LMFDB - Embedded newform 572.2.e.b.131.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(131,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("572.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.20
Character	$\chi$	$=$	572.131
Dual form			572.2.e.b.131.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.847391 + 1.13222i) q^{2} +1.51262i q^{3} +(-0.563856 - 1.91887i) q^{4} +4.09054 q^{5} +(-1.71262 - 1.28178i) q^{6} -1.07796 q^{7} +(2.65040 + 0.987625i) q^{8} +0.711990 q^{9} +O(q^{10})$	\(q+(-0.847391 + 1.13222i) q^{2} +1.51262i q^{3} +(-0.563856 - 1.91887i) q^{4} +4.09054 q^{5} +(-1.71262 - 1.28178i) q^{6} -1.07796 q^{7} +(2.65040 + 0.987625i) q^{8} +0.711990 q^{9} +(-3.46629 + 4.63140i) q^{10} +(2.01367 - 2.63537i) q^{11} +(2.90252 - 0.852898i) q^{12} -1.00000i q^{13} +(0.913452 - 1.22049i) q^{14} +6.18741i q^{15} +(-3.36413 + 2.16393i) q^{16} -4.95679i q^{17} +(-0.603334 + 0.806131i) q^{18} +4.25161 q^{19} +(-2.30647 - 7.84921i) q^{20} -1.63054i q^{21} +(1.27746 + 4.51310i) q^{22} -4.04090i q^{23} +(-1.49390 + 4.00903i) q^{24} +11.7325 q^{25} +(1.13222 + 0.847391i) q^{26} +5.61482i q^{27} +(0.607813 + 2.06846i) q^{28} +2.98962i q^{29} +(-7.00553 - 5.24316i) q^{30} -1.52418i q^{31} +(0.400684 - 5.64265i) q^{32} +(3.98630 + 3.04591i) q^{33} +(5.61219 + 4.20034i) q^{34} -4.40943 q^{35} +(-0.401460 - 1.36622i) q^{36} -4.04615 q^{37} +(-3.60278 + 4.81377i) q^{38} +1.51262 q^{39} +(10.8415 + 4.03991i) q^{40} +2.56650i q^{41} +(1.84613 + 1.38170i) q^{42} -11.6209 q^{43} +(-6.19234 - 2.37800i) q^{44} +2.91242 q^{45} +(4.57520 + 3.42422i) q^{46} +4.40319i q^{47} +(-3.27320 - 5.08865i) q^{48} -5.83801 q^{49} +(-9.94201 + 13.2838i) q^{50} +7.49773 q^{51} +(-1.91887 + 0.563856i) q^{52} -11.6487 q^{53} +(-6.35722 - 4.75795i) q^{54} +(8.23697 - 10.7801i) q^{55} +(-2.85702 - 1.06462i) q^{56} +6.43106i q^{57} +(-3.38491 - 2.53338i) q^{58} +2.32396i q^{59} +(11.8729 - 3.48881i) q^{60} +14.7660i q^{61} +(1.72571 + 1.29158i) q^{62} -0.767495 q^{63} +(6.04919 + 5.23519i) q^{64} -4.09054i q^{65} +(-6.82660 + 1.93230i) q^{66} +3.90608i q^{67} +(-9.51145 + 2.79492i) q^{68} +6.11233 q^{69} +(3.73651 - 4.99245i) q^{70} +10.7862i q^{71} +(1.88706 + 0.703179i) q^{72} -6.92125i q^{73} +(3.42867 - 4.58114i) q^{74} +17.7468i q^{75} +(-2.39729 - 8.15829i) q^{76} +(-2.17065 + 2.84081i) q^{77} +(-1.28178 + 1.71262i) q^{78} +8.45992 q^{79} +(-13.7611 + 8.85165i) q^{80} -6.35710 q^{81} +(-2.90585 - 2.17483i) q^{82} -8.36477 q^{83} +(-3.12879 + 0.919388i) q^{84} -20.2759i q^{85} +(9.84741 - 13.1574i) q^{86} -4.52215 q^{87} +(7.93976 - 4.99601i) q^{88} -3.18626 q^{89} +(-2.46796 + 3.29751i) q^{90} +1.07796i q^{91} +(-7.75396 + 2.27848i) q^{92} +2.30550 q^{93} +(-4.98539 - 3.73122i) q^{94} +17.3914 q^{95} +(8.53516 + 0.606081i) q^{96} -7.92283 q^{97} +(4.94708 - 6.60992i) q^{98} +(1.43371 - 1.87635i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9}+O(q^{10}) $ 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9	$ 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9} - 8 q^{12} - 34 q^{14} + 26 q^{16} + 14 q^{20} - 8 q^{22} + 76 q^{25} + 2 q^{26} - 16 q^{33} + 32 q^{34} - 24 q^{36} - 32 q^{37} - 30 q^{38} + 54 q^{42} + 10 q^{44} + 12 q^{45} + 34 q^{48} - 36 q^{49} - 32 q^{53} - 36 q^{56} + 62 q^{58} + 4 q^{60} - 18 q^{64} - 30 q^{66} - 24 q^{69} - 30 q^{70} + 88 q^{77} - 10 q^{78} - 46 q^{80} + 64 q^{81} - 46 q^{82} + 98 q^{86} + 16 q^{88} + 24 q^{89} + 84 q^{92} + 8 q^{93} - 88 q^{97}+O(q^{100}) $ 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9 - 8 * q^12 - 34 * q^14 + 26 * q^16 + 14 * q^20 - 8 * q^22 + 76 * q^25 + 2 * q^26 - 16 * q^33 + 32 * q^34 - 24 * q^36 - 32 * q^37 - 30 * q^38 + 54 * q^42 + 10 * q^44 + 12 * q^45 + 34 * q^48 - 36 * q^49 - 32 * q^53 - 36 * q^56 + 62 * q^58 + 4 * q^60 - 18 * q^64 - 30 * q^66 - 24 * q^69 - 30 * q^70 + 88 * q^77 - 10 * q^78 - 46 * q^80 + 64 * q^81 - 46 * q^82 + 98 * q^86 + 16 * q^88 + 24 * q^89 + 84 * q^92 + 8 * q^93 - 88 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.847391	+	1.13222i	−0.599196	+	0.800602i
$2$	−0.847391	+	1.13222i	−0.599196	+	0.800602i
$3$			1.51262i			0.873310i	0.899629	+	0.436655i	$0.143837\pi$
$3$			1.51262i			0.873310i	−0.899629	+	0.436655i	$0.856163\pi$
$4$	−0.563856	−	1.91887i	−0.281928	−	0.959436i
$5$	4.09054			1.82934			0.914672	−	0.404198i	$-0.132449\pi$
$5$	4.09054			1.82934			0.914672	+	0.404198i	$0.132449\pi$
$6$	−1.71262	−	1.28178i	−0.699174	−	0.523284i
$7$	−1.07796			−0.407430			−0.203715	−	0.979030i	$-0.565302\pi$
$7$	−1.07796			−0.407430			−0.203715	+	0.979030i	$0.565302\pi$
$8$	2.65040	+	0.987625i	0.937056	+	0.349178i
$9$	0.711990			0.237330
$10$	−3.46629	+	4.63140i	−1.09614	+	1.46458i
$11$	2.01367	−	2.63537i	0.607143	−	0.794592i
$11$	2.01367	−	2.63537i	0.607143	−	0.794592i
$12$	2.90252	−	0.852898i	0.837885	−	0.246210i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	0.913452	−	1.22049i	0.244130	−	0.326189i
$15$			6.18741i			1.59758i
$16$	−3.36413	+	2.16393i	−0.841033	+	0.540983i
$17$		−	4.95679i		−	1.20220i	−0.799174	−	0.601099i	$-0.794730\pi$
$17$		−	4.95679i		−	1.20220i	0.799174	−	0.601099i	$-0.205270\pi$
$18$	−0.603334	+	0.806131i	−0.142207	+	0.190007i
$19$	4.25161			0.975386			0.487693	−	0.873015i	$-0.337839\pi$
$19$	4.25161			0.975386			0.487693	+	0.873015i	$0.337839\pi$
$20$	−2.30647	−	7.84921i	−0.515743	−	1.75514i
$21$		−	1.63054i		−	0.355812i
$22$	1.27746	+	4.51310i	0.272355	+	0.962197i
$23$		−	4.04090i		−	0.842585i	−0.906925	−	0.421293i	$-0.861577\pi$
$23$		−	4.04090i		−	0.842585i	0.906925	−	0.421293i	$-0.138423\pi$
$24$	−1.49390	+	4.00903i	−0.304941	+	0.818341i
$25$	11.7325			2.34650
$26$	1.13222	+	0.847391i	0.222047	+	0.166187i
$27$			5.61482i			1.08057i
$28$	0.607813	+	2.06846i	0.114866	+	0.390903i
$29$			2.98962i			0.555158i	0.960703	+	0.277579i	$0.0895321\pi$
$29$			2.98962i			0.555158i	−0.960703	+	0.277579i	$0.910468\pi$
$30$	−7.00553	−	5.24316i	−1.27903	−	0.957266i
$31$		−	1.52418i		−	0.273751i	−0.990588	−	0.136875i	$-0.956294\pi$
$31$		−	1.52418i		−	0.273751i	0.990588	−	0.136875i	$-0.0437060\pi$
$32$	0.400684	−	5.64265i	0.0708316	−	0.997488i
$33$	3.98630	+	3.04591i	0.693925	+	0.530224i
$34$	5.61219	+	4.20034i	0.962483	+	0.720353i
$35$	−4.40943			−0.745329
$36$	−0.401460	−	1.36622i	−0.0669099	−	0.227703i
$37$	−4.04615			−0.665182			−0.332591	−	0.943071i	$-0.607923\pi$
$37$	−4.04615			−0.665182			−0.332591	+	0.943071i	$0.607923\pi$
$38$	−3.60278	+	4.81377i	−0.584448	+	0.780896i
$39$	1.51262			0.242213
$40$	10.8415	+	4.03991i	1.71420	+	0.638767i
$41$			2.56650i			0.400821i	0.979712	+	0.200410i	$0.0642275\pi$
$41$			2.56650i			0.400821i	−0.979712	+	0.200410i	$0.935772\pi$
$42$	1.84613	+	1.38170i	0.284864	+	0.213201i
$43$	−11.6209			−1.77216			−0.886082	−	0.463528i	$-0.846583\pi$
$43$	−11.6209			−1.77216			−0.886082	+	0.463528i	$0.846583\pi$
$44$	−6.19234	−	2.37800i	−0.933531	−	0.358497i
$45$	2.91242			0.434158
$46$	4.57520	+	3.42422i	0.674576	+	0.504874i
$47$			4.40319i			0.642271i	0.947033	+	0.321136i	$0.104065\pi$
$47$			4.40319i			0.642271i	−0.947033	+	0.321136i	$0.895935\pi$
$48$	−3.27320	−	5.08865i	−0.472446	−	0.734483i
$49$	−5.83801			−0.834001
$50$	−9.94201	+	13.2838i	−1.40601	+	1.87861i
$51$	7.49773			1.04989
$52$	−1.91887	+	0.563856i	−0.266100	+	0.0781927i
$53$	−11.6487			−1.60008			−0.800038	−	0.599950i	$-0.795187\pi$
$53$	−11.6487			−1.60008			−0.800038	+	0.599950i	$0.795187\pi$
$54$	−6.35722	−	4.75795i	−0.865109	−	0.647475i
$55$	8.23697	−	10.7801i	1.11067	−	1.45358i
$56$	−2.85702	−	1.06462i	−0.381785	−	0.142266i
$57$			6.43106i			0.851814i
$58$	−3.38491	−	2.53338i	−0.444461	−	0.332649i
$59$			2.32396i			0.302554i	0.988491	+	0.151277i	$0.0483385\pi$
$59$			2.32396i			0.302554i	−0.988491	+	0.151277i	$0.951661\pi$
$60$	11.8729	−	3.48881i	1.53278	−	0.450403i
$61$			14.7660i			1.89059i	0.326220	+	0.945294i	$0.394225\pi$
$61$			14.7660i			1.89059i	−0.326220	+	0.945294i	$0.605775\pi$
$62$	1.72571	+	1.29158i	0.219165	+	0.164030i
$63$	−0.767495			−0.0966953
