LMFDB - Embedded newform 1728.2.bc.b.721.1

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:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			721.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1728.721
Dual form			1728.2.bc.b.1009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.133975i) q^{5} +(2.13397 + 1.23205i) q^{7} +O(q^{10})$	$q+(-0.500000 - 0.133975i) q^{5} +(2.13397 + 1.23205i) q^{7} +(0.133975 + 0.500000i) q^{11} +(-1.23205 + 4.59808i) q^{13} -4.00000 q^{17} +(3.00000 + 3.00000i) q^{19} +(0.401924 - 0.232051i) q^{23} +(-4.09808 - 2.36603i) q^{25} +(3.23205 - 0.866025i) q^{29} +(-0.598076 - 1.03590i) q^{31} +(-0.901924 - 0.901924i) q^{35} +(-7.73205 + 7.73205i) q^{37} +(-9.69615 + 5.59808i) q^{41} +(2.33013 + 8.69615i) q^{43} +(4.59808 - 7.96410i) q^{47} +(-0.464102 - 0.803848i) q^{49} +(-2.26795 + 2.26795i) q^{53} -0.267949i q^{55} +(5.59808 + 1.50000i) q^{59} +(14.4282 - 3.86603i) q^{61} +(1.23205 - 2.13397i) q^{65} +(0.330127 - 1.23205i) q^{67} +10.9282i q^{71} +0.535898i q^{73} +(-0.330127 + 1.23205i) q^{77} +(-0.866025 + 1.50000i) q^{79} +(-11.7942 + 3.16025i) q^{83} +(2.00000 + 0.535898i) q^{85} +11.8564i q^{89} +(-8.29423 + 8.29423i) q^{91} +(-1.09808 - 1.90192i) q^{95} +(-0.500000 + 0.866025i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{5} + 12 q^{7}+O(q^{10}) $ 4 * q - 2 * q^5 + 12 * q^7	$ 4 q - 2 q^{5} + 12 q^{7} + 4 q^{11} + 2 q^{13} - 16 q^{17} + 12 q^{19} + 12 q^{23} - 6 q^{25} + 6 q^{29} + 8 q^{31} - 14 q^{35} - 24 q^{37} - 18 q^{41} - 8 q^{43} + 8 q^{47} + 12 q^{49} - 16 q^{53} + 12 q^{59} + 30 q^{61} - 2 q^{65} - 16 q^{67} + 16 q^{77} - 16 q^{83} + 8 q^{85} - 2 q^{91} + 6 q^{95} - 2 q^{97}+O(q^{100}) $ 4 * q - 2 * q^5 + 12 * q^7 + 4 * q^11 + 2 * q^13 - 16 * q^17 + 12 * q^19 + 12 * q^23 - 6 * q^25 + 6 * q^29 + 8 * q^31 - 14 * q^35 - 24 * q^37 - 18 * q^41 - 8 * q^43 + 8 * q^47 + 12 * q^49 - 16 * q^53 + 12 * q^59 + 30 * q^61 - 2 * q^65 - 16 * q^67 + 16 * q^77 - 16 * q^83 + 8 * q^85 - 2 * q^91 + 6 * q^95 - 2 * 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
$5$	−0.500000	−	0.133975i	−0.223607	−	0.0599153i	0.145276	−	0.989391i	$-0.453593\pi$
$5$	−0.500000	−	0.133975i	−0.223607	−	0.0599153i	−0.368883	+	0.929476i	$0.620260\pi$
$6$		0			0
$7$	2.13397	+	1.23205i	0.806567	+	0.465671i	0.845762	−	0.533560i	$-0.179146\pi$
$7$	2.13397	+	1.23205i	0.806567	+	0.465671i	−0.0391956	+	0.999232i	$0.512480\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.133975	+	0.500000i	0.0403949	+	0.150756i	0.983178	−	0.182652i	$-0.0584681\pi$
$11$	0.133975	+	0.500000i	0.0403949	+	0.150756i	−0.942783	+	0.333408i	$0.891801\pi$
$12$		0			0
$13$	−1.23205	+	4.59808i	−0.341709	+	1.27528i	0.554700	+	0.832050i	$0.312833\pi$
$13$	−1.23205	+	4.59808i	−0.341709	+	1.27528i	−0.896410	+	0.443227i	$0.853834\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.00000			−0.970143			−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000			−0.970143			−0.485071	+	0.874475i	$0.661206\pi$
$18$		0			0
$19$	3.00000	+	3.00000i	0.688247	+	0.688247i	0.961844	−	0.273597i	$-0.0882135\pi$
$19$	3.00000	+	3.00000i	0.688247	+	0.688247i	−0.273597	+	0.961844i	$0.588214\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.401924	−	0.232051i	0.0838069	−	0.0483859i	−0.457511	−	0.889204i	$-0.651259\pi$
$23$	0.401924	−	0.232051i	0.0838069	−	0.0483859i	0.541318	+	0.840818i	$0.317926\pi$
$24$		0			0
$25$	−4.09808	−	2.36603i	−0.819615	−	0.473205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.23205	−	0.866025i	0.600177	−	0.160817i	0.0540766	−	0.998537i	$-0.482778\pi$
$29$	3.23205	−	0.866025i	0.600177	−	0.160817i	0.546100	+	0.837720i	$0.316112\pi$
$30$		0			0
$31$	−0.598076	−	1.03590i	−0.107418	−	0.186053i	0.807306	−	0.590133i	$-0.200925\pi$
$31$	−0.598076	−	1.03590i	−0.107418	−	0.186053i	−0.914723	+	0.404081i	$0.867592\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.901924	−	0.901924i	−0.152453	−	0.152453i
$36$		0			0
$37$	−7.73205	+	7.73205i	−1.27114	+	1.27114i	−0.325651	+	0.945490i	$0.605584\pi$
$37$	−7.73205	+	7.73205i	−1.27114	+	1.27114i	−0.945490	+	0.325651i	$0.894416\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−9.69615	+	5.59808i	−1.51428	+	0.874273i	−0.514425	+	0.857536i	$0.671994\pi$
$41$	−9.69615	+	5.59808i	−1.51428	+	0.874273i	−0.999860	+	0.0167371i	$0.994672\pi$
$42$		0			0
$43$	2.33013	+	8.69615i	0.355341	+	1.32615i	0.880055	+	0.474872i	$0.157506\pi$
$43$	2.33013	+	8.69615i	0.355341	+	1.32615i	−0.524714	+	0.851279i	$0.675828\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.59808	−	7.96410i	0.670698	−	1.16168i	−0.307008	−	0.951707i	$-0.599328\pi$
$47$	4.59808	−	7.96410i	0.670698	−	1.16168i	0.977706	−	0.209977i	$-0.0673388\pi$
$48$		0			0
$49$	−0.464102	−	0.803848i	−0.0663002	−	0.114835i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.26795	+	2.26795i	−0.311527	+	0.311527i	−0.845501	−	0.533974i	$-0.820698\pi$
$53$	−2.26795	+	2.26795i	−0.311527	+	0.311527i	0.533974	+	0.845501i	$0.320698\pi$
$54$		0			0
$55$		−	0.267949i		−	0.0361303i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.59808	+	1.50000i	0.728807	+	0.195283i	0.604098	−	0.796910i	$-0.293533\pi$
$59$	5.59808	+	1.50000i	0.728807	+	0.195283i	0.124709	+	0.992193i	$0.460200\pi$
$60$		0			0
$61$	14.4282	−	3.86603i	1.84734	−	0.494994i	0.847957	−	0.530065i	$-0.177832\pi$
$61$	14.4282	−	3.86603i	1.84734	−	0.494994i	0.999385	+	0.0350707i	$0.0111656\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.23205	−	2.13397i	0.152817	−	0.264687i
$66$		0			0
$67$	0.330127	−	1.23205i	0.0403314	−	0.150519i	−0.942824	−	0.333292i	$-0.891841\pi$
$67$	0.330127	−	1.23205i	0.0403314	−	0.150519i	0.983155	+	0.182773i	$0.0585073\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			10.9282i			1.29694i	0.761241	+	0.648470i	$0.224591\pi$
$71$			10.9282i			1.29694i	−0.761241	+	0.648470i	$0.775409\pi$
$72$		0			0
$73$			0.535898i			0.0627222i	0.999508	+	0.0313611i	$0.00998418\pi$
$73$			0.535898i			0.0627222i	−0.999508	+	0.0313611i	$0.990016\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.330127	+	1.23205i	−0.0376215	+	0.140405i
$78$		0			0
