LMFDB - Embedded newform 144.3.j.a.53.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(53,144)]

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([0, 1, 2]))

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

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

chi := DirichletCharacter("144.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.j (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:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.6
Character	$\chi$	$=$	144.53
Dual form			144.3.j.a.125.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11574 + 1.65986i) q^{2} +(-1.51025 - 3.70394i) q^{4} +(-0.900179 + 0.900179i) q^{5} -7.66460i q^{7} +(7.83305 + 1.62583i) q^{8} +O(q^{10})$	\(q+(-1.11574 + 1.65986i) q^{2} +(-1.51025 - 3.70394i) q^{4} +(-0.900179 + 0.900179i) q^{5} -7.66460i q^{7} +(7.83305 + 1.62583i) q^{8} +(-0.489803 - 2.49853i) q^{10} +(4.57563 - 4.57563i) q^{11} +(10.9824 - 10.9824i) q^{13} +(12.7221 + 8.55170i) q^{14} +(-11.4383 + 11.1877i) q^{16} +0.0435225i q^{17} +(12.9849 - 12.9849i) q^{19} +(4.69370 + 1.97471i) q^{20} +(2.48968 + 12.7001i) q^{22} +18.3139 q^{23} +23.3794i q^{25} +(5.97571 + 30.4827i) q^{26} +(-28.3892 + 11.5755i) q^{28} +(-34.9759 - 34.9759i) q^{29} +38.4592 q^{31} +(-5.80790 - 31.4685i) q^{32} +(-0.0722411 - 0.0485598i) q^{34} +(6.89951 + 6.89951i) q^{35} +(11.3885 + 11.3885i) q^{37} +(7.06529 + 36.0407i) q^{38} +(-8.51469 + 5.58761i) q^{40} -45.6887 q^{41} +(-51.4657 - 51.4657i) q^{43} +(-23.8582 - 10.0375i) q^{44} +(-20.4335 + 30.3984i) q^{46} -56.5712i q^{47} -9.74608 q^{49} +(-38.8064 - 26.0853i) q^{50} +(-57.2642 - 24.0919i) q^{52} +(-44.6596 + 44.6596i) q^{53} +8.23778i q^{55} +(12.4613 - 60.0372i) q^{56} +(97.0790 - 19.0310i) q^{58} +(-20.7614 + 20.7614i) q^{59} +(-2.42706 + 2.42706i) q^{61} +(-42.9105 + 63.8368i) q^{62} +(58.7134 + 25.4704i) q^{64} +19.7722i q^{65} +(-18.9097 + 18.9097i) q^{67} +(0.161205 - 0.0657298i) q^{68} +(-19.1503 + 3.75414i) q^{70} +114.872 q^{71} +127.648i q^{73} +(-31.6098 + 6.19667i) q^{74} +(-67.7055 - 28.4847i) q^{76} +(-35.0704 - 35.0704i) q^{77} +37.0284 q^{79} +(0.225539 - 20.3675i) q^{80} +(50.9766 - 75.8366i) q^{82} +(84.4337 + 84.4337i) q^{83} +(-0.0391780 - 0.0391780i) q^{85} +(142.848 - 28.0034i) q^{86} +(43.2804 - 28.4020i) q^{88} +136.172 q^{89} +(-84.1756 - 84.1756i) q^{91} +(-27.6586 - 67.8335i) q^{92} +(93.9002 + 63.1188i) q^{94} +23.3774i q^{95} -173.475 q^{97} +(10.8741 - 16.1771i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 40 q^{10} + 48 q^{16} + 64 q^{19} - 88 q^{22} - 120 q^{28} - 248 q^{34} - 184 q^{40} + 128 q^{43} + 24 q^{46} - 224 q^{49} + 632 q^{52} + 456 q^{58} + 64 q^{61} - 48 q^{64} - 64 q^{67} - 312 q^{70} - 576 q^{76} - 512 q^{79} - 720 q^{82} + 320 q^{85} - 400 q^{88} - 192 q^{91} + 696 q^{94}+O(q^{100}) $ 32 * q + 40 * q^10 + 48 * q^16 + 64 * q^19 - 88 * q^22 - 120 * q^28 - 248 * q^34 - 184 * q^40 + 128 * q^43 + 24 * q^46 - 224 * q^49 + 632 * q^52 + 456 * q^58 + 64 * q^61 - 48 * q^64 - 64 * q^67 - 312 * q^70 - 576 * q^76 - 512 * q^79 - 720 * q^82 + 320 * q^85 - 400 * q^88 - 192 * q^91 + 696 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.11574	+	1.65986i	−0.557870	+	0.829928i
$2$	−1.11574	+	1.65986i	−0.557870	+	0.829928i
$3$		0			0
$3$		0			0
$4$	−1.51025	−	3.70394i	−0.377563	−	0.925984i
$5$	−0.900179	+	0.900179i	−0.180036	+	0.180036i	−0.791371	−	0.611336i	$-0.790633\pi$
$5$	−0.900179	+	0.900179i	−0.180036	+	0.180036i	0.611336	+	0.791371i	$0.290633\pi$
$6$		0			0
$7$		−	7.66460i		−	1.09494i	−0.836824	−	0.547471i	$-0.815591\pi$
$7$		−	7.66460i		−	1.09494i	0.836824	−	0.547471i	$-0.184409\pi$
$8$	7.83305	+	1.62583i	0.979131	+	0.203229i
$9$		0			0
$10$	−0.489803	−	2.49853i	−0.0489803	−	0.249853i
$11$	4.57563	−	4.57563i	0.415967	−	0.415967i	−0.467844	−	0.883811i	$-0.654969\pi$
$11$	4.57563	−	4.57563i	0.415967	−	0.415967i	0.883811	+	0.467844i	$0.154969\pi$
$12$		0			0
$13$	10.9824	−	10.9824i	0.844799	−	0.844799i	−0.144679	−	0.989479i	$-0.546215\pi$
$13$	10.9824	−	10.9824i	0.844799	−	0.844799i	0.989479	+	0.144679i	$0.0462150\pi$
$14$	12.7221	+	8.55170i	0.908724	+	0.610835i
$15$		0			0
$16$	−11.4383	+	11.1877i	−0.714893	+	0.699234i
$17$			0.0435225i			0.00256015i	0.999999	+	0.00128007i	$0.000407460\pi$
$17$			0.0435225i			0.00256015i	−0.999999	+	0.00128007i	$0.999593\pi$
$18$		0			0
$19$	12.9849	−	12.9849i	0.683414	−	0.683414i	−0.277354	−	0.960768i	$-0.589457\pi$
$19$	12.9849	−	12.9849i	0.683414	−	0.683414i	0.960768	+	0.277354i	$0.0894575\pi$
$20$	4.69370	+	1.97471i	0.234685	+	0.0987355i
$21$		0			0
$22$	2.48968	+	12.7001i	0.113167	+	0.577278i
$23$	18.3139			0.796256			0.398128	−	0.917330i	$-0.369660\pi$
$23$	18.3139			0.796256			0.398128	+	0.917330i	$0.369660\pi$
$24$		0			0
$25$			23.3794i			0.935174i
$26$	5.97571	+	30.4827i	0.229835	+	1.17241i
$27$		0			0
$28$	−28.3892	+	11.5755i	−1.01390	+	0.413409i
$29$	−34.9759	−	34.9759i	−1.20607	−	1.20607i	−0.972291	−	0.233774i	$-0.924892\pi$
$29$	−34.9759	−	34.9759i	−1.20607	−	1.20607i	−0.233774	−	0.972291i	$-0.575108\pi$
$30$		0			0
$31$	38.4592			1.24062			0.620310	−	0.784356i	$-0.287007\pi$
$31$	38.4592			1.24062			0.620310	+	0.784356i	$0.287007\pi$
$32$	−5.80790	−	31.4685i	−0.181497	−	0.983392i
$33$		0			0
$34$	−0.0722411	−	0.0485598i	−0.00212474	−	0.00142823i
$35$	6.89951	+	6.89951i	0.197129	+	0.197129i
$36$		0			0
$37$	11.3885	+	11.3885i	0.307797	+	0.307797i	0.844054	−	0.536258i	$-0.180162\pi$
$37$	11.3885	+	11.3885i	0.307797	+	0.307797i	−0.536258	+	0.844054i	$0.680162\pi$
$38$	7.06529	+	36.0407i	0.185929	+	0.948440i
$39$		0			0
$40$	−8.51469	+	5.58761i	−0.212867	+	0.139690i
$41$	−45.6887			−1.11436			−0.557179	−	0.830393i	$-0.688116\pi$
$41$	−45.6887			−1.11436			−0.557179	+	0.830393i	$0.688116\pi$
$42$		0			0
$43$	−51.4657	−	51.4657i	−1.19688	−	1.19688i	−0.975097	−	0.221781i	$-0.928813\pi$
$43$	−51.4657	−	51.4657i	−1.19688	−	1.19688i	−0.221781	−	0.975097i	$-0.571187\pi$
$44$	−23.8582	−	10.0375i	−0.542232	−	0.228125i
$45$		0			0
$46$	−20.4335	+	30.3984i	−0.444207	+	0.660836i
$47$		−	56.5712i		−	1.20364i	−0.798631	−	0.601822i	$-0.794442\pi$
$47$		−	56.5712i		−	1.20364i	0.798631	−	0.601822i	$-0.205558\pi$
$48$		0			0
$49$	−9.74608			−0.198900
$50$	−38.8064	−	26.0853i	−0.776128	−	0.521705i
$51$		0			0
$52$	−57.2642	−	24.0919i	−1.10124	−	0.463306i
$53$	−44.6596	+	44.6596i	−0.842634	+	0.842634i	−0.989201	−	0.146567i	$-0.953178\pi$
$53$	−44.6596	+	44.6596i	−0.842634	+	0.842634i	0.146567	+	0.989201i	$0.453178\pi$
$54$		0			0
$55$			8.23778i			0.149778i
$56$	12.4613	−	60.0372i	0.222524	−	1.07209i
$57$		0			0
$58$	97.0790	−	19.0310i	1.67378	−	0.328120i
$59$	−20.7614	+	20.7614i	−0.351887	+	0.351887i	−0.860811	−	0.508924i	$-0.830043\pi$
$59$	−20.7614	+	20.7614i	−0.351887	+	0.351887i	0.508924	+	0.860811i	$0.330043\pi$
$60$		0			0
$61$	−2.42706	+	2.42706i	−0.0397878	+	0.0397878i	−0.726721	−	0.686933i	$-0.758957\pi$
$61$	−2.42706	+	2.42706i	−0.0397878	+	0.0397878i	0.686933	+	0.726721i	$0.258957\pi$
$62$	−42.9105	+	63.8368i	−0.692105	+	1.02963i
$63$		0			0
$64$	58.7134	+	25.4704i	0.917396	+	0.397975i
$65$			19.7722i			0.304188i
$66$		0			0
$67$	−18.9097	+	18.9097i	−0.282234	+	0.282234i	−0.833999	−	0.551766i	$-0.813954\pi$
$67$	−18.9097	+	18.9097i	−0.282234	+	0.282234i	0.551766	+	0.833999i	$0.313954\pi$
$68$	0.161205	−	0.0657298i	0.00237065	−	0.000966615i
