LMFDB - Embedded newform 288.3.u.a.163.1

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			163.1
Character	$\chi$	$=$	288.163
Dual form			288.3.u.a.235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93931 + 0.488972i) q^{2} +(3.52181 - 1.89653i) q^{4} +(1.85856 + 4.48696i) q^{5} +(-5.27676 - 5.27676i) q^{7} +(-5.90252 + 5.40002i) q^{8} +O(q^{10})$	\(q+(-1.93931 + 0.488972i) q^{2} +(3.52181 - 1.89653i) q^{4} +(1.85856 + 4.48696i) q^{5} +(-5.27676 - 5.27676i) q^{7} +(-5.90252 + 5.40002i) q^{8} +(-5.79831 - 7.79280i) q^{10} +(-6.20050 - 14.9693i) q^{11} +(-4.22532 + 10.2008i) q^{13} +(12.8134 + 7.65307i) q^{14} +(8.80634 - 13.3585i) q^{16} +2.84356i q^{17} +(-12.4276 - 5.14768i) q^{19} +(15.0551 + 12.2774i) q^{20} +(19.3443 + 25.9983i) q^{22} +(1.43918 - 1.43918i) q^{23} +(0.999126 - 0.999126i) q^{25} +(3.20628 - 21.8486i) q^{26} +(-28.5913 - 8.57623i) q^{28} +(-36.9596 - 15.3092i) q^{29} -4.73823i q^{31} +(-10.5463 + 30.2122i) q^{32} +(-1.39042 - 5.51453i) q^{34} +(13.8694 - 33.4838i) q^{35} +(-6.68390 - 16.1364i) q^{37} +(26.6180 + 3.90618i) q^{38} +(-35.1998 - 16.4481i) q^{40} +(-40.4523 - 40.4523i) q^{41} +(-24.5000 - 59.1482i) q^{43} +(-50.2268 - 40.9598i) q^{44} +(-2.08729 + 3.49473i) q^{46} +16.5262 q^{47} +6.68842i q^{49} +(-1.44907 + 2.42615i) q^{50} +(4.46539 + 43.9389i) q^{52} +(46.9950 - 19.4659i) q^{53} +(55.6428 - 55.6428i) q^{55} +(59.6408 + 2.65160i) q^{56} +(79.1617 + 11.6170i) q^{58} +(-50.0578 + 20.7346i) q^{59} +(-54.3116 - 22.4966i) q^{61} +(2.31686 + 9.18889i) q^{62} +(5.67958 - 63.7475i) q^{64} -53.6237 q^{65} +(-25.5017 + 61.5665i) q^{67} +(5.39290 + 10.0145i) q^{68} +(-10.5245 + 71.7170i) q^{70} +(-7.12641 - 7.12641i) q^{71} +(55.3669 + 55.3669i) q^{73} +(20.8524 + 28.0251i) q^{74} +(-53.5304 + 5.44015i) q^{76} +(-46.2711 + 111.708i) q^{77} +11.0986 q^{79} +(76.3059 + 14.6862i) q^{80} +(98.2293 + 58.6693i) q^{82} +(29.9476 + 12.4047i) q^{83} +(-12.7589 + 5.28492i) q^{85} +(76.4348 + 102.727i) q^{86} +(117.433 + 54.8740i) q^{88} +(-16.7667 + 16.7667i) q^{89} +(76.1234 - 31.5313i) q^{91} +(2.33907 - 7.79797i) q^{92} +(-32.0494 + 8.08086i) q^{94} -65.3294i q^{95} -67.8301 q^{97} +(-3.27045 - 12.9709i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$	$-1$

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 $

$2$	−1.93931	+	0.488972i	−0.969653	+	0.244486i
$2$	−1.93931	+	0.488972i	−0.969653	+	0.244486i
$3$		0			0
$3$		0			0
$4$	3.52181	−	1.89653i	0.880453	−	0.474133i
$5$	1.85856	+	4.48696i	0.371712	+	0.897391i	0.993461	+	0.114175i	$0.0364224\pi$
$5$	1.85856	+	4.48696i	0.371712	+	0.897391i	−0.621749	+	0.783217i	$0.713578\pi$
$6$		0			0
$7$	−5.27676	−	5.27676i	−0.753823	−	0.753823i	0.221367	−	0.975190i	$-0.428948\pi$
$7$	−5.27676	−	5.27676i	−0.753823	−	0.753823i	−0.975190	+	0.221367i	$0.928948\pi$
$8$	−5.90252	+	5.40002i	−0.737816	+	0.675002i
$9$		0			0
$10$	−5.79831	−	7.79280i	−0.579831	−	0.779280i
$11$	−6.20050	−	14.9693i	−0.563682	−	1.36085i	−0.906802	−	0.421557i	$-0.861484\pi$
$11$	−6.20050	−	14.9693i	−0.563682	−	1.36085i	0.343120	−	0.939292i	$-0.388516\pi$
$12$		0			0
$13$	−4.22532	+	10.2008i	−0.325025	+	0.784680i	0.673922	+	0.738802i	$0.264608\pi$
$13$	−4.22532	+	10.2008i	−0.325025	+	0.784680i	−0.998947	+	0.0458772i	$0.985392\pi$
$14$	12.8134	+	7.65307i	0.915246	+	0.546648i
$15$		0			0
$16$	8.80634	−	13.3585i	0.550396	−	0.834903i
$17$			2.84356i			0.167268i	0.996497	+	0.0836341i	$0.0266527\pi$
$17$			2.84356i			0.167268i	−0.996497	+	0.0836341i	$0.973347\pi$
$18$		0			0
$19$	−12.4276	−	5.14768i	−0.654084	−	0.270931i	0.0308626	−	0.999524i	$-0.490175\pi$
$19$	−12.4276	−	5.14768i	−0.654084	−	0.270931i	−0.684947	+	0.728593i	$0.740175\pi$
$20$	15.0551	+	12.2774i	0.752757	+	0.613871i
$21$		0			0
$22$	19.3443	+	25.9983i	0.879284	+	1.18174i
$23$	1.43918	−	1.43918i	0.0625730	−	0.0625730i	−0.675128	−	0.737701i	$-0.735912\pi$
$23$	1.43918	−	1.43918i	0.0625730	−	0.0625730i	0.737701	+	0.675128i	$0.235912\pi$
$24$		0			0
$25$	0.999126	−	0.999126i	0.0399650	−	0.0399650i
$26$	3.20628	−	21.8486i	0.123318	−	0.840331i
$27$		0			0
$28$	−28.5913	−	8.57623i	−1.02112	−	0.306294i
$29$	−36.9596	−	15.3092i	−1.27447	−	0.527902i	−0.360148	−	0.932895i	$-0.617274\pi$
$29$	−36.9596	−	15.3092i	−1.27447	−	0.527902i	−0.914320	+	0.404993i	$0.867274\pi$
$30$		0			0
$31$		−	4.73823i		−	0.152846i	−0.997075	−	0.0764231i	$-0.975650\pi$
$31$		−	4.73823i		−	0.152846i	0.997075	−	0.0764231i	$-0.0243500\pi$
$32$	−10.5463	+	30.2122i	−0.329572	+	0.944131i
$33$		0			0
$34$	−1.39042	−	5.51453i	−0.0408947	−	0.162192i
$35$	13.8694	−	33.4838i	0.396269	−	0.956679i
$36$		0			0
$37$	−6.68390	−	16.1364i	−0.180646	−	0.436118i	0.807454	−	0.589930i	$-0.200845\pi$
$37$	−6.68390	−	16.1364i	−0.180646	−	0.436118i	−0.988100	+	0.153812i	$0.950845\pi$
$38$	26.6180	+	3.90618i	0.700473	+	0.102794i
$39$		0			0
$40$	−35.1998	−	16.4481i	−0.879996	−	0.411203i
$41$	−40.4523	−	40.4523i	−0.986641	−	0.986641i	0.0132711	−	0.999912i	$-0.495776\pi$
$41$	−40.4523	−	40.4523i	−0.986641	−	0.986641i	−0.999912	+	0.0132711i	$0.995776\pi$
$42$		0			0
$43$	−24.5000	−	59.1482i	−0.569767	−	1.37554i	−0.901751	−	0.432255i	$-0.857718\pi$
$43$	−24.5000	−	59.1482i	−0.569767	−	1.37554i	0.331984	−	0.943285i	$-0.392282\pi$
$44$	−50.2268	−	40.9598i	−1.14152	−	0.930904i
$45$		0			0
$46$	−2.08729	+	3.49473i	−0.0453759	+	0.0759723i
$47$	16.5262			0.351622			0.175811	−	0.984424i	$-0.443745\pi$
$47$	16.5262			0.351622			0.175811	+	0.984424i	$0.443745\pi$
$48$		0			0
$49$			6.68842i			0.136498i
$50$	−1.44907	+	2.42615i	−0.0289813	+	0.0485231i
$51$		0			0
$52$	4.46539	+	43.9389i	0.0858729	+	0.844979i
$53$	46.9950	−	19.4659i	0.886697	−	0.367282i	0.107607	−	0.994194i	$-0.465681\pi$
$53$	46.9950	−	19.4659i	0.886697	−	0.367282i	0.779090	+	0.626912i	$0.215681\pi$
$54$		0			0
$55$	55.6428	−	55.6428i	1.01169	−	1.01169i
$56$	59.6408	+	2.65160i	1.06501	+	0.0473500i
$57$		0			0
$58$	79.1617	+	11.6170i	1.36486	+	0.200292i
$59$	−50.0578	+	20.7346i	−0.848437	+	0.351434i	−0.764174	−	0.645010i	$-0.776853\pi$
$59$	−50.0578	+	20.7346i	−0.848437	+	0.351434i	−0.0842623	+	0.996444i	$0.526853\pi$
$60$		0			0
$61$	−54.3116	−	22.4966i	−0.890353	−	0.368796i	−0.109850	−	0.993948i	$-0.535037\pi$
$61$	−54.3116	−	22.4966i	−0.890353	−	0.368796i	−0.780503	+	0.625152i	$0.785037\pi$
$62$	2.31686	+	9.18889i	0.0373687	+	0.148208i
$63$		0			0
$64$	5.67958	−	63.7475i	0.0887435	−	0.996055i
$65$	−53.6237			−0.824980
$66$		0			0
$67$	−25.5017	+	61.5665i	−0.380622	+	0.918904i	0.611223	+	0.791458i	$0.290678\pi$
$67$	−25.5017	+	61.5665i	−0.380622	+	0.918904i	−0.991846	+	0.127445i	$0.959322\pi$
$68$	5.39290	+	10.0145i	0.0793073	+	0.147272i
$69$		0			0
$70$	−10.5245	+	71.7170i	−0.150349	+	1.02453i
$71$	−7.12641	−	7.12641i	−0.100372	−	0.100372i	0.655138	−	0.755510i	$-0.272611\pi$
$71$	−7.12641	−	7.12641i	−0.100372	−	0.100372i	−0.755510	+	0.655138i	$0.772611\pi$
$72$		0			0
$73$	55.3669	+	55.3669i	0.758451	+	0.758451i	0.976040	−	0.217590i	$-0.0698194\pi$
$73$	55.3669	+	55.3669i	0.758451	+	0.758451i	−0.217590	+	0.976040i	$0.569819\pi$
$74$	20.8524	+	28.0251i	0.281789	+	0.378718i
$75$		0			0
$76$	−53.5304	+	5.44015i	−0.704348	+	0.0715809i
$77$	−46.2711	+	111.708i	−0.600923	+	1.45076i
$78$		0			0
$79$	11.0986			0.140489			0.0702446	−	0.997530i	$-0.477622\pi$
$79$	11.0986			0.140489			0.0702446	+	0.997530i	$0.477622\pi$
$80$	76.3059	+	14.6862i	0.953824	+	0.183578i
$81$		0			0
