LMFDB - Embedded newform 144.3.m.c.19.5

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			19.5
Root			$0.125358 - 1.99607i$ of defining polynomial
Character	$\chi$	$=$	144.19
Dual form			144.3.m.c.91.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.125358 + 1.99607i) q^{2} +(-3.96857 + 0.500444i) q^{4} +(-3.32679 + 3.32679i) q^{5} -4.04088 q^{7} +(-1.49641 - 7.85880i) q^{8} +O(q^{10})$	\(q+(0.125358 + 1.99607i) q^{2} +(-3.96857 + 0.500444i) q^{4} +(-3.32679 + 3.32679i) q^{5} -4.04088 q^{7} +(-1.49641 - 7.85880i) q^{8} +(-7.05755 - 6.22347i) q^{10} +(-6.82458 - 6.82458i) q^{11} +(4.29091 + 4.29091i) q^{13} +(-0.506555 - 8.06588i) q^{14} +(15.4991 - 3.97210i) q^{16} -30.1192 q^{17} +(-19.7548 + 19.7548i) q^{19} +(11.5377 - 14.8675i) q^{20} +(12.7668 - 14.4778i) q^{22} +28.2345 q^{23} +2.86488i q^{25} +(-8.02705 + 9.10285i) q^{26} +(16.0365 - 2.02224i) q^{28} +(21.3607 + 21.3607i) q^{29} -38.0396i q^{31} +(9.87151 + 30.4393i) q^{32} +(-3.77567 - 60.1200i) q^{34} +(13.4432 - 13.4432i) q^{35} +(-42.8916 + 42.8916i) q^{37} +(-41.9084 - 36.9556i) q^{38} +(31.1229 + 21.1664i) q^{40} +48.2343i q^{41} +(32.6765 + 32.6765i) q^{43} +(30.4991 + 23.6685i) q^{44} +(3.53941 + 56.3580i) q^{46} -15.8305i q^{47} -32.6713 q^{49} +(-5.71849 + 0.359134i) q^{50} +(-19.1761 - 14.8814i) q^{52} +(0.476870 - 0.476870i) q^{53} +45.4079 q^{55} +(6.04682 + 31.7565i) q^{56} +(-39.9596 + 45.3151i) q^{58} +(-9.97719 - 9.97719i) q^{59} +(37.9455 + 37.9455i) q^{61} +(75.9296 - 4.76855i) q^{62} +(-59.5215 + 23.5200i) q^{64} -28.5500 q^{65} +(20.0705 - 20.0705i) q^{67} +(119.530 - 15.0730i) q^{68} +(28.5187 + 25.1483i) q^{70} -40.0818 q^{71} -30.8095i q^{73} +(-90.9912 - 80.2377i) q^{74} +(68.5123 - 88.2846i) q^{76} +(27.5773 + 27.5773i) q^{77} -130.125i q^{79} +(-38.3480 + 64.7767i) q^{80} +(-96.2789 + 6.04653i) q^{82} +(2.26155 - 2.26155i) q^{83} +(100.200 - 100.200i) q^{85} +(-61.1282 + 69.3207i) q^{86} +(-43.4206 + 63.8454i) q^{88} -72.2232i q^{89} +(-17.3391 - 17.3391i) q^{91} +(-112.051 + 14.1298i) q^{92} +(31.5986 - 1.98447i) q^{94} -131.441i q^{95} -112.343 q^{97} +(-4.09559 - 65.2140i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.125358	+	1.99607i	0.0626788	+	0.998034i
$2$	0.125358	+	1.99607i	0.0626788	+	0.998034i
$3$		0			0
$3$		0			0
$4$	−3.96857	+	0.500444i	−0.992143	+	0.125111i
$5$	−3.32679	+	3.32679i	−0.665359	+	0.665359i	−0.956638	−	0.291279i	$-0.905919\pi$
$5$	−3.32679	+	3.32679i	−0.665359	+	0.665359i	0.291279	+	0.956638i	$0.405919\pi$
$6$		0			0
$7$	−4.04088			−0.577269			−0.288635	−	0.957439i	$-0.593201\pi$
$7$	−4.04088			−0.577269			−0.288635	+	0.957439i	$0.593201\pi$
$8$	−1.49641	−	7.85880i	−0.187051	−	0.982350i
$9$		0			0
$10$	−7.05755	−	6.22347i	−0.705755	−	0.622347i
$11$	−6.82458	−	6.82458i	−0.620416	−	0.620416i	0.325222	−	0.945638i	$-0.394561\pi$
$11$	−6.82458	−	6.82458i	−0.620416	−	0.620416i	−0.945638	+	0.325222i	$0.894561\pi$
$12$		0			0
$13$	4.29091	+	4.29091i	0.330070	+	0.330070i	0.852613	−	0.522543i	$-0.175017\pi$
$13$	4.29091	+	4.29091i	0.330070	+	0.330070i	−0.522543	+	0.852613i	$0.675017\pi$
$14$	−0.506555	−	8.06588i	−0.0361825	−	0.576134i
$15$		0			0
$16$	15.4991	−	3.97210i	0.968694	−	0.248256i
$17$	−30.1192			−1.77172			−0.885859	−	0.463954i	$-0.846430\pi$
$17$	−30.1192			−1.77172			−0.885859	+	0.463954i	$0.846430\pi$
$18$		0			0
$19$	−19.7548	+	19.7548i	−1.03973	+	1.03973i	−0.0405505	+	0.999177i	$0.512911\pi$
$19$	−19.7548	+	19.7548i	−1.03973	+	1.03973i	−0.999177	+	0.0405505i	$0.987089\pi$
$20$	11.5377	−	14.8675i	0.576887	−	0.743375i
$21$		0			0
$22$	12.7668	−	14.4778i	0.580309	−	0.658083i
$23$	28.2345			1.22759			0.613794	−	0.789466i	$-0.289642\pi$
$23$	28.2345			1.22759			0.613794	+	0.789466i	$0.289642\pi$
$24$		0			0
$25$			2.86488i			0.114595i
$26$	−8.02705	+	9.10285i	−0.308733	+	0.350109i
$27$		0			0
$28$	16.0365	−	2.02224i	0.572733	−	0.0722227i
$29$	21.3607	+	21.3607i	0.736575	+	0.736575i	0.971914	−	0.235338i	$-0.0756198\pi$
$29$	21.3607	+	21.3607i	0.736575	+	0.736575i	−0.235338	+	0.971914i	$0.575620\pi$
$30$		0			0
$31$		−	38.0396i		−	1.22708i	−0.789662	−	0.613541i	$-0.789744\pi$
$31$		−	38.0396i		−	1.22708i	0.789662	−	0.613541i	$-0.210256\pi$
$32$	9.87151	+	30.4393i	0.308485	+	0.951229i
$33$		0			0
$34$	−3.77567	−	60.1200i	−0.111049	−	1.76823i
$35$	13.4432	−	13.4432i	0.384091	−	0.384091i
$36$		0			0
$37$	−42.8916	+	42.8916i	−1.15923	+	1.15923i	−0.174590	+	0.984641i	$0.555860\pi$
$37$	−42.8916	+	42.8916i	−1.15923	+	1.15923i	−0.984641	+	0.174590i	$0.944140\pi$
$38$	−41.9084	−	36.9556i	−1.10285	−	0.972515i
$39$		0			0
$40$	31.1229	+	21.1664i	0.778072	+	0.529159i
$41$			48.2343i			1.17645i	0.808699	+	0.588223i	$0.200172\pi$
$41$			48.2343i			1.17645i	−0.808699	+	0.588223i	$0.799828\pi$
$42$		0			0
$43$	32.6765	+	32.6765i	0.759918	+	0.759918i	0.976307	−	0.216389i	$-0.0694281\pi$
$43$	32.6765	+	32.6765i	0.759918	+	0.759918i	−0.216389	+	0.976307i	$0.569428\pi$
$44$	30.4991	+	23.6685i	0.693162	+	0.537921i
$45$		0			0
$46$	3.53941	+	56.3580i	0.0769437	+	1.22517i
$47$		−	15.8305i		−	0.336818i	−0.985717	−	0.168409i	$-0.946137\pi$
$47$		−	15.8305i		−	0.336818i	0.985717	−	0.168409i	$-0.0538630\pi$
$48$		0			0
$49$	−32.6713			−0.666760
$50$	−5.71849	+	0.359134i	−0.114370	+	0.00718268i
$51$		0			0
$52$	−19.1761	−	14.8814i	−0.368772	−	0.286181i
$53$	0.476870	−	0.476870i	0.00899755	−	0.00899755i	−0.702594	−	0.711591i	$-0.747975\pi$
$53$	0.476870	−	0.476870i	0.00899755	−	0.00899755i	0.711591	+	0.702594i	$0.247975\pi$
$54$		0			0
$55$	45.4079			0.825599
$56$	6.04682	+	31.7565i	0.107979	+	0.567080i
$57$		0			0
$58$	−39.9596	+	45.3151i	−0.688959	+	0.781295i
$59$	−9.97719	−	9.97719i	−0.169105	−	0.169105i	0.617481	−	0.786586i	$-0.288153\pi$
$59$	−9.97719	−	9.97719i	−0.169105	−	0.169105i	−0.786586	+	0.617481i	$0.788153\pi$
$60$		0			0
$61$	37.9455	+	37.9455i	0.622057	+	0.622057i	0.946057	−	0.324000i	$-0.105028\pi$
$61$	37.9455	+	37.9455i	0.622057	+	0.622057i	−0.324000	+	0.946057i	$0.605028\pi$
$62$	75.9296	−	4.76855i	1.22467	−	0.0769121i
$63$		0			0
$64$	−59.5215	+	23.5200i	−0.930024	+	0.367500i
$65$	−28.5500			−0.439230
$66$		0			0
$67$	20.0705	−	20.0705i	0.299559	−	0.299559i	−0.541282	−	0.840841i	$-0.682061\pi$
$67$	20.0705	−	20.0705i	0.299559	−	0.299559i	0.840841	+	0.541282i	$0.182061\pi$
$68$	119.530	−	15.0730i	1.75780	−	0.221662i
$69$		0			0
$70$	28.5187	+	25.1483i	0.407410	+	0.359261i
$71$	−40.0818			−0.564532			−0.282266	−	0.959336i	$-0.591086\pi$
$71$	−40.0818			−0.564532			−0.282266	+	0.959336i	$0.591086\pi$
$72$		0			0
$73$		−	30.8095i		−	0.422049i	−0.977481	−	0.211024i	$-0.932320\pi$
$73$		−	30.8095i		−	0.422049i	0.977481	−	0.211024i	$-0.0676799\pi$
$74$	−90.9912	−	80.2377i	−1.22961	−	1.08429i
$75$		0			0
$76$	68.5123	−	88.2846i	0.901477	−	1.16164i
$77$	27.5773	+	27.5773i	0.358147	+	0.358147i
$78$		0			0
$79$		−	130.125i		−	1.64716i	−0.567203	−	0.823578i	$-0.691975\pi$
$79$		−	130.125i		−	1.64716i	0.567203	−	0.823578i	$-0.308025\pi$
$80$	−38.3480	+	64.7767i	−0.479350	+	0.809709i
$81$		0			0
$82$	−96.2789	+	6.04653i	−1.17413	+	0.0737382i
$83$	2.26155	−	2.26155i	0.0272476	−	0.0272476i	−0.693352	−	0.720599i	$-0.743867\pi$
