LMFDB - Embedded newform 288.3.u.a.235.3

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			235.3
Character	$\chi$	$=$	288.235
Dual form			288.3.u.a.163.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.682385 - 1.87999i) q^{2} +(-3.06870 + 2.56575i) q^{4} +(-1.34740 + 3.25291i) q^{5} +(0.583225 - 0.583225i) q^{7} +(6.91761 + 4.01829i) q^{8} +O(q^{10})$	\(q+(-0.682385 - 1.87999i) q^{2} +(-3.06870 + 2.56575i) q^{4} +(-1.34740 + 3.25291i) q^{5} +(0.583225 - 0.583225i) q^{7} +(6.91761 + 4.01829i) q^{8} +(7.03487 + 0.313357i) q^{10} +(3.03620 - 7.33003i) q^{11} +(-6.38385 - 15.4120i) q^{13} +(-1.49444 - 0.698471i) q^{14} +(2.83386 - 15.7470i) q^{16} -19.0889i q^{17} +(-29.6679 + 12.2888i) q^{19} +(-4.21138 - 13.4393i) q^{20} +(-15.8522 - 0.706111i) q^{22} +(-15.2998 - 15.2998i) q^{23} +(8.91173 + 8.91173i) q^{25} +(-24.6181 + 22.5185i) q^{26} +(-0.293334 + 3.28615i) q^{28} +(20.5148 - 8.49749i) q^{29} -53.6582i q^{31} +(-31.5380 + 5.41792i) q^{32} +(-35.8868 + 13.0260i) q^{34} +(1.11134 + 2.68301i) q^{35} +(-3.80237 + 9.17973i) q^{37} +(43.3477 + 47.3895i) q^{38} +(-22.3919 + 17.0881i) q^{40} +(-14.5108 + 14.5108i) q^{41} +(20.3685 - 49.1739i) q^{43} +(9.48983 + 30.2838i) q^{44} +(-18.3230 + 39.2037i) q^{46} -4.73351 q^{47} +48.3197i q^{49} +(10.6727 - 22.8352i) q^{50} +(59.1334 + 30.9154i) q^{52} +(-61.4006 - 25.4330i) q^{53} +(19.7530 + 19.7530i) q^{55} +(6.37809 - 1.69095i) q^{56} +(-29.9741 - 32.7689i) q^{58} +(-42.4656 - 17.5898i) q^{59} +(-27.7452 + 11.4924i) q^{61} +(-100.877 + 36.6155i) q^{62} +(31.7067 + 55.5939i) q^{64} +58.7354 q^{65} +(-9.42323 - 22.7497i) q^{67} +(48.9772 + 58.5780i) q^{68} +(4.28567 - 3.92015i) q^{70} +(95.1299 - 95.1299i) q^{71} +(37.1241 - 37.1241i) q^{73} +(19.8524 + 0.884295i) q^{74} +(59.5118 - 113.831i) q^{76} +(-2.50427 - 6.04584i) q^{77} -70.3394 q^{79} +(47.4053 + 30.4358i) q^{80} +(37.1821 + 17.3782i) q^{82} +(-14.5221 + 6.01526i) q^{83} +(62.0944 + 25.7203i) q^{85} +(-106.345 - 4.73698i) q^{86} +(50.4574 - 38.5060i) q^{88} +(60.8411 + 60.8411i) q^{89} +(-12.7119 - 5.26543i) q^{91} +(86.2059 + 7.69507i) q^{92} +(3.23007 + 8.89893i) q^{94} -113.065i q^{95} +31.8287 q^{97} +(90.8404 - 32.9726i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$	$-1$

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 $

$2$	−0.682385	−	1.87999i	−0.341192	−	0.939993i
$2$	−0.682385	−	1.87999i	−0.341192	−	0.939993i
$3$		0			0
$3$		0			0
$4$	−3.06870	+	2.56575i	−0.767175	+	0.641437i
$5$	−1.34740	+	3.25291i	−0.269480	+	0.650582i	−0.999459	−	0.0328874i	$-0.989530\pi$
$5$	−1.34740	+	3.25291i	−0.269480	+	0.650582i	0.729979	+	0.683469i	$0.239530\pi$
$6$		0			0
$7$	0.583225	−	0.583225i	0.0833178	−	0.0833178i	−0.664220	−	0.747537i	$-0.731236\pi$
$7$	0.583225	−	0.583225i	0.0833178	−	0.0833178i	0.747537	+	0.664220i	$0.231236\pi$
$8$	6.91761	+	4.01829i	0.864701	+	0.502286i
$9$		0			0
$10$	7.03487	+	0.313357i	0.703487	+	0.0313357i
$11$	3.03620	−	7.33003i	0.276018	−	0.666366i	−0.723700	−	0.690115i	$-0.757560\pi$
$11$	3.03620	−	7.33003i	0.276018	−	0.666366i	0.999718	+	0.0237484i	$0.00756007\pi$
$12$		0			0
$13$	−6.38385	−	15.4120i	−0.491065	−	1.18554i	−0.954179	−	0.299238i	$-0.903268\pi$
$13$	−6.38385	−	15.4120i	−0.491065	−	1.18554i	0.463113	−	0.886299i	$-0.346732\pi$
$14$	−1.49444	−	0.698471i	−0.106746	−	0.0498908i
$15$		0			0
$16$	2.83386	−	15.7470i	0.177116	−	0.984190i
$17$		−	19.0889i		−	1.12287i	−0.827519	−	0.561437i	$-0.810249\pi$
$17$		−	19.0889i		−	1.12287i	0.827519	−	0.561437i	$-0.189751\pi$
$18$		0			0
$19$	−29.6679	+	12.2888i	−1.56147	+	0.646781i	−0.985343	−	0.170582i	$-0.945435\pi$
$19$	−29.6679	+	12.2888i	−1.56147	+	0.646781i	−0.576123	+	0.817363i	$0.695435\pi$
$20$	−4.21138	−	13.4393i	−0.210569	−	0.671965i
$21$		0			0
$22$	−15.8522	−	0.706111i	−0.720555	−	0.0320959i
$23$	−15.2998	−	15.2998i	−0.665208	−	0.665208i	0.291395	−	0.956603i	$-0.405881\pi$
$23$	−15.2998	−	15.2998i	−0.665208	−	0.665208i	−0.956603	+	0.291395i	$0.905881\pi$
$24$		0			0
$25$	8.91173	+	8.91173i	0.356469	+	0.356469i
$26$	−24.6181	+	22.5185i	−0.946849	+	0.866094i
$27$		0			0
$28$	−0.293334	+	3.28615i	−0.0104762	+	0.117363i
$29$	20.5148	−	8.49749i	0.707405	−	0.293017i	0.000174983	−	1.00000i	$-0.499944\pi$
$29$	20.5148	−	8.49749i	0.707405	−	0.293017i	0.707231	+	0.706983i	$0.249944\pi$
$30$		0			0
$31$		−	53.6582i		−	1.73091i	−0.500988	−	0.865454i	$-0.667030\pi$
$31$		−	53.6582i		−	1.73091i	0.500988	−	0.865454i	$-0.332970\pi$
$32$	−31.5380	+	5.41792i	−0.985563	+	0.169310i
$33$		0			0
$34$	−35.8868	+	13.0260i	−1.05549	+	0.383116i
$35$	1.11134	+	2.68301i	0.0317526	+	0.0766575i
$36$		0			0
$37$	−3.80237	+	9.17973i	−0.102767	+	0.248101i	−0.966897	−	0.255168i	$-0.917869\pi$
$37$	−3.80237	+	9.17973i	−0.102767	+	0.248101i	0.864130	+	0.503268i	$0.167869\pi$
$38$	43.3477	+	47.3895i	1.14073	+	1.24709i
$39$		0			0
$40$	−22.3919	+	17.0881i	−0.559798	+	0.427203i
$41$	−14.5108	+	14.5108i	−0.353922	+	0.353922i	−0.861567	−	0.507644i	$-0.830516\pi$
$41$	−14.5108	+	14.5108i	−0.353922	+	0.353922i	0.507644	+	0.861567i	$0.330516\pi$
$42$		0			0
$43$	20.3685	−	49.1739i	0.473686	−	1.14358i	−0.488837	−	0.872375i	$-0.662579\pi$
$43$	20.3685	−	49.1739i	0.473686	−	1.14358i	0.962522	−	0.271203i	$-0.0874214\pi$
$44$	9.48983	+	30.2838i	0.215678	+	0.688268i
$45$		0			0
$46$	−18.3230	+	39.2037i	−0.398327	+	0.852255i
$47$	−4.73351			−0.100713			−0.0503565	−	0.998731i	$-0.516036\pi$
$47$	−4.73351			−0.100713			−0.0503565	+	0.998731i	$0.516036\pi$
$48$		0			0
$49$			48.3197i			0.986116i
$50$	10.6727	−	22.8352i	0.213454	−	0.456703i
$51$		0			0
$52$	59.1334	+	30.9154i	1.13718	+	0.594527i
$53$	−61.4006	−	25.4330i	−1.15850	−	0.479867i	−0.281126	−	0.959671i	$-0.590708\pi$
$53$	−61.4006	−	25.4330i	−1.15850	−	0.479867i	−0.877376	+	0.479803i	$0.840708\pi$
$54$		0			0
$55$	19.7530	+	19.7530i	0.359145	+	0.359145i
$56$	6.37809	−	1.69095i	0.113894	−	0.0301956i
$57$		0			0
$58$	−29.9741	−	32.7689i	−0.516795	−	0.564981i
$59$	−42.4656	−	17.5898i	−0.719757	−	0.298133i	−0.00742152	−	0.999972i	$-0.502362\pi$
$59$	−42.4656	−	17.5898i	−0.719757	−	0.298133i	−0.712335	+	0.701840i	$0.752362\pi$
$60$		0			0
$61$	−27.7452	+	11.4924i	−0.454839	+	0.188400i	−0.598328	−	0.801251i	$-0.704168\pi$
$61$	−27.7452	+	11.4924i	−0.454839	+	0.188400i	0.143489	+	0.989652i	$0.454168\pi$
$62$	−100.877	+	36.6155i	−1.62704	+	0.590573i
$63$		0			0
$64$	31.7067	+	55.5939i	0.495417	+	0.868655i
$65$	58.7354			0.903621
$66$		0			0
$67$	−9.42323	−	22.7497i	−0.140645	−	0.339548i	0.837824	−	0.545940i	$-0.183828\pi$
$67$	−9.42323	−	22.7497i	−0.140645	−	0.339548i	−0.978469	+	0.206393i	$0.933828\pi$
$68$	48.9772	+	58.5780i	0.720254	+	0.861442i
$69$		0			0
$70$	4.28567	−	3.92015i	0.0612238	−	0.0560022i
$71$	95.1299	−	95.1299i	1.33986	−	1.33986i	0.443664	−	0.896193i	$-0.353678\pi$
$71$	95.1299	−	95.1299i	1.33986	−	1.33986i	0.896193	−	0.443664i	$-0.146322\pi$
$72$		0			0
$73$	37.1241	−	37.1241i	0.508550	−	0.508550i	−0.405531	−	0.914081i	$-0.632913\pi$
$73$	37.1241	−	37.1241i	0.508550	−	0.508550i	0.914081	+	0.405531i	$0.132913\pi$
$74$	19.8524	+	0.884295i	0.268276	+	0.0119499i
$75$		0			0
$76$	59.5118	−	113.831i	0.783050	−	1.49778i
$77$	−2.50427	−	6.04584i	−0.0325230	−	0.0785174i
$78$		0			0
$79$	−70.3394			−0.890372			−0.445186	−	0.895438i	$-0.646862\pi$
$79$	−70.3394			−0.890372			−0.445186	+	0.895438i	$0.646862\pi$
$80$	47.4053	+	30.4358i	0.592567	+	0.380448i
$81$		0			0
