LMFDB - Embedded newform 1800.2.m.d.899.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1800.899");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1800.m (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.3730723638$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 360)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			899.1
Root			$-0.394157 + 1.35818i$ of defining polynomial
Character	$\chi$	$=$	1800.899
Dual form			1800.2.m.d.899.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23909 - 0.681664i) q^{2} +(1.07067 + 1.68928i) q^{4} +1.41421 q^{7} +(-0.175128 - 2.82300i) q^{8} +O(q^{10})$	\(q+(-1.23909 - 0.681664i) q^{2} +(1.07067 + 1.68928i) q^{4} +1.41421 q^{7} +(-0.175128 - 2.82300i) q^{8} +6.37056i q^{11} +3.54213 q^{13} +(-1.75233 - 0.964019i) q^{14} +(-1.70734 + 3.61732i) q^{16} -3.92870 q^{17} -1.27334 q^{19} +(4.34258 - 7.89367i) q^{22} +6.28267i q^{23} +(-4.38900 - 2.41454i) q^{26} +(1.51415 + 2.38900i) q^{28} -9.00933 q^{29} +3.92870i q^{31} +(4.58134 - 3.31834i) q^{32} +(4.86799 + 2.67805i) q^{34} -2.51448 q^{37} +(1.57778 + 0.867993i) q^{38} -5.27029i q^{41} -1.55602i q^{43} +(-10.7617 + 6.82075i) q^{44} +(4.28267 - 7.78477i) q^{46} -9.73599i q^{47} -5.00000 q^{49} +(3.79245 + 5.98365i) q^{52} +5.55602i q^{53} +(-0.247668 - 3.99233i) q^{56} +(11.1633 + 6.14134i) q^{58} -0.313944i q^{59} +12.7411i q^{61} +(2.67805 - 4.86799i) q^{62} +(-7.93866 + 0.988770i) q^{64} -7.00933i q^{67} +(-4.20633 - 6.63667i) q^{68} +0.990671 q^{71} -12.0187i q^{73} +(3.11566 + 1.71403i) q^{74} +(-1.36333 - 2.15103i) q^{76} +9.00933i q^{77} +8.18453i q^{79} +(-3.59257 + 6.53034i) q^{82} -5.02897 q^{83} +(-1.06068 + 1.92804i) q^{86} +(17.9841 - 1.11566i) q^{88} -0.386566i q^{89} +5.00933 q^{91} +(-10.6132 + 6.72666i) q^{92} +(-6.63667 + 12.0637i) q^{94} +10.4626i q^{97} +(6.19543 + 3.40832i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{4}+O(q^{10}) $ 12 * q - 4 * q^4	$ 12 q - 4 q^{4} - 12 q^{16} - 32 q^{19} - 40 q^{26} - 24 q^{29} + 8 q^{34} - 24 q^{44} - 16 q^{46} - 60 q^{49} - 24 q^{56} - 28 q^{64} + 96 q^{71} + 8 q^{74} - 8 q^{76} + 80 q^{86} - 24 q^{91} - 88 q^{94}+O(q^{100}) $ 12 * q - 4 * q^4 - 12 * q^16 - 32 * q^19 - 40 * q^26 - 24 * q^29 + 8 * q^34 - 24 * q^44 - 16 * q^46 - 60 * q^49 - 24 * q^56 - 28 * q^64 + 96 * q^71 + 8 * q^74 - 8 * q^76 + 80 * q^86 - 24 * q^91 - 88 * 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 $

$2$	−1.23909	−	0.681664i	−0.876166	−	0.482009i
$2$	−1.23909	−	0.681664i	−0.876166	−	0.482009i
$3$		0			0
$3$		0			0
$4$	1.07067	+	1.68928i	0.535334	+	0.844640i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.41421			0.534522			0.267261	−	0.963624i	$-0.413881\pi$
$7$	1.41421			0.534522			0.267261	+	0.963624i	$0.413881\pi$
$8$	−0.175128	−	2.82300i	−0.0619170	−	0.998081i
$9$		0			0
$10$		0			0
$11$			6.37056i			1.92080i	0.278633	+	0.960398i	$0.410119\pi$
$11$			6.37056i			1.92080i	−0.278633	+	0.960398i	$0.589881\pi$
$12$		0			0
$13$	3.54213			0.982410			0.491205	−	0.871044i	$-0.336557\pi$
$13$	3.54213			0.982410			0.491205	+	0.871044i	$0.336557\pi$
$14$	−1.75233	−	0.964019i	−0.468330	−	0.257645i
$15$		0			0
$16$	−1.70734	+	3.61732i	−0.426835	+	0.904330i
$17$	−3.92870			−0.952849			−0.476424	−	0.879215i	$-0.658067\pi$
$17$	−3.92870			−0.952849			−0.476424	+	0.879215i	$0.658067\pi$
$18$		0			0
$19$	−1.27334			−0.292125			−0.146063	−	0.989275i	$-0.546660\pi$
$19$	−1.27334			−0.292125			−0.146063	+	0.989275i	$0.546660\pi$
$20$		0			0
$21$		0			0
$22$	4.34258	−	7.89367i	0.925841	−	1.68294i
$23$			6.28267i			1.31003i	0.755617	+	0.655014i	$0.227337\pi$
$23$			6.28267i			1.31003i	−0.755617	+	0.655014i	$0.772663\pi$
$24$		0			0
$25$		0			0
$26$	−4.38900	−	2.41454i	−0.860754	−	0.473531i
$27$		0			0
$28$	1.51415	+	2.38900i	0.286148	+	0.451479i
$29$	−9.00933			−1.67299			−0.836495	−	0.547974i	$-0.815399\pi$
$29$	−9.00933			−1.67299			−0.836495	+	0.547974i	$0.815399\pi$
$30$		0			0
$31$			3.92870i			0.705615i	0.935696	+	0.352807i	$0.114773\pi$
$31$			3.92870i			0.705615i	−0.935696	+	0.352807i	$0.885227\pi$
$32$	4.58134	−	3.31834i	0.809874	−	0.586604i
$33$		0			0
$34$	4.86799	+	2.67805i	0.834854	+	0.459282i
$35$		0			0
$36$		0			0
$37$	−2.51448			−0.413378			−0.206689	−	0.978407i	$-0.566269\pi$
$37$	−2.51448			−0.413378			−0.206689	+	0.978407i	$0.566269\pi$
$38$	1.57778	+	0.867993i	0.255950	+	0.140807i
$39$		0			0
$40$		0			0
$41$		−	5.27029i		−	0.823081i	−0.911392	−	0.411540i	$-0.864991\pi$
$41$		−	5.27029i		−	0.823081i	0.911392	−	0.411540i	$-0.135009\pi$
$42$		0			0
$43$		−	1.55602i		−	0.237290i	−0.992937	−	0.118645i	$-0.962145\pi$
$43$		−	1.55602i		−	0.237290i	0.992937	−	0.118645i	$-0.0378551\pi$
$44$	−10.7617	+	6.82075i	−1.62238	+	1.02827i
$45$		0			0
$46$	4.28267	−	7.78477i	0.631446	−	1.14780i
$47$		−	9.73599i		−	1.42014i	−0.704131	−	0.710070i	$-0.748663\pi$
$47$		−	9.73599i		−	1.42014i	0.704131	−	0.710070i	$-0.251337\pi$
$48$		0			0
$49$	−5.00000			−0.714286
$50$		0			0
$51$		0			0
$52$	3.79245	+	5.98365i	0.525918	+	0.829783i
$53$			5.55602i			0.763177i	0.924332	+	0.381589i	$0.124623\pi$
$53$			5.55602i			0.763177i	−0.924332	+	0.381589i	$0.875377\pi$
$54$		0			0
$55$		0			0
$56$	−0.247668	−	3.99233i	−0.0330960	−	0.533497i
$57$		0			0
$58$	11.1633	+	6.14134i	1.46582	+	0.806397i
$59$		−	0.313944i		−	0.0408721i	−0.999791	−	0.0204360i	$-0.993495\pi$
$59$		−	0.313944i		−	0.0408721i	0.999791	−	0.0204360i	$-0.00650544\pi$
$60$		0			0
$61$			12.7411i			1.63133i	0.578523	+	0.815666i	$0.303629\pi$
$61$			12.7411i			1.63133i	−0.578523	+	0.815666i	$0.696371\pi$
$62$	2.67805	−	4.86799i	0.340113	−	0.618236i
$63$		0			0
$64$	−7.93866	+	0.988770i	−0.992333	+	0.123596i
$65$		0			0
$66$		0			0
$67$		−	7.00933i		−	0.856326i	−0.903702	−	0.428163i	$-0.859161\pi$
$67$		−	7.00933i		−	0.856326i	0.903702	−	0.428163i	$-0.140839\pi$
$68$	−4.20633	−	6.63667i	−0.510092	−	0.804815i
$69$		0			0
$70$		0			0
$71$	0.990671			0.117571			0.0587855	−	0.998271i	$-0.481277\pi$
$71$	0.990671			0.117571			0.0587855	+	0.998271i	$0.481277\pi$
$72$		0			0
$73$		−	12.0187i		−	1.40668i	−0.710855	−	0.703339i	$-0.751692\pi$
$73$		−	12.0187i		−	1.40668i	0.710855	−	0.703339i	$-0.248308\pi$
$74$	3.11566	+	1.71403i	0.362188	+	0.199252i
$75$		0			0
$76$	−1.36333	−	2.15103i	−0.156384	−	0.246741i
