LMFDB - Embedded newform 288.3.u.a.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,3,Mod(19,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 0]))

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

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

chi := DirichletCharacter("288.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	288.u (of order $8$, degree $4$, 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:	$7.84743161358$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			19.5
Character	$\chi$	$=$	288.19
Dual form			288.3.u.a.91.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.360897 - 1.96717i) q^{2} +(-3.73951 - 1.41989i) q^{4} +(0.452310 - 0.187353i) q^{5} +(0.429965 + 0.429965i) q^{7} +(-4.14274 + 6.84381i) q^{8} +O(q^{10})$	\(q+(0.360897 - 1.96717i) q^{2} +(-3.73951 - 1.41989i) q^{4} +(0.452310 - 0.187353i) q^{5} +(0.429965 + 0.429965i) q^{7} +(-4.14274 + 6.84381i) q^{8} +(-0.205317 - 0.957385i) q^{10} +(-17.3350 + 7.18039i) q^{11} +(-19.9596 - 8.26755i) q^{13} +(1.00099 - 0.690640i) q^{14} +(11.9678 + 10.6194i) q^{16} -13.5961i q^{17} +(-3.45810 + 8.34859i) q^{19} +(-1.95744 + 0.0583763i) q^{20} +(7.86888 + 36.6922i) q^{22} +(16.8850 - 16.8850i) q^{23} +(-17.5082 + 17.5082i) q^{25} +(-23.4670 + 36.2802i) q^{26} +(-0.997353 - 2.21836i) q^{28} +(-13.8385 + 33.4091i) q^{29} +24.5614i q^{31} +(25.2093 - 19.7102i) q^{32} +(-26.7458 - 4.90679i) q^{34} +(0.275033 + 0.113922i) q^{35} +(9.89595 - 4.09904i) q^{37} +(15.1751 + 9.81565i) q^{38} +(-0.591598 + 3.87168i) q^{40} +(-14.4867 - 14.4867i) q^{41} +(17.8494 - 7.39348i) q^{43} +(75.0197 - 2.23730i) q^{44} +(-27.1219 - 39.3094i) q^{46} -43.6087 q^{47} -48.6303i q^{49} +(28.1229 + 40.7602i) q^{50} +(62.9001 + 59.2571i) q^{52} +(-28.0630 - 67.7501i) q^{53} +(-6.49552 + 6.49552i) q^{55} +(-4.72383 + 1.16136i) q^{56} +(60.7270 + 39.2799i) q^{58} +(-1.70130 - 4.10730i) q^{59} +(3.53360 - 8.53087i) q^{61} +(48.3165 + 8.86416i) q^{62} +(-29.6753 - 56.7043i) q^{64} -10.5769 q^{65} +(-0.300169 - 0.124334i) q^{67} +(-19.3050 + 50.8427i) q^{68} +(0.323363 - 0.499921i) q^{70} +(29.0914 + 29.0914i) q^{71} +(-68.2273 - 68.2273i) q^{73} +(-4.49208 - 20.9463i) q^{74} +(24.7857 - 26.3095i) q^{76} +(-10.5408 - 4.36612i) q^{77} +67.7588 q^{79} +(7.40274 + 2.56105i) q^{80} +(-33.7260 + 23.2695i) q^{82} +(16.4008 - 39.5950i) q^{83} +(-2.54727 - 6.14965i) q^{85} +(-8.10241 - 37.7811i) q^{86} +(22.6733 - 148.384i) q^{88} +(45.3745 - 45.3745i) q^{89} +(-5.02718 - 12.1367i) q^{91} +(-87.1165 + 39.1667i) q^{92} +(-15.7383 + 85.7857i) q^{94} +4.42403i q^{95} -119.312 q^{97} +(-95.6639 - 17.5505i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8	$ 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 44 q^{10} + 4 q^{11} - 4 q^{13} + 20 q^{14} + 16 q^{16} - 4 q^{19} - 76 q^{20} + 144 q^{22} + 68 q^{23} - 4 q^{25} - 96 q^{26} + 56 q^{28} + 4 q^{29} + 24 q^{32} - 48 q^{34} - 92 q^{35} - 4 q^{37} + 396 q^{38} - 408 q^{40} + 4 q^{41} + 92 q^{43} + 188 q^{44} - 36 q^{46} + 8 q^{47} - 308 q^{50} + 420 q^{52} + 164 q^{53} + 252 q^{55} - 552 q^{56} + 528 q^{58} - 124 q^{59} - 68 q^{61} - 216 q^{62} - 232 q^{64} + 8 q^{65} - 164 q^{67} + 368 q^{68} - 664 q^{70} + 260 q^{71} - 4 q^{73} + 532 q^{74} - 516 q^{76} - 220 q^{77} - 520 q^{79} - 312 q^{80} + 636 q^{82} + 484 q^{83} + 96 q^{85} - 688 q^{86} + 672 q^{88} + 4 q^{89} - 196 q^{91} - 616 q^{92} + 40 q^{94} - 8 q^{97} + 328 q^{98}+O(q^{100}) $ 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8 - 44 * q^10 + 4 * q^11 - 4 * q^13 + 20 * q^14 + 16 * q^16 - 4 * q^19 - 76 * q^20 + 144 * q^22 + 68 * q^23 - 4 * q^25 - 96 * q^26 + 56 * q^28 + 4 * q^29 + 24 * q^32 - 48 * q^34 - 92 * q^35 - 4 * q^37 + 396 * q^38 - 408 * q^40 + 4 * q^41 + 92 * q^43 + 188 * q^44 - 36 * q^46 + 8 * q^47 - 308 * q^50 + 420 * q^52 + 164 * q^53 + 252 * q^55 - 552 * q^56 + 528 * q^58 - 124 * q^59 - 68 * q^61 - 216 * q^62 - 232 * q^64 + 8 * q^65 - 164 * q^67 + 368 * q^68 - 664 * q^70 + 260 * q^71 - 4 * q^73 + 532 * q^74 - 516 * q^76 - 220 * q^77 - 520 * q^79 - 312 * q^80 + 636 * q^82 + 484 * q^83 + 96 * q^85 - 688 * q^86 + 672 * q^88 + 4 * q^89 - 196 * q^91 - 616 * q^92 + 40 * q^94 - 8 * q^97 + 328 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.360897	−	1.96717i	0.180449	−	0.983584i
$2$	0.360897	−	1.96717i	0.180449	−	0.983584i
$3$		0			0
$3$		0			0
$4$	−3.73951	−	1.41989i	−0.934877	−	0.354973i
$5$	0.452310	−	0.187353i	0.0904620	−	0.0374706i	−0.336994	−	0.941507i	$-0.609410\pi$
$5$	0.452310	−	0.187353i	0.0904620	−	0.0374706i	0.427456	+	0.904036i	$0.359410\pi$
$6$		0			0
$7$	0.429965	+	0.429965i	0.0614236	+	0.0614236i	0.737151	−	0.675728i	$-0.236170\pi$
$7$	0.429965	+	0.429965i	0.0614236	+	0.0614236i	−0.675728	+	0.737151i	$0.736170\pi$
$8$	−4.14274	+	6.84381i	−0.517843	+	0.855476i
$9$		0			0
$10$	−0.205317	−	0.957385i	−0.0205317	−	0.0957385i
$11$	−17.3350	+	7.18039i	−1.57591	+	0.652763i	−0.987759	−	0.155990i	$-0.950143\pi$
$11$	−17.3350	+	7.18039i	−1.57591	+	0.652763i	−0.588149	+	0.808752i	$0.700143\pi$
$12$		0			0
$13$	−19.9596	−	8.26755i	−1.53536	−	0.635965i	−0.554761	−	0.832010i	$-0.687190\pi$
$13$	−19.9596	−	8.26755i	−1.53536	−	0.635965i	−0.980595	+	0.196044i	$0.937190\pi$
$14$	1.00099	−	0.690640i	0.0714991	−	0.0493315i
$15$		0			0
$16$	11.9678	+	10.6194i	0.747988	+	0.663712i
$17$		−	13.5961i		−	0.799770i	−0.916565	−	0.399885i	$-0.869050\pi$
$17$		−	13.5961i		−	0.799770i	0.916565	−	0.399885i	$-0.130950\pi$
$18$		0			0
$19$	−3.45810	+	8.34859i	−0.182005	+	0.439399i	−0.988380	−	0.152006i	$-0.951427\pi$
$19$	−3.45810	+	8.34859i	−0.182005	+	0.439399i	0.806374	+	0.591405i	$0.201427\pi$
$20$	−1.95744	+	0.0583763i	−0.0978718	+	0.00291881i
$21$		0			0
$22$	7.86888	+	36.6922i	0.357677	+	1.66783i
$23$	16.8850	−	16.8850i	0.734131	−	0.734131i	−0.237304	−	0.971435i	$-0.576264\pi$
$23$	16.8850	−	16.8850i	0.734131	−	0.734131i	0.971435	+	0.237304i	$0.0762639\pi$
$24$		0			0
$25$	−17.5082	+	17.5082i	−0.700327	+	0.700327i
$26$	−23.4670	+	36.2802i	−0.902579	+	1.39539i
$27$		0			0
$28$	−0.997353	−	2.21836i	−0.0356197	−	0.0792271i
$29$	−13.8385	+	33.4091i	−0.477190	+	1.15204i	0.483732	+	0.875216i	$0.339281\pi$
$29$	−13.8385	+	33.4091i	−0.477190	+	1.15204i	−0.960921	+	0.276821i	$0.910719\pi$
$30$		0			0
$31$			24.5614i			0.792305i	0.918185	+	0.396152i	$0.129655\pi$
$31$			24.5614i			0.792305i	−0.918185	+	0.396152i	$0.870345\pi$
$32$	25.2093	−	19.7102i	0.787790	−	0.615944i
$33$		0			0
$34$	−26.7458	−	4.90679i	−0.786642	−	0.144317i
$35$	0.275033	+	0.113922i	0.00785807	+	0.00325492i
$36$		0			0
$37$	9.89595	−	4.09904i	0.267458	−	0.110785i	−0.244924	−	0.969542i	$-0.578763\pi$
$37$	9.89595	−	4.09904i	0.267458	−	0.110785i	0.512382	+	0.858757i	$0.328763\pi$
$38$	15.1751	+	9.81565i	0.399344	+	0.258306i
$39$		0			0
$40$	−0.591598	+	3.87168i	−0.0147899	+	0.0967919i
$41$	−14.4867	−	14.4867i	−0.353334	−	0.353334i	0.508015	−	0.861348i	$-0.330380\pi$
$41$	−14.4867	−	14.4867i	−0.353334	−	0.353334i	−0.861348	+	0.508015i	$0.830380\pi$
$42$		0			0
$43$	17.8494	−	7.39348i	0.415103	−	0.171941i	−0.165350	−	0.986235i	$-0.552875\pi$
$43$	17.8494	−	7.39348i	0.415103	−	0.171941i	0.580453	+	0.814294i	$0.302875\pi$
$44$	75.0197	−	2.23730i	1.70499	−	0.0508477i
$45$		0			0
$46$	−27.1219	−	39.3094i	−0.589607	−	0.854553i
$47$	−43.6087			−0.927845			−0.463922	−	0.885876i	$-0.653558\pi$
$47$	−43.6087			−0.927845			−0.463922	+	0.885876i	$0.653558\pi$
$48$		0			0
$49$		−	48.6303i		−	0.992454i
$50$	28.1229	+	40.7602i	0.562458	+	0.815204i
$51$		0			0
$52$	62.9001	+	59.2571i	1.20962	+	1.13956i
$53$	−28.0630	−	67.7501i	−0.529490	−	1.27830i	−0.931857	−	0.362825i	$-0.881812\pi$
$53$	−28.0630	−	67.7501i	−0.529490	−	1.27830i	0.402367	−	0.915478i	$-0.368188\pi$
$54$		0			0
$55$	−6.49552	+	6.49552i	−0.118100	+	0.118100i
$56$	−4.72383	+	1.16136i	−0.0843541	+	0.0207386i
$57$		0			0
$58$	60.7270	+	39.2799i	1.04702	+	0.677240i
