LMFDB - Embedded newform 384.3.i.a.353.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,3,Mod(161,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("384.161");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	384.i (of order $4$, degree $2$, not 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:	$10.4632421514$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.629407744.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 2x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 2x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			353.2
Root			$-0.767178 - 1.18804i$ of defining polynomial
Character	$\chi$	$=$	384.353
Dual form			384.3.i.a.161.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13234 - 2.77809i) q^{3} +(-6.28651 + 6.28651i) q^{5} +1.64575i q^{7} +(-6.43560 + 6.29150i) q^{9} +O(q^{10})$	\(q+(-1.13234 - 2.77809i) q^{3} +(-6.28651 + 6.28651i) q^{5} +1.64575i q^{7} +(-6.43560 + 6.29150i) q^{9} +(4.75216 - 4.75216i) q^{11} +(9.35425 - 9.35425i) q^{13} +(24.5830 + 10.3460i) q^{15} -11.4859i q^{17} +(8.58301 - 8.58301i) q^{19} +(4.57205 - 1.86355i) q^{21} +16.2381 q^{23} -54.0405i q^{25} +(24.7657 + 10.7546i) q^{27} +(10.7405 + 10.7405i) q^{29} +6.35425 q^{31} +(-18.5830 - 7.82087i) q^{33} +(-10.3460 - 10.3460i) q^{35} +(-27.2288 - 27.2288i) q^{37} +(-36.5792 - 15.3948i) q^{39} +1.98162 q^{41} +(19.4170 + 19.4170i) q^{43} +(0.905893 - 80.0091i) q^{45} -74.9474i q^{47} +46.2915 q^{49} +(-31.9090 + 13.0060i) q^{51} +(-4.00671 + 4.00671i) q^{53} +59.7490i q^{55} +(-33.5633 - 14.1255i) q^{57} +(27.9694 - 27.9694i) q^{59} +(-39.2288 + 39.2288i) q^{61} +(-10.3542 - 10.5914i) q^{63} +117.611i q^{65} +(68.6863 - 68.6863i) q^{67} +(-18.3871 - 45.1110i) q^{69} +40.6822 q^{71} +59.0405i q^{73} +(-150.130 + 61.1923i) q^{75} +(7.82087 + 7.82087i) q^{77} +17.3948 q^{79} +(1.83399 - 80.9792i) q^{81} +(75.1400 + 75.1400i) q^{83} +(72.2065 + 72.2065i) q^{85} +(17.6762 - 42.0000i) q^{87} +78.8051 q^{89} +(15.3948 + 15.3948i) q^{91} +(-7.19518 - 17.6527i) q^{93} +107.914i q^{95} -38.8340 q^{97} +(-0.684791 + 60.4812i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3}+O(q^{10}) $ 8 * q - 4 * q^3	$ 8 q - 4 q^{3} + 96 q^{13} + 112 q^{15} - 16 q^{19} + 32 q^{21} + 68 q^{27} + 72 q^{31} - 64 q^{33} - 112 q^{37} + 240 q^{43} + 112 q^{45} + 328 q^{49} + 32 q^{51} - 208 q^{61} - 104 q^{63} + 232 q^{67} - 324 q^{75} - 136 q^{79} + 184 q^{81} + 112 q^{85} - 152 q^{91} - 64 q^{93} - 480 q^{97} - 160 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 + 96 * q^13 + 112 * q^15 - 16 * q^19 + 32 * q^21 + 68 * q^27 + 72 * q^31 - 64 * q^33 - 112 * q^37 + 240 * q^43 + 112 * q^45 + 328 * q^49 + 32 * q^51 - 208 * q^61 - 104 * q^63 + 232 * q^67 - 324 * q^75 - 136 * q^79 + 184 * q^81 + 112 * q^85 - 152 * q^91 - 64 * q^93 - 480 * q^97 - 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.13234	−	2.77809i	−0.377447	−	0.926031i
$3$	−1.13234	−	2.77809i	−0.377447	−	0.926031i
$4$		0			0
$5$	−6.28651	+	6.28651i	−1.25730	+	1.25730i	−0.304927	+	0.952376i	$0.598632\pi$
$5$	−6.28651	+	6.28651i	−1.25730	+	1.25730i	−0.952376	+	0.304927i	$0.901368\pi$
$6$		0			0
$7$			1.64575i			0.235107i	0.993067	+	0.117554i	$0.0375052\pi$
$7$			1.64575i			0.235107i	−0.993067	+	0.117554i	$0.962495\pi$
$8$		0			0
$9$	−6.43560	+	6.29150i	−0.715067	+	0.699056i
$10$		0			0
$11$	4.75216	−	4.75216i	0.432014	−	0.432014i	−0.457299	−	0.889313i	$-0.651183\pi$
$11$	4.75216	−	4.75216i	0.432014	−	0.432014i	0.889313	+	0.457299i	$0.151183\pi$
$12$		0			0
$13$	9.35425	−	9.35425i	0.719558	−	0.719558i	−0.248957	−	0.968515i	$-0.580088\pi$
$13$	9.35425	−	9.35425i	0.719558	−	0.719558i	0.968515	+	0.248957i	$0.0800878\pi$
$14$		0			0
$15$	24.5830	+	10.3460i	1.63887	+	0.689736i
$16$		0			0
$17$		−	11.4859i		−	0.675644i	−0.941210	−	0.337822i	$-0.890310\pi$
$17$		−	11.4859i		−	0.675644i	0.941210	−	0.337822i	$-0.109690\pi$
$18$		0			0
$19$	8.58301	−	8.58301i	0.451737	−	0.451737i	−0.444194	−	0.895931i	$-0.646510\pi$
$19$	8.58301	−	8.58301i	0.451737	−	0.451737i	0.895931	+	0.444194i	$0.146510\pi$
$20$		0			0
$21$	4.57205	−	1.86355i	0.217717	−	0.0887406i
$22$		0			0
$23$	16.2381			0.706004			0.353002	−	0.935623i	$-0.385161\pi$
$23$	16.2381			0.706004			0.353002	+	0.935623i	$0.385161\pi$
$24$		0			0
$25$		−	54.0405i		−	2.16162i
$26$		0			0
$27$	24.7657	+	10.7546i	0.917248	+	0.398318i
$28$		0			0
$29$	10.7405	+	10.7405i	0.370362	+	0.370362i	0.867609	−	0.497247i	$-0.165656\pi$
$29$	10.7405	+	10.7405i	0.370362	+	0.370362i	−0.497247	+	0.867609i	$0.665656\pi$
$30$		0			0
$31$	6.35425			0.204976			0.102488	−	0.994734i	$-0.467320\pi$
$31$	6.35425			0.204976			0.102488	+	0.994734i	$0.467320\pi$
$32$		0			0
$33$	−18.5830	−	7.82087i	−0.563121	−	0.236996i
$34$		0			0
$35$	−10.3460	−	10.3460i	−0.295601	−	0.295601i
$36$		0			0
$37$	−27.2288	−	27.2288i	−0.735912	−	0.735912i	0.235872	−	0.971784i	$-0.424205\pi$
$37$	−27.2288	−	27.2288i	−0.735912	−	0.735912i	−0.971784	+	0.235872i	$0.924205\pi$
$38$		0			0
$39$	−36.5792	−	15.3948i	−0.937928	−	0.394738i
$40$		0			0
$41$	1.98162			0.0483323			0.0241662	−	0.999708i	$-0.492307\pi$
$41$	1.98162			0.0483323			0.0241662	+	0.999708i	$0.492307\pi$
$42$		0			0
$43$	19.4170	+	19.4170i	0.451558	+	0.451558i	0.895871	−	0.444313i	$-0.146552\pi$
$43$	19.4170	+	19.4170i	0.451558	+	0.451558i	−0.444313	+	0.895871i	$0.646552\pi$
$44$		0			0
$45$	0.905893	−	80.0091i	0.0201310	−	1.77798i
$46$		0			0
$47$		−	74.9474i		−	1.59463i	−0.603566	−	0.797313i	$-0.706254\pi$
$47$		−	74.9474i		−	1.59463i	0.603566	−	0.797313i	$-0.293746\pi$
$48$		0			0
$49$	46.2915			0.944725
$50$		0			0
$51$	−31.9090	+	13.0060i	−0.625667	+	0.255020i
$52$		0			0
$53$	−4.00671	+	4.00671i	−0.0755983	+	0.0755983i	−0.743895	−	0.668297i	$-0.767024\pi$
$53$	−4.00671	+	4.00671i	−0.0755983	+	0.0755983i	0.668297	+	0.743895i	$0.267024\pi$
$54$		0			0
$55$			59.7490i			1.08635i
$56$		0			0
$57$	−33.5633	−	14.1255i	−0.588830	−	0.247816i
$58$		0			0
$59$	27.9694	−	27.9694i	0.474058	−	0.474058i	−0.429167	−	0.903225i	$-0.641193\pi$
$59$	27.9694	−	27.9694i	0.474058	−	0.474058i	0.903225	+	0.429167i	$0.141193\pi$
$60$		0			0
$61$	−39.2288	+	39.2288i	−0.643094	+	0.643094i	−0.951315	−	0.308221i	$-0.900267\pi$
$61$	−39.2288	+	39.2288i	−0.643094	+	0.643094i	0.308221	+	0.951315i	$0.400267\pi$
$62$		0			0
$63$	−10.3542	−	10.5914i	−0.164353	−	0.168118i
$64$		0			0
$65$			117.611i			1.80940i
$66$		0			0
$67$	68.6863	−	68.6863i	1.02517	−	1.02517i	0.0254932	−	0.999675i	$-0.491884\pi$
