LMFDB - Embedded newform 1350.2.q.h.557.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,2,Mod(143,1350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1350, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 9]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1350.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1350.q (of order $12$, degree $4$, 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:	$10.7798042729$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.4
Root			$0.500000 + 0.589118i$ of defining polynomial
Character	$\chi$	$=$	1350.557
Dual form			1350.2.q.h.143.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(0.521929 - 1.94786i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.70563 - 0.984748i) q^{11} +(-1.05248 - 3.92790i) q^{13} +(1.00829 - 1.74641i) q^{14} +(0.500000 + 0.866025i) q^{16} +(2.35877 - 2.35877i) q^{17} -3.70753i q^{19} +(1.90239 - 0.509743i) q^{22} +(-6.05338 + 1.62200i) q^{23} -4.06647i q^{26} +(1.42594 - 1.42594i) q^{28} +(3.74863 + 6.49281i) q^{29} +(3.48837 - 6.04204i) q^{31} +(0.258819 + 0.965926i) q^{32} +(2.88889 - 1.66790i) q^{34} +(-4.26692 - 4.26692i) q^{37} +(0.959578 - 3.58120i) q^{38} +(-6.13601 - 3.54263i) q^{41} +(9.09714 + 2.43757i) q^{43} +1.96950 q^{44} -6.26692 q^{46} +(7.49533 + 2.00837i) q^{47} +(2.54041 + 1.46671i) q^{49} +(1.05248 - 3.92790i) q^{52} +(7.03027 + 7.03027i) q^{53} +(1.74641 - 1.00829i) q^{56} +(1.94043 + 7.24179i) q^{58} +(-1.34967 + 2.33769i) q^{59} +(-4.37353 - 7.57518i) q^{61} +(4.93330 - 4.93330i) q^{62} +1.00000i q^{64} +(8.18285 - 2.19259i) q^{67} +(3.22213 - 0.863368i) q^{68} -5.68481i q^{71} +(-1.14928 + 1.14928i) q^{73} +(-3.01717 - 5.22589i) q^{74} +(1.85376 - 3.21081i) q^{76} +(-1.02794 - 3.83631i) q^{77} +(-10.0535 + 5.80440i) q^{79} +(-5.01003 - 5.01003i) q^{82} +(-0.440961 + 1.64569i) q^{83} +(8.15627 + 4.70902i) q^{86} +(1.90239 + 0.509743i) q^{88} +2.04989 q^{89} -8.20034 q^{91} +(-6.05338 - 1.62200i) q^{92} +(6.72013 + 3.87987i) q^{94} +(-2.60421 + 9.71905i) q^{97} +(2.07424 + 2.07424i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7} + 8 q^{16} - 8 q^{22} - 24 q^{23} + 16 q^{28} - 8 q^{31} + 24 q^{38} - 24 q^{41} - 32 q^{46} + 48 q^{47} - 24 q^{56} - 16 q^{58} - 24 q^{61} + 16 q^{67} - 24 q^{68} - 16 q^{73} + 16 q^{76}+ \cdots + 48 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 + 8 * q^16 - 8 * q^22 - 24 * q^23 + 16 * q^28 - 8 * q^31 + 24 * q^38 - 24 * q^41 - 32 * q^46 + 48 * q^47 - 24 * q^56 - 16 * q^58 - 24 * q^61 + 16 * q^67 - 24 * q^68 - 16 * q^73 + 16 * q^76 - 72 * q^77 + 16 * q^82 + 48 * q^83 + 48 * q^86 - 8 * q^88 - 24 * q^92 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.521929	−	1.94786i	0.197270	−	0.736223i	−0.794397	−	0.607399i	$-0.792213\pi$
$7$	0.521929	−	1.94786i	0.197270	−	0.736223i	0.991667	−	0.128824i	$-0.0411204\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$		0			0
$11$	1.70563	−	0.984748i	0.514268	−	0.296913i	−0.220318	−	0.975428i	$-0.570710\pi$
$11$	1.70563	−	0.984748i	0.514268	−	0.296913i	0.734586	+	0.678515i	$0.237376\pi$
$12$		0			0
$13$	−1.05248	−	3.92790i	−0.291905	−	1.08940i	−0.943644	−	0.330961i	$-0.892627\pi$
$13$	−1.05248	−	3.92790i	−0.291905	−	1.08940i	0.651739	−	0.758443i	$-0.274040\pi$
$14$	1.00829	−	1.74641i	0.269476	−	0.466747i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.35877	−	2.35877i	0.572085	−	0.572085i	−0.360626	−	0.932711i	$-0.617437\pi$
$17$	2.35877	−	2.35877i	0.572085	−	0.572085i	0.932711	+	0.360626i	$0.117437\pi$
$18$		0			0
$19$		−	3.70753i		−	0.850565i	−0.905061	−	0.425282i	$-0.860175\pi$
$19$		−	3.70753i		−	0.850565i	0.905061	−	0.425282i	$-0.139825\pi$
$20$		0			0
$21$		0			0
$22$	1.90239	−	0.509743i	0.405590	−	0.108678i
$23$	−6.05338	+	1.62200i	−1.26222	+	0.338210i	−0.827044	−	0.562137i	$-0.809979\pi$
$23$	−6.05338	+	1.62200i	−1.26222	+	0.338210i	−0.435173	+	0.900347i	$0.643313\pi$
$24$		0			0
$25$		0			0
$26$		−	4.06647i		−	0.797499i
$27$		0			0
$28$	1.42594	−	1.42594i	0.269476	−	0.269476i
$29$	3.74863	+	6.49281i	0.696103	+	1.20569i	0.969808	+	0.243872i	$0.0784175\pi$
$29$	3.74863	+	6.49281i	0.696103	+	1.20569i	−0.273705	+	0.961814i	$0.588249\pi$
$30$		0			0
$31$	3.48837	−	6.04204i	0.626530	−	1.08518i	−0.361713	−	0.932289i	$-0.617808\pi$
$31$	3.48837	−	6.04204i	0.626530	−	1.08518i	0.988243	−	0.152892i	$-0.0488587\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$		0			0
$34$	2.88889	−	1.66790i	0.495440	−	0.286042i
$35$		0			0
$36$		0			0
$37$	−4.26692	−	4.26692i	−0.701478	−	0.701478i	0.263250	−	0.964728i	$-0.415206\pi$
$37$	−4.26692	−	4.26692i	−0.701478	−	0.701478i	−0.964728	+	0.263250i	$0.915206\pi$
$38$	0.959578	−	3.58120i	0.155664	−	0.580947i
$39$		0			0
$40$		0			0
$41$	−6.13601	−	3.54263i	−0.958284	−	0.553266i	−0.0626396	−	0.998036i	$-0.519952\pi$
$41$	−6.13601	−	3.54263i	−0.958284	−	0.553266i	−0.895644	+	0.444771i	$0.853285\pi$
$42$		0			0
$43$	9.09714	+	2.43757i	1.38730	+	0.371726i	0.873767	−	0.486344i	$-0.161670\pi$
$43$	9.09714	+	2.43757i	1.38730	+	0.371726i	0.513533	+	0.858070i	$0.328336\pi$
$44$	1.96950			0.296913
$45$		0			0
$46$	−6.26692			−0.924007
$47$	7.49533	+	2.00837i	1.09331	+	0.292951i	0.760036	−	0.649881i	$-0.225181\pi$
$47$	7.49533	+	2.00837i	1.09331	+	0.292951i	0.333270	+	0.942831i	$0.391848\pi$
$48$		0			0
$49$	2.54041	+	1.46671i	0.362916	+	0.209530i
$50$		0			0
$51$		0			0
$52$	1.05248	−	3.92790i	0.145953	−	0.544702i
$53$	7.03027	+	7.03027i	0.965682	+	0.965682i	0.999430	−	0.0337485i	$-0.0107445\pi$
$53$	7.03027	+	7.03027i	0.965682	+	0.965682i	−0.0337485	+	0.999430i	$0.510745\pi$
$54$		0			0
$55$		0			0
$56$	1.74641	−	1.00829i	0.233373	−	0.134738i
$57$		0			0
$58$	1.94043	+	7.24179i	0.254791	+	0.950894i
$59$	−1.34967	+	2.33769i	−0.175712	+	0.304341i	−0.940407	−	0.340050i	$-0.889556\pi$
$59$	−1.34967	+	2.33769i	−0.175712	+	0.304341i	0.764696	+	0.644392i	$0.222889\pi$
$60$		0			0
$61$	−4.37353	−	7.57518i	−0.559973	−	0.969902i	−0.997498	−	0.0706960i	$-0.977478\pi$
$61$	−4.37353	−	7.57518i	−0.559973	−	0.969902i	0.437524	−	0.899207i	$-0.355855\pi$
$62$	4.93330	−	4.93330i	0.626530	−	0.626530i
$63$		0			0
$64$			1.00000i			0.125000i
$65$		0			0
$66$		0			0
$67$	8.18285	−	2.19259i	0.999694	−	0.267867i	0.278377	−	0.960472i	$-0.410204\pi$
$67$	8.18285	−	2.19259i	0.999694	−	0.267867i	0.721317	+	0.692605i	$0.243537\pi$
$68$	3.22213	−	0.863368i	0.390741	−	0.104699i
$69$		0			0
$70$		0			0
$71$		−	5.68481i		−	0.674663i	−0.941386	−	0.337332i	$-0.890476\pi$
$71$		−	5.68481i		−	0.674663i	0.941386	−	0.337332i	$-0.109524\pi$
$72$		0			0
$73$	−1.14928	+	1.14928i	−0.134513	+	0.134513i	−0.771157	−	0.636645i	$-0.780322\pi$
$73$	−1.14928	+	1.14928i	−0.134513	+	0.134513i	0.636645	+	0.771157i	$0.280322\pi$
$74$	−3.01717	−	5.22589i	−0.350739	−	0.607498i
$75$		0			0
$76$	1.85376	−	3.21081i	0.212641	−	0.368305i
$77$	−1.02794	−	3.83631i	−0.117144	−	0.437188i
$78$		0			0
$79$	−10.0535	+	5.80440i	−1.13111	+	0.653046i	−0.944214	−	0.329334i	$-0.893176\pi$