$83$	2.26155	−	2.26155i	0.0272476	−	0.0272476i	0.720599	+	0.693352i	$0.243867\pi$
$84$		0			0
$85$	100.200	−	100.200i	1.17883	−	1.17883i
$86$	−61.1282	+	69.3207i	−0.710793	+	0.806054i
$87$		0			0
$88$	−43.4206	+	63.8454i	−0.493416	+	0.725516i
$89$		−	72.2232i		−	0.811496i	−0.913985	−	0.405748i	$-0.867011\pi$
$89$		−	72.2232i		−	0.811496i	0.913985	−	0.405748i	$-0.132989\pi$
$90$		0			0
$91$	−17.3391	−	17.3391i	−0.190539	−	0.190539i
$92$	−112.051	+	14.1298i	−1.21794	+	0.153585i
$93$		0			0
$94$	31.5986	−	1.98447i	0.336156	−	0.0211113i
$95$		−	131.441i		−	1.38358i
$96$		0			0
$97$	−112.343			−1.15817			−0.579085	−	0.815267i	$-0.696590\pi$
$97$	−112.343			−1.15817			−0.579085	+	0.815267i	$0.696590\pi$
$98$	−4.09559	−	65.2140i	−0.0417917	−	0.665449i
$99$		0			0
$100$	−1.43371	−	11.3695i	−0.0143371	−	0.113695i
$101$	1.61933	−	1.61933i	0.0160330	−	0.0160330i	−0.699045	−	0.715078i	$-0.746391\pi$
$101$	1.61933	−	1.61933i	0.0160330	−	0.0160330i	0.715078	+	0.699045i	$0.246391\pi$
$102$		0			0
$103$	27.9974			0.271819			0.135910	−	0.990721i	$-0.456604\pi$
$103$	27.9974			0.271819			0.135910	+	0.990721i	$0.456604\pi$
$104$	27.3005	−	40.1424i	0.262504	−	0.385984i
$105$		0			0
$106$	1.01164	+	0.892086i	0.00954381	+	0.00841590i
$107$	40.3835	+	40.3835i	0.377416	+	0.377416i	0.870169	−	0.492753i	$-0.164010\pi$
$107$	40.3835	+	40.3835i	0.377416	+	0.377416i	−0.492753	+	0.870169i	$0.664010\pi$
$108$		0			0
$109$	36.8336	+	36.8336i	0.337923	+	0.337923i	0.855585	−	0.517662i	$-0.173198\pi$
$109$	36.8336	+	36.8336i	0.337923	+	0.337923i	−0.517662	+	0.855585i	$0.673198\pi$
$110$	5.69223	+	90.6373i	0.0517475	+	0.823976i
$111$		0			0
$112$	−62.6301	+	16.0508i	−0.559197	+	0.143311i
$113$	55.5952			0.491993			0.245997	−	0.969271i	$-0.420885\pi$
$113$	55.5952			0.491993			0.245997	+	0.969271i	$0.420885\pi$
$114$		0			0
$115$	−93.9305	+	93.9305i	−0.816787	+	0.816787i
$116$	−95.4612	−	74.0815i	−0.822941	−	0.638634i
$117$		0			0
$118$	18.6644	−	21.1659i	0.158173	−	0.179372i
$119$	121.708			1.02276
$120$		0			0
$121$		−	27.8503i		−	0.230167i
$122$	−70.9850	+	80.4985i	−0.581844	+	0.659824i
$123$		0			0
$124$	19.0367	+	150.963i	0.153522	+	1.21744i
$125$	−92.7007	−	92.7007i	−0.741606	−	0.741606i
$126$		0			0
$127$			109.927i			0.865569i	0.901497	+	0.432785i	$0.142469\pi$
$127$			109.927i			0.865569i	−0.901497	+	0.432785i	$0.857531\pi$
$128$	−54.4090	−	115.861i	−0.425070	−	0.905160i
$129$		0			0
$130$	−3.57895	−	56.9876i	−0.0275304	−	0.438367i
$131$	−75.6795	+	75.6795i	−0.577706	+	0.577706i	−0.934271	−	0.356565i	$-0.883948\pi$
$131$	−75.6795	+	75.6795i	−0.577706	+	0.577706i	0.356565	+	0.934271i	$0.383948\pi$
$132$		0			0
$133$	79.8270	−	79.8270i	0.600203	−	0.600203i
$134$	42.5780	+	37.5460i	0.317746	+	0.280194i
$135$		0			0
$136$	45.0707	+	236.701i	0.331402	+	1.74045i
$137$		−	2.14751i		−	0.0156752i	−0.999969	−	0.00783762i	$-0.997505\pi$
$137$		−	2.14751i		−	0.0156752i	0.999969	−	0.00783762i	$-0.00249482\pi$
$138$		0			0
$139$	−109.246	−	109.246i	−0.785941	−	0.785941i	0.194885	−	0.980826i	$-0.437567\pi$
$139$	−109.246	−	109.246i	−0.785941	−	0.785941i	−0.980826	+	0.194885i	$0.937567\pi$
$140$	−46.6227	+	60.0778i	−0.333019	+	0.429127i
$141$		0			0
$142$	−5.02455	−	80.0059i	−0.0353842	−	0.563422i
$143$		−	58.5673i		−	0.409562i
$144$		0			0
$145$	−142.125			−0.980174
$146$	61.4979	−	3.86221i	0.421219	−	0.0264535i
$147$		0			0
$148$	148.753	−	191.683i	1.00509	−	1.29516i
$149$	−79.6950	+	79.6950i	−0.534866	+	0.534866i	−0.922016	−	0.387151i	$-0.873459\pi$
$149$	−79.6950	+	79.6950i	−0.534866	+	0.534866i	0.387151	+	0.922016i	$0.373459\pi$
$150$		0			0
$151$	105.546			0.698982			0.349491	−	0.936940i	$-0.386355\pi$
$151$	105.546			0.698982			0.349491	+	0.936940i	$0.386355\pi$
$152$	184.811	+	125.688i	1.21586	+	0.826894i
$153$		0			0
$154$	−51.5892	+	58.5032i	−0.334995	+	0.379891i
$155$	126.550	+	126.550i	0.816451	+	0.816451i
$156$		0			0
$157$	190.060	+	190.060i	1.21057	+	1.21057i	0.970839	+	0.239733i	$0.0770598\pi$
$157$	190.060	+	190.060i	1.21057	+	1.21057i	0.239733	+	0.970839i	$0.422940\pi$
$158$	259.739	−	16.3122i	1.64392	−	0.103242i
$159$		0			0
$160$	−134.106	−	68.4250i	−0.838162	−	0.427656i
$161$	−114.092			−0.708649
$162$		0			0
$163$	−59.4130	+	59.4130i	−0.364497	+	0.364497i	−0.865465	−	0.500969i	$-0.832977\pi$
$163$	−59.4130	+	59.4130i	−0.364497	+	0.364497i	0.500969	+	0.865465i	$0.332977\pi$
$164$	−24.1386	−	191.421i	−0.147186	−	1.16720i
$165$		0			0
$166$	4.79772	+	4.23071i	0.0289019	+	0.0254862i
$167$	−65.3894			−0.391553			−0.195777	−	0.980649i	$-0.562723\pi$
$167$	−65.3894			−0.391553			−0.195777	+	0.980649i	$0.562723\pi$
$168$		0			0
$169$		−	132.176i		−	0.782107i
$170$	212.568	+	187.446i	1.25040	+	1.10262i
$171$		0			0
$172$	−146.032	−	113.326i	−0.849021	−	0.658873i
$173$	212.939	+	212.939i	1.23086	+	1.23086i	0.963633	+	0.267228i	$0.0861077\pi$
$173$	212.939	+	212.939i	1.23086	+	1.23086i	0.267228	+	0.963633i	$0.413892\pi$
$174$		0			0
$175$		−	11.5766i		−	0.0661522i
$176$	−132.883	−	78.6670i	−0.755016	−	0.446972i
$177$		0			0
$178$	144.162	−	9.05372i	0.809901	−	0.0508636i
$179$	−196.852	+	196.852i	−1.09973	+	1.09973i	−0.105289	+	0.994442i	$0.533577\pi$
$179$	−196.852	+	196.852i	−1.09973	+	1.09973i	−0.994442	+	0.105289i	$0.966423\pi$
$180$		0			0
$181$	−27.4330	+	27.4330i	−0.151564	+	0.151564i	−0.778816	−	0.627252i	$-0.784179\pi$
$181$	−27.4330	+	27.4330i	−0.151564	+	0.151564i	0.627252	+	0.778816i	$0.284179\pi$
$182$	32.4364	−	36.7835i	0.178222	−	0.202107i
$183$		0			0
$184$	−42.2505	−	221.890i	−0.229622	−	1.20592i
$185$		−	285.383i		−	1.54261i
$186$		0			0
$187$	205.551	+	205.551i	1.09920	+	1.09920i
$188$	7.92226	+	62.8243i	0.0421397	+	0.334172i
$189$		0			0
$190$	262.364	−	16.4771i	1.38086	−	0.0867214i
$191$			244.409i			1.27963i	0.768530	+	0.639814i	$0.220989\pi$
$191$			244.409i			1.27963i	−0.768530	+	0.639814i	$0.779011\pi$
$192$		0			0
$193$	255.040			1.32145			0.660726	−	0.750627i	$-0.270249\pi$
$193$	255.040			1.32145			0.660726	+	0.750627i	$0.270249\pi$
$194$	−14.0830	−	224.243i	−0.0725927	−	1.15589i
$195$		0			0
$196$	129.658	−	16.3501i	0.661522	−	0.0834191i
$197$	194.229	−	194.229i	0.985936	−	0.985936i	−0.0139666	−	0.999902i	$-0.504446\pi$
$197$	194.229	−	194.229i	0.985936	−	0.985936i	0.999902	+	0.0139666i	$0.00444586\pi$
$198$		0			0
$199$	−169.797			−0.853252			−0.426626	−	0.904428i	$-0.640298\pi$
$199$	−169.797			−0.853252			−0.426626	+	0.904428i	$0.640298\pi$
$200$	22.5145	−	4.28703i	0.112573	−	0.0214352i
$201$		0			0
$202$	3.43529	+	3.02930i	0.0170064	+	0.0149965i
$203$	−86.3160	−	86.3160i	−0.425202	−	0.425202i
$204$		0			0
$205$	−160.466	−	160.466i	−0.782759	−	0.782759i
$206$	3.50969	+	55.8847i	0.0170373	+	0.271285i
$207$		0			0
$208$	83.5492	+	49.4614i	0.401679	+	0.237795i
$209$	269.637			1.29013
$210$		0			0
$211$	−132.691	+	132.691i	−0.628868	+	0.628868i	−0.947783	−	0.318915i	$-0.896681\pi$
$211$	−132.691	+	132.691i	−0.628868	+	0.628868i	0.318915	+	0.947783i	$0.396681\pi$
$212$	−1.65385	+	2.13114i	−0.00780116	+	0.0100525i
$213$		0			0
$214$	−75.5458	+	85.6705i	−0.353018	+	0.400330i
