LMFDB - Embedded newform 464.3.l.c.273.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [464,3,Mod(17,464)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(464, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("464.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	464.l (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:	$12.6430842663$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 91x^{4} + 126x^{2} + 25 $ x^8 + 18x^6 + 91x^4 + 126*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			273.4
Root			$0.486981i$ of defining polynomial
Character	$\chi$	$=$	464.273
Dual form			464.3.l.c.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.11190 + 3.11190i) q^{3} -4.53053i q^{5} +0.745339 q^{7} +10.3678i q^{9} +O(q^{10})$	\(q+(3.11190 + 3.11190i) q^{3} -4.53053i q^{5} +0.745339 q^{7} +10.3678i q^{9} +(-0.0423096 - 0.0423096i) q^{11} +8.30191i q^{13} +(14.0985 - 14.0985i) q^{15} +(15.2625 + 15.2625i) q^{17} +(25.1348 + 25.1348i) q^{19} +(2.31942 + 2.31942i) q^{21} -8.64367 q^{23} +4.47430 q^{25} +(-4.25644 + 4.25644i) q^{27} +(22.0908 - 18.7882i) q^{29} +(5.09325 + 5.09325i) q^{31} -0.263326i q^{33} -3.37678i q^{35} +(10.0725 - 10.0725i) q^{37} +(-25.8347 + 25.8347i) q^{39} +(2.50571 - 2.50571i) q^{41} +(11.2668 + 11.2668i) q^{43} +46.9716 q^{45} +(23.0132 - 23.0132i) q^{47} -48.4445 q^{49} +94.9907i q^{51} -42.8979 q^{53} +(-0.191685 + 0.191685i) q^{55} +156.434i q^{57} -106.413 q^{59} +(-42.3211 - 42.3211i) q^{61} +7.72752i q^{63} +37.6120 q^{65} -75.7926i q^{67} +(-26.8982 - 26.8982i) q^{69} -71.2051i q^{71} +(-73.7928 + 73.7928i) q^{73} +(13.9236 + 13.9236i) q^{75} +(-0.0315350 - 0.0315350i) q^{77} +(78.7399 + 78.7399i) q^{79} +66.8190 q^{81} -15.1749 q^{83} +(69.1473 - 69.1473i) q^{85} +(127.211 + 10.2773i) q^{87} +(-22.8417 - 22.8417i) q^{89} +6.18773i q^{91} +31.6993i q^{93} +(113.874 - 113.874i) q^{95} +(42.8298 - 42.8298i) q^{97} +(0.438657 - 0.438657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 4 q^{7}+O(q^{10}) $ 8 * q + 2 * q^3 + 4 * q^7	$ 8 q + 2 q^{3} + 4 q^{7} + 6 q^{11} + 10 q^{15} + 12 q^{17} + 16 q^{19} - 36 q^{21} + 104 q^{25} + 98 q^{27} + 128 q^{29} + 10 q^{31} - 84 q^{37} + 90 q^{39} + 20 q^{41} + 190 q^{43} + 292 q^{45} - 58 q^{47} - 72 q^{49} + 252 q^{53} + 74 q^{55} + 40 q^{59} - 208 q^{61} + 36 q^{65} + 120 q^{69} - 188 q^{73} + 12 q^{75} + 180 q^{77} + 382 q^{79} - 124 q^{81} - 280 q^{83} + 32 q^{85} - 34 q^{87} - 64 q^{89} + 380 q^{95} - 44 q^{97} - 552 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 4 * q^7 + 6 * q^11 + 10 * q^15 + 12 * q^17 + 16 * q^19 - 36 * q^21 + 104 * q^25 + 98 * q^27 + 128 * q^29 + 10 * q^31 - 84 * q^37 + 90 * q^39 + 20 * q^41 + 190 * q^43 + 292 * q^45 - 58 * q^47 - 72 * q^49 + 252 * q^53 + 74 * q^55 + 40 * q^59 - 208 * q^61 + 36 * q^65 + 120 * q^69 - 188 * q^73 + 12 * q^75 + 180 * q^77 + 382 * q^79 - 124 * q^81 - 280 * q^83 + 32 * q^85 - 34 * q^87 - 64 * q^89 + 380 * q^95 - 44 * q^97 - 552 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	3.11190	+	3.11190i	1.03730	+	1.03730i	0.999277	+	0.0380218i	$0.0121056\pi$
$3$	3.11190	+	3.11190i	1.03730	+	1.03730i	0.0380218	+	0.999277i	$0.487894\pi$
$4$		0			0
$5$		−	4.53053i		−	0.906106i	−0.891484	−	0.453053i	$-0.850335\pi$
$5$		−	4.53053i		−	0.906106i	0.891484	−	0.453053i	$-0.149665\pi$
$6$		0			0
$7$	0.745339			0.106477			0.0532385	−	0.998582i	$-0.483046\pi$
$7$	0.745339			0.106477			0.0532385	+	0.998582i	$0.483046\pi$
$8$		0			0
$9$			10.3678i			1.15198i
$10$		0			0
$11$	−0.0423096	−	0.0423096i	−0.00384632	−	0.00384632i	0.705181	−	0.709027i	$-0.250866\pi$
$11$	−0.0423096	−	0.0423096i	−0.00384632	−	0.00384632i	−0.709027	+	0.705181i	$0.750866\pi$
$12$		0			0
$13$			8.30191i			0.638608i	0.947652	+	0.319304i	$0.103449\pi$
$13$			8.30191i			0.638608i	−0.947652	+	0.319304i	$0.896551\pi$
$14$		0			0
$15$	14.0985	−	14.0985i	0.939903	−	0.939903i
$16$		0			0
$17$	15.2625	+	15.2625i	0.897795	+	0.897795i	0.995241	−	0.0974461i	$-0.0310673\pi$
$17$	15.2625	+	15.2625i	0.897795	+	0.897795i	−0.0974461	+	0.995241i	$0.531067\pi$
$18$		0			0
$19$	25.1348	+	25.1348i	1.32288	+	1.32288i	0.911431	+	0.411453i	$0.134979\pi$
$19$	25.1348	+	25.1348i	1.32288	+	1.32288i	0.411453	+	0.911431i	$0.365021\pi$
$20$		0			0
$21$	2.31942	+	2.31942i	0.110448	+	0.110448i
$22$		0			0
$23$	−8.64367			−0.375812			−0.187906	−	0.982187i	$-0.560170\pi$
$23$	−8.64367			−0.375812			−0.187906	+	0.982187i	$0.560170\pi$
$24$		0			0
$25$	4.47430			0.178972
$26$		0			0
$27$	−4.25644	+	4.25644i	−0.157646	+	0.157646i
$28$		0			0
$29$	22.0908	−	18.7882i	0.761752	−	0.647869i
$29$	22.0908	−	18.7882i	0.761752	−	0.647869i
$30$		0			0
$31$	5.09325	+	5.09325i	0.164298	+	0.164298i	0.784468	−	0.620169i	$-0.212936\pi$
$31$	5.09325	+	5.09325i	0.164298	+	0.164298i	−0.620169	+	0.784468i	$0.712936\pi$
$32$		0			0
$33$		−	0.263326i		−	0.00797957i
$34$		0			0
$35$		−	3.37678i		−	0.0964794i
$36$		0			0
$37$	10.0725	−	10.0725i	0.272230	−	0.272230i	−0.557767	−	0.829997i	$-0.688342\pi$
$37$	10.0725	−	10.0725i	0.272230	−	0.272230i	0.829997	+	0.557767i	$0.188342\pi$
$38$		0			0
$39$	−25.8347	+	25.8347i	−0.662427	+	0.662427i
$40$		0			0
$41$	2.50571	−	2.50571i	0.0611149	−	0.0611149i	−0.675889	−	0.737004i	$-0.736240\pi$
$41$	2.50571	−	2.50571i	0.0611149	−	0.0611149i	0.737004	+	0.675889i	$0.236240\pi$
$42$		0			0
$43$	11.2668	+	11.2668i	0.262018	+	0.262018i	0.825874	−	0.563855i	$-0.190682\pi$
$43$	11.2668	+	11.2668i	0.262018	+	0.262018i	−0.563855	+	0.825874i	$0.690682\pi$
$44$		0			0
$45$	46.9716			1.04381
$46$		0			0
$47$	23.0132	−	23.0132i	0.489643	−	0.489643i	−0.418550	−	0.908194i	$-0.637462\pi$
$47$	23.0132	−	23.0132i	0.489643	−	0.489643i	0.908194	+	0.418550i	$0.137462\pi$
$48$		0			0
$49$	−48.4445			−0.988663
$50$		0			0
$51$			94.9907i			1.86256i
$52$		0			0
$53$	−42.8979			−0.809394			−0.404697	−	0.914451i	$-0.632623\pi$
$53$	−42.8979			−0.809394			−0.404697	+	0.914451i	$0.632623\pi$
$54$		0			0
$55$	−0.191685	+	0.191685i	−0.00348518	+	0.00348518i
$56$		0			0
$57$			156.434i			2.74445i
$58$		0			0
$59$	−106.413			−1.80361			−0.901806	−	0.432140i	$-0.857759\pi$
$59$	−106.413			−1.80361			−0.901806	+	0.432140i	$0.857759\pi$
$60$		0			0
$61$	−42.3211	−	42.3211i	−0.693788	−	0.693788i	0.269275	−	0.963063i	$-0.413216\pi$