$59$	−1.70130	−	4.10730i	−0.0288356	−	0.0696153i	0.908806	−	0.417219i	$-0.136995\pi$
$59$	−1.70130	−	4.10730i	−0.0288356	−	0.0696153i	−0.937641	+	0.347604i	$0.886995\pi$
$60$		0			0
$61$	3.53360	−	8.53087i	0.0579279	−	0.139850i	−0.892266	−	0.451511i	$-0.850885\pi$
$61$	3.53360	−	8.53087i	0.0579279	−	0.139850i	0.950193	+	0.311661i	$0.100885\pi$
$62$	48.3165	+	8.86416i	0.779299	+	0.142970i
$63$		0			0
$64$	−29.6753	−	56.7043i	−0.463677	−	0.886004i
$65$	−10.5769			−0.162721
$66$		0			0
$67$	−0.300169	−	0.124334i	−0.00448013	−	0.00185573i	0.380442	−	0.924805i	$-0.375772\pi$
$67$	−0.300169	−	0.124334i	−0.00448013	−	0.00185573i	−0.384922	+	0.922949i	$0.625772\pi$
$68$	−19.3050	+	50.8427i	−0.283897	+	0.747686i
$69$		0			0
$70$	0.323363	−	0.499921i	0.00461947	−	0.00714173i
$71$	29.0914	+	29.0914i	0.409738	+	0.409738i	0.881647	−	0.471909i	$-0.156435\pi$
$71$	29.0914	+	29.0914i	0.409738	+	0.409738i	−0.471909	+	0.881647i	$0.656435\pi$
$72$		0			0
$73$	−68.2273	−	68.2273i	−0.934620	−	0.934620i	0.0633700	−	0.997990i	$-0.479815\pi$
$73$	−68.2273	−	68.2273i	−0.934620	−	0.934620i	−0.997990	+	0.0633700i	$0.979815\pi$
$74$	−4.49208	−	20.9463i	−0.0607037	−	0.283059i
$75$		0			0
$76$	24.7857	−	26.3095i	0.326127	−	0.346177i
$77$	−10.5408	−	4.36612i	−0.136893	−	0.0567029i
$78$		0			0
$79$	67.7588			0.857706			0.428853	−	0.903374i	$-0.358918\pi$
$79$	67.7588			0.857706			0.428853	+	0.903374i	$0.358918\pi$
$80$	7.40274	+	2.56105i	0.0925342	+	0.0320131i
$81$		0			0
$82$	−33.7260	+	23.2695i	−0.411292	+	0.283775i
$83$	16.4008	−	39.5950i	0.197600	−	0.477048i	−0.793758	−	0.608234i	$-0.791878\pi$
$83$	16.4008	−	39.5950i	0.197600	−	0.477048i	0.991358	+	0.131186i	$0.0418784\pi$
$84$		0			0
$85$	−2.54727	−	6.14965i	−0.0299679	−	0.0723488i
$86$	−8.10241	−	37.7811i	−0.0942140	−	0.439315i
$87$		0			0
$88$	22.6733	−	148.384i	0.257651	−	1.68618i
$89$	45.3745	−	45.3745i	0.509825	−	0.509825i	−0.404647	−	0.914473i	$-0.632606\pi$
$89$	45.3745	−	45.3745i	0.509825	−	0.509825i	0.914473	+	0.404647i	$0.132606\pi$
$90$		0			0
$91$	−5.02718	−	12.1367i	−0.0552438	−	0.133370i
$92$	−87.1165	+	39.1667i	−0.946919	+	0.425725i
$93$		0			0
$94$	−15.7383	+	85.7857i	−0.167428	+	0.912614i
$95$			4.42403i			0.0465688i
$96$		0			0
$97$	−119.312			−1.23002			−0.615012	−	0.788518i	$-0.710849\pi$
$97$	−119.312			−1.23002			−0.615012	+	0.788518i	$0.710849\pi$
$98$	−95.6639	−	17.5505i	−0.976163	−	0.179087i
$99$		0			0
$100$	90.3317	−	40.6122i	0.903317	−	0.406122i
$101$	−98.7914	+	40.9207i	−0.978133	+	0.405156i	−0.813734	−	0.581238i	$-0.802569\pi$
$101$	−98.7914	+	40.9207i	−0.978133	+	0.405156i	−0.164399	+	0.986394i	$0.552569\pi$
$102$		0			0
$103$	127.634	+	127.634i	1.23916	+	1.23916i	0.960344	+	0.278817i	$0.0899423\pi$
$103$	127.634	+	127.634i	1.23916	+	1.23916i	0.278817	+	0.960344i	$0.410058\pi$
$104$	139.269	−	102.349i	1.33913	−	0.984130i
$105$		0			0
$106$	−143.404	+	30.7538i	−1.35286	+	0.290131i
$107$	−94.9289	+	39.3208i	−0.887186	+	0.367484i	−0.779279	−	0.626677i	$-0.784415\pi$
$107$	−94.9289	+	39.3208i	−0.887186	+	0.367484i	−0.107906	+	0.994161i	$0.534415\pi$
$108$		0			0
$109$	−27.8610	−	11.5404i	−0.255605	−	0.105875i	0.251202	−	0.967935i	$-0.419174\pi$
$109$	−27.8610	−	11.5404i	−0.255605	−	0.105875i	−0.506807	+	0.862060i	$0.669174\pi$
$110$	10.4336	+	15.1220i	0.0948507	+	0.137473i
$111$		0			0
$112$	0.579776	+	9.71170i	0.00517658	+	0.0867116i
$113$		−	140.786i		−	1.24590i	−0.782263	−	0.622948i	$-0.785935\pi$
$113$		−	140.786i		−	1.24590i	0.782263	−	0.622948i	$-0.214065\pi$
$114$		0			0
$115$	4.47380	−	10.8007i	0.0389026	−	0.0939193i
$116$	99.1864	−	105.284i	0.855055	−	0.907623i
$117$		0			0
$118$	−8.69375	+	1.86443i	−0.0736758	+	0.0158003i
$119$	5.84584	−	5.84584i	0.0491247	−	0.0491247i
$120$		0			0
$121$	163.384	−	163.384i	1.35028	−	1.35028i
$122$	−15.5064	−	10.0300i	−0.127102	−	0.0822128i
$123$		0			0
$124$	34.8746	−	91.8477i	0.281247	−	0.740707i
$125$	−9.32274	+	22.5071i	−0.0745819	+	0.180057i
$126$		0			0
$127$		−	163.979i		−	1.29117i	−0.763687	−	0.645587i	$-0.776613\pi$
$127$		−	163.979i		−	1.29117i	0.763687	−	0.645587i	$-0.223387\pi$
$128$	−122.257	+	37.9120i	−0.955130	+	0.296187i
$129$		0			0
$130$	−3.81717	+	20.8065i	−0.0293629	+	0.160050i
$131$	11.2279	+	4.65074i	0.0857090	+	0.0355018i	0.425126	−	0.905134i	$-0.360230\pi$
$131$	11.2279	+	4.65074i	0.0857090	+	0.0355018i	−0.339417	+	0.940636i	$0.610230\pi$
$132$		0			0
$133$	−5.07646	+	2.10274i	−0.0381689	+	0.0158101i
$134$	−0.352916	+	0.545611i	−0.00263370	+	0.00407172i
$135$		0			0
$136$	93.0490	+	56.3251i	0.684184	+	0.414155i
$137$	−21.2983	−	21.2983i	−0.155462	−	0.155462i	0.625090	−	0.780552i	$-0.285062\pi$
$137$	−21.2983	−	21.2983i	−0.155462	−	0.155462i	−0.780552	+	0.625090i	$0.785062\pi$
$138$		0			0
$139$	−154.836	+	64.1351i	−1.11393	+	0.461404i	−0.862288	−	0.506418i	$-0.830969\pi$
$139$	−154.836	+	64.1351i	−1.11393	+	0.461404i	−0.251639	+	0.967821i	$0.580969\pi$
$140$	−0.866729	−	0.816529i	−0.00619092	−	0.00583235i
$141$		0			0
$142$	67.7268	−	46.7287i	0.476949	−	0.329076i
$143$	405.364			2.83471
$144$		0			0
$145$			17.7039i			0.122096i
$146$	−158.838	+	109.592i	−1.08793	+	0.750627i
$147$		0			0
$148$	−42.8262	+	1.27720i	−0.289366	+	0.00862971i
$149$	90.9258	+	219.514i	0.610240	+	1.47325i	0.862737	+	0.505653i	$0.168748\pi$
$149$	90.9258	+	219.514i	0.610240	+	1.47325i	−0.252497	+	0.967598i	$0.581252\pi$
$150$		0			0
$151$	−82.0484	+	82.0484i	−0.543367	+	0.543367i	−0.924514	−	0.381147i	$-0.875529\pi$
$151$	−82.0484	+	82.0484i	−0.543367	+	0.543367i	0.381147	+	0.924514i	$0.375529\pi$
$152$	−42.8101	−	58.2526i	−0.281645	−	0.383241i
$153$		0			0
$154$	−12.3930	+	19.1597i	−0.0804742	+	0.124414i
$155$	4.60166	+	11.1094i	0.0296881	+	0.0716735i
$156$		0			0
$157$	−52.8906	+	127.689i	−0.336883	+	0.813307i	0.661129	+	0.750272i	$0.270078\pi$
$157$	−52.8906	+	127.689i	−0.336883	+	0.813307i	−0.998011	+	0.0630341i	$0.979922\pi$
$158$	24.4540	−	133.293i	0.154772	−	0.843627i
$159$		0			0
$160$	7.70964	−	13.6382i	0.0481853	−	0.0852385i
$161$	14.5199			0.0901859
$162$		0			0
$163$	54.8297	+	22.7112i	0.336379	+	0.139333i	0.544478	−	0.838775i	$-0.316728\pi$
$163$	54.8297	+	22.7112i	0.336379	+	0.139333i	−0.208099	+	0.978108i	$0.566728\pi$
$164$	33.6035	+	74.7426i	0.204900	+	0.455747i
$165$		0			0
$166$	−71.9710	−	46.5528i	−0.433560	−	0.280439i
$167$	98.7296	+	98.7296i	0.591195	+	0.591195i	0.937954	−	0.346759i	$-0.112718\pi$
$167$	98.7296	+	98.7296i	0.591195	+	0.591195i	−0.346759	+	0.937954i	$0.612718\pi$
$168$		0			0
$169$	210.533	+	210.533i	1.24576	+	1.24576i
$170$	−13.0167	+	2.79151i	−0.0765688	+	0.0164207i
$171$		0			0
$172$	−77.2460	+	2.30369i	−0.449105	+	0.0133936i
$173$	6.09221	+	2.52348i	0.0352151	+	0.0145866i	0.400221	−	0.916418i	$-0.368933\pi$
$173$	6.09221	+	2.52348i	0.0352151	+	0.0145866i	−0.365006	+	0.931005i	$0.618933\pi$
$174$		0			0
$175$	−15.0558			−0.0860332
$176$	−283.713	−	98.1534i	−1.61201	−	0.557690i
$177$		0			0
$178$	−72.8837	−	105.635i	−0.409459	−	0.593454i
$179$	−80.6673	+	194.748i	−0.450655	+	1.08798i	0.521418	+	0.853301i	$0.325403\pi$
$179$	−80.6673	+	194.748i	−0.450655	+	1.08798i	−0.972073	+	0.234677i	$0.924597\pi$
$180$		0			0
$181$	−59.7464	−	144.241i	−0.330091	−	0.796910i	−0.998584	−	0.0531918i	$-0.983061\pi$
$181$	−59.7464	−	144.241i	−0.330091	−	0.796910i	0.668493	−	0.743718i	$-0.266939\pi$
$182$	−25.6892	+	5.50922i	−0.141150	+	0.0302704i
$183$		0			0
$184$	45.6075	+	185.508i	0.247867	+	1.00820i
$185$	3.70807	−	3.70807i	0.0200436	−	0.0200436i
$186$		0			0
$187$	97.6252	+	235.688i	0.522060	+	1.26036i
$188$	163.075	+	61.9196i	0.867421	+	0.329360i
$189$		0			0
$190$	8.70282	+	1.59662i	0.0458043	+	0.00840327i
$191$			107.812i			0.564460i	0.959347	+	0.282230i	$0.0910741\pi$
$191$			107.812i			0.564460i	−0.959347	+	0.282230i	$0.908926\pi$
$192$		0			0
$193$	−174.830			−0.905855			−0.452927	−	0.891547i	$-0.649620\pi$