$215$	−217.416			−1.01124
$216$		0			0
$217$			153.713i			0.708357i
$218$	−68.9050	+	78.1398i	−0.316078	+	0.358439i
$219$		0			0
$220$	−180.205	+	22.7241i	−0.819112	+	0.103292i
$221$	−129.239	−	129.239i	−0.584791	−	0.584791i
$222$		0			0
$223$			26.3436i			0.118133i	0.998254	+	0.0590664i	$0.0188124\pi$
$223$			26.3436i			0.118133i	−0.998254	+	0.0590664i	$0.981188\pi$
$224$	−39.8896	−	123.002i	−0.178079	−	0.549115i
$225$		0			0
$226$	6.96928	+	110.972i	0.0308375	+	0.491026i
$227$	70.3362	−	70.3362i	0.309851	−	0.309851i	−0.535001	−	0.844852i	$-0.679689\pi$
$227$	70.3362	−	70.3362i	0.309851	−	0.309851i	0.844852	+	0.535001i	$0.179689\pi$
$228$		0			0
$229$	−215.607	+	215.607i	−0.941516	+	0.941516i	−0.998382	−	0.0568658i	$-0.981889\pi$
$229$	−215.607	+	215.607i	−0.941516	+	0.941516i	0.0568658	+	0.998382i	$0.481889\pi$
$230$	−199.266	−	175.717i	−0.866376	−	0.763986i
$231$		0			0
$232$	135.905	−	199.834i	0.585797	−	0.861352i
$233$			183.853i			0.789069i	0.918881	+	0.394534i	$0.129094\pi$
$233$			183.853i			0.789069i	−0.918881	+	0.394534i	$0.870906\pi$
$234$		0			0
$235$	52.6647	+	52.6647i	0.224105	+	0.224105i
$236$	44.5882	+	34.6021i	0.188933	+	0.146619i
$237$		0			0
$238$	15.2570	+	242.938i	0.0641052	+	1.02075i
$239$			315.183i			1.31876i	0.751811	+	0.659379i	$0.229181\pi$
$239$			315.183i			1.31876i	−0.751811	+	0.659379i	$0.770819\pi$
$240$		0			0
$241$	−327.804			−1.36018			−0.680090	−	0.733128i	$-0.738059\pi$
$241$	−327.804			−1.36018			−0.680090	+	0.733128i	$0.738059\pi$
$242$	55.5910	−	3.49124i	0.229715	−	0.0144266i
$243$		0			0
$244$	−169.579	−	131.600i	−0.694996	−	0.539343i
$245$	108.691	−	108.691i	0.443635	−	0.443635i
$246$		0			0
$247$	−169.532			−0.686366
$248$	−298.945	+	56.9228i	−1.20543	+	0.229528i
$249$		0			0
$250$	173.416	−	196.658i	0.693665	−	0.786631i
$251$	−219.813	−	219.813i	−0.875747	−	0.875747i	0.117344	−	0.993091i	$-0.462562\pi$
$251$	−219.813	−	219.813i	−0.875747	−	0.875747i	−0.993091	+	0.117344i	$0.962562\pi$
$252$		0			0
$253$	−192.689	−	192.689i	−0.761616	−	0.761616i
$254$	−219.422	+	13.7802i	−0.863867	+	0.0542528i
$255$		0			0
$256$	224.445	−	123.128i	0.876738	−	0.480969i
$257$	−150.042			−0.583823			−0.291911	−	0.956445i	$-0.594291\pi$
$257$	−150.042			−0.583823			−0.291911	+	0.956445i	$0.594291\pi$
$258$		0			0
$259$	173.320	−	173.320i	0.669188	−	0.669188i
$260$	113.303	−	14.2877i	0.435779	−	0.0549526i
$261$		0			0
$262$	−160.548	−	141.574i	−0.612780	−	0.540360i
$263$	−14.8922			−0.0566242			−0.0283121	−	0.999599i	$-0.509013\pi$
$263$	−14.8922			−0.0566242			−0.0283121	+	0.999599i	$0.509013\pi$
$264$		0			0
$265$			3.17290i			0.0119732i
$266$	169.347	+	149.333i	0.636643	+	0.561403i
$267$		0			0
$268$	−69.6069	+	89.6952i	−0.259727	+	0.334684i
$269$	−95.4169	−	95.4169i	−0.354710	−	0.354710i	0.507149	−	0.861858i	$-0.330699\pi$
$269$	−95.4169	−	95.4169i	−0.354710	−	0.354710i	−0.861858	+	0.507149i	$0.830699\pi$
$270$		0			0
$271$			46.4991i			0.171583i	0.996313	+	0.0857917i	$0.0273420\pi$
$271$			46.4991i			0.171583i	−0.996313	+	0.0857917i	$0.972658\pi$
$272$	−466.821	+	119.636i	−1.71625	+	0.439840i
$273$		0			0
$274$	4.28657	−	0.269206i	0.0156444	−	0.000982505i
$275$	19.5516	−	19.5516i	0.0710967	−	0.0710967i
$276$		0			0
$277$	30.5071	−	30.5071i	0.110134	−	0.110134i	−0.649892	−	0.760026i	$-0.725186\pi$
$277$	30.5071	−	30.5071i	0.110134	−	0.110134i	0.760026	+	0.649892i	$0.225186\pi$
$278$	204.367	−	231.757i	0.735134	−	0.833657i
$279$		0			0
$280$	−125.764	−	85.5308i	−0.449157	−	0.305467i
$281$			217.239i			0.773093i	0.922270	+	0.386547i	$0.126332\pi$
$281$			217.239i			0.773093i	−0.922270	+	0.386547i	$0.873668\pi$
$282$		0			0
$283$	−136.055	−	136.055i	−0.480760	−	0.480760i	0.424614	−	0.905374i	$-0.360410\pi$
$283$	−136.055	−	136.055i	−0.480760	−	0.480760i	−0.905374	+	0.424614i	$0.860410\pi$
$284$	159.067	−	20.0587i	0.560096	−	0.0706292i
$285$		0			0
$286$	116.904	−	7.34186i	0.408756	−	0.0256708i
$287$		−	194.909i		−	0.679126i
$288$		0			0
$289$	618.167			2.13898
$290$	−17.8165	−	283.691i	−0.0614361	−	0.978246i
$291$		0			0
$292$	15.4185	+	122.270i	0.0528030	+	0.418732i
$293$	56.8362	−	56.8362i	0.193980	−	0.193980i	−0.603433	−	0.797414i	$-0.706201\pi$
$293$	56.8362	−	56.8362i	0.193980	−	0.193980i	0.797414	+	0.603433i	$0.206201\pi$
$294$		0			0
$295$	66.3841			0.225031
$296$	401.260	+	272.893i	1.35561	+	0.921935i
$297$		0			0
$298$	−169.067	−	149.086i	−0.567339	−	0.500289i
$299$	121.152	+	121.152i	0.405190	+	0.405190i
$300$		0			0
$301$	−132.042	−	132.042i	−0.438677	−	0.438677i
$302$	13.2310	+	210.677i	0.0438113	+	0.697608i
$303$		0			0
$304$	−227.714	+	384.650i	−0.749060	+	1.26530i
$305$	−252.474			−0.827782
$306$		0			0
$307$	245.927	−	245.927i	0.801067	−	0.801067i	−0.182196	−	0.983262i	$-0.558320\pi$
$307$	245.927	−	245.927i	0.801067	−	0.801067i	0.983262	+	0.182196i	$0.0583205\pi$
$308$	−123.243	−	95.6416i	−0.400141	−	0.310525i
$309$		0			0
$310$	−236.738	+	268.466i	−0.763671	+	0.866019i
$311$	359.964			1.15744			0.578721	−	0.815526i	$-0.303552\pi$
$311$	359.964			1.15744			0.578721	+	0.815526i	$0.303552\pi$
$312$		0			0
$313$			131.023i			0.418605i	0.977851	+	0.209303i	$0.0671194\pi$
$313$			131.023i			0.418605i	−0.977851	+	0.209303i	$0.932881\pi$
$314$	−355.547	+	403.198i	−1.13231	+	1.28407i
$315$		0			0
$316$	65.1205	+	516.412i	0.206077	+	1.63421i
$317$	−89.0470	−	89.0470i	−0.280905	−	0.280905i	0.552565	−	0.833470i	$-0.313649\pi$
$317$	−89.0470	−	89.0470i	−0.280905	−	0.280905i	−0.833470	+	0.552565i	$0.813649\pi$
$318$		0			0
$319$		−	291.555i		−	0.913966i
$320$	119.770	−	276.262i	0.374280	−	0.863319i
$321$		0			0
$322$	−14.3024	−	227.736i	−0.0444172	−	0.707255i
$323$	595.000	−	595.000i	1.84210	−	1.84210i
$324$		0			0
$325$	−12.2929	+	12.2929i	−0.0378244	+	0.0378244i
$326$	−126.040	−	111.144i	−0.386626	−	0.340934i
$327$		0			0
$328$	379.064	−	72.1783i	1.15568	−	0.220056i
$329$			63.9690i			0.194435i
$330$		0			0
$331$	95.5992	+	95.5992i	0.288819	+	0.288819i	0.836613	−	0.547794i	$-0.184532\pi$
$331$	95.5992	+	95.5992i	0.288819	+	0.288819i	−0.547794	+	0.836613i	$0.684532\pi$
$332$	−7.84336	+	10.1069i	−0.0236246	+	0.0304425i
$333$		0			0
$334$	−8.19706	−	130.522i	−0.0245421	−	0.390783i
$335$			133.541i			0.398629i
$336$		0			0
$337$	583.717			1.73210			0.866050	−	0.499958i	$-0.166651\pi$
$337$	583.717			1.73210			0.866050	+	0.499958i	$0.166651\pi$
$338$	263.833	−	16.5693i	0.780570	−	0.0490215i
$339$		0			0
$340$	−347.508	+	447.797i	−1.02208	+	1.31705i
$341$	−259.604	+	259.604i	−0.761302	+	0.761302i
$342$		0			0
$343$	330.024			0.962169
$344$	207.900	−	305.695i	0.604362	−	0.888649i
$345$		0			0
$346$	−398.347	+	451.734i	−1.15129	+	1.30559i
$347$	−191.655	−	191.655i	−0.552320	−	0.552320i	0.374790	−	0.927110i	$-0.377715\pi$
$347$	−191.655	−	191.655i	−0.552320	−	0.552320i	−0.927110	+	0.374790i	$0.877715\pi$
$348$		0			0
$349$	−19.4781	−	19.4781i	−0.0558112	−	0.0558112i	0.678650	−	0.734462i	$-0.262565\pi$
$349$	−19.4781	−	19.4781i	−0.0558112	−	0.0558112i	−0.734462	+	0.678650i	$0.762565\pi$
$350$	23.1077	−	1.45122i	0.0660221	−	0.00414634i
$351$		0			0
