LMFDB - Embedded newform 1800.2.m.c.899.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1800,2,Mod(899,1800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1800, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1800.899");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1800.m (of order $2$, degree $1$, 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:	$14.3730723638$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			899.5
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1800.899
Dual form			1800.2.m.c.899.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} -3.46410 q^{7} -2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} -3.46410 q^{7} -2.82843 q^{8} -2.82843i q^{11} -3.46410 q^{13} +(-2.44949 + 4.24264i) q^{14} +(-2.00000 + 3.46410i) q^{16} +1.41421 q^{17} +4.00000 q^{19} +(-3.46410 - 2.00000i) q^{22} +4.89898i q^{23} +(-2.44949 + 4.24264i) q^{26} +(3.46410 + 6.00000i) q^{28} -2.44949 q^{29} +3.46410i q^{31} +(2.82843 + 4.89898i) q^{32} +(1.00000 - 1.73205i) q^{34} +(2.82843 - 4.89898i) q^{38} +1.41421i q^{41} +8.00000i q^{43} +(-4.89898 + 2.82843i) q^{44} +(6.00000 + 3.46410i) q^{46} +4.89898i q^{47} +5.00000 q^{49} +(3.46410 + 6.00000i) q^{52} +7.34847i q^{53} +9.79796 q^{56} +(-1.73205 + 3.00000i) q^{58} +11.3137i q^{59} -13.8564i q^{61} +(4.24264 + 2.44949i) q^{62} +8.00000 q^{64} +4.00000i q^{67} +(-1.41421 - 2.44949i) q^{68} -14.6969 q^{71} -4.00000i q^{73} +(-4.00000 - 6.92820i) q^{76} +9.79796i q^{77} +3.46410i q^{79} +(1.73205 + 1.00000i) q^{82} -14.1421 q^{83} +(9.79796 + 5.65685i) q^{86} +8.00000i q^{88} +7.07107i q^{89} +12.0000 q^{91} +(8.48528 - 4.89898i) q^{92} +(6.00000 + 3.46410i) q^{94} -8.00000i q^{97} +(3.53553 - 6.12372i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4}+O(q^{10}) $ 8 * q - 8 * q^4	$ 8 q - 8 q^{4} - 16 q^{16} + 32 q^{19} + 8 q^{34} + 48 q^{46} + 40 q^{49} + 64 q^{64} - 32 q^{76} + 96 q^{91} + 48 q^{94}+O(q^{100}) $ 8 * q - 8 * q^4 - 16 * q^16 + 32 * q^19 + 8 * q^34 + 48 * q^46 + 40 * q^49 + 64 * q^64 - 32 * q^76 + 96 * q^91 + 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1001$	$1351$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	0.707107	−	1.22474i	0.500000	−	0.866025i
$2$	0.707107	−	1.22474i	0.500000	−	0.866025i
$3$		0			0
$3$		0			0
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−3.46410			−1.30931			−0.654654	−	0.755929i	$-0.727186\pi$
$7$	−3.46410			−1.30931			−0.654654	+	0.755929i	$0.727186\pi$
$8$	−2.82843			−1.00000
$9$		0			0
$10$		0			0
$11$		−	2.82843i		−	0.852803i	−0.904534	−	0.426401i	$-0.859781\pi$
$11$		−	2.82843i		−	0.852803i	0.904534	−	0.426401i	$-0.140219\pi$
$12$		0			0
$13$	−3.46410			−0.960769			−0.480384	−	0.877058i	$-0.659503\pi$
$13$	−3.46410			−0.960769			−0.480384	+	0.877058i	$0.659503\pi$
$14$	−2.44949	+	4.24264i	−0.654654	+	1.13389i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	1.41421			0.342997			0.171499	−	0.985184i	$-0.445139\pi$
$17$	1.41421			0.342997			0.171499	+	0.985184i	$0.445139\pi$
$18$		0			0
$19$	4.00000			0.917663			0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000			0.917663			0.458831	+	0.888523i	$0.348268\pi$
$20$		0			0
$21$		0			0
$22$	−3.46410	−	2.00000i	−0.738549	−	0.426401i
$23$			4.89898i			1.02151i	0.859727	+	0.510754i	$0.170634\pi$
$23$			4.89898i			1.02151i	−0.859727	+	0.510754i	$0.829366\pi$
$24$		0			0
$25$		0			0
$26$	−2.44949	+	4.24264i	−0.480384	+	0.832050i
$27$		0			0
$28$	3.46410	+	6.00000i	0.654654	+	1.13389i
$29$	−2.44949			−0.454859			−0.227429	−	0.973795i	$-0.573032\pi$
$29$	−2.44949			−0.454859			−0.227429	+	0.973795i	$0.573032\pi$
$30$		0			0
$31$			3.46410i			0.622171i	0.950382	+	0.311086i	$0.100693\pi$
$31$			3.46410i			0.622171i	−0.950382	+	0.311086i	$0.899307\pi$
$32$	2.82843	+	4.89898i	0.500000	+	0.866025i
$33$		0			0
$34$	1.00000	−	1.73205i	0.171499	−	0.297044i
$35$		0			0
$36$		0			0
$37$		0			0			−	1.00000i	$-0.5\pi$
$37$		0			0				1.00000i	$0.5\pi$
$38$	2.82843	−	4.89898i	0.458831	−	0.794719i
$39$		0			0
$40$		0			0
$41$			1.41421i			0.220863i	0.993884	+	0.110432i	$0.0352233\pi$
$41$			1.41421i			0.220863i	−0.993884	+	0.110432i	$0.964777\pi$
$42$		0			0
$43$			8.00000i			1.21999i	0.792406	+	0.609994i	$0.208828\pi$
$43$			8.00000i			1.21999i	−0.792406	+	0.609994i	$0.791172\pi$
$44$	−4.89898	+	2.82843i	−0.738549	+	0.426401i
$45$		0			0
$46$	6.00000	+	3.46410i	0.884652	+	0.510754i
$47$			4.89898i			0.714590i	0.933992	+	0.357295i	$0.116301\pi$
$47$			4.89898i			0.714590i	−0.933992	+	0.357295i	$0.883699\pi$
$48$		0			0
$49$	5.00000			0.714286
$50$		0			0
$51$		0			0
$52$	3.46410	+	6.00000i	0.480384	+	0.832050i
$53$			7.34847i			1.00939i	0.863298	+	0.504695i	$0.168395\pi$
$53$			7.34847i			1.00939i	−0.863298	+	0.504695i	$0.831605\pi$
$54$		0			0
$55$		0			0
$56$	9.79796			1.30931
$57$		0			0
$58$	−1.73205	+	3.00000i	−0.227429	+	0.393919i
$59$			11.3137i			1.47292i	0.676481	+	0.736460i	$0.263504\pi$
$59$			11.3137i			1.47292i	−0.676481	+	0.736460i	$0.736496\pi$
$60$		0			0
$61$		−	13.8564i		−	1.77413i	−0.461644	−	0.887066i	$-0.652740\pi$
$61$		−	13.8564i		−	1.77413i	0.461644	−	0.887066i	$-0.347260\pi$
$62$	4.24264	+	2.44949i	0.538816	+	0.311086i
$63$		0			0
$64$	8.00000			1.00000
$65$		0			0
$66$		0			0
$67$			4.00000i			0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$			4.00000i			0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$	−1.41421	−	2.44949i	−0.171499	−	0.297044i
$69$		0			0
$70$		0			0
$71$	−14.6969			−1.74421			−0.872103	−	0.489323i	$-0.837244\pi$
$71$	−14.6969			−1.74421			−0.872103	+	0.489323i	$0.837244\pi$
$72$		0			0
$73$		−	4.00000i		−	0.468165i	−0.972217	−	0.234082i	$-0.924791\pi$
$73$		−	4.00000i		−	0.468165i	0.972217	−	0.234082i	$-0.0752085\pi$
$74$		0			0
$75$		0			0
$76$	−4.00000	−	6.92820i	−0.458831	−	0.794719i
$77$			9.79796i			1.11658i
$78$		0			0
$79$			3.46410i			0.389742i	0.980829	+	0.194871i	$0.0624288\pi$
$79$			3.46410i			0.389742i	−0.980829	+	0.194871i	$0.937571\pi$
$80$		0			0
$81$		0			0
$82$	1.73205	+	1.00000i	0.191273	+	0.110432i
$83$	−14.1421			−1.55230			−0.776151	−	0.630548i	$-0.782830\pi$
$83$	−14.1421			−1.55230			−0.776151	+	0.630548i	$0.782830\pi$
