LMFDB - Embedded newform 538.3.c.a.187.1

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			187.1
Character	$\chi$	$=$	538.187
Dual form			538.3.c.a.351.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{2} +(-3.89974 - 3.89974i) q^{3} +2.00000i q^{4} -6.52679 q^{5} -7.79948i q^{6} +(-0.905272 + 0.905272i) q^{7} +(-2.00000 + 2.00000i) q^{8} +21.4159i q^{9} +(-6.52679 - 6.52679i) q^{10} +15.4536i q^{11} +(7.79948 - 7.79948i) q^{12} -12.6290i q^{13} -1.81054 q^{14} +(25.4528 + 25.4528i) q^{15} -4.00000 q^{16} +(-6.26998 - 6.26998i) q^{17} +(-21.4159 + 21.4159i) q^{18} +(6.97194 - 6.97194i) q^{19} -13.0536i q^{20} +7.06065 q^{21} +(-15.4536 + 15.4536i) q^{22} -16.3343 q^{23} +15.5990 q^{24} +17.5990 q^{25} +(12.6290 - 12.6290i) q^{26} +(48.4188 - 48.4188i) q^{27} +(-1.81054 - 1.81054i) q^{28} +(7.27465 - 7.27465i) q^{29} +50.9055i q^{30} +(15.4185 - 15.4185i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(60.2649 - 60.2649i) q^{33} -12.5400i q^{34} +(5.90852 - 5.90852i) q^{35} -42.8318 q^{36} +54.6130 q^{37} +13.9439 q^{38} +(-49.2498 + 49.2498i) q^{39} +(13.0536 - 13.0536i) q^{40} +53.6271 q^{41} +(7.06065 + 7.06065i) q^{42} -47.0638i q^{43} -30.9072 q^{44} -139.777i q^{45} +(-16.3343 - 16.3343i) q^{46} -30.3411 q^{47} +(15.5990 + 15.5990i) q^{48} +47.3610i q^{49} +(17.5990 + 17.5990i) q^{50} +48.9025i q^{51} +25.2580 q^{52} -44.1715 q^{53} +96.8376 q^{54} -100.862i q^{55} -3.62109i q^{56} -54.3775 q^{57} +14.5493 q^{58} +(24.8127 - 24.8127i) q^{59} +(-50.9055 + 50.9055i) q^{60} +26.4546 q^{61} +30.8370 q^{62} +(-19.3872 - 19.3872i) q^{63} -8.00000i q^{64} +82.4268i q^{65} +120.530 q^{66} +124.062 q^{67} +(12.5400 - 12.5400i) q^{68} +(63.6993 + 63.6993i) q^{69} +11.8170 q^{70} +(-9.09848 + 9.09848i) q^{71} +(-42.8318 - 42.8318i) q^{72} +115.086i q^{73} +(54.6130 + 54.6130i) q^{74} +(-68.6314 - 68.6314i) q^{75} +(13.9439 + 13.9439i) q^{76} +(-13.9897 - 13.9897i) q^{77} -98.4996 q^{78} -40.7905i q^{79} +26.1072 q^{80} -184.898 q^{81} +(53.6271 + 53.6271i) q^{82} +(11.4648 - 11.4648i) q^{83} +14.1213i q^{84} +(40.9228 + 40.9228i) q^{85} +(47.0638 - 47.0638i) q^{86} -56.7384 q^{87} +(-30.9072 - 30.9072i) q^{88} +127.857i q^{89} +(139.777 - 139.777i) q^{90} +(11.4327 + 11.4327i) q^{91} -32.6685i q^{92} -120.256 q^{93} +(-30.3411 - 30.3411i) q^{94} +(-45.5044 + 45.5044i) q^{95} +31.1979i q^{96} -53.6789i q^{97} +(-47.3610 + 47.3610i) q^{98} -330.952 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
$3$	−3.89974	−	3.89974i	−1.29991	−	1.29991i	−0.928446	−	0.371466i	$-0.878855\pi$
$3$	−3.89974	−	3.89974i	−1.29991	−	1.29991i	−0.371466	−	0.928446i	$-0.621145\pi$
$4$			2.00000i			0.500000i
$5$	−6.52679			−1.30536			−0.652679	−	0.757635i	$-0.726355\pi$
$5$	−6.52679			−1.30536			−0.652679	+	0.757635i	$0.726355\pi$
$6$		−	7.79948i		−	1.29991i
$7$	−0.905272	+	0.905272i	−0.129325	+	0.129325i	−0.768806	−	0.639482i	$-0.779149\pi$
$7$	−0.905272	+	0.905272i	−0.129325	+	0.129325i	0.639482	+	0.768806i	$0.279149\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$			21.4159i			2.37955i
$10$	−6.52679	−	6.52679i	−0.652679	−	0.652679i
$11$			15.4536i			1.40487i	0.711748	+	0.702435i	$0.247904\pi$
$11$			15.4536i			1.40487i	−0.711748	+	0.702435i	$0.752096\pi$
$12$	7.79948	−	7.79948i	0.649956	−	0.649956i
$13$		−	12.6290i		−	0.971461i	−0.874109	−	0.485731i	$-0.838554\pi$
$13$		−	12.6290i		−	0.971461i	0.874109	−	0.485731i	$-0.161446\pi$
$14$	−1.81054			−0.129325
$15$	25.4528	+	25.4528i	1.69685	+	1.69685i
$16$	−4.00000			−0.250000
$17$	−6.26998	−	6.26998i	−0.368822	−	0.368822i	0.498225	−	0.867048i	$-0.333985\pi$
$17$	−6.26998	−	6.26998i	−0.368822	−	0.368822i	−0.867048	+	0.498225i	$0.833985\pi$
$18$	−21.4159	+	21.4159i	−1.18977	+	1.18977i
$19$	6.97194	−	6.97194i	0.366944	−	0.366944i	−0.499417	−	0.866362i	$-0.666453\pi$
$19$	6.97194	−	6.97194i	0.366944	−	0.366944i	0.866362	+	0.499417i	$0.166453\pi$
$20$		−	13.0536i		−	0.652679i
$21$	7.06065			0.336221
$22$	−15.4536	+	15.4536i	−0.702435	+	0.702435i
$23$	−16.3343			−0.710185			−0.355092	−	0.934831i	$-0.615551\pi$
$23$	−16.3343			−0.710185			−0.355092	+	0.934831i	$0.615551\pi$
$24$	15.5990			0.649956
$25$	17.5990			0.703960
$26$	12.6290	−	12.6290i	0.485731	−	0.485731i
$27$	48.4188	−	48.4188i	1.79329	−	1.79329i
$28$	−1.81054	−	1.81054i	−0.0646623	−	0.0646623i
$29$	7.27465	−	7.27465i	0.250850	−	0.250850i	−0.570469	−	0.821319i	$-0.693239\pi$
$29$	7.27465	−	7.27465i	0.250850	−	0.250850i	0.821319	+	0.570469i	$0.193239\pi$
$30$			50.9055i			1.69685i
$31$	15.4185	−	15.4185i	0.497372	−	0.497372i	−0.413247	−	0.910619i	$-0.635605\pi$
$31$	15.4185	−	15.4185i	0.497372	−	0.497372i	0.910619	+	0.413247i	$0.135605\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	60.2649	−	60.2649i	1.82621	−	1.82621i
$34$		−	12.5400i		−	0.368822i
$35$	5.90852	−	5.90852i	0.168815	−	0.168815i
$36$	−42.8318			−1.18977
$37$	54.6130			1.47603			0.738014	−	0.674786i	$-0.235764\pi$
$37$	54.6130			1.47603			0.738014	+	0.674786i	$0.235764\pi$
$38$	13.9439			0.366944
$39$	−49.2498	+	49.2498i	−1.26282	+	1.26282i
$40$	13.0536	−	13.0536i	0.326340	−	0.326340i
$41$	53.6271			1.30798			0.653989	−	0.756504i	$-0.273094\pi$
$41$	53.6271			1.30798			0.653989	+	0.756504i	$0.273094\pi$
$42$	7.06065	+	7.06065i	0.168111	+	0.168111i
$43$		−	47.0638i		−	1.09451i	−0.836967	−	0.547253i	$-0.815673\pi$
$43$		−	47.0638i		−	1.09451i	0.836967	−	0.547253i	$-0.184327\pi$
$44$	−30.9072			−0.702435
$45$		−	139.777i		−	3.10616i
$46$	−16.3343	−	16.3343i	−0.355092	−	0.355092i
$47$	−30.3411			−0.645555			−0.322778	−	0.946475i	$-0.604617\pi$
$47$	−30.3411			−0.645555			−0.322778	+	0.946475i	$0.604617\pi$
$48$	15.5990	+	15.5990i	0.324978	+	0.324978i
$49$			47.3610i			0.966550i
$50$	17.5990	+	17.5990i	0.351980	+	0.351980i
$51$			48.9025i			0.958873i
$52$	25.2580			0.485731
$53$	−44.1715			−0.833424			−0.416712	−	0.909039i	$-0.636818\pi$
$53$	−44.1715			−0.833424			−0.416712	+	0.909039i	$0.636818\pi$
$54$	96.8376			1.79329
$55$		−	100.862i		−	1.83386i
$56$		−	3.62109i		−	0.0646623i
$57$	−54.3775			−0.953991
$58$	14.5493			0.250850
$59$	24.8127	−	24.8127i	0.420555	−	0.420555i	−0.464840	−	0.885395i	$-0.653888\pi$
$59$	24.8127	−	24.8127i	0.420555	−	0.420555i	0.885395	+	0.464840i	$0.153888\pi$
$60$	−50.9055	+	50.9055i	−0.848426	+	0.848426i
$61$	26.4546			0.433681			0.216841	−	0.976207i	$-0.430425\pi$
$61$	26.4546			0.433681			0.216841	+	0.976207i	$0.430425\pi$
$62$	30.8370			0.497372
$63$	−19.3872	−	19.3872i	−0.307734	−	0.307734i
$64$		−	8.00000i		−	0.125000i
$65$			82.4268i			1.26810i
$66$	120.530			1.82621
$67$	124.062			1.85167			0.925835	−	0.377927i	$-0.123363\pi$
$67$	124.062			1.85167			0.925835	+	0.377927i	$0.123363\pi$
$68$	12.5400	−	12.5400i	0.184411	−	0.184411i
$69$	63.6993	+	63.6993i	0.923178	+	0.923178i
$70$	11.8170			0.168815
$71$	−9.09848	+	9.09848i	−0.128148	+	0.128148i	−0.768272	−	0.640124i	$-0.778883\pi$
$71$	−9.09848	+	9.09848i	−0.128148	+	0.128148i	0.640124	+	0.768272i	$0.278883\pi$
$72$	−42.8318	−	42.8318i	−0.594887	−	0.594887i
$73$			115.086i			1.57652i	0.615343	+	0.788259i	$0.289017\pi$
$73$			115.086i			1.57652i	−0.615343	+	0.788259i	$0.710983\pi$
$74$	54.6130	+	54.6130i	0.738014	+	0.738014i
$75$	−68.6314	−	68.6314i	−0.915086	−	0.915086i
$76$	13.9439	+	13.9439i	0.183472	+	0.183472i
$77$	−13.9897	−	13.9897i	−0.181684	−	0.181684i
$78$	−98.4996			−1.26282
$79$		−	40.7905i		−	0.516336i	−0.966100	−	0.258168i	$-0.916881\pi$
$79$		−	40.7905i		−	0.516336i	0.966100	−	0.258168i	$-0.0831188\pi$
$80$	26.1072			0.326340
$81$	−184.898			−2.28269
$82$	53.6271	+	53.6271i	0.653989	+	0.653989i
$83$	11.4648	−	11.4648i	0.138131	−	0.138131i	−0.634661	−	0.772791i	$-0.718860\pi$
