LMFDB - Embedded newform 1728.2.bc.e.721.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1728,2,Mod(145,1728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1728, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 4]))

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

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

chi := DirichletCharacter("1728.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1728.bc (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:	$13.7981494693$
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			721.2
Character	$\chi$	$=$	1728.721
Dual form			1728.2.bc.e.1009.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.30105 - 0.884514i) q^{5} +(-2.63210 - 1.51965i) q^{7} +O(q^{10})$	$q+(-3.30105 - 0.884514i) q^{5} +(-2.63210 - 1.51965i) q^{7} +(-1.39766 - 5.21614i) q^{11} +(-0.378541 + 1.41274i) q^{13} -0.259408 q^{17} +(-0.228947 - 0.228947i) q^{19} +(-2.69713 + 1.55719i) q^{23} +(5.78446 + 3.33966i) q^{25} +(-1.63556 + 0.438247i) q^{29} +(3.30458 + 5.72370i) q^{31} +(7.34457 + 7.34457i) q^{35} +(1.24139 - 1.24139i) q^{37} +(8.85221 - 5.11082i) q^{41} +(-0.722202 - 2.69530i) q^{43} +(-6.08240 + 10.5350i) q^{47} +(1.11865 + 1.93755i) q^{49} +(-1.24325 + 1.24325i) q^{53} +18.4550i q^{55} +(0.725362 + 0.194360i) q^{59} +(4.36145 - 1.16865i) q^{61} +(2.49917 - 4.32869i) q^{65} +(-0.411250 + 1.53481i) q^{67} +4.68290i q^{71} +15.1606i q^{73} +(-4.24790 + 15.8534i) q^{77} +(0.738050 - 1.27834i) q^{79} +(-3.39108 + 0.908637i) q^{83} +(0.856321 + 0.229451i) q^{85} +15.7450i q^{89} +(3.14322 - 3.14322i) q^{91} +(0.553260 + 0.958274i) q^{95} +(5.94343 - 10.2943i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4 q^{5}+O(q^{10}) $ 72 * q - 4 * q^5	$ 72 q - 4 q^{5} - 2 q^{11} - 16 q^{13} + 16 q^{17} - 28 q^{19} - 4 q^{29} - 28 q^{31} - 16 q^{35} + 16 q^{37} + 10 q^{43} - 56 q^{47} + 4 q^{49} + 8 q^{53} - 14 q^{59} - 32 q^{61} + 64 q^{65} + 18 q^{67} + 36 q^{77} - 44 q^{79} + 20 q^{83} - 8 q^{85} + 80 q^{91} + 48 q^{95} + 40 q^{97}+O(q^{100}) $ 72 * q - 4 * q^5 - 2 * q^11 - 16 * q^13 + 16 * q^17 - 28 * q^19 - 4 * q^29 - 28 * q^31 - 16 * q^35 + 16 * q^37 + 10 * q^43 - 56 * q^47 + 4 * q^49 + 8 * q^53 - 14 * q^59 - 32 * q^61 + 64 * q^65 + 18 * q^67 + 36 * q^77 - 44 * q^79 + 20 * q^83 - 8 * q^85 + 80 * q^91 + 48 * q^95 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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			0
$3$		0			0
$4$		0			0
$5$	−3.30105	−	0.884514i	−1.47628	−	0.395567i	−0.571198	−	0.820812i	$-0.693521\pi$
$5$	−3.30105	−	0.884514i	−1.47628	−	0.395567i	−0.905078	+	0.425246i	$0.860188\pi$
$6$		0			0
$7$	−2.63210	−	1.51965i	−0.994842	−	0.574372i	−0.0881237	−	0.996110i	$-0.528087\pi$
$7$	−2.63210	−	1.51965i	−0.994842	−	0.574372i	−0.906718	+	0.421737i	$0.861420\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.39766	−	5.21614i	−0.421411	−	1.57273i	−0.771638	−	0.636062i	$-0.780562\pi$
$11$	−1.39766	−	5.21614i	−0.421411	−	1.57273i	0.350227	−	0.936665i	$-0.386104\pi$
$12$		0			0
$13$	−0.378541	+	1.41274i	−0.104988	+	0.391822i	−0.998344	−	0.0575285i	$-0.981678\pi$
$13$	−0.378541	+	1.41274i	−0.104988	+	0.391822i	0.893355	+	0.449351i	$0.148345\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.259408			−0.0629158			−0.0314579	−	0.999505i	$-0.510015\pi$
$17$	−0.259408			−0.0629158			−0.0314579	+	0.999505i	$0.510015\pi$
$18$		0			0
$19$	−0.228947	−	0.228947i	−0.0525241	−	0.0525241i	0.680357	−	0.732881i	$-0.261825\pi$
$19$	−0.228947	−	0.228947i	−0.0525241	−	0.0525241i	−0.732881	+	0.680357i	$0.761825\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.69713	+	1.55719i	−0.562391	+	0.324697i	−0.754105	−	0.656754i	$-0.771929\pi$
$23$	−2.69713	+	1.55719i	−0.562391	+	0.324697i	0.191714	+	0.981451i	$0.438596\pi$
$24$		0			0
$25$	5.78446	+	3.33966i	1.15689	+	0.667932i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.63556	+	0.438247i	−0.303716	+	0.0813803i	−0.407458	−	0.913224i	$-0.633585\pi$
$29$	−1.63556	+	0.438247i	−0.303716	+	0.0813803i	0.103743	+	0.994604i	$0.466918\pi$
$30$		0			0
$31$	3.30458	+	5.72370i	0.593520	+	1.02801i	0.993754	+	0.111594i	$0.0355957\pi$
$31$	3.30458	+	5.72370i	0.593520	+	1.02801i	−0.400233	+	0.916413i	$0.631071\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	7.34457	+	7.34457i	1.24146	+	1.24146i
$36$		0			0
$37$	1.24139	−	1.24139i	0.204084	−	0.204084i	−0.597663	−	0.801747i	$-0.703904\pi$
$37$	1.24139	−	1.24139i	0.204084	−	0.204084i	0.801747	+	0.597663i	$0.203904\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	8.85221	−	5.11082i	1.38248	−	0.798177i	0.390030	−	0.920802i	$-0.372465\pi$
$41$	8.85221	−	5.11082i	1.38248	−	0.798177i	0.992453	+	0.122626i	$0.0391314\pi$
$42$		0			0
$43$	−0.722202	−	2.69530i	−0.110135	−	0.411029i	0.888742	−	0.458407i	$-0.151580\pi$
$43$	−0.722202	−	2.69530i	−0.110135	−	0.411029i	−0.998877	+	0.0473786i	$0.984913\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.08240	+	10.5350i	−0.887209	+	1.53669i	−0.0440493	+	0.999029i	$0.514026\pi$
$47$	−6.08240	+	10.5350i	−0.887209	+	1.53669i	−0.843160	+	0.537662i	$0.819307\pi$
$48$		0			0
$49$	1.11865	+	1.93755i	0.159807	+	0.276793i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.24325	+	1.24325i	−0.170773	+	0.170773i	−0.787319	−	0.616546i	$-0.788532\pi$
$53$	−1.24325	+	1.24325i	−0.170773	+	0.170773i	0.616546	+	0.787319i	$0.288532\pi$
$54$		0			0
$55$			18.4550i			2.48847i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.725362	+	0.194360i	0.0944341	+	0.0253036i	0.305727	−	0.952119i	$-0.401101\pi$
$59$	0.725362	+	0.194360i	0.0944341	+	0.0253036i	−0.211293	+	0.977423i	$0.567767\pi$
$60$		0			0