$82$	98.2293	+	58.6693i	1.19792	+	0.715480i
$83$	29.9476	+	12.4047i	0.360814	+	0.149454i	0.555724	−	0.831367i	$-0.312441\pi$
$83$	29.9476	+	12.4047i	0.360814	+	0.149454i	−0.194909	+	0.980821i	$0.562441\pi$
$84$		0			0
$85$	−12.7589	+	5.28492i	−0.150105	+	0.0621755i
$86$	76.4348	+	102.727i	0.888777	+	1.19450i
$87$		0			0
$88$	117.433	+	54.8740i	1.33447	+	0.623569i
$89$	−16.7667	+	16.7667i	−0.188390	+	0.188390i	−0.795000	−	0.606610i	$-0.792529\pi$
$89$	−16.7667	+	16.7667i	−0.188390	+	0.188390i	0.606610	+	0.795000i	$0.292529\pi$
$90$		0			0
$91$	76.1234	−	31.5313i	0.836521	−	0.346498i
$92$	2.33907	−	7.79797i	0.0254247	−	0.0847606i
$93$		0			0
$94$	−32.0494	+	8.08086i	−0.340951	+	0.0859666i
$95$		−	65.3294i		−	0.687678i
$96$		0			0
$97$	−67.8301			−0.699280			−0.349640	−	0.936884i	$-0.613696\pi$
$97$	−67.8301			−0.699280			−0.349640	+	0.936884i	$0.613696\pi$
$98$	−3.27045	−	12.9709i	−0.0333719	−	0.132356i
$99$		0			0
$100$	1.62386	−	5.41361i	0.0162386	−	0.0541361i
$101$	45.6943	+	110.316i	0.452419	+	1.09224i	0.971400	+	0.237450i	$0.0763115\pi$
$101$	45.6943	+	110.316i	0.452419	+	1.09224i	−0.518981	+	0.854786i	$0.673689\pi$
$102$		0			0
$103$	61.7093	+	61.7093i	0.599120	+	0.599120i	0.940078	−	0.340959i	$-0.110752\pi$
$103$	61.7093	+	61.7093i	0.599120	+	0.599120i	−0.340959	+	0.940078i	$0.610752\pi$
$104$	−30.1446	−	83.0275i	−0.289852	−	0.798341i
$105$		0			0
$106$	−81.6193	+	60.7296i	−0.769993	+	0.572921i
$107$	−7.13652	−	17.2291i	−0.0666965	−	0.161020i	0.887017	−	0.461737i	$-0.152774\pi$
$107$	−7.13652	−	17.2291i	−0.0666965	−	0.161020i	−0.953713	+	0.300718i	$0.902774\pi$
$108$		0			0
$109$	−75.1681	+	181.472i	−0.689616	+	1.66488i	0.0559384	+	0.998434i	$0.482185\pi$
$109$	−75.1681	+	181.472i	−0.689616	+	1.66488i	−0.745554	+	0.666445i	$0.767815\pi$
$110$	−80.7006	+	135.116i	−0.733642	+	1.22833i
$111$		0			0
$112$	−116.958	+	24.0204i	−1.04427	+	0.214468i
$113$		−	156.784i		−	1.38747i	−0.720232	−	0.693734i	$-0.755965\pi$
$113$		−	156.784i		−	1.38747i	0.720232	−	0.693734i	$-0.244035\pi$
$114$		0			0
$115$	9.13234	+	3.78274i	0.0794116	+	0.0328934i
$116$	−159.199	+	16.1790i	−1.37241	+	0.139474i
$117$		0			0
$118$	86.9387	−	64.6876i	0.736769	−	0.548200i
$119$	15.0048	−	15.0048i	0.126091	−	0.126091i
$120$		0			0
$121$	−100.075	+	100.075i	−0.827066	+	0.827066i
$122$	116.327	+	17.0710i	0.953499	+	0.139926i
$123$		0			0
$124$	−8.98621	−	16.6872i	−0.0724694	−	0.134574i
$125$	118.514	+	49.0901i	0.948111	+	0.392720i
$126$		0			0
$127$		−	192.971i		−	1.51946i	−0.650240	−	0.759729i	$-0.725332\pi$
$127$		−	192.971i		−	1.51946i	0.650240	−	0.759729i	$-0.274668\pi$
$128$	20.1563	+	126.403i	0.157471	+	0.987524i
$129$		0			0
$130$	103.993	−	26.2205i	0.799944	−	0.201696i
$131$	−18.2599	+	44.0834i	−0.139389	+	0.336515i	−0.978123	−	0.208026i	$-0.933296\pi$
$131$	−18.2599	+	44.0834i	−0.139389	+	0.336515i	0.838734	+	0.544541i	$0.183296\pi$
$132$		0			0
$133$	38.4144	+	92.7406i	0.288830	+	0.697297i
$134$	19.3513	−	131.866i	0.144413	−	0.984074i
$135$		0			0
$136$	−15.3553	−	16.7842i	−0.112906	−	0.123413i
$137$	27.8671	+	27.8671i	0.203409	+	0.203409i	0.801459	−	0.598050i	$-0.204057\pi$
$137$	27.8671	+	27.8671i	0.203409	+	0.203409i	−0.598050	+	0.801459i	$0.704057\pi$
$138$		0			0
$139$	33.3447	+	80.5013i	0.239890	+	0.579146i	0.997271	−	0.0738274i	$-0.0235214\pi$
$139$	33.3447	+	80.5013i	0.239890	+	0.579146i	−0.757381	+	0.652973i	$0.773521\pi$
$140$	−14.6574	−	144.227i	−0.104696	−	1.03020i
$141$		0			0
$142$	17.3049	+	10.3357i	0.121866	+	0.0727865i
$143$	178.899			1.25104
$144$		0			0
$145$		−	194.289i		−	1.33992i
$146$	−134.446	−	80.3005i	−0.920864	−	0.550004i
$147$		0			0
$148$	−54.1426	−	44.1531i	−0.365828	−	0.298331i
$149$	125.860	−	52.1327i	0.844695	−	0.349884i	0.0819919	−	0.996633i	$-0.473872\pi$
$149$	125.860	−	52.1327i	0.844695	−	0.349884i	0.762703	+	0.646749i	$0.223872\pi$
$150$		0			0
$151$	106.254	−	106.254i	0.703672	−	0.703672i	−0.261525	−	0.965197i	$-0.584225\pi$
$151$	106.254	−	106.254i	0.703672	−	0.703672i	0.965197	+	0.261525i	$0.0842254\pi$
$152$	101.152	−	36.7250i	0.665472	−	0.241612i
$153$		0			0
$154$	35.1116	−	239.262i	0.227997	−	1.55365i
$155$	21.2603	−	8.80629i	0.137163	−	0.0568147i
$156$		0			0
$157$	209.345	+	86.7136i	1.33341	+	0.552316i	0.931626	−	0.363419i	$-0.118391\pi$
$157$	209.345	+	86.7136i	1.33341	+	0.552316i	0.401783	+	0.915735i	$0.368391\pi$
$158$	−21.5237	+	5.42692i	−0.136226	+	0.0343476i
$159$		0			0
$160$	−155.162	+	8.83036i	−0.969760	+	0.0551897i
$161$	−15.1884			−0.0943380
$162$		0			0
$163$	−0.176018	+	0.424946i	−0.00107987	+	0.00260703i	−0.924419	−	0.381380i	$-0.875449\pi$
$163$	−0.176018	+	0.424946i	−0.00107987	+	0.00260703i	0.923339	+	0.383987i	$0.125449\pi$
$164$	−219.184	−	65.7464i	−1.33649	−	0.400893i
$165$		0			0
$166$	−64.1431	−	9.41298i	−0.386404	−	0.0567047i
$167$	−96.7499	−	96.7499i	−0.579341	−	0.579341i	0.355381	−	0.934722i	$-0.384351\pi$
$167$	−96.7499	−	96.7499i	−0.579341	−	0.579341i	−0.934722	+	0.355381i	$0.884351\pi$
$168$		0			0
$169$	33.2974	+	33.2974i	0.197026	+	0.197026i
$170$	22.1593	−	16.4878i	0.130349	−	0.0969872i
$171$		0			0
$172$	−198.461	−	161.844i	−1.15384	−	0.940954i
$173$	−102.242	+	246.834i	−0.590994	+	1.42678i	0.291551	+	0.956555i	$0.405829\pi$
$173$	−102.242	+	246.834i	−0.590994	+	1.42678i	−0.882544	+	0.470229i	$0.844171\pi$
$174$		0			0
$175$	−10.5443			−0.0602531
$176$	−254.571	−	48.9960i	−1.44643	−	0.278386i
$177$		0			0
$178$	24.3174	−	40.7143i	0.136614	−	0.228732i
$179$	−269.771	−	111.743i	−1.50710	−	0.624262i	−0.532144	−	0.846654i	$-0.678613\pi$
$179$	−269.771	−	111.743i	−1.50710	−	0.624262i	−0.974957	+	0.222393i	$0.928613\pi$
$180$		0			0
$181$	−33.2079	+	13.7552i	−0.183469	+	0.0759954i	−0.472527	−	0.881316i	$-0.656658\pi$
$181$	−33.2079	+	13.7552i	−0.183469	+	0.0759954i	0.289058	+	0.957312i	$0.406658\pi$
$182$	−132.209	+	98.3711i	−0.726421	+	0.540500i
$183$		0			0
$184$	−0.723195	+	16.2664i	−0.00393041	+	0.0884043i
$185$	59.9808	−	59.9808i	0.324220	−	0.324220i
$186$		0			0
$187$	42.5662	−	17.6315i	0.227627	−	0.0942861i
$188$	58.2023	−	31.3425i	0.309587	−	0.166715i
$189$		0			0
$190$	31.9442	+	126.694i	0.168127	+	0.666809i
$191$			47.7299i			0.249895i	0.992163	+	0.124947i	$0.0398762\pi$
$191$			47.7299i			0.249895i	−0.992163	+	0.124947i	$0.960124\pi$
$192$		0			0
$193$	−302.171			−1.56565			−0.782827	−	0.622240i	$-0.786223\pi$
$193$	−302.171			−1.56565			−0.782827	+	0.622240i	$0.786223\pi$
$194$	131.543	−	33.1670i	0.678059	−	0.170964i
$195$		0			0
$196$	12.6848	+	23.5554i	0.0647183	+	0.120180i
$197$	−18.2996	−	44.1791i	−0.0928913	−	0.224259i	0.870604	−	0.491984i	$-0.163728\pi$
$197$	−18.2996	−	44.1791i	−0.0928913	−	0.224259i	−0.963495	+	0.267725i	$0.913728\pi$
$198$		0			0
$199$	−94.2590	−	94.2590i	−0.473663	−	0.473663i	0.429435	−	0.903098i	$-0.358713\pi$
$199$	−94.2590	−	94.2590i	−0.473663	−	0.473663i	−0.903098	+	0.429435i	$0.858713\pi$
$200$	−0.502066	+	11.2927i	−0.00251033	+	0.0564633i
$201$		0			0
$202$	−142.556	−	191.593i	−0.705725	−	0.948479i
$203$	114.244	+	275.810i	0.562779	+	1.35867i
$204$		0			0
$205$	106.325	−	256.691i	0.518657	−	1.25215i
$206$	−149.847	−	89.4992i	−0.727414	−	0.434462i
$207$		0			0
$208$	99.0577	+	146.276i	0.476239	+	0.703249i
$209$			217.951i			1.04283i
$210$		0			0
$211$	−267.734	−	110.899i	−1.26888	−	0.525589i	−0.356259	−	0.934387i	$-0.615948\pi$
$211$	−267.734	−	110.899i	−1.26888	−	0.525589i	−0.912625	+	0.408799i	$0.865948\pi$
