−	0.374646i	−0.299309	−	0.954156i	$-0.596756\pi$
$439$	10.8042	−	7.84970i	0.515656	−	0.374646i	0.814965	+	0.579510i	$0.196756\pi$
$440$		0			0
$441$	1.85265	+	1.34603i	0.0882214	+	0.0640966i
$442$		0			0
$443$	8.94435	+	6.49845i	0.424959	+	0.308751i	0.779630	−	0.626240i	$-0.215407\pi$
$443$	8.94435	+	6.49845i	0.424959	+	0.308751i	−0.354671	+	0.934991i	$0.615407\pi$
$444$		0			0
$445$	−4.30239	−	13.2414i	−0.203953	−	0.627703i
$446$		0			0
$447$	−8.15927	+	5.92806i	−0.385920	+	0.280388i
$448$		0			0
$449$	−6.35375	−	19.5548i	−0.299852	−	0.922849i	−0.981548	−	0.191214i	$-0.938758\pi$
$449$	−6.35375	−	19.5548i	−0.299852	−	0.922849i	0.681697	−	0.731635i	$-0.261242\pi$
$450$		0			0
$451$	−3.46317	−	4.28619i	−0.163074	−	0.201829i
$452$		0			0
$453$	−0.522352	−	1.60763i	−0.0245422	−	0.0755332i
$454$		0			0
$455$	10.6007	−	7.70186i	0.496969	−	0.361069i
$456$		0			0
$457$	−6.50065	−	20.0069i	−0.304088	−	0.935885i	−0.980016	−	0.198918i	$-0.936257\pi$
$457$	−6.50065	−	20.0069i	−0.304088	−	0.935885i	0.675929	−	0.736967i	$-0.263743\pi$
$458$		0			0
$459$	−17.8004	−	12.9327i	−0.830850	−	0.603648i
$460$		0			0
$461$	−6.27253	−	4.55726i	−0.292141	−	0.212253i	0.432055	−	0.901847i	$-0.357789\pi$
$461$	−6.27253	−	4.55726i	−0.292141	−	0.212253i	−0.724196	+	0.689595i	$0.757789\pi$
$462$		0			0
$463$	−6.76652	+	4.91617i	−0.314467	+	0.228474i	−0.733811	−	0.679354i	$-0.762260\pi$
$463$	−6.76652	+	4.91617i	−0.314467	+	0.228474i	0.419344	+	0.907827i	$0.362260\pi$
$464$		0			0
$465$	5.44335			0.252430
$466$		0			0
$467$	−8.39198	+	25.8278i	−0.388334	+	1.19517i	0.545698	+	0.837982i	$0.316265\pi$
$467$	−8.39198	+	25.8278i	−0.388334	+	1.19517i	−0.934032	+	0.357188i	$0.883735\pi$
$468$		0			0
$469$	−1.04436	−	3.21422i	−0.0482242	−	0.148419i
$470$		0			0
$471$	4.66562	−	14.3593i	0.214980	−	0.661641i
$472$		0			0
$473$	−0.965111	+	2.97031i	−0.0443759	+	0.136575i
$474$		0			0
$475$	−4.89992	−	3.56000i	−0.224824	−	0.163344i
$476$		0			0
$477$	−4.38443	+	3.18548i	−0.200749	+	0.145853i
$478$		0			0
$479$	10.4574	+	32.1845i	0.477810	+	1.47055i	0.842130	+	0.539275i	$0.181302\pi$
$479$	10.4574	+	32.1845i	0.477810	+	1.47055i	−0.364319	+	0.931274i	$0.618698\pi$
$480$		0			0
$481$	12.6254	+	9.17288i	0.575668	+	0.418247i
$482$		0			0
$483$	−2.30561			−0.104909
$484$		0			0
$485$	3.35787	−	10.3345i	0.152473	−	0.469264i
$486$		0			0
$487$	2.23903	−	1.62675i	0.101460	−	0.0737151i	−0.535898	−	0.844282i	$-0.680027\pi$
$487$	2.23903	−	1.62675i	0.101460	−	0.0737151i	0.637359	+	0.770567i	$0.280027\pi$
$488$		0			0
$489$	9.70023			0.438659
$490$		0			0
$491$	5.28764			0.238628			0.119314	−	0.992857i	$-0.461930\pi$
$491$	5.28764			0.238628			0.119314	+	0.992857i	$0.461930\pi$
$492$		0			0
$493$	−17.7095			−0.797596
$494$		0			0
$495$	−6.21042			−0.279137
$496$		0			0
$497$	−2.37728	+	1.72720i	−0.106636	+	0.0774754i
$498$		0			0
$499$	−7.99239	+	24.5981i	−0.357789	+	1.10116i	0.596586	+	0.802549i	$0.296523\pi$
$499$	−7.99239	+	24.5981i	−0.357789	+	1.10116i	−0.954375	+	0.298611i	$0.903477\pi$
$500$		0			0
$501$	10.5533			0.471488
$502$		0			0
$503$	−3.47576	−	2.52529i	−0.154977	−	0.112597i	0.507595	−	0.861596i	$-0.330535\pi$
$503$	−3.47576	−	2.52529i	−0.154977	−	0.112597i	−0.662571	+	0.748999i	$0.730535\pi$
$504$		0			0
$505$	−5.50668	−	16.9478i	−0.245044	−	0.754168i
$506$		0			0
$507$	2.92383	−	2.12429i	0.129852	−	0.0943429i
$508$		0			0
$509$	3.74312	+	2.71954i	0.165911	+	0.120541i	0.667643	−	0.744482i	$-0.267303\pi$
$509$	3.74312	+	2.71954i	0.165911	+	0.120541i	−0.501732	+	0.865023i	$0.667303\pi$
$510$		0			0
$511$	4.07022	−	12.5269i	0.180056	−	0.554155i
