LMFDB - Embedded newform 1728.2.bc.e.1585.1

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:	$72$
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			1585.1
Character	$\chi$	$=$	1728.1585
Dual form			1728.2.bc.e.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10094 + 4.10876i) q^{5} +(-1.63313 - 0.942891i) q^{7} +O(q^{10})$	$q+(-1.10094 + 4.10876i) q^{5} +(-1.63313 - 0.942891i) q^{7} +(-1.18389 + 0.317223i) q^{11} +(-2.31428 - 0.620109i) q^{13} -3.44622 q^{17} +(4.17726 - 4.17726i) q^{19} +(-1.34867 + 0.778655i) q^{23} +(-11.3397 - 6.54701i) q^{25} +(0.343336 + 1.28135i) q^{29} +(-1.25840 - 2.17961i) q^{31} +(5.67210 - 5.67210i) q^{35} +(5.77154 + 5.77154i) q^{37} +(3.43245 - 1.98173i) q^{41} +(2.96053 - 0.793272i) q^{43} +(0.230692 - 0.399570i) q^{47} +(-1.72191 - 2.98244i) q^{49} +(-5.61507 - 5.61507i) q^{53} -5.21358i q^{55} +(2.92766 - 10.9262i) q^{59} +(1.27078 + 4.74261i) q^{61} +(5.09576 - 8.82612i) q^{65} +(-0.286572 - 0.0767867i) q^{67} -13.9935i q^{71} +0.0279090i q^{73} +(2.23256 + 0.598214i) q^{77} +(-2.19067 + 3.79435i) q^{79} +(-0.915902 - 3.41819i) q^{83} +(3.79408 - 14.1597i) q^{85} +4.74894i q^{89} +(3.19483 + 3.19483i) q^{91} +(12.5645 + 21.7623i) q^{95} +(4.17352 - 7.22875i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

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

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
$5$	−1.10094	+	4.10876i	−0.492355	+	1.83750i	0.0520092	+	0.998647i	$0.483437\pi$
$5$	−1.10094	+	4.10876i	−0.492355	+	1.83750i	−0.544365	+	0.838849i	$0.683229\pi$
$6$		0			0
$7$	−1.63313	−	0.942891i	−0.617267	−	0.356379i	0.158537	−	0.987353i	$-0.449322\pi$
$7$	−1.63313	−	0.942891i	−0.617267	−	0.356379i	−0.775804	+	0.630974i	$0.782656\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.18389	+	0.317223i	−0.356957	+	0.0956464i	−0.432841	−	0.901470i	$-0.642489\pi$
$11$	−1.18389	+	0.317223i	−0.356957	+	0.0956464i	0.0758838	+	0.997117i	$0.475822\pi$
$12$		0			0
$13$	−2.31428	−	0.620109i	−0.641865	−	0.171987i	−0.0768171	−	0.997045i	$-0.524476\pi$
$13$	−2.31428	−	0.620109i	−0.641865	−	0.171987i	−0.565048	+	0.825058i	$0.691142\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.44622			−0.835831			−0.417915	−	0.908486i	$-0.637239\pi$
$17$	−3.44622			−0.835831			−0.417915	+	0.908486i	$0.637239\pi$
$18$		0			0
$19$	4.17726	−	4.17726i	0.958328	−	0.958328i	−0.0408377	−	0.999166i	$-0.513003\pi$
$19$	4.17726	−	4.17726i	0.958328	−	0.958328i	0.999166	+	0.0408377i	$0.0130027\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.34867	+	0.778655i	−0.281217	+	0.162361i	−0.633974	−	0.773354i	$-0.718578\pi$
$23$	−1.34867	+	0.778655i	−0.281217	+	0.162361i	0.352757	+	0.935715i	$0.385244\pi$
$24$		0			0
$25$	−11.3397	−	6.54701i	−2.26795	−	1.30940i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.343336	+	1.28135i	0.0637558	+	0.237940i	0.990449	−	0.137878i	$-0.0440283\pi$
$29$	0.343336	+	1.28135i	0.0637558	+	0.237940i	−0.926693	+	0.375818i	$0.877362\pi$
$30$		0			0
$31$	−1.25840	−	2.17961i	−0.226015	−	0.391469i	0.730609	−	0.682796i	$-0.239236\pi$
$31$	−1.25840	−	2.17961i	−0.226015	−	0.391469i	−0.956623	+	0.291327i	$0.905903\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	5.67210	−	5.67210i	0.958760	−	0.958760i
$36$		0			0
$37$	5.77154	+	5.77154i	0.948836	+	0.948836i	0.998753	−	0.0499178i	$-0.0158959\pi$
$37$	5.77154	+	5.77154i	0.948836	+	0.948836i	−0.0499178	+	0.998753i	$0.515896\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.43245	−	1.98173i	0.536058	−	0.309493i	−0.207422	−	0.978252i	$-0.566507\pi$
$41$	3.43245	−	1.98173i	0.536058	−	0.309493i	0.743480	+	0.668758i	$0.233174\pi$
$42$		0			0
$43$	2.96053	−	0.793272i	0.451477	−	0.120973i	−0.0259136	−	0.999664i	$-0.508249\pi$
$43$	2.96053	−	0.793272i	0.451477	−	0.120973i	0.477390	+	0.878691i	$0.341583\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.230692	−	0.399570i	0.0336498	−	0.0582832i	−0.848710	−	0.528858i	$-0.822620\pi$
$47$	0.230692	−	0.399570i	0.0336498	−	0.0582832i	0.882360	+	0.470575i	$0.155954\pi$
$48$		0			0
$49$	−1.72191	−	2.98244i	−0.245988	−	0.426063i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−5.61507	−	5.61507i	−0.771289	−	0.771289i	0.207043	−	0.978332i	$-0.433616\pi$
$53$	−5.61507	−	5.61507i	−0.771289	−	0.771289i	−0.978332	+	0.207043i	$0.933616\pi$
$54$		0			0
$55$		−	5.21358i		−	0.702999i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.92766	−	10.9262i	0.381148	−	1.42247i	−0.463001	−	0.886358i	$-0.653227\pi$
$59$	2.92766	−	10.9262i	0.381148	−	1.42247i	0.844150	−	0.536108i	$-0.180106\pi$
$60$		0			0
$61$	1.27078	+	4.74261i	0.162707	+	0.607229i	0.998322	+	0.0579138i	$0.0184448\pi$
$61$	1.27078	+	4.74261i	0.162707	+	0.607229i	−0.835615	+	0.549316i	$0.814888\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	5.09576	−	8.82612i	0.632052	−	1.09475i
$66$		0			0
$67$	−0.286572	−	0.0767867i	−0.0350103	−	0.00938099i	0.241271	−	0.970458i	$-0.422436\pi$
$67$	−0.286572	−	0.0767867i	−0.0350103	−	0.00938099i	−0.276282	+	0.961077i	$0.589102\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	13.9935i		−	1.66073i	−0.557221	−	0.830364i	$-0.688133\pi$
$71$		−	13.9935i		−	1.66073i	0.557221	−	0.830364i	$-0.311867\pi$
$72$		0			0
$73$			0.0279090i			0.00326650i	0.999999	+	0.00163325i	$0.000519880\pi$
$73$			0.0279090i			0.00326650i	−0.999999	+	0.00163325i	$0.999480\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.23256	+	0.598214i	0.254424	+	0.0681728i
$78$		0			0
$79$	−2.19067	+	3.79435i	−0.246470	+	0.426898i	−0.962544	−	0.271126i	$-0.912604\pi$
$79$	−2.19067	+	3.79435i	−0.246470	+	0.426898i	0.716074	+	0.698024i	$0.245937\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.915902	−	3.41819i	−0.100533	−	0.375195i	0.897267	−	0.441489i	$-0.145549\pi$
$83$	−0.915902	−	3.41819i	−0.100533	−	0.375195i	−0.997800	+	0.0662931i	$0.978883\pi$
$84$		0			0
$85$	3.79408	−	14.1597i	0.411526	−	1.53584i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			4.74894i			0.503386i	0.967807	+	0.251693i	$0.0809874\pi$
