LMFDB - Embedded newform 1350.2.q.h.1043.3

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			1043.3
Root			$0.500000 + 0.331082i$ of defining polynomial
Character	$\chi$	$=$	1350.1043
Dual form			1350.2.q.h.1007.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-1.94786 - 0.521929i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-1.94786 - 0.521929i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.70563 - 0.984748i) q^{11} +(3.92790 - 1.05248i) q^{13} +(-1.00829 + 1.74641i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-2.35877 - 2.35877i) q^{17} +3.70753i q^{19} +(-0.509743 - 1.90239i) q^{22} +(-1.62200 - 6.05338i) q^{23} -4.06647i q^{26} +(1.42594 + 1.42594i) q^{28} +(-3.74863 - 6.49281i) q^{29} +(3.48837 - 6.04204i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-2.88889 + 1.66790i) q^{34} +(-4.26692 + 4.26692i) q^{37} +(3.58120 + 0.959578i) q^{38} +(-6.13601 - 3.54263i) q^{41} +(-2.43757 + 9.09714i) q^{43} -1.96950 q^{44} -6.26692 q^{46} +(2.00837 - 7.49533i) q^{47} +(-2.54041 - 1.46671i) q^{49} +(-3.92790 - 1.05248i) q^{52} +(-7.03027 + 7.03027i) q^{53} +(1.74641 - 1.00829i) q^{56} +(-7.24179 + 1.94043i) q^{58} +(1.34967 - 2.33769i) q^{59} +(-4.37353 - 7.57518i) q^{61} +(-4.93330 - 4.93330i) q^{62} -1.00000i q^{64} +(-2.19259 - 8.18285i) q^{67} +(0.863368 + 3.22213i) q^{68} -5.68481i q^{71} +(-1.14928 - 1.14928i) q^{73} +(3.01717 + 5.22589i) q^{74} +(1.85376 - 3.21081i) q^{76} +(-3.83631 + 1.02794i) q^{77} +(10.0535 - 5.80440i) q^{79} +(-5.01003 + 5.01003i) q^{82} +(-1.64569 - 0.440961i) q^{83} +(8.15627 + 4.70902i) q^{86} +(-0.509743 + 1.90239i) q^{88} -2.04989 q^{89} -8.20034 q^{91} +(-1.62200 + 6.05338i) q^{92} +(-6.72013 - 3.87987i) q^{94} +(9.71905 + 2.60421i) q^{97} +(-2.07424 + 2.07424i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.94786	−	0.521929i	−0.736223	−	0.197270i	−0.128824	−	0.991667i	$-0.541120\pi$
$7$	−1.94786	−	0.521929i	−0.736223	−	0.197270i	−0.607399	+	0.794397i	$0.707787\pi$
$8$	−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
$13$	3.92790	−	1.05248i	1.08940	−	0.291905i	0.330961	−	0.943644i	$-0.392627\pi$
$13$	3.92790	−	1.05248i	1.08940	−	0.291905i	0.758443	+	0.651739i	$0.225960\pi$
$14$	−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	$-0.382563\pi$
$17$	−2.35877	−	2.35877i	−0.572085	−	0.572085i	−0.932711	+	0.360626i	$0.882563\pi$
$18$		0			0
$19$			3.70753i			0.850565i	0.905061	+	0.425282i	$0.139825\pi$
$19$			3.70753i			0.850565i	−0.905061	+	0.425282i	$0.860175\pi$
$20$		0			0
$21$		0			0
$22$	−0.509743	−	1.90239i	−0.108678	−	0.405590i
$23$	−1.62200	−	6.05338i	−0.338210	−	1.26222i	−0.900347	−	0.435173i	$-0.856687\pi$
$23$	−1.62200	−	6.05338i	−0.338210	−	1.26222i	0.562137	−	0.827044i	$-0.309979\pi$
$24$		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	$-0.921582\pi$
$29$	−3.74863	−	6.49281i	−0.696103	−	1.20569i	0.273705	−	0.961814i	$-0.411751\pi$
$30$		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	$-0.0488587\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$		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	−0.964728	−	0.263250i	$-0.915206\pi$
$37$	−4.26692	+	4.26692i	−0.701478	+	0.701478i	0.263250	+	0.964728i	$0.415206\pi$
$38$	3.58120	+	0.959578i	0.580947	+	0.155664i
$39$		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
$43$	−2.43757	+	9.09714i	−0.371726	+	1.38730i	0.486344	+	0.873767i	$0.338330\pi$
$43$	−2.43757	+	9.09714i	−0.371726	+	1.38730i	−0.858070	+	0.513533i	$0.828336\pi$
$44$	−1.96950			−0.296913
$45$		0			0
$46$	−6.26692			−0.924007
$47$	2.00837	−	7.49533i	0.292951	−	1.09331i	−0.649881	−	0.760036i	$-0.725181\pi$
$47$	2.00837	−	7.49533i	0.292951	−	1.09331i	0.942831	−	0.333270i	$-0.108152\pi$
$48$		0			0
$49$	−2.54041	−	1.46671i	−0.362916	−	0.209530i
$50$		0			0
$51$		0			0
$52$	−3.92790	−	1.05248i	−0.544702	−	0.145953i
$53$	−7.03027	+	7.03027i	−0.965682	+	0.965682i	−0.999430	−	0.0337485i	$-0.989255\pi$
$53$	−7.03027	+	7.03027i	−0.965682	+	0.965682i	0.0337485	+	0.999430i	$0.489255\pi$
$54$		0			0
$55$		0			0
$56$	1.74641	−	1.00829i	0.233373	−	0.134738i
$57$		0			0
$58$	−7.24179	+	1.94043i	−0.950894	+	0.254791i
$59$	1.34967	−	2.33769i	0.175712	−	0.304341i	−0.764696	−	0.644392i	$-0.777111\pi$
$59$	1.34967	−	2.33769i	0.175712	−	0.304341i	0.940407	+	0.340050i	$0.110444\pi$
$60$		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
$67$	−2.19259	−	8.18285i	−0.267867	−	0.999694i	−0.960472	−	0.278377i	$-0.910204\pi$
$67$	−2.19259	−	8.18285i	−0.267867	−	0.999694i	0.692605	−	0.721317i	$-0.256463\pi$
$68$	0.863368	+	3.22213i	0.104699	+	0.390741i
$69$		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	0.636645	−	0.771157i	$-0.280322\pi$
$73$	−1.14928	−	1.14928i	−0.134513	−	0.134513i	−0.771157	+	0.636645i	$0.780322\pi$
$74$	3.01717	+	5.22589i	0.350739	+	0.607498i
$75$		0			0
$76$	1.85376	−	3.21081i	0.212641	−	0.368305i
$77$	−3.83631	+	1.02794i	−0.437188	+	0.117144i
$78$		0			0
$79$	10.0535	−	5.80440i	1.13111	−	0.653046i	0.186895	−	0.982380i	$-0.440158\pi$
$79$	10.0535	−	5.80440i	1.13111	−	0.653046i	0.944214	+	0.329334i	$0.106824\pi$
$80$		0			0
$81$		0			0
$82$	−5.01003	+	5.01003i	−0.553266	+	0.553266i
$83$	−1.64569	−	0.440961i	−0.180638	−	0.0484017i	0.167366	−	0.985895i	$-0.446474\pi$
$83$	−1.64569	−	0.440961i	−0.180638	−	0.0484017i	−0.348004	+	0.937493i	$0.613140\pi$
