LMFDB - Embedded newform 288.3.u.a.91.3

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			91.3
Character	$\chi$	$=$	288.91
Dual form			288.3.u.a.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.345994 - 1.96984i) q^{2} +(-3.76058 + 1.36311i) q^{4} +(-7.20074 - 2.98264i) q^{5} +(4.26150 - 4.26150i) q^{7} +(3.98625 + 6.93612i) q^{8} +O(q^{10})$	\(q+(-0.345994 - 1.96984i) q^{2} +(-3.76058 + 1.36311i) q^{4} +(-7.20074 - 2.98264i) q^{5} +(4.26150 - 4.26150i) q^{7} +(3.98625 + 6.93612i) q^{8} +(-3.38393 + 15.2163i) q^{10} +(-6.19818 - 2.56737i) q^{11} +(-8.05345 + 3.33585i) q^{13} +(-9.86895 - 6.92004i) q^{14} +(12.2839 - 10.2522i) q^{16} +24.5802i q^{17} +(4.96459 + 11.9856i) q^{19} +(31.1446 + 1.40106i) q^{20} +(-2.91279 + 13.0978i) q^{22} +(9.72199 + 9.72199i) q^{23} +(25.2768 + 25.2768i) q^{25} +(9.35754 + 14.7099i) q^{26} +(-10.2168 + 21.8346i) q^{28} +(5.86371 + 14.1563i) q^{29} +17.5320i q^{31} +(-24.4453 - 20.6501i) q^{32} +(48.4192 - 8.50460i) q^{34} +(-43.3965 + 17.9754i) q^{35} +(-36.0346 - 14.9260i) q^{37} +(21.8920 - 13.9264i) q^{38} +(-8.01597 - 61.8348i) q^{40} +(-10.9784 + 10.9784i) q^{41} +(-22.4024 - 9.27937i) q^{43} +(26.8084 + 1.20599i) q^{44} +(15.7871 - 22.5146i) q^{46} -27.0104 q^{47} +12.6792i q^{49} +(41.0458 - 58.5371i) q^{50} +(25.7385 - 23.5224i) q^{52} +(34.0172 - 82.1247i) q^{53} +(36.9740 + 36.9740i) q^{55} +(46.5457 + 12.5709i) q^{56} +(25.8568 - 16.4486i) q^{58} +(-27.8391 + 67.2095i) q^{59} +(-6.37082 - 15.3805i) q^{61} +(34.5354 - 6.06598i) q^{62} +(-32.2196 + 55.2983i) q^{64} +67.9404 q^{65} +(-99.2165 + 41.0968i) q^{67} +(-33.5055 - 92.4357i) q^{68} +(50.4237 + 79.2650i) q^{70} +(2.55754 - 2.55754i) q^{71} +(30.7498 - 30.7498i) q^{73} +(-16.9342 + 76.1469i) q^{74} +(-35.0074 - 38.3054i) q^{76} +(-37.3544 + 15.4727i) q^{77} -90.6600 q^{79} +(-119.031 + 37.1847i) q^{80} +(25.4241 + 17.8272i) q^{82} +(39.3191 + 94.9247i) q^{83} +(73.3140 - 176.996i) q^{85} +(-10.5278 + 47.3398i) q^{86} +(-6.89991 - 53.2256i) q^{88} +(-109.290 - 109.290i) q^{89} +(-20.1040 + 48.5355i) q^{91} +(-49.8124 - 23.3081i) q^{92} +(9.34545 + 53.2063i) q^{94} -101.113i q^{95} +63.7161 q^{97} +(24.9761 - 4.38694i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.345994	−	1.96984i	−0.172997	−	0.984922i
$2$	−0.345994	−	1.96984i	−0.172997	−	0.984922i
$3$		0			0
$3$		0			0
$4$	−3.76058	+	1.36311i	−0.940144	+	0.340777i
$5$	−7.20074	−	2.98264i	−1.44015	−	0.596529i	−0.480314	−	0.877097i	$-0.659477\pi$
$5$	−7.20074	−	2.98264i	−1.44015	−	0.596529i	−0.959834	+	0.280568i	$0.909477\pi$
$6$		0			0
$7$	4.26150	−	4.26150i	0.608786	−	0.608786i	−0.333843	−	0.942629i	$-0.608346\pi$
$7$	4.26150	−	4.26150i	0.608786	−	0.608786i	0.942629	+	0.333843i	$0.108346\pi$
$8$	3.98625	+	6.93612i	0.498281	+	0.867015i
$9$		0			0
$10$	−3.38393	+	15.2163i	−0.338393	+	1.52163i
$11$	−6.19818	−	2.56737i	−0.563471	−	0.233397i	0.0827202	−	0.996573i	$-0.473639\pi$
$11$	−6.19818	−	2.56737i	−0.563471	−	0.233397i	−0.646191	+	0.763175i	$0.723639\pi$
$12$		0			0
$13$	−8.05345	+	3.33585i	−0.619496	+	0.256604i	−0.670283	−	0.742106i	$-0.733827\pi$
$13$	−8.05345	+	3.33585i	−0.619496	+	0.256604i	0.0507868	+	0.998710i	$0.483827\pi$
$14$	−9.86895	−	6.92004i	−0.704925	−	0.494288i
$15$		0			0
$16$	12.2839	−	10.2522i	0.767742	−	0.640760i
$17$			24.5802i			1.44589i	0.690904	+	0.722947i	$0.257213\pi$
$17$			24.5802i			1.44589i	−0.690904	+	0.722947i	$0.742787\pi$
$18$		0			0
$19$	4.96459	+	11.9856i	0.261294	+	0.630820i	0.999019	−	0.0442815i	$-0.0140998\pi$
$19$	4.96459	+	11.9856i	0.261294	+	0.630820i	−0.737725	+	0.675101i	$0.764100\pi$
$20$	31.1446	+	1.40106i	1.55723	+	0.0700532i
$21$		0			0
$22$	−2.91279	+	13.0978i	−0.132399	+	0.595353i
$23$	9.72199	+	9.72199i	0.422695	+	0.422695i	0.886131	−	0.463435i	$-0.153383\pi$
$23$	9.72199	+	9.72199i	0.422695	+	0.422695i	−0.463435	+	0.886131i	$0.653383\pi$
$24$		0			0
$25$	25.2768	+	25.2768i	1.01107	+	1.01107i
$26$	9.35754	+	14.7099i	0.359906	+	0.565764i
$27$		0			0
$28$	−10.2168	+	21.8346i	−0.364886	+	0.779807i
$29$	5.86371	+	14.1563i	0.202197	+	0.488147i	0.992155	−	0.125014i	$-0.0398977\pi$
$29$	5.86371	+	14.1563i	0.202197	+	0.488147i	−0.789958	+	0.613161i	$0.789898\pi$
$30$		0			0
$31$			17.5320i			0.565550i	0.959186	+	0.282775i	$0.0912549\pi$
$31$			17.5320i			0.565550i	−0.959186	+	0.282775i	$0.908745\pi$
$32$	−24.4453	−	20.6501i	−0.763915	−	0.645316i
$33$		0			0
$34$	48.4192	−	8.50460i	1.42409	−	0.250135i
$35$	−43.3965	+	17.9754i	−1.23990	+	0.513583i
$36$		0			0
$37$	−36.0346	−	14.9260i	−0.973909	−	0.403406i	−0.161743	−	0.986833i	$-0.551712\pi$
$37$	−36.0346	−	14.9260i	−0.973909	−	0.403406i	−0.812166	+	0.583427i	$0.801712\pi$
$38$	21.8920	−	13.9264i	0.576106	−	0.366485i
$39$		0			0
$40$	−8.01597	−	61.8348i	−0.200399	−	1.54587i
$41$	−10.9784	+	10.9784i	−0.267765	+	0.267765i	−0.828199	−	0.560434i	$-0.810634\pi$
$41$	−10.9784	+	10.9784i	−0.267765	+	0.267765i	0.560434	+	0.828199i	$0.310634\pi$
$42$		0			0
$43$	−22.4024	−	9.27937i	−0.520985	−	0.215799i	0.106664	−	0.994295i	$-0.465983\pi$
$43$	−22.4024	−	9.27937i	−0.520985	−	0.215799i	−0.627650	+	0.778496i	$0.715983\pi$
$44$	26.8084	+	1.20599i	0.609281	+	0.0274090i
$45$		0			0
$46$	15.7871	−	22.5146i	0.343197	−	0.489447i
$47$	−27.0104			−0.574690			−0.287345	−	0.957827i	$-0.592773\pi$
$47$	−27.0104			−0.574690			−0.287345	+	0.957827i	$0.592773\pi$
$48$		0			0
$49$			12.6792i			0.258760i
$50$	41.0458	−	58.5371i	0.820916	−	1.17074i
$51$		0			0
$52$	25.7385	−	23.5224i	0.494971	−	0.452354i
$53$	34.0172	−	82.1247i	0.641833	−	1.54952i	−0.182371	−	0.983230i	$-0.558377\pi$
$53$	34.0172	−	82.1247i	0.641833	−	1.54952i	0.824204	−	0.566293i	$-0.191623\pi$
$54$		0			0
$55$	36.9740	+	36.9740i	0.672254	+	0.672254i
$56$	46.5457	+	12.5709i	0.831173	+	0.224480i
$57$		0			0
$58$	25.8568	−	16.4486i	0.445807	−	0.283596i
$59$	−27.8391	+	67.2095i	−0.471849	+	1.13914i	0.491497	+	0.870879i	$0.336450\pi$
$59$	−27.8391	+	67.2095i	−0.471849	+	1.13914i	−0.963345	+	0.268264i	$0.913550\pi$
$60$		0			0
$61$	−6.37082	−	15.3805i	−0.104440	−	0.252140i	0.863018	−	0.505174i	$-0.168572\pi$
$61$	−6.37082	−	15.3805i	−0.104440	−	0.252140i	−0.967457	+	0.253034i	$0.918572\pi$
$62$	34.5354	−	6.06598i	0.557022	−	0.0978384i
$63$		0			0
$64$	−32.2196	+	55.2983i	−0.503431	+	0.864035i
$65$	67.9404			1.04524
$66$		0			0
$67$	−99.2165	+	41.0968i	−1.48084	+	0.613386i	−0.969302	−	0.245873i	$-0.920925\pi$
$67$	−99.2165	+	41.0968i	−1.48084	+	0.613386i	−0.511542	+	0.859258i	$0.670925\pi$
$68$	−33.5055	−	92.4357i	−0.492728	−	1.35935i
$69$		0			0
$70$	50.4237	+	79.2650i	0.720339	+	1.13236i
$71$	2.55754	−	2.55754i	0.0360217	−	0.0360217i	−0.688867	−	0.724888i	$-0.741891\pi$
$71$	2.55754	−	2.55754i	0.0360217	−	0.0360217i	0.724888	+	0.688867i	$0.241891\pi$
$72$		0			0
$73$	30.7498	−	30.7498i	0.421230	−	0.421230i	−0.464397	−	0.885627i	$-0.653729\pi$
$73$	30.7498	−	30.7498i	0.421230	−	0.421230i	0.885627	+	0.464397i	$0.153729\pi$
$74$	−16.9342	+	76.1469i	−0.228840	+	1.02901i
$75$		0			0
$76$	−35.0074	−	38.3054i	−0.460623	−	0.504019i
$77$	−37.3544	+	15.4727i	−0.485122	+	0.200944i
$78$		0			0
$79$	−90.6600			−1.14759			−0.573797	−	0.818997i	$-0.694530\pi$
$79$	−90.6600			−1.14759			−0.573797	+	0.818997i	$0.694530\pi$
$80$	−119.031	+	37.1847i	−1.48789	+	0.464809i
$81$		0			0
$82$	25.4241	+	17.8272i	0.310051	+	0.217405i
