LMFDB - Embedded newform 288.3.u.a.91.5

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			91.5
Character	$\chi$	$=$	288.91
Dual form			288.3.u.a.19.5

$q$-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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

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

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	0.427456	−	0.904036i	$-0.359410\pi$
$5$	0.452310	+	0.187353i	0.0904620	+	0.0374706i	−0.336994	+	0.941507i	$0.609410\pi$
$6$		0			0
$7$	0.429965	−	0.429965i	0.0614236	−	0.0614236i	−0.675728	−	0.737151i	$-0.736170\pi$
$7$	0.429965	−	0.429965i	0.0614236	−	0.0614236i	0.737151	+	0.675728i	$0.236170\pi$
$8$	−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	−0.588149	−	0.808752i	$-0.700143\pi$
$11$	−17.3350	−	7.18039i	−1.57591	−	0.652763i	−0.987759	+	0.155990i	$0.950143\pi$
$12$		0			0
$13$	−19.9596	+	8.26755i	−1.53536	+	0.635965i	−0.980595	−	0.196044i	$-0.937190\pi$
$13$	−19.9596	+	8.26755i	−1.53536	+	0.635965i	−0.554761	+	0.832010i	$0.687190\pi$
$14$	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	$0.130950\pi$
$17$			13.5961i			0.799770i	−0.916565	+	0.399885i	$0.869050\pi$
$18$		0			0
$19$	−3.45810	−	8.34859i	−0.182005	−	0.439399i	0.806374	−	0.591405i	$-0.201427\pi$
$19$	−3.45810	−	8.34859i	−0.182005	−	0.439399i	−0.988380	+	0.152006i	$0.951427\pi$
$20$	−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	0.971435	−	0.237304i	$-0.0762639\pi$
$23$	16.8850	+	16.8850i	0.734131	+	0.734131i	−0.237304	+	0.971435i	$0.576264\pi$
$24$		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	−0.960921	−	0.276821i	$-0.910719\pi$
$29$	−13.8385	−	33.4091i	−0.477190	−	1.15204i	0.483732	−	0.875216i	$-0.339281\pi$
$30$		0			0
$31$		−	24.5614i		−	0.792305i	−0.918185	−	0.396152i	$-0.870345\pi$
$31$		−	24.5614i		−	0.792305i	0.918185	−	0.396152i	$-0.129655\pi$
$32$	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	0.512382	−	0.858757i	$-0.328763\pi$
$37$	9.89595	+	4.09904i	0.267458	+	0.110785i	−0.244924	+	0.969542i	$0.578763\pi$
$38$	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	−0.861348	−	0.508015i	$-0.830380\pi$
$41$	−14.4867	+	14.4867i	−0.353334	+	0.353334i	0.508015	+	0.861348i	$0.330380\pi$
$42$		0			0
$43$	17.8494	+	7.39348i	0.415103	+	0.171941i	0.580453	−	0.814294i	$-0.302875\pi$
$43$	17.8494	+	7.39348i	0.415103	+	0.171941i	−0.165350	+	0.986235i	$0.552875\pi$
$44$	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	0.402367	+	0.915478i	$0.368188\pi$
$53$	−28.0630	+	67.7501i	−0.529490	+	1.27830i	−0.931857	+	0.362825i	$0.881812\pi$
$54$		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	−0.937641	−	0.347604i	$-0.886995\pi$
$59$	−1.70130	+	4.10730i	−0.0288356	+	0.0696153i	0.908806	+	0.417219i	$0.136995\pi$
$60$		0			0
$61$	3.53360	+	8.53087i	0.0579279	+	0.139850i	0.950193	−	0.311661i	$-0.100885\pi$
$61$	3.53360	+	8.53087i	0.0579279	+	0.139850i	−0.892266	+	0.451511i	$0.850885\pi$
$62$	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	−0.384922	−	0.922949i	$-0.625772\pi$
$67$	−0.300169	+	0.124334i	−0.00448013	+	0.00185573i	0.380442	+	0.924805i	$0.375772\pi$
$68$	−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	−0.471909	−	0.881647i	$-0.656435\pi$
$71$	29.0914	−	29.0914i	0.409738	−	0.409738i	0.881647	+	0.471909i	$0.156435\pi$
$72$		0			0
$73$	−68.2273	+	68.2273i	−0.934620	+	0.934620i	−0.997990	−	0.0633700i	$-0.979815\pi$