$83$	11.4648	−	11.4648i	0.138131	−	0.138131i	0.772791	+	0.634661i	$0.218860\pi$
$84$			14.1213i			0.168111i
$85$	40.9228	+	40.9228i	0.481445	+	0.481445i
$86$	47.0638	−	47.0638i	0.547253	−	0.547253i
$87$	−56.7384			−0.652166
$88$	−30.9072	−	30.9072i	−0.351218	−	0.351218i
$89$			127.857i			1.43659i	0.695738	+	0.718295i	$0.255077\pi$
$89$			127.857i			1.43659i	−0.695738	+	0.718295i	$0.744923\pi$
$90$	139.777	−	139.777i	1.55308	−	1.55308i
$91$	11.4327	+	11.4327i	0.125634	+	0.125634i
$92$		−	32.6685i		−	0.355092i
$93$	−120.256			−1.29308
$94$	−30.3411	−	30.3411i	−0.322778	−	0.322778i
$95$	−45.5044	+	45.5044i	−0.478994	+	0.478994i
$96$			31.1979i			0.324978i
$97$		−	53.6789i		−	0.553391i	−0.960958	−	0.276695i	$-0.910761\pi$
$97$		−	53.6789i		−	0.553391i	0.960958	−	0.276695i	$-0.0892393\pi$
$98$	−47.3610	+	47.3610i	−0.483275	+	0.483275i
$99$	−330.952			−3.34295
$100$			35.1980i			0.351980i
$101$	93.6070	+	93.6070i	0.926802	+	0.926802i	0.997498	−	0.0706962i	$-0.0225221\pi$
$101$	93.6070	+	93.6070i	0.926802	+	0.926802i	−0.0706962	+	0.997498i	$0.522522\pi$
$102$	−48.9025	+	48.9025i	−0.479437	+	0.479437i
$103$		−	138.512i		−	1.34478i	−0.740197	−	0.672390i	$-0.765268\pi$
$103$		−	138.512i		−	1.34478i	0.740197	−	0.672390i	$-0.234732\pi$
$104$	25.2580	+	25.2580i	0.242865	+	0.242865i
$105$	−46.0834			−0.438889
$106$	−44.1715	−	44.1715i	−0.416712	−	0.416712i
$107$	3.88684	−	3.88684i	0.0363256	−	0.0363256i	−0.688711	−	0.725036i	$-0.741823\pi$
$107$	3.88684	−	3.88684i	0.0363256	−	0.0363256i	0.725036	+	0.688711i	$0.241823\pi$
$108$	96.8376	+	96.8376i	0.896645	+	0.896645i
$109$	−70.6901	+	70.6901i	−0.648533	+	0.648533i	−0.952639	−	0.304105i	$-0.901643\pi$
$109$	−70.6901	+	70.6901i	−0.648533	+	0.648533i	0.304105	+	0.952639i	$0.401643\pi$
$110$	100.862	−	100.862i	0.916930	−	0.916930i
$111$	−212.976	−	212.976i	−1.91871	−	1.91871i
$112$	3.62109	−	3.62109i	0.0323311	−	0.0323311i
$113$	92.2740	−	92.2740i	0.816584	−	0.816584i	−0.169027	−	0.985611i	$-0.554063\pi$
$113$	92.2740	−	92.2740i	0.816584	−	0.816584i	0.985611	+	0.169027i	$0.0540626\pi$
$114$	−54.3775	−	54.3775i	−0.476996	−	0.476996i
$115$	106.610			0.927045
$116$	14.5493	+	14.5493i	0.125425	+	0.125425i
$117$	270.462			2.31164
$118$	49.6255			0.420555
$119$	11.3521			0.0953955
$120$	−101.811			−0.848426
$121$	−117.813			−0.973661
$122$	26.4546	+	26.4546i	0.216841	+	0.216841i
$123$	−209.132	−	209.132i	−1.70026	−	1.70026i
$124$	30.8370	+	30.8370i	0.248686	+	0.248686i
$125$	48.3048			0.386439
$126$		−	38.7745i		−	0.307734i
$127$			111.655i			0.879176i	0.898200	+	0.439588i	$0.144876\pi$
$127$			111.655i			0.879176i	−0.898200	+	0.439588i	$0.855124\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$	−183.536	+	183.536i	−1.42276	+	1.42276i
$130$	−82.4268	+	82.4268i	−0.634052	+	0.634052i
$131$	110.923			0.846738			0.423369	−	0.905957i	$-0.360847\pi$
$131$	110.923			0.846738			0.423369	+	0.905957i	$0.360847\pi$
$132$	120.530	+	120.530i	0.913105	+	0.913105i
$133$			12.6230i			0.0949099i
$134$	124.062	+	124.062i	0.925835	+	0.925835i
$135$	−316.019	+	316.019i	−2.34088	+	2.34088i
$136$	25.0799			0.184411
$137$	58.1590	−	58.1590i	0.424518	−	0.424518i	−0.462238	−	0.886756i	$-0.652953\pi$
$137$	58.1590	−	58.1590i	0.424518	−	0.424518i	0.886756	+	0.462238i	$0.152953\pi$
$138$			127.399i			0.923178i
$139$	−79.6194	−	79.6194i	−0.572801	−	0.572801i	0.360109	−	0.932910i	$-0.382739\pi$
$139$	−79.6194	−	79.6194i	−0.572801	−	0.572801i	−0.932910	+	0.360109i	$0.882739\pi$
$140$	11.8170	+	11.8170i	0.0844074	+	0.0844074i
$141$	118.322	+	118.322i	0.839165	+	0.839165i
$142$	−18.1970			−0.128148
$143$	195.163			1.36478
$144$		−	85.6637i		−	0.594887i
$145$	−47.4801	+	47.4801i	−0.327449	+	0.327449i
$146$	−115.086	+	115.086i	−0.788259	+	0.788259i
$147$	184.695	−	184.695i	1.25643	−	1.25643i
$148$			109.226i			0.738014i
$149$			214.603i			1.44029i	0.693823	+	0.720145i	$0.255925\pi$
$149$			214.603i			1.44029i	−0.693823	+	0.720145i	$0.744075\pi$
$150$		−	137.263i		−	0.915086i
$151$			173.292i			1.14763i	0.818986	+	0.573813i	$0.194536\pi$
$151$			173.292i			1.14763i	−0.818986	+	0.573813i	$0.805464\pi$
$152$			27.8878i			0.183472i
$153$	134.277	−	134.277i	0.877629	−	0.877629i
$154$		−	27.9794i		−	0.181684i
$155$	−100.633	+	100.633i	−0.649248	+	0.649248i
$156$	−98.4996	−	98.4996i	−0.631408	−	0.631408i
$157$	−156.060	−	156.060i	−0.994013	−	0.994013i	0.00596899	−	0.999982i	$-0.498100\pi$
$157$	−156.060	−	156.060i	−0.994013	−	0.994013i	−0.999982	+	0.00596899i	$0.998100\pi$
$158$	40.7905	−	40.7905i	0.258168	−	0.258168i
$159$	172.257	+	172.257i	1.08338	+	1.08338i
$160$	26.1072	+	26.1072i	0.163170	+	0.163170i
$161$	14.7869	−	14.7869i	0.0918444	−	0.0918444i
$162$	−184.898	−	184.898i	−1.14135	−	1.14135i
$163$	52.8516	−	52.8516i	0.324243	−	0.324243i	−0.526149	−	0.850392i	$-0.676365\pi$
$163$	52.8516	−	52.8516i	0.324243	−	0.324243i	0.850392	+	0.526149i	$0.176365\pi$
$164$			107.254i			0.653989i
$165$	−393.336	+	393.336i	−2.38386	+	2.38386i
$166$	22.9297			0.138131
$167$	−53.6813	−	53.6813i	−0.321445	−	0.321445i	0.527876	−	0.849321i	$-0.322988\pi$
$167$	−53.6813	−	53.6813i	−0.321445	−	0.321445i	−0.849321	+	0.527876i	$0.822988\pi$
$168$	−14.1213	+	14.1213i	−0.0840553	+	0.0840553i
$169$	9.50839			0.0562627
$170$			81.8456i			0.481445i
$171$	149.311	+	149.311i	0.873161	+	0.873161i
$172$	94.1276			0.547253
$173$	−46.2648			−0.267427			−0.133713	−	0.991020i	$-0.542690\pi$
$173$	−46.2648			−0.267427			−0.133713	+	0.991020i	$0.542690\pi$
$174$	−56.7384	−	56.7384i	−0.326083	−	0.326083i
$175$	−15.9319	+	15.9319i	−0.0910393	+	0.0910393i
$176$		−	61.8143i		−	0.351218i
$177$	−193.526			−1.09337
$178$	−127.857	+	127.857i	−0.718295	+	0.718295i
$179$	83.7868	+	83.7868i	0.468083	+	0.468083i	0.901293	−	0.433210i	$-0.142619\pi$
$179$	83.7868	+	83.7868i	0.468083	+	0.468083i	−0.433210	+	0.901293i	$0.642619\pi$
$180$	279.554			1.55308
$181$	142.813	−	142.813i	0.789025	−	0.789025i	−0.192310	−	0.981334i	$-0.561598\pi$
$181$	142.813	−	142.813i	0.789025	−	0.789025i	0.981334	+	0.192310i	$0.0615978\pi$
$182$			22.8654i			0.125634i
$183$	−103.166	−	103.166i	−0.563748	−	0.563748i
$184$	32.6685	−	32.6685i	0.177546	−	0.177546i
$185$	−356.448			−1.92674
$186$	−120.256	−	120.256i	−0.646540	−	0.646540i
$187$	96.8935	−	96.8935i	0.518147	−	0.518147i
$188$		−	60.6822i		−	0.322778i
$189$			87.6644i			0.463833i
$190$	−91.0088			−0.478994
$191$		−	267.738i		−	1.40177i	−0.713274	−	0.700885i	$-0.752789\pi$
$191$		−	267.738i		−	1.40177i	0.713274	−	0.700885i	$-0.247211\pi$
$192$	−31.1979	+	31.1979i	−0.162489	+	0.162489i
$193$	84.3735	−	84.3735i	0.437168	−	0.437168i	−0.453890	−	0.891058i	$-0.649964\pi$
$193$	84.3735	−	84.3735i	0.437168	−	0.437168i	0.891058	+	0.453890i	$0.149964\pi$
$194$	53.6789	−	53.6789i	0.276695	−	0.276695i
$195$	321.443	−	321.443i	1.64843	−	1.64843i
$196$	−94.7219			−0.483275
$197$	259.612	−	259.612i	1.31783	−	1.31783i	0.402338	−	0.915491i	$-0.368198\pi$
$197$	259.612	−	259.612i	1.31783	−	1.31783i	0.915491	−	0.402338i	$-0.131802\pi$
$198$	−330.952	−	330.952i	−1.67148	−	1.67148i
$199$			81.2115i			0.408098i	0.978961	+	0.204049i	$0.0654102\pi$
$199$			81.2115i			0.408098i	−0.978961	+	0.204049i	$0.934590\pi$
$200$	−35.1980	+	35.1980i	−0.175990	+	0.175990i
$201$	−483.809	−	483.809i	−2.40701	−	2.40701i
$202$			187.214i			0.926802i
$203$			13.1711i			0.0648821i
$204$	−97.8050			−0.479437
$205$	−350.013			−1.70738
$206$	138.512	−	138.512i	0.672390	−	0.672390i
$207$		−	349.813i		−	1.68992i
$208$			50.5160i			0.242865i
$209$	107.741	+	107.741i	0.515509	+	0.515509i
$210$	−46.0834	−	46.0834i	−0.219445	−	0.219445i
$211$		−	402.369i		−	1.90696i	−0.301456	−	0.953480i	$-0.597473\pi$