$352$	140.367	−	275.105i	0.398769	−	0.781547i
$353$	82.9610			0.235017			0.117509	−	0.993072i	$-0.462509\pi$
$353$	82.9610			0.235017			0.117509	+	0.993072i	$0.462509\pi$
$354$		0			0
$355$	133.344	−	133.344i	0.375616	−	0.375616i
$356$	36.1437	+	286.623i	0.101527	+	0.805120i
$357$		0			0
$358$	−417.606	−	368.253i	−1.16650	−	1.02864i
$359$	−357.792			−0.996634			−0.498317	−	0.866995i	$-0.666048\pi$
$359$	−357.792			−0.996634			−0.498317	+	0.866995i	$0.666048\pi$
$360$		0			0
$361$		−	419.507i		−	1.16207i
$362$	−58.1971	−	51.3193i	−0.160766	−	0.141766i
$363$		0			0
$364$	77.4886	+	60.1341i	0.212881	+	0.165204i
$365$	102.497	+	102.497i	0.280814	+	0.280814i
$366$		0			0
$367$			651.729i			1.77583i	0.460010	+	0.887914i	$0.347846\pi$
$367$			651.729i			1.77583i	−0.460010	+	0.887914i	$0.652154\pi$
$368$	437.610	−	112.150i	1.18916	−	0.304756i
$369$		0			0
$370$	569.643	−	35.7749i	1.53958	−	0.0966889i
$371$	−1.92698	+	1.92698i	−0.00519401	+	0.00519401i
$372$		0			0
$373$	199.720	−	199.720i	0.535442	−	0.535442i	−0.386745	−	0.922187i	$-0.626401\pi$
$373$	199.720	−	199.720i	0.535442	−	0.535442i	0.922187	+	0.386745i	$0.126401\pi$
$374$	−384.526	+	436.061i	−1.02814	+	1.16594i
$375$		0			0
$376$	−124.408	+	23.6889i	−0.330873	+	0.0630023i
$377$			183.314i			0.486243i
$378$		0			0
$379$	−330.204	−	330.204i	−0.871251	−	0.871251i	0.121358	−	0.992609i	$-0.461275\pi$
$379$	−330.204	−	330.204i	−0.871251	−	0.871251i	−0.992609	+	0.121358i	$0.961275\pi$
$380$	65.7787	+	521.631i	0.173102	+	1.37271i
$381$		0			0
$382$	−487.857	+	30.6385i	−1.27711	+	0.0802055i
$383$		−	174.284i		−	0.455049i	−0.973772	−	0.227524i	$-0.926937\pi$
$383$		−	174.284i		−	0.455049i	0.973772	−	0.227524i	$-0.0730631\pi$
$384$		0			0
$385$	−183.488			−0.476593
$386$	31.9712	+	509.077i	0.0828270	+	1.31885i
$387$		0			0
$388$	445.839	−	56.2212i	1.14907	−	0.144900i
$389$	−207.835	+	207.835i	−0.534279	+	0.534279i	−0.921843	−	0.387564i	$-0.873317\pi$
$389$	−207.835	+	207.835i	−0.534279	+	0.534279i	0.387564	+	0.921843i	$0.373317\pi$
$390$		0			0
$391$	−850.402			−2.17494
$392$	48.8896	+	256.757i	0.124718	+	0.654992i
$393$		0			0
$394$	412.043	+	363.347i	1.04579	+	0.922200i
$395$	432.900	+	432.900i	1.09595	+	1.09595i
$396$		0			0
$397$	−37.2994	−	37.2994i	−0.0939533	−	0.0939533i	0.658568	−	0.752521i	$-0.271162\pi$
$397$	−37.2994	−	37.2994i	−0.0939533	−	0.0939533i	−0.752521	+	0.658568i	$0.771162\pi$
$398$	−21.2854	−	338.927i	−0.0534808	−	0.851574i
$399$		0			0
$400$	11.3796	+	44.4031i	0.0284489	+	0.111008i
$401$	524.704			1.30849			0.654244	−	0.756284i	$-0.272987\pi$
$401$	524.704			1.30849			0.654244	+	0.756284i	$0.272987\pi$
$402$		0			0
$403$	163.224	−	163.224i	0.405023	−	0.405023i
$404$	−5.61605	+	7.23682i	−0.0139011	+	0.0179129i
$405$		0			0
$406$	161.472	−	183.113i	0.397715	−	0.451017i
$407$	585.434			1.43841
$408$		0			0
$409$			787.357i			1.92508i	0.271141	+	0.962540i	$0.412599\pi$
$409$			787.357i			1.92508i	−0.271141	+	0.962540i	$0.587401\pi$
$410$	300.184	−	340.416i	0.732157	−	0.830282i
$411$		0			0
$412$	−111.110	+	14.0111i	−0.269684	+	0.0340076i
$413$	40.3166	+	40.3166i	0.0976190	+	0.0976190i
$414$		0			0
$415$			15.0475i			0.0362589i
$416$	−88.2548	+	172.970i	−0.212151	+	0.415794i
$417$		0			0
$418$	33.8010	+	538.213i	0.0808637	+	1.28759i
$419$	−30.1767	+	30.1767i	−0.0720209	+	0.0720209i	−0.742200	−	0.670179i	$-0.766217\pi$
$419$	−30.1767	+	30.1767i	−0.0720209	+	0.0720209i	0.670179	+	0.742200i	$0.266217\pi$
$420$		0			0
$421$	−261.021	+	261.021i	−0.620003	+	0.620003i	−0.945532	−	0.325529i	$-0.894458\pi$
$421$	−261.021	+	261.021i	−0.620003	+	0.620003i	0.325529	+	0.945532i	$0.394458\pi$
$422$	−281.494	−	248.227i	−0.667048	−	0.588215i
$423$		0			0
$424$	−4.46122	−	3.03403i	−0.0105217	−	0.00715574i
$425$		−	86.2878i		−	0.203030i
$426$		0			0
$427$	−153.333	−	153.333i	−0.359094	−	0.359094i
$428$	−180.474	−	140.055i	−0.421669	−	0.327231i
$429$		0			0
$430$	−27.2547	−	433.977i	−0.0633830	−	1.00925i
$431$		−	459.989i		−	1.06726i	−0.845718	−	0.533630i	$-0.820828\pi$
$431$		−	459.989i		−	1.06726i	0.845718	−	0.533630i	$-0.179172\pi$
$432$		0			0
$433$	−445.246			−1.02828			−0.514140	−	0.857706i	$-0.671889\pi$
$433$	−445.246			−1.02828			−0.514140	+	0.857706i	$0.671889\pi$
$434$	−306.822	+	19.2691i	−0.706964	+	0.0443989i
$435$		0			0
$436$	−164.610	−	127.744i	−0.377546	−	0.292990i
$437$	−557.768	+	557.768i	−1.27636	+	1.27636i
$438$		0			0
$439$	356.467			0.811998			0.405999	−	0.913874i	$-0.366924\pi$
$439$	356.467			0.811998			0.405999	+	0.913874i	$0.366924\pi$
$440$	−67.9489	−	356.852i	−0.154429	−	0.811027i
$441$		0			0
$442$	241.768	−	274.171i	0.546987	−	0.620295i
$443$	−358.752	−	358.752i	−0.809824	−	0.809824i	0.174783	−	0.984607i	$-0.444078\pi$
$443$	−358.752	−	358.752i	−0.809824	−	0.809824i	−0.984607	+	0.174783i	$0.944078\pi$
$444$		0			0
$445$	240.272	+	240.272i	0.539936	+	0.539936i
$446$	−52.5837	+	3.30237i	−0.117901	+	0.00740442i
$447$		0			0
$448$	240.519	−	95.0415i	0.536874	−	0.212146i
$449$	44.6564			0.0994576			0.0497288	−	0.998763i	$-0.484164\pi$
$449$	44.6564			0.0994576			0.0497288	+	0.998763i	$0.484164\pi$
$450$		0			0
$451$	329.179	−	329.179i	0.729886	−	0.729886i
$452$	−220.634	+	27.8223i	−0.488128	+	0.0615538i
$453$		0			0
$454$	149.213	+	131.579i	0.328663	+	0.289821i
$455$	115.367			0.253554
$456$		0			0
$457$			84.2332i			0.184318i	0.995744	+	0.0921589i	$0.0293768\pi$
$457$			84.2332i			0.184318i	−0.995744	+	0.0921589i	$0.970623\pi$
$458$	−457.394	−	403.338i	−0.998678	−	0.880652i
$459$		0			0
$460$	325.763	−	419.777i	0.708180	−	0.912558i
$461$	−205.347	−	205.347i	−0.445438	−	0.445438i	0.448397	−	0.893835i	$-0.351995\pi$
$461$	−205.347	−	205.347i	−0.445438	−	0.445438i	−0.893835	+	0.448397i	$0.851995\pi$
$462$		0			0
$463$			270.647i			0.584550i	0.956334	+	0.292275i	$0.0944123\pi$
$463$			270.647i			0.584550i	−0.956334	+	0.292275i	$0.905588\pi$
$464$	415.918	+	246.225i	0.896376	+	0.530657i
$465$		0			0
$466$	−366.983	+	23.0474i	−0.787517	+	0.0494579i
$467$	−230.389	+	230.389i	−0.493338	+	0.493338i	−0.909356	−	0.416018i	$-0.863425\pi$
$467$	−230.389	+	230.389i	−0.493338	+	0.493338i	0.416018	+	0.909356i	$0.363425\pi$
$468$		0			0
$469$	−81.1024	+	81.1024i	−0.172926	+	0.172926i
$470$	−98.5203	+	111.724i	−0.209618	+	0.237711i
$471$		0			0
$472$	−63.4788	+	93.3387i	−0.134489	+	0.197751i
$473$		−	446.006i		−	0.942931i
$474$		0			0
$475$	−56.5952	−	56.5952i	−0.119148	−	0.119148i
$476$	−483.008	+	60.9082i	−1.01472	+	0.127958i
$477$		0			0
$478$	−629.127	+	39.5106i	−1.31616	+	0.0826581i
$479$		−	575.911i		−	1.20232i	−0.799129	−	0.601159i	$-0.794706\pi$
$479$		−	575.911i		−	1.20232i	0.799129	−	0.601159i	$-0.205294\pi$
$480$		0			0
$481$	−368.088			−0.765255
$482$	−41.0926	−	654.318i	−0.0852545	−	1.35751i
$483$		0			0
$484$	13.9375	+	110.526i	0.0287965	+	0.228359i
$485$	373.740	−	373.740i	0.770599	−	0.770599i
$486$		0			0
$487$	600.355			1.23276			0.616381	−	0.787448i	$-0.288598\pi$
$487$	600.355			1.23276			0.616381	+	0.787448i	$0.288598\pi$
$488$	241.424	−	354.988i	0.494721	−	0.727434i
$489$		0			0
$490$	230.579	+	203.329i	0.470569	+	0.414956i
