LMFDB - Embedded newform 384.3.l.b.31.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,3,Mod(31,384)]

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([2, 1, 0]))

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

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

chi := DirichletCharacter("384.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	384.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:	$10.4632421514$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + \cdots + 65536 $ x^16 - 6x^14 - 4x^13 + 10x^12 + 56x^11 + 88x^10 - 128x^9 - 496x^8 - 512x^7 + 1408x^6 + 3584x^5 + 2560x^4 - 4096x^3 - 24576*x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{24} $
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.8
Root			$-1.87459 + 0.697079i$ of defining polynomial
Character	$\chi$	$=$	384.31
Dual form			384.3.l.b.223.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 + 1.22474i) q^{3} +(5.24354 + 5.24354i) q^{5} +5.32796 q^{7} +3.00000i q^{9} +O(q^{10})$	\(q+(1.22474 + 1.22474i) q^{3} +(5.24354 + 5.24354i) q^{5} +5.32796 q^{7} +3.00000i q^{9} +(12.2863 - 12.2863i) q^{11} +(5.73657 - 5.73657i) q^{13} +12.8440i q^{15} -23.3997 q^{17} +(11.7492 + 11.7492i) q^{19} +(6.52540 + 6.52540i) q^{21} -5.80841 q^{23} +29.9894i q^{25} +(-3.67423 + 3.67423i) q^{27} +(-18.3914 + 18.3914i) q^{29} -16.9053i q^{31} +30.0951 q^{33} +(27.9374 + 27.9374i) q^{35} +(-15.3391 - 15.3391i) q^{37} +14.0517 q^{39} +29.2351i q^{41} +(33.4099 - 33.4099i) q^{43} +(-15.7306 + 15.7306i) q^{45} -18.2125i q^{47} -20.6128 q^{49} +(-28.6586 - 28.6586i) q^{51} +(66.9856 + 66.9856i) q^{53} +128.847 q^{55} +28.7796i q^{57} +(-27.1523 + 27.1523i) q^{59} +(-65.2399 + 65.2399i) q^{61} +15.9839i q^{63} +60.1599 q^{65} +(-37.6951 - 37.6951i) q^{67} +(-7.11382 - 7.11382i) q^{69} -42.6559 q^{71} -106.391i q^{73} +(-36.7294 + 36.7294i) q^{75} +(65.4607 - 65.4607i) q^{77} -21.2821i q^{79} -9.00000 q^{81} +(24.1638 + 24.1638i) q^{83} +(-122.697 - 122.697i) q^{85} -45.0495 q^{87} -52.8029i q^{89} +(30.5643 - 30.5643i) q^{91} +(20.7047 - 20.7047i) q^{93} +123.215i q^{95} -21.0222 q^{97} +(36.8588 + 36.8588i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 32 q^{11} - 32 q^{19} + 128 q^{23} - 32 q^{29} + 96 q^{35} + 96 q^{37} + 160 q^{43} + 112 q^{49} - 96 q^{51} + 160 q^{53} + 256 q^{55} - 128 q^{59} + 32 q^{61} - 32 q^{65} + 320 q^{67} - 96 q^{69} - 512 q^{71} + 192 q^{75} - 224 q^{77} - 144 q^{81} - 160 q^{83} - 160 q^{85} - 480 q^{91} + 96 q^{99}+O(q^{100}) $ 16 * q + 32 * q^11 - 32 * q^19 + 128 * q^23 - 32 * q^29 + 96 * q^35 + 96 * q^37 + 160 * q^43 + 112 * q^49 - 96 * q^51 + 160 * q^53 + 256 * q^55 - 128 * q^59 + 32 * q^61 - 32 * q^65 + 320 * q^67 - 96 * q^69 - 512 * q^71 + 192 * q^75 - 224 * q^77 - 144 * q^81 - 160 * q^83 - 160 * q^85 - 480 * q^91 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$		0			0
$5$	5.24354	+	5.24354i	1.04871	+	1.04871i	0.998751	+	0.0499563i	$0.0159082\pi$
$5$	5.24354	+	5.24354i	1.04871	+	1.04871i	0.0499563	+	0.998751i	$0.484092\pi$
$6$		0			0
$7$	5.32796			0.761138			0.380569	−	0.924753i	$-0.375728\pi$
$7$	5.32796			0.761138			0.380569	+	0.924753i	$0.375728\pi$
$8$		0			0
$9$			3.00000i			0.333333i
$10$		0			0
$11$	12.2863	−	12.2863i	1.11693	−	1.11693i	0.124743	−	0.992189i	$-0.460189\pi$
$11$	12.2863	−	12.2863i	1.11693	−	1.11693i	0.992189	−	0.124743i	$-0.0398107\pi$
$12$		0			0
$13$	5.73657	−	5.73657i	0.441275	−	0.441275i	−0.451165	−	0.892440i	$-0.648992\pi$
$13$	5.73657	−	5.73657i	0.441275	−	0.441275i	0.892440	+	0.451165i	$0.148992\pi$
$14$		0			0
$15$			12.8440i			0.856266i
$16$		0			0
$17$	−23.3997			−1.37645			−0.688226	−	0.725496i	$-0.741610\pi$
$17$	−23.3997			−1.37645			−0.688226	+	0.725496i	$0.741610\pi$
$18$		0			0
$19$	11.7492	+	11.7492i	0.618380	+	0.618380i	0.945116	−	0.326736i	$-0.105949\pi$
$19$	11.7492	+	11.7492i	0.618380	+	0.618380i	−0.326736	+	0.945116i	$0.605949\pi$
$20$		0			0
$21$	6.52540	+	6.52540i	0.310733	+	0.310733i
$22$		0			0
$23$	−5.80841			−0.252540			−0.126270	−	0.991996i	$-0.540301\pi$
$23$	−5.80841			−0.252540			−0.126270	+	0.991996i	$0.540301\pi$
$24$		0			0
$25$			29.9894i			1.19958i
$26$		0			0
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$		0			0
$29$	−18.3914	+	18.3914i	−0.634185	+	0.634185i	−0.949115	−	0.314930i	$-0.898019\pi$
$29$	−18.3914	+	18.3914i	−0.634185	+	0.634185i	0.314930	+	0.949115i	$0.398019\pi$
$30$		0			0
$31$		−	16.9053i		−	0.545332i	−0.962109	−	0.272666i	$-0.912095\pi$
$31$		−	16.9053i		−	0.545332i	0.962109	−	0.272666i	$-0.0879053\pi$
$32$		0			0
$33$	30.0951			0.911971
$34$		0			0
$35$	27.9374	+	27.9374i	0.798211	+	0.798211i
$36$		0			0
$37$	−15.3391	−	15.3391i	−0.414571	−	0.414571i	0.468756	−	0.883327i	$-0.344702\pi$
$37$	−15.3391	−	15.3391i	−0.414571	−	0.414571i	−0.883327	+	0.468756i	$0.844702\pi$
$38$		0			0
$39$	14.0517			0.360299
$40$		0			0
$41$			29.2351i			0.713051i	0.934286	+	0.356526i	$0.116039\pi$
$41$			29.2351i			0.713051i	−0.934286	+	0.356526i	$0.883961\pi$
$42$		0			0
$43$	33.4099	−	33.4099i	0.776975	−	0.776975i	−0.202340	−	0.979315i	$-0.564855\pi$
$43$	33.4099	−	33.4099i	0.776975	−	0.776975i	0.979315	+	0.202340i	$0.0648546\pi$
$44$		0			0
$45$	−15.7306	+	15.7306i	−0.349569	+	0.349569i
$46$		0			0
$47$		−	18.2125i		−	0.387500i	−0.981051	−	0.193750i	$-0.937935\pi$
$47$		−	18.2125i		−	0.387500i	0.981051	−	0.193750i	$-0.0620650\pi$
$48$		0			0
$49$	−20.6128			−0.420670
$50$		0			0
$51$	−28.6586	−	28.6586i	−0.561934	−	0.561934i
$52$		0			0
$53$	66.9856	+	66.9856i	1.26388	+	1.26388i	0.949197	+	0.314681i	$0.101898\pi$
$53$	66.9856	+	66.9856i	1.26388	+	1.26388i	0.314681	+	0.949197i	$0.398102\pi$
$54$		0			0
$55$	128.847			2.34267
$56$		0			0
$57$			28.7796i			0.504905i
$58$		0			0
$59$	−27.1523	+	27.1523i	−0.460209	+	0.460209i	−0.898724	−	0.438515i	$-0.855505\pi$
$59$	−27.1523	+	27.1523i	−0.460209	+	0.460209i	0.438515	+	0.898724i	$0.355505\pi$
$60$		0			0
$61$	−65.2399	+	65.2399i	−1.06951	+	1.06951i	−0.0721103	+	0.997397i	$0.522973\pi$
$61$	−65.2399	+	65.2399i	−1.06951	+	1.06951i	−0.997397	+	0.0721103i	$0.977027\pi$
$62$		0			0
$63$			15.9839i			0.253713i
$64$		0			0
$65$	60.1599			0.925537
$66$		0			0
$67$	−37.6951	−	37.6951i	−0.562614	−	0.562614i	0.367435	−	0.930049i	$-0.380236\pi$
