LMFDB - Embedded newform 144.3.m.b.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} - 6x^{14} + 10x^{12} + 88x^{10} - 752x^{8} + 1408x^{6} + 2560x^{4} - 24576x^{2} + 65536 $ x^16 - 6x^14 + 10x^12 + 88x^10 - 752x^8 + 1408x^6 + 2560x^4 - 24576*x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.2
Root			$1.64663 - 1.13516i$ of defining polynomial
Character	$\chi$	$=$	144.19
Dual form			144.3.m.b.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13516 - 1.64663i) q^{2} +(-1.42280 + 3.73840i) q^{4} +(2.41234 - 2.41234i) q^{5} -11.8718 q^{7} +(7.77089 - 1.90087i) q^{8} +O(q^{10})$	\(q+(-1.13516 - 1.64663i) q^{2} +(-1.42280 + 3.73840i) q^{4} +(2.41234 - 2.41234i) q^{5} -11.8718 q^{7} +(7.77089 - 1.90087i) q^{8} +(-6.71063 - 1.23383i) q^{10} +(-11.9421 - 11.9421i) q^{11} +(2.08177 + 2.08177i) q^{13} +(13.4765 + 19.5486i) q^{14} +(-11.9513 - 10.6380i) q^{16} -23.1512 q^{17} +(-6.77297 + 6.77297i) q^{19} +(5.58600 + 12.4506i) q^{20} +(-6.10800 + 33.2205i) q^{22} +3.92781 q^{23} +13.3613i q^{25} +(1.06476 - 5.79105i) q^{26} +(16.8913 - 44.3817i) q^{28} +(0.782548 + 0.782548i) q^{29} -2.65295i q^{31} +(-3.95022 + 31.7552i) q^{32} +(26.2805 + 38.1216i) q^{34} +(-28.6389 + 28.6389i) q^{35} +(37.2078 - 37.2078i) q^{37} +(18.8410 + 3.46416i) q^{38} +(14.1605 - 23.3315i) q^{40} -69.1259i q^{41} +(-29.2978 - 29.2978i) q^{43} +(61.6355 - 27.6531i) q^{44} +(-4.45872 - 6.46767i) q^{46} -68.0631i q^{47} +91.9405 q^{49} +(22.0011 - 15.1672i) q^{50} +(-10.7444 + 4.82053i) q^{52} +(-40.3674 + 40.3674i) q^{53} -57.6167 q^{55} +(-92.2547 + 22.5668i) q^{56} +(0.400249 - 2.17689i) q^{58} +(23.5544 + 23.5544i) q^{59} +(65.9304 + 65.9304i) q^{61} +(-4.36844 + 3.01154i) q^{62} +(56.7734 - 29.5429i) q^{64} +10.0438 q^{65} +(-40.9626 + 40.9626i) q^{67} +(32.9396 - 86.5486i) q^{68} +(79.6675 + 14.6479i) q^{70} +98.1885 q^{71} -74.2864i q^{73} +(-103.505 - 19.0306i) q^{74} +(-15.6835 - 34.9567i) q^{76} +(141.774 + 141.774i) q^{77} -0.779953i q^{79} +(-54.4929 + 3.16805i) q^{80} +(-113.825 + 78.4693i) q^{82} +(-91.7887 + 91.7887i) q^{83} +(-55.8486 + 55.8486i) q^{85} +(-14.9849 + 81.5005i) q^{86} +(-115.501 - 70.1003i) q^{88} -20.1568i q^{89} +(-24.7144 - 24.7144i) q^{91} +(-5.58850 + 14.6837i) q^{92} +(-112.075 + 77.2629i) q^{94} +32.6774i q^{95} -86.6476 q^{97} +(-104.368 - 151.392i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{4}+O(q^{10}) $ 16 * q - 12 * q^4	$ 16 q - 12 q^{4} + 16 q^{10} + 32 q^{16} - 32 q^{19} + 104 q^{22} - 24 q^{34} + 96 q^{37} - 312 q^{40} - 32 q^{43} - 224 q^{46} + 112 q^{49} - 264 q^{52} - 256 q^{55} + 312 q^{58} - 32 q^{61} + 456 q^{64} - 256 q^{67} + 744 q^{70} + 264 q^{76} - 280 q^{82} + 160 q^{85} - 912 q^{88} + 288 q^{91} - 1104 q^{94}+O(q^{100}) $ 16 * q - 12 * q^4 + 16 * q^10 + 32 * q^16 - 32 * q^19 + 104 * q^22 - 24 * q^34 + 96 * q^37 - 312 * q^40 - 32 * q^43 - 224 * q^46 + 112 * q^49 - 264 * q^52 - 256 * q^55 + 312 * q^58 - 32 * q^61 + 456 * q^64 - 256 * q^67 + 744 * q^70 + 264 * q^76 - 280 * q^82 + 160 * q^85 - 912 * q^88 + 288 * q^91 - 1104 * q^94

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 $

$2$	−1.13516	−	1.64663i	−0.567582	−	0.823317i
$2$	−1.13516	−	1.64663i	−0.567582	−	0.823317i
$3$		0			0
$3$		0			0
$4$	−1.42280	+	3.73840i	−0.355700	+	0.934600i
$5$	2.41234	−	2.41234i	0.482467	−	0.482467i	−0.423451	−	0.905919i	$-0.639182\pi$
$5$	2.41234	−	2.41234i	0.482467	−	0.482467i	0.905919	+	0.423451i	$0.139182\pi$
$6$		0			0
$7$	−11.8718			−1.69598			−0.847988	−	0.530015i	$-0.822186\pi$
$7$	−11.8718			−1.69598			−0.847988	+	0.530015i	$0.822186\pi$
$8$	7.77089	−	1.90087i	0.971361	−	0.237609i
$9$		0			0
$10$	−6.71063	−	1.23383i	−0.671063	−	0.123383i
$11$	−11.9421	−	11.9421i	−1.08564	−	1.08564i	−0.995971	−	0.0896729i	$-0.971418\pi$
$11$	−11.9421	−	11.9421i	−1.08564	−	1.08564i	−0.0896729	−	0.995971i	$-0.528582\pi$
$12$		0			0
$13$	2.08177	+	2.08177i	0.160136	+	0.160136i	0.782627	−	0.622491i	$-0.213879\pi$
$13$	2.08177	+	2.08177i	0.160136	+	0.160136i	−0.622491	+	0.782627i	$0.713879\pi$
$14$	13.4765	+	19.5486i	0.962607	+	1.39633i
$15$		0			0
$16$	−11.9513	−	10.6380i	−0.746955	−	0.664875i
$17$	−23.1512			−1.36184			−0.680919	−	0.732359i	$-0.738419\pi$
$17$	−23.1512			−1.36184			−0.680919	+	0.732359i	$0.738419\pi$
$18$		0			0
$19$	−6.77297	+	6.77297i	−0.356472	+	0.356472i	−0.862511	−	0.506039i	$-0.831109\pi$
$19$	−6.77297	+	6.77297i	−0.356472	+	0.356472i	0.506039	+	0.862511i	$0.331109\pi$
$20$	5.58600	+	12.4506i	0.279300	+	0.622528i
$21$		0			0
$22$	−6.10800	+	33.2205i	−0.277636	+	1.51002i
$23$	3.92781			0.170774			0.0853872	−	0.996348i	$-0.472787\pi$
$23$	3.92781			0.170774			0.0853872	+	0.996348i	$0.472787\pi$
$24$		0			0
$25$			13.3613i			0.534450i
$26$	1.06476	−	5.79105i	0.0409522	−	0.222733i
$27$		0			0
$28$	16.8913	−	44.3817i	0.603259	−	1.58506i
$29$	0.782548	+	0.782548i	0.0269844	+	0.0269844i	0.720470	−	0.693486i	$-0.243926\pi$
$29$	0.782548	+	0.782548i	0.0269844	+	0.0269844i	−0.693486	+	0.720470i	$0.743926\pi$
$30$		0			0
$31$		−	2.65295i		−	0.0855792i	−0.999084	−	0.0427896i	$-0.986375\pi$
$31$		−	2.65295i		−	0.0855792i	0.999084	−	0.0427896i	$-0.0136245\pi$
$32$	−3.95022	+	31.7552i	−0.123444	+	0.992351i
$33$		0			0
$34$	26.2805	+	38.1216i	0.772955	+	1.12122i
$35$	−28.6389	+	28.6389i	−0.818253	+	0.818253i
$36$		0			0
$37$	37.2078	−	37.2078i	1.00562	−	1.00562i	0.00563338	−	0.999984i	$-0.498207\pi$
$37$	37.2078	−	37.2078i	1.00562	−	1.00562i	0.999984	−	0.00563338i	$-0.00179317\pi$
$38$	18.8410	+	3.46416i	0.495817	+	0.0911621i
$39$		0			0
$40$	14.1605	−	23.3315i	0.354012	−	0.583288i
$41$		−	69.1259i		−	1.68600i	−0.537916	−	0.842998i	$-0.680788\pi$
$41$		−	69.1259i		−	1.68600i	0.537916	−	0.842998i	$-0.319212\pi$
$42$		0			0
$43$	−29.2978	−	29.2978i	−0.681343	−	0.681343i	0.278960	−	0.960303i	$-0.410010\pi$
$43$	−29.2978	−	29.2978i	−0.681343	−	0.681343i	−0.960303	+	0.278960i	$0.910010\pi$
$44$	61.6355	−	27.6531i	1.40081	−	0.628479i
$45$		0			0
$46$	−4.45872	−	6.46767i	−0.0969286	−	0.140601i
$47$		−	68.0631i		−	1.44815i	−0.689720	−	0.724076i	$-0.742266\pi$
$47$		−	68.0631i		−	1.44815i	0.689720	−	0.724076i	$-0.257734\pi$
$48$		0			0
$49$	91.9405			1.87634
$50$	22.0011	−	15.1672i	0.440022	−	0.303345i
$51$		0			0
$52$	−10.7444	+	4.82053i	−0.206623	+	0.0927026i
$53$	−40.3674	+	40.3674i	−0.761649	+	0.761649i	−0.976620	−	0.214971i	$-0.931034\pi$
$53$	−40.3674	+	40.3674i	−0.761649	+	0.761649i	0.214971	+	0.976620i	$0.431034\pi$
$54$		0			0
$55$	−57.6167			−1.04758
$56$	−92.2547	+	22.5668i	−1.64741	+	0.402979i
$57$		0			0
$58$	0.400249	−	2.17689i	0.00690084	−	0.0375326i
$59$	23.5544	+	23.5544i	0.399227	+	0.399227i	0.877960	−	0.478734i	$-0.158904\pi$
$59$	23.5544	+	23.5544i	0.399227	+	0.399227i	−0.478734	+	0.877960i	$0.658904\pi$
$60$		0			0
$61$	65.9304	+	65.9304i	1.08083	+	1.08083i	0.996433	+	0.0843932i	$0.0268952\pi$
$61$	65.9304	+	65.9304i	1.08083	+	1.08083i	0.0843932	+	0.996433i	$0.473105\pi$
$62$	−4.36844	+	3.01154i	−0.0704588	+	0.0485732i
$63$		0			0
$64$	56.7734	−	29.5429i	0.887084	−	0.461607i
$65$	10.0438			0.154521
$66$		0			0
$67$	−40.9626	+	40.9626i	−0.611381	+	0.611381i	−0.943306	−	0.331925i	$-0.892302\pi$
$67$	−40.9626	+	40.9626i	−0.611381	+	0.611381i	0.331925	+	0.943306i	$0.392302\pi$
$68$	32.9396	−	86.5486i	0.484406	−	1.27277i
$69$		0			0
$70$	79.6675	+	14.6479i	1.13811	+	0.209255i
