LMFDB - Embedded newform 576.2.bb.e.49.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(49,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("576.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bb (of order $12$, degree $4$, not 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			49.10
Character	$\chi$	$=$	576.49
Dual form			576.2.bb.e.529.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.409248 - 1.68301i) q^{3} +(3.30105 - 0.884514i) q^{5} +(-2.63210 + 1.51965i) q^{7} +(-2.66503 - 1.37753i) q^{9} +O(q^{10})$	\(q+(0.409248 - 1.68301i) q^{3} +(3.30105 - 0.884514i) q^{5} +(-2.63210 + 1.51965i) q^{7} +(-2.66503 - 1.37753i) q^{9} +(1.39766 - 5.21614i) q^{11} +(-0.378541 - 1.41274i) q^{13} +(-0.137697 - 5.91768i) q^{15} +0.259408 q^{17} +(-0.228947 + 0.228947i) q^{19} +(1.48039 + 5.05176i) q^{21} +(2.69713 + 1.55719i) q^{23} +(5.78446 - 3.33966i) q^{25} +(-3.40906 + 3.92152i) q^{27} +(1.63556 + 0.438247i) q^{29} +(3.30458 - 5.72370i) q^{31} +(-8.20682 - 4.48697i) q^{33} +(-7.34457 + 7.34457i) q^{35} +(1.24139 + 1.24139i) q^{37} +(-2.53256 + 0.0589295i) q^{39} +(-8.85221 - 5.11082i) q^{41} +(-0.722202 + 2.69530i) q^{43} +(-10.0159 - 2.19005i) q^{45} +(6.08240 + 10.5350i) q^{47} +(1.11865 - 1.93755i) q^{49} +(0.106162 - 0.436587i) q^{51} +(1.24325 + 1.24325i) q^{53} -18.4550i q^{55} +(0.291624 + 0.479016i) q^{57} +(-0.725362 + 0.194360i) q^{59} +(4.36145 + 1.16865i) q^{61} +(9.10801 - 0.424093i) q^{63} +(-2.49917 - 4.32869i) q^{65} +(-0.411250 - 1.53481i) q^{67} +(3.72456 - 3.90202i) q^{69} +4.68290i q^{71} -15.1606i q^{73} +(-3.25340 - 11.1020i) q^{75} +(4.24790 + 15.8534i) q^{77} +(0.738050 + 1.27834i) q^{79} +(5.20480 + 7.34235i) q^{81} +(3.39108 + 0.908637i) q^{83} +(0.856321 - 0.229451i) q^{85} +(1.40692 - 2.57331i) q^{87} +15.7450i q^{89} +(3.14322 + 3.14322i) q^{91} +(-8.28065 - 7.90405i) q^{93} +(-0.553260 + 0.958274i) q^{95} +(5.94343 + 10.2943i) q^{97} +(-10.9102 + 11.9759i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) $ 72 * q - 2 * q^3 + 4 * q^5	$ 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) $ 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.409248	−	1.68301i	0.236279	−	0.971685i
$3$	0.409248	−	1.68301i	0.236279	−	0.971685i
$4$		0			0
$5$	3.30105	−	0.884514i	1.47628	−	0.395567i	0.571198	−	0.820812i	$-0.306479\pi$
$5$	3.30105	−	0.884514i	1.47628	−	0.395567i	0.905078	+	0.425246i	$0.139812\pi$
$6$		0			0
$7$	−2.63210	+	1.51965i	−0.994842	+	0.574372i	−0.906718	−	0.421737i	$-0.861420\pi$
$7$	−2.63210	+	1.51965i	−0.994842	+	0.574372i	−0.0881237	+	0.996110i	$0.528087\pi$
$8$		0			0
$9$	−2.66503	−	1.37753i	−0.888344	−	0.459178i
$10$		0			0
$11$	1.39766	−	5.21614i	0.421411	−	1.57273i	−0.350227	−	0.936665i	$-0.613896\pi$
$11$	1.39766	−	5.21614i	0.421411	−	1.57273i	0.771638	−	0.636062i	$-0.219438\pi$
$12$		0			0
$13$	−0.378541	−	1.41274i	−0.104988	−	0.391822i	0.893355	−	0.449351i	$-0.148345\pi$
$13$	−0.378541	−	1.41274i	−0.104988	−	0.391822i	−0.998344	+	0.0575285i	$0.981678\pi$
$14$		0			0
$15$	−0.137697	−	5.91768i	−0.0355532	−	1.52794i
$16$		0			0
$17$	0.259408			0.0629158			0.0314579	−	0.999505i	$-0.489985\pi$
$17$	0.259408			0.0629158			0.0314579	+	0.999505i	$0.489985\pi$
$18$		0			0
$19$	−0.228947	+	0.228947i	−0.0525241	+	0.0525241i	−0.732881	−	0.680357i	$-0.761825\pi$
$19$	−0.228947	+	0.228947i	−0.0525241	+	0.0525241i	0.680357	+	0.732881i	$0.261825\pi$
$20$		0			0
$21$	1.48039	+	5.05176i	0.323048	+	1.10239i
$22$		0			0
$23$	2.69713	+	1.55719i	0.562391	+	0.324697i	0.754105	−	0.656754i	$-0.228071\pi$
$23$	2.69713	+	1.55719i	0.562391	+	0.324697i	−0.191714	+	0.981451i	$0.561404\pi$
$24$		0			0
$25$	5.78446	−	3.33966i	1.15689	−	0.667932i
$26$		0			0
$27$	−3.40906	+	3.92152i	−0.656074	+	0.754697i
$28$		0			0
$29$	1.63556	+	0.438247i	0.303716	+	0.0813803i	0.407458	−	0.913224i	$-0.366415\pi$
$29$	1.63556	+	0.438247i	0.303716	+	0.0813803i	−0.103743	+	0.994604i	$0.533082\pi$
$30$		0			0
$31$	3.30458	−	5.72370i	0.593520	−	1.02801i	−0.400233	−	0.916413i	$-0.631071\pi$
$31$	3.30458	−	5.72370i	0.593520	−	1.02801i	0.993754	−	0.111594i	$-0.0355957\pi$
$32$		0			0
$33$	−8.20682	−	4.48697i	−1.42862	−	0.781081i
$34$		0			0
$35$	−7.34457	+	7.34457i	−1.24146	+	1.24146i
$36$		0			0
$37$	1.24139	+	1.24139i	0.204084	+	0.204084i	0.801747	−	0.597663i	$-0.203904\pi$
$37$	1.24139	+	1.24139i	0.204084	+	0.204084i	−0.597663	+	0.801747i	$0.703904\pi$
$38$		0			0
$39$	−2.53256	+	0.0589295i	−0.405535	+	0.00943627i
$40$		0			0
$41$	−8.85221	−	5.11082i	−1.38248	−	0.798177i	−0.390030	−	0.920802i	$-0.627535\pi$
$41$	−8.85221	−	5.11082i	−1.38248	−	0.798177i	−0.992453	+	0.122626i	$0.960869\pi$
$42$		0			0
$43$	−0.722202	+	2.69530i	−0.110135	+	0.411029i	−0.998877	−	0.0473786i	$-0.984913\pi$
$43$	−0.722202	+	2.69530i	−0.110135	+	0.411029i	0.888742	+	0.458407i	$0.151580\pi$
$44$		0			0
$45$	−10.0159	−	2.19005i	−1.49308	−	0.326474i
$46$		0			0
$47$	6.08240	+	10.5350i	0.887209	+	1.53669i	0.843160	+	0.537662i	$0.180693\pi$
$47$	6.08240	+	10.5350i	0.887209	+	1.53669i	0.0440493	+	0.999029i	$0.485974\pi$
$48$		0			0
$49$	1.11865	−	1.93755i	0.159807	−	0.276793i
$50$		0			0
$51$	0.106162	−	0.436587i	0.0148657	−	0.0611343i
$52$		0			0
$53$	1.24325	+	1.24325i	0.170773	+	0.170773i	0.787319	−	0.616546i	$-0.211468\pi$
$53$	1.24325	+	1.24325i	0.170773	+	0.170773i	−0.616546	+	0.787319i	$0.711468\pi$
$54$		0			0
$55$		−	18.4550i		−	2.48847i
$56$		0			0
$57$	0.291624	+	0.479016i	0.0386266	+	0.0634473i
$58$		0			0
$59$	−0.725362	+	0.194360i	−0.0944341	+	0.0253036i	−0.305727	−	0.952119i	$-0.598899\pi$
$59$	−0.725362	+	0.194360i	−0.0944341	+	0.0253036i	0.211293	+	0.977423i	$0.432233\pi$
$60$		0			0
$61$	4.36145	+	1.16865i	0.558427	+	0.149630i	0.526983	−	0.849876i	$-0.323323\pi$
$61$	4.36145	+	1.16865i	0.558427	+	0.149630i	0.0314432	+	0.999506i	$0.489990\pi$
$62$		0			0
$63$	9.10801	−	0.424093i	1.14750	−	0.0534307i
$64$		0			0
$65$	−2.49917	−	4.32869i	−0.309984	−	0.536908i
$66$		0			0
$67$	−0.411250	−	1.53481i	−0.0502422	−	0.187506i	0.936244	−	0.351350i	$-0.114277\pi$
$67$	−0.411250	−	1.53481i	−0.0502422	−	0.187506i	−0.986486	+	0.163844i	$0.947611\pi$
$68$		0			0
$69$	3.72456	−	3.90202i	0.448384	−	0.469748i
$70$		0			0
$71$			4.68290i			0.555758i	0.960616	+	0.277879i	$0.0896315\pi$
$71$			4.68290i			0.555758i	−0.960616	+	0.277879i	$0.910368\pi$
$72$		0			0
$73$		−	15.1606i		−	1.77441i	−0.461373	−	0.887206i	$-0.652643\pi$
$73$		−	15.1606i		−	1.77441i	0.461373	−	0.887206i	$-0.347357\pi$
$74$		0			0
$75$	−3.25340	−	11.1020i	−0.375670	−	1.28195i
$76$		0			0
$77$	4.24790	+	15.8534i	0.484093	+	1.80666i
$78$		0			0
$79$	0.738050	+	1.27834i	0.0830371	+	0.143824i	0.904553	−	0.426361i	$-0.140205\pi$
$79$	0.738050	+	1.27834i	0.0830371	+	0.143824i	−0.821516	+	0.570185i	$0.806871\pi$
$80$		0			0
