LMFDB - Embedded newform 1800.2.k.p.901.2

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:	$6$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			901.2
Root			$-0.671462 - 1.24464i$ of defining polynomial
Character	$\chi$	$=$	1800.901
Dual form			1800.2.k.p.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.671462 + 1.24464i) q^{2} +(-1.09828 - 1.67146i) q^{4} -4.68585 q^{7} +(2.81783 - 0.244644i) q^{8} +O(q^{10})$	\(q+(-0.671462 + 1.24464i) q^{2} +(-1.09828 - 1.67146i) q^{4} -4.68585 q^{7} +(2.81783 - 0.244644i) q^{8} -2.29273i q^{11} +4.97858i q^{13} +(3.14637 - 5.83221i) q^{14} +(-1.58757 + 3.67146i) q^{16} -2.97858 q^{17} +2.68585i q^{19} +(2.85363 + 1.53948i) q^{22} +2.68585 q^{23} +(-6.19656 - 3.34292i) q^{26} +(5.14637 + 7.83221i) q^{28} -2.00000i q^{29} -6.97858 q^{31} +(-3.50367 - 4.44120i) q^{32} +(2.00000 - 3.70727i) q^{34} -4.39312i q^{37} +(-3.34292 - 1.80344i) q^{38} +11.3717 q^{41} -9.37169i q^{43} +(-3.83221 + 2.51806i) q^{44} +(-1.80344 + 3.34292i) q^{46} +7.27131 q^{47} +14.9572 q^{49} +(8.32150 - 5.46787i) q^{52} -2.00000i q^{53} +(-13.2039 + 1.14637i) q^{56} +(2.48929 + 1.34292i) q^{58} -1.70727i q^{59} +4.58546i q^{61} +(4.68585 - 8.68585i) q^{62} +(7.88030 - 1.37873i) q^{64} -4.00000i q^{67} +(3.27131 + 4.97858i) q^{68} -0.585462 q^{71} +6.00000 q^{73} +(5.46787 + 2.94981i) q^{74} +(4.48929 - 2.94981i) q^{76} +10.7434i q^{77} +1.02142 q^{79} +(-7.63565 + 14.1537i) q^{82} -13.3717i q^{83} +(11.6644 + 6.29273i) q^{86} +(-0.560904 - 6.46052i) q^{88} -3.37169 q^{89} -23.3288i q^{91} +(-2.94981 - 4.48929i) q^{92} +(-4.88240 + 9.05019i) q^{94} +3.95715 q^{97} +(-10.0432 + 18.6163i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 2 q^{4} - 4 q^{7} + 8 q^{8}+O(q^{10}) $ 6 * q + 2 * q^2 - 2 * q^4 - 4 * q^7 + 8 * q^8	$ 6 q + 2 q^{2} - 2 q^{4} - 4 q^{7} + 8 q^{8} + 16 q^{14} + 10 q^{16} + 12 q^{17} + 20 q^{22} - 8 q^{23} - 28 q^{26} + 28 q^{28} - 12 q^{31} + 12 q^{32} + 12 q^{34} - 8 q^{38} + 20 q^{41} + 4 q^{44} - 20 q^{46} + 8 q^{47} + 30 q^{49} + 8 q^{52} - 4 q^{56} + 4 q^{62} + 22 q^{64} - 16 q^{68} + 8 q^{71} + 36 q^{73} - 12 q^{74} + 12 q^{76} + 36 q^{79} - 28 q^{82} + 16 q^{86} - 12 q^{88} + 28 q^{89} - 24 q^{92} + 4 q^{94} - 36 q^{97} - 6 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 - 2 * q^4 - 4 * q^7 + 8 * q^8 + 16 * q^14 + 10 * q^16 + 12 * q^17 + 20 * q^22 - 8 * q^23 - 28 * q^26 + 28 * q^28 - 12 * q^31 + 12 * q^32 + 12 * q^34 - 8 * q^38 + 20 * q^41 + 4 * q^44 - 20 * q^46 + 8 * q^47 + 30 * q^49 + 8 * q^52 - 4 * q^56 + 4 * q^62 + 22 * q^64 - 16 * q^68 + 8 * q^71 + 36 * q^73 - 12 * q^74 + 12 * q^76 + 36 * q^79 - 28 * q^82 + 16 * q^86 - 12 * q^88 + 28 * q^89 - 24 * q^92 + 4 * q^94 - 36 * q^97 - 6 * q^98

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 $

$2$	−0.671462	+	1.24464i	−0.474795	+	0.880096i
$2$	−0.671462	+	1.24464i	−0.474795	+	0.880096i
$3$		0			0
$3$		0			0
$4$	−1.09828	−	1.67146i	−0.549139	−	0.835731i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−4.68585			−1.77108			−0.885542	−	0.464560i	$-0.846213\pi$
$7$	−4.68585			−1.77108			−0.885542	+	0.464560i	$0.846213\pi$
$8$	2.81783	−	0.244644i	0.996252	−	0.0864948i
$9$		0			0
$10$		0			0
$11$		−	2.29273i		−	0.691284i	−0.938366	−	0.345642i	$-0.887661\pi$
$11$		−	2.29273i		−	0.691284i	0.938366	−	0.345642i	$-0.112339\pi$
$12$		0			0
$13$			4.97858i			1.38081i	0.723424	+	0.690404i	$0.242567\pi$
$13$			4.97858i			1.38081i	−0.723424	+	0.690404i	$0.757433\pi$
$14$	3.14637	−	5.83221i	0.840902	−	1.55872i
$15$		0			0
$16$	−1.58757	+	3.67146i	−0.396892	+	0.917865i
$17$	−2.97858			−0.722411			−0.361206	−	0.932486i	$-0.617635\pi$
$17$	−2.97858			−0.722411			−0.361206	+	0.932486i	$0.617635\pi$
$18$		0			0
$19$			2.68585i			0.616175i	0.951358	+	0.308088i	$0.0996890\pi$
$19$			2.68585i			0.616175i	−0.951358	+	0.308088i	$0.900311\pi$
$20$		0			0
$21$		0			0
$22$	2.85363	+	1.53948i	0.608397	+	0.328218i
$23$	2.68585			0.560038			0.280019	−	0.959995i	$-0.409659\pi$
$23$	2.68585			0.560038			0.280019	+	0.959995i	$0.409659\pi$
$24$		0			0
$25$		0			0
$26$	−6.19656	−	3.34292i	−1.21524	−	0.655601i
$27$		0			0
$28$	5.14637	+	7.83221i	0.972572	+	1.48015i
$29$		−	2.00000i		−	0.371391i	−0.982607	−	0.185695i	$-0.940546\pi$
$29$		−	2.00000i		−	0.371391i	0.982607	−	0.185695i	$-0.0594537\pi$
$30$		0			0
$31$	−6.97858			−1.25339			−0.626695	−	0.779265i	$-0.715593\pi$
$31$	−6.97858			−1.25339			−0.626695	+	0.779265i	$0.715593\pi$
$32$	−3.50367	−	4.44120i	−0.619368	−	0.785101i
$33$		0			0
$34$	2.00000	−	3.70727i	0.342997	−	0.635791i
$35$		0			0
$36$		0			0
$37$		−	4.39312i		−	0.722224i	−0.932523	−	0.361112i	$-0.882397\pi$
$37$		−	4.39312i		−	0.722224i	0.932523	−	0.361112i	$-0.117603\pi$
$38$	−3.34292	−	1.80344i	−0.542294	−	0.292557i
$39$		0			0
$40$		0			0
$41$	11.3717			1.77596			0.887980	−	0.459882i	$-0.152108\pi$
$41$	11.3717			1.77596			0.887980	+	0.459882i	$0.152108\pi$
$42$		0			0
$43$		−	9.37169i		−	1.42917i	−0.699549	−	0.714585i	$-0.746616\pi$
$43$		−	9.37169i		−	1.42917i	0.699549	−	0.714585i	$-0.253384\pi$
$44$	−3.83221	+	2.51806i	−0.577728	+	0.379611i
$45$		0			0
$46$	−1.80344	+	3.34292i	−0.265903	+	0.492887i
$47$	7.27131			1.06063			0.530315	−	0.847801i	$-0.322074\pi$
$47$	7.27131			1.06063			0.530315	+	0.847801i	$0.322074\pi$
$48$		0			0
$49$	14.9572			2.13674
$50$		0			0
$51$		0			0
$52$	8.32150	−	5.46787i	1.15398	−	0.758257i
$53$		−	2.00000i		−	0.274721i	−0.990521	−	0.137361i	$-0.956138\pi$
$53$		−	2.00000i		−	0.274721i	0.990521	−	0.137361i	$-0.0438619\pi$
$54$		0			0
$55$		0			0
$56$	−13.2039	+	1.14637i	−1.76445	+	0.153190i
$57$		0			0
$58$	2.48929	+	1.34292i	0.326860	+	0.176334i
$59$		−	1.70727i		−	0.222267i	−0.993805	−	0.111134i	$-0.964552\pi$
$59$		−	1.70727i		−	0.222267i	0.993805	−	0.111134i	$-0.0354482\pi$
$60$		0			0
$61$			4.58546i			0.587108i	0.955942	+	0.293554i	$0.0948381\pi$
$61$			4.58546i			0.587108i	−0.955942	+	0.293554i	$0.905162\pi$
$62$	4.68585	−	8.68585i	0.595103	−	1.10310i
$63$		0			0
$64$	7.88030	−	1.37873i	0.985037	−	0.172341i
$65$		0			0
$66$		0			0
$67$		−	4.00000i		−	0.488678i	−0.969690	−	0.244339i	$-0.921429\pi$
$67$		−	4.00000i		−	0.488678i	0.969690	−	0.244339i	$-0.0785709\pi$
$68$	3.27131	+	4.97858i	0.396704	+	0.603741i
$69$		0			0
$70$		0			0
$71$	−0.585462			−0.0694816			−0.0347408	−	0.999396i	$-0.511061\pi$
$71$	−0.585462			−0.0694816			−0.0347408	+	0.999396i	$0.511061\pi$