$71$	98.1885			1.38294			0.691468	−	0.722407i	$-0.256964\pi$
$71$	98.1885			1.38294			0.691468	+	0.722407i	$0.256964\pi$
$72$		0			0
$73$		−	74.2864i		−	1.01762i	−0.860878	−	0.508811i	$-0.830085\pi$
$73$		−	74.2864i		−	1.01762i	0.860878	−	0.508811i	$-0.169915\pi$
$74$	−103.505	−	19.0306i	−1.39871	−	0.257171i
$75$		0			0
$76$	−15.6835	−	34.9567i	−0.206362	−	0.459956i
$77$	141.774	+	141.774i	1.84123	+	1.84123i
$78$		0			0
$79$		−	0.779953i		−	0.00987283i	−0.999988	−	0.00493641i	$-0.998429\pi$
$79$		−	0.779953i		−	0.00987283i	0.999988	−	0.00493641i	$-0.00157132\pi$
$80$	−54.4929	+	3.16805i	−0.681162	+	0.0396006i
$81$		0			0
$82$	−113.825	+	78.4693i	−1.38811	+	0.956942i
$83$	−91.7887	+	91.7887i	−1.10589	+	1.10589i	−0.112202	+	0.993685i	$0.535790\pi$
$83$	−91.7887	+	91.7887i	−1.10589	+	1.10589i	−0.993685	+	0.112202i	$0.964210\pi$
$84$		0			0
$85$	−55.8486	+	55.8486i	−0.657042	+	0.657042i
$86$	−14.9849	+	81.5005i	−0.174243	+	0.947680i
$87$		0			0
$88$	−115.501	−	70.1003i	−1.31251	−	0.796594i
$89$		−	20.1568i		−	0.226481i	−0.993568	−	0.113240i	$-0.963877\pi$
$89$		−	20.1568i		−	0.226481i	0.993568	−	0.113240i	$-0.0361230\pi$
$90$		0			0
$91$	−24.7144	−	24.7144i	−0.271587	−	0.271587i
$92$	−5.58850	+	14.6837i	−0.0607445	+	0.159606i
$93$		0			0
$94$	−112.075	+	77.2629i	−1.19229	+	0.821946i
$95$			32.6774i			0.343972i
$96$		0			0
$97$	−86.6476			−0.893275			−0.446637	−	0.894715i	$-0.647379\pi$
$97$	−86.6476			−0.893275			−0.446637	+	0.894715i	$0.647379\pi$
$98$	−104.368	−	151.392i	−1.06498	−	1.54482i
$99$		0			0
$100$	−49.9497	−	19.0104i	−0.499497	−	0.190104i
$101$	58.6920	−	58.6920i	0.581109	−	0.581109i	−0.354099	−	0.935208i	$-0.615212\pi$
$101$	58.6920	−	58.6920i	0.581109	−	0.581109i	0.935208	+	0.354099i	$0.115212\pi$
$102$		0			0
$103$	34.6530			0.336436			0.168218	−	0.985750i	$-0.446199\pi$
$103$	34.6530			0.336436			0.168218	+	0.985750i	$0.446199\pi$
$104$	20.1343	+	12.2200i	0.193599	+	0.117500i
$105$		0			0
$106$	112.294	+	20.6466i	1.05938	+	0.194780i
$107$	−46.7828	−	46.7828i	−0.437223	−	0.437223i	0.453854	−	0.891076i	$-0.350049\pi$
$107$	−46.7828	−	46.7828i	−0.437223	−	0.437223i	−0.891076	+	0.453854i	$0.850049\pi$
$108$		0			0
$109$	−93.0565	−	93.0565i	−0.853729	−	0.853729i	0.136861	−	0.990590i	$-0.456299\pi$
$109$	−93.0565	−	93.0565i	−0.853729	−	0.853729i	−0.990590	+	0.136861i	$0.956299\pi$
$110$	65.4044	+	94.8735i	0.594586	+	0.862487i
$111$		0			0
$112$	141.884	+	126.293i	1.26682	+	1.12761i
$113$	−143.982			−1.27418			−0.637088	−	0.770791i	$-0.719861\pi$
$113$	−143.982			−1.27418			−0.637088	+	0.770791i	$0.719861\pi$
$114$		0			0
$115$	9.47521	−	9.47521i	0.0823931	−	0.0823931i
$116$	−4.03889	+	1.81207i	−0.0348180	+	0.0156213i
$117$		0			0
$118$	12.0473	−	65.5235i	0.102096	−	0.555284i
$119$	274.848			2.30965
$120$		0			0
$121$			164.227i			1.35725i
$122$	33.7213	−	183.405i	0.276404	−	1.50332i
$123$		0			0
$124$	9.91781	+	3.77463i	0.0799823	+	0.0304405i
$125$	92.5403	+	92.5403i	0.740322	+	0.740322i
$126$		0			0
$127$			47.3047i			0.372478i	0.982504	+	0.186239i	$0.0596299\pi$
$127$			47.3047i			0.372478i	−0.982504	+	0.186239i	$0.940370\pi$
$128$	−113.093	−	59.9489i	−0.883543	−	0.468351i
$129$		0			0
$130$	−11.4014	−	16.5385i	−0.0877032	−	0.127219i
$131$	−26.5360	+	26.5360i	−0.202565	+	0.202565i	−0.801098	−	0.598533i	$-0.795750\pi$
$131$	−26.5360	+	26.5360i	−0.202565	+	0.202565i	0.598533	+	0.801098i	$0.295750\pi$
$132$		0			0
$133$	80.4076	−	80.4076i	0.604568	−	0.604568i
$134$	113.950	+	20.9510i	0.850370	+	0.156351i
$135$		0			0
$136$	−179.906	+	44.0075i	−1.32284	+	0.323584i
$137$		−	122.806i		−	0.896391i	−0.893936	−	0.448196i	$-0.852067\pi$
$137$		−	122.806i		−	0.896391i	0.893936	−	0.448196i	$-0.147933\pi$
$138$		0			0
$139$	44.5369	+	44.5369i	0.320410	+	0.320410i	0.848924	−	0.528515i	$-0.177251\pi$
$139$	44.5369	+	44.5369i	0.320410	+	0.320410i	−0.528515	+	0.848924i	$0.677251\pi$
$140$	−66.3161	−	147.811i	−0.473687	−	1.05579i
$141$		0			0
$142$	−111.460	−	161.680i	−0.784930	−	1.13859i
$143$		−	49.7212i		−	0.347701i
$144$		0			0
$145$	3.77554			0.0260382
$146$	−122.322	+	84.3273i	−0.837825	+	0.577584i
$147$		0			0
$148$	86.1584	+	192.037i	0.582152	+	1.29755i
$149$	−27.5232	+	27.5232i	−0.184719	+	0.184719i	−0.793409	−	0.608689i	$-0.791696\pi$
$149$	−27.5232	+	27.5232i	−0.184719	+	0.184719i	0.608689	+	0.793409i	$0.291696\pi$
$150$		0			0
$151$	59.6723			0.395181			0.197590	−	0.980285i	$-0.436688\pi$
$151$	59.6723			0.395181			0.197590	+	0.980285i	$0.436688\pi$
$152$	−39.7575	+	65.5065i	−0.261562	+	0.430964i
$153$		0			0
$154$	72.5132	−	394.388i	0.470865	−	2.56096i
$155$	−6.39982	−	6.39982i	−0.0412892	−	0.0412892i
$156$		0			0
$157$	23.4479	+	23.4479i	0.149350	+	0.149350i	0.777827	−	0.628478i	$-0.216322\pi$
$157$	23.4479	+	23.4479i	0.149350	+	0.149350i	−0.628478	+	0.777827i	$0.716322\pi$
$158$	−1.28430	+	0.885376i	−0.00812846	+	0.00560364i
$159$		0			0
$160$	67.0751	+	86.1336i	0.419219	+	0.538335i
$161$	−46.6304			−0.289630
$162$		0			0
$163$	119.673	−	119.673i	0.734189	−	0.734189i	−0.237258	−	0.971447i	$-0.576249\pi$
$163$	119.673	−	119.673i	0.734189	−	0.734189i	0.971447	+	0.237258i	$0.0762487\pi$
$164$	258.420	+	98.3524i	1.57573	+	0.599710i
$165$		0			0
$166$	255.338	+	46.9470i	1.53818	+	0.282813i
$167$	−225.083			−1.34780			−0.673902	−	0.738820i	$-0.735383\pi$
$167$	−225.083			−1.34780			−0.673902	+	0.738820i	$0.735383\pi$
$168$		0			0
$169$		−	160.333i		−	0.948713i
$170$	155.360	+	28.5648i	0.913880	+	0.168028i
$171$		0			0
$172$	151.212	−	67.8419i	0.879138	−	0.394429i
$173$	−85.4327	−	85.4327i	−0.493830	−	0.493830i	0.415680	−	0.909511i	$-0.363544\pi$
$173$	−85.4327	−	85.4327i	−0.493830	−	0.493830i	−0.909511	+	0.415680i	$0.863544\pi$
$174$		0			0
$175$		−	158.623i		−	0.906415i
$176$	15.6832	+	269.763i	0.0891090	+	1.53274i
$177$		0			0
$178$	−33.1908	+	22.8813i	−0.186465	+	0.128546i
$179$	−159.342	+	159.342i	−0.890180	+	0.890180i	−0.994540	−	0.104360i	$-0.966721\pi$
$179$	−159.342	+	159.342i	−0.890180	+	0.890180i	0.104360	+	0.994540i	$0.466721\pi$
$180$		0			0
$181$	−127.296	+	127.296i	−0.703295	+	0.703295i	−0.965116	−	0.261821i	$-0.915677\pi$
$181$	−127.296	+	127.296i	−0.703295	+	0.703295i	0.261821	+	0.965116i	$0.415677\pi$
$182$	−12.6406	+	68.7504i	−0.0694539	+	0.377749i
$183$		0			0
$184$	30.5226	−	7.46626i	0.165884	−	0.0405775i
$185$		−	179.516i		−	0.970355i
$186$		0			0
$187$	276.474	+	276.474i	1.47847	+	1.47847i
$188$	254.447	+	96.8403i	1.35344	+	0.515108i
$189$		0			0
$190$	53.8076	−	37.0942i	0.283198	−	0.195233i
$191$		−	269.623i		−	1.41164i	−0.708392	−	0.705819i	$-0.750579\pi$
$191$		−	269.623i		−	1.41164i	0.708392	−	0.705819i	$-0.249421\pi$
$192$		0			0
$193$	−245.619			−1.27264			−0.636318	−	0.771427i	$-0.719544\pi$
$193$	−245.619			−1.27264			−0.636318	+	0.771427i	$0.719544\pi$
$194$	98.3593	+	142.677i	0.507007	+	0.735448i
$195$		0			0
$196$	−130.813	+	343.710i	−0.667414	+	1.75362i
$197$	−220.753	+	220.753i	−1.12057	+	1.12057i	−0.128917	+	0.991655i	$0.541150\pi$
$197$	−220.753	+	220.753i	−1.12057	+	1.12057i	−0.991655	+	0.128917i	$0.958850\pi$
$198$		0			0
$199$	231.414			1.16288			0.581441	−	0.813588i	$-0.302489\pi$
$199$	231.414			1.16288			0.581441	+	0.813588i	$0.302489\pi$
$200$	25.3980	+	103.829i	0.126990	+	0.519144i
$201$		0			0
$202$	−163.269	−	30.0191i	−0.808264	−	0.148609i
