LMFDB - Embedded newform 538.3.c.a.187.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,3,Mod(187,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("538.187");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	538.c (of order $4$, degree $2$, 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:	$14.6594382226$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			187.15
Character	$\chi$	$=$	538.187
Dual form			538.3.c.a.351.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{2} +(1.79446 + 1.79446i) q^{3} +2.00000i q^{4} -4.75177 q^{5} +3.58893i q^{6} +(9.51668 - 9.51668i) q^{7} +(-2.00000 + 2.00000i) q^{8} -2.55979i q^{9} +(-4.75177 - 4.75177i) q^{10} -11.4091i q^{11} +(-3.58893 + 3.58893i) q^{12} -22.1551i q^{13} +19.0334 q^{14} +(-8.52688 - 8.52688i) q^{15} -4.00000 q^{16} +(0.892657 + 0.892657i) q^{17} +(2.55979 - 2.55979i) q^{18} +(4.21546 - 4.21546i) q^{19} -9.50354i q^{20} +34.1547 q^{21} +(11.4091 - 11.4091i) q^{22} -13.0222 q^{23} -7.17786 q^{24} -2.42070 q^{25} +(22.1551 - 22.1551i) q^{26} +(20.7436 - 20.7436i) q^{27} +(19.0334 + 19.0334i) q^{28} +(-27.9599 + 27.9599i) q^{29} -17.0538i q^{30} +(-24.2071 + 24.2071i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(20.4732 - 20.4732i) q^{33} +1.78531i q^{34} +(-45.2211 + 45.2211i) q^{35} +5.11959 q^{36} +53.9522 q^{37} +8.43092 q^{38} +(39.7565 - 39.7565i) q^{39} +(9.50354 - 9.50354i) q^{40} +38.7731 q^{41} +(34.1547 + 34.1547i) q^{42} +63.1369i q^{43} +22.8182 q^{44} +12.1636i q^{45} +(-13.0222 - 13.0222i) q^{46} +7.00296 q^{47} +(-7.17786 - 7.17786i) q^{48} -132.134i q^{49} +(-2.42070 - 2.42070i) q^{50} +3.20368i q^{51} +44.3102 q^{52} -41.7361 q^{53} +41.4873 q^{54} +54.2133i q^{55} +38.0667i q^{56} +15.1290 q^{57} -55.9199 q^{58} +(-25.7489 + 25.7489i) q^{59} +(17.0538 - 17.0538i) q^{60} +41.7906 q^{61} -48.4141 q^{62} +(-24.3607 - 24.3607i) q^{63} -8.00000i q^{64} +105.276i q^{65} +40.9464 q^{66} +60.2833 q^{67} +(-1.78531 + 1.78531i) q^{68} +(-23.3678 - 23.3678i) q^{69} -90.4421 q^{70} +(24.6805 - 24.6805i) q^{71} +(5.11959 + 5.11959i) q^{72} -100.890i q^{73} +(53.9522 + 53.9522i) q^{74} +(-4.34385 - 4.34385i) q^{75} +(8.43092 + 8.43092i) q^{76} +(-108.577 - 108.577i) q^{77} +79.5130 q^{78} +147.725i q^{79} +19.0071 q^{80} +51.4093 q^{81} +(38.7731 + 38.7731i) q^{82} +(-14.3693 + 14.3693i) q^{83} +68.3094i q^{84} +(-4.24170 - 4.24170i) q^{85} +(-63.1369 + 63.1369i) q^{86} -100.346 q^{87} +(22.8182 + 22.8182i) q^{88} +146.915i q^{89} +(-12.1636 + 12.1636i) q^{90} +(-210.843 - 210.843i) q^{91} -26.0443i q^{92} -86.8774 q^{93} +(7.00296 + 7.00296i) q^{94} +(-20.0309 + 20.0309i) q^{95} -14.3557i q^{96} -52.1351i q^{97} +(132.134 - 132.134i) q^{98} -29.2049 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 44 q^{2} + 2 q^{3} + 4 q^{7} - 88 q^{8} - 4 q^{12} + 8 q^{14} + 38 q^{15} - 176 q^{16} - 120 q^{18} + 18 q^{19} - 16 q^{21} + 68 q^{23} - 8 q^{24} + 196 q^{25} + 16 q^{26} - 22 q^{27} + 8 q^{28}+ \cdots - 188 q^{99}+O(q^{100}) $ 44 * q + 44 * q^2 + 2 * q^3 + 4 * q^7 - 88 * q^8 - 4 * q^12 + 8 * q^14 + 38 * q^15 - 176 * q^16 - 120 * q^18 + 18 * q^19 - 16 * q^21 + 68 * q^23 - 8 * q^24 + 196 * q^25 + 16 * q^26 - 22 * q^27 + 8 * q^28 + 18 * q^29 + 88 * q^31 - 176 * q^32 + 96 * q^33 + 10 * q^35 - 240 * q^36 + 180 * q^37 + 36 * q^38 - 54 * q^39 + 144 * q^41 - 16 * q^42 + 68 * q^46 - 156 * q^47 - 8 * q^48 + 196 * q^50 + 32 * q^52 - 188 * q^53 - 44 * q^54 - 88 * q^57 + 36 * q^58 - 98 * q^59 - 76 * q^60 - 244 * q^61 + 176 * q^62 - 10 * q^63 + 192 * q^66 + 220 * q^67 - 70 * q^69 + 20 * q^70 + 156 * q^71 - 240 * q^72 + 180 * q^74 - 102 * q^75 + 36 * q^76 - 28 * q^77 - 108 * q^78 + 392 * q^81 + 144 * q^82 - 250 * q^83 - 342 * q^85 - 44 * q^86 - 60 * q^87 - 192 * q^90 + 66 * q^91 - 536 * q^93 - 156 * q^94 - 472 * q^95 + 404 * q^98 - 188 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/538\mathbb{Z}\right)^\times$.

$n$	$271$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	1.79446	+	1.79446i	0.598155	+	0.598155i	0.939821	−	0.341666i	$-0.110991\pi$
$3$	1.79446	+	1.79446i	0.598155	+	0.598155i	−0.341666	+	0.939821i	$0.610991\pi$
$4$			2.00000i			0.500000i
$5$	−4.75177			−0.950354			−0.475177	−	0.879890i	$-0.657616\pi$
$5$	−4.75177			−0.950354			−0.475177	+	0.879890i	$0.657616\pi$
$6$			3.58893i			0.598155i
$7$	9.51668	−	9.51668i	1.35953	−	1.35953i	0.485026	−	0.874500i	$-0.338810\pi$
$7$	9.51668	−	9.51668i	1.35953	−	1.35953i	0.874500	−	0.485026i	$-0.161190\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	2.55979i		−	0.284422i
$10$	−4.75177	−	4.75177i	−0.475177	−	0.475177i
$11$		−	11.4091i		−	1.03719i	−0.855020	−	0.518595i	$-0.826455\pi$
$11$		−	11.4091i		−	1.03719i	0.855020	−	0.518595i	$-0.173545\pi$
$12$	−3.58893	+	3.58893i	−0.299077	+	0.299077i
$13$		−	22.1551i		−	1.70424i	−0.523349	−	0.852119i	$-0.675317\pi$
$13$		−	22.1551i		−	1.70424i	0.523349	−	0.852119i	$-0.324683\pi$
$14$	19.0334			1.35953
$15$	−8.52688	−	8.52688i	−0.568459	−	0.568459i
$16$	−4.00000			−0.250000
$17$	0.892657	+	0.892657i	0.0525092	+	0.0525092i	0.732874	−	0.680365i	$-0.238179\pi$
$17$	0.892657	+	0.892657i	0.0525092	+	0.0525092i	−0.680365	+	0.732874i	$0.738179\pi$
$18$	2.55979	−	2.55979i	0.142211	−	0.142211i
$19$	4.21546	−	4.21546i	0.221866	−	0.221866i	−0.587418	−	0.809284i	$-0.699855\pi$
$19$	4.21546	−	4.21546i	0.221866	−	0.221866i	0.809284	+	0.587418i	$0.199855\pi$
$20$		−	9.50354i		−	0.475177i
$21$	34.1547			1.62641
$22$	11.4091	−	11.4091i	0.518595	−	0.518595i
$23$	−13.0222			−0.566181			−0.283090	−	0.959093i	$-0.591360\pi$
$23$	−13.0222			−0.566181			−0.283090	+	0.959093i	$0.591360\pi$
$24$	−7.17786			−0.299077
$25$	−2.42070			−0.0968278
$26$	22.1551	−	22.1551i	0.852119	−	0.852119i
$27$	20.7436	−	20.7436i	0.768283	−	0.768283i
$28$	19.0334	+	19.0334i	0.679763	+	0.679763i
$29$	−27.9599	+	27.9599i	−0.964136	+	0.964136i	−0.999379	−	0.0352427i	$-0.988780\pi$
$29$	−27.9599	+	27.9599i	−0.964136	+	0.964136i	0.0352427	+	0.999379i	$0.488780\pi$
$30$		−	17.0538i		−	0.568459i
$31$	−24.2071	+	24.2071i	−0.780873	+	0.780873i	−0.979978	−	0.199105i	$-0.936196\pi$
$31$	−24.2071	+	24.2071i	−0.780873	+	0.780873i	0.199105	+	0.979978i	$0.436196\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	20.4732	−	20.4732i	0.620400	−	0.620400i
$34$			1.78531i			0.0525092i
$35$	−45.2211	+	45.2211i	−1.29203	+	1.29203i
$36$	5.11959			0.142211
$37$	53.9522			1.45817			0.729084	−	0.684424i	$-0.239946\pi$
$37$	53.9522			1.45817			0.729084	+	0.684424i	$0.239946\pi$
$38$	8.43092			0.221866
$39$	39.7565	−	39.7565i	1.01940	−	1.01940i
$40$	9.50354	−	9.50354i	0.237588	−	0.237588i
$41$	38.7731			0.945685			0.472843	−	0.881147i	$-0.343228\pi$
$41$	38.7731			0.945685			0.472843	+	0.881147i	$0.343228\pi$
$42$	34.1547	+	34.1547i	0.813207	+	0.813207i
$43$			63.1369i			1.46830i	0.678988	+	0.734150i	$0.262419\pi$
$43$			63.1369i			1.46830i	−0.678988	+	0.734150i	$0.737581\pi$
$44$	22.8182			0.518595
$45$			12.1636i			0.270301i
$46$	−13.0222	−	13.0222i	−0.283090	−	0.283090i
$47$	7.00296			0.148999			0.0744996	−	0.997221i	$-0.476264\pi$
$47$	7.00296			0.148999			0.0744996	+	0.997221i	$0.476264\pi$
$48$	−7.17786	−	7.17786i	−0.149539	−	0.149539i
$49$		−	132.134i		−	2.69662i
$50$	−2.42070	−	2.42070i	−0.0484139	−	0.0484139i
$51$			3.20368i			0.0628173i
$52$	44.3102			0.852119
$53$	−41.7361			−0.787473			−0.393737	−	0.919223i	$-0.628818\pi$
$53$	−41.7361			−0.787473			−0.393737	+	0.919223i	$0.628818\pi$
$54$	41.4873			0.768283
$55$			54.2133i			0.985697i
$56$			38.0667i			0.679763i
$57$	15.1290			0.265421
$58$	−55.9199			−0.964136
$59$	−25.7489	+	25.7489i	−0.436423	+	0.436423i	−0.890806	−	0.454384i	$-0.849860\pi$
$59$	−25.7489	+	25.7489i	−0.436423	+	0.436423i	0.454384	+	0.890806i	$0.349860\pi$
$60$	17.0538	−	17.0538i	0.284229	−	0.284229i
$61$	41.7906			0.685092			0.342546	−	0.939501i	$-0.388711\pi$
$61$	41.7906			0.685092			0.342546	+	0.939501i	$0.388711\pi$
$62$	−48.4141			−0.780873
$63$	−24.3607	−	24.3607i	−0.386679	−	0.386679i
$64$		−	8.00000i		−	0.125000i
$65$			105.276i			1.61963i
$66$	40.9464			0.620400