$67$	−37.6951	−	37.6951i	−0.562614	−	0.562614i	−0.930049	+	0.367435i	$0.880236\pi$
$68$		0			0
$69$	−7.11382	−	7.11382i	−0.103099	−	0.103099i
$70$		0			0
$71$	−42.6559			−0.600788			−0.300394	−	0.953815i	$-0.597118\pi$
$71$	−42.6559			−0.600788			−0.300394	+	0.953815i	$0.597118\pi$
$72$		0			0
$73$		−	106.391i		−	1.45742i	−0.684825	−	0.728708i	$-0.740121\pi$
$73$		−	106.391i		−	1.45742i	0.684825	−	0.728708i	$-0.259879\pi$
$74$		0			0
$75$	−36.7294	+	36.7294i	−0.489725	+	0.489725i
$76$		0			0
$77$	65.4607	−	65.4607i	0.850139	−	0.850139i
$78$		0			0
$79$		−	21.2821i		−	0.269394i	−0.990887	−	0.134697i	$-0.956994\pi$
$79$		−	21.2821i		−	0.269394i	0.990887	−	0.134697i	$-0.0430061\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$		0			0
$83$	24.1638	+	24.1638i	0.291130	+	0.291130i	0.837527	−	0.546396i	$-0.184001\pi$
$83$	24.1638	+	24.1638i	0.291130	+	0.291130i	−0.546396	+	0.837527i	$0.684001\pi$
$84$		0			0
$85$	−122.697	−	122.697i	−1.44350	−	1.44350i
$86$		0			0
$87$	−45.0495			−0.517810
$88$		0			0
$89$		−	52.8029i		−	0.593291i	−0.954988	−	0.296645i	$-0.904132\pi$
$89$		−	52.8029i		−	0.593291i	0.954988	−	0.296645i	$-0.0958679\pi$
$90$		0			0
$91$	30.5643	−	30.5643i	0.335871	−	0.335871i
$92$		0			0
$93$	20.7047	−	20.7047i	0.222631	−	0.222631i
$94$		0			0
$95$			123.215i			1.29700i
$96$		0			0
$97$	−21.0222			−0.216724			−0.108362	−	0.994112i	$-0.534560\pi$
$97$	−21.0222			−0.216724			−0.108362	+	0.994112i	$0.534560\pi$
$98$		0			0
$99$	36.8588	+	36.8588i	0.372311	+	0.372311i
$100$		0			0
$101$	3.24960	+	3.24960i	0.0321743	+	0.0321743i	0.723011	−	0.690837i	$-0.242758\pi$
$101$	3.24960	+	3.24960i	0.0321743	+	0.0321743i	−0.690837	+	0.723011i	$0.742758\pi$
$102$		0			0
$103$	−105.112			−1.02050			−0.510252	−	0.860025i	$-0.670448\pi$
$103$	−105.112			−1.02050			−0.510252	+	0.860025i	$0.670448\pi$
$104$		0			0
$105$			68.4323i			0.651736i
$106$		0			0
$107$	−99.6160	+	99.6160i	−0.930991	+	0.930991i	−0.997768	−	0.0667770i	$-0.978728\pi$
$107$	−99.6160	+	99.6160i	−0.930991	+	0.930991i	0.0667770	+	0.997768i	$0.478728\pi$
$108$		0			0
$109$	108.050	−	108.050i	0.991282	−	0.991282i	−0.00868078	−	0.999962i	$-0.502763\pi$
$109$	108.050	−	108.050i	0.991282	−	0.991282i	0.999962	+	0.00868078i	$0.00276321\pi$
$110$		0			0
$111$		−	37.5730i		−	0.338496i
$112$		0			0
$113$	−23.2835			−0.206048			−0.103024	−	0.994679i	$-0.532852\pi$
$113$	−23.2835			−0.206048			−0.103024	+	0.994679i	$0.532852\pi$
$114$		0			0
$115$	−30.4566	−	30.4566i	−0.264840	−	0.264840i
$116$		0			0
$117$	17.2097	+	17.2097i	0.147092	+	0.147092i
$118$		0			0
$119$	−124.673			−1.04767
$120$		0			0
$121$		−	180.904i		−	1.49508i
$122$		0			0
$123$	−35.8055	+	35.8055i	−0.291102	+	0.291102i
$124$		0			0
$125$	−26.1621	+	26.1621i	−0.209297	+	0.209297i
$126$		0			0
$127$		−	118.180i		−	0.930550i	−0.885166	−	0.465275i	$-0.845955\pi$
$127$		−	118.180i		−	0.930550i	0.885166	−	0.465275i	$-0.154045\pi$
$128$		0			0
$129$	81.8373			0.634398
$130$		0			0
$131$	−69.2067	−	69.2067i	−0.528296	−	0.528296i	0.391768	−	0.920064i	$-0.371863\pi$
$131$	−69.2067	−	69.2067i	−0.528296	−	0.528296i	−0.920064	+	0.391768i	$0.871863\pi$
$132$		0			0
$133$	62.5994	+	62.5994i	0.470672	+	0.470672i
$134$		0			0
$135$	−38.5320			−0.285422
$136$		0			0
$137$			124.474i			0.908572i	0.890856	+	0.454286i	$0.150106\pi$
$137$			124.474i			0.908572i	−0.890856	+	0.454286i	$0.849894\pi$
$138$		0			0
$139$	169.014	−	169.014i	1.21593	−	1.21593i	0.246881	−	0.969046i	$-0.420594\pi$
$139$	169.014	−	169.014i	1.21593	−	1.21593i	0.969046	−	0.246881i	$-0.0794057\pi$
$140$		0			0
$141$	22.3057	−	22.3057i	0.158196	−	0.158196i
$142$		0			0
$143$		−	140.962i		−	0.985749i
$144$		0			0
$145$	−192.872			−1.33015
$146$		0			0
$147$	−25.2454	−	25.2454i	−0.171738	−	0.171738i
$148$		0			0
$149$	−146.988	−	146.988i	−0.986495	−	0.986495i	0.0134145	−	0.999910i	$-0.495730\pi$
$149$	−146.988	−	146.988i	−0.986495	−	0.986495i	−0.999910	+	0.0134145i	$0.995730\pi$
$150$		0			0
$151$	−75.5456			−0.500302			−0.250151	−	0.968207i	$-0.580480\pi$
$151$	−75.5456			−0.500302			−0.250151	+	0.968207i	$0.580480\pi$
$152$		0			0
$153$		−	70.1991i		−	0.458817i
$154$		0			0
$155$	88.6435	−	88.6435i	0.571893	−	0.571893i
$156$		0			0
$157$	81.5356	−	81.5356i	0.519335	−	0.519335i	−0.398035	−	0.917370i	$-0.630308\pi$
$157$	81.5356	−	81.5356i	0.519335	−	0.519335i	0.917370	+	0.398035i	$0.130308\pi$
$158$		0			0
$159$			164.080i			1.03195i
$160$		0			0
$161$	−30.9470			−0.192217
$162$		0			0
$163$	55.8065	+	55.8065i	0.342371	+	0.342371i	0.857258	−	0.514887i	$-0.172166\pi$
$163$	55.8065	+	55.8065i	0.342371	+	0.342371i	−0.514887	+	0.857258i	$0.672166\pi$
$164$		0			0
$165$	157.805	+	157.805i	0.956391	+	0.956391i
$166$		0			0
$167$	24.6339			0.147508			0.0737540	−	0.997276i	$-0.476502\pi$
$167$	24.6339			0.147508			0.0737540	+	0.997276i	$0.476502\pi$
$168$		0			0
$169$			103.183i			0.610553i
$170$		0			0
$171$	−35.2476	+	35.2476i	−0.206127	+	0.206127i
$172$		0			0
$173$	−4.88551	+	4.88551i	−0.0282399	+	0.0282399i	−0.721086	−	0.692846i	$-0.756357\pi$
$173$	−4.88551	+	4.88551i	−0.0282399	+	0.0282399i	0.692846	+	0.721086i	$0.256357\pi$
$174$		0			0
$175$			159.782i			0.913042i
$176$		0			0
$177$	−66.5094			−0.375759
$178$		0			0
$179$	−229.504	−	229.504i	−1.28215	−	1.28215i	−0.939444	−	0.342702i	$-0.888658\pi$
$179$	−229.504	−	229.504i	−1.28215	−	1.28215i	−0.342702	−	0.939444i	$-0.611342\pi$
$180$		0			0
$181$	−116.607	−	116.607i	−0.644238	−	0.644238i	0.307356	−	0.951595i	$-0.400556\pi$
$181$	−116.607	−	116.607i	−0.644238	−	0.644238i	−0.951595	+	0.307356i	$0.900556\pi$
$182$		0			0
$183$	−159.805			−0.873249
$184$		0			0
$185$		−	160.863i		−	0.869528i
$186$		0			0
$187$	−287.495	+	287.495i	−1.53740	+	1.53740i
$188$		0			0
$189$	−19.5762	+	19.5762i	−0.103578	+	0.103578i
$190$		0			0
$191$			94.2316i			0.493359i	0.969097	+	0.246680i	$0.0793395\pi$
$191$			94.2316i			0.493359i	−0.969097	+	0.246680i	$0.920660\pi$
$192$		0			0
$193$	84.2667			0.436615			0.218308	−	0.975880i	$-0.429946\pi$
$193$	84.2667			0.436615			0.218308	+	0.975880i	$0.429946\pi$
$194$		0			0
$195$	73.6805	+	73.6805i	0.377849	+	0.377849i
$196$		0			0
$197$	56.9578	+	56.9578i	0.289126	+	0.289126i	0.836734	−	0.547609i	$-0.184462\pi$