$84$		0			0
$85$		0			0
$86$	9.79796	+	5.65685i	1.05654	+	0.609994i
$87$		0			0
$88$			8.00000i			0.852803i
$89$			7.07107i			0.749532i	0.927119	+	0.374766i	$0.122277\pi$
$89$			7.07107i			0.749532i	−0.927119	+	0.374766i	$0.877723\pi$
$90$		0			0
$91$	12.0000			1.25794
$92$	8.48528	−	4.89898i	0.884652	−	0.510754i
$93$		0			0
$94$	6.00000	+	3.46410i	0.618853	+	0.357295i
$95$		0			0
$96$		0			0
$97$		−	8.00000i		−	0.812277i	−0.913812	−	0.406138i	$-0.866875\pi$
$97$		−	8.00000i		−	0.812277i	0.913812	−	0.406138i	$-0.133125\pi$
$98$	3.53553	−	6.12372i	0.357143	−	0.618590i
$99$		0			0
$100$		0			0
$101$	2.44949			0.243733			0.121867	−	0.992546i	$-0.461112\pi$
$101$	2.44949			0.243733			0.121867	+	0.992546i	$0.461112\pi$
$102$		0			0
$103$	−3.46410			−0.341328			−0.170664	−	0.985329i	$-0.554591\pi$
$103$	−3.46410			−0.341328			−0.170664	+	0.985329i	$0.554591\pi$
$104$	9.79796			0.960769
$105$		0			0
$106$	9.00000	+	5.19615i	0.874157	+	0.504695i
$107$	−11.3137			−1.09374			−0.546869	−	0.837218i	$-0.684180\pi$
$107$	−11.3137			−1.09374			−0.546869	+	0.837218i	$0.684180\pi$
$108$		0			0
$109$		−	10.3923i		−	0.995402i	−0.867349	−	0.497701i	$-0.834178\pi$
$109$		−	10.3923i		−	0.995402i	0.867349	−	0.497701i	$-0.165822\pi$
$110$		0			0
$111$		0			0
$112$	6.92820	−	12.0000i	0.654654	−	1.13389i
$113$	−18.3848			−1.72949			−0.864747	−	0.502208i	$-0.832521\pi$
$113$	−18.3848			−1.72949			−0.864747	+	0.502208i	$0.832521\pi$
$114$		0			0
$115$		0			0
$116$	2.44949	+	4.24264i	0.227429	+	0.393919i
$117$		0			0
$118$	13.8564	+	8.00000i	1.27559	+	0.736460i
$119$	−4.89898			−0.449089
$120$		0			0
$121$	3.00000			0.272727
$122$	−16.9706	−	9.79796i	−1.53644	−	0.887066i
$123$		0			0
$124$	6.00000	−	3.46410i	0.538816	−	0.311086i
$125$		0			0
$126$		0			0
$127$	−10.3923			−0.922168			−0.461084	−	0.887357i	$-0.652539\pi$
$127$	−10.3923			−0.922168			−0.461084	+	0.887357i	$0.652539\pi$
$128$	5.65685	−	9.79796i	0.500000	−	0.866025i
$129$		0			0
$130$		0			0
$131$			5.65685i			0.494242i	0.968985	+	0.247121i	$0.0794845\pi$
$131$			5.65685i			0.494242i	−0.968985	+	0.247121i	$0.920516\pi$
$132$		0			0
$133$	−13.8564			−1.20150
$134$	4.89898	+	2.82843i	0.423207	+	0.244339i
$135$		0			0
$136$	−4.00000			−0.342997
$137$	9.89949			0.845771			0.422885	−	0.906183i	$-0.361017\pi$
$137$	9.89949			0.845771			0.422885	+	0.906183i	$0.361017\pi$
$138$		0			0
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$		0			0
$142$	−10.3923	+	18.0000i	−0.872103	+	1.51053i
$143$			9.79796i			0.819346i
$144$		0			0
$145$		0			0
$146$	−4.89898	−	2.82843i	−0.405442	−	0.234082i
$147$		0			0
$148$		0			0
$149$	17.1464			1.40469			0.702345	−	0.711837i	$-0.252136\pi$
$149$	17.1464			1.40469			0.702345	+	0.711837i	$0.252136\pi$
$150$		0			0
$151$		−	3.46410i		−	0.281905i	−0.990016	−	0.140952i	$-0.954984\pi$
$151$		−	3.46410i		−	0.281905i	0.990016	−	0.140952i	$-0.0450164\pi$
$152$	−11.3137			−0.917663
$153$		0			0
$154$	12.0000	+	6.92820i	0.966988	+	0.558291i
$155$		0			0
$156$		0			0
$157$	13.8564			1.10586			0.552931	−	0.833227i	$-0.313509\pi$
$157$	13.8564			1.10586			0.552931	+	0.833227i	$0.313509\pi$
$158$	4.24264	+	2.44949i	0.337526	+	0.194871i
$159$		0			0
$160$		0			0
$161$		−	16.9706i		−	1.33747i
$162$		0			0
$163$		−	16.0000i		−	1.25322i	−0.779334	−	0.626608i	$-0.784443\pi$
$163$		−	16.0000i		−	1.25322i	0.779334	−	0.626608i	$-0.215557\pi$
$164$	2.44949	−	1.41421i	0.191273	−	0.110432i
$165$		0			0
$166$	−10.0000	+	17.3205i	−0.776151	+	1.34433i
$167$		−	19.5959i		−	1.51638i	−0.652035	−	0.758189i	$-0.726085\pi$
$167$		−	19.5959i		−	1.51638i	0.652035	−	0.758189i	$-0.273915\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$		0			0
$171$		0			0
$172$	13.8564	−	8.00000i	1.05654	−	0.609994i
$173$			2.44949i			0.186231i	0.995655	+	0.0931156i	$0.0296826\pi$
$173$			2.44949i			0.186231i	−0.995655	+	0.0931156i	$0.970317\pi$
$174$		0			0
$175$		0			0
$176$	9.79796	+	5.65685i	0.738549	+	0.426401i
$177$		0			0
$178$	8.66025	+	5.00000i	0.649113	+	0.374766i
$179$		−	5.65685i		−	0.422813i	−0.977398	−	0.211407i	$-0.932196\pi$
$179$		−	5.65685i		−	0.422813i	0.977398	−	0.211407i	$-0.0678044\pi$
$180$		0			0
$181$		−	10.3923i		−	0.772454i	−0.922404	−	0.386227i	$-0.873778\pi$
$181$		−	10.3923i		−	0.772454i	0.922404	−	0.386227i	$-0.126222\pi$
$182$	8.48528	−	14.6969i	0.628971	−	1.08941i
$183$		0			0
$184$		−	13.8564i		−	1.02151i
$185$		0			0
$186$		0			0
$187$		−	4.00000i		−	0.292509i
$188$	8.48528	−	4.89898i	0.618853	−	0.357295i
$189$		0			0
$190$		0			0
$191$	−19.5959			−1.41791			−0.708955	−	0.705253i	$-0.750833\pi$
$191$	−19.5959			−1.41791			−0.708955	+	0.705253i	$0.750833\pi$
$192$		0			0
$193$			14.0000i			1.00774i	0.863779	+	0.503871i	$0.168091\pi$
$193$			14.0000i			1.00774i	−0.863779	+	0.503871i	$0.831909\pi$
$194$	−9.79796	−	5.65685i	−0.703452	−	0.406138i
$195$		0			0
$196$	−5.00000	−	8.66025i	−0.357143	−	0.618590i
$197$			7.34847i			0.523557i	0.965128	+	0.261778i	$0.0843089\pi$
$197$			7.34847i			0.523557i	−0.965128	+	0.261778i	$0.915691\pi$
$198$		0			0
$199$			10.3923i			0.736691i	0.929689	+	0.368345i	$0.120076\pi$
$199$			10.3923i			0.736691i	−0.929689	+	0.368345i	$0.879924\pi$
$200$		0			0
$201$		0			0
$202$	1.73205	−	3.00000i	0.121867	−	0.211079i
$203$	8.48528			0.595550
$204$		0			0
$205$		0			0
$206$	−2.44949	+	4.24264i	−0.170664	+	0.295599i
$207$		0			0
$208$	6.92820	−	12.0000i	0.480384	−	0.832050i
$209$		−	11.3137i		−	0.782586i
$210$		0			0
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$	12.7279	−	7.34847i	0.874157	−	0.504695i
$213$		0			0
$214$	−8.00000	+	13.8564i	−0.546869	+	0.947204i
$215$		0			0
$216$		0			0
$217$		−	12.0000i		−	0.814613i
$218$	−12.7279	−	7.34847i	−0.862044	−	0.497701i
$219$		0			0
$220$		0			0
$221$	−4.89898			−0.329541
$222$		0			0
$223$	−17.3205			−1.15987			−0.579934	−	0.814664i	$-0.696921\pi$
$223$	−17.3205			−1.15987			−0.579934	+	0.814664i	$0.696921\pi$
$224$	−9.79796	−	16.9706i	−0.654654	−	1.13389i
$225$		0			0
$226$	−13.0000	+	22.5167i	−0.864747	+	1.49779i
$227$	−2.82843			−0.187729			−0.0938647	−	0.995585i	$-0.529922\pi$
$227$	−2.82843			−0.187729			−0.0938647	+	0.995585i	$0.529922\pi$
$228$		0			0