$69$		0			0
$70$	−19.1503	+	3.75414i	−0.273575	+	0.0536306i
$71$	114.872			1.61791			0.808956	−	0.587869i	$-0.200033\pi$
$71$	114.872			1.61791			0.808956	+	0.587869i	$0.200033\pi$
$72$		0			0
$73$			127.648i			1.74860i	0.485388	+	0.874299i	$0.338678\pi$
$73$			127.648i			1.74860i	−0.485388	+	0.874299i	$0.661322\pi$
$74$	−31.6098	+	6.19667i	−0.427160	+	0.0837388i
$75$		0			0
$76$	−67.7055	−	28.4847i	−0.890862	−	0.374799i
$77$	−35.0704	−	35.0704i	−0.455460	−	0.455460i
$78$		0			0
$79$	37.0284			0.468714			0.234357	−	0.972151i	$-0.424701\pi$
$79$	37.0284			0.468714			0.234357	+	0.972151i	$0.424701\pi$
$80$	0.225539	−	20.3675i	0.00281923	−	0.254594i
$81$		0			0
$82$	50.9766	−	75.8366i	0.621666	−	0.924837i
$83$	84.4337	+	84.4337i	1.01727	+	1.01727i	0.999848	+	0.0174254i	$0.00554695\pi$
$83$	84.4337	+	84.4337i	1.01727	+	1.01727i	0.0174254	+	0.999848i	$0.494453\pi$
$84$		0			0
$85$	−0.0391780	−	0.0391780i	−0.000460918	−	0.000460918i
$86$	142.848	−	28.0034i	1.66102	−	0.325621i
$87$		0			0
$88$	43.2804	−	28.4020i	0.491822	−	0.322750i
$89$	136.172			1.53002			0.765012	−	0.644017i	$-0.222733\pi$
$89$	136.172			1.53002			0.765012	+	0.644017i	$0.222733\pi$
$90$		0			0
$91$	−84.1756	−	84.1756i	−0.925007	−	0.925007i
$92$	−27.6586	−	67.8335i	−0.300636	−	0.737320i
$93$		0			0
$94$	93.9002	+	63.1188i	0.998938	+	0.671476i
$95$			23.3774i			0.246078i
$96$		0			0
$97$	−173.475			−1.78840			−0.894202	−	0.447663i	$-0.852256\pi$
$97$	−173.475			−1.78840			−0.894202	+	0.447663i	$0.852256\pi$
$98$	10.8741	−	16.1771i	0.110960	−	0.165072i
$99$		0			0
$100$	86.5956	−	35.3087i	0.865956	−	0.353087i
$101$	18.4286	−	18.4286i	0.182462	−	0.182462i	−0.609966	−	0.792428i	$-0.708817\pi$
$101$	18.4286	−	18.4286i	0.182462	−	0.182462i	0.792428	+	0.609966i	$0.208817\pi$
$102$		0			0
$103$			88.8974i			0.863082i	0.902093	+	0.431541i	$0.142030\pi$
$103$			88.8974i			0.863082i	−0.902093	+	0.431541i	$0.857970\pi$
$104$	103.881	−	68.1701i	0.998857	−	0.655482i
$105$		0			0
$106$	−24.3001	−	123.957i	−0.229246	−	1.16941i
$107$	−54.3773	+	54.3773i	−0.508199	+	0.508199i	−0.913973	−	0.405774i	$-0.867002\pi$
$107$	−54.3773	+	54.3773i	−0.508199	+	0.508199i	0.405774	+	0.913973i	$0.367002\pi$
$108$		0			0
$109$	122.019	−	122.019i	1.11944	−	1.11944i	0.127620	−	0.991823i	$-0.459266\pi$
$109$	122.019	−	122.019i	1.11944	−	1.11944i	0.991823	−	0.127620i	$-0.0407339\pi$
$110$	−13.6735	−	9.19122i	−0.124305	−	0.0835566i
$111$		0			0
$112$	85.7495	+	87.6699i	0.765621	+	0.782767i
$113$			162.624i			1.43915i	0.694415	+	0.719575i	$0.255663\pi$
$113$			162.624i			1.43915i	−0.694415	+	0.719575i	$0.744337\pi$
$114$		0			0
$115$	−16.4858	+	16.4858i	−0.143355	+	0.143355i
$116$	−76.7261	+	182.371i	−0.661432	+	1.57216i
$117$		0			0
$118$	−11.2966	−	57.6251i	−0.0957340	−	0.488349i
$119$	0.333582			0.00280321
$120$		0			0
$121$			79.1271i			0.653943i
$122$	−1.32060	−	6.73653i	−0.0108246	−	0.0552175i
$123$		0			0
$124$	−58.0831	−	142.451i	−0.468412	−	1.14880i
$125$	−43.5501	−	43.5501i	−0.348401	−	0.348401i
$126$		0			0
$127$	36.2712			0.285600			0.142800	−	0.989752i	$-0.454389\pi$
$127$	36.2712			0.285600			0.142800	+	0.989752i	$0.454389\pi$
$128$	−107.786	+	69.0374i	−0.842079	+	0.539355i
$129$		0			0
$130$	−32.8191	−	22.0607i	−0.252455	−	0.169698i
$131$	−59.9003	−	59.9003i	−0.457254	−	0.457254i	0.440499	−	0.897753i	$-0.354802\pi$
$131$	−59.9003	−	59.9003i	−0.457254	−	0.457254i	−0.897753	+	0.440499i	$0.854802\pi$
$132$		0			0
$133$	−99.5238	−	99.5238i	−0.748299	−	0.748299i
$134$	−10.2891	−	52.4856i	−0.0767841	−	0.391684i
$135$		0			0
$136$	−0.0707601	+	0.340914i	−0.000520295	+	0.00250672i
$137$	98.5118			0.719064			0.359532	−	0.933133i	$-0.382936\pi$
$137$	98.5118			0.719064			0.359532	+	0.933133i	$0.382936\pi$
$138$		0			0
$139$	3.39960	+	3.39960i	0.0244575	+	0.0244575i	0.719230	−	0.694772i	$-0.244495\pi$
$139$	3.39960	+	3.39960i	0.0244575	+	0.0244575i	−0.694772	+	0.719230i	$0.744495\pi$
$140$	15.1354	−	35.9753i	0.108110	−	0.256967i
$141$		0			0
$142$	−128.167	+	190.671i	−0.902585	+	1.34275i
$143$		−	100.503i		−	0.702817i
$144$		0			0
$145$	62.9691			0.434270
$146$	−211.877	−	142.422i	−1.45121	−	0.975490i
$147$		0			0
$148$	24.9828	−	59.3817i	0.168802	−	0.401228i
$149$	−9.03169	+	9.03169i	−0.0606154	+	0.0606154i	−0.736765	−	0.676149i	$-0.763647\pi$
$149$	−9.03169	+	9.03169i	−0.0606154	+	0.0606154i	0.676149	+	0.736765i	$0.263647\pi$
$150$		0			0
$151$			69.0548i			0.457316i	0.973507	+	0.228658i	$0.0734338\pi$
$151$			69.0548i			0.457316i	−0.973507	+	0.228658i	$0.926566\pi$
$152$	122.822	−	80.5999i	0.808041	−	0.530263i
$153$		0			0
$154$	97.3413	−	19.0824i	0.632086	−	0.123912i
$155$	−34.6202	+	34.6202i	−0.223356	+	0.223356i
$156$		0			0
$157$	63.7071	−	63.7071i	0.405778	−	0.405778i	−0.474486	−	0.880263i	$-0.657366\pi$
$157$	63.7071	−	63.7071i	0.405778	−	0.405778i	0.880263	+	0.474486i	$0.157366\pi$
$158$	−41.3141	+	61.4619i	−0.261482	+	0.388999i
$159$		0			0
$160$	33.5555	+	23.0992i	0.209722	+	0.144370i
$161$		−	140.369i		−	0.871855i
$162$		0			0
$163$	−105.629	+	105.629i	−0.648033	+	0.648033i	−0.952517	−	0.304484i	$-0.901516\pi$
$163$	−105.629	+	105.629i	−0.648033	+	0.648033i	0.304484	+	0.952517i	$0.401516\pi$
$164$	69.0013	+	169.228i	0.420740	+	1.03188i
$165$		0			0
$166$	−234.354	+	45.9418i	−1.41177	+	0.276758i
$167$	−255.722			−1.53127			−0.765634	−	0.643276i	$-0.777575\pi$
$167$	−255.722			−1.53127			−0.765634	+	0.643276i	$0.777575\pi$
$168$		0			0
$169$		−	72.2259i		−	0.427372i
$170$	0.108742	−	0.0213175i	0.000639661	−	0.000125397i
$171$		0			0
$172$	−112.900	+	268.352i	−0.656393	+	1.56019i
$173$	56.9554	+	56.9554i	0.329222	+	0.329222i	0.852291	−	0.523069i	$-0.175213\pi$
$173$	56.9554	+	56.9554i	0.329222	+	0.329222i	−0.523069	+	0.852291i	$0.675213\pi$
$174$		0			0
$175$	179.193			1.02396
$176$	−1.14642	+	103.528i	−0.00651374	+	0.588230i
$177$		0			0
$178$	−151.933	+	226.026i	−0.853554	+	1.26981i
$179$	−171.658	−	171.658i	−0.958982	−	0.958982i	0.0402097	−	0.999191i	$-0.487197\pi$
$179$	−171.658	−	171.658i	−0.958982	−	0.958982i	−0.999191	+	0.0402097i	$0.987197\pi$
$180$		0			0
$181$	55.5135	+	55.5135i	0.306704	+	0.306704i	0.843630	−	0.536925i	$-0.180414\pi$
$181$	55.5135	+	55.5135i	0.306704	+	0.306704i	−0.536925	+	0.843630i	$0.680414\pi$
$182$	233.638	−	45.8014i	1.28372	−	0.251656i
$183$		0			0
$184$	143.454	+	29.7753i	0.779639	+	0.161822i
$185$	−20.5034			−0.110829
$186$		0			0
$187$	0.199143	+	0.199143i	0.00106494	+	0.00106494i
$188$	−209.536	+	85.4367i	−1.11455	+	0.454451i
$189$		0			0
$190$	−38.8032	−	26.0831i	−0.204227	−	0.137279i
$191$		−	101.947i		−	0.533755i	−0.963730	−	0.266878i	$-0.914008\pi$
$191$		−	101.947i		−	0.533755i	0.963730	−	0.266878i	$-0.0859920\pi$
$192$		0			0
$193$	81.5007			0.422284			0.211142	−	0.977455i	$-0.432282\pi$
$193$	81.5007			0.422284			0.211142	+	0.977455i	$0.432282\pi$
$194$	193.553	−	287.944i	0.997697	−	1.48425i
$195$		0			0
$196$	14.7190	+	36.0988i	0.0750970	+	0.184178i
$197$	170.676	−	170.676i	0.866377	−	0.866377i	−0.125692	−	0.992069i	$-0.540115\pi$
$197$	170.676	−	170.676i	0.866377	−	0.866377i	0.992069	+	0.125692i	$0.0401151\pi$
$198$		0			0
$199$			187.424i			0.941831i	0.882178	+	0.470916i	$0.156076\pi$
$199$			187.424i			0.941831i	−0.882178	+	0.470916i	$0.843924\pi$
$200$	−38.0108	+	183.132i	−0.190054	+	0.915658i
$201$		0			0
