LMFDB - Embedded newform 144.3.m.c.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(19,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("144.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.m (of order $4$, degree $2$, 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:	$3.92371580679$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.2
Root			$-1.87459 - 0.697079i$ of defining polynomial
Character	$\chi$	$=$	144.19
Dual form			144.3.m.c.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87459 + 0.697079i) q^{2} +(3.02816 - 2.61347i) q^{4} +(5.24354 - 5.24354i) q^{5} -5.32796 q^{7} +(-3.85476 + 7.01005i) q^{8} +O(q^{10})$	\(q+(-1.87459 + 0.697079i) q^{2} +(3.02816 - 2.61347i) q^{4} +(5.24354 - 5.24354i) q^{5} -5.32796 q^{7} +(-3.85476 + 7.01005i) q^{8} +(-6.17431 + 13.4846i) q^{10} +(-12.2863 - 12.2863i) q^{11} +(-5.73657 - 5.73657i) q^{13} +(9.98774 - 3.71401i) q^{14} +(2.33953 - 15.8280i) q^{16} +23.3997 q^{17} +(11.7492 - 11.7492i) q^{19} +(2.17444 - 29.5821i) q^{20} +(31.5962 + 14.4672i) q^{22} -5.80841 q^{23} -29.9894i q^{25} +(14.7526 + 6.75487i) q^{26} +(-16.1339 + 13.9245i) q^{28} +(-18.3914 - 18.3914i) q^{29} -16.9053i q^{31} +(6.64774 + 31.3019i) q^{32} +(-43.8648 + 16.3114i) q^{34} +(-27.9374 + 27.9374i) q^{35} +(15.3391 - 15.3391i) q^{37} +(-13.8348 + 30.2151i) q^{38} +(16.5449 + 56.9701i) q^{40} +29.2351i q^{41} +(33.4099 + 33.4099i) q^{43} +(-69.3146 - 5.09498i) q^{44} +(10.8884 - 4.04892i) q^{46} +18.2125i q^{47} -20.6128 q^{49} +(20.9050 + 56.2178i) q^{50} +(-32.3637 - 2.37890i) q^{52} +(66.9856 - 66.9856i) q^{53} -128.847 q^{55} +(20.5380 - 37.3493i) q^{56} +(47.2965 + 21.6560i) q^{58} +(27.1523 + 27.1523i) q^{59} +(65.2399 + 65.2399i) q^{61} +(11.7843 + 31.6904i) q^{62} +(-34.2817 - 54.0441i) q^{64} -60.1599 q^{65} +(-37.6951 + 37.6951i) q^{67} +(70.8580 - 61.1544i) q^{68} +(32.8965 - 71.8456i) q^{70} -42.6559 q^{71} +106.391i q^{73} +(-18.0620 + 39.4471i) q^{74} +(4.87228 - 66.2847i) q^{76} +(65.4607 + 65.4607i) q^{77} -21.2821i q^{79} +(-70.7275 - 95.2623i) q^{80} +(-20.3792 - 54.8038i) q^{82} +(-24.1638 + 24.1638i) q^{83} +(122.697 - 122.697i) q^{85} +(-85.9192 - 39.3405i) q^{86} +(133.488 - 38.7667i) q^{88} -52.8029i q^{89} +(30.5643 + 30.5643i) q^{91} +(-17.5888 + 15.1801i) q^{92} +(-12.6955 - 34.1409i) q^{94} -123.215i q^{95} -21.0222 q^{97} +(38.6405 - 14.3688i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} + 12 q^{8}+O(q^{10}) $ 16 * q + 12 * q^4 + 12 * q^8	$ 16 q + 12 q^{4} + 12 q^{8} - 56 q^{10} - 32 q^{11} + 44 q^{14} + 32 q^{16} - 32 q^{19} - 80 q^{20} + 32 q^{22} + 128 q^{23} + 100 q^{26} - 120 q^{28} - 32 q^{29} - 160 q^{32} + 96 q^{34} - 96 q^{35} - 96 q^{37} - 168 q^{38} + 48 q^{40} + 160 q^{43} - 88 q^{44} + 136 q^{46} + 112 q^{49} + 236 q^{50} - 48 q^{52} + 160 q^{53} - 256 q^{55} + 224 q^{56} + 144 q^{58} + 128 q^{59} - 32 q^{61} + 276 q^{62} - 408 q^{64} + 32 q^{65} + 320 q^{67} + 448 q^{68} - 384 q^{70} - 512 q^{71} - 348 q^{74} + 72 q^{76} - 224 q^{77} - 552 q^{80} - 40 q^{82} + 160 q^{83} + 160 q^{85} - 528 q^{86} + 480 q^{88} - 480 q^{91} - 496 q^{92} + 312 q^{94} + 440 q^{98}+O(q^{100}) $ 16 * q + 12 * q^4 + 12 * q^8 - 56 * q^10 - 32 * q^11 + 44 * q^14 + 32 * q^16 - 32 * q^19 - 80 * q^20 + 32 * q^22 + 128 * q^23 + 100 * q^26 - 120 * q^28 - 32 * q^29 - 160 * q^32 + 96 * q^34 - 96 * q^35 - 96 * q^37 - 168 * q^38 + 48 * q^40 + 160 * q^43 - 88 * q^44 + 136 * q^46 + 112 * q^49 + 236 * q^50 - 48 * q^52 + 160 * q^53 - 256 * q^55 + 224 * q^56 + 144 * q^58 + 128 * q^59 - 32 * q^61 + 276 * q^62 - 408 * q^64 + 32 * q^65 + 320 * q^67 + 448 * q^68 - 384 * q^70 - 512 * q^71 - 348 * q^74 + 72 * q^76 - 224 * q^77 - 552 * q^80 - 40 * q^82 + 160 * q^83 + 160 * q^85 - 528 * q^86 + 480 * q^88 - 480 * q^91 - 496 * q^92 + 312 * q^94 + 440 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.87459	+	0.697079i	−0.937294	+	0.348540i
$2$	−1.87459	+	0.697079i	−0.937294	+	0.348540i
$3$		0			0
$3$		0			0
$4$	3.02816	−	2.61347i	0.757040	−	0.653368i
$5$	5.24354	−	5.24354i	1.04871	−	1.04871i	0.0499563	−	0.998751i	$-0.484092\pi$
$5$	5.24354	−	5.24354i	1.04871	−	1.04871i	0.998751	−	0.0499563i	$-0.0159082\pi$
$6$		0			0
$7$	−5.32796			−0.761138			−0.380569	−	0.924753i	$-0.624272\pi$
$7$	−5.32796			−0.761138			−0.380569	+	0.924753i	$0.624272\pi$
$8$	−3.85476	+	7.01005i	−0.481845	+	0.876256i
$9$		0			0
$10$	−6.17431	+	13.4846i	−0.617431	+	1.34846i
$11$	−12.2863	−	12.2863i	−1.11693	−	1.11693i	−0.992189	−	0.124743i	$-0.960189\pi$
$11$	−12.2863	−	12.2863i	−1.11693	−	1.11693i	−0.124743	−	0.992189i	$-0.539811\pi$
$12$		0			0
$13$	−5.73657	−	5.73657i	−0.441275	−	0.441275i	0.451165	−	0.892440i	$-0.351008\pi$
$13$	−5.73657	−	5.73657i	−0.441275	−	0.441275i	−0.892440	+	0.451165i	$0.851008\pi$
$14$	9.98774	−	3.71401i	0.713410	−	0.265287i
$15$		0			0
$16$	2.33953	−	15.8280i	0.146220	−	0.989252i
$17$	23.3997			1.37645			0.688226	−	0.725496i	$-0.258390\pi$
$17$	23.3997			1.37645			0.688226	+	0.725496i	$0.258390\pi$
$18$		0			0
$19$	11.7492	−	11.7492i	0.618380	−	0.618380i	−0.326736	−	0.945116i	$-0.605949\pi$
$19$	11.7492	−	11.7492i	0.618380	−	0.618380i	0.945116	+	0.326736i	$0.105949\pi$
$20$	2.17444	−	29.5821i	0.108722	−	1.47911i
$21$		0			0
$22$	31.5962	+	14.4672i	1.43619	+	0.657599i
$23$	−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
$26$	14.7526	+	6.75487i	0.567406	+	0.259803i
$27$		0			0
$28$	−16.1339	+	13.9245i	−0.576212	+	0.497303i
$29$	−18.3914	−	18.3914i	−0.634185	−	0.634185i	0.314930	−	0.949115i	$-0.398019\pi$
$29$	−18.3914	−	18.3914i	−0.634185	−	0.634185i	−0.949115	+	0.314930i	$0.898019\pi$
$30$		0			0
$31$		−	16.9053i		−	0.545332i	−0.962109	−	0.272666i	$-0.912095\pi$
$31$		−	16.9053i		−	0.545332i	0.962109	−	0.272666i	$-0.0879053\pi$
$32$	6.64774	+	31.3019i	0.207742	+	0.978184i
$33$		0			0
$34$	−43.8648	+	16.3114i	−1.29014	+	0.479748i
$35$	−27.9374	+	27.9374i	−0.798211	+	0.798211i
$36$		0			0
$37$	15.3391	−	15.3391i	0.414571	−	0.414571i	−0.468756	−	0.883327i	$-0.655298\pi$
$37$	15.3391	−	15.3391i	0.414571	−	0.414571i	0.883327	+	0.468756i	$0.155298\pi$
$38$	−13.8348	+	30.2151i	−0.364074	+	0.795133i
$39$		0			0
$40$	16.5449	+	56.9701i	0.413622	+	1.42425i
$41$			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	0.979315	−	0.202340i	$-0.0648546\pi$
$43$	33.4099	+	33.4099i	0.776975	+	0.776975i	−0.202340	+	0.979315i	$0.564855\pi$
$44$	−69.3146	−	5.09498i	−1.57533	−	0.115795i
$45$		0			0
$46$	10.8884	−	4.04892i	0.236704	−	0.0880201i
$47$			18.2125i			0.387500i	0.981051	+	0.193750i	$0.0620650\pi$
$47$			18.2125i			0.387500i	−0.981051	+	0.193750i	$0.937935\pi$
$48$		0			0
$49$	−20.6128			−0.420670
$50$	20.9050	+	56.2178i	0.418100	+	1.12436i
$51$		0			0
$52$	−32.3637	−	2.37890i	−0.622378	−	0.0457480i