$229$			17.3205i			1.14457i	0.820054	+	0.572286i	$0.193943\pi$
$229$			17.3205i			1.14457i	−0.820054	+	0.572286i	$0.806057\pi$
$230$		0			0
$231$		0			0
$232$	6.92820			0.454859
$233$	−1.41421			−0.0926482			−0.0463241	−	0.998926i	$-0.514751\pi$
$233$	−1.41421			−0.0926482			−0.0463241	+	0.998926i	$0.514751\pi$
$234$		0			0
$235$		0			0
$236$	19.5959	−	11.3137i	1.27559	−	0.736460i
$237$		0			0
$238$	−3.46410	+	6.00000i	−0.224544	+	0.388922i
$239$	9.79796			0.633777			0.316889	−	0.948463i	$-0.397362\pi$
$239$	9.79796			0.633777			0.316889	+	0.948463i	$0.397362\pi$
$240$		0			0
$241$	−28.0000			−1.80364			−0.901819	−	0.432113i	$-0.857768\pi$
$241$	−28.0000			−1.80364			−0.901819	+	0.432113i	$0.857768\pi$
$242$	2.12132	−	3.67423i	0.136364	−	0.236189i
$243$		0			0
$244$	−24.0000	+	13.8564i	−1.53644	+	0.887066i
$245$		0			0
$246$		0			0
$247$	−13.8564			−0.881662
$248$		−	9.79796i		−	0.622171i
$249$		0			0
$250$		0			0
$251$			14.1421i			0.892644i	0.894873	+	0.446322i	$0.147266\pi$
$251$			14.1421i			0.892644i	−0.894873	+	0.446322i	$0.852734\pi$
$252$		0			0
$253$	13.8564			0.871145
$254$	−7.34847	+	12.7279i	−0.461084	+	0.798621i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−24.0416			−1.49968			−0.749838	−	0.661622i	$-0.769869\pi$
$257$	−24.0416			−1.49968			−0.749838	+	0.661622i	$0.769869\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	6.92820	+	4.00000i	0.428026	+	0.247121i
$263$			9.79796i			0.604168i	0.953281	+	0.302084i	$0.0976823\pi$
$263$			9.79796i			0.604168i	−0.953281	+	0.302084i	$0.902318\pi$
$264$		0			0
$265$		0			0
$266$	−9.79796	+	16.9706i	−0.600751	+	1.04053i
$267$		0			0
$268$	6.92820	−	4.00000i	0.423207	−	0.244339i
$269$	−7.34847			−0.448044			−0.224022	−	0.974584i	$-0.571919\pi$
$269$	−7.34847			−0.448044			−0.224022	+	0.974584i	$0.571919\pi$
$270$		0			0
$271$			31.1769i			1.89386i	0.321436	+	0.946931i	$0.395835\pi$
$271$			31.1769i			1.89386i	−0.321436	+	0.946931i	$0.604165\pi$
$272$	−2.82843	+	4.89898i	−0.171499	+	0.297044i
$273$		0			0
$274$	7.00000	−	12.1244i	0.422885	−	0.732459i
$275$		0			0
$276$		0			0
$277$	17.3205			1.04069			0.520344	−	0.853957i	$-0.325804\pi$
$277$	17.3205			1.04069			0.520344	+	0.853957i	$0.325804\pi$
$278$	2.82843	−	4.89898i	0.169638	−	0.293821i
$279$		0			0
$280$		0			0
$281$		−	24.0416i		−	1.43420i	−0.696969	−	0.717102i	$-0.745468\pi$
$281$		−	24.0416i		−	1.43420i	0.696969	−	0.717102i	$-0.254532\pi$
$282$		0			0
$283$		−	16.0000i		−	0.951101i	−0.879688	−	0.475551i	$-0.842249\pi$
$283$		−	16.0000i		−	0.951101i	0.879688	−	0.475551i	$-0.157751\pi$
$284$	14.6969	+	25.4558i	0.872103	+	1.51053i
$285$		0			0
$286$	12.0000	+	6.92820i	0.709575	+	0.409673i
$287$		−	4.89898i		−	0.289178i
$288$		0			0
$289$	−15.0000			−0.882353
$290$		0			0
$291$		0			0
$292$	−6.92820	+	4.00000i	−0.405442	+	0.234082i
$293$			26.9444i			1.57411i	0.616884	+	0.787054i	$0.288395\pi$
$293$			26.9444i			1.57411i	−0.616884	+	0.787054i	$0.711605\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$	12.1244	−	21.0000i	0.702345	−	1.21650i
$299$		−	16.9706i		−	0.981433i
$300$		0			0
$301$		−	27.7128i		−	1.59734i
$302$	−4.24264	−	2.44949i	−0.244137	−	0.140952i
$303$		0			0
$304$	−8.00000	+	13.8564i	−0.458831	+	0.794719i
$305$		0			0
$306$		0			0
$307$			4.00000i			0.228292i	0.993464	+	0.114146i	$0.0364132\pi$
$307$			4.00000i			0.228292i	−0.993464	+	0.114146i	$0.963587\pi$
$308$	16.9706	−	9.79796i	0.966988	−	0.558291i
$309$		0			0
$310$		0			0
$311$	−9.79796			−0.555591			−0.277796	−	0.960640i	$-0.589604\pi$
$311$	−9.79796			−0.555591			−0.277796	+	0.960640i	$0.589604\pi$
$312$		0			0
$313$		−	10.0000i		−	0.565233i	−0.959233	−	0.282617i	$-0.908798\pi$
$313$		−	10.0000i		−	0.565233i	0.959233	−	0.282617i	$-0.0912024\pi$
$314$	9.79796	−	16.9706i	0.552931	−	0.957704i
$315$		0			0
$316$	6.00000	−	3.46410i	0.337526	−	0.194871i
$317$			12.2474i			0.687885i	0.938991	+	0.343943i	$0.111763\pi$
$317$			12.2474i			0.687885i	−0.938991	+	0.343943i	$0.888237\pi$
$318$		0			0
$319$			6.92820i			0.387905i
$320$		0			0
$321$		0			0
$322$	−20.7846	−	12.0000i	−1.15828	−	0.668734i
$323$	5.65685			0.314756
$324$		0			0
$325$		0			0
$326$	−19.5959	−	11.3137i	−1.08532	−	0.626608i
$327$		0			0
$328$		−	4.00000i		−	0.220863i
$329$		−	16.9706i		−	0.935617i
$330$		0			0
$331$	−4.00000			−0.219860			−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000			−0.219860			−0.109930	+	0.993939i	$0.535063\pi$
$332$	14.1421	+	24.4949i	0.776151	+	1.34433i
$333$		0			0
$334$	−24.0000	−	13.8564i	−1.31322	−	0.758189i
$335$		0			0
$336$		0			0
$337$			4.00000i			0.217894i	0.994048	+	0.108947i	$0.0347479\pi$
$337$			4.00000i			0.217894i	−0.994048	+	0.108947i	$0.965252\pi$
$338$	−0.707107	+	1.22474i	−0.0384615	+	0.0666173i
$339$		0			0
$340$		0			0
$341$	9.79796			0.530589
$342$		0			0
$343$	6.92820			0.374088
$344$		−	22.6274i		−	1.21999i
$345$		0			0
$346$	3.00000	+	1.73205i	0.161281	+	0.0931156i
$347$	14.1421			0.759190			0.379595	−	0.925153i	$-0.376063\pi$
$347$	14.1421			0.759190			0.379595	+	0.925153i	$0.376063\pi$
$348$		0			0
$349$		−	27.7128i		−	1.48343i	−0.670714	−	0.741716i	$-0.734012\pi$
$349$		−	27.7128i		−	1.48343i	0.670714	−	0.741716i	$-0.265988\pi$
$350$		0			0
$351$		0			0
$352$	13.8564	−	8.00000i	0.738549	−	0.426401i
$353$	15.5563			0.827981			0.413990	−	0.910281i	$-0.364135\pi$
$353$	15.5563			0.827981			0.413990	+	0.910281i	$0.364135\pi$
$354$		0			0
$355$		0			0
$356$	12.2474	−	7.07107i	0.649113	−	0.374766i
$357$		0			0
$358$	−6.92820	−	4.00000i	−0.366167	−	0.211407i
$359$	−14.6969			−0.775675			−0.387837	−	0.921728i	$-0.626778\pi$
$359$	−14.6969			−0.775675			−0.387837	+	0.921728i	$0.626778\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$	−12.7279	−	7.34847i	−0.668965	−	0.386227i
$363$		0			0
$364$	−12.0000	−	20.7846i	−0.628971	−	1.08941i
$365$		0			0
$366$		0			0
$367$	−24.2487			−1.26577			−0.632886	−	0.774245i	$-0.718130\pi$
$367$	−24.2487			−1.26577			−0.632886	+	0.774245i	$0.718130\pi$
$368$	−16.9706	−	9.79796i	−0.884652	−	0.510754i
$369$		0			0
$370$		0			0
$371$		−	25.4558i		−	1.32160i
$372$		0			0
$373$	−13.8564			−0.717458			−0.358729	−	0.933442i	$-0.616790\pi$