$84$		0			0
$85$		0			0
$86$	8.15627	+	4.70902i	0.879513	+	0.507787i
$87$		0			0
$88$	−0.509743	+	1.90239i	−0.0543388	+	0.202795i
$89$	−2.04989			−0.217288			−0.108644	−	0.994081i	$-0.534651\pi$
$89$	−2.04989			−0.217288			−0.108644	+	0.994081i	$0.534651\pi$
$90$		0			0
$91$	−8.20034			−0.859629
$92$	−1.62200	+	6.05338i	−0.169105	+	0.631109i
$93$		0			0
$94$	−6.72013	−	3.87987i	−0.693128	−	0.400178i
$95$		0			0
$96$		0			0
$97$	9.71905	+	2.60421i	0.986820	+	0.264418i	0.715914	−	0.698188i	$-0.246010\pi$
$97$	9.71905	+	2.60421i	0.986820	+	0.264418i	0.270906	+	0.962606i	$0.412677\pi$
$98$	−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
$103$	3.86872	−	1.03662i	0.381196	−	0.102141i	−0.0631321	−	0.998005i	$-0.520109\pi$
$103$	3.86872	−	1.03662i	0.381196	−	0.102141i	0.444329	+	0.895864i	$0.353442\pi$
$104$	−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	$-0.129584\pi$
$107$	5.40296	+	5.40296i	0.522324	+	0.522324i	−0.395949	+	0.918273i	$0.629584\pi$
$108$		0			0
$109$			4.35357i			0.416996i	0.978023	+	0.208498i	$0.0668575\pi$
$109$			4.35357i			0.416996i	−0.978023	+	0.208498i	$0.933142\pi$
$110$		0			0
$111$		0			0
$112$	−0.521929	−	1.94786i	−0.0493176	−	0.184056i
$113$	0.767544	+	2.86451i	0.0722045	+	0.269471i	0.992585	−	0.121553i	$-0.0387876\pi$
$113$	0.767544	+	2.86451i	0.0722045	+	0.269471i	−0.920380	+	0.391024i	$0.872121\pi$
$114$		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
$122$	−8.44902	+	2.26391i	−0.764938	+	0.204965i
$123$		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	−0.539040	−	0.842280i	$-0.681213\pi$
$127$	3.41734	−	3.41734i	0.303240	−	0.303240i	0.842280	+	0.539040i	$0.181213\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$		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
$133$	1.93506	−	7.22176i	0.167791	−	0.626206i
$134$	−8.47151			−0.731827
$135$		0			0
$136$	3.33580			0.286042
$137$	2.54985	−	9.51618i	0.217849	−	0.813022i	−0.767296	−	0.641293i	$-0.778398\pi$
$137$	2.54985	−	9.51618i	0.217849	−	0.813022i	0.985144	−	0.171728i	$-0.0549352\pi$
$138$		0			0
$139$	−0.608318	−	0.351212i	−0.0515968	−	0.0297894i	0.473980	−	0.880536i	$-0.342817\pi$
$139$	−0.608318	−	0.351212i	−0.0515968	−	0.0297894i	−0.525577	+	0.850746i	$0.676150\pi$
$140$		0			0
$141$		0			0
$142$	−5.49111	−	1.47134i	−0.460803	−	0.123472i
$143$	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
$148$	5.82872	−	1.56180i	0.479118	−	0.128379i
$149$	4.05609	−	7.02536i	0.332288	−	0.575540i	−0.650672	−	0.759359i	$-0.725513\pi$
$149$	4.05609	−	7.02536i	0.332288	−	0.575540i	0.982960	+	0.183819i	$0.0588460\pi$
$150$		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
$157$	2.80938	+	10.4848i	0.224213	+	0.836775i	0.982718	+	0.185108i	$0.0592635\pi$
$157$	2.80938	+	10.4848i	0.224213	+	0.836775i	−0.758505	+	0.651667i	$0.774070\pi$
$158$	−3.00458	−	11.2132i	−0.239031	−	0.892077i
$159$		0			0
$160$		0			0
$161$			12.6377i			0.995993i
$162$		0			0
$163$	−9.68197	−	9.68197i	−0.758351	−	0.758351i	0.217671	−	0.976022i	$-0.430154\pi$
$163$	−9.68197	−	9.68197i	−0.758351	−	0.758351i	−0.976022	+	0.217671i	$0.930154\pi$
$164$	3.54263	+	6.13601i	0.276633	+	0.479142i
$165$		0			0
$166$	−0.851871	+	1.47548i	−0.0661180	+	0.114520i
$167$	4.93579	−	1.32254i	0.381943	−	0.102341i	−0.0627387	−	0.998030i	$-0.519983\pi$
$167$	4.93579	−	1.32254i	0.381943	−	0.102341i	0.444682	+	0.895689i	$0.353317\pi$
$168$		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
$173$	−7.16239	−	1.91916i	−0.544546	−	0.145911i	−0.0239492	−	0.999713i	$-0.507624\pi$
$173$	−7.16239	−	1.91916i	−0.544546	−	0.145911i	−0.520597	+	0.853802i	$0.674291\pi$
$174$		0			0
$175$		0			0
$176$	1.70563	+	0.984748i	0.128567	+	0.0742282i
$177$		0			0
$178$	−0.530550	+	1.98004i	−0.0397664	+	0.148410i
$179$	2.73426			0.204369			0.102184	−	0.994765i	$-0.467417\pi$
$179$	2.73426			0.204369			0.102184	+	0.994765i	$0.467417\pi$
$180$		0			0
$181$	−22.7081			−1.68788			−0.843941	−	0.536437i	$-0.819770\pi$
$181$	−22.7081			−1.68788			−0.843941	+	0.536437i	$0.819770\pi$
$182$	−2.12240	+	7.92092i	−0.157323	+	0.587138i
$183$		0			0
$184$	5.42731	+	3.13346i	0.400107	+	0.231002i
$185$		0			0
$186$		0			0
$187$	−6.34598	−	1.70040i	−0.464064	−	0.124346i
$188$	−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
$193$	5.28063	−	1.41494i	0.380108	−	0.101850i	−0.0637057	−	0.997969i	$-0.520292\pi$
$193$	5.28063	−	1.41494i	0.380108	−	0.101850i	0.443814	+	0.896119i	$0.353625\pi$
$194$	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	$-0.0425744\pi$
$197$	12.0386	+	12.0386i	0.857716	+	0.857716i	−0.133353	+	0.991069i	$0.542574\pi$
$198$		0			0
$199$			4.43831i			0.314623i	0.987549	+	0.157312i	$0.0502827\pi$
$199$			4.43831i			0.314623i	−0.987549	+	0.157312i	$0.949717\pi$
$200$		0			0
$201$		0			0
$202$	−1.22237	−	4.56196i	−0.0860058	−	0.320978i
$203$	3.91303	+	14.6036i	0.274641	+	1.02497i
$204$		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	$-0.144445\pi$
$212$	9.60353	−	2.57326i	0.659573	−	0.176732i
$213$		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
$218$	4.20523	+	1.12679i	0.284814	+	0.0763156i
$219$		0			0
$220$		0			0
$221$	−11.7476	−	6.78245i	−0.790226	−	0.456237i
$222$		0			0
$223$	−4.34272	+	16.2073i	−0.290810	+	1.08532i	0.653678	+	0.756773i	$0.273225\pi$