$81$	5.20480	+	7.34235i	0.578311	+	0.815816i
$82$		0			0
$83$	3.39108	+	0.908637i	0.372219	+	0.0997358i	0.440079	−	0.897959i	$-0.354950\pi$
$83$	3.39108	+	0.908637i	0.372219	+	0.0997358i	−0.0678599	+	0.997695i	$0.521617\pi$
$84$		0			0
$85$	0.856321	−	0.229451i	0.0928811	−	0.0248874i
$86$		0			0
$87$	1.40692	−	2.57331i	0.150838	−	0.275887i
$88$		0			0
$89$			15.7450i			1.66897i	0.551029	+	0.834486i	$0.314235\pi$
$89$			15.7450i			1.66897i	−0.551029	+	0.834486i	$0.685765\pi$
$90$		0			0
$91$	3.14322	+	3.14322i	0.329499	+	0.329499i
$92$		0			0
$93$	−8.28065	−	7.90405i	−0.858663	−	0.819612i
$94$		0			0
$95$	−0.553260	+	0.958274i	−0.0567633	+	0.0983169i
$96$		0			0
$97$	5.94343	+	10.2943i	0.603464	+	1.04523i	0.992292	+	0.123919i	$0.0395465\pi$
$97$	5.94343	+	10.2943i	0.603464	+	1.04523i	−0.388829	+	0.921310i	$0.627120\pi$
$98$		0			0
$99$	−10.9102	+	11.9759i	−1.09652	+	1.20362i
$100$		0			0
$101$	1.93153	−	7.20855i	0.192194	−	0.717278i	−0.800781	−	0.598957i	$-0.795582\pi$
$101$	1.93153	−	7.20855i	0.192194	−	0.717278i	0.992975	−	0.118321i	$-0.0377512\pi$
$102$		0			0
$103$	9.83030	+	5.67553i	0.968609	+	0.559227i	0.898812	−	0.438335i	$-0.144432\pi$
$103$	9.83030	+	5.67553i	0.968609	+	0.559227i	0.0697969	+	0.997561i	$0.477765\pi$
$104$		0			0
$105$	9.35522	+	15.3667i	0.912976	+	1.49964i
$106$		0			0
$107$	6.81697	+	6.81697i	0.659022	+	0.659022i	0.955149	−	0.296127i	$-0.0956952\pi$
$107$	6.81697	+	6.81697i	0.659022	+	0.659022i	−0.296127	+	0.955149i	$0.595695\pi$
$108$		0			0
$109$	−7.08227	+	7.08227i	−0.678359	+	0.678359i	−0.959629	−	0.281270i	$-0.909244\pi$
$109$	−7.08227	+	7.08227i	−0.678359	+	0.678359i	0.281270	+	0.959629i	$0.409244\pi$
$110$		0			0
$111$	2.59731	−	1.58124i	0.246526	−	0.150084i
$112$		0			0
$113$	−3.22342	+	5.58312i	−0.303234	+	0.525216i	−0.976866	−	0.213850i	$-0.931400\pi$
$113$	−3.22342	+	5.58312i	−0.303234	+	0.525216i	0.673633	+	0.739066i	$0.264733\pi$
$114$		0			0
$115$	10.2807	+	2.75471i	0.958684	+	0.256878i
$116$		0			0
$117$	−0.937266	+	4.28644i	−0.0866503	+	0.396282i
$118$		0			0
$119$	−0.682790	+	0.394209i	−0.0625913	+	0.0361371i
$120$		0			0
$121$	−15.7284	−	9.08080i	−1.42986	−	0.825528i
$122$		0			0
$123$	−12.2243	+	12.8067i	−1.10223	+	1.15475i
$124$		0			0
$125$	4.05813	−	4.05813i	0.362970	−	0.362970i
$126$		0			0
$127$	−14.1695			−1.25734			−0.628669	−	0.777673i	$-0.716400\pi$
$127$	−14.1695			−1.25734			−0.628669	+	0.777673i	$0.716400\pi$
$128$		0			0
$129$	4.24065	+	2.31852i	0.373368	+	0.204134i
$130$		0			0
$131$	2.33608	+	8.71838i	0.204104	+	0.761728i	0.989721	+	0.143014i	$0.0456794\pi$
$131$	2.33608	+	8.71838i	0.204104	+	0.761728i	−0.785616	+	0.618714i	$0.787654\pi$
$132$		0			0
$133$	0.254694	−	0.950532i	0.0220848	−	0.0824216i
$134$		0			0
$135$	−7.78485	+	15.9605i	−0.670013	+	1.37366i
$136$		0			0
$137$	8.48376	−	4.89810i	0.724817	−	0.418473i	−0.0917063	−	0.995786i	$-0.529232\pi$
$137$	8.48376	−	4.89810i	0.724817	−	0.418473i	0.816523	+	0.577313i	$0.195899\pi$
$138$		0			0
$139$	−0.532255	+	0.142617i	−0.0451453	+	0.0120967i	−0.281321	−	0.959614i	$-0.590773\pi$
$139$	−0.532255	+	0.142617i	−0.0451453	+	0.0120967i	0.236176	+	0.971710i	$0.424106\pi$
$140$		0			0
$141$	20.2197	−	5.92530i	1.70281	−	0.499000i
$142$		0			0
$143$	−7.89810			−0.660473
$144$		0			0
$145$	5.78670			0.480559
$146$		0			0
$147$	−2.80312	−	2.67563i	−0.231197	−	0.220682i
$148$		0			0
$149$	−11.0511	+	2.96113i	−0.905342	+	0.242586i	−0.681309	−	0.731996i	$-0.738589\pi$
$149$	−11.0511	+	2.96113i	−0.905342	+	0.242586i	−0.224033	+	0.974582i	$0.571922\pi$
$150$		0			0
$151$	−0.427774	+	0.246975i	−0.0348117	+	0.0200986i	−0.517305	−	0.855801i	$-0.673065\pi$
$151$	−0.427774	+	0.246975i	−0.0348117	+	0.0200986i	0.482493	+	0.875900i	$0.339731\pi$
$152$		0			0
$153$	−0.691332	−	0.357344i	−0.0558909	−	0.0288896i
$154$		0			0
$155$	5.84590	−	21.8172i	0.469554	−	1.75240i
$156$		0			0
$157$	3.71179	+	13.8526i	0.296233	+	1.10556i	0.940233	+	0.340532i	$0.110607\pi$
$157$	3.71179	+	13.8526i	0.296233	+	1.10556i	−0.644000	+	0.765026i	$0.722726\pi$
$158$		0			0
$159$	2.60119	−	1.58360i	0.206288	−	0.125588i
$160$		0			0
$161$	−9.46551			−0.745987
$162$		0			0
$163$	11.4938	−	11.4938i	0.900262	−	0.900262i	−0.0951968	−	0.995458i	$-0.530348\pi$
$163$	11.4938	−	11.4938i	0.900262	−	0.900262i	0.995458	+	0.0951968i	$0.0303480\pi$
$164$		0			0
$165$	−31.0599	−	7.55267i	−2.41801	−	0.587975i
$166$		0			0
$167$	−12.6295	−	7.29166i	−0.977302	−	0.564245i	−0.0758473	−	0.997119i	$-0.524166\pi$
$167$	−12.6295	−	7.29166i	−0.977302	−	0.564245i	−0.901454	+	0.432874i	$0.857499\pi$
$168$		0			0
$169$	9.40580	−	5.43044i	0.723523	−	0.417726i
$170$		0			0
$171$	0.925535	−	0.294769i	0.0707774	−	0.0225416i
$172$		0			0
$173$	14.7841	+	3.96139i	1.12402	+	0.301179i	0.772508	−	0.635005i	$-0.219002\pi$
$173$	14.7841	+	3.96139i	1.12402	+	0.301179i	0.351509	+	0.936185i	$0.385669\pi$
$174$		0			0
$175$	−10.1502	+	17.5807i	−0.767283	+	1.32897i
$176$		0			0
$177$	0.0302571	+	1.30033i	0.00227426	+	0.0977390i
$178$		0			0
$179$	13.0007	−	13.0007i	0.971722	−	0.971722i	−0.0278895	−	0.999611i	$-0.508879\pi$
$179$	13.0007	−	13.0007i	0.971722	−	0.971722i	0.999611	+	0.0278895i	$0.00887864\pi$
$180$		0			0
$181$	12.7435	+	12.7435i	0.947219	+	0.947219i	0.998675	−	0.0514563i	$-0.0163863\pi$
$181$	12.7435	+	12.7435i	0.947219	+	0.947219i	−0.0514563	+	0.998675i	$0.516386\pi$
$182$		0			0
$183$	3.75176	−	6.86209i	0.277338	−	0.507260i
$184$		0			0
$185$	5.19593	+	2.99987i	0.382013	+	0.220555i
$186$		0			0
$187$	0.362565	−	1.35311i	0.0265134	−	0.0989493i
$188$		0			0
$189$	3.01368	−	15.5024i	0.219213	−	1.12763i
$190$		0			0
$191$	−1.45841	−	2.52604i	−0.105527	−	0.182778i	0.808426	−	0.588597i	$-0.200320\pi$
$191$	−1.45841	−	2.52604i	−0.105527	−	0.182778i	−0.913953	+	0.405819i	$0.866986\pi$
$192$		0			0
$193$	1.33436	−	2.31118i	0.0960494	−	0.166362i	−0.813997	−	0.580870i	$-0.802713\pi$
$193$	1.33436	−	2.31118i	0.0960494	−	0.166362i	0.910046	+	0.414507i	$0.136046\pi$
$194$		0			0
$195$	−8.30800	+	2.43462i	−0.594948	+	0.174347i
$196$		0			0
$197$	10.9442	+	10.9442i	0.779739	+	0.779739i	0.979786	−	0.200048i	$-0.0641097\pi$
$197$	10.9442	+	10.9442i	0.779739	+	0.779739i	−0.200048	+	0.979786i	$0.564110\pi$
$198$		0			0
$199$			4.55405i			0.322828i	0.986887	+	0.161414i	$0.0516054\pi$
$199$			4.55405i			0.322828i	−0.986887	+	0.161414i	$0.948395\pi$
$200$		0			0
$201$	−2.75139	+	0.0640214i	−0.194068	+	0.00451572i
$202$		0			0
$203$	−4.97094	+	1.33196i	−0.348892	+	0.0934852i
$204$		0			0
$205$	−33.7422	−	9.04120i	−2.35666	−	0.631465i
$206$		0			0
$207$	−5.04286	−	7.86536i	−0.350503	−	0.546680i
$208$		0			0
$209$	0.874231	+	1.51421i	0.0604718	+	0.104740i
$210$		0			0
$211$	−2.12190	−	7.91903i	−0.146077	−	0.545168i	−0.999705	−	0.0242846i	$-0.992269\pi$