$373$	−13.8564			−0.717458			−0.358729	+	0.933442i	$0.616790\pi$
$374$	−4.89898	−	2.82843i	−0.253320	−	0.146254i
$375$		0			0
$376$		−	13.8564i		−	0.714590i
$377$	8.48528			0.437014
$378$		0			0
$379$	4.00000			0.205466			0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000			0.205466			0.102733	+	0.994709i	$0.467241\pi$
$380$		0			0
$381$		0			0
$382$	−13.8564	+	24.0000i	−0.708955	+	1.22795i
$383$		−	9.79796i		−	0.500652i	−0.968162	−	0.250326i	$-0.919462\pi$
$383$		−	9.79796i		−	0.500652i	0.968162	−	0.250326i	$-0.0805379\pi$
$384$		0			0
$385$		0			0
$386$	17.1464	+	9.89949i	0.872730	+	0.503871i
$387$		0			0
$388$	−13.8564	+	8.00000i	−0.703452	+	0.406138i
$389$	26.9444			1.36613			0.683067	−	0.730355i	$-0.260646\pi$
$389$	26.9444			1.36613			0.683067	+	0.730355i	$0.260646\pi$
$390$		0			0
$391$			6.92820i			0.350374i
$392$	−14.1421			−0.714286
$393$		0			0
$394$	9.00000	+	5.19615i	0.453413	+	0.261778i
$395$		0			0
$396$		0			0
$397$		0			0			−	1.00000i	$-0.5\pi$
$397$		0			0				1.00000i	$0.5\pi$
$398$	12.7279	+	7.34847i	0.637993	+	0.368345i
$399$		0			0
$400$		0			0
$401$			1.41421i			0.0706225i	0.999376	+	0.0353112i	$0.0112422\pi$
$401$			1.41421i			0.0706225i	−0.999376	+	0.0353112i	$0.988758\pi$
$402$		0			0
$403$		−	12.0000i		−	0.597763i
$404$	−2.44949	−	4.24264i	−0.121867	−	0.211079i
$405$		0			0
$406$	6.00000	−	10.3923i	0.297775	−	0.515761i
$407$		0			0
$408$		0			0
$409$	−32.0000			−1.58230			−0.791149	−	0.611623i	$-0.790517\pi$
$409$	−32.0000			−1.58230			−0.791149	+	0.611623i	$0.790517\pi$
$410$		0			0
$411$		0			0
$412$	3.46410	+	6.00000i	0.170664	+	0.295599i
$413$		−	39.1918i		−	1.92850i
$414$		0			0
$415$		0			0
$416$	−9.79796	−	16.9706i	−0.480384	−	0.832050i
$417$		0			0
$418$	−13.8564	−	8.00000i	−0.677739	−	0.391293i
$419$			19.7990i			0.967244i	0.875277	+	0.483622i	$0.160679\pi$
$419$			19.7990i			0.967244i	−0.875277	+	0.483622i	$0.839321\pi$
$420$		0			0
$421$		−	24.2487i		−	1.18181i	−0.806741	−	0.590905i	$-0.798771\pi$
$421$		−	24.2487i		−	1.18181i	0.806741	−	0.590905i	$-0.201229\pi$
$422$	14.1421	−	24.4949i	0.688428	−	1.19239i
$423$		0			0
$424$		−	20.7846i		−	1.00939i
$425$		0			0
$426$		0			0
$427$			48.0000i			2.32288i
$428$	11.3137	+	19.5959i	0.546869	+	0.947204i
$429$		0			0
$430$		0			0
$431$	14.6969			0.707927			0.353963	−	0.935259i	$-0.384834\pi$
$431$	14.6969			0.707927			0.353963	+	0.935259i	$0.384834\pi$
$432$		0			0
$433$		−	22.0000i		−	1.05725i	−0.848855	−	0.528626i	$-0.822707\pi$
$433$		−	22.0000i		−	1.05725i	0.848855	−	0.528626i	$-0.177293\pi$
$434$	−14.6969	−	8.48528i	−0.705476	−	0.407307i
$435$		0			0
$436$	−18.0000	+	10.3923i	−0.862044	+	0.497701i
$437$			19.5959i			0.937400i
$438$		0			0
$439$			3.46410i			0.165333i	0.996577	+	0.0826663i	$0.0263436\pi$
$439$			3.46410i			0.165333i	−0.996577	+	0.0826663i	$0.973656\pi$
$440$		0			0
$441$		0			0
$442$	−3.46410	+	6.00000i	−0.164771	+	0.285391i
$443$	2.82843			0.134383			0.0671913	−	0.997740i	$-0.478596\pi$
$443$	2.82843			0.134383			0.0671913	+	0.997740i	$0.478596\pi$
$444$		0			0
$445$		0			0
$446$	−12.2474	+	21.2132i	−0.579934	+	1.00447i
$447$		0			0
$448$	−27.7128			−1.30931
$449$			24.0416i			1.13459i	0.823513	+	0.567297i	$0.192011\pi$
$449$			24.0416i			1.13459i	−0.823513	+	0.567297i	$0.807989\pi$
$450$		0			0
$451$	4.00000			0.188353
$452$	18.3848	+	31.8434i	0.864747	+	1.49779i
$453$		0			0
$454$	−2.00000	+	3.46410i	−0.0938647	+	0.162578i
$455$		0			0
$456$		0			0
$457$		−	8.00000i		−	0.374224i	−0.982339	−	0.187112i	$-0.940087\pi$
$457$		−	8.00000i		−	0.374224i	0.982339	−	0.187112i	$-0.0599128\pi$
$458$	21.2132	+	12.2474i	0.991228	+	0.572286i
$459$		0			0
$460$		0			0
$461$	17.1464			0.798589			0.399294	−	0.916823i	$-0.369255\pi$
$461$	17.1464			0.798589			0.399294	+	0.916823i	$0.369255\pi$
$462$		0			0
$463$	17.3205			0.804952			0.402476	−	0.915430i	$-0.368150\pi$
$463$	17.3205			0.804952			0.402476	+	0.915430i	$0.368150\pi$
$464$	4.89898	−	8.48528i	0.227429	−	0.393919i
$465$		0			0
$466$	−1.00000	+	1.73205i	−0.0463241	+	0.0802357i
$467$	−36.7696			−1.70149			−0.850746	−	0.525577i	$-0.823849\pi$
$467$	−36.7696			−1.70149			−0.850746	+	0.525577i	$0.823849\pi$
$468$		0			0
$469$		−	13.8564i		−	0.639829i
$470$		0			0
$471$		0			0
$472$		−	32.0000i		−	1.47292i
$473$	22.6274			1.04041
$474$		0			0
$475$		0			0
$476$	4.89898	+	8.48528i	0.224544	+	0.388922i
$477$		0			0
$478$	6.92820	−	12.0000i	0.316889	−	0.548867i
$479$	−24.4949			−1.11920			−0.559600	−	0.828763i	$-0.689045\pi$
$479$	−24.4949			−1.11920			−0.559600	+	0.828763i	$0.689045\pi$
$480$		0			0
$481$		0			0
$482$	−19.7990	+	34.2929i	−0.901819	+	1.56200i
$483$		0			0
$484$	−3.00000	−	5.19615i	−0.136364	−	0.236189i
$485$		0			0
$486$		0			0
$487$	−10.3923			−0.470920			−0.235460	−	0.971884i	$-0.575660\pi$
$487$	−10.3923			−0.470920			−0.235460	+	0.971884i	$0.575660\pi$
$488$			39.1918i			1.77413i
$489$		0			0
$490$		0			0
$491$			39.5980i			1.78703i	0.449032	+	0.893516i	$0.351769\pi$
$491$			39.5980i			1.78703i	−0.449032	+	0.893516i	$0.648231\pi$
$492$		0			0
$493$	−3.46410			−0.156015
$494$	−9.79796	+	16.9706i	−0.440831	+	0.763542i
$495$		0			0
$496$	−12.0000	−	6.92820i	−0.538816	−	0.311086i
$497$	50.9117			2.28370
$498$		0			0
$499$	−32.0000			−1.43252			−0.716258	−	0.697835i	$-0.754147\pi$
$499$	−32.0000			−1.43252			−0.716258	+	0.697835i	$0.754147\pi$
$500$		0			0
$501$		0			0
$502$	17.3205	+	10.0000i	0.773052	+	0.446322i
$503$			14.6969i			0.655304i	0.944798	+	0.327652i	$0.106257\pi$
$503$			14.6969i			0.655304i	−0.944798	+	0.327652i	$0.893743\pi$
$504$		0			0
$505$		0			0
$506$	9.79796	−	16.9706i	0.435572	−	0.754434i
$507$		0			0
$508$	10.3923	+	18.0000i	0.461084	+	0.798621i
$509$	−41.6413			−1.84572			−0.922860	−	0.385136i	$-0.874154\pi$
$509$	−41.6413			−1.84572			−0.922860	+	0.385136i	$0.874154\pi$
$510$		0			0
$511$			13.8564i			0.612971i
$512$	−22.6274			−1.00000
$513$		0			0
$514$	−17.0000	+	29.4449i	−0.749838	+	1.29876i
$515$		0			0
$516$		0			0
$517$	13.8564			0.609404
$518$		0			0
$519$		0			0
$520$		0			0
$521$			26.8701i			1.17720i	0.808425	+	0.588599i	$0.200320\pi$
$521$			26.8701i			1.17720i	−0.808425	+	0.588599i	$0.799680\pi$
$522$		0			0
