LMFDB - Embedded newform 108.4.i.a.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,4,Mod(13,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("108.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	108.i (of order $9$, degree $6$, 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:	$6.37220628062$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			49.5
Character	$\chi$	$=$	108.49
Dual form			108.4.i.a.97.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.320339 - 5.18627i) q^{3} +(19.7528 - 7.18944i) q^{5} +(0.723940 + 4.10567i) q^{7} +(-26.7948 - 3.32273i) q^{9} +O(q^{10})$	\(q+(0.320339 - 5.18627i) q^{3} +(19.7528 - 7.18944i) q^{5} +(0.723940 + 4.10567i) q^{7} +(-26.7948 - 3.32273i) q^{9} +(-5.68204 - 2.06810i) q^{11} +(22.8525 + 19.1756i) q^{13} +(-30.9588 - 104.747i) q^{15} +(48.7365 - 84.4141i) q^{17} +(-63.0708 - 109.242i) q^{19} +(21.5250 - 2.43934i) q^{21} +(-26.2243 + 148.725i) q^{23} +(242.731 - 203.675i) q^{25} +(-25.8160 + 137.900i) q^{27} +(-179.445 + 150.572i) q^{29} +(-2.62143 + 14.8669i) q^{31} +(-12.5459 + 28.8061i) q^{33} +(43.8173 + 75.8939i) q^{35} +(-0.488402 + 0.845938i) q^{37} +(106.770 - 112.377i) q^{39} +(185.869 + 155.962i) q^{41} +(31.0450 + 11.2995i) q^{43} +(-553.161 + 127.006i) q^{45} +(66.6849 + 378.189i) q^{47} +(305.982 - 111.368i) q^{49} +(-422.182 - 279.802i) q^{51} +245.113 q^{53} -127.105 q^{55} +(-586.761 + 292.108i) q^{57} +(-399.605 + 145.444i) q^{59} +(134.131 + 760.693i) q^{61} +(-5.75579 - 112.416i) q^{63} +(589.264 + 214.475i) q^{65} +(-321.243 - 269.555i) q^{67} +(762.929 + 183.649i) q^{69} +(-113.989 + 197.435i) q^{71} +(265.093 + 459.155i) q^{73} +(-978.558 - 1324.11i) q^{75} +(4.37745 - 24.8258i) q^{77} +(848.570 - 712.034i) q^{79} +(706.919 + 178.063i) q^{81} +(406.829 - 341.370i) q^{83} +(355.794 - 2017.81i) q^{85} +(723.423 + 978.882i) q^{87} +(84.1224 + 145.704i) q^{89} +(-62.1846 + 107.707i) q^{91} +(76.2639 + 18.3579i) q^{93} +(-2031.21 - 1704.39i) q^{95} +(-1375.96 - 500.807i) q^{97} +(145.377 + 74.2940i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 12 q^{5} - 48 q^{9}+O(q^{10}) $ 54 * q + 12 * q^5 - 48 * q^9	$ 54 q + 12 q^{5} - 48 q^{9} - 87 q^{11} + 234 q^{15} + 204 q^{17} - 12 q^{21} + 96 q^{23} - 216 q^{25} + 27 q^{27} + 318 q^{29} - 54 q^{31} + 63 q^{33} + 6 q^{35} + 66 q^{39} + 867 q^{41} - 513 q^{43} - 306 q^{45} - 1548 q^{47} + 594 q^{49} - 1368 q^{51} - 1068 q^{53} - 1269 q^{57} - 1218 q^{59} - 54 q^{61} + 30 q^{63} + 96 q^{65} - 2997 q^{67} + 1476 q^{69} - 120 q^{71} - 216 q^{73} + 732 q^{75} + 3480 q^{77} + 2808 q^{79} + 3348 q^{81} + 4464 q^{83} + 2160 q^{85} + 4824 q^{87} + 4029 q^{89} + 270 q^{91} + 1164 q^{93} - 1650 q^{95} - 3483 q^{97} - 5076 q^{99}+O(q^{100}) $ 54 * q + 12 * q^5 - 48 * q^9 - 87 * q^11 + 234 * q^15 + 204 * q^17 - 12 * q^21 + 96 * q^23 - 216 * q^25 + 27 * q^27 + 318 * q^29 - 54 * q^31 + 63 * q^33 + 6 * q^35 + 66 * q^39 + 867 * q^41 - 513 * q^43 - 306 * q^45 - 1548 * q^47 + 594 * q^49 - 1368 * q^51 - 1068 * q^53 - 1269 * q^57 - 1218 * q^59 - 54 * q^61 + 30 * q^63 + 96 * q^65 - 2997 * q^67 + 1476 * q^69 - 120 * q^71 - 216 * q^73 + 732 * q^75 + 3480 * q^77 + 2808 * q^79 + 3348 * q^81 + 4464 * q^83 + 2160 * q^85 + 4824 * q^87 + 4029 * q^89 + 270 * q^91 + 1164 * q^93 - 1650 * q^95 - 3483 * q^97 - 5076 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.320339	−	5.18627i	0.0616492	−	0.998098i
$3$	0.320339	−	5.18627i	0.0616492	−	0.998098i
$4$		0			0
$5$	19.7528	−	7.18944i	1.76675	−	0.643043i	0.766747	−	0.641949i	$-0.221874\pi$
$5$	19.7528	−	7.18944i	1.76675	−	0.643043i	0.999999	−	0.00109400i	$-0.000348232\pi$
$6$		0			0
$7$	0.723940	+	4.10567i	0.0390891	+	0.221685i	0.998095	−	0.0617021i	$-0.0196529\pi$
$7$	0.723940	+	4.10567i	0.0390891	+	0.221685i	−0.959006	+	0.283387i	$0.908542\pi$
$8$		0			0
$9$	−26.7948	−	3.32273i	−0.992399	−	0.123064i
$10$		0			0
$11$	−5.68204	−	2.06810i	−0.155746	−	0.0566867i	0.262971	−	0.964804i	$-0.415298\pi$
$11$	−5.68204	−	2.06810i	−0.155746	−	0.0566867i	−0.418716	+	0.908117i	$0.637520\pi$
$12$		0			0
$13$	22.8525	+	19.1756i	0.487550	+	0.409103i	0.853147	−	0.521670i	$-0.174691\pi$
$13$	22.8525	+	19.1756i	0.487550	+	0.409103i	−0.365597	+	0.930773i	$0.619135\pi$
$14$		0			0
$15$	−30.9588	−	104.747i	−0.532901	−	1.80303i
$16$		0			0
$17$	48.7365	−	84.4141i	0.695314	−	1.20432i	−0.274760	−	0.961513i	$-0.588599\pi$
$17$	48.7365	−	84.4141i	0.695314	−	1.20432i	0.970075	−	0.242807i	$-0.0780681\pi$
$18$		0			0
$19$	−63.0708	−	109.242i	−0.761549	−	1.31904i	−0.942052	−	0.335467i	$-0.891106\pi$
$19$	−63.0708	−	109.242i	−0.761549	−	1.31904i	0.180503	−	0.983574i	$-0.442227\pi$
$20$		0			0
$21$	21.5250	−	2.43934i	0.223673	−	0.0253480i
$22$		0			0
$23$	−26.2243	+	148.725i	−0.237745	+	1.34832i	0.599009	+	0.800743i	$0.295561\pi$
$23$	−26.2243	+	148.725i	−0.237745	+	1.34832i	−0.836754	+	0.547579i	$0.815550\pi$
$24$		0			0
$25$	242.731	−	203.675i	1.94184	−	1.62940i
$26$		0			0
$27$	−25.8160	+	137.900i	−0.184011	+	0.982924i
$28$		0			0
$29$	−179.445	+	150.572i	−1.14904	+	0.964155i	−0.999697	−	0.0246306i	$-0.992159\pi$
$29$	−179.445	+	150.572i	−1.14904	+	0.964155i	−0.149339	+	0.988786i	$0.547715\pi$
$30$		0			0
$31$	−2.62143	+	14.8669i	−0.0151879	+	0.0861346i	−0.991460	−	0.130415i	$-0.958369\pi$
$31$	−2.62143	+	14.8669i	−0.0151879	+	0.0861346i	0.976272	+	0.216549i	$0.0694802\pi$
$32$		0			0
$33$	−12.5459	+	28.8061i	−0.0661805	+	0.151955i
$34$		0			0
$35$	43.8173	+	75.8939i	0.211614	+	0.366526i
$36$		0			0
$37$	−0.488402	+	0.845938i	−0.00217008	+	0.00375868i	−0.867108	−	0.498119i	$-0.834024\pi$
$37$	−0.488402	+	0.845938i	−0.00217008	+	0.00375868i	0.864938	+	0.501878i	$0.167357\pi$
$38$		0			0
$39$	106.770	−	112.377i	0.438382	−	0.461402i
$40$		0			0
$41$	185.869	+	155.962i	0.707995	+	0.594078i	0.924036	−	0.382306i	$-0.124870\pi$
$41$	185.869	+	155.962i	0.707995	+	0.594078i	−0.216041	+	0.976384i	$0.569314\pi$
$42$		0			0
$43$	31.0450	+	11.2995i	0.110101	+	0.0400733i	0.396483	−	0.918042i	$-0.370231\pi$
$43$	31.0450	+	11.2995i	0.110101	+	0.0400733i	−0.286382	+	0.958115i	$0.592453\pi$
$44$		0			0
$45$	−553.161	+	127.006i	−1.83245	+	0.420732i
$46$		0			0
$47$	66.6849	+	378.189i	0.206957	+	1.17371i	0.894330	+	0.447409i	$0.147653\pi$
$47$	66.6849	+	378.189i	0.206957	+	1.17371i	−0.687372	+	0.726305i	$0.741236\pi$
$48$		0			0
$49$	305.982	−	111.368i	0.892076	−	0.324689i
$50$		0			0
$51$	−422.182	−	279.802i	−1.15916	−	0.768237i
$52$		0			0
$53$	245.113			0.635261			0.317631	−	0.948215i	$-0.397113\pi$
$53$	245.113			0.635261			0.317631	+	0.948215i	$0.397113\pi$
$54$		0			0
$55$	−127.105			−0.311615
$56$		0			0
$57$	−586.761	+	292.108i	−1.36348	+	0.678782i
$58$		0			0
$59$	−399.605	+	145.444i	−0.881765	+	0.320936i	−0.742922	−	0.669378i	$-0.766561\pi$
$59$	−399.605	+	145.444i	−0.881765	+	0.320936i	−0.138843	+	0.990314i	$0.544338\pi$
$60$		0			0
$61$	134.131	+	760.693i	0.281536	+	1.59667i	0.717403	+	0.696658i	$0.245331\pi$
$61$	134.131	+	760.693i	0.281536	+	1.59667i	−0.435867	+	0.900011i	$0.643558\pi$
