LMFDB - Embedded newform 900.3.u.d.149.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(149,900)]

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, 5, 3]))

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

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

chi := DirichletCharacter("900.149");

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.u (of order $6$, degree $2$, 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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.8
Character	$\chi$	$=$	900.149
Dual form			900.3.u.d.749.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.386835 - 2.97496i) q^{3} +(4.03103 - 2.32731i) q^{7} +(-8.70072 + 2.30163i) q^{9} +O(q^{10})$	\(q+(-0.386835 - 2.97496i) q^{3} +(4.03103 - 2.32731i) q^{7} +(-8.70072 + 2.30163i) q^{9} +(-12.4900 + 7.21110i) q^{11} +(21.2885 + 12.2909i) q^{13} -6.56655 q^{17} +33.0870 q^{19} +(-8.48300 - 11.0918i) q^{21} +(-18.4543 + 31.9638i) q^{23} +(10.2130 + 24.9939i) q^{27} +(17.4825 - 10.0935i) q^{29} +(6.48775 - 11.2371i) q^{31} +(26.2843 + 34.3676i) q^{33} +19.9373i q^{37} +(28.3298 - 68.0870i) q^{39} +(44.9196 + 25.9344i) q^{41} +(6.41757 - 3.70519i) q^{43} +(-13.6910 - 23.7134i) q^{47} +(-13.6672 + 23.6723i) q^{49} +(2.54017 + 19.5352i) q^{51} +79.3730 q^{53} +(-12.7992 - 98.4324i) q^{57} +(-63.3853 - 36.5955i) q^{59} +(-12.3357 - 21.3660i) q^{61} +(-29.7162 + 29.5273i) q^{63} +(-35.4645 - 20.4754i) q^{67} +(102.230 + 42.5360i) q^{69} -117.149i q^{71} +40.1824i q^{73} +(-33.5650 + 58.1363i) q^{77} +(11.1389 + 19.2931i) q^{79} +(70.4050 - 40.0517i) q^{81} +(67.3085 + 116.582i) q^{83} +(-36.7906 - 48.1051i) q^{87} +4.69877i q^{89} +114.419 q^{91} +(-35.9396 - 14.9538i) q^{93} +(120.319 - 69.4664i) q^{97} +(92.0745 - 91.4891i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 28 q^{9}+O(q^{10}) $ 32 * q - 28 * q^9	$ 32 q - 28 q^{9} - 4 q^{19} + 2 q^{21} - 18 q^{29} + 16 q^{31} - 38 q^{39} + 108 q^{41} + 90 q^{49} + 180 q^{51} - 18 q^{59} - 110 q^{61} + 294 q^{69} - 22 q^{79} - 260 q^{81} - 268 q^{91} - 504 q^{99}+O(q^{100}) $ 32 * q - 28 * q^9 - 4 * q^19 + 2 * q^21 - 18 * q^29 + 16 * q^31 - 38 * q^39 + 108 * q^41 + 90 * q^49 + 180 * q^51 - 18 * q^59 - 110 * q^61 + 294 * q^69 - 22 * q^79 - 260 * q^81 - 268 * q^91 - 504 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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
$3$	−0.386835	−	2.97496i	−0.128945	−	0.991652i
$3$	−0.386835	−	2.97496i	−0.128945	−	0.991652i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	4.03103	−	2.32731i	0.575861	−	0.332474i	−0.183626	−	0.982996i	$-0.558783\pi$
$7$	4.03103	−	2.32731i	0.575861	−	0.332474i	0.759487	+	0.650523i	$0.225450\pi$
$8$		0			0
$9$	−8.70072	+	2.30163i	−0.966746	+	0.255737i
$10$		0			0
$11$	−12.4900	+	7.21110i	−1.13545	+	0.655554i	−0.945301	−	0.326200i	$-0.894232\pi$
$11$	−12.4900	+	7.21110i	−1.13545	+	0.655554i	−0.190153	+	0.981755i	$0.560898\pi$
$12$		0			0
$13$	21.2885	+	12.2909i	1.63758	+	0.945456i	0.981664	+	0.190621i	$0.0610503\pi$
$13$	21.2885	+	12.2909i	1.63758	+	0.945456i	0.655915	+	0.754835i	$0.272283\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.56655			−0.386268			−0.193134	−	0.981172i	$-0.561865\pi$
$17$	−6.56655			−0.386268			−0.193134	+	0.981172i	$0.561865\pi$
$18$		0			0
$19$	33.0870			1.74142			0.870711	−	0.491795i	$-0.163659\pi$
$19$	33.0870			1.74142			0.870711	+	0.491795i	$0.163659\pi$
$20$		0			0
$21$	−8.48300	−	11.0918i	−0.403952	−	0.528183i
$22$		0			0
$23$	−18.4543	+	31.9638i	−0.802361	+	1.38973i	0.115697	+	0.993285i	$0.463090\pi$
$23$	−18.4543	+	31.9638i	−0.802361	+	1.38973i	−0.918058	+	0.396446i	$0.870243\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	10.2130	+	24.9939i	0.378259	+	0.925700i
$28$		0			0
$29$	17.4825	−	10.0935i	0.602844	−	0.348052i	−0.167315	−	0.985903i	$-0.553510\pi$
$29$	17.4825	−	10.0935i	0.602844	−	0.348052i	0.770160	+	0.637851i	$0.220176\pi$
$30$		0			0
$31$	6.48775	−	11.2371i	0.209282	−	0.362487i	−0.742206	−	0.670171i	$-0.766221\pi$
$31$	6.48775	−	11.2371i	0.209282	−	0.362487i	0.951489	+	0.307684i	$0.0995540\pi$
$32$		0			0
$33$	26.2843	+	34.3676i	0.796493	+	1.04144i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			19.9373i			0.538845i	0.963022	+	0.269423i	$0.0868328\pi$
$37$			19.9373i			0.538845i	−0.963022	+	0.269423i	$0.913167\pi$
$38$		0			0
$39$	28.3298	−	68.0870i	0.726406	−	1.74582i
$40$		0			0
$41$	44.9196	+	25.9344i	1.09560	+	0.632546i	0.935062	−	0.354484i	$-0.115343\pi$
$41$	44.9196	+	25.9344i	1.09560	+	0.632546i	0.160539	+	0.987029i	$0.448677\pi$
$42$		0			0
$43$	6.41757	−	3.70519i	0.149246	−	0.0861672i	−0.423517	−	0.905888i	$-0.639205\pi$
$43$	6.41757	−	3.70519i	0.149246	−	0.0861672i	0.572763	+	0.819721i	$0.305871\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−13.6910	−	23.7134i	−0.291297	−	0.504541i	0.682820	−	0.730587i	$-0.260753\pi$
$47$	−13.6910	−	23.7134i	−0.291297	−	0.504541i	−0.974117	+	0.226046i	$0.927420\pi$
$48$		0			0
$49$	−13.6672	+	23.6723i	−0.278923	+	0.483108i
$50$		0			0
$51$	2.54017	+	19.5352i	0.0498073	+	0.383043i
$52$		0			0
$53$	79.3730			1.49760			0.748802	−	0.662794i	$-0.230630\pi$
$53$	79.3730			1.49760			0.748802	+	0.662794i	$0.230630\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−12.7992	−	98.4324i	−0.224548	−	1.72688i
$58$		0			0
$59$	−63.3853	−	36.5955i	−1.07433	−	0.620263i	−0.144966	−	0.989437i	$-0.546307\pi$
$59$	−63.3853	−	36.5955i	−1.07433	−	0.620263i	−0.929360	+	0.369174i	$0.879641\pi$
$60$		0			0
$61$	−12.3357	−	21.3660i	−0.202224	−	0.350263i	0.747020	−	0.664801i	$-0.231484\pi$
$61$	−12.3357	−	21.3660i	−0.202224	−	0.350263i	−0.949245	+	0.314538i	$0.898150\pi$
$62$		0			0
$63$	−29.7162	+	29.5273i	−0.471686	+	0.468687i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−35.4645	−	20.4754i	−0.529321	−	0.305603i	0.211419	−	0.977396i	$-0.432192\pi$
$67$	−35.4645	−	20.4754i	−0.529321	−	0.305603i	−0.740740	+	0.671792i	$0.765525\pi$
$68$		0			0
$69$	102.230	+	42.5360i	1.48159	+	0.616464i
$70$		0			0
$71$		−	117.149i		−	1.64998i	−0.565145	−	0.824992i	$-0.691180\pi$
$71$		−	117.149i		−	1.64998i	0.565145	−	0.824992i	$-0.308820\pi$
$72$		0			0
$73$			40.1824i			0.550444i	0.961381	+	0.275222i	$0.0887514\pi$
