LMFDB - Embedded newform 1800.2.d.s.1549.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1800,2,Mod(1549,1800)]

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, 1]))

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

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

chi := DirichletCharacter("1800.1549");

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.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.3730723638$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.214798336.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 2x^{5} + 9x^{4} - 4x^{3} - 16x + 16 $ x^8 - 2x^7 - 2x^5 + 9x^4 - 4x^3 - 16*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 600)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1549.2
Root			$-1.08003 + 0.912978i$ of defining polynomial
Character	$\chi$	$=$	1800.1549
Dual form			1800.2.d.s.1549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41298 + 0.0591148i) q^{2} +(1.99301 - 0.167056i) q^{4} -1.33411i q^{7} +(-2.80620 + 0.353863i) q^{8} +O(q^{10})$	\(q+(-1.41298 + 0.0591148i) q^{2} +(1.99301 - 0.167056i) q^{4} -1.33411i q^{7} +(-2.80620 + 0.353863i) q^{8} +2.94418i q^{11} -2.04184 q^{13} +(0.0788658 + 1.88507i) q^{14} +(3.94418 - 0.665888i) q^{16} +3.61241i q^{17} +5.35964i q^{19} +(-0.174045 - 4.16007i) q^{22} -8.59609i q^{23} +(2.88507 - 0.120703i) q^{26} +(-0.222871 - 2.65890i) q^{28} -5.26432i q^{29} -2.08134 q^{31} +(-5.53368 + 1.17404i) q^{32} +(-0.213547 - 5.10425i) q^{34} -6.55659 q^{37} +(-0.316834 - 7.57304i) q^{38} -7.02786 q^{41} -8.50078 q^{43} +(0.491843 + 5.86779i) q^{44} +(0.508157 + 12.1461i) q^{46} +9.97204i q^{47} +5.22015 q^{49} +(-4.06940 + 0.341101i) q^{52} +6.12318 q^{53} +(0.472092 + 3.74379i) q^{56} +(0.311199 + 7.43836i) q^{58} -4.75190i q^{59} +8.51476i q^{61} +(2.94089 - 0.123038i) q^{62} +(7.74956 - 1.98602i) q^{64} -10.6961 q^{67} +(0.603474 + 7.19957i) q^{68} +2.62405 q^{71} -15.3875i q^{73} +(9.26432 - 0.387592i) q^{74} +(0.895358 + 10.6818i) q^{76} +3.92787 q^{77} -10.4450 q^{79} +(9.93021 - 0.415451i) q^{82} -1.52708 q^{83} +(12.0114 - 0.502522i) q^{86} +(-1.04184 - 8.26198i) q^{88} -12.7193 q^{89} +2.72404i q^{91} +(-1.43603 - 17.1321i) q^{92} +(-0.589496 - 14.0903i) q^{94} +13.4450i q^{97} +(-7.37595 + 0.308588i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 4 q^{4} - 8 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 - 4 * q^4 - 8 * q^8	$ 8 q - 2 q^{2} - 4 q^{4} - 8 q^{8} - 6 q^{14} + 8 q^{16} - 20 q^{22} + 2 q^{26} - 24 q^{28} + 8 q^{31} - 12 q^{32} - 12 q^{34} + 14 q^{38} + 8 q^{43} - 12 q^{44} + 20 q^{46} - 24 q^{52} + 8 q^{53} - 8 q^{56} + 20 q^{58} + 26 q^{62} + 32 q^{64} - 24 q^{67} + 36 q^{68} + 40 q^{71} + 8 q^{74} - 20 q^{76} - 24 q^{77} + 16 q^{79} + 16 q^{82} - 32 q^{83} + 18 q^{86} + 8 q^{88} + 28 q^{92} + 4 q^{94} - 40 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 4 * q^4 - 8 * q^8 - 6 * q^14 + 8 * q^16 - 20 * q^22 + 2 * q^26 - 24 * q^28 + 8 * q^31 - 12 * q^32 - 12 * q^34 + 14 * q^38 + 8 * q^43 - 12 * q^44 + 20 * q^46 - 24 * q^52 + 8 * q^53 - 8 * q^56 + 20 * q^58 + 26 * q^62 + 32 * q^64 - 24 * q^67 + 36 * q^68 + 40 * q^71 + 8 * q^74 - 20 * q^76 - 24 * q^77 + 16 * q^79 + 16 * q^82 - 32 * q^83 + 18 * q^86 + 8 * q^88 + 28 * q^92 + 4 * q^94 - 40 * 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 $

$2$	−1.41298	+	0.0591148i	−0.999126	+	0.0418005i
$2$	−1.41298	+	0.0591148i	−0.999126	+	0.0418005i
$3$		0			0
$3$		0			0
$4$	1.99301	−	0.167056i	0.996505	−	0.0835279i
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	1.33411i		−	0.504247i	−0.967695	−	0.252123i	$-0.918871\pi$
$7$		−	1.33411i		−	0.504247i	0.967695	−	0.252123i	$-0.0811289\pi$
$8$	−2.80620	+	0.353863i	−0.992143	+	0.125109i
$9$		0			0
$10$		0			0
$11$			2.94418i			0.887705i	0.896100	+	0.443853i	$0.146389\pi$
$11$			2.94418i			0.887705i	−0.896100	+	0.443853i	$0.853611\pi$
$12$		0			0
$13$	−2.04184			−0.566304			−0.283152	−	0.959075i	$-0.591380\pi$
$13$	−2.04184			−0.566304			−0.283152	+	0.959075i	$0.591380\pi$
$14$	0.0788658	+	1.88507i	0.0210778	+	0.503806i
$15$		0			0
$16$	3.94418	−	0.665888i	0.986046	−	0.166472i
$17$			3.61241i			0.876138i	0.898941	+	0.438069i	$0.144337\pi$
$17$			3.61241i			0.876138i	−0.898941	+	0.438069i	$0.855663\pi$
$18$		0			0
$19$			5.35964i			1.22958i	0.788689	+	0.614792i	$0.210760\pi$
$19$			5.35964i			1.22958i	−0.788689	+	0.614792i	$0.789240\pi$
$20$		0			0
$21$		0			0
$22$	−0.174045	−	4.16007i	−0.0371065	−	0.886929i
$23$		−	8.59609i		−	1.79241i	−0.443641	−	0.896205i	$-0.646313\pi$
$23$		−	8.59609i		−	1.79241i	0.443641	−	0.896205i	$-0.353687\pi$
$24$		0			0
$25$		0			0
$26$	2.88507	−	0.120703i	0.565809	−	0.0236718i
$27$		0			0
$28$	−0.222871	−	2.65890i	−0.0421187	−	0.502485i
$29$		−	5.26432i		−	0.977559i	−0.872407	−	0.488780i	$-0.837442\pi$
$29$		−	5.26432i		−	0.977559i	0.872407	−	0.488780i	$-0.162558\pi$
$30$		0			0
$31$	−2.08134			−0.373820			−0.186910	−	0.982377i	$-0.559847\pi$
$31$	−2.08134			−0.373820			−0.186910	+	0.982377i	$0.559847\pi$
$32$	−5.53368	+	1.17404i	−0.978226	+	0.207544i
$33$		0			0
$34$	−0.213547	−	5.10425i	−0.0366230	−	0.875372i
$35$		0			0
$36$		0			0
$37$	−6.55659			−1.07790			−0.538949	−	0.842339i	$-0.681178\pi$
$37$	−6.55659			−1.07790			−0.538949	+	0.842339i	$0.681178\pi$
$38$	−0.316834	−	7.57304i	−0.0513973	−	1.22851i
$39$		0			0
$40$		0			0
$41$	−7.02786			−1.09757			−0.548784	−	0.835964i	$-0.684909\pi$
$41$	−7.02786			−1.09757			−0.548784	+	0.835964i	$0.684909\pi$
$42$		0			0
$43$	−8.50078			−1.29636			−0.648178	−	0.761489i	$-0.724469\pi$
$43$	−8.50078			−1.29636			−0.648178	+	0.761489i	$0.724469\pi$
$44$	0.491843	+	5.86779i	0.0741482	+	0.884603i
$45$		0			0
$46$	0.508157	+	12.1461i	0.0749236	+	1.79084i
$47$			9.97204i			1.45457i	0.686334	+	0.727286i	$0.259219\pi$
$47$			9.97204i			1.45457i	−0.686334	+	0.727286i	$0.740781\pi$
$48$		0			0
$49$	5.22015			0.745735
$50$		0			0
$51$		0			0
$52$	−4.06940	+	0.341101i	−0.564325	+	0.0473022i
$53$	6.12318			0.841083			0.420541	−	0.907273i	$-0.361840\pi$
$53$	6.12318			0.841083			0.420541	+	0.907273i	$0.361840\pi$
$54$		0			0
$55$		0			0
$56$	0.472092	+	3.74379i	0.0630860	+	0.500285i
$57$		0			0
$58$	0.311199	+	7.43836i	0.0408625	+	0.976705i
$59$		−	4.75190i		−	0.618644i	−0.950957	−	0.309322i	$-0.899898\pi$
$59$		−	4.75190i		−	0.618644i	0.950957	−	0.309322i	$-0.100102\pi$
$60$		0			0
$61$			8.51476i			1.09020i	0.838370	+	0.545101i	$0.183509\pi$
$61$			8.51476i			1.09020i	−0.838370	+	0.545101i	$0.816491\pi$
