LMFDB - Embedded newform 216.4.d.d.109.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,4,Mod(109,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("216.109");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	216.d (of order $2$, degree $1$, 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:	$12.7444125612$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.8
Character	$\chi$	$=$	216.109
Dual form			216.4.d.d.109.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.94701 + 2.05162i) q^{2} +(-0.418326 - 7.98906i) q^{4} +13.3613i q^{5} +33.2593 q^{7} +(17.2050 + 14.6965i) q^{8} +O(q^{10})$	\(q+(-1.94701 + 2.05162i) q^{2} +(-0.418326 - 7.98906i) q^{4} +13.3613i q^{5} +33.2593 q^{7} +(17.2050 + 14.6965i) q^{8} +(-27.4125 - 26.0146i) q^{10} -42.9405i q^{11} -73.9216i q^{13} +(-64.7560 + 68.2355i) q^{14} +(-63.6500 + 6.68406i) q^{16} -9.83895 q^{17} +39.7046i q^{19} +(106.745 - 5.58940i) q^{20} +(88.0978 + 83.6055i) q^{22} +182.876 q^{23} -53.5255 q^{25} +(151.659 + 143.926i) q^{26} +(-13.9132 - 265.710i) q^{28} +133.382i q^{29} +160.290 q^{31} +(110.214 - 143.600i) q^{32} +(19.1565 - 20.1858i) q^{34} +444.389i q^{35} +66.4666i q^{37} +(-81.4589 - 77.3051i) q^{38} +(-196.365 + 229.882i) q^{40} +301.253 q^{41} +53.4876i q^{43} +(-343.054 + 17.9632i) q^{44} +(-356.061 + 375.193i) q^{46} -576.665 q^{47} +763.179 q^{49} +(104.215 - 109.814i) q^{50} +(-590.564 + 30.9234i) q^{52} -317.543i q^{53} +573.743 q^{55} +(572.227 + 488.795i) q^{56} +(-273.649 - 259.695i) q^{58} +240.089i q^{59} +327.329i q^{61} +(-312.085 + 328.855i) q^{62} +(80.0258 + 505.707i) q^{64} +987.692 q^{65} +426.914i q^{67} +(4.11589 + 78.6039i) q^{68} +(-911.718 - 865.228i) q^{70} -506.816 q^{71} +66.7763 q^{73} +(-136.365 - 129.411i) q^{74} +(317.202 - 16.6095i) q^{76} -1428.17i q^{77} -35.3259 q^{79} +(-89.3081 - 850.450i) q^{80} +(-586.541 + 618.058i) q^{82} -304.430i q^{83} -131.462i q^{85} +(-109.736 - 104.141i) q^{86} +(631.075 - 738.793i) q^{88} -1100.06 q^{89} -2458.58i q^{91} +(-76.5018 - 1461.01i) q^{92} +(1122.77 - 1183.10i) q^{94} -530.507 q^{95} +1299.31 q^{97} +(-1485.91 + 1565.76i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4}+O(q^{10}) $ 24 * q - 12 * q^4	$ 24 q - 12 q^{4} - 24 q^{10} - 288 q^{16} + 336 q^{22} - 600 q^{25} + 84 q^{28} + 528 q^{31} + 24 q^{34} + 648 q^{40} - 864 q^{46} + 1536 q^{49} - 636 q^{52} + 144 q^{55} + 96 q^{58} - 888 q^{64} - 384 q^{70} + 216 q^{73} - 444 q^{76} - 2352 q^{79} + 336 q^{82} + 1896 q^{88} + 1200 q^{94} + 696 q^{97}+O(q^{100}) $ 24 * q - 12 * q^4 - 24 * q^10 - 288 * q^16 + 336 * q^22 - 600 * q^25 + 84 * q^28 + 528 * q^31 + 24 * q^34 + 648 * q^40 - 864 * q^46 + 1536 * q^49 - 636 * q^52 + 144 * q^55 + 96 * q^58 - 888 * q^64 - 384 * q^70 + 216 * q^73 - 444 * q^76 - 2352 * q^79 + 336 * q^82 + 1896 * q^88 + 1200 * q^94 + 696 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.94701	+	2.05162i	−0.688371	+	0.725359i
$2$	−1.94701	+	2.05162i	−0.688371	+	0.725359i
$3$		0			0
$3$		0			0
$4$	−0.418326	−	7.98906i	−0.0522908	−	0.998632i
$5$			13.3613i			1.19507i	0.801841	+	0.597537i	$0.203854\pi$
$5$			13.3613i			1.19507i	−0.801841	+	0.597537i	$0.796146\pi$
$6$		0			0
$7$	33.2593			1.79583			0.897916	−	0.440167i	$-0.145081\pi$
$7$	33.2593			1.79583			0.897916	+	0.440167i	$0.145081\pi$
$8$	17.2050	+	14.6965i	0.760362	+	0.649500i
$9$		0			0
$10$	−27.4125	−	26.0146i	−0.866858	−	0.822655i
$11$		−	42.9405i		−	1.17701i	−0.808495	−	0.588503i	$-0.799718\pi$
$11$		−	42.9405i		−	1.17701i	0.808495	−	0.588503i	$-0.200282\pi$
$12$		0			0
$13$		−	73.9216i		−	1.57709i	−0.614977	−	0.788545i	$-0.710835\pi$
$13$		−	73.9216i		−	1.57709i	0.614977	−	0.788545i	$-0.289165\pi$
$14$	−64.7560	+	68.2355i	−1.23620	+	1.30262i
$15$		0			0
$16$	−63.6500	+	6.68406i	−0.994531	+	0.104438i
$17$	−9.83895			−0.140370			−0.0701852	−	0.997534i	$-0.522359\pi$
$17$	−9.83895			−0.140370			−0.0701852	+	0.997534i	$0.522359\pi$
$18$		0			0
$19$			39.7046i			0.479414i	0.970845	+	0.239707i	$0.0770513\pi$
$19$			39.7046i			0.479414i	−0.970845	+	0.239707i	$0.922949\pi$
$20$	106.745	−	5.58940i	1.19344	−	0.0624914i
$21$		0			0
$22$	88.0978	+	83.6055i	0.853751	+	0.810216i
$23$	182.876			1.65792			0.828962	−	0.559305i	$-0.188932\pi$
$23$	182.876			1.65792			0.828962	+	0.559305i	$0.188932\pi$
$24$		0			0
$25$	−53.5255			−0.428204
$26$	151.659	+	143.926i	1.14396	+	1.08562i
$27$		0			0
$28$	−13.9132	−	265.710i	−0.0939055	−	1.79337i
$29$			133.382i			0.854082i	0.904232	+	0.427041i	$0.140444\pi$
$29$			133.382i			0.854082i	−0.904232	+	0.427041i	$0.859556\pi$
$30$		0			0
$31$	160.290			0.928674			0.464337	−	0.885659i	$-0.346293\pi$
$31$	160.290			0.928674			0.464337	+	0.885659i	$0.346293\pi$
$32$	110.214	−	143.600i	0.608851	−	0.793284i
$33$		0			0
$34$	19.1565	−	20.1858i	0.0966269	−	0.101819i
$35$			444.389i			2.14615i
$36$		0			0
$37$			66.4666i			0.295326i	0.989038	+	0.147663i	$0.0471750\pi$
$37$			66.4666i			0.295326i	−0.989038	+	0.147663i	$0.952825\pi$
$38$	−81.4589	−	77.3051i	−0.347747	−	0.330014i
$39$		0			0
$40$	−196.365	+	229.882i	−0.776201	+	0.908689i
$41$	301.253			1.14751			0.573753	−	0.819028i	$-0.305487\pi$
$41$	301.253			1.14751			0.573753	+	0.819028i	$0.305487\pi$
$42$		0			0
$43$			53.4876i			0.189693i	0.995492	+	0.0948463i	$0.0302359\pi$
$43$			53.4876i			0.189693i	−0.995492	+	0.0948463i	$0.969764\pi$
$44$	−343.054	+	17.9632i	−1.17539	+	0.0615465i
$45$		0			0
$46$	−356.061	+	375.193i	−1.14127	+	1.20259i
$47$	−576.665			−1.78969			−0.894843	−	0.446380i	$-0.852713\pi$
$47$	−576.665			−1.78969			−0.894843	+	0.446380i	$0.852713\pi$
$48$		0			0
$49$	763.179			2.22501
$50$	104.215	−	109.814i	0.294763	−	0.310602i
$51$		0			0
$52$	−590.564	+	30.9234i	−1.57493	+	0.0824673i
$53$		−	317.543i		−	0.822979i	−0.911415	−	0.411489i	$-0.865009\pi$
$53$		−	317.543i		−	0.822979i	0.911415	−	0.411489i	$-0.134991\pi$
$54$		0			0
$55$	573.743			1.40661
$56$	572.227	+	488.795i	1.36548	+	1.16639i
$57$		0			0
$58$	−273.649	−	259.695i	−0.619516	−	0.587925i
$59$			240.089i			0.529778i	0.964279	+	0.264889i	$0.0853354\pi$
$59$			240.089i			0.529778i	−0.964279	+	0.264889i	$0.914665\pi$
$60$		0			0
$61$			327.329i			0.687053i	0.939143	+	0.343527i	$0.111622\pi$
$61$			327.329i			0.687053i	−0.939143	+	0.343527i	$0.888378\pi$
$62$	−312.085	+	328.855i	−0.639272	+	0.673622i
$63$		0			0
$64$	80.0258	+	505.707i	0.156300	+	0.987710i
$65$	987.692			1.88474
$66$		0			0
$67$			426.914i			0.778445i	0.921144	+	0.389222i	$0.127256\pi$
$67$			426.914i			0.778445i	−0.921144	+	0.389222i	$0.872744\pi$
$68$	4.11589	+	78.6039i	0.00734007	+	0.140178i