$61$	−42.3211	−	42.3211i	−0.693788	−	0.693788i	−0.963063	+	0.269275i	$0.913216\pi$
$62$		0			0
$63$			7.72752i			0.122659i
$64$		0			0
$65$	37.6120			0.578647
$66$		0			0
$67$		−	75.7926i		−	1.13123i	−0.824668	−	0.565616i	$-0.808638\pi$
$67$		−	75.7926i		−	1.13123i	0.824668	−	0.565616i	$-0.191362\pi$
$68$		0			0
$69$	−26.8982	−	26.8982i	−0.389829	−	0.389829i
$70$		0			0
$71$		−	71.2051i		−	1.00289i	−0.865190	−	0.501445i	$-0.832802\pi$
$71$		−	71.2051i		−	1.00289i	0.865190	−	0.501445i	$-0.167198\pi$
$72$		0			0
$73$	−73.7928	+	73.7928i	−1.01086	+	1.01086i	−0.0109201	+	0.999940i	$0.503476\pi$
$73$	−73.7928	+	73.7928i	−1.01086	+	1.01086i	−0.999940	+	0.0109201i	$0.996524\pi$
$74$		0			0
$75$	13.9236	+	13.9236i	0.185647	+	0.185647i
$76$		0			0
$77$	−0.0315350	−	0.0315350i	−0.000409545	−	0.000409545i
$78$		0			0
$79$	78.7399	+	78.7399i	0.996707	+	0.996707i	0.999995	−	0.00328762i	$-0.00104648\pi$
$79$	78.7399	+	78.7399i	0.996707	+	0.996707i	−0.00328762	+	0.999995i	$0.501046\pi$
$80$		0			0
$81$	66.8190			0.824925
$82$		0			0
$83$	−15.1749			−0.182830			−0.0914152	−	0.995813i	$-0.529139\pi$
$83$	−15.1749			−0.182830			−0.0914152	+	0.995813i	$0.529139\pi$
$84$		0			0
$85$	69.1473	−	69.1473i	0.813497	−	0.813497i
$86$		0			0
$87$	127.211	+	10.2773i	1.46220	+	0.118130i
$88$		0			0
$89$	−22.8417	−	22.8417i	−0.256648	−	0.256648i	0.567041	−	0.823689i	$-0.308088\pi$
$89$	−22.8417	−	22.8417i	−0.256648	−	0.256648i	−0.823689	+	0.567041i	$0.808088\pi$
$90$		0			0
$91$			6.18773i			0.0679971i
$92$		0			0
$93$			31.6993i			0.340853i
$94$		0			0
$95$	113.874	−	113.874i	1.19867	−	1.19867i
$96$		0			0
$97$	42.8298	−	42.8298i	0.441544	−	0.441544i	−0.450987	−	0.892531i	$-0.648928\pi$
$97$	42.8298	−	42.8298i	0.441544	−	0.441544i	0.892531	+	0.450987i	$0.148928\pi$
$98$		0			0
$99$	0.438657	−	0.438657i	0.00443088	−	0.00443088i
$100$		0			0
$101$	36.4365	+	36.4365i	0.360757	+	0.360757i	0.864092	−	0.503334i	$-0.167894\pi$
$101$	36.4365	+	36.4365i	0.360757	+	0.360757i	−0.503334	+	0.864092i	$0.667894\pi$
$102$		0			0
$103$	−111.751			−1.08496			−0.542479	−	0.840070i	$-0.682514\pi$
$103$	−111.751			−1.08496			−0.542479	+	0.840070i	$0.682514\pi$
$104$		0			0
$105$	10.5082	−	10.5082i	0.100078	−	0.100078i
$106$		0			0
$107$	−88.9678			−0.831475			−0.415737	−	0.909485i	$-0.636476\pi$
$107$	−88.9678			−0.831475			−0.415737	+	0.909485i	$0.636476\pi$
$108$		0			0
$109$			41.1196i			0.377244i	0.982050	+	0.188622i	$0.0604020\pi$
$109$			41.1196i			0.377244i	−0.982050	+	0.188622i	$0.939598\pi$
$110$		0			0
$111$	62.6893			0.564768
$112$		0			0
$113$	104.104	−	104.104i	0.921275	−	0.921275i	−0.0758450	−	0.997120i	$-0.524165\pi$
$113$	104.104	−	104.104i	0.921275	−	0.921275i	0.997120	+	0.0758450i	$0.0241654\pi$
$114$		0			0
$115$			39.1604i			0.340525i
$116$		0			0
$117$	−86.0725			−0.735662
$118$		0			0
$119$	11.3757	+	11.3757i	0.0955945	+	0.0955945i
$120$		0			0
$121$		−	120.996i		−	0.999970i
$122$		0			0
$123$	15.5950			0.126789
$124$		0			0
$125$		−	133.534i		−	1.06827i
$126$		0			0
$127$	−8.26743	−	8.26743i	−0.0650978	−	0.0650978i	0.673808	−	0.738906i	$-0.264657\pi$
$127$	−8.26743	−	8.26743i	−0.0650978	−	0.0650978i	−0.738906	+	0.673808i	$0.764657\pi$
$128$		0			0
$129$			70.1221i			0.543582i
$130$		0			0
$131$	0.361622	−	0.361622i	0.00276047	−	0.00276047i	−0.705725	−	0.708486i	$-0.749379\pi$
$131$	0.361622	−	0.361622i	0.00276047	−	0.00276047i	0.708486	+	0.705725i	$0.249379\pi$
$132$		0			0
$133$	18.7339	+	18.7339i	0.140857	+	0.140857i
$134$		0			0
$135$	19.2839	+	19.2839i	0.142844	+	0.142844i
$136$		0			0
$137$	−69.5740	−	69.5740i	−0.507840	−	0.507840i	0.406023	−	0.913863i	$-0.366915\pi$
$137$	−69.5740	−	69.5740i	−0.507840	−	0.507840i	−0.913863	+	0.406023i	$0.866915\pi$
$138$		0			0
$139$	−111.380			−0.801297			−0.400649	−	0.916232i	$-0.631215\pi$
$139$	−111.380			−0.801297			−0.400649	+	0.916232i	$0.631215\pi$
$140$		0			0
$141$	143.230			1.01581
$142$		0			0
$143$	0.351250	−	0.351250i	0.00245629	−	0.00245629i
$144$		0			0
$145$	−85.1205	−	100.083i	−0.587038	−	0.690228i
$146$		0			0
$147$	−150.754	−	150.754i	−1.02554	−	1.02554i
$148$		0			0
$149$			44.5177i			0.298776i	0.988779	+	0.149388i	$0.0477304\pi$
$149$			44.5177i			0.298776i	−0.988779	+	0.149388i	$0.952270\pi$
$150$		0			0
$151$		−	70.6402i		−	0.467816i	−0.972259	−	0.233908i	$-0.924849\pi$
$151$		−	70.6402i		−	0.467816i	0.972259	−	0.233908i	$-0.0751514\pi$
$152$		0			0
$153$	−158.239	+	158.239i	−1.03424	+	1.03424i
$154$		0			0
$155$	23.0751	−	23.0751i	0.148872	−	0.148872i
$156$		0			0
$157$	−127.354	+	127.354i	−0.811173	+	0.811173i	−0.984810	−	0.173636i	$-0.944448\pi$
$157$	−127.354	+	127.354i	−0.811173	+	0.811173i	0.173636	+	0.984810i	$0.444448\pi$
$158$		0			0
$159$	−133.494	−	133.494i	−0.839583	−	0.839583i
$160$		0			0
$161$	−6.44246			−0.0400153
$162$		0			0
$163$	−83.4261	+	83.4261i	−0.511817	+	0.511817i	−0.915083	−	0.403266i	$-0.867875\pi$
$163$	−83.4261	+	83.4261i	−0.511817	+	0.511817i	0.403266	+	0.915083i	$0.367875\pi$
$164$		0			0
$165$	−1.19301			−0.00723034
$166$		0			0
$167$		−	221.605i		−	1.32697i	−0.748188	−	0.663487i	$-0.769076\pi$
$167$		−	221.605i		−	1.32697i	0.748188	−	0.663487i	$-0.230924\pi$
$168$		0			0
$169$	100.078			0.592180
$170$		0			0
$171$	−260.592	+	260.592i	−1.52393	+	1.52393i
$172$		0			0
$173$			6.62034i			0.0382679i	0.999817	+	0.0191339i	$0.00609089\pi$
$173$			6.62034i			0.0382679i	−0.999817	+	0.0191339i	$0.993909\pi$
$174$		0			0
$175$	3.33487			0.0190564
$176$		0			0
$177$	−331.147	−	331.147i	−1.87089	−	1.87089i
$178$		0			0
$179$			36.9603i			0.206482i	0.994656	+	0.103241i	$0.0329213\pi$
$179$			36.9603i			0.206482i	−0.994656	+	0.103241i	$0.967079\pi$
$180$		0			0
$181$	−192.039			−1.06099			−0.530494	−	0.847689i	$-0.677994\pi$
$181$	−192.039			−1.06099			−0.530494	+	0.847689i	$0.677994\pi$
$182$		0			0
$183$		−	263.398i		−	1.43933i
$184$		0			0
$185$	−45.6339	−	45.6339i	−0.246669	−	0.246669i
$186$		0			0
$187$		−	1.29150i		−	0.00690642i
$188$		0			0
$189$	−3.17249	+	3.17249i	−0.0167857	+	0.0167857i
$190$		0			0
$191$	215.351	+	215.351i	1.12749	+	1.12749i	0.990584	+	0.136906i	$0.0437158\pi$
$191$	215.351	+	215.351i	1.12749	+	1.12749i	0.136906	+	0.990584i	$0.456284\pi$
$192$		0			0
$193$	130.679	+	130.679i	0.677095	+	0.677095i	0.959342	−	0.282247i	$-0.0910797\pi$
