LMFDB - Embedded newform 900.3.u.a.149.2

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			149.2
Root			$-1.26217 - 1.18614i$ of defining polynomial
Character	$\chi$	$=$	900.149
Dual form			900.3.u.a.749.2

$q$-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 $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−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	$-0.863526\pi$
$7$	−7.02939	+	4.05842i	−1.00420	+	0.579775i	−0.0947110	+	0.995505i	$0.530193\pi$
$8$		0			0
$9$	−0.558422	+	8.98266i	−0.0620469	+	0.998073i
$10$		0			0
$11$	−17.6168	+	10.1711i	−1.60153	+	0.924645i	−0.610350	+	0.792132i	$0.708971\pi$
$11$	−17.6168	+	10.1711i	−1.60153	+	0.924645i	−0.991181	+	0.132513i	$0.957695\pi$
$12$		0			0
$13$	5.29734	+	3.05842i	0.407488	+	0.235263i	0.689710	−	0.724086i	$-0.257738\pi$
$13$	5.29734	+	3.05842i	0.407488	+	0.235263i	−0.282222	+	0.959349i	$0.591071\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	17.9653			1.05678			0.528392	−	0.849001i	$-0.322795\pi$
$17$	17.9653			1.05678			0.528392	+	0.849001i	$0.322795\pi$
$18$		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	−0.227695	−	0.973733i	$-0.573119\pi$
$23$	16.7769	−	29.0584i	0.729430	−	1.26341i	0.957124	−	0.289677i	$-0.0935479\pi$
$24$		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	−0.727416	−	0.686197i	$-0.759279\pi$
$29$	−14.4090	+	8.31901i	−0.496860	+	0.286863i	0.230556	+	0.973059i	$0.425946\pi$
$30$		0			0
$31$	11.1753	−	19.3561i	0.360492	−	0.624391i	−0.627549	−	0.778577i	$-0.715942\pi$
$31$	11.1753	−	19.3561i	0.360492	−	0.624391i	0.988042	+	0.154185i	$0.0492753\pi$
$32$		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	0.818756	−	0.574142i	$-0.194664\pi$
$41$	29.9674	+	17.3017i	0.730912	+	0.421992i	−0.0878440	+	0.996134i	$0.527998\pi$
$42$		0			0
$43$	−19.9186	+	11.5000i	−0.463223	+	0.267442i	−0.713398	−	0.700759i	$-0.752845\pi$
$43$	−19.9186	+	11.5000i	−0.463223	+	0.267442i	0.250176	+	0.968200i	$0.419512\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−19.1537	−	33.1753i	−0.407527	−	0.705857i	0.587085	−	0.809525i	$-0.300275\pi$
$47$	−19.1537	−	33.1753i	−0.407527	−	0.705857i	−0.994612	+	0.103668i	$0.966942\pi$
$48$		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	$-0.557411\pi$
$53$	−19.0149			−0.358771			−0.179386	+	0.983779i	$0.557411\pi$
$54$		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	0.524936	−	0.851141i	$-0.324089\pi$
$59$	2.96738	+	1.71322i	0.0502945	+	0.0290375i	−0.474642	+	0.880179i	$0.657422\pi$
$60$		0			0
$61$	23.1753	+	40.1407i	0.379922	+	0.658045i	0.991051	−	0.133487i	$-0.0426174\pi$
$61$	23.1753	+	40.1407i	0.379922	+	0.658045i	−0.611128	+	0.791532i	$0.709284\pi$
$62$		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	$-0.318365\pi$
$67$	5.45504	+	3.14947i	0.0814185	+	0.0470070i	−0.458738	+	0.888572i	$0.651698\pi$
$68$		0			0
$69$	−97.9932	+	23.0226i	−1.42019	+	0.333661i
$70$		0			0
$71$			35.9306i			0.506065i	0.967458	+	0.253033i	$0.0814280\pi$
$71$			35.9306i			0.506065i	−0.967458	+	0.253033i	$0.918572\pi$
$72$		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	−0.999147	−	0.0413035i	$-0.986849\pi$
$79$	−42.2921	−	73.2521i	−0.535343	−	0.927242i	0.463803	−	0.885938i	$-0.346484\pi$
$80$		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	$-0.0925428\pi$
$83$	19.1537	+	33.1753i	0.230768	+	0.399702i	−0.727266	+	0.686355i	$0.759209\pi$