$223$	−4.34272	+	16.2073i	−0.290810	+	1.08532i	−0.944488	+	0.328546i	$0.893441\pi$
$224$	−2.01658			−0.134738
$225$		0			0
$226$	2.96556			0.197266
$227$	1.92533	−	7.18543i	0.127789	−	0.476914i	−0.872135	−	0.489265i	$-0.837265\pi$
$227$	1.92533	−	7.18543i	0.127789	−	0.476914i	0.999924	+	0.0123515i	$0.00393171\pi$
$228$		0			0
$229$	7.74183	+	4.46975i	0.511595	+	0.295369i	0.733489	−	0.679701i	$-0.237891\pi$
$229$	7.74183	+	4.46975i	0.511595	+	0.295369i	−0.221894	+	0.975071i	$0.571224\pi$
$230$		0			0
$231$		0			0
$232$	7.24179	+	1.94043i	0.475447	+	0.127396i
$233$	15.0591	−	15.0591i	0.986558	−	0.986558i	−0.0133533	−	0.999911i	$-0.504251\pi$
$233$	15.0591	−	15.0591i	0.986558	−	0.986558i	0.999911	+	0.0133533i	$0.00425061\pi$
$234$		0			0
$235$		0			0
$236$	−2.33769	+	1.34967i	−0.152171	+	0.0878558i
$237$		0			0
$238$	6.49768	−	1.74105i	0.421182	−	0.112855i
$239$	5.42731	−	9.40038i	0.351064	−	0.608060i	−0.635372	−	0.772206i	$-0.719153\pi$
$239$	5.42731	−	9.40038i	0.351064	−	0.608060i	0.986436	+	0.164146i	$0.0524867\pi$
$240$		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
$247$	3.90209	+	14.5628i	0.248284	+	0.926609i
$248$	1.80571	+	6.73901i	0.114663	+	0.427928i
$249$		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
$257$	−7.29595	+	1.95494i	−0.455109	+	0.121946i	−0.479089	−	0.877766i	$-0.659033\pi$
$257$	−7.29595	+	1.95494i	−0.455109	+	0.121946i	0.0239802	+	0.999712i	$0.492366\pi$
$258$		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
$263$	10.7695	+	2.88569i	0.664078	+	0.177939i	0.575086	−	0.818093i	$-0.304969\pi$
$263$	10.7695	+	2.88569i	0.664078	+	0.177939i	0.0889923	+	0.996032i	$0.471635\pi$
$264$		0			0
$265$		0			0
$266$	−6.47485	−	3.73826i	−0.396998	−	0.229207i
$267$		0			0
$268$	−2.19259	+	8.18285i	−0.133934	+	0.499847i
$269$	13.4707			0.821326			0.410663	−	0.911787i	$-0.365297\pi$
$269$	13.4707			0.821326			0.410663	+	0.911787i	$0.365297\pi$
$270$		0			0
$271$	20.4402			1.24165			0.620827	−	0.783947i	$-0.286797\pi$
$271$	20.4402			1.24165			0.620827	+	0.783947i	$0.286797\pi$
$272$	0.863368	−	3.22213i	0.0523494	−	0.195371i
$273$		0			0
$274$	−8.53197	−	4.92594i	−0.515435	−	0.297587i
$275$		0			0
$276$		0			0
$277$	23.4121	+	6.27326i	1.40670	+	0.376924i	0.880745	−	0.473590i	$-0.157042\pi$
$277$	23.4121	+	6.27326i	1.40670	+	0.376924i	0.525953	+	0.850514i	$0.323709\pi$
$278$	−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
$283$	2.05136	−	0.549660i	0.121941	−	0.0326739i	−0.197333	−	0.980337i	$-0.563228\pi$
$283$	2.05136	−	0.549660i	0.121941	−	0.0326739i	0.319273	+	0.947663i	$0.396561\pi$
$284$	−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
$292$	0.420664	+	1.56994i	0.0246175	+	0.0918738i
$293$	−0.946406	−	3.53204i	−0.0552896	−	0.206344i	0.932755	−	0.360510i	$-0.117397\pi$
$293$	−0.946406	−	3.53204i	−0.0552896	−	0.206344i	−0.988045	+	0.154167i	$0.950731\pi$
$294$		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
$302$	8.92011	−	2.39014i	0.513295	−	0.137537i
$303$		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	−0.339024	−	0.940778i	$-0.610097\pi$
$307$	10.5436	−	10.5436i	0.601754	−	0.601754i	0.940778	+	0.339024i	$0.110097\pi$
$308$	3.83631	+	1.02794i	0.218594	+	0.0585721i
$309$		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
$313$	4.56901	−	17.0518i	0.258256	−	0.963824i	−0.707994	−	0.706218i	$-0.750400\pi$
$313$	4.56901	−	17.0518i	0.258256	−	0.963824i	0.966250	−	0.257606i	$-0.0829337\pi$
$314$	10.8546			0.612562
$315$		0			0
$316$	−11.6088			−0.653046
$317$	−6.00131	+	22.3972i	−0.337067	+	1.25795i	0.564543	+	0.825403i	$0.309052\pi$
$317$	−6.00131	+	22.3972i	−0.337067	+	1.25795i	−0.901611	+	0.432549i	$0.857614\pi$
$318$		0			0
$319$	−12.7876	−	7.38291i	−0.715966	−	0.413363i
$320$		0			0
$321$		0			0
$322$	12.2071	+	3.27089i	0.680276	+	0.182279i
$323$	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
$328$	6.84383	−	1.83380i	0.377887	−	0.101255i
$329$	−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
$337$	−8.30344	−	30.9889i	−0.452317	−	1.68807i	−0.695858	−	0.718180i	$-0.744976\pi$
$337$	−8.30344	−	30.9889i	−0.452317	−	1.68807i	0.243541	−	0.969891i	$-0.421691\pi$
$338$	−0.915220	−	3.41565i	−0.0497814	−	0.185787i
$339$		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
$347$	−14.3001	+	3.83170i	−0.767670	+	0.205696i	−0.621342	−	0.783540i	$-0.713412\pi$
$347$	−14.3001	+	3.83170i	−0.767670	+	0.205696i	−0.146328	+	0.989236i	$0.546745\pi$
$348$		0			0
$349$	−13.3741	+	7.72151i	−0.715897	+	0.413323i	−0.813241	−	0.581928i	$-0.802299\pi$
$349$	−13.3741	+	7.72151i	−0.715897	+	0.413323i	0.0973439	+	0.995251i	$0.468965\pi$
$350$		0			0
$351$		0			0
$352$	1.39264	−	1.39264i	0.0742282	−	0.0742282i
$353$	−20.1446	−	5.39774i	−1.07219	−	0.287293i	−0.320798	−	0.947148i	$-0.603951\pi$
$353$	−20.1446	−	5.39774i	−1.07219	−	0.287293i	−0.751393	+	0.659855i	$0.770618\pi$
$354$		0			0
$355$		0			0
$356$	1.77526	+	1.02494i	0.0940883	+	0.0543219i
$357$		0			0
$358$	0.707680	−	2.64110i	0.0374020	−	0.139586i
$359$	−3.39466			−0.179163			−0.0895815	−	0.995979i	$-0.528553\pi$
$359$	−3.39466			−0.179163			−0.0895815	+	0.995979i	$0.528553\pi$
$360$		0			0
$361$	5.25425			0.276540
$362$	−5.87729	+	21.9344i	−0.308904	+	1.15284i
$363$		0			0
$364$	7.10170	+	4.10017i	0.372230	+	0.214907i
$365$		0			0
$366$		0			0