$82$	37.1821	+	17.3782i	0.453440	+	0.211929i
$83$	−14.5221	+	6.01526i	−0.174965	+	0.0724730i	−0.468447	−	0.883492i	$-0.655186\pi$
$83$	−14.5221	+	6.01526i	−0.174965	+	0.0724730i	0.293481	+	0.955965i	$0.405186\pi$
$84$		0			0
$85$	62.0944	+	25.7203i	0.730522	+	0.302592i
$86$	−106.345	−	4.73698i	−1.23657	−	0.0550812i
$87$		0			0
$88$	50.4574	−	38.5060i	0.573380	−	0.437568i
$89$	60.8411	+	60.8411i	0.683608	+	0.683608i	0.960811	−	0.277204i	$-0.0894076\pi$
$89$	60.8411	+	60.8411i	0.683608	+	0.683608i	−0.277204	+	0.960811i	$0.589408\pi$
$90$		0			0
$91$	−12.7119	−	5.26543i	−0.139691	−	0.0578618i
$92$	86.2059	+	7.69507i	0.937020	+	0.0836420i
$93$		0			0
$94$	3.23007	+	8.89893i	0.0343625	+	0.0946695i
$95$		−	113.065i		−	1.19016i
$96$		0			0
$97$	31.8287			0.328131			0.164066	−	0.986449i	$-0.447539\pi$
$97$	31.8287			0.328131			0.164066	+	0.986449i	$0.447539\pi$
$98$	90.8404	−	32.9726i	0.926943	−	0.336455i
$99$		0			0
$100$	−50.2127	−	4.48218i	−0.502127	−	0.0448218i
$101$	−11.0397	+	26.6521i	−0.109304	+	0.263883i	−0.969061	−	0.246820i	$-0.920615\pi$
$101$	−11.0397	+	26.6521i	−0.109304	+	0.263883i	0.859758	+	0.510702i	$0.170615\pi$
$102$		0			0
$103$	56.0862	−	56.0862i	0.544526	−	0.544526i	−0.380326	−	0.924852i	$-0.624188\pi$
$103$	56.0862	−	56.0862i	0.544526	−	0.544526i	0.924852	+	0.380326i	$0.124188\pi$
$104$	17.7688	−	132.266i	0.170854	−	1.27179i
$105$		0			0
$106$	−5.91480	+	132.787i	−0.0558000	+	1.25271i
$107$	−5.85623	+	14.1382i	−0.0547311	+	0.132133i	−0.948880	−	0.315637i	$-0.897782\pi$
$107$	−5.85623	+	14.1382i	−0.0547311	+	0.132133i	0.894149	+	0.447770i	$0.147782\pi$
$108$		0			0
$109$	37.6258	+	90.8367i	0.345191	+	0.833364i	0.997174	+	0.0751304i	$0.0239373\pi$
$109$	37.6258	+	90.8367i	0.345191	+	0.833364i	−0.651983	+	0.758233i	$0.726063\pi$
$110$	23.6562	−	50.6144i	0.215056	−	0.460131i
$111$		0			0
$112$	−7.53128	−	10.8368i	−0.0672436	−	0.0967575i
$113$			82.4104i			0.729295i	0.931146	+	0.364648i	$0.118811\pi$
$113$			82.4104i			0.729295i	−0.931146	+	0.364648i	$0.881189\pi$
$114$		0			0
$115$	70.3837	−	29.1539i	0.612032	−	0.253512i
$116$	−41.1512	+	78.7120i	−0.354752	+	0.678552i
$117$		0			0
$118$	−4.09077	+	91.8379i	−0.0346675	+	0.778287i
$119$	−11.1331	−	11.1331i	−0.0935555	−	0.0935555i
$120$		0			0
$121$	41.0491	+	41.0491i	0.339249	+	0.339249i
$122$	40.5385	+	44.3183i	0.332283	+	0.363265i
$123$		0			0
$124$	137.673	+	164.661i	1.11027	+	1.32791i
$125$	−122.319	+	50.6664i	−0.978556	+	0.405331i
$126$		0			0
$127$		−	60.4972i		−	0.476356i	−0.971221	−	0.238178i	$-0.923450\pi$
$127$		−	60.4972i		−	0.476356i	0.971221	−	0.238178i	$-0.0765502\pi$
$128$	82.8797	−	97.5446i	0.647498	−	0.762067i
$129$		0			0
$130$	−40.0801	−	110.422i	−0.308309	−	0.849398i
$131$	56.4124	+	136.192i	0.430629	+	1.03963i	0.979085	+	0.203451i	$0.0652157\pi$
$131$	56.4124	+	136.192i	0.430629	+	1.03963i	−0.548456	+	0.836179i	$0.684784\pi$
$132$		0			0
$133$	−10.1359	+	24.4702i	−0.0762096	+	0.183986i
$134$	−36.3389	+	33.2396i	−0.271185	+	0.248057i
$135$		0			0
$136$	76.7046	−	132.049i	0.564005	−	0.970951i
$137$	139.949	−	139.949i	1.02152	−	1.02152i	0.0217604	−	0.999763i	$-0.493073\pi$
$137$	139.949	−	139.949i	1.02152	−	1.02152i	0.999763	−	0.0217604i	$-0.00692709\pi$
$138$		0			0
$139$	−2.63118	+	6.35223i	−0.0189293	+	0.0456995i	−0.933062	−	0.359717i	$-0.882873\pi$
$139$	−2.63118	+	6.35223i	−0.0189293	+	0.0456995i	0.914132	+	0.405416i	$0.132873\pi$
$140$	−10.2943	−	5.38195i	−0.0735308	−	0.0384425i
$141$		0			0
$142$	−243.758	−	113.928i	−1.71661	−	0.802308i
$143$	−132.353			−0.925545
$144$		0			0
$145$			78.1822i			0.539187i
$146$	−95.1258	−	44.4599i	−0.651547	−	0.304520i
$147$		0			0
$148$	−11.8845	−	37.9258i	−0.0803010	−	0.256255i
$149$	134.849	+	55.8563i	0.905027	+	0.374874i	0.786151	−	0.618035i	$-0.212071\pi$
$149$	134.849	+	55.8563i	0.905027	+	0.374874i	0.118876	+	0.992909i	$0.462071\pi$
$150$		0			0
$151$	−131.423	−	131.423i	−0.870353	−	0.870353i	0.122158	−	0.992511i	$-0.461019\pi$
$151$	−131.423	−	131.423i	−0.870353	−	0.870353i	−0.992511	+	0.122158i	$0.961019\pi$
$152$	−254.611	−	34.2048i	−1.67507	−	0.225031i
$153$		0			0
$154$	−9.65723	+	8.83358i	−0.0627093	+	0.0573609i
$155$	174.545	+	72.2990i	1.12610	+	0.466445i
$156$		0			0
$157$	−151.775	+	62.8673i	−0.966720	+	0.400429i	−0.809490	−	0.587133i	$-0.800256\pi$
$157$	−151.775	+	62.8673i	−0.966720	+	0.400429i	−0.157230	+	0.987562i	$0.550256\pi$
$158$	47.9985	+	132.237i	0.303788	+	0.836944i
$159$		0			0
$160$	24.8703	−	109.890i	0.155439	−	0.686815i
$161$	−17.8464			−0.110847
$162$		0			0
$163$	75.6492	+	182.633i	0.464106	+	1.12045i	0.966696	+	0.255926i	$0.0823802\pi$
$163$	75.6492	+	182.633i	0.464106	+	1.12045i	−0.502591	+	0.864524i	$0.667620\pi$
$164$	7.29825	−	81.7605i	0.0445015	−	0.498540i
$165$		0			0
$166$	21.2183	+	23.1967i	0.127821	+	0.139739i
$167$	−148.515	+	148.515i	−0.889310	+	0.889310i	−0.994457	−	0.105147i	$-0.966469\pi$
$167$	−148.515	+	148.515i	−0.889310	+	0.889310i	0.105147	+	0.994457i	$0.466469\pi$
$168$		0			0
$169$	−77.2745	+	77.2745i	−0.457246	+	0.457246i
$170$	5.98163	−	134.288i	0.0351860	−	0.789928i
$171$		0			0
$172$	63.6630	+	203.160i	0.370134	+	1.18116i
$173$	−14.9093	−	35.9942i	−0.0861808	−	0.208059i	0.874914	−	0.484279i	$-0.160918\pi$
$173$	−14.9093	−	35.9942i	−0.0861808	−	0.208059i	−0.961094	+	0.276220i	$0.910918\pi$
$174$		0			0
$175$	10.3951			0.0594005
$176$	−106.822	−	68.5834i	−0.606944	−	0.389678i
$177$		0			0
$178$	72.8634	−	155.897i	0.409345	−	0.875829i
$179$	−276.876	+	114.686i	−1.54679	+	0.640703i	−0.982733	−	0.185029i	$-0.940762\pi$
$179$	−276.876	+	114.686i	−1.54679	+	0.640703i	−0.564062	+	0.825733i	$0.690762\pi$
$180$		0			0
$181$	−82.1686	−	34.0354i	−0.453970	−	0.188041i	0.143969	−	0.989582i	$-0.454014\pi$
$181$	−82.1686	−	34.0354i	−0.453970	−	0.188041i	−0.597939	+	0.801542i	$0.704014\pi$
$182$	−1.22455	+	27.4912i	−0.00672830	+	0.151051i
$183$		0			0
$184$	−44.3590	−	167.317i	−0.241081	−	0.909331i
$185$	−24.7375	−	24.7375i	−0.133716	−	0.133716i
$186$		0			0
$187$	−139.922	−	57.9576i	−0.748246	−	0.309933i
$188$	14.5257	−	12.1450i	0.0772645	−	0.0646010i
$189$		0			0
$190$	−212.560	+	77.1537i	−1.11874	+	0.406072i
$191$		−	178.857i		−	0.936426i	−0.883616	−	0.468213i	$-0.844898\pi$
$191$		−	178.857i		−	0.936426i	0.883616	−	0.468213i	$-0.155102\pi$
$192$		0			0
$193$	197.034			1.02090			0.510450	−	0.859908i	$-0.329479\pi$
$193$	197.034			1.02090			0.510450	+	0.859908i	$0.329479\pi$
$194$	−21.7194	−	59.8376i	−0.111956	−	0.308441i
$195$		0			0
$196$	−123.976	−	148.279i	−0.632532	−	0.756524i
$197$	−62.3398	+	150.502i	−0.316446	+	0.763968i	0.682992	+	0.730426i	$0.260679\pi$
$197$	−62.3398	+	150.502i	−0.316446	+	0.763968i	−0.999437	+	0.0335413i	$0.989321\pi$
$198$		0			0
$199$	22.3835	−	22.3835i	0.112480	−	0.112480i	−0.648627	−	0.761107i	$-0.724656\pi$
$199$	22.3835	−	22.3835i	0.112480	−	0.112480i	0.761107	+	0.648627i	$0.224656\pi$
$200$	25.8380	+	97.4578i	0.129190	+	0.487289i
$201$		0			0
$202$	57.6390	+	2.56744i	0.285342	+	0.0127101i
$203$	7.00877	−	16.9207i	0.0345260	−	0.0833530i
$204$		0			0
$205$	−27.6505	−	66.7542i	−0.134881	−	0.325630i
$206$	−143.714	−	67.1690i	−0.697640	−	0.326063i
$207$		0			0
$208$	−260.784	+	56.8513i	−1.25377	+	0.273324i
$209$			254.778i			1.21903i
$210$		0			0
$211$	−315.926	+	130.861i	−1.49728	+	0.620194i	−0.972887	−	0.231282i	$-0.925708\pi$
$211$	−315.926	+	130.861i	−1.49728	+	0.620194i	−0.524394	+	0.851476i	$0.675708\pi$