$193$	−174.830			−0.905855			−0.452927	+	0.891547i	$0.649620\pi$
$194$	−43.0595	+	234.707i	−0.221956	+	1.20983i
$195$		0			0
$196$	−69.0497	+	181.853i	−0.352294	+	0.927822i
$197$	108.472	−	44.9304i	0.550618	−	0.228073i	−0.0899887	−	0.995943i	$-0.528683\pi$
$197$	108.472	−	44.9304i	0.550618	−	0.228073i	0.640606	+	0.767870i	$0.278683\pi$
$198$		0			0
$199$	190.347	+	190.347i	0.956516	+	0.956516i	0.999093	−	0.0425770i	$-0.0135568\pi$
$199$	190.347	+	190.347i	0.956516	+	0.956516i	−0.0425770	+	0.999093i	$0.513557\pi$
$200$	−47.2907	−	192.355i	−0.236453	−	0.961773i
$201$		0			0
$202$	44.8445	+	209.108i	0.222002	+	1.03519i
$203$	−20.3148	+	8.41467i	−0.100073	+	0.0414516i
$204$		0			0
$205$	−9.26659	−	3.83835i	−0.0452029	−	0.0187237i
$206$	297.140	−	205.014i	1.44242	−	0.995215i
$207$		0			0
$208$	−151.077	−	310.904i	−0.726331	−	1.49473i
$209$		−	169.553i		−	0.811259i
$210$		0			0
$211$	86.6725	−	209.246i	0.410770	−	0.991686i	−0.574162	−	0.818742i	$-0.694672\pi$
$211$	86.6725	−	209.246i	0.410770	−	0.991686i	0.984932	−	0.172944i	$-0.0553281\pi$
$212$	8.74400	+	293.198i	0.0412453	+	1.38301i
$213$		0			0
$214$	43.0911	+	200.932i	0.201360	+	0.938934i
$215$	6.68829	−	6.68829i	0.0311083	−	0.0311083i
$216$		0			0
$217$	−10.5606	+	10.5606i	−0.0486662	+	0.0486662i
$218$	−32.7569	+	50.6423i	−0.150261	+	0.232304i
$219$		0			0
$220$	33.5130	−	15.0671i	0.152332	−	0.0684869i
$221$	−112.406	+	271.373i	−0.508626	+	1.22793i
$222$		0			0
$223$			103.845i			0.465671i	0.972516	+	0.232836i	$0.0748004\pi$
$223$			103.845i			0.465671i	−0.972516	+	0.232836i	$0.925200\pi$
$224$	19.3138	+	2.36441i	0.0862223	+	0.0105554i
$225$		0			0
$226$	−276.951	−	50.8094i	−1.22544	−	0.224820i
$227$	−106.086	−	43.9421i	−0.467338	−	0.193578i	0.136572	−	0.990630i	$-0.456391\pi$
$227$	−106.086	−	43.9421i	−0.467338	−	0.193578i	−0.603910	+	0.797052i	$0.706391\pi$
$228$		0			0
$229$	46.1162	−	19.1019i	0.201381	−	0.0834146i	−0.279714	−	0.960083i	$-0.590240\pi$
$229$	46.1162	−	19.1019i	0.201381	−	0.0834146i	0.481094	+	0.876669i	$0.340240\pi$
$230$	−19.6322	−	12.6987i	−0.0853576	−	0.0552116i
$231$		0			0
$232$	−171.316	−	233.113i	−0.738431	−	1.00480i
$233$	62.7031	+	62.7031i	0.269112	+	0.269112i	0.828742	−	0.559630i	$-0.189057\pi$
$233$	62.7031	+	62.7031i	0.269112	+	0.269112i	−0.559630	+	0.828742i	$0.689057\pi$
$234$		0			0
$235$	−19.7247	+	8.17022i	−0.0839347	+	0.0347669i
$236$	0.530099	+	17.7749i	0.00224618	+	0.0753175i
$237$		0			0
$238$	−9.39001	−	13.6095i	−0.0394538	−	0.0571828i
$239$	−306.080			−1.28067			−0.640335	−	0.768095i	$-0.721205\pi$
$239$	−306.080			−1.28067			−0.640335	+	0.768095i	$0.721205\pi$
$240$		0			0
$241$		−	245.242i		−	1.01760i	−0.860884	−	0.508801i	$-0.830089\pi$
$241$		−	245.242i		−	1.01760i	0.860884	−	0.508801i	$-0.169911\pi$
$242$	−262.439	−	380.369i	−1.08446	−	1.57177i
$243$		0			0
$244$	−25.3268	+	26.8839i	−0.103799	+	0.110180i
$245$	−9.11102	−	21.9960i	−0.0371878	−	0.0897794i
$246$		0			0
$247$	138.045	−	138.045i	0.558886	−	0.558886i
$248$	−168.094	−	101.752i	−0.677797	−	0.410290i
$249$		0			0
$250$	40.9107	+	26.4621i	0.163643	+	0.105849i
$251$	−132.845	−	320.715i	−0.529261	−	1.27775i	−0.932008	−	0.362438i	$-0.881944\pi$
$251$	−132.845	−	320.715i	−0.529261	−	1.27775i	0.402747	−	0.915311i	$-0.368056\pi$
$252$		0			0
$253$	−171.461	+	413.942i	−0.677710	+	1.63614i
$254$	−322.574	−	59.1796i	−1.26998	−	0.232990i
$255$		0			0
$256$	30.4572	+	254.182i	0.118973	+	0.992897i
$257$	108.814			0.423399			0.211700	−	0.977335i	$-0.432100\pi$
$257$	108.814			0.423399			0.211700	+	0.977335i	$0.432100\pi$
$258$		0			0
$259$	6.01735	+	2.49247i	0.0232330	+	0.00962343i
$260$	39.5523	+	15.0180i	0.152124	+	0.0577617i
$261$		0			0
$262$	13.2009	−	20.4087i	0.0503851	−	0.0778958i
$263$	150.151	+	150.151i	0.570916	+	0.570916i	0.932384	−	0.361468i	$-0.117724\pi$
$263$	150.151	+	150.151i	0.570916	+	0.570916i	−0.361468	+	0.932384i	$0.617724\pi$
$264$		0			0
$265$	−25.3863	−	25.3863i	−0.0957975	−	0.0957975i
$266$	2.30436	+	10.7451i	0.00866301	+	0.0403952i
$267$		0			0
$268$	0.945942	+	0.891155i	0.00352963	+	0.00332520i
$269$	255.485	+	105.825i	0.949758	+	0.393403i	0.803140	−	0.595791i	$-0.203161\pi$
$269$	255.485	+	105.825i	0.949758	+	0.393403i	0.146618	+	0.989193i	$0.453161\pi$
$270$		0			0
$271$	−261.648			−0.965492			−0.482746	−	0.875760i	$-0.660361\pi$
$271$	−261.648			−0.965492			−0.482746	+	0.875760i	$0.660361\pi$
$272$	144.382	−	162.716i	0.530817	−	0.598219i
$273$		0			0
$274$	−49.5839	+	34.2109i	−0.180963	+	0.124857i
$275$	177.789	−	429.220i	0.646504	−	1.56080i
$276$		0			0
$277$	120.123	+	290.003i	0.433658	+	1.04694i	0.978098	+	0.208143i	$0.0667420\pi$
$277$	120.123	+	290.003i	0.433658	+	1.04694i	−0.544440	+	0.838799i	$0.683258\pi$
$278$	70.2848	+	327.734i	0.252823	+	1.17890i
$279$		0			0
$280$	−1.91905	+	1.41032i	−0.00685375	+	0.00503685i
$281$	−21.7898	+	21.7898i	−0.0775437	+	0.0775437i	−0.744815	−	0.667271i	$-0.767462\pi$
$281$	−21.7898	+	21.7898i	−0.0775437	+	0.0775437i	0.667271	+	0.744815i	$0.267462\pi$
$282$		0			0
$283$	−155.937	−	376.466i	−0.551016	−	1.33027i	−0.916717	−	0.399537i	$-0.869171\pi$
$283$	−155.937	−	376.466i	−0.551016	−	1.33027i	0.365702	−	0.930732i	$-0.380829\pi$
$284$	−67.4809	−	150.094i	−0.237609	−	0.528501i
$285$		0			0
$286$	146.295	−	797.420i	0.511520	−	2.78818i
$287$		−	12.4575i		−	0.0434060i
$288$		0			0
$289$	104.146			0.360368
$290$	34.8266	+	6.38930i	0.120092	+	0.0220321i
$291$		0			0
$292$	158.261	+	352.012i	0.541990	+	1.20552i
$293$	37.2090	−	15.4125i	0.126993	−	0.0526023i	−0.318282	−	0.947996i	$-0.603106\pi$
$293$	37.2090	−	15.4125i	0.126993	−	0.0526023i	0.445275	+	0.895394i	$0.353106\pi$
$294$		0			0
$295$	−1.53903	−	1.53903i	−0.00521705	−	0.00521705i
$296$	−12.9434	+	84.7072i	−0.0437276	+	0.286173i
$297$		0			0
$298$	464.637	−	99.6443i	1.55918	−	0.334377i
$299$	−476.616	+	197.421i	−1.59403	+	0.660271i
$300$		0			0
$301$	10.8536	+	4.49569i	0.0360584	+	0.0149359i
$302$	131.792	+	191.014i	0.436397	+	0.632497i
$303$		0			0
$304$	−130.043	+	63.1915i	−0.427772	+	0.207867i
$305$		−	4.52063i		−	0.0148217i
$306$		0			0
$307$	−101.089	+	244.049i	−0.329279	+	0.794949i	0.669368	+	0.742931i	$0.266565\pi$
$307$	−101.089	+	244.049i	−0.329279	+	0.794949i	−0.998646	+	0.0520174i	$0.983435\pi$
$308$	33.2178	+	31.2939i	0.107850	+	0.101603i
$309$		0			0
$310$	23.5148	−	5.04289i	0.0758541	−	0.0162674i
$311$	181.395	−	181.395i	0.583264	−	0.583264i	−0.352534	−	0.935799i	$-0.614680\pi$
$311$	181.395	−	181.395i	0.583264	−	0.583264i	0.935799	+	0.352534i	$0.114680\pi$
$312$		0			0
$313$	110.963	−	110.963i	0.354513	−	0.354513i	−0.507273	−	0.861786i	$-0.669346\pi$
$313$	110.963	−	110.963i	0.354513	−	0.354513i	0.861786	+	0.507273i	$0.169346\pi$
$314$	232.098	+	150.127i	0.739166	+	0.478113i
$315$		0			0
$316$	−253.384	−	96.2102i	−0.801850	−	0.304463i
$317$	−134.161	+	323.892i	−0.423219	+	1.02174i	0.558172	+	0.829725i	$0.311503\pi$
$317$	−134.161	+	323.892i	−0.423219	+	1.02174i	−0.981392	+	0.192017i	$0.938497\pi$
$318$		0			0
$319$		−	678.512i		−	2.12700i
$320$	−24.0462	−	20.0881i	−0.0751443	−	0.0627755i
$321$		0			0
$322$	5.24020	−	28.5631i	0.0162739	−	0.0887054i
$323$	113.508	+	47.0166i	0.351419	+	0.145562i
$324$		0			0
$325$	494.207	−	204.707i	1.52064	−	0.629868i
$326$	64.4647	−	99.6629i	0.197744	−	0.305714i
$327$		0			0
$328$	159.159	−	39.1294i	0.485240	−	0.119297i
$329$	−18.7502	−	18.7502i	−0.0569915	−	0.0569915i
$330$		0			0
$331$	−580.238	+	240.342i	−1.75298	+	0.726110i	−0.755506	+	0.655141i	$0.772609\pi$
$331$	−580.238	+	240.342i	−1.75298	+	0.726110i	−0.997479	+	0.0709686i	$0.977391\pi$
$332$	−117.551	+	124.778i	−0.354071	+	0.375839i
$333$		0			0
$334$	229.849	−	158.587i	0.688171	−	0.474810i
$335$	−0.159064			−0.000474817
$336$		0			0
$337$		−	130.257i		−	0.386519i	−0.981148	−	0.193259i	$-0.938094\pi$
$337$		−	130.257i		−	0.386519i	0.981148	−	0.193259i	$-0.0619059\pi$