$62$	2.94089	−	0.123038i	0.373493	−	0.0156258i
$63$		0			0
$64$	7.74956	−	1.98602i	0.968695	−	0.248253i
$65$		0			0
$66$		0			0
$67$	−10.6961			−1.30673			−0.653367	−	0.757041i	$-0.726644\pi$
$67$	−10.6961			−1.30673			−0.653367	+	0.757041i	$0.726644\pi$
$68$	0.603474	+	7.19957i	0.0731820	+	0.873076i
$69$		0			0
$70$		0			0
$71$	2.62405			0.311418			0.155709	−	0.987803i	$-0.450234\pi$
$71$	2.62405			0.311418			0.155709	+	0.987803i	$0.450234\pi$
$72$		0			0
$73$		−	15.3875i		−	1.80097i	−0.434887	−	0.900485i	$-0.643212\pi$
$73$		−	15.3875i		−	1.80097i	0.434887	−	0.900485i	$-0.356788\pi$
$74$	9.26432	−	0.387592i	1.07696	−	0.0450566i
$75$		0			0
$76$	0.895358	+	10.6818i	0.102705	+	1.22529i
$77$	3.92787			0.447622
$78$		0			0
$79$	−10.4450			−1.17515			−0.587575	−	0.809170i	$-0.699917\pi$
$79$	−10.4450			−1.17515			−0.587575	+	0.809170i	$0.699917\pi$
$80$		0			0
$81$		0			0
$82$	9.93021	−	0.415451i	1.09661	−	0.0458789i
$83$	−1.52708			−0.167619			−0.0838095	−	0.996482i	$-0.526709\pi$
$83$	−1.52708			−0.167619			−0.0838095	+	0.996482i	$0.526709\pi$
$84$		0			0
$85$		0			0
$86$	12.0114	−	0.502522i	1.29522	−	0.0541883i
$87$		0			0
$88$	−1.04184	−	8.26198i	−0.111060	−	0.880730i
$89$	−12.7193			−1.34824			−0.674120	−	0.738622i	$-0.735477\pi$
$89$	−12.7193			−1.34824			−0.674120	+	0.738622i	$0.735477\pi$
$90$		0			0
$91$			2.72404i			0.285557i
$92$	−1.43603	−	17.1321i	−0.149716	−	1.78615i
$93$		0			0
$94$	−0.589496	−	14.0903i	−0.0608018	−	1.45330i
$95$		0			0
$96$		0			0
$97$			13.4450i			1.36513i	0.730825	+	0.682565i	$0.239135\pi$
$97$			13.4450i			1.36513i	−0.730825	+	0.682565i	$0.760865\pi$
$98$	−7.37595	+	0.308588i	−0.745083	+	0.0311721i
$99$		0			0
$100$		0			0
$101$			10.1232i			1.00729i	0.863910	+	0.503647i	$0.168009\pi$
$101$			10.1232i			1.00729i	−0.863910	+	0.503647i	$0.831991\pi$
$102$		0			0
$103$			10.7472i			1.05896i	0.848324	+	0.529478i	$0.177612\pi$
$103$			10.7472i			1.05896i	−0.848324	+	0.529478i	$0.822388\pi$
$104$	5.72981	−	0.722530i	0.561854	−	0.0708499i
$105$		0			0
$106$	−8.65191	+	0.361971i	−0.840348	+	0.0351577i
$107$	−4.86518			−0.470335			−0.235167	−	0.971955i	$-0.575564\pi$
$107$	−4.86518			−0.470335			−0.235167	+	0.971955i	$0.575564\pi$
$108$		0			0
$109$		−	15.4573i		−	1.48054i	−0.672310	−	0.740270i	$-0.734698\pi$
$109$		−	15.4573i		−	1.48054i	0.672310	−	0.740270i	$-0.265302\pi$
$110$		0			0
$111$		0			0
$112$	−0.888369	−	5.26198i	−0.0839430	−	0.497211i
$113$			9.88837i			0.930220i	0.885253	+	0.465110i	$0.153985\pi$
$113$			9.88837i			0.930220i	−0.885253	+	0.465110i	$0.846015\pi$
$114$		0			0
$115$		0			0
$116$	−0.879435	−	10.4918i	−0.0816535	−	0.974143i
$117$		0			0
$118$	0.280908	+	6.71432i	0.0258596	+	0.618104i
$119$	4.81936			0.441790
$120$		0			0
$121$	2.33178			0.211980
$122$	−0.503348	−	12.0312i	−0.0455710	−	1.08925i
$123$		0			0
$124$	−4.14813	+	0.347700i	−0.372513	+	0.0312244i
$125$		0			0
$126$		0			0
$127$			8.75190i			0.776605i	0.921532	+	0.388303i	$0.126938\pi$
$127$			8.75190i			0.776605i	−0.921532	+	0.388303i	$0.873062\pi$
$128$	−10.8326	+	3.26432i	−0.957472	+	0.288528i
$129$		0			0
$130$		0			0
$131$		−	0.471266i		−	0.0411747i	−0.999788	−	0.0205874i	$-0.993446\pi$
$131$		−	0.471266i		−	0.0411747i	0.999788	−	0.0205874i	$-0.00655362\pi$
$132$		0			0
$133$	7.15035			0.620014
$134$	15.1133	−	0.632297i	1.30559	−	0.0546222i
$135$		0			0
$136$	−1.27830	−	10.1372i	−0.109613	−	0.869254i
$137$			1.30382i			0.111393i	0.998448	+	0.0556964i	$0.0177379\pi$
$137$			1.30382i			0.111393i	−0.998448	+	0.0556964i	$0.982262\pi$
$138$		0			0
$139$			8.74723i			0.741930i	0.928647	+	0.370965i	$0.120973\pi$
$139$			8.74723i			0.741930i	−0.928647	+	0.370965i	$0.879027\pi$
$140$		0			0
$141$		0			0
$142$	−3.70773	+	0.155120i	−0.311145	+	0.0130174i
$143$		−	6.01155i		−	0.502711i
$144$		0			0
$145$		0			0
$146$	0.909629	+	21.7422i	0.0752814	+	1.79940i
$147$		0			0
$148$	−13.0674	+	1.09532i	−1.07413	+	0.0900345i
$149$		−	15.1411i		−	1.24041i	−0.784439	−	0.620205i	$-0.787049\pi$
$149$		−	15.1411i		−	1.24041i	0.784439	−	0.620205i	$-0.212951\pi$
$150$		0			0
$151$	−23.2782			−1.89435			−0.947176	−	0.320713i	$-0.896078\pi$
$151$	−23.2782			−1.89435			−0.947176	+	0.320713i	$0.896078\pi$
$152$	−1.89657	−	15.0402i	−0.153833	−	1.21992i
$153$		0			0
$154$	−5.54999	+	0.232195i	−0.447231	+	0.0187108i
$155$		0			0
$156$		0			0
$157$	21.8976			1.74762			0.873809	−	0.486270i	$-0.161643\pi$
$157$	21.8976			1.74762			0.873809	+	0.486270i	$0.161643\pi$
$158$	14.7585	−	0.617452i	1.17412	−	0.0491219i
$159$		0			0
$160$		0			0
$161$	−11.4682			−0.903817
$162$		0			0
$163$	−11.1643			−0.874458			−0.437229	−	0.899350i	$-0.644040\pi$
$163$	−11.1643			−0.874458			−0.437229	+	0.899350i	$0.644040\pi$
$164$	−14.0066	+	1.17404i	−1.09373	+	0.0916775i
$165$		0			0
$166$	2.15773	−	0.0902732i	0.167472	−	0.00700656i
$167$			10.0952i			0.781192i	0.920562	+	0.390596i	$0.127731\pi$
$167$			10.0952i			0.781192i	−0.920562	+	0.390596i	$0.872269\pi$
$168$		0			0
$169$	−8.83090			−0.679300
$170$		0			0
$171$		0			0
$172$	−16.9421	+	1.42010i	−1.29183	+	0.108282i
$173$	−13.8162			−1.05043			−0.525215	−	0.850970i	$-0.676015\pi$
$173$	−13.8162			−1.05043			−0.525215	+	0.850970i	$0.676015\pi$
$174$		0			0
$175$		0			0
$176$	1.96050	+	11.6124i	0.147778	+	0.875318i
$177$		0			0
$178$	17.9720	−	0.751898i	1.34706	−	0.0563571i
$179$			21.9441i			1.64018i	0.572236	+	0.820089i	$0.306076\pi$
$179$			21.9441i			1.64018i	−0.572236	+	0.820089i	$0.693924\pi$
$180$		0			0
$181$			1.93021i			0.143471i	0.997424	+	0.0717356i	$0.0228538\pi$
$181$			1.93021i			0.143471i	−0.997424	+	0.0717356i	$0.977146\pi$
$182$	−0.161031	−	3.84901i	−0.0119364	−	0.285307i
$183$		0			0
$184$	3.04184	+	24.1224i	0.224247	+	1.77833i
$185$		0			0
$186$		0			0
$187$	−10.6356			−0.777752
$188$	1.66589	+	19.8744i	0.121497	+	1.44949i
$189$		0			0
$190$		0			0
$191$	−12.1232			−0.877202			−0.438601	−	0.898682i	$-0.644526\pi$
$191$	−12.1232			−0.877202			−0.438601	+	0.898682i	$0.644526\pi$
$192$		0			0
$193$		−	1.27431i		−	0.0917267i	−0.998948	−	0.0458634i	$-0.985396\pi$
$193$		−	1.27431i		−	0.0917267i	0.998948	−	0.0458634i	$-0.0146039\pi$
$194$	−0.794797	−	18.9974i	−0.0570631	−	1.36394i
$195$		0			0
$196$	10.4038	−	0.872056i	0.743129	−	0.0622897i
$197$	−3.30849			−0.235720			−0.117860	−	0.993030i	$-0.537603\pi$
$197$	−3.30849			−0.235720			−0.117860	+	0.993030i	$0.537603\pi$
$198$		0			0
$199$	−9.02718			−0.639920			−0.319960	−	0.947431i	$-0.603669\pi$