$203$	−9.29029	−	9.29029i	−0.0457650	−	0.0457650i
$204$		0			0
$205$	−166.755	−	166.755i	−0.813438	−	0.813438i
$206$	−39.3368	−	57.0607i	−0.190955	−	0.276994i
$207$		0			0
$208$	−2.73392	−	47.0256i	−0.0131438	−	0.226084i
$209$	161.767			0.774004
$210$		0			0
$211$	226.721	−	226.721i	1.07451	−	1.07451i	0.0775144	−	0.996991i	$-0.475302\pi$
$211$	226.721	−	226.721i	1.07451	−	1.07451i	0.996991	−	0.0775144i	$-0.0246984\pi$
$212$	−93.4747	−	208.344i	−0.440918	−	0.982756i
$213$		0			0
$214$	−23.9279	+	130.140i	−0.111813	+	0.608132i
$215$	−141.352			−0.657452
$216$		0			0
$217$			31.4954i			0.145140i
$218$	−47.5954	+	258.864i	−0.218328	+	1.18745i
$219$		0			0
$220$	81.9771	−	215.394i	0.372623	−	0.979064i
$221$	−48.1955	−	48.1955i	−0.218079	−	0.218079i
$222$		0			0
$223$			205.578i			0.921874i	0.887433	+	0.460937i	$0.152487\pi$
$223$			205.578i			0.921874i	−0.887433	+	0.460937i	$0.847513\pi$
$224$	46.8964	−	376.993i	0.209359	−	1.68300i
$225$		0			0
$226$	163.443	+	237.085i	0.723200	+	1.04905i
$227$	170.299	−	170.299i	0.750215	−	0.750215i	−0.224304	−	0.974519i	$-0.572011\pi$
$227$	170.299	−	170.299i	0.750215	−	0.750215i	0.974519	+	0.224304i	$0.0720109\pi$
$228$		0			0
$229$	−140.673	+	140.673i	−0.614293	+	0.614293i	−0.944062	−	0.329769i	$-0.893029\pi$
$229$	−140.673	+	140.673i	−0.614293	+	0.614293i	0.329769	+	0.944062i	$0.393029\pi$
$230$	−26.3581	−	4.84627i	−0.114601	−	0.0210707i
$231$		0			0
$232$	7.56862	+	4.59357i	0.0326234	+	0.0197999i
$233$			140.555i			0.603238i	0.953428	+	0.301619i	$0.0975271\pi$
$233$			140.555i			0.603238i	−0.953428	+	0.301619i	$0.902473\pi$
$234$		0			0
$235$	−164.191	−	164.191i	−0.698686	−	0.698686i
$236$	−121.569	+	54.5425i	−0.515122	+	0.231112i
$237$		0			0
$238$	−311.998	−	452.573i	−1.31091	−	1.90157i
$239$		−	48.3886i		−	0.202463i	−0.994863	−	0.101231i	$-0.967722\pi$
$239$		−	48.3886i		−	0.202463i	0.994863	−	0.101231i	$-0.0322783\pi$
$240$		0			0
$241$	−129.557			−0.537582			−0.268791	−	0.963198i	$-0.586624\pi$
$241$	−129.557			−0.537582			−0.268791	+	0.963198i	$0.586624\pi$
$242$	270.421	−	186.425i	1.11744	−	0.770349i
$243$		0			0
$244$	−340.280	+	152.668i	−1.39459	+	0.625690i
$245$	221.791	−	221.791i	0.905271	−	0.905271i
$246$		0			0
$247$	−28.1995			−0.114168
$248$	−5.04292	−	20.6158i	−0.0203344	−	0.0831283i
$249$		0			0
$250$	47.3314	−	257.428i	0.189326	−	1.02971i
$251$	−61.7026	−	61.7026i	−0.245827	−	0.245827i	0.573428	−	0.819256i	$-0.305613\pi$
$251$	−61.7026	−	61.7026i	−0.245827	−	0.245827i	−0.819256	+	0.573428i	$0.805613\pi$
$252$		0			0
$253$	−46.9063	−	46.9063i	−0.185400	−	0.185400i
$254$	77.8936	−	53.6987i	0.306668	−	0.211412i
$255$		0			0
$256$	29.6658	+	254.275i	0.115882	+	0.993263i
$257$	−242.911			−0.945181			−0.472590	−	0.881282i	$-0.656681\pi$
$257$	−242.911			−0.945181			−0.472590	+	0.881282i	$0.656681\pi$
$258$		0			0
$259$	−441.725	+	441.725i	−1.70550	+	1.70550i
$260$	−14.2904	+	37.5479i	−0.0549630	+	0.144415i
$261$		0			0
$262$	73.8177	+	13.5723i	0.281747	+	0.0518027i
$263$	5.18268			0.0197060			0.00985301	−	0.999951i	$-0.496864\pi$
$263$	5.18268			0.0197060			0.00985301	+	0.999951i	$0.496864\pi$
$264$		0			0
$265$			194.760i			0.734942i
$266$	−223.678	−	41.1259i	−0.840894	−	0.154609i
$267$		0			0
$268$	−94.8528	−	211.416i	−0.353929	−	0.788866i
$269$	−202.350	−	202.350i	−0.752230	−	0.752230i	0.222665	−	0.974895i	$-0.428524\pi$
$269$	−202.350	−	202.350i	−0.752230	−	0.752230i	−0.974895	+	0.222665i	$0.928524\pi$
$270$		0			0
$271$		−	42.0616i		−	0.155209i	−0.996984	−	0.0776044i	$-0.975273\pi$
$271$		−	42.0616i		−	0.155209i	0.996984	−	0.0776044i	$-0.0247271\pi$
$272$	276.687	+	246.283i	1.01723	+	0.905452i
$273$		0			0
$274$	−202.216	+	139.405i	−0.738014	+	0.508776i
$275$	159.561	−	159.561i	0.580223	−	0.580223i
$276$		0			0
$277$	117.767	−	117.767i	0.425151	−	0.425151i	−0.461822	−	0.886973i	$-0.652804\pi$
$277$	117.767	−	117.767i	0.425151	−	0.425151i	0.886973	+	0.461822i	$0.152804\pi$
$278$	22.7792	−	123.893i	0.0819397	−	0.445657i
$279$		0			0
$280$	−168.111	+	276.988i	−0.600395	+	0.989243i
$281$			186.670i			0.664307i	0.943225	+	0.332153i	$0.107775\pi$
$281$			186.670i			0.664307i	−0.943225	+	0.332153i	$0.892225\pi$
$282$		0			0
$283$	−233.633	−	233.633i	−0.825557	−	0.825557i	0.161342	−	0.986899i	$-0.448418\pi$
$283$	−233.633	−	233.633i	−0.825557	−	0.825557i	−0.986899	+	0.161342i	$0.948418\pi$
$284$	−139.703	+	367.068i	−0.491911	+	1.29249i
$285$		0			0
$286$	−81.8726	+	56.4418i	−0.286268	+	0.197349i
$287$			820.651i			2.85941i
$288$		0			0
$289$	246.980			0.854603
$290$	−4.28586	−	6.21693i	−0.0147788	−	0.0214377i
$291$		0			0
$292$	277.712	+	105.695i	0.951069	+	0.361968i
$293$	189.454	−	189.454i	0.646602	−	0.646602i	−0.305568	−	0.952170i	$-0.598846\pi$
$293$	189.454	−	189.454i	0.646602	−	0.646602i	0.952170	+	0.305568i	$0.0988464\pi$
$294$		0			0
$295$	113.642			0.385228
$296$	218.411	−	359.865i	0.737874	−	1.21576i
$297$		0			0
$298$	76.5639	+	14.0772i	0.256926	+	0.0472390i
$299$	8.17678	+	8.17678i	0.0273471	+	0.0273471i
$300$		0			0
$301$	347.818	+	347.818i	1.15554	+	1.15554i
$302$	−67.7379	−	98.2583i	−0.224298	−	0.325359i
$303$		0			0
$304$	152.996	−	8.89474i	0.503278	−	0.0292590i
$305$	318.093			1.04293
$306$		0			0
$307$	37.1123	−	37.1123i	0.120887	−	0.120887i	−0.644075	−	0.764962i	$-0.722758\pi$
$307$	37.1123	−	37.1123i	0.120887	−	0.120887i	0.764962	+	0.644075i	$0.222758\pi$
$308$	−731.727	+	328.293i	−2.37574	+	1.06589i
$309$		0			0
$310$	−3.27331	+	17.8030i	−0.0105590	+	0.0574291i
$311$	18.2210			0.0585884			0.0292942	−	0.999571i	$-0.490674\pi$
$311$	18.2210			0.0585884			0.0292942	+	0.999571i	$0.490674\pi$
$312$		0			0
$313$		−	481.905i		−	1.53963i	−0.638265	−	0.769816i	$-0.720348\pi$
$313$		−	481.905i		−	1.53963i	0.638265	−	0.769816i	$-0.279652\pi$
$314$	11.9928	−	65.2273i	0.0381938	−	0.207730i
$315$		0			0
$316$	2.91578	+	1.10972i	0.00922715	+	0.00351177i
$317$	63.1197	+	63.1197i	0.199116	+	0.199116i	0.799621	−	0.600505i	$-0.205034\pi$
$317$	63.1197	+	63.1197i	0.199116	+	0.199116i	−0.600505	+	0.799621i	$0.705034\pi$
$318$		0			0
$319$		−	18.6905i		−	0.0585910i
$320$	65.6892	−	208.224i	0.205279	−	0.650700i
$321$		0			0
$322$	52.9331	+	76.7831i	0.164389	+	0.238457i
$323$	156.803	−	156.803i	0.485457	−	0.485457i
$324$		0			0
$325$	−27.8150	+	27.8150i	−0.0855846	+	0.0855846i
$326$	−332.905	−	61.2088i	−1.02118	−	0.187757i
$327$		0			0
$328$	−131.399	−	537.169i	−0.400607	−	1.63771i
$329$			808.034i			2.45603i
$330$		0			0
$331$	21.7753	+	21.7753i	0.0657865	+	0.0657865i	0.739235	−	0.673448i	$-0.235187\pi$
$331$	21.7753	+	21.7753i	0.0657865	+	0.0657865i	−0.673448	+	0.739235i	$0.735187\pi$
$332$	−212.546	−	473.740i	−0.640198	−	1.42693i
$333$		0			0
$334$	255.507	+	370.630i	0.764990	+	1.10967i
$335$			197.631i			0.589943i
$336$		0			0
$337$	91.1781			0.270558			0.135279	−	0.990808i	$-0.456807\pi$
$337$	91.1781			0.270558			0.135279	+	0.990808i	$0.456807\pi$
$338$	−264.009	+	182.004i	−0.781091	+	0.538473i
$339$		0			0
$340$	−129.323	−	288.246i	−0.380362	−	0.847782i
$341$	−31.6818	+	31.6818i	−0.0929085	+	0.0929085i
$342$		0			0
$343$	−509.782			−1.48625
$344$	−283.361	−	171.978i	−0.823723	−	0.499937i
$345$		0			0
$346$	−43.6961	+	237.656i	−0.126289	+	0.686868i
$347$	375.508	+	375.508i	1.08216	+	1.08216i	0.996308	+	0.0858482i	$0.0273600\pi$
