LMFDB - Embedded newform 1800.2.k.u.901.7

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:	$12$
Coefficient field:	12.0.180227832610816.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + x^{10} - 8x^{6} + 16x^{2} + 64 $ x^12 + x^10 - 8x^6 + 16x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			901.7
Root			$0.450129 + 1.34067i$ of defining polynomial
Character	$\chi$	$=$	1800.901
Dual form			1800.2.k.u.901.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.450129 - 1.34067i) q^{2} +(-1.59477 - 1.20695i) q^{4} +2.64265 q^{7} +(-2.33596 + 1.59477i) q^{8} +O(q^{10})$	\(q+(0.450129 - 1.34067i) q^{2} +(-1.59477 - 1.20695i) q^{4} +2.64265 q^{7} +(-2.33596 + 1.59477i) q^{8} +1.51363i q^{11} +3.87086i q^{13} +(1.18953 - 3.54291i) q^{14} +(1.08656 + 3.84959i) q^{16} -3.31415 q^{17} +7.08582i q^{19} +(2.02927 + 0.681331i) q^{22} -4.82778 q^{23} +(5.18953 + 1.74239i) q^{26} +(-4.21441 - 3.18953i) q^{28} +2.18513i q^{29} -7.36266 q^{31} +(5.65011 + 0.276098i) q^{32} +(-1.49180 + 4.44317i) q^{34} +7.87086i q^{37} +(9.49971 + 3.18953i) q^{38} -8.72532 q^{41} +1.01641i q^{43} +(1.82687 - 2.41389i) q^{44} +(-2.17313 + 6.47244i) q^{46} +7.08582 q^{47} -0.0164068 q^{49} +(4.67192 - 6.17313i) q^{52} -4.50820i q^{53} +(-6.17313 + 4.21441i) q^{56} +(2.92953 + 0.983593i) q^{58} +6.79893i q^{59} -3.60104i q^{61} +(-3.31415 + 9.87086i) q^{62} +(2.91344 - 7.45063i) q^{64} +1.01641i q^{67} +(5.28530 + 4.00000i) q^{68} +6.72532 q^{71} +15.5146 q^{73} +(10.5522 + 3.54291i) q^{74} +(8.55220 - 11.3002i) q^{76} +4.00000i q^{77} -7.36266 q^{79} +(-3.92752 + 11.6977i) q^{82} -7.74173i q^{83} +(1.36266 + 0.457515i) q^{86} +(-2.41389 - 3.53579i) q^{88} -14.7581 q^{89} +10.2293i q^{91} +(7.69919 + 5.82687i) q^{92} +(3.18953 - 9.49971i) q^{94} +11.1444 q^{97} +(-0.00738516 + 0.0219960i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{4}+O(q^{10}) $ 12 * q - 2 * q^4	$ 12 q - 2 q^{4} - 20 q^{14} + 2 q^{16} + 28 q^{26} - 32 q^{31} - 24 q^{34} + 8 q^{41} + 44 q^{44} - 4 q^{46} + 12 q^{49} - 52 q^{56} + 46 q^{64} - 32 q^{71} + 36 q^{74} + 12 q^{76} - 32 q^{79} - 40 q^{86} - 40 q^{89} + 4 q^{94}+O(q^{100}) $ 12 * q - 2 * q^4 - 20 * q^14 + 2 * q^16 + 28 * q^26 - 32 * q^31 - 24 * q^34 + 8 * q^41 + 44 * q^44 - 4 * q^46 + 12 * q^49 - 52 * q^56 + 46 * q^64 - 32 * q^71 + 36 * q^74 + 12 * q^76 - 32 * q^79 - 40 * q^86 - 40 * q^89 + 4 * 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 $

$2$	0.450129	−	1.34067i	0.318290	−	0.947994i
$2$	0.450129	−	1.34067i	0.318290	−	0.947994i
$3$		0			0
$3$		0			0
$4$	−1.59477	−	1.20695i	−0.797384	−	0.603473i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.64265			0.998827			0.499414	−	0.866364i	$-0.333549\pi$
$7$	2.64265			0.998827			0.499414	+	0.866364i	$0.333549\pi$
$8$	−2.33596	+	1.59477i	−0.825887	+	0.563835i
$9$		0			0
$10$		0			0
$11$			1.51363i			0.456377i	0.973617	+	0.228189i	$0.0732803\pi$
$11$			1.51363i			0.456377i	−0.973617	+	0.228189i	$0.926720\pi$
$12$		0			0
$13$			3.87086i			1.07358i	0.843714	+	0.536792i	$0.180364\pi$
$13$			3.87086i			1.07358i	−0.843714	+	0.536792i	$0.819636\pi$
$14$	1.18953	−	3.54291i	0.317916	−	0.946882i
$15$		0			0
$16$	1.08656	+	3.84959i	0.271641	+	0.962399i
$17$	−3.31415			−0.803800			−0.401900	−	0.915684i	$-0.631650\pi$
$17$	−3.31415			−0.803800			−0.401900	+	0.915684i	$0.631650\pi$
$18$		0			0
$19$			7.08582i			1.62560i	0.582545	+	0.812799i	$0.302057\pi$
$19$			7.08582i			1.62560i	−0.582545	+	0.812799i	$0.697943\pi$
$20$		0			0
$21$		0			0
$22$	2.02927	+	0.681331i	0.432643	+	0.145260i
$23$	−4.82778			−1.00666			−0.503331	−	0.864094i	$-0.667892\pi$
$23$	−4.82778			−1.00666			−0.503331	+	0.864094i	$0.667892\pi$
$24$		0			0
$25$		0			0
$26$	5.18953	+	1.74239i	1.01775	+	0.341711i
$27$		0			0
$28$	−4.21441	−	3.18953i	−0.796448	−	0.602765i
$29$			2.18513i			0.405769i	0.979203	+	0.202885i	$0.0650316\pi$
$29$			2.18513i			0.405769i	−0.979203	+	0.202885i	$0.934968\pi$
$30$		0			0
$31$	−7.36266			−1.32237			−0.661187	−	0.750222i	$-0.729947\pi$
$31$	−7.36266			−1.32237			−0.661187	+	0.750222i	$0.729947\pi$
$32$	5.65011	+	0.276098i	0.998808	+	0.0488076i
$33$		0			0
$34$	−1.49180	+	4.44317i	−0.255841	+	0.761997i
$35$		0			0
$36$		0			0
$37$			7.87086i			1.29396i	0.762506	+	0.646981i	$0.223969\pi$
$37$			7.87086i			1.29396i	−0.762506	+	0.646981i	$0.776031\pi$
$38$	9.49971	+	3.18953i	1.54106	+	0.517411i
$39$		0			0
$40$		0			0
$41$	−8.72532			−1.36267			−0.681333	−	0.731973i	$-0.738600\pi$
$41$	−8.72532			−1.36267			−0.681333	+	0.731973i	$0.738600\pi$
$42$		0			0
$43$			1.01641i			0.155001i	0.996992	+	0.0775003i	$0.0246939\pi$
$43$			1.01641i			0.155001i	−0.996992	+	0.0775003i	$0.975306\pi$
$44$	1.82687	−	2.41389i	0.275411	−	0.363908i
$45$		0			0
$46$	−2.17313	+	6.47244i	−0.320410	+	0.954309i
$47$	7.08582			1.03357			0.516786	−	0.856114i	$-0.327128\pi$
$47$	7.08582			1.03357			0.516786	+	0.856114i	$0.327128\pi$
$48$		0			0
$49$	−0.0164068			−0.00234382
$50$		0			0
$51$		0			0
$52$	4.67192	−	6.17313i	0.647879	−	0.856059i
$53$		−	4.50820i		−	0.619249i	−0.950859	−	0.309625i	$-0.899797\pi$
$53$		−	4.50820i		−	0.619249i	0.950859	−	0.309625i	$-0.100203\pi$
$54$		0			0
$55$		0			0
$56$	−6.17313	+	4.21441i	−0.824919	+	0.563174i
$57$		0			0
$58$	2.92953	+	0.983593i	0.384667	+	0.129152i
$59$			6.79893i			0.885145i	0.896733	+	0.442573i	$0.145934\pi$
$59$			6.79893i			0.885145i	−0.896733	+	0.442573i	$0.854066\pi$
$60$		0			0
$61$		−	3.60104i		−	0.461065i	−0.973065	−	0.230533i	$-0.925953\pi$
$61$		−	3.60104i		−	0.461065i	0.973065	−	0.230533i	$-0.0740469\pi$
$62$	−3.31415	+	9.87086i	−0.420898	+	1.25360i
$63$		0			0
$64$	2.91344	−	7.45063i	0.364180	−	0.931329i
$65$		0			0
$66$		0			0
$67$			1.01641i			0.124174i	0.998071	+	0.0620869i	$0.0197756\pi$
$67$			1.01641i			0.124174i	−0.998071	+	0.0620869i	$0.980224\pi$
$68$	5.28530	+	4.00000i	0.640937	+	0.485071i
$69$		0			0
$70$		0			0
$71$	6.72532			0.798149			0.399074	−	0.916919i	$-0.369331\pi$
$71$	6.72532			0.798149			0.399074	+	0.916919i	$0.369331\pi$
$72$		0			0
$73$	15.5146			1.81585			0.907925	−	0.419132i	$-0.137666\pi$
$73$	15.5146			1.81585			0.907925	+	0.419132i	$0.137666\pi$
$74$	10.5522	+	3.54291i	1.22667	+	0.411855i
$75$		0			0
$76$	8.55220	−	11.3002i	0.981004	−	1.29622i
$77$			4.00000i			0.455842i
$78$		0			0
$79$	−7.36266			−0.828364			−0.414182	−	0.910194i	$-0.635932\pi$
