LMFDB - Embedded newform 1800.2.k.j.901.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1800,2,Mod(901,1800)]

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([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("1800.901");

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.k (of order $2$, degree $1$, 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:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			901.3
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1800.901
Dual form			1800.2.k.j.901.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +2.73205 q^{7} +(-2.00000 + 2.00000i) q^{8} -2.00000i q^{11} +3.46410i q^{13} +(1.00000 - 3.73205i) q^{14} +(2.00000 + 3.46410i) q^{16} -3.46410 q^{17} -7.46410i q^{19} +(-2.73205 - 0.732051i) q^{22} +4.19615 q^{23} +(4.73205 + 1.26795i) q^{26} +(-4.73205 - 2.73205i) q^{28} -6.92820i q^{29} +1.46410 q^{31} +(5.46410 - 1.46410i) q^{32} +(-1.26795 + 4.73205i) q^{34} -2.00000i q^{37} +(-10.1962 - 2.73205i) q^{38} +5.46410 q^{41} -8.73205i q^{43} +(-2.00000 + 3.46410i) q^{44} +(1.53590 - 5.73205i) q^{46} +6.73205 q^{47} +0.464102 q^{49} +(3.46410 - 6.00000i) q^{52} -4.53590i q^{53} +(-5.46410 + 5.46410i) q^{56} +(-9.46410 - 2.53590i) q^{58} -0.535898i q^{59} -4.92820i q^{61} +(0.535898 - 2.00000i) q^{62} -8.00000i q^{64} +7.26795i q^{67} +(6.00000 + 3.46410i) q^{68} +1.46410 q^{71} -0.535898 q^{73} +(-2.73205 - 0.732051i) q^{74} +(-7.46410 + 12.9282i) q^{76} -5.46410i q^{77} -14.9282 q^{79} +(2.00000 - 7.46410i) q^{82} -4.73205i q^{83} +(-11.9282 - 3.19615i) q^{86} +(4.00000 + 4.00000i) q^{88} +4.92820 q^{89} +9.46410i q^{91} +(-7.26795 - 4.19615i) q^{92} +(2.46410 - 9.19615i) q^{94} -6.39230 q^{97} +(0.169873 - 0.633975i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 4 q^{7} - 8 q^{8} + 4 q^{14} + 8 q^{16} - 4 q^{22} - 4 q^{23} + 12 q^{26} - 12 q^{28} - 8 q^{31} + 8 q^{32} - 12 q^{34} - 20 q^{38} + 8 q^{41} - 8 q^{44} + 20 q^{46} + 20 q^{47} - 12 q^{49}+ \cdots + 18 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 + 4 * q^7 - 8 * q^8 + 4 * q^14 + 8 * q^16 - 4 * q^22 - 4 * q^23 + 12 * q^26 - 12 * q^28 - 8 * q^31 + 8 * q^32 - 12 * q^34 - 20 * q^38 + 8 * q^41 - 8 * q^44 + 20 * q^46 + 20 * q^47 - 12 * q^49 - 8 * q^56 - 24 * q^58 + 16 * q^62 + 24 * q^68 - 8 * q^71 - 16 * q^73 - 4 * q^74 - 16 * q^76 - 32 * q^79 + 8 * q^82 - 20 * q^86 + 16 * q^88 - 8 * q^89 - 36 * q^92 - 4 * q^94 + 16 * q^97 + 18 * q^98

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 $

$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$3$		0			0
$3$		0			0
$4$	−1.73205	−	1.00000i	−0.866025	−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.73205			1.03262			0.516309	−	0.856402i	$-0.327306\pi$
$7$	2.73205			1.03262			0.516309	+	0.856402i	$0.327306\pi$
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$		0			0
$10$		0			0
$11$		−	2.00000i		−	0.603023i	−0.953463	−	0.301511i	$-0.902509\pi$
$11$		−	2.00000i		−	0.603023i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$		0			0
$13$			3.46410i			0.960769i	0.877058	+	0.480384i	$0.159503\pi$
$13$			3.46410i			0.960769i	−0.877058	+	0.480384i	$0.840497\pi$
$14$	1.00000	−	3.73205i	0.267261	−	0.997433i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−3.46410			−0.840168			−0.420084	−	0.907485i	$-0.637999\pi$
$17$	−3.46410			−0.840168			−0.420084	+	0.907485i	$0.637999\pi$
$18$		0			0
$19$		−	7.46410i		−	1.71238i	−0.516659	−	0.856191i	$-0.672825\pi$
$19$		−	7.46410i		−	1.71238i	0.516659	−	0.856191i	$-0.327175\pi$
$20$		0			0
$21$		0			0
$22$	−2.73205	−	0.732051i	−0.582475	−	0.156074i
$23$	4.19615			0.874958			0.437479	−	0.899229i	$-0.355871\pi$
$23$	4.19615			0.874958			0.437479	+	0.899229i	$0.355871\pi$
$24$		0			0
$25$		0			0
$26$	4.73205	+	1.26795i	0.928032	+	0.248665i
$27$		0			0
$28$	−4.73205	−	2.73205i	−0.894274	−	0.516309i
$29$		−	6.92820i		−	1.28654i	−0.765641	−	0.643268i	$-0.777578\pi$
$29$		−	6.92820i		−	1.28654i	0.765641	−	0.643268i	$-0.222422\pi$
$30$		0			0
$31$	1.46410			0.262960			0.131480	−	0.991319i	$-0.458027\pi$
$31$	1.46410			0.262960			0.131480	+	0.991319i	$0.458027\pi$
$32$	5.46410	−	1.46410i	0.965926	−	0.258819i
$33$		0			0
$34$	−1.26795	+	4.73205i	−0.217451	+	0.811540i
$35$		0			0
$36$		0			0
$37$		−	2.00000i		−	0.328798i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$		−	2.00000i		−	0.328798i	0.986394	−	0.164399i	$-0.0525685\pi$
$38$	−10.1962	−	2.73205i	−1.65403	−	0.443197i
$39$		0			0
$40$		0			0
$41$	5.46410			0.853349			0.426675	−	0.904405i	$-0.359685\pi$
$41$	5.46410			0.853349			0.426675	+	0.904405i	$0.359685\pi$
$42$		0			0
$43$		−	8.73205i		−	1.33163i	−0.746119	−	0.665813i	$-0.768085\pi$
$43$		−	8.73205i		−	1.33163i	0.746119	−	0.665813i	$-0.231915\pi$
$44$	−2.00000	+	3.46410i	−0.301511	+	0.522233i
$45$		0			0
$46$	1.53590	−	5.73205i	0.226456	−	0.845145i
$47$	6.73205			0.981971			0.490985	−	0.871168i	$-0.336637\pi$
$47$	6.73205			0.981971			0.490985	+	0.871168i	$0.336637\pi$
$48$		0			0
$49$	0.464102			0.0663002
$50$		0			0
$51$		0			0
$52$	3.46410	−	6.00000i	0.480384	−	0.832050i
$53$		−	4.53590i		−	0.623054i	−0.950237	−	0.311527i	$-0.899160\pi$
$53$		−	4.53590i		−	0.623054i	0.950237	−	0.311527i	$-0.100840\pi$
$54$		0			0
$55$		0			0
$56$	−5.46410	+	5.46410i	−0.730171	+	0.730171i
$57$		0			0
$58$	−9.46410	−	2.53590i	−1.24270	−	0.332980i
$59$		−	0.535898i		−	0.0697680i	−0.999391	−	0.0348840i	$-0.988894\pi$
$59$		−	0.535898i		−	0.0697680i	0.999391	−	0.0348840i	$-0.0111062\pi$
$60$		0			0
$61$		−	4.92820i		−	0.630992i	−0.948927	−	0.315496i	$-0.897829\pi$
$61$		−	4.92820i		−	0.630992i	0.948927	−	0.315496i	$-0.102171\pi$
$62$	0.535898	−	2.00000i	0.0680592	−	0.254000i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$		0			0
$66$		0			0
$67$			7.26795i			0.887921i	0.896046	+	0.443961i	$0.146427\pi$
$67$			7.26795i			0.887921i	−0.896046	+	0.443961i	$0.853573\pi$
$68$	6.00000	+	3.46410i	0.727607	+	0.420084i
$69$		0			0
$70$		0			0
$71$	1.46410			0.173757			0.0868784	−	0.996219i	$-0.472311\pi$
$71$	1.46410			0.173757			0.0868784	+	0.996219i	$0.472311\pi$
$72$		0			0
$73$	−0.535898			−0.0627222			−0.0313611	−	0.999508i	$-0.509984\pi$
$73$	−0.535898			−0.0627222			−0.0313611	+	0.999508i	$0.509984\pi$
$74$	−2.73205	−	0.732051i	−0.317594	−	0.0850992i
$75$		0			0
$76$	−7.46410	+	12.9282i	−0.856191	+	1.48297i