$347$	375.508	+	375.508i	1.08216	+	1.08216i	0.0858482	+	0.996308i	$0.472640\pi$
$348$		0			0
$349$	−175.613	−	175.613i	−0.503189	−	0.503189i	0.409238	−	0.912428i	$-0.365794\pi$
$349$	−175.613	−	175.613i	−0.503189	−	0.503189i	−0.912428	+	0.409238i	$0.865794\pi$
$350$	−261.193	+	180.063i	−0.746267	+	0.514465i
$351$		0			0
$352$	426.398	−	332.050i	1.21136	−	0.943324i
$353$	322.470			0.913514			0.456757	−	0.889592i	$-0.349011\pi$
$353$	322.470			0.913514			0.456757	+	0.889592i	$0.349011\pi$
$354$		0			0
$355$	236.864	−	236.864i	0.667222	−	0.667222i
$356$	75.3541	+	28.6791i	0.211669	+	0.0805592i
$357$		0			0
$358$	443.258	+	81.4985i	1.23815	+	0.227649i
$359$	−100.748			−0.280636			−0.140318	−	0.990107i	$-0.544812\pi$
$359$	−100.748			−0.280636			−0.140318	+	0.990107i	$0.544812\pi$
$360$		0			0
$361$			269.254i			0.745855i
$362$	354.113	+	65.1081i	0.978213	+	0.179857i
$363$		0			0
$364$	127.556	−	57.2286i	0.350428	−	0.157221i
$365$	−179.204	−	179.204i	−0.490969	−	0.490969i
$366$		0			0
$367$		−	220.387i		−	0.600509i	−0.953859	−	0.300255i	$-0.902928\pi$
$367$		−	220.387i		−	0.600509i	0.953859	−	0.300255i	$-0.0970717\pi$
$368$	−46.9424	−	41.7841i	−0.127561	−	0.113544i
$369$		0			0
$370$	−295.597	+	203.780i	−0.798910	+	0.550757i
$371$	479.235	−	479.235i	1.29174	−	1.29174i
$372$		0			0
$373$	257.247	−	257.247i	0.689671	−	0.689671i	−0.272488	−	0.962159i	$-0.587846\pi$
$373$	257.247	−	257.247i	0.689671	−	0.689671i	0.962159	+	0.272488i	$0.0878464\pi$
$374$	141.408	−	769.095i	0.378096	−	2.05640i
$375$		0			0
$376$	−129.379	−	528.911i	−0.344093	−	1.40668i
$377$			3.25816i			0.00864234i
$378$		0			0
$379$	466.048	+	466.048i	1.22968	+	1.22968i	0.964086	+	0.265592i	$0.0855674\pi$
$379$	466.048	+	466.048i	1.22968	+	1.22968i	0.265592	+	0.964086i	$0.414433\pi$
$380$	−122.161	−	46.4934i	−0.321477	−	0.122351i
$381$		0			0
$382$	−443.970	+	306.066i	−1.16222	+	0.801221i
$383$		−	416.164i		−	1.08659i	−0.839541	−	0.543296i	$-0.817176\pi$
$383$		−	416.164i		−	1.08659i	0.839541	−	0.543296i	$-0.182824\pi$
$384$		0			0
$385$	684.016			1.77666
$386$	278.818	+	404.444i	0.722326	+	1.04778i
$387$		0			0
$388$	123.282	−	323.924i	0.317738	−	0.834854i
$389$	−80.1982	+	80.1982i	−0.206165	+	0.206165i	−0.802635	−	0.596470i	$-0.796569\pi$
$389$	−80.1982	+	80.1982i	−0.206165	+	0.206165i	0.596470	+	0.802635i	$0.296569\pi$
$390$		0			0
$391$	−90.9338			−0.232567
$392$	714.459	−	174.767i	1.82260	−	0.445834i
$393$		0			0
$394$	614.089	+	112.908i	1.55860	+	0.286569i
$395$	−1.88151	−	1.88151i	−0.00476332	−	0.00476332i
$396$		0			0
$397$	347.220	+	347.220i	0.874610	+	0.874610i	0.992971	−	0.118360i	$-0.0377638\pi$
$397$	347.220	+	347.220i	0.874610	+	0.874610i	−0.118360	+	0.992971i	$0.537764\pi$
$398$	−262.693	−	381.053i	−0.660032	−	0.957420i
$399$		0			0
$400$	142.137	−	159.684i	0.355343	−	0.399210i
$401$	464.444			1.15821			0.579107	−	0.815251i	$-0.303401\pi$
$401$	464.444			1.15821			0.579107	+	0.815251i	$0.303401\pi$
$402$		0			0
$403$	5.52283	−	5.52283i	0.0137043	−	0.0137043i
$404$	135.907	+	302.921i	0.336404	+	0.749806i
$405$		0			0
$406$	−4.75169	+	25.8437i	−0.0117037	+	0.0636544i
$407$	−888.679			−2.18349
$408$		0			0
$409$			93.6191i			0.228898i	0.993429	+	0.114449i	$0.0365102\pi$
$409$			93.6191i			0.228898i	−0.993429	+	0.114449i	$0.963490\pi$
$410$	−85.2898	+	463.878i	−0.208024	+	1.13141i
$411$		0			0
$412$	−49.3043	+	129.547i	−0.119671	+	0.314434i
$413$	−279.634	−	279.634i	−0.677079	−	0.677079i
$414$		0			0
$415$			442.850i			1.06711i
$416$	−74.3304	+	57.8835i	−0.178679	+	0.139143i
$417$		0			0
$418$	−183.632	−	266.371i	−0.439311	−	0.637250i
$419$	−166.970	+	166.970i	−0.398497	+	0.398497i	−0.877703	−	0.479206i	$-0.840925\pi$
$419$	−166.970	+	166.970i	−0.398497	+	0.398497i	0.479206	+	0.877703i	$0.340925\pi$
$420$		0			0
$421$	201.491	−	201.491i	0.478600	−	0.478600i	−0.426083	−	0.904684i	$-0.640107\pi$
$421$	201.491	−	201.491i	0.478600	−	0.478600i	0.904684	+	0.426083i	$0.140107\pi$
$422$	−630.691	−	115.960i	−1.49453	−	0.274788i
$423$		0			0
$424$	−236.957	+	390.424i	−0.558862	+	0.920811i
$425$		−	309.330i		−	0.727835i
$426$		0			0
$427$	−782.715	−	782.715i	−1.83306	−	1.83306i
$428$	241.456	−	108.330i	0.564148	−	0.253108i
$429$		0			0
$430$	160.458	+	232.755i	0.373158	+	0.541291i
$431$			158.438i			0.367606i	0.982963	+	0.183803i	$0.0588409\pi$
$431$			158.438i			0.367606i	−0.982963	+	0.183803i	$0.941159\pi$
$432$		0			0
$433$	−178.566			−0.412393			−0.206197	−	0.978511i	$-0.566109\pi$
$433$	−178.566			−0.412393			−0.206197	+	0.978511i	$0.566109\pi$
$434$	51.8614	−	35.7525i	0.119496	−	0.0823791i
$435$		0			0
$436$	480.283	−	215.481i	1.10157	−	0.494223i
$437$	−26.6030	+	26.6030i	−0.0608763	+	0.0608763i
$438$		0			0
$439$	−702.502			−1.60023			−0.800116	−	0.599845i	$-0.795229\pi$
$439$	−702.502			−1.60023			−0.800116	+	0.599845i	$0.795229\pi$
$440$	−447.733	+	109.522i	−1.01757	+	0.248913i
$441$		0			0
$442$	−24.6504	+	134.070i	−0.0557702	+	0.303326i
$443$	118.984	+	118.984i	0.268587	+	0.268587i	0.828531	−	0.559943i	$-0.189177\pi$
$443$	118.984	+	118.984i	0.268587	+	0.268587i	−0.559943	+	0.828531i	$0.689177\pi$
$444$		0			0
$445$	−48.6249	−	48.6249i	−0.109270	−	0.109270i
$446$	338.511	−	233.365i	0.758994	−	0.523239i
$447$		0			0
$448$	−674.004	+	350.728i	−1.50447	+	0.782875i
$449$	504.107			1.12273			0.561366	−	0.827567i	$-0.310276\pi$
$449$	504.107			1.12273			0.561366	+	0.827567i	$0.310276\pi$
$450$		0			0
$451$	−825.507	+	825.507i	−1.83039	+	1.83039i
$452$	204.858	−	538.262i	0.453225	−	1.19085i
$453$		0			0
$454$	−473.737	−	87.1024i	−1.04347	−	0.191856i
$455$	−119.239			−0.262063
$456$		0			0
$457$			392.141i			0.858077i	0.903286	+	0.429039i	$0.141148\pi$
$457$			392.141i			0.858077i	−0.903286	+	0.429039i	$0.858852\pi$
$458$	391.324	+	71.9498i	0.854420	+	0.157096i
$459$		0			0
$460$	21.9408	+	48.9035i	0.0476974	+	0.106312i
$461$	−174.727	−	174.727i	−0.379017	−	0.379017i	0.491731	−	0.870747i	$-0.336365\pi$
$461$	−174.727	−	174.727i	−0.379017	−	0.379017i	−0.870747	+	0.491731i	$0.836365\pi$
$462$		0			0
$463$		−	769.387i		−	1.66174i	−0.556464	−	0.830872i	$-0.687842\pi$
$463$		−	769.387i		−	1.66174i	0.556464	−	0.830872i	$-0.312158\pi$
$464$	−1.02770	−	17.6772i	−0.00221487	−	0.0380974i
$465$		0			0
$466$	231.442	−	159.553i	0.496656	−	0.342387i
$467$	238.009	−	238.009i	0.509656	−	0.509656i	−0.404765	−	0.914421i	$-0.632647\pi$
$467$	238.009	−	238.009i	0.509656	−	0.509656i	0.914421	+	0.404765i	$0.132647\pi$
$468$		0			0
$469$	486.301	−	486.301i	1.03689	−	1.03689i
$470$	−83.9786	+	456.747i	−0.178678	+	0.971802i
$471$		0			0
$472$	227.812	+	138.265i	0.482653	+	0.292934i
$473$			699.753i			1.47939i
$474$		0			0
$475$	−90.4954	−	90.4954i	−0.190517	−	0.190517i
$476$	−391.054	+	1027.49i	−0.821542	+	2.15859i
$477$		0			0
$478$	−79.6783	+	54.9291i	−0.166691	+	0.114914i
$479$			98.2671i			0.205151i	0.994725	+	0.102575i	$0.0327083\pi$
$479$			98.2671i			0.205151i	−0.994725	+	0.102575i	$0.967292\pi$
$480$		0			0
$481$	154.916			0.322071
$482$	147.069	+	213.333i	0.305122	+	0.442600i
$483$		0			0
$484$	−613.946	−	233.662i	−1.26848	−	0.482773i
$485$	−209.023	+	209.023i	−0.430976	+	0.430976i
$486$		0			0
$487$	385.471			0.791522			0.395761	−	0.918353i	$-0.370481\pi$
$487$	385.471			0.791522			0.395761	+	0.918353i	$0.370481\pi$