$61$	4.36145	−	1.16865i	0.558427	−	0.149630i	0.0314432	−	0.999506i	$-0.489990\pi$
$61$	4.36145	−	1.16865i	0.558427	−	0.149630i	0.526983	+	0.849876i	$0.323323\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.49917	−	4.32869i	0.309984	−	0.536908i
$66$		0			0
$67$	−0.411250	+	1.53481i	−0.0502422	+	0.187506i	−0.986486	−	0.163844i	$-0.947611\pi$
$67$	−0.411250	+	1.53481i	−0.0502422	+	0.187506i	0.936244	+	0.351350i	$0.114277\pi$
$68$		0			0
$69$		0			0
$70$		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	$0.347357\pi$
$73$			15.1606i			1.77441i	−0.461373	+	0.887206i	$0.652643\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.24790	+	15.8534i	−0.484093	+	1.80666i
$78$		0			0
$79$	0.738050	−	1.27834i	0.0830371	−	0.143824i	−0.821516	−	0.570185i	$-0.806871\pi$
$79$	0.738050	−	1.27834i	0.0830371	−	0.143824i	0.904553	+	0.426361i	$0.140205\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.39108	+	0.908637i	−0.372219	+	0.0997358i	−0.440079	−	0.897959i	$-0.645050\pi$
$83$	−3.39108	+	0.908637i	−0.372219	+	0.0997358i	0.0678599	+	0.997695i	$0.478383\pi$
$84$		0			0
$85$	0.856321	+	0.229451i	0.0928811	+	0.0248874i
$86$		0			0
$87$		0			0
$88$		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
$93$		0			0
$94$		0			0
$95$	0.553260	+	0.958274i	0.0567633	+	0.0983169i
$96$		0			0
$97$	5.94343	−	10.2943i	0.603464	−	1.04523i	−0.388829	−	0.921310i	$-0.627120\pi$
$97$	5.94343	−	10.2943i	0.603464	−	1.04523i	0.992292	−	0.123919i	$-0.0395465\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.93153	−	7.20855i	−0.192194	−	0.717278i	−0.992975	−	0.118321i	$-0.962249\pi$
$101$	−1.93153	−	7.20855i	−0.192194	−	0.717278i	0.800781	−	0.598957i	$-0.204418\pi$
$102$		0			0
$103$	9.83030	−	5.67553i	0.968609	−	0.559227i	0.0697969	−	0.997561i	$-0.477765\pi$
$103$	9.83030	−	5.67553i	0.968609	−	0.559227i	0.898812	+	0.438335i	$0.144432\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.81697	+	6.81697i	−0.659022	+	0.659022i	−0.955149	−	0.296127i	$-0.904305\pi$
$107$	−6.81697	+	6.81697i	−0.659022	+	0.659022i	0.296127	+	0.955149i	$0.404305\pi$
$108$		0			0
$109$	−7.08227	−	7.08227i	−0.678359	−	0.678359i	0.281270	−	0.959629i	$-0.409244\pi$
$109$	−7.08227	−	7.08227i	−0.678359	−	0.678359i	−0.959629	+	0.281270i	$0.909244\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.22342	+	5.58312i	0.303234	+	0.525216i	0.976866	−	0.213850i	$-0.0686004\pi$
$113$	3.22342	+	5.58312i	0.303234	+	0.525216i	−0.673633	+	0.739066i	$0.735267\pi$
$114$		0			0
$115$	10.2807	−	2.75471i	0.958684	−	0.256878i
$116$		0			0
$117$		0			0
$118$		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
$123$		0			0
$124$		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
$129$		0			0
$130$		0			0
$131$	−2.33608	+	8.71838i	−0.204104	+	0.761728i	0.785616	+	0.618714i	$0.212346\pi$
$131$	−2.33608	+	8.71838i	−0.204104	+	0.761728i	−0.989721	+	0.143014i	$0.954321\pi$
$132$		0			0
$133$	0.254694	+	0.950532i	0.0220848	+	0.0824216i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−8.48376	−	4.89810i	−0.724817	−	0.418473i	0.0917063	−	0.995786i	$-0.470768\pi$
$137$	−8.48376	−	4.89810i	−0.724817	−	0.418473i	−0.816523	+	0.577313i	$0.804101\pi$
$138$		0			0
$139$	−0.532255	−	0.142617i	−0.0451453	−	0.0120967i	0.236176	−	0.971710i	$-0.424106\pi$
$139$	−0.532255	−	0.142617i	−0.0451453	−	0.0120967i	−0.281321	+	0.959614i	$0.590773\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	7.89810			0.660473
$144$		0			0
$145$	5.78670			0.480559
$146$		0			0
$147$		0			0
$148$		0			0
$149$	11.0511	+	2.96113i	0.905342	+	0.242586i	0.681309	−	0.731996i	$-0.261411\pi$
$149$	11.0511	+	2.96113i	0.905342	+	0.242586i	0.224033	+	0.974582i	$0.428078\pi$
$150$		0			0
$151$	−0.427774	−	0.246975i	−0.0348117	−	0.0200986i	0.482493	−	0.875900i	$-0.339731\pi$
$151$	−0.427774	−	0.246975i	−0.0348117	−	0.0200986i	−0.517305	+	0.855801i	$0.673065\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−5.84590	−	21.8172i	−0.469554	−	1.75240i
$156$		0			0
$157$	3.71179	−	13.8526i	0.296233	−	1.10556i	−0.644000	−	0.765026i	$-0.722726\pi$
$157$	3.71179	−	13.8526i	0.296233	−	1.10556i	0.940233	−	0.340532i	$-0.110607\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	9.46551			0.745987
$162$		0			0
$163$	11.4938	+	11.4938i	0.900262	+	0.900262i	0.995458	−	0.0951968i	$-0.0303480\pi$
$163$	11.4938	+	11.4938i	0.900262	+	0.900262i	−0.0951968	+	0.995458i	$0.530348\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.6295	−	7.29166i	0.977302	−	0.564245i	0.0758473	−	0.997119i	$-0.475834\pi$
$167$	12.6295	−	7.29166i	0.977302	−	0.564245i	0.901454	+	0.432874i	$0.142501\pi$
$168$		0			0
$169$	9.40580	+	5.43044i	0.723523	+	0.417726i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−14.7841	+	3.96139i	−1.12402	+	0.301179i	−0.772508	−	0.635005i	$-0.780998\pi$
$173$	−14.7841	+	3.96139i	−1.12402	+	0.301179i	−0.351509	+	0.936185i	$0.614331\pi$
$174$		0			0
$175$	−10.1502	−	17.5807i	−0.767283	−	1.32897i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−13.0007	−	13.0007i	−0.971722	−	0.971722i	0.0278895	−	0.999611i	$-0.491121\pi$
$179$	−13.0007	−	13.0007i	−0.971722	−	0.971722i	−0.999611	+	0.0278895i	$0.991121\pi$
$180$		0			0
$181$	12.7435	−	12.7435i	0.947219	−	0.947219i	−0.0514563	−	0.998675i	$-0.516386\pi$
$181$	12.7435	−	12.7435i	0.947219	−	0.947219i	0.998675	+	0.0514563i	$0.0163863\pi$
$182$		0			0
$183$		0			0
$184$		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
$189$		0			0
$190$		0			0
$191$	1.45841	−	2.52604i	0.105527	−	0.182778i	−0.808426	−	0.588597i	$-0.799680\pi$
$191$	1.45841	−	2.52604i	0.105527	−	0.182778i	0.913953	+	0.405819i	$0.133014\pi$
$192$		0			0