$211$	−2.12190	−	7.91903i	−0.146077	−	0.545168i	0.853628	−	0.520884i	$-0.174397\pi$
$212$		0			0
$213$	7.88137	+	1.91647i	0.540022	+	0.131314i
$214$		0			0
$215$			9.53611i			0.650357i
$216$		0			0
$217$			20.0872i			1.36361i
$218$		0			0
$219$	−25.5154	−	6.20443i	−1.72417	−	0.419257i
$220$		0			0
$221$	−0.0981968	−	0.366476i	−0.00660543	−	0.0246518i
$222$		0			0
$223$	−1.97029	−	3.41265i	−0.131941	−	0.228528i	0.792484	−	0.609893i	$-0.208787\pi$
$223$	−1.97029	−	3.41265i	−0.131941	−	0.228528i	−0.924425	+	0.381365i	$0.875454\pi$
$224$		0			0
$225$	−20.0163	+	0.932010i	−1.33442	+	0.0621340i
$226$		0			0
$227$	−11.1712	−	2.99331i	−0.741458	−	0.198673i	−0.131732	−	0.991285i	$-0.542054\pi$
$227$	−11.1712	−	2.99331i	−0.741458	−	0.198673i	−0.609726	+	0.792612i	$0.708721\pi$
$228$		0			0
$229$	−13.3738	+	3.58349i	−0.883764	+	0.236804i	−0.672030	−	0.740524i	$-0.734578\pi$
$229$	−13.3738	+	3.58349i	−0.883764	+	0.236804i	−0.211734	+	0.977327i	$0.567911\pi$
$230$		0			0
$231$	28.4198	−	0.661293i	1.86989	−	0.0435099i
$232$		0			0
$233$			6.01983i			0.394372i	0.980366	+	0.197186i	$0.0631803\pi$
$233$			6.01983i			0.394372i	−0.980366	+	0.197186i	$0.936820\pi$
$234$		0			0
$235$	29.3967	+	29.3967i	1.91763	+	1.91763i
$236$		0			0
$237$	2.45350	−	0.718987i	0.159372	−	0.0467032i
$238$		0			0
$239$	−7.92968	+	13.7346i	−0.512929	+	0.888418i	0.486959	+	0.873425i	$0.338106\pi$
$239$	−7.92968	+	13.7346i	−0.512929	+	0.888418i	−0.999888	+	0.0149936i	$0.995227\pi$
$240$		0			0
$241$	−7.70313	−	13.3422i	−0.496202	−	0.859447i	0.503788	−	0.863827i	$-0.331939\pi$
$241$	−7.70313	−	13.3422i	−0.496202	−	0.859447i	−0.999990	+	0.00437981i	$0.998606\pi$
$242$		0			0
$243$	14.4873	−	5.75488i	0.929360	−	0.369176i
$244$		0			0
$245$	1.97892	−	7.38543i	0.126429	−	0.471838i
$246$		0			0
$247$	0.410108	+	0.236776i	0.0260946	+	0.0150657i
$248$		0			0
$249$	2.91703	−	5.33535i	0.184859	−	0.338114i
$250$		0			0
$251$	−2.60640	−	2.60640i	−0.164514	−	0.164514i	0.620049	−	0.784563i	$-0.287113\pi$
$251$	−2.60640	−	2.60640i	−0.164514	−	0.164514i	−0.784563	+	0.620049i	$0.787113\pi$
$252$		0			0
$253$	11.8922	−	11.8922i	0.747657	−	0.747657i
$254$		0			0
$255$	−0.0357198	−	1.53510i	−0.00223686	−	0.0961315i
$256$		0			0
$257$	14.1100	−	24.4393i	0.880160	−	1.52448i	0.0289977	−	0.999579i	$-0.490768\pi$
$257$	14.1100	−	24.4393i	0.880160	−	1.52448i	0.851162	−	0.524902i	$-0.175898\pi$
$258$		0			0
$259$	−5.15395	−	1.38100i	−0.320251	−	0.0858110i
$260$		0			0
$261$	−3.75512	−	3.42098i	−0.232436	−	0.211753i
$262$		0			0
$263$	5.17419	−	2.98732i	0.319054	−	0.184206i	−0.331917	−	0.943309i	$-0.607695\pi$
$263$	5.17419	−	2.98732i	0.319054	−	0.184206i	0.650971	+	0.759103i	$0.274362\pi$
$264$		0			0
$265$	5.20370	+	3.00436i	0.319661	+	0.184556i
$266$		0			0
$267$	26.4990	+	6.44362i	1.62172	+	0.394343i
$268$		0			0
$269$	−7.44878	+	7.44878i	−0.454160	+	0.454160i	−0.896733	−	0.442573i	$-0.854066\pi$
$269$	−7.44878	+	7.44878i	−0.454160	+	0.454160i	0.442573	+	0.896733i	$0.354066\pi$
$270$		0			0
$271$	−12.6471			−0.768254			−0.384127	−	0.923280i	$-0.625498\pi$
$271$	−12.6471			−0.768254			−0.384127	+	0.923280i	$0.625498\pi$
$272$		0			0
$273$	6.57642	−	4.00371i	0.398023	−	0.242315i
$274$		0			0
$275$	−9.33542	−	34.8403i	−0.562947	−	2.10095i
$276$		0			0
$277$	6.12271	−	22.8503i	0.367878	−	1.37294i	−0.495600	−	0.868551i	$-0.665052\pi$
$277$	6.12271	−	22.8503i	0.367878	−	1.37294i	0.863477	−	0.504387i	$-0.168282\pi$
$278$		0			0
$279$	−16.6914	+	10.7017i	−0.999289	+	0.640693i
$280$		0			0
$281$	−20.8897	+	12.0607i	−1.24618	+	0.719480i	−0.970345	−	0.241726i	$-0.922287\pi$
$281$	−20.8897	+	12.0607i	−1.24618	+	0.719480i	−0.275832	+	0.961206i	$0.588953\pi$
$282$		0			0
$283$	−2.04741	+	0.548601i	−0.121706	+	0.0326110i	−0.319158	−	0.947702i	$-0.603400\pi$
$283$	−2.04741	+	0.548601i	−0.121706	+	0.0326110i	0.197452	+	0.980313i	$0.436733\pi$
$284$		0			0
$285$	1.38636	+	1.32331i	0.0821211	+	0.0783863i
$286$		0			0
$287$	31.0666			1.83380
$288$		0			0
$289$	−16.9327			−0.996042
$290$		0			0
$291$	19.7578	−	5.78991i	1.15822	−	0.339411i
$292$		0			0
$293$	−1.98386	+	0.531574i	−0.115898	+	0.0310549i	−0.316302	−	0.948659i	$-0.602441\pi$
$293$	−1.98386	+	0.531574i	−0.115898	+	0.0310549i	0.200404	+	0.979713i	$0.435775\pi$
$294$		0			0
$295$	−2.22255	+	1.28319i	−0.129402	+	0.0747100i
$296$		0			0
$297$	15.6905	+	23.2631i	0.910455	+	1.34986i
$298$		0			0
$299$	1.17892	−	4.39980i	0.0681788	−	0.254447i
$300$		0			0
$301$	−2.19498	−	8.19179i	−0.126517	−	0.472167i
$302$		0			0
$303$	−11.3416	−	6.20086i	−0.651557	−	0.356230i
$304$		0			0
$305$	15.4311			0.883580
$306$		0			0
$307$	−6.13676	+	6.13676i	−0.350243	+	0.350243i	−0.860200	−	0.509957i	$-0.829661\pi$
$307$	−6.13676	+	6.13676i	−0.350243	+	0.350243i	0.509957	+	0.860200i	$0.329661\pi$
$308$		0			0
$309$	13.5750	−	14.2218i	0.772254	−	0.809049i
$310$		0			0
$311$	−19.1722	−	11.0691i	−1.08716	−	0.627670i	−0.154339	−	0.988018i	$-0.549325\pi$
$311$	−19.1722	−	11.0691i	−1.08716	−	0.627670i	−0.932818	+	0.360348i	$0.882658\pi$
$312$		0			0
$313$	3.88285	−	2.24176i	0.219472	−	0.126712i	−0.386234	−	0.922401i	$-0.626224\pi$
$313$	3.88285	−	2.24176i	0.219472	−	0.126712i	0.605706	+	0.795689i	$0.292891\pi$
$314$		0			0
$315$	29.6909	−	9.45612i	1.67289	−	0.532792i
$316$		0			0
$317$	−0.0626747	−	0.0167936i	−0.00352016	−	0.000943225i	0.257059	−	0.966396i	$-0.417247\pi$
$317$	−0.0626747	−	0.0167936i	−0.00352016	−	0.000943225i	−0.260579	+	0.965453i	$0.583913\pi$
$318$		0			0
$319$	4.57191	−	7.91879i	0.255978	−	0.443367i
$320$		0			0
$321$	14.2628	−	8.68319i	0.796075	−	0.484648i
$322$		0			0
$323$	−0.0593909	+	0.0593909i	−0.00330460	+	0.00330460i
$324$		0			0
$325$	−6.90771	−	6.90771i	−0.383171	−	0.383171i
$326$		0			0
$327$	9.02112	+	14.8179i	0.498869	+	0.819433i
$328$		0			0
$329$	−32.0190	−	18.4862i	−1.76527	−	1.01918i
$330$		0			0
$331$	2.23703	−	8.34869i	0.122958	−	0.458886i	−0.876801	−	0.480854i	$-0.840327\pi$
$331$	2.23703	−	8.34869i	0.122958	−	0.458886i	0.999759	+	0.0219684i	$0.00699332\pi$
$332$		0			0
$333$	−1.59829	−	5.01841i	−0.0875858	−	0.275007i
$334$		0			0
$335$	−2.71512	−	4.70272i	−0.148343	−	0.256937i
$336$		0			0
$337$	15.6738	−	27.1477i	0.853804	−	1.47883i	−0.0239463	−	0.999713i	$-0.507623\pi$
$337$	15.6738	−	27.1477i	0.853804	−	1.47883i	0.877750	−	0.479119i	$-0.159044\pi$
$338$		0			0
$339$	8.07726	+	7.70992i	0.438697	+	0.418745i
$340$		0			0
$341$	−25.2370	−	25.2370i	−1.36666	−	1.36666i
$342$		0			0
$343$		−	14.4753i		−	0.781590i
$344$		0			0
$345$	8.84357	−	16.1752i	0.476122	−	0.870844i
$346$		0			0
$347$	2.46409	−	0.660251i	0.132279	−	0.0354441i	−0.192072	−	0.981381i	$-0.561521\pi$
$347$	2.46409	−	0.660251i	0.132279	−	0.0354441i	0.324351	+	0.945937i	$0.394854\pi$
$348$		0			0
$349$	−5.78691	−	1.55060i	−0.309766	−	0.0830016i	0.100587	−	0.994928i	$-0.467928\pi$