$83$	39.3191	+	94.9247i	0.473724	+	1.14367i	0.962505	+	0.271264i	$0.0874417\pi$
$83$	39.3191	+	94.9247i	0.473724	+	1.14367i	−0.488781	+	0.872407i	$0.662558\pi$
$84$		0			0
$85$	73.3140	−	176.996i	0.862517	−	2.08230i
$86$	−10.5278	+	47.3398i	−0.122417	+	0.550463i
$87$		0			0
$88$	−6.89991	−	53.2256i	−0.0784081	−	0.604836i
$89$	−109.290	−	109.290i	−1.22798	−	1.22798i	−0.964728	−	0.263248i	$-0.915206\pi$
$89$	−109.290	−	109.290i	−1.22798	−	1.22798i	−0.263248	−	0.964728i	$-0.584794\pi$
$90$		0			0
$91$	−20.1040	+	48.5355i	−0.220924	+	0.533357i
$92$	−49.8124	−	23.3081i	−0.541439	−	0.253349i
$93$		0			0
$94$	9.34545	+	53.2063i	0.0994196	+	0.566025i
$95$		−	101.113i		−	1.06434i
$96$		0			0
$97$	63.7161			0.656867			0.328433	−	0.944527i	$-0.393479\pi$
$97$	63.7161			0.656867			0.328433	+	0.944527i	$0.393479\pi$
$98$	24.9761	−	4.38694i	0.254859	−	0.0447647i
$99$		0			0
$100$	−129.511	−	60.6004i	−1.29511	−	0.606004i
$101$	14.4312	+	5.97761i	0.142883	+	0.0591842i	0.452979	−	0.891521i	$-0.350361\pi$
$101$	14.4312	+	5.97761i	0.142883	+	0.0591842i	−0.310096	+	0.950705i	$0.600361\pi$
$102$		0			0
$103$	−9.69681	+	9.69681i	−0.0941438	+	0.0941438i	−0.752610	−	0.658466i	$-0.771205\pi$
$103$	−9.69681	+	9.69681i	−0.0941438	+	0.0941438i	0.658466	+	0.752610i	$0.271205\pi$
$104$	−55.2409	−	42.5622i	−0.531163	−	0.409252i
$105$		0			0
$106$	−173.543	−	38.5939i	−1.63719	−	0.364093i
$107$	−138.127	−	57.2140i	−1.29091	−	0.534710i	−0.371650	−	0.928373i	$-0.621208\pi$
$107$	−138.127	−	57.2140i	−1.29091	−	0.534710i	−0.919255	+	0.393662i	$0.871208\pi$
$108$		0			0
$109$	−32.0941	+	13.2938i	−0.294442	+	0.121962i	−0.525014	−	0.851093i	$-0.675940\pi$
$109$	−32.0941	+	13.2938i	−0.294442	+	0.121962i	0.230573	+	0.973055i	$0.425940\pi$
$110$	60.0402	−	85.6257i	0.545820	−	0.778416i
$111$		0			0
$112$	8.65814	−	96.0372i	0.0773048	−	0.857475i
$113$			125.923i			1.11436i	0.830392	+	0.557180i	$0.188117\pi$
$113$			125.923i			1.11436i	−0.830392	+	0.557180i	$0.811883\pi$
$114$		0			0
$115$	−41.0083	−	99.0028i	−0.356594	−	0.860894i
$116$	−41.3475	−	45.2428i	−0.356444	−	0.390024i
$117$		0			0
$118$	142.024	+	31.5846i	1.20360	+	0.267666i
$119$	104.748	+	104.748i	0.880239	+	0.880239i
$120$		0			0
$121$	−53.7338	−	53.7338i	−0.444081	−	0.444081i
$122$	−28.0930	+	17.8711i	−0.230270	+	0.146484i
$123$		0			0
$124$	−23.8981	−	65.9306i	−0.192727	−	0.531698i
$125$	−32.0540	−	77.3852i	−0.256432	−	0.619081i
$126$		0			0
$127$			79.4160i			0.625322i	0.949865	+	0.312661i	$0.101220\pi$
$127$			79.4160i			0.625322i	−0.949865	+	0.312661i	$0.898780\pi$
$128$	120.077	+	44.3347i	0.938100	+	0.346365i
$129$		0			0
$130$	−23.5070	−	133.832i	−0.180823	−	1.02948i
$131$	−53.2656	+	22.0633i	−0.406608	+	0.168422i	−0.576607	−	0.817022i	$-0.695624\pi$
$131$	−53.2656	+	22.0633i	−0.406608	+	0.168422i	0.169999	+	0.985444i	$0.445624\pi$
$132$		0			0
$133$	72.2331	+	29.9199i	0.543106	+	0.224962i
$134$	115.283	+	181.222i	0.860319	+	1.35240i
$135$		0			0
$136$	−170.491	+	97.9828i	−1.25361	+	0.720462i
$137$	−50.7359	+	50.7359i	−0.370335	+	0.370335i	−0.867599	−	0.497264i	$-0.834338\pi$
$137$	−50.7359	+	50.7359i	−0.370335	+	0.370335i	0.497264	+	0.867599i	$0.334338\pi$
$138$		0			0
$139$	133.213	+	55.1786i	0.958366	+	0.396968i	0.806369	−	0.591413i	$-0.201430\pi$
$139$	133.213	+	55.1786i	0.958366	+	0.396968i	0.151997	+	0.988381i	$0.451430\pi$
$140$	138.693	−	126.752i	0.990667	−	0.905372i
$141$		0			0
$142$	−5.92286	−	4.15307i	−0.0417102	−	0.0292469i
$143$	58.4811			0.408959
$144$		0			0
$145$		−	119.425i		−	0.823620i
$146$	−71.2116	−	49.9331i	−0.487751	−	0.342007i
$147$		0			0
$148$	155.857	+	7.01134i	1.05309	+	0.0473739i
$149$	−5.00779	+	12.0899i	−0.0336093	+	0.0811401i	−0.939793	−	0.341744i	$-0.888982\pi$
$149$	−5.00779	+	12.0899i	−0.0336093	+	0.0811401i	0.906184	+	0.422884i	$0.138982\pi$
$150$		0			0
$151$	−17.6867	−	17.6867i	−0.117130	−	0.117130i	0.646112	−	0.763243i	$-0.276394\pi$
$151$	−17.6867	−	17.6867i	−0.117130	−	0.117130i	−0.763243	+	0.646112i	$0.776394\pi$
$152$	−63.3434	+	82.2125i	−0.416733	+	0.540872i
$153$		0			0
$154$	43.4032	+	68.2289i	0.281839	+	0.443045i
$155$	52.2918	−	126.244i	0.337367	−	0.814475i
$156$		0			0
$157$	73.8536	+	178.298i	0.470405	+	1.13566i	0.963985	+	0.265958i	$0.0856882\pi$
$157$	73.8536	+	178.298i	0.470405	+	1.13566i	−0.493580	+	0.869701i	$0.664312\pi$
$158$	31.3678	+	178.586i	0.198531	+	1.13029i
$159$		0			0
$160$	114.432	+	221.608i	0.715202	+	1.38505i
$161$	82.8605			0.514662
$162$		0			0
$163$	−132.246	+	54.7779i	−0.811322	+	0.336061i	−0.749481	−	0.662025i	$-0.769697\pi$
$163$	−132.246	+	54.7779i	−0.811322	+	0.336061i	−0.0618408	+	0.998086i	$0.519697\pi$
$164$	26.3203	−	56.2497i	0.160490	−	0.342986i
$165$		0			0
$166$	173.383	−	110.296i	1.04447	−	0.664433i
$167$	109.750	−	109.750i	0.657187	−	0.657187i	−0.297526	−	0.954714i	$-0.596162\pi$
$167$	109.750	−	109.750i	0.657187	−	0.657187i	0.954714	+	0.297526i	$0.0961616\pi$
$168$		0			0
$169$	−65.7709	+	65.7709i	−0.389177	+	0.389177i
$170$	−374.020	−	83.1777i	−2.20012	−	0.489281i
$171$		0			0
$172$	96.8946	+	4.35888i	0.563341	+	0.0253423i
$173$	287.188	−	118.957i	1.66005	−	0.687613i	0.661964	−	0.749535i	$-0.269723\pi$
$173$	287.188	−	118.957i	1.66005	−	0.687613i	0.998081	+	0.0619221i	$0.0197230\pi$
$174$		0			0
$175$	215.434			1.23105
$176$	−102.459	+	32.0075i	−0.582152	+	0.181861i
$177$		0			0
$178$	−177.470	+	253.098i	−0.997025	+	1.42190i
$179$	−48.9443	−	118.162i	−0.273432	−	0.660122i	0.726194	−	0.687490i	$-0.241288\pi$
$179$	−48.9443	−	118.162i	−0.273432	−	0.660122i	−0.999625	+	0.0273677i	$0.991288\pi$
$180$		0			0
$181$	38.9220	−	93.9660i	0.215039	−	0.519149i	−0.779145	−	0.626843i	$-0.784347\pi$
$181$	38.9220	−	93.9660i	0.215039	−	0.519149i	0.994184	+	0.107694i	$0.0343466\pi$
$182$	102.563	+	22.8089i	0.563534	+	0.125323i
$183$		0			0
$184$	−28.6786	+	106.187i	−0.155862	+	0.577104i
$185$	214.957	+	214.957i	1.16193	+	1.16193i
$186$		0			0
$187$	63.1065	−	152.353i	0.337468	−	0.814719i
$188$	101.575	−	36.8182i	0.540291	−	0.195841i
$189$		0			0
$190$	−199.176	+	34.9844i	−1.04830	+	0.184128i
$191$		−	66.5635i		−	0.348500i	−0.984701	−	0.174250i	$-0.944250\pi$
$191$		−	66.5635i		−	0.348500i	0.984701	−	0.174250i	$-0.0557500\pi$
$192$		0			0
$193$	275.880			1.42943			0.714714	−	0.699417i	$-0.246557\pi$
$193$	275.880			1.42943			0.714714	+	0.699417i	$0.246557\pi$
$194$	−22.0454	−	125.511i	−0.113636	−	0.646962i
$195$		0			0
$196$	−17.2832	−	47.6813i	−0.0881796	−	0.243272i
$197$	−167.300	−	69.2980i	−0.849240	−	0.351767i	−0.0847497	−	0.996402i	$-0.527009\pi$
$197$	−167.300	−	69.2980i	−0.849240	−	0.351767i	−0.764490	+	0.644636i	$0.777009\pi$
$198$		0			0
$199$	−233.526	+	233.526i	−1.17350	+	1.17350i	−0.192125	+	0.981370i	$0.561538\pi$
$199$	−233.526	+	233.526i	−1.17350	+	1.17350i	−0.981370	+	0.192125i	$0.938462\pi$
$200$	−74.5634	+	276.083i	−0.372817	+	1.38041i
$201$		0			0
$202$	6.78184	−	30.4955i	0.0335735	−	0.150968i
$203$	85.3151	+	35.3387i	0.420271	+	0.174082i
$204$		0			0
$205$	111.797	−	46.3078i	0.545351	−	0.225892i
$206$	22.4562	+	15.7462i	0.109011	+	0.0764377i
$207$		0			0
$208$	−64.7278	+	123.542i	−0.311192	+	0.593953i
$209$		−	87.0348i		−	0.416434i
$210$		0			0
$211$	32.7097	+	78.9682i	0.155022	+	0.374257i	0.982241	−	0.187623i	$-0.0600783\pi$
$211$	32.7097	+	78.9682i	0.155022	+	0.374257i	−0.827219	+	0.561880i	$0.810078\pi$
$212$	−15.9792	+	355.205i	−0.0753735	+	1.67550i