$89$			4.74894i			0.503386i	−0.967807	+	0.251693i	$0.919013\pi$
$90$		0			0
$91$	3.19483	+	3.19483i	0.334909	+	0.334909i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	12.5645	+	21.7623i	1.28909	+	2.23276i
$96$		0			0
$97$	4.17352	−	7.22875i	0.423757	−	0.733968i	−0.572547	−	0.819872i	$-0.694045\pi$
$97$	4.17352	−	7.22875i	0.423757	−	0.733968i	0.996303	+	0.0859041i	$0.0273779\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.20785	−	1.93134i	0.717208	−	0.192175i	0.118282	−	0.992980i	$-0.462261\pi$
$101$	7.20785	−	1.93134i	0.717208	−	0.192175i	0.598926	+	0.800805i	$0.295594\pi$
$102$		0			0
$103$	−12.2204	+	7.05547i	−1.20411	+	0.695196i	−0.961468	−	0.274919i	$-0.911349\pi$
$103$	−12.2204	+	7.05547i	−1.20411	+	0.695196i	−0.242647	+	0.970115i	$0.578016\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.84992	−	3.84992i	−0.372186	−	0.372186i	0.496087	−	0.868273i	$-0.334770\pi$
$107$	−3.84992	−	3.84992i	−0.372186	−	0.372186i	−0.868273	+	0.496087i	$0.834770\pi$
$108$		0			0
$109$	2.08616	−	2.08616i	0.199818	−	0.199818i	−0.600104	−	0.799922i	$-0.704874\pi$
$109$	2.08616	−	2.08616i	0.199818	−	0.199818i	0.799922	+	0.600104i	$0.204874\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.04799	+	3.54722i	0.192658	+	0.333694i	0.946130	−	0.323786i	$-0.104956\pi$
$113$	2.04799	+	3.54722i	0.192658	+	0.333694i	−0.753472	+	0.657480i	$0.771622\pi$
$114$		0			0
$115$	−1.71451	−	6.39862i	−0.159878	−	0.596674i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	5.62814	+	3.24941i	0.515931	+	0.297873i
$120$		0			0
$121$	−8.22531	+	4.74888i	−0.747755	+	0.431717i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	24.3454	−	24.3454i	2.17752	−	2.17752i
$126$		0			0
$127$	−4.89832			−0.434656			−0.217328	−	0.976099i	$-0.569734\pi$
$127$	−4.89832			−0.434656			−0.217328	+	0.976099i	$0.569734\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−17.7751	−	4.76283i	−1.55302	−	0.416130i	−0.622574	−	0.782561i	$-0.713913\pi$
$131$	−17.7751	−	4.76283i	−1.55302	−	0.416130i	−0.930446	+	0.366430i	$0.880580\pi$
$132$		0			0
$133$	−10.7607	+	2.88332i	−0.933072	+	0.250016i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−13.4198	−	7.74793i	−1.14653	−	0.661950i	−0.198492	−	0.980103i	$-0.563604\pi$
$137$	−13.4198	−	7.74793i	−1.14653	−	0.661950i	−0.948040	+	0.318153i	$0.896938\pi$
$138$		0			0
$139$	1.90836	−	7.12209i	0.161865	−	0.604088i	−0.836555	−	0.547884i	$-0.815434\pi$
$139$	1.90836	−	7.12209i	0.161865	−	0.604088i	0.998419	−	0.0562039i	$-0.0178997\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.93657			0.245568
$144$		0			0
$145$	−5.64274			−0.468604
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.99897	−	7.46026i	0.163762	−	0.611168i	−0.834433	−	0.551110i	$-0.814205\pi$
$149$	1.99897	−	7.46026i	0.163762	−	0.611168i	0.998195	−	0.0600585i	$-0.0191287\pi$
$150$		0			0
$151$	−3.36540	−	1.94301i	−0.273872	−	0.158120i	0.356774	−	0.934191i	$-0.383877\pi$
$151$	−3.36540	−	1.94301i	−0.273872	−	0.158120i	−0.630646	+	0.776071i	$0.717210\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	10.3409	−	2.77084i	0.830602	−	0.222559i
$156$		0			0
$157$	6.23351	+	1.67026i	0.497488	+	0.133302i	0.498834	−	0.866698i	$-0.333762\pi$
$157$	6.23351	+	1.67026i	0.497488	+	0.133302i	−0.00134577	+	0.999999i	$0.500428\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.93675			0.231448
$162$		0			0
$163$	−10.5783	+	10.5783i	−0.828556	+	0.828556i	−0.987317	−	0.158761i	$-0.949250\pi$
$163$	−10.5783	+	10.5783i	−0.828556	+	0.828556i	0.158761	+	0.987317i	$0.449250\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−18.7147	+	10.8050i	−1.44819	+	0.836112i	−0.998374	−	0.0570092i	$-0.981844\pi$
$167$	−18.7147	+	10.8050i	−1.44819	+	0.836112i	−0.449815	+	0.893122i	$0.648510\pi$
$168$		0			0
$169$	−6.28698	−	3.62979i	−0.483614	−	0.279215i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.00981	+	18.6969i	0.380889	+	1.42150i	0.844546	+	0.535483i	$0.179870\pi$
$173$	5.00981	+	18.6969i	0.380889	+	1.42150i	−0.463657	+	0.886015i	$0.653463\pi$
$174$		0			0
$175$	12.3462	+	21.3843i	0.933287	+	1.61650i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−2.88152	+	2.88152i	−0.215375	+	0.215375i	−0.806546	−	0.591171i	$-0.798666\pi$
$179$	−2.88152	+	2.88152i	−0.215375	+	0.215375i	0.591171	+	0.806546i	$0.298666\pi$
$180$		0			0
$181$	−9.50186	−	9.50186i	−0.706268	−	0.706268i	0.259480	−	0.965748i	$-0.416449\pi$
$181$	−9.50186	−	9.50186i	−0.706268	−	0.706268i	−0.965748	+	0.259480i	$0.916449\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−30.0680	+	17.3598i	−2.21065	+	1.27632i
$186$		0			0
$187$	4.07996	−	1.09322i	0.298356	−	0.0799442i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.36417	−	4.09487i	0.171066	−	0.296294i	−0.767727	−	0.640777i	$-0.778612\pi$
$191$	2.36417	−	4.09487i	0.171066	−	0.296294i	0.938793	+	0.344483i	$0.111946\pi$
$192$		0			0
$193$	9.76542	+	16.9142i	0.702931	+	1.21751i	0.967433	+	0.253127i	$0.0814589\pi$
$193$	9.76542	+	16.9142i	0.702931	+	1.21751i	−0.264503	+	0.964385i	$0.585208\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.89966	−	6.89966i	−0.491581	−	0.491581i	0.417223	−	0.908804i	$-0.363003\pi$
$197$	−6.89966	−	6.89966i	−0.491581	−	0.491581i	−0.908804	+	0.417223i	$0.863003\pi$
$198$		0			0
$199$		−	24.4752i		−	1.73500i	−0.497438	−	0.867500i	$-0.665726\pi$
$199$		−	24.4752i		−	1.73500i	0.497438	−	0.867500i	$-0.334274\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.647456	−	2.41634i	0.0454425	−	0.169594i
$204$		0			0
$205$	4.36352	+	16.2849i	0.304762	+	1.13739i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.62030	+	6.27055i	−0.250422	+	0.433743i
$210$		0			0
$211$	−21.1840	−	5.67623i	−1.45837	−	0.390768i	−0.559441	−	0.828870i	$-0.688984\pi$
$211$	−21.1840	−	5.67623i	−1.45837	−	0.390768i	−0.898925	+	0.438102i	$0.855651\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			13.0375i			0.889148i
$216$		0			0
