LMFDB - Embedded newform 192.3.l.a.175.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,3,Mod(79,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("192.79");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	192.l (of order $4$, degree $2$, 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:	$5.23162107572$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + \cdots + 65536 $ x^16 - 6x^14 - 4x^13 + 10x^12 + 56x^11 + 88x^10 - 128x^9 - 496x^8 - 512x^7 + 1408x^6 + 3584x^5 + 2560x^4 - 4096x^3 - 24576*x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{24} $
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			175.3
Root			$1.78012 + 0.911682i$ of defining polynomial
Character	$\chi$	$=$	192.175
Dual form			192.3.l.a.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 1.22474i) q^{3} +(1.00772 - 1.00772i) q^{5} -10.0236 q^{7} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.22474 + 1.22474i) q^{3} +(1.00772 - 1.00772i) q^{5} -10.0236 q^{7} -3.00000i q^{9} +(-2.26517 - 2.26517i) q^{11} +(-6.88229 - 6.88229i) q^{13} +2.46840i q^{15} -22.3801 q^{17} +(16.8918 - 16.8918i) q^{19} +(12.2763 - 12.2763i) q^{21} -33.2007 q^{23} +22.9690i q^{25} +(3.67423 + 3.67423i) q^{27} +(-24.6412 - 24.6412i) q^{29} -41.3761i q^{31} +5.54852 q^{33} +(-10.1010 + 10.1010i) q^{35} +(-6.60031 + 6.60031i) q^{37} +16.8581 q^{39} +47.1477i q^{41} +(48.8218 + 48.8218i) q^{43} +(-3.02316 - 3.02316i) q^{45} +45.6048i q^{47} +51.4717 q^{49} +(27.4100 - 27.4100i) q^{51} +(25.1401 - 25.1401i) q^{53} -4.56532 q^{55} +41.3762i q^{57} +(-6.23974 - 6.23974i) q^{59} +(35.9513 + 35.9513i) q^{61} +30.0707i q^{63} -13.8709 q^{65} +(-10.2045 + 10.2045i) q^{67} +(40.6624 - 40.6624i) q^{69} -11.9529 q^{71} -111.332i q^{73} +(-28.1312 - 28.1312i) q^{75} +(22.7051 + 22.7051i) q^{77} +4.46031i q^{79} -9.00000 q^{81} +(-10.1751 + 10.1751i) q^{83} +(-22.5530 + 22.5530i) q^{85} +60.3583 q^{87} +21.9364i q^{89} +(68.9850 + 68.9850i) q^{91} +(50.6752 + 50.6752i) q^{93} -34.0444i q^{95} +107.309 q^{97} +(-6.79552 + 6.79552i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 32 q^{11} + 32 q^{19} + 128 q^{23} + 32 q^{29} - 96 q^{35} - 96 q^{37} - 160 q^{43} + 112 q^{49} + 96 q^{51} - 160 q^{53} + 256 q^{55} + 128 q^{59} - 32 q^{61} - 32 q^{65} - 320 q^{67} + 96 q^{69} - 512 q^{71} - 192 q^{75} + 224 q^{77} - 144 q^{81} + 160 q^{83} + 160 q^{85} + 480 q^{91} - 96 q^{99}+O(q^{100}) $ 16 * q - 32 * q^11 + 32 * q^19 + 128 * q^23 + 32 * q^29 - 96 * q^35 - 96 * q^37 - 160 * q^43 + 112 * q^49 + 96 * q^51 - 160 * q^53 + 256 * q^55 + 128 * q^59 - 32 * q^61 - 32 * q^65 - 320 * q^67 + 96 * q^69 - 512 * q^71 - 192 * q^75 + 224 * q^77 - 144 * q^81 + 160 * q^83 + 160 * q^85 + 480 * q^91 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$		0			0
$5$	1.00772	−	1.00772i	0.201544	−	0.201544i	−0.599117	−	0.800661i	$-0.704482\pi$
$5$	1.00772	−	1.00772i	0.201544	−	0.201544i	0.800661	+	0.599117i	$0.204482\pi$
$6$		0			0
$7$	−10.0236			−1.43194			−0.715969	−	0.698133i	$-0.754015\pi$
$7$	−10.0236			−1.43194			−0.715969	+	0.698133i	$0.754015\pi$
$8$		0			0
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	−2.26517	−	2.26517i	−0.205925	−	0.205925i	0.596608	−	0.802533i	$-0.296515\pi$
$11$	−2.26517	−	2.26517i	−0.205925	−	0.205925i	−0.802533	+	0.596608i	$0.796515\pi$
$12$		0			0
$13$	−6.88229	−	6.88229i	−0.529407	−	0.529407i	0.390989	−	0.920395i	$-0.372133\pi$
$13$	−6.88229	−	6.88229i	−0.529407	−	0.529407i	−0.920395	+	0.390989i	$0.872133\pi$
$14$		0			0
$15$			2.46840i			0.164560i
$16$		0			0
$17$	−22.3801			−1.31648			−0.658240	−	0.752809i	$-0.728699\pi$
$17$	−22.3801			−1.31648			−0.658240	+	0.752809i	$0.728699\pi$
$18$		0			0
$19$	16.8918	−	16.8918i	0.889041	−	0.889041i	−0.105390	−	0.994431i	$-0.533609\pi$
$19$	16.8918	−	16.8918i	0.889041	−	0.889041i	0.994431	+	0.105390i	$0.0336092\pi$
$20$		0			0
$21$	12.2763	−	12.2763i	0.584586	−	0.584586i
$22$		0			0
$23$	−33.2007			−1.44351			−0.721755	−	0.692149i	$-0.756664\pi$
$23$	−33.2007			−1.44351			−0.721755	+	0.692149i	$0.756664\pi$
$24$		0			0
$25$			22.9690i			0.918760i
$26$		0			0
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$		0			0
$29$	−24.6412	−	24.6412i	−0.849696	−	0.849696i	0.140399	−	0.990095i	$-0.455161\pi$
$29$	−24.6412	−	24.6412i	−0.849696	−	0.849696i	−0.990095	+	0.140399i	$0.955161\pi$
$30$		0			0
$31$		−	41.3761i		−	1.33471i	−0.744738	−	0.667357i	$-0.767426\pi$
$31$		−	41.3761i		−	1.33471i	0.744738	−	0.667357i	$-0.232574\pi$
$32$		0			0
$33$	5.54852			0.168137
$34$		0			0
$35$	−10.1010	+	10.1010i	−0.288599	+	0.288599i
$36$		0			0
$37$	−6.60031	+	6.60031i	−0.178387	+	0.178387i	−0.790652	−	0.612266i	$-0.790258\pi$
$37$	−6.60031	+	6.60031i	−0.178387	+	0.178387i	0.612266	+	0.790652i	$0.290258\pi$
$38$		0			0
$39$	16.8581			0.432259
$40$		0			0
$41$			47.1477i			1.14994i	0.818173	+	0.574972i	$0.194987\pi$
$41$			47.1477i			1.14994i	−0.818173	+	0.574972i	$0.805013\pi$
$42$		0			0
$43$	48.8218	+	48.8218i	1.13539	+	1.13539i	0.989266	+	0.146124i	$0.0466799\pi$
$43$	48.8218	+	48.8218i	1.13539	+	1.13539i	0.146124	+	0.989266i	$0.453320\pi$
$44$		0			0
$45$	−3.02316	−	3.02316i	−0.0671814	−	0.0671814i
$46$		0			0
$47$			45.6048i			0.970315i	0.874427	+	0.485157i	$0.161238\pi$
$47$			45.6048i			0.970315i	−0.874427	+	0.485157i	$0.838762\pi$
$48$		0			0
$49$	51.4717			1.05044
$50$		0			0
$51$	27.4100	−	27.4100i	0.537450	−	0.537450i
$52$		0			0
$53$	25.1401	−	25.1401i	0.474341	−	0.474341i	−0.428975	−	0.903316i	$-0.641125\pi$
$53$	25.1401	−	25.1401i	0.474341	−	0.474341i	0.903316	+	0.428975i	$0.141125\pi$
$54$		0			0
$55$	−4.56532			−0.0830059
$56$		0			0
$57$			41.3762i			0.725899i
$58$		0			0
$59$	−6.23974	−	6.23974i	−0.105758	−	0.105758i	0.652248	−	0.758006i	$-0.273826\pi$
$59$	−6.23974	−	6.23974i	−0.105758	−	0.105758i	−0.758006	+	0.652248i	$0.773826\pi$
$60$		0			0
$61$	35.9513	+	35.9513i	0.589366	+	0.589366i	0.937460	−	0.348093i	$-0.113171\pi$
$61$	35.9513	+	35.9513i	0.589366	+	0.589366i	−0.348093	+	0.937460i	$0.613171\pi$
$62$		0			0
$63$			30.0707i			0.477312i
$64$		0			0
$65$	−13.8709			−0.213398
$66$		0			0
$67$	−10.2045	+	10.2045i	−0.152307	+	0.152307i	−0.779147	−	0.626841i	$-0.784348\pi$
$67$	−10.2045	+	10.2045i	−0.152307	+	0.152307i	0.626841	+	0.779147i	$0.284348\pi$