$79$	−10.0535	+	5.80440i	−1.13111	+	0.653046i	−0.186895	+	0.982380i	$0.559842\pi$
$80$		0			0
$81$		0			0
$82$	−5.01003	−	5.01003i	−0.553266	−	0.553266i
$83$	−0.440961	+	1.64569i	−0.0484017	+	0.180638i	−0.985895	−	0.167366i	$-0.946474\pi$
$83$	−0.440961	+	1.64569i	−0.0484017	+	0.180638i	0.937493	+	0.348004i	$0.113140\pi$
$84$		0			0
$85$		0			0
$86$	8.15627	+	4.70902i	0.879513	+	0.507787i
$87$		0			0
$88$	1.90239	+	0.509743i	0.202795	+	0.0543388i
$89$	2.04989			0.217288			0.108644	−	0.994081i	$-0.465349\pi$
$89$	2.04989			0.217288			0.108644	+	0.994081i	$0.465349\pi$
$90$		0			0
$91$	−8.20034			−0.859629
$92$	−6.05338	−	1.62200i	−0.631109	−	0.169105i
$93$		0			0
$94$	6.72013	+	3.87987i	0.693128	+	0.400178i
$95$		0			0
$96$		0			0
$97$	−2.60421	+	9.71905i	−0.264418	+	0.986820i	0.698188	+	0.715914i	$0.253990\pi$
$97$	−2.60421	+	9.71905i	−0.264418	+	0.986820i	−0.962606	+	0.270906i	$0.912677\pi$
$98$	2.07424	+	2.07424i	0.209530	+	0.209530i
$99$		0			0
$100$		0			0
$101$	4.09014	−	2.36144i	0.406984	−	0.234972i	−0.282509	−	0.959265i	$-0.591167\pi$
$101$	4.09014	−	2.36144i	0.406984	−	0.234972i	0.689493	+	0.724292i	$0.257833\pi$
$102$		0			0
$103$	−1.03662	−	3.86872i	−0.102141	−	0.381196i	0.895864	−	0.444329i	$-0.146558\pi$
$103$	−1.03662	−	3.86872i	−0.102141	−	0.381196i	−0.998005	+	0.0631321i	$0.979891\pi$
$104$	2.03323	−	3.52166i	0.199375	−	0.345327i
$105$		0			0
$106$	4.97115	+	8.61029i	0.482841	+	0.836305i
$107$	−5.40296	+	5.40296i	−0.522324	+	0.522324i	−0.918273	−	0.395949i	$-0.870416\pi$
$107$	−5.40296	+	5.40296i	−0.522324	+	0.522324i	0.395949	+	0.918273i	$0.370416\pi$
$108$		0			0
$109$		−	4.35357i		−	0.416996i	−0.978023	−	0.208498i	$-0.933142\pi$
$109$		−	4.35357i		−	0.416996i	0.978023	−	0.208498i	$-0.0668575\pi$
$110$		0			0
$111$		0			0
$112$	1.94786	−	0.521929i	0.184056	−	0.0493176i
$113$	2.86451	−	0.767544i	0.269471	−	0.0722045i	−0.121553	−	0.992585i	$-0.538788\pi$
$113$	2.86451	−	0.767544i	0.269471	−	0.0722045i	0.391024	+	0.920380i	$0.372121\pi$
$114$		0			0
$115$		0			0
$116$			7.49726i			0.696103i
$117$		0			0
$118$	−1.90872	+	1.90872i	−0.175712	+	0.175712i
$119$	−3.36345	−	5.82566i	−0.308327	−	0.534037i
$120$		0			0
$121$	−3.56054	+	6.16704i	−0.323686	+	0.560640i
$122$	−2.26391	−	8.44902i	−0.204965	−	0.764938i
$123$		0			0
$124$	6.04204	−	3.48837i	0.542591	−	0.313265i
$125$		0			0
$126$		0			0
$127$	3.41734	+	3.41734i	0.303240	+	0.303240i	0.842280	−	0.539040i	$-0.181213\pi$
$127$	3.41734	+	3.41734i	0.303240	+	0.303240i	−0.539040	+	0.842280i	$0.681213\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$		0			0
$130$		0			0
$131$	0.411267	+	0.237445i	0.0359326	+	0.0207457i	0.517859	−	0.855466i	$-0.326729\pi$
$131$	0.411267	+	0.237445i	0.0359326	+	0.0207457i	−0.481926	+	0.876212i	$0.660063\pi$
$132$		0			0
$133$	−7.22176	−	1.93506i	−0.626206	−	0.167791i
$134$	8.47151			0.731827
$135$		0			0
$136$	3.33580			0.286042
$137$	9.51618	+	2.54985i	0.813022	+	0.217849i	0.641293	−	0.767296i	$-0.278398\pi$
$137$	9.51618	+	2.54985i	0.813022	+	0.217849i	0.171728	+	0.985144i	$0.445065\pi$
$138$		0			0
$139$	0.608318	+	0.351212i	0.0515968	+	0.0297894i	0.525577	−	0.850746i	$-0.323850\pi$
$139$	0.608318	+	0.351212i	0.0515968	+	0.0297894i	−0.473980	+	0.880536i	$0.657183\pi$
$140$		0			0
$141$		0			0
$142$	1.47134	−	5.49111i	0.123472	−	0.460803i
$143$	−5.66314	−	5.66314i	−0.473575	−	0.473575i
$144$		0			0
$145$		0			0
$146$	−1.40757	+	0.812661i	−0.116491	+	0.0672563i
$147$		0			0
$148$	−1.56180	−	5.82872i	−0.128379	−	0.479118i
$149$	−4.05609	+	7.02536i	−0.332288	+	0.575540i	−0.982960	−	0.183819i	$-0.941154\pi$
$149$	−4.05609	+	7.02536i	−0.332288	+	0.575540i	0.650672	+	0.759359i	$0.274487\pi$
$150$		0			0
$151$	4.61739	+	7.99755i	0.375758	+	0.650832i	0.990440	−	0.137943i	$-0.0440491\pi$
$151$	4.61739	+	7.99755i	0.375758	+	0.650832i	−0.614682	+	0.788775i	$0.710716\pi$
$152$	2.62162	−	2.62162i	0.212641	−	0.212641i
$153$		0			0
$154$		−	3.97164i		−	0.320044i
$155$		0			0
$156$		0			0
$157$	−10.4848	+	2.80938i	−0.836775	+	0.224213i	−0.651667	−	0.758505i	$-0.725930\pi$
$157$	−10.4848	+	2.80938i	−0.836775	+	0.224213i	−0.185108	+	0.982718i	$0.559264\pi$
$158$	−11.2132	+	3.00458i	−0.892077	+	0.239031i
$159$		0			0
$160$		0			0
$161$			12.6377i			0.995993i
$162$		0			0
$163$	−9.68197	+	9.68197i	−0.758351	+	0.758351i	−0.976022	−	0.217671i	$-0.930154\pi$
$163$	−9.68197	+	9.68197i	−0.758351	+	0.758351i	0.217671	+	0.976022i	$0.430154\pi$
$164$	−3.54263	−	6.13601i	−0.276633	−	0.479142i
$165$		0			0
$166$	−0.851871	+	1.47548i	−0.0661180	+	0.114520i
$167$	1.32254	+	4.93579i	0.102341	+	0.381943i	0.998030	−	0.0627387i	$-0.0199835\pi$
$167$	1.32254	+	4.93579i	0.102341	+	0.381943i	−0.895689	+	0.444682i	$0.853317\pi$
$168$		0			0
$169$	−3.06239	+	1.76807i	−0.235568	+	0.136005i
$170$		0			0
$171$		0			0
$172$	6.65957	+	6.65957i	0.507787	+	0.507787i
$173$	−1.91916	+	7.16239i	−0.145911	+	0.544546i	0.853802	+	0.520597i	$0.174291\pi$
$173$	−1.91916	+	7.16239i	−0.145911	+	0.544546i	−0.999713	+	0.0239492i	$0.992376\pi$
$174$		0			0
$175$		0			0
$176$	1.70563	+	0.984748i	0.128567	+	0.0742282i
$177$		0			0
$178$	1.98004	+	0.530550i	0.148410	+	0.0397664i
$179$	−2.73426			−0.204369			−0.102184	−	0.994765i	$-0.532583\pi$
$179$	−2.73426			−0.204369			−0.102184	+	0.994765i	$0.532583\pi$
$180$		0			0
$181$	−22.7081			−1.68788			−0.843941	−	0.536437i	$-0.819770\pi$
$181$	−22.7081			−1.68788			−0.843941	+	0.536437i	$0.819770\pi$
$182$	−7.92092	−	2.12240i	−0.587138	−	0.157323i
$183$		0			0
$184$	−5.42731	−	3.13346i	−0.400107	−	0.231002i
$185$		0			0
$186$		0			0
$187$	1.70040	−	6.34598i	0.124346	−	0.464064i
$188$	5.48696	+	5.48696i	0.400178	+	0.400178i
$189$		0			0
$190$		0			0
$191$	1.11154	−	0.641749i	0.0804283	−	0.0464353i	−0.459246	−	0.888309i	$-0.651881\pi$
$191$	1.11154	−	0.641749i	0.0804283	−	0.0464353i	0.539675	+	0.841874i	$0.318547\pi$
$192$		0			0
$193$	−1.41494	−	5.28063i	−0.101850	−	0.380108i	0.896119	−	0.443814i	$-0.146375\pi$
$193$	−1.41494	−	5.28063i	−0.101850	−	0.380108i	−0.997969	+	0.0637057i	$0.979708\pi$
$194$	−5.03095	+	8.71386i	−0.361201	+	0.625619i
$195$		0			0
$196$	1.46671	+	2.54041i	0.104765	+	0.181458i
$197$	−12.0386	+	12.0386i	−0.857716	+	0.857716i	−0.991069	−	0.133353i	$-0.957426\pi$
$197$	−12.0386	+	12.0386i	−0.857716	+	0.857716i	0.133353	+	0.991069i	$0.457426\pi$
$198$		0			0
$199$		−	4.43831i		−	0.314623i	−0.987549	−	0.157312i	$-0.949717\pi$
$199$		−	4.43831i		−	0.314623i	0.987549	−	0.157312i	$-0.0502827\pi$
$200$		0			0
$201$		0			0
$202$	4.56196	−	1.22237i	0.320978	−	0.0860058i
$203$	14.6036	−	3.91303i	1.02497	−	0.274641i
$204$		0			0
$205$		0			0
$206$		−	4.00520i		−	0.279055i
$207$		0			0
$208$	2.87542	−	2.87542i	0.199375	−	0.199375i
$209$	−3.65098	−	6.32368i	−0.252543	−	0.437418i
$210$		0			0
$211$	12.0425	−	20.8582i	0.829038	−	1.43594i	−0.0697556	−	0.997564i	$-0.522222\pi$
$211$	12.0425	−	20.8582i	0.829038	−	1.43594i	0.898794	−	0.438372i	$-0.144445\pi$