$349$	−5.78691	−	1.55060i	−0.309766	−	0.0830016i	−0.410353	+	0.911927i	$0.634595\pi$
$350$		0			0
$351$	6.83054	+	3.33164i	0.364587	+	0.177830i
$352$		0			0
$353$	0.129293	+	0.223941i	0.00688155	+	0.0119192i	0.869446	−	0.494029i	$-0.164476\pi$
$353$	0.129293	+	0.223941i	0.00688155	+	0.0119192i	−0.862564	+	0.505948i	$0.831143\pi$
$354$		0			0
$355$	4.14210	+	15.4585i	0.219840	+	0.820453i
$356$		0			0
$357$	0.384027	+	1.31047i	0.0203249	+	0.0693574i
$358$		0			0
$359$			11.3079i			0.596808i	0.954440	+	0.298404i	$0.0964543\pi$
$359$			11.3079i			0.596808i	−0.954440	+	0.298404i	$0.903546\pi$
$360$		0			0
$361$			18.8952i			0.994482i
$362$		0			0
$363$	−21.7199	+	22.7547i	−1.14000	+	1.19431i
$364$		0			0
$365$	−13.4098	−	50.0459i	−0.701899	−	2.61952i
$366$		0			0
$367$	−14.0557	−	24.3452i	−0.733701	−	1.27081i	−0.955291	−	0.295667i	$-0.904458\pi$
$367$	−14.0557	−	24.3452i	−0.733701	−	1.27081i	0.221590	−	0.975140i	$-0.428875\pi$
$368$		0			0
$369$	16.5511	+	25.8147i	0.861615	+	1.34386i
$370$		0			0
$371$	−5.16165	−	1.38306i	−0.267980	−	0.0718049i
$372$		0			0
$373$	−28.9876	+	7.76720i	−1.50092	+	0.402170i	−0.913408	−	0.407045i	$-0.866559\pi$
$373$	−28.9876	+	7.76720i	−1.50092	+	0.402170i	−0.587512	+	0.809215i	$0.699893\pi$
$374$		0			0
$375$	−5.16909	−	8.49065i	−0.266931	−	0.438455i
$376$		0			0
$377$		−	2.47651i		−	0.127547i
$378$		0			0
$379$	−22.9932	−	22.9932i	−1.18108	−	1.18108i	−0.979465	−	0.201616i	$-0.935381\pi$
$379$	−22.9932	−	22.9932i	−1.18108	−	1.18108i	−0.201616	−	0.979465i	$-0.564619\pi$
$380$		0			0
$381$	−5.79883	+	23.8473i	−0.297083	+	1.22174i
$382$		0			0
$383$	−1.35411	+	2.34539i	−0.0691919	+	0.119844i	−0.898546	−	0.438880i	$-0.855375\pi$
$383$	−1.35411	+	2.34539i	−0.0691919	+	0.119844i	0.829354	+	0.558724i	$0.188709\pi$
$384$		0			0
$385$	28.0451	+	48.5755i	1.42931	+	2.47564i
$386$		0			0
$387$	5.63756	−	6.18819i	0.286573	−	0.314564i
$388$		0			0
$389$	3.57208	−	13.3312i	0.181112	−	0.675918i	−0.814318	−	0.580419i	$-0.802889\pi$
$389$	3.57208	−	13.3312i	0.181112	−	0.675918i	0.995430	−	0.0954990i	$-0.0304447\pi$
$390$		0			0
$391$	0.699659	+	0.403948i	0.0353833	+	0.0204285i
$392$		0			0
$393$	15.6291	−	0.363670i	0.788386	−	0.0183447i
$394$		0			0
$395$	3.56705	+	3.56705i	0.179478	+	0.179478i
$396$		0			0
$397$	−2.91803	+	2.91803i	−0.146452	+	0.146452i	−0.776531	−	0.630079i	$-0.783022\pi$
$397$	−2.91803	+	2.91803i	−0.146452	+	0.146452i	0.630079	+	0.776531i	$0.283022\pi$
$398$		0			0
$399$	−1.49552	−	0.817656i	−0.0748697	−	0.0409340i
$400$		0			0
$401$	−6.93768	+	12.0164i	−0.346451	+	0.600071i	−0.985616	−	0.168999i	$-0.945947\pi$
$401$	−6.93768	+	12.0164i	−0.346451	+	0.600071i	0.639165	+	0.769069i	$0.279280\pi$
$402$		0			0
$403$	−9.33700	−	2.50184i	−0.465109	−	0.124626i
$404$		0			0
$405$	23.6757	+	19.6338i	1.17646	+	0.975609i
$406$		0			0
$407$	8.21033	−	4.74024i	0.406971	−	0.234965i
$408$		0			0
$409$	15.7740	+	9.10712i	0.779974	+	0.450318i	0.836421	−	0.548087i	$-0.184644\pi$
$409$	15.7740	+	9.10712i	0.779974	+	0.450318i	−0.0564472	+	0.998406i	$0.517977\pi$
$410$		0			0
$411$	−4.77159	−	16.2828i	−0.235365	−	0.803170i
$412$		0			0
$413$	1.61387	−	1.61387i	0.0794134	−	0.0794134i
$414$		0			0
$415$	11.9978			0.588950
$416$		0			0
$417$	0.0222020	+	0.954156i	0.00108724	+	0.0467252i
$418$		0			0
$419$	−0.708792	−	2.64525i	−0.0346268	−	0.129229i	0.946449	−	0.322854i	$-0.104642\pi$
$419$	−0.708792	−	2.64525i	−0.0346268	−	0.129229i	−0.981076	+	0.193625i	$0.937976\pi$
$420$		0			0
$421$	−5.57629	+	20.8110i	−0.271772	+	1.01427i	0.686202	+	0.727411i	$0.259276\pi$
$421$	−5.57629	+	20.8110i	−0.271772	+	1.01427i	−0.957974	+	0.286855i	$0.907390\pi$
$422$		0			0
$423$	−1.69744	−	36.4549i	−0.0825322	−	1.77250i
$424$		0			0
$425$	1.50054	−	0.866336i	0.0727867	−	0.0420234i
$426$		0			0
$427$	−13.2557	+	3.55186i	−0.641489	+	0.171887i
$428$		0			0
$429$	−3.23228	+	13.2926i	−0.156056	+	0.641771i
$430$		0			0
$431$	−17.4155			−0.838873			−0.419436	−	0.907785i	$-0.637772\pi$
$431$	−17.4155			−0.838873			−0.419436	+	0.907785i	$0.637772\pi$
$432$		0			0
$433$	−27.7567			−1.33390			−0.666952	−	0.745101i	$-0.732401\pi$
$433$	−27.7567			−1.33390			−0.666952	+	0.745101i	$0.732401\pi$
$434$		0			0
$435$	2.36819	−	9.73906i	0.113546	−	0.466952i
$436$		0			0
$437$	−0.974016	+	0.260987i	−0.0465935	+	0.0124847i
$438$		0			0
$439$	−34.3074	+	19.8074i	−1.63740	+	0.945354i	−0.655677	+	0.755042i	$0.727617\pi$
$439$	−34.3074	+	19.8074i	−1.63740	+	0.945354i	−0.981724	+	0.190312i	$0.939050\pi$
$440$		0			0
$441$	−5.65028	+	3.62267i	−0.269061	+	0.172508i
$442$		0			0
$443$	−6.05978	+	22.6154i	−0.287909	+	1.07449i	0.658779	+	0.752337i	$0.271073\pi$
$443$	−6.05978	+	22.6154i	−0.287909	+	1.07449i	−0.946687	+	0.322154i	$0.895593\pi$
$444$		0			0
$445$	13.9267	+	51.9752i	0.660190	+	2.46386i
$446$		0			0
$447$	0.460975	+	19.8109i	0.0218034	+	0.937025i
$448$		0			0
$449$	−1.41103			−0.0665906			−0.0332953	−	0.999446i	$-0.510600\pi$
$449$	−1.41103			−0.0665906			−0.0332953	+	0.999446i	$0.510600\pi$
$450$		0			0
$451$	−39.0312	+	39.0312i	−1.83791	+	1.83791i
$452$		0			0
$453$	0.240596	+	0.821021i	0.0113042	+	0.0385749i
$454$		0			0
$455$	13.1562	+	7.59571i	0.616770	+	0.356092i
$456$		0			0
$457$	−21.3692	+	12.3375i	−0.999609	+	0.577124i	−0.908132	−	0.418683i	$-0.862492\pi$
$457$	−21.3692	+	12.3375i	−0.999609	+	0.577124i	−0.0914761	+	0.995807i	$0.529159\pi$
$458$		0			0
$459$	−0.884339	+	1.01728i	−0.0412774	+	0.0474823i
$460$		0			0
$461$	31.8645	+	8.53806i	1.48408	+	0.397657i	0.907733	−	0.419549i	$-0.137812\pi$
$461$	31.8645	+	8.53806i	1.48408	+	0.397657i	0.576345	+	0.817207i	$0.304479\pi$
$462$		0			0
$463$	14.0805	−	24.3881i	0.654376	−	1.13341i	−0.327674	−	0.944791i	$-0.606265\pi$
$463$	14.0805	−	24.3881i	0.654376	−	1.13341i	0.982050	−	0.188621i	$-0.0604018\pi$
$464$		0			0
$465$	−34.3261	−	18.7673i	−1.59183	−	0.870314i
$466$		0			0
$467$	−26.3173	+	26.3173i	−1.21782	+	1.21782i	−0.249427	+	0.968394i	$0.580242\pi$
$467$	−26.3173	+	26.3173i	−1.21782	+	1.21782i	−0.968394	+	0.249427i	$0.919758\pi$
$468$		0			0
$469$	3.41481	+	3.41481i	0.157681	+	0.157681i
$470$		0			0
$471$	24.8331	−	0.577834i	1.14425	−	0.0266252i
$472$		0			0
$473$	13.0497	+	7.53422i	0.600024	+	0.346424i
$474$		0			0
$475$	−0.559730	+	2.08894i	−0.0256822	+	0.0958472i
$476$		0			0
$477$	−1.60068	−	5.02591i	−0.0732901	−	0.230121i
$478$		0			0
$479$	−1.55507	−	2.69347i	−0.0710531	−	0.123068i	0.828310	−	0.560270i	$-0.189303\pi$
$479$	−1.55507	−	2.69347i	−0.0710531	−	0.123068i	−0.899363	+	0.437202i	$0.855969\pi$
$480$		0			0
$481$	1.28384	−	2.22368i	0.0585381	−	0.101391i
$482$		0			0
$483$	−3.87374	+	15.9305i	−0.176261	+	0.724864i
$484$		0			0
$485$	28.7250	+	28.7250i	1.30434	+	1.30434i
$486$		0			0
