LMFDB - Embedded newform 538.3.c.a.187.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [538,3,Mod(187,538)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [44] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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			187.8
Character	$\chi$	$=$	538.187
Dual form			538.3.c.a.351.8

$q$-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} +(-1.45158 - 1.45158i) q^{3} +2.00000i q^{4} +1.48345 q^{5} -2.90315i q^{6} +(-2.38989 + 2.38989i) q^{7} +(-2.00000 + 2.00000i) q^{8} -4.78586i q^{9} +(1.48345 + 1.48345i) q^{10} +16.7247i q^{11} +(2.90315 - 2.90315i) q^{12} -15.4852i q^{13} -4.77978 q^{14} +(-2.15334 - 2.15334i) q^{15} -4.00000 q^{16} +(19.4852 + 19.4852i) q^{17} +(4.78586 - 4.78586i) q^{18} +(-23.8056 + 23.8056i) q^{19} +2.96690i q^{20} +6.93821 q^{21} +(-16.7247 + 16.7247i) q^{22} +35.8637 q^{23} +5.80630 q^{24} -22.7994 q^{25} +(15.4852 - 15.4852i) q^{26} +(-20.0112 + 20.0112i) q^{27} +(-4.77978 - 4.77978i) q^{28} +(-17.0186 + 17.0186i) q^{29} -4.30668i q^{30} +(-5.30618 + 5.30618i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(24.2772 - 24.2772i) q^{33} +38.9705i q^{34} +(-3.54528 + 3.54528i) q^{35} +9.57171 q^{36} -13.2056 q^{37} -47.6112 q^{38} +(-22.4780 + 22.4780i) q^{39} +(-2.96690 + 2.96690i) q^{40} +63.9737 q^{41} +(6.93821 + 6.93821i) q^{42} +56.2586i q^{43} -33.4495 q^{44} -7.09959i q^{45} +(35.8637 + 35.8637i) q^{46} +52.9582 q^{47} +(5.80630 + 5.80630i) q^{48} +37.5769i q^{49} +(-22.7994 - 22.7994i) q^{50} -56.5686i q^{51} +30.9705 q^{52} -38.2821 q^{53} -40.0224 q^{54} +24.8103i q^{55} -9.55955i q^{56} +69.1113 q^{57} -34.0372 q^{58} +(-64.4046 + 64.4046i) q^{59} +(4.30668 - 4.30668i) q^{60} -61.9667 q^{61} -10.6124 q^{62} +(11.4377 + 11.4377i) q^{63} -8.00000i q^{64} -22.9716i q^{65} +48.5545 q^{66} +54.1353 q^{67} +(-38.9705 + 38.9705i) q^{68} +(-52.0588 - 52.0588i) q^{69} -7.09057 q^{70} +(-44.3714 + 44.3714i) q^{71} +(9.57171 + 9.57171i) q^{72} +55.0459i q^{73} +(-13.2056 - 13.2056i) q^{74} +(33.0950 + 33.0950i) q^{75} +(-47.6112 - 47.6112i) q^{76} +(-39.9703 - 39.9703i) q^{77} -44.9560 q^{78} -86.7105i q^{79} -5.93381 q^{80} +15.0229 q^{81} +(63.9737 + 63.9737i) q^{82} +(12.3562 - 12.3562i) q^{83} +13.8764i q^{84} +(28.9054 + 28.9054i) q^{85} +(-56.2586 + 56.2586i) q^{86} +49.4076 q^{87} +(-33.4495 - 33.4495i) q^{88} -78.7503i q^{89} +(7.09959 - 7.09959i) q^{90} +(37.0080 + 37.0080i) q^{91} +71.7273i q^{92} +15.4046 q^{93} +(52.9582 + 52.9582i) q^{94} +(-35.3145 + 35.3145i) q^{95} +11.6126i q^{96} +37.8520i q^{97} +(-37.5769 + 37.5769i) q^{98} +80.0422 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
$3$	−1.45158	−	1.45158i	−0.483859	−	0.483859i	0.422503	−	0.906362i	$-0.361152\pi$
$3$	−1.45158	−	1.45158i	−0.483859	−	0.483859i	−0.906362	+	0.422503i	$0.861152\pi$
$4$			2.00000i			0.500000i
$5$	1.48345			0.296690			0.148345	−	0.988936i	$-0.452605\pi$
$5$	1.48345			0.296690			0.148345	+	0.988936i	$0.452605\pi$
$6$		−	2.90315i		−	0.483859i
$7$	−2.38989	+	2.38989i	−0.341413	+	0.341413i	−0.856898	−	0.515486i	$-0.827612\pi$
$7$	−2.38989	+	2.38989i	−0.341413	+	0.341413i	0.515486	+	0.856898i	$0.327612\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	4.78586i		−	0.531762i
$10$	1.48345	+	1.48345i	0.148345	+	0.148345i
$11$			16.7247i			1.52043i	0.649671	+	0.760215i	$0.274907\pi$
$11$			16.7247i			1.52043i	−0.649671	+	0.760215i	$0.725093\pi$
$12$	2.90315	−	2.90315i	0.241929	−	0.241929i
$13$		−	15.4852i		−	1.19117i	−0.803291	−	0.595586i	$-0.796920\pi$
$13$		−	15.4852i		−	1.19117i	0.803291	−	0.595586i	$-0.203080\pi$
$14$	−4.77978			−0.341413
$15$	−2.15334	−	2.15334i	−0.143556	−	0.143556i
$16$	−4.00000			−0.250000
$17$	19.4852	+	19.4852i	1.14619	+	1.14619i	0.987296	+	0.158894i	$0.0507929\pi$
$17$	19.4852	+	19.4852i	1.14619	+	1.14619i	0.158894	+	0.987296i	$0.449207\pi$
$18$	4.78586	−	4.78586i	0.265881	−	0.265881i
$19$	−23.8056	+	23.8056i	−1.25293	+	1.25293i	−0.298525	+	0.954402i	$0.596495\pi$
$19$	−23.8056	+	23.8056i	−1.25293	+	1.25293i	−0.954402	+	0.298525i	$0.903505\pi$
$20$			2.96690i			0.148345i
$21$	6.93821			0.330391
$22$	−16.7247	+	16.7247i	−0.760215	+	0.760215i
$23$	35.8637			1.55929			0.779645	−	0.626222i	$-0.215399\pi$
$23$	35.8637			1.55929			0.779645	+	0.626222i	$0.215399\pi$
$24$	5.80630			0.241929
$25$	−22.7994			−0.911975
$26$	15.4852	−	15.4852i	0.595586	−	0.595586i
$27$	−20.0112	+	20.0112i	−0.741156	+	0.741156i
$28$	−4.77978	−	4.77978i	−0.170706	−	0.170706i
$29$	−17.0186	+	17.0186i	−0.586849	+	0.586849i	−0.936777	−	0.349928i	$-0.886206\pi$
$29$	−17.0186	+	17.0186i	−0.586849	+	0.586849i	0.349928	+	0.936777i	$0.386206\pi$
$30$		−	4.30668i		−	0.143556i
$31$	−5.30618	+	5.30618i	−0.171167	+	0.171167i	−0.787492	−	0.616325i	$-0.788621\pi$
$31$	−5.30618	+	5.30618i	−0.171167	+	0.171167i	0.616325	+	0.787492i	$0.288621\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	24.2772	−	24.2772i	0.735674	−	0.735674i
$34$			38.9705i			1.14619i
$35$	−3.54528	+	3.54528i	−0.101294	+	0.101294i
$36$	9.57171			0.265881
$37$	−13.2056			−0.356907			−0.178454	−	0.983948i	$-0.557109\pi$
$37$	−13.2056			−0.356907			−0.178454	+	0.983948i	$0.557109\pi$
$38$	−47.6112			−1.25293
$39$	−22.4780	+	22.4780i	−0.576359	+	0.576359i
$40$	−2.96690	+	2.96690i	−0.0741726	+	0.0741726i
$41$	63.9737			1.56033			0.780167	−	0.625571i	$-0.215134\pi$
$41$	63.9737			1.56033			0.780167	+	0.625571i	$0.215134\pi$
$42$	6.93821	+	6.93821i	0.165195	+	0.165195i
$43$			56.2586i			1.30834i	0.756347	+	0.654170i	$0.226982\pi$
$43$			56.2586i			1.30834i	−0.756347	+	0.654170i	$0.773018\pi$
$44$	−33.4495			−0.760215
$45$		−	7.09959i		−	0.157769i
$46$	35.8637	+	35.8637i	0.779645	+	0.779645i
$47$	52.9582			1.12677			0.563385	−	0.826194i	$-0.309499\pi$
$47$	52.9582			1.12677			0.563385	+	0.826194i	$0.309499\pi$
$48$	5.80630	+	5.80630i	0.120965	+	0.120965i
$49$			37.5769i			0.766875i
$50$	−22.7994	−	22.7994i	−0.455987	−	0.455987i
$51$		−	56.5686i		−	1.10919i
$52$	30.9705			0.595586
$53$	−38.2821			−0.722305			−0.361152	−	0.932507i	$-0.617617\pi$
$53$	−38.2821			−0.722305			−0.361152	+	0.932507i	$0.617617\pi$
$54$	−40.0224			−0.741156
$55$			24.8103i			0.451097i
$56$		−	9.55955i		−	0.170706i
$57$	69.1113			1.21248
$58$	−34.0372			−0.586849
$59$	−64.4046	+	64.4046i	−1.09160	+	1.09160i	−0.0962457	+	0.995358i	$0.530683\pi$
$59$	−64.4046	+	64.4046i	−1.09160	+	1.09160i	−0.995358	+	0.0962457i	$0.969317\pi$
$60$	4.30668	−	4.30668i	0.0717781	−	0.0717781i
$61$	−61.9667			−1.01585			−0.507924	−	0.861402i	$-0.669587\pi$
$61$	−61.9667			−1.01585			−0.507924	+	0.861402i	$0.669587\pi$
$62$	−10.6124			−0.171167
$63$	11.4377	+	11.4377i	0.181550	+	0.181550i
$64$		−	8.00000i		−	0.125000i
$65$		−	22.9716i		−	0.353409i
$66$	48.5545			0.735674
$67$	54.1353			0.807989			0.403995	−	0.914761i	$-0.367621\pi$
$67$	54.1353			0.807989			0.403995	+	0.914761i	$0.367621\pi$
$68$	−38.9705	+	38.9705i	−0.573095	+	0.573095i
$69$	−52.0588	−	52.0588i	−0.754476	−	0.754476i
$70$	−7.09057			−0.101294
$71$	−44.3714	+	44.3714i	−0.624949	+	0.624949i	−0.946793	−	0.321844i	$-0.895697\pi$
$71$	−44.3714	+	44.3714i	−0.624949	+	0.624949i	0.321844	+	0.946793i	$0.395697\pi$
$72$	9.57171	+	9.57171i	0.132940	+	0.132940i
$73$			55.0459i			0.754054i	0.926202	+	0.377027i	$0.123054\pi$
$73$			55.0459i			0.754054i	−0.926202	+	0.377027i	$0.876946\pi$
$74$	−13.2056	−	13.2056i	−0.178454	−	0.178454i
$75$	33.0950	+	33.0950i	0.441267	+	0.441267i
$76$	−47.6112	−	47.6112i	−0.626463	−	0.626463i
$77$	−39.9703	−	39.9703i	−0.519094	−	0.519094i
$78$	−44.9560			−0.576359
$79$		−	86.7105i		−	1.09760i	−0.835953	−	0.548801i	$-0.815085\pi$
$79$		−	86.7105i		−	1.09760i	0.835953	−	0.548801i	$-0.184915\pi$
$80$	−5.93381			−0.0741726
$81$	15.0229			0.185468