$212$	2.57326	+	9.60353i	0.176732	+	0.659573i
$213$		0			0
$214$	−6.61725	+	3.82047i	−0.452346	+	0.261162i
$215$		0			0
$216$		0			0
$217$	−9.94838	−	9.94838i	−0.675340	−	0.675340i
$218$	1.12679	−	4.20523i	0.0763156	−	0.284814i
$219$		0			0
$220$		0			0
$221$	−11.7476	−	6.78245i	−0.790226	−	0.456237i
$222$		0			0
$223$	16.2073	+	4.34272i	1.08532	+	0.290810i	0.756773	−	0.653678i	$-0.226775\pi$
$223$	16.2073	+	4.34272i	1.08532	+	0.290810i	0.328546	+	0.944488i	$0.393441\pi$
$224$	2.01658			0.134738
$225$		0			0
$226$	2.96556			0.197266
$227$	7.18543	+	1.92533i	0.476914	+	0.127789i	0.489265	−	0.872135i	$-0.337265\pi$
$227$	7.18543	+	1.92533i	0.476914	+	0.127789i	−0.0123515	+	0.999924i	$0.503932\pi$
$228$		0			0
$229$	−7.74183	−	4.46975i	−0.511595	−	0.295369i	0.221894	−	0.975071i	$-0.428776\pi$
$229$	−7.74183	−	4.46975i	−0.511595	−	0.295369i	−0.733489	+	0.679701i	$0.762109\pi$
$230$		0			0
$231$		0			0
$232$	−1.94043	+	7.24179i	−0.127396	+	0.475447i
$233$	−15.0591	−	15.0591i	−0.986558	−	0.986558i	0.0133533	−	0.999911i	$-0.495749\pi$
$233$	−15.0591	−	15.0591i	−0.986558	−	0.986558i	−0.999911	+	0.0133533i	$0.995749\pi$
$234$		0			0
$235$		0			0
$236$	−2.33769	+	1.34967i	−0.152171	+	0.0878558i
$237$		0			0
$238$	−1.74105	−	6.49768i	−0.112855	−	0.421182i
$239$	−5.42731	+	9.40038i	−0.351064	+	0.608060i	−0.986436	−	0.164146i	$-0.947513\pi$
$239$	−5.42731	+	9.40038i	−0.351064	+	0.608060i	0.635372	+	0.772206i	$0.280847\pi$
$240$		0			0
$241$	11.6659	+	20.2059i	0.751467	+	1.30158i	0.947112	+	0.320904i	$0.103987\pi$
$241$	11.6659	+	20.2059i	0.751467	+	1.30158i	−0.195645	+	0.980675i	$0.562680\pi$
$242$	−5.03537	+	5.03537i	−0.323686	+	0.323686i
$243$		0			0
$244$		−	8.74707i		−	0.559973i
$245$		0			0
$246$		0			0
$247$	−14.5628	+	3.90209i	−0.926609	+	0.248284i
$248$	6.73901	−	1.80571i	0.427928	−	0.114663i
$249$		0			0
$250$		0			0
$251$			13.3860i			0.844914i	0.906383	+	0.422457i	$0.138832\pi$
$251$			13.3860i			0.844914i	−0.906383	+	0.422457i	$0.861168\pi$
$252$		0			0
$253$	−8.72759	+	8.72759i	−0.548699	+	0.548699i
$254$	2.41643	+	4.18538i	0.151620	+	0.262614i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.95494	−	7.29595i	−0.121946	−	0.455109i	0.877766	−	0.479089i	$-0.159033\pi$
$257$	−1.95494	−	7.29595i	−0.121946	−	0.455109i	−0.999712	+	0.0239802i	$0.992366\pi$
$258$		0			0
$259$	−10.5384	+	6.08436i	−0.654825	+	0.378063i
$260$		0			0
$261$		0			0
$262$	0.335798	+	0.335798i	0.0207457	+	0.0207457i
$263$	2.88569	−	10.7695i	0.177939	−	0.664078i	−0.818093	−	0.575086i	$-0.804969\pi$
$263$	2.88569	−	10.7695i	0.177939	−	0.664078i	0.996032	−	0.0889923i	$-0.0283647\pi$
$264$		0			0
$265$		0			0
$266$	−6.47485	−	3.73826i	−0.396998	−	0.229207i
$267$		0			0
$268$	8.18285	+	2.19259i	0.499847	+	0.133934i
$269$	−13.4707			−0.821326			−0.410663	−	0.911787i	$-0.634703\pi$
$269$	−13.4707			−0.821326			−0.410663	+	0.911787i	$0.634703\pi$
$270$		0			0
$271$	20.4402			1.24165			0.620827	−	0.783947i	$-0.286797\pi$
$271$	20.4402			1.24165			0.620827	+	0.783947i	$0.286797\pi$
$272$	3.22213	+	0.863368i	0.195371	+	0.0523494i
$273$		0			0
$274$	8.53197	+	4.92594i	0.515435	+	0.297587i
$275$		0			0
$276$		0			0
$277$	−6.27326	+	23.4121i	−0.376924	+	1.40670i	0.473590	+	0.880745i	$0.342958\pi$
$277$	−6.27326	+	23.4121i	−0.376924	+	1.40670i	−0.850514	+	0.525953i	$0.823709\pi$
$278$	0.496689	+	0.496689i	0.0297894	+	0.0297894i
$279$		0			0
$280$		0			0
$281$	−19.5424	+	11.2828i	−1.16580	+	0.673076i	−0.952687	−	0.303952i	$-0.901694\pi$
$281$	−19.5424	+	11.2828i	−1.16580	+	0.673076i	−0.213114	+	0.977027i	$0.568360\pi$
$282$		0			0
$283$	−0.549660	−	2.05136i	−0.0326739	−	0.121941i	0.947663	−	0.319273i	$-0.103439\pi$
$283$	−0.549660	−	2.05136i	−0.0326739	−	0.121941i	−0.980337	+	0.197333i	$0.936772\pi$
$284$	2.84241	−	4.92319i	0.168666	−	0.292138i
$285$		0			0
$286$	−4.00444	−	6.93590i	−0.236788	−	0.410128i
$287$	−10.1031	+	10.1031i	−0.596368	+	0.596368i
$288$		0			0
$289$			5.87245i			0.345438i
$290$		0			0
$291$		0			0
$292$	−1.56994	+	0.420664i	−0.0918738	+	0.0246175i
$293$	−3.53204	+	0.946406i	−0.206344	+	0.0552896i	−0.360510	−	0.932755i	$-0.617397\pi$
$293$	−3.53204	+	0.946406i	−0.206344	+	0.0552896i	0.154167	+	0.988045i	$0.450731\pi$
$294$		0			0
$295$		0			0
$296$		−	6.03434i		−	0.350739i
$297$		0			0
$298$	−5.73618	+	5.73618i	−0.332288	+	0.332288i
$299$	12.7421	+	22.0700i	0.736895	+	1.27634i
$300$		0			0
$301$	9.49611	−	16.4477i	0.547347	−	0.948032i
$302$	2.39014	+	8.92011i	0.137537	+	0.513295i
$303$		0			0
$304$	3.21081	−	1.85376i	0.184153	−	0.106321i
$305$		0			0
$306$		0			0
$307$	10.5436	+	10.5436i	0.601754	+	0.601754i	0.940778	−	0.339024i	$-0.110097\pi$
$307$	10.5436	+	10.5436i	0.601754	+	0.601754i	−0.339024	+	0.940778i	$0.610097\pi$
$308$	1.02794	−	3.83631i	0.0585721	−	0.218594i
$309$		0			0
$310$		0			0
$311$	9.08436	+	5.24485i	0.515127	+	0.297408i	0.734938	−	0.678134i	$-0.237211\pi$
$311$	9.08436	+	5.24485i	0.515127	+	0.297408i	−0.219812	+	0.975542i	$0.570544\pi$
$312$		0			0
$313$	−17.0518	−	4.56901i	−0.963824	−	0.258256i	−0.257606	−	0.966250i	$-0.582934\pi$
$313$	−17.0518	−	4.56901i	−0.963824	−	0.258256i	−0.706218	+	0.707994i	$0.749600\pi$
$314$	−10.8546			−0.612562
$315$		0			0
$316$	−11.6088			−0.653046
$317$	−22.3972	−	6.00131i	−1.25795	−	0.337067i	−0.432549	−	0.901611i	$-0.642386\pi$
$317$	−22.3972	−	6.00131i	−1.25795	−	0.337067i	−0.825403	+	0.564543i	$0.809052\pi$
$318$		0			0
$319$	12.7876	+	7.38291i	0.715966	+	0.413363i
$320$		0			0
$321$		0			0
$322$	−3.27089	+	12.2071i	−0.182279	+	0.680276i
$323$	−8.74518	−	8.74518i	−0.486595	−	0.486595i
$324$		0			0
$325$		0			0
$326$	−11.8579	+	6.84619i	−0.656751	+	0.379175i
$327$		0			0
$328$	−1.83380	−	6.84383i	−0.101255	−	0.377887i
$329$	7.82405	−	13.5517i	0.431354	−	0.747127i
$330$		0			0
$331$	12.9130	+	22.3659i	0.709761	+	1.22934i	0.964946	+	0.262450i	$0.0845303\pi$
$331$	12.9130	+	22.3659i	0.709761	+	1.22934i	−0.255185	+	0.966892i	$0.582136\pi$
$332$	−1.20473	+	1.20473i	−0.0661180	+	0.0661180i
$333$		0			0
$334$			5.10991i			0.279602i
$335$		0			0
$336$		0			0
$337$	30.9889	−	8.30344i	1.68807	−	0.452317i	0.718180	−	0.695858i	$-0.244976\pi$
$337$	30.9889	−	8.30344i	1.68807	−	0.452317i	0.969891	+	0.243541i	$0.0783089\pi$
$338$	−3.41565	+	0.915220i	−0.185787	+	0.0497814i
$339$		0			0
$340$		0			0
$341$		−	13.7407i		−	0.744099i
$342$		0			0
$343$	14.1644	−	14.1644i	0.764806	−	0.764806i
$344$	4.70902	+	8.15627i	0.253894	+	0.439757i
$345$		0			0
$346$	−3.70753	+	6.42162i	−0.199318	+	0.345229i
$347$	−3.83170	−	14.3001i	−0.205696	−	0.767670i	−0.989236	−	0.146328i	$-0.953255\pi$
$347$	−3.83170	−	14.3001i	−0.205696	−	0.767670i	0.783540	−	0.621342i	$-0.213412\pi$
$348$		0			0
$349$	13.3741	−	7.72151i	0.715897	−	0.413323i	−0.0973439	−	0.995251i	$-0.531035\pi$
$349$	13.3741	−	7.72151i	0.715897	−	0.413323i	0.813241	+	0.581928i	$0.197701\pi$
$350$		0			0
$351$		0			0