$67$	68.6863	−	68.6863i	1.02517	−	1.02517i	0.999675	−	0.0254932i	$-0.00811562\pi$
$68$		0			0
$69$	−18.3871	−	45.1110i	−0.266479	−	0.653782i
$70$		0			0
$71$	40.6822			0.572988			0.286494	−	0.958082i	$-0.407510\pi$
$71$	40.6822			0.572988			0.286494	+	0.958082i	$0.407510\pi$
$72$		0			0
$73$			59.0405i			0.808774i	0.914588	+	0.404387i	$0.132515\pi$
$73$			59.0405i			0.808774i	−0.914588	+	0.404387i	$0.867485\pi$
$74$		0			0
$75$	−150.130	+	61.1923i	−2.00173	+	0.815898i
$76$		0			0
$77$	7.82087	+	7.82087i	0.101570	+	0.101570i
$78$		0			0
$79$	17.3948			0.220187			0.110093	−	0.993921i	$-0.464885\pi$
$79$	17.3948			0.220187			0.110093	+	0.993921i	$0.464885\pi$
$80$		0			0
$81$	1.83399	−	80.9792i	0.0226418	−	0.999744i
$82$		0			0
$83$	75.1400	+	75.1400i	0.905301	+	0.905301i	0.995889	−	0.0905874i	$-0.0288745\pi$
$83$	75.1400	+	75.1400i	0.905301	+	0.905301i	−0.0905874	+	0.995889i	$0.528874\pi$
$84$		0			0
$85$	72.2065	+	72.2065i	0.849489	+	0.849489i
$86$		0			0
$87$	17.6762	−	42.0000i	0.203174	−	0.482759i
$88$		0			0
$89$	78.8051			0.885450			0.442725	−	0.896657i	$-0.354012\pi$
$89$	78.8051			0.885450			0.442725	+	0.896657i	$0.354012\pi$
$90$		0			0
$91$	15.3948	+	15.3948i	0.169173	+	0.169173i
$92$		0			0
$93$	−7.19518	−	17.6527i	−0.0773675	−	0.189814i
$94$		0			0
$95$			107.914i			1.13594i
$96$		0			0
$97$	−38.8340			−0.400350			−0.200175	−	0.979760i	$-0.564151\pi$
$97$	−38.8340			−0.400350			−0.200175	+	0.979760i	$0.564151\pi$
$98$		0			0
$99$	−0.684791	+	60.4812i	−0.00691708	+	0.610921i
$100$		0			0
$101$	41.5332	−	41.5332i	0.411220	−	0.411220i	−0.470943	−	0.882164i	$-0.656086\pi$
$101$	41.5332	−	41.5332i	0.411220	−	0.411220i	0.882164	+	0.470943i	$0.156086\pi$
$102$		0			0
$103$		−	98.8118i		−	0.959337i	−0.877450	−	0.479669i	$-0.840757\pi$
$103$		−	98.8118i		−	0.959337i	0.877450	−	0.479669i	$-0.159243\pi$
$104$		0			0
$105$	−17.0270	+	40.4575i	−0.162162	+	0.385310i
$106$		0			0
$107$	98.8480	−	98.8480i	0.923813	−	0.923813i	−0.0734837	−	0.997296i	$-0.523412\pi$
$107$	98.8480	−	98.8480i	0.923813	−	0.923813i	0.997296	+	0.0734837i	$0.0234117\pi$
$108$		0			0
$109$	−68.8523	+	68.8523i	−0.631672	+	0.631672i	−0.948487	−	0.316815i	$-0.897387\pi$
$109$	−68.8523	+	68.8523i	−0.631672	+	0.631672i	0.316815	+	0.948487i	$0.397387\pi$
$110$		0			0
$111$	−44.8118	+	106.476i	−0.403710	+	0.959246i
$112$		0			0
$113$		−	8.31160i		−	0.0735540i	−0.999323	−	0.0367770i	$-0.988291\pi$
$113$		−	8.31160i		−	0.0735540i	0.999323	−	0.0367770i	$-0.0117091\pi$
$114$		0			0
$115$	−102.081	+	102.081i	−0.887661	+	0.887661i
$116$		0			0
$117$	−1.34796	+	119.053i	−0.0115210	+	1.01754i
$118$		0			0
$119$	18.9030			0.158849
$120$		0			0
$121$			75.8340i			0.626727i
$122$		0			0
$123$	−2.24388	−	5.50514i	−0.0182429	−	0.0447572i
$124$		0			0
$125$	182.564	+	182.564i	1.46051	+	1.46051i
$126$		0			0
$127$	−195.933			−1.54278			−0.771391	−	0.636361i	$-0.780439\pi$
$127$	−195.933			−1.54278			−0.771391	+	0.636361i	$0.780439\pi$
$128$		0			0
$129$	31.9555	−	75.9289i	0.247717	−	0.588596i
$130$		0			0
$131$	−142.127	−	142.127i	−1.08494	−	1.08494i	−0.996041	−	0.0888967i	$-0.971666\pi$
$131$	−142.127	−	142.127i	−1.08494	−	1.08494i	−0.0888967	−	0.996041i	$-0.528334\pi$
$132$		0			0
$133$	14.1255	+	14.1255i	0.106207	+	0.106207i
$134$		0			0
$135$	−223.299	+	88.0810i	−1.65406	+	0.652452i
$136$		0			0
$137$	−50.4847			−0.368501			−0.184251	−	0.982879i	$-0.558986\pi$
$137$	−50.4847			−0.368501			−0.184251	+	0.982879i	$0.558986\pi$
$138$		0			0
$139$	−171.727	−	171.727i	−1.23544	−	1.23544i	−0.961843	−	0.273601i	$-0.911785\pi$
$139$	−171.727	−	171.727i	−1.23544	−	1.23544i	−0.273601	−	0.961843i	$-0.588215\pi$
$140$		0			0
$141$	−208.211	+	84.8661i	−1.47667	+	0.601887i
$142$		0			0
$143$		−	88.9057i		−	0.621718i
$144$		0			0
$145$	−135.041			−0.931314
$146$		0			0
$147$	−52.4178	−	128.602i	−0.356584	−	0.874844i
$148$		0			0
$149$	−84.4952	+	84.4952i	−0.567082	+	0.567082i	−0.931310	−	0.364228i	$-0.881333\pi$
$149$	−84.4952	+	84.4952i	−0.567082	+	0.567082i	0.364228	+	0.931310i	$0.381333\pi$
$150$		0			0
$151$			30.1033i			0.199359i	0.995020	+	0.0996797i	$0.0317818\pi$
$151$			30.1033i			0.199359i	−0.995020	+	0.0996797i	$0.968218\pi$
$152$		0			0
$153$	72.2638	+	73.9190i	0.472313	+	0.483130i
$154$		0			0
$155$	−39.9461	+	39.9461i	−0.257717	+	0.257717i
$156$		0			0
$157$	181.265	−	181.265i	1.15456	−	1.15456i	0.168928	−	0.985628i	$-0.445970\pi$
$157$	181.265	−	181.265i	1.15456	−	1.15456i	0.985628	−	0.168928i	$-0.0540305\pi$
$158$		0			0
$159$	15.6680	+	6.59405i	0.0985407	+	0.0414720i
$160$		0			0
$161$			26.7239i			0.165987i
$162$		0			0
$163$	−200.081	+	200.081i	−1.22749	+	1.22749i	−0.262581	+	0.964910i	$0.584574\pi$
$163$	−200.081	+	200.081i	−1.22749	+	1.22749i	−0.964910	+	0.262581i	$0.915426\pi$
$164$		0			0
$165$	165.988	−	67.6563i	1.00599	−	0.410038i
$166$		0			0
$167$	172.656			1.03387			0.516933	−	0.856026i	$-0.327074\pi$
$167$	172.656			1.03387			0.516933	+	0.856026i	$0.327074\pi$
$168$		0			0
$169$		−	6.00394i		−	0.0355263i
$170$		0			0
$171$	−1.23682	+	109.237i	−0.00723287	+	0.638812i
$172$		0			0
$173$	−40.8313	−	40.8313i	−0.236019	−	0.236019i	0.579181	−	0.815199i	$-0.303373\pi$
$173$	−40.8313	−	40.8313i	−0.236019	−	0.236019i	−0.815199	+	0.579181i	$0.803373\pi$
$174$		0			0
$175$	88.9373			0.508213
$176$		0			0
$177$	−109.373	−	46.0307i	−0.617924	−	0.260060i
$178$		0			0
$179$	152.613	+	152.613i	0.852584	+	0.852584i	0.990451	−	0.137866i	$-0.0440245\pi$
$179$	152.613	+	152.613i	0.852584	+	0.852584i	−0.137866	+	0.990451i	$0.544024\pi$
$180$		0			0
$181$	−166.601	−	166.601i	−0.920449	−	0.920449i	0.0766118	−	0.997061i	$-0.475590\pi$
$181$	−166.601	−	166.601i	−0.920449	−	0.920449i	−0.997061	+	0.0766118i	$0.975590\pi$
$182$		0			0
$183$	153.402	+	64.5608i	0.838260	+	0.352791i
$184$		0			0
$185$	342.348			1.85053
$186$		0			0
$187$	−54.5830	−	54.5830i	−0.291888	−	0.291888i
$188$		0			0
$189$	−17.6994	+	40.7582i	−0.0936474	+	0.215652i
$190$		0			0
$191$			14.3434i			0.0750963i	0.999295	+	0.0375482i	$0.0119548\pi$
$191$			14.3434i			0.0750963i	−0.999295	+	0.0375482i	$0.988045\pi$
$192$		0			0
$193$	207.373			1.07447			0.537235	−	0.843433i	$-0.319469\pi$
$193$	207.373			1.07447			0.537235	+	0.843433i	$0.319469\pi$
$194$		0			0
$195$	326.735	−	133.176i	1.67556	−	0.682954i
$196$		0			0
$197$	97.2608	−	97.2608i	0.493710	−	0.493710i	−0.415763	−	0.909473i	$-0.636486\pi$
$197$	97.2608	−	97.2608i	0.493710	−	0.493710i	0.909473	+	0.415763i	$0.136486\pi$
$198$		0			0