$82$	63.9737	+	63.9737i	0.780167	+	0.780167i
$83$	12.3562	−	12.3562i	0.148870	−	0.148870i	−0.628743	−	0.777613i	$-0.716430\pi$
$83$	12.3562	−	12.3562i	0.148870	−	0.148870i	0.777613	+	0.628743i	$0.216430\pi$
$84$			13.8764i			0.165195i
$85$	28.9054	+	28.9054i	0.340063	+	0.340063i
$86$	−56.2586	+	56.2586i	−0.654170	+	0.654170i
$87$	49.4076			0.567904
$88$	−33.4495	−	33.4495i	−0.380108	−	0.380108i
$89$		−	78.7503i		−	0.884835i	−0.896809	−	0.442418i	$-0.854121\pi$
$89$		−	78.7503i		−	0.884835i	0.896809	−	0.442418i	$-0.145879\pi$
$90$	7.09959	−	7.09959i	0.0788843	−	0.0788843i
$91$	37.0080	+	37.0080i	0.406681	+	0.406681i
$92$			71.7273i			0.779645i
$93$	15.4046			0.165641
$94$	52.9582	+	52.9582i	0.563385	+	0.563385i
$95$	−35.3145	+	35.3145i	−0.371731	+	0.371731i
$96$			11.6126i			0.120965i
$97$			37.8520i			0.390226i	0.980781	+	0.195113i	$0.0625074\pi$
$97$			37.8520i			0.390226i	−0.980781	+	0.195113i	$0.937493\pi$
$98$	−37.5769	+	37.5769i	−0.383437	+	0.383437i
$99$	80.0422			0.808507
$100$		−	45.5987i		−	0.455987i
$101$	1.19352	+	1.19352i	0.0118170	+	0.0118170i	0.712991	−	0.701174i	$-0.247340\pi$
$101$	1.19352	+	1.19352i	0.0118170	+	0.0118170i	−0.701174	+	0.712991i	$0.747340\pi$
$102$	56.5686	−	56.5686i	0.554594	−	0.554594i
$103$		−	146.180i		−	1.41922i	−0.704595	−	0.709610i	$-0.748871\pi$
$103$		−	146.180i		−	1.41922i	0.704595	−	0.709610i	$-0.251129\pi$
$104$	30.9705	+	30.9705i	0.297793	+	0.297793i
$105$	10.2925			0.0980238
$106$	−38.2821	−	38.2821i	−0.361152	−	0.361152i
$107$	100.468	−	100.468i	0.938957	−	0.938957i	−0.0592840	−	0.998241i	$-0.518882\pi$
$107$	100.468	−	100.468i	0.938957	−	0.938957i	0.998241	+	0.0592840i	$0.0188818\pi$
$108$	−40.0224	−	40.0224i	−0.370578	−	0.370578i
$109$	91.9046	−	91.9046i	0.843162	−	0.843162i	−0.146107	−	0.989269i	$-0.546674\pi$
$109$	91.9046	−	91.9046i	0.843162	−	0.843162i	0.989269	+	0.146107i	$0.0466744\pi$
$110$	−24.8103	+	24.8103i	−0.225549	+	0.225549i
$111$	19.1689	+	19.1689i	0.172693	+	0.172693i
$112$	9.55955	−	9.55955i	0.0853532	−	0.0853532i
$113$	25.3183	−	25.3183i	0.224056	−	0.224056i	−0.586148	−	0.810204i	$-0.699356\pi$
$113$	25.3183	−	25.3183i	0.224056	−	0.224056i	0.810204	+	0.586148i	$0.199356\pi$
$114$	69.1113	+	69.1113i	0.606239	+	0.606239i
$115$	53.2020			0.462626
$116$	−34.0372	−	34.0372i	−0.293424	−	0.293424i
$117$	−74.1101			−0.633420
$118$	−128.809			−1.09160
$119$	−93.1351			−0.782648
$120$	8.61337			0.0717781
$121$	−158.717			−1.31171
$122$	−61.9667	−	61.9667i	−0.507924	−	0.507924i
$123$	−92.8627	−	92.8627i	−0.754981	−	0.754981i
$124$	−10.6124	−	10.6124i	−0.0855835	−	0.0855835i
$125$	−70.9080			−0.567264
$126$			22.8753i			0.181550i
$127$		−	86.0078i		−	0.677226i	−0.940926	−	0.338613i	$-0.890042\pi$
$127$		−	86.0078i		−	0.677226i	0.940926	−	0.338613i	$-0.109958\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$	81.6636	−	81.6636i	0.633052	−	0.633052i
$130$	22.9716	−	22.9716i	0.176705	−	0.176705i
$131$	247.488			1.88923			0.944613	−	0.328188i	$-0.106438\pi$
$131$	247.488			1.88923			0.944613	+	0.328188i	$0.106438\pi$
$132$	48.5545	+	48.5545i	0.367837	+	0.367837i
$133$		−	113.786i		−	0.855530i
$134$	54.1353	+	54.1353i	0.403995	+	0.403995i
$135$	−29.6857	+	29.6857i	−0.219894	+	0.219894i
$136$	−77.9409			−0.573095
$137$	−127.784	+	127.784i	−0.932728	+	0.932728i	−0.997876	−	0.0651474i	$-0.979248\pi$
$137$	−127.784	+	127.784i	−0.932728	+	0.932728i	0.0651474	+	0.997876i	$0.479248\pi$
$138$		−	104.118i		−	0.754476i
$139$	−29.7644	−	29.7644i	−0.214132	−	0.214132i	0.591888	−	0.806020i	$-0.298383\pi$
$139$	−29.7644	−	29.7644i	−0.214132	−	0.214132i	−0.806020	+	0.591888i	$0.798383\pi$
$140$	−7.09057	−	7.09057i	−0.0506469	−	0.0506469i
$141$	−76.8729	−	76.8729i	−0.545198	−	0.545198i
$142$	−88.7428			−0.624949
$143$	258.987			1.81110
$144$			19.1434i			0.132940i
$145$	−25.2463	+	25.2463i	−0.174112	+	0.174112i
$146$	−55.0459	+	55.0459i	−0.377027	+	0.377027i
$147$	54.5457	−	54.5457i	0.371059	−	0.371059i
$148$		−	26.4111i		−	0.178454i
$149$		−	230.447i		−	1.54662i	−0.634027	−	0.773311i	$-0.718599\pi$
$149$		−	230.447i		−	1.54662i	0.634027	−	0.773311i	$-0.281401\pi$
$150$			66.1900i			0.441267i
$151$		−	59.4678i		−	0.393826i	−0.980421	−	0.196913i	$-0.936908\pi$
$151$		−	59.4678i		−	0.393826i	0.980421	−	0.196913i	$-0.0630917\pi$
$152$		−	95.2224i		−	0.626463i
$153$	93.2535	−	93.2535i	0.609500	−	0.609500i
$154$		−	79.9405i		−	0.519094i
$155$	−7.87145	+	7.87145i	−0.0507836	+	0.0507836i
$156$	−44.9560	−	44.9560i	−0.288179	−	0.288179i
$157$	110.186	+	110.186i	0.701820	+	0.701820i	0.964801	−	0.262981i	$-0.0847056\pi$
$157$	110.186	+	110.186i	0.701820	+	0.701820i	−0.262981	+	0.964801i	$0.584706\pi$
$158$	86.7105	−	86.7105i	0.548801	−	0.548801i
$159$	55.5694	+	55.5694i	0.349493	+	0.349493i
$160$	−5.93381	−	5.93381i	−0.0370863	−	0.0370863i
$161$	−85.7102	+	85.7102i	−0.532361	+	0.532361i
$162$	15.0229	+	15.0229i	0.0927338	+	0.0927338i
$163$	64.4420	−	64.4420i	0.395350	−	0.395350i	−0.481239	−	0.876589i	$-0.659813\pi$
$163$	64.4420	−	64.4420i	0.395350	−	0.395350i	0.876589	+	0.481239i	$0.159813\pi$
$164$			127.947i			0.780167i
$165$	36.0141	−	36.0141i	0.218267	−	0.218267i
$166$	24.7124			0.148870
$167$	76.6572	+	76.6572i	0.459025	+	0.459025i	0.898335	−	0.439310i	$-0.144777\pi$
$167$	76.6572	+	76.6572i	0.459025	+	0.459025i	−0.439310	+	0.898335i	$0.644777\pi$
$168$	−13.8764	+	13.8764i	−0.0825977	+	0.0825977i
$169$	−70.7927			−0.418891
$170$			57.8108i			0.340063i
$171$	113.930	+	113.930i	0.666259	+	0.666259i
$172$	−112.517			−0.654170
$173$	−263.472			−1.52296			−0.761481	−	0.648187i	$-0.775527\pi$
$173$	−263.472			−1.52296			−0.761481	+	0.648187i	$0.775527\pi$
$174$	49.4076	+	49.4076i	0.283952	+	0.283952i
$175$	54.4880	−	54.4880i	0.311360	−	0.311360i
$176$		−	66.8990i		−	0.380108i
$177$	186.976			1.05636
$178$	78.7503	−	78.7503i	0.442418	−	0.442418i
$179$	180.188	+	180.188i	1.00664	+	1.00664i	0.999978	+	0.00666055i	$0.00212013\pi$
$179$	180.188	+	180.188i	1.00664	+	1.00664i	0.00666055	+	0.999978i	$0.497880\pi$
$180$	14.1992			0.0788843
$181$	44.4320	−	44.4320i	0.245480	−	0.245480i	−0.573632	−	0.819113i	$-0.694466\pi$
$181$	44.4320	−	44.4320i	0.245480	−	0.245480i	0.819113	+	0.573632i	$0.194466\pi$
$182$			74.0160i			0.406681i
$183$	89.9494	+	89.9494i	0.491527	+	0.491527i
$184$	−71.7273	+	71.7273i	−0.389823	+	0.389823i
$185$	−19.5898			−0.105891
$186$	15.4046	+	15.4046i	0.0828206	+	0.0828206i
$187$	−325.885	+	325.885i	−1.74270	+	1.74270i
$188$			105.916i			0.563385i
$189$		−	95.6491i		−	0.506080i
$190$	−70.6289			−0.371731
$191$			29.6682i			0.155331i	0.996979	+	0.0776653i	$0.0247466\pi$
$191$			29.6682i			0.155331i	−0.996979	+	0.0776653i	$0.975253\pi$
$192$	−11.6126	+	11.6126i	−0.0604823	+	0.0604823i
$193$	101.866	−	101.866i	0.527804	−	0.527804i	−0.392113	−	0.919917i	$-0.628256\pi$
$193$	101.866	−	101.866i	0.527804	−	0.527804i	0.919917	+	0.392113i	$0.128256\pi$
$194$	−37.8520	+	37.8520i	−0.195113	+	0.195113i
$195$	−33.3450	+	33.3450i	−0.171000	+	0.171000i
$196$	−75.1537			−0.383437
$197$	−157.348	+	157.348i	−0.798721	+	0.798721i	−0.982894	−	0.184173i	$-0.941039\pi$
$197$	−157.348	+	157.348i	−0.798721	+	0.798721i	0.184173	+	0.982894i	$0.441039\pi$
$198$	80.0422	+	80.0422i	0.404254	+	0.404254i
$199$		−	320.060i		−	1.60834i	−0.594397	−	0.804172i	$-0.702609\pi$
$199$		−	320.060i		−	1.60834i	0.594397	−	0.804172i	$-0.297391\pi$
$200$	45.5987	−	45.5987i	0.227994	−	0.227994i
$201$	−78.5814	−	78.5814i	−0.390952	−	0.390952i
$202$			2.38703i			0.0118170i
$203$		−	81.3452i		−	0.400715i
$204$	113.137			0.554594
$205$	94.9019			0.462936
$206$	146.180	−	146.180i	0.709610	−	0.709610i
$207$		−	171.638i		−	0.829171i
$208$			61.9410i			0.297793i
$209$	−398.143	−	398.143i	−1.90499	−	1.90499i