$62$		0			0
$63$	−5.75579	−	112.416i	−0.0115105	−	0.224811i
$64$		0			0
$65$	589.264	+	214.475i	1.12445	+	0.409266i
$66$		0			0
$67$	−321.243	−	269.555i	−0.585762	−	0.491512i	0.301072	−	0.953601i	$-0.402656\pi$
$67$	−321.243	−	269.555i	−0.585762	−	0.491512i	−0.886833	+	0.462089i	$0.847100\pi$
$68$		0			0
$69$	762.929	+	183.649i	1.33110	+	0.320416i
$70$		0			0
$71$	−113.989	+	197.435i	−0.190535	+	0.330016i	−0.945428	−	0.325832i	$-0.894356\pi$
$71$	−113.989	+	197.435i	−0.190535	+	0.330016i	0.754893	+	0.655848i	$0.227689\pi$
$72$		0			0
$73$	265.093	+	459.155i	0.425025	+	0.736165i	0.996423	−	0.0845083i	$-0.0269320\pi$
$73$	265.093	+	459.155i	0.425025	+	0.736165i	−0.571398	+	0.820673i	$0.693599\pi$
$74$		0			0
$75$	−978.558	−	1324.11i	−1.50659	−	2.03860i
$76$		0			0
$77$	4.37745	−	24.8258i	0.00647866	−	0.0367423i
$78$		0			0
$79$	848.570	−	712.034i	1.20850	−	1.01405i	0.209155	−	0.977883i	$-0.432929\pi$
$79$	848.570	−	712.034i	1.20850	−	1.01405i	0.999346	−	0.0361698i	$-0.0115157\pi$
$80$		0			0
$81$	706.919	+	178.063i	0.969711	+	0.244257i
$82$		0			0
$83$	406.829	−	341.370i	0.538015	−	0.451449i	−0.332843	−	0.942982i	$-0.608008\pi$
$83$	406.829	−	341.370i	0.538015	−	0.451449i	0.870859	+	0.491534i	$0.163564\pi$
$84$		0			0
$85$	355.794	−	2017.81i	0.454015	−	2.57484i
$86$		0			0
$87$	723.423	+	978.882i	0.891484	+	1.20629i
$88$		0			0
$89$	84.1224	+	145.704i	0.100190	+	0.173535i	0.911763	−	0.410717i	$-0.134721\pi$
$89$	84.1224	+	145.704i	0.100190	+	0.173535i	−0.811573	+	0.584252i	$0.801388\pi$
$90$		0			0
$91$	−62.1846	+	107.707i	−0.0716343	+	0.124074i
$92$		0			0
$93$	76.2639	+	18.3579i	0.0850344	+	0.0204691i
$94$		0			0
$95$	−2031.21	−	1704.39i	−2.19366	−	1.84070i
$96$		0			0
$97$	−1375.96	−	500.807i	−1.44028	−	0.524219i	−0.500421	−	0.865782i	$-0.666822\pi$
$97$	−1375.96	−	500.807i	−1.44028	−	0.524219i	−0.939859	+	0.341563i	$0.889044\pi$
$98$		0			0
$99$	145.377	+	74.2940i	0.147586	+	0.0754225i
$100$		0			0
$101$	180.078	+	1021.27i	0.177410	+	1.00614i	0.935325	+	0.353788i	$0.115107\pi$
$101$	180.078	+	1021.27i	0.177410	+	1.00614i	−0.757916	+	0.652353i	$0.773782\pi$
$102$		0			0
$103$	159.205	−	57.9460i	0.152301	−	0.0554329i	−0.264745	−	0.964318i	$-0.585288\pi$
$103$	159.205	−	57.9460i	0.152301	−	0.0554329i	0.417046	+	0.908886i	$0.363066\pi$
$104$		0			0
$105$	407.642	−	202.937i	0.378874	−	0.188615i
$106$		0			0
$107$	−125.729			−0.113595			−0.0567974	−	0.998386i	$-0.518089\pi$
$107$	−125.729			−0.113595			−0.0567974	+	0.998386i	$0.518089\pi$
$108$		0			0
$109$	−722.542			−0.634927			−0.317463	−	0.948271i	$-0.602831\pi$
$109$	−722.542			−0.634927			−0.317463	+	0.948271i	$0.602831\pi$
$110$		0			0
$111$	4.23081	+	2.80397i	0.00361775	+	0.00239767i
$112$		0			0
$113$	−372.502	+	135.580i	−0.310107	+	0.112870i	−0.492385	−	0.870377i	$-0.663875\pi$
$113$	−372.502	+	135.580i	−0.310107	+	0.112870i	0.182279	+	0.983247i	$0.441653\pi$
$114$		0			0
$115$	551.248	+	3126.29i	0.446993	+	2.53502i
$116$		0			0
$117$	−548.613	−	589.737i	−0.433499	−	0.465994i
$118$		0			0
$119$	381.859	+	138.985i	0.294159	+	0.107065i
$120$		0			0
$121$	−991.597	−	832.048i	−0.745001	−	0.625130i
$122$		0			0
$123$	868.403	−	914.003i	0.636595	−	0.670024i
$124$		0			0
$125$	2016.52	−	3492.72i	1.44291	−	2.49919i
$126$		0			0
$127$	24.8188	+	42.9874i	0.0173410	+	0.0300356i	0.874566	−	0.484907i	$-0.161147\pi$
$127$	24.8188	+	42.9874i	0.0173410	+	0.0300356i	−0.857225	+	0.514943i	$0.827813\pi$
$128$		0			0
$129$	68.5470	−	157.388i	0.0467847	−	0.107421i
$130$		0			0
$131$	142.167	−	806.266i	0.0948179	−	0.537739i	−0.899985	−	0.435921i	$-0.856423\pi$
$131$	142.167	−	806.266i	0.0948179	−	0.537739i	0.994803	−	0.101818i	$-0.0324661\pi$
$132$		0			0
$133$	402.851	−	338.032i	0.262644	−	0.220384i
$134$		0			0
$135$	481.489	+	2909.53i	0.306963	+	1.85490i
$136$		0			0
$137$	−446.492	+	374.651i	−0.278441	+	0.233639i	−0.771303	−	0.636468i	$-0.780395\pi$
$137$	−446.492	+	374.651i	−0.278441	+	0.233639i	0.492863	+	0.870107i	$0.335950\pi$
$138$		0			0
$139$	−330.670	+	1875.32i	−0.201777	+	1.14433i	0.700654	+	0.713501i	$0.252892\pi$
$139$	−330.670	+	1875.32i	−0.201777	+	1.14433i	−0.902431	+	0.430834i	$0.858219\pi$
$140$		0			0
$141$	1982.75	−	224.697i	1.18424	−	0.134205i
$142$		0			0
$143$	−90.1923	−	156.218i	−0.0527431	−	0.0913537i
$144$		0			0
$145$	−2462.01	+	4264.33i	−1.41006	+	2.44230i
$146$		0			0
$147$	−479.568	−	1622.58i	−0.269076	−	0.910396i
$148$		0			0
$149$	979.169	+	821.621i	0.538367	+	0.451744i	0.870979	−	0.491320i	$-0.163486\pi$
$149$	979.169	+	821.621i	0.538367	+	0.451744i	−0.332612	+	0.943064i	$0.607930\pi$
$150$		0			0
$151$	2893.47	+	1053.14i	1.55939	+	0.567571i	0.970596	−	0.240713i	$-0.0773814\pi$
$151$	2893.47	+	1053.14i	1.55939	+	0.567571i	0.588792	+	0.808284i	$0.299604\pi$
$152$		0			0
$153$	−1586.37	+	2099.92i	−0.838237	+	1.10960i
$154$		0			0
$155$	55.1039	+	312.510i	0.0285552	+	0.161944i
$156$		0			0
$157$	−909.442	+	331.010i	−0.462302	+	0.168264i	−0.562662	−	0.826687i	$-0.690223\pi$
$157$	−909.442	+	331.010i	−0.462302	+	0.168264i	0.100360	+	0.994951i	$0.468000\pi$
$158$		0			0
$159$	78.5192	−	1271.22i	0.0391634	−	0.634053i
$160$		0			0
$161$	−629.602			−0.308196
$162$		0			0
$163$	−3732.36			−1.79350			−0.896752	−	0.442534i	$-0.854079\pi$
$163$	−3732.36			−1.79350			−0.896752	+	0.442534i	$0.854079\pi$
$164$		0			0
$165$	−40.7166	+	659.200i	−0.0192108	+	0.311022i
$166$		0			0
$167$	−3395.70	+	1235.93i	−1.57346	+	0.572691i	−0.973768	−	0.227544i	$-0.926931\pi$
$167$	−3395.70	+	1235.93i	−1.57346	+	0.572691i	−0.599687	+	0.800235i	$0.704708\pi$
$168$		0			0
$169$	−226.968	−	1287.20i	−0.103308	−	0.585891i
$170$		0			0
$171$	1326.99	+	3136.68i	0.593434	+	1.40273i
$172$		0			0
$173$	−949.268	−	345.505i	−0.417176	−	0.151840i	0.124899	−	0.992169i	$-0.460139\pi$
$173$	−949.268	−	345.505i	−0.417176	−	0.151840i	−0.542076	+	0.840330i	$0.682361\pi$
$174$		0			0
$175$	1011.95	+	849.123i	0.437119	+	0.366787i
$176$		0			0
$177$	626.304	+	2119.05i	0.265966	+	0.899873i
$178$		0			0
$179$	2154.60	−	3731.88i	0.899678	−	1.55829i	0.0717728	−	0.997421i	$-0.477134\pi$
$179$	2154.60	−	3731.88i	0.899678	−	1.55829i	0.827906	−	0.560868i	$-0.189532\pi$
$180$		0			0
$181$	−1997.35	−	3459.52i	−0.820232	−	1.42068i	−0.905509	−	0.424327i	$-0.860511\pi$
$181$	−1997.35	−	3459.52i	−0.820232	−	1.42068i	0.0852767	−	0.996357i	$-0.472823\pi$
$182$		0			0
$183$	3988.13	−	451.959i	1.61099	−	0.182567i
$184$		0			0
$185$	−3.56551	+	20.2210i	−0.00141698	+	0.00803609i
$186$		0			0
$187$	−451.500	+	378.853i	−0.176561	+	0.148152i
$188$		0			0
$189$	−584.863	−	6.16010i	−0.225093	−	0.00237080i
$190$		0			0
$191$	−3232.23	+	2712.16i	−1.22448	+	1.02746i	−0.225903	+	0.974150i	$0.572533\pi$
$191$	−3232.23	+	2712.16i	−1.22448	+	1.02746i	−0.998578	+	0.0533113i	$0.983022\pi$
$192$		0			0
$193$	399.764	−	2267.17i	0.149097	−	0.845569i	−0.814890	−	0.579616i	$-0.803202\pi$
$193$	399.764	−	2267.17i	0.149097	−	0.845569i	0.963986	−	0.265952i	$-0.0856864\pi$
$194$		0			0