$199$		−	82.7673i		−	0.415916i	−0.978138	−	0.207958i	$-0.933318\pi$
$199$		−	82.7673i		−	0.415916i	0.978138	−	0.207958i	$-0.0666818\pi$
$200$		0			0
$201$	−268.593	−	113.041i	−1.33628	−	0.562391i
$202$		0			0
$203$	−17.6762	+	17.6762i	−0.0870748	+	0.0870748i
$204$		0			0
$205$	−12.4575	+	12.4575i	−0.0607684	+	0.0607684i
$206$		0			0
$207$	−104.502	+	102.162i	−0.504840	+	0.493536i
$208$		0			0
$209$		−	81.5756i		−	0.390314i
$210$		0			0
$211$	201.646	−	201.646i	0.955667	−	0.955667i	−0.0433911	−	0.999058i	$-0.513816\pi$
$211$	201.646	−	201.646i	0.955667	−	0.955667i	0.999058	+	0.0433911i	$0.0138162\pi$
$212$		0			0
$213$	−46.0661	−	113.019i	−0.216273	−	0.530605i
$214$		0			0
$215$	−244.130			−1.13549
$216$		0			0
$217$			10.4575i			0.0481913i
$218$		0			0
$219$	164.020	−	66.8541i	0.748950	−	0.305270i
$220$		0			0
$221$	−107.442	−	107.442i	−0.486164	−	0.486164i
$222$		0			0
$223$	233.261			1.04602			0.523008	−	0.852328i	$-0.324810\pi$
$223$	233.261			1.04602			0.523008	+	0.852328i	$0.324810\pi$
$224$		0			0
$225$	339.996	+	347.783i	1.51109	+	1.54570i
$226$		0			0
$227$	94.3599	+	94.3599i	0.415682	+	0.415682i	0.883712	−	0.468030i	$-0.155036\pi$
$227$	94.3599	+	94.3599i	0.415682	+	0.415682i	−0.468030	+	0.883712i	$0.655036\pi$
$228$		0			0
$229$	138.063	+	138.063i	0.602894	+	0.602894i	0.941080	−	0.338185i	$-0.109813\pi$
$229$	138.063	+	138.063i	0.602894	+	0.602894i	−0.338185	+	0.941080i	$0.609813\pi$
$230$		0			0
$231$	12.8712	−	30.5830i	0.0557195	−	0.132394i
$232$		0			0
$233$	−396.796			−1.70299			−0.851493	−	0.524366i	$-0.824303\pi$
$233$	−396.796			−1.70299			−0.851493	+	0.524366i	$0.824303\pi$
$234$		0			0
$235$	471.158	+	471.158i	2.00493	+	2.00493i
$236$		0			0
$237$	−19.6968	−	48.3243i	−0.0831090	−	0.203900i
$238$		0			0
$239$		−	284.813i		−	1.19168i	−0.803102	−	0.595842i	$-0.796818\pi$
$239$		−	284.813i		−	1.19168i	0.803102	−	0.595842i	$-0.203182\pi$
$240$		0			0
$241$	−266.531			−1.10594			−0.552968	−	0.833202i	$-0.686505\pi$
$241$	−266.531			−1.10594			−0.552968	+	0.833202i	$0.686505\pi$
$242$		0			0
$243$	−227.045	+	86.6012i	−0.934340	+	0.356383i
$244$		0			0
$245$	−291.012	+	291.012i	−1.18780	+	1.18780i
$246$		0			0
$247$		−	160.575i		−	0.650102i
$248$		0			0
$249$	123.662	−	293.830i	0.496633	−	1.18004i
$250$		0			0
$251$	−153.945	+	153.945i	−0.613327	+	0.613327i	−0.943811	−	0.330485i	$-0.892788\pi$
$251$	−153.945	+	153.945i	−0.613327	+	0.613327i	0.330485	+	0.943811i	$0.392788\pi$
$252$		0			0
$253$	77.1660	−	77.1660i	0.305004	−	0.305004i
$254$		0			0
$255$	118.834	−	282.359i	0.466016	−	1.10729i
$256$		0			0
$257$			240.167i			0.934503i	0.884125	+	0.467251i	$0.154756\pi$
$257$			240.167i			0.934503i	−0.884125	+	0.467251i	$0.845244\pi$
$258$		0			0
$259$	44.8118	−	44.8118i	0.173018	−	0.173018i
$260$		0			0
$261$	−136.695	−	1.54772i	−0.523737	−	0.00592995i
$262$		0			0
$263$	140.707			0.535009			0.267505	−	0.963557i	$-0.413801\pi$
$263$	140.707			0.535009			0.267505	+	0.963557i	$0.413801\pi$
$264$		0			0
$265$		−	50.3765i		−	0.190100i
$266$		0			0
$267$	−89.2343	−	218.928i	−0.334211	−	0.819954i
$268$		0			0
$269$	−229.830	−	229.830i	−0.854388	−	0.854388i	0.136282	−	0.990670i	$-0.456485\pi$
$269$	−229.830	−	229.830i	−0.854388	−	0.854388i	−0.990670	+	0.136282i	$0.956485\pi$
$270$		0			0
$271$	228.731			0.844025			0.422012	−	0.906590i	$-0.361324\pi$
$271$	228.731			0.844025			0.422012	+	0.906590i	$0.361324\pi$
$272$		0			0
$273$	25.3360	−	60.2002i	0.0928057	−	0.220514i
$274$		0			0
$275$	−256.809	−	256.809i	−0.933851	−	0.933851i
$276$		0			0
$277$	103.265	+	103.265i	0.372799	+	0.372799i	0.868496	−	0.495697i	$-0.165087\pi$
$277$	103.265	+	103.265i	0.372799	+	0.372799i	−0.495697	+	0.868496i	$0.665087\pi$
$278$		0			0
$279$	−40.8934	+	39.9778i	−0.146571	+	0.143290i
$280$		0			0
$281$	−283.552			−1.00908			−0.504540	−	0.863388i	$-0.668338\pi$
$281$	−283.552			−1.00908			−0.504540	+	0.863388i	$0.668338\pi$
$282$		0			0
$283$	−23.4758	−	23.4758i	−0.0829534	−	0.0829534i	0.664413	−	0.747366i	$-0.268682\pi$
$283$	−23.4758	−	23.4758i	−0.0829534	−	0.0829534i	−0.747366	+	0.664413i	$0.768682\pi$
$284$		0			0
$285$	299.796	−	122.196i	1.05192	−	0.428758i
$286$		0			0
$287$			3.26126i			0.0113633i
$288$		0			0
$289$	157.073			0.543506
$290$		0			0
$291$	43.9734	+	107.884i	0.151111	+	0.370737i
$292$		0			0
$293$	381.409	−	381.409i	1.30174	−	1.30174i	0.374516	−	0.927220i	$-0.377809\pi$
$293$	381.409	−	381.409i	1.30174	−	1.30174i	0.927220	−	0.374516i	$-0.122191\pi$
$294$		0			0
$295$			351.660i			1.19207i
$296$		0			0
$297$	168.798	−	66.5830i	0.568343	−	0.224185i
$298$		0			0
$299$	151.895	−	151.895i	0.508011	−	0.508011i
$300$		0			0
$301$	−31.9555	+	31.9555i	−0.106165	+	0.106165i
$302$		0			0
$303$	−162.413	−	68.3534i	−0.536017	−	0.225589i
$304$		0			0
$305$		−	493.224i		−	1.61713i
$306$		0			0
$307$	209.055	−	209.055i	0.680960	−	0.680960i	−0.279256	−	0.960217i	$-0.590088\pi$
$307$	209.055	−	209.055i	0.680960	−	0.680960i	0.960217	+	0.279256i	$0.0900879\pi$
$308$		0			0
$309$	−274.508	+	111.889i	−0.888376	+	0.362099i
$310$		0			0
$311$	−111.176			−0.357478			−0.178739	−	0.983897i	$-0.557202\pi$
$311$	−111.176			−0.357478			−0.178739	+	0.983897i	$0.557202\pi$
$312$		0			0
$313$		−	282.280i		−	0.901852i	−0.892561	−	0.450926i	$-0.851094\pi$
$313$		−	282.280i		−	0.901852i	0.892561	−	0.450926i	$-0.148906\pi$
$314$		0			0
$315$	131.675	+	1.49088i	0.418016	+	0.00473294i
$316$		0			0
$317$	206.983	+	206.983i	0.652943	+	0.652943i	0.953701	−	0.300758i	$-0.0972395\pi$
$317$	206.983	+	206.983i	0.652943	+	0.652943i	−0.300758	+	0.953701i	$0.597240\pi$
$318$		0			0
$319$	102.081			0.320003
$320$		0			0
$321$	−386.539	−	162.679i	−1.20417	−	0.506789i
$322$		0			0
$323$	−98.5839	−	98.5839i	−0.305213	−	0.305213i
$324$		0			0
$325$	−505.508	−	505.508i	−1.55541	−	1.55541i
$326$		0			0
$327$	269.242	+	113.314i	0.823371	+	0.346525i
$328$		0			0
$329$	123.345			0.374908
$330$		0			0
$331$	−127.431	−	127.431i	−0.384989	−	0.384989i	0.487907	−	0.872896i	$-0.337761\pi$
$331$	−127.431	−	127.431i	−0.384989	−	0.384989i	−0.872896	+	0.487907i	$0.837761\pi$
$332$		0			0
$333$	346.543	+	3.92369i	1.04067	+	0.0117829i
$334$		0			0
$335$			863.594i			2.57789i
$336$		0			0
$337$	68.9595			0.204628			0.102314	−	0.994752i	$-0.467375\pi$
$337$	68.9595			0.204628			0.102314	+	0.994752i	$0.467375\pi$
$338$		0			0
$339$	−23.0904	+	9.41157i	−0.0681133	+	0.0277627i
$340$		0			0
$341$	30.1964	−	30.1964i	0.0885525	−	0.0885525i
$342$		0			0
$343$			156.826i			0.457219i
$344$		0			0