$212$	128.590	−	157.683i	0.606555	−	0.743787i
$213$		0			0
$214$	22.2644	+	29.9229i	0.104039	+	0.139827i
$215$	219.861	−	219.861i	1.02261	−	1.02261i
$216$		0			0
$217$	−25.0025	+	25.0025i	−0.115219	+	0.115219i
$218$	57.0394	−	388.684i	0.261648	−	1.78296i
$219$		0			0
$220$	90.4353	−	301.492i	0.411069	−	1.37042i
$221$	−29.0067	−	12.0150i	−0.131252	−	0.0543663i
$222$		0			0
$223$			408.363i			1.83123i	0.402061	+	0.915613i	$0.368294\pi$
$223$			408.363i			1.83123i	−0.402061	+	0.915613i	$0.631706\pi$
$224$	215.073	−	103.772i	0.960146	−	0.463269i
$225$		0			0
$226$	76.6628	+	304.052i	0.339216	+	1.34536i
$227$	−82.5132	+	199.204i	−0.363494	+	0.877553i	0.631290	+	0.775547i	$0.282526\pi$
$227$	−82.5132	+	199.204i	−0.363494	+	0.877553i	−0.994784	+	0.102005i	$0.967474\pi$
$228$		0			0
$229$	22.6069	+	54.5778i	0.0987200	+	0.238331i	0.965522	−	0.260321i	$-0.0838284\pi$
$229$	22.6069	+	54.5778i	0.0987200	+	0.238331i	−0.866802	+	0.498652i	$0.833828\pi$
$230$	−19.5600	−	2.87043i	−0.0850437	−	0.0124801i
$231$		0			0
$232$	300.824	−	109.220i	1.29666	−	0.470775i
$233$	−58.2826	−	58.2826i	−0.250140	−	0.250140i	0.570888	−	0.821028i	$-0.306599\pi$
$233$	−58.2826	−	58.2826i	−0.250140	−	0.250140i	−0.821028	+	0.570888i	$0.806599\pi$
$234$		0			0
$235$	30.7150	+	74.1525i	0.130702	+	0.315543i
$236$	−136.970	+	167.960i	−0.580383	+	0.711693i
$237$		0			0
$238$	−21.7619	+	36.4358i	−0.0914368	+	0.153091i
$239$	367.366			1.53710			0.768548	−	0.639792i	$-0.220979\pi$
$239$	367.366			1.53710			0.768548	+	0.639792i	$0.220979\pi$
$240$		0			0
$241$		−	312.345i		−	1.29604i	−0.761624	−	0.648020i	$-0.775597\pi$
$241$		−	312.345i		−	1.29604i	0.761624	−	0.648020i	$-0.224403\pi$
$242$	145.142	−	243.010i	0.599761	−	1.00417i
$243$		0			0
$244$	−233.941	+	23.7748i	−0.958773	+	0.0974375i
$245$	−30.0106	+	12.4308i	−0.122492	+	0.0507380i
$246$		0			0
$247$	105.021	−	105.021i	0.425187	−	0.425187i
$248$	25.5866	+	27.9675i	0.103172	+	0.112772i
$249$		0			0
$250$	−253.838	−	37.2507i	−1.01535	−	0.149003i
$251$	−223.120	+	92.4192i	−0.888923	+	0.368204i	−0.779951	−	0.625841i	$-0.784756\pi$
$251$	−223.120	+	92.4192i	−0.888923	+	0.368204i	−0.108972	+	0.994045i	$0.534756\pi$
$252$		0			0
$253$	−30.4672	−	12.6199i	−0.120424	−	0.0498811i
$254$	94.3574	+	374.230i	0.371486	+	1.47335i
$255$		0			0
$256$	−100.897	−	235.278i	−0.394127	−	0.919056i
$257$	−178.176			−0.693293			−0.346646	−	0.937996i	$-0.612680\pi$
$257$	−178.176			−0.693293			−0.346646	+	0.937996i	$0.612680\pi$
$258$		0			0
$259$	−49.8784	+	120.417i	−0.192581	+	0.464931i
$260$	−188.853	+	101.699i	−0.726357	+	0.391150i
$261$		0			0
$262$	13.8561	−	94.4198i	0.0528858	−	0.360381i
$263$	147.164	+	147.164i	0.559558	+	0.559558i	0.929182	−	0.369623i	$-0.120513\pi$
$263$	147.164	+	147.164i	0.559558	+	0.559558i	−0.369623	+	0.929182i	$0.620513\pi$
$264$		0			0
$265$	174.686	+	174.686i	0.659191	+	0.659191i
$266$	−119.845	−	161.069i	−0.450544	−	0.605522i
$267$		0			0
$268$	26.9506	+	265.191i	0.100562	+	0.989517i
$269$	138.119	−	333.450i	0.513455	−	1.23959i	−0.428405	−	0.903587i	$-0.640924\pi$
$269$	138.119	−	333.450i	0.513455	−	1.23959i	0.941861	−	0.336004i	$-0.109076\pi$
$270$		0			0
$271$	218.643			0.806801			0.403400	−	0.915024i	$-0.367828\pi$
$271$	218.643			0.806801			0.403400	+	0.915024i	$0.367828\pi$
$272$	37.9856	+	25.0414i	0.139653	+	0.0920638i
$273$		0			0
$274$	−67.6690	−	40.4166i	−0.246967	−	0.147506i
$275$	−21.1513	−	8.76117i	−0.0769139	−	0.0318588i
$276$		0			0
$277$	256.038	−	106.054i	0.924323	−	0.382867i	0.130801	−	0.991409i	$-0.458245\pi$
$277$	256.038	−	106.054i	0.924323	−	0.382867i	0.793522	+	0.608541i	$0.208245\pi$
$278$	−104.028	−	139.812i	−0.374203	−	0.502921i
$279$		0			0
$280$	98.9483	+	272.534i	0.353387	+	0.973336i
$281$	49.4126	−	49.4126i	0.175845	−	0.175845i	−0.613697	−	0.789542i	$-0.710318\pi$
$281$	49.4126	−	49.4126i	0.175845	−	0.175845i	0.789542	+	0.613697i	$0.210318\pi$
$282$		0			0
$283$	118.290	−	48.9975i	0.417987	−	0.173136i	−0.163770	−	0.986499i	$-0.552365\pi$
$283$	118.290	−	48.9975i	0.417987	−	0.173136i	0.581757	+	0.813363i	$0.302365\pi$
$284$	−38.6133	−	11.5824i	−0.135962	−	0.0407832i
$285$		0			0
$286$	−346.940	+	87.4765i	−1.21308	+	0.305862i
$287$			426.914i			1.48751i
$288$		0			0
$289$	280.914			0.972021
$290$	95.0018	+	376.786i	0.327592	+	1.29926i
$291$		0			0
$292$	299.997	+	89.9869i	1.02739	+	0.308174i
$293$	100.203	+	241.910i	0.341988	+	0.825633i	0.997515	+	0.0704605i	$0.0224469\pi$
$293$	100.203	+	241.910i	0.341988	+	0.825633i	−0.655526	+	0.755172i	$0.727553\pi$
$294$		0			0
$295$	−186.071	−	186.071i	−0.630748	−	0.630748i
$296$	126.589	+	59.1521i	0.427664	+	0.199838i
$297$		0			0
$298$	−218.589	+	162.643i	−0.733519	+	0.545782i
$299$	8.59983	+	20.7618i	0.0287620	+	0.0694376i
$300$		0			0
$301$	−182.830	+	441.392i	−0.607410	+	1.46642i
$302$	−154.104	+	258.015i	−0.510280	+	0.854355i
$303$		0			0
$304$	−178.207	+	120.681i	−0.586206	+	0.396978i
$305$		−	285.505i		−	0.936081i
$306$		0			0
$307$	−371.163	−	153.741i	−1.20900	−	0.500784i	−0.315103	−	0.949058i	$-0.602039\pi$
$307$	−371.163	−	153.741i	−1.20900	−	0.500784i	−0.893896	+	0.448274i	$0.852039\pi$
$308$	48.9000	+	481.170i	0.158766	+	1.56224i
$309$		0			0
$310$	−36.9241	+	27.4737i	−0.119110	+	0.0886250i
$311$	312.733	−	312.733i	1.00557	−	1.00557i	0.00558671	−	0.999984i	$-0.498222\pi$
$311$	312.733	−	312.733i	1.00557	−	1.00557i	0.999984	−	0.00558671i	$-0.00177831\pi$
$312$		0			0
$313$	358.245	−	358.245i	1.14455	−	1.14455i	0.156946	−	0.987607i	$-0.449835\pi$
$313$	358.245	−	358.245i	1.14455	−	1.14455i	0.987607	−	0.156946i	$-0.0501649\pi$
$314$	−448.385	−	65.8004i	−1.42798	−	0.209555i
$315$		0			0
$316$	39.0874	−	21.0489i	0.123694	−	0.0666105i
$317$	−164.720	−	68.2292i	−0.519621	−	0.215234i	0.107429	−	0.994213i	$-0.465738\pi$
$317$	−164.720	−	68.2292i	−0.519621	−	0.215234i	−0.627051	+	0.778979i	$0.715738\pi$
$318$		0			0
$319$			648.185i			2.03193i
$320$	296.588	−	92.9944i	0.926838	−	0.290607i
$321$		0			0
$322$	29.4550	−	7.42670i	0.0914751	−	0.0230643i
$323$	14.6377	−	35.3386i	0.0453181	−	0.109407i
$324$		0			0
$325$	5.97029	+	14.4135i	0.0183701	+	0.0443494i
$326$	0.133567	−	0.910167i	0.000409714	−	0.00279192i
$327$		0			0
$328$	457.214	+	20.3275i	1.39394	+	0.0619740i
$329$	−87.2050	−	87.2050i	−0.265061	−	0.265061i
$330$		0			0
$331$	21.3130	+	51.4542i	0.0643898	+	0.155451i	0.952799	−	0.303601i	$-0.0981891\pi$
$331$	21.3130	+	51.4542i	0.0643898	+	0.155451i	−0.888409	+	0.459052i	$0.848189\pi$
$332$	128.996	−	13.1095i	0.388541	−	0.0394864i
$333$		0			0
$334$	234.936	+	140.320i	0.703400	+	0.420119i
$335$	−323.643			−0.966098
$336$		0			0
$337$			173.028i			0.513437i	0.966486	+	0.256718i	$0.0826413\pi$
$337$			173.028i			0.513437i	−0.966486	+	0.256718i	$0.917359\pi$
$338$	−80.8553	−	48.2924i	−0.239217	−	0.142877i
$339$		0			0
$340$	−34.9115	+	42.8102i	−0.102681	+	0.125912i
$341$	−70.9282	+	29.3794i	−0.208001	+	0.0861567i
$342$		0			0
$343$	−223.268	+	223.268i	−0.650927	+	0.650927i
$344$	464.013	+	216.823i	1.34888	+	0.630301i
$345$		0			0
$346$	77.5836	−	528.679i	0.224230	−	1.52798i
$347$	−48.9563	+	20.2784i	−0.141085	+	0.0584391i	−0.452109	−	0.891963i	$-0.649328\pi$
$347$	−48.9563	+	20.2784i	−0.141085	+	0.0584391i	0.311024	+	0.950402i	$0.399328\pi$
$348$		0			0
$349$	−222.227	−	92.0495i	−0.636754	−	0.263752i	0.0408656	−	0.999165i	$-0.486988\pi$