$69$		0			0
$70$	−911.718	−	865.228i	−1.55673	−	1.47735i
$71$	−506.816			−0.847154			−0.423577	−	0.905860i	$-0.639226\pi$
$71$	−506.816			−0.847154			−0.423577	+	0.905860i	$0.639226\pi$
$72$		0			0
$73$	66.7763			0.107063			0.0535313	−	0.998566i	$-0.482952\pi$
$73$	66.7763			0.107063			0.0535313	+	0.998566i	$0.482952\pi$
$74$	−136.365	−	129.411i	−0.214217	−	0.203294i
$75$		0			0
$76$	317.202	−	16.6095i	0.478758	−	0.0250689i
$77$		−	1428.17i		−	2.11370i
$78$		0			0
$79$	−35.3259			−0.0503097			−0.0251549	−	0.999684i	$-0.508008\pi$
$79$	−35.3259			−0.0503097			−0.0251549	+	0.999684i	$0.508008\pi$
$80$	−89.3081	−	850.450i	−0.124812	−	1.18854i
$81$		0			0
$82$	−586.541	+	618.058i	−0.789910	+	0.832354i
$83$		−	304.430i		−	0.402596i	−0.979530	−	0.201298i	$-0.935484\pi$
$83$		−	304.430i		−	0.402596i	0.979530	−	0.201298i	$-0.0645160\pi$
$84$		0			0
$85$		−	131.462i		−	0.167753i
$86$	−109.736	−	104.141i	−0.137595	−	0.130579i
$87$		0			0
$88$	631.075	−	738.793i	0.764464	−	0.894950i
$89$	−1100.06			−1.31018			−0.655092	−	0.755549i	$-0.727370\pi$
$89$	−1100.06			−1.31018			−0.655092	+	0.755549i	$0.727370\pi$
$90$		0			0
$91$		−	2458.58i		−	2.83219i
$92$	−76.5018	−	1461.01i	−0.0866942	−	1.65566i
$93$		0			0
$94$	1122.77	−	1183.10i	1.23197	−	1.29816i
$95$	−530.507			−0.572935
$96$		0			0
$97$	1299.31			1.36005			0.680024	−	0.733190i	$-0.261969\pi$
$97$	1299.31			1.36005			0.680024	+	0.733190i	$0.261969\pi$
$98$	−1485.91	+	1565.76i	−1.53163	+	1.61393i
$99$		0			0
$100$	22.3911	+	427.618i	0.0223911	+	0.427618i
$101$		−	493.365i		−	0.486056i	−0.970019	−	0.243028i	$-0.921859\pi$
$101$		−	493.365i		−	0.486056i	0.970019	−	0.243028i	$-0.0781407\pi$
$102$		0			0
$103$	−406.486			−0.388857			−0.194429	−	0.980917i	$-0.562285\pi$
$103$	−406.486			−0.388857			−0.194429	+	0.980917i	$0.562285\pi$
$104$	1086.39	−	1271.82i	1.02432	−	1.19916i
$105$		0			0
$106$	651.479	+	618.258i	0.596955	+	0.566515i
$107$			555.563i			0.501947i	0.967994	+	0.250973i	$0.0807507\pi$
$107$			555.563i			0.501947i	−0.967994	+	0.250973i	$0.919249\pi$
$108$		0			0
$109$		−	427.544i		−	0.375700i	−0.982198	−	0.187850i	$-0.939848\pi$
$109$		−	427.544i		−	0.375700i	0.982198	−	0.187850i	$-0.0601519\pi$
$110$	−1117.08	+	1177.11i	−0.968269	+	1.02030i
$111$		0			0
$112$	−2116.95	+	222.307i	−1.78601	+	0.187554i
$113$	495.723			0.412687			0.206344	−	0.978480i	$-0.433844\pi$
$113$	495.723			0.412687			0.206344	+	0.978480i	$0.433844\pi$
$114$		0			0
$115$			2443.47i			1.98134i
$116$	1065.59	−	55.7971i	0.852914	−	0.0446606i
$117$		0			0
$118$	−492.572	−	467.455i	−0.384279	−	0.364684i
$119$	−327.236			−0.252081
$120$		0			0
$121$	−512.889			−0.385341
$122$	−671.557	−	637.313i	−0.498360	−	0.472947i
$123$		0			0
$124$	−67.0534	−	1280.56i	−0.0485611	−	0.927404i
$125$			954.995i			0.683339i
$126$		0			0
$127$	903.203			0.631073			0.315537	−	0.948913i	$-0.397815\pi$
$127$	903.203			0.631073			0.315537	+	0.948913i	$0.397815\pi$
$128$	−1193.33	−	820.433i	−0.824037	−	0.566537i
$129$		0			0
$130$	−1923.04	+	2026.37i	−1.29740	+	1.36711i
$131$			790.884i			0.527479i	0.964594	+	0.263740i	$0.0849560\pi$
$131$			790.884i			0.527479i	−0.964594	+	0.263740i	$0.915044\pi$
$132$		0			0
$133$			1320.55i			0.860946i
$134$	−875.867	−	831.204i	−0.564652	−	0.535859i
$135$		0			0
$136$	−169.279	−	144.598i	−0.106732	−	0.0911705i
$137$	706.792			0.440768			0.220384	−	0.975413i	$-0.429269\pi$
$137$	706.792			0.440768			0.220384	+	0.975413i	$0.429269\pi$
$138$		0			0
$139$		−	719.036i		−	0.438762i	−0.975639	−	0.219381i	$-0.929596\pi$
$139$		−	719.036i		−	0.438762i	0.975639	−	0.219381i	$-0.0704037\pi$
$140$	3550.24	−	185.899i	2.14322	−	0.112224i
$141$		0			0
$142$	986.774	−	1039.80i	0.583156	−	0.614491i
$143$	−3174.23			−1.85624
$144$		0			0
$145$	−1782.16			−1.02069
$146$	−130.014	+	137.000i	−0.0736988	+	0.0776588i
$147$		0			0
$148$	531.006	−	27.8047i	0.294922	−	0.0154428i
$149$		−	1929.05i		−	1.06063i	−0.847801	−	0.530315i	$-0.822074\pi$
$149$		−	1929.05i		−	1.06063i	0.847801	−	0.530315i	$-0.177926\pi$
$150$		0			0
$151$	301.398			0.162433			0.0812167	−	0.996696i	$-0.474119\pi$
$151$	301.398			0.162433			0.0812167	+	0.996696i	$0.474119\pi$
$152$	−583.518	+	683.118i	−0.311379	+	0.364528i
$153$		0			0
$154$	2930.07	+	2780.66i	1.53319	+	1.45501i
$155$			2141.69i			1.10984i
$156$		0			0
$157$		−	1849.07i		−	0.939950i	−0.882680	−	0.469975i	$-0.844263\pi$
$157$		−	1849.07i		−	0.939950i	0.882680	−	0.469975i	$-0.155737\pi$
$158$	68.7797	−	72.4754i	0.0346318	−	0.0364926i
$159$		0			0
$160$	1918.69	+	1472.60i	0.948034	+	0.727623i
$161$	6082.32			2.97735
$162$		0			0
$163$			3098.24i			1.48879i	0.667738	+	0.744397i	$0.267263\pi$
$163$			3098.24i			1.48879i	−0.667738	+	0.744397i	$0.732737\pi$
$164$	−126.022	−	2406.73i	−0.0600040	−	1.14594i
$165$		0			0
$166$	624.575	+	592.727i	0.292027	+	0.277136i
$167$	741.954			0.343797			0.171899	−	0.985115i	$-0.445010\pi$
$167$	741.954			0.343797			0.171899	+	0.985115i	$0.445010\pi$
$168$		0			0
$169$	−3267.40			−1.48721
$170$	269.710	+	255.957i	0.121681	+	0.115476i
$171$		0			0
$172$	427.315	−	22.3753i	0.189433	−	0.00991917i
$173$		−	2799.26i		−	1.23019i	−0.788451	−	0.615097i	$-0.789117\pi$
$173$		−	2799.26i		−	1.23019i	0.788451	−	0.615097i	$-0.210883\pi$
$174$		0			0
$175$	−1780.22			−0.768983
$176$	287.017	+	2733.16i	0.122925	+	1.17057i
$177$		0			0
$178$	2141.83	−	2256.91i	0.901892	−	0.950353i
$179$			1667.32i			0.696207i	0.937456	+	0.348104i	$0.113174\pi$
$179$			1667.32i			0.696207i	−0.937456	+	0.348104i	$0.886826\pi$
$180$		0			0
$181$		−	2914.47i		−	1.19686i	−0.801177	−	0.598428i	$-0.795792\pi$
$181$		−	2914.47i		−	1.19686i	0.801177	−	0.598428i	$-0.204208\pi$
$182$	5044.08	+	4786.87i	2.05435	+	1.94960i
$183$		0			0
$184$	3146.38	+	2687.64i	1.26062	+	1.07682i
$185$	−888.084			−0.352936
$186$		0			0
$187$			422.490i			0.165217i
$188$	241.234	+	4607.01i	0.0935841	+	1.78724i
$189$		0			0
$190$	1032.90	−	1088.40i	0.394392	−	0.415583i
$191$	−917.438			−0.347557			−0.173779	−	0.984785i	$-0.555598\pi$
$191$	−917.438			−0.347557			−0.173779	+	0.984785i	$0.555598\pi$
$192$		0			0
$193$	−4550.79			−1.69727			−0.848634	−	0.528980i	$-0.822575\pi$
$193$	−4550.79			−1.69727			−0.848634	+	0.528980i	$0.822575\pi$
$194$	−2529.76	+	2665.69i	−0.936217	+	0.986523i
$195$		0			0
$196$	−319.258	−	6097.08i	−0.116348	−	2.22197i
$197$		−	1392.68i		−	0.503675i	−0.967770	−	0.251838i	$-0.918965\pi$
$197$		−	1392.68i		−	0.503675i	0.967770	−	0.251838i	$-0.0810349\pi$
$198$		0			0
$199$	−5099.53			−1.81656			−0.908282	−	0.418359i	$-0.862606\pi$