$193$	1.33436	+	2.31118i	0.0960494	+	0.166362i	0.910046	−	0.414507i	$-0.136046\pi$
$193$	1.33436	+	2.31118i	0.0960494	+	0.166362i	−0.813997	+	0.580870i	$0.802713\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.9442	+	10.9442i	−0.779739	+	0.779739i	−0.979786	−	0.200048i	$-0.935890\pi$
$197$	−10.9442	+	10.9442i	−0.779739	+	0.779739i	0.200048	+	0.979786i	$0.435890\pi$
$198$		0			0
$199$		−	4.55405i		−	0.322828i	−0.986887	−	0.161414i	$-0.948395\pi$
$199$		−	4.55405i		−	0.322828i	0.986887	−	0.161414i	$-0.0516054\pi$
$200$		0			0
$201$		0			0
$202$		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
$207$		0			0
$208$		0			0
$209$	−0.874231	+	1.51421i	−0.0604718	+	0.104740i
$210$		0			0
$211$	−2.12190	+	7.91903i	−0.146077	+	0.545168i	0.853628	+	0.520884i	$0.174397\pi$
$211$	−2.12190	+	7.91903i	−0.146077	+	0.545168i	−0.999705	+	0.0242846i	$0.992269\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			9.53611i			0.650357i
$216$		0			0
$217$		−	20.0872i		−	1.36361i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.0981968	−	0.366476i	0.00660543	−	0.0246518i
$222$		0			0
$223$	−1.97029	+	3.41265i	−0.131941	+	0.228528i	−0.924425	−	0.381365i	$-0.875454\pi$
$223$	−1.97029	+	3.41265i	−0.131941	+	0.228528i	0.792484	+	0.609893i	$0.208787\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	11.1712	−	2.99331i	0.741458	−	0.198673i	0.131732	−	0.991285i	$-0.457946\pi$
$227$	11.1712	−	2.99331i	0.741458	−	0.198673i	0.609726	+	0.792612i	$0.291279\pi$
$228$		0			0
$229$	−13.3738	−	3.58349i	−0.883764	−	0.236804i	−0.211734	−	0.977327i	$-0.567911\pi$
$229$	−13.3738	−	3.58349i	−0.883764	−	0.236804i	−0.672030	+	0.740524i	$0.734578\pi$
$230$		0			0
$231$		0			0
$232$		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
$237$		0			0
$238$		0			0
$239$	7.92968	+	13.7346i	0.512929	+	0.888418i	0.999888	+	0.0149936i	$0.00477279\pi$
$239$	7.92968	+	13.7346i	0.512929	+	0.888418i	−0.486959	+	0.873425i	$0.661894\pi$
$240$		0			0
$241$	−7.70313	+	13.3422i	−0.496202	+	0.859447i	−0.999990	−	0.00437981i	$-0.998606\pi$
$241$	−7.70313	+	13.3422i	−0.496202	+	0.859447i	0.503788	+	0.863827i	$0.331939\pi$
$242$		0			0
$243$		0			0
$244$		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
$249$		0			0
$250$		0			0
$251$	2.60640	−	2.60640i	0.164514	−	0.164514i	−0.620049	−	0.784563i	$-0.712887\pi$
$251$	2.60640	−	2.60640i	0.164514	−	0.164514i	0.784563	+	0.620049i	$0.212887\pi$
$252$		0			0
$253$	11.8922	+	11.8922i	0.747657	+	0.747657i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−14.1100	−	24.4393i	−0.880160	−	1.52448i	−0.851162	−	0.524902i	$-0.824102\pi$
$257$	−14.1100	−	24.4393i	−0.880160	−	1.52448i	−0.0289977	−	0.999579i	$-0.509232\pi$
$258$		0			0
$259$	−5.15395	+	1.38100i	−0.320251	+	0.0858110i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−5.17419	−	2.98732i	−0.319054	−	0.184206i	0.331917	−	0.943309i	$-0.392305\pi$
$263$	−5.17419	−	2.98732i	−0.319054	−	0.184206i	−0.650971	+	0.759103i	$0.725638\pi$
$264$		0			0
$265$	5.20370	−	3.00436i	0.319661	−	0.184556i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	7.44878	+	7.44878i	0.454160	+	0.454160i	0.896733	−	0.442573i	$-0.145934\pi$
$269$	7.44878	+	7.44878i	0.454160	+	0.454160i	−0.442573	+	0.896733i	$0.645934\pi$
$270$		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
$273$		0			0
$274$		0			0
$275$	9.33542	−	34.8403i	0.562947	−	2.10095i
$276$		0			0
$277$	6.12271	+	22.8503i	0.367878	+	1.37294i	0.863477	+	0.504387i	$0.168282\pi$
$277$	6.12271	+	22.8503i	0.367878	+	1.37294i	−0.495600	+	0.868551i	$0.665052\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	20.8897	+	12.0607i	1.24618	+	0.719480i	0.970345	−	0.241726i	$-0.0777135\pi$
$281$	20.8897	+	12.0607i	1.24618	+	0.719480i	0.275832	+	0.961206i	$0.411047\pi$
$282$		0			0
$283$	−2.04741	−	0.548601i	−0.121706	−	0.0326110i	0.197452	−	0.980313i	$-0.436733\pi$
$283$	−2.04741	−	0.548601i	−0.121706	−	0.0326110i	−0.319158	+	0.947702i	$0.603400\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−31.0666			−1.83380
$288$		0			0
$289$	−16.9327			−0.996042
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.98386	+	0.531574i	0.115898	+	0.0310549i	0.316302	−	0.948659i	$-0.397559\pi$
$293$	1.98386	+	0.531574i	0.115898	+	0.0310549i	−0.200404	+	0.979713i	$0.564225\pi$
$294$		0			0
$295$	−2.22255	−	1.28319i	−0.129402	−	0.0747100i
$296$		0			0
$297$		0			0
$298$		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
$303$		0			0
$304$		0			0
$305$	−15.4311			−0.883580
$306$		0			0
$307$	−6.13676	−	6.13676i	−0.350243	−	0.350243i	0.509957	−	0.860200i	$-0.329661\pi$
$307$	−6.13676	−	6.13676i	−0.350243	−	0.350243i	−0.860200	+	0.509957i	$0.829661\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	19.1722	−	11.0691i	1.08716	−	0.627670i	0.154339	−	0.988018i	$-0.450675\pi$
$311$	19.1722	−	11.0691i	1.08716	−	0.627670i	0.932818	+	0.360348i	$0.117342\pi$
$312$		0			0
$313$	3.88285	+	2.24176i	0.219472	+	0.126712i	0.605706	−	0.795689i	$-0.292891\pi$
$313$	3.88285	+	2.24176i	0.219472	+	0.126712i	−0.386234	+	0.922401i	$0.626224\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.0626747	−	0.0167936i	0.00352016	−	0.000943225i	−0.257059	−	0.966396i	$-0.582753\pi$
$317$	0.0626747	−	0.0167936i	0.00352016	−	0.000943225i	0.260579	+	0.965453i	$0.416087\pi$
$318$		0			0
$319$	4.57191	+	7.91879i	0.255978	+	0.443367i
$320$		0			0
$321$		0			0
$322$		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
$327$		0			0
$328$		0			0
$329$	32.0190	−	18.4862i	1.76527	−	1.01918i
$330$		0			0
$331$	2.23703	+	8.34869i	0.122958	+	0.458886i	0.999759	−	0.0219684i	$-0.00699332\pi$