$349$	−222.227	−	92.0495i	−0.636754	−	0.263752i	−0.677620	+	0.735412i	$0.736988\pi$
$350$	20.4486	−	5.15586i	0.0584246	−	0.0147310i
$351$		0			0
$352$	517.649	−	29.4597i	1.47059	−	0.0836924i
$353$	75.1997			0.213030			0.106515	−	0.994311i	$-0.466031\pi$
$353$	75.1997			0.213030			0.106515	+	0.994311i	$0.466031\pi$
$354$		0			0
$355$	18.7310	−	45.2208i	0.0527635	−	0.127382i
$356$	−27.2507	+	90.8479i	−0.0765469	+	0.255191i
$357$		0			0
$358$	577.808	+	84.7931i	1.61399	+	0.236852i
$359$	−369.532	−	369.532i	−1.02934	−	1.02934i	−0.999556	−	0.0297806i	$-0.990519\pi$
$359$	−369.532	−	369.532i	−1.02934	−	1.02934i	−0.0297806	−	0.999556i	$-0.509481\pi$
$360$		0			0
$361$	−127.319	−	127.319i	−0.352684	−	0.352684i
$362$	57.6744	−	42.9132i	0.159322	−	0.118545i
$363$		0			0
$364$	208.292	−	255.418i	0.572231	−	0.701697i
$365$	−145.526	+	351.332i	−0.398702	+	0.962552i
$366$		0			0
$367$	−482.888			−1.31577			−0.657885	−	0.753118i	$-0.728549\pi$
$367$	−482.888			−1.31577			−0.657885	+	0.753118i	$0.728549\pi$
$368$	−6.55131	−	31.8991i	−0.0178025	−	0.0866824i
$369$		0			0
$370$	−86.9922	+	145.650i	−0.235114	+	0.393648i
$371$	−350.698	−	145.264i	−0.945278	−	0.391547i
$372$		0			0
$373$	459.056	−	190.147i	1.23071	−	0.509778i	0.329913	−	0.944011i	$-0.392980\pi$
$373$	459.056	−	190.147i	1.23071	−	0.509778i	0.900801	+	0.434233i	$0.142980\pi$
$374$	−73.9276	+	55.0065i	−0.197667	+	0.147076i
$375$		0			0
$376$	−97.5465	+	89.2420i	−0.259432	+	0.237346i
$377$	312.332	−	312.332i	0.828468	−	0.828468i
$378$		0			0
$379$	209.167	−	86.6398i	0.551891	−	0.228601i	−0.0892693	−	0.996008i	$-0.528453\pi$
$379$	209.167	−	86.6398i	0.551891	−	0.228601i	0.641161	+	0.767407i	$0.278453\pi$
$380$	−123.899	−	230.078i	−0.326050	−	0.605468i
$381$		0			0
$382$	−23.3386	−	92.5629i	−0.0610958	−	0.242311i
$383$		−	243.083i		−	0.634682i	−0.948312	−	0.317341i	$-0.897210\pi$
$383$		−	243.083i		−	0.634682i	0.948312	−	0.317341i	$-0.102790\pi$
$384$		0			0
$385$	−587.227			−1.52527
$386$	586.002	−	147.753i	1.51814	−	0.382780i
$387$		0			0
$388$	−238.885	+	128.642i	−0.615683	+	0.331551i
$389$	−100.024	−	241.479i	−0.257131	−	0.620768i	0.741616	−	0.670825i	$-0.234060\pi$
$389$	−100.024	−	241.479i	−0.257131	−	0.620768i	−0.998746	+	0.0500566i	$0.984060\pi$
$390$		0			0
$391$	4.09239	+	4.09239i	0.0104665	+	0.0104665i
$392$	−36.1176	−	39.4786i	−0.0921367	−	0.100711i
$393$		0			0
$394$	57.0908	+	76.7288i	0.144901	+	0.194743i
$395$	20.6275	+	49.7992i	0.0522215	+	0.126074i
$396$		0			0
$397$	−177.617	+	428.806i	−0.447399	+	1.08012i	0.525894	+	0.850550i	$0.323731\pi$
$397$	−177.617	+	428.806i	−0.447399	+	1.08012i	−0.973293	+	0.229566i	$0.926269\pi$
$398$	228.887	+	136.707i	0.575093	+	0.343485i
$399$		0			0
$400$	−4.54813	−	22.1454i	−0.0113703	−	0.0553636i
$401$		−	539.233i		−	1.34472i	−0.740224	−	0.672360i	$-0.765281\pi$
$401$		−	539.233i		−	1.34472i	0.740224	−	0.672360i	$-0.234719\pi$
$402$		0			0
$403$	48.3339	+	20.0206i	0.119935	+	0.0496788i
$404$	370.144	+	301.851i	0.916198	+	0.747156i
$405$		0			0
$406$	−356.417	−	479.017i	−0.877875	−	1.17984i
$407$	−200.107	+	200.107i	−0.491664	+	0.491664i
$408$		0			0
$409$	177.821	−	177.821i	0.434769	−	0.434769i	−0.455478	−	0.890247i	$-0.650532\pi$
$409$	177.821	−	177.821i	0.434769	−	0.434769i	0.890247	+	0.455478i	$0.150532\pi$
$410$	−80.6817	+	549.791i	−0.196785	+	1.34095i
$411$		0			0
$412$	334.362	+	100.295i	0.811559	+	0.243435i
$413$	373.554	+	154.731i	0.904490	+	0.374652i
$414$		0			0
$415$			157.428i			0.379345i
$416$	−263.628	−	235.237i	−0.633721	−	0.565474i
$417$		0			0
$418$	−106.572	−	422.674i	−0.254957	−	1.01118i
$419$	−55.0604	+	132.927i	−0.131409	+	0.317249i	−0.975865	−	0.218376i	$-0.929924\pi$
$419$	−55.0604	+	132.927i	−0.131409	+	0.317249i	0.844456	+	0.535625i	$0.179924\pi$
$420$		0			0
$421$	−292.384	−	705.877i	−0.694498	−	1.67667i	−0.735514	−	0.677509i	$-0.763059\pi$
$421$	−292.384	−	705.877i	−0.694498	−	1.67667i	0.0410159	−	0.999158i	$-0.486941\pi$
$422$	573.445	+	84.1530i	1.35888	+	0.199415i
$423$		0			0
$424$	−172.272	+	368.672i	−0.406303	+	0.869509i
$425$	2.84107	+	2.84107i	0.00668488	+	0.00668488i
$426$		0			0
$427$	167.880	+	405.298i	0.393162	+	0.949176i
$428$	−57.8090	−	47.1430i	−0.135068	−	0.110147i
$429$		0			0
$430$	−318.872	+	533.883i	−0.741562	+	1.24159i
$431$	−810.711			−1.88100			−0.940500	−	0.339794i	$-0.889643\pi$
$431$	−810.711			−1.88100			−0.940500	+	0.339794i	$0.889643\pi$
$432$		0			0
$433$		−	753.072i		−	1.73920i	−0.493759	−	0.869599i	$-0.664378\pi$
$433$		−	753.072i		−	1.73920i	0.493759	−	0.869599i	$-0.335622\pi$
$434$	36.2620	−	60.7131i	0.0835531	−	0.139892i
$435$		0			0
$436$	79.4389	+	781.669i	0.182199	+	1.79282i
$437$	−25.2940	+	10.4771i	−0.0578810	+	0.0239751i
$438$		0			0
$439$	504.938	−	504.938i	1.15020	−	1.15020i	0.163689	−	0.986512i	$-0.447661\pi$
$439$	504.938	−	504.938i	1.15020	−	1.15020i	0.986512	−	0.163689i	$-0.0523392\pi$
$440$	−27.9608	+	628.905i	−0.0635472	+	1.42933i
$441$		0			0
$442$	62.1278	+	9.11724i	0.140561	+	0.0206272i
$443$	697.291	−	288.827i	1.57402	−	0.651981i	0.586569	−	0.809899i	$-0.300478\pi$
$443$	697.291	−	288.827i	1.57402	−	0.651981i	0.987452	+	0.157919i	$0.0504784\pi$
$444$		0			0
$445$	−106.394	−	44.0697i	−0.239087	−	0.0990330i
$446$	−199.678	−	791.942i	−0.447709	−	1.77565i
$447$		0			0
$448$	−366.350	+	306.410i	−0.817746	+	0.683952i
$449$	294.056			0.654913			0.327457	−	0.944866i	$-0.393808\pi$
$449$	294.056			0.654913			0.327457	+	0.944866i	$0.393808\pi$
$450$		0			0
$451$	−354.719	+	856.368i	−0.786517	+	1.89882i
$452$	−297.345	−	552.163i	−0.657843	−	1.22160i
$453$		0			0
$454$	62.6130	−	426.665i	0.137914	−	0.939791i
$455$	282.960	+	282.960i	0.621889	+	0.621889i
$456$		0			0
$457$	175.139	+	175.139i	0.383237	+	0.383237i	0.872267	−	0.489030i	$-0.162649\pi$
$457$	175.139	+	175.139i	0.383237	+	0.383237i	−0.489030	+	0.872267i	$0.662649\pi$
$458$	−70.5287	−	94.7890i	−0.153993	−	0.206963i
$459$		0			0
$460$	39.3365	−	3.99766i	0.0855141	−	0.00869056i
$461$	107.290	−	259.020i	0.232732	−	0.561866i	−0.763765	−	0.645495i	$-0.776651\pi$
$461$	107.290	−	259.020i	0.232732	−	0.561866i	0.996497	+	0.0836293i	$0.0266512\pi$
$462$		0			0
$463$	53.7059			0.115996			0.0579978	−	0.998317i	$-0.481528\pi$
$463$	53.7059			0.115996			0.0579978	+	0.998317i	$0.481528\pi$
$464$	−529.985	+	358.905i	−1.14221	+	0.773502i
$465$		0			0
$466$	141.526	+	84.5292i	0.303704	+	0.181393i
$467$	−101.550	−	42.0634i	−0.217452	−	0.0900716i	0.271298	−	0.962495i	$-0.412547\pi$
$467$	−101.550	−	42.0634i	−0.217452	−	0.0900716i	−0.488750	+	0.872424i	$0.662547\pi$
$468$		0			0
$469$	459.438	−	190.306i	0.979613	−	0.405769i
$470$	−95.8242	−	128.786i	−0.203881	−	0.274012i
$471$		0			0
$472$	183.500	−	392.699i	0.388771	−	0.831990i
$473$	−733.498	+	733.498i	−1.55074	+	1.55074i
$474$		0			0
$475$	−17.5599	+	7.27355i	−0.0369682	+	0.0153127i
$476$	24.3870	−	81.3011i	0.0512332	−	0.170801i
$477$		0			0
$478$	−712.435	+	179.632i	−1.49045	+	0.375798i
$479$			40.7997i			0.0851769i	0.999093	+	0.0425884i	$0.0135604\pi$
$479$			40.7997i			0.0851769i	−0.999093	+	0.0425884i	$0.986440\pi$
$480$		0			0
$481$	192.846			0.400927
$482$	152.728	+	605.733i	0.316863	+	1.25671i
$483$		0			0
$484$	−162.650	+	542.241i	−0.336054	+	1.12033i
$485$	−126.066	−	304.351i	−0.259931	−	0.627528i
$486$		0			0
$487$	−143.660	−	143.660i	−0.294989	−	0.294989i	0.544058	−	0.839047i	$-0.316887\pi$