$67$	60.2833			0.899750			0.449875	−	0.893092i	$-0.351469\pi$
$67$	60.2833			0.899750			0.449875	+	0.893092i	$0.351469\pi$
$68$	−1.78531	+	1.78531i	−0.0262546	+	0.0262546i
$69$	−23.3678	−	23.3678i	−0.338664	−	0.338664i
$70$	−90.4421			−1.29203
$71$	24.6805	−	24.6805i	0.347613	−	0.347613i	−0.511607	−	0.859220i	$-0.670949\pi$
$71$	24.6805	−	24.6805i	0.347613	−	0.347613i	0.859220	+	0.511607i	$0.170949\pi$
$72$	5.11959	+	5.11959i	0.0711054	+	0.0711054i
$73$		−	100.890i		−	1.38205i	−0.722830	−	0.691026i	$-0.757159\pi$
$73$		−	100.890i		−	1.38205i	0.722830	−	0.691026i	$-0.242841\pi$
$74$	53.9522	+	53.9522i	0.729084	+	0.729084i
$75$	−4.34385	−	4.34385i	−0.0579180	−	0.0579180i
$76$	8.43092	+	8.43092i	0.110933	+	0.110933i
$77$	−108.577	−	108.577i	−1.41009	−	1.41009i
$78$	79.5130			1.01940
$79$			147.725i			1.86994i	0.354732	+	0.934968i	$0.384572\pi$
$79$			147.725i			1.86994i	−0.354732	+	0.934968i	$0.615428\pi$
$80$	19.0071			0.237588
$81$	51.4093			0.634683
$82$	38.7731	+	38.7731i	0.472843	+	0.472843i
$83$	−14.3693	+	14.3693i	−0.173124	+	0.173124i	−0.788350	−	0.615226i	$-0.789065\pi$
$83$	−14.3693	+	14.3693i	−0.173124	+	0.173124i	0.615226	+	0.788350i	$0.289065\pi$
$84$			68.3094i			0.813207i
$85$	−4.24170	−	4.24170i	−0.0499023	−	0.0499023i
$86$	−63.1369	+	63.1369i	−0.734150	+	0.734150i
$87$	−100.346			−1.15341
$88$	22.8182	+	22.8182i	0.259297	+	0.259297i
$89$			146.915i			1.65073i	0.564603	+	0.825363i	$0.309029\pi$
$89$			146.915i			1.65073i	−0.564603	+	0.825363i	$0.690971\pi$
$90$	−12.1636	+	12.1636i	−0.135151	+	0.135151i
$91$	−210.843	−	210.843i	−2.31695	−	2.31695i
$92$		−	26.0443i		−	0.283090i
$93$	−86.8774			−0.934166
$94$	7.00296	+	7.00296i	0.0744996	+	0.0744996i
$95$	−20.0309	+	20.0309i	−0.210852	+	0.210852i
$96$		−	14.3557i		−	0.149539i
$97$		−	52.1351i		−	0.537476i	−0.963213	−	0.268738i	$-0.913393\pi$
$97$		−	52.1351i		−	0.537476i	0.963213	−	0.268738i	$-0.0866065\pi$
$98$	132.134	−	132.134i	1.34831	−	1.34831i
$99$	−29.2049			−0.294999
$100$		−	4.84139i		−	0.0484139i
$101$	37.0283	+	37.0283i	0.366617	+	0.366617i	0.866242	−	0.499625i	$-0.166529\pi$
$101$	37.0283	+	37.0283i	0.366617	+	0.366617i	−0.499625	+	0.866242i	$0.666529\pi$
$102$	−3.20368	+	3.20368i	−0.0314086	+	0.0314086i
$103$		−	93.4599i		−	0.907377i	−0.891160	−	0.453689i	$-0.850108\pi$
$103$		−	93.4599i		−	0.907377i	0.891160	−	0.453689i	$-0.149892\pi$
$104$	44.3102	+	44.3102i	0.426059	+	0.426059i
$105$	−162.295			−1.54567
$106$	−41.7361	−	41.7361i	−0.393737	−	0.393737i
$107$	−50.0728	+	50.0728i	−0.467970	+	0.467970i	−0.901256	−	0.433286i	$-0.857354\pi$
$107$	−50.0728	+	50.0728i	−0.467970	+	0.467970i	0.433286	+	0.901256i	$0.357354\pi$
$108$	41.4873	+	41.4873i	0.384141	+	0.384141i
$109$	105.381	−	105.381i	0.966796	−	0.966796i	−0.0326701	−	0.999466i	$-0.510401\pi$
$109$	105.381	−	105.381i	0.966796	−	0.966796i	0.999466	+	0.0326701i	$0.0104011\pi$
$110$	−54.2133	+	54.2133i	−0.492848	+	0.492848i
$111$	96.8154	+	96.8154i	0.872210	+	0.872210i
$112$	−38.0667	+	38.0667i	−0.339881	+	0.339881i
$113$	109.427	−	109.427i	0.968382	−	0.968382i	−0.0311328	−	0.999515i	$-0.509911\pi$
$113$	109.427	−	109.427i	0.968382	−	0.968382i	0.999515	+	0.0311328i	$0.00991148\pi$
$114$	15.1290	+	15.1290i	0.132710	+	0.132710i
$115$	61.8783			0.538072
$116$	−55.9199	−	55.9199i	−0.482068	−	0.482068i
$117$	−56.7125			−0.484722
$118$	−51.4979			−0.436423
$119$	16.9903			0.142775
$120$	34.1075			0.284229
$121$	−9.16714			−0.0757615
$122$	41.7906	+	41.7906i	0.342546	+	0.342546i
$123$	69.5769	+	69.5769i	0.565666	+	0.565666i
$124$	−48.4141	−	48.4141i	−0.390436	−	0.390436i
$125$	130.297			1.04237
$126$		−	48.7215i		−	0.386679i
$127$		−	70.9217i		−	0.558439i	−0.960227	−	0.279219i	$-0.909924\pi$
$127$		−	70.9217i		−	0.558439i	0.960227	−	0.279219i	$-0.0900757\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$	−113.297	+	113.297i	−0.878270	+	0.878270i
$130$	−105.276	+	105.276i	−0.809814	+	0.809814i
$131$	237.667			1.81425			0.907125	−	0.420861i	$-0.138272\pi$
$131$	237.667			1.81425			0.907125	+	0.420861i	$0.138272\pi$
$132$	40.9464	+	40.9464i	0.310200	+	0.310200i
$133$		−	80.2344i		−	0.603266i
$134$	60.2833	+	60.2833i	0.449875	+	0.449875i
$135$	−98.5690	+	98.5690i	−0.730141	+	0.730141i
$136$	−3.57063			−0.0262546
$137$	61.8934	−	61.8934i	0.451777	−	0.451777i	−0.444167	−	0.895944i	$-0.646500\pi$
$137$	61.8934	−	61.8934i	0.451777	−	0.451777i	0.895944	+	0.444167i	$0.146500\pi$
$138$		−	46.7356i		−	0.338664i
$139$	−61.6648	−	61.6648i	−0.443632	−	0.443632i	0.449599	−	0.893231i	$-0.351567\pi$
$139$	−61.6648	−	61.6648i	−0.443632	−	0.443632i	−0.893231	+	0.449599i	$0.851567\pi$
$140$	−90.4421	−	90.4421i	−0.646015	−	0.646015i
$141$	12.5666	+	12.5666i	0.0891246	+	0.0891246i
$142$	49.3611			0.347613
$143$	−252.769			−1.76762
$144$			10.2392i			0.0711054i
$145$	132.859	−	132.859i	0.916270	−	0.916270i
$146$	100.890	−	100.890i	0.691026	−	0.691026i
$147$	237.110	−	237.110i	1.61300	−	1.61300i
$148$			107.904i			0.729084i
$149$			145.158i			0.974214i	0.873342	+	0.487107i	$0.161948\pi$
$149$			145.158i			0.974214i	−0.873342	+	0.487107i	$0.838052\pi$
$150$		−	8.68770i		−	0.0579180i
$151$			198.815i			1.31666i	0.752731	+	0.658328i	$0.228736\pi$
$151$			198.815i			1.31666i	−0.752731	+	0.658328i	$0.771264\pi$
$152$			16.8618i			0.110933i
$153$	2.28502	−	2.28502i	0.0149348	−	0.0149348i
$154$		−	217.153i		−	1.41009i
$155$	115.026	−	115.026i	0.742105	−	0.742105i
$156$	79.5130	+	79.5130i	0.509699	+	0.509699i
$157$	150.750	+	150.750i	0.960188	+	0.960188i	0.999237	−	0.0390494i	$-0.0124330\pi$
$157$	150.750	+	150.750i	0.960188	+	0.960188i	−0.0390494	+	0.999237i	$0.512433\pi$
$158$	−147.725	+	147.725i	−0.934968	+	0.934968i
$159$	−74.8939	−	74.8939i	−0.471031	−	0.471031i
$160$	19.0071	+	19.0071i	0.118794	+	0.118794i
$161$	−123.928	+	123.928i	−0.769737	+	0.769737i
$162$	51.4093	+	51.4093i	0.317341	+	0.317341i
$163$	158.766	−	158.766i	0.974022	−	0.974022i	−0.0256486	−	0.999671i	$-0.508165\pi$
$163$	158.766	−	158.766i	0.974022	−	0.974022i	0.999671	+	0.0256486i	$0.00816510\pi$
$164$			77.5462i			0.472843i
$165$	−97.2839	+	97.2839i	−0.589599	+	0.589599i
$166$	−28.7386			−0.173124
$167$	60.5109	+	60.5109i	0.362341	+	0.362341i	0.864674	−	0.502333i	$-0.167525\pi$
$167$	60.5109	+	60.5109i	0.362341	+	0.362341i	−0.502333	+	0.864674i	$0.667525\pi$
$168$	−68.3094	+	68.3094i	−0.406603	+	0.406603i
$169$	−321.848			−1.90443
$170$		−	8.48340i		−	0.0499023i
$171$	−10.7907	−	10.7907i	−0.0631036	−	0.0631036i
$172$	−126.274			−0.734150
$173$	−304.092			−1.75775			−0.878877	−	0.477048i	$-0.841707\pi$
$173$	−304.092			−1.75775			−0.878877	+	0.477048i	$0.841707\pi$
$174$	−100.346	−	100.346i	−0.576703	−	0.576703i
$175$	−23.0370	+	23.0370i	−0.131640	+	0.131640i
$176$			45.6363i			0.259297i
$177$	−92.4111			−0.522097
$178$	−146.915	+	146.915i	−0.825363	+	0.825363i
$179$	−10.1235	−	10.1235i	−0.0565560	−	0.0565560i	0.678263	−	0.734819i	$-0.262733\pi$
$179$	−10.1235	−	10.1235i	−0.0565560	−	0.0565560i	−0.734819	+	0.678263i	$0.762733\pi$
$180$	−24.3271			−0.135151
$181$	−202.916	+	202.916i	−1.12108	+	1.12108i	−0.129501	+	0.991579i	$0.541338\pi$
$181$	−202.916	+	202.916i	−1.12108	+	1.12108i	−0.991579	+	0.129501i	$0.958662\pi$
$182$		−	421.686i		−	2.31695i
$183$	74.9918	+	74.9918i	0.409791	+	0.409791i
$184$	26.0443	−	26.0443i	0.141545	−	0.141545i
$185$	−256.369			−1.38578
$186$	−86.8774	−	86.8774i	−0.467083	−	0.467083i
$187$	10.1844	−	10.1844i	0.0544620	−	0.0544620i
$188$			14.0059i			0.0744996i
$189$		−	394.821i		−	2.08900i
$190$	−40.0618			−0.210852
$191$		−	266.822i		−	1.39697i	−0.715623	−	0.698486i	$-0.753857\pi$
$191$		−	266.822i		−	1.39697i	0.715623	−	0.698486i	$-0.246143\pi$
$192$	14.3557	−	14.3557i	0.0747694	−	0.0747694i
$193$	−7.36026	+	7.36026i	−0.0381361	+	0.0381361i	−0.725918	−	0.687782i	$-0.758585\pi$
$193$	−7.36026	+	7.36026i	−0.0381361	+	0.0381361i	0.687782	+	0.725918i	$0.258585\pi$
$194$	52.1351	−	52.1351i	0.268738	−	0.268738i
$195$	−188.914	+	188.914i	−0.968789	+	0.968789i
$196$	264.269			1.34831
