LMFDB - Embedded newform 900.3.p.f.101.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(101,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("900.101");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.p (of order $6$, degree $2$, 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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.9
Character	$\chi$	$=$	900.101
Dual form			900.3.p.f.401.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.92469 + 2.30121i) q^{3} +(-0.382345 + 0.662241i) q^{7} +(-1.59110 + 8.85824i) q^{9} +O(q^{10})$	\(q+(1.92469 + 2.30121i) q^{3} +(-0.382345 + 0.662241i) q^{7} +(-1.59110 + 8.85824i) q^{9} +(6.98717 + 4.03404i) q^{11} +(-1.08339 - 1.87649i) q^{13} +24.9128i q^{17} -20.7672 q^{19} +(-2.25985 + 0.394757i) q^{21} +(14.5841 - 8.42014i) q^{23} +(-23.4470 + 13.3880i) q^{27} +(-10.1651 - 5.86885i) q^{29} +(-0.334707 - 0.579730i) q^{31} +(4.16500 + 23.8432i) q^{33} +48.2956 q^{37} +(2.23299 - 6.10478i) q^{39} +(-54.1835 + 31.2829i) q^{41} +(-35.6645 + 61.7728i) q^{43} +(17.5663 + 10.1419i) q^{47} +(24.2076 + 41.9288i) q^{49} +(-57.3296 + 47.9496i) q^{51} -82.8011i q^{53} +(-39.9705 - 47.7896i) q^{57} +(-4.66958 + 2.69598i) q^{59} +(-41.6097 + 72.0702i) q^{61} +(-5.25794 - 4.44060i) q^{63} +(5.31727 + 9.20978i) q^{67} +(47.4464 + 17.3549i) q^{69} +87.9667i q^{71} +15.5340 q^{73} +(-5.34302 + 3.08479i) q^{77} +(16.8772 - 29.2322i) q^{79} +(-75.9368 - 28.1887i) q^{81} +(-48.2517 - 27.8581i) q^{83} +(-6.05936 - 34.6878i) q^{87} +22.3583i q^{89} +1.65692 q^{91} +(0.689869 - 1.88603i) q^{93} +(34.4755 - 59.7133i) q^{97} +(-46.8518 + 55.4754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{9}+O(q^{10}) $ 24 * q - 2 * q^9	$ 24 q - 2 q^{9} - 18 q^{11} - 26 q^{21} - 36 q^{29} + 30 q^{31} - 6 q^{39} - 36 q^{41} - 108 q^{49} + 124 q^{51} + 306 q^{59} + 48 q^{61} + 268 q^{69} - 114 q^{79} - 14 q^{81} - 84 q^{91} - 418 q^{99}+O(q^{100}) $ 24 * q - 2 * q^9 - 18 * q^11 - 26 * q^21 - 36 * q^29 + 30 * q^31 - 6 * q^39 - 36 * q^41 - 108 * q^49 + 124 * q^51 + 306 * q^59 + 48 * q^61 + 268 * q^69 - 114 * q^79 - 14 * q^81 - 84 * q^91 - 418 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	1.92469	+	2.30121i	0.641565	+	0.767069i
$3$	1.92469	+	2.30121i	0.641565	+	0.767069i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.382345	+	0.662241i	−0.0546207	+	0.0946058i	−0.892043	−	0.451951i	$-0.850728\pi$
$7$	−0.382345	+	0.662241i	−0.0546207	+	0.0946058i	0.837422	+	0.546557i	$0.184062\pi$
$8$		0			0
$9$	−1.59110	+	8.85824i	−0.176789	+	0.984249i
$10$		0			0
$11$	6.98717	+	4.03404i	0.635197	+	0.366731i	0.782762	−	0.622321i	$-0.213810\pi$
$11$	6.98717	+	4.03404i	0.635197	+	0.366731i	−0.147565	+	0.989052i	$0.547144\pi$
$12$		0			0
$13$	−1.08339	−	1.87649i	−0.0833378	−	0.144345i	0.821344	−	0.570433i	$-0.193225\pi$
$13$	−1.08339	−	1.87649i	−0.0833378	−	0.144345i	−0.904682	+	0.426088i	$0.859891\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			24.9128i			1.46546i	0.680519	+	0.732731i	$0.261755\pi$
$17$			24.9128i			1.46546i	−0.680519	+	0.732731i	$0.738245\pi$
$18$		0			0
$19$	−20.7672			−1.09301			−0.546505	−	0.837456i	$-0.684042\pi$
$19$	−20.7672			−1.09301			−0.546505	+	0.837456i	$0.684042\pi$
$20$		0			0
$21$	−2.25985	+	0.394757i	−0.107612	+	0.0187979i
$22$		0			0
$23$	14.5841	−	8.42014i	0.634092	−	0.366093i	−0.148243	−	0.988951i	$-0.547362\pi$
$23$	14.5841	−	8.42014i	0.634092	−	0.366093i	0.782335	+	0.622858i	$0.214029\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−23.4470	+	13.3880i	−0.868408	+	0.495850i
$28$		0			0
$29$	−10.1651	−	5.86885i	−0.350522	−	0.202374i	0.314393	−	0.949293i	$-0.398199\pi$
$29$	−10.1651	−	5.86885i	−0.350522	−	0.202374i	−0.664915	+	0.746919i	$0.731532\pi$
$30$		0			0
$31$	−0.334707	−	0.579730i	−0.0107970	−	0.0187010i	0.860576	−	0.509321i	$-0.170104\pi$
$31$	−0.334707	−	0.579730i	−0.0107970	−	0.0187010i	−0.871373	+	0.490620i	$0.836770\pi$
$32$		0			0
$33$	4.16500	+	23.8432i	0.126212	+	0.722522i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	48.2956			1.30529			0.652644	−	0.757665i	$-0.273660\pi$
$37$	48.2956			1.30529			0.652644	+	0.757665i	$0.273660\pi$
$38$		0			0
$39$	2.23299	−	6.10478i	0.0572562	−	0.156533i
$40$		0			0
$41$	−54.1835	+	31.2829i	−1.32155	+	0.762997i	−0.983976	−	0.178303i	$-0.942939\pi$
$41$	−54.1835	+	31.2829i	−1.32155	+	0.762997i	−0.337573	+	0.941299i	$0.609606\pi$
$42$		0			0
$43$	−35.6645	+	61.7728i	−0.829408	+	1.43658i	0.0690957	+	0.997610i	$0.477989\pi$
$43$	−35.6645	+	61.7728i	−0.829408	+	1.43658i	−0.898503	+	0.438966i	$0.855345\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	17.5663	+	10.1419i	0.373751	+	0.215785i	0.675096	−	0.737730i	$-0.264102\pi$
$47$	17.5663	+	10.1419i	0.373751	+	0.215785i	−0.301345	+	0.953515i	$0.597436\pi$
$48$		0			0
$49$	24.2076	+	41.9288i	0.494033	+	0.855691i
$50$		0			0
$51$	−57.3296	+	47.9496i	−1.12411	+	0.940189i
$52$		0			0
$53$		−	82.8011i		−	1.56228i	−0.624353	−	0.781142i	$-0.714637\pi$
$53$		−	82.8011i		−	1.56228i	0.624353	−	0.781142i	$-0.285363\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−39.9705	−	47.7896i	−0.701237	−	0.838414i
$58$		0			0
$59$	−4.66958	+	2.69598i	−0.0791454	+	0.0456946i	−0.539050	−	0.842273i	$-0.681217\pi$
$59$	−4.66958	+	2.69598i	−0.0791454	+	0.0456946i	0.459905	+	0.887968i	$0.347883\pi$
$60$		0			0
$61$	−41.6097	+	72.0702i	−0.682127	+	1.18148i	0.292203	+	0.956356i	$0.405612\pi$
$61$	−41.6097	+	72.0702i	−0.682127	+	1.18148i	−0.974330	+	0.225122i	$0.927722\pi$
$62$		0			0
$63$	−5.25794	−	4.44060i	−0.0834593	−	0.0704856i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	5.31727	+	9.20978i	0.0793622	+	0.137459i	0.902975	−	0.429693i	$-0.141378\pi$
$67$	5.31727	+	9.20978i	0.0793622	+	0.137459i	−0.823613	+	0.567153i	$0.808045\pi$
$68$		0			0
$69$	47.4464	+	17.3549i	0.687630	+	0.251520i
$70$		0			0
$71$			87.9667i			1.23897i	0.785010	+	0.619484i	$0.212658\pi$
$71$			87.9667i			1.23897i	−0.785010	+	0.619484i	$0.787342\pi$
$72$		0			0
$73$	15.5340			0.212794			0.106397	−	0.994324i	$-0.466069\pi$
$73$	15.5340			0.212794			0.106397	+	0.994324i	$0.466069\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.34302	+	3.08479i	−0.0693898	+	0.0400622i
$78$		0			0
$79$	16.8772	−	29.2322i	0.213635	−	0.370027i	−0.739214	−	0.673470i	$-0.764803\pi$