$217$			4.74612i			0.322188i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	7.97551	+	2.13703i	0.536491	+	0.143752i
$222$		0			0
$223$	1.56986	−	2.71908i	0.105126	−	0.182083i	−0.808664	−	0.588271i	$-0.799809\pi$
$223$	1.56986	−	2.71908i	0.105126	−	0.182083i	0.913790	+	0.406188i	$0.133142\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.64479	+	13.6026i	0.241913	+	0.902833i	0.974910	+	0.222601i	$0.0714546\pi$
$227$	3.64479	+	13.6026i	0.241913	+	0.902833i	−0.732996	+	0.680233i	$0.761879\pi$
$228$		0			0
$229$	−4.91218	+	18.3325i	−0.324606	+	1.21145i	0.590101	+	0.807330i	$0.299088\pi$
$229$	−4.91218	+	18.3325i	−0.324606	+	1.21145i	−0.914707	+	0.404117i	$0.867579\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	12.6802i		−	0.830708i	−0.909660	−	0.415354i	$-0.863658\pi$
$233$		−	12.6802i		−	0.830708i	0.909660	−	0.415354i	$-0.136342\pi$
$234$		0			0
$235$	1.38776	+	1.38776i	0.0905275	+	0.0905275i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−3.69405	−	6.39829i	−0.238948	−	0.413871i	0.721464	−	0.692451i	$-0.243469\pi$
$239$	−3.69405	−	6.39829i	−0.238948	−	0.413871i	−0.960413	+	0.278581i	$0.910136\pi$
$240$		0			0
$241$	11.1955	−	19.3912i	0.721167	−	1.24910i	−0.239366	−	0.970929i	$-0.576940\pi$
$241$	11.1955	−	19.3912i	0.721167	−	1.24910i	0.960533	−	0.278168i	$-0.0897271\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	14.1499	−	3.79145i	0.904003	−	0.242227i
$246$		0			0
$247$	−12.2577	+	7.07698i	−0.779938	+	0.450297i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−7.52339	−	7.52339i	−0.474872	−	0.474872i	0.428615	−	0.903487i	$-0.359002\pi$
$251$	−7.52339	−	7.52339i	−0.474872	−	0.474872i	−0.903487	+	0.428615i	$0.859002\pi$
$252$		0			0
$253$	1.34967	−	1.34967i	0.0848533	−	0.0848533i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2.21664	−	3.83934i	−0.138270	−	0.239491i	0.788572	−	0.614943i	$-0.210821\pi$
$257$	−2.21664	−	3.83934i	−0.138270	−	0.239491i	−0.926842	+	0.375452i	$0.877488\pi$
$258$		0			0
$259$	−3.98377	−	14.8676i	−0.247539	−	0.923830i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.61948	+	2.66706i	0.284850	+	0.164458i	0.635617	−	0.772005i	$-0.280746\pi$
$263$	4.61948	+	2.66706i	0.284850	+	0.164458i	−0.350767	+	0.936463i	$0.614079\pi$
$264$		0			0
$265$	29.2529	−	16.8891i	1.79699	−	1.03749i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−20.6406	+	20.6406i	−1.25848	+	1.25848i	−0.306663	+	0.951818i	$0.599212\pi$
$269$	−20.6406	+	20.6406i	−1.25848	+	1.25848i	−0.951818	+	0.306663i	$0.900788\pi$
$270$		0			0
$271$	−23.2339			−1.41136			−0.705680	−	0.708530i	$-0.749358\pi$
$271$	−23.2339			−1.41136			−0.705680	+	0.708530i	$0.749358\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	15.5019	+	4.15373i	0.934801	+	0.250479i
$276$		0			0
$277$	19.0092	−	5.09351i	1.14215	−	0.306039i	0.362338	−	0.932047i	$-0.381979\pi$
$277$	19.0092	−	5.09351i	1.14215	−	0.306039i	0.779817	+	0.626007i	$0.215312\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	16.3011	+	9.41146i	0.972444	+	0.561441i	0.899980	−	0.435930i	$-0.143581\pi$
$281$	16.3011	+	9.41146i	0.972444	+	0.561441i	0.0724633	+	0.997371i	$0.476914\pi$
$282$		0			0
$283$	3.43848	−	12.8326i	0.204397	−	0.762819i	−0.785236	−	0.619197i	$-0.787458\pi$
$283$	3.43848	−	12.8326i	0.204397	−	0.762819i	0.989633	−	0.143622i	$-0.0458749\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−7.47420			−0.441188
$288$		0			0
$289$	−5.12358			−0.301387
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−2.20679	+	8.23584i	−0.128922	+	0.481143i	−0.999949	−	0.0100919i	$-0.996788\pi$
$293$	−2.20679	+	8.23584i	−0.128922	+	0.481143i	0.871027	+	0.491235i	$0.163454\pi$
$294$		0			0
$295$	41.6699	+	24.0581i	2.42611	+	1.40072i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.60405	−	0.965702i	0.208427	−	0.0558480i
$300$		0			0
$301$	−5.58291	−	1.49594i	−0.321794	−	0.0862244i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−20.8853			−1.19589
$306$		0			0
$307$	7.13558	−	7.13558i	0.407249	−	0.407249i	−0.473529	−	0.880778i	$-0.657020\pi$
$307$	7.13558	−	7.13558i	0.407249	−	0.407249i	0.880778	+	0.473529i	$0.157020\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	10.0741	−	5.81630i	0.571252	−	0.329812i	−0.186397	−	0.982474i	$-0.559681\pi$
$311$	10.0741	−	5.81630i	0.571252	−	0.329812i	0.757649	+	0.652662i	$0.226348\pi$
$312$		0			0
$313$	5.76956	+	3.33106i	0.326115	+	0.188282i	0.654115	−	0.756395i	$-0.273041\pi$
$313$	5.76956	+	3.33106i	0.326115	+	0.188282i	−0.328000	+	0.944678i	$0.606375\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.708583	−	2.64447i	−0.0397980	−	0.148528i	0.943168	−	0.332317i	$-0.107830\pi$
$317$	−0.708583	−	2.64447i	−0.0397980	−	0.148528i	−0.982966	+	0.183789i	$0.941164\pi$
$318$		0			0
$319$	−0.812945	−	1.40806i	−0.0455162	−	0.0788364i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−14.3957	+	14.3957i	−0.801000	+	0.801000i
$324$		0			0
$325$	22.1835	+	22.1835i	1.23052	+	1.23052i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.753501	+	0.435034i	−0.0415418	+	0.0239842i
$330$		0			0
$331$	19.6789	−	5.27295i	1.08165	−	0.289827i	0.326379	−	0.945239i	$-0.394171\pi$
$331$	19.6789	−	5.27295i	1.08165	−	0.289827i	0.755272	+	0.655412i	$0.227505\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.630997	−	1.09292i	0.0344751	−	0.0597126i
$336$		0			0
$337$	−0.514533	−	0.891197i	−0.0280284	−	0.0485466i	0.851671	−	0.524077i	$-0.175590\pi$
$337$	−0.514533	−	0.891197i	−0.0280284	−	0.0485466i	−0.879699	+	0.475530i	$0.842256\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.18123	+	2.18123i	0.118120	+	0.118120i
$342$		0			0
$343$			19.6948i			1.06342i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−8.08026	+	30.1559i	−0.433771	+	1.61886i	0.310219	+	0.950665i	$0.399598\pi$
$347$	−8.08026	+	30.1559i	−0.433771	+	1.61886i	−0.743990	+	0.668191i	$0.767069\pi$
$348$		0			0
$349$	4.62320	+	17.2540i	0.247474	+	0.923587i	0.972124	+	0.234469i	$0.0753352\pi$
