LMFDB - Embedded newform 900.3.u.a.749.3

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.303595776.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			749.3
Root			$1.26217 - 1.18614i$ of defining polynomial
Character	$\chi$	$=$	900.749
Dual form			900.3.u.a.149.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.05446 - 2.18614i) q^{3} +(7.02939 + 4.05842i) q^{7} +(-0.558422 - 8.98266i) q^{9} +O(q^{10})$	\(q+(2.05446 - 2.18614i) q^{3} +(7.02939 + 4.05842i) q^{7} +(-0.558422 - 8.98266i) q^{9} +(-17.6168 - 10.1711i) q^{11} +(-5.29734 + 3.05842i) q^{13} -17.9653 q^{17} -9.11684 q^{19} +(23.3139 - 7.02939i) q^{21} +(-16.7769 - 29.0584i) q^{23} +(-20.7846 - 17.2337i) q^{27} +(-14.4090 - 8.31901i) q^{29} +(11.1753 + 19.3561i) q^{31} +(-58.4285 + 17.6168i) q^{33} -50.4674i q^{37} +(-4.19702 + 17.8641i) q^{39} +(29.9674 - 17.3017i) q^{41} +(19.9186 + 11.5000i) q^{43} +(19.1537 - 33.1753i) q^{47} +(8.44158 + 14.6212i) q^{49} +(-36.9090 + 39.2747i) q^{51} +19.0149 q^{53} +(-18.7302 + 19.9307i) q^{57} +(2.96738 - 1.71322i) q^{59} +(23.1753 - 40.1407i) q^{61} +(32.5301 - 65.4090i) q^{63} +(-5.45504 + 3.14947i) q^{67} +(-97.9932 - 23.0226i) q^{69} -35.9306i q^{71} -47.3505i q^{73} +(-82.5571 - 142.993i) q^{77} +(-42.2921 + 73.2521i) q^{79} +(-80.3763 + 10.0322i) q^{81} +(-19.1537 + 33.1753i) q^{83} +(-47.7891 + 14.4090i) q^{87} +143.723i q^{89} -49.6495 q^{91} +(65.2743 + 15.3356i) q^{93} +(-69.9457 - 40.3832i) q^{97} +(-81.5258 + 163.926i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 30 q^{9}+O(q^{10}) $ 8 * q + 30 * q^9	$ 8 q + 30 q^{9} - 72 q^{11} - 4 q^{19} + 198 q^{21} + 126 q^{29} - 14 q^{31} - 114 q^{39} - 36 q^{41} + 102 q^{49} - 54 q^{51} - 252 q^{59} + 82 q^{61} - 198 q^{69} - 166 q^{79} - 126 q^{81} - 604 q^{91} - 342 q^{99}+O(q^{100}) $ 8 * q + 30 * q^9 - 72 * q^11 - 4 * q^19 + 198 * q^21 + 126 * q^29 - 14 * q^31 - 114 * q^39 - 36 * q^41 + 102 * q^49 - 54 * q^51 - 252 * q^59 + 82 * q^61 - 198 * q^69 - 166 * q^79 - 126 * q^81 - 604 * q^91 - 342 * 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
$3$	2.05446	−	2.18614i	0.684819	−	0.728714i
$3$	2.05446	−	2.18614i	0.684819	−	0.728714i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	7.02939	+	4.05842i	1.00420	+	0.579775i	0.909488	−	0.415730i	$-0.136474\pi$
$7$	7.02939	+	4.05842i	1.00420	+	0.579775i	0.0947110	+	0.995505i	$0.469807\pi$
$8$		0			0
$9$	−0.558422	−	8.98266i	−0.0620469	−	0.998073i
$10$		0			0
$11$	−17.6168	−	10.1711i	−1.60153	−	0.924645i	−0.991181	−	0.132513i	$-0.957695\pi$
$11$	−17.6168	−	10.1711i	−1.60153	−	0.924645i	−0.610350	−	0.792132i	$-0.708971\pi$
$12$		0			0
$13$	−5.29734	+	3.05842i	−0.407488	+	0.235263i	−0.689710	−	0.724086i	$-0.742262\pi$
$13$	−5.29734	+	3.05842i	−0.407488	+	0.235263i	0.282222	+	0.959349i	$0.408929\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−17.9653			−1.05678			−0.528392	−	0.849001i	$-0.677205\pi$
$17$	−17.9653			−1.05678			−0.528392	+	0.849001i	$0.677205\pi$
$18$		0			0
$19$	−9.11684			−0.479834			−0.239917	−	0.970793i	$-0.577120\pi$
$19$	−9.11684			−0.479834			−0.239917	+	0.970793i	$0.577120\pi$
$20$		0			0
$21$	23.3139	−	7.02939i	1.11018	−	0.334733i
$22$		0			0
$23$	−16.7769	−	29.0584i	−0.729430	−	1.26341i	−0.957124	−	0.289677i	$-0.906452\pi$
$23$	−16.7769	−	29.0584i	−0.729430	−	1.26341i	0.227695	−	0.973733i	$-0.426881\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−20.7846	−	17.2337i	−0.769800	−	0.638285i
$28$		0			0
$29$	−14.4090	−	8.31901i	−0.496860	−	0.286863i	0.230556	−	0.973059i	$-0.425946\pi$
$29$	−14.4090	−	8.31901i	−0.496860	−	0.286863i	−0.727416	+	0.686197i	$0.759279\pi$
$30$		0			0
$31$	11.1753	+	19.3561i	0.360492	+	0.624391i	0.988042	−	0.154185i	$-0.0492753\pi$
$31$	11.1753	+	19.3561i	0.360492	+	0.624391i	−0.627549	+	0.778577i	$0.715942\pi$
$32$		0			0
$33$	−58.4285	+	17.6168i	−1.77056	+	0.533844i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	50.4674i		−	1.36398i	−0.731360	−	0.681992i	$-0.761114\pi$
$37$		−	50.4674i		−	1.36398i	0.731360	−	0.681992i	$-0.238886\pi$
$38$		0			0
$39$	−4.19702	+	17.8641i	−0.107616	+	0.458055i
$40$		0			0
$41$	29.9674	−	17.3017i	0.730912	−	0.421992i	−0.0878440	−	0.996134i	$-0.527998\pi$
$41$	29.9674	−	17.3017i	0.730912	−	0.421992i	0.818756	+	0.574142i	$0.194664\pi$
$42$		0			0
$43$	19.9186	+	11.5000i	0.463223	+	0.267442i	0.713398	−	0.700759i	$-0.247155\pi$
$43$	19.9186	+	11.5000i	0.463223	+	0.267442i	−0.250176	+	0.968200i	$0.580488\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	19.1537	−	33.1753i	0.407527	−	0.705857i	−0.587085	−	0.809525i	$-0.699725\pi$
$47$	19.1537	−	33.1753i	0.407527	−	0.705857i	0.994612	+	0.103668i	$0.0330580\pi$
$48$		0			0
$49$	8.44158	+	14.6212i	0.172277	+	0.298393i
$50$		0			0
$51$	−36.9090	+	39.2747i	−0.723705	+	0.770092i
$52$		0			0
$53$	19.0149			0.358771			0.179386	−	0.983779i	$-0.442589\pi$
$53$	19.0149			0.358771			0.179386	+	0.983779i	$0.442589\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−18.7302	+	19.9307i	−0.328599	+	0.349661i
$58$		0			0
$59$	2.96738	−	1.71322i	0.0502945	−	0.0290375i	−0.474642	−	0.880179i	$-0.657422\pi$
$59$	2.96738	−	1.71322i	0.0502945	−	0.0290375i	0.524936	+	0.851141i	$0.324089\pi$
$60$		0			0
$61$	23.1753	−	40.1407i	0.379922	−	0.658045i	−0.611128	−	0.791532i	$-0.709284\pi$
$61$	23.1753	−	40.1407i	0.379922	−	0.658045i	0.991051	+	0.133487i	$0.0426174\pi$
$62$		0			0
$63$	32.5301	−	65.4090i	0.516350	−	1.03824i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−5.45504	+	3.14947i	−0.0814185	+	0.0470070i	−0.540157	−	0.841565i	$-0.681635\pi$
$67$	−5.45504	+	3.14947i	−0.0814185	+	0.0470070i	0.458738	+	0.888572i	$0.348302\pi$
$68$		0			0
$69$	−97.9932	−	23.0226i	−1.42019	−	0.333661i
$70$		0			0
$71$		−	35.9306i		−	0.506065i	−0.967458	−	0.253033i	$-0.918572\pi$
$71$		−	35.9306i		−	0.506065i	0.967458	−	0.253033i	$-0.0814280\pi$
$72$		0			0
$73$		−	47.3505i		−	0.648637i	−0.945948	−	0.324319i	$-0.894865\pi$
$73$		−	47.3505i		−	0.648637i	0.945948	−	0.324319i	$-0.105135\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−82.5571	−	142.993i	−1.07217	−	1.85705i
$78$		0			0
$79$	−42.2921	+	73.2521i	−0.535343	+	0.927242i	0.463803	+	0.885938i	$0.346484\pi$
$79$	−42.2921	+	73.2521i	−0.535343	+	0.927242i	−0.999147	+	0.0413035i	$0.986849\pi$
$80$		0			0
$81$	−80.3763	+	10.0322i	−0.992300	+	0.123855i
$82$		0			0