$64$	6.04919	+	5.23519i	0.756149	+	0.654399i
$65$		−	4.09054i		−	0.507369i
$66$	−6.82660	+	1.93230i	−0.840296	+	0.237850i
$67$			3.90608i			0.477204i	0.971117	+	0.238602i	$0.0766891\pi$
$67$			3.90608i			0.477204i	−0.971117	+	0.238602i	$0.923311\pi$
$68$	−9.51145	+	2.79492i	−1.15343	+	0.338933i
$69$	6.11233			0.735838
$70$	3.73651	−	4.99245i	0.446598	−	0.596712i
$71$			10.7862i			1.28009i	0.768337	+	0.640046i	$0.221085\pi$
$71$			10.7862i			1.28009i	−0.768337	+	0.640046i	$0.778915\pi$
$72$	1.88706	+	0.703179i	0.222392	+	0.0828704i
$73$		−	6.92125i		−	0.810071i	−0.914301	−	0.405036i	$-0.867259\pi$
$73$		−	6.92125i		−	0.810071i	0.914301	−	0.405036i	$-0.132741\pi$
$74$	3.42867	−	4.58114i	0.398575	−	0.532547i
$75$			17.7468i			2.04922i
$76$	−2.39729	−	8.15829i	−0.274988	−	0.935820i
$77$	−2.17065	+	2.84081i	−0.247368	+	0.323741i
$78$	−1.28178	+	1.71262i	−0.145133	+	0.193916i
$79$	8.45992			0.951815			0.475908	−	0.879495i	$-0.342120\pi$
$79$	8.45992			0.951815			0.475908	+	0.879495i	$0.342120\pi$
$80$	−13.7611	+	8.85165i	−1.53854	+	0.989644i
$81$	−6.35710			−0.706345
$82$	−2.90585	−	2.17483i	−0.320898	−	0.240170i
$83$	−8.36477			−0.918153			−0.459077	−	0.888397i	$-0.651820\pi$
$83$	−8.36477			−0.918153			−0.459077	+	0.888397i	$0.651820\pi$
$84$	−3.12879	+	0.919388i	−0.341379	+	0.100313i
$85$		−	20.2759i		−	2.19923i
$86$	9.84741	−	13.1574i	1.06187	−	1.41880i
$87$	−4.52215			−0.484825
$88$	7.93976	−	4.99601i	0.846382	−	0.532577i
$89$	−3.18626			−0.337743			−0.168872	−	0.985638i	$-0.554012\pi$
$89$	−3.18626			−0.337743			−0.168872	+	0.985638i	$0.554012\pi$
$90$	−2.46796	+	3.29751i	−0.260146	+	0.347588i
$91$			1.07796i			0.113001i
$92$	−7.75396	+	2.27848i	−0.808406	+	0.237548i
$93$	2.30550			0.239069
$94$	−4.98539	−	3.73122i	−0.514204	−	0.384846i
$95$	17.3914			1.78432
$96$	8.53516	+	0.606081i	0.871116	+	0.0618579i
$97$	−7.92283			−0.804441			−0.402221	−	0.915543i	$-0.631762\pi$
$97$	−7.92283			−0.804441			−0.402221	+	0.915543i	$0.631762\pi$
$98$	4.94708	−	6.60992i	0.499730	−	0.667703i
$99$	1.43371	−	1.87635i	0.144093	−	0.188581i
$100$	−6.61543	−	22.5131i	−0.661543	−	2.25131i
$101$			2.28086i			0.226954i	0.993541	+	0.113477i	$0.0361988\pi$
$101$			2.28086i			0.226954i	−0.993541	+	0.113477i	$0.963801\pi$
$102$	−6.35351	+	8.48910i	−0.629091	+	0.840546i
$103$		−	4.48563i		−	0.441982i	−0.975276	−	0.220991i	$-0.929071\pi$
$103$		−	4.48563i		−	0.441982i	0.975276	−	0.220991i	$-0.0709292\pi$
$104$	0.987625	−	2.65040i	0.0968446	−	0.259893i
$105$		−	6.66977i		−	0.650903i
$106$	9.87103	−	13.1890i	0.958759	−	1.28102i
$107$	15.6436			1.51233			0.756164	−	0.654382i	$-0.227071\pi$
$107$	15.6436			1.51233			0.756164	+	0.654382i	$0.227071\pi$
$108$	10.7741	−	3.16595i	1.03674	−	0.304643i
$109$		−	6.01133i		−	0.575781i	−0.957663	−	0.287890i	$-0.907046\pi$
$109$		−	6.01133i		−	0.575781i	0.957663	−	0.287890i	$-0.0929539\pi$
$110$	5.22548	+	18.4610i	0.498230	+	1.76019i
$111$		−	6.12027i		−	0.580910i
$112$	3.62639	−	2.33263i	0.342662	−	0.220413i
$113$	10.4704			0.984970			0.492485	−	0.870321i	$-0.336089\pi$
$113$	10.4704			0.984970			0.492485	+	0.870321i	$0.336089\pi$
$114$	−7.28139	−	5.44962i	−0.681964	−	0.510404i
$115$		−	16.5294i		−	1.54138i
$116$	5.73669	−	1.68571i	0.532639	−	0.156515i
$117$		−	0.711990i		−	0.0658235i
$118$	−2.63124	−	1.96930i	−0.242225	−	0.181289i
$119$			5.34321i			0.489812i
$120$	−6.11084	+	16.3991i	−0.557841	+	1.49703i
$121$	−2.89030	−	10.6135i	−0.262754	−	0.964863i
$122$	−16.7184	−	12.5125i	−1.51361	−	1.13283i
$123$	−3.88214			−0.350041
$124$	−2.92470	+	0.859417i	−0.262646	+	0.0771779i
$125$	27.5395			2.46321
$126$	0.650369	−	0.868975i	0.0579395	−	0.0774145i
$127$	−1.64674			−0.146124			−0.0730622	−	0.997327i	$-0.523277\pi$
$127$	−1.64674			−0.146124			−0.0730622	+	0.997327i	$0.523277\pi$
$128$	−11.0534	+	2.41278i	−0.976995	+	0.213261i
$129$		−	17.5779i		−	1.54765i
$130$	4.63140	+	3.46629i	0.406200	+	0.304013i
$131$	9.77356			0.853920			0.426960	−	0.904270i	$-0.359584\pi$
$131$	9.77356			0.853920			0.426960	+	0.904270i	$0.359584\pi$
$132$	3.59700	−	9.36664i	0.313079	−	0.815262i
$133$	−4.58306			−0.397401
$134$	−4.42255	−	3.30998i	−0.382050	−	0.285939i
$135$			22.9676i			1.97674i
$136$	4.89545	−	13.1375i	0.419781	−	1.12653i
$137$	−22.2473			−1.90071			−0.950357	−	0.311160i	$-0.899282\pi$
$137$	−22.2473			−1.90071			−0.950357	+	0.311160i	$0.899282\pi$
$138$	−5.17954	+	6.92052i	−0.440911	+	0.589114i
$139$	−10.3410			−0.877110			−0.438555	−	0.898704i	$-0.644510\pi$
$139$	−10.3410			−0.877110			−0.438555	+	0.898704i	$0.644510\pi$
$140$	2.48628	+	8.46112i	0.210129	+	0.715095i
$141$	−6.66034			−0.560902
$142$	−12.2124	−	9.14017i	−1.02484	−	0.767026i
$143$	−2.63537	−	2.01367i	−0.220380	−	0.168391i
$144$	−2.39523	+	1.54070i	−0.199602	+	0.128392i
$145$			12.2291i			1.01558i
$146$	7.83640	+	5.86501i	0.648545	+	0.485392i
$147$		−	8.83067i		−	0.728341i
$148$	2.28144	+	7.76403i	0.187533	+	0.638200i
$149$			2.30555i			0.188878i	0.995531	+	0.0944391i	$0.0301058\pi$
$149$			2.30555i			0.188878i	−0.995531	+	0.0944391i	$0.969894\pi$
$150$	−20.0933	−	15.0384i	−1.64061	−	1.22788i
$151$	0.548563			0.0446415			0.0223207	−	0.999751i	$-0.492895\pi$
$151$	0.548563			0.0446415			0.0223207	+	0.999751i	$0.492895\pi$
$152$	11.2684	+	4.19899i	0.913992	+	0.340583i
$153$		−	3.52919i		−	0.285318i
$154$	−1.37704	−	4.86494i	−0.110965	−	0.392028i
$155$		−	6.23471i		−	0.500784i
$156$	−0.852898	−	2.90252i	−0.0682865	−	0.232387i
$157$	7.82772			0.624720			0.312360	−	0.949964i	$-0.398880\pi$
$157$	7.82772			0.624720			0.312360	+	0.949964i	$0.398880\pi$
$158$	−7.16886	+	9.57851i	−0.570324	+	0.762026i
$159$		−	17.6201i		−	1.39736i
$160$	1.63901	−	23.0814i	0.129575	−	1.82475i
$161$			4.35592i			0.343294i
$162$	5.38695	−	7.19765i	0.423239	−	0.565501i
$163$			9.91982i			0.776980i	0.921453	+	0.388490i	$0.127003\pi$
$163$			9.91982i			0.776980i	−0.921453	+	0.388490i	$0.872997\pi$
$164$	4.92479	−	1.44714i	0.384562	−	0.113003i
$165$	16.3061	+	12.4594i	1.26943	+	0.969962i
$166$	7.08824	−	9.47079i	0.550154	−	0.735076i
$167$	1.89119			0.146345			0.0731724	−	0.997319i	$-0.476688\pi$
$167$	1.89119			0.146345			0.0731724	+	0.997319i	$0.476688\pi$
$168$	1.61036	−	4.32157i	0.124242	−	0.333416i
$169$	−1.00000			−0.0769231
$170$	22.9569	+	17.1817i	1.76071	+	1.31777i
$171$	3.02710			0.231488
$172$	6.55249	+	22.2989i	0.499622	+	1.70028i
$173$			20.8605i			1.58600i	0.609224	+	0.792998i	$0.291481\pi$
$173$			20.8605i			1.58600i	−0.609224	+	0.792998i	$0.708519\pi$
$174$	3.83203	−	5.12008i	0.290505	−	0.388152i
$175$	−12.6471			−0.956033
$176$	−1.07149	+	13.2232i	−0.0807664	+	0.996733i
$177$	−3.51526			−0.264223
$178$	2.70001	−	3.60756i	0.202375	−	0.270398i
$179$		−	21.0688i		−	1.57475i	−0.616472	−	0.787377i	$-0.711439\pi$
$179$		−	21.0688i		−	1.57475i	0.616472	−	0.787377i	$-0.288561\pi$
$180$	−1.64219	−	5.58856i	−0.122401	−	0.416547i
$181$	12.2952			0.913893			0.456947	−	0.889494i	$-0.348943\pi$
$181$	12.2952			0.913893			0.456947	+	0.889494i	$0.348943\pi$
$182$	−1.22049	−	0.913452i	−0.0904686	−	0.0677096i
$183$	−22.3352			−1.65107
$184$	3.99089	−	10.7100i	0.294212	−	0.789550i
$185$	−16.5509			−1.21685
$186$	−1.95366	+	2.61034i	−0.143249	+	0.191399i
$187$	−13.0630	−	9.98132i	−0.955258	−	0.729907i
$188$	8.44915	−	2.48276i	0.616218	−	0.181074i
$189$		−	6.05254i		−	0.440257i
$190$	−14.7373	+	19.6909i	−1.06916	+	1.42853i
$191$			6.55027i			0.473961i	0.971514	+	0.236981i	$0.0761578\pi$
$191$			6.55027i			0.473961i	−0.971514	+	0.236981i	$0.923842\pi$
$192$	−7.91884	+	9.15011i	−0.571493	+	0.660353i
$193$		−	26.2758i		−	1.89137i	−0.325080	−	0.945686i	$-0.605391\pi$
$193$		−	26.2758i		−	1.89137i	0.325080	−	0.945686i	$-0.394609\pi$
$194$	6.71374	−	8.97040i	0.482018	−	0.644037i
$195$	6.18741			0.443090
$196$	3.29179	+	11.2024i	0.235128	+	0.800170i
$197$			0.723430i			0.0515423i	0.999668	+	0.0257711i	$0.00820412\pi$
$197$			0.723430i			0.0515423i	−0.999668	+	0.0257711i	$0.991796\pi$
$198$	0.909536	+	3.21328i	0.0646379	+	0.228358i