$197$	−185.966	+	185.966i	−0.943992	+	0.943992i	−0.998513	−	0.0545205i	$-0.982637\pi$
$197$	−185.966	+	185.966i	−0.943992	+	0.943992i	0.0545205	+	0.998513i	$0.482637\pi$
$198$	−29.2049	−	29.2049i	−0.147500	−	0.147500i
$199$			106.214i			0.533740i	0.963733	+	0.266870i	$0.0859894\pi$
$199$			106.214i			0.533740i	−0.963733	+	0.266870i	$0.914011\pi$
$200$	4.84139	−	4.84139i	0.0242070	−	0.0242070i
$201$	108.176	+	108.176i	0.538190	+	0.538190i
$202$			74.0567i			0.366617i
$203$			532.172i			2.62154i
$204$	−6.40736			−0.0314086
$205$	−184.241			−0.898735
$206$	93.4599	−	93.4599i	0.453689	−	0.453689i
$207$			33.3340i			0.161034i
$208$			88.6203i			0.426059i
$209$	−48.0945	−	48.0945i	−0.230117	−	0.230117i
$210$	−162.295	−	162.295i	−0.772834	−	0.772834i
$211$		−	9.73196i		−	0.0461230i	−0.999734	−	0.0230615i	$-0.992659\pi$
$211$		−	9.73196i		−	0.0461230i	0.999734	−	0.0230615i	$-0.00734136\pi$
$212$		−	83.4722i		−	0.393737i
$213$	88.5767			0.415853
$214$	−100.146			−0.467970
$215$		−	300.012i		−	1.39540i
$216$			82.9746i			0.384141i
$217$			460.742i			2.12323i
$218$	210.762			0.966796
$219$	181.043	−	181.043i	0.826681	−	0.826681i
$220$	−108.427			−0.492848
$221$	19.7769	−	19.7769i	0.0894882	−	0.0894882i
$222$			193.631i			0.872210i
$223$	97.2776	−	97.2776i	0.436223	−	0.436223i	−0.454516	−	0.890739i	$-0.650188\pi$
$223$	97.2776	−	97.2776i	0.436223	−	0.436223i	0.890739	+	0.454516i	$0.150188\pi$
$224$	−76.1334			−0.339881
$225$			6.19648i			0.0275399i
$226$	218.854			0.968382
$227$	40.8865	−	40.8865i	0.180117	−	0.180117i	−0.611290	−	0.791407i	$-0.709349\pi$
$227$	40.8865	−	40.8865i	0.180117	−	0.180117i	0.791407	+	0.611290i	$0.209349\pi$
$228$			30.2580i			0.132710i
$229$	39.5071	+	39.5071i	0.172520	+	0.172520i	0.788086	−	0.615566i	$-0.211072\pi$
$229$	39.5071	+	39.5071i	0.172520	+	0.172520i	−0.615566	+	0.788086i	$0.711072\pi$
$230$	61.8783	+	61.8783i	0.269036	+	0.269036i
$231$		−	389.674i		−	1.68690i
$232$		−	111.840i		−	0.482068i
$233$		−	424.358i		−	1.82128i	−0.413202	−	0.910639i	$-0.635590\pi$
$233$		−	424.358i		−	1.82128i	0.413202	−	0.910639i	$-0.364410\pi$
$234$	−56.7125	−	56.7125i	−0.242361	−	0.242361i
$235$	−33.2764			−0.141602
$236$	−51.4979	−	51.4979i	−0.218211	−	0.218211i
$237$	−265.087	+	265.087i	−1.11851	+	1.11851i
$238$	16.9903	+	16.9903i	0.0713876	+	0.0713876i
$239$	−6.22089			−0.0260288			−0.0130144	−	0.999915i	$-0.504143\pi$
$239$	−6.22089			−0.0260288			−0.0130144	+	0.999915i	$0.504143\pi$
$240$	34.1075	+	34.1075i	0.142115	+	0.142115i
$241$	−2.33206	+	2.33206i	−0.00967658	+	0.00967658i	−0.711929	−	0.702252i	$-0.752178\pi$
$241$	−2.33206	+	2.33206i	−0.00967658	+	0.00967658i	0.702252	+	0.711929i	$0.252178\pi$
$242$	−9.16714	−	9.16714i	−0.0378808	−	0.0378808i
$243$	−94.4406	−	94.4406i	−0.388644	−	0.388644i
$244$			83.5812i			0.342546i
$245$			627.872i			2.56274i
$246$			139.154i			0.565666i
$247$	−93.3939	−	93.3939i	−0.378113	−	0.378113i
$248$		−	96.8282i		−	0.390436i
$249$	−51.5704			−0.207110
$250$	130.297	+	130.297i	0.521187	+	0.521187i
$251$	269.043	+	269.043i	1.07189	+	1.07189i	0.997208	+	0.0746774i	$0.0237927\pi$
$251$	269.043	+	269.043i	1.07189	+	1.07189i	0.0746774	+	0.997208i	$0.476207\pi$
$252$	48.7215	−	48.7215i	0.193339	−	0.193339i
$253$			148.571i			0.587237i
$254$	70.9217	−	70.9217i	0.279219	−	0.279219i
$255$		−	15.2232i		−	0.0596986i
$256$	16.0000			0.0625000
$257$	−19.1102	−	19.1102i	−0.0743586	−	0.0743586i	0.668949	−	0.743308i	$-0.266744\pi$
$257$	−19.1102	−	19.1102i	−0.0743586	−	0.0743586i	−0.743308	+	0.668949i	$0.766744\pi$
$258$	−226.594			−0.878270
$259$	513.446	−	513.446i	1.98242	−	1.98242i
$260$	−210.552			−0.809814
$261$	71.5717	+	71.5717i	0.274221	+	0.274221i
$262$	237.667	+	237.667i	0.907125	+	0.907125i
$263$	−368.542			−1.40130			−0.700650	−	0.713505i	$-0.747106\pi$
$263$	−368.542			−1.40130			−0.700650	+	0.713505i	$0.747106\pi$
$264$			81.8928i			0.310200i
$265$	198.320			0.748378
$266$	80.2344	−	80.2344i	0.301633	−	0.301633i
$267$	−263.633	+	263.633i	−0.987389	+	0.987389i
$268$			120.567i			0.449875i
$269$	35.7347	+	266.616i	0.132843	+	0.991137i
$269$	35.7347	+	266.616i	0.132843	+	0.991137i
$270$	−197.138			−0.730141
$271$	134.797	+	134.797i	0.497405	+	0.497405i	0.910629	−	0.413224i	$-0.135597\pi$
$271$	134.797	+	134.797i	0.497405	+	0.497405i	−0.413224	+	0.910629i	$0.635597\pi$
$272$	−3.57063	−	3.57063i	−0.0131273	−	0.0131273i
$273$		−	756.700i		−	2.77180i
$274$	123.787			0.451777
$275$			27.6179i			0.100429i
$276$	46.7356	−	46.7356i	0.169332	−	0.169332i
$277$	−122.099	+	122.099i	−0.440791	+	0.440791i	−0.892278	−	0.451487i	$-0.850894\pi$
$277$	−122.099	+	122.099i	−0.440791	+	0.440791i	0.451487	+	0.892278i	$0.350894\pi$
$278$		−	123.330i		−	0.443632i
$279$	61.9651	+	61.9651i	0.222097	+	0.222097i
$280$		−	180.884i		−	0.646015i
$281$	185.961	−	185.961i	0.661784	−	0.661784i	−0.294017	−	0.955800i	$-0.594992\pi$
$281$	185.961	−	185.961i	0.661784	−	0.661784i	0.955800	+	0.294017i	$0.0949921\pi$
$282$			25.1331i			0.0891246i
$283$	−267.368			−0.944763			−0.472381	−	0.881394i	$-0.656606\pi$
$283$	−267.368			−0.944763			−0.472381	+	0.881394i	$0.656606\pi$
$284$	49.3611	+	49.3611i	0.173807	+	0.173807i
$285$	−71.8895			−0.252244
$286$	−252.769	−	252.769i	−0.883808	−	0.883808i
$287$	368.991	−	368.991i	1.28568	−	1.28568i
$288$	−10.2392	+	10.2392i	−0.0355527	+	0.0355527i
$289$		−	287.406i		−	0.994486i
$290$	265.718			0.916270
$291$	93.5547	−	93.5547i	0.321494	−	0.321494i
$292$	201.779			0.691026
$293$	200.890			0.685631			0.342815	−	0.939403i	$-0.388619\pi$
$293$	200.890			0.685631			0.342815	+	0.939403i	$0.388619\pi$
$294$	474.221			1.61300
$295$	122.353	−	122.353i	0.414756	−	0.414756i
$296$	−107.904	+	107.904i	−0.364542	+	0.364542i
$297$	−236.666	−	236.666i	−0.796855	−	0.796855i
$298$	−145.158	+	145.158i	−0.487107	+	0.487107i
$299$			288.507i			0.964906i
$300$	8.68770	−	8.68770i	0.0289590	−	0.0289590i
$301$	600.854	+	600.854i	1.99619	+	1.99619i
$302$	−198.815	+	198.815i	−0.658328	+	0.658328i
$303$			132.892i			0.438588i
$304$	−16.8618	+	16.8618i	−0.0554666	+	0.0554666i
$305$	−198.579			−0.651080
$306$	4.57004			0.0149348
$307$	436.068			1.42042			0.710209	−	0.703991i	$-0.248600\pi$
$307$	436.068			1.42042			0.710209	+	0.703991i	$0.248600\pi$
$308$	217.153	−	217.153i	0.705043	−	0.705043i
$309$	167.710	−	167.710i	0.542752	−	0.542752i
$310$	230.053			0.742105
$311$	−232.477	−	232.477i	−0.747514	−	0.747514i	0.226498	−	0.974012i	$-0.427272\pi$
$311$	−232.477	−	232.477i	−0.747514	−	0.747514i	−0.974012	+	0.226498i	$0.927272\pi$
$312$			159.026i			0.509699i
$313$	−305.654			−0.976531			−0.488265	−	0.872695i	$-0.662370\pi$
$313$	−305.654			−0.976531			−0.488265	+	0.872695i	$0.662370\pi$
$314$			301.499i			0.960188i
$315$	115.757	+	115.757i	0.367481	+	0.367481i
$316$	−295.450			−0.934968
$317$	−129.153	−	129.153i	−0.407423	−	0.407423i	0.473416	−	0.880839i	$-0.343021\pi$
$317$	−129.153	−	129.153i	−0.407423	−	0.407423i	−0.880839	+	0.473416i	$0.843021\pi$
$318$		−	149.788i		−	0.471031i
$319$	318.997	+	318.997i	0.999992	+	0.999992i
$320$			38.0141i			0.118794i
$321$	−179.708			−0.559837
$322$	−247.855			−0.769737
$323$	7.52592			0.0233001
$324$			102.819i			0.317341i
$325$			53.6307i			0.165018i
$326$	317.531			0.974022
$327$	378.204			1.15659
$328$	−77.5462	+	77.5462i	−0.236421	+	0.236421i
$329$	66.6449	−	66.6449i	0.202568	−	0.202568i
$330$	−194.568			−0.589599
$331$	−385.720			−1.16532			−0.582658	−	0.812717i	$-0.697987\pi$
$331$	−385.720			−1.16532			−0.582658	+	0.812717i	$0.697987\pi$
$332$	−28.7386	−	28.7386i	−0.0865621	−	0.0865621i
$333$		−	138.107i		−	0.414735i
$334$			121.022i			0.362341i
$335$	−286.452			−0.855081
$336$	−136.619			−0.406603
$337$	67.0198	−	67.0198i	0.198872	−	0.198872i	−0.600644	−	0.799516i	$-0.705089\pi$
$337$	67.0198	−	67.0198i	0.198872	−	0.198872i	0.799516	+	0.600644i	$0.205089\pi$
$338$	−321.848	−	321.848i	−0.952213	−	0.952213i
$339$	392.727			1.15849
$340$	8.48340	−	8.48340i	0.0249512	−	0.0249512i
$341$	276.180	+	276.180i	0.809913	+	0.809913i
$342$		−	21.5814i		−	0.0631036i
$343$	−791.164	−	791.164i	−2.30660	−	2.30660i