$72$		0			0
$73$	6.00000			0.702247			0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000			0.702247			0.351123	+	0.936329i	$0.385800\pi$
$74$	5.46787	+	2.94981i	0.635626	+	0.342908i
$75$		0			0
$76$	4.48929	−	2.94981i	0.514957	−	0.338366i
$77$			10.7434i			1.22432i
$78$		0			0
$79$	1.02142			0.114919			0.0574595	−	0.998348i	$-0.481700\pi$
$79$	1.02142			0.114919			0.0574595	+	0.998348i	$0.481700\pi$
$80$		0			0
$81$		0			0
$82$	−7.63565	+	14.1537i	−0.843217	+	1.56302i
$83$		−	13.3717i		−	1.46773i	−0.679293	−	0.733867i	$-0.737714\pi$
$83$		−	13.3717i		−	1.46773i	0.679293	−	0.733867i	$-0.262286\pi$
$84$		0			0
$85$		0			0
$86$	11.6644	+	6.29273i	1.25781	+	0.678563i
$87$		0			0
$88$	−0.560904	−	6.46052i	−0.0597925	−	0.688694i
$89$	−3.37169			−0.357399			−0.178699	−	0.983904i	$-0.557189\pi$
$89$	−3.37169			−0.357399			−0.178699	+	0.983904i	$0.557189\pi$
$90$		0			0
$91$		−	23.3288i		−	2.44553i
$92$	−2.94981	−	4.48929i	−0.307539	−	0.468041i
$93$		0			0
$94$	−4.88240	+	9.05019i	−0.503581	+	0.933456i
$95$		0			0
$96$		0			0
$97$	3.95715			0.401788			0.200894	−	0.979613i	$-0.435615\pi$
$97$	3.95715			0.401788			0.200894	+	0.979613i	$0.435615\pi$
$98$	−10.0432	+	18.6163i	−1.01451	+	1.88053i
$99$		0			0
$100$		0			0
$101$			2.00000i			0.199007i	0.995037	+	0.0995037i	$0.0317255\pi$
$101$			2.00000i			0.199007i	−0.995037	+	0.0995037i	$0.968274\pi$
$102$		0			0
$103$	14.6430			1.44282			0.721409	−	0.692509i	$-0.243495\pi$
$103$	14.6430			1.44282			0.721409	+	0.692509i	$0.243495\pi$
$104$	1.21798	+	14.0288i	0.119433	+	1.37563i
$105$		0			0
$106$	2.48929	+	1.34292i	0.241781	+	0.130436i
$107$		−	11.3288i		−	1.09520i	−0.836740	−	0.547600i	$-0.815541\pi$
$107$		−	11.3288i		−	1.09520i	0.836740	−	0.547600i	$-0.184459\pi$
$108$		0			0
$109$		−	9.37169i		−	0.897645i	−0.893621	−	0.448823i	$-0.851843\pi$
$109$		−	9.37169i		−	0.897645i	0.893621	−	0.448823i	$-0.148157\pi$
$110$		0			0
$111$		0			0
$112$	7.43910	−	17.2039i	0.702929	−	1.62562i
$113$	19.7648			1.85932			0.929658	−	0.368423i	$-0.120102\pi$
$113$	19.7648			1.85932			0.929658	+	0.368423i	$0.120102\pi$
$114$		0			0
$115$		0			0
$116$	−3.34292	+	2.19656i	−0.310383	+	0.203945i
$117$		0			0
$118$	2.12494	+	1.14637i	0.195617	+	0.105531i
$119$	13.9572			1.27945
$120$		0			0
$121$	5.74338			0.522126
$122$	−5.70727	−	3.07896i	−0.516712	−	0.278756i
$123$		0			0
$124$	7.66442	+	11.6644i	0.688286	+	1.04750i
$125$		0			0
$126$		0			0
$127$	−6.64300			−0.589471			−0.294735	−	0.955579i	$-0.595232\pi$
$127$	−6.64300			−0.589471			−0.294735	+	0.955579i	$0.595232\pi$
$128$	−3.57529	+	10.7339i	−0.316014	+	0.948755i
$129$		0			0
$130$		0			0
$131$		−	7.07896i		−	0.618492i	−0.950982	−	0.309246i	$-0.899923\pi$
$131$		−	7.07896i		−	0.618492i	0.950982	−	0.309246i	$-0.100077\pi$
$132$		0			0
$133$		−	12.5855i		−	1.09130i
$134$	4.97858	+	2.68585i	0.430084	+	0.232022i
$135$		0			0
$136$	−8.39312	+	0.728692i	−0.719704	+	0.0624848i
$137$	−14.9786			−1.27971			−0.639853	−	0.768497i	$-0.721005\pi$
$137$	−14.9786			−1.27971			−0.639853	+	0.768497i	$0.721005\pi$
$138$		0			0
$139$			4.64300i			0.393814i	0.980422	+	0.196907i	$0.0630897\pi$
$139$			4.64300i			0.393814i	−0.980422	+	0.196907i	$0.936910\pi$
$140$		0			0
$141$		0			0
$142$	0.393115	−	0.728692i	0.0329895	−	0.0611505i
$143$	11.4145			0.954532
$144$		0			0
$145$		0			0
$146$	−4.02877	+	7.46787i	−0.333423	+	0.618045i
$147$		0			0
$148$	−7.34292	+	4.82487i	−0.603585	+	0.396601i
$149$		−	2.00000i		−	0.163846i	−0.996639	−	0.0819232i	$-0.973894\pi$
$149$		−	2.00000i		−	0.163846i	0.996639	−	0.0819232i	$-0.0261062\pi$
$150$		0			0
$151$	−8.35027			−0.679535			−0.339768	−	0.940509i	$-0.610348\pi$
$151$	−8.35027			−0.679535			−0.339768	+	0.940509i	$0.610348\pi$
$152$	0.657077	+	7.56825i	0.0532960	+	0.613866i
$153$		0			0
$154$	−13.3717	−	7.21377i	−1.07752	−	0.581302i
$155$		0			0
$156$		0			0
$157$			22.3503i			1.78375i	0.452286	+	0.891873i	$0.350609\pi$
$157$			22.3503i			1.78375i	−0.452286	+	0.891873i	$0.649391\pi$
$158$	−0.685846	+	1.27131i	−0.0545630	+	0.101140i
$159$		0			0
$160$		0			0
$161$	−12.5855			−0.991873
$162$		0			0
$163$			1.37169i			0.107439i	0.998556	+	0.0537196i	$0.0171077\pi$
$163$			1.37169i			0.107439i	−0.998556	+	0.0537196i	$0.982892\pi$
$164$	−12.4893	−	19.0073i	−0.975250	−	1.48422i
$165$		0			0
$166$	16.6430	+	8.97858i	1.29175	+	0.696873i
$167$	11.2713			0.872200			0.436100	−	0.899898i	$-0.356359\pi$
$167$	11.2713			0.872200			0.436100	+	0.899898i	$0.356359\pi$
$168$		0			0
$169$	−11.7862			−0.906633
$170$		0			0
$171$		0			0
$172$	−15.6644	+	10.2927i	−1.19440	+	0.784813i
$173$		−	10.7862i		−	0.820062i	−0.912072	−	0.410031i	$-0.865518\pi$
$173$		−	10.7862i		−	0.820062i	0.912072	−	0.410031i	$-0.134482\pi$
$174$		0			0
$175$		0			0
$176$	8.41767	+	3.63986i	0.634506	+	0.274365i
$177$		0			0
$178$	2.26396	−	4.19656i	0.169691	−	0.314545i
$179$		−	3.66442i		−	0.273892i	−0.990579	−	0.136946i	$-0.956271\pi$
$179$		−	3.66442i		−	0.273892i	0.990579	−	0.136946i	$-0.0437287\pi$
$180$		0			0
$181$		−	6.62831i		−	0.492678i	−0.969184	−	0.246339i	$-0.920772\pi$
$181$		−	6.62831i		−	0.492678i	0.969184	−	0.246339i	$-0.0792277\pi$
$182$	29.0361	+	15.6644i	2.15230	+	1.16112i
$183$		0			0
$184$	7.56825	−	0.657077i	0.557939	−	0.0484404i
$185$		0			0
$186$		0			0
$187$			6.82908i			0.499392i
$188$	−7.98592	−	12.1537i	−0.582433	−	0.886401i
$189$		0			0
$190$		0			0
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$		0			0
$193$	−1.21377			−0.0873690			−0.0436845	−	0.999045i	$-0.513910\pi$
$193$	−1.21377			−0.0873690			−0.0436845	+	0.999045i	$0.513910\pi$
$194$	−2.65708	+	4.92525i	−0.190767	+	0.353612i
$195$		0			0
$196$	−16.4271	−	25.0003i	−1.17337	−	1.78574i
$197$			23.9572i			1.70688i	0.521194	+	0.853438i	$0.325487\pi$
$197$			23.9572i			1.70688i	−0.521194	+	0.853438i	$0.674513\pi$
$198$		0			0
$199$	0.350269			0.0248299			0.0124150	−	0.999923i	$-0.496048\pi$
$199$	0.350269			0.0248299			0.0124150	+	0.999923i	$0.496048\pi$
$200$		0			0
$201$		0			0
$202$	−2.48929	−	1.34292i	−0.175146	−	0.0944877i
$203$			9.37169i			0.657764i
$204$		0			0
$205$		0			0
$206$	−9.83221	+	18.2253i	−0.685043	+	1.26982i
$207$		0			0
$208$	−18.2787	−	7.90383i	−1.26740	−	0.548032i
$209$	6.15792			0.425952
$210$		0			0
$211$			14.1004i			0.970710i	0.874317	+	0.485355i	$0.161310\pi$
$211$			14.1004i			0.970710i	−0.874317	+	0.485355i	$0.838690\pi$