$193$	130.679	+	130.679i	0.677095	+	0.677095i	−0.282247	+	0.959342i	$0.591080\pi$
$194$		0			0
$195$	117.045	+	117.045i	0.600229	+	0.600229i
$196$		0			0
$197$	−254.953			−1.29418			−0.647090	−	0.762414i	$-0.724014\pi$
$197$	−254.953			−1.29418			−0.647090	+	0.762414i	$0.724014\pi$
$198$		0			0
$199$	−168.018			−0.844311			−0.422155	−	0.906524i	$-0.638726\pi$
$199$	−168.018			−0.844311			−0.422155	+	0.906524i	$0.638726\pi$
$200$		0			0
$201$	235.859	−	235.859i	1.17343	−	1.17343i
$202$		0			0
$203$	16.4651	−	14.0036i	0.0811090	−	0.0689832i
$204$		0			0
$205$	−11.3522	−	11.3522i	−0.0553766	−	0.0553766i
$206$		0			0
$207$		−	89.6158i		−	0.432926i
$208$		0			0
$209$		−	2.12688i		−	0.0101765i
$210$		0			0
$211$	111.890	−	111.890i	0.530285	−	0.530285i	−0.390372	−	0.920657i	$-0.627654\pi$
$211$	111.890	−	111.890i	0.530285	−	0.530285i	0.920657	+	0.390372i	$0.127654\pi$
$212$		0			0
$213$	221.583	−	221.583i	1.04030	−	1.04030i
$214$		0			0
$215$	51.0445	−	51.0445i	0.237416	−	0.237416i
$216$		0			0
$217$	3.79620	+	3.79620i	0.0174940	+	0.0174940i
$218$		0			0
$219$	−459.271			−2.09713
$220$		0			0
$221$	−126.708	+	126.708i	−0.573339	+	0.573339i
$222$		0			0
$223$	57.0256			0.255720			0.127860	−	0.991792i	$-0.459189\pi$
$223$	57.0256			0.255720			0.127860	+	0.991792i	$0.459189\pi$
$224$		0			0
$225$			46.3886i			0.206172i
$226$		0			0
$227$	173.750			0.765418			0.382709	−	0.923869i	$-0.374991\pi$
$227$	173.750			0.765418			0.382709	+	0.923869i	$0.374991\pi$
$228$		0			0
$229$	−144.696	+	144.696i	−0.631859	+	0.631859i	−0.948534	−	0.316675i	$-0.897433\pi$
$229$	−144.696	+	144.696i	−0.631859	+	0.631859i	0.316675	+	0.948534i	$0.397433\pi$
$230$		0			0
$231$		−	0.196267i		−	0.000849641i
$232$		0			0
$233$	102.871			0.441507			0.220754	−	0.975330i	$-0.429148\pi$
$233$	102.871			0.441507			0.220754	+	0.975330i	$0.429148\pi$
$234$		0			0
$235$	−104.262	−	104.262i	−0.443669	−	0.443669i
$236$		0			0
$237$			490.060i			2.06777i
$238$		0			0
$239$	312.152			1.30607			0.653037	−	0.757326i	$-0.273495\pi$
$239$	312.152			1.30607			0.653037	+	0.757326i	$0.273495\pi$
$240$		0			0
$241$		−	313.004i		−	1.29877i	−0.760460	−	0.649385i	$-0.775026\pi$
$241$		−	313.004i		−	1.29877i	0.760460	−	0.649385i	$-0.224974\pi$
$242$		0			0
$243$	246.242	+	246.242i	1.01334	+	1.01334i
$244$		0			0
$245$			219.479i			0.895833i
$246$		0			0
$247$	−208.667	+	208.667i	−0.844805	+	0.844805i
$248$		0			0
$249$	−47.2228	−	47.2228i	−0.189650	−	0.189650i
$250$		0			0
$251$	−7.83425	−	7.83425i	−0.0312121	−	0.0312121i	0.691328	−	0.722541i	$-0.257026\pi$
$251$	−7.83425	−	7.83425i	−0.0312121	−	0.0312121i	−0.722541	+	0.691328i	$0.757026\pi$
$252$		0			0
$253$	0.365710	+	0.365710i	0.00144549	+	0.00144549i
$254$		0			0
$255$	430.358			1.68768
$256$		0			0
$257$	68.5603			0.266771			0.133386	−	0.991064i	$-0.457415\pi$
$257$	68.5603			0.266771			0.133386	+	0.991064i	$0.457415\pi$
$258$		0			0
$259$	7.50744	−	7.50744i	0.0289863	−	0.0289863i
$260$		0			0
$261$	194.792	+	229.033i	0.746331	+	0.877521i
$262$		0			0
$263$	−153.717	−	153.717i	−0.584477	−	0.584477i	0.351653	−	0.936130i	$-0.385620\pi$
$263$	−153.717	−	153.717i	−0.584477	−	0.584477i	−0.936130	+	0.351653i	$0.885620\pi$
$264$		0			0
$265$			194.350i			0.733397i
$266$		0			0
$267$		−	142.162i		−	0.532441i
$268$		0			0
$269$	272.419	−	272.419i	1.01271	−	1.01271i	0.0127932	−	0.999918i	$-0.495928\pi$
$269$	272.419	−	272.419i	1.01271	−	1.01271i	0.999918	−	0.0127932i	$-0.00407231\pi$
$270$		0			0
$271$	304.778	−	304.778i	1.12464	−	1.12464i	0.133607	−	0.991034i	$-0.457344\pi$
$271$	304.778	−	304.778i	1.12464	−	1.12464i	0.991034	−	0.133607i	$-0.0426559\pi$
$272$		0			0
$273$	−19.2556	+	19.2556i	−0.0705333	+	0.0705333i
$274$		0			0
$275$	−0.189306	−	0.189306i	−0.000688384	−	0.000688384i
$276$		0			0
$277$	−26.7259			−0.0964834			−0.0482417	−	0.998836i	$-0.515362\pi$
$277$	−26.7259			−0.0964834			−0.0482417	+	0.998836i	$0.515362\pi$
$278$		0			0
$279$	−52.8058	+	52.8058i	−0.189268	+	0.189268i
$280$		0			0
$281$	468.922			1.66876			0.834380	−	0.551189i	$-0.185826\pi$
$281$	468.922			1.66876			0.834380	+	0.551189i	$0.185826\pi$
$282$		0			0
$283$			263.495i			0.931079i	0.885027	+	0.465540i	$0.154140\pi$
$283$			263.495i			0.931079i	−0.885027	+	0.465540i	$0.845860\pi$
$284$		0			0
$285$	708.728			2.48676
$286$		0			0
$287$	1.86760	−	1.86760i	0.00650733	−	0.00650733i
$288$		0			0
$289$			176.888i			0.612071i
$290$		0			0
$291$	266.564			0.916026
$292$		0			0
$293$	−84.4413	−	84.4413i	−0.288196	−	0.288196i	0.548171	−	0.836366i	$-0.315324\pi$
$293$	−84.4413	−	84.4413i	−0.288196	−	0.288196i	−0.836366	+	0.548171i	$0.815324\pi$
$294$		0			0
$295$			482.108i			1.63426i
$296$		0			0
$297$	0.360176			0.00121271
$298$		0			0
$299$		−	71.7589i		−	0.239996i
$300$		0			0
$301$	8.39757	+	8.39757i	0.0278989	+	0.0278989i
$302$		0			0
$303$			226.773i			0.748426i
$304$		0			0
$305$	−191.737	+	191.737i	−0.628646	+	0.628646i
$306$		0			0
$307$	−193.086	−	193.086i	−0.628945	−	0.628945i	0.318858	−	0.947803i	$-0.396701\pi$
$307$	−193.086	−	193.086i	−0.628945	−	0.628945i	−0.947803	+	0.318858i	$0.896701\pi$
$308$		0			0
$309$	−347.756	−	347.756i	−1.12542	−	1.12542i
$310$		0			0
$311$	138.374	+	138.374i	0.444932	+	0.444932i	0.893666	−	0.448734i	$-0.148125\pi$
$311$	138.374	+	138.374i	0.444932	+	0.444932i	−0.448734	+	0.893666i	$0.648125\pi$
$312$		0			0
$313$	316.089			1.00987			0.504934	−	0.863158i	$-0.331517\pi$
$313$	316.089			1.00987			0.504934	+	0.863158i	$0.331517\pi$
$314$		0			0
$315$	35.0098			0.111142
$316$		0			0
$317$	222.503	−	222.503i	0.701902	−	0.701902i	−0.262916	−	0.964819i	$-0.584684\pi$
$317$	222.503	−	222.503i	0.701902	−	0.701902i	0.964819	+	0.262916i	$0.0846843\pi$
$318$		0			0
$319$	−1.72957	−	0.139731i	−0.00542186	−	0.000438028i
$320$		0			0
$321$	−276.859	−	276.859i	−0.862488	−	0.862488i
$322$		0			0
$323$			767.240i			2.37536i
$324$		0			0
$325$			37.1452i			0.114293i
$326$		0			0
$327$	−127.960	+	127.960i	−0.391314	+	0.391314i
$328$		0			0
$329$	17.1527	−	17.1527i	0.0521358	−	0.0521358i
$330$		0			0
$331$	−240.645	+	240.645i	−0.727024	+	0.727024i	−0.970026	−	0.243002i	$-0.921868\pi$
$331$	−240.645	+	240.645i	−0.727024	+	0.727024i	0.243002	+	0.970026i	$0.421868\pi$
$332$		0			0
$333$	104.430	+	104.430i	0.313603	+	0.313603i
$334$		0			0