$344$	−126.274	−	126.274i	−0.367075	−	0.367075i
$345$	111.038	+	111.038i	0.321850	+	0.321850i
$346$	−304.092	−	304.092i	−0.878877	−	0.878877i
$347$	386.357			1.11342			0.556710	−	0.830707i	$-0.312063\pi$
$347$	386.357			1.11342			0.556710	+	0.830707i	$0.312063\pi$
$348$		−	200.693i		−	0.576703i
$349$	377.388			1.08134			0.540670	−	0.841235i	$-0.318171\pi$
$349$	377.388			1.08134			0.540670	+	0.841235i	$0.318171\pi$
$350$	−46.0740			−0.131640
$351$	−459.577	−	459.577i	−1.30934	−	1.30934i
$352$	−45.6363	+	45.6363i	−0.129649	+	0.129649i
$353$			471.661i			1.33615i	0.744093	+	0.668076i	$0.232882\pi$
$353$			471.661i			1.33615i	−0.744093	+	0.668076i	$0.767118\pi$
$354$	−92.4111	−	92.4111i	−0.261048	−	0.261048i
$355$	−117.276	+	117.276i	−0.330356	+	0.330356i
$356$	−293.829			−0.825363
$357$	30.4884	+	30.4884i	0.0854017	+	0.0854017i
$358$		−	20.2470i		−	0.0565560i
$359$	318.793	−	318.793i	0.888002	−	0.888002i	−0.106329	−	0.994331i	$-0.533910\pi$
$359$	318.793	−	318.793i	0.888002	−	0.888002i	0.994331	+	0.106329i	$0.0339098\pi$
$360$	−24.3271	−	24.3271i	−0.0675753	−	0.0675753i
$361$			325.460i			0.901551i
$362$	−405.831			−1.12108
$363$	−16.4501	−	16.4501i	−0.0453171	−	0.0453171i
$364$	421.686	−	421.686i	1.15848	−	1.15848i
$365$			479.405i			1.31344i
$366$			149.984i			0.409791i
$367$	−65.2673	+	65.2673i	−0.177840	+	0.177840i	−0.790414	−	0.612573i	$-0.790134\pi$
$367$	−65.2673	+	65.2673i	−0.177840	+	0.177840i	0.612573	+	0.790414i	$0.290134\pi$
$368$	52.0886			0.141545
$369$		−	99.2512i		−	0.268973i
$370$	−256.369	−	256.369i	−0.692888	−	0.692888i
$371$	−397.189	+	397.189i	−1.07059	+	1.07059i
$372$		−	173.755i		−	0.467083i
$373$	42.7381	+	42.7381i	0.114579	+	0.114579i	0.762072	−	0.647493i	$-0.224182\pi$
$373$	42.7381	+	42.7381i	0.114579	+	0.114579i	−0.647493	+	0.762072i	$0.724182\pi$
$374$	20.3688			0.0544620
$375$	233.813	+	233.813i	0.623501	+	0.623501i
$376$	−14.0059	+	14.0059i	−0.0372498	+	0.0372498i
$377$	619.455	+	619.455i	1.64312	+	1.64312i
$378$	394.821	−	394.821i	1.04450	−	1.04450i
$379$	170.947	−	170.947i	0.451047	−	0.451047i	−0.444655	−	0.895702i	$-0.646674\pi$
$379$	170.947	−	170.947i	0.451047	−	0.451047i	0.895702	+	0.444655i	$0.146674\pi$
$380$	−40.0618	−	40.0618i	−0.105426	−	0.105426i
$381$	127.266	−	127.266i	0.334033	−	0.334033i
$382$	266.822	−	266.822i	0.698486	−	0.698486i
$383$	−111.848	−	111.848i	−0.292031	−	0.292031i	0.545851	−	0.837882i	$-0.316206\pi$
$383$	−111.848	−	111.848i	−0.292031	−	0.292031i	−0.837882	+	0.545851i	$0.816206\pi$
$384$	28.7114			0.0747694
$385$	515.931	+	515.931i	1.34008	+	1.34008i
$386$	−14.7205			−0.0381361
$387$	161.617			0.417616
$388$	104.270			0.268738
$389$	182.560			0.469306			0.234653	−	0.972079i	$-0.424605\pi$
$389$	182.560			0.469306			0.234653	+	0.972079i	$0.424605\pi$
$390$	−377.828			−0.968789
$391$	−11.6243	−	11.6243i	−0.0297297	−	0.0297297i
$392$	264.269	+	264.269i	0.674155	+	0.674155i
$393$	426.485	+	426.485i	1.08520	+	1.08520i
$394$	−371.933			−0.943992
$395$		−	701.955i		−	1.77710i
$396$		−	58.4098i		−	0.147500i
$397$	−188.940	+	188.940i	−0.475920	+	0.475920i	−0.903824	−	0.427904i	$-0.859252\pi$
$397$	−188.940	+	188.940i	−0.475920	+	0.475920i	0.427904	+	0.903824i	$0.359252\pi$
$398$	−106.214	+	106.214i	−0.266870	+	0.266870i
$399$	143.978	−	143.978i	0.360847	−	0.360847i
$400$	9.68278			0.0242070
$401$	380.746	+	380.746i	0.949491	+	0.949491i	0.998784	−	0.0492930i	$-0.0156968\pi$
$401$	380.746	+	380.746i	0.949491	+	0.949491i	−0.0492930	+	0.998784i	$0.515697\pi$
$402$			216.352i			0.538190i
$403$	536.309	+	536.309i	1.33079	+	1.33079i
$404$	−74.0567	+	74.0567i	−0.183309	+	0.183309i
$405$	−244.285			−0.603173
$406$	−532.172	+	532.172i	−1.31077	+	1.31077i
$407$		−	615.545i		−	1.51240i
$408$	−6.40736	−	6.40736i	−0.0157043	−	0.0157043i
$409$	89.2298	+	89.2298i	0.218166	+	0.218166i	0.807725	−	0.589559i	$-0.200699\pi$
$409$	89.2298	+	89.2298i	0.218166	+	0.218166i	−0.589559	+	0.807725i	$0.700699\pi$
$410$	−184.241	−	184.241i	−0.449368	−	0.449368i
$411$	222.131			0.540465
$412$	186.920			0.453689
$413$			490.089i			1.18666i
$414$	−33.3340	+	33.3340i	−0.0805170	+	0.0805170i
$415$	68.2796	−	68.2796i	0.164529	−	0.164529i
$416$	−88.6203	+	88.6203i	−0.213030	+	0.213030i
$417$		−	221.311i		−	0.530721i
$418$		−	96.1891i		−	0.230117i
$419$			240.384i			0.573709i	0.957974	+	0.286855i	$0.0926097\pi$
$419$			240.384i			0.573709i	−0.957974	+	0.286855i	$0.907390\pi$
$420$		−	324.590i		−	0.772834i
$421$		−	399.203i		−	0.948225i	−0.880464	−	0.474113i	$-0.842769\pi$
$421$		−	399.203i		−	0.948225i	0.880464	−	0.474113i	$-0.157231\pi$
$422$	9.73196	−	9.73196i	0.0230615	−	0.0230615i
$423$		−	17.9261i		−	0.0423786i
$424$	83.4722	−	83.4722i	0.196868	−	0.196868i
$425$	−2.16085	−	2.16085i	−0.00508435	−	0.00508435i
$426$	88.5767	+	88.5767i	0.207927	+	0.207927i
$427$	397.708	−	397.708i	0.931400	−	0.931400i
$428$	−100.146	−	100.146i	−0.233985	−	0.233985i
$429$	−453.585	−	453.585i	−1.05731	−	1.05731i
$430$	300.012	−	300.012i	0.697702	−	0.697702i
$431$	116.865	+	116.865i	0.271149	+	0.271149i	0.829563	−	0.558413i	$-0.188590\pi$
$431$	116.865	+	116.865i	0.271149	+	0.271149i	−0.558413	+	0.829563i	$0.688590\pi$
$432$	−82.9746	+	82.9746i	−0.192071	+	0.192071i
$433$			429.883i			0.992802i	0.868093	+	0.496401i	$0.165345\pi$
$433$			429.883i			0.992802i	−0.868093	+	0.496401i	$0.834655\pi$
$434$	−460.742	+	460.742i	−1.06162	+	1.06162i
$435$	476.822			1.09614
$436$	210.762	+	210.762i	0.483398	+	0.483398i
$437$	−54.8944	+	54.8944i	−0.125616	+	0.125616i
$438$	362.086			0.826681
$439$		−	565.480i		−	1.28811i	−0.764980	−	0.644054i	$-0.777251\pi$
$439$		−	565.480i		−	1.28811i	0.764980	−	0.644054i	$-0.222749\pi$
$440$	−108.427	−	108.427i	−0.246424	−	0.246424i
$441$	−338.237			−0.766977
$442$	39.5538			0.0894882
$443$	−14.7763	−	14.7763i	−0.0333550	−	0.0333550i	0.690233	−	0.723588i	$-0.257508\pi$
$443$	−14.7763	−	14.7763i	−0.0333550	−	0.0333550i	−0.723588	+	0.690233i	$0.757508\pi$
$444$	−193.631	+	193.631i	−0.436105	+	0.436105i
$445$		−	698.104i		−	1.56877i
$446$	194.555			0.436223
$447$	−260.481	+	260.481i	−0.582731	+	0.582731i
$448$	−76.1334	−	76.1334i	−0.169941	−	0.169941i
$449$	−15.5790			−0.0346971			−0.0173486	−	0.999850i	$-0.505522\pi$
$449$	−15.5790			−0.0346971			−0.0173486	+	0.999850i	$0.505522\pi$
$450$	−6.19648	+	6.19648i	−0.0137700	+	0.0137700i
$451$		−	442.365i		−	0.980854i
$452$	218.854	+	218.854i	0.484191	+	0.484191i
$453$	−356.766	+	356.766i	−0.787564	+	0.787564i
$454$	81.7730			0.180117
$455$	1001.88	+	1001.88i	2.20193	+	2.20193i
$456$	−30.2580	+	30.2580i	−0.0663552	+	0.0663552i
$457$		−	676.235i		−	1.47973i	−0.672758	−	0.739863i	$-0.734890\pi$
$457$		−	676.235i		−	1.47973i	0.672758	−	0.739863i	$-0.265110\pi$
$458$			79.0142i			0.172520i
$459$	37.0339			0.0806839
$460$			123.757i			0.269036i
$461$	−409.407	+	409.407i	−0.888084	+	0.888084i	−0.994339	−	0.106255i	$-0.966114\pi$
$461$	−409.407	+	409.407i	−0.888084	+	0.888084i	0.106255	+	0.994339i	$0.466114\pi$
$462$	389.674	−	389.674i	0.843449	−	0.843449i
$463$	−97.7188	+	97.7188i	−0.211056	+	0.211056i	−0.804716	−	0.593660i	$-0.797682\pi$
$463$	−97.7188	+	97.7188i	−0.211056	+	0.211056i	0.593660	+	0.804716i	$0.297682\pi$
$464$	111.840	−	111.840i	0.241034	−	0.241034i
$465$	412.821			0.887788
$466$	424.358	−	424.358i	0.910639	−	0.910639i
$467$	402.844	+	402.844i	0.862622	+	0.862622i	0.991642	−	0.129020i	$-0.0411833\pi$
$467$	402.844	+	402.844i	0.862622	+	0.862622i	−0.129020	+	0.991642i	$0.541183\pi$
$468$		−	113.425i		−	0.242361i
$469$	573.696	−	573.696i	1.22323	−	1.22323i
$470$	−33.2764	−	33.2764i	−0.0708009	−	0.0708009i
$471$			541.029i			1.14868i
$472$		−	102.996i		−	0.218211i
$473$	720.334			1.52290
$474$	−530.174			−1.11851
$475$	−10.2043	+	10.2043i	−0.0214828	+	0.0214828i
$476$			33.9805i			0.0713876i
$477$			106.836i			0.223974i
$478$	−6.22089	−	6.22089i	−0.0130144	−	0.0130144i
$479$	144.194	+	144.194i	0.301032	+	0.301032i	0.841418	−	0.540385i	$-0.181722\pi$
$479$	144.194	+	144.194i	0.301032	+	0.301032i	−0.540385	+	0.841418i	$0.681722\pi$
