LMFDB - Embedded newform 216.3.b.a.163.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(163,216)]

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([1, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("216.163");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.b (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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 8x^{12} + 4x^{10} + 160x^{8} + 64x^{6} - 2048x^{4} + 4096x^{2} + 65536 $ x^16 + x^14 - 8x^12 + 4x^10 + 160x^8 + 64x^6 - 2048x^4 + 4096x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.11
Root			$0.941181 - 1.76470i$ of defining polynomial
Character	$\chi$	$=$	216.163
Dual form			216.3.b.a.163.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.941181 - 1.76470i) q^{2} +(-2.22836 - 3.32181i) q^{4} -8.60639i q^{5} +4.81948i q^{7} +(-7.95930 + 0.805966i) q^{8} +O(q^{10})$	\(q+(0.941181 - 1.76470i) q^{2} +(-2.22836 - 3.32181i) q^{4} -8.60639i q^{5} +4.81948i q^{7} +(-7.95930 + 0.805966i) q^{8} +(-15.1877 - 8.10017i) q^{10} -9.93139 q^{11} -5.78729i q^{13} +(8.50495 + 4.53600i) q^{14} +(-6.06885 + 14.8044i) q^{16} +30.8667 q^{17} -18.5944 q^{19} +(-28.5888 + 19.1781i) q^{20} +(-9.34723 + 17.5260i) q^{22} -15.6966i q^{23} -49.0699 q^{25} +(-10.2128 - 5.44688i) q^{26} +(16.0094 - 10.7395i) q^{28} -25.9792i q^{29} +12.7847i q^{31} +(20.4134 + 24.6433i) q^{32} +(29.0511 - 54.4705i) q^{34} +41.4783 q^{35} -63.2921i q^{37} +(-17.5007 + 32.8136i) q^{38} +(6.93646 + 68.5008i) q^{40} -14.4473 q^{41} +62.4861 q^{43} +(22.1307 + 32.9902i) q^{44} +(-27.6998 - 14.7733i) q^{46} -26.7557i q^{47} +25.7726 q^{49} +(-46.1837 + 86.5939i) q^{50} +(-19.2243 + 12.8961i) q^{52} +14.2150i q^{53} +85.4734i q^{55} +(-3.88434 - 38.3597i) q^{56} +(-45.8456 - 24.4512i) q^{58} +76.7922 q^{59} +44.5930i q^{61} +(22.5612 + 12.0327i) q^{62} +(62.7008 - 12.8298i) q^{64} -49.8076 q^{65} +88.6047 q^{67} +(-68.7820 - 102.533i) q^{68} +(39.0386 - 73.1969i) q^{70} -114.263i q^{71} +28.3077 q^{73} +(-111.692 - 59.5693i) q^{74} +(41.4350 + 61.7671i) q^{76} -47.8641i q^{77} +115.116i q^{79} +(127.412 + 52.2309i) q^{80} +(-13.5975 + 25.4952i) q^{82} -46.2135 q^{83} -265.651i q^{85} +(58.8107 - 110.269i) q^{86} +(79.0469 - 8.00436i) q^{88} +33.8625 q^{89} +27.8917 q^{91} +(-52.1410 + 34.9775i) q^{92} +(-47.2158 - 25.1819i) q^{94} +160.031i q^{95} -93.6047 q^{97} +(24.2567 - 45.4810i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{4}+O(q^{10}) $ 16 * q - 2 * q^4	$ 16 q - 2 q^{4} - 18 q^{10} + 34 q^{16} + 32 q^{19} - 22 q^{22} - 80 q^{25} + 102 q^{28} + 68 q^{34} - 6 q^{40} + 128 q^{43} + 60 q^{46} - 80 q^{49} - 180 q^{52} - 156 q^{58} - 74 q^{64} + 128 q^{67} - 378 q^{70} - 160 q^{73} + 188 q^{76} - 508 q^{82} + 542 q^{88} - 96 q^{91} + 24 q^{94} - 208 q^{97}+O(q^{100}) $ 16 * q - 2 * q^4 - 18 * q^10 + 34 * q^16 + 32 * q^19 - 22 * q^22 - 80 * q^25 + 102 * q^28 + 68 * q^34 - 6 * q^40 + 128 * q^43 + 60 * q^46 - 80 * q^49 - 180 * q^52 - 156 * q^58 - 74 * q^64 + 128 * q^67 - 378 * q^70 - 160 * q^73 + 188 * q^76 - 508 * q^82 + 542 * q^88 - 96 * q^91 + 24 * q^94 - 208 * 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 $

$2$	0.941181	−	1.76470i	0.470590	−	0.882352i
$2$	0.941181	−	1.76470i	0.470590	−	0.882352i
$3$		0			0
$3$		0			0
$4$	−2.22836	−	3.32181i	−0.557089	−	0.830453i
$5$		−	8.60639i		−	1.72128i	−0.509216	−	0.860639i	$-0.670065\pi$
$5$		−	8.60639i		−	1.72128i	0.509216	−	0.860639i	$-0.329935\pi$
$6$		0			0
$7$			4.81948i			0.688497i	0.938879	+	0.344249i	$0.111866\pi$
$7$			4.81948i			0.688497i	−0.938879	+	0.344249i	$0.888134\pi$
$8$	−7.95930	+	0.805966i	−0.994912	+	0.100746i
$9$		0			0
$10$	−15.1877	−	8.10017i	−1.51877	−	0.810017i
$11$	−9.93139			−0.902854			−0.451427	−	0.892308i	$-0.649085\pi$
$11$	−9.93139			−0.902854			−0.451427	+	0.892308i	$0.649085\pi$
$12$		0			0
$13$		−	5.78729i		−	0.445176i	−0.974913	−	0.222588i	$-0.928550\pi$
$13$		−	5.78729i		−	0.445176i	0.974913	−	0.222588i	$-0.0714504\pi$
$14$	8.50495	+	4.53600i	0.607497	+	0.324000i
$15$		0			0
$16$	−6.06885	+	14.8044i	−0.379303	+	0.925273i
$17$	30.8667			1.81569			0.907843	−	0.419309i	$-0.137728\pi$
$17$	30.8667			1.81569			0.907843	+	0.419309i	$0.137728\pi$
$18$		0			0
$19$	−18.5944			−0.978653			−0.489327	−	0.872101i	$-0.662757\pi$
$19$	−18.5944			−0.978653			−0.489327	+	0.872101i	$0.662757\pi$
$20$	−28.5888	+	19.1781i	−1.42944	+	0.958905i
$21$		0			0
$22$	−9.34723	+	17.5260i	−0.424874	+	0.796635i
$23$		−	15.6966i		−	0.682459i	−0.939980	−	0.341230i	$-0.889157\pi$
$23$		−	15.6966i		−	0.682459i	0.939980	−	0.341230i	$-0.110843\pi$
$24$		0			0
$25$	−49.0699			−1.96280
$26$	−10.2128	−	5.44688i	−0.392802	−	0.209495i
$27$		0			0
$28$	16.0094	−	10.7395i	0.571764	−	0.383554i
$29$		−	25.9792i		−	0.895836i	−0.894075	−	0.447918i	$-0.852166\pi$
$29$		−	25.9792i		−	0.895836i	0.894075	−	0.447918i	$-0.147834\pi$
$30$		0			0
$31$			12.7847i			0.412409i	0.978509	+	0.206204i	$0.0661112\pi$
$31$			12.7847i			0.412409i	−0.978509	+	0.206204i	$0.933889\pi$
$32$	20.4134	+	24.6433i	0.637920	+	0.770103i
$33$		0			0
$34$	29.0511	−	54.4705i	0.854445	−	1.60207i
$35$	41.4783			1.18509
$36$		0			0
$37$		−	63.2921i		−	1.71060i	−0.518136	−	0.855298i	$-0.673374\pi$
$37$		−	63.2921i		−	1.71060i	0.518136	−	0.855298i	$-0.326626\pi$
$38$	−17.5007	+	32.8136i	−0.460545	+	0.863516i
$39$		0			0
$40$	6.93646	+	68.5008i	0.173411	+	1.71252i
$41$	−14.4473			−0.352373			−0.176187	−	0.984357i	$-0.556376\pi$
$41$	−14.4473			−0.352373			−0.176187	+	0.984357i	$0.556376\pi$
$42$		0			0
$43$	62.4861			1.45317			0.726583	−	0.687079i	$-0.241107\pi$
$43$	62.4861			1.45317			0.726583	+	0.687079i	$0.241107\pi$
$44$	22.1307	+	32.9902i	0.502970	+	0.749777i
$45$		0			0
$46$	−27.6998	−	14.7733i	−0.602169	−	0.321159i
$47$		−	26.7557i		−	0.569269i	−0.958636	−	0.284635i	$-0.908128\pi$
$47$		−	26.7557i		−	0.569269i	0.958636	−	0.284635i	$-0.0918723\pi$
$48$		0			0
$49$	25.7726			0.525972
$50$	−46.1837	+	86.5939i	−0.923673	+	1.73188i
$51$		0			0
$52$	−19.2243	+	12.8961i	−0.369697	+	0.248003i
$53$			14.2150i			0.268207i	0.990967	+	0.134104i	$0.0428155\pi$
$53$			14.2150i			0.268207i	−0.990967	+	0.134104i	$0.957184\pi$
$54$		0			0
$55$			85.4734i			1.55406i
$56$	−3.88434	−	38.3597i	−0.0693631	−	0.684994i
$57$		0			0
$58$	−45.8456	−	24.4512i	−0.790442	−	0.421572i
$59$	76.7922			1.30156			0.650782	−	0.759265i	$-0.274441\pi$
$59$	76.7922			1.30156			0.650782	+	0.759265i	$0.274441\pi$
$60$		0			0
$61$			44.5930i			0.731032i	0.930805	+	0.365516i	$0.119107\pi$
$61$			44.5930i			0.731032i	−0.930805	+	0.365516i	$0.880893\pi$
$62$	22.5612	+	12.0327i	0.363890	+	0.194076i