$79$	−0.866025	+	1.50000i	−0.0974355	+	0.168763i	−0.910622	−	0.413239i	$-0.864397\pi$
$79$	−0.866025	+	1.50000i	−0.0974355	+	0.168763i	0.813187	+	0.582003i	$0.197731\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−11.7942	+	3.16025i	−1.29458	+	0.346883i	−0.839400	−	0.543514i	$-0.817093\pi$
$83$	−11.7942	+	3.16025i	−1.29458	+	0.346883i	−0.455185	+	0.890397i	$0.650427\pi$
$84$		0			0
$85$	2.00000	+	0.535898i	0.216930	+	0.0581263i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			11.8564i			1.25678i	0.777900	+	0.628388i	$0.216285\pi$
$89$			11.8564i			1.25678i	−0.777900	+	0.628388i	$0.783715\pi$
$90$		0			0
$91$	−8.29423	+	8.29423i	−0.869471	+	0.869471i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.09808	−	1.90192i	−0.112660	−	0.195133i
$96$		0			0
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	−0.890292	−	0.455389i	$-0.849500\pi$
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	0.839525	+	0.543321i	$0.182833\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.500000	−	1.86603i	−0.0497519	−	0.185676i	0.936578	−	0.350459i	$-0.113974\pi$
$101$	−0.500000	−	1.86603i	−0.0497519	−	0.185676i	−0.986330	+	0.164783i	$0.947308\pi$
$102$		0			0
$103$	−1.79423	+	1.03590i	−0.176791	+	0.102070i	−0.585784	−	0.810467i	$-0.699213\pi$
$103$	−1.79423	+	1.03590i	−0.176791	+	0.102070i	0.408993	+	0.912537i	$0.365880\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−11.3923	+	11.3923i	−1.10134	+	1.10134i	−0.107086	+	0.994250i	$0.534152\pi$
$107$	−11.3923	+	11.3923i	−1.10134	+	1.10134i	−0.994250	+	0.107086i	$0.965848\pi$
$108$		0			0
$109$	1.73205	+	1.73205i	0.165900	+	0.165900i	0.785175	−	0.619274i	$-0.212573\pi$
$109$	1.73205	+	1.73205i	0.165900	+	0.165900i	−0.619274	+	0.785175i	$0.712573\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.76795	+	4.79423i	0.260387	+	0.451003i	0.966345	−	0.257251i	$-0.0828166\pi$
$113$	2.76795	+	4.79423i	0.260387	+	0.451003i	−0.705958	+	0.708254i	$0.749483\pi$
$114$		0			0
$115$	−0.232051	+	0.0621778i	−0.0216388	+	0.00579811i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−8.53590	−	4.92820i	−0.782485	−	0.451768i
$120$		0			0
$121$	9.29423	−	5.36603i	0.844930	−	0.487820i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	3.56218	+	3.56218i	0.318611	+	0.318611i
$126$		0			0
$127$	20.3923			1.80952			0.904762	−	0.425917i	$-0.140048\pi$
$127$	20.3923			1.80952			0.904762	+	0.425917i	$0.140048\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.13397	+	11.6962i	−0.273817	+	1.02190i	0.682814	+	0.730593i	$0.260756\pi$
$131$	−3.13397	+	11.6962i	−0.273817	+	1.02190i	−0.956630	+	0.291305i	$0.905911\pi$
$132$		0			0
$133$	2.70577	+	10.0981i	0.234620	+	0.875614i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−14.4282	−	8.33013i	−1.23268	−	0.711691i	−0.265096	−	0.964222i	$-0.585404\pi$
$137$	−14.4282	−	8.33013i	−1.23268	−	0.711691i	−0.967589	+	0.252531i	$0.918737\pi$
$138$		0			0
$139$	−4.33013	−	1.16025i	−0.367277	−	0.0984115i	0.0704603	−	0.997515i	$-0.477553\pi$
$139$	−4.33013	−	1.16025i	−0.367277	−	0.0984115i	−0.437737	+	0.899103i	$0.644220\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.46410			−0.206059
$144$		0			0
$145$	−1.73205			−0.143839
$146$		0			0
$147$		0			0
$148$		0			0
$149$	14.6962	+	3.93782i	1.20396	+	0.322599i	0.804388	−	0.594105i	$-0.202493\pi$
$149$	14.6962	+	3.93782i	1.20396	+	0.322599i	0.399568	+	0.916704i	$0.369160\pi$
$150$		0			0
$151$	6.06218	+	3.50000i	0.493333	+	0.284826i	0.725956	−	0.687741i	$-0.241398\pi$
$151$	6.06218	+	3.50000i	0.493333	+	0.284826i	−0.232623	+	0.972567i	$0.574731\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.160254	+	0.598076i	0.0128719	+	0.0480386i
$156$		0			0
$157$	−0.232051	+	0.866025i	−0.0185197	+	0.0691164i	−0.974567	−	0.224095i	$-0.928057\pi$
$157$	−0.232051	+	0.866025i	−0.0185197	+	0.0691164i	0.956048	+	0.293212i	$0.0947240\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1.14359			0.0901278
$162$		0			0
$163$	−11.9282	−	11.9282i	−0.934289	−	0.934289i	0.0636813	−	0.997970i	$-0.479716\pi$
$163$	−11.9282	−	11.9282i	−0.934289	−	0.934289i	−0.997970	+	0.0636813i	$0.979716\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.25833	+	4.76795i	−0.639049	+	0.368955i	−0.784248	−	0.620447i	$-0.786951\pi$
$167$	−8.25833	+	4.76795i	−0.639049	+	0.368955i	0.145199	+	0.989402i	$0.453618\pi$
$168$		0			0
$169$	−8.36603	−	4.83013i	−0.643540	−	0.371548i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	8.96410	−	2.40192i	0.681528	−	0.182615i	0.0985859	−	0.995129i	$-0.468568\pi$
$173$	8.96410	−	2.40192i	0.681528	−	0.182615i	0.582942	+	0.812514i	$0.301901\pi$
$174$		0			0
$175$	−5.83013	−	10.0981i	−0.440716	−	0.763343i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	7.92820	+	7.92820i	0.592582	+	0.592582i	0.938328	−	0.345746i	$-0.112374\pi$
$179$	7.92820	+	7.92820i	0.592582	+	0.592582i	−0.345746	+	0.938328i	$0.612374\pi$
$180$		0			0
$181$	−4.26795	+	4.26795i	−0.317234	+	0.317234i	−0.847704	−	0.530470i	$-0.822016\pi$
$181$	−4.26795	+	4.26795i	−0.317234	+	0.317234i	0.530470	+	0.847704i	$0.322016\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	4.90192	−	2.83013i	0.360397	−	0.208075i
$186$		0			0
$187$	−0.535898	−	2.00000i	−0.0391888	−	0.146254i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.59808	−	11.4282i	0.477420	−	0.826916i	−0.522245	−	0.852795i	$-0.674905\pi$
$191$	6.59808	−	11.4282i	0.477420	−	0.826916i	0.999665	+	0.0258797i	$0.00823869\pi$
$192$		0			0
$193$	−1.23205	−	2.13397i	−0.0886850	−	0.153607i	0.818271	−	0.574833i	$-0.194933\pi$
$193$	−1.23205	−	2.13397i	−0.0886850	−	0.153607i	−0.906956	+	0.421226i	$0.861600\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.4641	+	10.4641i	−0.745536	+	0.745536i	−0.973637	−	0.228101i	$-0.926748\pi$
$197$	−10.4641	+	10.4641i	−0.745536	+	0.745536i	0.228101	+	0.973637i	$0.426748\pi$
$198$		0			0
$199$		−	5.85641i		−	0.415150i	−0.978219	−	0.207575i	$-0.933443\pi$
$199$		−	5.85641i		−	0.415150i	0.978219	−	0.207575i	$-0.0665570\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	7.96410	+	2.13397i	0.558970	+	0.149776i
$204$		0			0
$205$	5.59808	−	1.50000i	0.390987	−	0.104765i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.09808	+	1.90192i	−0.0759555	+	0.131559i