$77$			9.00933i			1.02671i
$78$		0			0
$79$			8.18453i			0.920832i	0.887703	+	0.460416i	$0.152300\pi$
$79$			8.18453i			0.920832i	−0.887703	+	0.460416i	$0.847700\pi$
$80$		0			0
$81$		0			0
$82$	−3.59257	+	6.53034i	−0.396733	+	0.721155i
$83$	−5.02897			−0.552001			−0.276000	−	0.961158i	$-0.589009\pi$
$83$	−5.02897			−0.552001			−0.276000	+	0.961158i	$0.589009\pi$
$84$		0			0
$85$		0			0
$86$	−1.06068	+	1.92804i	−0.114376	+	0.207906i
$87$		0			0
$88$	17.9841	−	1.11566i	1.91711	−	0.118930i
$89$		−	0.386566i		−	0.0409759i	−0.999790	−	0.0204880i	$-0.993478\pi$
$89$		−	0.386566i		−	0.0409759i	0.999790	−	0.0204880i	$-0.00652198\pi$
$90$		0			0
$91$	5.00933			0.525120
$92$	−10.6132	+	6.72666i	−1.10650	+	0.701302i
$93$		0			0
$94$	−6.63667	+	12.0637i	−0.684520	+	1.24428i
$95$		0			0
$96$		0			0
$97$			10.4626i			1.06232i	0.847271	+	0.531160i	$0.178244\pi$
$97$			10.4626i			1.06232i	−0.847271	+	0.531160i	$0.821756\pi$
$98$	6.19543	+	3.40832i	0.625833	+	0.344292i
$99$		0			0
$100$		0			0
$101$	13.1120			1.30470			0.652348	−	0.757920i	$-0.273784\pi$
$101$	13.1120			1.30470			0.652348	+	0.757920i	$0.273784\pi$
$102$		0			0
$103$	−6.04342			−0.595476			−0.297738	−	0.954648i	$-0.596232\pi$
$103$	−6.04342			−0.595476			−0.297738	+	0.954648i	$0.596232\pi$
$104$	−0.620325	−	9.99943i	−0.0608278	−	0.980525i
$105$		0			0
$106$	3.78734	−	6.88438i	0.367859	−	0.668670i
$107$	−2.82843			−0.273434			−0.136717	−	0.990610i	$-0.543655\pi$
$107$	−2.82843			−0.273434			−0.136717	+	0.990610i	$0.543655\pi$
$108$		0			0
$109$			7.08426i			0.678549i	0.940687	+	0.339275i	$0.110182\pi$
$109$			7.08426i			0.678549i	−0.940687	+	0.339275i	$0.889818\pi$
$110$		0			0
$111$		0			0
$112$	−2.41454	+	5.11566i	−0.228153	+	0.483384i
$113$	−16.6698			−1.56816			−0.784082	−	0.620657i	$-0.786866\pi$
$113$	−16.6698			−1.56816			−0.784082	+	0.620657i	$0.786866\pi$
$114$		0			0
$115$		0			0
$116$	−9.64600	−	15.2193i	−0.895609	−	1.41308i
$117$		0			0
$118$	−0.214005	+	0.389004i	−0.0197007	+	0.0358107i
$119$	−5.55602			−0.509319
$120$		0			0
$121$	−29.5840			−2.68945
$122$	8.68516	−	15.7873i	0.786318	−	1.42932i
$123$		0			0
$124$	−6.63667	+	4.20633i	−0.595991	+	0.377740i
$125$		0			0
$126$		0			0
$127$	−16.5840			−1.47159			−0.735796	−	0.677203i	$-0.763192\pi$
$127$	−16.5840			−1.47159			−0.735796	+	0.677203i	$0.763192\pi$
$128$	10.5107	+	4.18633i	0.929023	+	0.370023i
$129$		0			0
$130$		0			0
$131$			4.96954i			0.434190i	0.976150	+	0.217095i	$0.0696582\pi$
$131$			4.96954i			0.434190i	−0.976150	+	0.217095i	$0.930342\pi$
$132$		0			0
$133$	−1.80078			−0.156147
$134$	−4.77801	+	8.68516i	−0.412757	+	0.750284i
$135$		0			0
$136$	0.688023	+	11.0907i	0.0589975	+	0.951021i
$137$	2.50129			0.213700			0.106850	−	0.994275i	$-0.465924\pi$
$137$	2.50129			0.213700			0.106850	+	0.994275i	$0.465924\pi$
$138$		0			0
$139$	18.8480			1.59867			0.799334	−	0.600887i	$-0.205186\pi$
$139$	18.8480			1.59867			0.799334	+	0.600887i	$0.205186\pi$
$140$		0			0
$141$		0			0
$142$	−1.22753	−	0.675305i	−0.103012	−	0.0566703i
$143$			22.5653i			1.88701i
$144$		0			0
$145$		0			0
$146$	−8.19269	+	14.8921i	−0.678032	+	1.23248i
$147$		0			0
$148$	−2.69218	−	4.24767i	−0.221296	−	0.349156i
$149$	−1.00933			−0.0826874			−0.0413437	−	0.999145i	$-0.513164\pi$
$149$	−1.00933			−0.0826874			−0.0413437	+	0.999145i	$0.513164\pi$
$150$		0			0
$151$		−	16.5246i		−	1.34475i	−0.740211	−	0.672375i	$-0.765274\pi$
$151$		−	16.5246i		−	1.34475i	0.740211	−	0.672375i	$-0.234726\pi$
$152$	0.222998	+	3.59465i	0.0180875	+	0.291565i
$153$		0			0
$154$	6.14134	−	11.1633i	0.494883	−	0.899567i
$155$		0			0
$156$		0			0
$157$	10.2266			0.816174			0.408087	−	0.912943i	$-0.366196\pi$
$157$	10.2266			0.816174			0.408087	+	0.912943i	$0.366196\pi$
$158$	5.57910	−	10.1413i	0.443849	−	0.806801i
$159$		0			0
$160$		0			0
$161$			8.88504i			0.700239i
$162$		0			0
$163$			6.54669i			0.512776i	0.966574	+	0.256388i	$0.0825325\pi$
$163$			6.54669i			0.512776i	−0.966574	+	0.256388i	$0.917468\pi$
$164$	8.90300	−	5.64273i	0.695207	−	0.440623i
$165$		0			0
$166$	6.23132	+	3.42807i	0.483644	+	0.266069i
$167$			22.8480i			1.76803i	0.467456	+	0.884016i	$0.345171\pi$
$167$			22.8480i			1.76803i	−0.467456	+	0.884016i	$0.654829\pi$
$168$		0			0
$169$	−0.453313			−0.0348702
$170$		0			0
$171$		0			0
$172$	2.62855	−	1.66598i	0.200425	−	0.127030i
$173$			17.5560i			1.33476i	0.744718	+	0.667380i	$0.232584\pi$
$173$			17.5560i			1.33476i	−0.744718	+	0.667380i	$0.767416\pi$
$174$		0			0
$175$		0			0
$176$	−23.0443	−	10.8767i	−1.73703	−	0.819863i
$177$		0			0
$178$	−0.263508	+	0.478989i	−0.0197508	+	0.0359017i
$179$		−	1.48684i		−	0.111131i	−0.998455	−	0.0555656i	$-0.982304\pi$
$179$		−	1.48684i		−	0.111131i	0.998455	−	0.0555656i	$-0.0176962\pi$
$180$		0			0
$181$			16.1974i			1.20395i	0.798517	+	0.601973i	$0.205618\pi$
$181$			16.1974i			1.20395i	−0.798517	+	0.601973i	$0.794382\pi$
$182$	−6.20699	−	3.41468i	−0.460093	−	0.253113i
$183$		0			0
$184$	17.7360	−	1.10027i	1.30751	−	0.0811129i
$185$		0			0
$186$		0			0
$187$		−	25.0280i		−	1.83023i
$188$	16.4468	−	10.4240i	1.19951	−	0.760249i
$189$		0			0
$190$		0			0
$191$	24.0373			1.73928			0.869640	−	0.493687i	$-0.164351\pi$
$191$	24.0373			1.73928			0.869640	+	0.493687i	$0.164351\pi$
$192$		0			0
$193$			18.4626i			1.32897i	0.747302	+	0.664485i	$0.231349\pi$
$193$			18.4626i			1.32897i	−0.747302	+	0.664485i	$0.768651\pi$
$194$	7.13201	−	12.9641i	0.512048	−	0.930769i
$195$		0			0
$196$	−5.35334	−	8.44640i	−0.382381	−	0.603315i
$197$			11.4533i			0.816015i	0.912979	+	0.408007i	$0.133776\pi$
$197$			11.4533i			0.816015i	−0.912979	+	0.408007i	$0.866224\pi$
$198$		0			0
$199$			2.50129i			0.177312i	0.996062	+	0.0886559i	$0.0282571\pi$
$199$			2.50129i			0.177312i	−0.996062	+	0.0886559i	$0.971743\pi$
$200$		0			0
$201$		0			0
$202$	−16.2469	−	8.93800i	−1.14313	−	0.628876i
$203$	−12.7411			−0.894251
$204$		0			0
$205$		0			0
$206$	7.48832	+	4.11958i	0.521736	+	0.287025i
$207$		0			0
$208$	−6.04762	+	12.8130i	−0.419327	+	0.888423i
$209$		−	8.11191i		−	0.561112i
$210$		0			0
$211$	17.1893			1.18336			0.591680	−	0.806173i	$-0.298465\pi$
$211$	17.1893			1.18336			0.591680	+	0.806173i	$0.298465\pi$
$212$	−9.38567	+	5.94865i	−0.644611	+	0.408555i
$213$		0			0