$199$	−9.02718			−0.639920			−0.319960	+	0.947431i	$0.603669\pi$
$200$		0			0
$201$		0			0
$202$	−0.598430	−	14.3038i	−0.0421054	−	1.00641i
$203$	−7.02319			−0.492931
$204$		0			0
$205$		0			0
$206$	−0.635321	−	15.1856i	−0.0442649	−	1.05803i
$207$		0			0
$208$	−8.05338	+	1.35964i	−0.558402	+	0.0942738i
$209$	−15.7798			−1.09151
$210$		0			0
$211$		−	6.61241i		−	0.455217i	−0.973753	−	0.227608i	$-0.926909\pi$
$211$		−	6.61241i		−	0.455217i	0.973753	−	0.227608i	$-0.0730906\pi$
$212$	12.2036	−	1.02291i	0.838144	−	0.0702539i
$213$		0			0
$214$	6.87439	−	0.287604i	0.469924	−	0.0196602i
$215$		0			0
$216$		0			0
$217$			2.77674i			0.188497i
$218$	0.913755	+	21.8408i	0.0618873	+	1.47925i
$219$		0			0
$220$		0			0
$221$		−	7.37595i		−	0.496160i
$222$		0			0
$223$			0.833237i			0.0557976i	0.999611	+	0.0278988i	$0.00888162\pi$
$223$			0.833237i			0.0557976i	−0.999611	+	0.0278988i	$0.991118\pi$
$224$	1.56631	+	7.38255i	0.104653	+	0.493267i
$225$		0			0
$226$	−0.584549	−	13.9720i	−0.0388836	−	0.929407i
$227$	−10.9999			−0.730089			−0.365045	−	0.930990i	$-0.618946\pi$
$227$	−10.9999			−0.730089			−0.365045	+	0.930990i	$0.618946\pi$
$228$		0			0
$229$		−	15.2061i		−	1.00485i	−0.864622	−	0.502423i	$-0.832442\pi$
$229$		−	15.2061i		−	1.00485i	0.864622	−	0.502423i	$-0.167558\pi$
$230$		0			0
$231$		0			0
$232$	1.86285	+	14.7728i	0.122302	+	0.969879i
$233$		−	2.47594i		−	0.162204i	−0.996706	−	0.0811020i	$-0.974156\pi$
$233$		−	2.47594i		−	0.162204i	0.996706	−	0.0811020i	$-0.0258439\pi$
$234$		0			0
$235$		0			0
$236$	−0.793832	−	9.47058i	−0.0516741	−	0.616482i
$237$		0			0
$238$	−6.80964	+	0.284895i	−0.441404	+	0.0184670i
$239$	−21.0737			−1.36314			−0.681572	−	0.731751i	$-0.738703\pi$
$239$	−21.0737			−1.36314			−0.681572	+	0.731751i	$0.738703\pi$
$240$		0			0
$241$	−6.10852			−0.393484			−0.196742	−	0.980455i	$-0.563036\pi$
$241$	−6.10852			−0.393484			−0.196742	+	0.980455i	$0.563036\pi$
$242$	−3.29475	+	0.137843i	−0.211794	+	0.00886086i
$243$		0			0
$244$	1.42244	+	16.9700i	0.0910624	+	1.08639i
$245$		0			0
$246$		0			0
$247$		−	10.9435i		−	0.696318i
$248$	5.84066	−	0.736508i	0.370882	−	0.0467683i
$249$		0			0
$250$		0			0
$251$		−	22.5286i		−	1.42199i	−0.703195	−	0.710997i	$-0.748244\pi$
$251$		−	22.5286i		−	1.42199i	0.703195	−	0.710997i	$-0.251756\pi$
$252$		0			0
$253$	25.3085			1.59113
$254$	−0.517367	−	12.3662i	−0.0324625	−	0.775927i
$255$		0			0
$256$	15.1132	−	5.25277i	0.944574	−	0.328298i
$257$			14.5286i			0.906271i	0.891442	+	0.453136i	$0.149695\pi$
$257$			14.5286i			0.906271i	−0.891442	+	0.453136i	$0.850305\pi$
$258$		0			0
$259$			8.74723i			0.543526i
$260$		0			0
$261$		0			0
$262$	0.0278588	+	0.665888i	0.00172112	+	0.0411387i
$263$		−	5.29694i		−	0.326624i	−0.986575	−	0.163312i	$-0.947782\pi$
$263$		−	5.29694i		−	0.326624i	0.986575	−	0.163312i	$-0.0522177\pi$
$264$		0			0
$265$		0			0
$266$	−10.1033	+	0.422692i	−0.619472	+	0.0259169i
$267$		0			0
$268$	−21.3174	+	1.78684i	−1.30217	+	0.109149i
$269$			27.0737i			1.65071i	0.564613	+	0.825356i	$0.309025\pi$
$269$			27.0737i			1.65071i	−0.564613	+	0.825356i	$0.690975\pi$
$270$		0			0
$271$	15.8604			0.963451			0.481726	−	0.876322i	$-0.340010\pi$
$271$	15.8604			0.963451			0.481726	+	0.876322i	$0.340010\pi$
$272$	2.40546	+	14.2480i	0.145852	+	0.863912i
$273$		0			0
$274$	−0.0770751	−	1.84227i	−0.00465628	−	0.111296i
$275$		0			0
$276$		0			0
$277$	9.98592			0.599996			0.299998	−	0.953940i	$-0.403014\pi$
$277$	9.98592			0.599996			0.299998	+	0.953940i	$0.403014\pi$
$278$	−0.517091	−	12.3596i	−0.0310130	−	0.741282i
$279$		0			0
$280$		0			0
$281$	−13.4218			−0.800676			−0.400338	−	0.916368i	$-0.631107\pi$
$281$	−13.4218			−0.800676			−0.400338	+	0.916368i	$0.631107\pi$
$282$		0			0
$283$	3.83722			0.228099			0.114050	−	0.993475i	$-0.463618\pi$
$283$	3.83722			0.228099			0.114050	+	0.993475i	$0.463618\pi$
$284$	5.22976	−	0.438363i	0.310329	−	0.0260121i
$285$		0			0
$286$	0.355372	+	8.49418i	0.0210136	+	0.502271i
$287$			9.37595i			0.553445i
$288$		0			0
$289$	3.95051			0.232383
$290$		0			0
$291$		0			0
$292$	−2.57057	−	30.6674i	−0.150431	−	1.79468i
$293$	26.4450			1.54493			0.772466	−	0.635057i	$-0.219023\pi$
$293$	26.4450			1.54493			0.772466	+	0.635057i	$0.219023\pi$
$294$		0			0
$295$		0			0
$296$	18.3991	−	2.32013i	1.06943	−	0.134855i
$297$		0			0
$298$	0.895066	+	21.3941i	0.0518498	+	1.23933i
$299$			17.5518i			1.01505i
$300$		0			0
$301$			11.3410i			0.653684i
$302$	32.8916	−	1.37609i	1.89270	−	0.0791849i
$303$		0			0
$304$	3.56892	+	21.1394i	0.204692	+	1.21243i
$305$		0			0
$306$		0			0
$307$	−1.27596			−0.0728230			−0.0364115	−	0.999337i	$-0.511593\pi$
$307$	−1.27596			−0.0728230			−0.0364115	+	0.999337i	$0.511593\pi$
$308$	7.82829	−	0.656174i	0.446058	−	0.0373890i
$309$		0			0
$310$		0			0
$311$	−2.44496			−0.138641			−0.0693205	−	0.997594i	$-0.522083\pi$
$311$	−2.44496			−0.138641			−0.0693205	+	0.997594i	$0.522083\pi$
$312$		0			0
$313$			22.8325i			1.29057i	0.763943	+	0.645283i	$0.223261\pi$
$313$			22.8325i			1.29057i	−0.763943	+	0.645283i	$0.776739\pi$
$314$	−30.9408	+	1.29447i	−1.74609	+	0.0730513i
$315$		0			0
$316$	−20.8169	+	1.74489i	−1.17104	+	0.0981579i
$317$	−2.11163			−0.118601			−0.0593005	−	0.998240i	$-0.518887\pi$
$317$	−2.11163			−0.118601			−0.0593005	+	0.998240i	$0.518887\pi$
$318$		0			0
$319$	15.4991			0.867784
$320$		0			0
$321$		0			0
$322$	16.2042	−	0.677938i	0.903027	−	0.0377800i
$323$	−19.3612			−1.07729
$324$		0			0
$325$		0			0
$326$	15.7749	−	0.659978i	0.873694	−	0.0365528i
$327$		0			0
$328$	19.7216	−	2.48690i	1.08894	−	0.137316i
$329$	13.3038			0.733463
$330$		0			0
$331$		−	23.2248i		−	1.27655i	−0.769808	−	0.638276i	$-0.779648\pi$
$331$		−	23.2248i		−	1.27655i	0.769808	−	0.638276i	$-0.220352\pi$
$332$	−3.04349	+	0.255108i	−0.167033	+	0.0140009i
$333$		0			0
$334$	−0.596777	−	14.2643i	−0.0326542	−	0.780509i
$335$		0			0
$336$		0			0
$337$		−	12.8884i		−	0.702074i	−0.936362	−	0.351037i	$-0.885829\pi$
$337$		−	12.8884i		−	0.702074i	0.936362	−	0.351037i	$-0.114171\pi$
$338$	12.4779	−	0.522037i	0.678706	−	0.0283951i
$339$		0			0
$340$		0			0
$341$		−	6.12785i		−	0.331841i
$342$		0			0
$343$		−	16.3030i		−	0.880281i
$344$	23.8549	−	3.00811i	1.28617	−	0.162186i
$345$		0			0
$346$	19.5220	−	0.816745i	1.04951	−	0.0439085i
$347$	−6.79827			−0.364951			−0.182475	−	0.983210i	$-0.558411\pi$
$347$	−6.79827			−0.364951			−0.182475	+	0.983210i	$0.558411\pi$
$348$		0			0