$79$	−7.36266			−0.828364			−0.414182	+	0.910194i	$0.635932\pi$
$80$		0			0
$81$		0			0
$82$	−3.92752	+	11.6977i	−0.433723	+	1.29180i
$83$		−	7.74173i		−	0.849765i	−0.905248	−	0.424883i	$-0.860315\pi$
$83$		−	7.74173i		−	0.849765i	0.905248	−	0.424883i	$-0.139685\pi$
$84$		0			0
$85$		0			0
$86$	1.36266	+	0.457515i	0.146940	+	0.0493351i
$87$		0			0
$88$	−2.41389	−	3.53579i	−0.257322	−	0.376916i
$89$	−14.7581			−1.56436			−0.782180	−	0.623053i	$-0.785892\pi$
$89$	−14.7581			−1.56436			−0.782180	+	0.623053i	$0.785892\pi$
$90$		0			0
$91$			10.2293i			1.07233i
$92$	7.69919	+	5.82687i	0.802696	+	0.607493i
$93$		0			0
$94$	3.18953	−	9.49971i	0.328975	−	0.979820i
$95$		0			0
$96$		0			0
$97$	11.1444			1.13154			0.565769	−	0.824563i	$-0.308579\pi$
$97$	11.1444			1.13154			0.565769	+	0.824563i	$0.308579\pi$
$98$	−0.00738516	+	0.0219960i	−0.000746014	+	0.00222193i
$99$		0			0
$100$		0			0
$101$			13.3295i			1.32633i	0.748471	+	0.663167i	$0.230788\pi$
$101$			13.3295i			1.32633i	−0.748471	+	0.663167i	$0.769212\pi$
$102$		0			0
$103$	−0.958386			−0.0944326			−0.0472163	−	0.998885i	$-0.515035\pi$
$103$	−0.958386			−0.0944326			−0.0472163	+	0.998885i	$0.515035\pi$
$104$	−6.17313	−	9.04219i	−0.605325	−	0.886660i
$105$		0			0
$106$	−6.04399	−	2.02927i	−0.587044	−	0.197101i
$107$		−	4.00000i		−	0.386695i	−0.981130	−	0.193347i	$-0.938066\pi$
$107$		−	4.00000i		−	0.386695i	0.981130	−	0.193347i	$-0.0619344\pi$
$108$		0			0
$109$			0.769233i			0.0736792i	0.999321	+	0.0368396i	$0.0117291\pi$
$109$			0.769233i			0.0736792i	−0.999321	+	0.0368396i	$0.988271\pi$
$110$		0			0
$111$		0			0
$112$	2.87141	+	10.1731i	0.271322	+	0.961270i
$113$	14.4585			1.36014			0.680071	−	0.733146i	$-0.261949\pi$
$113$	14.4585			1.36014			0.680071	+	0.733146i	$0.261949\pi$
$114$		0			0
$115$		0			0
$116$	2.63734	−	3.48478i	0.244871	−	0.323554i
$117$		0			0
$118$	9.11509	+	3.06040i	0.839112	+	0.281733i
$119$	−8.75814			−0.802857
$120$		0			0
$121$	8.70892			0.791720
$122$	−4.82778	−	1.62093i	−0.437087	−	0.146752i
$123$		0			0
$124$	11.7417	+	8.88633i	1.05444	+	0.798016i
$125$		0			0
$126$		0			0
$127$	11.5290			1.02303			0.511516	−	0.859274i	$-0.329084\pi$
$127$	11.5290			1.02303			0.511516	+	0.859274i	$0.329084\pi$
$128$	−8.67738	−	7.25969i	−0.766979	−	0.641672i
$129$		0			0
$130$		0			0
$131$		−	7.37270i		−	0.644156i	−0.946713	−	0.322078i	$-0.895619\pi$
$131$		−	7.37270i		−	0.644156i	0.946713	−	0.322078i	$-0.104381\pi$
$132$		0			0
$133$			18.7253i			1.62369i
$134$	1.36266	+	0.457515i	0.117716	+	0.0395232i
$135$		0			0
$136$	7.74173	−	5.28530i	0.663848	−	0.453211i
$137$	3.88792			0.332167			0.166084	−	0.986112i	$-0.446888\pi$
$137$	3.88792			0.332167			0.166084	+	0.986112i	$0.446888\pi$
$138$		0			0
$139$		−	14.6291i		−	1.24083i	−0.784275	−	0.620414i	$-0.786965\pi$
$139$		−	14.6291i		−	1.24083i	0.784275	−	0.620414i	$-0.213035\pi$
$140$		0			0
$141$		0			0
$142$	3.02727	−	9.01641i	0.254042	−	0.756640i
$143$	−5.85907			−0.489960
$144$		0			0
$145$		0			0
$146$	6.98359	−	20.7999i	0.577966	−	1.72141i
$147$		0			0
$148$	9.49971	−	12.5522i	0.780871	−	1.03178i
$149$			11.0715i			0.907010i	0.891254	+	0.453505i	$0.149827\pi$
$149$			11.0715i			0.907010i	−0.891254	+	0.453505i	$0.850173\pi$
$150$		0			0
$151$	0.637339			0.0518659			0.0259329	−	0.999664i	$-0.491744\pi$
$151$	0.637339			0.0518659			0.0259329	+	0.999664i	$0.491744\pi$
$152$	−11.3002	−	16.5522i	−0.916569	−	1.34256i
$153$		0			0
$154$	5.36266	+	1.80052i	0.432136	+	0.145090i
$155$		0			0
$156$		0			0
$157$		−	0.129135i		−	0.0103061i	−0.999987	−	0.00515306i	$-0.998360\pi$
$157$		−	0.129135i		−	0.0103061i	0.999987	−	0.00515306i	$-0.00164028\pi$
$158$	−3.31415	+	9.87086i	−0.263660	+	0.785284i
$159$		0			0
$160$		0			0
$161$	−12.7581			−1.00548
$162$		0			0
$163$		−	19.4835i		−	1.52606i	−0.646362	−	0.763031i	$-0.723710\pi$
$163$		−	19.4835i		−	1.52606i	0.646362	−	0.763031i	$-0.276290\pi$
$164$	13.9149	+	10.5310i	1.08657	+	0.822332i
$165$		0			0
$166$	−10.3791	−	3.48478i	−0.805572	−	0.270471i
$167$	−1.80052			−0.139328			−0.0696641	−	0.997571i	$-0.522193\pi$
$167$	−1.80052			−0.139328			−0.0696641	+	0.997571i	$0.522193\pi$
$168$		0			0
$169$	−1.98359			−0.152584
$170$		0			0
$171$		0			0
$172$	1.22675	−	1.62093i	0.0935386	−	0.123595i
$173$			23.2335i			1.76641i	0.468985	+	0.883206i	$0.344620\pi$
$173$			23.2335i			1.76641i	−0.468985	+	0.883206i	$0.655380\pi$
$174$		0			0
$175$		0			0
$176$	−5.82687	+	1.64466i	−0.439217	+	0.123971i
$177$		0			0
$178$	−6.64307	+	19.7857i	−0.497919	+	1.48300i
$179$			2.85664i			0.213515i	0.994285	+	0.106757i	$0.0340468\pi$
$179$			2.85664i			0.213515i	−0.994285	+	0.106757i	$0.965953\pi$
$180$		0			0
$181$			5.28530i			0.392853i	0.980519	+	0.196427i	$0.0629337\pi$
$181$			5.28530i			0.392853i	−0.980519	+	0.196427i	$0.937066\pi$
$182$	13.7141	+	4.60453i	1.01656	+	0.341310i
$183$		0			0
$184$	11.2775	−	7.69919i	0.831390	−	0.567592i
$185$		0			0
$186$		0			0
$187$		−	5.01641i		−	0.366836i
$188$	−11.3002	−	8.55220i	−0.824154	−	0.623733i
$189$		0			0
$190$		0			0
$191$	5.96719			0.431770			0.215885	−	0.976419i	$-0.430736\pi$
$191$	5.96719			0.431770			0.215885	+	0.976419i	$0.430736\pi$
$192$		0			0
$193$	−14.9409			−1.07547			−0.537733	−	0.843115i	$-0.680719\pi$
$193$	−14.9409			−1.07547			−0.537733	+	0.843115i	$0.680719\pi$
$194$	5.01641	−	14.9409i	0.360157	−	1.07269i
$195$		0			0
$196$	0.0261649	+	0.0198021i	0.00186892	+	0.00141443i
$197$			3.23353i			0.230379i	0.993344	+	0.115190i	$0.0367476\pi$
$197$			3.23353i			0.230379i	−0.993344	+	0.115190i	$0.963252\pi$
$198$		0			0
$199$	−8.12080			−0.575668			−0.287834	−	0.957680i	$-0.592935\pi$
$199$	−8.12080			−0.575668			−0.287834	+	0.957680i	$0.592935\pi$
$200$		0			0
$201$		0			0
$202$	17.8704	+	6.00000i	1.25736	+	0.422159i
$203$			5.77454i			0.405293i
$204$		0			0
$205$		0			0
$206$	−0.431398	+	1.28488i	−0.0300569	+	0.0895215i
$207$		0			0
$208$	−14.9013	+	4.20594i	−1.03322	+	0.291630i
$209$	−10.7253			−0.741886
$210$		0			0
$211$		−	13.7141i		−	0.944119i	−0.881567	−	0.472059i	$-0.843511\pi$
$211$		−	13.7141i		−	0.944119i	0.881567	−	0.472059i	$-0.156489\pi$
$212$	−5.44116	+	7.18953i	−0.373700	+	0.493779i
$213$		0			0
$214$	−5.36266	−	1.80052i	−0.366584	−	0.123081i
$215$		0			0
$216$		0			0
$217$	−19.4569			−1.32082
$218$	1.03128	+	0.346255i	0.0698474	+	0.0234513i