$68$		0			0
$69$	40.6624	−	40.6624i	0.589310	−	0.589310i
$70$		0			0
$71$	−11.9529			−0.168350			−0.0841752	−	0.996451i	$-0.526826\pi$
$71$	−11.9529			−0.168350			−0.0841752	+	0.996451i	$0.526826\pi$
$72$		0			0
$73$		−	111.332i		−	1.52510i	−0.646929	−	0.762550i	$-0.723947\pi$
$73$		−	111.332i		−	1.52510i	0.646929	−	0.762550i	$-0.276053\pi$
$74$		0			0
$75$	−28.1312	−	28.1312i	−0.375082	−	0.375082i
$76$		0			0
$77$	22.7051	+	22.7051i	0.294871	+	0.294871i
$78$		0			0
$79$			4.46031i			0.0564596i	0.999601	+	0.0282298i	$0.00898702\pi$
$79$			4.46031i			0.0564596i	−0.999601	+	0.0282298i	$0.991013\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$		0			0
$83$	−10.1751	+	10.1751i	−0.122592	+	0.122592i	−0.765741	−	0.643149i	$-0.777627\pi$
$83$	−10.1751	+	10.1751i	−0.122592	+	0.122592i	0.643149	+	0.765741i	$0.277627\pi$
$84$		0			0
$85$	−22.5530	+	22.5530i	−0.265329	+	0.265329i
$86$		0			0
$87$	60.3583			0.693774
$88$		0			0
$89$			21.9364i			0.246476i	0.992377	+	0.123238i	$0.0393279\pi$
$89$			21.9364i			0.246476i	−0.992377	+	0.123238i	$0.960672\pi$
$90$		0			0
$91$	68.9850	+	68.9850i	0.758077	+	0.758077i
$92$		0			0
$93$	50.6752	+	50.6752i	0.544895	+	0.544895i
$94$		0			0
$95$		−	34.0444i		−	0.358362i
$96$		0			0
$97$	107.309			1.10628			0.553140	−	0.833088i	$-0.313429\pi$
$97$	107.309			1.10628			0.553140	+	0.833088i	$0.313429\pi$
$98$		0			0
$99$	−6.79552	+	6.79552i	−0.0686416	+	0.0686416i
$100$		0			0
$101$	−100.780	+	100.780i	−0.997824	+	0.997824i	−0.999998	−	0.00217389i	$-0.999308\pi$
$101$	−100.780	+	100.780i	−0.997824	+	0.997824i	0.00217389	+	0.999998i	$0.499308\pi$
$102$		0			0
$103$	−58.0562			−0.563653			−0.281826	−	0.959465i	$-0.590940\pi$
$103$	−58.0562			−0.563653			−0.281826	+	0.959465i	$0.590940\pi$
$104$		0			0
$105$		−	24.7422i		−	0.235640i
$106$		0			0
$107$	−112.747	−	112.747i	−1.05371	−	1.05371i	−0.998473	−	0.0552381i	$-0.982408\pi$
$107$	−112.747	−	112.747i	−1.05371	−	1.05371i	−0.0552381	−	0.998473i	$-0.517592\pi$
$108$		0			0
$109$	−81.1384	−	81.1384i	−0.744389	−	0.744389i	0.229030	−	0.973419i	$-0.426445\pi$
$109$	−81.1384	−	81.1384i	−0.744389	−	0.744389i	−0.973419	+	0.229030i	$0.926445\pi$
$110$		0			0
$111$		−	16.1674i		−	0.145652i
$112$		0			0
$113$	−171.844			−1.52074			−0.760371	−	0.649489i	$-0.774983\pi$
$113$	−171.844			−1.52074			−0.760371	+	0.649489i	$0.774983\pi$
$114$		0			0
$115$	−33.4571	+	33.4571i	−0.290931	+	0.290931i
$116$		0			0
$117$	−20.6469	+	20.6469i	−0.176469	+	0.176469i
$118$		0			0
$119$	224.329			1.88512
$120$		0			0
$121$		−	110.738i		−	0.915190i
$122$		0			0
$123$	−57.7439	−	57.7439i	−0.469463	−	0.469463i
$124$		0			0
$125$	48.3394	+	48.3394i	0.386715	+	0.386715i
$126$		0			0
$127$		−	36.8333i		−	0.290026i	−0.989430	−	0.145013i	$-0.953678\pi$
$127$		−	36.8333i		−	0.290026i	0.989430	−	0.145013i	$-0.0463224\pi$
$128$		0			0
$129$	−119.588			−0.927042
$130$		0			0
$131$	12.3686	−	12.3686i	0.0944170	−	0.0944170i	−0.658321	−	0.752738i	$-0.728733\pi$
$131$	12.3686	−	12.3686i	0.0944170	−	0.0944170i	0.752738	+	0.658321i	$0.228733\pi$
$132$		0			0
$133$	−169.316	+	169.316i	−1.27305	+	1.27305i
$134$		0			0
$135$	7.40521			0.0548534
$136$		0			0
$137$		−	145.679i		−	1.06335i	−0.846949	−	0.531674i	$-0.821563\pi$
$137$		−	145.679i		−	1.06335i	0.846949	−	0.531674i	$-0.178437\pi$
$138$		0			0
$139$	−82.5709	−	82.5709i	−0.594035	−	0.594035i	0.344684	−	0.938719i	$-0.387986\pi$
$139$	−82.5709	−	82.5709i	−0.594035	−	0.594035i	−0.938719	+	0.344684i	$0.887986\pi$
$140$		0			0
$141$	−55.8542	−	55.8542i	−0.396129	−	0.396129i
$142$		0			0
$143$			31.1791i			0.218036i
$144$		0			0
$145$	−49.6629			−0.342503
$146$		0			0
$147$	−63.0398	+	63.0398i	−0.428842	+	0.428842i
$148$		0			0
$149$	196.248	−	196.248i	1.31710	−	1.31710i	0.401043	−	0.916059i	$-0.368648\pi$
$149$	196.248	−	196.248i	1.31710	−	1.31710i	0.916059	−	0.401043i	$-0.131352\pi$
$150$		0			0
$151$	−64.5007			−0.427157			−0.213578	−	0.976926i	$-0.568512\pi$
$151$	−64.5007			−0.427157			−0.213578	+	0.976926i	$0.568512\pi$
$152$		0			0
$153$			67.1404i			0.438826i
$154$		0			0
$155$	−41.6956	−	41.6956i	−0.269004	−	0.269004i
$156$		0			0
$157$	54.4202	+	54.4202i	0.346625	+	0.346625i	0.858851	−	0.512226i	$-0.171179\pi$
$157$	54.4202	+	54.4202i	0.346625	+	0.346625i	−0.512226	+	0.858851i	$0.671179\pi$
$158$		0			0
$159$			61.5803i			0.387298i
$160$		0			0
$161$	332.789			2.06701
$162$		0			0
$163$	−104.803	+	104.803i	−0.642961	+	0.642961i	−0.951282	−	0.308321i	$-0.900233\pi$
$163$	−104.803	+	104.803i	−0.642961	+	0.642961i	0.308321	+	0.951282i	$0.400233\pi$
$164$		0			0
$165$	5.59136	−	5.59136i	0.0338870	−	0.0338870i
$166$		0			0
$167$	−53.3110			−0.319228			−0.159614	−	0.987180i	$-0.551025\pi$
$167$	−53.3110			−0.319228			−0.159614	+	0.987180i	$0.551025\pi$
$168$		0			0
$169$		−	74.2683i		−	0.439457i
$170$		0			0
$171$	−50.6753	−	50.6753i	−0.296347	−	0.296347i
$172$		0			0
$173$	−41.5780	−	41.5780i	−0.240335	−	0.240335i	0.576654	−	0.816989i	$-0.304358\pi$
$173$	−41.5780	−	41.5780i	−0.240335	−	0.240335i	−0.816989	+	0.576654i	$0.804358\pi$
$174$		0			0
$175$		−	230.231i		−	1.31561i
$176$		0			0
$177$	15.2842			0.0863513
$178$		0			0
$179$	−53.0709	+	53.0709i	−0.296486	+	0.296486i	−0.839636	−	0.543150i	$-0.817231\pi$
$179$	−53.0709	+	53.0709i	−0.296486	+	0.296486i	0.543150	+	0.839636i	$0.317231\pi$
$180$		0			0
$181$	−66.6042	+	66.6042i	−0.367979	+	0.367979i	−0.866740	−	0.498761i	$-0.833789\pi$
$181$	−66.6042	+	66.6042i	−0.367979	+	0.367979i	0.498761	+	0.866740i	$0.333789\pi$
$182$		0			0
$183$	−88.0625			−0.481216
$184$		0			0
$185$			13.3025i			0.0719056i
$186$		0			0
$187$	50.6949	+	50.6949i	0.271096	+	0.271096i
$188$		0			0
$189$	−36.8289	−	36.8289i	−0.194862	−	0.194862i
$190$		0			0
$191$			113.753i			0.595567i	0.954633	+	0.297784i	$0.0962474\pi$
$191$			113.753i			0.595567i	−0.954633	+	0.297784i	$0.903753\pi$
$192$		0			0
$193$	−26.5596			−0.137615			−0.0688073	−	0.997630i	$-0.521919\pi$
$193$	−26.5596			−0.137615			−0.0688073	+	0.997630i	$0.521919\pi$
$194$		0			0
$195$	16.9883	−	16.9883i	0.0871193	−	0.0871193i
$196$		0			0
$197$	51.8935	−	51.8935i	0.263419	−	0.263419i	−0.563023	−	0.826442i	$-0.690362\pi$
$197$	51.8935	−	51.8935i	0.263419	−	0.263419i	0.826442	+	0.563023i	$0.190362\pi$