$212$	253.675	−	79.4924i	1.19658	−	0.374964i
$213$		0			0
$214$	30.5758	+	1.36195i	0.142878	+	0.00636425i
$215$	132.514	+	132.514i	0.616343	+	0.616343i
$216$		0			0
$217$	−31.2948	−	31.2948i	−0.144216	−	0.144216i
$218$	145.096	−	132.722i	0.665580	−	0.608814i
$219$		0			0
$220$	−111.297	−	9.93480i	−0.505896	−	0.0451582i
$221$	−294.197	+	121.860i	−1.33121	+	0.551405i
$222$		0			0
$223$		−	103.995i		−	0.466346i	−0.972435	−	0.233173i	$-0.925089\pi$
$223$		−	103.995i		−	0.466346i	0.972435	−	0.233173i	$-0.0749109\pi$
$224$	−15.2339	+	21.5536i	−0.0680084	+	0.0962215i
$225$		0			0
$226$	154.930	−	56.2356i	0.685533	−	0.248830i
$227$	−19.9655	−	48.2010i	−0.0879538	−	0.212339i	0.873782	−	0.486318i	$-0.161660\pi$
$227$	−19.9655	−	48.2010i	−0.0879538	−	0.212339i	−0.961736	+	0.273979i	$0.911660\pi$
$228$		0			0
$229$	52.0405	−	125.637i	0.227251	−	0.548633i	−0.768590	−	0.639742i	$-0.779041\pi$
$229$	52.0405	−	125.637i	0.227251	−	0.548633i	0.995841	+	0.0911090i	$0.0290412\pi$
$230$	−102.838	−	112.426i	−0.447120	−	0.488810i
$231$		0			0
$232$	176.059	+	23.6519i	0.758873	+	0.101948i
$233$	0.497550	−	0.497550i	0.00213541	−	0.00213541i	−0.706038	−	0.708174i	$-0.749519\pi$
$233$	0.497550	−	0.497550i	0.00213541	−	0.00213541i	0.708174	+	0.706038i	$0.249519\pi$
$234$		0			0
$235$	6.37793	−	15.3977i	0.0271401	−	0.0655220i
$236$	175.446	−	54.9782i	0.743413	−	0.232958i
$237$		0			0
$238$	−13.3330	+	28.5271i	−0.0560211	+	0.119862i
$239$	80.2602			0.335817			0.167908	−	0.985803i	$-0.446299\pi$
$239$	80.2602			0.335817			0.167908	+	0.985803i	$0.446299\pi$
$240$		0			0
$241$			9.94799i			0.0412780i	0.999787	+	0.0206390i	$0.00657006\pi$
$241$			9.94799i			0.0412780i	−0.999787	+	0.0206390i	$0.993430\pi$
$242$	49.1605	−	105.183i	0.203142	−	0.434641i
$243$		0			0
$244$	55.6550	−	106.454i	0.228094	−	0.436287i
$245$	−157.180	−	65.1059i	−0.641549	−	0.265738i
$246$		0			0
$247$	378.790	+	378.790i	1.53356	+	1.53356i
$248$	215.614	−	371.186i	0.869412	−	1.49672i
$249$		0			0
$250$	178.721	+	195.385i	0.714884	+	0.781540i
$251$	37.4569	+	15.5152i	0.149231	+	0.0618134i	0.456049	−	0.889955i	$-0.349264\pi$
$251$	37.4569	+	15.5152i	0.149231	+	0.0618134i	−0.306818	+	0.951768i	$0.599264\pi$
$252$		0			0
$253$	−158.601	+	65.6947i	−0.626881	+	0.259663i
$254$	−113.734	+	41.2824i	−0.447772	+	0.162529i
$255$		0			0
$256$	−239.938	−	89.2499i	−0.937260	−	0.348632i
$257$	351.412			1.36736			0.683680	−	0.729782i	$-0.260378\pi$
$257$	351.412			1.36736			0.683680	+	0.729782i	$0.260378\pi$
$258$		0			0
$259$	3.13621	+	7.57148i	0.0121089	+	0.0292335i
$260$	−180.241	+	150.700i	−0.693236	+	0.579616i
$261$		0			0
$262$	217.543	−	198.990i	0.830318	−	0.759502i
$263$	347.609	−	347.609i	1.32171	−	1.32171i	0.409316	−	0.912393i	$-0.365767\pi$
$263$	347.609	−	347.609i	1.32171	−	1.32171i	0.912393	−	0.409316i	$-0.134233\pi$
$264$		0			0
$265$	165.462	−	165.462i	0.624386	−	0.624386i
$266$	52.9202	+	2.35724i	0.198948	+	0.00886182i
$267$		0			0
$268$	87.2871	+	45.6344i	0.325698	+	0.170278i
$269$	−77.8419	−	187.927i	−0.289375	−	0.698613i	0.710613	−	0.703584i	$-0.248418\pi$
$269$	−77.8419	−	187.927i	−0.289375	−	0.698613i	−0.999988	+	0.00497024i	$0.998418\pi$
$270$		0			0
$271$	−380.417			−1.40375			−0.701876	−	0.712299i	$-0.747654\pi$
$271$	−380.417			−1.40375			−0.701876	+	0.712299i	$0.747654\pi$
$272$	−300.593	−	54.0952i	−1.10512	−	0.198879i
$273$		0			0
$274$	−358.601	−	167.603i	−1.30876	−	0.611689i
$275$	92.3810	−	38.2655i	0.335931	−	0.139147i
$276$		0			0
$277$	130.082	+	53.8819i	0.469612	+	0.194519i	0.604924	−	0.796284i	$-0.293204\pi$
$277$	130.082	+	53.8819i	0.469612	+	0.194519i	−0.135312	+	0.990803i	$0.543204\pi$
$278$	13.7376	+	0.611918i	0.0494158	+	0.00220114i
$279$		0			0
$280$	−3.09331	+	23.0257i	−0.0110475	+	0.0822348i
$281$	40.5881	+	40.5881i	0.144442	+	0.144442i	0.775630	−	0.631188i	$-0.217432\pi$
$281$	40.5881	+	40.5881i	0.144442	+	0.144442i	−0.631188	+	0.775630i	$0.717432\pi$
$282$		0			0
$283$	442.450	+	183.269i	1.56343	+	0.647593i	0.985681	−	0.168622i	$-0.0539316\pi$
$283$	442.450	+	183.269i	1.56343	+	0.647593i	0.577748	+	0.816215i	$0.303932\pi$
$284$	−47.8458	+	536.005i	−0.168471	+	1.88734i
$285$		0			0
$286$	90.3156	+	248.822i	0.315789	+	0.870006i
$287$			16.9261i			0.0589761i
$288$		0			0
$289$	−75.3848			−0.260847
$290$	146.981	−	53.3503i	0.506833	−	0.183967i
$291$		0			0
$292$	−18.6717	+	209.174i	−0.0639441	+	0.716350i
$293$	141.261	−	341.035i	0.482120	−	1.16394i	−0.476479	−	0.879186i	$-0.658087\pi$
$293$	141.261	−	341.035i	0.482120	−	1.16394i	0.958600	−	0.284756i	$-0.0919127\pi$
$294$		0			0
$295$	114.436	−	114.436i	0.387920	−	0.387920i
$296$	−63.1901	+	48.2228i	−0.213480	+	0.162915i
$297$		0			0
$298$	12.9902	−	291.630i	0.0435912	−	0.978623i
$299$	−138.128	+	333.471i	−0.461968	+	1.11529i
$300$		0			0
$301$	−16.8000	−	40.5588i	−0.0558140	−	0.134747i
$302$	−157.393	+	336.755i	−0.521168	+	1.11508i
$303$		0			0
$304$	109.438	+	502.006i	0.359994	+	1.65134i
$305$		−	105.737i		−	0.346680i
$306$		0			0
$307$	27.5569	−	11.4145i	0.0897620	−	0.0371807i	−0.337351	−	0.941379i	$-0.609531\pi$
$307$	27.5569	−	11.4145i	0.0897620	−	0.0371807i	0.427113	+	0.904198i	$0.359531\pi$
$308$	23.1970	+	12.1276i	0.0753148	+	0.0393752i
$309$		0			0
$310$	16.8142	−	377.478i	0.0542392	−	1.21767i
$311$	−262.516	−	262.516i	−0.844102	−	0.844102i	0.145288	−	0.989389i	$-0.453589\pi$
$311$	−262.516	−	262.516i	−0.844102	−	0.844102i	−0.989389	+	0.145288i	$0.953589\pi$
$312$		0			0
$313$	−346.338	−	346.338i	−1.10651	−	1.10651i	−0.993606	−	0.112907i	$-0.963984\pi$
$313$	−346.338	−	346.338i	−1.10651	−	1.10651i	−0.112907	−	0.993606i	$-0.536016\pi$
$314$	221.759	+	242.435i	0.706238	+	0.772087i
$315$		0			0
$316$	215.851	−	180.473i	0.683071	−	0.571118i
$317$	−37.8371	+	15.6726i	−0.119360	+	0.0494405i	−0.441564	−	0.897230i	$-0.645576\pi$
$317$	−37.8371	+	15.6726i	−0.119360	+	0.0494405i	0.322204	+	0.946670i	$0.395576\pi$
$318$		0			0
$319$		−	176.174i		−	0.552269i
$320$	−223.564	+	28.2317i	−0.698636	+	0.0882241i
$321$		0			0
$322$	12.1781	+	33.5510i	0.0378203	+	0.104196i
$323$	234.580	+	566.326i	0.726253	+	1.75333i
$324$		0			0
$325$	80.4563	−	194.239i	0.247558	−	0.597657i
$326$	291.726	−	266.846i	0.894866	−	0.818545i
$327$		0			0
$328$	−158.689	+	42.0715i	−0.483807	+	0.128267i
$329$	−2.76070	+	2.76070i	−0.00839118	+	0.00839118i
$330$		0			0
$331$	123.850	−	298.999i	0.374168	−	0.903321i	−0.618867	−	0.785496i	$-0.712408\pi$
$331$	123.850	−	298.999i	0.374168	−	0.903321i	0.993034	−	0.117825i	$-0.0375921\pi$
$332$	29.1304	−	55.7192i	0.0877422	−	0.167829i
$333$		0			0
$334$	380.550	+	177.862i	1.13937	+	0.532520i
$335$	86.6995			0.258805
$336$		0			0
$337$			553.901i			1.64362i	0.569759	+	0.821812i	$0.307037\pi$
$337$			553.901i			1.64362i	−0.569759	+	0.821812i	$0.692963\pi$
$338$	198.006	+	92.5441i	0.585817	+	0.273799i
$339$		0			0
$340$	−256.541	+	80.3905i	−0.754532	+	0.236443i
$341$	−393.316	−	162.917i	−1.15342	−	0.477762i
$342$		0			0
$343$	56.7593	+	56.7593i	0.165479	+	0.165479i
$344$	338.496	−	258.319i	0.984000	−	0.750928i
$345$		0			0
$346$	−57.4947	+	52.5912i	−0.166170	+	0.151998i
$347$	−149.596	−	61.9645i	−0.431111	−	0.178572i	0.156566	−	0.987667i	$-0.449958\pi$
$347$	−149.596	−	61.9645i	−0.431111	−	0.178572i	−0.587677	+	0.809095i	$0.699958\pi$
$348$		0			0
$349$	−354.488	+	146.834i	−1.01572	+	0.420727i	−0.827540	−	0.561407i	$-0.810260\pi$