$73$			40.1824i			0.550444i	−0.961381	+	0.275222i	$0.911249\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−33.5650	+	58.1363i	−0.435909	+	0.755016i
$78$		0			0
$79$	11.1389	+	19.2931i	0.140998	+	0.244216i	0.927873	−	0.372897i	$-0.121635\pi$
$79$	11.1389	+	19.2931i	0.140998	+	0.244216i	−0.786874	+	0.617113i	$0.788302\pi$
$80$		0			0
$81$	70.4050	−	40.0517i	0.869197	−	0.494466i
$82$		0			0
$83$	67.3085	+	116.582i	0.810945	+	1.40460i	0.912203	+	0.409738i	$0.134380\pi$
$83$	67.3085	+	116.582i	0.810945	+	1.40460i	−0.101258	+	0.994860i	$0.532287\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−36.7906	−	48.1051i	−0.422880	−	0.552932i
$88$		0			0
$89$			4.69877i			0.0527951i	0.999652	+	0.0263976i	$0.00840358\pi$
$89$			4.69877i			0.0527951i	−0.999652	+	0.0263976i	$0.991596\pi$
$90$		0			0
$91$	114.419			1.25736
$92$		0			0
$93$	−35.9396	−	14.9538i	−0.386447	−	0.160794i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	120.319	−	69.4664i	1.24040	−	0.716148i	0.271228	−	0.962515i	$-0.412570\pi$
$97$	120.319	−	69.4664i	1.24040	−	0.716148i	0.969177	+	0.246367i	$0.0792369\pi$
$98$		0			0
$99$	92.0745	−	91.4891i	0.930046	−	0.924132i
$100$		0			0
$101$	83.0415	−	47.9440i	0.822193	−	0.474693i	−0.0289792	−	0.999580i	$-0.509226\pi$
$101$	83.0415	−	47.9440i	0.822193	−	0.474693i	0.851172	+	0.524887i	$0.175892\pi$
$102$		0			0
$103$	111.574	+	64.4175i	1.08325	+	0.625413i	0.931770	−	0.363048i	$-0.118264\pi$
$103$	111.574	+	64.4175i	1.08325	+	0.625413i	0.151476	+	0.988461i	$0.451597\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	19.4712			0.181974			0.0909870	−	0.995852i	$-0.470998\pi$
$107$	19.4712			0.181974			0.0909870	+	0.995852i	$0.470998\pi$
$108$		0			0
$109$	27.4421			0.251762			0.125881	−	0.992045i	$-0.459824\pi$
$109$	27.4421			0.251762			0.125881	+	0.992045i	$0.459824\pi$
$110$		0			0
$111$	59.3125	−	7.71243i	0.534347	−	0.0694814i
$112$		0			0
$113$	−27.4597	+	47.5616i	−0.243006	+	0.420899i	−0.961569	−	0.274563i	$-0.911467\pi$
$113$	−27.4597	+	47.5616i	−0.243006	+	0.420899i	0.718563	+	0.695462i	$0.244800\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−213.515	−	57.9416i	−1.82491	−	0.495227i
$118$		0			0
$119$	−26.4699	+	15.2824i	−0.222437	+	0.128424i
$120$		0			0
$121$	43.4999	−	75.3440i	0.359503	−	0.622677i
$122$		0			0
$123$	59.7771	−	143.666i	0.485993	−	1.16802i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	93.6328i		−	0.737266i	−0.929575	−	0.368633i	$-0.879826\pi$
$127$		−	93.6328i		−	0.737266i	0.929575	−	0.368633i	$-0.120174\pi$
$128$		0			0
$129$	−13.5053	−	17.6587i	−0.104692	−	0.136889i
$130$		0			0
$131$	161.160	+	93.0460i	1.23023	+	0.710274i	0.967078	−	0.254480i	$-0.0819042\pi$
$131$	161.160	+	93.0460i	1.23023	+	0.710274i	0.263153	+	0.964754i	$0.415238\pi$
$132$		0			0
$133$	133.375	−	77.0039i	1.00282	−	0.578977i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	35.2630	+	61.0773i	0.257394	+	0.445820i	0.965543	−	0.260243i	$-0.0838027\pi$
$137$	35.2630	+	61.0773i	0.257394	+	0.445820i	−0.708149	+	0.706063i	$0.750469\pi$
$138$		0			0
$139$	−24.3745	+	42.2179i	−0.175356	+	0.303726i	−0.940285	−	0.340389i	$-0.889441\pi$
$139$	−24.3745	+	42.2179i	−0.175356	+	0.303726i	0.764928	+	0.644116i	$0.222774\pi$
$140$		0			0
$141$	−65.2503	+	49.9032i	−0.462768	+	0.353923i
$142$		0			0
$143$	−354.524			−2.47919
$144$		0			0
$145$		0			0
$146$		0			0
$147$	75.7110	+	31.5021i	0.515041	+	0.214300i
$148$		0			0
$149$	−125.457	−	72.4324i	−0.841990	−	0.486123i	0.0159500	−	0.999873i	$-0.494923\pi$
$149$	−125.457	−	72.4324i	−0.841990	−	0.486123i	−0.857940	+	0.513750i	$0.828256\pi$
$150$		0			0
$151$	−116.217	−	201.293i	−0.769647	−	1.33307i	−0.937755	−	0.347299i	$-0.887099\pi$
$151$	−116.217	−	201.293i	−0.769647	−	1.33307i	0.168108	−	0.985769i	$-0.446234\pi$
$152$		0			0
$153$	57.1337	−	15.1138i	0.373423	−	0.0987830i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	53.4545	+	30.8620i	0.340474	+	0.196573i	0.660482	−	0.750842i	$-0.270352\pi$
$157$	53.4545	+	30.8620i	0.340474	+	0.196573i	−0.320007	+	0.947415i	$0.603685\pi$
$158$		0			0
$159$	−30.7042	−	236.131i	−0.193108	−	1.48510i
$160$		0			0
$161$			171.796i			1.06706i
$162$		0			0
$163$			53.3693i			0.327419i	0.986509	+	0.163710i	$0.0523460\pi$
$163$			53.3693i			0.327419i	−0.986509	+	0.163710i	$0.947654\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−67.1898	+	116.376i	−0.402334	+	0.696863i	−0.994007	−	0.109315i	$-0.965134\pi$
$167$	−67.1898	+	116.376i	−0.402334	+	0.696863i	0.591673	+	0.806178i	$0.298468\pi$
$168$		0			0
$169$	217.634	+	376.953i	1.28778	+	2.23049i
$170$		0			0
$171$	−287.881	+	76.1542i	−1.68351	+	0.445346i
$172$		0			0
$173$	117.944	+	204.285i	0.681758	+	1.18084i	0.974444	+	0.224630i	$0.0721175\pi$
$173$	117.944	+	204.285i	0.681758	+	1.18084i	−0.292686	+	0.956208i	$0.594549\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−84.3503	+	202.725i	−0.476556	+	1.14534i
$178$		0			0
$179$		−	324.935i		−	1.81528i	−0.419752	−	0.907639i	$-0.637883\pi$
$179$		−	324.935i		−	1.81528i	0.419752	−	0.907639i	$-0.362117\pi$
$180$		0			0
$181$	−205.548			−1.13563			−0.567813	−	0.823158i	$-0.692210\pi$
$181$	−205.548			−1.13563			−0.567813	+	0.823158i	$0.692210\pi$
$182$		0			0
$183$	−58.7911	+	44.9633i	−0.321263	+	0.245701i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	82.0161	−	47.3520i	0.438589	−	0.253219i
$188$		0			0
$189$	99.3375	+	76.9822i	0.525595	+	0.407313i
$190$		0			0
$191$	−55.6781	+	32.1458i	−0.291508	+	0.168302i	−0.638622	−	0.769521i	$-0.720495\pi$
$191$	−55.6781	+	32.1458i	−0.291508	+	0.168302i	0.347114	+	0.937823i	$0.387162\pi$
$192$		0			0
$193$	114.196	+	65.9311i	0.591689	+	0.341612i	0.765765	−	0.643120i	$-0.222361\pi$
$193$	114.196	+	65.9311i	0.591689	+	0.341612i	−0.174076	+	0.984732i	$0.555694\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−97.7058			−0.495968			−0.247984	−	0.968764i	$-0.579768\pi$
$197$	−97.7058			−0.495968			−0.247984	+	0.968764i	$0.579768\pi$
$198$		0			0
$199$	67.9123			0.341268			0.170634	−	0.985334i	$-0.445418\pi$
$199$	67.9123			0.341268			0.170634	+	0.985334i	$0.445418\pi$
$200$		0			0
$201$	−47.1946	+	113.426i	−0.234799	+	0.564308i
$202$		0			0
$203$	46.9816	−	81.3745i	0.231436	−	0.400859i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	86.9968	−	320.583i	0.420274	−	1.54871i
$208$		0			0