$197$	56.9578	+	56.9578i	0.289126	+	0.289126i	−0.547609	+	0.836734i	$0.684462\pi$
$198$		0			0
$199$	196.179			0.985827			0.492913	−	0.870078i	$-0.335932\pi$
$199$	196.179			0.985827			0.492913	+	0.870078i	$0.335932\pi$
$200$		0			0
$201$		−	92.3338i		−	0.459372i
$202$		0			0
$203$	−97.9886	+	97.9886i	−0.482702	+	0.482702i
$204$		0			0
$205$	−153.295	+	153.295i	−0.747782	+	0.747782i
$206$		0			0
$207$		−	17.4252i		−	0.0841799i
$208$		0			0
$209$	288.708			1.38138
$210$		0			0
$211$	177.340	+	177.340i	0.840475	+	0.840475i	0.988921	−	0.148445i	$-0.0474269\pi$
$211$	177.340	+	177.340i	0.840475	+	0.840475i	−0.148445	+	0.988921i	$0.547427\pi$
$212$		0			0
$213$	−52.2426	−	52.2426i	−0.245271	−	0.245271i
$214$		0			0
$215$	350.373			1.62964
$216$		0			0
$217$		−	90.0707i		−	0.415072i
$218$		0			0
$219$	130.302	−	130.302i	0.594987	−	0.594987i
$220$		0			0
$221$	−134.234	+	134.234i	−0.607394	+	0.607394i
$222$		0			0
$223$		−	377.924i		−	1.69473i	−0.531012	−	0.847364i	$-0.678188\pi$
$223$		−	377.924i		−	1.69473i	0.531012	−	0.847364i	$-0.321812\pi$
$224$		0			0
$225$	−89.9682			−0.399859
$226$		0			0
$227$	103.909	+	103.909i	0.457750	+	0.457750i	0.897916	−	0.440166i	$-0.145080\pi$
$227$	103.909	+	103.909i	0.457750	+	0.457750i	−0.440166	+	0.897916i	$0.645080\pi$
$228$		0			0
$229$	101.055	+	101.055i	0.441290	+	0.441290i	0.892445	−	0.451156i	$-0.148988\pi$
$229$	101.055	+	101.055i	0.441290	+	0.441290i	−0.451156	+	0.892445i	$0.648988\pi$
$230$		0			0
$231$	160.345			0.694136
$232$		0			0
$233$			287.259i			1.23287i	0.787405	+	0.616436i	$0.211424\pi$
$233$			287.259i			1.23287i	−0.787405	+	0.616436i	$0.788576\pi$
$234$		0			0
$235$	95.4979	−	95.4979i	0.406374	−	0.406374i
$236$		0			0
$237$	26.0651	−	26.0651i	0.109980	−	0.109980i
$238$		0			0
$239$			150.941i			0.631554i	0.948833	+	0.315777i	$0.102265\pi$
$239$			150.941i			0.631554i	−0.948833	+	0.315777i	$0.897735\pi$
$240$		0			0
$241$	37.7817			0.156771			0.0783853	−	0.996923i	$-0.475024\pi$
$241$	37.7817			0.156771			0.0783853	+	0.996923i	$0.475024\pi$
$242$		0			0
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	−108.084	−	108.084i	−0.441159	−	0.441159i
$246$		0			0
$247$	134.800			0.545751
$248$		0			0
$249$			59.1890i			0.237707i
$250$		0			0
$251$	100.915	−	100.915i	0.402050	−	0.402050i	−0.476905	−	0.878955i	$-0.658241\pi$
$251$	100.915	−	100.915i	0.402050	−	0.402050i	0.878955	+	0.476905i	$0.158241\pi$
$252$		0			0
$253$	−71.3637	+	71.3637i	−0.282070	+	0.282070i
$254$		0			0
$255$		−	300.545i		−	1.17861i
$256$		0			0
$257$	241.295			0.938891			0.469446	−	0.882961i	$-0.344454\pi$
$257$	241.295			0.938891			0.469446	+	0.882961i	$0.344454\pi$
$258$		0			0
$259$	−81.7263	−	81.7263i	−0.315546	−	0.315546i
$260$		0			0
$261$	−55.1741	−	55.1741i	−0.211395	−	0.211395i
$262$		0			0
$263$	118.747			0.451509			0.225754	−	0.974184i	$-0.427515\pi$
$263$	118.747			0.451509			0.225754	+	0.974184i	$0.427515\pi$
$264$		0			0
$265$			702.483i			2.65088i
$266$		0			0
$267$	64.6700	−	64.6700i	0.242210	−	0.242210i
$268$		0			0
$269$	−7.74853	+	7.74853i	−0.0288050	+	0.0288050i	−0.721363	−	0.692558i	$-0.756484\pi$
$269$	−7.74853	+	7.74853i	−0.0288050	+	0.0288050i	0.692558	+	0.721363i	$0.256484\pi$
$270$		0			0
$271$			131.899i			0.486712i	0.969937	+	0.243356i	$0.0782484\pi$
$271$			131.899i			0.486712i	−0.969937	+	0.243356i	$0.921752\pi$
$272$		0			0
$273$	74.8668			0.274237
$274$		0			0
$275$	368.457	+	368.457i	1.33984	+	1.33984i
$276$		0			0
$277$	202.352	+	202.352i	0.730513	+	0.730513i	0.970721	−	0.240208i	$-0.0772157\pi$
$277$	202.352	+	202.352i	0.730513	+	0.730513i	−0.240208	+	0.970721i	$0.577216\pi$
$278$		0			0
$279$	50.7158			0.181777
$280$		0			0
$281$		−	68.8493i		−	0.245015i	−0.992468	−	0.122508i	$-0.960906\pi$
$281$		−	68.8493i		−	0.245015i	0.992468	−	0.122508i	$-0.0390936\pi$
$282$		0			0
$283$	206.773	−	206.773i	0.730646	−	0.730646i	−0.240102	−	0.970748i	$-0.577181\pi$
$283$	206.773	−	206.773i	0.730646	−	0.730646i	0.970748	+	0.240102i	$0.0771808\pi$
$284$		0			0
$285$	−150.907	+	150.907i	−0.529498	+	0.529498i
$286$		0			0
$287$			155.764i			0.542730i
$288$		0			0
$289$	258.545			0.894620
$290$		0			0
$291$	−25.7468	−	25.7468i	−0.0884770	−	0.0884770i
$292$		0			0
$293$	361.237	+	361.237i	1.23289	+	1.23289i	0.962848	+	0.270043i	$0.0870379\pi$
$293$	361.237	+	361.237i	1.23289	+	1.23289i	0.270043	+	0.962848i	$0.412962\pi$
$294$		0			0
$295$	−284.749			−0.965250
$296$		0			0
$297$			90.2852i			0.303990i
$298$		0			0
$299$	−33.3204	+	33.3204i	−0.111439	+	0.111439i
$300$		0			0
$301$	178.007	−	178.007i	0.591385	−	0.591385i
$302$		0			0
$303$			7.95987i			0.0262702i
$304$		0			0
$305$	−684.176			−2.24320
$306$		0			0
$307$	−10.9073	−	10.9073i	−0.0355286	−	0.0355286i	0.689119	−	0.724648i	$-0.257998\pi$
$307$	−10.9073	−	10.9073i	−0.0355286	−	0.0355286i	−0.724648	+	0.689119i	$0.757998\pi$
$308$		0			0
$309$	−128.735	−	128.735i	−0.416619	−	0.416619i
$310$		0			0
$311$	160.251			0.515278			0.257639	−	0.966241i	$-0.417055\pi$
$311$	160.251			0.515278			0.257639	+	0.966241i	$0.417055\pi$
$312$		0			0
$313$		−	355.500i		−	1.13578i	−0.823103	−	0.567892i	$-0.807759\pi$
$313$		−	355.500i		−	1.13578i	0.823103	−	0.567892i	$-0.192241\pi$
$314$		0			0
$315$	−83.8121	+	83.8121i	−0.266070	+	0.266070i
$316$		0			0
$317$	−72.5192	+	72.5192i	−0.228767	+	0.228767i	−0.812178	−	0.583410i	$-0.801718\pi$
$317$	−72.5192	+	72.5192i	−0.228767	+	0.228767i	0.583410	+	0.812178i	$0.301718\pi$
$318$		0			0
$319$			451.922i			1.41668i
$320$		0			0
$321$	−244.008			−0.760151
$322$		0			0
$323$	−274.928	−	274.928i	−0.851170	−	0.851170i
$324$		0			0
$325$	172.036	+	172.036i	0.529343	+	0.529343i
$326$		0			0
$327$	264.667			0.809378
$328$		0			0
$329$		−	97.0355i		−	0.294941i
$330$		0			0
$331$	−248.096	+	248.096i	−0.749536	+	0.749536i	−0.974392	−	0.224856i	$-0.927809\pi$
$331$	−248.096	+	248.096i	−0.749536	+	0.749536i	0.224856	+	0.974392i	$0.427809\pi$
$332$		0			0
$333$	46.0174	−	46.0174i	0.138190	−	0.138190i
$334$		0			0
$335$		−	395.312i		−	1.18003i
$336$		0			0
$337$	−467.271			−1.38656			−0.693280	−	0.720668i	$-0.743835\pi$
$337$	−467.271			−1.38656			−0.693280	+	0.720668i	$0.743835\pi$
$338$		0			0
$339$	−28.5163	−	28.5163i	−0.0841189	−	0.0841189i
$340$		0			0