$487$			33.0078i			1.49572i	0.663854	+	0.747862i	$0.268920\pi$
$487$			33.0078i			1.49572i	−0.663854	+	0.747862i	$0.731080\pi$
$488$		0			0
$489$	−14.6403	−	24.0479i	−0.662058	−	1.08748i
$490$		0			0
$491$	19.9915	−	5.35669i	0.902202	−	0.241744i	0.222240	−	0.974992i	$-0.428663\pi$
$491$	19.9915	−	5.35669i	0.902202	−	0.241744i	0.679962	+	0.733248i	$0.261996\pi$
$492$		0			0
$493$	0.424278	+	0.113685i	0.0191085	+	0.00512011i
$494$		0			0
$495$	−25.4224	+	49.1832i	−1.14265	+	2.21062i
$496$		0			0
$497$	−7.11636	−	12.3259i	−0.319212	−	0.552892i
$498$		0			0
$499$	−9.38014	−	35.0072i	−0.419913	−	1.56714i	−0.774787	−	0.632222i	$-0.782143\pi$
$499$	−9.38014	−	35.0072i	−0.419913	−	1.56714i	0.354875	−	0.934914i	$-0.384524\pi$
$500$		0			0
$501$	−17.4405	+	18.2715i	−0.779185	+	0.816310i
$502$		0			0
$503$		−	37.1847i		−	1.65798i	−0.559261	−	0.828992i	$-0.688915\pi$
$503$		−	37.1847i		−	1.65798i	0.559261	−	0.828992i	$-0.311085\pi$
$504$		0			0
$505$		−	25.5043i		−	1.13493i
$506$		0			0
$507$	−5.29018	−	18.0524i	−0.234945	−	0.801737i
$508$		0			0
$509$	−2.85800	−	10.6662i	−0.126679	−	0.472771i	0.873215	−	0.487335i	$-0.162031\pi$
$509$	−2.85800	−	10.6662i	−0.126679	−	0.472771i	−0.999894	+	0.0145635i	$0.995364\pi$
$510$		0			0
$511$	23.0387	+	39.9042i	1.01917	+	1.76526i
$512$		0			0
$513$	−0.117326	−	1.67832i	−0.00518008	−	0.0740995i
$514$		0			0
$515$	37.4704	+	10.0402i	1.65115	+	0.442423i
$516$		0			0
$517$	63.4534	−	17.0023i	2.79068	−	0.747759i
$518$		0			0
$519$	12.7174	−	23.2606i	0.558233	−	1.02103i
$520$		0			0
$521$		−	38.7570i		−	1.69797i	−0.528413	−	0.848987i	$-0.677213\pi$
$521$		−	38.7570i		−	1.69797i	0.528413	−	0.848987i	$-0.322787\pi$
$522$		0			0
$523$	11.9219	+	11.9219i	0.521310	+	0.521310i	0.917967	−	0.396657i	$-0.129830\pi$
$523$	11.9219	+	11.9219i	0.521310	+	0.521310i	−0.396657	+	0.917967i	$0.629830\pi$
$524$		0			0
$525$	25.4344	+	24.2777i	1.11005	+	1.05957i
$526$		0			0
$527$	0.857236	−	1.48478i	0.0373418	−	0.0646779i
$528$		0			0
$529$	−6.65032	−	11.5187i	−0.289144	−	0.500812i
$530$		0			0
$531$	2.20085	+	0.481235i	0.0955089	+	0.0208838i
$532$		0			0
$533$	−3.86932	+	14.4405i	−0.167599	+	0.625487i
$534$		0			0
$535$	28.5329	+	16.4735i	1.23358	+	0.712210i
$536$		0			0
$537$	−16.5598	−	27.2009i	−0.714610	−	1.17381i
$538$		0			0
$539$	−8.54307	−	8.54307i	−0.367976	−	0.367976i
$540$		0			0
$541$	15.9175	−	15.9175i	0.684346	−	0.684346i	−0.276630	−	0.960976i	$-0.589218\pi$
$541$	15.9175	−	15.9175i	0.684346	−	0.684346i	0.960976	+	0.276630i	$0.0892177\pi$
$542$		0			0
$543$	26.6627	−	16.2322i	1.14421	−	0.696590i
$544$		0			0
$545$	−17.1146	+	29.6433i	−0.733108	+	1.26978i
$546$		0			0
$547$	15.4827	+	4.14859i	0.661994	+	0.177381i	0.574146	−	0.818753i	$-0.305334\pi$
$547$	15.4827	+	4.14859i	0.661994	+	0.177381i	0.0878483	+	0.996134i	$0.472001\pi$
$548$		0			0
$549$	−10.0136	−	9.12253i	−0.427368	−	0.389340i
$550$		0			0
$551$	−0.474792	+	0.274121i	−0.0202268	+	0.0116780i
$552$		0			0
$553$	−3.88525	−	2.24315i	−0.165218	−	0.0953884i
$554$		0			0
$555$	7.17523	−	7.51711i	0.304572	−	0.319083i
$556$		0			0
$557$	0.878593	−	0.878593i	0.0372272	−	0.0372272i	−0.688248	−	0.725475i	$-0.741620\pi$
$557$	0.878593	−	0.878593i	0.0372272	−	0.0372272i	0.725475	+	0.688248i	$0.241620\pi$
$558$		0			0
$559$	4.08112			0.172613
$560$		0			0
$561$	−2.12892	−	1.16396i	−0.0898830	−	0.0491423i
$562$		0			0
$563$	4.88030	+	18.2135i	0.205680	+	0.767609i	0.989241	+	0.146294i	$0.0467345\pi$
$563$	4.88030	+	18.2135i	0.205680	+	0.767609i	−0.783561	+	0.621315i	$0.786599\pi$
$564$		0			0
$565$	−5.70232	+	21.2813i	−0.239898	+	0.895313i
$566$		0			0
$567$	−24.8573	−	11.4164i	−1.04391	−	0.479442i
$568$		0			0
$569$	23.9512	−	13.8282i	1.00409	−	0.579710i	0.0946316	−	0.995512i	$-0.469833\pi$
$569$	23.9512	−	13.8282i	1.00409	−	0.579710i	0.909455	+	0.415803i	$0.136499\pi$
$570$		0			0
$571$	−24.9864	+	6.69509i	−1.04565	+	0.280181i	−0.740453	−	0.672108i	$-0.765389\pi$
$571$	−24.9864	+	6.69509i	−1.04565	+	0.280181i	−0.305197	+	0.952289i	$0.598722\pi$
$572$		0			0
$573$	−4.84820	+	1.42074i	−0.202537	+	0.0593524i
$574$		0			0
$575$	20.8019			0.867501
$576$		0			0
$577$	−13.3014			−0.553744			−0.276872	−	0.960907i	$-0.589298\pi$
$577$	−13.3014			−0.553744			−0.276872	+	0.960907i	$0.589298\pi$
$578$		0			0
$579$	−3.34365	−	3.19159i	−0.138957	−	0.132638i
$580$		0			0
$581$	−10.3065	+	2.76161i	−0.427585	+	0.114571i
$582$		0			0
$583$	8.22260	−	4.74732i	0.340545	−	0.196614i
$584$		0			0
$585$	0.697452	+	14.9788i	0.0288361	+	0.619297i
$586$		0			0
$587$	−8.65445	+	32.2988i	−0.357207	+	1.33312i	0.520477	+	0.853876i	$0.325754\pi$
$587$	−8.65445	+	32.2988i	−0.357207	+	1.33312i	−0.877684	+	0.479240i	$0.840912\pi$
$588$		0			0
$589$	0.553851	+	2.06700i	0.0228211	+	0.0851693i
$590$		0			0
$591$	22.8980	−	13.9402i	0.941896	−	0.573424i
$592$		0			0
$593$	25.3926			1.04275			0.521374	−	0.853328i	$-0.325420\pi$
$593$	25.3926			1.04275			0.521374	+	0.853328i	$0.325420\pi$
$594$		0			0
$595$	−1.90524	+	1.90524i	−0.0781073	+	0.0781073i
$596$		0			0
$597$	7.66450	+	1.86373i	0.313687	+	0.0762775i
$598$		0			0
$599$	4.74083	+	2.73712i	0.193705	+	0.111836i	0.593716	−	0.804675i	$-0.297660\pi$
$599$	4.74083	+	2.73712i	0.193705	+	0.111836i	−0.400011	+	0.916510i	$0.630994\pi$
$600$		0			0
$601$	2.04493	−	1.18064i	0.0834143	−	0.0481593i	−0.457713	−	0.889100i	$-0.651331\pi$
$601$	2.04493	−	1.18064i	0.0834143	−	0.0481593i	0.541127	+	0.840941i	$0.317998\pi$
$602$		0			0
$603$	−1.01825	+	4.65682i	−0.0414665	+	0.189640i
$604$		0			0
$605$	−59.9524	−	16.0642i	−2.43741	−	0.653103i
$606$		0			0
$607$	2.67439	−	4.63219i	0.108550	−	0.188015i	−0.806633	−	0.591053i	$-0.798712\pi$
$607$	2.67439	−	4.63219i	0.108550	−	0.188015i	0.915183	+	0.403038i	$0.132046\pi$
$608$		0			0
$609$	0.207353	+	8.91123i	0.00840237	+	0.361101i
$610$		0			0
$611$	12.5808	−	12.5808i	0.508963	−	0.508963i
$612$		0			0
$613$	−0.799430	−	0.799430i	−0.0322887	−	0.0322887i	0.690778	−	0.723067i	$-0.257268\pi$
$613$	−0.799430	−	0.799430i	−0.0322887	−	0.0322887i	−0.723067	+	0.690778i	$0.757268\pi$
$614$		0			0
$615$	−29.0253	+	53.0883i	−1.17041	+	2.14073i
$616$		0			0
$617$	19.2117	+	11.0919i	0.773432	+	0.446541i	0.834098	−	0.551617i	$-0.185989\pi$
$617$	19.2117	+	11.0919i	0.773432	+	0.446541i	−0.0606655	+	0.998158i	$0.519322\pi$
$618$		0			0
$619$	11.4867	−	42.8691i	0.461691	−	1.72305i	−0.205943	−	0.978564i	$-0.566026\pi$
$619$	11.4867	−	42.8691i	0.461691	−	1.72305i	0.667634	−	0.744490i	$-0.267307\pi$
$620$		0			0
$621$	−15.3012	+	5.26830i	−0.614018	+	0.211410i
$622$		0			0
$623$	−23.9269	−	41.4426i	−0.958611	−	1.66036i
$624$		0			0
$625$	−6.89166	+	11.9367i	−0.275666	+	0.477468i
$626$		0			0
$627$	2.90621	−	0.851650i	0.116063	−	0.0340116i
$628$		0			0
$629$	0.322028	+	0.322028i	0.0128401	+	0.0128401i