$209$	−413.257	+	238.594i	−1.97730	+	1.14160i
$210$		0			0
$211$	4.53364	−	7.85250i	0.0214865	−	0.0372156i	−0.855082	−	0.518492i	$-0.826493\pi$
$211$	4.53364	−	7.85250i	0.0214865	−	0.0372156i	0.876569	+	0.481277i	$0.159827\pi$
$212$		0			0
$213$	−348.513	+	45.3173i	−1.63621	+	0.212757i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	60.3961i		−	0.278323i
$218$		0			0
$219$	119.541	−	15.5440i	0.545849	−	0.0709770i
$220$		0			0
$221$	−139.792	−	80.7090i	−0.632544	−	0.365199i
$222$		0			0
$223$	111.146	−	64.1704i	0.498415	−	0.287760i	−0.229644	−	0.973275i	$-0.573756\pi$
$223$	111.146	−	64.1704i	0.498415	−	0.287760i	0.728059	+	0.685515i	$0.240423\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	103.886	+	179.936i	0.457649	+	0.792671i	0.998836	−	0.0482311i	$-0.0153584\pi$
$227$	103.886	+	179.936i	0.457649	+	0.792671i	−0.541187	+	0.840902i	$0.682025\pi$
$228$		0			0
$229$	−195.885	+	339.283i	−0.855394	+	1.48159i	0.0208858	+	0.999782i	$0.493351\pi$
$229$	−195.885	+	339.283i	−0.855394	+	1.48159i	−0.876279	+	0.481803i	$0.839982\pi$
$230$		0			0
$231$	185.937	+	77.3652i	0.804922	+	0.334914i
$232$		0			0
$233$	152.713			0.655419			0.327709	−	0.944779i	$-0.393723\pi$
$233$	152.713			0.655419			0.327709	+	0.944779i	$0.393723\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	53.0872	−	40.6009i	0.223997	−	0.171312i
$238$		0			0
$239$	−63.4669	−	36.6426i	−0.265552	−	0.153316i	0.361313	−	0.932445i	$-0.382329\pi$
$239$	−63.4669	−	36.6426i	−0.265552	−	0.153316i	−0.626865	+	0.779128i	$0.715662\pi$
$240$		0			0
$241$	214.984	+	372.364i	0.892051	+	1.54508i	0.837413	+	0.546571i	$0.184067\pi$
$241$	214.984	+	372.364i	0.892051	+	1.54508i	0.0546375	+	0.998506i	$0.482600\pi$
$242$		0			0
$243$	−146.387	−	193.958i	−0.602417	−	0.798182i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	704.374	+	406.670i	2.85172	+	1.64644i
$248$		0			0
$249$	320.788	−	245.338i	1.28831	−	0.985291i
$250$		0			0
$251$		−	165.235i		−	0.658309i	−0.944276	−	0.329154i	$-0.893236\pi$
$251$		−	165.235i		−	0.658309i	0.944276	−	0.329154i	$-0.106764\pi$
$252$		0			0
$253$		−	532.303i		−	2.10397i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−234.388	+	405.971i	−0.912014	+	1.57965i	−0.100798	+	0.994907i	$0.532140\pi$
$257$	−234.388	+	405.971i	−0.912014	+	1.57965i	−0.811216	+	0.584747i	$0.801194\pi$
$258$		0			0
$259$	46.4003	+	80.3677i	0.179152	+	0.310300i
$260$		0			0
$261$	−128.879	+	128.059i	−0.493788	+	0.490648i
$262$		0			0
$263$	−17.7143	−	30.6821i	−0.0673549	−	0.116662i	0.830381	−	0.557196i	$-0.188123\pi$
$263$	−17.7143	−	30.6821i	−0.0673549	−	0.116662i	−0.897736	+	0.440533i	$0.854789\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	13.9786	−	1.81765i	0.0523544	−	0.00680767i
$268$		0			0
$269$		−	141.461i		−	0.525876i	−0.964813	−	0.262938i	$-0.915309\pi$
$269$		−	141.461i		−	0.525876i	0.964813	−	0.262938i	$-0.0846914\pi$
$270$		0			0
$271$	−372.478			−1.37446			−0.687229	−	0.726441i	$-0.741173\pi$
$271$	−372.478			−1.37446			−0.687229	+	0.726441i	$0.741173\pi$
$272$		0			0
$273$	−44.2615	−	340.393i	−0.162130	−	1.24686i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−223.619	+	129.107i	−0.807289	+	0.466089i	−0.846014	−	0.533161i	$-0.821004\pi$
$277$	−223.619	+	129.107i	−0.807289	+	0.466089i	0.0387244	+	0.999250i	$0.487671\pi$
$278$		0			0
$279$	−30.5843	+	112.703i	−0.109621	+	0.403954i
$280$		0			0
$281$	−283.705	+	163.797i	−1.00963	+	0.582908i	−0.911082	−	0.412224i	$-0.864752\pi$
$281$	−283.705	+	163.797i	−1.00963	+	0.582908i	−0.0985444	+	0.995133i	$0.531419\pi$
$282$		0			0
$283$	−358.781	−	207.142i	−1.26778	−	0.731952i	−0.293210	−	0.956048i	$-0.594724\pi$
$283$	−358.781	−	207.142i	−1.26778	−	0.731952i	−0.974567	+	0.224096i	$0.928057\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	241.430			0.841219
$288$		0			0
$289$	−245.880			−0.850797
$290$		0			0
$291$	−253.203	−	331.072i	−0.870113	−	1.13771i
$292$		0			0
$293$	−207.824	+	359.962i	−0.709298	+	1.22854i	0.255820	+	0.966724i	$0.417655\pi$
$293$	−207.824	+	359.962i	−0.709298	+	1.22854i	−0.965118	+	0.261816i	$0.915679\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−307.794	−	238.526i	−1.03634	−	0.803119i
$298$		0			0
$299$	−785.730	+	453.641i	−2.62786	+	1.51720i
$300$		0			0
$301$	17.2463	−	29.8714i	0.0572966	−	0.0992406i
$302$		0			0
$303$	−174.755	−	228.498i	−0.576748	−	0.754120i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			91.4750i			0.297964i	0.988840	+	0.148982i	$0.0475997\pi$
$307$			91.4750i			0.297964i	−0.988840	+	0.148982i	$0.952400\pi$
$308$		0			0
$309$	148.478	−	356.848i	0.480512	−	1.15485i
$310$		0			0
$311$	385.023	+	222.293i	1.23802	+	0.714769i	0.968688	−	0.248280i	$-0.0798652\pi$
$311$	385.023	+	222.293i	1.23802	+	0.714769i	0.269328	+	0.963049i	$0.413199\pi$
$312$		0			0
$313$	117.114	−	67.6156i	0.374165	−	0.216024i	−0.301111	−	0.953589i	$-0.597358\pi$
$313$	117.114	−	67.6156i	0.374165	−	0.216024i	0.675277	+	0.737565i	$0.264024\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−171.876	−	297.699i	−0.542197	−	0.939113i	−0.998778	−	0.0494307i	$-0.984259\pi$
$317$	−171.876	−	297.699i	−0.542197	−	0.939113i	0.456580	−	0.889682i	$-0.349074\pi$
$318$		0			0
$319$	−145.571	+	252.136i	−0.456334	+	0.790394i
$320$		0			0
$321$	−7.53215	−	57.9260i	−0.0234646	−	0.180455i
$322$		0			0
$323$	−217.268			−0.672655
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−10.6156	−	81.6389i	−0.0324635	−	0.249660i
$328$		0			0
$329$	−110.377	−	63.7263i	−0.335493	−	0.193697i
$330$		0			0
$331$	−269.871	−	467.430i	−0.815319	−	1.41217i	−0.909098	−	0.416581i	$-0.863228\pi$
$331$	−269.871	−	467.430i	−0.815319	−	1.41217i	0.0937793	−	0.995593i	$-0.470105\pi$
$332$		0			0
$333$	−45.8883	−	173.469i	−0.137803	−	0.520926i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−475.164	−	274.336i	−1.40998	−	0.814054i	−0.414597	−	0.910005i	$-0.636077\pi$
$337$	−475.164	−	274.336i	−1.40998	−	0.814054i	−0.995386	+	0.0959512i	$0.969411\pi$
$338$		0			0
$339$	152.116	+	63.2929i	0.448720	+	0.186705i
$340$		0			0
$341$			187.135i			0.548783i
$342$		0			0
$343$			355.308i			1.03588i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−58.0540	+	100.553i	−0.167303	+	0.289777i	−0.937471	−	0.348064i	$-0.886839\pi$
