LMFDB - Embedded newform 384.3.i.b.161.1

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			161.1
Root			$0.767178 - 1.18804i$ of defining polynomial
Character	$\chi$	$=$	384.161
Dual form			384.3.i.b.353.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.77809 + 1.13234i) q^{3} +(6.28651 + 6.28651i) q^{5} +1.64575i q^{7} +(6.43560 - 6.29150i) q^{9} +O(q^{10})$	\(q+(-2.77809 + 1.13234i) q^{3} +(6.28651 + 6.28651i) q^{5} +1.64575i q^{7} +(6.43560 - 6.29150i) q^{9} +(4.75216 + 4.75216i) q^{11} +(9.35425 + 9.35425i) q^{13} +(-24.5830 - 10.3460i) q^{15} -11.4859i q^{17} +(-8.58301 - 8.58301i) q^{19} +(-1.86355 - 4.57205i) q^{21} +16.2381 q^{23} +54.0405i q^{25} +(-10.7546 + 24.7657i) q^{27} +(-10.7405 + 10.7405i) q^{29} -6.35425 q^{31} +(-18.5830 - 7.82087i) q^{33} +(-10.3460 + 10.3460i) q^{35} +(-27.2288 + 27.2288i) q^{37} +(-36.5792 - 15.3948i) q^{39} -1.98162 q^{41} +(-19.4170 + 19.4170i) q^{43} +(80.0091 + 0.905893i) q^{45} +74.9474i q^{47} +46.2915 q^{49} +(13.0060 + 31.9090i) q^{51} +(4.00671 + 4.00671i) q^{53} +59.7490i q^{55} +(33.5633 + 14.1255i) q^{57} +(27.9694 + 27.9694i) q^{59} +(-39.2288 - 39.2288i) q^{61} +(10.3542 + 10.5914i) q^{63} +117.611i q^{65} +(-68.6863 - 68.6863i) q^{67} +(-45.1110 + 18.3871i) q^{69} +40.6822 q^{71} -59.0405i q^{73} +(-61.1923 - 150.130i) q^{75} +(-7.82087 + 7.82087i) q^{77} -17.3948 q^{79} +(1.83399 - 80.9792i) q^{81} +(75.1400 - 75.1400i) q^{83} +(72.2065 - 72.2065i) q^{85} +(17.6762 - 42.0000i) q^{87} -78.8051 q^{89} +(-15.3948 + 15.3948i) q^{91} +(17.6527 - 7.19518i) q^{93} -107.914i q^{95} -38.8340 q^{97} +(60.4812 + 0.684791i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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
$3$	−2.77809	+	1.13234i	−0.926031	+	0.377447i
$3$	−2.77809	+	1.13234i	−0.926031	+	0.377447i
$4$		0			0
$5$	6.28651	+	6.28651i	1.25730	+	1.25730i	0.952376	+	0.304927i	$0.0986321\pi$
$5$	6.28651	+	6.28651i	1.25730	+	1.25730i	0.304927	+	0.952376i	$0.401368\pi$
$6$		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	0.889313	−	0.457299i	$-0.151183\pi$
$11$	4.75216	+	4.75216i	0.432014	+	0.432014i	−0.457299	+	0.889313i	$0.651183\pi$
$12$		0			0
$13$	9.35425	+	9.35425i	0.719558	+	0.719558i	0.968515	−	0.248957i	$-0.0800878\pi$
$13$	9.35425	+	9.35425i	0.719558	+	0.719558i	−0.248957	+	0.968515i	$0.580088\pi$
$14$		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	$-0.353490\pi$
$19$	−8.58301	−	8.58301i	−0.451737	−	0.451737i	−0.895931	+	0.444194i	$0.853490\pi$
$20$		0			0
$21$	−1.86355	−	4.57205i	−0.0887406	−	0.217717i
$22$		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
$27$	−10.7546	+	24.7657i	−0.398318	+	0.917248i
$28$		0			0
$29$	−10.7405	+	10.7405i	−0.370362	+	0.370362i	−0.867609	−	0.497247i	$-0.834344\pi$
$29$	−10.7405	+	10.7405i	−0.370362	+	0.370362i	0.497247	+	0.867609i	$0.334344\pi$
$30$		0			0
$31$	−6.35425			−0.204976			−0.102488	−	0.994734i	$-0.532680\pi$
$31$	−6.35425			−0.204976			−0.102488	+	0.994734i	$0.532680\pi$
$32$		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	−0.971784	−	0.235872i	$-0.924205\pi$
$37$	−27.2288	+	27.2288i	−0.735912	+	0.735912i	0.235872	+	0.971784i	$0.424205\pi$
$38$		0			0
$39$	−36.5792	−	15.3948i	−0.937928	−	0.394738i
$40$		0			0
$41$	−1.98162			−0.0483323			−0.0241662	−	0.999708i	$-0.507693\pi$
$41$	−1.98162			−0.0483323			−0.0241662	+	0.999708i	$0.507693\pi$
$42$		0			0
$43$	−19.4170	+	19.4170i	−0.451558	+	0.451558i	−0.895871	−	0.444313i	$-0.853448\pi$
$43$	−19.4170	+	19.4170i	−0.451558	+	0.451558i	0.444313	+	0.895871i	$0.353448\pi$
$44$		0			0
$45$	80.0091	+	0.905893i	1.77798	+	0.0201310i
$46$		0			0
$47$			74.9474i			1.59463i	0.603566	+	0.797313i	$0.293746\pi$
$47$			74.9474i			1.59463i	−0.603566	+	0.797313i	$0.706254\pi$
$48$		0			0
$49$	46.2915			0.944725
$50$		0			0
$51$	13.0060	+	31.9090i	0.255020	+	0.625667i
$52$		0			0
$53$	4.00671	+	4.00671i	0.0755983	+	0.0755983i	0.743895	−	0.668297i	$-0.232976\pi$
$53$	4.00671	+	4.00671i	0.0755983	+	0.0755983i	−0.668297	+	0.743895i	$0.732976\pi$