$213$		0			0
$214$	−64.9117	+	291.884i	−0.303325	+	1.36394i
$215$	133.637	+	133.637i	0.621566	+	0.621566i
$216$		0			0
$217$	74.7128	+	74.7128i	0.344298	+	0.344298i
$218$	37.2912	+	58.6209i	0.171060	+	0.268903i
$219$		0			0
$220$	−189.443	−	88.6438i	−0.861104	−	0.402927i
$221$	−81.9957	−	197.955i	−0.371021	−	0.895725i
$222$		0			0
$223$		−	373.446i		−	1.67465i	−0.546708	−	0.837323i	$-0.684119\pi$
$223$		−	373.446i		−	1.67465i	0.546708	−	0.837323i	$-0.315881\pi$
$224$	−192.174	+	16.1731i	−0.857920	+	0.0722015i
$225$		0			0
$226$	248.048	−	43.5685i	1.09756	−	0.192781i
$227$	−7.71962	+	3.19757i	−0.0340071	+	0.0140862i	−0.399622	−	0.916680i	$-0.630859\pi$
$227$	−7.71962	+	3.19757i	−0.0340071	+	0.0140862i	0.365615	+	0.930766i	$0.380859\pi$
$228$		0			0
$229$	−165.203	−	68.4293i	−0.721410	−	0.298818i	−0.00839310	−	0.999965i	$-0.502672\pi$
$229$	−165.203	−	68.4293i	−0.721410	−	0.298818i	−0.713017	+	0.701147i	$0.752672\pi$
$230$	−180.831	+	115.034i	−0.786224	+	0.500149i
$231$		0			0
$232$	−74.8153	+	97.1018i	−0.322480	+	0.418542i
$233$	−14.0197	+	14.0197i	−0.0601703	+	0.0601703i	−0.736552	−	0.676381i	$-0.763547\pi$
$233$	−14.0197	+	14.0197i	−0.0601703	+	0.0601703i	0.676381	+	0.736552i	$0.263547\pi$
$234$		0			0
$235$	194.495	+	80.5625i	0.827638	+	0.342819i
$236$	13.0771	−	290.694i	0.0554114	−	1.23175i
$237$		0			0
$238$	170.096	−	242.581i	0.714688	−	1.01925i
$239$	230.951			0.966321			0.483161	−	0.875532i	$-0.339489\pi$
$239$	230.951			0.966321			0.483161	+	0.875532i	$0.339489\pi$
$240$		0			0
$241$		−	111.407i		−	0.462269i	−0.972922	−	0.231135i	$-0.925756\pi$
$241$		−	111.407i		−	0.462269i	0.972922	−	0.231135i	$-0.0742438\pi$
$242$	−87.2557	+	124.439i	−0.360561	+	0.514210i
$243$		0			0
$244$	44.9233	+	49.1555i	0.184112	+	0.201457i
$245$	37.8177	−	91.3000i	0.154358	−	0.372653i
$246$		0			0
$247$	−79.9641	−	79.9641i	−0.323741	−	0.323741i
$248$	−121.604	+	69.8871i	−0.490340	+	0.281803i
$249$		0			0
$250$	−141.346	+	89.9162i	−0.565385	+	0.359665i
$251$	−93.4234	+	225.544i	−0.372205	+	0.898581i	0.621172	+	0.783675i	$0.286657\pi$
$251$	−93.4234	+	225.544i	−0.372205	+	0.898581i	−0.993376	+	0.114907i	$0.963343\pi$
$252$		0			0
$253$	−35.2987	−	85.2186i	−0.139521	−	0.336833i
$254$	156.437	−	27.4775i	0.615894	−	0.108179i
$255$		0			0
$256$	45.7867	−	251.872i	0.178854	−	0.983876i
$257$	278.684			1.08437			0.542187	−	0.840258i	$-0.317597\pi$
$257$	278.684			1.08437			0.542187	+	0.840258i	$0.317597\pi$
$258$		0			0
$259$	−217.169	+	89.9543i	−0.838490	+	0.347314i
$260$	−255.495	+	92.6102i	−0.982674	+	0.356193i
$261$		0			0
$262$	61.8909	+	97.2912i	0.236225	+	0.371340i
$263$	−271.210	+	271.210i	−1.03122	+	1.03122i	−0.0317197	+	0.999497i	$0.510098\pi$
$263$	−271.210	+	271.210i	−1.03122	+	1.03122i	−0.999497	+	0.0317197i	$0.989902\pi$
$264$		0			0
$265$	−489.898	+	489.898i	−1.84867	+	1.84867i
$266$	33.9454	−	152.640i	0.127614	−	0.573835i
$267$		0			0
$268$	317.092	−	289.791i	1.18318	−	1.08131i
$269$	−54.9518	+	22.7618i	−0.204282	+	0.0846163i	−0.482478	−	0.875908i	$-0.660263\pi$
$269$	−54.9518	+	22.7618i	−0.204282	+	0.0846163i	0.278197	+	0.960524i	$0.410263\pi$
$270$		0			0
$271$	443.976			1.63829			0.819143	−	0.573589i	$-0.194449\pi$
$271$	443.976			1.63829			0.819143	+	0.573589i	$0.194449\pi$
$272$	252.000	+	301.940i	0.926470	+	1.11007i
$273$		0			0
$274$	117.496	+	82.3875i	0.428818	+	0.300684i
$275$	−91.7754	−	221.565i	−0.333729	−	0.805693i
$276$		0			0
$277$	23.1329	−	55.8478i	0.0835124	−	0.201617i	−0.876607	−	0.481207i	$-0.840199\pi$
$277$	23.1329	−	55.8478i	0.0835124	−	0.201617i	0.960119	+	0.279590i	$0.0901986\pi$
$278$	62.6023	−	281.500i	0.225188	−	1.01259i
$279$		0			0
$280$	−297.669	−	229.349i	−1.06310	−	0.819103i
$281$	159.772	+	159.772i	0.568582	+	0.568582i	0.931731	−	0.363149i	$-0.118298\pi$
$281$	159.772	+	159.772i	0.568582	+	0.568582i	−0.363149	+	0.931731i	$0.618298\pi$
$282$		0			0
$283$	−185.468	+	447.761i	−0.655366	+	1.58219i	0.149517	+	0.988759i	$0.452228\pi$
$283$	−185.468	+	447.761i	−0.655366	+	1.58219i	−0.804883	+	0.593434i	$0.797772\pi$
$284$	−6.13162	+	13.1040i	−0.0215902	+	0.0461410i
$285$		0			0
$286$	−20.2341	−	115.199i	−0.0707487	−	0.402793i
$287$			93.5687i			0.326023i
$288$		0			0
$289$	−315.186			−1.09061
$290$	−235.249	+	41.3203i	−0.811202	+	0.142484i
$291$		0			0
$292$	−73.7216	+	157.552i	−0.252471	+	0.539563i
$293$	−476.574	−	197.403i	−1.62653	−	0.673732i	−0.631696	−	0.775216i	$-0.717641\pi$
$293$	−476.574	−	197.403i	−1.62653	−	0.673732i	−0.994837	+	0.101485i	$0.967641\pi$
$294$		0			0
$295$	400.924	−	400.924i	1.35906	−	1.35906i
$296$	−40.1143	−	309.439i	−0.135521	−	1.04540i
$297$		0			0
$298$	25.5479	+	5.68155i	0.0857310	+	0.0190656i
$299$	−110.727	−	45.8645i	−0.370323	−	0.153393i
$300$		0			0
$301$	−135.012	+	55.9237i	−0.448544	+	0.185793i
$302$	−28.7206	+	40.9595i	−0.0951012	+	0.135628i
$303$		0			0
$304$	183.862	+	96.3315i	0.604810	+	0.316880i
$305$			129.753i			0.425420i
$306$		0			0
$307$	−196.212	−	473.698i	−0.639127	−	1.54299i	−0.827844	−	0.560959i	$-0.810433\pi$
$307$	−196.212	−	473.698i	−0.639127	−	1.54299i	0.188716	−	0.982032i	$-0.439567\pi$
$308$	119.383	−	109.104i	0.387608	−	0.354235i
$309$		0			0
$310$	−266.773	−	59.3272i	−0.860558	−	0.191378i
$311$	−386.346	−	386.346i	−1.24227	−	1.24227i	−0.959057	−	0.283215i	$-0.908599\pi$
$311$	−386.346	−	386.346i	−1.24227	−	1.24227i	−0.283215	−	0.959057i	$-0.591401\pi$
$312$		0			0
$313$	127.090	+	127.090i	0.406038	+	0.406038i	0.880354	−	0.474316i	$-0.157305\pi$
$313$	127.090	+	127.090i	0.406038	+	0.406038i	−0.474316	+	0.880354i	$0.657305\pi$
$314$	325.667	−	207.170i	1.03716	−	0.659778i
$315$		0			0
$316$	340.934	−	123.579i	1.07890	−	0.391074i
$317$	24.4377	+	58.9979i	0.0770906	+	0.186113i	0.957726	−	0.287681i	$-0.0928842\pi$
$317$	24.4377	+	58.9979i	0.0770906	+	0.186113i	−0.880636	+	0.473794i	$0.842884\pi$
$318$		0			0
$319$		−	102.797i		−	0.322249i
$320$	396.940	−	302.089i	1.24044	−	0.944027i
$321$		0			0
$322$	−28.6693	−	163.222i	−0.0890349	−	0.506902i
$323$	−294.608	+	122.031i	−0.912099	+	0.377804i
$324$		0			0
$325$	−287.885	−	119.246i	−0.885801	−	0.366911i
$326$	153.660	+	241.550i	0.471350	+	0.740952i
$327$		0			0
$328$	−119.910	−	32.3848i	−0.365579	−	0.0987341i
$329$	−115.105	+	115.105i	−0.349863	+	0.349863i
$330$		0			0
$331$	53.7512	+	22.2645i	0.162390	+	0.0672643i	0.462398	−	0.886673i	$-0.346989\pi$
$331$	53.7512	+	22.2645i	0.162390	+	0.0672643i	−0.300007	+	0.953937i	$0.596989\pi$
$332$	−277.255	−	303.375i	−0.835106	−	0.913781i
$333$		0			0
$334$	−254.164	−	178.218i	−0.760970	−	0.533587i
$335$	837.010			2.49854
$336$		0			0
$337$			368.803i			1.09437i	0.837012	+	0.547185i	$0.184300\pi$
$337$			368.803i			1.09437i	−0.837012	+	0.547185i	$0.815700\pi$
$338$	152.315	+	106.802i	0.450636	+	0.315983i
$339$		0			0
$340$	−34.4384	+	765.540i	−0.101289	+	2.25159i
$341$	45.0113	−	108.667i	0.131998	−	0.318671i
$342$		0			0
$343$	262.846	+	262.846i	0.766315	+	0.766315i
$344$	−24.9387	−	192.376i	−0.0724961	−	0.559231i
$345$		0			0
$346$	−333.692	−	524.557i	−0.964429	−	1.51606i
$347$	−166.265	+	401.400i	−0.479151	+	1.15677i	0.480857	+	0.876799i	$0.340325\pi$
$347$	−166.265	+	401.400i	−0.479151	+	1.15677i	−0.960008	+	0.279973i	$0.909675\pi$
$348$		0			0
$349$	−24.6685	−	59.5550i	−0.0706833	−	0.170645i	0.884590	−	0.466370i	$-0.154439\pi$
$349$	−24.6685	−	59.5550i	−0.0706833	−	0.170645i	−0.955273	+	0.295726i	$0.904439\pi$