$210$		0			0
$211$	0.526279	−	1.96410i	0.0362306	−	0.135214i	−0.945442	−	0.325791i	$-0.894369\pi$
$211$	0.526279	−	1.96410i	0.0362306	−	0.135214i	0.981672	+	0.190577i	$0.0610359\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	4.66025i		−	0.317827i
$216$		0			0
$217$		−	2.94744i		−	0.200085i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	4.92820	−	18.3923i	0.331507	−	1.23720i
$222$		0			0
$223$	7.79423	−	13.5000i	0.521940	−	0.904027i	−0.477734	−	0.878504i	$-0.658542\pi$
$223$	7.79423	−	13.5000i	0.521940	−	0.904027i	0.999674	−	0.0255224i	$-0.00812491\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	17.2583	−	4.62436i	1.14548	−	0.306929i	0.364325	−	0.931272i	$-0.381300\pi$
$227$	17.2583	−	4.62436i	1.14548	−	0.306929i	0.781151	+	0.624343i	$0.214633\pi$
$228$		0			0
$229$	9.42820	+	2.52628i	0.623033	+	0.166941i	0.556506	−	0.830843i	$-0.312142\pi$
$229$	9.42820	+	2.52628i	0.623033	+	0.166941i	0.0665269	+	0.997785i	$0.478808\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	22.9282i		−	1.50208i	−0.660259	−	0.751038i	$-0.729553\pi$
$233$		−	22.9282i		−	1.50208i	0.660259	−	0.751038i	$-0.270447\pi$
$234$		0			0
$235$	−3.36603	+	3.36603i	−0.219575	+	0.219575i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−5.59808	−	9.69615i	−0.362109	−	0.627192i	0.626198	−	0.779664i	$-0.284610\pi$
$239$	−5.59808	−	9.69615i	−0.362109	−	0.627192i	−0.988308	+	0.152472i	$0.951277\pi$
$240$		0			0
$241$	−6.23205	+	10.7942i	−0.401442	+	0.695317i	−0.993900	−	0.110284i	$-0.964824\pi$
$241$	−6.23205	+	10.7942i	−0.401442	+	0.695317i	0.592458	+	0.805601i	$0.298157\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.124356	+	0.464102i	0.00794479	+	0.0296504i
$246$		0			0
$247$	−17.4904	+	10.0981i	−1.11289	+	0.642525i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	7.39230	−	7.39230i	0.466598	−	0.466598i	−0.434212	−	0.900811i	$-0.642973\pi$
$251$	7.39230	−	7.39230i	0.466598	−	0.466598i	0.900811	+	0.434212i	$0.142973\pi$
$252$		0			0
$253$	0.169873	+	0.169873i	0.0106798	+	0.0106798i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.16025	+	8.93782i	0.321888	+	0.557526i	0.980878	−	0.194626i	$-0.0623493\pi$
$257$	5.16025	+	8.93782i	0.321888	+	0.557526i	−0.658990	+	0.752152i	$0.729016\pi$
$258$		0			0
$259$	−26.0263	+	6.97372i	−1.61719	+	0.433326i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	3.40192	+	1.96410i	0.209772	+	0.121112i	0.601205	−	0.799095i	$-0.294687\pi$
$263$	3.40192	+	1.96410i	0.209772	+	0.121112i	−0.391434	+	0.920206i	$0.628021\pi$
$264$		0			0
$265$	1.43782	−	0.830127i	0.0883247	−	0.0509943i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7.73205	−	7.73205i	−0.471431	−	0.471431i	0.430946	−	0.902378i	$-0.358180\pi$
$269$	−7.73205	−	7.73205i	−0.471431	−	0.471431i	−0.902378	+	0.430946i	$0.858180\pi$
$270$		0			0
$271$	14.9282			0.906824			0.453412	−	0.891301i	$-0.350207\pi$
$271$	14.9282			0.906824			0.453412	+	0.891301i	$0.350207\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.633975	−	2.36603i	0.0382301	−	0.142677i
$276$		0			0
$277$	−3.69615	−	13.7942i	−0.222080	−	0.828815i	−0.983553	−	0.180618i	$-0.942190\pi$
$277$	−3.69615	−	13.7942i	−0.222080	−	0.828815i	0.761473	−	0.648197i	$-0.224477\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−16.9641	−	9.79423i	−1.01199	−	0.584275i	−0.100219	−	0.994965i	$-0.531954\pi$
$281$	−16.9641	−	9.79423i	−1.01199	−	0.584275i	−0.911775	+	0.410691i	$0.865288\pi$
$282$		0			0
$283$	15.5263	+	4.16025i	0.922942	+	0.247301i	0.688842	−	0.724911i	$-0.258119\pi$
$283$	15.5263	+	4.16025i	0.922942	+	0.247301i	0.234099	+	0.972213i	$0.424786\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−27.5885			−1.62850
$288$		0			0
$289$	−1.00000			−0.0588235
$290$		0			0
$291$		0			0
$292$		0			0
$293$	14.4282	+	3.86603i	0.842905	+	0.225856i	0.654336	−	0.756204i	$-0.272948\pi$
$293$	14.4282	+	3.86603i	0.842905	+	0.225856i	0.188569	+	0.982060i	$0.439615\pi$
$294$		0			0
$295$	−2.59808	−	1.50000i	−0.151266	−	0.0873334i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.571797	+	2.13397i	0.0330679	+	0.123411i
$300$		0			0
$301$	−5.74167	+	21.4282i	−0.330944	+	1.23510i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−7.73205			−0.442736
$306$		0			0
$307$	5.92820	+	5.92820i	0.338340	+	0.338340i	0.855742	−	0.517402i	$-0.173101\pi$
$307$	5.92820	+	5.92820i	0.338340	+	0.338340i	−0.517402	+	0.855742i	$0.673101\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	27.1865	−	15.6962i	1.54161	−	0.890047i	0.542869	−	0.839817i	$-0.317338\pi$
$311$	27.1865	−	15.6962i	1.54161	−	0.890047i	0.998738	−	0.0502299i	$-0.0159954\pi$
$312$		0			0
$313$	−7.83975	−	4.52628i	−0.443129	−	0.255840i	0.261795	−	0.965123i	$-0.415686\pi$
$313$	−7.83975	−	4.52628i	−0.443129	−	0.255840i	−0.704924	+	0.709283i	$0.749019\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.03590	+	0.545517i	−0.114347	+	0.0306393i	−0.315539	−	0.948913i	$-0.602185\pi$
$317$	−2.03590	+	0.545517i	−0.114347	+	0.0306393i	0.201192	+	0.979552i	$0.435519\pi$
$318$		0			0
$319$	0.866025	+	1.50000i	0.0484881	+	0.0839839i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−12.0000	−	12.0000i	−0.667698	−	0.667698i
$324$		0			0
$325$	15.9282	−	15.9282i	0.883538	−	0.883538i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	19.6244	−	11.3301i	1.08193	−	0.624650i
$330$		0			0
$331$	−7.06218	−	26.3564i	−0.388172	−	1.44868i	−0.833105	−	0.553115i	$-0.813439\pi$
$331$	−7.06218	−	26.3564i	−0.388172	−	1.44868i	0.444933	−	0.895564i	$-0.353228\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.330127	+	0.571797i	−0.0180368	+	0.0312406i
$336$		0			0
$337$	0.696152	+	1.20577i	0.0379218	+	0.0656826i	0.884363	−	0.466799i	$-0.154593\pi$
$337$	0.696152	+	1.20577i	0.0379218	+	0.0656826i	−0.846442	+	0.532482i	$0.821260\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.437822	−	0.437822i	0.0237094	−	0.0237094i
$342$		0			0
$343$		−	19.5359i		−	1.05484i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	19.5263	+	5.23205i	1.04823	+	0.280871i	0.741518	−	0.670933i	$-0.234106\pi$
$347$	19.5263	+	5.23205i	1.04823	+	0.280871i	0.306707	+	0.951804i	$0.400773\pi$