$487$	−143.660	−	143.660i	−0.294989	−	0.294989i	−0.839047	+	0.544058i	$0.816887\pi$
$488$	442.057	−	160.497i	0.905855	−	0.328887i
$489$		0			0
$490$	52.1215	−	38.7815i	0.106370	−	0.0791459i
$491$	−182.575	−	440.775i	−0.371843	−	0.897709i	−0.993438	−	0.114370i	$-0.963515\pi$
$491$	−182.575	−	440.775i	−0.371843	−	0.897709i	0.621595	−	0.783339i	$-0.286485\pi$
$492$		0			0
$493$	43.5325	−	105.097i	0.0883012	−	0.213178i
$494$	−152.316	+	255.021i	−0.308332	+	0.516236i
$495$		0			0
$496$	−63.2955	−	41.7265i	−0.127612	−	0.0841261i
$497$			75.2087i			0.151325i
$498$		0			0
$499$	−409.850	−	169.766i	−0.821343	−	0.340211i	−0.0678733	−	0.997694i	$-0.521621\pi$
$499$	−409.850	−	169.766i	−0.821343	−	0.340211i	−0.753470	+	0.657482i	$0.771621\pi$
$500$	510.485	−	51.8792i	1.02097	−	0.103758i
$501$		0			0
$502$	387.507	−	288.328i	0.771926	−	0.574359i
$503$	−453.715	+	453.715i	−0.902019	+	0.902019i	−0.995611	−	0.0935920i	$-0.970165\pi$
$503$	−453.715	+	453.715i	−0.902019	+	0.902019i	0.0935920	+	0.995611i	$0.470165\pi$
$504$		0			0
$505$	−410.057	+	410.057i	−0.811993	+	0.811993i
$506$	65.2560	+	9.57631i	0.128964	+	0.0189255i
$507$		0			0
$508$	−365.976	−	679.608i	−0.720425	−	1.33781i
$509$	71.5029	+	29.6175i	0.140477	+	0.0581876i	0.451815	−	0.892112i	$-0.350777\pi$
$509$	71.5029	+	29.6175i	0.140477	+	0.0581876i	−0.311337	+	0.950299i	$0.600777\pi$
$510$		0			0
$511$		−	584.316i		−	1.14348i
$512$	310.714	+	406.941i	0.606863	+	0.794807i
$513$		0			0
$514$	345.538	−	87.1231i	0.672253	−	0.169500i
$515$	−162.197	+	391.578i	−0.314945	+	0.760345i
$516$		0			0
$517$	−102.471	−	247.387i	−0.198203	−	0.478504i
$518$	37.8489	−	257.915i	0.0730674	−	0.497905i
$519$		0			0
$520$	316.515	−	289.569i	0.608683	−	0.556864i
$521$	565.729	+	565.729i	1.08585	+	1.08585i	0.995951	+	0.0899020i	$0.0286554\pi$
$521$	565.729	+	565.729i	1.08585	+	1.08585i	0.0899020	+	0.995951i	$0.471345\pi$
$522$		0			0
$523$	−1.50925	−	3.64366i	−0.00288576	−	0.00696685i	0.922430	−	0.386164i	$-0.126200\pi$
$523$	−1.50925	−	3.64366i	−0.00288576	−	0.00696685i	−0.925316	+	0.379197i	$0.876200\pi$
$524$	19.2974	+	189.884i	0.0368271	+	0.362374i
$525$		0			0
$526$	−357.355	−	213.437i	−0.679381	−	0.405773i
$527$	13.4734			0.0255663
$528$		0			0
$529$			524.858i			0.992169i
$530$	−424.185	−	253.353i	−0.800350	−	0.478024i
$531$		0			0
$532$	311.174	+	253.761i	0.584913	+	0.476994i
$533$	583.571	−	241.723i	1.09488	−	0.453514i
$534$		0			0
$535$	64.0426	−	64.0426i	0.119706	−	0.119706i
$536$	−181.936	−	501.108i	−0.339433	−	0.934902i
$537$		0			0
$538$	−104.808	+	714.198i	−0.194811	+	1.32751i
$539$	100.121	−	41.4716i	0.185754	−	0.0769417i
$540$		0			0
$541$	−746.681	−	309.286i	−1.38019	−	0.571692i	−0.435656	−	0.900113i	$-0.643483\pi$
$541$	−746.681	−	309.286i	−1.38019	−	0.571692i	−0.944531	+	0.328421i	$0.893483\pi$
$542$	−424.016	+	106.910i	−0.782317	+	0.197251i
$543$		0			0
$544$	−85.9101	−	29.9890i	−0.157923	−	0.0551268i
$545$	−953.961			−1.75039
$546$		0			0
$547$	298.176	−	719.861i	0.545112	−	1.31602i	−0.375964	−	0.926634i	$-0.622688\pi$
$547$	298.176	−	719.861i	0.545112	−	1.31602i	0.921076	−	0.389383i	$-0.127312\pi$
$548$	150.993	+	45.2919i	0.275535	+	0.0826494i
$549$		0			0
$550$	45.3029	+	6.64819i	0.0823688	+	0.0120876i
$551$	380.512	+	380.512i	0.690585	+	0.690585i
$552$		0			0
$553$	−58.5649	−	58.5649i	−0.105904	−	0.105904i
$554$	−444.678	+	330.867i	−0.802667	+	0.597232i
$555$		0			0
$556$	270.107	+	220.271i	0.485804	+	0.396171i
$557$	−83.4142	+	201.380i	−0.149756	+	0.361544i	−0.980900	−	0.194515i	$-0.937687\pi$
$557$	−83.4142	+	201.380i	−0.149756	+	0.361544i	0.831143	+	0.556058i	$0.187687\pi$
$558$		0			0
$559$	706.882			1.26455
$560$	−325.152	−	480.144i	−0.580629	−	0.857400i
$561$		0			0
$562$	−71.6647	+	119.987i	−0.127517	+	0.213501i
$563$	19.5811	+	8.11076i	0.0347800	+	0.0144063i	0.400006	−	0.916513i	$-0.369008\pi$
$563$	19.5811	+	8.11076i	0.0347800	+	0.0144063i	−0.365226	+	0.930919i	$0.619008\pi$
$564$		0			0
$565$	703.482	−	291.392i	1.24510	−	0.515738i
$566$	−205.443	+	152.862i	−0.362973	+	0.270074i
$567$		0			0
$568$	80.5466	+	3.58106i	0.141807	+	0.00630468i
$569$	366.760	−	366.760i	0.644569	−	0.644569i	−0.307106	−	0.951675i	$-0.599361\pi$
$569$	366.760	−	366.760i	0.644569	−	0.644569i	0.951675	+	0.307106i	$0.0993606\pi$
$570$		0			0
$571$	−121.285	+	50.2378i	−0.212408	+	0.0879822i	−0.486350	−	0.873764i	$-0.661672\pi$
$571$	−121.285	+	50.2378i	−0.212408	+	0.0879822i	0.273943	+	0.961746i	$0.411672\pi$
$572$	630.049	−	339.287i	1.10148	−	0.593159i
$573$		0			0
$574$	−208.749	−	827.917i	−0.363674	−	1.44236i
$575$		−	2.87584i		−	0.00500147i
$576$		0			0
$577$	464.948			0.805802			0.402901	−	0.915244i	$-0.368002\pi$
$577$	464.948			0.805802			0.402901	+	0.915244i	$0.368002\pi$
$578$	−544.778	+	137.359i	−0.942523	+	0.237645i
$579$		0			0
$580$	−368.475	−	684.250i	−0.635302	−	1.17974i
$581$	−92.5696	−	223.483i	−0.159328	−	0.384652i
$582$		0			0
$583$	−582.785	−	582.785i	−0.999631	−	0.999631i
$584$	−625.787	−	27.8221i	−1.07155	−	0.0476407i
$585$		0			0
$586$	−312.611	−	420.142i	−0.533465	−	0.716966i
$587$	−159.551	−	385.190i	−0.271807	−	0.656201i	0.727753	−	0.685839i	$-0.240565\pi$
$587$	−159.551	−	385.190i	−0.271807	−	0.656201i	−0.999561	+	0.0296380i	$0.990565\pi$
$588$		0			0
$589$	−24.3909	+	58.8849i	−0.0414107	+	0.0999743i
$590$	451.831	+	269.865i	0.765815	+	0.457398i
$591$		0			0
$592$	−274.418	−	52.8158i	−0.463543	−	0.0892159i
$593$		−	470.422i		−	0.793292i	−0.917972	−	0.396646i	$-0.870174\pi$
$593$		−	470.422i		−	0.793292i	0.917972	−	0.396646i	$-0.129826\pi$
$594$		0			0
$595$	95.2131	+	39.4385i	0.160022	+	0.0662833i
$596$	344.383	−	422.298i	0.577823	−	0.708554i
$597$		0			0
$598$	−26.8296	−	36.0585i	−0.0448656	−	0.0602984i
$599$	506.817	−	506.817i	0.846105	−	0.846105i	−0.143540	−	0.989645i	$-0.545849\pi$
$599$	506.817	−	506.817i	0.846105	−	0.846105i	0.989645	+	0.143540i	$0.0458485\pi$
$600$		0			0
$601$	−261.398	+	261.398i	−0.434939	+	0.434939i	−0.890305	−	0.455366i	$-0.849509\pi$
$601$	−261.398	+	261.398i	−0.434939	+	0.434939i	0.455366	+	0.890305i	$0.349509\pi$
$602$	138.736	−	945.393i	0.230459	−	1.57042i
$603$		0			0
$604$	172.694	−	575.723i	0.285916	−	0.953184i
$605$	−635.027	−	263.037i	−1.04963	−	0.434772i
$606$		0			0
$607$			812.089i			1.33787i	0.743319	+	0.668937i	$0.233250\pi$
$607$			812.089i			1.33787i	−0.743319	+	0.668937i	$0.766750\pi$
$608$	286.588	−	321.176i	0.471361	−	0.528250i
$609$		0			0
$610$	139.604	+	553.681i	0.228859	+	0.907674i
$611$	−69.8287	+	168.581i	−0.114286	+	0.275911i
$612$		0			0
$613$	105.168	+	253.898i	0.171563	+	0.414190i	0.986151	−	0.165850i	$-0.0530369\pi$
$613$	105.168	+	253.898i	0.171563	+	0.414190i	−0.814588	+	0.580040i	$0.803037\pi$
$614$	794.973	+	116.662i	1.29474	+	0.190003i
$615$		0			0
$616$	−330.110	−	909.225i	−0.535894	−	1.47601i
$617$	508.739	+	508.739i	0.824536	+	0.824536i	0.986755	−	0.162218i	$-0.0518649\pi$
$617$	508.739	+	508.739i	0.824536	+	0.824536i	−0.162218	+	0.986755i	$0.551865\pi$
$618$		0			0
$619$	−6.64960	−	16.0536i	−0.0107425	−	0.0259347i	0.918417	−	0.395613i	$-0.129468\pi$
$619$	−6.64960	−	16.0536i	−0.0107425	−	0.0259347i	−0.929160	+	0.369678i	$0.879468\pi$
$620$	58.1733	−	71.3348i	0.0938278	−	0.115056i
$621$		0			0
$622$	−453.567	+	759.402i	−0.729207	+	1.22090i
$623$	176.948			0.284026
$624$		0			0
$625$			587.679i			0.940287i
$626$	−519.575	+	869.919i	−0.829992	+	1.38965i
$627$		0			0
