LMFDB - Embedded newform 900.3.p.e.101.8

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 10 x^{14} - 12 x^{13} + 6 x^{12} - 27 x^{11} - 585 x^{10} + 3618 x^{9} + \cdots + 43046721 $ x^16 - 2x^15 + 10x^14 - 12x^13 + 6x^12 - 27x^11 - 585x^10 + 3618x^9 - 12150x^8 + 32562x^7 - 47385x^6 - 19683x^5 + 39366x^4 - 708588x^3 + 5314410x^2 - 9565938*x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{41}]$
Coefficient ring index:	$ 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.8
Root			$-1.82249 + 2.38297i$ of defining polynomial
Character	$\chi$	$=$	900.101
Dual form			900.3.p.e.401.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.97496 + 0.386835i) q^{3} +(-2.32731 + 4.03103i) q^{7} +(8.70072 + 2.30163i) q^{9} +O(q^{10})$	\(q+(2.97496 + 0.386835i) q^{3} +(-2.32731 + 4.03103i) q^{7} +(8.70072 + 2.30163i) q^{9} +(-12.4900 - 7.21110i) q^{11} +(-12.2909 - 21.2885i) q^{13} -6.56655i q^{17} -33.0870 q^{19} +(-8.48300 + 11.0918i) q^{21} +(-31.9638 + 18.4543i) q^{23} +(24.9939 + 10.2130i) q^{27} +(-17.4825 - 10.0935i) q^{29} +(6.48775 + 11.2371i) q^{31} +(-34.3676 - 26.2843i) q^{33} +19.9373 q^{37} +(-28.3298 - 68.0870i) q^{39} +(44.9196 - 25.9344i) q^{41} +(3.70519 - 6.41757i) q^{43} +(-23.7134 - 13.6910i) q^{47} +(13.6672 + 23.6723i) q^{49} +(2.54017 - 19.5352i) q^{51} -79.3730i q^{53} +(-98.4324 - 12.7992i) q^{57} +(63.3853 - 36.5955i) q^{59} +(-12.3357 + 21.3660i) q^{61} +(-29.5273 + 29.7162i) q^{63} +(-20.4754 - 35.4645i) q^{67} +(-102.230 + 42.5360i) q^{69} +117.149i q^{71} -40.1824 q^{73} +(58.1363 - 33.5650i) q^{77} +(-11.1389 + 19.2931i) q^{79} +(70.4050 + 40.0517i) q^{81} +(-116.582 - 67.3085i) q^{83} +(-48.1051 - 36.7906i) q^{87} +4.69877i q^{89} +114.419 q^{91} +(14.9538 + 35.9396i) q^{93} +(-69.4664 + 120.319i) q^{97} +(-92.0745 - 91.4891i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{3} - q^{7} + 14 q^{9}+O(q^{10}) $ 16 * q + 2 * q^3 - q^7 + 14 * q^9	$ 16 q + 2 q^{3} - q^{7} + 14 q^{9} - 10 q^{13} + 2 q^{19} + q^{21} + 27 q^{23} - 16 q^{27} + 9 q^{29} + 8 q^{31} + 36 q^{33} - 22 q^{37} + 19 q^{39} + 54 q^{41} + 44 q^{43} - 108 q^{47} - 45 q^{49} + 90 q^{51} - 68 q^{57} + 9 q^{59} - 55 q^{61} - 107 q^{63} - 28 q^{67} - 147 q^{69} + 86 q^{73} + 342 q^{77} + 11 q^{79} - 130 q^{81} - 306 q^{83} + 375 q^{87} - 134 q^{91} - 83 q^{93} + 41 q^{97} + 252 q^{99}+O(q^{100}) $ 16 * q + 2 * q^3 - q^7 + 14 * q^9 - 10 * q^13 + 2 * q^19 + q^21 + 27 * q^23 - 16 * q^27 + 9 * q^29 + 8 * q^31 + 36 * q^33 - 22 * q^37 + 19 * q^39 + 54 * q^41 + 44 * q^43 - 108 * q^47 - 45 * q^49 + 90 * q^51 - 68 * q^57 + 9 * q^59 - 55 * q^61 - 107 * q^63 - 28 * q^67 - 147 * q^69 + 86 * q^73 + 342 * q^77 + 11 * q^79 - 130 * q^81 - 306 * q^83 + 375 * q^87 - 134 * q^91 - 83 * q^93 + 41 * q^97 + 252 * 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
$3$	2.97496	+	0.386835i	0.991652	+	0.128945i
$3$	2.97496	+	0.386835i	0.991652	+	0.128945i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.32731	+	4.03103i	−0.332474	+	0.575861i	−0.982996	−	0.183626i	$-0.941217\pi$
$7$	−2.32731	+	4.03103i	−0.332474	+	0.575861i	0.650523	+	0.759487i	$0.274550\pi$
$8$		0			0
$9$	8.70072	+	2.30163i	0.966746	+	0.255737i
$10$		0			0
$11$	−12.4900	−	7.21110i	−1.13545	−	0.655554i	−0.190153	−	0.981755i	$-0.560898\pi$
$11$	−12.4900	−	7.21110i	−1.13545	−	0.655554i	−0.945301	+	0.326200i	$0.894232\pi$
$12$		0			0
$13$	−12.2909	−	21.2885i	−0.945456	−	1.63758i	−0.754835	−	0.655915i	$-0.772283\pi$
$13$	−12.2909	−	21.2885i	−0.945456	−	1.63758i	−0.190621	−	0.981664i	$-0.561050\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	6.56655i		−	0.386268i	−0.981172	−	0.193134i	$-0.938135\pi$
$17$		−	6.56655i		−	0.386268i	0.981172	−	0.193134i	$-0.0618652\pi$
$18$		0			0
$19$	−33.0870			−1.74142			−0.870711	−	0.491795i	$-0.836341\pi$
$19$	−33.0870			−1.74142			−0.870711	+	0.491795i	$0.836341\pi$
$20$		0			0
$21$	−8.48300	+	11.0918i	−0.403952	+	0.528183i
$22$		0			0
$23$	−31.9638	+	18.4543i	−1.38973	+	0.802361i	−0.993285	−	0.115697i	$-0.963090\pi$
$23$	−31.9638	+	18.4543i	−1.38973	+	0.802361i	−0.396446	+	0.918058i	$0.629757\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	24.9939	+	10.2130i	0.925700	+	0.378259i
$28$		0			0
$29$	−17.4825	−	10.0935i	−0.602844	−	0.348052i	0.167315	−	0.985903i	$-0.446490\pi$
$29$	−17.4825	−	10.0935i	−0.602844	−	0.348052i	−0.770160	+	0.637851i	$0.779824\pi$
$30$		0			0
$31$	6.48775	+	11.2371i	0.209282	+	0.362487i	0.951489	−	0.307684i	$-0.0995540\pi$
$31$	6.48775	+	11.2371i	0.209282	+	0.362487i	−0.742206	+	0.670171i	$0.766221\pi$
$32$		0			0
$33$	−34.3676	−	26.2843i	−1.04144	−	0.796493i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	19.9373			0.538845			0.269423	−	0.963022i	$-0.413167\pi$
$37$	19.9373			0.538845			0.269423	+	0.963022i	$0.413167\pi$
$38$		0			0
$39$	−28.3298	−	68.0870i	−0.726406	−	1.74582i
$40$		0			0
$41$	44.9196	−	25.9344i	1.09560	−	0.632546i	0.160539	−	0.987029i	$-0.448677\pi$
$41$	44.9196	−	25.9344i	1.09560	−	0.632546i	0.935062	+	0.354484i	$0.115343\pi$
$42$		0			0
$43$	3.70519	−	6.41757i	0.0861672	−	0.149246i	−0.819721	−	0.572763i	$-0.805871\pi$
$43$	3.70519	−	6.41757i	0.0861672	−	0.149246i	0.905888	+	0.423517i	$0.139205\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−23.7134	−	13.6910i	−0.504541	−	0.291297i	0.226046	−	0.974117i	$-0.427420\pi$
$47$	−23.7134	−	13.6910i	−0.504541	−	0.291297i	−0.730587	+	0.682820i	$0.760753\pi$
$48$		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
$53$		−	79.3730i		−	1.49760i	−0.662794	−	0.748802i	$-0.730630\pi$
$53$		−	79.3730i		−	1.49760i	0.662794	−	0.748802i	$-0.269370\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−98.4324	−	12.7992i	−1.72688	−	0.224548i
$58$		0			0
$59$	63.3853	−	36.5955i	1.07433	−	0.620263i	0.144966	−	0.989437i	$-0.453693\pi$
$59$	63.3853	−	36.5955i	1.07433	−	0.620263i	0.929360	+	0.369174i	$0.120359\pi$
$60$		0			0
$61$	−12.3357	+	21.3660i	−0.202224	+	0.350263i	−0.949245	−	0.314538i	$-0.898150\pi$