$335$	−343.381			−1.02502
$336$		0			0
$337$	−294.375	+	294.375i	−0.873517	+	0.873517i	−0.992854	−	0.119336i	$-0.961923\pi$
$337$	−294.375	+	294.375i	−0.873517	+	0.873517i	0.119336	+	0.992854i	$0.461923\pi$
$338$		0			0
$339$	647.922			1.91127
$340$		0			0
$341$		−	0.430987i		−	0.00126389i
$342$		0			0
$343$	−72.6291			−0.211747
$344$		0			0
$345$	−121.863	+	121.863i	−0.353226	+	0.353226i
$346$		0			0
$347$			355.572i			1.02470i	0.858776	+	0.512351i	$0.171225\pi$
$347$			355.572i			1.02470i	−0.858776	+	0.512351i	$0.828775\pi$
$348$		0			0
$349$	−239.336			−0.685775			−0.342888	−	0.939376i	$-0.611405\pi$
$349$	−239.336			−0.685775			−0.342888	+	0.939376i	$0.611405\pi$
$350$		0			0
$351$	−35.3366	−	35.3366i	−0.100674	−	0.100674i
$352$		0			0
$353$		−	31.2450i		−	0.0885128i	−0.999020	−	0.0442564i	$-0.985908\pi$
$353$		−	31.2450i		−	0.0885128i	0.999020	−	0.0442564i	$-0.0140919\pi$
$354$		0			0
$355$	−322.597			−0.908724
$356$		0			0
$357$			70.8003i			0.198320i
$358$		0			0
$359$	−259.580	−	259.580i	−0.723064	−	0.723064i	0.246164	−	0.969228i	$-0.420830\pi$
$359$	−259.580	−	259.580i	−0.723064	−	0.723064i	−0.969228	+	0.246164i	$0.920830\pi$
$360$		0			0
$361$			902.516i			2.50004i
$362$		0			0
$363$	376.528	−	376.528i	1.03727	−	1.03727i
$364$		0			0
$365$	334.321	+	334.321i	0.915947	+	0.915947i
$366$		0			0
$367$	−130.207	−	130.207i	−0.354786	−	0.354786i	0.507100	−	0.861887i	$-0.330717\pi$
$367$	−130.207	−	130.207i	−0.354786	−	0.354786i	−0.861887	+	0.507100i	$0.830717\pi$
$368$		0			0
$369$	25.9787	+	25.9787i	0.0704030	+	0.0704030i
$370$		0			0
$371$	−31.9735			−0.0861818
$372$		0			0
$373$	−638.263			−1.71116			−0.855581	−	0.517669i	$-0.826800\pi$
$373$	−638.263			−1.71116			−0.855581	+	0.517669i	$0.826800\pi$
$374$		0			0
$375$	415.545	−	415.545i	1.10812	−	1.10812i
$376$		0			0
$377$	155.978	+	183.396i	0.413735	+	0.486461i
$378$		0			0
$379$	−91.7710	−	91.7710i	−0.242140	−	0.242140i	0.575595	−	0.817735i	$-0.304771\pi$
$379$	−91.7710	−	91.7710i	−0.242140	−	0.242140i	−0.817735	+	0.575595i	$0.804771\pi$
$380$		0			0
$381$		−	51.4547i		−	0.135052i
$382$		0			0
$383$		−	290.256i		−	0.757848i	−0.925428	−	0.378924i	$-0.876294\pi$
$383$		−	290.256i		−	0.757848i	0.925428	−	0.378924i	$-0.123706\pi$
$384$		0			0
$385$	−0.142870	+	0.142870i	−0.000371091	+	0.000371091i
$386$		0			0
$387$	−116.812	+	116.812i	−0.301839	+	0.301839i
$388$		0			0
$389$	404.811	−	404.811i	1.04065	−	1.04065i	0.0415071	−	0.999138i	$-0.486784\pi$
$389$	404.811	−	404.811i	1.04065	−	1.04065i	0.999138	−	0.0415071i	$-0.0132159\pi$
$390$		0			0
$391$	−131.924	−	131.924i	−0.337402	−	0.337402i
$392$		0			0
$393$	2.25066			0.00572686
$394$		0			0
$395$	356.733	−	356.733i	0.903122	−	0.903122i
$396$		0			0
$397$	−485.501			−1.22292			−0.611462	−	0.791274i	$-0.709418\pi$
$397$	−485.501			−1.22292			−0.611462	+	0.791274i	$0.709418\pi$
$398$		0			0
$399$			116.596i			0.292221i
$400$		0			0
$401$	−144.170			−0.359527			−0.179763	−	0.983710i	$-0.557533\pi$
$401$	−144.170			−0.359527			−0.179763	+	0.983710i	$0.557533\pi$
$402$		0			0
$403$	−42.2837	+	42.2837i	−0.104922	+	0.104922i
$404$		0			0
$405$		−	302.725i		−	0.747470i
$406$		0			0
$407$	−0.852328			−0.00209417
$408$		0			0
$409$	118.758	+	118.758i	0.290361	+	0.290361i	0.837223	−	0.546862i	$-0.184178\pi$
$409$	118.758	+	118.758i	0.290361	+	0.290361i	−0.546862	+	0.837223i	$0.684178\pi$
$410$		0			0
$411$		−	433.014i		−	1.05356i
$412$		0			0
$413$	−79.3139			−0.192043
$414$		0			0
$415$			68.7504i			0.165664i
$416$		0			0
$417$	−346.604	−	346.604i	−0.831185	−	0.831185i
$418$		0			0
$419$			20.8124i			0.0496715i	0.999692	+	0.0248357i	$0.00790628\pi$
$419$			20.8124i			0.0496715i	−0.999692	+	0.0248357i	$0.992094\pi$
$420$		0			0
$421$	199.204	−	199.204i	0.473168	−	0.473168i	−0.429770	−	0.902938i	$-0.641405\pi$
$421$	199.204	−	199.204i	0.473168	−	0.473168i	0.902938	+	0.429770i	$0.141405\pi$
$422$		0			0
$423$	238.597	+	238.597i	0.564058	+	0.564058i
$424$		0			0
$425$	68.2891	+	68.2891i	0.160680	+	0.160680i
$426$		0			0
$427$	−31.5436	−	31.5436i	−0.0738725	−	0.0738725i
$428$		0			0
$429$	2.18611			0.00509582
$430$		0			0
$431$	193.044			0.447898			0.223949	−	0.974601i	$-0.428105\pi$
$431$	193.044			0.447898			0.223949	+	0.974601i	$0.428105\pi$
$432$		0			0
$433$	118.795	−	118.795i	0.274353	−	0.274353i	−0.556497	−	0.830850i	$-0.687855\pi$
$433$	118.795	−	118.795i	0.274353	−	0.274353i	0.830850	+	0.556497i	$0.187855\pi$
$434$		0			0
$435$	46.5616	−	576.334i	0.107038	−	1.32491i
$436$		0			0
$437$	−217.257	−	217.257i	−0.497155	−	0.497155i
$438$		0			0
$439$			660.370i			1.50426i	0.659015	+	0.752130i	$0.270973\pi$
$439$			660.370i			1.50426i	−0.659015	+	0.752130i	$0.729027\pi$
$440$		0			0
$441$		−	502.262i		−	1.13892i
$442$		0			0
$443$	−222.343	+	222.343i	−0.501904	+	0.501904i	−0.912029	−	0.410125i	$-0.865485\pi$
$443$	−222.343	+	222.343i	−0.501904	+	0.501904i	0.410125	+	0.912029i	$0.365485\pi$
$444$		0			0
$445$	−103.485	+	103.485i	−0.232550	+	0.232550i
$446$		0			0
$447$	−138.534	+	138.534i	−0.309920	+	0.309920i
$448$		0			0
$449$	289.500	+	289.500i	0.644765	+	0.644765i	0.951723	−	0.306958i	$-0.0993111\pi$
$449$	289.500	+	289.500i	0.644765	+	0.644765i	−0.306958	+	0.951723i	$0.599311\pi$
$450$		0			0
$451$	−0.212031			−0.000470135
$452$		0			0
$453$	219.825	−	219.825i	0.485265	−	0.485265i
$454$		0			0
$455$	28.0337			0.0616125
$456$		0			0
$457$			263.854i			0.577361i	0.957426	+	0.288680i	$0.0932165\pi$
$457$			263.854i			0.577361i	−0.957426	+	0.288680i	$0.906784\pi$
$458$		0			0
$459$	−129.928			−0.283067
$460$		0			0
$461$	−489.859	+	489.859i	−1.06260	+	1.06260i	−0.0646957	+	0.997905i	$0.520608\pi$
$461$	−489.859	+	489.859i	−1.06260	+	1.06260i	−0.997905	+	0.0646957i	$0.979392\pi$
$462$		0			0
$463$			606.327i			1.30956i	0.755819	+	0.654781i	$0.227239\pi$
$463$			606.327i			1.30956i	−0.755819	+	0.654781i	$0.772761\pi$
$464$		0			0
$465$	143.615			0.308849
$466$		0			0
$467$	−337.667	−	337.667i	−0.723056	−	0.723056i	0.246171	−	0.969227i	$-0.420828\pi$
$467$	−337.667	−	337.667i	−0.723056	−	0.723056i	−0.969227	+	0.246171i	$0.920828\pi$
$468$		0			0
$469$		−	56.4912i		−	0.120450i
$470$		0			0
$471$	−792.626			−1.68286
$472$		0			0
$473$		−	0.953385i		−	0.00201561i
$474$		0			0
$475$	112.461	+	112.461i	0.236759	+	0.236759i