$54$		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	0.903225	−	0.429167i	$-0.141193\pi$
$59$	27.9694	+	27.9694i	0.474058	+	0.474058i	−0.429167	+	0.903225i	$0.641193\pi$
$60$		0			0
$61$	−39.2288	−	39.2288i	−0.643094	−	0.643094i	0.308221	−	0.951315i	$-0.400267\pi$
$61$	−39.2288	−	39.2288i	−0.643094	−	0.643094i	−0.951315	+	0.308221i	$0.900267\pi$
$62$		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	−0.999675	−	0.0254932i	$-0.991884\pi$
$67$	−68.6863	−	68.6863i	−1.02517	−	1.02517i	−0.0254932	−	0.999675i	$-0.508116\pi$
$68$		0			0
$69$	−45.1110	+	18.3871i	−0.653782	+	0.266479i
$70$		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	$-0.867485\pi$
$73$		−	59.0405i		−	0.808774i	0.914588	−	0.404387i	$-0.132515\pi$
$74$		0			0
$75$	−61.1923	−	150.130i	−0.815898	−	2.00173i
$76$		0			0
$77$	−7.82087	+	7.82087i	−0.101570	+	0.101570i
$78$		0			0
$79$	−17.3948			−0.220187			−0.110093	−	0.993921i	$-0.535115\pi$
$79$	−17.3948			−0.220187			−0.110093	+	0.993921i	$0.535115\pi$
$80$		0			0
$81$	1.83399	−	80.9792i	0.0226418	−	0.999744i
$82$		0			0
$83$	75.1400	−	75.1400i	0.905301	−	0.905301i	−0.0905874	−	0.995889i	$-0.528874\pi$
$83$	75.1400	−	75.1400i	0.905301	−	0.905301i	0.995889	+	0.0905874i	$0.0288745\pi$
$84$		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	$-0.645988\pi$
$89$	−78.8051			−0.885450			−0.442725	+	0.896657i	$0.645988\pi$
$90$		0			0
$91$	−15.3948	+	15.3948i	−0.169173	+	0.169173i
$92$		0			0
$93$	17.6527	−	7.19518i	0.189814	−	0.0773675i
$94$		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
$99$	60.4812	+	0.684791i	0.610921	+	0.00691708i
$100$		0			0
$101$	−41.5332	−	41.5332i	−0.411220	−	0.411220i	0.470943	−	0.882164i	$-0.343914\pi$
$101$	−41.5332	−	41.5332i	−0.411220	−	0.411220i	−0.882164	+	0.470943i	$0.843914\pi$
$102$		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	0.997296	−	0.0734837i	$-0.0234117\pi$
$107$	98.8480	+	98.8480i	0.923813	+	0.923813i	−0.0734837	+	0.997296i	$0.523412\pi$
$108$		0			0
$109$	−68.8523	−	68.8523i	−0.631672	−	0.631672i	0.316815	−	0.948487i	$-0.397387\pi$
$109$	−68.8523	−	68.8523i	−0.631672	−	0.631672i	−0.948487	+	0.316815i	$0.897387\pi$
$110$		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
$117$	119.053	+	1.34796i	1.01754	+	0.0115210i
$118$		0			0
$119$	18.9030			0.158849
$120$		0			0
$121$		−	75.8340i		−	0.626727i
$122$		0			0
$123$	5.50514	−	2.24388i	0.0447572	−	0.0182429i
$124$		0			0
$125$	−182.564	+	182.564i	−1.46051	+	1.46051i
$126$		0			0
$127$	195.933			1.54278			0.771391	−	0.636361i	$-0.219561\pi$
$127$	195.933			1.54278			0.771391	+	0.636361i	$0.219561\pi$
$128$		0			0
$129$	31.9555	−	75.9289i	0.247717	−	0.588596i
$130$		0			0
$131$	−142.127	+	142.127i	−1.08494	+	1.08494i	−0.0888967	+	0.996041i	$0.528334\pi$
$131$	−142.127	+	142.127i	−1.08494	+	1.08494i	−0.996041	+	0.0888967i	$0.971666\pi$
$132$		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	$-0.441014\pi$
$137$	50.4847			0.368501			0.184251	+	0.982879i	$0.441014\pi$
$138$		0			0
$139$	171.727	−	171.727i	1.23544	−	1.23544i	0.273601	−	0.961843i	$-0.411785\pi$
$139$	171.727	−	171.727i	1.23544	−	1.23544i	0.961843	−	0.273601i	$-0.0882149\pi$
$140$		0			0
$141$	−84.8661	−	208.211i	−0.601887	−	1.47667i
$142$		0			0
$143$			88.9057i			0.621718i
$144$		0			0
$145$	−135.041			−0.931314
$146$		0			0
$147$	−128.602	+	52.4178i	−0.874844	+	0.356584i
$148$		0			0
$149$	84.4952	+	84.4952i	0.567082	+	0.567082i	0.931310	−	0.364228i	$-0.118667\pi$
$149$	84.4952	+	84.4952i	0.567082	+	0.567082i	−0.364228	+	0.931310i	$0.618667\pi$
$150$		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	0.985628	+	0.168928i	$0.0540305\pi$
$157$	181.265	+	181.265i	1.15456	+	1.15456i	0.168928	+	0.985628i	$0.445970\pi$
$158$		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	0.964910	+	0.262581i	$0.0845737\pi$
$163$	200.081	+	200.081i	1.22749	+	1.22749i	0.262581	+	0.964910i	$0.415426\pi$
$164$		0			0
$165$	−67.6563	−	165.988i	−0.410038	−	1.00599i
$166$		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