$73$	−68.2273	+	68.2273i	−0.934620	+	0.934620i	0.0633700	+	0.997990i	$0.479815\pi$
$74$	−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	0.991358	−	0.131186i	$-0.0418784\pi$
$83$	16.4008	+	39.5950i	0.197600	+	0.477048i	−0.793758	+	0.608234i	$0.791878\pi$
$84$		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	0.914473	−	0.404647i	$-0.132606\pi$
$89$	45.3745	+	45.3745i	0.509825	+	0.509825i	−0.404647	+	0.914473i	$0.632606\pi$
$90$		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	−0.164399	−	0.986394i	$-0.552569\pi$
$101$	−98.7914	−	40.9207i	−0.978133	−	0.405156i	−0.813734	+	0.581238i	$0.802569\pi$
$102$		0			0
$103$	127.634	−	127.634i	1.23916	−	1.23916i	0.278817	−	0.960344i	$-0.410058\pi$
$103$	127.634	−	127.634i	1.23916	−	1.23916i	0.960344	−	0.278817i	$-0.0899423\pi$
$104$	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	−0.107906	−	0.994161i	$-0.534415\pi$
$107$	−94.9289	−	39.3208i	−0.887186	−	0.367484i	−0.779279	+	0.626677i	$0.784415\pi$
$108$		0			0
$109$	−27.8610	+	11.5404i	−0.255605	+	0.105875i	−0.506807	−	0.862060i	$-0.669174\pi$
$109$	−27.8610	+	11.5404i	−0.255605	+	0.105875i	0.251202	+	0.967935i	$0.419174\pi$
$110$	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	$0.214065\pi$
$113$			140.786i			1.24590i	−0.782263	+	0.622948i	$0.785935\pi$
$114$		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	$0.223387\pi$
$127$			163.979i			1.29117i	−0.763687	+	0.645587i	$0.776613\pi$
$128$	−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	−0.339417	−	0.940636i	$-0.610230\pi$
$131$	11.2279	−	4.65074i	0.0857090	−	0.0355018i	0.425126	+	0.905134i	$0.360230\pi$
$132$		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	−0.780552	−	0.625090i	$-0.785062\pi$
$137$	−21.2983	+	21.2983i	−0.155462	+	0.155462i	0.625090	+	0.780552i	$0.285062\pi$
$138$		0			0
$139$	−154.836	−	64.1351i	−1.11393	−	0.461404i	−0.251639	−	0.967821i	$-0.580969\pi$
$139$	−154.836	−	64.1351i	−1.11393	−	0.461404i	−0.862288	+	0.506418i	$0.830969\pi$
$140$	−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	−0.252497	−	0.967598i	$-0.581252\pi$
$149$	90.9258	−	219.514i	0.610240	−	1.47325i	0.862737	−	0.505653i	$-0.168748\pi$
$150$		0			0
$151$	−82.0484	−	82.0484i	−0.543367	−	0.543367i	0.381147	−	0.924514i	$-0.375529\pi$
$151$	−82.0484	−	82.0484i	−0.543367	−	0.543367i	−0.924514	+	0.381147i	$0.875529\pi$
$152$	−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	−0.998011	−	0.0630341i	$-0.979922\pi$
$157$	−52.8906	−	127.689i	−0.336883	−	0.813307i	0.661129	−	0.750272i	$-0.270078\pi$
$158$	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	−0.208099	−	0.978108i	$-0.566728\pi$
$163$	54.8297	−	22.7112i	0.336379	−	0.139333i	0.544478	+	0.838775i	$0.316728\pi$
$164$	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	−0.346759	−	0.937954i	$-0.612718\pi$
$167$	98.7296	−	98.7296i	0.591195	−	0.591195i	0.937954	+	0.346759i	$0.112718\pi$
$168$		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	−0.365006	−	0.931005i	$-0.618933\pi$
$173$	6.09221	−	2.52348i	0.0352151	−	0.0145866i	0.400221	+	0.916418i	$0.368933\pi$
$174$		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	−0.972073	−	0.234677i	$-0.924597\pi$
$179$	−80.6673	−	194.748i	−0.450655	−	1.08798i	0.521418	−	0.853301i	$-0.325403\pi$
$180$		0			0
$181$	−59.7464	+	144.241i	−0.330091	+	0.796910i	0.668493	+	0.743718i	$0.266939\pi$