$349$		−	34.6076i		−	1.85250i	−0.376904	−	0.926252i	$-0.623011\pi$
$349$		−	34.6076i		−	1.85250i	0.376904	−	0.926252i	$-0.376989\pi$
$350$		0			0
$351$		0			0
$352$	−3.45661	−	16.2922i	−0.184238	−	0.868376i
$353$		−	12.2433i		−	0.651647i	−0.945431	−	0.325823i	$-0.894358\pi$
$353$		−	12.2433i		−	0.651647i	0.945431	−	0.325823i	$-0.105642\pi$
$354$		0			0
$355$		0			0
$356$	−25.3496	+	2.12483i	−1.34353	+	0.112616i
$357$		0			0
$358$	−1.29722	−	31.0065i	−0.0685603	−	1.63874i
$359$	−2.01622			−0.106412			−0.0532059	−	0.998584i	$-0.516944\pi$
$359$	−2.01622			−0.106412			−0.0532059	+	0.998584i	$0.516944\pi$
$360$		0			0
$361$	−9.72569			−0.511878
$362$	−0.114104	−	2.72734i	−0.00599716	−	0.143346i
$363$		0			0
$364$	0.455067	+	5.42904i	0.0238520	+	0.284559i
$365$		0			0
$366$		0			0
$367$			13.4131i			0.700159i	0.936720	+	0.350079i	$0.113845\pi$
$367$			13.4131i			0.700159i	−0.936720	+	0.350079i	$0.886155\pi$
$368$	−5.72404	−	33.9046i	−0.298386	−	1.76740i
$369$		0			0
$370$		0			0
$371$		−	8.16900i		−	0.424113i
$372$		0			0
$373$	10.0976			0.522832			0.261416	−	0.965226i	$-0.415811\pi$
$373$	10.0976			0.522832			0.261416	+	0.965226i	$0.415811\pi$
$374$	15.0279	−	0.628722i	0.777072	−	0.0325104i
$375$		0			0
$376$	−3.52873	−	27.9836i	−0.181981	−	1.44314i
$377$			10.7489i			0.553595i
$378$		0			0
$379$			18.2775i			0.938853i	0.882972	+	0.469426i	$0.155539\pi$
$379$			18.2775i			0.938853i	−0.882972	+	0.469426i	$0.844461\pi$
$380$		0			0
$381$		0			0
$382$	17.1298	−	0.716660i	0.876436	−	0.0366675i
$383$			11.7734i			0.601594i	0.953688	+	0.300797i	$0.0972527\pi$
$383$			11.7734i			0.601594i	−0.953688	+	0.300797i	$0.902747\pi$
$384$		0			0
$385$		0			0
$386$	0.0753305	+	1.80057i	0.00383422	+	0.0916466i
$387$		0			0
$388$	2.24606	+	26.7960i	0.114026	+	1.36036i
$389$		−	33.4270i		−	1.69482i	−0.530942	−	0.847408i	$-0.678162\pi$
$389$		−	33.4270i		−	1.69482i	0.530942	−	0.847408i	$-0.321838\pi$
$390$		0			0
$391$	31.0526			1.57040
$392$	−14.6488	+	1.84721i	−0.739876	+	0.0932984i
$393$		0			0
$394$	4.67482	−	0.195581i	0.235514	−	0.00985322i
$395$		0			0
$396$		0			0
$397$	39.0434			1.95953			0.979766	−	0.200147i	$-0.0641420\pi$
$397$	39.0434			1.95953			0.979766	+	0.200147i	$0.0641420\pi$
$398$	12.7552	−	0.533640i	0.639360	−	0.0267490i
$399$		0			0
$400$		0			0
$401$	24.6140			1.22916			0.614581	−	0.788853i	$-0.289325\pi$
$401$	24.6140			1.22916			0.614581	+	0.788853i	$0.289325\pi$
$402$		0			0
$403$	4.24976			0.211695
$404$	1.69114	+	20.1756i	0.0841372	+	1.00377i
$405$		0			0
$406$	9.92361	−	0.415175i	0.492500	−	0.0206048i
$407$		−	19.3038i		−	0.956855i
$408$		0			0
$409$	14.5024			0.717099			0.358550	−	0.933511i	$-0.383271\pi$
$409$	14.5024			0.717099			0.358550	+	0.933511i	$0.383271\pi$
$410$		0			0
$411$		0			0
$412$	1.79539	+	21.4193i	0.0884524	+	1.05526i
$413$	−6.33956			−0.311949
$414$		0			0
$415$		0			0
$416$	11.2989	−	2.39721i	0.553973	−	0.117533i
$417$		0			0
$418$	22.2964	−	0.932818i	1.09055	−	0.0456256i
$419$		−	12.6419i		−	0.617598i	−0.951127	−	0.308799i	$-0.900073\pi$
$419$		−	12.6419i		−	0.617598i	0.951127	−	0.308799i	$-0.0999271\pi$
$420$		0			0
$421$		−	16.8389i		−	0.820677i	−0.911933	−	0.410338i	$-0.865411\pi$
$421$		−	16.8389i		−	0.820677i	0.911933	−	0.410338i	$-0.134589\pi$
$422$	0.390891	+	9.34318i	0.0190283	+	0.454819i
$423$		0			0
$424$	−17.1829	+	2.16676i	−0.834474	+	0.105227i
$425$		0			0
$426$		0			0
$427$	11.3596			0.549731
$428$	−9.69636	+	0.812757i	−0.468691	+	0.0392861i
$429$		0			0
$430$		0			0
$431$	−5.98845			−0.288454			−0.144227	−	0.989545i	$-0.546070\pi$
$431$	−5.98845			−0.288454			−0.144227	+	0.989545i	$0.546070\pi$
$432$		0			0
$433$		−	2.22482i		−	0.106918i	−0.998570	−	0.0534589i	$-0.982975\pi$
$433$		−	2.22482i		−	0.106918i	0.998570	−	0.0534589i	$-0.0170246\pi$
$434$	−0.164146	−	3.92347i	−0.00787928	−	0.188333i
$435$		0			0
$436$	−2.58223	−	30.8065i	−0.123666	−	1.47537i
$437$	46.0719			2.20392
$438$		0			0
$439$	2.30460			0.109993			0.0549963	−	0.998487i	$-0.482485\pi$
$439$	2.30460			0.109993			0.0549963	+	0.998487i	$0.482485\pi$
$440$		0			0
$441$		0			0
$442$	0.436028	+	10.4220i	0.0207397	+	0.495726i
$443$	22.1347			1.05165			0.525826	−	0.850592i	$-0.323756\pi$
$443$	22.1347			1.05165			0.525826	+	0.850592i	$0.323756\pi$
$444$		0			0
$445$		0			0
$446$	−0.0492566	−	1.17734i	−0.00233237	−	0.0557489i
$447$		0			0
$448$	−2.64957	−	10.3388i	−0.125181	−	0.488462i
$449$	21.5861			1.01871			0.509356	−	0.860556i	$-0.329884\pi$
$449$	21.5861			1.01871			0.509356	+	0.860556i	$0.329884\pi$
$450$		0			0
$451$		−	20.6913i		−	0.974316i
$452$	1.65191	+	19.7076i	0.0776993	+	0.926969i
$453$		0			0
$454$	15.5426	−	0.650257i	0.729451	−	0.0305181i
$455$		0			0
$456$		0			0
$457$			2.50088i			0.116986i	0.998288	+	0.0584930i	$0.0186295\pi$
$457$			2.50088i			0.116986i	−0.998288	+	0.0584930i	$0.981370\pi$
$458$	0.898904	+	21.4858i	0.0420030	+	1.00397i
$459$		0			0
$460$		0			0
$461$			2.59609i			0.120912i	0.998171	+	0.0604561i	$0.0192555\pi$
$461$			2.59609i			0.120912i	−0.998171	+	0.0604561i	$0.980744\pi$
$462$		0			0
$463$		−	27.8604i		−	1.29478i	−0.762158	−	0.647392i	$-0.775860\pi$
$463$		−	27.8604i		−	1.29478i	0.762158	−	0.647392i	$-0.224140\pi$
$464$	−3.50545	−	20.7634i	−0.162736	−	0.963919i
$465$		0			0
$466$	0.146365	+	3.49844i	0.00678021	+	0.162062i
$467$	−5.75200			−0.266171			−0.133085	−	0.991105i	$-0.542488\pi$
$467$	−5.75200			−0.266171			−0.133085	+	0.991105i	$0.542488\pi$
$468$		0			0
$469$			14.2698i			0.658917i
$470$		0			0
$471$		0			0
$472$	1.68152	+	13.3348i	0.0773982	+	0.613784i
$473$		−	25.0279i		−	1.15078i
$474$		0			0
$475$		0			0
$476$	9.60503	−	0.805102i	0.440246	−	0.0369018i
$477$		0			0
$478$	29.7766	−	1.24577i	1.36195	−	0.0569801i
$479$	−12.5473			−0.573299			−0.286649	−	0.958036i	$-0.592541\pi$
$479$	−12.5473			−0.573299			−0.286649	+	0.958036i	$0.592541\pi$
$480$		0			0
$481$	13.3875			0.610417
$482$	8.63119	−	0.361104i	0.393140	−	0.0164478i
$483$		0			0
$484$	4.64726	−	0.389537i	0.211239	−	0.0177062i
$485$		0			0
$486$		0			0
$487$			8.60530i			0.389944i	0.980809	+	0.194972i	$0.0624615\pi$
$487$			8.60530i			0.389944i	−0.980809	+	0.194972i	$0.937538\pi$
$488$	−3.01305	−	23.8941i	−0.136395	−	1.08164i
$489$		0			0
$490$		0			0
$491$			36.8866i			1.66467i	0.554273	+	0.832335i	$0.312996\pi$
$491$			36.8866i			1.66467i	−0.554273	+	0.832335i	$0.687004\pi$
$492$		0			0
$493$	19.0169			0.856477
$494$	0.646923	+	15.4629i	0.0291065	+	0.695710i
$495$		0			0