$350$	−74.5390	−	424.372i	−0.212969	−	1.21249i
$351$		0			0
$352$	98.4999	+	190.753i	0.279829	+	0.541913i
$353$	−245.534			−0.695563			−0.347782	−	0.937576i	$-0.613065\pi$
$353$	−245.534			−0.695563			−0.347782	+	0.937576i	$0.613065\pi$
$354$		0			0
$355$	−26.0444	+	10.7880i	−0.0733646	+	0.0303886i
$356$	559.967	+	262.019i	1.57294	+	0.736008i
$357$		0			0
$358$	−215.826	+	137.296i	−0.602866	+	0.383508i
$359$	−61.7019	+	61.7019i	−0.171872	+	0.171872i	−0.787801	−	0.615930i	$-0.788781\pi$
$359$	−61.7019	+	61.7019i	−0.171872	+	0.171872i	0.615930	+	0.787801i	$0.288781\pi$
$360$		0			0
$361$	136.259	−	136.259i	0.377448	−	0.377448i
$362$	−198.565	−	44.1586i	−0.548523	−	0.121985i
$363$		0			0
$364$	9.44365	−	209.925i	0.0259441	−	0.576718i
$365$	−313.137	+	129.706i	−0.857910	+	0.355358i
$366$		0			0
$367$	123.349			0.336102			0.168051	−	0.985778i	$-0.446253\pi$
$367$	123.349			0.336102			0.168051	+	0.985778i	$0.446253\pi$
$368$	219.095	+	19.7523i	0.595367	+	0.0536747i
$369$		0			0
$370$	349.058	−	497.806i	0.943400	−	1.34542i
$371$	−205.010	−	494.939i	−0.552588	−	1.33407i
$372$		0			0
$373$	−11.5942	+	27.9909i	−0.0310836	+	0.0750425i	−0.938659	−	0.344846i	$-0.887931\pi$
$373$	−11.5942	+	27.9909i	−0.0310836	+	0.0750425i	0.907575	+	0.419889i	$0.137931\pi$
$374$	−321.945	−	71.5969i	−0.860816	−	0.191436i
$375$		0			0
$376$	−107.670	−	187.348i	−0.286357	−	0.498265i
$377$	−94.4462	−	94.4462i	−0.250520	−	0.250520i
$378$		0			0
$379$	205.083	−	495.114i	0.541115	−	1.30637i	−0.382821	−	0.923823i	$-0.625047\pi$
$379$	205.083	−	495.114i	0.541115	−	1.30637i	0.923937	−	0.382546i	$-0.124953\pi$
$380$	137.828	+	380.242i	0.362704	+	1.00064i
$381$		0			0
$382$	−131.120	+	23.0306i	−0.343245	+	0.0602894i
$383$		−	605.809i		−	1.58175i	−0.611979	−	0.790874i	$-0.709626\pi$
$383$		−	605.809i		−	1.58175i	0.611979	−	0.790874i	$-0.290374\pi$
$384$		0			0
$385$	315.129			0.818517
$386$	−95.4528	−	543.440i	−0.247287	−	1.40788i
$387$		0			0
$388$	−239.609	+	86.8519i	−0.617549	+	0.223845i
$389$	426.567	+	176.690i	1.09657	+	0.454215i	0.856294	−	0.516489i	$-0.172761\pi$
$389$	426.567	+	176.690i	1.09657	+	0.454215i	0.240279	+	0.970704i	$0.422761\pi$
$390$		0			0
$391$	−238.968	+	238.968i	−0.611172	+	0.611172i
$392$	−87.9448	+	50.5427i	−0.224349	+	0.128935i
$393$		0			0
$394$	−78.6214	+	353.532i	−0.199547	+	0.897290i
$395$	652.819	+	270.407i	1.65271	+	0.684573i
$396$		0			0
$397$	294.458	−	121.969i	0.741708	−	0.307226i	0.0203548	−	0.999793i	$-0.493520\pi$
$397$	294.458	−	121.969i	0.741708	−	0.307226i	0.721353	+	0.692567i	$0.243520\pi$
$398$	540.808	+	379.211i	1.35881	+	0.952791i
$399$		0			0
$400$	569.639	+	51.3552i	1.42410	+	0.128388i
$401$		−	48.4544i		−	0.120834i	−0.998173	−	0.0604169i	$-0.980757\pi$
$401$		−	48.4544i		−	0.120834i	0.998173	−	0.0604169i	$-0.0192430\pi$
$402$		0			0
$403$	−58.4842	−	141.193i	−0.145122	−	0.350356i
$404$	−62.4178	−	2.80791i	−0.154500	−	0.00695028i
$405$		0			0
$406$	40.0932	−	180.284i	0.0987516	−	0.444050i
$407$	185.029	+	185.029i	0.454616	+	0.454616i
$408$		0			0
$409$	−242.037	−	242.037i	−0.591778	−	0.591778i	0.346334	−	0.938111i	$-0.387427\pi$
$409$	−242.037	−	242.037i	−0.591778	−	0.591778i	−0.938111	+	0.346334i	$0.887427\pi$
$410$	−129.900	−	204.201i	−0.316830	−	0.498050i
$411$		0			0
$412$	23.2478	−	49.6834i	0.0564266	−	0.120591i
$413$	167.777	+	405.049i	0.406239	+	0.980749i
$414$		0			0
$415$		−	800.803i		−	1.92965i
$416$	265.755	+	84.7589i	0.638833	+	0.203747i
$417$		0			0
$418$	−171.445	+	30.1135i	−0.410155	+	0.0720419i
$419$	−163.261	+	67.6248i	−0.389644	+	0.161396i	−0.568900	−	0.822407i	$-0.692631\pi$
$419$	−163.261	+	67.6248i	−0.389644	+	0.161396i	0.179256	+	0.983802i	$0.442631\pi$
$420$		0			0
$421$	−624.400	−	258.635i	−1.48314	−	0.614335i	−0.513325	−	0.858195i	$-0.671586\pi$
$421$	−624.400	−	258.635i	−1.48314	−	0.614335i	−0.969810	+	0.243860i	$0.921586\pi$
$422$	144.238	−	91.7555i	0.341795	−	0.217430i
$423$		0			0
$424$	705.228	−	91.4225i	1.66327	−	0.215619i
$425$	−621.309	+	621.309i	−1.46190	+	1.46190i
$426$		0			0
$427$	−92.6933	−	38.3948i	−0.217080	−	0.0899176i
$428$	597.426	+	26.8757i	1.39585	+	0.0627936i
$429$		0			0
$430$	217.006	−	309.481i	0.504665	−	0.719723i
$431$	−606.510			−1.40722			−0.703608	−	0.710588i	$-0.748429\pi$
$431$	−606.510			−1.40722			−0.703608	+	0.710588i	$0.748429\pi$
$432$		0			0
$433$			3.82972i			0.00884462i	0.999990	+	0.00442231i	$0.00140767\pi$
$433$			3.82972i			0.00884462i	−0.999990	+	0.00442231i	$0.998592\pi$
$434$	121.322	−	173.023i	0.279545	−	0.398670i
$435$		0			0
$436$	102.572	−	93.7403i	0.235256	−	0.215001i
$437$	−68.2580	+	164.789i	−0.156197	+	0.377092i
$438$		0			0
$439$	−36.3389	−	36.3389i	−0.0827765	−	0.0827765i	0.664506	−	0.747283i	$-0.268642\pi$
$439$	−36.3389	−	36.3389i	−0.0827765	−	0.0827765i	−0.747283	+	0.664506i	$0.768642\pi$
$440$	−109.068	+	403.843i	−0.247883	+	0.917826i
$441$		0			0
$442$	−361.571	+	230.010i	−0.818034	+	0.520385i
$443$	208.435	−	503.207i	0.470508	−	1.13591i	−0.493431	−	0.869785i	$-0.664258\pi$
$443$	208.435	−	503.207i	0.470508	−	1.13591i	0.963939	−	0.266122i	$-0.0857425\pi$
$444$		0			0
$445$	460.995	+	1112.94i	1.03594	+	2.50099i
$446$	−735.631	+	129.210i	−1.64940	+	0.289709i
$447$		0			0
$448$	98.3497	+	372.957i	0.219530	+	0.832494i
$449$	−431.670			−0.961402			−0.480701	−	0.876884i	$-0.659618\pi$
$449$	−431.670			−0.961402			−0.480701	+	0.876884i	$0.659618\pi$
$450$		0			0
$451$	96.2316	−	39.8604i	0.213374	−	0.0883823i
$452$	−171.646	−	473.542i	−0.379749	−	1.04766i
$453$		0			0
$454$	8.96966	+	14.1001i	0.0197570	+	0.0310575i
$455$	289.528	−	289.528i	0.636325	−	0.636325i
$456$		0			0
$457$	−187.054	+	187.054i	−0.409309	+	0.409309i	−0.881497	−	0.472189i	$-0.843464\pi$
$457$	−187.054	+	187.054i	−0.409309	+	0.409309i	0.472189	+	0.881497i	$0.343464\pi$
$458$	−77.6358	+	349.100i	−0.169510	+	0.762227i
$459$		0			0
$460$	289.166	+	316.409i	0.628623	+	0.687845i
$461$	−253.784	+	105.121i	−0.550508	+	0.228028i	−0.640558	−	0.767909i	$-0.721297\pi$
$461$	−253.784	+	105.121i	−0.550508	+	0.228028i	0.0900508	+	0.995937i	$0.471297\pi$
$462$		0			0
$463$	−765.246			−1.65280			−0.826400	−	0.563084i	$-0.809615\pi$
$463$	−765.246			−1.65280			−0.826400	+	0.563084i	$0.809615\pi$
$464$	217.161	+	113.778i	0.468020	+	0.245211i
$465$		0			0
$466$	32.4673	+	22.7659i	0.0696723	+	0.0488538i
$467$	110.687	+	267.223i	0.237018	+	0.572211i	0.996972	−	0.0777657i	$-0.0247786\pi$
$467$	110.687	+	267.223i	0.237018	+	0.572211i	−0.759954	+	0.649977i	$0.774779\pi$
$468$		0			0
$469$	−247.677	+	597.945i	−0.528096	+	1.27494i
$470$	91.4014	−	410.999i	0.194471	−	0.874466i
$471$		0			0
$472$	−577.147	+	74.8186i	−1.22277	+	0.158514i
$473$	115.030	+	115.030i	0.243193	+	0.243193i
$474$		0			0
$475$	−177.468	+	428.447i	−0.373618	+	0.901993i
$476$	−536.698	−	251.131i	−1.12752	−	0.527586i
$477$		0			0
$478$	−79.9076	−	454.937i	−0.167171	−	0.951751i
$479$			158.059i			0.329977i	0.986296	+	0.164988i	$0.0527586\pi$
$479$			158.059i			0.329977i	−0.986296	+	0.164988i	$0.947241\pi$
$480$		0			0
$481$	339.994			0.706848
$482$	−219.454	+	38.5461i	−0.455299	+	0.0799712i
$483$		0			0
$484$	275.315	+	128.825i	0.568833	+	0.266168i
$485$	−458.803	−	190.042i	−0.945985	−	0.391840i
$486$		0			0
$487$	−675.116	+	675.116i	−1.38628	+	1.38628i	−0.553280	+	0.832996i	$0.686624\pi$