$523$			20.0000i			0.874539i	0.899331	+	0.437269i	$0.144054\pi$
$523$			20.0000i			0.874539i	−0.899331	+	0.437269i	$0.855946\pi$
$524$	9.79796	−	5.65685i	0.428026	−	0.247121i
$525$		0			0
$526$	12.0000	+	6.92820i	0.523225	+	0.302084i
$527$			4.89898i			0.213403i
$528$		0			0
$529$	−1.00000			−0.0434783
$530$		0			0
$531$		0			0
$532$	13.8564	+	24.0000i	0.600751	+	1.04053i
$533$		−	4.89898i		−	0.212198i
$534$		0			0
$535$		0			0
$536$		−	11.3137i		−	0.488678i
$537$		0			0
$538$	−5.19615	+	9.00000i	−0.224022	+	0.388018i
$539$		−	14.1421i		−	0.609145i
$540$		0			0
$541$			10.3923i			0.446800i	0.974727	+	0.223400i	$0.0717156\pi$
$541$			10.3923i			0.446800i	−0.974727	+	0.223400i	$0.928284\pi$
$542$	38.1838	+	22.0454i	1.64013	+	0.946931i
$543$		0			0
$544$	4.00000	+	6.92820i	0.171499	+	0.297044i
$545$		0			0
$546$		0			0
$547$		−	8.00000i		−	0.342055i	−0.985266	−	0.171028i	$-0.945291\pi$
$547$		−	8.00000i		−	0.342055i	0.985266	−	0.171028i	$-0.0547087\pi$
$548$	−9.89949	−	17.1464i	−0.422885	−	0.732459i
$549$		0			0
$550$		0			0
$551$	−9.79796			−0.417407
$552$		0			0
$553$		−	12.0000i		−	0.510292i
$554$	12.2474	−	21.2132i	0.520344	−	0.901263i
$555$		0			0
$556$	−4.00000	−	6.92820i	−0.169638	−	0.293821i
$557$		−	7.34847i		−	0.311365i	−0.987807	−	0.155682i	$-0.950242\pi$
$557$		−	7.34847i		−	0.311365i	0.987807	−	0.155682i	$-0.0497576\pi$
$558$		0			0
$559$		−	27.7128i		−	1.17213i
$560$		0			0
$561$		0			0
$562$	−29.4449	−	17.0000i	−1.24206	−	0.717102i
$563$	−14.1421			−0.596020			−0.298010	−	0.954563i	$-0.596323\pi$
$563$	−14.1421			−0.596020			−0.298010	+	0.954563i	$0.596323\pi$
$564$		0			0
$565$		0			0
$566$	−19.5959	−	11.3137i	−0.823678	−	0.475551i
$567$		0			0
$568$	41.5692			1.74421
$569$		−	9.89949i		−	0.415008i	−0.978234	−	0.207504i	$-0.933466\pi$
$569$		−	9.89949i		−	0.415008i	0.978234	−	0.207504i	$-0.0665341\pi$
$570$		0			0
$571$	−40.0000			−1.67395			−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000			−1.67395			−0.836974	+	0.547243i	$0.815677\pi$
$572$	16.9706	−	9.79796i	0.709575	−	0.409673i
$573$		0			0
$574$	−6.00000	−	3.46410i	−0.250435	−	0.144589i
$575$		0			0
$576$		0			0
$577$		−	14.0000i		−	0.582828i	−0.956597	−	0.291414i	$-0.905874\pi$
$577$		−	14.0000i		−	0.582828i	0.956597	−	0.291414i	$-0.0941257\pi$
$578$	−10.6066	+	18.3712i	−0.441176	+	0.764140i
$579$		0			0
$580$		0			0
$581$	48.9898			2.03244
$582$		0			0
$583$	20.7846			0.860811
$584$			11.3137i			0.468165i
$585$		0			0
$586$	33.0000	+	19.0526i	1.36322	+	0.787054i
$587$	22.6274			0.933933			0.466967	−	0.884275i	$-0.345347\pi$
$587$	22.6274			0.933933			0.466967	+	0.884275i	$0.345347\pi$
$588$		0			0
$589$			13.8564i			0.570943i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	7.07107			0.290374			0.145187	−	0.989404i	$-0.453622\pi$
$593$	7.07107			0.290374			0.145187	+	0.989404i	$0.453622\pi$
$594$		0			0
$595$		0			0
$596$	−17.1464	−	29.6985i	−0.702345	−	1.21650i
$597$		0			0
$598$	−20.7846	−	12.0000i	−0.849946	−	0.490716i
$599$	−4.89898			−0.200167			−0.100083	−	0.994979i	$-0.531911\pi$
$599$	−4.89898			−0.200167			−0.100083	+	0.994979i	$0.531911\pi$
$600$		0			0
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$	−33.9411	−	19.5959i	−1.38334	−	0.798670i
$603$		0			0
$604$	−6.00000	+	3.46410i	−0.244137	+	0.140952i
$605$		0			0
$606$		0			0
$607$	45.0333			1.82785			0.913923	−	0.405887i	$-0.133038\pi$
$607$	45.0333			1.82785			0.913923	+	0.405887i	$0.133038\pi$
$608$	11.3137	+	19.5959i	0.458831	+	0.794719i
$609$		0			0
$610$		0			0
$611$		−	16.9706i		−	0.686555i
$612$		0			0
$613$		0			0			−	1.00000i	$-0.5\pi$
$613$		0			0				1.00000i	$0.5\pi$
$614$	4.89898	+	2.82843i	0.197707	+	0.114146i
$615$		0			0
$616$		−	27.7128i		−	1.11658i
$617$	−24.0416			−0.967880			−0.483940	−	0.875101i	$-0.660795\pi$
$617$	−24.0416			−0.967880			−0.483940	+	0.875101i	$0.660795\pi$
$618$		0			0
$619$	−8.00000			−0.321547			−0.160774	−	0.986991i	$-0.551399\pi$
$619$	−8.00000			−0.321547			−0.160774	+	0.986991i	$0.551399\pi$
$620$		0			0
$621$		0			0
$622$	−6.92820	+	12.0000i	−0.277796	+	0.481156i
$623$		−	24.4949i		−	0.981367i
$624$		0			0
$625$		0			0
$626$	−12.2474	−	7.07107i	−0.489506	−	0.282617i
$627$		0			0
$628$	−13.8564	−	24.0000i	−0.552931	−	0.957704i
$629$		0			0
$630$		0			0
$631$			31.1769i			1.24113i	0.784154	+	0.620567i	$0.213097\pi$
$631$			31.1769i			1.24113i	−0.784154	+	0.620567i	$0.786903\pi$
$632$		−	9.79796i		−	0.389742i
$633$		0			0
$634$	15.0000	+	8.66025i	0.595726	+	0.343943i
$635$		0			0
$636$		0			0
$637$	−17.3205			−0.686264
$638$	8.48528	+	4.89898i	0.335936	+	0.193952i
$639$		0			0
$640$		0			0
$641$		−	15.5563i		−	0.614439i	−0.951639	−	0.307219i	$-0.900601\pi$
$641$		−	15.5563i		−	0.614439i	0.951639	−	0.307219i	$-0.0993986\pi$
$642$		0			0
$643$			32.0000i			1.26196i	0.775800	+	0.630978i	$0.217346\pi$
$643$			32.0000i			1.26196i	−0.775800	+	0.630978i	$0.782654\pi$
$644$	−29.3939	+	16.9706i	−1.15828	+	0.668734i
$645$		0			0
$646$	4.00000	−	6.92820i	0.157378	−	0.272587i
$647$		−	14.6969i		−	0.577796i	−0.957360	−	0.288898i	$-0.906711\pi$
$647$		−	14.6969i		−	0.577796i	0.957360	−	0.288898i	$-0.0932889\pi$
$648$		0			0
$649$	32.0000			1.25611
$650$		0			0
$651$		0			0
$652$	−27.7128	+	16.0000i	−1.08532	+	0.626608i
$653$		−	17.1464i		−	0.670992i	−0.942042	−	0.335496i	$-0.891096\pi$
$653$		−	17.1464i		−	0.670992i	0.942042	−	0.335496i	$-0.108904\pi$
$654$		0			0
$655$		0			0
$656$	−4.89898	−	2.82843i	−0.191273	−	0.110432i
$657$		0			0
$658$	−20.7846	−	12.0000i	−0.810268	−	0.467809i
$659$			11.3137i			0.440720i	0.975419	+	0.220360i	$0.0707231\pi$
$659$			11.3137i			0.440720i	−0.975419	+	0.220360i	$0.929277\pi$
$660$		0			0
$661$			13.8564i			0.538952i	0.963007	+	0.269476i	$0.0868504\pi$
$661$			13.8564i			0.538952i	−0.963007	+	0.269476i	$0.913150\pi$
$662$	−2.82843	+	4.89898i	−0.109930	+	0.190404i
$663$		0			0
$664$	40.0000			1.55230
$665$		0			0
$666$		0			0
$667$		−	12.0000i		−	0.464642i
$668$	−33.9411	+	19.5959i	−1.31322	+	0.758189i
$669$		0			0
$670$		0			0
$671$	−39.1918			−1.51298
$672$		0			0
$673$			14.0000i			0.539660i	0.962908	+	0.269830i	$0.0869676\pi$
$673$			14.0000i			0.539660i	−0.962908	+	0.269830i	$0.913032\pi$