$480$			68.2150i			0.142115i
$481$		−	1195.32i		−	2.48507i
$482$	−4.66411			−0.00967658
$483$	−444.768			−0.920844
$484$		−	18.3343i		−	0.0378808i
$485$			247.734i			0.510792i
$486$		−	188.881i		−	0.388644i
$487$	−541.406			−1.11172			−0.555859	−	0.831277i	$-0.687610\pi$
$487$	−541.406			−1.11172			−0.555859	+	0.831277i	$0.687610\pi$
$488$	−83.5812	+	83.5812i	−0.171273	+	0.171273i
$489$	569.799			1.16523
$490$	−627.872	+	627.872i	−1.28137	+	1.28137i
$491$		−	279.654i		−	0.569560i	−0.958593	−	0.284780i	$-0.908080\pi$
$491$		−	279.654i		−	0.569560i	0.958593	−	0.284780i	$-0.0919205\pi$
$492$	−139.154	+	139.154i	−0.282833	+	0.282833i
$493$	−49.9173			−0.101252
$494$		−	186.788i		−	0.378113i
$495$	138.775			0.280353
$496$	96.8282	−	96.8282i	0.195218	−	0.195218i
$497$		−	469.754i		−	0.945179i
$498$	−51.5704	−	51.5704i	−0.103555	−	0.103555i
$499$	−105.935	−	105.935i	−0.212295	−	0.212295i	0.592947	−	0.805242i	$-0.297964\pi$
$499$	−105.935	−	105.935i	−0.212295	−	0.212295i	−0.805242	+	0.592947i	$0.797964\pi$
$500$			260.594i			0.521187i
$501$			217.169i			0.433472i
$502$			538.086i			1.07189i
$503$	−468.820	−	468.820i	−0.932048	−	0.932048i	0.0657862	−	0.997834i	$-0.479044\pi$
$503$	−468.820	−	468.820i	−0.932048	−	0.932048i	−0.997834	+	0.0657862i	$0.979044\pi$
$504$	97.4430			0.193339
$505$	−175.950	−	175.950i	−0.348416	−	0.348416i
$506$	−148.571	+	148.571i	−0.293618	+	0.293618i
$507$	−577.545	−	577.545i	−1.13914	−	1.13914i
$508$	141.843			0.279219
$509$	−271.626	−	271.626i	−0.533646	−	0.533646i	0.388009	−	0.921655i	$-0.373163\pi$
$509$	−271.626	−	271.626i	−0.533646	−	0.533646i	−0.921655	+	0.388009i	$0.873163\pi$
$510$	15.2232	−	15.2232i	0.0298493	−	0.0298493i
$511$	−960.135	−	960.135i	−1.87893	−	1.87893i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$		−	174.888i		−	0.340912i
$514$		−	38.2203i		−	0.0743586i
$515$			444.100i			0.862329i
$516$	−226.594	−	226.594i	−0.439135	−	0.439135i
$517$		−	79.8973i		−	0.154540i
$518$	1026.89			1.98242
$519$	−545.682	−	545.682i	−1.05141	−	1.05141i
$520$	−210.552	−	210.552i	−0.404907	−	0.404907i
$521$	−339.802	+	339.802i	−0.652211	+	0.652211i	−0.953525	−	0.301314i	$-0.902575\pi$
$521$	−339.802	+	339.802i	−0.652211	+	0.652211i	0.301314	+	0.953525i	$0.402575\pi$
$522$			143.143i			0.274221i
$523$	−221.682	+	221.682i	−0.423865	+	0.423865i	−0.886532	−	0.462667i	$-0.846893\pi$
$523$	−221.682	+	221.682i	−0.423865	+	0.423865i	0.462667	+	0.886532i	$0.346893\pi$
$524$			475.334i			0.907125i
$525$	−82.6781			−0.157482
$526$	−368.542	−	368.542i	−0.700650	−	0.700650i
$527$	−43.2172			−0.0820060
$528$	−81.8928	+	81.8928i	−0.155100	+	0.155100i
$529$	−359.423			−0.679439
$530$	198.320	+	198.320i	0.374189	+	0.374189i
$531$	65.9120	+	65.9120i	0.124128	+	0.124128i
$532$	160.469			0.301633
$533$		−	859.021i		−	1.61167i
$534$	−527.266			−0.987389
$535$	237.934	−	237.934i	0.444737	−	0.444737i
$536$	−120.567	+	120.567i	−0.224938	+	0.224938i
$537$		−	36.3326i		−	0.0676585i
$538$	−230.881	+	302.351i	−0.429147	+	0.561990i
$539$	−1507.53			−2.79691
$540$	−197.138	−	197.138i	−0.365070	−	0.365070i
$541$	−181.302	−	181.302i	−0.335124	−	0.335124i	0.519404	−	0.854529i	$-0.326154\pi$
$541$	−181.302	−	181.302i	−0.335124	−	0.335124i	−0.854529	+	0.519404i	$0.826154\pi$
$542$			269.594i			0.497405i
$543$	−728.250			−1.34116
$544$		−	7.14125i		−	0.0131273i
$545$	−500.745	+	500.745i	−0.918798	+	0.918798i
$546$	756.700	−	756.700i	1.38590	−	1.38590i
$547$			453.445i			0.828967i	0.910057	+	0.414483i	$0.136038\pi$
$547$			453.445i			0.828967i	−0.910057	+	0.414483i	$0.863962\pi$
$548$	123.787	+	123.787i	0.225888	+	0.225888i
$549$		−	106.975i		−	0.194855i
$550$	−27.6179	+	27.6179i	−0.0502144	+	0.0502144i
$551$			235.728i			0.427819i
$552$	93.4712			0.169332
$553$	1405.85	+	1405.85i	2.54223	+	2.54223i
$554$	−244.198			−0.440791
$555$	−460.044	−	460.044i	−0.828908	−	0.828908i
$556$	123.330	−	123.330i	0.221816	−	0.221816i
$557$	−191.888	+	191.888i	−0.344502	+	0.344502i	−0.858057	−	0.513555i	$-0.828328\pi$
$557$	−191.888	+	191.888i	−0.344502	+	0.344502i	0.513555	+	0.858057i	$0.328328\pi$
$558$			123.930i			0.222097i
$559$	1398.80			2.50233
$560$	180.884	−	180.884i	0.323008	−	0.323008i
$561$	36.5511			0.0651534
$562$	371.922			0.661784
$563$	299.551			0.532062			0.266031	−	0.963965i	$-0.414288\pi$
$563$	299.551			0.532062			0.266031	+	0.963965i	$0.414288\pi$
$564$	−25.1331	+	25.1331i	−0.0445623	+	0.0445623i
$565$	−519.973	+	519.973i	−0.920306	+	0.920306i
$566$	−267.368	−	267.368i	−0.472381	−	0.472381i
$567$	489.246	−	489.246i	0.862867	−	0.862867i
$568$			98.7222i			0.173807i
$569$	−535.376	+	535.376i	−0.940907	+	0.940907i	−0.998349	−	0.0574414i	$-0.981706\pi$
$569$	−535.376	+	535.376i	−0.940907	+	0.940907i	0.0574414	+	0.998349i	$0.481706\pi$
$570$	−71.8895	−	71.8895i	−0.126122	−	0.126122i
$571$	−238.022	+	238.022i	−0.416852	+	0.416852i	−0.884117	−	0.467265i	$-0.845239\pi$
$571$	−238.022	+	238.022i	−0.416852	+	0.416852i	0.467265	+	0.884117i	$0.345239\pi$
$572$		−	505.538i		−	0.883808i
$573$	478.802	−	478.802i	0.835606	−	0.835606i
$574$	737.982			1.28568
$575$	31.5227			0.0548220
$576$	−20.4784			−0.0355527
$577$	83.6317	−	83.6317i	0.144942	−	0.144942i	−0.630912	−	0.775854i	$-0.717319\pi$
$577$	83.6317	−	83.6317i	0.144942	−	0.144942i	0.775854	+	0.630912i	$0.217319\pi$
$578$	287.406	−	287.406i	0.497243	−	0.497243i
$579$	−26.4155			−0.0456226
$580$	265.718	+	265.718i	0.458135	+	0.458135i
$581$			273.496i			0.470733i
$582$	187.109			0.321494
$583$			476.170i			0.816759i
$584$	201.779	+	201.779i	0.345513	+	0.345513i
$585$	269.485			0.460657
$586$	200.890	+	200.890i	0.342815	+	0.342815i
$587$			224.995i			0.383297i	0.981464	+	0.191649i	$0.0613834\pi$
$587$			224.995i			0.383297i	−0.981464	+	0.191649i	$0.938617\pi$
$588$	474.221	+	474.221i	0.806498	+	0.806498i
$589$			204.088i			0.346499i
$590$	244.706			0.414756
$591$	−667.420			−1.12931
$592$	−215.809			−0.364542
$593$		−	724.039i		−	1.22098i	−0.792025	−	0.610489i	$-0.790973\pi$
$593$		−	724.039i		−	1.22098i	0.792025	−	0.610489i	$-0.209027\pi$
$594$		−	473.332i		−	0.796855i
$595$	−80.7338			−0.135687
$596$	−290.316			−0.487107
$597$	−190.598	+	190.598i	−0.319259	+	0.319259i
$598$	−288.507	+	288.507i	−0.482453	+	0.482453i
$599$	177.995			0.297153			0.148577	−	0.988901i	$-0.452531\pi$
$599$	177.995			0.297153			0.148577	+	0.988901i	$0.452531\pi$
$600$	17.3754			0.0289590
$601$	90.4397	+	90.4397i	0.150482	+	0.150482i	0.778333	−	0.627851i	$-0.216065\pi$
$601$	90.4397	+	90.4397i	0.150482	+	0.150482i	−0.627851	+	0.778333i	$0.716065\pi$
$602$			1201.71i			1.99619i
$603$		−	154.313i		−	0.255908i
$604$	−397.630			−0.658328
$605$	43.5601			0.0720002
$606$	−132.892	+	132.892i	−0.219294	+	0.219294i
$607$	25.2699	+	25.2699i	0.0416308	+	0.0416308i	0.727616	−	0.685985i	$-0.240628\pi$
$607$	25.2699	+	25.2699i	0.0416308	+	0.0416308i	−0.685985	+	0.727616i	$0.740628\pi$
$608$	−33.7237			−0.0554666
$609$	−954.963	+	954.963i	−1.56808	+	1.56808i
$610$	−198.579	−	198.579i	−0.325540	−	0.325540i
$611$		−	155.151i		−	0.253930i
$612$	4.57004	+	4.57004i	0.00746738	+	0.00746738i
$613$	−654.493	−	654.493i	−1.06769	−	1.06769i	−0.997536	−	0.0701529i	$-0.977651\pi$
$613$	−654.493	−	654.493i	−1.06769	−	1.06769i	−0.0701529	−	0.997536i	$-0.522349\pi$
$614$	436.068	+	436.068i	0.710209	+	0.710209i
$615$	−330.613	−	330.613i	−0.537583	−	0.537583i
$616$	434.306			0.705043
$617$		−	329.981i		−	0.534815i	−0.963583	−	0.267408i	$-0.913833\pi$
$617$		−	329.981i		−	0.534815i	0.963583	−	0.267408i	$-0.0861670\pi$
$618$	335.421			0.542752
$619$	648.468			1.04761			0.523803	−	0.851839i	$-0.324513\pi$
$619$	648.468			1.04761			0.523803	+	0.851839i	$0.324513\pi$
$620$	230.053	+	230.053i	0.371053	+	0.371053i
$621$	−270.127	+	270.127i	−0.434987	+	0.434987i
$622$		−	464.954i		−	0.747514i
$623$	1398.14	+	1398.14i	2.24420	+	2.24420i
$624$	−159.026	+	159.026i	−0.254849	+	0.254849i
$625$	−558.623			−0.893797
$626$	−305.654	−	305.654i	−0.488265	−	0.488265i
$627$		−	172.608i		−	0.275292i
$628$	−301.499	+	301.499i	−0.480094	+	0.480094i