$210$	10.2925	+	10.2925i	0.0490119	+	0.0490119i
$211$			204.819i			0.970706i	0.874318	+	0.485353i	$0.161309\pi$
$211$			204.819i			0.970706i	−0.874318	+	0.485353i	$0.838691\pi$
$212$		−	76.5643i		−	0.361152i
$213$	128.817			0.604774
$214$	200.937			0.938957
$215$			83.4569i			0.388172i
$216$		−	80.0449i		−	0.370578i
$217$		−	25.3623i		−	0.116877i
$218$	183.809			0.843162
$219$	79.9033	−	79.9033i	0.364855	−	0.364855i
$220$	−49.6207			−0.225549
$221$	301.733	−	301.733i	1.36531	−	1.36531i
$222$			38.3377i			0.172693i
$223$	−146.712	+	146.712i	−0.657900	+	0.657900i	−0.954883	−	0.296983i	$-0.904020\pi$
$223$	−146.712	+	146.712i	−0.657900	+	0.657900i	0.296983	+	0.954883i	$0.404020\pi$
$224$	19.1191			0.0853532
$225$			109.115i			0.484953i
$226$	50.6366			0.224056
$227$	−229.636	+	229.636i	−1.01161	+	1.01161i	−0.0116807	+	0.999932i	$0.503718\pi$
$227$	−229.636	+	229.636i	−1.01161	+	1.01161i	−0.999932	+	0.0116807i	$0.996282\pi$
$228$			138.223i			0.606239i
$229$	156.971	+	156.971i	0.685461	+	0.685461i	0.961225	−	0.275764i	$-0.0889308\pi$
$229$	156.971	+	156.971i	0.685461	+	0.685461i	−0.275764	+	0.961225i	$0.588931\pi$
$230$	53.2020	+	53.2020i	0.231313	+	0.231313i
$231$			116.040i			0.502337i
$232$		−	68.0745i		−	0.293424i
$233$		−	307.922i		−	1.32156i	−0.750582	−	0.660778i	$-0.770227\pi$
$233$		−	307.922i		−	1.32156i	0.750582	−	0.660778i	$-0.229773\pi$
$234$	−74.1101	−	74.1101i	−0.316710	−	0.316710i
$235$	78.5609			0.334302
$236$	−128.809	−	128.809i	−0.545802	−	0.545802i
$237$	−125.867	+	125.867i	−0.531084	+	0.531084i
$238$	−93.1351	−	93.1351i	−0.391324	−	0.391324i
$239$	−64.9095			−0.271588			−0.135794	−	0.990737i	$-0.543359\pi$
$239$	−64.9095			−0.271588			−0.135794	+	0.990737i	$0.543359\pi$
$240$	8.61337	+	8.61337i	0.0358890	+	0.0358890i
$241$	−3.46495	+	3.46495i	−0.0143774	+	0.0143774i	−0.714259	−	0.699882i	$-0.753236\pi$
$241$	−3.46495	+	3.46495i	−0.0143774	+	0.0143774i	0.699882	+	0.714259i	$0.253236\pi$
$242$	−158.717	−	158.717i	−0.655855	−	0.655855i
$243$	158.294	+	158.294i	0.651416	+	0.651416i
$244$		−	123.933i		−	0.507924i
$245$			55.7435i			0.227524i
$246$		−	185.725i		−	0.754981i
$247$	368.636	+	368.636i	1.49245	+	1.49245i
$248$		−	21.2247i		−	0.0855835i
$249$	−35.8720			−0.144064
$250$	−70.9080	−	70.9080i	−0.283632	−	0.283632i
$251$	−164.176	−	164.176i	−0.654086	−	0.654086i	0.299888	−	0.953974i	$-0.403051\pi$
$251$	−164.176	−	164.176i	−0.654086	−	0.654086i	−0.953974	+	0.299888i	$0.903051\pi$
$252$	−22.8753	+	22.8753i	−0.0907751	+	0.0907751i
$253$			599.811i			2.37079i
$254$	86.0078	−	86.0078i	0.338613	−	0.338613i
$255$		−	83.9167i		−	0.329085i
$256$	16.0000			0.0625000
$257$	263.218	+	263.218i	1.02420	+	1.02420i	0.999700	+	0.0244965i	$0.00779825\pi$
$257$	263.218	+	263.218i	1.02420	+	1.02420i	0.0244965	+	0.999700i	$0.492202\pi$
$258$	163.327			0.633052
$259$	31.5598	−	31.5598i	0.121853	−	0.121853i
$260$	45.9432			0.176705
$261$	81.4486	+	81.4486i	0.312064	+	0.312064i
$262$	247.488	+	247.488i	0.944613	+	0.944613i
$263$	−225.288			−0.856610			−0.428305	−	0.903634i	$-0.640889\pi$
$263$	−225.288			−0.856610			−0.428305	+	0.903634i	$0.640889\pi$
$264$			97.1089i			0.367837i
$265$	−56.7897			−0.214301
$266$	113.786	−	113.786i	0.427765	−	0.427765i
$267$	−114.312	+	114.312i	−0.428135	+	0.428135i
$268$			108.271i			0.403995i
$269$	182.574	−	197.554i	0.678716	−	0.734401i
$269$	182.574	−	197.554i	0.678716	−	0.734401i
$270$	−59.3713			−0.219894
$271$	213.289	+	213.289i	0.787043	+	0.787043i	0.981008	−	0.193966i	$-0.0621350\pi$
$271$	213.289	+	213.289i	0.787043	+	0.787043i	−0.193966	+	0.981008i	$0.562135\pi$
$272$	−77.9409	−	77.9409i	−0.286547	−	0.286547i
$273$		−	107.440i		−	0.393552i
$274$	−255.568			−0.932728
$275$		−	381.314i		−	1.38659i
$276$	104.118	−	104.118i	0.377238	−	0.377238i
$277$	300.555	−	300.555i	1.08504	−	1.08504i	0.0890042	−	0.996031i	$-0.471632\pi$
$277$	300.555	−	300.555i	1.08504	−	1.08504i	0.996031	−	0.0890042i	$-0.0283684\pi$
$278$		−	59.5287i		−	0.214132i
$279$	25.3946	+	25.3946i	0.0910201	+	0.0910201i
$280$		−	14.1811i		−	0.0506469i
$281$	−89.5044	+	89.5044i	−0.318521	+	0.318521i	−0.848199	−	0.529678i	$-0.822313\pi$
$281$	−89.5044	+	89.5044i	−0.318521	+	0.318521i	0.529678	+	0.848199i	$0.322313\pi$
$282$		−	153.746i		−	0.545198i
$283$	−355.075			−1.25468			−0.627341	−	0.778744i	$-0.715857\pi$
$283$	−355.075			−1.25468			−0.627341	+	0.778744i	$0.715857\pi$
$284$	−88.7428	−	88.7428i	−0.312474	−	0.312474i
$285$	102.523			0.359731
$286$	258.987	+	258.987i	0.905548	+	0.905548i
$287$	−152.890	+	152.890i	−0.532718	+	0.532718i
$288$	−19.1434	+	19.1434i	−0.0664702	+	0.0664702i
$289$			470.348i			1.62750i
$290$	−50.4926			−0.174112
$291$	54.9450	−	54.9450i	0.188814	−	0.188814i
$292$	−110.092			−0.377027
$293$	−26.4056			−0.0901213			−0.0450607	−	0.998984i	$-0.514348\pi$
$293$	−26.4056			−0.0901213			−0.0450607	+	0.998984i	$0.514348\pi$
$294$	109.091			0.371059
$295$	−95.5411	+	95.5411i	−0.323868	+	0.323868i
$296$	26.4111	−	26.4111i	0.0892268	−	0.0892268i
$297$	−334.682	−	334.682i	−1.12688	−	1.12688i
$298$	230.447	−	230.447i	0.773311	−	0.773311i
$299$		−	555.358i		−	1.85738i
$300$	−66.1900	+	66.1900i	−0.220633	+	0.220633i
$301$	−134.452	−	134.452i	−0.446684	−	0.446684i
$302$	59.4678	−	59.4678i	0.196913	−	0.196913i
$303$		−	3.46496i		−	0.0114355i
$304$	95.2224	−	95.2224i	0.313232	−	0.313232i
$305$	−91.9246			−0.301392
$306$	186.507			0.609500
$307$	−19.4030			−0.0632020			−0.0316010	−	0.999501i	$-0.510061\pi$
$307$	−19.4030			−0.0632020			−0.0316010	+	0.999501i	$0.510061\pi$
$308$	79.9405	−	79.9405i	0.259547	−	0.259547i
$309$	−212.191	+	212.191i	−0.686702	+	0.686702i
$310$	−15.7429			−0.0507836
$311$	−101.590	−	101.590i	−0.326656	−	0.326656i	0.524657	−	0.851313i	$-0.324193\pi$
$311$	−101.590	−	101.590i	−0.326656	−	0.326656i	−0.851313	+	0.524657i	$0.824193\pi$
$312$		−	89.9120i		−	0.288179i
$313$	−279.679			−0.893544			−0.446772	−	0.894648i	$-0.647426\pi$
$313$	−279.679			−0.893544			−0.446772	+	0.894648i	$0.647426\pi$
$314$			220.372i			0.701820i
$315$	16.9672	+	16.9672i	0.0538642	+	0.0538642i
$316$	173.421			0.548801
$317$	−365.382	−	365.382i	−1.15262	−	1.15262i	−0.986025	−	0.166600i	$-0.946721\pi$
$317$	−365.382	−	365.382i	−1.15262	−	1.15262i	−0.166600	−	0.986025i	$-0.553279\pi$
$318$			111.139i			0.349493i
$319$	−284.632	−	284.632i	−0.892263	−	0.892263i
$320$		−	11.8676i		−	0.0370863i
$321$	−291.675			−0.908645
$322$	−171.420			−0.532361
$323$	−927.715			−2.87218
$324$			30.0457i			0.0927338i
$325$			353.054i			1.08632i
$326$	128.884			0.395350
$327$	−266.813			−0.815942
$328$	−127.947	+	127.947i	−0.390084	+	0.390084i
$329$	−126.564	+	126.564i	−0.384694	+	0.384694i
$330$	72.0282			0.218267
$331$	87.4154			0.264095			0.132047	−	0.991243i	$-0.457845\pi$
$331$	87.4154			0.264095			0.132047	+	0.991243i	$0.457845\pi$
$332$	24.7124	+	24.7124i	0.0744351	+	0.0744351i
$333$			63.1999i			0.189790i
$334$			153.314i			0.459025i
$335$	80.3071			0.239723
$336$	−27.7528			−0.0825977
$337$	424.119	−	424.119i	1.25851	−	1.25851i	0.306710	−	0.951803i	$-0.400772\pi$
$337$	424.119	−	424.119i	1.25851	−	1.25851i	0.951803	−	0.306710i	$-0.0992281\pi$
$338$	−70.7927	−	70.7927i	−0.209446	−	0.209446i
$339$	−73.5028			−0.216822
$340$	−57.8108	+	57.8108i	−0.170032	+	0.170032i
$341$	−88.7444	−	88.7444i	−0.260248	−	0.260248i
$342$			227.860i			0.666259i
$343$	−206.909	−	206.909i	−0.603233	−	0.603233i
$344$	−112.517	−	112.517i	−0.327085	−	0.327085i
$345$	−77.2268	−	77.2268i	−0.223846	−	0.223846i
$346$	−263.472	−	263.472i	−0.761481	−	0.761481i
$347$	−350.568			−1.01028			−0.505141	−	0.863037i	$-0.668559\pi$
$347$	−350.568			−1.01028			−0.505141	+	0.863037i	$0.668559\pi$
$348$			98.8152i			0.283952i
$349$	159.379			0.456672			0.228336	−	0.973582i	$-0.426671\pi$