$349$	−354.488	+	146.834i	−1.01572	+	0.420727i	−0.188184	+	0.982134i	$0.560260\pi$
$350$	−7.09345	−	19.5426i	−0.0202670	−	0.0558361i
$351$		0			0
$352$	−56.0421	+	247.624i	−0.159211	+	0.703478i
$353$	360.254			1.02055			0.510275	−	0.860011i	$-0.329544\pi$
$353$	360.254			1.02055			0.510275	+	0.860011i	$0.329544\pi$
$354$		0			0
$355$	181.271	+	437.627i	0.510622	+	1.23275i
$356$	−342.806	−	30.6002i	−0.962939	−	0.0859556i
$357$		0			0
$358$	404.544	+	442.264i	1.13001	+	1.23537i
$359$	−92.0047	+	92.0047i	−0.256280	+	0.256280i	−0.823539	−	0.567259i	$-0.808004\pi$
$359$	−92.0047	+	92.0047i	−0.256280	+	0.256280i	0.567259	+	0.823539i	$0.308004\pi$
$360$		0			0
$361$	473.901	−	473.901i	1.31275	−	1.31275i
$362$	−7.91541	+	177.701i	−0.0218658	+	0.490887i
$363$		0			0
$364$	52.5187	−	16.4574i	0.144282	−	0.0452127i
$365$	70.7404	+	170.782i	0.193809	+	0.467897i
$366$		0			0
$367$	254.513			0.693496			0.346748	−	0.937958i	$-0.387286\pi$
$367$	254.513			0.693496			0.346748	+	0.937958i	$0.387286\pi$
$368$	−284.284	+	197.569i	−0.772510	+	0.536872i
$369$		0			0
$370$	−29.6257	+	63.3867i	−0.0800695	+	0.171315i
$371$	−50.6435	+	20.9772i	−0.136505	+	0.0565424i
$372$		0			0
$373$	440.477	+	182.452i	1.18090	+	0.489147i	0.884783	−	0.466004i	$-0.154307\pi$
$373$	440.477	+	182.452i	1.18090	+	0.489147i	0.296122	+	0.955150i	$0.404307\pi$
$374$	−13.4789	+	302.601i	−0.0360397	+	0.809093i
$375$		0			0
$376$	−32.7446	−	19.0206i	−0.0870866	−	0.0505867i
$377$	−261.926	−	261.926i	−0.694765	−	0.694765i
$378$		0			0
$379$	124.964	+	51.7618i	0.329720	+	0.136575i	0.541402	−	0.840764i	$-0.317894\pi$
$379$	124.964	+	51.7618i	0.329720	+	0.136575i	−0.211681	+	0.977339i	$0.567894\pi$
$380$	290.096	+	346.962i	0.763411	+	0.913059i
$381$		0			0
$382$	−336.250	+	122.050i	−0.880235	+	0.319502i
$383$			182.483i			0.476458i	0.971209	+	0.238229i	$0.0765669\pi$
$383$			182.483i			0.476458i	−0.971209	+	0.238229i	$0.923433\pi$
$384$		0			0
$385$	23.0408			0.0598463
$386$	−134.453	−	370.421i	−0.348323	−	0.959639i
$387$		0			0
$388$	−97.6728	+	81.6645i	−0.251734	+	0.210476i
$389$	134.979	−	325.868i	0.346990	−	0.837708i	−0.649982	−	0.759949i	$-0.725224\pi$
$389$	134.979	−	325.868i	0.346990	−	0.837708i	0.996972	−	0.0777583i	$-0.0247763\pi$
$390$		0			0
$391$	−292.055	+	292.055i	−0.746945	+	0.746945i
$392$	−194.163	+	334.257i	−0.495313	+	0.852696i
$393$		0			0
$394$	325.481	+	14.4980i	0.826093	+	0.0367970i
$395$	94.7752	−	228.808i	0.239937	−	0.579260i
$396$		0			0
$397$	−272.283	−	657.350i	−0.685852	−	1.65579i	−0.752976	−	0.658048i	$-0.771382\pi$
$397$	−272.283	−	657.350i	−0.685852	−	1.65579i	0.0671236	−	0.997745i	$-0.478618\pi$
$398$	−57.3549	−	26.8066i	−0.144108	−	0.0673532i
$399$		0			0
$400$	165.588	−	115.079i	0.413970	−	0.287697i
$401$		−	74.4996i		−	0.185785i	−0.995676	−	0.0928923i	$-0.970389\pi$
$401$		−	74.4996i		−	0.185785i	0.995676	−	0.0928923i	$-0.0296112\pi$
$402$		0			0
$403$	−826.978	+	342.546i	−2.05206	+	0.849989i
$404$	−34.5052	−	110.113i	−0.0854090	−	0.272556i
$405$		0			0
$406$	−36.5933	−	1.62999i	−0.0901313	−	0.00401475i
$407$	55.7429	+	55.7429i	0.136961	+	0.136961i
$408$		0			0
$409$	−289.633	−	289.633i	−0.708149	−	0.708149i	0.257997	−	0.966146i	$-0.416938\pi$
$409$	−289.633	−	289.633i	−0.708149	−	0.708149i	−0.966146	+	0.257997i	$0.916938\pi$
$410$	−106.629	+	97.5347i	−0.260070	+	0.237889i
$411$		0			0
$412$	−28.2087	+	316.015i	−0.0684678	+	0.767027i
$413$	−35.0258	+	14.5082i	−0.0848083	+	0.0351288i
$414$		0			0
$415$		−	55.3441i		−	0.133359i
$416$	284.835	+	451.476i	0.684699	+	1.08528i
$417$		0			0
$418$	478.979	−	173.856i	1.14588	−	0.415924i
$419$	−234.290	−	565.626i	−0.559165	−	1.34994i	−0.910428	−	0.413667i	$-0.864248\pi$
$419$	−234.290	−	565.626i	−0.559165	−	1.34994i	0.351264	−	0.936277i	$-0.385752\pi$
$420$		0			0
$421$	205.463	−	496.031i	0.488035	−	1.17822i	−0.467672	−	0.883902i	$-0.654907\pi$
$421$	205.463	−	496.031i	0.488035	−	1.17822i	0.955707	−	0.294319i	$-0.0950929\pi$
$422$	461.600	+	504.640i	1.09384	+	1.19583i
$423$		0			0
$424$	−322.549	−	422.661i	−0.760728	−	0.996842i
$425$	170.115	−	170.115i	0.400270	−	0.400270i
$426$		0			0
$427$	−9.47901	+	22.8843i	−0.0221991	+	0.0535933i
$428$	−18.3040	−	58.4115i	−0.0427664	−	0.136476i
$429$		0			0
$430$	158.699	−	339.549i	0.369067	−	0.789649i
$431$	94.1706			0.218493			0.109247	−	0.994015i	$-0.465156\pi$
$431$	94.1706			0.218493			0.109247	+	0.994015i	$0.465156\pi$
$432$		0			0
$433$			66.2703i			0.153049i	0.997068	+	0.0765246i	$0.0243824\pi$
$433$			66.2703i			0.153049i	−0.997068	+	0.0765246i	$0.975618\pi$
$434$	−37.4787	+	80.1888i	−0.0863564	+	0.184767i
$435$		0			0
$436$	−348.526	−	182.212i	−0.799372	−	0.417918i
$437$	641.928	+	265.895i	1.46894	+	0.608456i
$438$		0			0
$439$	393.404	+	393.404i	0.896137	+	0.896137i	0.995092	−	0.0989551i	$-0.0315500\pi$
$439$	393.404	+	393.404i	0.896137	+	0.896137i	−0.0989551	+	0.995092i	$0.531550\pi$
$440$	57.2701	+	216.016i	0.130159	+	0.490946i
$441$		0			0
$442$	429.852	+	469.931i	0.972515	+	1.06319i
$443$	−124.298	−	51.4859i	−0.280583	−	0.116221i	0.237954	−	0.971276i	$-0.423523\pi$
$443$	−124.298	−	51.4859i	−0.280583	−	0.116221i	−0.518537	+	0.855055i	$0.673523\pi$
$444$		0			0
$445$	−279.888	+	115.933i	−0.628961	+	0.260524i
$446$	−195.510	+	70.9647i	−0.438362	+	0.159114i
$447$		0			0
$448$	50.9159	+	13.9317i	0.113652	+	0.0310974i
$449$	−621.505			−1.38420			−0.692099	−	0.721802i	$-0.743314\pi$
$449$	−621.505			−1.38420			−0.692099	+	0.721802i	$0.743314\pi$
$450$		0			0
$451$	62.3070	+	150.422i	0.138153	+	0.333531i
$452$	−211.444	−	252.893i	−0.467797	−	0.559498i
$453$		0			0
$454$	−76.9931	+	70.4265i	−0.169588	+	0.155124i
$455$	34.2559	−	34.2559i	0.0752877	−	0.0752877i
$456$		0			0
$457$	−121.890	+	121.890i	−0.266718	+	0.266718i	−0.827776	−	0.561058i	$-0.810394\pi$
$457$	−121.890	+	121.890i	−0.266718	+	0.266718i	0.561058	+	0.827776i	$0.310394\pi$
$458$	−271.708	−	12.1028i	−0.593248	−	0.0264253i
$459$		0			0
$460$	−141.185	+	270.052i	−0.306924	+	0.587069i
$461$	−92.0148	−	222.143i	−0.199598	−	0.481873i	0.792111	−	0.610378i	$-0.208982\pi$
$461$	−92.0148	−	222.143i	−0.199598	−	0.481873i	−0.991709	+	0.128505i	$0.958982\pi$
$462$		0			0
$463$	−133.158			−0.287598			−0.143799	−	0.989607i	$-0.545932\pi$
$463$	−133.158			−0.287598			−0.143799	+	0.989607i	$0.545932\pi$
$464$	−75.6743	−	347.127i	−0.163091	−	0.748119i
$465$		0			0
$466$	−1.27491	−	0.595867i	−0.00273586	−	0.00127869i
$467$	414.267	−	171.595i	0.887082	−	0.367441i	0.107843	−	0.994168i	$-0.465606\pi$
$467$	414.267	−	171.595i	0.887082	−	0.367441i	0.779239	+	0.626727i	$0.215606\pi$
$468$		0			0
$469$	−18.7640	−	7.77232i	−0.0400086	−	0.0165721i
$470$	−33.2996	−	1.48328i	−0.0708503	−	0.00315591i
$471$		0			0
$472$	−223.080	−	292.319i	−0.472626	−	0.619320i
$473$	−298.603	−	298.603i	−0.631296	−	0.631296i
$474$		0			0
$475$	−373.907	−	154.877i	−0.787172	−	0.326058i
$476$	62.7289	+	5.59942i	0.131783	+	0.0117635i
$477$		0			0
$478$	−54.7683	−	150.888i	−0.114578	−	0.315665i
$479$		−	293.655i		−	0.613059i	−0.951861	−	0.306530i	$-0.900832\pi$
$479$		−	293.655i		−	0.613059i	0.951861	−	0.306530i	$-0.0991679\pi$
$480$		0			0
$481$	165.752			0.344598
$482$	18.7021	−	6.78836i	0.0388010	−	0.0140837i
$483$		0			0
$484$	−231.289	−	20.6458i	−0.477870	−	0.0426565i
$485$	−42.8860	+	103.536i	−0.0884247	+	0.213476i
$486$		0			0
$487$	468.368	−	468.368i	0.961741	−	0.961741i	−0.0375532	−	0.999295i	$-0.511956\pi$