$84$		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	$-0.700858\pi$
$89$		−	143.723i		−	1.61486i	0.589963	−	0.807430i	$-0.299142\pi$
$90$		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	$-0.529986\pi$
$97$	69.9457	−	40.3832i	0.721089	−	0.416321i	0.815154	+	0.579245i	$0.196653\pi$
$98$		0			0
$99$	−81.5258	−	163.926i	−0.823493	−	1.65582i
$100$		0			0
$101$	105.942	−	61.1654i	1.04893	−	0.605598i	0.126578	−	0.991957i	$-0.459601\pi$
$101$	105.942	−	61.1654i	1.04893	−	0.605598i	0.922349	+	0.386359i	$0.126267\pi$
$102$		0			0
$103$	63.7823	+	36.8247i	0.619246	+	0.357522i	0.776575	−	0.630024i	$-0.216955\pi$
$103$	63.7823	+	36.8247i	0.619246	+	0.357522i	−0.157330	+	0.987546i	$0.550288\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	72.9108			0.681410			0.340705	−	0.940170i	$-0.389334\pi$
$107$	72.9108			0.681410			0.340705	+	0.940170i	$0.389334\pi$
$108$		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	$-0.806913\pi$
$113$	9.36858	−	16.2269i	0.0829078	−	0.143601i	0.904498	+	0.426478i	$0.140246\pi$
$114$		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	0.929272	−	0.369396i	$-0.120435\pi$
$131$	140.694	+	81.2299i	1.07400	+	0.620075i	0.144730	+	0.989471i	$0.453769\pi$
$132$		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	$-0.0422823\pi$
$137$	52.1827	+	90.3832i	0.380896	+	0.659731i	−0.610295	+	0.792174i	$0.708949\pi$
$138$		0			0
$139$	30.6168	−	53.0299i	0.220265	−	0.381510i	−0.734623	−	0.678475i	$-0.762641\pi$
$139$	30.6168	−	53.0299i	0.220265	−	0.381510i	0.954888	+	0.296965i	$0.0959744\pi$
$140$		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	0.864470	−	0.502685i	$-0.167654\pi$
$149$	128.344	+	74.0993i	0.861367	+	0.497311i	−0.00310272	+	0.999995i	$0.500988\pi$
$150$		0			0
$151$	−127.526	−	220.881i	−0.844542	−	1.46279i	−0.886019	−	0.463650i	$-0.846540\pi$
$151$	−127.526	−	220.881i	−0.844542	−	1.46279i	0.0414769	−	0.999139i	$-0.486794\pi$
$152$		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	−0.988622	−	0.150418i	$-0.951938\pi$
$157$	−253.272	−	146.227i	−1.61320	−	0.931381i	−0.624577	−	0.780963i	$-0.714729\pi$
$158$		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	$-0.724215\pi$
$167$	56.1340	−	97.2269i	0.336131	−	0.582197i	0.983702	+	0.179809i	$0.0575480\pi$
$168$		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	0.973468	+	0.228823i	$0.0734877\pi$
$173$	118.488	+	205.227i	0.684900	+	1.18628i	−0.288568	+	0.957460i	$0.593179\pi$
$174$		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	$0.227459\pi$
$179$			234.599i			1.31061i	−0.755366	+	0.655304i	$0.772541\pi$
$180$		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	−0.800410	−	0.599452i	$-0.795385\pi$
$191$	−130.162	+	75.1488i	−0.681474	+	0.393449i	0.118936	+	0.992902i	$0.462052\pi$
$192$		0			0
$193$	−42.4352	−	24.5000i	−0.219872	−	0.126943i	0.386019	−	0.922491i	$-0.373850\pi$
$193$	−42.4352	−	24.5000i	−0.219872	−	0.126943i	−0.605891	+	0.795548i	$0.707183\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	276.827			1.40521			0.702606	−	0.711579i	$-0.252020\pi$
$197$	276.827			1.40521			0.702606	+	0.711579i	$0.252020\pi$
$198$		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	−0.955651	−	0.294500i	$-0.904847\pi$
$211$	−47.0068	+	81.4182i	−0.222781	+	0.385868i	0.732870	+	0.680368i	$0.238180\pi$
$212$		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	$-0.553113\pi$