$77$		−	5.46410i		−	0.622692i
$78$		0			0
$79$	−14.9282			−1.67955			−0.839777	−	0.542931i	$-0.817314\pi$
$79$	−14.9282			−1.67955			−0.839777	+	0.542931i	$0.817314\pi$
$80$		0			0
$81$		0			0
$82$	2.00000	−	7.46410i	0.220863	−	0.824272i
$83$		−	4.73205i		−	0.519410i	−0.965688	−	0.259705i	$-0.916375\pi$
$83$		−	4.73205i		−	0.519410i	0.965688	−	0.259705i	$-0.0836253\pi$
$84$		0			0
$85$		0			0
$86$	−11.9282	−	3.19615i	−1.28625	−	0.344650i
$87$		0			0
$88$	4.00000	+	4.00000i	0.426401	+	0.426401i
$89$	4.92820			0.522388			0.261194	−	0.965286i	$-0.415884\pi$
$89$	4.92820			0.522388			0.261194	+	0.965286i	$0.415884\pi$
$90$		0			0
$91$			9.46410i			0.992107i
$92$	−7.26795	−	4.19615i	−0.757736	−	0.437479i
$93$		0			0
$94$	2.46410	−	9.19615i	0.254153	−	0.948511i
$95$		0			0
$96$		0			0
$97$	−6.39230			−0.649040			−0.324520	−	0.945879i	$-0.605203\pi$
$97$	−6.39230			−0.649040			−0.324520	+	0.945879i	$0.605203\pi$
$98$	0.169873	−	0.633975i	0.0171598	−	0.0640411i
$99$		0			0
$100$		0			0
$101$		−	10.9282i		−	1.08740i	−0.839281	−	0.543698i	$-0.817024\pi$
$101$		−	10.9282i		−	1.08740i	0.839281	−	0.543698i	$-0.182976\pi$
$102$		0			0
$103$	1.66025			0.163590			0.0817948	−	0.996649i	$-0.473935\pi$
$103$	1.66025			0.163590			0.0817948	+	0.996649i	$0.473935\pi$
$104$	−6.92820	−	6.92820i	−0.679366	−	0.679366i
$105$		0			0
$106$	−6.19615	−	1.66025i	−0.601824	−	0.161258i
$107$			0.732051i			0.0707700i	0.999374	+	0.0353850i	$0.0112658\pi$
$107$			0.732051i			0.0707700i	−0.999374	+	0.0353850i	$0.988734\pi$
$108$		0			0
$109$		−	3.07180i		−	0.294225i	−0.989120	−	0.147112i	$-0.953002\pi$
$109$		−	3.07180i		−	0.294225i	0.989120	−	0.147112i	$-0.0469979\pi$
$110$		0			0
$111$		0			0
$112$	5.46410	+	9.46410i	0.516309	+	0.894274i
$113$	0.928203			0.0873180			0.0436590	−	0.999046i	$-0.486098\pi$
$113$	0.928203			0.0873180			0.0436590	+	0.999046i	$0.486098\pi$
$114$		0			0
$115$		0			0
$116$	−6.92820	+	12.0000i	−0.643268	+	1.11417i
$117$		0			0
$118$	−0.732051	−	0.196152i	−0.0673907	−	0.0180573i
$119$	−9.46410			−0.867573
$120$		0			0
$121$	7.00000			0.636364
$122$	−6.73205	−	1.80385i	−0.609491	−	0.163313i
$123$		0			0
$124$	−2.53590	−	1.46410i	−0.227730	−	0.131480i
$125$		0			0
$126$		0			0
$127$	−13.2679			−1.17734			−0.588670	−	0.808373i	$-0.700348\pi$
$127$	−13.2679			−1.17734			−0.588670	+	0.808373i	$0.700348\pi$
$128$	−10.9282	−	2.92820i	−0.965926	−	0.258819i
$129$		0			0
$130$		0			0
$131$			7.85641i			0.686417i	0.939259	+	0.343209i	$0.111514\pi$
$131$			7.85641i			0.686417i	−0.939259	+	0.343209i	$0.888486\pi$
$132$		0			0
$133$		−	20.3923i		−	1.76824i
$134$	9.92820	+	2.66025i	0.857666	+	0.229811i
$135$		0			0
$136$	6.92820	−	6.92820i	0.594089	−	0.594089i
$137$	−8.92820			−0.762788			−0.381394	−	0.924413i	$-0.624556\pi$
$137$	−8.92820			−0.762788			−0.381394	+	0.924413i	$0.624556\pi$
$138$		0			0
$139$			7.46410i			0.633097i	0.948576	+	0.316548i	$0.102524\pi$
$139$			7.46410i			0.633097i	−0.948576	+	0.316548i	$0.897476\pi$
$140$		0			0
$141$		0			0
$142$	0.535898	−	2.00000i	0.0449716	−	0.167836i
$143$	6.92820			0.579365
$144$		0			0
$145$		0			0
$146$	−0.196152	+	0.732051i	−0.0162337	+	0.0605850i
$147$		0			0
$148$	−2.00000	+	3.46410i	−0.164399	+	0.284747i
$149$			19.8564i			1.62670i	0.581775	+	0.813350i	$0.302359\pi$
$149$			19.8564i			1.62670i	−0.581775	+	0.813350i	$0.697641\pi$
$150$		0			0
$151$	8.39230			0.682956			0.341478	−	0.939890i	$-0.389073\pi$
$151$	8.39230			0.682956			0.341478	+	0.939890i	$0.389073\pi$
$152$	14.9282	+	14.9282i	1.21084	+	1.21084i
$153$		0			0
$154$	−7.46410	−	2.00000i	−0.601474	−	0.161165i
$155$		0			0
$156$		0			0
$157$		−	16.9282i		−	1.35102i	−0.737352	−	0.675509i	$-0.763924\pi$
$157$		−	16.9282i		−	1.35102i	0.737352	−	0.675509i	$-0.236076\pi$
$158$	−5.46410	+	20.3923i	−0.434701	+	1.62232i
$159$		0			0
$160$		0			0
$161$	11.4641			0.903498
$162$		0			0
$163$			10.1962i			0.798624i	0.916815	+	0.399312i	$0.130751\pi$
$163$			10.1962i			0.798624i	−0.916815	+	0.399312i	$0.869249\pi$
$164$	−9.46410	−	5.46410i	−0.739022	−	0.426675i
$165$		0			0
$166$	−6.46410	−	1.73205i	−0.501712	−	0.134433i
$167$	−20.1962			−1.56283			−0.781413	−	0.624015i	$-0.785501\pi$
$167$	−20.1962			−1.56283			−0.781413	+	0.624015i	$0.785501\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$		0			0
$172$	−8.73205	+	15.1244i	−0.665813	+	1.15322i
$173$		−	2.00000i		−	0.152057i	−0.997106	−	0.0760286i	$-0.975776\pi$
$173$		−	2.00000i		−	0.152057i	0.997106	−	0.0760286i	$-0.0242240\pi$
$174$		0			0
$175$		0			0
$176$	6.92820	−	4.00000i	0.522233	−	0.301511i
$177$		0			0
$178$	1.80385	−	6.73205i	0.135204	−	0.504589i
$179$		−	15.4641i		−	1.15584i	−0.816093	−	0.577921i	$-0.803864\pi$
$179$		−	15.4641i		−	1.15584i	0.816093	−	0.577921i	$-0.196136\pi$
$180$		0			0
$181$		−	16.0000i		−	1.18927i	−0.803996	−	0.594635i	$-0.797296\pi$
$181$		−	16.0000i		−	1.18927i	0.803996	−	0.594635i	$-0.202704\pi$
$182$	12.9282	+	3.46410i	0.958302	+	0.256776i
$183$		0			0
$184$	−8.39230	+	8.39230i	−0.618689	+	0.618689i
$185$		0			0
$186$		0			0
$187$			6.92820i			0.506640i
$188$	−11.6603	−	6.73205i	−0.850411	−	0.490985i
$189$		0			0
$190$		0			0
$191$	19.3205			1.39798			0.698991	−	0.715130i	$-0.253633\pi$
$191$	19.3205			1.39798			0.698991	+	0.715130i	$0.253633\pi$
$192$		0			0
$193$	−7.46410			−0.537278			−0.268639	−	0.963241i	$-0.586574\pi$
$193$	−7.46410			−0.537278			−0.268639	+	0.963241i	$0.586574\pi$
$194$	−2.33975	+	8.73205i	−0.167984	+	0.626925i
$195$		0			0
$196$	−0.803848	−	0.464102i	−0.0574177	−	0.0331501i
$197$			12.5359i			0.893146i	0.894747	+	0.446573i	$0.147356\pi$
$197$			12.5359i			0.893146i	−0.894747	+	0.446573i	$0.852644\pi$
$198$		0			0
$199$	25.8564			1.83291			0.916456	−	0.400135i	$-0.131037\pi$
$199$	25.8564			1.83291			0.916456	+	0.400135i	$0.131037\pi$
$200$		0			0
$201$		0			0
$202$	−14.9282	−	4.00000i	−1.05034	−	0.281439i
$203$		−	18.9282i		−	1.32850i
$204$		0			0
$205$		0			0
$206$	0.607695	−	2.26795i	0.0423401	−	0.158016i
$207$		0			0
$208$	−12.0000	+	6.92820i	−0.832050	+	0.480384i
$209$	−14.9282			−1.03261
$210$		0			0
$211$			14.7846i			1.01781i	0.860821	+	0.508907i	$0.169950\pi$
$211$			14.7846i			1.01781i	−0.860821	+	0.508907i	$0.830050\pi$
$212$	−4.53590	+	7.85641i	−0.311527	+	0.539580i
$213$		0			0