$628$	901.730	−	91.6403i	1.43588	−	0.145924i
$629$	45.8847	−	19.0061i	0.0729487	−	0.0302163i
$630$		0			0
$631$	−177.518	+	177.518i	−0.281329	+	0.281329i	−0.833639	−	0.552310i	$-0.813746\pi$
$631$	−177.518	+	177.518i	−0.281329	+	0.281329i	0.552310	+	0.833639i	$0.313746\pi$
$632$	−65.5100	+	59.9329i	−0.103655	+	0.0948306i
$633$		0			0
$634$	352.804	+	51.7740i	0.556474	+	0.0816624i
$635$	865.853	−	358.648i	1.36355	−	0.564800i
$636$		0			0
$637$	−68.2274	−	28.2607i	−0.107107	−	0.0443654i
$638$	−316.944	−	1257.03i	−0.496777	−	1.97026i
$639$		0			0
$640$	−529.703	+	325.368i	−0.827662	+	0.508387i
$641$	−334.058			−0.521151			−0.260575	−	0.965454i	$-0.583912\pi$
$641$	−334.058			−0.521151			−0.260575	+	0.965454i	$0.583912\pi$
$642$		0			0
$643$	−19.9758	+	48.2257i	−0.0310665	+	0.0750011i	−0.938651	−	0.344867i	$-0.887924\pi$
$643$	−19.9758	+	48.2257i	−0.0310665	+	0.0750011i	0.907585	+	0.419869i	$0.137924\pi$
$644$	−53.4908	+	28.8053i	−0.0830602	+	0.0447287i
$645$		0			0
$646$	−11.1075	+	75.6898i	−0.0171942	+	0.117167i
$647$	−443.581	−	443.581i	−0.685596	−	0.685596i	0.275659	−	0.961255i	$-0.411104\pi$
$647$	−443.581	−	443.581i	−0.685596	−	0.685596i	−0.961255	+	0.275659i	$0.911104\pi$
$648$		0			0
$649$	620.767	+	620.767i	0.956497	+	0.956497i
$650$	−18.6260	−	25.0330i	−0.0286554	−	0.0385123i
$651$		0			0
$652$	0.186019	+	1.83040i	0.000285305	+	0.00280737i
$653$	14.0746	−	33.9792i	0.0215538	−	0.0520355i	−0.912736	−	0.408549i	$-0.866035\pi$
$653$	14.0746	−	33.9792i	0.0215538	−	0.0520355i	0.934290	+	0.356514i	$0.116035\pi$
$654$		0			0
$655$	−231.737			−0.353798
$656$	−896.617	+	184.143i	−1.36679	+	0.280706i
$657$		0			0
$658$	211.758	+	126.476i	0.321821	+	0.192213i
$659$	845.778	+	350.333i	1.28343	+	0.531613i	0.917020	−	0.398842i	$-0.130588\pi$
$659$	845.778	+	350.333i	1.28343	+	0.531613i	0.366407	+	0.930455i	$0.380588\pi$
$660$		0			0
$661$	−1022.39	+	423.490i	−1.54674	+	0.640680i	−0.982723	−	0.185083i	$-0.940745\pi$
$661$	−1022.39	+	423.490i	−1.54674	+	0.640680i	−0.564017	+	0.825763i	$0.690745\pi$
$662$	−66.4921	−	89.3640i	−0.100441	−	0.134991i
$663$		0			0
$664$	−243.752	+	88.4985i	−0.367096	+	0.133281i
$665$	−344.727	+	344.727i	−0.518387	+	0.518387i
$666$		0			0
$667$	−75.2241	+	31.1588i	−0.112780	+	0.0467149i
$668$	−524.224	−	157.246i	−0.784767	−	0.235398i
$669$		0			0
$670$	627.642	−	158.252i	0.936780	−	0.236197i
$671$			952.498i			1.41952i
$672$		0			0
$673$	−441.074			−0.655385			−0.327693	−	0.944784i	$-0.606271\pi$
$673$	−441.074			−0.655385			−0.327693	+	0.944784i	$0.606271\pi$
$674$	−84.6059	−	335.555i	−0.125528	−	0.497856i
$675$		0			0
$676$	180.417	+	54.1177i	0.266889	+	0.0800558i
$677$	3.12869	+	7.55333i	0.00462140	+	0.0111571i	0.926173	−	0.377098i	$-0.123078\pi$
$677$	3.12869	+	7.55333i	0.00462140	+	0.0111571i	−0.921552	+	0.388255i	$0.873078\pi$
$678$		0			0
$679$	357.923	+	357.923i	0.527133	+	0.527133i
$680$	46.7712	−	100.093i	0.0687812	−	0.147195i
$681$		0			0
$682$	123.186	−	91.6576i	0.180624	−	0.134395i
$683$	198.853	+	480.073i	0.291146	+	0.702889i	0.999997	−	0.00246964i	$-0.000786112\pi$
$683$	198.853	+	480.073i	0.291146	+	0.702889i	−0.708851	+	0.705358i	$0.750786\pi$
$684$		0			0
$685$	−73.2458	+	176.831i	−0.106928	+	0.258147i
$686$	323.813	−	542.157i	0.472031	−	0.790316i
$687$		0			0
$688$	−1005.88	−	193.598i	−1.46204	−	0.281392i
$689$			561.638i			0.815149i
$690$		0			0
$691$	260.304	+	107.822i	0.376707	+	0.156037i	0.563000	−	0.826457i	$-0.309647\pi$
$691$	260.304	+	107.822i	0.376707	+	0.156037i	−0.186293	+	0.982494i	$0.559647\pi$
$692$	108.051	+	1063.21i	0.156143	+	1.53643i
$693$		0			0
$694$	85.0257	−	63.2642i	0.122515	−	0.0911588i
$695$	−299.233	+	299.233i	−0.430551	+	0.430551i
$696$		0			0
$697$	115.028	−	115.028i	0.165034	−	0.165034i
$698$	475.976	+	69.8494i	0.681914	+	0.100071i
$699$		0			0
$700$	−37.1350	+	19.9976i	−0.0530501	+	0.0285680i
$701$	487.328	+	201.858i	0.695189	+	0.287957i	0.702160	−	0.712019i	$-0.252219\pi$
$701$	487.328	+	201.858i	0.695189	+	0.287957i	−0.00697111	+	0.999976i	$0.502219\pi$
$702$		0			0
$703$			234.943i			0.334200i
$704$	−989.474	+	310.247i	−1.40550	+	0.440692i
$705$		0			0
$706$	−145.835	+	36.7705i	−0.206565	+	0.0520829i
$707$	340.992	−	823.228i	0.482309	−	1.16440i
$708$		0			0
$709$	260.932	+	629.945i	0.368028	+	0.888498i	0.994073	+	0.108711i	$0.0346724\pi$
$709$	260.932	+	629.945i	0.368028	+	0.888498i	−0.626046	+	0.779786i	$0.715328\pi$
$710$	−14.2136	+	96.8558i	−0.0200191	+	0.136417i
$711$		0			0
$712$	8.42537	−	189.507i	0.0118334	−	0.266161i
$713$	−6.81917	−	6.81917i	−0.00956405	−	0.00956405i
$714$		0			0
$715$	332.494	+	802.712i	0.465027	+	1.12267i
$716$	−1162.01	+	118.092i	−1.62291	+	0.164932i
$717$		0			0
$718$	897.326	+	535.945i	1.24976	+	0.746441i
$719$	349.854			0.486585			0.243292	−	0.969953i	$-0.421773\pi$
$719$	349.854			0.486585			0.243292	+	0.969953i	$0.421773\pi$
$720$		0			0
$721$		−	651.251i		−	0.903261i
$722$	309.166	+	184.655i	0.428207	+	0.255755i
$723$		0			0
$724$	−90.8650	+	111.423i	−0.125504	+	0.153899i
$725$	−52.2230	+	21.6315i	−0.0720318	+	0.0298365i
$726$		0			0
$727$	−58.3736	+	58.3736i	−0.0802938	+	0.0802938i	−0.746113	−	0.665819i	$-0.768082\pi$
$727$	−58.3736	+	58.3736i	−0.0802938	+	0.0802938i	0.665819	+	0.746113i	$0.268082\pi$
$728$	−279.050	+	597.182i	−0.383311	+	0.820305i
$729$		0			0
$730$	110.429	−	752.498i	0.151272	−	1.03082i
$731$	168.191	−	69.6672i	0.230084	−	0.0953040i
$732$		0			0
$733$	327.632	+	135.710i	0.446975	+	0.185143i	0.594805	−	0.803870i	$-0.297229\pi$
$733$	327.632	+	135.710i	0.446975	+	0.185143i	−0.147831	+	0.989013i	$0.547229\pi$
$734$	936.467	−	236.118i	1.27584	−	0.321687i
$735$		0			0
$736$	28.3027	+	58.6588i	0.0384548	+	0.0796994i
$737$	1079.73			1.46504
$738$		0			0
$739$	328.523	−	793.126i	0.444551	−	1.07324i	−0.529783	−	0.848134i	$-0.677726\pi$
$739$	328.523	−	793.126i	0.444551	−	1.07324i	0.974334	−	0.225108i	$-0.0722736\pi$
$740$	97.4857	−	324.996i	0.131737	−	0.439184i
$741$		0			0
$742$	751.141	+	110.230i	1.01232	+	0.148558i
$743$	−79.8532	−	79.8532i	−0.107474	−	0.107474i	0.651325	−	0.758799i	$-0.274214\pi$
$743$	−79.8532	−	79.8532i	−0.107474	−	0.107474i	−0.758799	+	0.651325i	$0.774214\pi$
$744$		0			0
$745$	467.835	+	467.835i	0.627966	+	0.627966i
$746$	−797.274	+	593.219i	−1.06873	+	0.795200i
$747$		0			0
$748$	116.472	−	142.823i	0.155711	−	0.190940i
$749$	−53.2561	+	128.572i	−0.0711029	+	0.171658i
$750$		0			0
$751$	−729.615			−0.971524			−0.485762	−	0.874091i	$-0.661458\pi$
$751$	−729.615			−0.971524			−0.485762	+	0.874091i	$0.661458\pi$
$752$	145.536	−	220.765i	0.193532	−	0.293570i
$753$		0			0
$754$	−452.986	+	758.429i	−0.600778	+	1.00587i
$755$	674.239	+	279.279i	0.893032	+	0.369906i
$756$		0			0
$757$	565.974	−	234.434i	0.747654	−	0.309688i	0.0238700	−	0.999715i	$-0.492401\pi$
$757$	565.974	−	234.434i	0.747654	−	0.309688i	0.723784	+	0.690027i	$0.242401\pi$
$758$	−363.274	+	270.298i	−0.479253	+	0.356593i
$759$		0			0
$760$	352.780	+	385.608i	0.464184	+	0.507379i
$761$	−186.563	+	186.563i	−0.245155	+	0.245155i	−0.818979	−	0.573824i	$-0.805459\pi$
$761$	−186.563	+	186.563i	−0.245155	+	0.245155i	0.573824	+	0.818979i	$0.305459\pi$
$762$		0			0
$763$	1354.23	−	560.940i	1.77487	−	0.735176i
$764$	90.5213	+	168.096i	0.118483	+	0.220021i
$765$		0			0
$766$	118.861	+	471.413i	0.155171	+	0.615421i
$767$		−	598.241i		−	0.779976i
$768$		0			0
$769$	134.178			0.174484			0.0872420	−	0.996187i	$-0.472195\pi$