$53$	66.9856	−	66.9856i	1.26388	−	1.26388i	0.314681	−	0.949197i	$-0.398102\pi$
$53$	66.9856	−	66.9856i	1.26388	−	1.26388i	0.949197	−	0.314681i	$-0.101898\pi$
$54$		0			0
$55$	−128.847			−2.34267
$56$	20.5380	−	37.3493i	0.366750	−	0.666952i
$57$		0			0
$58$	47.2965	+	21.6560i	0.815457	+	0.373380i
$59$	27.1523	+	27.1523i	0.460209	+	0.460209i	0.898724	−	0.438515i	$-0.144495\pi$
$59$	27.1523	+	27.1523i	0.460209	+	0.460209i	−0.438515	+	0.898724i	$0.644495\pi$
$60$		0			0
$61$	65.2399	+	65.2399i	1.06951	+	1.06951i	0.997397	+	0.0721103i	$0.0229733\pi$
$61$	65.2399	+	65.2399i	1.06951	+	1.06951i	0.0721103	+	0.997397i	$0.477027\pi$
$62$	11.7843	+	31.6904i	0.190070	+	0.511136i
$63$		0			0
$64$	−34.2817	−	54.0441i	−0.535651	−	0.844440i
$65$	−60.1599			−0.925537
$66$		0			0
$67$	−37.6951	+	37.6951i	−0.562614	+	0.562614i	−0.930049	−	0.367435i	$-0.880236\pi$
$67$	−37.6951	+	37.6951i	−0.562614	+	0.562614i	0.367435	+	0.930049i	$0.380236\pi$
$68$	70.8580	−	61.1544i	1.04203	−	0.899330i
$69$		0			0
$70$	32.8965	−	71.8456i	0.469950	−	1.02637i
$71$	−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	$0.259879\pi$
$73$			106.391i			1.45742i	−0.684825	+	0.728708i	$0.740121\pi$
$74$	−18.0620	+	39.4471i	−0.244081	+	0.533069i
$75$		0			0
$76$	4.87228	−	66.2847i	0.0641089	−	0.872168i
$77$	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	$-0.0430061\pi$
$80$	−70.7275	−	95.2623i	−0.884094	−	1.19078i
$81$		0			0
$82$	−20.3792	−	54.8038i	−0.248527	−	0.668339i
$83$	−24.1638	+	24.1638i	−0.291130	+	0.291130i	−0.837527	−	0.546396i	$-0.815999\pi$
$83$	−24.1638	+	24.1638i	−0.291130	+	0.291130i	0.546396	+	0.837527i	$0.315999\pi$
$84$		0			0
$85$	122.697	−	122.697i	1.44350	−	1.44350i
$86$	−85.9192	−	39.3405i	−0.999061	−	0.457448i
$87$		0			0
$88$	133.488	−	38.7667i	1.51691	−	0.440531i
$89$		−	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
$92$	−17.5888	+	15.1801i	−0.191183	+	0.165001i
$93$		0			0
$94$	−12.6955	−	34.1409i	−0.135059	−	0.363201i
$95$		−	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	$0.534560\pi$
$98$	38.6405	−	14.3688i	0.394291	−	0.146620i
$99$		0			0
$100$	−78.3764	−	90.8127i	−0.783764	−	0.908127i
$101$	3.24960	−	3.24960i	0.0321743	−	0.0321743i	−0.690837	−	0.723011i	$-0.742758\pi$
$101$	3.24960	−	3.24960i	0.0321743	−	0.0321743i	0.723011	+	0.690837i	$0.242758\pi$
$102$		0			0
$103$	105.112			1.02050			0.510252	−	0.860025i	$-0.329552\pi$
$103$	105.112			1.02050			0.510252	+	0.860025i	$0.329552\pi$
$104$	62.3268	−	18.1006i	0.599296	−	0.174044i
$105$		0			0
$106$	−78.8761	+	172.265i	−0.744114	+	1.62514i
$107$	99.6160	+	99.6160i	0.930991	+	0.930991i	0.997768	−	0.0667770i	$-0.0212716\pi$
$107$	99.6160	+	99.6160i	0.930991	+	0.930991i	−0.0667770	+	0.997768i	$0.521272\pi$
$108$		0			0
$109$	−108.050	−	108.050i	−0.991282	−	0.991282i	0.00868078	−	0.999962i	$-0.497237\pi$
$109$	−108.050	−	108.050i	−0.991282	−	0.991282i	−0.999962	+	0.00868078i	$0.997237\pi$
$110$	241.535	−	89.8165i	2.19577	−	0.816513i
$111$		0			0
$112$	−12.4649	+	84.3312i	−0.111294	+	0.752957i
$113$	23.2835			0.206048			0.103024	−	0.994679i	$-0.467148\pi$
$113$	23.2835			0.206048			0.103024	+	0.994679i	$0.467148\pi$
$114$		0			0
$115$	−30.4566	+	30.4566i	−0.264840	+	0.264840i
$116$	−103.757	−	7.62671i	−0.894460	−	0.0657475i
$117$		0			0
$118$	−69.8268	−	31.9721i	−0.591752	−	0.270950i
$119$	−124.673			−1.04767
$120$		0			0
$121$			180.904i			1.49508i
$122$	−167.775	−	76.8206i	−1.37521	−	0.629677i
$123$		0			0
$124$	−44.1815	−	51.1919i	−0.356302	−	0.412838i
$125$	−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	$-0.154045\pi$
$128$	101.937	+	77.4135i	0.796383	+	0.604793i
$129$		0			0
$130$	112.775	−	41.9362i	0.867500	−	0.322586i
$131$	69.2067	−	69.2067i	0.528296	−	0.528296i	−0.391768	−	0.920064i	$-0.628137\pi$
$131$	69.2067	−	69.2067i	0.528296	−	0.528296i	0.920064	+	0.391768i	$0.128137\pi$
$132$		0			0
$133$	−62.5994	+	62.5994i	−0.470672	+	0.470672i
$134$	44.3864	−	96.9393i	0.331241	−	0.723428i
$135$		0			0
$136$	−90.2002	+	164.033i	−0.663237	+	1.20613i
$137$			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	0.969046	+	0.246881i	$0.0794057\pi$
$139$	169.014	+	169.014i	1.21593	+	1.21593i	0.246881	+	0.969046i	$0.420594\pi$
$140$	−11.5853	+	157.612i	−0.0827524	+	1.12580i
$141$		0			0
$142$	79.9623	−	29.7346i	0.563115	−	0.209398i
$143$			140.962i			0.985749i
$144$		0			0
$145$	−192.872			−1.33015
$146$	−74.1632	−	199.440i	−0.507967	−	1.36603i
$147$		0			0
$148$	6.36098	−	86.5377i	0.0429796	−	0.584714i
$149$	−146.988	+	146.988i	−0.986495	+	0.986495i	−0.999910	−	0.0134145i	$-0.995730\pi$
$149$	−146.988	+	146.988i	−0.986495	+	0.986495i	0.0134145	+	0.999910i	$0.495730\pi$
$150$		0			0
$151$	75.5456			0.500302			0.250151	−	0.968207i	$-0.419520\pi$
$151$	75.5456			0.500302			0.250151	+	0.968207i	$0.419520\pi$
$152$	37.0722	+	127.653i	0.243896	+	0.839822i
$153$		0			0
$154$	−168.343	−	77.0806i	−1.09314	−	0.500523i
$155$	−88.6435	−	88.6435i	−0.571893	−	0.571893i
$156$		0			0
$157$	−81.5356	−	81.5356i	−0.519335	−	0.519335i	0.398035	−	0.917370i	$-0.369692\pi$
$157$	−81.5356	−	81.5356i	−0.519335	−	0.519335i	−0.917370	+	0.398035i	$0.869692\pi$
$158$	14.8353	+	39.8952i	0.0938943	+	0.252501i
$159$		0			0
$160$	198.990	+	129.275i	1.24369	+	0.807968i
$161$	30.9470			0.192217
$162$		0			0
$163$	55.8065	−	55.8065i	0.342371	−	0.342371i	−0.514887	−	0.857258i	$-0.672166\pi$
$163$	55.8065	−	55.8065i	0.342371	−	0.342371i	0.857258	+	0.514887i	$0.172166\pi$
$164$	76.4051	+	88.5286i	0.465885	+	0.539809i
$165$		0			0
$166$	28.4531	−	62.1413i	0.171404	−	0.374345i
$167$	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
$170$	−144.477	+	315.536i	−0.849865	+	1.85610i
$171$		0			0
$172$	188.487	+	13.8548i	1.09585	+	0.0805509i
$173$	−4.88551	−	4.88551i	−0.0282399	−	0.0282399i	0.692846	−	0.721086i	$-0.256357\pi$
$173$	−4.88551	−	4.88551i	−0.0282399	−	0.0282399i	−0.721086	+	0.692846i	$0.756357\pi$
$174$		0			0
$175$			159.782i			0.913042i
$176$	−223.211	+	165.723i	−1.26825	+	0.941609i
$177$		0			0
$178$	36.8078	+	98.9836i	0.206785	+	0.556088i
$179$	229.504	−	229.504i	1.28215	−	1.28215i	0.342702	−	0.939444i	$-0.388658\pi$
$179$	229.504	−	229.504i	1.28215	−	1.28215i	0.939444	−	0.342702i	$-0.111342\pi$
$180$		0			0
$181$	116.607	−	116.607i	0.644238	−	0.644238i	−0.307356	−	0.951595i	$-0.599444\pi$
$181$	116.607	−	116.607i	0.644238	−	0.644238i	0.951595	+	0.307356i	$0.0994443\pi$
$182$	−78.6011	−	35.9897i	−0.431874	−	0.197746i
$183$		0			0
$184$	22.3900	−	40.7173i	0.121685	−	0.221290i
$185$		−	160.863i		−	0.869528i
$186$		0			0
$187$	−287.495	−	287.495i	−1.53740	−	1.53740i
$188$	47.5978	+	55.1504i	0.253180	+	0.293353i
$189$		0			0
$190$	85.8905	+	230.977i	0.452055	+	1.21567i
$191$		−	94.2316i		−	0.493359i	−0.969097	−	0.246680i	$-0.920660\pi$