$487$	−675.116	+	675.116i	−1.38628	+	1.38628i	−0.832996	+	0.553280i	$0.813376\pi$
$488$	81.2855	−	105.499i	0.166569	−	0.216187i
$489$		0			0
$490$	−192.931	−	42.9057i	−0.393738	−	0.0875627i
$491$	−87.1226	−	36.0874i	−0.177439	−	0.0734977i	0.292195	−	0.956359i	$-0.405614\pi$
$491$	−87.1226	−	36.0874i	−0.177439	−	0.0734977i	−0.469634	+	0.882861i	$0.655614\pi$
$492$		0			0
$493$	−347.963	+	144.131i	−0.705808	+	0.292355i
$494$	−129.850	+	185.184i	−0.262854	+	0.374866i
$495$		0			0
$496$	179.741	+	215.361i	0.362381	+	0.434196i
$497$		−	21.7979i		−	0.0438590i
$498$		0			0
$499$	164.812	+	397.892i	0.330285	+	0.797378i	0.998569	+	0.0534724i	$0.0170289\pi$
$499$	164.812	+	397.892i	0.330285	+	0.797378i	−0.668284	+	0.743906i	$0.732971\pi$
$500$	226.026	+	247.320i	0.452052	+	0.494640i
$501$		0			0
$502$	476.610	+	105.993i	0.949423	+	0.211141i
$503$	270.905	+	270.905i	0.538578	+	0.538578i	0.923111	−	0.384533i	$-0.125638\pi$
$503$	270.905	+	270.905i	0.538578	+	0.538578i	−0.384533	+	0.923111i	$0.625638\pi$
$504$		0			0
$505$	−86.0864	−	86.0864i	−0.170468	−	0.170468i
$506$	−155.654	+	99.0181i	−0.307617	+	0.195688i
$507$		0			0
$508$	−108.253	−	298.650i	−0.213096	−	0.587893i
$509$	194.137	+	468.689i	0.381409	+	0.920803i	0.991694	+	0.128621i	$0.0410551\pi$
$509$	194.137	+	468.689i	0.381409	+	0.920803i	−0.610285	+	0.792182i	$0.708945\pi$
$510$		0			0
$511$		−	262.081i		−	0.512878i
$512$	−511.991	−	3.04640i	−0.999982	−	0.00595000i
$513$		0			0
$514$	−96.4230	−	548.964i	−0.187593	−	1.06802i
$515$	98.7463	−	40.9021i	0.191740	−	0.0794215i
$516$		0			0
$517$	167.416	+	69.3458i	0.323821	+	0.134131i
$518$	252.335	+	396.665i	0.487133	+	0.765763i
$519$		0			0
$520$	270.828	+	471.243i	0.520822	+	0.906237i
$521$	240.434	−	240.434i	0.461486	−	0.461486i	−0.437656	−	0.899142i	$-0.644191\pi$
$521$	240.434	−	240.434i	0.461486	−	0.461486i	0.899142	+	0.437656i	$0.144191\pi$
$522$		0			0
$523$	846.467	+	350.618i	1.61848	+	0.670398i	0.993872	−	0.110538i	$-0.0352574\pi$
$523$	846.467	+	350.618i	1.61848	+	0.670398i	0.624611	+	0.780936i	$0.285257\pi$
$524$	170.235	−	155.578i	0.324875	−	0.296904i
$525$		0			0
$526$	628.078	+	440.404i	1.19407	+	0.837271i
$527$	−430.941			−0.817725
$528$		0			0
$529$		−	339.966i		−	0.642657i
$530$	1134.52	+	795.521i	2.14061	+	1.50098i
$531$		0			0
$532$	−312.422	−	14.0546i	−0.587260	−	0.0264183i
$533$	51.7916	−	125.036i	0.0971699	−	0.234589i
$534$		0			0
$535$	823.967	+	823.967i	1.54012	+	1.54012i
$536$	−680.555	−	524.356i	−1.26969	−	0.978276i
$537$		0			0
$538$	63.8502	+	100.371i	0.118681	+	0.186563i
$539$	32.5523	−	78.5883i	0.0603939	−	0.145804i
$540$		0			0
$541$	−6.87337	−	16.5938i	−0.0127049	−	0.0306724i	0.917400	−	0.397967i	$-0.130284\pi$
$541$	−6.87337	−	16.5938i	−0.0127049	−	0.0306724i	−0.930105	+	0.367294i	$0.880284\pi$
$542$	−153.613	−	874.563i	−0.283419	−	1.61358i
$543$		0			0
$544$	507.584	−	600.870i	0.933059	−	1.10454i
$545$	270.752			0.496793
$546$		0			0
$547$	354.417	−	146.804i	0.647929	−	0.268381i	−0.0344200	−	0.999407i	$-0.510958\pi$
$547$	354.417	−	146.804i	0.647929	−	0.268381i	0.682349	+	0.731026i	$0.260958\pi$
$548$	121.638	−	259.955i	0.221967	−	0.474370i
$549$		0			0
$550$	−404.696	+	257.444i	−0.735811	+	0.468079i
$551$	−140.560	+	140.560i	−0.255100	+	0.255100i
$552$		0			0
$553$	−386.348	+	386.348i	−0.698639	+	0.698639i
$554$	−118.015	−	26.2452i	−0.213024	−	0.0473741i
$555$		0			0
$556$	−576.171	−	25.9195i	−1.03628	−	0.0466178i
$557$	549.588	−	227.647i	0.986692	−	0.408701i	0.169792	−	0.985480i	$-0.445690\pi$
$557$	549.588	−	227.647i	0.986692	−	0.408701i	0.816900	+	0.576779i	$0.195690\pi$
$558$		0			0
$559$	211.371			0.378123
$560$	−348.790	+	665.715i	−0.622839	+	1.18878i
$561$		0			0
$562$	259.445	−	370.005i	0.461646	−	0.658372i
$563$	150.445	+	363.205i	0.267219	+	0.645125i	0.999350	−	0.0360391i	$-0.0114741\pi$
$563$	150.445	+	363.205i	0.267219	+	0.645125i	−0.732131	+	0.681164i	$0.761474\pi$
$564$		0			0
$565$	375.583	−	906.737i	0.664748	−	1.60484i
$566$	946.190	+	210.422i	1.67171	+	0.371770i
$567$		0			0
$568$	27.9344	+	7.54442i	0.0491803	+	0.0132824i
$569$	−510.987	−	510.987i	−0.898045	−	0.898045i	0.0972186	−	0.995263i	$-0.469005\pi$
$569$	−510.987	−	510.987i	−0.898045	−	0.898045i	−0.995263	+	0.0972186i	$0.969005\pi$
$570$		0			0
$571$	328.247	−	792.459i	0.574864	−	1.38784i	−0.322507	−	0.946567i	$-0.604526\pi$
$571$	328.247	−	792.459i	0.574864	−	1.38784i	0.897371	−	0.441277i	$-0.145474\pi$
$572$	−219.923	+	79.7161i	−0.384480	+	0.139364i
$573$		0			0
$574$	184.316	−	32.3742i	0.321108	−	0.0564011i
$575$			491.482i			0.854752i
$576$		0			0
$577$	305.039			0.528663			0.264332	−	0.964432i	$-0.414849\pi$
$577$	305.039			0.528663			0.264332	+	0.964432i	$0.414849\pi$
$578$	109.052	+	620.867i	0.188672	+	1.07416i
$579$		0			0
$580$	162.789	+	449.106i	0.280671	+	0.774322i
$581$	572.080	+	236.963i	0.984647	+	0.407854i
$582$		0			0
$583$	−421.689	+	421.689i	−0.723309	+	0.723309i
$584$	335.861	+	90.7080i	0.575104	+	0.155322i
$585$		0			0
$586$	−223.962	+	1007.08i	−0.382188	+	1.71856i
$587$	388.900	+	161.088i	0.662521	+	0.274425i	0.688499	−	0.725237i	$-0.258270\pi$
$587$	388.900	+	161.088i	0.662521	+	0.274425i	−0.0259780	+	0.999663i	$0.508270\pi$
$588$		0			0
$589$	−210.132	+	87.0394i	−0.356760	+	0.147775i
$590$	−928.475	−	651.040i	−1.57369	−	1.10346i
$591$		0			0
$592$	−595.668	+	186.083i	−1.00620	+	0.314330i
$593$		−	1039.64i		−	1.75319i	−0.481228	−	0.876595i	$-0.659809\pi$
$593$		−	1039.64i		−	1.75319i	0.481228	−	0.876595i	$-0.340191\pi$
$594$		0			0
$595$	−441.839	−	1066.69i	−0.742587	−	1.79276i
$596$	2.35235	−	52.2911i	0.00394690	−	0.0877367i
$597$		0			0
$598$	−52.0351	+	233.983i	−0.0870152	+	0.391276i
$599$	−22.4929	−	22.4929i	−0.0375507	−	0.0375507i	0.688082	−	0.725633i	$-0.258453\pi$
$599$	−22.4929	−	22.4929i	−0.0375507	−	0.0375507i	−0.725633	+	0.688082i	$0.758453\pi$
$600$		0			0
$601$	−640.653	−	640.653i	−1.06598	−	1.06598i	−0.997664	−	0.0683147i	$-0.978238\pi$
$601$	−640.653	−	640.653i	−1.06598	−	1.06598i	−0.0683147	−	0.997664i	$-0.521762\pi$
$602$	156.874	+	246.603i	0.260588	+	0.409639i
$603$		0			0
$604$	90.6211	+	42.4033i	0.150035	+	0.0702041i
$605$	226.654	+	547.192i	0.374636	+	0.904450i
$606$		0			0
$607$			860.149i			1.41705i	0.705686	+	0.708524i	$0.250639\pi$
$607$			860.149i			1.41705i	−0.705686	+	0.708524i	$0.749361\pi$
$608$	126.143	−	395.510i	0.207472	−	0.650511i
$609$		0			0
$610$	255.593	−	44.8938i	0.419005	−	0.0735964i
$611$	217.527	−	90.1026i	0.356018	−	0.147467i
$612$		0			0
$613$	724.830	+	300.235i	1.18243	+	0.489779i	0.885283	−	0.465052i	$-0.153965\pi$
$613$	724.830	+	300.235i	1.18243	+	0.489779i	0.297148	+	0.954831i	$0.403965\pi$
$614$	−865.223	+	550.404i	−1.40916	+	0.896424i
$615$		0			0
$616$	−256.225	−	197.417i	−0.415949	−	0.320482i
$617$	704.685	−	704.685i	1.14212	−	1.14212i	0.154052	−	0.988063i	$-0.450768\pi$
$617$	704.685	−	704.685i	1.14212	−	1.14212i	0.988063	−	0.154052i	$-0.0492324\pi$
$618$		0			0
$619$	−33.0442	−	13.6874i	−0.0533832	−	0.0221121i	0.355832	−	0.934550i	$-0.384198\pi$
$619$	−33.0442	−	13.6874i	−0.0533832	−	0.0221121i	−0.409215	+	0.912438i	$0.634198\pi$
$620$	−24.5635	+	546.028i	−0.0396186	+	0.880691i
$621$		0			0
$622$	−627.369	+	894.716i	−1.00863	+	1.43845i
$623$	−931.477			−1.49515
$624$		0			0
$625$		−	240.835i		−	0.385335i
$626$	206.375	−	294.320i	0.329673	−	0.470159i
$627$		0			0