$341$	−207.703	−	207.703i	−0.609098	−	0.609098i
$342$		0			0
$343$	−370.894			−1.08133
$344$		0			0
$345$		−	74.6032i		−	0.216241i
$346$		0			0
$347$	292.821	−	292.821i	0.843863	−	0.843863i	−0.145496	−	0.989359i	$-0.546478\pi$
$347$	292.821	−	292.821i	0.843863	−	0.843863i	0.989359	+	0.145496i	$0.0464776\pi$
$348$		0			0
$349$	−346.260	+	346.260i	−0.992150	+	0.992150i	−0.999969	−	0.00781941i	$-0.997511\pi$
$349$	−346.260	+	346.260i	−0.992150	+	0.992150i	0.00781941	+	0.999969i	$0.497511\pi$
$350$		0			0
$351$			42.1550i			0.120100i
$352$		0			0
$353$	8.01816			0.0227143			0.0113572	−	0.999936i	$-0.496385\pi$
$353$	8.01816			0.0227143			0.0113572	+	0.999936i	$0.496385\pi$
$354$		0			0
$355$	−223.668	−	223.668i	−0.630051	−	0.630051i
$356$		0			0
$357$	−152.692	−	152.692i	−0.427709	−	0.427709i
$358$		0			0
$359$	−590.403			−1.64458			−0.822289	−	0.569071i	$-0.807303\pi$
$359$	−590.403			−1.64458			−0.822289	+	0.569071i	$0.807303\pi$
$360$		0			0
$361$		−	84.9121i		−	0.235213i
$362$		0			0
$363$	221.561	−	221.561i	0.610362	−	0.610362i
$364$		0			0
$365$	557.867	−	557.867i	1.52840	−	1.52840i
$366$		0			0
$367$			397.100i			1.08202i	0.841017	+	0.541008i	$0.181957\pi$
$367$			397.100i			1.08202i	−0.841017	+	0.541008i	$0.818043\pi$
$368$		0			0
$369$	−87.7053			−0.237684
$370$		0			0
$371$	356.897	+	356.897i	0.961986	+	0.961986i
$372$		0			0
$373$	165.010	+	165.010i	0.442387	+	0.442387i	0.892814	−	0.450427i	$-0.148728\pi$
$373$	165.010	+	165.010i	0.442387	+	0.442387i	−0.450427	+	0.892814i	$0.648728\pi$
$374$		0			0
$375$	−64.0837			−0.170890
$376$		0			0
$377$			211.007i			0.559700i
$378$		0			0
$379$	−206.669	+	206.669i	−0.545300	+	0.545300i	−0.925078	−	0.379778i	$-0.876000\pi$
$379$	−206.669	+	206.669i	−0.545300	+	0.545300i	0.379778	+	0.925078i	$0.376000\pi$
$380$		0			0
$381$	144.740	−	144.740i	0.379895	−	0.379895i
$382$		0			0
$383$		−	598.414i		−	1.56244i	−0.624257	−	0.781219i	$-0.714598\pi$
$383$		−	598.414i		−	1.56244i	0.624257	−	0.781219i	$-0.285402\pi$
$384$		0			0
$385$	686.492			1.78310
$386$		0			0
$387$	100.230	+	100.230i	0.258992	+	0.258992i
$388$		0			0
$389$	−186.696	−	186.696i	−0.479939	−	0.479939i	0.425173	−	0.905112i	$-0.360213\pi$
$389$	−186.696	−	186.696i	−0.479939	−	0.479939i	−0.905112	+	0.425173i	$0.860213\pi$
$390$		0			0
$391$	135.915			0.347609
$392$		0			0
$393$		−	169.521i		−	0.431352i
$394$		0			0
$395$	111.594	−	111.594i	0.282515	−	0.282515i
$396$		0			0
$397$	57.3727	−	57.3727i	0.144516	−	0.144516i	−0.631147	−	0.775663i	$-0.717416\pi$
$397$	57.3727	−	57.3727i	0.144516	−	0.144516i	0.775663	+	0.631147i	$0.217416\pi$
$398$		0			0
$399$			153.337i			0.384302i
$400$		0			0
$401$	−466.082			−1.16230			−0.581149	−	0.813797i	$-0.697397\pi$
$401$	−466.082			−1.16230			−0.581149	+	0.813797i	$0.697397\pi$
$402$		0			0
$403$	−96.9784	−	96.9784i	−0.240641	−	0.240641i
$404$		0			0
$405$	−47.1918	−	47.1918i	−0.116523	−	0.116523i
$406$		0			0
$407$	−376.921			−0.926096
$408$		0			0
$409$			597.952i			1.46198i	0.682386	+	0.730992i	$0.260942\pi$
$409$			597.952i			1.46198i	−0.682386	+	0.730992i	$0.739058\pi$
$410$		0			0
$411$	−152.449	+	152.449i	−0.370923	+	0.370923i
$412$		0			0
$413$	−144.667	+	144.667i	−0.350282	+	0.350282i
$414$		0			0
$415$			253.408i			0.610621i
$416$		0			0
$417$	413.998			0.992800
$418$		0			0
$419$	−4.65301	−	4.65301i	−0.0111050	−	0.0111050i	0.701532	−	0.712638i	$-0.252500\pi$
$419$	−4.65301	−	4.65301i	−0.0111050	−	0.0111050i	−0.712638	+	0.701532i	$0.752500\pi$
$420$		0			0
$421$	−34.3754	−	34.3754i	−0.0816519	−	0.0816519i	0.665101	−	0.746753i	$-0.268388\pi$
$421$	−34.3754	−	34.3754i	−0.0816519	−	0.0816519i	−0.746753	+	0.665101i	$0.768388\pi$
$422$		0			0
$423$	54.6375			0.129167
$424$		0			0
$425$		−	701.742i		−	1.65116i
$426$		0			0
$427$	−347.596	+	347.596i	−0.814042	+	0.814042i
$428$		0			0
$429$	172.643	−	172.643i	0.402430	−	0.402430i
$430$		0			0
$431$		−	423.823i		−	0.983347i	−0.870780	−	0.491674i	$-0.836385\pi$
$431$		−	423.823i		−	0.983347i	0.870780	−	0.491674i	$-0.163615\pi$
$432$		0			0
$433$	833.377			1.92466			0.962330	−	0.271885i	$-0.0876472\pi$
$433$	833.377			1.92466			0.962330	+	0.271885i	$0.0876472\pi$
$434$		0			0
$435$	−236.219	−	236.219i	−0.543031	−	0.543031i
$436$		0			0
$437$	−68.2443	−	68.2443i	−0.156165	−	0.156165i
$438$		0			0
$439$	−32.3193			−0.0736203			−0.0368102	−	0.999322i	$-0.511720\pi$
$439$	−32.3193			−0.0736203			−0.0368102	+	0.999322i	$0.511720\pi$
$440$		0			0
$441$		−	61.8384i		−	0.140223i
$442$		0			0
$443$	119.527	−	119.527i	0.269813	−	0.269813i	−0.559212	−	0.829025i	$-0.688896\pi$
$443$	119.527	−	119.527i	0.269813	−	0.269813i	0.829025	+	0.559212i	$0.188896\pi$
$444$		0			0
$445$	276.874	−	276.874i	0.622189	−	0.622189i
$446$		0			0
$447$		−	360.045i		−	0.805470i
$448$		0			0
$449$	−182.359			−0.406146			−0.203073	−	0.979164i	$-0.565093\pi$
$449$	−182.359			−0.406146			−0.203073	+	0.979164i	$0.565093\pi$
$450$		0			0
$451$	359.190	+	359.190i	0.796430	+	0.796430i
$452$		0			0
$453$	−92.5241	−	92.5241i	−0.204248	−	0.204248i
$454$		0			0
$455$	320.530			0.704461
$456$		0			0
$457$		−	272.942i		−	0.597246i	−0.954371	−	0.298623i	$-0.903473\pi$
$457$		−	272.942i		−	0.597246i	0.954371	−	0.298623i	$-0.0965274\pi$
$458$		0			0
$459$	85.9759	−	85.9759i	0.187311	−	0.187311i
$460$		0			0
$461$	−188.323	+	188.323i	−0.408510	+	0.408510i	−0.881219	−	0.472709i	$-0.843276\pi$
$461$	−188.323	+	188.323i	−0.408510	+	0.408510i	0.472709	+	0.881219i	$0.343276\pi$
$462$		0			0
$463$		−	116.023i		−	0.250590i	−0.992120	−	0.125295i	$-0.960012\pi$
$463$		−	116.023i		−	0.250590i	0.992120	−	0.125295i	$-0.0399877\pi$
$464$		0			0
$465$	217.131			0.466949
$466$		0			0
$467$	−271.914	−	271.914i	−0.582257	−	0.582257i	0.353266	−	0.935523i	$-0.385071\pi$
$467$	−271.914	−	271.914i	−0.582257	−	0.582257i	−0.935523	+	0.353266i	$0.885071\pi$
$468$		0			0
$469$	−200.838	−	200.838i	−0.428227	−	0.428227i
$470$		0			0
$471$	199.721			0.424035
$472$		0			0
$473$		−	820.966i		−	1.73566i
$474$		0			0
$475$	−352.352	+	352.352i	−0.741793	+	0.741793i
$476$		0			0
$477$	−200.957	+	200.957i	−0.421293	+	0.421293i
$478$		0			0
$479$			775.808i			1.61964i	0.586678	+	0.809820i	$0.300435\pi$
$479$			775.808i			1.61964i	−0.586678	+	0.809820i	$0.699565\pi$
$480$		0			0