$214$	3.50466	+	1.92804i	0.239574	+	0.131798i
$215$		0			0
$216$		0			0
$217$			5.55602i			0.377167i
$218$	4.82909	−	8.77801i	0.327067	−	0.594522i
$219$		0			0
$220$		0			0
$221$	−13.9160			−0.936088
$222$		0			0
$223$	2.04210			0.136749			0.0683746	−	0.997660i	$-0.478219\pi$
$223$	2.04210			0.136749			0.0683746	+	0.997660i	$0.478219\pi$
$224$	6.47899	−	4.69284i	0.432896	−	0.313553i
$225$		0			0
$226$	20.6553	+	11.3632i	1.37397	+	0.755870i
$227$	21.2264			1.40885			0.704423	−	0.709781i	$-0.251206\pi$
$227$	21.2264			1.40885			0.704423	+	0.709781i	$0.251206\pi$
$228$		0			0
$229$			13.3690i			0.883449i	0.897151	+	0.441724i	$0.145633\pi$
$229$			13.3690i			0.883449i	−0.897151	+	0.441724i	$0.854367\pi$
$230$		0			0
$231$		0			0
$232$	1.57778	+	25.4333i	0.103586	+	1.66978i
$233$	17.2977			1.13321			0.566605	−	0.823990i	$-0.308257\pi$
$233$	17.2977			1.13321			0.566605	+	0.823990i	$0.308257\pi$
$234$		0			0
$235$		0			0
$236$	0.530340	−	0.336130i	0.0345222	−	0.0218802i
$237$		0			0
$238$	6.88438	+	3.78734i	0.446248	+	0.245497i
$239$	13.4533			0.870222			0.435111	−	0.900377i	$-0.356709\pi$
$239$	13.4533			0.870222			0.435111	+	0.900377i	$0.356709\pi$
$240$		0			0
$241$	−4.56534			−0.294080			−0.147040	−	0.989131i	$-0.546975\pi$
$241$	−4.56534			−0.294080			−0.147040	+	0.989131i	$0.546975\pi$
$242$	36.6571	+	20.1664i	2.35641	+	1.29634i
$243$		0			0
$244$	−21.5233	+	13.6415i	−1.37789	+	0.873308i
$245$		0			0
$246$		0			0
$247$	−4.51035			−0.286987
$248$	11.0907	−	0.688023i	0.704261	−	0.0436895i
$249$		0			0
$250$		0			0
$251$			25.9414i			1.63741i	0.574216	+	0.818704i	$0.305307\pi$
$251$			25.9414i			1.63741i	−0.574216	+	0.818704i	$0.694693\pi$
$252$		0			0
$253$	−40.0241			−2.51630
$254$	20.5490	+	11.3047i	1.28936	+	0.709321i
$255$		0			0
$256$	−10.1700	−	12.3520i	−0.635624	−	0.771999i
$257$	−24.3820			−1.52090			−0.760452	−	0.649394i	$-0.775023\pi$
$257$	−24.3820			−1.52090			−0.760452	+	0.649394i	$0.775023\pi$
$258$		0			0
$259$	−3.55602			−0.220960
$260$		0			0
$261$		0			0
$262$	3.38755	−	6.15768i	0.209284	−	0.380423i
$263$		−	11.7360i		−	0.723672i	−0.932242	−	0.361836i	$-0.882150\pi$
$263$		−	11.7360i		−	0.723672i	0.932242	−	0.361836i	$-0.117850\pi$
$264$		0			0
$265$		0			0
$266$	2.23132	+	1.22753i	0.136811	+	0.0752645i
$267$		0			0
$268$	11.8407	−	7.50466i	0.723287	−	0.458420i
$269$	11.0280			0.672388			0.336194	−	0.941793i	$-0.390860\pi$
$269$	11.0280			0.672388			0.336194	+	0.941793i	$0.390860\pi$
$270$		0			0
$271$			20.2714i			1.23140i	0.787981	+	0.615699i	$0.211126\pi$
$271$			20.2714i			1.23140i	−0.787981	+	0.615699i	$0.788874\pi$
$272$	6.70762	−	14.2113i	0.406709	−	0.861689i
$273$		0			0
$274$	−3.09931	−	1.70504i	−0.187236	−	0.103005i
$275$		0			0
$276$		0			0
$277$	−3.28762			−0.197534			−0.0987668	−	0.995111i	$-0.531490\pi$
$277$	−3.28762			−0.197534			−0.0987668	+	0.995111i	$0.531490\pi$
$278$	−23.3543	−	12.8480i	−1.40070	−	0.770573i
$279$		0			0
$280$		0			0
$281$		−	23.4401i		−	1.39832i	−0.714965	−	0.699160i	$-0.753557\pi$
$281$		−	23.4401i		−	1.39832i	0.714965	−	0.699160i	$-0.246443\pi$
$282$		0			0
$283$		−	27.0093i		−	1.60554i	−0.596290	−	0.802769i	$-0.703359\pi$
$283$		−	27.0093i		−	1.60554i	0.596290	−	0.802769i	$-0.296641\pi$
$284$	1.06068	+	1.67352i	0.0629398	+	0.0993053i
$285$		0			0
$286$	15.3820	−	27.9604i	0.909556	−	1.65333i
$287$		−	7.45331i		−	0.439955i
$288$		0			0
$289$	−1.56534			−0.0920791
$290$		0			0
$291$		0			0
$292$	20.3029	−	12.8680i	1.18814	−	0.753042i
$293$		−	6.00000i		−	0.350524i	−0.984522	−	0.175262i	$-0.943923\pi$
$293$		−	6.00000i		−	0.350524i	0.984522	−	0.175262i	$-0.0560772\pi$
$294$		0			0
$295$		0			0
$296$	0.440355	+	7.09839i	0.0255951	+	0.412585i
$297$		0			0
$298$	1.25065	+	0.688023i	0.0724479	+	0.0398561i
$299$			22.2540i			1.28698i
$300$		0			0
$301$		−	2.20054i		−	0.126837i
$302$	−11.2642	+	20.4754i	−0.648182	+	1.17822i
$303$		0			0
$304$	2.17403	−	4.60609i	0.124689	−	0.264177i
$305$		0			0
$306$		0			0
$307$		−	0.565344i		−	0.0322659i	−0.999870	−	0.0161330i	$-0.994864\pi$
$307$		−	0.565344i		−	0.0322659i	0.999870	−	0.0161330i	$-0.00513550\pi$
$308$	−15.2193	+	9.64600i	−0.867199	+	0.549632i
$309$		0			0
$310$		0			0
$311$	25.4533			1.44332			0.721662	−	0.692245i	$-0.243378\pi$
$311$	25.4533			1.44332			0.721662	+	0.692245i	$0.243378\pi$
$312$		0			0
$313$		−	29.5747i		−	1.67166i	−0.548989	−	0.835830i	$-0.684987\pi$
$313$		−	29.5747i		−	1.67166i	0.548989	−	0.835830i	$-0.315013\pi$
$314$	−12.6717	−	6.97113i	−0.715104	−	0.393404i
$315$		0			0
$316$	−13.8260	+	8.76291i	−0.777772	+	0.492952i
$317$		−	6.56534i		−	0.368746i	−0.982856	−	0.184373i	$-0.940974\pi$
$317$		−	6.56534i		−	0.368746i	0.982856	−	0.184373i	$-0.0590255\pi$
$318$		0			0
$319$		−	57.3944i		−	3.21347i
$320$		0			0
$321$		0			0
$322$	6.05661	−	11.0093i	0.337522	−	0.613526i
$323$	5.00258			0.278351
$324$		0			0
$325$		0			0
$326$	4.46264	−	8.11191i	0.247163	−	0.449277i
$327$		0			0
$328$	−14.8780	+	0.922973i	−0.821501	+	0.0509627i
$329$		−	13.7688i		−	0.759096i
$330$		0			0
$331$	7.29200			0.400805			0.200402	−	0.979714i	$-0.435775\pi$
$331$	7.29200			0.400805			0.200402	+	0.979714i	$0.435775\pi$
$332$	−5.38435	−	8.49534i	−0.295505	−	0.466242i
$333$		0			0
$334$	15.5747	−	28.3107i	0.852208	−	1.54909i
$335$		0			0
$336$		0			0
$337$			19.1307i			1.04212i	0.853522	+	0.521058i	$0.174462\pi$
$337$			19.1307i			1.04212i	−0.853522	+	0.521058i	$0.825538\pi$
$338$	0.561694	+	0.309007i	0.0305521	+	0.0168078i
$339$		0			0
$340$		0			0
$341$	−25.0280			−1.35534
$342$		0			0
$343$	−16.9706			−0.916324
$344$	−4.39263	+	0.272501i	−0.236835	+	0.0146923i
$345$		0			0
$346$	11.9673	−	21.7534i	0.643366	−	1.16947i
$347$	21.8807			1.17462			0.587308	−	0.809364i	$-0.300188\pi$
$347$	21.8807			1.17462			0.587308	+	0.809364i	$0.300188\pi$
$348$		0			0
$349$		−	24.8543i		−	1.33042i	−0.746655	−	0.665211i	$-0.768342\pi$
$349$		−	24.8543i		−	1.33042i	0.746655	−	0.665211i	$-0.231658\pi$
$350$		0			0
$351$		0			0
$352$	21.1396	+	29.1857i	1.12675	+	1.55560i
$353$	−8.18453			−0.435619			−0.217809	−	0.975991i	$-0.569891\pi$
$353$	−8.18453			−0.435619			−0.217809	+	0.975991i	$0.569891\pi$
$354$		0			0
$355$		0			0
$356$	0.653019	−	0.413884i	0.0346099	−	0.0219358i
$357$		0			0
$358$	−1.01352	+	1.84232i	−0.0535663	+	0.0973695i