$223$	134.886	−	77.8763i	0.604869	−	0.349221i	0.770955	+	0.636890i	$0.219780\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−79.9332	−	138.448i	−0.352129	−	0.609905i	0.634493	−	0.772928i	$-0.281209\pi$
$227$	−79.9332	−	138.448i	−0.352129	−	0.609905i	−0.986622	+	0.163023i	$0.947875\pi$
$228$		0			0
$229$	−19.1237	+	33.1232i	−0.0835095	+	0.144643i	−0.904755	−	0.425932i	$-0.859946\pi$
$229$	−19.1237	+	33.1232i	−0.0835095	+	0.144643i	0.821246	+	0.570575i	$0.193280\pi$
$230$		0			0
$231$	−482.213	+	113.292i	−2.08750	+	0.490440i
$232$		0			0
$233$	−157.490			−0.675921			−0.337960	−	0.941160i	$-0.609737\pi$
$233$	−157.490			−0.675921			−0.337960	+	0.941160i	$0.609737\pi$
$234$		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	0.624972	−	0.780647i	$-0.285110\pi$
$239$	62.4742	+	36.0695i	0.261398	+	0.150918i	−0.363574	+	0.931565i	$0.618444\pi$
$240$		0			0
$241$	−113.370	−	196.362i	−0.470413	−	0.814779i	0.529015	−	0.848613i	$-0.322562\pi$
$241$	−113.370	−	196.362i	−0.470413	−	0.814779i	−0.999427	+	0.0338337i	$0.989228\pi$
$242$		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	$0.146471\pi$
$251$			222.931i			0.888171i	−0.895985	+	0.444085i	$0.853529\pi$
$252$		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	$-0.899746\pi$
$257$	−53.2323	+	92.2011i	−0.207130	+	0.358759i	0.743680	+	0.668536i	$0.233079\pi$
$258$		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	$-0.277438\pi$
$263$	−89.6877	−	155.344i	−0.341018	−	0.590660i	−0.984622	+	0.174698i	$0.944105\pi$
$264$		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	$0.281690\pi$
$269$			416.351i			1.54777i	−0.633324	+	0.773887i	$0.718310\pi$
$270$		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	$-0.733547\pi$
$277$	−100.066	+	57.7731i	−0.361249	+	0.208567i	0.308379	+	0.951263i	$0.400213\pi$
$278$		0			0
$279$	167.629	+	111.192i	0.600821	+	0.398539i
$280$		0			0
$281$	422.564	−	243.967i	1.50379	−	0.868211i	0.503795	−	0.863823i	$-0.331937\pi$
$281$	422.564	−	243.967i	1.50379	−	0.868211i	0.999990	−	0.00438786i	$-0.00139670\pi$
$282$		0			0
$283$	−294.145	−	169.825i	−1.03938	−	0.600087i	−0.119724	−	0.992807i	$-0.538201\pi$
$283$	−294.145	−	169.825i	−1.03938	−	0.600087i	−0.919658	+	0.392720i	$0.871534\pi$
$284$		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	$-0.755791\pi$
$293$	70.6728	−	122.409i	0.241204	−	0.417778i	0.961058	+	0.276348i	$0.0891243\pi$
$294$		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	0.295866	−	0.955229i	$-0.404392\pi$
$311$	−119.254	−	68.8514i	−0.383454	−	0.221387i	−0.679320	+	0.733842i	$0.737725\pi$
$312$		0			0
$313$	−223.896	+	129.266i	−0.715322	+	0.412991i	−0.813029	−	0.582224i	$-0.802183\pi$
$313$	−223.896	+	129.266i	−0.715322	+	0.412991i	0.0977064	+	0.995215i	$0.468849\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.64630	−	16.7079i	−0.0304300	−	0.0527063i	0.850409	−	0.526122i	$-0.176354\pi$
$317$	−9.64630	−	16.7079i	−0.0304300	−	0.0527063i	−0.880839	+	0.473415i	$0.843021\pi$
$318$		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	0.975510	−	0.219957i	$-0.0705916\pi$
$331$	98.3953	+	170.426i	0.297267	+	0.514881i	−0.678243	+	0.734838i	$0.737258\pi$
$332$		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	$-0.489433\pi$
$337$	−274.911	−	158.720i	−0.815760	−	0.470979i	−0.848952	+	0.528470i	$0.822766\pi$