$349$	4.62320	+	17.2540i	0.247474	+	0.923587i	−0.724649	+	0.689118i	$0.757998\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.02827	−	1.78101i	0.0547291	−	0.0947935i	−0.837363	−	0.546647i	$-0.815904\pi$
$353$	1.02827	−	1.78101i	0.0547291	−	0.0947935i	0.892092	+	0.451854i	$0.149237\pi$
$354$		0			0
$355$	57.4962	+	15.4061i	3.05158	+	0.817668i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			4.76579i			0.251529i	0.992060	+	0.125764i	$0.0401383\pi$
$359$			4.76579i			0.251529i	−0.992060	+	0.125764i	$0.959862\pi$
$360$		0			0
$361$		−	15.8989i		−	0.836785i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.114672	−	0.0307261i	−0.00600218	−	0.00160828i
$366$		0			0
$367$	−8.61021	+	14.9133i	−0.449449	+	0.778469i	−0.998350	−	0.0574187i	$-0.981713\pi$
$367$	−8.61021	+	14.9133i	−0.449449	+	0.778469i	0.548901	+	0.835887i	$0.315046\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.87577	+	14.4646i	0.201220	+	0.750963i
$372$		0			0
$373$	4.29744	−	16.0383i	0.222513	−	0.830430i	−0.760872	−	0.648901i	$-0.775229\pi$
$373$	4.29744	−	16.0383i	0.222513	−	0.830430i	0.983386	−	0.181529i	$-0.0581046\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	3.17830i		−	0.163691i
$378$		0			0
$379$	22.5741	+	22.5741i	1.15955	+	1.15955i	0.984572	+	0.174981i	$0.0559865\pi$
$379$	22.5741	+	22.5741i	1.15955	+	1.15955i	0.174981	+	0.984572i	$0.444013\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−12.6153	−	21.8504i	−0.644614	−	1.11650i	−0.984391	−	0.175997i	$-0.943685\pi$
$383$	−12.6153	−	21.8504i	−0.644614	−	1.11650i	0.339777	−	0.940506i	$-0.389648\pi$
$384$		0			0
$385$	−4.91584	+	8.51448i	−0.250534	+	0.433938i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−7.09570	+	1.90129i	−0.359766	+	0.0963991i	−0.434175	−	0.900829i	$-0.642960\pi$
$389$	−7.09570	+	1.90129i	−0.359766	+	0.0963991i	0.0744082	+	0.997228i	$0.476293\pi$
$390$		0			0
$391$	4.64781	−	2.68342i	0.235050	−	0.135706i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−13.1783	−	13.1783i	−0.663073	−	0.663073i
$396$		0			0
$397$	−2.23236	+	2.23236i	−0.112039	+	0.112039i	−0.760904	−	0.648865i	$-0.775244\pi$
$397$	−2.23236	+	2.23236i	−0.112039	+	0.112039i	0.648865	+	0.760904i	$0.275244\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.10949	−	15.7781i	−0.454906	−	0.787921i	0.543777	−	0.839230i	$-0.316994\pi$
$401$	−9.10949	−	15.7781i	−0.454906	−	0.787921i	−0.998683	+	0.0513094i	$0.983661\pi$
$402$		0			0
$403$	1.56069	+	5.82456i	0.0777433	+	0.290142i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−8.66376	−	5.00202i	−0.429447	−	0.247941i
$408$		0			0
$409$	−22.6986	+	13.1050i	−1.12237	+	0.648002i	−0.942006	−	0.335597i	$-0.891062\pi$
$409$	−22.6986	+	13.1050i	−1.12237	+	0.648002i	−0.180368	+	0.983599i	$0.557729\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−15.0834	+	15.0834i	−0.742207	+	0.742207i
$414$		0			0
$415$	15.0529			0.738918
$416$		0			0
$417$		0			0
$418$		0			0
$419$	11.2202	+	3.00645i	0.548144	+	0.146875i	0.522254	−	0.852790i	$-0.325091\pi$
$419$	11.2202	+	3.00645i	0.548144	+	0.146875i	0.0258901	+	0.999665i	$0.491758\pi$
$420$		0			0
$421$	−9.74548	+	2.61129i	−0.474966	+	0.127267i	−0.488358	−	0.872644i	$-0.662404\pi$
$421$	−9.74548	+	2.61129i	−0.474966	+	0.127267i	0.0133918	+	0.999910i	$0.495737\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	39.0793	+	22.5624i	1.89562	+	1.09444i
$426$		0			0
$427$	2.39641	−	8.94353i	0.115970	−	0.432808i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−4.07825			−0.196442			−0.0982211	−	0.995165i	$-0.531315\pi$
$431$	−4.07825			−0.196442			−0.0982211	+	0.995165i	$0.531315\pi$
$432$		0			0
$433$	−25.1331			−1.20782			−0.603910	−	0.797052i	$-0.706392\pi$
$433$	−25.1331			−1.20782			−0.603910	+	0.797052i	$0.706392\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.38110	+	8.88638i	−0.113903	+	0.425093i
$438$		0			0
$439$	−13.5272	−	7.80991i	−0.645616	−	0.372747i	0.141158	−	0.989987i	$-0.454917\pi$
$439$	−13.5272	−	7.80991i	−0.645616	−	0.372747i	−0.786775	+	0.617240i	$0.788251\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	32.6709	−	8.75415i	1.55224	−	0.415922i	0.622045	−	0.782982i	$-0.286302\pi$
$443$	32.6709	−	8.75415i	1.55224	−	0.415922i	0.930197	+	0.367060i	$0.119636\pi$
$444$		0			0
$445$	−19.5123	−	5.22830i	−0.924970	−	0.247845i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	28.0284			1.32274			0.661370	−	0.750060i	$-0.269975\pi$
$449$	28.0284			1.32274			0.661370	+	0.750060i	$0.269975\pi$
$450$		0			0
$451$	−3.43500	+	3.43500i	−0.161748	+	0.161748i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−16.6441	+	9.60949i	−0.780289	+	0.450500i
$456$		0			0
$457$	14.8363	+	8.56574i	0.694012	+	0.400688i	0.805113	−	0.593121i	$-0.202104\pi$
$457$	14.8363	+	8.56574i	0.694012	+	0.400688i	−0.111101	+	0.993809i	$0.535438\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.43727	−	9.09603i	−0.113515	−	0.423644i	0.885656	−	0.464341i	$-0.153709\pi$
$461$	−2.43727	−	9.09603i	−0.113515	−	0.423644i	−0.999172	+	0.0406970i	$0.987042\pi$
$462$		0			0
$463$	0.777204	+	1.34616i	0.0361197	+	0.0625612i	0.883520	−	0.468393i	$-0.155167\pi$
$463$	0.777204	+	1.34616i	0.0361197	+	0.0625612i	−0.847400	+	0.530954i	$0.821834\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	9.81211	−	9.81211i	0.454050	−	0.454050i	−0.442646	−	0.896696i	$-0.645960\pi$
$467$	9.81211	−	9.81211i	0.454050	−	0.454050i	0.896696	+	0.442646i	$0.145960\pi$
$468$		0			0
$469$	0.395609	+	0.395609i	0.0182675	+	0.0182675i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−3.25331	+	1.87830i	−0.149587	+	0.0863643i
$474$		0			0
$475$	−74.7175	+	20.0205i	−3.42828	+	0.918604i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−11.7030	+	20.2702i	−0.534724	+	0.926169i	0.464453	+	0.885598i	$0.346251\pi$
$479$	−11.7030	+	20.2702i	−0.534724	+	0.926169i	−0.999177	+	0.0405710i	$0.987082\pi$
$480$		0			0
$481$	−9.77797	−	16.9359i	−0.445837	−	0.772212i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	25.1064	+	25.1064i	1.14002	+	1.14002i
$486$		0			0
$487$		−	21.0301i		−	0.952967i	−0.879183	−	0.476483i	$-0.841911\pi$