$359$	−11.8973			−0.627915			−0.313958	−	0.949437i	$-0.601655\pi$
$359$	−11.8973			−0.627915			−0.313958	+	0.949437i	$0.601655\pi$
$360$		0			0
$361$	−17.3786			−0.914663
$362$	11.0412	−	20.0700i	0.580313	−	1.05486i
$363$		0			0
$364$	5.36333	+	8.46216i	0.281115	+	0.443538i
$365$		0			0
$366$		0			0
$367$	−6.67131			−0.348239			−0.174120	−	0.984724i	$-0.555708\pi$
$367$	−6.67131			−0.348239			−0.174120	+	0.984724i	$0.555708\pi$
$368$	−22.7264	−	10.7267i	−1.18470	−	0.559166i
$369$		0			0
$370$		0			0
$371$			7.85739i			0.407936i
$372$		0			0
$373$	−0.340330			−0.0176216			−0.00881081	−	0.999961i	$-0.502805\pi$
$373$	−0.340330			−0.0176216			−0.00881081	+	0.999961i	$0.502805\pi$
$374$	−17.0607	+	31.0118i	−0.882187	+	1.60358i
$375$		0			0
$376$	−27.4847	+	1.70504i	−1.41741	+	0.0879307i
$377$	−31.9122			−1.64356
$378$		0			0
$379$	−20.3013			−1.04281			−0.521405	−	0.853310i	$-0.674592\pi$
$379$	−20.3013			−1.04281			−0.521405	+	0.853310i	$0.674592\pi$
$380$		0			0
$381$		0			0
$382$	−29.7843	−	16.3854i	−1.52390	−	0.838349i
$383$		−	10.3013i		−	0.526373i	−0.964745	−	0.263187i	$-0.915226\pi$
$383$		−	10.3013i		−	0.526373i	0.964745	−	0.263187i	$-0.0847735\pi$
$384$		0			0
$385$		0			0
$386$	12.5853	−	22.8768i	0.640576	−	1.16440i
$387$		0			0
$388$	−17.6743	+	11.2020i	−0.897279	+	0.568696i
$389$	19.1307			0.969964			0.484982	−	0.874524i	$-0.338826\pi$
$389$	19.1307			0.969964			0.484982	+	0.874524i	$0.338826\pi$
$390$		0			0
$391$		−	24.6827i		−	1.24826i
$392$	0.875638	+	14.1150i	0.0442264	+	0.712915i
$393$		0			0
$394$	7.80731	−	14.1916i	0.393327	−	0.714964i
$395$		0			0
$396$		0			0
$397$	3.39689			0.170485			0.0852424	−	0.996360i	$-0.472834\pi$
$397$	3.39689			0.170485			0.0852424	+	0.996360i	$0.472834\pi$
$398$	1.70504	−	3.09931i	0.0854659	−	0.155355i
$399$		0			0
$400$		0			0
$401$		−	10.2993i		−	0.514320i	−0.966369	−	0.257160i	$-0.917213\pi$
$401$		−	10.2993i		−	0.514320i	0.966369	−	0.257160i	$-0.0827868\pi$
$402$		0			0
$403$			13.9160i			0.693203i
$404$	14.0386	+	22.1499i	0.698448	+	1.10200i
$405$		0			0
$406$	15.7873	+	8.68516i	0.783512	+	0.431037i
$407$		−	16.0187i		−	0.794015i
$408$		0			0
$409$	−9.11203			−0.450561			−0.225280	−	0.974294i	$-0.572330\pi$
$409$	−9.11203			−0.450561			−0.225280	+	0.974294i	$0.572330\pi$
$410$		0			0
$411$		0			0
$412$	−6.47050	−	10.2090i	−0.318779	−	0.502963i
$413$		−	0.443984i		−	0.0218470i
$414$		0			0
$415$		0			0
$416$	16.2277	−	11.7540i	0.795628	−	0.576286i
$417$		0			0
$418$	−5.52960	+	10.0514i	−0.270461	+	0.491628i
$419$			8.17134i			0.399196i	0.979878	+	0.199598i	$0.0639636\pi$
$419$			8.17134i			0.399196i	−0.979878	+	0.199598i	$0.936036\pi$
$420$		0			0
$421$		−	3.60156i		−	0.175529i	−0.996141	−	0.0877646i	$-0.972028\pi$
$421$		−	3.60156i		−	0.175529i	0.996141	−	0.0877646i	$-0.0279723\pi$
$422$	−21.2990	−	11.7173i	−1.03682	−	0.570391i
$423$		0			0
$424$	15.6846	−	0.973012i	0.761713	−	0.0472536i
$425$		0			0
$426$		0			0
$427$			18.0187i			0.871984i
$428$	−3.02831	−	4.77801i	−0.146379	−	0.230954i
$429$		0			0
$430$		0			0
$431$	−8.10270			−0.390293			−0.195147	−	0.980774i	$-0.562518\pi$
$431$	−8.10270			−0.390293			−0.195147	+	0.980774i	$0.562518\pi$
$432$		0			0
$433$			8.01866i			0.385352i	0.981262	+	0.192676i	$0.0617166\pi$
$433$			8.01866i			0.385352i	−0.981262	+	0.192676i	$0.938283\pi$
$434$	3.78734	−	6.88438i	0.181798	−	0.330461i
$435$		0			0
$436$	−11.9673	+	7.58489i	−0.573130	+	0.363250i
$437$		−	8.00000i		−	0.382692i
$438$		0			0
$439$			13.8150i			0.659354i	0.944094	+	0.329677i	$0.106940\pi$
$439$			13.8150i			0.659354i	−0.944094	+	0.329677i	$0.893060\pi$
$440$		0			0
$441$		0			0
$442$	17.2431	+	9.48601i	0.820169	+	0.451203i
$443$	−12.7147			−0.604095			−0.302048	−	0.953293i	$-0.597670\pi$
$443$	−12.7147			−0.604095			−0.302048	+	0.953293i	$0.597670\pi$
$444$		0			0
$445$		0			0
$446$	−2.53034	−	1.39203i	−0.119815	−	0.0659144i
$447$		0			0
$448$	−11.2270	+	1.39833i	−0.530424	+	0.0660650i
$449$		−	4.24264i		−	0.200223i	−0.994976	−	0.100111i	$-0.968080\pi$
$449$		−	4.24264i		−	0.200223i	0.994976	−	0.100111i	$-0.0319199\pi$
$450$		0			0
$451$	33.5747			1.58097
$452$	−17.8478	−	28.1600i	−0.839492	−	1.32453i
$453$		0			0
$454$	−26.3013	−	14.4693i	−1.23438	−	0.679077i
$455$		0			0
$456$		0			0
$457$			3.35061i			0.156735i	0.996925	+	0.0783675i	$0.0249707\pi$
$457$			3.35061i			0.156735i	−0.996925	+	0.0783675i	$0.975029\pi$
$458$	9.11317	−	16.5653i	0.425830	−	0.774048i
$459$		0			0
$460$		0			0
$461$	18.1400			0.844865			0.422432	−	0.906394i	$-0.361176\pi$
$461$	18.1400			0.844865			0.422432	+	0.906394i	$0.361176\pi$
$462$		0			0
$463$	32.9267			1.53023			0.765116	−	0.643892i	$-0.222682\pi$
$463$	32.9267			1.53023			0.765116	+	0.643892i	$0.222682\pi$
$464$	15.3820	−	32.5896i	0.714091	−	1.51293i
$465$		0			0
$466$	−21.4333	−	11.7912i	−0.992880	−	0.546218i
$467$	−6.42999			−0.297544			−0.148772	−	0.988872i	$-0.547532\pi$
$467$	−6.42999			−0.297544			−0.148772	+	0.988872i	$0.547532\pi$
$468$		0			0
$469$		−	9.91269i		−	0.457725i
$470$		0			0
$471$		0			0
$472$	−0.886265	+	0.0549803i	−0.0407936	+	0.00253067i
$473$	9.91269			0.455786
$474$		0			0
$475$		0			0
$476$	−5.94865	−	9.38567i	−0.272656	−	0.430192i
$477$		0			0
$478$	−16.6698	−	9.17064i	−0.762459	−	0.419455i
$479$	29.0280			1.32632			0.663161	−	0.748477i	$-0.269214\pi$
$479$	29.0280			1.32632			0.663161	+	0.748477i	$0.269214\pi$
$480$		0			0
$481$	−8.90663			−0.406107
$482$	5.65685	+	3.11203i	0.257663	+	0.141749i
$483$		0			0
$484$	−31.6746	−	49.9757i	−1.43976	−	2.27162i
$485$		0			0
$486$		0			0
$487$	−11.7267			−0.531386			−0.265693	−	0.964058i	$-0.585601\pi$
$487$	−11.7267			−0.531386			−0.265693	+	0.964058i	$0.585601\pi$
$488$	35.9682	−	2.23132i	1.62820	−	0.101007i
$489$		0			0
$490$		0			0
$491$			8.02609i			0.362213i	0.983464	+	0.181106i	$0.0579678\pi$
$491$			8.02609i			0.362213i	−0.983464	+	0.181106i	$0.942032\pi$
$492$		0			0
$493$	35.3949			1.59411
$494$	5.58871	+	3.07454i	0.251448	+	0.138330i
$495$		0			0
$496$	−14.2113	−	6.70762i	−0.638108	−	0.301181i
$497$	1.40102			0.0628444
$498$		0			0
$499$	26.4040			1.18201			0.591003	−	0.806669i	$-0.298732\pi$
$499$	26.4040			1.18201			0.591003	+	0.806669i	$0.298732\pi$
$500$		0			0
$501$		0			0