$348$		0			0
$349$	7.96410	−	2.13397i	0.426309	−	0.114229i	−0.0392843	−	0.999228i	$-0.512508\pi$
$349$	7.96410	−	2.13397i	0.426309	−	0.114229i	0.465593	+	0.884999i	$0.345841\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	15.2321	−	26.3827i	0.810720	−	1.40421i	−0.101640	−	0.994821i	$-0.532409\pi$
$353$	15.2321	−	26.3827i	0.810720	−	1.40421i	0.912361	−	0.409387i	$-0.134258\pi$
$354$		0			0
$355$	1.46410	−	5.46410i	0.0777064	−	0.290004i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	15.0718i		−	0.795459i	−0.917503	−	0.397730i	$-0.869798\pi$
$359$		−	15.0718i		−	0.795459i	0.917503	−	0.397730i	$-0.130202\pi$
$360$		0			0
$361$		−	1.00000i		−	0.0526316i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.0717968	−	0.267949i	0.00375801	−	0.0140251i
$366$		0			0
$367$	−15.4545	+	26.7679i	−0.806717	+	1.39728i	0.108408	+	0.994106i	$0.465425\pi$
$367$	−15.4545	+	26.7679i	−0.806717	+	1.39728i	−0.915125	+	0.403169i	$0.867909\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−7.63397	+	2.04552i	−0.396336	+	0.106198i
$372$		0			0
$373$	−13.4282	−	3.59808i	−0.695286	−	0.186301i	−0.106168	−	0.994348i	$-0.533858\pi$
$373$	−13.4282	−	3.59808i	−0.695286	−	0.186301i	−0.589118	+	0.808047i	$0.700525\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			15.9282i			0.820344i
$378$		0			0
$379$	−15.5885	+	15.5885i	−0.800725	+	0.800725i	−0.983209	−	0.182484i	$-0.941586\pi$
$379$	−15.5885	+	15.5885i	−0.800725	+	0.800725i	0.182484	+	0.983209i	$0.441586\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	12.3301	+	21.3564i	0.630040	+	1.09126i	0.987543	+	0.157349i	$0.0502949\pi$
$383$	12.3301	+	21.3564i	0.630040	+	1.09126i	−0.357503	+	0.933912i	$0.616372\pi$
$384$		0			0
$385$	0.330127	−	0.571797i	0.0168248	−	0.0291415i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	2.03590	+	7.59808i	0.103224	+	0.385238i	0.998138	−	0.0610019i	$-0.0194296\pi$
$389$	2.03590	+	7.59808i	0.103224	+	0.385238i	−0.894914	+	0.446240i	$0.852763\pi$
$390$		0			0
$391$	−1.60770	+	0.928203i	−0.0813046	+	0.0469413i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.633975	−	0.633975i	0.0318987	−	0.0318987i
$396$		0			0
$397$	−21.0526	−	21.0526i	−1.05660	−	1.05660i	−0.998299	−	0.0582984i	$-0.981433\pi$
$397$	−21.0526	−	21.0526i	−1.05660	−	1.05660i	−0.0582984	−	0.998299i	$-0.518567\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.16025	−	2.00962i	−0.0579403	−	0.100356i	0.835600	−	0.549338i	$-0.185120\pi$
$401$	−1.16025	−	2.00962i	−0.0579403	−	0.100356i	−0.893541	+	0.448982i	$0.851787\pi$
$402$		0			0
$403$	5.50000	−	1.47372i	0.273975	−	0.0734112i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.90192	−	2.83013i	−0.242979	−	0.140284i
$408$		0			0
$409$	−4.62436	+	2.66987i	−0.228660	+	0.132017i	−0.609954	−	0.792437i	$-0.708812\pi$
$409$	−4.62436	+	2.66987i	−0.228660	+	0.132017i	0.381294	+	0.924454i	$0.375479\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	10.0981	+	10.0981i	0.496894	+	0.496894i
$414$		0			0
$415$	6.32051			0.310262
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.526279	+	1.96410i	−0.0257104	+	0.0959526i	−0.977589	−	0.210523i	$-0.932483\pi$
$419$	−0.526279	+	1.96410i	−0.0257104	+	0.0959526i	0.951878	+	0.306476i	$0.0991499\pi$
$420$		0			0
$421$	−2.89230	−	10.7942i	−0.140962	−	0.526079i	−0.999902	−	0.0140017i	$-0.995543\pi$
$421$	−2.89230	−	10.7942i	−0.140962	−	0.526079i	0.858940	−	0.512077i	$-0.171124\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	16.3923	+	9.46410i	0.795144	+	0.459076i
$426$		0			0
$427$	35.5526	+	9.52628i	1.72051	+	0.461009i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	31.3205			1.50866			0.754328	−	0.656498i	$-0.227963\pi$
$431$	31.3205			1.50866			0.754328	+	0.656498i	$0.227963\pi$
$432$		0			0
$433$	24.3923			1.17222			0.586110	−	0.810232i	$-0.300659\pi$
$433$	24.3923			1.17222			0.586110	+	0.810232i	$0.300659\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.90192	+	0.509619i	0.0909814	+	0.0243784i
$438$		0			0
$439$	18.0622	+	10.4282i	0.862061	+	0.497711i	0.864702	−	0.502286i	$-0.167507\pi$
$439$	18.0622	+	10.4282i	0.862061	+	0.497711i	−0.00264111	+	0.999997i	$0.500841\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4.33013	−	16.1603i	−0.205731	−	0.767797i	−0.989226	−	0.146399i	$-0.953232\pi$
$443$	−4.33013	−	16.1603i	−0.205731	−	0.767797i	0.783495	−	0.621398i	$-0.213435\pi$
$444$		0			0
$445$	1.58846	−	5.92820i	0.0753001	−	0.281024i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.679492			−0.0320672			−0.0160336	−	0.999871i	$-0.505104\pi$
$449$	−0.679492			−0.0320672			−0.0160336	+	0.999871i	$0.505104\pi$
$450$		0			0
$451$	−4.09808	−	4.09808i	−0.192971	−	0.192971i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	5.25833	−	3.03590i	0.246514	−	0.142325i
$456$		0			0
$457$	−19.0359	−	10.9904i	−0.890462	−	0.514108i	−0.0163683	−	0.999866i	$-0.505210\pi$
$457$	−19.0359	−	10.9904i	−0.890462	−	0.514108i	−0.874094	+	0.485758i	$0.838544\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.23205	+	0.598076i	−0.103957	+	0.0278552i	−0.310423	−	0.950599i	$-0.600471\pi$
$461$	−2.23205	+	0.598076i	−0.103957	+	0.0278552i	0.206466	+	0.978454i	$0.433804\pi$
$462$		0			0
$463$	−3.33013	−	5.76795i	−0.154764	−	0.268059i	0.778209	−	0.628005i	$-0.216128\pi$
$463$	−3.33013	−	5.76795i	−0.154764	−	0.268059i	−0.932973	+	0.359946i	$0.882795\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−19.7846	−	19.7846i	−0.915523	−	0.915523i	0.0811771	−	0.996700i	$-0.474132\pi$
$467$	−19.7846	−	19.7846i	−0.915523	−	0.915523i	−0.996700	+	0.0811771i	$0.974132\pi$
$468$		0			0
$469$	2.22243	−	2.22243i	0.102622	−	0.102622i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.03590	+	2.33013i	−0.185571	+	0.107139i
$474$		0			0
$475$	−5.19615	−	19.3923i	−0.238416	−	0.889780i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	0.669873	−	1.16025i	0.0306073	−	0.0530134i	−0.850316	−	0.526272i	$-0.823589\pi$
$479$	0.669873	−	1.16025i	0.0306073	−	0.0530134i	0.880923	+	0.473259i	$0.156923\pi$
$480$		0			0
$481$	−26.0263	−	45.0788i	−1.18670	−	2.05542i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	0.366025	−	0.366025i	0.0166204	−	0.0166204i