$63$		0			0
$64$	62.7008	−	12.8298i	0.979701	−	0.200466i
$65$	−49.8076			−0.766271
$66$		0			0
$67$	88.6047			1.32246			0.661229	−	0.750184i	$-0.270035\pi$
$67$	88.6047			1.32246			0.661229	+	0.750184i	$0.270035\pi$
$68$	−68.7820	−	102.533i	−1.01150	−	1.50784i
$69$		0			0
$70$	39.0386	−	73.1969i	0.557694	−	1.04567i
$71$		−	114.263i		−	1.60933i	−0.593728	−	0.804666i	$-0.702345\pi$
$71$		−	114.263i		−	1.60933i	0.593728	−	0.804666i	$-0.297655\pi$
$72$		0			0
$73$	28.3077			0.387777			0.193889	−	0.981024i	$-0.437890\pi$
$73$	28.3077			0.387777			0.193889	+	0.981024i	$0.437890\pi$
$74$	−111.692	−	59.5693i	−1.50935	−	0.804990i
$75$		0			0
$76$	41.4350	+	61.7671i	0.545197	+	0.812725i
$77$		−	47.8641i		−	0.621612i
$78$		0			0
$79$			115.116i			1.45716i	0.684960	+	0.728581i	$0.259820\pi$
$79$			115.116i			1.45716i	−0.684960	+	0.728581i	$0.740180\pi$
$80$	127.412	+	52.2309i	1.59265	+	0.652886i
$81$		0			0
$82$	−13.5975	+	25.4952i	−0.165823	+	0.310917i
$83$	−46.2135			−0.556790			−0.278395	−	0.960467i	$-0.589802\pi$
$83$	−46.2135			−0.556790			−0.278395	+	0.960467i	$0.589802\pi$
$84$		0			0
$85$		−	265.651i		−	3.12530i
$86$	58.8107	−	110.269i	0.683846	−	1.28220i
$87$		0			0
$88$	79.0469	−	8.00436i	0.898260	−	0.0909587i
$89$	33.8625			0.380478			0.190239	−	0.981738i	$-0.439074\pi$
$89$	33.8625			0.380478			0.190239	+	0.981738i	$0.439074\pi$
$90$		0			0
$91$	27.8917			0.306502
$92$	−52.1410	+	34.9775i	−0.566750	+	0.380191i
$93$		0			0
$94$	−47.2158	−	25.1819i	−0.502296	−	0.267893i
$95$			160.031i			1.68453i
$96$		0			0
$97$	−93.6047			−0.964997			−0.482499	−	0.875897i	$-0.660271\pi$
$97$	−93.6047			−0.964997			−0.482499	+	0.875897i	$0.660271\pi$
$98$	24.2567	−	45.4810i	0.247517	−	0.464092i
$99$		0			0
$100$	109.345	+	163.001i	1.09345	+	1.63001i
$101$			28.2006i			0.279214i	0.990207	+	0.139607i	$0.0445839\pi$
$101$			28.2006i			0.279214i	−0.990207	+	0.139607i	$0.955416\pi$
$102$		0			0
$103$		−	55.9057i		−	0.542774i	−0.962470	−	0.271387i	$-0.912518\pi$
$103$		−	55.9057i		−	0.542774i	0.962470	−	0.271387i	$-0.0874823\pi$
$104$	4.66436	+	46.0627i	0.0448496	+	0.442911i
$105$		0			0
$106$	25.0852	+	13.3789i	0.236653	+	0.126216i
$107$	−169.036			−1.57977			−0.789886	−	0.613253i	$-0.789860\pi$
$107$	−169.036			−1.57977			−0.789886	+	0.613253i	$0.789860\pi$
$108$		0			0
$109$			84.7359i			0.777393i	0.921366	+	0.388697i	$0.127075\pi$
$109$			84.7359i			0.777393i	−0.921366	+	0.388697i	$0.872925\pi$
$110$	150.835	+	80.4459i	1.37123	+	0.731327i
$111$		0			0
$112$	−71.3493	−	29.2487i	−0.637047	−	0.261149i
$113$	75.2321			0.665771			0.332885	−	0.942967i	$-0.391978\pi$
$113$	75.2321			0.665771			0.332885	+	0.942967i	$0.391978\pi$
$114$		0			0
$115$	−135.091			−1.17470
$116$	−86.2981	+	57.8910i	−0.743949	+	0.499061i
$117$		0			0
$118$	72.2754	−	135.516i	0.612503	−	1.14844i
$119$			148.761i			1.25009i
$120$		0			0
$121$	−22.3675			−0.184855
$122$	78.6933	+	41.9700i	0.645027	+	0.344017i
$123$		0			0
$124$	42.4682	−	28.4888i	0.342486	−	0.229748i
$125$			207.155i			1.65724i
$126$		0			0
$127$			58.4530i			0.460260i	0.973160	+	0.230130i	$0.0739151\pi$
$127$			58.4530i			0.460260i	−0.973160	+	0.230130i	$0.926085\pi$
$128$	36.3720	−	122.724i	0.284156	−	0.958778i
$129$		0			0
$130$	−46.8780	+	87.8957i	−0.360600	+	0.676121i
$131$	−115.102			−0.878639			−0.439320	−	0.898331i	$-0.644780\pi$
$131$	−115.102			−0.878639			−0.439320	+	0.898331i	$0.644780\pi$
$132$		0			0
$133$		−	89.6154i		−	0.673800i
$134$	83.3931	−	156.361i	0.622336	−	1.16687i
$135$		0			0
$136$	−245.677	+	24.8775i	−1.80645	+	0.182923i
$137$	−50.2245			−0.366602			−0.183301	−	0.983057i	$-0.558678\pi$
$137$	−50.2245			−0.366602			−0.183301	+	0.983057i	$0.558678\pi$
$138$		0			0
$139$	58.1186			0.418120			0.209060	−	0.977903i	$-0.432960\pi$
$139$	58.1186			0.418120			0.209060	+	0.977903i	$0.432960\pi$
$140$	−92.4285	−	137.783i	−0.660203	−	0.984165i
$141$		0			0
$142$	−201.639	−	107.542i	−1.42000	−	0.757336i
$143$			57.4758i			0.401929i
$144$		0			0
$145$	−223.587			−1.54198
$146$	26.6427	−	49.9547i	0.182484	−	0.342156i
$147$		0			0
$148$	−210.244	+	141.037i	−1.42057	+	0.952955i
$149$		−	125.603i		−	0.842974i	−0.906834	−	0.421487i	$-0.861508\pi$
$149$		−	125.603i		−	0.842974i	0.906834	−	0.421487i	$-0.138492\pi$
$150$		0			0
$151$			162.225i			1.07433i	0.843476	+	0.537167i	$0.180506\pi$
$151$			162.225i			1.07433i	−0.843476	+	0.537167i	$0.819494\pi$
$152$	147.998	−	14.9865i	0.973674	−	0.0985951i
$153$		0			0
$154$	−84.4660	−	45.0488i	−0.548480	−	0.292525i
$155$	110.030			0.709870
$156$		0			0
$157$			157.397i			1.00253i	0.865293	+	0.501266i	$0.167132\pi$
$157$			157.397i			1.00253i	−0.865293	+	0.501266i	$0.832868\pi$
$158$	203.145	+	108.345i	1.28573	+	0.685726i
$159$		0			0
$160$	212.090	−	175.686i	1.32556	−	1.09804i
$161$	75.6492			0.469871
$162$		0			0
$163$	166.269			1.02006			0.510029	−	0.860157i	$-0.329635\pi$
$163$	166.269			1.02006			0.510029	+	0.860157i	$0.329635\pi$
$164$	32.1937	+	47.9912i	0.196303	+	0.292629i
$165$		0			0
$166$	−43.4953	+	81.5532i	−0.262020	+	0.491284i
$167$			158.709i			0.950355i	0.879890	+	0.475177i	$0.157616\pi$
$167$			158.709i			0.950355i	−0.879890	+	0.475177i	$0.842384\pi$
$168$		0			0
$169$	135.507			0.801818
$170$	−468.795	−	250.025i	−2.75761	−	1.47074i
$171$		0			0
$172$	−139.241	−	207.567i	−0.809543	−	1.20678i
$173$			45.2251i			0.261417i	0.991421	+	0.130708i	$0.0417251\pi$
$173$			45.2251i			0.261417i	−0.991421	+	0.130708i	$0.958275\pi$
$174$		0			0
$175$		−	236.491i		−	1.35138i
$176$	60.2721	−	147.028i	0.342455	−	0.835386i
$177$		0			0
$178$	31.8708	−	59.7574i	0.179049	−	0.335715i
$179$	−34.1175			−0.190601			−0.0953003	−	0.995449i	$-0.530381\pi$
$179$	−34.1175			−0.190601			−0.0953003	+	0.995449i	$0.530381\pi$
$180$		0			0
$181$		−	21.4438i		−	0.118474i	−0.998244	−	0.0592370i	$-0.981133\pi$
$181$		−	21.4438i		−	0.118474i	0.998244	−	0.0592370i	$-0.0188668\pi$
$182$	26.2511	−	49.2206i	0.144237	−	0.270443i
$183$		0			0
$184$	12.6509	+	124.934i	0.0687548	+	0.678987i
$185$	−544.716			−2.94441
$186$		0			0
$187$	−306.549			−1.63930
$188$	−88.8772	+	59.6212i	−0.472751	+	0.317134i
$189$		0			0
$190$	282.407	+	150.618i	1.48635	+	0.792725i
$191$		−	172.809i		−	0.904759i	−0.891826	−	0.452380i	$-0.850575\pi$
$191$		−	172.809i		−	0.904759i	0.891826	−	0.452380i	$-0.149425\pi$
$192$		0			0
$193$	140.210			0.726475			0.363238	−	0.931697i	$-0.381671\pi$
$193$	140.210			0.726475			0.363238	+	0.931697i	$0.381671\pi$
$194$	−88.0990	+	165.185i	−0.454118	+	0.851467i
$195$		0			0
$196$	−57.4306	−	85.6118i	−0.293013	−	0.436795i