$502$	17.6833	−	32.1436i	0.789246	−	1.43464i
$503$		−	31.3947i		−	1.39982i	−0.714231	−	0.699910i	$-0.753223\pi$
$503$		−	31.3947i		−	1.39982i	0.714231	−	0.699910i	$-0.246777\pi$
$504$		0			0
$505$		0			0
$506$	49.5933	+	27.2830i	2.20469	+	1.21288i
$507$		0			0
$508$	−17.7560	−	28.0150i	−0.787793	−	1.24297i
$509$	−26.9253			−1.19344			−0.596721	−	0.802449i	$-0.703530\pi$
$509$	−26.9253			−1.19344			−0.596721	+	0.802449i	$0.703530\pi$
$510$		0			0
$511$		−	16.9969i		−	0.751901i
$512$	4.18158	+	22.2377i	0.184801	+	0.982776i
$513$		0			0
$514$	30.2113	+	16.6203i	1.33257	+	0.733090i
$515$		0			0
$516$		0			0
$517$	62.0237			2.72780
$518$	4.40621	+	2.42401i	0.193598	+	0.106505i
$519$		0			0
$520$		0			0
$521$		−	0.641081i		−	0.0280863i	−0.999901	−	0.0140431i	$-0.995530\pi$
$521$		−	0.641081i		−	0.0280863i	0.999901	−	0.0140431i	$-0.00447022\pi$
$522$		0			0
$523$			13.1307i			0.574165i	0.957906	+	0.287082i	$0.0926854\pi$
$523$			13.1307i			0.574165i	−0.957906	+	0.287082i	$0.907315\pi$
$524$	−8.39494	+	5.32072i	−0.366735	+	0.232437i
$525$		0			0
$526$	−8.00000	+	14.5419i	−0.348817	+	0.634057i
$527$		−	15.4347i		−	0.672344i
$528$		0			0
$529$	−16.4720			−0.716173
$530$		0			0
$531$		0			0
$532$	−1.92804	−	3.04202i	−0.0835910	−	0.131888i
$533$		−	18.6680i		−	0.808603i
$534$		0			0
$535$		0			0
$536$	−19.7873	+	1.22753i	−0.854683	+	0.0530211i
$537$		0			0
$538$	−13.6646	−	7.51738i	−0.589124	−	0.324097i
$539$		−	31.8528i		−	1.37200i
$540$		0			0
$541$		−	12.8864i		−	0.554028i	−0.960866	−	0.277014i	$-0.910655\pi$
$541$		−	12.8864i		−	0.554028i	0.960866	−	0.277014i	$-0.0893448\pi$
$542$	13.8183	−	25.1180i	0.593545	−	1.07891i
$543$		0			0
$544$	−17.9987	+	13.0367i	−0.771687	+	0.558945i
$545$		0			0
$546$		0			0
$547$		−	30.4813i		−	1.30329i	−0.758526	−	0.651643i	$-0.774080\pi$
$547$		−	30.4813i		−	1.30329i	0.758526	−	0.651643i	$-0.225920\pi$
$548$	2.67805	+	4.22538i	0.114401	+	0.180499i
$549$		0			0
$550$		0			0
$551$	11.4720			0.488722
$552$		0			0
$553$			11.5747i			0.492205i
$554$	4.07364	+	2.24105i	0.173072	+	0.0952131i
$555$		0			0
$556$	20.1800	+	31.8396i	0.855821	+	1.35030i
$557$			0.462642i			0.0196028i	0.999952	+	0.00980138i	$0.00311993\pi$
$557$			0.462642i			0.0196028i	−0.999952	+	0.00980138i	$0.996880\pi$
$558$		0			0
$559$		−	5.51161i		−	0.233116i
$560$		0			0
$561$		0			0
$562$	−15.9783	+	29.0443i	−0.674004	+	1.22516i
$563$	36.7959			1.55076			0.775382	−	0.631493i	$-0.217557\pi$
$563$	36.7959			1.55076			0.775382	+	0.631493i	$0.217557\pi$
$564$		0			0
$565$		0			0
$566$	−18.4113	+	33.4669i	−0.773884	+	1.40672i
$567$		0			0
$568$	−0.173494	−	2.79667i	−0.00727964	−	0.117345i
$569$			7.44444i			0.312087i	0.987750	+	0.156044i	$0.0498740\pi$
$569$			7.44444i			0.312087i	−0.987750	+	0.156044i	$0.950126\pi$
$570$		0			0
$571$	10.1986			0.426799			0.213400	−	0.976965i	$-0.431546\pi$
$571$	10.1986			0.426799			0.213400	+	0.976965i	$0.431546\pi$
$572$	−38.1192	+	24.1600i	−1.59384	+	1.01018i
$573$		0			0
$574$	−5.08066	+	9.23530i	−0.212062	+	0.385474i
$575$		0			0
$576$		0			0
$577$			0.443984i			0.0184833i	0.999957	+	0.00924165i	$0.00294175\pi$
$577$			0.443984i			0.0184833i	−0.999957	+	0.00924165i	$0.997058\pi$
$578$	1.93960	+	1.06704i	0.0806766	+	0.0443830i
$579$		0			0
$580$		0			0
$581$	−7.11203			−0.295057
$582$		0			0
$583$	−35.3949			−1.46591
$584$	−33.9287	+	2.10480i	−1.40398	+	0.0870972i
$585$		0			0
$586$	−4.08998	+	7.43452i	−0.168956	+	0.307117i
$587$	−30.3660			−1.25334			−0.626668	−	0.779286i	$-0.715582\pi$
$587$	−30.3660			−1.25334			−0.626668	+	0.779286i	$0.715582\pi$
$588$		0			0
$589$		−	5.00258i		−	0.206128i
$590$		0			0
$591$		0			0
$592$	4.29308	−	9.09568i	0.176444	−	0.373830i
$593$	23.1262			0.949679			0.474839	−	0.880073i	$-0.342506\pi$
$593$	23.1262			0.949679			0.474839	+	0.880073i	$0.342506\pi$
$594$		0			0
$595$		0			0
$596$	−1.08066	−	1.70504i	−0.0442654	−	0.0698411i
$597$		0			0
$598$	15.1698	−	27.5747i	0.620339	−	1.12761i
$599$	−16.1027			−0.657939			−0.328969	−	0.944341i	$-0.606701\pi$
$599$	−16.1027			−0.657939			−0.328969	+	0.944341i	$0.606701\pi$
$600$		0			0
$601$	−8.20541			−0.334705			−0.167353	−	0.985897i	$-0.553522\pi$
$601$	−8.20541			−0.334705			−0.167353	+	0.985897i	$0.553522\pi$
$602$	−1.50003	+	2.72666i	−0.0611366	+	0.111130i
$603$		0			0
$604$	27.9146	−	17.6923i	1.13583	−	0.719891i
$605$		0			0
$606$		0			0
$607$	5.81529			0.236035			0.118018	−	0.993011i	$-0.462346\pi$
$607$	5.81529			0.236035			0.118018	+	0.993011i	$0.462346\pi$
$608$	−5.83362	+	4.22538i	−0.236584	+	0.171362i
$609$		0			0
$610$		0			0
$611$		−	34.4861i		−	1.39516i
$612$		0			0
$613$	0.0858146			0.00346602			0.00173301	−	0.999998i	$-0.499448\pi$
$613$	0.0858146			0.00346602			0.00173301	+	0.999998i	$0.499448\pi$
$614$	−0.385375	+	0.700510i	−0.0155525	+	0.0282703i
$615$		0			0
$616$	25.4333	−	1.57778i	1.02474	−	0.0635707i
$617$	39.3236			1.58311			0.791555	−	0.611099i	$-0.209272\pi$
$617$	39.3236			1.58311			0.791555	+	0.611099i	$0.209272\pi$
$618$		0			0
$619$	28.0959			1.12927			0.564635	−	0.825341i	$-0.309017\pi$
$619$	28.0959			1.12927			0.564635	+	0.825341i	$0.309017\pi$
$620$		0			0
$621$		0			0
$622$	−31.5388	−	17.3506i	−1.26459	−	0.695696i
$623$		−	0.546687i		−	0.0219026i
$624$		0			0
$625$		0			0
$626$	−20.1600	+	36.6456i	−0.805755	+	1.46465i
$627$		0			0
$628$	10.9493	+	17.2757i	0.436926	+	0.689374i
$629$	9.87864			0.393887
$630$		0			0
$631$		−	18.8440i		−	0.750166i	−0.926991	−	0.375083i	$-0.877614\pi$
$631$		−	18.8440i		−	0.750166i	0.926991	−	0.375083i	$-0.122386\pi$
$632$	23.1049	−	1.43334i	0.919065	−	0.0570151i
$633$		0			0
$634$	−4.47536	+	8.13503i	−0.177739	+	0.323083i
$635$		0			0
$636$		0			0
$637$	−17.7107			−0.701722
$638$	−39.1237	+	71.1167i	−1.54892	+	2.81554i
$639$		0			0
$640$		0			0
$641$		−	14.1817i		−	0.560144i	−0.959979	−	0.280072i	$-0.909642\pi$
$641$		−	14.1817i		−	0.560144i	0.959979	−	0.280072i	$-0.0903583\pi$
$642$		0			0
$643$			18.5467i			0.731410i	0.930731	+	0.365705i	$0.119172\pi$
$643$			18.5467i			0.731410i	−0.930731	+	0.365705i	$0.880828\pi$
$644$	−15.0093	+	9.51293i	−0.591450	+	0.374862i
$645$		0			0
$646$	−6.19863	−	3.41008i	−0.243882	−	0.134168i
$647$		−	7.75464i		−	0.304866i	−0.988314	−	0.152433i	$-0.951289\pi$