$219$		0			0
$220$		0			0
$221$		−	12.8286i		−	0.862947i
$222$		0			0
$223$	−9.84472			−0.659251			−0.329626	−	0.944112i	$-0.606923\pi$
$223$	−9.84472			−0.659251			−0.329626	+	0.944112i	$0.606923\pi$
$224$	14.9313	+	0.729629i	0.997637	+	0.0487504i
$225$		0			0
$226$	6.50820	−	19.3840i	0.432919	−	1.28941i
$227$		−	5.70892i		−	0.378914i	−0.981889	−	0.189457i	$-0.939327\pi$
$227$		−	5.70892i		−	0.378914i	0.981889	−	0.189457i	$-0.0606728\pi$
$228$		0			0
$229$		−	0.769233i		−	0.0508324i	−0.999677	−	0.0254162i	$-0.991909\pi$
$229$		−	0.769233i		−	0.0508324i	0.999677	−	0.0254162i	$-0.00809109\pi$
$230$		0			0
$231$		0			0
$232$	−3.48478	−	5.10439i	−0.228787	−	0.335120i
$233$	−18.4008			−1.20548			−0.602739	−	0.797939i	$-0.705924\pi$
$233$	−18.4008			−1.20548			−0.602739	+	0.797939i	$0.705924\pi$
$234$		0			0
$235$		0			0
$236$	8.20594	−	10.8427i	0.534161	−	0.705800i
$237$		0			0
$238$	−3.94229	+	11.7417i	−0.255541	+	0.761103i
$239$	−10.0328			−0.648969			−0.324484	−	0.945891i	$-0.605191\pi$
$239$	−10.0328			−0.648969			−0.324484	+	0.945891i	$0.605191\pi$
$240$		0			0
$241$	10.7581			0.692992			0.346496	−	0.938051i	$-0.387371\pi$
$241$	10.7581			0.692992			0.346496	+	0.938051i	$0.387371\pi$
$242$	3.92014	−	11.6757i	0.251996	−	0.750545i
$243$		0			0
$244$	−4.34625	+	5.74281i	−0.278240	+	0.367646i
$245$		0			0
$246$		0			0
$247$	−27.4282			−1.74522
$248$	17.1989	−	11.7417i	1.09213	−	0.745601i
$249$		0			0
$250$		0			0
$251$			12.6580i			0.798966i	0.916741	+	0.399483i	$0.130810\pi$
$251$			12.6580i			0.798966i	−0.916741	+	0.399483i	$0.869190\pi$
$252$		0			0
$253$		−	7.30749i		−	0.459418i
$254$	5.18953	−	15.4565i	0.325620	−	0.969827i
$255$		0			0
$256$	−13.6388	+	8.36566i	−0.852422	+	0.522854i
$257$	13.3110			0.830316			0.415158	−	0.909749i	$-0.363726\pi$
$257$	13.3110			0.830316			0.415158	+	0.909749i	$0.363726\pi$
$258$		0			0
$259$			20.7999i			1.29244i
$260$		0			0
$261$		0			0
$262$	−9.88432	−	3.31867i	−0.610656	−	0.205028i
$263$	18.4256			1.13617			0.568087	−	0.822969i	$-0.307684\pi$
$263$	18.4256			1.13617			0.568087	+	0.822969i	$0.307684\pi$
$264$		0			0
$265$		0			0
$266$	25.1044	+	8.42882i	1.53925	+	0.516804i
$267$		0			0
$268$	1.22675	−	1.62093i	0.0749356	−	0.0990142i
$269$			3.86940i			0.235921i	0.993018	+	0.117961i	$0.0376357\pi$
$269$			3.86940i			0.235921i	−0.993018	+	0.117961i	$0.962364\pi$
$270$		0			0
$271$	−17.3955			−1.05670			−0.528350	−	0.849027i	$-0.677189\pi$
$271$	−17.3955			−1.05670			−0.528350	+	0.849027i	$0.677189\pi$
$272$	−3.60104	−	12.7581i	−0.218345	−	0.773576i
$273$		0			0
$274$	1.75007	−	5.21240i	0.105725	−	0.314893i
$275$		0			0
$276$		0			0
$277$		−	0.887271i		−	0.0533110i	−0.999645	−	0.0266555i	$-0.991514\pi$
$277$		−	0.887271i		−	0.0533110i	0.999645	−	0.0266555i	$-0.00848571\pi$
$278$	−19.6128	−	6.58501i	−1.17630	−	0.394943i
$279$		0			0
$280$		0			0
$281$	13.4835			0.804356			0.402178	−	0.915562i	$-0.368253\pi$
$281$	13.4835			0.804356			0.402178	+	0.915562i	$0.368253\pi$
$282$		0			0
$283$		−	28.4342i		−	1.69024i	−0.534577	−	0.845120i	$-0.679529\pi$
$283$		−	28.4342i		−	1.69024i	0.534577	−	0.845120i	$-0.320471\pi$
$284$	−10.7253	−	8.11710i	−0.636431	−	0.481661i
$285$		0			0
$286$	−2.63734	+	7.85505i	−0.155949	+	0.464479i
$287$	−23.0580			−1.36107
$288$		0			0
$289$	−6.01641			−0.353906
$290$		0			0
$291$		0			0
$292$	−24.7422	−	18.7253i	−1.44793	−	1.09582i
$293$			7.99166i			0.466878i	0.972371	+	0.233439i	$0.0749979\pi$
$293$			7.99166i			0.466878i	−0.972371	+	0.233439i	$0.925002\pi$
$294$		0			0
$295$		0			0
$296$	−12.5522	−	18.3860i	−0.729582	−	1.06867i
$297$		0			0
$298$	14.8431	+	4.98359i	0.859840	+	0.288692i
$299$		−	18.6877i		−	1.08074i
$300$		0			0
$301$			2.68601i			0.154819i
$302$	0.286885	−	0.854458i	0.0165084	−	0.0491685i
$303$		0			0
$304$	−27.2775	+	7.69919i	−1.56447	+	0.441579i
$305$		0			0
$306$		0			0
$307$		−	17.4506i		−	0.995961i	−0.867188	−	0.497980i	$-0.834075\pi$
$307$		−	17.4506i		−	0.995961i	0.867188	−	0.497980i	$-0.165925\pi$
$308$	4.82778	−	6.37907i	0.275088	−	0.363481i
$309$		0			0
$310$		0			0
$311$	−21.4506			−1.21635			−0.608177	−	0.793801i	$-0.708099\pi$
$311$	−21.4506			−1.21635			−0.608177	+	0.793801i	$0.708099\pi$
$312$		0			0
$313$	−7.73879			−0.437422			−0.218711	−	0.975790i	$-0.570185\pi$
$313$	−7.73879			−0.437422			−0.218711	+	0.975790i	$0.570185\pi$
$314$	−0.173127	−	0.0581276i	−0.00977014	−	0.00328033i
$315$		0			0
$316$	11.7417	+	8.88633i	0.660524	+	0.499895i
$317$			11.2335i			0.630938i	0.948936	+	0.315469i	$0.102162\pi$
$317$			11.2335i			0.630938i	−0.948936	+	0.315469i	$0.897838\pi$
$318$		0			0
$319$	−3.30749			−0.185184
$320$		0			0
$321$		0			0
$322$	−5.74281	+	17.1044i	−0.320034	+	0.953190i
$323$		−	23.4835i		−	1.30665i
$324$		0			0
$325$		0			0
$326$	−26.1208	−	8.77008i	−1.44670	−	0.485730i
$327$		0			0
$328$	20.3820	−	13.9149i	1.12541	−	0.768319i
$329$	18.7253			1.03236
$330$		0			0
$331$			8.00084i			0.439766i	0.975526	+	0.219883i	$0.0705676\pi$
$331$			8.00084i			0.439766i	−0.975526	+	0.219883i	$0.929432\pi$
$332$	−9.34385	+	12.3463i	−0.512810	+	0.677589i
$333$		0			0
$334$	−0.810466	+	2.41389i	−0.0443467	+	0.132082i
$335$		0			0
$336$		0			0
$337$	21.5692			1.17495			0.587474	−	0.809243i	$-0.300123\pi$
$337$	21.5692			1.17495			0.587474	+	0.809243i	$0.300123\pi$
$338$	−0.892874	+	2.65933i	−0.0485659	+	0.144649i
$339$		0			0
$340$		0			0
$341$		−	11.1444i		−	0.603501i
$342$		0			0
$343$	−18.5419			−1.00117
$344$	−1.62093	−	2.37429i	−0.0873948	−	0.128013i
$345$		0			0
$346$	31.1484	+	10.4581i	1.67455	+	0.562231i
$347$			21.7089i			1.16540i	0.812689	+	0.582698i	$0.198003\pi$
$347$			21.7089i			1.16540i	−0.812689	+	0.582698i	$0.801997\pi$
$348$		0			0
$349$			24.7422i			1.32442i	0.749318	+	0.662211i	$0.230382\pi$
$349$			24.7422i			1.32442i	−0.749318	+	0.662211i	$0.769618\pi$
$350$		0			0
$351$		0			0
$352$	−0.417910	+	8.55220i	−0.0222747	+	0.455834i
$353$	3.31415			0.176394			0.0881972	−	0.996103i	$-0.471889\pi$
$353$	3.31415			0.176394			0.0881972	+	0.996103i	$0.471889\pi$
$354$		0			0
$355$		0			0
$356$	23.5358	+	17.8123i	1.24739	+	0.944048i
$357$		0			0
$358$	3.82979	+	1.28586i	0.202411	+	0.0679596i
$359$	16.7581			0.884461			0.442230	−	0.896902i	$-0.354187\pi$
$359$	16.7581			0.884461			0.442230	+	0.896902i	$0.354187\pi$
$360$		0			0