$212$	−3.34292	+	2.19656i	−0.229593	+	0.150860i
$213$		0			0
$214$	14.1004	+	7.60688i	0.963882	+	0.519996i
$215$		0			0
$216$		0			0
$217$	32.7005			2.21986
$218$	11.6644	+	6.29273i	0.790014	+	0.426198i
$219$		0			0
$220$		0			0
$221$		−	14.8291i		−	0.997512i
$222$		0			0
$223$	6.72869			0.450587			0.225293	−	0.974291i	$-0.427666\pi$
$223$	6.72869			0.450587			0.225293	+	0.974291i	$0.427666\pi$
$224$	16.4177	+	20.8108i	1.09695	+	1.39048i
$225$		0			0
$226$	−13.2713	+	24.6002i	−0.882794	+	1.63638i
$227$			9.95715i			0.660880i	0.943827	+	0.330440i	$0.107197\pi$
$227$			9.95715i			0.660880i	−0.943827	+	0.330440i	$0.892803\pi$
$228$		0			0
$229$		−	11.3288i		−	0.748631i	−0.927301	−	0.374316i	$-0.877878\pi$
$229$		−	11.3288i		−	0.748631i	0.927301	−	0.374316i	$-0.122122\pi$
$230$		0			0
$231$		0			0
$232$	−0.489289	−	5.63565i	−0.0321234	−	0.369999i
$233$	−18.9786			−1.24333			−0.621664	−	0.783284i	$-0.713543\pi$
$233$	−18.9786			−1.24333			−0.621664	+	0.783284i	$0.713543\pi$
$234$		0			0
$235$		0			0
$236$	−2.85363	+	1.87506i	−0.185756	+	0.122056i
$237$		0			0
$238$	−9.37169	+	17.3717i	−0.607477	+	1.12604i
$239$	−2.62831			−0.170011			−0.0850055	−	0.996380i	$-0.527091\pi$
$239$	−2.62831			−0.170011			−0.0850055	+	0.996380i	$0.527091\pi$
$240$		0			0
$241$	10.7862			0.694802			0.347401	−	0.937717i	$-0.387064\pi$
$241$	10.7862			0.694802			0.347401	+	0.937717i	$0.387064\pi$
$242$	−3.85646	+	7.14847i	−0.247903	+	0.459521i
$243$		0			0
$244$	7.66442	−	5.03612i	0.490664	−	0.322404i
$245$		0			0
$246$		0			0
$247$	−13.3717			−0.850820
$248$	−19.6644	+	1.70727i	−1.24869	+	0.108412i
$249$		0			0
$250$		0			0
$251$		−	30.9933i		−	1.95628i	−0.207952	−	0.978139i	$-0.566680\pi$
$251$		−	30.9933i		−	1.95628i	0.207952	−	0.978139i	$-0.433320\pi$
$252$		0			0
$253$		−	6.15792i		−	0.387145i
$254$	4.46052	−	8.26817i	0.279878	−	0.518791i
$255$		0			0
$256$	−10.9593	−	11.6574i	−0.684954	−	0.728587i
$257$	20.9357			1.30594			0.652968	−	0.757386i	$-0.273524\pi$
$257$	20.9357			1.30594			0.652968	+	0.757386i	$0.273524\pi$
$258$		0			0
$259$			20.5855i			1.27912i
$260$		0			0
$261$		0			0
$262$	8.81079	+	4.75325i	0.544332	+	0.293657i
$263$	−19.2713			−1.18832			−0.594160	−	0.804347i	$-0.702515\pi$
$263$	−19.2713			−1.18832			−0.594160	+	0.804347i	$0.702515\pi$
$264$		0			0
$265$		0			0
$266$	15.6644	+	8.45065i	0.960447	+	0.518143i
$267$		0			0
$268$	−6.68585	+	4.39312i	−0.408403	+	0.268352i
$269$			24.7434i			1.50863i	0.656512	+	0.754315i	$0.272031\pi$
$269$			24.7434i			1.50863i	−0.656512	+	0.754315i	$0.727969\pi$
$270$		0			0
$271$	27.5640			1.67440			0.837198	−	0.546900i	$-0.184192\pi$
$271$	27.5640			1.67440			0.837198	+	0.546900i	$0.184192\pi$
$272$	4.72869	−	10.9357i	0.286719	−	0.663076i
$273$		0			0
$274$	10.0575	−	18.6430i	0.607598	−	1.12626i
$275$		0			0
$276$		0			0
$277$			20.3074i			1.22015i	0.792342	+	0.610077i	$0.208862\pi$
$277$			20.3074i			1.22015i	−0.792342	+	0.610077i	$0.791138\pi$
$278$	−5.77888	−	3.11760i	−0.346594	−	0.186981i
$279$		0			0
$280$		0			0
$281$	10.7862			0.643453			0.321726	−	0.946833i	$-0.395737\pi$
$281$	10.7862			0.643453			0.321726	+	0.946833i	$0.395737\pi$
$282$		0			0
$283$			20.0000i			1.18888i	0.804141	+	0.594438i	$0.202626\pi$
$283$			20.0000i			1.18888i	−0.804141	+	0.594438i	$0.797374\pi$
$284$	0.643000	+	0.978577i	0.0381551	+	0.0580679i
$285$		0			0
$286$	−7.66442	+	14.2070i	−0.453207	+	0.840080i
$287$	−53.2860			−3.14537
$288$		0			0
$289$	−8.12808			−0.478122
$290$		0			0
$291$		0			0
$292$	−6.58967	−	10.0288i	−0.385631	−	0.586889i
$293$		−	21.9143i		−	1.28025i	−0.768272	−	0.640124i	$-0.778883\pi$
$293$		−	21.9143i		−	1.28025i	0.768272	−	0.640124i	$-0.221117\pi$
$294$		0			0
$295$		0			0
$296$	−1.07475	−	12.3790i	−0.0624686	−	0.719517i
$297$		0			0
$298$	2.48929	+	1.34292i	0.144201	+	0.0777934i
$299$			13.3717i			0.773305i
$300$		0			0
$301$			43.9143i			2.53118i
$302$	5.60688	−	10.3931i	0.322640	−	0.598057i
$303$		0			0
$304$	−9.86098	−	4.26396i	−0.565566	−	0.244555i
$305$		0			0
$306$		0			0
$307$		−	26.5426i		−	1.51487i	−0.652912	−	0.757434i	$-0.726453\pi$
$307$		−	26.5426i		−	1.51487i	0.652912	−	0.757434i	$-0.273547\pi$
$308$	17.9572	−	11.7992i	1.02320	−	0.672324i
$309$		0			0
$310$		0			0
$311$	−12.2008			−0.691842			−0.345921	−	0.938264i	$-0.612434\pi$
$311$	−12.2008			−0.691842			−0.345921	+	0.938264i	$0.612434\pi$
$312$		0			0
$313$	−15.9572			−0.901952			−0.450976	−	0.892536i	$-0.648924\pi$
$313$	−15.9572			−0.901952			−0.450976	+	0.892536i	$0.648924\pi$
$314$	−27.8181	−	15.0073i	−1.56987	−	0.846914i
$315$		0			0
$316$	−1.12181	−	1.70727i	−0.0631066	−	0.0960414i
$317$		−	33.5296i		−	1.88321i	−0.336718	−	0.941605i	$-0.609317\pi$
$317$		−	33.5296i		−	1.88321i	0.336718	−	0.941605i	$-0.390683\pi$
$318$		0			0
$319$	−4.58546			−0.256737
$320$		0			0
$321$		0			0
$322$	8.45065	−	15.6644i	0.470937	−	0.872944i
$323$		−	8.00000i		−	0.445132i
$324$		0			0
$325$		0			0
$326$	−1.70727	−	0.921039i	−0.0945569	−	0.0510116i
$327$		0			0
$328$	32.0435	−	2.78202i	1.76930	−	0.153611i
$329$	−34.0722			−1.87846
$330$		0			0
$331$		−	19.8568i		−	1.09143i	−0.837972	−	0.545713i	$-0.816259\pi$
$331$		−	19.8568i		−	1.09143i	0.837972	−	0.545713i	$-0.183741\pi$
$332$	−22.3503	+	14.6858i	−1.22663	+	0.805991i
$333$		0			0
$334$	−7.56825	+	14.0288i	−0.414116	+	0.767620i
$335$		0			0
$336$		0			0
$337$	−7.17092			−0.390625			−0.195313	−	0.980741i	$-0.562572\pi$
$337$	−7.17092			−0.390625			−0.195313	+	0.980741i	$0.562572\pi$
$338$	7.91400	−	14.6697i	0.430465	−	0.797925i
$339$		0			0
$340$		0			0
$341$			16.0000i			0.866449i
$342$		0			0
$343$	−37.2860			−2.01325
$344$	−2.29273	−	26.4078i	−0.123616	−	1.42381i
$345$		0			0
$346$	13.4250	+	7.24254i	0.721734	+	0.389361i
$347$			0.786230i			0.0422071i	0.999777	+	0.0211035i	$0.00671796\pi$
$347$			0.786230i			0.0422071i	−0.999777	+	0.0211035i	$0.993282\pi$
$348$		0			0
$349$			6.15792i			0.329626i	0.986325	+	0.164813i	$0.0527021\pi$
$349$			6.15792i			0.329626i	−0.986325	+	0.164813i	$0.947298\pi$
$350$		0			0
$351$		0			0
$352$	−10.1825	+	8.03298i	−0.542728	+	0.428159i
$353$	21.7220			1.15614			0.578072	−	0.815986i	$-0.303805\pi$
$353$	21.7220			1.15614			0.578072	+	0.815986i	$0.303805\pi$
$354$		0			0
$355$		0			0
$356$	3.70306	+	5.63565i	0.196262	+	0.298689i
$357$		0			0
$358$	4.56090	+	2.46052i	0.241051	+	0.130042i