$512$		0			0
$513$	1.69194	−	5.20726i	0.0747010	−	0.229906i
$514$		0			0
$515$	−2.69087	−	8.28163i	−0.118574	−	0.364932i
$516$		0			0
$517$	−0.0596350	+	0.183538i	−0.00262274	+	0.00807197i
$518$		0			0
$519$	−19.7741			−0.867986
$520$		0			0
$521$	0.363110	−	0.263815i	0.0159081	−	0.0115579i	−0.579803	−	0.814757i	$-0.696870\pi$
$521$	0.363110	−	0.263815i	0.0159081	−	0.0115579i	0.595711	+	0.803199i	$0.296870\pi$
$522$		0			0
$523$	24.6501	+	17.9094i	1.07788	+	0.783122i	0.977311	−	0.211808i	$-0.0679352\pi$
$523$	24.6501	+	17.9094i	1.07788	+	0.783122i	0.100564	+	0.994931i	$0.467935\pi$
$524$		0			0
$525$	−3.36124	−	2.44208i	−0.146696	−	0.106581i
$526$		0			0
$527$	3.12691	+	9.62365i	0.136210	+	0.419213i
$528$		0			0
$529$	12.5502	−	9.11827i	0.545662	−	0.396446i
$530$		0			0
$531$	9.82160	+	30.2278i	0.426221	+	1.31177i
$532$		0			0
$533$	1.36447	+	26.5893i	0.0591016	+	1.15171i
$534$		0			0
$535$	0.465200	+	1.43174i	0.0201123	+	0.0618994i
$536$		0			0
$537$	13.1641	−	9.56425i	0.568071	−	0.412728i
$538$		0			0
$539$	−0.265936	−	0.818466i	−0.0114547	−	0.0352538i
$540$		0			0
$541$	−30.1261	−	21.8879i	−1.29522	−	0.941034i	−0.295326	−	0.955397i	$-0.595428\pi$
$541$	−30.1261	−	21.8879i	−1.29522	−	0.941034i	−0.999897	+	0.0143620i	$0.995428\pi$
$542$		0			0
$543$	−15.1804	−	11.0292i	−0.651452	−	0.473307i
$544$		0			0
$545$	−10.4255	+	7.57454i	−0.446578	+	0.324458i
$546$		0			0
$547$	−40.9132			−1.74932			−0.874660	−	0.484737i	$-0.838915\pi$
$547$	−40.9132			−1.74932			−0.874660	+	0.484737i	$0.838915\pi$
$548$		0			0
$549$	−6.62200	+	20.3804i	−0.282620	+	0.869815i
$550$		0			0
$551$	−1.36182	−	4.19126i	−0.0580156	−	0.178554i
$552$		0			0
$553$	−0.722343	+	2.22314i	−0.0307172	+	0.0945377i
$554$		0			0
$555$	3.07966	−	9.47822i	0.130724	−	0.402328i
$556$		0			0
$557$	−13.8548	−	10.0661i	−0.587046	−	0.426514i	0.254211	−	0.967149i	$-0.418184\pi$
$557$	−13.8548	−	10.0661i	−0.587046	−	0.426514i	−0.841257	+	0.540635i	$0.818184\pi$
$558$		0			0
$559$	12.2080	−	8.86964i	0.516344	−	0.375146i
$560$		0			0
$561$	1.10609	+	3.40421i	0.0466993	+	0.143726i
$562$		0			0
$563$	−30.7170	−	22.3172i	−1.29457	−	0.940558i	−0.294679	−	0.955596i	$-0.595213\pi$
$563$	−30.7170	−	22.3172i	−1.29457	−	0.940558i	−0.999887	+	0.0150386i	$0.995213\pi$
$564$		0			0
$565$	−28.5116			−1.19949
$566$		0			0
$567$	−0.962313	+	2.96169i	−0.0404133	+	0.124379i
$568$		0			0
$569$	20.7191	−	15.0533i	0.868588	−	0.631066i	−0.0616193	−	0.998100i	$-0.519626\pi$
$569$	20.7191	−	15.0533i	0.868588	−	0.631066i	0.930208	+	0.367033i	$0.119626\pi$
$570$		0			0
$571$	8.56866			0.358587			0.179294	−	0.983796i	$-0.442619\pi$
$571$	8.56866			0.358587			0.179294	+	0.983796i	$0.442619\pi$
$572$		0			0
$573$	−16.6723			−0.696493
$574$		0			0
$575$	−13.4918			−0.562646
$576$		0			0
$577$	−10.9886			−0.457463			−0.228731	−	0.973490i	$-0.573458\pi$
$577$	−10.9886			−0.457463			−0.228731	+	0.973490i	$0.573458\pi$
$578$		0			0
$579$	0.0582301	−	0.0423066i	0.00241996	−	0.00175820i
$580$		0			0
$581$	−4.10986	+	12.6488i	−0.170506	+	0.524762i
$582$		0			0
$583$	2.03664			0.0843490
$584$		0			0
$585$	24.2756	+	17.6373i	1.00367	+	0.729212i
$586$		0			0
$587$	3.94442	+	12.1397i	0.162804	+	0.501059i	0.998868	−	0.0475734i	$-0.0151488\pi$
$587$	3.94442	+	12.1397i	0.162804	+	0.501059i	−0.836064	+	0.548632i	$0.815149\pi$
$588$		0			0
$589$	−2.03715	+	1.48008i	−0.0839393	+	0.0609854i
$590$		0			0
$591$	4.97275	+	3.61291i	0.204552	+	0.148615i
$592$		0			0
$593$	4.16005	−	12.8033i	0.170833	−	0.525769i	−0.828586	−	0.559862i	$-0.810854\pi$
$593$	4.16005	−	12.8033i	0.170833	−	0.525769i	0.999419	+	0.0340929i	$0.0108542\pi$