$214$	1.00000	+	0.267949i	0.0683586	+	0.0183166i
$215$		0			0
$216$		0			0
$217$	4.00000			0.271538
$218$	−4.19615	−	1.12436i	−0.284199	−	0.0761510i
$219$		0			0
$220$		0			0
$221$		−	12.0000i		−	0.807207i
$222$		0			0
$223$	16.1962			1.08457			0.542287	−	0.840193i	$-0.317558\pi$
$223$	16.1962			1.08457			0.542287	+	0.840193i	$0.317558\pi$
$224$	14.9282	−	4.00000i	0.997433	−	0.267261i
$225$		0			0
$226$	0.339746	−	1.26795i	0.0225996	−	0.0843427i
$227$			28.0526i			1.86191i	0.365129	+	0.930957i	$0.381025\pi$
$227$			28.0526i			1.86191i	−0.365129	+	0.930957i	$0.618975\pi$
$228$		0			0
$229$			4.00000i			0.264327i	0.991228	+	0.132164i	$0.0421925\pi$
$229$			4.00000i			0.264327i	−0.991228	+	0.132164i	$0.957808\pi$
$230$		0			0
$231$		0			0
$232$	13.8564	+	13.8564i	0.909718	+	0.909718i
$233$	29.3205			1.92085			0.960425	−	0.278538i	$-0.0898499\pi$
$233$	29.3205			1.92085			0.960425	+	0.278538i	$0.0898499\pi$
$234$		0			0
$235$		0			0
$236$	−0.535898	+	0.928203i	−0.0348840	+	0.0604209i
$237$		0			0
$238$	−3.46410	+	12.9282i	−0.224544	+	0.838011i
$239$	20.0000			1.29369			0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000			1.29369			0.646846	+	0.762620i	$0.276088\pi$
$240$		0			0
$241$	−4.39230			−0.282933			−0.141467	−	0.989943i	$-0.545182\pi$
$241$	−4.39230			−0.282933			−0.141467	+	0.989943i	$0.545182\pi$
$242$	2.56218	−	9.56218i	0.164703	−	0.614680i
$243$		0			0
$244$	−4.92820	+	8.53590i	−0.315496	+	0.546455i
$245$		0			0
$246$		0			0
$247$	25.8564			1.64520
$248$	−2.92820	+	2.92820i	−0.185941	+	0.185941i
$249$		0			0
$250$		0			0
$251$			11.0718i			0.698846i	0.936965	+	0.349423i	$0.113622\pi$
$251$			11.0718i			0.698846i	−0.936965	+	0.349423i	$0.886378\pi$
$252$		0			0
$253$		−	8.39230i		−	0.527620i
$254$	−4.85641	+	18.1244i	−0.304718	+	1.13722i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−2.00000			−0.124757			−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000			−0.124757			−0.0623783	+	0.998053i	$0.519869\pi$
$258$		0			0
$259$		−	5.46410i		−	0.339523i
$260$		0			0
$261$		0			0
$262$	10.7321	+	2.87564i	0.663028	+	0.177658i
$263$	5.66025			0.349026			0.174513	−	0.984655i	$-0.444165\pi$
$263$	5.66025			0.349026			0.174513	+	0.984655i	$0.444165\pi$
$264$		0			0
$265$		0			0
$266$	−27.8564	−	7.46410i	−1.70799	−	0.457653i
$267$		0			0
$268$	7.26795	−	12.5885i	0.443961	−	0.768962i
$269$			4.92820i			0.300478i	0.988650	+	0.150239i	$0.0480043\pi$
$269$			4.92820i			0.300478i	−0.988650	+	0.150239i	$0.951996\pi$
$270$		0			0
$271$	15.3205			0.930655			0.465327	−	0.885139i	$-0.345937\pi$
$271$	15.3205			0.930655			0.465327	+	0.885139i	$0.345937\pi$
$272$	−6.92820	−	12.0000i	−0.420084	−	0.727607i
$273$		0			0
$274$	−3.26795	+	12.1962i	−0.197424	+	0.736797i
$275$		0			0
$276$		0			0
$277$			2.00000i			0.120168i	0.998193	+	0.0600842i	$0.0191369\pi$
$277$			2.00000i			0.120168i	−0.998193	+	0.0600842i	$0.980863\pi$
$278$	10.1962	+	2.73205i	0.611525	+	0.163858i
$279$		0			0
$280$		0			0
$281$	−17.4641			−1.04182			−0.520910	−	0.853611i	$-0.674407\pi$
$281$	−17.4641			−1.04182			−0.520910	+	0.853611i	$0.674407\pi$
$282$		0			0
$283$			7.66025i			0.455355i	0.973737	+	0.227677i	$0.0731132\pi$
$283$			7.66025i			0.455355i	−0.973737	+	0.227677i	$0.926887\pi$
$284$	−2.53590	−	1.46410i	−0.150478	−	0.0868784i
$285$		0			0
$286$	2.53590	−	9.46410i	0.149951	−	0.559624i
$287$	14.9282			0.881184
$288$		0			0
$289$	−5.00000			−0.294118
$290$		0			0
$291$		0			0
$292$	0.928203	+	0.535898i	0.0543190	+	0.0313611i
$293$		−	11.8564i		−	0.692659i	−0.938113	−	0.346329i	$-0.887428\pi$
$293$		−	11.8564i		−	0.692659i	0.938113	−	0.346329i	$-0.112572\pi$
$294$		0			0
$295$		0			0
$296$	4.00000	+	4.00000i	0.232495	+	0.232495i
$297$		0			0
$298$	27.1244	+	7.26795i	1.57127	+	0.421021i
$299$			14.5359i			0.840633i
$300$		0			0
$301$		−	23.8564i		−	1.37506i
$302$	3.07180	−	11.4641i	0.176762	−	0.659685i
$303$		0			0
$304$	25.8564	−	14.9282i	1.48297	−	0.856191i
$305$		0			0
$306$		0			0
$307$			26.9808i			1.53987i	0.638120	+	0.769937i	$0.279712\pi$
$307$			26.9808i			1.53987i	−0.638120	+	0.769937i	$0.720288\pi$
$308$	−5.46410	+	9.46410i	−0.311346	+	0.539267i
$309$		0			0
$310$		0			0
$311$	3.32051			0.188289			0.0941444	−	0.995559i	$-0.469988\pi$
$311$	3.32051			0.188289			0.0941444	+	0.995559i	$0.469988\pi$
$312$		0			0
$313$	31.8564			1.80063			0.900315	−	0.435238i	$-0.143336\pi$
$313$	31.8564			1.80063			0.900315	+	0.435238i	$0.143336\pi$
$314$	−23.1244	−	6.19615i	−1.30498	−	0.349669i
$315$		0			0
$316$	25.8564	+	14.9282i	1.45454	+	0.839777i
$317$		−	15.4641i		−	0.868550i	−0.900780	−	0.434275i	$-0.857005\pi$
$317$		−	15.4641i		−	0.868550i	0.900780	−	0.434275i	$-0.142995\pi$
$318$		0			0
$319$	−13.8564			−0.775810
$320$		0			0
$321$		0			0
$322$	4.19615	−	15.6603i	0.233842	−	0.872712i
$323$			25.8564i			1.43869i
$324$		0			0
$325$		0			0
$326$	13.9282	+	3.73205i	0.771412	+	0.206699i
$327$		0			0
$328$	−10.9282	+	10.9282i	−0.603409	+	0.603409i
$329$	18.3923			1.01400
$330$		0			0
$331$			14.0000i			0.769510i	0.923019	+	0.384755i	$0.125714\pi$
$331$			14.0000i			0.769510i	−0.923019	+	0.384755i	$0.874286\pi$
$332$	−4.73205	+	8.19615i	−0.259705	+	0.449822i
$333$		0			0
$334$	−7.39230	+	27.5885i	−0.404489	+	1.50957i
$335$		0			0
$336$		0			0
$337$	−7.85641			−0.427966			−0.213983	−	0.976837i	$-0.568644\pi$
$337$	−7.85641			−0.427966			−0.213983	+	0.976837i	$0.568644\pi$
$338$	0.366025	−	1.36603i	0.0199092	−	0.0743020i
$339$		0			0
$340$		0			0
$341$		−	2.92820i		−	0.158571i
$342$		0			0
$343$	−17.8564			−0.964155
$344$	17.4641	+	17.4641i	0.941601	+	0.941601i
$345$		0			0
$346$	−2.73205	−	0.732051i	−0.146876	−	0.0393553i
$347$		−	15.6603i		−	0.840686i	−0.907365	−	0.420343i	$-0.861910\pi$
$347$		−	15.6603i		−	0.840686i	0.907365	−	0.420343i	$-0.138090\pi$
$348$		0			0
$349$			28.0000i			1.49881i	0.662114	+	0.749403i	$0.269659\pi$
$349$			28.0000i			1.49881i	−0.662114	+	0.749403i	$0.730341\pi$
$350$		0			0
$351$		0			0
$352$	−2.92820	−	10.9282i	−0.156074	−	0.582475i
$353$	−0.928203			−0.0494033			−0.0247016	−	0.999695i	$-0.507864\pi$
$353$	−0.928203			−0.0494033			−0.0247016	+	0.999695i	$0.507864\pi$
$354$		0			0
$355$		0			0
$356$	−8.53590	−	4.92820i	−0.452402	−	0.261194i
$357$		0			0
$358$	−21.1244	−	5.66025i	−1.11646	−	0.299154i