$338$		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	0.0593116	−	0.998240i	$-0.481109\pi$
$347$	310.272	−	537.407i	0.894157	−	1.54872i	0.834845	−	0.550485i	$-0.185557\pi$
$348$		0			0
$349$	−189.512	−	328.245i	−0.543015	−	0.940529i	−0.998729	−	0.0504030i	$-0.983949\pi$
$349$	−189.512	−	328.245i	−0.543015	−	0.940529i	0.455714	−	0.890126i	$-0.349384\pi$
$350$		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	$-0.0531157\pi$
$353$	123.272	+	213.514i	0.349213	+	0.604855i	−0.636897	+	0.770949i	$0.719782\pi$
$354$		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	$-0.706019\pi$
$359$		−	572.791i		−	1.59552i	0.602976	−	0.797759i	$-0.293981\pi$
$360$		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	$-0.749050\pi$
$367$	−162.688	+	93.9279i	−0.443291	+	0.255934i	0.261701	+	0.965149i	$0.415716\pi$
$368$		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	$-0.268840\pi$
$373$	130.005	+	75.0584i	0.348539	+	0.201229i	−0.315503	+	0.948925i	$0.602173\pi$
$374$		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	0.306929	+	0.951733i	$0.400699\pi$
$383$	−256.901	+	444.966i	−0.670760	+	1.16179i	−0.977689	+	0.210058i	$0.932635\pi$
$384$		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	−0.471244	−	0.882003i	$-0.656195\pi$
$389$	22.1616	−	12.7950i	0.0569707	−	0.0328921i	0.528215	+	0.849111i	$0.322862\pi$
$390$		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	0.456899	−	0.889519i	$-0.348960\pi$
$401$	−34.0842	−	19.6785i	−0.0849981	−	0.0490736i	−0.541897	+	0.840445i	$0.682294\pi$
$402$		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	−0.740320	−	0.672255i	$-0.765326\pi$
$409$	86.7200	−	150.204i	0.212029	−	0.367246i	0.952350	+	0.305009i	$0.0986594\pi$
$410$		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	0.356411	−	0.934329i	$-0.384000\pi$
$419$	−115.031	−	66.4132i	−0.274537	−	0.158504i	−0.630948	+	0.775825i	$0.717334\pi$
$420$		0			0
$421$	−317.447	−	549.834i	−0.754031	−	1.30602i	−0.945855	−	0.324590i	$-0.894774\pi$
$421$	−317.447	−	549.834i	−0.754031	−	1.30602i	0.191824	−	0.981429i	$-0.438560\pi$
$422$		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	$0.246313\pi$
$431$			602.424i			1.39774i	−0.715251	+	0.698868i	$0.753687\pi$
$432$		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	0.996542	+	0.0830886i	$0.0264784\pi$
$439$	250.330	+	433.584i	0.570228	+	0.987664i	−0.426314	+	0.904575i	$0.640188\pi$
$440$		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	$-0.0561441\pi$
$443$	150.745	+	261.098i	0.340282	+	0.589386i	−0.644203	+	0.764855i	$0.722811\pi$
$444$		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	$0.216754\pi$
$449$			565.321i			1.25907i	−0.776973	+	0.629534i	$0.783246\pi$
$450$		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	$-0.648443\pi$
$457$	45.2922	−	26.1495i	0.0991077	−	0.0572198i	0.548735	+	0.835997i	$0.315110\pi$
$458$		0			0
$459$	373.402	−	309.609i	0.813512	−	0.674529i
$460$		0			0
$461$	166.357	−	96.0465i	0.360862	−	0.208344i	−0.308597	−	0.951193i	$-0.599859\pi$
$461$	166.357	−	96.0465i	0.360862	−	0.208344i	0.669459	+	0.742849i	$0.266526\pi$
$462$		0			0
$463$	490.361	+	283.110i	1.05909	+	0.611469i	0.925182	−	0.379524i	$-0.123912\pi$
$463$	490.361	+	283.110i	1.05909	+	0.611469i	0.133913	+	0.990993i	$0.457246\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	174.405			0.373459			0.186729	−	0.982411i	$-0.440211\pi$