$359$	−0.585462			−0.0308995			−0.0154498	−	0.999881i	$-0.504918\pi$
$359$	−0.585462			−0.0308995			−0.0154498	+	0.999881i	$0.504918\pi$
$360$		0			0
$361$	11.7862			0.620328
$362$	8.24989	+	4.45065i	0.433604	+	0.233921i
$363$		0			0
$364$	−38.9933	+	25.6216i	−2.04380	+	1.34294i
$365$		0			0
$366$		0			0
$367$	0.485078			0.0253209			0.0126604	−	0.999920i	$-0.495970\pi$
$367$	0.485078			0.0253209			0.0126604	+	0.999920i	$0.495970\pi$
$368$	−4.26396	+	9.86098i	−0.222274	+	0.514039i
$369$		0			0
$370$		0			0
$371$			9.37169i			0.486554i
$372$		0			0
$373$			12.3931i			0.641691i	0.947132	+	0.320846i	$0.103967\pi$
$373$			12.3931i			0.641691i	−0.947132	+	0.320846i	$0.896033\pi$
$374$	−8.49977	−	4.58546i	−0.439513	−	0.237109i
$375$		0			0
$376$	20.4893	−	1.77888i	1.05665	−	0.0917389i
$377$	9.95715			0.512820
$378$		0			0
$379$		−	26.0147i		−	1.33629i	−0.744033	−	0.668143i	$-0.767090\pi$
$379$		−	26.0147i		−	1.33629i	0.744033	−	0.668143i	$-0.232910\pi$
$380$		0			0
$381$		0			0
$382$	−5.37169	+	9.95715i	−0.274840	+	0.509452i
$383$	6.68585			0.341631			0.170815	−	0.985303i	$-0.445360\pi$
$383$	6.68585			0.341631			0.170815	+	0.985303i	$0.445360\pi$
$384$		0			0
$385$		0			0
$386$	0.815000	−	1.51071i	0.0414824	−	0.0768932i
$387$		0			0
$388$	−4.34606	−	6.61423i	−0.220638	−	0.335787i
$389$		−	29.9143i		−	1.51672i	−0.651838	−	0.758358i	$-0.726002\pi$
$389$		−	29.9143i		−	1.51672i	0.651838	−	0.758358i	$-0.273998\pi$
$390$		0			0
$391$	−8.00000			−0.404577
$392$	42.1467	−	3.65918i	2.12873	−	0.184817i
$393$		0			0
$394$	−29.8181	−	16.0863i	−1.50222	−	0.810416i
$395$		0			0
$396$		0			0
$397$		−	9.76481i		−	0.490082i	−0.969513	−	0.245041i	$-0.921199\pi$
$397$		−	9.76481i		−	0.490082i	0.969513	−	0.245041i	$-0.0788014\pi$
$398$	−0.235192	+	0.435961i	−0.0117891	+	0.0218527i
$399$		0			0
$400$		0			0
$401$	6.58546			0.328862			0.164431	−	0.986389i	$-0.447421\pi$
$401$	6.58546			0.328862			0.164431	+	0.986389i	$0.447421\pi$
$402$		0			0
$403$		−	34.7434i		−	1.73069i
$404$	3.34292	−	2.19656i	0.166317	−	0.109283i
$405$		0			0
$406$	−11.6644	−	6.29273i	−0.578896	−	0.312303i
$407$	−10.0722			−0.499262
$408$		0			0
$409$	−25.9143			−1.28138			−0.640690	−	0.767800i	$-0.721352\pi$
$409$	−25.9143			−1.28138			−0.640690	+	0.767800i	$0.721352\pi$
$410$		0			0
$411$		0			0
$412$	−16.0821	−	24.4752i	−0.792308	−	1.20581i
$413$			8.00000i			0.393654i
$414$		0			0
$415$		0			0
$416$	22.1109	−	17.4433i	1.08407	−	0.855229i
$417$		0			0
$418$	−4.13481	+	7.66442i	−0.202240	+	0.374879i
$419$			12.2499i			0.598446i	0.954183	+	0.299223i	$0.0967275\pi$
$419$			12.2499i			0.598446i	−0.954183	+	0.299223i	$0.903273\pi$
$420$		0			0
$421$		−	4.67115i		−	0.227658i	−0.993500	−	0.113829i	$-0.963688\pi$
$421$		−	4.67115i		−	0.227658i	0.993500	−	0.113829i	$-0.0363116\pi$
$422$	−17.5500	−	9.46787i	−0.854319	−	0.460888i
$423$		0			0
$424$	−0.489289	−	5.63565i	−0.0237620	−	0.273692i
$425$		0			0
$426$		0			0
$427$		−	21.4868i		−	1.03982i
$428$	−18.9357	+	12.4422i	−0.915293	+	0.601418i
$429$		0			0
$430$		0			0
$431$	−0.585462			−0.0282007			−0.0141004	−	0.999901i	$-0.504488\pi$
$431$	−0.585462			−0.0282007			−0.0141004	+	0.999901i	$0.504488\pi$
$432$		0			0
$433$	21.9143			1.05313			0.526567	−	0.850133i	$-0.323479\pi$
$433$	21.9143			1.05313			0.526567	+	0.850133i	$0.323479\pi$
$434$	−21.9572	+	40.7005i	−1.05398	+	1.95369i
$435$		0			0
$436$	−15.6644	+	10.2927i	−0.750190	+	0.492932i
$437$			7.21377i			0.345081i
$438$		0			0
$439$	−2.39312			−0.114217			−0.0571086	−	0.998368i	$-0.518188\pi$
$439$	−2.39312			−0.114217			−0.0571086	+	0.998368i	$0.518188\pi$
$440$		0			0
$441$		0			0
$442$	18.4569	+	9.95715i	0.877906	+	0.473614i
$443$		−	20.7005i		−	0.983512i	−0.870733	−	0.491756i	$-0.836355\pi$
$443$		−	20.7005i		−	0.983512i	0.870733	−	0.491756i	$-0.163645\pi$
$444$		0			0
$445$		0			0
$446$	−4.51806	+	8.37483i	−0.213936	+	0.396560i
$447$		0			0
$448$	−36.9259	+	6.46052i	−1.74458	+	0.305231i
$449$	37.9143			1.78929			0.894643	−	0.446781i	$-0.147430\pi$
$449$	37.9143			1.78929			0.894643	+	0.446781i	$0.147430\pi$
$450$		0			0
$451$		−	26.0722i		−	1.22769i
$452$	−21.7073	−	33.0361i	−1.02102	−	1.55389i
$453$		0			0
$454$	−12.3931	−	6.68585i	−0.581638	−	0.313782i
$455$		0			0
$456$		0			0
$457$	−38.7005			−1.81033			−0.905167	−	0.425055i	$-0.860255\pi$
$457$	−38.7005			−1.81033			−0.905167	+	0.425055i	$0.860255\pi$
$458$	14.1004	+	7.60688i	0.658868	+	0.355446i
$459$		0			0
$460$		0			0
$461$			4.74338i			0.220921i	0.993880	+	0.110461i	$0.0352326\pi$
$461$			4.74338i			0.220921i	−0.993880	+	0.110461i	$0.964767\pi$
$462$		0			0
$463$	−15.3142			−0.711709			−0.355855	−	0.934541i	$-0.615810\pi$
$463$	−15.3142			−0.711709			−0.355855	+	0.934541i	$0.615810\pi$
$464$	7.34292	+	3.17513i	0.340887	+	0.147402i
$465$		0			0
$466$	12.7434	−	23.6216i	0.590326	−	1.09425i
$467$		−	30.5426i		−	1.41334i	−0.707541	−	0.706672i	$-0.750196\pi$
$467$		−	30.5426i		−	1.41334i	0.707541	−	0.706672i	$-0.249804\pi$
$468$		0			0
$469$			18.7434i			0.865489i
$470$		0			0
$471$		0			0
$472$	−0.417674	−	4.81079i	−0.0192250	−	0.221435i
$473$	−21.4868			−0.987963
$474$		0			0
$475$		0			0
$476$	−15.3288	−	23.3288i	−0.702597	−	1.06928i
$477$		0			0
$478$	1.76481	−	3.27131i	0.0807204	−	0.149626i
$479$	−3.32885			−0.152099			−0.0760494	−	0.997104i	$-0.524231\pi$
$479$	−3.32885			−0.152099			−0.0760494	+	0.997104i	$0.524231\pi$
$480$		0			0
$481$	21.8715			0.997253
$482$	−7.24254	+	13.4250i	−0.329889	+	0.611493i
$483$		0			0
$484$	−6.30784	−	9.59985i	−0.286720	−	0.436357i
$485$		0			0
$486$		0			0
$487$	12.1004			0.548321			0.274160	−	0.961684i	$-0.411600\pi$
$487$	12.1004			0.548321			0.274160	+	0.961684i	$0.411600\pi$
$488$	1.12181	+	12.9210i	0.0507818	+	0.584908i
$489$		0			0
$490$		0			0
$491$		−	14.2927i		−	0.645022i	−0.946566	−	0.322511i	$-0.895473\pi$
$491$		−	14.2927i		−	0.645022i	0.946566	−	0.322511i	$-0.104527\pi$
$492$		0			0
$493$			5.95715i			0.268297i
$494$	8.97858	−	16.6430i	0.403965	−	0.748804i
$495$		0			0
$496$	11.0790	−	25.6216i	0.497460	−	1.15044i
$497$	2.74338			0.123058
$498$		0			0
$499$		−	9.22846i		−	0.413123i	−0.978434	−	0.206561i	$-0.933773\pi$
$499$		−	9.22846i		−	0.413123i	0.978434	−	0.206561i	$-0.0662273\pi$
$500$		0			0
$501$		0			0
$502$	38.5756	+	20.8108i	1.72171	+	0.928831i
$503$	−14.1004			−0.628705			−0.314353	−	0.949306i	$-0.601787\pi$