$476$		0			0
$477$		−	444.757i		−	0.932404i
$478$		0			0
$479$	−431.509	+	431.509i	−0.900854	+	0.900854i	−0.995510	−	0.0946564i	$-0.969825\pi$
$479$	−431.509	+	431.509i	−0.900854	+	0.900854i	0.0946564	+	0.995510i	$0.469825\pi$
$480$		0			0
$481$	83.6211	+	83.6211i	0.173848	+	0.173848i
$482$		0			0
$483$	−20.0483	−	20.0483i	−0.0415078	−	0.0415078i
$484$		0			0
$485$	−194.042	−	194.042i	−0.400086	−	0.400086i
$486$		0			0
$487$	317.203			0.651341			0.325670	−	0.945483i	$-0.394410\pi$
$487$	317.203			0.651341			0.325670	+	0.945483i	$0.394410\pi$
$488$		0			0
$489$	−519.227			−1.06181
$490$		0			0
$491$	440.067	−	440.067i	0.896266	−	0.896266i	−0.0988377	−	0.995104i	$-0.531512\pi$
$491$	440.067	−	440.067i	0.896266	−	0.896266i	0.995104	+	0.0988377i	$0.0315125\pi$
$492$		0			0
$493$	623.916	+	50.4057i	1.26555	+	0.102243i
$494$		0			0
$495$	−1.98735	−	1.98735i	−0.00401485	−	0.00401485i
$496$		0			0
$497$		−	53.0720i		−	0.106785i
$498$		0			0
$499$		−	847.151i		−	1.69770i	−0.528635	−	0.848849i	$-0.677296\pi$
$499$		−	847.151i		−	1.69770i	0.528635	−	0.848849i	$-0.322704\pi$
$500$		0			0
$501$	689.610	−	689.610i	1.37647	−	1.37647i
$502$		0			0
$503$	6.42815	−	6.42815i	0.0127796	−	0.0127796i	−0.700688	−	0.713468i	$-0.747124\pi$
$503$	6.42815	−	6.42815i	0.0127796	−	0.0127796i	0.713468	+	0.700688i	$0.247124\pi$
$504$		0			0
$505$	165.077	−	165.077i	0.326884	−	0.326884i
$506$		0			0
$507$	311.433	+	311.433i	0.614267	+	0.614267i
$508$		0			0
$509$	−476.056			−0.935277			−0.467638	−	0.883920i	$-0.654895\pi$
$509$	−476.056			−0.935277			−0.467638	+	0.883920i	$0.654895\pi$
$510$		0			0
$511$	−55.0007	+	55.0007i	−0.107633	+	0.107633i
$512$		0			0
$513$	−213.970			−0.417095
$514$		0			0
$515$			506.289i			0.983086i
$516$		0			0
$517$	−1.94736			−0.00376665
$518$		0			0
$519$	−20.6018	+	20.6018i	−0.0396952	+	0.0396952i
$520$		0			0
$521$			557.186i			1.06946i	0.845024	+	0.534728i	$0.179586\pi$
$521$			557.186i			1.06946i	−0.845024	+	0.534728i	$0.820414\pi$
$522$		0			0
$523$	−456.134			−0.872149			−0.436074	−	0.899911i	$-0.643632\pi$
$523$	−456.134			−0.872149			−0.436074	+	0.899911i	$0.643632\pi$
$524$		0			0
$525$	10.3778	+	10.3778i	0.0197672	+	0.0197672i
$526$		0			0
$527$			155.472i			0.295013i
$528$		0			0
$529$	−454.287			−0.858766
$530$		0			0
$531$		−	1103.27i		−	2.07772i
$532$		0			0
$533$	20.8022	+	20.8022i	0.0390285	+	0.0390285i
$534$		0			0
$535$			403.071i			0.753404i
$536$		0			0
$537$	−115.017	+	115.017i	−0.214184	+	0.214184i
$538$		0			0
$539$	2.04966	+	2.04966i	0.00380272	+	0.00380272i
$540$		0			0
$541$	537.048	+	537.048i	0.992694	+	0.992694i	0.999974	−	0.00727934i	$-0.00231711\pi$
$541$	537.048	+	537.048i	0.992694	+	0.992694i	−0.00727934	+	0.999974i	$0.502317\pi$
$542$		0			0
$543$	−597.605	−	597.605i	−1.10056	−	1.10056i
$544$		0			0
$545$	186.293			0.341823
$546$		0			0
$547$	−353.235			−0.645768			−0.322884	−	0.946439i	$-0.604652\pi$
$547$	−353.235			−0.645768			−0.322884	+	0.946439i	$0.604652\pi$
$548$		0			0
$549$	438.776	−	438.776i	0.799229	−	0.799229i
$550$		0			0
$551$	1027.49	+	83.0098i	1.86477	+	0.150653i
$552$		0			0
$553$	58.6879	+	58.6879i	0.106126	+	0.106126i
$554$		0			0
$555$		−	284.016i		−	0.511740i
$556$		0			0
$557$		−	916.424i		−	1.64529i	−0.568558	−	0.822643i	$-0.692499\pi$
$557$		−	916.424i		−	1.64529i	0.568558	−	0.822643i	$-0.307501\pi$
$558$		0			0
$559$	−93.5358	+	93.5358i	−0.167327	+	0.167327i
$560$		0			0
$561$	4.01902	−	4.01902i	0.00716402	−	0.00716402i
$562$		0			0
$563$	526.927	−	526.927i	0.935928	−	0.935928i	−0.0621396	−	0.998067i	$-0.519792\pi$
$563$	526.927	−	526.927i	0.935928	−	0.935928i	0.998067	+	0.0621396i	$0.0197924\pi$
$564$		0			0
$565$	−471.646	−	471.646i	−0.834772	−	0.834772i
$566$		0			0
$567$	49.8028			0.0878356
$568$		0			0
$569$	394.074	−	394.074i	0.692573	−	0.692573i	−0.270224	−	0.962797i	$-0.587098\pi$
$569$	394.074	−	394.074i	0.692573	−	0.692573i	0.962797	+	0.270224i	$0.0870979\pi$
$570$		0			0
$571$	552.975			0.968432			0.484216	−	0.874949i	$-0.339105\pi$
$571$	552.975			0.968432			0.484216	+	0.874949i	$0.339105\pi$
$572$		0			0
$573$			1340.30i			2.33909i
$574$		0			0
$575$	−38.6744			−0.0672598
$576$		0			0
$577$	167.445	−	167.445i	0.290200	−	0.290200i	−0.546959	−	0.837159i	$-0.684215\pi$
$577$	167.445	−	167.445i	0.290200	−	0.290200i	0.837159	+	0.546959i	$0.184215\pi$
$578$		0			0
$579$			813.321i			1.40470i
$580$		0			0
$581$	−11.3105			−0.0194672
$582$		0			0
$583$	1.81499	+	1.81499i	0.00311319	+	0.00311319i
$584$		0			0
$585$			389.954i			0.666588i
$586$		0			0
$587$	−38.0082			−0.0647500			−0.0323750	−	0.999476i	$-0.510307\pi$
$587$	−38.0082			−0.0647500			−0.0323750	+	0.999476i	$0.510307\pi$
$588$		0			0
$589$			256.036i			0.434696i
$590$		0			0
$591$	−793.388	−	793.388i	−1.34245	−	1.34245i
$592$		0			0
$593$		−	627.850i		−	1.05877i	−0.848382	−	0.529385i	$-0.822423\pi$
$593$		−	627.850i		−	1.05877i	0.848382	−	0.529385i	$-0.177577\pi$
$594$		0			0
$595$	51.5381	−	51.5381i	0.0866187	−	0.0866187i
$596$		0			0
$597$	−522.854	−	522.854i	−0.875802	−	0.875802i
$598$		0			0
$599$	−674.702	−	674.702i	−1.12638	−	1.12638i	−0.990761	−	0.135619i	$-0.956698\pi$
$599$	−674.702	−	674.702i	−1.12638	−	1.12638i	−0.135619	−	0.990761i	$-0.543302\pi$
$600$		0			0
$601$	−500.527	−	500.527i	−0.832823	−	0.832823i	0.155079	−	0.987902i	$-0.450437\pi$
$601$	−500.527	−	500.527i	−0.832823	−	0.832823i	−0.987902	+	0.155079i	$0.950437\pi$
$602$		0			0
$603$	785.802			1.30315
$604$		0			0
$605$	−548.178			−0.906079
$606$		0			0
$607$	−780.373	+	780.373i	−1.28562	+	1.28562i	−0.348204	+	0.937419i	$0.613208\pi$
$607$	−780.373	+	780.373i	−1.28562	+	1.28562i	−0.937419	+	0.348204i	$0.886792\pi$
$608$		0			0
$609$	94.8155	+	7.66007i	0.155690	+	0.0125781i
$610$		0			0
$611$	191.054	+	191.054i	0.312690	+	0.312690i
$612$		0			0
$613$			830.453i			1.35473i	0.735645	+	0.677367i	$0.236879\pi$
$613$			830.453i			1.35473i	−0.735645	+	0.677367i	$0.763121\pi$
$614$		0			0
$615$		−	70.6537i		−	0.114884i
$616$		0			0
$617$	69.2239	−	69.2239i	0.112194	−	0.112194i	−0.648781	−	0.760975i	$-0.724721\pi$
$617$	69.2239	−	69.2239i	0.112194	−	0.112194i	0.760975	+	0.648781i	$0.224721\pi$
$618$		0			0
$619$	331.072	−	331.072i	0.534849	−	0.534849i	−0.387162	−	0.922012i	$-0.626545\pi$