$345$	399.181	+	168.000i	1.15705	+	0.486957i
$346$		0			0
$347$	−54.0628	+	54.0628i	−0.155801	+	0.155801i	−0.780703	−	0.624902i	$-0.785139\pi$
$347$	−54.0628	+	54.0628i	−0.155801	+	0.155801i	0.624902	+	0.780703i	$0.285139\pi$
$348$		0			0
$349$	−0.107201	+	0.107201i	−0.000307168	+	0.000307168i	−0.707260	−	0.706953i	$-0.750069\pi$
$349$	−0.107201	+	0.107201i	−0.000307168	+	0.000307168i	0.706953	+	0.707260i	$0.250069\pi$
$350$		0			0
$351$	332.265	−	131.063i	0.946625	−	0.373400i
$352$		0			0
$353$		−	194.223i		−	0.550208i	−0.961414	−	0.275104i	$-0.911288\pi$
$353$		−	194.223i		−	0.550208i	0.961414	−	0.275104i	$-0.0887123\pi$
$354$		0			0
$355$	−255.749	+	255.749i	−0.720420	+	0.720420i
$356$		0			0
$357$	−21.4047	−	52.5143i	−0.0599570	−	0.147099i
$358$		0			0
$359$	−437.689			−1.21919			−0.609595	−	0.792713i	$-0.708668\pi$
$359$	−437.689			−1.21919			−0.609595	+	0.792713i	$0.708668\pi$
$360$		0			0
$361$			213.664i			0.591867i
$362$		0			0
$363$	210.674	−	85.8700i	0.580369	−	0.236556i
$364$		0			0
$365$	−371.159	−	371.159i	−1.01687	−	1.01687i
$366$		0			0
$367$	−246.678			−0.672148			−0.336074	−	0.941836i	$-0.609099\pi$
$367$	−246.678			−0.672148			−0.336074	+	0.941836i	$0.609099\pi$
$368$		0			0
$369$	−12.7530	+	12.4674i	−0.0345608	+	0.0337870i
$370$		0			0
$371$	−6.59405	−	6.59405i	−0.0177737	−	0.0177737i
$372$		0			0
$373$	349.678	+	349.678i	0.937476	+	0.937476i	0.998157	−	0.0606816i	$-0.0193274\pi$
$373$	349.678	+	349.678i	0.937476	+	0.937476i	−0.0606816	+	0.998157i	$0.519327\pi$
$374$		0			0
$375$	300.454	−	713.903i	0.801212	−	1.90374i
$376$		0			0
$377$	200.938			0.532993
$378$		0			0
$379$	−235.668	−	235.668i	−0.621815	−	0.621815i	0.324180	−	0.945995i	$-0.394912\pi$
$379$	−235.668	−	235.668i	−0.621815	−	0.621815i	−0.945995	+	0.324180i	$0.894912\pi$
$380$		0			0
$381$	221.864	+	544.321i	0.582319	+	1.42866i
$382$		0			0
$383$		−	64.2130i		−	0.167658i	−0.996480	−	0.0838290i	$-0.973285\pi$
$383$		−	64.2130i		−	0.167658i	0.996480	−	0.0838290i	$-0.0267149\pi$
$384$		0			0
$385$	−98.3320			−0.255408
$386$		0			0
$387$	−247.122	−	2.79801i	−0.638559	−	0.00723000i
$388$		0			0
$389$	−273.321	+	273.321i	−0.702624	+	0.702624i	−0.964973	−	0.262349i	$-0.915503\pi$
$389$	−273.321	+	273.321i	−0.702624	+	0.702624i	0.262349	+	0.964973i	$0.415503\pi$
$390$		0			0
$391$		−	186.510i		−	0.477007i
$392$		0			0
$393$	−233.905	+	555.778i	−0.595179	+	1.41419i
$394$		0			0
$395$	−109.352	+	109.352i	−0.276842	+	0.276842i
$396$		0			0
$397$	−141.678	+	141.678i	−0.356873	+	0.356873i	−0.862659	−	0.505786i	$-0.831202\pi$
$397$	−141.678	+	141.678i	−0.356873	+	0.356873i	0.505786	+	0.862659i	$0.331202\pi$
$398$		0			0
$399$	23.2470	−	55.2368i	0.0582633	−	0.138438i
$400$		0			0
$401$		−	194.801i		−	0.485788i	−0.970053	−	0.242894i	$-0.921903\pi$
$401$		−	194.801i		−	0.485788i	0.970053	−	0.242894i	$-0.0780967\pi$
$402$		0			0
$403$	59.4392	−	59.4392i	0.147492	−	0.147492i
$404$		0			0
$405$	497.548	+	520.607i	1.22851	+	1.28545i
$406$		0			0
$407$	−258.791			−0.635849
$408$		0			0
$409$		−	420.826i		−	1.02891i	−0.857516	−	0.514457i	$-0.827993\pi$
$409$		−	420.826i		−	1.02891i	0.857516	−	0.514457i	$-0.172007\pi$
$410$		0			0
$411$	57.1659	+	140.251i	0.139090	+	0.341244i
$412$		0			0
$413$	46.0307	+	46.0307i	0.111454	+	0.111454i
$414$		0			0
$415$	−944.737			−2.27648
$416$		0			0
$417$	−282.620	+	671.526i	−0.677745	+	1.61038i
$418$		0			0
$419$	186.421	+	186.421i	0.444919	+	0.444919i	0.893661	−	0.448742i	$-0.148128\pi$
$419$	186.421	+	186.421i	0.444919	+	0.444919i	−0.448742	+	0.893661i	$0.648128\pi$
$420$		0			0
$421$	186.889	+	186.889i	0.443917	+	0.443917i	0.893326	−	0.449409i	$-0.148366\pi$
$421$	186.889	+	186.889i	0.443917	+	0.443917i	−0.449409	+	0.893326i	$0.648366\pi$
$422$		0			0
$423$	471.532	+	482.332i	1.11473	+	1.14026i
$424$		0			0
$425$	−620.706			−1.46049
$426$		0			0
$427$	−64.5608	−	64.5608i	−0.151196	−	0.151196i
$428$		0			0
$429$	−246.988	+	100.672i	−0.575731	+	0.234666i
$430$		0			0
$431$		−	128.395i		−	0.297901i	−0.988845	−	0.148950i	$-0.952411\pi$
$431$		−	128.395i		−	0.297901i	0.988845	−	0.148950i	$-0.0475895\pi$
$432$		0			0
$433$	684.737			1.58138			0.790690	−	0.612217i	$-0.209722\pi$
$433$	684.737			1.58138			0.790690	+	0.612217i	$0.209722\pi$
$434$		0			0
$435$	152.912	+	375.155i	0.351522	+	0.862426i
$436$		0			0
$437$	139.372	−	139.372i	0.318928	−	0.318928i
$438$		0			0
$439$			239.107i			0.544663i	0.962203	+	0.272332i	$0.0877948\pi$
$439$			239.107i			0.544663i	−0.962203	+	0.272332i	$0.912205\pi$
$440$		0			0
$441$	−297.914	+	291.243i	−0.675541	+	0.660415i
$442$		0			0
$443$	−310.189	+	310.189i	−0.700200	+	0.700200i	−0.964453	−	0.264253i	$-0.914875\pi$
$443$	−310.189	+	310.189i	−0.700200	+	0.700200i	0.264253	+	0.964453i	$0.414875\pi$
$444$		0			0
$445$	−495.409	+	495.409i	−1.11328	+	1.11328i
$446$		0			0
$447$	330.413	+	139.058i	0.739179	+	0.311092i
$448$		0			0
$449$			545.902i			1.21582i	0.794007	+	0.607908i	$0.207991\pi$
$449$			545.902i			1.21582i	−0.794007	+	0.607908i	$0.792009\pi$
$450$		0			0
$451$	9.41699	−	9.41699i	0.0208803	−	0.0208803i
$452$		0			0
$453$	83.6297	−	34.0872i	0.184613	−	0.0752477i
$454$		0			0
$455$	−193.559			−0.425404
$456$		0			0
$457$			289.579i			0.633652i	0.948484	+	0.316826i	$0.102617\pi$
$457$			289.579i			0.633652i	−0.948484	+	0.316826i	$0.897383\pi$
$458$		0			0
$459$	123.526	−	284.457i	0.269121	−	0.619732i
$460$		0			0
$461$	−160.511	−	160.511i	−0.348180	−	0.348180i	0.511251	−	0.859431i	$-0.329182\pi$
$461$	−160.511	−	160.511i	−0.348180	−	0.348180i	−0.859431	+	0.511251i	$0.829182\pi$
$462$		0			0
$463$	−197.573			−0.426723			−0.213361	−	0.976973i	$-0.568441\pi$
$463$	−197.573			−0.426723			−0.213361	+	0.976973i	$0.568441\pi$
$464$		0			0
$465$	156.207	+	65.7413i	0.335928	+	0.141379i
$466$		0			0
$467$	−52.7645	−	52.7645i	−0.112986	−	0.112986i	0.648353	−	0.761339i	$-0.275458\pi$
$467$	−52.7645	−	52.7645i	−0.112986	−	0.112986i	−0.761339	+	0.648353i	$0.775458\pi$
$468$		0			0
$469$	113.041	+	113.041i	0.241025	+	0.241025i
$470$		0			0
$471$	−708.826	−	298.318i	−1.50494	−	0.633371i
$472$		0			0
$473$	184.545			0.390159
$474$		0			0
$475$	−463.830	−	463.830i	−0.976484	−	0.976484i
$476$		0			0
$477$	0.577371	−	50.9938i	0.00121042	−	0.106905i
$478$		0			0
$479$			175.985i			0.367401i	0.982982	+	0.183700i	$0.0588076\pi$
$479$			175.985i			0.367401i	−0.982982	+	0.183700i	$0.941192\pi$
$480$		0			0
$481$	−509.409			−1.05906
$482$		0			0
$483$	74.2414	−	30.2606i	0.153709	−	0.0626513i