$181$	−59.7464	+	144.241i	−0.330091	+	0.796910i	−0.998584	+	0.0531918i	$0.983061\pi$
$182$	−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	$-0.908926\pi$
$191$		−	107.812i		−	0.564460i	0.959347	−	0.282230i	$-0.0910741\pi$
$192$		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	0.640606	−	0.767870i	$-0.278683\pi$
$197$	108.472	+	44.9304i	0.550618	+	0.228073i	−0.0899887	+	0.995943i	$0.528683\pi$
$198$		0			0
$199$	190.347	−	190.347i	0.956516	−	0.956516i	−0.0425770	−	0.999093i	$-0.513557\pi$
$199$	190.347	−	190.347i	0.956516	−	0.956516i	0.999093	+	0.0425770i	$0.0135568\pi$
$200$	−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	0.984932	+	0.172944i	$0.0553281\pi$
$211$	86.6725	+	209.246i	0.410770	+	0.991686i	−0.574162	+	0.818742i	$0.694672\pi$
$212$	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	$-0.925200\pi$
$223$		−	103.845i		−	0.465671i	0.972516	−	0.232836i	$-0.0748004\pi$
$224$	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	−0.603910	−	0.797052i	$-0.706391\pi$
$227$	−106.086	+	43.9421i	−0.467338	+	0.193578i	0.136572	+	0.990630i	$0.456391\pi$
$228$		0			0
$229$	46.1162	+	19.1019i	0.201381	+	0.0834146i	0.481094	−	0.876669i	$-0.340240\pi$
$229$	46.1162	+	19.1019i	0.201381	+	0.0834146i	−0.279714	+	0.960083i	$0.590240\pi$
$230$	−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	−0.559630	−	0.828742i	$-0.689057\pi$
$233$	62.7031	−	62.7031i	0.269112	−	0.269112i	0.828742	+	0.559630i	$0.189057\pi$
$234$		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	$0.169911\pi$
$241$			245.242i			1.01760i	−0.860884	+	0.508801i	$0.830089\pi$
$242$	−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	0.402747	+	0.915311i	$0.368056\pi$
$251$	−132.845	+	320.715i	−0.529261	+	1.27775i	−0.932008	+	0.362438i	$0.881944\pi$
$252$		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	−0.361468	−	0.932384i	$-0.617724\pi$
$263$	150.151	−	150.151i	0.570916	−	0.570916i	0.932384	+	0.361468i	$0.117724\pi$
$264$		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	0.146618	−	0.989193i	$-0.453161\pi$
$269$	255.485	−	105.825i	0.949758	−	0.393403i	0.803140	+	0.595791i	$0.203161\pi$
$270$		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	−0.544440	−	0.838799i	$-0.683258\pi$
$277$	120.123	−	290.003i	0.433658	−	1.04694i	0.978098	−	0.208143i	$-0.0667420\pi$
$278$	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	0.667271	−	0.744815i	$-0.267462\pi$
$281$	−21.7898	−	21.7898i	−0.0775437	−	0.0775437i	−0.744815	+	0.667271i	$0.767462\pi$
$282$		0			0
$283$	−155.937	+	376.466i	−0.551016	+	1.33027i	0.365702	+	0.930732i	$0.380829\pi$
$283$	−155.937	+	376.466i	−0.551016	+	1.33027i	−0.916717	+	0.399537i	$0.869171\pi$
$284$	−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	0.445275	−	0.895394i	$-0.353106\pi$
$293$	37.2090	+	15.4125i	0.126993	+	0.0526023i	−0.318282	+	0.947996i	$0.603106\pi$
$294$		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	−0.998646	−	0.0520174i	$-0.983435\pi$
$307$	−101.089	−	244.049i	−0.329279	−	0.794949i	0.669368	−	0.742931i	$-0.266565\pi$
$308$	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	0.935799	−	0.352534i	$-0.114680\pi$
$311$	181.395	+	181.395i	0.583264	+	0.583264i	−0.352534	+	0.935799i	$0.614680\pi$
$312$		0			0
$313$	110.963	+	110.963i	0.354513	+	0.354513i	0.861786	−	0.507273i	$-0.169346\pi$