$496$	−8.20919	+	1.38594i	−0.368603	+	0.0622305i
$497$		−	3.50078i		−	0.157031i
$498$		0			0
$499$			36.2496i			1.62275i	0.584524	+	0.811377i	$0.301281\pi$
$499$			36.2496i			1.62275i	−0.584524	+	0.811377i	$0.698719\pi$
$500$		0			0
$501$		0			0
$502$	1.33178	+	31.8325i	0.0594401	+	1.42075i
$503$			23.3527i			1.04124i	0.853787	+	0.520622i	$0.174300\pi$
$503$			23.3527i			1.04124i	−0.853787	+	0.520622i	$0.825700\pi$
$504$		0			0
$505$		0			0
$506$	−35.7603	+	1.49611i	−1.58974	+	0.0665101i
$507$		0			0
$508$	1.46206	+	17.4426i	0.0648682	+	0.773891i
$509$			3.35506i			0.148711i	0.997232	+	0.0743553i	$0.0236899\pi$
$509$			3.35506i			0.148711i	−0.997232	+	0.0743553i	$0.976310\pi$
$510$		0			0
$511$	−20.5286			−0.908133
$512$	−21.0441	+	8.31546i	−0.930025	+	0.367495i
$513$		0			0
$514$	−0.858858	−	20.5286i	−0.0378826	−	0.905479i
$515$		0			0
$516$		0			0
$517$	−29.3595			−1.29123
$518$	−0.517091	−	12.3596i	−0.0227197	−	0.543051i
$519$		0			0
$520$		0			0
$521$	33.6029			1.47217			0.736084	−	0.676890i	$-0.236673\pi$
$521$	33.6029			1.47217			0.736084	+	0.676890i	$0.236673\pi$
$522$		0			0
$523$	−0.965721			−0.0422280			−0.0211140	−	0.999777i	$-0.506721\pi$
$523$	−0.965721			−0.0422280			−0.0211140	+	0.999777i	$0.506721\pi$
$524$	−0.0787277	−	0.939238i	−0.00343924	−	0.0410308i
$525$		0			0
$526$	0.313128	+	7.48446i	0.0136530	+	0.326338i
$527$		−	7.51865i		−	0.327517i
$528$		0			0
$529$	−50.8928			−2.21273
$530$		0			0
$531$		0			0
$532$	14.2507	−	1.19451i	0.617848	−	0.0517885i
$533$	14.3497			0.621556
$534$		0			0
$535$		0			0
$536$	30.0154	−	3.78494i	1.29647	−	0.163485i
$537$		0			0
$538$	−1.60046	−	38.2545i	−0.0690006	−	1.64927i
$539$			15.3691i			0.661993i
$540$		0			0
$541$			6.34877i			0.272955i	0.990643	+	0.136478i	$0.0435781\pi$
$541$			6.34877i			0.272955i	−0.990643	+	0.136478i	$0.956422\pi$
$542$	−22.4104	+	0.937586i	−0.962609	+	0.0402728i
$543$		0			0
$544$	−4.24113	−	19.9899i	−0.181837	−	0.857060i
$545$		0			0
$546$		0			0
$547$	−2.07433			−0.0886921			−0.0443460	−	0.999016i	$-0.514120\pi$
$547$	−2.07433			−0.0886921			−0.0443460	+	0.999016i	$0.514120\pi$
$548$	0.217811	+	2.59853i	0.00930442	+	0.111004i
$549$		0			0
$550$		0			0
$551$	28.2148			1.20199
$552$		0			0
$553$			13.9347i			0.592566i
$554$	−14.1099	+	0.590316i	−0.599472	+	0.0250801i
$555$		0			0
$556$	1.46128	+	17.4333i	0.0619719	+	0.739337i
$557$	−27.6931			−1.17339			−0.586696	−	0.809807i	$-0.699572\pi$
$557$	−27.6931			−1.17339			−0.586696	+	0.809807i	$0.699572\pi$
$558$		0			0
$559$	17.3572			0.734131
$560$		0			0
$561$		0			0
$562$	18.9647	−	0.793426i	0.799976	−	0.0334687i
$563$	3.80771			0.160476			0.0802380	−	0.996776i	$-0.474432\pi$
$563$	3.80771			0.160476			0.0802380	+	0.996776i	$0.474432\pi$
$564$		0			0
$565$		0			0
$566$	−5.42191	+	0.226837i	−0.227900	+	0.00953467i
$567$		0			0
$568$	−7.36362	+	0.928554i	−0.308971	+	0.0389613i
$569$	38.6371			1.61975			0.809875	−	0.586603i	$-0.199535\pi$
$569$	38.6371			1.61975			0.809875	+	0.586603i	$0.199535\pi$
$570$		0			0
$571$			6.24976i			0.261544i	0.991412	+	0.130772i	$0.0417456\pi$
$571$			6.24976i			0.261544i	−0.991412	+	0.130772i	$0.958254\pi$
$572$	−1.00426	−	11.9811i	−0.0419904	−	0.500954i
$573$		0			0
$574$	−0.554258	−	13.2480i	−0.0231343	−	0.552961i
$575$		0			0
$576$		0			0
$577$			2.17377i			0.0904952i	0.998976	+	0.0452476i	$0.0144077\pi$
$577$			2.17377i			0.0904952i	−0.998976	+	0.0452476i	$0.985592\pi$
$578$	−5.58198	+	0.233534i	−0.232180	+	0.00971372i
$579$		0			0
$580$		0			0
$581$			2.03730i			0.0845213i
$582$		0			0
$583$			18.0278i			0.746634i
$584$	5.44506	+	43.1804i	0.225318	+	1.78682i
$585$		0			0
$586$	−37.3661	+	1.56329i	−1.54358	+	0.0645789i
$587$	34.1688			1.41030			0.705149	−	0.709059i	$-0.250880\pi$
$587$	34.1688			1.41030			0.705149	+	0.709059i	$0.250880\pi$
$588$		0			0
$589$		−	11.1552i		−	0.459643i
$590$		0			0
$591$		0			0
$592$	−25.8604	+	4.36596i	−1.06286	+	0.179440i
$593$		−	12.9952i		−	0.533650i	−0.963745	−	0.266825i	$-0.914025\pi$
$593$		−	12.9952i		−	0.533650i	0.963745	−	0.266825i	$-0.0859746\pi$
$594$		0			0
$595$		0			0
$596$	−2.52942	−	30.1765i	−0.103609	−	1.23608i
$597$		0			0
$598$	−1.03757	−	24.8003i	−0.0424295	−	1.01416i
$599$	47.2572			1.93088			0.965439	−	0.260628i	$-0.0839295\pi$
$599$	47.2572			1.93088			0.965439	+	0.260628i	$0.0839295\pi$
$600$		0			0
$601$	−23.5007			−0.958613			−0.479306	−	0.877648i	$-0.659112\pi$
$601$	−23.5007			−0.958613			−0.479306	+	0.877648i	$0.659112\pi$
$602$	−0.670421	−	16.0246i	−0.0273243	−	0.653112i
$603$		0			0
$604$	−46.3937	+	3.88876i	−1.88773	+	0.158231i
$605$		0			0
$606$		0			0
$607$			0.218591i			0.00887233i	0.999990	+	0.00443617i	$0.00141208\pi$
$607$			0.218591i			0.00887233i	−0.999990	+	0.00443617i	$0.998588\pi$
$608$	−6.29245	−	29.6585i	−0.255193	−	1.20281i
$609$		0			0
$610$		0			0
$611$		−	20.3613i		−	0.823730i
$612$		0			0
$613$	−35.7488			−1.44388			−0.721940	−	0.691956i	$-0.756749\pi$
$613$	−35.7488			−1.44388			−0.721940	+	0.691956i	$0.756749\pi$
$614$	1.80290	−	0.0754282i	0.0727593	−	0.00304404i
$615$		0			0
$616$	−11.0224	+	1.38993i	−0.444105	+	0.0560018i
$617$		−	33.0836i		−	1.33189i	−0.745999	−	0.665947i	$-0.768028\pi$
$617$		−	33.0836i		−	1.33189i	0.745999	−	0.665947i	$-0.231972\pi$
$618$		0			0
$619$			25.1084i			1.00919i	0.863355	+	0.504596i	$0.168359\pi$
$619$			25.1084i			1.00919i	−0.863355	+	0.504596i	$0.831641\pi$
$620$		0			0
$621$		0			0
$622$	3.45468	−	0.144534i	0.138520	−	0.00579527i
$623$			16.9689i			0.679846i
$624$		0			0
$625$		0			0
$626$	−1.34974	−	32.2617i	−0.0539463	−	1.28944i
$627$		0			0
$628$	43.6421	−	3.65812i	1.74151	−	0.145975i
$629$		−	23.6851i		−	0.944386i
$630$		0			0
$631$	23.2829			0.926876			0.463438	−	0.886129i	$-0.346616\pi$
$631$	23.2829			0.926876			0.463438	+	0.886129i	$0.346616\pi$
$632$	29.3107	−	3.69608i	1.16592	−	0.147022i
$633$		0			0
$634$	2.98369	−	0.124829i	0.118497	−	0.00495758i
$635$		0			0
$636$		0			0
$637$	−10.6587			−0.422313
$638$	−21.8999	+	0.916228i	−0.867026	+	0.0362738i
$639$		0			0
$640$		0			0
$641$	38.3021			1.51284			0.756420	−	0.654086i	$-0.226946\pi$
$641$	38.3021			1.51284			0.756420	+	0.654086i	$0.226946\pi$
$642$		0			0
$643$	−45.8045			−1.80635			−0.903177	−	0.429269i	$-0.858771\pi$
$643$	−45.8045			−1.80635			−0.903177	+	0.429269i	$0.858771\pi$
$644$	−22.8561	+	1.91582i	−0.900658	+	0.0754940i
$645$		0			0
$646$	27.3569	−	1.14453i	1.07634	−	0.0450311i
$647$		−	48.1114i		−	1.89146i	−0.324960	−	0.945728i	$-0.605351\pi$