$197$			329.507i			1.67262i	0.548253	+	0.836312i	$0.315293\pi$
$197$			329.507i			1.67262i	−0.548253	+	0.836312i	$0.684707\pi$
$198$		0			0
$199$		−	249.916i		−	1.25586i	−0.778270	−	0.627930i	$-0.783902\pi$
$199$		−	249.916i		−	1.25586i	0.778270	−	0.627930i	$-0.216098\pi$
$200$	390.562	−	39.5487i	1.95281	−	0.197743i
$201$		0			0
$202$	49.7657	+	26.5419i	0.246365	+	0.131395i
$203$	125.206			0.616780
$204$		0			0
$205$			124.339i			0.606532i
$206$	−98.6570	−	52.6174i	−0.478917	−	0.255424i
$207$		0			0
$208$	85.6771	+	35.1222i	0.411909	+	0.168857i
$209$	184.668			0.883581
$210$		0			0
$211$	−84.9300			−0.402512			−0.201256	−	0.979539i	$-0.564502\pi$
$211$	−84.9300			−0.402512			−0.201256	+	0.979539i	$0.564502\pi$
$212$	47.2195	−	31.6761i	0.222733	−	0.149415i
$213$		0			0
$214$	−159.093	+	298.298i	−0.743426	+	1.39392i
$215$		−	537.780i		−	2.50130i
$216$		0			0
$217$	−61.6154			−0.283942
$218$	149.534	+	79.7518i	0.685934	+	0.365834i
$219$		0			0
$220$	283.926	−	190.465i	1.29057	−	0.865751i
$221$		−	178.634i		−	0.808300i
$222$		0			0
$223$			1.94316i			0.00871371i	0.999991	+	0.00435686i	$0.00138683\pi$
$223$			1.94316i			0.00871371i	−0.999991	+	0.00435686i	$0.998613\pi$
$224$	−118.768	+	98.3821i	−0.530214	+	0.439206i
$225$		0			0
$226$	70.8070	−	132.762i	0.313305	−	0.587444i
$227$	203.658			0.897171			0.448586	−	0.893740i	$-0.351928\pi$
$227$	203.658			0.897171			0.448586	+	0.893740i	$0.351928\pi$
$228$		0			0
$229$			19.9963i			0.0873202i	0.999046	+	0.0436601i	$0.0139019\pi$
$229$			19.9963i			0.0873202i	−0.999046	+	0.0436601i	$0.986098\pi$
$230$	−127.145	+	238.395i	−0.552803	+	1.03650i
$231$		0			0
$232$	20.9384	+	206.776i	0.0902516	+	0.891278i
$233$	−91.1197			−0.391072			−0.195536	−	0.980697i	$-0.562645\pi$
$233$	−91.1197			−0.391072			−0.195536	+	0.980697i	$0.562645\pi$
$234$		0			0
$235$	−230.270			−0.979870
$236$	−171.121	−	255.089i	−0.725087	−	1.08089i
$237$		0			0
$238$	262.520	+	140.011i	1.10302	+	0.588283i
$239$			36.8504i			0.154186i	0.997024	+	0.0770929i	$0.0245638\pi$
$239$			36.8504i			0.154186i	−0.997024	+	0.0770929i	$0.975436\pi$
$240$		0			0
$241$	308.182			1.27876			0.639381	−	0.768890i	$-0.279191\pi$
$241$	308.182			1.27876			0.639381	+	0.768890i	$0.279191\pi$
$242$	−21.0519	+	39.4720i	−0.0869911	+	0.163107i
$243$		0			0
$244$	148.129	−	99.3690i	0.607087	−	0.407250i
$245$		−	221.809i		−	0.905344i
$246$		0			0
$247$			107.611i			0.435673i
$248$	−10.3040	−	101.757i	−0.0415484	−	0.410310i
$249$		0			0
$250$	365.567	+	194.970i	1.46227	+	0.779881i
$251$	−228.334			−0.909696			−0.454848	−	0.890569i	$-0.650306\pi$
$251$	−228.334			−0.909696			−0.454848	+	0.890569i	$0.650306\pi$
$252$		0			0
$253$			155.889i			0.616161i
$254$	103.152	+	55.0149i	0.406111	+	0.216594i
$255$		0			0
$256$	−182.338	−	179.691i	−0.712259	−	0.701917i
$257$	292.265			1.13722			0.568609	−	0.822608i	$-0.307482\pi$
$257$	292.265			1.13722			0.568609	+	0.822608i	$0.307482\pi$
$258$		0			0
$259$	305.035			1.17774
$260$	110.989	+	165.451i	0.426881	+	0.636352i
$261$		0			0
$262$	−108.332	+	203.120i	−0.413479	+	0.775269i
$263$			488.233i			1.85640i	0.372083	+	0.928199i	$0.378644\pi$
$263$			488.233i			1.85640i	−0.372083	+	0.928199i	$0.621356\pi$
$264$		0			0
$265$	122.340			0.461659
$266$	−158.145	−	84.3443i	−0.594528	−	0.317084i
$267$		0			0
$268$	−197.443	−	294.328i	−0.736728	−	1.09824i
$269$		−	38.8093i		−	0.144273i	−0.997395	−	0.0721363i	$-0.977018\pi$
$269$		−	38.8093i		−	0.144273i	0.997395	−	0.0721363i	$-0.0229816\pi$
$270$		0			0
$271$		−	327.987i		−	1.21028i	−0.796118	−	0.605142i	$-0.793116\pi$
$271$		−	327.987i		−	1.21028i	0.796118	−	0.605142i	$-0.206884\pi$
$272$	−187.325	+	456.961i	−0.688695	+	1.68001i
$273$		0			0
$274$	−47.2703	+	88.6313i	−0.172519	+	0.323472i
$275$	487.332			1.77212
$276$		0			0
$277$			418.966i			1.51251i	0.654275	+	0.756257i	$0.272974\pi$
$277$			418.966i			1.51251i	−0.654275	+	0.756257i	$0.727026\pi$
$278$	54.7001	−	102.562i	0.196763	−	0.368929i
$279$		0			0
$280$	−330.138	+	33.4301i	−1.17906	+	0.119393i
$281$	201.185			0.715960			0.357980	−	0.933729i	$-0.383466\pi$
$281$	201.185			0.715960			0.357980	+	0.933729i	$0.383466\pi$
$282$		0			0
$283$	242.161			0.855692			0.427846	−	0.903852i	$-0.359273\pi$
$283$	242.161			0.855692			0.427846	+	0.903852i	$0.359273\pi$
$284$	−379.558	+	254.618i	−1.33647	+	0.896541i
$285$		0			0
$286$	101.428	+	54.0951i	0.354642	+	0.189144i
$287$		−	69.6285i		−	0.242608i
$288$		0			0
$289$	663.752			2.29672
$290$	−210.436	+	394.565i	−0.725642	+	1.36057i
$291$		0			0
$292$	−63.0797	−	94.0329i	−0.216026	−	0.322030i
$293$		−	268.900i		−	0.917749i	−0.888501	−	0.458874i	$-0.848253\pi$
$293$		−	268.900i		−	0.917749i	0.888501	−	0.458874i	$-0.151747\pi$
$294$		0			0
$295$		−	660.904i		−	2.24035i
$296$	51.0112	+	503.760i	0.172335	+	1.70189i
$297$		0			0
$298$	−221.652	−	118.215i	−0.743800	−	0.396696i
$299$	−90.8405			−0.303814
$300$		0			0
$301$			301.151i			1.00050i
$302$	286.278	+	152.683i	0.947941	+	0.505572i
$303$		0			0
$304$	112.847	−	275.278i	0.371206	−	0.905521i
$305$	383.784			1.25831
$306$		0			0
$307$	−88.1714			−0.287203			−0.143602	−	0.989636i	$-0.545868\pi$
$307$	−88.1714			−0.287203			−0.143602	+	0.989636i	$0.545868\pi$
$308$	−158.996	+	106.658i	−0.516219	+	0.346293i
$309$		0			0
$310$	103.558	−	194.170i	0.334058	−	0.626355i
$311$			175.687i			0.564909i	0.959281	+	0.282455i	$0.0911486\pi$
$311$			175.687i			0.564909i	−0.959281	+	0.282455i	$0.908851\pi$
$312$		0			0
$313$	−298.025			−0.952157			−0.476078	−	0.879403i	$-0.657942\pi$
$313$	−298.025			−0.952157			−0.476078	+	0.879403i	$0.657942\pi$
$314$	277.760	+	148.140i	0.884586	+	0.471782i
$315$		0			0
$316$	382.393	−	256.519i	1.21010	−	0.811769i
$317$		−	157.658i		−	0.497343i	−0.968588	−	0.248671i	$-0.920006\pi$
$317$		−	157.658i		−	0.497343i	0.968588	−	0.248671i	$-0.0799939\pi$
$318$		0			0
$319$			258.010i			0.808809i
$320$	−110.419	−	539.628i	−0.345058	−	1.68634i
$321$		0			0
$322$	71.1996	−	133.498i	0.221117	−	0.414592i
$323$	−573.948			−1.77693
$324$		0			0
$325$			283.982i			0.873790i
$326$	156.490	−	293.416i	0.480029	−	0.900049i
$327$		0			0
$328$	114.990	−	11.6440i	0.350580	−	0.0355001i
$329$	128.948			0.391940
$330$		0			0
$331$	171.458			0.518000			0.259000	−	0.965877i	$-0.416607\pi$
$331$	171.458			0.518000			0.259000	+	0.965877i	$0.416607\pi$
$332$	102.980	+	153.513i	0.310182	+	0.462387i
$333$		0			0
$334$	280.075	+	149.374i	0.838547	+	0.447228i
$335$		−	762.567i		−	2.27632i
$336$		0			0
$337$	−358.818			−1.06474			−0.532371	−	0.846511i	$-0.678699\pi$
$337$	−358.818			−1.06474			−0.532371	+	0.846511i	$0.678699\pi$