$83$	−19.1537	+	33.1753i	−0.230768	+	0.399702i	−0.958034	−	0.286653i	$-0.907457\pi$
$83$	−19.1537	+	33.1753i	−0.230768	+	0.399702i	0.727266	+	0.686355i	$0.240791\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−47.7891	+	14.4090i	−0.549300	+	0.165620i
$88$		0			0
$89$			143.723i			1.61486i	0.589963	+	0.807430i	$0.299142\pi$
$89$			143.723i			1.61486i	−0.589963	+	0.807430i	$0.700858\pi$
$90$		0			0
$91$	−49.6495			−0.545599
$92$		0			0
$93$	65.2743	+	15.3356i	0.701874	+	0.164899i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−69.9457	−	40.3832i	−0.721089	−	0.416321i	0.0940641	−	0.995566i	$-0.470014\pi$
$97$	−69.9457	−	40.3832i	−0.721089	−	0.416321i	−0.815154	+	0.579245i	$0.803347\pi$
$98$		0			0
$99$	−81.5258	+	163.926i	−0.823493	+	1.65582i
$100$		0			0
$101$	105.942	+	61.1654i	1.04893	+	0.605598i	0.922349	−	0.386359i	$-0.126267\pi$
$101$	105.942	+	61.1654i	1.04893	+	0.605598i	0.126578	+	0.991957i	$0.459601\pi$
$102$		0			0
$103$	−63.7823	+	36.8247i	−0.619246	+	0.357522i	−0.776575	−	0.630024i	$-0.783045\pi$
$103$	−63.7823	+	36.8247i	−0.619246	+	0.357522i	0.157330	+	0.987546i	$0.449712\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−72.9108			−0.681410			−0.340705	−	0.940170i	$-0.610666\pi$
$107$	−72.9108			−0.681410			−0.340705	+	0.940170i	$0.610666\pi$
$108$		0			0
$109$	−31.2989			−0.287146			−0.143573	−	0.989640i	$-0.545859\pi$
$109$	−31.2989			−0.287146			−0.143573	+	0.989640i	$0.545859\pi$
$110$		0			0
$111$	−110.329	−	103.683i	−0.993953	−	0.934081i
$112$		0			0
$113$	−9.36858	−	16.2269i	−0.0829078	−	0.143601i	0.821590	−	0.570079i	$-0.193087\pi$
$113$	−9.36858	−	16.2269i	−0.0829078	−	0.143601i	−0.904498	+	0.426478i	$0.859754\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	30.4309	+	45.8763i	0.260093	+	0.392105i
$118$		0			0
$119$	−126.285	−	72.9108i	−1.06122	−	0.612696i
$120$		0			0
$121$	146.402	+	253.576i	1.20993	+	2.09567i
$122$		0			0
$123$	23.7428	−	101.058i	0.193031	−	0.821613i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	126.103i		−	0.992939i	−0.868054	−	0.496469i	$-0.834630\pi$
$127$		−	126.103i		−	0.992939i	0.868054	−	0.496469i	$-0.165370\pi$
$128$		0			0
$129$	66.0625	−	19.9186i	0.512112	−	0.154408i
$130$		0			0
$131$	140.694	−	81.2299i	1.07400	−	0.620075i	0.144730	−	0.989471i	$-0.453769\pi$
$131$	140.694	−	81.2299i	1.07400	−	0.620075i	0.929272	+	0.369396i	$0.120435\pi$
$132$		0			0
$133$	−64.0859	−	37.0000i	−0.481849	−	0.278195i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−52.1827	+	90.3832i	−0.380896	+	0.659731i	−0.991191	−	0.132443i	$-0.957718\pi$
$137$	−52.1827	+	90.3832i	−0.380896	+	0.659731i	0.610295	+	0.792174i	$0.291051\pi$
$138$		0			0
$139$	30.6168	+	53.0299i	0.220265	+	0.381510i	0.954888	−	0.296965i	$-0.0959744\pi$
$139$	30.6168	+	53.0299i	0.220265	+	0.381510i	−0.734623	+	0.678475i	$0.762641\pi$
$140$		0			0
$141$	−33.1753	−	110.030i	−0.235286	−	0.780354i
$142$		0			0
$143$	124.430			0.870139
$144$		0			0
$145$		0			0
$146$		0			0
$147$	49.3069	+	11.5842i	0.335421	+	0.0788042i
$148$		0			0
$149$	128.344	−	74.0993i	0.861367	−	0.497311i	−0.00310272	−	0.999995i	$-0.500988\pi$
$149$	128.344	−	74.0993i	0.861367	−	0.497311i	0.864470	+	0.502685i	$0.167654\pi$
$150$		0			0
$151$	−127.526	+	220.881i	−0.844542	+	1.46279i	0.0414769	+	0.999139i	$0.486794\pi$
$151$	−127.526	+	220.881i	−0.844542	+	1.46279i	−0.886019	+	0.463650i	$0.846540\pi$
$152$		0			0
$153$	10.0322	+	161.376i	0.0655701	+	1.05475i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	253.272	−	146.227i	1.61320	−	0.931381i	0.624577	−	0.780963i	$-0.285271\pi$
$157$	253.272	−	146.227i	1.61320	−	0.931381i	0.988622	−	0.150418i	$-0.0480620\pi$
$158$		0			0
$159$	39.0652	−	41.5692i	0.245693	−	0.261442i
$160$		0			0
$161$		−	272.351i		−	1.69162i
$162$		0			0
$163$		−	93.5326i		−	0.573820i	−0.957958	−	0.286910i	$-0.907372\pi$
$163$		−	93.5326i		−	0.573820i	0.957958	−	0.286910i	$-0.0926280\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−56.1340	−	97.2269i	−0.336131	−	0.582197i	0.647570	−	0.762006i	$-0.275785\pi$
$167$	−56.1340	−	97.2269i	−0.336131	−	0.582197i	−0.983702	+	0.179809i	$0.942452\pi$
$168$		0			0
$169$	−65.7921	+	113.955i	−0.389302	+	0.674292i
$170$		0			0
$171$	5.09105	+	81.8935i	0.0297722	+	0.478909i
$172$		0			0
$173$	−118.488	+	205.227i	−0.684900	+	1.18628i	0.288568	+	0.957460i	$0.406821\pi$
$173$	−118.488	+	205.227i	−0.684900	+	1.18628i	−0.973468	+	0.228823i	$0.926512\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.35101	−	10.0068i	0.0132826	−	0.0565357i
$178$		0			0
$179$		−	234.599i		−	1.31061i	−0.755366	−	0.655304i	$-0.772541\pi$
$179$		−	234.599i		−	1.31061i	0.755366	−	0.655304i	$-0.227459\pi$
$180$		0			0
$181$	221.636			1.22451			0.612254	−	0.790661i	$-0.290263\pi$
$181$	221.636			1.22451			0.612254	+	0.790661i	$0.290263\pi$
$182$		0			0
$183$	−40.1407	−	133.132i	−0.219348	−	0.727496i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	316.492	+	182.727i	1.69247	+	0.977149i
$188$		0			0
$189$	−76.1616	−	205.495i	−0.402971	−	1.08728i
$190$		0			0
$191$	−130.162	−	75.1488i	−0.681474	−	0.393449i	0.118936	−	0.992902i	$-0.462052\pi$
$191$	−130.162	−	75.1488i	−0.681474	−	0.393449i	−0.800410	+	0.599452i	$0.795385\pi$
$192$		0			0
$193$	42.4352	−	24.5000i	0.219872	−	0.126943i	−0.386019	−	0.922491i	$-0.626150\pi$
$193$	42.4352	−	24.5000i	0.219872	−	0.126943i	0.605891	+	0.795548i	$0.292817\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−276.827			−1.40521			−0.702606	−	0.711579i	$-0.747980\pi$
$197$	−276.827			−1.40521			−0.702606	+	0.711579i	$0.747980\pi$
$198$		0			0
$199$	198.935			0.999672			0.499836	−	0.866120i	$-0.333394\pi$
$199$	198.935			0.999672			0.499836	+	0.866120i	$0.333394\pi$
$200$		0			0
$201$	−4.32196	+	18.3959i	−0.0215023	+	0.0915220i
$202$		0			0
$203$	−67.5241	−	116.955i	−0.332631	−	0.576134i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−251.653	+	166.928i	−1.21572	+	0.806415i
$208$		0			0
$209$	160.610	+	92.7282i	0.768469	+	0.443676i
$210$		0			0
$211$	−47.0068	−	81.4182i	−0.222781	−	0.385868i	0.732870	−	0.680368i	$-0.238180\pi$
$211$	−47.0068	−	81.4182i	−0.222781	−	0.385868i	−0.955651	+	0.294500i	$0.904847\pi$
$212$		0			0
$213$	−78.5494	−	73.8179i	−0.368777	−	0.346563i
$214$		0			0
$215$		0			0
$216$		0			0
$217$			181.416i			0.836017i
$218$		0			0
$219$	−103.515	−	97.2796i	−0.472671	−	0.444199i