$629$	48.1608	+	48.1608i	0.0765673	+	0.0765673i
$630$			231.513i			0.367481i
$631$	−619.619			−0.981963			−0.490981	−	0.871170i	$-0.663362\pi$
$631$	−619.619			−0.981963			−0.490981	+	0.871170i	$0.663362\pi$
$632$	−295.450	−	295.450i	−0.467484	−	0.467484i
$633$	17.4637	−	17.4637i	0.0275887	−	0.0275887i
$634$		−	258.306i		−	0.407423i
$635$			337.004i			0.530714i
$636$	149.788	−	149.788i	0.235515	−	0.235515i
$637$	−2927.45			−4.59568
$638$			637.995i			0.999992i
$639$	−63.1771	−	63.1771i	−0.0988688	−	0.0988688i
$640$	−38.0141	+	38.0141i	−0.0593971	+	0.0593971i
$641$		−	48.9919i		−	0.0764304i	−0.999270	−	0.0382152i	$-0.987833\pi$
$641$		−	48.9919i		−	0.0764304i	0.999270	−	0.0382152i	$-0.0121672\pi$
$642$	−179.708	−	179.708i	−0.279919	−	0.279919i
$643$	1234.26			1.91953			0.959763	−	0.280812i	$-0.0906036\pi$
$643$	1234.26			1.91953			0.959763	+	0.280812i	$0.0906036\pi$
$644$	−247.855	−	247.855i	−0.384869	−	0.384869i
$645$	538.361	−	538.361i	0.834668	−	0.834668i
$646$	7.52592	+	7.52592i	0.0116500	+	0.0116500i
$647$	345.808	−	345.808i	0.534480	−	0.534480i	−0.387423	−	0.921902i	$-0.626635\pi$
$647$	345.808	−	345.808i	0.534480	−	0.534480i	0.921902	+	0.387423i	$0.126635\pi$
$648$	−102.819	+	102.819i	−0.158671	+	0.158671i
$649$	293.772	+	293.772i	0.452653	+	0.452653i
$650$	−53.6307	+	53.6307i	−0.0825088	+	0.0825088i
$651$	−826.784	+	826.784i	−1.27002	+	1.27002i
$652$	317.531	+	317.531i	0.487011	+	0.487011i
$653$	614.311			0.940751			0.470376	−	0.882466i	$-0.344118\pi$
$653$	614.311			0.940751			0.470376	+	0.882466i	$0.344118\pi$
$654$	378.204	+	378.204i	0.578294	+	0.578294i
$655$	−1129.34			−1.72418
$656$	−155.092			−0.236421
$657$	−258.257			−0.393085
$658$	133.290			0.202568
$659$	−297.742			−0.451808			−0.225904	−	0.974150i	$-0.572534\pi$
$659$	−297.742			−0.451808			−0.225904	+	0.974150i	$0.572534\pi$
$660$	−194.568	−	194.568i	−0.294800	−	0.294800i
$661$	496.795	+	496.795i	0.751581	+	0.751581i	0.974774	−	0.223193i	$-0.0716481\pi$
$661$	496.795	+	496.795i	0.751581	+	0.751581i	−0.223193	+	0.974774i	$0.571648\pi$
$662$	−385.720	−	385.720i	−0.582658	−	0.582658i
$663$	70.9778			0.107056
$664$		−	57.4772i		−	0.0865621i
$665$			381.255i			0.573316i
$666$	138.107	−	138.107i	0.207367	−	0.207367i
$667$	364.099	−	364.099i	0.545875	−	0.545875i
$668$	−121.022	+	121.022i	−0.181170	+	0.181170i
$669$	349.123			0.521857
$670$	−286.452	−	286.452i	−0.427540	−	0.427540i
$671$		−	476.792i		−	0.710570i
$672$	−136.619	−	136.619i	−0.203302	−	0.203302i
$673$	−712.652	+	712.652i	−1.05892	+	1.05892i	−0.0607666	+	0.998152i	$0.519355\pi$
$673$	−712.652	+	712.652i	−1.05892	+	1.05892i	−0.998152	+	0.0607666i	$0.980645\pi$
$674$	134.040			0.198872
$675$	−50.2140	+	50.2140i	−0.0743912	+	0.0743912i
$676$		−	643.696i		−	0.952213i
$677$	−82.0217	−	82.0217i	−0.121155	−	0.121155i	0.643930	−	0.765084i	$-0.277303\pi$
$677$	−82.0217	−	82.0217i	−0.121155	−	0.121155i	−0.765084	+	0.643930i	$0.777303\pi$
$678$	392.727	+	392.727i	0.579243	+	0.579243i
$679$	−496.153	−	496.153i	−0.730712	−	0.730712i
$680$	16.9668			0.0249512
$681$	146.739			0.215476
$682$			552.361i			0.809913i
$683$	−592.867	+	592.867i	−0.868033	+	0.868033i	−0.992255	−	0.124221i	$-0.960357\pi$
$683$	−592.867	+	592.867i	−0.868033	+	0.868033i	0.124221	+	0.992255i	$0.460357\pi$
$684$	21.5814	−	21.5814i	0.0315518	−	0.0315518i
$685$	−294.103	+	294.103i	−0.429348	+	0.429348i
$686$		−	1582.33i		−	2.30660i
$687$			141.788i			0.206387i
$688$		−	252.548i		−	0.367075i
$689$			924.667i			1.34204i
$690$			222.077i			0.321850i
$691$	40.2932	−	40.2932i	0.0583115	−	0.0583115i	−0.677350	−	0.735661i	$-0.736872\pi$
$691$	40.2932	−	40.2932i	0.0583115	−	0.0583115i	0.735661	+	0.677350i	$0.236872\pi$
$692$		−	608.183i		−	0.878877i
$693$	−277.934	+	277.934i	−0.401059	+	0.401059i
$694$	386.357	+	386.357i	0.556710	+	0.556710i
$695$	293.017	+	293.017i	0.421607	+	0.421607i
$696$	200.693	−	200.693i	0.288351	−	0.288351i
$697$	34.6111	+	34.6111i	0.0496572	+	0.0496572i
$698$	377.388	+	377.388i	0.540670	+	0.540670i
$699$	761.495	−	761.495i	1.08941	−	1.08941i
$700$	−46.0740	−	46.0740i	−0.0658200	−	0.0658200i
$701$	−555.051	+	555.051i	−0.791799	+	0.791799i	−0.981787	−	0.189987i	$-0.939155\pi$
$701$	−555.051	+	555.051i	−0.791799	+	0.791799i	0.189987	+	0.981787i	$0.439155\pi$
$702$		−	919.154i		−	1.30934i
$703$	227.434	−	227.434i	0.323519	−	0.323519i
$704$	−91.2727			−0.129649
$705$	−59.7134	−	59.7134i	−0.0846998	−	0.0846998i
$706$	−471.661	+	471.661i	−0.668076	+	0.668076i
$707$	704.774			0.996851
$708$		−	184.822i		−	0.261048i
$709$	−535.874	−	535.874i	−0.755816	−	0.755816i	0.219742	−	0.975558i	$-0.429478\pi$
$709$	−535.874	−	535.874i	−0.755816	−	0.755816i	−0.975558	+	0.219742i	$0.929478\pi$
$710$	−234.552			−0.330356
$711$	378.146			0.531850
$712$	−293.829	−	293.829i	−0.412681	−	0.412681i
$713$	315.228	−	315.228i	0.442115	−	0.442115i
$714$			60.9768i			0.0854017i
$715$	1201.10			1.67986
$716$	20.2470	−	20.2470i	0.0282780	−	0.0282780i
$717$	−11.1632	−	11.1632i	−0.0155693	−	0.0155693i
$718$	637.585			0.888002
$719$	−172.918	+	172.918i	−0.240498	+	0.240498i	−0.817056	−	0.576558i	$-0.804395\pi$
$719$	−172.918	+	172.918i	−0.240498	+	0.240498i	0.576558	+	0.817056i	$0.304395\pi$
$720$		−	48.6542i		−	0.0675753i
$721$	−889.428	−	889.428i	−1.23360	−	1.23360i
$722$	−325.460	+	325.460i	−0.450775	+	0.450775i
$723$	−8.36959			−0.0115762
$724$	−405.831	−	405.831i	−0.560540	−	0.560540i
$725$	67.6825	−	67.6825i	0.0933552	−	0.0933552i
$726$		−	32.9002i		−	0.0453171i
$727$		−	976.300i		−	1.34292i	−0.741043	−	0.671458i	$-0.765668\pi$
$727$		−	976.300i		−	1.34292i	0.741043	−	0.671458i	$-0.234332\pi$
$728$	843.372			1.15848
$729$		−	801.624i		−	1.09962i
$730$	−479.405	+	479.405i	−0.656719	+	0.656719i
$731$	−56.3596	+	56.3596i	−0.0770993	+	0.0770993i
$732$	−149.984	+	149.984i	−0.204896	+	0.204896i
$733$	−922.393	+	922.393i	−1.25838	+	1.25838i	−0.306515	+	0.951866i	$0.599163\pi$
$733$	−922.393	+	922.393i	−1.25838	+	1.25838i	−0.951866	+	0.306515i	$0.900837\pi$
$734$	−130.535			−0.177840
$735$	−1126.69	+	1126.69i	−1.53292	+	1.53292i
$736$	52.0886	+	52.0886i	0.0707726	+	0.0707726i
$737$		−	687.777i		−	0.933211i
$738$	99.2512	−	99.2512i	0.134487	−	0.134487i
$739$	122.586	+	122.586i	0.165880	+	0.165880i	0.785166	−	0.619285i	$-0.212578\pi$
$739$	122.586	+	122.586i	0.165880	+	0.165880i	−0.619285	+	0.785166i	$0.712578\pi$
$740$		−	512.737i		−	0.692888i
$741$		−	335.184i		−	0.452340i
$742$	−794.378			−1.07059
$743$	−628.224			−0.845524			−0.422762	−	0.906241i	$-0.638939\pi$
$743$	−628.224			−0.845524			−0.422762	+	0.906241i	$0.638939\pi$
$744$	173.755	−	173.755i	0.233541	−	0.233541i
$745$		−	689.757i		−	0.925848i
$746$			85.4761i			0.114579i
$747$	36.7825	+	36.7825i	0.0492402	+	0.0492402i
$748$	20.3688	+	20.3688i	0.0272310	+	0.0272310i
$749$			953.054i			1.27243i
$750$			467.626i			0.623501i
$751$	−676.940			−0.901385			−0.450692	−	0.892679i	$-0.648823\pi$
$751$	−676.940			−0.901385			−0.450692	+	0.892679i	$0.648823\pi$
$752$	−28.0118			−0.0372498
$753$			965.577i			1.28231i
$754$			1238.91i			1.64312i
$755$		−	944.723i		−	1.25129i
$756$	789.642			1.04450
$757$	−72.5433	+	72.5433i	−0.0958300	+	0.0958300i	−0.753396	−	0.657567i	$-0.771586\pi$
$757$	−72.5433	+	72.5433i	−0.0958300	+	0.0958300i	0.657567	+	0.753396i	$0.271586\pi$
$758$	341.894			0.451047
$759$	−266.605	+	266.605i	−0.351258	+	0.351258i
$760$		−	80.1236i		−	0.105426i
$761$	−133.650	+	133.650i	−0.175624	+	0.175624i	−0.789445	−	0.613821i	$-0.789632\pi$
$761$	−133.650	+	133.650i	−0.175624	+	0.175624i	0.613821	+	0.789445i	$0.289632\pi$
$762$	254.533			0.334033
$763$		−	2005.75i		−	2.62877i
$764$	533.644			0.698486
$765$	−10.8579	+	10.8579i	−0.0141933	+	0.0141933i
$766$		−	223.695i		−	0.292031i
$767$	570.470	+	570.470i	0.743768	+	0.743768i
$768$	28.7114	+	28.7114i	0.0373847	+	0.0373847i
$769$			1006.01i			1.30821i	0.756404	+	0.654104i	$0.226954\pi$
$769$			1006.01i			1.30821i	−0.756404	+	0.654104i	$0.773046\pi$
$770$			1031.86i			1.34008i
$771$		−	68.5850i		−	0.0889559i