$211$		−	402.369i		−	1.90696i	0.301456	−	0.953480i	$-0.402527\pi$
$212$		−	88.3429i		−	0.416712i
$213$	70.9634			0.333161
$214$	7.77369			0.0363256
$215$			307.175i			1.42872i
$216$			193.675i			0.896645i
$217$			27.9159i			0.128645i
$218$	−141.380			−0.648533
$219$	448.805	−	448.805i	2.04934	−	2.04934i
$220$	201.724			0.916930
$221$	−79.1835	+	79.1835i	−0.358296	+	0.358296i
$222$		−	425.953i		−	1.91871i
$223$	−259.449	+	259.449i	−1.16345	+	1.16345i	−0.179734	+	0.983715i	$0.557524\pi$
$223$	−259.449	+	259.449i	−1.16345	+	1.16345i	−0.983715	+	0.179734i	$0.942476\pi$
$224$	7.24218			0.0323311
$225$			376.898i			1.67510i
$226$	184.548			0.816584
$227$	−215.701	+	215.701i	−0.950225	+	0.950225i	−0.998819	−	0.0485937i	$-0.984526\pi$
$227$	−215.701	+	215.701i	−0.950225	+	0.950225i	0.0485937	+	0.998819i	$0.484526\pi$
$228$		−	108.755i		−	0.476996i
$229$	151.547	+	151.547i	0.661776	+	0.661776i	0.955798	−	0.294023i	$-0.0949941\pi$
$229$	151.547	+	151.547i	0.661776	+	0.661776i	−0.294023	+	0.955798i	$0.594994\pi$
$230$	106.610	+	106.610i	0.463523	+	0.463523i
$231$			109.112i			0.472347i
$232$			29.0986i			0.125425i
$233$			349.895i			1.50170i	0.660475	+	0.750848i	$0.270355\pi$
$233$			349.895i			1.50170i	−0.660475	+	0.750848i	$0.729645\pi$
$234$	270.462	+	270.462i	1.15582	+	1.15582i
$235$	198.030			0.842680
$236$	49.6255	+	49.6255i	0.210277	+	0.210277i
$237$	−159.072	+	159.072i	−0.671192	+	0.671192i
$238$	11.3521	+	11.3521i	0.0476978	+	0.0476978i
$239$	273.894			1.14600			0.573000	−	0.819555i	$-0.305780\pi$
$239$	273.894			1.14600			0.573000	+	0.819555i	$0.305780\pi$
$240$	−101.811	−	101.811i	−0.424213	−	0.424213i
$241$	253.168	−	253.168i	1.05049	−	1.05049i	0.0518357	−	0.998656i	$-0.483493\pi$
$241$	253.168	−	253.168i	1.05049	−	1.05049i	0.998656	−	0.0518357i	$-0.0165072\pi$
$242$	−117.813	−	117.813i	−0.486831	−	0.486831i
$243$	285.285	+	285.285i	1.17401	+	1.17401i
$244$			52.9091i			0.216841i
$245$		−	309.115i		−	1.26169i
$246$		−	418.263i		−	1.70026i
$247$	−88.0487	−	88.0487i	−0.356472	−	0.356472i
$248$			61.6741i			0.248686i
$249$	−89.4197			−0.359115
$250$	48.3048	+	48.3048i	0.193219	+	0.193219i
$251$	−255.977	−	255.977i	−1.01983	−	1.01983i	−0.999799	−	0.0200305i	$-0.993624\pi$
$251$	−255.977	−	255.977i	−1.01983	−	1.01983i	−0.0200305	−	0.999799i	$-0.506376\pi$
$252$	38.7745	−	38.7745i	0.153867	−	0.153867i
$253$		−	252.423i		−	0.997718i
$254$	−111.655	+	111.655i	−0.439588	+	0.439588i
$255$		−	319.177i		−	1.25167i
$256$	16.0000			0.0625000
$257$	−306.383	−	306.383i	−1.19215	−	1.19215i	−0.976462	−	0.215692i	$-0.930799\pi$
$257$	−306.383	−	306.383i	−1.19215	−	1.19215i	−0.215692	−	0.976462i	$-0.569201\pi$
$258$	−367.073			−1.42276
$259$	−49.4396	+	49.4396i	−0.190887	+	0.190887i
$260$	−164.854			−0.634052
$261$	155.793	+	155.793i	0.596909	+	0.596909i
$262$	110.923	+	110.923i	0.423369	+	0.423369i
$263$	−379.430			−1.44270			−0.721350	−	0.692571i	$-0.756478\pi$
$263$	−379.430			−1.44270			−0.721350	+	0.692571i	$0.756478\pi$
$264$			241.060i			0.913105i
$265$	288.298			1.08792
$266$	−12.6230	+	12.6230i	−0.0474549	+	0.0474549i
$267$	498.607	−	498.607i	1.86744	−	1.86744i
$268$			248.124i			0.925835i
$269$	46.4159	+	264.965i	0.172550	+	0.985001i
$269$	46.4159	+	264.965i	0.172550	+	0.985001i
$270$	−632.039			−2.34088
$271$	−112.559	−	112.559i	−0.415346	−	0.415346i	0.468250	−	0.883596i	$-0.344885\pi$
$271$	−112.559	−	112.559i	−0.415346	−	0.415346i	−0.883596	+	0.468250i	$0.844885\pi$
$272$	25.0799	+	25.0799i	0.0922055	+	0.0922055i
$273$		−	89.1689i		−	0.326626i
$274$	116.318			0.424518
$275$			271.967i			0.988972i
$276$	−127.399	+	127.399i	−0.461589	+	0.461589i
$277$	117.612	−	117.612i	0.424591	−	0.424591i	−0.462190	−	0.886781i	$-0.652936\pi$
$277$	117.612	−	117.612i	0.424591	−	0.424591i	0.886781	+	0.462190i	$0.152936\pi$
$278$		−	159.239i		−	0.572801i
$279$	330.202	+	330.202i	1.18352	+	1.18352i
$280$			23.6341i			0.0844074i
$281$	−214.416	+	214.416i	−0.763046	+	0.763046i	−0.976872	−	0.213825i	$-0.931408\pi$
$281$	−214.416	+	214.416i	−0.763046	+	0.763046i	0.213825	+	0.976872i	$0.431408\pi$
$282$			236.645i			0.839165i
$283$	273.475			0.966341			0.483171	−	0.875526i	$-0.339485\pi$
$283$	273.475			0.966341			0.483171	+	0.875526i	$0.339485\pi$
$284$	−18.1970	−	18.1970i	−0.0640738	−	0.0640738i
$285$	354.911			1.24530
$286$	195.163	+	195.163i	0.682389	+	0.682389i
$287$	−48.5471	+	48.5471i	−0.169154	+	0.169154i
$288$	85.6637	−	85.6637i	0.297443	−	0.297443i
$289$		−	210.375i		−	0.727941i
$290$	−94.9602			−0.327449
$291$	−209.334	+	209.334i	−0.719359	+	0.719359i
$292$	−230.172			−0.788259
$293$	473.642			1.61652			0.808262	−	0.588822i	$-0.200408\pi$
$293$	473.642			1.61652			0.808262	+	0.588822i	$0.200408\pi$
$294$	369.391			1.25643
$295$	−161.947	+	161.947i	−0.548975	+	0.548975i
$296$	−109.226	+	109.226i	−0.369007	+	0.369007i
$297$	748.244	+	748.244i	2.51934	+	2.51934i
$298$	−214.603	+	214.603i	−0.720145	+	0.720145i
$299$			206.285i			0.689917i
$300$	137.263	−	137.263i	0.457543	−	0.457543i
$301$	42.6055	+	42.6055i	0.141547	+	0.141547i
$302$	−173.292	+	173.292i	−0.573813	+	0.573813i
$303$		−	730.085i		−	2.40952i
$304$	−27.8878	+	27.8878i	−0.0917361	+	0.0917361i
$305$	−172.663			−0.566110
$306$	268.555			0.877629
$307$	190.785			0.621451			0.310725	−	0.950500i	$-0.399428\pi$
$307$	190.785			0.621451			0.310725	+	0.950500i	$0.399428\pi$
$308$	27.9794	−	27.9794i	0.0908421	−	0.0908421i
$309$	−540.162	+	540.162i	−1.74810	+	1.74810i
$310$	−201.267			−0.649248
$311$	−90.1837	−	90.1837i	−0.289980	−	0.289980i	0.547092	−	0.837072i	$-0.315735\pi$
$311$	−90.1837	−	90.1837i	−0.289980	−	0.289980i	−0.837072	+	0.547092i	$0.815735\pi$
$312$		−	196.999i		−	0.631408i
$313$	248.677			0.794496			0.397248	−	0.917711i	$-0.369965\pi$
$313$	248.677			0.794496			0.397248	+	0.917711i	$0.369965\pi$
$314$		−	312.120i		−	0.994013i
$315$	126.536	+	126.536i	0.401703	+	0.401703i
$316$	81.5811			0.258168
$317$	126.242	+	126.242i	0.398238	+	0.398238i	0.877611	−	0.479373i	$-0.159136\pi$
$317$	126.242	+	126.242i	0.398238	+	0.398238i	−0.479373	+	0.877611i	$0.659136\pi$
$318$			344.514i			1.08338i
$319$	112.419	+	112.419i	0.352412	+	0.352412i
$320$			52.2143i			0.163170i
$321$	−30.3154			−0.0944403
$322$	29.5739			0.0918444
$323$	−87.4278			−0.270674
$324$		−	369.796i		−	1.14135i
$325$		−	222.258i		−	0.683870i
$326$	105.703			0.324243
$327$	551.346			1.68607
$328$	−107.254	+	107.254i	−0.326994	+	0.326994i
$329$	27.4669	−	27.4669i	0.0834861	−	0.0834861i
$330$	−786.673			−2.38386
$331$	584.868			1.76697			0.883487	−	0.468456i	$-0.155190\pi$
$331$	584.868			1.76697			0.883487	+	0.468456i	$0.155190\pi$
$332$	22.9297	+	22.9297i	0.0690653	+	0.0690653i
$333$			1169.59i			3.51228i
$334$		−	107.363i		−	0.321445i
$335$	−809.726			−2.41709
$336$	−28.2426			−0.0840553
$337$	−387.839	+	387.839i	−1.15086	+	1.15086i	−0.164475	+	0.986381i	$0.552593\pi$
$337$	−387.839	+	387.839i	−1.15086	+	1.15086i	−0.986381	+	0.164475i	$0.947407\pi$
$338$	9.50839	+	9.50839i	0.0281313	+	0.0281313i
$339$	−719.689			−2.12298
$340$	−81.8456	+	81.8456i	−0.240722	+	0.240722i
$341$	238.271	+	238.271i	0.698743	+	0.698743i
$342$			298.621i			0.873161i
$343$	−87.2329	−	87.2329i	−0.254323	−	0.254323i
$344$	94.1276	+	94.1276i	0.273627	+	0.273627i
$345$	−415.752	−	415.752i	−1.20508	−	1.20508i
$346$	−46.2648	−	46.2648i	−0.133713	−	0.133713i
$347$	304.297			0.876936			0.438468	−	0.898747i	$-0.355521\pi$
$347$	304.297			0.876936			0.438468	+	0.898747i	$0.355521\pi$
$348$		−	113.477i		−	0.326083i
$349$	−307.304			−0.880528			−0.440264	−	0.897868i	$-0.645115\pi$
$349$	−307.304			−0.880528			−0.440264	+	0.897868i	$0.645115\pi$
$350$	−31.8637			−0.0910393