$594$		0			0
$595$	4.80684	−	14.7939i	0.197061	−	0.606492i
$596$		0			0
$597$	−4.46537	−	13.7430i	−0.182755	−	0.562463i
$598$		0			0
$599$	−7.23816	+	22.2768i	−0.295743	+	0.910205i	0.687227	+	0.726442i	$0.258828\pi$
$599$	−7.23816	+	22.2768i	−0.295743	+	0.910205i	−0.982971	+	0.183762i	$0.941172\pi$
$600$		0			0
$601$	26.8365			1.09468			0.547342	−	0.836909i	$-0.315640\pi$
$601$	26.8365			1.09468			0.547342	+	0.836909i	$0.315640\pi$
$602$		0			0
$603$	6.26126	−	4.54907i	0.254978	−	0.185253i
$604$		0			0
$605$	−26.1559	−	19.0034i	−1.06339	−	0.772598i
$606$		0			0
$607$	−36.8008	−	26.7374i	−1.49370	−	1.08524i	−0.972808	−	0.231615i	$-0.925599\pi$
$607$	−36.8008	−	26.7374i	−1.49370	−	1.08524i	−0.520893	−	0.853622i	$-0.674401\pi$
$608$		0			0
$609$	−0.934181	−	2.87511i	−0.0378549	−	0.116505i
$610$		0			0
$611$	0.754342	−	0.548062i	0.0305174	−	0.0221722i
$612$		0			0
$613$	−1.23029	−	3.78645i	−0.0496910	−	0.152933i	0.923132	−	0.384483i	$-0.125620\pi$
$613$	−1.23029	−	3.78645i	−0.0496910	−	0.152933i	−0.972823	+	0.231550i	$0.925620\pi$
$614$		0			0
$615$	15.8798	−	6.07585i	0.640335	−	0.245002i
$616$		0			0
$617$	2.36430	+	7.27657i	0.0951831	+	0.292944i	0.987301	−	0.158858i	$-0.0507813\pi$
$617$	2.36430	+	7.27657i	0.0951831	+	0.292944i	−0.892118	+	0.451802i	$0.850781\pi$
$618$		0			0
$619$	33.2238	−	24.1385i	1.33538	−	0.970208i	0.335776	−	0.941942i	$-0.391001\pi$
$619$	33.2238	−	24.1385i	1.33538	−	0.970208i	0.999600	−	0.0282663i	$-0.00899864\pi$
$620$		0			0
$621$	−3.76897	−	11.5997i	−0.151244	−	0.465480i
$622$		0			0
$623$	3.57433	+	2.59690i	0.143202	+	0.104043i
$624$		0			0
$625$	20.5017	+	14.8953i	0.820067	+	0.595814i
$626$		0			0
$627$	−0.720608	+	0.523552i	−0.0287783	+	0.0209087i
$628$		0			0
$629$	18.5262			0.738690
$630$		0			0
$631$	3.87406	−	11.9231i	0.154224	−	0.474652i	−0.843858	−	0.536567i	$-0.819721\pi$
$631$	3.87406	−	11.9231i	0.154224	−	0.474652i	0.998081	+	0.0619153i	$0.0197209\pi$
$632$		0			0
$633$	−0.708288	−	2.17989i	−0.0281519	−	0.0866427i
$634$		0			0
$635$	8.78887	−	27.0494i	0.348776	−	1.07342i
$636$		0			0
$637$	−1.28490	+	3.95451i	−0.0509095	+	0.156683i
$638$		0			0
$639$	−5.44398	−	3.95529i	−0.215361	−	0.156469i
$640$		0			0
$641$	20.5950	−	14.9631i	0.813454	−	0.591009i	−0.101376	−	0.994848i	$-0.532325\pi$
$641$	20.5950	−	14.9631i	0.813454	−	0.591009i	0.914830	+	0.403840i	$0.132325\pi$
$642$		0			0
$643$	−4.83408	−	14.8778i	−0.190638	−	0.586722i	0.809362	−	0.587310i	$-0.199813\pi$
$643$	−4.83408	−	14.8778i	−0.190638	−	0.586722i	−1.00000		0.000587570i	$0.999813\pi$
$644$		0			0
$645$	−7.79612	−	5.66421i	−0.306972	−	0.223028i
$646$		0			0
$647$	−38.2019			−1.50187			−0.750936	−	0.660375i	$-0.770397\pi$
$647$	−38.2019			−1.50187			−0.750936	+	0.660375i	$0.770397\pi$
$648$		0			0
$649$	3.69097	−	11.3596i	0.144883	−	0.445905i
$650$		0			0
$651$	−1.39744	+	1.01530i	−0.0547700	+	0.0397927i
$652$		0			0
$653$	−5.68140			−0.222330			−0.111165	−	0.993802i	$-0.535458\pi$
$653$	−5.68140			−0.222330			−0.111165	+	0.993802i	$0.535458\pi$
$654$		0			0
$655$	36.2579			1.41671
$656$		0			0
$657$	30.1628			1.17676
$658$		0			0
$659$	20.1127			0.783479			0.391740	−	0.920076i	$-0.371873\pi$
$659$	20.1127			0.783479			0.391740	+	0.920076i	$0.371873\pi$
$660$		0			0
$661$	−14.5696	+	10.5854i	−0.566692	+	0.411726i	−0.833902	−	0.551913i	$-0.813898\pi$
$661$	−14.5696	+	10.5854i	−0.566692	+	0.411726i	0.267210	+	0.963638i	$0.413898\pi$
$662$		0			0
$663$	5.34421	−	16.4478i	0.207552	−	0.638780i
$664$		0			0
$665$	3.87088			0.150106
$666$		0			0
$667$	−7.94207	−	5.77025i	−0.307518	−	0.223425i