$674$	4.89898	+	2.82843i	0.188702	+	0.108947i
$675$		0			0
$676$	1.00000	+	1.73205i	0.0384615	+	0.0666173i
$677$		−	17.1464i		−	0.658991i	−0.944157	−	0.329495i	$-0.893121\pi$
$677$		−	17.1464i		−	0.658991i	0.944157	−	0.329495i	$-0.106879\pi$
$678$		0			0
$679$			27.7128i			1.06352i
$680$		0			0
$681$		0			0
$682$	6.92820	−	12.0000i	0.265295	−	0.459504i
$683$	36.7696			1.40695			0.703474	−	0.710721i	$-0.251631\pi$
$683$	36.7696			1.40695			0.703474	+	0.710721i	$0.251631\pi$
$684$		0			0
$685$		0			0
$686$	4.89898	−	8.48528i	0.187044	−	0.323970i
$687$		0			0
$688$	−27.7128	−	16.0000i	−1.05654	−	0.609994i
$689$		−	25.4558i		−	0.969790i
$690$		0			0
$691$	32.0000			1.21734			0.608669	−	0.793424i	$-0.291704\pi$
$691$	32.0000			1.21734			0.608669	+	0.793424i	$0.291704\pi$
$692$	4.24264	−	2.44949i	0.161281	−	0.0931156i
$693$		0			0
$694$	10.0000	−	17.3205i	0.379595	−	0.657477i
$695$		0			0
$696$		0			0
$697$			2.00000i			0.0757554i
$698$	−33.9411	−	19.5959i	−1.28469	−	0.741716i
$699$		0			0
$700$		0			0
$701$	−7.34847			−0.277548			−0.138774	−	0.990324i	$-0.544316\pi$
$701$	−7.34847			−0.277548			−0.138774	+	0.990324i	$0.544316\pi$
$702$		0			0
$703$		0			0
$704$		−	22.6274i		−	0.852803i
$705$		0			0
$706$	11.0000	−	19.0526i	0.413990	−	0.717053i
$707$	−8.48528			−0.319122
$708$		0			0
$709$			3.46410i			0.130097i	0.997882	+	0.0650485i	$0.0207202\pi$
$709$			3.46410i			0.130097i	−0.997882	+	0.0650485i	$0.979280\pi$
$710$		0			0
$711$		0			0
$712$		−	20.0000i		−	0.749532i
$713$	−16.9706			−0.635553
$714$		0			0
$715$		0			0
$716$	−9.79796	+	5.65685i	−0.366167	+	0.211407i
$717$		0			0
$718$	−10.3923	+	18.0000i	−0.387837	+	0.671754i
$719$	44.0908			1.64431			0.822155	−	0.569264i	$-0.192772\pi$
$719$	44.0908			1.64431			0.822155	+	0.569264i	$0.192772\pi$
$720$		0			0
$721$	12.0000			0.446903
$722$	−2.12132	+	3.67423i	−0.0789474	+	0.136741i
$723$		0			0
$724$	−18.0000	+	10.3923i	−0.668965	+	0.386227i
$725$		0			0
$726$		0			0
$727$	−24.2487			−0.899335			−0.449667	−	0.893196i	$-0.648458\pi$
$727$	−24.2487			−0.899335			−0.449667	+	0.893196i	$0.648458\pi$
$728$	−33.9411			−1.25794
$729$		0			0
$730$		0			0
$731$			11.3137i			0.418453i
$732$		0			0
$733$	38.1051			1.40744			0.703722	−	0.710475i	$-0.251520\pi$
$733$	38.1051			1.40744			0.703722	+	0.710475i	$0.251520\pi$
$734$	−17.1464	+	29.6985i	−0.632886	+	1.09619i
$735$		0			0
$736$	−24.0000	+	13.8564i	−0.884652	+	0.510754i
$737$	11.3137			0.416746
$738$		0			0
$739$	40.0000			1.47142			0.735712	−	0.677295i	$-0.236848\pi$
$739$	40.0000			1.47142			0.735712	+	0.677295i	$0.236848\pi$
$740$		0			0
$741$		0			0
$742$	−31.1769	−	18.0000i	−1.14454	−	0.660801i
$743$		−	39.1918i		−	1.43781i	−0.695109	−	0.718905i	$-0.744644\pi$
$743$		−	39.1918i		−	1.43781i	0.695109	−	0.718905i	$-0.255356\pi$
$744$		0			0
$745$		0			0
$746$	−9.79796	+	16.9706i	−0.358729	+	0.621336i
$747$		0			0
$748$	−6.92820	+	4.00000i	−0.253320	+	0.146254i
$749$	39.1918			1.43204
$750$		0			0
$751$			3.46410i			0.126407i	0.998001	+	0.0632034i	$0.0201317\pi$
$751$			3.46410i			0.126407i	−0.998001	+	0.0632034i	$0.979868\pi$
$752$	−16.9706	−	9.79796i	−0.618853	−	0.357295i
$753$		0			0
$754$	6.00000	−	10.3923i	0.218507	−	0.378465i
$755$		0			0
$756$		0			0
$757$	10.3923			0.377715			0.188857	−	0.982005i	$-0.439522\pi$
$757$	10.3923			0.377715			0.188857	+	0.982005i	$0.439522\pi$
$758$	2.82843	−	4.89898i	0.102733	−	0.177939i
$759$		0			0
$760$		0			0
$761$			18.3848i			0.666448i	0.942848	+	0.333224i	$0.108136\pi$
$761$			18.3848i			0.666448i	−0.942848	+	0.333224i	$0.891864\pi$
$762$		0			0
$763$			36.0000i			1.30329i
$764$	19.5959	+	33.9411i	0.708955	+	1.22795i
$765$		0			0
$766$	−12.0000	−	6.92820i	−0.433578	−	0.250326i
$767$		−	39.1918i		−	1.41514i
$768$		0			0
$769$	−2.00000			−0.0721218			−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	−2.00000			−0.0721218			−0.0360609	+	0.999350i	$0.511481\pi$
$770$		0			0
$771$		0			0
$772$	24.2487	−	14.0000i	0.872730	−	0.503871i
$773$		−	22.0454i		−	0.792918i	−0.918052	−	0.396459i	$-0.870239\pi$
$773$		−	22.0454i		−	0.792918i	0.918052	−	0.396459i	$-0.129761\pi$
$774$		0			0
$775$		0			0
$776$			22.6274i			0.812277i
$777$		0			0
$778$	19.0526	−	33.0000i	0.683067	−	1.18311i
$779$			5.65685i			0.202678i
$780$		0			0
$781$			41.5692i			1.48746i
$782$	8.48528	+	4.89898i	0.303433	+	0.175187i
$783$		0			0
$784$	−10.0000	+	17.3205i	−0.357143	+	0.618590i
$785$		0			0
$786$		0			0
$787$		−	20.0000i		−	0.712923i	−0.934310	−	0.356462i	$-0.883983\pi$
$787$		−	20.0000i		−	0.712923i	0.934310	−	0.356462i	$-0.116017\pi$
$788$	12.7279	−	7.34847i	0.453413	−	0.261778i
$789$		0			0
$790$		0			0
$791$	63.6867			2.26444
$792$		0			0
$793$			48.0000i			1.70453i
$794$		0			0
$795$		0			0
$796$	18.0000	−	10.3923i	0.637993	−	0.368345i
$797$		−	12.2474i		−	0.433827i	−0.976191	−	0.216913i	$-0.930401\pi$
$797$		−	12.2474i		−	0.433827i	0.976191	−	0.216913i	$-0.0695989\pi$
$798$		0			0
$799$			6.92820i			0.245102i
$800$		0			0
$801$		0			0
$802$	1.73205	+	1.00000i	0.0611608	+	0.0353112i
$803$	−11.3137			−0.399252
$804$		0			0
$805$		0			0
$806$	−14.6969	−	8.48528i	−0.517678	−	0.298881i
$807$		0			0
$808$	−6.92820			−0.243733
$809$		−	1.41421i		−	0.0497211i	−0.999691	−	0.0248606i	$-0.992086\pi$
$809$		−	1.41421i		−	0.0497211i	0.999691	−	0.0248606i	$-0.00791417\pi$
$810$		0			0
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$	−8.48528	−	14.6969i	−0.297775	−	0.515761i
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$			32.0000i			1.11954i
$818$	−22.6274	+	39.1918i	−0.791149	+	1.37031i
$819$		0			0
$820$		0			0
$821$	2.44949			0.0854878			0.0427439	−	0.999086i	$-0.486390\pi$
$821$	2.44949			0.0854878			0.0427439	+	0.999086i	$0.486390\pi$
$822$		0			0
$823$	17.3205			0.603755			0.301877	−	0.953347i	$-0.402387\pi$
$823$	17.3205			0.603755			0.301877	+	0.953347i	$0.402387\pi$
$824$	9.79796			0.341328
$825$		0			0
$826$	−48.0000	−	27.7128i	−1.67013	−	0.964252i
$827$	5.65685			0.196708			0.0983540	−	0.995151i	$-0.468642\pi$
$827$	5.65685			0.196708			0.0983540	+	0.995151i	$0.468642\pi$
$828$		0			0
$829$		−	10.3923i		−	0.360940i	−0.983581	−	0.180470i	$-0.942238\pi$