$220$		0			0
$221$	95.1684	−	54.9455i	0.430626	−	0.248622i
$222$		0			0
$223$	−134.886	−	77.8763i	−0.604869	−	0.349221i	0.166086	−	0.986111i	$-0.446887\pi$
$223$	−134.886	−	77.8763i	−0.604869	−	0.349221i	−0.770955	+	0.636890i	$0.780220\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	79.9332	−	138.448i	0.352129	−	0.609905i	−0.634493	−	0.772928i	$-0.718791\pi$
$227$	79.9332	−	138.448i	0.352129	−	0.609905i	0.986622	+	0.163023i	$0.0521246\pi$
$228$		0			0
$229$	−19.1237	−	33.1232i	−0.0835095	−	0.144643i	0.821246	−	0.570575i	$-0.193280\pi$
$229$	−19.1237	−	33.1232i	−0.0835095	−	0.144643i	−0.904755	+	0.425932i	$0.859946\pi$
$230$		0			0
$231$	−482.213	−	113.292i	−2.08750	−	0.490440i
$232$		0			0
$233$	157.490			0.675921			0.337960	−	0.941160i	$-0.390263\pi$
$233$	157.490			0.675921			0.337960	+	0.941160i	$0.390263\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	73.2521	+	242.950i	0.309081	+	1.02510i
$238$		0			0
$239$	62.4742	−	36.0695i	0.261398	−	0.150918i	−0.363574	−	0.931565i	$-0.618444\pi$
$239$	62.4742	−	36.0695i	0.261398	−	0.150918i	0.624972	+	0.780647i	$0.285110\pi$
$240$		0			0
$241$	−113.370	+	196.362i	−0.470413	+	0.814779i	−0.999427	−	0.0338337i	$-0.989228\pi$
$241$	−113.370	+	196.362i	−0.470413	+	0.814779i	0.529015	+	0.848613i	$0.322562\pi$
$242$		0			0
$243$	−143.198	+	196.325i	−0.589291	+	0.807921i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	48.2950	−	27.8832i	0.195526	−	0.112887i
$248$		0			0
$249$	33.1753	+	110.030i	0.133234	+	0.441887i
$250$		0			0
$251$		−	222.931i		−	0.888171i	−0.895985	−	0.444085i	$-0.853529\pi$
$251$		−	222.931i		−	0.888171i	0.895985	−	0.444085i	$-0.146471\pi$
$252$		0			0
$253$			682.557i			2.69785i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	53.2323	+	92.2011i	0.207130	+	0.358759i	0.950809	−	0.309777i	$-0.100254\pi$
$257$	53.2323	+	92.2011i	0.207130	+	0.358759i	−0.743680	+	0.668536i	$0.766921\pi$
$258$		0			0
$259$	204.818	−	354.755i	0.790803	−	1.36971i
$260$		0			0
$261$	−66.6806	+	134.076i	−0.255481	+	0.513702i
$262$		0			0
$263$	89.6877	−	155.344i	0.341018	−	0.590660i	−0.643604	−	0.765359i	$-0.722562\pi$
$263$	89.6877	−	155.344i	0.341018	−	0.590660i	0.984622	+	0.174698i	$0.0558950\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	314.198	+	295.272i	1.17677	+	1.10589i
$268$		0			0
$269$		−	416.351i		−	1.54777i	−0.633324	−	0.773887i	$-0.718310\pi$
$269$		−	416.351i		−	1.54777i	0.633324	−	0.773887i	$-0.281690\pi$
$270$		0			0
$271$	396.907			1.46460			0.732302	−	0.680980i	$-0.238446\pi$
$271$	396.907			1.46460			0.732302	+	0.680980i	$0.238446\pi$
$272$		0			0
$273$	−102.003	+	108.541i	−0.373636	+	0.397585i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	100.066	+	57.7731i	0.361249	+	0.208567i	0.669629	−	0.742696i	$-0.266453\pi$
$277$	100.066	+	57.7731i	0.361249	+	0.208567i	−0.308379	+	0.951263i	$0.599787\pi$
$278$		0			0
$279$	167.629	−	111.192i	0.600821	−	0.398539i
$280$		0			0
$281$	422.564	+	243.967i	1.50379	+	0.868211i	0.999990	+	0.00438786i	$0.00139670\pi$
$281$	422.564	+	243.967i	1.50379	+	0.868211i	0.503795	+	0.863823i	$0.331937\pi$
$282$		0			0
$283$	294.145	−	169.825i	1.03938	−	0.600087i	0.119724	−	0.992807i	$-0.461799\pi$
$283$	294.145	−	169.825i	1.03938	−	0.600087i	0.919658	+	0.392720i	$0.128466\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	280.870			0.978641
$288$		0			0
$289$	33.7527			0.116791
$290$		0			0
$291$	−231.984	+	69.9457i	−0.797194	+	0.240363i
$292$		0			0
$293$	−70.6728	−	122.409i	−0.241204	−	0.417778i	0.719853	−	0.694126i	$-0.244209\pi$
$293$	−70.6728	−	122.409i	−0.241204	−	0.417778i	−0.961058	+	0.276348i	$0.910876\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	190.874	+	515.005i	0.642673	+	1.73402i
$298$		0			0
$299$	177.746	+	102.622i	0.594468	+	0.343216i
$300$		0			0
$301$	93.3437	+	161.676i	0.310112	+	0.537130i
$302$		0			0
$303$	351.368	−	105.942i	1.15963	−	0.349642i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	120.649i		−	0.392995i	−0.980504	−	0.196498i	$-0.937043\pi$
$307$		−	120.649i		−	0.392995i	0.980504	−	0.196498i	$-0.0629568\pi$
$308$		0			0
$309$	−50.5339	+	215.092i	−0.163540	+	0.696090i
$310$		0			0
$311$	−119.254	+	68.8514i	−0.383454	+	0.221387i	−0.679320	−	0.733842i	$-0.737725\pi$
$311$	−119.254	+	68.8514i	−0.383454	+	0.221387i	0.295866	+	0.955229i	$0.404392\pi$
$312$		0			0
$313$	223.896	+	129.266i	0.715322	+	0.412991i	0.813029	−	0.582224i	$-0.197817\pi$
$313$	223.896	+	129.266i	0.715322	+	0.412991i	−0.0977064	+	0.995215i	$0.531151\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.64630	−	16.7079i	0.0304300	−	0.0527063i	−0.850409	−	0.526122i	$-0.823646\pi$
$317$	9.64630	−	16.7079i	0.0304300	−	0.0527063i	0.880839	+	0.473415i	$0.156979\pi$
$318$		0			0
$319$	169.227	+	293.110i	0.530492	+	0.918839i
$320$		0			0
$321$	−149.792	+	159.393i	−0.466642	+	0.496553i
$322$		0			0
$323$	163.787			0.507081
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−64.3023	+	68.4239i	−0.196643	+	0.209247i
$328$		0			0
$329$	269.278	−	155.468i	0.818476	−	0.472547i
$330$		0			0
$331$	98.3953	−	170.426i	0.297267	−	0.514881i	−0.678243	−	0.734838i	$-0.737258\pi$
$331$	98.3953	−	170.426i	0.297267	−	0.514881i	0.975510	+	0.219957i	$0.0705916\pi$
$332$		0			0
$333$	−453.331	+	28.1821i	−1.36136	+	0.0846309i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	274.911	−	158.720i	0.815760	−	0.470979i	−0.0331921	−	0.999449i	$-0.510567\pi$
$337$	274.911	−	158.720i	0.815760	−	0.470979i	0.848952	+	0.528470i	$0.177234\pi$
$338$		0			0
$339$	−54.7215	−	12.8563i	−0.161420	−	0.0379243i
$340$		0			0
$341$		−	454.659i		−	1.33331i
$342$		0			0
$343$		−	260.687i		−	0.760022i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−310.272	−	537.407i	−0.894157	−	1.54872i	−0.834845	−	0.550485i	$-0.814443\pi$
$347$	−310.272	−	537.407i	−0.894157	−	1.54872i	−0.0593116	−	0.998240i	$-0.518891\pi$
$348$		0			0
$349$	−189.512	+	328.245i	−0.543015	+	0.940529i	0.455714	+	0.890126i	$0.349384\pi$
$349$	−189.512	+	328.245i	−0.543015	+	0.940529i	−0.998729	+	0.0504030i	$0.983949\pi$
$350$		0			0
$351$	162.811	+	27.7246i	0.463849	+	0.0789876i
$352$		0			0
$353$	−123.272	+	213.514i	−0.349213	+	0.604855i	−0.986110	−	0.166094i	$-0.946884\pi$
$353$	−123.272	+	213.514i	−0.349213	+	0.604855i	0.636897	+	0.770949i	$0.280218\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−418.841	+	126.285i	−1.17322	+	0.353740i