$647$		−	7.75464i		−	0.304866i	0.988314	−	0.152433i	$-0.0487109\pi$
$648$		0			0
$649$	2.00000			0.0785069
$650$		0			0
$651$		0			0
$652$	−11.0592	+	7.00933i	−0.433111	+	0.274506i
$653$		−	27.6960i		−	1.08383i	−0.840433	−	0.541915i	$-0.817700\pi$
$653$		−	27.6960i		−	1.08383i	0.840433	−	0.541915i	$-0.182300\pi$
$654$		0			0
$655$		0			0
$656$	19.0643	+	8.99817i	0.744336	+	0.351320i
$657$		0			0
$658$	−9.38567	+	17.0607i	−0.365892	+	0.665095i
$659$			28.1420i			1.09625i	0.836395	+	0.548127i	$0.184659\pi$
$659$			28.1420i			1.09625i	−0.836395	+	0.548127i	$0.815341\pi$
$660$		0			0
$661$			19.7990i			0.770091i	0.922897	+	0.385046i	$0.125814\pi$
$661$			19.7990i			0.770091i	−0.922897	+	0.385046i	$0.874186\pi$
$662$	−9.03542	−	4.97070i	−0.351171	−	0.193192i
$663$		0			0
$664$	0.880711	+	14.1968i	0.0341782	+	0.550942i
$665$		0			0
$666$		0			0
$667$		−	56.6027i		−	2.19166i
$668$	−38.5967	+	24.4626i	−1.49335	+	0.946488i
$669$		0			0
$670$		0			0
$671$	−81.1680			−3.13346
$672$		0			0
$673$		−	11.8133i		−	0.455367i	−0.973735	−	0.227684i	$-0.926885\pi$
$673$		−	11.8133i		−	0.455367i	0.973735	−	0.227684i	$-0.0731152\pi$
$674$	13.0407	−	23.7046i	0.502309	−	0.913066i
$675$		0			0
$676$	−0.485348	−	0.765773i	−0.0186672	−	0.0294528i
$677$			11.4533i			0.440187i	0.975479	+	0.220093i	$0.0706362\pi$
$677$			11.4533i			0.440187i	−0.975479	+	0.220093i	$0.929364\pi$
$678$		0			0
$679$			14.7964i			0.567834i
$680$		0			0
$681$		0			0
$682$	31.0118	+	17.0607i	1.18750	+	0.653287i
$683$	−41.0254			−1.56979			−0.784896	−	0.619627i	$-0.787284\pi$
$683$	−41.0254			−1.56979			−0.784896	+	0.619627i	$0.787284\pi$
$684$		0			0
$685$		0			0
$686$	21.0280	+	11.5682i	0.802852	+	0.441677i
$687$		0			0
$688$	5.62860	+	2.65665i	0.214589	+	0.101284i
$689$			19.6801i			0.749753i
$690$		0			0
$691$	4.38538			0.166828			0.0834138	−	0.996515i	$-0.473418\pi$
$691$	4.38538			0.166828			0.0834138	+	0.996515i	$0.473418\pi$
$692$	−29.6570	+	18.7967i	−1.12739	+	0.714542i
$693$		0			0
$694$	−27.1120	−	14.9153i	−1.02916	−	0.566176i
$695$		0			0
$696$		0			0
$697$			20.7054i			0.784272i
$698$	−16.9423	+	30.7967i	−0.641276	+	1.16567i
$699$		0			0
$700$		0			0
$701$	−5.11203			−0.193079			−0.0965394	−	0.995329i	$-0.530777\pi$
$701$	−5.11203			−0.193079			−0.0965394	+	0.995329i	$0.530777\pi$
$702$		0			0
$703$	3.20180			0.120758
$704$	−6.29902	−	50.5737i	−0.237403	−	1.90607i
$705$		0			0
$706$	10.1413	+	5.57910i	0.381674	+	0.209972i
$707$	18.5432			0.697389
$708$		0			0
$709$			32.6853i			1.22752i	0.789491	+	0.613762i	$0.210345\pi$
$709$			32.6853i			1.22752i	−0.789491	+	0.613762i	$0.789655\pi$
$710$		0			0
$711$		0			0
$712$	−1.09128	+	0.0676984i	−0.0408973	+	0.00253710i
$713$	−24.6827			−0.924375
$714$		0			0
$715$		0			0
$716$	2.51168	−	1.59191i	0.0938660	−	0.0594924i
$717$		0			0
$718$	14.7418	+	8.10996i	0.550158	+	0.302661i
$719$	−10.4813			−0.390886			−0.195443	−	0.980715i	$-0.562615\pi$
$719$	−10.4813			−0.390886			−0.195443	+	0.980715i	$0.562615\pi$
$720$		0			0
$721$	−8.54669			−0.318295
$722$	21.5336	+	11.8464i	0.801397	+	0.440876i
$723$		0			0
$724$	−27.3620	+	17.3421i	−1.01690	+	0.644513i
$725$		0			0
$726$		0			0
$727$	48.5226			1.79960			0.899802	−	0.436299i	$-0.143711\pi$
$727$	48.5226			1.79960			0.899802	+	0.436299i	$0.143711\pi$
$728$	−0.877272	−	14.1413i	−0.0325139	−	0.524113i
$729$		0			0
$730$		0			0
$731$			6.11311i			0.226102i
$732$		0			0
$733$	8.94447			0.330372			0.165186	−	0.986262i	$-0.447178\pi$
$733$	8.94447			0.330372			0.165186	+	0.986262i	$0.447178\pi$
$734$	8.26633	+	4.54759i	0.305116	+	0.167855i
$735$		0			0
$736$	20.8480	+	28.7830i	0.768468	+	1.06096i
$737$	44.6533			1.64483
$738$		0			0
$739$	−4.17997			−0.153763			−0.0768813	−	0.997040i	$-0.524496\pi$
$739$	−4.17997			−0.153763			−0.0768813	+	0.997040i	$0.524496\pi$
$740$		0			0
$741$		0			0
$742$	5.35610	−	9.73599i	0.196629	−	0.357419i
$743$		−	0.245357i		−	0.00900129i	−0.999990	−	0.00450065i	$-0.998567\pi$
$743$		−	0.245357i		−	0.00900129i	0.999990	−	0.00450065i	$-0.00143260\pi$
$744$		0			0
$745$		0			0
$746$	0.421698	+	0.231991i	0.0154395	+	0.00849378i
$747$		0			0
$748$	42.2793	−	26.7967i	1.54588	−	0.979783i
$749$	−4.00000			−0.146157
$750$		0			0
$751$			8.78603i			0.320607i	0.987068	+	0.160303i	$0.0512473\pi$
$751$			8.78603i			0.320607i	−0.987068	+	0.160303i	$0.948753\pi$
$752$	35.2182	+	16.6226i	1.28427	+	0.606165i
$753$		0			0
$754$	39.5420	+	21.7534i	1.44003	+	0.792213i
$755$		0			0
$756$		0			0
$757$	−41.3393			−1.50250			−0.751252	−	0.660016i	$-0.770550\pi$
$757$	−41.3393			−1.50250			−0.751252	+	0.660016i	$0.770550\pi$
$758$	25.1551	+	13.8387i	0.913674	+	0.502644i
$759$		0			0
$760$		0			0
$761$		−	10.6726i		−	0.386882i	−0.981112	−	0.193441i	$-0.938035\pi$
$761$		−	10.6726i		−	0.386882i	0.981112	−	0.193441i	$-0.0619649\pi$
$762$		0			0
$763$			10.0187i			0.362700i
$764$	25.7360	+	40.6058i	0.931095	+	1.46907i
$765$		0			0
$766$	−7.02205	+	12.7642i	−0.253717	+	0.461190i
$767$		−	1.11203i		−	0.0401531i
$768$		0			0
$769$	28.2427			1.01846			0.509229	−	0.860631i	$-0.329931\pi$
$769$	28.2427			1.01846			0.509229	+	0.860631i	$0.329931\pi$
$770$		0			0
$771$		0			0
$772$	−31.1886	+	19.7674i	−1.12250	+	0.711443i
$773$		−	41.4720i		−	1.49164i	−0.666146	−	0.745822i	$-0.732057\pi$
$773$		−	41.4720i		−	1.49164i	0.666146	−	0.745822i	$-0.267943\pi$
$774$		0			0
$775$		0			0
$776$	29.5360	−	1.83230i	1.06028	−	0.0657756i
$777$		0			0
$778$	−23.7046	−	13.0407i	−0.849850	−	0.467532i
$779$			6.71089i			0.240442i
$780$		0			0
$781$			6.31113i			0.225830i
$782$	−16.8253	+	30.5840i	−0.601672	+	1.09368i
$783$		0			0
$784$	8.53670	−	18.0866i	0.304882	−	0.645950i
$785$		0			0
$786$		0			0
$787$			45.1680i			1.61007i	0.593230	+	0.805033i	$0.297852\pi$
$787$			45.1680i			1.61007i	−0.593230	+	0.805033i	$0.702148\pi$
$788$	−19.3479	+	12.2627i	−0.689239	+	0.436840i
$789$		0			0
$790$		0			0
$791$	−23.5747			−0.838219
$792$		0			0
$793$			45.1307i			1.60264i
$794$	−4.20903	−	2.31554i	−0.149373	−	0.0821753i
$795$		0			0
$796$	−4.22538	+	2.67805i	−0.149765	+	0.0949210i
$797$			12.4626i			0.441449i	0.975336	+	0.220725i	$0.0708422\pi$
$797$			12.4626i			0.441449i	−0.975336	+	0.220725i	$0.929158\pi$
$798$		0			0
$799$			38.2497i			1.35318i
$800$		0			0
$801$		0			0
