LMFDB - Embedded newform 1350.2.q.h.1043.4

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			1043.4
Root			$0.500000 - 2.74530i$ of defining polynomial
Character	$\chi$	$=$	1350.1043
Dual form			1350.2.q.h.1007.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(2.56188 + 0.686453i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-4.15512 + 2.39896i) q^{11} +(-0.581838 + 0.155903i) q^{13} +(1.32613 - 2.29692i) q^{14} +(0.500000 + 0.866025i) q^{16} +(4.40865 + 4.40865i) q^{17} +5.19145i q^{19} +(1.24179 + 4.63444i) q^{22} +(-0.681226 - 2.54237i) q^{23} +0.602363i q^{26} +(-1.87542 - 1.87542i) q^{28} +(0.920201 + 1.59383i) q^{29} +(-2.03888 + 3.53145i) q^{31} +(0.965926 - 0.258819i) q^{32} +(5.39948 - 3.11739i) q^{34} +(-0.632057 + 0.632057i) q^{37} +(5.01456 + 1.34365i) q^{38} +(5.58550 + 3.22479i) q^{41} +(0.644420 - 2.40501i) q^{43} +4.79792 q^{44} -2.63206 q^{46} +(-1.02538 + 3.82678i) q^{47} +(0.0298240 + 0.0172189i) q^{49} +(0.581838 + 0.155903i) q^{52} +(-1.31215 + 1.31215i) q^{53} +(-2.29692 + 1.32613i) q^{56} +(1.77769 - 0.476331i) q^{58} +(0.0645473 - 0.111799i) q^{59} +(6.27251 + 10.8643i) q^{61} +(2.88341 + 2.88341i) q^{62} -1.00000i q^{64} +(-2.85782 - 10.6655i) q^{67} +(-1.61368 - 6.02233i) q^{68} +10.4203i q^{71} +(-3.30021 - 3.30021i) q^{73} +(0.446932 + 0.774109i) q^{74} +(2.59573 - 4.49593i) q^{76} +(-12.2917 + 3.29355i) q^{77} +(3.62792 - 2.09458i) q^{79} +(4.56054 - 4.56054i) q^{82} +(11.1098 + 2.97686i) q^{83} +(-2.15627 - 1.24492i) q^{86} +(1.24179 - 4.63444i) q^{88} -2.04989 q^{89} -1.59762 q^{91} +(-0.681226 + 2.54237i) q^{92} +(3.43100 + 1.98089i) q^{94} +(16.7115 + 4.47782i) q^{97} +(0.0243512 - 0.0243512i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

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

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
$7$	2.56188	+	0.686453i	0.968299	+	0.259455i	0.708109	−	0.706103i	$-0.249548\pi$
$7$	2.56188	+	0.686453i	0.968299	+	0.259455i	0.260189	+	0.965558i	$0.416215\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$		0			0
$11$	−4.15512	+	2.39896i	−1.25282	+	0.723314i	−0.971668	−	0.236350i	$-0.924049\pi$
$11$	−4.15512	+	2.39896i	−1.25282	+	0.723314i	−0.281149	+	0.959664i	$0.590715\pi$
$12$		0			0
$13$	−0.581838	+	0.155903i	−0.161373	+	0.0432397i	−0.338601	−	0.940930i	$-0.609954\pi$
$13$	−0.581838	+	0.155903i	−0.161373	+	0.0432397i	0.177228	+	0.984170i	$0.443287\pi$
$14$	1.32613	−	2.29692i	0.354422	−	0.613877i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	4.40865	+	4.40865i	1.06926	+	1.06926i	0.997416	+	0.0718393i	$0.0228869\pi$
$17$	4.40865	+	4.40865i	1.06926	+	1.06926i	0.0718393	+	0.997416i	$0.477113\pi$
$18$		0			0
$19$			5.19145i			1.19100i	0.803355	+	0.595501i	$0.203046\pi$
$19$			5.19145i			1.19100i	−0.803355	+	0.595501i	$0.796954\pi$
$20$		0			0
$21$		0			0
$22$	1.24179	+	4.63444i	0.264751	+	0.988065i
$23$	−0.681226	−	2.54237i	−0.142046	−	0.530121i	−0.999869	−	0.0161770i	$-0.994850\pi$
$23$	−0.681226	−	2.54237i	−0.142046	−	0.530121i	0.857824	−	0.513944i	$-0.171816\pi$
$24$		0			0
$25$		0			0
$26$			0.602363i			0.118133i