$202$	10.0273	+	51.1504i	0.0496403	+	0.253220i
$203$	−268.076	+	268.076i	−1.32057	+	1.32057i
$204$		0			0
$205$	41.1280	−	41.1280i	0.200624	−	0.200624i
$206$	−147.557	−	99.1864i	−0.716296	−	0.481487i
$207$		0			0
$208$	−2.75162	+	248.488i	−0.0132289	+	1.19465i
$209$		−	118.828i		−	0.568555i
$210$		0			0
$211$	111.675	−	111.675i	0.529265	−	0.529265i	−0.391088	−	0.920353i	$-0.627901\pi$
$211$	111.675	−	111.675i	0.529265	−	0.529265i	0.920353	+	0.391088i	$0.127901\pi$
$212$	232.863	+	97.9691i	1.09841	+	0.462119i
$213$		0			0
$214$	−29.5876	−	150.929i	−0.138260	−	0.705278i
$215$	92.6567			0.430962
$216$		0			0
$217$		−	294.775i		−	1.35841i
$218$	66.3928	+	338.676i	0.304554	+	1.55356i
$219$		0			0
$220$	30.5122	−	12.4411i	0.138692	−	0.0565505i
$221$	0.477981	+	0.477981i	0.00216281	+	0.00216281i
$222$		0			0
$223$	135.329			0.606857			0.303429	−	0.952854i	$-0.401869\pi$
$223$	135.329			0.606857			0.303429	+	0.952854i	$0.401869\pi$
$224$	−241.194	+	44.5152i	−1.07676	+	0.198729i
$225$		0			0
$226$	−269.932	−	181.446i	−1.19439	−	0.802858i
$227$	6.74050	+	6.74050i	0.0296938	+	0.0296938i	0.721798	−	0.692104i	$-0.243316\pi$
$227$	6.74050	+	6.74050i	0.0296938	+	0.0296938i	−0.692104	+	0.721798i	$0.743316\pi$
$228$		0			0
$229$	−48.9527	−	48.9527i	−0.213767	−	0.213767i	0.592098	−	0.805866i	$-0.298300\pi$
$229$	−48.9527	−	48.9527i	−0.213767	−	0.213767i	−0.805866	+	0.592098i	$0.798300\pi$
$230$	−8.97020	−	45.7579i	−0.0390009	−	0.198947i
$231$		0			0
$232$	−217.103	−	330.833i	−0.935789	−	1.42600i
$233$	101.494			0.435595			0.217797	−	0.975994i	$-0.430113\pi$
$233$	101.494			0.435595			0.217797	+	0.975994i	$0.430113\pi$
$234$		0			0
$235$	50.9243	+	50.9243i	0.216699	+	0.216699i
$236$	108.254	+	45.5439i	0.458702	+	0.192983i
$237$		0			0
$238$	−0.372191	+	0.553699i	−0.00156383	+	0.00232647i
$239$			47.7817i			0.199923i	0.994991	+	0.0999617i	$0.0318720\pi$
$239$			47.7817i			0.199923i	−0.994991	+	0.0999617i	$0.968128\pi$
$240$		0			0
$241$	−18.2775			−0.0758402			−0.0379201	−	0.999281i	$-0.512073\pi$
$241$	−18.2775			−0.0758402			−0.0379201	+	0.999281i	$0.512073\pi$
$242$	−131.340	−	88.2853i	−0.542726	−	0.364815i
$243$		0			0
$244$	12.6551	+	5.32420i	0.0518653	+	0.0218205i
$245$	8.77322	−	8.77322i	0.0358090	−	0.0358090i
$246$		0			0
$247$		−	285.210i		−	1.15470i
$248$	301.253	+	62.5282i	1.21473	+	0.252130i
$249$		0			0
$250$	120.877	−	23.6964i	0.483510	−	0.0947854i
$251$	300.658	−	300.658i	1.19784	−	1.19784i	0.223027	−	0.974812i	$-0.428406\pi$
$251$	300.658	−	300.658i	1.19784	−	1.19784i	0.974812	−	0.223027i	$-0.0715938\pi$
$252$		0			0
$253$	83.7977	−	83.7977i	0.331216	−	0.331216i
$254$	−40.4692	+	60.2050i	−0.159328	+	0.237027i
$255$		0			0
$256$	5.66892	−	255.937i	0.0221442	−	0.999755i
$257$			170.456i			0.663254i	0.943411	+	0.331627i	$0.107598\pi$
$257$			170.456i			0.663254i	−0.943411	+	0.331627i	$0.892402\pi$
$258$		0			0
$259$	87.2882	−	87.2882i	0.337020	−	0.337020i
$260$	73.2351	−	29.8610i	0.281674	−	0.114850i
$261$		0			0
$262$	166.259	−	32.5928i	0.634577	−	0.124400i
$263$	−294.979			−1.12159			−0.560797	−	0.827953i	$-0.689505\pi$
$263$	−294.979			−1.12159			−0.560797	+	0.827953i	$0.689505\pi$
$264$		0			0
$265$		−	80.4033i		−	0.303409i
$266$	276.238	−	54.1526i	1.03849	−	0.203581i
$267$		0			0
$268$	98.5985	+	41.4819i	0.367905	+	0.154783i
$269$	129.972	+	129.972i	0.483165	+	0.483165i	0.906141	−	0.422976i	$-0.139014\pi$
$269$	129.972	+	129.972i	0.483165	+	0.483165i	−0.422976	+	0.906141i	$0.639014\pi$
$270$		0			0
$271$	−535.196			−1.97489			−0.987447	−	0.157953i	$-0.949511\pi$
$271$	−535.196			−1.97489			−0.987447	+	0.157953i	$0.949511\pi$
$272$	−0.486918	−	0.497823i	−0.00179014	−	0.00183023i
$273$		0			0
$274$	−109.914	+	163.516i	−0.401144	+	0.596772i
$275$	106.975	+	106.975i	0.389001	+	0.389001i
$276$		0			0
$277$	−62.0846	−	62.0846i	−0.224132	−	0.224132i	0.586104	−	0.810236i	$-0.300661\pi$
$277$	−62.0846	−	62.0846i	−0.224132	−	0.224132i	−0.810236	+	0.586104i	$0.800661\pi$
$278$	−9.43592	+	1.84978i	−0.0339421	+	0.00665389i
$279$		0			0
$280$	42.8268	+	65.2617i	0.152953	+	0.233077i
$281$	102.299			0.364055			0.182027	−	0.983293i	$-0.441734\pi$
$281$	102.299			0.364055			0.182027	+	0.983293i	$0.441734\pi$
$282$		0			0
$283$	164.906	+	164.906i	0.582705	+	0.582705i	0.935646	−	0.352940i	$-0.114818\pi$
$283$	164.906	+	164.906i	0.582705	+	0.582705i	−0.352940	+	0.935646i	$0.614818\pi$
$284$	−173.485	−	425.478i	−0.610863	−	1.49816i
$285$		0			0
$286$	166.820	+	112.135i	0.583288	+	0.392080i
$287$			350.185i			1.22016i
$288$		0			0
$289$	288.998			0.999993
$290$	−70.2572	+	104.520i	−0.242266	+	0.360413i
$291$		0			0
$292$	472.799	−	192.780i	1.61917	−	0.660205i
$293$	−203.242	+	203.242i	−0.693658	+	0.693658i	−0.963035	−	0.269377i	$-0.913182\pi$
$293$	−203.242	+	203.242i	−0.693658	+	0.693658i	0.269377	+	0.963035i	$0.413182\pi$
$294$		0			0
$295$		−	37.3779i		−	0.126705i
$296$	70.6909	+	107.722i	0.238820	+	0.363927i
$297$		0			0
$298$	−4.91430	−	25.0683i	−0.0164909	−	0.0841219i
$299$	201.130	−	201.130i	0.672677	−	0.672677i
$300$		0			0
$301$	−394.464	+	394.464i	−1.31051	+	1.31051i
$302$	−114.621	−	77.0471i	−0.379540	−	0.255123i
$303$		0			0
$304$	−3.25334	+	293.796i	−0.0107018	+	0.966434i
$305$		−	4.36957i		−	0.0143265i
$306$		0			0
$307$	−133.116	+	133.116i	−0.433602	+	0.433602i	−0.889852	−	0.456250i	$-0.849192\pi$
$307$	−133.116	+	133.116i	−0.433602	+	0.433602i	0.456250	+	0.889852i	$0.349192\pi$
$308$	−76.9335	+	182.864i	−0.249784	+	0.593713i
$309$		0			0
$310$	−18.8375	−	96.0918i	−0.0607660	−	0.309973i
$311$	260.983			0.839175			0.419587	−	0.907715i	$-0.362175\pi$
$311$	260.983			0.839175			0.419587	+	0.907715i	$0.362175\pi$
$312$		0			0
$313$			157.967i			0.504686i	0.967638	+	0.252343i	$0.0812011\pi$
$313$			157.967i			0.504686i	−0.967638	+	0.252343i	$0.918799\pi$
$314$	34.6641	+	176.825i	0.110395	+	0.563138i
$315$		0			0
$316$	−55.9222	−	137.151i	−0.176969	−	0.434022i
$317$	136.209	+	136.209i	0.429683	+	0.429683i	0.888520	−	0.458838i	$-0.151734\pi$
$317$	136.209	+	136.209i	0.429683	+	0.429683i	−0.458838	+	0.888520i	$0.651734\pi$
$318$		0			0
$319$	−320.074			−1.00337
$320$	−75.7805	+	29.9246i	−0.236814	+	0.0935144i
$321$		0			0
$322$	232.992	+	156.615i	0.723577	+	0.486381i
$323$	0.565134	+	0.565134i	0.00174964	+	0.00174964i
$324$		0			0
$325$	256.761	+	256.761i	0.790035	+	0.790035i
$326$	−57.4748	−	293.185i	−0.176303	−	0.899340i
$327$		0			0
$328$	−357.882	−	74.2820i	−1.09110	−	0.226469i
$329$	−433.596			−1.31792
$330$		0			0
$331$	432.414	+	432.414i	1.30639	+	1.30639i	0.924003	+	0.382385i	$0.124897\pi$
$331$	432.414	+	432.414i	1.30639	+	1.30639i	0.382385	+	0.924003i	$0.375103\pi$
$332$	185.221	−	440.253i	0.557895	−	1.32606i
$333$		0			0
$334$	285.319	−	424.462i	0.854248	−	1.27084i
$335$		−	34.0442i		−	0.101624i
$336$		0			0
$337$	−383.585			−1.13823			−0.569117	−	0.822256i	$-0.692715\pi$
$337$	−383.585			−1.13823			−0.569117	+	0.822256i	$0.692715\pi$
$338$	119.885	+	80.5853i	0.354688	+	0.238418i
$339$		0			0
$340$	−0.0859443	+	0.204282i	−0.000252777	+	0.000600828i
$341$	175.975	−	175.975i	0.516057	−	0.516057i
$342$		0			0
$343$		−	300.866i		−	0.877159i
$344$	−319.459	−	486.808i	−0.928660	−	1.41514i
$345$		0			0
$346$	−158.085	+	30.9904i	−0.456893	+	0.0895676i
$347$	111.739	−	111.739i	0.322014	−	0.322014i	−0.527526	−	0.849539i	$-0.676880\pi$