$338$	490.136	−	338.174i	1.45011	−	1.00051i
$339$		0			0
$340$	0.793689	+	26.6135i	0.00233438	+	0.0782750i
$341$	−176.361	−	425.772i	−0.517187	−	1.24860i
$342$		0			0
$343$	41.9776	−	41.9776i	0.122384	−	0.122384i
$344$	−23.3461	+	152.787i	−0.0678666	+	0.444149i
$345$		0			0
$346$	7.16277	−	11.0737i	0.0207016	−	0.0320049i
$347$	54.6775	+	132.003i	0.157572	+	0.380412i	0.982874	−	0.184279i	$-0.0589951\pi$
$347$	54.6775	+	132.003i	0.157572	+	0.380412i	−0.825302	+	0.564692i	$0.808995\pi$
$348$		0			0
$349$	−46.7936	+	112.970i	−0.134079	+	0.323696i	−0.976632	−	0.214918i	$-0.931052\pi$
$349$	−46.7936	+	112.970i	−0.134079	+	0.323696i	0.842553	+	0.538613i	$0.181052\pi$
$350$	−5.43360	+	29.6173i	−0.0155246	+	0.0846209i
$351$		0			0
$352$	−295.476	+	522.689i	−0.839420	+	1.48491i
$353$	−382.113			−1.08247			−0.541236	−	0.840871i	$-0.682043\pi$
$353$	−382.113			−1.08247			−0.541236	+	0.840871i	$0.682043\pi$
$354$		0			0
$355$	18.6087	+	7.70798i	0.0524189	+	0.0217126i
$356$	−234.105	+	105.251i	−0.657598	+	0.295650i
$357$		0			0
$358$	353.990	+	228.970i	0.988798	+	0.639582i
$359$	81.2910	+	81.2910i	0.226437	+	0.226437i	0.811203	−	0.584765i	$-0.198813\pi$
$359$	81.2910	+	81.2910i	0.226437	+	0.226437i	−0.584765	+	0.811203i	$0.698813\pi$
$360$		0			0
$361$	197.525	+	197.525i	0.547161	+	0.547161i
$362$	−305.308	+	65.4753i	−0.843392	+	0.180871i
$363$		0			0
$364$	1.56639	+	52.5233i	0.00430328	+	0.144295i
$365$	−43.6425	−	18.0773i	−0.119568	−	0.0495268i
$366$		0			0
$367$	456.145			1.24290			0.621452	−	0.783453i	$-0.286543\pi$
$367$	456.145			1.24290			0.621452	+	0.783453i	$0.286543\pi$
$368$	381.385	−	22.7682i	1.03637	−	0.0618701i
$369$		0			0
$370$	−5.95617	−	8.63263i	−0.0160977	−	0.0233314i
$371$	17.0640	−	41.1963i	0.0459947	−	0.111041i
$372$		0			0
$373$	−184.108	−	444.476i	−0.493588	−	1.19163i	−0.952882	−	0.303342i	$-0.901898\pi$
$373$	−184.108	−	444.476i	−0.493588	−	1.19163i	0.459294	−	0.888284i	$-0.348102\pi$
$374$	498.871	−	106.986i	1.33388	−	0.286059i
$375$		0			0
$376$	180.660	−	298.450i	0.480478	−	0.793749i
$377$	552.423	−	552.423i	1.46531	−	1.46531i
$378$		0			0
$379$	−108.900	−	262.908i	−0.287336	−	0.693690i	0.712634	−	0.701536i	$-0.247502\pi$
$379$	−108.900	−	262.908i	−0.287336	−	0.693690i	−0.999969	+	0.00784682i	$0.997502\pi$
$380$	6.28165	−	16.5437i	0.0165307	−	0.0435361i
$381$		0			0
$382$	212.084	+	38.9090i	0.555194	+	0.101856i
$383$		−	476.810i		−	1.24493i	−0.782646	−	0.622467i	$-0.786131\pi$
$383$		−	476.810i		−	1.24493i	0.782646	−	0.622467i	$-0.213869\pi$
$384$		0			0
$385$	−5.58569			−0.0145083
$386$	−63.0957	+	343.920i	−0.163460	+	0.890985i
$387$		0			0
$388$	446.169	+	169.411i	1.14992	+	0.436625i
$389$	71.5472	−	29.6358i	0.183926	−	0.0761846i	−0.288820	−	0.957383i	$-0.593263\pi$
$389$	71.5472	−	29.6358i	0.183926	−	0.0761846i	0.472746	+	0.881199i	$0.343263\pi$
$390$		0			0
$391$	−229.570	−	229.570i	−0.587136	−	0.587136i
$392$	332.816	+	201.463i	0.849020	+	0.513936i
$393$		0			0
$394$	−49.2386	−	229.597i	−0.124971	−	0.582734i
$395$	30.6480	−	12.6948i	0.0775898	−	0.0321388i
$396$		0			0
$397$	120.360	+	49.8545i	0.303173	+	0.125578i	0.529084	−	0.848570i	$-0.322536\pi$
$397$	120.360	+	49.8545i	0.303173	+	0.125578i	−0.225911	+	0.974148i	$0.572536\pi$
$398$	443.140	−	305.749i	1.11342	−	0.768212i
$399$		0			0
$400$	−395.461	+	23.6085i	−0.988652	+	0.0590213i
$401$			174.015i			0.433953i	0.976177	+	0.216976i	$0.0696195\pi$
$401$			174.015i			0.433953i	−0.976177	+	0.216976i	$0.930381\pi$
$402$		0			0
$403$	203.063	−	490.237i	0.503878	−	1.21647i
$404$	427.534	−	12.7503i	1.05825	−	0.0315601i
$405$		0			0
$406$	9.22151	+	42.9995i	0.0227131	+	0.105910i
$407$	−142.114	+	142.114i	−0.349173	+	0.349173i
$408$		0			0
$409$	−108.736	+	108.736i	−0.265857	+	0.265857i	−0.827428	−	0.561571i	$-0.810197\pi$
$409$	−108.736	+	108.736i	−0.265857	+	0.265857i	0.561571	+	0.827428i	$0.310197\pi$
$410$	−10.8950	+	16.8437i	−0.0265731	+	0.0410822i
$411$		0			0
$412$	−296.061	−	658.513i	−0.718594	−	1.59833i
$413$	1.03450	−	2.49749i	0.00250483	−	0.00604720i
$414$		0			0
$415$		−	20.9819i		−	0.0505589i
$416$	−666.123	+	184.989i	−1.60126	+	0.444686i
$417$		0			0
$418$	−333.540	−	61.1913i	−0.797942	−	0.146391i
$419$	−370.373	−	153.414i	−0.883946	−	0.366142i	−0.105920	−	0.994375i	$-0.533779\pi$
$419$	−370.373	−	153.414i	−0.883946	−	0.366142i	−0.778026	+	0.628232i	$0.783779\pi$
$420$		0			0
$421$	−600.339	+	248.669i	−1.42598	+	0.590662i	−0.956357	−	0.292202i	$-0.905612\pi$
$421$	−600.339	+	248.669i	−1.42598	+	0.590662i	−0.469628	+	0.882864i	$0.655612\pi$
$422$	−380.342	−	246.016i	−0.901284	−	0.582975i
$423$		0			0
$424$	579.926	+	88.6135i	1.36775	+	0.208994i
$425$	238.043	+	238.043i	0.560101	+	0.560101i
$426$		0			0
$427$	5.18730	−	2.14865i	0.0121482	−	0.00503197i
$428$	410.818	−	12.2518i	0.959856	−	0.0286256i
$429$		0			0
$430$	−10.7432	−	15.5708i	−0.0249842	−	0.0362111i
$431$	−289.906			−0.672636			−0.336318	−	0.941749i	$-0.609182\pi$
$431$	−289.906			−0.672636			−0.336318	+	0.941749i	$0.609182\pi$
$432$		0			0
$433$			314.414i			0.726129i	0.931764	+	0.363064i	$0.118269\pi$
$433$			314.414i			0.726129i	−0.931764	+	0.363064i	$0.881731\pi$
$434$	16.9631	+	24.5857i	0.0390856	+	0.0566490i
$435$		0			0
$436$	87.8002	+	82.7149i	0.201377	+	0.189713i
$437$	82.5760	+	199.356i	0.188961	+	0.456192i
$438$		0			0
$439$	−579.455	+	579.455i	−1.31994	+	1.31994i	−0.406125	+	0.913818i	$0.633120\pi$
$439$	−579.455	+	579.455i	−1.31994	+	1.31994i	−0.913818	+	0.406125i	$0.866880\pi$
$440$	−17.5448	−	71.3634i	−0.0398745	−	0.162189i
$441$		0			0
$442$	493.269	+	319.060i	1.11599	+	0.721855i
$443$	−107.736	−	260.098i	−0.243197	−	0.587130i	0.754400	−	0.656415i	$-0.227928\pi$
$443$	−107.736	−	260.098i	−0.243197	−	0.587130i	−0.997597	+	0.0692856i	$0.977928\pi$
$444$		0			0
$445$	12.0223	−	29.0244i	0.0270164	−	0.0652233i
$446$	204.280	+	37.4773i	0.458027	+	0.0840297i
$447$		0			0
$448$	11.6215	−	37.1402i	0.0259408	−	0.0829022i
$449$	−470.997			−1.04899			−0.524496	−	0.851413i	$-0.675746\pi$
$449$	−470.997			−1.04899			−0.524496	+	0.851413i	$0.675746\pi$
$450$		0			0
$451$	355.147	+	147.107i	0.787465	+	0.326179i
$452$	−199.901	+	526.471i	−0.442260	+	1.16476i
$453$		0			0
$454$	−124.728	+	192.830i	−0.274730	+	0.424735i
$455$	−4.54769	−	4.54769i	−0.00999493	−	0.00999493i
$456$		0			0
$457$	447.868	+	447.868i	0.980018	+	0.980018i	0.999804	−	0.0197861i	$-0.00629852\pi$
$457$	447.868	+	447.868i	0.980018	+	0.980018i	−0.0197861	+	0.999804i	$0.506299\pi$
$458$	−20.9335	−	97.6121i	−0.0457064	−	0.213127i
$459$		0			0
$460$	−32.0657	+	34.0370i	−0.0697080	+	0.0739935i
$461$	−253.222	−	104.888i	−0.549288	−	0.227523i	0.0907394	−	0.995875i	$-0.471077\pi$
$461$	−253.222	−	104.888i	−0.549288	−	0.227523i	−0.640027	+	0.768352i	$0.721077\pi$
$462$		0			0
$463$	−653.753			−1.41199			−0.705996	−	0.708215i	$-0.749501\pi$
$463$	−653.753			−1.41199			−0.705996	+	0.708215i	$0.749501\pi$
$464$	−520.401	+	252.877i	−1.12155	+	0.544994i
$465$		0			0
$466$	145.977	−	100.718i	0.313255	−	0.216133i
$467$	−39.3875	+	95.0899i	−0.0843416	+	0.203619i	−0.960424	−	0.278544i	$-0.910148\pi$
$467$	−39.3875	+	95.0899i	−0.0843416	+	0.203619i	0.876082	+	0.482162i	$0.160148\pi$
$468$		0			0
$469$	−0.0756028	−	0.182521i	−0.000161200	−	0.000389171i
$470$	8.95363	+	41.7503i	0.0190503	+	0.0888305i
$471$		0			0
$472$	35.1576	+	5.37213i	0.0744865	+	0.0113816i
$473$	−256.332	+	256.332i	−0.541927	+	0.541927i
$474$		0			0
$475$	−85.6236	−	206.714i	−0.180260	−	0.435187i
$476$	−30.1610	+	13.5601i	−0.0633635	+	0.0284876i
$477$		0			0
$478$	−110.464	+	602.112i	−0.231095	+	1.25965i
$479$		−	857.713i		−	1.79063i	−0.445432	−	0.895316i	$-0.646950\pi$
$479$		−	857.713i		−	1.79063i	0.445432	−	0.895316i	$-0.353050\pi$
$480$		0			0
$481$	−231.408			−0.481099
$482$	−482.433	−	88.5072i	−1.00090	−	0.183625i
$483$		0			0
$484$	−842.963	+	378.988i	−1.74166	+	0.783033i