$349$	159.379			0.456672			0.228336	+	0.973582i	$0.426671\pi$
$350$	108.976			0.311360
$351$	309.878	+	309.878i	0.882845	+	0.882845i
$352$	66.8990	−	66.8990i	0.190054	−	0.190054i
$353$			410.791i			1.16371i	0.813291	+	0.581857i	$0.197674\pi$
$353$			410.791i			1.16371i	−0.813291	+	0.581857i	$0.802326\pi$
$354$	186.976	+	186.976i	0.528182	+	0.528182i
$355$	−65.8228	+	65.8228i	−0.185416	+	0.185416i
$356$	157.501			0.442418
$357$	135.193	+	135.193i	0.378691	+	0.378691i
$358$			360.377i			1.00664i
$359$	−280.044	+	280.044i	−0.780066	+	0.780066i	−0.979842	−	0.199775i	$-0.935979\pi$
$359$	−280.044	+	280.044i	−0.780066	+	0.780066i	0.199775	+	0.979842i	$0.435979\pi$
$360$	14.1992	+	14.1992i	0.0394421	+	0.0394421i
$361$		−	772.414i		−	2.13965i
$362$	88.8639			0.245480
$363$	230.390	+	230.390i	0.634682	+	0.634682i
$364$	−74.0160	+	74.0160i	−0.203341	+	0.203341i
$365$			81.6580i			0.223720i
$366$			179.899i			0.491527i
$367$	−325.936	+	325.936i	−0.888109	+	0.888109i	−0.994341	−	0.106232i	$-0.966121\pi$
$367$	−325.936	+	325.936i	−0.888109	+	0.888109i	0.106232	+	0.994341i	$0.466121\pi$
$368$	−143.455			−0.389823
$369$		−	306.169i		−	0.829726i
$370$	−19.5898	−	19.5898i	−0.0529454	−	0.0529454i
$371$	91.4901	−	91.4901i	0.246604	−	0.246604i
$372$			30.8093i			0.0828206i
$373$	113.962	+	113.962i	0.305527	+	0.305527i	0.843172	−	0.537645i	$-0.180686\pi$
$373$	113.962	+	113.962i	0.305527	+	0.305527i	−0.537645	+	0.843172i	$0.680686\pi$
$374$	−651.771			−1.74270
$375$	102.928	+	102.928i	0.274476	+	0.274476i
$376$	−105.916	+	105.916i	−0.281693	+	0.281693i
$377$	263.537	+	263.537i	0.699038	+	0.699038i
$378$	95.6491	−	95.6491i	0.253040	−	0.253040i
$379$	−84.8069	+	84.8069i	−0.223765	+	0.223765i	−0.810082	−	0.586317i	$-0.800577\pi$
$379$	−84.8069	+	84.8069i	−0.223765	+	0.223765i	0.586317	+	0.810082i	$0.300577\pi$
$380$	−70.6289	−	70.6289i	−0.185866	−	0.185866i
$381$	−124.847	+	124.847i	−0.327682	+	0.327682i
$382$	−29.6682	+	29.6682i	−0.0776653	+	0.0776653i
$383$	462.145	+	462.145i	1.20665	+	1.20665i	0.972107	+	0.234539i	$0.0753579\pi$
$383$	462.145	+	462.145i	1.20665	+	1.20665i	0.234539	+	0.972107i	$0.424642\pi$
$384$	−23.2252			−0.0604823
$385$	−59.2940	−	59.2940i	−0.154010	−	0.154010i
$386$	203.732			0.527804
$387$	269.246			0.695725
$388$	−75.7039			−0.195113
$389$	662.847			1.70398			0.851988	−	0.523562i	$-0.175397\pi$
$389$	662.847			1.70398			0.851988	+	0.523562i	$0.175397\pi$
$390$	−66.6900			−0.171000
$391$	698.812	+	698.812i	1.78724	+	1.78724i
$392$	−75.1537	−	75.1537i	−0.191719	−	0.191719i
$393$	−359.248	−	359.248i	−0.914118	−	0.914118i
$394$	−314.696			−0.798721
$395$		−	128.631i		−	0.325648i
$396$			160.084i			0.404254i
$397$	−164.172	+	164.172i	−0.413532	+	0.413532i	−0.882967	−	0.469435i	$-0.844458\pi$
$397$	−164.172	+	164.172i	−0.413532	+	0.413532i	0.469435	+	0.882967i	$0.344458\pi$
$398$	320.060	−	320.060i	0.804172	−	0.804172i
$399$	−165.168	+	165.168i	−0.413956	+	0.413956i
$400$	91.1975			0.227994
$401$	281.823	+	281.823i	0.702801	+	0.702801i	0.965011	−	0.262210i	$-0.0844513\pi$
$401$	281.823	+	281.823i	0.702801	+	0.702801i	−0.262210	+	0.965011i	$0.584451\pi$
$402$		−	157.163i		−	0.390952i
$403$	82.1674	+	82.1674i	0.203889	+	0.203889i
$404$	−2.38703	+	2.38703i	−0.00590850	+	0.00590850i
$405$	22.2857			0.0550264
$406$	81.3452	−	81.3452i	0.200358	−	0.200358i
$407$		−	220.860i		−	0.542653i
$408$	113.137	+	113.137i	0.277297	+	0.277297i
$409$	−60.8514	−	60.8514i	−0.148781	−	0.148781i	0.628792	−	0.777573i	$-0.283550\pi$
$409$	−60.8514	−	60.8514i	−0.148781	−	0.148781i	−0.777573	+	0.628792i	$0.783550\pi$
$410$	94.9019	+	94.9019i	0.231468	+	0.231468i
$411$	370.976			0.902617
$412$	292.359			0.709610
$413$		−	307.840i		−	0.745374i
$414$	171.638	−	171.638i	0.414585	−	0.414585i
$415$	18.3299	−	18.3299i	0.0441683	−	0.0441683i
$416$	−61.9410	+	61.9410i	−0.148897	+	0.148897i
$417$			86.4105i			0.207219i
$418$		−	796.285i		−	1.90499i
$419$			454.438i			1.08458i	0.840193	+	0.542288i	$0.182442\pi$
$419$			454.438i			1.08458i	−0.840193	+	0.542288i	$0.817558\pi$
$420$			20.5850i			0.0490119i
$421$		−	119.783i		−	0.284520i	−0.989829	−	0.142260i	$-0.954563\pi$
$421$		−	119.783i		−	0.284520i	0.989829	−	0.142260i	$-0.0454370\pi$
$422$	−204.819	+	204.819i	−0.485353	+	0.485353i
$423$		−	253.450i		−	0.599174i
$424$	76.5643	−	76.5643i	0.180576	−	0.180576i
$425$	−444.251	−	444.251i	−1.04530	−	1.04530i
$426$	128.817	+	128.817i	0.302387	+	0.302387i
$427$	148.094	−	148.094i	0.346823	−	0.346823i
$428$	200.937	+	200.937i	0.469479	+	0.469479i
$429$	−375.939	−	375.939i	−0.876314	−	0.876314i
$430$	−83.4569	+	83.4569i	−0.194086	+	0.194086i
$431$	507.394	+	507.394i	1.17725	+	1.17725i	0.980442	+	0.196807i	$0.0630571\pi$
$431$	507.394	+	507.394i	1.17725	+	1.17725i	0.196807	+	0.980442i	$0.436943\pi$
$432$	80.0449	−	80.0449i	0.185289	−	0.185289i
$433$		−	29.3204i		−	0.0677145i	−0.999427	−	0.0338572i	$-0.989221\pi$
$433$		−	29.3204i		−	0.0677145i	0.999427	−	0.0338572i	$-0.0107792\pi$
$434$	25.3623	−	25.3623i	0.0584386	−	0.0584386i
$435$	73.2938			0.168491
$436$	183.809	+	183.809i	0.421581	+	0.421581i
$437$	−853.757	+	853.757i	−1.95368	+	1.95368i
$438$	159.807			0.364855
$439$			650.874i			1.48263i	0.671158	+	0.741314i	$0.265797\pi$
$439$			650.874i			1.48263i	−0.671158	+	0.741314i	$0.734203\pi$
$440$	−49.6207	−	49.6207i	−0.112774	−	0.112774i
$441$	179.837			0.407795
$442$	603.467			1.36531
$443$	279.547	+	279.547i	0.631031	+	0.631031i	0.948327	−	0.317295i	$-0.102775\pi$
$443$	279.547	+	279.547i	0.631031	+	0.631031i	−0.317295	+	0.948327i	$0.602775\pi$
$444$	−38.3377	+	38.3377i	−0.0863463	+	0.0863463i
$445$		−	116.822i		−	0.262522i
$446$	−293.423			−0.657900
$447$	−334.511	+	334.511i	−0.748346	+	0.748346i
$448$	19.1191	+	19.1191i	0.0426766	+	0.0426766i
$449$	487.472			1.08568			0.542842	−	0.839835i	$-0.317348\pi$
$449$	487.472			1.08568			0.542842	+	0.839835i	$0.317348\pi$
$450$	−109.115	+	109.115i	−0.242477	+	0.242477i
$451$			1069.94i			2.37238i
$452$	50.6366	+	50.6366i	0.112028	+	0.112028i
$453$	−86.3220	+	86.3220i	−0.190556	+	0.190556i
$454$	−459.272			−1.01161
$455$	54.8996	+	54.8996i	0.120658	+	0.120658i
$456$	−138.223	+	138.223i	−0.303120	+	0.303120i
$457$			389.253i			0.851756i	0.904780	+	0.425878i	$0.140035\pi$
$457$			389.253i			0.851756i	−0.904780	+	0.425878i	$0.859965\pi$
$458$			313.941i			0.685461i
$459$	−779.846			−1.69901
$460$			106.404i			0.231313i
$461$	−113.397	+	113.397i	−0.245981	+	0.245981i	−0.819319	−	0.573338i	$-0.805648\pi$
$461$	−113.397	+	113.397i	−0.245981	+	0.245981i	0.573338	+	0.819319i	$0.305648\pi$
$462$	−116.040	+	116.040i	−0.251168	+	0.251168i
$463$	316.766	−	316.766i	0.684159	−	0.684159i	−0.276775	−	0.960935i	$-0.589266\pi$
$463$	316.766	−	316.766i	0.684159	−	0.684159i	0.960935	+	0.276775i	$0.0892658\pi$
$464$	68.0745	−	68.0745i	0.146712	−	0.146712i
$465$	22.8520			0.0491441
$466$	307.922	−	307.922i	0.660778	−	0.660778i
$467$	114.556	+	114.556i	0.245301	+	0.245301i	0.819039	−	0.573738i	$-0.194507\pi$
$467$	114.556	+	114.556i	0.245301	+	0.245301i	−0.573738	+	0.819039i	$0.694507\pi$
$468$		−	148.220i		−	0.316710i
$469$	−129.377	+	129.377i	−0.275858	+	0.275858i
$470$	78.5609	+	78.5609i	0.167151	+	0.167151i
$471$		−	319.886i		−	0.679163i
$472$		−	257.618i		−	0.545802i
$473$	−940.911			−1.98924
$474$	−251.734			−0.531084
$475$	542.753	−	542.753i	1.14264	−	1.14264i
$476$		−	186.270i		−	0.391324i
$477$			183.213i			0.384094i
$478$	−64.9095	−	64.9095i	−0.135794	−	0.135794i
$479$	−609.039	−	609.039i	−1.27148	−	1.27148i	−0.945312	−	0.326169i	$-0.894242\pi$
$479$	−609.039	−	609.039i	−1.27148	−	1.27148i	−0.326169	−	0.945312i	$-0.605758\pi$
$480$			17.2267i			0.0358890i
$481$			204.491i			0.425138i