$313$	110.963	+	110.963i	0.354513	+	0.354513i	−0.507273	+	0.861786i	$0.669346\pi$
$314$	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	−0.981392	−	0.192017i	$-0.938497\pi$
$317$	−134.161	−	323.892i	−0.423219	−	1.02174i	0.558172	−	0.829725i	$-0.311503\pi$
$318$		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	−0.997479	−	0.0709686i	$-0.977391\pi$
$331$	−580.238	−	240.342i	−1.75298	−	0.726110i	−0.755506	−	0.655141i	$-0.772609\pi$
$332$	−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	$0.0619059\pi$
$337$			130.257i			0.386519i	−0.981148	+	0.193259i	$0.938094\pi$
$338$	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	−0.825302	−	0.564692i	$-0.808995\pi$
$347$	54.6775	−	132.003i	0.157572	−	0.380412i	0.982874	+	0.184279i	$0.0589951\pi$
$348$		0			0
$349$	−46.7936	−	112.970i	−0.134079	−	0.323696i	0.842553	−	0.538613i	$-0.181052\pi$
$349$	−46.7936	−	112.970i	−0.134079	−	0.323696i	−0.976632	+	0.214918i	$0.931052\pi$
$350$	−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	−0.584765	−	0.811203i	$-0.698813\pi$
$359$	81.2910	−	81.2910i	0.226437	−	0.226437i	0.811203	+	0.584765i	$0.198813\pi$
$360$		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	0.459294	+	0.888284i	$0.348102\pi$
$373$	−184.108	+	444.476i	−0.493588	+	1.19163i	−0.952882	+	0.303342i	$0.901898\pi$
$374$	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	−0.999969	−	0.00784682i	$-0.997502\pi$
$379$	−108.900	+	262.908i	−0.287336	+	0.693690i	0.712634	+	0.701536i	$0.247502\pi$
$380$	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	$0.213869\pi$
$383$			476.810i			1.24493i	−0.782646	+	0.622467i	$0.786131\pi$
$384$		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	0.472746	−	0.881199i	$-0.343263\pi$
$389$	71.5472	+	29.6358i	0.183926	+	0.0761846i	−0.288820	+	0.957383i	$0.593263\pi$
$390$		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	−0.225911	−	0.974148i	$-0.572536\pi$
$397$	120.360	−	49.8545i	0.303173	−	0.125578i	0.529084	+	0.848570i	$0.322536\pi$
$398$	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	$-0.930381\pi$
$401$		−	174.015i		−	0.433953i	0.976177	−	0.216976i	$-0.0696195\pi$
$402$		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	0.561571	−	0.827428i	$-0.310197\pi$
$409$	−108.736	−	108.736i	−0.265857	−	0.265857i	−0.827428	+	0.561571i	$0.810197\pi$
$410$	−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	−0.778026	−	0.628232i	$-0.783779\pi$
$419$	−370.373	+	153.414i	−0.883946	+	0.366142i	−0.105920	+	0.994375i	$0.533779\pi$
$420$		0			0
$421$	−600.339	−	248.669i	−1.42598	−	0.590662i	−0.469628	−	0.882864i	$-0.655612\pi$
$421$	−600.339	−	248.669i	−1.42598	−	0.590662i	−0.956357	+	0.292202i	$0.905612\pi$
$422$	−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	$-0.881731\pi$
$433$		−	314.414i		−	0.726129i	0.931764	−	0.363064i	$-0.118269\pi$
$434$	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	−0.913818	−	0.406125i	$-0.866880\pi$
$439$	−579.455	−	579.455i	−1.31994	−	1.31994i	−0.406125	−	0.913818i	$-0.633120\pi$
$440$	−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	−0.997597	−	0.0692856i	$-0.977928\pi$
$443$	−107.736	+	260.098i	−0.243197	+	0.587130i	0.754400	+	0.656415i	$0.227928\pi$
$444$		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	−0.0197861	−	0.999804i	$-0.506299\pi$
$457$	447.868	−	447.868i	0.980018	−	0.980018i	0.999804	+	0.0197861i	$0.00629852\pi$