$802$	−7.02063	+	12.7617i	−0.247907	+	0.450630i
$803$	76.5655			2.70194
$804$		0			0
$805$		0			0
$806$	9.48601	−	17.2431i	0.334130	−	0.607361i
$807$		0			0
$808$	−2.29628	−	37.0153i	−0.0807828	−	1.30219i
$809$			34.7802i			1.22281i	0.791319	+	0.611404i	$0.209395\pi$
$809$			34.7802i			1.22281i	−0.791319	+	0.611404i	$0.790605\pi$
$810$		0			0
$811$	−31.7360			−1.11440			−0.557201	−	0.830378i	$-0.688125\pi$
$811$	−31.7360			−1.11440			−0.557201	+	0.830378i	$0.688125\pi$
$812$	−13.6415	−	21.5233i	−0.478723	−	0.755321i
$813$		0			0
$814$	−10.9193	+	19.8485i	−0.382723	+	0.695689i
$815$		0			0
$816$		0			0
$817$			1.98134i			0.0693184i
$818$	11.2906	+	6.21134i	0.394766	+	0.217175i
$819$		0			0
$820$		0			0
$821$	−4.97201			−0.173524			−0.0867622	−	0.996229i	$-0.527652\pi$
$821$	−4.97201			−0.173524			−0.0867622	+	0.996229i	$0.527652\pi$
$822$		0			0
$823$	44.0386			1.53509			0.767545	−	0.640995i	$-0.221478\pi$
$823$	44.0386			1.53509			0.767545	+	0.640995i	$0.221478\pi$
$824$	1.05837	+	17.0606i	0.0368701	+	0.594333i
$825$		0			0
$826$	−0.302648	+	0.550135i	−0.0105305	+	0.0191416i
$827$	32.0838			1.11566			0.557832	−	0.829954i	$-0.311633\pi$
$827$	32.0838			1.11566			0.557832	+	0.829954i	$0.311633\pi$
$828$		0			0
$829$			41.1706i			1.42992i	0.699168	+	0.714958i	$0.253554\pi$
$829$			41.1706i			1.42992i	−0.699168	+	0.714958i	$0.746446\pi$
$830$		0			0
$831$		0			0
$832$	−28.1198	+	3.50235i	−0.974878	+	0.121422i
$833$	19.6435			0.680606
$834$		0			0
$835$		0			0
$836$	13.7033	−	8.68516i	0.473938	−	0.300383i
$837$		0			0
$838$	5.57011	−	10.1250i	0.192416	−	0.349762i
$839$	39.9346			1.37870			0.689348	−	0.724430i	$-0.257897\pi$
$839$	39.9346			1.37870			0.689348	+	0.724430i	$0.257897\pi$
$840$		0			0
$841$	52.1680			1.79890
$842$	−2.45505	+	4.46264i	−0.0846067	+	0.153793i
$843$		0			0
$844$	18.4040	+	29.0376i	0.633493	+	0.999514i
$845$		0			0
$846$		0			0
$847$	−41.8381			−1.43757
$848$	−20.0979	−	9.48601i	−0.690164	−	0.325751i
$849$		0			0
$850$		0			0
$851$		−	15.7977i		−	0.541537i
$852$		0			0
$853$	36.0822			1.23543			0.617716	−	0.786401i	$-0.288058\pi$
$853$	36.0822			1.23543			0.617716	+	0.786401i	$0.288058\pi$
$854$	12.2827	−	22.3267i	0.420304	−	0.764003i
$855$		0			0
$856$	0.495336	+	7.98465i	0.0169302	+	0.272910i
$857$	−23.0998			−0.789074			−0.394537	−	0.918880i	$-0.629095\pi$
$857$	−23.0998			−0.789074			−0.394537	+	0.918880i	$0.629095\pi$
$858$		0			0
$859$	−44.3013			−1.51154			−0.755771	−	0.654836i	$-0.772738\pi$
$859$	−44.3013			−1.51154			−0.755771	+	0.654836i	$0.772738\pi$
$860$		0			0
$861$		0			0
$862$	10.0399	+	5.52332i	0.341962	+	0.188125i
$863$			25.5492i			0.869706i	0.900501	+	0.434853i	$0.143200\pi$
$863$			25.5492i			0.869706i	−0.900501	+	0.434853i	$0.856800\pi$
$864$		0			0
$865$		0			0
$866$	5.46603	−	9.93581i	0.185743	−	0.337632i
$867$		0			0
$868$	−9.38567	+	5.94865i	−0.318570	+	0.201910i
$869$	−52.1400			−1.76873
$870$		0			0
$871$		−	24.8280i		−	0.841263i
$872$	19.9989	−	1.24065i	0.677247	−	0.0420137i
$873$		0			0
$874$	−5.45331	+	9.91269i	−0.184461	+	0.335302i
$875$		0			0
$876$		0			0
$877$	−0.168701			−0.00569661			−0.00284831	−	0.999996i	$-0.500907\pi$
$877$	−0.168701			−0.00569661			−0.00284831	+	0.999996i	$0.500907\pi$
$878$	9.41719	−	17.1180i	0.317815	−	0.577704i
$879$		0			0
$880$		0			0
$881$		−	29.4704i		−	0.992881i	−0.868071	−	0.496441i	$-0.834640\pi$
$881$		−	29.4704i		−	0.992881i	0.868071	−	0.496441i	$-0.165360\pi$
$882$		0			0
$883$			3.43466i			0.115585i	0.998329	+	0.0577927i	$0.0184062\pi$
$883$			3.43466i			0.115585i	−0.998329	+	0.0577927i	$0.981594\pi$
$884$	−14.8994	−	23.5080i	−0.501120	−	0.790658i
$885$		0			0
$886$	15.7546	+	8.66717i	0.529288	+	0.291179i
$887$			16.6240i			0.558178i	0.960265	+	0.279089i	$0.0900324\pi$
$887$			16.6240i			0.558178i	−0.960265	+	0.279089i	$0.909968\pi$
$888$		0			0
$889$	−23.4533			−0.786599
$890$		0			0
$891$		0			0
$892$	2.18641	+	3.44968i	0.0732065	+	0.115504i
$893$			12.3973i			0.414858i
$894$		0			0
$895$		0			0
$896$	14.8644	+	5.92036i	0.496584	+	0.197785i
$897$		0			0
$898$	−2.89206	+	5.25700i	−0.0965092	+	0.175428i
$899$		−	35.3949i		−	1.18049i
$900$		0			0
$901$		−	21.8279i		−	0.727193i
$902$	−41.6019	−	22.8867i	−1.38519	−	0.762042i
$903$		0			0
$904$	2.91934	+	47.0589i	0.0970959	+	1.56516i
$905$		0			0
$906$		0			0
$907$			50.1587i			1.66549i	0.553656	+	0.832746i	$0.313232\pi$
$907$			50.1587i			1.66549i	−0.553656	+	0.832746i	$0.686768\pi$
$908$	22.7264	+	35.8573i	0.754203	+	1.18997i
$909$		0			0
$910$		0			0
$911$	26.5467			0.879531			0.439765	−	0.898113i	$-0.355062\pi$
$911$	26.5467			0.879531			0.439765	+	0.898113i	$0.355062\pi$
$912$		0			0
$913$		−	32.0373i		−	1.06028i
$914$	2.28399	−	4.15169i	0.0755477	−	0.137326i
$915$		0			0
$916$	−22.5840	+	14.3138i	−0.746196	+	0.472940i
$917$			7.02799i			0.232085i
$918$		0			0
$919$			39.3236i			1.29717i	0.761144	+	0.648583i	$0.224638\pi$
$919$			39.3236i			1.29717i	−0.761144	+	0.648583i	$0.775362\pi$
$920$		0			0
$921$		0			0
$922$	−22.4770	−	12.3654i	−0.740242	−	0.407233i
$923$	3.50909			0.115503
$924$		0			0
$925$		0			0
$926$	−40.7990	−	22.4449i	−1.34074	−	0.737586i
$927$		0			0
$928$	−41.2748	+	29.8960i	−1.35491	+	0.981384i
$929$		−	38.9833i		−	1.27900i	−0.768791	−	0.639500i	$-0.779141\pi$
$929$		−	38.9833i		−	1.27900i	0.768791	−	0.639500i	$-0.220859\pi$
$930$		0			0
$931$	6.36672			0.208661
$932$	18.5201	+	29.2207i	0.606646	+	0.957155i
$933$		0			0
$934$	7.96731	+	4.38309i	0.260698	+	0.143419i
$935$		0			0
$936$		0			0
$937$		−	11.1307i		−	0.363624i	−0.983333	−	0.181812i	$-0.941804\pi$
$937$		−	11.1307i		−	0.363624i	0.983333	−	0.181812i	$-0.0581962\pi$
$938$	−6.75712	+	12.2827i	−0.220628	+	0.401043i
$939$		0			0
$940$		0			0
$941$	−46.2427			−1.50747			−0.753735	−	0.657179i	$-0.771750\pi$
$941$	−46.2427			−1.50747			−0.753735	+	0.657179i	$0.771750\pi$
$942$		0			0
$943$	33.1115			1.07826
$944$	1.13564	+	0.536010i	0.0369618	+	0.0174456i
$945$		0			0
$946$	−12.2827	−	6.75712i	−0.399344	−	0.219693i
$947$	16.3163			0.530208			0.265104	−	0.964220i	$-0.414594\pi$
$947$	16.3163			0.530208			0.265104	+	0.964220i	$0.414594\pi$
$948$		0			0
$949$		−	42.5717i		−	1.38193i
$950$		0			0
$951$		0			0
$952$	0.973012	+	15.6846i	0.0315355	+	0.508342i
$953$	−8.01290			−0.259563			−0.129782	−	0.991543i	$-0.541428\pi$