$488$	637.662	+	387.013i	1.30669	+	0.793058i
$489$		0			0
$490$	−616.979	−	113.439i	−1.25914	−	0.231509i
$491$	118.148	+	118.148i	0.240627	+	0.240627i	0.817109	−	0.576483i	$-0.195575\pi$
$491$	118.148	+	118.148i	0.240627	+	0.240627i	−0.576483	+	0.817109i	$0.695575\pi$
$492$		0			0
$493$	−18.1170	−	18.1170i	−0.0367484	−	0.0367484i
$494$	32.0110	+	46.4342i	0.0647997	+	0.0939963i
$495$		0			0
$496$	−28.2221	+	31.7062i	−0.0568995	+	0.0639238i
$497$	−1165.68			−2.34543
$498$		0			0
$499$	215.550	−	215.550i	0.431964	−	0.431964i	−0.457332	−	0.889296i	$-0.651195\pi$
$499$	215.550	−	215.550i	0.431964	−	0.431964i	0.889296	+	0.457332i	$0.151195\pi$
$500$	−477.619	+	214.286i	−0.955238	+	0.428572i
$501$		0			0
$502$	−31.5589	+	171.644i	−0.0628664	+	0.341921i
$503$	58.9526			0.117202			0.0586010	−	0.998281i	$-0.481336\pi$
$503$	58.9526			0.117202			0.0586010	+	0.998281i	$0.481336\pi$
$504$		0			0
$505$		−	283.170i		−	0.560733i
$506$	−23.9911	+	130.484i	−0.0474132	+	0.257873i
$507$		0			0
$508$	−176.844	−	67.3053i	−0.348118	−	0.132491i
$509$	−612.268	−	612.268i	−1.20288	−	1.20288i	−0.973285	−	0.229600i	$-0.926258\pi$
$509$	−612.268	−	612.268i	−1.20288	−	1.20288i	−0.229600	−	0.973285i	$-0.573742\pi$
$510$		0			0
$511$			881.916i			1.72586i
$512$	385.023	−	337.493i	0.751997	−	0.659166i
$513$		0			0
$514$	275.745	+	399.986i	0.536468	+	0.778183i
$515$	83.5946	−	83.5946i	0.162320	−	0.162320i
$516$		0			0
$517$	−812.816	+	812.816i	−1.57218	+	1.57218i
$518$	1228.79	+	225.929i	2.37218	+	0.436156i
$519$		0			0
$520$	78.0495	−	19.0920i	0.150095	−	0.0367154i
$521$		−	562.971i		−	1.08056i	−0.841486	−	0.540279i	$-0.818319\pi$
$521$		−	562.971i		−	1.08056i	0.841486	−	0.540279i	$-0.181681\pi$
$522$		0			0
$523$	104.076	+	104.076i	0.198998	+	0.198998i	0.799571	−	0.600572i	$-0.205060\pi$
$523$	104.076	+	104.076i	0.198998	+	0.198998i	−0.600572	+	0.799571i	$0.705060\pi$
$524$	−61.4467	−	136.958i	−0.117265	−	0.261369i
$525$		0			0
$526$	−5.88320	−	8.53398i	−0.0111848	−	0.0162243i
$527$			61.4192i			0.116545i
$528$		0			0
$529$	−513.572			−0.970836
$530$	320.698	−	221.084i	0.605090	−	0.417140i
$531$		0			0
$532$	186.192	+	415.000i	0.349984	+	0.780075i
$533$	143.904	−	143.904i	0.269988	−	0.269988i
$534$		0			0
$535$	−225.712			−0.421891
$536$	−240.451	+	396.180i	−0.448603	+	0.739141i
$537$		0			0
$538$	−103.496	+	562.897i	−0.192371	+	1.04628i
$539$	−1097.96	−	1097.96i	−2.03703	−	2.03703i
$540$		0			0
$541$	−209.794	−	209.794i	−0.387788	−	0.387788i	0.486109	−	0.873898i	$-0.338416\pi$
$541$	−209.794	−	209.794i	−0.387788	−	0.387788i	−0.873898	+	0.486109i	$0.838416\pi$
$542$	−69.2600	+	47.7468i	−0.127786	+	0.0880938i
$543$		0			0
$544$	91.4526	−	735.174i	0.168111	−	1.35142i
$545$	−448.967			−0.823793
$546$		0			0
$547$	283.251	−	283.251i	0.517827	−	0.517827i	−0.399086	−	0.916913i	$-0.630673\pi$
$547$	283.251	−	283.251i	0.517827	−	0.517827i	0.916913	+	0.399086i	$0.130673\pi$
$548$	459.096	+	174.728i	0.837767	+	0.318847i
$549$		0			0
$550$	−443.867	−	81.6106i	−0.807032	−	0.148383i
$551$	−10.6004			−0.0192384
$552$		0			0
$553$			9.25948i			0.0167441i
$554$	−327.604	−	60.2340i	−0.591342	−	0.108726i
$555$		0			0
$556$	−229.864	+	103.130i	−0.413425	+	0.185485i
$557$	316.798	+	316.798i	0.568758	+	0.568758i	0.931781	−	0.363022i	$-0.118255\pi$
$557$	316.798	+	316.798i	0.568758	+	0.568758i	−0.363022	+	0.931781i	$0.618255\pi$
$558$		0			0
$559$		−	121.982i		−	0.218215i
$560$	646.931	−	37.6106i	1.15523	−	0.0671617i
$561$		0			0
$562$	307.377	−	211.901i	0.546935	−	0.377049i
$563$	−298.317	+	298.317i	−0.529871	+	0.529871i	−0.920534	−	0.390663i	$-0.872246\pi$
$563$	−298.317	+	298.317i	−0.529871	+	0.529871i	0.390663	+	0.920534i	$0.372246\pi$
$564$		0			0
$565$	−347.333	+	347.333i	−0.614748	+	0.614748i
$566$	−119.496	+	649.919i	−0.211123	+	1.14827i
$567$		0			0
$568$	763.012	−	186.643i	1.34333	−	0.328598i
$569$			24.9852i			0.0439107i	0.999759	+	0.0219553i	$0.00698916\pi$
$569$			24.9852i			0.0439107i	−0.999759	+	0.0219553i	$0.993011\pi$
$570$		0			0
$571$	739.901	+	739.901i	1.29580	+	1.29580i	0.931142	+	0.364657i	$0.118814\pi$
$571$	739.901	+	739.901i	1.29580	+	1.29580i	0.364657	+	0.931142i	$0.381186\pi$
$572$	185.878	+	70.7434i	0.324961	+	0.123677i
$573$		0			0
$574$	1351.31	−	931.574i	2.35420	−	1.62295i
$575$			52.4805i			0.0912705i
$576$		0			0
$577$	−120.741			−0.209256			−0.104628	−	0.994511i	$-0.533365\pi$
$577$	−120.741			−0.209256			−0.104628	+	0.994511i	$0.533365\pi$
$578$	−280.363	−	406.686i	−0.485057	−	0.703608i
$579$		0			0
$580$	−5.37185	+	14.1145i	−0.00926180	+	0.0243353i
$581$	1089.70	−	1089.70i	1.87556	−	1.87556i
$582$		0			0
$583$	964.142			1.65376
$584$	−141.209	−	577.271i	−0.241796	−	0.988478i
$585$		0			0
$586$	−527.024	−	96.8999i	−0.899358	−	0.165358i
$587$	83.1502	+	83.1502i	0.141653	+	0.141653i	0.774377	−	0.632724i	$-0.218063\pi$
$587$	83.1502	+	83.1502i	0.141653	+	0.141653i	−0.632724	+	0.774377i	$0.718063\pi$
$588$		0			0
$589$	17.9684	+	17.9684i	0.0305066	+	0.0305066i
$590$	−129.003	−	187.127i	−0.218648	−	0.317164i
$591$		0			0
$592$	−840.498	+	48.8640i	−1.41976	+	0.0825405i
$593$	135.037			0.227719			0.113859	−	0.993497i	$-0.463679\pi$
$593$	135.037			0.227719			0.113859	+	0.993497i	$0.463679\pi$
$594$		0			0
$595$	663.025	−	663.025i	1.11433	−	1.11433i
$596$	−63.7326	−	142.053i	−0.106934	−	0.238343i
$597$		0			0
$598$	4.18217	−	22.7462i	0.00699359	−	0.0380371i
$599$	244.844			0.408755			0.204377	−	0.978892i	$-0.434483\pi$
$599$	244.844			0.408755			0.204377	+	0.978892i	$0.434483\pi$
$600$		0			0
$601$		−	765.274i		−	1.27333i	−0.771139	−	0.636667i	$-0.780313\pi$
$601$		−	765.274i		−	1.27333i	0.771139	−	0.636667i	$-0.219687\pi$
$602$	177.898	−	967.560i	0.295512	−	1.60724i
$603$		0			0
$604$	−84.9018	+	223.079i	−0.140566	+	0.369336i
$605$	396.171	+	396.171i	0.654827	+	0.654827i
$606$		0			0
$607$		−	546.253i		−	0.899923i	−0.893048	−	0.449961i	$-0.851438\pi$
$607$		−	546.253i		−	0.899923i	0.893048	−	0.449961i	$-0.148562\pi$
$608$	−188.323	−	241.832i	−0.309741	−	0.397750i
$609$		0			0
$610$	−361.087	−	523.782i	−0.591947	−	0.858659i
$611$	141.691	−	141.691i	0.231901	−	0.231901i
$612$		0			0
$613$	11.8818	−	11.8818i	0.0193830	−	0.0193830i	−0.697349	−	0.716732i	$-0.745637\pi$
$613$	11.8818	−	11.8818i	0.0193830	−	0.0193830i	0.716732	+	0.697349i	$0.245637\pi$
$614$	−103.239	−	18.9818i	−0.168142	−	0.0309150i
$615$		0			0
$616$	1371.21	+	832.219i	2.22599	+	1.35100i
$617$		−	72.2000i		−	0.117018i	−0.998287	−	0.0585089i	$-0.981365\pi$
$617$		−	72.2000i		−	0.117018i	0.998287	−	0.0585089i	$-0.0186346\pi$
$618$		0			0
$619$	−265.473	−	265.473i	−0.428874	−	0.428874i	0.459371	−	0.888245i	$-0.348075\pi$
$619$	−265.473	−	265.473i	−0.428874	−	0.428874i	−0.888245	+	0.459371i	$0.848075\pi$
$620$	33.0308	−	14.8194i	0.0532754	−	0.0239023i
$621$		0			0
$622$	−20.6838	−	30.0033i	−0.0332537	−	0.0482368i
$623$			239.298i			0.384106i
$624$		0			0
$625$	112.445			0.179912
$626$	−793.521	+	547.042i	−1.26761	+	0.873868i
$627$		0			0
$628$	−121.019	+	54.2959i	−0.192706	+	0.0864584i
$629$	−861.408	+	861.408i	−1.36949	+	1.36949i
$630$		0			0
$631$	343.644			0.544602			0.272301	−	0.962212i	$-0.412215\pi$
$631$	343.644			0.544602			0.272301	+	0.962212i	$0.412215\pi$
$632$	−1.48259	−	6.06093i	−0.00234587	−	0.00959008i
$633$		0			0
$634$	32.2837	−	175.586i	0.0509207	−	0.276950i