$61$	−12.3357	+	21.3660i	−0.202224	+	0.350263i	0.747020	+	0.664801i	$0.231484\pi$
$62$		0			0
$63$	−29.5273	+	29.7162i	−0.468687	+	0.471686i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−20.4754	−	35.4645i	−0.305603	−	0.529321i	0.671792	−	0.740740i	$-0.265525\pi$
$67$	−20.4754	−	35.4645i	−0.305603	−	0.529321i	−0.977396	+	0.211419i	$0.932192\pi$
$68$		0			0
$69$	−102.230	+	42.5360i	−1.48159	+	0.616464i
$70$		0			0
$71$			117.149i			1.64998i	0.565145	+	0.824992i	$0.308820\pi$
$71$			117.149i			1.64998i	−0.565145	+	0.824992i	$0.691180\pi$
$72$		0			0
$73$	−40.1824			−0.550444			−0.275222	−	0.961381i	$-0.588751\pi$
$73$	−40.1824			−0.550444			−0.275222	+	0.961381i	$0.588751\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	58.1363	−	33.5650i	0.755016	−	0.435909i
$78$		0			0
$79$	−11.1389	+	19.2931i	−0.140998	+	0.244216i	−0.927873	−	0.372897i	$-0.878365\pi$
$79$	−11.1389	+	19.2931i	−0.140998	+	0.244216i	0.786874	+	0.617113i	$0.211698\pi$
$80$		0			0
$81$	70.4050	+	40.0517i	0.869197	+	0.494466i
$82$		0			0
$83$	−116.582	−	67.3085i	−1.40460	−	0.810945i	−0.409738	−	0.912203i	$-0.634380\pi$
$83$	−116.582	−	67.3085i	−1.40460	−	0.810945i	−0.994860	+	0.101258i	$0.967713\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−48.1051	−	36.7906i	−0.552932	−	0.422880i
$88$		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
$93$	14.9538	+	35.9396i	0.160794	+	0.386447i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−69.4664	+	120.319i	−0.716148	+	1.24040i	0.246367	+	0.969177i	$0.420763\pi$
$97$	−69.4664	+	120.319i	−0.716148	+	1.24040i	−0.962515	+	0.271228i	$0.912570\pi$
$98$		0			0
$99$	−92.0745	−	91.4891i	−0.930046	−	0.924132i
$100$		0			0
$101$	83.0415	+	47.9440i	0.822193	+	0.474693i	0.851172	−	0.524887i	$-0.175892\pi$
$101$	83.0415	+	47.9440i	0.822193	+	0.474693i	−0.0289792	+	0.999580i	$0.509226\pi$
$102$		0			0
$103$	−64.4175	−	111.574i	−0.625413	−	1.08325i	−0.988461	−	0.151476i	$-0.951597\pi$
$103$	−64.4175	−	111.574i	−0.625413	−	1.08325i	0.363048	−	0.931770i	$-0.381736\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			19.4712i			0.181974i	0.995852	+	0.0909870i	$0.0290022\pi$
$107$			19.4712i			0.181974i	−0.995852	+	0.0909870i	$0.970998\pi$
$108$		0			0
$109$	−27.4421			−0.251762			−0.125881	−	0.992045i	$-0.540176\pi$
$109$	−27.4421			−0.251762			−0.125881	+	0.992045i	$0.540176\pi$
$110$		0			0
$111$	59.3125	+	7.71243i	0.534347	+	0.0694814i
$112$		0			0
$113$	−47.5616	+	27.4597i	−0.420899	+	0.243006i	−0.695462	−	0.718563i	$-0.744800\pi$
$113$	−47.5616	+	27.4597i	−0.420899	+	0.243006i	0.274563	+	0.961569i	$0.411467\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−57.9416	−	213.515i	−0.495227	−	1.82491i
$118$		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
$123$	143.666	−	59.7771i	1.16802	−	0.485993i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−93.6328			−0.737266			−0.368633	−	0.929575i	$-0.620174\pi$
$127$	−93.6328			−0.737266			−0.368633	+	0.929575i	$0.620174\pi$
$128$		0			0
$129$	13.5053	−	17.6587i	0.104692	−	0.136889i
$130$		0			0
$131$	161.160	−	93.0460i	1.23023	−	0.710274i	0.263153	−	0.964754i	$-0.415238\pi$
$131$	161.160	−	93.0460i	1.23023	−	0.710274i	0.967078	+	0.254480i	$0.0819042\pi$
$132$		0			0
$133$	77.0039	−	133.375i	0.578977	−	1.00282i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	61.0773	+	35.2630i	0.445820	+	0.257394i	0.706063	−	0.708149i	$-0.250469\pi$
$137$	61.0773	+	35.2630i	0.445820	+	0.257394i	−0.260243	+	0.965543i	$0.583803\pi$
$138$		0			0
$139$	24.3745	+	42.2179i	0.175356	+	0.303726i	0.940285	−	0.340389i	$-0.110559\pi$
$139$	24.3745	+	42.2179i	0.175356	+	0.303726i	−0.764928	+	0.644116i	$0.777226\pi$
$140$		0			0
$141$	−65.2503	−	49.9032i	−0.462768	−	0.353923i
$142$		0			0
$143$			354.524i			2.47919i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	31.5021	+	75.7110i	0.214300	+	0.515041i
$148$		0			0
$149$	125.457	−	72.4324i	0.841990	−	0.486123i	−0.0159500	−	0.999873i	$-0.505077\pi$
$149$	125.457	−	72.4324i	0.841990	−	0.486123i	0.857940	+	0.513750i	$0.171744\pi$
$150$		0			0
$151$	−116.217	+	201.293i	−0.769647	+	1.33307i	0.168108	+	0.985769i	$0.446234\pi$
$151$	−116.217	+	201.293i	−0.769647	+	1.33307i	−0.937755	+	0.347299i	$0.887099\pi$
$152$		0			0
$153$	15.1138	−	57.1337i	0.0987830	−	0.373423i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	30.8620	+	53.4545i	0.196573	+	0.340474i	0.947415	−	0.320007i	$-0.103685\pi$
$157$	30.8620	+	53.4545i	0.196573	+	0.340474i	−0.750842	+	0.660482i	$0.770352\pi$
$158$		0			0
$159$	30.7042	−	236.131i	0.193108	−	1.48510i
$160$		0			0
$161$		−	171.796i		−	1.06706i
$162$		0			0
$163$	−53.3693			−0.327419			−0.163710	−	0.986509i	$-0.552346\pi$
$163$	−53.3693			−0.327419			−0.163710	+	0.986509i	$0.552346\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	116.376	−	67.1898i	0.696863	−	0.402334i	−0.109315	−	0.994007i	$-0.534866\pi$
$167$	116.376	−	67.1898i	0.696863	−	0.402334i	0.806178	+	0.591673i	$0.201532\pi$
$168$		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
$173$	−204.285	−	117.944i	−1.18084	−	0.681758i	−0.224630	−	0.974444i	$-0.572117\pi$
$173$	−204.285	−	117.944i	−1.18084	−	0.681758i	−0.956208	+	0.292686i	$0.905451\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	202.725	−	84.3503i	1.14534	−	0.476556i
$178$		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
$183$	−44.9633	+	58.7911i	−0.245701	+	0.321263i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−47.3520	+	82.0161i	−0.253219	+	0.438589i
$188$		0			0
$189$	−99.3375	+	76.9822i	−0.525595	+	0.407313i
$190$		0			0
$191$	−55.6781	−	32.1458i	−0.291508	−	0.168302i	0.347114	−	0.937823i	$-0.387162\pi$
$191$	−55.6781	−	32.1458i	−0.291508	−	0.168302i	−0.638622	+	0.769521i	$0.720495\pi$
$192$		0			0
$193$	−65.9311	−	114.196i	−0.341612	−	0.591689i	0.643120	−	0.765765i	$-0.277639\pi$