$482$	−6.92991			−0.0143774
$483$	248.830			0.515175
$484$		−	317.434i		−	0.655855i
$485$			56.1516i			0.115776i
$486$			316.588i			0.651416i
$487$	317.453			0.651854			0.325927	−	0.945395i	$-0.394324\pi$
$487$	317.453			0.651854			0.325927	+	0.945395i	$0.394324\pi$
$488$	123.933	−	123.933i	0.253962	−	0.253962i
$489$	−187.085			−0.382587
$490$	−55.7435	+	55.7435i	−0.113762	+	0.113762i
$491$		−	714.712i		−	1.45563i	−0.685776	−	0.727813i	$-0.740537\pi$
$491$		−	714.712i		−	1.45563i	0.685776	−	0.727813i	$-0.259463\pi$
$492$	185.725	−	185.725i	0.377491	−	0.377491i
$493$	−663.223			−1.34528
$494$			737.271i			1.49245i
$495$	118.739			0.239876
$496$	21.2247	−	21.2247i	0.0427917	−	0.0427917i
$497$		−	212.085i		−	0.426731i
$498$	−35.8720	−	35.8720i	−0.0720321	−	0.0720321i
$499$	−271.717	−	271.717i	−0.544523	−	0.544523i	0.380329	−	0.924851i	$-0.375811\pi$
$499$	−271.717	−	271.717i	−0.544523	−	0.544523i	−0.924851	+	0.380329i	$0.875811\pi$
$500$		−	141.816i		−	0.283632i
$501$		−	222.547i		−	0.444207i
$502$		−	328.351i		−	0.654086i
$503$	253.136	+	253.136i	0.503253	+	0.503253i	0.912447	−	0.409194i	$-0.134190\pi$
$503$	253.136	+	253.136i	0.503253	+	0.503253i	−0.409194	+	0.912447i	$0.634190\pi$
$504$	−45.7507			−0.0907751
$505$	1.77052	+	1.77052i	0.00350599	+	0.00350599i
$506$	−599.811	+	599.811i	−1.18540	+	1.18540i
$507$	102.761	+	102.761i	0.202684	+	0.202684i
$508$	172.016			0.338613
$509$	418.999	+	418.999i	0.823181	+	0.823181i	0.986563	−	0.163382i	$-0.0522403\pi$
$509$	418.999	+	418.999i	0.823181	+	0.823181i	−0.163382	+	0.986563i	$0.552240\pi$
$510$	83.9167	−	83.9167i	0.164543	−	0.164543i
$511$	−131.554	−	131.554i	−0.257444	−	0.257444i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$		−	952.758i		−	1.85723i
$514$			526.437i			1.02420i
$515$		−	216.850i		−	0.421069i
$516$	163.327	+	163.327i	0.316526	+	0.316526i
$517$			885.712i			1.71318i
$518$	63.1197			0.121853
$519$	382.450	+	382.450i	0.736898	+	0.736898i
$520$	45.9432	+	45.9432i	0.0883523	+	0.0883523i
$521$	548.945	−	548.945i	1.05364	−	1.05364i	0.0551602	−	0.998478i	$-0.482433\pi$
$521$	548.945	−	548.945i	1.05364	−	1.05364i	0.998478	−	0.0551602i	$-0.0175669\pi$
$522$			162.897i			0.312064i
$523$	−99.1601	+	99.1601i	−0.189599	+	0.189599i	−0.795523	−	0.605924i	$-0.792804\pi$
$523$	−99.1601	+	99.1601i	−0.189599	+	0.189599i	0.605924	+	0.795523i	$0.292804\pi$
$524$			494.977i			0.944613i
$525$	−158.187			−0.301308
$526$	−225.288	−	225.288i	−0.428305	−	0.428305i
$527$	−206.784			−0.392380
$528$	−97.1089	+	97.1089i	−0.183918	+	0.183918i
$529$	757.203			1.43139
$530$	−56.7897	−	56.7897i	−0.107150	−	0.107150i
$531$	308.231	+	308.231i	0.580473	+	0.580473i
$532$	227.571			0.427765
$533$		−	990.648i		−	1.85863i
$534$	−228.624			−0.428135
$535$	149.040	−	149.040i	0.278579	−	0.278579i
$536$	−108.271	+	108.271i	−0.201997	+	0.201997i
$537$		−	523.114i		−	0.974141i
$538$	380.128	−	14.9794i	0.706558	−	0.0278428i
$539$	−628.463			−1.16598
$540$	−59.3713	−	59.3713i	−0.109947	−	0.109947i
$541$	−125.464	−	125.464i	−0.231911	−	0.231911i	0.581579	−	0.813490i	$-0.302435\pi$
$541$	−125.464	−	125.464i	−0.231911	−	0.231911i	−0.813490	+	0.581579i	$0.802435\pi$
$542$			426.577i			0.787043i
$543$	−128.993			−0.237556
$544$		−	155.882i		−	0.286547i
$545$	136.336	−	136.336i	0.250158	−	0.250158i
$546$	107.440	−	107.440i	0.196776	−	0.196776i
$547$			439.337i			0.803176i	0.915820	+	0.401588i	$0.131542\pi$
$547$			439.337i			0.803176i	−0.915820	+	0.401588i	$0.868458\pi$
$548$	−255.568	−	255.568i	−0.466364	−	0.466364i
$549$			296.564i			0.540189i
$550$	381.314	−	381.314i	0.693297	−	0.693297i
$551$		−	810.277i		−	1.47056i
$552$	208.235			0.377238
$553$	207.229	+	207.229i	0.374735	+	0.374735i
$554$	601.110			1.08504
$555$	28.4361	+	28.4361i	0.0512362	+	0.0512362i
$556$	59.5287	−	59.5287i	0.107066	−	0.107066i
$557$	234.353	−	234.353i	0.420741	−	0.420741i	−0.464718	−	0.885459i	$-0.653844\pi$
$557$	234.353	−	234.353i	0.420741	−	0.420741i	0.885459	+	0.464718i	$0.153844\pi$
$558$			50.7892i			0.0910201i
$559$	871.178			1.55846
$560$	14.1811	−	14.1811i	0.0253235	−	0.0253235i
$561$	946.095			1.68644
$562$	−179.009			−0.318521
$563$	−122.898			−0.218292			−0.109146	−	0.994026i	$-0.534812\pi$
$563$	−122.898			−0.218292			−0.109146	+	0.994026i	$0.534812\pi$
$564$	153.746	−	153.746i	0.272599	−	0.272599i
$565$	37.5584	−	37.5584i	0.0664751	−	0.0664751i
$566$	−355.075	−	355.075i	−0.627341	−	0.627341i
$567$	−35.9030	+	35.9030i	−0.0633210	+	0.0633210i
$568$		−	177.486i		−	0.312474i
$569$	27.5868	−	27.5868i	0.0484830	−	0.0484830i	−0.682450	−	0.730933i	$-0.739085\pi$
$569$	27.5868	−	27.5868i	0.0484830	−	0.0484830i	0.730933	+	0.682450i	$0.239085\pi$
$570$	102.523	+	102.523i	0.179865	+	0.179865i
$571$	−250.973	+	250.973i	−0.439532	+	0.439532i	−0.891854	−	0.452323i	$-0.850596\pi$
$571$	−250.973	+	250.973i	−0.439532	+	0.439532i	0.452323	+	0.891854i	$0.350596\pi$
$572$			517.973i			0.905548i
$573$	43.0656	−	43.0656i	0.0751581	−	0.0751581i
$574$	−305.780			−0.532718
$575$	−817.669			−1.42203
$576$	−38.2869			−0.0664702
$577$	−47.1126	+	47.1126i	−0.0816510	+	0.0816510i	−0.746753	−	0.665102i	$-0.768388\pi$
$577$	−47.1126	+	47.1126i	−0.0816510	+	0.0816510i	0.665102	+	0.746753i	$0.268388\pi$
$578$	−470.348	+	470.348i	−0.813751	+	0.813751i
$579$	−295.733			−0.510765
$580$	−50.4926	−	50.4926i	−0.0870562	−	0.0870562i
$581$			59.0600i			0.101652i
$582$	109.890			0.188814
$583$		−	640.259i		−	1.09821i
$584$	−110.092	−	110.092i	−0.188513	−	0.188513i
$585$	−109.939			−0.187930
$586$	−26.4056	−	26.4056i	−0.0450607	−	0.0450607i
$587$		−	198.837i		−	0.338734i	−0.985553	−	0.169367i	$-0.945828\pi$
$587$		−	198.837i		−	0.338734i	0.985553	−	0.169367i	$-0.0541724\pi$
$588$	109.091	+	109.091i	0.185529	+	0.185529i
$589$		−	252.633i		−	0.428919i
$590$	−191.082			−0.323868
$591$	456.805			0.772936
$592$	52.8223			0.0892268
$593$		−	665.761i		−	1.12270i	−0.827579	−	0.561350i	$-0.810282\pi$
$593$		−	665.761i		−	1.12270i	0.827579	−	0.561350i	$-0.189718\pi$
$594$		−	669.365i		−	1.12688i
$595$	−138.161			−0.232204
$596$	460.893			0.773311
$597$	−464.592	+	464.592i	−0.778211	+	0.778211i
$598$	555.358	−	555.358i	0.928692	−	0.928692i
$599$	−73.5083			−0.122718			−0.0613592	−	0.998116i	$-0.519544\pi$
$599$	−73.5083			−0.122718			−0.0613592	+	0.998116i	$0.519544\pi$
$600$	−132.380			−0.220633
$601$	217.542	+	217.542i	0.361967	+	0.361967i	0.864537	−	0.502570i	$-0.167612\pi$
$601$	217.542	+	217.542i	0.361967	+	0.361967i	−0.502570	+	0.864537i	$0.667612\pi$
$602$		−	268.904i		−	0.446684i
$603$		−	259.084i		−	0.429658i
$604$	118.936			0.196913
$605$	−235.449			−0.389172
$606$	3.46496	−	3.46496i	0.00571776	−	0.00571776i
$607$	−266.305	−	266.305i	−0.438723	−	0.438723i	0.452859	−	0.891582i	$-0.350404\pi$
$607$	−266.305	−	266.305i	−0.438723	−	0.438723i	−0.891582	+	0.452859i	$0.850404\pi$
$608$	190.445			0.313232
$609$	−118.079	+	118.079i	−0.193889	+	0.193889i
$610$	−91.9246	−	91.9246i	−0.150696	−	0.150696i
$611$		−	820.071i		−	1.34218i
$612$	186.507	+	186.507i	0.304750	+	0.304750i
$613$	−217.417	−	217.417i	−0.354677	−	0.354677i	0.507170	−	0.861846i	$-0.330692\pi$
$613$	−217.417	−	217.417i	−0.354677	−	0.354677i	−0.861846	+	0.507170i	$0.830692\pi$
$614$	−19.4030	−	19.4030i	−0.0316010	−	0.0316010i
$615$	−137.757	−	137.757i	−0.223996	−	0.223996i
$616$	159.881			0.259547
$617$			649.130i			1.05207i	0.850462	+	0.526037i	$0.176323\pi$
$617$			649.130i			1.05207i	−0.850462	+	0.526037i	$0.823677\pi$
$618$	−424.382			−0.686702
$619$	−170.857			−0.276021			−0.138011	−	0.990431i	$-0.544071\pi$
$619$	−170.857			−0.276021			−0.138011	+	0.990431i	$0.544071\pi$
$620$	−15.7429	−	15.7429i	−0.0253918	−	0.0253918i
$621$	−717.676	+	717.676i	−1.15568	+	1.15568i
$622$		−	203.180i		−	0.326656i