$467$	174.405			0.373459			0.186729	+	0.982411i	$0.440211\pi$
$468$		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	−0.905008	−	0.425394i	$-0.860135\pi$
$479$	−473.784	+	273.539i	−0.989110	+	0.571063i	−0.0841020	+	0.996457i	$0.526802\pi$
$480$		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	0.333879	−	0.942616i	$-0.391642\pi$
$491$	−154.916	−	89.4407i	−0.315511	−	0.182160i	−0.649390	+	0.760456i	$0.724976\pi$
$492$		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	−0.991919	−	0.126876i	$-0.959505\pi$
$499$	−192.655	+	333.688i	−0.386082	+	0.668713i	0.605837	+	0.795589i	$0.292838\pi$
$500$		0			0
$501$	−327.876	+	77.0316i	−0.654444	+	0.153756i
$502$		0			0
$503$	−67.6630			−0.134519			−0.0672594	−	0.997736i	$-0.521426\pi$
$503$	−67.6630			−0.134519			−0.0672594	+	0.997736i	$0.521426\pi$
$504$		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	−0.111645	−	0.993748i	$-0.535612\pi$
$509$	−523.292	−	302.123i	−1.02808	−	0.593562i	−0.916434	+	0.400187i	$0.868945\pi$
$510$		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	$-0.915405\pi$
$521$		−	273.678i		−	0.525294i	0.964892	−	0.262647i	$-0.0845954\pi$
$522$		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	$-0.509261\pi$
$547$	449.646	−	259.603i	0.822022	−	0.474594i	0.851113	+	0.524982i	$0.175928\pi$
$548$		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	$-0.623869\pi$
$557$	−422.648			−0.758794			−0.379397	+	0.925234i	$0.623869\pi$
$558$		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	−0.0871428	−	0.996196i	$-0.527774\pi$
$563$	461.187	−	798.799i	0.819159	−	1.41883i	0.906302	−	0.422630i	$-0.138893\pi$
$564$		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	0.617097	−	0.786887i	$-0.288309\pi$
$569$	914.445	−	527.955i	1.60711	−	0.927865i	0.990013	−	0.140978i	$-0.0450247\pi$
$570$		0			0
$571$	−401.524	+	695.460i	−0.703195	+	1.21797i	0.264144	+	0.964483i	$0.414911\pi$
$571$	−401.524	+	695.460i	−0.703195	+	1.21797i	−0.967339	+	0.253486i	$0.918423\pi$
$572$		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	−0.875540	−	0.483146i	$-0.839494\pi$
$587$	−502.582	−	870.497i	−0.856187	−	1.48296i	0.0193528	−	0.999813i	$-0.493839\pi$
$588$		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	$-0.718769\pi$
$593$	−752.444			−1.26888			−0.634439	+	0.772973i	$0.718769\pi$
$594$		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	0.519970	−	0.854184i	$-0.325943\pi$
$599$	24.0857	+	13.9059i	0.0402099	+	0.0232152i	−0.479760	+	0.877400i	$0.659276\pi$
$600$		0			0
$601$	475.356	+	823.340i	0.790942	+	1.36995i	0.925385	+	0.379030i	$0.123742\pi$
$601$	475.356	+	823.340i	0.790942	+	1.36995i	−0.134443	+	0.990921i	$0.542925\pi$
$602$		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	$-0.247716\pi$
$607$	279.390	+	161.306i	0.460280	+	0.265743i	−0.251882	+	0.967758i	$0.581050\pi$
$608$		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	−0.347564	−	0.937656i	$-0.612991\pi$
$617$	393.802	−	682.084i	0.638252	−	1.10548i	0.985816	−	0.167829i	$-0.0536756\pi$
$618$		0			0
$619$	−121.747	−	210.873i	−0.196684	−	0.340667i	0.750767	−	0.660567i	$-0.229684\pi$
$619$	−121.747	−	210.873i	−0.196684	−	0.340667i	−0.947451	+	0.319900i	$0.896351\pi$
$620$		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	0.0819990	−	0.996632i	$-0.473870\pi$
$641$	632.095	−	364.940i	0.986107	−	0.569329i	0.904108	+	0.427303i	$0.140536\pi$