$367$	21.2279	+	5.68801i	1.10809	+	0.296912i	0.766054	−	0.642776i	$-0.222217\pi$
$367$	21.2279	+	5.68801i	1.10809	+	0.296912i	0.342035	+	0.939687i	$0.388884\pi$
$368$	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
$373$	−1.42207	+	0.381044i	−0.0736322	+	0.0197297i	−0.295447	−	0.955359i	$-0.595469\pi$
$373$	−1.42207	+	0.381044i	−0.0736322	+	0.0197297i	0.221815	+	0.975089i	$0.428802\pi$
$374$	−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	$-0.718306\pi$
$379$		−	30.1323i		−	1.54779i	0.633314	−	0.773895i	$-0.281694\pi$
$380$		0			0
$381$		0			0
$382$	−0.332194	−	1.23976i	−0.0169965	−	0.0634318i
$383$	−4.43826	−	16.5638i	−0.226785	−	0.846372i	−0.981682	−	0.190528i	$-0.938980\pi$
$383$	−4.43826	−	16.5638i	−0.226785	−	0.846372i	0.754897	−	0.655843i	$-0.227687\pi$
$384$		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	$0.111066\pi$
$389$	15.1070	+	26.1660i	0.765953	+	1.32667i	−0.173789	+	0.984783i	$0.555601\pi$
$390$		0			0
$391$	−10.4526	+	18.1044i	−0.528610	+	0.915580i
$392$	2.83346	−	0.759224i	0.143112	−	0.0383466i
$393$		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	−0.650561	−	0.759454i	$-0.725466\pi$
$397$	2.16969	−	2.16969i	0.108893	−	0.108893i	0.759454	+	0.650561i	$0.225466\pi$
$398$	4.28708	+	1.14872i	0.214892	+	0.0575801i
$399$		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
$403$	7.34287	−	27.4040i	0.365774	−	1.36509i
$404$	−4.72288			−0.234972
$405$		0			0
$406$	15.1188			0.750333
$407$	−3.07596	+	11.4796i	−0.152470	+	0.569025i
$408$		0			0
$409$	10.2963	+	5.94456i	0.509118	+	0.293939i	0.732471	−	0.680798i	$-0.238367\pi$
$409$	10.2963	+	5.94456i	0.509118	+	0.293939i	−0.223353	+	0.974738i	$0.571700\pi$
$410$		0			0
$411$		0			0
$412$	−3.86872	−	1.03662i	−0.190598	−	0.0510706i
$413$	−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
$418$	7.05315	−	1.88989i	0.344981	−	0.0924373i
$419$	−19.6354	+	34.0095i	−0.959251	+	1.66147i	−0.234926	+	0.972013i	$0.575485\pi$
$419$	−19.6354	+	34.0095i	−0.959251	+	1.66147i	−0.724325	+	0.689458i	$0.757849\pi$
$420$		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
$427$	4.56534	+	17.0381i	0.220932	+	0.824531i
$428$	−1.97762	−	7.38058i	−0.0955920	−	0.356754i
$429$		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	0.416190	−	0.909278i	$-0.363365\pi$
$433$	−10.2605	−	10.2605i	−0.493088	−	0.493088i	−0.909278	+	0.416190i	$0.863365\pi$
$434$	7.03457	+	12.1842i	0.337670	+	0.584862i
$435$		0			0
$436$	2.17679	−	3.77030i	0.104249	−	0.180565i
$437$	22.4431	−	6.01360i	1.07360	−	0.287670i
$438$		0			0
$439$	−1.96604	+	1.13510i	−0.0938342	+	0.0541752i	−0.546183	−	0.837666i	$-0.683920\pi$
$439$	−1.96604	+	1.13510i	−0.0938342	+	0.0541752i	0.452349	+	0.891841i	$0.350586\pi$
$440$		0			0
$441$		0			0
$442$	−9.59184	+	9.59184i	−0.456237	+	0.456237i
$443$	26.8719	+	7.20031i	1.27672	+	0.342097i	0.832603	−	0.553870i	$-0.186850\pi$
$443$	26.8719	+	7.20031i	1.27672	+	0.342097i	0.444120	+	0.895967i	$0.353516\pi$
$444$		0			0
$445$		0			0
$446$	14.5310	+	8.38950i	0.688065	+	0.397254i
$447$		0			0
$448$	−0.521929	+	1.94786i	−0.0246588	+	0.0920279i
$449$	11.7712			0.555516			0.277758	−	0.960651i	$-0.410409\pi$
$449$	11.7712			0.555516			0.277758	+	0.960651i	$0.410409\pi$
$450$		0			0
$451$	−13.9544			−0.657086
$452$	0.767544	−	2.86451i	0.0361022	−	0.134735i
$453$		0			0
$454$	−6.44228	−	3.71945i	−0.302351	−	0.174562i
$455$		0			0
$456$		0			0
$457$	−37.5970	−	10.0741i	−1.75871	−	0.471246i	−0.772263	−	0.635303i	$-0.780875\pi$
$457$	−37.5970	−	10.0741i	−1.75871	−	0.471246i	−0.986451	+	0.164058i	$0.947542\pi$
$458$	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
$463$	6.60350	−	1.76940i	0.306891	−	0.0822311i	−0.102087	−	0.994775i	$-0.532552\pi$
$463$	6.60350	−	1.76940i	0.306891	−	0.0822311i	0.408978	+	0.912544i	$0.365885\pi$
$464$	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	$-0.165116\pi$
$467$	8.05359	+	8.05359i	0.372676	+	0.372676i	−0.495775	+	0.868451i	$0.665116\pi$
$468$		0			0
$469$			17.0835i			0.788841i
$470$		0			0
$471$		0			0
$472$	0.698639	+	2.60736i	0.0321575	+	0.120013i
$473$	4.80079	+	17.9168i	0.220740	+	0.823814i
$474$		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	$-0.893256\pi$
$479$	−16.5711	−	28.7020i	−0.757154	−	1.31143i	0.187142	−	0.982333i	$-0.440078\pi$
$480$		0			0
$481$	−12.2692	+	21.2509i	−0.559428	+	0.968958i
$482$	22.5368	−	6.03872i	1.02652	−	0.275056i
$483$		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	−0.286349	−	0.958126i	$-0.592442\pi$
$487$	14.8248	−	14.8248i	0.671777	−	0.671777i	0.958126	+	0.286349i	$0.0924415\pi$
$488$	8.44902	+	2.26391i	0.382469	+	0.102482i
$489$		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
$493$	−6.47289	+	24.1572i	−0.291524	+	1.08798i
$494$	15.0765			0.678325
$495$		0			0
$496$	6.97674			0.313265
$497$	−2.96707	+	11.0732i	−0.133091	+	0.496703i
$498$		0			0
$499$	−19.6189	−	11.3270i	−0.878263	−	0.507065i	−0.00817742	−	0.999967i	$-0.502603\pi$
$499$	−19.6189	−	11.3270i	−0.878263	−	0.507065i	−0.870085	+	0.492901i	$0.835936\pi$
$500$		0			0
$501$		0			0
$502$	12.9298	+	3.46454i	0.577087	+	0.154630i
$503$	−9.64801	+	9.64801i	−0.430183	+	0.430183i	−0.888691	−	0.458507i	$-0.848384\pi$
$503$	−9.64801	+	9.64801i	−0.430183	+	0.430183i	0.458507	+	0.888691i	$0.348384\pi$
$504$		0			0
$505$		0			0