$953$	−8.01290			−0.259563			−0.129782	+	0.991543i	$0.541428\pi$
$954$		0			0
$955$		0			0
$956$	14.4040	+	22.7264i	0.465860	+	0.735025i
$957$		0			0
$958$	−35.9682	−	19.7873i	−1.16208	−	0.639300i
$959$	3.53736			0.114227
$960$		0			0
$961$	15.5653			0.502108
$962$	11.0361	+	6.07133i	0.355817	+	0.195747i
$963$		0			0
$964$	−4.88797	−	7.71215i	−0.157431	−	0.248392i
$965$		0			0
$966$		0			0
$967$	61.0092			1.96192			0.980962	−	0.194201i	$-0.0622114\pi$
$967$	61.0092			1.96192			0.980962	+	0.194201i	$0.0622114\pi$
$968$	5.18098	+	83.5156i	0.166523	+	2.68429i
$969$		0			0
$970$		0			0
$971$			16.0023i			0.513540i	0.966473	+	0.256770i	$0.0826582\pi$
$971$			16.0023i			0.513540i	−0.966473	+	0.256770i	$0.917342\pi$
$972$		0			0
$973$	26.6551			0.854524
$974$	14.5303	+	7.99364i	0.465582	+	0.256133i
$975$		0			0
$976$	−46.0887	−	21.7534i	−1.47526	−	0.696310i
$977$	−34.2683			−1.09634			−0.548169	−	0.836367i	$-0.684675\pi$
$977$	−34.2683			−1.09634			−0.548169	+	0.836367i	$0.684675\pi$
$978$		0			0
$979$	2.46264			0.0787064
$980$		0			0
$981$		0			0
$982$	5.47110	−	9.94502i	0.174590	−	0.317358i
$983$			15.3947i			0.491015i	0.969395	+	0.245507i	$0.0789546\pi$
$983$			15.3947i			0.491015i	−0.969395	+	0.245507i	$0.921045\pi$
$984$		0			0
$985$		0			0
$986$	−43.8573	−	24.1274i	−1.39670	−	0.768374i
$987$		0			0
$988$	−4.82909	−	7.61925i	−0.153634	−	0.242401i
$989$	9.77594			0.310857
$990$		0			0
$991$		−	14.6145i		−	0.464245i	−0.972687	−	0.232123i	$-0.925433\pi$
$991$		−	14.6145i		−	0.464245i	0.972687	−	0.232123i	$-0.0745671\pi$
$992$	13.0367	+	17.9987i	0.413917	+	0.571459i
$993$		0			0
$994$	−1.73599	−	0.955026i	−0.0550621	−	0.0302916i
$995$		0			0
$996$		0			0
$997$	−44.7655			−1.41774			−0.708869	−	0.705340i	$-0.750794\pi$
$997$	−44.7655			−1.41774			−0.708869	+	0.705340i	$0.750794\pi$
$998$	−32.7169	−	17.9987i	−1.03563	−	0.569738i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.m.d.899.1		12
3.2	odd	2		1800.2.m.e.899.12		12
4.3	odd	2		7200.2.m.d.3599.1		12
5.2	odd	4		1800.2.b.e.251.3		6
5.3	odd	4		360.2.b.c.251.4	yes	6
5.4	even	2	inner	1800.2.m.d.899.12		12
8.3	odd	2		1800.2.m.e.899.2		12
8.5	even	2		7200.2.m.e.3599.7		12
12.11	even	2		7200.2.m.e.3599.6		12
15.2	even	4		1800.2.b.d.251.4		6
15.8	even	4		360.2.b.d.251.3	yes	6
15.14	odd	2		1800.2.m.e.899.1		12
20.3	even	4		1440.2.b.c.431.4		6
20.7	even	4		7200.2.b.d.4751.1		6
20.19	odd	2		7200.2.m.d.3599.7		12
24.5	odd	2		7200.2.m.d.3599.12		12
24.11	even	2	inner	1800.2.m.d.899.11		12
40.3	even	4		360.2.b.d.251.4	yes	6
40.13	odd	4		1440.2.b.d.431.1		6
40.19	odd	2		1800.2.m.e.899.11		12
40.27	even	4		1800.2.b.d.251.3		6
40.29	even	2		7200.2.m.e.3599.1		12
40.37	odd	4		7200.2.b.e.4751.4		6
60.23	odd	4		1440.2.b.d.431.6		6
60.47	odd	4		7200.2.b.e.4751.3		6
60.59	even	2		7200.2.m.e.3599.12		12
120.29	odd	2		7200.2.m.d.3599.6		12
120.53	even	4		1440.2.b.c.431.3		6
120.59	even	2	inner	1800.2.m.d.899.2		12
120.77	even	4		7200.2.b.d.4751.6		6
120.83	odd	4		360.2.b.c.251.3	✓	6
120.107	odd	4		1800.2.b.e.251.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.b.c.251.3	✓	6	120.83	odd	4
360.2.b.c.251.4	yes	6	5.3	odd	4
360.2.b.d.251.3	yes	6	15.8	even	4
360.2.b.d.251.4	yes	6	40.3	even	4
1440.2.b.c.431.3		6	120.53	even	4
1440.2.b.c.431.4		6	20.3	even	4
1440.2.b.d.431.1		6	40.13	odd	4
1440.2.b.d.431.6		6	60.23	odd	4
1800.2.b.d.251.3		6	40.27	even	4
1800.2.b.d.251.4		6	15.2	even	4
1800.2.b.e.251.3		6	5.2	odd	4
1800.2.b.e.251.4		6	120.107	odd	4
1800.2.m.d.899.1		12	1.1	even	1	trivial
1800.2.m.d.899.2		12	120.59	even	2	inner
1800.2.m.d.899.11		12	24.11	even	2	inner
1800.2.m.d.899.12		12	5.4	even	2	inner
1800.2.m.e.899.1		12	15.14	odd	2
1800.2.m.e.899.2		12	8.3	odd	2
1800.2.m.e.899.11		12	40.19	odd	2
1800.2.m.e.899.12		12	3.2	odd	2
7200.2.b.d.4751.1		6	20.7	even	4
7200.2.b.d.4751.6		6	120.77	even	4
7200.2.b.e.4751.3		6	60.47	odd	4
7200.2.b.e.4751.4		6	40.37	odd	4
7200.2.m.d.3599.1		12	4.3	odd	2
7200.2.m.d.3599.6		12	120.29	odd	2
7200.2.m.d.3599.7		12	20.19	odd	2
7200.2.m.d.3599.12		12	24.5	odd	2
7200.2.m.e.3599.1		12	40.29	even	2
7200.2.m.e.3599.6		12	12.11	even	2
7200.2.m.e.3599.7		12	8.5	even	2
7200.2.m.e.3599.12		12	60.59	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1800.m (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.23909 - 0.681664i) q^{2} +(1.07067 + 1.68928i) q^{4} +1.41421 q^{7} +(-0.175128 - 2.82300i) q^{8} +O(q^{10})\)	\(q+(-1.23909 - 0.681664i) q^{2} +(1.07067 + 1.68928i) q^{4} +1.41421 q^{7} +(-0.175128 - 2.82300i) q^{8} +6.37056i q^{11} +3.54213 q^{13} +(-1.75233 - 0.964019i) q^{14} +(-1.70734 + 3.61732i) q^{16} -3.92870 q^{17} -1.27334 q^{19} +(4.34258 - 7.89367i) q^{22} +6.28267i q^{23} +(-4.38900 - 2.41454i) q^{26} +(1.51415 + 2.38900i) q^{28} -9.00933 q^{29} +3.92870i q^{31} +(4.58134 - 3.31834i) q^{32} +(4.86799 + 2.67805i) q^{34} -2.51448 q^{37} +(1.57778 + 0.867993i) q^{38} -5.27029i q^{41} -1.55602i q^{43} +(-10.7617 + 6.82075i) q^{44} +(4.28267 - 7.78477i) q^{46} -9.73599i q^{47} -5.00000 q^{49} +(3.79245 + 5.98365i) q^{52} +5.55602i q^{53} +(-0.247668 - 3.99233i) q^{56} +(11.1633 + 6.14134i) q^{58} -0.313944i q^{59} +12.7411i q^{61} +(2.67805 - 4.86799i) q^{62} +(-7.93866 + 0.988770i) q^{64} -7.00933i q^{67} +(-4.20633 - 6.63667i) q^{68} +0.990671 q^{71} -12.0187i q^{73} +(3.11566 + 1.71403i) q^{74} +(-1.36333 - 2.15103i) q^{76} +9.00933i q^{77} +8.18453i q^{79} +(-3.59257 + 6.53034i) q^{82} -5.02897 q^{83} +(-1.06068 + 1.92804i) q^{86} +(17.9841 - 1.11566i) q^{88} -0.386566i q^{89} +5.00933 q^{91} +(-10.6132 + 6.72666i) q^{92} +(-6.63667 + 12.0637i) q^{94} +10.4626i q^{97} +(6.19543 + 3.40832i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{4}+O(q^{10}) \) 12 * q - 4 * q^4	\( 12 q - 4 q^{4} - 12 q^{16} - 32 q^{19} - 40 q^{26} - 24 q^{29} + 8 q^{34} - 24 q^{44} - 16 q^{46} - 60 q^{49} - 24 q^{56} - 28 q^{64} + 96 q^{71} + 8 q^{74} - 8 q^{76} + 80 q^{86} - 24 q^{91} - 88 q^{94}+O(q^{100}) \) 12 * q - 4 * q^4 - 12 * q^16 - 32 * q^19 - 40 * q^26 - 24 * q^29 + 8 * q^34 - 24 * q^44 - 16 * q^46 - 60 * q^49 - 24 * q^56 - 28 * q^64 + 96 * q^71 + 8 * q^74 - 8 * q^76 + 80 * q^86 - 24 * q^91 - 88 * q^94

Introduction

L-functions

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