$195$	1301.09	−	2987.38i	0.477809	−	1.09708i
$196$		0			0
$197$	−709.523	−	1228.93i	−0.256606	−	0.444455i	0.708724	−	0.705486i	$-0.249271\pi$
$197$	−709.523	−	1228.93i	−0.256606	−	0.444455i	−0.965331	+	0.261030i	$0.915938\pi$
$198$		0			0
$199$	994.545	−	1722.60i	0.354278	−	0.613628i	−0.632716	−	0.774384i	$-0.718060\pi$
$199$	994.545	−	1722.60i	0.354278	−	0.613628i	0.986994	+	0.160756i	$0.0513932\pi$
$200$		0			0
$201$	−1500.89	+	1579.70i	−0.526689	+	0.554346i
$202$		0			0
$203$	−748.106	−	627.735i	−0.258654	−	0.217036i
$204$		0			0
$205$	4792.71	+	1744.40i	1.63287	+	0.594314i
$206$		0			0
$207$	1196.85	−	3897.93i	0.401868	−	1.30881i
$208$		0			0
$209$	132.449	+	751.153i	0.0438357	+	0.248605i
$210$		0			0
$211$	280.745	−	102.183i	0.0915985	−	0.0333391i	−0.295814	−	0.955245i	$-0.595591\pi$
$211$	280.745	−	102.183i	0.0915985	−	0.0333391i	0.387413	+	0.921906i	$0.373369\pi$
$212$		0			0
$213$	987.434	+	654.423i	0.317642	+	0.210518i
$214$		0			0
$215$	694.464			0.220289
$216$		0			0
$217$	−62.9363			−0.0196884
$218$		0			0
$219$	2466.22	−	1227.76i	0.760967	−	0.378833i
$220$		0			0
$221$	2732.44	−	994.527i	0.831692	−	0.302711i
$222$		0			0
$223$	−559.273	−	3171.80i	−0.167945	−	0.952463i	−0.945976	−	0.324237i	$-0.894893\pi$
$223$	−559.273	−	3171.80i	−0.167945	−	0.952463i	0.778031	−	0.628226i	$-0.216219\pi$
$224$		0			0
$225$	−7180.67	+	4650.90i	−2.12760	+	1.37804i
$226$		0			0
$227$	3153.27	+	1147.70i	0.921983	+	0.335574i	0.759027	−	0.651059i	$-0.225675\pi$
$227$	3153.27	+	1147.70i	0.921983	+	0.335574i	0.162956	+	0.986633i	$0.447897\pi$
$228$		0			0
$229$	−3053.24	−	2561.97i	−0.881064	−	0.739301i	0.0853333	−	0.996352i	$-0.472804\pi$
$229$	−3053.24	−	2561.97i	−0.881064	−	0.739301i	−0.966398	+	0.257052i	$0.917249\pi$
$230$		0			0
$231$	−127.351	−	30.6553i	−0.0362730	−	0.00873148i
$232$		0			0
$233$	180.603	−	312.813i	0.0507797	−	0.0879531i	−0.839518	−	0.543331i	$-0.817163\pi$
$233$	180.603	−	312.813i	0.0507797	−	0.0879531i	0.890298	+	0.455378i	$0.150496\pi$
$234$		0			0
$235$	4036.18	+	6990.88i	1.12039	+	1.94057i
$236$		0			0
$237$	−3420.97	−	4629.00i	−0.937620	−	1.26872i
$238$		0			0
$239$	−66.7780	+	378.717i	−0.0180733	+	0.102499i	−0.992510	−	0.122164i	$-0.961017\pi$
$239$	−66.7780	+	378.717i	−0.0180733	+	0.102499i	0.974437	+	0.224662i	$0.0721278\pi$
$240$		0			0
$241$	−1868.30	+	1567.69i	−0.499368	+	0.419019i	−0.857369	−	0.514702i	$-0.827903\pi$
$241$	−1868.30	+	1567.69i	−0.499368	+	0.419019i	0.358002	+	0.933721i	$0.383458\pi$
$242$		0			0
$243$	1149.94	−	3609.23i	0.303574	−	0.952808i
$244$		0			0
$245$	5243.34	−	4399.68i	1.36728	−	1.14729i
$246$		0			0
$247$	653.445	−	3705.87i	0.168331	−	0.954651i
$248$		0			0
$249$	−1640.11	−	2219.28i	−0.417422	−	0.564823i
$250$		0			0
$251$	3340.30	+	5785.57i	0.839992	+	1.45491i	0.889900	+	0.456155i	$0.150774\pi$
$251$	3340.30	+	5785.57i	0.839992	+	1.45491i	−0.0499080	+	0.998754i	$0.515893\pi$
$252$		0			0
$253$	456.586	−	790.830i	0.113460	−	0.196518i
$254$		0			0
$255$	−10350.9	−	2491.62i	−2.54196	−	0.611888i
$256$		0			0
$257$	−3562.33	−	2989.15i	−0.864638	−	0.725517i	0.0983240	−	0.995154i	$-0.468652\pi$
$257$	−3562.33	−	2989.15i	−0.864638	−	0.725517i	−0.962962	+	0.269637i	$0.913096\pi$
$258$		0			0
$259$	−3.82671	−	1.39281i	−0.000918071	−	0.000334151i
$260$		0			0
$261$	5308.49	−	3438.29i	1.25895	−	0.815422i
$262$		0			0
$263$	407.176	+	2309.21i	0.0954659	+	0.541414i	0.994604	+	0.103748i	$0.0330836\pi$
$263$	407.176	+	2309.21i	0.0954659	+	0.541414i	−0.899138	+	0.437666i	$0.855805\pi$
$264$		0			0
$265$	4841.67	−	1762.22i	1.12235	−	0.408500i
$266$		0			0
$267$	782.609	−	389.607i	0.179382	−	0.0893016i
$268$		0			0
$269$	−5351.31			−1.21292			−0.606459	−	0.795115i	$-0.707411\pi$
$269$	−5351.31			−1.21292			−0.606459	+	0.795115i	$0.707411\pi$
$270$		0			0
$271$	2895.83			0.649112			0.324556	−	0.945867i	$-0.394785\pi$
$271$	2895.83			0.649112			0.324556	+	0.945867i	$0.394785\pi$
$272$		0			0
$273$	538.677	+	357.009i	0.119422	+	0.0791471i
$274$		0			0
$275$	−1800.43	+	655.301i	−0.394799	+	0.143695i
$276$		0			0
$277$	−461.311	−	2616.22i	−0.100063	−	0.567486i	−0.993078	−	0.117458i	$-0.962525\pi$
$277$	−461.311	−	2616.22i	−0.100063	−	0.567486i	0.893015	−	0.450027i	$-0.148586\pi$
$278$		0			0
$279$	119.639	−	389.644i	0.0256725	−	0.0836108i
$280$		0			0
$281$	3820.36	+	1390.50i	0.811046	+	0.295196i	0.714056	−	0.700089i	$-0.246856\pi$
$281$	3820.36	+	1390.50i	0.811046	+	0.295196i	0.0969900	+	0.995285i	$0.469079\pi$
$282$		0			0
$283$	1665.70	+	1397.69i	0.349879	+	0.293583i	0.800741	−	0.599010i	$-0.204439\pi$
$283$	1665.70	+	1397.69i	0.349879	+	0.293583i	−0.450863	+	0.892593i	$0.648884\pi$
$284$		0			0
$285$	−9490.11	+	9988.44i	−1.97244	+	2.07601i
$286$		0			0
$287$	−505.771	+	876.022i	−0.104024	+	0.180174i
$288$		0			0
$289$	−2294.00	−	3973.32i	−0.466924	−	0.808736i
$290$		0			0
$291$	−3038.09	+	6975.65i	−0.612014	+	1.40522i
$292$		0			0
$293$	−705.493	+	4001.05i	−0.140667	+	0.797760i	0.830078	+	0.557647i	$0.188296\pi$
$293$	−705.493	+	4001.05i	−0.140667	+	0.797760i	−0.970745	+	0.240113i	$0.922815\pi$
$294$		0			0
$295$	−6847.67	+	5745.87i	−1.35148	+	1.13403i
$296$		0			0
$297$	431.879	−	730.167i	0.0843776	−	0.142655i
$298$		0			0
$299$	−3451.18	+	2895.89i	−0.667516	+	0.560112i
$300$		0			0
$301$	−23.9171	+	135.641i	−0.00457993	+	0.0259741i
$302$		0			0
$303$	5354.27	−	606.778i	1.01516	−	0.115045i
$304$		0			0
$305$	8118.42	+	14061.5i	1.52413	+	2.63987i
$306$		0			0
$307$	3875.27	−	6712.17i	0.720435	−	1.24783i	−0.240391	−	0.970676i	$-0.577276\pi$
$307$	3875.27	−	6712.17i	0.720435	−	1.24783i	0.960826	−	0.277154i	$-0.0893912\pi$
$308$		0			0
$309$	−249.524	−	844.243i	−0.0459382	−	0.155428i
$310$		0			0
$311$	4511.08	+	3785.24i	0.822507	+	0.690166i	0.953558	−	0.301210i	$-0.0973906\pi$
$311$	4511.08	+	3785.24i	0.822507	+	0.690166i	−0.131050	+	0.991376i	$0.541835\pi$
$312$		0			0
$313$	2898.37	+	1054.92i	0.523404	+	0.190504i	0.590191	−	0.807264i	$-0.299052\pi$
$313$	2898.37	+	1054.92i	0.523404	+	0.190504i	−0.0667865	+	0.997767i	$0.521275\pi$
$314$		0			0
$315$	−921.901	−	2179.15i	−0.164899	−	0.389782i
$316$		0			0
$317$	73.4339	+	416.464i	0.0130109	+	0.0737885i	0.990622	−	0.136632i	$-0.0436278\pi$
$317$	73.4339	+	416.464i	0.0130109	+	0.0737885i	−0.977611	+	0.210421i	$0.932517\pi$
$318$		0			0
$319$	1331.01	−	484.448i	0.233612	−	0.0850278i
$320$		0			0
$321$	−40.2758	+	652.063i	−0.00700304	+	0.113379i
$322$		0			0
$323$	−12295.4			−2.11806
$324$		0			0
$325$	9452.60			1.61334
$326$		0			0
$327$	−231.458	+	3747.30i	−0.0391427	+	0.633719i
$328$		0			0
$329$	−1504.44	+	547.573i	−0.252105	+	0.0917588i
$330$		0			0
$331$	−1281.12	−	7265.62i	−0.212740	−	1.20651i	−0.884785	−	0.465999i	$-0.845695\pi$
$331$	−1281.12	−	7265.62i	−0.212740	−	1.20651i	0.672045	−	0.740510i	$-0.265416\pi$
$332$		0			0
$333$	15.8974	−	21.0439i	0.00261614	−	0.00346305i
$334$		0			0
$335$	−8283.40	−	3014.91i	−1.35096	−	0.491708i
$336$		0			0
$337$	−1222.42	−	1025.74i	−0.197596	−	0.165802i	0.538621	−	0.842548i	$-0.318945\pi$