$486$		0			0
$487$		−	34.7846i		−	1.57624i	−0.615521	−	0.788121i	$-0.711054\pi$
$487$		−	34.7846i		−	1.57624i	0.615521	−	0.788121i	$-0.288946\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.86603	−	0.500000i	−0.0842125	−	0.0225647i	0.216467	−	0.976290i	$-0.430547\pi$
$491$	−1.86603	−	0.500000i	−0.0842125	−	0.0225647i	−0.300679	+	0.953725i	$0.597213\pi$
$492$		0			0
$493$	−12.9282	+	3.46410i	−0.582257	+	0.156015i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−13.4641	+	23.3205i	−0.603947	+	1.04607i
$498$		0			0
$499$	−0.669873	+	2.50000i	−0.0299876	+	0.111915i	−0.979297	−	0.202427i	$-0.935117\pi$
$499$	−0.669873	+	2.50000i	−0.0299876	+	0.111915i	0.949310	+	0.314342i	$0.101784\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	13.8564i		−	0.617827i	−0.951090	−	0.308913i	$-0.900035\pi$
$503$		−	13.8564i		−	0.617827i	0.951090	−	0.308913i	$-0.0999653\pi$
$504$		0			0
$505$			1.00000i			0.0444994i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−5.69615	+	21.2583i	−0.252478	+	0.942259i	0.716999	+	0.697074i	$0.245515\pi$
$509$	−5.69615	+	21.2583i	−0.252478	+	0.942259i	−0.969476	+	0.245185i	$0.921151\pi$
$510$		0			0
$511$	−0.660254	+	1.14359i	−0.0292079	+	0.0505896i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.03590	−	0.277568i	0.0456471	−	0.0122311i
$516$		0			0
$517$	4.59808	+	1.23205i	0.202223	+	0.0541855i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			14.1436i			0.619642i	0.950795	+	0.309821i	$0.100269\pi$
$521$			14.1436i			0.619642i	−0.950795	+	0.309821i	$0.899731\pi$
$522$		0			0
$523$	2.12436	−	2.12436i	0.0928916	−	0.0928916i	−0.659134	−	0.752026i	$-0.729077\pi$
$523$	2.12436	−	2.12436i	0.0928916	−	0.0928916i	0.752026	+	0.659134i	$0.229077\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.39230	+	4.14359i	0.104210	+	0.180498i
$528$		0			0
$529$	−11.3923	+	19.7321i	−0.495318	+	0.857915i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−13.7942	−	51.4808i	−0.597494	−	2.22988i
$534$		0			0
$535$	7.22243	−	4.16987i	0.312253	−	0.180279i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.339746	−	0.339746i	0.0146339	−	0.0146339i
$540$		0			0
$541$	−15.0000	−	15.0000i	−0.644900	−	0.644900i	0.306856	−	0.951756i	$-0.400723\pi$
$541$	−15.0000	−	15.0000i	−0.644900	−	0.644900i	−0.951756	+	0.306856i	$0.900723\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.633975	−	1.09808i	−0.0271565	−	0.0470364i
$546$		0			0
$547$	28.2583	−	7.57180i	1.20824	−	0.323747i	0.402168	−	0.915566i	$-0.368257\pi$
$547$	28.2583	−	7.57180i	1.20824	−	0.323747i	0.806071	+	0.591819i	$0.201590\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	12.2942	+	7.09808i	0.523752	+	0.302388i
$552$		0			0
$553$	−3.69615	+	2.13397i	−0.157176	+	0.0907458i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−27.9808	−	27.9808i	−1.18558	−	1.18558i	−0.978276	−	0.207307i	$-0.933530\pi$
$557$	−27.9808	−	27.9808i	−1.18558	−	1.18558i	−0.207307	−	0.978276i	$-0.566470\pi$
$558$		0			0
$559$	−42.8564			−1.81263
$560$		0			0
$561$		0			0
$562$		0			0
$563$	7.86603	−	29.3564i	0.331513	−	1.23723i	−0.576086	−	0.817389i	$-0.695421\pi$
$563$	7.86603	−	29.3564i	0.331513	−	1.23723i	0.907600	−	0.419836i	$-0.137912\pi$
$564$		0			0
$565$	−0.741670	−	2.76795i	−0.0312023	−	0.116448i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	24.4808	+	14.1340i	1.02629	+	0.592527i	0.915919	−	0.401364i	$-0.131464\pi$
$569$	24.4808	+	14.1340i	1.02629	+	0.592527i	0.110368	+	0.993891i	$0.464797\pi$
$570$		0			0
$571$	5.40192	+	1.44744i	0.226063	+	0.0605735i	0.370073	−	0.929003i	$-0.379333\pi$
$571$	5.40192	+	1.44744i	0.226063	+	0.0605735i	−0.144009	+	0.989576i	$0.545999\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−2.19615			−0.0915859
$576$		0			0
$577$	37.1769			1.54770			0.773848	−	0.633372i	$-0.218330\pi$
$577$	37.1769			1.54770			0.773848	+	0.633372i	$0.218330\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−29.0622	−	7.78719i	−1.20570	−	0.323067i
$582$		0			0
$583$	−1.43782	−	0.830127i	−0.0595485	−	0.0343803i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.794229	+	2.96410i	0.0327813	+	0.122342i	0.980378	−	0.197129i	$-0.0631617\pi$
$587$	0.794229	+	2.96410i	0.0327813	+	0.122342i	−0.947596	+	0.319470i	$0.896495\pi$
$588$		0			0
$589$	1.31347	−	4.90192i	0.0541204	−	0.201980i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.46410			−0.0601234			−0.0300617	−	0.999548i	$-0.509570\pi$
$593$	−1.46410			−0.0601234			−0.0300617	+	0.999548i	$0.509570\pi$
$594$		0			0
$595$	3.60770	+	3.60770i	0.147901	+	0.147901i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−30.3109	+	17.5000i	−1.23847	+	0.715031i	−0.968781	−	0.247917i	$-0.920254\pi$
$599$	−30.3109	+	17.5000i	−1.23847	+	0.715031i	−0.269688	+	0.962948i	$0.586921\pi$
$600$		0			0
$601$	30.2321	+	17.4545i	1.23319	+	0.711983i	0.967694	−	0.252128i	$-0.0811305\pi$
$601$	30.2321	+	17.4545i	1.23319	+	0.711983i	0.265497	+	0.964112i	$0.414464\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−5.36603	+	1.43782i	−0.218160	+	0.0584558i
$606$		0			0
$607$	4.59808	+	7.96410i	0.186630	+	0.323253i	0.944125	−	0.329589i	$-0.106910\pi$
$607$	4.59808	+	7.96410i	0.186630	+	0.323253i	−0.757494	+	0.652842i	$0.773577\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	30.9545	+	30.9545i	1.25228	+	1.25228i
$612$		0			0
$613$	−7.58846	+	7.58846i	−0.306495	+	0.306495i	−0.843548	−	0.537053i	$-0.819537\pi$
$613$	−7.58846	+	7.58846i	−0.306495	+	0.306495i	0.537053	+	0.843548i	$0.319537\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−8.08846	+	4.66987i	−0.325629	+	0.188002i	−0.653899	−	0.756582i	$-0.726868\pi$
$617$	−8.08846	+	4.66987i	−0.325629	+	0.188002i	0.328270	+	0.944584i	$0.393534\pi$
$618$		0			0
$619$	−8.86603	−	33.0885i	−0.356356	−	1.32994i	−0.878770	−	0.477246i	$-0.841635\pi$
$619$	−8.86603	−	33.0885i	−0.356356	−	1.32994i	0.522414	−	0.852692i	$-0.325031\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−14.6077	+	25.3013i	−0.585245	+	1.01367i
$624$		0			0
$625$	10.5263	+	18.2321i	0.421051	+	0.729282i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	30.9282	−	30.9282i	1.23319	−	1.23319i