$503$	−14.1004			−0.628705			−0.314353	+	0.949306i	$0.601787\pi$
$504$		0			0
$505$		0			0
$506$	7.66442	+	4.13481i	0.340725	+	0.183815i
$507$		0			0
$508$	7.29587	+	11.1035i	0.323702	+	0.492639i
$509$		−	43.4011i		−	1.92372i	−0.273544	−	0.961859i	$-0.588196\pi$
$509$		−	43.4011i		−	1.92372i	0.273544	−	0.961859i	$-0.411804\pi$
$510$		0			0
$511$	−28.1151			−1.24374
$512$	21.8680	−	5.81289i	0.966439	−	0.256896i
$513$		0			0
$514$	−14.0575	+	26.0575i	−0.620051	+	1.14935i
$515$		0			0
$516$		0			0
$517$		−	16.6712i		−	0.733196i
$518$	−25.6216	−	13.8223i	−1.12575	−	0.607319i
$519$		0			0
$520$		0			0
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$		0			0
$523$			13.5725i			0.593482i	0.954958	+	0.296741i	$0.0958998\pi$
$523$			13.5725i			0.593482i	−0.954958	+	0.296741i	$0.904100\pi$
$524$	−11.8322	+	7.77467i	−0.516893	+	0.339638i
$525$		0			0
$526$	12.9399	−	23.9859i	0.564208	−	1.04584i
$527$	20.7862			0.905462
$528$		0			0
$529$	−15.7862			−0.686358
$530$		0			0
$531$		0			0
$532$	−21.0361	+	13.8223i	−0.912031	+	0.599275i
$533$			56.6148i			2.45226i
$534$		0			0
$535$		0			0
$536$	−0.978577	−	11.2713i	−0.0422681	−	0.486846i
$537$		0			0
$538$	−30.7967	−	16.6142i	−1.32774	−	0.716290i
$539$		−	34.2927i		−	1.47709i
$540$		0			0
$541$			37.2860i			1.60305i	0.597961	+	0.801525i	$0.295978\pi$
$541$			37.2860i			1.60305i	−0.597961	+	0.801525i	$0.704022\pi$
$542$	−18.5082	+	34.3074i	−0.794995	+	1.47363i
$543$		0			0
$544$	10.4360	+	13.2285i	0.447438	+	0.567166i
$545$		0			0
$546$		0			0
$547$		−	0.200768i		−	0.00858424i	−0.999991	−	0.00429212i	$-0.998634\pi$
$547$		−	0.200768i		−	0.00858424i	0.999991	−	0.00429212i	$-0.00136623\pi$
$548$	16.4507	+	25.0361i	0.702737	+	1.06949i
$549$		0			0
$550$		0			0
$551$	5.37169			0.228842
$552$		0			0
$553$	−4.78623			−0.203531
$554$	−25.2755	−	13.6357i	−1.07385	−	0.579323i
$555$		0			0
$556$	7.76060	−	5.09931i	0.329123	−	0.216259i
$557$		−	9.21377i		−	0.390400i	−0.980763	−	0.195200i	$-0.937464\pi$
$557$		−	9.21377i		−	0.390400i	0.980763	−	0.195200i	$-0.0625356\pi$
$558$		0			0
$559$	46.6577			1.97341
$560$		0			0
$561$		0			0
$562$	−7.24254	+	13.4250i	−0.305508	+	0.566300i
$563$			36.7005i			1.54674i	0.633953	+	0.773372i	$0.281431\pi$
$563$			36.7005i			1.54674i	−0.633953	+	0.773372i	$0.718569\pi$
$564$		0			0
$565$		0			0
$566$	−24.8929	−	13.4292i	−1.04633	−	0.564473i
$567$		0			0
$568$	−1.64973	+	0.143230i	−0.0692212	+	0.00600979i
$569$	−13.4145			−0.562367			−0.281183	−	0.959654i	$-0.590727\pi$
$569$	−13.4145			−0.562367			−0.281183	+	0.959654i	$0.590727\pi$
$570$		0			0
$571$		−	18.6858i		−	0.781978i	−0.920395	−	0.390989i	$-0.872133\pi$
$571$		−	18.6858i		−	0.781978i	0.920395	−	0.390989i	$-0.127867\pi$
$572$	−12.5363	−	19.0790i	−0.524171	−	0.797731i
$573$		0			0
$574$	35.7795	−	66.3221i	1.49341	−	2.76823i
$575$		0			0
$576$		0			0
$577$	2.78623			0.115992			0.0579961	−	0.998317i	$-0.481529\pi$
$577$	2.78623			0.115992			0.0579961	+	0.998317i	$0.481529\pi$
$578$	5.45769	−	10.1166i	0.227010	−	0.420794i
$579$		0			0
$580$		0			0
$581$			62.6577i			2.59948i
$582$		0			0
$583$	−4.58546			−0.189910
$584$	16.9070	−	1.46787i	0.699615	−	0.0607407i
$585$		0			0
$586$	27.2755	+	14.7146i	1.12674	+	0.607855i
$587$			27.3288i			1.12798i	0.825781	+	0.563991i	$0.190735\pi$
$587$			27.3288i			1.12798i	−0.825781	+	0.563991i	$0.809265\pi$
$588$		0			0
$589$		−	18.7434i		−	0.772308i
$590$		0			0
$591$		0			0
$592$	16.1292	+	6.97437i	0.662904	+	0.286645i
$593$	−6.97858			−0.286576			−0.143288	−	0.989681i	$-0.545767\pi$
$593$	−6.97858			−0.286576			−0.143288	+	0.989681i	$0.545767\pi$
$594$		0			0
$595$		0			0
$596$	−3.34292	+	2.19656i	−0.136931	+	0.0899745i
$597$		0			0
$598$	−16.6430	−	8.97858i	−0.680583	−	0.367161i
$599$	−36.4998			−1.49134			−0.745670	−	0.666315i	$-0.767870\pi$
$599$	−36.4998			−1.49134			−0.745670	+	0.666315i	$0.767870\pi$
$600$		0			0
$601$	−15.5725			−0.635214			−0.317607	−	0.948222i	$-0.602879\pi$
$601$	−15.5725			−0.635214			−0.317607	+	0.948222i	$0.602879\pi$
$602$	−54.6577	−	29.4868i	−2.22768	−	1.20179i
$603$		0			0
$604$	9.17092	+	13.9572i	0.373160	+	0.567909i
$605$		0			0
$606$		0			0
$607$	31.2285			1.26752			0.633762	−	0.773528i	$-0.281510\pi$
$607$	31.2285			1.26752			0.633762	+	0.773528i	$0.281510\pi$
$608$	11.9284	−	9.41033i	0.483760	−	0.381639i
$609$		0			0
$610$		0			0
$611$			36.2008i			1.46453i
$612$		0			0
$613$		−	0.978577i		−	0.0395244i	−0.999805	−	0.0197622i	$-0.993709\pi$
$613$		−	0.978577i		−	0.0395244i	0.999805	−	0.0197622i	$-0.00629091\pi$
$614$	33.0361	+	17.8223i	1.33323	+	0.719251i
$615$		0			0
$616$	2.62831	+	30.2730i	0.105898	+	1.21973i
$617$	32.9357			1.32594			0.662971	−	0.748645i	$-0.269295\pi$
$617$	32.9357			1.32594			0.662971	+	0.748645i	$0.269295\pi$
$618$		0			0
$619$		−	3.35700i		−	0.134929i	−0.997722	−	0.0674646i	$-0.978509\pi$
$619$		−	3.35700i		−	0.134929i	0.997722	−	0.0674646i	$-0.0214910\pi$
$620$		0			0
$621$		0			0
$622$	8.19235	−	15.1856i	0.328483	−	0.608888i
$623$	15.7992			0.632983
$624$		0			0
$625$		0			0
$626$	10.7146	−	19.8610i	0.428242	−	0.793804i
$627$		0			0
$628$	37.3576	−	24.5468i	1.49073	−	0.979525i
$629$			13.0852i			0.521742i
$630$		0			0
$631$	−27.7648			−1.10530			−0.552650	−	0.833414i	$-0.686383\pi$
$631$	−27.7648			−1.10530			−0.552650	+	0.833414i	$0.686383\pi$
$632$	2.87819	−	0.249885i	0.114488	−	0.00993990i
$633$		0			0
$634$	41.7324	+	22.5138i	1.65741	+	0.894139i
$635$		0			0
$636$		0			0
$637$			74.4653i			2.95042i
$638$	3.07896	−	5.70727i	0.121897	−	0.225953i
$639$		0			0
$640$		0			0
$641$	21.1281			0.834509			0.417254	−	0.908790i	$-0.362992\pi$
$641$	21.1281			0.834509			0.417254	+	0.908790i	$0.362992\pi$
$642$		0			0
$643$		−	29.2860i		−	1.15493i	−0.816416	−	0.577464i	$-0.804043\pi$
$643$		−	29.2860i		−	1.15493i	0.816416	−	0.577464i	$-0.195957\pi$
$644$	13.8223	+	21.0361i	0.544677	+	0.828939i
$645$		0			0
$646$	9.95715	+	5.37169i	0.391759	+	0.211346i
$647$	15.6728			0.616163			0.308082	−	0.951360i	$-0.400313\pi$
$647$	15.6728			0.616163			0.308082	+	0.951360i	$0.400313\pi$
$648$		0			0
$649$	−3.91431			−0.153650
$650$		0			0
$651$		0			0
$652$	2.29273	−	1.50650i	0.0897903	−	0.0589991i
$653$			17.5296i			0.685987i	0.939338	+	0.342993i	$0.111441\pi$
$653$			17.5296i			0.685987i	−0.939338	+	0.342993i	$0.888559\pi$
$654$		0			0
$655$		0			0
$656$	−18.0533	+	41.7507i	−0.704864	+	1.63009i