$337$	−1222.42	−	1025.74i	−0.197596	−	0.165802i	−0.736217	+	0.676745i	$0.763390\pi$
$338$		0			0
$339$	583.826	+	1975.33i	0.0935371	+	0.316475i
$340$		0			0
$341$	45.6412	−	79.0529i	0.00724813	−	0.0125541i
$342$		0			0
$343$	1393.74	+	2414.03i	0.219402	+	0.380015i
$344$		0			0
$345$	16390.3	−	1857.45i	2.55776	−	0.289860i
$346$		0			0
$347$	1332.82	−	7558.82i	0.206195	−	1.16939i	−0.689352	−	0.724426i	$-0.742105\pi$
$347$	1332.82	−	7558.82i	0.206195	−	1.16939i	0.895548	−	0.444966i	$-0.146784\pi$
$348$		0			0
$349$	3679.04	−	3087.08i	0.564282	−	0.473489i	−0.315461	−	0.948939i	$-0.602159\pi$
$349$	3679.04	−	3087.08i	0.564282	−	0.473489i	0.879743	+	0.475450i	$0.157715\pi$
$350$		0			0
$351$	−3234.28	+	2656.34i	−0.491832	+	0.403946i
$352$		0			0
$353$	3351.24	−	2812.02i	0.505293	−	0.423991i	−0.354176	−	0.935179i	$-0.615239\pi$
$353$	3351.24	−	2812.02i	0.505293	−	0.423991i	0.859469	+	0.511187i	$0.170794\pi$
$354$		0			0
$355$	−832.159	+	4719.41i	−0.124412	+	0.705578i
$356$		0			0
$357$	843.139	−	1935.90i	0.124996	−	0.286999i
$358$		0			0
$359$	−161.158	−	279.135i	−0.0236925	−	0.0410366i	0.853936	−	0.520378i	$-0.174209\pi$
$359$	−161.158	−	279.135i	−0.0236925	−	0.0410366i	−0.877629	+	0.479341i	$0.840876\pi$
$360$		0			0
$361$	−4526.35	+	7839.86i	−0.659914	+	1.14300i
$362$		0			0
$363$	−4632.87	+	4876.15i	−0.669870	+	0.705045i
$364$		0			0
$365$	8537.41	+	7163.74i	1.22430	+	1.02731i
$366$		0			0
$367$	−5880.80	−	2140.43i	−0.836444	−	0.304441i	−0.111943	−	0.993715i	$-0.535708\pi$
$367$	−5880.80	−	2140.43i	−0.836444	−	0.304441i	−0.724501	+	0.689274i	$0.757930\pi$
$368$		0			0
$369$	−4462.08	−	4796.56i	−0.629503	−	0.676691i
$370$		0			0
$371$	177.447	+	1006.35i	0.0248318	+	0.140828i
$372$		0			0
$373$	−10764.1	+	3917.82i	−1.49422	+	0.543852i	−0.954557	−	0.298028i	$-0.903671\pi$
$373$	−10764.1	+	3917.82i	−1.49422	+	0.543852i	−0.539664	+	0.841880i	$0.681449\pi$
$374$		0			0
$375$	−17468.2	−	11577.1i	−2.40548	−	1.59423i
$376$		0			0
$377$	−6988.07			−0.954652
$378$		0			0
$379$	−2145.56			−0.290791			−0.145396	−	0.989374i	$-0.546446\pi$
$379$	−2145.56			−0.290791			−0.145396	+	0.989374i	$0.546446\pi$
$380$		0			0
$381$	230.895	−	114.946i	0.0310475	−	0.0154564i
$382$		0			0
$383$	8574.14	−	3120.73i	1.14391	−	0.416350i	0.300587	−	0.953754i	$-0.402817\pi$
$383$	8574.14	−	3120.73i	1.14391	−	0.416350i	0.843324	+	0.537405i	$0.180595\pi$
$384$		0			0
$385$	−92.0164	−	521.851i	−0.0121807	−	0.0690804i
$386$		0			0
$387$	−794.299	−	405.921i	−0.104332	−	0.0533181i
$388$		0			0
$389$	−1226.29	−	446.334i	−0.159834	−	0.0581749i	0.260864	−	0.965376i	$-0.415993\pi$
$389$	−1226.29	−	446.334i	−0.159834	−	0.0581749i	−0.420698	+	0.907201i	$0.638215\pi$
$390$		0			0
$391$	11276.4	+	9462.06i	1.45850	+	1.22383i
$392$		0			0
$393$	−4135.97	−	995.592i	−0.530871	−	0.127789i
$394$		0			0
$395$	11642.5	−	20165.4i	1.48303	−	2.56869i
$396$		0			0
$397$	−5594.33	−	9689.67i	−0.707233	−	1.22496i	−0.965880	−	0.258991i	$-0.916610\pi$
$397$	−5594.33	−	9689.67i	−0.707233	−	1.22496i	0.258647	−	0.965972i	$-0.416723\pi$
$398$		0			0
$399$	−1624.08	−	2197.58i	−0.203773	−	0.275731i
$400$		0			0
$401$	−1540.68	+	8737.63i	−0.191865	+	1.08812i	0.724948	+	0.688804i	$0.241864\pi$
$401$	−1540.68	+	8737.63i	−0.191865	+	1.08812i	−0.916813	+	0.399317i	$0.869247\pi$
$402$		0			0
$403$	−344.987	+	289.479i	−0.0426428	+	0.0357815i
$404$		0			0
$405$	15243.8	−	1565.10i	1.87030	−	0.192025i
$406$		0			0
$407$	4.52460	−	3.79659i	0.000551047	−	0.000462384i
$408$		0			0
$409$	−2427.17	+	13765.2i	−0.293437	+	1.66417i	0.380049	+	0.924967i	$0.375907\pi$
$409$	−2427.17	+	13765.2i	−0.293437	+	1.66417i	−0.673486	+	0.739200i	$0.735204\pi$
$410$		0			0
$411$	1800.01	+	2435.64i	0.216029	+	0.292315i
$412$		0			0
$413$	−886.437	−	1535.35i	−0.105614	−	0.182929i
$414$		0			0
$415$	5581.76	−	9667.90i	0.660236	−	1.14356i
$416$		0			0
$417$	9619.99	+	2315.68i	1.12972	+	0.271941i
$418$		0			0
$419$	−2230.07	−	1871.25i	−0.260014	−	0.218178i	0.503456	−	0.864021i	$-0.332062\pi$
$419$	−2230.07	−	1871.25i	−0.260014	−	0.218178i	−0.763470	+	0.645843i	$0.776506\pi$
$420$		0			0
$421$	1669.95	+	607.813i	0.193322	+	0.0703634i	0.436867	−	0.899526i	$-0.356088\pi$
$421$	1669.95	+	607.813i	0.193322	+	0.0703634i	−0.243545	+	0.969890i	$0.578310\pi$
$422$		0			0
$423$	−530.188	−	10355.1i	−0.0609424	−	1.19026i
$424$		0			0
$425$	−5363.22	−	30416.3i	−0.612127	−	3.47155i
$426$		0			0
$427$	−3026.05	+	1101.39i	−0.342953	+	0.124825i
$428$		0			0
$429$	−839.079	+	417.719i	−0.0944315	+	0.0470109i
$430$		0			0
$431$	2943.86			0.329004			0.164502	−	0.986377i	$-0.447398\pi$
$431$	2943.86			0.329004			0.164502	+	0.986377i	$0.447398\pi$
$432$		0			0
$433$	−5093.05			−0.565257			−0.282628	−	0.959229i	$-0.591206\pi$
$433$	−5093.05			−0.565257			−0.282628	+	0.959229i	$0.591206\pi$
$434$		0			0
$435$	21327.3	+	14134.7i	2.35072	+	1.55795i
$436$		0			0
$437$	17901.0	−	6515.44i	1.95955	−	0.713217i
$438$		0			0
$439$	−114.587	−	649.855i	−0.0124577	−	0.0706512i	0.977945	−	0.208862i	$-0.0669760\pi$
$439$	−114.587	−	649.855i	−0.0124577	−	0.0706512i	−0.990403	+	0.138211i	$0.955865\pi$
$440$		0			0
$441$	−8568.77	+	1967.39i	−0.925253	+	0.212439i
$442$		0			0
$443$	−14988.3	−	5455.28i	−1.60748	−	0.585075i	−0.626541	−	0.779389i	$-0.715530\pi$
$443$	−14988.3	−	5455.28i	−1.60748	−	0.585075i	−0.980939	+	0.194314i	$0.937752\pi$
$444$		0			0
$445$	2709.19	+	2273.28i	0.288602	+	0.242166i
$446$		0			0
$447$	4574.81	−	4815.04i	0.484074	−	0.509493i
$448$		0			0
$449$	−6982.02	+	12093.2i	−0.733858	+	1.27108i	0.221365	+	0.975191i	$0.428949\pi$
$449$	−6982.02	+	12093.2i	−0.733858	+	1.27108i	−0.955223	+	0.295888i	$0.904385\pi$
$450$		0			0
$451$	−733.568	−	1270.58i	−0.0765907	−	0.132659i
$452$		0			0
$453$	6388.75	−	14669.0i	0.662626	−	1.52143i
$454$		0			0
$455$	−453.970	+	2574.59i	−0.0467746	+	0.265272i
$456$		0			0
$457$	9944.76	−	8344.65i	1.01794	−	0.854149i	0.0285686	−	0.999592i	$-0.490905\pi$
$457$	9944.76	−	8344.65i	1.01794	−	0.854149i	0.989367	+	0.145443i	$0.0464607\pi$
$458$		0			0
$459$	10382.6	+	8900.02i	1.05581	+	0.905049i
$460$		0			0
$461$	−3090.41	+	2593.17i	−0.312223	+	0.261986i	−0.785410	−	0.618976i	$-0.787548\pi$
$461$	−3090.41	+	2593.17i	−0.312223	+	0.261986i	0.473187	+	0.880962i	$0.343104\pi$
$462$		0			0
$463$	−1711.84	+	9708.30i	−0.171827	+	0.974477i	0.769917	+	0.638145i	$0.220298\pi$
$463$	−1711.84	+	9708.30i	−0.171827	+	0.974477i	−0.941743	+	0.336333i	$0.890813\pi$
$464$		0			0
$465$	1638.41	−	185.675i	0.163397	−	0.0185171i
$466$		0			0
$467$	3974.08	+	6883.30i	0.393787	+	0.682058i	0.992945	−	0.118572i	$-0.0378316\pi$
$467$	3974.08	+	6883.30i	0.393787	+	0.682058i	−0.599159	+	0.800630i	$0.704498\pi$
$468$		0			0
$469$	874.141	−	1514.06i	0.0860642	−	0.149068i
$470$		0			0
$471$	1425.38	+	4822.65i	0.139443	+	0.471796i
$472$		0			0
$473$	−153.031	−	128.408i	−0.0148760	−	0.0124825i
$474$		0			0
$475$	−37559.0	−	13670.4i	−3.62806	−	1.32050i
$476$		0			0
$477$	−6567.74	−	814.443i	−0.630432	−	0.0781778i