$630$		0			0
$631$		−	12.0156i		−	0.478334i	−0.970978	−	0.239167i	$-0.923126\pi$
$631$		−	12.0156i		−	0.478334i	0.970978	−	0.239167i	$-0.0768744\pi$
$632$		0			0
$633$	−14.1962	+	0.330327i	−0.564247	+	0.0131293i
$634$		0			0
$635$	−46.7742	+	12.5331i	−1.85618	+	0.497361i
$636$		0			0
$637$	−3.16071	−	0.846909i	−0.125232	−	0.0335557i
$638$		0			0
$639$	6.45086	−	12.4801i	0.255192	−	0.493705i
$640$		0			0
$641$	−8.47322	−	14.6760i	−0.334672	−	0.579669i	0.648750	−	0.761002i	$-0.275292\pi$
$641$	−8.47322	−	14.6760i	−0.334672	−	0.579669i	−0.983422	+	0.181333i	$0.941959\pi$
$642$		0			0
$643$	5.96216	+	22.2511i	0.235124	+	0.877496i	0.978093	+	0.208170i	$0.0667506\pi$
$643$	5.96216	+	22.2511i	0.235124	+	0.877496i	−0.742968	+	0.669327i	$0.766583\pi$
$644$		0			0
$645$	16.0494	+	3.90263i	0.631943	+	0.153666i
$646$		0			0
$647$			30.4726i			1.19800i	0.800749	+	0.599000i	$0.204435\pi$
$647$			30.4726i			1.19800i	−0.800749	+	0.599000i	$0.795565\pi$
$648$		0			0
$649$			4.05524i			0.159182i
$650$		0			0
$651$	33.8069	+	8.22063i	1.32500	+	0.322192i
$652$		0			0
$653$	7.67978	+	28.6613i	0.300533	+	1.12160i	0.936723	+	0.350072i	$0.113843\pi$
$653$	7.67978	+	28.6613i	0.300533	+	1.12160i	−0.636190	+	0.771533i	$0.719490\pi$
$654$		0			0
$655$	15.4231	+	26.7135i	0.602629	+	1.04378i
$656$		0			0
$657$	−20.8842	+	40.4035i	−0.814771	+	1.57629i
$658$		0			0
$659$	31.3170	+	8.39137i	1.21994	+	0.326882i	0.810654	−	0.585525i	$-0.199112\pi$
$659$	31.3170	+	8.39137i	1.21994	+	0.326882i	0.409284	+	0.912407i	$0.365778\pi$
$660$		0			0
$661$	2.79494	−	0.748903i	0.108711	−	0.0291290i	−0.204054	−	0.978960i	$-0.565412\pi$
$661$	2.79494	−	0.748903i	0.108711	−	0.0291290i	0.312764	+	0.949831i	$0.398745\pi$
$662$		0			0
$663$	−0.656968	+	0.0152868i	−0.0255145	+	0.000593691i
$664$		0			0
$665$		−	3.36304i		−	0.130413i
$666$		0			0
$667$	3.72888	+	3.72888i	0.144383	+	0.144383i
$668$		0			0
$669$	−6.54985	+	1.91940i	−0.253232	+	0.0742083i
$670$		0			0
$671$	12.1917	−	21.1166i	0.470654	−	0.815197i
$672$		0			0
$673$	−5.83527	−	10.1070i	−0.224933	−	0.389595i	0.731366	−	0.681985i	$-0.238883\pi$
$673$	−5.83527	−	10.1070i	−0.224933	−	0.389595i	−0.956299	+	0.292389i	$0.905550\pi$
$674$		0			0
$675$	−6.62303	+	34.0690i	−0.254920	+	1.31131i
$676$		0			0
$677$	−12.1843	+	45.4726i	−0.468282	+	1.74765i	0.177489	+	0.984123i	$0.443202\pi$
$677$	−12.1843	+	45.4726i	−0.468282	+	1.74765i	−0.645772	+	0.763531i	$0.723464\pi$
$678$		0			0
$679$	−31.2874	−	18.0638i	−1.20070	−	0.693225i
$680$		0			0
$681$	−9.60955	+	17.5762i	−0.368239	+	0.673522i
$682$		0			0
$683$	−19.7598	−	19.7598i	−0.756087	−	0.756087i	0.219521	−	0.975608i	$-0.429551\pi$
$683$	−19.7598	−	19.7598i	−0.756087	−	0.756087i	−0.975608	+	0.219521i	$0.929551\pi$
$684$		0			0
$685$	23.6729	−	23.6729i	0.904495	−	0.904495i
$686$		0			0
$687$	0.557861	+	23.9747i	0.0212837	+	0.914692i
$688$		0			0
$689$	1.28576	−	2.22700i	0.0489835	−	0.0848420i
$690$		0			0
$691$	25.6957	+	6.88515i	0.977511	+	0.261923i	0.711996	−	0.702183i	$-0.247791\pi$
$691$	25.6957	+	6.88515i	0.977511	+	0.261923i	0.265515	+	0.964107i	$0.414458\pi$
$692$		0			0
$693$	10.5178	−	48.1014i	0.399537	−	1.82722i
$694$		0			0
$695$	−1.63086	+	0.941575i	−0.0618619	+	0.0357160i
$696$		0			0
$697$	−2.29634	−	1.32579i	−0.0869800	−	0.0502179i
$698$		0			0
$699$	10.1314	+	2.46360i	0.383206	+	0.0931820i
$700$		0			0
$701$	−32.6887	+	32.6887i	−1.23463	+	1.23463i	−0.272471	+	0.962164i	$0.587841\pi$
$701$	−32.6887	+	32.6887i	−1.23463	+	1.23463i	−0.962164	+	0.272471i	$0.912159\pi$
$702$		0			0
$703$	−0.568427			−0.0214386
$704$		0			0
$705$	61.5054	−	37.4444i	2.31643	−	1.41024i
$706$		0			0
$707$	5.87047	+	21.9089i	0.220782	+	0.823969i
$708$		0			0
$709$	11.4514	−	42.7374i	0.430068	−	1.60504i	−0.322533	−	0.946558i	$-0.604534\pi$
$709$	11.4514	−	42.7374i	0.430068	−	1.60504i	0.752601	−	0.658477i	$-0.228799\pi$
$710$		0			0
$711$	−0.205970	−	4.42351i	−0.00772449	−	0.165894i
$712$		0			0
$713$	17.8258	−	10.2917i	0.667581	−	0.385428i
$714$		0			0
$715$	−26.0721	+	6.98599i	−0.975040	+	0.261261i
$716$		0			0
$717$	19.8703	+	18.9666i	0.742069	+	0.708320i
$718$		0			0
$719$	−5.93945			−0.221504			−0.110752	−	0.993848i	$-0.535326\pi$
$719$	−5.93945			−0.221504			−0.110752	+	0.993848i	$0.535326\pi$
$720$		0			0
$721$	−34.4992			−1.28482
$722$		0			0
$723$	−25.6075	+	7.50416i	−0.952355	+	0.279083i
$724$		0			0
$725$	10.9244	−	2.92719i	0.405722	−	0.108713i
$726$		0			0
$727$	8.81201	−	5.08761i	0.326819	−	0.188689i	−0.327609	−	0.944813i	$-0.606243\pi$
$727$	8.81201	−	5.08761i	0.326819	−	0.188689i	0.654428	+	0.756124i	$0.272909\pi$
$728$		0			0
$729$	−3.75663	−	26.7374i	−0.139134	−	0.990274i
$730$		0			0
$731$	−0.187345	+	0.699183i	−0.00692922	+	0.0258602i
$732$		0			0
$733$	−8.23211	−	30.7227i	−0.304060	−	1.13477i	−0.933752	−	0.357922i	$-0.883485\pi$
$733$	−8.23211	−	30.7227i	−0.304060	−	1.13477i	0.629692	−	0.776845i	$-0.283181\pi$
$734$		0			0
$735$	−11.6199	−	6.35301i	−0.428605	−	0.234334i
$736$		0			0
$737$	−8.58056			−0.316069
$738$		0			0
$739$	24.0006	−	24.0006i	0.882876	−	0.882876i	−0.110950	−	0.993826i	$-0.535389\pi$
$739$	24.0006	−	24.0006i	0.882876	−	0.882876i	0.993826	+	0.110950i	$0.0353894\pi$
$740$		0			0
$741$	0.566332	−	0.593315i	0.0208047	−	0.0217960i
$742$		0			0
$743$	8.54415	+	4.93297i	0.313454	+	0.180973i	0.648471	−	0.761239i	$-0.275409\pi$
$743$	8.54415	+	4.93297i	0.313454	+	0.180973i	−0.335017	+	0.942212i	$0.608742\pi$
$744$		0			0
$745$	−33.8611	+	19.5497i	−1.24057	+	0.716246i
$746$		0			0
$747$	−7.78566	−	7.09287i	−0.284862	−	0.259515i
$748$		0			0
$749$	−28.3024	−	7.58360i	−1.03415	−	0.277099i
$750$		0			0
$751$	−22.9226	+	39.7031i	−0.836458	+	1.44879i	0.0563807	+	0.998409i	$0.482044\pi$
$751$	−22.9226	+	39.7031i	−0.836458	+	1.44879i	−0.892838	+	0.450378i	$0.851289\pi$
$752$		0			0
$753$	−5.45325	+	3.31993i	−0.198728	+	0.120985i
$754$		0			0
$755$	−1.19365	+	1.19365i	−0.0434414	+	0.0434414i
$756$		0			0
$757$	−13.9071	−	13.9071i	−0.505462	−	0.505462i	0.407668	−	0.913130i	$-0.366342\pi$
$757$	−13.9071	−	13.9071i	−0.505462	−	0.505462i	−0.913130	+	0.407668i	$0.866342\pi$
$758$		0			0
$759$	−15.1478	−	24.8815i	−0.549831	−	0.903143i
$760$		0			0
$761$	23.7610	+	13.7184i	0.861334	+	0.497291i	0.864459	−	0.502704i	$-0.167661\pi$
$761$	23.7610	+	13.7184i	0.861334	+	0.497291i	−0.00312490	+	0.999995i	$0.500995\pi$
$762$		0			0
$763$	7.87873	−	29.4038i	0.285229	−	1.06449i
$764$		0			0
$765$	−2.59820	−	0.568118i	−0.0939381	−	0.0205404i
$766$		0			0
$767$	0.549159	+	0.951172i	0.0198290	+	0.0343448i
$768$		0			0
$769$	−0.377145	+	0.653234i	−0.0136002	+	0.0235562i	−0.872745	−	0.488176i	$-0.837663\pi$
$769$	−0.377145	+	0.653234i	−0.0136002	+	0.0235562i	0.859145	+	0.511732i	$0.170996\pi$
$770$		0			0
$771$	−35.3570	−	33.7490i	−1.27335	−	1.21544i