$199$			3.85429i			0.273224i	0.990625	+	0.136612i	$0.0436213\pi$
$199$			3.85429i			0.273224i	−0.990625	+	0.136612i	$0.956379\pi$
$200$	31.0957	+	11.5873i	2.19880	+	0.819345i
$201$	−5.90840			−0.416747
$202$	−2.58244	−	1.93278i	−0.181700	−	0.135990i
$203$		−	3.22268i		−	0.226188i
$204$	−4.22764	−	14.3872i	−0.295994	−	1.00730i
$205$			10.4984i			0.733239i
$206$	5.07873	+	3.80109i	0.353852	+	0.264834i
$207$		−	2.87708i		−	0.199971i
$208$	2.16393	+	3.36413i	0.150042	+	0.233261i
$209$	8.56132	−	11.2045i	0.592199	−	0.775034i
$210$	7.55167	+	5.65191i	0.521115	+	0.390019i
$211$	21.3594			1.47044			0.735219	−	0.677829i	$-0.237079\pi$
$211$	21.3594			1.47044			0.735219	+	0.677829i	$0.237079\pi$
$212$	6.56820	+	22.3524i	0.451106	+	1.53517i
$213$	−16.3154			−1.11792
$214$	−13.2563	+	17.7121i	−0.906182	+	1.21077i
$215$	−47.5355			−3.24190
$216$	−5.54533	+	14.8815i	−0.377312	+	1.01256i
$217$			1.64300i			0.111534i
$218$	6.80616	+	5.09395i	0.460971	+	0.345006i
$219$	10.4692			0.707443
$220$	−25.3300	−	9.72730i	−1.70775	−	0.655814i
$221$	−4.95679			−0.333430
$222$	6.92951	+	5.18626i	0.465078	+	0.348079i
$223$		−	15.4630i		−	1.03548i	−0.855538	−	0.517741i	$-0.826773\pi$
$223$		−	15.4630i		−	1.03548i	0.855538	−	0.517741i	$-0.173227\pi$
$224$	−0.431920	+	6.08254i	−0.0288589	+	0.406406i
$225$	8.35341			0.556894
$226$	−8.87251	+	11.8548i	−0.590190	+	0.788569i
$227$	−23.2591			−1.54376			−0.771880	−	0.635768i	$-0.780684\pi$
$227$	−23.2591			−1.54376			−0.771880	+	0.635768i	$0.780684\pi$
$228$	12.3404	−	3.62619i	0.817261	−	0.240150i
$229$	−3.69206			−0.243978			−0.121989	−	0.992531i	$-0.538927\pi$
$229$	−3.69206			−0.243978			−0.121989	+	0.992531i	$0.538927\pi$
$230$	18.7150	+	14.0069i	1.23403	+	0.923588i
$231$	−4.29706	−	3.28336i	−0.282726	−	0.216029i
$232$	−2.95262	+	7.92367i	−0.193849	+	0.520215i
$233$			19.7269i			1.29235i	0.763189	+	0.646175i	$0.223632\pi$
$233$			19.7269i			1.29235i	−0.763189	+	0.646175i	$0.776368\pi$
$234$	0.806131	+	0.603334i	0.0526984	+	0.0394412i
$235$			18.0114i			1.17493i
$236$	4.45938	−	1.31038i	0.290281	−	0.0852984i
$237$			12.7966i			0.831230i
$238$	−6.04971	−	4.52779i	−0.392144	−	0.293493i
$239$	−23.7930			−1.53904			−0.769519	−	0.638624i	$-0.779504\pi$
$239$	−23.7930			−1.53904			−0.769519	+	0.638624i	$0.779504\pi$
$240$	−13.3892	−	20.8153i	−0.864266	−	1.34362i
$241$			8.01660i			0.516395i	0.966092	+	0.258197i	$0.0831285\pi$
$241$			8.01660i			0.516395i	−0.966092	+	0.258197i	$0.916872\pi$
$242$	14.4660	+	5.72132i	0.929913	+	0.367780i
$243$			7.22860i			0.463715i
$244$	28.3340	−	8.32587i	1.81390	−	0.533009i
$245$	−23.8806			−1.52567
$246$	3.28969	−	4.39545i	0.209743	−	0.280243i
$247$		−	4.25161i		−	0.270523i
$248$	1.50532	−	4.03968i	0.0955877	−	0.256520i
$249$		−	12.6527i		−	0.801832i
$250$	−23.3367	+	31.1808i	−1.47594	+	1.97205i
$251$		−	25.5367i		−	1.61186i	−0.592010	−	0.805931i	$-0.701665\pi$
$251$		−	25.5367i		−	1.61186i	0.592010	−	0.805931i	$-0.298335\pi$
$252$	0.432757	+	1.47272i	0.0272611	+	0.0927729i
$253$	−10.6492	−	8.13702i	−0.669512	−	0.511570i
$254$	1.39543	−	1.86448i	0.0875572	−	0.116988i
$255$	30.6697			1.92061
$256$	6.63479	−	14.5595i	0.414674	−	0.909970i
$257$	21.0282			1.31170			0.655852	−	0.754889i	$-0.272309\pi$
$257$	21.0282			1.31170			0.655852	+	0.754889i	$0.272309\pi$
$258$	19.9021	+	14.8954i	1.23905	+	0.927345i
$259$	4.36158			0.271015
$260$	−7.84921	+	2.30647i	−0.486787	+	0.143041i
$261$			2.12858i			0.131756i
$262$	−8.28203	+	11.0658i	−0.511666	+	0.683650i
$263$	−29.3614			−1.81050			−0.905251	−	0.424878i	$-0.860317\pi$
$263$	−29.3614			−1.81050			−0.905251	+	0.424878i	$0.860317\pi$
$264$	7.55706	+	12.0098i	0.465105	+	0.739153i
$265$	−47.6495			−2.92709
$266$	3.88364	−	5.18904i	0.238121	−	0.318160i
$267$		−	4.81960i		−	0.294955i
$268$	7.49527	−	2.20247i	0.457846	−	0.134537i
$269$	4.76880			0.290759			0.145379	−	0.989376i	$-0.453560\pi$
$269$	4.76880			0.290759			0.145379	+	0.989376i	$0.453560\pi$
$270$	−26.0045	−	19.4626i	−1.58258	−	1.18445i
$271$	15.5207			0.942817			0.471408	−	0.881915i	$-0.343746\pi$
$271$	15.5207			0.942817			0.471408	+	0.881915i	$0.343746\pi$
$272$	10.7262	+	16.6753i	0.650369	+	1.01109i
$273$	−1.63054			−0.0986846
$274$	18.8522	−	25.1889i	1.13890	−	1.52172i
$275$	23.6253	−	30.9194i	1.42466	−	1.86451i
$276$	−3.44647	−	11.7288i	−0.207453	−	0.705989i
$277$		−	17.6684i		−	1.06159i	−0.847500	−	0.530796i	$-0.821893\pi$
$277$		−	17.6684i		−	1.06159i	0.847500	−	0.530796i	$-0.178107\pi$
$278$	8.76286	−	11.7083i	0.525561	−	0.702217i
$279$		−	1.08520i		−	0.0649692i
$280$	−11.6867	−	4.35486i	−0.698415	−	0.260253i
$281$			5.69436i			0.339697i	0.985470	+	0.169849i	$0.0543278\pi$
$281$			5.69436i			0.339697i	−0.985470	+	0.169849i	$0.945672\pi$
$282$	5.64391	−	7.54099i	0.336090	−	0.449059i
$283$	0.316676			0.0188245			0.00941223	−	0.999956i	$-0.497004\pi$
$283$	0.316676			0.0188245			0.00941223	+	0.999956i	$0.497004\pi$
$284$	20.6974	−	6.08188i	1.22816	−	0.360893i
$285$			26.3065i			1.55826i
$286$	4.51310	−	1.27746i	0.266865	−	0.0755376i
$287$		−	2.76658i		−	0.163306i
$288$	0.285283	−	4.01751i	0.0168105	−	0.236734i
$289$	−7.56979			−0.445282
$290$	−13.8461	−	10.3629i	−0.813072	−	0.608529i
$291$		−	11.9842i		−	0.702526i
$292$	−13.2810	+	3.90259i	−0.777211	+	0.228382i
$293$			16.6341i			0.971775i	0.874021	+	0.485887i	$0.161503\pi$
$293$			16.6341i			0.971775i	−0.874021	+	0.485887i	$0.838497\pi$
$294$	9.99828	+	7.48303i	0.583112	+	0.436419i
$295$			9.50625i			0.553475i
$296$	−10.7239	−	3.99607i	−0.623313	−	0.232267i
$297$	14.7971	+	11.3064i	0.858615	+	0.656062i
$298$	−2.61040	−	1.95370i	−0.151216	−	0.113175i
$299$	−4.04090			−0.233691
$300$	34.0537	−	10.0066i	1.96609	−	0.577732i
$301$	12.5268			0.722033
$302$	−0.464848	+	0.621096i	−0.0267490	+	0.0357400i
$303$	−3.45006			−0.198201
$304$	−14.3030	+	9.20020i	−0.820332	+	0.527667i
$305$			60.4007i			3.45853i
$306$	3.99582	+	2.99060i	0.228426	+	0.170961i
$307$	11.2561			0.642419			0.321209	−	0.947008i	$-0.395911\pi$
$307$	11.2561			0.642419			0.321209	+	0.947008i	$0.395911\pi$
$308$	6.67509	+	2.56338i	0.380348	+	0.146062i
$309$	6.78504			0.385988
$310$	7.05908	+	5.28324i	0.400929	+	0.300068i
$311$			27.4383i			1.55589i	0.628335	+	0.777943i	$0.283737\pi$
$311$			27.4383i			1.55589i	−0.628335	+	0.777943i	$0.716263\pi$
$312$	4.00903	+	1.49390i	0.226967	+	0.0845753i
$313$	28.9030			1.63369			0.816847	−	0.576854i	$-0.195720\pi$
$313$	28.9030			1.63369			0.816847	+	0.576854i	$0.195720\pi$
$314$	−6.63314	+	8.86272i	−0.374330	+	0.500152i
$315$	−3.13947			−0.176889
$316$	−4.77017	−	16.2335i	−0.268343	−	0.913206i
$317$	−1.02885			−0.0577860			−0.0288930	−	0.999583i	$-0.509198\pi$
$317$	−1.02885			−0.0577860			−0.0288930	+	0.999583i	$0.509198\pi$
$318$	19.9498	+	14.9311i	1.11873	+	0.837294i
$319$	7.87874	+	6.02009i	0.441125	+	0.337061i
$320$	24.7445	+	21.4147i	1.38326	+	1.19712i
$321$			23.6628i			1.32073i
$322$	−4.93187	−	3.69117i	−0.274842	−	0.205701i
$323$		−	21.0743i		−	1.17261i
$324$	3.58449	+	12.1985i	0.199138	+	0.677692i
$325$		−	11.7325i		−	0.650801i
$326$	−11.2314	−	8.40597i	−0.622052	−	0.465564i
$327$	9.09283			0.502835
$328$	−2.53474	+	6.80225i	−0.139958	+	0.375592i
$329$		−	4.74645i		−	0.261680i
$330$	−27.9244	+	7.90415i	−1.53719	+	0.435109i
$331$			16.3751i			0.900055i	0.893015	+	0.450028i	$0.148586\pi$
$331$			16.3751i			0.900055i	−0.893015	+	0.450028i	$0.851414\pi$
$332$	4.71653	+	16.0509i	0.258853	+	0.880909i
$333$	−2.88082			−0.157868
$334$	−1.60258	+	2.14125i	−0.0876892	+	0.117164i
$335$			15.9780i			0.872970i
$336$	3.52837	+	5.48535i	0.192489	+	0.299250i
$337$			14.9651i			0.815203i	0.913160	+	0.407602i	$0.133635\pi$
$337$			14.9651i			0.815203i	−0.913160	+	0.407602i	$0.866365\pi$
$338$	0.847391	−	1.13222i	0.0460920	−	0.0615848i
$339$			15.8377i			0.860184i
$340$	−38.9069	+	11.4327i	−2.11002	+	0.620025i
$341$	−4.01677	−	3.06919i	−0.217520	−	0.166206i
$342$	−2.56514	+	3.42735i	−0.138707	+	0.185330i
$343$	13.8388			0.747227
$344$	−30.7999	−	11.4770i	−1.66062	−	0.618801i