$668$		0			0
$669$	1.13196	+	3.48383i	0.0437642	+	0.134692i
$670$		0			0
$671$	6.51512	−	4.73351i	0.251513	−	0.182735i
$672$		0			0
$673$	7.38494	+	5.36547i	0.284668	+	0.206824i	0.720951	−	0.692986i	$-0.243705\pi$
$673$	7.38494	+	5.36547i	0.284668	+	0.206824i	−0.436283	+	0.899810i	$0.643705\pi$
$674$		0			0
$675$	6.79172	−	20.9028i	0.261413	−	0.804548i
$676$		0			0
$677$	0.423412	−	1.30313i	0.0162730	−	0.0500833i	−0.942590	−	0.333951i	$-0.891618\pi$
$677$	0.423412	−	1.30313i	0.0162730	−	0.0500833i	0.958863	+	0.283868i	$0.0916178\pi$
$678$		0			0
$679$	1.06555	+	3.27942i	0.0408920	+	0.125853i
$680$		0			0
$681$	5.13765	−	15.8121i	0.196875	−	0.605920i
$682$		0			0
$683$	11.2574			0.430751			0.215376	−	0.976531i	$-0.430902\pi$
$683$	11.2574			0.430751			0.215376	+	0.976531i	$0.430902\pi$
$684$		0			0
$685$	−30.1643	+	21.9156i	−1.15252	+	0.837353i
$686$		0			0
$687$	−2.28919	−	1.66319i	−0.0873380	−	0.0634548i
$688$		0			0
$689$	−7.96093	−	5.78395i	−0.303287	−	0.220351i
$690$		0			0
$691$	−1.21966	−	3.75373i	−0.0463981	−	0.142799i	0.925174	−	0.379544i	$-0.123919\pi$
$691$	−1.21966	−	3.75373i	−0.0463981	−	0.142799i	−0.971572	+	0.236746i	$0.923919\pi$
$692$		0			0
$693$	1.59436	−	1.15837i	0.0605649	−	0.0440030i
$694$		0			0
$695$	4.99850	+	15.3838i	0.189604	+	0.583541i
$696$		0			0
$697$	19.8640	+	24.5846i	0.752401	+	0.931209i
$698$		0			0
$699$	−4.83038	−	14.8664i	−0.182702	−	0.562298i
$700$		0			0
$701$	25.5344	−	18.5518i	0.964422	−	0.700693i	0.0102482	−	0.999947i	$-0.496738\pi$
$701$	25.5344	−	18.5518i	0.964422	−	0.700693i	0.954173	+	0.299254i	$0.0967378\pi$
$702$		0			0
$703$	1.42463	+	4.38455i	0.0537309	+	0.165367i
$704$		0			0
$705$	−0.481728	−	0.349996i	−0.0181429	−	0.0131816i
$706$		0			0
$707$	4.57482	+	3.32380i	0.172054	+	0.125004i
$708$		0			0
$709$	−19.5435	+	14.1992i	−0.733972	+	0.533262i	−0.890817	−	0.454361i	$-0.849867\pi$
$709$	−19.5435	+	14.1992i	−0.733972	+	0.533262i	0.156846	+	0.987623i	$0.449867\pi$
$710$		0			0
$711$	−5.35300			−0.200753
$712$		0			0
$713$	−1.73335	+	5.33469i	−0.0649144	+	0.199786i
$714$		0			0
$715$	−3.48460	−	10.7245i	−0.130317	−	0.401074i
$716$		0			0
$717$	3.84831	−	11.8439i	0.143718	−	0.442318i
$718$		0			0
$719$	3.51843	−	10.8286i	0.131215	−	0.403839i	−0.863767	−	0.503892i	$-0.831901\pi$
$719$	3.51843	−	10.8286i	0.131215	−	0.403839i	0.994982	+	0.100053i	$0.0319011\pi$
$720$		0			0
$721$	2.23551	+	1.62419i	0.0832547	+	0.0604881i
$722$		0			0
$723$	−13.7103	+	9.96113i	−0.509892	+	0.370459i
$724$		0			0
$725$	−5.46657	−	16.8244i	−0.203023	−	0.624841i
$726$		0			0
$727$	−41.5683	−	30.2011i	−1.54168	−	1.12010i	−0.949269	−	0.314464i	$-0.898175\pi$
$727$	−41.5683	−	30.2011i	−1.54168	−	1.12010i	−0.592413	−	0.805634i	$-0.701825\pi$
$728$		0			0
$729$	4.13637			0.153199
$730$		0			0
$731$	5.53567	−	17.0370i	0.204744	−	0.630137i
$732$		0			0
$733$	−10.0283	+	7.28600i	−0.370404	+	0.269115i	−0.757379	−	0.652976i	$-0.773520\pi$
$733$	−10.0283	+	7.28600i	−0.370404	+	0.269115i	0.386974	+	0.922091i	$0.373520\pi$
$734$		0			0
$735$	2.65534			0.0979436
$736$		0			0
$737$	−2.90846			−0.107134
$738$		0			0
$739$	−53.1562			−1.95538			−0.977691	−	0.210050i	$-0.932637\pi$
$739$	−53.1562			−1.95538			−0.977691	+	0.210050i	$0.932637\pi$
$740$		0			0
$741$	4.30361			0.158097
$742$		0			0
$743$	41.0024	−	29.7900i	1.50423	−	1.09289i	0.535573	−	0.844489i	$-0.320096\pi$
$743$	41.0024	−	29.7900i	1.50423	−	1.09289i	0.968658	−	0.248399i	$-0.0799043\pi$
$744$		0			0
$745$	11.6557	−	35.8726i	0.427032	−	1.31427i
$746$		0			0
$747$	−30.4565			−1.11435
$748$		0			0