$351$	−611.481	−	611.481i	−1.74211	−	1.74211i
$352$	61.8143	−	61.8143i	0.175609	−	0.175609i
$353$			567.201i			1.60680i	0.595438	+	0.803401i	$0.296978\pi$
$353$			567.201i			1.60680i	−0.595438	+	0.803401i	$0.703022\pi$
$354$	−193.526	−	193.526i	−0.546685	−	0.546685i
$355$	59.3839	−	59.3839i	0.167278	−	0.167278i
$356$	−255.713			−0.718295
$357$	−44.2701	−	44.2701i	−0.124006	−	0.124006i
$358$			167.574i			0.468083i
$359$	377.586	−	377.586i	1.05177	−	1.05177i	0.0531874	−	0.998585i	$-0.483062\pi$
$359$	377.586	−	377.586i	1.05177	−	1.05177i	0.998585	−	0.0531874i	$-0.0169381\pi$
$360$	279.554	+	279.554i	0.776540	+	0.776540i
$361$			263.784i			0.730704i
$362$	285.627			0.789025
$363$	459.440	+	459.440i	1.26567	+	1.26567i
$364$	−22.8654	+	22.8654i	−0.0628169	+	0.0628169i
$365$		−	751.141i		−	2.05792i
$366$		−	206.332i		−	0.563748i
$367$	430.806	−	430.806i	1.17386	−	1.17386i	0.192576	−	0.981282i	$-0.438316\pi$
$367$	430.806	−	430.806i	1.17386	−	1.17386i	0.981282	−	0.192576i	$-0.0616843\pi$
$368$	65.3370			0.177546
$369$			1148.47i			3.11239i
$370$	−356.448	−	356.448i	−0.963372	−	0.963372i
$371$	39.9872	−	39.9872i	0.107782	−	0.107782i
$372$		−	240.513i		−	0.646540i
$373$	334.180	+	334.180i	0.895926	+	0.895926i	0.995073	−	0.0991469i	$-0.0316114\pi$
$373$	334.180	+	334.180i	0.895926	+	0.895926i	−0.0991469	+	0.995073i	$0.531611\pi$
$374$	193.787			0.518147
$375$	−188.376	−	188.376i	−0.502337	−	0.502337i
$376$	60.6822	−	60.6822i	0.161389	−	0.161389i
$377$	−91.8715	−	91.8715i	−0.243691	−	0.243691i
$378$	−87.6644	+	87.6644i	−0.231916	+	0.231916i
$379$	−463.927	+	463.927i	−1.22408	+	1.22408i	−0.257913	+	0.966168i	$0.583035\pi$
$379$	−463.927	+	463.927i	−1.22408	+	1.22408i	−0.966168	+	0.257913i	$0.916965\pi$
$380$	−91.0088	−	91.0088i	−0.239497	−	0.239497i
$381$	435.427	−	435.427i	1.14285	−	1.14285i
$382$	267.738	−	267.738i	0.700885	−	0.700885i
$383$	−15.9896	−	15.9896i	−0.0417483	−	0.0417483i	0.685924	−	0.727673i	$-0.259398\pi$
$383$	−15.9896	−	15.9896i	−0.0417483	−	0.0417483i	−0.727673	+	0.685924i	$0.759398\pi$
$384$	−62.3958			−0.162489
$385$	91.3078	+	91.3078i	0.237163	+	0.237163i
$386$	168.747			0.437168
$387$	1007.91			2.60443
$388$	107.358			0.276695
$389$	−599.214			−1.54040			−0.770198	−	0.637804i	$-0.779843\pi$
$389$	−599.214			−1.54040			−0.770198	+	0.637804i	$0.779843\pi$
$390$	642.886			1.64843
$391$	102.415	+	102.415i	0.261932	+	0.261932i
$392$	−94.7219	−	94.7219i	−0.241638	−	0.241638i
$393$	−432.570	−	432.570i	−1.10069	−	1.10069i
$394$	519.225			1.31783
$395$			266.231i			0.674003i
$396$		−	661.905i		−	1.67148i
$397$	127.683	−	127.683i	0.321621	−	0.321621i	−0.527768	−	0.849389i	$-0.676971\pi$
$397$	127.683	−	127.683i	0.321621	−	0.321621i	0.849389	+	0.527768i	$0.176971\pi$
$398$	−81.2115	+	81.2115i	−0.204049	+	0.204049i
$399$	49.2264	−	49.2264i	0.123375	−	0.123375i
$400$	−70.3960			−0.175990
$401$	429.679	+	429.679i	1.07152	+	1.07152i	0.997237	+	0.0742824i	$0.0236666\pi$
$401$	429.679	+	429.679i	1.07152	+	1.07152i	0.0742824	+	0.997237i	$0.476333\pi$
$402$		−	967.618i		−	2.40701i
$403$	−194.721	−	194.721i	−0.483177	−	0.483177i
$404$	−187.214	+	187.214i	−0.463401	+	0.463401i
$405$	1206.79			2.97973
$406$	−13.1711	+	13.1711i	−0.0324411	+	0.0324411i
$407$			843.966i			2.07363i
$408$	−97.8050	−	97.8050i	−0.239718	−	0.239718i
$409$	−388.988	−	388.988i	−0.951070	−	0.951070i	0.0477878	−	0.998858i	$-0.484783\pi$
$409$	−388.988	−	388.988i	−0.951070	−	0.951070i	−0.998858	+	0.0477878i	$0.984783\pi$
$410$	−350.013	−	350.013i	−0.853689	−	0.853689i
$411$	−453.609			−1.10367
$412$	277.025			0.672390
$413$			44.9245i			0.108776i
$414$	349.813	−	349.813i	0.844959	−	0.844959i
$415$	−74.8286	+	74.8286i	−0.180310	+	0.180310i
$416$	−50.5160	+	50.5160i	−0.121433	+	0.121433i
$417$			620.989i			1.48918i
$418$			215.483i			0.515509i
$419$		−	194.897i		−	0.465149i	−0.972579	−	0.232574i	$-0.925285\pi$
$419$		−	194.897i		−	0.465149i	0.972579	−	0.232574i	$-0.0747149\pi$
$420$		−	92.1667i		−	0.219445i
$421$		−	557.136i		−	1.32336i	−0.749785	−	0.661682i	$-0.769843\pi$
$421$		−	557.136i		−	1.32336i	0.749785	−	0.661682i	$-0.230157\pi$
$422$	402.369	−	402.369i	0.953480	−	0.953480i
$423$		−	649.782i		−	1.53613i
$424$	88.3429	−	88.3429i	0.208356	−	0.208356i
$425$	−110.345	−	110.345i	−0.259636	−	0.259636i
$426$	70.9634	+	70.9634i	0.166581	+	0.166581i
$427$	−23.9486	+	23.9486i	−0.0560857	+	0.0560857i
$428$	7.77369	+	7.77369i	0.0181628	+	0.0181628i
$429$	−761.085	−	761.085i	−1.77409	−	1.77409i
$430$	−307.175	+	307.175i	−0.714361	+	0.714361i
$431$	−367.049	−	367.049i	−0.851622	−	0.851622i	0.138711	−	0.990333i	$-0.455704\pi$
$431$	−367.049	−	367.049i	−0.851622	−	0.851622i	−0.990333	+	0.138711i	$0.955704\pi$
$432$	−193.675	+	193.675i	−0.448322	+	0.448322i
$433$		−	18.8613i		−	0.0435597i	−0.999763	−	0.0217798i	$-0.993067\pi$
$433$		−	18.8613i		−	0.0435597i	0.999763	−	0.0217798i	$-0.00693329\pi$
$434$	−27.9159	+	27.9159i	−0.0643224	+	0.0643224i
$435$	370.320			0.851310
$436$	−141.380	−	141.380i	−0.324267	−	0.324267i
$437$	−113.881	+	113.881i	−0.260598	+	0.260598i
$438$	897.610			2.04934
$439$		−	432.350i		−	0.984852i	−0.870354	−	0.492426i	$-0.836110\pi$
$439$		−	432.350i		−	0.984852i	0.870354	−	0.492426i	$-0.163890\pi$
$440$	201.724	+	201.724i	0.458465	+	0.458465i
$441$	−1014.28			−2.29995
$442$	−158.367			−0.358296
$443$	402.242	+	402.242i	0.907995	+	0.907995i	0.996110	−	0.0881153i	$-0.0280844\pi$
$443$	402.242	+	402.242i	0.907995	+	0.907995i	−0.0881153	+	0.996110i	$0.528084\pi$
$444$	425.953	−	425.953i	0.959353	−	0.959353i
$445$		−	834.493i		−	1.87527i
$446$	−518.898			−1.16345
$447$	836.897	−	836.897i	1.87225	−	1.87225i
$448$	7.24218	+	7.24218i	0.0161656	+	0.0161656i
$449$	842.474			1.87633			0.938167	−	0.346183i	$-0.112522\pi$
$449$	842.474			1.87633			0.938167	+	0.346183i	$0.112522\pi$
$450$	−376.898	+	376.898i	−0.837552	+	0.837552i
$451$			828.730i			1.83754i
$452$	184.548	+	184.548i	0.408292	+	0.408292i
$453$	675.792	−	675.792i	1.49181	−	1.49181i
$454$	−431.402			−0.950225
$455$	−74.6187	−	74.6187i	−0.163997	−	0.163997i
$456$	108.755	−	108.755i	0.238498	−	0.238498i
$457$			321.109i			0.702646i	0.936254	+	0.351323i	$0.114268\pi$
$457$			321.109i			0.702646i	−0.936254	+	0.351323i	$0.885732\pi$
$458$			303.093i			0.661776i
$459$	−607.170			−1.32281
$460$			213.220i			0.463523i
$461$	101.857	−	101.857i	0.220948	−	0.220948i	−0.587949	−	0.808898i	$-0.700065\pi$
$461$	101.857	−	101.857i	0.220948	−	0.220948i	0.808898	+	0.587949i	$0.200065\pi$
$462$	−109.112	+	109.112i	−0.236174	+	0.236174i
$463$	−114.254	+	114.254i	−0.246770	+	0.246770i	−0.819644	−	0.572874i	$-0.805829\pi$
$463$	−114.254	+	114.254i	−0.246770	+	0.246770i	0.572874	+	0.819644i	$0.305829\pi$
$464$	−29.0986	+	29.0986i	−0.0627125	+	0.0627125i
$465$	784.888			1.68793
$466$	−349.895	+	349.895i	−0.750848	+	0.750848i
$467$	−186.494	−	186.494i	−0.399346	−	0.399346i	0.478657	−	0.878002i	$-0.341124\pi$
$467$	−186.494	−	186.494i	−0.399346	−	0.399346i	−0.878002	+	0.478657i	$0.841124\pi$
$468$			540.923i			1.15582i
$469$	−112.310	+	112.310i	−0.239467	+	0.239467i
$470$	198.030	+	198.030i	0.421340	+	0.421340i
$471$			1217.19i			2.58426i
$472$			99.2509i			0.210277i
$473$	727.304			1.53764
$474$	−318.145			−0.671192
$475$	122.699	−	122.699i	0.258314	−	0.258314i
$476$			22.7041i			0.0476978i
$477$		−	945.972i		−	1.98317i
$478$	273.894	+	273.894i	0.573000	+	0.573000i
$479$	6.26608	+	6.26608i	0.0130816	+	0.0130816i	0.713617	−	0.700536i	$-0.247056\pi$
$479$	6.26608	+	6.26608i	0.0130816	+	0.0130816i	−0.700536	+	0.713617i	$0.747056\pi$
$480$		−	203.622i		−	0.424213i
$481$		−	689.708i		−	1.43390i
$482$	506.337			1.05049
$483$	−115.330			−0.238779