$358$		0			0
$359$			572.791i			1.59552i	0.602976	+	0.797759i	$0.293981\pi$
$359$			572.791i			1.59552i	−0.602976	+	0.797759i	$0.706019\pi$
$360$		0			0
$361$	−277.883			−0.769759
$362$		0			0
$363$	855.129	+	200.905i	2.35573	+	0.553457i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	162.688	+	93.9279i	0.443291	+	0.255934i	0.704993	−	0.709214i	$-0.250950\pi$
$367$	162.688	+	93.9279i	0.443291	+	0.255934i	−0.261701	+	0.965149i	$0.584284\pi$
$368$		0			0
$369$	−172.149	−	259.525i	−0.466530	−	0.703320i
$370$		0			0
$371$	133.663	+	77.1704i	0.360278	+	0.208007i
$372$		0			0
$373$	−130.005	+	75.0584i	−0.348539	+	0.201229i	−0.664042	−	0.747696i	$-0.731160\pi$
$373$	−130.005	+	75.0584i	−0.348539	+	0.201229i	0.315503	+	0.948925i	$0.397827\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	101.772			0.269953
$378$		0			0
$379$	26.6222			0.0702432			0.0351216	−	0.999383i	$-0.488818\pi$
$379$	26.6222			0.0702432			0.0351216	+	0.999383i	$0.488818\pi$
$380$		0			0
$381$	−275.679	−	259.073i	−0.723568	−	0.679983i
$382$		0			0
$383$	256.901	+	444.966i	0.670760	+	1.16179i	0.977689	+	0.210058i	$0.0673654\pi$
$383$	256.901	+	444.966i	0.670760	+	1.16179i	−0.306929	+	0.951733i	$0.599301\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	92.1776	−	185.344i	0.238185	−	0.478924i
$388$		0			0
$389$	22.1616	+	12.7950i	0.0569707	+	0.0328921i	0.528215	−	0.849111i	$-0.322862\pi$
$389$	22.1616	+	12.7950i	0.0569707	+	0.0328921i	−0.471244	+	0.882003i	$0.656195\pi$
$390$		0			0
$391$	301.402	+	522.044i	0.770849	+	1.33515i
$392$		0			0
$393$	111.470	−	474.461i	0.283639	−	1.20728i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			388.804i			0.979356i	0.871903	+	0.489678i	$0.162886\pi$
$397$			388.804i			0.979356i	−0.871903	+	0.489678i	$0.837114\pi$
$398$		0			0
$399$	−212.549	+	64.0859i	−0.532704	+	0.160616i
$400$		0			0
$401$	−34.0842	+	19.6785i	−0.0849981	+	0.0490736i	−0.541897	−	0.840445i	$-0.682294\pi$
$401$	−34.0842	+	19.6785i	−0.0849981	+	0.0490736i	0.456899	+	0.889519i	$0.348960\pi$
$402$		0			0
$403$	−118.398	−	68.3574i	−0.293793	−	0.169621i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−513.308	+	889.076i	−1.26120	+	2.18446i
$408$		0			0
$409$	86.7200	+	150.204i	0.212029	+	0.367246i	0.952350	−	0.305009i	$-0.0986594\pi$
$409$	86.7200	+	150.204i	0.212029	+	0.367246i	−0.740320	+	0.672255i	$0.765326\pi$
$410$		0			0
$411$	90.3832	+	299.767i	0.219910	+	0.729360i
$412$		0			0
$413$	27.8118			0.0673409
$414$		0			0
$415$		0			0
$416$		0			0
$417$	178.832	+	42.0149i	0.428853	+	0.100755i
$418$		0			0
$419$	−115.031	+	66.4132i	−0.274537	+	0.158504i	−0.630948	−	0.775825i	$-0.717334\pi$
$419$	−115.031	+	66.4132i	−0.274537	+	0.158504i	0.356411	+	0.934329i	$0.384000\pi$
$420$		0			0
$421$	−317.447	+	549.834i	−0.754031	+	1.30602i	0.191824	+	0.981429i	$0.438560\pi$
$421$	−317.447	+	549.834i	−0.754031	+	1.30602i	−0.945855	+	0.324590i	$0.894774\pi$
$422$		0			0
$423$	−308.698	−	153.526i	−0.729782	−	0.362945i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	325.816	−	188.110i	0.763035	−	0.440539i
$428$		0			0
$429$	255.636	−	272.021i	0.595888	−	0.634082i
$430$		0			0
$431$		−	602.424i		−	1.39774i	−0.715251	−	0.698868i	$-0.753687\pi$
$431$		−	602.424i		−	1.39774i	0.715251	−	0.698868i	$-0.246313\pi$
$432$		0			0
$433$		−	266.155i		−	0.614676i	−0.951600	−	0.307338i	$-0.900562\pi$
$433$		−	266.155i		−	0.614676i	0.951600	−	0.307338i	$-0.0994382\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	152.952	+	264.921i	0.350005	+	0.606227i
$438$		0			0
$439$	250.330	−	433.584i	0.570228	−	0.987664i	−0.426314	−	0.904575i	$-0.640188\pi$
$439$	250.330	−	433.584i	0.570228	−	0.987664i	0.996542	−	0.0830886i	$-0.0264784\pi$
$440$		0			0
$441$	126.624	−	83.9926i	0.287129	−	0.190460i
$442$		0			0
$443$	−150.745	+	261.098i	−0.340282	+	0.589386i	−0.984485	−	0.175469i	$-0.943856\pi$
$443$	−150.745	+	261.098i	−0.340282	+	0.589386i	0.644203	+	0.764855i	$0.277189\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	101.685	−	432.811i	0.227483	−	0.968257i
$448$		0			0
$449$		−	565.321i		−	1.25907i	−0.776973	−	0.629534i	$-0.783246\pi$
$449$		−	565.321i		−	1.25907i	0.776973	−	0.629534i	$-0.216754\pi$
$450$		0			0
$451$	−703.907			−1.56077
$452$		0			0
$453$	220.881	+	732.580i	0.487596	+	1.61717i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−45.2922	−	26.1495i	−0.0991077	−	0.0572198i	0.449627	−	0.893216i	$-0.351557\pi$
$457$	−45.2922	−	26.1495i	−0.0991077	−	0.0572198i	−0.548735	+	0.835997i	$0.684890\pi$
$458$		0			0
$459$	373.402	+	309.609i	0.813512	+	0.674529i
$460$		0			0
$461$	166.357	+	96.0465i	0.360862	+	0.208344i	0.669459	−	0.742849i	$-0.266526\pi$
$461$	166.357	+	96.0465i	0.360862	+	0.208344i	−0.308597	+	0.951193i	$0.599859\pi$
$462$		0			0
$463$	−490.361	+	283.110i	−1.05909	+	0.611469i	−0.925182	−	0.379524i	$-0.876088\pi$
$463$	−490.361	+	283.110i	−1.05909	+	0.611469i	−0.133913	+	0.990993i	$0.542754\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−174.405			−0.373459			−0.186729	−	0.982411i	$-0.559789\pi$
$467$	−174.405			−0.373459			−0.186729	+	0.982411i	$0.559789\pi$
$468$		0			0
$469$	−51.1275			−0.109014
$470$		0			0
$471$	200.664	−	854.106i	0.426039	−	1.81339i
$472$		0			0
$473$	−233.935	−	405.187i	−0.494577	−	0.856633i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−10.6183	−	170.804i	−0.0222607	−	0.358080i
$478$		0			0
$479$	−473.784	−	273.539i	−0.989110	−	0.571063i	−0.0841020	−	0.996457i	$-0.526802\pi$
$479$	−473.784	−	273.539i	−0.989110	−	0.571063i	−0.905008	+	0.425394i	$0.860135\pi$
$480$		0			0
$481$	154.351	+	267.343i	0.320895	+	0.555807i
$482$		0			0
$483$	−595.397	−	559.533i	−1.23271	−	1.15845i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	769.945i		−	1.58100i	−0.612464	−	0.790498i	$-0.709822\pi$
$487$		−	769.945i		−	1.58100i	0.612464	−	0.790498i	$-0.290178\pi$
$488$		0			0
$489$	−204.475	−	192.159i	−0.418150	−	0.392962i
$490$		0			0
$491$	−154.916	+	89.4407i	−0.315511	+	0.182160i	−0.649390	−	0.760456i	$-0.724976\pi$
$491$	−154.916	+	89.4407i	−0.315511	+	0.182160i	0.333879	+	0.942616i	$0.391642\pi$
$492$		0			0
$493$	258.861	+	149.454i	0.525074	+	0.303152i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	145.822	−	252.571i	0.293404	−	0.508190i
$498$		0			0
$499$	−192.655	−	333.688i	−0.386082	−	0.668713i	0.605837	−	0.795589i	$-0.292838\pi$