$772$		0			0
$773$	9.72090	+	9.72090i	0.349637	+	0.349637i	0.859974	−	0.510338i	$-0.170480\pi$
$773$	9.72090	+	9.72090i	0.349637	+	0.349637i	−0.510338	+	0.859974i	$0.670480\pi$
$774$		0			0
$775$		−	44.1447i		−	1.58572i
$776$		0			0
$777$	−4.43347	+	8.10897i	−0.159050	+	0.290908i
$778$		0			0
$779$	3.19680	−	0.856580i	0.114537	−	0.0306902i
$780$		0			0
$781$	24.4267	+	6.54511i	0.874056	+	0.234203i
$782$		0			0
$783$	−7.29431	+	4.91986i	−0.260677	+	0.175822i
$784$		0			0
$785$	24.5056	+	42.4450i	0.874644	+	1.51493i
$786$		0			0
$787$	−6.76494	−	25.2471i	−0.241144	−	0.899962i	−0.975282	−	0.220962i	$-0.929080\pi$
$787$	−6.76494	−	25.2471i	−0.241144	−	0.899962i	0.734138	−	0.679000i	$-0.237586\pi$
$788$		0			0
$789$	−2.91016	−	9.93075i	−0.103604	−	0.353544i
$790$		0			0
$791$		−	19.5938i		−	0.696676i
$792$		0			0
$793$		−	6.60396i		−	0.234513i
$794$		0			0
$795$	7.18596	−	7.52834i	0.254860	−	0.267003i
$796$		0			0
$797$	8.11835	+	30.2981i	0.287567	+	1.07321i	0.946943	+	0.321401i	$0.104154\pi$
$797$	8.11835	+	30.2981i	0.287567	+	1.07321i	−0.659377	+	0.751813i	$0.729180\pi$
$798$		0			0
$799$	1.57783	+	2.73288i	0.0558195	+	0.0966822i
$800$		0			0
$801$	21.6893	−	41.9611i	0.766355	−	1.48262i
$802$		0			0
$803$	−79.0798	−	21.1894i	−2.79066	−	0.747756i
$804$		0			0
$805$	−31.2462	+	8.37238i	−1.10128	+	0.295088i
$806$		0			0
$807$	9.48796	+	15.5848i	0.333992	+	0.548609i
$808$		0			0
$809$		−	6.53194i		−	0.229651i	−0.993386	−	0.114825i	$-0.963369\pi$
$809$		−	6.53194i		−	0.229651i	0.993386	−	0.114825i	$-0.0366309\pi$
$810$		0			0
$811$	−4.79744	−	4.79744i	−0.168461	−	0.168461i	0.617842	−	0.786303i	$-0.288007\pi$
$811$	−4.79744	−	4.79744i	−0.168461	−	0.168461i	−0.786303	+	0.617842i	$0.788007\pi$
$812$		0			0
$813$	−5.17578	+	21.2851i	−0.181522	+	0.746501i
$814$		0			0
$815$	27.7751	−	48.1080i	0.972921	−	1.68515i
$816$		0			0
$817$	−0.451735	−	0.782427i	−0.0158042	−	0.0273737i
$818$		0			0
$819$	−4.04689	−	12.7067i	−0.141410	−	0.444007i
$820$		0			0
$821$	7.43764	−	27.7576i	0.259575	−	0.968748i	−0.705912	−	0.708299i	$-0.749463\pi$
$821$	7.43764	−	27.7576i	0.259575	−	0.968748i	0.965488	−	0.260449i	$-0.0838706\pi$
$822$		0			0
$823$	22.9167	+	13.2310i	0.798826	+	0.461202i	0.843060	−	0.537819i	$-0.180752\pi$
$823$	22.9167	+	13.2310i	0.798826	+	0.461202i	−0.0442346	+	0.999021i	$0.514085\pi$
$824$		0			0
$825$	−62.4570	+	1.45329i	−2.17447	+	0.0505972i
$826$		0			0
$827$	28.6969	+	28.6969i	0.997888	+	0.997888i	0.999998	−	0.00211025i	$-0.000671713\pi$
$827$	28.6969	+	28.6969i	0.997888	+	0.997888i	−0.00211025	+	0.999998i	$0.500672\pi$
$828$		0			0
$829$	16.5920	−	16.5920i	0.576263	−	0.576263i	−0.357609	−	0.933872i	$-0.616408\pi$
$829$	16.5920	−	16.5920i	0.576263	−	0.576263i	0.933872	+	0.357609i	$0.116408\pi$
$830$		0			0
$831$	−35.9515	−	19.6560i	−1.24714	−	0.681858i
$832$		0			0
$833$	0.290187	−	0.502618i	0.0100544	−	0.0174147i
$834$		0			0
$835$	−48.1403	−	12.8992i	−1.66596	−	0.446394i
$836$		0			0
$837$	11.1801	+	32.4714i	0.386441	+	1.12238i
$838$		0			0
$839$	5.80231	−	3.34997i	0.200318	−	0.115654i	−0.396486	−	0.918041i	$-0.629770\pi$
$839$	5.80231	−	3.34997i	0.200318	−	0.115654i	0.596804	+	0.802387i	$0.296437\pi$
$840$		0			0
$841$	−22.6317	−	13.0664i	−0.780405	−	0.450567i
$842$		0			0
$843$	11.7492	+	40.0934i	0.404663	+	1.38089i
$844$		0			0
$845$	26.2457	−	26.2457i	0.902881	−	0.902881i
$846$		0			0
$847$	55.1984			1.89664
$848$		0			0
$849$	0.0854036	+	3.67032i	0.00293104	+	0.125965i
$850$		0			0
$851$	1.41512	+	5.28129i	0.0485096	+	0.181040i
$852$		0			0
$853$	−5.16181	+	19.2641i	−0.176737	+	0.659592i	0.819512	+	0.573062i	$0.194245\pi$
$853$	−5.16181	+	19.2641i	−0.176737	+	0.659592i	−0.996249	+	0.0865300i	$0.972422\pi$
$854$		0			0
$855$	2.79451	−	1.79170i	0.0955703	−	0.0612748i
$856$		0			0
$857$	−12.5164	+	7.22635i	−0.427552	+	0.246848i	−0.698303	−	0.715802i	$-0.746061\pi$
$857$	−12.5164	+	7.22635i	−0.427552	+	0.246848i	0.270751	+	0.962649i	$0.412728\pi$
$858$		0			0
$859$	4.24540	−	1.13755i	0.144851	−	0.0388127i	−0.185665	−	0.982613i	$-0.559444\pi$
$859$	4.24540	−	1.13755i	0.144851	−	0.0388127i	0.330516	+	0.943800i	$0.392777\pi$
$860$		0			0
$861$	12.7139	−	52.2853i	0.433289	−	1.78188i
$862$		0			0
$863$	−43.8649			−1.49318			−0.746589	−	0.665286i	$-0.768310\pi$
$863$	−43.8649			−1.49318			−0.746589	+	0.665286i	$0.768310\pi$
$864$		0			0
$865$	52.3071			1.77849
$866$		0			0
$867$	−6.92967	+	28.4979i	−0.235344	+	0.967839i
$868$		0			0
$869$	7.69955	−	2.06309i	0.261189	−	0.0699855i
$870$		0			0
$871$	−2.01260	+	1.16198i	−0.0681943	+	0.0393720i
$872$		0			0
$873$	−1.65865	−	35.6220i	−0.0561369	−	1.20562i
$874$		0			0
$875$	−4.51450	+	16.8484i	−0.152618	+	0.569578i
$876$		0			0
$877$	−9.87004	−	36.8355i	−0.333288	−	1.24385i	−0.905714	−	0.423890i	$-0.860664\pi$
$877$	−9.87004	−	36.8355i	−0.333288	−	1.24385i	0.572426	−	0.819956i	$-0.306002\pi$
$878$		0			0
$879$	0.0827529	+	3.55640i	0.00279118	+	0.119954i
$880$		0			0
$881$	−17.2270			−0.580392			−0.290196	−	0.956967i	$-0.593721\pi$
$881$	−17.2270			−0.580392			−0.290196	+	0.956967i	$0.593721\pi$
$882$		0			0
$883$	−8.52615	+	8.52615i	−0.286928	+	0.286928i	−0.835864	−	0.548936i	$-0.815033\pi$
$883$	−8.52615	+	8.52615i	−0.286928	+	0.286928i	0.548936	+	0.835864i	$0.315033\pi$
$884$		0			0
$885$	1.25004	+	4.26570i	0.0420197	+	0.143390i
$886$		0			0
$887$	−0.898979	−	0.519026i	−0.0301847	−	0.0174272i	0.484832	−	0.874607i	$-0.338881\pi$
$887$	−0.898979	−	0.519026i	−0.0301847	−	0.0174272i	−0.515016	+	0.857180i	$0.672214\pi$
$888$		0			0
$889$	37.2955	−	21.5326i	1.25085	−	0.722180i
$890$		0			0
$891$	45.5733	−	16.8869i	1.52676	−	0.565731i
$892$		0			0
$893$	−3.80452	−	1.01942i	−0.127313	−	0.0341135i
$894$		0			0
$895$	31.4168	−	54.4155i	1.05015	−	1.81891i
$896$		0			0
$897$	−6.92242	−	3.78474i	−0.231133	−	0.126369i
$898$		0			0
$899$	7.91323	−	7.91323i	0.263921	−	0.263921i
$900$		0			0
$901$	0.322509	+	0.322509i	0.0107443	+	0.0107443i
$902$		0			0
$903$	−14.6851	+	0.341705i	−0.488691	+	0.0113712i
$904$		0			0
$905$	53.3389	+	30.7952i	1.77304	+	1.02367i
$906$		0			0
$907$	13.8612	−	51.7308i	0.460255	−	1.71769i	−0.211907	−	0.977290i	$-0.567968\pi$
$907$	13.8612	−	51.7308i	0.460255	−	1.71769i	0.672162	−	0.740404i	$-0.265366\pi$
$908$		0			0
$909$	−15.0776	+	16.5503i	−0.500093	+	0.548938i
$910$		0			0
$911$	24.2632	+	42.0250i	0.803875	+	1.39235i	0.917048	+	0.398777i	$0.130565\pi$
$911$	24.2632	+	42.0250i	0.803875	+	1.39235i	−0.113173	+	0.993575i	$0.536102\pi$
$912$		0			0
$913$	9.47916	−	16.4184i	0.313714	−	0.543369i
$914$		0			0
$915$	6.31513	−	25.9706i	0.208772	−	0.858562i
$916$		0			0
$917$	−19.3977	−	19.3977i	−0.640567	−	0.640567i
$918$		0			0
$919$		−	1.68133i		−	0.0554620i	−0.999615	−	0.0277310i	$-0.991172\pi$