$478$		0			0
$479$	324.074	+	1837.91i	0.0309130	+	0.175316i	0.996355	−	0.0853009i	$-0.0271851\pi$
$479$	324.074	+	1837.91i	0.0309130	+	0.175316i	−0.965442	+	0.260617i	$0.916074\pi$
$480$		0			0
$481$	−27.3826	+	9.96644i	−0.00259571	+	0.000944762i
$482$		0			0
$483$	−201.686	+	3265.29i	−0.0190001	+	0.307610i
$484$		0			0
$485$	−30779.5			−2.88171
$486$		0			0
$487$	1560.17			0.145171			0.0725854	−	0.997362i	$-0.476875\pi$
$487$	1560.17			0.145171			0.0725854	+	0.997362i	$0.476875\pi$
$488$		0			0
$489$	−1195.62	+	19357.0i	−0.110568	+	1.79009i
$490$		0			0
$491$	−3956.47	+	1440.04i	−0.363652	+	0.132358i	−0.517382	−	0.855754i	$-0.673093\pi$
$491$	−3956.47	+	1440.04i	−0.363652	+	0.132358i	0.153731	+	0.988113i	$0.450871\pi$
$492$		0			0
$493$	3964.89	+	22486.0i	0.362210	+	2.05420i
$494$		0			0
$495$	3405.75	+	422.335i	0.309246	+	0.0383486i
$496$		0			0
$497$	−893.122	−	325.070i	−0.0806076	−	0.0293388i
$498$		0			0
$499$	−8986.51	−	7540.58i	−0.806196	−	0.676478i	0.143501	−	0.989650i	$-0.454164\pi$
$499$	−8986.51	−	7540.58i	−0.806196	−	0.676478i	−0.949697	+	0.313172i	$0.898608\pi$
$500$		0			0
$501$	5322.11	+	18006.9i	0.474599	+	1.60577i
$502$		0			0
$503$	1066.88	−	1847.89i	0.0945720	−	0.163803i	−0.814858	−	0.579661i	$-0.803185\pi$
$503$	1066.88	−	1847.89i	0.0945720	−	0.163803i	0.909430	+	0.415857i	$0.136518\pi$
$504$		0			0
$505$	10899.4	+	18878.3i	0.960430	+	1.66351i
$506$		0			0
$507$	−6748.48	+	764.778i	−0.591145	+	0.0669921i
$508$		0			0
$509$	2281.35	−	12938.2i	0.198662	−	1.12667i	−0.708443	−	0.705768i	$-0.750602\pi$
$509$	2281.35	−	12938.2i	0.198662	−	1.12667i	0.907106	−	0.420903i	$-0.138287\pi$
$510$		0			0
$511$	−1693.23	+	1420.79i	−0.146583	+	0.122998i
$512$		0			0
$513$	16692.7	−	5877.31i	1.43665	−	0.505827i
$514$		0			0
$515$	2728.15	−	2289.19i	0.233431	−	0.195872i
$516$		0			0
$517$	403.224	−	2286.80i	0.0343013	−	0.194532i
$518$		0			0
$519$	−2095.97	+	4812.48i	−0.177270	+	0.407022i
$520$		0			0
$521$	305.345	+	528.873i	0.0256764	+	0.0444728i	0.878578	−	0.477599i	$-0.158493\pi$
$521$	305.345	+	528.873i	0.0256764	+	0.0444728i	−0.852902	+	0.522072i	$0.825159\pi$
$522$		0			0
$523$	4132.80	−	7158.22i	0.345535	−	0.598484i	−0.639916	−	0.768445i	$-0.721031\pi$
$523$	4132.80	−	7158.22i	0.345535	−	0.598484i	0.985451	+	0.169961i	$0.0543641\pi$
$524$		0			0
$525$	4727.94	−	4976.21i	0.393037	−	0.413676i
$526$		0			0
$527$	1127.22	+	945.846i	0.0931732	+	0.0781816i
$528$		0			0
$529$	−9998.29	−	3639.08i	−0.821755	−	0.299094i
$530$		0			0
$531$	11190.6	−	2569.37i	0.914558	−	0.209983i
$532$		0			0
$533$	1256.91	+	7128.27i	0.102144	+	0.579286i
$534$		0			0
$535$	−2483.50	+	903.919i	−0.200693	+	0.0730464i
$536$		0			0
$537$	−18664.3	−	12369.8i	−1.49986	−	0.994034i
$538$		0			0
$539$	−1968.92			−0.157342
$540$		0			0
$541$	11983.2			0.952304			0.476152	−	0.879363i	$-0.342031\pi$
$541$	11983.2			0.952304			0.476152	+	0.879363i	$0.342031\pi$
$542$		0			0
$543$	−18581.8	+	9250.59i	−1.46855	+	0.731088i
$544$		0			0
$545$	−14272.3	+	5194.68i	−1.12175	+	0.408285i
$546$		0			0
$547$	2258.20	+	12806.9i	0.176515	+	1.00107i	0.936381	+	0.350986i	$0.114154\pi$
$547$	2258.20	+	12806.9i	0.176515	+	1.00107i	−0.759866	+	0.650080i	$0.774735\pi$
$548$		0			0
$549$	−1066.43	−	20828.3i	−0.0829034	−	1.61918i
$550$		0			0
$551$	27766.5	+	10106.2i	2.14681	+	0.781374i
$552$		0			0
$553$	3537.69	+	2968.48i	0.272040	+	0.228268i
$554$		0			0
$555$	103.729	+	24.9693i	0.00793345	+	0.00190970i
$556$		0			0
$557$	7371.70	−	12768.2i	0.560770	−	0.971283i	−0.436659	−	0.899627i	$-0.643838\pi$
$557$	7371.70	−	12768.2i	0.560770	−	0.971283i	0.997429	−	0.0716556i	$-0.0228283\pi$
$558$		0			0
$559$	492.784	+	853.527i	0.0372854	+	0.0645803i
$560$		0			0
$561$	1820.20	+	2462.96i	0.136986	+	0.185359i
$562$		0			0
$563$	2093.29	−	11871.6i	0.156699	−	0.888683i	−0.800517	−	0.599310i	$-0.795442\pi$
$563$	2093.29	−	11871.6i	0.156699	−	0.888683i	0.957216	−	0.289374i	$-0.0934470\pi$
$564$		0			0
$565$	−6383.23	+	5356.17i	−0.475300	+	0.398824i
$566$		0			0
$567$	−219.302	+	3031.28i	−0.0162431	+	0.224518i
$568$		0			0
$569$	14312.2	−	12009.4i	1.05448	−	0.884813i	0.0609216	−	0.998143i	$-0.480596\pi$
$569$	14312.2	−	12009.4i	1.05448	−	0.884813i	0.993557	+	0.113330i	$0.0361516\pi$
$570$		0			0
$571$	−2434.29	+	13805.6i	−0.178410	+	1.01181i	0.755724	+	0.654890i	$0.227285\pi$
$571$	−2434.29	+	13805.6i	−0.178410	+	1.01181i	−0.934134	+	0.356923i	$0.883826\pi$
$572$		0			0
$573$	13030.6	+	17632.0i	0.950019	+	1.28549i
$574$		0			0
$575$	23926.2	+	41441.4i	1.73529	+	3.00561i
$576$		0			0
$577$	−8845.23	+	15320.4i	−0.638183	+	1.10537i	0.347648	+	0.937625i	$0.386980\pi$
$577$	−8845.23	+	15320.4i	−0.638183	+	1.10537i	−0.985831	+	0.167741i	$0.946353\pi$
$578$		0			0
$579$	−11630.1	−	2799.55i	−0.834769	−	0.200942i
$580$		0			0
$581$	1696.07	+	1423.17i	0.121110	+	0.101623i
$582$		0			0
$583$	−1392.74	−	506.917i	−0.0989391	−	0.0360109i
$584$		0			0
$585$	−15076.5	−	7704.76i	−1.06554	−	0.544534i
$586$		0			0
$587$	−1937.34	−	10987.2i	−0.136222	−	0.772555i	−0.974001	−	0.226545i	$-0.927257\pi$
$587$	−1937.34	−	10987.2i	−0.136222	−	0.772555i	0.837778	−	0.546010i	$-0.183854\pi$
$588$		0			0
$589$	1789.42	−	651.296i	0.125181	−	0.0455623i
$590$		0			0
$591$	−6600.85	+	3286.10i	−0.459429	+	0.228718i
$592$		0			0
$593$	−10171.0			−0.704336			−0.352168	−	0.935937i	$-0.614555\pi$
$593$	−10171.0			−0.704336			−0.352168	+	0.935937i	$0.614555\pi$
$594$		0			0
$595$	8542.02			0.588552
$596$		0			0
$597$	−8615.28	−	5709.79i	−0.590620	−	0.391434i
$598$		0			0
$599$	4550.73	−	1656.33i	0.310414	−	0.112981i	−0.182116	−	0.983277i	$-0.558295\pi$
$599$	4550.73	−	1656.33i	0.310414	−	0.112981i	0.492529	+	0.870296i	$0.336072\pi$
$600$		0			0
$601$	−2049.47	−	11623.1i	−0.139101	−	0.788880i	−0.971916	−	0.235329i	$-0.924383\pi$
$601$	−2049.47	−	11623.1i	−0.139101	−	0.788880i	0.832815	−	0.553552i	$-0.186728\pi$
$602$		0			0
$603$	7711.96	+	8290.05i	0.520822	+	0.559862i
$604$		0			0
$605$	−25568.8	−	9306.28i	−1.71821	−	0.625379i
$606$		0			0
$607$	3586.38	+	3009.33i	0.239813	+	0.201227i	0.754771	−	0.655988i	$-0.227748\pi$
$607$	3586.38	+	3009.33i	0.239813	+	0.201227i	−0.514958	+	0.857216i	$0.672192\pi$
$608$		0			0
$609$	−3495.25	+	3678.79i	−0.232569	+	0.244782i
$610$		0			0
$611$	−5728.07	+	9921.31i	−0.379268	+	0.656912i
$612$		0			0
$613$	1434.25	+	2484.19i	0.0945005	+	0.163680i	0.909400	−	0.415923i	$-0.136541\pi$
$613$	1434.25	+	2484.19i	0.0945005	+	0.163680i	−0.814900	+	0.579602i	$0.803208\pi$
$614$		0			0
$615$	10582.2	−	24297.5i	0.693849	−	1.59312i
$616$		0			0
$617$	−955.679	+	5419.93i	−0.0623569	+	0.353643i	0.937625	+	0.347648i	$0.113020\pi$
$617$	−955.679	+	5419.93i	−0.0623569	+	0.353643i	−0.999982	+	0.00599552i	$0.998092\pi$
$618$		0			0
$619$	7221.69	−	6059.72i	0.468925	−	0.393475i	−0.377477	−	0.926019i	$-0.623208\pi$
$619$	7221.69	−	6059.72i	0.468925	−	0.393475i	0.846402	+	0.532544i	$0.178764\pi$
$620$		0			0
$621$	−19832.3	−	7455.83i	−1.28155	−	0.481791i