$487$		−	21.0301i		−	0.952967i	0.879183	−	0.476483i	$-0.158089\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−6.82214	+	25.4606i	−0.307879	+	1.14902i	0.622560	+	0.782572i	$0.286093\pi$
$491$	−6.82214	+	25.4606i	−0.307879	+	1.14902i	−0.930439	+	0.366447i	$0.880574\pi$
$492$		0			0
$493$	−1.18321	−	4.41580i	−0.0532891	−	0.198877i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−13.1944	+	22.8533i	−0.591849	+	1.02511i
$498$		0			0
$499$	−12.8466	−	3.44223i	−0.575092	−	0.154095i	−0.0404610	−	0.999181i	$-0.512883\pi$
$499$	−12.8466	−	3.44223i	−0.575092	−	0.154095i	−0.534631	+	0.845086i	$0.679549\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	7.97796i		−	0.355720i	−0.984056	−	0.177860i	$-0.943083\pi$
$503$		−	7.97796i		−	0.355720i	0.984056	−	0.177860i	$-0.0569174\pi$
$504$		0			0
$505$			31.7417i			1.41249i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−33.3037	−	8.92371i	−1.47616	−	0.395536i	−0.571123	−	0.820865i	$-0.693492\pi$
$509$	−33.3037	−	8.92371i	−1.47616	−	0.395536i	−0.905039	+	0.425328i	$0.860159\pi$
$510$		0			0
$511$	0.0263151	−	0.0455792i	0.00116411	−	0.00201630i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−15.5353	−	57.9785i	−0.684567	−	2.55484i
$516$		0			0
$517$	−0.146362	+	0.546229i	−0.00643697	+	0.0240231i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			20.0111i			0.876703i	0.898804	+	0.438352i	$0.144438\pi$
$521$			20.0111i			0.876703i	−0.898804	+	0.438352i	$0.855562\pi$
$522$		0			0
$523$	11.2432	+	11.2432i	0.491633	+	0.491633i	0.908820	−	0.417188i	$-0.136984\pi$
$523$	11.2432	+	11.2432i	0.491633	+	0.491633i	−0.417188	+	0.908820i	$0.636984\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.33671	+	7.51140i	0.188910	+	0.327202i
$528$		0			0
$529$	−10.2874	+	17.8183i	−0.447278	+	0.774708i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−9.17253	+	2.45777i	−0.397306	+	0.106458i
$534$		0			0
$535$	20.0569	−	11.5799i	0.867137	−	0.500642i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	2.98466	+	2.98466i	0.128559	+	0.128559i
$540$		0			0
$541$	9.38252	−	9.38252i	0.403386	−	0.403386i	−0.476038	−	0.879424i	$-0.657928\pi$
$541$	9.38252	−	9.38252i	0.403386	−	0.403386i	0.879424	+	0.476038i	$0.157928\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	6.27481	+	10.8683i	0.268783	+	0.465546i
$546$		0			0
$547$	9.70067	+	36.2034i	0.414770	+	1.54794i	0.785295	+	0.619122i	$0.212511\pi$
$547$	9.70067	+	36.2034i	0.414770	+	1.54794i	−0.370524	+	0.928823i	$0.620822\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	6.78671	+	3.91831i	0.289123	+	0.166926i
$552$		0			0
$553$	7.15532	−	4.13113i	0.304275	−	0.175673i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−9.01169	+	9.01169i	−0.381838	+	0.381838i	−0.871764	−	0.489926i	$-0.837024\pi$
$557$	−9.01169	+	9.01169i	−0.381838	+	0.381838i	0.489926	+	0.871764i	$0.337024\pi$
$558$		0			0
$559$	−7.34341			−0.310593
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−16.4015	−	4.39477i	−0.691241	−	0.185218i	−0.103937	−	0.994584i	$-0.533144\pi$
$563$	−16.4015	−	4.39477i	−0.691241	−	0.185218i	−0.587304	+	0.809366i	$0.699811\pi$
$564$		0			0
$565$	−16.8294	+	4.50942i	−0.708018	+	0.189713i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−14.1855	−	8.19001i	−0.594688	−	0.343343i	0.172261	−	0.985051i	$-0.444893\pi$
$569$	−14.1855	−	8.19001i	−0.594688	−	0.343343i	−0.766949	+	0.641708i	$0.778226\pi$
$570$		0			0
$571$	9.58794	−	35.7827i	0.401243	−	1.49746i	−0.409638	−	0.912248i	$-0.634345\pi$
$571$	9.58794	−	35.7827i	0.401243	−	1.49746i	0.810881	−	0.585211i	$-0.198988\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	20.3914			0.850382
$576$		0			0
$577$	−2.14863			−0.0894487			−0.0447243	−	0.998999i	$-0.514241\pi$
$577$	−2.14863			−0.0894487			−0.0447243	+	0.998999i	$0.514241\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.72719	+	6.44597i	−0.0716560	+	0.267424i
$582$		0			0
$583$	8.42888	+	4.86642i	0.349088	+	0.201546i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−21.6014	+	5.78807i	−0.891585	+	0.238899i	−0.675399	−	0.737453i	$-0.736028\pi$
$587$	−21.6014	+	5.78807i	−0.891585	+	0.238899i	−0.216186	+	0.976352i	$0.569362\pi$
$588$		0			0
$589$	−14.3614	−	3.84813i	−0.591752	−	0.158559i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−10.7128			−0.439921			−0.219960	−	0.975509i	$-0.570593\pi$
$593$	−10.7128			−0.439921			−0.219960	+	0.975509i	$0.570593\pi$
$594$		0			0
$595$	−19.5473	+	19.5473i	−0.801361	+	0.801361i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	23.8944	−	13.7955i	0.976300	−	0.563667i	0.0751489	−	0.997172i	$-0.476057\pi$
$599$	23.8944	−	13.7955i	0.976300	−	0.563667i	0.901151	+	0.433505i	$0.142723\pi$
$600$		0			0
$601$	−9.37490	−	5.41260i	−0.382410	−	0.220785i	0.296456	−	0.955046i	$-0.404195\pi$
$601$	−9.37490	−	5.41260i	−0.382410	−	0.220785i	−0.678866	+	0.734262i	$0.737528\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−10.4565	−	39.0241i	−0.425116	−	1.58655i
$606$		0			0
$607$	−19.0270	−	32.9557i	−0.772282	−	1.33763i	−0.936310	−	0.351175i	$-0.885782\pi$
$607$	−19.0270	−	32.9557i	−0.772282	−	1.33763i	0.164028	−	0.986456i	$-0.447551\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.781661	+	0.781661i	−0.0316226	+	0.0316226i
$612$		0			0
$613$	−34.9758	−	34.9758i	−1.41266	−	1.41266i	−0.739489	−	0.673168i	$-0.764933\pi$
$613$	−34.9758	−	34.9758i	−1.41266	−	1.41266i	−0.673168	−	0.739489i	$-0.735067\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	11.9478	−	6.89807i	0.481001	−	0.277706i	−0.239833	−	0.970814i	$-0.577093\pi$
$617$	11.9478	−	6.89807i	0.481001	−	0.277706i	0.720834	+	0.693108i	$0.243759\pi$
$618$		0			0
$619$	−32.9231	+	8.82171i	−1.32329	+	0.354574i	−0.850209	−	0.526445i	$-0.823525\pi$
$619$	−32.9231	+	8.82171i	−1.32329	+	0.354574i	−0.473080	+	0.881019i	$0.656858\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	4.47773	−	7.75565i	0.179396	−	0.310724i
$624$		0			0