$345$	25.0027			1.34610
$346$	−23.6188	−	17.6770i	−1.26975	−	0.950323i
$347$	5.69618			0.305787			0.152893	−	0.988243i	$-0.451141\pi$
$347$	5.69618			0.305787			0.152893	+	0.988243i	$0.451141\pi$
$348$	2.54984	+	8.67742i	0.136686	+	0.465158i
$349$		−	9.88019i		−	0.528875i	−0.964403	−	0.264437i	$-0.914814\pi$
$349$		−	9.88019i		−	0.528875i	0.964403	−	0.264437i	$-0.0851862\pi$
$350$	10.7171	−	14.3194i	0.572851	−	0.765402i
$351$	5.61482			0.299697
$352$	−14.0636	−	12.4184i	−0.749592	−	0.661900i
$353$	1.94910			0.103740			0.0518700	−	0.998654i	$-0.483482\pi$
$353$	1.94910			0.103740			0.0518700	+	0.998654i	$0.483482\pi$
$354$	2.97880	−	3.98006i	0.158322	−	0.211538i
$355$			44.1215i			2.34173i
$356$	1.79659	+	6.11403i	0.0952193	+	0.324043i
$357$	−8.08224			−0.427757
$358$	23.8545	+	17.8535i	1.26075	+	0.943587i
$359$	−28.8245			−1.52130			−0.760648	−	0.649164i	$-0.775119\pi$
$359$	−28.8245			−1.52130			−0.760648	+	0.649164i	$0.775119\pi$
$360$	7.71907	+	2.87638i	0.406831	+	0.151598i
$361$	−0.923822			−0.0486222
$362$	−10.4188	+	13.9209i	−0.547601	+	0.731665i
$363$	16.0541	−	4.37191i	0.842624	−	0.229466i
$364$	2.06846	−	0.607813i	0.108417	−	0.0318580i
$365$		−	28.3116i		−	1.48190i
$366$	18.9267	−	25.2885i	0.989314	−	1.32185i
$367$		−	8.94084i		−	0.466708i	−0.972392	−	0.233354i	$-0.925030\pi$
$367$		−	8.94084i		−	0.466708i	0.972392	−	0.233354i	$-0.0749701\pi$
$368$	8.74423	+	13.5941i	0.455825	+	0.708642i
$369$			1.82733i			0.0951268i
$370$	14.0251	−	18.7393i	0.729130	−	0.974210i
$371$	12.5568			0.651919
$372$	−1.29997	−	4.42396i	−0.0674002	−	0.229371i
$373$		−	14.0380i		−	0.726860i	−0.931621	−	0.363430i	$-0.881606\pi$
$373$		−	14.0380i		−	0.726860i	0.931621	−	0.363430i	$-0.118394\pi$
$374$	22.3705	−	6.33209i	1.15675	−	0.327424i
$375$			41.6567i			2.15114i
$376$	−4.34870	+	11.6702i	−0.224267	+	0.601844i
$377$	2.98962			0.153973
$378$	6.85282	+	5.12887i	0.352471	+	0.263801i
$379$		−	2.70770i		−	0.139085i	−0.997579	−	0.0695427i	$-0.977846\pi$
$379$		−	2.70770i		−	0.139085i	0.997579	−	0.0695427i	$-0.0221540\pi$
$380$	−9.80622	−	33.3718i	−0.503048	−	1.71194i
$381$		−	2.49089i		−	0.127612i
$382$	−7.41637	−	5.55064i	−0.379454	−	0.283996i
$383$		−	11.2916i		−	0.576975i	−0.957484	−	0.288487i	$-0.906848\pi$
$383$		−	11.2916i		−	0.576975i	0.957484	−	0.288487i	$-0.0931523\pi$
$384$	−3.64961	−	16.7196i	−0.186243	−	0.853219i
$385$	−8.87911	+	11.6204i	−0.452521	+	0.592233i
$386$	29.7500	+	22.2659i	1.51424	+	1.13330i
$387$	−8.27393			−0.420588
$388$	4.46733	+	15.2029i	0.226794	+	0.771810i
$389$	12.8635			0.652204			0.326102	−	0.945335i	$-0.394265\pi$
$389$	12.8635			0.652204			0.326102	+	0.945335i	$0.394265\pi$
$390$	−5.24316	+	7.00553i	−0.265498	+	0.354739i
$391$	−20.0299			−1.01296
$392$	−15.4730	−	5.76576i	−0.781506	−	0.291215i
$393$			14.7837i			0.745737i
$394$	−0.819084	−	0.613029i	−0.0412649	−	0.0308839i
$395$	34.6056			1.74120
$396$	−4.40889	−	1.69311i	−0.221555	−	0.0850821i
$397$	−3.36703			−0.168986			−0.0844931	−	0.996424i	$-0.526927\pi$
$397$	−3.36703			−0.168986			−0.0844931	+	0.996424i	$0.526927\pi$
$398$	−4.36392	−	3.26609i	−0.218743	−	0.163714i
$399$		−	6.93241i		−	0.347054i
$400$	−39.4696	+	25.3883i	−1.97348	+	1.26942i
$401$	7.87297			0.393157			0.196579	−	0.980488i	$-0.437017\pi$
$401$	7.87297			0.393157			0.196579	+	0.980488i	$0.437017\pi$
$402$	5.00673	−	6.68963i	0.249713	−	0.333648i
$403$	−1.52418			−0.0759248
$404$	4.37667	−	1.28607i	0.217747	−	0.0639846i
$405$	−26.0039			−1.29215
$406$	3.64879	+	2.73087i	0.181087	+	0.135531i
$407$	−8.14759	+	10.6631i	−0.403861	+	0.528549i
$408$	19.8719	+	7.40494i	0.983808	+	0.366599i
$409$		−	22.2967i		−	1.10250i	−0.834339	−	0.551252i	$-0.814150\pi$
$409$		−	22.2967i		−	1.10250i	0.834339	−	0.551252i	$-0.185850\pi$
$410$	−11.8865	−	8.89624i	−0.587033	−	0.439354i
$411$		−	33.6516i		−	1.65991i
$412$	−8.60735	+	2.52925i	−0.424054	+	0.124607i
$413$		−	2.50513i		−	0.123269i
$414$	3.25749	+	2.43801i	0.160097	+	0.119822i
$415$	−34.2164			−1.67962
$416$	−5.64265	−	0.400684i	−0.276653	−	0.0196451i
$417$		−	15.6419i		−	0.765989i
$418$	5.43125	+	19.1880i	0.265651	+	0.938513i
$419$		−	18.2677i		−	0.892435i	−0.894925	−	0.446217i	$-0.852771\pi$
$419$		−	18.2677i		−	0.892435i	0.894925	−	0.446217i	$-0.147229\pi$
$420$	−12.7984	+	3.76079i	−0.624500	+	0.183508i
$421$	20.2791			0.988344			0.494172	−	0.869364i	$-0.335471\pi$
$421$	20.2791			0.988344			0.494172	+	0.869364i	$0.335471\pi$
$422$	−18.0997	+	24.1835i	−0.881081	+	1.17724i
$423$			3.13503i			0.152430i
$424$	−30.8737	−	11.5046i	−1.49936	−	0.558711i
$425$		−	58.1555i		−	2.82096i
$426$	13.8256	−	18.4727i	0.669851	−	0.895006i
$427$		−	15.9171i		−	0.770282i
$428$	−8.82076	−	30.0181i	−0.426368	−	1.45098i
$429$	3.04591	−	3.98630i	0.147058	−	0.192460i
$430$	40.2812	−	53.8208i	1.94253	−	2.59547i
$431$	−22.8213			−1.09926			−0.549632	−	0.835407i	$-0.685232\pi$
$431$	−22.8213			−1.09926			−0.549632	+	0.835407i	$0.685232\pi$
$432$	−12.1501	−	18.8890i	−0.584572	−	0.908797i
$433$	20.8201			1.00055			0.500276	−	0.865866i	$-0.333232\pi$
$433$	20.8201			1.00055			0.500276	+	0.865866i	$0.333232\pi$
$434$	−1.86024	−	1.39226i	−0.0892945	−	0.0668308i
$435$	−18.4980			−0.886912
$436$	−11.5350	+	3.38952i	−0.552424	+	0.162329i
$437$		−	17.1803i		−	0.821846i
$438$	−8.87151	+	11.8535i	−0.423897	+	0.566381i
$439$	−26.2018			−1.25055			−0.625273	−	0.780406i	$-0.715012\pi$
$439$	−26.2018			−1.25055			−0.625273	+	0.780406i	$0.715012\pi$
$440$	32.4779	−	20.4364i	1.54832	−	0.974266i
$441$	−4.15660			−0.197933
$442$	4.20034	−	5.61219i	0.199790	−	0.266945i
$443$		−	18.0414i		−	0.857171i	−0.903501	−	0.428586i	$-0.859012\pi$
$443$		−	18.0414i		−	0.857171i	0.903501	−	0.428586i	$-0.140988\pi$
$444$	−11.7440	+	3.45095i	−0.557346	+	0.163775i
$445$	−13.0335			−0.617849
$446$	17.5076	+	13.1032i	0.829008	+	0.620456i
$447$	−3.48742			−0.164949
$448$	−6.52078	−	5.64332i	−0.308078	−	0.266622i
$449$	−15.9393			−0.752223			−0.376111	−	0.926574i	$-0.622739\pi$
$449$	−15.9393			−0.752223			−0.376111	+	0.926574i	$0.622739\pi$
$450$	−7.07861	+	9.45792i	−0.333689	+	0.445851i
$451$	6.76368	+	5.16808i	0.318489	+	0.243356i
$452$	−5.90378	−	20.0913i	−0.277691	−	0.945015i
$453$			0.829766i			0.0389858i
$454$	19.7096	−	26.3345i	0.925016	−	1.23594i
$455$			4.40943i			0.206717i
$456$	−6.35147	+	17.0448i	−0.297435	+	0.798198i
$457$		−	25.2965i		−	1.18332i	−0.806187	−	0.591661i	$-0.798472\pi$
$457$		−	25.2965i		−	1.18332i	0.806187	−	0.591661i	$-0.201528\pi$
$458$	3.12862	−	4.18023i	0.146191	−	0.195329i
$459$	27.8315			1.29906
$460$	−31.7179	+	9.32022i	−1.47885	+	0.434557i
$461$			11.2336i			0.523201i	0.965176	+	0.261601i	$0.0842503\pi$
$461$			11.2336i			0.523201i	−0.965176	+	0.261601i	$0.915750\pi$
$462$	7.35878	−	2.08294i	0.342362	−	0.0969072i
$463$			14.7217i			0.684174i	0.939668	+	0.342087i	$0.111134\pi$
$463$			14.7217i			0.684174i	−0.939668	+	0.342087i	$0.888866\pi$
$464$	−6.46933	−	10.0575i	−0.300331	−	0.466907i
$465$	9.43073			0.437339
$466$	−22.3352	−	16.7164i	−1.03466	−	0.774371i
$467$			4.92066i			0.227701i	0.993498	+	0.113850i	$0.0363185\pi$
$467$			4.92066i			0.227701i	−0.993498	+	0.113850i	$0.963682\pi$
$468$	−1.36622	+	0.401460i	−0.0631534	+	0.0185575i
$469$		−	4.21059i		−	0.194427i
$470$	−20.3929	−	15.2627i	−0.940655	−	0.704016i
$471$			11.8403i			0.545574i
$472$	−2.29520	+	6.15942i	−0.105645	+	0.283510i
$473$	−23.4005	+	30.6252i	−1.07596	+	1.40815i
$474$	−14.4886	−	10.8437i	−0.665484	−	0.498070i
$475$	49.8819			2.28874
$476$	10.2529	−	3.01280i	0.469943	−	0.138092i
$477$	−8.29378			−0.379746
$478$	20.1619	−	26.9389i	0.922186	−	1.23216i
$479$	13.7022			0.626069			0.313034	−	0.949742i	$-0.398655\pi$
$479$	13.7022			0.626069			0.313034	+	0.949742i	$0.398655\pi$
$480$	34.9134	+	2.47920i	1.59357	+	0.113159i
$481$			4.04615i			0.184488i
$482$	−9.07657	−	6.79320i	−0.413427	−	0.309422i
$483$	−6.58884			−0.299802
$484$	−18.7362	+	11.5306i	−0.851646	+	0.524118i
$485$	−32.4086			−1.47160
$486$	−8.18438	−	6.12545i	−0.371251	−	0.277856i