$657$		0			0
$658$	22.8782	−	42.4078i	0.891885	−	1.65323i
$659$			23.8652i			0.929656i	0.885401	+	0.464828i	$0.153884\pi$
$659$			23.8652i			0.929656i	−0.885401	+	0.464828i	$0.846116\pi$
$660$		0			0
$661$		−	30.1579i		−	1.17301i	−0.809947	−	0.586504i	$-0.800504\pi$
$661$		−	30.1579i		−	1.17301i	0.809947	−	0.586504i	$-0.199496\pi$
$662$	24.7146	+	13.3331i	0.960561	+	0.518204i
$663$		0			0
$664$	−3.27131	−	37.6791i	−0.126951	−	1.46223i
$665$		0			0
$666$		0			0
$667$		−	5.37169i		−	0.207993i
$668$	−12.3790	−	18.8396i	−0.478959	−	0.728924i
$669$		0			0
$670$		0			0
$671$	10.5132			0.405859
$672$		0			0
$673$	18.0000			0.693849			0.346925	−	0.937893i	$-0.387226\pi$
$673$	18.0000			0.693849			0.346925	+	0.937893i	$0.387226\pi$
$674$	4.81500	−	8.92525i	0.185467	−	0.343788i
$675$		0			0
$676$	12.9446	+	19.7002i	0.497868	+	0.757701i
$677$			9.61531i			0.369546i	0.982781	+	0.184773i	$0.0591550\pi$
$677$			9.61531i			0.369546i	−0.982781	+	0.184773i	$0.940845\pi$
$678$		0			0
$679$	−18.5426			−0.711600
$680$		0			0
$681$		0			0
$682$	−19.9143	−	10.7434i	−0.762558	−	0.411385i
$683$			18.6283i			0.712792i	0.934335	+	0.356396i	$0.115995\pi$
$683$			18.6283i			0.712792i	−0.934335	+	0.356396i	$0.884005\pi$
$684$		0			0
$685$		0			0
$686$	25.0361	−	46.4078i	0.955883	−	1.77186i
$687$		0			0
$688$	34.4078	+	14.8782i	1.31179	+	0.567226i
$689$	9.95715			0.379337
$690$		0			0
$691$		−	13.4292i		−	0.510872i	−0.966826	−	0.255436i	$-0.917781\pi$
$691$		−	13.4292i		−	0.510872i	0.966826	−	0.255436i	$-0.0822190\pi$
$692$	−18.0288	+	11.8463i	−0.685351	+	0.450328i
$693$		0			0
$694$	−0.978577	−	0.527923i	−0.0371463	−	0.0200397i
$695$		0			0
$696$		0			0
$697$	−33.8715			−1.28297
$698$	−7.66442	−	4.13481i	−0.290103	−	0.156505i
$699$		0			0
$700$		0			0
$701$		−	19.1709i		−	0.724076i	−0.932163	−	0.362038i	$-0.882081\pi$
$701$		−	19.1709i		−	0.724076i	0.932163	−	0.362038i	$-0.117919\pi$
$702$		0			0
$703$	11.7992			0.445016
$704$	−3.16106	−	18.0674i	−0.119137	−	0.680941i
$705$		0			0
$706$	−14.5855	+	27.0361i	−0.548931	+	1.01752i
$707$		−	9.37169i		−	0.352459i
$708$		0			0
$709$			15.4145i			0.578905i	0.957192	+	0.289453i	$0.0934732\pi$
$709$			15.4145i			0.578905i	−0.957192	+	0.289453i	$0.906527\pi$
$710$		0			0
$711$		0			0
$712$	−9.50085	+	0.824865i	−0.356059	+	0.0309131i
$713$	−18.7434			−0.701945
$714$		0			0
$715$		0			0
$716$	−6.12494	+	4.02456i	−0.228900	+	0.150405i
$717$		0			0
$718$	0.393115	−	0.728692i	0.0146709	−	0.0271945i
$719$	−20.7862			−0.775196			−0.387598	−	0.921829i	$-0.626695\pi$
$719$	−20.7862			−0.775196			−0.387598	+	0.921829i	$0.626695\pi$
$720$		0			0
$721$	−68.6148			−2.55535
$722$	−7.91400	+	14.6697i	−0.294529	+	0.545948i
$723$		0			0
$724$	−11.0790	+	7.27973i	−0.411746	+	0.270549i
$725$		0			0
$726$		0			0
$727$	−12.3012			−0.456224			−0.228112	−	0.973635i	$-0.573255\pi$
$727$	−12.3012			−0.456224			−0.228112	+	0.973635i	$0.573255\pi$
$728$	−5.70727	−	65.7367i	−0.211525	−	2.43636i
$729$		0			0
$730$		0			0
$731$			27.9143i			1.03245i
$732$		0			0
$733$			35.9227i			1.32684i	0.748249	+	0.663418i	$0.230895\pi$
$733$			35.9227i			1.32684i	−0.748249	+	0.663418i	$0.769105\pi$
$734$	−0.325711	+	0.603749i	−0.0120222	+	0.0222848i
$735$		0			0
$736$	−9.41033	−	11.9284i	−0.346869	−	0.439686i
$737$	−9.17092			−0.337815
$738$		0			0
$739$			29.0277i			1.06780i	0.845547	+	0.533900i	$0.179274\pi$
$739$			29.0277i			1.06780i	−0.845547	+	0.533900i	$0.820726\pi$
$740$		0			0
$741$		0			0
$742$	−11.6644	−	6.29273i	−0.428214	−	0.231013i
$743$	2.60015			0.0953904			0.0476952	−	0.998862i	$-0.484812\pi$
$743$	2.60015			0.0953904			0.0476952	+	0.998862i	$0.484812\pi$
$744$		0			0
$745$		0			0
$746$	−15.4250	−	8.32150i	−0.564750	−	0.304672i
$747$		0			0
$748$	11.4145	−	7.50023i	0.417357	−	0.274236i
$749$			53.0852i			1.93969i
$750$		0			0
$751$	−10.8929			−0.397487			−0.198744	−	0.980052i	$-0.563686\pi$
$751$	−10.8929			−0.397487			−0.198744	+	0.980052i	$0.563686\pi$
$752$	−11.5437	+	26.6963i	−0.420955	+	0.973515i
$753$		0			0
$754$	−6.68585	+	12.3931i	−0.243484	+	0.451331i
$755$		0			0
$756$		0			0
$757$		−	34.3503i		−	1.24848i	−0.781232	−	0.624241i	$-0.785408\pi$
$757$		−	34.3503i		−	1.24848i	0.781232	−	0.624241i	$-0.214592\pi$
$758$	32.3790	+	17.4679i	1.17606	+	0.634461i
$759$		0			0
$760$		0			0
$761$	19.0852			0.691839			0.345920	−	0.938264i	$-0.387567\pi$
$761$	19.0852			0.691839			0.345920	+	0.938264i	$0.387567\pi$
$762$		0			0
$763$			43.9143i			1.58980i
$764$	−8.78623	−	13.3717i	−0.317875	−	0.483771i
$765$		0			0
$766$	−4.48929	+	8.32150i	−0.162205	+	0.300668i
$767$	8.49977			0.306909
$768$		0			0
$769$	31.8715			1.14931			0.574657	−	0.818394i	$-0.305135\pi$
$769$	31.8715			1.14931			0.574657	+	0.818394i	$0.305135\pi$
$770$		0			0
$771$		0			0
$772$	1.33306	+	2.02877i	0.0479778	+	0.0730170i
$773$		−	11.9572i		−	0.430069i	−0.976606	−	0.215034i	$-0.931014\pi$
$773$		−	11.9572i		−	0.430069i	0.976606	−	0.215034i	$-0.0689864\pi$
$774$		0			0
$775$		0			0
$776$	11.1506	−	0.968095i	0.400282	−	0.0347526i
$777$		0			0
$778$	37.2327	+	20.0863i	1.33486	+	0.720129i
$779$			30.5426i			1.09430i
$780$		0			0
$781$			1.34231i			0.0480315i
$782$	5.37169	−	9.95715i	0.192091	−	0.356067i
$783$		0			0
$784$	−23.7455	+	54.9146i	−0.848053	+	1.96124i
$785$		0			0
$786$		0			0
$787$		−	33.0852i		−	1.17936i	−0.807637	−	0.589681i	$-0.799254\pi$
$787$		−	33.0852i		−	1.17936i	0.807637	−	0.589681i	$-0.200746\pi$
$788$	40.0435	−	26.3116i	1.42649	−	0.937313i
$789$		0			0
$790$		0			0
$791$	−92.6148			−3.29300
$792$		0			0
$793$	−22.8291			−0.810684
$794$	12.1537	+	6.55669i	0.431319	+	0.232688i
$795$		0			0
$796$	−0.384694	−	0.585462i	−0.0136351	−	0.0207511i
$797$		−	10.0000i		−	0.354218i	−0.984191	−	0.177109i	$-0.943325\pi$
$797$		−	10.0000i		−	0.354218i	0.984191	−	0.177109i	$-0.0566745\pi$
$798$		0			0
$799$	−21.6582			−0.766210
$800$		0			0
$801$		0			0
$802$	−4.42188	+	8.19656i	−0.156142	+	0.289431i
$803$		−	13.7564i		−	0.485452i
$804$		0			0
$805$		0			0
$806$	43.2432	+	23.3288i	1.52318	+	0.821724i
$807$		0			0
$808$	0.489289	+	5.63565i	0.0172131	+	0.198262i
$809$	30.6148			1.07636			0.538180	−	0.842830i	$-0.319112\pi$
$809$	30.6148			1.07636			0.538180	+	0.842830i	$0.319112\pi$
$810$		0			0
$811$			53.9290i			1.89370i	0.321670	+	0.946852i	$0.395756\pi$
$811$			53.9290i			1.89370i	−0.321670	+	0.946852i	$0.604244\pi$