$27$		0			0
$28$	−1.87542	−	1.87542i	−0.354422	−	0.354422i
$29$	0.920201	+	1.59383i	0.170877	+	0.295968i	0.938727	−	0.344662i	$-0.112007\pi$
$29$	0.920201	+	1.59383i	0.170877	+	0.295968i	−0.767850	+	0.640630i	$0.778673\pi$
$30$		0			0
$31$	−2.03888	+	3.53145i	−0.366194	+	0.634266i	−0.988967	−	0.148136i	$-0.952673\pi$
$31$	−2.03888	+	3.53145i	−0.366194	+	0.634266i	0.622773	+	0.782402i	$0.286006\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$		0			0
$34$	5.39948	−	3.11739i	0.926002	−	0.534628i
$35$		0			0
$36$		0			0
$37$	−0.632057	+	0.632057i	−0.103910	+	0.103910i	−0.757150	−	0.653241i	$-0.773409\pi$
$37$	−0.632057	+	0.632057i	−0.103910	+	0.103910i	0.653241	+	0.757150i	$0.273409\pi$
$38$	5.01456	+	1.34365i	0.813469	+	0.217968i
$39$		0			0
$40$		0			0
$41$	5.58550	+	3.22479i	0.872309	+	0.503628i	0.868115	−	0.496363i	$-0.165332\pi$
$41$	5.58550	+	3.22479i	0.872309	+	0.503628i	0.00419400	+	0.999991i	$0.498665\pi$
$42$		0			0
$43$	0.644420	−	2.40501i	0.0982731	−	0.366760i	−0.899222	−	0.437492i	$-0.855867\pi$
$43$	0.644420	−	2.40501i	0.0982731	−	0.366760i	0.997495	+	0.0707320i	$0.0225335\pi$
$44$	4.79792			0.723314
$45$		0			0
$46$	−2.63206			−0.388076
$47$	−1.02538	+	3.82678i	−0.149568	+	0.558194i	0.849942	+	0.526876i	$0.176637\pi$
$47$	−1.02538	+	3.82678i	−0.149568	+	0.558194i	−0.999509	+	0.0313173i	$0.990030\pi$
$48$		0			0
$49$	0.0298240	+	0.0172189i	0.00426058	+	0.00245984i
$50$		0			0
$51$		0			0
$52$	0.581838	+	0.155903i	0.0806865	+	0.0216199i
$53$	−1.31215	+	1.31215i	−0.180237	+	0.180237i	−0.791459	−	0.611222i	$-0.790678\pi$
$53$	−1.31215	+	1.31215i	−0.180237	+	0.180237i	0.611222	+	0.791459i	$0.290678\pi$
$54$		0			0
$55$		0			0
$56$	−2.29692	+	1.32613i	−0.306938	+	0.177211i
$57$		0			0
$58$	1.77769	−	0.476331i	0.233422	−	0.0625453i
$59$	0.0645473	−	0.111799i	0.00840334	−	0.0145550i	−0.861793	−	0.507260i	$-0.830658\pi$
$59$	0.0645473	−	0.111799i	0.00840334	−	0.0145550i	0.870196	+	0.492705i	$0.163992\pi$
$60$		0			0
$61$	6.27251	+	10.8643i	0.803113	+	1.39103i	0.917558	+	0.397603i	$0.130158\pi$
$61$	6.27251	+	10.8643i	0.803113	+	1.39103i	−0.114445	+	0.993430i	$0.536509\pi$
$62$	2.88341	+	2.88341i	0.366194	+	0.366194i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$		0			0
$67$	−2.85782	−	10.6655i	−0.349138	−	1.30300i	−0.887703	−	0.460416i	$-0.847700\pi$
$67$	−2.85782	−	10.6655i	−0.349138	−	1.30300i	0.538566	−	0.842584i	$-0.318966\pi$
$68$	−1.61368	−	6.02233i	−0.195687	−	0.730315i
$69$		0			0
$70$		0			0
$71$			10.4203i			1.23666i	0.785919	+	0.618329i	$0.212190\pi$
$71$			10.4203i			1.23666i	−0.785919	+	0.618329i	$0.787810\pi$
$72$		0			0
$73$	−3.30021	−	3.30021i	−0.386261	−	0.386261i	0.487091	−	0.873351i	$-0.338058\pi$
$73$	−3.30021	−	3.30021i	−0.386261	−	0.386261i	−0.873351	+	0.487091i	$0.838058\pi$
$74$	0.446932	+	0.774109i	0.0519548	+	0.0899883i
$75$		0			0
$76$	2.59573	−	4.49593i	0.297750	−	0.515719i
$77$	−12.2917	+	3.29355i	−1.40077	+	0.375335i
$78$		0			0
$79$	3.62792	−	2.09458i	0.408173	−	0.235659i	−0.281832	−	0.959464i	$-0.590942\pi$
$79$	3.62792	−	2.09458i	0.408173	−	0.235659i	0.690004	+	0.723805i	$0.257609\pi$