$481$	−175.988			−0.365880
$482$		0			0
$483$	−37.9022	−	37.9022i	−0.0784725	−	0.0784725i
$484$		0			0
$485$	−110.231	−	110.231i	−0.227280	−	0.227280i
$486$		0			0
$487$	−174.891			−0.359118			−0.179559	−	0.983747i	$-0.557467\pi$
$487$	−174.891			−0.359118			−0.179559	+	0.983747i	$0.557467\pi$
$488$		0			0
$489$			136.697i			0.279545i
$490$		0			0
$491$	−348.578	+	348.578i	−0.709934	+	0.709934i	−0.966521	−	0.256587i	$-0.917402\pi$
$491$	−348.578	+	348.578i	−0.709934	+	0.709934i	0.256587	+	0.966521i	$0.417402\pi$
$492$		0			0
$493$	430.352	−	430.352i	0.872926	−	0.872926i
$494$		0			0
$495$			386.541i			0.780890i
$496$		0			0
$497$	−227.269			−0.457282
$498$		0			0
$499$	−607.544	−	607.544i	−1.21752	−	1.21752i	−0.968496	−	0.249027i	$-0.919889\pi$
$499$	−607.544	−	607.544i	−1.21752	−	1.21752i	−0.249027	−	0.968496i	$-0.580111\pi$
$500$		0			0
$501$	30.1702	+	30.1702i	0.0602199	+	0.0602199i
$502$		0			0
$503$	130.935			0.260309			0.130154	−	0.991494i	$-0.458453\pi$
$503$	130.935			0.260309			0.130154	+	0.991494i	$0.458453\pi$
$504$		0			0
$505$			34.0789i			0.0674829i
$506$		0			0
$507$	−126.373	+	126.373i	−0.249257	+	0.249257i
$508$		0			0
$509$	61.5539	−	61.5539i	0.120931	−	0.120931i	−0.644051	−	0.764982i	$-0.722748\pi$
$509$	61.5539	−	61.5539i	0.120931	−	0.120931i	0.764982	+	0.644051i	$0.222748\pi$
$510$		0			0
$511$		−	566.849i		−	1.10929i
$512$		0			0
$513$	−86.3387			−0.168302
$514$		0			0
$515$	−551.159	−	551.159i	−1.07021	−	1.07021i
$516$		0			0
$517$	−223.763	−	223.763i	−0.432811	−	0.432811i
$518$		0			0
$519$	−11.9670			−0.0230578
$520$		0			0
$521$		−	32.5929i		−	0.0625584i	−0.999511	−	0.0312792i	$-0.990042\pi$
$521$		−	32.5929i		−	0.0625584i	0.999511	−	0.0312792i	$-0.00995810\pi$
$522$		0			0
$523$	−226.407	+	226.407i	−0.432900	+	0.432900i	−0.889614	−	0.456713i	$-0.849026\pi$
$523$	−226.407	+	226.407i	−0.432900	+	0.432900i	0.456713	+	0.889614i	$0.349026\pi$
$524$		0			0
$525$	−195.693	+	195.693i	−0.372748	+	0.372748i
$526$		0			0
$527$			395.578i			0.750623i
$528$		0			0
$529$	−495.262			−0.936224
$530$		0			0
$531$	−81.4570	−	81.4570i	−0.153403	−	0.153403i
$532$		0			0
$533$	167.709	+	167.709i	0.314652	+	0.314652i
$534$		0			0
$535$	−1044.68			−1.95267
$536$		0			0
$537$		−	562.168i		−	1.04687i
$538$		0			0
$539$	−253.254	+	253.254i	−0.469859	+	0.469859i
$540$		0			0
$541$	−510.912	+	510.912i	−0.944385	+	0.944385i	−0.998533	−	0.0541480i	$-0.982756\pi$
$541$	−510.912	+	510.912i	−0.944385	+	0.944385i	0.0541480	+	0.998533i	$0.482756\pi$
$542$		0			0
$543$		−	285.628i		−	0.526018i
$544$		0			0
$545$	1133.13			2.07913
$546$		0			0
$547$	512.889	+	512.889i	0.937639	+	0.937639i	0.998167	−	0.0605271i	$-0.0192782\pi$
$547$	512.889	+	512.889i	0.937639	+	0.937639i	−0.0605271	+	0.998167i	$0.519278\pi$
$548$		0			0
$549$	−195.720	−	195.720i	−0.356502	−	0.356502i
$550$		0			0
$551$	−432.168			−0.784334
$552$		0			0
$553$		−	113.390i		−	0.205046i
$554$		0			0
$555$	197.016	−	197.016i	0.354983	−	0.354983i
$556$		0			0
$557$	−566.691	+	566.691i	−1.01740	+	1.01740i	−0.0175529	+	0.999846i	$0.505588\pi$
$557$	−566.691	+	566.691i	−1.01740	+	1.01740i	−0.999846	+	0.0175529i	$0.994412\pi$
$558$		0			0
$559$		−	383.317i		−	0.685720i
$560$		0			0
$561$	−704.215			−1.25529
$562$		0			0
$563$	548.653	+	548.653i	0.974517	+	0.974517i	0.999683	−	0.0251665i	$-0.00801159\pi$
$563$	548.653	+	548.653i	0.974517	+	0.974517i	−0.0251665	+	0.999683i	$0.508012\pi$
$564$		0			0
$565$	−122.088	−	122.088i	−0.216085	−	0.216085i
$566$		0			0
$567$	−47.9517			−0.0845708
$568$		0			0
$569$			551.224i			0.968760i	0.874858	+	0.484380i	$0.160955\pi$
$569$			551.224i			0.968760i	−0.874858	+	0.484380i	$0.839045\pi$
$570$		0			0
$571$	458.387	−	458.387i	0.802780	−	0.802780i	−0.180749	−	0.983529i	$-0.557852\pi$
$571$	458.387	−	458.387i	0.802780	−	0.802780i	0.983529	+	0.180749i	$0.0578522\pi$
$572$		0			0
$573$	−115.410	+	115.410i	−0.201413	+	0.201413i
$574$		0			0
$575$		−	174.191i		−	0.302941i
$576$		0			0
$577$	−718.488			−1.24521			−0.622607	−	0.782535i	$-0.713926\pi$
$577$	−718.488			−1.24521			−0.622607	+	0.782535i	$0.713926\pi$
$578$		0			0
$579$	103.205	+	103.205i	0.178247	+	0.178247i
$580$		0			0
$581$	128.744	+	128.744i	0.221590	+	0.221590i
$582$		0			0
$583$	1646.00			2.82333
$584$		0			0
$585$			180.480i			0.308512i
$586$		0			0
$587$	3.02450	−	3.02450i	0.00515247	−	0.00515247i	−0.704526	−	0.709678i	$-0.748840\pi$
$587$	3.02450	−	3.02450i	0.00515247	−	0.00515247i	0.709678	+	0.704526i	$0.248840\pi$
$588$		0			0
$589$	198.624	−	198.624i	0.337222	−	0.337222i
$590$		0			0
$591$			139.517i			0.236070i
$592$		0			0
$593$	576.193			0.971657			0.485829	−	0.874054i	$-0.338518\pi$
$593$	576.193			0.971657			0.485829	+	0.874054i	$0.338518\pi$
$594$		0			0
$595$	−653.726	−	653.726i	−1.09870	−	1.09870i
$596$		0			0
$597$	240.270	+	240.270i	0.402462	+	0.402462i
$598$		0			0
$599$	1101.40			1.83873			0.919365	−	0.393406i	$-0.128703\pi$
$599$	1101.40			1.83873			0.919365	+	0.393406i	$0.128703\pi$
$600$		0			0
$601$			7.11053i			0.0118312i	0.999983	+	0.00591558i	$0.00188300\pi$
$601$			7.11053i			0.0118312i	−0.999983	+	0.00591558i	$0.998117\pi$
$602$		0			0
$603$	113.085	−	113.085i	0.187538	−	0.187538i
$604$		0			0
$605$	948.578	−	948.578i	1.56790	−	1.56790i
$606$		0			0
$607$			528.384i			0.870485i	0.900313	+	0.435242i	$0.143337\pi$
$607$			528.384i			0.870485i	−0.900313	+	0.435242i	$0.856663\pi$
$608$		0			0
$609$	−240.022			−0.394125
$610$		0			0
$611$	−104.477	−	104.477i	−0.170994	−	0.170994i
$612$		0			0
$613$	642.364	+	642.364i	1.04790	+	1.04790i	0.998793	+	0.0491093i	$0.0156383\pi$
$613$	642.364	+	642.364i	1.04790	+	1.04790i	0.0491093	+	0.998793i	$0.484362\pi$
$614$		0			0
$615$	−375.496			−0.610562
$616$		0			0
$617$			1068.16i			1.73122i	0.500717	+	0.865611i	$0.333070\pi$
$617$			1068.16i			1.73122i	−0.500717	+	0.865611i	$0.666930\pi$
$618$		0			0
$619$	691.136	−	691.136i	1.11654	−	1.11654i	0.124290	−	0.992246i	$-0.460335\pi$
$619$	691.136	−	691.136i	1.11654	−	1.11654i	0.992246	−	0.124290i	$-0.0396653\pi$
$620$		0			0
$621$	21.3415	−	21.3415i	0.0343663	−	0.0343663i
$622$		0			0
$623$		−	281.332i		−	0.451576i
$624$		0			0
$625$	475.371			0.760594
$626$		0			0
$627$	353.593	+	353.593i	0.563945	+	0.563945i
$628$		0			0