$484$		−	235.626i		−	0.486831i
$485$			350.351i			0.722373i
$486$			570.570i			1.17401i
$487$	271.941			0.558401			0.279200	−	0.960233i	$-0.409931\pi$
$487$	271.941			0.558401			0.279200	+	0.960233i	$0.409931\pi$
$488$	−52.9091	+	52.9091i	−0.108420	+	0.108420i
$489$	−412.215			−0.842976
$490$	309.115	−	309.115i	0.630847	−	0.630847i
$491$		−	470.437i		−	0.958121i	−0.877782	−	0.479060i	$-0.840978\pi$
$491$		−	470.437i		−	0.958121i	0.877782	−	0.479060i	$-0.159022\pi$
$492$	418.263	−	418.263i	0.850128	−	0.850128i
$493$	−91.2237			−0.185038
$494$		−	176.097i		−	0.356472i
$495$	2160.06			4.36375
$496$	−61.6741	+	61.6741i	−0.124343	+	0.124343i
$497$		−	16.4732i		−	0.0331453i
$498$	−89.4197	−	89.4197i	−0.179558	−	0.179558i
$499$	83.5111	+	83.5111i	0.167357	+	0.167357i	0.785817	−	0.618460i	$-0.212243\pi$
$499$	83.5111	+	83.5111i	0.167357	+	0.167357i	−0.618460	+	0.785817i	$0.712243\pi$
$500$			96.6097i			0.193219i
$501$			418.686i			0.835701i
$502$		−	511.955i		−	1.01983i
$503$	86.9474	+	86.9474i	0.172858	+	0.172858i	0.788234	−	0.615376i	$-0.210996\pi$
$503$	86.9474	+	86.9474i	0.172858	+	0.172858i	−0.615376	+	0.788234i	$0.710996\pi$
$504$	77.5489			0.153867
$505$	−610.953	−	610.953i	−1.20981	−	1.20981i
$506$	252.423	−	252.423i	0.498859	−	0.498859i
$507$	−37.0802	−	37.0802i	−0.0731366	−	0.0731366i
$508$	−223.311			−0.439588
$509$	−463.621	−	463.621i	−0.910847	−	0.910847i	0.0854915	−	0.996339i	$-0.472754\pi$
$509$	−463.621	−	463.621i	−0.910847	−	0.910847i	−0.996339	+	0.0854915i	$0.972754\pi$
$510$	319.177	−	319.177i	0.625836	−	0.625836i
$511$	−104.184	−	104.184i	−0.203883	−	0.203883i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$		−	675.147i		−	1.31608i
$514$		−	612.767i		−	1.19215i
$515$			904.041i			1.75542i
$516$	−367.073	−	367.073i	−0.711381	−	0.711381i
$517$		−	468.878i		−	0.906921i
$518$	−98.8793			−0.190887
$519$	180.421	+	180.421i	0.347631	+	0.347631i
$520$	−164.854	−	164.854i	−0.317026	−	0.317026i
$521$	47.2548	−	47.2548i	0.0907001	−	0.0907001i	−0.660301	−	0.751001i	$-0.729571\pi$
$521$	47.2548	−	47.2548i	0.0907001	−	0.0907001i	0.751001	+	0.660301i	$0.229571\pi$
$522$			311.587i			0.596909i
$523$	−283.189	+	283.189i	−0.541470	+	0.541470i	−0.923960	−	0.382489i	$-0.875067\pi$
$523$	−283.189	+	283.189i	−0.541470	+	0.541470i	0.382489	+	0.923960i	$0.375067\pi$
$524$			221.845i			0.423369i
$525$	124.260			0.236686
$526$	−379.430	−	379.430i	−0.721350	−	0.721350i
$527$	−193.348			−0.366883
$528$	−241.060	+	241.060i	−0.456552	+	0.456552i
$529$	−262.192			−0.495637
$530$	288.298	+	288.298i	0.543958	+	0.543958i
$531$	531.387	+	531.387i	1.00073	+	1.00073i
$532$	−25.2460			−0.0474549
$533$		−	677.256i		−	1.27065i
$534$	997.214			1.86744
$535$	−25.3686	+	25.3686i	−0.0474180	+	0.0474180i
$536$	−248.124	+	248.124i	−0.462918	+	0.462918i
$537$		−	653.493i		−	1.21693i
$538$	−218.549	+	311.381i	−0.406226	+	0.578775i
$539$	−731.896			−1.35788
$540$	−632.039	−	632.039i	−1.17044	−	1.17044i
$541$	163.006	+	163.006i	0.301305	+	0.301305i	0.841524	−	0.540220i	$-0.181659\pi$
$541$	163.006	+	163.006i	0.301305	+	0.301305i	−0.540220	+	0.841524i	$0.681659\pi$
$542$		−	225.118i		−	0.415346i
$543$	−1113.87			−2.05133
$544$			50.1598i			0.0922055i
$545$	461.380	−	461.380i	0.846568	−	0.846568i
$546$	89.1689	−	89.1689i	0.163313	−	0.163313i
$547$		−	165.860i		−	0.303218i	−0.988441	−	0.151609i	$-0.951555\pi$
$547$		−	165.860i		−	0.303218i	0.988441	−	0.151609i	$-0.0484454\pi$
$548$	116.318	+	116.318i	0.212259	+	0.212259i
$549$			566.549i			1.03196i
$550$	−271.967	+	271.967i	−0.494486	+	0.494486i
$551$		−	101.437i		−	0.184096i
$552$	−254.797			−0.461589
$553$	36.9265	+	36.9265i	0.0667749	+	0.0667749i
$554$	235.224			0.424591
$555$	1390.05	+	1390.05i	2.50460	+	2.50460i
$556$	159.239	−	159.239i	0.286401	−	0.286401i
$557$	−358.595	+	358.595i	−0.643797	+	0.643797i	−0.951487	−	0.307690i	$-0.900444\pi$
$557$	−358.595	+	358.595i	−0.643797	+	0.643797i	0.307690	+	0.951487i	$0.400444\pi$
$558$			660.404i			1.18352i
$559$	−594.368			−1.06327
$560$	−23.6341	+	23.6341i	−0.0422037	+	0.0422037i
$561$	−755.719			−1.34709
$562$	−428.832			−0.763046
$563$	−657.191			−1.16730			−0.583651	−	0.812005i	$-0.698376\pi$
$563$	−657.191			−1.16730			−0.583651	+	0.812005i	$0.698376\pi$
$564$	−236.645	+	236.645i	−0.419583	+	0.419583i
$565$	−602.253	+	602.253i	−1.06593	+	1.06593i
$566$	273.475	+	273.475i	0.483171	+	0.483171i
$567$	167.383	−	167.383i	0.295208	−	0.295208i
$568$		−	36.3939i		−	0.0640738i
$569$	−62.8867	+	62.8867i	−0.110521	+	0.110521i	−0.760205	−	0.649683i	$-0.774901\pi$
$569$	−62.8867	+	62.8867i	−0.110521	+	0.110521i	0.649683	+	0.760205i	$0.274901\pi$
$570$	354.911	+	354.911i	0.622650	+	0.622650i
$571$	559.497	−	559.497i	0.979854	−	0.979854i	−0.0199470	−	0.999801i	$-0.506350\pi$
$571$	559.497	−	559.497i	0.979854	−	0.979854i	0.999801	+	0.0199470i	$0.00634974\pi$
$572$			390.326i			0.682389i
$573$	−1044.11	+	1044.11i	−1.82218	+	1.82218i
$574$	−97.0942			−0.169154
$575$	−287.466			−0.499941
$576$	171.327			0.297443
$577$	208.070	−	208.070i	0.360607	−	0.360607i	−0.503429	−	0.864036i	$-0.667929\pi$
$577$	208.070	−	208.070i	0.360607	−	0.360607i	0.864036	+	0.503429i	$0.167929\pi$
$578$	210.375	−	210.375i	0.363970	−	0.363970i
$579$	−658.069			−1.13656
$580$	−94.9602	−	94.9602i	−0.163724	−	0.163724i
$581$			20.7576i			0.0357274i
$582$	−418.667			−0.719359
$583$		−	682.607i		−	1.17085i
$584$	−230.172	−	230.172i	−0.394130	−	0.394130i
$585$	−1765.25			−3.01751
$586$	473.642	+	473.642i	0.808262	+	0.808262i
$587$			746.743i			1.27213i	0.771634	+	0.636067i	$0.219440\pi$
$587$			746.743i			1.27213i	−0.771634	+	0.636067i	$0.780560\pi$
$588$	369.391	+	369.391i	0.628216	+	0.628216i
$589$		−	214.994i		−	0.365016i
$590$	−323.895			−0.548975
$591$	−2024.84			−3.42613
$592$	−218.452			−0.369007
$593$			281.034i			0.473919i	0.971520	+	0.236959i	$0.0761508\pi$
$593$			281.034i			0.473919i	−0.971520	+	0.236959i	$0.923849\pi$
$594$			1496.49i			2.51934i
$595$	−74.0926			−0.124525
$596$	−429.207			−0.720145
$597$	316.704	−	316.704i	0.530492	−	0.530492i
$598$	−206.285	+	206.285i	−0.344959	+	0.344959i
$599$	245.727			0.410229			0.205115	−	0.978738i	$-0.434243\pi$
$599$	245.727			0.410229			0.205115	+	0.978738i	$0.434243\pi$
$600$	274.526			0.457543
$601$	−538.142	−	538.142i	−0.895411	−	0.895411i	0.0996146	−	0.995026i	$-0.468239\pi$
$601$	−538.142	−	538.142i	−0.895411	−	0.895411i	−0.995026	+	0.0996146i	$0.968239\pi$
$602$			85.2110i			0.141547i
$603$			2656.90i			4.40614i
$604$	−346.583			−0.573813
$605$	768.941			1.27098
$606$	730.085	−	730.085i	1.20476	−	1.20476i
$607$	−437.437	−	437.437i	−0.720654	−	0.720654i	0.248085	−	0.968738i	$-0.420199\pi$
$607$	−437.437	−	437.437i	−0.720654	−	0.720654i	−0.968738	+	0.248085i	$0.920199\pi$
$608$	−55.7755			−0.0917361
$609$	51.3637	−	51.3637i	0.0843411	−	0.0843411i
$610$	−172.663	−	172.663i	−0.283055	−	0.283055i
$611$			383.178i			0.627132i
$612$	268.555	+	268.555i	0.438815	+	0.438815i
$613$	−303.946	−	303.946i	−0.495834	−	0.495834i	0.414304	−	0.910138i	$-0.364025\pi$
$613$	−303.946	−	303.946i	−0.495834	−	0.495834i	−0.910138	+	0.414304i	$0.864025\pi$
$614$	190.785	+	190.785i	0.310725	+	0.310725i
$615$	1364.96	+	1364.96i	2.21944	+	2.21944i
$616$	55.9588			0.0908421
$617$			498.398i			0.807777i	0.914808	+	0.403888i	$0.132342\pi$
$617$			498.398i			0.807777i	−0.914808	+	0.403888i	$0.867658\pi$
$618$	−1080.32			−1.74810
$619$	89.7201			0.144944			0.0724718	−	0.997370i	$-0.476911\pi$
$619$	89.7201			0.144944			0.0724718	+	0.997370i	$0.476911\pi$
$620$	−201.267	−	201.267i	−0.324624	−	0.324624i
$621$	−790.885	+	790.885i	−1.27357	+	1.27357i
$622$		−	180.367i		−	0.289980i
$623$	−115.745	−	115.745i	−0.185786	−	0.185786i