$79$	16.8772	−	29.2322i	0.213635	−	0.370027i	0.952850	+	0.303443i	$0.0981362\pi$
$80$		0			0
$81$	−75.9368	−	28.1887i	−0.937491	−	0.348009i
$82$		0			0
$83$	−48.2517	−	27.8581i	−0.581346	−	0.335640i	0.180322	−	0.983608i	$-0.442286\pi$
$83$	−48.2517	−	27.8581i	−0.581346	−	0.335640i	−0.761668	+	0.647967i	$0.775619\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−6.05936	−	34.6878i	−0.0696479	−	0.398711i
$88$		0			0
$89$			22.3583i			0.251217i	0.992080	+	0.125608i	$0.0400883\pi$
$89$			22.3583i			0.251217i	−0.992080	+	0.125608i	$0.959912\pi$
$90$		0			0
$91$	1.65692			0.0182079
$92$		0			0
$93$	0.689869	−	1.88603i	0.00741794	−	0.0202799i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	34.4755	−	59.7133i	0.355418	−	0.615601i	−0.631772	−	0.775154i	$-0.717672\pi$
$97$	34.4755	−	59.7133i	0.355418	−	0.615601i	0.987189	+	0.159553i	$0.0510053\pi$
$98$		0			0
$99$	−46.8518	+	55.4754i	−0.473250	+	0.560358i
$100$		0			0
$101$	−48.8636	−	28.2114i	−0.483798	−	0.279321i	0.238200	−	0.971216i	$-0.423443\pi$
$101$	−48.8636	−	28.2114i	−0.483798	−	0.279321i	−0.721998	+	0.691895i	$0.756776\pi$
$102$		0			0
$103$	65.1243	+	112.799i	0.632275	+	1.09513i	0.987086	+	0.160194i	$0.0512119\pi$
$103$	65.1243	+	112.799i	0.632275	+	1.09513i	−0.354811	+	0.934938i	$0.615455\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	109.062i		−	1.01927i	−0.860390	−	0.509635i	$-0.829780\pi$
$107$		−	109.062i		−	1.01927i	0.860390	−	0.509635i	$-0.170220\pi$
$108$		0			0
$109$	−193.169			−1.77219			−0.886095	−	0.463503i	$-0.846592\pi$
$109$	−193.169			−1.77219			−0.886095	+	0.463503i	$0.846592\pi$
$110$		0			0
$111$	92.9544	+	111.138i	0.837427	+	1.00125i
$112$		0			0
$113$	157.797	−	91.1040i	1.39643	−	0.806230i	0.402414	−	0.915458i	$-0.368171\pi$
$113$	157.797	−	91.1040i	1.39643	−	0.806230i	0.994017	+	0.109228i	$0.0348378\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	18.3462	−	6.61126i	0.156805	−	0.0565065i
$118$		0			0
$119$	−16.4983	−	9.52530i	−0.138641	−	0.0800446i
$120$		0			0
$121$	−27.9530	−	48.4160i	−0.231017	−	0.400132i
$122$		0			0
$123$	−176.275	−	64.4775i	−1.43313	−	0.524207i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−166.528			−1.31125			−0.655623	−	0.755088i	$-0.727594\pi$
$127$	−166.528			−1.31125			−0.655623	+	0.755088i	$0.727594\pi$
$128$		0			0
$129$	−210.795	+	36.8223i	−1.63407	+	0.285444i
$130$		0			0
$131$	63.4040	−	36.6063i	0.484000	−	0.279438i	−0.238082	−	0.971245i	$-0.576519\pi$
$131$	63.4040	−	36.6063i	0.484000	−	0.279438i	0.722082	+	0.691807i	$0.243185\pi$
$132$		0			0
$133$	7.94023	−	13.7529i	0.0597010	−	0.103405i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−84.9384	−	49.0392i	−0.619988	−	0.357950i	0.156876	−	0.987618i	$-0.449858\pi$
$137$	−84.9384	−	49.0392i	−0.619988	−	0.357950i	−0.776864	+	0.629668i	$0.783191\pi$
$138$		0			0
$139$	72.1548	+	124.976i	0.519099	+	0.899106i	0.999754	+	0.0221962i	$0.00706586\pi$
$139$	72.1548	+	124.976i	0.519099	+	0.899106i	−0.480654	+	0.876910i	$0.659601\pi$
$140$		0			0
$141$	10.4711	+	59.9437i	0.0742634	+	0.425133i
$142$		0			0
$143$		−	17.4818i		−	0.122250i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−49.8946	+	136.407i	−0.339419	+	0.927938i
$148$		0			0
$149$	6.27949	−	3.62546i	0.0421442	−	0.0243320i	−0.478780	−	0.877935i	$-0.658921\pi$
$149$	6.27949	−	3.62546i	0.0421442	−	0.0243320i	0.520924	+	0.853603i	$0.325587\pi$
$150$		0			0
$151$	−93.7906	+	162.450i	−0.621130	+	1.07583i	0.368146	+	0.929768i	$0.379993\pi$
$151$	−93.7906	+	162.450i	−0.621130	+	1.07583i	−0.989276	+	0.146060i	$0.953341\pi$
$152$		0			0
$153$	−220.684	−	39.6389i	−1.44238	−	0.259077i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	138.219	+	239.402i	0.880375	+	1.52485i	0.850924	+	0.525289i	$0.176043\pi$
$157$	138.219	+	239.402i	0.880375	+	1.52485i	0.0294513	+	0.999566i	$0.490624\pi$
$158$		0			0
$159$	190.542	−	159.367i	1.19838	−	1.00231i
$160$		0			0
$161$			12.8776i			0.0799851i
$162$		0			0
$163$	314.271			1.92804			0.964021	−	0.265826i	$-0.0856447\pi$
$163$	314.271			1.92804			0.964021	+	0.265826i	$0.0856447\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	233.059	−	134.557i	1.39556	−	0.805728i	0.401638	−	0.915799i	$-0.368441\pi$
$167$	233.059	−	134.557i	1.39556	−	0.805728i	0.993924	+	0.110071i	$0.0351078\pi$
$168$		0			0
$169$	82.1525	−	142.292i	0.486110	−	0.841967i
$170$		0			0
$171$	33.0427	−	183.961i	0.193232	−	1.07579i
$172$		0			0
$173$	156.688	+	90.4637i	0.905710	+	0.522912i	0.879048	−	0.476733i	$-0.158179\pi$
$173$	156.688	+	90.4637i	0.905710	+	0.522912i	0.0266614	+	0.999645i	$0.491512\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−15.1915	−	5.55672i	−0.0858278	−	0.0313939i
$178$		0			0
$179$			234.728i			1.31133i	0.755053	+	0.655664i	$0.227611\pi$
$179$			234.728i			1.31133i	−0.755053	+	0.655664i	$0.772389\pi$
$180$		0			0
$181$	118.215			0.653119			0.326560	−	0.945177i	$-0.394111\pi$
$181$	118.215			0.653119			0.326560	+	0.945177i	$0.394111\pi$
$182$		0			0
$183$	−245.934	+	42.9605i	−1.34390	+	0.234757i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−100.499	+	174.070i	−0.537430	+	0.930857i
$188$		0			0
$189$	0.0987989	−	20.6464i	0.000522745	−	0.109240i
$190$		0			0
$191$	−67.1836	−	38.7885i	−0.351747	−	0.203081i	0.313708	−	0.949520i	$-0.398429\pi$
$191$	−67.1836	−	38.7885i	−0.351747	−	0.203081i	−0.665454	+	0.746439i	$0.731762\pi$
$192$		0			0
$193$	97.0806	+	168.149i	0.503008	+	0.871236i	0.999994	+	0.00347712i	$0.00110680\pi$
$193$	97.0806	+	168.149i	0.503008	+	0.871236i	−0.496986	+	0.867759i	$0.665560\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	121.122i		−	0.614835i	−0.951575	−	0.307417i	$-0.900535\pi$
$197$		−	121.122i		−	0.614835i	0.951575	−	0.307417i	$-0.0994647\pi$
$198$		0			0
$199$	305.074			1.53304			0.766518	−	0.642223i	$-0.221988\pi$
$199$	305.074			1.53304			0.766518	+	0.642223i	$0.221988\pi$
$200$		0			0
$201$	−10.9595	+	29.9621i	−0.0545248	+	0.149065i
$202$		0			0
$203$	7.77318	−	4.48785i	0.0382915	−	0.0221076i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	51.3828	+	142.587i	0.248226	+	0.688825i
$208$		0			0
$209$	−145.104	−	83.7757i	−0.694277	−	0.400841i
$210$		0			0
$211$	−99.1129	−	171.669i	−0.469730	−	0.813595i	0.529671	−	0.848203i	$-0.322315\pi$