$628$	−520.772	−	569.834i	−0.829255	−	0.907379i
$629$	366.885	−	885.738i	0.583282	−	1.40817i
$630$		0			0
$631$	−718.112	−	718.112i	−1.13805	−	1.13805i	−0.988799	−	0.149255i	$-0.952312\pi$
$631$	−718.112	−	718.112i	−1.13805	−	1.13805i	−0.149255	−	0.988799i	$-0.547688\pi$
$632$	−361.393	−	628.829i	−0.571825	−	0.994982i
$633$		0			0
$634$	107.761	−	68.5514i	0.169971	−	0.108125i
$635$	236.870	−	571.854i	0.373023	−	0.900557i
$636$		0			0
$637$	−42.2960	−	102.112i	−0.0663988	−	0.160301i
$638$	−202.495	+	35.5673i	−0.317390	+	0.0557481i
$639$		0			0
$640$	−732.407	−	677.389i	−1.14439	−	1.05842i
$641$	338.159			0.527549			0.263774	−	0.964584i	$-0.415033\pi$
$641$	338.159			0.527549			0.263774	+	0.964584i	$0.415033\pi$
$642$		0			0
$643$	332.477	−	137.716i	0.517071	−	0.214178i	−0.108859	−	0.994057i	$-0.534720\pi$
$643$	332.477	−	137.716i	0.517071	−	0.214178i	0.625930	+	0.779879i	$0.284720\pi$
$644$	−311.603	+	112.948i	−0.483856	+	0.175385i
$645$		0			0
$646$	342.314	+	538.110i	0.529898	+	0.832987i
$647$	31.2745	−	31.2745i	0.0483377	−	0.0483377i	−0.682525	−	0.730862i	$-0.739118\pi$
$647$	31.2745	−	31.2745i	0.0483377	−	0.0483377i	0.730862	+	0.682525i	$0.239118\pi$
$648$		0			0
$649$	345.103	−	345.103i	0.531746	−	0.531746i
$650$	−135.289	+	608.348i	−0.208138	+	0.935919i
$651$		0			0
$652$	422.651	−	386.262i	0.648238	−	0.592426i
$653$	−355.409	+	147.215i	−0.544271	+	0.225445i	−0.637841	−	0.770168i	$-0.720172\pi$
$653$	−355.409	+	147.215i	−0.544271	+	0.225445i	0.0935696	+	0.995613i	$0.470172\pi$
$654$		0			0
$655$	449.359			0.686044
$656$	−22.3049	+	247.409i	−0.0340014	+	0.377148i
$657$		0			0
$658$	266.564	+	186.913i	0.405113	+	0.284062i
$659$	116.271	+	280.702i	0.176435	+	0.425952i	0.987214	−	0.159401i	$-0.0509562\pi$
$659$	116.271	+	280.702i	0.176435	+	0.425952i	−0.810779	+	0.585352i	$0.800956\pi$
$660$		0			0
$661$	179.920	−	434.366i	0.272194	−	0.657134i	−0.727383	−	0.686232i	$-0.759263\pi$
$661$	179.920	−	434.366i	0.272194	−	0.657134i	0.999577	+	0.0290979i	$0.00926347\pi$
$662$	25.2600	−	113.585i	0.0381571	−	0.171579i
$663$		0			0
$664$	−501.673	+	651.116i	−0.755532	+	0.980596i
$665$	−430.892	−	430.892i	−0.647957	−	0.647957i
$666$		0			0
$667$	−80.6200	+	194.634i	−0.120870	+	0.291805i
$668$	−263.123	+	562.326i	−0.393896	+	0.841805i
$669$		0			0
$670$	−289.600	−	1648.78i	−0.432240	−	2.46086i
$671$			111.688i			0.166449i
$672$		0			0
$673$	1168.06			1.73561			0.867803	−	0.496908i	$-0.165531\pi$
$673$	1168.06			1.73561			0.867803	+	0.496908i	$0.165531\pi$
$674$	726.484	−	127.604i	1.07787	−	0.189323i
$675$		0			0
$676$	157.684	−	336.990i	0.233260	−	0.498505i
$677$	604.882	+	250.550i	0.893474	+	0.370089i	0.781707	−	0.623645i	$-0.214349\pi$
$677$	604.882	+	250.550i	0.893474	+	0.370089i	0.111767	+	0.993734i	$0.464349\pi$
$678$		0			0
$679$	271.526	−	271.526i	0.399891	−	0.399891i
$680$	1519.91	−	197.034i	2.23516	−	0.289756i
$681$		0			0
$682$	−229.630	−	51.0671i	−0.336701	−	0.0748785i
$683$	369.863	+	153.202i	0.541527	+	0.224308i	0.636644	−	0.771158i	$-0.280322\pi$
$683$	369.863	+	153.202i	0.541527	+	0.224308i	−0.0951163	+	0.995466i	$0.530322\pi$
$684$		0			0
$685$	516.663	−	214.009i	0.754253	−	0.312422i
$686$	426.823	−	608.709i	0.622191	−	0.887331i
$687$		0			0
$688$	−370.321	+	115.686i	−0.538258	+	0.168148i
$689$			774.863i			1.12462i
$690$		0			0
$691$	74.8080	+	180.602i	0.108260	+	0.261364i	0.968721	−	0.248154i	$-0.0798239\pi$
$691$	74.8080	+	180.602i	0.108260	+	0.261364i	−0.860460	+	0.509518i	$0.829824\pi$
$692$	−917.840	+	838.816i	−1.32636	+	1.21216i
$693$		0			0
$694$	848.222	+	188.635i	1.22222	+	0.271808i
$695$	−794.653	−	794.653i	−1.14339	−	1.14339i
$696$		0			0
$697$	−269.851	−	269.851i	−0.387160	−	0.387160i
$698$	−108.779	+	69.1987i	−0.155844	+	0.0991386i
$699$		0			0
$700$	−810.157	+	293.661i	−1.15737	+	0.419515i
$701$	−250.206	−	604.050i	−0.356927	−	0.861698i	−0.995729	−	0.0923265i	$-0.970570\pi$
$701$	−250.206	−	604.050i	−0.356927	−	0.861698i	0.638802	−	0.769371i	$-0.279430\pi$
$702$		0			0
$703$		−	505.998i		−	0.719769i
$704$	341.674	−	260.029i	0.485333	−	0.369359i
$705$		0			0
$706$	84.9533	+	483.663i	0.120330	+	0.685076i
$707$	86.9722	−	36.0251i	0.123016	−	0.0509548i
$708$		0			0
$709$	−771.157	−	319.424i	−1.08767	−	0.450527i	−0.234476	−	0.972122i	$-0.575337\pi$
$709$	−771.157	−	319.424i	−1.08767	−	0.450527i	−0.853193	+	0.521595i	$0.825337\pi$
$710$	30.2618	+	47.5709i	0.0426223	+	0.0670013i
$711$		0			0
$712$	322.391	−	1193.70i	0.452796	−	1.67655i
$713$	−170.446	+	170.446i	−0.239055	+	0.239055i
$714$		0			0
$715$	−421.107	−	174.428i	−0.588961	−	0.243956i
$716$	345.126	+	377.640i	0.482020	+	0.527431i
$717$		0			0
$718$	142.892	+	100.195i	0.199013	+	0.139547i
$719$	−263.077			−0.365893			−0.182947	−	0.983123i	$-0.558564\pi$
$719$	−263.077			−0.365893			−0.182947	+	0.983123i	$0.558564\pi$
$720$		0			0
$721$			82.6459i			0.114627i
$722$	−315.553	−	221.264i	−0.437054	−	0.306459i
$723$		0			0
$724$	−18.2832	+	406.421i	−0.0252530	+	0.561355i
$725$	−209.609	+	506.041i	−0.289116	+	0.697988i
$726$		0			0
$727$	320.334	+	320.334i	0.440625	+	0.440625i	0.892222	−	0.451597i	$-0.149146\pi$
$727$	320.334	+	320.334i	0.440625	+	0.440625i	−0.451597	+	0.892222i	$0.649146\pi$
$728$	−416.788	+	54.0304i	−0.572511	+	0.0742176i
$729$		0			0
$730$	363.844	+	571.954i	0.498416	+	0.783499i
$731$	228.089	−	550.655i	0.312023	−	0.753289i
$732$		0			0
$733$	119.193	+	287.758i	0.162610	+	0.392575i	0.984092	−	0.177659i	$-0.0568524\pi$
$733$	119.193	+	287.758i	0.162610	+	0.392575i	−0.821482	+	0.570234i	$0.806852\pi$
$734$	−42.6782	−	242.979i	−0.0581446	−	0.331034i
$735$		0			0
$736$	−36.8966	−	438.417i	−0.0501313	−	0.595676i
$737$	720.473			0.977576
$738$		0			0
$739$	−760.509	+	315.013i	−1.02911	+	0.426269i	−0.832389	−	0.554191i	$-0.813028\pi$
$739$	−760.509	+	315.013i	−1.02911	+	0.426269i	−0.196716	+	0.980461i	$0.563028\pi$
$740$	−1101.37	−	515.352i	−1.48834	−	0.696422i
$741$		0			0
$742$	−904.020	+	575.084i	−1.21836	+	0.775046i
$743$	−89.2306	+	89.2306i	−0.120095	+	0.120095i	−0.764600	−	0.644505i	$-0.777063\pi$
$743$	−89.2306	+	89.2306i	−0.120095	+	0.120095i	0.644505	+	0.764600i	$0.277063\pi$
$744$		0			0
$745$	72.1196	−	72.1196i	0.0968049	−	0.0968049i
$746$	59.1492	+	13.1541i	0.0792885	+	0.0176328i
$747$		0			0
$748$	−29.6436	+	658.954i	−0.0396304	+	0.880955i
$749$	−832.445	+	344.810i	−1.11141	+	0.460361i
$750$		0			0
$751$	−418.271			−0.556953			−0.278476	−	0.960443i	$-0.589829\pi$
$751$	−418.271			−0.556953			−0.278476	+	0.960443i	$0.589829\pi$
$752$	−331.792	+	276.915i	−0.441213	+	0.368238i
$753$		0			0
$754$	−153.367	+	218.722i	−0.203404	+	0.290082i
$755$	74.6042	+	180.110i	0.0988135	+	0.238557i
$756$		0			0
$757$	−212.675	+	513.443i	−0.280944	+	0.678260i	−0.999858	−	0.0168395i	$-0.994640\pi$
$757$	−212.675	+	513.443i	−0.280944	+	0.678260i	0.718914	+	0.695099i	$0.244640\pi$
$758$	−1046.25	−	232.675i	−1.38028	−	0.306959i
$759$		0			0
$760$	701.330	−	403.060i	0.922802	−	0.530343i
$761$	−60.9342	−	60.9342i	−0.0800712	−	0.0800712i	0.665937	−	0.746008i	$-0.268032\pi$
$761$	−60.9342	−	60.9342i	−0.0800712	−	0.0800712i	−0.746008	+	0.665937i	$0.768032\pi$
$762$		0			0
$763$	−80.1175	+	193.421i	−0.105003	+	0.253500i
$764$	90.7333	+	250.317i	0.118761	+	0.327640i
$765$		0			0
$766$	−1193.35	+	209.607i	−1.55790	+	0.273638i
$767$		−	634.135i		−	0.826773i
$768$		0			0