$499$	−192.655	−	333.688i	−0.386082	−	0.668713i	−0.991919	+	0.126876i	$0.959505\pi$
$500$		0			0
$501$	−327.876	−	77.0316i	−0.654444	−	0.153756i
$502$		0			0
$503$	67.6630			0.134519			0.0672594	−	0.997736i	$-0.478574\pi$
$503$	67.6630			0.134519			0.0672594	+	0.997736i	$0.478574\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	113.955	+	377.947i	0.224764	+	0.745457i
$508$		0			0
$509$	−523.292	+	302.123i	−1.02808	+	0.593562i	−0.916434	−	0.400187i	$-0.868945\pi$
$509$	−523.292	+	302.123i	−1.02808	+	0.593562i	−0.111645	+	0.993748i	$0.535612\pi$
$510$		0			0
$511$	192.168	−	332.846i	0.376063	−	0.651361i
$512$		0			0
$513$	189.490	+	157.117i	0.369376	+	0.306271i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−674.857	+	389.629i	−1.30533	+	0.753634i
$518$		0			0
$519$	205.227	+	680.660i	0.395427	+	1.31148i
$520$		0			0
$521$			273.678i			0.525294i	0.964892	+	0.262647i	$0.0845954\pi$
$521$			273.678i			0.525294i	−0.964892	+	0.262647i	$0.915405\pi$
$522$		0			0
$523$		−	687.402i		−	1.31434i	−0.753740	−	0.657172i	$-0.771752\pi$
$523$		−	687.402i		−	1.31434i	0.753740	−	0.657172i	$-0.228248\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−200.767	−	347.739i	−0.380962	−	0.659846i
$528$		0			0
$529$	−298.428	+	516.892i	−0.564136	+	0.977112i
$530$		0			0
$531$	−17.0463	−	25.6982i	−0.0321022	−	0.0483959i
$532$		0			0
$533$	−105.832	+	183.306i	−0.198558	+	0.343913i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−512.866	−	481.973i	−0.955057	−	0.897528i
$538$		0			0
$539$		−	343.440i		−	0.637180i
$540$		0			0
$541$	664.543			1.22836			0.614180	−	0.789166i	$-0.289487\pi$
$541$	664.543			1.22836			0.614180	+	0.789166i	$0.289487\pi$
$542$		0			0
$543$	455.341	−	484.527i	0.838565	−	0.892315i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−449.646	−	259.603i	−0.822022	−	0.474594i	0.0290914	−	0.999577i	$-0.490739\pi$
$547$	−449.646	−	259.603i	−0.822022	−	0.474594i	−0.851113	+	0.524982i	$0.824072\pi$
$548$		0			0
$549$	−373.512	−	185.760i	−0.680350	−	0.338361i
$550$		0			0
$551$	131.364	+	75.8431i	0.238410	+	0.137646i
$552$		0			0
$553$	−594.576	+	343.278i	−1.07518	+	0.620757i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	422.648			0.758794			0.379397	−	0.925234i	$-0.376131\pi$
$557$	422.648			0.758794			0.379397	+	0.925234i	$0.376131\pi$
$558$		0			0
$559$	−140.687			−0.251677
$560$		0			0
$561$	1049.69	−	316.492i	1.87110	−	0.564157i
$562$		0			0
$563$	−461.187	−	798.799i	−0.819159	−	1.41883i	−0.906302	−	0.422630i	$-0.861107\pi$
$563$	−461.187	−	798.799i	−0.819159	−	1.41883i	0.0871428	−	0.996196i	$-0.472226\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−605.712	−	255.681i	−1.06827	−	0.450936i
$568$		0			0
$569$	914.445	+	527.955i	1.60711	+	0.927865i	0.990013	+	0.140978i	$0.0450247\pi$
$569$	914.445	+	527.955i	1.60711	+	0.927865i	0.617097	+	0.786887i	$0.288309\pi$
$570$		0			0
$571$	−401.524	−	695.460i	−0.703195	−	1.21797i	−0.967339	−	0.253486i	$-0.918423\pi$
$571$	−401.524	−	695.460i	−0.703195	−	1.21797i	0.264144	−	0.964483i	$-0.414911\pi$
$572$		0			0
$573$	−431.697	+	130.162i	−0.753398	+	0.227158i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	96.6495i		−	0.167503i	−0.996487	−	0.0837517i	$-0.973310\pi$
$577$		−	96.6495i		−	0.167503i	0.996487	−	0.0837517i	$-0.0266903\pi$
$578$		0			0
$579$	33.6209	−	143.104i	0.0580672	−	0.247156i
$580$		0			0
$581$	−269.278	+	155.468i	−0.463474	+	0.267587i
$582$		0			0
$583$	−334.982	−	193.402i	−0.574584	−	0.331736i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	502.582	−	870.497i	0.856187	−	1.48296i	−0.0193528	−	0.999813i	$-0.506161\pi$
$587$	502.582	−	870.497i	0.856187	−	1.48296i	0.875540	−	0.483146i	$-0.160506\pi$
$588$		0			0
$589$	−101.883	−	176.467i	−0.172976	−	0.299604i
$590$		0			0
$591$	−568.728	+	605.182i	−0.962315	+	1.02400i
$592$		0			0
$593$	752.444			1.26888			0.634439	−	0.772973i	$-0.281231\pi$
$593$	752.444			1.26888			0.634439	+	0.772973i	$0.281231\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	408.703	−	434.899i	0.684594	−	0.728475i
$598$		0			0
$599$	24.0857	−	13.9059i	0.0402099	−	0.0232152i	−0.479760	−	0.877400i	$-0.659276\pi$
$599$	24.0857	−	13.9059i	0.0402099	−	0.0232152i	0.519970	+	0.854184i	$0.325943\pi$
$600$		0			0
$601$	475.356	−	823.340i	0.790942	−	1.36995i	−0.134443	−	0.990921i	$-0.542925\pi$
$601$	475.356	−	823.340i	0.790942	−	1.36995i	0.925385	−	0.379030i	$-0.123742\pi$
$602$		0			0
$603$	31.3368	+	47.2420i	0.0519682	+	0.0783450i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−279.390	+	161.306i	−0.460280	+	0.265743i	−0.712162	−	0.702015i	$-0.752284\pi$
$607$	−279.390	+	161.306i	−0.460280	+	0.265743i	0.251882	+	0.967758i	$0.418950\pi$
$608$		0			0
$609$	−394.406	−	92.6621i	−0.647629	−	0.152155i
$610$		0			0
$611$			234.321i			0.383504i
$612$		0			0
$613$		−	138.206i		−	0.225459i	−0.993626	−	0.112730i	$-0.964041\pi$
$613$		−	138.206i		−	0.225459i	0.993626	−	0.112730i	$-0.0359594\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−393.802	−	682.084i	−0.638252	−	1.10548i	−0.985816	−	0.167829i	$-0.946324\pi$
$617$	−393.802	−	682.084i	−0.638252	−	1.10548i	0.347564	−	0.937656i	$-0.387009\pi$
$618$		0			0
$619$	−121.747	+	210.873i	−0.196684	+	0.340667i	−0.947451	−	0.319900i	$-0.896351\pi$
$619$	−121.747	+	210.873i	−0.196684	+	0.340667i	0.750767	+	0.660567i	$0.229684\pi$
$620$		0			0
$621$	−152.083	+	893.096i	−0.244900	+	1.43816i
$622$		0			0
$623$	−583.287	+	1010.28i	−0.936255	+	1.62164i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	532.683	−	160.610i	0.849574	−	0.256156i
$628$		0			0
$629$			906.662i			1.44143i
$630$		0			0
$631$	111.924			0.177376			0.0886879	−	0.996059i	$-0.471733\pi$
$631$	111.924			0.177376			0.0886879	+	0.996059i	$0.471733\pi$
$632$		0			0
$633$	−274.565	−	64.5066i	−0.433752	−	0.101906i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−89.4359	−	51.6358i	−0.140402	−	0.0810609i
$638$		0			0
$639$	−322.753	+	20.0645i	−0.505090	+	0.0313998i
$640$		0			0
$641$	632.095	+	364.940i	0.986107	+	0.569329i	0.904108	−	0.427303i	$-0.140536\pi$
$641$	632.095	+	364.940i	0.986107	+	0.569329i	0.0819990	+	0.996632i	$0.473870\pi$
$642$		0			0
$643$	499.697	−	288.500i	0.777133	−	0.448678i	−0.0582801	−	0.998300i	$-0.518562\pi$
$643$	499.697	−	288.500i	0.777133	−	0.448678i	0.835413	+	0.549622i	$0.185228\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−129.029			−0.199426			−0.0997130	−	0.995016i	$-0.531792\pi$