$625$	40.4916	+	70.1335i	1.61966	+	2.80534i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−19.8900	−	19.8900i	−0.793066	−	0.793066i
$630$		0			0
$631$			7.97657i			0.317542i	0.987315	+	0.158771i	$0.0507532\pi$
$631$			7.97657i			0.317542i	−0.987315	+	0.158771i	$0.949247\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	5.39276	−	20.1260i	0.214005	−	0.798677i
$636$		0			0
$637$	2.13555	+	7.96998i	0.0846135	+	0.315782i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	18.6956	−	32.3818i	0.738434	−	1.27900i	−0.214767	−	0.976665i	$-0.568899\pi$
$641$	18.6956	−	32.3818i	0.738434	−	1.27900i	0.953200	−	0.302339i	$-0.0977676\pi$
$642$		0			0
$643$	−12.4765	−	3.34308i	−0.492026	−	0.131838i	0.00427070	−	0.999991i	$-0.498641\pi$
$643$	−12.4765	−	3.34308i	−0.492026	−	0.131838i	−0.496297	+	0.868153i	$0.665307\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	4.85394i		−	0.190828i	−0.995438	−	0.0954140i	$-0.969582\pi$
$647$		−	4.85394i		−	0.190828i	0.995438	−	0.0954140i	$-0.0304175\pi$
$648$		0			0
$649$			13.8641i			0.544215i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	37.4249	+	10.0280i	1.46455	+	0.392425i	0.901059	−	0.433696i	$-0.142791\pi$
$653$	37.4249	+	10.0280i	1.46455	+	0.392425i	0.563492	+	0.826121i	$0.309458\pi$
$654$		0			0
$655$	39.1387	−	67.7902i	1.52928	−	2.64878i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	9.85502	+	36.7794i	0.383897	+	1.43272i	0.839898	+	0.542744i	$0.182615\pi$
$659$	9.85502	+	36.7794i	0.383897	+	1.43272i	−0.456001	+	0.889979i	$0.650719\pi$
$660$		0			0
$661$	3.10339	−	11.5820i	0.120708	−	0.450488i	−0.878943	−	0.476927i	$-0.841750\pi$
$661$	3.10339	−	11.5820i	0.120708	−	0.450488i	0.999650	+	0.0264400i	$0.00841709\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	47.3876i		−	1.83761i
$666$		0			0
$667$	−1.46077	−	1.46077i	−0.0565613	−	0.0565613i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−3.00893	−	5.21163i	−0.116159	−	0.201193i
$672$		0			0
$673$	14.9076	−	25.8207i	0.574645	−	0.995314i	−0.421435	−	0.906858i	$-0.638474\pi$
$673$	14.9076	−	25.8207i	0.574645	−	0.995314i	0.996080	−	0.0884554i	$-0.0281931\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−27.4303	+	7.34993i	−1.05423	+	0.282481i	−0.744000	−	0.668180i	$-0.767074\pi$
$677$	−27.4303	+	7.34993i	−1.05423	+	0.282481i	−0.310233	+	0.950661i	$0.600407\pi$
$678$		0			0
$679$	−13.6318	+	7.87034i	−0.523142	+	0.302036i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	34.9639	+	34.9639i	1.33786	+	1.33786i	0.898134	+	0.439721i	$0.144923\pi$
$683$	34.9639	+	34.9639i	1.33786	+	1.33786i	0.439721	+	0.898134i	$0.355077\pi$
$684$		0			0
$685$	46.6088	−	46.6088i	1.78083	−	1.78083i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	9.51288	+	16.4768i	0.362412	+	0.627716i
$690$		0			0
$691$	3.37585	+	12.5989i	0.128424	+	0.479283i	0.999939	−	0.0110856i	$-0.00352872\pi$
$691$	3.37585	+	12.5989i	0.128424	+	0.479283i	−0.871515	+	0.490369i	$0.836862\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	27.1620	+	15.6820i	1.03031	+	0.594851i
$696$		0			0
$697$	−11.8290	+	6.82946i	−0.448054	+	0.258684i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1.18582	−	1.18582i	0.0447879	−	0.0447879i	−0.684358	−	0.729146i	$-0.739917\pi$
$701$	1.18582	−	1.18582i	0.0447879	−	0.0447879i	0.729146	+	0.684358i	$0.239917\pi$
$702$		0			0
$703$	48.2184			1.81859
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−13.5924	−	3.64208i	−0.511196	−	0.136975i
$708$		0			0
$709$	13.3909	−	3.58808i	0.502906	−	0.134753i	0.00155784	−	0.999999i	$-0.499504\pi$
$709$	13.3909	−	3.58808i	0.502906	−	0.134753i	0.501349	+	0.865245i	$0.332837\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	3.39432	+	1.95971i	0.127118	+	0.0733919i
$714$		0			0
$715$	−3.23299	+	12.0657i	−0.120907	+	0.451231i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	22.9314			0.855198			0.427599	−	0.903968i	$-0.359359\pi$
$719$	22.9314			0.855198			0.427599	+	0.903968i	$0.359359\pi$
$720$		0			0
$721$	26.6101			0.991013
$722$		0			0
$723$		0			0
$724$		0			0
$725$	4.49564	−	16.7780i	0.166964	−	0.623118i
$726$		0			0
$727$	−14.6244	−	8.44338i	−0.542387	−	0.313147i	0.203659	−	0.979042i	$-0.434717\pi$
$727$	−14.6244	−	8.44338i	−0.542387	−	0.313147i	−0.746046	+	0.665894i	$0.768050\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−10.2026	+	2.73379i	−0.377358	+	0.101113i
$732$		0			0
$733$	−39.1181	−	10.4817i	−1.44486	−	0.387149i	−0.550626	−	0.834752i	$-0.685611\pi$
$733$	−39.1181	−	10.4817i	−1.44486	−	0.387149i	−0.894232	+	0.447603i	$0.852278\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.363629			0.0133945
$738$		0			0
$739$	−20.2719	+	20.2719i	−0.745713	+	0.745713i	−0.973671	−	0.227958i	$-0.926795\pi$
$739$	−20.2719	+	20.2719i	−0.745713	+	0.745713i	0.227958	+	0.973671i	$0.426795\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	33.3722	−	19.2674i	1.22431	−	0.706853i	0.258473	−	0.966019i	$-0.416781\pi$
$743$	33.3722	−	19.2674i	1.22431	−	0.706853i	0.965833	+	0.259165i	$0.0834474\pi$
$744$		0			0
$745$	28.4517	+	16.4266i	1.04239	+	0.601824i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.65738	+	9.91749i	0.0970987	+	0.362377i
$750$		0			0
$751$	2.59701	+	4.49815i	0.0947663	+	0.164140i	0.909511	−	0.415680i	$-0.136456\pi$
$751$	2.59701	+	4.49815i	0.0947663	+	0.164140i	−0.814745	+	0.579820i	$0.803123\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	11.6885	−	11.6885i	0.425388	−	0.425388i
$756$		0			0
$757$	16.3310	+	16.3310i	0.593562	+	0.593562i	0.938592	−	0.345030i	$-0.112131\pi$
$757$	16.3310	+	16.3310i	0.593562	+	0.593562i	−0.345030	+	0.938592i	$0.612131\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	30.2706	−	17.4767i	1.09731	−	0.633530i	0.161794	−	0.986824i	$-0.448272\pi$
$761$	30.2706	−	17.4767i	1.09731	−	0.633530i	0.935512	+	0.353294i	$0.114939\pi$
$762$		0			0
$763$	−5.37400	+	1.43996i	−0.194552	+	0.0521300i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−13.5508	+	23.4707i	−0.489292	+	0.847478i
$768$		0			0
$769$	−11.5439	−	19.9946i	−0.416284	−	0.721024i	0.579279	−	0.815130i	$-0.303334\pi$