$347$	111.739	−	111.739i	0.322014	−	0.322014i	0.849539	+	0.527526i	$0.176880\pi$
$348$		0			0
$349$	−431.263	+	431.263i	−1.23571	+	1.23571i	−0.273971	+	0.961738i	$0.588337\pi$
$349$	−431.263	+	431.263i	−1.23571	+	1.23571i	−0.961738	+	0.273971i	$0.911663\pi$
$350$	−199.933	+	297.435i	−0.571238	+	0.849815i
$351$		0			0
$352$	−170.563	−	117.414i	−0.484555	−	0.333562i
$353$		−	290.324i		−	0.822448i	−0.911534	−	0.411224i	$-0.865101\pi$
$353$		−	290.324i		−	0.822448i	0.911534	−	0.411224i	$-0.134899\pi$
$354$		0			0
$355$	−103.405	+	103.405i	−0.291282	+	0.291282i
$356$	−205.654	−	504.373i	−0.577679	−	1.41678i
$357$		0			0
$358$	476.453	−	93.4019i	1.33087	−	0.260899i
$359$	81.9699			0.228329			0.114164	−	0.993462i	$-0.463581\pi$
$359$	81.9699			0.228329			0.114164	+	0.993462i	$0.463581\pi$
$360$		0			0
$361$			23.7867i			0.0658912i
$362$	−154.083	+	30.2058i	−0.425644	+	0.0834416i
$363$		0			0
$364$	−184.655	+	438.907i	−0.507294	+	1.20579i
$365$	−114.906	−	114.906i	−0.314810	−	0.314810i
$366$		0			0
$367$	−112.713			−0.307121			−0.153560	−	0.988139i	$-0.549074\pi$
$367$	−112.713			−0.307121			−0.153560	+	0.988139i	$0.549074\pi$
$368$	−209.480	+	204.891i	−0.569238	+	0.556769i
$369$		0			0
$370$	22.8764	−	34.0326i	0.0618281	−	0.0919801i
$371$	342.298	+	342.298i	0.922636	+	0.922636i
$372$		0			0
$373$	−32.7139	−	32.7139i	−0.0877049	−	0.0877049i	0.661893	−	0.749598i	$-0.269753\pi$
$373$	−32.7139	−	32.7139i	−0.0877049	−	0.0877049i	−0.749598	+	0.661893i	$0.769753\pi$
$374$	−0.552741	+	0.108357i	−0.00147792	+	0.000289725i
$375$		0			0
$376$	91.9752	−	443.125i	0.244615	−	1.17852i
$377$	−768.238			−2.03777
$378$		0			0
$379$	−413.066	−	413.066i	−1.08988	−	1.08988i	−0.995540	−	0.0943432i	$-0.969925\pi$
$379$	−413.066	−	413.066i	−1.08988	−	1.08988i	−0.0943432	−	0.995540i	$-0.530075\pi$
$380$	86.5884	−	35.3057i	0.227864	−	0.0929098i
$381$		0			0
$382$	169.218	+	113.747i	0.442979	+	0.297766i
$383$			616.895i			1.61069i	0.592805	+	0.805346i	$0.298020\pi$
$383$			616.895i			1.61069i	−0.592805	+	0.805346i	$0.701980\pi$
$384$		0			0
$385$	63.1393			0.163998
$386$	−90.9336	+	135.280i	−0.235579	+	0.350465i
$387$		0			0
$388$	261.991	+	642.541i	0.675235	+	1.65603i
$389$	−414.902	+	414.902i	−1.06659	+	1.06659i	−0.0689668	+	0.997619i	$0.521970\pi$
$389$	−414.902	+	414.902i	−1.06659	+	1.06659i	−0.997619	+	0.0689668i	$0.978030\pi$
$390$		0			0
$391$			0.797066i			0.00203853i
$392$	−76.3415	−	15.8455i	−0.194749	−	0.0404221i
$393$		0			0
$394$	92.8680	+	473.729i	0.235705	+	1.20236i
$395$	−33.3322	+	33.3322i	−0.0843854	+	0.0843854i
$396$		0			0
$397$	−252.200	+	252.200i	−0.635266	+	0.635266i	−0.949384	−	0.314118i	$-0.898291\pi$
$397$	−252.200	+	252.200i	−0.635266	+	0.635266i	0.314118	+	0.949384i	$0.398291\pi$
$398$	−311.098	−	209.117i	−0.781653	−	0.525419i
$399$		0			0
$400$	−261.562	−	267.420i	−0.653905	−	0.668550i
$401$		−	161.463i		−	0.402651i	−0.979524	−	0.201325i	$-0.935475\pi$
$401$		−	161.463i		−	0.402651i	0.979524	−	0.201325i	$-0.0645249\pi$
$402$		0			0
$403$	422.375	−	422.375i	1.04808	−	1.04808i
$404$	−96.0903	−	40.4266i	−0.237847	−	0.100066i
$405$		0			0
$406$	−145.865	−	744.071i	−0.359273	−	1.83269i
$407$	104.219			0.256067
$408$		0			0
$409$		−	156.176i		−	0.381847i	−0.981605	−	0.190924i	$-0.938852\pi$
$409$		−	156.176i		−	0.381847i	0.981605	−	0.190924i	$-0.0611483\pi$
$410$	22.3784	+	114.155i	0.0545816	+	0.278426i
$411$		0			0
$412$	329.270	−	134.257i	0.799200	−	0.325867i
$413$	159.127	+	159.127i	0.385296	+	0.385296i
$414$		0			0
$415$	−152.011			−0.366291
$416$	−409.384	−	281.815i	−0.984097	−	0.677440i
$417$		0			0
$418$	197.237	+	132.581i	0.471860	+	0.317180i
$419$	−530.843	−	530.843i	−1.26693	−	1.26693i	−0.947667	−	0.319260i	$-0.896566\pi$
$419$	−530.843	−	530.843i	−1.26693	−	1.26693i	−0.319260	−	0.947667i	$-0.603434\pi$
$420$		0			0
$421$	198.004	+	198.004i	0.470318	+	0.470318i	0.902017	−	0.431700i	$-0.142086\pi$
$421$	198.004	+	198.004i	0.470318	+	0.470318i	−0.431700	+	0.902017i	$0.642086\pi$
$422$	60.7643	+	309.965i	0.143991	+	0.734513i
$423$		0			0
$424$	−422.430	+	277.212i	−0.996297	+	0.653802i
$425$	−1.01753			−0.00239418
$426$		0			0
$427$	18.6024	+	18.6024i	0.0435654	+	0.0435654i
$428$	283.533	+	119.287i	0.662461	+	0.278707i
$429$		0			0
$430$	−103.381	+	153.797i	−0.240420	+	0.357667i
$431$		−	418.584i		−	0.971192i	−0.874183	−	0.485596i	$-0.838603\pi$
$431$		−	418.584i		−	0.971192i	0.874183	−	0.485596i	$-0.161397\pi$
$432$		0			0
$433$	747.383			1.72606			0.863029	−	0.505154i	$-0.168564\pi$
$433$	747.383			1.72606			0.863029	+	0.505154i	$0.168564\pi$
$434$	489.284	+	328.892i	1.12738	+	0.757815i
$435$		0			0
$436$	−636.232	−	267.672i	−1.45925	−	0.613927i
$437$	237.803	−	237.803i	0.544172	−	0.544172i
$438$		0			0
$439$		−	304.573i		−	0.693789i	−0.937904	−	0.346894i	$-0.887236\pi$
$439$		−	304.573i		−	0.693789i	0.937904	−	0.346894i	$-0.112764\pi$
$440$	−13.3932	+	64.5270i	−0.0304392	+	0.146652i
$441$		0			0
$442$	−1.32668	+	0.260078i	−0.00300154	+	0.000588411i
$443$	479.719	−	479.719i	1.08289	−	1.08289i	0.0866493	−	0.996239i	$-0.472384\pi$
$443$	479.719	−	479.719i	1.08289	−	1.08289i	0.996239	−	0.0866493i	$-0.0276159\pi$
$444$		0			0
$445$	−122.579	+	122.579i	−0.275459	+	0.275459i
$446$	−150.992	+	224.627i	−0.338547	+	0.503648i
$447$		0			0
$448$	195.220	−	450.014i	0.435760	−	1.00450i
$449$			485.831i			1.08203i	0.841013	+	0.541015i	$0.181960\pi$
$449$			485.831i			1.08203i	−0.841013	+	0.541015i	$0.818040\pi$
$450$		0			0
$451$	−209.055	+	209.055i	−0.463536	+	0.463536i
$452$	602.348	−	245.603i	1.33263	−	0.543369i
$453$		0			0
$454$	−18.7089	+	3.66762i	−0.0412091	+	0.00807847i
$455$	151.546			0.333069
$456$		0			0
$457$		−	413.632i		−	0.905102i	−0.891738	−	0.452551i	$-0.850514\pi$
$457$		−	413.632i		−	0.905102i	0.891738	−	0.452551i	$-0.149486\pi$
$458$	135.873	−	26.6360i	0.296666	−	0.0581573i
$459$		0			0
$460$	85.9600	+	36.1646i	0.186869	+	0.0786188i
$461$	54.2195	+	54.2195i	0.117613	+	0.117613i	0.763464	−	0.645851i	$-0.223497\pi$
$461$	54.2195	+	54.2195i	0.117613	+	0.117613i	−0.645851	+	0.763464i	$0.723497\pi$
$462$		0			0
$463$	−135.028			−0.291637			−0.145819	−	0.989311i	$-0.546582\pi$
$463$	−135.028			−0.291637			−0.145819	+	0.989311i	$0.546582\pi$
$464$	791.366	+	8.76315i	1.70553	+	0.0188861i
$465$		0			0
$466$	−113.240	+	168.465i	−0.243005	+	0.361513i
$467$	583.642	+	583.642i	1.24977	+	1.24977i	0.955822	+	0.293947i	$0.0949689\pi$
$467$	583.642	+	583.642i	1.24977	+	1.24977i	0.293947	+	0.955822i	$0.405031\pi$
$468$		0			0
$469$	144.935	+	144.935i	0.309030	+	0.309030i
$470$	−141.345	+	27.7088i	−0.300734	+	0.0589548i
$471$		0			0
$472$	−196.379	+	128.870i	−0.416058	+	0.273030i
$473$	−470.977			−0.995722
$474$		0			0
$475$	303.578	+	303.578i	0.639111	+	0.639111i
$476$	−0.503793	−	1.23557i	−0.00105839	−	0.00259573i
$477$		0			0
$478$	−79.3108	−	53.3119i	−0.165922	−	0.111531i
$479$			51.0721i			0.106622i	0.998578	+	0.0533112i	$0.0169775\pi$
$479$			51.0721i			0.106622i	−0.998578	+	0.0533112i	$0.983022\pi$
$480$		0			0
$481$	250.146			0.520053
$482$	20.3929	−	30.3380i	0.0423089	−	0.0629419i
$483$		0			0
$484$	293.082	−	119.502i	0.605541	−	0.246904i
$485$	156.159	−	156.159i	0.321977	−	0.321977i
$486$		0			0
$487$		−	490.285i		−	1.00674i	−0.864070	−	0.503372i	$-0.832092\pi$
$487$		−	490.285i		−	1.00674i	0.864070	−	0.503372i	$-0.167908\pi$
