LMFDB - Embedded newform 572.2.e.b.131.19

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

$q$-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	$-0.856163\pi$
$3$		−	1.51262i		−	0.873310i	0.899629	−	0.436655i	$-0.143837\pi$
$4$	−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	$0.205270\pi$
$17$			4.95679i			1.20220i	−0.799174	+	0.601099i	$0.794730\pi$
$18$	−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	$0.138423\pi$
$23$			4.04090i			0.842585i	−0.906925	+	0.421293i	$0.861577\pi$
$24$	−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	$-0.910468\pi$
$29$		−	2.98962i		−	0.555158i	0.960703	−	0.277579i	$-0.0895321\pi$
$30$	−7.00553	+	5.24316i	−1.27903	+	0.957266i
$31$			1.52418i			0.273751i	0.990588	+	0.136875i	$0.0437060\pi$
$31$			1.52418i			0.273751i	−0.990588	+	0.136875i	$0.956294\pi$
$32$	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	$-0.935772\pi$
$41$		−	2.56650i		−	0.400821i	0.979712	−	0.200410i	$-0.0642275\pi$
$42$	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	$-0.895935\pi$
$47$		−	4.40319i		−	0.642271i	0.947033	−	0.321136i	$-0.104065\pi$
$48$	−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	$-0.951661\pi$
$59$		−	2.32396i		−	0.302554i	0.988491	−	0.151277i	$-0.0483385\pi$
$60$	11.8729	+	3.48881i	1.53278	+	0.450403i
$61$		−	14.7660i		−	1.89059i	−0.326220	−	0.945294i	$-0.605775\pi$
$61$		−	14.7660i		−	1.89059i	0.326220	−	0.945294i	$-0.394225\pi$
$62$	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	$-0.923311\pi$
$67$		−	3.90608i		−	0.477204i	0.971117	−	0.238602i	$-0.0766891\pi$
$68$	−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	$-0.778915\pi$
$71$		−	10.7862i		−	1.28009i	0.768337	−	0.640046i	$-0.221085\pi$
$72$	1.88706	−	0.703179i	0.222392	−	0.0828704i
$73$			6.92125i			0.810071i	0.914301	+	0.405036i	$0.132741\pi$
$73$			6.92125i			0.810071i	−0.914301	+	0.405036i	$0.867259\pi$
$74$	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	$-0.963801\pi$
$101$		−	2.28086i		−	0.226954i	0.993541	−	0.113477i	$-0.0361988\pi$
$102$	−6.35351	−	8.48910i	−0.629091	−	0.840546i
$103$			4.48563i			0.441982i	0.975276	+	0.220991i	$0.0709292\pi$
$103$			4.48563i			0.441982i	−0.975276	+	0.220991i	$0.929071\pi$
$104$	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	$0.0929539\pi$
$109$			6.01133i			0.575781i	−0.957663	+	0.287890i	$0.907046\pi$
$110$	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	$-0.969894\pi$
$149$		−	2.30555i		−	0.188878i	0.995531	−	0.0944391i	$-0.0301058\pi$
$150$	−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	$-0.872997\pi$
$163$		−	9.91982i		−	0.776980i	0.921453	−	0.388490i	$-0.127003\pi$
$164$	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	$-0.708519\pi$
$173$		−	20.8605i		−	1.58600i	0.609224	−	0.792998i	$-0.291481\pi$
$174$	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	$0.288561\pi$
$179$			21.0688i			1.57475i	−0.616472	+	0.787377i	$0.711439\pi$
$180$	−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	$-0.923842\pi$
$191$		−	6.55027i		−	0.473961i	0.971514	−	0.236981i	$-0.0761578\pi$
$192$	−7.91884	−	9.15011i	−0.571493	−	0.660353i
$193$			26.2758i			1.89137i	0.325080	+	0.945686i	$0.394609\pi$
$193$			26.2758i			1.89137i	−0.325080	+	0.945686i	$0.605391\pi$
$194$	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	$-0.991796\pi$
$197$		−	0.723430i		−	0.0515423i	0.999668	−	0.0257711i	$-0.00820412\pi$
$198$	0.909536	−	3.21328i	0.0646379	−	0.228358i
$199$		−	3.85429i		−	0.273224i	−0.990625	−	0.136612i	$-0.956379\pi$
$199$		−	3.85429i		−	0.273224i	0.990625	−	0.136612i	$-0.0436213\pi$
$200$	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	$0.173227\pi$
$223$			15.4630i			1.03548i	−0.855538	+	0.517741i	$0.826773\pi$
$224$	−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	$-0.776368\pi$
$233$		−	19.7269i		−	1.29235i	0.763189	−	0.646175i	$-0.223632\pi$
$234$	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	$-0.916872\pi$
$241$		−	8.01660i		−	0.516395i	0.966092	−	0.258197i	$-0.0831285\pi$
$242$	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	$0.298335\pi$
$251$			25.5367i			1.61186i	−0.592010	+	0.805931i	$0.701665\pi$
$252$	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	$0.178107\pi$
$277$			17.6684i			1.06159i	−0.847500	+	0.530796i	$0.821893\pi$
$278$	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	$-0.945672\pi$
$281$		−	5.69436i		−	0.339697i	0.985470	−	0.169849i	$-0.0543278\pi$
$282$	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	$-0.838497\pi$
$293$		−	16.6341i		−	0.971775i	0.874021	−	0.485887i	$-0.161503\pi$