$619$	331.072	−	331.072i	0.534849	−	0.534849i	0.922012	+	0.387162i	$0.126545\pi$
$620$		0			0
$621$	36.7912	−	36.7912i	0.0592452	−	0.0592452i
$622$		0			0
$623$	−17.0248	−	17.0248i	−0.0273271	−	0.0273271i
$624$		0			0
$625$	−493.123			−0.788997
$626$		0			0
$627$	6.61864	−	6.61864i	0.0105561	−	0.0105561i
$628$		0			0
$629$	307.464			0.488814
$630$		0			0
$631$		−	681.376i		−	1.07984i	−0.841718	−	0.539918i	$-0.818455\pi$
$631$		−	681.376i		−	1.07984i	0.841718	−	0.539918i	$-0.181545\pi$
$632$		0			0
$633$	696.381			1.10013
$634$		0			0
$635$	−37.4558	+	37.4558i	−0.0589855	+	0.0589855i
$636$		0			0
$637$		−	402.181i		−	0.631368i
$638$		0			0
$639$	738.240			1.15531
$640$		0			0
$641$	−517.626	−	517.626i	−0.807529	−	0.807529i	0.176730	−	0.984259i	$-0.443448\pi$
$641$	−517.626	−	517.626i	−0.807529	−	0.807529i	−0.984259	+	0.176730i	$0.943448\pi$
$642$		0			0
$643$			867.657i			1.34939i	0.738097	+	0.674694i	$0.235725\pi$
$643$			867.657i			1.34939i	−0.738097	+	0.674694i	$0.764275\pi$
$644$		0			0
$645$	317.690			0.492543
$646$		0			0
$647$		−	357.347i		−	0.552314i	−0.961113	−	0.276157i	$-0.910939\pi$
$647$		−	357.347i		−	0.552314i	0.961113	−	0.276157i	$-0.0890609\pi$
$648$		0			0
$649$	4.50229	+	4.50229i	0.00693728	+	0.00693728i
$650$		0			0
$651$			23.6268i			0.0362930i
$652$		0			0
$653$	−700.906	+	700.906i	−1.07336	+	1.07336i	−0.0762758	+	0.997087i	$0.524303\pi$
$653$	−700.906	+	700.906i	−1.07336	+	1.07336i	−0.997087	+	0.0762758i	$0.975697\pi$
$654$		0			0
$655$	−1.63834	−	1.63834i	−0.00250128	−	0.00250128i
$656$		0			0
$657$	−765.069	−	765.069i	−1.16449	−	1.16449i
$658$		0			0
$659$	−760.878	−	760.878i	−1.15459	−	1.15459i	−0.985621	−	0.168974i	$-0.945955\pi$
$659$	−760.878	−	760.878i	−1.15459	−	1.15459i	−0.168974	−	0.985621i	$-0.554045\pi$
$660$		0			0
$661$	−204.176			−0.308889			−0.154444	−	0.988001i	$-0.549359\pi$
$661$	−204.176			−0.308889			−0.154444	+	0.988001i	$0.549359\pi$
$662$		0			0
$663$	−788.604			−1.18945
$664$		0			0
$665$	84.8747	−	84.8747i	0.127631	−	0.127631i
$666$		0			0
$667$	−190.945	+	162.399i	−0.286275	+	0.243477i
$668$		0			0
$669$	177.458	+	177.458i	0.265258	+	0.265258i
$670$		0			0
$671$			3.58117i			0.00533707i
$672$		0			0
$673$		−	255.714i		−	0.379962i	−0.981788	−	0.189981i	$-0.939157\pi$
$673$		−	255.714i		−	0.379962i	0.981788	−	0.189981i	$-0.0608426\pi$
$674$		0			0
$675$	−19.0446	+	19.0446i	−0.0282142	+	0.0282142i
$676$		0			0
$677$	−778.876	+	778.876i	−1.15048	+	1.15048i	−0.164026	+	0.986456i	$0.552448\pi$
$677$	−778.876	+	778.876i	−1.15048	+	1.15048i	−0.986456	+	0.164026i	$0.947552\pi$
$678$		0			0
$679$	31.9227	−	31.9227i	0.0470143	−	0.0470143i
$680$		0			0
$681$	540.692	+	540.692i	0.793967	+	0.793967i
$682$		0			0
$683$	712.500			1.04319			0.521596	−	0.853193i	$-0.325337\pi$
$683$	712.500			1.04319			0.521596	+	0.853193i	$0.325337\pi$
$684$		0			0
$685$	−315.207	+	315.207i	−0.460156	+	0.460156i
$686$		0			0
$687$	−900.556			−1.31085
$688$		0			0
$689$		−	356.134i		−	0.516886i
$690$		0			0
$691$	−85.2702			−0.123401			−0.0617006	−	0.998095i	$-0.519652\pi$
$691$	−85.2702			−0.123401			−0.0617006	+	0.998095i	$0.519652\pi$
$692$		0			0
$693$	0.326948	−	0.326948i	0.000471787	−	0.000471787i
$694$		0			0
$695$			504.612i			0.726060i
$696$		0			0
$697$	76.4869			0.109737
$698$		0			0
$699$	320.124	+	320.124i	0.457975	+	0.457975i
$700$		0			0
$701$		−	389.567i		−	0.555731i	−0.960620	−	0.277865i	$-0.910373\pi$
$701$		−	389.567i		−	0.555731i	0.960620	−	0.277865i	$-0.0896269\pi$
$702$		0			0
$703$	506.342			0.720258
$704$		0			0
$705$		−	648.906i		−	0.920434i
$706$		0			0
$707$	27.1575	+	27.1575i	0.0384123	+	0.0384123i
$708$		0			0
$709$		−	616.933i		−	0.870145i	−0.900396	−	0.435072i	$-0.856723\pi$
$709$		−	616.933i		−	0.870145i	0.900396	−	0.435072i	$-0.143277\pi$
$710$		0			0
$711$	−816.359	+	816.359i	−1.14818	+	1.14818i
$712$		0			0
$713$	−44.0244	−	44.0244i	−0.0617452	−	0.0617452i
$714$		0			0
$715$	−1.59135	−	1.59135i	−0.00222566	−	0.00222566i
$716$		0			0
$717$	971.384	+	971.384i	1.35479	+	1.35479i
$718$		0			0
$719$	−273.210			−0.379986			−0.189993	−	0.981785i	$-0.560847\pi$
$719$	−273.210			−0.379986			−0.189993	+	0.981785i	$0.560847\pi$
$720$		0			0
$721$	−83.2920			−0.115523
$722$		0			0
$723$	974.035	−	974.035i	1.34721	−	1.34721i
$724$		0			0
$725$	98.8409	−	84.0641i	0.136332	−	0.115950i
$726$		0			0
$727$	−136.415	−	136.415i	−0.187641	−	0.187641i	0.607034	−	0.794676i	$-0.292359\pi$
$727$	−136.415	−	136.415i	−0.187641	−	0.187641i	−0.794676	+	0.607034i	$0.792359\pi$
$728$		0			0
$729$			931.186i			1.27735i
$730$		0			0
$731$			343.919i			0.470477i
$732$		0			0
$733$	−580.859	+	580.859i	−0.792441	+	0.792441i	−0.981890	−	0.189449i	$-0.939330\pi$
$733$	−580.859	+	580.859i	−0.792441	+	0.792441i	0.189449	+	0.981890i	$0.439330\pi$
$734$		0			0
$735$	−682.996	+	682.996i	−0.929247	+	0.929247i
$736$		0			0
$737$	−3.20675	+	3.20675i	−0.00435109	+	0.00435109i
$738$		0			0
$739$	688.432	+	688.432i	0.931572	+	0.931572i	0.997804	−	0.0662318i	$-0.0210977\pi$
$739$	688.432	+	688.432i	0.931572	+	0.931572i	−0.0662318	+	0.997804i	$0.521098\pi$
$740$		0			0
$741$	−1298.70			−1.75263
$742$		0			0
$743$	−108.284	+	108.284i	−0.145739	+	0.145739i	−0.776212	−	0.630472i	$-0.782861\pi$
$743$	−108.284	+	108.284i	−0.145739	+	0.145739i	0.630472	+	0.776212i	$0.282861\pi$
$744$		0			0
$745$	201.689			0.270723
$746$		0			0
$747$		−	157.330i		−	0.210616i
$748$		0			0
$749$	−66.3112			−0.0885329
$750$		0			0
$751$	−474.687	+	474.687i	−0.632074	+	0.632074i	−0.948588	−	0.316514i	$-0.897488\pi$
$751$	−474.687	+	474.687i	−0.632074	+	0.632074i	0.316514	+	0.948588i	$0.397488\pi$
$752$		0			0
$753$		−	48.7587i		−	0.0647526i
$754$		0			0
$755$	−320.037			−0.423891
$756$		0			0
$757$	144.571	+	144.571i	0.190979	+	0.190979i	0.796119	−	0.605140i	$-0.206883\pi$
$757$	144.571	+	144.571i	0.190979	+	0.190979i	−0.605140	+	0.796119i	$0.706883\pi$
$758$		0			0
$759$			2.27610i			0.00299882i
$760$		0			0
$761$	279.009			0.366635			0.183318	−	0.983054i	$-0.441316\pi$
$761$	279.009			0.366635			0.183318	+	0.983054i	$0.441316\pi$
$762$		0			0
$763$			30.6480i			0.0401678i
$764$		0			0
$765$	716.905	+	716.905i	0.937130	+	0.937130i
$766$		0			0
$767$		−	883.432i		−	1.15180i
$768$		0			0
$769$	270.425	−	270.425i	0.351658	−	0.351658i	−0.509068	−	0.860726i	$-0.670010\pi$