$491$	−79.7182	−	79.7182i	−0.162359	−	0.162359i	0.621252	−	0.783611i	$-0.286624\pi$
$491$	−79.7182	−	79.7182i	−0.162359	−	0.162359i	−0.783611	+	0.621252i	$0.786624\pi$
$492$		0			0
$493$	−643.367	−	643.367i	−1.30500	−	1.30500i
$494$	−21.2522	−	338.398i	−0.0430206	−	0.685017i
$495$		0			0
$496$	−151.097	−	589.580i	−0.304631	−	1.18867i
$497$	161.966			0.325887
$498$		0			0
$499$	−13.4912	+	13.4912i	−0.0270365	+	0.0270365i	−0.720496	−	0.693459i	$-0.756086\pi$
$499$	−13.4912	+	13.4912i	−0.0270365	+	0.0270365i	0.693459	+	0.720496i	$0.256086\pi$
$500$	414.281	+	321.498i	0.828562	+	0.642996i
$501$		0			0
$502$	411.205	−	466.316i	0.819134	−	0.928916i
$503$	−892.196			−1.77375			−0.886875	−	0.462009i	$-0.847129\pi$
$503$	−892.196			−1.77375			−0.886875	+	0.462009i	$0.847129\pi$
$504$		0			0
$505$			10.7744i			0.0213354i
$506$	360.465	−	408.775i	0.712381	−	0.807855i
$507$		0			0
$508$	−55.0125	−	436.254i	−0.108292	−	0.858768i
$509$	44.9128	+	44.9128i	0.0882374	+	0.0882374i	0.749848	−	0.661610i	$-0.230127\pi$
$509$	44.9128	+	44.9128i	0.0882374	+	0.0882374i	−0.661610	+	0.749848i	$0.730127\pi$
$510$		0			0
$511$			124.498i			0.243636i
$512$	273.908	+	432.572i	0.534976	+	0.844867i
$513$		0			0
$514$	−18.8090	−	299.495i	−0.0365933	−	0.582675i
$515$	−93.1416	+	93.1416i	−0.180857	+	0.180857i
$516$		0			0
$517$	−108.036	+	108.036i	−0.208967	+	0.208967i
$518$	367.685	+	324.231i	0.709816	+	0.625929i
$519$		0			0
$520$	42.7225	+	224.368i	0.0821586	+	0.431478i
$521$			866.038i			1.66226i	0.556078	+	0.831130i	$0.312306\pi$
$521$			866.038i			1.66226i	−0.556078	+	0.831130i	$0.687694\pi$
$522$		0			0
$523$	359.579	+	359.579i	0.687531	+	0.687531i	0.961686	−	0.274155i	$-0.0883981\pi$
$523$	359.579	+	359.579i	0.687531	+	0.687531i	−0.274155	+	0.961686i	$0.588398\pi$
$524$	262.466	−	338.213i	0.500889	−	0.645444i
$525$		0			0
$526$	−1.86684	−	29.7257i	−0.00354913	−	0.0565128i
$527$			1145.72i			2.17405i
$528$		0			0
$529$	268.189			0.506973
$530$	−6.33332	+	0.397747i	−0.0119497	+	0.000750466i
$531$		0			0
$532$	−276.850	+	356.748i	−0.520395	+	0.670579i
$533$	−206.969	+	206.969i	−0.388310	+	0.388310i
$534$		0			0
$535$	−268.695			−0.502234
$536$	−187.764	−	127.696i	−0.350305	−	0.238239i
$537$		0			0
$538$	178.497	−	202.420i	0.331779	−	0.376245i
$539$	222.968	+	222.968i	0.413669	+	0.413669i
$540$		0			0
$541$	−9.41176	−	9.41176i	−0.0173970	−	0.0173970i	0.698355	−	0.715752i	$-0.253916\pi$
$541$	−9.41176	−	9.41176i	−0.0173970	−	0.0173970i	−0.715752	+	0.698355i	$0.753916\pi$
$542$	−92.8154	+	5.82902i	−0.171246	+	0.0107546i
$543$		0			0
$544$	−297.322	−	916.809i	−0.546548	−	1.68531i
$545$	−245.076			−0.449680
$546$		0			0
$547$	−37.6377	+	37.6377i	−0.0688075	+	0.0688075i	−0.740673	−	0.671866i	$-0.765493\pi$
$547$	−37.6377	+	37.6377i	−0.0688075	+	0.0688075i	0.671866	+	0.740673i	$0.265493\pi$
$548$	1.07471	+	8.52253i	0.00196115	+	0.0155521i
$549$		0			0
$550$	41.4772	+	36.5753i	0.0754131	+	0.0665006i
$551$	−843.953			−1.53168
$552$		0			0
$553$			525.821i			0.950852i
$554$	64.7186	+	57.0700i	0.116821	+	0.103014i
$555$		0			0
$556$	488.221	+	378.878i	0.878096	+	0.681436i
$557$	−369.172	−	369.172i	−0.662786	−	0.662786i	0.293250	−	0.956036i	$-0.405263\pi$
$557$	−369.172	−	369.172i	−0.662786	−	0.662786i	−0.956036	+	0.293250i	$0.905263\pi$
$558$		0			0
$559$			280.424i			0.501652i
$560$	154.960	−	261.755i	0.276714	−	0.467420i
$561$		0			0
$562$	−433.624	+	27.2326i	−0.771573	+	0.0484565i
$563$	141.210	−	141.210i	0.250817	−	0.250817i	−0.570489	−	0.821306i	$-0.693246\pi$
$563$	141.210	−	141.210i	0.250817	−	0.250817i	0.821306	+	0.570489i	$0.193246\pi$
$564$		0			0
$565$	−184.954	+	184.954i	−0.327352	+	0.327352i
$566$	254.520	−	288.631i	0.449682	−	0.509949i
$567$		0			0
$568$	59.9788	+	314.995i	0.105596	+	0.554568i
$569$		−	134.928i		−	0.237131i	−0.992946	−	0.118566i	$-0.962170\pi$
$569$		−	134.928i		−	0.237131i	0.992946	−	0.118566i	$-0.0378296\pi$
$570$		0			0
$571$	−486.485	−	486.485i	−0.851988	−	0.851988i	0.138390	−	0.990378i	$-0.455807\pi$
$571$	−486.485	−	486.485i	−0.851988	−	0.851988i	−0.990378	+	0.138390i	$0.955807\pi$
$572$	29.3097	+	232.429i	0.0512407	+	0.406344i
$573$		0			0
$574$	389.052	−	24.4333i	0.677790	−	0.0425668i
$575$			80.8885i			0.140676i
$576$		0			0
$577$	−310.050			−0.537349			−0.268674	−	0.963231i	$-0.586586\pi$
$577$	−310.050			−0.537349			−0.268674	+	0.963231i	$0.586586\pi$
$578$	77.4919	+	1233.90i	0.134069	+	2.13478i
$579$		0			0
$580$	564.034	−	71.1257i	0.972472	−	0.122631i
$581$	−9.13868	+	9.13868i	−0.0157292	+	0.0157292i
$582$		0			0
$583$	−6.50888			−0.0111645
$584$	−242.126	+	46.1037i	−0.414599	+	0.0789448i
$585$		0			0
$586$	120.574	+	106.324i	0.205757	+	0.181440i
$587$	301.021	+	301.021i	0.512812	+	0.512812i	0.915387	−	0.402575i	$-0.131885\pi$
$587$	301.021	+	301.021i	0.512812	+	0.512812i	−0.402575	+	0.915387i	$0.631885\pi$
$588$		0			0
$589$	751.465	+	751.465i	1.27583	+	1.27583i
$590$	8.32175	+	132.507i	0.0141047	+	0.224588i
$591$		0			0
$592$	−494.412	+	835.150i	−0.835155	+	1.41073i
$593$	−6.08782			−0.0102661			−0.00513307	−	0.999987i	$-0.501634\pi$
$593$	−6.08782			−0.0102661			−0.00513307	+	0.999987i	$0.501634\pi$
$594$		0			0
$595$	−404.898	+	404.898i	−0.680501	+	0.680501i
$596$	276.392	−	356.158i	0.463746	−	0.597581i
$597$		0			0
$598$	−226.640	+	257.015i	−0.378997	+	0.429790i
$599$	756.472			1.26289			0.631446	−	0.775420i	$-0.282462\pi$
$599$	756.472			1.26289			0.631446	+	0.775420i	$0.282462\pi$
$600$		0			0
$601$		−	753.072i		−	1.25303i	−0.779409	−	0.626516i	$-0.784480\pi$
$601$		−	753.072i		−	1.25303i	0.779409	−	0.626516i	$-0.215520\pi$
$602$	247.012	−	280.117i	0.410319	−	0.465310i
$603$		0			0
$604$	−418.868	+	52.8200i	−0.693490	+	0.0874504i
$605$	92.6521	+	92.6521i	0.153144	+	0.153144i
$606$		0			0
$607$			47.1200i			0.0776277i	0.999246	+	0.0388139i	$0.0123579\pi$
$607$			47.1200i			0.0776277i	−0.999246	+	0.0388139i	$0.987642\pi$
$608$	−796.334	−	406.314i	−1.30976	−	0.668280i
$609$		0			0
$610$	−31.6495	−	503.954i	−0.0518844	−	0.826155i
$611$	67.9271	−	67.9271i	0.111174	−	0.111174i
$612$		0			0
$613$	637.192	−	637.192i	1.03947	−	1.03947i	0.0402769	−	0.999189i	$-0.487176\pi$
$613$	637.192	−	637.192i	1.03947	−	1.03947i	0.999189	−	0.0402769i	$-0.0128240\pi$
$614$	521.717	+	460.059i	0.849701	+	0.749282i
$615$		0			0
$616$	175.458	−	257.992i	0.284834	−	0.418818i
$617$		−	514.635i		−	0.834092i	−0.908885	−	0.417046i	$-0.863065\pi$
$617$		−	514.635i		−	0.834092i	0.908885	−	0.417046i	$-0.136935\pi$
$618$		0			0
$619$	313.704	+	313.704i	0.506791	+	0.506791i	0.913540	−	0.406749i	$-0.133338\pi$
$619$	313.704	+	313.704i	0.506791	+	0.506791i	−0.406749	+	0.913540i	$0.633338\pi$
$620$	−565.553	−	438.891i	−0.912182	−	0.707888i
$621$		0			0
$622$	45.1243	+	718.513i	0.0725471	+	1.15517i
$623$			291.845i			0.468452i
$624$		0			0
$625$	545.171			0.872273
$626$	−261.532	+	16.4248i	−0.417782	+	0.0262377i
$627$		0			0
$628$	−849.380	−	659.151i	−1.35252	−	1.04960i
$629$	1291.86	−	1291.86i	2.05383	−	2.05383i
$630$		0			0
$631$	−1226.20			−1.94326			−0.971631	−	0.236502i	$-0.923999\pi$
$631$	−1226.20			−1.94326			−0.971631	+	0.236502i	$0.923999\pi$