$919$		−	1.68133i		−	0.0554620i	0.999615	−	0.0277310i	$-0.00882819\pi$
$920$		0			0
$921$	7.81676	+	12.8397i	0.257571	+	0.423081i
$922$		0			0
$923$	6.61571	−	1.77267i	0.217759	−	0.0583482i
$924$		0			0
$925$	11.3266	+	3.03496i	0.372417	+	0.0997887i
$926$		0			0
$927$	−18.3798	−	28.6671i	−0.603673	−	0.941550i
$928$		0			0
$929$	11.7821	+	20.4072i	0.386559	+	0.669540i	0.991984	−	0.126363i	$-0.0403303\pi$
$929$	11.7821	+	20.4072i	0.386559	+	0.669540i	−0.605425	+	0.795902i	$0.706997\pi$
$930$		0			0
$931$	0.187487	+	0.699709i	0.00614462	+	0.0229320i
$932$		0			0
$933$	−26.4755	+	27.7370i	−0.866770	+	0.908069i
$934$		0			0
$935$		−	4.78739i		−	0.156564i
$936$		0			0
$937$			41.8215i			1.36625i	0.730302	+	0.683125i	$0.239380\pi$
$937$			41.8215i			1.36625i	−0.730302	+	0.683125i	$0.760620\pi$
$938$		0			0
$939$	−2.18386	−	7.45231i	−0.0712676	−	0.243197i
$940$		0			0
$941$	−7.02041	−	26.2005i	−0.228859	−	0.854113i	−0.980822	−	0.194907i	$-0.937559\pi$
$941$	−7.02041	−	26.2005i	−0.228859	−	0.854113i	0.751963	−	0.659205i	$-0.229107\pi$
$942$		0			0
$943$	−15.9171	−	27.5691i	−0.518331	−	0.897775i
$944$		0			0
$945$	−3.76379	−	53.8399i	−0.122436	−	1.75141i
$946$		0			0
$947$	8.69902	+	2.33090i	0.282680	+	0.0757439i	0.397373	−	0.917657i	$-0.369922\pi$
$947$	8.69902	+	2.33090i	0.282680	+	0.0757439i	−0.114693	+	0.993401i	$0.536588\pi$
$948$		0			0
$949$	−21.4179	+	5.73891i	−0.695254	+	0.186293i
$950$		0			0
$951$	−0.0539133	+	0.0986093i	−0.00174826	+	0.00319763i
$952$		0			0
$953$			15.4588i			0.500758i	0.968148	+	0.250379i	$0.0805553\pi$
$953$			15.4588i			0.500758i	−0.968148	+	0.250379i	$0.919445\pi$
$954$		0			0
$955$	−7.04862	−	7.04862i	−0.228088	−	0.228088i
$956$		0			0
$957$	−11.4563	−	10.9353i	−0.370331	−	0.353488i
$958$		0			0
$959$	−14.8868	+	25.7846i	−0.480719	+	0.832629i
$960$		0			0
$961$	−6.34052	−	10.9821i	−0.204533	−	0.354261i
$962$		0			0
$963$	−8.77684	−	27.5581i	−0.282830	−	0.888046i
$964$		0			0
$965$	2.36052	−	8.80959i	0.0759879	−	0.283591i
$966$		0			0
$967$	38.0224	+	21.9523i	1.22272	+	0.705937i	0.965497	−	0.260415i	$-0.0838594\pi$
$967$	38.0224	+	21.9523i	1.22272	+	0.705937i	0.257222	+	0.966352i	$0.417193\pi$
$968$		0			0
$969$	0.0756497	+	0.124261i	0.00243022	+	0.00399184i
$970$		0			0
$971$	13.7775	+	13.7775i	0.442142	+	0.442142i	0.892731	−	0.450590i	$-0.148786\pi$
$971$	13.7775	+	13.7775i	0.442142	+	0.442142i	−0.450590	+	0.892731i	$0.648786\pi$
$972$		0			0
$973$	1.18422	−	1.18422i	0.0379645	−	0.0379645i
$974$		0			0
$975$	−14.4527	+	8.79877i	−0.462857	+	0.281786i
$976$		0			0
$977$	8.47350	−	14.6765i	0.271091	−	0.469544i	−0.698050	−	0.716049i	$-0.745949\pi$
$977$	8.47350	−	14.6765i	0.271091	−	0.469544i	0.969142	+	0.246505i	$0.0792822\pi$
$978$		0			0
$979$	82.1284	+	22.0062i	2.62484	+	0.703323i
$980$		0			0
$981$	28.6306	−	9.11842i	0.914104	−	0.291129i
$982$		0			0
$983$	−1.93132	+	1.11505i	−0.0615996	+	0.0355645i	−0.530483	−	0.847695i	$-0.677990\pi$
$983$	−1.93132	+	1.11505i	−0.0615996	+	0.0355645i	0.468884	+	0.883260i	$0.344656\pi$
$984$		0			0
$985$	45.8075	+	26.4470i	1.45955	+	0.842670i
$986$		0			0
$987$	−44.2161	+	46.3229i	−1.40741	+	1.47447i
$988$		0			0
$989$	−6.14496	+	6.14496i	−0.195399	+	0.195399i
$990$		0			0
$991$	21.4329			0.680838			0.340419	−	0.940274i	$-0.389431\pi$
$991$	21.4329			0.680838			0.340419	+	0.940274i	$0.389431\pi$
$992$		0			0
$993$	−13.1354	−	7.18162i	−0.416840	−	0.227902i
$994$		0			0
$995$	4.02812	+	15.0332i	0.127700	+	0.476583i
$996$		0			0
$997$	10.9118	−	40.7234i	0.345581	−	1.28972i	−0.546352	−	0.837556i	$-0.683984\pi$
$997$	10.9118	−	40.7234i	0.345581	−	1.28972i	0.891932	−	0.452169i	$-0.149349\pi$
$998$		0			0
$999$	−9.10013	+	0.636164i	−0.287915	+	0.0201273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bb.e.49.10		72
3.2	odd	2		1728.2.bc.e.1009.2		72
4.3	odd	2		144.2.x.e.85.5	yes	72
9.2	odd	6		1728.2.bc.e.1585.17		72
9.7	even	3	inner	576.2.bb.e.241.18		72
12.11	even	2		432.2.y.e.37.14		72
16.3	odd	4		144.2.x.e.13.16	✓	72
16.13	even	4	inner	576.2.bb.e.337.18		72
36.7	odd	6		144.2.x.e.133.16	yes	72
36.11	even	6		432.2.y.e.181.3		72
48.29	odd	4		1728.2.bc.e.145.17		72
48.35	even	4		432.2.y.e.253.3		72
144.29	odd	12		1728.2.bc.e.721.2		72
144.61	even	12	inner	576.2.bb.e.529.10		72
144.83	even	12		432.2.y.e.397.14		72
144.115	odd	12		144.2.x.e.61.5	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.16	✓	72	16.3	odd	4
144.2.x.e.61.5	yes	72	144.115	odd	12
144.2.x.e.85.5	yes	72	4.3	odd	2
144.2.x.e.133.16	yes	72	36.7	odd	6
432.2.y.e.37.14		72	12.11	even	2
432.2.y.e.181.3		72	36.11	even	6
432.2.y.e.253.3		72	48.35	even	4
432.2.y.e.397.14		72	144.83	even	12
576.2.bb.e.49.10		72	1.1	even	1	trivial
576.2.bb.e.241.18		72	9.7	even	3	inner
576.2.bb.e.337.18		72	16.13	even	4	inner
576.2.bb.e.529.10		72	144.61	even	12	inner
1728.2.bc.e.145.17		72	48.29	odd	4
1728.2.bc.e.721.2		72	144.29	odd	12
1728.2.bc.e.1009.2		72	3.2	odd	2
1728.2.bc.e.1585.17		72	9.2	odd	6

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.409248 - 1.68301i) q^{3} +(3.30105 - 0.884514i) q^{5} +(-2.63210 + 1.51965i) q^{7} +(-2.66503 - 1.37753i) q^{9} +O(q^{10})\)	\(q+(0.409248 - 1.68301i) q^{3} +(3.30105 - 0.884514i) q^{5} +(-2.63210 + 1.51965i) q^{7} +(-2.66503 - 1.37753i) q^{9} +(1.39766 - 5.21614i) q^{11} +(-0.378541 - 1.41274i) q^{13} +(-0.137697 - 5.91768i) q^{15} +0.259408 q^{17} +(-0.228947 + 0.228947i) q^{19} +(1.48039 + 5.05176i) q^{21} +(2.69713 + 1.55719i) q^{23} +(5.78446 - 3.33966i) q^{25} +(-3.40906 + 3.92152i) q^{27} +(1.63556 + 0.438247i) q^{29} +(3.30458 - 5.72370i) q^{31} +(-8.20682 - 4.48697i) q^{33} +(-7.34457 + 7.34457i) q^{35} +(1.24139 + 1.24139i) q^{37} +(-2.53256 + 0.0589295i) q^{39} +(-8.85221 - 5.11082i) q^{41} +(-0.722202 + 2.69530i) q^{43} +(-10.0159 - 2.19005i) q^{45} +(6.08240 + 10.5350i) q^{47} +(1.11865 - 1.93755i) q^{49} +(0.106162 - 0.436587i) q^{51} +(1.24325 + 1.24325i) q^{53} -18.4550i q^{55} +(0.291624 + 0.479016i) q^{57} +(-0.725362 + 0.194360i) q^{59} +(4.36145 + 1.16865i) q^{61} +(9.10801 - 0.424093i) q^{63} +(-2.49917 - 4.32869i) q^{65} +(-0.411250 - 1.53481i) q^{67} +(3.72456 - 3.90202i) q^{69} +4.68290i q^{71} -15.1606i q^{73} +(-3.25340 - 11.1020i) q^{75} +(4.24790 + 15.8534i) q^{77} +(0.738050 + 1.27834i) q^{79} +(5.20480 + 7.34235i) q^{81} +(3.39108 + 0.908637i) q^{83} +(0.856321 - 0.229451i) q^{85} +(1.40692 - 2.57331i) q^{87} +15.7450i q^{89} +(3.14322 + 3.14322i) q^{91} +(-8.28065 - 7.90405i) q^{93} +(-0.553260 + 0.958274i) q^{95} +(5.94343 + 10.2943i) q^{97} +(-10.9102 + 11.9759i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) \) 72 * q - 2 * q^3 + 4 * q^5	\( 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) \) 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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