$347$	−58.0540	+	100.553i	−0.167303	+	0.289777i	0.770168	+	0.637841i	$0.220172\pi$
$348$		0			0
$349$	119.155	+	206.383i	0.341419	+	0.591355i	0.984696	−	0.174278i	$-0.0557592\pi$
$349$	119.155	+	206.383i	0.341419	+	0.591355i	−0.643278	+	0.765633i	$0.722426\pi$
$350$		0			0
$351$	−89.7786	+	657.610i	−0.255779	+	1.87353i
$352$		0			0
$353$	−278.006	−	481.520i	−0.787551	−	1.36408i	−0.927463	−	0.373915i	$-0.878015\pi$
$353$	−278.006	−	481.520i	−0.787551	−	1.36408i	0.139912	−	0.990164i	$-0.455318\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	55.7041	+	72.8351i	0.156034	+	0.204020i
$358$		0			0
$359$			119.443i			0.332710i	0.986066	+	0.166355i	$0.0531998\pi$
$359$			119.443i			0.332710i	−0.986066	+	0.166355i	$0.946800\pi$
$360$		0			0
$361$	733.751			2.03255
$362$		0			0
$363$	−240.972	−	100.264i	−0.663835	−	0.276211i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	497.713	−	287.355i	1.35617	−	0.782983i	0.367062	−	0.930197i	$-0.380364\pi$
$367$	497.713	−	287.355i	1.35617	−	0.782983i	0.989105	+	0.147214i	$0.0470305\pi$
$368$		0			0
$369$	−450.525	−	122.259i	−1.22093	−	0.331325i
$370$		0			0
$371$	319.955	−	184.726i	0.862411	−	0.497913i
$372$		0			0
$373$	187.298	+	108.136i	0.502139	+	0.289910i	0.729596	−	0.683878i	$-0.239708\pi$
$373$	187.298	+	108.136i	0.502139	+	0.289910i	−0.227458	+	0.973788i	$0.573041\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	496.235			1.31627
$378$		0			0
$379$	252.187			0.665400			0.332700	−	0.943033i	$-0.392040\pi$
$379$	252.187			0.665400			0.332700	+	0.943033i	$0.392040\pi$
$380$		0			0
$381$	−278.553	+	36.2204i	−0.731111	+	0.0950668i
$382$		0			0
$383$	64.3180	−	111.402i	0.167932	−	0.290867i	−0.769761	−	0.638333i	$-0.779624\pi$
$383$	64.3180	−	111.402i	0.167932	−	0.290867i	0.937693	+	0.347466i	$0.112958\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−47.3095	+	47.0087i	−0.122247	+	0.121470i
$388$		0			0
$389$	214.436	−	123.805i	0.551250	−	0.318264i	−0.198376	−	0.980126i	$-0.563567\pi$
$389$	214.436	−	123.805i	0.551250	−	0.318264i	0.749626	+	0.661862i	$0.230233\pi$
$390$		0			0
$391$	121.181	−	209.892i	0.309926	−	0.536808i
$392$		0			0
$393$	214.465	−	515.438i	0.545713	−	1.31155i
$394$		0			0
$395$		0			0
$396$		0			0
$397$		−	123.266i		−	0.310493i	−0.987876	−	0.155246i	$-0.950383\pi$
$397$		−	123.266i		−	0.310493i	0.987876	−	0.155246i	$-0.0496171\pi$
$398$		0			0
$399$	−280.677	−	366.996i	−0.703452	−	0.919789i
$400$		0			0
$401$	397.425	+	229.454i	0.991085	+	0.572203i	0.905599	−	0.424136i	$-0.139422\pi$
$401$	397.425	+	229.454i	0.991085	+	0.572203i	0.0854868	+	0.996339i	$0.472755\pi$
$402$		0			0
$403$	276.229	−	159.481i	0.685432	−	0.395734i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−143.770	−	249.016i	−0.353242	−	0.611833i
$408$		0			0
$409$	38.8984	−	67.3740i	0.0951061	−	0.164729i	−0.814547	−	0.580098i	$-0.803014\pi$
$409$	38.8984	−	67.3740i	0.0951061	−	0.164729i	0.909653	+	0.415369i	$0.136348\pi$
$410$		0			0
$411$	168.061	−	128.533i	0.408908	−	0.312732i
$412$		0			0
$413$	−340.677			−0.824884
$414$		0			0
$415$		0			0
$416$		0			0
$417$	135.025	+	56.1818i	0.323802	+	0.134728i
$418$		0			0
$419$	−363.032	−	209.597i	−0.866425	−	0.500230i	−0.000266138	−	1.00000i	$-0.500085\pi$
$419$	−363.032	−	209.597i	−0.866425	−	0.500230i	−0.866158	+	0.499770i	$0.833418\pi$
$420$		0			0
$421$	−41.7402	−	72.2962i	−0.0991454	−	0.171725i	0.812186	−	0.583399i	$-0.198278\pi$
$421$	−41.7402	−	72.2962i	−0.0991454	−	0.171725i	−0.911331	+	0.411674i	$0.864944\pi$
$422$		0			0
$423$	173.701	+	174.812i	0.410640	+	0.413268i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−99.4510	−	57.4181i	−0.232906	−	0.134469i
$428$		0			0
$429$	137.142	+	1054.69i	0.319679	+	2.45850i
$430$		0			0
$431$		−	464.864i		−	1.07857i	−0.842123	−	0.539285i	$-0.818694\pi$
$431$		−	464.864i		−	1.07857i	0.842123	−	0.539285i	$-0.181306\pi$
$432$		0			0
$433$		−	201.140i		−	0.464525i	−0.972653	−	0.232263i	$-0.925387\pi$
$433$		−	201.140i		−	0.464525i	0.972653	−	0.232263i	$-0.0746129\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−610.598	+	1057.59i	−1.39725	+	2.42011i
$438$		0			0
$439$	252.879	+	437.999i	0.576033	+	0.997719i	0.995929	+	0.0901465i	$0.0287335\pi$
$439$	252.879	+	437.999i	0.576033	+	0.997719i	−0.419895	+	0.907573i	$0.637933\pi$
$440$		0			0
$441$	64.4296	−	237.423i	0.146099	−	0.538374i
$442$		0			0
$443$	113.753	+	197.026i	0.256779	+	0.444755i	0.965377	−	0.260858i	$-0.0840054\pi$
$443$	113.753	+	197.026i	0.256779	+	0.444755i	−0.708598	+	0.705612i	$0.750672\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−166.952	+	401.247i	−0.373495	+	0.897644i
$448$		0			0
$449$		−	224.825i		−	0.500724i	−0.968152	−	0.250362i	$-0.919450\pi$
$449$		−	224.825i		−	0.500724i	0.968152	−	0.250362i	$-0.0805496\pi$
$450$		0			0
$451$	−748.061			−1.65867
$452$		0			0
$453$	−553.881	+	423.607i	−1.22270	+	0.935114i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	533.780	−	308.178i	1.16801	−	0.674350i	0.214798	−	0.976659i	$-0.431091\pi$
$457$	533.780	−	308.178i	1.16801	−	0.674350i	0.953210	+	0.302309i	$0.0977574\pi$
$458$		0			0
$459$	−67.0642	−	164.124i	−0.146109	−	0.357568i
$460$		0			0
$461$	−616.599	+	355.994i	−1.33753	+	0.772221i	−0.986440	−	0.164122i	$-0.947521\pi$
$461$	−616.599	+	355.994i	−1.33753	+	0.772221i	−0.351086	+	0.936343i	$0.614188\pi$
$462$		0			0
$463$	218.788	+	126.318i	0.472545	+	0.272824i	0.717304	−	0.696760i	$-0.245376\pi$
$463$	218.788	+	126.318i	0.472545	+	0.272824i	−0.244759	+	0.969584i	$0.578709\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	508.789			1.08948			0.544742	−	0.838604i	$-0.316628\pi$
$467$	508.789			1.08948			0.544742	+	0.838604i	$0.316628\pi$
$468$		0			0
$469$	−190.611			−0.406420
$470$		0			0
$471$	71.1349	−	170.963i	0.151029	−	0.362979i
$472$		0			0
$473$	−53.4370	+	92.5555i	−0.112975	+	0.195678i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−690.602	+	182.687i	−1.44780	+	0.382993i
$478$		0			0
$479$	683.840	−	394.815i	1.42764	−	0.824249i	0.430706	−	0.902492i	$-0.358265\pi$
$479$	683.840	−	394.815i	1.42764	−	0.824249i	0.996934	+	0.0782437i	$0.0249312\pi$
$480$		0			0
$481$	−245.048	+	424.435i	−0.509454	+	0.882401i
$482$		0			0
$483$	511.085	−	66.4567i	1.05815	−	0.137592i
$484$		0			0
$485$		0			0
$486$		0			0