$829$		−	10.3923i		−	0.360940i	0.983581	−	0.180470i	$-0.0577618\pi$
$830$		0			0
$831$		0			0
$832$	−27.7128			−0.960769
$833$	7.07107			0.244998
$834$		0			0
$835$		0			0
$836$	−19.5959	+	11.3137i	−0.677739	+	0.391293i
$837$		0			0
$838$	24.2487	+	14.0000i	0.837658	+	0.483622i
$839$	4.89898			0.169132			0.0845658	−	0.996418i	$-0.473050\pi$
$839$	4.89898			0.169132			0.0845658	+	0.996418i	$0.473050\pi$
$840$		0			0
$841$	−23.0000			−0.793103
$842$	−29.6985	−	17.1464i	−1.02348	−	0.590905i
$843$		0			0
$844$	−20.0000	−	34.6410i	−0.688428	−	1.19239i
$845$		0			0
$846$		0			0
$847$	−10.3923			−0.357084
$848$	−25.4558	−	14.6969i	−0.874157	−	0.504695i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	13.8564			0.474434			0.237217	−	0.971457i	$-0.423765\pi$
$853$	13.8564			0.474434			0.237217	+	0.971457i	$0.423765\pi$
$854$	58.7878	+	33.9411i	2.01168	+	1.16144i
$855$		0			0
$856$	32.0000			1.09374
$857$	1.41421			0.0483086			0.0241543	−	0.999708i	$-0.492311\pi$
$857$	1.41421			0.0483086			0.0241543	+	0.999708i	$0.492311\pi$
$858$		0			0
$859$	40.0000			1.36478			0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000			1.36478			0.682391	+	0.730987i	$0.260940\pi$
$860$		0			0
$861$		0			0
$862$	10.3923	−	18.0000i	0.353963	−	0.613082i
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$		0			0
$865$		0			0
$866$	−26.9444	−	15.5563i	−0.915608	−	0.528626i
$867$		0			0
$868$	−20.7846	+	12.0000i	−0.705476	+	0.407307i
$869$	9.79796			0.332373
$870$		0			0
$871$		−	13.8564i		−	0.469506i
$872$			29.3939i			0.995402i
$873$		0			0
$874$	24.0000	+	13.8564i	0.811812	+	0.468700i
$875$		0			0
$876$		0			0
$877$	55.4256			1.87159			0.935795	−	0.352544i	$-0.114683\pi$
$877$	55.4256			1.87159			0.935795	+	0.352544i	$0.114683\pi$
$878$	4.24264	+	2.44949i	0.143182	+	0.0826663i
$879$		0			0
$880$		0			0
$881$			43.8406i			1.47703i	0.674238	+	0.738514i	$0.264472\pi$
$881$			43.8406i			1.47703i	−0.674238	+	0.738514i	$0.735528\pi$
$882$		0			0
$883$		−	40.0000i		−	1.34611i	−0.739594	−	0.673054i	$-0.764982\pi$
$883$		−	40.0000i		−	1.34611i	0.739594	−	0.673054i	$-0.235018\pi$
$884$	4.89898	+	8.48528i	0.164771	+	0.285391i
$885$		0			0
$886$	2.00000	−	3.46410i	0.0671913	−	0.116379i
$887$			9.79796i			0.328983i	0.986378	+	0.164492i	$0.0525984\pi$
$887$			9.79796i			0.328983i	−0.986378	+	0.164492i	$0.947402\pi$
$888$		0			0
$889$	36.0000			1.20740
$890$		0			0
$891$		0			0
$892$	17.3205	+	30.0000i	0.579934	+	1.00447i
$893$			19.5959i			0.655752i
$894$		0			0
$895$		0			0
$896$	−19.5959	+	33.9411i	−0.654654	+	1.13389i
$897$		0			0
$898$	29.4449	+	17.0000i	0.982588	+	0.567297i
$899$		−	8.48528i		−	0.283000i
$900$		0			0
$901$			10.3923i			0.346218i
$902$	2.82843	−	4.89898i	0.0941763	−	0.163118i
$903$		0			0
$904$	52.0000			1.72949
$905$		0			0
$906$		0			0
$907$		−	8.00000i		−	0.265636i	−0.991140	−	0.132818i	$-0.957597\pi$
$907$		−	8.00000i		−	0.265636i	0.991140	−	0.132818i	$-0.0424025\pi$
$908$	2.82843	+	4.89898i	0.0938647	+	0.162578i
$909$		0			0
$910$		0			0
$911$	39.1918			1.29848			0.649242	−	0.760582i	$-0.275086\pi$
$911$	39.1918			1.29848			0.649242	+	0.760582i	$0.275086\pi$
$912$		0			0
$913$			40.0000i			1.32381i
$914$	−9.79796	−	5.65685i	−0.324088	−	0.187112i
$915$		0			0
$916$	30.0000	−	17.3205i	0.991228	−	0.572286i
$917$		−	19.5959i		−	0.647114i
$918$		0			0
$919$		−	10.3923i		−	0.342811i	−0.985201	−	0.171405i	$-0.945169\pi$
$919$		−	10.3923i		−	0.342811i	0.985201	−	0.171405i	$-0.0548307\pi$
$920$		0			0
$921$		0			0
$922$	12.1244	−	21.0000i	0.399294	−	0.691598i
$923$	50.9117			1.67578
$924$		0			0
$925$		0			0
$926$	12.2474	−	21.2132i	0.402476	−	0.697109i
$927$		0			0
$928$	−6.92820	−	12.0000i	−0.227429	−	0.393919i
$929$		−	1.41421i		−	0.0463988i	−0.999731	−	0.0231994i	$-0.992615\pi$
$929$		−	1.41421i		−	0.0463988i	0.999731	−	0.0231994i	$-0.00738527\pi$
$930$		0			0
$931$	20.0000			0.655474
$932$	1.41421	+	2.44949i	0.0463241	+	0.0802357i
$933$		0			0
$934$	−26.0000	+	45.0333i	−0.850746	+	1.47354i
$935$		0			0
$936$		0			0
$937$		−	2.00000i		−	0.0653372i	−0.999466	−	0.0326686i	$-0.989599\pi$
$937$		−	2.00000i		−	0.0653372i	0.999466	−	0.0326686i	$-0.0104006\pi$
$938$	−16.9706	−	9.79796i	−0.554109	−	0.319915i
$939$		0			0
$940$		0			0
$941$	−2.44949			−0.0798511			−0.0399255	−	0.999203i	$-0.512712\pi$
$941$	−2.44949			−0.0798511			−0.0399255	+	0.999203i	$0.512712\pi$
$942$		0			0
$943$	−6.92820			−0.225613
$944$	−39.1918	−	22.6274i	−1.27559	−	0.736460i
$945$		0			0
$946$	16.0000	−	27.7128i	0.520205	−	0.901021i
$947$	22.6274			0.735292			0.367646	−	0.929966i	$-0.380164\pi$
$947$	22.6274			0.735292			0.367646	+	0.929966i	$0.380164\pi$
$948$		0			0
$949$			13.8564i			0.449798i
$950$		0			0
$951$		0			0
$952$	13.8564			0.449089
$953$	−26.8701			−0.870407			−0.435203	−	0.900332i	$-0.643323\pi$
$953$	−26.8701			−0.870407			−0.435203	+	0.900332i	$0.643323\pi$
$954$		0			0
$955$		0			0
$956$	−9.79796	−	16.9706i	−0.316889	−	0.548867i
$957$		0			0
$958$	−17.3205	+	30.0000i	−0.559600	+	0.969256i
$959$	−34.2929			−1.10737
$960$		0			0
$961$	19.0000			0.612903
$962$		0			0
$963$		0			0
$964$	28.0000	+	48.4974i	0.901819	+	1.56200i
$965$		0			0
$966$		0			0
$967$	45.0333			1.44817			0.724087	−	0.689709i	$-0.242261\pi$
$967$	45.0333			1.44817			0.724087	+	0.689709i	$0.242261\pi$
$968$	−8.48528			−0.272727
$969$		0			0
$970$		0			0
$971$			31.1127i			0.998454i	0.866471	+	0.499227i	$0.166383\pi$
$971$			31.1127i			0.998454i	−0.866471	+	0.499227i	$0.833617\pi$
$972$		0			0
$973$	−13.8564			−0.444216
$974$	−7.34847	+	12.7279i	−0.235460	+	0.407829i
$975$		0			0
$976$	48.0000	+	27.7128i	1.53644	+	0.887066i
$977$	−24.0416			−0.769160			−0.384580	−	0.923092i	$-0.625654\pi$
$977$	−24.0416			−0.769160			−0.384580	+	0.923092i	$0.625654\pi$
$978$		0			0
$979$	20.0000			0.639203
$980$		0			0
$981$		0			0
$982$	48.4974	+	28.0000i	1.54761	+	0.893516i
$983$		−	48.9898i		−	1.56253i	−0.624198	−	0.781266i	$-0.714574\pi$
$983$		−	48.9898i		−	1.56253i	0.624198	−	0.781266i	$-0.285426\pi$
$984$		0			0
$985$		0			0
$986$	−2.44949	+	4.24264i	−0.0780076	+	0.135113i
$987$		0			0
$988$	13.8564	+	24.0000i	0.440831	+	0.763542i