$749$	−0.386477	−	0.280792i	−0.0141216	−	0.0102599i
$750$		0			0
$751$	−13.1820	−	40.5701i	−0.481019	−	1.48042i	−0.837665	−	0.546184i	$-0.816080\pi$
$751$	−13.1820	−	40.5701i	−0.481019	−	1.48042i	0.356646	−	0.934240i	$-0.383920\pi$
$752$		0			0
$753$	−15.5303	+	11.2834i	−0.565955	+	0.411191i
$754$		0			0
$755$	5.11447	+	3.71588i	0.186135	+	0.135235i
$756$		0			0
$757$	1.29825	−	3.99560i	0.0471857	−	0.145223i	−0.924688	−	0.380726i	$-0.875674\pi$
$757$	1.29825	−	3.99560i	0.0471857	−	0.145223i	0.971873	+	0.235504i	$0.0756740\pi$
$758$		0			0
$759$	−0.613143	+	1.88706i	−0.0222557	+	0.0684959i
$760$		0			0
$761$	0.890249	+	2.73991i	0.0322715	+	0.0993215i	0.965895	−	0.258935i	$-0.0833714\pi$
$761$	0.890249	+	2.73991i	0.0322715	+	0.0993215i	−0.933623	+	0.358256i	$0.883371\pi$
$762$		0			0
$763$	1.26366	−	3.88914i	0.0457475	−	0.140796i
$764$		0			0
$765$	35.6216			1.28790
$766$		0			0
$767$	−46.6883	+	33.9210i	−1.68582	+	1.22482i
$768$		0			0
$769$	−7.68094	−	5.58053i	−0.276982	−	0.201239i	0.440618	−	0.897695i	$-0.354759\pi$
$769$	−7.68094	−	5.58053i	−0.276982	−	0.201239i	−0.717600	+	0.696456i	$0.754759\pi$
$770$		0			0
$771$	−16.1411	−	11.7272i	−0.581306	−	0.422344i
$772$		0			0
$773$	9.62711	+	29.6292i	0.346263	+	1.06569i	0.960904	+	0.276881i	$0.0893009\pi$
$773$	9.62711	+	29.6292i	0.346263	+	1.06569i	−0.614641	+	0.788807i	$0.710699\pi$
$774$		0			0
$775$	−8.17744	+	5.94126i	−0.293742	+	0.213416i
$776$		0			0
$777$	0.977264	+	3.00771i	0.0350592	+	0.107901i
$778$		0			0
$779$	−4.29088	+	6.59165i	−0.153737	+	0.236170i
$780$		0			0
$781$	0.781448	+	2.40505i	0.0279624	+	0.0860594i
$782$		0			0
$783$	12.9378	−	9.39989i	0.462361	−	0.335925i
$784$		0			0
$785$	17.4490	+	53.7026i	0.622783	+	1.91673i
$786$		0			0
$787$	−25.1777	−	18.2926i	−0.897487	−	0.652063i	0.0403323	−	0.999186i	$-0.487158\pi$
$787$	−25.1777	−	18.2926i	−0.897487	−	0.652063i	−0.937819	+	0.347124i	$0.887158\pi$
$788$		0			0
$789$	−7.65664	−	5.56288i	−0.272584	−	0.198044i
$790$		0			0
$791$	7.31961	−	5.31801i	0.260256	−	0.189087i
$792$		0			0
$793$	−38.9096			−1.38172
$794$		0			0
$795$	−1.94188	+	5.97649i	−0.0688713	+	0.211964i
$796$		0			0
$797$	4.44678	+	13.6858i	0.157513	+	0.484775i	0.998407	−	0.0564250i	$-0.0179702\pi$
$797$	4.44678	+	13.6858i	0.157513	+	0.484775i	−0.840894	+	0.541200i	$0.817970\pi$
$798$		0			0
$799$	0.342053	−	1.05273i	0.0121010	−	0.0372430i
$800$		0			0
$801$	−3.12647	+	9.62230i	−0.110469	+	0.339987i
$802$		0			0
$803$	−9.17038	−	6.66267i	−0.323616	−	0.235121i
$804$		0			0
$805$	6.97597	−	5.06834i	0.245871	−	0.178636i
$806$		0			0
$807$	0.214796	+	0.661073i	0.00756116	+	0.0232709i
$808$		0			0
$809$	6.93734	+	5.04027i	0.243904	+	0.177207i	0.703021	−	0.711169i	$-0.251834\pi$
$809$	6.93734	+	5.04027i	0.243904	+	0.177207i	−0.459117	+	0.888376i	$0.651834\pi$
$810$		0			0
$811$	52.6637			1.84927			0.924637	−	0.380851i	$-0.124369\pi$
$811$	52.6637			1.84927			0.924637	+	0.380851i	$0.124369\pi$
$812$		0			0
$813$	−0.759945	+	2.33887i	−0.0266524	+	0.0820277i
$814$		0			0
$815$	−29.3496	+	21.3237i	−1.02807	+	0.746937i
$816$		0			0
$817$	4.45779			0.155958
$818$		0			0
$819$	−9.52186			−0.332721
$820$		0			0
$821$	20.1200			0.702192			0.351096	−	0.936339i	$-0.385809\pi$
$821$	20.1200			0.702192			0.351096	+	0.936339i	$0.385809\pi$
$822$		0			0
$823$	−31.4812			−1.09736			−0.548682	−	0.836031i	$-0.684870\pi$
$823$	−31.4812			−1.09736			−0.548682	+	0.836031i	$0.684870\pi$
$824$		0			0
$825$	−2.89263	+	2.10162i	−0.100709	+	0.0731690i
$826$		0			0
$827$	5.15944	−	15.8791i	0.179411	−	0.552172i	−0.820396	−	0.571796i	$-0.806247\pi$