$772$	−14.7205	−	14.7205i	−0.0190680	−	0.0190680i
$773$	−792.686			−1.02547			−0.512734	−	0.858548i	$-0.671367\pi$
$773$	−792.686			−1.02547			−0.512734	+	0.858548i	$0.671367\pi$
$774$	161.617	+	161.617i	0.208808	+	0.208808i
$775$	58.5979	−	58.5979i	0.0756102	−	0.0756102i
$776$	104.270	+	104.270i	0.134369	+	0.134369i
$777$	1842.72			2.37159
$778$	182.560	+	182.560i	0.234653	+	0.234653i
$779$	163.446	−	163.446i	0.209816	−	0.209816i
$780$	−377.828	−	377.828i	−0.484394	−	0.484394i
$781$	−281.582	−	281.582i	−0.360541	−	0.360541i
$782$		−	23.2486i		−	0.0297297i
$783$			1159.98i			1.48146i
$784$			528.538i			0.674155i
$785$	−716.327	−	716.327i	−0.912518	−	0.912518i
$786$			852.969i			1.08520i
$787$	−681.424			−0.865850			−0.432925	−	0.901430i	$-0.642518\pi$
$787$	−681.424			−0.865850			−0.432925	+	0.901430i	$0.642518\pi$
$788$	−371.933	−	371.933i	−0.471996	−	0.471996i
$789$	−661.335	−	661.335i	−0.838194	−	0.838194i
$790$	701.955	−	701.955i	0.888550	−	0.888550i
$791$		−	2082.77i		−	2.63308i
$792$	58.4098	−	58.4098i	0.0737498	−	0.0737498i
$793$		−	925.875i		−	1.16756i
$794$	−377.880			−0.475920
$795$	355.879	+	355.879i	0.447646	+	0.447646i
$796$	−212.429			−0.266870
$797$	646.500	−	646.500i	0.811167	−	0.811167i	−0.173642	−	0.984809i	$-0.555554\pi$
$797$	646.500	−	646.500i	0.811167	−	0.811167i	0.984809	+	0.173642i	$0.0555536\pi$
$798$	287.956			0.360847
$799$	6.25124	+	6.25124i	0.00782383	+	0.00782383i
$800$	9.68278	+	9.68278i	0.0121035	+	0.0121035i
$801$	376.071			0.469502
$802$			761.492i			0.949491i
$803$	−1151.06			−1.43345
$804$	−216.352	+	216.352i	−0.269095	+	0.269095i
$805$	588.876	−	588.876i	0.731523	−	0.731523i
$806$			1072.62i			1.33079i
$807$	−414.308	+	542.557i	−0.513393	+	0.672314i
$808$	−148.113			−0.183309
$809$	286.713	+	286.713i	0.354405	+	0.354405i	0.861745	−	0.507341i	$-0.169371\pi$
$809$	286.713	+	286.713i	0.354405	+	0.354405i	−0.507341	+	0.861745i	$0.669371\pi$
$810$	−244.285	−	244.285i	−0.301587	−	0.301587i
$811$			1213.32i			1.49607i	0.663657	+	0.748037i	$0.269004\pi$
$811$			1213.32i			1.49607i	−0.663657	+	0.748037i	$0.730996\pi$
$812$	−1064.34			−1.31077
$813$			483.776i			0.595051i
$814$	615.545	−	615.545i	0.756198	−	0.756198i
$815$	−754.418	+	754.418i	−0.925666	+	0.925666i
$816$		−	12.8147i		−	0.0157043i
$817$	266.151	+	266.151i	0.325766	+	0.325766i
$818$			178.460i			0.218166i
$819$	−539.715	+	539.715i	−0.658992	+	0.658992i
$820$		−	368.481i		−	0.449368i
$821$	−512.109			−0.623763			−0.311881	−	0.950121i	$-0.600959\pi$
$821$	−512.109			−0.623763			−0.311881	+	0.950121i	$0.600959\pi$
$822$	222.131	+	222.131i	0.270232	+	0.270232i
$823$	650.504			0.790406			0.395203	−	0.918594i	$-0.370674\pi$
$823$	650.504			0.790406			0.395203	+	0.918594i	$0.370674\pi$
$824$	186.920	+	186.920i	0.226844	+	0.226844i
$825$	−49.5594	+	49.5594i	−0.0600720	+	0.0600720i
$826$	−490.089	+	490.089i	−0.593328	+	0.593328i
$827$			1087.15i			1.31457i	0.753643	+	0.657284i	$0.228295\pi$
$827$			1087.15i			1.31457i	−0.753643	+	0.657284i	$0.771705\pi$
$828$	−66.6681			−0.0805170
$829$	−569.606	+	569.606i	−0.687100	+	0.687100i	−0.961590	−	0.274490i	$-0.911491\pi$
$829$	−569.606	+	569.606i	−0.687100	+	0.687100i	0.274490	+	0.961590i	$0.411491\pi$
$830$	136.559			0.164529
$831$	−438.205			−0.527323
$832$	−177.241			−0.213030
$833$	117.951	−	117.951i	0.141597	−	0.141597i
$834$	221.311	−	221.311i	0.265360	−	0.265360i
$835$	−287.534	−	287.534i	−0.344352	−	0.344352i
$836$	96.1891	−	96.1891i	0.115059	−	0.115059i
$837$			1004.28i			1.19986i
$838$	−240.384	+	240.384i	−0.286855	+	0.286855i
$839$	907.852	+	907.852i	1.08206	+	1.08206i	0.996317	+	0.0857472i	$0.0273278\pi$
$839$	907.852	+	907.852i	1.08206	+	1.08206i	0.0857472	+	0.996317i	$0.472672\pi$
$840$	324.590	−	324.590i	0.386417	−	0.386417i
$841$		−	722.517i		−	0.859117i
$842$	399.203	−	399.203i	0.474113	−	0.474113i
$843$	667.401			0.791698
$844$	19.4639			0.0230615
$845$	1529.35			1.80988
$846$	17.9261	−	17.9261i	0.0211893	−	0.0211893i
$847$	−87.2408	+	87.2408i	−0.103000	+	0.103000i
$848$	166.944			0.196868
$849$	−479.782	−	479.782i	−0.565114	−	0.565114i
$850$		−	4.32170i		−	0.00508435i
$851$	−702.574			−0.825587
$852$			177.153i			0.207927i
$853$	−753.895	−	753.895i	−0.883816	−	0.883816i	0.110104	−	0.993920i	$-0.464882\pi$
$853$	−753.895	−	753.895i	−0.883816	−	0.883816i	−0.993920	+	0.110104i	$0.964882\pi$
$854$	795.416			0.931400
$855$	51.2750	+	51.2750i	0.0599707	+	0.0599707i
$856$		−	200.291i		−	0.233985i
$857$	−492.147	−	492.147i	−0.574267	−	0.574267i	0.359051	−	0.933318i	$-0.383100\pi$
$857$	−492.147	−	492.147i	−0.574267	−	0.574267i	−0.933318	+	0.359051i	$0.883100\pi$
$858$		−	907.171i		−	1.05731i
$859$	878.234			1.02239			0.511196	−	0.859464i	$-0.329203\pi$
$859$	878.234			1.02239			0.511196	+	0.859464i	$0.329203\pi$
$860$	600.024			0.697702
$861$	1324.28			1.53808
$862$			233.731i			0.271149i
$863$			553.270i			0.641101i	0.947231	+	0.320550i	$0.103868\pi$
$863$			553.270i			0.641101i	−0.947231	+	0.320550i	$0.896132\pi$
$864$	−165.949			−0.192071
$865$	1444.97			1.67049
$866$	−429.883	+	429.883i	−0.496401	+	0.496401i
$867$	515.740	−	515.740i	0.594856	−	0.594856i
$868$	−921.483			−1.06162
$869$	1685.41			1.93948
$870$	476.822	+	476.822i	0.548071	+	0.548071i
$871$		−	1335.58i		−	1.53339i
$872$			421.523i			0.483398i
$873$	−133.455			−0.152870
$874$	−109.789			−0.125616
$875$	1239.99	−	1239.99i	1.41713	−	1.41713i
$876$	362.086	+	362.086i	0.413340	+	0.413340i
$877$	−282.253			−0.321839			−0.160919	−	0.986968i	$-0.551446\pi$
$877$	−282.253			−0.321839			−0.160919	+	0.986968i	$0.551446\pi$
$878$	565.480	−	565.480i	0.644054	−	0.644054i
$879$	360.490	+	360.490i	0.410113	+	0.410113i
$880$		−	216.853i		−	0.246424i
$881$	72.1331	+	72.1331i	0.0818763	+	0.0818763i	0.746859	−	0.664983i	$-0.231561\pi$
$881$	72.1331	+	72.1331i	0.0818763	+	0.0818763i	−0.664983	+	0.746859i	$0.731561\pi$
$882$	−338.237	−	338.237i	−0.383489	−	0.383489i
$883$	422.957	+	422.957i	0.479000	+	0.479000i	0.904812	−	0.425811i	$-0.140011\pi$
$883$	422.957	+	422.957i	0.479000	+	0.479000i	−0.425811	+	0.904812i	$0.640011\pi$
$884$	39.5538	+	39.5538i	0.0447441	+	0.0447441i
$885$	439.116			0.496176
$886$		−	29.5525i		−	0.0333550i
$887$	−148.042			−0.166902			−0.0834509	−	0.996512i	$-0.526594\pi$
$887$	−148.042			−0.166902			−0.0834509	+	0.996512i	$0.526594\pi$
$888$	−387.261			−0.436105
$889$	−674.939	−	674.939i	−0.759212	−	0.759212i
$890$	698.104	−	698.104i	0.784386	−	0.784386i
$891$		−	586.533i		−	0.658286i
$892$	194.555	+	194.555i	0.218111	+	0.218111i
$893$	29.5207	−	29.5207i	0.0330579	−	0.0330579i
$894$	−520.962			−0.582731
$895$	48.1046	+	48.1046i	0.0537482	+	0.0537482i
$896$		−	152.267i		−	0.169941i
$897$	−517.716	+	517.716i	−0.577163	+	0.577163i
$898$	−15.5790	−	15.5790i	−0.0173486	−	0.0173486i
$899$		−	1353.66i		−	1.50574i
$900$	−12.3930			−0.0137700
$901$	−37.2560	−	37.2560i	−0.0413496	−	0.0413496i
$902$	442.365	−	442.365i	0.490427	−	0.490427i
$903$			2156.42i			2.38806i
$904$			437.709i			0.484191i
$905$	964.208	−	964.208i	1.06542	−	1.06542i
$906$	−713.533			−0.787564
$907$			791.820i			0.873010i	0.899702	+	0.436505i	$0.143784\pi$
$907$			791.820i			0.873010i	−0.899702	+	0.436505i	$0.856216\pi$
$908$	81.7730	+	81.7730i	0.0900584	+	0.0900584i
$909$	94.7850	−	94.7850i	0.104274	−	0.104274i
$910$			2003.75i			2.20193i
$911$	−983.982	−	983.982i	−1.08011	−	1.08011i	−0.996498	−	0.0836132i	$-0.973354\pi$
$911$	−983.982	−	983.982i	−1.08011	−	1.08011i	−0.0836132	−	0.996498i	$-0.526646\pi$
$912$	−60.5160			−0.0663552
$913$	163.941	+	163.941i	0.179562	+	0.179562i
$914$	676.235	−	676.235i	0.739863	−	0.739863i
$915$	−356.343	−	356.343i	−0.389446	−	0.389446i
$916$	−79.0142	+	79.0142i	−0.0862600	+	0.0862600i
$917$	2261.80	−	2261.80i	2.46652	−	2.46652i
$918$	37.0339	+	37.0339i	0.0403419	+	0.0403419i
$919$	369.811	−	369.811i	0.402406	−	0.402406i	−0.476674	−	0.879080i	$-0.658158\pi$
$919$	369.811	−	369.811i	0.402406	−	0.402406i	0.879080	+	0.476674i	$0.158158\pi$
$920$	−123.757	+	123.757i	−0.134518	+	0.134518i
$921$	782.509	+	782.509i	0.849630	+	0.849630i