$331$	2.23703	+	8.34869i	0.122958	+	0.458886i	−0.876801	+	0.480854i	$0.840327\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.71512	−	4.70272i	0.148343	−	0.256937i
$336$		0			0
$337$	15.6738	+	27.1477i	0.853804	+	1.47883i	0.877750	+	0.479119i	$0.159044\pi$
$337$	15.6738	+	27.1477i	0.853804	+	1.47883i	−0.0239463	+	0.999713i	$0.507623\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	25.2370	−	25.2370i	1.36666	−	1.36666i
$342$		0			0
$343$			14.4753i			0.781590i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.46409	−	0.660251i	−0.132279	−	0.0354441i	0.192072	−	0.981381i	$-0.438479\pi$
$347$	−2.46409	−	0.660251i	−0.132279	−	0.0354441i	−0.324351	+	0.945937i	$0.605146\pi$
$348$		0			0
$349$	−5.78691	+	1.55060i	−0.309766	+	0.0830016i	−0.410353	−	0.911927i	$-0.634595\pi$
$349$	−5.78691	+	1.55060i	−0.309766	+	0.0830016i	0.100587	+	0.994928i	$0.467928\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.129293	+	0.223941i	−0.00688155	+	0.0119192i	−0.869446	−	0.494029i	$-0.835524\pi$
$353$	−0.129293	+	0.223941i	−0.00688155	+	0.0119192i	0.862564	+	0.505948i	$0.168857\pi$
$354$		0			0
$355$	4.14210	−	15.4585i	0.219840	−	0.820453i
$356$		0			0
$357$		0			0
$358$		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
$363$		0			0
$364$		0			0
$365$	13.4098	−	50.0459i	0.701899	−	2.61952i
$366$		0			0
$367$	−14.0557	+	24.3452i	−0.733701	+	1.27081i	0.221590	+	0.975140i	$0.428875\pi$
$367$	−14.0557	+	24.3452i	−0.733701	+	1.27081i	−0.955291	+	0.295667i	$0.904458\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	5.16165	−	1.38306i	0.267980	−	0.0718049i
$372$		0			0
$373$	−28.9876	−	7.76720i	−1.50092	−	0.402170i	−0.587512	−	0.809215i	$-0.699893\pi$
$373$	−28.9876	−	7.76720i	−1.50092	−	0.402170i	−0.913408	+	0.407045i	$0.866559\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	2.47651i		−	0.127547i
$378$		0			0
$379$	−22.9932	+	22.9932i	−1.18108	+	1.18108i	−0.201616	+	0.979465i	$0.564619\pi$
$379$	−22.9932	+	22.9932i	−1.18108	+	1.18108i	−0.979465	+	0.201616i	$0.935381\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.35411	+	2.34539i	0.0691919	+	0.119844i	0.898546	−	0.438880i	$-0.144625\pi$
$383$	1.35411	+	2.34539i	0.0691919	+	0.119844i	−0.829354	+	0.558724i	$0.811291\pi$
$384$		0			0
$385$	28.0451	−	48.5755i	1.42931	−	2.47564i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−3.57208	−	13.3312i	−0.181112	−	0.675918i	−0.995430	−	0.0954990i	$-0.969555\pi$
$389$	−3.57208	−	13.3312i	−0.181112	−	0.675918i	0.814318	−	0.580419i	$-0.197111\pi$
$390$		0			0
$391$	0.699659	−	0.403948i	0.0353833	−	0.0204285i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.56705	+	3.56705i	−0.179478	+	0.179478i
$396$		0			0
$397$	−2.91803	−	2.91803i	−0.146452	−	0.146452i	0.630079	−	0.776531i	$-0.283022\pi$
$397$	−2.91803	−	2.91803i	−0.146452	−	0.146452i	−0.776531	+	0.630079i	$0.783022\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6.93768	+	12.0164i	0.346451	+	0.600071i	0.985616	−	0.168999i	$-0.0540533\pi$
$401$	6.93768	+	12.0164i	0.346451	+	0.600071i	−0.639165	+	0.769069i	$0.720720\pi$
$402$		0			0
$403$	−9.33700	+	2.50184i	−0.465109	+	0.124626i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−8.21033	−	4.74024i	−0.406971	−	0.234965i
$408$		0			0
$409$	15.7740	−	9.10712i	0.779974	−	0.450318i	−0.0564472	−	0.998406i	$-0.517977\pi$
$409$	15.7740	−	9.10712i	0.779974	−	0.450318i	0.836421	+	0.548087i	$0.184644\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−1.61387	−	1.61387i	−0.0794134	−	0.0794134i
$414$		0			0
$415$	11.9978			0.588950
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.708792	−	2.64525i	0.0346268	−	0.129229i	−0.946449	−	0.322854i	$-0.895358\pi$
$419$	0.708792	−	2.64525i	0.0346268	−	0.129229i	0.981076	+	0.193625i	$0.0620245\pi$
$420$		0			0
$421$	−5.57629	−	20.8110i	−0.271772	−	1.01427i	−0.957974	−	0.286855i	$-0.907390\pi$
$421$	−5.57629	−	20.8110i	−0.271772	−	1.01427i	0.686202	−	0.727411i	$-0.259276\pi$
$422$		0			0
$423$		0			0
$424$		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
$429$		0			0
$430$		0			0
$431$	17.4155			0.838873			0.419436	−	0.907785i	$-0.362228\pi$
$431$	17.4155			0.838873			0.419436	+	0.907785i	$0.362228\pi$
$432$		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
$435$		0			0
$436$		0			0
$437$	0.974016	+	0.260987i	0.0465935	+	0.0124847i
$438$		0			0
$439$	−34.3074	−	19.8074i	−1.63740	−	0.945354i	−0.981724	−	0.190312i	$-0.939050\pi$
$439$	−34.3074	−	19.8074i	−1.63740	−	0.945354i	−0.655677	−	0.755042i	$-0.727617\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6.05978	+	22.6154i	0.287909	+	1.07449i	0.946687	+	0.322154i	$0.104407\pi$
$443$	6.05978	+	22.6154i	0.287909	+	1.07449i	−0.658779	+	0.752337i	$0.728927\pi$
$444$		0			0
$445$	13.9267	−	51.9752i	0.660190	−	2.46386i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	1.41103			0.0665906			0.0332953	−	0.999446i	$-0.489400\pi$
$449$	1.41103			0.0665906			0.0332953	+	0.999446i	$0.489400\pi$
$450$		0			0
$451$	−39.0312	−	39.0312i	−1.83791	−	1.83791i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−13.1562	+	7.59571i	−0.616770	+	0.356092i
$456$		0			0
$457$	−21.3692	−	12.3375i	−0.999609	−	0.577124i	−0.0914761	−	0.995807i	$-0.529159\pi$
$457$	−21.3692	−	12.3375i	−0.999609	−	0.577124i	−0.908132	+	0.418683i	$0.862492\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−31.8645	+	8.53806i	−1.48408	+	0.397657i	−0.907733	−	0.419549i	$-0.862188\pi$
$461$	−31.8645	+	8.53806i	−1.48408	+	0.397657i	−0.576345	+	0.817207i	$0.695521\pi$
$462$		0			0
$463$	14.0805	+	24.3881i	0.654376	+	1.13341i	0.982050	+	0.188621i	$0.0604018\pi$
$463$	14.0805	+	24.3881i	0.654376	+	1.13341i	−0.327674	+	0.944791i	$0.606265\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	26.3173	+	26.3173i	1.21782	+	1.21782i	0.968394	+	0.249427i	$0.0802423\pi$