$458$	−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	−0.640027	−	0.768352i	$-0.721077\pi$
$461$	−253.222	+	104.888i	−0.549288	+	0.227523i	0.0907394	+	0.995875i	$0.471077\pi$
$462$		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	0.876082	−	0.482162i	$-0.160148\pi$
$467$	−39.3875	−	95.0899i	−0.0843416	−	0.203619i	−0.960424	+	0.278544i	$0.910148\pi$
$468$		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	$0.353050\pi$
$479$			857.713i			1.79063i	−0.445432	+	0.895316i	$0.646950\pi$
$480$		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	−0.694108	−	0.719871i	$-0.744201\pi$
$487$	12.5467	−	12.5467i	0.0257633	−	0.0257633i	0.719871	+	0.694108i	$0.244201\pi$
$488$	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	0.287341	−	0.957828i	$-0.407229\pi$
$491$	−91.7015	−	37.9840i	−0.186765	−	0.0773605i	−0.474106	+	0.880468i	$0.657229\pi$
$492$		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	0.990336	+	0.138688i	$0.0442886\pi$
$499$	193.677	+	467.577i	0.388130	+	0.937029i	−0.602206	+	0.798341i	$0.705711\pi$
$500$	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	−0.920459	−	0.390840i	$-0.872184\pi$
$503$	−659.583	−	659.583i	−1.31130	−	1.31130i	−0.390840	−	0.920459i	$-0.627816\pi$
$504$		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	0.999041	−	0.0437918i	$-0.0139438\pi$
$509$	133.178	+	321.521i	0.261647	+	0.631671i	−0.737394	+	0.675463i	$0.763944\pi$
$510$		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	−0.772207	−	0.635371i	$-0.780847\pi$
$521$	−71.2918	+	71.2918i	−0.136837	+	0.136837i	0.635371	+	0.772207i	$0.280847\pi$
$522$		0			0
$523$	−376.338	−	155.884i	−0.719576	−	0.298058i	−0.00731529	−	0.999973i	$-0.502329\pi$
$523$	−376.338	−	155.884i	−0.719576	−	0.298058i	−0.712261	+	0.701915i	$0.752329\pi$
$524$	−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	0.754948	−	0.655785i	$-0.227662\pi$
$541$	−131.242	−	316.846i	−0.242591	−	0.585667i	−0.997539	+	0.0701185i	$0.977662\pi$
$542$	−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	−0.434772	−	0.900541i	$-0.643171\pi$
$547$	−57.6667	+	23.8863i	−0.105424	+	0.0436679i	0.329348	+	0.944209i	$0.393171\pi$
$548$	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	−0.714589	−	0.699544i	$-0.753386\pi$
$557$	−403.952	+	167.322i	−0.725228	+	0.300399i	−0.0106383	+	0.999943i	$0.503386\pi$
$558$		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	0.921546	−	0.388270i	$-0.126927\pi$
$563$	−2.60893	−	6.29851i	−0.00463398	−	0.0111874i	−0.926180	+	0.377083i	$0.876927\pi$
$564$		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	0.480818	−	0.876820i	$-0.340340\pi$
$569$	−225.325	−	225.325i	−0.396002	−	0.396002i	−0.876820	+	0.480818i	$0.840340\pi$
$570$		0			0
$571$	203.081	−	490.280i	0.355658	−	0.858634i	−0.640242	−	0.768173i	$-0.721166\pi$
$571$	203.081	−	490.280i	0.355658	−	0.858634i	0.995900	−	0.0904608i	$-0.0288340\pi$
$572$	−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	0.900149	−	0.435583i	$-0.143458\pi$
$587$	721.215	+	298.737i	1.22865	+	0.508922i	0.328498	+	0.944505i	$0.393458\pi$
$588$		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	$0.146116\pi$
$593$			525.499i			0.886170i	−0.896479	+	0.443085i	$0.853884\pi$
$594$		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	0.940213	−	0.340587i	$-0.110626\pi$
$599$	359.176	+	359.176i	0.599626	+	0.599626i	−0.340587	+	0.940213i	$0.610626\pi$