$338$	127.537	−	239.130i	0.377328	−	0.707486i
$339$		0			0
$340$	−882.441	+	591.964i	−2.59541	+	1.74107i
$341$		−	126.970i		−	0.372345i
$342$		0			0
$343$			360.365i			1.05063i
$344$	−497.346	+	50.3617i	−1.44577	+	0.146400i
$345$		0			0
$346$	79.8088	+	42.5650i	0.230661	+	0.123020i
$347$	−167.974			−0.484075			−0.242037	−	0.970267i	$-0.577816\pi$
$347$	−167.974			−0.484075			−0.242037	+	0.970267i	$0.577816\pi$
$348$		0			0
$349$		−	496.148i		−	1.42163i	−0.703380	−	0.710814i	$-0.748327\pi$
$349$		−	496.148i		−	1.42163i	0.703380	−	0.710814i	$-0.251673\pi$
$350$	−417.337	−	222.581i	−1.19239	−	0.635946i
$351$		0			0
$352$	−202.734	−	244.742i	−0.575948	−	0.695290i
$353$	132.906			0.376505			0.188253	−	0.982121i	$-0.439718\pi$
$353$	132.906			0.376505			0.188253	+	0.982121i	$0.439718\pi$
$354$		0			0
$355$	−983.388			−2.77011
$356$	−75.4578	−	112.485i	−0.211960	−	0.315969i
$357$		0			0
$358$	−32.1107	+	60.2073i	−0.0896948	+	0.168177i
$359$		−	565.184i		−	1.57433i	−0.616743	−	0.787164i	$-0.711548\pi$
$359$		−	565.184i		−	1.57433i	0.616743	−	0.787164i	$-0.288452\pi$
$360$		0			0
$361$	−15.2479			−0.0422381
$362$	−37.8420	−	20.1825i	−0.104536	−	0.0557528i
$363$		0			0
$364$	−62.1527	−	92.6509i	−0.170749	−	0.254536i
$365$		−	243.627i		−	0.667472i
$366$		0			0
$367$		−	615.679i		−	1.67760i	−0.544441	−	0.838799i	$-0.683258\pi$
$367$		−	615.679i		−	1.67760i	0.544441	−	0.838799i	$-0.316742\pi$
$368$	232.377	+	95.2600i	0.631461	+	0.258859i
$369$		0			0
$370$	−512.676	+	961.262i	−1.38561	+	2.59801i
$371$	−68.5088			−0.184660
$372$		0			0
$373$			455.597i			1.22144i	0.791847	+	0.610720i	$0.209120\pi$
$373$			455.597i			1.22144i	−0.791847	+	0.610720i	$0.790880\pi$
$374$	−288.518	+	540.968i	−0.771439	+	1.44644i
$375$		0			0
$376$	21.5641	+	212.956i	0.0573514	+	0.566373i
$377$	−150.349			−0.398804
$378$		0			0
$379$	−337.902			−0.891562			−0.445781	−	0.895142i	$-0.647074\pi$
$379$	−337.902			−0.891562			−0.445781	+	0.895142i	$0.647074\pi$
$380$	531.592	−	356.606i	1.39893	−	0.938436i
$381$		0			0
$382$	−304.957	−	162.644i	−0.798316	−	0.425771i
$383$			218.893i			0.571522i	0.958301	+	0.285761i	$0.0922464\pi$
$383$			218.893i			0.571522i	−0.958301	+	0.285761i	$0.907754\pi$
$384$		0			0
$385$	−411.937			−1.06997
$386$	131.963	−	247.429i	0.341872	−	0.641007i
$387$		0			0
$388$	208.585	+	310.937i	0.537590	+	0.801384i
$389$			142.868i			0.367270i	0.982994	+	0.183635i	$0.0587865\pi$
$389$			142.868i			0.367270i	−0.982994	+	0.183635i	$0.941214\pi$
$390$		0			0
$391$		−	484.501i		−	1.23913i
$392$	−205.132	+	20.7719i	−0.523296	+	0.0529894i
$393$		0			0
$394$	581.482	+	310.126i	1.47584	+	0.787121i
$395$	990.731			2.50818
$396$		0			0
$397$		−	709.501i		−	1.78716i	−0.448907	−	0.893579i	$-0.648186\pi$
$397$		−	709.501i		−	1.78716i	0.448907	−	0.893579i	$-0.351814\pi$
$398$	−441.028	−	235.216i	−1.10811	−	0.590996i
$399$		0			0
$400$	297.798	−	726.449i	0.744495	−	1.81612i
$401$	−157.900			−0.393766			−0.196883	−	0.980427i	$-0.563082\pi$
$401$	−157.900			−0.393766			−0.196883	+	0.980427i	$0.563082\pi$
$402$		0			0
$403$	73.9885			0.183594
$404$	93.6771	−	62.8410i	0.231874	−	0.155547i
$405$		0			0
$406$	117.842	−	220.952i	0.290251	−	0.544217i
$407$			628.578i			1.54442i
$408$		0			0
$409$	121.735			0.297641			0.148820	−	0.988864i	$-0.452452\pi$
$409$	121.735			0.297641			0.148820	+	0.988864i	$0.452452\pi$
$410$	219.422	+	117.026i	0.535175	+	0.285428i
$411$		0			0
$412$	−185.708	+	124.578i	−0.450748	+	0.302373i
$413$			370.099i			0.896123i
$414$		0			0
$415$			397.732i			0.958390i
$416$	142.618	−	118.138i	0.342831	−	0.283986i
$417$		0			0
$418$	173.806	−	325.885i	0.415805	−	0.779629i
$419$	24.2370			0.0578449			0.0289224	−	0.999582i	$-0.490792\pi$
$419$	24.2370			0.0578449			0.0289224	+	0.999582i	$0.490792\pi$
$420$		0			0
$421$			280.461i			0.666177i	0.942895	+	0.333089i	$0.108091\pi$
$421$			280.461i			0.666177i	−0.942895	+	0.333089i	$0.891909\pi$
$422$	−79.9345	+	149.876i	−0.189418	+	0.355157i
$423$		0			0
$424$	−11.4568	−	113.141i	−0.0270208	−	0.266843i
$425$	−1514.63			−3.56382
$426$		0			0
$427$	−214.915			−0.503313
$428$	376.672	+	561.504i	0.880074	+	1.31193i
$429$		0			0
$430$	−949.022	−	506.148i	−2.20703	−	1.17709i
$431$			537.398i			1.24686i	0.781878	+	0.623432i	$0.214262\pi$
$431$			537.398i			1.24686i	−0.781878	+	0.623432i	$0.785738\pi$
$432$		0			0
$433$	−103.584			−0.239224			−0.119612	−	0.992821i	$-0.538165\pi$
$433$	−103.584			−0.239224			−0.119612	+	0.992821i	$0.538165\pi$
$434$	−57.9913	+	108.733i	−0.133620	+	0.250537i
$435$		0			0
$436$	281.476	−	188.822i	0.645588	−	0.433078i
$437$			291.868i			0.667891i
$438$		0			0
$439$			557.858i			1.27075i	0.772205	+	0.635373i	$0.219154\pi$
$439$			557.858i			1.27075i	−0.772205	+	0.635373i	$0.780846\pi$
$440$	−68.8886	−	680.308i	−0.156565	−	1.54615i
$441$		0			0
$442$	−315.237	−	168.127i	−0.713205	−	0.380378i
$443$	4.79025			0.0108132			0.00540660	−	0.999985i	$-0.498279\pi$
$443$	4.79025			0.0108132			0.00540660	+	0.999985i	$0.498279\pi$
$444$		0			0
$445$		−	291.434i		−	0.654908i
$446$	3.42910	+	1.82886i	0.00768856	+	0.00410059i
$447$		0			0
$448$	61.8332	+	302.185i	0.138020	+	0.674521i
$449$	838.004			1.86638			0.933190	−	0.359384i	$-0.117013\pi$
$449$	838.004			1.86638			0.933190	+	0.359384i	$0.117013\pi$
$450$		0			0
$451$	143.482			0.318141
$452$	−167.644	−	249.907i	−0.370894	−	0.552891i
$453$		0			0
$454$	191.679	−	359.396i	0.422200	−	0.791620i
$455$		−	240.047i		−	0.527575i
$456$		0			0
$457$	537.817			1.17684			0.588422	−	0.808554i	$-0.299750\pi$
$457$	537.817			1.17684			0.588422	+	0.808554i	$0.299750\pi$
$458$	35.2876	+	18.8202i	0.0770471	+	0.0410920i
$459$		0			0
$460$	301.030	+	448.746i	0.654414	+	0.975534i
$461$			161.391i			0.350088i	0.984561	+	0.175044i	$0.0560068\pi$
$461$			161.391i			0.350088i	−0.984561	+	0.175044i	$0.943993\pi$
$462$		0			0
$463$			485.576i			1.04876i	0.851484	+	0.524381i	$0.175703\pi$
$463$			485.576i			1.04876i	−0.851484	+	0.524381i	$0.824297\pi$
$464$	384.606	+	157.664i	0.828892	+	0.339793i
$465$		0			0
$466$	−85.7601	+	160.799i	−0.184035	+	0.345063i
$467$	239.041			0.511864			0.255932	−	0.966695i	$-0.417618\pi$
$467$	239.041			0.511864			0.255932	+	0.966695i	$0.417618\pi$
$468$		0			0
$469$			427.029i			0.910509i
$470$	−216.725	+	406.357i	−0.461118	+	0.864590i
$471$		0			0
$472$	−611.212	+	61.8919i	−1.29494	+	0.131127i
$473$	−620.574			−1.31200
$474$		0			0
$475$	912.426			1.92090
$476$	494.157	−	331.493i	1.03814	−	0.696415i
$477$		0			0
$478$	65.0300	+	34.6829i	0.136046	+	0.0725583i
$479$		−	416.528i		−	0.869579i	−0.900532	−	0.434789i	$-0.856823\pi$