$80$		0			0
$81$		0			0
$82$	4.56054	−	4.56054i	0.503628	−	0.503628i
$83$	11.1098	+	2.97686i	1.21946	+	0.326753i	0.810466	−	0.585785i	$-0.199214\pi$
$83$	11.1098	+	2.97686i	1.21946	+	0.326753i	0.408992	+	0.912538i	$0.365881\pi$
$84$		0			0
$85$		0			0
$86$	−2.15627	−	1.24492i	−0.232517	−	0.134243i
$87$		0			0
$88$	1.24179	−	4.63444i	0.132376	−	0.494033i
$89$	−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
$91$	−1.59762			−0.167476
$92$	−0.681226	+	2.54237i	−0.0710228	+	0.265061i
$93$		0			0
$94$	3.43100	+	1.98089i	0.353881	+	0.204313i
$95$		0			0
$96$		0			0
$97$	16.7115	+	4.47782i	1.69679	+	0.454654i	0.972128	−	0.234450i	$-0.0753290\pi$
$97$	16.7115	+	4.47782i	1.69679	+	0.454654i	0.724663	+	0.689104i	$0.241996\pi$
$98$	0.0243512	−	0.0243512i	0.00245984	−	0.00245984i
$99$		0			0
$100$		0			0
$101$	10.3594	−	5.98097i	1.03079	−	0.595129i	0.113582	−	0.993529i	$-0.463768\pi$
$101$	10.3594	−	5.98097i	1.03079	−	0.595129i	0.917212	+	0.398399i	$0.130434\pi$
$102$		0			0
$103$	10.4055	−	2.78816i	1.02529	−	0.274725i	0.293285	−	0.956025i	$-0.405252\pi$
$103$	10.4055	−	2.78816i	1.02529	−	0.274725i	0.732004	+	0.681300i	$0.238585\pi$
$104$	0.301182	−	0.521662i	0.0295333	−	0.0511532i
$105$		0			0
$106$	0.927828	+	1.60704i	0.0901186	+	0.156090i
$107$	4.35367	+	4.35367i	0.420885	+	0.420885i	0.885508	−	0.464623i	$-0.153810\pi$
$107$	4.35367	+	4.35367i	0.420885	+	0.420885i	−0.464623	+	0.885508i	$0.653810\pi$
$108$		0			0
$109$		−	15.4546i		−	1.48028i	−0.672452	−	0.740141i	$-0.734759\pi$
$109$		−	15.4546i		−	1.48028i	0.672452	−	0.740141i	$-0.265241\pi$
$110$		0			0
$111$		0			0
$112$	0.686453	+	2.56188i	0.0648637	+	0.242075i
$113$	1.53568	+	5.73124i	0.144465	+	0.539150i	0.999779	+	0.0210396i	$0.00669762\pi$
$113$	1.53568	+	5.73124i	0.144465	+	0.539150i	−0.855314	+	0.518110i	$0.826636\pi$
$114$		0			0
$115$		0			0
$116$		−	1.84040i		−	0.170877i
$117$		0			0
$118$	−0.0912837	−	0.0912837i	−0.00840334	−	0.00840334i
$119$	8.26810	+	14.3208i	0.757935	+	1.31278i
$120$		0			0
$121$	6.01003	−	10.4097i	0.546367	−	0.946335i
$122$	12.1176	−	3.24689i	1.09707	−	0.293960i
$123$		0			0
$124$	3.53145	−	2.03888i	0.317133	−	0.183097i
$125$		0			0
$126$		0			0
$127$	−2.51837	+	2.51837i	−0.223469	+	0.223469i	−0.809957	−	0.586489i	$-0.800510\pi$
$127$	−2.51837	+	2.51837i	−0.223469	+	0.223469i	0.586489	+	0.809957i	$0.300510\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$		0			0
$130$		0			0
$131$	−11.3102	−	6.52997i	−0.988181	−	0.570526i	−0.0834508	−	0.996512i	$-0.526594\pi$
$131$	−11.3102	−	6.52997i	−0.988181	−	0.570526i	−0.904730	+	0.425985i	$0.859927\pi$
$132$		0			0
$133$	−3.56369	+	13.2999i	−0.309011	+	1.15325i
$134$	−11.0417			−0.953862
$135$		0			0
$136$	−6.23478			−0.534628
$137$	0.840942	−	3.13844i	0.0718465	−	0.268135i	−0.920653	−	0.390381i	$-0.872343\pi$
$137$	0.840942	−	3.13844i	0.0718465	−	0.268135i	0.992500	+	0.122246i	$0.0390098\pi$
$138$		0			0
$139$	−19.0478	−	10.9973i	−1.61561	−	0.932775i	−0.988036	−	0.154221i	$-0.950713\pi$
$139$	−19.0478	−	10.9973i	−1.61561	−	0.932775i	−0.627578	−	0.778554i	$-0.715953\pi$