$487$			23.9531i			1.08542i	0.839920	+	0.542710i	$0.182602\pi$
$487$			23.9531i			1.08542i	−0.839920	+	0.542710i	$0.817398\pi$
$488$	−14.5832	+	39.1356i	−0.660152	+	1.77159i
$489$	−15.0049			−0.678544
$490$	20.2362	−	27.0381i	0.914178	−	1.22146i
$491$	−16.7372			−0.755338			−0.377669	−	0.925941i	$-0.623274\pi$
$491$	−16.7372			−0.755338			−0.377669	+	0.925941i	$0.623274\pi$
$492$	2.18897	+	7.44932i	0.0986862	+	0.335841i
$493$	14.8189			0.667411
$494$	4.81377	+	3.60278i	0.216582	+	0.162097i
$495$	5.86464	−	7.67529i	0.263596	−	0.344979i
$496$	3.29822	+	5.12754i	0.148094	+	0.230233i
$497$		−	11.6271i		−	0.521547i
$498$	14.3257	+	10.7218i	0.641949	+	0.480455i
$499$		−	32.9555i		−	1.47529i	−0.675188	−	0.737646i	$-0.735937\pi$
$499$		−	32.9555i		−	1.47529i	0.675188	−	0.737646i	$-0.264063\pi$
$500$	−15.5283	−	52.8447i	−0.694446	−	2.36329i
$501$			2.86065i			0.127804i
$502$	28.9132	+	21.6396i	1.29046	+	0.965821i
$503$	−10.9791			−0.489534			−0.244767	−	0.969582i	$-0.578711\pi$
$503$	−10.9791			−0.489534			−0.244767	+	0.969582i	$0.578711\pi$
$504$	−2.03417	−	0.757997i	−0.0906090	−	0.0337639i
$505$			9.32993i			0.415176i
$506$	18.2370	−	5.16207i	0.810733	−	0.229482i
$507$		−	1.51262i		−	0.0671777i
$508$	0.928523	+	3.15988i	0.0411966	+	0.140197i
$509$	−7.25004			−0.321352			−0.160676	−	0.987007i	$-0.551367\pi$
$509$	−7.25004			−0.321352			−0.160676	+	0.987007i	$0.551367\pi$
$510$	−25.9893	+	34.7250i	−1.15082	+	1.53765i
$511$			7.46082i			0.330047i
$512$	10.8624	+	19.8497i	0.480053	+	0.877240i
$513$			23.8720i			1.05398i
$514$	−17.8191	+	23.8086i	−0.785968	+	1.05015i
$515$		−	18.3486i		−	0.808538i
$516$	−33.7297	+	9.91140i	−1.48487	+	0.436325i
$517$	11.6040	+	8.86655i	0.510344	+	0.389951i
$518$	−3.69596	+	4.93827i	−0.162391	+	0.216975i
$519$	−31.5540			−1.38507
$520$	4.03991	−	10.8415i	0.177162	−	0.475433i
$521$	−17.3845			−0.761627			−0.380813	−	0.924652i	$-0.624356\pi$
$521$	−17.3845			−0.761627			−0.380813	+	0.924652i	$0.624356\pi$
$522$	−2.41002	−	1.80374i	−0.105484	−	0.0789475i
$523$	13.6792			0.598147			0.299074	−	0.954230i	$-0.403322\pi$
$523$	13.6792			0.598147			0.299074	+	0.954230i	$0.403322\pi$
$524$	−5.51088	−	18.7542i	−0.240744	−	0.819281i
$525$		−	19.1303i		−	0.834913i
$526$	24.8806	−	33.2436i	1.08485	−	1.44949i
$527$	−7.55504			−0.329103
$528$	−20.0016	−	1.62075i	−0.870457	−	0.0705341i
$529$	6.67115			0.290050
$530$	40.3778	−	53.9499i	1.75390	−	2.34343i
$531$			1.65464i			0.0718051i
$532$	2.58418	+	8.79429i	0.112039	+	0.381281i
$533$	2.56650			0.111168
$534$	5.45686	+	4.08408i	0.236141	+	0.176736i
$535$	63.9909			2.76657
$536$	−3.85774	+	10.3527i	−0.166629	+	0.447167i
$537$	31.8690			1.37525
$538$	−4.04104	+	5.39934i	−0.174222	+	0.232782i
$539$	−11.7558	+	15.3853i	−0.506358	+	0.662691i
$540$	44.0719	−	12.9504i	1.89655	−	0.557298i
$541$		−	15.4491i		−	0.664210i	−0.943242	−	0.332105i	$-0.892241\pi$
$541$		−	15.4491i		−	0.664210i	0.943242	−	0.332105i	$-0.107759\pi$
$542$	−13.1521	+	17.5729i	−0.564932	+	0.754821i
$543$			18.5979i			0.798112i
$544$	−27.9694	−	1.98611i	−1.19918	−	0.0851536i
$545$		−	24.5895i		−	1.05330i
$546$	1.38170	−	1.84613i	0.0591314	−	0.0790071i
$547$	16.6247			0.710819			0.355410	−	0.934711i	$-0.384341\pi$
$547$	16.6247			0.710819			0.355410	+	0.934711i	$0.384341\pi$
$548$	12.5443	+	42.6897i	0.535864	+	1.82361i
$549$			10.5132i			0.448693i
$550$	14.9877	+	52.9499i	0.639079	+	2.25779i
$551$			12.7107i			0.541494i
$552$	16.2001	+	6.03669i	0.689522	+	0.256939i
$553$	−9.11944			−0.387798
$554$	20.0046	+	14.9721i	0.849912	+	0.636102i
$555$		−	25.0352i		−	1.06268i
$556$	5.83082	+	19.8430i	0.247282	+	0.841531i
$557$			43.7652i			1.85439i	0.374577	+	0.927196i	$0.377788\pi$
$557$			43.7652i			1.85439i	−0.374577	+	0.927196i	$0.622212\pi$
$558$	1.22869	+	0.919589i	0.0520145	+	0.0389293i
$559$			11.6209i			0.491510i
$560$	14.8339	−	9.54170i	0.626847	−	0.403211i
$561$	15.0979	−	19.7593i	0.637435	−	0.834236i
$562$	−6.44728	−	4.82535i	−0.271962	−	0.203545i
$563$	25.1988			1.06200			0.531001	−	0.847371i	$-0.321816\pi$
$563$	25.1988			1.06200			0.531001	+	0.847371i	$0.321816\pi$
$564$	3.75547	+	12.7803i	0.158134	+	0.538149i
$565$	42.8294			1.80185
$566$	−0.268349	+	0.358548i	−0.0112795	+	0.0150709i
$567$	6.85269			0.287786
$568$	−10.6528	+	28.5878i	−0.446980	+	1.19952i
$569$		−	1.77335i		−	0.0743426i	−0.999309	−	0.0371713i	$-0.988165\pi$
$569$		−	1.77335i		−	0.0743426i	0.999309	−	0.0371713i	$-0.0118347\pi$
$570$	−29.7848	−	22.2919i	−1.24755	−	0.933704i
$571$	−28.0078			−1.17209			−0.586046	−	0.810278i	$-0.699316\pi$
$571$	−28.0078			−1.17209			−0.586046	+	0.810278i	$0.699316\pi$
$572$	−2.37800	+	6.19234i	−0.0994292	+	0.258915i
$573$	−9.90805			−0.413915
$574$	3.13239	+	2.34438i	0.130743	+	0.0978525i
$575$		−	47.4098i		−	1.97712i
$576$	4.30697	+	3.72740i	0.179457	+	0.155309i
$577$	2.22053			0.0924419			0.0462210	−	0.998931i	$-0.485282\pi$
$577$	2.22053			0.0924419			0.0462210	+	0.998931i	$0.485282\pi$
$578$	6.41458	−	8.57069i	0.266811	−	0.356494i
$579$	39.7452			1.65175
$580$	23.4662	−	6.89547i	0.974379	−	0.286319i
$581$	9.01688			0.374083
$582$	13.5688	+	10.1553i	0.562444	+	0.420951i
$583$	−23.4566	+	30.6986i	−0.971475	+	1.27141i
$584$	6.83560	−	18.3441i	0.282859	−	0.759083i
$585$		−	2.91242i		−	0.120414i
$586$	−18.8335	−	14.0956i	−0.778005	−	0.582284i
$587$		−	48.1296i		−	1.98652i	−0.115898	−	0.993261i	$-0.536974\pi$
$587$		−	48.1296i		−	1.98652i	0.115898	−	0.993261i	$-0.463026\pi$
$588$	−16.9449	+	4.97922i	−0.698796	+	0.205340i
$589$		−	6.48021i		−	0.267012i
$590$	−10.7632	−	8.05551i	−0.443113	−	0.331640i
$591$	−1.09427			−0.0450124
$592$	13.6118	−	8.75559i	0.559441	−	0.359853i
$593$		−	38.5953i		−	1.58492i	−0.609924	−	0.792460i	$-0.708800\pi$
$593$		−	38.5953i		−	1.58492i	0.609924	−	0.792460i	$-0.291200\pi$
$594$	−25.3403	+	7.17269i	−1.03972	+	0.294299i
$595$			21.8566i			0.896034i
$596$	4.42406	−	1.30000i	0.181216	−	0.0532500i
$597$	−5.83007			−0.238609
$598$	3.42422	−	4.57520i	0.140027	−	0.187094i
$599$		−	22.5857i		−	0.922827i	−0.887185	−	0.461414i	$-0.847342\pi$
$599$		−	22.5857i		−	0.922827i	0.887185	−	0.461414i	$-0.152658\pi$
$600$	−17.5271	+	47.0359i	−0.715542	+	1.92023i
$601$		−	20.9336i		−	0.853898i	−0.904276	−	0.426949i	$-0.859588\pi$
$601$		−	20.9336i		−	0.853898i	0.904276	−	0.426949i	$-0.140412\pi$
$602$	−10.6151	+	14.1831i	−0.432639	+	0.578061i
$603$			2.78109i			0.113255i
$604$	−0.309311	−	1.05262i	−0.0125857	−	0.0428306i
$605$	−11.8229	−	43.4149i	−0.480668	−	1.76507i
$606$	2.92355	−	3.90624i	0.118761	−	0.158680i
$607$	6.92979			0.281271			0.140636	−	0.990061i	$-0.455085\pi$
$607$	6.92979			0.281271			0.140636	+	0.990061i	$0.455085\pi$
$608$	1.70355	−	23.9903i	0.0690881	−	0.972936i
$609$	4.87469			0.197532
$610$	−68.3870	−	51.1830i	−2.76891	−	2.07234i
$611$	4.40319			0.178134
$612$	−6.77205	+	1.98995i	−0.273744	+	0.0804390i
$613$			13.9094i			0.561794i	0.959738	+	0.280897i	$0.0906320\pi$
$613$			13.9094i			0.561794i	−0.959738	+	0.280897i	$0.909368\pi$
$614$	−9.53831	+	12.7444i	−0.384935	+	0.514322i
$615$	−15.8800			−0.640345
$616$	−8.55873	+	5.38549i	−0.344841	+	0.216988i
$617$	6.16312			0.248118			0.124059	−	0.992275i	$-0.460409\pi$
$617$	6.16312			0.248118			0.124059	+	0.992275i	$0.460409\pi$
$618$	−5.74959	+	7.68218i	−0.231282	+	0.309022i
$619$			37.1366i			1.49265i	0.665584	+	0.746323i	$0.268183\pi$
$619$			37.1366i			1.49265i	−0.665584	+	0.746323i	$0.731817\pi$
$620$	−11.9636	+	3.51548i	−0.480470	+	0.141185i
$621$	22.6889			0.910475
$622$	−31.0663	−	23.2510i	−1.24565	−	0.932281i
$623$	3.43466			0.137607
$624$	−5.08865	+	3.27320i	−0.203709	+	0.131033i
$625$	53.9888			2.15955
$626$	−24.4922	+	32.7246i	−0.978903	+	1.30794i
$627$	16.9482	+	12.9500i	0.676845	+	0.517173i
$628$	−4.41371	−	15.0204i	−0.176126	−	0.599379i
$629$			20.0559i			0.799681i
$630$	2.66036	−	3.55458i	0.105991	−	0.141618i
$631$			3.86111i			0.153708i	0.997042	+	0.0768542i	$0.0244876\pi$
$631$			3.86111i			0.153708i	−0.997042	+	0.0768542i	$0.975512\pi$
$632$	22.4221	+	8.35523i	0.891905	+	0.332353i