$199$	−5099.53			−1.81656			−0.908282	+	0.418359i	$0.862606\pi$
$200$	−920.908	−	786.638i	−0.325590	−	0.278118i
$201$		0			0
$202$	1012.20	+	960.586i	0.352565	+	0.334587i
$203$			4436.18i			1.53379i
$204$		0			0
$205$			4025.14i			1.37136i
$206$	791.431	−	833.957i	0.267678	−	0.282061i
$207$		0			0
$208$	494.097	+	4705.11i	0.164709	+	1.56847i
$209$	1704.94			0.564272
$210$		0			0
$211$		−	3249.71i		−	1.06028i	−0.847910	−	0.530141i	$-0.822139\pi$
$211$		−	3249.71i		−	1.06028i	0.847910	−	0.530141i	$-0.177861\pi$
$212$	−2536.87	+	132.837i	−0.821853	+	0.0430342i
$213$		0			0
$214$	−1139.81	−	1081.69i	−0.364092	−	0.345526i
$215$	−714.666			−0.226697
$216$		0			0
$217$	5331.12			1.66774
$218$	877.160	+	832.431i	0.272517	+	0.258621i
$219$		0			0
$220$	−240.012	−	4583.67i	−0.0735527	−	1.40468i
$221$			727.311i			0.221377i
$222$		0			0
$223$	−1469.99			−0.441425			−0.220713	−	0.975339i	$-0.570838\pi$
$223$	−1469.99			−0.441425			−0.220713	+	0.975339i	$0.570838\pi$
$224$	3665.63	−	4776.03i	1.09339	−	1.42461i
$225$		0			0
$226$	−965.176	+	1017.04i	−0.284082	+	0.299346i
$227$		−	955.754i		−	0.279452i	−0.990190	−	0.139726i	$-0.955378\pi$
$227$		−	955.754i		−	0.279452i	0.990190	−	0.139726i	$-0.0446222\pi$
$228$		0			0
$229$			3691.75i			1.06532i	0.846330	+	0.532659i	$0.178807\pi$
$229$			3691.75i			1.06532i	−0.846330	+	0.532659i	$0.821193\pi$
$230$	−5013.08	−	4757.45i	−1.43719	−	1.36390i
$231$		0			0
$232$	−1960.25	+	2294.84i	−0.554726	+	0.649412i
$233$	−2966.84			−0.834181			−0.417091	−	0.908865i	$-0.636950\pi$
$233$	−2966.84			−0.834181			−0.417091	+	0.908865i	$0.636950\pi$
$234$		0			0
$235$		−	7705.02i		−	2.13881i
$236$	1918.08	−	100.436i	0.529053	−	0.0277025i
$237$		0			0
$238$	637.131	−	671.366i	0.173526	−	0.182850i
$239$	5838.66			1.58022			0.790108	−	0.612968i	$-0.210025\pi$
$239$	5838.66			1.58022			0.790108	+	0.612968i	$0.210025\pi$
$240$		0			0
$241$	327.690			0.0875866			0.0437933	−	0.999041i	$-0.486056\pi$
$241$	327.690			0.0875866			0.0437933	+	0.999041i	$0.486056\pi$
$242$	998.598	−	1052.26i	0.265258	−	0.279510i
$243$		0			0
$244$	2615.05	−	136.931i	0.686113	−	0.0359266i
$245$			10197.1i			2.65906i
$246$		0			0
$247$	2935.03			0.756078
$248$	2757.79	+	2355.70i	0.706128	+	0.603174i
$249$		0			0
$250$	−1959.29	−	1859.38i	−0.495666	−	0.470391i
$251$		−	7493.65i		−	1.88444i	−0.334992	−	0.942221i	$-0.608734\pi$
$251$		−	7493.65i		−	1.88444i	0.334992	−	0.942221i	$-0.391266\pi$
$252$		0			0
$253$		−	7852.79i		−	1.95139i
$254$	−1758.54	+	1853.03i	−0.434413	+	0.457755i
$255$		0			0
$256$	4006.65	−	850.881i	0.978185	−	0.207735i
$257$	−2034.92			−0.493911			−0.246955	−	0.969027i	$-0.579430\pi$
$257$	−2034.92			−0.493911			−0.246955	+	0.969027i	$0.579430\pi$
$258$		0			0
$259$			2210.63i			0.530355i
$260$	−413.178	−	7890.73i	−0.0985546	−	1.88216i
$261$		0			0
$262$	−1622.60	−	1539.86i	−0.382612	−	0.363102i
$263$	−5776.20			−1.35428			−0.677140	−	0.735854i	$-0.736781\pi$
$263$	−5776.20			−1.35428			−0.677140	+	0.735854i	$0.736781\pi$
$264$		0			0
$265$	4242.80			0.983521
$266$	−2709.26	−	2571.11i	−0.624495	−	0.592650i
$267$		0			0
$268$	3410.64	−	178.589i	0.777380	−	0.0407055i
$269$			1787.25i			0.405095i	0.979272	+	0.202548i	$0.0649221\pi$
$269$			1787.25i			0.405095i	−0.979272	+	0.202548i	$0.935078\pi$
$270$		0			0
$271$	−3504.63			−0.785577			−0.392789	−	0.919629i	$-0.628490\pi$
$271$	−3504.63			−0.785577			−0.392789	+	0.919629i	$0.628490\pi$
$272$	626.249	−	65.7642i	0.139603	−	0.0146601i
$273$		0			0
$274$	−1376.13	+	1450.07i	−0.303412	+	0.319715i
$275$			2298.41i			0.503998i
$276$		0			0
$277$			5398.60i			1.17101i	0.810668	+	0.585507i	$0.199104\pi$
$277$			5398.60i			1.17101i	−0.810668	+	0.585507i	$0.800896\pi$
$278$	1475.19	+	1399.97i	0.318260	+	0.302031i
$279$		0			0
$280$	−6530.96	+	7645.72i	−1.39393	+	1.63185i
$281$	−720.817			−0.153026			−0.0765131	−	0.997069i	$-0.524379\pi$
$281$	−720.817			−0.153026			−0.0765131	+	0.997069i	$0.524379\pi$
$282$		0			0
$283$			3888.21i			0.816713i	0.912822	+	0.408357i	$0.133898\pi$
$283$			3888.21i			0.816713i	−0.912822	+	0.408357i	$0.866102\pi$
$284$	212.014	+	4048.98i	0.0442984	+	0.845995i
$285$		0			0
$286$	6180.25	−	6512.33i	1.27778	−	1.34644i
$287$	10019.4			2.06073
$288$		0			0
$289$	−4816.20			−0.980296
$290$	3469.88	−	3656.32i	0.702615	−	0.740368i
$291$		0			0
$292$	−27.9343	−	533.479i	−0.00559839	−	0.106916i
$293$		−	7803.10i		−	1.55584i	−0.628361	−	0.777922i	$-0.716274\pi$
$293$		−	7803.10i		−	1.55584i	0.628361	−	0.777922i	$-0.283726\pi$
$294$		0			0
$295$	−3207.91			−0.633125
$296$	−976.827	+	1143.56i	−0.191814	+	0.224554i
$297$		0			0
$298$	3957.68	+	3755.87i	0.769337	+	0.730106i
$299$		−	13518.5i		−	2.61470i
$300$		0			0
$301$			1778.96i			0.340656i
$302$	−586.824	+	618.356i	−0.111814	+	0.117822i
$303$		0			0
$304$	−265.388	−	2527.20i	−0.0500692	−	0.476792i
$305$	−4373.56			−0.821080
$306$		0			0
$307$			2663.26i			0.495115i	0.968873	+	0.247557i	$0.0796279\pi$
$307$			2663.26i			0.495115i	−0.968873	+	0.247557i	$0.920372\pi$
$308$	−11409.7	+	597.441i	−2.11081	+	0.110527i
$309$		0			0
$310$	−4393.94	−	4169.88i	−0.805029	−	0.763978i
$311$	−2555.22			−0.465895			−0.232948	−	0.972489i	$-0.574837\pi$
$311$	−2555.22			−0.465895			−0.232948	+	0.972489i	$0.574837\pi$
$312$		0			0
$313$	−4254.74			−0.768345			−0.384173	−	0.923261i	$-0.625513\pi$
$313$	−4254.74			−0.768345			−0.384173	+	0.923261i	$0.625513\pi$
$314$	3793.60	+	3600.16i	0.681801	+	0.647034i
$315$		0			0
$316$	14.7777	+	282.220i	0.00263074	+	0.0502409i
$317$			1300.06i			0.230342i	0.993346	+	0.115171i	$0.0367417\pi$
$317$			1300.06i			0.230342i	−0.993346	+	0.115171i	$0.963258\pi$
$318$		0			0
$319$	5727.49			1.00526
$320$	−6756.93	+	1069.25i	−1.18039	+	0.186791i
$321$		0			0
$322$	−11842.3	+	12478.6i	−2.04952	+	2.15965i
$323$		−	390.651i		−	0.0672954i
$324$		0			0
$325$			3956.69i			0.675316i
$326$	−6356.44	−	6032.30i	−1.07991	−	1.02484i
$327$		0			0
$328$	5183.06	+	4427.36i	0.872520	+	0.745305i
$329$	−19179.5			−3.21398
$330$		0			0
$331$			6949.46i			1.15401i	0.816741	+	0.577004i	$0.195778\pi$
$331$			6949.46i			1.15401i	−0.816741	+	0.577004i	$0.804222\pi$
$332$	−2432.10	+	127.351i	−0.402045	+	0.0210521i
$333$		0			0
$334$	−1444.59	+	1522.21i	−0.236660	+	0.249376i
$335$	−5704.14			−0.930300
$336$		0			0
$337$	2694.10			0.435480			0.217740	−	0.976007i	$-0.430132\pi$
$337$	2694.10			0.435480			0.217740	+	0.976007i	$0.430132\pi$
$338$	6361.66	−	6703.49i	1.02375	−	1.07876i
$339$		0			0
$340$	−1050.25	+	54.9938i	−0.167524	+	0.00877194i
$341$		−	6882.93i		−	1.09305i
$342$		0			0
$343$	13974.8			2.19991