$630$		0			0
$631$			32.2487i			1.28380i	0.766788	+	0.641900i	$0.221854\pi$
$631$			32.2487i			1.28380i	−0.766788	+	0.641900i	$0.778146\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−10.1962	−	2.73205i	−0.404622	−	0.108418i
$636$		0			0
$637$	4.26795	−	1.14359i	0.169102	−	0.0453108i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−5.76795	+	9.99038i	−0.227820	+	0.394596i	−0.957162	−	0.289553i	$-0.906493\pi$
$641$	−5.76795	+	9.99038i	−0.227820	+	0.394596i	0.729342	+	0.684150i	$0.239827\pi$
$642$		0			0
$643$	0.277568	−	1.03590i	0.0109462	−	0.0408518i	−0.960237	−	0.279187i	$-0.909935\pi$
$643$	0.277568	−	1.03590i	0.0109462	−	0.0408518i	0.971183	+	0.238335i	$0.0766017\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			46.3923i			1.82387i	0.410335	+	0.911935i	$0.365412\pi$
$647$			46.3923i			1.82387i	−0.410335	+	0.911935i	$0.634588\pi$
$648$		0			0
$649$			3.00000i			0.117760i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.71539	+	21.3301i	−0.223661	+	0.834712i	0.759276	+	0.650768i	$0.225553\pi$
$653$	−5.71539	+	21.3301i	−0.223661	+	0.834712i	−0.982937	+	0.183944i	$0.941114\pi$
$654$		0			0
$655$	3.13397	−	5.42820i	0.122455	−	0.212097i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	8.33013	−	2.23205i	0.324496	−	0.0869484i	−0.0928939	−	0.995676i	$-0.529612\pi$
$659$	8.33013	−	2.23205i	0.324496	−	0.0869484i	0.417390	+	0.908728i	$0.362945\pi$
$660$		0			0
$661$	−15.6962	−	4.20577i	−0.610510	−	0.163586i	−0.0596998	−	0.998216i	$-0.519014\pi$
$661$	−15.6962	−	4.20577i	−0.610510	−	0.163586i	−0.550810	+	0.834631i	$0.685681\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	5.41154i		−	0.209851i
$666$		0			0
$667$	1.09808	−	1.09808i	0.0425177	−	0.0425177i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	3.86603	+	6.69615i	0.149246	+	0.258502i
$672$		0			0
$673$	3.83975	−	6.65064i	0.148011	−	0.256363i	−0.782481	−	0.622674i	$-0.786046\pi$
$673$	3.83975	−	6.65064i	0.148011	−	0.256363i	0.930492	+	0.366311i	$0.119379\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	12.2321	+	45.6506i	0.470116	+	1.75450i	0.639345	+	0.768920i	$0.279205\pi$
$677$	12.2321	+	45.6506i	0.470116	+	1.75450i	−0.169229	+	0.985577i	$0.554128\pi$
$678$		0			0
$679$	−2.13397	+	1.23205i	−0.0818944	+	0.0472818i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−5.39230	+	5.39230i	−0.206331	+	0.206331i	−0.802706	−	0.596375i	$-0.796607\pi$
$683$	−5.39230	+	5.39230i	−0.206331	+	0.206331i	0.596375	+	0.802706i	$0.296607\pi$
$684$		0			0
$685$	6.09808	+	6.09808i	0.232996	+	0.232996i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−7.63397	−	13.2224i	−0.290831	−	0.503735i
$690$		0			0
$691$	18.5263	−	4.96410i	0.704773	−	0.188843i	0.111405	−	0.993775i	$-0.464465\pi$
$691$	18.5263	−	4.96410i	0.704773	−	0.188843i	0.593367	+	0.804932i	$0.297798\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.00962	+	1.16025i	0.0762292	+	0.0440109i
$696$		0			0
$697$	38.7846	−	22.3923i	1.46907	−	0.848169i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	21.0526	+	21.0526i	0.795144	+	0.795144i	0.982325	−	0.187181i	$-0.0599352\pi$
$701$	21.0526	+	21.0526i	0.795144	+	0.795144i	−0.187181	+	0.982325i	$0.559935\pi$
$702$		0			0
$703$	−46.3923			−1.74972
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.23205	−	4.59808i	0.0463360	−	0.172928i
$708$		0			0
$709$	10.7487	+	40.1147i	0.403676	+	1.50654i	0.806484	+	0.591256i	$0.201368\pi$
$709$	10.7487	+	40.1147i	0.403676	+	1.50654i	−0.402808	+	0.915285i	$0.631966\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.480762	−	0.277568i	−0.0180047	−	0.0103950i
$714$		0			0
$715$	1.23205	+	0.330127i	0.0460761	+	0.0123461i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	23.3205			0.869708			0.434854	−	0.900501i	$-0.356800\pi$
$719$	23.3205			0.869708			0.434854	+	0.900501i	$0.356800\pi$
$720$		0			0
$721$	−5.10512			−0.190125
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−15.2942	−	4.09808i	−0.568013	−	0.152199i
$726$		0			0
$727$	−9.06218	−	5.23205i	−0.336098	−	0.194046i	0.322447	−	0.946587i	$-0.395494\pi$
$727$	−9.06218	−	5.23205i	−0.336098	−	0.194046i	−0.658545	+	0.752541i	$0.728828\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−9.32051	−	34.7846i	−0.344731	−	1.28656i
$732$		0			0
$733$	−7.37564	+	27.5263i	−0.272426	+	1.01671i	0.685121	+	0.728429i	$0.259749\pi$
$733$	−7.37564	+	27.5263i	−0.272426	+	1.01671i	−0.957547	+	0.288277i	$0.906917\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.660254			0.0243208
$738$		0			0
$739$	29.7321	+	29.7321i	1.09371	+	1.09371i	0.995129	+	0.0985823i	$0.0314308\pi$
$739$	29.7321	+	29.7321i	1.09371	+	1.09371i	0.0985823	+	0.995129i	$0.468569\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	25.1147	−	14.5000i	0.921370	−	0.531953i	0.0372984	−	0.999304i	$-0.488125\pi$
$743$	25.1147	−	14.5000i	0.921370	−	0.531953i	0.884072	+	0.467351i	$0.154791\pi$
$744$		0			0
$745$	−6.82051	−	3.93782i	−0.249884	−	0.144271i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−38.3468	+	10.2750i	−1.40116	+	0.375440i
$750$		0			0
$751$	−4.72243	−	8.17949i	−0.172324	−	0.298474i	0.766908	−	0.641757i	$-0.221794\pi$
$751$	−4.72243	−	8.17949i	−0.172324	−	0.298474i	−0.939232	+	0.343283i	$0.888461\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−2.56218	−	2.56218i	−0.0932472	−	0.0932472i
$756$		0			0
$757$	8.46410	−	8.46410i	0.307633	−	0.307633i	−0.536358	−	0.843991i	$-0.680200\pi$
$757$	8.46410	−	8.46410i	0.307633	−	0.307633i	0.843991	+	0.536358i	$0.180200\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	25.2846	−	14.5981i	0.916566	−	0.529180i	0.0340283	−	0.999421i	$-0.489166\pi$
$761$	25.2846	−	14.5981i	0.916566	−	0.529180i	0.882538	+	0.470241i	$0.155833\pi$
$762$		0			0
$763$	1.56218	+	5.83013i	0.0565546	+	0.211065i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−13.7942	+	23.8923i	−0.498081	+	0.862701i
$768$		0			0
$769$	−3.50000	−	6.06218i	−0.126213	−	0.218608i	0.795993	−	0.605305i	$-0.206949\pi$
$769$	−3.50000	−	6.06218i	−0.126213	−	0.218608i	−0.922207	+	0.386698i	$0.873616\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−7.58846	+	7.58846i	−0.272938	+	0.272938i	−0.830282	−	0.557344i	$-0.811821\pi$