$140$		0			0
$141$		0			0
$142$	10.0652	+	2.69696i	0.844653	+	0.226324i
$143$	2.04360	−	2.04360i	0.170895	−	0.170895i
$144$		0			0
$145$		0			0
$146$	−4.04192	+	2.33360i	−0.334512	+	0.193130i
$147$		0			0
$148$	0.863406	−	0.231349i	0.0709715	−	0.0190168i
$149$	−6.56668	+	11.3738i	−0.537964	+	0.931780i	0.461050	+	0.887374i	$0.347473\pi$
$149$	−6.56668	+	11.3738i	−0.537964	+	0.931780i	−0.999014	+	0.0444061i	$0.985860\pi$
$150$		0			0
$151$	−0.167899	−	0.290810i	−0.0136634	−	0.0236658i	0.859113	−	0.511786i	$-0.171016\pi$
$151$	−0.167899	−	0.290810i	−0.0136634	−	0.0236658i	−0.872776	+	0.488120i	$0.837683\pi$
$152$	−3.67091	−	3.67091i	−0.297750	−	0.297750i
$153$		0			0
$154$			12.7253i			1.02543i
$155$		0			0
$156$		0			0
$157$	1.17992	+	4.40352i	0.0941678	+	0.351439i	0.996892	−	0.0787808i	$-0.0251027\pi$
$157$	1.17992	+	4.40352i	0.0941678	+	0.351439i	−0.902724	+	0.430220i	$0.858436\pi$
$158$	−1.08423	−	4.04642i	−0.0862571	−	0.321916i
$159$		0			0
$160$		0			0
$161$		−	6.98088i		−	0.550170i
$162$		0			0
$163$	−9.01496	−	9.01496i	−0.706106	−	0.706106i	0.259608	−	0.965714i	$-0.416407\pi$
$163$	−9.01496	−	9.01496i	−0.706106	−	0.706106i	−0.965714	+	0.259608i	$0.916407\pi$
$164$	−3.22479	−	5.58550i	−0.251814	−	0.436154i
$165$		0			0
$166$	5.75085	−	9.96076i	0.446353	−	0.773105i
$167$	−0.00858342	+	0.00229992i	−0.000664205	+	0.000177973i	−0.259151	−	0.965837i	$-0.583443\pi$
$167$	−0.00858342	+	0.00229992i	−0.000664205	+	0.000177973i	0.258487	+	0.966015i	$0.416776\pi$
$168$		0			0
$169$	−10.9441	+	6.31858i	−0.841854	+	0.486045i
$170$		0			0
$171$		0			0
$172$	−1.76059	+	1.76059i	−0.134243	+	0.134243i
$173$	−10.0291	−	2.68729i	−0.762500	−	0.204311i	−0.143444	−	0.989658i	$-0.545818\pi$
$173$	−10.0291	−	2.68729i	−0.762500	−	0.204311i	−0.619056	+	0.785347i	$0.712484\pi$
$174$		0			0
$175$		0			0
$176$	−4.15512	−	2.39896i	−0.313204	−	0.180829i
$177$		0			0
$178$	−0.530550	+	1.98004i	−0.0397664	+	0.148410i
$179$	−1.46292			−0.109343			−0.0546717	−	0.998504i	$-0.517411\pi$
$179$	−1.46292			−0.109343			−0.0546717	+	0.998504i	$0.517411\pi$
$180$		0			0
$181$	−8.68576			−0.645607			−0.322804	−	0.946466i	$-0.604625\pi$
$181$	−8.68576			−0.645607			−0.322804	+	0.946466i	$0.604625\pi$
$182$	−0.413494	+	1.54318i	−0.0306502	+	0.114388i
$183$		0			0
$184$	2.27943	+	1.31603i	0.168042	+	0.0970189i
$185$		0			0
$186$		0			0
$187$	−28.8947	−	7.74231i	−2.11299	−	0.566174i
$188$	2.80140	−	2.80140i	0.204313	−	0.204313i
$189$		0			0
$190$		0			0
$191$	4.33795	−	2.50452i	0.313883	−	0.181220i	−0.334780	−	0.942296i	$-0.608662\pi$
$191$	4.33795	−	2.50452i	0.313883	−	0.181220i	0.648663	+	0.761076i	$0.275329\pi$
$192$		0			0
$193$	3.25355	−	0.871785i	0.234195	−	0.0627524i	−0.139812	−	0.990178i	$-0.544650\pi$
$193$	3.25355	−	0.871785i	0.234195	−	0.0627524i	0.374008	+	0.927426i	$0.377983\pi$
$194$	8.65048	−	14.9831i	0.621069	−	1.07572i
$195$		0			0
$196$	−0.0172189	−	0.0298240i	−0.00122992	−	0.00213029i
$197$	−15.5027	−	15.5027i	−1.10452	−	1.10452i	−0.993858	−	0.110665i	$-0.964702\pi$
$197$	−15.5027	−	15.5027i	−1.10452	−	1.10452i	−0.110665	−	0.993858i	$-0.535298\pi$