$344$	−786.080	+	920.255i	−0.123205	+	0.144235i
$345$		0			0
$346$	5743.03	+	5450.18i	0.892333	+	0.846830i
$347$			10412.7i			1.61091i	0.592658	+	0.805455i	$0.298079\pi$
$347$			10412.7i			1.61091i	−0.592658	+	0.805455i	$0.701921\pi$
$348$		0			0
$349$		−	10474.2i		−	1.60651i	−0.595634	−	0.803256i	$-0.703099\pi$
$349$		−	10474.2i		−	1.60651i	0.595634	−	0.803256i	$-0.296901\pi$
$350$	3466.10	−	3652.34i	0.529345	−	0.557788i
$351$		0			0
$352$	−6166.25	−	4732.64i	−0.933700	−	0.716621i
$353$	12192.6			1.83838			0.919190	−	0.393814i	$-0.128845\pi$
$353$	12192.6			1.83838			0.919190	+	0.393814i	$0.128845\pi$
$354$		0			0
$355$		−	6771.74i		−	1.01241i
$356$	460.185	+	8788.45i	0.0685105	+	1.30839i
$357$		0			0
$358$	−3420.71	−	3246.28i	−0.505000	−	0.479249i
$359$	5356.02			0.787410			0.393705	−	0.919237i	$-0.371193\pi$
$359$	5356.02			0.787410			0.393705	+	0.919237i	$0.371193\pi$
$360$		0			0
$361$	5282.55			0.770163
$362$	5979.40	+	5674.49i	0.868149	+	0.823880i
$363$		0			0
$364$	−19641.7	+	1028.49i	−2.82831	+	0.148097i
$365$			892.221i			0.127948i
$366$		0			0
$367$	6716.09			0.955250			0.477625	−	0.878564i	$-0.341498\pi$
$367$	6716.09			0.955250			0.477625	+	0.878564i	$0.341498\pi$
$368$	−11640.1	+	1222.35i	−1.64886	+	0.173151i
$369$		0			0
$370$	1729.11	−	1822.01i	0.242951	−	0.256005i
$371$		−	10561.2i		−	1.47793i
$372$		0			0
$373$		−	5325.75i		−	0.739294i	−0.929172	−	0.369647i	$-0.879479\pi$
$373$		−	5325.75i		−	0.739294i	0.929172	−	0.369647i	$-0.120521\pi$
$374$	−866.790	−	822.590i	−0.119841	−	0.113730i
$375$		0			0
$376$	−9921.54	−	8474.96i	−1.36081	−	1.16240i
$377$	9859.80			1.34696
$378$		0			0
$379$			6980.22i			0.946041i	0.881051	+	0.473021i	$0.156836\pi$
$379$			6980.22i			0.946041i	−0.881051	+	0.473021i	$0.843164\pi$
$380$	221.925	+	4238.25i	0.0299592	+	0.572151i
$381$		0			0
$382$	1786.26	−	1882.24i	0.239248	−	0.252104i
$383$	5385.60			0.718515			0.359257	−	0.933239i	$-0.383030\pi$
$383$	5385.60			0.718515			0.359257	+	0.933239i	$0.383030\pi$
$384$		0			0
$385$	19082.3			2.52603
$386$	8860.42	−	9336.51i	1.16835	−	1.23113i
$387$		0			0
$388$	−543.534	−	10380.2i	−0.0711180	−	1.35819i
$389$			14629.3i			1.90677i	0.301753	+	0.953386i	$0.402428\pi$
$389$			14629.3i			1.90677i	−0.301753	+	0.953386i	$0.597572\pi$
$390$		0			0
$391$	−1799.31			−0.232723
$392$	13130.5	+	11216.1i	1.69181	+	1.44514i
$393$		0			0
$394$	2857.25	+	2711.55i	0.365345	+	0.346715i
$395$		−	472.001i		−	0.0601239i
$396$		0			0
$397$			9651.00i			1.22008i	0.792372	+	0.610038i	$0.208846\pi$
$397$			9651.00i			1.22008i	−0.792372	+	0.610038i	$0.791154\pi$
$398$	9928.83	−	10462.3i	1.25047	−	1.31766i
$399$		0			0
$400$	3406.90	−	357.768i	0.425862	−	0.0447210i
$401$	−9742.56			−1.21327			−0.606634	−	0.794981i	$-0.707481\pi$
$401$	−9742.56			−1.21327			−0.606634	+	0.794981i	$0.707481\pi$
$402$		0			0
$403$		−	11848.9i		−	1.46460i
$404$	−3941.52	+	206.388i	−0.485391	+	0.0254163i
$405$		0			0
$406$	−9101.38	−	8637.28i	−1.11255	−	1.05582i
$407$	2854.11			0.347600
$408$		0			0
$409$	49.5016			0.00598459			0.00299229	−	0.999996i	$-0.499048\pi$
$409$	49.5016			0.00598459			0.00299229	+	0.999996i	$0.499048\pi$
$410$	−8258.08	−	7836.98i	−0.994726	−	0.944002i
$411$		0			0
$412$	170.044	+	3247.44i	0.0203336	+	0.388325i
$413$			7985.18i			0.951393i
$414$		0			0
$415$	4067.59			0.481133
$416$	−10615.1	−	8147.18i	−1.25108	−	0.960213i
$417$		0			0
$418$	−3319.52	+	3497.89i	−0.388429	+	0.409300i
$419$		−	10212.9i		−	1.19077i	−0.803439	−	0.595387i	$-0.796999\pi$
$419$		−	10212.9i		−	1.19077i	0.803439	−	0.595387i	$-0.203001\pi$
$420$		0			0
$421$		−	1979.98i		−	0.229213i	−0.993411	−	0.114606i	$-0.963439\pi$
$421$		−	1979.98i		−	0.229213i	0.993411	−	0.114606i	$-0.0365607\pi$
$422$	6667.19	+	6327.21i	0.769085	+	0.729867i
$423$		0			0
$424$	4666.77	−	5463.34i	0.534524	−	0.625762i
$425$	526.635			0.0601072
$426$		0			0
$427$			10886.7i			1.23383i
$428$	4438.42	−	232.407i	0.501260	−	0.0262472i
$429$		0			0
$430$	1391.46	−	1466.23i	0.156051	−	0.164436i
$431$	−6771.53			−0.756783			−0.378391	−	0.925646i	$-0.623523\pi$
$431$	−6771.53			−0.756783			−0.378391	+	0.925646i	$0.623523\pi$
$432$		0			0
$433$	−5653.12			−0.627417			−0.313708	−	0.949519i	$-0.601571\pi$
$433$	−5653.12			−0.627417			−0.313708	+	0.949519i	$0.601571\pi$
$434$	−10379.7	+	10937.5i	−1.14803	+	1.20971i
$435$		0			0
$436$	−3415.67	+	178.853i	−0.375186	+	0.0196456i
$437$			7261.01i			0.794831i
$438$		0			0
$439$	5073.72			0.551607			0.275803	−	0.961214i	$-0.411056\pi$
$439$	5073.72			0.551607			0.275803	+	0.961214i	$0.411056\pi$
$440$	9871.27	+	8432.02i	1.06953	+	0.913592i
$441$		0			0
$442$	−1492.17	−	1416.08i	−0.160577	−	0.152389i
$443$			4991.42i			0.535326i	0.963513	+	0.267663i	$0.0862514\pi$
$443$			4991.42i			0.535326i	−0.963513	+	0.267663i	$0.913749\pi$
$444$		0			0
$445$		−	14698.3i		−	1.56577i
$446$	2862.08	−	3015.87i	0.303864	−	0.320192i
$447$		0			0
$448$	2661.60	+	16819.5i	0.280689	+	1.77376i
$449$	−15075.5			−1.58454			−0.792270	−	0.610171i	$-0.791101\pi$
$449$	−15075.5			−1.58454			−0.792270	+	0.610171i	$0.791101\pi$
$450$		0			0
$451$		−	12936.0i		−	1.35062i
$452$	−207.374	−	3960.36i	−0.0215797	−	0.412123i
$453$		0			0
$454$	1960.85	+	1860.86i	0.202703	+	0.192367i
$455$	32849.9			3.38468
$456$		0			0
$457$	−16021.3			−1.63992			−0.819962	−	0.572418i	$-0.806006\pi$
$457$	−16021.3			−1.63992			−0.819962	+	0.572418i	$0.806006\pi$
$458$	−7574.08	−	7187.86i	−0.772737	−	0.733333i
$459$		0			0
$460$	19521.0	−	1022.17i	1.97863	−	0.103606i
$461$			14219.4i			1.43658i	0.695742	+	0.718292i	$0.255076\pi$
$461$			14219.4i			1.43658i	−0.695742	+	0.718292i	$0.744924\pi$
$462$		0			0
$463$	−10324.2			−1.03630			−0.518152	−	0.855289i	$-0.673380\pi$
$463$	−10324.2			−1.03630			−0.518152	+	0.855289i	$0.673380\pi$
$464$	−891.533	−	8489.75i	−0.0891991	−	0.849411i
$465$		0			0
$466$	5776.46	−	6086.85i	0.574226	−	0.605081i
$467$			2548.47i			0.252525i	0.991997	+	0.126263i	$0.0402982\pi$
$467$			2548.47i			0.252525i	−0.991997	+	0.126263i	$0.959702\pi$
$468$		0			0
$469$			14198.8i			1.39796i
$470$	15807.8	+	15001.7i	1.55140	+	1.47229i
$471$		0			0
$472$	−3528.47	+	4130.74i	−0.344091	+	0.402823i
$473$	2296.78			0.223269
$474$		0			0
$475$		−	2125.21i		−	0.205287i
$476$	136.892	+	2614.31i	0.0131815	+	0.251737i
$477$		0			0
$478$	−11367.9	+	11978.7i	−1.08777	+	1.14622i
$479$	12868.6			1.22752			0.613760	−	0.789493i	$-0.289656\pi$
$479$	12868.6			1.22752			0.613760	+	0.789493i	$0.289656\pi$
$480$		0			0
$481$	4913.32			0.465755
$482$	−638.015	+	672.297i	−0.0602921	+	0.0635317i
$483$		0			0