$600$		0			0
$601$	163.858	+	163.858i	0.272642	+	0.272642i	0.830163	−	0.557521i	$-0.188247\pi$
$601$	163.858	+	163.858i	0.272642	+	0.272642i	−0.557521	+	0.830163i	$0.688247\pi$
$602$	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	$0.0548587\pi$
$607$			208.191i			0.342984i	−0.985186	+	0.171492i	$0.945141\pi$
$608$	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	0.839640	−	0.543144i	$-0.182766\pi$
$613$	643.217	+	266.429i	1.04929	+	0.434632i	0.209654	+	0.977776i	$0.432766\pi$
$614$	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	−0.136838	−	0.990593i	$-0.543694\pi$
$617$	526.767	−	526.767i	0.853755	−	0.853755i	0.990593	+	0.136838i	$0.0436941\pi$
$618$		0			0
$619$	−316.799	−	131.222i	−0.511791	−	0.211991i	0.111816	−	0.993729i	$-0.464333\pi$
$619$	−316.799	−	131.222i	−0.511791	−	0.211991i	−0.623607	+	0.781738i	$0.714333\pi$
$620$	−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	0.985582	−	0.169199i	$-0.0541179\pi$
$631$	515.138	+	515.138i	0.816383	+	0.816383i	−0.169199	+	0.985582i	$0.554118\pi$
$632$	−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	−0.136779	−	0.990602i	$-0.543675\pi$
$643$	300.259	−	124.371i	0.466965	−	0.193423i	0.603744	+	0.797178i	$0.293675\pi$
$644$	−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	−0.552027	−	0.833827i	$-0.686145\pi$
$647$	182.325	−	182.325i	0.281800	−	0.281800i	0.833827	+	0.552027i	$0.186145\pi$
$648$		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	−0.317868	−	0.948135i	$-0.602967\pi$
$653$	83.4520	−	34.5670i	0.127798	−	0.0529356i	0.445666	+	0.895199i	$0.352967\pi$
$654$		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	0.893837	−	0.448393i	$-0.148003\pi$
$659$	−36.4182	−	87.9213i	−0.0552628	−	0.133416i	−0.949099	+	0.314976i	$0.898003\pi$
$660$		0			0
$661$	−420.501	+	1015.18i	−0.636159	+	1.53582i	0.195597	+	0.980684i	$0.437335\pi$
$661$	−420.501	+	1015.18i	−0.636159	+	1.53582i	−0.831757	+	0.555140i	$0.812665\pi$
$662$	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	0.948312	−	0.317339i	$-0.102789\pi$
$677$	944.061	+	391.043i	1.39448	+	0.577611i	0.446165	+	0.894951i	$0.352789\pi$
$678$		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	0.506353	−	0.862326i	$-0.330993\pi$
$683$	173.921	+	72.0404i	0.254643	+	0.105476i	−0.251711	+	0.967803i	$0.580993\pi$
$684$		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	0.999438	−	0.0335109i	$-0.0106688\pi$
$691$	185.902	+	448.807i	0.269033	+	0.649503i	−0.730405	+	0.683014i	$0.760669\pi$
$692$	−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	0.994214	−	0.107416i	$-0.0342576\pi$
$701$	150.886	+	364.271i	0.215244	+	0.519645i	−0.778970	+	0.627061i	$0.784258\pi$
$702$		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	0.0362043	−	0.999344i	$-0.488473\pi$
$709$	−457.191	−	189.375i	−0.644839	−	0.267101i	−0.681043	+	0.732243i	$0.738473\pi$
$710$	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	0.952432	−	0.304753i	$-0.0985738\pi$
$727$	470.863	+	470.863i	0.647679	+	0.647679i	−0.304753	+	0.952432i	$0.598574\pi$
$728$	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	0.950982	+	0.309246i	$0.100077\pi$
$733$	364.452	+	879.866i	0.497206	+	1.20036i	−0.453776	+	0.891116i	$0.649923\pi$
$734$	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	0.568016	−	0.823018i	$-0.307711\pi$
$739$	1146.65	−	474.958i	1.55162	−	0.642704i	0.983609	+	0.180314i	$0.0577112\pi$