$352$	1.39264	+	1.39264i	0.0742282	+	0.0742282i
$353$	−5.39774	+	20.1446i	−0.287293	+	1.07219i	0.659855	+	0.751393i	$0.270618\pi$
$353$	−5.39774	+	20.1446i	−0.287293	+	1.07219i	−0.947148	+	0.320798i	$0.896049\pi$
$354$		0			0
$355$		0			0
$356$	1.77526	+	1.02494i	0.0940883	+	0.0543219i
$357$		0			0
$358$	−2.64110	−	0.707680i	−0.139586	−	0.0374020i
$359$	3.39466			0.179163			0.0895815	−	0.995979i	$-0.471447\pi$
$359$	3.39466			0.179163			0.0895815	+	0.995979i	$0.471447\pi$
$360$		0			0
$361$	5.25425			0.276540
$362$	−21.9344	−	5.87729i	−1.15284	−	0.308904i
$363$		0			0
$364$	−7.10170	−	4.10017i	−0.372230	−	0.214907i
$365$		0			0
$366$		0			0
$367$	−5.68801	+	21.2279i	−0.296912	+	1.10809i	0.642776	+	0.766054i	$0.277783\pi$
$367$	−5.68801	+	21.2279i	−0.296912	+	1.10809i	−0.939687	+	0.342035i	$0.888884\pi$
$368$	−4.43138	−	4.43138i	−0.231002	−	0.231002i
$369$		0			0
$370$		0			0
$371$	17.3633	−	10.0247i	0.901458	−	0.520457i
$372$		0			0
$373$	0.381044	+	1.42207i	0.0197297	+	0.0736322i	0.975089	−	0.221815i	$-0.0711981\pi$
$373$	0.381044	+	1.42207i	0.0197297	+	0.0736322i	−0.955359	+	0.295447i	$0.904531\pi$
$374$	3.28492	−	5.68965i	0.169859	−	0.294205i
$375$		0			0
$376$	3.87987	+	6.72013i	0.200089	+	0.346564i
$377$	21.5578	−	21.5578i	1.11028	−	1.11028i
$378$		0			0
$379$			30.1323i			1.54779i	0.633314	+	0.773895i	$0.281694\pi$
$379$			30.1323i			1.54779i	−0.633314	+	0.773895i	$0.718306\pi$
$380$		0			0
$381$		0			0
$382$	1.23976	−	0.332194i	0.0634318	−	0.0169965i
$383$	−16.5638	+	4.43826i	−0.846372	+	0.226785i	−0.655843	−	0.754897i	$-0.727687\pi$
$383$	−16.5638	+	4.43826i	−0.846372	+	0.226785i	−0.190528	+	0.981682i	$0.561020\pi$
$384$		0			0
$385$		0			0
$386$		−	5.46691i		−	0.278258i
$387$		0			0
$388$	−7.11484	+	7.11484i	−0.361201	+	0.361201i
$389$	−15.1070	−	26.1660i	−0.765953	−	1.32667i	−0.939741	−	0.341886i	$-0.888934\pi$
$389$	−15.1070	−	26.1660i	−0.765953	−	1.32667i	0.173789	−	0.984783i	$-0.444399\pi$
$390$		0			0
$391$	−10.4526	+	18.1044i	−0.528610	+	0.915580i
$392$	0.759224	+	2.83346i	0.0383466	+	0.143112i
$393$		0			0
$394$	−14.7442	+	8.51258i	−0.742803	+	0.428858i
$395$		0			0
$396$		0			0
$397$	2.16969	+	2.16969i	0.108893	+	0.108893i	0.759454	−	0.650561i	$-0.225466\pi$
$397$	2.16969	+	2.16969i	0.108893	+	0.108893i	−0.650561	+	0.759454i	$0.725466\pi$
$398$	1.14872	−	4.28708i	0.0575801	−	0.214892i
$399$		0			0
$400$		0			0
$401$	12.3209	+	7.11346i	0.615275	+	0.355229i	0.775027	−	0.631928i	$-0.217736\pi$
$401$	12.3209	+	7.11346i	0.615275	+	0.355229i	−0.159752	+	0.987157i	$0.551069\pi$
$402$		0			0
$403$	−27.4040	−	7.34287i	−1.36509	−	0.365774i
$404$	4.72288			0.234972
$405$		0			0
$406$	15.1188			0.750333
$407$	−11.4796	−	3.07596i	−0.569025	−	0.152470i
$408$		0			0
$409$	−10.2963	−	5.94456i	−0.509118	−	0.293939i	0.223353	−	0.974738i	$-0.428300\pi$
$409$	−10.2963	−	5.94456i	−0.509118	−	0.293939i	−0.732471	+	0.680798i	$0.761633\pi$
$410$		0			0
$411$		0			0
$412$	1.03662	−	3.86872i	0.0510706	−	0.190598i
$413$	3.84907	+	3.84907i	0.189401	+	0.189401i
$414$		0			0
$415$		0			0
$416$	3.52166	−	2.03323i	0.172664	−	0.0996874i
$417$		0			0
$418$	−1.88989	−	7.05315i	−0.0924373	−	0.344981i
$419$	19.6354	−	34.0095i	0.959251	−	1.66147i	0.234926	−	0.972013i	$-0.424515\pi$
$419$	19.6354	−	34.0095i	0.959251	−	1.66147i	0.724325	−	0.689458i	$-0.242151\pi$
$420$		0			0
$421$	−12.2493	−	21.2163i	−0.596992	−	1.03402i	−0.993262	−	0.115887i	$-0.963029\pi$
$421$	−12.2493	−	21.2163i	−0.596992	−	1.03402i	0.396270	−	0.918134i	$-0.370304\pi$
$422$	17.0306	−	17.0306i	0.829038	−	0.829038i
$423$		0			0
$424$			9.94230i			0.482841i
$425$		0			0
$426$		0			0
$427$	−17.0381	+	4.56534i	−0.824531	+	0.220932i
$428$	−7.38058	+	1.97762i	−0.356754	+	0.0955920i
$429$		0			0
$430$		0			0
$431$			6.10703i			0.294165i	0.989124	+	0.147083i	$0.0469883\pi$
$431$			6.10703i			0.294165i	−0.989124	+	0.147083i	$0.953012\pi$
$432$		0			0
$433$	−10.2605	+	10.2605i	−0.493088	+	0.493088i	−0.909278	−	0.416190i	$-0.863365\pi$
$433$	−10.2605	+	10.2605i	−0.493088	+	0.493088i	0.416190	+	0.909278i	$0.363365\pi$
$434$	−7.03457	−	12.1842i	−0.337670	−	0.584862i
$435$		0			0
$436$	2.17679	−	3.77030i	0.104249	−	0.180565i
$437$	6.01360	+	22.4431i	0.287670	+	1.07360i
$438$		0			0
$439$	1.96604	−	1.13510i	0.0938342	−	0.0541752i	−0.452349	−	0.891841i	$-0.649414\pi$
$439$	1.96604	−	1.13510i	0.0938342	−	0.0541752i	0.546183	+	0.837666i	$0.316080\pi$
$440$		0			0
$441$		0			0
$442$	−9.59184	−	9.59184i	−0.456237	−	0.456237i
$443$	7.20031	−	26.8719i	0.342097	−	1.27672i	−0.553870	−	0.832603i	$-0.686850\pi$
$443$	7.20031	−	26.8719i	0.342097	−	1.27672i	0.895967	−	0.444120i	$-0.146484\pi$
$444$		0			0
$445$		0			0
$446$	14.5310	+	8.38950i	0.688065	+	0.397254i
$447$		0			0
$448$	1.94786	+	0.521929i	0.0920279	+	0.0246588i
$449$	−11.7712			−0.555516			−0.277758	−	0.960651i	$-0.589591\pi$
$449$	−11.7712			−0.555516			−0.277758	+	0.960651i	$0.589591\pi$
$450$		0			0
$451$	−13.9544			−0.657086
$452$	2.86451	+	0.767544i	0.134735	+	0.0361022i
$453$		0			0
$454$	6.44228	+	3.71945i	0.302351	+	0.174562i
$455$		0			0
$456$		0			0
$457$	10.0741	−	37.5970i	0.471246	−	1.75871i	−0.164058	−	0.986451i	$-0.552458\pi$
$457$	10.0741	−	37.5970i	0.471246	−	1.75871i	0.635303	−	0.772263i	$-0.280875\pi$
$458$	−6.32118	−	6.32118i	−0.295369	−	0.295369i
$459$		0			0
$460$		0			0
$461$	2.62200	−	1.51381i	0.122119	−	0.0705053i	−0.437696	−	0.899123i	$-0.644205\pi$
$461$	2.62200	−	1.51381i	0.122119	−	0.0705053i	0.559815	+	0.828618i	$0.310872\pi$
$462$		0			0
$463$	−1.76940	−	6.60350i	−0.0822311	−	0.306891i	0.912544	−	0.408978i	$-0.134115\pi$
$463$	−1.76940	−	6.60350i	−0.0822311	−	0.306891i	−0.994775	+	0.102087i	$0.967448\pi$
$464$	−3.74863	+	6.49281i	−0.174026	+	0.301421i
$465$		0			0
$466$	−10.6484	−	18.4436i	−0.493279	−	0.854384i
$467$	−8.05359	+	8.05359i	−0.372676	+	0.372676i	−0.868451	−	0.495775i	$-0.834884\pi$
$467$	−8.05359	+	8.05359i	−0.372676	+	0.372676i	0.495775	+	0.868451i	$0.334884\pi$
$468$		0			0
$469$		−	17.0835i		−	0.788841i
$470$		0			0
$471$		0			0
$472$	−2.60736	+	0.698639i	−0.120013	+	0.0321575i
$473$	17.9168	−	4.80079i	0.823814	−	0.220740i
$474$		0			0
$475$		0			0
$476$		−	6.72689i		−	0.308327i
$477$		0			0
$478$	−7.67538	+	7.67538i	−0.351064	+	0.351064i
$479$	16.5711	+	28.7020i	0.757154	+	1.31143i	0.944296	+	0.329097i	$0.106744\pi$
$479$	16.5711	+	28.7020i	0.757154	+	1.31143i	−0.187142	+	0.982333i	$0.559922\pi$
$480$		0			0
$481$	−12.2692	+	21.2509i	−0.559428	+	0.968958i
$482$	6.03872	+	22.5368i	0.275056	+	1.02652i
$483$		0			0
$484$	−6.16704	+	3.56054i	−0.280320	+	0.161843i
$485$		0			0
$486$		0			0
$487$	14.8248	+	14.8248i	0.671777	+	0.671777i	0.958126	−	0.286349i	$-0.0924415\pi$
$487$	14.8248	+	14.8248i	0.671777	+	0.671777i	−0.286349	+	0.958126i	$0.592442\pi$
$488$	2.26391	−	8.44902i	0.102482	−	0.382469i
$489$		0			0
$490$		0			0
$491$	−16.1505	−	9.32449i	−0.728861	−	0.420808i	0.0891441	−	0.996019i	$-0.471587\pi$