$479$		−	416.528i		−	0.869579i	0.900532	−	0.434789i	$-0.143177\pi$
$480$		0			0
$481$	−366.289			−0.761516
$482$	290.055	−	543.849i	0.601773	−	1.12832i
$483$		0			0
$484$	49.8428	+	74.3006i	0.102981	+	0.153514i
$485$			805.599i			1.66103i
$486$		0			0
$487$		−	404.821i		−	0.831254i	−0.909535	−	0.415627i	$-0.863562\pi$
$487$		−	404.821i		−	0.831254i	0.909535	−	0.415627i	$-0.136438\pi$
$488$	−35.9404	−	354.929i	−0.0736484	−	0.727313i
$489$		0			0
$490$	−391.427	−	208.763i	−0.798832	−	0.426046i
$491$	−508.547			−1.03574			−0.517869	−	0.855460i	$-0.673275\pi$
$491$	−508.547			−1.03574			−0.517869	+	0.855460i	$0.673275\pi$
$492$		0			0
$493$		−	801.893i		−	1.62656i
$494$	189.902	+	101.282i	0.384417	+	0.205023i
$495$		0			0
$496$	−189.269	−	77.5882i	−0.381590	−	0.156428i
$497$	550.686			1.10802
$498$		0			0
$499$	745.549			1.49409			0.747043	−	0.664776i	$-0.231473\pi$
$499$	745.549			1.49409			0.747043	+	0.664776i	$0.231473\pi$
$500$	688.130	−	461.615i	1.37626	−	0.923231i
$501$		0			0
$502$	−214.903	+	402.941i	−0.428094	+	0.802672i
$503$			290.768i			0.578068i	0.957319	+	0.289034i	$0.0933341\pi$
$503$			290.768i			0.578068i	−0.957319	+	0.289034i	$0.906666\pi$
$504$		0			0
$505$	242.705			0.480605
$506$	275.097	+	146.719i	0.543670	+	0.289959i
$507$		0			0
$508$	194.170	−	130.254i	0.382224	−	0.256406i
$509$			215.775i			0.423920i	0.977278	+	0.211960i	$0.0679846\pi$
$509$			215.775i			0.423920i	−0.977278	+	0.211960i	$0.932015\pi$
$510$		0			0
$511$			136.428i			0.266983i
$512$	−488.714	+	152.651i	−0.954520	+	0.298147i
$513$		0			0
$514$	275.074	−	515.761i	0.535164	−	1.00343i
$515$	−481.146			−0.934264
$516$		0			0
$517$			265.721i			0.513967i
$518$	287.093	−	538.296i	0.554233	−	1.03918i
$519$		0			0
$520$	396.434	−	40.1433i	0.762373	−	0.0771986i
$521$	−747.187			−1.43414			−0.717070	−	0.697001i	$-0.754517\pi$
$521$	−747.187			−1.43414			−0.717070	+	0.697001i	$0.754517\pi$
$522$		0			0
$523$	289.683			0.553886			0.276943	−	0.960886i	$-0.410679\pi$
$523$	289.683			0.553886			0.276943	+	0.960886i	$0.410679\pi$
$524$	256.488	+	382.346i	0.489481	+	0.729668i
$525$		0			0
$526$	861.586	+	459.515i	1.63800	+	0.873604i
$527$			394.620i			0.748805i
$528$		0			0
$529$	282.618			0.534250
$530$	115.144	−	215.893i	0.217252	−	0.407346i
$531$		0			0
$532$	−297.685	+	199.695i	−0.559559	+	0.375367i
$533$			83.6107i			0.156868i
$534$		0			0
$535$			1454.79i			2.71923i
$536$	−705.231	+	71.4124i	−1.31573	+	0.133232i
$537$		0			0
$538$	−68.4869	−	36.5266i	−0.127299	−	0.0678933i
$539$	−255.958			−0.474876
$540$		0			0
$541$		−	348.783i		−	0.644700i	−0.946621	−	0.322350i	$-0.895527\pi$
$541$		−	348.783i		−	0.644700i	0.946621	−	0.322350i	$-0.104473\pi$
$542$	−578.800	−	308.695i	−1.06790	−	0.569548i
$543$		0			0
$544$	630.095	+	760.657i	1.15826	+	1.39827i
$545$	729.270			1.33811
$546$		0			0
$547$	−730.849			−1.33610			−0.668052	−	0.744115i	$-0.732872\pi$
$547$	−730.849			−1.33610			−0.668052	+	0.744115i	$0.732872\pi$
$548$	111.918	+	166.836i	0.204230	+	0.304446i
$549$		0			0
$550$	458.668	−	859.997i	0.833942	−	1.56363i
$551$			483.069i			0.876712i
$552$		0			0
$553$	−554.798			−1.00325
$554$	739.351	+	394.323i	1.33457	+	0.711774i
$555$		0			0
$556$	−129.509	−	193.059i	−0.232930	−	0.347228i
$557$		−	462.185i		−	0.829776i	−0.909872	−	0.414888i	$-0.863821\pi$
$557$		−	462.185i		−	0.829776i	0.909872	−	0.414888i	$-0.136179\pi$
$558$		0			0
$559$		−	361.625i		−	0.646914i
$560$	−251.726	+	614.060i	−0.449510	+	1.09654i
$561$		0			0
$562$	189.351	−	355.032i	0.336924	−	0.631729i
$563$	−161.225			−0.286367			−0.143184	−	0.989696i	$-0.545734\pi$
$563$	−161.225			−0.286367			−0.143184	+	0.989696i	$0.545734\pi$
$564$		0			0
$565$		−	647.476i		−	1.14598i
$566$	227.917	−	427.342i	0.402680	−	0.755021i
$567$		0			0
$568$	92.0917	+	909.449i	0.162133	+	1.60114i
$569$	−63.2844			−0.111220			−0.0556102	−	0.998453i	$-0.517710\pi$
$569$	−63.2844			−0.111220			−0.0556102	+	0.998453i	$0.517710\pi$
$570$		0			0
$571$	268.584			0.470375			0.235188	−	0.971950i	$-0.424430\pi$
$571$	268.584			0.470375			0.235188	+	0.971950i	$0.424430\pi$
$572$	190.924	−	128.077i	0.333783	−	0.223910i
$573$		0			0
$574$	−122.874	−	65.5330i	−0.214066	−	0.114169i
$575$			770.229i			1.33953i
$576$		0			0
$577$	−989.322			−1.71460			−0.857298	−	0.514821i	$-0.827858\pi$
$577$	−989.322			−1.71460			−0.857298	+	0.514821i	$0.827858\pi$
$578$	624.710	−	1171.33i	1.08081	−	2.02651i
$579$		0			0
$580$	498.233	+	742.715i	0.859022	+	1.28054i
$581$		−	222.725i		−	0.383348i
$582$		0			0
$583$		−	141.175i		−	0.242152i
$584$	−225.310	+	22.8151i	−0.385804	+	0.0390669i
$585$		0			0
$586$	−474.529	−	253.084i	−0.809777	−	0.431884i
$587$	−856.358			−1.45887			−0.729436	−	0.684049i	$-0.760217\pi$
$587$	−856.358			−1.45887			−0.729436	+	0.684049i	$0.760217\pi$
$588$		0			0
$589$		−	237.723i		−	0.403605i
$590$	−1166.30	−	622.030i	−1.97678	−	1.05429i
$591$		0			0
$592$	936.998	+	384.110i	1.58277	+	0.648834i
$593$	108.067			0.182238			0.0911189	−	0.995840i	$-0.470956\pi$
$593$	108.067			0.182238			0.0911189	+	0.995840i	$0.470956\pi$
$594$		0			0
$595$	1280.30			2.15176
$596$	−417.230	+	279.889i	−0.700050	+	0.469612i
$597$		0			0
$598$	−85.4973	+	160.306i	−0.142972	+	0.268071i
$599$		−	556.750i		−	0.929466i	−0.885451	−	0.464733i	$-0.846150\pi$
$599$		−	556.750i		−	0.929466i	0.885451	−	0.464733i	$-0.153850\pi$
$600$		0			0
$601$	260.078			0.432742			0.216371	−	0.976311i	$-0.430578\pi$
$601$	260.078			0.432742			0.216371	+	0.976311i	$0.430578\pi$
$602$	531.441	+	283.437i	0.882793	+	0.470826i
$603$		0			0
$604$	538.879	−	361.494i	0.892184	−	0.598500i
$605$			192.503i			0.318187i
$606$		0			0
$607$			8.91926i			0.0146940i	0.999973	+	0.00734701i	$0.00233865\pi$
$607$			8.91926i			0.0146940i	−0.999973	+	0.00734701i	$0.997661\pi$
$608$	−379.576	−	458.228i	−0.624302	−	0.753664i
$609$		0			0
$610$	361.210	−	677.265i	0.592148	−	1.11027i
$611$	−154.843			−0.253425
$612$		0			0
$613$		−	738.776i		−	1.20518i	−0.798051	−	0.602590i	$-0.794135\pi$
$613$		−	738.776i		−	1.20518i	0.798051	−	0.602590i	$-0.205865\pi$
$614$	−82.9852	+	155.596i	−0.135155	+	0.253414i
$615$		0			0
$616$	38.5769	+	380.965i	0.0626248	+	0.618449i
$617$	357.548			0.579495			0.289747	−	0.957103i	$-0.406429\pi$
$617$	357.548			0.579495			0.289747	+	0.957103i	$0.406429\pi$
$618$		0			0
$619$	−408.256			−0.659541			−0.329770	−	0.944061i	$-0.606971\pi$
$619$	−408.256			−0.659541			−0.329770	+	0.944061i	$0.606971\pi$
$620$	−245.186	−	365.498i	−0.395461	−	0.589513i
$621$		0			0
$622$	310.035	+	165.353i	0.498449	+	0.265841i
$623$			163.200i			0.261958i
$624$		0			0
$625$	556.109			0.889774