$198$		0			0
$199$	136.741			0.687140			0.343570	−	0.939127i	$-0.388364\pi$
$199$	136.741			0.687140			0.343570	+	0.939127i	$0.388364\pi$
$200$		0			0
$201$		−	24.9959i		−	0.124358i
$202$		0			0
$203$	246.992	+	246.992i	1.21671	+	1.21671i
$204$		0			0
$205$	47.5118	+	47.5118i	0.231765	+	0.231765i
$206$		0			0
$207$			99.6022i			0.481170i
$208$		0			0
$209$	−76.5255			−0.366151
$210$		0			0
$211$	141.171	−	141.171i	0.669057	−	0.669057i	−0.288441	−	0.957498i	$-0.593137\pi$
$211$	141.171	−	141.171i	0.669057	−	0.669057i	0.957498	+	0.288441i	$0.0931368\pi$
$212$		0			0
$213$	14.6392	−	14.6392i	0.0687288	−	0.0687288i
$214$		0			0
$215$	98.3975			0.457663
$216$		0			0
$217$			414.736i			1.91123i
$218$		0			0
$219$	136.354	+	136.354i	0.622620	+	0.622620i
$220$		0			0
$221$	154.027	+	154.027i	0.696953	+	0.696953i
$222$		0			0
$223$			122.607i			0.549806i	0.961472	+	0.274903i	$0.0886457\pi$
$223$			122.607i			0.549806i	−0.961472	+	0.274903i	$0.911354\pi$
$224$		0			0
$225$	68.9070			0.306253
$226$		0			0
$227$	295.844	−	295.844i	1.30328	−	1.30328i	0.377112	−	0.926168i	$-0.376917\pi$
$227$	295.844	−	295.844i	1.30328	−	1.30328i	0.926168	−	0.377112i	$-0.123083\pi$
$228$		0			0
$229$	73.3817	−	73.3817i	0.320444	−	0.320444i	−0.528493	−	0.848937i	$-0.677243\pi$
$229$	73.3817	−	73.3817i	0.320444	−	0.320444i	0.848937	+	0.528493i	$0.177243\pi$
$230$		0			0
$231$	−55.6159			−0.240761
$232$		0			0
$233$			156.229i			0.670509i	0.942128	+	0.335255i	$0.108822\pi$
$233$			156.229i			0.670509i	−0.942128	+	0.335255i	$0.891178\pi$
$234$		0			0
$235$	45.9569	+	45.9569i	0.195561	+	0.195561i
$236$		0			0
$237$	−5.46274	−	5.46274i	−0.0230495	−	0.0230495i
$238$		0			0
$239$			13.1716i			0.0551113i	0.999620	+	0.0275557i	$0.00877235\pi$
$239$			13.1716i			0.0551113i	−0.999620	+	0.0275557i	$0.991228\pi$
$240$		0			0
$241$	−189.519			−0.786386			−0.393193	−	0.919456i	$-0.628630\pi$
$241$	−189.519			−0.786386			−0.393193	+	0.919456i	$0.628630\pi$
$242$		0			0
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$		0			0
$245$	51.8692	−	51.8692i	0.211711	−	0.211711i
$246$		0			0
$247$	−232.508			−0.941328
$248$		0			0
$249$		−	24.9238i		−	0.100096i
$250$		0			0
$251$	27.4434	+	27.4434i	0.109336	+	0.109336i	0.759658	−	0.650322i	$-0.225366\pi$
$251$	27.4434	+	27.4434i	0.109336	+	0.109336i	−0.650322	+	0.759658i	$0.725366\pi$
$252$		0			0
$253$	75.2053	+	75.2053i	0.297254	+	0.297254i
$254$		0			0
$255$		−	55.2432i		−	0.216640i
$256$		0			0
$257$	135.375			0.526752			0.263376	−	0.964693i	$-0.415164\pi$
$257$	135.375			0.526752			0.263376	+	0.964693i	$0.415164\pi$
$258$		0			0
$259$	66.1586	−	66.1586i	0.255438	−	0.255438i
$260$		0			0
$261$	−73.9236	+	73.9236i	−0.283232	+	0.283232i
$262$		0			0
$263$	−31.6123			−0.120199			−0.0600994	−	0.998192i	$-0.519142\pi$
$263$	−31.6123			−0.120199			−0.0600994	+	0.998192i	$0.519142\pi$
$264$		0			0
$265$		−	50.6684i		−	0.191201i
$266$		0			0
$267$	−26.8665	−	26.8665i	−0.100624	−	0.100624i
$268$		0			0
$269$	−194.213	−	194.213i	−0.721981	−	0.721981i	0.247028	−	0.969008i	$-0.420546\pi$
$269$	−194.213	−	194.213i	−0.721981	−	0.721981i	−0.969008	+	0.247028i	$0.920546\pi$
$270$		0			0
$271$			291.647i			1.07619i	0.842884	+	0.538095i	$0.180856\pi$
$271$			291.647i			1.07619i	−0.842884	+	0.538095i	$0.819144\pi$
$272$		0			0
$273$	−168.978			−0.618967
$274$		0			0
$275$	52.0287	−	52.0287i	0.189195	−	0.189195i
$276$		0			0
$277$	305.166	−	305.166i	1.10168	−	1.10168i	0.107475	−	0.994208i	$-0.465723\pi$
$277$	305.166	−	305.166i	1.10168	−	1.10168i	0.994208	−	0.107475i	$-0.0342765\pi$
$278$		0			0
$279$	−124.128			−0.444905
$280$		0			0
$281$			211.861i			0.753955i	0.926222	+	0.376978i	$0.123037\pi$
$281$			211.861i			0.753955i	−0.926222	+	0.376978i	$0.876963\pi$
$282$		0			0
$283$	−105.325	−	105.325i	−0.372175	−	0.372175i	0.496094	−	0.868269i	$-0.334767\pi$
$283$	−105.325	−	105.325i	−0.372175	−	0.372175i	−0.868269	+	0.496094i	$0.834767\pi$
$284$		0			0
$285$	41.6957	+	41.6957i	0.146301	+	0.146301i
$286$		0			0
$287$		−	472.588i		−	1.64665i
$288$		0			0
$289$	211.871			0.733117
$290$		0			0
$291$	−131.426	+	131.426i	−0.451637	+	0.451637i
$292$		0			0
$293$	−171.289	+	171.289i	−0.584603	+	0.584603i	−0.936165	−	0.351562i	$-0.885651\pi$
$293$	−171.289	+	171.289i	−0.584603	+	0.584603i	0.351562	+	0.936165i	$0.385651\pi$
$294$		0			0
$295$	−12.5758			−0.0426300
$296$		0			0
$297$		−	16.6455i		−	0.0560456i
$298$		0			0
$299$	228.497	+	228.497i	0.764204	+	0.764204i
$300$		0			0
$301$	−489.368	−	489.368i	−1.62581	−	1.62581i
$302$		0			0
$303$		−	246.860i		−	0.814720i
$304$		0			0
$305$	72.4579			0.237567
$306$		0			0
$307$	27.1124	−	27.1124i	0.0883140	−	0.0883140i	−0.661570	−	0.749884i	$-0.730109\pi$
$307$	27.1124	−	27.1124i	0.0883140	−	0.0883140i	0.749884	+	0.661570i	$0.230109\pi$
$308$		0			0
$309$	71.1041	−	71.1041i	0.230110	−	0.230110i
$310$		0			0
$311$	−371.124			−1.19333			−0.596663	−	0.802492i	$-0.703507\pi$
$311$	−371.124			−1.19333			−0.596663	+	0.802492i	$0.703507\pi$
$312$		0			0
$313$			374.501i			1.19649i	0.801313	+	0.598245i	$0.204135\pi$
$313$			374.501i			1.19649i	−0.801313	+	0.598245i	$0.795865\pi$
$314$		0			0
$315$	30.3029	+	30.3029i	0.0961996	+	0.0961996i
$316$		0			0
$317$	−48.5840	−	48.5840i	−0.153262	−	0.153262i	0.626311	−	0.779573i	$-0.284564\pi$
$317$	−48.5840	−	48.5840i	−0.153262	−	0.153262i	−0.779573	+	0.626311i	$0.784564\pi$
$318$		0			0
$319$			111.633i			0.349947i
$320$		0			0
$321$	276.173			0.860352
$322$		0			0
$323$	−378.040	+	378.040i	−1.17040	+	1.17040i
$324$		0			0
$325$	158.079	−	158.079i	0.486398	−	0.486398i
$326$		0			0
$327$	198.748			0.607791
$328$		0			0
$329$		−	457.122i		−	1.38943i
$330$		0			0
$331$	1.88883	+	1.88883i	0.00570644	+	0.00570644i	0.709954	−	0.704248i	$-0.248716\pi$
$331$	1.88883	+	1.88883i	0.00570644	+	0.00570644i	−0.704248	+	0.709954i	$0.748716\pi$
$332$		0			0
$333$	19.8009	+	19.8009i	0.0594622	+	0.0594622i
$334$		0			0
$335$			20.5667i			0.0613931i
$336$		0			0
$337$	−386.980			−1.14831			−0.574154	−	0.818747i	$-0.694669\pi$
$337$	−386.980			−1.14831			−0.574154	+	0.818747i	$0.694669\pi$
$338$		0			0
$339$	210.465	−	210.465i	0.620840	−	0.620840i
$340$		0			0
$341$	−93.7240	+	93.7240i	−0.274851	+	0.274851i