$191$		−	94.2316i		−	0.493359i	0.969097	−	0.246680i	$-0.0793395\pi$
$192$		0			0
$193$	84.2667			0.436615			0.218308	−	0.975880i	$-0.429946\pi$
$193$	84.2667			0.436615			0.218308	+	0.975880i	$0.429946\pi$
$194$	39.4079	−	14.6541i	0.203134	−	0.0755367i
$195$		0			0
$196$	−62.4189	+	53.8710i	−0.318464	+	0.274852i
$197$	56.9578	−	56.9578i	0.289126	−	0.289126i	−0.547609	−	0.836734i	$-0.684462\pi$
$197$	56.9578	−	56.9578i	0.289126	−	0.289126i	0.836734	+	0.547609i	$0.184462\pi$
$198$		0			0
$199$	−196.179			−0.985827			−0.492913	−	0.870078i	$-0.664068\pi$
$199$	−196.179			−0.985827			−0.492913	+	0.870078i	$0.664068\pi$
$200$	210.227	+	115.602i	1.05114	+	0.578009i
$201$		0			0
$202$	−3.82644	+	8.35690i	−0.0189428	+	0.0413708i
$203$	97.9886	+	97.9886i	0.482702	+	0.482702i
$204$		0			0
$205$	153.295	+	153.295i	0.747782	+	0.747782i
$206$	−197.042	+	73.2714i	−0.956513	+	0.355686i
$207$		0			0
$208$	−104.220	+	77.3778i	−0.501056	+	0.372009i
$209$	−288.708			−1.38138
$210$		0			0
$211$	177.340	−	177.340i	0.840475	−	0.840475i	−0.148445	−	0.988921i	$-0.547427\pi$
$211$	177.340	−	177.340i	0.840475	−	0.840475i	0.988921	+	0.148445i	$0.0474269\pi$
$212$	27.7782	−	377.908i	0.131029	−	1.78259i
$213$		0			0
$214$	−256.179	−	117.299i	−1.19710	−	0.548125i
$215$	350.373			1.62964
$216$		0			0
$217$			90.0707i			0.415072i
$218$	277.868	+	127.229i	1.27462	+	0.583622i
$219$		0			0
$220$	−390.169	+	336.738i	−1.77350	+	1.53063i
$221$	−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	$-0.321812\pi$
$224$	−35.4189	−	166.775i	−0.158120	−	0.744532i
$225$		0			0
$226$	−43.6469	+	16.2304i	−0.193128	+	0.0718160i
$227$	−103.909	+	103.909i	−0.457750	+	0.457750i	−0.897916	−	0.440166i	$-0.854920\pi$
$227$	−103.909	+	103.909i	−0.457750	+	0.457750i	0.440166	+	0.897916i	$0.354920\pi$
$228$		0			0
$229$	−101.055	+	101.055i	−0.441290	+	0.441290i	−0.892445	−	0.451156i	$-0.851012\pi$
$229$	−101.055	+	101.055i	−0.441290	+	0.441290i	0.451156	+	0.892445i	$0.351012\pi$
$230$	35.8630	−	78.3243i	0.155926	−	0.340541i
$231$		0			0
$232$	199.819	−	58.0302i	0.861288	−	0.250130i
$233$			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
$236$	153.184	+	11.2598i	0.649083	+	0.0477110i
$237$		0			0
$238$	233.710	−	86.9067i	0.981974	−	0.365154i
$239$		−	150.941i		−	0.631554i	−0.948833	−	0.315777i	$-0.897735\pi$
$239$		−	150.941i		−	0.631554i	0.948833	−	0.315777i	$-0.102265\pi$
$240$		0			0
$241$	37.7817			0.156771			0.0783853	−	0.996923i	$-0.475024\pi$
$241$	37.7817			0.156771			0.0783853	+	0.996923i	$0.475024\pi$
$242$	−126.105	−	339.121i	−0.521093	−	1.40133i
$243$		0			0
$244$	368.060	+	27.0543i	1.50844	+	0.110878i
$245$	−108.084	+	108.084i	−0.441159	+	0.441159i
$246$		0			0
$247$	−134.800			−0.545751
$248$	118.507	+	65.1658i	0.477850	+	0.262765i
$249$		0			0
$250$	67.2801	+	30.8061i	0.269121	+	0.123224i
$251$	−100.915	−	100.915i	−0.402050	−	0.402050i	0.476905	−	0.878955i	$-0.341759\pi$
$251$	−100.915	−	100.915i	−0.402050	−	0.402050i	−0.878955	+	0.476905i	$0.841759\pi$
$252$		0			0
$253$	71.3637	+	71.3637i	0.282070	+	0.282070i
$254$	82.3807	+	221.539i	0.324333	+	0.872199i
$255$		0			0
$256$	−245.053	−	74.0602i	−0.957239	−	0.289298i
$257$	−241.295			−0.938891			−0.469446	−	0.882961i	$-0.655546\pi$
$257$	−241.295			−0.938891			−0.469446	+	0.882961i	$0.655546\pi$
$258$		0			0
$259$	−81.7263	+	81.7263i	−0.315546	+	0.315546i
$260$	−182.174	+	157.226i	−0.700669	+	0.604716i
$261$		0			0
$262$	−81.4916	+	177.977i	−0.311037	+	0.679300i
$263$	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
$266$	73.7113	−	160.985i	0.277110	−	0.605206i
$267$		0			0
$268$	−15.6318	+	212.662i	−0.0583275	+	0.793515i
$269$	−7.74853	−	7.74853i	−0.0288050	−	0.0288050i	0.692558	−	0.721363i	$-0.256484\pi$
$269$	−7.74853	−	7.74853i	−0.0288050	−	0.0288050i	−0.721363	+	0.692558i	$0.756484\pi$
$270$		0			0
$271$			131.899i			0.486712i	0.969937	+	0.243356i	$0.0782484\pi$
$271$			131.899i			0.486712i	−0.969937	+	0.243356i	$0.921752\pi$
$272$	54.7442	−	370.371i	0.201265	−	1.36166i
$273$		0			0
$274$	−86.7685	−	233.338i	−0.316673	−	0.851599i
$275$	−368.457	+	368.457i	−1.33984	+	1.33984i
$276$		0			0
$277$	−202.352	+	202.352i	−0.730513	+	0.730513i	−0.970721	−	0.240208i	$-0.922784\pi$
$277$	−202.352	+	202.352i	−0.730513	+	0.730513i	0.240208	+	0.970721i	$0.422784\pi$
$278$	−434.647	−	199.015i	−1.56348	−	0.715883i
$279$		0			0
$280$	−88.1506	−	303.534i	−0.314824	−	1.08405i
$281$		−	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	0.970748	−	0.240102i	$-0.0771808\pi$
$283$	206.773	+	206.773i	0.730646	+	0.730646i	−0.240102	+	0.970748i	$0.577181\pi$
$284$	−129.169	+	111.480i	−0.454821	+	0.392535i
$285$		0			0
$286$	−98.2617	−	264.246i	−0.343572	−	0.923936i
$287$		−	155.764i		−	0.542730i
$288$		0			0
$289$	258.545			0.894620
$290$	361.555	−	134.447i	1.24674	−	0.463610i
$291$		0			0
$292$	278.051	+	322.170i	0.952229	+	1.10332i
$293$	361.237	−	361.237i	1.23289	−	1.23289i	0.270043	−	0.962848i	$-0.412962\pi$
$293$	361.237	−	361.237i	1.23289	−	1.23289i	0.962848	−	0.270043i	$-0.0870379\pi$
$294$		0			0
$295$	284.749			0.965250
$296$	48.3994	+	166.657i	0.163512	+	0.563029i
$297$		0			0
$298$	173.080	−	378.004i	0.580804	−	1.26847i
$299$	33.3204	+	33.3204i	0.111439	+	0.111439i
$300$		0			0
$301$	−178.007	−	178.007i	−0.591385	−	0.591385i
$302$	−141.617	+	52.6613i	−0.468930	+	0.174375i
$303$		0			0
$304$	−158.479	−	213.454i	−0.521314	−	0.702153i
$305$	684.176			2.24320
$306$		0			0
$307$	−10.9073	+	10.9073i	−0.0355286	+	0.0355286i	−0.724648	−	0.689119i	$-0.757998\pi$
$307$	−10.9073	+	10.9073i	−0.0355286	+	0.0355286i	0.689119	+	0.724648i	$0.257998\pi$
$308$	369.305	+	27.1459i	1.19904	+	0.0881360i
$309$		0			0
$310$	227.962	+	104.379i	0.735360	+	0.336705i
$311$	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	$0.192241\pi$
$313$			355.500i			1.13578i	−0.823103	+	0.567892i	$0.807759\pi$
$314$	209.682	+	96.0089i	0.667778	+	0.305761i
$315$		0			0
$316$	−55.6202	−	64.4456i	−0.176013	−	0.203942i
$317$	−72.5192	−	72.5192i	−0.228767	−	0.228767i	0.583410	−	0.812178i	$-0.301718\pi$
$317$	−72.5192	−	72.5192i	−0.228767	−	0.228767i	−0.812178	+	0.583410i	$0.801718\pi$
$318$		0			0
$319$			451.922i			1.41668i
$320$	−463.140	−	103.625i	−1.44731	−	0.323829i
$321$		0			0
$322$	−58.0129	+	21.5725i	−0.180164	+	0.0669954i
$323$	274.928	−	274.928i	0.851170	−	0.851170i
$324$		0			0
$325$	−172.036	+	172.036i	−0.529343	+	0.529343i
$326$	−65.7127	+	143.516i	−0.201573	+	0.440233i
$327$		0			0
$328$	−204.940	−	112.694i	−0.624816	−	0.343580i
$329$		−	97.0355i		−	0.294941i
$330$		0			0
$331$	−248.096	−	248.096i	−0.749536	−	0.749536i	0.224856	−	0.974392i	$-0.427809\pi$
$331$	−248.096	−	248.096i	−0.749536	−	0.749536i	−0.974392	+	0.224856i	$0.927809\pi$
$332$	−10.0205	+	136.323i	−0.0301822	+	0.410613i
$333$		0			0