$812$	15.6644	−	10.2927i	0.549713	−	0.361204i
$813$		0			0
$814$	6.76312	−	12.5363i	0.237047	−	0.439399i
$815$		0			0
$816$		0			0
$817$	25.1709			0.880619
$818$	17.4005	−	32.2541i	0.608393	−	1.12774i
$819$		0			0
$820$		0			0
$821$		−	12.6577i		−	0.441757i	−0.975301	−	0.220878i	$-0.929108\pi$
$821$		−	12.6577i		−	0.441757i	0.975301	−	0.220878i	$-0.0708924\pi$
$822$		0			0
$823$	19.8139			0.690670			0.345335	−	0.938479i	$-0.387765\pi$
$823$	19.8139			0.690670			0.345335	+	0.938479i	$0.387765\pi$
$824$	41.2614	−	3.58233i	1.43741	−	0.124796i
$825$		0			0
$826$	−9.95715	−	5.37169i	−0.346454	−	0.186905i
$827$			20.0000i			0.695468i	0.937593	+	0.347734i	$0.113049\pi$
$827$			20.0000i			0.695468i	−0.937593	+	0.347734i	$0.886951\pi$
$828$		0			0
$829$		−	41.3717i		−	1.43690i	−0.695580	−	0.718449i	$-0.744852\pi$
$829$		−	41.3717i		−	1.43690i	0.695580	−	0.718449i	$-0.255148\pi$
$830$		0			0
$831$		0			0
$832$	6.86412	+	39.2327i	0.237970	+	1.36015i
$833$	−44.5510			−1.54360
$834$		0			0
$835$		0			0
$836$	−6.76312	−	10.2927i	−0.233907	−	0.355982i
$837$		0			0
$838$	−15.2467	−	8.22533i	−0.526690	−	0.284139i
$839$	−20.9013			−0.721593			−0.360797	−	0.932645i	$-0.617495\pi$
$839$	−20.9013			−0.721593			−0.360797	+	0.932645i	$0.617495\pi$
$840$		0			0
$841$	25.0000			0.862069
$842$	5.81392	+	3.13650i	0.200361	+	0.108091i
$843$		0			0
$844$	23.5682	−	15.4862i	0.811253	−	0.533055i
$845$		0			0
$846$		0			0
$847$	−26.9126			−0.924728
$848$	7.34292	+	3.17513i	0.252157	+	0.109035i
$849$		0			0
$850$		0			0
$851$		−	11.7992i		−	0.404472i
$852$		0			0
$853$		−	6.63673i		−	0.227237i	−0.993524	−	0.113619i	$-0.963756\pi$
$853$		−	6.63673i		−	0.227237i	0.993524	−	0.113619i	$-0.0362442\pi$
$854$	26.7434	+	14.4275i	0.915140	+	0.493700i
$855$		0			0
$856$	−2.77154	−	31.9227i	−0.0947292	−	1.09110i
$857$	9.80765			0.335023			0.167512	−	0.985870i	$-0.446427\pi$
$857$	9.80765			0.335023			0.167512	+	0.985870i	$0.446427\pi$
$858$		0			0
$859$			39.3864i			1.34385i	0.740621	+	0.671923i	$0.234531\pi$
$859$			39.3864i			1.34385i	−0.740621	+	0.671923i	$0.765469\pi$
$860$		0			0
$861$		0			0
$862$	0.393115	−	0.728692i	0.0133896	−	0.0248193i
$863$	7.07054			0.240684			0.120342	−	0.992732i	$-0.461601\pi$
$863$	7.07054			0.240684			0.120342	+	0.992732i	$0.461601\pi$
$864$		0			0
$865$		0			0
$866$	−14.7146	+	27.2755i	−0.500023	+	0.926860i
$867$		0			0
$868$	−35.9143	−	54.6577i	−1.21901	−	1.85520i
$869$		−	2.34185i		−	0.0794417i
$870$		0			0
$871$	19.9143			0.674771
$872$	−2.29273	−	26.4078i	−0.0776417	−	0.894281i
$873$		0			0
$874$	−8.97858	−	4.84377i	−0.303705	−	0.163843i
$875$		0			0
$876$		0			0
$877$		−	23.1365i		−	0.781264i	−0.920547	−	0.390632i	$-0.872256\pi$
$877$		−	23.1365i		−	0.781264i	0.920547	−	0.390632i	$-0.127744\pi$
$878$	1.60688	−	2.97858i	0.0542297	−	0.100522i
$879$		0			0
$880$		0			0
$881$	−28.4569			−0.958738			−0.479369	−	0.877613i	$-0.659134\pi$
$881$	−28.4569			−0.958738			−0.479369	+	0.877613i	$0.659134\pi$
$882$		0			0
$883$			41.2003i			1.38650i	0.720697	+	0.693250i	$0.243822\pi$
$883$			41.2003i			1.38650i	−0.720697	+	0.693250i	$0.756178\pi$
$884$	−24.7862	+	16.2865i	−0.833651	+	0.547773i
$885$		0			0
$886$	25.7648	+	13.8996i	0.865586	+	0.466967i
$887$	−3.55777			−0.119458			−0.0597291	−	0.998215i	$-0.519024\pi$
$887$	−3.55777			−0.119458			−0.0597291	+	0.998215i	$0.519024\pi$
$888$		0			0
$889$	31.1281			1.04400
$890$		0			0
$891$		0			0
$892$	−7.38998	−	11.2467i	−0.247435	−	0.376569i
$893$			19.5296i			0.653534i
$894$		0			0
$895$		0			0
$896$	16.7533	−	50.2976i	0.559687	−	1.68032i
$897$		0			0
$898$	−25.4580	+	47.1898i	−0.849544	+	1.57474i
$899$			13.9572i			0.465497i
$900$		0			0
$901$			5.95715i			0.198462i
$902$	32.4507	+	17.5065i	1.08049	+	0.582903i
$903$		0			0
$904$	55.6938	−	4.83535i	1.85235	−	0.160821i
$905$		0			0
$906$		0			0
$907$			50.6577i			1.68206i	0.540988	+	0.841031i	$0.318051\pi$
$907$			50.6577i			1.68206i	−0.540988	+	0.841031i	$0.681949\pi$
$908$	16.6430	−	10.9357i	0.552317	−	0.362915i
$909$		0			0
$910$		0			0
$911$	26.4569			0.876557			0.438279	−	0.898839i	$-0.355588\pi$
$911$	26.4569			0.876557			0.438279	+	0.898839i	$0.355588\pi$
$912$		0			0
$913$	−30.6577			−1.01462
$914$	25.9859	−	48.1684i	0.859538	−	1.59327i
$915$		0			0
$916$	−18.9357	+	12.4422i	−0.625654	+	0.411103i
$917$			33.1709i			1.09540i
$918$		0			0
$919$	29.8077			0.983264			0.491632	−	0.870803i	$-0.336401\pi$
$919$	29.8077			0.983264			0.491632	+	0.870803i	$0.336401\pi$
$920$		0			0
$921$		0			0
$922$	−5.90383	−	3.18500i	−0.194432	−	0.104892i
$923$		−	2.91477i		−	0.0959407i
$924$		0			0
$925$		0			0
$926$	10.2829	−	19.0607i	0.337916	−	0.626373i
$927$		0			0
$928$	−8.88240	+	7.00735i	−0.291579	+	0.230027i
$929$	8.82908			0.289673			0.144836	−	0.989456i	$-0.453734\pi$
$929$	8.82908			0.289673			0.144836	+	0.989456i	$0.453734\pi$
$930$		0			0
$931$			40.1726i			1.31660i
$932$	20.8438	+	31.7220i	0.682760	+	1.03909i
$933$		0			0
$934$	38.0147	+	20.5082i	1.24388	+	0.671049i
$935$		0			0
$936$		0			0
$937$	42.2302			1.37960			0.689799	−	0.724000i	$-0.257699\pi$
$937$	42.2302			1.37960			0.689799	+	0.724000i	$0.257699\pi$
$938$	−23.3288	−	12.5855i	−0.761714	−	0.410930i
$939$		0			0
$940$		0			0
$941$		−	32.7434i		−	1.06740i	−0.845673	−	0.533702i	$-0.820800\pi$
$941$		−	32.7434i		−	1.06740i	0.845673	−	0.533702i	$-0.179200\pi$
$942$		0			0
$943$	30.5426			0.994604
$944$	6.26817	+	2.71040i	0.204012	+	0.0882162i
$945$		0			0
$946$	14.4275	−	26.7434i	0.469080	−	0.869502i
$947$		−	15.9143i		−	0.517146i	−0.965992	−	0.258573i	$-0.916748\pi$
$947$		−	15.9143i		−	0.517146i	0.965992	−	0.258573i	$-0.0832522\pi$
$948$		0			0
$949$			29.8715i			0.969669i
$950$		0			0
$951$		0			0
$952$	39.3288	−	3.41454i	1.27466	−	0.110666i
$953$	55.6791			1.80362			0.901812	−	0.432129i	$-0.142238\pi$
$953$	55.6791			1.80362			0.901812	+	0.432129i	$0.142238\pi$
$954$		0			0
$955$		0			0
$956$	2.88661	+	4.39312i	0.0933598	+	0.142083i
$957$		0			0
$958$	2.23519	−	4.14323i	0.0722158	−	0.133862i
$959$	70.1873			2.26647
$960$		0			0
$961$	17.7005			0.570985
$962$	−14.6858	+	27.2222i	−0.473491	+	0.877679i
$963$		0			0
$964$	−11.8463	−	18.0288i	−0.381543	−	0.580668i
$965$		0			0
$966$		0			0
$967$	54.7581			1.76090			0.880451	−	0.474138i	$-0.157240\pi$
$967$	54.7581			1.76090			0.880451	+	0.474138i	$0.157240\pi$