$488$	−22.9572	+	15.0653i	−0.0470435	+	0.0308715i
$489$		0			0
$490$	4.77366	+	24.3509i	0.00974216	+	0.0496957i
$491$	219.757	−	219.757i	0.447570	−	0.447570i	−0.446976	−	0.894546i	$-0.647499\pi$
$491$	219.757	−	219.757i	0.447570	−	0.447570i	0.894546	+	0.446976i	$0.147499\pi$
$492$		0			0
$493$	1.52224	−	1.52224i	0.00308770	−	0.00308770i
$494$	473.407	+	318.220i	0.958314	+	0.644170i
$495$		0			0
$496$	−439.908	+	430.272i	−0.886911	+	0.867484i
$497$		−	880.446i		−	1.77152i
$498$		0			0
$499$	435.155	−	435.155i	0.872054	−	0.872054i	−0.120642	−	0.992696i	$-0.538495\pi$
$499$	435.155	−	435.155i	0.872054	−	0.872054i	0.992696	+	0.120642i	$0.0384955\pi$
$500$	−95.5352	+	227.078i	−0.191070	+	0.454157i
$501$		0			0
$502$	163.593	+	834.504i	0.325883	+	1.66236i
$503$	46.8803			0.0932014			0.0466007	−	0.998914i	$-0.485161\pi$
$503$	46.8803			0.0932014			0.0466007	+	0.998914i	$0.485161\pi$
$504$		0			0
$505$			33.1781i			0.0656993i
$506$	45.5958	+	232.589i	0.0901102	+	0.459661i
$507$		0			0
$508$	−54.7786	−	134.346i	−0.107832	−	0.264461i
$509$	166.731	+	166.731i	0.327566	+	0.327566i	0.851660	−	0.524094i	$-0.175596\pi$
$509$	166.731	+	166.731i	0.327566	+	0.327566i	−0.524094	+	0.851660i	$0.675596\pi$
$510$		0			0
$511$	978.368			1.91461
$512$	418.494	+	294.969i	0.817371	+	0.576111i
$513$		0			0
$514$	−282.933	−	190.185i	−0.550453	−	0.370009i
$515$	−80.0236	−	80.0236i	−0.155386	−	0.155386i
$516$		0			0
$517$	−258.849	−	258.849i	−0.500676	−	0.500676i
$518$	47.4950	+	242.277i	0.0916892	+	0.467716i
$519$		0			0
$520$	−32.1463	+	154.877i	−0.0618198	+	0.297840i
$521$	351.071			0.673840			0.336920	−	0.941533i	$-0.390615\pi$
$521$	351.071			0.673840			0.336920	+	0.941533i	$0.390615\pi$
$522$		0			0
$523$	214.780	+	214.780i	0.410670	+	0.410670i	0.881972	−	0.471302i	$-0.156216\pi$
$523$	214.780	+	214.780i	0.410670	+	0.410670i	−0.471302	+	0.881972i	$0.656216\pi$
$524$	−131.402	+	312.331i	−0.250768	+	0.596052i
$525$		0			0
$526$	329.120	−	489.624i	0.625704	−	0.930843i
$527$			1.67384i			0.00317617i
$528$		0			0
$529$	−193.601			−0.365976
$530$	133.458	+	89.7091i	0.251807	+	0.169263i
$531$		0			0
$532$	−218.324	+	518.935i	−0.410383	+	0.975443i
$533$	−501.771	+	501.771i	−0.941409	+	0.941409i
$534$		0			0
$535$		−	97.8986i		−	0.182988i
$536$	−178.864	+	117.376i	−0.333702	+	0.218986i
$537$		0			0
$538$	−360.748	+	70.7197i	−0.670536	+	0.131449i
$539$	−44.5945	+	44.5945i	−0.0827356	+	0.0827356i
$540$		0			0
$541$	579.728	−	579.728i	1.07159	−	1.07159i	0.0743548	−	0.997232i	$-0.476310\pi$
$541$	579.728	−	579.728i	1.07159	−	1.07159i	0.997232	−	0.0743548i	$-0.0236897\pi$
$542$	597.139	−	888.349i	1.10173	−	1.63902i
$543$		0			0
$544$	1.36959	−	0.252774i	0.00251763	−	0.000464658i
$545$			219.679i			0.403080i
$546$		0			0
$547$	100.142	−	100.142i	0.183075	−	0.183075i	−0.609619	−	0.792694i	$-0.708678\pi$
$547$	100.142	−	100.142i	0.183075	−	0.183075i	0.792694	+	0.609619i	$0.208678\pi$
$548$	−148.777	−	364.882i	−0.271492	−	0.665842i
$549$		0			0
$550$	−296.920	+	58.2072i	−0.539855	+	0.105831i
$551$	−908.314			−1.64848
$552$		0			0
$553$		−	283.808i		−	0.513215i
$554$	172.322	−	33.7813i	0.311050	−	0.0609771i
$555$		0			0
$556$	7.45765	−	17.7261i	0.0134130	−	0.0318816i
$557$	−644.771	−	644.771i	−1.15758	−	1.15758i	−0.984995	−	0.172584i	$-0.944788\pi$
$557$	−644.771	−	644.771i	−1.15758	−	1.15758i	−0.172584	−	0.984995i	$-0.555212\pi$
$558$		0			0
$559$	−1130.43			−2.02224
$560$	−156.109	−	1.72866i	−0.278765	−	0.00308690i
$561$		0			0
$562$	−114.139	+	169.802i	−0.203095	+	0.302139i
$563$	−418.555	−	418.555i	−0.743436	−	0.743436i	0.229801	−	0.973238i	$-0.426192\pi$
$563$	−418.555	−	418.555i	−0.743436	−	0.743436i	−0.973238	+	0.229801i	$0.926192\pi$
$564$		0			0
$565$	−146.391	−	146.391i	−0.259098	−	0.259098i
$566$	−457.711	+	89.7280i	−0.808677	+	0.158530i
$567$		0			0
$568$	899.797	+	186.762i	1.58415	+	0.328806i
$569$	652.285			1.14637			0.573186	−	0.819426i	$-0.305707\pi$
$569$	652.285			1.14637			0.573186	+	0.819426i	$0.305707\pi$
$570$		0			0
$571$	13.6933	+	13.6933i	0.0239813	+	0.0239813i	0.718996	−	0.695014i	$-0.244602\pi$
$571$	13.6933	+	13.6933i	0.0239813	+	0.0239813i	−0.695014	+	0.718996i	$0.744602\pi$
$572$	−372.256	+	151.784i	−0.650797	+	0.265357i
$573$		0			0
$574$	−581.257	−	390.716i	−1.01264	−	0.680689i
$575$			428.167i			0.744638i
$576$		0			0
$577$	−269.997			−0.467932			−0.233966	−	0.972245i	$-0.575170\pi$
$577$	−269.997			−0.467932			−0.233966	+	0.972245i	$0.575170\pi$
$578$	−322.447	+	479.696i	−0.557866	+	0.829923i
$579$		0			0
$580$	−95.0992	−	233.234i	−0.163964	−	0.402127i
$581$	647.150	−	647.150i	1.11386	−	1.11386i
$582$		0			0
$583$			408.692i			0.701015i
$584$	−207.533	+	999.871i	−0.355365	+	1.71211i
$585$		0			0
$586$	−110.587	−	564.117i	−0.188716	−	0.962658i
$587$	−784.885	+	784.885i	−1.33711	+	1.33711i	−0.438269	+	0.898844i	$0.644408\pi$
$587$	−784.885	+	784.885i	−1.33711	+	1.33711i	−0.898844	+	0.438269i	$0.855592\pi$
$588$		0			0
$589$	499.388	−	499.388i	0.847857	−	0.847857i
$590$	62.0419	+	41.7040i	0.105156	+	0.0706847i
$591$		0			0
$592$	−257.676	−	2.85337i	−0.435264	−	0.00481988i
$593$			451.885i			0.762032i	0.924569	+	0.381016i	$0.124426\pi$
$593$			451.885i			0.762032i	−0.924569	+	0.381016i	$0.875574\pi$
$594$		0			0
$595$	−0.300284	+	0.300284i	−0.000504679	+	0.000504679i
$596$	47.0929	+	19.8127i	0.0790150	+	0.0332428i
$597$		0			0
$598$	109.438	+	558.257i	0.183008	+	0.933540i
$599$	664.313			1.10904			0.554518	−	0.832171i	$-0.312902\pi$
$599$	664.313			1.10904			0.554518	+	0.832171i	$0.312902\pi$
$600$		0			0
$601$			496.693i			0.826444i	0.910630	+	0.413222i	$0.135597\pi$
$601$			496.693i			0.826444i	−0.910630	+	0.413222i	$0.864403\pi$
$602$	−214.635	−	1094.87i	−0.356536	−	1.81873i
$603$		0			0
$604$	255.774	−	104.290i	0.423468	−	0.172666i
$605$	−71.2286	−	71.2286i	−0.117733	−	0.117733i
$606$		0			0
$607$	595.964			0.981819			0.490910	−	0.871210i	$-0.336665\pi$
$607$	595.964			0.981819			0.490910	+	0.871210i	$0.336665\pi$
$608$	−484.029	−	333.200i	−0.796101	−	0.548026i
$609$		0			0
$610$	7.25287	+	4.87531i	0.0118899	+	0.00799230i
$611$	−621.287	−	621.287i	−1.01684	−	1.01684i
$612$		0			0
$613$	228.109	+	228.109i	0.372119	+	0.372119i	0.868249	−	0.496129i	$-0.165246\pi$
$613$	228.109	+	228.109i	0.372119	+	0.372119i	−0.496129	+	0.868249i	$0.665246\pi$
$614$	−72.4306	−	369.476i	−0.117965	−	0.601752i
$615$		0			0
$616$	−217.690	−	331.727i	−0.353392	−	0.538517i
$617$	199.680			0.323631			0.161815	−	0.986821i	$-0.448265\pi$
$617$	199.680			0.323631			0.161815	+	0.986821i	$0.448265\pi$
$618$		0			0
$619$	−8.72024	−	8.72024i	−0.0140876	−	0.0140876i	0.700028	−	0.714116i	$-0.253171\pi$
$619$	−8.72024	−	8.72024i	−0.0140876	−	0.0140876i	−0.714116	+	0.700028i	$0.753171\pi$
$620$	180.516	+	75.9459i	0.291155	+	0.122493i
$621$		0			0
$622$	−291.189	+	433.195i	−0.468150	+	0.696455i
$623$		−	1043.70i		−	1.67529i
$624$		0			0
$625$	−506.078			−0.809725
$626$	−262.202	−	176.250i	−0.418853	−	0.281549i
$627$		0			0
$628$	−332.181	−	139.753i	−0.528950	−	0.222537i
$629$	−0.495655	+	0.495655i	−0.000788005	+	0.000788005i
$630$		0			0
$631$			558.798i			0.885575i	0.896627	+	0.442788i	$0.146010\pi$
$631$			558.798i			0.885575i	−0.896627	+	0.442788i	$0.853990\pi$
$632$	290.046	+	60.2019i	0.458933	+	0.0952562i
$633$		0			0