$624$	196.999	−	196.999i	0.315704	−	0.315704i
$625$	−755.250			−1.20840
$626$	248.677	+	248.677i	0.397248	+	0.397248i
$627$		−	840.327i		−	1.34023i
$628$	312.120	−	312.120i	0.497007	−	0.497007i
$629$	−342.422	−	342.422i	−0.544391	−	0.544391i
$630$			253.073i			0.401703i
$631$	−337.884			−0.535475			−0.267737	−	0.963492i	$-0.586276\pi$
$631$	−337.884			−0.535475			−0.267737	+	0.963492i	$0.586276\pi$
$632$	81.5811	+	81.5811i	0.129084	+	0.129084i
$633$	−1569.13	+	1569.13i	−2.47888	+	2.47888i
$634$			252.483i			0.398238i
$635$		−	728.751i		−	1.14764i
$636$	−344.514	+	344.514i	−0.541689	+	0.541689i
$637$	598.122			0.938966
$638$			224.839i			0.352412i
$639$	−194.852	−	194.852i	−0.304933	−	0.304933i
$640$	−52.2143	+	52.2143i	−0.0815849	+	0.0815849i
$641$			656.279i			1.02384i	0.859034	+	0.511918i	$0.171065\pi$
$641$			656.279i			1.02384i	−0.859034	+	0.511918i	$0.828935\pi$
$642$	−30.3154	−	30.3154i	−0.0472202	−	0.0472202i
$643$	792.811			1.23299			0.616494	−	0.787360i	$-0.288552\pi$
$643$	792.811			1.23299			0.616494	+	0.787360i	$0.288552\pi$
$644$	29.5739	+	29.5739i	0.0459222	+	0.0459222i
$645$	1197.90	−	1197.90i	1.85721	−	1.85721i
$646$	−87.4278	−	87.4278i	−0.135337	−	0.135337i
$647$	112.270	−	112.270i	0.173525	−	0.173525i	−0.615001	−	0.788526i	$-0.710845\pi$
$647$	112.270	−	112.270i	0.173525	−	0.173525i	0.788526	+	0.615001i	$0.210845\pi$
$648$	369.796	−	369.796i	0.570673	−	0.570673i
$649$	383.445	+	383.445i	0.590825	+	0.590825i
$650$	222.258	−	222.258i	0.341935	−	0.341935i
$651$	108.865	−	108.865i	0.167227	−	0.167227i
$652$	105.703	+	105.703i	0.162122	+	0.162122i
$653$	−25.8733			−0.0396223			−0.0198111	−	0.999804i	$-0.506306\pi$
$653$	−25.8733			−0.0396223			−0.0198111	+	0.999804i	$0.506306\pi$
$654$	551.346	+	551.346i	0.843037	+	0.843037i
$655$	−723.969			−1.10530
$656$	−214.508			−0.326994
$657$	−2464.67			−3.75140
$658$	54.9339			0.0834861
$659$	−276.514			−0.419597			−0.209798	−	0.977745i	$-0.567281\pi$
$659$	−276.514			−0.419597			−0.209798	+	0.977745i	$0.567281\pi$
$660$	−786.673	−	786.673i	−1.19193	−	1.19193i
$661$	883.854	+	883.854i	1.33715	+	1.33715i	0.898811	+	0.438336i	$0.144432\pi$
$661$	883.854	+	883.854i	1.33715	+	1.33715i	0.438336	+	0.898811i	$0.355568\pi$
$662$	584.868	+	584.868i	0.883487	+	0.883487i
$663$	617.590			0.931508
$664$			45.8593i			0.0690653i
$665$		−	82.3877i		−	0.123891i
$666$	−1169.59	+	1169.59i	−1.75614	+	1.75614i
$667$	−118.826	+	118.826i	−0.178150	+	0.178150i
$668$	107.363	−	107.363i	0.160722	−	0.160722i
$669$	2023.57			3.02477
$670$	−809.726	−	809.726i	−1.20855	−	1.20855i
$671$			408.818i			0.609266i
$672$	−28.2426	−	28.2426i	−0.0420277	−	0.0420277i
$673$	−142.265	+	142.265i	−0.211390	+	0.211390i	−0.804858	−	0.593468i	$-0.797758\pi$
$673$	−142.265	+	142.265i	−0.211390	+	0.211390i	0.593468	+	0.804858i	$0.297758\pi$
$674$	−775.677			−1.15086
$675$	852.122	−	852.122i	1.26240	−	1.26240i
$676$			19.0168i			0.0281313i
$677$	−444.539	−	444.539i	−0.656631	−	0.656631i	0.297950	−	0.954581i	$-0.403697\pi$
$677$	−444.539	−	444.539i	−0.656631	−	0.656631i	−0.954581	+	0.297950i	$0.903697\pi$
$678$	−719.689	−	719.689i	−1.06149	−	1.06149i
$679$	48.5940	+	48.5940i	0.0715670	+	0.0715670i
$680$	−163.691			−0.240722
$681$	1682.36			2.47042
$682$			476.543i			0.698743i
$683$	320.153	−	320.153i	0.468745	−	0.468745i	−0.432763	−	0.901508i	$-0.642461\pi$
$683$	320.153	−	320.153i	0.468745	−	0.468745i	0.901508	+	0.432763i	$0.142461\pi$
$684$	−298.621	+	298.621i	−0.436581	+	0.436581i
$685$	−379.591	+	379.591i	−0.554148	+	0.554148i
$686$		−	174.466i		−	0.254323i
$687$		−	1181.98i		−	1.72050i
$688$			188.255i			0.273627i
$689$			557.841i			0.809639i
$690$		−	831.504i		−	1.20508i
$691$	452.233	−	452.233i	0.654462	−	0.654462i	−0.299602	−	0.954064i	$-0.596854\pi$
$691$	452.233	−	452.233i	0.654462	−	0.654462i	0.954064	+	0.299602i	$0.0968539\pi$
$692$		−	92.5296i		−	0.133713i
$693$	299.602	−	299.602i	0.432326	−	0.432326i
$694$	304.297	+	304.297i	0.438468	+	0.438468i
$695$	519.659	+	519.659i	0.747711	+	0.747711i
$696$	113.477	−	113.477i	0.163042	−	0.163042i
$697$	−336.240	−	336.240i	−0.482411	−	0.482411i
$698$	−307.304	−	307.304i	−0.440264	−	0.440264i
$699$	1364.50	−	1364.50i	1.95207	−	1.95207i
$700$	−31.8637	−	31.8637i	−0.0455196	−	0.0455196i
$701$	353.765	−	353.765i	0.504657	−	0.504657i	−0.408225	−	0.912882i	$-0.633852\pi$
$701$	353.765	−	353.765i	0.504657	−	0.504657i	0.912882	+	0.408225i	$0.133852\pi$
$702$		−	1222.96i		−	1.74211i
$703$	380.759	−	380.759i	0.541620	−	0.541620i
$704$	123.629			0.175609
$705$	−772.265	−	772.265i	−1.09541	−	1.09541i
$706$	−567.201	+	567.201i	−0.803401	+	0.803401i
$707$	−169.480			−0.239716
$708$		−	387.053i		−	0.546685i
$709$	−451.390	−	451.390i	−0.636657	−	0.636657i	0.313072	−	0.949729i	$-0.398642\pi$
$709$	−451.390	−	451.390i	−0.636657	−	0.636657i	−0.949729	+	0.313072i	$0.898642\pi$
$710$	118.768			0.167278
$711$	873.567			1.22865
$712$	−255.713	−	255.713i	−0.359148	−	0.359148i
$713$	−251.850	+	251.850i	−0.353226	+	0.353226i
$714$		−	88.5402i		−	0.124006i
$715$	−1273.79			−1.78152
$716$	−167.574	+	167.574i	−0.234041	+	0.234041i
$717$	−1068.11	−	1068.11i	−1.48970	−	1.48970i
$718$	755.172			1.05177
$719$	106.012	−	106.012i	0.147443	−	0.147443i	−0.629532	−	0.776975i	$-0.716753\pi$
$719$	106.012	−	106.012i	0.147443	−	0.147443i	0.776975	+	0.629532i	$0.216753\pi$
$720$			559.109i			0.776540i
$721$	125.391	+	125.391i	0.173913	+	0.173913i
$722$	−263.784	+	263.784i	−0.365352	+	0.365352i
$723$	−1974.58			−2.73109
$724$	285.627	+	285.627i	0.394512	+	0.394512i
$725$	128.026	−	128.026i	0.176588	−	0.176588i
$726$			918.880i			1.26567i
$727$			221.291i			0.304389i	0.988351	+	0.152194i	$0.0486340\pi$
$727$			221.291i			0.304389i	−0.988351	+	0.152194i	$0.951366\pi$
$728$	−45.7307			−0.0628169
$729$		−	560.991i		−	0.769535i
$730$	751.141	−	751.141i	1.02896	−	1.02896i
$731$	−295.089	+	295.089i	−0.403678	+	0.403678i
$732$	206.332	−	206.332i	0.281874	−	0.281874i
$733$	414.108	−	414.108i	0.564949	−	0.564949i	−0.365760	−	0.930709i	$-0.619191\pi$
$733$	414.108	−	414.108i	0.564949	−	0.564949i	0.930709	+	0.365760i	$0.119191\pi$
$734$	861.612			1.17386
$735$	−1205.47	+	1205.47i	−1.64009	+	1.64009i
$736$	65.3370	+	65.3370i	0.0887731	+	0.0887731i
$737$			1917.20i			2.60136i
$738$	−1148.47	+	1148.47i	−1.55620	+	1.55620i
$739$	−753.962	−	753.962i	−1.02025	−	1.02025i	−0.999791	−	0.0204550i	$-0.993489\pi$
$739$	−753.962	−	753.962i	−1.02025	−	1.02025i	−0.0204550	−	0.999791i	$-0.506511\pi$
$740$		−	712.895i		−	0.963372i
$741$			686.733i			0.926766i
$742$	79.9744			0.107782
$743$	908.110			1.22222			0.611110	−	0.791545i	$-0.290723\pi$
$743$	908.110			1.22222			0.611110	+	0.791545i	$0.290723\pi$
$744$	240.513	−	240.513i	0.323270	−	0.323270i
$745$		−	1400.67i		−	1.88010i
$746$			668.361i			0.895926i
$747$	245.530	+	245.530i	0.328688	+	0.328688i
$748$	193.787	+	193.787i	0.259074	+	0.259074i
$749$			7.03730i			0.00939560i
$750$		−	376.753i		−	0.502337i
$751$	1098.76			1.46307			0.731535	−	0.681804i	$-0.238804\pi$
$751$	1098.76			1.46307			0.731535	+	0.681804i	$0.238804\pi$
$752$	121.364			0.161389
$753$			1996.49i			2.65138i
$754$		−	183.743i		−	0.243691i
$755$		−	1131.04i		−	1.49806i
$756$	−175.329			−0.231916
$757$	965.094	−	965.094i	1.27489	−	1.27489i	0.331405	−	0.943489i	$-0.392477\pi$
$757$	965.094	−	965.094i	1.27489	−	1.27489i	0.943489	−	0.331405i	$-0.107523\pi$
$758$	−927.854			−1.22408
$759$	−984.382	+	984.382i	−1.29695	+	1.29695i
$760$		−	182.018i		−	0.239497i
$761$	731.448	−	731.448i	0.961167	−	0.961167i	−0.0381066	−	0.999274i	$-0.512133\pi$
$761$	731.448	−	731.448i	0.961167	−	0.961167i	0.999274	+	0.0381066i	$0.0121326\pi$