$487$	468.368	−	468.368i	0.961741	−	0.961741i	0.999295	+	0.0375532i	$0.0119564\pi$
$488$	−238.110	−	31.9881i	−0.487931	−	0.0655493i
$489$		0			0
$490$	−15.1413	+	339.923i	−0.0309006	+	0.693720i
$491$	120.443	−	290.775i	0.245301	−	0.592210i	−0.752492	−	0.658601i	$-0.771149\pi$
$491$	120.443	−	290.775i	0.245301	−	0.592210i	0.997794	+	0.0663911i	$0.0211485\pi$
$492$		0			0
$493$	−162.207	−	391.603i	−0.329021	−	0.794328i
$494$	453.640	−	970.602i	0.918300	−	1.96478i
$495$		0			0
$496$	−844.957	−	152.060i	−1.70354	−	0.306572i
$497$		−	110.964i		−	0.223268i
$498$		0			0
$499$	572.626	−	237.190i	1.14755	−	0.475330i	0.273837	−	0.961776i	$-0.411707\pi$
$499$	572.626	−	237.190i	1.14755	−	0.475330i	0.873711	+	0.486446i	$0.161707\pi$
$500$	245.365	−	469.321i	0.490729	−	0.938642i
$501$		0			0
$502$	3.60827	−	81.0058i	0.00718779	−	0.161366i
$503$	397.129	+	397.129i	0.789520	+	0.789520i	0.981415	−	0.191895i	$-0.0614634\pi$
$503$	397.129	+	397.129i	0.789520	+	0.789520i	−0.191895	+	0.981415i	$0.561463\pi$
$504$		0			0
$505$	−71.8222	−	71.8222i	−0.142222	−	0.142222i
$506$	231.732	+	253.339i	0.457968	+	0.500669i
$507$		0			0
$508$	155.221	+	185.648i	0.305553	+	0.365449i
$509$	16.5014	−	6.83509i	0.0324192	−	0.0134285i	−0.366415	−	0.930452i	$-0.619415\pi$
$509$	16.5014	−	6.83509i	0.0324192	−	0.0134285i	0.398834	+	0.917023i	$0.369415\pi$
$510$		0			0
$511$		−	43.3034i		−	0.0847425i
$512$	−4.05825	+	511.984i	−0.00792626	+	0.999969i
$513$		0			0
$514$	−239.798	−	660.649i	−0.466533	−	1.28531i
$515$	106.873	+	258.014i	0.207520	+	0.500998i
$516$		0			0
$517$	−14.3719	+	34.6968i	−0.0277986	+	0.0671117i
$518$	12.0942	−	11.0627i	0.0233478	−	0.0213566i
$519$		0			0
$520$	406.308	+	236.016i	0.781362	+	0.453877i
$521$	11.8175	−	11.8175i	0.0226824	−	0.0226824i	−0.695675	−	0.718357i	$-0.744894\pi$
$521$	11.8175	−	11.8175i	0.0226824	−	0.0226824i	0.718357	+	0.695675i	$0.244894\pi$
$522$		0			0
$523$	141.420	−	341.417i	0.270401	−	0.652806i	−0.729100	−	0.684408i	$-0.760061\pi$
$523$	141.420	−	341.417i	0.270401	−	0.652806i	0.999501	+	0.0316019i	$0.0100609\pi$
$524$	−522.546	−	273.191i	−0.997225	−	0.521357i
$525$		0			0
$526$	−890.705	−	416.298i	−1.69335	−	0.791441i
$527$	−1024.27			−1.94359
$528$		0			0
$529$		−	60.8334i		−	0.114997i
$530$	−423.976	−	198.158i	−0.799955	−	0.373883i
$531$		0			0
$532$	−31.6804	−	101.098i	−0.0595495	−	0.190034i
$533$	316.275	+	131.006i	0.593387	+	0.245789i
$534$		0			0
$535$	−38.0996	−	38.0996i	−0.0712142	−	0.0712142i
$536$	26.2286	−	195.239i	0.0489340	−	0.364251i
$537$		0			0
$538$	−300.182	+	274.580i	−0.557959	+	0.510372i
$539$	354.185	+	146.708i	0.657115	+	0.272186i
$540$		0			0
$541$	−117.048	+	48.4829i	−0.216355	+	0.0896172i	−0.488229	−	0.872716i	$-0.662357\pi$
$541$	−117.048	+	48.4829i	−0.216355	+	0.0896172i	0.271874	+	0.962333i	$0.412357\pi$
$542$	259.591	+	715.178i	0.478949	+	1.31952i
$543$		0			0
$544$	103.422	+	602.025i	0.190114	+	1.10666i
$545$	−346.180			−0.635193
$546$		0			0
$547$	−113.911	−	275.005i	−0.208247	−	0.502752i	0.784901	−	0.619622i	$-0.212714\pi$
$547$	−113.911	−	275.005i	−0.208247	−	0.502752i	−0.993147	+	0.116870i	$0.962714\pi$
$548$	−70.3876	+	788.534i	−0.128445	+	1.43893i
$549$		0			0
$550$	−134.978	−	147.563i	−0.245415	−	0.268297i
$551$	−504.205	+	504.205i	−0.915072	+	0.915072i
$552$		0			0
$553$	−41.0237	+	41.0237i	−0.0741838	+	0.0741838i
$554$	12.5310	−	281.321i	0.0226191	−	0.507800i
$555$		0			0
$556$	−8.22392	−	26.2440i	−0.0147912	−	0.0472015i
$557$	−87.2197	−	210.567i	−0.156588	−	0.378037i	0.826043	−	0.563607i	$-0.190587\pi$
$557$	−87.2197	−	210.567i	−0.156588	−	0.378037i	−0.982631	+	0.185570i	$0.940587\pi$
$558$		0			0
$559$	−887.896			−1.58836
$560$	45.3989	−	9.89703i	0.0810695	−	0.0176733i
$561$		0			0
$562$	48.6084	−	104.002i	0.0864918	−	0.185057i
$563$	−697.221	+	288.798i	−1.23840	+	0.512963i	−0.903215	−	0.429188i	$-0.858800\pi$
$563$	−697.221	+	288.798i	−1.23840	+	0.512963i	−0.335188	+	0.942151i	$0.608800\pi$
$564$		0			0
$565$	−268.074	−	111.040i	−0.474466	−	0.196530i
$566$	42.6218	−	956.861i	0.0753035	−	1.69057i
$567$		0			0
$568$	1040.33	−	275.812i	1.83157	−	0.485584i
$569$	252.850	+	252.850i	0.444376	+	0.444376i	0.893480	−	0.449104i	$-0.148257\pi$
$569$	252.850	+	252.850i	0.444376	+	0.444376i	−0.449104	+	0.893480i	$0.648257\pi$
$570$		0			0
$571$	352.993	+	146.215i	0.618202	+	0.256068i	0.669731	−	0.742604i	$-0.266409\pi$
$571$	352.993	+	146.215i	0.618202	+	0.256068i	−0.0515290	+	0.998672i	$0.516409\pi$
$572$	406.152	−	339.584i	0.710055	−	0.593679i
$573$		0			0
$574$	31.8209	−	11.5501i	0.0554371	−	0.0201222i
$575$		−	272.695i		−	0.474252i
$576$		0			0
$577$	−197.099			−0.341593			−0.170797	−	0.985306i	$-0.554634\pi$
$577$	−197.099			−0.341593			−0.170797	+	0.985306i	$0.554634\pi$
$578$	51.4414	+	141.722i	0.0889990	+	0.245194i
$579$		0			0
$580$	−200.596	−	239.918i	−0.345855	−	0.413651i
$581$	−4.96141	+	11.9779i	−0.00853944	+	0.0206160i
$582$		0			0
$583$	−372.849	+	372.849i	−0.639535	+	0.639535i
$584$	405.986	−	107.635i	0.695181	−	0.184306i
$585$		0			0
$586$	−737.536	−	32.8523i	−1.25859	−	0.0560620i
$587$	238.745	−	576.382i	0.406721	−	0.981912i	−0.579273	−	0.815134i	$-0.696664\pi$
$587$	238.745	−	576.382i	0.406721	−	0.981912i	0.985994	−	0.166778i	$-0.0533365\pi$
$588$		0			0
$589$	659.396	+	1591.92i	1.11952	+	2.70276i
$590$	−293.228	−	137.049i	−0.496997	−	0.232287i
$591$		0			0
$592$	133.778	+	85.8901i	0.225977	+	0.145085i
$593$			276.598i			0.466438i	0.972424	+	0.233219i	$0.0749260\pi$
$593$			276.598i			0.466438i	−0.972424	+	0.233219i	$0.925074\pi$
$594$		0			0
$595$	51.2157	−	21.2142i	0.0860768	−	0.0356542i
$596$	−557.124	+	174.582i	−0.934772	+	0.292923i
$597$		0			0
$598$	721.179	+	32.1237i	1.20598	+	0.0537186i
$599$	710.727	+	710.727i	1.18652	+	1.18652i	0.978022	+	0.208501i	$0.0668585\pi$
$599$	710.727	+	710.727i	1.18652	+	1.18652i	0.208501	+	0.978022i	$0.433141\pi$
$600$		0			0
$601$	−215.219	−	215.219i	−0.358102	−	0.358102i	0.505011	−	0.863113i	$-0.331488\pi$
$601$	−215.219	−	215.219i	−0.358102	−	0.358102i	−0.863113	+	0.505011i	$0.831488\pi$
$602$	−64.7860	+	59.2605i	−0.107618	+	0.0984394i
$603$		0			0
$604$	740.498	+	66.0997i	1.22599	+	0.109437i
$605$	−188.839	+	78.2195i	−0.312130	+	0.129288i
$606$		0			0
$607$			683.779i			1.12649i	0.826290	+	0.563245i	$0.190447\pi$
$607$			683.779i			1.12649i	−0.826290	+	0.563245i	$0.809553\pi$
$608$	869.086	−	548.303i	1.42942	−	0.901815i
$609$		0			0
$610$	−198.785	+	72.1536i	−0.325877	+	0.118285i
$611$	30.2180	+	72.9527i	0.0494566	+	0.119399i
$612$		0			0
$613$	−296.111	+	714.875i	−0.483052	+	1.16619i	0.475100	+	0.879932i	$0.342412\pi$
$613$	−296.111	+	714.875i	−0.483052	+	1.16619i	−0.958152	+	0.286259i	$0.907588\pi$
$614$	−40.2635	−	44.0176i	−0.0655757	−	0.0716900i
$615$		0			0
$616$	6.97039	−	51.8856i	0.0113156	−	0.0842299i
$617$	275.822	−	275.822i	0.447037	−	0.447037i	−0.447331	−	0.894368i	$-0.647626\pi$
$617$	275.822	−	275.822i	0.447037	−	0.447037i	0.894368	+	0.447331i	$0.147626\pi$
$618$		0			0
$619$	201.130	−	485.570i	0.324927	−	0.784443i	−0.674027	−	0.738707i	$-0.735437\pi$
$619$	201.130	−	485.570i	0.324927	−	0.784443i	0.998954	−	0.0457357i	$-0.0145632\pi$
$620$	−721.128	+	225.975i	−1.16311	+	0.364476i
$621$		0			0
$622$	−314.389	+	672.663i	−0.505449	+	1.08145i
$623$	70.9681			0.113913
$624$		0			0
$625$		−	151.085i		−	0.241735i
$626$	−414.775	+	887.448i	−0.662581	+	1.41765i