$171$	−109.237	−	1.23682i	−0.638812	−	0.00723287i
$172$		0			0
$173$	40.8313	−	40.8313i	0.236019	−	0.236019i	−0.579181	−	0.815199i	$-0.696627\pi$
$173$	40.8313	−	40.8313i	0.236019	−	0.236019i	0.815199	+	0.579181i	$0.196627\pi$
$174$		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	−0.137866	−	0.990451i	$-0.544024\pi$
$179$	152.613	−	152.613i	0.852584	−	0.852584i	0.990451	+	0.137866i	$0.0440245\pi$
$180$		0			0
$181$	−166.601	+	166.601i	−0.920449	+	0.920449i	−0.997061	−	0.0766118i	$-0.975590\pi$
$181$	−166.601	+	166.601i	−0.920449	+	0.920449i	0.0766118	+	0.997061i	$0.475590\pi$
$182$		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
$189$	−40.7582	−	17.6994i	−0.215652	−	0.0936474i
$190$		0			0
$191$		−	14.3434i		−	0.0750963i	−0.999295	−	0.0375482i	$-0.988045\pi$
$191$		−	14.3434i		−	0.0750963i	0.999295	−	0.0375482i	$-0.0119548\pi$
$192$		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
$195$	−133.176	−	326.735i	−0.682954	−	1.67556i
$196$		0			0
$197$	−97.2608	−	97.2608i	−0.493710	−	0.493710i	0.415763	−	0.909473i	$-0.363514\pi$
$197$	−97.2608	−	97.2608i	−0.493710	−	0.493710i	−0.909473	+	0.415763i	$0.863514\pi$
$198$		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	$-0.486184\pi$
$211$	−201.646	−	201.646i	−0.955667	−	0.955667i	−0.999058	+	0.0433911i	$0.986184\pi$
$212$		0			0
$213$	−113.019	+	46.0661i	−0.530605	+	0.216273i
$214$		0			0
$215$	−244.130			−1.13549
$216$		0			0
$217$		−	10.4575i		−	0.0481913i
$218$		0			0
$219$	66.8541	+	164.020i	0.305270	+	0.748950i
$220$		0			0
$221$	107.442	−	107.442i	0.486164	−	0.486164i
$222$		0			0
$223$	−233.261			−1.04602			−0.523008	−	0.852328i	$-0.675190\pi$
$223$	−233.261			−1.04602			−0.523008	+	0.852328i	$0.675190\pi$
$224$		0			0
$225$	339.996	+	347.783i	1.51109	+	1.54570i
$226$		0			0
$227$	94.3599	−	94.3599i	0.415682	−	0.415682i	−0.468030	−	0.883712i	$-0.655036\pi$
$227$	94.3599	−	94.3599i	0.415682	−	0.415682i	0.883712	+	0.468030i	$0.155036\pi$
$228$		0			0
$229$	138.063	−	138.063i	0.602894	−	0.602894i	−0.338185	−	0.941080i	$-0.609813\pi$
$229$	138.063	−	138.063i	0.602894	−	0.602894i	0.941080	+	0.338185i	$0.109813\pi$
$230$		0			0
$231$	12.8712	−	30.5830i	0.0557195	−	0.132394i
$232$		0			0
$233$	396.796			1.70299			0.851493	−	0.524366i	$-0.175697\pi$
$233$	396.796			1.70299			0.851493	+	0.524366i	$0.175697\pi$
$234$		0			0
$235$	−471.158	+	471.158i	−2.00493	+	2.00493i
$236$		0			0
$237$	48.3243	−	19.6968i	0.203900	−	0.0831090i
$238$		0			0
$239$			284.813i			1.19168i	0.803102	+	0.595842i	$0.203182\pi$
$239$			284.813i			1.19168i	−0.803102	+	0.595842i	$0.796818\pi$
$240$		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
$243$	86.6012	+	227.045i	0.356383	+	0.934340i
$244$		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	0.330485	−	0.943811i	$-0.392788\pi$
$251$	−153.945	−	153.945i	−0.613327	−	0.613327i	−0.943811	+	0.330485i	$0.892788\pi$
$252$		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
$261$	−1.54772	+	136.695i	−0.00592995	+	0.523737i
$262$		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
$267$	218.928	−	89.2343i	0.819954	−	0.334211i
$268$		0			0
$269$	229.830	−	229.830i	0.854388	−	0.854388i	−0.136282	−	0.990670i	$-0.543515\pi$
$269$	229.830	−	229.830i	0.854388	−	0.854388i	0.990670	+	0.136282i	$0.0435152\pi$
$270$		0			0
$271$	−228.731			−0.844025			−0.422012	−	0.906590i	$-0.638676\pi$
$271$	−228.731			−0.844025			−0.422012	+	0.906590i	$0.638676\pi$
$272$		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	−0.495697	−	0.868496i	$-0.665087\pi$
$277$	103.265	−	103.265i	0.372799	−	0.372799i	0.868496	+	0.495697i	$0.165087\pi$
$278$		0			0
$279$	−40.8934	+	39.9778i	−0.146571	+	0.143290i
$280$		0			0
$281$	283.552			1.00908			0.504540	−	0.863388i	$-0.331662\pi$
$281$	283.552			1.00908			0.504540	+	0.863388i	$0.331662\pi$
$282$		0			0
$283$	23.4758	−	23.4758i	0.0829534	−	0.0829534i	−0.664413	−	0.747366i	$-0.731318\pi$
$283$	23.4758	−	23.4758i	0.0829534	−	0.0829534i	0.747366	+	0.664413i	$0.231318\pi$
$284$		0			0
$285$	122.196	+	299.796i	0.428758	+	1.05192i