$635$	114.115	+	114.115i	0.179709	+	0.179709i
$636$		0			0
$637$	191.398	+	191.398i	0.300469	+	0.300469i
$638$	−30.7764	+	21.2168i	−0.0482389	+	0.0332552i
$639$		0			0
$640$	−417.436	+	128.202i	−0.652245	+	0.200316i
$641$	158.821			0.247771			0.123885	−	0.992297i	$-0.460465\pi$
$641$	158.821			0.247771			0.123885	+	0.992297i	$0.460465\pi$
$642$		0			0
$643$	−576.120	+	576.120i	−0.895988	+	0.895988i	−0.995078	−	0.0990902i	$-0.968407\pi$
$643$	−576.120	+	576.120i	−0.895988	+	0.895988i	0.0990902	+	0.995078i	$0.468407\pi$
$644$	66.3457	−	174.323i	0.103021	−	0.270688i
$645$		0			0
$646$	−436.193	−	80.1996i	−0.675222	−	0.124148i
$647$	750.114			1.15937			0.579686	−	0.814840i	$-0.303175\pi$
$647$	750.114			1.15937			0.579686	+	0.814840i	$0.303175\pi$
$648$		0			0
$649$		−	562.577i		−	0.866836i
$650$	77.3757	+	14.2265i	0.119040	+	0.0218869i
$651$		0			0
$652$	277.114	+	617.655i	0.425022	+	0.947324i
$653$	631.097	+	631.097i	0.966458	+	0.966458i	0.999455	−	0.0329977i	$-0.0105054\pi$
$653$	631.097	+	631.097i	0.966458	+	0.966458i	−0.0329977	+	0.999455i	$0.510505\pi$
$654$		0			0
$655$			128.027i			0.195462i
$656$	−735.361	+	826.142i	−1.12098	+	1.25936i
$657$		0			0
$658$	1330.54	−	917.252i	2.02209	−	1.39400i
$659$	−555.313	+	555.313i	−0.842659	+	0.842659i	−0.989204	−	0.146545i	$-0.953185\pi$
$659$	−555.313	+	555.313i	−0.842659	+	0.842659i	0.146545	+	0.989204i	$0.453185\pi$
$660$		0			0
$661$	75.6151	−	75.6151i	0.114395	−	0.114395i	−0.647592	−	0.761987i	$-0.724224\pi$
$661$	75.6151	−	75.6151i	0.114395	−	0.114395i	0.761987	+	0.647592i	$0.224224\pi$
$662$	11.1374	−	60.5745i	0.0168238	−	0.0915023i
$663$		0			0
$664$	−538.801	+	887.758i	−0.811448	+	1.33698i
$665$		−	387.940i		−	0.583369i
$666$		0			0
$667$	3.07370	+	3.07370i	0.00460825	+	0.00460825i
$668$	320.249	−	841.452i	0.479415	−	1.25966i
$669$		0			0
$670$	325.426	−	224.344i	0.485710	−	0.334841i
$671$		−	1574.69i		−	2.34678i
$672$		0			0
$673$	−317.869			−0.472317			−0.236158	−	0.971715i	$-0.575888\pi$
$673$	−317.869			−0.472317			−0.236158	+	0.971715i	$0.575888\pi$
$674$	−103.502	−	150.137i	−0.153564	−	0.222755i
$675$		0			0
$676$	599.387	+	228.121i	0.886667	+	0.337458i
$677$	−621.736	+	621.736i	−0.918370	+	0.918370i	−0.996911	−	0.0785409i	$-0.974974\pi$
$677$	−621.736	+	621.736i	−0.918370	+	0.918370i	0.0785409	+	0.996911i	$0.474974\pi$
$678$		0			0
$679$	1028.67			1.51497
$680$	−327.832	+	540.154i	−0.482106	+	0.794344i
$681$		0			0
$682$	88.1324	+	16.2042i	0.129226	+	0.0237599i
$683$	438.781	+	438.781i	0.642431	+	0.642431i	0.951153	−	0.308721i	$-0.0999010\pi$
$683$	438.781	+	438.781i	0.642431	+	0.642431i	−0.308721	+	0.951153i	$0.599901\pi$
$684$		0			0
$685$	−296.248	−	296.248i	−0.432480	−	0.432480i
$686$	578.687	+	839.425i	0.843567	+	1.22365i
$687$		0			0
$688$	38.4759	+	661.815i	0.0559242	+	0.961941i
$689$	−168.071			−0.243935
$690$		0			0
$691$	418.978	−	418.978i	0.606336	−	0.606336i	−0.335651	−	0.941987i	$-0.608956\pi$
$691$	418.978	−	418.978i	0.606336	−	0.606336i	0.941987	+	0.335651i	$0.108956\pi$
$692$	440.935	−	197.828i	0.637190	−	0.285878i
$693$		0			0
$694$	192.061	−	1044.59i	0.276744	−	1.50517i
$695$	214.876			0.309174
$696$		0			0
$697$			1600.35i			2.29605i
$698$	−89.8205	+	488.520i	−0.128683	+	0.699885i
$699$		0			0
$700$	592.995	+	225.689i	0.847136	+	0.322412i
$701$	244.043	+	244.043i	0.348136	+	0.348136i	0.859415	−	0.511279i	$-0.170828\pi$
$701$	244.043	+	244.043i	0.348136	+	0.348136i	−0.511279	+	0.859415i	$0.670828\pi$
$702$		0			0
$703$			504.015i			0.716949i
$704$	−1030.80	−	325.189i	−1.46420	−	0.461917i
$705$		0			0
$706$	−366.057	−	530.990i	−0.518494	−	0.752111i
$707$	−696.782	+	696.782i	−0.985548	+	0.985548i
$708$		0			0
$709$	580.549	−	580.549i	0.818828	−	0.818828i	−0.167111	−	0.985938i	$-0.553444\pi$
$709$	580.549	−	580.549i	0.818828	−	0.818828i	0.985938	+	0.167111i	$0.0534437\pi$
$710$	−658.907	−	121.148i	−0.928038	−	0.170631i
$711$		0			0
$712$	−38.3154	−	156.636i	−0.0538137	−	0.219994i
$713$		−	10.4203i		−	0.0146147i
$714$		0			0
$715$	−119.944	−	119.944i	−0.167754	−	0.167754i
$716$	−368.973	−	822.397i	−0.515325	−	1.14860i
$717$		0			0
$718$	114.366	+	165.895i	0.159284	+	0.231052i
$719$			404.510i			0.562600i	0.959620	+	0.281300i	$0.0907657\pi$
$719$			404.510i			0.562600i	−0.959620	+	0.281300i	$0.909234\pi$
$720$		0			0
$721$	−411.394			−0.570588
$722$	443.362	−	305.647i	0.614075	−	0.423334i
$723$		0			0
$724$	−294.768	−	657.003i	−0.407138	−	0.907462i
$725$	−10.4558	+	10.4558i	−0.0144218	+	0.0144218i
$726$		0			0
$727$	−449.531			−0.618337			−0.309169	−	0.951007i	$-0.600051\pi$
$727$	−449.531			−0.618337			−0.309169	+	0.951007i	$0.600051\pi$
$728$	−239.031	−	145.074i	−0.328340	−	0.199277i
$729$		0			0
$730$	−91.6570	+	498.509i	−0.125558	+	0.682889i
$731$	678.280	+	678.280i	0.927879	+	0.927879i
$732$		0			0
$733$	−418.626	−	418.626i	−0.571113	−	0.571113i	0.361326	−	0.932440i	$-0.382324\pi$
$733$	−418.626	−	418.626i	−0.571113	−	0.571113i	−0.932440	+	0.361326i	$0.882324\pi$
$734$	−362.896	+	250.175i	−0.494409	+	0.340839i
$735$		0			0
$736$	−15.5157	+	124.729i	−0.0210812	+	0.169468i
$737$	978.357			1.32749
$738$		0			0
$739$	−54.2122	+	54.2122i	−0.0733588	+	0.0733588i	−0.742834	−	0.669475i	$-0.766519\pi$
$739$	−54.2122	+	54.2122i	−0.0733588	+	0.0733588i	0.669475	+	0.742834i	$0.266519\pi$
$740$	671.102	+	255.415i	0.906894	+	0.345156i
$741$		0			0
$742$	−1333.14	−	245.114i	−1.79668	−	0.330342i
$743$	119.012			0.160178			0.0800891	−	0.996788i	$-0.474480\pi$
$743$	119.012			0.160178			0.0800891	+	0.996788i	$0.474480\pi$
$744$		0			0
$745$			132.790i			0.178242i
$746$	−715.610	−	131.574i	−0.959263	−	0.176373i
$747$		0			0
$748$	−1426.94	+	640.203i	−1.90767	+	0.855887i
$749$	555.398	+	555.398i	0.741519	+	0.741519i
$750$		0			0
$751$		−	758.619i		−	1.01015i	−0.863077	−	0.505073i	$-0.831466\pi$
$751$		−	758.619i		−	1.01015i	0.863077	−	0.505073i	$-0.168534\pi$
$752$	−724.056	+	813.441i	−0.962840	+	1.08170i
$753$		0			0
$754$	5.36500	−	3.69855i	0.00711539	−	0.00490524i
$755$	143.950	−	143.950i	0.190662	−	0.190662i
$756$		0			0
$757$	−980.581	+	980.581i	−1.29535	+	1.29535i	−0.363922	+	0.931429i	$0.618563\pi$
$757$	−980.581	+	980.581i	−1.29535	+	1.29535i	−0.931429	+	0.363922i	$0.881437\pi$
$758$	238.369	−	1296.45i	0.314470	−	1.71036i
$759$		0			0
$760$	62.1154	+	253.932i	0.0817308	+	0.334121i
$761$		−	1119.28i		−	1.47080i	−0.677634	−	0.735399i	$-0.736995\pi$
$761$		−	1119.28i		−	1.47080i	0.677634	−	0.735399i	$-0.263005\pi$
$762$		0			0
$763$	1104.75	+	1104.75i	1.44790	+	1.44790i
$764$	1007.96	+	383.620i	1.31932	+	0.502120i
$765$		0			0
$766$	−685.270	+	472.415i	−0.894609	+	0.616730i
$767$			98.0693i			0.127861i
$768$		0			0
$769$	−1268.90			−1.65006			−0.825032	−	0.565087i	$-0.808843\pi$
$769$	−1268.90			−1.65006			−0.825032	+	0.565087i	$0.808843\pi$
$770$	−776.471	−	1126.32i	−1.00840	−	1.46276i
$771$		0			0
$772$	349.467	−	918.222i	0.452677	−	1.18941i
$773$	−213.869	+	213.869i	−0.276674	+	0.276674i	−0.831780	−	0.555106i	$-0.812678\pi$
$773$	−213.869	+	213.869i	−0.276674	+	0.276674i	0.555106	+	0.831780i	$0.312678\pi$
$774$		0			0
$775$	35.4468			0.0457378
$776$	−673.329	+	164.706i	−0.867692	+	0.212250i
$777$		0			0
$778$	223.095	+	41.0188i	0.286755	+	0.0527234i
$779$	468.187	+	468.187i	0.601011	+	0.601011i
$780$		0			0