$506$	−10.6891	+	6.17134i	−0.475187	+	0.274349i
$507$		0			0
$508$	−4.66818	+	1.25084i	−0.207117	+	0.0554968i
$509$	−13.5882	+	23.5355i	−0.602286	+	1.04319i	0.390188	+	0.920735i	$0.372410\pi$
$509$	−13.5882	+	23.5355i	−0.602286	+	1.04319i	−0.992474	+	0.122455i	$0.960923\pi$
$510$		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
$517$	−3.95547	−	14.7620i	−0.173961	−	0.649233i
$518$	−3.14949	−	11.7541i	−0.138381	−	0.516444i
$519$		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	0.990066	+	0.140607i	$0.0449053\pi$
$523$	25.8576	+	25.8576i	1.13067	+	1.13067i	0.140607	+	0.990066i	$0.455095\pi$
$524$	−0.237445	−	0.411267i	−0.0103728	−	0.0179663i
$525$		0			0
$526$	5.57472	−	9.65570i	0.243069	−	0.421009i
$527$	−22.4800	+	6.02350i	−0.979244	+	0.262388i
$528$		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
$533$	−27.8302	−	7.45708i	−1.20546	−	0.323002i
$534$		0			0
$535$		0			0
$536$	7.33654	+	4.23576i	0.316890	+	0.182957i
$537$		0			0
$538$	3.48649	−	13.0117i	0.150313	−	0.560976i
$539$	−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	$0.531170\pi$
$542$	5.29032	−	19.7437i	0.227239	−	0.848066i
$543$		0			0
$544$	−2.88889	−	1.66790i	−0.123860	−	0.0715106i
$545$		0			0
$546$		0			0
$547$	−21.6180	−	5.79252i	−0.924319	−	0.247670i	−0.234888	−	0.972022i	$-0.575472\pi$
$547$	−21.6180	−	5.79252i	−0.924319	−	0.247670i	−0.689430	+	0.724352i	$0.742139\pi$
$548$	−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
$553$	−22.6124	+	6.05896i	−0.961575	+	0.257653i
$554$	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	$-0.0385825\pi$
$557$	20.5740	+	20.5740i	0.871749	+	0.871749i	−0.120914	+	0.992663i	$0.538583\pi$
$558$		0			0
$559$			38.2982i			1.61984i
$560$		0			0
$561$		0			0
$562$	5.84041	+	21.7967i	0.246363	+	0.919438i
$563$	9.17805	+	34.2529i	0.386809	+	1.44359i	0.835296	+	0.549800i	$0.185296\pi$
$563$	9.17805	+	34.2529i	0.386809	+	1.44359i	−0.448487	+	0.893789i	$0.648037\pi$
$564$		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	$-0.997956\pi$
$569$	−12.0592	−	20.8872i	−0.505549	−	0.875637i	0.494430	−	0.869217i	$-0.335377\pi$
$570$		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	$0.136687\pi$
$572$	−7.73599	+	2.07285i	−0.323458	+	0.0866703i
$573$		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	−0.710979	−	0.703214i	$-0.751748\pi$
$577$	−0.186522	+	0.186522i	−0.00776502	+	0.00776502i	0.703214	+	0.710979i	$0.251748\pi$
$578$	−5.67235	−	1.51990i	−0.235939	−	0.0632196i
$579$		0			0
$580$		0			0
$581$	2.97543	+	1.71786i	0.123441	+	0.0712689i
$582$		0			0
$583$	−5.06802	+	18.9141i	−0.209896	+	0.783342i
$584$	1.62532			0.0672563
$585$		0			0
$586$	−3.65663			−0.151054
$587$	11.6992	−	43.6620i	0.482878	−	1.80212i	−0.106555	−	0.994307i	$-0.533982\pi$
$587$	11.6992	−	43.6620i	0.482878	−	1.80212i	0.589433	−	0.807818i	$-0.299351\pi$
$588$		0			0
$589$	22.4010	+	12.9332i	0.923017	+	0.532904i
$590$		0			0
$591$		0			0
$592$	−5.82872	−	1.56180i	−0.239559	−	0.0641897i
$593$	−3.60323	+	3.60323i	−0.147967	+	0.147967i	−0.777209	−	0.629242i	$-0.783365\pi$
$593$	−3.60323	+	3.60323i	−0.147967	+	0.147967i	0.629242	+	0.777209i	$0.283365\pi$
$594$		0			0
$595$		0			0
$596$	−7.02536	+	4.05609i	−0.287770	+	0.166144i
$597$		0			0
$598$	−24.6159	+	6.59580i	−1.00662	+	0.269722i
$599$	23.4581	−	40.6307i	0.958473	−	1.66012i	0.232260	−	0.972654i	$-0.425388\pi$
$599$	23.4581	−	40.6307i	0.958473	−	1.66012i	0.726213	−	0.687470i	$-0.241279\pi$
$600$		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
$607$	−4.28061	−	15.9755i	−0.173745	−	0.648424i	−0.996762	−	0.0804079i	$-0.974378\pi$
$607$	−4.28061	−	15.9755i	−0.173745	−	0.648424i	0.823017	−	0.568016i	$-0.192289\pi$
$608$	0.959578	+	3.58120i	0.0389160	+	0.145237i
$609$		0			0
$610$		0			0
$611$		−	31.5547i		−	1.27657i
$612$		0			0
$613$	21.1512	+	21.1512i	0.854290	+	0.854290i	0.990658	−	0.136368i	$-0.0435429\pi$
$613$	21.1512	+	21.1512i	0.854290	+	0.854290i	−0.136368	+	0.990658i	$0.543543\pi$
$614$	−7.45544	−	12.9132i	−0.300877	−	0.521134i
$615$		0			0
$616$	1.98582	−	3.43954i	0.0800110	−	0.138583i
$617$	−10.1671	+	2.72427i	−0.409312	+	0.109675i	−0.457599	−	0.889159i	$-0.651290\pi$
$617$	−10.1671	+	2.72427i	−0.409312	+	0.109675i	0.0482869	+	0.998834i	$0.484624\pi$
$618$		0			0
$619$	2.77044	−	1.59951i	0.111353	−	0.0642898i	−0.443289	−	0.896379i	$-0.646188\pi$
$619$	2.77044	−	1.59951i	0.111353	−	0.0642898i	0.554642	+	0.832089i	$0.312855\pi$
$620$		0			0
$621$		0			0
$622$	7.41734	−	7.41734i	0.297408	−	0.297408i
$623$	3.99290	+	1.06990i	0.159972	+	0.0428644i
$624$		0			0
$625$		0			0
$626$	−15.2882	−	8.82666i	−0.611040	−	0.352784i
$627$		0			0
$628$	2.80938	−	10.4848i	0.112107	−	0.418388i
$629$	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	$0.361102\pi$
$632$	−3.00458	+	11.2132i	−0.119516	+	0.446039i
$633$		0			0
$634$	20.0808	+	11.5936i	0.797510	+	0.460442i
$635$		0			0
$636$		0			0
$637$	−11.5222	−	3.08736i	−0.456525	−	0.122326i
$638$	−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
$643$	−19.6155	+	5.25595i	−0.773559	+	0.207274i	−0.623943	−	0.781470i	$-0.714470\pi$
$643$	−19.6155	+	5.25595i	−0.773559	+	0.207274i	−0.149616	+	0.988744i	$0.547804\pi$
$644$	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	−0.987974	−	0.154619i	$-0.950585\pi$