$485$	−53.9661	+	22.3535i	−0.111270	+	0.0460897i
$486$		0			0
$487$	12.5467	+	12.5467i	0.0257633	+	0.0257633i	0.719871	−	0.694108i	$-0.244201\pi$
$487$	12.5467	+	12.5467i	0.0257633	+	0.0257633i	−0.694108	+	0.719871i	$0.744201\pi$
$488$	43.7448	+	59.5245i	0.0896410	+	0.121976i
$489$		0			0
$490$	−46.5579	+	9.98464i	−0.0950161	+	0.0203768i
$491$	−91.7015	+	37.9840i	−0.186765	+	0.0773605i	−0.474106	−	0.880468i	$-0.657229\pi$
$491$	−91.7015	+	37.9840i	−0.186765	+	0.0773605i	0.287341	+	0.957828i	$0.407229\pi$
$492$		0			0
$493$	454.233	+	188.149i	0.921365	+	0.381642i
$494$	−221.737	−	321.377i	−0.448861	−	0.650561i
$495$		0			0
$496$	−260.828	+	293.947i	−0.525862	+	0.592635i
$497$			25.0166i			0.0503352i
$498$		0			0
$499$	193.677	−	467.577i	0.388130	−	0.937029i	−0.602206	−	0.798341i	$-0.705711\pi$
$499$	193.677	−	467.577i	0.388130	−	0.937029i	0.990336	−	0.138688i	$-0.0442886\pi$
$500$	66.8201	−	70.9281i	0.133640	−	0.141856i
$501$		0			0
$502$	−678.844	+	145.582i	−1.35228	+	0.290005i
$503$	−659.583	+	659.583i	−1.31130	+	1.31130i	−0.390840	+	0.920459i	$0.627816\pi$
$503$	−659.583	+	659.583i	−1.31130	+	1.31130i	−0.920459	+	0.390840i	$0.872184\pi$
$504$		0			0
$505$	−37.0177	+	37.0177i	−0.0733024	+	0.0733024i
$506$	752.415	+	486.683i	1.48699	+	0.961823i
$507$		0			0
$508$	−232.832	+	613.201i	−0.458332	+	1.20709i
$509$	133.178	−	321.521i	0.261647	−	0.631671i	−0.737394	−	0.675463i	$-0.763944\pi$
$509$	133.178	−	321.521i	0.261647	−	0.631671i	0.999041	+	0.0437918i	$0.0139438\pi$
$510$		0			0
$511$		−	58.6707i		−	0.114815i
$512$	511.010	+	31.8190i	0.998067	+	0.0621466i
$513$		0			0
$514$	39.2705	−	214.055i	0.0764018	−	0.416449i
$515$	81.6425	+	33.8174i	0.158529	+	0.0656649i
$516$		0			0
$517$	755.957	−	313.127i	1.46220	−	0.605662i
$518$	7.07475	−	10.9376i	0.0136578	−	0.0211151i
$519$		0			0
$520$	43.8173	−	72.3862i	0.0842641	−	0.139204i
$521$	−71.2918	−	71.2918i	−0.136837	−	0.136837i	0.635371	−	0.772207i	$-0.280847\pi$
$521$	−71.2918	−	71.2918i	−0.136837	−	0.136837i	−0.772207	+	0.635371i	$0.780847\pi$
$522$		0			0
$523$	−376.338	+	155.884i	−0.719576	+	0.298058i	−0.712261	−	0.701915i	$-0.752329\pi$
$523$	−376.338	+	155.884i	−0.719576	+	0.298058i	−0.00731529	+	0.999973i	$0.502329\pi$
$524$	−35.3832	−	33.3338i	−0.0675252	−	0.0636142i
$525$		0			0
$526$	349.562	−	241.183i	0.664566	−	0.458523i
$527$	333.940			0.633662
$528$		0			0
$529$		−	41.2074i		−	0.0778968i
$530$	−59.1011	+	40.7774i	−0.111511	+	0.0769384i
$531$		0			0
$532$	21.9691	−	0.655181i	0.0412953	−	0.00123154i
$533$	169.379	+	408.918i	0.317785	+	0.767201i
$534$		0			0
$535$	−35.5704	+	35.5704i	−0.0664867	+	0.0664867i
$536$	2.09444	−	1.53921i	0.00390754	−	0.00287167i
$537$		0			0
$538$	300.380	−	464.390i	0.558327	−	0.863178i
$539$	349.184	+	843.005i	0.647837	+	1.56402i
$540$		0			0
$541$	−131.242	+	316.846i	−0.242591	+	0.585667i	−0.997539	−	0.0701185i	$-0.977662\pi$
$541$	−131.242	+	316.846i	−0.242591	+	0.585667i	0.754948	+	0.655785i	$0.227662\pi$
$542$	−94.4281	+	514.706i	−0.174222	+	0.949643i
$543$		0			0
$544$	−267.982	−	342.748i	−0.492614	−	0.630051i
$545$	−14.7639			−0.0270898
$546$		0			0
$547$	−57.6667	−	23.8863i	−0.105424	−	0.0436679i	0.329348	−	0.944209i	$-0.393171\pi$
$547$	−57.6667	−	23.8863i	−0.105424	−	0.0436679i	−0.434772	+	0.900541i	$0.643171\pi$
$548$	49.4039	+	109.886i	0.0901531	+	0.200523i
$549$		0			0
$550$	−780.184	−	504.645i	−1.41852	−	0.917536i
$551$	−231.064	−	231.064i	−0.419354	−	0.419354i
$552$		0			0
$553$	29.1339	+	29.1339i	0.0526834	+	0.0526834i
$554$	613.837	−	131.641i	1.10801	−	0.237620i
$555$		0			0
$556$	670.075	−	19.9835i	1.20517	−	0.0359416i
$557$	−403.952	−	167.322i	−0.725228	−	0.300399i	−0.0106383	−	0.999943i	$-0.503386\pi$
$557$	−403.952	−	167.322i	−0.725228	−	0.300399i	−0.714589	+	0.699544i	$0.753386\pi$
$558$		0			0
$559$	−417.394			−0.746680
$560$	2.08175	+	4.28408i	0.00371742	+	0.00765014i
$561$		0			0
$562$	35.0003	+	50.7280i	0.0622781	+	0.0902634i
$563$	−2.60893	+	6.29851i	−0.00463398	+	0.0111874i	−0.926180	−	0.377083i	$-0.876927\pi$
$563$	−2.60893	+	6.29851i	−0.00463398	+	0.0111874i	0.921546	+	0.388270i	$0.126927\pi$
$564$		0			0
$565$	−26.3767	−	63.6791i	−0.0466845	−	0.112706i
$566$	−796.850	+	170.890i	−1.40786	+	0.301925i
$567$		0			0
$568$	−319.614	+	78.5777i	−0.562702	+	0.138341i
$569$	−225.325	+	225.325i	−0.396002	+	0.396002i	−0.876820	−	0.480818i	$-0.840340\pi$
$569$	−225.325	+	225.325i	−0.396002	+	0.396002i	0.480818	+	0.876820i	$0.340340\pi$
$570$		0			0
$571$	203.081	+	490.280i	0.355658	+	0.858634i	0.995900	+	0.0904608i	$0.0288340\pi$
$571$	203.081	+	490.280i	0.355658	+	0.858634i	−0.640242	+	0.768173i	$0.721166\pi$
$572$	−1515.86	−	575.573i	−2.65011	−	1.00625i
$573$		0			0
$574$	−24.5061	−	4.49589i	−0.0426935	−	0.00783256i
$575$			591.252i			1.02826i
$576$		0			0
$577$	−1017.81			−1.76396			−0.881980	−	0.471286i	$-0.843790\pi$
$577$	−1017.81			−1.76396			−0.881980	+	0.471286i	$0.843790\pi$
$578$	37.5861	−	204.873i	0.0650278	−	0.354452i
$579$		0			0
$580$	25.1377	−	66.2040i	0.0433408	−	0.114145i
$581$	24.0762	−	9.97270i	0.0414393	−	0.0171647i
$582$		0			0
$583$	972.943	+	972.943i	1.66886	+	1.66886i
$584$	749.582	−	184.286i	1.28353	−	0.315558i
$585$		0			0
$586$	−16.8903	−	78.7587i	−0.0288230	−	0.134400i
$587$	721.215	−	298.737i	1.22865	−	0.508922i	0.328498	−	0.944505i	$-0.393458\pi$
$587$	721.215	−	298.737i	1.22865	−	0.508922i	0.900149	+	0.435583i	$0.143458\pi$
$588$		0			0
$589$	−205.053	−	84.9359i	−0.348138	−	0.144204i
$590$	−3.58296	+	2.47210i	−0.00607282	+	0.00419000i
$591$		0			0
$592$	161.962	+	56.0324i	0.273585	+	0.0946493i
$593$		−	525.499i		−	0.886170i	−0.896479	−	0.443085i	$-0.853884\pi$
$593$		−	525.499i		−	0.886170i	0.896479	−	0.443085i	$-0.146116\pi$
$594$		0			0
$595$	1.54890	−	3.73937i	0.00260319	−	0.00628465i
$596$	−28.3311	−	949.980i	−0.0475354	−	1.59393i
$597$		0			0
$598$	216.351	+	1008.83i	0.361791	+	1.68701i
$599$	359.176	−	359.176i	0.599626	−	0.599626i	−0.340587	−	0.940213i	$-0.610626\pi$
$599$	359.176	−	359.176i	0.599626	−	0.599626i	0.940213	+	0.340587i	$0.110626\pi$
$600$		0			0
$601$	163.858	−	163.858i	0.272642	−	0.272642i	−0.557521	−	0.830163i	$-0.688247\pi$
$601$	163.858	−	163.858i	0.272642	−	0.272642i	0.830163	+	0.557521i	$0.188247\pi$
$602$	12.7608	−	19.7283i	0.0211974	−	0.0327713i
$603$		0			0
$604$	423.320	−	190.321i	0.700862	−	0.315101i
$605$	43.2897	−	104.511i	0.0715533	−	0.172745i
$606$		0			0
$607$		−	208.191i		−	0.342984i	−0.985186	−	0.171492i	$-0.945141\pi$
$607$		−	208.191i		−	0.342984i	0.985186	−	0.171492i	$-0.0548587\pi$
$608$	77.3762	+	278.622i	0.127263	+	0.458259i
$609$		0			0
$610$	−8.89284	−	1.63148i	−0.0145784	−	0.00267456i
$611$	870.414	+	360.537i	1.42457	+	0.590077i
$612$		0			0
$613$	643.217	−	266.429i	1.04929	−	0.434632i	0.209654	−	0.977776i	$-0.432766\pi$
$613$	643.217	−	266.429i	1.04929	−	0.434632i	0.839640	+	0.543144i	$0.182766\pi$
$614$	443.604	+	286.935i	0.722481	+	0.467321i
$615$		0			0
$616$	73.5485	−	54.0511i	0.119397	−	0.0877453i
$617$	526.767	+	526.767i	0.853755	+	0.853755i	0.990593	−	0.136838i	$-0.0436941\pi$
$617$	526.767	+	526.767i	0.853755	+	0.853755i	−0.136838	+	0.990593i	$0.543694\pi$
$618$		0			0
$619$	−316.799	+	131.222i	−0.511791	+	0.211991i	−0.623607	−	0.781738i	$-0.714333\pi$
$619$	−316.799	+	131.222i	−0.511791	+	0.211991i	0.111816	+	0.993729i	$0.464333\pi$
$620$	−1.43381	−	48.0775i	−0.00231259	−	0.0775443i
$621$		0			0
$622$	−291.370	−	422.300i	−0.468441	−	0.678939i
$623$	39.0188			0.0626306
$624$		0			0
$625$		−	607.081i		−	0.971330i
$626$	−178.236	−	258.328i	−0.284722	−	0.412665i
$627$		0			0
$628$	379.089	−	402.395i	0.603645	−	0.640757i
$629$	−55.7309	−	134.546i	−0.0886024	−	0.213905i
$630$		0			0
$631$	515.138	−	515.138i	0.816383	−	0.816383i	−0.169199	−	0.985582i	$-0.554118\pi$
$631$	515.138	−	515.138i	0.816383	−	0.816383i	0.985582	+	0.169199i	$0.0541179\pi$