$629$	358.931	+	358.931i	0.570637	+	0.570637i
$630$		0			0
$631$	−486.622			−0.771191			−0.385596	−	0.922668i	$-0.626004\pi$
$631$	−486.622			−0.771191			−0.385596	+	0.922668i	$0.626004\pi$
$632$		0			0
$633$			434.393i			0.686245i
$634$		0			0
$635$	619.681	−	619.681i	0.975875	−	0.975875i
$636$		0			0
$637$	−118.247	+	118.247i	−0.185631	+	0.185631i
$638$		0			0
$639$		−	127.968i		−	0.200263i
$640$		0			0
$641$	−691.017			−1.07803			−0.539015	−	0.842296i	$-0.681203\pi$
$641$	−691.017			−1.07803			−0.539015	+	0.842296i	$0.681203\pi$
$642$		0			0
$643$	652.605	+	652.605i	1.01494	+	1.01494i	0.999887	+	0.0150512i	$0.00479113\pi$
$643$	652.605	+	652.605i	1.01494	+	1.01494i	0.0150512	+	0.999887i	$0.495209\pi$
$644$		0			0
$645$	429.117	+	429.117i	0.665298	+	0.665298i
$646$		0			0
$647$	−1156.72			−1.78782			−0.893911	−	0.448245i	$-0.852049\pi$
$647$	−1156.72			−1.78782			−0.893911	+	0.448245i	$0.852049\pi$
$648$		0			0
$649$			667.201i			1.02804i
$650$		0			0
$651$	110.314	−	110.314i	0.169453	−	0.169453i
$652$		0			0
$653$	209.105	−	209.105i	0.320222	−	0.320222i	−0.528630	−	0.848852i	$-0.677294\pi$
$653$	209.105	−	209.105i	0.320222	−	0.320222i	0.848852	+	0.528630i	$0.177294\pi$
$654$		0			0
$655$		−	725.776i		−	1.10806i
$656$		0			0
$657$	319.174			0.485805
$658$		0			0
$659$	533.902	+	533.902i	0.810170	+	0.810170i	0.984659	−	0.174489i	$-0.0558274\pi$
$659$	533.902	+	533.902i	0.810170	+	0.810170i	−0.174489	+	0.984659i	$0.555827\pi$
$660$		0			0
$661$	−283.120	−	283.120i	−0.428320	−	0.428320i	0.459736	−	0.888056i	$-0.347944\pi$
$661$	−283.120	−	283.120i	−0.428320	−	0.428320i	−0.888056	+	0.459736i	$0.847944\pi$
$662$		0			0
$663$	−328.805			−0.495935
$664$		0			0
$665$			656.484i			0.987195i
$666$		0			0
$667$	106.825	−	106.825i	0.160157	−	0.160157i
$668$		0			0
$669$	462.861	−	462.861i	0.691870	−	0.691870i
$670$		0			0
$671$			1603.11i			2.38913i
$672$		0			0
$673$	−397.854			−0.591164			−0.295582	−	0.955317i	$-0.595514\pi$
$673$	−397.854			−0.591164			−0.295582	+	0.955317i	$0.595514\pi$
$674$		0			0
$675$	−110.188	−	110.188i	−0.163242	−	0.163242i
$676$		0			0
$677$	−289.959	−	289.959i	−0.428299	−	0.428299i	0.459749	−	0.888049i	$-0.347939\pi$
$677$	−289.959	−	289.959i	−0.428299	−	0.428299i	−0.888049	+	0.459749i	$0.847939\pi$
$678$		0			0
$679$	−112.005			−0.164956
$680$		0			0
$681$			254.525i			0.373751i
$682$		0			0
$683$	−150.197	+	150.197i	−0.219908	+	0.219908i	−0.808460	−	0.588551i	$-0.799698\pi$
$683$	−150.197	+	150.197i	−0.219908	+	0.219908i	0.588551	+	0.808460i	$0.299698\pi$
$684$		0			0
$685$	−652.686	+	652.686i	−0.952826	+	0.952826i
$686$		0			0
$687$			247.534i			0.360312i
$688$		0			0
$689$	768.535			1.11544
$690$		0			0
$691$	791.212	+	791.212i	1.14502	+	1.14502i	0.987518	+	0.157506i	$0.0503453\pi$
$691$	791.212	+	791.212i	1.14502	+	1.14502i	0.157506	+	0.987518i	$0.449655\pi$
$692$		0			0
$693$	196.382	+	196.382i	0.283380	+	0.283380i
$694$		0			0
$695$	1772.46			2.55030
$696$		0			0
$697$		−	684.092i		−	0.981481i
$698$		0			0
$699$	−351.819	+	351.819i	−0.503318	+	0.503318i
$700$		0			0
$701$	−900.201	+	900.201i	−1.28417	+	1.28417i	−0.345893	+	0.938274i	$0.612424\pi$
$701$	−900.201	+	900.201i	−1.28417	+	1.28417i	−0.938274	+	0.345893i	$0.887576\pi$
$702$		0			0
$703$		−	360.445i		−	0.512724i
$704$		0			0
$705$	233.921			0.331803
$706$		0			0
$707$	17.3138	+	17.3138i	0.0244891	+	0.0244891i
$708$		0			0
$709$	−128.490	−	128.490i	−0.181227	−	0.181227i	0.610663	−	0.791891i	$-0.290903\pi$
$709$	−128.490	−	128.490i	−0.181227	−	0.181227i	−0.791891	+	0.610663i	$0.790903\pi$
$710$		0			0
$711$	63.8463			0.0897979
$712$		0			0
$713$			98.1928i			0.137718i
$714$		0			0
$715$	739.140	−	739.140i	1.03376	−	1.03376i
$716$		0			0
$717$	−184.865	+	184.865i	−0.257831	+	0.257831i
$718$		0			0
$719$		−	1246.14i		−	1.73315i	−0.499045	−	0.866576i	$-0.666316\pi$
$719$		−	1246.14i		−	1.73315i	0.499045	−	0.866576i	$-0.333684\pi$
$720$		0			0
$721$	−560.033			−0.776745
$722$		0			0
$723$	46.2730	+	46.2730i	0.0640014	+	0.0640014i
$724$		0			0
$725$	−551.546	−	551.546i	−0.760753	−	0.760753i
$726$		0			0
$727$	1130.07			1.55443			0.777216	−	0.629234i	$-0.216631\pi$
$727$	1130.07			1.55443			0.777216	+	0.629234i	$0.216631\pi$
$728$		0			0
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	−781.782	+	781.782i	−1.06947	+	1.06947i
$732$		0			0
$733$	708.087	−	708.087i	0.966012	−	0.966012i	−0.0334292	−	0.999441i	$-0.510643\pi$
$733$	708.087	−	708.087i	0.966012	−	0.966012i	0.999441	+	0.0334292i	$0.0106428\pi$
$734$		0			0
$735$		−	264.751i		−	0.360205i
$736$		0			0
$737$	−926.264			−1.25680
$738$		0			0
$739$	−32.7516	−	32.7516i	−0.0443188	−	0.0443188i	0.684600	−	0.728919i	$-0.259977\pi$
$739$	−32.7516	−	32.7516i	−0.0443188	−	0.0443188i	−0.728919	+	0.684600i	$0.759977\pi$
$740$		0			0
$741$	165.096	+	165.096i	0.222802	+	0.222802i
$742$		0			0
$743$	−708.128			−0.953066			−0.476533	−	0.879157i	$-0.658107\pi$
$743$	−708.128			−0.953066			−0.476533	+	0.879157i	$0.658107\pi$
$744$		0			0
$745$		−	1541.47i		−	2.06909i
$746$		0			0
$747$	−72.4914	+	72.4914i	−0.0970434	+	0.0970434i
$748$		0			0
$749$	−530.751	+	530.751i	−0.708612	+	0.708612i
$750$		0			0
$751$			1242.37i			1.65429i	0.561990	+	0.827144i	$0.310036\pi$
$751$			1242.37i			1.65429i	−0.561990	+	0.827144i	$0.689964\pi$
$752$		0			0
$753$	247.189			0.328272
$754$		0			0
$755$	−396.127	−	396.127i	−0.524671	−	0.524671i
$756$		0			0
$757$	311.304	+	311.304i	0.411233	+	0.411233i	0.882168	−	0.470935i	$-0.156083\pi$
$757$	311.304	+	311.304i	0.411233	+	0.411233i	−0.470935	+	0.882168i	$0.656083\pi$
$758$		0			0
$759$	−174.805			−0.230309
$760$		0			0
$761$		−	179.137i		−	0.235397i	−0.993049	−	0.117699i	$-0.962448\pi$
$761$		−	179.137i		−	0.235397i	0.993049	−	0.117699i	$-0.0375517\pi$
$762$		0			0
$763$	575.685	−	575.685i	0.754502	−	0.754502i
$764$		0			0
$765$	368.091	−	368.091i	0.481165	−	0.481165i
$766$		0			0
$767$			311.523i			0.406158i
$768$		0			0
$769$	−967.409			−1.25801			−0.629005	−	0.777402i	$-0.716537\pi$
$769$	−967.409			−1.25801			−0.629005	+	0.777402i	$0.716537\pi$
$770$		0			0
$771$	295.525	+	295.525i	0.383301	+	0.383301i
$772$		0			0
$773$	96.7342	+	96.7342i	0.125141	+	0.125141i	0.766904	−	0.641762i	$-0.221796\pi$