$294$	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	$-0.716263\pi$
$311$		−	27.4383i		−	1.55589i	0.628335	−	0.777943i	$-0.283737\pi$
$312$	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	$-0.851414\pi$
$331$		−	16.3751i		−	0.900055i	0.893015	−	0.450028i	$-0.148586\pi$
$332$	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	$-0.866365\pi$
$337$		−	14.9651i		−	0.815203i	0.913160	−	0.407602i	$-0.133635\pi$
$338$	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	$0.0851862\pi$
$349$			9.88019i			0.528875i	−0.964403	+	0.264437i	$0.914814\pi$
$350$	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	$0.0749701\pi$
$367$			8.94084i			0.466708i	−0.972392	+	0.233354i	$0.925030\pi$
$368$	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	$0.118394\pi$
$373$			14.0380i			0.726860i	−0.931621	+	0.363430i	$0.881606\pi$
$374$	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	$0.0221540\pi$
$379$			2.70770i			0.139085i	−0.997579	+	0.0695427i	$0.977846\pi$
$380$	−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	$0.0931523\pi$
$383$			11.2916i			0.576975i	−0.957484	+	0.288487i	$0.906848\pi$
$384$	−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	$0.185850\pi$
$409$			22.2967i			1.10250i	−0.834339	+	0.551252i	$0.814150\pi$
$410$	−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	$0.147229\pi$
$419$			18.2677i			0.892435i	−0.894925	+	0.446217i	$0.852771\pi$
$420$	−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	$0.140988\pi$
$443$			18.0414i			0.857171i	−0.903501	+	0.428586i	$0.859012\pi$
$444$	−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	$0.201528\pi$
$457$			25.2965i			1.18332i	−0.806187	+	0.591661i	$0.798472\pi$
$458$	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	$-0.915750\pi$
$461$		−	11.2336i		−	0.523201i	0.965176	−	0.261601i	$-0.0842503\pi$
$462$	7.35878	+	2.08294i	0.342362	+	0.0969072i
$463$		−	14.7217i		−	0.684174i	−0.939668	−	0.342087i	$-0.888866\pi$
$463$		−	14.7217i		−	0.684174i	0.939668	−	0.342087i	$-0.111134\pi$
$464$	−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	$-0.963682\pi$
$467$		−	4.92066i		−	0.227701i	0.993498	−	0.113850i	$-0.0363185\pi$
$468$	−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	$-0.817398\pi$
$487$		−	23.9531i		−	1.08542i	0.839920	−	0.542710i	$-0.182602\pi$
$488$	−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	$0.264063\pi$
$499$			32.9555i			1.47529i	−0.675188	+	0.737646i	$0.735937\pi$
$500$	−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	$0.107759\pi$
$541$			15.4491i			0.664210i	−0.943242	+	0.332105i	$0.892241\pi$
$542$	−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	$-0.622212\pi$
$557$		−	43.7652i		−	1.85439i	0.374577	−	0.927196i	$-0.377788\pi$
$558$	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	$0.0118347\pi$
$569$			1.77335i			0.0743426i	−0.999309	+	0.0371713i	$0.988165\pi$
$570$	−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	$0.463026\pi$
$587$			48.1296i			1.98652i	−0.115898	+	0.993261i	$0.536974\pi$
$588$	−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	$0.291200\pi$
$593$			38.5953i			1.58492i	−0.609924	+	0.792460i	$0.708800\pi$
$594$	−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	$0.152658\pi$
$599$			22.5857i			0.922827i	−0.887185	+	0.461414i	$0.847342\pi$
$600$	−17.5271	−	47.0359i	−0.715542	−	1.92023i
$601$			20.9336i			0.853898i	0.904276	+	0.426949i	$0.140412\pi$
$601$			20.9336i			0.853898i	−0.904276	+	0.426949i	$0.859588\pi$
$602$	−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	$-0.909368\pi$
$613$		−	13.9094i		−	0.561794i	0.959738	−	0.280897i	$-0.0906320\pi$
$614$	−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	$-0.731817\pi$
$619$		−	37.1366i		−	1.49265i	0.665584	−	0.746323i	$-0.268183\pi$
$620$	−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	$-0.975512\pi$
$631$		−	3.86111i		−	0.153708i	0.997042	−	0.0768542i	$-0.0244876\pi$
$632$	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	$0.291652\pi$
$643$			40.2334i			1.58665i	−0.608798	+	0.793325i	$0.708348\pi$
$644$	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	$-0.683538\pi$
$647$		−	42.6474i		−	1.67664i	0.545178	−	0.838320i	$-0.316462\pi$
$648$	−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	$-0.698909\pi$
$673$		−	42.0797i		−	1.62205i	0.585009	−	0.811027i	$-0.301091\pi$
$674$	−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	$-0.848018\pi$
$677$		−	23.9132i		−	0.919058i	0.888163	−	0.459529i	$-0.151982\pi$
$678$	−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	$-0.874769\pi$