$361$	−31.2088			−1.64257
$362$	7.08582	+	2.37907i	0.372422	+	0.125041i
$363$		0			0
$364$	12.3463	−	16.3134i	0.647120	−	0.855055i
$365$		0			0
$366$		0			0
$367$	−28.5324			−1.48938			−0.744690	−	0.667411i	$-0.767403\pi$
$367$	−28.5324			−1.48938			−0.744690	+	0.667411i	$0.767403\pi$
$368$	−5.24569	−	18.5850i	−0.273451	−	0.968811i
$369$		0			0
$370$		0			0
$371$		−	11.9136i		−	0.618523i
$372$		0			0
$373$			37.5798i			1.94581i	0.231211	+	0.972904i	$0.425731\pi$
$373$			37.5798i			1.94581i	−0.231211	+	0.972904i	$0.574269\pi$
$374$	−6.72532	−	2.25803i	−0.347758	−	0.116760i
$375$		0			0
$376$	−16.5522	+	11.3002i	−0.853614	+	0.582765i
$377$	−8.45836			−0.435628
$378$		0			0
$379$		−	6.74456i		−	0.346445i	−0.984883	−	0.173222i	$-0.944582\pi$
$379$		−	6.74456i		−	0.346445i	0.984883	−	0.173222i	$-0.0554179\pi$
$380$		0			0
$381$		0			0
$382$	2.68601	−	8.00000i	0.137428	−	0.409316i
$383$	21.8312			1.11552			0.557762	−	0.830001i	$-0.311660\pi$
$383$	21.8312			1.11552			0.557762	+	0.830001i	$0.311660\pi$
$384$		0			0
$385$		0			0
$386$	−6.72532	+	20.0307i	−0.342310	+	1.01954i
$387$		0			0
$388$	−17.7727	−	13.4506i	−0.902270	−	0.682853i
$389$		−	8.81344i		−	0.446859i	−0.974720	−	0.223429i	$-0.928275\pi$
$389$		−	8.81344i		−	0.446859i	0.974720	−	0.223429i	$-0.0717252\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$	0.0383256	−	0.0261649i	0.00193573	−	0.00132153i
$393$		0			0
$394$	4.33508	+	1.45551i	0.218398	+	0.0733273i
$395$		0			0
$396$		0			0
$397$			0.821644i			0.0412372i	0.999787	+	0.0206186i	$0.00656356\pi$
$397$			0.821644i			0.0412372i	−0.999787	+	0.0206186i	$0.993436\pi$
$398$	−3.65541	+	10.8873i	−0.183229	+	0.545730i
$399$		0			0
$400$		0			0
$401$	12.7253			0.635472			0.317736	−	0.948179i	$-0.397077\pi$
$401$	12.7253			0.635472			0.317736	+	0.948179i	$0.397077\pi$
$402$		0			0
$403$		−	28.4999i		−	1.41968i
$404$	16.0880	−	21.2574i	0.800407	−	1.05760i
$405$		0			0
$406$	7.74173	+	2.59929i	0.384216	+	0.129001i
$407$	−11.9136			−0.590535
$408$		0			0
$409$	2.25827			0.111664			0.0558321	−	0.998440i	$-0.482219\pi$
$409$	2.25827			0.111664			0.0558321	+	0.998440i	$0.482219\pi$
$410$		0			0
$411$		0			0
$412$	1.52840	+	1.15672i	0.0752990	+	0.0569875i
$413$			17.9672i			0.884107i
$414$		0			0
$415$		0			0
$416$	−1.06874	+	21.8708i	−0.0523991	+	1.07231i
$417$		0			0
$418$	−4.82778	+	14.3791i	−0.236135	+	0.703303i
$419$			33.4579i			1.63453i	0.576264	+	0.817263i	$0.304510\pi$
$419$			33.4579i			1.63453i	−0.576264	+	0.817263i	$0.695490\pi$
$420$		0			0
$421$		−	11.3398i		−	0.552669i	−0.961061	−	0.276335i	$-0.910880\pi$
$421$		−	11.3398i		−	0.552669i	0.961061	−	0.276335i	$-0.0891198\pi$
$422$	−18.3860	−	6.17313i	−0.895018	−	0.300503i
$423$		0			0
$424$	7.18953	+	10.5310i	0.349155	+	0.511430i
$425$		0			0
$426$		0			0
$427$		−	9.51627i		−	0.460525i
$428$	−4.82778	+	6.37907i	−0.233360	+	0.308344i
$429$		0			0
$430$		0			0
$431$	−10.6597			−0.513459			−0.256730	−	0.966483i	$-0.582645\pi$
$431$	−10.6597			−0.513459			−0.256730	+	0.966483i	$0.582645\pi$
$432$		0			0
$433$	26.5132			1.27414			0.637072	−	0.770805i	$-0.280146\pi$
$433$	26.5132			1.27414			0.637072	+	0.770805i	$0.280146\pi$
$434$	−8.75814	+	26.0852i	−0.420404	+	1.25213i
$435$		0			0
$436$	0.928423	−	1.22675i	0.0444634	−	0.0587506i
$437$		−	34.2088i		−	1.63643i
$438$		0			0
$439$	32.8789			1.56923			0.784613	−	0.619986i	$-0.212862\pi$
$439$	32.8789			1.56923			0.784613	+	0.619986i	$0.212862\pi$
$440$		0			0
$441$		0			0
$442$	−17.1989	−	5.77454i	−0.818068	−	0.274667i
$443$		−	5.70892i		−	0.271239i	−0.990761	−	0.135619i	$-0.956698\pi$
$443$		−	5.70892i		−	0.271239i	0.990761	−	0.135619i	$-0.0433024\pi$
$444$		0			0
$445$		0			0
$446$	−4.43140	+	13.1985i	−0.209833	+	0.624966i
$447$		0			0
$448$	7.69919	−	19.6894i	0.363753	−	0.930237i
$449$	2.00000			0.0943858			0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000			0.0943858			0.0471929	+	0.998886i	$0.484972\pi$
$450$		0			0
$451$		−	13.2069i		−	0.621890i
$452$	−23.0580	−	17.4506i	−1.08456	−	0.820809i
$453$		0			0
$454$	−7.65375	−	2.56975i	−0.359208	−	0.120604i
$455$		0			0
$456$		0			0
$457$	−3.94229			−0.184413			−0.0922064	−	0.995740i	$-0.529392\pi$
$457$	−3.94229			−0.184413			−0.0922064	+	0.995740i	$0.529392\pi$
$458$	−1.03128	−	0.346255i	−0.0481888	−	0.0161794i
$459$		0			0
$460$		0			0
$461$			33.8969i			1.57874i	0.613920	+	0.789369i	$0.289592\pi$
$461$			33.8969i			1.57874i	−0.613920	+	0.789369i	$0.710408\pi$
$462$		0			0
$463$	22.8688			1.06280			0.531402	−	0.847120i	$-0.321665\pi$
$463$	22.8688			1.06280			0.531402	+	0.847120i	$0.321665\pi$
$464$	−8.41188	+	2.37429i	−0.390512	+	0.110224i
$465$		0			0
$466$	−8.28275	+	24.6693i	−0.383691	+	1.14278i
$467$		−	15.7417i		−	0.728440i	−0.931313	−	0.364220i	$-0.881336\pi$
$467$		−	15.7417i		−	0.728440i	0.931313	−	0.364220i	$-0.118664\pi$
$468$		0			0
$469$			2.68601i			0.124028i
$470$		0			0
$471$		0			0
$472$	−10.8427	−	15.8820i	−0.499076	−	0.731030i
$473$	−1.53847			−0.0707388
$474$		0			0
$475$		0			0
$476$	13.9672	+	10.5706i	0.640185	+	0.484502i
$477$		0			0
$478$	−4.51606	+	13.4506i	−0.206560	+	0.615218i
$479$	−20.6925			−0.945465			−0.472732	−	0.881206i	$-0.656732\pi$
$479$	−20.6925			−0.945465			−0.472732	+	0.881206i	$0.656732\pi$
$480$		0			0
$481$	−30.4671			−1.38918
$482$	4.84255	−	14.4231i	0.220572	−	0.656952i
$483$		0			0
$484$	−13.8887	−	10.5112i	−0.631304	−	0.477781i
$485$		0			0
$486$		0			0
$487$	30.8401			1.39750			0.698750	−	0.715366i	$-0.253740\pi$
$487$	30.8401			1.39750			0.698750	+	0.715366i	$0.253740\pi$
$488$	5.74281	+	8.41188i	0.259965	+	0.380788i
$489$		0			0
$490$		0			0
$491$			10.9737i			0.495238i	0.968858	+	0.247619i	$0.0796481\pi$
$491$			10.9737i			0.495238i	−0.968858	+	0.247619i	$0.920352\pi$
$492$		0			0
$493$		−	7.24186i		−	0.326157i
$494$	−12.3463	+	36.7721i	−0.555484	+	1.65445i
$495$		0			0
$496$	−8.00000	−	28.3433i	−0.359211	−	1.27265i
$497$	17.7727			0.797213
$498$		0			0
$499$			3.71729i			0.166409i	0.996533	+	0.0832044i	$0.0265154\pi$
$499$			3.71729i			0.166409i	−0.996533	+	0.0832044i	$0.973485\pi$
$500$		0			0
$501$		0			0
$502$	16.9701	+	5.69774i	0.757414	+	0.254302i
$503$	−39.9451			−1.78107			−0.890533	−	0.454919i	$-0.849668\pi$
$503$	−39.9451			−1.78107			−0.890533	+	0.454919i	$0.849668\pi$
$504$		0			0
$505$		0			0
$506$	−9.79690	−	3.28932i	−0.435525	−	0.146228i