$773$	96.7342	+	96.7342i	0.125141	+	0.125141i	−0.641762	+	0.766904i	$0.721796\pi$
$774$		0			0
$775$	506.979			0.654166
$776$		0			0
$777$		−	200.188i		−	0.257642i
$778$		0			0
$779$	−343.489	+	343.489i	−0.440936	+	0.440936i
$780$		0			0
$781$	−524.082	+	524.082i	−0.671039	+	0.671039i
$782$		0			0
$783$		−	135.148i		−	0.172603i
$784$		0			0
$785$	855.070			1.08926
$786$		0			0
$787$	−381.038	−	381.038i	−0.484166	−	0.484166i	0.422293	−	0.906459i	$-0.361225\pi$
$787$	−381.038	−	381.038i	−0.484166	−	0.484166i	−0.906459	+	0.422293i	$0.861225\pi$
$788$		0			0
$789$	145.435	+	145.435i	0.184328	+	0.184328i
$790$		0			0
$791$	−124.054			−0.156831
$792$		0			0
$793$			748.507i			0.943893i
$794$		0			0
$795$	−860.362	+	860.362i	−1.08222	+	1.08222i
$796$		0			0
$797$	371.148	−	371.148i	0.465681	−	0.465681i	−0.434831	−	0.900512i	$-0.643192\pi$
$797$	371.148	−	371.148i	0.465681	−	0.465681i	0.900512	+	0.434831i	$0.143192\pi$
$798$		0			0
$799$			426.167i			0.533375i
$800$		0			0
$801$	158.409			0.197764
$802$		0			0
$803$	−1307.15	−	1307.15i	−1.62783	−	1.62783i
$804$		0			0
$805$	−162.272	−	162.272i	−0.201580	−	0.201580i
$806$		0			0
$807$	−18.9799			−0.0235191
$808$		0			0
$809$			309.566i			0.382653i	0.981526	+	0.191326i	$0.0612789\pi$
$809$			309.566i			0.382653i	−0.981526	+	0.191326i	$0.938721\pi$
$810$		0			0
$811$	−27.2916	+	27.2916i	−0.0336517	+	0.0336517i	−0.723732	−	0.690081i	$-0.757575\pi$
$811$	−27.2916	+	27.2916i	−0.0336517	+	0.0336517i	0.690081	+	0.723732i	$0.257575\pi$
$812$		0			0
$813$	−161.543	+	161.543i	−0.198699	+	0.198699i
$814$		0			0
$815$			585.247i			0.718095i
$816$		0			0
$817$	785.081			0.960931
$818$		0			0
$819$	91.6928	+	91.6928i	0.111957	+	0.111957i
$820$		0			0
$821$	879.903	+	879.903i	1.07175	+	1.07175i	0.997219	+	0.0745264i	$0.0237445\pi$
$821$	879.903	+	879.903i	1.07175	+	1.07175i	0.0745264	+	0.997219i	$0.476255\pi$
$822$		0			0
$823$	−68.6842			−0.0834559			−0.0417280	−	0.999129i	$-0.513286\pi$
$823$	−68.6842			−0.0834559			−0.0417280	+	0.999129i	$0.513286\pi$
$824$		0			0
$825$			902.533i			1.09398i
$826$		0			0
$827$	942.097	−	942.097i	1.13917	−	1.13917i	0.150575	−	0.988599i	$-0.451887\pi$
$827$	942.097	−	942.097i	1.13917	−	1.13917i	0.988599	−	0.150575i	$-0.0481126\pi$
$828$		0			0
$829$	568.532	−	568.532i	0.685805	−	0.685805i	−0.275497	−	0.961302i	$-0.588842\pi$
$829$	568.532	−	568.532i	0.685805	−	0.685805i	0.961302	+	0.275497i	$0.0888424\pi$
$830$		0			0
$831$			495.660i			0.596462i
$832$		0			0
$833$	482.333			0.579031
$834$		0			0
$835$	129.169	+	129.169i	0.154693	+	0.154693i
$836$		0			0
$837$	62.1140	+	62.1140i	0.0742102	+	0.0742102i
$838$		0			0
$839$	1346.87			1.60533			0.802666	−	0.596429i	$-0.203414\pi$
$839$	1346.87			1.60533			0.802666	+	0.596429i	$0.203414\pi$
$840$		0			0
$841$			164.515i			0.195618i
$842$		0			0
$843$	84.3228	−	84.3228i	0.100027	−	0.100027i
$844$		0			0
$845$	−541.046	+	541.046i	−0.640291	+	0.640291i
$846$		0			0
$847$		−	963.851i		−	1.13796i
$848$		0			0
$849$	506.488			0.596570
$850$		0			0
$851$	89.0960	+	89.0960i	0.104696	+	0.104696i
$852$		0			0
$853$	−74.4816	−	74.4816i	−0.0873172	−	0.0873172i	0.662099	−	0.749416i	$-0.269666\pi$
$853$	−74.4816	−	74.4816i	−0.0873172	−	0.0873172i	−0.749416	+	0.662099i	$0.769666\pi$
$854$		0			0
$855$	−369.645			−0.432333
$856$		0			0
$857$		−	53.7221i		−	0.0626862i	−0.999509	−	0.0313431i	$-0.990022\pi$
$857$		−	53.7221i		−	0.0626862i	0.999509	−	0.0313431i	$-0.00997845\pi$
$858$		0			0
$859$	−537.704	+	537.704i	−0.625965	+	0.625965i	−0.947050	−	0.321085i	$-0.895952\pi$
$859$	−537.704	+	537.704i	−0.625965	+	0.625965i	0.321085	+	0.947050i	$0.395952\pi$
$860$		0			0
$861$	−190.771	+	190.771i	−0.221569	+	0.221569i
$862$		0			0
$863$		−	1390.97i		−	1.61178i	−0.592064	−	0.805891i	$-0.701687\pi$
$863$		−	1390.97i		−	1.61178i	0.592064	−	0.805891i	$-0.298313\pi$
$864$		0			0
$865$	−51.2347			−0.0592309
$866$		0			0
$867$	316.652	+	316.652i	0.365227	+	0.365227i
$868$		0			0
$869$	−261.477	−	261.477i	−0.300895	−	0.300895i
$870$		0			0
$871$	−432.482			−0.496535
$872$		0			0
$873$		−	63.0666i		−	0.0722412i
$874$		0			0
$875$	−139.391	+	139.391i	−0.159303	+	0.159303i
$876$		0			0
$877$	−940.115	+	940.115i	−1.07197	+	1.07197i	−0.0747652	+	0.997201i	$0.523821\pi$
$877$	−940.115	+	940.115i	−1.07197	+	1.07197i	−0.997201	+	0.0747652i	$0.976179\pi$
$878$		0			0
$879$			884.847i			1.00665i
$880$		0			0
$881$	−140.985			−0.160029			−0.0800143	−	0.996794i	$-0.525497\pi$
$881$	−140.985			−0.160029			−0.0800143	+	0.996794i	$0.525497\pi$
$882$		0			0
$883$	−482.231	−	482.231i	−0.546127	−	0.546127i	0.379191	−	0.925318i	$-0.376202\pi$
$883$	−482.231	−	482.231i	−0.546127	−	0.546127i	−0.925318	+	0.379191i	$0.876202\pi$
$884$		0			0
$885$	−348.744	−	348.744i	−0.394062	−	0.394062i
$886$		0			0
$887$	−266.180			−0.300091			−0.150045	−	0.988679i	$-0.547942\pi$
$887$	−266.180			−0.300091			−0.150045	+	0.988679i	$0.547942\pi$
$888$		0			0
$889$		−	629.658i		−	0.708277i
$890$		0			0
$891$	−110.576	+	110.576i	−0.124104	+	0.124104i
$892$		0			0
$893$	213.982	−	213.982i	0.239622	−	0.239622i
$894$		0			0
$895$		−	2406.83i		−	2.68919i
$896$		0			0
$897$	−81.6180			−0.0909899
$898$		0			0
$899$	310.911	+	310.911i	0.345841	+	0.345841i
$900$		0			0
$901$	−1567.44	−	1567.44i	−1.73967	−	1.73967i
$902$		0			0
$903$	436.026			0.482864
$904$		0			0
$905$		−	1222.87i		−	1.35124i
$906$		0			0
$907$	−303.117	+	303.117i	−0.334197	+	0.334197i	−0.854178	−	0.519981i	$-0.825939\pi$
$907$	−303.117	+	303.117i	−0.334197	+	0.334197i	0.519981	+	0.854178i	$0.325939\pi$
$908$		0			0
$909$	−9.74881	+	9.74881i	−0.0107248	+	0.0107248i
$910$		0			0
$911$		−	296.228i		−	0.325168i	−0.986695	−	0.162584i	$-0.948017\pi$
$911$		−	296.228i		−	0.325168i	0.986695	−	0.162584i	$-0.0519829\pi$
$912$		0			0
$913$	593.765			0.650346
$914$		0			0
$915$	−837.941	−	837.941i	−0.915783	−	0.915783i
$916$		0			0
$917$	−368.731	−	368.731i	−0.402106	−	0.402106i
$918$		0			0
$919$	228.052			0.248153			0.124076	−	0.992273i	$-0.460403\pi$
$919$	228.052			0.248153			0.124076	+	0.992273i	$0.460403\pi$
$920$		0			0
$921$		−	26.7172i		−	0.0290090i
$922$		0			0
$923$	−244.699	+	244.699i	−0.265113	+	0.265113i
$924$		0			0
$925$	460.011	−	460.011i	0.497309	−	0.497309i
$926$		0			0