$342$		0			0
$343$	−24.7757			−0.0722325
$344$		0			0
$345$		−	81.9528i		−	0.237544i
$346$		0			0
$347$	−441.887	−	441.887i	−1.27345	−	1.27345i	−0.944266	−	0.329183i	$-0.893227\pi$
$347$	−441.887	−	441.887i	−1.27345	−	1.27345i	−0.329183	−	0.944266i	$-0.606773\pi$
$348$		0			0
$349$	119.382	+	119.382i	0.342068	+	0.342068i	0.857144	−	0.515076i	$-0.172236\pi$
$349$	119.382	+	119.382i	0.342068	+	0.342068i	−0.515076	+	0.857144i	$0.672236\pi$
$350$		0			0
$351$		−	50.5743i		−	0.144086i
$352$		0			0
$353$	−515.642			−1.46074			−0.730371	−	0.683050i	$-0.760653\pi$
$353$	−515.642			−1.46074			−0.730371	+	0.683050i	$0.760653\pi$
$354$		0			0
$355$	−12.0452	+	12.0452i	−0.0339301	+	0.0339301i
$356$		0			0
$357$	−274.745	+	274.745i	−0.769595	+	0.769595i
$358$		0			0
$359$	−428.264			−1.19294			−0.596468	−	0.802637i	$-0.703430\pi$
$359$	−428.264			−1.19294			−0.596468	+	0.802637i	$0.703430\pi$
$360$		0			0
$361$		−	209.664i		−	0.580786i
$362$		0			0
$363$	135.626	+	135.626i	0.373625	+	0.373625i
$364$		0			0
$365$	−112.192	−	112.192i	−0.307375	−	0.307375i
$366$		0			0
$367$			219.482i			0.598043i	0.954246	+	0.299021i	$0.0966602\pi$
$367$			219.482i			0.598043i	−0.954246	+	0.299021i	$0.903340\pi$
$368$		0			0
$369$	141.443			0.383315
$370$		0			0
$371$	−251.993	+	251.993i	−0.679226	+	0.679226i
$372$		0			0
$373$	425.005	−	425.005i	1.13942	−	1.13942i	0.150870	−	0.988554i	$-0.451793\pi$
$373$	425.005	−	425.005i	1.13942	−	1.13942i	0.988554	−	0.150870i	$-0.0482075\pi$
$374$		0			0
$375$	−118.407			−0.315752
$376$		0			0
$377$			339.175i			0.899669i
$378$		0			0
$379$	−365.916	−	365.916i	−0.965476	−	0.965476i	0.0339473	−	0.999424i	$-0.489192\pi$
$379$	−365.916	−	365.916i	−0.965476	−	0.965476i	−0.999424	+	0.0339473i	$0.989192\pi$
$380$		0			0
$381$	45.1114	+	45.1114i	0.118403	+	0.118403i
$382$		0			0
$383$			213.276i			0.556857i	0.960457	+	0.278428i	$0.0898135\pi$
$383$			213.276i			0.556857i	−0.960457	+	0.278428i	$0.910187\pi$
$384$		0			0
$385$	45.7608			0.118859
$386$		0			0
$387$	146.465	−	146.465i	0.378464	−	0.378464i
$388$		0			0
$389$	−210.798	+	210.798i	−0.541898	+	0.541898i	−0.924085	−	0.382187i	$-0.875171\pi$
$389$	−210.798	+	210.798i	−0.541898	+	0.541898i	0.382187	+	0.924085i	$0.375171\pi$
$390$		0			0
$391$	743.037			1.90035
$392$		0			0
$393$			30.2968i			0.0770912i
$394$		0			0
$395$	4.49475	+	4.49475i	0.0113791	+	0.0113791i
$396$		0			0
$397$	392.907	+	392.907i	0.989690	+	0.989690i	0.999947	−	0.0102579i	$-0.00326524\pi$
$397$	392.907	+	392.907i	0.989690	+	0.989690i	−0.0102579	+	0.999947i	$0.503265\pi$
$398$		0			0
$399$		−	414.737i		−	1.03944i
$400$		0			0
$401$	29.3290			0.0731396			0.0365698	−	0.999331i	$-0.488357\pi$
$401$	29.3290			0.0731396			0.0365698	+	0.999331i	$0.488357\pi$
$402$		0			0
$403$	−284.762	+	284.762i	−0.706606	+	0.706606i
$404$		0			0
$405$	−9.06949	+	9.06949i	−0.0223938	+	0.0223938i
$406$		0			0
$407$	29.9017			0.0734684
$408$		0			0
$409$		−	601.115i		−	1.46972i	−0.678219	−	0.734860i	$-0.737248\pi$
$409$		−	601.115i		−	1.46972i	0.678219	−	0.734860i	$-0.262752\pi$
$410$		0			0
$411$	178.419	+	178.419i	0.434110	+	0.434110i
$412$		0			0
$413$	62.5444	+	62.5444i	0.151439	+	0.151439i
$414$		0			0
$415$			20.5073i			0.0494153i
$416$		0			0
$417$	202.257			0.485028
$418$		0			0
$419$	518.885	−	518.885i	1.23839	−	1.23839i	0.277729	−	0.960659i	$-0.410418\pi$
$419$	518.885	−	518.885i	1.23839	−	1.23839i	0.960659	−	0.277729i	$-0.0895819\pi$
$420$		0			0
$421$	−411.213	+	411.213i	−0.976754	+	0.976754i	−0.999736	−	0.0229817i	$-0.992684\pi$
$421$	−411.213	+	411.213i	−0.976754	+	0.976754i	0.0229817	+	0.999736i	$0.492684\pi$
$422$		0			0
$423$	136.814			0.323438
$424$		0			0
$425$		−	514.049i		−	1.20953i
$426$		0			0
$427$	−360.360	−	360.360i	−0.843936	−	0.843936i
$428$		0			0
$429$	−38.1865	−	38.1865i	−0.0890128	−	0.0890128i
$430$		0			0
$431$			41.1083i			0.0953789i	0.998862	+	0.0476895i	$0.0151858\pi$
$431$			41.1083i			0.0953789i	−0.998862	+	0.0476895i	$0.984814\pi$
$432$		0			0
$433$	−351.682			−0.812199			−0.406100	−	0.913829i	$-0.633111\pi$
$433$	−351.682			−0.812199			−0.406100	+	0.913829i	$0.633111\pi$
$434$		0			0
$435$	60.8244	−	60.8244i	0.139826	−	0.139826i
$436$		0			0
$437$	−560.819	+	560.819i	−1.28334	+	1.28334i
$438$		0			0
$439$	775.613			1.76677			0.883386	−	0.468646i	$-0.155258\pi$
$439$	775.613			1.76677			0.883386	+	0.468646i	$0.155258\pi$
$440$		0			0
$441$		−	154.415i		−	0.350148i
$442$		0			0
$443$	241.372	+	241.372i	0.544858	+	0.544858i	0.924949	−	0.380091i	$-0.124107\pi$
$443$	241.372	+	241.372i	0.544858	+	0.544858i	−0.380091	+	0.924949i	$0.624107\pi$
$444$		0			0
$445$	22.1058	+	22.1058i	0.0496759	+	0.0496759i
$446$		0			0
$447$			480.708i			1.07541i
$448$		0			0
$449$	266.360			0.593228			0.296614	−	0.954997i	$-0.404142\pi$
$449$	266.360			0.593228			0.296614	+	0.954997i	$0.404142\pi$
$450$		0			0
$451$	106.798	−	106.798i	0.236802	−	0.236802i
$452$		0			0
$453$	78.9969	−	78.9969i	0.174386	−	0.174386i
$454$		0			0
$455$	139.035			0.305572
$456$		0			0
$457$			515.244i			1.12745i	0.825963	+	0.563725i	$0.190632\pi$
$457$			515.244i			1.12745i	−0.825963	+	0.563725i	$0.809368\pi$
$458$		0			0
$459$	−82.2299	−	82.2299i	−0.179150	−	0.179150i
$460$		0			0
$461$	5.67717	+	5.67717i	0.0123149	+	0.0123149i	0.713237	−	0.700923i	$-0.247228\pi$
$461$	5.67717	+	5.67717i	0.0123149	+	0.0123149i	−0.700923	+	0.713237i	$0.747228\pi$
$462$		0			0
$463$		−	464.510i		−	1.00326i	−0.865082	−	0.501631i	$-0.832733\pi$
$463$		−	464.510i		−	1.00326i	0.865082	−	0.501631i	$-0.167267\pi$
$464$		0			0
$465$	102.133			0.219641
$466$		0			0
$467$	−495.985	+	495.985i	−1.06207	+	1.06207i	−0.0641248	+	0.997942i	$0.520426\pi$
$467$	−495.985	+	495.985i	−1.06207	+	1.06207i	−0.997942	+	0.0641248i	$0.979574\pi$
$468$		0			0
$469$	102.286	−	102.286i	0.218094	−	0.218094i
$470$		0			0
$471$	−133.302			−0.283018
$472$		0			0
$473$		−	221.180i		−	0.467610i
$474$		0			0
$475$	387.987	+	387.987i	0.816815	+	0.816815i
$476$		0			0
$477$	−75.4202	−	75.4202i	−0.158114	−	0.158114i
$478$		0			0
$479$		−	378.802i		−	0.790818i	−0.918505	−	0.395409i	$-0.870603\pi$
$479$		−	378.802i		−	0.790818i	0.918505	−	0.395409i	$-0.129397\pi$
$480$		0			0
$481$	90.8504			0.188878
$482$		0			0