$989$	−39.1918			−1.24623
$990$		0			0
$991$		−	51.9615i		−	1.65061i	−0.564686	−	0.825306i	$-0.691003\pi$
$991$		−	51.9615i		−	1.65061i	0.564686	−	0.825306i	$-0.308997\pi$
$992$	−16.9706	+	9.79796i	−0.538816	+	0.311086i
$993$		0			0
$994$	36.0000	−	62.3538i	1.14185	−	1.97774i
$995$		0			0
$996$		0			0
$997$	−13.8564			−0.438837			−0.219418	−	0.975631i	$-0.570416\pi$
$997$	−13.8564			−0.438837			−0.219418	+	0.975631i	$0.570416\pi$
$998$	−22.6274	+	39.1918i	−0.716258	+	1.24060i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.m.c.899.5		8
3.2	odd	2	inner	1800.2.m.c.899.3		8
4.3	odd	2		7200.2.m.c.3599.8		8
5.2	odd	4		72.2.f.a.35.4	yes	4
5.3	odd	4		1800.2.b.c.251.1		4
5.4	even	2	inner	1800.2.m.c.899.4		8
8.3	odd	2	inner	1800.2.m.c.899.8		8
8.5	even	2		7200.2.m.c.3599.4		8
12.11	even	2		7200.2.m.c.3599.5		8
15.2	even	4		72.2.f.a.35.1	✓	4
15.8	even	4		1800.2.b.c.251.4		4
15.14	odd	2	inner	1800.2.m.c.899.6		8
20.3	even	4		7200.2.b.c.4751.2		4
20.7	even	4		288.2.f.a.143.2		4
20.19	odd	2		7200.2.m.c.3599.3		8
24.5	odd	2		7200.2.m.c.3599.1		8
24.11	even	2	inner	1800.2.m.c.899.2		8
40.3	even	4		1800.2.b.c.251.3		4
40.13	odd	4		7200.2.b.c.4751.4		4
40.19	odd	2	inner	1800.2.m.c.899.1		8
40.27	even	4		72.2.f.a.35.2	yes	4
40.29	even	2		7200.2.m.c.3599.7		8
40.37	odd	4		288.2.f.a.143.3		4
45.2	even	12		648.2.l.a.539.2		4
45.7	odd	12		648.2.l.a.539.1		4
45.22	odd	12		648.2.l.c.107.1		4
45.32	even	12		648.2.l.c.107.2		4
60.23	odd	4		7200.2.b.c.4751.1		4
60.47	odd	4		288.2.f.a.143.4		4
60.59	even	2		7200.2.m.c.3599.2		8
80.27	even	4		2304.2.c.i.2303.2		8
80.37	odd	4		2304.2.c.i.2303.4		8
80.67	even	4		2304.2.c.i.2303.5		8
80.77	odd	4		2304.2.c.i.2303.7		8
120.29	odd	2		7200.2.m.c.3599.6		8
120.53	even	4		7200.2.b.c.4751.3		4
120.59	even	2	inner	1800.2.m.c.899.7		8
120.77	even	4		288.2.f.a.143.1		4
120.83	odd	4		1800.2.b.c.251.2		4
120.107	odd	4		72.2.f.a.35.3	yes	4
180.7	even	12		2592.2.p.c.2159.2		4
180.47	odd	12		2592.2.p.c.2159.1		4
180.67	even	12		2592.2.p.a.431.2		4
180.167	odd	12		2592.2.p.a.431.1		4
240.77	even	4		2304.2.c.i.2303.3		8
240.107	odd	4		2304.2.c.i.2303.6		8
240.197	even	4		2304.2.c.i.2303.8		8
240.227	odd	4		2304.2.c.i.2303.1		8
360.67	even	12		648.2.l.a.107.1		4
360.77	even	12		2592.2.p.c.431.2		4
360.157	odd	12		2592.2.p.c.431.1		4
360.187	even	12		648.2.l.c.539.2		4
360.227	odd	12		648.2.l.c.539.1		4
360.277	odd	12		2592.2.p.a.2159.1		4
360.317	even	12		2592.2.p.a.2159.2		4
360.347	odd	12		648.2.l.a.107.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.f.a.35.1	✓	4	15.2	even	4
72.2.f.a.35.2	yes	4	40.27	even	4
72.2.f.a.35.3	yes	4	120.107	odd	4
72.2.f.a.35.4	yes	4	5.2	odd	4
288.2.f.a.143.1		4	120.77	even	4
288.2.f.a.143.2		4	20.7	even	4
288.2.f.a.143.3		4	40.37	odd	4
288.2.f.a.143.4		4	60.47	odd	4
648.2.l.a.107.1		4	360.67	even	12
648.2.l.a.107.2		4	360.347	odd	12
648.2.l.a.539.1		4	45.7	odd	12
648.2.l.a.539.2		4	45.2	even	12
648.2.l.c.107.1		4	45.22	odd	12
648.2.l.c.107.2		4	45.32	even	12
648.2.l.c.539.1		4	360.227	odd	12
648.2.l.c.539.2		4	360.187	even	12
1800.2.b.c.251.1		4	5.3	odd	4
1800.2.b.c.251.2		4	120.83	odd	4
1800.2.b.c.251.3		4	40.3	even	4
1800.2.b.c.251.4		4	15.8	even	4
1800.2.m.c.899.1		8	40.19	odd	2	inner
1800.2.m.c.899.2		8	24.11	even	2	inner
1800.2.m.c.899.3		8	3.2	odd	2	inner
1800.2.m.c.899.4		8	5.4	even	2	inner
1800.2.m.c.899.5		8	1.1	even	1	trivial
1800.2.m.c.899.6		8	15.14	odd	2	inner
1800.2.m.c.899.7		8	120.59	even	2	inner
1800.2.m.c.899.8		8	8.3	odd	2	inner
2304.2.c.i.2303.1		8	240.227	odd	4
2304.2.c.i.2303.2		8	80.27	even	4
2304.2.c.i.2303.3		8	240.77	even	4
2304.2.c.i.2303.4		8	80.37	odd	4
2304.2.c.i.2303.5		8	80.67	even	4
2304.2.c.i.2303.6		8	240.107	odd	4
2304.2.c.i.2303.7		8	80.77	odd	4
2304.2.c.i.2303.8		8	240.197	even	4
2592.2.p.a.431.1		4	180.167	odd	12
2592.2.p.a.431.2		4	180.67	even	12
2592.2.p.a.2159.1		4	360.277	odd	12
2592.2.p.a.2159.2		4	360.317	even	12
2592.2.p.c.431.1		4	360.157	odd	12
2592.2.p.c.431.2		4	360.77	even	12
2592.2.p.c.2159.1		4	180.47	odd	12
2592.2.p.c.2159.2		4	180.7	even	12
7200.2.b.c.4751.1		4	60.23	odd	4
7200.2.b.c.4751.2		4	20.3	even	4
7200.2.b.c.4751.3		4	120.53	even	4
7200.2.b.c.4751.4		4	40.13	odd	4
7200.2.m.c.3599.1		8	24.5	odd	2
7200.2.m.c.3599.2		8	60.59	even	2
7200.2.m.c.3599.3		8	20.19	odd	2
7200.2.m.c.3599.4		8	8.5	even	2
7200.2.m.c.3599.5		8	12.11	even	2
7200.2.m.c.3599.6		8	120.29	odd	2
7200.2.m.c.3599.7		8	40.29	even	2
7200.2.m.c.3599.8		8	4.3	odd	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:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1800.m (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} -3.46410 q^{7} -2.82843 q^{8} +O(q^{10})\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} -3.46410 q^{7} -2.82843 q^{8} -2.82843i q^{11} -3.46410 q^{13} +(-2.44949 + 4.24264i) q^{14} +(-2.00000 + 3.46410i) q^{16} +1.41421 q^{17} +4.00000 q^{19} +(-3.46410 - 2.00000i) q^{22} +4.89898i q^{23} +(-2.44949 + 4.24264i) q^{26} +(3.46410 + 6.00000i) q^{28} -2.44949 q^{29} +3.46410i q^{31} +(2.82843 + 4.89898i) q^{32} +(1.00000 - 1.73205i) q^{34} +(2.82843 - 4.89898i) q^{38} +1.41421i q^{41} +8.00000i q^{43} +(-4.89898 + 2.82843i) q^{44} +(6.00000 + 3.46410i) q^{46} +4.89898i q^{47} +5.00000 q^{49} +(3.46410 + 6.00000i) q^{52} +7.34847i q^{53} +9.79796 q^{56} +(-1.73205 + 3.00000i) q^{58} +11.3137i q^{59} -13.8564i q^{61} +(4.24264 + 2.44949i) q^{62} +8.00000 q^{64} +4.00000i q^{67} +(-1.41421 - 2.44949i) q^{68} -14.6969 q^{71} -4.00000i q^{73} +(-4.00000 - 6.92820i) q^{76} +9.79796i q^{77} +3.46410i q^{79} +(1.73205 + 1.00000i) q^{82} -14.1421 q^{83} +(9.79796 + 5.65685i) q^{86} +8.00000i q^{88} +7.07107i q^{89} +12.0000 q^{91} +(8.48528 - 4.89898i) q^{92} +(6.00000 + 3.46410i) q^{94} -8.00000i q^{97} +(3.53553 - 6.12372i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4}+O(q^{10}) \) 8 * q - 8 * q^4	\( 8 q - 8 q^{4} - 16 q^{16} + 32 q^{19} + 8 q^{34} + 48 q^{46} + 40 q^{49} + 64 q^{64} - 32 q^{76} + 96 q^{91} + 48 q^{94}+O(q^{100}) \) 8 * q - 8 * q^4 - 16 * q^16 + 32 * q^19 + 8 * q^34 + 48 * q^46 + 40 * q^49 + 64 * q^64 - 32 * q^76 + 96 * q^91 + 48 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more