$507$		0			0
$508$	−18.3860	−	13.9149i	−0.815749	−	0.617372i
$509$			0.0728979i			0.00323114i	0.999999	+	0.00161557i	$0.000514253\pi$
$509$			0.0728979i			0.00323114i	−0.999999	+	0.00161557i	$0.999486\pi$
$510$		0			0
$511$	40.9997			1.81372
$512$	5.07634	+	22.0506i	0.224345	+	0.974510i
$513$		0			0
$514$	5.99166	−	17.8456i	0.264281	−	0.787134i
$515$		0			0
$516$		0			0
$517$			10.7253i			0.471699i
$518$	27.8857	+	9.36266i	1.22523	+	0.411372i
$519$		0			0
$520$		0			0
$521$	11.9672			0.524292			0.262146	−	0.965028i	$-0.415570\pi$
$521$	11.9672			0.524292			0.262146	+	0.965028i	$0.415570\pi$
$522$		0			0
$523$			16.0656i			0.702501i	0.936282	+	0.351250i	$0.114243\pi$
$523$			16.0656i			0.702501i	−0.936282	+	0.351250i	$0.885757\pi$
$524$	−8.89845	+	11.7577i	−0.388731	+	0.513639i
$525$		0			0
$526$	8.29392	−	24.7026i	0.361632	−	1.07709i
$527$	24.4010			1.06292
$528$		0			0
$529$	0.307491			0.0133692
$530$		0			0
$531$		0			0
$532$	22.6004	−	29.8625i	0.979854	−	1.29470i
$533$		−	33.7745i		−	1.46294i
$534$		0			0
$535$		0			0
$536$	−1.62093	−	2.37429i	−0.0700136	−	0.102554i
$537$		0			0
$538$	5.18757	+	1.74173i	0.223652	+	0.0750913i
$539$		−	0.0248338i		−	0.00106967i
$540$		0			0
$541$			15.8559i			0.681698i	0.940118	+	0.340849i	$0.110715\pi$
$541$			15.8559i			0.681698i	−0.940118	+	0.340849i	$0.889285\pi$
$542$	−7.83021	+	23.3215i	−0.336337	+	1.00174i
$543$		0			0
$544$	−18.7253	−	0.915029i	−0.802842	−	0.0392316i
$545$		0			0
$546$		0			0
$547$		−	4.95078i		−	0.211680i	−0.994383	−	0.105840i	$-0.966247\pi$
$547$		−	4.95078i		−	0.211680i	0.994383	−	0.105840i	$-0.0337531\pi$
$548$	−6.20033	−	4.69251i	−0.264865	−	0.200454i
$549$		0			0
$550$		0			0
$551$	−15.4835			−0.659618
$552$		0			0
$553$	−19.4569			−0.827393
$554$	−1.18953	−	0.399387i	−0.0505385	−	0.0169683i
$555$		0			0
$556$	−17.6566	+	23.3301i	−0.748806	+	0.989416i
$557$		−	1.26634i		−	0.0536565i	−0.999640	−	0.0268283i	$-0.991459\pi$
$557$		−	1.26634i		−	0.0536565i	0.999640	−	0.0268283i	$-0.00854073\pi$
$558$		0			0
$559$	−3.93437			−0.166406
$560$		0			0
$561$		0			0
$562$	6.06930	−	18.0768i	0.256018	−	0.762524i
$563$			5.70892i			0.240602i	0.992737	+	0.120301i	$0.0383860\pi$
$563$			5.70892i			0.240602i	−0.992737	+	0.120301i	$0.961614\pi$
$564$		0			0
$565$		0			0
$566$	−38.1208	−	12.7991i	−1.60234	−	0.537986i
$567$		0			0
$568$	−15.7101	+	10.7253i	−0.659181	+	0.450025i
$569$	2.75814			0.115627			0.0578135	−	0.998327i	$-0.481587\pi$
$569$	2.75814			0.115627			0.0578135	+	0.998327i	$0.481587\pi$
$570$		0			0
$571$			25.7735i			1.07859i	0.842118	+	0.539294i	$0.181309\pi$
$571$			25.7735i			1.07859i	−0.842118	+	0.539294i	$0.818691\pi$
$572$	9.34385	+	7.07158i	0.390686	+	0.295677i
$573$		0			0
$574$	−10.3791	+	30.9130i	−0.433214	+	1.29028i
$575$		0			0
$576$		0			0
$577$	−32.7135			−1.36188			−0.680941	−	0.732338i	$-0.738429\pi$
$577$	−32.7135			−1.36188			−0.680941	+	0.732338i	$0.738429\pi$
$578$	−2.70816	+	8.06599i	−0.112645	+	0.335501i
$579$		0			0
$580$		0			0
$581$		−	20.4587i		−	0.848769i
$582$		0			0
$583$	6.82376			0.282611
$584$	−36.2416	+	24.7422i	−1.49969	+	1.02384i
$585$		0			0
$586$	10.7141	+	3.59728i	0.442597	+	0.148602i
$587$		−	43.4835i		−	1.79475i	−0.441264	−	0.897377i	$-0.645470\pi$
$587$		−	43.4835i		−	1.79475i	0.441264	−	0.897377i	$-0.354530\pi$
$588$		0			0
$589$		−	52.1705i		−	2.14965i
$590$		0			0
$591$		0			0
$592$	−30.2996	+	8.55220i	−1.24531	+	0.351493i
$593$	−7.83021			−0.321548			−0.160774	−	0.986991i	$-0.551399\pi$
$593$	−7.83021			−0.321548			−0.160774	+	0.986991i	$0.551399\pi$
$594$		0			0
$595$		0			0
$596$	13.3627	−	17.6564i	0.547356	−	0.723235i
$597$		0			0
$598$	−25.0539	−	8.41188i	−1.02453	−	0.343987i
$599$	32.7581			1.33846			0.669231	−	0.743055i	$-0.266624\pi$
$599$	32.7581			1.33846			0.669231	+	0.743055i	$0.266624\pi$
$600$		0			0
$601$	17.8074			0.726377			0.363189	−	0.931716i	$-0.381688\pi$
$601$	17.8074			0.726377			0.363189	+	0.931716i	$0.381688\pi$
$602$	3.60104	+	1.20905i	0.146767	+	0.0492772i
$603$		0			0
$604$	−1.01641	−	0.769233i	−0.0413570	−	0.0312997i
$605$		0			0
$606$		0			0
$607$	−3.41188			−0.138484			−0.0692420	−	0.997600i	$-0.522058\pi$
$607$	−3.41188			−0.138484			−0.0692420	+	0.997600i	$0.522058\pi$
$608$	−1.95638	+	40.0357i	−0.0793416	+	1.62366i
$609$		0			0
$610$		0			0
$611$			27.4282i			1.10963i
$612$		0			0
$613$			36.6290i			1.47943i	0.672920	+	0.739716i	$0.265040\pi$
$613$			36.6290i			1.47943i	−0.672920	+	0.739716i	$0.734960\pi$
$614$	−23.3955	−	7.85505i	−0.944165	−	0.317004i
$615$		0			0
$616$	−6.37907	−	9.34385i	−0.257020	−	0.376474i
$617$	−40.3979			−1.62636			−0.813180	−	0.582012i	$-0.802266\pi$
$617$	−40.3979			−1.62636			−0.813180	+	0.582012i	$0.802266\pi$
$618$		0			0
$619$		−	24.5172i		−	0.985430i	−0.870191	−	0.492715i	$-0.836004\pi$
$619$		−	24.5172i		−	0.985430i	0.870191	−	0.492715i	$-0.163996\pi$
$620$		0			0
$621$		0			0
$622$	−9.65557	+	28.7581i	−0.387153	+	1.15310i
$623$	−39.0006			−1.56252
$624$		0			0
$625$		0			0
$626$	−3.48346	+	10.3751i	−0.139227	+	0.414674i
$627$		0			0
$628$	−0.155859	+	0.205941i	−0.00621947	+	0.00821793i
$629$		−	26.0852i		−	1.04009i
$630$		0			0
$631$	18.7805			0.747640			0.373820	−	0.927501i	$-0.378048\pi$
$631$	18.7805			0.747640			0.373820	+	0.927501i	$0.378048\pi$
$632$	17.1989	−	11.7417i	0.684135	−	0.467061i
$633$		0			0
$634$	15.0604	+	5.05654i	0.598125	+	0.200821i
$635$		0			0
$636$		0			0
$637$		−	0.0635083i		−	0.00251629i
$638$	−1.48880	+	4.43424i	−0.0589421	+	0.175553i
$639$		0			0
$640$		0			0
$641$	15.5163			0.612856			0.306428	−	0.951894i	$-0.400866\pi$
$641$	15.5163			0.612856			0.306428	+	0.951894i	$0.400866\pi$
$642$		0			0
$643$			17.4506i			0.688186i	0.938936	+	0.344093i	$0.111814\pi$
$643$			17.4506i			0.688186i	−0.938936	+	0.344093i	$0.888186\pi$
$644$	20.3463	+	15.3984i	0.801755	+	0.606781i
$645$		0			0
$646$	−31.4835	−	10.5706i	−1.23870	−	0.415895i
$647$	13.1403			0.516600			0.258300	−	0.966065i	$-0.416838\pi$
$647$	13.1403			0.516600			0.258300	+	0.966065i	$0.416838\pi$
$648$		0			0
$649$	−10.2911			−0.403960
$650$		0			0
$651$		0			0
$652$	−23.5155	+	31.0716i	−0.920937	+	1.21686i
$653$			14.7993i			0.579141i	0.957157	+	0.289570i	$0.0935124\pi$
$653$			14.7993i			0.579141i	−0.957157	+	0.289570i	$0.906488\pi$
$654$		0			0
$655$		0			0