$483$	−407.582	+	407.582i	−0.843855	+	0.843855i
$484$		0			0
$485$	108.138	−	108.138i	0.222964	−	0.222964i
$486$		0			0
$487$	−147.446			−0.302764			−0.151382	−	0.988475i	$-0.548372\pi$
$487$	−147.446			−0.302764			−0.151382	+	0.988475i	$0.548372\pi$
$488$		0			0
$489$		−	256.713i		−	0.524976i
$490$		0			0
$491$	−109.547	−	109.547i	−0.223110	−	0.223110i	0.586697	−	0.809807i	$-0.300428\pi$
$491$	−109.547	−	109.547i	−0.223110	−	0.223110i	−0.809807	+	0.586697i	$0.800428\pi$
$492$		0			0
$493$	551.473	+	551.473i	1.11861	+	1.11861i
$494$		0			0
$495$			13.6960i			0.0276686i
$496$		0			0
$497$	119.810			0.241067
$498$		0			0
$499$	360.523	−	360.523i	0.722491	−	0.722491i	−0.246621	−	0.969112i	$-0.579320\pi$
$499$	360.523	−	360.523i	0.722491	−	0.722491i	0.969112	+	0.246621i	$0.0793202\pi$
$500$		0			0
$501$	65.2924	−	65.2924i	0.130324	−	0.130324i
$502$		0			0
$503$	927.420			1.84378			0.921889	−	0.387454i	$-0.126645\pi$
$503$	927.420			1.84378			0.921889	+	0.387454i	$0.126645\pi$
$504$		0			0
$505$			203.117i			0.402211i
$506$		0			0
$507$	90.9597	+	90.9597i	0.179408	+	0.179408i
$508$		0			0
$509$	677.931	+	677.931i	1.33189	+	1.33189i	0.903680	+	0.428208i	$0.140855\pi$
$509$	677.931	+	677.931i	1.33189	+	1.33189i	0.428208	+	0.903680i	$0.359145\pi$
$510$		0			0
$511$			1115.95i			2.18385i
$512$		0			0
$513$	124.129			0.241966
$514$		0			0
$515$	−58.5045	+	58.5045i	−0.113601	+	0.113601i
$516$		0			0
$517$	103.303	−	103.303i	0.199812	−	0.199812i
$518$		0			0
$519$	101.845			0.196233
$520$		0			0
$521$			143.173i			0.274804i	0.990515	+	0.137402i	$0.0438753\pi$
$521$			143.173i			0.274804i	−0.990515	+	0.137402i	$0.956125\pi$
$522$		0			0
$523$	−226.187	−	226.187i	−0.432481	−	0.432481i	0.456991	−	0.889471i	$-0.348927\pi$
$523$	−226.187	−	226.187i	−0.432481	−	0.432481i	−0.889471	+	0.456991i	$0.848927\pi$
$524$		0			0
$525$	281.974	+	281.974i	0.537094	+	0.537094i
$526$		0			0
$527$			926.004i			1.75712i
$528$		0			0
$529$	573.288			1.08372
$530$		0			0
$531$	−18.7192	+	18.7192i	−0.0352528	+	0.0352528i
$532$		0			0
$533$	324.484	−	324.484i	0.608788	−	0.608788i
$534$		0			0
$535$	−227.235			−0.424739
$536$		0			0
$537$		−	129.997i		−	0.242080i
$538$		0			0
$539$	−116.592	−	116.592i	−0.216312	−	0.216312i
$540$		0			0
$541$	−156.708	−	156.708i	−0.289663	−	0.289663i	0.547284	−	0.836947i	$-0.315662\pi$
$541$	−156.708	−	156.708i	−0.289663	−	0.289663i	−0.836947	+	0.547284i	$0.815662\pi$
$542$		0			0
$543$		−	163.146i		−	0.300454i
$544$		0			0
$545$	−163.530			−0.300055
$546$		0			0
$547$	−247.357	+	247.357i	−0.452207	+	0.452207i	−0.896086	−	0.443880i	$-0.853602\pi$
$547$	−247.357	+	247.357i	−0.452207	+	0.452207i	0.443880	+	0.896086i	$0.353602\pi$
$548$		0			0
$549$	107.854	−	107.854i	0.196455	−	0.196455i
$550$		0			0
$551$	−832.466			−1.51083
$552$		0			0
$553$		−	44.7082i		−	0.0808466i
$554$		0			0
$555$	−16.2922	−	16.2922i	−0.0293553	−	0.0293553i
$556$		0			0
$557$	−661.193	−	661.193i	−1.18706	−	1.18706i	−0.977876	−	0.209184i	$-0.932919\pi$
$557$	−661.193	−	661.193i	−1.18706	−	1.18706i	−0.209184	−	0.977876i	$-0.567081\pi$
$558$		0			0
$559$		−	672.011i		−	1.20217i
$560$		0			0
$561$	−124.177			−0.221349
$562$		0			0
$563$	−246.685	+	246.685i	−0.438162	+	0.438162i	−0.891393	−	0.453231i	$-0.850271\pi$
$563$	−246.685	+	246.685i	−0.438162	+	0.438162i	0.453231	+	0.891393i	$0.350271\pi$
$564$		0			0
$565$	−173.171	+	173.171i	−0.306497	+	0.306497i
$566$		0			0
$567$	90.2120			0.159104
$568$		0			0
$569$			243.567i			0.428061i	0.976827	+	0.214030i	$0.0686592\pi$
$569$			243.567i			0.428061i	−0.976827	+	0.214030i	$0.931341\pi$
$570$		0			0
$571$	−59.9229	−	59.9229i	−0.104944	−	0.104944i	0.652685	−	0.757629i	$-0.273642\pi$
$571$	−59.9229	−	59.9229i	−0.104944	−	0.104944i	−0.757629	+	0.652685i	$0.773642\pi$
$572$		0			0
$573$	−139.319	−	139.319i	−0.243139	−	0.243139i
$574$		0			0
$575$		−	762.587i		−	1.32624i
$576$		0			0
$577$	136.609			0.236757			0.118378	−	0.992969i	$-0.462230\pi$
$577$	136.609			0.236757			0.118378	+	0.992969i	$0.462230\pi$
$578$		0			0
$579$	32.5287	−	32.5287i	0.0561809	−	0.0561809i
$580$		0			0
$581$	101.991	−	101.991i	0.175543	−	0.175543i
$582$		0			0
$583$	−113.893			−0.195357
$584$		0			0
$585$			41.6126i			0.0711326i
$586$		0			0
$587$	331.817	+	331.817i	0.565276	+	0.565276i	0.930801	−	0.365525i	$-0.119111\pi$
$587$	331.817	+	331.817i	0.565276	+	0.565276i	−0.365525	+	0.930801i	$0.619111\pi$
$588$		0			0
$589$	−698.916	−	698.916i	−1.18661	−	1.18661i
$590$		0			0
$591$			127.113i			0.215081i
$592$		0			0
$593$	131.285			0.221391			0.110695	−	0.993854i	$-0.464692\pi$
$593$	131.285			0.221391			0.110695	+	0.993854i	$0.464692\pi$
$594$		0			0
$595$	226.061	−	226.061i	0.379934	−	0.379934i
$596$		0			0
$597$	−167.473	+	167.473i	−0.280524	+	0.280524i
$598$		0			0
$599$	136.119			0.227243			0.113621	−	0.993524i	$-0.463755\pi$
$599$	136.119			0.227243			0.113621	+	0.993524i	$0.463755\pi$
$600$		0			0
$601$			498.566i			0.829561i	0.909922	+	0.414780i	$0.136142\pi$
$601$			498.566i			0.829561i	−0.909922	+	0.414780i	$0.863858\pi$
$602$		0			0
$603$	30.6136	+	30.6136i	0.0507689	+	0.0507689i
$604$		0			0
$605$	−111.593	−	111.593i	−0.184451	−	0.184451i
$606$		0			0
$607$		−	568.740i		−	0.936969i	−0.883472	−	0.468484i	$-0.844800\pi$
$607$		−	568.740i		−	0.936969i	0.883472	−	0.468484i	$-0.155200\pi$
$608$		0			0
$609$	−605.005			−0.993441
$610$		0			0
$611$	313.865	−	313.865i	0.513691	−	0.513691i
$612$		0			0
$613$	−168.441	+	168.441i	−0.274782	+	0.274782i	−0.831022	−	0.556240i	$-0.812244\pi$
$613$	−168.441	+	168.441i	−0.274782	+	0.274782i	0.556240	+	0.831022i	$0.312244\pi$
$614$		0			0
$615$	−116.380			−0.189235
$616$		0			0
$617$		−	599.157i		−	0.971081i	−0.874214	−	0.485541i	$-0.838623\pi$
$617$		−	599.157i		−	0.971081i	0.874214	−	0.485541i	$-0.161377\pi$
$618$		0			0
$619$	−126.719	−	126.719i	−0.204715	−	0.204715i	0.597301	−	0.802017i	$-0.296240\pi$
$619$	−126.719	−	126.719i	−0.204715	−	0.204715i	−0.802017	+	0.597301i	$0.796240\pi$
$620$		0			0
$621$	−121.987	−	121.987i	−0.196437	−	0.196437i
$622$		0			0
$623$		−	219.881i		−	0.352939i
$624$		0			0
$625$	−476.800			−0.762879
$626$		0			0
$627$	93.7242	−	93.7242i	0.149480	−	0.149480i
$628$		0			0
$629$	147.716	−	147.716i	0.234842	−	0.234842i