$198$		0			0
$199$			18.4607i			1.30864i	0.756217	+	0.654321i	$0.227045\pi$
$199$			18.4607i			1.30864i	−0.756217	+	0.654321i	$0.772955\pi$
$200$		0			0
$201$		0			0
$202$	−3.09598	−	11.5544i	−0.217832	−	0.812962i
$203$	1.26335	+	4.71488i	0.0886697	+	0.330920i
$204$		0			0
$205$		0			0
$206$		−	10.7726i		−	0.750564i
$207$		0			0
$208$	−0.425935	−	0.425935i	−0.0295333	−	0.0295333i
$209$	−12.4541	−	21.5711i	−0.861468	−	1.49211i
$210$		0			0
$211$	0.654465	−	1.13357i	0.0450552	−	0.0780380i	−0.842618	−	0.538511i	$-0.818987\pi$
$211$	0.654465	−	1.13357i	0.0450552	−	0.0780380i	0.887674	+	0.460473i	$0.152320\pi$
$212$	1.79243	−	0.480279i	0.123104	−	0.0329857i
$213$		0			0
$214$	5.33213	−	3.07851i	0.364497	−	0.210442i
$215$		0			0
$216$		0			0
$217$	−7.64754	+	7.64754i	−0.519149	+	0.519149i
$218$	−14.9280	−	3.99994i	−1.01105	−	0.270910i
$219$		0			0
$220$		0			0
$221$	−3.25245	−	1.87780i	−0.218783	−	0.126315i
$222$		0			0
$223$	−5.42903	+	20.2614i	−0.363555	+	1.35681i	0.505814	+	0.862643i	$0.331192\pi$
$223$	−5.42903	+	20.2614i	−0.363555	+	1.35681i	−0.869369	+	0.494163i	$0.835474\pi$
$224$	2.65225			0.177211
$225$		0			0
$226$	5.93342			0.394685
$227$	1.54126	−	5.75206i	0.102297	−	0.381778i	−0.895727	−	0.444604i	$-0.853345\pi$
$227$	1.54126	−	5.75206i	0.102297	−	0.381778i	0.998025	+	0.0628257i	$0.0200112\pi$
$228$		0			0
$229$	10.1822	+	5.87872i	0.672862	+	0.388477i	0.797160	−	0.603768i	$-0.206335\pi$
$229$	10.1822	+	5.87872i	0.672862	+	0.388477i	−0.124298	+	0.992245i	$0.539668\pi$
$230$		0			0
$231$		0			0
$232$	−1.77769	−	0.476331i	−0.116711	−	0.0312727i
$233$	13.4322	−	13.4322i	0.879973	−	0.879973i	−0.113558	−	0.993531i	$-0.536225\pi$
$233$	13.4322	−	13.4322i	0.879973	−	0.879973i	0.993531	+	0.113558i	$0.0362249\pi$
$234$		0			0
$235$		0			0
$236$	−0.111799	+	0.0645473i	−0.00727751	+	0.00420167i
$237$		0			0
$238$	15.9727	−	4.27988i	1.03536	−	0.277424i
$239$	2.27943	−	3.94809i	0.147444	−	0.255380i	−0.782838	−	0.622225i	$-0.786229\pi$
$239$	2.27943	−	3.94809i	0.147444	−	0.255380i	0.930282	+	0.366845i	$0.119562\pi$
$240$		0			0
$241$	8.03104	+	13.9102i	0.517325	+	0.896032i	0.999798	+	0.0201215i	$0.00640532\pi$
$241$	8.03104	+	13.9102i	0.517325	+	0.896032i	−0.482473	+	0.875911i	$0.660261\pi$
$242$	−8.49947	−	8.49947i	−0.546367	−	0.546367i
$243$		0			0
$244$		−	12.5450i		−	0.803113i
$245$		0			0
$246$		0			0
$247$	−0.809364	−	3.02059i	−0.0514986	−	0.192195i
$248$	−1.05540	−	3.93882i	−0.0670181	−	0.250115i
$249$		0			0
$250$		0			0
$251$			18.9981i			1.19915i	0.800319	+	0.599574i	$0.204663\pi$
$251$			18.9981i			1.19915i	−0.800319	+	0.599574i	$0.795337\pi$
$252$		0			0
$253$	8.92963	+	8.92963i	0.561401	+	0.561401i
$254$	1.78075	+	3.08436i	0.111734	+	0.193530i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.23709	−	0.867374i	0.201924	−	0.0541053i	−0.156439	−	0.987688i	$-0.550002\pi$
$257$	3.23709	−	0.867374i	0.201924	−	0.0541053i	0.358363	+	0.933582i	$0.383335\pi$
$258$		0			0
$259$	−2.05313	+	1.18538i	−0.127575	+	0.0736557i
$260$		0			0
$261$		0			0
$262$	−9.23478	+	9.23478i	−0.570526	+	0.570526i