$286$		0			0
$287$		−	3.26126i		−	0.0113633i
$288$		0			0
$289$	157.073			0.543506
$290$		0			0
$291$	107.884	−	43.9734i	0.370737	−	0.151111i
$292$		0			0
$293$	−381.409	−	381.409i	−1.30174	−	1.30174i	−0.927220	−	0.374516i	$-0.877809\pi$
$293$	−381.409	−	381.409i	−1.30174	−	1.30174i	−0.374516	−	0.927220i	$-0.622191\pi$
$294$		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	$-0.409912\pi$
$307$	−209.055	−	209.055i	−0.680960	−	0.680960i	−0.960217	+	0.279256i	$0.909912\pi$
$308$		0			0
$309$	111.889	+	274.508i	0.362099	+	0.888376i
$310$		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	$0.148906\pi$
$313$			282.280i			0.901852i	−0.892561	+	0.450926i	$0.851094\pi$
$314$		0			0
$315$	−1.49088	+	131.675i	−0.00473294	+	0.418016i
$316$		0			0
$317$	−206.983	+	206.983i	−0.652943	+	0.652943i	−0.953701	−	0.300758i	$-0.902760\pi$
$317$	−206.983	+	206.983i	−0.652943	+	0.652943i	0.300758	+	0.953701i	$0.402760\pi$
$318$		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	$-0.662239\pi$
$331$	127.431	−	127.431i	0.384989	−	0.384989i	0.872896	+	0.487907i	$0.162239\pi$
$332$		0			0
$333$	−3.92369	+	346.543i	−0.0117829	+	1.04067i
$334$		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
$339$	9.41157	+	23.0904i	0.0277627	+	0.0681133i
$340$		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	0.624902	−	0.780703i	$-0.285139\pi$
$347$	−54.0628	−	54.0628i	−0.155801	−	0.155801i	−0.780703	+	0.624902i	$0.785139\pi$
$348$		0			0
$349$	−0.107201	−	0.107201i	−0.000307168	−	0.000307168i	0.706953	−	0.707260i	$-0.250069\pi$
$349$	−0.107201	−	0.107201i	−0.000307168	−	0.000307168i	−0.707260	+	0.706953i	$0.750069\pi$
$350$		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
$357$	−52.5143	+	21.4047i	−0.147099	+	0.0599570i
$358$		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
$363$	85.8700	+	210.674i	0.236556	+	0.580369i
$364$		0			0
$365$	371.159	−	371.159i	1.01687	−	1.01687i
$366$		0			0
$367$	246.678			0.672148			0.336074	−	0.941836i	$-0.390901\pi$
$367$	246.678			0.672148			0.336074	+	0.941836i	$0.390901\pi$
$368$		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	−0.0606816	−	0.998157i	$-0.519327\pi$
$373$	349.678	−	349.678i	0.937476	−	0.937476i	0.998157	+	0.0606816i	$0.0193274\pi$
$374$		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	$-0.605088\pi$
$379$	235.668	−	235.668i	0.621815	−	0.621815i	0.945995	+	0.324180i	$0.105088\pi$
$380$		0			0
$381$	−544.321	+	221.864i	−1.42866	+	0.582319i
$382$		0			0
$383$			64.2130i			0.167658i	0.996480	+	0.0838290i	$0.0267149\pi$
$383$			64.2130i			0.167658i	−0.996480	+	0.0838290i	$0.973285\pi$
$384$		0			0
$385$	−98.3320			−0.255408
$386$		0			0
$387$	−2.79801	+	247.122i	−0.00723000	+	0.638559i
$388$		0			0
$389$	273.321	+	273.321i	0.702624	+	0.702624i	0.964973	−	0.262349i	$-0.0844973\pi$
$389$	273.321	+	273.321i	0.702624	+	0.702624i	−0.262349	+	0.964973i	$0.584497\pi$
$390$		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	0.505786	−	0.862659i	$-0.331202\pi$
$397$	−141.678	−	141.678i	−0.356873	−	0.356873i	−0.862659	+	0.505786i	$0.831202\pi$
$398$		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
$405$	520.607	−	497.548i	1.28545	−	1.22851i
$406$		0			0
$407$	−258.791			−0.635849
$408$		0			0
$409$			420.826i			1.02891i	0.857516	+	0.514457i	$0.172007\pi$
$409$			420.826i			1.02891i	−0.857516	+	0.514457i	$0.827993\pi$
$410$		0			0
$411$	−140.251	+	57.1659i	−0.341244	+	0.139090i
$412$		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	−0.448742	−	0.893661i	$-0.648128\pi$
$419$	186.421	−	186.421i	0.444919	−	0.444919i	0.893661	+	0.448742i	$0.148128\pi$
$420$		0			0
$421$	186.889	−	186.889i	0.443917	−	0.443917i	−0.449409	−	0.893326i	$-0.648366\pi$
$421$	186.889	−	186.889i	0.443917	−	0.443917i	0.893326	+	0.449409i	$0.148366\pi$
$422$		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
$429$	−100.672	−	246.988i	−0.234666	−	0.575731i
$430$		0			0
$431$			128.395i			0.297901i	0.988845	+	0.148950i	$0.0475895\pi$
$431$			128.395i			0.297901i	−0.988845	+	0.148950i	$0.952411\pi$