$630$		0			0
$631$	−668.283			−1.05909			−0.529543	−	0.848283i	$-0.677637\pi$
$631$	−668.283			−1.05909			−0.529543	+	0.848283i	$0.677637\pi$
$632$		0			0
$633$			345.797i			0.546283i
$634$		0			0
$635$	−37.1177	−	37.1177i	−0.0584531	−	0.0584531i
$636$		0			0
$637$	−354.243	−	354.243i	−0.556112	−	0.556112i
$638$		0			0
$639$			35.8586i			0.0561168i
$640$		0			0
$641$	484.574			0.755966			0.377983	−	0.925813i	$-0.376618\pi$
$641$	484.574			0.755966			0.377983	+	0.925813i	$0.376618\pi$
$642$		0			0
$643$	−75.2980	+	75.2980i	−0.117104	+	0.117104i	−0.763230	−	0.646126i	$-0.776388\pi$
$643$	−75.2980	+	75.2980i	−0.117104	+	0.117104i	0.646126	+	0.763230i	$0.276388\pi$
$644$		0			0
$645$	−120.512	+	120.512i	−0.186840	+	0.186840i
$646$		0			0
$647$	582.307			0.900011			0.450006	−	0.893026i	$-0.351422\pi$
$647$	582.307			0.900011			0.450006	+	0.893026i	$0.351422\pi$
$648$		0			0
$649$			28.2682i			0.0435565i
$650$		0			0
$651$	−507.946	−	507.946i	−0.780255	−	0.780255i
$652$		0			0
$653$	457.453	+	457.453i	0.700541	+	0.700541i	0.964527	−	0.263986i	$-0.0850371\pi$
$653$	457.453	+	457.453i	0.700541	+	0.700541i	−0.263986	+	0.964527i	$0.585037\pi$
$654$		0			0
$655$		−	24.9283i		−	0.0380584i
$656$		0			0
$657$	−333.997			−0.508367
$658$		0			0
$659$	430.079	−	430.079i	0.652623	−	0.652623i	−0.301001	−	0.953624i	$-0.597321\pi$
$659$	430.079	−	430.079i	0.652623	−	0.652623i	0.953624	+	0.301001i	$0.0973207\pi$
$660$		0			0
$661$	−513.622	+	513.622i	−0.777038	+	0.777038i	−0.979326	−	0.202288i	$-0.935162\pi$
$661$	−513.622	+	513.622i	−0.777038	+	0.777038i	0.202288	+	0.979326i	$0.435162\pi$
$662$		0			0
$663$	−377.287			−0.569060
$664$		0			0
$665$			341.246i			0.513152i
$666$		0			0
$667$	818.105	+	818.105i	1.22654	+	1.22654i
$668$		0			0
$669$	−150.162	−	150.162i	−0.224457	−	0.224457i
$670$		0			0
$671$		−	162.872i		−	0.242730i
$672$		0			0
$673$	−1112.68			−1.65332			−0.826659	−	0.562703i	$-0.809761\pi$
$673$	−1112.68			−1.65332			−0.826659	+	0.562703i	$0.809761\pi$
$674$		0			0
$675$	−84.3935	+	84.3935i	−0.125027	+	0.125027i
$676$		0			0
$677$	633.271	−	633.271i	0.935408	−	0.935408i	−0.0626291	−	0.998037i	$-0.519949\pi$
$677$	633.271	−	633.271i	0.935408	−	0.935408i	0.998037	+	0.0626291i	$0.0199485\pi$
$678$		0			0
$679$	−1075.62			−1.58412
$680$		0			0
$681$			724.668i			1.06412i
$682$		0			0
$683$	429.651	+	429.651i	0.629065	+	0.629065i	0.947833	−	0.318768i	$-0.103269\pi$
$683$	429.651	+	429.651i	0.629065	+	0.629065i	−0.318768	+	0.947833i	$0.603269\pi$
$684$		0			0
$685$	−146.803	−	146.803i	−0.214312	−	0.214312i
$686$		0			0
$687$			179.748i			0.261642i
$688$		0			0
$689$	−346.042			−0.502239
$690$		0			0
$691$	151.617	−	151.617i	0.219417	−	0.219417i	−0.588836	−	0.808253i	$-0.700414\pi$
$691$	151.617	−	151.617i	0.219417	−	0.219417i	0.808253	+	0.588836i	$0.200414\pi$
$692$		0			0
$693$	68.1153	−	68.1153i	0.0982904	−	0.0982904i
$694$		0			0
$695$	−166.417			−0.239449
$696$		0			0
$697$		−	1055.17i		−	1.51388i
$698$		0			0
$699$	−191.340	−	191.340i	−0.273734	−	0.273734i
$700$		0			0
$701$	−920.704	−	920.704i	−1.31341	−	1.31341i	−0.918882	−	0.394533i	$-0.870906\pi$
$701$	−920.704	−	920.704i	−1.31341	−	1.31341i	−0.394533	−	0.918882i	$-0.629094\pi$
$702$		0			0
$703$			222.982i			0.317186i
$704$		0			0
$705$	−112.571			−0.159675
$706$		0			0
$707$	1010.18	−	1010.18i	1.42882	−	1.42882i
$708$		0			0
$709$	405.348	−	405.348i	0.571718	−	0.571718i	−0.360890	−	0.932608i	$-0.617527\pi$
$709$	405.348	−	405.348i	0.571718	−	0.571718i	0.932608	+	0.360890i	$0.117527\pi$
$710$		0			0
$711$	13.3809			0.0188199
$712$		0			0
$713$			1373.72i			1.92667i
$714$		0			0
$715$	31.4199	+	31.4199i	0.0439439	+	0.0439439i
$716$		0			0
$717$	−16.1319	−	16.1319i	−0.0224991	−	0.0224991i
$718$		0			0
$719$			880.704i			1.22490i	0.790509	+	0.612450i	$0.209816\pi$
$719$			880.704i			1.22490i	−0.790509	+	0.612450i	$0.790184\pi$
$720$		0			0
$721$	581.930			0.807115
$722$		0			0
$723$	232.112	−	232.112i	0.321041	−	0.321041i
$724$		0			0
$725$	565.983	−	565.983i	0.780667	−	0.780667i
$726$		0			0
$727$	−1000.46			−1.37615			−0.688077	−	0.725637i	$-0.741545\pi$
$727$	−1000.46			−1.37615			−0.688077	+	0.725637i	$0.741545\pi$
$728$		0			0
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	−1092.64	−	1092.64i	−1.49472	−	1.49472i
$732$		0			0
$733$	540.306	+	540.306i	0.737116	+	0.737116i	0.972019	−	0.234903i	$-0.0754772\pi$
$733$	540.306	+	540.306i	0.737116	+	0.737116i	−0.234903	+	0.972019i	$0.575477\pi$
$734$		0			0
$735$			127.053i			0.172861i
$736$		0			0
$737$	46.2301			0.0627274
$738$		0			0
$739$	−893.726	+	893.726i	−1.20937	+	1.20937i	−0.238142	+	0.971230i	$0.576538\pi$
$739$	−893.726	+	893.726i	−1.20937	+	1.20937i	−0.971230	+	0.238142i	$0.923462\pi$
$740$		0			0
$741$	284.763	−	284.763i	0.384296	−	0.384296i
$742$		0			0
$743$	−1295.75			−1.74394			−0.871969	−	0.489561i	$-0.837157\pi$
$743$	−1295.75			−1.74394			−0.871969	+	0.489561i	$0.837157\pi$
$744$		0			0
$745$		−	395.527i		−	0.530909i
$746$		0			0
$747$	30.5253	+	30.5253i	0.0408639	+	0.0408639i
$748$		0			0
$749$	1130.13	+	1130.13i	1.50885	+	1.50885i
$750$		0			0
$751$		−	229.818i		−	0.306016i	−0.988225	−	0.153008i	$-0.951104\pi$
$751$		−	229.818i		−	0.306016i	0.988225	−	0.153008i	$-0.0488961\pi$
$752$		0			0
$753$	−67.2223			−0.0892726
$754$		0			0
$755$	−64.9987	+	64.9987i	−0.0860910	+	0.0860910i
$756$		0			0
$757$	−373.678	+	373.678i	−0.493630	+	0.493630i	−0.909448	−	0.415818i	$-0.863495\pi$
$757$	−373.678	+	373.678i	−0.493630	+	0.493630i	0.415818	+	0.909448i	$0.363495\pi$
$758$		0			0
$759$	−184.215			−0.242707
$760$		0			0
$761$		−	384.012i		−	0.504615i	−0.967647	−	0.252307i	$-0.918811\pi$
$761$		−	384.012i		−	0.504615i	0.967647	−	0.252307i	$-0.0811894\pi$
$762$		0			0
$763$	813.296	+	813.296i	1.06592	+	1.06592i
$764$		0			0
$765$	67.6589	+	67.6589i	0.0884429	+	0.0884429i
$766$		0			0
$767$			85.8874i			0.111978i
$768$		0			0
$769$	865.026			1.12487			0.562436	−	0.826841i	$-0.309864\pi$
$769$	865.026			1.12487			0.562436	+	0.826841i	$0.309864\pi$
$770$		0			0
$771$	−165.800	+	165.800i	−0.215045	+	0.215045i
$772$		0			0
$773$	−1.78859	+	1.78859i	−0.00231383	+	0.00231383i	−0.708263	−	0.705949i	$-0.750521\pi$
$773$	−1.78859	+	1.78859i	−0.00231383	+	0.00231383i	0.705949	+	0.708263i	$0.250521\pi$