$781$	−1172.58	−	1172.58i	−1.50138	−	1.50138i
$782$	103.225	+	149.735i	0.132001	+	0.191476i
$783$		0			0
$784$	−1098.81	−	978.063i	−1.40154	−	1.24753i
$785$	113.128			0.144113
$786$		0			0
$787$	760.645	−	760.645i	0.966512	−	0.966512i	−0.0329453	−	0.999457i	$-0.510489\pi$
$787$	760.645	−	760.645i	0.966512	−	0.966512i	0.999457	+	0.0329453i	$0.0104887\pi$
$788$	−511.175	−	1139.35i	−0.648699	−	1.44587i
$789$		0			0
$790$	−0.962333	+	5.23398i	−0.00121814	+	0.00662529i
$791$	1709.33			2.16097
$792$		0			0
$793$			274.503i			0.346158i
$794$	177.592	−	965.897i	0.223668	−	1.21649i
$795$		0			0
$796$	−329.256	+	865.117i	−0.413638	+	1.08683i
$797$	801.178	+	801.178i	1.00524	+	1.00524i	0.999986	+	0.00525555i	$0.00167290\pi$
$797$	801.178	+	801.178i	1.00524	+	1.00524i	0.00525555	+	0.999986i	$0.498327\pi$
$798$		0			0
$799$			1575.75i			1.97215i
$800$	−424.290	−	52.7799i	−0.530363	−	0.0659749i
$801$		0			0
$802$	−527.221	−	764.769i	−0.657382	−	0.953578i
$803$	−887.134	+	887.134i	−1.10477	+	1.10477i
$804$		0			0
$805$	−112.488	+	112.488i	−0.139737	+	0.139737i
$806$	−15.3634	−	2.82475i	−0.0190613	−	0.00350465i
$807$		0			0
$808$	344.523	−	567.655i	0.426390	−	0.702543i
$809$		−	1311.28i		−	1.62087i	−0.585831	−	0.810433i	$-0.699232\pi$
$809$		−	1311.28i		−	1.62087i	0.585831	−	0.810433i	$-0.300768\pi$
$810$		0			0
$811$	−358.552	−	358.552i	−0.442112	−	0.442112i	0.450610	−	0.892721i	$-0.351207\pi$
$811$	−358.552	−	358.552i	−0.442112	−	0.442112i	−0.892721	+	0.450610i	$0.851207\pi$
$812$	47.9490	−	21.5126i	0.0590505	−	0.0264933i
$813$		0			0
$814$	1008.80	+	1463.33i	1.23931	+	1.79770i
$815$		−	577.382i		−	0.708444i
$816$		0			0
$817$	396.866			0.485760
$818$	154.156	−	106.273i	0.188455	−	0.129918i
$819$		0			0
$820$	860.656	−	386.137i	1.04958	−	0.470899i
$821$	526.464	−	526.464i	0.641247	−	0.641247i	−0.309615	−	0.950862i	$-0.600200\pi$
$821$	526.464	−	526.464i	0.641247	−	0.641247i	0.950862	+	0.309615i	$0.100200\pi$
$822$		0			0
$823$	−947.410			−1.15117			−0.575583	−	0.817743i	$-0.695225\pi$
$823$	−947.410			−1.15117			−0.575583	+	0.817743i	$0.695225\pi$
$824$	269.284	−	65.8707i	0.326801	−	0.0799402i
$825$		0			0
$826$	−143.024	+	777.884i	−0.173152	+	0.941749i
$827$	−856.014	−	856.014i	−1.03508	−	1.03508i	−0.999362	−	0.0357214i	$-0.988627\pi$
$827$	−856.014	−	856.014i	−1.03508	−	1.03508i	−0.0357214	−	0.999362i	$-0.511373\pi$
$828$		0			0
$829$	741.590	+	741.590i	0.894560	+	0.894560i	0.994948	−	0.100389i	$-0.0320086\pi$
$829$	741.590	+	741.590i	0.894560	+	0.894560i	−0.100389	+	0.994948i	$0.532009\pi$
$830$	729.212	−	502.708i	0.878569	−	0.605673i
$831$		0			0
$832$	179.690	+	56.6875i	0.215974	+	0.0681341i
$833$	−2128.54			−2.55527
$834$		0			0
$835$	−542.977	+	542.977i	−0.650272	+	0.650272i
$836$	−230.162	+	604.749i	−0.275313	+	0.723384i
$837$		0			0
$838$	464.477	+	85.3999i	0.554269	+	0.101909i
$839$	607.471			0.724042			0.362021	−	0.932170i	$-0.382087\pi$
$839$	607.471			0.724042			0.362021	+	0.932170i	$0.382087\pi$
$840$		0			0
$841$		−	839.775i		−	0.998544i
$842$	−560.507	−	103.056i	−0.665685	−	0.122394i
$843$		0			0
$844$	524.994	+	1170.15i	0.622031	+	1.38644i
$845$	−386.776	−	386.776i	−0.457723	−	0.457723i
$846$		0			0
$847$		−	1949.67i		−	2.30186i
$848$	911.870	−	53.0133i	1.07532	−	0.0625157i
$849$		0			0
$850$	−509.353	+	351.140i	−0.599238	+	0.413106i
$851$	146.145	−	146.145i	0.171734	−	0.171734i
$852$		0			0
$853$	−156.942	+	156.942i	−0.183989	+	0.183989i	−0.793091	−	0.609103i	$-0.791530\pi$
$853$	−156.942	+	156.942i	−0.183989	+	0.183989i	0.609103	+	0.793091i	$0.291530\pi$
$854$	−400.334	+	2177.35i	−0.468775	+	2.54959i
$855$		0			0
$856$	−452.472	−	274.616i	−0.528589	−	0.320813i
$857$			915.604i			1.06838i	0.845364	+	0.534191i	$0.179384\pi$
$857$			915.604i			1.06838i	−0.845364	+	0.534191i	$0.820616\pi$
$858$		0			0
$859$	379.829	+	379.829i	0.442176	+	0.442176i	0.892743	−	0.450567i	$-0.148778\pi$
$859$	379.829	+	379.829i	0.442176	+	0.442176i	−0.450567	+	0.892743i	$0.648778\pi$
$860$	201.116	−	528.431i	0.233856	−	0.614455i
$861$		0			0
$862$	260.890	−	179.854i	0.302656	−	0.208647i
$863$		−	49.7576i		−	0.0576565i	−0.999584	−	0.0288283i	$-0.990822\pi$
$863$		−	49.7576i		−	0.0576565i	0.999584	−	0.0288283i	$-0.00917759\pi$
$864$		0			0
$865$	−412.185			−0.476514
$866$	202.702	+	294.033i	0.234067	+	0.339530i
$867$		0			0
$868$	−117.743	−	44.8118i	−0.135648	−	0.0516265i
$869$	−9.31427	+	9.31427i	−0.0107184	+	0.0107184i
$870$		0			0
$871$	−170.549			−0.195808
$872$	−900.019	−	546.243i	−1.03213	−	0.626426i
$873$		0			0
$874$	74.0041	+	13.6066i	0.0846729	+	0.0155682i
$875$	−1098.62	−	1098.62i	−1.25557	−	1.25557i
$876$		0			0
$877$	963.055	+	963.055i	1.09812	+	1.09812i	0.994630	+	0.103494i	$0.0330022\pi$
$877$	963.055	+	963.055i	1.09812	+	1.09812i	0.103494	+	0.994630i	$0.466998\pi$
$878$	797.456	+	1156.76i	0.908264	+	1.31750i
$879$		0			0
$880$	688.593	+	612.926i	0.782492	+	0.696507i
$881$	−159.518			−0.181064			−0.0905322	−	0.995894i	$-0.528857\pi$
$881$	−159.518			−0.181064			−0.0905322	+	0.995894i	$0.528857\pi$
$882$		0			0
$883$	−53.9632	+	53.9632i	−0.0611134	+	0.0611134i	−0.737003	−	0.675890i	$-0.763760\pi$
$883$	−53.9632	+	53.9632i	−0.0611134	+	0.0611134i	0.675890	+	0.737003i	$0.263760\pi$
$884$	248.746	−	111.601i	0.281387	−	0.126246i
$885$		0			0
$886$	60.8567	−	330.990i	0.0686870	−	0.373578i
$887$	−1215.94			−1.37085			−0.685424	−	0.728144i	$-0.740383\pi$
$887$	−1215.94			−1.37085			−0.685424	+	0.728144i	$0.740383\pi$
$888$		0			0
$889$		−	561.594i		−	0.631714i
$890$	−24.8701	+	135.265i	−0.0279439	+	0.151983i
$891$		0			0
$892$	−768.532	−	292.496i	−0.861583	−	0.327911i
$893$	460.990	+	460.990i	0.516226	+	0.516226i
$894$		0			0
$895$			768.774i			0.858966i
$896$	1342.63	+	711.704i	1.49847	+	0.794312i
$897$		0			0
$898$	−572.245	−	830.079i	−0.637243	−	0.924364i
$899$	2.07607	−	2.07607i	0.00230931	−	0.00230931i
$900$		0			0
$901$	934.556	−	934.556i	1.03724	−	1.03724i
$902$	2296.39	+	422.221i	2.54589	+	0.468094i
$903$		0			0
$904$	−1118.87	+	273.691i	−1.23769	+	0.302755i
$905$			614.164i			0.678634i
$906$		0			0
$907$	−780.678	−	780.678i	−0.860726	−	0.860726i	0.130697	−	0.991422i	$-0.458279\pi$
$907$	−780.678	−	780.678i	−0.860726	−	0.860726i	−0.991422	+	0.130697i	$0.958279\pi$
$908$	394.344	+	878.946i	0.434299	+	0.968003i
$909$		0			0
$910$	135.356	+	196.343i	0.148743	+	0.215761i
$911$		−	760.487i		−	0.834782i	−0.908727	−	0.417391i	$-0.862945\pi$
$911$		−	760.487i		−	0.834782i	0.908727	−	0.417391i	$-0.137055\pi$
$912$		0			0
$913$	2192.30			2.40120
$914$	645.713	−	445.145i	0.706469	−	0.487029i
$915$		0			0
$916$	−325.743	−	726.042i	−0.355614	−	0.792623i
$917$	315.031	−	315.031i	0.343545	−	0.343545i
$918$		0			0
$919$	−905.928			−0.985776			−0.492888	−	0.870093i	$-0.664059\pi$
$919$	−905.928			−0.985776			−0.492888	+	0.870093i	$0.664059\pi$
$920$	55.6197	−	91.6419i	0.0604562	−	0.0996108i
$921$		0			0
$922$	−89.3672	+	486.055i	−0.0969275	+	0.527174i
$923$	204.405	+	204.405i	0.221458	+	0.221458i
$924$		0			0
$925$	497.144	+	497.144i	0.537453	+	0.537453i
$926$	−1266.90	+	873.381i	−1.36814	+	0.943176i
$927$		0			0
$928$	−27.9413	+	21.7588i	−0.0301091	+	0.0234470i
$929$	−932.848			−1.00414			−0.502071	−	0.864826i	$-0.667428\pi$
$929$	−932.848			−1.00414			−0.502071	+	0.864826i	$0.667428\pi$
$930$		0			0
$931$	−622.710	+	622.710i	−0.668862	+	0.668862i