$740$	−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	−0.962039	−	0.272913i	$-0.912013\pi$
$743$	−512.021	+	512.021i	−0.689126	+	0.689126i	0.272913	+	0.962039i	$0.412013\pi$
$744$		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	−0.988921	−	0.148444i	$-0.952573\pi$
$757$	−139.805	+	337.518i	−0.184682	+	0.445863i	0.804238	+	0.594307i	$0.202573\pi$
$758$	−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	0.302064	−	0.953288i	$-0.402324\pi$
$761$	−495.581	−	495.581i	−0.651223	−	0.651223i	−0.953288	+	0.302064i	$0.902324\pi$
$762$		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	0.700759	−	0.713398i	$-0.252845\pi$
$773$	534.778	+	221.512i	0.691822	+	0.286562i	−0.00893708	+	0.999960i	$0.502845\pi$
$774$		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	−0.995844	−	0.0910769i	$-0.970969\pi$
$787$	−280.233	−	676.541i	−0.356077	−	0.859646i	0.639767	−	0.768569i	$-0.279031\pi$
$788$	−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	0.855148	−	0.518384i	$-0.173466\pi$
$797$	−92.5205	−	223.364i	−0.116086	−	0.280256i	−0.971234	+	0.238128i	$0.923466\pi$
$798$		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	−0.236358	+	0.971666i	$0.575954\pi$
$809$	−977.291	+	977.291i	−1.20802	+	1.20802i	−0.971666	+	0.236358i	$0.924046\pi$
$810$		0			0
$811$	553.320	+	229.193i	0.682269	+	0.282605i	0.696775	−	0.717290i	$-0.254618\pi$
$811$	553.320	+	229.193i	0.682269	+	0.282605i	−0.0145062	+	0.999895i	$0.504618\pi$
$812$	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	0.486665	+	0.873589i	$0.338213\pi$
$821$	−390.123	+	941.839i	−0.475180	+	1.14719i	−0.961844	+	0.273597i	$0.911787\pi$
$822$		0			0
$823$	−692.747	−	692.747i	−0.841734	−	0.841734i	0.147350	−	0.989084i	$-0.452926\pi$
$823$	−692.747	−	692.747i	−0.841734	−	0.841734i	−0.989084	+	0.147350i	$0.952926\pi$
$824$	−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	−0.471173	−	0.882041i	$-0.656169\pi$
$827$	401.669	−	969.714i	0.485694	−	1.17257i	0.956867	−	0.290528i	$-0.0938309\pi$
$828$		0			0
$829$	562.011	+	1356.81i	0.677938	+	1.63669i	0.767766	+	0.640730i	$0.221368\pi$
$829$	562.011	+	1356.81i	0.677938	+	1.63669i	−0.0898281	+	0.995957i	$0.528632\pi$
$830$	−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	−0.144862	−	0.989452i	$-0.546274\pi$
$839$	708.611	−	708.611i	0.844590	−	0.844590i	0.989452	+	0.144862i	$0.0462737\pi$
$840$		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	−0.993250	−	0.115992i	$-0.962995\pi$
$853$	−178.189	+	430.187i	−0.208897	+	0.504322i	0.784353	+	0.620315i	$0.212995\pi$
$854$	−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	0.812142	−	0.583459i	$-0.198301\pi$
$857$	195.982	+	195.982i	0.228683	+	0.228683i	−0.583459	+	0.812142i	$0.698301\pi$
$858$		0			0
$859$	−155.060	+	374.347i	−0.180512	+	0.435794i	−0.988072	−	0.153991i	$-0.950787\pi$
$859$	−155.060	+	374.347i	−0.180512	+	0.435794i	0.807560	+	0.589785i	$0.200787\pi$
$860$	−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	$0.0117895\pi$
$863$			63.9126i			0.0740586i	−0.999314	+	0.0370293i	$0.988211\pi$
$864$		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	−0.402130	−	0.915583i	$-0.631730\pi$
$877$	−34.2590	+	14.1905i	−0.0390638	+	0.0161808i	0.363066	+	0.931763i	$0.381730\pi$
$878$	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	$0.220677\pi$
$881$			1126.03i			1.27812i	−0.769155	+	0.639062i	$0.779323\pi$