$211$	−99.1129	−	171.669i	−0.469730	−	0.813595i	−0.999401	+	0.0346075i	$0.988982\pi$
$212$		0			0
$213$	−202.429	+	169.309i	−0.950373	+	0.794878i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.511894			0.00235896
$218$		0			0
$219$	29.8982	+	35.7469i	0.136521	+	0.163228i
$220$		0			0
$221$	46.7487	−	26.9904i	0.211533	−	0.122128i
$222$		0			0
$223$	−99.6112	+	172.532i	−0.446687	+	0.773685i	−0.998168	−	0.0605029i	$-0.980730\pi$
$223$	−99.6112	+	172.532i	−0.446687	+	0.773685i	0.551481	+	0.834187i	$0.314063\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	109.496	+	63.2175i	0.482361	+	0.278491i	0.721400	−	0.692519i	$-0.243499\pi$
$227$	109.496	+	63.2175i	0.482361	+	0.278491i	−0.239039	+	0.971010i	$0.576832\pi$
$228$		0			0
$229$	−69.3360	−	120.094i	−0.302777	−	0.524426i	0.673987	−	0.738744i	$-0.264581\pi$
$229$	−69.3360	−	120.094i	−0.302777	−	0.524426i	−0.976764	+	0.214318i	$0.931247\pi$
$230$		0			0
$231$	−17.3824	−	6.35810i	−0.0752486	−	0.0275242i
$232$		0			0
$233$		−	306.314i		−	1.31465i	−0.753606	−	0.657326i	$-0.771687\pi$
$233$		−	306.314i		−	1.31465i	0.753606	−	0.657326i	$-0.228313\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	99.7527	−	17.4251i	0.420897	−	0.0735235i
$238$		0			0
$239$	325.596	−	187.983i	1.36233	−	0.786539i	0.372393	−	0.928075i	$-0.378537\pi$
$239$	325.596	−	187.983i	1.36233	−	0.786539i	0.989933	+	0.141536i	$0.0452041\pi$
$240$		0			0
$241$	43.1442	−	74.7280i	0.179022	−	0.310075i	−0.762524	−	0.646960i	$-0.776040\pi$
$241$	43.1442	−	74.7280i	0.179022	−	0.310075i	0.941546	+	0.336885i	$0.109373\pi$
$242$		0			0
$243$	−81.2871	−	229.001i	−0.334515	−	0.942390i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	22.4990	+	38.9694i	0.0910891	+	0.157771i
$248$		0			0
$249$	−28.7625	−	164.656i	−0.115512	−	0.661268i
$250$		0			0
$251$		−	280.285i		−	1.11667i	−0.829615	−	0.558336i	$-0.811440\pi$
$251$		−	280.285i		−	1.11667i	0.829615	−	0.558336i	$-0.188560\pi$
$252$		0			0
$253$	135.869			0.537031
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−157.053	+	90.6747i	−0.611102	+	0.352820i	−0.773397	−	0.633922i	$-0.781444\pi$
$257$	−157.053	+	90.6747i	−0.611102	+	0.352820i	0.162295	+	0.986742i	$0.448111\pi$
$258$		0			0
$259$	−18.4656	+	31.9833i	−0.0712957	+	0.123488i
$260$		0			0
$261$	68.1614	−	80.7073i	0.261155	−	0.309223i
$262$		0			0
$263$	12.3265	+	7.11669i	0.0468687	+	0.0270597i	0.523251	−	0.852178i	$-0.324719\pi$
$263$	12.3265	+	7.11669i	0.0468687	+	0.0270597i	−0.476383	+	0.879238i	$0.658052\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−51.4510	+	43.0329i	−0.192701	+	0.161172i
$268$		0			0
$269$		−	90.7714i		−	0.337440i	−0.985664	−	0.168720i	$-0.946037\pi$
$269$		−	90.7714i		−	0.337440i	0.985664	−	0.168720i	$-0.0539634\pi$
$270$		0			0
$271$	219.809			0.811105			0.405553	−	0.914072i	$-0.367079\pi$
$271$	219.809			0.811105			0.405553	+	0.914072i	$0.367079\pi$
$272$		0			0
$273$	3.18906	+	3.81291i	0.0116815	+	0.0139667i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	11.3522	−	19.6626i	0.0409827	−	0.0709841i	−0.844806	−	0.535072i	$-0.820284\pi$
$277$	11.3522	−	19.6626i	0.0409827	−	0.0709841i	0.885789	+	0.464088i	$0.153618\pi$
$278$		0			0
$279$	5.66794	−	2.04251i	0.0203152	−	0.00732081i
$280$		0			0
$281$	136.094	+	78.5742i	0.484322	+	0.279623i	0.722216	−	0.691668i	$-0.243124\pi$
$281$	136.094	+	78.5742i	0.484322	+	0.279623i	−0.237894	+	0.971291i	$0.576457\pi$
$282$		0			0
$283$	201.880	+	349.667i	0.713357	+	1.23557i	0.963590	+	0.267385i	$0.0861596\pi$
$283$	201.880	+	349.667i	0.713357	+	1.23557i	−0.250233	+	0.968186i	$0.580507\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	47.8434i		−	0.166702i
$288$		0			0
$289$	−331.650			−1.14758
$290$		0			0
$291$	203.768	−	35.5947i	0.700232	−	0.122318i
$292$		0			0
$293$	340.324	−	196.486i	1.16152	−	0.670601i	0.209849	−	0.977734i	$-0.432703\pi$
$293$	340.324	−	196.486i	1.16152	−	0.670601i	0.951667	+	0.307133i	$0.0993696\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−217.836	−	1.04241i	−0.733454	−	0.00350979i
$298$		0			0
$299$	−31.6006	−	18.2446i	−0.105688	−	0.0610188i
$300$		0			0
$301$	−27.2723	−	47.2370i	−0.0906057	−	0.156934i
$302$		0			0
$303$	−29.1272	−	166.744i	−0.0961295	−	0.550309i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	349.575			1.13868			0.569340	−	0.822102i	$-0.307199\pi$
$307$	349.575			1.13868			0.569340	+	0.822102i	$0.307199\pi$
$308$		0			0
$309$	−134.228	+	366.967i	−0.434396	+	1.18760i
$310$		0			0
$311$	340.304	−	196.474i	1.09422	−	0.631751i	0.159526	−	0.987194i	$-0.449003\pi$
$311$	340.304	−	196.474i	1.09422	−	0.631751i	0.934698	+	0.355443i	$0.115670\pi$
$312$		0			0
$313$	−190.027	+	329.137i	−0.607116	+	1.05156i	0.384597	+	0.923084i	$0.374340\pi$
$313$	−190.027	+	329.137i	−0.607116	+	1.05156i	−0.991713	+	0.128471i	$0.958993\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−152.907	−	88.2809i	−0.482356	−	0.278489i	0.239042	−	0.971009i	$-0.423167\pi$
$317$	−152.907	−	88.2809i	−0.482356	−	0.278489i	−0.721398	+	0.692521i	$0.756500\pi$
$318$		0			0
$319$	−47.3503	−	82.0132i	−0.148434	−	0.257095i
$320$		0			0
$321$	250.974	−	209.911i	0.781851	−	0.653928i
$322$		0			0
$323$		−	517.370i		−	1.60176i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−371.791	−	444.521i	−1.13698	−	1.35939i
$328$		0			0
$329$	−13.4328	+	7.75541i	−0.0408291	+	0.0235727i
$330$		0			0
$331$	325.552	−	563.872i	0.983540	−	1.70354i	0.335288	−	0.942116i	$-0.391167\pi$
$331$	325.552	−	563.872i	0.983540	−	1.70354i	0.648253	−	0.761425i	$-0.275500\pi$
$332$		0			0
$333$	−76.8432	+	427.814i	−0.230760	+	1.28473i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−95.8762	−	166.063i	−0.284499	−	0.492767i	0.687988	−	0.725722i	$-0.258494\pi$
$337$	−95.8762	−	166.063i	−0.284499	−	0.492767i	−0.972488	+	0.232955i	$0.925161\pi$
$338$		0			0
$339$	513.360	+	187.775i	1.51434	+	0.553910i
$340$		0			0
$341$		−	5.40089i		−	0.0158384i
$342$		0			0
$343$	−74.4925			−0.217179
$344$		0			0
$345$		0			0
$346$		0			0
$347$	251.512	−	145.210i	0.724817	−	0.418473i	−0.0917059	−	0.995786i	$-0.529232\pi$
$347$	251.512	−	145.210i	0.724817	−	0.418473i	0.816523	+	0.577313i	$0.195899\pi$
$348$		0			0
$349$	−26.0785	+	45.1693i	−0.0747235	+	0.129425i	−0.900966	−	0.433890i	$-0.857141\pi$
$349$	−26.0785	+	45.1693i	−0.0747235	+	0.129425i	0.826243	+	0.563315i	$0.190474\pi$