$633$			32.3085i			1.28415i
$634$	0.871839	−	1.16489i	0.0346251	−	0.0462636i
$635$	−6.73605			−0.267312
$636$	−33.8106	+	9.93517i	−1.34068	+	0.393955i
$637$			5.83801i			0.231310i
$638$	−13.4925	+	3.81911i	−0.534172	+	0.151200i
$639$			7.67969i			0.303804i
$640$	−45.2145	+	9.86955i	−1.78726	+	0.390128i
$641$	−17.3177			−0.684007			−0.342003	−	0.939699i	$-0.611105\pi$
$641$	−17.3177			−0.684007			−0.342003	+	0.939699i	$0.611105\pi$
$642$	−26.7916	−	20.0517i	−1.05738	−	0.791377i
$643$		−	40.2334i		−	1.58665i	−0.608798	−	0.793325i	$-0.708348\pi$
$643$		−	40.2334i		−	1.58665i	0.608798	−	0.793325i	$-0.291652\pi$
$644$	8.35845	−	2.45611i	0.329369	−	0.0967843i
$645$		−	71.9031i		−	2.83118i
$646$	23.8608	+	17.8582i	0.938792	+	0.702622i
$647$			42.6474i			1.67664i	0.545178	+	0.838320i	$0.316462\pi$
$647$			42.6474i			1.67664i	−0.545178	+	0.838320i	$0.683538\pi$
$648$	−16.8488	−	6.27843i	−0.661885	−	0.246640i
$649$	6.12448	+	4.67968i	0.240407	+	0.183694i
$650$	13.2838	+	9.94201i	0.521033	+	0.389958i
$651$	−2.48523			−0.0974039
$652$	19.0349	−	5.59335i	0.745462	−	0.219052i
$653$	20.0564			0.784867			0.392433	−	0.919780i	$-0.371633\pi$
$653$	20.0564			0.784867			0.392433	+	0.919780i	$0.371633\pi$
$654$	−7.70519	+	10.2951i	−0.301297	+	0.402571i
$655$	39.9791			1.56211
$656$	−5.55374	−	8.63406i	−0.216837	−	0.337104i
$657$		−	4.92786i		−	0.192254i
$658$	5.37404	+	4.02210i	0.209502	+	0.156798i
$659$	29.8518			1.16286			0.581430	−	0.813597i	$-0.302494\pi$
$659$	29.8518			1.16286			0.581430	+	0.813597i	$0.302494\pi$
$660$	14.7137	−	38.3146i	0.572729	−	1.49139i
$661$	−8.90179			−0.346239			−0.173120	−	0.984901i	$-0.555385\pi$
$661$	−8.90179			−0.346239			−0.173120	+	0.984901i	$0.555385\pi$
$662$	−18.5402	−	13.8761i	−0.720586	−	0.539310i
$663$		−	7.49773i		−	0.291188i
$664$	−22.1700	−	8.26126i	−0.860361	−	0.320599i
$665$	−18.7472			−0.726984
$666$	2.44118	−	3.26172i	0.0945937	−	0.126389i
$667$	12.0807			0.467768
$668$	−1.06636	−	3.62895i	−0.0412587	−	0.140408i
$669$	23.3896			0.904296
$670$	−18.0906	−	13.5396i	−0.698901	−	0.523080i
$671$	38.9137	+	29.7337i	1.50225	+	1.14786i
$672$	−9.20055	−	0.653330i	−0.354919	−	0.0252028i
$673$			42.0797i			1.62205i	0.585009	+	0.811027i	$0.301091\pi$
$673$			42.0797i			1.62205i	−0.585009	+	0.811027i	$0.698909\pi$
$674$	−16.9439	−	12.6813i	−0.652654	−	0.488467i
$675$			65.8758i			2.53556i
$676$	0.563856	+	1.91887i	0.0216868	+	0.0738027i
$677$			23.9132i			0.919058i	0.888163	+	0.459529i	$0.151982\pi$
$677$			23.9132i			0.919058i	−0.888163	+	0.459529i	$0.848018\pi$
$678$	−17.9318	−	13.4207i	−0.688665	−	0.515419i
$679$	8.54048			0.327753
$680$	20.0250	−	53.7393i	0.767924	−	2.06081i
$681$		−	35.1821i		−	1.34818i
$682$	6.87878	−	1.94707i	0.263402	−	0.0745572i
$683$			20.0373i			0.766707i	0.923602	+	0.383353i	$0.125231\pi$
$683$			20.0373i			0.766707i	−0.923602	+	0.383353i	$0.874769\pi$
$684$	−1.70685	−	5.80862i	−0.0652630	−	0.222098i
$685$	−91.0034			−3.47706
$686$	−11.7269	+	15.6686i	−0.447735	+	0.598231i
$687$		−	5.58467i		−	0.213068i
$688$	39.0941	−	25.1468i	1.49045	−	0.958711i
$689$			11.6487i			0.443781i
$690$	−21.1871	+	28.3086i	−0.806578	+	1.07769i
$691$			30.4481i			1.15830i	0.815221	+	0.579151i	$0.196616\pi$
$691$			30.4481i			1.15830i	−0.815221	+	0.579151i	$0.803384\pi$
$692$	40.0287	−	11.7623i	1.52166	−	0.447137i
$693$	−1.54548	+	2.02263i	−0.0587079	+	0.0768334i
$694$	−4.82689	+	6.44934i	−0.183226	+	0.244814i
$695$	−42.3002			−1.60454
$696$	−11.9855	−	4.46618i	−0.454308	−	0.169290i
$697$	12.7216			0.481866
$698$	11.1866	+	8.37239i	0.423418	+	0.316900i
$699$	−29.8392			−1.12862
$700$	7.13116	+	24.2682i	0.269532	+	0.917252i
$701$		−	11.0535i		−	0.417484i	−0.977971	−	0.208742i	$-0.933063\pi$
$701$		−	11.0535i		−	0.417484i	0.977971	−	0.208742i	$-0.0669369\pi$
$702$	−4.75795	+	6.35722i	−0.179577	+	0.239938i
$703$	−17.2026			−0.648810
$704$	25.9777	−	5.39991i	0.979071	−	0.203517i
$705$	−27.2444			−1.02608
$706$	−1.65165	+	2.20681i	−0.0621606	+	0.0830544i
$707$		−	2.45867i		−	0.0924677i
$708$	1.98210	+	6.74534i	0.0744919	+	0.253505i
$709$	9.23034			0.346653			0.173326	−	0.984864i	$-0.444548\pi$
$709$	9.23034			0.346653			0.173326	+	0.984864i	$0.444548\pi$
$710$	−49.9554	−	37.3882i	−1.87479	−	1.40315i
$711$	6.02338			0.225894
$712$	−8.44486	−	3.14683i	−0.316485	−	0.117933i
$713$	−6.15905			−0.230658
$714$	6.84882	−	9.15089i	0.256311	−	0.342463i
$715$	−10.7801	−	8.23697i	−0.403151	−	0.308045i
$716$	−40.4283	+	11.8797i	−1.51087	+	0.443967i
$717$		−	35.9896i		−	1.34406i
$718$	24.4256	−	32.6357i	0.911555	−	1.21795i
$719$		−	41.2165i		−	1.53711i	−0.639781	−	0.768557i	$-0.720975\pi$
$719$		−	41.2165i		−	1.53711i	0.639781	−	0.768557i	$-0.279025\pi$
$720$	−9.79777	+	6.30228i	−0.365141	+	0.234872i
$721$			4.83532i			0.180077i
$722$	0.782839	−	1.04597i	0.0291343	−	0.0389271i
$723$	−12.1260			−0.450972
$724$	−6.93271	−	23.5929i	−0.257652	−	0.876822i
$725$			35.0757i			1.30268i
$726$	−8.65417	+	21.8816i	−0.321186	+	0.812102i
$727$			28.8970i			1.07173i	0.844303	+	0.535866i	$0.180015\pi$
$727$			28.8970i			1.07173i	−0.844303	+	0.535866i	$0.819985\pi$
$728$	−1.06462	+	2.85702i	−0.0394574	+	0.105888i
$729$	−30.0054			−1.11131
$730$	32.0551	+	23.9910i	1.18641	+	0.887948i
$731$			57.6022i			2.13049i
$732$	12.5939	+	42.8585i	0.465482	+	1.58409i
$733$		−	12.9916i		−	0.479854i	−0.970791	−	0.239927i	$-0.922876\pi$
$733$		−	12.9916i		−	0.479854i	0.970791	−	0.239927i	$-0.0771236\pi$
$734$	10.1230	+	7.57639i	0.373647	+	0.279650i
$735$		−	36.1222i		−	1.33239i
$736$	−22.8014	−	1.61912i	−0.840469	−	0.0596816i
$737$	10.2939	+	7.86554i	0.379183	+	0.289731i
$738$	−2.06894	−	1.54846i	−0.0761587	−	0.0569996i
$739$	−15.4904			−0.569824			−0.284912	−	0.958554i	$-0.591964\pi$
$739$	−15.4904			−0.569824			−0.284912	+	0.958554i	$0.591964\pi$
$740$	9.33233	+	31.7591i	0.343063	+	1.16749i
$741$	6.43106			0.236251
$742$	−10.6406	+	14.2171i	−0.390627	+	0.521927i
$743$	9.59836			0.352130			0.176065	−	0.984379i	$-0.443663\pi$
$743$	9.59836			0.352130			0.176065	+	0.984379i	$0.443663\pi$
$744$	6.11048	+	2.27697i	0.224021	+	0.0834777i
$745$			9.43094i			0.345523i
$746$	15.8941	+	11.8957i	0.581926	+	0.435532i
$747$	−5.95564			−0.217905
$748$	−11.7873	+	30.6942i	−0.430985	+	1.12229i
$749$	−16.8632			−0.616168
$750$	−47.1646	−	35.2995i	−1.72221	−	1.28896i
$751$			35.3232i			1.28896i	0.764621	+	0.644480i	$0.222926\pi$
$751$			35.3232i			1.28896i	−0.764621	+	0.644480i	$0.777074\pi$
$752$	−9.52821	−	14.8129i	−0.347458	−	0.540172i
$753$	38.6272			1.40765
$754$	−2.53338	+	3.38491i	−0.0922601	+	0.123271i
$755$	2.24392			0.0816645
$756$	−11.6140	+	3.41276i	−0.422399	+	0.124121i
$757$	−15.2389			−0.553866			−0.276933	−	0.960889i	$-0.589318\pi$
$757$	−15.2389			−0.553866			−0.276933	+	0.960889i	$0.589318\pi$
$758$	3.06572	+	2.29449i	0.111352	+	0.0833395i
$759$	12.3082	−	16.1082i	0.446759	−	0.584691i
$760$	46.0940	+	17.1761i	1.67200	+	0.623044i
$761$		−	3.85293i		−	0.139669i	−0.997559	−	0.0698343i	$-0.977753\pi$
$761$		−	3.85293i		−	0.139669i	0.997559	−	0.0698343i	$-0.0222471\pi$
$762$	2.82024	+	2.11076i	0.102166	+	0.0764646i
$763$			6.47996i			0.234590i
$764$	12.5691	−	3.69341i	0.454735	−	0.133623i
$765$		−	14.4363i		−	0.521944i
$766$	12.7846	+	9.56842i	0.461927	+	0.345721i
$767$	2.32396			0.0839134
$768$	22.0230	+	10.0359i	0.794686	+	0.362139i
$769$		−	37.2562i		−	1.34349i	−0.740782	−	0.671746i	$-0.765545\pi$
$769$		−	37.2562i		−	1.34349i	0.740782	−	0.671746i	$-0.234455\pi$
$770$	−5.63285	−	19.9002i	−0.202994	−	0.717153i
$771$			31.8076i			1.14552i
$772$	−50.4199	+	14.8158i	−1.81465	+	0.533231i
$773$	6.99877			0.251728			0.125864	−	0.992047i	$-0.459830\pi$
$773$	6.99877			0.251728			0.125864	+	0.992047i	$0.459830\pi$
$774$	7.01126	−	9.36793i	0.252015	−	0.336723i
$775$		−	17.8824i		−	0.642355i
$776$	−20.9986	−	7.82478i	−0.753807	−	0.280893i
$777$			6.59739i			0.236680i
$778$	−10.9004	+	14.5643i	−0.390798	+	0.522156i
$779$			10.9118i			0.390955i
$780$	−3.48881	−	11.8729i	−0.124919	−	0.425116i