$334$	−46.1783	+	17.1717i	−0.138258	+	0.0514124i
$335$			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	$0.743835\pi$
$338$	71.9270	+	193.426i	0.212802	+	0.572268i
$339$		0			0
$340$	50.8812	−	692.212i	0.149651	−	2.03592i
$341$	−207.703	+	207.703i	−0.609098	+	0.609098i
$342$		0			0
$343$	370.894			1.08133
$344$	−362.993	+	105.418i	−1.05521	+	0.306448i
$345$		0			0
$346$	12.5639	+	5.75273i	0.0363118	+	0.0166264i
$347$	−292.821	−	292.821i	−0.843863	−	0.843863i	0.145496	−	0.989359i	$-0.453522\pi$
$347$	−292.821	−	292.821i	−0.843863	−	0.843863i	−0.989359	+	0.145496i	$0.953522\pi$
$348$		0			0
$349$	346.260	+	346.260i	0.992150	+	0.992150i	0.999969	−	0.00781941i	$-0.00248902\pi$
$349$	346.260	+	346.260i	0.992150	+	0.992150i	−0.00781941	+	0.999969i	$0.502489\pi$
$350$	−111.381	−	299.526i	−0.318231	−	0.855789i
$351$		0			0
$352$	302.907	−	466.259i	0.860531	−	1.32460i
$353$	−8.01816			−0.0227143			−0.0113572	−	0.999936i	$-0.503615\pi$
$353$	−8.01816			−0.0227143			−0.0113572	+	0.999936i	$0.503615\pi$
$354$		0			0
$355$	−223.668	+	223.668i	−0.630051	+	0.630051i
$356$	−137.999	−	159.896i	−0.387637	−	0.449145i
$357$		0			0
$358$	−270.243	+	590.208i	−0.754869	+	1.64863i
$359$	−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
$362$	−137.306	+	299.875i	−0.379298	+	0.828383i
$363$		0			0
$364$	172.432	+	12.6747i	0.473715	+	0.0348205i
$365$	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	$0.818043\pi$
$368$	−13.5889	+	91.9358i	−0.0369265	+	0.249825i
$369$		0			0
$370$	112.134	+	301.551i	0.303065	+	0.815003i
$371$	−356.897	+	356.897i	−0.961986	+	0.961986i
$372$		0			0
$373$	−165.010	+	165.010i	−0.442387	+	0.442387i	−0.892814	−	0.450427i	$-0.851272\pi$
$373$	−165.010	+	165.010i	−0.442387	+	0.442387i	0.450427	+	0.892814i	$0.351272\pi$
$374$	739.340	+	338.527i	1.97685	+	0.905154i
$375$		0			0
$376$	−127.671	−	70.2048i	−0.339549	−	0.186715i
$377$			211.007i			0.559700i
$378$		0			0
$379$	−206.669	−	206.669i	−0.545300	−	0.545300i	0.379778	−	0.925078i	$-0.376000\pi$
$379$	−206.669	−	206.669i	−0.545300	−	0.545300i	−0.925078	+	0.379778i	$0.876000\pi$
$380$	−322.019	−	373.115i	−0.847418	−	0.981881i
$381$		0			0
$382$	65.6869	+	176.645i	0.171955	+	0.462423i
$383$			598.414i			1.56244i	0.624257	+	0.781219i	$0.285402\pi$
$383$			598.414i			1.56244i	−0.624257	+	0.781219i	$0.714598\pi$
$384$		0			0
$385$	686.492			1.78310
$386$	−157.965	+	58.7405i	−0.409237	+	0.152178i
$387$		0			0
$388$	−63.6586	+	54.9409i	−0.164069	+	0.141600i
$389$	−186.696	+	186.696i	−0.479939	+	0.479939i	−0.905112	−	0.425173i	$-0.860213\pi$
$389$	−186.696	+	186.696i	−0.479939	+	0.479939i	0.425173	+	0.905112i	$0.360213\pi$
$390$		0			0
$391$	−135.915			−0.347609
$392$	79.4574	−	144.497i	0.202697	−	0.368614i
$393$		0			0
$394$	−67.0683	+	146.476i	−0.170224	+	0.371768i
$395$	−111.594	−	111.594i	−0.282515	−	0.282515i
$396$		0			0
$397$	−57.3727	−	57.3727i	−0.144516	−	0.144516i	0.631147	−	0.775663i	$-0.282584\pi$
$397$	−57.3727	−	57.3727i	−0.144516	−	0.144516i	−0.775663	+	0.631147i	$0.782584\pi$
$398$	367.756	−	136.753i	0.924009	−	0.343600i
$399$		0			0
$400$	−474.673	−	70.1610i	−1.18668	−	0.175402i
$401$	466.082			1.16230			0.581149	−	0.813797i	$-0.302603\pi$
$401$	466.082			1.16230			0.581149	+	0.813797i	$0.302603\pi$
$402$		0			0
$403$	−96.9784	+	96.9784i	−0.240641	+	0.240641i
$404$	1.34758	−	18.3331i	0.00333559	−	0.0453789i
$405$		0			0
$406$	−251.994	−	115.382i	−0.620675	−	0.284193i
$407$	−376.921			−0.926096
$408$		0			0
$409$		−	597.952i		−	1.46198i	−0.682386	−	0.730992i	$-0.739058\pi$
$409$		−	597.952i		−	1.46198i	0.682386	−	0.730992i	$-0.260942\pi$
$410$	−394.225	−	180.507i	−0.961524	−	0.440260i
$411$		0			0
$412$	318.296	−	274.707i	0.772563	−	0.666765i
$413$	−144.667	−	144.667i	−0.350282	−	0.350282i
$414$		0			0
$415$			253.408i			0.610621i
$416$	141.430	−	217.701i	0.339977	−	0.523319i
$417$		0			0
$418$	541.208	−	201.252i	1.29476	−	0.481464i
$419$	4.65301	−	4.65301i	0.0111050	−	0.0111050i	−0.701532	−	0.712638i	$-0.747500\pi$
$419$	4.65301	−	4.65301i	0.0111050	−	0.0111050i	0.712638	+	0.701532i	$0.247500\pi$
$420$		0			0
$421$	34.3754	−	34.3754i	0.0816519	−	0.0816519i	−0.665101	−	0.746753i	$-0.731612\pi$
$421$	34.3754	−	34.3754i	0.0816519	−	0.0816519i	0.746753	+	0.665101i	$0.231612\pi$
$422$	−208.820	+	456.060i	−0.494834	+	1.08071i
$423$		0			0
$424$	211.359	+	727.786i	0.498488	+	1.71648i
$425$		−	701.742i		−	1.65116i
$426$		0			0
$427$	−347.596	−	347.596i	−0.814042	−	0.814042i
$428$	561.997	+	41.3097i	1.31308	+	0.0965181i
$429$		0			0
$430$	−656.804	+	244.237i	−1.52745	+	0.567994i
$431$			423.823i			0.983347i	0.870780	+	0.491674i	$0.163615\pi$
$431$			423.823i			0.983347i	−0.870780	+	0.491674i	$0.836385\pi$
$432$		0			0
$433$	833.377			1.92466			0.962330	−	0.271885i	$-0.0876472\pi$
$433$	833.377			1.92466			0.962330	+	0.271885i	$0.0876472\pi$
$434$	−62.7864	−	168.845i	−0.144669	−	0.389045i
$435$		0			0
$436$	−609.577	−	44.8071i	−1.39811	−	0.102769i
$437$	−68.2443	+	68.2443i	−0.156165	+	0.156165i
$438$		0			0
$439$	32.3193			0.0736203			0.0368102	−	0.999322i	$-0.488280\pi$
$439$	32.3193			0.0736203			0.0368102	+	0.999322i	$0.488280\pi$
$440$	496.674	−	903.224i	1.12880	−	2.05278i
$441$		0			0
$442$	345.205	+	158.062i	0.781007	+	0.357606i
$443$	−119.527	−	119.527i	−0.269813	−	0.269813i	0.559212	−	0.829025i	$-0.311104\pi$
$443$	−119.527	−	119.527i	−0.269813	−	0.269813i	−0.829025	+	0.559212i	$0.811104\pi$
$444$		0			0
$445$	−276.874	−	276.874i	−0.622189	−	0.622189i
$446$	263.443	+	708.453i	0.590680	+	1.58846i
$447$		0			0
$448$	182.651	+	287.945i	0.407704	+	0.642735i
$449$	182.359			0.406146			0.203073	−	0.979164i	$-0.434907\pi$
$449$	182.359			0.406146			0.203073	+	0.979164i	$0.434907\pi$
$450$		0			0
$451$	359.190	−	359.190i	0.796430	−	0.796430i
$452$	70.5061	−	60.8507i	0.155987	−	0.134625i
$453$		0			0
$454$	122.354	−	267.220i	0.269502	−	0.588591i
$455$	320.530			0.704461
$456$		0			0
$457$			272.942i			0.597246i	0.954371	+	0.298623i	$0.0965274\pi$
$457$			272.942i			0.597246i	−0.954371	+	0.298623i	$0.903473\pi$
$458$	118.994	−	259.881i	0.259811	−	0.567425i
$459$		0			0
$460$	−12.6301	+	171.825i	−0.0274566	+	0.373533i
$461$	−188.323	−	188.323i	−0.408510	−	0.408510i	0.472709	−	0.881219i	$-0.343276\pi$
$461$	−188.323	−	188.323i	−0.408510	−	0.408510i	−0.881219	+	0.472709i	$0.843276\pi$
$462$		0			0
$463$		−	116.023i		−	0.250590i	−0.992120	−	0.125295i	$-0.960012\pi$
$463$		−	116.023i		−	0.250590i	0.992120	−	0.125295i	$-0.0399877\pi$
$464$	−334.126	+	248.072i	−0.720100	+	0.534638i
$465$		0			0
$466$	−200.242	−	538.492i	−0.429704	−	1.15556i
$467$	271.914	−	271.914i	0.582257	−	0.582257i	−0.353266	−	0.935523i	$-0.614929\pi$
$467$	271.914	−	271.914i	0.582257	−	0.582257i	0.935523	+	0.353266i	$0.114929\pi$
$468$		0			0