$484$		0			0
$485$	244.130	−	244.130i	0.503362	−	0.503362i
$486$		0			0
$487$		−	965.217i		−	1.98196i	−0.133991	−	0.990982i	$-0.542779\pi$
$487$		−	965.217i		−	1.98196i	0.133991	−	0.990982i	$-0.457221\pi$
$488$		0			0
$489$	782.404	+	329.284i	1.60001	+	0.673382i
$490$		0			0
$491$	−600.614	+	600.614i	−1.22325	+	1.22325i	−0.256775	+	0.966471i	$0.582660\pi$
$491$	−600.614	+	600.614i	−1.22325	+	1.22325i	−0.966471	+	0.256775i	$0.917340\pi$
$492$		0			0
$493$	123.365	−	123.365i	0.250233	−	0.250233i
$494$		0			0
$495$	−375.911	−	384.521i	−0.759416	−	0.776810i
$496$		0			0
$497$			66.9527i			0.134714i
$498$		0			0
$499$	51.6092	−	51.6092i	0.103425	−	0.103425i	−0.653501	−	0.756926i	$-0.726700\pi$
$499$	51.6092	−	51.6092i	0.103425	−	0.103425i	0.756926	+	0.653501i	$0.226700\pi$
$500$		0			0
$501$	−195.505	−	479.653i	−0.390230	−	0.957391i
$502$		0			0
$503$	847.530			1.68495			0.842475	−	0.538735i	$-0.181098\pi$
$503$	847.530			1.68495			0.842475	+	0.538735i	$0.181098\pi$
$504$		0			0
$505$			522.199i			1.03406i
$506$		0			0
$507$	−16.6795	+	6.79851i	−0.0328984	+	0.0134093i
$508$		0			0
$509$	128.457	+	128.457i	0.252372	+	0.252372i	0.821942	−	0.569570i	$-0.192890\pi$
$509$	128.457	+	128.457i	0.252372	+	0.252372i	−0.569570	+	0.821942i	$0.692890\pi$
$510$		0			0
$511$	−97.1660			−0.190149
$512$		0			0
$513$	304.871	−	120.257i	0.594290	−	0.234420i
$514$		0			0
$515$	621.182	+	621.182i	1.20618	+	1.20618i
$516$		0			0
$517$	−356.162	−	356.162i	−0.688901	−	0.688901i
$518$		0			0
$519$	−67.1981	+	159.668i	−0.129476	+	0.307645i
$520$		0			0
$521$	676.366			1.29821			0.649103	−	0.760700i	$-0.275144\pi$
$521$	676.366			1.29821			0.649103	+	0.760700i	$0.275144\pi$
$522$		0			0
$523$	600.494	+	600.494i	1.14817	+	1.14817i	0.986912	+	0.161260i	$0.0515559\pi$
$523$	600.494	+	600.494i	1.14817	+	1.14817i	0.161260	+	0.986912i	$0.448444\pi$
$524$		0			0
$525$	−100.707	−	247.076i	−0.191824	−	0.470621i
$526$		0			0
$527$		−	72.9845i		−	0.138491i
$528$		0			0
$529$	−265.324			−0.501558
$530$		0			0
$531$	−4.03042	+	355.970i	−0.00759025	+	0.670376i
$532$		0			0
$533$	18.5366	−	18.5366i	0.0347779	−	0.0347779i
$534$		0			0
$535$			1242.82i			2.32302i
$536$		0			0
$537$	251.162	−	596.782i	0.467714	−	1.11133i
$538$		0			0
$539$	219.985	−	219.985i	0.408135	−	0.408135i
$540$		0			0
$541$	−43.4797	+	43.4797i	−0.0803692	+	0.0803692i	−0.746149	−	0.665779i	$-0.768099\pi$
$541$	−43.4797	+	43.4797i	−0.0803692	+	0.0803692i	0.665779	+	0.746149i	$0.268099\pi$
$542$		0			0
$543$	−274.184	+	651.484i	−0.504943	+	1.19979i
$544$		0			0
$545$		−	865.682i		−	1.58841i
$546$		0			0
$547$	125.498	−	125.498i	0.229430	−	0.229430i	−0.583025	−	0.812454i	$-0.698131\pi$
$547$	125.498	−	125.498i	0.229430	−	0.229430i	0.812454	+	0.583025i	$0.198131\pi$
$548$		0			0
$549$	5.65291	−	499.269i	0.0102967	−	0.909414i
$550$		0			0
$551$	184.371			0.334612
$552$		0			0
$553$			28.6275i			0.0517676i
$554$		0			0
$555$	−387.655	−	951.074i	−0.698477	−	1.71365i
$556$		0			0
$557$	184.272	+	184.272i	0.330829	+	0.330829i	0.852901	−	0.522072i	$-0.174841\pi$
$557$	184.272	+	184.272i	0.330829	+	0.330829i	−0.522072	+	0.852901i	$0.674841\pi$
$558$		0			0
$559$	363.263			0.649844
$560$		0			0
$561$	−89.8301	+	213.443i	−0.160125	+	0.380469i
$562$		0			0
$563$	−523.489	−	523.489i	−0.929820	−	0.929820i	0.0678736	−	0.997694i	$-0.478379\pi$
$563$	−523.489	−	523.489i	−0.929820	−	0.929820i	−0.997694	+	0.0678736i	$0.978379\pi$
$564$		0			0
$565$	52.2510	+	52.2510i	0.0924796	+	0.0924796i
$566$		0			0
$567$	133.272	+	3.01829i	0.235047	+	0.00532326i
$568$		0			0
$569$	−52.6214			−0.0924805			−0.0462403	−	0.998930i	$-0.514724\pi$
$569$	−52.6214			−0.0924805			−0.0462403	+	0.998930i	$0.514724\pi$
$570$		0			0
$571$	114.561	+	114.561i	0.200632	+	0.200632i	0.800271	−	0.599639i	$-0.204689\pi$
$571$	114.561	+	114.561i	0.200632	+	0.200632i	−0.599639	+	0.800271i	$0.704689\pi$
$572$		0			0
$573$	39.8473	−	16.2416i	0.0695415	−	0.0283449i
$574$		0			0
$575$		−	877.515i		−	1.52611i
$576$		0			0
$577$	496.442			0.860384			0.430192	−	0.902737i	$-0.358446\pi$
$577$	496.442			0.860384			0.430192	+	0.902737i	$0.358446\pi$
$578$		0			0
$579$	−234.817	−	576.100i	−0.405555	−	0.994992i
$580$		0			0
$581$	−123.662	+	123.662i	−0.212843	+	0.212843i
$582$		0			0
$583$			38.0810i			0.0653191i
$584$		0			0
$585$	−739.951	−	756.899i	−1.26487	−	1.29384i
$586$		0			0
$587$	−115.260	+	115.260i	−0.196354	+	0.196354i	−0.798435	−	0.602081i	$-0.794338\pi$
$587$	−115.260	+	115.260i	−0.196354	+	0.196354i	0.602081	+	0.798435i	$0.294338\pi$
$588$		0			0
$589$	54.5385	−	54.5385i	0.0925952	−	0.0925952i
$590$		0			0
$591$	−380.332	−	160.067i	−0.643540	−	0.270841i
$592$		0			0
$593$		−	227.756i		−	0.384074i	−0.981388	−	0.192037i	$-0.938491\pi$
$593$		−	227.756i		−	0.384074i	0.981388	−	0.192037i	$-0.0615094\pi$
$594$		0			0
$595$	−118.834	+	118.834i	−0.199721	+	0.199721i
$596$		0			0
$597$	−229.935	+	93.7209i	−0.385151	+	0.156986i
$598$		0			0
$599$	−760.308			−1.26930			−0.634648	−	0.772802i	$-0.718855\pi$
$599$	−760.308			−1.26930			−0.634648	+	0.772802i	$0.718855\pi$
$600$		0			0
$601$			85.7856i			0.142738i	0.997450	+	0.0713690i	$0.0227368\pi$
$601$			85.7856i			0.142738i	−0.997450	+	0.0713690i	$0.977263\pi$
$602$		0			0
$603$	−9.89776	+	874.177i	−0.0164142	+	1.44971i
$604$		0			0
$605$	−476.731	−	476.731i	−0.787986	−	0.787986i
$606$		0			0
$607$	685.217			1.12886			0.564429	−	0.825482i	$-0.309096\pi$
$607$	685.217			1.12886			0.564429	+	0.825482i	$0.309096\pi$
$608$		0			0
$609$	69.1216	+	29.0906i	0.113500	+	0.0477678i
$610$		0			0
$611$	−701.077	−	701.077i	−1.14743	−	1.14743i
$612$		0			0
$613$	544.727	+	544.727i	0.888624	+	0.888624i	0.994391	−	0.105767i	$-0.0337296\pi$
$613$	544.727	+	544.727i	0.888624	+	0.888624i	−0.105767	+	0.994391i	$0.533730\pi$
$614$		0			0
$615$	48.7143	+	20.5020i	0.0792102	+	0.0333365i
$616$		0			0
$617$	−383.577			−0.621681			−0.310840	−	0.950462i	$-0.600610\pi$
$617$	−383.577			−0.621681			−0.310840	+	0.950462i	$0.600610\pi$
$618$		0			0
$619$	−81.7634	−	81.7634i	−0.132089	−	0.132089i	0.637971	−	0.770060i	$-0.279774\pi$
$619$	−81.7634	−	81.7634i	−0.132089	−	0.132089i	−0.770060	+	0.637971i	$0.779774\pi$
$620$		0			0
$621$	402.148	+	174.634i	0.647581	+	0.281214i
$622$		0			0
$623$			129.694i			0.208176i
$624$		0			0
$625$	−944.365			−1.51098
$626$		0			0
$627$	−226.625	+	92.3715i	−0.361443	+	0.147323i
$628$		0			0
$629$	−312.748	+	312.748i	−0.497214	+	0.497214i
$630$		0			0
$631$		−	944.242i		−	1.49642i	−0.663461	−	0.748211i	$-0.730913\pi$