$769$	134.178			0.174484			0.0872420	+	0.996187i	$0.472195\pi$
$770$	1138.81	−	287.137i	1.47898	−	0.372906i
$771$		0			0
$772$	−1064.19	+	573.077i	−1.37849	+	0.742328i
$773$	155.016	+	374.241i	0.200538	+	0.484141i	0.991872	−	0.127243i	$-0.0406130\pi$
$773$	155.016	+	374.241i	0.200538	+	0.484141i	−0.791334	+	0.611384i	$0.790613\pi$
$774$		0			0
$775$	−4.73409	−	4.73409i	−0.00610851	−	0.00610851i
$776$	400.369	−	366.284i	0.515940	−	0.472016i
$777$		0			0
$778$	312.053	+	419.393i	0.401097	+	0.539065i
$779$	294.489	+	710.960i	0.378035	+	0.912657i
$780$		0			0
$781$	−62.4903	+	150.865i	−0.0800132	+	0.193169i
$782$	−9.93746	−	5.93534i	−0.0127078	−	0.00758994i
$783$		0			0
$784$	89.3469	+	58.9005i	0.113963	+	0.0751282i
$785$			1100.49i			1.40189i
$786$		0			0
$787$	464.245	+	192.297i	0.589892	+	0.244341i	0.657604	−	0.753364i	$-0.271570\pi$
$787$	464.245	+	192.297i	0.589892	+	0.244341i	−0.0677120	+	0.997705i	$0.521570\pi$
$788$	−148.235	−	120.885i	−0.188115	−	0.153407i
$789$		0			0
$790$	−64.3534	−	86.4895i	−0.0814600	−	0.109480i
$791$	−827.311	+	827.311i	−1.04590	+	1.04590i
$792$		0			0
$793$	458.968	−	458.968i	0.578774	−	0.578774i
$794$	134.780	−	918.436i	0.169749	−	1.15672i
$795$		0			0
$796$	−510.728	−	153.198i	−0.641618	−	0.192459i
$797$	−1426.93	−	591.055i	−1.79038	−	0.741600i	−0.989816	−	0.142353i	$-0.954533\pi$
$797$	−1426.93	−	591.055i	−1.79038	−	0.741600i	−0.800564	−	0.599247i	$-0.795467\pi$
$798$		0			0
$799$			46.9933i			0.0588152i
$800$	19.6487	+	40.7228i	0.0245609	+	0.0509035i
$801$		0			0
$802$	263.669	+	1045.74i	0.328765	+	1.30391i
$803$	485.503	−	1172.11i	0.604612	−	1.45966i
$804$		0			0
$805$	−28.2286	−	68.1498i	−0.0350665	−	0.0846581i
$806$	−103.524	−	15.1921i	−0.128441	−	0.0188488i
$807$		0			0
$808$	−865.419	−	404.391i	−1.07106	−	0.500485i
$809$	950.297	+	950.297i	1.17466	+	1.17466i	0.981086	+	0.193570i	$0.0620067\pi$
$809$	950.297	+	950.297i	1.17466	+	1.17466i	0.193570	+	0.981086i	$0.437993\pi$
$810$		0			0
$811$	−580.036	−	1400.33i	−0.715210	−	1.72667i	−0.686552	−	0.727081i	$-0.740876\pi$
$811$	−580.036	−	1400.33i	−0.715210	−	1.72667i	−0.0286586	−	0.999589i	$-0.509124\pi$
$812$	925.428	+	754.683i	1.13969	+	0.929412i
$813$		0			0
$814$	290.222	−	485.916i	0.356538	−	0.596948i
$815$	−2.23385			−0.00274092
$816$		0			0
$817$			861.189i			1.05409i
$818$	−257.899	+	431.798i	−0.315280	+	0.527870i
$819$		0			0
$820$	−112.366	−	1105.66i	−0.137031	−	1.34837i
$821$	−646.816	+	267.920i	−0.787839	+	0.326334i	−0.740074	−	0.672525i	$-0.765210\pi$
$821$	−646.816	+	267.920i	−0.787839	+	0.326334i	−0.0477645	+	0.998859i	$0.515210\pi$
$822$		0			0
$823$	−262.313	+	262.313i	−0.318728	+	0.318728i	−0.848278	−	0.529551i	$-0.822361\pi$
$823$	−262.313	+	262.313i	−0.318728	+	0.318728i	0.529551	+	0.848278i	$0.322361\pi$
$824$	−697.472	−	31.0092i	−0.846447	−	0.0376326i
$825$		0			0
$826$	−800.096	−	117.414i	−0.968639	−	0.142148i
$827$	−893.204	+	369.977i	−1.08005	+	0.447373i	−0.850528	−	0.525930i	$-0.823717\pi$
$827$	−893.204	+	369.977i	−1.08005	+	0.447373i	−0.229525	+	0.973303i	$0.573717\pi$
$828$		0			0
$829$	−161.439	−	66.8701i	−0.194739	−	0.0806635i	0.283183	−	0.959066i	$-0.408610\pi$
$829$	−161.439	−	66.8701i	−0.194739	−	0.0806635i	−0.477922	+	0.878402i	$0.658610\pi$
$830$	−76.9780	−	305.302i	−0.0927446	−	0.367833i
$831$		0			0
$832$	626.279	+	327.290i	0.752740	+	0.393378i
$833$	−19.0189			−0.0228318
$834$		0			0
$835$	254.297	−	613.928i	0.304548	−	0.735243i
$836$	413.351	+	767.583i	0.494439	+	0.918162i
$837$		0			0
$838$	41.7811	−	284.710i	0.0498582	−	0.339749i
$839$	−552.802	−	552.802i	−0.658882	−	0.658882i	0.296234	−	0.955116i	$-0.404269\pi$
$839$	−552.802	−	552.802i	−0.658882	−	0.658882i	−0.955116	+	0.296234i	$0.904269\pi$
$840$		0			0
$841$	536.963	+	536.963i	0.638481	+	0.638481i
$842$	912.175	+	1225.94i	1.08334	+	1.45599i
$843$		0			0
$844$	−1153.23	+	117.200i	−1.36639	+	0.138863i
$845$	−87.5188	+	211.289i	−0.103573	+	0.250046i
$846$		0			0
$847$	1056.14			1.24692
$848$	153.819	−	799.204i	0.181390	−	0.942457i
$849$		0			0
$850$	−6.89891	−	4.12051i	−0.00811637	−	0.00484765i
$851$	−32.8425	−	13.6038i	−0.0385928	−	0.0159857i
$852$		0			0
$853$	−653.395	+	270.645i	−0.765997	+	0.317286i	−0.731250	−	0.682110i	$-0.761063\pi$
$853$	−653.395	+	270.645i	−0.765997	+	0.317286i	−0.0347472	+	0.999396i	$0.511063\pi$
$854$	−523.750	−	703.909i	−0.613290	−	0.824249i
$855$		0			0
$856$	135.161	+	63.1578i	0.157898	+	0.0737824i
$857$	26.5894	−	26.5894i	0.0310261	−	0.0310261i	−0.691424	−	0.722450i	$-0.743016\pi$
$857$	26.5894	−	26.5894i	0.0310261	−	0.0310261i	0.722450	+	0.691424i	$0.243016\pi$
$858$		0			0
$859$	149.594	−	61.9638i	0.174149	−	0.0721349i	−0.293906	−	0.955834i	$-0.594955\pi$
$859$	149.594	−	61.9638i	0.174149	−	0.0721349i	0.468054	+	0.883700i	$0.344955\pi$
$860$	357.336	−	1191.28i	0.415507	−	1.38521i
$861$		0			0
$862$	1572.22	−	396.414i	1.82392	−	0.459878i
$863$			448.190i			0.519339i	0.965698	+	0.259670i	$0.0836137\pi$
$863$			448.190i			0.519339i	−0.965698	+	0.259670i	$0.916386\pi$
$864$		0			0
$865$	−1297.55			−1.50006
$866$	368.231	+	1460.44i	0.425209	+	1.68642i
$867$		0			0
$868$	−40.6362	+	135.472i	−0.0468159	+	0.156074i
$869$	−68.8172	−	166.139i	−0.0791913	−	0.191185i
$870$		0			0
$871$	−520.277	−	520.277i	−0.597333	−	0.597333i
$872$	−536.270	−	1477.05i	−0.614988	−	1.69387i
$873$		0			0
$874$	43.9298	−	32.6864i	0.0502629	−	0.0373986i
$875$	−366.333	−	884.406i	−0.418666	−	1.01075i
$876$		0			0
$877$	−285.210	+	688.559i	−0.325211	+	0.785130i	0.673723	+	0.738984i	$0.264694\pi$
$877$	−285.210	+	688.559i	−0.325211	+	0.785130i	−0.998935	+	0.0461461i	$0.985306\pi$
$878$	−732.329	+	1226.13i	−0.834088	+	1.39650i
$879$		0			0
$880$	−253.292	−	1233.31i	−0.287832	−	1.40149i
$881$			140.757i			0.159770i	0.996804	+	0.0798849i	$0.0254553\pi$
$881$			140.757i			0.159770i	−0.996804	+	0.0798849i	$0.974545\pi$
$882$		0			0
$883$	−644.358	−	266.902i	−0.729737	−	0.302267i	−0.0132930	−	0.999912i	$-0.504231\pi$
$883$	−644.358	−	266.902i	−0.729737	−	0.302267i	−0.716444	+	0.697645i	$0.754231\pi$
$884$	−124.943	+	12.6976i	−0.141338	+	0.0143638i
$885$		0			0
$886$	−1211.03	+	901.080i	−1.36685	+	1.01702i
$887$	251.938	−	251.938i	0.284034	−	0.284034i	−0.550682	−	0.834715i	$-0.685632\pi$
$887$	251.938	−	251.938i	0.284034	−	0.284034i	0.834715	+	0.550682i	$0.185632\pi$
$888$		0			0
$889$	−1018.26	+	1018.26i	−1.14540	+	1.14540i
$890$	227.878	+	33.4411i	0.256043	+	0.0375743i
$891$		0			0
$892$	774.474	+	1438.18i	0.868244	+	1.61231i
$893$	−205.381	−	85.0718i	−0.229990	−	0.0952651i
$894$		0			0
$895$		−	1418.13i		−	1.58450i
$896$	560.639	−	773.358i	0.625713	−	0.863123i
$897$		0			0
$898$	−570.264	+	143.785i	−0.635038	+	0.160117i
$899$	−72.5384	+	175.123i	−0.0806878	+	0.194798i
$900$		0			0
$901$	55.3526	+	133.633i	0.0614346	+	0.148316i
$902$	269.170	−	1834.21i	0.298414	−	2.03349i
$903$		0			0
$904$	846.635	+	925.420i	0.936544	+	1.02369i
$905$	−123.438	−	123.438i	−0.136395	−	0.136395i
$906$		0			0
$907$	17.5960	+	42.4804i	0.0194002	+	0.0468362i	0.933283	−	0.359142i	$-0.116931\pi$
$907$	17.5960	+	42.4804i	0.0194002	+	0.0468362i	−0.913883	+	0.405979i	$0.866931\pi$
$908$	87.2013	+	858.050i	0.0960366	+	0.944989i
$909$		0			0
$910$	−687.104	−	410.386i	−0.755060	−	0.450974i
$911$	−425.886			−0.467493			−0.233747	−	0.972298i	$-0.575099\pi$
$911$	−425.886			−0.467493			−0.233747	+	0.972298i	$0.575099\pi$