$469$	200.838	−	200.838i	0.428227	−	0.428227i
$470$	−245.589	−	112.450i	−0.522530	−	0.239255i
$471$		0			0
$472$	−295.005	+	85.6736i	−0.625011	+	0.181512i
$473$		−	820.966i		−	1.73566i
$474$		0			0
$475$	−352.352	−	352.352i	−0.741793	−	0.741793i
$476$	−377.529	+	325.829i	−0.793128	+	0.684514i
$477$		0			0
$478$	105.218	+	282.953i	0.220121	+	0.591952i
$479$		−	775.808i		−	1.61964i	−0.586678	−	0.809820i	$-0.699565\pi$
$479$		−	775.808i		−	1.61964i	0.586678	−	0.809820i	$-0.300435\pi$
$480$		0			0
$481$	−175.988			−0.365880
$482$	−70.8252	+	26.3369i	−0.146940	+	0.0546408i
$483$		0			0
$484$	472.788	+	547.807i	0.976835	+	1.13183i
$485$	−110.231	+	110.231i	−0.227280	+	0.227280i
$486$		0			0
$487$	174.891			0.359118			0.179559	−	0.983747i	$-0.442533\pi$
$487$	174.891			0.359118			0.179559	+	0.983747i	$0.442533\pi$
$488$	−708.819	+	205.851i	−1.45250	+	0.421826i
$489$		0			0
$490$	127.270	−	277.956i	0.259735	−	0.567258i
$491$	348.578	+	348.578i	0.709934	+	0.709934i	0.966521	−	0.256587i	$-0.0825980\pi$
$491$	348.578	+	348.578i	0.709934	+	0.709934i	−0.256587	+	0.966521i	$0.582598\pi$
$492$		0			0
$493$	−430.352	−	430.352i	−0.872926	−	0.872926i
$494$	252.695	−	93.9666i	0.511529	−	0.190216i
$495$		0			0
$496$	−267.577	−	39.5503i	−0.539470	−	0.0797386i
$497$	227.269			0.457282
$498$		0			0
$499$	−607.544	+	607.544i	−1.21752	+	1.21752i	−0.249027	+	0.968496i	$0.580111\pi$
$499$	−607.544	+	607.544i	−1.21752	+	1.21752i	−0.968496	+	0.249027i	$0.919889\pi$
$500$	−147.597	−	10.8491i	−0.295194	−	0.0216983i
$501$		0			0
$502$	259.519	+	118.828i	0.516969	+	0.236709i
$503$	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
$506$	−183.524	−	84.0314i	−0.362695	−	0.166070i
$507$		0			0
$508$	−308.860	−	357.868i	−0.607992	−	0.704464i
$509$	61.5539	+	61.5539i	0.120931	+	0.120931i	0.764982	−	0.644051i	$-0.222748\pi$
$509$	61.5539	+	61.5539i	0.120931	+	0.120931i	−0.644051	+	0.764982i	$0.722748\pi$
$510$		0			0
$511$		−	566.849i		−	1.10929i
$512$	511.000	−	31.9891i	0.998046	−	0.0624786i
$513$		0			0
$514$	452.329	−	168.202i	0.880017	−	0.327241i
$515$	551.159	−	551.159i	1.07021	−	1.07021i
$516$		0			0
$517$	223.763	−	223.763i	0.432811	−	0.432811i
$518$	96.2335	−	210.173i	0.185779	−	0.405739i
$519$		0			0
$520$	231.902	−	421.724i	0.445965	−	0.811008i
$521$		−	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	0.456713	−	0.889614i	$-0.349026\pi$
$523$	−226.407	−	226.407i	−0.432900	−	0.432900i	−0.889614	+	0.456713i	$0.849026\pi$
$524$	28.6993	−	390.439i	0.0547697	−	0.745113i
$525$		0			0
$526$	−222.601	+	82.7759i	−0.423196	+	0.157369i
$527$		−	395.578i		−	0.750623i
$528$		0			0
$529$	−495.262			−0.936224
$530$	489.686	+	1316.87i	0.923936	+	2.48465i
$531$		0			0
$532$	−25.9593	+	353.163i	−0.0487957	+	0.663840i
$533$	167.709	−	167.709i	0.314652	−	0.314652i
$534$		0			0
$535$	1044.68			1.95267
$536$	−118.939	−	409.550i	−0.221901	−	0.764087i
$537$		0			0
$538$	19.9266	+	9.12397i	0.0370384	+	0.0169590i
$539$	253.254	+	253.254i	0.469859	+	0.469859i
$540$		0			0
$541$	510.912	+	510.912i	0.944385	+	0.944385i	0.998533	−	0.0541480i	$-0.0172443\pi$
$541$	510.912	+	510.912i	0.944385	+	0.944385i	−0.0541480	+	0.998533i	$0.517244\pi$
$542$	−91.9440	−	247.256i	−0.169638	−	0.456192i
$543$		0			0
$544$	155.555	+	732.454i	0.285947	+	1.34642i
$545$	−1133.13			−2.07913
$546$		0			0
$547$	512.889	−	512.889i	0.937639	−	0.937639i	−0.0605271	−	0.998167i	$-0.519278\pi$
$547$	512.889	−	512.889i	0.937639	−	0.937639i	0.998167	+	0.0605271i	$0.0192782\pi$
$548$	325.310	+	376.929i	0.593632	+	0.687826i
$549$		0			0
$550$	433.862	−	947.550i	0.788840	−	1.72282i
$551$	−432.168			−0.784334
$552$		0			0
$553$			113.390i			0.205046i
$554$	238.272	−	520.382i	0.430093	−	0.939318i
$555$		0			0
$556$	953.514	+	70.0883i	1.71495	+	0.126058i
$557$	−566.691	−	566.691i	−1.01740	−	1.01740i	−0.999846	−	0.0175529i	$-0.994412\pi$
$557$	−566.691	−	566.691i	−1.01740	−	1.01740i	−0.0175529	−	0.999846i	$-0.505588\pi$
$558$		0			0
$559$		−	383.317i		−	0.685720i
$560$	376.834	+	507.554i	0.672917	+	0.906346i
$561$		0			0
$562$	47.9934	+	129.064i	0.0853975	+	0.229651i
$563$	−548.653	+	548.653i	−0.974517	+	0.974517i	−0.999683	−	0.0251665i	$-0.991988\pi$
$563$	−548.653	+	548.653i	−0.974517	+	0.974517i	0.0251665	+	0.999683i	$0.491988\pi$
$564$		0			0
$565$	122.088	−	122.088i	0.216085	−	0.216085i
$566$	−531.751	−	243.477i	−0.939489	−	0.430171i
$567$		0			0
$568$	164.428	−	299.020i	0.289487	−	0.526444i
$569$			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	0.983529	−	0.180749i	$-0.0578522\pi$
$571$	458.387	+	458.387i	0.802780	+	0.802780i	−0.180749	+	0.983529i	$0.557852\pi$
$572$	368.400	+	426.856i	0.644057	+	0.746251i
$573$		0			0
$574$	108.580	+	291.993i	0.189163	+	0.508698i
$575$			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	$0.713926\pi$
$578$	−484.666	+	180.227i	−0.838522	+	0.311811i
$579$		0			0
$580$	−584.047	+	504.065i	−1.00698	+	0.869078i
$581$	128.744	−	128.744i	0.221590	−	0.221590i
$582$		0			0
$583$	−1646.00			−2.82333
$584$	−745.809	−	410.113i	−1.27707	−	0.702248i
$585$		0			0
$586$	−425.360	+	928.982i	−0.725870	+	1.58529i
$587$	−3.02450	−	3.02450i	−0.00515247	−	0.00515247i	0.704526	−	0.709678i	$-0.251160\pi$
$587$	−3.02450	−	3.02450i	−0.00515247	−	0.00515247i	−0.709678	+	0.704526i	$0.751160\pi$
$588$		0			0
$589$	−198.624	−	198.624i	−0.337222	−	0.337222i
$590$	−533.786	+	198.492i	−0.904723	+	0.336428i
$591$		0			0
$592$	−206.902	−	278.674i	−0.349496	−	0.470734i
$593$	−576.193			−0.971657			−0.485829	−	0.874054i	$-0.661482\pi$
$593$	−576.193			−0.971657			−0.485829	+	0.874054i	$0.661482\pi$
$594$		0			0
$595$	−653.726	+	653.726i	−1.09870	+	1.09870i
$596$	−60.9543	+	829.252i	−0.102272	+	1.39136i
$597$		0			0
$598$	−85.6890	−	39.2351i	−0.143293	−	0.0656105i
$599$	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	$-0.998117\pi$
$601$		−	7.11053i		−	0.0118312i	0.999983	−	0.00591558i	$-0.00188300\pi$
$602$	457.775	+	209.605i	0.760423	+	0.348181i
$603$		0			0
$604$	228.764	−	197.436i	0.378749	−	0.326882i
$605$	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	$0.856663\pi$
$608$	445.878	+	289.667i	0.733352	+	0.476425i
$609$		0			0
$610$	−1282.55	+	476.925i	−2.10254	+	0.781844i
$611$	104.477	−	104.477i	0.170994	−	0.170994i
$612$		0			0
$613$	−642.364	+	642.364i	−1.04790	+	1.04790i	−0.0491093	+	0.998793i	$0.515638\pi$
$613$	−642.364	+	642.364i	−1.04790	+	1.04790i	−0.998793	+	0.0491093i	$0.984362\pi$
$614$	12.8434	−	28.0499i	0.0209176	−	0.0456838i
$615$		0			0
$616$	−711.218	+	206.548i	−1.15458	+	0.335305i
$617$			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	0.992246	+	0.124290i	$0.0396653\pi$
$619$	691.136	+	691.136i	1.11654	+	1.11654i	0.124290	+	0.992246i	$0.460335\pi$
$620$	−500.094	−	36.7595i	−0.806603	−	0.0592896i
$621$		0			0