$631$		−	944.242i		−	1.49642i	0.663461	−	0.748211i	$-0.269087\pi$
$632$		0			0
$633$	−788.523	−	331.859i	−1.24569	−	0.524263i
$634$		0			0
$635$	1231.74	−	1231.74i	1.93974	−	1.93974i
$636$		0			0
$637$	433.022	−	433.022i	0.679784	−	0.679784i
$638$		0			0
$639$	−261.814	+	255.952i	−0.409725	+	0.400551i
$640$		0			0
$641$			1102.48i			1.71994i	0.510344	+	0.859970i	$0.329518\pi$
$641$			1102.48i			1.71994i	−0.510344	+	0.859970i	$0.670482\pi$
$642$		0			0
$643$	−794.664	+	794.664i	−1.23587	+	1.23587i	−0.274195	+	0.961674i	$0.588412\pi$
$643$	−794.664	+	794.664i	−1.23587	+	1.23587i	−0.961674	+	0.274195i	$0.911588\pi$
$644$		0			0
$645$	276.439	+	678.217i	0.428588	+	1.05150i
$646$		0			0
$647$	−768.446			−1.18771			−0.593853	−	0.804574i	$-0.702394\pi$
$647$	−768.446			−1.18771			−0.593853	+	0.804574i	$0.702394\pi$
$648$		0			0
$649$		−	265.830i		−	0.409599i
$650$		0			0
$651$	29.0519	−	11.8415i	0.0446266	−	0.0181897i
$652$		0			0
$653$	829.478	+	829.478i	1.27026	+	1.27026i	0.945953	+	0.324305i	$0.105130\pi$
$653$	829.478	+	829.478i	1.27026	+	1.27026i	0.324305	+	0.945953i	$0.394870\pi$
$654$		0			0
$655$	1786.96			2.72819
$656$		0			0
$657$	−371.454	−	379.961i	−0.565378	−	0.578328i
$658$		0			0
$659$	653.956	+	653.956i	0.992346	+	0.992346i	0.999971	−	0.00762509i	$-0.00242716\pi$
$659$	653.956	+	653.956i	0.992346	+	0.992346i	−0.00762509	+	0.999971i	$0.502427\pi$
$660$		0			0
$661$	−734.342	−	734.342i	−1.11096	−	1.11096i	−0.993021	−	0.117936i	$-0.962372\pi$
$661$	−734.342	−	734.342i	−1.11096	−	1.11096i	−0.117936	−	0.993021i	$-0.537628\pi$
$662$		0			0
$663$	−176.823	+	420.146i	−0.266702	+	0.633705i
$664$		0			0
$665$	−177.600			−0.267068
$666$		0			0
$667$	174.405	+	174.405i	0.261477	+	0.261477i
$668$		0			0
$669$	−264.132	−	648.022i	−0.394816	−	0.968643i
$670$		0			0
$671$			372.842i			0.555652i
$672$		0			0
$673$	514.259			0.764129			0.382065	−	0.924136i	$-0.375213\pi$
$673$	514.259			0.764129			0.382065	+	0.924136i	$0.375213\pi$
$674$		0			0
$675$	581.183	−	1338.35i	0.861012	−	1.98274i
$676$		0			0
$677$	−662.519	+	662.519i	−0.978610	+	0.978610i	−0.999776	−	0.0211661i	$-0.993262\pi$
$677$	−662.519	+	662.519i	−0.978610	+	0.978610i	0.0211661	+	0.999776i	$0.493262\pi$
$678$		0			0
$679$		−	63.9111i		−	0.0941253i
$680$		0			0
$681$	155.293	−	368.988i	0.228037	−	0.541833i
$682$		0			0
$683$	280.446	−	280.446i	0.410608	−	0.410608i	−0.471342	−	0.881950i	$-0.656230\pi$
$683$	280.446	−	280.446i	0.410608	−	0.410608i	0.881950	+	0.471342i	$0.156230\pi$
$684$		0			0
$685$	317.373	−	317.373i	0.463318	−	0.463318i
$686$		0			0
$687$	227.217	−	539.885i	0.330738	−	0.785859i
$688$		0			0
$689$			74.9595i			0.108795i
$690$		0			0
$691$	631.830	−	631.830i	0.914371	−	0.914371i	−0.0822418	−	0.996612i	$-0.526208\pi$
$691$	631.830	−	631.830i	0.914371	−	0.914371i	0.996612	+	0.0822418i	$0.0262080\pi$
$692$		0			0
$693$	−99.5370	−	1.12700i	−0.143632	−	0.00162626i
$694$		0			0
$695$	2159.13			3.10666
$696$		0			0
$697$		−	22.7608i		−	0.0326554i
$698$		0			0
$699$	449.309	+	1102.34i	0.642788	+	1.57702i
$700$		0			0
$701$	−160.480	−	160.480i	−0.228930	−	0.228930i	0.583315	−	0.812246i	$-0.301755\pi$
$701$	−160.480	−	160.480i	−0.228930	−	0.228930i	−0.812246	+	0.583315i	$0.801755\pi$
$702$		0			0
$703$	−467.409			−0.664878
$704$		0			0
$705$	775.409	−	1842.43i	1.09987	−	2.61338i
$706$		0			0
$707$	68.3534	+	68.3534i	0.0966809	+	0.0966809i
$708$		0			0
$709$	410.261	+	410.261i	0.578648	+	0.578648i	0.934531	−	0.355883i	$-0.115820\pi$
$709$	410.261	+	410.261i	0.578648	+	0.578648i	−0.355883	+	0.934531i	$0.615820\pi$
$710$		0			0
$711$	−111.946	+	109.439i	−0.157448	+	0.153923i
$712$		0			0
$713$	103.181			0.144714
$714$		0			0
$715$	558.907	+	558.907i	0.781688	+	0.781688i
$716$		0			0
$717$	−791.236	+	322.505i	−1.10354	+	0.449798i
$718$		0			0
$719$			1069.18i			1.48704i	0.668716	+	0.743518i	$0.266844\pi$
$719$			1069.18i			1.48704i	−0.668716	+	0.743518i	$0.733156\pi$
$720$		0			0
$721$	162.620			0.225547
$722$		0			0
$723$	301.804	+	740.447i	0.417433	+	1.02413i
$724$		0			0
$725$	580.422	−	580.422i	0.800582	−	0.800582i
$726$		0			0
$727$		−	148.864i		−	0.204765i	−0.994745	−	0.102382i	$-0.967353\pi$
$727$		−	148.864i		−	0.204765i	0.994745	−	0.102382i	$-0.0326466\pi$
$728$		0			0
$729$	497.678	+	532.689i	0.682686	+	0.730712i
$730$		0			0
$731$	223.022	−	223.022i	0.305092	−	0.305092i
$732$		0			0
$733$	690.136	−	690.136i	0.941522	−	0.941522i	−0.0568598	−	0.998382i	$-0.518109\pi$
$733$	690.136	−	690.136i	0.941522	−	0.941522i	0.998382	+	0.0568598i	$0.0181088\pi$
$734$		0			0
$735$	1137.98	+	478.934i	1.54828	+	0.651610i
$736$		0			0
$737$		−	652.816i		−	0.885775i
$738$		0			0
$739$	535.593	−	535.593i	0.724754	−	0.724754i	−0.244815	−	0.969570i	$-0.578727\pi$
$739$	535.593	−	535.593i	0.724754	−	0.724754i	0.969570	+	0.244815i	$0.0787274\pi$
$740$		0			0
$741$	−446.093	+	181.826i	−0.602014	+	0.245379i
$742$		0			0
$743$	20.5116			0.0276065			0.0138032	−	0.999905i	$-0.495606\pi$
$743$	20.5116			0.0276065			0.0138032	+	0.999905i	$0.495606\pi$
$744$		0			0
$745$		−	1062.36i		−	1.42599i
$746$		0			0
$747$	−956.315	−	10.8278i	−1.28021	−	0.0144950i
$748$		0			0
$749$	162.679	+	162.679i	0.217195	+	0.217195i
$750$		0			0
$751$	−15.8000			−0.0210385			−0.0105193	−	0.999945i	$-0.503348\pi$
$751$	−15.8000			−0.0210385			−0.0105193	+	0.999945i	$0.503348\pi$
$752$		0			0
$753$	601.992	+	253.355i	0.799458	+	0.336461i
$754$		0			0
$755$	−189.245	−	189.245i	−0.250655	−	0.250655i
$756$		0			0
$757$	−810.497	−	810.497i	−1.07067	−	1.07067i	−0.997305	−	0.0733640i	$-0.976627\pi$
$757$	−810.497	−	810.497i	−1.07067	−	1.07067i	−0.0733640	−	0.997305i	$-0.523373\pi$
$758$		0			0
$759$	−301.753	−	126.996i	−0.397566	−	0.167320i
$760$		0			0
$761$	212.194			0.278836			0.139418	−	0.990234i	$-0.455477\pi$
$761$	212.194			0.278836			0.139418	+	0.990234i	$0.455477\pi$
$762$		0			0
$763$	−113.314	−	113.314i	−0.148511	−	0.148511i
$764$		0			0
$765$	−918.980	−	10.4050i	−1.20128	−	0.0136014i
$766$		0			0
$767$		−	523.266i		−	0.682224i
$768$		0			0
$769$	−883.681			−1.14913			−0.574565	−	0.818459i	$-0.694829\pi$
$769$	−883.681			−1.14913			−0.574565	+	0.818459i	$0.694829\pi$
$770$		0			0
$771$	667.207	−	271.951i	0.865378	−	0.352725i
$772$		0			0
$773$	515.805	−	515.805i	0.667277	−	0.667277i	−0.289808	−	0.957085i	$-0.593591\pi$
$773$	515.805	−	515.805i	0.667277	−	0.667277i	0.957085	+	0.289808i	$0.0935914\pi$
$774$		0			0
$775$		−	343.387i		−	0.443080i