$647$		−	48.1114i		−	1.89146i	0.324960	−	0.945728i	$-0.394649\pi$
$648$		0			0
$649$	13.9905			0.549174
$650$		0			0
$651$		0			0
$652$	−22.2506	+	1.86507i	−0.871402	+	0.0730417i
$653$	38.3331			1.50009			0.750046	−	0.661386i	$-0.230031\pi$
$653$	38.3331			1.50009			0.750046	+	0.661386i	$0.230031\pi$
$654$		0			0
$655$		0			0
$656$	−27.7192	+	4.67977i	−1.08225	+	0.182714i
$657$		0			0
$658$	−18.7980	+	0.786453i	−0.732822	+	0.0306591i
$659$		−	5.03253i		−	0.196040i	−0.995184	−	0.0980198i	$-0.968749\pi$
$659$		−	5.03253i		−	0.196040i	0.995184	−	0.0980198i	$-0.0312508\pi$
$660$		0			0
$661$		−	17.4665i		−	0.679368i	−0.940540	−	0.339684i	$-0.889680\pi$
$661$		−	17.4665i		−	0.679368i	0.940540	−	0.339684i	$-0.110320\pi$
$662$	1.37293	+	32.8161i	0.0533605	+	1.27544i
$663$		0			0
$664$	4.28530	−	0.540377i	0.166302	−	0.0209707i
$665$		0			0
$666$		0			0
$667$	−45.2526			−1.75219
$668$	1.68647	+	20.1199i	0.0652513	+	0.778462i
$669$		0			0
$670$		0			0
$671$	−25.0690			−0.967779
$672$		0			0
$673$			32.4448i			1.25065i	0.780363	+	0.625327i	$0.215034\pi$
$673$			32.4448i			1.25065i	−0.780363	+	0.625327i	$0.784966\pi$
$674$	0.761894	+	18.2110i	0.0293471	+	0.701461i
$675$		0			0
$676$	−17.6001	+	1.47525i	−0.676926	+	0.0567405i
$677$	8.07213			0.310237			0.155119	−	0.987896i	$-0.450424\pi$
$677$	8.07213			0.310237			0.155119	+	0.987896i	$0.450424\pi$
$678$		0			0
$679$	17.9371			0.688362
$680$		0			0
$681$		0			0
$682$	0.362247	+	8.65851i	0.0138711	+	0.331551i
$683$	−36.3380			−1.39043			−0.695217	−	0.718799i	$-0.744692\pi$
$683$	−36.3380			−1.39043			−0.695217	+	0.718799i	$0.744692\pi$
$684$		0			0
$685$		0			0
$686$	0.963751	+	23.0358i	0.0367962	+	0.879512i
$687$		0			0
$688$	−33.5286	+	5.66057i	−1.27827	+	0.215807i
$689$	−12.5025			−0.476308
$690$		0			0
$691$			15.0016i			0.570686i	0.958425	+	0.285343i	$0.0921075\pi$
$691$			15.0016i			0.570686i	−0.958425	+	0.285343i	$0.907892\pi$
$692$	−27.5359	+	2.30808i	−1.04676	+	0.0877402i
$693$		0			0
$694$	9.60581	−	0.401879i	0.364632	−	0.0152551i
$695$		0			0
$696$		0			0
$697$		−	25.3875i		−	0.961620i
$698$	2.04582	+	48.8998i	0.0774356	+	1.85089i
$699$		0			0
$700$		0			0
$701$			13.2874i			0.501859i	0.968005	+	0.250929i	$0.0807362\pi$
$701$			13.2874i			0.501859i	−0.968005	+	0.250929i	$0.919264\pi$
$702$		0			0
$703$		−	35.1409i		−	1.32537i
$704$	5.84721	+	22.8161i	0.220375	+	0.859916i
$705$		0			0
$706$	0.723763	+	17.2996i	0.0272392	+	0.651077i
$707$	13.5054			0.507925
$708$		0			0
$709$			37.8976i			1.42327i	0.702548	+	0.711637i	$0.252046\pi$
$709$			37.8976i			1.42327i	−0.702548	+	0.711637i	$0.747954\pi$
$710$		0			0
$711$		0			0
$712$	35.6929	−	4.50088i	1.33765	−	0.168677i
$713$			17.8914i			0.670038i
$714$		0			0
$715$		0			0
$716$	3.66589	+	43.7348i	0.137001	+	1.63445i
$717$		0			0
$718$	2.84887	−	0.119188i	0.106319	−	0.00444807i
$719$	−4.17909			−0.155854			−0.0779269	−	0.996959i	$-0.524830\pi$
$719$	−4.17909			−0.155854			−0.0779269	+	0.996959i	$0.524830\pi$
$720$		0			0
$721$	14.3380			0.533975
$722$	13.7422	−	0.574933i	0.511431	−	0.0213968i
$723$		0			0
$724$	0.322452	+	3.84692i	0.0119838	+	0.142970i
$725$		0			0
$726$		0			0
$727$		−	26.7727i		−	0.992943i	−0.868053	−	0.496471i	$-0.834629\pi$
$727$		−	26.7727i		−	0.992943i	0.868053	−	0.496471i	$-0.165371\pi$
$728$	−0.963936	−	7.64421i	−0.0357258	−	0.283313i
$729$		0			0
$730$		0			0
$731$		−	30.7083i		−	1.13579i
$732$		0			0
$733$	21.3364			0.788080			0.394040	−	0.919093i	$-0.371077\pi$
$733$	21.3364			0.788080			0.394040	+	0.919093i	$0.371077\pi$
$734$	−0.792914	−	18.9524i	−0.0292670	−	0.699547i
$735$		0			0
$736$	10.0922	+	47.5680i	0.372003	+	1.75338i
$737$		−	31.4912i		−	1.15999i
$738$		0			0
$739$		−	13.1038i		−	0.482033i	−0.970521	−	0.241016i	$-0.922519\pi$
$739$		−	13.1038i		−	0.482033i	0.970521	−	0.241016i	$-0.0774807\pi$
$740$		0			0
$741$		0			0
$742$	0.482909	+	11.5426i	0.0177282	+	0.423743i
$743$			33.3595i			1.22384i	0.790919	+	0.611921i	$0.209603\pi$
$743$			33.3595i			1.22384i	−0.790919	+	0.611921i	$0.790397\pi$
$744$		0			0
$745$		0			0
$746$	−14.2676	+	0.596915i	−0.522375	+	0.0218546i
$747$		0			0
$748$	−21.1969	+	1.77674i	−0.775034	+	0.0649640i
$749$			6.49069i			0.237165i
$750$		0			0
$751$	−1.92100			−0.0700981			−0.0350491	−	0.999386i	$-0.511159\pi$
$751$	−1.92100			−0.0700981			−0.0350491	+	0.999386i	$0.511159\pi$
$752$	6.64027	+	39.3316i	0.242146	+	1.43428i
$753$		0			0
$754$	−0.635418	−	15.1879i	−0.0231406	−	0.553112i
$755$		0			0
$756$		0			0
$757$	−13.9908			−0.508504			−0.254252	−	0.967138i	$-0.581829\pi$
$757$	−13.9908			−0.508504			−0.254252	+	0.967138i	$0.581829\pi$
$758$	−1.08047	−	25.8257i	−0.0392445	−	0.938032i
$759$		0			0
$760$		0			0
$761$	−25.6618			−0.930240			−0.465120	−	0.885248i	$-0.653989\pi$
$761$	−25.6618			−0.930240			−0.465120	+	0.885248i	$0.653989\pi$
$762$		0			0
$763$	−20.6217			−0.746557
$764$	−24.1616	+	2.02525i	−0.874137	+	0.0732709i
$765$		0			0
$766$	−0.695985	−	16.6356i	−0.0251469	−	0.601069i
$767$			9.70260i			0.350341i
$768$		0			0
$769$	12.3922			0.446873			0.223436	−	0.974719i	$-0.428272\pi$
$769$	12.3922			0.446873			0.223436	+	0.974719i	$0.428272\pi$
$770$		0			0
$771$		0			0
$772$	−0.212881	−	2.53971i	−0.00766174	−	0.0914062i
$773$	−38.4843			−1.38418			−0.692091	−	0.721810i	$-0.743311\pi$
$773$	−38.4843			−1.38418			−0.692091	+	0.721810i	$0.743311\pi$
$774$		0			0
$775$		0			0
$776$	−4.75767	−	37.7293i	−0.170790	−	1.35440i
$777$		0			0
$778$	1.97603	+	47.2316i	0.0708442	+	1.69333i
$779$		−	37.6668i		−	1.34955i
$780$		0			0
$781$			7.72569i			0.276447i
$782$	−43.8766	+	1.83567i	−1.56903	+	0.0656434i
$783$		0			0
$784$	20.5892	−	3.47603i	0.735329	−	0.124144i
$785$		0			0
$786$		0			0
$787$	−0.389147			−0.0138716			−0.00693579	−	0.999976i	$-0.502208\pi$
$787$	−0.389147			−0.0138716			−0.00693579	+	0.999976i	$0.502208\pi$
$788$	−6.59386	+	0.552703i	−0.234896	+	0.0196892i
$789$		0			0
$790$		0			0
$791$	13.1922			0.469060
$792$		0			0
$793$		−	17.3857i		−	0.617386i
$794$	−55.1674	+	2.30804i	−1.95782	+	0.0819094i
$795$		0			0
$796$	−17.9913	+	1.50804i	−0.637683	+	0.0534512i
$797$	−0.854188			−0.0302569			−0.0151284	−	0.999886i	$-0.504816\pi$
$797$	−0.854188			−0.0302569			−0.0151284	+	0.999886i	$0.504816\pi$
$798$		0			0
$799$	−36.0231			−1.27441
$800$		0			0
$801$		0			0
$802$	−34.7790	+	1.45505i	−1.22809	+	0.0513796i
$803$	45.3036			1.59873
$804$		0			0
$805$		0			0