$622$	−300.405	+	111.708i	−0.482967	+	0.179595i
$623$			281.332i			0.451576i
$624$		0			0
$625$	475.371			0.760594
$626$	−247.812	−	666.417i	−0.395866	−	1.06456i
$627$		0			0
$628$	−459.994	−	33.8120i	−0.732474	−	0.0538407i
$629$	358.931	−	358.931i	0.570637	−	0.570637i
$630$		0			0
$631$	486.622			0.771191			0.385596	−	0.922668i	$-0.373996\pi$
$631$	486.622			0.771191			0.385596	+	0.922668i	$0.373996\pi$
$632$	149.189	+	82.0374i	0.236058	+	0.129806i
$633$		0			0
$634$	186.495	+	85.3920i	0.294156	+	0.134688i
$635$	−619.681	−	619.681i	−0.975875	−	0.975875i
$636$		0			0
$637$	118.247	+	118.247i	0.185631	+	0.185631i
$638$	−315.026	−	847.168i	−0.493770	−	1.32785i
$639$		0			0
$640$	940.431	−	128.590i	1.46942	−	0.200922i
$641$	691.017			1.07803			0.539015	−	0.842296i	$-0.318797\pi$
$641$	691.017			1.07803			0.539015	+	0.842296i	$0.318797\pi$
$642$		0			0
$643$	652.605	−	652.605i	1.01494	−	1.01494i	0.0150512	−	0.999887i	$-0.495209\pi$
$643$	652.605	−	652.605i	1.01494	−	1.01494i	0.999887	−	0.0150512i	$-0.00479113\pi$
$644$	93.7126	−	80.8792i	0.145516	−	0.125589i
$645$		0			0
$646$	−323.730	+	707.023i	−0.501130	+	1.09446i
$647$	−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
$650$	202.574	−	442.420i	0.311653	−	0.680647i
$651$		0			0
$652$	23.1424	−	314.840i	0.0354945	−	0.482883i
$653$	209.105	+	209.105i	0.320222	+	0.320222i	0.848852	−	0.528630i	$-0.177294\pi$
$653$	209.105	+	209.105i	0.320222	+	0.320222i	−0.528630	+	0.848852i	$0.677294\pi$
$654$		0			0
$655$		−	725.776i		−	1.10806i
$656$	462.734	+	68.3963i	0.705388	+	0.104263i
$657$		0			0
$658$	67.6414	+	181.902i	0.102799	+	0.276446i
$659$	−533.902	+	533.902i	−0.810170	+	0.810170i	−0.984659	−	0.174489i	$-0.944173\pi$
$659$	−533.902	+	533.902i	−0.810170	+	0.810170i	0.174489	+	0.984659i	$0.444173\pi$
$660$		0			0
$661$	283.120	−	283.120i	0.428320	−	0.428320i	−0.459736	−	0.888056i	$-0.652056\pi$
$661$	283.120	−	283.120i	0.428320	−	0.428320i	0.888056	+	0.459736i	$0.152056\pi$
$662$	638.021	+	292.136i	0.963779	+	0.441293i
$663$		0			0
$664$	−76.2439	−	262.535i	−0.114825	−	0.395384i
$665$			656.484i			0.987195i
$666$		0			0
$667$	106.825	+	106.825i	0.160157	+	0.160157i
$668$	74.5953	−	64.3799i	0.111670	−	0.0963771i
$669$		0			0
$670$	−275.563	−	741.047i	−0.411289	−	1.10604i
$671$		−	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	$0.595514\pi$
$674$	875.941	−	325.725i	1.29962	−	0.483271i
$675$		0			0
$676$	−269.667	−	312.456i	−0.398916	−	0.462213i
$677$	−289.959	+	289.959i	−0.428299	+	0.428299i	−0.888049	−	0.459749i	$-0.847939\pi$
$677$	−289.959	+	289.959i	−0.428299	+	0.428299i	0.459749	+	0.888049i	$0.347939\pi$
$678$		0			0
$679$	112.005			0.164956
$680$	387.145	+	1333.08i	0.569331	+	1.96041i
$681$		0			0
$682$	244.572	−	534.142i	0.358609	−	0.783199i
$683$	150.197	+	150.197i	0.219908	+	0.219908i	0.808460	−	0.588551i	$-0.200302\pi$
$683$	150.197	+	150.197i	0.219908	+	0.219908i	−0.588551	+	0.808460i	$0.700302\pi$
$684$		0			0
$685$	652.686	+	652.686i	0.952826	+	0.952826i
$686$	−695.274	+	258.543i	−1.01352	+	0.376884i
$687$		0			0
$688$	606.977	−	450.650i	0.882234	−	0.655015i
$689$	−768.535			−1.11544
$690$		0			0
$691$	791.212	−	791.212i	1.14502	−	1.14502i	0.157506	−	0.987518i	$-0.449655\pi$
$691$	791.212	−	791.212i	1.14502	−	1.14502i	0.987518	−	0.157506i	$-0.0503453\pi$
$692$	−27.5622	−	2.02597i	−0.0398298	−	0.00292770i
$693$		0			0
$694$	753.037	+	344.799i	1.08507	+	0.496828i
$695$	1772.46			2.55030
$696$		0			0
$697$			684.092i			0.981481i
$698$	−890.466	−	407.725i	−1.27574	−	0.584133i
$699$		0			0
$700$	417.587	+	483.847i	0.596553	+	0.691210i
$701$	−900.201	−	900.201i	−1.28417	−	1.28417i	−0.938274	−	0.345893i	$-0.887576\pi$
$701$	−900.201	−	900.201i	−1.28417	−	1.28417i	−0.345893	−	0.938274i	$-0.612424\pi$
$702$		0			0
$703$		−	360.445i		−	0.512724i
$704$	−242.807	+	1085.19i	−0.344896	+	1.54147i
$705$		0			0
$706$	15.0308	−	5.58929i	0.0212900	−	0.00791685i
$707$	−17.3138	+	17.3138i	−0.0244891	+	0.0244891i
$708$		0			0
$709$	128.490	−	128.490i	0.181227	−	0.181227i	−0.610663	−	0.791891i	$-0.709097\pi$
$709$	128.490	−	128.490i	0.181227	−	0.181227i	0.791891	+	0.610663i	$0.209097\pi$
$710$	263.371	−	575.200i	0.370945	−	0.810140i
$711$		0			0
$712$	370.151	+	203.542i	0.519875	+	0.285874i
$713$			98.1928i			0.137718i
$714$		0			0
$715$	739.140	+	739.140i	1.03376	+	1.03376i
$716$	95.1730	−	1294.78i	0.132923	−	1.80835i
$717$		0			0
$718$	1106.76	−	411.558i	1.54145	−	0.573200i
$719$			1246.14i			1.73315i	0.499045	+	0.866576i	$0.333684\pi$
$719$			1246.14i			1.73315i	−0.499045	+	0.866576i	$0.666316\pi$
$720$		0			0
$721$	−560.033			−0.776745
$722$	−59.1904	−	159.175i	−0.0819812	−	0.220464i
$723$		0			0
$724$	48.3558	−	657.855i	0.0667897	−	0.908639i
$725$	−551.546	+	551.546i	−0.760753	+	0.760753i
$726$		0			0
$727$	−1130.07			−1.55443			−0.777216	−	0.629234i	$-0.783369\pi$
$727$	−1130.07			−1.55443			−0.777216	+	0.629234i	$0.783369\pi$
$728$	−332.075	+	96.4392i	−0.456147	+	0.132471i
$729$		0			0
$730$	−1434.65	−	656.893i	−1.96527	−	0.899854i
$731$	781.782	+	781.782i	1.06947	+	1.06947i
$732$		0			0
$733$	−708.087	−	708.087i	−0.966012	−	0.966012i	0.0334292	−	0.999441i	$-0.489357\pi$
$733$	−708.087	−	708.087i	−0.966012	−	0.966012i	−0.999441	+	0.0334292i	$0.989357\pi$
$734$	−276.810	−	744.399i	−0.377126	−	1.01417i
$735$		0			0
$736$	−38.6128	−	181.814i	−0.0524631	−	0.247030i
$737$	926.264			1.25680
$738$		0			0
$739$	−32.7516	+	32.7516i	−0.0443188	+	0.0443188i	−0.728919	−	0.684600i	$-0.759977\pi$
$739$	−32.7516	+	32.7516i	−0.0443188	+	0.0443188i	0.684600	+	0.728919i	$0.259977\pi$
$740$	−420.410	−	487.118i	−0.568122	−	0.658268i
$741$		0			0
$742$	420.249	−	917.819i	0.566373	−	1.23695i
$743$	−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
$746$	194.301	−	424.352i	0.260457	−	0.568836i
$747$		0			0
$748$	−1621.94	−	119.221i	−2.16837	−	0.159386i
$749$	−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	$0.689964\pi$
$752$	288.268	+	42.6086i	0.383335	+	0.0566604i
$753$		0			0
$754$	−147.089	−	395.551i	−0.195078	−	0.524604i
$755$	396.127	−	396.127i	0.524671	−	0.524671i
$756$		0			0
$757$	−311.304	+	311.304i	−0.411233	+	0.411233i	−0.882168	−	0.470935i	$-0.843917\pi$
$757$	−311.304	+	311.304i	−0.411233	+	0.411233i	0.470935	+	0.882168i	$0.343917\pi$
$758$	531.483	+	243.354i	0.701165	+	0.321048i
$759$		0			0
$760$	863.743	+	474.964i	1.13650	+	0.624952i
$761$		−	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
$764$	−246.272	−	285.348i	−0.322345	−	0.373493i
$765$		0			0
$766$	−417.142	−	1121.78i	−0.544572	−	1.46446i
$767$		−	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	$0.716537\pi$
$770$	−1286.89	+	478.539i	−1.67128	+	0.621479i
$771$		0			0
$772$	255.173	−	220.229i	0.330535	−	0.285270i