$776$		0			0
$777$	−175.233	−	73.7490i	−0.225526	−	0.0949151i
$778$		0			0
$779$	17.0083	−	17.0083i	0.0218335	−	0.0218335i
$780$		0			0
$781$	193.328	−	193.328i	0.247539	−	0.247539i
$782$		0			0
$783$	150.486	+	381.505i	0.192192	+	0.487235i
$784$		0			0
$785$			2279.05i			2.90325i
$786$		0			0
$787$	−279.150	+	279.150i	−0.354702	+	0.354702i	−0.861856	−	0.507154i	$-0.830698\pi$
$787$	−279.150	+	279.150i	−0.354702	+	0.354702i	0.507154	+	0.861856i	$0.330698\pi$
$788$		0			0
$789$	−159.329	−	390.898i	−0.201938	−	0.495435i
$790$		0			0
$791$	13.6788			0.0172931
$792$		0			0
$793$			733.911i			0.925487i
$794$		0			0
$795$	−139.951	+	57.0434i	−0.176038	+	0.0717527i
$796$		0			0
$797$	409.431	+	409.431i	0.513715	+	0.513715i	0.915663	−	0.401947i	$-0.131667\pi$
$797$	409.431	+	409.431i	0.513715	+	0.513715i	−0.401947	+	0.915663i	$0.631667\pi$
$798$		0			0
$799$	−860.842			−1.07740
$800$		0			0
$801$	−507.158	+	495.802i	−0.633156	+	0.618979i
$802$		0			0
$803$	280.570	+	280.570i	0.349402	+	0.349402i
$804$		0			0
$805$	−168.000	−	168.000i	−0.208696	−	0.208696i
$806$		0			0
$807$	−378.244	+	898.737i	−0.468704	+	1.11368i
$808$		0			0
$809$	285.148			0.352470			0.176235	−	0.984348i	$-0.443608\pi$
$809$	285.148			0.352470			0.176235	+	0.984348i	$0.443608\pi$
$810$		0			0
$811$	−819.150	−	819.150i	−1.01005	−	1.01005i	−0.999949	−	0.0101007i	$-0.996785\pi$
$811$	−819.150	−	819.150i	−1.01005	−	1.01005i	−0.0101007	−	0.999949i	$-0.503215\pi$
$812$		0			0
$813$	−259.001	−	635.435i	−0.318575	−	0.781593i
$814$		0			0
$815$		−	2515.62i		−	3.08666i
$816$		0			0
$817$	333.312			0.407971
$818$		0			0
$819$	−195.931	−	2.21840i	−0.239232	−	0.00270867i
$820$		0			0
$821$	−116.499	+	116.499i	−0.141899	+	0.141899i	−0.774488	−	0.632589i	$-0.781992\pi$
$821$	−116.499	+	116.499i	−0.141899	+	0.141899i	0.632589	+	0.774488i	$0.281992\pi$
$822$		0			0
$823$			1551.22i			1.88484i	0.334429	+	0.942421i	$0.391457\pi$
$823$			1551.22i			1.88484i	−0.334429	+	0.942421i	$0.608543\pi$
$824$		0			0
$825$	−422.644	+	1004.24i	−0.512296	+	1.21725i
$826$		0			0
$827$	−139.847	+	139.847i	−0.169102	+	0.169102i	−0.786584	−	0.617483i	$-0.788153\pi$
$827$	−139.847	+	139.847i	−0.169102	+	0.169102i	0.617483	+	0.786584i	$0.288153\pi$
$828$		0			0
$829$	454.593	−	454.593i	0.548364	−	0.548364i	−0.377604	−	0.925967i	$-0.623252\pi$
$829$	454.593	−	454.593i	0.548364	−	0.548364i	0.925967	+	0.377604i	$0.123252\pi$
$830$		0			0
$831$	169.949	−	403.812i	0.204512	−	0.485936i
$832$		0			0
$833$		−	531.701i		−	0.638297i
$834$		0			0
$835$	−1085.40	+	1085.40i	−1.29988	+	1.29988i
$836$		0			0
$837$	157.367	+	68.3372i	0.188014	+	0.0816455i
$838$		0			0
$839$	34.1596			0.0407147			0.0203574	−	0.999793i	$-0.493520\pi$
$839$	34.1596			0.0407147			0.0203574	+	0.999793i	$0.493520\pi$
$840$		0			0
$841$		−	610.284i		−	0.725664i
$842$		0			0
$843$	321.077	+	787.733i	0.380875	+	0.934440i
$844$		0			0
$845$	37.7438	+	37.7438i	0.0446673	+	0.0446673i
$846$		0			0
$847$	−124.804			−0.147348
$848$		0			0
$849$	−38.6353	+	91.8006i	−0.0455069	+	0.108128i
$850$		0			0
$851$	−442.143	−	442.143i	−0.519557	−	0.519557i
$852$		0			0
$853$	514.933	+	514.933i	0.603673	+	0.603673i	0.941285	−	0.337612i	$-0.109619\pi$
$853$	514.933	+	514.933i	0.603673	+	0.603673i	−0.337612	+	0.941285i	$0.609619\pi$
$854$		0			0
$855$	−678.944	−	694.494i	−0.794086	−	0.812274i
$856$		0			0
$857$	−1165.96			−1.36051			−0.680254	−	0.732976i	$-0.738131\pi$
$857$	−1165.96			−1.36051			−0.680254	+	0.732976i	$0.738131\pi$
$858$		0			0
$859$	−246.162	−	246.162i	−0.286568	−	0.286568i	0.549153	−	0.835722i	$-0.314950\pi$
$859$	−246.162	−	246.162i	−0.286568	−	0.286568i	−0.835722	+	0.549153i	$0.814950\pi$
$860$		0			0
$861$	9.06009	−	3.69286i	0.0105228	−	0.00428904i
$862$		0			0
$863$		−	196.851i		−	0.228101i	−0.993475	−	0.114050i	$-0.963617\pi$
$863$		−	196.851i		−	0.228101i	0.993475	−	0.114050i	$-0.0363825\pi$
$864$		0			0
$865$	513.373			0.593494
$866$		0			0
$867$	−177.861	−	436.364i	−0.205145	−	0.503303i
$868$		0			0
$869$	82.6627	−	82.6627i	0.0951239	−	0.0951239i
$870$		0			0
$871$		−	1285.02i		−	1.47534i
$872$		0			0
$873$	249.920	−	244.324i	0.286277	−	0.279867i
$874$		0			0
$875$	−300.454	+	300.454i	−0.343376	+	0.343376i
$876$		0			0
$877$	−1123.93	+	1123.93i	−1.28156	+	1.28156i	−0.341782	+	0.939779i	$0.611031\pi$
$877$	−1123.93	+	1123.93i	−1.28156	+	1.28156i	−0.939779	+	0.341782i	$0.888969\pi$
$878$		0			0
$879$	−1491.47	−	627.704i	−1.69679	−	0.714112i
$880$		0			0
$881$			776.024i			0.880845i	0.897791	+	0.440422i	$0.145171\pi$
$881$			776.024i			0.880845i	−0.897791	+	0.440422i	$0.854829\pi$
$882$		0			0
$883$	157.587	−	157.587i	0.178468	−	0.178468i	−0.612220	−	0.790688i	$-0.709723\pi$
$883$	157.587	−	157.587i	0.178468	−	0.178468i	0.790688	+	0.612220i	$0.209723\pi$
$884$		0			0
$885$	976.945	−	398.199i	1.10389	−	0.449943i
$886$		0			0
$887$	−469.259			−0.529040			−0.264520	−	0.964380i	$-0.585214\pi$
$887$	−469.259			−0.529040			−0.264520	+	0.964380i	$0.585214\pi$
$888$		0			0
$889$		−	322.458i		−	0.362719i
$890$		0			0
$891$	−376.111	−	393.542i	−0.422122	−	0.441685i
$892$		0			0
$893$	−643.274	−	643.274i	−0.720352	−	0.720352i
$894$		0			0
$895$	−1918.80			−2.14391
$896$		0			0
$897$	−593.976	−	249.982i	−0.662181	−	0.278686i
$898$		0			0
$899$	68.2478	+	68.2478i	0.0759152	+	0.0759152i
$900$		0			0
$901$	46.0208	+	46.0208i	0.0510775	+	0.0510775i
$902$		0			0
$903$	124.960	+	52.5909i	0.138383	+	0.0582402i
$904$		0			0
$905$	2094.68			2.31457
$906$		0			0
$907$	684.081	+	684.081i	0.754224	+	0.754224i	0.975265	−	0.221041i	$-0.0709454\pi$
$907$	684.081	+	684.081i	0.754224	+	0.754224i	−0.221041	+	0.975265i	$0.570945\pi$
$908$		0			0
$909$	−5.98498	+	528.598i	−0.00658414	+	0.581516i
$910$		0			0
$911$			1109.61i			1.21802i	0.793164	+	0.609008i	$0.208432\pi$
$911$			1109.61i			1.21802i	−0.793164	+	0.609008i	$0.791568\pi$
$912$		0			0
$913$	714.154			0.782206
$914$		0			0
$915$	−1370.22	+	558.498i	−1.49751	+	0.610381i
$916$		0			0
$917$	233.905	−	233.905i	0.255077	−	0.255077i
$918$		0			0
$919$			740.861i			0.806160i	0.915165	+	0.403080i	$0.132060\pi$
$919$			740.861i			0.806160i	−0.915165	+	0.403080i	$0.867940\pi$
$920$		0			0
$921$	−817.496	−	344.052i	−0.887617	−	0.373564i
$922$		0			0
$923$	380.551	−	380.551i	0.412298	−	0.412298i
$924$		0			0
$925$	−1471.46	+	1471.46i	−1.59076	+	1.59076i
$926$		0			0
$927$	621.674	+	635.913i	0.670630	+	0.685991i
$928$		0			0
$929$		−	621.861i		−	0.669388i	−0.942327	−	0.334694i	$-0.891367\pi$