$827$	5.15944	−	15.8791i	0.179411	−	0.552172i	0.999807	+	0.0196242i	$0.00624697\pi$
$828$		0			0
$829$	−43.6618			−1.51644			−0.758219	−	0.652000i	$-0.773930\pi$
$829$	−43.6618			−1.51644			−0.758219	+	0.652000i	$0.773930\pi$
$830$		0			0
$831$	15.1851	+	11.0326i	0.526765	+	0.382717i
$832$		0			0
$833$	1.52535	+	4.69454i	0.0528502	+	0.162656i
$834$		0			0
$835$	−31.9307	+	23.1990i	−1.10501	+	0.802836i
$836$		0			0
$837$	−7.39246	−	5.37094i	−0.255521	−	0.185647i
$838$		0			0
$839$	12.6735	−	39.0051i	0.437539	−	1.34661i	−0.452924	−	0.891549i	$-0.649619\pi$
$839$	12.6735	−	39.0051i	0.437539	−	1.34661i	0.890463	−	0.455056i	$-0.150381\pi$
$840$		0			0
$841$	−4.98389	+	15.3388i	−0.171858	+	0.528925i
$842$		0			0
$843$	−6.72562	−	20.6993i	−0.231643	−	0.712923i
$844$		0			0
$845$	−4.17675	+	12.8547i	−0.143685	+	0.442216i
$846$		0			0
$847$	10.2594			0.352517
$848$		0			0
$849$	−8.13834	+	5.91285i	−0.279307	+	0.202928i
$850$		0			0
$851$	8.30835	+	6.03637i	0.284806	+	0.206924i
$852$		0			0
$853$	0.781005	+	0.567433i	0.0267411	+	0.0194285i	0.601076	−	0.799192i	$-0.294739\pi$
$853$	0.781005	+	0.567433i	0.0267411	+	0.0194285i	−0.574334	+	0.818621i	$0.694739\pi$
$854$		0			0
$855$	2.73922	+	8.43046i	0.0936794	+	0.288316i
$856$		0			0
$857$	0.414216	−	0.300946i	0.0141494	−	0.0102801i	−0.580688	−	0.814126i	$-0.697216\pi$
$857$	0.414216	−	0.300946i	0.0141494	−	0.0102801i	0.594837	+	0.803846i	$0.297216\pi$
$858$		0			0
$859$	13.0986	+	40.3135i	0.446920	+	1.37548i	0.880365	+	0.474298i	$0.157298\pi$
$859$	13.0986	+	40.3135i	0.446920	+	1.37548i	−0.433445	+	0.901180i	$0.642702\pi$
$860$		0			0
$861$	−2.94345	+	4.52173i	−0.100312	+	0.154100i
$862$		0			0
$863$	−6.15231	−	18.9349i	−0.209427	−	0.644550i	−0.999502	−	0.0315407i	$-0.989959\pi$
$863$	−6.15231	−	18.9349i	−0.209427	−	0.644550i	0.790075	−	0.613010i	$-0.210041\pi$
$864$		0			0
$865$	59.8296	−	43.4687i	2.03427	−	1.47798i
$866$		0			0
$867$	−1.91781	−	5.90242i	−0.0651323	−	0.200457i
$868$		0			0
$869$	1.62747	+	1.18243i	0.0552081	+	0.0401111i
$870$		0			0
$871$	11.3687	+	8.25988i	0.385215	+	0.279875i
$872$		0			0
$873$	−6.38828	+	4.64136i	−0.216211	+	0.157086i
$874$		0			0
$875$	−0.218236			−0.00737773
$876$		0			0
$877$	−5.45680	+	16.7943i	−0.184263	+	0.567103i	−0.999935	−	0.0114117i	$-0.996367\pi$
$877$	−5.45680	+	16.7943i	−0.184263	+	0.567103i	0.815672	+	0.578515i	$0.196367\pi$
$878$		0			0
$879$	0.847932	+	2.60967i	0.0286001	+	0.0880219i
$880$		0			0
$881$	7.38110	−	22.7167i	0.248676	−	0.765345i	−0.746335	−	0.665571i	$-0.768188\pi$
$881$	7.38110	−	22.7167i	0.248676	−	0.765345i	0.995010	−	0.0997738i	$-0.0318119\pi$
$882$		0			0
$883$	−14.5158	+	44.6750i	−0.488496	+	1.50343i	0.338358	+	0.941018i	$0.390129\pi$
$883$	−14.5158	+	44.6750i	−0.488496	+	1.50343i	−0.826853	+	0.562417i	$0.809871\pi$
$884$		0			0
$885$	29.8155	+	21.6622i	1.00224	+	0.728167i
$886$		0			0
$887$	−11.1579	+	8.10672i	−0.374647	+	0.272197i	−0.759135	−	0.650933i	$-0.774378\pi$
$887$	−11.1579	+	8.10672i	−0.374647	+	0.272197i	0.384488	+	0.923130i	$0.374378\pi$
$888$		0			0
$889$	2.78896	+	8.58354i	0.0935387	+	0.287883i
$890$		0			0
$891$	2.16813	+	1.57524i	0.0726351	+	0.0527725i
$892$		0			0
$893$	0.275450			0.00921759
$894$		0			0
$895$	−18.8051	+	57.8763i	−0.628587	+	1.93459i
$896$		0			0
$897$	7.75584	−	5.63495i	0.258960	−	0.188145i
$898$		0			0
$899$	−7.35473			−0.245294
$900$		0			0
$901$	−11.6817			−0.389174
$902$		0			0
$903$	3.05795			0.101762
$904$		0			0
$905$	70.1757			2.33272
$906$		0			0
$907$	37.7770	−	27.4466i	1.25437	−	0.911350i	0.255899	−	0.966703i	$-0.417628\pi$