$623$	188.205	+	188.205i	0.302094	+	0.302094i
$624$	89.9120	−	89.9120i	0.144090	−	0.144090i
$625$	464.796			0.743673
$626$	−279.679	−	279.679i	−0.446772	−	0.446772i
$627$			1155.87i			1.84349i
$628$	−220.372	+	220.372i	−0.350910	+	0.350910i
$629$	−257.313	−	257.313i	−0.409083	−	0.409083i
$630$			33.9344i			0.0538642i
$631$	−1170.63			−1.85520			−0.927598	−	0.373579i	$-0.878130\pi$
$631$	−1170.63			−1.85520			−0.927598	+	0.373579i	$0.878130\pi$
$632$	173.421	+	173.421i	0.274400	+	0.274400i
$633$	297.310	−	297.310i	0.469684	−	0.469684i
$634$		−	730.764i		−	1.15262i
$635$		−	127.588i		−	0.200927i
$636$	−111.139	+	111.139i	−0.174747	+	0.174747i
$637$	581.887			0.913480
$638$		−	569.264i		−	0.892263i
$639$	212.355	+	212.355i	0.332324	+	0.332324i
$640$	11.8676	−	11.8676i	0.0185431	−	0.0185431i
$641$		−	832.894i		−	1.29937i	−0.760205	−	0.649683i	$-0.774902\pi$
$641$		−	832.894i		−	1.29937i	0.760205	−	0.649683i	$-0.225098\pi$
$642$	−291.675	−	291.675i	−0.454322	−	0.454322i
$643$	1189.28			1.84959			0.924793	−	0.380471i	$-0.124238\pi$
$643$	1189.28			1.84959			0.924793	+	0.380471i	$0.124238\pi$
$644$	−171.420	−	171.420i	−0.266181	−	0.266181i
$645$	121.144	−	121.144i	0.187820	−	0.187820i
$646$	−927.715	−	927.715i	−1.43609	−	1.43609i
$647$	349.154	−	349.154i	0.539651	−	0.539651i	−0.383775	−	0.923426i	$-0.625376\pi$
$647$	349.154	−	349.154i	0.539651	−	0.539651i	0.923426	+	0.383775i	$0.125376\pi$
$648$	−30.0457	+	30.0457i	−0.0463669	+	0.0463669i
$649$	−1077.15	−	1077.15i	−1.65971	−	1.65971i
$650$	−353.054	+	353.054i	−0.543160	+	0.543160i
$651$	−36.8154	+	36.8154i	−0.0565520	+	0.0565520i
$652$	128.884	+	128.884i	0.197675	+	0.197675i
$653$	823.923			1.26175			0.630875	−	0.775884i	$-0.282696\pi$
$653$	823.923			1.26175			0.630875	+	0.775884i	$0.282696\pi$
$654$	−266.813	−	266.813i	−0.407971	−	0.407971i
$655$	367.137			0.560515
$656$	−255.895			−0.390084
$657$	263.442			0.400977
$658$	−253.128			−0.384694
$659$	149.041			0.226163			0.113081	−	0.993586i	$-0.463928\pi$
$659$	149.041			0.226163			0.113081	+	0.993586i	$0.463928\pi$
$660$	72.0282	+	72.0282i	0.109134	+	0.109134i
$661$	115.313	+	115.313i	0.174452	+	0.174452i	0.788932	−	0.614480i	$-0.210634\pi$
$661$	115.313	+	115.313i	0.174452	+	0.174452i	−0.614480	+	0.788932i	$0.710634\pi$
$662$	87.4154	+	87.4154i	0.132047	+	0.132047i
$663$	−875.978			−1.32123
$664$			49.4249i			0.0744351i
$665$		−	168.795i		−	0.253827i
$666$	−63.1999	+	63.1999i	−0.0948948	+	0.0948948i
$667$	−610.350	+	610.350i	−0.915068	+	0.915068i
$668$	−153.314	+	153.314i	−0.229513	+	0.229513i
$669$	425.926			0.636661
$670$	80.3071	+	80.3071i	0.119861	+	0.119861i
$671$		−	1036.38i		−	1.54453i
$672$	−27.7528	−	27.7528i	−0.0412989	−	0.0412989i
$673$	723.480	−	723.480i	1.07501	−	1.07501i	0.0780593	−	0.996949i	$-0.475128\pi$
$673$	723.480	−	723.480i	1.07501	−	1.07501i	0.996949	−	0.0780593i	$-0.0248723\pi$
$674$	848.238			1.25851
$675$	456.243	−	456.243i	0.675916	−	0.675916i
$676$		−	141.585i		−	0.209446i
$677$	−737.948	−	737.948i	−1.09003	−	1.09003i	−0.995525	−	0.0945020i	$-0.969874\pi$
$677$	−737.948	−	737.948i	−1.09003	−	1.09003i	−0.0945020	−	0.995525i	$-0.530126\pi$
$678$	−73.5028	−	73.5028i	−0.108411	−	0.108411i
$679$	−90.4620	−	90.4620i	−0.133228	−	0.133228i
$680$	−115.622			−0.170032
$681$	666.668			0.978955
$682$		−	177.489i		−	0.260248i
$683$	367.695	−	367.695i	0.538353	−	0.538353i	−0.384692	−	0.923045i	$-0.625692\pi$
$683$	367.695	−	367.695i	0.538353	−	0.538353i	0.923045	+	0.384692i	$0.125692\pi$
$684$	−227.860	+	227.860i	−0.333129	+	0.333129i
$685$	−189.561	+	189.561i	−0.276731	+	0.276731i
$686$		−	413.818i		−	0.603233i
$687$		−	455.710i		−	0.663333i
$688$		−	225.035i		−	0.327085i
$689$			592.808i			0.860389i
$690$		−	154.454i		−	0.223846i
$691$	−54.3680	+	54.3680i	−0.0786802	+	0.0786802i	−0.745352	−	0.666671i	$-0.767718\pi$
$691$	−54.3680	+	54.3680i	−0.0786802	+	0.0786802i	0.666671	+	0.745352i	$0.267718\pi$
$692$		−	526.945i		−	0.761481i
$693$	−191.292	+	191.292i	−0.276035	+	0.276035i
$694$	−350.568	−	350.568i	−0.505141	−	0.505141i
$695$	−44.1540	−	44.1540i	−0.0635309	−	0.0635309i
$696$	−98.8152	+	98.8152i	−0.141976	+	0.141976i
$697$	1246.54	+	1246.54i	1.78844	+	1.78844i
$698$	159.379	+	159.379i	0.228336	+	0.228336i
$699$	−446.973	+	446.973i	−0.639446	+	0.639446i
$700$	108.976	+	108.976i	0.155680	+	0.155680i
$701$	159.161	−	159.161i	0.227048	−	0.227048i	−0.584410	−	0.811458i	$-0.698674\pi$
$701$	159.161	−	159.161i	0.227048	−	0.227048i	0.811458	+	0.584410i	$0.198674\pi$
$702$			619.757i			0.882845i
$703$	314.366	−	314.366i	0.447178	−	0.447178i
$704$	133.798			0.190054
$705$	−114.037	−	114.037i	−0.161755	−	0.161755i
$706$	−410.791	+	410.791i	−0.581857	+	0.581857i
$707$	−5.70474			−0.00806895
$708$			373.953i			0.528182i
$709$	463.429	+	463.429i	0.653638	+	0.653638i	0.953867	−	0.300229i	$-0.0970632\pi$
$709$	463.429	+	463.429i	0.653638	+	0.653638i	−0.300229	+	0.953867i	$0.597063\pi$
$710$	−131.646			−0.185416
$711$	−414.984			−0.583663
$712$	157.501	+	157.501i	0.221209	+	0.221209i
$713$	−190.299	+	190.299i	−0.266899	+	0.266899i
$714$			270.385i			0.378691i
$715$	384.194			0.537334
$716$	−360.377	+	360.377i	−0.503319	+	0.503319i
$717$	94.2211	+	94.2211i	0.131410	+	0.131410i
$718$	−560.088			−0.780066
$719$	601.498	−	601.498i	0.836576	−	0.836576i	−0.151831	−	0.988407i	$-0.548517\pi$
$719$	601.498	−	601.498i	0.836576	−	0.836576i	0.988407	+	0.151831i	$0.0485168\pi$
$720$			28.3983i			0.0394421i
$721$	349.353	+	349.353i	0.484540	+	0.484540i
$722$	772.414	−	772.414i	1.06983	−	1.06983i
$723$	10.0593			0.0139133
$724$	88.8639	+	88.8639i	0.122740	+	0.122740i
$725$	388.014	−	388.014i	0.535191	−	0.535191i
$726$			460.779i			0.634682i
$727$		−	485.676i		−	0.668055i	−0.942563	−	0.334028i	$-0.891592\pi$
$727$		−	485.676i		−	0.668055i	0.942563	−	0.334028i	$-0.108408\pi$
$728$	−148.032			−0.203341
$729$		−	594.758i		−	0.815854i
$730$	−81.6580	+	81.6580i	−0.111860	+	0.111860i
$731$	−1096.21	+	1096.21i	−1.49961	+	1.49961i
$732$	−179.899	+	179.899i	−0.245763	+	0.245763i
$733$	56.7078	−	56.7078i	0.0773640	−	0.0773640i	−0.667366	−	0.744730i	$-0.732578\pi$
$733$	56.7078	−	56.7078i	0.0773640	−	0.0773640i	0.744730	+	0.667366i	$0.232578\pi$
$734$	−651.872			−0.888109
$735$	80.9158	−	80.9158i	0.110090	−	0.110090i
$736$	−143.455	−	143.455i	−0.194911	−	0.194911i
$737$			905.398i			1.22849i
$738$	306.169	−	306.169i	0.414863	−	0.414863i
$739$	−93.1093	−	93.1093i	−0.125994	−	0.125994i	0.641298	−	0.767292i	$-0.278396\pi$
$739$	−93.1093	−	93.1093i	−0.125994	−	0.125994i	−0.767292	+	0.641298i	$0.778396\pi$
$740$		−	39.1796i		−	0.0529454i
$741$		−	1070.20i		−	1.44427i
$742$	182.980			0.246604
$743$	1213.32			1.63301			0.816503	−	0.577342i	$-0.195910\pi$
$743$	1213.32			1.63301			0.816503	+	0.577342i	$0.195910\pi$
$744$	−30.8093	+	30.8093i	−0.0414103	+	0.0414103i
$745$		−	341.856i		−	0.458868i
$746$			227.923i			0.305527i
$747$	−59.1351	−	59.1351i	−0.0791635	−	0.0791635i
$748$	−651.771	−	651.771i	−0.871351	−	0.871351i
$749$			480.217i			0.641144i
$750$			205.857i			0.274476i
$751$	310.835			0.413895			0.206947	−	0.978352i	$-0.433647\pi$
$751$	310.835			0.413895			0.206947	+	0.978352i	$0.433647\pi$
$752$	−211.833			−0.281693
$753$			476.627i			0.632971i
$754$			527.075i			0.699038i
$755$		−	88.2175i		−	0.116844i
$756$	191.298			0.253040
$757$	980.801	−	980.801i	1.29564	−	1.29564i	0.364399	−	0.931243i	$-0.381275\pi$
$757$	980.801	−	980.801i	1.29564	−	1.29564i	0.931243	−	0.364399i	$-0.118725\pi$
$758$	−169.614			−0.223765
$759$	870.671	−	870.671i	1.14713	−	1.14713i
$760$		−	141.258i		−	0.185866i
$761$	76.9778	−	76.9778i	0.101153	−	0.101153i	−0.654719	−	0.755872i	$-0.727213\pi$
$761$	76.9778	−	76.9778i	0.101153	−	0.101153i	0.755872	+	0.654719i	$0.227213\pi$