$487$			317.579i			0.652112i	0.945350	+	0.326056i	$0.105720\pi$
$487$			317.579i			0.652112i	−0.945350	+	0.326056i	$0.894280\pi$
$488$		0			0
$489$	158.771	−	20.6451i	0.324686	−	0.0422190i
$490$		0			0
$491$	−597.835	−	345.160i	−1.21759	−	0.702973i	−0.253185	−	0.967418i	$-0.581478\pi$
$491$	−597.835	−	345.160i	−1.21759	−	0.702973i	−0.964401	+	0.264444i	$0.914811\pi$
$492$		0			0
$493$	−114.800	+	66.2796i	−0.232859	+	0.134441i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−272.642	−	472.230i	−0.548576	−	0.950161i
$498$		0			0
$499$	−25.6761	+	44.4723i	−0.0514550	+	0.0891228i	−0.890606	−	0.454776i	$-0.849719\pi$
$499$	−25.6761	+	44.4723i	−0.0514550	+	0.0891228i	0.839151	+	0.543899i	$0.183053\pi$
$500$		0			0
$501$	372.205	+	154.868i	0.742924	+	0.309118i
$502$		0			0
$503$	239.928			0.476994			0.238497	−	0.971143i	$-0.423345\pi$
$503$	239.928			0.476994			0.238497	+	0.971143i	$0.423345\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1037.23	−	793.270i	2.04582	−	1.56464i
$508$		0			0
$509$	440.034	+	254.054i	0.864507	+	0.499123i	0.865519	−	0.500876i	$-0.166989\pi$
$509$	440.034	+	254.054i	0.864507	+	0.499123i	−0.00101197	+	0.999999i	$0.500322\pi$
$510$		0			0
$511$	93.5171	+	161.976i	0.183008	+	0.316979i
$512$		0			0
$513$	337.918	+	826.974i	0.658709	+	1.61203i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	342.000	+	197.454i	0.661508	+	0.381922i
$518$		0			0
$519$	562.114	−	429.903i	1.08307	−	0.828329i
$520$		0			0
$521$			66.1586i			0.126984i	0.997982	+	0.0634920i	$0.0202237\pi$
$521$			66.1586i			0.126984i	−0.997982	+	0.0634920i	$0.979776\pi$
$522$		0			0
$523$		−	133.503i		−	0.255264i	−0.991822	−	0.127632i	$-0.959262\pi$
$523$		−	133.503i		−	0.255264i	0.991822	−	0.127632i	$-0.0407377\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−42.6021	+	73.7890i	−0.0808389	+	0.140017i
$528$		0			0
$529$	−416.623	−	721.613i	−0.787568	−	1.36411i
$530$		0			0
$531$	635.727	+	172.517i	1.19723	+	0.324892i
$532$		0			0
$533$	637.515	+	1104.21i	1.19609	+	2.07169i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−966.666	+	125.696i	−1.80012	+	0.234071i
$538$		0			0
$539$		−	394.222i		−	0.731396i
$540$		0			0
$541$	263.866			0.487737			0.243868	−	0.969808i	$-0.421584\pi$
$541$	263.866			0.487737			0.243868	+	0.969808i	$0.421584\pi$
$542$		0			0
$543$	79.5133	+	611.497i	0.146433	+	1.12615i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−523.690	+	302.353i	−0.957386	+	0.552747i	−0.895368	−	0.445328i	$-0.853087\pi$
$547$	−523.690	+	302.353i	−0.957386	+	0.552747i	−0.0620188	+	0.998075i	$0.519754\pi$
$548$		0			0
$549$	156.506	+	157.508i	0.285075	+	0.286899i
$550$		0			0
$551$	578.443	−	333.964i	1.04981	−	0.606106i
$552$		0			0
$553$	89.8022	+	51.8473i	0.162391	+	0.0937565i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	510.522			0.916556			0.458278	−	0.888809i	$-0.348466\pi$
$557$	510.522			0.916556			0.458278	+	0.888809i	$0.348466\pi$
$558$		0			0
$559$	182.161			0.325869
$560$		0			0
$561$	−172.597	−	225.677i	−0.307659	−	0.402276i
$562$		0			0
$563$	192.705	−	333.774i	0.342282	−	0.592849i	−0.642574	−	0.766223i	$-0.722134\pi$
$563$	192.705	−	333.774i	0.342282	−	0.592849i	0.984856	+	0.173374i	$0.0554669\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	190.591	−	325.304i	0.336140	−	0.573729i
$568$		0			0
$569$	−192.215	+	110.975i	−0.337812	+	0.195036i	−0.659304	−	0.751877i	$-0.729149\pi$
$569$	−192.215	+	110.975i	−0.337812	+	0.195036i	0.321492	+	0.946912i	$0.395816\pi$
$570$		0			0
$571$	−187.067	+	324.010i	−0.327613	+	0.567443i	−0.982038	−	0.188685i	$-0.939578\pi$
$571$	−187.067	+	324.010i	−0.327613	+	0.567443i	0.654425	+	0.756127i	$0.272911\pi$
$572$		0			0
$573$	117.170	+	153.205i	0.204486	+	0.267373i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	237.121i		−	0.410955i	−0.978662	−	0.205478i	$-0.934125\pi$
$577$		−	237.121i		−	0.410955i	0.978662	−	0.205478i	$-0.0658748\pi$
$578$		0			0
$579$	151.967	−	365.232i	0.262465	−	0.630799i
$580$		0			0
$581$	542.645	+	313.296i	0.933984	+	0.539236i
$582$		0			0
$583$	−991.367	+	572.366i	−1.70046	+	0.981760i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−473.676	−	820.431i	−0.806944	−	1.39767i	−0.914971	−	0.403519i	$-0.867787\pi$
$587$	−473.676	−	820.431i	−0.806944	−	1.39767i	0.108028	−	0.994148i	$-0.465547\pi$
$588$		0			0
$589$	214.660	−	371.802i	0.364449	−	0.631243i
$590$		0			0
$591$	37.7960	+	290.670i	0.0639527	+	0.491828i
$592$		0			0
$593$	744.224			1.25502			0.627508	−	0.778610i	$-0.284075\pi$
$593$	744.224			1.25502			0.627508	+	0.778610i	$0.284075\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−26.2709	−	202.036i	−0.0440048	−	0.338419i
$598$		0			0
$599$	532.457	+	307.414i	0.888910	+	0.513212i	0.873586	−	0.486670i	$-0.161789\pi$
$599$	532.457	+	307.414i	0.888910	+	0.513212i	0.0153242	+	0.999883i	$0.495122\pi$
$600$		0			0
$601$	−156.574	−	271.195i	−0.260523	−	0.451239i	0.705858	−	0.708353i	$-0.250562\pi$
$601$	−156.574	−	271.195i	−0.260523	−	0.451239i	−0.966381	+	0.257114i	$0.917228\pi$
$602$		0			0
$603$	355.693	+	96.5247i	0.589873	+	0.160074i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−840.192	−	485.085i	−1.38417	−	0.799152i	−0.391521	−	0.920169i	$-0.628051\pi$
$607$	−840.192	−	485.085i	−1.38417	−	0.799152i	−0.992650	+	0.121018i	$0.961384\pi$
$608$		0			0
$609$	−260.260	−	108.290i	−0.427356	−	0.177815i
$610$		0			0
$611$		−	673.099i		−	1.10163i
$612$		0			0
$613$			758.446i			1.23727i	0.785679	+	0.618635i	$0.212314\pi$
$613$			758.446i			1.23727i	−0.785679	+	0.618635i	$0.787686\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	156.323	−	270.760i	0.253360	−	0.438833i	−0.711089	−	0.703102i	$-0.751798\pi$
$617$	156.323	−	270.760i	0.253360	−	0.438833i	0.964449	+	0.264270i	$0.0851309\pi$
$618$		0			0
$619$	−488.656	−	846.377i	−0.789428	−	1.36733i	−0.926318	−	0.376744i	$-0.877044\pi$
$619$	−488.656	−	846.377i	−0.789428	−	1.36733i	0.136889	−	0.990586i	$-0.456290\pi$
$620$		0			0
$621$	−987.374	−	134.799i	−1.58997	−	0.217067i
$622$		0			0
$623$	10.9355	+	18.9409i	0.0175530	+	0.0304027i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	869.668	+	1137.12i	1.38703	+	1.81359i
$628$		0			0
$629$		−	130.919i		−	0.208138i
$630$		0			0
$631$	904.406			1.43329			0.716645	−	0.697438i	$-0.245677\pi$