$193$	−65.9311	−	114.196i	−0.341612	−	0.591689i	−0.984732	+	0.174076i	$0.944306\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	97.7058i		−	0.495968i	−0.968764	−	0.247984i	$-0.920232\pi$
$197$		−	97.7058i		−	0.495968i	0.968764	−	0.247984i	$-0.0797681\pi$
$198$		0			0
$199$	−67.9123			−0.341268			−0.170634	−	0.985334i	$-0.554582\pi$
$199$	−67.9123			−0.341268			−0.170634	+	0.985334i	$0.554582\pi$
$200$		0			0
$201$	−47.1946	−	113.426i	−0.234799	−	0.564308i
$202$		0			0
$203$	81.3745	−	46.9816i	0.400859	−	0.231436i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−320.583	+	86.9968i	−1.54871	+	0.420274i
$208$		0			0
$209$	413.257	+	238.594i	1.97730	+	1.14160i
$210$		0			0
$211$	4.53364	+	7.85250i	0.0214865	+	0.0372156i	0.876569	−	0.481277i	$-0.159827\pi$
$211$	4.53364	+	7.85250i	0.0214865	+	0.0372156i	−0.855082	+	0.518492i	$0.826493\pi$
$212$		0			0
$213$	−45.3173	+	348.513i	−0.212757	+	1.63621i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−60.3961			−0.278323
$218$		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
$223$	64.1704	−	111.146i	0.287760	−	0.498415i	−0.685515	−	0.728059i	$-0.740423\pi$
$223$	64.1704	−	111.146i	0.287760	−	0.498415i	0.973275	+	0.229644i	$0.0737562\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	179.936	+	103.886i	0.792671	+	0.457649i	0.840902	−	0.541187i	$-0.182025\pi$
$227$	179.936	+	103.886i	0.792671	+	0.457649i	−0.0482311	+	0.998836i	$0.515358\pi$
$228$		0			0
$229$	195.885	+	339.283i	0.855394	+	1.48159i	0.876279	+	0.481803i	$0.160018\pi$
$229$	195.885	+	339.283i	0.855394	+	1.48159i	−0.0208858	+	0.999782i	$0.506649\pi$
$230$		0			0
$231$	185.937	−	77.3652i	0.804922	−	0.334914i
$232$		0			0
$233$		−	152.713i		−	0.655419i	−0.944779	−	0.327709i	$-0.893723\pi$
$233$		−	152.713i		−	0.655419i	0.944779	−	0.327709i	$-0.106277\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−40.6009	+	53.0872i	−0.171312	+	0.223997i
$238$		0			0
$239$	63.4669	−	36.6426i	0.265552	−	0.153316i	−0.361313	−	0.932445i	$-0.617671\pi$
$239$	63.4669	−	36.6426i	0.265552	−	0.153316i	0.626865	+	0.779128i	$0.284338\pi$
$240$		0			0
$241$	214.984	−	372.364i	0.892051	−	1.54508i	0.0546375	−	0.998506i	$-0.482600\pi$
$241$	214.984	−	372.364i	0.892051	−	1.54508i	0.837413	−	0.546571i	$-0.184067\pi$
$242$		0			0
$243$	193.958	+	146.387i	0.798182	+	0.602417i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	406.670	+	704.374i	1.64644	+	2.85172i
$248$		0			0
$249$	−320.788	−	245.338i	−1.28831	−	0.985291i
$250$		0			0
$251$			165.235i			0.658309i	0.944276	+	0.329154i	$0.106764\pi$
$251$			165.235i			0.658309i	−0.944276	+	0.329154i	$0.893236\pi$
$252$		0			0
$253$	532.303			2.10397
$254$		0			0
$255$		0			0
$256$		0			0
$257$	405.971	−	234.388i	1.57965	−	0.912014i	0.584747	−	0.811216i	$-0.301194\pi$
$257$	405.971	−	234.388i	1.57965	−	0.912014i	0.994907	−	0.100798i	$-0.0321397\pi$
$258$		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
$263$	30.6821	+	17.7143i	0.116662	+	0.0673549i	0.557196	−	0.830381i	$-0.311877\pi$
$263$	30.6821	+	17.7143i	0.116662	+	0.0673549i	−0.440533	+	0.897736i	$0.645211\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.81765	+	13.9786i	−0.00680767	+	0.0523544i
$268$		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
$273$	340.393	+	44.2615i	1.24686	+	0.162130i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	129.107	−	223.619i	0.466089	−	0.807289i	−0.533161	−	0.846014i	$-0.678996\pi$
$277$	129.107	−	223.619i	0.466089	−	0.807289i	0.999250	+	0.0387244i	$0.0123294\pi$
$278$		0			0
$279$	30.5843	+	112.703i	0.109621	+	0.403954i
$280$		0			0
$281$	−283.705	−	163.797i	−1.00963	−	0.582908i	−0.0985444	−	0.995133i	$-0.531419\pi$
$281$	−283.705	−	163.797i	−1.00963	−	0.582908i	−0.911082	+	0.412224i	$0.864752\pi$
$282$		0			0
$283$	207.142	+	358.781i	0.731952	+	1.26778i	0.956048	+	0.293210i	$0.0947237\pi$
$283$	207.142	+	358.781i	0.731952	+	1.26778i	−0.224096	+	0.974567i	$0.571943\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			241.430i			0.841219i
$288$		0			0
$289$	245.880			0.850797
$290$		0			0
$291$	−253.203	+	331.072i	−0.870113	+	1.13771i
$292$		0			0
$293$	−359.962	+	207.824i	−1.22854	+	0.709298i	−0.966724	−	0.255820i	$-0.917655\pi$
$293$	−359.962	+	207.824i	−1.22854	+	0.709298i	−0.261816	+	0.965118i	$0.584321\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−238.526	−	307.794i	−0.803119	−	1.03634i
$298$		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
$303$	228.498	+	174.755i	0.754120	+	0.576748i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	91.4750			0.297964			0.148982	−	0.988840i	$-0.452400\pi$
$307$	91.4750			0.297964			0.148982	+	0.988840i	$0.452400\pi$
$308$		0			0
$309$	−148.478	−	356.848i	−0.480512	−	1.15485i
$310$		0			0
$311$	385.023	−	222.293i	1.23802	−	0.714769i	0.269328	−	0.963049i	$-0.413199\pi$
$311$	385.023	−	222.293i	1.23802	−	0.714769i	0.968688	+	0.248280i	$0.0798652\pi$
$312$		0			0
$313$	67.6156	−	117.114i	0.216024	−	0.374165i	−0.737565	−	0.675277i	$-0.764024\pi$
$313$	67.6156	−	117.114i	0.216024	−	0.374165i	0.953589	+	0.301111i	$0.0973576\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−297.699	−	171.876i	−0.939113	−	0.542197i	−0.0494307	−	0.998778i	$-0.515741\pi$
$317$	−297.699	−	171.876i	−0.939113	−	0.542197i	−0.889682	+	0.456580i	$0.849074\pi$
$318$		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
$323$			217.268i			0.672655i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−81.6389	−	10.6156i	−0.249660	−	0.0324635i
$328$		0			0
$329$	110.377	−	63.7263i	0.335493	−	0.193697i
$330$		0			0
$331$	−269.871	+	467.430i	−0.815319	+	1.41217i	0.0937793	+	0.995593i	$0.470105\pi$
$331$	−269.871	+	467.430i	−0.815319	+	1.41217i	−0.909098	+	0.416581i	$0.863228\pi$
$332$		0			0
$333$	173.469	+	45.8883i	0.520926	+	0.137803i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−274.336	−	475.164i	−0.814054	−	1.40998i	−0.910005	−	0.414597i	$-0.863923\pi$
$337$	−274.336	−	475.164i	−0.814054	−	1.40998i	0.0959512	−	0.995386i	$-0.469411\pi$