$350$		0			0
$351$	50.5247	+	29.4937i	0.143945	+	0.0840276i
$352$		0			0
$353$	−508.816	−	293.765i	−1.44140	−	0.832195i	−0.443461	−	0.896294i	$-0.646250\pi$
$353$	−508.816	−	293.765i	−1.44140	−	0.832195i	−0.997944	+	0.0640982i	$0.979583\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−9.83452	−	56.2993i	−0.0275477	−	0.157701i
$358$		0			0
$359$			112.104i			0.312268i	0.987736	+	0.156134i	$0.0499031\pi$
$359$			112.104i			0.312268i	−0.987736	+	0.156134i	$0.950097\pi$
$360$		0			0
$361$	70.2762			0.194671
$362$		0			0
$363$	57.6143	−	157.512i	0.158717	−	0.433917i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−27.3260	+	47.3300i	−0.0744577	+	0.128965i	−0.900850	−	0.434130i	$-0.857056\pi$
$367$	−27.3260	+	47.3300i	−0.0744577	+	0.128965i	0.826393	+	0.563094i	$0.190389\pi$
$368$		0			0
$369$	−190.900	−	529.745i	−0.517343	−	1.43562i
$370$		0			0
$371$	54.8342	+	31.6586i	0.147801	+	0.0853331i
$372$		0			0
$373$	−13.7449	−	23.8068i	−0.0368495	−	0.0638253i	0.847012	−	0.531573i	$-0.178399\pi$
$373$	−13.7449	−	23.8068i	−0.0368495	−	0.0638253i	−0.883862	+	0.467748i	$0.845066\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			25.4330i			0.0674616i
$378$		0			0
$379$	396.721			1.04676			0.523379	−	0.852100i	$-0.324671\pi$
$379$	396.721			1.04676			0.523379	+	0.852100i	$0.324671\pi$
$380$		0			0
$381$	−320.516	−	383.216i	−0.841250	−	1.00582i
$382$		0			0
$383$	564.674	−	326.015i	1.47435	−	0.851214i	0.474763	−	0.880113i	$-0.342534\pi$
$383$	564.674	−	326.015i	1.47435	−	0.851214i	0.999582	+	0.0288996i	$0.00920030\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−490.452	−	414.212i	−1.26732	−	1.07031i
$388$		0			0
$389$	−465.136	−	268.546i	−1.19572	−	0.690350i	−0.236123	−	0.971723i	$-0.575877\pi$
$389$	−465.136	−	268.546i	−1.19572	−	0.690350i	−0.959599	+	0.281373i	$0.909210\pi$
$390$		0			0
$391$	209.770	+	363.332i	0.536495	+	0.929237i
$392$		0			0
$393$	206.272	+	75.4497i	0.524865	+	0.191984i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	428.508			1.07937			0.539683	−	0.841868i	$-0.318544\pi$
$397$	428.508			1.07937			0.539683	+	0.841868i	$0.318544\pi$
$398$		0			0
$399$	46.9307	−	8.19799i	0.117621	−	0.0205463i
$400$		0			0
$401$	−5.61792	+	3.24351i	−0.0140098	+	0.00808855i	−0.506989	−	0.861953i	$-0.669241\pi$
$401$	−5.61792	+	3.24351i	−0.0140098	+	0.00808855i	0.492979	+	0.870041i	$0.335908\pi$
$402$		0			0
$403$	−0.725238	+	1.25615i	−0.00179960	+	0.00311699i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	337.450	+	194.827i	0.829115	+	0.478690i
$408$		0			0
$409$	67.3741	+	116.695i	0.164729	+	0.285319i	0.936559	−	0.350510i	$-0.113992\pi$
$409$	67.3741	+	116.695i	0.164729	+	0.285319i	−0.771830	+	0.635829i	$0.780658\pi$
$410$		0			0
$411$	−50.6311	−	289.846i	−0.123190	−	0.705222i
$412$		0			0
$413$		−	4.12318i		−	0.00998349i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−148.719	+	406.583i	−0.356641	+	0.975020i
$418$		0			0
$419$	442.857	−	255.683i	1.05694	−	0.610223i	0.132354	−	0.991203i	$-0.457747\pi$
$419$	442.857	−	255.683i	1.05694	−	0.610223i	0.924583	+	0.380980i	$0.124413\pi$
$420$		0			0
$421$	−33.6290	+	58.2471i	−0.0798788	+	0.138354i	−0.903197	−	0.429225i	$-0.858787\pi$
$421$	−33.6290	+	58.2471i	−0.0798788	+	0.138354i	0.823319	+	0.567579i	$0.192120\pi$
$422$		0			0
$423$	−117.789	+	139.470i	−0.278461	+	0.329716i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−31.8186	−	55.1114i	−0.0745165	−	0.129066i
$428$		0			0
$429$	40.2292	−	33.6471i	0.0937744	−	0.0784315i
$430$		0			0
$431$			786.579i			1.82501i	0.409066	+	0.912505i	$0.365854\pi$
$431$			786.579i			1.82501i	−0.409066	+	0.912505i	$0.634146\pi$
$432$		0			0
$433$	−279.636			−0.645810			−0.322905	−	0.946431i	$-0.604659\pi$
$433$	−279.636			−0.645810			−0.322905	+	0.946431i	$0.604659\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−302.871	+	174.863i	−0.693069	+	0.400143i
$438$		0			0
$439$	−125.374	+	217.154i	−0.285590	+	0.494657i	−0.972752	−	0.231847i	$-0.925523\pi$
$439$	−125.374	+	217.154i	−0.285590	+	0.494657i	0.687162	+	0.726504i	$0.258856\pi$
$440$		0			0
$441$	−409.932	+	147.724i	−0.929552	+	0.334975i
$442$		0			0
$443$	406.996	+	234.979i	0.918728	+	0.530428i	0.883229	−	0.468942i	$-0.155365\pi$
$443$	406.996	+	234.979i	0.918728	+	0.530428i	0.0354987	+	0.999370i	$0.488698\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	20.4290	+	7.47249i	0.0457026	+	0.0167170i
$448$		0			0
$449$			471.154i			1.04934i	0.851306	+	0.524670i	$0.175811\pi$
$449$			471.154i			1.04934i	−0.851306	+	0.524670i	$0.824189\pi$
$450$		0			0
$451$	−504.786			−1.11926
$452$		0			0
$453$	−554.349	+	96.8353i	−1.22373	+	0.213764i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	270.196	−	467.993i	0.591239	−	1.02406i	−0.402827	−	0.915276i	$-0.631972\pi$
$457$	270.196	−	467.993i	0.591239	−	1.02406i	0.994066	−	0.108780i	$-0.0346943\pi$
$458$		0			0
$459$	−333.532	−	584.132i	−0.726649	−	1.27262i
$460$		0			0
$461$	−761.747	−	439.795i	−1.65238	−	0.954002i	−0.976090	−	0.217367i	$-0.930253\pi$
$461$	−761.747	−	439.795i	−1.65238	−	0.954002i	−0.676290	−	0.736635i	$-0.736414\pi$
$462$		0			0
$463$	140.953	+	244.138i	0.304434	+	0.527295i	0.977135	−	0.212619i	$-0.0681993\pi$
$463$	140.953	+	244.138i	0.304434	+	0.527295i	−0.672701	+	0.739914i	$0.734866\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			252.452i			0.540582i	0.962779	+	0.270291i	$0.0871199\pi$
$467$			252.452i			0.540582i	−0.962779	+	0.270291i	$0.912880\pi$
$468$		0			0
$469$	−8.13212			−0.0173393
$470$		0			0
$471$	−284.885	+	778.846i	−0.604851	+	1.65360i
$472$		0			0
$473$	−498.388	+	287.744i	−1.05367	+	0.608339i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	733.472	+	131.745i	1.53768	+	0.276195i
$478$		0			0
$479$	−84.7130	−	48.9091i	−0.176854	−	0.102107i	0.408960	−	0.912552i	$-0.365892\pi$
$479$	−84.7130	−	48.9091i	−0.176854	−	0.102107i	−0.585814	+	0.810446i	$0.699225\pi$
$480$		0			0
$481$	−52.3231	−	90.6263i	−0.108780	−	0.188412i
$482$		0			0
$483$	−29.6340	+	24.7854i	−0.0613540	+	0.0513156i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−235.388			−0.483344			−0.241672	−	0.970358i	$-0.577696\pi$
$487$	−235.388			−0.483344			−0.241672	+	0.970358i	$0.577696\pi$
$488$		0			0