$656$	−9.48062	−	33.5890i	−0.370156	−	1.31143i
$657$		0			0
$658$	8.42882	−	25.1044i	0.328590	−	0.978671i
$659$		−	7.99614i		−	0.311485i	−0.987798	−	0.155743i	$-0.950223\pi$
$659$		−	7.99614i		−	0.311485i	0.987798	−	0.155743i	$-0.0497771\pi$
$660$		0			0
$661$		−	0.915029i		−	0.0355905i	−0.999842	−	0.0177953i	$-0.994335\pi$
$661$		−	0.915029i		−	0.0355905i	0.999842	−	0.0177953i	$-0.00566470\pi$
$662$	10.7265	+	3.60142i	0.416896	+	0.139973i
$663$		0			0
$664$	12.3463	+	18.0844i	0.479128	+	0.701810i
$665$		0			0
$666$		0			0
$667$		−	10.5494i		−	0.408473i
$668$	2.87141	+	2.17313i	0.111098	+	0.0840808i
$669$		0			0
$670$		0			0
$671$	5.45065			0.210420
$672$		0			0
$673$	34.3978			1.32594			0.662969	−	0.748647i	$-0.269296\pi$
$673$	34.3978			1.32594			0.662969	+	0.748647i	$0.269296\pi$
$674$	9.70892	−	28.9170i	0.373973	−	1.11384i
$675$		0			0
$676$	3.16337	+	2.39409i	0.121668	+	0.0920804i
$677$			40.1676i			1.54377i	0.635764	+	0.771884i	$0.280685\pi$
$677$			40.1676i			1.54377i	−0.635764	+	0.771884i	$0.719315\pi$
$678$		0			0
$679$	29.4506			1.13021
$680$		0			0
$681$		0			0
$682$	−14.9409	−	5.01641i	−0.572115	−	0.192088i
$683$		−	33.2580i		−	1.27258i	−0.771449	−	0.636291i	$-0.780468\pi$
$683$		−	33.2580i		−	1.27258i	0.771449	−	0.636291i	$-0.219532\pi$
$684$		0			0
$685$		0			0
$686$	−8.34625	+	24.8585i	−0.318661	+	0.949101i
$687$		0			0
$688$	−3.91275	+	1.10439i	−0.149172	+	0.0421045i
$689$	17.4506			0.664817
$690$		0			0
$691$		−	50.2241i		−	1.91062i	−0.295611	−	0.955308i	$-0.595523\pi$
$691$		−	50.2241i		−	1.91062i	0.295611	−	0.955308i	$-0.404477\pi$
$692$	28.0416	−	37.0521i	1.06598	−	1.40851i
$693$		0			0
$694$	29.1044	+	9.77182i	1.10479	+	0.370933i
$695$		0			0
$696$		0			0
$697$	28.9170			1.09531
$698$	33.1710	+	11.1372i	1.25554	+	0.421549i
$699$		0			0
$700$		0			0
$701$		−	23.7543i		−	0.897188i	−0.893736	−	0.448594i	$-0.851925\pi$
$701$		−	23.7543i		−	0.897188i	0.893736	−	0.448594i	$-0.148075\pi$
$702$		0			0
$703$	−55.7715			−2.10346
$704$	11.2775	+	4.40987i	0.425037	+	0.166203i
$705$		0			0
$706$	1.49180	−	4.44317i	0.0561445	−	0.167221i
$707$			35.2252i			1.32478i
$708$		0			0
$709$		−	36.3146i		−	1.36382i	−0.731435	−	0.681911i	$-0.761149\pi$
$709$		−	36.3146i		−	1.36382i	0.731435	−	0.681911i	$-0.238851\pi$
$710$		0			0
$711$		0			0
$712$	34.4744	−	23.5358i	1.29198	−	0.882041i
$713$	35.5453			1.33118
$714$		0			0
$715$		0			0
$716$	3.44780	−	4.55567i	0.128851	−	0.170253i
$717$		0			0
$718$	7.54333	−	22.4671i	0.281515	−	0.838463i
$719$	−30.7253			−1.14586			−0.572931	−	0.819604i	$-0.694194\pi$
$719$	−30.7253			−1.14586			−0.572931	+	0.819604i	$0.694194\pi$
$720$		0			0
$721$	−2.53268			−0.0943219
$722$	−14.0480	+	41.8405i	−0.522812	+	1.55714i
$723$		0			0
$724$	6.37907	−	8.42882i	0.237076	−	0.313255i
$725$		0			0
$726$		0			0
$727$	5.47445			0.203036			0.101518	−	0.994834i	$-0.467630\pi$
$727$	5.47445			0.203036			0.101518	+	0.994834i	$0.467630\pi$
$728$	−16.3134	−	23.8953i	−0.604615	−	0.885620i
$729$		0			0
$730$		0			0
$731$		−	3.36852i		−	0.124589i
$732$		0			0
$733$		−	17.1455i		−	0.633285i	−0.948545	−	0.316643i	$-0.897444\pi$
$733$		−	17.1455i		−	0.633285i	0.948545	−	0.316643i	$-0.102556\pi$
$734$	−12.8433	+	38.2524i	−0.474054	+	1.41192i
$735$		0			0
$736$	−27.2775	−	1.33294i	−1.00546	−	0.0491328i
$737$	−1.53847			−0.0566701
$738$		0			0
$739$			11.6019i			0.426782i	0.976967	+	0.213391i	$0.0684508\pi$
$739$			11.6019i			0.426782i	−0.976967	+	0.213391i	$0.931549\pi$
$740$		0			0
$741$		0			0
$742$	−15.9721	−	5.36266i	−0.586356	−	0.196869i
$743$	23.6613			0.868048			0.434024	−	0.900901i	$-0.357093\pi$
$743$	23.6613			0.868048			0.434024	+	0.900901i	$0.357093\pi$
$744$		0			0
$745$		0			0
$746$	50.3819	+	16.9158i	1.84461	+	0.619330i
$747$		0			0
$748$	−6.05453	+	8.00000i	−0.221376	+	0.292509i
$749$		−	10.5706i		−	0.386241i
$750$		0			0
$751$	−11.4283			−0.417024			−0.208512	−	0.978020i	$-0.566862\pi$
$751$	−11.4283			−0.417024			−0.208512	+	0.978020i	$0.566862\pi$
$752$	7.69919	+	27.2775i	0.280761	+	0.994709i
$753$		0			0
$754$	−3.80736	+	11.3398i	−0.138656	+	0.412972i
$755$		0			0
$756$		0			0
$757$			19.1784i			0.697049i	0.937300	+	0.348525i	$0.113317\pi$
$757$			19.1784i			0.697049i	−0.937300	+	0.348525i	$0.886683\pi$
$758$	−9.04219	−	3.03592i	−0.328427	−	0.110270i
$759$		0			0
$760$		0			0
$761$	−4.03281			−0.146189			−0.0730947	−	0.997325i	$-0.523288\pi$
$761$	−4.03281			−0.146189			−0.0730947	+	0.997325i	$0.523288\pi$
$762$		0			0
$763$			2.03281i			0.0735928i
$764$	−9.51627	−	7.20207i	−0.344287	−	0.260562i
$765$		0			0
$766$	9.82687	−	29.2684i	0.355059	−	1.05751i
$767$	−26.3177			−0.950279
$768$		0			0
$769$	−2.95078			−0.106408			−0.0532039	−	0.998584i	$-0.516943\pi$
$769$	−2.95078			−0.106408			−0.0532039	+	0.998584i	$0.516943\pi$
$770$		0			0
$771$		0			0
$772$	23.8272	+	18.0328i	0.857560	+	0.649015i
$773$		−	45.2663i		−	1.62812i	−0.580783	−	0.814059i	$-0.697253\pi$
$773$		−	45.2663i		−	1.62812i	0.580783	−	0.814059i	$-0.302747\pi$
$774$		0			0
$775$		0			0
$776$	−26.0328	+	17.7727i	−0.934524	+	0.638002i
$777$		0			0
$778$	−11.8159	−	3.96719i	−0.423619	−	0.142231i
$779$		−	61.8260i		−	2.21515i
$780$		0			0
$781$			10.1797i			0.364257i
$782$	7.20207	−	21.4506i	0.257546	−	0.767074i
$783$		0			0
$784$	−0.0178270	−	0.0631594i	−0.000636678	−	0.00225569i
$785$		0			0
$786$		0			0
$787$			52.9997i			1.88924i	0.328171	+	0.944618i	$0.393568\pi$
$787$			52.9997i			1.88924i	−0.328171	+	0.944618i	$0.606432\pi$
$788$	3.90269	−	5.15672i	0.139028	−	0.183701i
$789$		0			0
$790$		0			0
$791$	38.2088			1.35855
$792$		0			0
$793$	13.9391			0.494993
$794$	1.10155	+	0.369846i	0.0390926	+	0.0131254i
$795$		0			0
$796$	12.9508	+	9.80136i	0.459028	+	0.347400i
$797$			16.5738i			0.587075i	0.955948	+	0.293538i	$0.0948326\pi$
$797$			16.5738i			0.587075i	−0.955948	+	0.293538i	$0.905167\pi$
$798$		0			0
$799$	−23.4835			−0.830785
$800$		0			0
$801$		0			0
$802$	5.72804	−	17.0604i	0.202264	−	0.602424i
$803$			23.4835i			0.828713i
$804$		0			0
$805$		0			0
$806$	−38.2088	−	12.8286i	−1.34585	−	0.451869i
$807$		0			0
$808$	−21.2574	−	31.1372i	−0.747834	−	1.09540i
$809$	37.5491			1.32016			0.660078	−	0.751197i	$-0.270523\pi$
$809$	37.5491			1.32016			0.660078	+	0.751197i	$0.270523\pi$
$810$		0			0
$811$			32.1102i			1.12754i	0.825931	+	0.563771i	$0.190650\pi$