$484$	214.555	+	4097.50i	0.0201498	+	0.384814i
$485$			17360.5i			1.62536i
$486$		0			0
$487$	−8885.79			−0.826804			−0.413402	−	0.910549i	$-0.635660\pi$
$487$	−8885.79			−0.826804			−0.413402	+	0.910549i	$0.635660\pi$
$488$	−4810.60	+	5631.71i	−0.446241	+	0.522409i
$489$		0			0
$490$	−20920.6	−	19853.8i	−1.92877	−	1.83042i
$491$			8718.23i			0.801320i	0.916227	+	0.400660i	$0.131219\pi$
$491$			8718.23i			0.801320i	−0.916227	+	0.400660i	$0.868781\pi$
$492$		0			0
$493$		−	1312.34i		−	0.119888i
$494$	−5714.52	+	6021.57i	−0.520462	+	0.548428i
$495$		0			0
$496$	−10202.4	+	1071.39i	−0.923596	+	0.0969893i
$497$	−16856.3			−1.52135
$498$		0			0
$499$			3340.62i			0.299693i	0.988709	+	0.149847i	$0.0478780\pi$
$499$			3340.62i			0.299693i	−0.988709	+	0.149847i	$0.952122\pi$
$500$	7629.51	−	399.500i	0.682404	−	0.0357323i
$501$		0			0
$502$	15374.2	+	14590.2i	1.36690	+	1.29720i
$503$	−7993.03			−0.708532			−0.354266	−	0.935145i	$-0.615269\pi$
$503$	−7993.03			−0.708532			−0.354266	+	0.935145i	$0.615269\pi$
$504$		0			0
$505$	6592.02			0.580874
$506$	16111.0	+	15289.4i	1.41545	+	1.34328i
$507$		0			0
$508$	−377.834	−	7215.74i	−0.0329993	−	0.630210i
$509$		−	19580.0i		−	1.70504i	−0.522692	−	0.852521i	$-0.675072\pi$
$509$		−	19580.0i		−	1.70504i	0.522692	−	0.852521i	$-0.324928\pi$
$510$		0			0
$511$	2220.93			0.192266
$512$	−6055.28	+	9876.81i	−0.522672	+	0.852534i
$513$		0			0
$514$	3962.01	−	4174.90i	0.339994	−	0.358262i
$515$		−	5431.20i		−	0.464713i
$516$		0			0
$517$			24762.3i			2.10647i
$518$	−4535.39	−	4304.12i	−0.384698	−	0.365081i
$519$		0			0
$520$	16993.3	+	14515.6i	1.43308	+	1.22414i
$521$	7294.04			0.613354			0.306677	−	0.951814i	$-0.400783\pi$
$521$	7294.04			0.613354			0.306677	+	0.951814i	$0.400783\pi$
$522$		0			0
$523$			16832.4i			1.40732i	0.710536	+	0.703661i	$0.248453\pi$
$523$			16832.4i			1.40732i	−0.710536	+	0.703661i	$0.751547\pi$
$524$	6318.41	−	330.847i	0.526758	−	0.0275823i
$525$		0			0
$526$	11246.3	−	11850.6i	0.932248	−	0.982340i
$527$	−1577.08			−0.130358
$528$		0			0
$529$	21276.6			1.74871
$530$	−8260.76	+	8704.63i	−0.677028	+	0.713406i
$531$		0			0
$532$	10549.9	−	552.419i	0.859768	−	0.0450195i
$533$		−	22269.1i		−	1.80972i
$534$		0			0
$535$	−7423.07			−0.599864
$536$	−6274.14	+	7345.06i	−0.505600	+	0.591900i
$537$		0			0
$538$	−3666.77	−	3479.79i	−0.293840	−	0.278856i
$539$		−	32771.3i		−	2.61885i
$540$		0			0
$541$		−	17134.8i		−	1.36170i	−0.732421	−	0.680852i	$-0.761610\pi$
$541$		−	17134.8i		−	1.36170i	0.732421	−	0.680852i	$-0.238390\pi$
$542$	6823.55	−	7190.20i	0.540769	−	0.569825i
$543$		0			0
$544$	−1084.39	+	1412.87i	−0.0854646	+	0.111354i
$545$	5712.56			0.448989
$546$		0			0
$547$		−	13773.0i		−	1.07658i	−0.842759	−	0.538290i	$-0.819070\pi$
$547$		−	13773.0i		−	1.07658i	0.842759	−	0.538290i	$-0.180930\pi$
$548$	−295.670	−	5646.60i	−0.0230481	−	0.440165i
$549$		0			0
$550$	−4715.48	−	4475.03i	−0.365580	−	0.346938i
$551$	−5295.87			−0.409459
$552$		0			0
$553$	−1174.91			−0.0903478
$554$	−11075.9	−	10511.1i	−0.849405	−	0.806092i
$555$		0			0
$556$	−5744.42	+	300.792i	−0.438161	+	0.0229432i
$557$			8769.14i			0.667074i	0.942737	+	0.333537i	$0.108242\pi$
$557$			8769.14i			0.667074i	−0.942737	+	0.333537i	$0.891758\pi$
$558$		0			0
$559$	3953.89			0.299162
$560$	−2970.32	−	28285.3i	−0.224141	−	2.13442i
$561$		0			0
$562$	1403.44	−	1478.85i	0.105339	−	0.110999i
$563$			1668.22i			0.124879i	0.998049	+	0.0624397i	$0.0198881\pi$
$563$			1668.22i			0.124879i	−0.998049	+	0.0624397i	$0.980112\pi$
$564$		0			0
$565$			6623.52i			0.493192i
$566$	−7977.14	−	7570.36i	−0.592410	−	0.562202i
$567$		0			0
$568$	−8719.77	−	7448.41i	−0.644144	−	0.550226i
$569$	12999.9			0.957792			0.478896	−	0.877872i	$-0.341037\pi$
$569$	12999.9			0.957792			0.478896	+	0.877872i	$0.341037\pi$
$570$		0			0
$571$		−	2095.17i		−	0.153555i	−0.997048	−	0.0767777i	$-0.975537\pi$
$571$		−	2095.17i		−	0.153555i	0.997048	−	0.0767777i	$-0.0244632\pi$
$572$	1327.87	+	25359.1i	0.0970644	+	1.85370i
$573$		0			0
$574$	−19507.9	+	20556.1i	−1.41855	+	1.49477i
$575$	−9788.53			−0.709930
$576$		0			0
$577$	−21999.2			−1.58725			−0.793623	−	0.608410i	$-0.791807\pi$
$577$	−21999.2			−1.58725			−0.793623	+	0.608410i	$0.791807\pi$
$578$	9377.17	−	9881.02i	0.674807	−	0.711066i
$579$		0			0
$580$	745.525	+	14237.8i	0.0533728	+	1.01930i
$581$		−	10125.1i		−	0.722995i
$582$		0			0
$583$	−13635.5			−0.968650
$584$	1148.89	+	981.377i	0.0814063	+	0.0695371i
$585$		0			0
$586$	16009.0	+	15192.7i	1.12854	+	1.07100i
$587$			4656.43i			0.327413i	0.986509	+	0.163707i	$0.0523451\pi$
$587$			4656.43i			0.327413i	−0.986509	+	0.163707i	$0.947655\pi$
$588$		0			0
$589$			6364.24i			0.445219i
$590$	6245.83	−	6581.43i	0.435825	−	0.459243i
$591$		0			0
$592$	−444.267	−	4230.60i	−0.0308434	−	0.293711i
$593$	2645.53			0.183202			0.0916011	−	0.995796i	$-0.470802\pi$
$593$	2645.53			0.183202			0.0916011	+	0.995796i	$0.470802\pi$
$594$		0			0
$595$		−	4372.32i		−	0.301256i
$596$	−15411.3	+	806.971i	−1.05918	+	0.0554611i
$597$		0			0
$598$	27734.8	+	26320.6i	1.89659	+	1.79988i
$599$	−17099.3			−1.16637			−0.583186	−	0.812339i	$-0.698194\pi$
$599$	−17099.3			−1.16637			−0.583186	+	0.812339i	$0.698194\pi$
$600$		0			0
$601$	−27599.8			−1.87325			−0.936623	−	0.350339i	$-0.886066\pi$
$601$	−27599.8			−1.87325			−0.936623	+	0.350339i	$0.886066\pi$
$602$	−3649.75	−	3463.64i	−0.247098	−	0.234498i
$603$		0			0
$604$	−126.083	−	2407.89i	−0.00849377	−	0.162211i
$605$		−	6852.88i		−	0.460511i
$606$		0			0
$607$	−13934.8			−0.931788			−0.465894	−	0.884841i	$-0.654267\pi$
$607$	−13934.8			−0.931788			−0.465894	+	0.884841i	$0.654267\pi$
$608$	5701.57	+	4375.99i	0.380311	+	0.291891i
$609$		0			0
$610$	8515.36	−	8972.91i	0.565208	−	0.595578i
$611$			42628.0i			2.82250i
$612$		0			0
$613$			21656.5i			1.42691i	0.700699	+	0.713457i	$0.252872\pi$
$613$			21656.5i			1.42691i	−0.700699	+	0.713457i	$0.747128\pi$
$614$	−5464.01	−	5185.38i	−0.359136	−	0.340823i
$615$		0			0
$616$	20989.1	−	24571.7i	1.37285	−	1.60718i
$617$	24406.9			1.59252			0.796260	−	0.604954i	$-0.206809\pi$
$617$	24406.9			1.59252			0.796260	+	0.604954i	$0.206809\pi$
$618$		0			0
$619$		−	15475.3i		−	1.00485i	−0.864620	−	0.502426i	$-0.832441\pi$
$619$		−	15475.3i		−	1.00485i	0.864620	−	0.502426i	$-0.167559\pi$
$620$	17110.1	−	895.924i	1.10832	−	0.0580342i
$621$		0			0
$622$	4975.04	−	5242.36i	0.320709	−	0.337941i
$623$	−36587.2			−2.35287
$624$		0			0
$625$	−19450.7			−1.24485
$626$	8284.01	−	8729.13i	0.528906	−	0.557326i
$627$		0			0
$628$	−14772.3	+	773.516i	−0.938664	+	0.0491507i
$629$		−	653.962i		−	0.0414550i