$263$	−16.1748	−	4.33402i	−0.997380	−	0.267247i	−0.277032	−	0.960861i	$-0.589351\pi$
$263$	−16.1748	−	4.33402i	−0.997380	−	0.267247i	−0.720347	+	0.693614i	$0.756018\pi$
$264$		0			0
$265$		0			0
$266$	11.9243	+	6.88452i	0.731128	+	0.422117i
$267$		0			0
$268$	−2.85782	+	10.6655i	−0.174569	+	0.651500i
$269$	−0.535741			−0.0326647			−0.0163324	−	0.999867i	$-0.505199\pi$
$269$	−0.535741			−0.0326647			−0.0163324	+	0.999867i	$0.505199\pi$
$270$		0			0
$271$	−15.5412			−0.944063			−0.472032	−	0.881582i	$-0.656479\pi$
$271$	−15.5412			−0.944063			−0.472032	+	0.881582i	$0.656479\pi$
$272$	−1.61368	+	6.02233i	−0.0978437	+	0.365158i
$273$		0			0
$274$	−2.81385	−	1.62458i	−0.169991	−	0.0981442i
$275$		0			0
$276$		0			0
$277$	−16.7200	−	4.48011i	−1.00461	−	0.269184i	−0.281232	−	0.959640i	$-0.590743\pi$
$277$	−16.7200	−	4.48011i	−1.00461	−	0.269184i	−0.723374	+	0.690456i	$0.757410\pi$
$278$	−15.5525	+	15.5525i	−0.932775	+	0.932775i
$279$		0			0
$280$		0			0
$281$	20.8909	−	12.0613i	1.24624	−	0.719519i	0.275886	−	0.961190i	$-0.411029\pi$
$281$	20.8909	−	12.0613i	1.24624	−	0.719519i	0.970358	+	0.241671i	$0.0776955\pi$
$282$		0			0
$283$	−15.9876	+	4.28387i	−0.950365	+	0.254649i	−0.700517	−	0.713636i	$-0.747047\pi$
$283$	−15.9876	+	4.28387i	−0.950365	+	0.254649i	−0.249848	+	0.968285i	$0.580381\pi$
$284$	5.21013	−	9.02421i	0.309164	−	0.535489i
$285$		0			0
$286$	−1.44505	−	2.50289i	−0.0854474	−	0.147999i
$287$	12.0957	+	12.0957i	0.713987	+	0.713987i
$288$		0			0
$289$			21.8725i			1.28661i
$290$		0			0
$291$		0			0
$292$	1.20796	+	4.50818i	0.0706906	+	0.263821i
$293$	4.18032	+	15.6012i	0.244217	+	0.911431i	0.973775	+	0.227512i	$0.0730591\pi$
$293$	4.18032	+	15.6012i	0.244217	+	0.911431i	−0.729558	+	0.683919i	$0.760274\pi$
$294$		0			0
$295$		0			0
$296$		−	0.893864i		−	0.0519548i
$297$		0			0
$298$	9.28669	+	9.28669i	0.537964	+	0.537964i
$299$	0.792727	+	1.37304i	0.0458446	+	0.0794052i
$300$		0			0
$301$	3.30185	−	5.71897i	0.190315	−	0.329636i
$302$	−0.324356	+	0.0869109i	−0.0186646	+	0.00500116i
$303$		0			0
$304$	−4.49593	+	2.59573i	−0.257859	+	0.148875i
$305$		0			0
$306$		0			0
$307$	1.45642	−	1.45642i	0.0831222	−	0.0831222i	−0.664323	−	0.747445i	$-0.731280\pi$
$307$	1.45642	−	1.45642i	0.0831222	−	0.0831222i	0.747445	+	0.664323i	$0.231280\pi$
$308$	12.2917	+	3.29355i	0.700384	+	0.187667i
$309$		0			0
$310$		0			0
$311$	1.81462	+	1.04767i	0.102898	+	0.0594081i	0.550566	−	0.834792i	$-0.314412\pi$
$311$	1.81462	+	1.04767i	0.102898	+	0.0594081i	−0.447668	+	0.894200i	$0.647745\pi$
$312$		0			0
$313$	5.11217	−	19.0789i	0.288957	−	1.07840i	−0.656942	−	0.753941i	$-0.728150\pi$
$313$	5.11217	−	19.0789i	0.288957	−	1.07840i	0.945899	−	0.324461i	$-0.105183\pi$
$314$	4.55886			0.257271
$315$		0			0
$316$	−4.18916			−0.235659
$317$	8.82217	−	32.9248i	0.495503	−	1.84924i	−0.0316937	−	0.999498i	$-0.510090\pi$
$317$	8.82217	−	32.9248i	0.495503	−	1.84924i	0.527196	−	0.849743i	$-0.323243\pi$
$318$		0			0
$319$	−7.64709	−	4.41505i	−0.428155	−	0.247195i
$320$		0			0
$321$		0			0
$322$	−6.74301	−	1.80678i	−0.375773	−	0.100688i