$647$	−29.0632	−	29.0632i	−1.14259	−	1.14259i	−0.154619	−	0.987974i	$-0.549415\pi$
$648$		0			0
$649$		−	5.31632i		−	0.208684i
$650$		0			0
$651$		0			0
$652$	3.54385	+	13.2258i	0.138788	+	0.517963i
$653$	0.736931	+	2.75027i	0.0288384	+	0.107626i	0.978845	−	0.204604i	$-0.0655906\pi$
$653$	0.736931	+	2.75027i	0.0288384	+	0.107626i	−0.950006	+	0.312230i	$0.898924\pi$
$654$		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	$0.0957928\pi$
$659$	18.8486	+	32.6467i	0.734236	+	1.27173i	−0.220822	+	0.975314i	$0.570874\pi$
$660$		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	$0.120835\pi$
$662$	24.9459	−	6.68424i	0.969551	−	0.259791i
$663$		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
$668$	−4.93579	−	1.32254i	−0.190971	−	0.0511707i
$669$		0			0
$670$		0			0
$671$	−14.9193	−	8.61365i	−0.575953	−	0.332526i
$672$		0			0
$673$	−1.84460	+	6.88414i	−0.0711041	+	0.265364i	−0.992322	−	0.123684i	$-0.960529\pi$
$673$	−1.84460	+	6.88414i	−0.0711041	+	0.265364i	0.921218	+	0.389048i	$0.127196\pi$
$674$	−32.0820			−1.23575
$675$		0			0
$676$	−3.53614			−0.136005
$677$	2.16966	−	8.09727i	0.0833867	−	0.311203i	−0.911617	−	0.411040i	$-0.865166\pi$
$677$	2.16966	−	8.09727i	0.0833867	−	0.311203i	0.995004	+	0.0998372i	$0.0318322\pi$
$678$		0			0
$679$	−17.5722	−	10.1453i	−0.674358	−	0.389341i
$680$		0			0
$681$		0			0
$682$	−13.2725	−	3.55635i	−0.508229	−	0.136180i
$683$	−15.8873	+	15.8873i	−0.607911	+	0.607911i	−0.942400	−	0.334488i	$-0.891436\pi$
$683$	−15.8873	+	15.8873i	−0.607911	+	0.607911i	0.334488	+	0.942400i	$0.391436\pi$
$684$		0			0
$685$		0			0
$686$	17.3478	−	10.0158i	0.662342	−	0.382403i
$687$		0			0
$688$	−9.09714	+	2.43757i	−0.346825	+	0.0929315i
$689$	−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
$697$	6.11718	+	22.8296i	0.231705	+	0.864734i
$698$	3.99695	+	14.9168i	0.151287	+	0.564610i
$699$		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
$707$	−9.19953	+	2.46501i	−0.345984	+	0.0927062i
$708$		0			0
$709$	−20.4846	+	11.8268i	−0.769316	+	0.444165i	−0.832631	−	0.553829i	$-0.813166\pi$
$709$	−20.4846	+	11.8268i	−0.769316	+	0.444165i	0.0633143	+	0.997994i	$0.479833\pi$
$710$		0			0
$711$		0			0
$712$	1.44949	−	1.44949i	0.0543219	−	0.0543219i
$713$	−42.2329	−	11.3163i	−1.58163	−	0.423798i
$714$		0			0
$715$		0			0
$716$	−2.36794	−	1.36713i	−0.0884942	−	0.0510921i
$717$		0			0
$718$	−0.878601	+	3.27899i	−0.0327891	+	0.122371i
$719$	−21.3695			−0.796947			−0.398473	−	0.917180i	$-0.630460\pi$
$719$	−21.3695			−0.796947			−0.398473	+	0.917180i	$0.630460\pi$
$720$		0			0
$721$	−8.07679			−0.300795
$722$	1.35990	−	5.07522i	0.0506102	−	0.188880i
$723$		0			0
$724$	19.6658	+	11.3541i	0.730874	+	0.421970i
$725$		0			0
$726$		0			0
$727$	−2.97151	−	0.796213i	−0.110207	−	0.0295299i	0.203294	−	0.979118i	$-0.434835\pi$
$727$	−2.97151	−	0.796213i	−0.110207	−	0.0295299i	−0.313501	+	0.949588i	$0.601502\pi$
$728$	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
$733$	−23.5366	+	6.30661i	−0.869343	+	0.232940i	−0.665804	−	0.746127i	$-0.731911\pi$
$733$	−23.5366	+	6.30661i	−0.869343	+	0.232940i	−0.203540	+	0.979067i	$0.565245\pi$
$734$	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	$-0.966638\pi$
$739$		−	5.68805i		−	0.209238i	0.994512	−	0.104619i	$-0.0333624\pi$
$740$		0			0
$741$		0			0
$742$	−5.18917	−	19.3663i	−0.190500	−	0.710958i
$743$	−4.04871	−	15.1100i	−0.148533	−	0.554332i	−0.999573	−	0.0292311i	$-0.990694\pi$
$743$	−4.04871	−	15.1100i	−0.148533	−	0.554332i	0.851040	−	0.525101i	$-0.175973\pi$
$744$		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	$0.877229\pi$
$752$	7.49533	−	2.00837i	0.273327	−	0.0732376i
$753$		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	−0.986963	−	0.160950i	$-0.948544\pi$
$757$	−22.7266	+	22.7266i	−0.826013	+	0.826013i	0.160950	+	0.986963i	$0.448544\pi$
$758$	−29.1055	−	7.79880i	−1.05716	−	0.283265i
$759$		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
$763$	2.27225	−	8.48016i	0.0822611	−	0.307002i
$764$	−1.28350			−0.0464353
$765$		0			0
$766$	−17.1481			−0.619587
$767$	2.84099	−	10.6027i	0.102582	−	0.382842i
$768$		0			0
$769$	−29.3558	−	16.9486i	−1.05860	−	0.611180i	−0.133552	−	0.991042i	$-0.542638\pi$
$769$	−29.3558	−	16.9486i	−1.05860	−	0.611180i	−0.925043	+	0.379861i	$0.875972\pi$
$770$		0			0
$771$		0			0
$772$	−5.28063	−	1.41494i	−0.190054	−	0.0509248i
$773$	30.1093	−	30.1093i	1.08296	−	1.08296i	0.0867231	−	0.996232i	$-0.472360\pi$
$773$	30.1093	−	30.1093i	1.08296	−	1.08296i	0.996232	−	0.0867231i	$-0.0276395\pi$
$774$		0			0
$775$		0			0
$776$	−8.71386	+	5.03095i	−0.312809	+	0.180601i
$777$		0			0
$778$	29.1844	−	7.81993i	1.04631	−	0.280358i
$779$	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
$787$	−2.73876	−	10.2212i	−0.0976263	−	0.364346i	0.899778	−	0.436347i	$-0.143728\pi$
$787$	−2.73876	−	10.2212i	−0.0976263	−	0.364346i	−0.997405	+	0.0720011i	$0.977061\pi$
$788$	−4.40644	−	16.4450i	−0.156973	−	0.585831i
$789$		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
$797$	−13.1409	+	3.52110i	−0.465476	+	0.124724i	−0.483932	−	0.875106i	$-0.660792\pi$
$797$	−13.1409	+	3.52110i	−0.465476	+	0.124724i	0.0184558	+	0.999830i	$0.494125\pi$
$798$		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
$803$	−3.09199	−	0.828496i	−0.109114	−	0.0292370i
$804$		0			0
$805$		0			0
$806$	−24.5697	−	14.1853i	−0.865432	−	0.499657i