$359$	−5.07180			−0.267679			−0.133840	−	0.991003i	$-0.542731\pi$
$359$	−5.07180			−0.267679			−0.133840	+	0.991003i	$0.542731\pi$
$360$		0			0
$361$	−36.7128			−1.93225
$362$	−21.8564	−	5.85641i	−1.14875	−	0.307806i
$363$		0			0
$364$	9.46410	−	16.3923i	0.496054	−	0.859190i
$365$		0			0
$366$		0			0
$367$	−27.1244			−1.41588			−0.707940	−	0.706273i	$-0.750375\pi$
$367$	−27.1244			−1.41588			−0.707940	+	0.706273i	$0.750375\pi$
$368$	8.39230	+	14.5359i	0.437479	+	0.757736i
$369$		0			0
$370$		0			0
$371$		−	12.3923i		−	0.643376i
$372$		0			0
$373$			29.7128i			1.53847i	0.638965	+	0.769236i	$0.279363\pi$
$373$			29.7128i			1.53847i	−0.638965	+	0.769236i	$0.720637\pi$
$374$	9.46410	+	2.53590i	0.489377	+	0.131128i
$375$		0			0
$376$	−13.4641	+	13.4641i	−0.694358	+	0.694358i
$377$	24.0000			1.23606
$378$		0			0
$379$		−	12.2487i		−	0.629174i	−0.949229	−	0.314587i	$-0.898134\pi$
$379$		−	12.2487i		−	0.629174i	0.949229	−	0.314587i	$-0.101866\pi$
$380$		0			0
$381$		0			0
$382$	7.07180	−	26.3923i	0.361825	−	1.35035i
$383$	−3.12436			−0.159647			−0.0798236	−	0.996809i	$-0.525436\pi$
$383$	−3.12436			−0.159647			−0.0798236	+	0.996809i	$0.525436\pi$
$384$		0			0
$385$		0			0
$386$	−2.73205	+	10.1962i	−0.139058	+	0.518970i
$387$		0			0
$388$	11.0718	+	6.39230i	0.562085	+	0.324520i
$389$		−	34.7846i		−	1.76365i	−0.471577	−	0.881825i	$-0.656315\pi$
$389$		−	34.7846i		−	1.76365i	0.471577	−	0.881825i	$-0.343685\pi$
$390$		0			0
$391$	−14.5359			−0.735112
$392$	−0.928203	+	0.928203i	−0.0468813	+	0.0468813i
$393$		0			0
$394$	17.1244	+	4.58846i	0.862713	+	0.231163i
$395$		0			0
$396$		0			0
$397$		−	16.2487i		−	0.815499i	−0.913094	−	0.407750i	$-0.866314\pi$
$397$		−	16.2487i		−	0.815499i	0.913094	−	0.407750i	$-0.133686\pi$
$398$	9.46410	−	35.3205i	0.474393	−	1.77046i
$399$		0			0
$400$		0			0
$401$	−19.8564			−0.991582			−0.495791	−	0.868442i	$-0.665122\pi$
$401$	−19.8564			−0.991582			−0.495791	+	0.868442i	$0.665122\pi$
$402$		0			0
$403$			5.07180i			0.252644i
$404$	−10.9282	+	18.9282i	−0.543698	+	0.941713i
$405$		0			0
$406$	−25.8564	−	6.92820i	−1.28323	−	0.343841i
$407$	−4.00000			−0.198273
$408$		0			0
$409$	23.3205			1.15312			0.576562	−	0.817053i	$-0.304394\pi$
$409$	23.3205			1.15312			0.576562	+	0.817053i	$0.304394\pi$
$410$		0			0
$411$		0			0
$412$	−2.87564	−	1.66025i	−0.141673	−	0.0817948i
$413$		−	1.46410i		−	0.0720437i
$414$		0			0
$415$		0			0
$416$	5.07180	+	18.9282i	0.248665	+	0.928032i
$417$		0			0
$418$	−5.46410	+	20.3923i	−0.267258	+	0.997420i
$419$		−	2.39230i		−	0.116872i	−0.998291	−	0.0584359i	$-0.981389\pi$
$419$		−	2.39230i		−	0.116872i	0.998291	−	0.0584359i	$-0.0186113\pi$
$420$		0			0
$421$		−	27.8564i		−	1.35764i	−0.734306	−	0.678819i	$-0.762492\pi$
$421$		−	27.8564i		−	1.35764i	0.734306	−	0.678819i	$-0.237508\pi$
$422$	20.1962	+	5.41154i	0.983133	+	0.263430i
$423$		0			0
$424$	9.07180	+	9.07180i	0.440565	+	0.440565i
$425$		0			0
$426$		0			0
$427$		−	13.4641i		−	0.651574i
$428$	0.732051	−	1.26795i	0.0353850	−	0.0612886i
$429$		0			0
$430$		0			0
$431$	14.5359			0.700170			0.350085	−	0.936718i	$-0.386153\pi$
$431$	14.5359			0.700170			0.350085	+	0.936718i	$0.386153\pi$
$432$		0			0
$433$	12.5359			0.602437			0.301218	−	0.953555i	$-0.402607\pi$
$433$	12.5359			0.602437			0.301218	+	0.953555i	$0.402607\pi$
$434$	1.46410	−	5.46410i	0.0702791	−	0.262285i
$435$		0			0
$436$	−3.07180	+	5.32051i	−0.147112	+	0.254806i
$437$		−	31.3205i		−	1.49826i
$438$		0			0
$439$	−0.784610			−0.0374474			−0.0187237	−	0.999825i	$-0.505960\pi$
$439$	−0.784610			−0.0374474			−0.0187237	+	0.999825i	$0.505960\pi$
$440$		0			0
$441$		0			0
$442$	−16.3923	−	4.39230i	−0.779702	−	0.208921i
$443$			30.9808i			1.47194i	0.677014	+	0.735970i	$0.263274\pi$
$443$			30.9808i			1.47194i	−0.677014	+	0.735970i	$0.736726\pi$
$444$		0			0
$445$		0			0
$446$	5.92820	−	22.1244i	0.280709	−	1.04762i
$447$		0			0
$448$		−	21.8564i		−	1.03262i
$449$	−11.3205			−0.534248			−0.267124	−	0.963662i	$-0.586073\pi$
$449$	−11.3205			−0.534248			−0.267124	+	0.963662i	$0.586073\pi$
$450$		0			0
$451$		−	10.9282i		−	0.514589i
$452$	−1.60770	−	0.928203i	−0.0756196	−	0.0436590i
$453$		0			0
$454$	38.3205	+	10.2679i	1.79847	+	0.481899i
$455$		0			0
$456$		0			0
$457$	−14.7846			−0.691595			−0.345797	−	0.938309i	$-0.612392\pi$
$457$	−14.7846			−0.691595			−0.345797	+	0.938309i	$0.612392\pi$
$458$	5.46410	+	1.46410i	0.255321	+	0.0684130i
$459$		0			0
$460$		0			0
$461$			2.92820i			0.136380i	0.997672	+	0.0681900i	$0.0217224\pi$
$461$			2.92820i			0.136380i	−0.997672	+	0.0681900i	$0.978278\pi$
$462$		0			0
$463$	14.7321			0.684656			0.342328	−	0.939580i	$-0.388785\pi$
$463$	14.7321			0.684656			0.342328	+	0.939580i	$0.388785\pi$
$464$	24.0000	−	13.8564i	1.11417	−	0.643268i
$465$		0			0
$466$	10.7321	−	40.0526i	0.497153	−	1.85540i
$467$			8.33975i			0.385917i	0.981207	+	0.192959i	$0.0618083\pi$
$467$			8.33975i			0.385917i	−0.981207	+	0.192959i	$0.938192\pi$
$468$		0			0
$469$			19.8564i			0.916884i
$470$		0			0
$471$		0			0
$472$	1.07180	+	1.07180i	0.0493334	+	0.0493334i
$473$	−17.4641			−0.803000
$474$		0			0
$475$		0			0
$476$	16.3923	+	9.46410i	0.751340	+	0.433786i
$477$		0			0
$478$	7.32051	−	27.3205i	0.334832	−	1.24961i
$479$	21.8564			0.998645			0.499322	−	0.866416i	$-0.333582\pi$
$479$	21.8564			0.998645			0.499322	+	0.866416i	$0.333582\pi$
$480$		0			0
$481$	6.92820			0.315899
$482$	−1.60770	+	6.00000i	−0.0732285	+	0.273293i
$483$		0			0
$484$	−12.1244	−	7.00000i	−0.551107	−	0.318182i
$485$		0			0
$486$		0			0
$487$	24.5885			1.11421			0.557105	−	0.830442i	$-0.311912\pi$
$487$	24.5885			1.11421			0.557105	+	0.830442i	$0.311912\pi$
$488$	9.85641	+	9.85641i	0.446179	+	0.446179i
$489$		0			0
$490$		0			0
$491$		−	3.07180i		−	0.138628i	−0.997595	−	0.0693141i	$-0.977919\pi$
$491$		−	3.07180i		−	0.138628i	0.997595	−	0.0693141i	$-0.0220811\pi$
$492$		0			0
$493$			24.0000i			1.08091i
$494$	9.46410	−	35.3205i	0.425810	−	1.58914i
$495$		0			0
$496$	2.92820	+	5.07180i	0.131480	+	0.227730i
$497$	4.00000			0.179425
$498$		0			0
$499$		−	24.5359i		−	1.09838i	−0.835698	−	0.549189i	$-0.814937\pi$
$499$		−	24.5359i		−	1.09838i	0.835698	−	0.549189i	$-0.185063\pi$
$500$		0			0
$501$		0			0
$502$	15.1244	+	4.05256i	0.675033	+	0.180875i
$503$	−17.6603			−0.787432			−0.393716	−	0.919232i	$-0.628811\pi$