$634$	−378.062	+	74.1139i	−0.596313	+	0.116899i
$635$	−32.6506	+	32.6506i	−0.0514182	+	0.0514182i
$636$		0			0
$637$	−107.035	+	107.035i	−0.168030	+	0.168030i
$638$	357.119	−	531.277i	0.559748	−	0.832722i
$639$		0			0
$640$	34.8807	−	159.173i	0.0545011	−	0.248708i
$641$		−	549.401i		−	0.857100i	−0.903518	−	0.428550i	$-0.859025\pi$
$641$		−	549.401i		−	0.857100i	0.903518	−	0.428550i	$-0.140975\pi$
$642$		0			0
$643$	−615.401	+	615.401i	−0.957078	+	0.957078i	−0.999116	−	0.0420379i	$-0.986615\pi$
$643$	−615.401	+	615.401i	−0.957078	+	0.957078i	0.0420379	+	0.999116i	$0.486615\pi$
$644$	−519.916	+	211.992i	−0.807324	+	0.329180i
$645$		0			0
$646$	−1.56858	+	0.307499i	−0.00242815	+	0.000476005i
$647$	−1040.44			−1.60810			−0.804051	−	0.594560i	$-0.797326\pi$
$647$	−1040.44			−1.60810			−0.804051	+	0.594560i	$0.797326\pi$
$648$		0			0
$649$			189.993i			0.292747i
$650$	−712.666	+	139.708i	−1.09641	+	0.214936i
$651$		0			0
$652$	550.772	+	231.718i	0.844742	+	0.355395i
$653$	359.946	+	359.946i	0.551218	+	0.551218i	0.926792	−	0.375574i	$-0.122554\pi$
$653$	359.946	+	359.946i	0.551218	+	0.551218i	−0.375574	+	0.926792i	$0.622554\pi$
$654$		0			0
$655$	107.842			0.164644
$656$	522.600	−	511.153i	0.796646	−	0.779196i
$657$		0			0
$658$	483.780	−	719.707i	0.735228	−	1.09378i
$659$	675.277	+	675.277i	1.02470	+	1.02470i	0.999687	+	0.0250117i	$0.00796231\pi$
$659$	675.277	+	675.277i	1.02470	+	1.02470i	0.0250117	+	0.999687i	$0.492038\pi$
$660$		0			0
$661$	−118.754	−	118.754i	−0.179659	−	0.179659i	0.611548	−	0.791207i	$-0.290547\pi$
$661$	−118.754	−	118.754i	−0.179659	−	0.179659i	−0.791207	+	0.611548i	$0.790547\pi$
$662$	−1200.21	+	235.284i	−1.81300	+	0.355414i
$663$		0			0
$664$	524.099	+	798.648i	0.789305	+	1.20278i
$665$	179.178			0.269441
$666$		0			0
$667$	−640.545	−	640.545i	−0.960337	−	0.960337i
$668$	386.204	+	947.177i	0.578149	+	1.41793i
$669$		0			0
$670$	56.5085	+	37.9844i	0.0843410	+	0.0566932i
$671$			22.2106i			0.0331008i
$672$		0			0
$673$	−226.637			−0.336757			−0.168378	−	0.985722i	$-0.553853\pi$
$673$	−226.637			−0.336757			−0.168378	+	0.985722i	$0.553853\pi$
$674$	427.981	−	636.696i	0.634987	−	0.944653i
$675$		0			0
$676$	−267.520	+	109.079i	−0.395740	+	0.161360i
$677$	−529.591	+	529.591i	−0.782261	+	0.782261i	−0.980212	−	0.197951i	$-0.936571\pi$
$677$	−529.591	+	529.591i	−0.782261	+	0.782261i	0.197951	+	0.980212i	$0.436571\pi$
$678$		0			0
$679$			1329.62i			1.95820i
$680$	−0.243187	−	0.370580i	−0.000357628	−	0.000544971i
$681$		0			0
$682$	95.7513	+	488.437i	0.140398	+	0.716183i
$683$	−582.521	+	582.521i	−0.852885	+	0.852885i	−0.990488	−	0.137602i	$-0.956060\pi$
$683$	−582.521	+	582.521i	−0.852885	+	0.852885i	0.137602	+	0.990488i	$0.456060\pi$
$684$		0			0
$685$	−88.6783	+	88.6783i	−0.129457	+	0.129457i
$686$	499.394	+	335.688i	0.727979	+	0.489341i
$687$		0			0
$688$	1164.46	+	12.8947i	1.69254	+	0.0187422i
$689$			980.938i			1.42371i
$690$		0			0
$691$	−670.134	+	670.134i	−0.969803	+	0.969803i	−0.999557	−	0.0297546i	$-0.990527\pi$
$691$	−670.134	+	670.134i	−0.969803	+	0.969803i	0.0297546	+	0.999557i	$0.490527\pi$
$692$	124.942	−	296.976i	0.180552	−	0.429156i
$693$		0			0
$694$	60.7990	+	310.142i	0.0876066	+	0.446890i
$695$	−6.12050			−0.00880647
$696$		0			0
$697$		−	1.98848i		−	0.00285292i
$698$	−234.657	−	1197.01i	−0.336185	−	1.71492i
$699$		0			0
$700$	−270.627	−	663.721i	−0.386610	−	0.948173i
$701$	291.428	+	291.428i	0.415732	+	0.415732i	0.883730	−	0.467998i	$-0.155024\pi$
$701$	291.428	+	291.428i	0.415732	+	0.415732i	−0.467998	+	0.883730i	$0.655024\pi$
$702$		0			0
$703$	295.756			0.420705
$704$	385.194	−	152.108i	0.547151	−	0.216062i
$705$		0			0
$706$	481.897	+	323.926i	0.682573	+	0.458819i
$707$	−141.248	−	141.248i	−0.199785	−	0.199785i
$708$		0			0
$709$	−459.988	−	459.988i	−0.648784	−	0.648784i	0.303915	−	0.952699i	$-0.401706\pi$
$709$	−459.988	−	459.988i	−0.648784	−	0.648784i	−0.952699	+	0.303915i	$0.901706\pi$
$710$	−56.2646	−	287.011i	−0.0792459	−	0.404241i
$711$		0			0
$712$	1066.64	+	221.393i	1.49809	+	0.310945i
$713$	704.338			0.987852
$714$		0			0
$715$	90.4706	+	90.4706i	0.126532	+	0.126532i
$716$	−376.563	+	895.055i	−0.525926	+	1.25008i
$717$		0			0
$718$	−91.4571	+	136.058i	−0.127378	+	0.189496i
$719$		−	285.232i		−	0.396707i	−0.980131	−	0.198353i	$-0.936441\pi$
$719$		−	285.232i		−	0.396707i	0.980131	−	0.198353i	$-0.0635594\pi$
$720$		0			0
$721$	681.363			0.945025
$722$	−39.4826	−	26.5398i	−0.0546850	−	0.0367587i
$723$		0			0
$724$	121.779	−	289.458i	0.168203	−	0.399803i
$725$	817.714	−	817.714i	1.12788	−	1.12788i
$726$		0			0
$727$		−	114.350i		−	0.157290i	−0.996903	−	0.0786451i	$-0.974941\pi$
$727$		−	114.350i		−	0.157290i	0.996903	−	0.0786451i	$-0.0250594\pi$
$728$	−522.497	−	796.207i	−0.717715	−	1.09369i
$729$		0			0
$730$	318.932	−	62.5222i	0.436893	−	0.0856469i
$731$	2.23992	−	2.23992i	0.00306418	−	0.00306418i
$732$		0			0
$733$	−158.553	+	158.553i	−0.216307	+	0.216307i	−0.806940	−	0.590633i	$-0.798878\pi$
$733$	−158.553	+	158.553i	−0.216307	+	0.216307i	0.590633	+	0.806940i	$0.298878\pi$
$734$	125.759	−	187.088i	0.171333	−	0.254888i
$735$		0			0
$736$	−106.365	−	576.311i	−0.144518	−	0.783032i
$737$			173.047i			0.234800i
$738$		0			0
$739$	−381.275	+	381.275i	−0.515933	+	0.515933i	−0.916338	−	0.400405i	$-0.868869\pi$
$739$	−381.275	+	381.275i	−0.515933	+	0.515933i	0.400405	+	0.916338i	$0.368869\pi$
$740$	30.9652	+	75.9431i	0.0418449	+	0.102626i
$741$		0			0
$742$	−950.081	+	186.250i	−1.28043	+	0.251011i
$743$	445.947			0.600198			0.300099	−	0.953908i	$-0.402980\pi$
$743$	445.947			0.600198			0.300099	+	0.953908i	$0.402980\pi$
$744$		0			0
$745$		−	16.2603i		−	0.0218259i
$746$	90.8006	−	17.8002i	0.121717	−	0.0238609i
$747$		0			0
$748$	0.436857	−	1.03837i	0.000584034	−	0.00138819i
$749$	416.780	+	416.780i	0.556449	+	0.556449i
$750$		0			0
$751$	774.061			1.03071			0.515353	−	0.856978i	$-0.327661\pi$
$751$	774.061			1.03071			0.515353	+	0.856978i	$0.327661\pi$
$752$	632.904	+	647.078i	0.841628	+	0.860476i
$753$		0			0
$754$	857.154	−	1275.17i	1.13681	−	1.69120i
$755$	−62.1617	−	62.1617i	−0.0823333	−	0.0823333i
$756$		0			0
$757$	−431.310	−	431.310i	−0.569763	−	0.569763i	0.362299	−	0.932062i	$-0.381992\pi$
$757$	−431.310	−	431.310i	−0.569763	−	0.569763i	−0.932062	+	0.362299i	$0.881992\pi$
$758$	1146.50	−	224.756i	1.51254	−	0.296512i
$759$		0			0
$760$	−38.0077	+	183.116i	−0.0500101	+	0.240943i
$761$	1493.05			1.96195			0.980977	−	0.194123i	$-0.0621861\pi$
$761$	1493.05			1.96195			0.980977	+	0.194123i	$0.0621861\pi$
$762$		0			0
$763$	−935.229	−	935.229i	−1.22573	−	1.22573i
$764$	−377.606	+	153.966i	−0.494249	+	0.201526i
$765$		0			0
$766$	−1023.96	−	688.294i	−1.33676	−	0.898556i
$767$			456.019i			0.594548i
$768$		0			0
$769$	−823.023			−1.07025			−0.535126	−	0.844772i	$-0.679736\pi$
$769$	−823.023			−1.07025			−0.535126	+	0.844772i	$0.679736\pi$
$770$	−70.4470	+	104.802i	−0.0914896	+	0.136107i
$771$		0			0
$772$	−123.087	−	301.874i	−0.159438	−	0.391028i
$773$	322.532	−	322.532i	0.417247	−	0.417247i	−0.467007	−	0.884254i	$-0.654668\pi$
$773$	322.532	−	322.532i	0.417247	−	0.417247i	0.884254	+	0.467007i	$0.154668\pi$
$774$		0			0
$775$			899.152i			1.16020i
$776$	−1358.84	−	282.041i	−1.75108	−	0.363455i
$777$		0			0
$778$	−225.755	−	1151.60i	−0.290174	−	1.48021i
$779$	−593.261	+	593.261i	−0.761567	+	0.761567i