$932$	−525.449	−	199.981i	−0.563787	−	0.214572i
$933$		0			0
$934$	−662.093	−	121.734i	−0.708880	−	0.130336i
$935$	1333.90			1.42663
$936$		0			0
$937$		−	26.1861i		−	0.0279468i	−0.999902	−	0.0139734i	$-0.995552\pi$
$937$		−	26.1861i		−	0.0279468i	0.999902	−	0.0139734i	$-0.00444801\pi$
$938$	−1352.79	−	248.727i	−1.44221	−	0.265168i
$939$		0			0
$940$	847.424	−	380.201i	0.901515	−	0.404469i
$941$	313.838	+	313.838i	0.333516	+	0.333516i	0.853920	−	0.520404i	$-0.174219\pi$
$941$	313.838	+	313.838i	0.333516	+	0.333516i	−0.520404	+	0.853920i	$0.674219\pi$
$942$		0			0
$943$		−	271.514i		−	0.287925i
$944$	−30.9333	−	532.076i	−0.0327683	−	0.563640i
$945$		0			0
$946$	1152.24	−	794.335i	1.21801	−	0.839677i
$947$	−1091.06	+	1091.06i	−1.15213	+	1.15213i	−0.166001	+	0.986126i	$0.553085\pi$
$947$	−1091.06	+	1091.06i	−1.15213	+	1.15213i	−0.986126	+	0.166001i	$0.946915\pi$
$948$		0			0
$949$	154.647	−	154.647i	0.162958	−	0.162958i
$950$	−46.2855	+	251.740i	−0.0487216	+	0.264989i
$951$		0			0
$952$	2135.81	−	522.450i	2.24350	−	0.548792i
$953$		−	1305.60i		−	1.36999i	−0.728546	−	0.684997i	$-0.759803\pi$
$953$		−	1305.60i		−	1.36999i	0.728546	−	0.684997i	$-0.240197\pi$
$954$		0			0
$955$	−650.421	−	650.421i	−0.681069	−	0.681069i
$956$	180.896	+	68.8474i	0.189222	+	0.0720161i
$957$		0			0
$958$	161.810	−	111.549i	0.168904	−	0.116440i
$959$			1457.93i			1.52026i
$960$		0			0
$961$	953.962			0.992676
$962$	−175.855	−	255.090i	−0.182802	−	0.265166i
$963$		0			0
$964$	184.334	−	484.337i	0.191218	−	0.502425i
$965$	−592.515	+	592.515i	−0.614006	+	0.614006i
$966$		0			0
$967$	1005.88			1.04021			0.520103	−	0.854104i	$-0.325894\pi$
$967$	1005.88			1.04021			0.520103	+	0.854104i	$0.325894\pi$
$968$	312.174	+	1276.19i	0.322493	+	1.31838i
$969$		0			0
$970$	581.461	+	106.909i	0.599444	+	0.110215i
$971$	−1310.71	−	1310.71i	−1.34985	−	1.34985i	−0.885815	−	0.464039i	$-0.846400\pi$
$971$	−1310.71	−	1310.71i	−1.34985	−	1.34985i	−0.464039	−	0.885815i	$-0.653600\pi$
$972$		0			0
$973$	−528.735	−	528.735i	−0.543407	−	0.543407i
$974$	−437.574	−	634.730i	−0.449254	−	0.651673i
$975$		0			0
$976$	−86.5844	−	1489.32i	−0.0887135	−	1.52594i
$977$	−257.041			−0.263092			−0.131546	−	0.991310i	$-0.541994\pi$
$977$	−257.041			−0.263092			−0.131546	+	0.991310i	$0.541994\pi$
$978$		0			0
$979$	−240.714	+	240.714i	−0.245877	+	0.245877i
$980$	513.580	+	1144.71i	0.524061	+	1.16807i
$981$		0			0
$982$	60.4289	−	328.663i	0.0615365	−	0.334688i
$983$	−405.819			−0.412837			−0.206419	−	0.978464i	$-0.566181\pi$
$983$	−405.819			−0.412837			−0.206419	+	0.978464i	$0.566181\pi$
$984$		0			0
$985$			1065.06i			1.08128i
$986$	−9.26626	+	50.3978i	−0.00939783	+	0.0511133i
$987$		0			0
$988$	40.1222	−	105.421i	0.0406096	−	0.106701i
$989$	−115.076	−	115.076i	−0.116356	−	0.116356i
$990$		0			0
$991$			143.499i			0.144802i	0.997376	+	0.0724010i	$0.0230661\pi$
$991$			143.499i			0.144802i	−0.997376	+	0.0724010i	$0.976934\pi$
$992$	84.2452	+	10.4798i	0.0849246	+	0.0105643i
$993$		0			0
$994$	1323.24	+	1919.44i	1.33122	+	1.93103i
$995$	558.248	−	558.248i	0.561053	−	0.561053i
$996$		0			0
$997$	595.333	−	595.333i	0.597124	−	0.597124i	−0.342422	−	0.939546i	$-0.611247\pi$
$997$	595.333	−	595.333i	0.597124	−	0.597124i	0.939546	+	0.342422i	$0.111247\pi$
$998$	−599.617	−	110.247i	−0.600818	−	0.110468i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.m.b.19.2	✓	16
3.2	odd	2	inner	144.3.m.b.19.7	yes	16
4.3	odd	2		576.3.m.b.559.6		16
8.3	odd	2		1152.3.m.d.991.3		16
8.5	even	2		1152.3.m.e.991.3		16
12.11	even	2		576.3.m.b.559.3		16
16.3	odd	4		1152.3.m.e.415.3		16
16.5	even	4		576.3.m.b.271.6		16
16.11	odd	4	inner	144.3.m.b.91.2	yes	16
16.13	even	4		1152.3.m.d.415.3		16
24.5	odd	2		1152.3.m.e.991.6		16
24.11	even	2		1152.3.m.d.991.6		16
48.5	odd	4		576.3.m.b.271.3		16
48.11	even	4	inner	144.3.m.b.91.7	yes	16
48.29	odd	4		1152.3.m.d.415.6		16
48.35	even	4		1152.3.m.e.415.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.m.b.19.2	✓	16	1.1	even	1	trivial
144.3.m.b.19.7	yes	16	3.2	odd	2	inner
144.3.m.b.91.2	yes	16	16.11	odd	4	inner
144.3.m.b.91.7	yes	16	48.11	even	4	inner
576.3.m.b.271.3		16	48.5	odd	4
576.3.m.b.271.6		16	16.5	even	4
576.3.m.b.559.3		16	12.11	even	2
576.3.m.b.559.6		16	4.3	odd	2
1152.3.m.d.415.3		16	16.13	even	4
1152.3.m.d.415.6		16	48.29	odd	4
1152.3.m.d.991.3		16	8.3	odd	2
1152.3.m.d.991.6		16	24.11	even	2
1152.3.m.e.415.3		16	16.3	odd	4
1152.3.m.e.415.6		16	48.35	even	4
1152.3.m.e.991.3		16	8.5	even	2
1152.3.m.e.991.6		16	24.5	odd	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)

\(f(q)\)	\(=\)	\(q+(-1.13516 - 1.64663i) q^{2} +(-1.42280 + 3.73840i) q^{4} +(2.41234 - 2.41234i) q^{5} -11.8718 q^{7} +(7.77089 - 1.90087i) q^{8} +O(q^{10})\)	\(q+(-1.13516 - 1.64663i) q^{2} +(-1.42280 + 3.73840i) q^{4} +(2.41234 - 2.41234i) q^{5} -11.8718 q^{7} +(7.77089 - 1.90087i) q^{8} +(-6.71063 - 1.23383i) q^{10} +(-11.9421 - 11.9421i) q^{11} +(2.08177 + 2.08177i) q^{13} +(13.4765 + 19.5486i) q^{14} +(-11.9513 - 10.6380i) q^{16} -23.1512 q^{17} +(-6.77297 + 6.77297i) q^{19} +(5.58600 + 12.4506i) q^{20} +(-6.10800 + 33.2205i) q^{22} +3.92781 q^{23} +13.3613i q^{25} +(1.06476 - 5.79105i) q^{26} +(16.8913 - 44.3817i) q^{28} +(0.782548 + 0.782548i) q^{29} -2.65295i q^{31} +(-3.95022 + 31.7552i) q^{32} +(26.2805 + 38.1216i) q^{34} +(-28.6389 + 28.6389i) q^{35} +(37.2078 - 37.2078i) q^{37} +(18.8410 + 3.46416i) q^{38} +(14.1605 - 23.3315i) q^{40} -69.1259i q^{41} +(-29.2978 - 29.2978i) q^{43} +(61.6355 - 27.6531i) q^{44} +(-4.45872 - 6.46767i) q^{46} -68.0631i q^{47} +91.9405 q^{49} +(22.0011 - 15.1672i) q^{50} +(-10.7444 + 4.82053i) q^{52} +(-40.3674 + 40.3674i) q^{53} -57.6167 q^{55} +(-92.2547 + 22.5668i) q^{56} +(0.400249 - 2.17689i) q^{58} +(23.5544 + 23.5544i) q^{59} +(65.9304 + 65.9304i) q^{61} +(-4.36844 + 3.01154i) q^{62} +(56.7734 - 29.5429i) q^{64} +10.0438 q^{65} +(-40.9626 + 40.9626i) q^{67} +(32.9396 - 86.5486i) q^{68} +(79.6675 + 14.6479i) q^{70} +98.1885 q^{71} -74.2864i q^{73} +(-103.505 - 19.0306i) q^{74} +(-15.6835 - 34.9567i) q^{76} +(141.774 + 141.774i) q^{77} -0.779953i q^{79} +(-54.4929 + 3.16805i) q^{80} +(-113.825 + 78.4693i) q^{82} +(-91.7887 + 91.7887i) q^{83} +(-55.8486 + 55.8486i) q^{85} +(-14.9849 + 81.5005i) q^{86} +(-115.501 - 70.1003i) q^{88} -20.1568i q^{89} +(-24.7144 - 24.7144i) q^{91} +(-5.58850 + 14.6837i) q^{92} +(-112.075 + 77.2629i) q^{94} +32.6774i q^{95} -86.6476 q^{97} +(-104.368 - 151.392i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{4}+O(q^{10}) \) 16 * q - 12 * q^4	\( 16 q - 12 q^{4} + 16 q^{10} + 32 q^{16} - 32 q^{19} + 104 q^{22} - 24 q^{34} + 96 q^{37} - 312 q^{40} - 32 q^{43} - 224 q^{46} + 112 q^{49} - 264 q^{52} - 256 q^{55} + 312 q^{58} - 32 q^{61} + 456 q^{64} - 256 q^{67} + 744 q^{70} + 264 q^{76} - 280 q^{82} + 160 q^{85} - 912 q^{88} + 288 q^{91} - 1104 q^{94}+O(q^{100}) \) 16 * q - 12 * q^4 + 16 * q^10 + 32 * q^16 - 32 * q^19 + 104 * q^22 - 24 * q^34 + 96 * q^37 - 312 * q^40 - 32 * q^43 - 224 * q^46 + 112 * q^49 - 264 * q^52 - 256 * q^55 + 312 * q^58 - 32 * q^61 + 456 * q^64 - 256 * q^67 + 744 * q^70 + 264 * q^76 - 280 * q^82 + 160 * q^85 - 912 * q^88 + 288 * q^91 - 1104 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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