$432$		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
$435$	375.155	−	152.912i	0.862426	−	0.351522i
$436$		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	0.264253	−	0.964453i	$-0.414875\pi$
$443$	−310.189	−	310.189i	−0.700200	−	0.700200i	−0.964453	+	0.264253i	$0.914875\pi$
$444$		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
$453$	−34.0872	−	83.6297i	−0.0752477	−	0.184613i
$454$		0			0
$455$	−193.559			−0.425404
$456$		0			0
$457$		−	289.579i		−	0.633652i	−0.948484	−	0.316826i	$-0.897383\pi$
$457$		−	289.579i		−	0.633652i	0.948484	−	0.316826i	$-0.102617\pi$
$458$		0			0
$459$	284.457	+	123.526i	0.619732	+	0.269121i
$460$		0			0
$461$	160.511	−	160.511i	0.348180	−	0.348180i	−0.511251	−	0.859431i	$-0.670818\pi$
$461$	160.511	−	160.511i	0.348180	−	0.348180i	0.859431	+	0.511251i	$0.170818\pi$
$462$		0			0
$463$	197.573			0.426723			0.213361	−	0.976973i	$-0.431559\pi$
$463$	197.573			0.426723			0.213361	+	0.976973i	$0.431559\pi$
$464$		0			0
$465$	156.207	+	65.7413i	0.335928	+	0.141379i
$466$		0			0
$467$	−52.7645	+	52.7645i	−0.112986	+	0.112986i	−0.761339	−	0.648353i	$-0.775458\pi$
$467$	−52.7645	+	52.7645i	−0.112986	+	0.112986i	0.648353	+	0.761339i	$0.275458\pi$
$468$		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
$477$	50.9938	+	0.577371i	0.106905	+	0.00121042i
$478$		0			0
$479$		−	175.985i		−	0.367401i	−0.982982	−	0.183700i	$-0.941192\pi$
$479$		−	175.985i		−	0.367401i	0.982982	−	0.183700i	$-0.0588076\pi$
$480$		0			0
$481$	−509.409			−1.05906
$482$		0			0
$483$	−30.2606	−	74.2414i	−0.0626513	−	0.153709i
$484$		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	−0.966471	−	0.256775i	$-0.917340\pi$
$491$	−600.614	−	600.614i	−1.22325	−	1.22325i	−0.256775	−	0.966471i	$-0.582660\pi$
$492$		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	$-0.273300\pi$
$499$	−51.6092	−	51.6092i	−0.103425	−	0.103425i	−0.756926	+	0.653501i	$0.773300\pi$
$500$		0			0
$501$	−479.653	+	195.505i	−0.957391	+	0.390230i
$502$		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
$507$	−6.79851	−	16.6795i	−0.0134093	−	0.0328984i
$508$		0			0
$509$	−128.457	+	128.457i	−0.252372	+	0.252372i	−0.821942	−	0.569570i	$-0.807110\pi$
$509$	−128.457	+	128.457i	−0.252372	+	0.252372i	0.569570	+	0.821942i	$0.307110\pi$
$510$		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	$-0.724856\pi$
$521$	−676.366			−1.29821			−0.649103	+	0.760700i	$0.724856\pi$
$522$		0			0
$523$	−600.494	+	600.494i	−1.14817	+	1.14817i	−0.161260	+	0.986912i	$0.551556\pi$
$523$	−600.494	+	600.494i	−1.14817	+	1.14817i	−0.986912	+	0.161260i	$0.948444\pi$
$524$		0			0
$525$	247.076	−	100.707i	0.470621	−	0.191824i
$526$		0			0
$527$			72.9845i			0.138491i
$528$		0			0
$529$	−265.324			−0.501558
$530$		0			0
$531$	355.970	+	4.03042i	0.670376	+	0.00759025i
$532$		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	0.665779	−	0.746149i	$-0.268099\pi$
$541$	−43.4797	−	43.4797i	−0.0803692	−	0.0803692i	−0.746149	+	0.665779i	$0.768099\pi$
$542$		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	$-0.301869\pi$
$547$	−125.498	−	125.498i	−0.229430	−	0.229430i	−0.812454	+	0.583025i	$0.801869\pi$
$548$		0			0
$549$	−499.269	−	5.65291i	−0.909414	−	0.0102967i
$550$		0			0
$551$	184.371			0.334612
$552$		0			0
$553$		−	28.6275i		−	0.0517676i
$554$		0			0
$555$	951.074	−	387.655i	1.71365	−	0.698477i
$556$		0			0
$557$	−184.272	+	184.272i	−0.330829	+	0.330829i	−0.852901	−	0.522072i	$-0.825159\pi$
$557$	−184.272	+	184.272i	−0.330829	+	0.330829i	0.522072	+	0.852901i	$0.325159\pi$
$558$		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	−0.997694	−	0.0678736i	$-0.978379\pi$
$563$	−523.489	+	523.489i	−0.929820	+	0.929820i	0.0678736	+	0.997694i	$0.478379\pi$
$564$		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	$-0.485276\pi$
$569$	52.6214			0.0924805			0.0462403	+	0.998930i	$0.485276\pi$
$570$		0			0
$571$	−114.561	+	114.561i	−0.200632	+	0.200632i	−0.800271	−	0.599639i	$-0.795311\pi$