$338$		0			0
$339$	−152.116	+	63.2929i	−0.448720	+	0.186705i
$340$		0			0
$341$		−	187.135i		−	0.548783i
$342$		0			0
$343$	−355.308			−1.03588
$344$		0			0
$345$		0			0
$346$		0			0
$347$	100.553	−	58.0540i	0.289777	−	0.167303i	−0.348064	−	0.937471i	$-0.613161\pi$
$347$	100.553	−	58.0540i	0.289777	−	0.167303i	0.637841	+	0.770168i	$0.279828\pi$
$348$		0			0
$349$	−119.155	+	206.383i	−0.341419	+	0.591355i	−0.984696	−	0.174278i	$-0.944241\pi$
$349$	−119.155	+	206.383i	−0.341419	+	0.591355i	0.643278	+	0.765633i	$0.277574\pi$
$350$		0			0
$351$	−89.7786	−	657.610i	−0.255779	−	1.87353i
$352$		0			0
$353$	481.520	+	278.006i	1.36408	+	0.787551i	0.990164	−	0.139912i	$-0.0446819\pi$
$353$	481.520	+	278.006i	1.36408	+	0.787551i	0.373915	+	0.927463i	$0.378015\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	72.8351	+	55.7041i	0.204020	+	0.156034i
$358$		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
$363$	100.264	+	240.972i	0.276211	+	0.663835i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−287.355	+	497.713i	−0.782983	+	1.35617i	0.147214	+	0.989105i	$0.452970\pi$
$367$	−287.355	+	497.713i	−0.782983	+	1.35617i	−0.930197	+	0.367062i	$0.880364\pi$
$368$		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
$373$	−108.136	−	187.298i	−0.289910	−	0.502139i	0.683878	−	0.729596i	$-0.260292\pi$
$373$	−108.136	−	187.298i	−0.289910	−	0.502139i	−0.973788	+	0.227458i	$0.926959\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			496.235i			1.31627i
$378$		0			0
$379$	−252.187			−0.665400			−0.332700	−	0.943033i	$-0.607960\pi$
$379$	−252.187			−0.665400			−0.332700	+	0.943033i	$0.607960\pi$
$380$		0			0
$381$	−278.553	−	36.2204i	−0.731111	−	0.0950668i
$382$		0			0
$383$	111.402	−	64.3180i	0.290867	−	0.167932i	−0.347466	−	0.937693i	$-0.612958\pi$
$383$	111.402	−	64.3180i	0.290867	−	0.167932i	0.638333	+	0.769761i	$0.279624\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	47.0087	−	47.3095i	0.121470	−	0.122247i
$388$		0			0
$389$	−214.436	−	123.805i	−0.551250	−	0.318264i	0.198376	−	0.980126i	$-0.436433\pi$
$389$	−214.436	−	123.805i	−0.551250	−	0.318264i	−0.749626	+	0.661862i	$0.769767\pi$
$390$		0			0
$391$	121.181	+	209.892i	0.309926	+	0.536808i
$392$		0			0
$393$	515.438	−	214.465i	1.31155	−	0.545713i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−123.266			−0.310493			−0.155246	−	0.987876i	$-0.549617\pi$
$397$	−123.266			−0.310493			−0.155246	+	0.987876i	$0.549617\pi$
$398$		0			0
$399$	280.677	−	366.996i	0.703452	−	0.919789i
$400$		0			0
$401$	397.425	−	229.454i	0.991085	−	0.572203i	0.0854868	−	0.996339i	$-0.472755\pi$
$401$	397.425	−	229.454i	0.991085	−	0.572203i	0.905599	+	0.424136i	$0.139422\pi$
$402$		0			0
$403$	159.481	−	276.229i	0.395734	−	0.685432i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−249.016	−	143.770i	−0.611833	−	0.353242i
$408$		0			0
$409$	−38.8984	−	67.3740i	−0.0951061	−	0.164729i	0.814547	−	0.580098i	$-0.196986\pi$
$409$	−38.8984	−	67.3740i	−0.0951061	−	0.164729i	−0.909653	+	0.415369i	$0.863652\pi$
$410$		0			0
$411$	168.061	+	128.533i	0.408908	+	0.312732i
$412$		0			0
$413$			340.677i			0.824884i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	56.1818	+	135.025i	0.134728	+	0.323802i
$418$		0			0
$419$	363.032	−	209.597i	0.866425	−	0.500230i	0.000266138	−	1.00000i	$-0.499915\pi$
$419$	363.032	−	209.597i	0.866425	−	0.500230i	0.866158	+	0.499770i	$0.166582\pi$
$420$		0			0
$421$	−41.7402	+	72.2962i	−0.0991454	+	0.171725i	−0.911331	−	0.411674i	$-0.864944\pi$
$421$	−41.7402	+	72.2962i	−0.0991454	+	0.171725i	0.812186	+	0.583399i	$0.198278\pi$
$422$		0			0
$423$	−174.812	−	173.701i	−0.413268	−	0.410640i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−57.4181	−	99.4510i	−0.134469	−	0.232906i
$428$		0			0
$429$	−137.142	+	1054.69i	−0.319679	+	2.45850i
$430$		0			0
$431$			464.864i			1.07857i	0.842123	+	0.539285i	$0.181306\pi$
$431$			464.864i			1.07857i	−0.842123	+	0.539285i	$0.818694\pi$
$432$		0			0
$433$	201.140			0.464525			0.232263	−	0.972653i	$-0.425387\pi$
$433$	201.140			0.464525			0.232263	+	0.972653i	$0.425387\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1057.59	−	610.598i	2.42011	−	1.39725i
$438$		0			0
$439$	−252.879	+	437.999i	−0.576033	+	0.997719i	0.419895	+	0.907573i	$0.362067\pi$
$439$	−252.879	+	437.999i	−0.576033	+	0.997719i	−0.995929	+	0.0901465i	$0.971266\pi$
$440$		0			0
$441$	64.4296	+	237.423i	0.146099	+	0.538374i
$442$		0			0
$443$	−197.026	−	113.753i	−0.444755	−	0.256779i	0.260858	−	0.965377i	$-0.415995\pi$
$443$	−197.026	−	113.753i	−0.444755	−	0.256779i	−0.705612	+	0.708598i	$0.749328\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	401.247	−	166.952i	0.897644	−	0.373495i
$448$		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
$453$	−423.607	+	553.881i	−0.935114	+	1.22270i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−308.178	+	533.780i	−0.674350	+	1.16801i	0.302309	+	0.953210i	$0.402243\pi$
$457$	−308.178	+	533.780i	−0.674350	+	1.16801i	−0.976659	+	0.214798i	$0.931091\pi$
$458$		0			0
$459$	67.0642	−	164.124i	0.146109	−	0.357568i
$460$		0			0
$461$	−616.599	−	355.994i	−1.33753	−	0.772221i	−0.351086	−	0.936343i	$-0.614188\pi$
$461$	−616.599	−	355.994i	−1.33753	−	0.772221i	−0.986440	+	0.164122i	$0.947521\pi$
$462$		0			0
$463$	−126.318	−	218.788i	−0.272824	−	0.472545i	0.696760	−	0.717304i	$-0.254624\pi$
$463$	−126.318	−	218.788i	−0.272824	−	0.472545i	−0.969584	+	0.244759i	$0.921291\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			508.789i			1.08948i	0.838604	+	0.544742i	$0.183372\pi$
$467$			508.789i			1.08948i	−0.838604	+	0.544742i	$0.816628\pi$
$468$		0			0
$469$	190.611			0.406420
$470$		0			0
$471$	71.1349	+	170.963i	0.151029	+	0.362979i
$472$		0			0
$473$	−92.5555	+	53.4370i	−0.195678	+	0.112975i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	182.687	−	690.602i	0.382993	−	1.44780i
$478$		0			0