$907$	37.7770	−	27.4466i	1.25437	−	0.911350i	0.998467	+	0.0553533i	$0.0176285\pi$
$908$		0			0
$909$	−4.00161	+	12.3157i	−0.132725	+	0.408485i
$910$		0			0
$911$	29.0566			0.962688			0.481344	−	0.876532i	$-0.340149\pi$
$911$	29.0566			0.962688			0.481344	+	0.876532i	$0.340149\pi$
$912$		0			0
$913$	9.25969	+	6.72756i	0.306451	+	0.222650i
$914$		0			0
$915$	7.67844	+	23.6318i	0.253841	+	0.781243i
$916$		0			0
$917$	−9.30829	+	6.76287i	−0.307387	+	0.223330i
$918$		0			0
$919$	−36.3560	−	26.4142i	−1.19927	−	0.871323i	−0.205060	−	0.978749i	$-0.565739\pi$
$919$	−36.3560	−	26.4142i	−1.19927	−	0.871323i	−0.994213	+	0.107427i	$0.965739\pi$
$920$		0			0
$921$	−6.21628	+	19.1317i	−0.204833	+	0.630412i
$922$		0			0
$923$	3.77565	−	11.6203i	0.124277	−	0.382486i
$924$		0			0
$925$	5.71868	+	17.6003i	0.188029	+	0.578694i
$926$		0			0
$927$	−1.95540	+	6.01812i	−0.0642239	+	0.197661i
$928$		0			0
$929$	36.0351			1.18227			0.591137	−	0.806571i	$-0.298679\pi$
$929$	36.0351			1.18227			0.591137	+	0.806571i	$0.298679\pi$
$930$		0			0
$931$	−0.993747	+	0.722000i	−0.0325688	+	0.0236626i
$932$		0			0
$933$	−6.46770	−	4.69906i	−0.211743	−	0.153840i
$934$		0			0
$935$	−10.8300	−	7.86847i	−0.354180	−	0.257327i
$936$		0			0
$937$	10.7324	+	33.0311i	0.350614	+	1.07908i	0.958509	+	0.285061i	$0.0920138\pi$
$937$	10.7324	+	33.0311i	0.350614	+	1.07908i	−0.607896	+	0.794017i	$0.707986\pi$
$938$		0			0
$939$	−23.1797	+	16.8410i	−0.756440	+	0.549586i
$940$		0			0
$941$	2.68494	+	8.26338i	0.0875264	+	0.269379i	0.985234	−	0.171213i	$-0.0547687\pi$
$941$	2.68494	+	8.26338i	0.0875264	+	0.269379i	−0.897708	+	0.440592i	$0.854769\pi$
$942$		0			0
$943$	0.897910	+	17.4975i	0.0292400	+	0.569798i
$944$		0			0
$945$	4.34068	+	13.3592i	0.141202	+	0.434576i
$946$		0			0
$947$	−35.5996	+	25.8647i	−1.15683	+	0.840488i	−0.989374	−	0.145391i	$-0.953556\pi$
$947$	−35.5996	+	25.8647i	−1.15683	+	0.840488i	−0.167459	+	0.985879i	$0.553556\pi$
$948$		0			0
$949$	16.9240	+	52.0868i	0.549378	+	1.69081i
$950$		0			0
$951$	−11.4688	−	8.33260i	−0.371903	−	0.270203i
$952$		0			0
$953$	16.7885	+	12.1976i	0.543834	+	0.395118i	0.825507	−	0.564392i	$-0.190889\pi$
$953$	16.7885	+	12.1976i	0.543834	+	0.395118i	−0.281673	+	0.959510i	$0.590889\pi$
$954$		0			0
$955$	50.4445	−	36.6501i	1.63235	−	1.18597i
$956$		0			0
$957$	−2.60161			−0.0840982
$958$		0			0
$959$	3.65617	−	11.2525i	0.118064	−	0.363363i
$960$		0			0
$961$	−8.28092	−	25.4861i	−0.267127	−	0.822131i
$962$		0			0
$963$	0.338053	−	1.04042i	0.0108936	−	0.0335270i
$964$		0			0
$965$	−0.0831830	+	0.256011i	−0.00267775	+	0.00824128i
$966$		0			0
$967$	45.3125	+	32.9215i	1.45715	+	1.05868i	0.984093	+	0.177652i	$0.0568503\pi$
$967$	45.3125	+	32.9215i	1.45715	+	1.05868i	0.473059	+	0.881031i	$0.343150\pi$
$968$		0			0
$969$	4.13325	−	3.00298i	0.132779	−	0.0964696i
$970$		0			0
$971$	−13.2980	−	40.9270i	−0.426753	−	1.31341i	−0.901306	−	0.433183i	$-0.857390\pi$
$971$	−13.2980	−	40.9270i	−0.426753	−	1.31341i	0.474553	−	0.880227i	$-0.342610\pi$
$972$		0			0
$973$	−4.15264	−	3.01707i	−0.133128	−	0.0967228i
$974$		0			0
$975$	17.2754			0.553255
$976$		0			0
$977$	12.5172	−	38.5241i	0.400462	−	1.23249i	−0.524164	−	0.851617i	$-0.675622\pi$
$977$	12.5172	−	38.5241i	0.400462	−	1.23249i	0.924626	−	0.380877i	$-0.124378\pi$
$978$		0			0
$979$	3.07602	−	2.23486i	0.0983099	−	0.0714263i
$980$		0			0
$981$	9.36446			0.298984
$982$		0			0
$983$	−50.3912			−1.60723			−0.803614	−	0.595151i	$-0.797092\pi$
$983$	−50.3912			−1.60723			−0.803614	+	0.595151i	$0.797092\pi$
$984$		0			0
$985$	−22.9880			−0.732458
$986$		0			0
$987$	0.188953			0.00601444
$988$		0			0