$762$	−249.694			−0.327682
$763$			439.284i			0.575732i
$764$	−59.3363			−0.0776653
$765$	138.337	−	138.337i	0.180833	−	0.180833i
$766$			924.290i			1.20665i
$767$	997.321	+	997.321i	1.30029	+	1.30029i
$768$	−23.2252	−	23.2252i	−0.0302412	−	0.0302412i
$769$		−	1169.72i		−	1.52109i	−0.649284	−	0.760546i	$-0.724931\pi$
$769$		−	1169.72i		−	1.52109i	0.649284	−	0.760546i	$-0.275069\pi$
$770$		−	118.588i		−	0.154010i
$771$		−	764.163i		−	0.991132i
$772$	203.732	+	203.732i	0.263902	+	0.263902i
$773$	−985.851			−1.27536			−0.637678	−	0.770303i	$-0.720105\pi$
$773$	−985.851			−1.27536			−0.637678	+	0.770303i	$0.720105\pi$
$774$	269.246	+	269.246i	0.347863	+	0.347863i
$775$	120.977	−	120.977i	0.156100	−	0.156100i
$776$	−75.7039	−	75.7039i	−0.0975566	−	0.0975566i
$777$	−91.6230			−0.117919
$778$	662.847	+	662.847i	0.851988	+	0.851988i
$779$	−1522.93	+	1522.93i	−1.95498	+	1.95498i
$780$	−66.6900	−	66.6900i	−0.0855000	−	0.0855000i
$781$	−742.100	−	742.100i	−0.950192	−	0.950192i
$782$			1397.62i			1.78724i
$783$		−	681.126i		−	0.869893i
$784$		−	150.307i		−	0.191719i
$785$	163.455	+	163.455i	0.208223	+	0.208223i
$786$		−	718.497i		−	0.914118i
$787$	874.742			1.11149			0.555744	−	0.831353i	$-0.312433\pi$
$787$	874.742			1.11149			0.555744	+	0.831353i	$0.312433\pi$
$788$	−314.696	−	314.696i	−0.399360	−	0.399360i
$789$	327.023	+	327.023i	0.414478	+	0.414478i
$790$	128.631	−	128.631i	0.162824	−	0.162824i
$791$			121.016i			0.152991i
$792$	−160.084	+	160.084i	−0.202127	+	0.202127i
$793$			959.569i			1.21005i
$794$	−328.344			−0.413532
$795$	82.4346	+	82.4346i	0.103691	+	0.103691i
$796$	640.121			0.804172
$797$	−56.4662	+	56.4662i	−0.0708484	+	0.0708484i	−0.741643	−	0.670795i	$-0.765953\pi$
$797$	−56.4662	+	56.4662i	−0.0708484	+	0.0708484i	0.670795	+	0.741643i	$0.265953\pi$
$798$	−330.337			−0.413956
$799$	1031.90	+	1031.90i	1.29149	+	1.29149i
$800$	91.1975	+	91.1975i	0.113997	+	0.113997i
$801$	−376.888			−0.470522
$802$			563.646i			0.702801i
$803$	−920.629			−1.14649
$804$	157.163	−	157.163i	0.195476	−	0.195476i
$805$	−127.147	+	127.147i	−0.157946	+	0.157946i
$806$			164.335i			0.203889i
$807$	−551.785	+	21.7438i	−0.683749	+	0.0269440i
$808$	−4.77407			−0.00590850
$809$	−1013.01	−	1013.01i	−1.25217	−	1.25217i	−0.954744	−	0.297429i	$-0.903871\pi$
$809$	−1013.01	−	1013.01i	−1.25217	−	1.25217i	−0.297429	−	0.954744i	$-0.596129\pi$
$810$	22.2857	+	22.2857i	0.0275132	+	0.0275132i
$811$			1520.11i			1.87436i	0.348844	+	0.937181i	$0.386574\pi$
$811$			1520.11i			1.87436i	−0.348844	+	0.937181i	$0.613426\pi$
$812$	162.690			0.200358
$813$		−	619.209i		−	0.761635i
$814$	220.860	−	220.860i	0.271326	−	0.271326i
$815$	95.5966	−	95.5966i	0.117296	−	0.117296i
$816$			226.274i			0.277297i
$817$	−1339.27	−	1339.27i	−1.63925	−	1.63925i
$818$		−	121.703i		−	0.148781i
$819$	177.115	−	177.115i	0.216258	−	0.216258i
$820$			189.804i			0.231468i
$821$	518.307			0.631311			0.315656	−	0.948874i	$-0.397776\pi$
$821$	518.307			0.631311			0.315656	+	0.948874i	$0.397776\pi$
$822$	370.976	+	370.976i	0.451309	+	0.451309i
$823$	−180.463			−0.219274			−0.109637	−	0.993972i	$-0.534969\pi$
$823$	−180.463			−0.219274			−0.109637	+	0.993972i	$0.534969\pi$
$824$	292.359	+	292.359i	0.354805	+	0.354805i
$825$	−553.505	+	553.505i	−0.670916	+	0.670916i
$826$	307.840	−	307.840i	0.372687	−	0.372687i
$827$			767.274i			0.927780i	0.885893	+	0.463890i	$0.153547\pi$
$827$			767.274i			0.927780i	−0.885893	+	0.463890i	$0.846453\pi$
$828$	343.277			0.414585
$829$	44.2063	−	44.2063i	0.0533249	−	0.0533249i	−0.679941	−	0.733266i	$-0.737995\pi$
$829$	44.2063	−	44.2063i	0.0533249	−	0.0533249i	0.733266	+	0.679941i	$0.237995\pi$
$830$	36.6597			0.0441683
$831$	−872.556			−1.05001
$832$	−123.882			−0.148897
$833$	−732.194	+	732.194i	−0.878984	+	0.878984i
$834$	−86.4105	+	86.4105i	−0.103610	+	0.103610i
$835$	113.717	+	113.717i	0.136188	+	0.136188i
$836$	796.285	−	796.285i	0.952494	−	0.952494i
$837$		−	212.366i		−	0.253723i
$838$	−454.438	+	454.438i	−0.542288	+	0.542288i
$839$	−256.099	−	256.099i	−0.305243	−	0.305243i	0.537818	−	0.843061i	$-0.319249\pi$
$839$	−256.099	−	256.099i	−0.305243	−	0.305243i	−0.843061	+	0.537818i	$0.819249\pi$
$840$	−20.5850	+	20.5850i	−0.0245059	+	0.0245059i
$841$			261.733i			0.311217i
$842$	119.783	−	119.783i	0.142260	−	0.142260i
$843$	259.845			0.308238
$844$	−409.638			−0.485353
$845$	−105.017			−0.124281
$846$	253.450	−	253.450i	0.299587	−	0.299587i
$847$	379.316	−	379.316i	0.447835	−	0.447835i
$848$	153.129			0.180576
$849$	515.419	+	515.419i	0.607089	+	0.607089i
$850$		−	888.502i		−	1.04530i
$851$	−473.600			−0.556522
$852$			257.634i			0.302387i
$853$	214.882	+	214.882i	0.251914	+	0.251914i	0.821755	−	0.569841i	$-0.192995\pi$
$853$	214.882	+	214.882i	0.251914	+	0.251914i	−0.569841	+	0.821755i	$0.692995\pi$
$854$	296.187			0.346823
$855$	169.010	+	169.010i	0.197672	+	0.197672i
$856$			401.874i			0.469479i
$857$	4.01980	+	4.01980i	0.00469054	+	0.00469054i	0.709448	−	0.704758i	$-0.248944\pi$
$857$	4.01980	+	4.01980i	0.00469054	+	0.00469054i	−0.704758	+	0.709448i	$0.748944\pi$
$858$		−	751.877i		−	0.876314i
$859$	−574.526			−0.668831			−0.334415	−	0.942426i	$-0.608539\pi$
$859$	−574.526			−0.668831			−0.334415	+	0.942426i	$0.608539\pi$
$860$	−166.914			−0.194086
$861$	443.863			0.515520
$862$			1014.79i			1.17725i
$863$			93.0275i			0.107796i	0.998546	+	0.0538978i	$0.0171645\pi$
$863$			93.0275i			0.107796i	−0.998546	+	0.0538978i	$0.982835\pi$
$864$	160.090			0.185289
$865$	−390.849			−0.451848
$866$	29.3204	−	29.3204i	0.0338572	−	0.0338572i
$867$	682.746	−	682.746i	0.787481	−	0.787481i
$868$	50.7247			0.0584386
$869$	1450.21			1.66883
$870$	73.2938	+	73.2938i	0.0842457	+	0.0842457i
$871$		−	838.298i		−	0.962454i
$872$			367.619i			0.421581i
$873$	181.154			0.207508
$874$	−1707.51			−1.95368
$875$	169.462	−	169.462i	0.193671	−	0.193671i
$876$	159.807	+	159.807i	0.182428	+	0.182428i
$877$	578.799			0.659976			0.329988	−	0.943985i	$-0.392955\pi$
$877$	578.799			0.659976			0.329988	+	0.943985i	$0.392955\pi$
$878$	−650.874	+	650.874i	−0.741314	+	0.741314i
$879$	38.3297	+	38.3297i	0.0436060	+	0.0436060i
$880$		−	99.2414i		−	0.112774i
$881$	−699.808	−	699.808i	−0.794334	−	0.794334i	0.187862	−	0.982195i	$-0.439844\pi$
$881$	−699.808	−	699.808i	−0.794334	−	0.794334i	−0.982195	+	0.187862i	$0.939844\pi$
$882$	179.837	+	179.837i	0.203897	+	0.203897i
$883$	623.282	+	623.282i	0.705869	+	0.705869i	0.965664	−	0.259795i	$-0.0836551\pi$
$883$	623.282	+	623.282i	0.705869	+	0.705869i	−0.259795	+	0.965664i	$0.583655\pi$
$884$	603.467	+	603.467i	0.682655	+	0.682655i
$885$	277.370			0.313413
$886$			559.094i			0.631031i
$887$	1414.07			1.59422			0.797109	−	0.603836i	$-0.206362\pi$
$887$	1414.07			1.59422			0.797109	+	0.603836i	$0.206362\pi$
$888$	−76.6755			−0.0863463
$889$	205.549	+	205.549i	0.231214	+	0.231214i
$890$	116.822	−	116.822i	0.131261	−	0.131261i
$891$			251.254i			0.281991i
$892$	−293.423	−	293.423i	−0.328950	−	0.328950i
$893$	−1260.70	+	1260.70i	−1.41176	+	1.41176i
$894$	−669.021			−0.748346
$895$	267.301	+	267.301i	0.298660	+	0.298660i
$896$			38.2382i			0.0426766i
$897$	−806.144	+	806.144i	−0.898711	+	0.898711i
$898$	487.472	+	487.472i	0.542842	+	0.542842i
$899$		−	180.608i		−	0.200898i
$900$	−218.229			−0.242477
$901$	−745.936	−	745.936i	−0.827898	−	0.827898i
$902$	−1069.94	+	1069.94i	−1.18619	+	1.18619i
$903$			390.334i			0.432264i
$904$			101.273i			0.112028i
$905$	65.9126	−	65.9126i	0.0728317	−	0.0728317i
$906$	−172.644			−0.190556
$907$			1601.45i			1.76566i	0.469697	+	0.882828i	$0.344363\pi$
$907$			1601.45i			1.76566i	−0.469697	+	0.882828i	$0.655637\pi$
$908$	−459.272	−	459.272i	−0.505806	−	0.505806i