$631$	904.406			1.43329			0.716645	+	0.697438i	$0.245677\pi$
$632$		0			0
$633$	−25.1146	−	10.4498i	−0.0396755	−	0.0165083i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−581.910	+	335.966i	−0.913516	+	0.527419i
$638$		0			0
$639$	269.634	+	1019.28i	0.421962	+	1.59512i
$640$		0			0
$641$	−764.357	+	441.302i	−1.19245	+	0.688459i	−0.958860	−	0.283878i	$-0.908379\pi$
$641$	−764.357	+	441.302i	−1.19245	+	0.688459i	−0.233585	+	0.972336i	$0.575046\pi$
$642$		0			0
$643$	495.184	+	285.894i	0.770114	+	0.444626i	0.832915	−	0.553400i	$-0.186670\pi$
$643$	495.184	+	285.894i	0.770114	+	0.444626i	−0.0628010	+	0.998026i	$0.520003\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−113.496			−0.175419			−0.0877096	−	0.996146i	$-0.527955\pi$
$647$	−113.496			−0.175419			−0.0877096	+	0.996146i	$0.527955\pi$
$648$		0			0
$649$	1055.58			1.62646
$650$		0			0
$651$	−179.676	+	23.3633i	−0.276000	+	0.0358884i
$652$		0			0
$653$	508.582	−	880.891i	0.778840	−	1.34899i	−0.153771	−	0.988106i	$-0.549142\pi$
$653$	508.582	−	880.891i	0.778840	−	1.34899i	0.932611	−	0.360884i	$-0.117525\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−92.4852	−	349.616i	−0.140769	−	0.532140i
$658$		0			0
$659$	−697.672	+	402.801i	−1.05868	+	0.611231i	−0.925068	−	0.379802i	$-0.875992\pi$
$659$	−697.672	+	402.801i	−1.05868	+	0.611231i	−0.133615	+	0.991033i	$0.542659\pi$
$660$		0			0
$661$	491.116	−	850.638i	0.742989	−	1.28690i	−0.208139	−	0.978099i	$-0.566741\pi$
$661$	491.116	−	850.638i	0.742989	−	1.28690i	0.951128	−	0.308796i	$-0.0999261\pi$
$662$		0			0
$663$	−186.029	+	447.097i	−0.280587	+	0.674354i
$664$		0			0
$665$		0			0
$666$		0			0
$667$			745.076i			1.11705i
$668$		0			0
$669$	−233.900	−	305.832i	−0.349626	−	0.457149i
$670$		0			0
$671$	308.145	+	177.908i	0.459233	+	0.265138i
$672$		0			0
$673$	246.268	−	142.183i	0.365926	−	0.211267i	−0.305751	−	0.952111i	$-0.598908\pi$
$673$	246.268	−	142.183i	0.365926	−	0.211267i	0.671677	+	0.740844i	$0.265574\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	128.253	+	222.141i	0.189443	+	0.328125i	0.945065	−	0.326883i	$-0.105998\pi$
$677$	128.253	+	222.141i	0.189443	+	0.328125i	−0.755621	+	0.655009i	$0.772665\pi$
$678$		0			0
$679$	323.340	−	560.042i	0.476200	−	0.824803i
$680$		0			0
$681$	495.116	−	378.663i	0.727042	−	0.556039i
$682$		0			0
$683$	−1126.46			−1.64928			−0.824639	−	0.565660i	$-0.808622\pi$
$683$	−1126.46			−1.64928			−0.824639	+	0.565660i	$0.808622\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	1085.13	+	451.503i	1.57952	+	0.657210i
$688$		0			0
$689$	1689.73	+	975.568i	2.45244	+	1.41592i
$690$		0			0
$691$	144.035	+	249.476i	0.208444	+	0.361036i	0.951225	−	0.308499i	$-0.0998267\pi$
$691$	144.035	+	249.476i	0.208444	+	0.361036i	−0.742780	+	0.669535i	$0.766493\pi$
$692$		0			0
$693$	158.231	−	583.081i	0.228328	−	0.841387i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−294.967	−	170.299i	−0.423195	−	0.244332i
$698$		0			0
$699$	−59.0746	−	454.313i	−0.0845130	−	0.649947i
$700$		0			0
$701$		−	854.593i		−	1.21911i	−0.792745	−	0.609553i	$-0.791349\pi$
$701$		−	854.593i		−	1.21911i	0.792745	−	0.609553i	$-0.208651\pi$
$702$		0			0
$703$			659.665i			0.938357i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	223.162	−	386.527i	0.315646	−	0.546715i
$708$		0			0
$709$	−183.387	−	317.636i	−0.258656	−	0.448006i	0.707226	−	0.706988i	$-0.249946\pi$
$709$	−183.387	−	317.636i	−0.258656	−	0.448006i	−0.965882	+	0.258982i	$0.916613\pi$
$710$		0			0
$711$	−141.322	−	142.226i	−0.198765	−	0.200037i
$712$		0			0
$713$	239.454	+	414.746i	0.335840	+	0.581692i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−84.4590	+	202.986i	−0.117795	+	0.283104i
$718$		0			0
$719$		−	167.078i		−	0.232376i	−0.993227	−	0.116188i	$-0.962932\pi$
$719$		−	167.078i		−	0.232376i	0.993227	−	0.116188i	$-0.0370675\pi$
$720$		0			0
$721$	599.679			0.831733
$722$		0			0
$723$	1024.60	−	783.612i	1.41715	−	1.08383i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−572.186	+	330.352i	−0.787051	+	0.454404i	−0.838923	−	0.544250i	$-0.816814\pi$
$727$	−572.186	+	330.352i	−0.787051	+	0.454404i	0.0518723	+	0.998654i	$0.483481\pi$
$728$		0			0
$729$	−520.389	+	510.525i	−0.713840	+	0.700309i
$730$		0			0
$731$	−42.1413	+	24.3303i	−0.0576489	+	0.0332836i
$732$		0			0
$733$	−23.6078	−	13.6300i	−0.0322071	−	0.0185947i	0.483810	−	0.875173i	$-0.339253\pi$
$733$	−23.6078	−	13.6300i	−0.0322071	−	0.0185947i	−0.516017	+	0.856578i	$0.672586\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	590.601			0.801359
$738$		0			0
$739$	−549.148			−0.743096			−0.371548	−	0.928414i	$-0.621173\pi$
$739$	−549.148			−0.743096			−0.371548	+	0.928414i	$0.621173\pi$
$740$		0			0
$741$	937.350	−	2252.80i	1.26498	−	3.04021i
$742$		0			0
$743$	−88.0673	+	152.537i	−0.118529	+	0.205299i	−0.919185	−	0.393826i	$-0.871151\pi$
$743$	−88.0673	+	152.537i	−0.118529	+	0.205299i	0.800656	+	0.599125i	$0.204485\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−853.960	−	859.425i	−1.14319	−	1.15050i
$748$		0			0
$749$	78.4890	−	45.3157i	0.104792	−	0.0605016i
$750$		0			0
$751$	108.231	−	187.462i	0.144116	−	0.249616i	−0.784927	−	0.619589i	$-0.787299\pi$
$751$	108.231	−	187.462i	0.144116	−	0.249616i	0.929043	+	0.369972i	$0.120633\pi$
$752$		0			0
$753$	−491.568	+	63.9189i	−0.652813	+	0.0848856i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	1104.91i		−	1.45959i	−0.683668	−	0.729793i	$-0.739616\pi$
$757$		−	1104.91i		−	1.45959i	0.683668	−	0.729793i	$-0.260384\pi$
$758$		0			0
$759$	−1583.58	+	205.914i	−2.08640	+	0.271296i
$760$		0			0
$761$	774.245	+	447.011i	1.01741	+	0.587399i	0.913351	−	0.407173i	$-0.133485\pi$
$761$	774.245	+	447.011i	1.01741	+	0.587399i	0.104054	+	0.994572i	$0.466819\pi$
$762$		0			0
$763$	110.620	−	63.8663i	0.144980	−	0.0837042i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−899.586	−	1558.13i	−1.17286	−	2.03146i
$768$		0			0
$769$	287.360	−	497.722i	0.373680	−	0.647233i	−0.616448	−	0.787395i	$-0.711429\pi$
$769$	287.360	−	497.722i	0.373680	−	0.647233i	0.990129	+	0.140162i	$0.0447624\pi$
$770$		0			0
$771$	1298.42	+	540.249i	1.68407	+	0.700711i
$772$		0			0
$773$	−71.2870			−0.0922212			−0.0461106	−	0.998936i	$-0.514683\pi$