$626$	−280.495	+	525.926i	−0.448076	+	0.840137i
$627$		0			0
$628$	522.845	−	350.738i	0.832555	−	0.558500i
$629$		−	1953.62i		−	3.10591i
$630$		0			0
$631$			230.148i			0.364735i	0.983230	+	0.182367i	$0.0583760\pi$
$631$			230.148i			0.364735i	−0.983230	+	0.182367i	$0.941624\pi$
$632$	−92.7794	−	916.241i	−0.146803	−	1.44975i
$633$		0			0
$634$	−278.219	−	148.384i	−0.438831	−	0.234045i
$635$	503.069			0.792235
$636$		0			0
$637$		−	149.154i		−	0.234150i
$638$	455.311	+	242.834i	0.713654	+	0.380618i
$639$		0			0
$640$	−1056.21	−	313.031i	−1.65032	−	0.489111i
$641$	736.093			1.14835			0.574176	−	0.818732i	$-0.305323\pi$
$641$	736.093			1.14835			0.574176	+	0.818732i	$0.305323\pi$
$642$		0			0
$643$	21.9654			0.0341609			0.0170804	−	0.999854i	$-0.494563\pi$
$643$	21.9654			0.0341609			0.0170804	+	0.999854i	$0.494563\pi$
$644$	−168.574	−	251.292i	−0.261760	−	0.390206i
$645$		0			0
$646$	−540.188	+	1012.85i	−0.836205	+	1.56788i
$647$		−	493.227i		−	0.762329i	−0.924507	−	0.381164i	$-0.875523\pi$
$647$		−	493.227i		−	0.762329i	0.924507	−	0.381164i	$-0.124477\pi$
$648$		0			0
$649$	−762.654			−1.17512
$650$	501.143	+	267.278i	0.770990	+	0.411197i
$651$		0			0
$652$	−370.508	−	552.315i	−0.568263	−	0.847109i
$653$			1024.37i			1.56871i	0.620310	+	0.784356i	$0.287007\pi$
$653$			1024.37i			1.56871i	−0.620310	+	0.784356i	$0.712993\pi$
$654$		0			0
$655$			990.610i			1.51238i
$656$	87.6785	−	213.883i	0.133656	−	0.326041i
$657$		0			0
$658$	121.364	−	227.556i	0.184443	−	0.345829i
$659$	759.973			1.15322			0.576611	−	0.817019i	$-0.304375\pi$
$659$	759.973			1.15322			0.576611	+	0.817019i	$0.304375\pi$
$660$		0			0
$661$		−	215.108i		−	0.325427i	−0.986673	−	0.162714i	$-0.947975\pi$
$661$		−	215.108i		−	0.325427i	0.986673	−	0.162714i	$-0.0520247\pi$
$662$	161.373	−	302.573i	0.243766	−	0.457058i
$663$		0			0
$664$	367.827	−	37.2465i	0.553957	−	0.0560942i
$665$	−771.265			−1.15980
$666$		0			0
$667$	−407.785			−0.611371
$668$	527.202	−	353.661i	0.789224	−	0.529432i
$669$		0			0
$670$	−1345.70	−	717.713i	−2.00851	−	1.07121i
$671$		−	442.870i		−	0.660015i
$672$		0			0
$673$	475.353			0.706320			0.353160	−	0.935563i	$-0.385107\pi$
$673$	475.353			0.706320			0.353160	+	0.935563i	$0.385107\pi$
$674$	−337.713	+	633.207i	−0.501057	+	0.939477i
$675$		0			0
$676$	−301.959	−	450.130i	−0.446685	−	0.665872i
$677$		−	47.6348i		−	0.0703615i	−0.999381	−	0.0351808i	$-0.988799\pi$
$677$		−	47.6348i		−	0.0703615i	0.999381	−	0.0351808i	$-0.0112007\pi$
$678$		0			0
$679$		−	451.126i		−	0.664398i
$680$	214.105	+	2114.39i	0.314861	+	3.10940i
$681$		0			0
$682$	−224.064	−	119.501i	−0.328539	−	0.175222i
$683$	−857.260			−1.25514			−0.627570	−	0.778561i	$-0.715950\pi$
$683$	−857.260			−1.25514			−0.627570	+	0.778561i	$0.715950\pi$
$684$		0			0
$685$			432.251i			0.631024i
$686$	635.938	+	339.169i	0.927023	+	0.494415i
$687$		0			0
$688$	−379.219	+	925.067i	−0.551190	+	1.34457i
$689$	82.2662			0.119399
$690$		0			0
$691$	−437.965			−0.633813			−0.316906	−	0.948457i	$-0.602644\pi$
$691$	−437.965			−0.633813			−0.316906	+	0.948457i	$0.602644\pi$
$692$	150.229	−	100.778i	0.217094	−	0.145632i
$693$		0			0
$694$	−158.094	+	296.424i	−0.227801	+	0.427124i
$695$		−	500.191i		−	0.719700i
$696$		0			0
$697$	−445.940			−0.639799
$698$	−875.554	−	466.965i	−1.25438	−	0.669004i
$699$		0			0
$700$	−785.580	+	526.987i	−1.12226	+	0.752839i
$701$		−	4.79962i		−	0.00684682i	−0.999994	−	0.00342341i	$-0.998910\pi$
$701$		−	4.79962i		−	0.00684682i	0.999994	−	0.00342341i	$-0.00108971\pi$
$702$		0			0
$703$			1176.88i			1.67408i
$704$	−622.706	+	127.418i	−0.884526	+	0.180992i
$705$		0			0
$706$	125.089	−	234.540i	0.177180	−	0.332210i
$707$	−135.912			−0.192238
$708$		0			0
$709$			117.092i			0.165151i	0.996585	+	0.0825753i	$0.0263145\pi$
$709$			117.092i			0.165151i	−0.996585	+	0.0825753i	$0.973685\pi$
$710$	−925.546	+	1735.39i	−1.30359	+	2.44421i
$711$		0			0
$712$	−269.522	+	27.2921i	−0.378542	+	0.0383315i
$713$	200.675			0.281452
$714$		0			0
$715$	494.659			0.691831
$716$	76.0260	+	113.332i	0.106182	+	0.158285i
$717$		0			0
$718$	−997.382	−	531.940i	−1.38911	−	0.740864i
$719$			430.448i			0.598676i	0.954147	+	0.299338i	$0.0967658\pi$
$719$			430.448i			0.598676i	−0.954147	+	0.299338i	$0.903234\pi$
$720$		0			0
$721$	269.436			0.373698
$722$	−14.3511	+	26.9081i	−0.0198768	+	0.0372688i
$723$		0			0
$724$	−71.2323	+	47.7845i	−0.0983871	+	0.0660007i
$725$			1274.80i			1.75834i
$726$		0			0
$727$			1080.06i			1.48564i	0.669493	+	0.742818i	$0.266511\pi$
$727$			1080.06i			1.48564i	−0.669493	+	0.742818i	$0.733489\pi$
$728$	−221.998	+	22.4798i	−0.304943	+	0.0308788i
$729$		0			0
$730$	−429.930	−	229.297i	−0.588945	−	0.314106i
$731$	1928.74			2.63849
$732$		0			0
$733$		−	756.874i		−	1.03257i	−0.856417	−	0.516285i	$-0.827315\pi$
$733$		−	756.874i		−	1.03257i	0.856417	−	0.516285i	$-0.172685\pi$
$734$	−1086.49	−	579.465i	−1.48023	−	0.789462i
$735$		0			0
$736$	386.815	−	320.420i	0.525564	−	0.435354i
$737$	−879.968			−1.19399
$738$		0			0
$739$	269.971			0.365319			0.182659	−	0.983176i	$-0.441529\pi$
$739$	269.971			0.365319			0.182659	+	0.983176i	$0.441529\pi$
$740$	1213.82	+	1809.44i	1.64030	+	2.44519i
$741$		0			0
$742$	−64.4792	+	120.898i	−0.0868992	+	0.162935i
$743$		−	412.457i		−	0.555123i	−0.960708	−	0.277562i	$-0.910474\pi$
$743$		−	412.457i		−	0.555123i	0.960708	−	0.277562i	$-0.0895263\pi$
$744$		0			0
$745$	−1080.99			−1.45099
$746$	803.994	+	428.799i	1.07774	+	0.574798i
$747$		0			0
$748$	683.101	+	1018.30i	0.913236	+	1.36136i
$749$		−	814.664i		−	1.08767i
$750$		0			0
$751$		−	982.058i		−	1.30767i	−0.756639	−	0.653833i	$-0.773160\pi$
$751$		−	982.058i		−	1.30767i	0.756639	−	0.653833i	$-0.226840\pi$
$752$	396.100	+	162.376i	0.526729	+	0.215925i
$753$		0			0
$754$	−141.506	+	265.322i	−0.187674	+	0.351886i
$755$	1396.17			1.84923
$756$		0			0
$757$		−	96.0126i		−	0.126833i	−0.997987	−	0.0634165i	$-0.979800\pi$
$757$		−	96.0126i		−	0.126833i	0.997987	−	0.0634165i	$-0.0201997\pi$
$758$	−318.027	+	596.297i	−0.419561	+	0.786671i
$759$		0			0
$760$	−128.979	−	1273.73i	−0.169710	−	1.67596i
$761$	−483.966			−0.635960			−0.317980	−	0.948097i	$-0.603005\pi$
$761$	−483.966			−0.635960			−0.317980	+	0.948097i	$0.603005\pi$
$762$		0			0
$763$	−408.383			−0.535233
$764$	−574.039	+	385.080i	−0.751359	+	0.504032i
$765$		0			0
$766$	386.281	+	206.018i	0.504284	+	0.268953i
$767$		−	444.419i		−	0.579425i
$768$		0			0
$769$	395.882			0.514801			0.257400	−	0.966305i	$-0.417134\pi$
$769$	395.882			0.514801			0.257400	+	0.966305i	$0.417134\pi$
$770$	−387.707	+	726.947i	−0.503516	+	0.944087i