$781$	28.4257	+	21.7199i	1.01715	+	0.777199i
$782$	16.9732	−	22.6783i	0.606959	−	0.810974i
$783$	−16.7862			−0.599889
$784$	19.6398	−	12.6331i	0.701423	−	0.451181i
$785$	32.0196			1.14283
$786$	−16.7384	−	12.5275i	−0.597039	−	0.446843i
$787$	−32.0371			−1.14200			−0.571000	−	0.820950i	$-0.693444\pi$
$787$	−32.0371			−1.14200			−0.571000	+	0.820950i	$0.693444\pi$
$788$	1.38817	−	0.407910i	0.0494515	−	0.0145312i
$789$		−	44.4126i		−	1.58113i
$790$	−29.3245	+	39.1813i	−1.04332	+	1.39401i
$791$	−11.2866			−0.401306
$792$	5.65303	−	3.55711i	0.200872	−	0.126396i
$793$	14.7660			0.524355
$794$	2.85319	−	3.81222i	0.101256	−	0.135291i
$795$		−	72.0755i		−	2.55625i
$796$	7.39589	−	2.17326i	0.262140	−	0.0770293i
$797$	49.7653			1.76278			0.881389	−	0.472390i	$-0.156609\pi$
$797$	49.7653			1.76278			0.881389	+	0.472390i	$0.156609\pi$
$798$	7.84903	+	5.87446i	0.277853	+	0.207954i
$799$	21.8257			0.772138
$800$	4.70102	−	66.2023i	0.166206	−	2.34060i
$801$	−2.26859			−0.0801566
$802$	−6.67148	+	8.91395i	−0.235578	+	0.314763i
$803$	−18.2400	−	13.9371i	−0.643677	−	0.491829i
$804$	3.33149	+	11.3375i	0.117493	+	0.399842i
$805$			17.8180i			0.628003i
$806$	1.29158	−	1.72571i	0.0454938	−	0.0607855i
$807$			7.21337i			0.253923i
$808$	−2.25263	+	6.04517i	−0.0792473	+	0.212668i
$809$			9.87870i			0.347317i	0.984806	+	0.173658i	$0.0555588\pi$
$809$			9.87870i			0.347317i	−0.984806	+	0.173658i	$0.944441\pi$
$810$	22.0355	−	29.4423i	0.774249	−	1.03450i
$811$	9.56800			0.335978			0.167989	−	0.985789i	$-0.446273\pi$
$811$	9.56800			0.335978			0.167989	+	0.985789i	$0.446273\pi$
$812$	−6.18391	+	1.81713i	−0.217013	+	0.0637687i
$813$			23.4769i			0.823371i
$814$	−5.16878	−	18.2607i	−0.181166	−	0.640036i
$815$			40.5774i			1.42136i
$816$	−25.2234	+	16.2246i	−0.882994	+	0.567974i
$817$	−49.4073			−1.72854
$818$	25.2449	+	18.8941i	0.882667	+	0.660616i
$819$			0.767495i			0.0268185i
$820$	20.1450	−	5.91957i	0.703495	−	0.206720i
$821$			2.41165i			0.0841670i	0.999114	+	0.0420835i	$0.0133996\pi$
$821$			2.41165i			0.0841670i	−0.999114	+	0.0420835i	$0.986600\pi$
$822$	38.1011	+	28.5161i	1.32893	+	0.994614i
$823$		−	44.5021i		−	1.55125i	−0.631196	−	0.775623i	$-0.717436\pi$
$823$		−	44.5021i		−	1.55125i	0.631196	−	0.775623i	$-0.282564\pi$
$824$	4.43012	−	11.8887i	0.154331	−	0.414162i
$825$	46.7692	+	35.7360i	1.62829	+	1.24417i
$826$	2.83637	+	2.12283i	0.0986898	+	0.0738626i
$827$	39.9929			1.39069			0.695344	−	0.718677i	$-0.255252\pi$
$827$	39.9929			1.39069			0.695344	+	0.718677i	$0.255252\pi$
$828$	−5.52074	+	1.62226i	−0.191859	+	0.0563773i
$829$	−29.0163			−1.00778			−0.503889	−	0.863769i	$-0.668098\pi$
$829$	−29.0163			−1.00778			−0.503889	+	0.863769i	$0.668098\pi$
$830$	28.9947	−	38.7406i	1.00642	−	1.34471i
$831$	26.7255			0.927098
$832$	5.23519	−	6.04919i	0.181498	−	0.209718i
$833$			28.9378i			1.00263i
$834$	17.7102	+	13.2548i	0.613253	+	0.458978i
$835$	7.73599			0.267715
$836$	−26.3274	−	10.1103i	−0.910553	−	0.349673i
$837$	8.55799			0.295807
$838$	20.6831	+	15.4799i	0.714485	+	0.534743i
$839$		−	35.7399i		−	1.23388i	−0.787011	−	0.616939i	$-0.788373\pi$
$839$		−	35.7399i		−	1.23388i	0.787011	−	0.616939i	$-0.211627\pi$
$840$	6.58723	−	17.6775i	0.227281	−	0.609933i
$841$	20.0622			0.691799
$842$	−17.1843	+	22.9605i	−0.592212	+	0.791270i
$843$	−8.61339			−0.296661
$844$	−12.0436	−	40.9858i	−0.414558	−	1.41079i
$845$	−4.09054			−0.140719
$846$	−3.54955	−	2.65659i	−0.122036	−	0.0913356i
$847$	3.11562	+	11.4409i	0.107054	+	0.393114i
$848$	39.1879	−	25.2071i	1.34572	−	0.865614i
$849$			0.479010i			0.0164396i
$850$	65.8450	+	49.2805i	2.25846	+	1.69031i
$851$			16.3501i			0.560473i
$852$	9.19956	+	31.3072i	0.315172	+	1.07257i
$853$			51.9977i			1.78037i	0.455603	+	0.890183i	$0.349424\pi$
$853$			51.9977i			1.78037i	−0.455603	+	0.890183i	$0.650576\pi$
$854$	18.0217	+	13.4880i	0.616689	+	0.461550i
$855$	12.3825			0.423472
$856$	41.4619	+	15.4501i	1.41714	+	0.528072i
$857$		−	26.0895i		−	0.891199i	−0.895232	−	0.445600i	$-0.852991\pi$
$857$		−	26.0895i		−	0.891199i	0.895232	−	0.445600i	$-0.147009\pi$
$858$	1.93230	+	6.82660i	0.0659677	+	0.233056i
$859$		−	24.0181i		−	0.819488i	−0.912200	−	0.409744i	$-0.865618\pi$
$859$		−	24.0181i		−	0.819488i	0.912200	−	0.409744i	$-0.134382\pi$
$860$	26.8032	+	91.2146i	0.913981	+	3.11039i
$861$	4.18478			0.142617
$862$	19.3386	−	25.8388i	0.658675	−	0.880073i
$863$		−	1.07867i		−	0.0367184i	−0.999831	−	0.0183592i	$-0.994156\pi$
$863$		−	1.07867i		−	0.0367184i	0.999831	−	0.0183592i	$-0.00584425\pi$
$864$	31.6824	+	2.24977i	1.07786	+	0.0765386i
$865$			85.3307i			2.90133i
$866$	−17.6428	+	23.5730i	−0.599527	+	0.801044i
$867$		−	11.4502i		−	0.388869i
$868$	3.15271	−	0.926415i	0.107010	−	0.0314446i
$869$	17.0355	−	22.2950i	0.577888	−	0.756305i
$870$	15.6751	−	20.9439i	0.531434	−	0.710063i
$871$	3.90608			0.132353
$872$	5.93693	−	15.9324i	0.201050	−	0.539539i
$873$	−5.64097			−0.190918
$874$	19.4519	+	14.5585i	0.657972	+	0.492447i
$875$	−29.6864			−1.00358
$876$	−5.90312	−	20.0891i	−0.199448	−	0.678746i
$877$			2.40683i			0.0812727i	0.999174	+	0.0406364i	$0.0129385\pi$
$877$			2.40683i			0.0812727i	−0.999174	+	0.0406364i	$0.987061\pi$
$878$	22.2032	−	29.6663i	0.749322	−	1.00119i
$879$	−25.1610			−0.848660
$880$	−4.38296	+	54.0898i	−0.147750	+	1.82337i
$881$	−30.7947			−1.03750			−0.518750	−	0.854926i	$-0.673603\pi$
$881$	−30.7947			−1.03750			−0.518750	+	0.854926i	$0.673603\pi$
$882$	3.52227	−	4.70620i	0.118601	−	0.158466i
$883$		−	27.8088i		−	0.935842i	−0.883770	−	0.467921i	$-0.845003\pi$
$883$		−	27.8088i		−	0.935842i	0.883770	−	0.467921i	$-0.154997\pi$
$884$	2.79492	+	9.51145i	0.0940032	+	0.319905i
$885$	−14.3793			−0.483355
$886$	20.4268	+	15.2881i	0.686253	+	0.513614i
$887$	−38.2723			−1.28506			−0.642529	−	0.766261i	$-0.722115\pi$
$887$	−38.2723			−1.28506			−0.642529	+	0.766261i	$0.722115\pi$
$888$	6.04453	−	16.2211i	0.202841	−	0.544346i
$889$	1.77512			0.0595355
$890$	11.0445	−	14.7569i	0.370212	−	0.494651i
$891$	−12.8011	+	16.7533i	−0.428852	+	0.561256i
$892$	−29.6716	+	8.71892i	−0.993477	+	0.291931i
$893$			18.7206i			0.626462i
$894$	2.95521	−	3.94853i	0.0988369	−	0.132059i
$895$		−	86.1826i		−	2.88077i
$896$	11.9151	−	2.60087i	0.398057	−	0.0868891i
$897$		−	6.11233i		−	0.204085i
$898$	13.5068	−	18.0469i	0.450729	−	0.602231i
$899$	4.55671			0.151975
$900$	−4.71012	−	16.0291i	−0.157004	−	0.534304i
$901$			57.7403i			1.92361i
$902$	−11.5829	+	3.27860i	−0.385668	+	0.109165i
$903$			18.9482i			0.630558i
$904$	27.7506	+	10.3408i	0.922972	+	0.343930i
$905$	50.2939			1.67182
$906$	−0.939480	−	0.703137i	−0.0312121	−	0.0233602i
$907$		−	3.57910i		−	0.118842i	−0.998233	−	0.0594211i	$-0.981075\pi$
$907$		−	3.57910i		−	0.118842i	0.998233	−	0.0594211i	$-0.0189255\pi$
$908$	13.1148	+	44.6312i	0.435229	+	1.48114i
$909$			1.62395i			0.0538629i
$910$	−4.99245	−	3.73651i	−0.165498	−	0.123864i
$911$			26.3928i			0.874433i	0.899356	+	0.437216i	$0.144036\pi$
$911$			26.3928i			0.874433i	−0.899356	+	0.437216i	$0.855964\pi$
$912$	−13.9164	−	21.6349i	−0.460817	−	0.716404i
$913$	−16.8439	+	22.0442i	−0.557451	+	0.729558i
$914$	28.6413	+	21.4361i	0.947371	+	0.709042i
$915$	−91.3631			−3.02037
$916$	2.08179	+	7.08458i	0.0687842	+	0.234081i
$917$	−10.5355			−0.347913
$918$	−23.5842	+	31.5114i	−0.778393	+	1.04003i
$919$	41.1806			1.35842			0.679212	−	0.733942i	$-0.262322\pi$
$919$	41.1806			1.35842			0.679212	+	0.733942i	$0.262322\pi$
$920$	16.3249	−	43.8096i	0.538215	−	1.44436i
$921$			17.0261i			0.561031i
$922$	−12.7189	−	9.51926i	−0.418876	−	0.313500i
$923$	10.7862			0.355033
$924$	−3.87742	+	10.0968i	−0.127558	+	0.332162i
$925$	−47.4714			−1.56085
$926$	−16.6682	−	12.4750i	−0.547751	−	0.409954i
$927$		−	3.19372i		−	0.104896i
$928$	16.8694	+	1.19789i	0.553764	+	0.0393227i
$929$	−29.4915			−0.967586			−0.483793	−	0.875182i	$-0.660741\pi$
$929$	−29.4915			−0.967586			−0.483793	+	0.875182i	$0.660741\pi$
$930$	−7.99152	+	10.6777i	−0.262052	+	0.350135i
$931$	−24.8209			−0.813473