$467$	26.3173	+	26.3173i	1.21782	+	1.21782i	0.249427	+	0.968394i	$0.419758\pi$
$468$		0			0
$469$	3.41481	−	3.41481i	0.157681	−	0.157681i
$470$		0			0
$471$		0			0
$472$		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
$477$		0			0
$478$		0			0
$479$	1.55507	−	2.69347i	0.0710531	−	0.123068i	−0.828310	−	0.560270i	$-0.810697\pi$
$479$	1.55507	−	2.69347i	0.0710531	−	0.123068i	0.899363	+	0.437202i	$0.144031\pi$
$480$		0			0
$481$	1.28384	+	2.22368i	0.0585381	+	0.101391i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−28.7250	+	28.7250i	−1.30434	+	1.30434i
$486$		0			0
$487$		−	33.0078i		−	1.49572i	−0.663854	−	0.747862i	$-0.731080\pi$
$487$		−	33.0078i		−	1.49572i	0.663854	−	0.747862i	$-0.268920\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−19.9915	−	5.35669i	−0.902202	−	0.241744i	−0.222240	−	0.974992i	$-0.571337\pi$
$491$	−19.9915	−	5.35669i	−0.902202	−	0.241744i	−0.679962	+	0.733248i	$0.738004\pi$
$492$		0			0
$493$	0.424278	−	0.113685i	0.0191085	−	0.00512011i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	7.11636	−	12.3259i	0.319212	−	0.552892i
$498$		0			0
$499$	−9.38014	+	35.0072i	−0.419913	+	1.56714i	0.354875	+	0.934914i	$0.384524\pi$
$499$	−9.38014	+	35.0072i	−0.419913	+	1.56714i	−0.774787	+	0.632222i	$0.782143\pi$
$500$		0			0
$501$		0			0
$502$		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
$507$		0			0
$508$		0			0
$509$	2.85800	−	10.6662i	0.126679	−	0.472771i	−0.873215	−	0.487335i	$-0.837969\pi$
$509$	2.85800	−	10.6662i	0.126679	−	0.472771i	0.999894	+	0.0145635i	$0.00463586\pi$
$510$		0			0
$511$	23.0387	−	39.9042i	1.01917	−	1.76526i
$512$		0			0
$513$		0			0
$514$		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
$519$		0			0
$520$		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	−0.396657	−	0.917967i	$-0.629830\pi$
$523$	11.9219	−	11.9219i	0.521310	−	0.521310i	0.917967	+	0.396657i	$0.129830\pi$
$524$		0			0
$525$		0			0
$526$		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
$531$		0			0
$532$		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
$537$		0			0
$538$		0			0
$539$	8.54307	−	8.54307i	0.367976	−	0.367976i
$540$		0			0
$541$	15.9175	+	15.9175i	0.684346	+	0.684346i	0.960976	−	0.276630i	$-0.0892177\pi$
$541$	15.9175	+	15.9175i	0.684346	+	0.684346i	−0.276630	+	0.960976i	$0.589218\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	17.1146	+	29.6433i	0.733108	+	1.26978i
$546$		0			0
$547$	15.4827	−	4.14859i	0.661994	−	0.177381i	0.0878483	−	0.996134i	$-0.472001\pi$
$547$	15.4827	−	4.14859i	0.661994	−	0.177381i	0.574146	+	0.818753i	$0.305334\pi$
$548$		0			0
$549$		0			0
$550$		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
$555$		0			0
$556$		0			0
$557$	−0.878593	−	0.878593i	−0.0372272	−	0.0372272i	0.688248	−	0.725475i	$-0.258380\pi$
$557$	−0.878593	−	0.878593i	−0.0372272	−	0.0372272i	−0.725475	+	0.688248i	$0.758380\pi$
$558$		0			0
$559$	4.08112			0.172613
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−4.88030	+	18.2135i	−0.205680	+	0.767609i	0.783561	+	0.621315i	$0.213401\pi$
$563$	−4.88030	+	18.2135i	−0.205680	+	0.767609i	−0.989241	+	0.146294i	$0.953265\pi$
$564$		0			0
$565$	−5.70232	−	21.2813i	−0.239898	−	0.895313i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−23.9512	−	13.8282i	−1.00409	−	0.579710i	−0.0946316	−	0.995512i	$-0.530167\pi$
$569$	−23.9512	−	13.8282i	−1.00409	−	0.579710i	−0.909455	+	0.415803i	$0.863501\pi$
$570$		0			0
$571$	−24.9864	−	6.69509i	−1.04565	−	0.280181i	−0.305197	−	0.952289i	$-0.598722\pi$
$571$	−24.9864	−	6.69509i	−1.04565	−	0.280181i	−0.740453	+	0.672108i	$0.765389\pi$
$572$		0			0
$573$		0			0
$574$		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
$579$		0			0
$580$		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			0
$586$		0			0
$587$	8.65445	+	32.2988i	0.357207	+	1.33312i	0.877684	+	0.479240i	$0.159088\pi$
$587$	8.65445	+	32.2988i	0.357207	+	1.33312i	−0.520477	+	0.853876i	$0.674246\pi$
$588$		0			0
$589$	0.553851	−	2.06700i	0.0228211	−	0.0851693i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−25.3926			−1.04275			−0.521374	−	0.853328i	$-0.674580\pi$
$593$	−25.3926			−1.04275			−0.521374	+	0.853328i	$0.674580\pi$
$594$		0			0
$595$	−1.90524	−	1.90524i	−0.0781073	−	0.0781073i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−4.74083	+	2.73712i	−0.193705	+	0.111836i	−0.593716	−	0.804675i	$-0.702340\pi$
$599$	−4.74083	+	2.73712i	−0.193705	+	0.111836i	0.400011	+	0.916510i	$0.369006\pi$
$600$		0			0
$601$	2.04493	+	1.18064i	0.0834143	+	0.0481593i	0.541127	−	0.840941i	$-0.317998\pi$
$601$	2.04493	+	1.18064i	0.0834143	+	0.0481593i	−0.457713	+	0.889100i	$0.651331\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	59.9524	−	16.0642i	2.43741	−	0.653103i
$606$		0			0
$607$	2.67439	+	4.63219i	0.108550	+	0.188015i	0.915183	−	0.403038i	$-0.132046\pi$
$607$	2.67439	+	4.63219i	0.108550	+	0.188015i	−0.806633	+	0.591053i	$0.798712\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−12.5808	−	12.5808i	−0.508963	−	0.508963i
$612$		0			0
$613$	−0.799430	+	0.799430i	−0.0322887	+	0.0322887i	−0.723067	−	0.690778i	$-0.757268\pi$
$613$	−0.799430	+	0.799430i	−0.0322887	+	0.0322887i	0.690778	+	0.723067i	$0.257268\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−19.2117	+	11.0919i	−0.773432	+	0.446541i	−0.834098	−	0.551617i	$-0.814011\pi$
$617$	−19.2117	+	11.0919i	−0.773432	+	0.446541i	0.0606655	+	0.998158i	$0.480678\pi$
$618$		0			0
$619$	11.4867	+	42.8691i	0.461691	+	1.72305i	0.667634	+	0.744490i	$0.267307\pi$
$619$	11.4867	+	42.8691i	0.461691	+	1.72305i	−0.205943	+	0.978564i	$0.566026\pi$