$912$		0			0
$913$		−	525.211i		−	0.575258i
$914$	−425.287	−	254.011i	−0.465303	−	0.277911i
$915$		0			0
$916$	183.126	+	149.338i	0.199919	+	0.163033i
$917$	328.971	−	136.264i	0.358747	−	0.148598i
$918$		0			0
$919$	339.201	−	339.201i	0.369098	−	0.369098i	−0.498050	−	0.867148i	$-0.665951\pi$
$919$	339.201	−	339.201i	0.369098	−	0.369098i	0.867148	+	0.498050i	$0.165951\pi$
$920$	−74.3307	+	26.9871i	−0.0807942	+	0.0293338i
$921$		0			0
$922$	−81.4139	+	554.781i	−0.0883015	+	0.601714i
$923$	102.807	−	42.5839i	0.111383	−	0.0461364i
$924$		0			0
$925$	−22.8003	−	9.44420i	−0.0246490	−	0.0102099i
$926$	−104.152	+	26.2607i	−0.112475	+	0.0283593i
$927$		0			0
$928$	852.309	−	955.174i	0.918437	−	1.02928i
$929$	674.156			0.725679			0.362839	−	0.931852i	$-0.381807\pi$
$929$	674.156			0.725679			0.362839	+	0.931852i	$0.381807\pi$
$930$		0			0
$931$	34.4298	−	83.1210i	0.0369816	−	0.0892814i
$932$	−315.795	−	94.7257i	−0.338836	−	0.101637i
$933$		0			0
$934$	217.505	+	31.9188i	0.232874	+	0.0341743i
$935$	158.224	+	158.224i	0.169223	+	0.169223i
$936$		0			0
$937$	−810.809	−	810.809i	−0.865325	−	0.865325i	0.126626	−	0.991951i	$-0.459585\pi$
$937$	−810.809	−	810.809i	−0.865325	−	0.865325i	−0.991951	+	0.126626i	$0.959585\pi$
$938$	−797.937	+	593.713i	−0.850680	+	0.632956i
$939$		0			0
$940$	248.805	+	202.899i	0.264686	+	0.215850i
$941$	372.431	−	899.128i	0.395782	−	0.955503i	−0.592873	−	0.805296i	$-0.702006\pi$
$941$	372.431	−	899.128i	0.395782	−	0.955503i	0.988655	−	0.150206i	$-0.0479938\pi$
$942$		0			0
$943$	−116.436			−0.123474
$944$	−163.844	+	851.291i	−0.173563	+	0.901791i
$945$		0			0
$946$	1063.82	−	1781.14i	1.12454	−	1.88281i
$947$	−647.322	−	268.130i	−0.683551	−	0.283136i	0.0137596	−	0.999905i	$-0.495620\pi$
$947$	−647.322	−	268.130i	−0.683551	−	0.283136i	−0.697310	+	0.716769i	$0.745620\pi$
$948$		0			0
$949$	−798.732	+	330.846i	−0.841656	+	0.348625i
$950$	30.4975	−	22.6919i	0.0321026	−	0.0238863i
$951$		0			0
$952$	−7.53998	+	169.592i	−0.00792014	+	0.178143i
$953$	584.883	−	584.883i	0.613728	−	0.613728i	−0.330187	−	0.943916i	$-0.607112\pi$
$953$	584.883	−	584.883i	0.613728	−	0.613728i	0.943916	+	0.330187i	$0.107112\pi$
$954$		0			0
$955$	−214.162	+	88.7089i	−0.224254	+	0.0928889i
$956$	1293.79	−	696.721i	1.35334	−	0.728788i
$957$		0			0
$958$	−19.9499	−	79.1232i	−0.0208245	−	0.0825920i
$959$		−	294.096i		−	0.306669i
$960$		0			0
$961$	938.549			0.976638
$962$	−373.987	+	94.2962i	−0.388760	+	0.0980210i
$963$		0			0
$964$	−592.373	−	1100.02i	−0.614495	−	1.14110i
$965$	−561.603	−	1355.83i	−0.581972	−	1.40500i
$966$		0			0
$967$	177.502	+	177.502i	0.183560	+	0.183560i	0.792905	−	0.609345i	$-0.208568\pi$
$967$	177.502	+	177.502i	0.183560	+	0.183560i	−0.609345	+	0.792905i	$0.708568\pi$
$968$	50.2882	−	1131.10i	0.0519506	−	1.16849i
$969$		0			0
$970$	393.300	+	528.587i	0.405464	+	0.544935i
$971$	−130.414	−	314.847i	−0.134309	−	0.324250i	0.842389	−	0.538870i	$-0.181149\pi$
$971$	−130.414	−	314.847i	−0.134309	−	0.324250i	−0.976698	+	0.214620i	$0.931149\pi$
$972$		0			0
$973$	248.834	−	600.738i	0.255739	−	0.617408i
$974$	348.846	+	208.355i	0.358158	+	0.213916i
$975$		0			0
$976$	−778.806	+	527.406i	−0.797957	+	0.540375i
$977$			73.1425i			0.0748644i	0.999299	+	0.0374322i	$0.0119178\pi$
$977$			73.1425i			0.0748644i	−0.999299	+	0.0374322i	$0.988082\pi$
$978$		0			0
$979$	354.949	+	147.025i	0.362563	+	0.150179i
$980$	−82.1165	+	100.695i	−0.0837923	+	0.102750i
$981$		0			0
$982$	569.595	+	765.524i	0.580036	+	0.779556i
$983$	614.269	−	614.269i	0.624892	−	0.624892i	−0.321886	−	0.946778i	$-0.604317\pi$
$983$	614.269	−	614.269i	0.624892	−	0.624892i	0.946778	+	0.321886i	$0.104317\pi$
$984$		0			0
$985$	164.219	−	164.219i	0.166720	−	0.166720i
$986$	−33.0335	+	225.101i	−0.0335025	+	0.228297i
$987$		0			0
$988$	170.689	−	569.041i	0.172762	−	0.575953i
$989$	−120.385	−	49.8650i	−0.121724	−	0.0504197i
$990$		0			0
$991$			763.403i			0.770336i	0.922847	+	0.385168i	$0.125856\pi$
$991$			763.403i			0.770336i	−0.922847	+	0.385168i	$0.874144\pi$
$992$	143.152	+	49.9708i	0.144307	+	0.0503738i
$993$		0			0
$994$	−36.7749	−	145.853i	−0.0369969	−	0.146733i
$995$	247.750	−	598.122i	0.248995	−	0.601128i
$996$		0			0
$997$	−752.731	−	1817.25i	−0.754996	−	1.82272i	−0.529073	−	0.848576i	$-0.677460\pi$
$997$	−752.731	−	1817.25i	−0.754996	−	1.82272i	−0.225923	−	0.974145i	$-0.572540\pi$
$998$	877.835	+	128.822i	0.879595	+	0.129080i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.3.u.a.163.1		28
3.2	odd	2		32.3.h.a.3.7	✓	28
12.11	even	2		128.3.h.a.47.7		28
24.5	odd	2		256.3.h.b.95.7		28
24.11	even	2		256.3.h.a.95.1		28
32.11	odd	8	inner	288.3.u.a.235.1		28
96.5	odd	8		256.3.h.a.159.1		28
96.11	even	8		32.3.h.a.11.7	yes	28
96.53	odd	8		128.3.h.a.79.7		28
96.59	even	8		256.3.h.b.159.7		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.7	✓	28	3.2	odd	2
32.3.h.a.11.7	yes	28	96.11	even	8
128.3.h.a.47.7		28	12.11	even	2
128.3.h.a.79.7		28	96.53	odd	8
256.3.h.a.95.1		28	24.11	even	2
256.3.h.a.159.1		28	96.5	odd	8
256.3.h.b.95.7		28	24.5	odd	2
256.3.h.b.159.7		28	96.59	even	8
288.3.u.a.163.1		28	1.1	even	1	trivial
288.3.u.a.235.1		28	32.11	odd	8	inner

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)

\(f(q)\)	\(=\)	\(q+(-1.93931 + 0.488972i) q^{2} +(3.52181 - 1.89653i) q^{4} +(1.85856 + 4.48696i) q^{5} +(-5.27676 - 5.27676i) q^{7} +(-5.90252 + 5.40002i) q^{8} +O(q^{10})\)	\(q+(-1.93931 + 0.488972i) q^{2} +(3.52181 - 1.89653i) q^{4} +(1.85856 + 4.48696i) q^{5} +(-5.27676 - 5.27676i) q^{7} +(-5.90252 + 5.40002i) q^{8} +(-5.79831 - 7.79280i) q^{10} +(-6.20050 - 14.9693i) q^{11} +(-4.22532 + 10.2008i) q^{13} +(12.8134 + 7.65307i) q^{14} +(8.80634 - 13.3585i) q^{16} +2.84356i q^{17} +(-12.4276 - 5.14768i) q^{19} +(15.0551 + 12.2774i) q^{20} +(19.3443 + 25.9983i) q^{22} +(1.43918 - 1.43918i) q^{23} +(0.999126 - 0.999126i) q^{25} +(3.20628 - 21.8486i) q^{26} +(-28.5913 - 8.57623i) q^{28} +(-36.9596 - 15.3092i) q^{29} -4.73823i q^{31} +(-10.5463 + 30.2122i) q^{32} +(-1.39042 - 5.51453i) q^{34} +(13.8694 - 33.4838i) q^{35} +(-6.68390 - 16.1364i) q^{37} +(26.6180 + 3.90618i) q^{38} +(-35.1998 - 16.4481i) q^{40} +(-40.4523 - 40.4523i) q^{41} +(-24.5000 - 59.1482i) q^{43} +(-50.2268 - 40.9598i) q^{44} +(-2.08729 + 3.49473i) q^{46} +16.5262 q^{47} +6.68842i q^{49} +(-1.44907 + 2.42615i) q^{50} +(4.46539 + 43.9389i) q^{52} +(46.9950 - 19.4659i) q^{53} +(55.6428 - 55.6428i) q^{55} +(59.6408 + 2.65160i) q^{56} +(79.1617 + 11.6170i) q^{58} +(-50.0578 + 20.7346i) q^{59} +(-54.3116 - 22.4966i) q^{61} +(2.31686 + 9.18889i) q^{62} +(5.67958 - 63.7475i) q^{64} -53.6237 q^{65} +(-25.5017 + 61.5665i) q^{67} +(5.39290 + 10.0145i) q^{68} +(-10.5245 + 71.7170i) q^{70} +(-7.12641 - 7.12641i) q^{71} +(55.3669 + 55.3669i) q^{73} +(20.8524 + 28.0251i) q^{74} +(-53.5304 + 5.44015i) q^{76} +(-46.2711 + 111.708i) q^{77} +11.0986 q^{79} +(76.3059 + 14.6862i) q^{80} +(98.2293 + 58.6693i) q^{82} +(29.9476 + 12.4047i) q^{83} +(-12.7589 + 5.28492i) q^{85} +(76.4348 + 102.727i) q^{86} +(117.433 + 54.8740i) q^{88} +(-16.7667 + 16.7667i) q^{89} +(76.1234 - 31.5313i) q^{91} +(2.33907 - 7.79797i) q^{92} +(-32.0494 + 8.08086i) q^{94} -65.3294i q^{95} -67.8301 q^{97} +(-3.27045 - 12.9709i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 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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