$630$		0			0
$631$	−15000.0			−0.946339			−0.473170	−	0.880971i	$-0.656890\pi$
$631$	−15000.0			−0.946339			−0.473170	+	0.880971i	$0.656890\pi$
$632$	−607.782	−	519.166i	−0.0382536	−	0.0326762i
$633$		0			0
$634$	−2667.23	−	2531.22i	−0.167081	−	0.158561i
$635$			12068.0i			0.754180i
$636$		0			0
$637$		−	56415.4i		−	3.50904i
$638$	−11151.5	+	11750.6i	−0.691991	+	0.729173i
$639$		0			0
$640$	10962.1	−	15944.5i	0.677054	−	0.984785i
$641$	−5446.05			−0.335579			−0.167789	−	0.985823i	$-0.553663\pi$
$641$	−5446.05			−0.335579			−0.167789	+	0.985823i	$0.553663\pi$
$642$		0			0
$643$			16491.4i			1.01144i	0.862697	+	0.505721i	$0.168773\pi$
$643$			16491.4i			1.01144i	−0.862697	+	0.505721i	$0.831227\pi$
$644$	−2544.39	−	48592.0i	−0.155688	−	2.97328i
$645$		0			0
$646$	801.470	+	760.601i	0.0488133	+	0.0463242i
$647$	−7083.27			−0.430405			−0.215202	−	0.976569i	$-0.569041\pi$
$647$	−7083.27			−0.430405			−0.215202	+	0.976569i	$0.569041\pi$
$648$		0			0
$649$	10309.5			0.623552
$650$	−8117.65	−	7703.71i	−0.489847	−	0.464868i
$651$		0			0
$652$	24752.0	−	1296.08i	1.48676	−	0.0778502i
$653$		−	15688.9i		−	0.940204i	−0.882612	−	0.470102i	$-0.844217\pi$
$653$		−	15688.9i		−	0.940204i	0.882612	−	0.470102i	$-0.155783\pi$
$654$		0			0
$655$	−10567.3			−0.630378
$656$	−19174.7	+	2013.59i	−1.14123	+	0.119844i
$657$		0			0
$658$	37342.6	−	39349.1i	2.21241	−	2.33129i
$659$		−	1945.69i		−	0.115012i	−0.998345	−	0.0575062i	$-0.981685\pi$
$659$		−	1945.69i		−	0.115012i	0.998345	−	0.0575062i	$-0.0183149\pi$
$660$		0			0
$661$		−	23029.1i		−	1.35511i	−0.735473	−	0.677554i	$-0.763040\pi$
$661$		−	23029.1i		−	1.35511i	0.735473	−	0.677554i	$-0.236960\pi$
$662$	−14257.7	−	13530.6i	−0.837070	−	0.794386i
$663$		0			0
$664$	4474.05	−	5237.72i	0.261486	−	0.306119i
$665$	−17644.3			−1.02889
$666$		0			0
$667$			24392.3i			1.41600i
$668$	−310.379	−	5927.51i	−0.0179774	−	0.343327i
$669$		0			0
$670$	11106.0	−	11702.8i	0.640392	−	0.674801i
$671$	14055.7			0.808665
$672$		0			0
$673$	−19866.4			−1.13788			−0.568939	−	0.822380i	$-0.692646\pi$
$673$	−19866.4			−1.13788			−0.568939	+	0.822380i	$0.692646\pi$
$674$	−5245.42	+	5527.27i	−0.299772	+	0.315879i
$675$		0			0
$676$	1366.84	+	26103.5i	0.0777675	+	1.48518i
$677$		−	4263.76i		−	0.242052i	−0.992649	−	0.121026i	$-0.961381\pi$
$677$		−	4263.76i		−	0.242052i	0.992649	−	0.121026i	$-0.0386185\pi$
$678$		0			0
$679$	43214.0			2.44242
$680$	1932.02	−	2261.80i	0.108956	−	0.127553i
$681$		0			0
$682$	14121.2	+	13401.1i	0.792857	+	0.752427i
$683$			264.761i			0.0148328i	0.999972	+	0.00741639i	$0.00236073\pi$
$683$			264.761i			0.0148328i	−0.999972	+	0.00741639i	$0.997639\pi$
$684$		0			0
$685$			9443.69i			0.526751i
$686$	−27209.1	+	28671.1i	−1.51436	+	1.59573i
$687$		0			0
$688$	−357.514	−	3404.48i	−0.0198112	−	0.188655i
$689$	−23473.3			−1.29791
$690$		0			0
$691$			10688.1i			0.588415i	0.955742	+	0.294207i	$0.0950556\pi$
$691$			10688.1i			0.588415i	−0.955742	+	0.294207i	$0.904944\pi$
$692$	−22363.4	+	1171.00i	−1.22851	+	0.0643279i
$693$		0			0
$694$	−21363.0	−	20273.7i	−1.16849	−	1.10890i
$695$	9607.29			0.524353
$696$		0			0
$697$	−2964.01			−0.161076
$698$	21489.2	+	20393.4i	1.16530	+	1.10588i
$699$		0			0
$700$	744.713	+	14222.3i	0.0402107	+	0.767931i
$701$		−	25577.1i		−	1.37808i	−0.724723	−	0.689041i	$-0.758032\pi$
$701$		−	25577.1i		−	1.37808i	0.724723	−	0.689041i	$-0.241968\pi$
$702$		0			0
$703$	−2639.03			−0.141583
$704$	21715.3	−	3436.35i	1.16254	−	0.183966i
$705$		0			0
$706$	−23739.1	+	25014.7i	−1.26549	+	1.33349i
$707$		−	16409.0i		−	0.872875i
$708$		0			0
$709$			3305.01i			0.175067i	0.996162	+	0.0875334i	$0.0278984\pi$
$709$			3305.01i			0.175067i	−0.996162	+	0.0875334i	$0.972102\pi$
$710$	13893.1	+	13184.6i	0.734362	+	0.696915i
$711$		0			0
$712$	−18926.6	−	16167.1i	−0.996213	−	0.850964i
$713$	29313.1			1.53967
$714$		0			0
$715$		−	42412.0i		−	2.21835i
$716$	13320.3	−	697.483i	0.695255	−	0.0364052i
$717$		0			0
$718$	−10428.2	+	10988.5i	−0.542030	+	0.571155i
$719$	−13268.0			−0.688198			−0.344099	−	0.938933i	$-0.611816\pi$
$719$	−13268.0			−0.688198			−0.344099	+	0.938933i	$0.611816\pi$
$720$		0			0
$721$	−13519.4			−0.698322
$722$	−10285.2	+	10837.8i	−0.530158	+	0.558644i
$723$		0			0
$724$	−23283.9	+	1219.20i	−1.19522	+	0.0625845i
$725$		−	7139.33i		−	0.365721i
$726$		0			0
$727$	−6305.89			−0.321696			−0.160848	−	0.986979i	$-0.551423\pi$
$727$	−6305.89			−0.321696			−0.160848	+	0.986979i	$0.551423\pi$
$728$	36132.5	−	42299.9i	1.83950	−	2.15349i
$729$		0			0
$730$	−1830.50	−	1737.16i	−0.0928081	−	0.0880756i
$731$		−	526.261i		−	0.0266272i
$732$		0			0
$733$		−	11396.5i		−	0.574267i	−0.957891	−	0.287133i	$-0.907298\pi$
$733$		−	11396.5i		−	0.574267i	0.957891	−	0.287133i	$-0.0927023\pi$
$734$	−13076.3	+	13778.9i	−0.657566	+	0.692899i
$735$		0			0
$736$	20155.4	−	26260.9i	1.00943	−	1.31521i
$737$	18331.9			0.916234
$738$		0			0
$739$			30149.5i			1.50077i	0.661003	+	0.750384i	$0.270131\pi$
$739$			30149.5i			1.50077i	−0.661003	+	0.750384i	$0.729869\pi$
$740$	371.509	+	7094.95i	0.0184553	+	0.352453i
$741$		0			0
$742$	21667.7	+	20562.8i	1.07203	+	1.01737i
$743$	−4136.17			−0.204228			−0.102114	−	0.994773i	$-0.532561\pi$
$743$	−4136.17			−0.204228			−0.102114	+	0.994773i	$0.532561\pi$
$744$		0			0
$745$	25774.7			1.26753
$746$	10926.4	+	10369.3i	0.536254	+	0.508909i
$747$		0			0
$748$	3375.29	−	176.739i	0.164991	−	0.00863931i
$749$			18477.6i			0.901412i
$750$		0			0
$751$	18734.2			0.910278			0.455139	−	0.890420i	$-0.349590\pi$
$751$	18734.2			0.910278			0.455139	+	0.890420i	$0.349590\pi$
$752$	36704.7	−	3854.47i	1.77990	−	0.186912i
$753$		0			0
$754$	−19197.1	+	20228.6i	−0.927211	+	0.977032i
$755$			4027.08i			0.194120i
$756$		0			0
$757$			7878.86i			0.378286i	0.981950	+	0.189143i	$0.0605709\pi$
$757$			7878.86i			0.378286i	−0.981950	+	0.189143i	$0.939429\pi$
$758$	−14320.8	−	13590.5i	−0.686219	−	0.651227i
$759$		0			0
$760$	−9127.38	−	7796.59i	−0.435638	−	0.372121i
$761$	2527.77			0.120410			0.0602048	−	0.998186i	$-0.480825\pi$
$761$	2527.77			0.120410			0.0602048	+	0.998186i	$0.480825\pi$
$762$		0			0
$763$		−	14219.8i		−	0.674694i
$764$	383.788	+	7329.46i	0.0181740	+	0.347082i
$765$		0			0
$766$	−10485.8	+	11049.2i	−0.494605	+	0.521181i
$767$	17747.8			0.835508
$768$		0			0
$769$	12262.0			0.575006			0.287503	−	0.957780i	$-0.407175\pi$
$769$	12262.0			0.575006			0.287503	+	0.957780i	$0.407175\pi$
$770$	−37153.3	+	39149.7i	−1.73885	+	1.83228i
$771$		0			0
$772$	1903.71	+	36356.5i	0.0887515	+	1.69495i
$773$		−	18696.3i		−	0.869935i	−0.900446	−	0.434968i	$-0.856760\pi$