$989$	8.03369	−	5.83682i	0.255456	−	0.185600i
$990$		0			0
$991$	−5.38325	+	16.5680i	−0.171005	+	0.526298i	−0.999429	−	0.0338034i	$-0.989238\pi$
$991$	−5.38325	+	16.5680i	−0.171005	+	0.526298i	0.828424	+	0.560102i	$0.189238\pi$
$992$		0			0
$993$	1.49503			0.0474433
$994$		0			0
$995$	43.7215	+	31.7655i	1.38606	+	1.00703i
$996$		0			0
$997$	−1.36859	−	4.21207i	−0.0433435	−	0.133398i	0.927043	−	0.374955i	$-0.122342\pi$
$997$	−1.36859	−	4.21207i	−0.0433435	−	0.133398i	−0.970387	+	0.241557i	$0.922342\pi$
$998$		0			0
$999$	−13.5345	+	9.83341i	−0.428213	+	0.311115i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.e.141.2	yes	24
41.16	even	5	inner	1148.2.n.e.57.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.e.57.2	✓	24	41.16	even	5	inner
1148.2.n.e.141.2	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-0.842614 q^{3} +(2.54946 - 1.85229i) q^{5} +(-0.309017 + 0.951057i) q^{7} -2.29000 q^{9} +O(q^{10})\)	\(q-0.842614 q^{3} +(2.54946 - 1.85229i) q^{5} +(-0.309017 + 0.951057i) q^{7} -2.29000 q^{9} +(0.696228 + 0.505840i) q^{11} +(-1.28490 - 3.95451i) q^{13} +(-2.14821 + 1.56077i) q^{15} +(-3.99341 - 2.90138i) q^{17} +(0.379578 - 1.16822i) q^{19} +(0.260382 - 0.801374i) q^{21} +(-0.845549 - 2.60233i) q^{23} +(1.52368 - 4.68942i) q^{25} +4.45743 q^{27} +(2.90253 - 2.10881i) q^{29} +(-1.65846 - 1.20494i) q^{31} +(-0.586652 - 0.426228i) q^{33} +(0.973808 + 2.99707i) q^{35} +(-3.03640 + 2.20607i) q^{37} +(1.08267 + 3.33212i) q^{39} +(-6.18314 - 1.66398i) q^{41} +(1.12146 + 3.45150i) q^{43} +(-5.83827 + 4.24175i) q^{45} +(0.0692958 + 0.213271i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(3.36491 + 2.44475i) q^{51} +(1.91460 - 1.39104i) q^{53} +2.71197 q^{55} +(-0.319838 + 0.984359i) q^{57} +(-4.28890 - 13.1999i) q^{59} +(2.89170 - 8.89974i) q^{61} +(0.707649 - 2.17792i) q^{63} +(-10.6007 - 7.70186i) q^{65} +(-2.73418 + 1.98649i) q^{67} +(0.712471 + 2.19276i) q^{69} +(2.37728 + 1.72720i) q^{71} -13.1715 q^{73} +(-1.28388 + 3.95137i) q^{75} +(-0.696228 + 0.505840i) q^{77} +2.33755 q^{79} +3.11411 q^{81} +13.2998 q^{83} -15.5553 q^{85} +(-2.44572 + 1.77692i) q^{87} +(1.36527 - 4.20187i) q^{89} +4.15802 q^{91} +(1.39744 + 1.01530i) q^{93} +(-1.19617 - 3.68142i) q^{95} +(2.78964 - 2.02679i) q^{97} +(-1.59436 - 1.15837i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9}+O(q^{10}) \) 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9	\( 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9} - 8 q^{11} + 10 q^{15} + 8 q^{17} - 28 q^{19} + 3 q^{21} - 23 q^{23} + 17 q^{25} + 12 q^{27} - 31 q^{29} + 2 q^{31} + 12 q^{33} + 13 q^{35} + 7 q^{37} - 16 q^{39} - q^{41} - 2 q^{43} + 71 q^{45} + 15 q^{47} - 6 q^{49} + 2 q^{51} + 28 q^{53} - 16 q^{55} - 15 q^{57} + 17 q^{59} + 35 q^{61} - q^{63} + 62 q^{65} - 10 q^{67} - 9 q^{69} - 25 q^{71} - 74 q^{73} + 17 q^{75} + 8 q^{77} + 64 q^{81} + 96 q^{83} - 94 q^{85} - q^{87} - 33 q^{89} - 15 q^{93} - 29 q^{95} - 34 q^{97} - 3 q^{99}+O(q^{100}) \) 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9 - 8 * q^11 + 10 * q^15 + 8 * q^17 - 28 * q^19 + 3 * q^21 - 23 * q^23 + 17 * q^25 + 12 * q^27 - 31 * q^29 + 2 * q^31 + 12 * q^33 + 13 * q^35 + 7 * q^37 - 16 * q^39 - q^41 - 2 * q^43 + 71 * q^45 + 15 * q^47 - 6 * q^49 + 2 * q^51 + 28 * q^53 - 16 * q^55 - 15 * q^57 + 17 * q^59 + 35 * q^61 - q^63 + 62 * q^65 - 10 * q^67 - 9 * q^69 - 25 * q^71 - 74 * q^73 + 17 * q^75 + 8 * q^77 + 64 * q^81 + 96 * q^83 - 94 * q^85 - q^87 - 33 * q^89 - 15 * q^93 - 29 * q^95 - 34 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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