$620$		0			0
$621$		0			0
$622$		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
$627$		0			0
$628$		0			0
$629$	−0.322028	+	0.322028i	−0.0128401	+	0.0128401i
$630$		0			0
$631$			12.0156i			0.478334i	0.970978	+	0.239167i	$0.0768744\pi$
$631$			12.0156i			0.478334i	−0.970978	+	0.239167i	$0.923126\pi$
$632$		0			0
$633$		0			0
$634$		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
$639$		0			0
$640$		0			0
$641$	8.47322	−	14.6760i	0.334672	−	0.579669i	−0.648750	−	0.761002i	$-0.724708\pi$
$641$	8.47322	−	14.6760i	0.334672	−	0.579669i	0.983422	+	0.181333i	$0.0580411\pi$
$642$		0			0
$643$	5.96216	−	22.2511i	0.235124	−	0.877496i	−0.742968	−	0.669327i	$-0.766583\pi$
$643$	5.96216	−	22.2511i	0.235124	−	0.877496i	0.978093	−	0.208170i	$-0.0667506\pi$
$644$		0			0
$645$		0			0
$646$		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
$651$		0			0
$652$		0			0
$653$	−7.67978	+	28.6613i	−0.300533	+	1.12160i	0.636190	+	0.771533i	$0.280510\pi$
$653$	−7.67978	+	28.6613i	−0.300533	+	1.12160i	−0.936723	+	0.350072i	$0.886157\pi$
$654$		0			0
$655$	15.4231	−	26.7135i	0.602629	−	1.04378i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−31.3170	+	8.39137i	−1.21994	+	0.326882i	−0.810654	−	0.585525i	$-0.800888\pi$
$659$	−31.3170	+	8.39137i	−1.21994	+	0.326882i	−0.409284	+	0.912407i	$0.634222\pi$
$660$		0			0
$661$	2.79494	+	0.748903i	0.108711	+	0.0291290i	0.312764	−	0.949831i	$-0.398745\pi$
$661$	2.79494	+	0.748903i	0.108711	+	0.0291290i	−0.204054	+	0.978960i	$0.565412\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	3.36304i		−	0.130413i
$666$		0			0
$667$	3.72888	−	3.72888i	0.144383	−	0.144383i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−12.1917	−	21.1166i	−0.470654	−	0.815197i
$672$		0			0
$673$	−5.83527	+	10.1070i	−0.224933	+	0.389595i	−0.956299	−	0.292389i	$-0.905550\pi$
$673$	−5.83527	+	10.1070i	−0.224933	+	0.389595i	0.731366	+	0.681985i	$0.238883\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	12.1843	+	45.4726i	0.468282	+	1.74765i	0.645772	+	0.763531i	$0.276536\pi$
$677$	12.1843	+	45.4726i	0.468282	+	1.74765i	−0.177489	+	0.984123i	$0.556798\pi$
$678$		0			0
$679$	−31.2874	+	18.0638i	−1.20070	+	0.693225i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	19.7598	−	19.7598i	0.756087	−	0.756087i	−0.219521	−	0.975608i	$-0.570449\pi$
$683$	19.7598	−	19.7598i	0.756087	−	0.756087i	0.975608	+	0.219521i	$0.0704495\pi$
$684$		0			0
$685$	23.6729	+	23.6729i	0.904495	+	0.904495i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.28576	−	2.22700i	−0.0489835	−	0.0848420i
$690$		0			0
$691$	25.6957	−	6.88515i	0.977511	−	0.261923i	0.265515	−	0.964107i	$-0.414458\pi$
$691$	25.6957	−	6.88515i	0.977511	−	0.261923i	0.711996	+	0.702183i	$0.247791\pi$
$692$		0			0
$693$		0			0
$694$		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
$699$		0			0
$700$		0			0
$701$	32.6887	+	32.6887i	1.23463	+	1.23463i	0.962164	+	0.272471i	$0.0878408\pi$
$701$	32.6887	+	32.6887i	1.23463	+	1.23463i	0.272471	+	0.962164i	$0.412159\pi$
$702$		0			0
$703$	−0.568427			−0.0214386
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−5.87047	+	21.9089i	−0.220782	+	0.823969i
$708$		0			0
$709$	11.4514	+	42.7374i	0.430068	+	1.60504i	0.752601	+	0.658477i	$0.228799\pi$
$709$	11.4514	+	42.7374i	0.430068	+	1.60504i	−0.322533	+	0.946558i	$0.604534\pi$
$710$		0			0
$711$		0			0
$712$		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
$717$		0			0
$718$		0			0
$719$	5.93945			0.221504			0.110752	−	0.993848i	$-0.464674\pi$
$719$	5.93945			0.221504			0.110752	+	0.993848i	$0.464674\pi$
$720$		0			0
$721$	−34.4992			−1.28482
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−10.9244	−	2.92719i	−0.405722	−	0.108713i
$726$		0			0
$727$	8.81201	+	5.08761i	0.326819	+	0.188689i	0.654428	−	0.756124i	$-0.272909\pi$
$727$	8.81201	+	5.08761i	0.326819	+	0.188689i	−0.327609	+	0.944813i	$0.606243\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.187345	+	0.699183i	0.00692922	+	0.0258602i
$732$		0			0
$733$	−8.23211	+	30.7227i	−0.304060	+	1.13477i	0.629692	+	0.776845i	$0.283181\pi$
$733$	−8.23211	+	30.7227i	−0.304060	+	1.13477i	−0.933752	+	0.357922i	$0.883485\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	8.58056			0.316069
$738$		0			0
$739$	24.0006	+	24.0006i	0.882876	+	0.882876i	0.993826	−	0.110950i	$-0.0353894\pi$
$739$	24.0006	+	24.0006i	0.882876	+	0.882876i	−0.110950	+	0.993826i	$0.535389\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−8.54415	+	4.93297i	−0.313454	+	0.180973i	−0.648471	−	0.761239i	$-0.724591\pi$
$743$	−8.54415	+	4.93297i	−0.313454	+	0.180973i	0.335017	+	0.942212i	$0.391258\pi$
$744$		0			0
$745$	−33.8611	−	19.5497i	−1.24057	−	0.716246i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	28.3024	−	7.58360i	1.03415	−	0.277099i
$750$		0			0
$751$	−22.9226	−	39.7031i	−0.836458	−	1.44879i	−0.892838	−	0.450378i	$-0.851289\pi$
$751$	−22.9226	−	39.7031i	−0.836458	−	1.44879i	0.0563807	−	0.998409i	$-0.482044\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1.19365	+	1.19365i	0.0434414	+	0.0434414i
$756$		0			0
$757$	−13.9071	+	13.9071i	−0.505462	+	0.505462i	−0.913130	−	0.407668i	$-0.866342\pi$
$757$	−13.9071	+	13.9071i	−0.505462	+	0.505462i	0.407668	+	0.913130i	$0.366342\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−23.7610	+	13.7184i	−0.861334	+	0.497291i	−0.864459	−	0.502704i	$-0.832339\pi$
$761$	−23.7610	+	13.7184i	−0.861334	+	0.497291i	0.00312490	+	0.999995i	$0.499005\pi$
$762$		0			0
$763$	7.87873	+	29.4038i	0.285229	+	1.06449i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.549159	+	0.951172i	−0.0198290	+	0.0343448i
$768$		0			0