$642$		0			0
$643$	−499.697	−	288.500i	−0.777133	−	0.448678i	0.0582801	−	0.998300i	$-0.481438\pi$
$643$	−499.697	−	288.500i	−0.777133	−	0.448678i	−0.835413	+	0.549622i	$0.814772\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	129.029			0.199426			0.0997130	−	0.995016i	$-0.468208\pi$
$647$	129.029			0.199426			0.0997130	+	0.995016i	$0.468208\pi$
$648$		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	0.0904070	−	0.995905i	$-0.471183\pi$
$653$	592.717	−	1026.62i	0.907682	−	1.57215i	0.817275	−	0.576247i	$-0.195483\pi$
$654$		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	−0.997728	−	0.0673658i	$-0.978541\pi$
$659$	−947.808	+	547.217i	−1.43825	+	0.830375i	−0.440524	+	0.897741i	$0.645207\pi$
$660$		0			0
$661$	−604.876	+	1047.68i	−0.915093	+	1.58499i	−0.108327	+	0.994115i	$0.534549\pi$
$661$	−604.876	+	1047.68i	−0.915093	+	1.58499i	−0.806765	+	0.590872i	$0.798784\pi$
$662$		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	$-0.939391\pi$
$673$	−880.948	+	508.615i	−1.30899	+	0.755743i	−0.327059	+	0.945004i	$0.606058\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	398.308	+	689.890i	0.588343	+	1.01904i	0.994450	+	0.105214i	$0.0335528\pi$
$677$	398.308	+	689.890i	0.588343	+	1.01904i	−0.406107	+	0.913826i	$0.633114\pi$
$678$		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	$-0.594714\pi$
$683$	−400.485			−0.586361			−0.293181	+	0.956057i	$0.594714\pi$
$684$		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	0.979054	−	0.203602i	$-0.0652650\pi$
$691$	216.423	+	374.855i	0.313202	+	0.542482i	−0.665852	+	0.746084i	$0.731932\pi$
$692$		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	$-0.985137\pi$
$701$		−	65.4412i		−	0.0933541i	0.998910	−	0.0466770i	$-0.0148632\pi$
$702$		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	0.928134	−	0.372245i	$-0.121412\pi$
$709$	100.461	+	174.003i	0.141693	+	0.245420i	−0.786441	+	0.617665i	$0.788079\pi$
$710$		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	$-0.735200\pi$
$719$		−	1062.98i		−	1.47841i	0.673478	−	0.739207i	$-0.264800\pi$
$720$		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	$-0.427888\pi$
$727$	858.455	−	495.629i	1.18082	−	0.681746i	0.956204	+	0.292702i	$0.0945545\pi$
$728$		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	$-0.631219\pi$
$733$	−1022.14	−	590.134i	−1.39446	−	0.805095i	−0.993806	+	0.111133i	$0.964552\pi$
$734$		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	$-0.761723\pi$
$743$	165.747	−	287.083i	0.223078	−	0.386383i	0.955741	+	0.294209i	$0.0950561\pi$
$744$		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	−0.912203	−	0.409738i	$-0.865620\pi$
$751$	−76.0448	+	131.713i	−0.101258	+	0.175384i	0.810945	+	0.585122i	$0.198953\pi$
$752$		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	−0.999458	−	0.0329205i	$-0.989519\pi$
$761$	−1162.58	−	671.214i	−1.52770	−	0.882016i	−0.528239	−	0.849096i	$-0.677147\pi$
$762$		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	−0.250339	−	0.968158i	$-0.580542\pi$
$769$	548.512	−	950.051i	0.713280	−	1.23544i	0.963619	−	0.267279i	$-0.0861244\pi$
$770$		0			0
$771$	310.928	−	73.0497i	0.403279	−	0.0947467i
$772$		0			0
$773$	−1181.39			−1.52832			−0.764159	−	0.645028i	$-0.776846\pi$
$773$	−1181.39			−1.52832			−0.764159	+	0.645028i	$0.776846\pi$