$632$	−1022.63	+	194.721i	−1.61808	+	0.308103i
$633$		0			0
$634$	166.581	−	188.906i	0.262746	−	0.297960i
$635$	−365.706	−	365.706i	−0.575914	−	0.575914i
$636$		0			0
$637$	−140.189	−	140.189i	−0.220078	−	0.220078i
$638$	581.964	−	36.5487i	0.912169	−	0.0572863i
$639$		0			0
$640$	566.452	+	204.437i	0.885081	+	0.319432i
$641$	−241.218			−0.376314			−0.188157	−	0.982139i	$-0.560251\pi$
$641$	−241.218			−0.376314			−0.188157	+	0.982139i	$0.560251\pi$
$642$		0			0
$643$	−736.141	+	736.141i	−1.14485	+	1.14485i	−0.157304	+	0.987550i	$0.550280\pi$
$643$	−736.141	+	736.141i	−1.14485	+	1.14485i	−0.987550	+	0.157304i	$0.949720\pi$
$644$	452.784	−	57.0969i	0.703081	−	0.0886598i
$645$		0			0
$646$	1262.25	+	1113.07i	1.95394	+	1.72302i
$647$	680.082			1.05113			0.525565	−	0.850753i	$-0.323854\pi$
$647$	680.082			1.05113			0.525565	+	0.850753i	$0.323854\pi$
$648$		0			0
$649$			136.180i			0.209831i
$650$	−26.0785	−	22.9965i	−0.0401208	−	0.0353793i
$651$		0			0
$652$	206.052	−	265.518i	0.316030	−	0.407235i
$653$	716.929	+	716.929i	1.09790	+	1.09790i	0.994656	+	0.103244i	$0.0329224\pi$
$653$	716.929	+	716.929i	1.09790	+	1.09790i	0.103244	+	0.994656i	$0.467078\pi$
$654$		0			0
$655$		−	503.540i		−	0.768763i
$656$	191.591	+	747.589i	0.292060	+	1.13962i
$657$		0			0
$658$	−127.686	+	8.01900i	−0.194052	+	0.0121869i
$659$	−276.868	+	276.868i	−0.420133	+	0.420133i	−0.885250	−	0.465116i	$-0.846012\pi$
$659$	−276.868	+	276.868i	−0.420133	+	0.420133i	0.465116	+	0.885250i	$0.346012\pi$
$660$		0			0
$661$	251.780	−	251.780i	0.380907	−	0.380907i	−0.490522	−	0.871429i	$-0.663194\pi$
$661$	251.780	−	251.780i	0.380907	−	0.380907i	0.871429	+	0.490522i	$0.163194\pi$
$662$	−178.838	+	202.807i	−0.270149	+	0.306354i
$663$		0			0
$664$	−21.1573	−	14.3889i	−0.0318634	−	0.0216700i
$665$			531.136i			0.798700i
$666$		0			0
$667$	603.109	+	603.109i	0.904211	+	0.904211i
$668$	259.502	−	32.7238i	0.388477	−	0.0489877i
$669$		0			0
$670$	−266.556	+	16.7403i	−0.397845	+	0.0249856i
$671$		−	517.924i		−	0.771869i
$672$		0			0
$673$	674.332			1.00198			0.500990	−	0.865453i	$-0.332969\pi$
$673$	674.332			1.00198			0.500990	+	0.865453i	$0.332969\pi$
$674$	73.1734	+	1165.14i	0.108566	+	1.72869i
$675$		0			0
$676$	66.1468	+	524.550i	0.0978503	+	0.775962i
$677$	−109.048	+	109.048i	−0.161075	+	0.161075i	−0.783043	−	0.621968i	$-0.786334\pi$
$677$	−109.048	+	109.048i	−0.161075	+	0.161075i	0.621968	+	0.783043i	$0.286334\pi$
$678$		0			0
$679$	453.963			0.668576
$680$	−937.396	−	637.514i	−1.37852	−	0.937521i
$681$		0			0
$682$	−550.731	−	485.644i	−0.807523	−	0.712088i
$683$	784.278	+	784.278i	1.14828	+	1.14828i	0.986890	+	0.161394i	$0.0515990\pi$
$683$	784.278	+	784.278i	1.14828	+	1.14828i	0.161394	+	0.986890i	$0.448401\pi$
$684$		0			0
$685$	7.14432	+	7.14432i	0.0104297	+	0.0104297i
$686$	41.3710	+	658.750i	0.0603076	+	0.960277i
$687$		0			0
$688$	636.250	+	376.662i	0.924782	+	0.547474i
$689$	4.09241			0.00593964
$690$		0			0
$691$	−99.4915	+	99.4915i	−0.143982	+	0.143982i	−0.775423	−	0.631442i	$-0.782464\pi$
$691$	−99.4915	+	99.4915i	−0.143982	+	0.143982i	0.631442	+	0.775423i	$0.282464\pi$
$692$	−951.628	−	738.500i	−1.37518	−	1.06720i
$693$		0			0
$694$	358.531	−	406.582i	0.516615	−	0.585853i
$695$	726.877			1.04587
$696$		0			0
$697$		−	1452.78i		−	2.08433i
$698$	36.4379	−	41.3213i	0.0522032	−	0.0591996i
$699$		0			0
$700$	5.79346	+	45.9427i	0.00827637	+	0.0656324i
$701$	−177.909	−	177.909i	−0.253794	−	0.253794i	0.568730	−	0.822524i	$-0.307435\pi$
$701$	−177.909	−	177.909i	−0.253794	−	0.253794i	−0.822524	+	0.568730i	$0.807435\pi$
$702$		0			0
$703$		−	1694.63i		−	2.41057i
$704$	566.723	+	245.695i	0.805005	+	0.348999i
$705$		0			0
$706$	10.3998	+	165.596i	0.0147306	+	0.234555i
$707$	−6.54353	+	6.54353i	−0.00925535	+	0.00925535i
$708$		0			0
$709$	−208.080	+	208.080i	−0.293484	+	0.293484i	−0.838455	−	0.544971i	$-0.816541\pi$
$709$	−208.080	+	208.080i	−0.293484	+	0.293484i	0.544971	+	0.838455i	$0.316541\pi$
$710$	282.879	+	249.448i	0.398421	+	0.351335i
$711$		0			0
$712$	−567.587	+	108.076i	−0.797173	+	0.151791i
$713$		−	1074.03i		−	1.50635i
$714$		0			0
$715$	194.841	+	194.841i	0.272506	+	0.272506i
$716$	682.707	−	879.734i	0.953501	−	1.22868i
$717$		0			0
$718$	−44.8519	−	714.176i	−0.0624678	−	0.994674i
$719$			1013.84i			1.41007i	0.709171	+	0.705036i	$0.249069\pi$
$719$			1013.84i			1.41007i	−0.709171	+	0.705036i	$0.750931\pi$
$720$		0			0
$721$	−113.134			−0.156913
$722$	837.364	−	52.5883i	1.15978	−	0.0728370i
$723$		0			0
$724$	95.1413	−	122.599i	0.131411	−	0.169335i
$725$	−61.1957	+	61.1957i	−0.0844079	+	0.0844079i
$726$		0			0
$727$	697.156			0.958949			0.479474	−	0.877556i	$-0.340827\pi$
$727$	697.156			0.958949			0.479474	+	0.877556i	$0.340827\pi$
$728$	−110.318	+	162.211i	−0.151536	+	0.222817i
$729$		0			0
$730$	−191.742	+	217.440i	−0.262661	+	0.297863i
$731$	−984.189	−	984.189i	−1.34636	−	1.34636i
$732$		0			0
$733$	−39.9608	−	39.9608i	−0.0545168	−	0.0545168i	0.679323	−	0.733840i	$-0.262274\pi$
$733$	−39.9608	−	39.9608i	−0.0545168	−	0.0545168i	−0.733840	+	0.679323i	$0.762274\pi$
$734$	−1300.89	+	81.6991i	−1.77234	+	0.111307i
$735$		0			0
$736$	278.717	+	859.441i	0.378692	+	1.16772i
$737$	−273.945			−0.371703
$738$		0			0
$739$	−236.377	+	236.377i	−0.319860	+	0.319860i	−0.848713	−	0.528853i	$-0.822622\pi$
$739$	−236.377	+	236.377i	−0.319860	+	0.319860i	0.528853	+	0.848713i	$0.322622\pi$
$740$	142.818	+	1132.56i	0.192998	+	1.53049i
$741$		0			0
$742$	−4.08794	−	3.60481i	−0.00550935	−	0.00485824i
$743$	−804.248			−1.08243			−0.541217	−	0.840883i	$-0.682036\pi$
$743$	−804.248			−1.08243			−0.541217	+	0.840883i	$0.682036\pi$
$744$		0			0
$745$		−	530.258i		−	0.711755i
$746$	423.691	+	373.618i	0.567950	+	0.500828i
$747$		0			0
$748$	−918.610	−	712.877i	−1.22809	−	0.953043i
$749$	−163.185	−	163.185i	−0.217870	−	0.217870i
$750$		0			0
$751$		−	607.492i		−	0.808911i	−0.914558	−	0.404456i	$-0.867461\pi$
$751$		−	607.492i		−	0.808911i	0.914558	−	0.404456i	$-0.132539\pi$
$752$	−62.8801	−	245.358i	−0.0836171	−	0.326274i
$753$		0			0
$754$	−365.906	+	22.9797i	−0.485287	+	0.0304771i
$755$	−351.131	+	351.131i	−0.465074	+	0.465074i
$756$		0			0
$757$	−11.6797	+	11.6797i	−0.0154289	+	0.0154289i	−0.714779	−	0.699350i	$-0.753473\pi$
$757$	−11.6797	+	11.6797i	−0.0154289	+	0.0154289i	0.699350	+	0.714779i	$0.253473\pi$
$758$	617.716	−	700.503i	0.814929	−	0.924147i
$759$		0			0
$760$	−1032.96	+	196.689i	−1.35916	+	0.258801i
$761$		−	659.125i		−	0.866130i	−0.901363	−	0.433065i	$-0.857432\pi$
$761$		−	659.125i		−	0.866130i	0.901363	−	0.433065i	$-0.142568\pi$
$762$		0			0
$763$	−148.840	−	148.840i	−0.195073	−	0.195073i
$764$	−122.313	−	969.954i	−0.160096	−	1.26957i
$765$		0			0
$766$	347.882	−	21.8478i	0.454154	−	0.0285219i
$767$		−	85.6224i		−	0.111633i
$768$		0			0
$769$	−178.802			−0.232512			−0.116256	−	0.993219i	$-0.537089\pi$
$769$	−178.802			−0.232512			−0.116256	+	0.993219i	$0.537089\pi$
$770$	−23.0016	−	366.255i	−0.0298722	−	0.475656i
$771$		0			0
$772$	−1012.15	+	127.633i	−1.31107	+	0.165328i
$773$	91.8171	−	91.8171i	0.118780	−	0.118780i	−0.645218	−	0.763998i	$-0.723234\pi$