$929$		−	621.861i		−	0.669388i	0.942327	−	0.334694i	$-0.108633\pi$
$930$		0			0
$931$	397.320	−	397.320i	0.426767	−	0.426767i
$932$		0			0
$933$	125.889	+	308.856i	0.134929	+	0.331036i
$934$		0			0
$935$	686.274			0.733983
$936$		0			0
$937$			1036.08i			1.10574i	0.833267	+	0.552871i	$0.186468\pi$
$937$			1036.08i			1.10574i	−0.833267	+	0.552871i	$0.813532\pi$
$938$		0			0
$939$	−784.199	+	319.637i	−0.835143	+	0.340402i
$940$		0			0
$941$	904.283	+	904.283i	0.960980	+	0.960980i	0.999267	−	0.0382864i	$-0.0121899\pi$
$941$	904.283	+	904.283i	0.960980	+	0.960980i	−0.0382864	+	0.999267i	$0.512190\pi$
$942$		0			0
$943$	32.1778			0.0341228
$944$		0			0
$945$	−144.959	−	367.494i	−0.153396	−	0.388883i
$946$		0			0
$947$	895.943	+	895.943i	0.946085	+	0.946085i	0.998619	−	0.0525337i	$-0.0167297\pi$
$947$	895.943	+	895.943i	0.946085	+	0.946085i	−0.0525337	+	0.998619i	$0.516730\pi$
$948$		0			0
$949$	552.280	+	552.280i	0.581960	+	0.581960i
$950$		0			0
$951$	340.642	−	809.393i	0.358194	−	0.851097i
$952$		0			0
$953$	1165.12			1.22259			0.611293	−	0.791405i	$-0.290650\pi$
$953$	1165.12			1.22259			0.611293	+	0.791405i	$0.290650\pi$
$954$		0			0
$955$	−90.1699	−	90.1699i	−0.0944188	−	0.0944188i
$956$		0			0
$957$	−115.591	−	283.591i	−0.120784	−	0.296333i
$958$		0			0
$959$		−	83.0852i		−	0.0866373i
$960$		0			0
$961$	−920.624			−0.957985
$962$		0			0
$963$	−14.2441	+	1258.05i	−0.0147914	+	1.30638i
$964$		0			0
$965$	−1303.65	+	1303.65i	−1.35093	+	1.35093i
$966$		0			0
$967$		−	453.248i		−	0.468716i	−0.972150	−	0.234358i	$-0.924701\pi$
$967$		−	453.248i		−	0.468716i	0.972150	−	0.234358i	$-0.0752988\pi$
$968$		0			0
$969$	−162.245	+	385.506i	−0.167435	+	0.397839i
$970$		0			0
$971$	678.155	−	678.155i	0.698408	−	0.698408i	−0.265659	−	0.964067i	$-0.585589\pi$
$971$	678.155	−	678.155i	0.698408	−	0.698408i	0.964067	+	0.265659i	$0.0855894\pi$
$972$		0			0
$973$	282.620	−	282.620i	0.290462	−	0.290462i
$974$		0			0
$975$	−831.941	+	1976.76i	−0.853273	+	2.02744i
$976$		0			0
$977$		−	544.399i		−	0.557215i	−0.960405	−	0.278607i	$-0.910127\pi$
$977$		−	544.399i		−	0.557215i	0.960405	−	0.278607i	$-0.0898728\pi$
$978$		0			0
$979$	374.494	−	374.494i	0.382527	−	0.382527i
$980$		0			0
$981$	9.92169	−	876.290i	0.0101138	−	0.893262i
$982$		0			0
$983$	−514.630			−0.523530			−0.261765	−	0.965132i	$-0.584305\pi$
$983$	−514.630			−0.523530			−0.261765	+	0.965132i	$0.584305\pi$
$984$		0			0
$985$			1222.86i			1.24148i
$986$		0			0
$987$	−139.669	−	342.663i	−0.141508	−	0.347177i
$988$		0			0
$989$	315.295	+	315.295i	0.318802	+	0.318802i
$990$		0			0
$991$	939.282			0.947813			0.473906	−	0.880575i	$-0.342844\pi$
$991$	939.282			0.947813			0.473906	+	0.880575i	$0.342844\pi$
$992$		0			0
$993$	−209.720	+	498.312i	−0.211199	+	0.501825i
$994$		0			0
$995$	520.318	+	520.318i	0.522932	+	0.522932i
$996$		0			0
$997$	−165.885	−	165.885i	−0.166384	−	0.166384i	0.619004	−	0.785388i	$-0.287537\pi$
$997$	−165.885	−	165.885i	−0.166384	−	0.166384i	−0.785388	+	0.619004i	$0.787537\pi$
$998$		0			0
$999$	−381.505	−	967.172i	−0.381887	−	0.968141i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.3.i.a.353.2		8
3.2	odd	2	inner	384.3.i.a.353.4		8
4.3	odd	2		384.3.i.b.353.3		8
8.3	odd	2		192.3.i.a.113.2		8
8.5	even	2		48.3.i.a.5.3	yes	8
12.11	even	2		384.3.i.b.353.1		8
16.3	odd	4		384.3.i.b.161.1		8
16.5	even	4		48.3.i.a.29.2	yes	8
16.11	odd	4		192.3.i.a.17.4		8
16.13	even	4	inner	384.3.i.a.161.4		8
24.5	odd	2		48.3.i.a.5.2	✓	8
24.11	even	2		192.3.i.a.113.4		8
48.5	odd	4		48.3.i.a.29.3	yes	8
48.11	even	4		192.3.i.a.17.2		8
48.29	odd	4	inner	384.3.i.a.161.2		8
48.35	even	4		384.3.i.b.161.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.i.a.5.2	✓	8	24.5	odd	2
48.3.i.a.5.3	yes	8	8.5	even	2
48.3.i.a.29.2	yes	8	16.5	even	4
48.3.i.a.29.3	yes	8	48.5	odd	4
192.3.i.a.17.2		8	48.11	even	4
192.3.i.a.17.4		8	16.11	odd	4
192.3.i.a.113.2		8	8.3	odd	2
192.3.i.a.113.4		8	24.11	even	2
384.3.i.a.161.2		8	48.29	odd	4	inner
384.3.i.a.161.4		8	16.13	even	4	inner
384.3.i.a.353.2		8	1.1	even	1	trivial
384.3.i.a.353.4		8	3.2	odd	2	inner
384.3.i.b.161.1		8	16.3	odd	4
384.3.i.b.161.3		8	48.35	even	4
384.3.i.b.353.1		8	12.11	even	2
384.3.i.b.353.3		8	4.3	odd	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	384.i (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.13234 - 2.77809i) q^{3} +(-6.28651 + 6.28651i) q^{5} +1.64575i q^{7} +(-6.43560 + 6.29150i) q^{9} +O(q^{10})\)	\(q+(-1.13234 - 2.77809i) q^{3} +(-6.28651 + 6.28651i) q^{5} +1.64575i q^{7} +(-6.43560 + 6.29150i) q^{9} +(4.75216 - 4.75216i) q^{11} +(9.35425 - 9.35425i) q^{13} +(24.5830 + 10.3460i) q^{15} -11.4859i q^{17} +(8.58301 - 8.58301i) q^{19} +(4.57205 - 1.86355i) q^{21} +16.2381 q^{23} -54.0405i q^{25} +(24.7657 + 10.7546i) q^{27} +(10.7405 + 10.7405i) q^{29} +6.35425 q^{31} +(-18.5830 - 7.82087i) q^{33} +(-10.3460 - 10.3460i) q^{35} +(-27.2288 - 27.2288i) q^{37} +(-36.5792 - 15.3948i) q^{39} +1.98162 q^{41} +(19.4170 + 19.4170i) q^{43} +(0.905893 - 80.0091i) q^{45} -74.9474i q^{47} +46.2915 q^{49} +(-31.9090 + 13.0060i) q^{51} +(-4.00671 + 4.00671i) q^{53} +59.7490i q^{55} +(-33.5633 - 14.1255i) q^{57} +(27.9694 - 27.9694i) q^{59} +(-39.2288 + 39.2288i) q^{61} +(-10.3542 - 10.5914i) q^{63} +117.611i q^{65} +(68.6863 - 68.6863i) q^{67} +(-18.3871 - 45.1110i) q^{69} +40.6822 q^{71} +59.0405i q^{73} +(-150.130 + 61.1923i) q^{75} +(7.82087 + 7.82087i) q^{77} +17.3948 q^{79} +(1.83399 - 80.9792i) q^{81} +(75.1400 + 75.1400i) q^{83} +(72.2065 + 72.2065i) q^{85} +(17.6762 - 42.0000i) q^{87} +78.8051 q^{89} +(15.3948 + 15.3948i) q^{91} +(-7.19518 - 17.6527i) q^{93} +107.914i q^{95} -38.8340 q^{97} +(-0.684791 + 60.4812i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3}+O(q^{10}) \) 8 * q - 4 * q^3	\( 8 q - 4 q^{3} + 96 q^{13} + 112 q^{15} - 16 q^{19} + 32 q^{21} + 68 q^{27} + 72 q^{31} - 64 q^{33} - 112 q^{37} + 240 q^{43} + 112 q^{45} + 328 q^{49} + 32 q^{51} - 208 q^{61} - 104 q^{63} + 232 q^{67} - 324 q^{75} - 136 q^{79} + 184 q^{81} + 112 q^{85} - 152 q^{91} - 64 q^{93} - 480 q^{97} - 160 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 + 96 * q^13 + 112 * q^15 - 16 * q^19 + 32 * q^21 + 68 * q^27 + 72 * q^31 - 64 * q^33 - 112 * q^37 + 240 * q^43 + 112 * q^45 + 328 * q^49 + 32 * q^51 - 208 * q^61 - 104 * q^63 + 232 * q^67 - 324 * q^75 - 136 * q^79 + 184 * q^81 + 112 * q^85 - 152 * q^91 - 64 * q^93 - 480 * q^97 - 160 * q^99

Introduction

L-functions

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