$479$	−683.840	−	394.815i	−1.42764	−	0.824249i	−0.430706	−	0.902492i	$-0.641735\pi$
$479$	−683.840	−	394.815i	−1.42764	−	0.824249i	−0.996934	+	0.0782437i	$0.975069\pi$
$480$		0			0
$481$	−245.048	−	424.435i	−0.509454	−	0.882401i
$482$		0			0
$483$	66.4567	−	511.085i	0.137592	−	1.05815i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	317.579			0.652112			0.326056	−	0.945350i	$-0.394280\pi$
$487$	317.579			0.652112			0.326056	+	0.945350i	$0.394280\pi$
$488$		0			0
$489$	−158.771	−	20.6451i	−0.324686	−	0.0422190i
$490$		0			0
$491$	−597.835	+	345.160i	−1.21759	+	0.702973i	−0.964401	−	0.264444i	$-0.914811\pi$
$491$	−597.835	+	345.160i	−1.21759	+	0.702973i	−0.253185	+	0.967418i	$0.581478\pi$
$492$		0			0
$493$	−66.2796	+	114.800i	−0.134441	+	0.232859i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−472.230	−	272.642i	−0.950161	−	0.548576i
$498$		0			0
$499$	25.6761	+	44.4723i	0.0514550	+	0.0891228i	0.890606	−	0.454776i	$-0.150281\pi$
$499$	25.6761	+	44.4723i	0.0514550	+	0.0891228i	−0.839151	+	0.543899i	$0.816947\pi$
$500$		0			0
$501$	372.205	−	154.868i	0.742924	−	0.309118i
$502$		0			0
$503$		−	239.928i		−	0.476994i	−0.971143	−	0.238497i	$-0.923345\pi$
$503$		−	239.928i		−	0.476994i	0.971143	−	0.238497i	$-0.0766547\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−793.270	+	1037.23i	−1.56464	+	2.04582i
$508$		0			0
$509$	−440.034	+	254.054i	−0.864507	+	0.499123i	−0.865519	−	0.500876i	$-0.833011\pi$
$509$	−440.034	+	254.054i	−0.864507	+	0.499123i	0.00101197	+	0.999999i	$0.499678\pi$
$510$		0			0
$511$	93.5171	−	161.976i	0.183008	−	0.316979i
$512$		0			0
$513$	−826.974	−	337.918i	−1.61203	−	0.658709i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	197.454	+	342.000i	0.381922	+	0.661508i
$518$		0			0
$519$	−562.114	−	429.903i	−1.08307	−	0.828329i
$520$		0			0
$521$		−	66.1586i		−	0.126984i	−0.997982	−	0.0634920i	$-0.979776\pi$
$521$		−	66.1586i		−	0.126984i	0.997982	−	0.0634920i	$-0.0202237\pi$
$522$		0			0
$523$	133.503			0.255264			0.127632	−	0.991822i	$-0.459262\pi$
$523$	133.503			0.255264			0.127632	+	0.991822i	$0.459262\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	73.7890	−	42.6021i	0.140017	−	0.0808389i
$528$		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
$533$	−1104.21	−	637.515i	−2.07169	−	1.19609i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	125.696	−	966.666i	0.234071	−	1.80012i
$538$		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
$543$	−611.497	−	79.5133i	−1.12615	−	0.146433i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	302.353	−	523.690i	0.552747	−	0.957386i	−0.445328	−	0.895368i	$-0.646913\pi$
$547$	302.353	−	523.690i	0.552747	−	0.957386i	0.998075	−	0.0620188i	$-0.0197539\pi$
$548$		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
$553$	−51.8473	−	89.8022i	−0.0937565	−	0.162391i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			510.522i			0.916556i	0.888809	+	0.458278i	$0.151534\pi$
$557$			510.522i			0.916556i	−0.888809	+	0.458278i	$0.848466\pi$
$558$		0			0
$559$	−182.161			−0.325869
$560$		0			0
$561$	−172.597	+	225.677i	−0.307659	+	0.402276i
$562$		0			0
$563$	333.774	−	192.705i	0.592849	−	0.342282i	−0.173374	−	0.984856i	$-0.555467\pi$
$563$	333.774	−	192.705i	0.592849	−	0.342282i	0.766223	+	0.642574i	$0.222134\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−325.304	+	190.591i	−0.573729	+	0.336140i
$568$		0			0
$569$	192.215	+	110.975i	0.337812	+	0.195036i	0.659304	−	0.751877i	$-0.270851\pi$
$569$	192.215	+	110.975i	0.337812	+	0.195036i	−0.321492	+	0.946912i	$0.604184\pi$
$570$		0			0
$571$	−187.067	−	324.010i	−0.327613	−	0.567443i	0.654425	−	0.756127i	$-0.272911\pi$
$571$	−187.067	−	324.010i	−0.327613	−	0.567443i	−0.982038	+	0.188685i	$0.939578\pi$
$572$		0			0
$573$	−153.205	−	117.170i	−0.267373	−	0.204486i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−237.121			−0.410955			−0.205478	−	0.978662i	$-0.565875\pi$
$577$	−237.121			−0.410955			−0.205478	+	0.978662i	$0.565875\pi$
$578$		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
$583$	−572.366	+	991.367i	−0.981760	+	1.70046i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−820.431	−	473.676i	−1.39767	−	0.806944i	−0.403519	−	0.914971i	$-0.632213\pi$
$587$	−820.431	−	473.676i	−1.39767	−	0.806944i	−0.994148	+	0.108028i	$0.965547\pi$
$588$		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
$593$		−	744.224i		−	1.25502i	−0.778610	−	0.627508i	$-0.784075\pi$
$593$		−	744.224i		−	1.25502i	0.778610	−	0.627508i	$-0.215925\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−202.036	−	26.2709i	−0.338419	−	0.0440048i
$598$		0			0
$599$	−532.457	+	307.414i	−0.888910	+	0.513212i	−0.873586	−	0.486670i	$-0.838211\pi$
$599$	−532.457	+	307.414i	−0.888910	+	0.513212i	−0.0153242	+	0.999883i	$0.504878\pi$
$600$		0			0
$601$	−156.574	+	271.195i	−0.260523	+	0.451239i	−0.966381	−	0.257114i	$-0.917228\pi$
$601$	−156.574	+	271.195i	−0.260523	+	0.451239i	0.705858	+	0.708353i	$0.250562\pi$
$602$		0			0
$603$	−96.5247	−	355.693i	−0.160074	−	0.589873i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−485.085	−	840.192i	−0.799152	−	1.38417i	−0.920169	−	0.391521i	$-0.871949\pi$
$607$	−485.085	−	840.192i	−0.799152	−	1.38417i	0.121018	−	0.992650i	$-0.461384\pi$
$608$		0			0
$609$	260.260	−	108.290i	0.427356	−	0.177815i
$610$		0			0
$611$			673.099i			1.10163i
$612$		0			0
$613$	−758.446			−1.23727			−0.618635	−	0.785679i	$-0.712314\pi$
$613$	−758.446			−1.23727			−0.618635	+	0.785679i	$0.712314\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−270.760	+	156.323i	−0.438833	+	0.253360i	−0.703102	−	0.711089i	$-0.748202\pi$
$617$	−270.760	+	156.323i	−0.438833	+	0.253360i	0.264270	+	0.964449i	$0.414869\pi$
$618$		0			0
$619$	488.656	−	846.377i	0.789428	−	1.36733i	−0.136889	−	0.990586i	$-0.543710\pi$
$619$	488.656	−	846.377i	0.789428	−	1.36733i	0.926318	−	0.376744i	$-0.122956\pi$
$620$		0			0
$621$	−987.374	+	134.799i	−1.58997	+	0.217067i