$927$		−	315.336i		−	0.340168i
$928$		0			0
$929$	−574.026			−0.617897			−0.308948	−	0.951079i	$-0.599977\pi$
$929$	−574.026			−0.617897			−0.308948	+	0.951079i	$0.599977\pi$
$930$		0			0
$931$	−242.184	−	242.184i	−0.260133	−	0.260133i
$932$		0			0
$933$	196.267	+	196.267i	0.210361	+	0.210361i
$934$		0			0
$935$	−3014.98			−3.22457
$936$		0			0
$937$		−	1098.22i		−	1.17206i	−0.810291	−	0.586028i	$-0.800691\pi$
$937$		−	1098.22i		−	1.17206i	0.810291	−	0.586028i	$-0.199309\pi$
$938$		0			0
$939$	435.397	−	435.397i	0.463682	−	0.463682i
$940$		0			0
$941$	857.669	−	857.669i	0.911444	−	0.911444i	−0.0849418	−	0.996386i	$-0.527070\pi$
$941$	857.669	−	857.669i	0.911444	−	0.911444i	0.996386	+	0.0849418i	$0.0270704\pi$
$942$		0			0
$943$		−	169.810i		−	0.180074i
$944$		0			0
$945$	−205.297			−0.217245
$946$		0			0
$947$	1041.67	+	1041.67i	1.09997	+	1.09997i	0.994413	+	0.105556i	$0.0336622\pi$
$947$	1041.67	+	1041.67i	1.09997	+	1.09997i	0.105556	+	0.994413i	$0.466338\pi$
$948$		0			0
$949$	−610.322	−	610.322i	−0.643121	−	0.643121i
$950$		0			0
$951$	−177.635			−0.186788
$952$		0			0
$953$			910.089i			0.954973i	0.878639	+	0.477486i	$0.158452\pi$
$953$			910.089i			0.954973i	−0.878639	+	0.477486i	$0.841548\pi$
$954$		0			0
$955$	−494.107	+	494.107i	−0.517389	+	0.517389i
$956$		0			0
$957$	−553.489	+	553.489i	−0.578359	+	0.578359i
$958$		0			0
$959$			663.195i			0.691548i
$960$		0			0
$961$	675.212			0.702614
$962$		0			0
$963$	−298.848	−	298.848i	−0.310330	−	0.310330i
$964$		0			0
$965$	441.856	+	441.856i	0.457882	+	0.457882i
$966$		0			0
$967$	695.071			0.718791			0.359396	−	0.933185i	$-0.382983\pi$
$967$	695.071			0.718791			0.359396	+	0.933185i	$0.382983\pi$
$968$		0			0
$969$		−	673.433i		−	0.694977i
$970$		0			0
$971$	−1208.40	+	1208.40i	−1.24449	+	1.24449i	−0.286366	+	0.958120i	$0.592447\pi$
$971$	−1208.40	+	1208.40i	−1.24449	+	1.24449i	−0.958120	+	0.286366i	$0.907553\pi$
$972$		0			0
$973$	900.500	−	900.500i	0.925488	−	0.925488i
$974$		0			0
$975$			421.401i			0.432206i
$976$		0			0
$977$	141.036			0.144356			0.0721780	−	0.997392i	$-0.477005\pi$
$977$	141.036			0.144356			0.0721780	+	0.997392i	$0.477005\pi$
$978$		0			0
$979$	−648.750	−	648.750i	−0.662666	−	0.662666i
$980$		0			0
$981$	324.149	+	324.149i	0.330427	+	0.330427i
$982$		0			0
$983$	−1692.71			−1.72199			−0.860994	−	0.508616i	$-0.830157\pi$
$983$	−1692.71			−1.72199			−0.860994	+	0.508616i	$0.830157\pi$
$984$		0			0
$985$			597.320i			0.606417i
$986$		0			0
$987$	118.844	−	118.844i	0.120409	−	0.120409i
$988$		0			0
$989$	−194.059	+	194.059i	−0.196217	+	0.196217i
$990$		0			0
$991$			1532.62i			1.54654i	0.634079	+	0.773268i	$0.281379\pi$
$991$			1532.62i			1.54654i	−0.634079	+	0.773268i	$0.718621\pi$
$992$		0			0
$993$	−607.710			−0.611994
$994$		0			0
$995$	1028.67	+	1028.67i	1.03384	+	1.03384i
$996$		0			0
$997$	−1131.91	−	1131.91i	−1.13532	−	1.13532i	−0.989279	−	0.146039i	$-0.953348\pi$
$997$	−1131.91	−	1131.91i	−1.13532	−	1.13532i	−0.146039	−	0.989279i	$-0.546652\pi$
$998$		0			0
$999$	112.719			0.112832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.3.l.b.31.8		16
3.2	odd	2		1152.3.m.c.415.1		16
4.3	odd	2		384.3.l.a.31.4		16
8.3	odd	2		48.3.l.a.43.7	yes	16
8.5	even	2		192.3.l.a.79.1		16
12.11	even	2		1152.3.m.f.415.1		16
16.3	odd	4	inner	384.3.l.b.223.8		16
16.5	even	4		48.3.l.a.19.7	✓	16
16.11	odd	4		192.3.l.a.175.1		16
16.13	even	4		384.3.l.a.223.4		16
24.5	odd	2		576.3.m.c.271.8		16
24.11	even	2		144.3.m.c.91.2		16
48.5	odd	4		144.3.m.c.19.2		16
48.11	even	4		576.3.m.c.559.8		16
48.29	odd	4		1152.3.m.f.991.1		16
48.35	even	4		1152.3.m.c.991.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.l.a.19.7	✓	16	16.5	even	4
48.3.l.a.43.7	yes	16	8.3	odd	2
144.3.m.c.19.2		16	48.5	odd	4
144.3.m.c.91.2		16	24.11	even	2
192.3.l.a.79.1		16	8.5	even	2
192.3.l.a.175.1		16	16.11	odd	4
384.3.l.a.31.4		16	4.3	odd	2
384.3.l.a.223.4		16	16.13	even	4
384.3.l.b.31.8		16	1.1	even	1	trivial
384.3.l.b.223.8		16	16.3	odd	4	inner
576.3.m.c.271.8		16	24.5	odd	2
576.3.m.c.559.8		16	48.11	even	4
1152.3.m.c.415.1		16	3.2	odd	2
1152.3.m.c.991.1		16	48.35	even	4
1152.3.m.f.415.1		16	12.11	even	2
1152.3.m.f.991.1		16	48.29	odd	4

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.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 1.22474i) q^{3} +(5.24354 + 5.24354i) q^{5} +5.32796 q^{7} +3.00000i q^{9} +O(q^{10})\)	\(q+(1.22474 + 1.22474i) q^{3} +(5.24354 + 5.24354i) q^{5} +5.32796 q^{7} +3.00000i q^{9} +(12.2863 - 12.2863i) q^{11} +(5.73657 - 5.73657i) q^{13} +12.8440i q^{15} -23.3997 q^{17} +(11.7492 + 11.7492i) q^{19} +(6.52540 + 6.52540i) q^{21} -5.80841 q^{23} +29.9894i q^{25} +(-3.67423 + 3.67423i) q^{27} +(-18.3914 + 18.3914i) q^{29} -16.9053i q^{31} +30.0951 q^{33} +(27.9374 + 27.9374i) q^{35} +(-15.3391 - 15.3391i) q^{37} +14.0517 q^{39} +29.2351i q^{41} +(33.4099 - 33.4099i) q^{43} +(-15.7306 + 15.7306i) q^{45} -18.2125i q^{47} -20.6128 q^{49} +(-28.6586 - 28.6586i) q^{51} +(66.9856 + 66.9856i) q^{53} +128.847 q^{55} +28.7796i q^{57} +(-27.1523 + 27.1523i) q^{59} +(-65.2399 + 65.2399i) q^{61} +15.9839i q^{63} +60.1599 q^{65} +(-37.6951 - 37.6951i) q^{67} +(-7.11382 - 7.11382i) q^{69} -42.6559 q^{71} -106.391i q^{73} +(-36.7294 + 36.7294i) q^{75} +(65.4607 - 65.4607i) q^{77} -21.2821i q^{79} -9.00000 q^{81} +(24.1638 + 24.1638i) q^{83} +(-122.697 - 122.697i) q^{85} -45.0495 q^{87} -52.8029i q^{89} +(30.5643 - 30.5643i) q^{91} +(20.7047 - 20.7047i) q^{93} +123.215i q^{95} -21.0222 q^{97} +(36.8588 + 36.8588i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 32 q^{11} - 32 q^{19} + 128 q^{23} - 32 q^{29} + 96 q^{35} + 96 q^{37} + 160 q^{43} + 112 q^{49} - 96 q^{51} + 160 q^{53} + 256 q^{55} - 128 q^{59} + 32 q^{61} - 32 q^{65} + 320 q^{67} - 96 q^{69} - 512 q^{71} + 192 q^{75} - 224 q^{77} - 144 q^{81} - 160 q^{83} - 160 q^{85} - 480 q^{91} + 96 q^{99}+O(q^{100}) \) 16 * q + 32 * q^11 - 32 * q^19 + 128 * q^23 - 32 * q^29 + 96 * q^35 + 96 * q^37 + 160 * q^43 + 112 * q^49 - 96 * q^51 + 160 * q^53 + 256 * q^55 - 128 * q^59 + 32 * q^61 - 32 * q^65 + 320 * q^67 - 96 * q^69 - 512 * q^71 + 192 * q^75 - 224 * q^77 - 144 * q^81 - 160 * q^83 - 160 * q^85 - 480 * q^91 + 96 * q^99

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