$627$		0			0
$628$	304.451	−	582.338i	0.484794	−	0.927289i
$629$	175.231	+	72.5829i	0.278586	+	0.115394i
$630$		0			0
$631$	48.9545	+	48.9545i	0.0775823	+	0.0775823i	0.744833	−	0.667251i	$-0.232529\pi$
$631$	48.9545	+	48.9545i	0.0775823	+	0.0775823i	−0.667251	+	0.744833i	$0.732529\pi$
$632$	−486.580	−	282.644i	−0.769906	−	0.447222i
$633$		0			0
$634$	55.2838	+	60.4385i	0.0871984	+	0.0953288i
$635$	196.792	+	81.5139i	0.309909	+	0.128368i
$636$		0			0
$637$	744.702	−	308.466i	1.16908	−	0.484248i
$638$	−331.205	+	120.218i	−0.519129	+	0.188430i
$639$		0			0
$640$	205.632	+	401.032i	0.321299	+	0.626612i
$641$	−320.295			−0.499680			−0.249840	−	0.968287i	$-0.580378\pi$
$641$	−320.295			−0.499680			−0.249840	+	0.968287i	$0.580378\pi$
$642$		0			0
$643$	39.8184	+	96.1302i	0.0619260	+	0.149503i	0.951813	−	0.306677i	$-0.0992173\pi$
$643$	39.8184	+	96.1302i	0.0619260	+	0.149503i	−0.889887	+	0.456180i	$0.849217\pi$
$644$	54.7653	−	45.7894i	0.0850394	−	0.0711016i
$645$		0			0
$646$	904.612	−	827.459i	1.40033	−	1.28090i
$647$	134.372	−	134.372i	0.207684	−	0.207684i	−0.595598	−	0.803282i	$-0.703085\pi$
$647$	134.372	−	134.372i	0.207684	−	0.207684i	0.803282	+	0.595598i	$0.203085\pi$
$648$		0			0
$649$	−257.868	+	257.868i	−0.397331	+	0.397331i
$650$	−420.068	−	18.7113i	−0.646259	−	0.0287865i
$651$		0			0
$652$	−700.736	−	366.350i	−1.07475	−	0.561887i
$653$	358.760	+	866.123i	0.549403	+	1.32638i	0.917924	+	0.396756i	$0.129864\pi$
$653$	358.760	+	866.123i	0.549403	+	1.32638i	−0.368521	+	0.929619i	$0.620136\pi$
$654$		0			0
$655$	−519.029			−0.792410
$656$	187.381	+	269.624i	0.285641	+	0.411012i
$657$		0			0
$658$	7.07394	+	3.30622i	0.0107507	+	0.00502465i
$659$	−596.224	+	246.964i	−0.904741	+	0.374756i	−0.786041	−	0.618174i	$-0.787873\pi$
$659$	−596.224	+	246.964i	−0.904741	+	0.374756i	−0.118700	+	0.992930i	$0.537873\pi$
$660$		0			0
$661$	16.3196	+	6.75978i	0.0246892	+	0.0102266i	0.394994	−	0.918684i	$-0.370747\pi$
$661$	16.3196	+	6.75978i	0.0246892	+	0.0102266i	−0.370305	+	0.928910i	$0.620747\pi$
$662$	−646.628	−	28.8030i	−0.976779	−	0.0435090i
$663$		0			0
$664$	−124.629	−	16.7429i	−0.187695	−	0.0252152i
$665$	−65.9422	−	65.9422i	−0.0991612	−	0.0991612i
$666$		0			0
$667$	−443.881	−	183.862i	−0.665489	−	0.275655i
$668$	74.6959	−	836.799i	0.111820	−	1.25269i
$669$		0			0
$670$	−59.1625	−	162.994i	−0.0883022	−	0.243275i
$671$			238.266i			0.355091i
$672$		0			0
$673$	−334.752			−0.497403			−0.248701	−	0.968580i	$-0.580004\pi$
$673$	−334.752			−0.497403			−0.248701	+	0.968580i	$0.580004\pi$
$674$	1041.33	−	377.974i	1.54500	−	0.560792i
$675$		0			0
$676$	38.8654	−	435.399i	0.0574932	−	0.644082i
$677$	−294.364	+	710.658i	−0.434807	+	1.04972i	0.542911	+	0.839790i	$0.317322\pi$
$677$	−294.364	+	710.658i	−0.434807	+	1.04972i	−0.977717	+	0.209926i	$0.932678\pi$
$678$		0			0
$679$	18.5633	−	18.5633i	0.0273392	−	0.0273392i
$680$	326.193	+	427.436i	0.479695	+	0.628583i
$681$		0			0
$682$	−37.8886	+	850.601i	−0.0555551	+	1.24721i
$683$	118.311	−	285.628i	0.173223	−	0.418196i	−0.813295	−	0.581851i	$-0.802328\pi$
$683$	118.311	−	285.628i	0.173223	−	0.418196i	0.986518	+	0.163655i	$0.0523285\pi$
$684$		0			0
$685$	266.674	+	643.807i	0.389305	+	0.939865i
$686$	67.9750	−	145.438i	0.0990889	−	0.212009i
$687$		0			0
$688$	−716.621	−	460.095i	−1.04160	−	0.668743i
$689$			1108.67i			1.60909i
$690$		0			0
$691$	−13.1275	+	5.43758i	−0.0189978	+	0.00786914i	−0.392162	−	0.919896i	$-0.628273\pi$
$691$	−13.1275	+	5.43758i	−0.0189978	+	0.00786914i	0.373164	+	0.927765i	$0.378273\pi$
$692$	138.104	+	72.2020i	0.199573	+	0.104338i
$693$		0			0
$694$	−14.4107	+	323.522i	−0.0207647	+	0.466169i
$695$	−17.1180	−	17.1180i	−0.0246302	−	0.0246302i
$696$		0			0
$697$	276.995	+	276.995i	0.397410	+	0.397410i
$698$	517.942	+	566.235i	0.742038	+	0.811225i
$699$		0			0
$700$	−31.8994	+	26.6712i	−0.0455706	+	0.0381017i
$701$	100.100	−	41.4627i	0.142796	−	0.0591480i	−0.310141	−	0.950691i	$-0.600376\pi$
$701$	100.100	−	41.4627i	0.142796	−	0.0591480i	0.452937	+	0.891543i	$0.350376\pi$
$702$		0			0
$703$		−	319.070i		−	0.453869i
$704$	503.773	−	63.6166i	0.715587	−	0.0903645i
$705$		0			0
$706$	−245.832	−	677.273i	−0.348204	−	0.959310i
$707$	9.10558	+	21.9828i	0.0128792	+	0.0310931i
$708$		0			0
$709$	273.663	−	660.681i	0.385985	−	0.931849i	−0.604797	−	0.796380i	$-0.706746\pi$
$709$	273.663	−	660.681i	0.385985	−	0.931849i	0.990781	−	0.135470i	$-0.0432543\pi$
$710$	699.036	−	639.417i	0.984558	−	0.900587i
$711$		0			0
$712$	176.398	+	665.352i	0.247750	+	0.934483i
$713$	−820.958	+	820.958i	−1.15141	+	1.15141i
$714$		0			0
$715$	178.332	−	430.532i	0.249416	−	0.602143i
$716$	555.395	−	1062.33i	0.775692	−	1.48370i
$717$		0			0
$718$	235.750	+	110.185i	0.328343	+	0.153461i
$719$	532.079			0.740026			0.370013	−	0.929026i	$-0.379353\pi$
$719$	532.079			0.740026			0.370013	+	0.929026i	$0.379353\pi$
$720$		0			0
$721$		−	65.4218i		−	0.0907375i
$722$	−1214.31	−	567.545i	−1.68187	−	0.786074i
$723$		0			0
$724$	339.477	−	106.380i	0.468891	−	0.146933i
$725$	258.549	+	107.095i	0.356620	+	0.147717i
$726$		0			0
$727$	305.054	+	305.054i	0.419606	+	0.419606i	0.885068	−	0.465462i	$-0.154112\pi$
$727$	305.054	+	305.054i	0.419606	+	0.419606i	−0.465462	+	0.885068i	$0.654112\pi$
$728$	−66.7777	−	87.5042i	−0.0917276	−	0.120198i
$729$		0			0
$730$	272.797	−	249.530i	0.373694	−	0.341823i
$731$	−938.673	−	388.811i	−1.28409	−	0.531889i
$732$		0			0
$733$	344.710	−	142.783i	0.470272	−	0.194793i	−0.134946	−	0.990853i	$-0.543086\pi$
$733$	344.710	−	142.783i	0.470272	−	0.194793i	0.605218	+	0.796060i	$0.293086\pi$
$734$	−173.676	−	478.481i	−0.236616	−	0.651882i
$735$		0			0
$736$	565.418	+	399.632i	0.768230	+	0.542978i
$737$	−195.367			−0.265084
$738$		0			0
$739$	107.676	+	259.954i	0.145706	+	0.351765i	0.979836	−	0.199803i	$-0.0640301\pi$
$739$	107.676	+	259.954i	0.145706	+	0.351765i	−0.834131	+	0.551567i	$0.814030\pi$
$740$	139.382	+	12.4418i	0.188354	+	0.0168132i
$741$		0			0
$742$	73.9953	+	80.8946i	0.0997241	+	0.109022i
$743$	470.112	−	470.112i	0.632721	−	0.632721i	−0.316029	−	0.948750i	$-0.602350\pi$
$743$	470.112	−	470.112i	0.632721	−	0.632721i	0.948750	+	0.316029i	$0.102350\pi$
$744$		0			0
$745$	−363.391	+	363.391i	−0.487773	+	0.487773i
$746$	42.4317	−	952.594i	0.0568790	−	1.27694i
$747$		0			0
$748$	578.083	−	181.150i	0.772839	−	0.242179i
$749$	4.83025	+	11.6612i	0.00644893	+	0.0155691i
$750$		0			0
$751$	844.801			1.12490			0.562451	−	0.826831i	$-0.309859\pi$
$751$	844.801			1.12490			0.562451	+	0.826831i	$0.309859\pi$
$752$	−13.4141	+	74.5387i	−0.0178379	+	0.0991207i
$753$		0			0
$754$	−313.684	+	671.153i	−0.416026	+	0.890123i
$755$	604.588	−	250.428i	0.800778	−	0.331693i
$756$		0			0
$757$	1050.78	+	435.247i	1.38808	+	0.574962i	0.946630	−	0.322322i	$-0.104464\pi$
$757$	1050.78	+	435.247i	1.38808	+	0.574962i	0.441452	+	0.897285i	$0.354464\pi$
$758$	12.0379	−	270.252i	0.0158812	−	0.356533i
$759$		0			0
$760$	454.327	−	782.139i	0.597799	−	1.02913i
$761$	44.1359	+	44.1359i	0.0579972	+	0.0579972i	0.735511	−	0.677513i	$-0.236942\pi$
$761$	44.1359	+	44.1359i	0.0579972	+	0.0579972i	−0.677513	+	0.735511i	$0.736942\pi$
$762$		0			0
$763$	74.9225	+	31.0339i	0.0981946	+	0.0406735i
$764$	458.903	+	548.860i	0.600659	+	0.718403i
$765$		0			0
$766$	343.066	−	124.524i	0.447867	−	0.162564i
$767$			766.771i			0.999701i
$768$		0			0