$882$		0			0
$883$	−114.384	−	276.148i	−0.129540	−	0.312738i	0.845780	−	0.533531i	$-0.179135\pi$
$883$	−114.384	−	276.148i	−0.129540	−	0.312738i	−0.975321	+	0.220793i	$0.929135\pi$
$884$	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	0.669453	−	0.742855i	$-0.266529\pi$
$887$	−65.1075	−	65.1075i	−0.0734020	−	0.0734020i	−0.742855	+	0.669453i	$0.766529\pi$
$888$		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	0.890070	−	0.455825i	$-0.150656\pi$
$907$	1085.79	+	449.751i	1.19713	+	0.495866i	0.307058	+	0.951691i	$0.400656\pi$
$908$	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	−0.920119	−	0.391640i	$-0.871908\pi$
$919$	−1205.51	−	1205.51i	−1.31176	−	1.31176i	−0.391640	−	0.920119i	$-0.628092\pi$
$920$	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	−0.921883	−	0.387467i	$-0.873350\pi$
$937$	−500.748	+	500.748i	−0.534416	+	0.534416i	0.387467	+	0.921883i	$0.373350\pi$
$938$	−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	0.446588	−	0.894740i	$-0.352639\pi$
$941$	1312.74	−	543.756i	1.39505	−	0.577849i	0.948462	+	0.316891i	$0.102639\pi$
$942$		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	0.999531	−	0.0306337i	$-0.00975255\pi$
$947$	256.726	+	619.792i	0.271094	+	0.654480i	−0.728436	+	0.685114i	$0.759753\pi$
$948$		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	0.00480927	−	0.999988i	$-0.498469\pi$
$953$	−948.406	−	948.406i	−0.995179	−	0.995179i	−0.999988	+	0.00480927i	$0.998469\pi$
$954$		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	−0.710096	−	0.704104i	$-0.751349\pi$
$967$	−5.79422	+	5.79422i	−0.00599196	+	0.00599196i	0.704104	+	0.710096i	$0.251349\pi$
$968$	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	−0.693457	−	0.720498i	$-0.743913\pi$
$971$	−1644.17	−	681.037i	−1.69327	−	0.701377i	−0.999817	+	0.0191210i	$0.993913\pi$
$972$		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	$-0.911054\pi$
$977$		−	538.935i		−	0.551623i	0.961212	−	0.275811i	$-0.0889465\pi$
$978$		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	0.614546	−	0.788881i	$-0.289339\pi$
$983$	−171.371	−	171.371i	−0.174335	−	0.174335i	−0.788881	+	0.614546i	$0.789339\pi$
$984$		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	$0.319166\pi$
$991$			1670.67i			1.68584i	−0.538038	+	0.842921i	$0.680834\pi$
$992$	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	0.908791	−	0.417252i	$-0.137007\pi$
$997$	1252.59	+	518.840i	1.25636	+	0.520402i	0.347570	+	0.937654i	$0.387007\pi$
$998$	−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.91.5		28
3.2	odd	2		32.3.h.a.27.3	yes	28
12.11	even	2		128.3.h.a.15.2		28
24.5	odd	2		256.3.h.b.31.2		28
24.11	even	2		256.3.h.a.31.6		28
32.19	odd	8	inner	288.3.u.a.19.5		28
96.29	odd	8		256.3.h.a.223.6		28
96.35	even	8		256.3.h.b.223.2		28
96.77	odd	8		128.3.h.a.111.2		28
96.83	even	8		32.3.h.a.19.3	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.19.3	✓	28	96.83	even	8
32.3.h.a.27.3	yes	28	3.2	odd	2
128.3.h.a.15.2		28	12.11	even	2
128.3.h.a.111.2		28	96.77	odd	8
256.3.h.a.31.6		28	24.11	even	2
256.3.h.a.223.6		28	96.29	odd	8
256.3.h.b.31.2		28	24.5	odd	2
256.3.h.b.223.2		28	96.35	even	8
288.3.u.a.19.5		28	32.19	odd	8	inner
288.3.u.a.91.5		28	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
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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