$774$		0			0
$775$	950.368			1.22628
$776$		0			0
$777$			162.055i			0.208565i
$778$		0			0
$779$	796.409	+	796.409i	1.02235	+	1.02235i
$780$		0			0
$781$	27.0753	+	27.0753i	0.0346675	+	0.0346675i
$782$		0			0
$783$		−	181.075i		−	0.231258i
$784$		0			0
$785$	109.681			0.139721
$786$		0			0
$787$	−143.702	+	143.702i	−0.182595	+	0.182595i	−0.792485	−	0.609891i	$-0.791213\pi$
$787$	−143.702	+	143.702i	−0.182595	+	0.182595i	0.609891	+	0.792485i	$0.291213\pi$
$788$		0			0
$789$	38.7170	−	38.7170i	0.0490710	−	0.0490710i
$790$		0			0
$791$	1722.49			2.17761
$792$		0			0
$793$		−	494.855i		−	0.624029i
$794$		0			0
$795$	62.0558	+	62.0558i	0.0780577	+	0.0780577i
$796$		0			0
$797$	−477.929	−	477.929i	−0.599660	−	0.599660i	0.340562	−	0.940222i	$-0.389383\pi$
$797$	−477.929	−	477.929i	−0.599660	−	0.599660i	−0.940222	+	0.340562i	$0.889383\pi$
$798$		0			0
$799$		−	1020.64i		−	1.27740i
$800$		0			0
$801$	65.8092			0.0821588
$802$		0			0
$803$	−252.187	+	252.187i	−0.314056	+	0.314056i
$804$		0			0
$805$	335.359	−	335.359i	0.416595	−	0.416595i
$806$		0			0
$807$	475.722			0.589495
$808$		0			0
$809$			1524.96i			1.88500i	0.334212	+	0.942498i	$0.391530\pi$
$809$			1524.96i			1.88500i	−0.334212	+	0.942498i	$0.608470\pi$
$810$		0			0
$811$	576.427	+	576.427i	0.710761	+	0.710761i	0.966694	−	0.255933i	$-0.0823828\pi$
$811$	576.427	+	576.427i	0.710761	+	0.710761i	−0.255933	+	0.966694i	$0.582383\pi$
$812$		0			0
$813$	−357.194	−	357.194i	−0.439353	−	0.439353i
$814$		0			0
$815$			211.224i			0.259170i
$816$		0			0
$817$	1649.37			2.01882
$818$		0			0
$819$	206.955	−	206.955i	0.252692	−	0.252692i
$820$		0			0
$821$	−386.324	+	386.324i	−0.470552	+	0.470552i	−0.902093	−	0.431541i	$-0.857970\pi$
$821$	−386.324	+	386.324i	−0.470552	+	0.470552i	0.431541	+	0.902093i	$0.357970\pi$
$822$		0			0
$823$	−377.870			−0.459138			−0.229569	−	0.973292i	$-0.573732\pi$
$823$	−377.870			−0.459138			−0.229569	+	0.973292i	$0.573732\pi$
$824$		0			0
$825$			127.444i			0.154477i
$826$		0			0
$827$	−140.900	−	140.900i	−0.170375	−	0.170375i	0.616769	−	0.787144i	$-0.288441\pi$
$827$	−140.900	−	140.900i	−0.170375	−	0.170375i	−0.787144	+	0.616769i	$0.788441\pi$
$828$		0			0
$829$	−522.203	−	522.203i	−0.629919	−	0.629919i	0.318128	−	0.948048i	$-0.396946\pi$
$829$	−522.203	−	522.203i	−0.629919	−	0.629919i	−0.948048	+	0.318128i	$0.896946\pi$
$830$		0			0
$831$			747.501i			0.899520i
$832$		0			0
$833$	−1151.95			−1.38289
$834$		0			0
$835$	−53.7226	+	53.7226i	−0.0643385	+	0.0643385i
$836$		0			0
$837$	152.026	−	152.026i	0.181632	−	0.181632i
$838$		0			0
$839$	442.133			0.526976			0.263488	−	0.964663i	$-0.415127\pi$
$839$	442.133			0.526976			0.263488	+	0.964663i	$0.415127\pi$
$840$		0			0
$841$			373.376i			0.443967i
$842$		0			0
$843$	−259.476	−	259.476i	−0.307801	−	0.307801i
$844$		0			0
$845$	−74.8417	−	74.8417i	−0.0885701	−	0.0885701i
$846$		0			0
$847$			1109.99i			1.31049i
$848$		0			0
$849$	257.994			0.303879
$850$		0			0
$851$	219.135	−	219.135i	0.257503	−	0.257503i
$852$		0			0
$853$	−494.617	+	494.617i	−0.579856	+	0.579856i	−0.934863	−	0.355007i	$-0.884478\pi$
$853$	−494.617	+	494.617i	−0.579856	+	0.579856i	0.355007	+	0.934863i	$0.384478\pi$
$854$		0			0
$855$	−102.133			−0.119454
$856$		0			0
$857$		−	1676.75i		−	1.95654i	−0.207340	−	0.978269i	$-0.566481\pi$
$857$		−	1676.75i		−	1.95654i	0.207340	−	0.978269i	$-0.433519\pi$
$858$		0			0
$859$	−228.948	−	228.948i	−0.266529	−	0.266529i	0.561171	−	0.827700i	$-0.310351\pi$
$859$	−228.948	−	228.948i	−0.266529	−	0.266529i	−0.827700	+	0.561171i	$0.810351\pi$
$860$		0			0
$861$	578.800	+	578.800i	0.672241	+	0.672241i
$862$		0			0
$863$		−	1603.23i		−	1.85774i	−0.370401	−	0.928872i	$-0.620780\pi$
$863$		−	1603.23i		−	1.85774i	0.370401	−	0.928872i	$-0.379220\pi$
$864$		0			0
$865$	−83.7981			−0.0968764
$866$		0			0
$867$	−259.488	+	259.488i	−0.299294	+	0.299294i
$868$		0			0
$869$	10.1034	−	10.1034i	0.0116264	−	0.0116264i
$870$		0			0
$871$	140.461			0.161264
$872$		0			0
$873$		−	321.927i		−	0.368760i
$874$		0			0
$875$	−484.533	−	484.533i	−0.553752	−	0.553752i
$876$		0			0
$877$	289.017	+	289.017i	0.329552	+	0.329552i	0.852416	−	0.522864i	$-0.175136\pi$
$877$	289.017	+	289.017i	0.329552	+	0.329552i	−0.522864	+	0.852416i	$0.675136\pi$
$878$		0			0
$879$		−	419.570i		−	0.477326i
$880$		0			0
$881$	937.450			1.06408			0.532038	−	0.846721i	$-0.321426\pi$
$881$	937.450			1.06408			0.532038	+	0.846721i	$0.321426\pi$
$882$		0			0
$883$	485.966	−	485.966i	0.550357	−	0.550357i	−0.376187	−	0.926544i	$-0.622765\pi$
$883$	485.966	−	485.966i	0.550357	−	0.550357i	0.926544	+	0.376187i	$0.122765\pi$
$884$		0			0
$885$	15.4022	−	15.4022i	0.0174036	−	0.0174036i
$886$		0			0
$887$	534.193			0.602247			0.301123	−	0.953585i	$-0.402638\pi$
$887$	534.193			0.602247			0.301123	+	0.953585i	$0.402638\pi$
$888$		0			0
$889$			369.201i			0.415299i
$890$		0			0
$891$	20.3865	+	20.3865i	0.0228805	+	0.0228805i
$892$		0			0
$893$	770.346	+	770.346i	0.862649	+	0.862649i
$894$		0			0
$895$			106.961i			0.119510i
$896$		0			0
$897$	−559.701			−0.623970
$898$		0			0
$899$	−1019.56	+	1019.56i	−1.13410	+	1.13410i
$900$		0			0
$901$	−562.638	+	562.638i	−0.624460	+	0.624460i
$902$		0			0
$903$	1198.70			1.32747
$904$		0			0
$905$			134.237i			0.148328i
$906$		0			0
$907$	−368.669	−	368.669i	−0.406471	−	0.406471i	0.474035	−	0.880506i	$-0.342797\pi$
$907$	−368.669	−	368.669i	−0.406471	−	0.406471i	−0.880506	+	0.474035i	$0.842797\pi$
$908$		0			0
$909$	302.341	+	302.341i	0.332608	+	0.332608i
$910$		0			0
$911$			1592.43i			1.74800i	0.485927	+	0.873999i	$0.338482\pi$
$911$			1592.43i			1.74800i	−0.485927	+	0.873999i	$0.661518\pi$
$912$		0			0
$913$	46.0967			0.0504893
$914$		0			0
$915$	−88.7424	+	88.7424i	−0.0969863	+	0.0969863i
$916$		0			0
$917$	−123.978	+	123.978i	−0.135199	+	0.135199i
$918$		0			0
$919$	403.500			0.439064			0.219532	−	0.975605i	$-0.429547\pi$
$919$	403.500			0.439064			0.219532	+	0.975605i	$0.429547\pi$
$920$		0			0
$921$			66.4116i			0.0721081i
$922$		0			0
$923$	82.2632	+	82.2632i	0.0891258	+	0.0891258i
$924$		0			0
$925$	−151.602	−	151.602i	−0.163894	−	0.163894i
$926$		0			0
$927$			174.169i			0.187884i
$928$		0			0