$773$	91.8171	−	91.8171i	0.118780	−	0.118780i	0.763998	+	0.645218i	$0.223234\pi$
$774$		0			0
$775$	108.979			0.140618
$776$	168.111	+	882.877i	0.216637	+	1.13773i
$777$		0			0
$778$	−440.906	−	388.798i	−0.566717	−	0.499741i
$779$	−952.860	−	952.860i	−1.22318	−	1.22318i
$780$		0			0
$781$	273.541	+	273.541i	0.350245	+	0.350245i
$782$	−106.604	−	1697.46i	−0.136323	−	2.17066i
$783$		0			0
$784$	−506.376	+	129.773i	−0.645887	+	0.165527i
$785$	−1264.58			−1.61093
$786$		0			0
$787$	214.856	−	214.856i	0.273006	−	0.273006i	−0.557303	−	0.830309i	$-0.688164\pi$
$787$	214.856	−	214.856i	0.273006	−	0.273006i	0.830309	+	0.557303i	$0.188164\pi$
$788$	−673.612	+	868.014i	−0.854838	+	1.10154i
$789$		0			0
$790$	−809.831	+	918.365i	−1.02510	+	1.16249i
$791$	−224.654			−0.284012
$792$		0			0
$793$			325.641i			0.410645i
$794$	69.7764	−	79.1280i	0.0878796	−	0.0996574i
$795$		0			0
$796$	673.852	−	84.9740i	0.846548	−	0.106751i
$797$	332.028	+	332.028i	0.416598	+	0.416598i	0.884029	−	0.467432i	$-0.154821\pi$
$797$	332.028	+	332.028i	0.416598	+	0.416598i	−0.467432	+	0.884029i	$0.654821\pi$
$798$		0			0
$799$			476.801i			0.596747i
$800$	−87.2050	+	28.2807i	−0.109006	+	0.0353508i
$801$		0			0
$802$	65.7756	+	1047.34i	0.0820144	+	1.30592i
$803$	−210.262	+	210.262i	−0.261846	+	0.261846i
$804$		0			0
$805$	379.562	−	379.562i	0.471506	−	0.471506i
$806$	346.268	+	305.346i	0.429613	+	0.378841i
$807$		0			0
$808$	−15.1492	−	10.3028i	−0.0187490	−	0.0127510i
$809$		−	421.989i		−	0.521618i	−0.965390	−	0.260809i	$-0.916011\pi$
$809$		−	421.989i		−	0.521618i	0.965390	−	0.260809i	$-0.0839893\pi$
$810$		0			0
$811$	532.822	+	532.822i	0.656994	+	0.656994i	0.954668	−	0.297674i	$-0.0962107\pi$
$811$	532.822	+	532.822i	0.656994	+	0.656994i	−0.297674	+	0.954668i	$0.596211\pi$
$812$	385.748	+	299.355i	0.475059	+	0.368664i
$813$		0			0
$814$	73.3885	+	1168.56i	0.0901579	+	1.43558i
$815$		−	395.310i		−	0.485042i
$816$		0			0
$817$	−1291.04			−1.58022
$818$	−1571.62	+	98.7012i	−1.92129	+	0.120662i
$819$		0			0
$820$	717.123	+	556.515i	0.874540	+	0.678677i
$821$	797.754	−	797.754i	0.971686	−	0.971686i	−0.0279241	−	0.999610i	$-0.508890\pi$
$821$	797.754	−	797.754i	0.971686	−	0.971686i	0.999610	+	0.0279241i	$0.00888968\pi$
$822$		0			0
$823$	863.777			1.04955			0.524773	−	0.851242i	$-0.324150\pi$
$823$	863.777			1.04955			0.524773	+	0.851242i	$0.324150\pi$
$824$	−41.8956	−	220.026i	−0.0508442	−	0.267022i
$825$		0			0
$826$	−75.4207	+	85.5287i	−0.0913084	+	0.103546i
$827$	1154.08	+	1154.08i	1.39550	+	1.39550i	0.812402	+	0.583098i	$0.198160\pi$
$827$	1154.08	+	1154.08i	1.39550	+	1.39550i	0.583098	+	0.812402i	$0.301840\pi$
$828$		0			0
$829$	473.183	+	473.183i	0.570788	+	0.570788i	0.932349	−	0.361561i	$-0.117756\pi$
$829$	473.183	+	473.183i	0.570788	+	0.570788i	−0.361561	+	0.932349i	$0.617756\pi$
$830$	−30.0357	+	1.88631i	−0.0361876	+	0.00227266i
$831$		0			0
$832$	−356.324	−	154.479i	−0.428274	−	0.185672i
$833$	984.033			1.18131
$834$		0			0
$835$	217.537	−	217.537i	0.260523	−	0.260523i
$836$	−1070.07	+	134.938i	−1.27999	+	0.161409i
$837$		0			0
$838$	−64.0177	−	56.4519i	−0.0763934	−	0.0673651i
$839$	−561.776			−0.669578			−0.334789	−	0.942293i	$-0.608665\pi$
$839$	−561.776			−0.669578			−0.334789	+	0.942293i	$0.608665\pi$
$840$		0			0
$841$			71.5574i			0.0850861i
$842$	−553.737	−	488.295i	−0.657645	−	0.579923i
$843$		0			0
$844$	460.189	−	592.998i	0.545248	−	0.702605i
$845$	439.723	+	439.723i	0.520382	+	0.520382i
$846$		0			0
$847$			112.540i			0.132869i
$848$	5.49689	−	9.28524i	0.00648218	−	0.0109496i
$849$		0			0
$850$	172.236	−	10.8168i	0.202631	−	0.0127257i
$851$	−1211.02	+	1211.02i	−1.42306	+	1.42306i
$852$		0			0
$853$	−431.517	+	431.517i	−0.505881	+	0.505881i	−0.913259	−	0.407378i	$-0.866443\pi$
$853$	−431.517	+	431.517i	−0.505881	+	0.505881i	0.407378	+	0.913259i	$0.366443\pi$
$854$	286.842	−	325.285i	0.335881	−	0.380896i
$855$		0			0
$856$	256.935	−	377.796i	0.300158	−	0.441350i
$857$			448.237i			0.523030i	0.965199	+	0.261515i	$0.0842221\pi$
$857$			448.237i			0.523030i	−0.965199	+	0.261515i	$0.915778\pi$
$858$		0			0
$859$	−617.299	−	617.299i	−0.718625	−	0.718625i	0.249699	−	0.968324i	$-0.419668\pi$
$859$	−617.299	−	617.299i	−0.718625	−	0.718625i	−0.968324	+	0.249699i	$0.919668\pi$
$860$	862.830	−	108.804i	1.00329	−	0.126517i
$861$		0			0
$862$	918.169	−	57.6631i	1.06516	−	0.0668946i
$863$		−	1588.33i		−	1.84047i	−0.391363	−	0.920236i	$-0.627996\pi$
$863$		−	1588.33i		−	1.84047i	0.391363	−	0.920236i	$-0.372004\pi$
$864$		0			0
$865$	−1416.81			−1.63793
$866$	−55.8149	−	888.740i	−0.0644514	−	1.02626i
$867$		0			0
$868$	−76.9250	−	610.023i	−0.0886233	−	0.702791i
$869$	−888.050	+	888.050i	−1.02192	+	1.02192i
$870$		0			0
$871$	172.241			0.197751
$872$	234.350	−	344.586i	0.268750	−	0.395168i
$873$		0			0
$874$	−1183.26	−	1043.42i	−1.35385	−	1.19385i
$875$	374.593	+	374.593i	0.428106	+	0.428106i
$876$		0			0
$877$	535.285	+	535.285i	0.610359	+	0.610359i	0.943040	−	0.332680i	$-0.107953\pi$
$877$	535.285	+	535.285i	0.610359	+	0.610359i	−0.332680	+	0.943040i	$0.607953\pi$
$878$	44.6858	+	711.532i	0.0508950	+	0.810401i
$879$		0			0
$880$	703.783	−	180.365i	0.799753	−	0.204960i
$881$	−517.437			−0.587330			−0.293665	−	0.955908i	$-0.594875\pi$
$881$	−517.437			−0.587330			−0.293665	+	0.955908i	$0.594875\pi$
$882$		0			0
$883$	−1192.91	+	1192.91i	−1.35097	+	1.35097i	−0.466399	+	0.884574i	$0.654449\pi$
$883$	−1192.91	+	1192.91i	−1.35097	+	1.35097i	−0.884574	+	0.466399i	$0.845551\pi$
$884$	577.570	+	448.217i	0.653360	+	0.507032i
$885$		0			0
$886$	671.121	−	761.066i	0.757473	−	0.858991i
$887$	1750.36			1.97335			0.986675	−	0.162704i	$-0.0520217\pi$
$887$	1750.36			1.97335			0.986675	+	0.162704i	$0.0520217\pi$
$888$		0			0
$889$		−	444.203i		−	0.499666i
$890$	−449.479	+	509.718i	−0.505032	+	0.572717i
$891$		0			0
$892$	−13.1835	−	104.547i	−0.0147797	−	0.117205i
$893$	312.728	+	312.728i	0.350199	+	0.350199i
$894$		0			0
$895$		−	1309.77i		−	1.46343i
$896$	219.860	+	468.179i	0.245380	+	0.522521i
$897$		0			0
$898$	5.59802	+	89.1373i	0.00623388	+	0.0992620i
$899$	812.551	−	812.551i	0.903839	−	0.903839i
$900$		0			0
$901$	−14.3630	+	14.3630i	−0.0159411	+	0.0159411i
$902$	698.328	+	615.798i	0.774199	+	0.682703i
$903$		0			0
$904$	−83.1933	−	436.912i	−0.0920280	−	0.483310i
$905$		−	182.528i		−	0.201689i
$906$		0			0
$907$	86.0833	+	86.0833i	0.0949099	+	0.0949099i	0.752968	−	0.658058i	$-0.228622\pi$
$907$	86.0833	+	86.0833i	0.0949099	+	0.0949099i	−0.658058	+	0.752968i	$0.728622\pi$
$908$	−243.935	+	314.333i	−0.268651	+	0.346182i
$909$		0			0
$910$	14.4621	+	230.280i	0.0158925	+	0.253055i
$911$		−	44.7701i		−	0.0491439i	−0.999698	−	0.0245719i	$-0.992178\pi$
$911$		−	44.7701i		−	0.0491439i	0.999698	−	0.0245719i	$-0.00782228\pi$
$912$		0			0
$913$	−30.8683			−0.0338098
$914$	−168.135	+	10.5593i	−0.183955	+	0.0115528i
$915$		0			0
$916$	747.753	−	963.552i	0.816324	−	1.05191i
$917$	305.812	−	305.812i	0.333492	−	0.333492i
$918$		0			0
$919$	498.982			0.542962			0.271481	−	0.962444i	$-0.412487\pi$