$503$	−17.6603			−0.787432			−0.393716	+	0.919232i	$0.628811\pi$
$504$		0			0
$505$		0			0
$506$	−11.4641	−	3.07180i	−0.509641	−	0.136558i
$507$		0			0
$508$	22.9808	+	13.2679i	1.01961	+	0.588670i
$509$			25.8564i			1.14607i	0.819533	+	0.573033i	$0.194233\pi$
$509$			25.8564i			1.14607i	−0.819533	+	0.573033i	$0.805767\pi$
$510$		0			0
$511$	−1.46410			−0.0647680
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$		0			0
$514$	−0.732051	+	2.73205i	−0.0322894	+	0.120506i
$515$		0			0
$516$		0			0
$517$		−	13.4641i		−	0.592151i
$518$	−7.46410	−	2.00000i	−0.327954	−	0.0878750i
$519$		0			0
$520$		0			0
$521$	16.1436			0.707264			0.353632	−	0.935385i	$-0.384947\pi$
$521$	16.1436			0.707264			0.353632	+	0.935385i	$0.384947\pi$
$522$		0			0
$523$		−	22.1962i		−	0.970570i	−0.874356	−	0.485285i	$-0.838716\pi$
$523$		−	22.1962i		−	0.970570i	0.874356	−	0.485285i	$-0.161284\pi$
$524$	7.85641	−	13.6077i	0.343209	−	0.594455i
$525$		0			0
$526$	2.07180	−	7.73205i	0.0903346	−	0.337133i
$527$	−5.07180			−0.220931
$528$		0			0
$529$	−5.39230			−0.234448
$530$		0			0
$531$		0			0
$532$	−20.3923	+	35.3205i	−0.884119	+	1.53134i
$533$			18.9282i			0.819871i
$534$		0			0
$535$		0			0
$536$	−14.5359	−	14.5359i	−0.627855	−	0.627855i
$537$		0			0
$538$	6.73205	+	1.80385i	0.290239	+	0.0777694i
$539$		−	0.928203i		−	0.0399805i
$540$		0			0
$541$			13.0718i			0.562000i	0.959708	+	0.281000i	$0.0906662\pi$
$541$			13.0718i			0.562000i	−0.959708	+	0.281000i	$0.909334\pi$
$542$	5.60770	−	20.9282i	0.240871	−	0.898943i
$543$		0			0
$544$	−18.9282	+	5.07180i	−0.811540	+	0.217451i
$545$		0			0
$546$		0			0
$547$			36.7321i			1.57055i	0.619148	+	0.785275i	$0.287478\pi$
$547$			36.7321i			1.57055i	−0.619148	+	0.785275i	$0.712522\pi$
$548$	15.4641	+	8.92820i	0.660594	+	0.381394i
$549$		0			0
$550$		0			0
$551$	−51.7128			−2.20304
$552$		0			0
$553$	−40.7846			−1.73434
$554$	2.73205	+	0.732051i	0.116074	+	0.0311019i
$555$		0			0
$556$	7.46410	−	12.9282i	0.316548	−	0.548278i
$557$			26.7846i			1.13490i	0.823408	+	0.567450i	$0.192070\pi$
$557$			26.7846i			1.13490i	−0.823408	+	0.567450i	$0.807930\pi$
$558$		0			0
$559$	30.2487			1.27938
$560$		0			0
$561$		0			0
$562$	−6.39230	+	23.8564i	−0.269643	+	1.00632i
$563$		−	16.0526i		−	0.676535i	−0.941050	−	0.338267i	$-0.890159\pi$
$563$		−	16.0526i		−	0.676535i	0.941050	−	0.338267i	$-0.109841\pi$
$564$		0			0
$565$		0			0
$566$	10.4641	+	2.80385i	0.439839	+	0.117855i
$567$		0			0
$568$	−2.92820	+	2.92820i	−0.122865	+	0.122865i
$569$	6.53590			0.273999			0.137000	−	0.990571i	$-0.456254\pi$
$569$	6.53590			0.273999			0.137000	+	0.990571i	$0.456254\pi$
$570$		0			0
$571$			34.7846i			1.45569i	0.685741	+	0.727845i	$0.259478\pi$
$571$			34.7846i			1.45569i	−0.685741	+	0.727845i	$0.740522\pi$
$572$	−12.0000	−	6.92820i	−0.501745	−	0.289683i
$573$		0			0
$574$	5.46410	−	20.3923i	0.228067	−	0.851158i
$575$		0			0
$576$		0			0
$577$	43.5692			1.81381			0.906905	−	0.421335i	$-0.138438\pi$
$577$	43.5692			1.81381			0.906905	+	0.421335i	$0.138438\pi$
$578$	−1.83013	+	6.83013i	−0.0761232	+	0.284096i
$579$		0			0
$580$		0			0
$581$		−	12.9282i		−	0.536352i
$582$		0			0
$583$	−9.07180			−0.375715
$584$	1.07180	−	1.07180i	0.0443513	−	0.0443513i
$585$		0			0
$586$	−16.1962	−	4.33975i	−0.669057	−	0.179273i
$587$			14.1962i			0.585938i	0.956122	+	0.292969i	$0.0946433\pi$
$587$			14.1962i			0.585938i	−0.956122	+	0.292969i	$0.905357\pi$
$588$		0			0
$589$		−	10.9282i		−	0.450289i
$590$		0			0
$591$		0			0
$592$	6.92820	−	4.00000i	0.284747	−	0.164399i
$593$	−36.6410			−1.50467			−0.752333	−	0.658783i	$-0.771072\pi$
$593$	−36.6410			−1.50467			−0.752333	+	0.658783i	$0.771072\pi$
$594$		0			0
$595$		0			0
$596$	19.8564	−	34.3923i	0.813350	−	1.40876i
$597$		0			0
$598$	19.8564	+	5.32051i	0.811989	+	0.217572i
$599$	−34.6410			−1.41539			−0.707697	−	0.706516i	$-0.750266\pi$
$599$	−34.6410			−1.41539			−0.707697	+	0.706516i	$0.750266\pi$
$600$		0			0
$601$	25.4641			1.03870			0.519351	−	0.854561i	$-0.326174\pi$
$601$	25.4641			1.03870			0.519351	+	0.854561i	$0.326174\pi$
$602$	−32.5885	−	8.73205i	−1.32821	−	0.355892i
$603$		0			0
$604$	−14.5359	−	8.39230i	−0.591457	−	0.341478i
$605$		0			0
$606$		0			0
$607$	20.9808			0.851583			0.425791	−	0.904821i	$-0.359996\pi$
$607$	20.9808			0.851583			0.425791	+	0.904821i	$0.359996\pi$
$608$	−10.9282	−	40.7846i	−0.443197	−	1.65403i
$609$		0			0
$610$		0			0
$611$			23.3205i			0.943447i
$612$		0			0
$613$			5.60770i			0.226493i	0.993567	+	0.113246i	$0.0361249\pi$
$613$			5.60770i			0.226493i	−0.993567	+	0.113246i	$0.963875\pi$
$614$	36.8564	+	9.87564i	1.48740	+	0.398549i
$615$		0			0
$616$	10.9282	+	10.9282i	0.440310	+	0.440310i
$617$	−27.4641			−1.10566			−0.552832	−	0.833293i	$-0.686453\pi$
$617$	−27.4641			−1.10566			−0.552832	+	0.833293i	$0.686453\pi$
$618$		0			0
$619$			33.3205i			1.33926i	0.742693	+	0.669632i	$0.233548\pi$
$619$			33.3205i			1.33926i	−0.742693	+	0.669632i	$0.766452\pi$
$620$		0			0
$621$		0			0
$622$	1.21539	−	4.53590i	0.0487327	−	0.181873i
$623$	13.4641			0.539428
$624$		0			0
$625$		0			0
$626$	11.6603	−	43.5167i	0.466037	−	1.73928i
$627$		0			0
$628$	−16.9282	+	29.3205i	−0.675509	+	1.17002i
$629$			6.92820i			0.276246i
$630$		0			0
$631$	11.3205			0.450662			0.225331	−	0.974282i	$-0.427654\pi$
$631$	11.3205			0.450662			0.225331	+	0.974282i	$0.427654\pi$
$632$	29.8564	−	29.8564i	1.18762	−	1.18762i
$633$		0			0
$634$	−21.1244	−	5.66025i	−0.838955	−	0.224797i
$635$		0			0
$636$		0			0
$637$			1.60770i			0.0636992i
$638$	−5.07180	+	18.9282i	−0.200794	+	0.749375i
$639$		0			0
$640$		0			0
$641$	20.3923			0.805448			0.402724	−	0.915322i	$-0.368064\pi$
$641$	20.3923			0.805448			0.402724	+	0.915322i	$0.368064\pi$
$642$		0			0
$643$			14.8756i			0.586638i	0.956015	+	0.293319i	$0.0947598\pi$
$643$			14.8756i			0.586638i	−0.956015	+	0.293319i	$0.905240\pi$
$644$	−19.8564	−	11.4641i	−0.782452	−	0.451749i
$645$		0			0
$646$	35.3205	+	9.46410i	1.38967	+	0.372360i
$647$	13.2679			0.521617			0.260808	−	0.965391i	$-0.416011\pi$
$647$	13.2679			0.521617			0.260808	+	0.965391i	$0.416011\pi$
$648$		0			0
$649$	−1.07180			−0.0420717
$650$		0			0
$651$		0			0
$652$	10.1962	−	17.6603i	0.399312	−	0.691629i
$653$			36.2487i			1.41852i	0.704946	+	0.709261i	$0.250971\pi$