$571$	−114.561	+	114.561i	−0.200632	+	0.200632i	0.599639	+	0.800271i	$0.295311\pi$
$572$		0			0
$573$	16.2416	+	39.8473i	0.0283449	+	0.0695415i
$574$		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
$579$	−576.100	+	234.817i	−0.994992	+	0.405555i
$580$		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	0.602081	−	0.798435i	$-0.294338\pi$
$587$	−115.260	−	115.260i	−0.196354	−	0.196354i	−0.798435	+	0.602081i	$0.794338\pi$
$588$		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
$597$	93.7209	+	229.935i	0.156986	+	0.385151i
$598$		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	$-0.977263\pi$
$601$		−	85.7856i		−	0.142738i	0.997450	−	0.0713690i	$-0.0227368\pi$
$602$		0			0
$603$	−874.177	−	9.89776i	−1.44971	−	0.0164142i
$604$		0			0
$605$	476.731	−	476.731i	0.787986	−	0.787986i
$606$		0			0
$607$	−685.217			−1.12886			−0.564429	−	0.825482i	$-0.690904\pi$
$607$	−685.217			−1.12886			−0.564429	+	0.825482i	$0.690904\pi$
$608$		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	−0.105767	−	0.994391i	$-0.533730\pi$
$613$	544.727	−	544.727i	0.888624	−	0.888624i	0.994391	+	0.105767i	$0.0337296\pi$
$614$		0			0
$615$	48.7143	+	20.5020i	0.0792102	+	0.0333365i
$616$		0			0
$617$	383.577			0.621681			0.310840	−	0.950462i	$-0.399390\pi$
$617$	383.577			0.621681			0.310840	+	0.950462i	$0.399390\pi$
$618$		0			0
$619$	81.7634	−	81.7634i	0.132089	−	0.132089i	−0.637971	−	0.770060i	$-0.720226\pi$
$619$	81.7634	−	81.7634i	0.132089	−	0.132089i	0.770060	+	0.637971i	$0.220226\pi$
$620$		0			0
$621$	−174.634	+	402.148i	−0.281214	+	0.647581i
$622$		0			0
$623$		−	129.694i		−	0.208176i
$624$		0			0
$625$	−944.365			−1.51098
$626$		0			0
$627$	92.3715	+	226.625i	0.147323	+	0.361443i
$628$		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	0.961674	+	0.274195i	$0.0884115\pi$
$643$	794.664	+	794.664i	1.23587	+	1.23587i	0.274195	+	0.961674i	$0.411588\pi$
$644$		0			0
$645$	678.217	−	276.439i	1.05150	−	0.428588i
$646$		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
$651$	11.8415	+	29.0519i	0.0181897	+	0.0446266i
$652$		0			0
$653$	−829.478	+	829.478i	−1.27026	+	1.27026i	−0.324305	+	0.945953i	$0.605130\pi$
$653$	−829.478	+	829.478i	−1.27026	+	1.27026i	−0.945953	+	0.324305i	$0.894870\pi$
$654$		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	−0.00762509	−	0.999971i	$-0.502427\pi$
$659$	653.956	−	653.956i	0.992346	−	0.992346i	0.999971	+	0.00762509i	$0.00242716\pi$
$660$		0			0
$661$	−734.342	+	734.342i	−1.11096	+	1.11096i	−0.117936	+	0.993021i	$0.537628\pi$
$661$	−734.342	+	734.342i	−1.11096	+	1.11096i	−0.993021	+	0.117936i	$0.962372\pi$
$662$		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
$669$	648.022	−	264.132i	0.968643	−	0.394816i
$670$		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
$675$	−1338.35	−	581.183i	−1.98274	−	0.861012i
$676$		0			0
$677$	662.519	+	662.519i	0.978610	+	0.978610i	0.999776	−	0.0211661i	$-0.00673787\pi$
$677$	662.519	+	662.519i	0.978610	+	0.978610i	−0.0211661	+	0.999776i	$0.506738\pi$
$678$		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	0.881950	−	0.471342i	$-0.156230\pi$
$683$	280.446	+	280.446i	0.410608	+	0.410608i	−0.471342	+	0.881950i	$0.656230\pi$
$684$		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	$-0.473792\pi$
$691$	−631.830	−	631.830i	−0.914371	−	0.914371i	−0.996612	+	0.0822418i	$0.973792\pi$
$692$		0			0
$693$	−1.12700	+	99.5370i	−0.00162626	+	0.143632i
$694$		0			0
$695$	2159.13			3.10666
$696$		0			0
$697$			22.7608i			0.0326554i
$698$		0			0
$699$	−1102.34	+	449.309i	−1.57702	+	0.642788i
$700$		0			0
$701$	160.480	−	160.480i	0.228930	−	0.228930i	−0.583315	−	0.812246i	$-0.698245\pi$
$701$	160.480	−	160.480i	0.228930	−	0.228930i	0.812246	+	0.583315i	$0.198245\pi$
$702$		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	−0.355883	−	0.934531i	$-0.615820\pi$
$709$	410.261	−	410.261i	0.578648	−	0.578648i	0.934531	+	0.355883i	$0.115820\pi$
$710$		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
$717$	−322.505	−	791.236i	−0.449798	−	1.10354i
$718$		0			0