$491$	−16.1505	−	9.32449i	−0.728861	−	0.420808i	−0.818005	+	0.575210i	$0.804920\pi$
$492$		0			0
$493$	24.1572	+	6.47289i	1.08798	+	0.291524i
$494$	−15.0765			−0.678325
$495$		0			0
$496$	6.97674			0.313265
$497$	−11.0732	−	2.96707i	−0.496703	−	0.133091i
$498$		0			0
$499$	19.6189	+	11.3270i	0.878263	+	0.507065i	0.870085	−	0.492901i	$-0.164064\pi$
$499$	19.6189	+	11.3270i	0.878263	+	0.507065i	0.00817742	+	0.999967i	$0.497397\pi$
$500$		0			0
$501$		0			0
$502$	−3.46454	+	12.9298i	−0.154630	+	0.577087i
$503$	9.64801	+	9.64801i	0.430183	+	0.430183i	0.888691	−	0.458507i	$-0.151616\pi$
$503$	9.64801	+	9.64801i	0.430183	+	0.430183i	−0.458507	+	0.888691i	$0.651616\pi$
$504$		0			0
$505$		0			0
$506$	−10.6891	+	6.17134i	−0.475187	+	0.274349i
$507$		0			0
$508$	1.25084	+	4.66818i	0.0554968	+	0.207117i
$509$	13.5882	−	23.5355i	0.602286	−	1.04319i	−0.390188	−	0.920735i	$-0.627590\pi$
$509$	13.5882	−	23.5355i	0.602286	−	1.04319i	0.992474	−	0.122455i	$-0.0390768\pi$
$510$		0			0
$511$	1.63879	+	2.83847i	0.0724959	+	0.125567i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	7.55332i		−	0.333163i
$515$		0			0
$516$		0			0
$517$	14.7620	−	3.95547i	0.649233	−	0.173961i
$518$	−11.7541	+	3.14949i	−0.516444	+	0.138381i
$519$		0			0
$520$		0			0
$521$			18.3542i			0.804114i	0.915615	+	0.402057i	$0.131705\pi$
$521$			18.3542i			0.804114i	−0.915615	+	0.402057i	$0.868295\pi$
$522$		0			0
$523$	25.8576	−	25.8576i	1.13067	−	1.13067i	0.140607	−	0.990066i	$-0.455095\pi$
$523$	25.8576	−	25.8576i	1.13067	−	1.13067i	0.990066	−	0.140607i	$-0.0449053\pi$
$524$	0.237445	+	0.411267i	0.0103728	+	0.0179663i
$525$		0			0
$526$	5.57472	−	9.65570i	0.243069	−	0.421009i
$527$	−6.02350	−	22.4800i	−0.262388	−	0.979244i
$528$		0			0
$529$	14.0940	−	8.13716i	0.612781	−	0.353789i
$530$		0			0
$531$		0			0
$532$	−5.28669	−	5.28669i	−0.229207	−	0.229207i
$533$	−7.45708	+	27.8302i	−0.323002	+	1.20546i
$534$		0			0
$535$		0			0
$536$	7.33654	+	4.23576i	0.316890	+	0.182957i
$537$		0			0
$538$	−13.0117	−	3.48649i	−0.560976	−	0.150313i
$539$	5.77735			0.248848
$540$		0			0
$541$	−4.54804			−0.195536			−0.0977678	−	0.995209i	$-0.531170\pi$
$541$	−4.54804			−0.195536			−0.0977678	+	0.995209i	$0.531170\pi$
$542$	19.7437	+	5.29032i	0.848066	+	0.227239i
$543$		0			0
$544$	2.88889	+	1.66790i	0.123860	+	0.0715106i
$545$		0			0
$546$		0			0
$547$	5.79252	−	21.6180i	0.247670	−	0.924319i	−0.724352	−	0.689430i	$-0.757861\pi$
$547$	5.79252	−	21.6180i	0.247670	−	0.924319i	0.972022	−	0.234888i	$-0.0754724\pi$
$548$	6.96632	+	6.96632i	0.297587	+	0.297587i
$549$		0			0
$550$		0			0
$551$	24.0723	−	13.8981i	1.02551	−	0.592080i
$552$		0			0
$553$	6.05896	+	22.6124i	0.257653	+	0.961575i
$554$	−12.1190	+	20.9907i	−0.514887	+	0.891811i
$555$		0			0
$556$	0.351212	+	0.608318i	0.0148947	+	0.0257984i
$557$	−20.5740	+	20.5740i	−0.871749	+	0.871749i	−0.992663	−	0.120914i	$-0.961417\pi$
$557$	−20.5740	+	20.5740i	−0.871749	+	0.871749i	0.120914	+	0.992663i	$0.461417\pi$
$558$		0			0
$559$		−	38.2982i		−	1.61984i
$560$		0			0
$561$		0			0
$562$	−21.7967	+	5.84041i	−0.919438	+	0.246363i
$563$	34.2529	−	9.17805i	1.44359	−	0.386809i	0.549800	−	0.835296i	$-0.314704\pi$
$563$	34.2529	−	9.17805i	1.44359	−	0.386809i	0.893789	+	0.448487i	$0.148037\pi$
$564$		0			0
$565$		0			0
$566$		−	2.12372i		−	0.0892668i
$567$		0			0
$568$	4.01977	−	4.01977i	0.168666	−	0.168666i
$569$	12.0592	+	20.8872i	0.505549	+	0.875637i	0.999979	+	0.00641982i	$0.00204351\pi$
$569$	12.0592	+	20.8872i	0.505549	+	0.875637i	−0.494430	+	0.869217i	$0.664623\pi$
$570$		0			0
$571$	2.24726	−	3.89236i	0.0940448	−	0.162890i	−0.815165	−	0.579229i	$-0.803354\pi$
$571$	2.24726	−	3.89236i	0.0940448	−	0.162890i	0.909210	+	0.416339i	$0.136687\pi$
$572$	−2.07285	−	7.73599i	−0.0866703	−	0.323458i
$573$		0			0
$574$	−12.3737	+	7.14398i	−0.516470	+	0.298184i
$575$		0			0
$576$		0			0
$577$	−0.186522	−	0.186522i	−0.00776502	−	0.00776502i	0.703214	−	0.710979i	$-0.251748\pi$
$577$	−0.186522	−	0.186522i	−0.00776502	−	0.00776502i	−0.710979	+	0.703214i	$0.751748\pi$
$578$	−1.51990	+	5.67235i	−0.0632196	+	0.235939i
$579$		0			0
$580$		0			0
$581$	2.97543	+	1.71786i	0.123441	+	0.0712689i
$582$		0			0
$583$	18.9141	+	5.06802i	0.783342	+	0.209896i
$584$	−1.62532			−0.0672563
$585$		0			0
$586$	−3.65663			−0.151054
$587$	43.6620	+	11.6992i	1.80212	+	0.482878i	0.994307	−	0.106555i	$-0.0339820\pi$
$587$	43.6620	+	11.6992i	1.80212	+	0.482878i	0.807818	+	0.589433i	$0.200649\pi$
$588$		0			0
$589$	−22.4010	−	12.9332i	−0.923017	−	0.532904i
$590$		0			0
$591$		0			0
$592$	1.56180	−	5.82872i	0.0641897	−	0.239559i
$593$	3.60323	+	3.60323i	0.147967	+	0.147967i	0.777209	−	0.629242i	$-0.216635\pi$
$593$	3.60323	+	3.60323i	0.147967	+	0.147967i	−0.629242	+	0.777209i	$0.716635\pi$
$594$		0			0
$595$		0			0
$596$	−7.02536	+	4.05609i	−0.287770	+	0.166144i
$597$		0			0
$598$	6.59580	+	24.6159i	0.269722	+	1.00662i
$599$	−23.4581	+	40.6307i	−0.958473	+	1.66012i	−0.232260	+	0.972654i	$0.574612\pi$
$599$	−23.4581	+	40.6307i	−0.958473	+	1.66012i	−0.726213	+	0.687470i	$0.758721\pi$
$600$		0			0
$601$	−20.5688	−	35.6263i	−0.839020	−	1.45323i	−0.890715	−	0.454563i	$-0.849795\pi$
$601$	−20.5688	−	35.6263i	−0.839020	−	1.45323i	0.0516943	−	0.998663i	$-0.483538\pi$
$602$	13.4295	−	13.4295i	0.547347	−	0.547347i
$603$		0			0
$604$			9.23478i			0.375758i
$605$		0			0
$606$		0			0
$607$	15.9755	−	4.28061i	0.648424	−	0.173745i	0.0804079	−	0.996762i	$-0.474378\pi$
$607$	15.9755	−	4.28061i	0.648424	−	0.173745i	0.568016	+	0.823017i	$0.307711\pi$
$608$	3.58120	−	0.959578i	0.145237	−	0.0389160i
$609$		0			0
$610$		0			0
$611$		−	31.5547i		−	1.27657i
$612$		0			0
$613$	21.1512	−	21.1512i	0.854290	−	0.854290i	−0.136368	−	0.990658i	$-0.543543\pi$
$613$	21.1512	−	21.1512i	0.854290	−	0.854290i	0.990658	+	0.136368i	$0.0435429\pi$
$614$	7.45544	+	12.9132i	0.300877	+	0.521134i
$615$		0			0
$616$	1.98582	−	3.43954i	0.0800110	−	0.138583i
$617$	−2.72427	−	10.1671i	−0.109675	−	0.409312i	0.889159	−	0.457599i	$-0.151290\pi$
$617$	−2.72427	−	10.1671i	−0.109675	−	0.409312i	−0.998834	+	0.0482869i	$0.984624\pi$
$618$		0			0
$619$	−2.77044	+	1.59951i	−0.111353	+	0.0642898i	−0.554642	−	0.832089i	$-0.687145\pi$
$619$	−2.77044	+	1.59951i	−0.111353	+	0.0642898i	0.443289	+	0.896379i	$0.353812\pi$
$620$		0			0
$621$		0			0
$622$	7.41734	+	7.41734i	0.297408	+	0.297408i
$623$	1.06990	−	3.99290i	0.0428644	−	0.159972i
$624$		0			0
$625$		0			0
$626$	−15.2882	−	8.82666i	−0.611040	−	0.352784i
$627$		0			0
$628$	−10.4848	−	2.80938i	−0.418388	−	0.112107i
$629$	−20.1293			−0.802609
$630$		0			0
$631$	21.2335			0.845291			0.422645	−	0.906295i	$-0.361102\pi$
$631$	21.2335			0.845291			0.422645	+	0.906295i	$0.361102\pi$
$632$	−11.2132	−	3.00458i	−0.446039	−	0.119516i
$633$		0			0
$634$	−20.0808	−	11.5936i	−0.797510	−	0.460442i
$635$		0			0
$636$		0			0
$637$	3.08736	−	11.5222i	0.122326	−	0.456525i
$638$	10.4410	+	10.4410i	0.413363	+	0.413363i
$639$		0			0