$806$	−6.00481	+	0.251224i	−0.211510	+	0.00884897i
$807$		0			0
$808$	−3.58221	−	28.4077i	−0.126022	−	0.999379i
$809$	−10.4107			−0.366020			−0.183010	−	0.983111i	$-0.558584\pi$
$809$	−10.4107			−0.366020			−0.183010	+	0.983111i	$0.558584\pi$
$810$		0			0
$811$			6.08825i			0.213787i	0.994270	+	0.106894i	$0.0340904\pi$
$811$			6.08825i			0.213787i	−0.994270	+	0.106894i	$0.965910\pi$
$812$	−13.9973	+	1.17326i	−0.491209	+	0.0411735i
$813$		0			0
$814$	1.14114	+	27.2759i	0.0399970	+	0.956019i
$815$		0			0
$816$		0			0
$817$		−	45.5611i		−	1.59398i
$818$	−20.4916	+	0.857309i	−0.716472	+	0.0299751i
$819$		0			0
$820$		0			0
$821$			35.3908i			1.23515i	0.786513	+	0.617574i	$0.211884\pi$
$821$			35.3908i			1.23515i	−0.786513	+	0.617574i	$0.788116\pi$
$822$		0			0
$823$			16.2846i			0.567646i	0.958877	+	0.283823i	$0.0916028\pi$
$823$			16.2846i			0.567646i	−0.958877	+	0.283823i	$0.908397\pi$
$824$	−3.80304	−	30.1589i	−0.132485	−	1.05064i
$825$		0			0
$826$	8.95766	−	0.374762i	0.311677	−	0.0130396i
$827$	−32.1362			−1.11748			−0.558742	−	0.829341i	$-0.688716\pi$
$827$	−32.1362			−1.11748			−0.558742	+	0.829341i	$0.688716\pi$
$828$		0			0
$829$		−	22.4682i		−	0.780355i	−0.920740	−	0.390177i	$-0.872414\pi$
$829$		−	22.4682i		−	0.780355i	0.920740	−	0.390177i	$-0.127586\pi$
$830$		0			0
$831$		0			0
$832$	−15.8233	+	4.05513i	−0.548576	+	0.140586i
$833$			18.8573i			0.653367i
$834$		0			0
$835$		0			0
$836$	−31.4492	+	2.63610i	−1.08769	+	0.0911715i
$837$		0			0
$838$	0.747325	+	17.8627i	0.0258159	+	0.617058i
$839$	−16.1358			−0.557070			−0.278535	−	0.960426i	$-0.589849\pi$
$839$	−16.1358			−0.557070			−0.278535	+	0.960426i	$0.589849\pi$
$840$		0			0
$841$	1.28695			0.0443777
$842$	0.995427	+	23.7930i	0.0343047	+	0.819959i
$843$		0			0
$844$	−1.10464	−	13.1786i	−0.0380233	−	0.453626i
$845$		0			0
$846$		0			0
$847$		−	3.11085i		−	0.106890i
$848$	24.1509	−	4.07735i	0.829347	−	0.140017i
$849$		0			0
$850$		0			0
$851$			56.3611i			1.93203i
$852$		0			0
$853$	−44.6262			−1.52797			−0.763986	−	0.645233i	$-0.776760\pi$
$853$	−44.6262			−1.52797			−0.763986	+	0.645233i	$0.776760\pi$
$854$	−16.0509	+	0.671523i	−0.549251	+	0.0229790i
$855$		0			0
$856$	13.6527	−	1.72161i	0.466639	−	0.0588433i
$857$			4.52553i			0.154589i	0.997008	+	0.0772945i	$0.0246282\pi$
$857$			4.52553i			0.154589i	−0.997008	+	0.0772945i	$0.975372\pi$
$858$		0			0
$859$		−	42.7783i		−	1.45958i	−0.683673	−	0.729788i	$-0.739619\pi$
$859$		−	42.7783i		−	1.45958i	0.683673	−	0.729788i	$-0.260381\pi$
$860$		0			0
$861$		0			0
$862$	8.46155	−	0.354006i	0.288202	−	0.0120575i
$863$		−	23.7734i		−	0.809257i	−0.914481	−	0.404629i	$-0.867401\pi$
$863$		−	23.7734i		−	0.809257i	0.914481	−	0.404629i	$-0.132599\pi$
$864$		0			0
$865$		0			0
$866$	0.131520	+	3.14362i	0.00446922	+	0.106824i
$867$		0			0
$868$	0.463870	+	5.53407i	0.0157448	+	0.187839i
$869$		−	30.7519i		−	1.04319i
$870$		0			0
$871$	21.8397			0.740009
$872$	5.46976	+	43.3763i	0.185229	+	1.46891i
$873$		0			0
$874$	−65.0986	+	2.72353i	−2.20199	+	0.0921249i
$875$		0			0
$876$		0			0
$877$	13.1470			0.443944			0.221972	−	0.975053i	$-0.428751\pi$
$877$	13.1470			0.443944			0.221972	+	0.975053i	$0.428751\pi$
$878$	−3.25635	+	0.136236i	−0.109896	+	0.00459774i
$879$		0			0
$880$		0			0
$881$	−38.9132			−1.31102			−0.655510	−	0.755187i	$-0.727546\pi$
$881$	−38.9132			−1.31102			−0.655510	+	0.755187i	$0.727546\pi$
$882$		0			0
$883$	44.5843			1.50038			0.750190	−	0.661223i	$-0.229962\pi$
$883$	44.5843			1.50038			0.750190	+	0.661223i	$0.229962\pi$
$884$	−1.23220	−	14.7003i	−0.0414432	−	0.494426i
$885$		0			0
$886$	−31.2759	+	1.30849i	−1.05073	+	0.0439596i
$887$		−	32.3240i		−	1.08533i	−0.839948	−	0.542667i	$-0.817415\pi$
$887$		−	32.3240i		−	1.08533i	0.839948	−	0.542667i	$-0.182585\pi$
$888$		0			0
$889$	11.6760			0.391601
$890$		0			0
$891$		0			0
$892$	0.139197	+	1.66065i	0.00466066	+	0.0556027i
$893$	−53.4465			−1.78852
$894$		0			0
$895$		0			0
$896$	4.35497	+	14.4518i	0.145489	+	0.482802i
$897$		0			0
$898$	−30.5007	+	1.27606i	−1.01782	+	0.0425826i
$899$			10.9568i			0.365431i
$900$		0			0
$901$			22.1194i			0.736904i
$902$	1.22316	+	29.2364i	0.0407269	+	0.973464i
$903$		0			0
$904$	−3.49912	−	27.7488i	−0.116379	−	0.922911i
$905$		0			0
$906$		0			0
$907$	14.8309			0.492452			0.246226	−	0.969212i	$-0.420809\pi$
$907$	14.8309			0.492452			0.246226	+	0.969212i	$0.420809\pi$
$908$	−21.9229	+	1.83760i	−0.727538	+	0.0609828i
$909$		0			0
$910$		0			0
$911$	−11.6108			−0.384681			−0.192341	−	0.981328i	$-0.561608\pi$
$911$	−11.6108			−0.384681			−0.192341	+	0.981328i	$0.561608\pi$
$912$		0			0
$913$		−	4.49601i		−	0.148796i
$914$	−0.147839	−	3.53368i	−0.00489007	−	0.116884i
$915$		0			0
$916$	−2.54026	−	30.3059i	−0.0839327	−	1.00133i
$917$	−0.628722			−0.0207622
$918$		0			0
$919$	58.2518			1.92155			0.960775	−	0.277330i	$-0.0894495\pi$
$919$	58.2518			1.92155			0.960775	+	0.277330i	$0.0894495\pi$
$920$		0			0
$921$		0			0
$922$	−0.153468	−	3.66822i	−0.00505419	−	0.120807i
$923$	−5.35789			−0.176357
$924$		0			0
$925$		0			0
$926$	1.64696	+	39.3661i	0.0541226	+	1.29365i
$927$		0			0
$928$	6.18055	+	29.1311i	0.202886	+	0.956274i
$929$	18.4433			0.605105			0.302553	−	0.953133i	$-0.402161\pi$
$929$	18.4433			0.605105			0.302553	+	0.953133i	$0.402161\pi$
$930$		0			0
$931$			27.9781i			0.916944i
$932$	−0.413620	−	4.93457i	−0.0135486	−	0.161637i
$933$		0			0
$934$	8.12744	−	0.340028i	0.265938	−	0.0111261i
$935$		0			0
$936$		0			0
$937$			16.1005i			0.525982i	0.964798	+	0.262991i	$0.0847089\pi$
$937$			16.1005i			0.525982i	−0.964798	+	0.262991i	$0.915291\pi$
$938$	−0.843555	−	20.1629i	−0.0275430	−	0.658341i
$939$		0			0
$940$		0			0
$941$		−	32.0974i		−	1.04635i	−0.852226	−	0.523173i	$-0.824748\pi$
$941$		−	32.0974i		−	1.04635i	0.852226	−	0.523173i	$-0.175252\pi$
$942$		0			0
$943$			60.4121i			1.96729i
$944$	−3.16423	−	18.7424i	−0.102987	−	0.610012i
$945$		0			0
$946$	1.47952	+	35.3638i	0.0481033	+	1.14978i
$947$	4.10998			0.133556			0.0667782	−	0.997768i	$-0.478728\pi$
$947$	4.10998			0.133556			0.0667782	+	0.997768i	$0.478728\pi$
$948$		0			0
$949$			31.4188i			1.01990i
$950$		0			0
$951$		0			0
$952$	−13.5241	+	1.70539i	−0.438318	+	0.0552720i
$953$			31.7208i			1.02754i	0.857928	+	0.513769i	$0.171751\pi$
$953$			31.7208i			1.02754i	−0.857928	+	0.513769i	$0.828249\pi$
$954$		0			0
$955$		0			0
$956$	−42.0001	+	3.52048i	−1.35838	+	0.113861i
$957$		0			0
$958$	17.7290	−	0.741729i	0.572798	−	0.0239642i