$773$	−7.58846	+	7.58846i	−0.272938	+	0.272938i	0.557344	+	0.830282i	$0.311821\pi$
$774$		0			0
$775$			5.66025i			0.203322i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−45.8827	−	12.2942i	−1.64392	−	0.440486i
$780$		0			0
$781$	−5.46410	+	1.46410i	−0.195521	+	0.0523897i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.232051	−	0.401924i	0.00828225	−	0.0143453i
$786$		0			0
$787$	−9.06218	+	33.8205i	−0.323032	+	1.20557i	0.593244	+	0.805023i	$0.297847\pi$
$787$	−9.06218	+	33.8205i	−0.323032	+	1.20557i	−0.916276	+	0.400548i	$0.868820\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			13.6410i			0.485019i
$792$		0			0
$793$			71.1051i			2.52502i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−0.284610	+	1.06218i	−0.0100814	+	0.0376243i	−0.970783	−	0.239958i	$-0.922866\pi$
$797$	−0.284610	+	1.06218i	−0.0100814	+	0.0376243i	0.960702	+	0.277582i	$0.0895331\pi$
$798$		0			0
$799$	−18.3923	+	31.8564i	−0.650673	+	1.12700i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.267949	+	0.0717968i	−0.00945572	+	0.00253365i
$804$		0			0
$805$	−0.571797	−	0.153212i	−0.0201532	−	0.00540003i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	32.6410i		−	1.14760i	−0.818997	−	0.573799i	$-0.805469\pi$
$809$		−	32.6410i		−	1.14760i	0.818997	−	0.573799i	$-0.194531\pi$
$810$		0			0
$811$	11.5359	−	11.5359i	0.405080	−	0.405080i	−0.474939	−	0.880019i	$-0.657530\pi$
$811$	11.5359	−	11.5359i	0.405080	−	0.405080i	0.880019	+	0.474939i	$0.157530\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	4.36603	+	7.56218i	0.152935	+	0.264892i
$816$		0			0
$817$	−19.0981	+	33.0788i	−0.668157	+	1.15728i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.01666	−	18.7224i	−0.175083	−	0.653417i	−0.996538	−	0.0831439i	$-0.973504\pi$
$821$	−5.01666	−	18.7224i	−0.175083	−	0.653417i	0.821455	−	0.570273i	$-0.193163\pi$
$822$		0			0
$823$	−6.65064	+	3.83975i	−0.231827	+	0.133845i	−0.611414	−	0.791311i	$-0.709399\pi$
$823$	−6.65064	+	3.83975i	−0.231827	+	0.133845i	0.379588	+	0.925156i	$0.376066\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−10.6077	+	10.6077i	−0.368866	+	0.368866i	−0.867063	−	0.498198i	$-0.833995\pi$
$827$	−10.6077	+	10.6077i	−0.368866	+	0.368866i	0.498198	+	0.867063i	$0.333995\pi$
$828$		0			0
$829$	−17.7321	−	17.7321i	−0.615860	−	0.615860i	0.328607	−	0.944467i	$-0.393421\pi$
$829$	−17.7321	−	17.7321i	−0.615860	−	0.615860i	−0.944467	+	0.328607i	$0.893421\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.85641	+	3.21539i	0.0643207	+	0.111407i
$834$		0			0
$835$	4.76795	−	1.27757i	0.165002	−	0.0442121i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−29.2583	−	16.8923i	−1.01011	−	0.583187i	−0.0988859	−	0.995099i	$-0.531528\pi$
$839$	−29.2583	−	16.8923i	−1.01011	−	0.583187i	−0.911224	+	0.411912i	$0.864861\pi$
$840$		0			0
$841$	−15.4186	+	8.90192i	−0.531675	+	0.306963i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	3.53590	+	3.53590i	0.121639	+	0.121639i
$846$		0			0
$847$	26.4449			0.908656
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.31347	+	4.90192i	−0.0450251	+	0.168036i
$852$		0			0
$853$	−2.69615	−	10.0622i	−0.0923145	−	0.344522i	0.904284	−	0.426931i	$-0.140405\pi$
$853$	−2.69615	−	10.0622i	−0.0923145	−	0.344522i	−0.996599	+	0.0824088i	$0.973739\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	42.3564	+	24.4545i	1.44687	+	0.835349i	0.998293	−	0.0583966i	$-0.0185988\pi$
$857$	42.3564	+	24.4545i	1.44687	+	0.835349i	0.448574	+	0.893746i	$0.351932\pi$
$858$		0			0
$859$	−16.7942	−	4.50000i	−0.573012	−	0.153538i	−0.0393342	−	0.999226i	$-0.512524\pi$
$859$	−16.7942	−	4.50000i	−0.573012	−	0.153538i	−0.533677	+	0.845688i	$0.679190\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−33.4641			−1.13913			−0.569566	−	0.821946i	$-0.692889\pi$
$863$	−33.4641			−1.13913			−0.569566	+	0.821946i	$0.692889\pi$
$864$		0			0
$865$	−4.80385			−0.163336
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.866025	−	0.232051i	−0.0293779	−	0.00787178i
$870$		0			0
$871$	5.25833	+	3.03590i	0.178172	+	0.102867i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	3.21281	+	11.9904i	0.108613	+	0.405349i
$876$		0			0
$877$	−8.94486	+	33.3827i	−0.302047	+	1.12725i	0.633411	+	0.773815i	$0.281654\pi$
$877$	−8.94486	+	33.3827i	−0.302047	+	1.12725i	−0.935458	+	0.353438i	$0.885013\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	3.32051			0.111871			0.0559354	−	0.998434i	$-0.482186\pi$
$881$	3.32051			0.111871			0.0559354	+	0.998434i	$0.482186\pi$
$882$		0			0
$883$	3.00000	+	3.00000i	0.100958	+	0.100958i	0.755782	−	0.654824i	$-0.227257\pi$
$883$	3.00000	+	3.00000i	0.100958	+	0.100958i	−0.654824	+	0.755782i	$0.727257\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−21.0622	+	12.1603i	−0.707199	+	0.408301i	−0.810023	−	0.586398i	$-0.800545\pi$
$887$	−21.0622	+	12.1603i	−0.707199	+	0.408301i	0.102824	+	0.994700i	$0.467212\pi$
$888$		0			0
$889$	43.5167	+	25.1244i	1.45950	+	0.842644i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	37.6865	−	10.0981i	1.26113	−	0.337919i
$894$		0			0
$895$	−2.90192	−	5.02628i	−0.0970006	−	0.168010i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.83013	−	2.83013i	−0.0943900	−	0.0943900i
$900$		0			0
$901$	9.07180	−	9.07180i	0.302225	−	0.302225i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.70577	−	1.56218i	0.0899429	−	0.0519285i
$906$		0			0
$907$	3.06218	+	11.4282i	0.101678	+	0.379467i	0.997947	−	0.0640432i	$-0.0203996\pi$
$907$	3.06218	+	11.4282i	0.101678	+	0.379467i	−0.896269	+	0.443510i	$0.853733\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−5.86603	+	10.1603i	−0.194350	+	0.336624i	−0.946687	−	0.322154i	$-0.895593\pi$
$911$	−5.86603	+	10.1603i	−0.194350	+	0.336624i	0.752337	+	0.658778i	$0.228926\pi$
$912$		0			0
$913$	−3.16025	−	5.47372i	−0.104589	−	0.181154i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−21.0981	+	21.0981i	−0.696720	+	0.696720i
$918$		0			0
$919$			43.4641i			1.43375i	0.697203	+	0.716874i	$0.254428\pi$
$919$			43.4641i			1.43375i	−0.697203	+	0.716874i	$0.745572\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−50.2487	−	13.4641i	−1.65396	−	0.443176i