$773$	−71.2870			−0.0922212			−0.0461106	+	0.998936i	$0.514683\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	221.141	−	169.128i	0.284609	−	0.217668i
$778$		0			0
$779$	1486.26	+	858.091i	1.90790	+	1.10153i
$780$		0			0
$781$	844.772	+	1463.19i	1.08165	+	1.87348i
$782$		0			0
$783$	430.825	+	333.870i	0.550223	+	0.426399i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	30.2005	+	17.4363i	0.0383742	+	0.0221554i	0.519064	−	0.854735i	$-0.326280\pi$
$787$	30.2005	+	17.4363i	0.0383742	+	0.0221554i	−0.480690	+	0.876891i	$0.659614\pi$
$788$		0			0
$789$	−84.4254	+	64.5683i	−0.107003	+	0.0818356i
$790$		0			0
$791$			255.629i			0.323172i
$792$		0			0
$793$		−	606.469i		−	0.764777i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	451.742	−	782.440i	0.566803	−	0.981731i	−0.430077	−	0.902792i	$-0.641513\pi$
$797$	451.742	−	782.440i	0.566803	−	0.981731i	0.996879	−	0.0789390i	$-0.0251532\pi$
$798$		0			0
$799$	89.9024	+	155.716i	0.112519	+	0.194888i
$800$		0			0
$801$	−10.8148	−	40.8826i	−0.0135017	−	0.0510395i
$802$		0			0
$803$	−289.759	−	501.878i	−0.360846	−	0.625004i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−420.839	+	54.7219i	−0.521485	+	0.0678090i
$808$		0			0
$809$		−	1019.43i		−	1.26011i	−0.776551	−	0.630054i	$-0.783033\pi$
$809$		−	1019.43i		−	1.26011i	0.776551	−	0.630054i	$-0.216967\pi$
$810$		0			0
$811$	−1022.62			−1.26093			−0.630467	−	0.776216i	$-0.717136\pi$
$811$	−1022.62			−1.26093			−0.630467	+	0.776216i	$0.717136\pi$
$812$		0			0
$813$	144.088	+	1108.11i	0.177229	+	1.36298i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	212.338	−	122.594i	0.259900	−	0.150053i
$818$		0			0
$819$	−995.531	+	263.352i	−1.21555	+	0.321553i
$820$		0			0
$821$	−1352.85	+	781.066i	−1.64780	+	0.951359i	−0.669859	+	0.742488i	$0.733646\pi$
$821$	−1352.85	+	781.066i	−1.64780	+	0.951359i	−0.977943	+	0.208871i	$0.933021\pi$
$822$		0			0
$823$	−1224.82	−	707.151i	−1.48824	−	0.859236i	−0.488331	−	0.872659i	$-0.662394\pi$
$823$	−1224.82	−	707.151i	−1.48824	−	0.859236i	−0.999910	+	0.0134224i	$0.995727\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−949.074			−1.14761			−0.573805	−	0.818992i	$-0.694533\pi$
$827$	−949.074			−1.14761			−0.573805	+	0.818992i	$0.694533\pi$
$828$		0			0
$829$	−1144.99			−1.38118			−0.690588	−	0.723249i	$-0.742648\pi$
$829$	−1144.99			−1.38118			−0.690588	+	0.723249i	$0.742648\pi$
$830$		0			0
$831$	470.590	+	615.314i	0.566294	+	0.740450i
$832$		0			0
$833$	89.7465	−	155.445i	0.107739	−	0.186609i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	347.118	+	47.3895i	0.414717	+	0.0566182i
$838$		0			0
$839$	218.826	−	126.340i	0.260818	−	0.150583i	−0.363890	−	0.931442i	$-0.618551\pi$
$839$	218.826	−	126.340i	0.260818	−	0.150583i	0.624708	+	0.780859i	$0.285218\pi$
$840$		0			0
$841$	−216.742	+	375.408i	−0.257719	+	0.446383i
$842$		0			0
$843$	597.037	+	780.648i	0.708228	+	0.926035i
$844$		0			0
$845$		0			0
$846$		0			0
$847$		−	404.951i		−	0.478101i
$848$		0			0
$849$	−477.450	+	1147.49i	−0.562368	+	1.35158i
$850$		0			0
$851$	−637.271	−	367.929i	−0.748849	−	0.432348i
$852$		0			0
$853$	236.510	−	136.549i	0.277269	−	0.160081i	−0.354917	−	0.934898i	$-0.615491\pi$
$853$	236.510	−	136.549i	0.277269	−	0.160081i	0.632186	+	0.774816i	$0.282158\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	206.740	+	358.085i	0.241237	+	0.417835i	0.961067	−	0.276315i	$-0.0891134\pi$
$857$	206.740	+	358.085i	0.241237	+	0.417835i	−0.719830	+	0.694151i	$0.755780\pi$
$858$		0			0
$859$	664.377	−	1150.73i	0.773431	−	1.33962i	−0.162242	−	0.986751i	$-0.551872\pi$
$859$	664.377	−	1150.73i	0.773431	−	1.33962i	0.935672	−	0.352870i	$-0.114794\pi$
$860$		0			0
$861$	−93.3935	−	718.243i	−0.108471	−	0.834196i
$862$		0			0
$863$	−283.552			−0.328565			−0.164283	−	0.986413i	$-0.552531\pi$
$863$	−283.552			−0.328565			−0.164283	+	0.986413i	$0.552531\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	95.1152	+	731.483i	0.109706	+	0.843695i
$868$		0			0
$869$	−278.249	−	160.647i	−0.320194	−	0.184864i
$870$		0			0
$871$	−503.324	−	871.783i	−0.577870	−	1.00090i
$872$		0			0
$873$	−886.978	+	881.338i	−1.01601	+	1.00955i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	396.843	+	229.117i	0.452500	+	0.261251i	0.708886	−	0.705323i	$-0.249198\pi$
$877$	396.843	+	229.117i	0.452500	+	0.261251i	−0.256385	+	0.966575i	$0.582532\pi$
$878$		0			0
$879$	1151.27	+	479.022i	1.30974	+	0.544962i
$880$		0			0
$881$		−	1408.20i		−	1.59841i	−0.601056	−	0.799207i	$-0.705253\pi$
$881$		−	1408.20i		−	1.59841i	0.601056	−	0.799207i	$-0.294747\pi$
$882$		0			0
$883$		−	200.279i		−	0.226817i	−0.993548	−	0.113408i	$-0.963823\pi$
$883$		−	200.279i		−	0.226817i	0.993548	−	0.113408i	$-0.0361768\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−592.748	+	1026.67i	−0.668262	+	1.15746i	0.310128	+	0.950695i	$0.399628\pi$
$887$	−592.748	+	1026.67i	−0.668262	+	1.15746i	−0.978390	+	0.206769i	$0.933705\pi$
$888$		0			0
$889$	−217.913	−	377.436i	−0.245121	−	0.424563i
$890$		0			0
$891$	−590.540	+	1007.94i	−0.662784	+	1.13125i
$892$		0			0
$893$	−452.993	−	784.607i	−0.507271	−	0.878620i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1653.51	+	2162.03i	1.84338	+	2.41029i
$898$		0			0
$899$		−	261.937i		−	0.291364i
$900$		0			0
$901$	−521.207			−0.578476
$902$		0			0
$903$	−95.5376	−	39.7516i	−0.105800	−	0.0440217i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−1152.23	+	665.240i	−1.27037	+	0.733451i	−0.975058	−	0.221949i	$-0.928758\pi$
$907$	−1152.23	+	665.240i	−1.27037	+	0.733451i	−0.295316	+	0.955400i	$0.595425\pi$
$908$		0			0
$909$	−612.171	+	608.278i	−0.673455	+	0.669173i
$910$		0			0
$911$	311.564	−	179.882i	0.342003	−	0.197455i	−0.319155	−	0.947703i	$-0.603399\pi$
$911$	311.564	−	179.882i	0.342003	−	0.197455i	0.661157	+	0.750247i	$0.270066\pi$
$912$		0			0
$913$	−1681.36	−	970.736i	−1.84158	−	1.06324i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	866.189			0.944590
$918$		0			0
$919$	−114.308			−0.124383			−0.0621913	−	0.998064i	$-0.519809\pi$
$919$	−114.308			−0.124383			−0.0621913	+	0.998064i	$0.519809\pi$
$920$		0			0
$921$	272.134	−	35.3858i	0.295477	−	0.0384210i
$922$		0			0
$923$	1439.87	−	2493.93i	1.55999	−	2.70198i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1119.04	−	303.675i	−1.20717	−	0.327589i
$928$		0			0