$909$	5.71200	−	5.71200i	0.00628383	−	0.00628383i
$910$			109.799i			0.120658i
$911$	344.275	+	344.275i	0.377909	+	0.377909i	0.870347	−	0.492438i	$-0.163894\pi$
$911$	344.275	+	344.275i	0.377909	+	0.377909i	−0.492438	+	0.870347i	$0.663894\pi$
$912$	−276.445			−0.303120
$913$	206.655	+	206.655i	0.226347	+	0.226347i
$914$	−389.253	+	389.253i	−0.425878	+	0.425878i
$915$	133.436	+	133.436i	0.145831	+	0.145831i
$916$	−313.941	+	313.941i	−0.342731	+	0.342731i
$917$	−591.470	+	591.470i	−0.645005	+	0.645005i
$918$	−779.846	−	779.846i	−0.849506	−	0.849506i
$919$	373.791	−	373.791i	0.406737	−	0.406737i	−0.473862	−	0.880599i	$-0.657141\pi$
$919$	373.791	−	373.791i	0.406737	−	0.406737i	0.880599	+	0.473862i	$0.157141\pi$
$920$	−106.404	+	106.404i	−0.115657	+	0.115657i
$921$	28.1649	+	28.1649i	0.0305808	+	0.0305808i
$922$	−226.794			−0.245981
$923$	687.101	+	687.101i	0.744422	+	0.744422i
$924$	−232.079			−0.251168
$925$	301.079			0.325490
$926$	633.531			0.684159
$927$	−699.595			−0.754687
$928$	136.149			0.146712
$929$	800.114	+	800.114i	0.861264	+	0.861264i	0.991485	−	0.130221i	$-0.0415687\pi$
$929$	800.114	+	800.114i	0.861264	+	0.861264i	−0.130221	+	0.991485i	$0.541569\pi$
$930$	22.8520	+	22.8520i	0.0245721	+	0.0245721i
$931$	−894.540	−	894.540i	−0.960838	−	0.960838i
$932$	615.845			0.660778
$933$			294.931i			0.316111i
$934$			229.111i			0.245301i
$935$	−483.435	+	483.435i	−0.517043	+	0.517043i
$936$	148.220	−	148.220i	0.158355	−	0.158355i
$937$	−691.254	+	691.254i	−0.737731	+	0.737731i	−0.972138	−	0.234407i	$-0.924685\pi$
$937$	−691.254	+	691.254i	−0.737731	+	0.737731i	0.234407	+	0.972138i	$0.424685\pi$
$938$	−258.755			−0.275858
$939$	405.975	+	405.975i	0.432349	+	0.432349i
$940$			157.122i			0.167151i
$941$	−41.4249	−	41.4249i	−0.0440222	−	0.0440222i	0.684753	−	0.728775i	$-0.259910\pi$
$941$	−41.4249	−	41.4249i	−0.0440222	−	0.0440222i	−0.728775	+	0.684753i	$0.759910\pi$
$942$	319.886	−	319.886i	0.339582	−	0.339582i
$943$	2294.33			2.43301
$944$	257.618	−	257.618i	0.272901	−	0.272901i
$945$		−	141.891i		−	0.150149i
$946$	−940.911	−	940.911i	−0.994620	−	0.994620i
$947$	−1073.37	−	1073.37i	−1.13344	−	1.13344i	−0.989601	−	0.143843i	$-0.954054\pi$
$947$	−1073.37	−	1073.37i	−1.13344	−	1.13344i	−0.143843	−	0.989601i	$-0.545946\pi$
$948$	−251.734	−	251.734i	−0.265542	−	0.265542i
$949$	852.400			0.898208
$950$	1085.51			1.14264
$951$			1060.76i			1.11541i
$952$	186.270	−	186.270i	0.195662	−	0.195662i
$953$	−470.334	+	470.334i	−0.493530	+	0.493530i	−0.909417	−	0.415886i	$-0.863471\pi$
$953$	−470.334	+	470.334i	−0.493530	+	0.493530i	0.415886	+	0.909417i	$0.363471\pi$
$954$	−183.213	+	183.213i	−0.192047	+	0.192047i
$955$			44.0113i			0.0460851i
$956$		−	129.819i		−	0.135794i
$957$			826.330i			0.863458i
$958$		−	1218.08i		−	1.27148i
$959$		−	610.778i		−	0.636891i
$960$	−17.2267	+	17.2267i	−0.0179445	+	0.0179445i
$961$			904.689i			0.941404i
$962$	−204.491	+	204.491i	−0.212569	+	0.212569i
$963$	−480.827	−	480.827i	−0.499302	−	0.499302i
$964$	−6.92991	−	6.92991i	−0.00718870	−	0.00718870i
$965$	151.113	−	151.113i	0.156594	−	0.156594i
$966$	248.830	+	248.830i	0.257588	+	0.257588i
$967$	−731.642	−	731.642i	−0.756610	−	0.756610i	0.219094	−	0.975704i	$-0.429690\pi$
$967$	−731.642	−	731.642i	−0.756610	−	0.756610i	−0.975704	+	0.219094i	$0.929690\pi$
$968$	317.434	−	317.434i	0.327928	−	0.327928i
$969$	1346.65	+	1346.65i	1.38973	+	1.38973i
$970$	−56.1516	+	56.1516i	−0.0578882	+	0.0578882i
$971$		−	1669.22i		−	1.71907i	−0.511076	−	0.859536i	$-0.670753\pi$
$971$		−	1669.22i		−	1.71907i	0.511076	−	0.859536i	$-0.329247\pi$
$972$	−316.588	+	316.588i	−0.325708	+	0.325708i
$973$	142.267			0.146215
$974$	317.453	+	317.453i	0.325927	+	0.325927i
$975$	512.484	−	512.484i	0.525625	−	0.525625i
$976$	247.867			0.253962
$977$		−	786.373i		−	0.804886i	−0.915445	−	0.402443i	$-0.868161\pi$
$977$		−	786.373i		−	0.804886i	0.915445	−	0.402443i	$-0.131839\pi$
$978$	−187.085	−	187.085i	−0.191293	−	0.191293i
$979$	1317.08			1.34533
$980$	−111.487			−0.113762
$981$	−439.842	−	439.842i	−0.448361	−	0.448361i
$982$	714.712	−	714.712i	0.727813	−	0.727813i
$983$		−	1129.81i		−	1.14935i	−0.818382	−	0.574675i	$-0.805128\pi$
$983$		−	1129.81i		−	1.14935i	0.818382	−	0.574675i	$-0.194872\pi$
$984$	371.451			0.377491
$985$	−233.418	+	233.418i	−0.236973	+	0.236973i
$986$	−663.223	−	663.223i	−0.672640	−	0.672640i
$987$	367.435			0.372275
$988$	−737.271	+	737.271i	−0.746226	+	0.746226i
$989$			2017.64i			2.04008i
$990$	118.739	+	118.739i	0.119938	+	0.119938i
$991$	301.024	−	301.024i	0.303758	−	0.303758i	−0.538724	−	0.842482i	$-0.681093\pi$
$991$	301.024	−	301.024i	0.303758	−	0.303758i	0.842482	+	0.538724i	$0.181093\pi$
$992$	42.4494			0.0427917
$993$	−126.890	−	126.890i	−0.127785	−	0.127785i
$994$	212.085	−	212.085i	0.213365	−	0.213365i
$995$		−	474.794i		−	0.477180i
$996$		−	71.7440i		−	0.0720321i
$997$	−1487.60			−1.49207			−0.746037	−	0.665904i	$-0.768046\pi$
$997$	−1487.60			−1.49207			−0.746037	+	0.665904i	$0.768046\pi$
$998$		−	543.434i		−	0.544523i
$999$	264.259	−	264.259i	0.264524	−	0.264524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.3.c.a.187.8	✓	44
269.82	odd	4	inner	538.3.c.a.351.8	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.3.c.a.187.8	✓	44	1.1	even	1	trivial
538.3.c.a.351.8	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 $\F_{q}$
Belyi maps

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} +(-1.45158 - 1.45158i) q^{3} +2.00000i q^{4} +1.48345 q^{5} -2.90315i q^{6} +(-2.38989 + 2.38989i) q^{7} +(-2.00000 + 2.00000i) q^{8} -4.78586i q^{9} +(1.48345 + 1.48345i) q^{10} +16.7247i q^{11} +(2.90315 - 2.90315i) q^{12} -15.4852i q^{13} -4.77978 q^{14} +(-2.15334 - 2.15334i) q^{15} -4.00000 q^{16} +(19.4852 + 19.4852i) q^{17} +(4.78586 - 4.78586i) q^{18} +(-23.8056 + 23.8056i) q^{19} +2.96690i q^{20} +6.93821 q^{21} +(-16.7247 + 16.7247i) q^{22} +35.8637 q^{23} +5.80630 q^{24} -22.7994 q^{25} +(15.4852 - 15.4852i) q^{26} +(-20.0112 + 20.0112i) q^{27} +(-4.77978 - 4.77978i) q^{28} +(-17.0186 + 17.0186i) q^{29} -4.30668i q^{30} +(-5.30618 + 5.30618i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(24.2772 - 24.2772i) q^{33} +38.9705i q^{34} +(-3.54528 + 3.54528i) q^{35} +9.57171 q^{36} -13.2056 q^{37} -47.6112 q^{38} +(-22.4780 + 22.4780i) q^{39} +(-2.96690 + 2.96690i) q^{40} +63.9737 q^{41} +(6.93821 + 6.93821i) q^{42} +56.2586i q^{43} -33.4495 q^{44} -7.09959i q^{45} +(35.8637 + 35.8637i) q^{46} +52.9582 q^{47} +(5.80630 + 5.80630i) q^{48} +37.5769i q^{49} +(-22.7994 - 22.7994i) q^{50} -56.5686i q^{51} +30.9705 q^{52} -38.2821 q^{53} -40.0224 q^{54} +24.8103i q^{55} -9.55955i q^{56} +69.1113 q^{57} -34.0372 q^{58} +(-64.4046 + 64.4046i) q^{59} +(4.30668 - 4.30668i) q^{60} -61.9667 q^{61} -10.6124 q^{62} +(11.4377 + 11.4377i) q^{63} -8.00000i q^{64} -22.9716i q^{65} +48.5545 q^{66} +54.1353 q^{67} +(-38.9705 + 38.9705i) q^{68} +(-52.0588 - 52.0588i) q^{69} -7.09057 q^{70} +(-44.3714 + 44.3714i) q^{71} +(9.57171 + 9.57171i) q^{72} +55.0459i q^{73} +(-13.2056 - 13.2056i) q^{74} +(33.0950 + 33.0950i) q^{75} +(-47.6112 - 47.6112i) q^{76} +(-39.9703 - 39.9703i) q^{77} -44.9560 q^{78} -86.7105i q^{79} -5.93381 q^{80} +15.0229 q^{81} +(63.9737 + 63.9737i) q^{82} +(12.3562 - 12.3562i) q^{83} +13.8764i q^{84} +(28.9054 + 28.9054i) q^{85} +(-56.2586 + 56.2586i) q^{86} +49.4076 q^{87} +(-33.4495 - 33.4495i) q^{88} -78.7503i q^{89} +(7.09959 - 7.09959i) q^{90} +(37.0080 + 37.0080i) q^{91} +71.7273i q^{92} +15.4046 q^{93} +(52.9582 + 52.9582i) q^{94} +(-35.3145 + 35.3145i) q^{95} +11.6126i q^{96} +37.8520i q^{97} +(-37.5769 + 37.5769i) q^{98} +80.0422 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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