$771$		0			0
$772$	−312.437	−	465.750i	−0.404712	−	0.603303i
$773$			51.0498i			0.0660411i	0.999455	+	0.0330206i	$0.0105127\pi$
$773$			51.0498i			0.0660411i	−0.999455	+	0.0330206i	$0.989487\pi$
$774$		0			0
$775$		−	627.343i		−	0.809474i
$776$	745.028	−	75.4422i	0.960087	−	0.0972194i
$777$		0			0
$778$	252.120	+	134.465i	0.324062	+	0.172834i
$779$	268.639			0.344851
$780$		0			0
$781$			1134.79i			1.45299i
$782$	−855.000	−	456.003i	−1.09335	−	0.583124i
$783$		0			0
$784$	−156.410	+	381.547i	−0.199503	+	0.486667i
$785$	1354.62			1.72564
$786$		0			0
$787$	−973.748			−1.23729			−0.618646	−	0.785670i	$-0.712318\pi$
$787$	−973.748			−1.23729			−0.618646	+	0.785670i	$0.712318\pi$
$788$	1094.56	−	734.260i	1.38904	−	0.931801i
$789$		0			0
$790$	932.457	−	1748.35i	1.18033	−	2.21310i
$791$			362.579i			0.458381i
$792$		0			0
$793$	258.072			0.325438
$794$	−1252.06	−	667.769i	−1.57690	−	0.841019i
$795$		0			0
$796$	−830.174	+	556.903i	−1.04293	+	0.699627i
$797$		−	849.870i		−	1.06634i	−0.846009	−	0.533168i	$-0.821001\pi$
$797$		−	849.870i		−	1.06634i	0.846009	−	0.533168i	$-0.178999\pi$
$798$		0			0
$799$		−	825.858i		−	1.03361i
$800$	−1001.69	−	1209.24i	−1.25211	−	1.51156i
$801$		0			0
$802$	−148.613	+	278.647i	−0.185303	+	0.347441i
$803$	−281.135			−0.350106
$804$		0			0
$805$		−	651.067i		−	0.808778i
$806$	69.6366	−	130.568i	0.0863977	−	0.161995i
$807$		0			0
$808$	−22.7287	−	224.457i	−0.0281296	−	0.277793i
$809$	−396.410			−0.490000			−0.245000	−	0.969523i	$-0.578788\pi$
$809$	−396.410			−0.490000			−0.245000	+	0.969523i	$0.578788\pi$
$810$		0			0
$811$	−1531.93			−1.88894			−0.944470	−	0.328598i	$-0.893424\pi$
$811$	−1531.93			−1.88894			−0.944470	+	0.328598i	$0.893424\pi$
$812$	−279.005	−	415.912i	−0.343602	−	0.512207i
$813$		0			0
$814$	1109.25	+	591.606i	1.36272	+	0.726788i
$815$		−	1430.98i		−	1.75580i
$816$		0			0
$817$	−1161.89			−1.42214
$818$	114.575	−	214.826i	0.140067	−	0.262624i
$819$		0			0
$820$	413.031	−	277.072i	0.503696	−	0.337893i
$821$			790.420i			0.962752i	0.876514	+	0.481376i	$0.159863\pi$
$821$			790.420i			0.962752i	−0.876514	+	0.481376i	$0.840137\pi$
$822$		0			0
$823$		−	1061.92i		−	1.29031i	−0.764054	−	0.645153i	$-0.776794\pi$
$823$		−	1061.92i		−	1.29031i	0.764054	−	0.645153i	$-0.223206\pi$
$824$	45.0581	+	444.970i	0.0546821	+	0.540012i
$825$		0			0
$826$	653.114	+	348.330i	0.790695	+	0.421707i
$827$	575.872			0.696339			0.348170	−	0.937432i	$-0.386803\pi$
$827$	575.872			0.696339			0.348170	+	0.937432i	$0.386803\pi$
$828$		0			0
$829$			849.875i			1.02518i	0.858633	+	0.512590i	$0.171314\pi$
$829$			849.875i			1.02518i	−0.858633	+	0.512590i	$0.828686\pi$
$830$	701.879	+	374.337i	0.845637	+	0.451009i
$831$		0			0
$832$	−74.2500	−	362.868i	−0.0892428	−	0.436139i
$833$	795.515			0.955000
$834$		0			0
$835$	1365.91			1.63582
$836$	−411.507	−	613.433i	−0.492233	−	0.733772i
$837$		0			0
$838$	22.8114	−	42.7711i	0.0272212	−	0.0510395i
$839$		−	1187.72i		−	1.41564i	−0.706394	−	0.707819i	$-0.749679\pi$
$839$		−	1187.72i		−	1.41564i	0.706394	−	0.707819i	$-0.250321\pi$
$840$		0			0
$841$	166.079			0.197478
$842$	494.930	+	263.964i	0.587803	+	0.313497i
$843$		0			0
$844$	189.254	+	282.121i	0.224235	+	0.334267i
$845$		−	1166.23i		−	1.38015i
$846$		0			0
$847$		−	107.800i		−	0.127272i
$848$	−210.444	−	86.2686i	−0.248165	−	0.101732i
$849$		0			0
$850$	−1425.54	+	2672.86i	−1.67710	+	3.14455i
$851$	−993.467			−1.16741
$852$		0			0
$853$		−	941.579i		−	1.10384i	−0.833896	−	0.551922i	$-0.813895\pi$
$853$		−	941.579i		−	1.10384i	0.833896	−	0.551922i	$-0.186105\pi$
$854$	−202.274	+	379.261i	−0.236854	+	0.444099i
$855$		0			0
$856$	1345.41	−	136.237i	1.57173	−	0.159155i
$857$	−1094.02			−1.27657			−0.638284	−	0.769801i	$-0.720355\pi$
$857$	−1094.02			−1.27657			−0.638284	+	0.769801i	$0.720355\pi$
$858$		0			0
$859$	811.069			0.944201			0.472101	−	0.881545i	$-0.343496\pi$
$859$	811.069			0.944201			0.472101	+	0.881545i	$0.343496\pi$
$860$	−1786.40	+	1198.37i	−2.07721	+	1.39345i
$861$		0			0
$862$	948.348	+	505.789i	1.10017	+	0.586762i
$863$			64.9665i			0.0752799i	0.999291	+	0.0376399i	$0.0119840\pi$
$863$			64.9665i			0.0752799i	−0.999291	+	0.0376399i	$0.988016\pi$
$864$		0			0
$865$	389.224			0.449970
$866$	−97.4912	+	182.795i	−0.112576	+	0.211079i
$867$		0			0
$868$	137.301	+	204.675i	0.158181	+	0.235800i
$869$		−	1143.26i		−	1.31560i
$870$		0			0
$871$		−	512.781i		−	0.588727i
$872$	−68.2942	−	674.438i	−0.0783191	−	0.773438i
$873$		0			0
$874$	515.061	+	274.701i	0.589314	+	0.314303i
$875$	−998.379			−1.14100
$876$		0			0
$877$			180.847i			0.206211i	0.994670	+	0.103106i	$0.0328779\pi$
$877$			180.847i			0.206211i	−0.994670	+	0.103106i	$0.967122\pi$
$878$	984.454	+	525.045i	1.12125	+	0.598001i
$879$		0			0
$880$	−1265.38	−	518.725i	−1.43793	−	0.589460i
$881$	896.400			1.01748			0.508740	−	0.860920i	$-0.330112\pi$
$881$	896.400			1.01748			0.508740	+	0.860920i	$0.330112\pi$
$882$		0			0
$883$	490.293			0.555258			0.277629	−	0.960688i	$-0.410451\pi$
$883$	490.293			0.555258			0.277629	+	0.960688i	$0.410451\pi$
$884$	−593.389	+	398.061i	−0.671255	+	0.450295i
$885$		0			0
$886$	4.50849	−	8.45336i	0.00508859	−	0.00954104i
$887$		−	450.485i		−	0.507875i	−0.967221	−	0.253938i	$-0.918274\pi$
$887$		−	450.485i		−	0.507875i	0.967221	−	0.253938i	$-0.0817258\pi$
$888$		0			0
$889$	−281.713			−0.316888
$890$	−514.295	−	274.292i	−0.577860	−	0.308194i
$891$		0			0
$892$	6.45480	−	4.33005i	0.00723632	−	0.00485432i
$893$			497.506i			0.557117i
$894$		0			0
$895$			293.629i			0.328077i
$896$	591.464	+	175.294i	0.660116	+	0.195640i
$897$		0			0
$898$	788.714	−	1478.83i	0.878300	−	1.64680i
$899$	332.136			0.369450
$900$		0			0
$901$			438.769i			0.486981i
$902$	135.042	−	253.203i	0.149714	−	0.280713i
$903$		0			0
$904$	−598.794	+	60.6345i	−0.662383	+	0.0670735i
$905$	−184.554			−0.203927
$906$		0			0
$907$	113.210			0.124818			0.0624091	−	0.998051i	$-0.480122\pi$
$907$	113.210			0.124818			0.0624091	+	0.998051i	$0.480122\pi$
$908$	−453.822	−	676.513i	−0.499804	−	0.745058i
$909$		0			0
$910$	−423.611	−	225.927i	−0.465507	−	0.248272i
$911$			1580.60i			1.73502i	0.497423	+	0.867508i	$0.334280\pi$
$911$			1580.60i			1.73502i	−0.497423	+	0.867508i	$0.665720\pi$
$912$		0			0
$913$	458.965			0.502700
$914$	506.183	−	949.088i	0.553811	−	1.03839i
$915$		0			0
$916$	66.4240	−	44.5589i	0.0725153	−	0.0486451i
$917$		−	554.730i		−	0.604941i
$918$		0			0
$919$			846.401i			0.921002i	0.887659	+	0.460501i	$0.152330\pi$
$919$			846.401i			0.921002i	−0.887659	+	0.460501i	$0.847670\pi$
$920$	1075.23	−	108.878i	1.16872	−	0.118346i