$622$		0			0
$623$	−537.314	+	450.860i	−0.0345538	+	0.0289941i
$624$		0			0
$625$	7843.50	−	44482.7i	0.501984	−	2.84689i
$626$		0			0
$627$	3938.11	−	446.290i	0.250834	−	0.0284260i
$628$		0			0
$629$	47.6061	+	82.4561i	0.00301777	+	0.00522693i
$630$		0			0
$631$	12997.8	−	22512.8i	0.820022	−	1.42032i	−0.0856432	−	0.996326i	$-0.527295\pi$
$631$	12997.8	−	22512.8i	0.820022	−	1.42032i	0.905665	−	0.423994i	$-0.139372\pi$
$632$		0			0
$633$	−440.014	−	1488.75i	−0.0276287	−	0.0934796i
$634$		0			0
$635$	799.297	+	670.690i	0.0499514	+	0.0419142i
$636$		0			0
$637$	9128.02	+	3322.33i	0.567764	+	0.206649i
$638$		0			0
$639$	3710.33	−	4911.46i	0.229700	−	0.304060i
$640$		0			0
$641$	1345.12	+	7628.57i	0.0828847	+	0.470063i	0.997793	+	0.0664010i	$0.0211516\pi$
$641$	1345.12	+	7628.57i	0.0828847	+	0.470063i	−0.914908	+	0.403662i	$0.867737\pi$
$642$		0			0
$643$	6591.22	−	2399.01i	0.404249	−	0.147135i	−0.131890	−	0.991264i	$-0.542105\pi$
$643$	6591.22	−	2399.01i	0.404249	−	0.147135i	0.536139	+	0.844130i	$0.319882\pi$
$644$		0			0
$645$	222.464	−	3601.68i	0.0135806	−	0.219870i
$646$		0			0
$647$	−6294.68			−0.382488			−0.191244	−	0.981543i	$-0.561252\pi$
$647$	−6294.68			−0.382488			−0.191244	+	0.981543i	$0.561252\pi$
$648$		0			0
$649$	2571.37			0.155524
$650$		0			0
$651$	−20.1609	+	326.404i	−0.00121378	+	0.0196510i
$652$		0			0
$653$	−4566.21	+	1661.97i	−0.273644	+	0.0995984i	−0.475197	−	0.879879i	$-0.657623\pi$
$653$	−4566.21	+	1661.97i	−0.273644	+	0.0995984i	0.201553	+	0.979478i	$0.435401\pi$
$654$		0			0
$655$	−2988.41	−	16948.1i	−0.178270	−	1.01102i
$656$		0			0
$657$	−5577.47	−	13183.8i	−0.331199	−	0.782874i
$658$		0			0
$659$	16715.1	+	6083.80i	0.988054	+	0.359622i	0.784966	−	0.619538i	$-0.212680\pi$
$659$	16715.1	+	6083.80i	0.988054	+	0.359622i	0.203088	+	0.979161i	$0.434902\pi$
$660$		0			0
$661$	−6238.48	−	5234.71i	−0.367093	−	0.308028i	0.440517	−	0.897744i	$-0.354795\pi$
$661$	−6238.48	−	5234.71i	−0.367093	−	0.308028i	−0.807610	+	0.589716i	$0.799240\pi$
$662$		0			0
$663$	−4282.58	−	14489.8i	−0.250862	−	0.848772i
$664$		0			0
$665$	5527.19	−	9573.37i	0.322308	−	0.558255i
$666$		0			0
$667$	−17688.1	−	30636.6i	−1.02681	−	1.77849i
$668$		0			0
$669$	−16628.9	+	1884.49i	−0.961005	+	0.108907i
$670$		0			0
$671$	811.049	−	4599.69i	0.0466620	−	0.264633i
$672$		0			0
$673$	730.692	−	613.124i	0.0418516	−	0.0351177i	−0.621622	−	0.783317i	$-0.713526\pi$
$673$	730.692	−	613.124i	0.0418516	−	0.0351177i	0.663474	+	0.748200i	$0.269082\pi$
$674$		0			0
$675$	21820.6	+	38730.7i	1.24426	+	2.20851i
$676$		0			0
$677$	−17325.9	+	14538.2i	−0.983589	+	0.825329i	−0.984627	−	0.174670i	$-0.944114\pi$
$677$	−17325.9	+	14538.2i	−0.983589	+	0.825329i	0.00103773	+	0.999999i	$0.499670\pi$
$678$		0			0
$679$	1060.04	−	6011.78i	0.0599124	−	0.339780i
$680$		0			0
$681$	6962.38	−	15986.1i	0.391776	−	0.899541i
$682$		0			0
$683$	−12017.4	−	20814.8i	−0.673257	−	1.16611i	−0.976975	−	0.213353i	$-0.931562\pi$
$683$	−12017.4	−	20814.8i	−0.673257	−	1.16611i	0.303718	−	0.952762i	$-0.401772\pi$
$684$		0			0
$685$	−6125.94	+	10610.4i	−0.341694	+	0.591831i
$686$		0			0
$687$	−14265.1	+	15014.2i	−0.792211	+	0.833811i
$688$		0			0
$689$	5601.45	+	4700.18i	0.309722	+	0.259887i
$690$		0			0
$691$	24335.6	+	8857.43i	1.33975	+	0.487630i	0.909735	−	0.415190i	$-0.136285\pi$
$691$	24335.6	+	8857.43i	1.33975	+	0.487630i	0.430019	+	0.902820i	$0.358507\pi$
$692$		0			0
$693$	−199.782	+	650.656i	−0.0109511	+	0.0356658i
$694$		0			0
$695$	6950.84	+	39420.2i	0.379368	+	2.15150i
$696$		0			0
$697$	22224.0	−	8088.87i	1.20774	−	0.439581i
$698$		0			0
$699$	−1564.48	−	1036.86i	−0.0846553	−	0.0561054i
$700$		0			0
$701$	−5879.83			−0.316802			−0.158401	−	0.987375i	$-0.550634\pi$
$701$	−5879.83			−0.316802			−0.158401	+	0.987375i	$0.550634\pi$
$702$		0			0
$703$	123.216			0.00661048
$704$		0			0
$705$	37549.5	−	18693.3i	2.00595	−	0.998624i
$706$		0			0
$707$	−4062.63	+	1478.68i	−0.216112	+	0.0786583i
$708$		0			0
$709$	386.211	+	2190.31i	0.0204576	+	0.116021i	0.993327	−	0.115336i	$-0.0367945\pi$
$709$	386.211	+	2190.31i	0.0204576	+	0.116021i	−0.972869	+	0.231357i	$0.925683\pi$
$710$		0			0
$711$	−25103.1	+	16259.2i	−1.32411	+	0.857621i
$712$		0			0
$713$	−2142.34	−	779.747i	−0.112526	−	0.0409562i
$714$		0			0
$715$	−2904.67	−	2437.31i	−0.151928	−	0.127483i
$716$		0			0
$717$	1942.73	+	467.646i	0.101189	+	0.0243578i
$718$		0			0
$719$	14710.5	−	25479.4i	0.763018	−	1.32159i	−0.178270	−	0.983982i	$-0.557050\pi$
$719$	14710.5	−	25479.4i	0.763018	−	1.32159i	0.941288	−	0.337605i	$-0.109617\pi$
$720$		0			0
$721$	353.162	+	611.694i	0.0182419	+	0.0315960i
$722$		0			0
$723$	7531.96	+	10191.7i	0.387437	+	0.524250i
$724$		0			0
$725$	−12888.9	+	73096.8i	−0.660253	+	3.74448i
$726$		0			0
$727$	25940.8	−	21766.9i	1.32337	−	1.11044i	0.337794	−	0.941220i	$-0.390319\pi$
$727$	25940.8	−	21766.9i	1.32337	−	1.11044i	0.985578	−	0.169220i	$-0.0541250\pi$
$728$		0			0
$729$	−18350.1	−	7120.07i	−0.932280	−	0.361737i
$730$		0			0
$731$	2466.86	−	2069.94i	0.124816	−	0.104733i
$732$		0			0
$733$	−2518.64	+	14283.9i	−0.126914	+	0.719766i	0.853238	+	0.521521i	$0.174635\pi$
$733$	−2518.64	+	14283.9i	−0.126914	+	0.719766i	−0.980153	+	0.198245i	$0.936476\pi$
$734$		0			0
$735$	−21138.3	−	28602.7i	−1.06081	−	1.43541i
$736$		0			0
$737$	1267.85	+	2195.98i	0.0633675	+	0.109756i
$738$		0			0
$739$	−5275.76	+	9137.89i	−0.262614	+	0.454862i	−0.966936	−	0.255020i	$-0.917918\pi$
$739$	−5275.76	+	9137.89i	−0.262614	+	0.454862i	0.704321	+	0.709881i	$0.251251\pi$
$740$		0			0
$741$	−19010.3	−	4576.08i	−0.942458	−	0.226864i
$742$		0			0
$743$	−17080.5	−	14332.3i	−0.843371	−	0.707672i	0.114949	−	0.993371i	$-0.463330\pi$
$743$	−17080.5	−	14332.3i	−0.843371	−	0.707672i	−0.958319	+	0.285699i	$0.907774\pi$
$744$		0			0
$745$	25248.4	+	9189.65i	1.24165	+	0.451923i
$746$		0			0
$747$	−12035.2	+	7795.15i	−0.589483	+	0.381807i
$748$		0			0
$749$	−91.0200	−	516.200i	−0.00444032	−	0.0251823i
$750$		0			0
$751$	−11137.3	+	4053.63i	−0.541151	+	0.196963i	−0.598110	−	0.801414i	$-0.704082\pi$
$751$	−11137.3	+	4053.63i	−0.541151	+	0.196963i	0.0569597	+	0.998376i	$0.481859\pi$
$752$		0			0
$753$	31075.6	−	15470.4i	1.50393	−	0.748700i
$754$		0			0
$755$	64725.8			3.12002
$756$		0			0
$757$	−33298.7			−1.59876			−0.799379	−	0.600827i	$-0.794838\pi$
$757$	−33298.7			−1.59876			−0.799379	+	0.600827i	$0.794838\pi$
$758$		0			0
$759$	−3955.19	−	2621.31i	−0.189150	−	0.125359i
$760$		0			0
$761$	37817.9	−	13764.6i	1.80144	−	0.655672i	0.803247	−	0.595647i	$-0.203104\pi$
$761$	37817.9	−	13764.6i	1.80144	−	0.655672i	0.998197	−	0.0600251i	$-0.0191181\pi$
$762$		0			0
$763$	−523.077	−	2966.52i	−0.0248187	−	0.140754i
$764$		0			0
$765$	−16238.0	+	52884.4i	−0.767434	+	2.49940i
$766$		0			0
$767$	−11921.0	−	4338.88i	−0.561201	−	0.204260i
$768$		0			0
$769$	−5901.10	−	4951.61i	−0.276722	−	0.232197i	0.493855	−	0.869544i	$-0.335587\pi$
$769$	−5901.10	−	4951.61i	−0.276722	−	0.232197i	−0.770577	+	0.637347i	$0.780032\pi$