$489$	604.875	+	723.202i	1.23696	+	1.47894i
$490$		0			0
$491$	31.7383	−	18.3241i	0.0646401	−	0.0373200i	−0.467332	−	0.884082i	$-0.654785\pi$
$491$	31.7383	−	18.3241i	0.0646401	−	0.0373200i	0.531972	+	0.846762i	$0.321451\pi$
$492$		0			0
$493$	146.210	−	253.243i	0.296571	−	0.513677i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−58.2551	−	33.6336i	−0.117214	−	0.0676733i
$498$		0			0
$499$	−262.287	−	454.294i	−0.525625	−	0.910409i	−0.999554	−	0.0298464i	$-0.990498\pi$
$499$	−262.287	−	454.294i	−0.525625	−	0.910409i	0.473929	−	0.880563i	$-0.342835\pi$
$500$		0			0
$501$	758.209	+	277.336i	1.51339	+	0.553565i
$502$		0			0
$503$			37.5712i			0.0746943i	0.999302	+	0.0373471i	$0.0118907\pi$
$503$			37.5712i			0.0746943i	−0.999302	+	0.0373471i	$0.988109\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	485.563	−	84.8194i	0.957717	−	0.167297i
$508$		0			0
$509$	540.966	−	312.327i	1.06280	−	0.613609i	0.136596	−	0.990627i	$-0.456384\pi$
$509$	540.966	−	312.327i	1.06280	−	0.613609i	0.926206	+	0.377018i	$0.123050\pi$
$510$		0			0
$511$	−5.93934	+	10.2872i	−0.0116230	+	0.0201316i
$512$		0			0
$513$	486.929	−	278.030i	0.949179	−	0.541969i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	81.8258	+	141.726i	0.158270	+	0.274132i
$518$		0			0
$519$	93.4004	+	534.686i	0.179962	+	1.03022i
$520$		0			0
$521$		−	7.40805i		−	0.0142189i	−0.999975	−	0.00710945i	$-0.997737\pi$
$521$		−	7.40805i		−	0.0142189i	0.999975	−	0.00710945i	$-0.00226303\pi$
$522$		0			0
$523$	−438.767			−0.838943			−0.419472	−	0.907768i	$-0.637785\pi$
$523$	−438.767			−0.838943			−0.419472	+	0.907768i	$0.637785\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	14.4427	−	8.33851i	0.0274055	−	0.0158226i
$528$		0			0
$529$	−122.702	+	212.527i	−0.231952	+	0.401752i
$530$		0			0
$531$	−16.4519	−	45.6538i	−0.0309828	−	0.0859771i
$532$		0			0
$533$	117.404	+	67.7832i	0.220270	+	0.127173i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−540.157	+	451.779i	−1.00588	+	0.841302i
$538$		0			0
$539$			390.618i			0.724709i
$540$		0			0
$541$	−566.949			−1.04797			−0.523983	−	0.851729i	$-0.675554\pi$
$541$	−566.949			−1.04797			−0.523983	+	0.851729i	$0.675554\pi$
$542$		0			0
$543$	227.527	+	272.036i	0.419019	+	0.500988i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−488.314	+	845.784i	−0.892713	+	1.54622i	−0.0561024	+	0.998425i	$0.517867\pi$
$547$	−488.314	+	845.784i	−0.892713	+	1.54622i	−0.836610	+	0.547799i	$0.815466\pi$
$548$		0			0
$549$	−572.210	−	483.260i	−1.04228	−	0.880255i
$550$		0			0
$551$	211.101	+	121.879i	0.383124	+	0.221197i
$552$		0			0
$553$	12.9058	+	22.3535i	0.0233378	+	0.0404223i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	55.7939i		−	0.100168i	−0.998745	−	0.0500842i	$-0.984051\pi$
$557$		−	55.7939i		−	0.100168i	0.998745	−	0.0500842i	$-0.0159490\pi$
$558$		0			0
$559$	154.555			0.276484
$560$		0			0
$561$	−594.002	+	103.762i	−1.05883	+	0.184959i
$562$		0			0
$563$	−306.442	+	176.924i	−0.544302	+	0.314253i	−0.746821	−	0.665025i	$-0.768421\pi$
$563$	−306.442	+	176.924i	−0.544302	+	0.314253i	0.202519	+	0.979278i	$0.435087\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	47.7018	−	39.5106i	0.0841301	−	0.0696837i
$568$		0			0
$569$	−419.282	−	242.072i	−0.736875	−	0.425435i	0.0840571	−	0.996461i	$-0.473212\pi$
$569$	−419.282	−	242.072i	−0.736875	−	0.425435i	−0.820932	+	0.571026i	$0.806546\pi$
$570$		0			0
$571$	469.887	+	813.868i	0.822920	+	1.42534i	0.903499	+	0.428591i	$0.140990\pi$
$571$	469.887	+	813.868i	0.822920	+	1.42534i	−0.0805791	+	0.996748i	$0.525677\pi$
$572$		0			0
$573$	−40.0476	−	229.259i	−0.0698912	−	0.400103i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−637.613			−1.10505			−0.552524	−	0.833497i	$-0.686335\pi$
$577$	−637.613			−1.10505			−0.552524	+	0.833497i	$0.686335\pi$
$578$		0			0
$579$	−200.094	+	547.037i	−0.345585	+	0.944796i
$580$		0			0
$581$	36.8976	−	21.3028i	0.0635071	−	0.0366658i
$582$		0			0
$583$	334.023	−	578.545i	0.572938	−	0.992358i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−63.9363	−	36.9136i	−0.108920	−	0.0628853i	0.444550	−	0.895754i	$-0.353364\pi$
$587$	−63.9363	−	36.9136i	−0.108920	−	0.0628853i	−0.553471	+	0.832869i	$0.686697\pi$
$588$		0			0
$589$	6.95093	+	12.0394i	0.0118012	+	0.0204403i
$590$		0			0
$591$	278.728	−	233.124i	0.471620	−	0.394456i
$592$		0			0
$593$			804.091i			1.35597i	0.735075	+	0.677986i	$0.237147\pi$
$593$			804.091i			1.35597i	−0.735075	+	0.677986i	$0.762853\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	587.174	+	702.038i	0.983542	+	1.17594i
$598$		0			0
$599$	−147.274	+	85.0287i	−0.245866	+	0.141951i	−0.617870	−	0.786280i	$-0.712004\pi$
$599$	−147.274	+	85.0287i	−0.245866	+	0.141951i	0.372004	+	0.928231i	$0.378671\pi$
$600$		0			0
$601$	−202.298	+	350.390i	−0.336602	+	0.583012i	−0.983791	−	0.179318i	$-0.942611\pi$
$601$	−202.298	+	350.390i	−0.336602	+	0.583012i	0.647189	+	0.762329i	$0.275944\pi$
$602$		0			0
$603$	−90.0427	+	32.4479i	−0.149325	+	0.0538108i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	312.235	+	540.806i	0.514390	+	0.890949i	0.999861	+	0.0166965i	$0.00531491\pi$
$607$	312.235	+	540.806i	0.514390	+	0.890949i	−0.485471	+	0.874253i	$0.661352\pi$
$608$		0			0
$609$	25.2885	+	9.24995i	0.0415246	+	0.0151888i
$610$		0			0
$611$		−	43.9506i		−	0.0719323i
$612$		0			0
$613$	1080.05			1.76191			0.880956	−	0.473199i	$-0.156901\pi$
$613$	1080.05			1.76191			0.880956	+	0.473199i	$0.156901\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	256.436	−	148.053i	0.415617	−	0.239957i	−0.277583	−	0.960702i	$-0.589533\pi$
$617$	256.436	−	148.053i	0.415617	−	0.239957i	0.693200	+	0.720745i	$0.256200\pi$
$618$		0			0
$619$	−168.651	+	292.111i	−0.272457	+	0.471909i	−0.969490	−	0.245130i	$-0.921169\pi$
$619$	−168.651	+	292.111i	−0.272457	+	0.471909i	0.697034	+	0.717038i	$0.254503\pi$
$620$		0			0
$621$	−229.226	+	392.679i	−0.369123	+	0.632333i
$622$		0			0
$623$	−14.8066	−	8.54858i	−0.0237666	−	0.0137216i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−86.4953	−	495.157i	−0.137951	−	0.789723i
$628$		0			0
$629$			1203.18i			1.91285i
$630$		0			0
$631$	−449.564			−0.712463			−0.356232	−	0.934398i	$-0.615939\pi$
$631$	−449.564			−0.712463			−0.356232	+	0.934398i	$0.615939\pi$
$632$		0			0