$921$		0			0
$922$	284.807	+	151.898i	0.308901	+	0.164748i
$923$	−661.270			−0.716435
$924$		0			0
$925$			3105.74i			3.35755i
$926$	856.898	+	457.015i	0.925376	+	0.493537i
$927$		0			0
$928$	640.214	−	530.325i	0.689886	−	0.571471i
$929$	579.755			0.624063			0.312032	−	0.950072i	$-0.398991\pi$
$929$	579.755			0.624063			0.312032	+	0.950072i	$0.398991\pi$
$930$		0			0
$931$	−479.227			−0.514744
$932$	203.047	+	302.682i	0.217862	+	0.324767i
$933$		0			0
$934$	224.980	−	421.836i	0.240878	−	0.451644i
$935$			2638.28i			2.82169i
$936$		0			0
$937$	1810.65			1.93239			0.966196	−	0.257808i	$-0.0830002\pi$
$937$	1810.65			1.93239			0.966196	+	0.257808i	$0.0830002\pi$
$938$	753.579	+	401.911i	0.803389	+	0.428477i
$939$		0			0
$940$	513.123	+	764.912i	0.545875	+	0.813736i
$941$			1154.89i			1.22730i	0.789579	+	0.613649i	$0.210299\pi$
$941$			1154.89i			1.22730i	−0.789579	+	0.613649i	$0.789701\pi$
$942$		0			0
$943$			226.773i			0.240480i
$944$	−466.040	+	1136.86i	−0.493687	+	1.20430i
$945$		0			0
$946$	−584.072	+	1095.13i	−0.617413	+	1.15764i
$947$	1.41679			0.00149608			0.000748039	−	1.00000i	$-0.499762\pi$
$947$	1.41679			0.00149608			0.000748039		1.00000i	$0.499762\pi$
$948$		0			0
$949$		−	163.825i		−	0.172629i
$950$	858.758	−	1610.16i	0.903956	−	1.69491i
$951$		0			0
$952$	−119.897	−	1184.04i	−0.125942	−	1.24373i
$953$	−662.875			−0.695566			−0.347783	−	0.937575i	$-0.613065\pi$
$953$	−662.875			−0.695566			−0.347783	+	0.937575i	$0.613065\pi$
$954$		0			0
$955$	−1487.26			−1.55734
$956$	122.410	−	82.1158i	0.128044	−	0.0858952i
$957$		0			0
$958$	−735.049	−	392.028i	−0.767274	−	0.409215i
$959$		−	242.056i		−	0.252404i
$960$		0			0
$961$	797.552			0.829919
$962$	−344.744	+	646.392i	−0.358362	+	0.671925i
$963$		0			0
$964$	−686.739	−	1023.72i	−0.712385	−	1.06195i
$965$		−	1206.70i		−	1.25047i
$966$		0			0
$967$		−	843.335i		−	0.872114i	−0.899919	−	0.436057i	$-0.856375\pi$
$967$		−	843.335i		−	0.872114i	0.899919	−	0.436057i	$-0.143625\pi$
$968$	178.030	−	18.0274i	0.183915	−	0.0186234i
$969$		0			0
$970$	1421.64	+	758.214i	1.46561	+	0.781664i
$971$	−289.643			−0.298293			−0.149147	−	0.988815i	$-0.547653\pi$
$971$	−289.643			−0.298293			−0.149147	+	0.988815i	$0.547653\pi$
$972$		0			0
$973$			280.101i			0.287874i
$974$	−714.388	−	381.009i	−0.733458	−	0.391180i
$975$		0			0
$976$	−660.170	−	270.628i	−0.676404	−	0.277283i
$977$	1403.92			1.43697			0.718484	−	0.695544i	$-0.244836\pi$
$977$	1403.92			1.43697			0.718484	+	0.695544i	$0.244836\pi$
$978$		0			0
$979$	−336.302			−0.343516
$980$	−736.808	+	494.270i	−0.751845	+	0.504357i
$981$		0			0
$982$	−478.635	+	897.435i	−0.487408	+	0.913885i
$983$		−	531.529i		−	0.540722i	−0.962759	−	0.270361i	$-0.912857\pi$
$983$		−	531.529i		−	0.540722i	0.962759	−	0.270361i	$-0.0871430\pi$
$984$		0			0
$985$	2835.87			2.87905
$986$	−1415.10	−	754.726i	−1.43520	−	0.765442i
$987$		0			0
$988$	357.464	−	239.796i	0.361806	−	0.242709i
$989$		−	980.817i		−	0.991726i
$990$		0			0
$991$		−	1549.03i		−	1.56310i	−0.623846	−	0.781548i	$-0.714431\pi$
$991$		−	1549.03i		−	1.56310i	0.623846	−	0.781548i	$-0.285569\pi$
$992$	−315.056	+	260.979i	−0.317597	+	0.263084i
$993$		0			0
$994$	518.295	−	971.797i	0.521423	−	0.977663i
$995$	−2150.88			−2.16168
$996$		0			0
$997$			411.253i			0.412491i	0.978500	+	0.206245i	$0.0661245\pi$
$997$			411.253i			0.412491i	−0.978500	+	0.206245i	$0.933876\pi$
$998$	701.696	−	1315.67i	0.703102	−	1.31831i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.b.a.163.11	yes	16
3.2	odd	2	inner	216.3.b.a.163.6	yes	16
4.3	odd	2		864.3.b.a.271.1		16
8.3	odd	2	inner	216.3.b.a.163.12	yes	16
8.5	even	2		864.3.b.a.271.16		16
12.11	even	2		864.3.b.a.271.15		16
24.5	odd	2		864.3.b.a.271.2		16
24.11	even	2	inner	216.3.b.a.163.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.b.a.163.5	✓	16	24.11	even	2	inner
216.3.b.a.163.6	yes	16	3.2	odd	2	inner
216.3.b.a.163.11	yes	16	1.1	even	1	trivial
216.3.b.a.163.12	yes	16	8.3	odd	2	inner
864.3.b.a.271.1		16	4.3	odd	2
864.3.b.a.271.2		16	24.5	odd	2
864.3.b.a.271.15		16	12.11	even	2
864.3.b.a.271.16		16	8.5	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.941181 - 1.76470i) q^{2} +(-2.22836 - 3.32181i) q^{4} -8.60639i q^{5} +4.81948i q^{7} +(-7.95930 + 0.805966i) q^{8} +O(q^{10})\)	\(q+(0.941181 - 1.76470i) q^{2} +(-2.22836 - 3.32181i) q^{4} -8.60639i q^{5} +4.81948i q^{7} +(-7.95930 + 0.805966i) q^{8} +(-15.1877 - 8.10017i) q^{10} -9.93139 q^{11} -5.78729i q^{13} +(8.50495 + 4.53600i) q^{14} +(-6.06885 + 14.8044i) q^{16} +30.8667 q^{17} -18.5944 q^{19} +(-28.5888 + 19.1781i) q^{20} +(-9.34723 + 17.5260i) q^{22} -15.6966i q^{23} -49.0699 q^{25} +(-10.2128 - 5.44688i) q^{26} +(16.0094 - 10.7395i) q^{28} -25.9792i q^{29} +12.7847i q^{31} +(20.4134 + 24.6433i) q^{32} +(29.0511 - 54.4705i) q^{34} +41.4783 q^{35} -63.2921i q^{37} +(-17.5007 + 32.8136i) q^{38} +(6.93646 + 68.5008i) q^{40} -14.4473 q^{41} +62.4861 q^{43} +(22.1307 + 32.9902i) q^{44} +(-27.6998 - 14.7733i) q^{46} -26.7557i q^{47} +25.7726 q^{49} +(-46.1837 + 86.5939i) q^{50} +(-19.2243 + 12.8961i) q^{52} +14.2150i q^{53} +85.4734i q^{55} +(-3.88434 - 38.3597i) q^{56} +(-45.8456 - 24.4512i) q^{58} +76.7922 q^{59} +44.5930i q^{61} +(22.5612 + 12.0327i) q^{62} +(62.7008 - 12.8298i) q^{64} -49.8076 q^{65} +88.6047 q^{67} +(-68.7820 - 102.533i) q^{68} +(39.0386 - 73.1969i) q^{70} -114.263i q^{71} +28.3077 q^{73} +(-111.692 - 59.5693i) q^{74} +(41.4350 + 61.7671i) q^{76} -47.8641i q^{77} +115.116i q^{79} +(127.412 + 52.2309i) q^{80} +(-13.5975 + 25.4952i) q^{82} -46.2135 q^{83} -265.651i q^{85} +(58.8107 - 110.269i) q^{86} +(79.0469 - 8.00436i) q^{88} +33.8625 q^{89} +27.8917 q^{91} +(-52.1410 + 34.9775i) q^{92} +(-47.2158 - 25.1819i) q^{94} +160.031i q^{95} -93.6047 q^{97} +(24.2567 - 45.4810i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{4}+O(q^{10}) \) 16 * q - 2 * q^4	\( 16 q - 2 q^{4} - 18 q^{10} + 34 q^{16} + 32 q^{19} - 22 q^{22} - 80 q^{25} + 102 q^{28} + 68 q^{34} - 6 q^{40} + 128 q^{43} + 60 q^{46} - 80 q^{49} - 180 q^{52} - 156 q^{58} - 74 q^{64} + 128 q^{67} - 378 q^{70} - 160 q^{73} + 188 q^{76} - 508 q^{82} + 542 q^{88} - 96 q^{91} + 24 q^{94} - 208 q^{97}+O(q^{100}) \) 16 * q - 2 * q^4 - 18 * q^10 + 34 * q^16 + 32 * q^19 - 22 * q^22 - 80 * q^25 + 102 * q^28 + 68 * q^34 - 6 * q^40 + 128 * q^43 + 60 * q^46 - 80 * q^49 - 180 * q^52 - 156 * q^58 - 74 * q^64 + 128 * q^67 - 378 * q^70 - 160 * q^73 + 188 * q^76 - 508 * q^82 + 542 * q^88 - 96 * q^91 + 24 * q^94 - 208 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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