$770$		0			0
$771$	−16643.7	+	17517.7i	−0.777442	+	0.818266i
$772$		0			0
$773$	−2618.83	+	4535.94i	−0.121853	+	0.211056i	−0.920499	−	0.390746i	$-0.872217\pi$
$773$	−2618.83	+	4535.94i	−0.121853	+	0.211056i	0.798645	+	0.601802i	$0.205550\pi$
$774$		0			0
$775$	2391.71	+	4142.57i	0.110855	+	0.192007i
$776$		0			0
$777$	−8.44933	+	19.4002i	−0.000390113	+	0.000895725i
$778$		0			0
$779$	5314.72	−	30141.3i	0.244441	−	1.38629i
$780$		0			0
$781$	1056.00	−	886.092i	0.0483826	−	0.0405978i
$782$		0			0
$783$	−16131.4	−	28632.7i	−0.736257	−	1.30683i
$784$		0			0
$785$	−15584.3	+	13076.8i	−0.708569	+	0.594560i
$786$		0			0
$787$	−5676.14	+	32191.0i	−0.257093	+	1.45805i	0.533549	+	0.845769i	$0.320858\pi$
$787$	−5676.14	+	32191.0i	−0.257093	+	1.45805i	−0.790642	+	0.612279i	$0.790253\pi$
$788$		0			0
$789$	12106.6	−	1371.99i	0.546270	−	0.0619066i
$790$		0			0
$791$	−826.315	−	1431.22i	−0.0371433	−	0.0643341i
$792$		0			0
$793$	−11521.5	+	19955.8i	−0.515940	+	0.893634i
$794$		0			0
$795$	−7588.39	−	25674.7i	−0.338532	−	1.14539i
$796$		0			0
$797$	15837.0	+	13288.8i	0.703857	+	0.590606i	0.922868	−	0.385116i	$-0.125839\pi$
$797$	15837.0	+	13288.8i	0.703857	+	0.590606i	−0.219011	+	0.975722i	$0.570283\pi$
$798$		0			0
$799$	35174.5	+	12802.5i	1.55743	+	0.566857i
$800$		0			0
$801$	−1769.90	−	4183.63i	−0.0780730	−	0.184546i
$802$		0			0
$803$	−556.696	−	3157.18i	−0.0244650	−	0.138748i
$804$		0			0
$805$	−12436.4	+	4526.49i	−0.544505	+	0.198184i
$806$		0			0
$807$	−1714.23	+	27753.3i	−0.0747755	+	1.21061i
$808$		0			0
$809$	−2618.04			−0.113777			−0.0568884	−	0.998381i	$-0.518118\pi$
$809$	−2618.04			−0.113777			−0.0568884	+	0.998381i	$0.518118\pi$
$810$		0			0
$811$	−28096.0			−1.21650			−0.608251	−	0.793744i	$-0.708129\pi$
$811$	−28096.0			−1.21650			−0.608251	+	0.793744i	$0.708129\pi$
$812$		0			0
$813$	927.647	−	15018.6i	0.0400172	−	0.647877i
$814$		0			0
$815$	−73724.7	+	26833.6i	−3.16867	+	1.15330i
$816$		0			0
$817$	−723.660	−	4104.08i	−0.0309886	−	0.175745i
$818$		0			0
$819$	2024.10	−	2679.36i	0.0863589	−	0.114316i
$820$		0			0
$821$	26718.4	+	9724.72i	1.13579	+	0.413392i	0.840390	−	0.541983i	$-0.182326\pi$
$821$	26718.4	+	9724.72i	1.13579	+	0.413392i	0.295396	+	0.955375i	$0.404548\pi$
$822$		0			0
$823$	19859.2	+	16663.9i	0.841128	+	0.705791i	0.957817	−	0.287378i	$-0.0927836\pi$
$823$	19859.2	+	16663.9i	0.841128	+	0.705791i	−0.116689	+	0.993169i	$0.537228\pi$
$824$		0			0
$825$	2821.82	+	9547.41i	0.119083	+	0.402907i
$826$		0			0
$827$	5254.81	−	9101.60i	0.220952	−	0.382701i	−0.734145	−	0.678993i	$-0.762417\pi$
$827$	5254.81	−	9101.60i	0.220952	−	0.382701i	0.955097	+	0.296292i	$0.0957501\pi$
$828$		0			0
$829$	6930.26	+	12003.6i	0.290347	+	0.502896i	0.973892	−	0.227012i	$-0.0728958\pi$
$829$	6930.26	+	12003.6i	0.290347	+	0.502896i	−0.683544	+	0.729909i	$0.739562\pi$
$830$		0			0
$831$	−13716.2	+	1554.40i	−0.572575	+	0.0648877i
$832$		0			0
$833$	5511.44	−	31256.9i	0.229244	−	1.30011i
$834$		0			0
$835$	−58189.0	+	48826.3i	−2.41163	+	2.02360i
$836$		0			0
$837$	−1982.48	−	745.300i	−0.0818690	−	0.0307782i
$838$		0			0
$839$	−28428.4	+	23854.3i	−1.16980	+	0.981575i	−0.999992	−	0.00390245i	$-0.998758\pi$
$839$	−28428.4	+	23854.3i	−1.16980	+	0.981575i	−0.169804	+	0.985478i	$0.554313\pi$
$840$		0			0
$841$	5293.37	−	30020.2i	0.217039	−	1.23089i
$842$		0			0
$843$	8435.31	−	19368.0i	0.344635	−	0.791304i
$844$		0			0
$845$	−13737.5	−	23794.1i	−0.559273	−	0.968689i
$846$		0			0
$847$	2698.26	−	4673.52i	0.109461	−	0.189592i
$848$		0			0
$849$	7782.38	−	8191.04i	0.314595	−	0.331114i
$850$		0			0
$851$	−113.004	−	94.8219i	−0.00455199	−	0.00381957i
$852$		0			0
$853$	20206.7	+	7354.62i	0.811093	+	0.295214i	0.714075	−	0.700069i	$-0.246847\pi$
$853$	20206.7	+	7354.62i	0.811093	+	0.295214i	0.0970180	+	0.995283i	$0.469070\pi$
$854$		0			0
$855$	48762.7	+	52417.9i	1.95047	+	2.09667i
$856$		0			0
$857$	4386.32	+	24876.0i	0.174835	+	0.991540i	0.938334	+	0.345730i	$0.112369\pi$
$857$	4386.32	+	24876.0i	0.174835	+	0.991540i	−0.763499	+	0.645809i	$0.776520\pi$
$858$		0			0
$859$	12789.1	−	4654.85i	0.507984	−	0.184891i	−0.0752975	−	0.997161i	$-0.523991\pi$
$859$	12789.1	−	4654.85i	0.507984	−	0.184891i	0.583282	+	0.812270i	$0.301768\pi$
$860$		0			0
$861$	4381.27	+	2903.69i	0.173418	+	0.114933i
$862$		0			0
$863$	−15562.5			−0.613850			−0.306925	−	0.951734i	$-0.599300\pi$
$863$	−15562.5			−0.613850			−0.306925	+	0.951734i	$0.599300\pi$
$864$		0			0
$865$	−21234.7			−0.834684
$866$		0			0
$867$	−21341.6	+	10624.5i	−0.835983	+	0.416178i
$868$		0			0
$869$	−6294.17	+	2290.89i	−0.245702	+	0.0894282i
$870$		0			0
$871$	−2172.35	−	12320.0i	−0.0845089	−	0.479274i
$872$		0			0
$873$	35204.4	+	17990.9i	1.36482	+	0.697481i
$874$		0			0
$875$	15799.8	+	5750.65i	0.610435	+	0.222180i
$876$		0			0
$877$	−18024.2	−	15124.1i	−0.693995	−	0.582331i	0.226063	−	0.974113i	$-0.427414\pi$
$877$	−18024.2	−	15124.1i	−0.693995	−	0.582331i	−0.920058	+	0.391782i	$0.871859\pi$
$878$		0			0
$879$	20524.5	+	4940.57i	0.787571	+	0.189580i
$880$		0			0
$881$	11773.4	−	20392.2i	0.450234	−	0.779829i	−0.548166	−	0.836370i	$-0.684674\pi$
$881$	11773.4	−	20392.2i	0.450234	−	0.779829i	0.998400	+	0.0565407i	$0.0180071\pi$
$882$		0			0
$883$	3943.58	+	6830.49i	0.150297	+	0.260322i	0.931337	−	0.364159i	$-0.118644\pi$
$883$	3943.58	+	6830.49i	0.150297	+	0.260322i	−0.781040	+	0.624481i	$0.785310\pi$
$884$		0			0
$885$	27606.1	+	37354.5i	1.04855	+	1.41882i
$886$		0			0
$887$	1461.95	−	8291.13i	0.0553410	−	0.313855i	−0.944554	−	0.328357i	$-0.893505\pi$
$887$	1461.95	−	8291.13i	0.0553410	−	0.313855i	0.999895	+	0.0145021i	$0.00461633\pi$
$888$		0			0
$889$	−158.525	+	133.018i	−0.00598060	+	0.00501832i
$890$		0			0
$891$	−3648.49	−	2473.74i	−0.137182	−	0.0930117i
$892$		0			0
$893$	37108.2	−	31137.5i	1.39057	−	1.16683i
$894$		0			0
$895$	15729.3	−	89205.5i	0.587457	−	3.33163i
$896$		0			0
$897$	13913.3	+	18826.4i	0.517895	+	0.700776i
$898$		0			0
$899$	−1768.13	−	3062.50i	−0.0655957	−	0.113615i
$900$		0			0
$901$	11945.9	−	20691.0i	0.441706	−	0.765057i
$902$		0			0
$903$	695.808	+	167.492i	0.0256423	+	0.00617251i
$904$		0			0
$905$	−64325.4	−	53975.4i	−2.36270	−	1.98254i
$906$		0			0
$907$	−4157.15	−	1513.08i	−0.152190	−	0.0553925i	0.264802	−	0.964303i	$-0.414693\pi$
$907$	−4157.15	−	1513.08i	−0.152190	−	0.0553925i	−0.416992	+	0.908910i	$0.636916\pi$
$908$		0			0
$909$	−1431.73	−	27963.1i	−0.0522416	−	1.02033i
$910$		0			0
$911$	−503.055	−	2852.97i	−0.0182952	−	0.103757i	0.974293	−	0.225286i	$-0.0723316\pi$
$911$	−503.055	−	2852.97i	−0.0182952	−	0.103757i	−0.992588	+	0.121528i	$0.961220\pi$
$912$		0			0
$913$	−3017.61	+	1098.32i	−0.109385	+	0.0398128i
$914$		0			0
$915$	75527.5	−	37599.9i	2.72881	−	1.35848i
$916$		0			0
$917$	3413.18			0.122915
$918$		0			0
$919$	24120.5			0.865790			0.432895	−	0.901444i	$-0.357492\pi$
$919$	24120.5			0.865790			0.432895	+	0.901444i	$0.357492\pi$
$920$		0			0
$921$	−33569.7	−	22248.4i	−1.20104	−	0.795992i
$922$		0			0