$762$	870.853			1.14285
$763$		−	127.988i		−	0.167743i
$764$	535.476			0.700885
$765$	−876.399	+	876.399i	−1.14562	+	1.14562i
$766$		−	31.9792i		−	0.0417483i
$767$	−313.360	−	313.360i	−0.408553	−	0.408553i
$768$	−62.3958	−	62.3958i	−0.0812445	−	0.0812445i
$769$			134.902i			0.175425i	0.996146	+	0.0877125i	$0.0279557\pi$
$769$			134.902i			0.175425i	−0.996146	+	0.0877125i	$0.972044\pi$
$770$			182.616i			0.237163i
$771$			2389.63i			3.09939i
$772$	168.747	+	168.747i	0.218584	+	0.218584i
$773$	1131.91			1.46431			0.732156	−	0.681137i	$-0.238514\pi$
$773$	1131.91			1.46431			0.732156	+	0.681137i	$0.238514\pi$
$774$	1007.91	+	1007.91i	1.30221	+	1.30221i
$775$	271.350	−	271.350i	0.350130	−	0.350130i
$776$	107.358	+	107.358i	0.138348	+	0.138348i
$777$	385.603			0.496272
$778$	−599.214	−	599.214i	−0.770198	−	0.770198i
$779$	373.885	−	373.885i	0.479955	−	0.479955i
$780$	642.886	+	642.886i	0.824213	+	0.824213i
$781$	−140.604	−	140.604i	−0.180031	−	0.180031i
$782$			204.831i			0.261932i
$783$		−	704.460i		−	0.899693i
$784$		−	189.444i		−	0.241638i
$785$	1018.57	+	1018.57i	1.29754	+	1.29754i
$786$		−	865.139i		−	1.10069i
$787$	1123.63			1.42773			0.713867	−	0.700282i	$-0.246942\pi$
$787$	1123.63			1.42773			0.713867	+	0.700282i	$0.246942\pi$
$788$	519.225	+	519.225i	0.658915	+	0.658915i
$789$	1479.68	+	1479.68i	1.87538	+	1.87538i
$790$	−266.231	+	266.231i	−0.337002	+	0.337002i
$791$			167.066i			0.211209i
$792$	661.905	−	661.905i	0.835739	−	0.835739i
$793$		−	334.095i		−	0.421305i
$794$	255.367			0.321621
$795$	−1124.29	−	1124.29i	−1.41420	−	1.41420i
$796$	−162.423			−0.204049
$797$	25.2801	−	25.2801i	0.0317191	−	0.0317191i	−0.691069	−	0.722788i	$-0.742860\pi$
$797$	25.2801	−	25.2801i	0.0317191	−	0.0317191i	0.722788	+	0.691069i	$0.242860\pi$
$798$	98.4529			0.123375
$799$	190.238	+	190.238i	0.238095	+	0.238095i
$800$	−70.3960	−	70.3960i	−0.0879949	−	0.0879949i
$801$	−2738.17			−3.41843
$802$			859.359i			1.07152i
$803$	−1778.49			−2.21480
$804$	967.618	−	967.618i	1.20351	−	1.20351i
$805$	−96.5113	+	96.5113i	−0.119890	+	0.119890i
$806$		−	389.441i		−	0.483177i
$807$	852.285	−	1214.30i	1.05612	−	1.50471i
$808$	−374.428			−0.463401
$809$	−183.521	−	183.521i	−0.226850	−	0.226850i	0.584526	−	0.811375i	$-0.301281\pi$
$809$	−183.521	−	183.521i	−0.226850	−	0.226850i	−0.811375	+	0.584526i	$0.801281\pi$
$810$	1206.79	+	1206.79i	1.48987	+	1.48987i
$811$			170.440i			0.210160i	0.994464	+	0.105080i	$0.0335098\pi$
$811$			170.440i			0.210160i	−0.994464	+	0.105080i	$0.966490\pi$
$812$	−26.3421			−0.0324411
$813$			877.899i			1.07983i
$814$	−843.966	+	843.966i	−1.03681	+	1.03681i
$815$	−344.952	+	344.952i	−0.423253	+	0.423253i
$816$		−	195.610i		−	0.239718i
$817$	−328.126	−	328.126i	−0.401623	−	0.401623i
$818$		−	777.975i		−	0.951070i
$819$	−244.841	+	244.841i	−0.298951	+	0.298951i
$820$		−	700.025i		−	0.853689i
$821$	1081.79			1.31765			0.658827	−	0.752294i	$-0.271053\pi$
$821$	1081.79			1.31765			0.658827	+	0.752294i	$0.271053\pi$
$822$	−453.609	−	453.609i	−0.551836	−	0.551836i
$823$	−1049.92			−1.27572			−0.637862	−	0.770150i	$-0.720181\pi$
$823$	−1049.92			−1.27572			−0.637862	+	0.770150i	$0.720181\pi$
$824$	277.025	+	277.025i	0.336195	+	0.336195i
$825$	1060.60	−	1060.60i	1.28558	−	1.28558i
$826$	−44.9245	+	44.9245i	−0.0543881	+	0.0543881i
$827$		−	711.634i		−	0.860501i	−0.902710	−	0.430251i	$-0.858425\pi$
$827$		−	711.634i		−	0.860501i	0.902710	−	0.430251i	$-0.141575\pi$
$828$	699.626			0.844959
$829$	357.565	−	357.565i	0.431320	−	0.431320i	−0.457757	−	0.889077i	$-0.651347\pi$
$829$	357.565	−	357.565i	0.431320	−	0.431320i	0.889077	+	0.457757i	$0.151347\pi$
$830$	−149.657			−0.180310
$831$	−917.311			−1.10386
$832$	−101.032			−0.121433
$833$	296.952	−	296.952i	0.356485	−	0.356485i
$834$	−620.989	+	620.989i	−0.744591	+	0.744591i
$835$	350.367	+	350.367i	0.419601	+	0.419601i
$836$	−215.483	+	215.483i	−0.257755	+	0.257755i
$837$		−	1493.09i		−	1.78386i
$838$	194.897	−	194.897i	0.232574	−	0.232574i
$839$	−1041.70	−	1041.70i	−1.24159	−	1.24159i	−0.959341	−	0.282251i	$-0.908919\pi$
$839$	−1041.70	−	1041.70i	−1.24159	−	1.24159i	−0.282251	−	0.959341i	$-0.591081\pi$
$840$	92.1667	−	92.1667i	0.109722	−	0.109722i
$841$			735.159i			0.874149i
$842$	557.136	−	557.136i	0.661682	−	0.661682i
$843$	1672.33			1.98379
$844$	804.737			0.953480
$845$	−62.0593			−0.0734430
$846$	649.782	−	649.782i	0.768064	−	0.768064i
$847$	106.653	−	106.653i	0.125918	−	0.125918i
$848$	176.686			0.208356
$849$	−1066.48	−	1066.48i	−1.25616	−	1.25616i
$850$		−	220.690i		−	0.259636i
$851$	−892.063			−1.04825
$852$			141.927i			0.166581i
$853$	−133.701	−	133.701i	−0.156742	−	0.156742i	0.624379	−	0.781121i	$-0.285352\pi$
$853$	−133.701	−	133.701i	−0.156742	−	0.156742i	−0.781121	+	0.624379i	$0.785352\pi$
$854$	−47.8972			−0.0560857
$855$	−974.519	−	974.519i	−1.13979	−	1.13979i
$856$			15.5474i			0.0181628i
$857$	−132.566	−	132.566i	−0.154686	−	0.154686i	0.625521	−	0.780207i	$-0.284886\pi$
$857$	−132.566	−	132.566i	−0.154686	−	0.154686i	−0.780207	+	0.625521i	$0.784886\pi$
$858$		−	1522.17i		−	1.77409i
$859$	−260.751			−0.303552			−0.151776	−	0.988415i	$-0.548499\pi$
$859$	−260.751			−0.303552			−0.151776	+	0.988415i	$0.548499\pi$
$860$	−614.351			−0.714361
$861$	378.642			0.439770
$862$		−	734.098i		−	0.851622i
$863$		−	301.521i		−	0.349387i	−0.984623	−	0.174693i	$-0.944107\pi$
$863$		−	301.521i		−	0.349387i	0.984623	−	0.174693i	$-0.0558934\pi$
$864$	−387.351			−0.448322
$865$	301.961			0.349088
$866$	18.8613	−	18.8613i	0.0217798	−	0.0217798i
$867$	−820.407	+	820.407i	−0.946259	+	0.946259i
$868$	−55.8318			−0.0643224
$869$	630.360			0.725385
$870$	370.320	+	370.320i	0.425655	+	0.425655i
$871$		−	1566.78i		−	1.79883i
$872$		−	282.761i		−	0.324267i
$873$	1149.58			1.31682
$874$	−227.763			−0.260598
$875$	−43.7290	+	43.7290i	−0.0499760	+	0.0499760i
$876$	897.610	+	897.610i	1.02467	+	1.02467i
$877$	107.153			0.122181			0.0610906	−	0.998132i	$-0.480542\pi$
$877$	107.153			0.122181			0.0610906	+	0.998132i	$0.480542\pi$
$878$	432.350	−	432.350i	0.492426	−	0.492426i
$879$	−1847.08	−	1847.08i	−2.10134	−	2.10134i
$880$			403.449i			0.458465i
$881$	755.999	+	755.999i	0.858115	+	0.858115i	0.991116	−	0.133001i	$-0.0424614\pi$
$881$	755.999	+	755.999i	0.858115	+	0.858115i	−0.133001	+	0.991116i	$0.542461\pi$
$882$	−1014.28	−	1014.28i	−1.14998	−	1.14998i
$883$	−321.307	−	321.307i	−0.363881	−	0.363881i	0.501359	−	0.865240i	$-0.332834\pi$
$883$	−321.307	−	321.307i	−0.363881	−	0.363881i	−0.865240	+	0.501359i	$0.832834\pi$
$884$	−158.367	−	158.367i	−0.179148	−	0.179148i
$885$	1263.11			1.42724
$886$			804.484i			0.907995i
$887$	450.433			0.507817			0.253908	−	0.967228i	$-0.418284\pi$
$887$	450.433			0.507817			0.253908	+	0.967228i	$0.418284\pi$
$888$	851.906			0.959353
$889$	−101.078	−	101.078i	−0.113699	−	0.113699i
$890$	834.493	−	834.493i	0.937633	−	0.937633i
$891$		−	2857.34i		−	3.20689i
$892$	−518.898	−	518.898i	−0.581725	−	0.581725i
$893$	−211.536	+	211.536i	−0.236883	+	0.236883i
$894$	1673.79			1.87225
$895$	−546.859	−	546.859i	−0.611016	−	0.611016i
$896$			14.4844i			0.0161656i
$897$	804.458	−	804.458i	0.896832	−	0.896832i
$898$	842.474	+	842.474i	0.938167	+	0.938167i
$899$		−	224.329i		−	0.249531i
$900$	−753.797			−0.837552
$901$	276.954	+	276.954i	0.307385	+	0.307385i
$902$	−828.730	+	828.730i	−0.918769	+	0.918769i
$903$		−	332.301i		−	0.367996i
$904$			369.096i			0.408292i
$905$	−932.114	+	932.114i	−1.02996	+	1.02996i
$906$	1351.58			1.49181
$907$			1483.18i			1.63525i	0.575748	+	0.817627i	$0.304711\pi$
$907$			1483.18i			1.63525i	−0.575748	+	0.817627i	$0.695289\pi$
$908$	−431.402	−	431.402i	−0.475112	−	0.475112i