$323$	−22.8873	+	22.8873i	−1.27348	+	1.27348i
$324$		0			0
$325$		0			0
$326$	−11.0410	+	6.37454i	−0.611506	+	0.353053i
$327$		0			0
$328$	−6.22982	+	1.66927i	−0.343984	+	0.0921703i
$329$	−5.25381	+	9.09987i	−0.289652	+	0.501692i
$330$		0			0
$331$	−12.0140	−	20.8088i	−0.660348	−	1.14376i	−0.980524	−	0.196399i	$-0.937075\pi$
$331$	−12.0140	−	20.8088i	−0.660348	−	1.14376i	0.320176	−	0.947358i	$-0.396258\pi$
$332$	−8.13293	−	8.13293i	−0.446353	−	0.446353i
$333$		0			0
$334$			0.00888621i			0.000486232i
$335$		0			0
$336$		0			0
$337$	−3.17090	−	11.8340i	−0.172730	−	0.644637i	−0.996927	−	0.0783338i	$-0.975040\pi$
$337$	−3.17090	−	11.8340i	−0.172730	−	0.644637i	0.824197	−	0.566303i	$-0.191627\pi$
$338$	3.27074	+	12.2066i	0.177905	+	0.663949i
$339$		0			0
$340$		0			0
$341$		−	19.5648i		−	1.05949i
$342$		0			0
$343$	−13.0634	−	13.0634i	−0.705357	−	0.705357i
$344$	1.24492	+	2.15627i	0.0671217	+	0.116258i
$345$		0			0
$346$	−5.19145	+	8.99186i	−0.279094	+	0.483405i
$347$	−17.9559	+	4.81127i	−0.963924	+	0.258283i	−0.706260	−	0.707952i	$-0.749619\pi$
$347$	−17.9559	+	4.81127i	−0.963924	+	0.258283i	−0.257663	+	0.966235i	$0.582953\pi$
$348$		0			0
$349$	27.2305	−	15.7215i	1.45761	−	0.841553i	0.458720	−	0.888581i	$-0.348308\pi$
$349$	27.2305	−	15.7215i	1.45761	−	0.841553i	0.998894	+	0.0470278i	$0.0149749\pi$
$350$		0			0
$351$		0			0
$352$	−3.39264	+	3.39264i	−0.180829	+	0.180829i
$353$	11.7440	+	3.14681i	0.625073	+	0.167488i	0.557433	−	0.830222i	$-0.311786\pi$
$353$	11.7440	+	3.14681i	0.625073	+	0.167488i	0.0676398	+	0.997710i	$0.478453\pi$
$354$		0			0
$355$		0			0
$356$	1.77526	+	1.02494i	0.0940883	+	0.0543219i
$357$		0			0
$358$	−0.378631	+	1.41307i	−0.0200112	+	0.0746830i
$359$	4.31606			0.227793			0.113896	−	0.993493i	$-0.463667\pi$
$359$	4.31606			0.227793			0.113896	+	0.993493i	$0.463667\pi$
$360$		0			0
$361$	−7.95119			−0.418484
$362$	−2.24804	+	8.38980i	−0.118154	+	0.440958i
$363$		0			0
$364$	1.38358	+	0.798810i	0.0725192	+	0.0418690i
$365$		0			0
$366$		0			0
$367$	19.2008	+	5.14485i	1.00228	+	0.268559i	0.722399	−	0.691477i	$-0.243040\pi$
$367$	19.2008	+	5.14485i	1.00228	+	0.268559i	0.279877	+	0.960036i	$0.409706\pi$
$368$	1.86115	−	1.86115i	0.0970189	−	0.0970189i
$369$		0			0
$370$		0			0
$371$	−4.26229	+	2.46083i	−0.221287	+	0.127760i
$372$		0			0
$373$	−2.53800	+	0.680056i	−0.131413	+	0.0352120i	−0.323926	−	0.946082i	$-0.605003\pi$
$373$	−2.53800	+	0.680056i	−0.131413	+	0.0352120i	0.192513	+	0.981294i	$0.438336\pi$
$374$	−14.9570	+	25.9063i	−0.773408	+	1.33958i
$375$		0			0
$376$	−1.98089	−	3.43100i	−0.102157	−	0.176940i
$377$	−0.783892	−	0.783892i	−0.0403725	−	0.0403725i
$378$		0			0
$379$			3.03124i			0.155705i	0.996965	+	0.0778523i	$0.0248063\pi$
$379$			3.03124i			0.155705i	−0.996965	+	0.0778523i	$0.975194\pi$
$380$		0			0
$381$		0			0
$382$	−1.29643	−	4.83835i	−0.0663313	−	0.247552i
$383$	−6.14717	−	22.9416i	−0.314106	−	1.17226i	−0.924819	−	0.380407i	$-0.875784\pi$
$383$	−6.14717	−	22.9416i	−0.314106	−	1.17226i	0.610713	−	0.791852i	$-0.290883\pi$
$384$		0			0
$385$		0			0
$386$		−	3.36832i		−	0.171443i
$387$		0			0