$923$	−6390.85	+	2326.08i	−0.227906	+	0.0829511i
$924$		0			0
$925$	53.7463	+	304.810i	0.00191045	+	0.0108347i
$926$		0			0
$927$	−4458.40	+	1023.65i	−0.157965	+	0.0362688i
$928$		0			0
$929$	15087.5	+	5491.40i	0.532836	+	0.193936i	0.594404	−	0.804166i	$-0.297388\pi$
$929$	15087.5	+	5491.40i	0.532836	+	0.193936i	−0.0615682	+	0.998103i	$0.519610\pi$
$930$		0			0
$931$	−31464.6	−	26401.9i	−1.10764	−	0.929419i
$932$		0			0
$933$	21076.4	−	22183.1i	0.739560	−	0.778395i
$934$		0			0
$935$	−6194.65	+	10729.4i	−0.216670	+	0.375284i
$936$		0			0
$937$	16037.8	+	27778.3i	0.559160	+	0.968494i	0.997567	+	0.0697170i	$0.0222096\pi$
$937$	16037.8	+	27778.3i	0.559160	+	0.968494i	−0.438407	+	0.898777i	$0.644457\pi$
$938$		0			0
$939$	6399.56	−	14693.8i	0.222409	−	0.510664i
$940$		0			0
$941$	−310.666	+	1761.87i	−0.0107624	+	0.0610366i	−0.989716	−	0.143046i	$-0.954310\pi$
$941$	−310.666	+	1761.87i	−0.0107624	+	0.0610366i	0.978954	+	0.204083i	$0.0654213\pi$
$942$		0			0
$943$	−28069.8	+	23553.4i	−0.969331	+	0.813365i
$944$		0			0
$945$	−11597.0	+	4083.16i	−0.399206	+	0.140556i
$946$		0			0
$947$	17838.2	−	14968.0i	0.612104	−	0.513616i	−0.283207	−	0.959059i	$-0.591398\pi$
$947$	17838.2	−	14968.0i	0.612104	−	0.513616i	0.895310	+	0.445443i	$0.146954\pi$
$948$		0			0
$949$	−2746.50	+	15576.2i	−0.0939464	+	0.532797i
$950$		0			0
$951$	2183.42	−	247.438i	0.0744503	−	0.00843715i
$952$		0			0
$953$	378.222	+	655.100i	0.0128561	+	0.0222673i	0.872382	−	0.488825i	$-0.162574\pi$
$953$	378.222	+	655.100i	0.0128561	+	0.0222673i	−0.859526	+	0.511092i	$0.829241\pi$
$954$		0			0
$955$	−44346.7	+	76810.8i	−1.50264	+	2.60266i
$956$		0			0
$957$	−2086.10	−	7058.16i	−0.0704641	−	0.238410i
$958$		0			0
$959$	−1861.43	−	1561.92i	−0.0626784	−	0.0525934i
$960$		0			0
$961$	27780.2	+	10111.2i	0.932504	+	0.339404i
$962$		0			0
$963$	3368.87	+	417.762i	0.112731	+	0.0139794i
$964$		0			0
$965$	−8403.25	−	47657.2i	−0.280321	−	1.58978i
$966$		0			0
$967$	−18140.2	+	6602.48i	−0.603256	+	0.219567i	−0.625550	−	0.780184i	$-0.715125\pi$
$967$	−18140.2	+	6602.48i	−0.603256	+	0.219567i	0.0222937	+	0.999751i	$0.492903\pi$
$968$		0			0
$969$	−3938.70	+	63767.3i	−0.130577	+	2.11403i
$970$		0			0
$971$	−11825.1			−0.390818			−0.195409	−	0.980722i	$-0.562603\pi$
$971$	−11825.1			−0.390818			−0.195409	+	0.980722i	$0.562603\pi$
$972$		0			0
$973$	−7938.83			−0.261570
$974$		0			0
$975$	3028.03	−	49023.7i	0.0994612	−	1.61027i
$976$		0			0
$977$	14594.2	−	5311.86i	0.477902	−	0.173942i	−0.0918267	−	0.995775i	$-0.529271\pi$
$977$	14594.2	−	5311.86i	0.477902	−	0.173942i	0.569729	+	0.821833i	$0.307048\pi$
$978$		0			0
$979$	−176.657	−	1001.87i	−0.00576709	−	0.0327068i
$980$		0			0
$981$	19360.4	+	2400.81i	0.630100	+	0.0781366i
$982$		0			0
$983$	−36816.8	−	13400.2i	−1.19458	−	0.434792i	−0.333251	−	0.942838i	$-0.608146\pi$
$983$	−36816.8	−	13400.2i	−1.19458	−	0.434792i	−0.861330	+	0.508046i	$0.830368\pi$
$984$		0			0
$985$	−22850.4	−	19173.8i	−0.739162	−	0.620231i
$986$		0			0
$987$	2357.93	+	7977.86i	0.0760422	+	0.257283i
$988$		0			0
$989$	−2494.65	+	4320.86i	−0.0802076	+	0.138924i
$990$		0			0
$991$	−20152.2	−	34904.6i	−0.645969	−	1.11885i	−0.984077	−	0.177743i	$-0.943120\pi$
$991$	−20152.2	−	34904.6i	−0.645969	−	1.11885i	0.338108	−	0.941107i	$-0.390213\pi$
$992$		0			0
$993$	−38091.8	+	4316.79i	−1.21733	+	0.137955i
$994$		0			0
$995$	7260.52	−	41176.5i	0.231331	−	1.31194i
$996$		0			0
$997$	−13367.5	+	11216.6i	−0.424626	+	0.356303i	−0.829919	−	0.557883i	$-0.811614\pi$
$997$	−13367.5	+	11216.6i	−0.424626	+	0.356303i	0.405294	+	0.914186i	$0.367169\pi$
$998$		0			0
$999$	−104.047	−	89.1896i	−0.00329518	−	0.00282466i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.i.a.49.5	✓	54
3.2	odd	2		324.4.i.a.37.1		54
27.11	odd	18		324.4.i.a.289.1		54
27.16	even	9	inner	108.4.i.a.97.5	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.4.i.a.49.5	✓	54	1.1	even	1	trivial
108.4.i.a.97.5	yes	54	27.16	even	9	inner
324.4.i.a.37.1		54	3.2	odd	2
324.4.i.a.289.1		54	27.11	odd	18

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.320339 - 5.18627i) q^{3} +(19.7528 - 7.18944i) q^{5} +(0.723940 + 4.10567i) q^{7} +(-26.7948 - 3.32273i) q^{9} +O(q^{10})\)	\(q+(0.320339 - 5.18627i) q^{3} +(19.7528 - 7.18944i) q^{5} +(0.723940 + 4.10567i) q^{7} +(-26.7948 - 3.32273i) q^{9} +(-5.68204 - 2.06810i) q^{11} +(22.8525 + 19.1756i) q^{13} +(-30.9588 - 104.747i) q^{15} +(48.7365 - 84.4141i) q^{17} +(-63.0708 - 109.242i) q^{19} +(21.5250 - 2.43934i) q^{21} +(-26.2243 + 148.725i) q^{23} +(242.731 - 203.675i) q^{25} +(-25.8160 + 137.900i) q^{27} +(-179.445 + 150.572i) q^{29} +(-2.62143 + 14.8669i) q^{31} +(-12.5459 + 28.8061i) q^{33} +(43.8173 + 75.8939i) q^{35} +(-0.488402 + 0.845938i) q^{37} +(106.770 - 112.377i) q^{39} +(185.869 + 155.962i) q^{41} +(31.0450 + 11.2995i) q^{43} +(-553.161 + 127.006i) q^{45} +(66.6849 + 378.189i) q^{47} +(305.982 - 111.368i) q^{49} +(-422.182 - 279.802i) q^{51} +245.113 q^{53} -127.105 q^{55} +(-586.761 + 292.108i) q^{57} +(-399.605 + 145.444i) q^{59} +(134.131 + 760.693i) q^{61} +(-5.75579 - 112.416i) q^{63} +(589.264 + 214.475i) q^{65} +(-321.243 - 269.555i) q^{67} +(762.929 + 183.649i) q^{69} +(-113.989 + 197.435i) q^{71} +(265.093 + 459.155i) q^{73} +(-978.558 - 1324.11i) q^{75} +(4.37745 - 24.8258i) q^{77} +(848.570 - 712.034i) q^{79} +(706.919 + 178.063i) q^{81} +(406.829 - 341.370i) q^{83} +(355.794 - 2017.81i) q^{85} +(723.423 + 978.882i) q^{87} +(84.1224 + 145.704i) q^{89} +(-62.1846 + 107.707i) q^{91} +(76.2639 + 18.3579i) q^{93} +(-2031.21 - 1704.39i) q^{95} +(-1375.96 - 500.807i) q^{97} +(145.377 + 74.2940i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 12 q^{5} - 48 q^{9}+O(q^{10}) \) 54 * q + 12 * q^5 - 48 * q^9	\( 54 q + 12 q^{5} - 48 q^{9} - 87 q^{11} + 234 q^{15} + 204 q^{17} - 12 q^{21} + 96 q^{23} - 216 q^{25} + 27 q^{27} + 318 q^{29} - 54 q^{31} + 63 q^{33} + 6 q^{35} + 66 q^{39} + 867 q^{41} - 513 q^{43} - 306 q^{45} - 1548 q^{47} + 594 q^{49} - 1368 q^{51} - 1068 q^{53} - 1269 q^{57} - 1218 q^{59} - 54 q^{61} + 30 q^{63} + 96 q^{65} - 2997 q^{67} + 1476 q^{69} - 120 q^{71} - 216 q^{73} + 732 q^{75} + 3480 q^{77} + 2808 q^{79} + 3348 q^{81} + 4464 q^{83} + 2160 q^{85} + 4824 q^{87} + 4029 q^{89} + 270 q^{91} + 1164 q^{93} - 1650 q^{95} - 3483 q^{97} - 5076 q^{99}+O(q^{100}) \) 54 * q + 12 * q^5 - 48 * q^9 - 87 * q^11 + 234 * q^15 + 204 * q^17 - 12 * q^21 + 96 * q^23 - 216 * q^25 + 27 * q^27 + 318 * q^29 - 54 * q^31 + 63 * q^33 + 6 * q^35 + 66 * q^39 + 867 * q^41 - 513 * q^43 - 306 * q^45 - 1548 * q^47 + 594 * q^49 - 1368 * q^51 - 1068 * q^53 - 1269 * q^57 - 1218 * q^59 - 54 * q^61 + 30 * q^63 + 96 * q^65 - 2997 * q^67 + 1476 * q^69 - 120 * q^71 - 216 * q^73 + 732 * q^75 + 3480 * q^77 + 2808 * q^79 + 3348 * q^81 + 4464 * q^83 + 2160 * q^85 + 4824 * q^87 + 4029 * q^89 + 270 * q^91 + 1164 * q^93 - 1650 * q^95 - 3483 * q^97 - 5076 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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