$769$	−11.5439	−	19.9946i	−0.416284	−	0.721024i	−0.995562	+	0.0941052i	$0.970001\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−14.4736	−	14.4736i	−0.520581	−	0.520581i	0.397166	−	0.917747i	$-0.369994\pi$
$773$	−14.4736	−	14.4736i	−0.520581	−	0.520581i	−0.917747	+	0.397166i	$0.869994\pi$
$774$		0			0
$775$			32.9549i			1.18378i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.06004	−	22.6164i	0.217124	−	0.810316i
$780$		0			0
$781$	4.43908	+	16.5669i	0.158843	+	0.592809i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−13.7254	+	23.7732i	−0.489882	+	0.848501i
$786$		0			0
$787$	33.2907	+	8.92022i	1.18669	+	0.317971i	0.797575	−	0.603220i	$-0.206116\pi$
$787$	33.2907	+	8.92022i	1.18669	+	0.317971i	0.389110	+	0.921191i	$0.372782\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	7.72411i		−	0.274638i
$792$		0			0
$793$		−	11.7637i		−	0.417743i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−19.0745	−	5.11099i	−0.675652	−	0.181040i	−0.0953525	−	0.995444i	$-0.530398\pi$
$797$	−19.0745	−	5.11099i	−0.675652	−	0.181040i	−0.580299	+	0.814403i	$0.697064\pi$
$798$		0			0
$799$	−0.795014	+	1.37700i	−0.0281256	+	0.0487149i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.00885339	−	0.0330413i	−0.000312429	−	0.00116600i
$804$		0			0
$805$	−3.23318	+	12.0664i	−0.113955	+	0.425285i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			2.32596i			0.0817763i	0.999164	+	0.0408882i	$0.0130187\pi$
$809$			2.32596i			0.0817763i	−0.999164	+	0.0408882i	$0.986981\pi$
$810$		0			0
$811$	−34.5092	−	34.5092i	−1.21178	−	1.21178i	−0.970440	−	0.241343i	$-0.922412\pi$
$811$	−34.5092	−	34.5092i	−1.21178	−	1.21178i	−0.241343	−	0.970440i	$-0.577588\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−31.8177	−	55.1098i	−1.11452	−	1.93041i
$816$		0			0
$817$	9.05319	−	15.6806i	0.316731	−	0.548594i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	51.3558	−	13.7607i	1.79233	−	0.480253i	0.799590	−	0.600547i	$-0.205050\pi$
$821$	51.3558	−	13.7607i	1.79233	−	0.480253i	0.992738	+	0.120294i	$0.0383836\pi$
$822$		0			0
$823$	−8.35343	+	4.82286i	−0.291182	+	0.168114i	−0.638475	−	0.769643i	$-0.720434\pi$
$823$	−8.35343	+	4.82286i	−0.291182	+	0.168114i	0.347293	+	0.937757i	$0.387101\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−18.2747	−	18.2747i	−0.635475	−	0.635475i	0.313961	−	0.949436i	$-0.398344\pi$
$827$	−18.2747	−	18.2747i	−0.635475	−	0.635475i	−0.949436	+	0.313961i	$0.898344\pi$
$828$		0			0
$829$	6.63529	−	6.63529i	0.230453	−	0.230453i	−0.582429	−	0.812882i	$-0.697897\pi$
$829$	6.63529	−	6.63529i	0.230453	−	0.230453i	0.812882	+	0.582429i	$0.197897\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	5.93409	+	10.2782i	0.205604	+	0.356117i
$834$		0			0
$835$	−23.7912	−	88.7900i	−0.823329	−	3.07271i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−34.7829	−	20.0819i	−1.20084	−	0.693306i	−0.240099	−	0.970749i	$-0.577180\pi$
$839$	−34.7829	−	20.0819i	−1.20084	−	0.693306i	−0.960742	+	0.277443i	$0.910513\pi$
$840$		0			0
$841$	23.5908	−	13.6201i	0.813475	−	0.469660i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	21.8355	−	21.8355i	0.751166	−	0.751166i
$846$		0			0
$847$	17.9107			0.615419
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−12.2779	−	3.28987i	−0.420883	−	0.112775i
$852$		0			0
$853$	−2.70204	+	0.724010i	−0.0925162	+	0.0247896i	−0.304780	−	0.952423i	$-0.598583\pi$
$853$	−2.70204	+	0.724010i	−0.0925162	+	0.0247896i	0.212264	+	0.977212i	$0.431916\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−32.4678	−	18.7453i	−1.10908	−	0.640326i	−0.170488	−	0.985360i	$-0.554534\pi$
$857$	−32.4678	−	18.7453i	−1.10908	−	0.640326i	−0.938590	+	0.345033i	$0.887868\pi$
$858$		0			0
$859$	−12.4963	+	46.6369i	−0.426369	+	1.59123i	0.334547	+	0.942379i	$0.391417\pi$
$859$	−12.4963	+	46.6369i	−0.426369	+	1.59123i	−0.760916	+	0.648850i	$0.775250\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−40.4745			−1.37777			−0.688883	−	0.724872i	$-0.741899\pi$
$863$	−40.4745			−1.37777			−0.688883	+	0.724872i	$0.741899\pi$
$864$		0			0
$865$	−82.3366			−2.79953
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1.38986	−	5.18704i	0.0471479	−	0.175958i
$870$		0			0
$871$	0.615591	+	0.355412i	0.0208585	+	0.0120427i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−62.7143	+	16.8042i	−2.12013	+	0.568087i
$876$		0			0
$877$	31.1530	+	8.34743i	1.05196	+	0.281873i	0.743063	−	0.669222i	$-0.233372\pi$
$877$	31.1530	+	8.34743i	1.05196	+	0.281873i	0.308901	+	0.951094i	$0.400039\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	44.0930			1.48553			0.742765	−	0.669552i	$-0.233514\pi$
$881$	44.0930			1.48553			0.742765	+	0.669552i	$0.233514\pi$
$882$		0			0
$883$	28.6867	−	28.6867i	0.965385	−	0.965385i	−0.0340356	−	0.999421i	$-0.510836\pi$
$883$	28.6867	−	28.6867i	0.965385	−	0.965385i	0.999421	+	0.0340356i	$0.0108359\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−6.66474	+	3.84789i	−0.223780	+	0.129199i	−0.607699	−	0.794167i	$-0.707907\pi$
$887$	−6.66474	+	3.84789i	−0.223780	+	0.129199i	0.383919	+	0.923367i	$0.374574\pi$
$888$		0			0
$889$	7.99961	+	4.61858i	0.268298	+	0.154902i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.705446	−	2.63276i	−0.0236069	−	0.0881020i
$894$		0			0
$895$	−8.66712	−	15.0119i	−0.289710	−	0.501792i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.36078	−	2.36078i	0.0787364	−	0.0787364i
$900$		0			0
$901$	19.3508	+	19.3508i	0.644667	+	0.644667i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	49.5019	−	28.5799i	1.64550	−	0.950029i
$906$		0			0
$907$	30.2432	−	8.10365i	1.00421	−	0.269077i	0.281002	−	0.959707i	$-0.409333\pi$
$907$	30.2432	−	8.10365i	1.00421	−	0.269077i	0.723208	+	0.690630i	$0.242667\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	11.1615	−	19.3322i	0.369796	−	0.640506i	−0.619737	−	0.784809i	$-0.712761\pi$
$911$	11.1615	−	19.3322i	0.369796	−	0.640506i	0.989533	+	0.144304i	$0.0460942\pi$
$912$		0			0