$773$		−	18696.3i		−	0.869935i	0.900446	−	0.434968i	$-0.143240\pi$
$774$		0			0
$775$	−8579.59			−0.397662
$776$	22354.6	+	19095.3i	1.03413	+	0.883351i
$777$		0			0
$778$	−30013.8	−	28483.3i	−1.38309	−	1.31257i
$779$			11961.1i			0.550130i
$780$		0			0
$781$			21762.9i			0.997105i
$782$	3503.26	−	3691.50i	0.160200	−	0.168808i
$783$		0			0
$784$	−48576.3	+	5101.14i	−2.21284	+	0.232377i
$785$	24706.1			1.12331
$786$		0			0
$787$			12270.8i			0.555791i	0.960611	+	0.277896i	$0.0896370\pi$
$787$			12270.8i			0.555791i	−0.960611	+	0.277896i	$0.910363\pi$
$788$	−11126.2	+	582.593i	−0.502986	+	0.0263376i
$789$		0			0
$790$	968.369	+	918.989i	0.0436114	+	0.0413876i
$791$	16487.4			0.741117
$792$		0			0
$793$	24196.7			1.08354
$794$	−19800.2	−	18790.6i	−0.884993	−	0.839865i
$795$		0			0
$796$	2133.27	+	40740.4i	0.0949896	+	1.81408i
$797$			39305.1i			1.74687i	0.486939	+	0.873436i	$0.338114\pi$
$797$			39305.1i			1.74687i	−0.486939	+	0.873436i	$0.661886\pi$
$798$		0			0
$799$	5673.78			0.251219
$800$	−5899.25	+	7686.26i	−0.260713	+	0.339688i
$801$		0			0
$802$	18968.8	−	19988.1i	0.835178	−	0.880054i
$803$		−	2867.41i		−	0.126013i
$804$		0			0
$805$			81267.9i			3.55816i
$806$	24309.5	+	23069.9i	1.06236	+	1.00819i
$807$		0			0
$808$	7250.74	−	8488.36i	0.315693	−	0.369579i
$809$	16175.7			0.702976			0.351488	−	0.936192i	$-0.385676\pi$
$809$	16175.7			0.702976			0.351488	+	0.936192i	$0.385676\pi$
$810$		0			0
$811$		−	11577.8i		−	0.501297i	−0.968078	−	0.250648i	$-0.919356\pi$
$811$		−	11577.8i		−	0.501297i	0.968078	−	0.250648i	$-0.0806438\pi$
$812$	35440.9	−	1855.77i	1.53169	−	0.0802030i
$813$		0			0
$814$	−5556.98	+	5855.57i	−0.239278	+	0.252135i
$815$	−41396.7			−1.77922
$816$		0			0
$817$	−2123.70			−0.0909411
$818$	−96.3800	+	101.559i	−0.00411962	+	0.00434097i
$819$		0			0
$820$	32157.1	−	1683.82i	1.36948	−	0.0717093i
$821$			14454.3i			0.614445i	0.951638	+	0.307223i	$0.0993997\pi$
$821$			14454.3i			0.614445i	−0.951638	+	0.307223i	$0.900600\pi$
$822$		0			0
$823$	−30914.5			−1.30937			−0.654685	−	0.755902i	$-0.727199\pi$
$823$	−30914.5			−1.30937			−0.654685	+	0.755902i	$0.727199\pi$
$824$	−6993.60	−	5973.92i	−0.295672	−	0.252562i
$825$		0			0
$826$	−16382.6	−	15547.2i	−0.690101	−	0.654911i
$827$			27336.9i			1.14945i	0.818346	+	0.574725i	$0.194891\pi$
$827$			27336.9i			1.14945i	−0.818346	+	0.574725i	$0.805109\pi$
$828$		0			0
$829$		−	46893.1i		−	1.96461i	−0.187280	−	0.982307i	$-0.559967\pi$
$829$		−	46893.1i		−	1.96461i	0.187280	−	0.982307i	$-0.440033\pi$
$830$	−7919.62	+	8345.16i	−0.331198	+	0.348994i
$831$		0			0
$832$	37382.7	−	5915.64i	1.55771	−	0.246500i
$833$	−7508.88			−0.312326
$834$		0			0
$835$			9913.51i			0.410864i
$836$	−713.219	−	13620.8i	−0.0295062	−	0.563500i
$837$		0			0
$838$	20953.1	+	19884.7i	0.863739	+	0.819695i
$839$	−28984.1			−1.19266			−0.596330	−	0.802740i	$-0.703375\pi$
$839$	−28984.1			−1.19266			−0.596330	+	0.802740i	$0.703375\pi$
$840$		0			0
$841$	6598.29			0.270544
$842$	4062.19	+	3855.04i	0.166261	+	0.157783i
$843$		0			0
$844$	−25962.1	+	1359.44i	−1.05883	+	0.0554430i
$845$		−	43656.9i		−	1.77733i
$846$		0			0
$847$	−17058.3			−0.692007
$848$	2122.48	+	20211.6i	0.0859507	+	0.818478i
$849$		0			0
$850$	−1025.36	+	1080.46i	−0.0413760	+	0.0435993i
$851$			12155.1i			0.489628i
$852$		0			0
$853$			30385.8i			1.21968i	0.792524	+	0.609841i	$0.208767\pi$
$853$			30385.8i			1.21968i	−0.792524	+	0.609841i	$0.791233\pi$
$854$	−22335.5	−	21196.6i	−0.894971	−	0.849334i
$855$		0			0
$856$	−8164.83	+	9558.48i	−0.326014	+	0.381661i
$857$	12014.5			0.478888			0.239444	−	0.970910i	$-0.423035\pi$
$857$	12014.5			0.478888			0.239444	+	0.970910i	$0.423035\pi$
$858$		0			0
$859$		−	8657.72i		−	0.343885i	−0.985107	−	0.171943i	$-0.944996\pi$
$859$		−	8657.72i		−	0.343885i	0.985107	−	0.171943i	$-0.0550044\pi$
$860$	298.964	+	5709.50i	0.0118542	+	0.226387i
$861$		0			0
$862$	13184.2	−	13892.6i	0.520947	−	0.548939i
$863$	32403.5			1.27813			0.639065	−	0.769153i	$-0.279321\pi$
$863$	32403.5			1.27813			0.639065	+	0.769153i	$0.279321\pi$
$864$		0			0
$865$	37401.9			1.47017
$866$	11006.7	−	11598.1i	0.431896	−	0.455102i
$867$		0			0
$868$	−2230.15	−	42590.6i	−0.0872076	−	1.66546i
$869$			1516.91i			0.0592148i
$870$		0			0
$871$	31558.1			1.22768
$872$	6283.40	−	7355.90i	0.244017	−	0.285668i
$873$		0			0
$874$	−14896.9	−	14137.2i	−0.576538	−	0.547139i
$875$			31762.4i			1.22716i
$876$		0			0
$877$		−	44207.2i		−	1.70213i	−0.525058	−	0.851066i	$-0.675956\pi$
$877$		−	44207.2i		−	1.70213i	0.525058	−	0.851066i	$-0.324044\pi$
$878$	−9878.56	+	10409.4i	−0.379710	+	0.400113i
$879$		0			0
$880$	−36518.8	+	3834.94i	−1.39892	+	0.146904i
$881$	13143.3			0.502621			0.251311	−	0.967906i	$-0.419138\pi$
$881$	13143.3			0.502621			0.251311	+	0.967906i	$0.419138\pi$
$882$		0			0
$883$		−	35509.0i		−	1.35331i	−0.736300	−	0.676656i	$-0.763429\pi$
$883$		−	35509.0i		−	1.35331i	0.736300	−	0.676656i	$-0.236571\pi$
$884$	5810.53	−	304.253i	0.221074	−	0.0115760i
$885$		0			0
$886$	−10240.5	−	9718.33i	−0.388304	−	0.368503i
$887$	−44049.6			−1.66746			−0.833731	−	0.552170i	$-0.813800\pi$
$887$	−44049.6			−1.66746			−0.833731	+	0.552170i	$0.813800\pi$
$888$		0			0
$889$	30039.9			1.13330
$890$	30155.4	+	28617.7i	1.13574	+	1.07783i
$891$		0			0
$892$	614.936	+	11743.8i	0.0230825	+	0.440821i
$893$		−	22896.3i		−	0.858000i
$894$		0			0
$895$	−22277.6			−0.832020
$896$	−39689.4	−	27287.0i	−1.47983	−	1.01740i
$897$		0			0
$898$	29352.2	−	30929.3i	1.09075	−	1.14936i
$899$			21379.7i			0.793164i
$900$		0			0
$901$			3124.29i			0.115522i
$902$	26539.7	+	25186.4i	0.979685	+	0.929729i
$903$		0			0
$904$	8528.92	+	7285.39i	0.313792	+	0.268040i
$905$	38941.2			1.43033
$906$		0			0
$907$		−	20821.7i		−	0.762265i	−0.924520	−	0.381132i	$-0.875534\pi$
$907$		−	20821.7i		−	0.762265i	0.924520	−	0.381132i	$-0.124466\pi$
$908$	−7635.57	+	399.817i	−0.279070	+	0.0146128i
$909$		0			0
$910$	−63959.0	+	67395.7i	−2.32991	+	2.45511i
$911$	14603.6			0.531106			0.265553	−	0.964096i	$-0.414446\pi$
$911$	14603.6			0.531106			0.265553	+	0.964096i	$0.414446\pi$
$912$		0			0
$913$	−13072.4			−0.473858
$914$	31193.6	−	32869.7i	1.12888	−	1.18953i
$915$		0			0
$916$	29493.6	−	1544.36i	1.06386	−	0.0557063i
$917$			26304.2i			0.947264i
$918$		0			0
$919$	47367.9			1.70024			0.850121	−	0.526587i	$-0.176529\pi$
$919$	47367.9			1.70024			0.850121	+	0.526587i	$0.176529\pi$
$920$	−35910.4	+	42039.9i	−1.28688	+	1.50654i
$921$		0			0
$922$	−29172.9	−	27685.3i	−1.04204	−	0.988902i
$923$			37464.6i			1.33604i
$924$		0			0