$922$	−818.814			−0.888084
$923$	−546.800	−	546.800i	−0.592416	−	0.592416i
$924$	779.347			0.843449
$925$	−130.602			−0.141191
$926$	−195.438			−0.211056
$927$	−239.238			−0.258078
$928$	223.680			0.241034
$929$	228.632	+	228.632i	0.246105	+	0.246105i	0.819370	−	0.573265i	$-0.194323\pi$
$929$	228.632	+	228.632i	0.246105	+	0.246105i	−0.573265	+	0.819370i	$0.694323\pi$
$930$	412.821	+	412.821i	0.443894	+	0.443894i
$931$	−557.008	−	557.008i	−0.598289	−	0.598289i
$932$	848.716			0.910639
$933$		−	834.343i		−	0.894258i
$934$			805.688i			0.862622i
$935$	−48.3939	+	48.3939i	−0.0517582	+	0.0517582i
$936$	113.425	−	113.425i	0.121181	−	0.121181i
$937$	1040.98	−	1040.98i	1.11097	−	1.11097i	0.117952	−	0.993019i	$-0.462367\pi$
$937$	1040.98	−	1040.98i	1.11097	−	1.11097i	0.993019	−	0.117952i	$-0.0376330\pi$
$938$	1147.39			1.22323
$939$	−548.486	−	548.486i	−0.584117	−	0.584117i
$940$		−	66.5529i		−	0.0708009i
$941$	−619.978	−	619.978i	−0.658850	−	0.658850i	0.296258	−	0.955108i	$-0.404261\pi$
$941$	−619.978	−	619.978i	−0.658850	−	0.658850i	−0.955108	+	0.296258i	$0.904261\pi$
$942$	−541.029	+	541.029i	−0.574341	+	0.574341i
$943$	−504.909			−0.535429
$944$	102.996	−	102.996i	0.109106	−	0.109106i
$945$			1876.10i			1.98529i
$946$	720.334	+	720.334i	0.761452	+	0.761452i
$947$	939.235	+	939.235i	0.991801	+	0.991801i	0.999967	−	0.00816604i	$-0.00259936\pi$
$947$	939.235	+	939.235i	0.991801	+	0.991801i	−0.00816604	+	0.999967i	$0.502599\pi$
$948$	−530.174	−	530.174i	−0.559256	−	0.559256i
$949$	−2235.22			−2.35534
$950$	−20.4087			−0.0214828
$951$		−	463.521i		−	0.487404i
$952$	−33.9805	+	33.9805i	−0.0356938	+	0.0356938i
$953$	1303.06	−	1303.06i	1.36733	−	1.36733i	0.503093	−	0.864233i	$-0.332195\pi$
$953$	1303.06	−	1303.06i	1.36733	−	1.36733i	0.864233	−	0.503093i	$-0.167805\pi$
$954$	−106.836	+	106.836i	−0.111987	+	0.111987i
$955$			1267.88i			1.32762i
$956$		−	12.4418i		−	0.0130144i
$957$			1144.86i			1.19630i
$958$			288.389i			0.301032i
$959$		−	1178.04i		−	1.22840i
$960$	−68.2150	+	68.2150i	−0.0710573	+	0.0710573i
$961$		−	210.963i		−	0.219524i
$962$	1195.32	−	1195.32i	1.24253	−	1.24253i
$963$	128.176	+	128.176i	0.133101	+	0.133101i
$964$	−4.66411	−	4.66411i	−0.00483829	−	0.00483829i
$965$	34.9743	−	34.9743i	0.0362428	−	0.0362428i
$966$	−444.768	−	444.768i	−0.460422	−	0.460422i
$967$	−470.586	−	470.586i	−0.486646	−	0.486646i	0.420600	−	0.907246i	$-0.361819\pi$
$967$	−470.586	−	470.586i	−0.486646	−	0.486646i	−0.907246	+	0.420600i	$0.861819\pi$
$968$	18.3343	−	18.3343i	0.0189404	−	0.0189404i
$969$	13.5050	+	13.5050i	0.0139370	+	0.0139370i
$970$	−247.734	+	247.734i	−0.255396	+	0.255396i
$971$			409.170i			0.421390i	0.977552	+	0.210695i	$0.0675727\pi$
$971$			409.170i			0.421390i	−0.977552	+	0.210695i	$0.932427\pi$
$972$	188.881	−	188.881i	0.194322	−	0.194322i
$973$	−1173.69			−1.20626
$974$	−541.406	−	541.406i	−0.555859	−	0.555859i
$975$	−96.2384	+	96.2384i	−0.0987061	+	0.0987061i
$976$	−167.162			−0.171273
$977$			1261.84i			1.29155i	0.763528	+	0.645774i	$0.223465\pi$
$977$			1261.84i			1.29155i	−0.763528	+	0.645774i	$0.776535\pi$
$978$	569.799	+	569.799i	0.582616	+	0.582616i
$979$	1676.16			1.71211
$980$	−1255.74			−1.28137
$981$	−269.753	−	269.753i	−0.274978	−	0.274978i
$982$	279.654	−	279.654i	0.284780	−	0.284780i
$983$			1858.50i			1.89064i	0.326139	+	0.945322i	$0.394252\pi$
$983$			1858.50i			1.89064i	−0.326139	+	0.945322i	$0.605748\pi$
$984$	−278.308			−0.282833
$985$	883.670	−	883.670i	0.897126	−	0.897126i
$986$	−49.9173	−	49.9173i	−0.0506260	−	0.0506260i
$987$	239.184			0.242334
$988$	186.788	−	186.788i	0.189057	−	0.189057i
$989$		−	822.178i		−	0.831323i
$990$	138.775	+	138.775i	0.140177	+	0.140177i
$991$	−233.156	+	233.156i	−0.235274	+	0.235274i	−0.814890	−	0.579616i	$-0.803203\pi$
$991$	−233.156	+	233.156i	−0.235274	+	0.235274i	0.579616	+	0.814890i	$0.303203\pi$
$992$	193.656			0.195218
$993$	−692.160	−	692.160i	−0.697039	−	0.697039i
$994$	469.754	−	469.754i	0.472589	−	0.472589i
$995$		−	504.706i		−	0.507242i
$996$		−	103.141i		−	0.103555i
$997$	1078.14			1.08138			0.540691	−	0.841221i	$-0.318163\pi$
$997$	1078.14			1.08138			0.540691	+	0.841221i	$0.318163\pi$
$998$		−	211.870i		−	0.212295i
$999$	1119.17	−	1119.17i	1.12029	−	1.12029i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.3.c.a.187.15	✓	44
269.82	odd	4	inner	538.3.c.a.351.15	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.3.c.a.187.15	✓	44	1.1	even	1	trivial
538.3.c.a.351.15	yes	44	269.82	odd	4	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:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	538.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.79446 + 1.79446i) q^{3} +2.00000i q^{4} -4.75177 q^{5} +3.58893i q^{6} +(9.51668 - 9.51668i) q^{7} +(-2.00000 + 2.00000i) q^{8} -2.55979i q^{9} +(-4.75177 - 4.75177i) q^{10} -11.4091i q^{11} +(-3.58893 + 3.58893i) q^{12} -22.1551i q^{13} +19.0334 q^{14} +(-8.52688 - 8.52688i) q^{15} -4.00000 q^{16} +(0.892657 + 0.892657i) q^{17} +(2.55979 - 2.55979i) q^{18} +(4.21546 - 4.21546i) q^{19} -9.50354i q^{20} +34.1547 q^{21} +(11.4091 - 11.4091i) q^{22} -13.0222 q^{23} -7.17786 q^{24} -2.42070 q^{25} +(22.1551 - 22.1551i) q^{26} +(20.7436 - 20.7436i) q^{27} +(19.0334 + 19.0334i) q^{28} +(-27.9599 + 27.9599i) q^{29} -17.0538i q^{30} +(-24.2071 + 24.2071i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(20.4732 - 20.4732i) q^{33} +1.78531i q^{34} +(-45.2211 + 45.2211i) q^{35} +5.11959 q^{36} +53.9522 q^{37} +8.43092 q^{38} +(39.7565 - 39.7565i) q^{39} +(9.50354 - 9.50354i) q^{40} +38.7731 q^{41} +(34.1547 + 34.1547i) q^{42} +63.1369i q^{43} +22.8182 q^{44} +12.1636i q^{45} +(-13.0222 - 13.0222i) q^{46} +7.00296 q^{47} +(-7.17786 - 7.17786i) q^{48} -132.134i q^{49} +(-2.42070 - 2.42070i) q^{50} +3.20368i q^{51} +44.3102 q^{52} -41.7361 q^{53} +41.4873 q^{54} +54.2133i q^{55} +38.0667i q^{56} +15.1290 q^{57} -55.9199 q^{58} +(-25.7489 + 25.7489i) q^{59} +(17.0538 - 17.0538i) q^{60} +41.7906 q^{61} -48.4141 q^{62} +(-24.3607 - 24.3607i) q^{63} -8.00000i q^{64} +105.276i q^{65} +40.9464 q^{66} +60.2833 q^{67} +(-1.78531 + 1.78531i) q^{68} +(-23.3678 - 23.3678i) q^{69} -90.4421 q^{70} +(24.6805 - 24.6805i) q^{71} +(5.11959 + 5.11959i) q^{72} -100.890i q^{73} +(53.9522 + 53.9522i) q^{74} +(-4.34385 - 4.34385i) q^{75} +(8.43092 + 8.43092i) q^{76} +(-108.577 - 108.577i) q^{77} +79.5130 q^{78} +147.725i q^{79} +19.0071 q^{80} +51.4093 q^{81} +(38.7731 + 38.7731i) q^{82} +(-14.3693 + 14.3693i) q^{83} +68.3094i q^{84} +(-4.24170 - 4.24170i) q^{85} +(-63.1369 + 63.1369i) q^{86} -100.346 q^{87} +(22.8182 + 22.8182i) q^{88} +146.915i q^{89} +(-12.1636 + 12.1636i) q^{90} +(-210.843 - 210.843i) q^{91} -26.0443i q^{92} -86.8774 q^{93} +(7.00296 + 7.00296i) q^{94} +(-20.0309 + 20.0309i) q^{95} -14.3557i q^{96} -52.1351i q^{97} +(132.134 - 132.134i) q^{98} -29.2049 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 44 q^{2} + 2 q^{3} + 4 q^{7} - 88 q^{8} - 4 q^{12} + 8 q^{14} + 38 q^{15} - 176 q^{16} - 120 q^{18} + 18 q^{19} - 16 q^{21} + 68 q^{23} - 8 q^{24} + 196 q^{25} + 16 q^{26} - 22 q^{27} + 8 q^{28}+ \cdots - 188 q^{99}+O(q^{100}) \) 44 * q + 44 * q^2 + 2 * q^3 + 4 * q^7 - 88 * q^8 - 4 * q^12 + 8 * q^14 + 38 * q^15 - 176 * q^16 - 120 * q^18 + 18 * q^19 - 16 * q^21 + 68 * q^23 - 8 * q^24 + 196 * q^25 + 16 * q^26 - 22 * q^27 + 8 * q^28 + 18 * q^29 + 88 * q^31 - 176 * q^32 + 96 * q^33 + 10 * q^35 - 240 * q^36 + 180 * q^37 + 36 * q^38 - 54 * q^39 + 144 * q^41 - 16 * q^42 + 68 * q^46 - 156 * q^47 - 8 * q^48 + 196 * q^50 + 32 * q^52 - 188 * q^53 - 44 * q^54 - 88 * q^57 + 36 * q^58 - 98 * q^59 - 76 * q^60 - 244 * q^61 + 176 * q^62 - 10 * q^63 + 192 * q^66 + 220 * q^67 - 70 * q^69 + 20 * q^70 + 156 * q^71 - 240 * q^72 + 180 * q^74 - 102 * q^75 + 36 * q^76 - 28 * q^77 - 108 * q^78 + 392 * q^81 + 144 * q^82 - 250 * q^83 - 342 * q^85 - 44 * q^86 - 60 * q^87 - 192 * q^90 + 66 * q^91 - 536 * q^93 - 156 * q^94 - 472 * q^95 + 404 * q^98 - 188 * q^99

Introduction

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