$811$			32.1102i			1.12754i	−0.825931	+	0.563771i	$0.809350\pi$
$812$	6.96956	−	9.20905i	0.244584	−	0.323174i
$813$		0			0
$814$	−5.36266	+	15.9721i	−0.187961	+	0.559824i
$815$		0			0
$816$		0			0
$817$	−7.20207			−0.251969
$818$	1.01651	−	3.02759i	0.0355416	−	0.105857i
$819$		0			0
$820$		0			0
$821$		−	29.3809i		−	1.02540i	−0.858568	−	0.512699i	$-0.828646\pi$
$821$		−	29.3809i		−	1.02540i	0.858568	−	0.512699i	$-0.171354\pi$
$822$		0			0
$823$	28.3866			0.989495			0.494748	−	0.869037i	$-0.335260\pi$
$823$	28.3866			0.989495			0.494748	+	0.869037i	$0.335260\pi$
$824$	2.23875	−	1.52840i	0.0779907	−	0.0532444i
$825$		0			0
$826$	24.0880	+	8.08756i	0.838128	+	0.281402i
$827$		−	1.45065i		−	0.0504439i	−0.999682	−	0.0252219i	$-0.991971\pi$
$827$		−	1.45065i		−	0.0504439i	0.999682	−	0.0252219i	$-0.00802924\pi$
$828$		0			0
$829$			37.4621i			1.30111i	0.759458	+	0.650556i	$0.225464\pi$
$829$			37.4621i			1.30111i	−0.759458	+	0.650556i	$0.774536\pi$
$830$		0			0
$831$		0			0
$832$	28.8404	+	11.2775i	0.999860	+	0.390978i
$833$	0.0543744			0.00188396
$834$		0			0
$835$		0			0
$836$	17.1044	+	12.9449i	0.591568	+	0.447708i
$837$		0			0
$838$	44.8559	+	15.0604i	1.54952	+	0.520253i
$839$	48.7581			1.68332			0.841659	−	0.540010i	$-0.181579\pi$
$839$	48.7581			1.68332			0.841659	+	0.540010i	$0.181579\pi$
$840$		0			0
$841$	24.2252			0.835351
$842$	−15.2029	−	5.10439i	−0.523927	−	0.175909i
$843$		0			0
$844$	−16.5522	+	21.8708i	−0.569750	+	0.752825i
$845$		0			0
$846$		0			0
$847$	23.0146			0.790791
$848$	17.3548	−	4.89845i	0.595965	−	0.168213i
$849$		0			0
$850$		0			0
$851$		−	37.9988i		−	1.30258i
$852$		0			0
$853$		−	4.37073i		−	0.149651i	−0.997197	−	0.0748255i	$-0.976160\pi$
$853$		−	4.37073i		−	0.149651i	0.997197	−	0.0748255i	$-0.0238400\pi$
$854$	−12.7581	−	4.28355i	−0.436574	−	0.146580i
$855$		0			0
$856$	6.37907	+	9.34385i	0.218032	+	0.319366i
$857$	−20.5130			−0.700712			−0.350356	−	0.936617i	$-0.613939\pi$
$857$	−20.5130			−0.700712			−0.350356	+	0.936617i	$0.613939\pi$
$858$		0			0
$859$		−	10.1131i		−	0.345054i	−0.985005	−	0.172527i	$-0.944807\pi$
$859$		−	10.1131i		−	0.345054i	0.985005	−	0.172527i	$-0.0551932\pi$
$860$		0			0
$861$		0			0
$862$	−4.79824	+	14.2911i	−0.163429	+	0.486756i
$863$	−13.2861			−0.452266			−0.226133	−	0.974096i	$-0.572608\pi$
$863$	−13.2861			−0.452266			−0.226133	+	0.974096i	$0.572608\pi$
$864$		0			0
$865$		0			0
$866$	11.9344	−	35.5453i	0.405547	−	1.20788i
$867$		0			0
$868$	31.0293	+	23.4835i	1.05320	+	0.797081i
$869$		−	11.1444i		−	0.378047i
$870$		0			0
$871$	−3.93437			−0.133311
$872$	−1.22675	−	1.79690i	−0.0415429	−	0.0608507i
$873$		0			0
$874$	−45.8625	−	15.3984i	−1.55132	−	0.520858i
$875$		0			0
$876$		0			0
$877$		−	33.6454i		−	1.13612i	−0.822986	−	0.568062i	$-0.807693\pi$
$877$		−	33.6454i		−	1.13612i	0.822986	−	0.568062i	$-0.192307\pi$
$878$	14.7998	−	44.0796i	0.499468	−	1.48762i
$879$		0			0
$880$		0			0
$881$	32.7909			1.10476			0.552378	−	0.833594i	$-0.313721\pi$
$881$	32.7909			1.10476			0.552378	+	0.833594i	$0.313721\pi$
$882$		0			0
$883$			33.4506i			1.12570i	0.826558	+	0.562852i	$0.190296\pi$
$883$			33.4506i			1.12570i	−0.826558	+	0.562852i	$0.809704\pi$
$884$	−15.4835	+	20.4587i	−0.520765	+	0.688100i
$885$		0			0
$886$	−7.65375	−	2.56975i	−0.257133	−	0.0863325i
$887$	34.8924			1.17157			0.585785	−	0.810466i	$-0.300786\pi$
$887$	34.8924			1.17157			0.585785	+	0.810466i	$0.300786\pi$
$888$		0			0
$889$	30.4671			1.02183
$890$		0			0
$891$		0			0
$892$	15.7000	+	11.8820i	0.525676	+	0.397840i
$893$			50.2088i			1.68017i
$894$		0			0
$895$		0			0
$896$	−22.9313	−	19.1848i	−0.766080	−	0.640920i
$897$		0			0
$898$	0.900259	−	2.68133i	0.0300420	−	0.0894772i
$899$		−	16.0884i		−	0.536578i
$900$		0			0
$901$			14.9409i			0.497752i
$902$	−17.7061	−	5.94483i	−0.589548	−	0.197941i
$903$		0			0
$904$	−33.7745	+	23.0580i	−1.12332	+	0.766896i
$905$		0			0
$906$		0			0
$907$			30.9836i			1.02879i	0.857552	+	0.514397i	$0.171984\pi$
$907$			30.9836i			1.02879i	−0.857552	+	0.514397i	$0.828016\pi$
$908$	−6.89035	+	9.10439i	−0.228664	+	0.302140i
$909$		0			0
$910$		0			0
$911$	−16.0000			−0.530104			−0.265052	−	0.964234i	$-0.585389\pi$
$911$	−16.0000			−0.530104			−0.265052	+	0.964234i	$0.585389\pi$
$912$		0			0
$913$	11.7181			0.387814
$914$	−1.77454	+	5.28530i	−0.0586967	+	0.174822i
$915$		0			0
$916$	−0.928423	+	1.22675i	−0.0306760	+	0.0405329i
$917$		−	19.4835i		−	0.643400i
$918$		0			0
$919$	−15.6043			−0.514737			−0.257368	−	0.966313i	$-0.582855\pi$
$919$	−15.6043			−0.514737			−0.257368	+	0.966313i	$0.582855\pi$
$920$		0			0
$921$		0			0
$922$	45.4444	+	15.2580i	1.49663	+	0.502496i
$923$			26.0328i			0.856880i
$924$		0			0
$925$		0			0
$926$	10.2939	−	30.6594i	0.338279	−	1.00753i
$927$		0			0
$928$	−0.603310	+	12.3463i	−0.0198046	+	0.405286i
$929$	38.9341			1.27739			0.638693	−	0.769461i	$-0.279475\pi$
$929$	38.9341			1.27739			0.638693	+	0.769461i	$0.279475\pi$
$930$		0			0
$931$		−	0.116255i		−	0.00381011i
$932$	29.3450	+	22.2088i	0.961228	+	0.727473i
$933$		0			0
$934$	−21.1044	−	7.08582i	−0.690557	−	0.231855i
$935$		0			0
$936$		0			0
$937$	19.6027			0.640393			0.320197	−	0.947351i	$-0.396251\pi$
$937$	19.6027			0.640393			0.320197	+	0.947351i	$0.396251\pi$
$938$	3.60104	+	1.20905i	0.117578	+	0.0394769i
$939$		0			0
$940$		0			0
$941$			25.0476i			0.816530i	0.912864	+	0.408265i	$0.133866\pi$
$941$			25.0476i			0.816530i	−0.912864	+	0.408265i	$0.866134\pi$
$942$		0			0
$943$	42.1240			1.37175
$944$	−26.1731	+	7.38747i	−0.851863	+	0.240442i
$945$		0			0
$946$	−0.692509	+	2.06257i	−0.0225154	+	0.0670599i
$947$		−	7.93437i		−	0.257832i	−0.991655	−	0.128916i	$-0.958850\pi$
$947$		−	7.93437i		−	0.257832i	0.991655	−	0.128916i	$-0.0411498\pi$
$948$		0			0
$949$			60.0550i			1.94947i
$950$		0			0
$951$		0			0
$952$	20.4587	−	13.9672i	0.663069	−	0.452679i
$953$	11.4809			0.371903			0.185952	−	0.982559i	$-0.440463\pi$
$953$	11.4809			0.371903			0.185952	+	0.982559i	$0.440463\pi$
$954$		0			0
$955$		0			0
$956$	16.0000	+	12.1091i	0.517477	+	0.391635i
$957$		0			0
$958$	−9.31431	+	27.7417i	−0.300932	+	0.896295i
$959$	10.2744			0.331778
$960$		0			0
$961$	23.2088			0.748670
$962$	−13.7141	+	40.8461i	−0.442161	+	1.31693i
$963$		0			0
$964$	−17.1567	−	12.9845i	−0.552581	−	0.418202i
$965$		0			0
$966$		0			0