$959$	1.73944			0.0561695
$960$		0			0
$961$	−26.6680			−0.860259
$962$	−18.9162	+	0.791399i	−0.609884	+	0.0255157i
$963$		0			0
$964$	−12.1743	+	1.02046i	−0.392109	+	0.0328669i
$965$		0			0
$966$		0			0
$967$		−	26.9936i		−	0.868055i	−0.900900	−	0.434027i	$-0.857092\pi$
$967$		−	26.9936i		−	0.868055i	0.900900	−	0.434027i	$-0.142908\pi$
$968$	−6.54344	+	0.825129i	−0.210314	+	0.0265206i
$969$		0			0
$970$		0			0
$971$			14.0559i			0.451076i	0.974234	+	0.225538i	$0.0724139\pi$
$971$			14.0559i			0.451076i	−0.974234	+	0.225538i	$0.927586\pi$
$972$		0			0
$973$	11.6698			0.374116
$974$	−0.508701	−	12.1591i	−0.0162998	−	0.389603i
$975$		0			0
$976$	5.66988	+	33.5838i	0.181488	+	1.07499i
$977$		−	1.14251i		−	0.0365520i	−0.999833	−	0.0182760i	$-0.994182\pi$
$977$		−	1.14251i		−	0.0365520i	0.999833	−	0.0182760i	$-0.00581776\pi$
$978$		0			0
$979$		−	37.4479i		−	1.19684i
$980$		0			0
$981$		0			0
$982$	−2.18055	−	52.1200i	−0.0695840	−	1.66321i
$983$			6.41720i			0.204677i	0.994750	+	0.102338i	$0.0326325\pi$
$983$			6.41720i			0.204677i	−0.994750	+	0.102338i	$0.967368\pi$
$984$		0			0
$985$		0			0
$986$	−26.8704	+	1.12418i	−0.855728	+	0.0358011i
$987$		0			0
$988$	−1.82818	−	21.8105i	−0.0581620	−	0.693885i
$989$			73.0735i			2.32360i
$990$		0			0
$991$	−7.39470			−0.234900			−0.117450	−	0.993079i	$-0.537472\pi$
$991$	−7.39470			−0.234900			−0.117450	+	0.993079i	$0.537472\pi$
$992$	11.5175	−	2.44359i	0.365680	−	0.0775839i
$993$		0			0
$994$	0.206948	+	4.94652i	0.00656399	+	0.156894i
$995$		0			0
$996$		0			0
$997$	31.6649			1.00284			0.501419	−	0.865205i	$-0.332812\pi$
$997$	31.6649			1.00284			0.501419	+	0.865205i	$0.332812\pi$
$998$	−2.14289	−	51.2198i	−0.0678319	−	1.62133i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.d.s.1549.2		8
3.2	odd	2		600.2.d.h.349.7		8
4.3	odd	2		7200.2.d.s.2449.6		8
5.2	odd	4		1800.2.k.t.901.3		8
5.3	odd	4		1800.2.k.q.901.6		8
5.4	even	2		1800.2.d.t.1549.7		8
8.3	odd	2		7200.2.d.t.2449.6		8
8.5	even	2		1800.2.d.t.1549.8		8
12.11	even	2		2400.2.d.g.49.6		8
15.2	even	4		600.2.k.d.301.6	yes	8
15.8	even	4		600.2.k.e.301.3	yes	8
15.14	odd	2		600.2.d.g.349.2		8
20.3	even	4		7200.2.k.s.3601.5		8
20.7	even	4		7200.2.k.r.3601.3		8
20.19	odd	2		7200.2.d.t.2449.3		8
24.5	odd	2		600.2.d.g.349.1		8
24.11	even	2		2400.2.d.h.49.6		8
40.3	even	4		7200.2.k.s.3601.6		8
40.13	odd	4		1800.2.k.q.901.5		8
40.19	odd	2		7200.2.d.s.2449.3		8
40.27	even	4		7200.2.k.r.3601.4		8
40.29	even	2	inner	1800.2.d.s.1549.1		8
40.37	odd	4		1800.2.k.t.901.4		8
60.23	odd	4		2400.2.k.e.1201.3		8
60.47	odd	4		2400.2.k.d.1201.6		8
60.59	even	2		2400.2.d.h.49.3		8
120.29	odd	2		600.2.d.h.349.8		8
120.53	even	4		600.2.k.e.301.4	yes	8
120.59	even	2		2400.2.d.g.49.3		8
120.77	even	4		600.2.k.d.301.5	✓	8
120.83	odd	4		2400.2.k.e.1201.7		8
120.107	odd	4		2400.2.k.d.1201.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.d.g.349.1		8	24.5	odd	2
600.2.d.g.349.2		8	15.14	odd	2
600.2.d.h.349.7		8	3.2	odd	2
600.2.d.h.349.8		8	120.29	odd	2
600.2.k.d.301.5	✓	8	120.77	even	4
600.2.k.d.301.6	yes	8	15.2	even	4
600.2.k.e.301.3	yes	8	15.8	even	4
600.2.k.e.301.4	yes	8	120.53	even	4
1800.2.d.s.1549.1		8	40.29	even	2	inner
1800.2.d.s.1549.2		8	1.1	even	1	trivial
1800.2.d.t.1549.7		8	5.4	even	2
1800.2.d.t.1549.8		8	8.5	even	2
1800.2.k.q.901.5		8	40.13	odd	4
1800.2.k.q.901.6		8	5.3	odd	4
1800.2.k.t.901.3		8	5.2	odd	4
1800.2.k.t.901.4		8	40.37	odd	4
2400.2.d.g.49.3		8	120.59	even	2
2400.2.d.g.49.6		8	12.11	even	2
2400.2.d.h.49.3		8	60.59	even	2
2400.2.d.h.49.6		8	24.11	even	2
2400.2.k.d.1201.2		8	120.107	odd	4
2400.2.k.d.1201.6		8	60.47	odd	4
2400.2.k.e.1201.3		8	60.23	odd	4
2400.2.k.e.1201.7		8	120.83	odd	4
7200.2.d.s.2449.3		8	40.19	odd	2
7200.2.d.s.2449.6		8	4.3	odd	2
7200.2.d.t.2449.3		8	20.19	odd	2
7200.2.d.t.2449.6		8	8.3	odd	2
7200.2.k.r.3601.3		8	20.7	even	4
7200.2.k.r.3601.4		8	40.27	even	4
7200.2.k.s.3601.5		8	20.3	even	4
7200.2.k.s.3601.6		8	40.3	even	4

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.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.41298 + 0.0591148i) q^{2} +(1.99301 - 0.167056i) q^{4} -1.33411i q^{7} +(-2.80620 + 0.353863i) q^{8} +O(q^{10})\)	\(q+(-1.41298 + 0.0591148i) q^{2} +(1.99301 - 0.167056i) q^{4} -1.33411i q^{7} +(-2.80620 + 0.353863i) q^{8} +2.94418i q^{11} -2.04184 q^{13} +(0.0788658 + 1.88507i) q^{14} +(3.94418 - 0.665888i) q^{16} +3.61241i q^{17} +5.35964i q^{19} +(-0.174045 - 4.16007i) q^{22} -8.59609i q^{23} +(2.88507 - 0.120703i) q^{26} +(-0.222871 - 2.65890i) q^{28} -5.26432i q^{29} -2.08134 q^{31} +(-5.53368 + 1.17404i) q^{32} +(-0.213547 - 5.10425i) q^{34} -6.55659 q^{37} +(-0.316834 - 7.57304i) q^{38} -7.02786 q^{41} -8.50078 q^{43} +(0.491843 + 5.86779i) q^{44} +(0.508157 + 12.1461i) q^{46} +9.97204i q^{47} +5.22015 q^{49} +(-4.06940 + 0.341101i) q^{52} +6.12318 q^{53} +(0.472092 + 3.74379i) q^{56} +(0.311199 + 7.43836i) q^{58} -4.75190i q^{59} +8.51476i q^{61} +(2.94089 - 0.123038i) q^{62} +(7.74956 - 1.98602i) q^{64} -10.6961 q^{67} +(0.603474 + 7.19957i) q^{68} +2.62405 q^{71} -15.3875i q^{73} +(9.26432 - 0.387592i) q^{74} +(0.895358 + 10.6818i) q^{76} +3.92787 q^{77} -10.4450 q^{79} +(9.93021 - 0.415451i) q^{82} -1.52708 q^{83} +(12.0114 - 0.502522i) q^{86} +(-1.04184 - 8.26198i) q^{88} -12.7193 q^{89} +2.72404i q^{91} +(-1.43603 - 17.1321i) q^{92} +(-0.589496 - 14.0903i) q^{94} +13.4450i q^{97} +(-7.37595 + 0.308588i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 4 q^{4} - 8 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 - 4 * q^4 - 8 * q^8	\( 8 q - 2 q^{2} - 4 q^{4} - 8 q^{8} - 6 q^{14} + 8 q^{16} - 20 q^{22} + 2 q^{26} - 24 q^{28} + 8 q^{31} - 12 q^{32} - 12 q^{34} + 14 q^{38} + 8 q^{43} - 12 q^{44} + 20 q^{46} - 24 q^{52} + 8 q^{53} - 8 q^{56} + 20 q^{58} + 26 q^{62} + 32 q^{64} - 24 q^{67} + 36 q^{68} + 40 q^{71} + 8 q^{74} - 20 q^{76} - 24 q^{77} + 16 q^{79} + 16 q^{82} - 32 q^{83} + 18 q^{86} + 8 q^{88} + 28 q^{92} + 4 q^{94} - 40 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 4 * q^4 - 8 * q^8 - 6 * q^14 + 8 * q^16 - 20 * q^22 + 2 * q^26 - 24 * q^28 + 8 * q^31 - 12 * q^32 - 12 * q^34 + 14 * q^38 + 8 * q^43 - 12 * q^44 + 20 * q^46 - 24 * q^52 + 8 * q^53 - 8 * q^56 + 20 * q^58 + 26 * q^62 + 32 * q^64 - 24 * q^67 + 36 * q^68 + 40 * q^71 + 8 * q^74 - 20 * q^76 - 24 * q^77 + 16 * q^79 + 16 * q^82 - 32 * q^83 + 18 * q^86 + 8 * q^88 + 28 * q^92 + 4 * q^94 - 40 * q^98

Introduction

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