$909$	−2004.68	+	2004.68i	−2.20537	+	2.20537i
$910$		−	149.237i		−	0.163997i
$911$	72.0980	+	72.0980i	0.0791416	+	0.0791416i	0.745570	−	0.666428i	$-0.232178\pi$
$911$	72.0980	+	72.0980i	0.0791416	+	0.0791416i	−0.666428	+	0.745570i	$0.732178\pi$
$912$	217.510			0.238498
$913$	177.173	+	177.173i	0.194056	+	0.194056i
$914$	−321.109	+	321.109i	−0.351323	+	0.351323i
$915$	673.342	+	673.342i	0.735893	+	0.735893i
$916$	−303.093	+	303.093i	−0.330888	+	0.330888i
$917$	−100.415	+	100.415i	−0.109504	+	0.109504i
$918$	−607.170	−	607.170i	−0.661405	−	0.661405i
$919$	−982.987	+	982.987i	−1.06963	+	1.06963i	−0.0722399	+	0.997387i	$0.523015\pi$
$919$	−982.987	+	982.987i	−1.06963	+	1.06963i	−0.997387	+	0.0722399i	$0.976985\pi$
$920$	−213.220	+	213.220i	−0.231761	+	0.231761i
$921$	−744.013	−	744.013i	−0.807832	−	0.807832i
$922$	203.714			0.220948
$923$	114.905	+	114.905i	0.124490	+	0.124490i
$924$	−218.225			−0.236174
$925$	961.134			1.03906
$926$	−228.509			−0.246770
$927$	2966.37			3.19997
$928$	−58.1972			−0.0627125
$929$	533.172	+	533.172i	0.573921	+	0.573921i	0.933222	−	0.359301i	$-0.116985\pi$
$929$	533.172	+	533.172i	0.573921	+	0.573921i	−0.359301	+	0.933222i	$0.616985\pi$
$930$	784.888	+	784.888i	0.843966	+	0.843966i
$931$	330.198	+	330.198i	0.354670	+	0.354670i
$932$	−699.790			−0.750848
$933$			703.386i			0.753897i
$934$		−	372.989i		−	0.399346i
$935$	−632.404	+	632.404i	−0.676368	+	0.676368i
$936$	−540.923	+	540.923i	−0.577909	+	0.577909i
$937$	168.993	−	168.993i	0.180355	−	0.180355i	−0.611156	−	0.791511i	$-0.709295\pi$
$937$	168.993	−	168.993i	0.180355	−	0.180355i	0.791511	+	0.611156i	$0.209295\pi$
$938$	−224.620			−0.239467
$939$	−969.777	−	969.777i	−1.03278	−	1.03278i
$940$			396.060i			0.421340i
$941$	212.690	+	212.690i	0.226026	+	0.226026i	0.811030	−	0.585004i	$-0.198907\pi$
$941$	212.690	+	212.690i	0.226026	+	0.226026i	−0.585004	+	0.811030i	$0.698907\pi$
$942$	−1217.19	+	1217.19i	−1.29213	+	1.29213i
$943$	−875.958			−0.928906
$944$	−99.2509	+	99.2509i	−0.105139	+	0.105139i
$945$		−	572.167i		−	0.605468i
$946$	727.304	+	727.304i	0.768820	+	0.768820i
$947$	−310.572	−	310.572i	−0.327953	−	0.327953i	0.523855	−	0.851808i	$-0.324494\pi$
$947$	−310.572	−	310.572i	−0.327953	−	0.327953i	−0.851808	+	0.523855i	$0.824494\pi$
$948$	−318.145	−	318.145i	−0.335596	−	0.335596i
$949$	1453.42			1.53153
$950$	245.398			0.258314
$951$		−	984.618i		−	1.03535i
$952$	−22.7041	+	22.7041i	−0.0238489	+	0.0238489i
$953$	956.479	−	956.479i	1.00365	−	1.00365i	0.00365755	−	0.999993i	$-0.498836\pi$
$953$	956.479	−	956.479i	1.00365	−	1.00365i	0.999993	−	0.00365755i	$-0.00116424\pi$
$954$	945.972	−	945.972i	0.991585	−	0.991585i
$955$			1747.47i			1.82981i
$956$			547.788i			0.573000i
$957$		−	876.812i		−	0.916209i
$958$			12.5322i			0.0130816i
$959$			105.299i			0.109801i
$960$	203.622	−	203.622i	0.212106	−	0.212106i
$961$			485.538i			0.505243i
$962$	689.708	−	689.708i	0.716952	−	0.716952i
$963$	83.2403	+	83.2403i	0.0864386	+	0.0864386i
$964$	506.337	+	506.337i	0.525246	+	0.525246i
$965$	−550.688	+	550.688i	−0.570661	+	0.570661i
$966$	−115.330	−	115.330i	−0.119390	−	0.119390i
$967$	553.748	+	553.748i	0.572645	+	0.572645i	0.932867	−	0.360222i	$-0.117299\pi$
$967$	553.748	+	553.748i	0.572645	+	0.572645i	−0.360222	+	0.932867i	$0.617299\pi$
$968$	235.626	−	235.626i	0.243415	−	0.243415i
$969$	340.946	+	340.946i	0.351853	+	0.351853i
$970$	−350.351	+	350.351i	−0.361186	+	0.361186i
$971$			1615.95i			1.66421i	0.554618	+	0.832105i	$0.312864\pi$
$971$			1615.95i			1.66421i	−0.554618	+	0.832105i	$0.687136\pi$
$972$	−570.570	+	570.570i	−0.587006	+	0.587006i
$973$	144.154			0.148155
$974$	271.941	+	271.941i	0.279200	+	0.279200i
$975$	−866.746	+	866.746i	−0.888971	+	0.888971i
$976$	−105.818			−0.108420
$977$			882.366i			0.903138i	0.892236	+	0.451569i	$0.149136\pi$
$977$			882.366i			0.903138i	−0.892236	+	0.451569i	$0.850864\pi$
$978$	−412.215	−	412.215i	−0.421488	−	0.421488i
$979$	−1975.84			−2.01822
$980$	618.230			0.630847
$981$	−1513.89	−	1513.89i	−1.54322	−	1.54322i
$982$	470.437	−	470.437i	0.479060	−	0.479060i
$983$		−	88.7858i		−	0.0903213i	−0.998980	−	0.0451606i	$-0.985620\pi$
$983$		−	88.7858i		−	0.0903213i	0.998980	−	0.0451606i	$-0.0143800\pi$
$984$	836.526			0.850128
$985$	−1694.44	+	1694.44i	−1.72024	+	1.72024i
$986$	−91.2237	−	91.2237i	−0.0925190	−	0.0925190i
$987$	−214.228			−0.217049
$988$	176.097	−	176.097i	0.178236	−	0.178236i
$989$			768.752i			0.777302i
$990$	2160.06	+	2160.06i	2.18188	+	2.18188i
$991$	309.154	−	309.154i	0.311962	−	0.311962i	−0.533708	−	0.845669i	$-0.679202\pi$
$991$	309.154	−	309.154i	0.311962	−	0.311962i	0.845669	+	0.533708i	$0.179202\pi$
$992$	−123.348			−0.124343
$993$	−2280.83	−	2280.83i	−2.29691	−	2.29691i
$994$	16.4732	−	16.4732i	0.0165726	−	0.0165726i
$995$		−	530.051i		−	0.532714i
$996$		−	178.839i		−	0.179558i
$997$	115.397			0.115744			0.0578722	−	0.998324i	$-0.481568\pi$
$997$	115.397			0.115744			0.0578722	+	0.998324i	$0.481568\pi$
$998$			167.022i			0.167357i
$999$	2644.30	−	2644.30i	2.64694	−	2.64694i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.3.c.a.187.1	✓	44
269.82	odd	4	inner	538.3.c.a.351.1	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.3.c.a.187.1	✓	44	1.1	even	1	trivial
538.3.c.a.351.1	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} +(-3.89974 - 3.89974i) q^{3} +2.00000i q^{4} -6.52679 q^{5} -7.79948i q^{6} +(-0.905272 + 0.905272i) q^{7} +(-2.00000 + 2.00000i) q^{8} +21.4159i q^{9} +(-6.52679 - 6.52679i) q^{10} +15.4536i q^{11} +(7.79948 - 7.79948i) q^{12} -12.6290i q^{13} -1.81054 q^{14} +(25.4528 + 25.4528i) q^{15} -4.00000 q^{16} +(-6.26998 - 6.26998i) q^{17} +(-21.4159 + 21.4159i) q^{18} +(6.97194 - 6.97194i) q^{19} -13.0536i q^{20} +7.06065 q^{21} +(-15.4536 + 15.4536i) q^{22} -16.3343 q^{23} +15.5990 q^{24} +17.5990 q^{25} +(12.6290 - 12.6290i) q^{26} +(48.4188 - 48.4188i) q^{27} +(-1.81054 - 1.81054i) q^{28} +(7.27465 - 7.27465i) q^{29} +50.9055i q^{30} +(15.4185 - 15.4185i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(60.2649 - 60.2649i) q^{33} -12.5400i q^{34} +(5.90852 - 5.90852i) q^{35} -42.8318 q^{36} +54.6130 q^{37} +13.9439 q^{38} +(-49.2498 + 49.2498i) q^{39} +(13.0536 - 13.0536i) q^{40} +53.6271 q^{41} +(7.06065 + 7.06065i) q^{42} -47.0638i q^{43} -30.9072 q^{44} -139.777i q^{45} +(-16.3343 - 16.3343i) q^{46} -30.3411 q^{47} +(15.5990 + 15.5990i) q^{48} +47.3610i q^{49} +(17.5990 + 17.5990i) q^{50} +48.9025i q^{51} +25.2580 q^{52} -44.1715 q^{53} +96.8376 q^{54} -100.862i q^{55} -3.62109i q^{56} -54.3775 q^{57} +14.5493 q^{58} +(24.8127 - 24.8127i) q^{59} +(-50.9055 + 50.9055i) q^{60} +26.4546 q^{61} +30.8370 q^{62} +(-19.3872 - 19.3872i) q^{63} -8.00000i q^{64} +82.4268i q^{65} +120.530 q^{66} +124.062 q^{67} +(12.5400 - 12.5400i) q^{68} +(63.6993 + 63.6993i) q^{69} +11.8170 q^{70} +(-9.09848 + 9.09848i) q^{71} +(-42.8318 - 42.8318i) q^{72} +115.086i q^{73} +(54.6130 + 54.6130i) q^{74} +(-68.6314 - 68.6314i) q^{75} +(13.9439 + 13.9439i) q^{76} +(-13.9897 - 13.9897i) q^{77} -98.4996 q^{78} -40.7905i q^{79} +26.1072 q^{80} -184.898 q^{81} +(53.6271 + 53.6271i) q^{82} +(11.4648 - 11.4648i) q^{83} +14.1213i q^{84} +(40.9228 + 40.9228i) q^{85} +(47.0638 - 47.0638i) q^{86} -56.7384 q^{87} +(-30.9072 - 30.9072i) q^{88} +127.857i q^{89} +(139.777 - 139.777i) q^{90} +(11.4327 + 11.4327i) q^{91} -32.6685i q^{92} -120.256 q^{93} +(-30.3411 - 30.3411i) q^{94} +(-45.5044 + 45.5044i) q^{95} +31.1979i q^{96} -53.6789i q^{97} +(-47.3610 + 47.3610i) q^{98} -330.952 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

L-functions

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