$769$	−0.377145	−	0.653234i	−0.0136002	−	0.0235562i	0.859145	−	0.511732i	$-0.170996\pi$
$769$	−0.377145	−	0.653234i	−0.0136002	−	0.0235562i	−0.872745	+	0.488176i	$0.837663\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−9.72090	+	9.72090i	−0.349637	+	0.349637i	−0.859974	−	0.510338i	$-0.829520\pi$
$773$	−9.72090	+	9.72090i	−0.349637	+	0.349637i	0.510338	+	0.859974i	$0.329520\pi$
$774$		0			0
$775$			44.1447i			1.58572i
$776$		0			0
$777$		0			0
$778$		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
$783$		0			0
$784$		0			0
$785$	−24.5056	+	42.4450i	−0.874644	+	1.51493i
$786$		0			0
$787$	−6.76494	+	25.2471i	−0.241144	+	0.899962i	0.734138	+	0.679000i	$0.237586\pi$
$787$	−6.76494	+	25.2471i	−0.241144	+	0.899962i	−0.975282	+	0.220962i	$0.929080\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	19.5938i		−	0.696676i
$792$		0			0
$793$			6.60396i			0.234513i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−8.11835	+	30.2981i	−0.287567	+	1.07321i	0.659377	+	0.751813i	$0.270820\pi$
$797$	−8.11835	+	30.2981i	−0.287567	+	1.07321i	−0.946943	+	0.321401i	$0.895846\pi$
$798$		0			0
$799$	1.57783	−	2.73288i	0.0558195	−	0.0966822i
$800$		0			0
$801$		0			0
$802$		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
$807$		0			0
$808$		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	−0.786303	−	0.617842i	$-0.788007\pi$
$811$	−4.79744	+	4.79744i	−0.168461	+	0.168461i	0.617842	+	0.786303i	$0.288007\pi$
$812$		0			0
$813$		0			0
$814$		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
$819$		0			0
$820$		0			0
$821$	−7.43764	−	27.7576i	−0.259575	−	0.968748i	−0.965488	−	0.260449i	$-0.916129\pi$
$821$	−7.43764	−	27.7576i	−0.259575	−	0.968748i	0.705912	−	0.708299i	$-0.250537\pi$
$822$		0			0
$823$	22.9167	−	13.2310i	0.798826	−	0.461202i	−0.0442346	−	0.999021i	$-0.514085\pi$
$823$	22.9167	−	13.2310i	0.798826	−	0.461202i	0.843060	+	0.537819i	$0.180752\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−28.6969	+	28.6969i	−0.997888	+	0.997888i	−0.999998	−	0.00211025i	$-0.999328\pi$
$827$	−28.6969	+	28.6969i	−0.997888	+	0.997888i	0.00211025	+	0.999998i	$0.499328\pi$
$828$		0			0
$829$	16.5920	+	16.5920i	0.576263	+	0.576263i	0.933872	−	0.357609i	$-0.116408\pi$
$829$	16.5920	+	16.5920i	0.576263	+	0.576263i	−0.357609	+	0.933872i	$0.616408\pi$
$830$		0			0
$831$		0			0
$832$		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
$837$		0			0
$838$		0			0
$839$	−5.80231	−	3.34997i	−0.200318	−	0.115654i	0.396486	−	0.918041i	$-0.370230\pi$
$839$	−5.80231	−	3.34997i	−0.200318	−	0.115654i	−0.596804	+	0.802387i	$0.703563\pi$
$840$		0			0
$841$	−22.6317	+	13.0664i	−0.780405	+	0.450567i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−26.2457	−	26.2457i	−0.902881	−	0.902881i
$846$		0			0
$847$	55.1984			1.89664
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.41512	+	5.28129i	−0.0485096	+	0.181040i
$852$		0			0
$853$	−5.16181	−	19.2641i	−0.176737	−	0.659592i	−0.996249	−	0.0865300i	$-0.972422\pi$
$853$	−5.16181	−	19.2641i	−0.176737	−	0.659592i	0.819512	−	0.573062i	$-0.194245\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	12.5164	+	7.22635i	0.427552	+	0.246848i	0.698303	−	0.715802i	$-0.253939\pi$
$857$	12.5164	+	7.22635i	0.427552	+	0.246848i	−0.270751	+	0.962649i	$0.587272\pi$
$858$		0			0
$859$	4.24540	+	1.13755i	0.144851	+	0.0388127i	0.330516	−	0.943800i	$-0.392777\pi$
$859$	4.24540	+	1.13755i	0.144851	+	0.0388127i	−0.185665	+	0.982613i	$0.559444\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	43.8649			1.49318			0.746589	−	0.665286i	$-0.231690\pi$
$863$	43.8649			1.49318			0.746589	+	0.665286i	$0.231690\pi$
$864$		0			0
$865$	52.3071			1.77849
$866$		0			0
$867$		0			0
$868$		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
$873$		0			0
$874$		0			0
$875$	4.51450	+	16.8484i	0.152618	+	0.569578i
$876$		0			0
$877$	−9.87004	+	36.8355i	−0.333288	+	1.24385i	0.572426	+	0.819956i	$0.306002\pi$
$877$	−9.87004	+	36.8355i	−0.333288	+	1.24385i	−0.905714	+	0.423890i	$0.860664\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	17.2270			0.580392			0.290196	−	0.956967i	$-0.406279\pi$
$881$	17.2270			0.580392			0.290196	+	0.956967i	$0.406279\pi$
$882$		0			0
$883$	−8.52615	−	8.52615i	−0.286928	−	0.286928i	0.548936	−	0.835864i	$-0.315033\pi$
$883$	−8.52615	−	8.52615i	−0.286928	−	0.286928i	−0.835864	+	0.548936i	$0.815033\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.898979	−	0.519026i	0.0301847	−	0.0174272i	−0.484832	−	0.874607i	$-0.661119\pi$
$887$	0.898979	−	0.519026i	0.0301847	−	0.0174272i	0.515016	+	0.857180i	$0.327786\pi$
$888$		0			0
$889$	37.2955	+	21.5326i	1.25085	+	0.722180i
$890$		0			0
$891$		0			0
$892$		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
$897$		0			0
$898$		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
$903$		0			0
$904$		0			0
$905$	−53.3389	+	30.7952i	−1.77304	+	1.02367i
$906$		0			0
$907$	13.8612	+	51.7308i	0.460255	+	1.71769i	0.672162	+	0.740404i	$0.265366\pi$
$907$	13.8612	+	51.7308i	0.460255	+	1.71769i	−0.211907	+	0.977290i	$0.567968\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−24.2632	+	42.0250i	−0.803875	+	1.39235i	0.113173	+	0.993575i	$0.463898\pi$
$911$	−24.2632	+	42.0250i	−0.803875	+	1.39235i	−0.917048	+	0.398777i	$0.869435\pi$
$912$		0			0
$913$	9.47916	+	16.4184i	0.313714	+	0.543369i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	19.3977	−	19.3977i	0.640567	−	0.640567i
$918$		0			0
$919$			1.68133i			0.0554620i	0.999615	+	0.0277310i	$0.00882819\pi$
$919$			1.68133i			0.0554620i	−0.999615	+	0.0277310i	$0.991172\pi$
$920$		0			0
$921$		0			0
$922$		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
$927$		0			0
$928$		0			0