$769$	270.425	−	270.425i	0.351658	−	0.351658i	0.860726	+	0.509068i	$0.170010\pi$
$770$		0			0
$771$	213.352	+	213.352i	0.276722	+	0.276722i
$772$		0			0
$773$	933.705	+	933.705i	1.20790	+	1.20790i	0.971707	+	0.236191i	$0.0758991\pi$
$773$	933.705	+	933.705i	1.20790	+	1.20790i	0.236191	+	0.971707i	$0.424101\pi$
$774$		0			0
$775$	22.7887	+	22.7887i	0.0294048	+	0.0294048i
$776$		0			0
$777$	46.7248			0.0601348
$778$		0			0
$779$	125.961			0.161696
$780$		0			0
$781$	−3.01266	+	3.01266i	−0.00385744	+	0.00385744i
$782$		0			0
$783$	−14.0573	+	173.999i	−0.0179531	+	0.222221i
$784$		0			0
$785$	576.982	+	576.982i	0.735009	+	0.735009i
$786$		0			0
$787$		−	377.592i		−	0.479786i	−0.970799	−	0.239893i	$-0.922888\pi$
$787$		−	377.592i		−	0.479786i	0.970799	−	0.239893i	$-0.0771124\pi$
$788$		0			0
$789$		−	956.705i		−	1.21255i
$790$		0			0
$791$	77.5928	−	77.5928i	0.0980945	−	0.0980945i
$792$		0			0
$793$	351.346	−	351.346i	0.443059	−	0.443059i
$794$		0			0
$795$	−604.797	+	604.797i	−0.760751	+	0.760751i
$796$		0			0
$797$	350.486	+	350.486i	0.439756	+	0.439756i	0.891930	−	0.452174i	$-0.149351\pi$
$797$	350.486	+	350.486i	0.439756	+	0.439756i	−0.452174	+	0.891930i	$0.649351\pi$
$798$		0			0
$799$	702.480			0.879199
$800$		0			0
$801$	236.818	−	236.818i	0.295653	−	0.295653i
$802$		0			0
$803$	6.24428			0.00777619
$804$		0			0
$805$			29.1878i			0.0362581i
$806$		0			0
$807$	1695.48			2.10097
$808$		0			0
$809$	−303.271	+	303.271i	−0.374872	+	0.374872i	−0.869248	−	0.494376i	$-0.835397\pi$
$809$	−303.271	+	303.271i	−0.374872	+	0.374872i	0.494376	+	0.869248i	$0.335397\pi$
$810$		0			0
$811$		−	1521.59i		−	1.87619i	−0.346380	−	0.938094i	$-0.612589\pi$
$811$		−	1521.59i		−	1.87619i	0.346380	−	0.938094i	$-0.387411\pi$
$812$		0			0
$813$	1896.87			2.33318
$814$		0			0
$815$	377.964	+	377.964i	0.463760	+	0.463760i
$816$		0			0
$817$			566.376i			0.693239i
$818$		0			0
$819$	−64.1532			−0.0783311
$820$		0			0
$821$		−	307.159i		−	0.374128i	−0.982348	−	0.187064i	$-0.940103\pi$
$821$		−	307.159i		−	0.374128i	0.982348	−	0.187064i	$-0.0598972\pi$
$822$		0			0
$823$	861.491	+	861.491i	1.04677	+	1.04677i	0.998851	+	0.0479183i	$0.0152587\pi$
$823$	861.491	+	861.491i	1.04677	+	1.04677i	0.0479183	+	0.998851i	$0.484741\pi$
$824$		0			0
$825$		−	1.17820i		−	0.00142812i
$826$		0			0
$827$	−18.3000	+	18.3000i	−0.0221282	+	0.0221282i	−0.718084	−	0.695956i	$-0.754981\pi$
$827$	−18.3000	+	18.3000i	−0.0221282	+	0.0221282i	0.695956	+	0.718084i	$0.254981\pi$
$828$		0			0
$829$	−211.234	−	211.234i	−0.254806	−	0.254806i	0.568132	−	0.822938i	$-0.307666\pi$
$829$	−211.234	−	211.234i	−0.254806	−	0.254806i	−0.822938	+	0.568132i	$0.807666\pi$
$830$		0			0
$831$	−83.1683	−	83.1683i	−0.100082	−	0.100082i
$832$		0			0
$833$	−739.384	−	739.384i	−0.887616	−	0.887616i
$834$		0			0
$835$	−1003.99			−1.20238
$836$		0			0
$837$	−43.3582			−0.0518020
$838$		0			0
$839$	−479.471	+	479.471i	−0.571479	+	0.571479i	−0.932542	−	0.361063i	$-0.882414\pi$
$839$	−479.471	+	479.471i	−0.571479	+	0.571479i	0.361063	+	0.932542i	$0.382414\pi$
$840$		0			0
$841$	135.006	−	830.093i	0.160531	−	0.987031i
$842$		0			0
$843$	1459.24	+	1459.24i	1.73100	+	1.73100i
$844$		0			0
$845$		−	453.408i		−	0.536577i
$846$		0			0
$847$		−	90.1833i		−	0.106474i
$848$		0			0
$849$	−819.970	+	819.970i	−0.965807	+	0.965807i
$850$		0			0
$851$	−87.0635	+	87.0635i	−0.102307	+	0.102307i
$852$		0			0
$853$	−74.8941	+	74.8941i	−0.0878008	+	0.0878008i	−0.749643	−	0.661842i	$-0.769775\pi$
$853$	−74.8941	+	74.8941i	−0.0878008	+	0.0878008i	0.661842	+	0.749643i	$0.269775\pi$
$854$		0			0
$855$	1180.62	+	1180.62i	1.38084	+	1.38084i
$856$		0			0
$857$	1145.50			1.33664			0.668321	−	0.743873i	$-0.267013\pi$
$857$	1145.50			1.33664			0.668321	+	0.743873i	$0.267013\pi$
$858$		0			0
$859$	307.151	−	307.151i	0.357568	−	0.357568i	−0.505348	−	0.862916i	$-0.668636\pi$
$859$	307.151	−	307.151i	0.357568	−	0.357568i	0.862916	+	0.505348i	$0.168636\pi$
$860$		0			0
$861$	11.6236			0.0135001
$862$		0			0
$863$			181.269i			0.210046i	0.994470	+	0.105023i	$0.0334916\pi$
$863$			181.269i			0.210046i	−0.994470	+	0.105023i	$0.966508\pi$
$864$		0			0
$865$	29.9937			0.0346747
$866$		0			0
$867$	−550.459	+	550.459i	−0.634900	+	0.634900i
$868$		0			0
$869$		−	6.66290i		−	0.00766732i
$870$		0			0
$871$	629.223			0.722415
$872$		0			0
$873$	444.050	+	444.050i	0.508649	+	0.508649i
$874$		0			0
$875$		−	99.5282i		−	0.113747i
$876$		0			0
$877$	1730.81			1.97355			0.986777	−	0.162083i	$-0.0518211\pi$
$877$	1730.81			1.97355			0.986777	+	0.162083i	$0.0518211\pi$
$878$		0			0
$879$		−	525.545i		−	0.597890i
$880$		0			0
$881$	433.391	+	433.391i	0.491931	+	0.491931i	0.908914	−	0.416983i	$-0.136913\pi$
$881$	433.391	+	433.391i	0.491931	+	0.491931i	−0.416983	+	0.908914i	$0.636913\pi$
$882$		0			0
$883$			589.072i			0.667126i	0.942728	+	0.333563i	$0.108251\pi$
$883$			589.072i			0.667126i	−0.942728	+	0.333563i	$0.891749\pi$
$884$		0			0
$885$	−1500.27	+	1500.27i	−1.69522	+	1.69522i
$886$		0			0
$887$	−136.134	−	136.134i	−0.153477	−	0.153477i	0.626192	−	0.779669i	$-0.284613\pi$
$887$	−136.134	−	136.134i	−0.153477	−	0.153477i	−0.779669	+	0.626192i	$0.784613\pi$
$888$		0			0
$889$	−6.16203	−	6.16203i	−0.00693142	−	0.00693142i
$890$		0			0
$891$	−2.82708	−	2.82708i	−0.00317293	−	0.00317293i
$892$		0			0
$893$	1156.87			1.29548
$894$		0			0
$895$	167.450			0.187095
$896$		0			0
$897$	223.306	−	223.306i	0.248948	−	0.248948i
$898$		0			0
$899$	208.207	+	16.8209i	0.231599	+	0.0187107i
$900$		0			0
$901$	−654.729	−	654.729i	−0.726670	−	0.726670i
$902$		0			0
$903$			52.2647i			0.0578790i
$904$		0			0
$905$			870.038i			0.961368i
$906$		0			0
$907$	490.744	−	490.744i	0.541063	−	0.541063i	−0.382778	−	0.923840i	$-0.625033\pi$
$907$	490.744	−	490.744i	0.541063	−	0.541063i	0.923840	+	0.382778i	$0.125033\pi$
$908$		0			0
$909$	−377.766	+	377.766i	−0.415584	+	0.415584i
$910$		0			0
$911$	−686.245	+	686.245i	−0.753287	+	0.753287i	−0.975091	−	0.221804i	$-0.928805\pi$
$911$	−686.245	+	686.245i	−0.753287	+	0.753287i	0.221804	+	0.975091i	$0.428805\pi$
$912$		0			0
$913$	0.642044	+	0.642044i	0.000703225	+	0.000703225i
$914$		0			0
$915$	−1193.33			−1.30419
$916$		0			0
$917$	0.269531	−	0.269531i	0.000293927	−	0.000293927i
$918$		0			0