$967$	15.8993			0.511285			0.255643	−	0.966771i	$-0.417713\pi$
$967$	15.8993			0.511285			0.255643	+	0.966771i	$0.417713\pi$
$968$	−20.3437	+	13.8887i	−0.653871	+	0.446399i
$969$		0			0
$970$		0			0
$971$		−	40.6600i		−	1.30484i	−0.757857	−	0.652421i	$-0.773754\pi$
$971$		−	40.6600i		−	1.30484i	0.757857	−	0.652421i	$-0.226246\pi$
$972$		0			0
$973$		−	38.6597i		−	1.23937i
$974$	13.8820	−	41.3463i	0.444809	−	1.32482i
$975$		0			0
$976$	13.8625	−	3.91275i	0.443729	−	0.125244i
$977$	26.5676			0.849972			0.424986	−	0.905200i	$-0.360279\pi$
$977$	26.5676			0.849972			0.424986	+	0.905200i	$0.360279\pi$
$978$		0			0
$979$		−	22.3384i		−	0.713938i
$980$		0			0
$981$		0			0
$982$	14.7121	+	4.93960i	0.469482	+	0.157629i
$983$	−9.88057			−0.315141			−0.157571	−	0.987508i	$-0.550366\pi$
$983$	−9.88057			−0.315141			−0.157571	+	0.987508i	$0.550366\pi$
$984$		0			0
$985$		0			0
$986$	−9.70892	−	3.25978i	−0.309195	−	0.103812i
$987$		0			0
$988$	43.7416	+	33.1044i	1.39161	+	1.05319i
$989$		−	4.90699i		−	0.156033i
$990$		0			0
$991$	−53.0549			−1.68534			−0.842672	−	0.538427i	$-0.819019\pi$
$991$	−53.0549			−1.68534			−0.842672	+	0.538427i	$0.819019\pi$
$992$	−41.5999	−	2.03281i	−1.32080	−	0.0645419i
$993$		0			0
$994$	8.00000	−	23.8272i	0.253745	−	0.755753i
$995$		0			0
$996$		0			0
$997$			32.3051i			1.02311i	0.859250	+	0.511556i	$0.170931\pi$
$997$			32.3051i			1.02311i	−0.859250	+	0.511556i	$0.829069\pi$
$998$	4.98364	+	1.67326i	0.157754	+	0.0529662i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.k.u.901.7		12
3.2	odd	2		600.2.k.f.301.6		12
4.3	odd	2		7200.2.k.u.3601.3		12
5.2	odd	4		360.2.d.f.109.6		6
5.3	odd	4		360.2.d.e.109.1		6
5.4	even	2	inner	1800.2.k.u.901.6		12
8.3	odd	2		7200.2.k.u.3601.4		12
8.5	even	2	inner	1800.2.k.u.901.8		12
12.11	even	2		2400.2.k.f.1201.2		12
15.2	even	4		120.2.d.a.109.1	✓	6
15.8	even	4		120.2.d.b.109.6	yes	6
15.14	odd	2		600.2.k.f.301.7		12
20.3	even	4		1440.2.d.f.1009.3		6
20.7	even	4		1440.2.d.e.1009.3		6
20.19	odd	2		7200.2.k.u.3601.9		12
24.5	odd	2		600.2.k.f.301.5		12
24.11	even	2		2400.2.k.f.1201.8		12
40.3	even	4		1440.2.d.e.1009.4		6
40.13	odd	4		360.2.d.f.109.5		6
40.19	odd	2		7200.2.k.u.3601.10		12
40.27	even	4		1440.2.d.f.1009.4		6
40.29	even	2	inner	1800.2.k.u.901.5		12
40.37	odd	4		360.2.d.e.109.2		6
60.23	odd	4		480.2.d.b.49.4		6
60.47	odd	4		480.2.d.a.49.4		6
60.59	even	2		2400.2.k.f.1201.11		12
120.29	odd	2		600.2.k.f.301.8		12
120.53	even	4		120.2.d.a.109.2	yes	6
120.59	even	2		2400.2.k.f.1201.5		12
120.77	even	4		120.2.d.b.109.5	yes	6
120.83	odd	4		480.2.d.a.49.3		6
120.107	odd	4		480.2.d.b.49.3		6
240.53	even	4		3840.2.f.l.769.7		12
240.77	even	4		3840.2.f.l.769.12		12
240.83	odd	4		3840.2.f.m.769.12		12
240.107	odd	4		3840.2.f.m.769.7		12
240.173	even	4		3840.2.f.l.769.6		12
240.197	even	4		3840.2.f.l.769.1		12
240.203	odd	4		3840.2.f.m.769.1		12
240.227	odd	4		3840.2.f.m.769.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.d.a.109.1	✓	6	15.2	even	4
120.2.d.a.109.2	yes	6	120.53	even	4
120.2.d.b.109.5	yes	6	120.77	even	4
120.2.d.b.109.6	yes	6	15.8	even	4
360.2.d.e.109.1		6	5.3	odd	4
360.2.d.e.109.2		6	40.37	odd	4
360.2.d.f.109.5		6	40.13	odd	4
360.2.d.f.109.6		6	5.2	odd	4
480.2.d.a.49.3		6	120.83	odd	4
480.2.d.a.49.4		6	60.47	odd	4
480.2.d.b.49.3		6	120.107	odd	4
480.2.d.b.49.4		6	60.23	odd	4
600.2.k.f.301.5		12	24.5	odd	2
600.2.k.f.301.6		12	3.2	odd	2
600.2.k.f.301.7		12	15.14	odd	2
600.2.k.f.301.8		12	120.29	odd	2
1440.2.d.e.1009.3		6	20.7	even	4
1440.2.d.e.1009.4		6	40.3	even	4
1440.2.d.f.1009.3		6	20.3	even	4
1440.2.d.f.1009.4		6	40.27	even	4
1800.2.k.u.901.5		12	40.29	even	2	inner
1800.2.k.u.901.6		12	5.4	even	2	inner
1800.2.k.u.901.7		12	1.1	even	1	trivial
1800.2.k.u.901.8		12	8.5	even	2	inner
2400.2.k.f.1201.2		12	12.11	even	2
2400.2.k.f.1201.5		12	120.59	even	2
2400.2.k.f.1201.8		12	24.11	even	2
2400.2.k.f.1201.11		12	60.59	even	2
3840.2.f.l.769.1		12	240.197	even	4
3840.2.f.l.769.6		12	240.173	even	4
3840.2.f.l.769.7		12	240.53	even	4
3840.2.f.l.769.12		12	240.77	even	4
3840.2.f.m.769.1		12	240.203	odd	4
3840.2.f.m.769.6		12	240.227	odd	4
3840.2.f.m.769.7		12	240.107	odd	4
3840.2.f.m.769.12		12	240.83	odd	4
7200.2.k.u.3601.3		12	4.3	odd	2
7200.2.k.u.3601.4		12	8.3	odd	2
7200.2.k.u.3601.9		12	20.19	odd	2
7200.2.k.u.3601.10		12	40.19	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)

\(f(q)\)	\(=\)	\(q+(0.450129 - 1.34067i) q^{2} +(-1.59477 - 1.20695i) q^{4} +2.64265 q^{7} +(-2.33596 + 1.59477i) q^{8} +O(q^{10})\)	\(q+(0.450129 - 1.34067i) q^{2} +(-1.59477 - 1.20695i) q^{4} +2.64265 q^{7} +(-2.33596 + 1.59477i) q^{8} +1.51363i q^{11} +3.87086i q^{13} +(1.18953 - 3.54291i) q^{14} +(1.08656 + 3.84959i) q^{16} -3.31415 q^{17} +7.08582i q^{19} +(2.02927 + 0.681331i) q^{22} -4.82778 q^{23} +(5.18953 + 1.74239i) q^{26} +(-4.21441 - 3.18953i) q^{28} +2.18513i q^{29} -7.36266 q^{31} +(5.65011 + 0.276098i) q^{32} +(-1.49180 + 4.44317i) q^{34} +7.87086i q^{37} +(9.49971 + 3.18953i) q^{38} -8.72532 q^{41} +1.01641i q^{43} +(1.82687 - 2.41389i) q^{44} +(-2.17313 + 6.47244i) q^{46} +7.08582 q^{47} -0.0164068 q^{49} +(4.67192 - 6.17313i) q^{52} -4.50820i q^{53} +(-6.17313 + 4.21441i) q^{56} +(2.92953 + 0.983593i) q^{58} +6.79893i q^{59} -3.60104i q^{61} +(-3.31415 + 9.87086i) q^{62} +(2.91344 - 7.45063i) q^{64} +1.01641i q^{67} +(5.28530 + 4.00000i) q^{68} +6.72532 q^{71} +15.5146 q^{73} +(10.5522 + 3.54291i) q^{74} +(8.55220 - 11.3002i) q^{76} +4.00000i q^{77} -7.36266 q^{79} +(-3.92752 + 11.6977i) q^{82} -7.74173i q^{83} +(1.36266 + 0.457515i) q^{86} +(-2.41389 - 3.53579i) q^{88} -14.7581 q^{89} +10.2293i q^{91} +(7.69919 + 5.82687i) q^{92} +(3.18953 - 9.49971i) q^{94} +11.1444 q^{97} +(-0.00738516 + 0.0219960i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{4}+O(q^{10}) \) 12 * q - 2 * q^4	\( 12 q - 2 q^{4} - 20 q^{14} + 2 q^{16} + 28 q^{26} - 32 q^{31} - 24 q^{34} + 8 q^{41} + 44 q^{44} - 4 q^{46} + 12 q^{49} - 52 q^{56} + 46 q^{64} - 32 q^{71} + 36 q^{74} + 12 q^{76} - 32 q^{79} - 40 q^{86} - 40 q^{89} + 4 q^{94}+O(q^{100}) \) 12 * q - 2 * q^4 - 20 * q^14 + 2 * q^16 + 28 * q^26 - 32 * q^31 - 24 * q^34 + 8 * q^41 + 44 * q^44 - 4 * q^46 + 12 * q^49 - 52 * q^56 + 46 * q^64 - 32 * q^71 + 36 * q^74 + 12 * q^76 - 32 * q^79 - 40 * q^86 - 40 * q^89 + 4 * q^94

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