$640$		0			0
$641$	−42.6583	+	24.6288i	−1.68490	+	0.972778i	−0.726582	+	0.687080i	$0.758892\pi$
$641$	−42.6583	+	24.6288i	−1.68490	+	0.972778i	−0.958320	+	0.285698i	$0.907775\pi$
$642$		0			0
$643$	5.25595	+	19.6155i	0.207274	+	0.773559i	0.988744	+	0.149616i	$0.0478036\pi$
$643$	5.25595	+	19.6155i	0.207274	+	0.773559i	−0.781470	+	0.623943i	$0.785530\pi$
$644$	−6.31887	+	10.9446i	−0.248998	+	0.431278i
$645$		0			0
$646$	−6.18378	−	10.7106i	−0.243298	−	0.421404i
$647$	29.0632	−	29.0632i	1.14259	−	1.14259i	0.154619	−	0.987974i	$-0.450585\pi$
$647$	29.0632	−	29.0632i	1.14259	−	1.14259i	0.987974	−	0.154619i	$-0.0494151\pi$
$648$		0			0
$649$			5.31632i			0.208684i
$650$		0			0
$651$		0			0
$652$	−13.2258	+	3.54385i	−0.517963	+	0.138788i
$653$	2.75027	−	0.736931i	0.107626	−	0.0288384i	−0.204604	−	0.978845i	$-0.565591\pi$
$653$	2.75027	−	0.736931i	0.107626	−	0.0288384i	0.312230	+	0.950006i	$0.398924\pi$
$654$		0			0
$655$		0			0
$656$		−	7.08526i		−	0.276633i
$657$		0			0
$658$	11.0649	−	11.0649i	0.431354	−	0.431354i
$659$	−18.8486	−	32.6467i	−0.734236	−	1.27173i	−0.955058	−	0.296420i	$-0.904207\pi$
$659$	−18.8486	−	32.6467i	−0.734236	−	1.27173i	0.220822	−	0.975314i	$-0.429126\pi$
$660$		0			0
$661$	3.68907	−	6.38966i	0.143488	−	0.248529i	−0.785320	−	0.619091i	$-0.787501\pi$
$661$	3.68907	−	6.38966i	0.143488	−	0.248529i	0.928808	+	0.370561i	$0.120835\pi$
$662$	6.68424	+	24.9459i	0.259791	+	0.969551i
$663$		0			0
$664$	−1.47548	+	0.851871i	−0.0572598	+	0.0330590i
$665$		0			0
$666$		0			0
$667$	−33.2232	−	33.2232i	−1.28641	−	1.28641i
$668$	−1.32254	+	4.93579i	−0.0511707	+	0.190971i
$669$		0			0
$670$		0			0
$671$	−14.9193	−	8.61365i	−0.575953	−	0.332526i
$672$		0			0
$673$	6.88414	+	1.84460i	0.265364	+	0.0711041i	0.389048	−	0.921218i	$-0.372804\pi$
$673$	6.88414	+	1.84460i	0.265364	+	0.0711041i	−0.123684	+	0.992322i	$0.539471\pi$
$674$	32.0820			1.23575
$675$		0			0
$676$	−3.53614			−0.136005
$677$	8.09727	+	2.16966i	0.311203	+	0.0833867i	0.411040	−	0.911617i	$-0.365166\pi$
$677$	8.09727	+	2.16966i	0.311203	+	0.0833867i	−0.0998372	+	0.995004i	$0.531832\pi$
$678$		0			0
$679$	17.5722	+	10.1453i	0.674358	+	0.389341i
$680$		0			0
$681$		0			0
$682$	3.55635	−	13.2725i	0.136180	−	0.508229i
$683$	15.8873	+	15.8873i	0.607911	+	0.607911i	0.942400	−	0.334488i	$-0.108564\pi$
$683$	15.8873	+	15.8873i	0.607911	+	0.607911i	−0.334488	+	0.942400i	$0.608564\pi$
$684$		0			0
$685$		0			0
$686$	17.3478	−	10.0158i	0.662342	−	0.382403i
$687$		0			0
$688$	2.43757	+	9.09714i	0.0929315	+	0.346825i
$689$	20.2150	−	35.0134i	0.770131	−	1.33391i
$690$		0			0
$691$	9.16297	+	15.8707i	0.348576	+	0.603751i	0.985997	−	0.166765i	$-0.0533321\pi$
$691$	9.16297	+	15.8707i	0.348576	+	0.603751i	−0.637421	+	0.770516i	$0.719999\pi$
$692$	−5.24323	+	5.24323i	−0.199318	+	0.199318i
$693$		0			0
$694$		−	14.8046i		−	0.561973i
$695$		0			0
$696$		0			0
$697$	−22.8296	+	6.11718i	−0.864734	+	0.231705i
$698$	14.9168	−	3.99695i	0.564610	−	0.151287i
$699$		0			0
$700$		0			0
$701$			21.1738i			0.799724i	0.916575	+	0.399862i	$0.130942\pi$
$701$			21.1738i			0.799724i	−0.916575	+	0.399862i	$0.869058\pi$
$702$		0			0
$703$	−15.8197	+	15.8197i	−0.596652	+	0.596652i
$704$	0.984748	+	1.70563i	0.0371141	+	0.0642835i
$705$		0			0
$706$	−10.4276	+	18.0612i	−0.392449	+	0.679742i
$707$	−2.46501	−	9.19953i	−0.0927062	−	0.345984i
$708$		0			0
$709$	20.4846	−	11.8268i	0.769316	−	0.444165i	−0.0633143	−	0.997994i	$-0.520167\pi$
$709$	20.4846	−	11.8268i	0.769316	−	0.444165i	0.832631	+	0.553829i	$0.186834\pi$
$710$		0			0
$711$		0			0
$712$	1.44949	+	1.44949i	0.0543219	+	0.0543219i
$713$	−11.3163	+	42.2329i	−0.423798	+	1.58163i
$714$		0			0
$715$		0			0
$716$	−2.36794	−	1.36713i	−0.0884942	−	0.0510921i
$717$		0			0
$718$	3.27899	+	0.878601i	0.122371	+	0.0327891i
$719$	21.3695			0.796947			0.398473	−	0.917180i	$-0.369540\pi$
$719$	21.3695			0.796947			0.398473	+	0.917180i	$0.369540\pi$
$720$		0			0
$721$	−8.07679			−0.300795
$722$	5.07522	+	1.35990i	0.188880	+	0.0506102i
$723$		0			0
$724$	−19.6658	−	11.3541i	−0.730874	−	0.421970i
$725$		0			0
$726$		0			0
$727$	0.796213	−	2.97151i	0.0295299	−	0.110207i	−0.949588	−	0.313501i	$-0.898498\pi$
$727$	0.796213	−	2.97151i	0.0295299	−	0.110207i	0.979118	+	0.203294i	$0.0651647\pi$
$728$	−5.79852	−	5.79852i	−0.214907	−	0.214907i
$729$		0			0
$730$		0			0
$731$	27.2077	−	15.7084i	1.00631	−	0.580994i
$732$		0			0
$733$	6.30661	+	23.5366i	0.232940	+	0.869343i	0.979067	+	0.203540i	$0.0652446\pi$
$733$	6.30661	+	23.5366i	0.232940	+	0.869343i	−0.746127	+	0.665804i	$0.768089\pi$
$734$	−10.9884	+	19.0324i	−0.405589	+	0.702500i
$735$		0			0
$736$	−3.13346	−	5.42731i	−0.115501	−	0.200053i
$737$	11.7978	−	11.7978i	0.434578	−	0.434578i
$738$		0			0
$739$			5.68805i			0.209238i	0.994512	+	0.104619i	$0.0333624\pi$
$739$			5.68805i			0.209238i	−0.994512	+	0.104619i	$0.966638\pi$
$740$		0			0
$741$		0			0
$742$	19.3663	−	5.18917i	0.710958	−	0.190500i
$743$	−15.1100	+	4.04871i	−0.554332	+	0.148533i	−0.525101	−	0.851040i	$-0.675973\pi$
$743$	−15.1100	+	4.04871i	−0.554332	+	0.148533i	−0.0292311	+	0.999573i	$0.509306\pi$
$744$		0			0
$745$		0			0
$746$			1.47224i			0.0539025i
$747$		0			0
$748$	4.64558	−	4.64558i	0.169859	−	0.169859i
$749$	7.70428	+	13.3442i	0.281508	+	0.487586i
$750$		0			0
$751$	−21.6240	+	37.4538i	−0.789070	+	1.36671i	0.137467	+	0.990506i	$0.456104\pi$
$751$	−21.6240	+	37.4538i	−0.789070	+	1.36671i	−0.926537	+	0.376203i	$0.877229\pi$
$752$	2.00837	+	7.49533i	0.0732376	+	0.273327i
$753$		0			0
$754$	26.4028	−	15.2437i	0.961533	−	0.555141i
$755$		0			0
$756$		0			0
$757$	−22.7266	−	22.7266i	−0.826013	−	0.826013i	0.160950	−	0.986963i	$-0.448544\pi$
$757$	−22.7266	−	22.7266i	−0.826013	−	0.826013i	−0.986963	+	0.160950i	$0.948544\pi$
$758$	−7.79880	+	29.1055i	−0.283265	+	1.05716i
$759$		0			0
$760$		0			0
$761$	24.8744	+	14.3612i	0.901696	+	0.520595i	0.877750	−	0.479119i	$-0.159044\pi$
$761$	24.8744	+	14.3612i	0.901696	+	0.520595i	0.0239461	+	0.999713i	$0.492377\pi$
$762$		0			0
$763$	−8.48016	−	2.27225i	−0.307002	−	0.0822611i
$764$	1.28350			0.0464353
$765$		0			0
$766$	−17.1481			−0.619587
$767$	10.6027	+	2.84099i	0.382842	+	0.102582i
$768$		0			0
$769$	29.3558	+	16.9486i	1.05860	+	0.611180i	0.925043	−	0.379861i	$-0.124028\pi$
$769$	29.3558	+	16.9486i	1.05860	+	0.611180i	0.133552	+	0.991042i	$0.457362\pi$
$770$		0			0
$771$		0			0
$772$	1.41494	−	5.28063i	0.0509248	−	0.190054i
$773$	−30.1093	−	30.1093i	−1.08296	−	1.08296i	−0.996232	−	0.0867231i	$-0.972360\pi$
$773$	−30.1093	−	30.1093i	−1.08296	−	1.08296i	−0.0867231	−	0.996232i	$-0.527640\pi$
$774$		0			0
$775$		0			0
$776$	−8.71386	+	5.03095i	−0.312809	+	0.180601i
$777$		0			0
$778$	−7.81993	−	29.1844i	−0.280358	−	1.04631i
$779$	−13.1344	+	22.7494i	−0.470588	+	0.815083i
$780$		0			0
$781$	−5.59811	−	9.69621i	−0.200316	−	0.346958i
$782$	−14.7822	+	14.7822i	−0.528610	+	0.528610i
$783$		0			0
$784$			2.93342i			0.104765i