$924$		0			0
$925$	49.9808	−	13.3923i	1.64336	−	0.440336i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	18.3564	−	31.7942i	0.602254	−	1.04313i	−0.390225	−	0.920720i	$-0.627603\pi$
$929$	18.3564	−	31.7942i	0.602254	−	1.04313i	0.992479	−	0.122415i	$-0.0390640\pi$
$930$		0			0
$931$	1.01924	−	3.80385i	0.0334042	−	0.124666i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			1.07180i			0.0350515i
$936$		0			0
$937$			32.9282i			1.07572i	0.843035	+	0.537859i	$0.180767\pi$
$937$			32.9282i			1.07572i	−0.843035	+	0.537859i	$0.819233\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	2.91154	−	10.8660i	0.0949136	−	0.354222i	−0.902093	−	0.431542i	$-0.857970\pi$
$941$	2.91154	−	10.8660i	0.0949136	−	0.354222i	0.997006	+	0.0773199i	$0.0246363\pi$
$942$		0			0
$943$	−2.59808	+	4.50000i	−0.0846050	+	0.146540i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−14.9904	+	4.01666i	−0.487122	+	0.130524i	−0.494017	−	0.869452i	$-0.664472\pi$
$947$	−14.9904	+	4.01666i	−0.487122	+	0.130524i	0.00689497	+	0.999976i	$0.497805\pi$
$948$		0			0
$949$	−2.46410	−	0.660254i	−0.0799881	−	0.0214328i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			39.4641i			1.27837i	0.769054	+	0.639184i	$0.220728\pi$
$953$			39.4641i			1.27837i	−0.769054	+	0.639184i	$0.779272\pi$
$954$		0			0
$955$	−4.83013	+	4.83013i	−0.156299	+	0.156299i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−20.5263	−	35.5526i	−0.662828	−	1.14805i
$960$		0			0
$961$	14.7846	−	25.6077i	0.476923	−	0.826055i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.330127	+	1.23205i	0.0106272	+	0.0396611i
$966$		0			0
$967$	−14.9378	+	8.62436i	−0.480368	+	0.277341i	−0.720570	−	0.693382i	$-0.756120\pi$
$967$	−14.9378	+	8.62436i	−0.480368	+	0.277341i	0.240202	+	0.970723i	$0.422786\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	27.9808	−	27.9808i	0.897945	−	0.897945i	−0.0973088	−	0.995254i	$-0.531023\pi$
$971$	27.9808	−	27.9808i	0.897945	−	0.897945i	0.995254	+	0.0973088i	$0.0310235\pi$
$972$		0			0
$973$	−7.81089	−	7.81089i	−0.250406	−	0.250406i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−17.2846	−	29.9378i	−0.552984	−	0.957796i	−0.998057	−	0.0623018i	$-0.980156\pi$
$977$	−17.2846	−	29.9378i	−0.552984	−	0.957796i	0.445074	−	0.895494i	$-0.353177\pi$
$978$		0			0
$979$	−5.92820	+	1.58846i	−0.189466	+	0.0507673i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	40.9186	+	23.6244i	1.30510	+	0.753500i	0.981274	−	0.192617i	$-0.0616974\pi$
$983$	40.9186	+	23.6244i	1.30510	+	0.753500i	0.323826	+	0.946117i	$0.395031\pi$
$984$		0			0
$985$	6.63397	−	3.83013i	0.211376	−	0.122038i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.95448	+	2.95448i	0.0939471	+	0.0939471i
$990$		0			0
$991$	23.6077			0.749923			0.374962	−	0.927040i	$-0.377656\pi$
$991$	23.6077			0.749923			0.374962	+	0.927040i	$0.377656\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−0.784610	+	2.92820i	−0.0248738	+	0.0928303i
$996$		0			0
$997$	−2.96410	−	11.0622i	−0.0938740	−	0.350343i	0.902972	−	0.429699i	$-0.141380\pi$
$997$	−2.96410	−	11.0622i	−0.0938740	−	0.350343i	−0.996846	+	0.0793561i	$0.974714\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.2.bc.b.721.1		4
3.2	odd	2		576.2.bb.b.529.1		4
4.3	odd	2		432.2.y.a.397.1		4
9.4	even	3		1728.2.bc.c.145.1		4
9.5	odd	6		576.2.bb.a.337.1		4
12.11	even	2		144.2.x.d.61.1	yes	4
16.5	even	4		1728.2.bc.c.1585.1		4
16.11	odd	4		432.2.y.d.181.1		4
36.23	even	6		144.2.x.a.13.1	✓	4
36.31	odd	6		432.2.y.d.253.1		4
48.5	odd	4		576.2.bb.a.241.1		4
48.11	even	4		144.2.x.a.133.1	yes	4
144.5	odd	12		576.2.bb.b.49.1		4
144.59	even	12		144.2.x.d.85.1	yes	4
144.85	even	12	inner	1728.2.bc.b.1009.1		4
144.139	odd	12		432.2.y.a.37.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.a.13.1	✓	4	36.23	even	6
144.2.x.a.133.1	yes	4	48.11	even	4
144.2.x.d.61.1	yes	4	12.11	even	2
144.2.x.d.85.1	yes	4	144.59	even	12
432.2.y.a.37.1		4	144.139	odd	12
432.2.y.a.397.1		4	4.3	odd	2
432.2.y.d.181.1		4	16.11	odd	4
432.2.y.d.253.1		4	36.31	odd	6
576.2.bb.a.241.1		4	48.5	odd	4
576.2.bb.a.337.1		4	9.5	odd	6
576.2.bb.b.49.1		4	144.5	odd	12
576.2.bb.b.529.1		4	3.2	odd	2
1728.2.bc.b.721.1		4	1.1	even	1	trivial
1728.2.bc.b.1009.1		4	144.85	even	12	inner
1728.2.bc.c.145.1		4	9.4	even	3
1728.2.bc.c.1585.1		4	16.5	even	4

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.133975i) q^{5} +(2.13397 + 1.23205i) q^{7} +O(q^{10})\)	\(q+(-0.500000 - 0.133975i) q^{5} +(2.13397 + 1.23205i) q^{7} +(0.133975 + 0.500000i) q^{11} +(-1.23205 + 4.59808i) q^{13} -4.00000 q^{17} +(3.00000 + 3.00000i) q^{19} +(0.401924 - 0.232051i) q^{23} +(-4.09808 - 2.36603i) q^{25} +(3.23205 - 0.866025i) q^{29} +(-0.598076 - 1.03590i) q^{31} +(-0.901924 - 0.901924i) q^{35} +(-7.73205 + 7.73205i) q^{37} +(-9.69615 + 5.59808i) q^{41} +(2.33013 + 8.69615i) q^{43} +(4.59808 - 7.96410i) q^{47} +(-0.464102 - 0.803848i) q^{49} +(-2.26795 + 2.26795i) q^{53} -0.267949i q^{55} +(5.59808 + 1.50000i) q^{59} +(14.4282 - 3.86603i) q^{61} +(1.23205 - 2.13397i) q^{65} +(0.330127 - 1.23205i) q^{67} +10.9282i q^{71} +0.535898i q^{73} +(-0.330127 + 1.23205i) q^{77} +(-0.866025 + 1.50000i) q^{79} +(-11.7942 + 3.16025i) q^{83} +(2.00000 + 0.535898i) q^{85} +11.8564i q^{89} +(-8.29423 + 8.29423i) q^{91} +(-1.09808 - 1.90192i) q^{95} +(-0.500000 + 0.866025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{5} + 12 q^{7}+O(q^{10}) \) 4 * q - 2 * q^5 + 12 * q^7	\( 4 q - 2 q^{5} + 12 q^{7} + 4 q^{11} + 2 q^{13} - 16 q^{17} + 12 q^{19} + 12 q^{23} - 6 q^{25} + 6 q^{29} + 8 q^{31} - 14 q^{35} - 24 q^{37} - 18 q^{41} - 8 q^{43} + 8 q^{47} + 12 q^{49} - 16 q^{53} + 12 q^{59} + 30 q^{61} - 2 q^{65} - 16 q^{67} + 16 q^{77} - 16 q^{83} + 8 q^{85} - 2 q^{91} + 6 q^{95} - 2 q^{97}+O(q^{100}) \) 4 * q - 2 * q^5 + 12 * q^7 + 4 * q^11 + 2 * q^13 - 16 * q^17 + 12 * q^19 + 12 * q^23 - 6 * q^25 + 6 * q^29 + 8 * q^31 - 14 * q^35 - 24 * q^37 - 18 * q^41 - 8 * q^43 + 8 * q^47 + 12 * q^49 - 16 * q^53 + 12 * q^59 + 30 * q^61 - 2 * q^65 - 16 * q^67 + 16 * q^77 - 16 * q^83 + 8 * q^85 - 2 * q^91 + 6 * q^95 - 2 * q^97

Introduction

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