$622$		0			0
$623$	−18.9409	−	10.9355i	−0.0304027	−	0.0175530i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	1137.12	+	869.668i	1.81359	+	1.38703i
$628$		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
$633$	10.4498	+	25.1146i	0.0165083	+	0.0396755i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	335.966	−	581.910i	0.527419	−	0.913516i
$638$		0			0
$639$	−269.634	+	1019.28i	−0.421962	+	1.59512i
$640$		0			0
$641$	−764.357	−	441.302i	−1.19245	−	0.688459i	−0.233585	−	0.972336i	$-0.575046\pi$
$641$	−764.357	−	441.302i	−1.19245	−	0.688459i	−0.958860	+	0.283878i	$0.908379\pi$
$642$		0			0
$643$	−285.894	−	495.184i	−0.444626	−	0.770114i	0.553400	−	0.832915i	$-0.313330\pi$
$643$	−285.894	−	495.184i	−0.444626	−	0.770114i	−0.998026	+	0.0628010i	$0.979997\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	113.496i		−	0.175419i	−0.996146	−	0.0877096i	$-0.972045\pi$
$647$		−	113.496i		−	0.175419i	0.996146	−	0.0877096i	$-0.0279547\pi$
$648$		0			0
$649$	−1055.58			−1.62646
$650$		0			0
$651$	−179.676	−	23.3633i	−0.276000	−	0.0358884i
$652$		0			0
$653$	880.891	−	508.582i	1.34899	−	0.778840i	0.360884	−	0.932611i	$-0.382475\pi$
$653$	880.891	−	508.582i	1.34899	−	0.778840i	0.988106	+	0.153771i	$0.0491418\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−349.616	−	92.4852i	−0.532140	−	0.140769i
$658$		0			0
$659$	697.672	+	402.801i	1.05868	+	0.611231i	0.925068	−	0.379802i	$-0.124008\pi$
$659$	697.672	+	402.801i	1.05868	+	0.611231i	0.133615	+	0.991033i	$0.457341\pi$
$660$		0			0
$661$	491.116	+	850.638i	0.742989	+	1.28690i	0.951128	+	0.308796i	$0.0999261\pi$
$661$	491.116	+	850.638i	0.742989	+	1.28690i	−0.208139	+	0.978099i	$0.566741\pi$
$662$		0			0
$663$	−447.097	+	186.029i	−0.674354	+	0.280587i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	745.076			1.11705
$668$		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
$673$	142.183	−	246.268i	0.211267	−	0.365926i	−0.740844	−	0.671677i	$-0.765574\pi$
$673$	142.183	−	246.268i	0.211267	−	0.365926i	0.952111	+	0.305751i	$0.0989076\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	222.141	+	128.253i	0.328125	+	0.189443i	0.655009	−	0.755621i	$-0.272665\pi$
$677$	222.141	+	128.253i	0.328125	+	0.189443i	−0.326883	+	0.945065i	$0.605998\pi$
$678$		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
$683$			1126.46i			1.64928i	0.565660	+	0.824639i	$0.308622\pi$
$683$			1126.46i			1.64928i	−0.565660	+	0.824639i	$0.691378\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	451.503	+	1085.13i	0.657210	+	1.57952i
$688$		0			0
$689$	−1689.73	+	975.568i	−2.45244	+	1.41592i
$690$		0			0
$691$	144.035	−	249.476i	0.208444	−	0.361036i	−0.742780	−	0.669535i	$-0.766493\pi$
$691$	144.035	−	249.476i	0.208444	−	0.361036i	0.951225	+	0.308499i	$0.0998267\pi$
$692$		0			0
$693$	583.081	−	158.231i	0.841387	−	0.228328i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−170.299	−	294.967i	−0.244332	−	0.423195i
$698$		0			0
$699$	59.0746	−	454.313i	0.0845130	−	0.649947i
$700$		0			0
$701$			854.593i			1.21911i	0.792745	+	0.609553i	$0.208651\pi$
$701$			854.593i			1.21911i	−0.792745	+	0.609553i	$0.791349\pi$
$702$		0			0
$703$	−659.665			−0.938357
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−386.527	+	223.162i	−0.546715	+	0.315646i
$708$		0			0
$709$	183.387	−	317.636i	0.258656	−	0.448006i	−0.707226	−	0.706988i	$-0.750054\pi$
$709$	183.387	−	317.636i	0.258656	−	0.448006i	0.965882	+	0.258982i	$0.0833870\pi$
$710$		0			0
$711$	−141.322	+	142.226i	−0.198765	+	0.200037i
$712$		0			0
$713$	−414.746	−	239.454i	−0.581692	−	0.335840i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	202.986	−	84.4590i	0.283104	−	0.117795i
$718$		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
$723$	783.612	−	1024.60i	1.08383	−	1.41715i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	330.352	−	572.186i	0.454404	−	0.787051i	−0.544250	−	0.838923i	$-0.683186\pi$
$727$	330.352	−	572.186i	0.454404	−	0.787051i	0.998654	+	0.0518723i	$0.0165189\pi$
$728$		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
$733$	13.6300	+	23.6078i	0.0185947	+	0.0322071i	0.875173	−	0.483810i	$-0.160747\pi$
$733$	13.6300	+	23.6078i	0.0185947	+	0.0322071i	−0.856578	+	0.516017i	$0.827414\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			590.601i			0.801359i
$738$		0			0
$739$	549.148			0.743096			0.371548	−	0.928414i	$-0.378827\pi$
$739$	549.148			0.743096			0.371548	+	0.928414i	$0.378827\pi$
$740$		0			0
$741$	937.350	+	2252.80i	1.26498	+	3.04021i
$742$		0			0
$743$	−152.537	+	88.0673i	−0.205299	+	0.118529i	−0.599125	−	0.800656i	$-0.704485\pi$
$743$	−152.537	+	88.0673i	−0.205299	+	0.118529i	0.393826	+	0.919185i	$0.371151\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−859.425	−	853.960i	−1.15050	−	1.14319i
$748$		0			0
$749$	−78.4890	−	45.3157i	−0.104792	−	0.0605016i
$750$		0			0
$751$	108.231	+	187.462i	0.144116	+	0.249616i	0.929043	−	0.369972i	$-0.120633\pi$
$751$	108.231	+	187.462i	0.144116	+	0.249616i	−0.784927	+	0.619589i	$0.787299\pi$
$752$		0			0
$753$	−63.9189	+	491.568i	−0.0848856	+	0.652813i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1104.91			−1.45959			−0.729793	−	0.683668i	$-0.760384\pi$
$757$	−1104.91			−1.45959			−0.729793	+	0.683668i	$0.760384\pi$
$758$		0			0
$759$	1583.58	+	205.914i	2.08640	+	0.271296i
$760$		0			0
$761$	774.245	−	447.011i	1.01741	−	0.587399i	0.104054	−	0.994572i	$-0.466819\pi$
$761$	774.245	−	447.011i	1.01741	−	0.587399i	0.913351	+	0.407173i	$0.133485\pi$
$762$		0			0
$763$	63.8663	−	110.620i	0.0837042	−	0.144980i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1558.13	−	899.586i	−2.03146	−	1.17286i
$768$		0			0
$769$	−287.360	−	497.722i	−0.373680	−	0.647233i	0.616448	−	0.787395i	$-0.288571\pi$
$769$	−287.360	−	497.722i	−0.373680	−	0.647233i	−0.990129	+	0.140162i	$0.955238\pi$
$770$		0			0
$771$	1298.42	−	540.249i	1.68407	−	0.700711i
$772$		0			0