$929$	−11.7821	+	20.4072i	−0.386559	+	0.669540i	−0.991984	−	0.126363i	$-0.959670\pi$
$929$	−11.7821	+	20.4072i	−0.386559	+	0.669540i	0.605425	+	0.795902i	$0.293003\pi$
$930$		0			0
$931$	0.187487	−	0.699709i	0.00614462	−	0.0229320i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	4.78739i		−	0.156564i
$936$		0			0
$937$		−	41.8215i		−	1.36625i	−0.730302	−	0.683125i	$-0.760620\pi$
$937$		−	41.8215i		−	1.36625i	0.730302	−	0.683125i	$-0.239380\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	7.02041	−	26.2005i	0.228859	−	0.854113i	−0.751963	−	0.659205i	$-0.770893\pi$
$941$	7.02041	−	26.2005i	0.228859	−	0.854113i	0.980822	−	0.194907i	$-0.0624406\pi$
$942$		0			0
$943$	−15.9171	+	27.5691i	−0.518331	+	0.897775i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.69902	+	2.33090i	−0.282680	+	0.0757439i	−0.397373	−	0.917657i	$-0.630078\pi$
$947$	−8.69902	+	2.33090i	−0.282680	+	0.0757439i	0.114693	+	0.993401i	$0.463412\pi$
$948$		0			0
$949$	−21.4179	−	5.73891i	−0.695254	−	0.186293i
$950$		0			0
$951$		0			0
$952$		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
$957$		0			0
$958$		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
$963$		0			0
$964$		0			0
$965$	−2.36052	−	8.80959i	−0.0759879	−	0.283591i
$966$		0			0
$967$	38.0224	−	21.9523i	1.22272	−	0.705937i	0.257222	−	0.966352i	$-0.417193\pi$
$967$	38.0224	−	21.9523i	1.22272	−	0.705937i	0.965497	+	0.260415i	$0.0838594\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−13.7775	+	13.7775i	−0.442142	+	0.442142i	−0.892731	−	0.450590i	$-0.851214\pi$
$971$	−13.7775	+	13.7775i	−0.442142	+	0.442142i	0.450590	+	0.892731i	$0.351214\pi$
$972$		0			0
$973$	1.18422	+	1.18422i	0.0379645	+	0.0379645i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−8.47350	−	14.6765i	−0.271091	−	0.469544i	0.698050	−	0.716049i	$-0.254051\pi$
$977$	−8.47350	−	14.6765i	−0.271091	−	0.469544i	−0.969142	+	0.246505i	$0.920718\pi$
$978$		0			0
$979$	82.1284	−	22.0062i	2.62484	−	0.703323i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.93132	+	1.11505i	0.0615996	+	0.0355645i	0.530483	−	0.847695i	$-0.322010\pi$
$983$	1.93132	+	1.11505i	0.0615996	+	0.0355645i	−0.468884	+	0.883260i	$0.655344\pi$
$984$		0			0
$985$	45.8075	−	26.4470i	1.45955	−	0.842670i
$986$		0			0
$987$		0			0
$988$		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
$993$		0			0
$994$		0			0
$995$	−4.02812	+	15.0332i	−0.127700	+	0.476583i
$996$		0			0
$997$	10.9118	+	40.7234i	0.345581	+	1.28972i	0.891932	+	0.452169i	$0.149349\pi$
$997$	10.9118	+	40.7234i	0.345581	+	1.28972i	−0.546352	+	0.837556i	$0.683984\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.2.bc.e.721.2		72
3.2	odd	2		576.2.bb.e.529.10		72
4.3	odd	2		432.2.y.e.397.14		72
9.4	even	3	inner	1728.2.bc.e.145.17		72
9.5	odd	6		576.2.bb.e.337.18		72
12.11	even	2		144.2.x.e.61.5	yes	72
16.5	even	4	inner	1728.2.bc.e.1585.17		72
16.11	odd	4		432.2.y.e.181.3		72
36.23	even	6		144.2.x.e.13.16	✓	72
36.31	odd	6		432.2.y.e.253.3		72
48.5	odd	4		576.2.bb.e.241.18		72
48.11	even	4		144.2.x.e.133.16	yes	72
144.5	odd	12		576.2.bb.e.49.10		72
144.59	even	12		144.2.x.e.85.5	yes	72
144.85	even	12	inner	1728.2.bc.e.1009.2		72
144.139	odd	12		432.2.y.e.37.14		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.16	✓	72	36.23	even	6
144.2.x.e.61.5	yes	72	12.11	even	2
144.2.x.e.85.5	yes	72	144.59	even	12
144.2.x.e.133.16	yes	72	48.11	even	4
432.2.y.e.37.14		72	144.139	odd	12
432.2.y.e.181.3		72	16.11	odd	4
432.2.y.e.253.3		72	36.31	odd	6
432.2.y.e.397.14		72	4.3	odd	2
576.2.bb.e.49.10		72	144.5	odd	12
576.2.bb.e.241.18		72	48.5	odd	4
576.2.bb.e.337.18		72	9.5	odd	6
576.2.bb.e.529.10		72	3.2	odd	2
1728.2.bc.e.145.17		72	9.4	even	3	inner
1728.2.bc.e.721.2		72	1.1	even	1	trivial
1728.2.bc.e.1009.2		72	144.85	even	12	inner
1728.2.bc.e.1585.17		72	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1728.bc (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.30105 - 0.884514i) q^{5} +(-2.63210 - 1.51965i) q^{7} +O(q^{10})\)	\(q+(-3.30105 - 0.884514i) q^{5} +(-2.63210 - 1.51965i) q^{7} +(-1.39766 - 5.21614i) q^{11} +(-0.378541 + 1.41274i) q^{13} -0.259408 q^{17} +(-0.228947 - 0.228947i) q^{19} +(-2.69713 + 1.55719i) q^{23} +(5.78446 + 3.33966i) q^{25} +(-1.63556 + 0.438247i) q^{29} +(3.30458 + 5.72370i) q^{31} +(7.34457 + 7.34457i) q^{35} +(1.24139 - 1.24139i) q^{37} +(8.85221 - 5.11082i) q^{41} +(-0.722202 - 2.69530i) q^{43} +(-6.08240 + 10.5350i) q^{47} +(1.11865 + 1.93755i) q^{49} +(-1.24325 + 1.24325i) q^{53} +18.4550i q^{55} +(0.725362 + 0.194360i) q^{59} +(4.36145 - 1.16865i) q^{61} +(2.49917 - 4.32869i) q^{65} +(-0.411250 + 1.53481i) q^{67} +4.68290i q^{71} +15.1606i q^{73} +(-4.24790 + 15.8534i) q^{77} +(0.738050 - 1.27834i) q^{79} +(-3.39108 + 0.908637i) q^{83} +(0.856321 + 0.229451i) q^{85} +15.7450i q^{89} +(3.14322 - 3.14322i) q^{91} +(0.553260 + 0.958274i) q^{95} +(5.94343 - 10.2943i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{5}+O(q^{10}) \) 72 * q - 4 * q^5	\( 72 q - 4 q^{5} - 2 q^{11} - 16 q^{13} + 16 q^{17} - 28 q^{19} - 4 q^{29} - 28 q^{31} - 16 q^{35} + 16 q^{37} + 10 q^{43} - 56 q^{47} + 4 q^{49} + 8 q^{53} - 14 q^{59} - 32 q^{61} + 64 q^{65} + 18 q^{67} + 36 q^{77} - 44 q^{79} + 20 q^{83} - 8 q^{85} + 80 q^{91} + 48 q^{95} + 40 q^{97}+O(q^{100}) \) 72 * q - 4 * q^5 - 2 * q^11 - 16 * q^13 + 16 * q^17 - 28 * q^19 - 4 * q^29 - 28 * q^31 - 16 * q^35 + 16 * q^37 + 10 * q^43 - 56 * q^47 + 4 * q^49 + 8 * q^53 - 14 * q^59 - 32 * q^61 + 64 * q^65 + 18 * q^67 + 36 * q^77 - 44 * q^79 + 20 * q^83 - 8 * q^85 + 80 * q^91 + 48 * q^95 + 40 * q^97

Introduction

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