$633$	204.283	−	558.489i	0.322722	−	0.882289i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	52.4527	−	90.8507i	0.0823433	−	0.142623i
$638$		0			0
$639$	−779.230	−	139.964i	−1.21945	−	0.219036i
$640$		0			0
$641$	328.996	+	189.946i	0.513254	+	0.296327i	0.734170	−	0.678966i	$-0.237571\pi$
$641$	328.996	+	189.946i	0.513254	+	0.296327i	−0.220916	+	0.975293i	$0.570905\pi$
$642$		0			0
$643$	−214.358	−	371.279i	−0.333372	−	0.577417i	0.649799	−	0.760106i	$-0.274853\pi$
$643$	−214.358	−	371.279i	−0.333372	−	0.577417i	−0.983171	+	0.182689i	$0.941520\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	485.842i		−	0.750916i	−0.926840	−	0.375458i	$-0.877486\pi$
$647$		−	485.842i		−	0.750916i	0.926840	−	0.375458i	$-0.122514\pi$
$648$		0			0
$649$	−43.5028			−0.0670305
$650$		0			0
$651$	0.985240	+	1.17797i	0.00151343	+	0.00180948i
$652$		0			0
$653$	−657.636	+	379.686i	−1.00710	+	0.581449i	−0.910341	−	0.413859i	$-0.864181\pi$
$653$	−657.636	+	379.686i	−1.00710	+	0.581449i	−0.0967581	+	0.995308i	$0.530847\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−24.7161	+	137.604i	−0.0376197	+	0.209442i
$658$		0			0
$659$	−874.981	−	505.171i	−1.32774	−	0.766572i	−0.342791	−	0.939412i	$-0.611372\pi$
$659$	−874.981	−	505.171i	−1.32774	−	0.766572i	−0.984950	+	0.172840i	$0.944706\pi$
$660$		0			0
$661$	−59.7150	−	103.429i	−0.0903404	−	0.156474i	0.817314	−	0.576193i	$-0.195462\pi$
$661$	−59.7150	−	103.429i	−0.0903404	−	0.156474i	−0.907654	+	0.419718i	$0.862129\pi$
$662$		0			0
$663$	152.087	+	55.6302i	0.229393	+	0.0839067i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−197.666			−0.296351
$668$		0			0
$669$	−588.752	+	102.845i	−0.880048	+	0.153729i
$670$		0			0
$671$	−581.468	+	335.711i	−0.866570	+	0.500314i
$672$		0			0
$673$	143.089	−	247.838i	0.212614	−	0.368258i	−0.739918	−	0.672697i	$-0.765136\pi$
$673$	143.089	−	247.838i	0.212614	−	0.368258i	0.952532	+	0.304439i	$0.0984690\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−679.115	−	392.087i	−1.00312	−	0.579154i	−0.0939532	−	0.995577i	$-0.529950\pi$
$677$	−679.115	−	392.087i	−1.00312	−	0.579154i	−0.909171	+	0.416422i	$0.863284\pi$
$678$		0			0
$679$	26.3631	+	45.6622i	0.0388263	+	0.0672492i
$680$		0			0
$681$	65.2697	+	373.647i	0.0958439	+	0.548674i
$682$		0			0
$683$			829.221i			1.21409i	0.794669	+	0.607043i	$0.207645\pi$
$683$			829.221i			1.21409i	−0.794669	+	0.607043i	$0.792355\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	142.909	−	390.700i	0.208019	−	0.568704i
$688$		0			0
$689$	−155.375	+	89.7060i	−0.225508	+	0.130197i
$690$		0			0
$691$	85.0309	−	147.278i	0.123055	−	0.213137i	−0.797916	−	0.602769i	$-0.794064\pi$
$691$	85.0309	−	147.278i	0.123055	−	0.213137i	0.920971	+	0.389631i	$0.127398\pi$
$692$		0			0
$693$	−18.8245	−	52.2379i	−0.0271638	−	0.0753794i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−779.345	−	1349.87i	−1.11814	−	1.93668i
$698$		0			0
$699$	704.892	−	589.561i	1.00843	−	0.843435i
$700$		0			0
$701$			780.669i			1.11365i	0.830630	+	0.556825i	$0.187981\pi$
$701$			780.669i			1.11365i	−0.830630	+	0.556825i	$0.812019\pi$
$702$		0			0
$703$	−1002.96			−1.42669
$704$		0			0
$705$		0			0
$706$		0			0
$707$	37.3655	−	21.5730i	0.0528508	−	0.0305134i
$708$		0			0
$709$	242.396	−	419.842i	0.341884	−	0.592161i	−0.642898	−	0.765952i	$-0.722268\pi$
$709$	242.396	−	419.842i	0.341884	−	0.592161i	0.984783	+	0.173790i	$0.0556015\pi$
$710$		0			0
$711$	232.092	+	196.014i	0.326431	+	0.275687i
$712$		0			0
$713$	−9.76281	−	5.63656i	−0.0136926	−	0.00790542i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1059.26	+	387.454i	1.47735	+	0.540382i
$718$		0			0
$719$			772.608i			1.07456i	0.843404	+	0.537280i	$0.180548\pi$
$719$			772.608i			1.07456i	−0.843404	+	0.537280i	$0.819452\pi$
$720$		0			0
$721$	−99.5998			−0.138141
$722$		0			0
$723$	255.004	−	44.5448i	0.352702	−	0.0616110i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−171.192	+	296.513i	−0.235477	+	0.407859i	−0.959411	−	0.282011i	$-0.908999\pi$
$727$	−171.192	+	296.513i	−0.235477	+	0.407859i	0.723934	+	0.689869i	$0.242332\pi$
$728$		0			0
$729$	370.525	−	627.815i	0.508265	−	0.861201i
$730$		0			0
$731$	−1538.94	−	888.505i	−2.10525	−	1.21547i
$732$		0			0
$733$	−572.225	−	991.122i	−0.780661	−	1.35214i	−0.931557	−	0.363595i	$-0.881549\pi$
$733$	−572.225	−	991.122i	−0.780661	−	1.35214i	0.150896	−	0.988550i	$-0.451784\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			85.8003i			0.116418i
$738$		0			0
$739$	310.428			0.420065			0.210032	−	0.977694i	$-0.432643\pi$
$739$	310.428			0.420065			0.210032	+	0.977694i	$0.432643\pi$
$740$		0			0
$741$	−46.3730	+	126.779i	−0.0625816	+	0.171092i
$742$		0			0
$743$	−70.6999	+	40.8186i	−0.0951546	+	0.0549375i	−0.546822	−	0.837249i	$-0.684163\pi$
$743$	−70.6999	+	40.8186i	−0.0951546	+	0.0549375i	0.451668	+	0.892186i	$0.350829\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	323.548	−	383.100i	0.433129	−	0.512852i
$748$		0			0
$749$	72.2253	+	41.6993i	0.0964290	+	0.0556733i
$750$		0			0
$751$	160.813	+	278.536i	0.214131	+	0.370886i	0.953003	−	0.302959i	$-0.0979746\pi$
$751$	160.813	+	278.536i	0.214131	+	0.370886i	−0.738872	+	0.673846i	$0.764641\pi$
$752$		0			0
$753$	644.993	−	539.463i	0.856565	−	0.716418i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	215.279			0.284384			0.142192	−	0.989839i	$-0.454585\pi$
$757$	215.279			0.284384			0.142192	+	0.989839i	$0.454585\pi$
$758$		0			0
$759$	261.506	+	312.662i	0.344540	+	0.411940i
$760$		0			0
$761$	128.185	−	74.0074i	0.168442	−	0.0972502i	−0.413409	−	0.910546i	$-0.635662\pi$
$761$	128.185	−	74.0074i	0.168442	−	0.0972502i	0.581851	+	0.813295i	$0.302329\pi$
$762$		0			0
$763$	73.8571	−	127.924i	0.0967983	−	0.167660i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	10.1180	+	5.84161i	0.0131916	+	0.00761618i
$768$		0			0
$769$	271.200	+	469.732i	0.352666	+	0.610835i	0.986716	−	0.162457i	$-0.0519419\pi$
$769$	271.200	+	469.732i	0.352666	+	0.610835i	−0.634050	+	0.773292i	$0.718609\pi$
$770$		0			0
$771$	−510.941	−	186.891i	−0.662699	−	0.242400i
$772$		0			0
$773$			441.852i			0.571607i	0.958288	+	0.285803i	$0.0922604\pi$
$773$			441.852i			0.571607i	−0.958288	+	0.285803i	$0.907740\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−109.141	+	19.0650i	−0.140464	+	0.0245367i
$778$		0			0