$719$		−	1069.18i		−	1.48704i	−0.668716	−	0.743518i	$-0.733156\pi$
$719$		−	1069.18i		−	1.48704i	0.668716	−	0.743518i	$-0.266844\pi$
$720$		0			0
$721$	162.620			0.225547
$722$		0			0
$723$	740.447	−	301.804i	1.02413	−	0.417433i
$724$		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	0.998382	−	0.0568598i	$-0.0181088\pi$
$733$	690.136	+	690.136i	0.941522	+	0.941522i	−0.0568598	+	0.998382i	$0.518109\pi$
$734$		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	$-0.421273\pi$
$739$	−535.593	−	535.593i	−0.724754	−	0.724754i	−0.969570	+	0.244815i	$0.921273\pi$
$740$		0			0
$741$	181.826	+	446.093i	0.245379	+	0.602014i
$742$		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
$747$	10.8278	−	956.315i	0.0144950	−	1.28021i
$748$		0			0
$749$	−162.679	+	162.679i	−0.217195	+	0.217195i
$750$		0			0
$751$	15.8000			0.0210385			0.0105193	−	0.999945i	$-0.496652\pi$
$751$	15.8000			0.0210385			0.0105193	+	0.999945i	$0.496652\pi$
$752$		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	−0.0733640	+	0.997305i	$0.523373\pi$
$757$	−810.497	+	810.497i	−1.07067	+	1.07067i	−0.997305	+	0.0733640i	$0.976627\pi$
$758$		0			0
$759$	−301.753	−	126.996i	−0.397566	−	0.167320i
$760$		0			0
$761$	−212.194			−0.278836			−0.139418	−	0.990234i	$-0.544523\pi$
$761$	−212.194			−0.278836			−0.139418	+	0.990234i	$0.544523\pi$
$762$		0			0
$763$	113.314	−	113.314i	0.148511	−	0.148511i
$764$		0			0
$765$	10.4050	−	918.980i	0.0136014	−	1.20128i
$766$		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
$771$	−271.951	−	667.207i	−0.352725	−	0.865378i
$772$		0			0
$773$	−515.805	−	515.805i	−0.667277	−	0.667277i	0.289808	−	0.957085i	$-0.406409\pi$
$773$	−515.805	−	515.805i	−0.667277	−	0.667277i	−0.957085	+	0.289808i	$0.906409\pi$
$774$		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	$-0.169302\pi$
$787$	279.150	+	279.150i	0.354702	+	0.354702i	−0.507154	+	0.861856i	$0.669302\pi$
$788$		0			0
$789$	−390.898	+	159.329i	−0.495435	+	0.201938i
$790$		0			0
$791$	13.6788			0.0172931
$792$		0			0
$793$		−	733.911i		−	0.925487i
$794$		0			0
$795$	−57.0434	−	139.951i	−0.0717527	−	0.176038i
$796$		0			0
$797$	−409.431	+	409.431i	−0.513715	+	0.513715i	−0.915663	−	0.401947i	$-0.868333\pi$
$797$	−409.431	+	409.431i	−0.513715	+	0.513715i	0.401947	+	0.915663i	$0.368333\pi$
$798$		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	$-0.556392\pi$
$809$	−285.148			−0.352470			−0.176235	+	0.984348i	$0.556392\pi$
$810$		0			0
$811$	819.150	−	819.150i	1.01005	−	1.01005i	0.0101007	−	0.999949i	$-0.496785\pi$
$811$	819.150	−	819.150i	1.01005	−	1.01005i	0.999949	−	0.0101007i	$-0.00321519\pi$
$812$		0			0
$813$	635.435	−	259.001i	0.781593	−	0.318575i
$814$		0			0
$815$			2515.62i			3.08666i
$816$		0			0
$817$	333.312			0.407971
$818$		0			0
$819$	−2.21840	+	195.931i	−0.00270867	+	0.239232i
$820$		0			0
$821$	116.499	+	116.499i	0.141899	+	0.141899i	0.774488	−	0.632589i	$-0.218008\pi$
$821$	116.499	+	116.499i	0.141899	+	0.141899i	−0.632589	+	0.774488i	$0.718008\pi$
$822$		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	0.617483	−	0.786584i	$-0.288153\pi$
$827$	−139.847	−	139.847i	−0.169102	−	0.169102i	−0.786584	+	0.617483i	$0.788153\pi$
$828$		0			0
$829$	454.593	+	454.593i	0.548364	+	0.548364i	0.925967	−	0.377604i	$-0.123252\pi$
$829$	454.593	+	454.593i	0.548364	+	0.548364i	−0.377604	+	0.925967i	$0.623252\pi$
$830$		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
$837$	68.3372	−	157.367i	0.0816455	−	0.188014i
$838$		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
$843$	−787.733	+	321.077i	−0.934440	+	0.380875i
$844$		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	−0.337612	−	0.941285i	$-0.609619\pi$
$853$	514.933	−	514.933i	0.603673	−	0.603673i	0.941285	+	0.337612i	$0.109619\pi$
$854$		0			0
$855$	−678.944	−	694.494i	−0.794086	−	0.812274i
$856$		0			0
$857$	1165.96			1.36051			0.680254	−	0.732976i	$-0.261869\pi$
$857$	1165.96			1.36051			0.680254	+	0.732976i	$0.261869\pi$
$858$		0			0
$859$	246.162	−	246.162i	0.286568	−	0.286568i	−0.549153	−	0.835722i	$-0.685050\pi$