$632$	−280.707	+	463.728i	−0.444157	+	0.733747i
$633$		0			0
$634$	588.732	+	380.808i	0.928600	+	0.600644i
$635$	−30.7220	−	74.1694i	−0.0483810	−	0.116802i
$636$		0			0
$637$	−402.053	+	970.642i	−0.631167	+	1.52377i
$638$	−1334.75	−	244.873i	−2.09208	−	0.383814i
$639$		0			0
$640$	−48.1950	+	40.0531i	−0.0753046	+	0.0625830i
$641$	827.282			1.29061			0.645306	−	0.763925i	$-0.276730\pi$
$641$	827.282			1.29061			0.645306	+	0.763925i	$0.276730\pi$
$642$		0			0
$643$	300.259	+	124.371i	0.466965	+	0.193423i	0.603744	−	0.797178i	$-0.293675\pi$
$643$	300.259	+	124.371i	0.466965	+	0.193423i	−0.136779	+	0.990602i	$0.543675\pi$
$644$	−54.2974	−	20.6167i	−0.0843127	−	0.0320135i
$645$		0			0
$646$	133.454	−	206.322i	0.206586	−	0.319383i
$647$	182.325	+	182.325i	0.281800	+	0.281800i	0.833827	−	0.552027i	$-0.186145\pi$
$647$	182.325	+	182.325i	0.281800	+	0.281800i	−0.552027	+	0.833827i	$0.686145\pi$
$648$		0			0
$649$	58.9840	+	58.9840i	0.0908845	+	0.0908845i
$650$	−224.336	−	1046.07i	−0.345132	−	1.60933i
$651$		0			0
$652$	−172.789	−	162.781i	−0.265013	−	0.249664i
$653$	83.4520	+	34.5670i	0.127798	+	0.0529356i	0.445666	−	0.895199i	$-0.352967\pi$
$653$	83.4520	+	34.5670i	0.127798	+	0.0529356i	−0.317868	+	0.948135i	$0.602967\pi$
$654$		0			0
$655$	5.94981			0.00908368
$656$	−19.5342	−	327.214i	−0.0297778	−	0.498801i
$657$		0			0
$658$	−43.6517	+	30.1179i	−0.0663400	+	0.0457719i
$659$	−36.4182	+	87.9213i	−0.0552628	+	0.133416i	−0.949099	−	0.314976i	$-0.898003\pi$
$659$	−36.4182	+	87.9213i	−0.0552628	+	0.133416i	0.893837	+	0.448393i	$0.148003\pi$
$660$		0			0
$661$	−420.501	−	1015.18i	−0.636159	−	1.53582i	−0.831757	−	0.555140i	$-0.812665\pi$
$661$	−420.501	−	1015.18i	−0.636159	−	1.53582i	0.195597	−	0.980684i	$-0.437335\pi$
$662$	263.388	+	1228.16i	0.397867	+	1.85523i
$663$		0			0
$664$	203.036	+	276.276i	0.305777	+	0.416078i
$665$	−1.90218	+	1.90218i	−0.00286042	+	0.00286042i
$666$		0			0
$667$	330.450	+	797.776i	0.495427	+	1.19607i
$668$	−229.015	−	509.385i	−0.342836	−	0.762553i
$669$		0			0
$670$	−0.0574056	+	0.312905i	−8.56800e−5	+	0.000467022i
$671$			173.255i			0.258205i
$672$		0			0
$673$	80.3370			0.119372			0.0596858	−	0.998217i	$-0.480990\pi$
$673$	80.3370			0.119372			0.0596858	+	0.998217i	$0.480990\pi$
$674$	−256.237	−	47.0094i	−0.380174	−	0.0697468i
$675$		0			0
$676$	−488.356	−	1086.23i	−0.722421	−	1.60684i
$677$	944.061	−	391.043i	1.39448	−	0.577611i	0.446165	−	0.894951i	$-0.352789\pi$
$677$	944.061	−	391.043i	1.39448	−	0.577611i	0.948312	+	0.317339i	$0.102789\pi$
$678$		0			0
$679$	−51.3001	−	51.3001i	−0.0755524	−	0.0755524i
$680$	52.6397	+	8.04342i	0.0774113	+	0.0118286i
$681$		0			0
$682$	−901.214	+	193.271i	−1.32143	+	0.283389i
$683$	173.921	−	72.0404i	0.254643	−	0.105476i	−0.251711	−	0.967803i	$-0.580993\pi$
$683$	173.921	−	72.0404i	0.254643	−	0.105476i	0.506353	+	0.862326i	$0.330993\pi$
$684$		0			0
$685$	−13.6237	−	5.64314i	−0.0198887	−	0.00823816i
$686$	−67.4274	−	97.7266i	−0.0982907	−	0.142459i
$687$		0			0
$688$	292.133	+	101.066i	0.424612	+	0.146899i
$689$			1584.28i			2.29939i
$690$		0			0
$691$	185.902	−	448.807i	0.269033	−	0.649503i	−0.730405	−	0.683014i	$-0.760669\pi$
$691$	185.902	−	448.807i	0.269033	−	0.649503i	0.999438	+	0.0335109i	$0.0106688\pi$
$692$	−19.1988	−	18.0868i	−0.0277439	−	0.0261370i
$693$		0			0
$694$	279.405	−	59.9203i	0.402601	−	0.0863404i
$695$	−58.0179	+	58.0179i	−0.0834790	+	0.0834790i
$696$		0			0
$697$	−196.962	+	196.962i	−0.282586	+	0.282586i
$698$	205.343	+	132.821i	0.294188	+	0.190289i
$699$		0			0
$700$	56.3013	+	21.3776i	0.0804304	+	0.0305395i
$701$	150.886	−	364.271i	0.215244	−	0.519645i	−0.778970	−	0.627061i	$-0.784258\pi$
$701$	150.886	−	364.271i	0.215244	−	0.519645i	0.994214	+	0.107416i	$0.0342576\pi$
$702$		0			0
$703$			96.7921i			0.137684i
$704$	921.580	+	769.887i	1.30906	+	1.09359i
$705$		0			0
$706$	−137.903	+	751.680i	−0.195331	+	1.06470i
$707$	−60.0713	−	24.8824i	−0.0849665	−	0.0351943i
$708$		0			0
$709$	−457.191	+	189.375i	−0.644839	+	0.267101i	−0.681043	−	0.732243i	$-0.738473\pi$
$709$	−457.191	+	189.375i	−0.644839	+	0.267101i	0.0362043	+	0.999344i	$0.488473\pi$
$710$	21.8787	−	33.8247i	0.0308151	−	0.0476404i
$711$		0			0
$712$	122.559	+	498.509i	0.172134	+	0.700153i
$713$	414.720	+	414.720i	0.581656	+	0.581656i
$714$		0			0
$715$	183.350	−	75.9462i	0.256434	−	0.106218i
$716$	578.177	−	613.723i	0.807510	−	0.857155i
$717$		0			0
$718$	189.251	−	130.575i	0.263581	−	0.181860i
$719$	−1277.00			−1.77608			−0.888039	−	0.459768i	$-0.847932\pi$
$719$	−1277.00			−1.77608			−0.888039	+	0.459768i	$0.847932\pi$
$720$		0			0
$721$			109.756i			0.152227i
$722$	459.851	−	317.279i	0.636913	−	0.439444i
$723$		0			0
$724$	18.6161	+	624.222i	0.0257128	+	0.862186i
$725$	−342.646	−	827.219i	−0.472614	−	1.14099i
$726$		0			0
$727$	470.863	−	470.863i	0.647679	−	0.647679i	−0.304753	−	0.952432i	$-0.598574\pi$
$727$	470.863	−	470.863i	0.647679	−	0.647679i	0.952432	+	0.304753i	$0.0985738\pi$
$728$	103.888	+	15.8742i	0.142703	+	0.0218052i
$729$		0			0
$730$	−51.3115	+	79.3280i	−0.0702898	+	0.108669i
$731$	−100.522	−	242.683i	−0.137514	−	0.331987i
$732$		0			0
$733$	364.452	−	879.866i	0.497206	−	1.20036i	−0.453776	−	0.891116i	$-0.649923\pi$
$733$	364.452	−	879.866i	0.497206	−	1.20036i	0.950982	−	0.309246i	$-0.100077\pi$
$734$	164.622	−	897.315i	0.224280	−	1.22250i
$735$		0			0
$736$	92.8520	−	758.466i	0.126158	−	1.03052i
$737$	6.09619			0.00827163
$738$		0			0
$739$	1146.65	+	474.958i	1.55162	+	0.642704i	0.983609	−	0.180314i	$-0.0577112\pi$
$739$	1146.65	+	474.958i	1.55162	+	0.642704i	0.568016	+	0.823018i	$0.307711\pi$
$740$	−19.1314	+	8.60129i	−0.0258533	+	0.0116234i
$741$		0			0
$742$	−74.8816	−	48.4355i	−0.100919	−	0.0652769i
$743$	−512.021	−	512.021i	−0.689126	−	0.689126i	0.272913	−	0.962039i	$-0.412013\pi$
$743$	−512.021	−	512.021i	−0.689126	−	0.689126i	−0.962039	+	0.272913i	$0.912013\pi$
$744$		0			0
$745$	82.2533	+	82.2533i	0.110407	+	0.110407i
$746$	−940.804	+	201.762i	−1.26113	+	0.270458i
$747$		0			0
$748$	−30.4185	−	1019.97i	−0.0406665	−	1.36360i
$749$	−57.7227	−	23.9095i	−0.0770663	−	0.0319219i
$750$		0			0
$751$	335.629			0.446910			0.223455	−	0.974714i	$-0.428266\pi$
$751$	335.629			0.446910			0.223455	+	0.974714i	$0.428266\pi$
$752$	−521.901	−	463.098i	−0.694017	−	0.615822i
$753$		0			0
$754$	−887.341	−	1286.08i	−1.17684	−	1.70567i
$755$	−21.7393	+	52.4833i	−0.0287938	+	0.0695143i
$756$		0			0
$757$	−139.805	−	337.518i	−0.184682	−	0.445863i	0.804238	−	0.594307i	$-0.202573\pi$
$757$	−139.805	−	337.518i	−0.184682	−	0.445863i	−0.988921	+	0.148444i	$0.952573\pi$
$758$	−556.487	+	119.342i	−0.734152	+	0.157444i
$759$		0			0
$760$	−30.2772	−	18.3276i	−0.0398385	−	0.0241153i
$761$	−495.581	+	495.581i	−0.651223	+	0.651223i	−0.953288	−	0.302064i	$-0.902324\pi$
$761$	−495.581	+	495.581i	−0.651223	+	0.651223i	0.302064	+	0.953288i	$0.402324\pi$
$762$		0			0
$763$	−7.01728	−	16.9412i	−0.00919696	−	0.0222034i
$764$	153.081	−	403.163i	0.200368	−	0.527700i
$765$		0			0
$766$	−937.965	−	172.079i	−1.22450	−	0.224647i
$767$			96.0458i			0.125223i
$768$		0			0
$769$	372.267			0.484092			0.242046	−	0.970265i	$-0.422181\pi$
$769$	372.267			0.484092			0.242046	+	0.970265i	$0.422181\pi$
$770$	−2.01586	+	10.9880i	−0.00261800	+	0.0142701i
$771$		0			0
$772$	653.778	+	248.240i	0.846862	+	0.321554i
$773$	534.778	−	221.512i	0.691822	−	0.286562i	−0.00893708	−	0.999960i	$-0.502845\pi$
$773$	534.778	−	221.512i	0.691822	−	0.286562i	0.700759	+	0.713398i	$0.252845\pi$
$774$		0			0
$775$	−430.026	−	430.026i	−0.554873	−	0.554873i
$776$	494.280	−	816.550i	0.636959	−	1.05226i
$777$		0			0
$778$	−32.4775	−	151.441i	−0.0417448	−	0.194654i
$779$	171.040	−	70.8470i	0.219563	−	0.0909461i
$780$		0			0
$781$	−713.187	−	295.412i	−0.913172	−	0.378248i
$782$	−534.455	+	368.752i	−0.683446	+	0.471550i
$783$		0			0
$784$	516.424	−	581.998i	0.658704	−	0.742344i