$780$		0			0
$781$	525.611	−	525.611i	0.672998	−	0.672998i
$782$	−1.32302	−	0.889318i	−0.00169184	−	0.00113724i
$783$		0			0
$784$	111.478	−	109.037i	0.142192	−	0.139077i
$785$			114.696i			0.146109i
$786$		0			0
$787$	470.300	−	470.300i	0.597586	−	0.597586i	−0.342083	−	0.939670i	$-0.611133\pi$
$787$	470.300	−	470.300i	0.597586	−	0.597586i	0.939670	+	0.342083i	$0.111133\pi$
$788$	−889.938	−	374.410i	−1.12936	−	0.475140i
$789$		0			0
$790$	−18.1366	−	92.5168i	−0.0229578	−	0.117110i
$791$	1246.45			1.57579
$792$		0			0
$793$			53.3098i			0.0672255i
$794$	−137.227	−	700.007i	−0.172829	−	0.881620i
$795$		0			0
$796$	694.208	−	283.058i	0.872121	−	0.355600i
$797$	−775.967	−	775.967i	−0.973610	−	0.973610i	0.0260505	−	0.999661i	$-0.491707\pi$
$797$	−775.967	−	775.967i	−0.973610	−	0.973610i	−0.999661	+	0.0260505i	$0.991707\pi$
$798$		0			0
$799$	2.46212			0.00308150
$800$	735.714	−	135.785i	0.919642	−	0.169731i
$801$		0			0
$802$	268.005	+	180.151i	0.334171	+	0.224627i
$803$	584.069	+	584.069i	0.727359	+	0.727359i
$804$		0			0
$805$	126.357	+	126.357i	0.156965	+	0.156965i
$806$	229.821	+	1172.34i	0.285138	+	1.45452i
$807$		0			0
$808$	174.314	−	114.391i	0.215735	−	0.141572i
$809$	−812.614			−1.00447			−0.502234	−	0.864732i	$-0.667488\pi$
$809$	−812.614			−1.00447			−0.502234	+	0.864732i	$0.667488\pi$
$810$		0			0
$811$	229.002	+	229.002i	0.282369	+	0.282369i	0.834053	−	0.551684i	$-0.186015\pi$
$811$	229.002	+	229.002i	0.282369	+	0.282369i	−0.551684	+	0.834053i	$0.686015\pi$
$812$	1397.80	+	588.075i	1.72143	+	0.724230i
$813$		0			0
$814$	−116.281	+	172.989i	−0.142852	+	0.212517i
$815$		−	190.171i		−	0.233338i
$816$		0			0
$817$	−1336.55			−1.63592
$818$	259.229	+	174.251i	0.316906	+	0.213021i
$819$		0			0
$820$	−214.449	−	90.2219i	−0.261523	−	0.110027i
$821$	−781.504	+	781.504i	−0.951893	+	0.951893i	−0.998895	−	0.0470014i	$-0.985033\pi$
$821$	−781.504	+	781.504i	−0.951893	+	0.951893i	0.0470014	+	0.998895i	$0.485033\pi$
$822$		0			0
$823$		−	757.548i		−	0.920472i	−0.887797	−	0.460236i	$-0.847765\pi$
$823$		−	757.548i		−	0.920472i	0.887797	−	0.460236i	$-0.152235\pi$
$824$	−144.532	+	696.338i	−0.175403	+	0.845070i
$825$		0			0
$826$	−441.674	+	86.5840i	−0.534714	+	0.104823i
$827$	−168.079	+	168.079i	−0.203240	+	0.203240i	−0.801387	−	0.598147i	$-0.795904\pi$
$827$	−168.079	+	168.079i	−0.203240	+	0.203240i	0.598147	+	0.801387i	$0.295904\pi$
$828$		0			0
$829$	1044.13	−	1044.13i	1.25950	−	1.25950i	0.308171	−	0.951331i	$-0.400283\pi$
$829$	1044.13	−	1044.13i	1.25950	−	1.25950i	0.951331	−	0.308171i	$-0.0997170\pi$
$830$	169.605	−	252.316i	0.204343	−	0.303996i
$831$		0			0
$832$	924.539	−	365.087i	1.11122	−	0.438807i
$833$		−	0.424174i		−	0.000509212i
$834$		0			0
$835$	230.195	−	230.195i	0.275683	−	0.275683i
$836$	−440.131	+	179.460i	−0.526473	+	0.214665i
$837$		0			0
$838$	1473.40	−	288.841i	1.75824	−	0.344679i
$839$	−1052.57			−1.25456			−0.627278	−	0.778796i	$-0.715831\pi$
$839$	−1052.57			−1.25456			−0.627278	+	0.778796i	$0.715831\pi$
$840$		0			0
$841$			1605.63i			1.90919i
$842$	−549.579	+	107.737i	−0.652706	+	0.127954i
$843$		0			0
$844$	−582.294	−	244.980i	−0.689922	−	0.290260i
$845$	65.0162	+	65.0162i	0.0769423	+	0.0769423i
$846$		0			0
$847$	606.478			0.716030
$848$	11.1894	−	1010.47i	0.0131950	−	1.19159i
$849$		0			0
$850$	1.13530	−	1.68895i	0.00133564	−	0.00198700i
$851$	208.567	+	208.567i	0.245085	+	0.245085i
$852$		0			0
$853$	−101.196	−	101.196i	−0.118636	−	0.118636i	0.645296	−	0.763932i	$-0.276734\pi$
$853$	−101.196	−	101.196i	−0.118636	−	0.118636i	−0.763932	+	0.645296i	$0.776734\pi$
$854$	−51.6328	+	10.1219i	−0.0604600	+	0.0118523i
$855$		0			0
$856$	−514.348	+	337.532i	−0.600874	+	0.394313i
$857$	280.731			0.327574			0.163787	−	0.986496i	$-0.447629\pi$
$857$	280.731			0.327574			0.163787	+	0.986496i	$0.447629\pi$
$858$		0			0
$859$	−743.635	−	743.635i	−0.865699	−	0.865699i	0.126294	−	0.991993i	$-0.459692\pi$
$859$	−743.635	−	743.635i	−0.865699	−	0.865699i	−0.991993	+	0.126294i	$0.959692\pi$
$860$	−139.935	−	343.195i	−0.162715	−	0.399064i
$861$		0			0
$862$	694.789	+	467.030i	0.806020	+	0.541799i
$863$			98.7005i			0.114369i	0.998364	+	0.0571845i	$0.0182123\pi$
$863$			98.7005i			0.114369i	−0.998364	+	0.0571845i	$0.981788\pi$
$864$		0			0
$865$	−102.540			−0.118543
$866$	−833.885	+	1240.55i	−0.962916	+	1.43250i
$867$		0			0
$868$	−1091.83	+	445.184i	−1.25786	+	0.512884i
$869$	169.429	−	169.429i	0.194970	−	0.194970i
$870$		0			0
$871$			415.347i			0.476862i
$872$	1154.17	−	757.401i	1.32358	−	0.868579i
$873$		0			0
$874$	129.393	+	660.046i	0.148047	+	0.755202i
$875$	−333.794	+	333.794i	−0.381479	+	0.381479i
$876$		0			0
$877$	552.841	−	552.841i	0.630378	−	0.630378i	−0.317785	−	0.948163i	$-0.602939\pi$
$877$	552.841	−	552.841i	0.630378	−	0.630378i	0.948163	+	0.317785i	$0.102939\pi$
$878$	505.548	+	339.824i	0.575795	+	0.387044i
$879$		0			0
$880$	−92.1622	−	94.2261i	−0.104730	−	0.107075i
$881$			316.248i			0.358965i	0.983761	+	0.179482i	$0.0574423\pi$
$881$			316.248i			0.358965i	−0.983761	+	0.179482i	$0.942558\pi$
$882$		0			0
$883$	−98.6469	+	98.6469i	−0.111718	+	0.111718i	−0.760756	−	0.649038i	$-0.775172\pi$
$883$	−98.6469	+	98.6469i	−0.111718	+	0.111718i	0.649038	+	0.760756i	$0.275172\pi$
$884$	1.04854	−	2.49228i	0.00118613	−	0.00281932i
$885$		0			0
$886$	261.024	+	1331.51i	0.294609	+	1.50283i
$887$	1426.43			1.60815			0.804074	−	0.594530i	$-0.202662\pi$
$887$	1426.43			1.60815			0.804074	+	0.594530i	$0.202662\pi$
$888$		0			0
$889$		−	278.004i		−	0.312715i
$890$	−66.6975	−	340.231i	−0.0749410	−	0.382282i
$891$		0			0
$892$	−204.381	−	501.251i	−0.229127	−	0.561940i
$893$	−734.570	−	734.570i	−0.822586	−	0.822586i
$894$		0			0
$895$	309.045			0.345302
$896$	529.144	+	826.137i	0.590563	+	0.922028i
$897$		0			0
$898$	−806.410	−	542.061i	−0.898007	−	0.603631i
$899$	−1345.15	−	1345.15i	−1.49627	−	1.49627i
$900$		0			0
$901$	−1.94370	−	1.94370i	−0.00215727	−	0.00215727i
$902$	−113.750	−	580.251i	−0.126109	−	0.643294i
$903$		0			0
$904$	−264.399	+	1273.84i	−0.292476	+	1.40912i
$905$	−99.9442			−0.110436
$906$		0			0
$907$	238.634	+	238.634i	0.263103	+	0.263103i	0.826313	−	0.563211i	$-0.190434\pi$
$907$	238.634	+	238.634i	0.263103	+	0.263103i	−0.563211	+	0.826313i	$0.690434\pi$
$908$	14.7865	−	35.1462i	0.0162847	−	0.0387073i
$909$		0			0
$910$	−169.086	+	251.545i	−0.185809	+	0.276423i
$911$		−	1309.38i		−	1.43730i	−0.695374	−	0.718648i	$-0.744761\pi$
$911$		−	1309.38i		−	1.43730i	0.695374	−	0.718648i	$-0.255239\pi$
$912$		0			0
$913$	772.676			0.846304
$914$	686.570	+	461.505i	0.751170	+	0.504929i
$915$		0			0
$916$	−107.387	+	255.249i	−0.117235	+	0.278656i
$917$	−459.112	+	459.112i	−0.500667	+	0.500667i
$918$		0			0
$919$		−	511.000i		−	0.556039i	−0.960575	−	0.278019i	$-0.910322\pi$
$919$		−	511.000i		−	0.556039i	0.960575	−	0.278019i	$-0.0896779\pi$
$920$	−155.937	+	102.331i	−0.169497	+	0.111229i
$921$		0			0
$922$	−150.492	+	29.5018i	−0.163223	+	0.0319976i
$923$	1261.57	−	1261.57i	1.36681	−	1.36681i
$924$		0			0
$925$	−266.255	+	266.255i	−0.287844	+	0.287844i
$926$	150.656	−	224.127i	0.162696	−	0.242038i
$927$		0			0
$928$	−897.504	+	1303.78i	−0.967137	+	1.40493i
$929$			386.394i			0.415924i	0.978137	+	0.207962i	$0.0666831\pi$
$929$			386.394i			0.415924i	−0.978137	+	0.207962i	$0.933317\pi$
$930$		0			0