$807$		0			0
$808$	−1.22237	+	4.56196i	−0.0430029	+	0.160489i
$809$	−33.4429			−1.17579			−0.587895	−	0.808937i	$-0.700043\pi$
$809$	−33.4429			−1.17579			−0.587895	+	0.808937i	$0.700043\pi$
$810$		0			0
$811$	21.1960			0.744294			0.372147	−	0.928174i	$-0.378622\pi$
$811$	21.1960			0.744294			0.372147	+	0.928174i	$0.378622\pi$
$812$	3.91303	−	14.6036i	0.137320	−	0.512487i
$813$		0			0
$814$	10.2924	+	5.94230i	0.360747	+	0.208278i
$815$		0			0
$816$		0			0
$817$	−33.7279	−	9.03736i	−1.17999	−	0.316177i
$818$	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
$823$	24.6311	−	6.59989i	0.858588	−	0.230058i	0.197441	−	0.980315i	$-0.436737\pi$
$823$	24.6311	−	6.59989i	0.858588	−	0.230058i	0.661146	+	0.750257i	$0.270070\pi$
$824$	−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	$-0.164600\pi$
$827$	10.7808	+	10.7808i	0.374885	+	0.374885i	−0.494368	+	0.869253i	$0.664600\pi$
$828$		0			0
$829$			4.02079i			0.139648i	0.997559	+	0.0698239i	$0.0222437\pi$
$829$			4.02079i			0.139648i	−0.997559	+	0.0698239i	$0.977756\pi$
$830$		0			0
$831$		0			0
$832$	−1.05248	−	3.92790i	−0.0364881	−	0.136176i
$833$	2.53262	+	9.45186i	0.0877500	+	0.327488i
$834$		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	$0.0301196\pi$
$839$	16.7880	+	29.0777i	0.579588	+	1.00388i	−0.415939	+	0.909393i	$0.636547\pi$
$840$		0			0
$841$	−13.6044	+	23.5635i	−0.469118	+	0.812536i
$842$	−23.6637	+	6.34068i	−0.815506	+	0.218514i
$843$		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
$848$	−9.60353	−	2.57326i	−0.329786	−	0.0883660i
$849$		0			0
$850$		0			0
$851$	32.7503	+	18.9084i	1.12266	+	0.648171i
$852$		0			0
$853$	6.15572	−	22.9734i	0.210768	−	0.786596i	−0.776846	−	0.629691i	$-0.783182\pi$
$853$	6.15572	−	22.9734i	0.210768	−	0.786596i	0.987614	−	0.156905i	$-0.0501517\pi$
$854$	17.6391			0.603599
$855$		0			0
$856$	−7.64094			−0.261162
$857$	3.06736	−	11.4475i	0.104779	−	0.391040i	−0.893541	−	0.448981i	$-0.851787\pi$
$857$	3.06736	−	11.4475i	0.104779	−	0.391040i	0.998320	+	0.0579412i	$0.0184536\pi$
$858$		0			0
$859$	34.6670	+	20.0150i	1.18282	+	0.682904i	0.956666	−	0.291187i	$-0.0940501\pi$
$859$	34.6670	+	20.0150i	1.18282	+	0.682904i	0.226158	+	0.974091i	$0.427383\pi$
$860$		0			0
$861$		0			0
$862$	5.89894	+	1.58062i	0.200919	+	0.0538360i
$863$	−1.78680	+	1.78680i	−0.0608233	+	0.0608233i	−0.736864	−	0.676041i	$-0.763694\pi$
$863$	−1.78680	+	1.78680i	−0.0608233	+	0.0608233i	0.676041	+	0.736864i	$0.263694\pi$
$864$		0			0
$865$		0			0
$866$	−12.5665	+	7.25527i	−0.427027	+	0.246544i
$867$		0			0
$868$	13.5897	−	3.64136i	0.461266	−	0.123596i
$869$	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
$877$	1.78537	+	6.66309i	0.0602876	+	0.224996i	0.989496	−	0.144559i	$-0.0461765\pi$
$877$	1.78537	+	6.66309i	0.0602876	+	0.224996i	−0.929208	+	0.369556i	$0.879510\pi$
$878$	0.587569	+	2.19284i	0.0198295	+	0.0740047i
$879$		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	0.835569	−	0.549385i	$-0.185138\pi$
$883$	8.50404	+	8.50404i	0.286184	+	0.286184i	−0.549385	+	0.835569i	$0.685138\pi$
$884$	6.78245	+	11.7476i	0.228119	+	0.395113i
$885$		0			0
$886$	13.9099	−	24.0927i	0.467313	−	0.809410i
$887$	−17.2055	+	4.61020i	−0.577705	+	0.154796i	−0.535828	−	0.844327i	$-0.680000\pi$
$887$	−17.2055	+	4.61020i	−0.577705	+	0.154796i	−0.0418769	+	0.999123i	$0.513334\pi$
$888$		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
$893$	27.7891	+	7.44607i	0.929928	+	0.249173i
$894$		0			0
$895$		0			0
$896$	1.74641	+	1.00829i	0.0583434	+	0.0336846i
$897$		0			0
$898$	3.04660	−	11.3701i	0.101666	−	0.379424i
$899$	−52.3064			−1.74452
$900$		0			0
$901$	33.1655			1.10490
$902$	−3.61166	+	13.4789i	−0.120255	+	0.448798i
$903$		0			0
$904$	−2.56825	−	1.48278i	−0.0854188	−	0.0493166i
$905$		0			0
$906$		0			0
$907$	1.21188	+	0.324723i	0.0402399	+	0.0107822i	0.278883	−	0.960325i	$-0.410036\pi$
$907$	1.21188	+	0.324723i	0.0402399	+	0.0107822i	−0.238643	+	0.971107i	$0.576703\pi$
$908$	−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
$913$	−3.24117	+	0.868470i	−0.107267	+	0.0287422i
$914$	−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	$-0.646511\pi$
$919$		−	54.3202i		−	1.79186i	0.444196	−	0.895930i	$-0.353489\pi$
$920$		0			0
$921$		0			0
$922$	−0.783607	−	2.92446i	−0.0258067	−	0.0963121i
$923$	−5.98314	−	22.3294i	−0.196938	−	0.734981i
$924$		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	0.998798	−	0.0490228i	$-0.0156107\pi$
$929$	13.9274	+	24.1230i	0.456944	+	0.791450i	−0.541854	+	0.840473i	$0.682277\pi$
$930$		0			0
$931$	5.43786	−	9.41865i	0.178219	−	0.308684i
$932$	−20.5712	+	5.51203i	−0.673831	+	0.180553i
$933$		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	−0.375481	−	0.926830i	$-0.622523\pi$
$937$	16.8770	−	16.8770i	0.551349	−	0.551349i	0.926830	+	0.375481i	$0.122523\pi$
$938$	16.5014	+	4.42152i	0.538788	+	0.144368i
$939$		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
$943$	−11.4923	+	42.8898i	−0.374240	+	1.39668i
$944$	2.69933			0.0878558
$945$		0			0
$946$	18.5488			0.603074
$947$	3.08335	−	11.5072i	0.100195	−	0.373934i	−0.897560	−	0.440891i	$-0.854662\pi$
$947$	3.08335	−	11.5072i	0.100195	−	0.373934i	0.997756	+	0.0669572i	$0.0213291\pi$
$948$		0			0
$949$	−5.72383	−	3.30466i	−0.185804	−	0.107274i
$950$		0			0
$951$		0			0