$653$			36.2487i			1.41852i	−0.704946	+	0.709261i	$0.749029\pi$
$654$		0			0
$655$		0			0
$656$	10.9282	+	18.9282i	0.426675	+	0.739022i
$657$		0			0
$658$	6.73205	−	25.1244i	0.262443	−	0.979449i
$659$			17.3205i			0.674711i	0.941377	+	0.337356i	$0.109532\pi$
$659$			17.3205i			0.674711i	−0.941377	+	0.337356i	$0.890468\pi$
$660$		0			0
$661$			35.8564i			1.39465i	0.716754	+	0.697326i	$0.245627\pi$
$661$			35.8564i			1.39465i	−0.716754	+	0.697326i	$0.754373\pi$
$662$	19.1244	+	5.12436i	0.743289	+	0.199164i
$663$		0			0
$664$	9.46410	+	9.46410i	0.367278	+	0.367278i
$665$		0			0
$666$		0			0
$667$		−	29.0718i		−	1.12566i
$668$	34.9808	+	20.1962i	1.35345	+	0.781413i
$669$		0			0
$670$		0			0
$671$	−9.85641			−0.380502
$672$		0			0
$673$	−19.4641			−0.750286			−0.375143	−	0.926967i	$-0.622406\pi$
$673$	−19.4641			−0.750286			−0.375143	+	0.926967i	$0.622406\pi$
$674$	−2.87564	+	10.7321i	−0.110766	+	0.413383i
$675$		0			0
$676$	−1.73205	−	1.00000i	−0.0666173	−	0.0384615i
$677$		−	38.3923i		−	1.47554i	−0.675054	−	0.737768i	$-0.735880\pi$
$677$		−	38.3923i		−	1.47554i	0.675054	−	0.737768i	$-0.264120\pi$
$678$		0			0
$679$	−17.4641			−0.670211
$680$		0			0
$681$		0			0
$682$	−4.00000	−	1.07180i	−0.153168	−	0.0410412i
$683$		−	34.9808i		−	1.33850i	−0.743037	−	0.669251i	$-0.766615\pi$
$683$		−	34.9808i		−	1.33850i	0.743037	−	0.669251i	$-0.233385\pi$
$684$		0			0
$685$		0			0
$686$	−6.53590	+	24.3923i	−0.249542	+	0.931303i
$687$		0			0
$688$	30.2487	−	17.4641i	1.15322	−	0.665813i
$689$	15.7128			0.598610
$690$		0			0
$691$		−	18.0000i		−	0.684752i	−0.939563	−	0.342376i	$-0.888768\pi$
$691$		−	18.0000i		−	0.684752i	0.939563	−	0.342376i	$-0.111232\pi$
$692$	−2.00000	+	3.46410i	−0.0760286	+	0.131685i
$693$		0			0
$694$	−21.3923	−	5.73205i	−0.812041	−	0.217586i
$695$		0			0
$696$		0			0
$697$	−18.9282			−0.716957
$698$	38.2487	+	10.2487i	1.44774	+	0.387919i
$699$		0			0
$700$		0			0
$701$			32.9282i			1.24368i	0.783144	+	0.621841i	$0.213615\pi$
$701$			32.9282i			1.24368i	−0.783144	+	0.621841i	$0.786385\pi$
$702$		0			0
$703$	−14.9282			−0.563028
$704$	−16.0000			−0.603023
$705$		0			0
$706$	−0.339746	+	1.26795i	−0.0127865	+	0.0477199i
$707$		−	29.8564i		−	1.12287i
$708$		0			0
$709$		−	28.7846i		−	1.08103i	−0.841335	−	0.540514i	$-0.818230\pi$
$709$		−	28.7846i		−	1.08103i	0.841335	−	0.540514i	$-0.181770\pi$
$710$		0			0
$711$		0			0
$712$	−9.85641	+	9.85641i	−0.369384	+	0.369384i
$713$	6.14359			0.230079
$714$		0			0
$715$		0			0
$716$	−15.4641	+	26.7846i	−0.577921	+	1.00099i
$717$		0			0
$718$	−1.85641	+	6.92820i	−0.0692805	+	0.258558i
$719$	−25.8564			−0.964281			−0.482141	−	0.876094i	$-0.660141\pi$
$719$	−25.8564			−0.964281			−0.482141	+	0.876094i	$0.660141\pi$
$720$		0			0
$721$	4.53590			0.168926
$722$	−13.4378	+	50.1506i	−0.500104	+	1.86641i
$723$		0			0
$724$	−16.0000	+	27.7128i	−0.594635	+	1.02994i
$725$		0			0
$726$		0			0
$727$	−14.0526			−0.521181			−0.260590	−	0.965449i	$-0.583917\pi$
$727$	−14.0526			−0.521181			−0.260590	+	0.965449i	$0.583917\pi$
$728$	−18.9282	−	18.9282i	−0.701526	−	0.701526i
$729$		0			0
$730$		0			0
$731$			30.2487i			1.11879i
$732$		0			0
$733$		−	48.9282i		−	1.80720i	−0.428373	−	0.903602i	$-0.640913\pi$
$733$		−	48.9282i		−	1.80720i	0.428373	−	0.903602i	$-0.359087\pi$
$734$	−9.92820	+	37.0526i	−0.366457	+	1.36763i
$735$		0			0
$736$	22.9282	−	6.14359i	0.845145	−	0.226456i
$737$	14.5359			0.535437
$738$		0			0
$739$			5.32051i			0.195718i	0.995200	+	0.0978590i	$0.0311994\pi$
$739$			5.32051i			0.195718i	−0.995200	+	0.0978590i	$0.968801\pi$
$740$		0			0
$741$		0			0
$742$	−16.9282	−	4.53590i	−0.621454	−	0.166518i
$743$	−40.9808			−1.50344			−0.751719	−	0.659483i	$-0.770775\pi$
$743$	−40.9808			−1.50344			−0.751719	+	0.659483i	$0.770775\pi$
$744$		0			0
$745$		0			0
$746$	40.5885	+	10.8756i	1.48605	+	0.398186i
$747$		0			0
$748$	6.92820	−	12.0000i	0.253320	−	0.438763i
$749$			2.00000i			0.0730784i
$750$		0			0
$751$	−22.2487			−0.811867			−0.405934	−	0.913903i	$-0.633054\pi$
$751$	−22.2487			−0.811867			−0.405934	+	0.913903i	$0.633054\pi$
$752$	13.4641	+	23.3205i	0.490985	+	0.850411i
$753$		0			0
$754$	8.78461	−	32.7846i	0.319917	−	1.19395i
$755$		0			0
$756$		0			0
$757$		−	32.9282i		−	1.19680i	−0.801199	−	0.598398i	$-0.795804\pi$
$757$		−	32.9282i		−	1.19680i	0.801199	−	0.598398i	$-0.204196\pi$
$758$	−16.7321	−	4.48334i	−0.607735	−	0.162842i
$759$		0			0
$760$		0			0
$761$	−49.7128			−1.80209			−0.901044	−	0.433728i	$-0.857198\pi$
$761$	−49.7128			−1.80209			−0.901044	+	0.433728i	$0.857198\pi$
$762$		0			0
$763$		−	8.39230i		−	0.303822i
$764$	−33.4641	−	19.3205i	−1.21069	−	0.698991i
$765$		0			0
$766$	−1.14359	+	4.26795i	−0.0413197	+	0.154207i
$767$	1.85641			0.0670310
$768$		0			0
$769$	−0.928203			−0.0334719			−0.0167359	−	0.999860i	$-0.505327\pi$
$769$	−0.928203			−0.0334719			−0.0167359	+	0.999860i	$0.505327\pi$
$770$		0			0
$771$		0			0
$772$	12.9282	+	7.46410i	0.465296	+	0.268639i
$773$			1.60770i			0.0578248i	0.999582	+	0.0289124i	$0.00920438\pi$
$773$			1.60770i			0.0578248i	−0.999582	+	0.0289124i	$0.990796\pi$
$774$		0			0
$775$		0			0
$776$	12.7846	−	12.7846i	0.458941	−	0.458941i
$777$		0			0
$778$	−47.5167	−	12.7321i	−1.70355	−	0.456466i
$779$		−	40.7846i		−	1.46126i
$780$		0			0
$781$		−	2.92820i		−	0.104779i
$782$	−5.32051	+	19.8564i	−0.190261	+	0.710064i
$783$		0			0
$784$	0.928203	+	1.60770i	0.0331501	+	0.0574177i
$785$		0			0
$786$		0			0
$787$		−	14.5885i		−	0.520022i	−0.965606	−	0.260011i	$-0.916274\pi$
$787$		−	14.5885i		−	0.520022i	0.965606	−	0.260011i	$-0.0837262\pi$
$788$	12.5359	−	21.7128i	0.446573	−	0.773487i
$789$		0			0
$790$		0			0
$791$	2.53590			0.0901662
$792$		0			0
$793$	17.0718			0.606237
$794$	−22.1962	−	5.94744i	−0.787712	−	0.211067i
$795$		0			0
$796$	−44.7846	−	25.8564i	−1.58735	−	0.916456i
$797$			26.1051i			0.924691i	0.886700	+	0.462345i	$0.152992\pi$
$797$			26.1051i			0.924691i	−0.886700	+	0.462345i	$0.847008\pi$
$798$		0			0
$799$	−23.3205			−0.825020
$800$		0			0
$801$		0			0
$802$	−7.26795	+	27.1244i	−0.256640	+	0.957794i
$803$			1.07180i			0.0378229i
$804$		0			0
$805$		0			0
$806$	6.92820	+	1.85641i	0.244036	+	0.0653891i
$807$		0			0
$808$	21.8564	+	21.8564i	0.768906	+	0.768906i
$809$	3.85641			0.135584			0.0677920	−	0.997699i	$-0.478405\pi$