$769$	387.688			0.504146			0.252073	−	0.967708i	$-0.418888\pi$
$769$	387.688			0.504146			0.252073	+	0.967708i	$0.418888\pi$
$770$	−109.033	−	620.755i	−0.141601	−	0.806176i
$771$		0			0
$772$	−1037.47	+	376.054i	−1.34387	+	0.487117i
$773$	−19.2892	−	7.98984i	−0.0249537	−	0.0103361i	0.370172	−	0.928963i	$-0.379299\pi$
$773$	−19.2892	−	7.98984i	−0.0249537	−	0.0103361i	−0.395125	+	0.918627i	$0.629299\pi$
$774$		0			0
$775$	−443.154	+	443.154i	−0.571812	+	0.571812i
$776$	253.988	+	441.942i	0.327304	+	0.569513i
$777$		0			0
$778$	200.462	−	901.404i	0.257663	−	1.15862i
$779$	−186.085	−	77.0791i	−0.238877	−	0.0989462i
$780$		0			0
$781$	−22.4183	+	9.28595i	−0.0287046	+	0.0118898i
$782$	553.412	+	388.049i	0.707688	+	0.496226i
$783$		0			0
$784$	129.990	+	155.750i	0.165803	+	0.198661i
$785$		−	1504.16i		−	1.91613i
$786$		0			0
$787$	521.707	+	1259.51i	0.662906	+	1.60040i	0.793228	+	0.608925i	$0.208399\pi$
$787$	521.707	+	1259.51i	0.662906	+	1.60040i	−0.130321	+	0.991472i	$0.541601\pi$
$788$	723.606	+	32.5520i	0.918282	+	0.0413096i
$789$		0			0
$790$	306.787	−	1379.51i	0.388338	−	1.74622i
$791$	536.619	+	536.619i	0.678406	+	0.678406i
$792$		0			0
$793$	102.614	+	102.614i	0.129400	+	0.129400i
$794$	−342.140	−	537.836i	−0.430907	−	0.677376i
$795$		0			0
$796$	559.870	−	1196.51i	0.703354	−	1.50316i
$797$	397.554	+	959.781i	0.498813	+	1.20424i	0.950123	+	0.311875i	$0.100957\pi$
$797$	397.554	+	959.781i	0.498813	+	1.20424i	−0.451310	+	0.892367i	$0.649043\pi$
$798$		0			0
$799$		−	663.921i		−	0.830940i
$800$	−95.9300	−	1139.87i	−0.119912	−	1.42484i
$801$		0			0
$802$	−95.4475	+	16.7649i	−0.119012	+	0.0209039i
$803$	−269.539	+	111.647i	−0.335665	+	0.139037i
$804$		0			0
$805$	−596.657	−	247.143i	−0.741189	−	0.307010i
$806$	−257.894	+	164.057i	−0.319967	+	0.203544i
$807$		0			0
$808$	16.0650	+	123.925i	0.0198825	+	0.153372i
$809$	349.674	−	349.674i	0.432230	−	0.432230i	−0.457157	−	0.889386i	$-0.651132\pi$
$809$	349.674	−	349.674i	0.432230	−	0.432230i	0.889386	+	0.457157i	$0.151132\pi$
$810$		0			0
$811$	179.312	+	74.2736i	0.221100	+	0.0915827i	0.490484	−	0.871450i	$-0.336820\pi$
$811$	179.312	+	74.2736i	0.221100	+	0.0915827i	−0.269384	+	0.963033i	$0.586820\pi$
$812$	−369.004	−	16.5999i	−0.454439	−	0.0204433i
$813$		0			0
$814$	300.459	−	428.496i	0.369114	−	0.526408i
$815$	1115.65			1.36889
$816$		0			0
$817$		−	314.574i		−	0.385035i
$818$	−393.032	+	560.519i	−0.480479	+	0.685231i
$819$		0			0
$820$	−357.299	+	326.536i	−0.435730	+	0.398214i
$821$	41.2552	−	99.5988i	0.0502499	−	0.121314i	−0.896761	−	0.442515i	$-0.854086\pi$
$821$	41.2552	−	99.5988i	0.0502499	−	0.121314i	0.947011	+	0.321201i	$0.104086\pi$
$822$		0			0
$823$	−818.928	−	818.928i	−0.995053	−	0.995053i	0.00493500	−	0.999988i	$-0.498429\pi$
$823$	−818.928	−	818.928i	−0.995053	−	0.995053i	−0.999988	+	0.00493500i	$0.998429\pi$
$824$	−105.912	−	28.6043i	−0.128534	−	0.0347140i
$825$		0			0
$826$	739.834	−	470.639i	0.895683	−	0.569781i
$827$	−30.9529	+	74.7270i	−0.0374280	+	0.0903591i	−0.941488	−	0.337046i	$-0.890572\pi$
$827$	−30.9529	+	74.7270i	−0.0374280	+	0.0903591i	0.904060	+	0.427405i	$0.140572\pi$
$828$		0			0
$829$	87.1070	+	210.295i	0.105075	+	0.253673i	0.967669	−	0.252223i	$-0.0811618\pi$
$829$	87.1070	+	210.295i	0.105075	+	0.253673i	−0.862594	+	0.505896i	$0.831162\pi$
$830$	−1577.46	+	277.073i	−1.90055	+	0.333823i
$831$		0			0
$832$	75.0123	−	552.821i	0.0901591	−	0.664449i
$833$	−311.658			−0.374140
$834$		0			0
$835$	−1117.63	+	462.937i	−1.33848	+	0.554416i
$836$	118.638	+	327.301i	0.141911	+	0.391508i
$837$		0			0
$838$	189.698	+	298.201i	0.226370	+	0.355848i
$839$	−500.637	+	500.637i	−0.596707	+	0.596707i	−0.939435	−	0.342728i	$-0.888649\pi$
$839$	−500.637	+	500.637i	−0.596707	+	0.596707i	0.342728	+	0.939435i	$0.388649\pi$
$840$		0			0
$841$	428.660	−	428.660i	0.509703	−	0.509703i
$842$	−293.432	+	1319.46i	−0.348494	+	1.56705i
$843$		0			0
$844$	−230.650	−	252.379i	−0.273281	−	0.299027i
$845$	669.771	−	277.428i	0.792628	−	0.328317i
$846$		0			0
$847$	−457.973			−0.540701
$848$	−424.093	−	1357.56i	−0.500109	−	1.60089i
$849$		0			0
$850$	1438.85	+	1008.91i	1.69277	+	1.18696i
$851$	−205.218	−	495.439i	−0.241149	−	0.582184i
$852$		0			0
$853$	222.935	−	538.212i	0.261354	−	0.630964i	−0.737669	−	0.675162i	$-0.764074\pi$
$853$	222.935	−	538.212i	0.261354	−	0.630964i	0.999023	+	0.0441988i	$0.0140735\pi$
$854$	−43.5605	+	195.876i	−0.0510076	+	0.229363i
$855$		0			0
$856$	−153.765	−	1186.13i	−0.179632	−	1.38567i
$857$	172.645	+	172.645i	0.201453	+	0.201453i	0.800622	−	0.599169i	$-0.204502\pi$
$857$	172.645	+	172.645i	0.201453	+	0.201453i	−0.599169	+	0.800622i	$0.704502\pi$
$858$		0			0
$859$	66.9122	−	161.540i	0.0778954	−	0.188056i	−0.880135	−	0.474724i	$-0.842548\pi$
$859$	66.9122	−	161.540i	0.0778954	−	0.188056i	0.958030	+	0.286668i	$0.0925477\pi$
$860$	−684.712	−	320.389i	−0.796177	−	0.372546i
$861$		0			0
$862$	209.849	+	1194.73i	0.243444	+	1.38600i
$863$			325.900i			0.377636i	0.982012	+	0.188818i	$0.0604656\pi$
$863$			325.900i			0.377636i	−0.982012	+	0.188818i	$0.939534\pi$
$864$		0			0
$865$	−2422.77			−2.80089
$866$	7.54396	−	1.32506i	0.00871127	−	0.00153009i
$867$		0			0
$868$	−382.805	−	179.121i	−0.441019	−	0.206361i
$869$	561.927	+	232.758i	0.646637	+	0.267846i
$870$		0			0
$871$	661.942	−	661.942i	0.759980	−	0.759980i
$872$	−220.143	−	169.616i	−0.252457	−	0.194514i
$873$		0			0
$874$	348.226	+	77.4415i	0.398428	+	0.0886058i
$875$	−466.375	−	193.179i	−0.533000	−	0.220776i
$876$		0			0
$877$	93.3817	−	38.6800i	0.106479	−	0.0441049i	−0.328808	−	0.944397i	$-0.606647\pi$
$877$	93.3817	−	38.6800i	0.106479	−	0.0441049i	0.435287	+	0.900292i	$0.356647\pi$
$878$	−59.0089	+	84.1550i	−0.0672083	+	0.0958485i
$879$		0			0
$880$	833.246	+	75.1204i	0.946870	+	0.0853641i
$881$			129.296i			0.146760i	0.997304	+	0.0733801i	$0.0233786\pi$
$881$			129.296i			0.146760i	−0.997304	+	0.0733801i	$0.976621\pi$
$882$		0			0
$883$	28.1493	+	67.9584i	0.0318792	+	0.0769631i	0.939017	−	0.343870i	$-0.111738\pi$
$883$	28.1493	+	67.9584i	0.0318792	+	0.0769631i	−0.907138	+	0.420833i	$0.861738\pi$
$884$	578.186	+	632.657i	0.654056	+	0.715675i
$885$		0			0
$886$	−1063.36	−	236.478i	−1.20018	−	0.266905i
$887$	−338.588	−	338.588i	−0.381723	−	0.381723i	0.490000	−	0.871723i	$-0.336997\pi$
$887$	−338.588	−	338.588i	−0.381723	−	0.381723i	−0.871723	+	0.490000i	$0.836997\pi$
$888$		0			0
$889$	338.431	+	338.431i	0.380687	+	0.380687i
$890$	2032.82	−	1293.16i	2.28407	−	1.45299i
$891$		0			0
$892$	509.048	+	1404.37i	0.570682	+	1.57441i
$893$	−134.096	−	323.736i	−0.150163	−	0.362526i
$894$		0			0
$895$			996.837i			1.11378i
$896$	700.640	−	322.775i	0.781964	−	0.360240i
$897$		0			0
$898$	149.355	+	850.322i	0.166320	+	0.946907i
$899$	−248.188	+	102.803i	−0.276071	+	0.114352i
$900$		0			0
$901$	2018.64	+	836.148i	2.24045	+	0.928023i
$902$	−111.814	−	175.770i	−0.123963	−	0.194867i
$903$		0			0
$904$	−873.415	+	501.959i	−0.966167	+	0.555265i
$905$	−560.535	+	560.535i	−0.619375	+	0.619375i
$906$		0			0
$907$	1031.84	+	427.401i	1.13764	+	0.471225i	0.870371	−	0.492397i	$-0.163879\pi$
$907$	1031.84	+	427.401i	1.13764	+	0.471225i	0.267268	+	0.963622i	$0.413879\pi$
$908$	24.6716	−	22.5474i	0.0271713	−	0.0248319i
$909$		0			0
$910$	−670.500	−	470.150i	−0.736814	−	0.516649i
$911$	−857.136			−0.940873			−0.470437	−	0.882434i	$-0.655904\pi$