$774$		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	$-0.326040\pi$
$787$	31.2308	+	18.0311i	0.0396834	+	0.0229112i	−0.480027	+	0.877254i	$0.659373\pi$
$788$		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	$-0.806642\pi$
$797$	66.7523	−	115.618i	0.0837544	−	0.145067i	0.904860	+	0.425710i	$0.139976\pi$
$798$		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	$-0.774262\pi$
$809$		−	1053.66i		−	1.30242i	0.758898	−	0.651209i	$-0.225738\pi$
$810$		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	−0.338322	−	0.941031i	$-0.609859\pi$
$821$	252.436	−	145.744i	0.307474	−	0.177520i	0.645796	+	0.763510i	$0.276526\pi$
$822$		0			0
$823$	291.693	+	168.409i	0.354426	+	0.204628i	0.666633	−	0.745386i	$-0.267735\pi$
$823$	291.693	+	168.409i	0.354426	+	0.204628i	−0.312207	+	0.950014i	$0.601068\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1029.27			−1.24458			−0.622292	−	0.782785i	$-0.713798\pi$
$827$	−1029.27			−1.24458			−0.622292	+	0.782785i	$0.713798\pi$
$828$		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	−0.836688	−	0.547679i	$-0.815511\pi$
$839$	−655.031	+	378.182i	−0.780728	+	0.450754i	0.0559600	+	0.998433i	$0.482178\pi$
$840$		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	$-0.418764\pi$
$853$	1037.80	−	599.175i	1.21665	−	0.702433i	0.964200	+	0.265177i	$0.0854304\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	349.660	+	605.629i	0.408005	+	0.706685i	0.994666	−	0.103147i	$-0.0328913\pi$
$857$	349.660	+	605.629i	0.408005	+	0.706685i	−0.586661	+	0.809832i	$0.699558\pi$
$858$		0			0
$859$	−278.734	+	482.781i	−0.324486	+	0.562027i	−0.981408	−	0.191932i	$-0.938525\pi$
$859$	−278.734	+	482.781i	−0.324486	+	0.562027i	0.656922	+	0.753959i	$0.271858\pi$
$860$		0			0
$861$	577.035	+	614.021i	0.670192	+	0.713149i
$862$		0			0
$863$	−99.3954			−0.115174			−0.0575871	−	0.998340i	$-0.518341\pi$
$863$	−99.3954			−0.115174			−0.0575871	+	0.998340i	$0.518341\pi$
$864$		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	$-0.484615\pi$
$877$	−695.058	−	401.292i	−0.792541	−	0.457574i	−0.840856	+	0.541258i	$0.817948\pi$
$878$		0			0
$879$	−412.797	+	96.9830i	−0.469622	+	0.110333i
$880$		0			0
$881$			524.266i			0.595080i	0.954709	+	0.297540i	$0.0961662\pi$
$881$			524.266i			0.595080i	−0.954709	+	0.297540i	$0.903834\pi$
$882$		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	$-0.964801\pi$
$887$	−356.019	+	616.643i	−0.401374	+	0.695200i	0.592518	+	0.805557i	$0.298134\pi$
$888$		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	$-0.802140\pi$
$907$	−648.606	+	374.473i	−0.715111	+	0.412870i	0.0978396	+	0.995202i	$0.468807\pi$
$908$		0			0
$909$	490.268	+	985.793i	0.539349	+	1.08448i
$910$		0			0
$911$	−3.87633	+	2.23800i	−0.00425503	+	0.00245664i	−0.502126	−	0.864794i	$-0.667449\pi$
$911$	−3.87633	+	2.23800i	−0.00425503	+	0.00245664i	0.497871	+	0.867251i	$0.334115\pi$
$912$		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	−0.0240553	−	0.999711i	$-0.507658\pi$
$929$	770.784	−	445.012i	0.829692	−	0.479023i	0.853747	+	0.520688i	$0.174324\pi$
$930$		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	0.462483	−	0.886628i	$-0.346959\pi$
$941$	−69.7458	−	40.2678i	−0.0741188	−	0.0427925i	−0.536601	+	0.843836i	$0.680292\pi$
$942$		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	$-0.118774\pi$
$947$	141.948	+	245.861i	0.149892	+	0.259621i	−0.781295	+	0.624162i	$0.785441\pi$