$919$	498.982			0.542962			0.271481	+	0.962444i	$0.412487\pi$
$920$	878.740	+	597.622i	0.955152	+	0.649590i
$921$		0			0
$922$	384.144	−	435.628i	0.416642	−	0.472481i
$923$	−171.987	−	171.987i	−0.186335	−	0.186335i
$924$		0			0
$925$	−122.879	−	122.879i	−0.132842	−	0.132842i
$926$	−540.229	+	33.9276i	−0.583401	+	0.0366389i
$927$		0			0
$928$	−439.343	+	861.067i	−0.473430	+	0.927874i
$929$	1460.97			1.57262			0.786311	−	0.617831i	$-0.211988\pi$
$929$	1460.97			1.57262			0.786311	+	0.617831i	$0.211988\pi$
$930$		0			0
$931$	645.415	−	645.415i	0.693250	−	0.693250i
$932$	−92.0082	−	729.634i	−0.0987213	−	0.782869i
$933$		0			0
$934$	−488.753	−	430.991i	−0.523290	−	0.461446i
$935$	−1367.65			−1.46273
$936$		0			0
$937$			594.005i			0.633943i	0.948435	+	0.316972i	$0.102666\pi$
$937$			594.005i			0.633943i	−0.948435	+	0.316972i	$0.897334\pi$
$938$	−172.053	−	151.719i	−0.183425	−	0.161747i
$939$		0			0
$940$	−235.359	−	182.648i	−0.250382	−	0.194306i
$941$	−767.764	−	767.764i	−0.815902	−	0.815902i	0.169610	−	0.985511i	$-0.445749\pi$
$941$	−767.764	−	767.764i	−0.815902	−	0.815902i	−0.985511	+	0.169610i	$0.945749\pi$
$942$		0			0
$943$			1361.87i			1.44419i
$944$	−194.268	−	115.007i	−0.205792	−	0.121830i
$945$		0			0
$946$	890.259	−	55.9102i	0.941077	−	0.0591017i
$947$	205.644	−	205.644i	0.217153	−	0.217153i	−0.590145	−	0.807297i	$-0.700929\pi$
$947$	205.644	−	205.644i	0.217153	−	0.217153i	0.807297	+	0.590145i	$0.200929\pi$
$948$		0			0
$949$	132.201	−	132.201i	0.139306	−	0.139306i
$950$	105.873	−	120.062i	0.111445	−	0.126381i
$951$		0			0
$952$	−182.125	−	956.480i	−0.191308	−	1.00471i
$953$			1714.17i			1.79871i	0.437215	+	0.899357i	$0.355965\pi$
$953$			1714.17i			1.79871i	−0.437215	+	0.899357i	$0.644035\pi$
$954$		0			0
$955$	−813.098	−	813.098i	−0.851412	−	0.851412i
$956$	−157.732	−	1250.83i	−0.164991	−	1.30840i
$957$		0			0
$958$	1149.56	−	72.1948i	1.19995	−	0.0753599i
$959$			8.67783i			0.00904883i
$960$		0			0
$961$	−486.009			−0.505733
$962$	−46.1426	−	734.728i	−0.0479653	−	0.763750i
$963$		0			0
$964$	1300.91	−	164.047i	1.34949	−	0.170174i
$965$	−848.466	+	848.466i	−0.879240	+	0.879240i
$966$		0			0
$967$	−1375.76			−1.42271			−0.711356	−	0.702832i	$-0.751919\pi$
$967$	−1375.76			−1.42271			−0.711356	+	0.702832i	$0.751919\pi$
$968$	−218.870	+	41.6754i	−0.226105	+	0.0430531i
$969$		0			0
$970$	792.862	+	699.160i	0.817384	+	0.720783i
$971$	1081.41	+	1081.41i	1.11371	+	1.11371i	0.992645	+	0.121062i	$0.0386300\pi$
$971$	1081.41	+	1081.41i	1.11371	+	1.11371i	0.121062	+	0.992645i	$0.461370\pi$
$972$		0			0
$973$	441.449	+	441.449i	0.453699	+	0.453699i
$974$	75.2590	+	1198.35i	0.0772680	+	1.23034i
$975$		0			0
$976$	738.844	+	437.398i	0.757013	+	0.448154i
$977$	18.0081			0.0184320			0.00921601	−	0.999958i	$-0.497066\pi$
$977$	18.0081			0.0184320			0.00921601	+	0.999958i	$0.497066\pi$
$978$		0			0
$979$	−492.893	+	492.893i	−0.503465	+	0.503465i
$980$	−376.953	+	485.740i	−0.384646	+	0.495653i
$981$		0			0
$982$	149.130	−	169.116i	0.151863	−	0.172216i
$983$	−579.164			−0.589180			−0.294590	−	0.955624i	$-0.595183\pi$
$983$	−579.164			−0.589180			−0.294590	+	0.955624i	$0.595183\pi$
$984$		0			0
$985$			1292.32i			1.31200i
$986$	1203.55	−	1364.85i	1.22064	−	1.38423i
$987$		0			0
$988$	672.802	−	84.8416i	0.680973	−	0.0858720i
$989$	922.605	+	922.605i	0.932866	+	0.932866i
$990$		0			0
$991$			1389.22i			1.40184i	0.713242	+	0.700918i	$0.247226\pi$
$991$			1389.22i			1.40184i	−0.713242	+	0.700918i	$0.752774\pi$
$992$	1157.90	−	375.508i	1.16724	−	0.378536i
$993$		0			0
$994$	20.3036	+	323.295i	0.0204262	+	0.325246i
$995$	564.880	−	564.880i	0.567719	−	0.567719i
$996$		0			0
$997$	867.073	−	867.073i	0.869682	−	0.869682i	−0.122755	−	0.992437i	$-0.539173\pi$
$997$	867.073	−	867.073i	0.869682	−	0.869682i	0.992437	+	0.122755i	$0.0391730\pi$
$998$	−28.6206	−	25.2381i	−0.0286779	−	0.0252887i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.m.c.19.5		16
3.2	odd	2		48.3.l.a.19.4	✓	16
4.3	odd	2		576.3.m.c.559.2		16
8.3	odd	2		1152.3.m.c.991.7		16
8.5	even	2		1152.3.m.f.991.7		16
12.11	even	2		192.3.l.a.175.4		16
16.3	odd	4		1152.3.m.f.415.7		16
16.5	even	4		576.3.m.c.271.2		16
16.11	odd	4	inner	144.3.m.c.91.5		16
16.13	even	4		1152.3.m.c.415.7		16
24.5	odd	2		384.3.l.a.223.1		16
24.11	even	2		384.3.l.b.223.5		16
48.5	odd	4		192.3.l.a.79.4		16
48.11	even	4		48.3.l.a.43.4	yes	16
48.29	odd	4		384.3.l.b.31.5		16
48.35	even	4		384.3.l.a.31.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.l.a.19.4	✓	16	3.2	odd	2
48.3.l.a.43.4	yes	16	48.11	even	4
144.3.m.c.19.5		16	1.1	even	1	trivial
144.3.m.c.91.5		16	16.11	odd	4	inner
192.3.l.a.79.4		16	48.5	odd	4
192.3.l.a.175.4		16	12.11	even	2
384.3.l.a.31.1		16	48.35	even	4
384.3.l.a.223.1		16	24.5	odd	2
384.3.l.b.31.5		16	48.29	odd	4
384.3.l.b.223.5		16	24.11	even	2
576.3.m.c.271.2		16	16.5	even	4
576.3.m.c.559.2		16	4.3	odd	2
1152.3.m.c.415.7		16	16.13	even	4
1152.3.m.c.991.7		16	8.3	odd	2
1152.3.m.f.415.7		16	16.3	odd	4
1152.3.m.f.991.7		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)

\(f(q)\)	\(=\)	\(q+(0.125358 + 1.99607i) q^{2} +(-3.96857 + 0.500444i) q^{4} +(-3.32679 + 3.32679i) q^{5} -4.04088 q^{7} +(-1.49641 - 7.85880i) q^{8} +O(q^{10})\)	\(q+(0.125358 + 1.99607i) q^{2} +(-3.96857 + 0.500444i) q^{4} +(-3.32679 + 3.32679i) q^{5} -4.04088 q^{7} +(-1.49641 - 7.85880i) q^{8} +(-7.05755 - 6.22347i) q^{10} +(-6.82458 - 6.82458i) q^{11} +(4.29091 + 4.29091i) q^{13} +(-0.506555 - 8.06588i) q^{14} +(15.4991 - 3.97210i) q^{16} -30.1192 q^{17} +(-19.7548 + 19.7548i) q^{19} +(11.5377 - 14.8675i) q^{20} +(12.7668 - 14.4778i) q^{22} +28.2345 q^{23} +2.86488i q^{25} +(-8.02705 + 9.10285i) q^{26} +(16.0365 - 2.02224i) q^{28} +(21.3607 + 21.3607i) q^{29} -38.0396i q^{31} +(9.87151 + 30.4393i) q^{32} +(-3.77567 - 60.1200i) q^{34} +(13.4432 - 13.4432i) q^{35} +(-42.8916 + 42.8916i) q^{37} +(-41.9084 - 36.9556i) q^{38} +(31.1229 + 21.1664i) q^{40} +48.2343i q^{41} +(32.6765 + 32.6765i) q^{43} +(30.4991 + 23.6685i) q^{44} +(3.53941 + 56.3580i) q^{46} -15.8305i q^{47} -32.6713 q^{49} +(-5.71849 + 0.359134i) q^{50} +(-19.1761 - 14.8814i) q^{52} +(0.476870 - 0.476870i) q^{53} +45.4079 q^{55} +(6.04682 + 31.7565i) q^{56} +(-39.9596 + 45.3151i) q^{58} +(-9.97719 - 9.97719i) q^{59} +(37.9455 + 37.9455i) q^{61} +(75.9296 - 4.76855i) q^{62} +(-59.5215 + 23.5200i) q^{64} -28.5500 q^{65} +(20.0705 - 20.0705i) q^{67} +(119.530 - 15.0730i) q^{68} +(28.5187 + 25.1483i) q^{70} -40.0818 q^{71} -30.8095i q^{73} +(-90.9912 - 80.2377i) q^{74} +(68.5123 - 88.2846i) q^{76} +(27.5773 + 27.5773i) q^{77} -130.125i q^{79} +(-38.3480 + 64.7767i) q^{80} +(-96.2789 + 6.04653i) q^{82} +(2.26155 - 2.26155i) q^{83} +(100.200 - 100.200i) q^{85} +(-61.1282 + 69.3207i) q^{86} +(-43.4206 + 63.8454i) q^{88} -72.2232i q^{89} +(-17.3391 - 17.3391i) q^{91} +(-112.051 + 14.1298i) q^{92} +(31.5986 - 1.98447i) q^{94} -131.441i q^{95} -112.343 q^{97} +(-4.09559 - 65.2140i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} + 12 q^{8}+O(q^{10}) \) 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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