$683$		−	20.0373i		−	0.766707i	0.923602	−	0.383353i	$-0.125231\pi$
$684$	−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	$-0.803384\pi$
$691$		−	30.4481i		−	1.15830i	0.815221	−	0.579151i	$-0.196616\pi$
$692$	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	$0.0669369\pi$
$701$			11.0535i			0.417484i	−0.977971	+	0.208742i	$0.933063\pi$
$702$	−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	$0.279025\pi$
$719$			41.2165i			1.53711i	−0.639781	+	0.768557i	$0.720975\pi$
$720$	−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	$-0.819985\pi$
$727$		−	28.8970i		−	1.07173i	0.844303	−	0.535866i	$-0.180015\pi$
$728$	−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	$0.0771236\pi$
$733$			12.9916i			0.479854i	−0.970791	+	0.239927i	$0.922876\pi$
$734$	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	$-0.777074\pi$
$751$		−	35.3232i		−	1.28896i	0.764621	−	0.644480i	$-0.222926\pi$
$752$	−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	$0.0222471\pi$
$761$			3.85293i			0.139669i	−0.997559	+	0.0698343i	$0.977753\pi$
$762$	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	$0.234455\pi$
$769$			37.2562i			1.34349i	−0.740782	+	0.671746i	$0.765545\pi$
$770$	−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	$-0.944441\pi$
$809$		−	9.87870i		−	0.347317i	0.984806	−	0.173658i	$-0.0555588\pi$
$810$	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	$-0.986600\pi$
$821$		−	2.41165i		−	0.0841670i	0.999114	−	0.0420835i	$-0.0133996\pi$
$822$	38.1011	−	28.5161i	1.32893	−	0.994614i
$823$			44.5021i			1.55125i	0.631196	+	0.775623i	$0.282564\pi$
$823$			44.5021i			1.55125i	−0.631196	+	0.775623i	$0.717436\pi$
$824$	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	$0.211627\pi$
$839$			35.7399i			1.23388i	−0.787011	+	0.616939i	$0.788373\pi$
$840$	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	$-0.650576\pi$
$853$		−	51.9977i		−	1.78037i	0.455603	−	0.890183i	$-0.349424\pi$
$854$	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	$0.147009\pi$
$857$			26.0895i			0.891199i	−0.895232	+	0.445600i	$0.852991\pi$
$858$	1.93230	−	6.82660i	0.0659677	−	0.233056i
$859$			24.0181i			0.819488i	0.912200	+	0.409744i	$0.134382\pi$
$859$			24.0181i			0.819488i	−0.912200	+	0.409744i	$0.865618\pi$
$860$	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	$0.00584425\pi$
$863$			1.07867i			0.0367184i	−0.999831	+	0.0183592i	$0.994156\pi$
$864$	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	$-0.987061\pi$
$877$		−	2.40683i		−	0.0812727i	0.999174	−	0.0406364i	$-0.0129385\pi$
$878$	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	$0.154997\pi$
$883$			27.8088i			0.935842i	−0.883770	+	0.467921i	$0.845003\pi$
$884$	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	$0.0189255\pi$
$907$			3.57910i			0.118842i	−0.998233	+	0.0594211i	$0.981075\pi$
$908$	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	$-0.855964\pi$
$911$		−	26.3928i		−	0.874433i	0.899356	−	0.437216i	$-0.144036\pi$
$912$	−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	$-0.928995\pi$
$937$		−	13.5434i		−	0.442445i	0.975223	−	0.221222i	$-0.0710046\pi$
$938$	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	$0.0177365\pi$
$941$			3.41679i			0.111384i	−0.998448	+	0.0556920i	$0.982263\pi$
$942$	−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	$-0.863409\pi$
$947$		−	25.6075i		−	0.832131i	0.909335	−	0.416066i	$-0.136591\pi$
$948$	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	$-0.949704\pi$
$953$		−	9.71512i		−	0.314704i	0.987543	−	0.157352i	$-0.0502957\pi$
$954$	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	$0.165230\pi$
$971$			30.9169i			0.992171i	−0.868274	+	0.496086i	$0.834770\pi$
$972$	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	$0.473731\pi$
$983$			62.4923i			1.99319i	−0.0824321	+	0.996597i	$0.526269\pi$
$984$	−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	$0.194526\pi$
$991$			36.1258i			1.14757i	−0.819005	+	0.573787i	$0.805474\pi$
$992$	−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	$0.0928107\pi$
$997$			18.1532i			0.574919i	−0.957793	+	0.287459i	$0.907189\pi$
$998$	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.131.19	✓	64
4.3	odd	2	inner	572.2.e.b.131.45	yes	64
11.10	odd	2	inner	572.2.e.b.131.46	yes	64
44.43	even	2	inner	572.2.e.b.131.20	yes	64

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

Varieties

Fields

Representations

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Database

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