$809$	3.85641			0.135584			0.0677920	+	0.997699i	$0.478405\pi$
$810$		0			0
$811$			15.0718i			0.529242i	0.964352	+	0.264621i	$0.0852469\pi$
$811$			15.0718i			0.529242i	−0.964352	+	0.264621i	$0.914753\pi$
$812$	−18.9282	+	32.7846i	−0.664250	+	1.15051i
$813$		0			0
$814$	−1.46410	+	5.46410i	−0.0513167	+	0.191517i
$815$		0			0
$816$		0			0
$817$	−65.1769			−2.28025
$818$	8.53590	−	31.8564i	0.298451	−	1.11383i
$819$		0			0
$820$		0			0
$821$		−	6.78461i		−	0.236785i	−0.992967	−	0.118392i	$-0.962226\pi$
$821$		−	6.78461i		−	0.236785i	0.992967	−	0.118392i	$-0.0377740\pi$
$822$		0			0
$823$	−15.1244			−0.527202			−0.263601	−	0.964632i	$-0.584910\pi$
$823$	−15.1244			−0.527202			−0.263601	+	0.964632i	$0.584910\pi$
$824$	−3.32051	+	3.32051i	−0.115675	+	0.115675i
$825$		0			0
$826$	−2.00000	−	0.535898i	−0.0695889	−	0.0186463i
$827$			1.12436i			0.0390977i	0.999809	+	0.0195488i	$0.00622298\pi$
$827$			1.12436i			0.0390977i	−0.999809	+	0.0195488i	$0.993777\pi$
$828$		0			0
$829$		−	15.0718i		−	0.523465i	−0.965140	−	0.261733i	$-0.915706\pi$
$829$		−	15.0718i		−	0.523465i	0.965140	−	0.261733i	$-0.0842938\pi$
$830$		0			0
$831$		0			0
$832$	27.7128			0.960769
$833$	−1.60770			−0.0557033
$834$		0			0
$835$		0			0
$836$	25.8564	+	14.9282i	0.894263	+	0.516303i
$837$		0			0
$838$	−3.26795	−	0.875644i	−0.112889	−	0.0302486i
$839$	16.7846			0.579469			0.289735	−	0.957107i	$-0.406433\pi$
$839$	16.7846			0.579469			0.289735	+	0.957107i	$0.406433\pi$
$840$		0			0
$841$	−19.0000			−0.655172
$842$	−38.0526	−	10.1962i	−1.31138	−	0.351383i
$843$		0			0
$844$	14.7846	−	25.6077i	0.508907	−	0.881453i
$845$		0			0
$846$		0			0
$847$	19.1244			0.657121
$848$	15.7128	−	9.07180i	0.539580	−	0.311527i
$849$		0			0
$850$		0			0
$851$		−	8.39230i		−	0.287685i
$852$		0			0
$853$		−	42.3923i		−	1.45148i	−0.687967	−	0.725742i	$-0.741496\pi$
$853$		−	42.3923i		−	1.45148i	0.687967	−	0.725742i	$-0.258504\pi$
$854$	−18.3923	−	4.92820i	−0.629372	−	0.168640i
$855$		0			0
$856$	−1.46410	−	1.46410i	−0.0500420	−	0.0500420i
$857$	7.85641			0.268370			0.134185	−	0.990956i	$-0.457158\pi$
$857$	7.85641			0.268370			0.134185	+	0.990956i	$0.457158\pi$
$858$		0			0
$859$			20.2487i			0.690877i	0.938441	+	0.345439i	$0.112270\pi$
$859$			20.2487i			0.690877i	−0.938441	+	0.345439i	$0.887730\pi$
$860$		0			0
$861$		0			0
$862$	5.32051	−	19.8564i	0.181217	−	0.676312i
$863$	30.3397			1.03278			0.516388	−	0.856354i	$-0.327276\pi$
$863$	30.3397			1.03278			0.516388	+	0.856354i	$0.327276\pi$
$864$		0			0
$865$		0			0
$866$	4.58846	−	17.1244i	0.155922	−	0.581909i
$867$		0			0
$868$	−6.92820	−	4.00000i	−0.235159	−	0.135769i
$869$			29.8564i			1.01281i
$870$		0			0
$871$	−25.1769			−0.853087
$872$	6.14359	+	6.14359i	0.208048	+	0.208048i
$873$		0			0
$874$	−42.7846	−	11.4641i	−1.44721	−	0.387779i
$875$		0			0
$876$		0			0
$877$			53.7128i			1.81375i	0.421397	+	0.906876i	$0.361540\pi$
$877$			53.7128i			1.81375i	−0.421397	+	0.906876i	$0.638460\pi$
$878$	−0.287187	+	1.07180i	−0.00969209	+	0.0361714i
$879$		0			0
$880$		0			0
$881$	−2.53590			−0.0854366			−0.0427183	−	0.999087i	$-0.513602\pi$
$881$	−2.53590			−0.0854366			−0.0427183	+	0.999087i	$0.513602\pi$
$882$		0			0
$883$			37.9090i			1.27574i	0.770145	+	0.637869i	$0.220184\pi$
$883$			37.9090i			1.27574i	−0.770145	+	0.637869i	$0.779816\pi$
$884$	−12.0000	+	20.7846i	−0.403604	+	0.699062i
$885$		0			0
$886$	42.3205	+	11.3397i	1.42179	+	0.380966i
$887$	51.9090			1.74293			0.871466	−	0.490455i	$-0.163170\pi$
$887$	51.9090			1.74293			0.871466	+	0.490455i	$0.163170\pi$
$888$		0			0
$889$	−36.2487			−1.21574
$890$		0			0
$891$		0			0
$892$	−28.0526	−	16.1962i	−0.939269	−	0.542287i
$893$		−	50.2487i		−	1.68151i
$894$		0			0
$895$		0			0
$896$	−29.8564	−	8.00000i	−0.997433	−	0.267261i
$897$		0			0
$898$	−4.14359	+	15.4641i	−0.138274	+	0.516044i
$899$		−	10.1436i		−	0.338308i
$900$		0			0
$901$			15.7128i			0.523470i
$902$	−14.9282	−	4.00000i	−0.497055	−	0.133185i
$903$		0			0
$904$	−1.85641	+	1.85641i	−0.0617432	+	0.0617432i
$905$		0			0
$906$		0			0
$907$			29.1244i			0.967058i	0.875328	+	0.483529i	$0.160645\pi$
$907$			29.1244i			0.967058i	−0.875328	+	0.483529i	$0.839355\pi$
$908$	28.0526	−	48.5885i	0.930957	−	1.61246i
$909$		0			0
$910$		0			0
$911$	−13.1769			−0.436571			−0.218285	−	0.975885i	$-0.570046\pi$
$911$	−13.1769			−0.436571			−0.218285	+	0.975885i	$0.570046\pi$
$912$		0			0
$913$	−9.46410			−0.313216
$914$	−5.41154	+	20.1962i	−0.178998	+	0.668029i
$915$		0			0
$916$	4.00000	−	6.92820i	0.132164	−	0.228914i
$917$			21.4641i			0.708807i
$918$		0			0
$919$	−25.0718			−0.827042			−0.413521	−	0.910495i	$-0.635701\pi$
$919$	−25.0718			−0.827042			−0.413521	+	0.910495i	$0.635701\pi$
$920$		0			0
$921$		0			0
$922$	4.00000	+	1.07180i	0.131733	+	0.0352977i
$923$			5.07180i			0.166940i
$924$		0			0
$925$		0			0
$926$	5.39230	−	20.1244i	0.177202	−	0.661327i
$927$		0			0
$928$	−10.1436	−	37.8564i	−0.332980	−	1.24270i
$929$	10.5359			0.345672			0.172836	−	0.984951i	$-0.444707\pi$
$929$	10.5359			0.345672			0.172836	+	0.984951i	$0.444707\pi$
$930$		0			0
$931$		−	3.46410i		−	0.113531i
$932$	−50.7846	−	29.3205i	−1.66351	−	0.960425i
$933$		0			0
$934$	11.3923	+	3.05256i	0.372768	+	0.0998828i
$935$		0			0
$936$		0			0
$937$	44.2487			1.44554			0.722771	−	0.691087i	$-0.242868\pi$
$937$	44.2487			1.44554			0.722771	+	0.691087i	$0.242868\pi$
$938$	27.1244	+	7.26795i	0.885642	+	0.237307i
$939$		0			0
$940$		0			0
$941$		−	32.0000i		−	1.04317i	−0.853199	−	0.521585i	$-0.825341\pi$
$941$		−	32.0000i		−	1.04317i	0.853199	−	0.521585i	$-0.174659\pi$
$942$		0			0
$943$	22.9282			0.746645
$944$	1.85641	−	1.07180i	0.0604209	−	0.0348840i
$945$		0			0
$946$	−6.39230	+	23.8564i	−0.207832	+	0.775639i
$947$		−	21.1244i		−	0.686449i	−0.939253	−	0.343225i	$-0.888481\pi$
$947$		−	21.1244i		−	0.686449i	0.939253	−	0.343225i	$-0.111519\pi$
$948$		0			0
$949$		−	1.85641i		−	0.0602615i
$950$		0			0
$951$		0			0
$952$	18.9282	−	18.9282i	0.613467	−	0.613467i
$953$	−58.7846			−1.90422			−0.952110	−	0.305755i	$-0.901091\pi$
$953$	−58.7846			−1.90422			−0.952110	+	0.305755i	$0.901091\pi$
$954$		0			0
$955$		0			0
$956$	−34.6410	−	20.0000i	−1.12037	−	0.646846i
$957$		0			0
$958$	8.00000	−	29.8564i	0.258468	−	0.964617i
$959$	−24.3923			−0.787669
$960$		0			0
$961$	−28.8564			−0.930852