$769$	794.025			1.03254			0.516271	−	0.856425i	$-0.327320\pi$
$769$	794.025			1.03254			0.516271	+	0.856425i	$0.327320\pi$
$770$	−15.7227	−	43.3164i	−0.0204191	−	0.0562551i
$771$		0			0
$772$	−604.637	+	505.539i	−0.783209	+	0.654843i
$773$	395.664	−	955.218i	0.511856	−	1.23573i	−0.430947	−	0.902377i	$-0.641820\pi$
$773$	395.664	−	955.218i	0.511856	−	1.23573i	0.942803	−	0.333351i	$-0.108180\pi$
$774$		0			0
$775$	478.187	−	478.187i	0.617016	−	0.617016i
$776$	220.179	+	127.897i	0.283735	+	0.164816i
$777$		0			0
$778$	−704.736	−	31.3913i	−0.905830	−	0.0403487i
$779$	252.184	−	608.826i	0.323728	−	0.781548i
$780$		0			0
$781$	−408.472	−	986.138i	−0.523011	−	1.26266i
$782$	748.355	+	349.766i	0.956975	+	0.447271i
$783$		0			0
$784$	760.892	+	136.931i	0.970526	+	0.174657i
$785$		−	578.418i		−	0.736838i
$786$		0			0
$787$	−445.085	+	184.360i	−0.565547	+	0.234257i	−0.647091	−	0.762413i	$-0.724015\pi$
$787$	−445.085	+	184.360i	−0.565547	+	0.234257i	0.0815444	+	0.996670i	$0.474015\pi$
$788$	−194.847	−	621.793i	−0.247268	−	0.789077i
$789$		0			0
$790$	−494.828	−	22.0413i	−0.626365	−	0.0279004i
$791$	48.0638	+	48.0638i	0.0607633	+	0.0607633i
$792$		0			0
$793$	354.242	+	354.242i	0.446711	+	0.446711i
$794$	−1050.01	+	960.455i	−1.32243	+	1.20964i
$795$		0			0
$796$	−11.2579	+	126.119i	−0.0141430	+	0.158441i
$797$	1384.22	−	573.363i	1.73679	−	0.719402i	0.737773	−	0.675049i	$-0.235877\pi$
$797$	1384.22	−	573.363i	1.73679	−	0.719402i	0.999016	−	0.0443527i	$-0.0141225\pi$
$798$		0			0
$799$			90.3573i			0.113088i
$800$	−329.341	−	232.775i	−0.411677	−	0.290969i
$801$		0			0
$802$	−140.058	+	50.8374i	−0.174636	+	0.0633883i
$803$	−159.405	−	384.837i	−0.198512	−	0.479249i
$804$		0			0
$805$	24.0463	−	58.0528i	0.0298711	−	0.0721153i
$806$	1208.30	+	1320.96i	1.49913	+	1.63891i
$807$		0			0
$808$	−183.464	+	140.009i	−0.227060	+	0.173278i
$809$	−462.148	+	462.148i	−0.571258	+	0.571258i	−0.932480	−	0.361222i	$-0.882360\pi$
$809$	−462.148	+	462.148i	−0.571258	+	0.571258i	0.361222	+	0.932480i	$0.382360\pi$
$810$		0			0
$811$	32.9003	−	79.4282i	0.0405675	−	0.0979386i	−0.902297	−	0.431115i	$-0.858120\pi$
$811$	32.9003	−	79.4282i	0.0405675	−	0.0979386i	0.942865	+	0.333176i	$0.108120\pi$
$812$	21.9064	+	69.9072i	0.0269783	+	0.0860926i
$813$		0			0
$814$	66.7578	−	142.834i	0.0820121	−	0.175472i
$815$	−696.019			−0.854012
$816$		0			0
$817$			1709.19i			2.09203i
$818$	−346.865	+	742.147i	−0.424040	+	0.907270i
$819$		0			0
$820$	256.126	+	133.905i	0.312349	+	0.163298i
$821$	724.768	+	300.209i	0.882787	+	0.365662i	0.777577	−	0.628788i	$-0.216449\pi$
$821$	724.768	+	300.209i	0.882787	+	0.365662i	0.105210	+	0.994450i	$0.466449\pi$
$822$		0			0
$823$	−378.179	−	378.179i	−0.459513	−	0.459513i	0.438982	−	0.898496i	$-0.355339\pi$
$823$	−378.179	−	378.179i	−0.459513	−	0.459513i	−0.898496	+	0.438982i	$0.855339\pi$
$824$	613.353	−	162.612i	0.744361	−	0.197345i
$825$		0			0
$826$	51.1763	+	55.9480i	0.0619568	+	0.0677336i
$827$	1071.43	+	443.801i	1.29556	+	0.536639i	0.920638	−	0.390416i	$-0.127669\pi$
$827$	1071.43	+	443.801i	1.29556	+	0.536639i	0.374924	+	0.927056i	$0.377669\pi$
$828$		0			0
$829$	−1023.61	+	423.991i	−1.23475	+	0.511449i	−0.902069	−	0.431592i	$-0.857952\pi$
$829$	−1023.61	+	423.991i	−1.23475	+	0.511449i	−0.332678	+	0.943041i	$0.607952\pi$
$830$	−104.046	+	37.7660i	−0.125357	+	0.0455012i
$831$		0			0
$832$	654.402	−	843.566i	0.786541	−	1.01390i
$833$	922.368			1.10728
$834$		0			0
$835$	−282.996	−	683.214i	−0.338918	−	0.818220i
$836$	−653.696	−	781.837i	−0.781932	−	0.935211i
$837$		0			0
$838$	−903.494	+	826.437i	−1.07815	+	0.986202i
$839$	−1157.38	+	1157.38i	−1.37947	+	1.37947i	−0.533966	+	0.845506i	$0.679299\pi$
$839$	−1157.38	+	1157.38i	−1.37947	+	1.37947i	−0.845506	+	0.533966i	$0.820701\pi$
$840$		0			0
$841$	−246.029	+	246.029i	−0.292543	+	0.292543i
$842$	−1072.74	−	47.7833i	−1.27403	−	0.0567498i
$843$		0			0
$844$	633.727	−	1212.16i	0.750862	−	1.43621i
$845$	−147.247	−	355.487i	−0.174257	−	0.420694i
$846$		0			0
$847$	47.8817			0.0565309
$848$	−574.495	+	894.805i	−0.677470	+	1.05519i
$849$		0			0
$850$	−435.898	−	203.730i	−0.512821	−	0.239682i
$851$	198.623	−	82.2724i	0.233400	−	0.0966773i
$852$		0			0
$853$	1189.88	+	492.862i	1.39493	+	0.577799i	0.948431	−	0.316985i	$-0.102671\pi$
$853$	1189.88	+	492.862i	1.39493	+	0.577799i	0.446499	+	0.894784i	$0.352671\pi$
$854$	49.4906	+	2.20448i	0.0579515	+	0.00258136i
$855$		0			0
$856$	−97.3225	+	74.2705i	−0.113695	+	0.0867646i
$857$	−240.773	−	240.773i	−0.280948	−	0.280948i	0.552539	−	0.833487i	$-0.313659\pi$
$857$	−240.773	−	240.773i	−0.280948	−	0.280948i	−0.833487	+	0.552539i	$0.813659\pi$
$858$		0			0
$859$	−577.833	−	239.346i	−0.672682	−	0.278634i	0.0200823	−	0.999798i	$-0.493607\pi$
$859$	−577.833	−	239.346i	−0.672682	−	0.278634i	−0.692764	+	0.721164i	$0.743607\pi$
$860$	−746.642	−	66.6481i	−0.868188	−	0.0774978i
$861$		0			0
$862$	−64.2606	−	177.040i	−0.0745483	−	0.205382i
$863$			1084.57i			1.25675i	0.777912	+	0.628373i	$0.216279\pi$
$863$			1084.57i			1.25675i	−0.777912	+	0.628373i	$0.783721\pi$
$864$		0			0
$865$	137.175			0.158583
$866$	124.587	−	45.2218i	0.143865	−	0.0522192i
$867$		0			0
$868$	176.329	+	15.7398i	0.203144	+	0.0181334i
$869$	−213.564	+	515.590i	−0.245759	+	0.593314i
$870$		0			0
$871$	−290.461	+	290.461i	−0.333480	+	0.333480i
$872$	−104.728	+	779.564i	−0.120101	+	0.893995i
$873$		0			0
$874$	61.8378	−	1388.26i	0.0707526	−	1.58840i
$875$	−41.7899	+	100.890i	−0.0477598	+	0.115302i
$876$		0			0
$877$	−331.246	−	799.700i	−0.377704	−	0.911858i	−0.992395	−	0.123090i	$-0.960719\pi$
$877$	−331.246	−	799.700i	−0.377704	−	0.911858i	0.614691	−	0.788768i	$-0.289281\pi$
$878$	471.142	−	1008.05i	0.536608	−	1.14812i
$879$		0			0
$880$	367.028	−	255.073i	0.417077	−	0.289856i
$881$		−	995.281i		−	1.12972i	−0.825188	−	0.564859i	$-0.808931\pi$
$881$		−	995.281i		−	1.12972i	0.825188	−	0.564859i	$-0.191069\pi$
$882$		0			0
$883$	−587.282	+	243.260i	−0.665098	+	0.275493i	−0.689582	−	0.724207i	$-0.742206\pi$
$883$	−587.282	+	243.260i	−0.665098	+	0.275493i	0.0244838	+	0.999700i	$0.492206\pi$
$884$	590.140	−	1128.79i	0.667579	−	1.27691i
$885$		0			0
$886$	−11.9738	+	268.812i	−0.0135144	+	0.303400i
$887$	−679.194	−	679.194i	−0.765720	−	0.765720i	0.211630	−	0.977350i	$-0.432123\pi$
$887$	−679.194	−	679.194i	−0.765720	−	0.765720i	−0.977350	+	0.211630i	$0.932123\pi$
$888$		0			0
$889$	−35.2835	−	35.2835i	−0.0396890	−	0.0396890i
$890$	408.944	+	447.074i	0.459488	+	0.502331i
$891$		0			0
$892$	266.826	+	319.130i	0.299132	+	0.357769i
$893$	140.433	−	58.1693i	0.157260	−	0.0651392i
$894$		0			0
$895$		−	1055.18i		−	1.17897i
$896$	−8.55291	−	105.228i	−0.00954566	−	0.117442i
$897$		0			0
$898$	424.106	+	1168.42i	0.472278	+	1.30114i
$899$	−455.960	−	1100.78i	−0.507185	−	1.22445i
$900$		0			0
$901$	−485.487	+	1172.07i	−0.538831	+	1.30085i
$902$	240.275	−	219.782i	0.266380	−	0.243661i
$903$		0			0
$904$	−331.149	+	570.083i	−0.366315	+	0.630623i
$905$	221.428	−	221.428i	0.244672	−	0.244672i
$906$		0			0
$907$	77.7483	−	187.701i	0.0857203	−	0.206947i	−0.875207	−	0.483749i	$-0.839275\pi$
$907$	77.7483	−	187.701i	0.0857203	−	0.206947i	0.960927	+	0.276802i	$0.0892746\pi$
$908$	184.940	+	96.6880i	0.203678	+	0.106485i
$909$		0			0
$910$	−87.7764	−	41.0250i	−0.0964576	−	0.0450824i
$911$	−300.365			−0.329710			−0.164855	−	0.986318i	$-0.552716\pi$
$911$	−300.365			−0.329710			−0.164855	+	0.986318i	$0.552716\pi$