$785$		0			0
$786$		0			0
$787$	10.2212	−	2.73876i	0.364346	−	0.0976263i	−0.0720011	−	0.997405i	$-0.522939\pi$
$787$	10.2212	−	2.73876i	0.364346	−	0.0976263i	0.436347	+	0.899778i	$0.356272\pi$
$788$	−16.4450	+	4.40644i	−0.585831	+	0.156973i
$789$		0			0
$790$		0			0
$791$		−	5.98028i		−	0.212634i
$792$		0			0
$793$	−25.1515	+	25.1515i	−0.893157	+	0.893157i
$794$	1.53420	+	2.65731i	0.0544467	+	0.0943045i
$795$		0			0
$796$	2.21916	−	3.84369i	0.0786559	−	0.136236i
$797$	−3.52110	−	13.1409i	−0.124724	−	0.465476i	0.875106	−	0.483932i	$-0.160792\pi$
$797$	−3.52110	−	13.1409i	−0.124724	−	0.465476i	−0.999830	+	0.0184558i	$0.994125\pi$
$798$		0			0
$799$	22.4170	−	12.9425i	0.793056	−	0.457871i
$800$		0			0
$801$		0			0
$802$	10.0599	+	10.0599i	0.355229	+	0.355229i
$803$	−0.828496	+	3.09199i	−0.0292370	+	0.109114i
$804$		0			0
$805$		0			0
$806$	−24.5697	−	14.1853i	−0.865432	−	0.499657i
$807$		0			0
$808$	4.56196	+	1.22237i	0.160489	+	0.0430029i
$809$	33.4429			1.17579			0.587895	−	0.808937i	$-0.299957\pi$
$809$	33.4429			1.17579			0.587895	+	0.808937i	$0.299957\pi$
$810$		0			0
$811$	21.1960			0.744294			0.372147	−	0.928174i	$-0.378622\pi$
$811$	21.1960			0.744294			0.372147	+	0.928174i	$0.378622\pi$
$812$	14.6036	+	3.91303i	0.512487	+	0.137320i
$813$		0			0
$814$	−10.2924	−	5.94230i	−0.360747	−	0.208278i
$815$		0			0
$816$		0			0
$817$	9.03736	−	33.7279i	0.316177	−	1.17999i
$818$	−8.40687	−	8.40687i	−0.293939	−	0.293939i
$819$		0			0
$820$		0			0
$821$	38.4941	−	22.2246i	1.34345	−	0.775643i	0.356141	−	0.934432i	$-0.384092\pi$
$821$	38.4941	−	22.2246i	1.34345	−	0.775643i	0.987313	+	0.158789i	$0.0507589\pi$
$822$		0			0
$823$	−6.59989	−	24.6311i	−0.230058	−	0.858588i	−0.980315	−	0.197441i	$-0.936737\pi$
$823$	−6.59989	−	24.6311i	−0.230058	−	0.858588i	0.750257	−	0.661146i	$-0.229930\pi$
$824$	2.00260	−	3.46860i	0.0697638	−	0.120834i
$825$		0			0
$826$	2.72171	+	4.71413i	0.0947003	+	0.164026i
$827$	−10.7808	+	10.7808i	−0.374885	+	0.374885i	−0.869253	−	0.494368i	$-0.835400\pi$
$827$	−10.7808	+	10.7808i	−0.374885	+	0.374885i	0.494368	+	0.869253i	$0.335400\pi$
$828$		0			0
$829$		−	4.02079i		−	0.139648i	−0.997559	−	0.0698239i	$-0.977756\pi$
$829$		−	4.02079i		−	0.139648i	0.997559	−	0.0698239i	$-0.0222437\pi$
$830$		0			0
$831$		0			0
$832$	3.92790	−	1.05248i	0.136176	−	0.0364881i
$833$	9.45186	−	2.53262i	0.327488	−	0.0877500i
$834$		0			0
$835$		0			0
$836$		−	7.30196i		−	0.252543i
$837$		0			0
$838$	27.7686	−	27.7686i	0.959251	−	0.959251i
$839$	−16.7880	−	29.0777i	−0.579588	−	1.00388i	−0.995527	−	0.0944825i	$-0.969880\pi$
$839$	−16.7880	−	29.0777i	−0.579588	−	1.00388i	0.415939	−	0.909393i	$-0.363453\pi$
$840$		0			0
$841$	−13.6044	+	23.5635i	−0.469118	+	0.812536i
$842$	−6.34068	−	23.6637i	−0.218514	−	0.815506i
$843$		0			0
$844$	20.8582	−	12.0425i	0.717968	−	0.414519i
$845$		0			0
$846$		0			0
$847$	10.1542	+	10.1542i	0.348903	+	0.348903i
$848$	−2.57326	+	9.60353i	−0.0883660	+	0.329786i
$849$		0			0
$850$		0			0
$851$	32.7503	+	18.9084i	1.12266	+	0.648171i
$852$		0			0
$853$	−22.9734	−	6.15572i	−0.786596	−	0.210768i	−0.156905	−	0.987614i	$-0.550152\pi$
$853$	−22.9734	−	6.15572i	−0.786596	−	0.210768i	−0.629691	+	0.776846i	$0.716818\pi$
$854$	−17.6391			−0.603599
$855$		0			0
$856$	−7.64094			−0.261162
$857$	11.4475	+	3.06736i	0.391040	+	0.104779i	0.448981	−	0.893541i	$-0.351787\pi$
$857$	11.4475	+	3.06736i	0.391040	+	0.104779i	−0.0579412	+	0.998320i	$0.518454\pi$
$858$		0			0
$859$	−34.6670	−	20.0150i	−1.18282	−	0.682904i	−0.226158	−	0.974091i	$-0.572617\pi$
$859$	−34.6670	−	20.0150i	−1.18282	−	0.682904i	−0.956666	+	0.291187i	$0.905950\pi$
$860$		0			0
$861$		0			0
$862$	−1.58062	+	5.89894i	−0.0538360	+	0.200919i
$863$	1.78680	+	1.78680i	0.0608233	+	0.0608233i	0.736864	−	0.676041i	$-0.236306\pi$
$863$	1.78680	+	1.78680i	0.0608233	+	0.0608233i	−0.676041	+	0.736864i	$0.736306\pi$
$864$		0			0
$865$		0			0
$866$	−12.5665	+	7.25527i	−0.427027	+	0.246544i
$867$		0			0
$868$	−3.64136	−	13.5897i	−0.123596	−	0.461266i
$869$	−11.4317	+	19.8004i	−0.387795	+	0.671681i
$870$		0			0
$871$	−17.2246	−	29.8338i	−0.583632	−	1.01088i
$872$	3.07844	−	3.07844i	0.104249	−	0.104249i
$873$		0			0
$874$			23.2348i			0.785928i
$875$		0			0
$876$		0			0
$877$	−6.66309	+	1.78537i	−0.224996	+	0.0602876i	−0.369556	−	0.929208i	$-0.620490\pi$
$877$	−6.66309	+	1.78537i	−0.224996	+	0.0602876i	0.144559	+	0.989496i	$0.453824\pi$
$878$	2.19284	−	0.587569i	0.0740047	−	0.0198295i
$879$		0			0
$880$		0			0
$881$			3.01999i			0.101746i	0.998705	+	0.0508731i	$0.0162004\pi$
$881$			3.01999i			0.101746i	−0.998705	+	0.0508731i	$0.983800\pi$
$882$		0			0
$883$	8.50404	−	8.50404i	0.286184	−	0.286184i	−0.549385	−	0.835569i	$-0.685138\pi$
$883$	8.50404	−	8.50404i	0.286184	−	0.286184i	0.835569	+	0.549385i	$0.185138\pi$
$884$	−6.78245	−	11.7476i	−0.228119	−	0.395113i
$885$		0			0
$886$	13.9099	−	24.0927i	0.467313	−	0.809410i
$887$	−4.61020	−	17.2055i	−0.154796	−	0.577705i	−0.999123	−	0.0418769i	$-0.986666\pi$
$887$	−4.61020	−	17.2055i	−0.154796	−	0.577705i	0.844327	−	0.535828i	$-0.180000\pi$
$888$		0			0
$889$	8.44013	−	4.87291i	0.283073	−	0.163432i
$890$		0			0
$891$		0			0
$892$	11.8645	+	11.8645i	0.397254	+	0.397254i
$893$	7.44607	−	27.7891i	0.249173	−	0.929928i
$894$		0			0
$895$		0			0
$896$	1.74641	+	1.00829i	0.0583434	+	0.0336846i
$897$		0			0
$898$	−11.3701	−	3.04660i	−0.379424	−	0.101666i
$899$	52.3064			1.74452
$900$		0			0
$901$	33.1655			1.10490
$902$	−13.4789	−	3.61166i	−0.448798	−	0.120255i
$903$		0			0
$904$	2.56825	+	1.48278i	0.0854188	+	0.0493166i
$905$		0			0
$906$		0			0
$907$	−0.324723	+	1.21188i	−0.0107822	+	0.0402399i	−0.971107	−	0.238643i	$-0.923297\pi$
$907$	−0.324723	+	1.21188i	−0.0107822	+	0.0402399i	0.960325	+	0.278883i	$0.0899641\pi$
$908$	5.26010	+	5.26010i	0.174562	+	0.174562i
$909$		0			0
$910$		0			0
$911$	23.3987	−	13.5092i	0.775232	−	0.447581i	−0.0595057	−	0.998228i	$-0.518952\pi$
$911$	23.3987	−	13.5092i	0.775232	−	0.447581i	0.834738	+	0.550647i	$0.185619\pi$
$912$		0			0
$913$	0.868470	+	3.24117i	0.0287422	+	0.107267i
$914$	19.4616	−	33.7085i	0.643734	−	1.11498i
$915$		0			0
$916$	−4.46975	−	7.74183i	−0.147685	−	0.255797i
$917$	0.677163	−	0.677163i	0.0223619	−	0.0223619i
$918$		0			0
$919$			54.3202i			1.79186i	0.444196	+	0.895930i	$0.353489\pi$
$919$			54.3202i			1.79186i	−0.444196	+	0.895930i	$0.646511\pi$
$920$		0			0
$921$		0			0
$922$	2.92446	−	0.783607i	0.0963121	−	0.0258067i
$923$	−22.3294	+	5.98314i	−0.734981	+	0.196938i
$924$		0			0
$925$		0			0
$926$		−	6.83645i		−	0.224660i
$927$		0			0
$928$	−5.30136	+	5.30136i	−0.174026	+	0.174026i
$929$	−13.9274	−	24.1230i	−0.456944	−	0.791450i	0.541854	−	0.840473i	$-0.317723\pi$
$929$	−13.9274	−	24.1230i	−0.456944	−	0.791450i	−0.998798	+	0.0490228i	$0.984389\pi$
$930$		0			0
$931$	5.43786	−	9.41865i	0.178219	−	0.308684i
$932$	−5.51203	−	20.5712i	−0.180553	−	0.673831i
$933$		0			0