$925$		−	3557.66i		−	0.126460i
$926$	20101.4	−	21181.5i	0.713361	−	0.751692i
$927$		0			0
$928$	19153.6	+	14700.5i	0.677530	+	0.520009i
$929$	−26130.2			−0.922823			−0.461411	−	0.887186i	$-0.652657\pi$
$929$	−26130.2			−0.922823			−0.461411	+	0.887186i	$0.652657\pi$
$930$		0			0
$931$			30301.7i			1.06670i
$932$	1241.11	+	23702.3i	0.0436200	+	0.833040i
$933$		0			0
$934$	−5228.51	−	4961.90i	−0.183171	−	0.173831i
$935$	−5645.03			−0.197446
$936$		0			0
$937$	−15796.3			−0.550738			−0.275369	−	0.961339i	$-0.588800\pi$
$937$	−15796.3			−0.550738			−0.275369	+	0.961339i	$0.588800\pi$
$938$	−29130.7	−	27645.2i	−1.01402	−	0.962312i
$939$		0			0
$940$	−61555.9	+	3223.21i	−2.13588	+	0.111840i
$941$		−	3239.15i		−	0.112214i	−0.998425	−	0.0561070i	$-0.982131\pi$
$941$		−	3239.15i		−	0.112214i	0.998425	−	0.0561070i	$-0.0178688\pi$
$942$		0			0
$943$	55091.9			1.90248
$944$	−1604.77	−	15281.7i	−0.0553292	−	0.526881i
$945$		0			0
$946$	−4471.86	+	4712.14i	−0.153692	+	0.161950i
$947$			44464.5i			1.52577i	0.646535	+	0.762884i	$0.276217\pi$
$947$			44464.5i			1.52577i	−0.646535	+	0.762884i	$0.723783\pi$
$948$		0			0
$949$		−	4936.21i		−	0.168847i
$950$	4360.13	+	4137.80i	0.148907	+	0.141314i
$951$		0			0
$952$	−5630.11	−	4809.23i	−0.191673	−	0.163727i
$953$	9758.46			0.331697			0.165849	−	0.986151i	$-0.446964\pi$
$953$	9758.46			0.331697			0.165849	+	0.986151i	$0.446964\pi$
$954$		0			0
$955$		−	12258.2i		−	0.415357i
$956$	−2442.46	−	46645.4i	−0.0826307	−	1.57805i
$957$		0			0
$958$	−25055.3	+	26401.6i	−0.844989	+	0.890392i
$959$	23507.4			0.791546
$960$		0			0
$961$	−4098.18			−0.137564
$962$	−9566.27	+	10080.3i	−0.320612	+	0.337840i
$963$		0			0
$964$	−137.081	−	2617.93i	−0.00457997	−	0.0874668i
$965$		−	60804.6i		−	2.02836i
$966$		0			0
$967$	37624.1			1.25120			0.625600	−	0.780144i	$-0.284854\pi$
$967$	37624.1			1.25120			0.625600	+	0.780144i	$0.284854\pi$
$968$	−8824.26	−	7537.67i	−0.292999	−	0.250279i
$969$		0			0
$970$	−35617.2	−	33801.0i	−1.17897	−	1.11885i
$971$		−	56799.4i		−	1.87722i	−0.344983	−	0.938609i	$-0.612115\pi$
$971$		−	56799.4i		−	1.87722i	0.344983	−	0.938609i	$-0.387885\pi$
$972$		0			0
$973$		−	23914.6i		−	0.787942i
$974$	17300.7	−	18230.3i	0.569148	−	0.599730i
$975$		0			0
$976$	−2187.89	−	20834.5i	−0.0717548	−	0.683296i
$977$	52512.9			1.71959			0.859793	−	0.510642i	$-0.170592\pi$
$977$	52512.9			1.71959			0.859793	+	0.510642i	$0.170592\pi$
$978$		0			0
$979$			47237.2i			1.54209i
$980$	81465.2	−	4265.71i	2.65542	−	0.139044i
$981$		0			0
$982$	−17886.5	−	16974.4i	−0.581244	−	0.551605i
$983$	−29065.5			−0.943077			−0.471538	−	0.881846i	$-0.656301\pi$
$983$	−29065.5			−0.943077			−0.471538	+	0.881846i	$0.656301\pi$
$984$		0			0
$985$	18608.0			0.601930
$986$	2692.42	+	2555.13i	0.0869617	+	0.0825273i
$987$		0			0
$988$	−1227.80	−	23448.1i	−0.0395359	−	0.755044i
$989$			9781.59i			0.314496i
$990$		0			0
$991$	28842.4			0.924530			0.462265	−	0.886742i	$-0.347037\pi$
$991$	28842.4			0.924530			0.462265	+	0.886742i	$0.347037\pi$
$992$	17666.2	−	23017.6i	0.565424	−	0.736703i
$993$		0			0
$994$	32819.4	−	34582.8i	1.04725	−	1.10352i
$995$		−	68136.6i		−	2.17093i
$996$		0			0
$997$			10685.8i			0.339440i	0.985492	+	0.169720i	$0.0542863\pi$
$997$			10685.8i			0.339440i	−0.985492	+	0.169720i	$0.945714\pi$
$998$	−6853.71	−	6504.22i	−0.217385	−	0.206300i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.4.d.d.109.8	yes	24
3.2	odd	2	inner	216.4.d.d.109.17	yes	24
4.3	odd	2		864.4.d.d.433.10		24
8.3	odd	2		864.4.d.d.433.9		24
8.5	even	2	inner	216.4.d.d.109.7	✓	24
12.11	even	2		864.4.d.d.433.23		24
24.5	odd	2	inner	216.4.d.d.109.18	yes	24
24.11	even	2		864.4.d.d.433.24		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.4.d.d.109.7	✓	24	8.5	even	2	inner
216.4.d.d.109.8	yes	24	1.1	even	1	trivial
216.4.d.d.109.17	yes	24	3.2	odd	2	inner
216.4.d.d.109.18	yes	24	24.5	odd	2	inner
864.4.d.d.433.9		24	8.3	odd	2
864.4.d.d.433.10		24	4.3	odd	2
864.4.d.d.433.23		24	12.11	even	2
864.4.d.d.433.24		24	24.11	even	2

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	216.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.94701 + 2.05162i) q^{2} +(-0.418326 - 7.98906i) q^{4} +13.3613i q^{5} +33.2593 q^{7} +(17.2050 + 14.6965i) q^{8} +O(q^{10})\)	\(q+(-1.94701 + 2.05162i) q^{2} +(-0.418326 - 7.98906i) q^{4} +13.3613i q^{5} +33.2593 q^{7} +(17.2050 + 14.6965i) q^{8} +(-27.4125 - 26.0146i) q^{10} -42.9405i q^{11} -73.9216i q^{13} +(-64.7560 + 68.2355i) q^{14} +(-63.6500 + 6.68406i) q^{16} -9.83895 q^{17} +39.7046i q^{19} +(106.745 - 5.58940i) q^{20} +(88.0978 + 83.6055i) q^{22} +182.876 q^{23} -53.5255 q^{25} +(151.659 + 143.926i) q^{26} +(-13.9132 - 265.710i) q^{28} +133.382i q^{29} +160.290 q^{31} +(110.214 - 143.600i) q^{32} +(19.1565 - 20.1858i) q^{34} +444.389i q^{35} +66.4666i q^{37} +(-81.4589 - 77.3051i) q^{38} +(-196.365 + 229.882i) q^{40} +301.253 q^{41} +53.4876i q^{43} +(-343.054 + 17.9632i) q^{44} +(-356.061 + 375.193i) q^{46} -576.665 q^{47} +763.179 q^{49} +(104.215 - 109.814i) q^{50} +(-590.564 + 30.9234i) q^{52} -317.543i q^{53} +573.743 q^{55} +(572.227 + 488.795i) q^{56} +(-273.649 - 259.695i) q^{58} +240.089i q^{59} +327.329i q^{61} +(-312.085 + 328.855i) q^{62} +(80.0258 + 505.707i) q^{64} +987.692 q^{65} +426.914i q^{67} +(4.11589 + 78.6039i) q^{68} +(-911.718 - 865.228i) q^{70} -506.816 q^{71} +66.7763 q^{73} +(-136.365 - 129.411i) q^{74} +(317.202 - 16.6095i) q^{76} -1428.17i q^{77} -35.3259 q^{79} +(-89.3081 - 850.450i) q^{80} +(-586.541 + 618.058i) q^{82} -304.430i q^{83} -131.462i q^{85} +(-109.736 - 104.141i) q^{86} +(631.075 - 738.793i) q^{88} -1100.06 q^{89} -2458.58i q^{91} +(-76.5018 - 1461.01i) q^{92} +(1122.77 - 1183.10i) q^{94} -530.507 q^{95} +1299.31 q^{97} +(-1485.91 + 1565.76i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4}+O(q^{10}) \) 24 * q - 12 * q^4	\( 24 q - 12 q^{4} - 24 q^{10} - 288 q^{16} + 336 q^{22} - 600 q^{25} + 84 q^{28} + 528 q^{31} + 24 q^{34} + 648 q^{40} - 864 q^{46} + 1536 q^{49} - 636 q^{52} + 144 q^{55} + 96 q^{58} - 888 q^{64} - 384 q^{70} + 216 q^{73} - 444 q^{76} - 2352 q^{79} + 336 q^{82} + 1896 q^{88} + 1200 q^{94} + 696 q^{97}+O(q^{100}) \) 24 * q - 12 * q^4 - 24 * q^10 - 288 * q^16 + 336 * q^22 - 600 * q^25 + 84 * q^28 + 528 * q^31 + 24 * q^34 + 648 * q^40 - 864 * q^46 + 1536 * q^49 - 636 * q^52 + 144 * q^55 + 96 * q^58 - 888 * q^64 - 384 * q^70 + 216 * q^73 - 444 * q^76 - 2352 * q^79 + 336 * q^82 + 1896 * q^88 + 1200 * q^94 + 696 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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