$647$	−129.029			−0.199426			−0.0997130	+	0.995016i	$0.531792\pi$
$648$		0			0
$649$	−69.7011			−0.107398
$650$		0			0
$651$	396.600	+	372.711i	0.609217	+	0.572520i
$652$		0			0
$653$	−592.717	−	1026.62i	−0.907682	−	1.57215i	−0.817275	−	0.576247i	$-0.804517\pi$
$653$	−592.717	−	1026.62i	−0.907682	−	1.57215i	−0.0904070	−	0.995905i	$-0.528817\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−425.334	+	26.4416i	−0.647388	+	0.0402459i
$658$		0			0
$659$	−947.808	−	547.217i	−1.43825	−	0.830375i	−0.440524	−	0.897741i	$-0.645207\pi$
$659$	−947.808	−	547.217i	−1.43825	−	0.830375i	−0.997728	+	0.0673658i	$0.978541\pi$
$660$		0			0
$661$	−604.876	−	1047.68i	−0.915093	−	1.58499i	−0.806765	−	0.590872i	$-0.798784\pi$
$661$	−604.876	−	1047.68i	−0.915093	−	1.58499i	−0.108327	−	0.994115i	$-0.534549\pi$
$662$		0			0
$663$	75.4007	−	320.935i	0.113727	−	0.484064i
$664$		0			0
$665$		0			0
$666$		0			0
$667$			558.269i			0.836984i
$668$		0			0
$669$	−447.365	+	134.886i	−0.668708	+	0.201623i
$670$		0			0
$671$	−816.550	+	471.435i	−1.21692	+	0.702586i
$672$		0			0
$673$	880.948	+	508.615i	1.30899	+	0.755743i	0.981927	−	0.189260i	$-0.0606090\pi$
$673$	880.948	+	508.615i	1.30899	+	0.755743i	0.327059	+	0.945004i	$0.393942\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−398.308	+	689.890i	−0.588343	+	1.01904i	0.406107	+	0.913826i	$0.366886\pi$
$677$	−398.308	+	689.890i	−0.588343	+	1.01904i	−0.994450	+	0.105214i	$0.966447\pi$
$678$		0			0
$679$	−327.784	−	567.738i	−0.482745	−	0.836139i
$680$		0			0
$681$	−138.448	−	459.181i	−0.203302	−	0.674275i
$682$		0			0
$683$	400.485			0.586361			0.293181	−	0.956057i	$-0.405286\pi$
$683$	400.485			0.586361			0.293181	+	0.956057i	$0.405286\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−111.701	−	26.2431i	−0.162592	−	0.0381995i
$688$		0			0
$689$	−100.728	+	58.1556i	−0.146195	+	0.0844057i
$690$		0			0
$691$	216.423	−	374.855i	0.313202	−	0.542482i	−0.665852	−	0.746084i	$-0.731932\pi$
$691$	216.423	−	374.855i	0.313202	−	0.542482i	0.979054	+	0.203602i	$0.0652650\pi$
$692$		0			0
$693$	−1238.36	+	821.433i	−1.78695	+	1.18533i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−538.373	+	310.830i	−0.772415	+	0.445954i
$698$		0			0
$699$	323.555	−	344.294i	0.462883	−	0.492553i
$700$		0			0
$701$			65.4412i			0.0933541i	0.998910	+	0.0466770i	$0.0148632\pi$
$701$			65.4412i			0.0933541i	−0.998910	+	0.0466770i	$0.985137\pi$
$702$		0			0
$703$			460.103i			0.654485i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	496.470	+	859.911i	0.702221	+	1.21628i
$708$		0			0
$709$	100.461	−	174.003i	0.141693	−	0.245420i	−0.786441	−	0.617665i	$-0.788079\pi$
$709$	100.461	−	174.003i	0.141693	−	0.245420i	0.928134	+	0.372245i	$0.121412\pi$
$710$		0			0
$711$	681.615	+	338.990i	0.958671	+	0.476779i
$712$		0			0
$713$	374.972	−	649.471i	0.525908	−	0.910899i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	49.4975	−	210.681i	0.0690342	−	0.293836i
$718$		0			0
$719$			1062.98i			1.47841i	0.673478	+	0.739207i	$0.264800\pi$
$719$			1062.98i			1.47841i	−0.673478	+	0.739207i	$0.735200\pi$
$720$		0			0
$721$	−597.801			−0.829128
$722$		0			0
$723$	196.362	+	651.258i	0.271593	+	0.900772i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−858.455	−	495.629i	−1.18082	−	0.681746i	−0.224614	−	0.974448i	$-0.572112\pi$
$727$	−858.455	−	495.629i	−1.18082	−	0.681746i	−0.956204	+	0.292702i	$0.905446\pi$
$728$		0			0
$729$	135.000	+	716.391i	0.185185	+	0.982704i
$730$		0			0
$731$	−357.844	−	206.601i	−0.489526	−	0.282628i
$732$		0			0
$733$	1022.14	−	590.134i	1.39446	−	0.805095i	0.400659	−	0.916227i	$-0.368781\pi$
$733$	1022.14	−	590.134i	1.39446	−	0.805095i	0.993806	+	0.111133i	$0.0354478\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	128.134			0.173859
$738$		0			0
$739$	−599.351			−0.811029			−0.405515	−	0.914089i	$-0.632908\pi$
$739$	−599.351			−0.811029			−0.405515	+	0.914089i	$0.632908\pi$
$740$		0			0
$741$	38.2635	−	162.864i	0.0516377	−	0.219790i
$742$		0			0
$743$	−165.747	−	287.083i	−0.223078	−	0.386383i	0.732663	−	0.680592i	$-0.238277\pi$
$743$	−165.747	−	287.083i	−0.223078	−	0.386383i	−0.955741	+	0.294209i	$0.904944\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	308.698	+	153.526i	0.413250	+	0.205523i
$748$		0			0
$749$	−512.519	−	295.903i	−0.684271	−	0.395064i
$750$		0			0
$751$	−76.0448	−	131.713i	−0.101258	−	0.175384i	0.810945	−	0.585122i	$-0.198953\pi$
$751$	−76.0448	−	131.713i	−0.101258	−	0.175384i	−0.912203	+	0.409738i	$0.865620\pi$
$752$		0			0
$753$	−487.358	−	458.002i	−0.647222	−	0.608236i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	1179.61i		−	1.55827i	−0.626858	−	0.779134i	$-0.715659\pi$
$757$		−	1179.61i		−	1.55827i	0.626858	−	0.779134i	$-0.284341\pi$
$758$		0			0
$759$	1492.17	+	1402.28i	1.96596	+	1.84754i
$760$		0			0
$761$	−1162.58	+	671.214i	−1.52770	+	0.882016i	−0.528239	+	0.849096i	$0.677147\pi$
$761$	−1162.58	+	671.214i	−1.52770	+	0.882016i	−0.999458	+	0.0329205i	$0.989519\pi$
$762$		0			0
$763$	−220.013	−	127.024i	−0.288352	−	0.166480i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−10.4795	+	18.1510i	−0.0136629	+	0.0236649i
$768$		0			0
$769$	548.512	+	950.051i	0.713280	+	1.23544i	0.963619	+	0.267279i	$0.0861244\pi$
$769$	548.512	+	950.051i	0.713280	+	1.23544i	−0.250339	+	0.968158i	$0.580542\pi$
$770$		0			0
$771$	310.928	+	73.0497i	0.403279	+	0.0947467i
$772$		0			0
$773$	1181.39			1.52832			0.764159	−	0.645028i	$-0.223154\pi$
$773$	1181.39			1.52832			0.764159	+	0.645028i	$0.223154\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−354.755	−	1176.59i	−0.456570	−	1.51427i
$778$		0			0
$779$	−273.208	+	157.737i	−0.350716	+	0.202486i
$780$		0			0
$781$	−365.454	+	632.984i	−0.467931	+	0.810479i
$782$		0			0
$783$	156.117	+	421.227i	0.199383	+	0.537965i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−31.2308	+	18.0311i	−0.0396834	+	0.0229112i	−0.519710	−	0.854342i	$-0.673960\pi$
$787$	−31.2308	+	18.0311i	−0.0396834	+	0.0229112i	0.480027	+	0.877254i	$0.340627\pi$
$788$		0			0
$789$	−155.344	−	515.217i	−0.196887	−	0.653000i
$790$		0			0
$791$		−	152.087i		−	0.192271i
$792$		0			0
$793$			283.519i			0.357527i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−66.7523	−	115.618i	−0.0837544	−	0.145067i	0.821105	−	0.570777i	$-0.193358\pi$