$785$			67.6643i			0.0861965i
$786$		0			0
$787$	−280.233	+	676.541i	−0.356077	+	0.859646i	0.639767	+	0.768569i	$0.279031\pi$
$787$	−280.233	+	676.541i	−0.356077	+	0.859646i	−0.995844	+	0.0910769i	$0.970969\pi$
$788$	−469.427	+	13.9996i	−0.595719	+	0.0177660i
$789$		0			0
$790$	−13.9121	−	64.8713i	−0.0176102	−	0.0821155i
$791$	60.5332	−	60.5332i	0.0765274	−	0.0765274i
$792$		0			0
$793$	−141.059	+	141.059i	−0.177880	+	0.177880i
$794$	141.510	−	218.775i	0.178224	−	0.275535i
$795$		0			0
$796$	−441.531	−	982.074i	−0.554687	−	1.23376i
$797$	−92.5205	+	223.364i	−0.116086	+	0.280256i	−0.971234	−	0.238128i	$-0.923466\pi$
$797$	−92.5205	+	223.364i	−0.116086	+	0.280256i	0.855148	+	0.518384i	$0.173466\pi$
$798$		0			0
$799$			592.908i			0.742063i
$800$	−96.2788	+	786.459i	−0.120349	+	0.983073i
$801$		0			0
$802$	342.317	+	62.8016i	0.426829	+	0.0783062i
$803$	1672.62	+	692.821i	2.08296	+	0.862790i
$804$		0			0
$805$	6.56751	−	2.72035i	0.00815839	−	0.00337932i
$806$	−891.095	−	576.385i	−1.10558	−	0.715117i
$807$		0			0
$808$	129.214	−	845.633i	0.159918	−	1.04658i
$809$	−977.291	−	977.291i	−1.20802	−	1.20802i	−0.971666	−	0.236358i	$-0.924046\pi$
$809$	−977.291	−	977.291i	−1.20802	−	1.20802i	−0.236358	−	0.971666i	$-0.575954\pi$
$810$		0			0
$811$	553.320	−	229.193i	0.682269	−	0.282605i	−0.0145062	−	0.999895i	$-0.504618\pi$
$811$	553.320	−	229.193i	0.682269	−	0.282605i	0.696775	+	0.717290i	$0.254618\pi$
$812$	87.9152	−	2.62188i	0.108270	−	0.00322892i
$813$		0			0
$814$	228.273	+	330.850i	0.280434	+	0.406449i
$815$	29.0550			0.0356503
$816$		0			0
$817$			174.585i			0.213690i
$818$	174.659	+	253.144i	0.213519	+	0.309467i
$819$		0			0
$820$	29.2024	+	27.5111i	0.0356127	+	0.0335501i
$821$	−390.123	−	941.839i	−0.475180	−	1.14719i	−0.961844	−	0.273597i	$-0.911787\pi$
$821$	−390.123	−	941.839i	−0.475180	−	1.14719i	0.486665	−	0.873589i	$-0.338213\pi$
$822$		0			0
$823$	−692.747	+	692.747i	−0.841734	+	0.841734i	−0.989084	−	0.147350i	$-0.952926\pi$
$823$	−692.747	+	692.747i	−0.841734	+	0.841734i	0.147350	+	0.989084i	$0.452926\pi$
$824$	−1402.25	+	344.746i	−1.70176	+	0.418381i
$825$		0			0
$826$	−4.53965	−	2.93637i	−0.00549594	−	0.00355492i
$827$	401.669	+	969.714i	0.485694	+	1.17257i	0.956867	+	0.290528i	$0.0938309\pi$
$827$	401.669	+	969.714i	0.485694	+	1.17257i	−0.471173	+	0.882041i	$0.656169\pi$
$828$		0			0
$829$	562.011	−	1356.81i	0.677938	−	1.63669i	−0.0898281	−	0.995957i	$-0.528632\pi$
$829$	562.011	−	1356.81i	0.677938	−	1.63669i	0.767766	−	0.640730i	$-0.221368\pi$
$830$	−41.2750	−	7.57233i	−0.0497289	−	0.00912328i
$831$		0			0
$832$	123.503	+	1377.14i	0.148442	+	1.65521i
$833$	−661.182			−0.793735
$834$		0			0
$835$	63.1537	+	26.1591i	0.0756331	+	0.0313283i
$836$	−240.747	+	634.045i	−0.287975	+	0.758427i
$837$		0			0
$838$	−435.457	+	673.220i	−0.519639	+	0.803365i
$839$	708.611	+	708.611i	0.844590	+	0.844590i	0.989452	−	0.144862i	$-0.0462737\pi$
$839$	708.611	+	708.611i	0.844590	+	0.844590i	−0.144862	+	0.989452i	$0.546274\pi$
$840$		0			0
$841$	−329.986	−	329.986i	−0.392374	−	0.392374i
$842$	272.513	+	1270.71i	0.323649	+	1.50916i
$843$		0			0
$844$	−621.219	+	659.411i	−0.736041	+	0.781292i
$845$	134.670	+	55.7823i	0.159373	+	0.0660146i
$846$		0			0
$847$	140.499			0.165878
$848$	383.611	−	1108.83i	0.452372	−	1.30758i
$849$		0			0
$850$	554.180	−	382.362i	0.651976	−	0.449837i
$851$	97.8810	−	236.306i	0.115019	−	0.277680i
$852$		0			0
$853$	−178.189	−	430.187i	−0.208897	−	0.504322i	0.784353	−	0.620315i	$-0.212995\pi$
$853$	−178.189	−	430.187i	−0.208897	−	0.504322i	−0.993250	+	0.115992i	$0.962995\pi$
$854$	−2.35468	−	10.9797i	−0.00275723	−	0.0128568i
$855$		0			0
$856$	124.162	−	812.571i	0.145049	−	0.949265i
$857$	195.982	−	195.982i	0.228683	−	0.228683i	−0.583459	−	0.812142i	$-0.698301\pi$
$857$	195.982	−	195.982i	0.228683	−	0.228683i	0.812142	+	0.583459i	$0.198301\pi$
$858$		0			0
$859$	−155.060	−	374.347i	−0.180512	−	0.435794i	0.807560	−	0.589785i	$-0.200787\pi$
$859$	−155.060	−	374.347i	−0.180512	−	0.435794i	−0.988072	+	0.153991i	$0.950787\pi$
$860$	−34.5075	+	15.5142i	−0.0401250	+	0.0180398i
$861$		0			0
$862$	−104.626	+	570.294i	−0.121376	+	0.661594i
$863$		−	63.9126i		−	0.0740586i	−0.999314	−	0.0370293i	$-0.988211\pi$
$863$		−	63.9126i		−	0.0740586i	0.999314	−	0.0370293i	$-0.0117895\pi$
$864$		0			0
$865$	3.22835			0.00373219
$866$	618.505	+	113.471i	0.714209	+	0.131029i
$867$		0			0
$868$	54.4861	−	24.4964i	0.0627720	−	0.0282217i
$869$	−1174.60	+	486.534i	−1.35167	+	0.559879i
$870$		0			0
$871$	4.96332	+	4.96332i	0.00569842	+	0.00569842i
$872$	194.401	−	142.866i	0.222937	−	0.163837i
$873$		0			0
$874$	421.968	−	90.4938i	0.482801	−	0.103540i
$875$	−13.6857	+	5.66881i	−0.0156408	+	0.00647864i
$876$		0			0
$877$	−34.2590	−	14.1905i	−0.0390638	−	0.0161808i	0.363066	−	0.931763i	$-0.381730\pi$
$877$	−34.2590	−	14.1905i	−0.0390638	−	0.0161808i	−0.402130	+	0.915583i	$0.631730\pi$
$878$	930.762	+	1349.01i	1.06009	+	1.53646i
$879$		0			0
$880$	−146.716	+	8.75874i	−0.166722	+	0.00995311i
$881$		−	1126.03i		−	1.27812i	−0.769155	−	0.639062i	$-0.779323\pi$
$881$		−	1126.03i		−	1.27812i	0.769155	−	0.639062i	$-0.220677\pi$
$882$		0			0
$883$	−114.384	+	276.148i	−0.129540	+	0.312738i	−0.975321	−	0.220793i	$-0.929135\pi$
$883$	−114.384	+	276.148i	−0.129540	+	0.312738i	0.845780	+	0.533531i	$0.179135\pi$
$884$	805.665	−	855.196i	0.911385	−	0.967417i
$885$		0			0
$886$	−550.539	+	118.067i	−0.621376	+	0.133258i
$887$	−65.1075	+	65.1075i	−0.0734020	+	0.0734020i	−0.742855	−	0.669453i	$-0.766529\pi$
$887$	−65.1075	+	65.1075i	−0.0734020	+	0.0734020i	0.669453	+	0.742855i	$0.266529\pi$
$888$		0			0
$889$	70.5052	−	70.5052i	0.0793085	−	0.0793085i
$890$	−52.7570	−	34.1247i	−0.0592775	−	0.0383423i
$891$		0			0
$892$	147.448	−	388.328i	0.165301	−	0.435345i
$893$	150.803	−	364.071i	0.168873	−	0.407694i
$894$		0			0
$895$			103.200i			0.115307i
$896$	−68.8669	−	36.2652i	−0.0768604	−	0.0404746i
$897$		0			0
$898$	−169.982	+	926.531i	−0.189289	+	1.03177i
$899$	−820.576	−	339.894i	−0.912765	−	0.378080i
$900$		0			0
$901$	−921.136	+	381.547i	−1.02235	+	0.423471i
$902$	417.555	−	645.543i	0.462921	−	0.715679i
$903$		0			0
$904$	963.514	+	583.242i	1.06583	+	0.645179i
$905$	−54.0478	−	54.0478i	−0.0597213	−	0.0597213i
$906$		0			0
$907$	1085.79	−	449.751i	1.19713	−	0.495866i	0.307058	−	0.951691i	$-0.400656\pi$
$907$	1085.79	−	449.751i	1.19713	−	0.495866i	0.890070	+	0.455825i	$0.150656\pi$
$908$	334.315	+	314.952i	0.368188	+	0.346864i
$909$		0			0
$910$	−10.5873	+	7.30483i	−0.0116344	+	0.00802728i
$911$	37.8649			0.0415641			0.0207821	−	0.999784i	$-0.493384\pi$
$911$	37.8649			0.0415641			0.0207821	+	0.999784i	$0.493384\pi$
$912$		0			0
$913$			804.143i			0.880770i
$914$	1042.67	−	719.398i	1.14077	−	0.787088i
$915$		0			0
$916$	−199.574	+	5.95187i	−0.217876	+	0.00649767i
$917$	2.82794	+	6.82725i	0.00308390	+	0.00744520i
$918$		0			0
$919$	−1205.51	+	1205.51i	−1.31176	+	1.31176i	−0.391640	+	0.920119i	$0.628092\pi$
$919$	−1205.51	+	1205.51i	−1.31176	+	1.31176i	−0.920119	+	0.391640i	$0.871908\pi$
$920$	55.3842	+	75.3624i	0.0602002	+	0.0819157i
$921$		0			0
$922$	−297.719	+	460.276i	−0.322906	+	0.499215i
$923$	−340.139	−	821.169i	−0.368515	−	0.889674i
$924$		0			0
$925$	−101.493	+	245.027i	−0.109723	+	0.264894i
$926$	−235.938	+	1286.04i	−0.254792	+	1.38881i
$927$		0			0
$928$	309.641	+	1114.98i	0.333665	+	1.20149i
$929$	−1384.29			−1.49009			−0.745045	−	0.667014i	$-0.767572\pi$
$929$	−1384.29			−1.49009			−0.745045	+	0.667014i	$0.767572\pi$
$930$		0			0
$931$	405.994	+	168.168i	0.436084	+	0.180632i
$932$	−145.447	−	323.510i	−0.156059	−	0.347114i
$933$		0			0
$934$	172.843	+	111.800i	0.185057	+	0.119700i
$935$	88.3137	+	88.3137i	0.0944532	+	0.0944532i
$936$		0			0
$937$	−500.748	−	500.748i	−0.534416	−	0.534416i	0.387467	−	0.921883i	$-0.373350\pi$