$773$	96.7342	−	96.7342i	0.125141	−	0.125141i	−0.641762	−	0.766904i	$-0.721796\pi$
$773$	96.7342	−	96.7342i	0.125141	−	0.125141i	0.766904	+	0.641762i	$0.221796\pi$
$774$		0			0
$775$	−506.979			−0.654166
$776$	81.0355	−	147.367i	0.104427	−	0.189905i
$777$		0			0
$778$	219.836	−	480.120i	0.282566	−	0.617121i
$779$	343.489	+	343.489i	0.440936	+	0.440936i
$780$		0			0
$781$	524.082	+	524.082i	0.671039	+	0.671039i
$782$	254.785	−	94.7435i	0.325812	−	0.121155i
$783$		0			0
$784$	−48.2242	+	326.260i	−0.0615105	+	0.416148i
$785$	−855.070			−1.08926
$786$		0			0
$787$	−381.038	+	381.038i	−0.484166	+	0.484166i	−0.906459	−	0.422293i	$-0.861225\pi$
$787$	−381.038	+	381.038i	−0.484166	+	0.484166i	0.422293	+	0.906459i	$0.361225\pi$
$788$	23.6198	−	321.335i	0.0299744	−	0.407785i
$789$		0			0
$790$	286.981	+	131.402i	0.363268	+	0.166332i
$791$	−124.054			−0.156831
$792$		0			0
$793$		−	748.507i		−	0.943893i
$794$	147.544	+	67.5569i	0.185823	+	0.0850842i
$795$		0			0
$796$	−594.063	+	512.710i	−0.746311	+	0.644108i
$797$	371.148	+	371.148i	0.465681	+	0.465681i	0.900512	−	0.434831i	$-0.143192\pi$
$797$	371.148	+	371.148i	0.465681	+	0.465681i	−0.434831	+	0.900512i	$0.643192\pi$
$798$		0			0
$799$			426.167i			0.533375i
$800$	938.724	−	199.362i	1.17341	−	0.249202i
$801$		0			0
$802$	−873.712	+	324.896i	−1.08942	+	0.405107i
$803$	1307.15	−	1307.15i	1.62783	−	1.62783i
$804$		0			0
$805$	162.272	−	162.272i	0.201580	−	0.201580i
$806$	114.193	−	249.396i	0.141679	−	0.309424i
$807$		0			0
$808$	10.2535	+	35.3063i	0.0126899	+	0.0436960i
$809$			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	0.690081	−	0.723732i	$-0.257575\pi$
$811$	−27.2916	−	27.2916i	−0.0336517	−	0.0336517i	−0.723732	+	0.690081i	$0.757575\pi$
$812$	552.816	+	40.6348i	0.680807	+	0.0500429i
$813$		0			0
$814$	706.571	−	262.744i	0.868024	−	0.322781i
$815$		−	585.247i		−	0.718095i
$816$		0			0
$817$	785.081			0.960931
$818$	416.820	+	1120.91i	0.509559	+	1.37031i
$819$		0			0
$820$	864.837	+	63.5700i	1.05468	+	0.0775244i
$821$	879.903	−	879.903i	1.07175	−	1.07175i	0.0745264	−	0.997219i	$-0.476255\pi$
$821$	879.903	−	879.903i	1.07175	−	1.07175i	0.997219	−	0.0745264i	$-0.0237445\pi$
$822$		0			0
$823$	68.6842			0.0834559			0.0417280	−	0.999129i	$-0.486714\pi$
$823$	68.6842			0.0834559			0.0417280	+	0.999129i	$0.486714\pi$
$824$	−405.181	+	736.841i	−0.491725	+	0.894224i
$825$		0			0
$826$	372.035	+	170.346i	0.450405	+	0.206230i
$827$	−942.097	−	942.097i	−1.13917	−	1.13917i	−0.988599	−	0.150575i	$-0.951887\pi$
$827$	−942.097	−	942.097i	−1.13917	−	1.13917i	−0.150575	−	0.988599i	$-0.548113\pi$
$828$		0			0
$829$	−568.532	−	568.532i	−0.685805	−	0.685805i	0.275497	−	0.961302i	$-0.411158\pi$
$829$	−568.532	−	568.532i	−0.685805	−	0.685805i	−0.961302	+	0.275497i	$0.911158\pi$
$830$	−176.645	−	475.035i	−0.212826	−	0.572331i
$831$		0			0
$832$	−113.369	+	506.687i	−0.136261	+	0.608999i
$833$	−482.333			−0.579031
$834$		0			0
$835$	129.169	−	129.169i	0.154693	−	0.154693i
$836$	−874.253	+	754.529i	−1.04576	+	0.902547i
$837$		0			0
$838$	−5.47897	+	11.9660i	−0.00653815	+	0.0142792i
$839$	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
$842$	−40.4774	+	88.4022i	−0.0480729	+	0.104991i
$843$		0			0
$844$	73.5412	−	1000.49i	0.0871341	−	1.18541i
$845$	−541.046	−	541.046i	−0.640291	−	0.640291i
$846$		0			0
$847$		−	963.851i		−	1.13796i
$848$	−903.535	−	1216.96i	−1.06549	−	1.43510i
$849$		0			0
$850$	489.170	+	1315.48i	0.575494	+	1.54762i
$851$	−89.0960	+	89.0960i	−0.104696	+	0.104696i
$852$		0			0
$853$	74.4816	−	74.4816i	0.0873172	−	0.0873172i	−0.662099	−	0.749416i	$-0.730334\pi$
$853$	74.4816	−	74.4816i	0.0873172	−	0.0873172i	0.749416	+	0.662099i	$0.230334\pi$
$854$	893.901	+	409.297i	1.04672	+	0.479271i
$855$		0			0
$856$	−1082.31	+	314.318i	−1.26438	+	0.367194i
$857$		−	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	0.321085	−	0.947050i	$-0.395952\pi$
$859$	−537.704	−	537.704i	−0.625965	−	0.625965i	−0.947050	+	0.321085i	$0.895952\pi$
$860$	1060.98	−	915.689i	1.23370	−	1.06475i
$861$		0			0
$862$	−295.438	−	794.493i	−0.342735	−	0.921686i
$863$			1390.97i			1.61178i	0.592064	+	0.805891i	$0.298313\pi$
$863$			1390.97i			1.61178i	−0.592064	+	0.805891i	$0.701687\pi$
$864$		0			0
$865$	−51.2347			−0.0592309
$866$	−1562.24	+	580.930i	−1.80397	+	0.670820i
$867$		0			0
$868$	235.397	+	272.749i	0.271195	+	0.314227i
$869$	−261.477	+	261.477i	−0.300895	+	0.300895i
$870$		0			0
$871$	432.482			0.496535
$872$	1173.94	−	340.928i	1.34626	−	0.390973i
$873$		0			0
$874$	80.3583	−	175.502i	0.0919431	−	0.200803i
$875$	139.391	+	139.391i	0.159303	+	0.159303i
$876$		0			0
$877$	940.115	+	940.115i	1.07197	+	1.07197i	0.997201	+	0.0747652i	$0.0238207\pi$
$877$	940.115	+	940.115i	1.07197	+	1.07197i	0.0747652	+	0.997201i	$0.476179\pi$
$878$	−60.5854	+	22.5291i	−0.0690039	+	0.0256596i
$879$		0			0
$880$	−301.441	+	2039.39i	−0.342546	+	2.31749i
$881$	140.985			0.160029			0.0800143	−	0.996794i	$-0.474503\pi$
$881$	140.985			0.160029			0.0800143	+	0.996794i	$0.474503\pi$
$882$		0			0
$883$	−482.231	+	482.231i	−0.546127	+	0.546127i	−0.925318	−	0.379191i	$-0.876202\pi$
$883$	−482.231	+	482.231i	−0.546127	+	0.546127i	0.379191	+	0.925318i	$0.376202\pi$
$884$	−757.299	−	55.6655i	−0.856673	−	0.0629700i
$885$		0			0
$886$	307.384	+	140.744i	0.346934	+	0.158854i
$887$	−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
$890$	712.028	+	326.022i	0.800031	+	0.366316i
$891$		0			0
$892$	−987.695	−	1144.42i	−1.10728	−	1.28298i
$893$	213.982	+	213.982i	0.239622	+	0.239622i
$894$		0			0
$895$		−	2406.83i		−	2.68919i
$896$	−543.117	−	412.456i	−0.606157	−	0.460330i
$897$		0			0
$898$	−341.849	+	127.119i	−0.380678	+	0.141558i
$899$	−310.911	+	310.911i	−0.345841	+	0.345841i
$900$		0			0
$901$	1567.44	−	1567.44i	1.73967	−	1.73967i
$902$	−422.950	+	923.717i	−0.468902	+	1.02408i
$903$		0			0
$904$	−89.7522	+	163.218i	−0.0992834	+	0.180551i
$905$		−	1222.87i		−	1.35124i
$906$		0			0
$907$	−303.117	−	303.117i	−0.334197	−	0.334197i	0.519981	−	0.854178i	$-0.325939\pi$
$907$	−303.117	−	303.117i	−0.334197	−	0.334197i	−0.854178	+	0.519981i	$0.825939\pi$
$908$	−43.0901	+	586.218i	−0.0474561	+	0.645615i
$909$		0			0
$910$	−600.861	+	223.435i	−0.660287	+	0.245532i
$911$			296.228i			0.325168i	0.986695	+	0.162584i	$0.0519829\pi$
$911$			296.228i			0.325168i	−0.986695	+	0.162584i	$0.948017\pi$
$912$		0			0
$913$	593.765			0.650346
$914$	−190.262	−	511.653i	−0.208164	−	0.559795i
$915$		0			0
$916$	−41.9066	+	570.117i	−0.0457496	+	0.622399i
$917$	−368.731	+	368.731i	−0.402106	+	0.402106i
$918$		0			0
$919$	−228.052			−0.248153			−0.124076	−	0.992273i	$-0.539597\pi$
$919$	−228.052			−0.248153			−0.124076	+	0.992273i	$0.539597\pi$
$920$	−96.0996	−	330.906i	−0.104456	−	0.359680i
$921$		0			0
$922$	484.305	+	221.752i	0.525276	+	0.240512i