$929$	692.105	−	399.587i	0.745000	−	0.430126i	−0.0788843	−	0.996884i	$-0.525136\pi$
$929$	692.105	−	399.587i	0.745000	−	0.430126i	0.823885	+	0.566758i	$0.191802\pi$
$930$		0			0
$931$	−452.207	+	783.246i	−0.485722	+	0.841296i
$932$		0			0
$933$	512.372	−	1231.42i	0.549166	−	1.31985i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			937.387i			1.00041i	0.865906	+	0.500206i	$0.166743\pi$
$937$			937.387i			1.00041i	−0.865906	+	0.500206i	$0.833257\pi$
$938$		0			0
$939$	−246.457	−	322.252i	−0.262468	−	0.343186i
$940$		0			0
$941$	−490.911	−	283.428i	−0.521691	−	0.301198i	0.215935	−	0.976408i	$-0.430720\pi$
$941$	−490.911	−	283.428i	−0.521691	−	0.301198i	−0.737626	+	0.675209i	$0.764053\pi$
$942$		0			0
$943$	−1657.92	+	957.202i	−1.75814	+	1.01506i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−357.494	−	619.197i	−0.377501	−	0.653851i	0.613197	−	0.789930i	$-0.289883\pi$
$947$	−357.494	−	619.197i	−0.377501	−	0.653851i	−0.990698	+	0.136079i	$0.956550\pi$
$948$		0			0
$949$	−493.880	+	855.424i	−0.520421	+	0.901396i
$950$		0			0
$951$	−819.153	+	626.485i	−0.861359	+	0.658765i
$952$		0			0
$953$	918.880			0.964197			0.482099	−	0.876117i	$-0.339875\pi$
$953$	918.880			0.964197			0.482099	+	0.876117i	$0.339875\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	806.405	+	335.531i	0.842638	+	0.350607i
$958$		0			0
$959$	284.292	+	164.136i	0.296447	+	0.171154i
$960$		0			0
$961$	396.318	+	686.443i	0.412402	+	0.714301i
$962$		0			0
$963$	−169.414	+	44.8156i	−0.175923	+	0.0465375i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	15.8660	+	9.16023i	0.0164074	+	0.00947283i	0.508181	−	0.861250i	$-0.330318\pi$
$967$	15.8660	+	9.16023i	0.0164074	+	0.00947283i	−0.491774	+	0.870723i	$0.663651\pi$
$968$		0			0
$969$	84.0468	+	646.362i	0.0867356	+	0.667040i
$970$		0			0
$971$		−	35.9529i		−	0.0370266i	−0.999829	−	0.0185133i	$-0.994107\pi$
$971$		−	35.9529i		−	0.0370266i	0.999829	−	0.0185133i	$-0.00589331\pi$
$972$		0			0
$973$			226.909i			0.233205i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	281.116	−	486.908i	0.287734	−	0.498370i	−0.685534	−	0.728040i	$-0.740431\pi$
$977$	281.116	−	486.908i	0.287734	−	0.498370i	0.973269	+	0.229670i	$0.0737647\pi$
$978$		0			0
$979$	−33.8833	−	58.6875i	−0.0346101	−	0.0599464i
$980$		0			0
$981$	−238.766	+	63.1616i	−0.243390	+	0.0643849i
$982$		0			0
$983$	−241.885	−	418.957i	−0.246068	−	0.426202i	0.716363	−	0.697727i	$-0.245805\pi$
$983$	−241.885	−	418.957i	−0.246068	−	0.426202i	−0.962431	+	0.271525i	$0.912472\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−146.885	+	353.019i	−0.148820	+	0.357669i
$988$		0			0
$989$			273.507i			0.276549i
$990$		0			0
$991$	−1071.66			−1.08139			−0.540695	−	0.841219i	$-0.681839\pi$
$991$	−1071.66			−1.08139			−0.540695	+	0.841219i	$0.681839\pi$
$992$		0			0
$993$	−1286.19	+	983.671i	−1.29525	+	0.990606i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	269.139	−	155.387i	0.269949	−	0.155855i	−0.358916	−	0.933370i	$-0.616853\pi$
$997$	269.139	−	155.387i	0.269949	−	0.155855i	0.628864	+	0.777515i	$0.283520\pi$
$998$		0			0
$999$	−498.310	+	203.619i	−0.498809	+	0.203823i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.u.d.149.8		32
3.2	odd	2		2700.3.u.d.449.11		32
5.2	odd	4		900.3.p.d.401.1	yes	16
5.3	odd	4		900.3.p.e.401.8	yes	16
5.4	even	2	inner	900.3.u.d.149.9		32
9.2	odd	6	inner	900.3.u.d.749.9		32
9.7	even	3		2700.3.u.d.2249.6		32
15.2	even	4		2700.3.p.e.2501.6		16
15.8	even	4		2700.3.p.d.2501.3		16
15.14	odd	2		2700.3.u.d.449.6		32
45.2	even	12		900.3.p.d.101.1	✓	16
45.7	odd	12		2700.3.p.e.1601.6		16
45.29	odd	6	inner	900.3.u.d.749.8		32
45.34	even	6		2700.3.u.d.2249.11		32
45.38	even	12		900.3.p.e.101.8	yes	16
45.43	odd	12		2700.3.p.d.1601.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.p.d.101.1	✓	16	45.2	even	12
900.3.p.d.401.1	yes	16	5.2	odd	4
900.3.p.e.101.8	yes	16	45.38	even	12
900.3.p.e.401.8	yes	16	5.3	odd	4
900.3.u.d.149.8		32	1.1	even	1	trivial
900.3.u.d.149.9		32	5.4	even	2	inner
900.3.u.d.749.8		32	45.29	odd	6	inner
900.3.u.d.749.9		32	9.2	odd	6	inner
2700.3.p.d.1601.3		16	45.43	odd	12
2700.3.p.d.2501.3		16	15.8	even	4
2700.3.p.e.1601.6		16	45.7	odd	12
2700.3.p.e.2501.6		16	15.2	even	4
2700.3.u.d.449.6		32	15.14	odd	2
2700.3.u.d.449.11		32	3.2	odd	2
2700.3.u.d.2249.6		32	9.7	even	3
2700.3.u.d.2249.11		32	45.34	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.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.386835 - 2.97496i) q^{3} +(4.03103 - 2.32731i) q^{7} +(-8.70072 + 2.30163i) q^{9} +O(q^{10})\)	\(q+(-0.386835 - 2.97496i) q^{3} +(4.03103 - 2.32731i) q^{7} +(-8.70072 + 2.30163i) q^{9} +(-12.4900 + 7.21110i) q^{11} +(21.2885 + 12.2909i) q^{13} -6.56655 q^{17} +33.0870 q^{19} +(-8.48300 - 11.0918i) q^{21} +(-18.4543 + 31.9638i) q^{23} +(10.2130 + 24.9939i) q^{27} +(17.4825 - 10.0935i) q^{29} +(6.48775 - 11.2371i) q^{31} +(26.2843 + 34.3676i) q^{33} +19.9373i q^{37} +(28.3298 - 68.0870i) q^{39} +(44.9196 + 25.9344i) q^{41} +(6.41757 - 3.70519i) q^{43} +(-13.6910 - 23.7134i) q^{47} +(-13.6672 + 23.6723i) q^{49} +(2.54017 + 19.5352i) q^{51} +79.3730 q^{53} +(-12.7992 - 98.4324i) q^{57} +(-63.3853 - 36.5955i) q^{59} +(-12.3357 - 21.3660i) q^{61} +(-29.7162 + 29.5273i) q^{63} +(-35.4645 - 20.4754i) q^{67} +(102.230 + 42.5360i) q^{69} -117.149i q^{71} +40.1824i q^{73} +(-33.5650 + 58.1363i) q^{77} +(11.1389 + 19.2931i) q^{79} +(70.4050 - 40.0517i) q^{81} +(67.3085 + 116.582i) q^{83} +(-36.7906 - 48.1051i) q^{87} +4.69877i q^{89} +114.419 q^{91} +(-35.9396 - 14.9538i) q^{93} +(120.319 - 69.4664i) q^{97} +(92.0745 - 91.4891i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 28 q^{9}+O(q^{10}) \) 32 * q - 28 * q^9	\( 32 q - 28 q^{9} - 4 q^{19} + 2 q^{21} - 18 q^{29} + 16 q^{31} - 38 q^{39} + 108 q^{41} + 90 q^{49} + 180 q^{51} - 18 q^{59} - 110 q^{61} + 294 q^{69} - 22 q^{79} - 260 q^{81} - 268 q^{91} - 504 q^{99}+O(q^{100}) \) 32 * q - 28 * q^9 - 4 * q^19 + 2 * q^21 - 18 * q^29 + 16 * q^31 - 38 * q^39 + 108 * q^41 + 90 * q^49 + 180 * q^51 - 18 * q^59 - 110 * q^61 + 294 * q^69 - 22 * q^79 - 260 * q^81 - 268 * q^91 - 504 * q^99

Introduction

L-functions

Modular forms

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Database

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