$919$	−94.8391			−0.103198			−0.0515991	−	0.998668i	$-0.516432\pi$
$919$	−94.8391			−0.103198			−0.0515991	+	0.998668i	$0.516432\pi$
$920$		0			0
$921$		−	1201.73i		−	1.30481i
$922$		0			0
$923$	591.138			0.640453
$924$		0			0
$925$	45.0675	−	45.0675i	0.0487216	−	0.0487216i
$926$		0			0
$927$		−	1158.61i		−	1.24985i
$928$		0			0
$929$	−382.605			−0.411846			−0.205923	−	0.978568i	$-0.566020\pi$
$929$	−382.605			−0.411846			−0.205923	+	0.978568i	$0.566020\pi$
$930$		0			0
$931$	−1217.64	−	1217.64i	−1.30789	−	1.30789i
$932$		0			0
$933$			861.210i			0.923054i
$934$		0			0
$935$	−5.85118			−0.00625795
$936$		0			0
$937$		−	1462.55i		−	1.56089i	−0.625227	−	0.780443i	$-0.714994\pi$
$937$		−	1462.55i		−	1.56089i	0.625227	−	0.780443i	$-0.285006\pi$
$938$		0			0
$939$	983.635	+	983.635i	1.04753	+	1.04753i
$940$		0			0
$941$			828.617i			0.880571i	0.897858	+	0.440285i	$0.145123\pi$
$941$			828.617i			0.880571i	−0.897858	+	0.440285i	$0.854877\pi$
$942$		0			0
$943$	−21.6585	+	21.6585i	−0.0229677	+	0.0229677i
$944$		0			0
$945$	14.3731	+	14.3731i	0.0152096	+	0.0152096i
$946$		0			0
$947$	612.076	+	612.076i	0.646331	+	0.646331i	0.952104	−	0.305773i	$-0.0989149\pi$
$947$	612.076	+	612.076i	0.646331	+	0.646331i	−0.305773	+	0.952104i	$0.598915\pi$
$948$		0			0
$949$	−612.621	−	612.621i	−0.645544	−	0.645544i
$950$		0			0
$951$	1384.81			1.45617
$952$		0			0
$953$	884.227			0.927835			0.463917	−	0.885878i	$-0.346443\pi$
$953$	884.227			0.927835			0.463917	+	0.885878i	$0.346443\pi$
$954$		0			0
$955$	975.652	−	975.652i	1.02163	−	1.02163i
$956$		0			0
$957$	−4.94742	−	5.81708i	−0.00516972	−	0.00607845i
$958$		0			0
$959$	−51.8562	−	51.8562i	−0.0540732	−	0.0540732i
$960$		0			0
$961$		−	909.118i		−	0.946012i
$962$		0			0
$963$		−	922.400i		−	0.957840i
$964$		0			0
$965$	592.047	−	592.047i	0.613520	−	0.613520i
$966$		0			0
$967$	1022.14	−	1022.14i	1.05702	−	1.05702i	0.0587468	−	0.998273i	$-0.481290\pi$
$967$	1022.14	−	1022.14i	1.05702	−	1.05702i	0.998273	−	0.0587468i	$-0.0187105\pi$
$968$		0			0
$969$	−2387.57	+	2387.57i	−2.46395	+	2.46395i
$970$		0			0
$971$	−118.570	−	118.570i	−0.122111	−	0.122111i	0.643410	−	0.765522i	$-0.277519\pi$
$971$	−118.570	−	118.570i	−0.122111	−	0.122111i	−0.765522	+	0.643410i	$0.777519\pi$
$972$		0			0
$973$	−83.0161			−0.0853197
$974$		0			0
$975$	−115.592	+	115.592i	−0.118556	+	0.118556i
$976$		0			0
$977$	722.204			0.739205			0.369603	−	0.929190i	$-0.379494\pi$
$977$	722.204			0.739205			0.369603	+	0.929190i	$0.379494\pi$
$978$		0			0
$979$			1.93284i			0.00197430i
$980$		0			0
$981$	−426.319			−0.434576
$982$		0			0
$983$	295.211	−	295.211i	0.300317	−	0.300317i	−0.540821	−	0.841138i	$-0.681886\pi$
$983$	295.211	−	295.211i	0.300317	−	0.300317i	0.841138	+	0.540821i	$0.181886\pi$
$984$		0			0
$985$			1155.07i			1.17266i
$986$		0			0
$987$	106.755			0.108161
$988$		0			0
$989$	−97.3863	−	97.3863i	−0.0984694	−	0.0984694i
$990$		0			0
$991$			1627.14i			1.64191i	0.570991	+	0.820956i	$0.306559\pi$
$991$			1627.14i			1.64191i	−0.570991	+	0.820956i	$0.693441\pi$
$992$		0			0
$993$	−1497.72			−1.50828
$994$		0			0
$995$			761.210i			0.765035i
$996$		0			0
$997$	472.423	+	472.423i	0.473845	+	0.473845i	0.903156	−	0.429312i	$-0.141244\pi$
$997$	472.423	+	472.423i	0.473845	+	0.473845i	−0.429312	+	0.903156i	$0.641244\pi$
$998$		0			0
$999$			85.7462i			0.0858320i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.3.l.c.273.4		8
4.3	odd	2		29.3.c.a.12.4	✓	8
12.11	even	2		261.3.f.a.244.1		8
29.17	odd	4	inner	464.3.l.c.17.4		8
116.75	even	4		29.3.c.a.17.4	yes	8
348.191	odd	4		261.3.f.a.46.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.c.a.12.4	✓	8	4.3	odd	2
29.3.c.a.17.4	yes	8	116.75	even	4
261.3.f.a.46.1		8	348.191	odd	4
261.3.f.a.244.1		8	12.11	even	2
464.3.l.c.17.4		8	29.17	odd	4	inner
464.3.l.c.273.4		8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	464.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.11190 + 3.11190i) q^{3} -4.53053i q^{5} +0.745339 q^{7} +10.3678i q^{9} +O(q^{10})\)	\(q+(3.11190 + 3.11190i) q^{3} -4.53053i q^{5} +0.745339 q^{7} +10.3678i q^{9} +(-0.0423096 - 0.0423096i) q^{11} +8.30191i q^{13} +(14.0985 - 14.0985i) q^{15} +(15.2625 + 15.2625i) q^{17} +(25.1348 + 25.1348i) q^{19} +(2.31942 + 2.31942i) q^{21} -8.64367 q^{23} +4.47430 q^{25} +(-4.25644 + 4.25644i) q^{27} +(22.0908 - 18.7882i) q^{29} +(5.09325 + 5.09325i) q^{31} -0.263326i q^{33} -3.37678i q^{35} +(10.0725 - 10.0725i) q^{37} +(-25.8347 + 25.8347i) q^{39} +(2.50571 - 2.50571i) q^{41} +(11.2668 + 11.2668i) q^{43} +46.9716 q^{45} +(23.0132 - 23.0132i) q^{47} -48.4445 q^{49} +94.9907i q^{51} -42.8979 q^{53} +(-0.191685 + 0.191685i) q^{55} +156.434i q^{57} -106.413 q^{59} +(-42.3211 - 42.3211i) q^{61} +7.72752i q^{63} +37.6120 q^{65} -75.7926i q^{67} +(-26.8982 - 26.8982i) q^{69} -71.2051i q^{71} +(-73.7928 + 73.7928i) q^{73} +(13.9236 + 13.9236i) q^{75} +(-0.0315350 - 0.0315350i) q^{77} +(78.7399 + 78.7399i) q^{79} +66.8190 q^{81} -15.1749 q^{83} +(69.1473 - 69.1473i) q^{85} +(127.211 + 10.2773i) q^{87} +(-22.8417 - 22.8417i) q^{89} +6.18773i q^{91} +31.6993i q^{93} +(113.874 - 113.874i) q^{95} +(42.8298 - 42.8298i) q^{97} +(0.438657 - 0.438657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 4 q^{7}+O(q^{10}) \) 8 * q + 2 * q^3 + 4 * q^7	\( 8 q + 2 q^{3} + 4 q^{7} + 6 q^{11} + 10 q^{15} + 12 q^{17} + 16 q^{19} - 36 q^{21} + 104 q^{25} + 98 q^{27} + 128 q^{29} + 10 q^{31} - 84 q^{37} + 90 q^{39} + 20 q^{41} + 190 q^{43} + 292 q^{45} - 58 q^{47} - 72 q^{49} + 252 q^{53} + 74 q^{55} + 40 q^{59} - 208 q^{61} + 36 q^{65} + 120 q^{69} - 188 q^{73} + 12 q^{75} + 180 q^{77} + 382 q^{79} - 124 q^{81} - 280 q^{83} + 32 q^{85} - 34 q^{87} - 64 q^{89} + 380 q^{95} - 44 q^{97} - 552 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 4 * q^7 + 6 * q^11 + 10 * q^15 + 12 * q^17 + 16 * q^19 - 36 * q^21 + 104 * q^25 + 98 * q^27 + 128 * q^29 + 10 * q^31 - 84 * q^37 + 90 * q^39 + 20 * q^41 + 190 * q^43 + 292 * q^45 - 58 * q^47 - 72 * q^49 + 252 * q^53 + 74 * q^55 + 40 * q^59 - 208 * q^61 + 36 * q^65 + 120 * q^69 - 188 * q^73 + 12 * q^75 + 180 * q^77 + 382 * q^79 - 124 * q^81 - 280 * q^83 + 32 * q^85 - 34 * q^87 - 64 * q^89 + 380 * q^95 - 44 * q^97 - 552 * q^99

Introduction

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