$913$	2.16866	+	3.75623i	0.0717722	+	0.124313i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	24.5383	+	24.5383i	0.810327	+	0.810327i
$918$		0			0
$919$		−	51.8070i		−	1.70895i	−0.519489	−	0.854477i	$-0.673877\pi$
$919$		−	51.8070i		−	1.70895i	0.519489	−	0.854477i	$-0.326123\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−8.67752	+	32.3849i	−0.285624	+	1.06596i
$924$		0			0
$925$	−27.6615	−	103.234i	−0.909505	−	3.39432i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	13.9260	−	24.1206i	0.456899	−	0.791372i	−0.541897	−	0.840445i	$-0.682294\pi$
$929$	13.9260	−	24.1206i	0.456899	−	0.791372i	0.998795	+	0.0490736i	$0.0156269\pi$
$930$		0			0
$931$	−19.6513	−	5.26555i	−0.644046	−	0.172571i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			17.9671i			0.587589i
$936$		0			0
$937$		−	35.0104i		−	1.14374i	−0.820344	−	0.571870i	$-0.806218\pi$
$937$		−	35.0104i		−	1.14374i	0.820344	−	0.571870i	$-0.193782\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−25.0151	−	6.70277i	−0.815468	−	0.218504i	−0.173104	−	0.984904i	$-0.555380\pi$
$941$	−25.0151	−	6.70277i	−0.815468	−	0.218504i	−0.642364	+	0.766400i	$0.722046\pi$
$942$		0			0
$943$	−3.08616	+	5.34539i	−0.100499	+	0.174070i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	5.18039	+	19.3335i	0.168340	+	0.628254i	0.997591	+	0.0693768i	$0.0221011\pi$
$947$	5.18039	+	19.3335i	0.168340	+	0.628254i	−0.829250	+	0.558877i	$0.811232\pi$
$948$		0			0
$949$	0.0173066	−	0.0645892i	0.000561797	−	0.00209665i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			6.37793i			0.206601i	0.994650	+	0.103301i	$0.0329404\pi$
$953$			6.37793i			0.206601i	−0.994650	+	0.103301i	$0.967060\pi$
$954$		0			0
$955$	14.2220	+	14.2220i	0.460215	+	0.460215i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	14.6109	+	25.3068i	0.471810	+	0.817199i
$960$		0			0
$961$	12.3329	−	21.3612i	0.397835	−	0.689070i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−80.2477	+	21.5023i	−2.58326	+	0.692183i
$966$		0			0
$967$	−32.7206	+	18.8912i	−1.05222	+	0.607501i	−0.923271	−	0.384149i	$-0.874495\pi$
$967$	−32.7206	+	18.8912i	−1.05222	+	0.607501i	−0.128952	+	0.991651i	$0.541161\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	39.2528	+	39.2528i	1.25968	+	1.25968i	0.951245	+	0.308436i	$0.0998057\pi$
$971$	39.2528	+	39.2528i	1.25968	+	1.25968i	0.308436	+	0.951245i	$0.400194\pi$
$972$		0			0
$973$	−9.83195	+	9.83195i	−0.315198	+	0.315198i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	13.9657	+	24.1893i	0.446803	+	0.773885i	0.998176	−	0.0603737i	$-0.0192293\pi$
$977$	13.9657	+	24.1893i	0.446803	+	0.773885i	−0.551373	+	0.834259i	$0.685896\pi$
$978$		0			0
$979$	−1.50647	−	5.62224i	−0.0481471	−	0.179687i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−31.3818	−	18.1183i	−1.00092	−	0.577883i	−0.0924017	−	0.995722i	$-0.529454\pi$
$983$	−31.3818	−	18.1183i	−1.00092	−	0.577883i	−0.908521	+	0.417839i	$0.862788\pi$
$984$		0			0
$985$	35.9452	−	20.7530i	1.14531	−	0.661245i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−3.37509	+	3.37509i	−0.107322	+	0.107322i
$990$		0			0
$991$	−52.0673			−1.65397			−0.826985	−	0.562223i	$-0.809946\pi$
$991$	−52.0673			−1.65397			−0.826985	+	0.562223i	$0.809946\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	100.563	+	26.9457i	3.18805	+	0.854236i
$996$		0			0
$997$	−52.9980	+	14.2008i	−1.67846	+	0.449743i	−0.967373	−	0.253357i	$-0.918465\pi$
$997$	−52.9980	+	14.2008i	−1.67846	+	0.449743i	−0.711091	+	0.703100i	$0.751798\pi$
$998$		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.1585.1		72
3.2	odd	2		576.2.bb.e.241.16		72
4.3	odd	2		432.2.y.e.181.4		72
9.4	even	3	inner	1728.2.bc.e.1009.18		72
9.5	odd	6		576.2.bb.e.49.6		72
12.11	even	2		144.2.x.e.133.15	yes	72
16.3	odd	4		432.2.y.e.397.15		72
16.13	even	4	inner	1728.2.bc.e.721.18		72
36.23	even	6		144.2.x.e.85.4	yes	72
36.31	odd	6		432.2.y.e.37.15		72
48.29	odd	4		576.2.bb.e.529.6		72
48.35	even	4		144.2.x.e.61.4	yes	72
144.13	even	12	inner	1728.2.bc.e.145.1		72
144.67	odd	12		432.2.y.e.253.4		72
144.77	odd	12		576.2.bb.e.337.16		72
144.131	even	12		144.2.x.e.13.15	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.15	✓	72	144.131	even	12
144.2.x.e.61.4	yes	72	48.35	even	4
144.2.x.e.85.4	yes	72	36.23	even	6
144.2.x.e.133.15	yes	72	12.11	even	2
432.2.y.e.37.15		72	36.31	odd	6
432.2.y.e.181.4		72	4.3	odd	2
432.2.y.e.253.4		72	144.67	odd	12
432.2.y.e.397.15		72	16.3	odd	4
576.2.bb.e.49.6		72	9.5	odd	6
576.2.bb.e.241.16		72	3.2	odd	2
576.2.bb.e.337.16		72	144.77	odd	12
576.2.bb.e.529.6		72	48.29	odd	4
1728.2.bc.e.145.1		72	144.13	even	12	inner
1728.2.bc.e.721.18		72	16.13	even	4	inner
1728.2.bc.e.1009.18		72	9.4	even	3	inner
1728.2.bc.e.1585.1		72	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-1.10094 + 4.10876i) q^{5} +(-1.63313 - 0.942891i) q^{7} +O(q^{10})\)	\(q+(-1.10094 + 4.10876i) q^{5} +(-1.63313 - 0.942891i) q^{7} +(-1.18389 + 0.317223i) q^{11} +(-2.31428 - 0.620109i) q^{13} -3.44622 q^{17} +(4.17726 - 4.17726i) q^{19} +(-1.34867 + 0.778655i) q^{23} +(-11.3397 - 6.54701i) q^{25} +(0.343336 + 1.28135i) q^{29} +(-1.25840 - 2.17961i) q^{31} +(5.67210 - 5.67210i) q^{35} +(5.77154 + 5.77154i) q^{37} +(3.43245 - 1.98173i) q^{41} +(2.96053 - 0.793272i) q^{43} +(0.230692 - 0.399570i) q^{47} +(-1.72191 - 2.98244i) q^{49} +(-5.61507 - 5.61507i) q^{53} -5.21358i q^{55} +(2.92766 - 10.9262i) q^{59} +(1.27078 + 4.74261i) q^{61} +(5.09576 - 8.82612i) q^{65} +(-0.286572 - 0.0767867i) q^{67} -13.9935i q^{71} +0.0279090i q^{73} +(2.23256 + 0.598214i) q^{77} +(-2.19067 + 3.79435i) q^{79} +(-0.915902 - 3.41819i) q^{83} +(3.79408 - 14.1597i) q^{85} +4.74894i q^{89} +(3.19483 + 3.19483i) q^{91} +(12.5645 + 21.7623i) q^{95} +(4.17352 - 7.22875i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{5}+O(q^{10}) \) 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

L-functions

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Database

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