$779$	1125.24	−	649.657i	1.44447	−	0.833963i
$780$		0			0
$781$	−354.861	+	614.638i	−0.454368	+	0.786988i
$782$		0			0
$783$	316.914	+	1.51652i	0.404743	+	0.00193681i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−239.559	−	414.928i	−0.304395	−	0.527228i	0.672731	−	0.739887i	$-0.265121\pi$
$787$	−239.559	−	414.928i	−0.304395	−	0.527228i	−0.977126	+	0.212659i	$0.931788\pi$
$788$		0			0
$789$	7.34772	+	42.0632i	0.00931270	+	0.0533121i
$790$		0			0
$791$			139.333i			0.176147i
$792$		0			0
$793$	180.319			0.227388
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−501.920	+	289.784i	−0.629762	+	0.363593i	−0.780660	−	0.624956i	$-0.785117\pi$
$797$	−501.920	+	289.784i	−0.629762	+	0.363593i	0.150898	+	0.988549i	$0.451783\pi$
$798$		0			0
$799$	−252.664	+	437.626i	−0.316225	+	0.547718i
$800$		0			0
$801$	−198.055	−	35.5743i	−0.247260	−	0.0444124i
$802$		0			0
$803$	108.538	+	62.6647i	0.135166	+	0.0780382i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	208.884	−	174.707i	0.258840	−	0.216490i
$808$		0			0
$809$		−	906.264i		−	1.12023i	−0.828416	−	0.560114i	$-0.810757\pi$
$809$		−	906.264i		−	1.12023i	0.828416	−	0.560114i	$-0.189243\pi$
$810$		0			0
$811$	−593.696			−0.732055			−0.366027	−	0.930604i	$-0.619282\pi$
$811$	−593.696			−0.732055			−0.366027	+	0.930604i	$0.619282\pi$
$812$		0			0
$813$	423.066	+	505.827i	0.520377	+	0.622173i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	740.652	−	1282.85i	0.906551	−	1.57019i
$818$		0			0
$819$	−2.63632	+	14.6774i	−0.00321895	+	0.0179211i
$820$		0			0
$821$	1053.43	+	608.200i	1.28311	+	0.740804i	0.977416	−	0.211326i	$-0.0677780\pi$
$821$	1053.43	+	608.200i	1.28311	+	0.740804i	0.305695	+	0.952130i	$0.401111\pi$
$822$		0			0
$823$	−579.655	−	1003.99i	−0.704320	−	1.21992i	−0.966936	−	0.255017i	$-0.917919\pi$
$823$	−579.655	−	1003.99i	−0.704320	−	1.21992i	0.262617	−	0.964900i	$-0.415415\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			676.065i			0.817491i	0.912648	+	0.408746i	$0.134034\pi$
$827$			676.065i			0.817491i	−0.912648	+	0.408746i	$0.865966\pi$
$828$		0			0
$829$	528.868			0.637959			0.318979	−	0.947762i	$-0.396660\pi$
$829$	528.868			0.637959			0.318979	+	0.947762i	$0.396660\pi$
$830$		0			0
$831$	67.0973	−	11.7207i	0.0807428	−	0.0141044i
$832$		0			0
$833$	−1044.57	+	603.081i	−1.25398	+	0.723987i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	15.6093	+	9.11189i	0.0186491	+	0.0108864i
$838$		0			0
$839$	453.025	+	261.554i	0.539958	+	0.311745i	0.745062	−	0.666995i	$-0.232420\pi$
$839$	453.025	+	261.554i	0.539958	+	0.311745i	−0.205104	+	0.978740i	$0.565753\pi$
$840$		0			0
$841$	−351.613	−	609.012i	−0.418090	−	0.724152i
$842$		0			0
$843$	81.1249	+	464.413i	0.0962336	+	0.550905i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	42.7508			0.0504732
$848$		0			0
$849$	−416.097	+	1137.57i	−0.490103	+	1.33989i
$850$		0			0
$851$	704.349	−	406.656i	0.827672	−	0.477857i
$852$		0			0
$853$	522.627	−	905.217i	0.612693	−	1.06122i	−0.378091	−	0.925768i	$-0.623419\pi$
$853$	522.627	−	905.217i	0.612693	−	1.06122i	0.990785	−	0.135448i	$-0.0432472\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	612.298	+	353.510i	0.714467	+	0.412497i	0.812713	−	0.582665i	$-0.197990\pi$
$857$	612.298	+	353.510i	0.714467	+	0.412497i	−0.0982461	+	0.995162i	$0.531323\pi$
$858$		0			0
$859$	−661.447	−	1145.66i	−0.770020	−	1.33371i	−0.937551	−	0.347847i	$-0.886913\pi$
$859$	−661.447	−	1145.66i	−0.770020	−	1.33371i	0.167532	−	0.985867i	$-0.446420\pi$
$860$		0			0
$861$	110.097	−	92.0839i	0.127872	−	0.106950i
$862$		0			0
$863$			559.626i			0.648466i	0.945977	+	0.324233i	$0.105106\pi$
$863$			559.626i			0.648466i	−0.945977	+	0.324233i	$0.894894\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−638.325	−	763.195i	−0.736246	−	0.880271i
$868$		0			0
$869$	235.848	−	136.167i	0.271401	−	0.156693i
$870$		0			0
$871$	11.5214	−	19.9556i	0.0132277	−	0.0229111i
$872$		0			0
$873$	474.101	+	400.402i	0.543071	+	0.458651i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−246.933	−	427.700i	−0.281565	−	0.487685i	0.690205	−	0.723614i	$-0.257520\pi$
$877$	−246.933	−	427.700i	−0.281565	−	0.487685i	−0.971770	+	0.235928i	$0.924187\pi$
$878$		0			0
$879$	1107.17	+	404.980i	1.25958	+	0.460728i
$880$		0			0
$881$		−	765.716i		−	0.869145i	−0.900637	−	0.434572i	$-0.856900\pi$
$881$		−	765.716i		−	0.869145i	0.900637	−	0.434572i	$-0.143100\pi$
$882$		0			0
$883$	−1647.52			−1.86582			−0.932908	−	0.360115i	$-0.882737\pi$
$883$	−1647.52			−1.86582			−0.932908	+	0.360115i	$0.882737\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−265.193	+	153.109i	−0.298977	+	0.172615i	−0.641983	−	0.766719i	$-0.721888\pi$
$887$	−265.193	+	153.109i	−0.298977	+	0.172615i	0.343006	+	0.939333i	$0.388555\pi$
$888$		0			0
$889$	63.6713	−	110.282i	0.0716212	−	0.124052i
$890$		0			0
$891$	−416.869	−	503.291i	−0.467866	−	0.564861i
$892$		0			0
$893$	−364.803	−	210.619i	−0.408514	−	0.235855i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−18.8369	−	107.835i	−0.0209999	−	0.120217i
$898$		0			0
$899$			7.85738i			0.00874013i
$900$		0			0
$901$	2062.81			2.28947
$902$		0			0
$903$	56.2113	−	153.676i	0.0622495	−	0.170184i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−286.265	+	495.826i	−0.315617	+	0.546665i	−0.979569	−	0.201111i	$-0.935545\pi$
$907$	−286.265	+	495.826i	−0.315617	+	0.546665i	0.663951	+	0.747776i	$0.268878\pi$
$908$		0			0
$909$	327.650	−	387.958i	0.360451	−	0.426797i
$910$		0			0
$911$	−223.086	−	128.799i	−0.244880	−	0.141382i	0.372538	−	0.928017i	$-0.378488\pi$
$911$	−223.086	−	128.799i	−0.244880	−	0.141382i	−0.617418	+	0.786636i	$0.711821\pi$
$912$		0			0
$913$	−224.762	−	389.299i	−0.246180	−	0.426395i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			55.9850i			0.0610523i
$918$		0			0
$919$	−935.435			−1.01788			−0.508942	−	0.860801i	$-0.669963\pi$
$919$	−935.435			−1.01788			−0.508942	+	0.860801i	$0.669963\pi$
$920$		0			0
$921$	672.824	+	804.443i	0.730537	+	0.873445i
$922$		0			0
$923$	165.069	−	95.3024i	0.178839	−	0.103253i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1102.82	+	397.413i	−1.18966	+	0.428708i
$928$		0			0
$929$	−1041.48	−	601.296i	−1.12107	−	0.647251i	−0.179398	−	0.983777i	$-0.557415\pi$