$797$	−66.7523	−	115.618i	−0.0837544	−	0.145067i	−0.904860	+	0.425710i	$0.860024\pi$
$798$		0			0
$799$	−344.103	+	596.004i	−0.430667	+	0.745938i
$800$		0			0
$801$	1291.01	−	80.2578i	1.61175	−	0.100197i
$802$		0			0
$803$	−481.607	+	834.167i	−0.599759	+	1.03881i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−910.202	−	855.375i	−1.12788	−	1.05994i
$808$		0			0
$809$			1053.66i			1.30242i	0.758898	+	0.651209i	$0.225738\pi$
$809$			1053.66i			1.30242i	−0.758898	+	0.651209i	$0.774262\pi$
$810$		0			0
$811$	434.464			0.535714			0.267857	−	0.963459i	$-0.413684\pi$
$811$	434.464			0.535714			0.267857	+	0.963459i	$0.413684\pi$
$812$		0			0
$813$	815.429	−	867.696i	1.00299	−	1.06728i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−181.595	−	104.844i	−0.222270	−	0.128328i
$818$		0			0
$819$	27.7254	+	445.984i	0.0338527	+	0.544547i
$820$		0			0
$821$	252.436	+	145.744i	0.307474	+	0.177520i	0.645796	−	0.763510i	$-0.276526\pi$
$821$	252.436	+	145.744i	0.307474	+	0.177520i	−0.338322	+	0.941031i	$0.609859\pi$
$822$		0			0
$823$	−291.693	+	168.409i	−0.354426	+	0.204628i	−0.666633	−	0.745386i	$-0.732265\pi$
$823$	−291.693	+	168.409i	−0.354426	+	0.204628i	0.312207	+	0.950014i	$0.398932\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1029.27			1.24458			0.622292	−	0.782785i	$-0.286202\pi$
$827$	1029.27			1.24458			0.622292	+	0.782785i	$0.286202\pi$
$828$		0			0
$829$	−790.674			−0.953768			−0.476884	−	0.878966i	$-0.658234\pi$
$829$	−790.674			−0.953768			−0.476884	+	0.878966i	$0.658234\pi$
$830$		0			0
$831$	331.881	−	100.066i	0.399376	−	0.120416i
$832$		0			0
$833$	−151.656	−	262.675i	−0.182060	−	0.315336i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	101.304	−	594.901i	0.121032	−	0.710753i
$838$		0			0
$839$	−655.031	−	378.182i	−0.780728	−	0.450754i	0.0559600	−	0.998433i	$-0.482178\pi$
$839$	−655.031	−	378.182i	−0.780728	−	0.450754i	−0.836688	+	0.547679i	$0.815511\pi$
$840$		0			0
$841$	−282.088	−	488.591i	−0.335420	−	0.580964i
$842$		0			0
$843$	1401.49	−	422.564i	1.66250	−	0.501262i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			2376.65i			2.80596i
$848$		0			0
$849$	233.047	−	991.940i	0.274496	−	1.16836i
$850$		0			0
$851$	−1466.50	+	846.686i	−1.72327	+	0.994930i
$852$		0			0
$853$	−1037.80	−	599.175i	−1.21665	−	0.702433i	−0.252450	−	0.967610i	$-0.581236\pi$
$853$	−1037.80	−	599.175i	−1.21665	−	0.702433i	−0.964200	+	0.265177i	$0.914570\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−349.660	+	605.629i	−0.408005	+	0.706685i	−0.994666	−	0.103147i	$-0.967109\pi$
$857$	−349.660	+	605.629i	−0.408005	+	0.706685i	0.586661	+	0.809832i	$0.300442\pi$
$858$		0			0
$859$	−278.734	−	482.781i	−0.324486	−	0.562027i	0.656922	−	0.753959i	$-0.271858\pi$
$859$	−278.734	−	482.781i	−0.324486	−	0.562027i	−0.981408	+	0.191932i	$0.938525\pi$
$860$		0			0
$861$	577.035	−	614.021i	0.670192	−	0.713149i
$862$		0			0
$863$	99.3954			0.115174			0.0575871	−	0.998340i	$-0.481659\pi$
$863$	99.3954			0.115174			0.0575871	+	0.998340i	$0.481659\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	69.3434	−	73.7881i	0.0799808	−	0.0851073i
$868$		0			0
$869$	1490.11	−	860.314i	1.71474	−	0.990004i
$870$		0			0
$871$	19.2648	−	33.3676i	0.0221180	−	0.0383096i
$872$		0			0
$873$	−323.689	+	650.849i	−0.370778	+	0.745532i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	695.058	−	401.292i	0.792541	−	0.457574i	−0.0483154	−	0.998832i	$-0.515385\pi$
$877$	695.058	−	401.292i	0.792541	−	0.457574i	0.840856	+	0.541258i	$0.182052\pi$
$878$		0			0
$879$	−412.797	−	96.9830i	−0.469622	−	0.110333i
$880$		0			0
$881$		−	524.266i		−	0.595080i	−0.954709	−	0.297540i	$-0.903834\pi$
$881$		−	524.266i		−	0.595080i	0.954709	−	0.297540i	$-0.0961662\pi$
$882$		0			0
$883$			993.894i			1.12559i	0.826597	+	0.562794i	$0.190273\pi$
$883$			993.894i			1.12559i	−0.826597	+	0.562794i	$0.809727\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	356.019	+	616.643i	0.401374	+	0.695200i	0.993892	−	0.110357i	$-0.0351994\pi$
$887$	356.019	+	616.643i	0.401374	+	0.695200i	−0.592518	+	0.805557i	$0.701866\pi$
$888$		0			0
$889$	511.780	−	886.429i	0.575681	−	0.997108i
$890$		0			0
$891$	1518.02	+	640.779i	1.70372	+	0.719168i
$892$		0			0
$893$	−174.622	+	302.454i	−0.195545	+	0.338694i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	589.516	−	177.746i	0.657209	−	0.198156i
$898$		0			0
$899$		−	371.869i		−	0.413647i
$900$		0			0
$901$	−341.609			−0.379144
$902$		0			0
$903$	545.217	+	128.094i	0.603784	+	0.141854i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	648.606	+	374.473i	0.715111	+	0.412870i	0.812951	−	0.582333i	$-0.197860\pi$
$907$	648.606	+	374.473i	0.715111	+	0.412870i	−0.0978396	+	0.995202i	$0.531193\pi$
$908$		0			0
$909$	490.268	−	985.793i	0.539349	−	1.08448i
$910$		0			0
$911$	−3.87633	−	2.23800i	−0.00425503	−	0.00245664i	0.497871	−	0.867251i	$-0.334115\pi$
$911$	−3.87633	−	2.23800i	−0.00425503	−	0.00245664i	−0.502126	+	0.864794i	$0.667449\pi$
$912$		0			0
$913$	674.857	−	389.629i	0.739165	−	0.426757i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1318.66			1.43802
$918$		0			0
$919$	1592.91			1.73331			0.866653	−	0.498912i	$-0.166267\pi$
$919$	1592.91			1.73331			0.866653	+	0.498912i	$0.166267\pi$
$920$		0			0
$921$	−263.757	−	247.869i	−0.286381	−	0.269130i
$922$		0			0
$923$	109.891	+	190.337i	0.119059	+	0.206215i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	366.401	+	552.371i	0.395255	+	0.595869i
$928$		0			0
$929$	770.784	+	445.012i	0.829692	+	0.479023i	0.853747	−	0.520688i	$-0.174324\pi$
$929$	770.784	+	445.012i	0.829692	+	0.479023i	−0.0240553	+	0.999711i	$0.507658\pi$
$930$		0			0
$931$	−76.9605	−	133.300i	−0.0826644	−	0.143179i
$932$		0			0
$933$	−94.4835	+	402.159i	−0.101269	+	0.431038i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			443.554i			0.473377i	0.971586	+	0.236688i	$0.0760620\pi$
$937$			443.554i			0.473377i	−0.971586	+	0.236688i	$0.923938\pi$
$938$		0			0
$939$	742.578	−	223.896i	0.790818	−	0.238441i
$940$		0			0
$941$	−69.7458	+	40.2678i	−0.0741188	+	0.0427925i	−0.536601	−	0.843836i	$-0.680292\pi$
$941$	−69.7458	+	40.2678i	−0.0741188	+	0.0427925i	0.462483	+	0.886628i	$0.346959\pi$
$942$		0			0
$943$	−1005.52	−	580.536i	−1.06630	−	0.615627i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−141.948	+	245.861i	−0.149892	+	0.259621i	−0.931187	−	0.364541i	$-0.881226\pi$