$912$		0			0
$913$			124.711i			0.136595i
$914$	312.328	+	145.976i	0.341716	+	0.159711i
$915$		0			0
$916$	162.656	+	519.065i	0.177572	+	0.566665i
$917$	112.331	+	46.5292i	0.122499	+	0.0507407i
$918$		0			0
$919$	−149.768	−	149.768i	−0.162968	−	0.162968i	0.620912	−	0.783880i	$-0.286762\pi$
$919$	−149.768	−	149.768i	−0.162968	−	0.162968i	−0.783880	+	0.620912i	$0.786762\pi$
$920$	604.036	+	81.1470i	0.656561	+	0.0882033i
$921$		0			0
$922$	−354.837	+	324.574i	−0.384856	+	0.352032i
$923$	−2073.43	−	858.845i	−2.24641	−	0.930493i
$924$		0			0
$925$	−115.693	+	47.9216i	−0.125073	+	0.0518071i
$926$	90.8649	+	250.335i	0.0981262	+	0.270340i
$927$		0			0
$928$	−600.956	+	379.141i	−0.647582	+	0.408557i
$929$	−1235.73			−1.33017			−0.665086	−	0.746767i	$-0.731605\pi$
$929$	−1235.73			−1.33017			−0.665086	+	0.746767i	$0.731605\pi$
$930$		0			0
$931$	−593.793	−	1433.54i	−0.637801	−	1.53979i
$932$	−0.250244	+	2.80342i	−0.000268502	+	0.00300796i
$933$		0			0
$934$	−605.286	−	661.723i	−0.648058	−	0.708483i
$935$	377.061	−	377.061i	0.403274	−	0.403274i
$936$		0			0
$937$	955.999	−	955.999i	1.02028	−	1.02028i	0.0204864	−	0.999790i	$-0.493479\pi$
$937$	955.999	−	955.999i	1.02028	−	1.02028i	0.999790	−	0.0204864i	$-0.00652149\pi$
$938$	−1.80756	+	40.5799i	−0.00192704	+	0.0432621i
$939$		0			0
$940$	19.9346	+	63.6150i	0.0212070	+	0.0676756i
$941$	337.224	+	814.132i	0.358368	+	0.865177i	0.995530	+	0.0944471i	$0.0301083\pi$
$941$	337.224	+	814.132i	0.358368	+	0.865177i	−0.637162	+	0.770730i	$0.719892\pi$
$942$		0			0
$943$	444.025			0.470864
$944$	−397.330	+	618.861i	−0.420900	+	0.655573i
$945$		0			0
$946$	−357.608	+	765.132i	−0.378021	+	0.808808i
$947$	1611.78	−	667.619i	1.70198	−	0.704983i	0.702007	−	0.712171i	$-0.252288\pi$
$947$	1611.78	−	667.619i	1.70198	−	0.704983i	0.999974	+	0.00718706i	$0.00228773\pi$
$948$		0			0
$949$	−809.151	−	335.161i	−0.852636	−	0.353173i
$950$	−36.0189	+	808.626i	−0.0379147	+	0.851185i
$951$		0			0
$952$	−32.2784	−	121.750i	−0.0339059	−	0.127889i
$953$	−661.490	−	661.490i	−0.694114	−	0.694114i	0.269021	−	0.963134i	$-0.413300\pi$
$953$	−661.490	−	661.490i	−0.694114	−	0.694114i	−0.963134	+	0.269021i	$0.913300\pi$
$954$		0			0
$955$	581.807	+	240.992i	0.609222	+	0.252348i
$956$	−246.295	+	205.927i	−0.257630	+	0.215405i
$957$		0			0
$958$	−552.068	+	200.386i	−0.576272	+	0.209171i
$959$		−	163.243i		−	0.170222i
$960$		0			0
$961$	−1918.20			−1.99604
$962$	−113.106	−	311.611i	−0.117574	−	0.323920i
$963$		0			0
$964$	−25.5241	−	30.5274i	−0.0264772	−	0.0316674i
$965$	−265.483	+	640.932i	−0.275112	+	0.664179i
$966$		0			0
$967$	38.7070	−	38.7070i	0.0400279	−	0.0400279i	−0.686810	−	0.726837i	$-0.740989\pi$
$967$	38.7070	−	38.7070i	0.0400279	−	0.0400279i	0.726837	+	0.686810i	$0.240989\pi$
$968$	119.014	+	448.909i	0.122949	+	0.463749i
$969$		0			0
$970$	223.911	+	9.97375i	0.230836	+	0.0102822i
$971$	−253.057	+	610.934i	−0.260615	+	0.629180i	−0.998977	−	0.0452246i	$-0.985600\pi$
$971$	−253.057	+	610.934i	−0.260615	+	0.629180i	0.738362	+	0.674405i	$0.235600\pi$
$972$		0			0
$973$	2.17021	+	5.23934i	0.00223043	+	0.00538473i
$974$	−1200.13	−	560.919i	−1.23217	−	0.575892i
$975$		0			0
$976$	102.346	+	469.472i	0.104862	+	0.481017i
$977$			122.372i			0.125253i	0.998037	+	0.0626263i	$0.0199476\pi$
$977$			122.372i			0.125253i	−0.998037	+	0.0626263i	$0.980052\pi$
$978$		0			0
$979$	630.692	−	261.241i	0.644221	−	0.266845i
$980$	649.383	−	203.493i	0.662636	−	0.207646i
$981$		0			0
$982$	−628.842	−	28.0107i	−0.640368	−	0.0285242i
$983$	−696.783	−	696.783i	−0.708833	−	0.708833i	0.257457	−	0.966290i	$-0.417116\pi$
$983$	−696.783	−	696.783i	−0.708833	−	0.708833i	−0.966290	+	0.257457i	$0.917116\pi$
$984$		0			0
$985$	−405.572	−	405.572i	−0.411748	−	0.411748i
$986$	−625.521	+	572.172i	−0.634403	+	0.580296i
$987$		0			0
$988$	−2134.28	−	190.514i	−2.16020	−	0.192828i
$989$	−1063.98	+	440.716i	−1.07582	+	0.445618i
$990$		0			0
$991$		−	536.777i		−	0.541652i	−0.962628	−	0.270826i	$-0.912703\pi$
$991$		−	536.777i		−	0.541652i	0.962628	−	0.270826i	$-0.0872968\pi$
$992$	290.715	+	1692.27i	0.293060	+	1.70592i
$993$		0			0
$994$	−208.611	+	75.7203i	−0.209870	+	0.0761773i
$995$	42.6521	+	102.971i	0.0428664	+	0.103489i
$996$		0			0
$997$	250.176	−	603.979i	0.250929	−	0.605796i	−0.747351	−	0.664430i	$-0.768674\pi$
$997$	250.176	−	603.979i	0.250929	−	0.605796i	0.998280	+	0.0586337i	$0.0186744\pi$
$998$	−836.665	−	914.676i	−0.838342	−	0.916509i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.3.u.a.235.3		28
3.2	odd	2		32.3.h.a.11.5	yes	28
12.11	even	2		128.3.h.a.79.4		28
24.5	odd	2		256.3.h.b.159.4		28
24.11	even	2		256.3.h.a.159.4		28
32.3	odd	8	inner	288.3.u.a.163.3		28
96.29	odd	8		128.3.h.a.47.4		28
96.35	even	8		32.3.h.a.3.5	✓	28
96.77	odd	8		256.3.h.a.95.4		28
96.83	even	8		256.3.h.b.95.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.5	✓	28	96.35	even	8
32.3.h.a.11.5	yes	28	3.2	odd	2
128.3.h.a.47.4		28	96.29	odd	8
128.3.h.a.79.4		28	12.11	even	2
256.3.h.a.95.4		28	96.77	odd	8
256.3.h.a.159.4		28	24.11	even	2
256.3.h.b.95.4		28	96.83	even	8
256.3.h.b.159.4		28	24.5	odd	2
288.3.u.a.163.3		28	32.3	odd	8	inner
288.3.u.a.235.3		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)

\(f(q)\)	\(=\)	\(q+(-0.682385 - 1.87999i) q^{2} +(-3.06870 + 2.56575i) q^{4} +(-1.34740 + 3.25291i) q^{5} +(0.583225 - 0.583225i) q^{7} +(6.91761 + 4.01829i) q^{8} +O(q^{10})\)	\(q+(-0.682385 - 1.87999i) q^{2} +(-3.06870 + 2.56575i) q^{4} +(-1.34740 + 3.25291i) q^{5} +(0.583225 - 0.583225i) q^{7} +(6.91761 + 4.01829i) q^{8} +(7.03487 + 0.313357i) q^{10} +(3.03620 - 7.33003i) q^{11} +(-6.38385 - 15.4120i) q^{13} +(-1.49444 - 0.698471i) q^{14} +(2.83386 - 15.7470i) q^{16} -19.0889i q^{17} +(-29.6679 + 12.2888i) q^{19} +(-4.21138 - 13.4393i) q^{20} +(-15.8522 - 0.706111i) q^{22} +(-15.2998 - 15.2998i) q^{23} +(8.91173 + 8.91173i) q^{25} +(-24.6181 + 22.5185i) q^{26} +(-0.293334 + 3.28615i) q^{28} +(20.5148 - 8.49749i) q^{29} -53.6582i q^{31} +(-31.5380 + 5.41792i) q^{32} +(-35.8868 + 13.0260i) q^{34} +(1.11134 + 2.68301i) q^{35} +(-3.80237 + 9.17973i) q^{37} +(43.3477 + 47.3895i) q^{38} +(-22.3919 + 17.0881i) q^{40} +(-14.5108 + 14.5108i) q^{41} +(20.3685 - 49.1739i) q^{43} +(9.48983 + 30.2838i) q^{44} +(-18.3230 + 39.2037i) q^{46} -4.73351 q^{47} +48.3197i q^{49} +(10.6727 - 22.8352i) q^{50} +(59.1334 + 30.9154i) q^{52} +(-61.4006 - 25.4330i) q^{53} +(19.7530 + 19.7530i) q^{55} +(6.37809 - 1.69095i) q^{56} +(-29.9741 - 32.7689i) q^{58} +(-42.4656 - 17.5898i) q^{59} +(-27.7452 + 11.4924i) q^{61} +(-100.877 + 36.6155i) q^{62} +(31.7067 + 55.5939i) q^{64} +58.7354 q^{65} +(-9.42323 - 22.7497i) q^{67} +(48.9772 + 58.5780i) q^{68} +(4.28567 - 3.92015i) q^{70} +(95.1299 - 95.1299i) q^{71} +(37.1241 - 37.1241i) q^{73} +(19.8524 + 0.884295i) q^{74} +(59.5118 - 113.831i) q^{76} +(-2.50427 - 6.04584i) q^{77} -70.3394 q^{79} +(47.4053 + 30.4358i) q^{80} +(37.1821 + 17.3782i) q^{82} +(-14.5221 + 6.01526i) q^{83} +(62.0944 + 25.7203i) q^{85} +(-106.345 - 4.73698i) q^{86} +(50.4574 - 38.5060i) q^{88} +(60.8411 + 60.8411i) q^{89} +(-12.7119 - 5.26543i) q^{91} +(86.2059 + 7.69507i) q^{92} +(3.23007 + 8.89893i) q^{94} -113.065i q^{95} +31.8287 q^{97} +(90.8404 - 32.9726i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 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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