$929$	348.546			0.375184			0.187592	−	0.982247i	$-0.439932\pi$
$929$	348.546			0.375184			0.187592	+	0.982247i	$0.439932\pi$
$930$		0			0
$931$	869.449	−	869.449i	0.933887	−	0.933887i
$932$		0			0
$933$	454.533	−	454.533i	0.487173	−	0.487173i
$934$		0			0
$935$	102.173			0.109276
$936$		0			0
$937$			248.875i			0.265609i	0.991142	+	0.132804i	$0.0423982\pi$
$937$			248.875i			0.265609i	−0.991142	+	0.132804i	$0.957602\pi$
$938$		0			0
$939$	−458.669	−	458.669i	−0.488465	−	0.488465i
$940$		0			0
$941$	884.188	+	884.188i	0.939626	+	0.939626i	0.998278	−	0.0586528i	$-0.0186805\pi$
$941$	884.188	+	884.188i	0.939626	+	0.939626i	−0.0586528	+	0.998278i	$0.518681\pi$
$942$		0			0
$943$		−	1565.34i		−	1.65996i
$944$		0			0
$945$	−74.2266			−0.0785466
$946$		0			0
$947$	−462.279	+	462.279i	−0.488151	+	0.488151i	−0.907722	−	0.419571i	$-0.862180\pi$
$947$	−462.279	+	462.279i	−0.488151	+	0.488151i	0.419571	+	0.907722i	$0.362180\pi$
$948$		0			0
$949$	−766.221	+	766.221i	−0.807398	+	0.807398i
$950$		0			0
$951$	119.006			0.125138
$952$		0			0
$953$		−	707.656i		−	0.742556i	−0.928522	−	0.371278i	$-0.878920\pi$
$953$		−	707.656i		−	0.742556i	0.928522	−	0.371278i	$-0.121080\pi$
$954$		0			0
$955$	114.632	+	114.632i	0.120033	+	0.120033i
$956$		0			0
$957$	−136.722	−	136.722i	−0.142865	−	0.142865i
$958$		0			0
$959$			1460.22i			1.52265i
$960$		0			0
$961$	−750.983			−0.781460
$962$		0			0
$963$	−338.241	+	338.241i	−0.351237	+	0.351237i
$964$		0			0
$965$	−26.7647	+	26.7647i	−0.0277354	+	0.0277354i
$966$		0			0
$967$	841.240			0.869949			0.434974	−	0.900443i	$-0.356757\pi$
$967$	841.240			0.869949			0.434974	+	0.900443i	$0.356757\pi$
$968$		0			0
$969$		−	926.006i		−	0.955630i
$970$		0			0
$971$	−308.415	−	308.415i	−0.317626	−	0.317626i	0.530229	−	0.847855i	$-0.322106\pi$
$971$	−308.415	−	308.415i	−0.317626	−	0.317626i	−0.847855	+	0.530229i	$0.822106\pi$
$972$		0			0
$973$	827.654	+	827.654i	0.850621	+	0.850621i
$974$		0			0
$975$			387.213i			0.397142i
$976$		0			0
$977$	−1316.85			−1.34786			−0.673928	−	0.738797i	$-0.735394\pi$
$977$	−1316.85			−1.34786			−0.673928	+	0.738797i	$0.735394\pi$
$978$		0			0
$979$	49.6897	−	49.6897i	0.0507556	−	0.0507556i
$980$		0			0
$981$	−243.415	+	243.415i	−0.248130	+	0.248130i
$982$		0			0
$983$	−504.538			−0.513263			−0.256632	−	0.966509i	$-0.582613\pi$
$983$	−504.538			−0.513263			−0.256632	+	0.966509i	$0.582613\pi$
$984$		0			0
$985$		−	104.588i		−	0.106181i
$986$		0			0
$987$	559.858	+	559.858i	0.567232	+	0.567232i
$988$		0			0
$989$	−1620.92	−	1620.92i	−1.63895	−	1.63895i
$990$		0			0
$991$		−	436.650i		−	0.440616i	−0.975430	−	0.220308i	$-0.929294\pi$
$991$		−	436.650i		−	0.440616i	0.975430	−	0.220308i	$-0.0707062\pi$
$992$		0			0
$993$	−4.62667			−0.00465929
$994$		0			0
$995$	137.797	−	137.797i	0.138489	−	0.138489i
$996$		0			0
$997$	−383.801	+	383.801i	−0.384956	+	0.384956i	−0.872884	−	0.487928i	$-0.837753\pi$
$997$	−383.801	+	383.801i	−0.384956	+	0.384956i	0.487928	+	0.872884i	$0.337753\pi$
$998$		0			0
$999$	−48.5021			−0.0485507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.3.l.a.175.3		16
3.2	odd	2		576.3.m.c.559.4		16
4.3	odd	2		48.3.l.a.19.3	✓	16
8.3	odd	2		384.3.l.a.223.2		16
8.5	even	2		384.3.l.b.223.6		16
12.11	even	2		144.3.m.c.19.6		16
16.3	odd	4		384.3.l.b.31.6		16
16.5	even	4		48.3.l.a.43.3	yes	16
16.11	odd	4	inner	192.3.l.a.79.3		16
16.13	even	4		384.3.l.a.31.2		16
24.5	odd	2		1152.3.m.c.991.5		16
24.11	even	2		1152.3.m.f.991.5		16
48.5	odd	4		144.3.m.c.91.6		16
48.11	even	4		576.3.m.c.271.4		16
48.29	odd	4		1152.3.m.f.415.5		16
48.35	even	4		1152.3.m.c.415.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.l.a.19.3	✓	16	4.3	odd	2
48.3.l.a.43.3	yes	16	16.5	even	4
144.3.m.c.19.6		16	12.11	even	2
144.3.m.c.91.6		16	48.5	odd	4
192.3.l.a.79.3		16	16.11	odd	4	inner
192.3.l.a.175.3		16	1.1	even	1	trivial
384.3.l.a.31.2		16	16.13	even	4
384.3.l.a.223.2		16	8.3	odd	2
384.3.l.b.31.6		16	16.3	odd	4
384.3.l.b.223.6		16	8.5	even	2
576.3.m.c.271.4		16	48.11	even	4
576.3.m.c.559.4		16	3.2	odd	2
1152.3.m.c.415.5		16	48.35	even	4
1152.3.m.c.991.5		16	24.5	odd	2
1152.3.m.f.415.5		16	48.29	odd	4
1152.3.m.f.991.5		16	24.11	even	2

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	192.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 1.22474i) q^{3} +(1.00772 - 1.00772i) q^{5} -10.0236 q^{7} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.22474 + 1.22474i) q^{3} +(1.00772 - 1.00772i) q^{5} -10.0236 q^{7} -3.00000i q^{9} +(-2.26517 - 2.26517i) q^{11} +(-6.88229 - 6.88229i) q^{13} +2.46840i q^{15} -22.3801 q^{17} +(16.8918 - 16.8918i) q^{19} +(12.2763 - 12.2763i) q^{21} -33.2007 q^{23} +22.9690i q^{25} +(3.67423 + 3.67423i) q^{27} +(-24.6412 - 24.6412i) q^{29} -41.3761i q^{31} +5.54852 q^{33} +(-10.1010 + 10.1010i) q^{35} +(-6.60031 + 6.60031i) q^{37} +16.8581 q^{39} +47.1477i q^{41} +(48.8218 + 48.8218i) q^{43} +(-3.02316 - 3.02316i) q^{45} +45.6048i q^{47} +51.4717 q^{49} +(27.4100 - 27.4100i) q^{51} +(25.1401 - 25.1401i) q^{53} -4.56532 q^{55} +41.3762i q^{57} +(-6.23974 - 6.23974i) q^{59} +(35.9513 + 35.9513i) q^{61} +30.0707i q^{63} -13.8709 q^{65} +(-10.2045 + 10.2045i) q^{67} +(40.6624 - 40.6624i) q^{69} -11.9529 q^{71} -111.332i q^{73} +(-28.1312 - 28.1312i) q^{75} +(22.7051 + 22.7051i) q^{77} +4.46031i q^{79} -9.00000 q^{81} +(-10.1751 + 10.1751i) q^{83} +(-22.5530 + 22.5530i) q^{85} +60.3583 q^{87} +21.9364i q^{89} +(68.9850 + 68.9850i) q^{91} +(50.6752 + 50.6752i) q^{93} -34.0444i q^{95} +107.309 q^{97} +(-6.79552 + 6.79552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 32 q^{11} + 32 q^{19} + 128 q^{23} + 32 q^{29} - 96 q^{35} - 96 q^{37} - 160 q^{43} + 112 q^{49} + 96 q^{51} - 160 q^{53} + 256 q^{55} + 128 q^{59} - 32 q^{61} - 32 q^{65} - 320 q^{67} + 96 q^{69} - 512 q^{71} - 192 q^{75} + 224 q^{77} - 144 q^{81} + 160 q^{83} + 160 q^{85} + 480 q^{91} - 96 q^{99}+O(q^{100}) \) 16 * q - 32 * q^11 + 32 * q^19 + 128 * q^23 + 32 * q^29 - 96 * q^35 - 96 * q^37 - 160 * q^43 + 112 * q^49 + 96 * q^51 - 160 * q^53 + 256 * q^55 + 128 * q^59 - 32 * q^61 - 32 * q^65 - 320 * q^67 + 96 * q^69 - 512 * q^71 - 192 * q^75 + 224 * q^77 - 144 * q^81 + 160 * q^83 + 160 * q^85 + 480 * q^91 - 96 * q^99

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