$947$	−141.948	+	245.861i	−0.149892	+	0.259621i	0.781295	+	0.624162i	$0.214559\pi$
$948$		0			0
$949$	144.818	+	250.832i	0.152601	+	0.264312i
$950$		0			0
$951$	−16.7079	−	55.4138i	−0.0175688	−	0.0582690i
$952$		0			0
$953$	−1123.17			−1.17857			−0.589283	−	0.807927i	$-0.700590\pi$
$953$	−1123.17			−1.17857			−0.589283	+	0.807927i	$0.700590\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	988.448	+	232.227i	1.03286	+	0.242661i
$958$		0			0
$959$	−733.626	+	423.559i	−0.764991	+	0.441668i
$960$		0			0
$961$	230.727	−	399.631i	0.240090	−	0.415849i
$962$		0			0
$963$	40.7150	+	654.933i	0.0422794	+	0.680097i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1211.63	+	699.536i	−1.25298	+	0.723409i	−0.971700	−	0.236217i	$-0.924093\pi$
$967$	−1211.63	+	699.536i	−1.25298	+	0.723409i	−0.281281	+	0.959626i	$0.590759\pi$
$968$		0			0
$969$	336.493	−	358.061i	0.347258	−	0.369516i
$970$		0			0
$971$			1705.41i			1.75634i	0.478345	+	0.878172i	$0.341237\pi$
$971$			1705.41i			1.75634i	−0.478345	+	0.878172i	$0.658763\pi$
$972$		0			0
$973$			497.024i			0.510816i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	580.524	+	1005.50i	0.594190	+	1.02917i	0.993661	+	0.112422i	$0.0358607\pi$
$977$	580.524	+	1005.50i	0.594190	+	1.02917i	−0.399470	+	0.916746i	$0.630806\pi$
$978$		0			0
$979$	1461.81	−	2531.94i	1.49317	−	2.58625i
$980$		0			0
$981$	17.4780	+	281.148i	0.0178165	+	0.286593i
$982$		0			0
$983$	−590.895	+	1023.46i	−0.601114	+	1.04116i	0.391539	+	0.920162i	$0.371943\pi$
$983$	−590.895	+	1023.46i	−0.601114	+	1.04116i	−0.992653	+	0.120999i	$0.961390\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	213.346	−	908.083i	0.216156	−	0.920043i
$988$		0			0
$989$		−	771.737i		−	0.780320i
$990$		0			0
$991$	−969.527			−0.978332			−0.489166	−	0.872191i	$-0.662699\pi$
$991$	−969.527			−0.978332			−0.489166	+	0.872191i	$0.662699\pi$
$992$		0			0
$993$	−170.426	−	565.238i	−0.171627	−	0.569223i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−675.714	−	390.124i	−0.677747	−	0.391298i	0.121258	−	0.992621i	$-0.461307\pi$
$997$	−675.714	−	390.124i	−0.677747	−	0.391298i	−0.799006	+	0.601323i	$0.794640\pi$
$998$		0			0
$999$	−869.739	+	1048.94i	−0.870610	+	1.04999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.u.a.749.3		8
3.2	odd	2		2700.3.u.b.2249.3		8
5.2	odd	4		900.3.p.a.101.1		4
5.3	odd	4		36.3.g.a.29.2	yes	4
5.4	even	2	inner	900.3.u.a.749.2		8
9.4	even	3		2700.3.u.b.449.2		8
9.5	odd	6	inner	900.3.u.a.149.2		8
15.2	even	4		2700.3.p.b.1601.1		4
15.8	even	4		108.3.g.a.89.2		4
15.14	odd	2		2700.3.u.b.2249.2		8
20.3	even	4		144.3.q.b.65.1		4
40.3	even	4		576.3.q.g.65.2		4
40.13	odd	4		576.3.q.d.65.1		4
45.4	even	6		2700.3.u.b.449.3		8
45.13	odd	12		108.3.g.a.17.2		4
45.14	odd	6	inner	900.3.u.a.149.3		8
45.22	odd	12		2700.3.p.b.2501.1		4
45.23	even	12		36.3.g.a.5.2	✓	4
45.32	even	12		900.3.p.a.401.1		4
45.38	even	12		324.3.c.b.161.3		4
45.43	odd	12		324.3.c.b.161.2		4
60.23	odd	4		432.3.q.b.305.2		4
120.53	even	4		1728.3.q.g.1601.1		4
120.83	odd	4		1728.3.q.h.1601.1		4
180.23	odd	12		144.3.q.b.113.1		4
180.43	even	12		1296.3.e.e.161.2		4
180.83	odd	12		1296.3.e.e.161.3		4
180.103	even	12		432.3.q.b.17.2		4
360.13	odd	12		1728.3.q.g.449.1		4
360.203	odd	12		576.3.q.g.257.2		4
360.283	even	12		1728.3.q.h.449.1		4
360.293	even	12		576.3.q.d.257.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.g.a.5.2	✓	4	45.23	even	12
36.3.g.a.29.2	yes	4	5.3	odd	4
108.3.g.a.17.2		4	45.13	odd	12
108.3.g.a.89.2		4	15.8	even	4
144.3.q.b.65.1		4	20.3	even	4
144.3.q.b.113.1		4	180.23	odd	12
324.3.c.b.161.2		4	45.43	odd	12
324.3.c.b.161.3		4	45.38	even	12
432.3.q.b.17.2		4	180.103	even	12
432.3.q.b.305.2		4	60.23	odd	4
576.3.q.d.65.1		4	40.13	odd	4
576.3.q.d.257.1		4	360.293	even	12
576.3.q.g.65.2		4	40.3	even	4
576.3.q.g.257.2		4	360.203	odd	12
900.3.p.a.101.1		4	5.2	odd	4
900.3.p.a.401.1		4	45.32	even	12
900.3.u.a.149.2		8	9.5	odd	6	inner
900.3.u.a.149.3		8	45.14	odd	6	inner
900.3.u.a.749.2		8	5.4	even	2	inner
900.3.u.a.749.3		8	1.1	even	1	trivial
1296.3.e.e.161.2		4	180.43	even	12
1296.3.e.e.161.3		4	180.83	odd	12
1728.3.q.g.449.1		4	360.13	odd	12
1728.3.q.g.1601.1		4	120.53	even	4
1728.3.q.h.449.1		4	360.283	even	12
1728.3.q.h.1601.1		4	120.83	odd	4
2700.3.p.b.1601.1		4	15.2	even	4
2700.3.p.b.2501.1		4	45.22	odd	12
2700.3.u.b.449.2		8	9.4	even	3
2700.3.u.b.449.3		8	45.4	even	6
2700.3.u.b.2249.2		8	15.14	odd	2
2700.3.u.b.2249.3		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.05446 - 2.18614i) q^{3} +(7.02939 + 4.05842i) q^{7} +(-0.558422 - 8.98266i) q^{9} +O(q^{10})\)	\(q+(2.05446 - 2.18614i) q^{3} +(7.02939 + 4.05842i) q^{7} +(-0.558422 - 8.98266i) q^{9} +(-17.6168 - 10.1711i) q^{11} +(-5.29734 + 3.05842i) q^{13} -17.9653 q^{17} -9.11684 q^{19} +(23.3139 - 7.02939i) q^{21} +(-16.7769 - 29.0584i) q^{23} +(-20.7846 - 17.2337i) q^{27} +(-14.4090 - 8.31901i) q^{29} +(11.1753 + 19.3561i) q^{31} +(-58.4285 + 17.6168i) q^{33} -50.4674i q^{37} +(-4.19702 + 17.8641i) q^{39} +(29.9674 - 17.3017i) q^{41} +(19.9186 + 11.5000i) q^{43} +(19.1537 - 33.1753i) q^{47} +(8.44158 + 14.6212i) q^{49} +(-36.9090 + 39.2747i) q^{51} +19.0149 q^{53} +(-18.7302 + 19.9307i) q^{57} +(2.96738 - 1.71322i) q^{59} +(23.1753 - 40.1407i) q^{61} +(32.5301 - 65.4090i) q^{63} +(-5.45504 + 3.14947i) q^{67} +(-97.9932 - 23.0226i) q^{69} -35.9306i q^{71} -47.3505i q^{73} +(-82.5571 - 142.993i) q^{77} +(-42.2921 + 73.2521i) q^{79} +(-80.3763 + 10.0322i) q^{81} +(-19.1537 + 33.1753i) q^{83} +(-47.7891 + 14.4090i) q^{87} +143.723i q^{89} -49.6495 q^{91} +(65.2743 + 15.3356i) q^{93} +(-69.9457 - 40.3832i) q^{97} +(-81.5258 + 163.926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 30 q^{9}+O(q^{10}) \) 8 * q + 30 * q^9	\( 8 q + 30 q^{9} - 72 q^{11} - 4 q^{19} + 198 q^{21} + 126 q^{29} - 14 q^{31} - 114 q^{39} - 36 q^{41} + 102 q^{49} - 54 q^{51} - 252 q^{59} + 82 q^{61} - 198 q^{69} - 166 q^{79} - 126 q^{81} - 604 q^{91} - 342 q^{99}+O(q^{100}) \) 8 * q + 30 * q^9 - 72 * q^11 - 4 * q^19 + 198 * q^21 + 126 * q^29 - 14 * q^31 - 114 * q^39 - 36 * q^41 + 102 * q^49 - 54 * q^51 - 252 * q^59 + 82 * q^61 - 198 * q^69 - 166 * q^79 - 126 * q^81 - 604 * q^91 - 342 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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