$859$	246.162	−	246.162i	0.286568	−	0.286568i	0.835722	+	0.549153i	$0.185050\pi$
$860$		0			0
$861$	3.69286	+	9.06009i	0.00428904	+	0.0105228i
$862$		0			0
$863$			196.851i			0.228101i	0.993475	+	0.114050i	$0.0363825\pi$
$863$			196.851i			0.228101i	−0.993475	+	0.114050i	$0.963617\pi$
$864$		0			0
$865$	513.373			0.593494
$866$		0			0
$867$	−436.364	+	177.861i	−0.503303	+	0.205145i
$868$		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	−0.939779	−	0.341782i	$-0.888969\pi$
$877$	−1123.93	−	1123.93i	−1.28156	−	1.28156i	−0.341782	−	0.939779i	$-0.611031\pi$
$878$		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	$-0.290277\pi$
$883$	−157.587	−	157.587i	−0.178468	−	0.178468i	−0.790688	+	0.612220i	$0.790277\pi$
$884$		0			0
$885$	−398.199	−	976.945i	−0.449943	−	1.10389i
$886$		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
$891$	393.542	−	376.111i	0.441685	−	0.422122i
$892$		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	$-0.929055\pi$
$907$	−684.081	+	684.081i	−0.754224	+	0.754224i	0.221041	+	0.975265i	$0.429055\pi$
$908$		0			0
$909$	−528.598	−	5.98498i	−0.581516	−	0.00658414i
$910$		0			0
$911$		−	1109.61i		−	1.21802i	−0.793164	−	0.609008i	$-0.791568\pi$
$911$		−	1109.61i		−	1.21802i	0.793164	−	0.609008i	$-0.208432\pi$
$912$		0			0
$913$	714.154			0.782206
$914$		0			0
$915$	558.498	+	1370.22i	0.610381	+	1.49751i
$916$		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
$933$	308.856	−	125.889i	0.331036	−	0.134929i
$934$		0			0
$935$	686.274			0.733983
$936$		0			0
$937$		−	1036.08i		−	1.10574i	−0.833267	−	0.552871i	$-0.813532\pi$
$937$		−	1036.08i		−	1.10574i	0.833267	−	0.552871i	$-0.186468\pi$
$938$		0			0
$939$	−319.637	−	784.199i	−0.340402	−	0.835143i
$940$		0			0
$941$	−904.283	+	904.283i	−0.960980	+	0.960980i	−0.999267	−	0.0382864i	$-0.987810\pi$
$941$	−904.283	+	904.283i	−0.960980	+	0.960980i	0.0382864	+	0.999267i	$0.487810\pi$
$942$		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	−0.0525337	−	0.998619i	$-0.516730\pi$
$947$	895.943	−	895.943i	0.946085	−	0.946085i	0.998619	+	0.0525337i	$0.0167297\pi$
$948$		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	$-0.709350\pi$
$953$	−1165.12			−1.22259			−0.611293	+	0.791405i	$0.709350\pi$
$954$		0			0
$955$	90.1699	−	90.1699i	0.0944188	−	0.0944188i
$956$		0			0
$957$	283.591	−	115.591i	0.296333	−	0.120784i
$958$		0			0
$959$			83.0852i			0.0866373i
$960$		0			0
$961$	−920.624			−0.957985
$962$		0			0
$963$	1258.05	+	14.2441i	1.30638	+	0.0147914i
$964$		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	0.964067	−	0.265659i	$-0.0855894\pi$
$971$	678.155	+	678.155i	0.698408	+	0.698408i	−0.265659	+	0.964067i	$0.585589\pi$
$972$		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
$981$	−876.290	−	9.92169i	−0.893262	−	0.0101138i
$982$		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
$987$	342.663	−	139.669i	0.347177	−	0.141508i
$988$		0			0
$989$	−315.295	+	315.295i	−0.318802	+	0.318802i
$990$		0			0
$991$	−939.282			−0.947813			−0.473906	−	0.880575i	$-0.657156\pi$
$991$	−939.282			−0.947813			−0.473906	+	0.880575i	$0.657156\pi$
$992$		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	−0.785388	−	0.619004i	$-0.787537\pi$
$997$	−165.885	+	165.885i	−0.166384	+	0.166384i	0.619004	+	0.785388i	$0.287537\pi$
$998$		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.b.161.1		8
3.2	odd	2	inner	384.3.i.b.161.3		8
4.3	odd	2		384.3.i.a.161.4		8
8.3	odd	2		48.3.i.a.29.2	yes	8
8.5	even	2		192.3.i.a.17.4		8
12.11	even	2		384.3.i.a.161.2		8
16.3	odd	4		48.3.i.a.5.3	yes	8
16.5	even	4	inner	384.3.i.b.353.3		8
16.11	odd	4		384.3.i.a.353.2		8
16.13	even	4		192.3.i.a.113.2		8
24.5	odd	2		192.3.i.a.17.2		8
24.11	even	2		48.3.i.a.29.3	yes	8
48.5	odd	4	inner	384.3.i.b.353.1		8
48.11	even	4		384.3.i.a.353.4		8
48.29	odd	4		192.3.i.a.113.4		8
48.35	even	4		48.3.i.a.5.2	✓	8

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

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)

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