$952$	−6.49768	−	1.74105i	−0.210591	−	0.0564277i
$953$	−13.4723	+	13.4723i	−0.436411	+	0.436411i	−0.890802	−	0.454391i	$-0.849857\pi$
$953$	−13.4723	+	13.4723i	−0.436411	+	0.436411i	0.454391	+	0.890802i	$0.349857\pi$
$954$		0			0
$955$		0			0
$956$	−9.40038	+	5.42731i	−0.304030	+	0.175532i
$957$		0			0
$958$	−32.0130	+	8.57785i	−1.03429	+	0.277138i
$959$	−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
$967$	2.40036	+	8.95826i	0.0771904	+	0.288078i	0.993721	−	0.111886i	$-0.0356892\pi$
$967$	2.40036	+	8.95826i	0.0771904	+	0.288078i	−0.916531	+	0.399964i	$0.869022\pi$
$968$	−1.84307	−	6.87844i	−0.0592386	−	0.221081i
$969$		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
$977$	23.7190	−	6.35548i	0.758837	−	0.203330i	0.141403	−	0.989952i	$-0.454839\pi$
$977$	23.7190	−	6.35548i	0.758837	−	0.203330i	0.617434	+	0.786622i	$0.288172\pi$
$978$		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
$983$	40.0954	+	10.7435i	1.27885	+	0.342666i	0.833414	−	0.552650i	$-0.186383\pi$
$983$	40.0954	+	10.7435i	1.27885	+	0.342666i	0.445433	+	0.895316i	$0.353050\pi$
$984$		0			0
$985$		0			0
$986$	21.6587	+	12.5047i	0.689754	+	0.398230i
$987$		0			0
$988$	3.90209	−	14.5628i	0.124142	−	0.463305i
$989$	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	$0.302481\pi$
$992$	1.80571	−	6.73901i	0.0573315	−	0.213964i
$993$		0			0
$994$	9.92800	+	5.73193i	0.314897	+	0.181806i
$995$		0			0
$996$		0			0
$997$	11.5550	+	3.09617i	0.365952	+	0.0980565i	0.437109	−	0.899409i	$-0.356002\pi$
$997$	11.5550	+	3.09617i	0.365952	+	0.0980565i	−0.0711569	+	0.997465i	$0.522669\pi$
$998$	−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.1043.3		16
3.2	odd	2		450.2.p.h.293.1		16
5.2	odd	4	inner	1350.2.q.h.557.4		16
5.3	odd	4		270.2.m.b.17.2		16
5.4	even	2		270.2.m.b.233.2		16
9.2	odd	6	inner	1350.2.q.h.143.4		16
9.7	even	3		450.2.p.h.443.1		16
15.2	even	4		450.2.p.h.257.1		16
15.8	even	4		90.2.l.b.77.4	yes	16
15.14	odd	2		90.2.l.b.23.4	✓	16
45.2	even	12	inner	1350.2.q.h.1007.3		16
45.4	even	6		810.2.f.c.323.2		16
45.7	odd	12		450.2.p.h.407.1		16
45.13	odd	12		810.2.f.c.647.7		16
45.14	odd	6		810.2.f.c.323.7		16
45.23	even	12		810.2.f.c.647.2		16
45.29	odd	6		270.2.m.b.143.2		16
45.34	even	6		90.2.l.b.83.4	yes	16
45.38	even	12		270.2.m.b.197.2		16
45.43	odd	12		90.2.l.b.47.4	yes	16
60.23	odd	4		720.2.cu.b.257.2		16
60.59	even	2		720.2.cu.b.113.1		16
180.43	even	12		720.2.cu.b.497.1		16
180.79	odd	6		720.2.cu.b.353.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.4	✓	16	15.14	odd	2
90.2.l.b.47.4	yes	16	45.43	odd	12
90.2.l.b.77.4	yes	16	15.8	even	4
90.2.l.b.83.4	yes	16	45.34	even	6
270.2.m.b.17.2		16	5.3	odd	4
270.2.m.b.143.2		16	45.29	odd	6
270.2.m.b.197.2		16	45.38	even	12
270.2.m.b.233.2		16	5.4	even	2
450.2.p.h.257.1		16	15.2	even	4
450.2.p.h.293.1		16	3.2	odd	2
450.2.p.h.407.1		16	45.7	odd	12
450.2.p.h.443.1		16	9.7	even	3
720.2.cu.b.113.1		16	60.59	even	2
720.2.cu.b.257.2		16	60.23	odd	4
720.2.cu.b.353.2		16	180.79	odd	6
720.2.cu.b.497.1		16	180.43	even	12
810.2.f.c.323.2		16	45.4	even	6
810.2.f.c.323.7		16	45.14	odd	6
810.2.f.c.647.2		16	45.23	even	12
810.2.f.c.647.7		16	45.13	odd	12
1350.2.q.h.143.4		16	9.2	odd	6	inner
1350.2.q.h.557.4		16	5.2	odd	4	inner
1350.2.q.h.1007.3		16	45.2	even	12	inner
1350.2.q.h.1043.3		16	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-1.94786 - 0.521929i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-1.94786 - 0.521929i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.70563 - 0.984748i) q^{11} +(3.92790 - 1.05248i) q^{13} +(-1.00829 + 1.74641i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-2.35877 - 2.35877i) q^{17} +3.70753i q^{19} +(-0.509743 - 1.90239i) q^{22} +(-1.62200 - 6.05338i) q^{23} -4.06647i q^{26} +(1.42594 + 1.42594i) q^{28} +(-3.74863 - 6.49281i) q^{29} +(3.48837 - 6.04204i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-2.88889 + 1.66790i) q^{34} +(-4.26692 + 4.26692i) q^{37} +(3.58120 + 0.959578i) q^{38} +(-6.13601 - 3.54263i) q^{41} +(-2.43757 + 9.09714i) q^{43} -1.96950 q^{44} -6.26692 q^{46} +(2.00837 - 7.49533i) q^{47} +(-2.54041 - 1.46671i) q^{49} +(-3.92790 - 1.05248i) q^{52} +(-7.03027 + 7.03027i) q^{53} +(1.74641 - 1.00829i) q^{56} +(-7.24179 + 1.94043i) q^{58} +(1.34967 - 2.33769i) q^{59} +(-4.37353 - 7.57518i) q^{61} +(-4.93330 - 4.93330i) q^{62} -1.00000i q^{64} +(-2.19259 - 8.18285i) q^{67} +(0.863368 + 3.22213i) q^{68} -5.68481i q^{71} +(-1.14928 - 1.14928i) q^{73} +(3.01717 + 5.22589i) q^{74} +(1.85376 - 3.21081i) q^{76} +(-3.83631 + 1.02794i) q^{77} +(10.0535 - 5.80440i) q^{79} +(-5.01003 + 5.01003i) q^{82} +(-1.64569 - 0.440961i) q^{83} +(8.15627 + 4.70902i) q^{86} +(-0.509743 + 1.90239i) q^{88} -2.04989 q^{89} -8.20034 q^{91} +(-1.62200 + 6.05338i) q^{92} +(-6.72013 - 3.87987i) q^{94} +(9.71905 + 2.60421i) q^{97} +(-2.07424 + 2.07424i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} + 8 q^{16} - 8 q^{22} - 24 q^{23} + 16 q^{28} - 8 q^{31} + 24 q^{38} - 24 q^{41} - 32 q^{46} + 48 q^{47} - 24 q^{56} - 16 q^{58} - 24 q^{61} + 16 q^{67} - 24 q^{68} - 16 q^{73} + 16 q^{76} - 72 q^{77} + 16 q^{82} + 48 q^{83} + 48 q^{86} - 8 q^{88} - 24 q^{92} + 48 q^{97}+O(q^{100}) \) 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

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