$911$	−857.136			−0.940873			−0.470437	+	0.882434i	$0.655904\pi$
$912$		0			0
$913$		−	689.307i		−	0.754992i
$914$	433.187	+	303.748i	0.473947	+	0.332328i
$915$		0			0
$916$	714.534	+	32.1439i	0.780059	+	0.0350916i
$917$	−132.968	+	321.014i	−0.145004	+	0.350070i
$918$		0			0
$919$	447.382	+	447.382i	0.486814	+	0.486814i	0.907299	−	0.420486i	$-0.138140\pi$
$919$	447.382	+	447.382i	0.486814	+	0.486814i	−0.420486	+	0.907299i	$0.638140\pi$
$920$	523.226	−	679.088i	0.568724	−	0.738140i
$921$		0			0
$922$	294.879	+	463.544i	0.319826	+	0.502759i
$923$	−12.0655	+	29.1286i	−0.0130720	+	0.0315586i
$924$		0			0
$925$	−533.558	−	1288.12i	−0.576820	−	1.39257i
$926$	264.771	+	1507.42i	0.285929	+	1.62788i
$927$		0			0
$928$	148.988	−	467.140i	0.160548	−	0.503384i
$929$	357.338			0.384648			0.192324	−	0.981332i	$-0.438398\pi$
$929$	357.338			0.384648			0.192324	+	0.981332i	$0.438398\pi$
$930$		0			0
$931$	−151.968	+	62.9473i	−0.163231	+	0.0676125i
$932$	33.6117	−	71.8324i	0.0360641	−	0.0770734i
$933$		0			0
$934$	488.090	−	310.494i	0.522580	−	0.332435i
$935$	−908.827	+	908.827i	−0.972007	+	0.972007i
$936$		0			0
$937$	−504.116	+	504.116i	−0.538011	+	0.538011i	−0.922944	−	0.384934i	$-0.874224\pi$
$937$	−504.116	+	504.116i	−0.538011	+	0.538011i	0.384934	+	0.922944i	$0.374224\pi$
$938$	1263.55	+	281.000i	1.34707	+	0.299573i
$939$		0			0
$940$	−841.229	−	37.8433i	−0.894924	−	0.0402589i
$941$	503.223	−	208.442i	0.534775	−	0.221511i	−0.0989183	−	0.995096i	$-0.531538\pi$
$941$	503.223	−	208.442i	0.534775	−	0.221511i	0.633693	+	0.773585i	$0.281538\pi$
$942$		0			0
$943$	−213.463			−0.226366
$944$	347.070	+	1111.00i	0.367659	+	1.17691i
$945$		0			0
$946$	186.792	−	266.392i	0.197455	−	0.281598i
$947$	137.566	+	332.113i	0.145265	+	0.350700i	0.979719	−	0.200378i	$-0.0642169\pi$
$947$	137.566	+	332.113i	0.145265	+	0.350700i	−0.834454	+	0.551077i	$0.814217\pi$
$948$		0			0
$949$	−145.065	+	350.219i	−0.152861	+	0.369040i
$950$	905.376	+	201.345i	0.953028	+	0.211942i
$951$		0			0
$952$	−308.995	+	1144.10i	−0.324574	+	1.20179i
$953$	−129.115	−	129.115i	−0.135483	−	0.135483i	0.636113	−	0.771596i	$-0.280541\pi$
$953$	−129.115	−	129.115i	−0.135483	−	0.135483i	−0.771596	+	0.636113i	$0.780541\pi$
$954$		0			0
$955$	−198.535	+	479.306i	−0.207890	+	0.501891i
$956$	−868.508	+	314.811i	−0.908481	+	0.329300i
$957$		0			0
$958$	311.351	−	54.6874i	0.325001	−	0.0570850i
$959$			432.422i			0.450909i
$960$		0			0
$961$	653.628			0.680154
$962$	−117.636	−	669.735i	−0.122283	−	0.696190i
$963$		0			0
$964$	151.860	+	418.954i	0.157531	+	0.434600i
$965$	−1986.54	−	822.851i	−2.05859	−	0.852695i
$966$		0			0
$967$	657.007	−	657.007i	0.679428	−	0.679428i	−0.280443	−	0.959871i	$-0.590481\pi$
$967$	657.007	−	657.007i	0.679428	−	0.679428i	0.959871	+	0.280443i	$0.0904813\pi$
$968$	158.508	−	586.901i	0.163748	−	0.606303i
$969$		0			0
$970$	−215.611	+	969.524i	−0.222279	+	0.999509i
$971$	654.912	+	271.274i	0.674472	+	0.279376i	0.693514	−	0.720443i	$-0.256062\pi$
$971$	654.912	+	271.274i	0.674472	+	0.279376i	−0.0190418	+	0.999819i	$0.506062\pi$
$972$		0			0
$973$	802.830	−	332.543i	0.825108	−	0.341771i
$974$	1563.46	+	1096.29i	1.60519	+	1.12555i
$975$		0			0
$976$	−235.942	−	123.618i	−0.241744	−	0.126657i
$977$			1493.20i			1.52835i	0.645010	+	0.764174i	$0.276853\pi$
$977$			1493.20i			1.52835i	−0.645010	+	0.764174i	$0.723147\pi$
$978$		0			0
$979$	396.811	+	957.986i	0.405323	+	0.978536i
$980$	−17.7644	+	394.890i	−0.0181270	+	0.402949i
$981$		0			0
$982$	−40.9426	+	184.104i	−0.0416931	+	0.187479i
$983$	856.189	+	856.189i	0.870996	+	0.870996i	0.992581	−	0.121585i	$-0.0387976\pi$
$983$	856.189	+	856.189i	0.870996	+	0.870996i	−0.121585	+	0.992581i	$0.538798\pi$
$984$		0			0
$985$	997.994	+	997.994i	1.01319	+	1.01319i
$986$	404.309	+	635.565i	0.410050	+	0.644590i
$987$		0			0
$988$	409.711	+	191.711i	0.414687	+	0.194040i
$989$	−127.582	−	308.010i	−0.129001	−	0.311435i
$990$		0			0
$991$			1223.32i			1.23443i	0.786793	+	0.617217i	$0.211740\pi$
$991$			1223.32i			1.23443i	−0.786793	+	0.617217i	$0.788260\pi$
$992$	362.039	−	428.576i	0.364958	−	0.432032i
$993$		0			0
$994$	−42.9385	+	7.54196i	−0.0431977	+	0.00758748i
$995$	2378.08	−	985.034i	2.39003	−	0.989984i
$996$		0			0
$997$	604.001	+	250.185i	0.605819	+	0.250938i	0.664440	−	0.747342i	$-0.268670\pi$
$997$	604.001	+	250.185i	0.605819	+	0.250938i	−0.0586209	+	0.998280i	$0.518670\pi$
$998$	726.761	−	462.323i	0.728217	−	0.463249i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.3.u.a.91.3		28
3.2	odd	2		32.3.h.a.27.5	yes	28
12.11	even	2		128.3.h.a.15.6		28
24.5	odd	2		256.3.h.b.31.6		28
24.11	even	2		256.3.h.a.31.2		28
32.19	odd	8	inner	288.3.u.a.19.3		28
96.29	odd	8		256.3.h.a.223.2		28
96.35	even	8		256.3.h.b.223.6		28
96.77	odd	8		128.3.h.a.111.6		28
96.83	even	8		32.3.h.a.19.5	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.19.5	✓	28	96.83	even	8
32.3.h.a.27.5	yes	28	3.2	odd	2
128.3.h.a.15.6		28	12.11	even	2
128.3.h.a.111.6		28	96.77	odd	8
256.3.h.a.31.2		28	24.11	even	2
256.3.h.a.223.2		28	96.29	odd	8
256.3.h.b.31.6		28	24.5	odd	2
256.3.h.b.223.6		28	96.35	even	8
288.3.u.a.19.3		28	32.19	odd	8	inner
288.3.u.a.91.3		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)

\(f(q)\)	\(=\)	\(q+(-0.345994 - 1.96984i) q^{2} +(-3.76058 + 1.36311i) q^{4} +(-7.20074 - 2.98264i) q^{5} +(4.26150 - 4.26150i) q^{7} +(3.98625 + 6.93612i) q^{8} +O(q^{10})\)	\(q+(-0.345994 - 1.96984i) q^{2} +(-3.76058 + 1.36311i) q^{4} +(-7.20074 - 2.98264i) q^{5} +(4.26150 - 4.26150i) q^{7} +(3.98625 + 6.93612i) q^{8} +(-3.38393 + 15.2163i) q^{10} +(-6.19818 - 2.56737i) q^{11} +(-8.05345 + 3.33585i) q^{13} +(-9.86895 - 6.92004i) q^{14} +(12.2839 - 10.2522i) q^{16} +24.5802i q^{17} +(4.96459 + 11.9856i) q^{19} +(31.1446 + 1.40106i) q^{20} +(-2.91279 + 13.0978i) q^{22} +(9.72199 + 9.72199i) q^{23} +(25.2768 + 25.2768i) q^{25} +(9.35754 + 14.7099i) q^{26} +(-10.2168 + 21.8346i) q^{28} +(5.86371 + 14.1563i) q^{29} +17.5320i q^{31} +(-24.4453 - 20.6501i) q^{32} +(48.4192 - 8.50460i) q^{34} +(-43.3965 + 17.9754i) q^{35} +(-36.0346 - 14.9260i) q^{37} +(21.8920 - 13.9264i) q^{38} +(-8.01597 - 61.8348i) q^{40} +(-10.9784 + 10.9784i) q^{41} +(-22.4024 - 9.27937i) q^{43} +(26.8084 + 1.20599i) q^{44} +(15.7871 - 22.5146i) q^{46} -27.0104 q^{47} +12.6792i q^{49} +(41.0458 - 58.5371i) q^{50} +(25.7385 - 23.5224i) q^{52} +(34.0172 - 82.1247i) q^{53} +(36.9740 + 36.9740i) q^{55} +(46.5457 + 12.5709i) q^{56} +(25.8568 - 16.4486i) q^{58} +(-27.8391 + 67.2095i) q^{59} +(-6.37082 - 15.3805i) q^{61} +(34.5354 - 6.06598i) q^{62} +(-32.2196 + 55.2983i) q^{64} +67.9404 q^{65} +(-99.2165 + 41.0968i) q^{67} +(-33.5055 - 92.4357i) q^{68} +(50.4237 + 79.2650i) q^{70} +(2.55754 - 2.55754i) q^{71} +(30.7498 - 30.7498i) q^{73} +(-16.9342 + 76.1469i) q^{74} +(-35.0074 - 38.3054i) q^{76} +(-37.3544 + 15.4727i) q^{77} -90.6600 q^{79} +(-119.031 + 37.1847i) q^{80} +(25.4241 + 17.8272i) q^{82} +(39.3191 + 94.9247i) q^{83} +(73.3140 - 176.996i) q^{85} +(-10.5278 + 47.3398i) q^{86} +(-6.89991 - 53.2256i) q^{88} +(-109.290 - 109.290i) q^{89} +(-20.1040 + 48.5355i) q^{91} +(-49.8124 - 23.3081i) q^{92} +(9.34545 + 53.2063i) q^{94} -101.113i q^{95} +63.7161 q^{97} +(24.9761 - 4.38694i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 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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