$773$			71.2870i			0.0922212i	0.998936	+	0.0461106i	$0.0146827\pi$
$773$			71.2870i			0.0922212i	−0.998936	+	0.0461106i	$0.985317\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−169.128	+	221.141i	−0.217668	+	0.284609i
$778$		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
$783$	−333.870	−	430.825i	−0.426399	−	0.550223i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	17.4363	+	30.2005i	0.0221554	+	0.0383742i	0.876891	−	0.480690i	$-0.159614\pi$
$787$	17.4363	+	30.2005i	0.0221554	+	0.0383742i	−0.854735	+	0.519064i	$0.826280\pi$
$788$		0			0
$789$	84.4254	+	64.5683i	0.107003	+	0.0818356i
$790$		0			0
$791$		−	255.629i		−	0.323172i
$792$		0			0
$793$	606.469			0.764777
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−782.440	+	451.742i	−0.981731	+	0.566803i	−0.902792	−	0.430077i	$-0.858487\pi$
$797$	−782.440	+	451.742i	−0.981731	+	0.566803i	−0.0789390	+	0.996879i	$0.525153\pi$
$798$		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
$803$	501.878	+	289.759i	0.625004	+	0.360846i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	54.7219	−	420.839i	0.0678090	−	0.521485i
$808$		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
$813$	−1108.11	−	144.088i	−1.36298	−	0.177229i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−122.594	+	212.338i	−0.150053	+	0.259900i
$818$		0			0
$819$	995.531	+	263.352i	1.21555	+	0.321553i
$820$		0			0
$821$	−1352.85	−	781.066i	−1.64780	−	0.951359i	−0.977943	−	0.208871i	$-0.933021\pi$
$821$	−1352.85	−	781.066i	−1.64780	−	0.951359i	−0.669859	−	0.742488i	$-0.733646\pi$
$822$		0			0
$823$	707.151	+	1224.82i	0.859236	+	1.48824i	0.872659	+	0.488331i	$0.162394\pi$
$823$	707.151	+	1224.82i	0.859236	+	1.48824i	−0.0134224	+	0.999910i	$0.504273\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	949.074i		−	1.14761i	−0.818992	−	0.573805i	$-0.805467\pi$
$827$		−	949.074i		−	1.14761i	0.818992	−	0.573805i	$-0.194533\pi$
$828$		0			0
$829$	1144.99			1.38118			0.690588	−	0.723249i	$-0.257352\pi$
$829$	1144.99			1.38118			0.690588	+	0.723249i	$0.257352\pi$
$830$		0			0
$831$	470.590	−	615.314i	0.566294	−	0.740450i
$832$		0			0
$833$	155.445	−	89.7465i	0.186609	−	0.107739i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	47.3895	+	347.118i	0.0566182	+	0.414717i
$838$		0			0
$839$	−218.826	−	126.340i	−0.260818	−	0.150583i	0.363890	−	0.931442i	$-0.381449\pi$
$839$	−218.826	−	126.340i	−0.260818	−	0.150583i	−0.624708	+	0.780859i	$0.714782\pi$
$840$		0			0
$841$	−216.742	−	375.408i	−0.257719	−	0.446383i
$842$		0			0
$843$	−780.648	−	597.037i	−0.926035	−	0.708228i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−404.951			−0.478101
$848$		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
$853$	136.549	−	236.510i	0.160081	−	0.277269i	−0.774816	−	0.632186i	$-0.782158\pi$
$853$	136.549	−	236.510i	0.160081	−	0.277269i	0.934898	+	0.354917i	$0.115491\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	358.085	+	206.740i	0.417835	+	0.241237i	0.694151	−	0.719830i	$-0.255780\pi$
$857$	358.085	+	206.740i	0.417835	+	0.241237i	−0.276315	+	0.961067i	$0.589113\pi$
$858$		0			0
$859$	−664.377	−	1150.73i	−0.773431	−	1.33962i	−0.935672	−	0.352870i	$-0.885206\pi$
$859$	−664.377	−	1150.73i	−0.773431	−	1.33962i	0.162242	−	0.986751i	$-0.448128\pi$
$860$		0			0
$861$	−93.3935	+	718.243i	−0.108471	+	0.834196i
$862$		0			0
$863$			283.552i			0.328565i	0.986413	+	0.164283i	$0.0525309\pi$
$863$			283.552i			0.328565i	−0.986413	+	0.164283i	$0.947469\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	731.483	+	95.1152i	0.843695	+	0.109706i
$868$		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
$873$	−881.338	+	886.978i	−1.00955	+	1.01601i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	229.117	+	396.843i	0.261251	+	0.452500i	0.966575	−	0.256385i	$-0.0825316\pi$
$877$	229.117	+	396.843i	0.261251	+	0.452500i	−0.705323	+	0.708886i	$0.749198\pi$
$878$		0			0
$879$	−1151.27	+	479.022i	−1.30974	+	0.544962i
$880$		0			0
$881$			1408.20i			1.59841i	0.601056	+	0.799207i	$0.294747\pi$
$881$			1408.20i			1.59841i	−0.601056	+	0.799207i	$0.705253\pi$
$882$		0			0
$883$	200.279			0.226817			0.113408	−	0.993548i	$-0.463823\pi$
$883$	200.279			0.226817			0.113408	+	0.993548i	$0.463823\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1026.67	−	592.748i	1.15746	−	0.668262i	0.206769	−	0.978390i	$-0.433705\pi$
$887$	1026.67	−	592.748i	1.15746	−	0.668262i	0.950695	+	0.310128i	$0.100372\pi$
$888$		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
$893$	784.607	+	452.993i	0.878620	+	0.507271i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	2162.03	+	1653.51i	2.41029	+	1.84338i
$898$		0			0
$899$		−	261.937i		−	0.291364i
$900$		0			0
$901$	−521.207			−0.578476
$902$		0			0
$903$	39.7516	+	95.5376i	0.0440217	+	0.105800i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	665.240	−	1152.23i	0.733451	−	1.27037i	−0.221949	−	0.975058i	$-0.571242\pi$
$907$	665.240	−	1152.23i	0.733451	−	1.27037i	0.955400	−	0.295316i	$-0.0954248\pi$
$908$		0			0
$909$	612.171	+	608.278i	0.673455	+	0.669173i
$910$		0			0
$911$	311.564	+	179.882i	0.342003	+	0.197455i	0.661157	−	0.750247i	$-0.270066\pi$
$911$	311.564	+	179.882i	0.342003	+	0.197455i	−0.319155	+	0.947703i	$0.603399\pi$
$912$		0			0
$913$	970.736	+	1681.36i	1.06324	+	1.84158i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			866.189i			0.944590i
$918$		0			0
$919$	114.308			0.124383			0.0621913	−	0.998064i	$-0.480191\pi$
$919$	114.308			0.124383			0.0621913	+	0.998064i	$0.480191\pi$
$920$		0			0
$921$	272.134	+	35.3858i	0.295477	+	0.0384210i
$922$		0			0
$923$	2493.93	−	1439.87i	2.70198	−	1.55999i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−303.675	−	1119.04i	−0.327589	−	1.20717i
$928$		0			0
$929$	−692.105	−	399.587i	−0.745000	−	0.430126i	0.0788843	−	0.996884i	$-0.474864\pi$
$929$	−692.105	−	399.587i	−0.745000	−	0.430126i	−0.823885	+	0.566758i	$0.808198\pi$
$930$		0			0