$929$	−1041.48	−	601.296i	−1.12107	−	0.647251i	−0.941674	+	0.336526i	$0.890748\pi$
$930$		0			0
$931$	−502.724	−	870.744i	−0.539983	−	0.935278i
$932$		0			0
$933$	1107.11	+	404.956i	1.18661	+	0.434036i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	627.406			0.669590			0.334795	−	0.942291i	$-0.391333\pi$
$937$	627.406			0.669590			0.334795	+	0.942291i	$0.391333\pi$
$938$		0			0
$939$	−1123.16	+	196.196i	−1.19612	+	0.208941i
$940$		0			0
$941$	−65.8189	+	38.0005i	−0.0699457	+	0.0403831i	−0.534565	−	0.845127i	$-0.679525\pi$
$941$	−65.8189	+	38.0005i	−0.0699457	+	0.0403831i	0.464619	+	0.885511i	$0.346191\pi$
$942$		0			0
$943$	−526.812	+	912.466i	−0.558656	+	0.967620i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1305.77	+	753.885i	1.37885	+	0.796077i	0.992021	−	0.126076i	$-0.0402382\pi$
$947$	1305.77	+	753.885i	1.37885	+	0.796077i	0.386826	+	0.922153i	$0.373571\pi$
$948$		0			0
$949$	−16.8294	−	29.1493i	−0.0177338	−	0.0307158i
$950$		0			0
$951$	−91.1467	−	521.784i	−0.0958430	−	0.548669i
$952$		0			0
$953$		−	355.068i		−	0.372580i	−0.982495	−	0.186290i	$-0.940354\pi$
$953$		−	355.068i		−	0.372580i	0.982495	−	0.186290i	$-0.0596463\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	97.5943	−	266.813i	0.101979	−	0.278802i
$958$		0			0
$959$	64.9515	−	37.4998i	0.0677284	−	0.0391030i
$960$		0			0
$961$	480.276	−	831.862i	0.499767	−	0.865622i
$962$		0			0
$963$	966.097	+	173.529i	1.00322	+	0.180196i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	591.262	+	1024.10i	0.611439	+	1.05904i	0.990998	+	0.133876i	$0.0427424\pi$
$967$	591.262	+	1024.10i	0.611439	+	1.05904i	−0.379559	+	0.925168i	$0.623924\pi$
$968$		0			0
$969$	1190.57	−	995.779i	1.22866	−	1.02764i
$970$		0			0
$971$			1230.36i			1.26711i	0.773698	+	0.633555i	$0.218405\pi$
$971$			1230.36i			1.26711i	−0.773698	+	0.633555i	$0.781595\pi$
$972$		0			0
$973$	−110.352			−0.113414
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1198.12	+	691.734i	−1.22632	+	0.708018i	−0.966259	−	0.257573i	$-0.917077\pi$
$977$	−1198.12	+	691.734i	−1.22632	+	0.708018i	−0.260064	+	0.965591i	$0.583744\pi$
$978$		0			0
$979$	−90.1943	+	156.221i	−0.0921290	+	0.159572i
$980$		0			0
$981$	307.351	−	1711.14i	0.313304	−	1.74428i
$982$		0			0
$983$	28.2445	+	16.3070i	0.0287330	+	0.0165890i	0.514298	−	0.857612i	$-0.328053\pi$
$983$	28.2445	+	16.3070i	0.0287330	+	0.0165890i	−0.485565	+	0.874201i	$0.661386\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−43.7008	−	15.9848i	−0.0442764	−	0.0161953i
$988$		0			0
$989$			1201.20i			1.21456i
$990$		0			0
$991$	1536.43			1.55039			0.775193	−	0.631724i	$-0.217653\pi$
$991$	1536.43			1.55039			0.775193	+	0.631724i	$0.217653\pi$
$992$		0			0
$993$	1924.17	−	336.120i	1.93774	−	0.338489i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	276.492	−	478.898i	0.277324	−	0.480339i	−0.693395	−	0.720558i	$-0.743886\pi$
$997$	276.492	−	478.898i	0.277324	−	0.480339i	0.970719	+	0.240219i	$0.0772193\pi$
$998$		0			0
$999$	−1132.39	+	646.580i	−1.13352	+	0.647227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.p.f.101.9		24
3.2	odd	2		2700.3.p.f.1601.5		24
5.2	odd	4		180.3.t.a.29.10	yes	24
5.3	odd	4		180.3.t.a.29.3	✓	24
5.4	even	2	inner	900.3.p.f.101.4		24
9.4	even	3		2700.3.p.f.2501.5		24
9.5	odd	6	inner	900.3.p.f.401.9		24
15.2	even	4		540.3.t.a.89.1		24
15.8	even	4		540.3.t.a.89.4		24
15.14	odd	2		2700.3.p.f.1601.8		24
45.2	even	12		1620.3.b.b.809.15		24
45.4	even	6		2700.3.p.f.2501.8		24
45.7	odd	12		1620.3.b.b.809.10		24
45.13	odd	12		540.3.t.a.449.1		24
45.14	odd	6	inner	900.3.p.f.401.4		24
45.22	odd	12		540.3.t.a.449.4		24
45.23	even	12		180.3.t.a.149.10	yes	24
45.32	even	12		180.3.t.a.149.3	yes	24
45.38	even	12		1620.3.b.b.809.9		24
45.43	odd	12		1620.3.b.b.809.16		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.t.a.29.3	✓	24	5.3	odd	4
180.3.t.a.29.10	yes	24	5.2	odd	4
180.3.t.a.149.3	yes	24	45.32	even	12
180.3.t.a.149.10	yes	24	45.23	even	12
540.3.t.a.89.1		24	15.2	even	4
540.3.t.a.89.4		24	15.8	even	4
540.3.t.a.449.1		24	45.13	odd	12
540.3.t.a.449.4		24	45.22	odd	12
900.3.p.f.101.4		24	5.4	even	2	inner
900.3.p.f.101.9		24	1.1	even	1	trivial
900.3.p.f.401.4		24	45.14	odd	6	inner
900.3.p.f.401.9		24	9.5	odd	6	inner
1620.3.b.b.809.9		24	45.38	even	12
1620.3.b.b.809.10		24	45.7	odd	12
1620.3.b.b.809.15		24	45.2	even	12
1620.3.b.b.809.16		24	45.43	odd	12
2700.3.p.f.1601.5		24	3.2	odd	2
2700.3.p.f.1601.8		24	15.14	odd	2
2700.3.p.f.2501.5		24	9.4	even	3
2700.3.p.f.2501.8		24	45.4	even	6

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.92469 + 2.30121i) q^{3} +(-0.382345 + 0.662241i) q^{7} +(-1.59110 + 8.85824i) q^{9} +O(q^{10})\)	\(q+(1.92469 + 2.30121i) q^{3} +(-0.382345 + 0.662241i) q^{7} +(-1.59110 + 8.85824i) q^{9} +(6.98717 + 4.03404i) q^{11} +(-1.08339 - 1.87649i) q^{13} +24.9128i q^{17} -20.7672 q^{19} +(-2.25985 + 0.394757i) q^{21} +(14.5841 - 8.42014i) q^{23} +(-23.4470 + 13.3880i) q^{27} +(-10.1651 - 5.86885i) q^{29} +(-0.334707 - 0.579730i) q^{31} +(4.16500 + 23.8432i) q^{33} +48.2956 q^{37} +(2.23299 - 6.10478i) q^{39} +(-54.1835 + 31.2829i) q^{41} +(-35.6645 + 61.7728i) q^{43} +(17.5663 + 10.1419i) q^{47} +(24.2076 + 41.9288i) q^{49} +(-57.3296 + 47.9496i) q^{51} -82.8011i q^{53} +(-39.9705 - 47.7896i) q^{57} +(-4.66958 + 2.69598i) q^{59} +(-41.6097 + 72.0702i) q^{61} +(-5.25794 - 4.44060i) q^{63} +(5.31727 + 9.20978i) q^{67} +(47.4464 + 17.3549i) q^{69} +87.9667i q^{71} +15.5340 q^{73} +(-5.34302 + 3.08479i) q^{77} +(16.8772 - 29.2322i) q^{79} +(-75.9368 - 28.1887i) q^{81} +(-48.2517 - 27.8581i) q^{83} +(-6.05936 - 34.6878i) q^{87} +22.3583i q^{89} +1.65692 q^{91} +(0.689869 - 1.88603i) q^{93} +(34.4755 - 59.7133i) q^{97} +(-46.8518 + 55.4754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{9}+O(q^{10}) \) 24 * q - 2 * q^9	\( 24 q - 2 q^{9} - 18 q^{11} - 26 q^{21} - 36 q^{29} + 30 q^{31} - 6 q^{39} - 36 q^{41} - 108 q^{49} + 124 q^{51} + 306 q^{59} + 48 q^{61} + 268 q^{69} - 114 q^{79} - 14 q^{81} - 84 q^{91} - 418 q^{99}+O(q^{100}) \) 24 * q - 2 * q^9 - 18 * q^11 - 26 * q^21 - 36 * q^29 + 30 * q^31 - 6 * q^39 - 36 * q^41 - 108 * q^49 + 124 * q^51 + 306 * q^59 + 48 * q^61 + 268 * q^69 - 114 * q^79 - 14 * q^81 - 84 * q^91 - 418 * q^99

Introduction

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