$937$	−500.748	−	500.748i	−0.534416	−	0.534416i	−0.921883	+	0.387467i	$0.873350\pi$
$938$	−0.386335	+	0.0828520i	−0.000411871	+	8.83284e-5i
$939$		0			0
$940$	85.3613	−	2.54571i	0.0908099	−	0.00270821i
$941$	1312.74	+	543.756i	1.39505	+	0.577849i	0.948462	−	0.316891i	$-0.102639\pi$
$941$	1312.74	+	543.756i	1.39505	+	0.577849i	0.446588	+	0.894740i	$0.352639\pi$
$942$		0			0
$943$	−489.216			−0.518787
$944$	23.2562	−	67.2222i	0.0246358	−	0.0712099i
$945$		0			0
$946$	411.738	+	596.757i	0.435241	+	0.630821i
$947$	256.726	−	619.792i	0.271094	−	0.654480i	−0.728436	−	0.685114i	$-0.759753\pi$
$947$	256.726	−	619.792i	0.271094	−	0.654480i	0.999531	+	0.0306337i	$0.00975255\pi$
$948$		0			0
$949$	797.719	+	1925.86i	0.840589	+	2.02936i
$950$	−437.542	+	93.8337i	−0.460571	+	0.0987723i
$951$		0			0
$952$	15.7900	+	64.2256i	0.0165861	+	0.0674639i
$953$	−948.406	+	948.406i	−0.995179	+	0.995179i	−0.999988	−	0.00480927i	$-0.998469\pi$
$953$	−948.406	+	948.406i	−0.995179	+	0.995179i	0.00480927	+	0.999988i	$0.498469\pi$
$954$		0			0
$955$	20.1989	+	48.7643i	0.0211506	+	0.0510621i
$956$	1144.59	+	434.601i	1.19727	+	0.454603i
$957$		0			0
$958$	−1687.27	−	309.546i	−1.76124	−	0.323117i
$959$		−	18.3151i		−	0.0190981i
$960$		0			0
$961$	357.735			0.372253
$962$	−83.5147	+	455.220i	−0.0868136	+	0.473201i
$963$		0			0
$964$	−348.217	+	917.084i	−0.361221	+	0.951332i
$965$	−79.0773	+	32.7549i	−0.0819454	+	0.0339429i
$966$		0			0
$967$	−5.79422	−	5.79422i	−0.00599196	−	0.00599196i	0.704104	−	0.710096i	$-0.251349\pi$
$967$	−5.79422	−	5.79422i	−0.00599196	−	0.00599196i	−0.710096	+	0.704104i	$0.751349\pi$
$968$	441.310	+	1795.03i	0.455899	+	1.85437i
$969$		0			0
$970$	24.4969	+	114.228i	0.0252545	+	0.117761i
$971$	−1644.17	+	681.037i	−1.69327	+	0.701377i	−0.999817	−	0.0191210i	$-0.993913\pi$
$971$	−1644.17	+	681.037i	−1.69327	+	0.701377i	−0.693457	+	0.720498i	$0.743913\pi$
$972$		0			0
$973$	−94.1498	−	38.9981i	−0.0967624	−	0.0400803i
$974$	29.2096	−	20.1534i	0.0299893	−	0.0206914i
$975$		0			0
$976$	132.882	−	64.5712i	0.136150	−	0.0661590i
$977$			538.935i			0.551623i	0.961212	+	0.275811i	$0.0889465\pi$
$977$			538.935i			0.551623i	−0.961212	+	0.275811i	$0.911054\pi$
$978$		0			0
$979$	−460.760	+	1112.37i	−0.470643	+	1.13623i
$980$	2.83885	+	95.1907i	0.00289679	+	0.0971333i
$981$		0			0
$982$	41.6261	+	194.101i	0.0423891	+	0.197658i
$983$	−171.371	+	171.371i	−0.174335	+	0.174335i	−0.788881	−	0.614546i	$-0.789339\pi$
$983$	−171.371	+	171.371i	−0.174335	+	0.174335i	0.614546	+	0.788881i	$0.289339\pi$
$984$		0			0
$985$	40.6450	−	40.6450i	0.0412639	−	0.0412639i
$986$	534.053	−	825.650i	0.541636	−	0.837374i
$987$		0			0
$988$	−712.228	+	320.211i	−0.720878	+	0.324100i
$989$	176.549	−	426.227i	0.178513	−	0.430967i
$990$		0			0
$991$		−	1670.67i		−	1.68584i	−0.538038	−	0.842921i	$-0.680834\pi$
$991$		−	1670.67i		−	1.68584i	0.538038	−	0.842921i	$-0.319166\pi$
$992$	484.111	+	619.176i	0.488015	+	0.624170i
$993$		0			0
$994$	49.2119	+	9.02842i	0.0495089	+	0.00908292i
$995$	121.758	+	50.4337i	0.122370	+	0.0506871i
$996$		0			0
$997$	1252.59	−	518.840i	1.25636	−	0.520402i	0.347570	−	0.937654i	$-0.387007\pi$
$997$	1252.59	−	518.840i	1.25636	−	0.520402i	0.908791	+	0.417252i	$0.137007\pi$
$998$	−849.906	−	549.743i	−0.851609	−	0.550844i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.3.u.a.19.5		28
3.2	odd	2		32.3.h.a.19.3	✓	28
12.11	even	2		128.3.h.a.111.2		28
24.5	odd	2		256.3.h.b.223.2		28
24.11	even	2		256.3.h.a.223.6		28
32.27	odd	8	inner	288.3.u.a.91.5		28
96.5	odd	8		128.3.h.a.15.2		28
96.11	even	8		256.3.h.b.31.2		28
96.53	odd	8		256.3.h.a.31.6		28
96.59	even	8		32.3.h.a.27.3	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.19.3	✓	28	3.2	odd	2
32.3.h.a.27.3	yes	28	96.59	even	8
128.3.h.a.15.2		28	96.5	odd	8
128.3.h.a.111.2		28	12.11	even	2
256.3.h.a.31.6		28	96.53	odd	8
256.3.h.a.223.6		28	24.11	even	2
256.3.h.b.31.2		28	96.11	even	8
256.3.h.b.223.2		28	24.5	odd	2
288.3.u.a.19.5		28	1.1	even	1	trivial
288.3.u.a.91.5		28	32.27	odd	8	inner

Overview	Random
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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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	288.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.360897 - 1.96717i) q^{2} +(-3.73951 - 1.41989i) q^{4} +(0.452310 - 0.187353i) q^{5} +(0.429965 + 0.429965i) q^{7} +(-4.14274 + 6.84381i) q^{8} +O(q^{10})\)	\(q+(0.360897 - 1.96717i) q^{2} +(-3.73951 - 1.41989i) q^{4} +(0.452310 - 0.187353i) q^{5} +(0.429965 + 0.429965i) q^{7} +(-4.14274 + 6.84381i) q^{8} +(-0.205317 - 0.957385i) q^{10} +(-17.3350 + 7.18039i) q^{11} +(-19.9596 - 8.26755i) q^{13} +(1.00099 - 0.690640i) q^{14} +(11.9678 + 10.6194i) q^{16} -13.5961i q^{17} +(-3.45810 + 8.34859i) q^{19} +(-1.95744 + 0.0583763i) q^{20} +(7.86888 + 36.6922i) q^{22} +(16.8850 - 16.8850i) q^{23} +(-17.5082 + 17.5082i) q^{25} +(-23.4670 + 36.2802i) q^{26} +(-0.997353 - 2.21836i) q^{28} +(-13.8385 + 33.4091i) q^{29} +24.5614i q^{31} +(25.2093 - 19.7102i) q^{32} +(-26.7458 - 4.90679i) q^{34} +(0.275033 + 0.113922i) q^{35} +(9.89595 - 4.09904i) q^{37} +(15.1751 + 9.81565i) q^{38} +(-0.591598 + 3.87168i) q^{40} +(-14.4867 - 14.4867i) q^{41} +(17.8494 - 7.39348i) q^{43} +(75.0197 - 2.23730i) q^{44} +(-27.1219 - 39.3094i) q^{46} -43.6087 q^{47} -48.6303i q^{49} +(28.1229 + 40.7602i) q^{50} +(62.9001 + 59.2571i) q^{52} +(-28.0630 - 67.7501i) q^{53} +(-6.49552 + 6.49552i) q^{55} +(-4.72383 + 1.16136i) q^{56} +(60.7270 + 39.2799i) q^{58} +(-1.70130 - 4.10730i) q^{59} +(3.53360 - 8.53087i) q^{61} +(48.3165 + 8.86416i) q^{62} +(-29.6753 - 56.7043i) q^{64} -10.5769 q^{65} +(-0.300169 - 0.124334i) q^{67} +(-19.3050 + 50.8427i) q^{68} +(0.323363 - 0.499921i) q^{70} +(29.0914 + 29.0914i) q^{71} +(-68.2273 - 68.2273i) q^{73} +(-4.49208 - 20.9463i) q^{74} +(24.7857 - 26.3095i) q^{76} +(-10.5408 - 4.36612i) q^{77} +67.7588 q^{79} +(7.40274 + 2.56105i) q^{80} +(-33.7260 + 23.2695i) q^{82} +(16.4008 - 39.5950i) q^{83} +(-2.54727 - 6.14965i) q^{85} +(-8.10241 - 37.7811i) q^{86} +(22.6733 - 148.384i) q^{88} +(45.3745 - 45.3745i) q^{89} +(-5.02718 - 12.1367i) q^{91} +(-87.1165 + 39.1667i) q^{92} +(-15.7383 + 85.7857i) q^{94} +4.42403i q^{95} -119.312 q^{97} +(-95.6639 - 17.5505i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8	\( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 44 q^{10} + 4 q^{11} - 4 q^{13} + 20 q^{14} + 16 q^{16} - 4 q^{19} - 76 q^{20} + 144 q^{22} + 68 q^{23} - 4 q^{25} - 96 q^{26} + 56 q^{28} + 4 q^{29} + 24 q^{32} - 48 q^{34} - 92 q^{35} - 4 q^{37} + 396 q^{38} - 408 q^{40} + 4 q^{41} + 92 q^{43} + 188 q^{44} - 36 q^{46} + 8 q^{47} - 308 q^{50} + 420 q^{52} + 164 q^{53} + 252 q^{55} - 552 q^{56} + 528 q^{58} - 124 q^{59} - 68 q^{61} - 216 q^{62} - 232 q^{64} + 8 q^{65} - 164 q^{67} + 368 q^{68} - 664 q^{70} + 260 q^{71} - 4 q^{73} + 532 q^{74} - 516 q^{76} - 220 q^{77} - 520 q^{79} - 312 q^{80} + 636 q^{82} + 484 q^{83} + 96 q^{85} - 688 q^{86} + 672 q^{88} + 4 q^{89} - 196 q^{91} - 616 q^{92} + 40 q^{94} - 8 q^{97} + 328 q^{98}+O(q^{100}) \) 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8 - 44 * q^10 + 4 * q^11 - 4 * q^13 + 20 * q^14 + 16 * q^16 - 4 * q^19 - 76 * q^20 + 144 * q^22 + 68 * q^23 - 4 * q^25 - 96 * q^26 + 56 * q^28 + 4 * q^29 + 24 * q^32 - 48 * q^34 - 92 * q^35 - 4 * q^37 + 396 * q^38 - 408 * q^40 + 4 * q^41 + 92 * q^43 + 188 * q^44 - 36 * q^46 + 8 * q^47 - 308 * q^50 + 420 * q^52 + 164 * q^53 + 252 * q^55 - 552 * q^56 + 528 * q^58 - 124 * q^59 - 68 * q^61 - 216 * q^62 - 232 * q^64 + 8 * q^65 - 164 * q^67 + 368 * q^68 - 664 * q^70 + 260 * q^71 - 4 * q^73 + 532 * q^74 - 516 * q^76 - 220 * q^77 - 520 * q^79 - 312 * q^80 + 636 * q^82 + 484 * q^83 + 96 * q^85 - 688 * q^86 + 672 * q^88 + 4 * q^89 - 196 * q^91 - 616 * q^92 + 40 * q^94 - 8 * q^97 + 328 * q^98

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