$923$	244.699	+	244.699i	0.265113	+	0.265113i
$924$		0			0
$925$	−460.011	−	460.011i	−0.497309	−	0.497309i
$926$	80.8772	+	217.495i	0.0873404	+	0.234876i
$927$		0			0
$928$	453.423	−	697.946i	0.488603	−	0.752097i
$929$	574.026			0.617897			0.308948	−	0.951079i	$-0.400023\pi$
$929$	574.026			0.617897			0.308948	+	0.951079i	$0.400023\pi$
$930$		0			0
$931$	−242.184	+	242.184i	−0.260133	+	0.260133i
$932$	750.744	+	869.867i	0.805519	+	0.933334i
$933$		0			0
$934$	−320.181	+	699.272i	−0.342806	+	0.748686i
$935$	−3014.98			−3.22457
$936$		0			0
$937$			1098.22i			1.17206i	0.810291	+	0.586028i	$0.199309\pi$
$937$			1098.22i			1.17206i	−0.810291	+	0.586028i	$0.800691\pi$
$938$	−236.489	+	516.489i	−0.252120	+	0.550628i
$939$		0			0
$940$	538.764	+	39.6020i	0.573154	+	0.0421298i
$941$	857.669	+	857.669i	0.911444	+	0.911444i	0.996386	−	0.0849418i	$-0.0270704\pi$
$941$	857.669	+	857.669i	0.911444	+	0.911444i	−0.0849418	+	0.996386i	$0.527070\pi$
$942$		0			0
$943$		−	169.810i		−	0.180074i
$944$	493.292	−	366.244i	0.522555	−	0.387971i
$945$		0			0
$946$	572.278	+	1538.97i	0.604945	+	1.62682i
$947$	−1041.67	+	1041.67i	−1.09997	+	1.09997i	−0.105556	+	0.994413i	$0.533662\pi$
$947$	−1041.67	+	1041.67i	−1.09997	+	1.09997i	−0.994413	+	0.105556i	$0.966338\pi$
$948$		0			0
$949$	610.322	−	610.322i	0.643121	−	0.643121i
$950$	906.131	+	414.897i	0.953822	+	0.436734i
$951$		0			0
$952$	480.583	−	873.962i	0.504814	−	0.918027i
$953$			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
$956$	−394.481	−	457.075i	−0.412637	−	0.478112i
$957$		0			0
$958$	540.799	+	1454.32i	0.564509	+	1.51808i
$959$		−	663.195i		−	0.691548i
$960$		0			0
$961$	675.212			0.702614
$962$	329.905	−	122.678i	0.342937	−	0.127523i
$963$		0			0
$964$	114.409	−	98.7415i	0.118682	−	0.102429i
$965$	441.856	−	441.856i	0.457882	−	0.457882i
$966$		0			0
$967$	−695.071			−0.718791			−0.359396	−	0.933185i	$-0.617017\pi$
$967$	−695.071			−0.718791			−0.359396	+	0.933185i	$0.617017\pi$
$968$	−1268.15	−	697.342i	−1.31007	−	0.720395i
$969$		0			0
$970$	129.798	−	283.477i	0.133812	−	0.292244i
$971$	1208.40	+	1208.40i	1.24449	+	1.24449i	0.958120	+	0.286366i	$0.0924472\pi$
$971$	1208.40	+	1208.40i	1.24449	+	1.24449i	0.286366	+	0.958120i	$0.407553\pi$
$972$		0			0
$973$	−900.500	−	900.500i	−0.925488	−	0.925488i
$974$	−327.848	+	121.913i	−0.336600	+	0.125167i
$975$		0			0
$976$	1185.25	−	879.989i	1.21440	−	0.901628i
$977$	−141.036			−0.144356			−0.0721780	−	0.997392i	$-0.522995\pi$
$977$	−141.036			−0.144356			−0.0721780	+	0.997392i	$0.522995\pi$
$978$		0			0
$979$	−648.750	+	648.750i	−0.662666	+	0.662666i
$980$	−44.8213	+	609.771i	−0.0457360	+	0.622215i
$981$		0			0
$982$	−896.426	−	410.453i	−0.912857	−	0.417977i
$983$	−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
$986$	1106.72	+	506.744i	1.12244	+	0.513939i
$987$		0			0
$988$	−408.198	+	352.297i	−0.413155	+	0.356576i
$989$	−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	$0.718621\pi$
$992$	529.167	−	112.382i	0.533434	−	0.113288i
$993$		0			0
$994$	−426.036	+	158.425i	−0.428608	+	0.159381i
$995$	−1028.67	+	1028.67i	−1.03384	+	1.03384i
$996$		0			0
$997$	1131.91	−	1131.91i	1.13532	−	1.13532i	0.146039	−	0.989279i	$-0.453348\pi$
$997$	1131.91	−	1131.91i	1.13532	−	1.13532i	0.989279	−	0.146039i	$-0.0466524\pi$
$998$	715.389	−	1562.40i	0.716823	−	1.56553i
$999$		0			0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.87459 + 0.697079i) q^{2} +(3.02816 - 2.61347i) q^{4} +(5.24354 - 5.24354i) q^{5} -5.32796 q^{7} +(-3.85476 + 7.01005i) q^{8} +O(q^{10})\)	\(q+(-1.87459 + 0.697079i) q^{2} +(3.02816 - 2.61347i) q^{4} +(5.24354 - 5.24354i) q^{5} -5.32796 q^{7} +(-3.85476 + 7.01005i) q^{8} +(-6.17431 + 13.4846i) q^{10} +(-12.2863 - 12.2863i) q^{11} +(-5.73657 - 5.73657i) q^{13} +(9.98774 - 3.71401i) q^{14} +(2.33953 - 15.8280i) q^{16} +23.3997 q^{17} +(11.7492 - 11.7492i) q^{19} +(2.17444 - 29.5821i) q^{20} +(31.5962 + 14.4672i) q^{22} -5.80841 q^{23} -29.9894i q^{25} +(14.7526 + 6.75487i) q^{26} +(-16.1339 + 13.9245i) q^{28} +(-18.3914 - 18.3914i) q^{29} -16.9053i q^{31} +(6.64774 + 31.3019i) q^{32} +(-43.8648 + 16.3114i) q^{34} +(-27.9374 + 27.9374i) q^{35} +(15.3391 - 15.3391i) q^{37} +(-13.8348 + 30.2151i) q^{38} +(16.5449 + 56.9701i) q^{40} +29.2351i q^{41} +(33.4099 + 33.4099i) q^{43} +(-69.3146 - 5.09498i) q^{44} +(10.8884 - 4.04892i) q^{46} +18.2125i q^{47} -20.6128 q^{49} +(20.9050 + 56.2178i) q^{50} +(-32.3637 - 2.37890i) q^{52} +(66.9856 - 66.9856i) q^{53} -128.847 q^{55} +(20.5380 - 37.3493i) q^{56} +(47.2965 + 21.6560i) q^{58} +(27.1523 + 27.1523i) q^{59} +(65.2399 + 65.2399i) q^{61} +(11.7843 + 31.6904i) q^{62} +(-34.2817 - 54.0441i) q^{64} -60.1599 q^{65} +(-37.6951 + 37.6951i) q^{67} +(70.8580 - 61.1544i) q^{68} +(32.8965 - 71.8456i) q^{70} -42.6559 q^{71} +106.391i q^{73} +(-18.0620 + 39.4471i) q^{74} +(4.87228 - 66.2847i) q^{76} +(65.4607 + 65.4607i) q^{77} -21.2821i q^{79} +(-70.7275 - 95.2623i) q^{80} +(-20.3792 - 54.8038i) q^{82} +(-24.1638 + 24.1638i) q^{83} +(122.697 - 122.697i) q^{85} +(-85.9192 - 39.3405i) q^{86} +(133.488 - 38.7667i) q^{88} -52.8029i q^{89} +(30.5643 + 30.5643i) q^{91} +(-17.5888 + 15.1801i) q^{92} +(-12.6955 - 34.1409i) q^{94} -123.215i q^{95} -21.0222 q^{97} +(38.6405 - 14.3688i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} + 12 q^{8}+O(q^{10}) \) 16 * q + 12 * q^4 + 12 * q^8	\( 16 q + 12 q^{4} + 12 q^{8} - 56 q^{10} - 32 q^{11} + 44 q^{14} + 32 q^{16} - 32 q^{19} - 80 q^{20} + 32 q^{22} + 128 q^{23} + 100 q^{26} - 120 q^{28} - 32 q^{29} - 160 q^{32} + 96 q^{34} - 96 q^{35} - 96 q^{37} - 168 q^{38} + 48 q^{40} + 160 q^{43} - 88 q^{44} + 136 q^{46} + 112 q^{49} + 236 q^{50} - 48 q^{52} + 160 q^{53} - 256 q^{55} + 224 q^{56} + 144 q^{58} + 128 q^{59} - 32 q^{61} + 276 q^{62} - 408 q^{64} + 32 q^{65} + 320 q^{67} + 448 q^{68} - 384 q^{70} - 512 q^{71} - 348 q^{74} + 72 q^{76} - 224 q^{77} - 552 q^{80} - 40 q^{82} + 160 q^{83} + 160 q^{85} - 528 q^{86} + 480 q^{88} - 480 q^{91} - 496 q^{92} + 312 q^{94} + 440 q^{98}+O(q^{100}) \) 16 * q + 12 * q^4 + 12 * q^8 - 56 * q^10 - 32 * q^11 + 44 * q^14 + 32 * q^16 - 32 * q^19 - 80 * q^20 + 32 * q^22 + 128 * q^23 + 100 * q^26 - 120 * q^28 - 32 * q^29 - 160 * q^32 + 96 * q^34 - 96 * q^35 - 96 * q^37 - 168 * q^38 + 48 * q^40 + 160 * q^43 - 88 * q^44 + 136 * q^46 + 112 * q^49 + 236 * q^50 - 48 * q^52 + 160 * q^53 - 256 * q^55 + 224 * q^56 + 144 * q^58 + 128 * q^59 - 32 * q^61 + 276 * q^62 - 408 * q^64 + 32 * q^65 + 320 * q^67 + 448 * q^68 - 384 * q^70 - 512 * q^71 - 348 * q^74 + 72 * q^76 - 224 * q^77 - 552 * q^80 - 40 * q^82 + 160 * q^83 + 160 * q^85 - 528 * q^86 + 480 * q^88 - 480 * q^91 - 496 * q^92 + 312 * q^94 + 440 * q^98

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