$931$	−126.551	+	126.551i	−0.135931	+	0.135931i
$932$	−153.281	−	375.926i	−0.164464	−	0.403354i
$933$		0			0
$934$	−1619.95	+	317.570i	−1.73443	+	0.340010i
$935$	−0.358529			−0.000383453
$936$		0			0
$937$			927.440i			0.989797i	0.868951	+	0.494898i	$0.164795\pi$
$937$			927.440i			0.989797i	−0.868951	+	0.494898i	$0.835205\pi$
$938$	−402.281	+	78.8616i	−0.428871	+	0.0840742i
$939$		0			0
$940$	111.712	−	265.529i	0.118842	−	0.282477i
$941$	−645.746	−	645.746i	−0.686234	−	0.686234i	0.275164	−	0.961397i	$-0.411268\pi$
$941$	−645.746	−	645.746i	−0.686234	−	0.686234i	−0.961397	+	0.275164i	$0.911268\pi$
$942$		0			0
$943$	−836.737			−0.887314
$944$	5.20172	−	469.747i	0.00551030	−	0.497613i
$945$		0			0
$946$	525.487	−	781.754i	0.555483	−	0.826378i
$947$	1017.28	+	1017.28i	1.07421	+	1.07421i	0.997016	+	0.0771972i	$0.0245971\pi$
$947$	1017.28	+	1017.28i	1.07421	+	1.07421i	0.0771972	+	0.997016i	$0.475403\pi$
$948$		0			0
$949$	1401.88	+	1401.88i	1.47721	+	1.47721i
$950$	−842.609	+	165.182i	−0.886957	+	0.173876i
$951$		0			0
$952$	2.61297	+	0.542348i	0.00274471	+	0.000569693i
$953$	−214.062			−0.224619			−0.112309	−	0.993673i	$-0.535825\pi$
$953$	−214.062			−0.224619			−0.112309	+	0.993673i	$0.535825\pi$
$954$		0			0
$955$	91.7708	+	91.7708i	0.0960951	+	0.0960951i
$956$	176.980	−	72.1623i	0.185126	−	0.0754836i
$957$		0			0
$958$	−84.7724	−	56.9832i	−0.0884890	−	0.0594814i
$959$		−	755.054i		−	0.787334i
$960$		0			0
$961$	518.114			0.539140
$962$	−279.097	+	415.206i	−0.290122	+	0.431607i
$963$		0			0
$964$	27.6036	+	67.6986i	0.0286344	+	0.0702268i
$965$	−73.3653	+	73.3653i	−0.0760262	+	0.0760262i
$966$		0			0
$967$		−	440.861i		−	0.455906i	−0.973672	−	0.227953i	$-0.926797\pi$
$967$		−	440.861i		−	0.455906i	0.973672	−	0.227953i	$-0.0732033\pi$
$968$	−128.647	+	619.807i	−0.132900	+	0.640296i
$969$		0			0
$970$	84.9687	+	433.434i	0.0875966	+	0.446839i
$971$	−343.159	+	343.159i	−0.353407	+	0.353407i	−0.861376	−	0.507968i	$-0.830397\pi$
$971$	−343.159	+	343.159i	−0.353407	+	0.353407i	0.507968	+	0.861376i	$0.330397\pi$
$972$		0			0
$973$	26.0566	−	26.0566i	0.0267796	−	0.0267796i
$974$	813.802	+	547.030i	0.835526	+	0.561632i
$975$		0			0
$976$	0.608095	−	54.9147i	0.000623048	−	0.0562650i
$977$		−	388.323i		−	0.397465i	−0.980054	−	0.198733i	$-0.936317\pi$
$977$		−	388.323i		−	0.397465i	0.980054	−	0.198733i	$-0.0636825\pi$
$978$		0			0
$979$	623.073	−	623.073i	0.636439	−	0.636439i
$980$	−45.7452	−	19.2457i	−0.0466788	−	0.0196385i
$981$		0			0
$982$	119.574	+	609.957i	0.121765	+	0.621137i
$983$	−1344.22			−1.36746			−0.683731	−	0.729734i	$-0.739644\pi$
$983$	−1344.22			−1.36746			−0.683731	+	0.729734i	$0.739644\pi$
$984$		0			0
$985$			307.279i			0.311958i
$986$	0.828276	+	4.22512i	0.000840037	+	0.00428511i
$987$		0			0
$988$	−1056.40	+	430.738i	−1.06923	+	0.435970i
$989$	−942.538	−	942.538i	−0.953021	−	0.953021i
$990$		0			0
$991$	1058.38			1.06799			0.533997	−	0.845486i	$-0.320689\pi$
$991$	1058.38			1.06799			0.533997	+	0.845486i	$0.320689\pi$
$992$	−223.367	−	1210.26i	−0.225169	−	1.22002i
$993$		0			0
$994$	1461.41	+	982.349i	1.47024	+	0.988278i
$995$	−168.716	−	168.716i	−0.169563	−	0.169563i
$996$		0			0
$997$	−554.656	−	554.656i	−0.556325	−	0.556325i	0.371934	−	0.928259i	$-0.378695\pi$
$997$	−554.656	−	554.656i	−0.556325	−	0.556325i	−0.928259	+	0.371934i	$0.878695\pi$
$998$	236.775	+	1207.81i	0.237250	+	1.21023i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.j.a.53.6	✓	32
3.2	odd	2	inner	144.3.j.a.53.11	yes	32
4.3	odd	2		576.3.j.a.305.8		32
8.3	odd	2		1152.3.j.b.737.9		32
8.5	even	2		1152.3.j.a.737.9		32
12.11	even	2		576.3.j.a.305.9		32
16.3	odd	4		576.3.j.a.17.9		32
16.5	even	4		1152.3.j.a.161.8		32
16.11	odd	4		1152.3.j.b.161.8		32
16.13	even	4	inner	144.3.j.a.125.11	yes	32
24.5	odd	2		1152.3.j.a.737.8		32
24.11	even	2		1152.3.j.b.737.8		32
48.5	odd	4		1152.3.j.a.161.9		32
48.11	even	4		1152.3.j.b.161.9		32
48.29	odd	4	inner	144.3.j.a.125.6	yes	32
48.35	even	4		576.3.j.a.17.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.j.a.53.6	✓	32	1.1	even	1	trivial
144.3.j.a.53.11	yes	32	3.2	odd	2	inner
144.3.j.a.125.6	yes	32	48.29	odd	4	inner
144.3.j.a.125.11	yes	32	16.13	even	4	inner
576.3.j.a.17.8		32	48.35	even	4
576.3.j.a.17.9		32	16.3	odd	4
576.3.j.a.305.8		32	4.3	odd	2
576.3.j.a.305.9		32	12.11	even	2
1152.3.j.a.161.8		32	16.5	even	4
1152.3.j.a.161.9		32	48.5	odd	4
1152.3.j.a.737.8		32	24.5	odd	2
1152.3.j.a.737.9		32	8.5	even	2
1152.3.j.b.161.8		32	16.11	odd	4
1152.3.j.b.161.9		32	48.11	even	4
1152.3.j.b.737.8		32	24.11	even	2
1152.3.j.b.737.9		32	8.3	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.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11574 + 1.65986i) q^{2} +(-1.51025 - 3.70394i) q^{4} +(-0.900179 + 0.900179i) q^{5} -7.66460i q^{7} +(7.83305 + 1.62583i) q^{8} +O(q^{10})\)	\(q+(-1.11574 + 1.65986i) q^{2} +(-1.51025 - 3.70394i) q^{4} +(-0.900179 + 0.900179i) q^{5} -7.66460i q^{7} +(7.83305 + 1.62583i) q^{8} +(-0.489803 - 2.49853i) q^{10} +(4.57563 - 4.57563i) q^{11} +(10.9824 - 10.9824i) q^{13} +(12.7221 + 8.55170i) q^{14} +(-11.4383 + 11.1877i) q^{16} +0.0435225i q^{17} +(12.9849 - 12.9849i) q^{19} +(4.69370 + 1.97471i) q^{20} +(2.48968 + 12.7001i) q^{22} +18.3139 q^{23} +23.3794i q^{25} +(5.97571 + 30.4827i) q^{26} +(-28.3892 + 11.5755i) q^{28} +(-34.9759 - 34.9759i) q^{29} +38.4592 q^{31} +(-5.80790 - 31.4685i) q^{32} +(-0.0722411 - 0.0485598i) q^{34} +(6.89951 + 6.89951i) q^{35} +(11.3885 + 11.3885i) q^{37} +(7.06529 + 36.0407i) q^{38} +(-8.51469 + 5.58761i) q^{40} -45.6887 q^{41} +(-51.4657 - 51.4657i) q^{43} +(-23.8582 - 10.0375i) q^{44} +(-20.4335 + 30.3984i) q^{46} -56.5712i q^{47} -9.74608 q^{49} +(-38.8064 - 26.0853i) q^{50} +(-57.2642 - 24.0919i) q^{52} +(-44.6596 + 44.6596i) q^{53} +8.23778i q^{55} +(12.4613 - 60.0372i) q^{56} +(97.0790 - 19.0310i) q^{58} +(-20.7614 + 20.7614i) q^{59} +(-2.42706 + 2.42706i) q^{61} +(-42.9105 + 63.8368i) q^{62} +(58.7134 + 25.4704i) q^{64} +19.7722i q^{65} +(-18.9097 + 18.9097i) q^{67} +(0.161205 - 0.0657298i) q^{68} +(-19.1503 + 3.75414i) q^{70} +114.872 q^{71} +127.648i q^{73} +(-31.6098 + 6.19667i) q^{74} +(-67.7055 - 28.4847i) q^{76} +(-35.0704 - 35.0704i) q^{77} +37.0284 q^{79} +(0.225539 - 20.3675i) q^{80} +(50.9766 - 75.8366i) q^{82} +(84.4337 + 84.4337i) q^{83} +(-0.0391780 - 0.0391780i) q^{85} +(142.848 - 28.0034i) q^{86} +(43.2804 - 28.4020i) q^{88} +136.172 q^{89} +(-84.1756 - 84.1756i) q^{91} +(-27.6586 - 67.8335i) q^{92} +(93.9002 + 63.1188i) q^{94} +23.3774i q^{95} -173.475 q^{97} +(10.8741 - 16.1771i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 40 q^{10} + 48 q^{16} + 64 q^{19} - 88 q^{22} - 120 q^{28} - 248 q^{34} - 184 q^{40} + 128 q^{43} + 24 q^{46} - 224 q^{49} + 632 q^{52} + 456 q^{58} + 64 q^{61} - 48 q^{64} - 64 q^{67} - 312 q^{70} - 576 q^{76} - 512 q^{79} - 720 q^{82} + 320 q^{85} - 400 q^{88} - 192 q^{91} + 696 q^{94}+O(q^{100}) \) 32 * q + 40 * q^10 + 48 * q^16 + 64 * q^19 - 88 * q^22 - 120 * q^28 - 248 * q^34 - 184 * q^40 + 128 * q^43 + 24 * q^46 - 224 * q^49 + 632 * q^52 + 456 * q^58 + 64 * q^61 - 48 * q^64 - 64 * q^67 - 312 * q^70 - 576 * q^76 - 512 * q^79 - 720 * q^82 + 320 * q^85 - 400 * q^88 - 192 * q^91 + 696 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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