$962$	2.53590	−	9.46410i	0.0817606	−	0.305135i
$963$		0			0
$964$	7.60770	+	4.39230i	0.245027	+	0.141467i
$965$		0			0
$966$		0			0
$967$	−33.6603			−1.08244			−0.541220	−	0.840881i	$-0.682038\pi$
$967$	−33.6603			−1.08244			−0.541220	+	0.840881i	$0.682038\pi$
$968$	−14.0000	+	14.0000i	−0.449977	+	0.449977i
$969$		0			0
$970$		0			0
$971$			23.0718i			0.740409i	0.928950	+	0.370205i	$0.120712\pi$
$971$			23.0718i			0.740409i	−0.928950	+	0.370205i	$0.879288\pi$
$972$		0			0
$973$			20.3923i			0.653747i
$974$	9.00000	−	33.5885i	0.288379	−	1.07624i
$975$		0			0
$976$	17.0718	−	9.85641i	0.546455	−	0.315496i
$977$	−31.4641			−1.00663			−0.503313	−	0.864104i	$-0.667886\pi$
$977$	−31.4641			−1.00663			−0.503313	+	0.864104i	$0.667886\pi$
$978$		0			0
$979$		−	9.85641i		−	0.315012i
$980$		0			0
$981$		0			0
$982$	−4.19615	−	1.12436i	−0.133905	−	0.0358796i
$983$	−45.2679			−1.44382			−0.721912	−	0.691985i	$-0.756736\pi$
$983$	−45.2679			−1.44382			−0.721912	+	0.691985i	$0.756736\pi$
$984$		0			0
$985$		0			0
$986$	32.7846	+	8.78461i	1.04407	+	0.279759i
$987$		0			0
$988$	−44.7846	−	25.8564i	−1.42479	−	0.822602i
$989$		−	36.6410i		−	1.16512i
$990$		0			0
$991$	34.5359			1.09707			0.548534	−	0.836128i	$-0.315186\pi$
$991$	34.5359			1.09707			0.548534	+	0.836128i	$0.315186\pi$
$992$	8.00000	−	2.14359i	0.254000	−	0.0680592i
$993$		0			0
$994$	1.46410	−	5.46410i	0.0464385	−	0.173311i
$995$		0			0
$996$		0			0
$997$			51.1769i			1.62079i	0.585884	+	0.810395i	$0.300747\pi$
$997$			51.1769i			1.62079i	−0.585884	+	0.810395i	$0.699253\pi$
$998$	−33.5167	−	8.98076i	−1.06095	−	0.284281i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.k.j.901.3		4
3.2	odd	2		200.2.d.f.101.2		4
4.3	odd	2		7200.2.k.j.3601.2		4
5.2	odd	4		1800.2.d.p.1549.4		4
5.3	odd	4		1800.2.d.l.1549.1		4
5.4	even	2		360.2.k.e.181.2		4
8.3	odd	2		7200.2.k.j.3601.1		4
8.5	even	2	inner	1800.2.k.j.901.4		4
12.11	even	2		800.2.d.e.401.3		4
15.2	even	4		200.2.f.c.149.1		4
15.8	even	4		200.2.f.e.149.4		4
15.14	odd	2		40.2.d.a.21.3	✓	4
20.3	even	4		7200.2.d.n.2449.4		4
20.7	even	4		7200.2.d.o.2449.1		4
20.19	odd	2		1440.2.k.e.721.2		4
24.5	odd	2		200.2.d.f.101.1		4
24.11	even	2		800.2.d.e.401.2		4
40.3	even	4		7200.2.d.o.2449.4		4
40.13	odd	4		1800.2.d.p.1549.3		4
40.19	odd	2		1440.2.k.e.721.4		4
40.27	even	4		7200.2.d.n.2449.1		4
40.29	even	2		360.2.k.e.181.1		4
40.37	odd	4		1800.2.d.l.1549.2		4
48.5	odd	4		6400.2.a.ce.1.1		2
48.11	even	4		6400.2.a.be.1.2		2
48.29	odd	4		6400.2.a.z.1.2		2
48.35	even	4		6400.2.a.cj.1.1		2
60.23	odd	4		800.2.f.e.49.2		4
60.47	odd	4		800.2.f.c.49.3		4
60.59	even	2		160.2.d.a.81.2		4
120.29	odd	2		40.2.d.a.21.4	yes	4
120.53	even	4		200.2.f.c.149.2		4
120.59	even	2		160.2.d.a.81.3		4
120.77	even	4		200.2.f.e.149.3		4
120.83	odd	4		800.2.f.c.49.4		4
120.107	odd	4		800.2.f.e.49.1		4
240.29	odd	4		1280.2.a.o.1.1		2
240.59	even	4		1280.2.a.n.1.1		2
240.149	odd	4		1280.2.a.a.1.2		2
240.179	even	4		1280.2.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.2.d.a.21.3	✓	4	15.14	odd	2
40.2.d.a.21.4	yes	4	120.29	odd	2
160.2.d.a.81.2		4	60.59	even	2
160.2.d.a.81.3		4	120.59	even	2
200.2.d.f.101.1		4	24.5	odd	2
200.2.d.f.101.2		4	3.2	odd	2
200.2.f.c.149.1		4	15.2	even	4
200.2.f.c.149.2		4	120.53	even	4
200.2.f.e.149.3		4	120.77	even	4
200.2.f.e.149.4		4	15.8	even	4
360.2.k.e.181.1		4	40.29	even	2
360.2.k.e.181.2		4	5.4	even	2
800.2.d.e.401.2		4	24.11	even	2
800.2.d.e.401.3		4	12.11	even	2
800.2.f.c.49.3		4	60.47	odd	4
800.2.f.c.49.4		4	120.83	odd	4
800.2.f.e.49.1		4	120.107	odd	4
800.2.f.e.49.2		4	60.23	odd	4
1280.2.a.a.1.2		2	240.149	odd	4
1280.2.a.d.1.2		2	240.179	even	4
1280.2.a.n.1.1		2	240.59	even	4
1280.2.a.o.1.1		2	240.29	odd	4
1440.2.k.e.721.2		4	20.19	odd	2
1440.2.k.e.721.4		4	40.19	odd	2
1800.2.d.l.1549.1		4	5.3	odd	4
1800.2.d.l.1549.2		4	40.37	odd	4
1800.2.d.p.1549.3		4	40.13	odd	4
1800.2.d.p.1549.4		4	5.2	odd	4
1800.2.k.j.901.3		4	1.1	even	1	trivial
1800.2.k.j.901.4		4	8.5	even	2	inner
6400.2.a.z.1.2		2	48.29	odd	4
6400.2.a.be.1.2		2	48.11	even	4
6400.2.a.ce.1.1		2	48.5	odd	4
6400.2.a.cj.1.1		2	48.35	even	4
7200.2.d.n.2449.1		4	40.27	even	4
7200.2.d.n.2449.4		4	20.3	even	4
7200.2.d.o.2449.1		4	20.7	even	4
7200.2.d.o.2449.4		4	40.3	even	4
7200.2.k.j.3601.1		4	8.3	odd	2
7200.2.k.j.3601.2		4	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.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +2.73205 q^{7} +(-2.00000 + 2.00000i) q^{8} -2.00000i q^{11} +3.46410i q^{13} +(1.00000 - 3.73205i) q^{14} +(2.00000 + 3.46410i) q^{16} -3.46410 q^{17} -7.46410i q^{19} +(-2.73205 - 0.732051i) q^{22} +4.19615 q^{23} +(4.73205 + 1.26795i) q^{26} +(-4.73205 - 2.73205i) q^{28} -6.92820i q^{29} +1.46410 q^{31} +(5.46410 - 1.46410i) q^{32} +(-1.26795 + 4.73205i) q^{34} -2.00000i q^{37} +(-10.1962 - 2.73205i) q^{38} +5.46410 q^{41} -8.73205i q^{43} +(-2.00000 + 3.46410i) q^{44} +(1.53590 - 5.73205i) q^{46} +6.73205 q^{47} +0.464102 q^{49} +(3.46410 - 6.00000i) q^{52} -4.53590i q^{53} +(-5.46410 + 5.46410i) q^{56} +(-9.46410 - 2.53590i) q^{58} -0.535898i q^{59} -4.92820i q^{61} +(0.535898 - 2.00000i) q^{62} -8.00000i q^{64} +7.26795i q^{67} +(6.00000 + 3.46410i) q^{68} +1.46410 q^{71} -0.535898 q^{73} +(-2.73205 - 0.732051i) q^{74} +(-7.46410 + 12.9282i) q^{76} -5.46410i q^{77} -14.9282 q^{79} +(2.00000 - 7.46410i) q^{82} -4.73205i q^{83} +(-11.9282 - 3.19615i) q^{86} +(4.00000 + 4.00000i) q^{88} +4.92820 q^{89} +9.46410i q^{91} +(-7.26795 - 4.19615i) q^{92} +(2.46410 - 9.19615i) q^{94} -6.39230 q^{97} +(0.169873 - 0.633975i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 4 q^{7} - 8 q^{8} + 4 q^{14} + 8 q^{16} - 4 q^{22} - 4 q^{23} + 12 q^{26} - 12 q^{28} - 8 q^{31} + 8 q^{32} - 12 q^{34} - 20 q^{38} + 8 q^{41} - 8 q^{44} + 20 q^{46} + 20 q^{47} - 12 q^{49}+ \cdots + 18 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 4 * q^7 - 8 * q^8 + 4 * q^14 + 8 * q^16 - 4 * q^22 - 4 * q^23 + 12 * q^26 - 12 * q^28 - 8 * q^31 + 8 * q^32 - 12 * q^34 - 20 * q^38 + 8 * q^41 - 8 * q^44 + 20 * q^46 + 20 * q^47 - 12 * q^49 - 8 * q^56 - 24 * q^58 + 16 * q^62 + 24 * q^68 - 8 * q^71 - 16 * q^73 - 4 * q^74 - 16 * q^76 - 32 * q^79 + 8 * q^82 - 20 * q^86 + 16 * q^88 - 8 * q^89 - 36 * q^92 - 4 * q^94 + 16 * q^97 + 18 * q^98

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