$948$		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	$-0.299410\pi$
$953$	1123.17			1.17857			0.589283	+	0.807927i	$0.299410\pi$
$954$		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	$-0.0759075\pi$
$967$	1211.63	+	699.536i	1.25298	+	0.723409i	0.281281	+	0.959626i	$0.409241\pi$
$968$		0			0
$969$	336.493	+	358.061i	0.347258	+	0.369516i
$970$		0			0
$971$		−	1705.41i		−	1.75634i	−0.478345	−	0.878172i	$-0.658763\pi$
$971$		−	1705.41i		−	1.75634i	0.478345	−	0.878172i	$-0.341237\pi$
$972$		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	0.399470	+	0.916746i	$0.369194\pi$
$977$	−580.524	+	1005.50i	−0.594190	+	1.02917i	−0.993661	+	0.112422i	$0.964139\pi$
$978$		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	0.992653	+	0.120999i	$0.0386096\pi$
$983$	590.895	+	1023.46i	0.601114	+	1.04116i	−0.391539	+	0.920162i	$0.628057\pi$
$984$		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	$-0.538693\pi$
$997$	675.714	−	390.124i	0.677747	−	0.391298i	0.799006	+	0.601323i	$0.205360\pi$
$998$		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.149.2		8
3.2	odd	2		2700.3.u.b.449.2		8
5.2	odd	4		900.3.p.a.401.1		4
5.3	odd	4		36.3.g.a.5.2	✓	4
5.4	even	2	inner	900.3.u.a.149.3		8
9.2	odd	6	inner	900.3.u.a.749.3		8
9.7	even	3		2700.3.u.b.2249.3		8
15.2	even	4		2700.3.p.b.2501.1		4
15.8	even	4		108.3.g.a.17.2		4
15.14	odd	2		2700.3.u.b.449.3		8
20.3	even	4		144.3.q.b.113.1		4
40.3	even	4		576.3.q.g.257.2		4
40.13	odd	4		576.3.q.d.257.1		4
45.2	even	12		900.3.p.a.101.1		4
45.7	odd	12		2700.3.p.b.1601.1		4
45.13	odd	12		324.3.c.b.161.3		4
45.23	even	12		324.3.c.b.161.2		4
45.29	odd	6	inner	900.3.u.a.749.2		8
45.34	even	6		2700.3.u.b.2249.2		8
45.38	even	12		36.3.g.a.29.2	yes	4
45.43	odd	12		108.3.g.a.89.2		4
60.23	odd	4		432.3.q.b.17.2		4
120.53	even	4		1728.3.q.g.449.1		4
120.83	odd	4		1728.3.q.h.449.1		4
180.23	odd	12		1296.3.e.e.161.2		4
180.43	even	12		432.3.q.b.305.2		4
180.83	odd	12		144.3.q.b.65.1		4
180.103	even	12		1296.3.e.e.161.3		4
360.43	even	12		1728.3.q.h.1601.1		4
360.83	odd	12		576.3.q.g.65.2		4
360.133	odd	12		1728.3.q.g.1601.1		4
360.173	even	12		576.3.q.d.65.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.g.a.5.2	✓	4	5.3	odd	4
36.3.g.a.29.2	yes	4	45.38	even	12
108.3.g.a.17.2		4	15.8	even	4
108.3.g.a.89.2		4	45.43	odd	12
144.3.q.b.65.1		4	180.83	odd	12
144.3.q.b.113.1		4	20.3	even	4
324.3.c.b.161.2		4	45.23	even	12
324.3.c.b.161.3		4	45.13	odd	12
432.3.q.b.17.2		4	60.23	odd	4
432.3.q.b.305.2		4	180.43	even	12
576.3.q.d.65.1		4	360.173	even	12
576.3.q.d.257.1		4	40.13	odd	4
576.3.q.g.65.2		4	360.83	odd	12
576.3.q.g.257.2		4	40.3	even	4
900.3.p.a.101.1		4	45.2	even	12
900.3.p.a.401.1		4	5.2	odd	4
900.3.u.a.149.2		8	1.1	even	1	trivial
900.3.u.a.149.3		8	5.4	even	2	inner
900.3.u.a.749.2		8	45.29	odd	6	inner
900.3.u.a.749.3		8	9.2	odd	6	inner
1296.3.e.e.161.2		4	180.23	odd	12
1296.3.e.e.161.3		4	180.103	even	12
1728.3.q.g.449.1		4	120.53	even	4
1728.3.q.g.1601.1		4	360.133	odd	12
1728.3.q.h.449.1		4	120.83	odd	4
1728.3.q.h.1601.1		4	360.43	even	12
2700.3.p.b.1601.1		4	45.7	odd	12
2700.3.p.b.2501.1		4	15.2	even	4
2700.3.u.b.449.2		8	3.2	odd	2
2700.3.u.b.449.3		8	15.14	odd	2
2700.3.u.b.2249.2		8	45.34	even	6
2700.3.u.b.2249.3		8	9.7	even	3

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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