$932$	37.8533	−	11.1231i	1.23993	−	0.364350i
$933$	−41.5037			−1.35877
$934$	−5.57128	−	4.16972i	−0.182298	−	0.136437i
$935$	−53.4345	−	40.8290i	−1.74750	−	1.33525i
$936$	0.703179	−	1.88706i	0.0229841	−	0.0616803i
$937$			13.5434i			0.442445i	0.975223	+	0.221222i	$0.0710046\pi$
$937$			13.5434i			0.442445i	−0.975223	+	0.221222i	$0.928995\pi$
$938$	4.76733	+	3.56802i	0.155659	+	0.116500i
$939$			43.7192i			1.42672i
$940$	34.5616	−	10.1558i	1.12727	−	0.331247i
$941$		−	3.41679i		−	0.111384i	−0.998448	−	0.0556920i	$-0.982263\pi$
$941$		−	3.41679i		−	0.111384i	0.998448	−	0.0556920i	$-0.0177365\pi$
$942$	−13.4059	−	10.0334i	−0.436788	−	0.326906i
$943$	10.3710			0.337726
$944$	−5.02890	−	7.81811i	−0.163677	−	0.254458i
$945$		−	24.7581i		−	0.805382i
$946$	−14.8451	−	52.4461i	−0.482657	−	1.70517i
$947$			25.6075i			0.832131i	0.909335	+	0.416066i	$0.136591\pi$
$947$			25.6075i			0.832131i	−0.909335	+	0.416066i	$0.863409\pi$
$948$	24.5551	−	7.21545i	0.797511	−	0.234347i
$949$	−6.92125			−0.224673
$950$	−42.2695	+	56.4775i	−1.37140	+	1.83237i
$951$		−	1.55626i		−	0.0504651i
$952$	−5.27709	+	14.1616i	−0.171031	+	0.458981i
$953$			9.71512i			0.314704i	0.987543	+	0.157352i	$0.0502957\pi$
$953$			9.71512i			0.314704i	−0.987543	+	0.157352i	$0.949704\pi$
$954$	7.02807	−	9.39040i	0.227542	−	0.304025i
$955$			26.7941i			0.867038i
$956$	13.4158	+	45.6556i	0.433898	+	1.47661i
$957$	−9.10610	+	11.9175i	−0.294358	+	0.385238i
$958$	−11.6111	+	15.5139i	−0.375138	+	0.501232i
$959$	23.9817			0.774408
$960$	−32.3923	+	37.4289i	−1.04546	+	1.20801i
$961$	28.6769			0.925061
$962$	−4.58114	−	3.42867i	−0.147702	−	0.110545i
$963$	11.1381			0.358921
$964$	15.3828	−	4.52021i	0.495447	−	0.145586i
$965$		−	107.482i		−	3.45997i
$966$	5.58332	−	7.46003i	0.179640	−	0.240022i
$967$	36.4829			1.17321			0.586605	−	0.809873i	$-0.300464\pi$
$967$	36.4829			1.17321			0.586605	+	0.809873i	$0.300464\pi$
$968$	2.82171	−	30.9845i	0.0906933	−	0.995879i
$969$	31.8774			1.02405
$970$	27.4628	−	36.6938i	0.881777	−	1.17817i
$971$		−	30.9169i		−	0.992171i	−0.868274	−	0.496086i	$-0.834770\pi$
$971$		−	30.9169i		−	0.992171i	0.868274	−	0.496086i	$-0.165230\pi$
$972$	13.8708	−	4.07589i	0.444905	−	0.130734i
$973$	11.1471			0.357361
$974$	−27.1203	−	20.2977i	−0.868989	−	0.650379i
$975$	17.7468			0.568351
$976$	−31.9526	−	49.6747i	−1.02278	−	1.59005i
$977$	−41.4638			−1.32654			−0.663272	−	0.748379i	$-0.730833\pi$
$977$	−41.4638			−1.32654			−0.663272	+	0.748379i	$0.730833\pi$
$978$	12.7150	−	16.9889i	0.406581	−	0.543244i
$979$	−6.41607	+	8.39697i	−0.205059	+	0.268368i
$980$	13.4652	+	45.8238i	0.430130	+	1.46379i
$981$		−	4.28000i		−	0.136650i
$982$	14.1829	−	18.9502i	0.452596	−	0.604726i
$983$		−	62.4923i		−	1.99319i	−0.0824321	−	0.996597i	$-0.526269\pi$
$983$		−	62.4923i		−	1.99319i	0.0824321	−	0.996597i	$-0.473731\pi$
$984$	−10.2892	−	3.83410i	−0.328008	−	0.122227i
$985$			2.95922i			0.0942885i
$986$	−12.5574	+	16.7783i	−0.399910	+	0.534330i
$987$	7.17957			0.228528
$988$	−8.15829	+	2.39729i	−0.259550	+	0.0762681i
$989$			46.9587i			1.49320i
$990$	3.72049	+	13.1441i	0.118245	+	0.417746i
$991$		−	36.1258i		−	1.14757i	−0.819005	−	0.573787i	$-0.805474\pi$
$991$		−	36.1258i		−	1.14757i	0.819005	−	0.573787i	$-0.194526\pi$
$992$	−8.60040	−	0.610714i	−0.273063	−	0.0193902i
$993$	−24.7692			−0.786027
$994$	13.1645	+	9.85272i	0.417552	+	0.312509i
$995$			15.7661i			0.499820i
$996$	−24.2789	+	7.13430i	−0.769306	+	0.226059i
$997$		−	18.1532i		−	0.574919i	−0.957793	−	0.287459i	$-0.907189\pi$
$997$		−	18.1532i		−	0.574919i	0.957793	−	0.287459i	$-0.0928107\pi$
$998$	37.3130	+	27.9262i	1.18112	+	0.883989i
$999$		−	22.7184i		−	0.718778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.e.b.131.20	yes	64
4.3	odd	2	inner	572.2.e.b.131.46	yes	64
11.10	odd	2	inner	572.2.e.b.131.45	yes	64
44.43	even	2	inner	572.2.e.b.131.19	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.e.b.131.19	✓	64	44.43	even	2	inner
572.2.e.b.131.20	yes	64	1.1	even	1	trivial
572.2.e.b.131.45	yes	64	11.10	odd	2	inner
572.2.e.b.131.46	yes	64	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.847391 + 1.13222i) q^{2} +1.51262i q^{3} +(-0.563856 - 1.91887i) q^{4} +4.09054 q^{5} +(-1.71262 - 1.28178i) q^{6} -1.07796 q^{7} +(2.65040 + 0.987625i) q^{8} +0.711990 q^{9} +O(q^{10})\)	\(q+(-0.847391 + 1.13222i) q^{2} +1.51262i q^{3} +(-0.563856 - 1.91887i) q^{4} +4.09054 q^{5} +(-1.71262 - 1.28178i) q^{6} -1.07796 q^{7} +(2.65040 + 0.987625i) q^{8} +0.711990 q^{9} +(-3.46629 + 4.63140i) q^{10} +(2.01367 - 2.63537i) q^{11} +(2.90252 - 0.852898i) q^{12} -1.00000i q^{13} +(0.913452 - 1.22049i) q^{14} +6.18741i q^{15} +(-3.36413 + 2.16393i) q^{16} -4.95679i q^{17} +(-0.603334 + 0.806131i) q^{18} +4.25161 q^{19} +(-2.30647 - 7.84921i) q^{20} -1.63054i q^{21} +(1.27746 + 4.51310i) q^{22} -4.04090i q^{23} +(-1.49390 + 4.00903i) q^{24} +11.7325 q^{25} +(1.13222 + 0.847391i) q^{26} +5.61482i q^{27} +(0.607813 + 2.06846i) q^{28} +2.98962i q^{29} +(-7.00553 - 5.24316i) q^{30} -1.52418i q^{31} +(0.400684 - 5.64265i) q^{32} +(3.98630 + 3.04591i) q^{33} +(5.61219 + 4.20034i) q^{34} -4.40943 q^{35} +(-0.401460 - 1.36622i) q^{36} -4.04615 q^{37} +(-3.60278 + 4.81377i) q^{38} +1.51262 q^{39} +(10.8415 + 4.03991i) q^{40} +2.56650i q^{41} +(1.84613 + 1.38170i) q^{42} -11.6209 q^{43} +(-6.19234 - 2.37800i) q^{44} +2.91242 q^{45} +(4.57520 + 3.42422i) q^{46} +4.40319i q^{47} +(-3.27320 - 5.08865i) q^{48} -5.83801 q^{49} +(-9.94201 + 13.2838i) q^{50} +7.49773 q^{51} +(-1.91887 + 0.563856i) q^{52} -11.6487 q^{53} +(-6.35722 - 4.75795i) q^{54} +(8.23697 - 10.7801i) q^{55} +(-2.85702 - 1.06462i) q^{56} +6.43106i q^{57} +(-3.38491 - 2.53338i) q^{58} +2.32396i q^{59} +(11.8729 - 3.48881i) q^{60} +14.7660i q^{61} +(1.72571 + 1.29158i) q^{62} -0.767495 q^{63} +(6.04919 + 5.23519i) q^{64} -4.09054i q^{65} +(-6.82660 + 1.93230i) q^{66} +3.90608i q^{67} +(-9.51145 + 2.79492i) q^{68} +6.11233 q^{69} +(3.73651 - 4.99245i) q^{70} +10.7862i q^{71} +(1.88706 + 0.703179i) q^{72} -6.92125i q^{73} +(3.42867 - 4.58114i) q^{74} +17.7468i q^{75} +(-2.39729 - 8.15829i) q^{76} +(-2.17065 + 2.84081i) q^{77} +(-1.28178 + 1.71262i) q^{78} +8.45992 q^{79} +(-13.7611 + 8.85165i) q^{80} -6.35710 q^{81} +(-2.90585 - 2.17483i) q^{82} -8.36477 q^{83} +(-3.12879 + 0.919388i) q^{84} -20.2759i q^{85} +(9.84741 - 13.1574i) q^{86} -4.52215 q^{87} +(7.93976 - 4.99601i) q^{88} -3.18626 q^{89} +(-2.46796 + 3.29751i) q^{90} +1.07796i q^{91} +(-7.75396 + 2.27848i) q^{92} +2.30550 q^{93} +(-4.98539 - 3.73122i) q^{94} +17.3914 q^{95} +(8.53516 + 0.606081i) q^{96} -7.92283 q^{97} +(4.94708 - 6.60992i) q^{98} +(1.43371 - 1.87635i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9}+O(q^{10}) \) 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9	\( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9} - 8 q^{12} - 34 q^{14} + 26 q^{16} + 14 q^{20} - 8 q^{22} + 76 q^{25} + 2 q^{26} - 16 q^{33} + 32 q^{34} - 24 q^{36} - 32 q^{37} - 30 q^{38} + 54 q^{42} + 10 q^{44} + 12 q^{45} + 34 q^{48} - 36 q^{49} - 32 q^{53} - 36 q^{56} + 62 q^{58} + 4 q^{60} - 18 q^{64} - 30 q^{66} - 24 q^{69} - 30 q^{70} + 88 q^{77} - 10 q^{78} - 46 q^{80} + 64 q^{81} - 46 q^{82} + 98 q^{86} + 16 q^{88} + 24 q^{89} + 84 q^{92} + 8 q^{93} - 88 q^{97}+O(q^{100}) \) 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9 - 8 * q^12 - 34 * q^14 + 26 * q^16 + 14 * q^20 - 8 * q^22 + 76 * q^25 + 2 * q^26 - 16 * q^33 + 32 * q^34 - 24 * q^36 - 32 * q^37 - 30 * q^38 + 54 * q^42 + 10 * q^44 + 12 * q^45 + 34 * q^48 - 36 * q^49 - 32 * q^53 - 36 * q^56 + 62 * q^58 + 4 * q^60 - 18 * q^64 - 30 * q^66 - 24 * q^69 - 30 * q^70 + 88 * q^77 - 10 * q^78 - 46 * q^80 + 64 * q^81 - 46 * q^82 + 98 * q^86 + 16 * q^88 + 24 * q^89 + 84 * q^92 + 8 * q^93 - 88 * q^97

Introduction

L-functions

Modular forms

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Representations

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Database

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