$931$	−452.207	−	783.246i	−0.485722	−	0.841296i
$932$		0			0
$933$	1231.42	−	512.372i	1.31985	−	0.549166i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	937.387			1.00041			0.500206	−	0.865906i	$-0.333257\pi$
$937$	937.387			1.00041			0.500206	+	0.865906i	$0.333257\pi$
$938$		0			0
$939$	246.457	−	322.252i	0.262468	−	0.343186i
$940$		0			0
$941$	−490.911	+	283.428i	−0.521691	+	0.301198i	−0.737626	−	0.675209i	$-0.764053\pi$
$941$	−490.911	+	283.428i	−0.521691	+	0.301198i	0.215935	+	0.976408i	$0.430720\pi$
$942$		0			0
$943$	−957.202	+	1657.92i	−1.01506	+	1.75814i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−619.197	−	357.494i	−0.653851	−	0.377501i	0.136079	−	0.990698i	$-0.456550\pi$
$947$	−619.197	−	357.494i	−0.653851	−	0.377501i	−0.789930	+	0.613197i	$0.789883\pi$
$948$		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
$953$		−	918.880i		−	0.964197i	−0.876117	−	0.482099i	$-0.839875\pi$
$953$		−	918.880i		−	0.964197i	0.876117	−	0.482099i	$-0.160125\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	335.531	+	806.405i	0.350607	+	0.842638i
$958$		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
$963$	−44.8156	+	169.414i	−0.0465375	+	0.175923i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	9.16023	+	15.8660i	0.00947283	+	0.0164074i	0.870723	−	0.491774i	$-0.163651\pi$
$967$	9.16023	+	15.8660i	0.00947283	+	0.0164074i	−0.861250	+	0.508181i	$0.830318\pi$
$968$		0			0
$969$	−84.0468	+	646.362i	−0.0867356	+	0.667040i
$970$		0			0
$971$			35.9529i			0.0370266i	0.999829	+	0.0185133i	$0.00589331\pi$
$971$			35.9529i			0.0370266i	−0.999829	+	0.0185133i	$0.994107\pi$
$972$		0			0
$973$	−226.909			−0.233205
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−486.908	+	281.116i	−0.498370	+	0.287734i	−0.728040	−	0.685534i	$-0.759569\pi$
$977$	−486.908	+	281.116i	−0.498370	+	0.287734i	0.229670	+	0.973269i	$0.426235\pi$
$978$		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
$983$	418.957	+	241.885i	0.426202	+	0.246068i	0.697727	−	0.716363i	$-0.254195\pi$
$983$	418.957	+	241.885i	0.426202	+	0.246068i	−0.271525	+	0.962431i	$0.587528\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	353.019	−	146.885i	0.357669	−	0.148820i
$988$		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
$993$	−983.671	+	1286.19i	−0.990606	+	1.29525i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−155.387	+	269.139i	−0.155855	+	0.269949i	−0.933370	−	0.358916i	$-0.883147\pi$
$997$	−155.387	+	269.139i	−0.155855	+	0.269949i	0.777515	+	0.628864i	$0.216480\pi$
$998$		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.p.e.101.8	yes	16
3.2	odd	2		2700.3.p.d.1601.3		16
5.2	odd	4		900.3.u.d.749.9		32
5.3	odd	4		900.3.u.d.749.8		32
5.4	even	2		900.3.p.d.101.1	✓	16
9.4	even	3		2700.3.p.d.2501.3		16
9.5	odd	6	inner	900.3.p.e.401.8	yes	16
15.2	even	4		2700.3.u.d.2249.6		32
15.8	even	4		2700.3.u.d.2249.11		32
15.14	odd	2		2700.3.p.e.1601.6		16
45.4	even	6		2700.3.p.e.2501.6		16
45.13	odd	12		2700.3.u.d.449.6		32
45.14	odd	6		900.3.p.d.401.1	yes	16
45.22	odd	12		2700.3.u.d.449.11		32
45.23	even	12		900.3.u.d.149.9		32
45.32	even	12		900.3.u.d.149.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.p.d.101.1	✓	16	5.4	even	2
900.3.p.d.401.1	yes	16	45.14	odd	6
900.3.p.e.101.8	yes	16	1.1	even	1	trivial
900.3.p.e.401.8	yes	16	9.5	odd	6	inner
900.3.u.d.149.8		32	45.32	even	12
900.3.u.d.149.9		32	45.23	even	12
900.3.u.d.749.8		32	5.3	odd	4
900.3.u.d.749.9		32	5.2	odd	4
2700.3.p.d.1601.3		16	3.2	odd	2
2700.3.p.d.2501.3		16	9.4	even	3
2700.3.p.e.1601.6		16	15.14	odd	2
2700.3.p.e.2501.6		16	45.4	even	6
2700.3.u.d.449.6		32	45.13	odd	12
2700.3.u.d.449.11		32	45.22	odd	12
2700.3.u.d.2249.6		32	15.2	even	4
2700.3.u.d.2249.11		32	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.97496 + 0.386835i) q^{3} +(-2.32731 + 4.03103i) q^{7} +(8.70072 + 2.30163i) q^{9} +O(q^{10})\)	\(q+(2.97496 + 0.386835i) q^{3} +(-2.32731 + 4.03103i) q^{7} +(8.70072 + 2.30163i) q^{9} +(-12.4900 - 7.21110i) q^{11} +(-12.2909 - 21.2885i) q^{13} -6.56655i q^{17} -33.0870 q^{19} +(-8.48300 + 11.0918i) q^{21} +(-31.9638 + 18.4543i) q^{23} +(24.9939 + 10.2130i) q^{27} +(-17.4825 - 10.0935i) q^{29} +(6.48775 + 11.2371i) q^{31} +(-34.3676 - 26.2843i) q^{33} +19.9373 q^{37} +(-28.3298 - 68.0870i) q^{39} +(44.9196 - 25.9344i) q^{41} +(3.70519 - 6.41757i) q^{43} +(-23.7134 - 13.6910i) q^{47} +(13.6672 + 23.6723i) q^{49} +(2.54017 - 19.5352i) q^{51} -79.3730i q^{53} +(-98.4324 - 12.7992i) q^{57} +(63.3853 - 36.5955i) q^{59} +(-12.3357 + 21.3660i) q^{61} +(-29.5273 + 29.7162i) q^{63} +(-20.4754 - 35.4645i) q^{67} +(-102.230 + 42.5360i) q^{69} +117.149i q^{71} -40.1824 q^{73} +(58.1363 - 33.5650i) q^{77} +(-11.1389 + 19.2931i) q^{79} +(70.4050 + 40.0517i) q^{81} +(-116.582 - 67.3085i) q^{83} +(-48.1051 - 36.7906i) q^{87} +4.69877i q^{89} +114.419 q^{91} +(14.9538 + 35.9396i) q^{93} +(-69.4664 + 120.319i) q^{97} +(-92.0745 - 91.4891i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{3} - q^{7} + 14 q^{9}+O(q^{10}) \) 16 * q + 2 * q^3 - q^7 + 14 * q^9	\( 16 q + 2 q^{3} - q^{7} + 14 q^{9} - 10 q^{13} + 2 q^{19} + q^{21} + 27 q^{23} - 16 q^{27} + 9 q^{29} + 8 q^{31} + 36 q^{33} - 22 q^{37} + 19 q^{39} + 54 q^{41} + 44 q^{43} - 108 q^{47} - 45 q^{49} + 90 q^{51} - 68 q^{57} + 9 q^{59} - 55 q^{61} - 107 q^{63} - 28 q^{67} - 147 q^{69} + 86 q^{73} + 342 q^{77} + 11 q^{79} - 130 q^{81} - 306 q^{83} + 375 q^{87} - 134 q^{91} - 83 q^{93} + 41 q^{97} + 252 q^{99}+O(q^{100}) \) 16 * q + 2 * q^3 - q^7 + 14 * q^9 - 10 * q^13 + 2 * q^19 + q^21 + 27 * q^23 - 16 * q^27 + 9 * q^29 + 8 * q^31 + 36 * q^33 - 22 * q^37 + 19 * q^39 + 54 * q^41 + 44 * q^43 - 108 * q^47 - 45 * q^49 + 90 * q^51 - 68 * q^57 + 9 * q^59 - 55 * q^61 - 107 * q^63 - 28 * q^67 - 147 * q^69 + 86 * q^73 + 342 * q^77 + 11 * q^79 - 130 * q^81 - 306 * q^83 + 375 * q^87 - 134 * q^91 - 83 * q^93 + 41 * q^97 + 252 * q^99

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