$934$	−9.86360	+	5.69475i	−0.322747	+	0.186338i
$935$		0			0
$936$		0			0
$937$	16.8770	+	16.8770i	0.551349	+	0.551349i	0.926830	−	0.375481i	$-0.122523\pi$
$937$	16.8770	+	16.8770i	0.551349	+	0.551349i	−0.375481	+	0.926830i	$0.622523\pi$
$938$	4.42152	−	16.5014i	0.144368	−	0.538788i
$939$		0			0
$940$		0			0
$941$	−28.5039	−	16.4567i	−0.929201	−	0.536474i	−0.0426420	−	0.999090i	$-0.513577\pi$
$941$	−28.5039	−	16.4567i	−0.929201	−	0.536474i	−0.886559	+	0.462616i	$0.846911\pi$
$942$		0			0
$943$	42.8898	+	11.4923i	1.39668	+	0.374240i
$944$	−2.69933			−0.0878558
$945$		0			0
$946$	18.5488			0.603074
$947$	11.5072	+	3.08335i	0.373934	+	0.100195i	0.440891	−	0.897560i	$-0.354662\pi$
$947$	11.5072	+	3.08335i	0.373934	+	0.100195i	−0.0669572	+	0.997756i	$0.521329\pi$
$948$		0			0
$949$	5.72383	+	3.30466i	0.185804	+	0.107274i
$950$		0			0
$951$		0			0
$952$	1.74105	−	6.49768i	0.0564277	−	0.210591i
$953$	13.4723	+	13.4723i	0.436411	+	0.436411i	0.890802	−	0.454391i	$-0.150143\pi$
$953$	13.4723	+	13.4723i	0.436411	+	0.436411i	−0.454391	+	0.890802i	$0.650143\pi$
$954$		0			0
$955$		0			0
$956$	−9.40038	+	5.42731i	−0.304030	+	0.175532i
$957$		0			0
$958$	8.57785	+	32.0130i	0.277138	+	1.03429i
$959$	9.93353	−	17.2054i	0.320770	−	0.555591i
$960$		0			0
$961$	−8.83746	−	15.3069i	−0.285079	−	0.493772i
$962$	−17.3513	+	17.3513i	−0.559428	+	0.559428i
$963$		0			0
$964$			23.3318i			0.751467i
$965$		0			0
$966$		0			0
$967$	−8.95826	+	2.40036i	−0.288078	+	0.0771904i	−0.399964	−	0.916531i	$-0.630978\pi$
$967$	−8.95826	+	2.40036i	−0.288078	+	0.0771904i	0.111886	+	0.993721i	$0.464311\pi$
$968$	−6.87844	+	1.84307i	−0.221081	+	0.0592386i
$969$		0			0
$970$		0			0
$971$			24.7290i			0.793590i	0.917907	+	0.396795i	$0.129878\pi$
$971$			24.7290i			0.793590i	−0.917907	+	0.396795i	$0.870122\pi$
$972$		0			0
$973$	1.00161	−	1.00161i	0.0321102	−	0.0321102i
$974$	10.4827	+	18.1566i	0.335889	+	0.581776i
$975$		0			0
$976$	4.37353	−	7.57518i	0.139993	−	0.242476i
$977$	6.35548	+	23.7190i	0.203330	+	0.758837i	0.989952	+	0.141403i	$0.0451612\pi$
$977$	6.35548	+	23.7190i	0.203330	+	0.758837i	−0.786622	+	0.617434i	$0.788172\pi$
$978$		0			0
$979$	3.49636	−	2.01862i	0.111744	−	0.0645155i
$980$		0			0
$981$		0			0
$982$	−13.1868	−	13.1868i	−0.420808	−	0.420808i
$983$	10.7435	−	40.0954i	0.342666	−	1.27885i	−0.552650	−	0.833414i	$-0.686383\pi$
$983$	10.7435	−	40.0954i	0.342666	−	1.27885i	0.895316	−	0.445433i	$-0.146950\pi$
$984$		0			0
$985$		0			0
$986$	21.6587	+	12.5047i	0.689754	+	0.398230i
$987$		0			0
$988$	−14.5628	−	3.90209i	−0.463305	−	0.124142i
$989$	−59.0222			−1.87680
$990$		0			0
$991$	36.6089			1.16292			0.581460	−	0.813575i	$-0.302481\pi$
$991$	36.6089			1.16292			0.581460	+	0.813575i	$0.302481\pi$
$992$	6.73901	+	1.80571i	0.213964	+	0.0573315i
$993$		0			0
$994$	−9.92800	−	5.73193i	−0.314897	−	0.181806i
$995$		0			0
$996$		0			0
$997$	−3.09617	+	11.5550i	−0.0980565	+	0.365952i	−0.997465	−	0.0711569i	$-0.977331\pi$
$997$	−3.09617	+	11.5550i	−0.0980565	+	0.365952i	0.899409	+	0.437109i	$0.143998\pi$
$998$	16.0188	+	16.0188i	0.507065	+	0.507065i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.2.q.h.557.4		16
3.2	odd	2		450.2.p.h.257.1		16
5.2	odd	4		270.2.m.b.233.2		16
5.3	odd	4	inner	1350.2.q.h.1043.3		16
5.4	even	2		270.2.m.b.17.2		16
9.2	odd	6	inner	1350.2.q.h.1007.3		16
9.7	even	3		450.2.p.h.407.1		16
15.2	even	4		90.2.l.b.23.4	✓	16
15.8	even	4		450.2.p.h.293.1		16
15.14	odd	2		90.2.l.b.77.4	yes	16
45.2	even	12		270.2.m.b.143.2		16
45.4	even	6		810.2.f.c.647.7		16
45.7	odd	12		90.2.l.b.83.4	yes	16
45.14	odd	6		810.2.f.c.647.2		16
45.22	odd	12		810.2.f.c.323.2		16
45.29	odd	6		270.2.m.b.197.2		16
45.32	even	12		810.2.f.c.323.7		16
45.34	even	6		90.2.l.b.47.4	yes	16
45.38	even	12	inner	1350.2.q.h.143.4		16
45.43	odd	12		450.2.p.h.443.1		16
60.47	odd	4		720.2.cu.b.113.1		16
60.59	even	2		720.2.cu.b.257.2		16
180.7	even	12		720.2.cu.b.353.2		16
180.79	odd	6		720.2.cu.b.497.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.4	✓	16	15.2	even	4
90.2.l.b.47.4	yes	16	45.34	even	6
90.2.l.b.77.4	yes	16	15.14	odd	2
90.2.l.b.83.4	yes	16	45.7	odd	12
270.2.m.b.17.2		16	5.4	even	2
270.2.m.b.143.2		16	45.2	even	12
270.2.m.b.197.2		16	45.29	odd	6
270.2.m.b.233.2		16	5.2	odd	4
450.2.p.h.257.1		16	3.2	odd	2
450.2.p.h.293.1		16	15.8	even	4
450.2.p.h.407.1		16	9.7	even	3
450.2.p.h.443.1		16	45.43	odd	12
720.2.cu.b.113.1		16	60.47	odd	4
720.2.cu.b.257.2		16	60.59	even	2
720.2.cu.b.353.2		16	180.7	even	12
720.2.cu.b.497.1		16	180.79	odd	6
810.2.f.c.323.2		16	45.22	odd	12
810.2.f.c.323.7		16	45.32	even	12
810.2.f.c.647.2		16	45.14	odd	6
810.2.f.c.647.7		16	45.4	even	6
1350.2.q.h.143.4		16	45.38	even	12	inner
1350.2.q.h.557.4		16	1.1	even	1	trivial
1350.2.q.h.1007.3		16	9.2	odd	6	inner
1350.2.q.h.1043.3		16	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1350.q (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(0.521929 - 1.94786i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.70563 - 0.984748i) q^{11} +(-1.05248 - 3.92790i) q^{13} +(1.00829 - 1.74641i) q^{14} +(0.500000 + 0.866025i) q^{16} +(2.35877 - 2.35877i) q^{17} -3.70753i q^{19} +(1.90239 - 0.509743i) q^{22} +(-6.05338 + 1.62200i) q^{23} -4.06647i q^{26} +(1.42594 - 1.42594i) q^{28} +(3.74863 + 6.49281i) q^{29} +(3.48837 - 6.04204i) q^{31} +(0.258819 + 0.965926i) q^{32} +(2.88889 - 1.66790i) q^{34} +(-4.26692 - 4.26692i) q^{37} +(0.959578 - 3.58120i) q^{38} +(-6.13601 - 3.54263i) q^{41} +(9.09714 + 2.43757i) q^{43} +1.96950 q^{44} -6.26692 q^{46} +(7.49533 + 2.00837i) q^{47} +(2.54041 + 1.46671i) q^{49} +(1.05248 - 3.92790i) q^{52} +(7.03027 + 7.03027i) q^{53} +(1.74641 - 1.00829i) q^{56} +(1.94043 + 7.24179i) q^{58} +(-1.34967 + 2.33769i) q^{59} +(-4.37353 - 7.57518i) q^{61} +(4.93330 - 4.93330i) q^{62} +1.00000i q^{64} +(8.18285 - 2.19259i) q^{67} +(3.22213 - 0.863368i) q^{68} -5.68481i q^{71} +(-1.14928 + 1.14928i) q^{73} +(-3.01717 - 5.22589i) q^{74} +(1.85376 - 3.21081i) q^{76} +(-1.02794 - 3.83631i) q^{77} +(-10.0535 + 5.80440i) q^{79} +(-5.01003 - 5.01003i) q^{82} +(-0.440961 + 1.64569i) q^{83} +(8.15627 + 4.70902i) q^{86} +(1.90239 + 0.509743i) q^{88} +2.04989 q^{89} -8.20034 q^{91} +(-6.05338 - 1.62200i) q^{92} +(6.72013 + 3.87987i) q^{94} +(-2.60421 + 9.71905i) q^{97} +(2.07424 + 2.07424i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} + 8 q^{16} - 8 q^{22} - 24 q^{23} + 16 q^{28} - 8 q^{31} + 24 q^{38} - 24 q^{41} - 32 q^{46} + 48 q^{47} - 24 q^{56} - 16 q^{58} - 24 q^{61} + 16 q^{67} - 24 q^{68} - 16 q^{73} + 16 q^{76}+ \cdots + 48 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 + 8 * q^16 - 8 * q^22 - 24 * q^23 + 16 * q^28 - 8 * q^31 + 24 * q^38 - 24 * q^41 - 32 * q^46 + 48 * q^47 - 24 * q^56 - 16 * q^58 - 24 * q^61 + 16 * q^67 - 24 * q^68 - 16 * q^73 + 16 * q^76 - 72 * q^77 + 16 * q^82 + 48 * q^83 + 48 * q^86 - 8 * q^88 - 24 * q^92 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more