$968$	16.1839	−	1.40509i	0.520169	−	0.0451612i
$969$		0			0
$970$		0			0
$971$			30.3221i			0.973083i	0.873657	+	0.486542i	$0.161742\pi$
$971$			30.3221i			0.973083i	−0.873657	+	0.486542i	$0.838258\pi$
$972$		0			0
$973$		−	21.7564i		−	0.697478i
$974$	−8.12494	+	15.0607i	−0.260340	+	0.482575i
$975$		0			0
$976$	−16.8353	−	7.27973i	−0.538886	−	0.233018i
$977$	−29.7220			−0.950890			−0.475445	−	0.879746i	$-0.657713\pi$
$977$	−29.7220			−0.950890			−0.475445	+	0.879746i	$0.657713\pi$
$978$		0			0
$979$			7.73038i			0.247064i
$980$		0			0
$981$		0			0
$982$	17.7894	+	9.59702i	0.567681	+	0.306253i
$983$	−49.5443			−1.58022			−0.790109	−	0.612966i	$-0.789976\pi$
$983$	−49.5443			−1.58022			−0.790109	+	0.612966i	$0.789976\pi$
$984$		0			0
$985$		0			0
$986$	−7.41454	−	4.00000i	−0.236127	−	0.127386i
$987$		0			0
$988$	14.6858	+	22.3503i	0.467219	+	0.711057i
$989$		−	25.1709i		−	0.800389i
$990$		0			0
$991$	19.0937			0.606530			0.303265	−	0.952906i	$-0.401923\pi$
$991$	19.0937			0.606530			0.303265	+	0.952906i	$0.401923\pi$
$992$	24.4507	+	30.9933i	0.776309	+	0.984037i
$993$		0			0
$994$	−1.84208	+	3.41454i	−0.0584271	+	0.108303i
$995$		0			0
$996$		0			0
$997$		−	38.8500i		−	1.23039i	−0.788374	−	0.615197i	$-0.789077\pi$
$997$		−	38.8500i		−	1.23039i	0.788374	−	0.615197i	$-0.210923\pi$
$998$	11.4862	+	6.19656i	0.363588	+	0.196149i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.k.p.901.2		6
3.2	odd	2		600.2.k.c.301.5		6
4.3	odd	2		7200.2.k.p.3601.6		6
5.2	odd	4		1800.2.d.r.1549.1		6
5.3	odd	4		1800.2.d.q.1549.6		6
5.4	even	2		360.2.k.f.181.5		6
8.3	odd	2		7200.2.k.p.3601.5		6
8.5	even	2	inner	1800.2.k.p.901.1		6
12.11	even	2		2400.2.k.c.1201.3		6
15.2	even	4		600.2.d.f.349.6		6
15.8	even	4		600.2.d.e.349.1		6
15.14	odd	2		120.2.k.b.61.2	yes	6
20.3	even	4		7200.2.d.q.2449.1		6
20.7	even	4		7200.2.d.r.2449.6		6
20.19	odd	2		1440.2.k.f.721.4		6
24.5	odd	2		600.2.k.c.301.6		6
24.11	even	2		2400.2.k.c.1201.6		6
40.3	even	4		7200.2.d.r.2449.1		6
40.13	odd	4		1800.2.d.r.1549.2		6
40.19	odd	2		1440.2.k.f.721.1		6
40.27	even	4		7200.2.d.q.2449.6		6
40.29	even	2		360.2.k.f.181.6		6
40.37	odd	4		1800.2.d.q.1549.5		6
60.23	odd	4		2400.2.d.f.49.1		6
60.47	odd	4		2400.2.d.e.49.6		6
60.59	even	2		480.2.k.b.241.4		6
120.29	odd	2		120.2.k.b.61.1	✓	6
120.53	even	4		600.2.d.f.349.5		6
120.59	even	2		480.2.k.b.241.1		6
120.77	even	4		600.2.d.e.349.2		6
120.83	odd	4		2400.2.d.e.49.1		6
120.107	odd	4		2400.2.d.f.49.6		6
240.29	odd	4		3840.2.a.bq.1.1		3
240.59	even	4		3840.2.a.br.1.3		3
240.149	odd	4		3840.2.a.bp.1.1		3
240.179	even	4		3840.2.a.bo.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.k.b.61.1	✓	6	120.29	odd	2
120.2.k.b.61.2	yes	6	15.14	odd	2
360.2.k.f.181.5		6	5.4	even	2
360.2.k.f.181.6		6	40.29	even	2
480.2.k.b.241.1		6	120.59	even	2
480.2.k.b.241.4		6	60.59	even	2
600.2.d.e.349.1		6	15.8	even	4
600.2.d.e.349.2		6	120.77	even	4
600.2.d.f.349.5		6	120.53	even	4
600.2.d.f.349.6		6	15.2	even	4
600.2.k.c.301.5		6	3.2	odd	2
600.2.k.c.301.6		6	24.5	odd	2
1440.2.k.f.721.1		6	40.19	odd	2
1440.2.k.f.721.4		6	20.19	odd	2
1800.2.d.q.1549.5		6	40.37	odd	4
1800.2.d.q.1549.6		6	5.3	odd	4
1800.2.d.r.1549.1		6	5.2	odd	4
1800.2.d.r.1549.2		6	40.13	odd	4
1800.2.k.p.901.1		6	8.5	even	2	inner
1800.2.k.p.901.2		6	1.1	even	1	trivial
2400.2.d.e.49.1		6	120.83	odd	4
2400.2.d.e.49.6		6	60.47	odd	4
2400.2.d.f.49.1		6	60.23	odd	4
2400.2.d.f.49.6		6	120.107	odd	4
2400.2.k.c.1201.3		6	12.11	even	2
2400.2.k.c.1201.6		6	24.11	even	2
3840.2.a.bo.1.3		3	240.179	even	4
3840.2.a.bp.1.1		3	240.149	odd	4
3840.2.a.bq.1.1		3	240.29	odd	4
3840.2.a.br.1.3		3	240.59	even	4
7200.2.d.q.2449.1		6	20.3	even	4
7200.2.d.q.2449.6		6	40.27	even	4
7200.2.d.r.2449.1		6	40.3	even	4
7200.2.d.r.2449.6		6	20.7	even	4
7200.2.k.p.3601.5		6	8.3	odd	2
7200.2.k.p.3601.6		6	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1800.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.671462 + 1.24464i) q^{2} +(-1.09828 - 1.67146i) q^{4} -4.68585 q^{7} +(2.81783 - 0.244644i) q^{8} +O(q^{10})\)	\(q+(-0.671462 + 1.24464i) q^{2} +(-1.09828 - 1.67146i) q^{4} -4.68585 q^{7} +(2.81783 - 0.244644i) q^{8} -2.29273i q^{11} +4.97858i q^{13} +(3.14637 - 5.83221i) q^{14} +(-1.58757 + 3.67146i) q^{16} -2.97858 q^{17} +2.68585i q^{19} +(2.85363 + 1.53948i) q^{22} +2.68585 q^{23} +(-6.19656 - 3.34292i) q^{26} +(5.14637 + 7.83221i) q^{28} -2.00000i q^{29} -6.97858 q^{31} +(-3.50367 - 4.44120i) q^{32} +(2.00000 - 3.70727i) q^{34} -4.39312i q^{37} +(-3.34292 - 1.80344i) q^{38} +11.3717 q^{41} -9.37169i q^{43} +(-3.83221 + 2.51806i) q^{44} +(-1.80344 + 3.34292i) q^{46} +7.27131 q^{47} +14.9572 q^{49} +(8.32150 - 5.46787i) q^{52} -2.00000i q^{53} +(-13.2039 + 1.14637i) q^{56} +(2.48929 + 1.34292i) q^{58} -1.70727i q^{59} +4.58546i q^{61} +(4.68585 - 8.68585i) q^{62} +(7.88030 - 1.37873i) q^{64} -4.00000i q^{67} +(3.27131 + 4.97858i) q^{68} -0.585462 q^{71} +6.00000 q^{73} +(5.46787 + 2.94981i) q^{74} +(4.48929 - 2.94981i) q^{76} +10.7434i q^{77} +1.02142 q^{79} +(-7.63565 + 14.1537i) q^{82} -13.3717i q^{83} +(11.6644 + 6.29273i) q^{86} +(-0.560904 - 6.46052i) q^{88} -3.37169 q^{89} -23.3288i q^{91} +(-2.94981 - 4.48929i) q^{92} +(-4.88240 + 9.05019i) q^{94} +3.95715 q^{97} +(-10.0432 + 18.6163i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 2 q^{4} - 4 q^{7} + 8 q^{8}+O(q^{10}) \) 6 * q + 2 * q^2 - 2 * q^4 - 4 * q^7 + 8 * q^8	\( 6 q + 2 q^{2} - 2 q^{4} - 4 q^{7} + 8 q^{8} + 16 q^{14} + 10 q^{16} + 12 q^{17} + 20 q^{22} - 8 q^{23} - 28 q^{26} + 28 q^{28} - 12 q^{31} + 12 q^{32} + 12 q^{34} - 8 q^{38} + 20 q^{41} + 4 q^{44} - 20 q^{46} + 8 q^{47} + 30 q^{49} + 8 q^{52} - 4 q^{56} + 4 q^{62} + 22 q^{64} - 16 q^{68} + 8 q^{71} + 36 q^{73} - 12 q^{74} + 12 q^{76} + 36 q^{79} - 28 q^{82} + 16 q^{86} - 12 q^{88} + 28 q^{89} - 24 q^{92} + 4 q^{94} - 36 q^{97} - 6 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 - 2 * q^4 - 4 * q^7 + 8 * q^8 + 16 * q^14 + 10 * q^16 + 12 * q^17 + 20 * q^22 - 8 * q^23 - 28 * q^26 + 28 * q^28 - 12 * q^31 + 12 * q^32 + 12 * q^34 - 8 * q^38 + 20 * q^41 + 4 * q^44 - 20 * q^46 + 8 * q^47 + 30 * q^49 + 8 * q^52 - 4 * q^56 + 4 * q^62 + 22 * q^64 - 16 * q^68 + 8 * q^71 + 36 * q^73 - 12 * q^74 + 12 * q^76 + 36 * q^79 - 28 * q^82 + 16 * q^86 - 12 * q^88 + 28 * q^89 - 24 * q^92 + 4 * q^94 - 36 * q^97 - 6 * q^98

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