$388$	−12.2336	−	12.2336i	−0.621069	−	0.621069i
$389$	−3.33254	−	5.77213i	−0.168966	−	0.292659i	0.769090	−	0.639140i	$-0.220710\pi$
$389$	−3.33254	−	5.77213i	−0.168966	−	0.292659i	−0.938057	+	0.346482i	$0.887376\pi$
$390$		0			0
$391$	8.20515	−	14.2117i	0.414952	−	0.718718i
$392$	−0.0332644	+	0.00891317i	−0.00168011	+	0.000450183i
$393$		0			0
$394$	−18.9869	+	10.9621i	−0.956545	+	0.552261i
$395$		0			0
$396$		0			0
$397$	13.2242	−	13.2242i	0.663703	−	0.663703i	−0.292548	−	0.956251i	$-0.594503\pi$
$397$	13.2242	−	13.2242i	0.663703	−	0.663703i	0.956251	+	0.292548i	$0.0945031\pi$
$398$	17.8316	+	4.77797i	0.893819	+	0.239498i
$399$		0			0
$400$		0			0
$401$	−4.66934	−	2.69585i	−0.233176	−	0.134624i	0.378860	−	0.925454i	$-0.376316\pi$
$401$	−4.66934	−	2.69585i	−0.233176	−	0.134624i	−0.612036	+	0.790830i	$0.709649\pi$
$402$		0			0
$403$	0.635736	−	2.37260i	0.0316683	−	0.118188i
$404$	−11.9619			−0.595129
$405$		0			0
$406$	4.88121			0.242250
$407$	1.10999	−	4.14256i	0.0550204	−	0.205339i
$408$		0			0
$409$	−7.43574	−	4.29303i	−0.367674	−	0.212277i	0.304768	−	0.952427i	$-0.401421\pi$
$409$	−7.43574	−	4.29303i	−0.367674	−	0.212277i	−0.672442	+	0.740150i	$0.734754\pi$
$410$		0			0
$411$		0			0
$412$	−10.4055	−	2.78816i	−0.512644	−	0.137363i
$413$	0.242107	−	0.242107i	0.0119133	−	0.0119133i
$414$		0			0
$415$		0			0
$416$	−0.521662	+	0.301182i	−0.0255766	+	0.0147666i
$417$		0			0
$418$	−24.0595	+	6.44672i	−1.17679	+	0.315319i
$419$	−7.72749	+	13.3844i	−0.377512	+	0.653871i	−0.990700	−	0.136067i	$-0.956554\pi$
$419$	−7.72749	+	13.3844i	−0.377512	+	0.653871i	0.613187	+	0.789938i	$0.289887\pi$
$420$		0			0
$421$	9.45129	+	16.3701i	0.460628	+	0.797831i	0.998992	−	0.0448812i	$-0.0142909\pi$
$421$	9.45129	+	16.3701i	0.460628	+	0.797831i	−0.538364	+	0.842712i	$0.680958\pi$
$422$	−0.925553	−	0.925553i	−0.0450552	−	0.0450552i
$423$		0			0
$424$		−	1.85566i		−	0.0901186i
$425$		0			0
$426$		0			0
$427$	8.61157	+	32.1388i	0.416743	+	1.55531i
$428$	−1.59355	−	5.94722i	−0.0770273	−	0.287470i
$429$		0			0
$430$		0			0
$431$		−	3.91428i		−	0.188544i	−0.995546	−	0.0942720i	$-0.969948\pi$
$431$		−	3.91428i		−	0.188544i	0.995546	−	0.0942720i	$-0.0300523\pi$
$432$		0			0
$433$	27.2049	+	27.2049i	1.30738	+	1.30738i	0.923297	+	0.384086i	$0.125483\pi$
$433$	27.2049	+	27.2049i	1.30738	+	1.30738i	0.384086	+	0.923297i	$0.374517\pi$
$434$	5.40762	+	9.36628i	0.259574	+	0.449596i
$435$		0			0
$436$	−7.72730	+	13.3841i	−0.370070	+	0.640981i
$437$	13.1986	−	3.53656i	0.631375	−	0.169176i
$438$		0			0
$439$	−13.2725	+	7.66286i	−0.633460	+	0.365728i	−0.782091	−	0.623164i	$-0.785847\pi$
$439$	−13.2725	+	7.66286i	−0.633460	+	0.365728i	0.148631	+	0.988893i	$0.452513\pi$
$440$		0			0
$441$		0			0
$442$	−2.65561	+	2.65561i	−0.126315	+	0.126315i
$443$	−26.8719	−	7.20031i	−1.27672	−	0.342097i	−0.444120	−	0.895967i	$-0.646484\pi$
$443$	−26.8719	−	7.20031i	−1.27672	−	0.342097i	−0.832603	+	0.553870i	$0.813150\pi$
$444$		0			0
$445$		0			0
$446$	18.1659	+	10.4881i	0.860180	+	0.496625i
$447$		0			0
$448$	0.686453	−	2.56188i	0.0324319	−	0.121037i
$449$	24.3627			1.14975			0.574874	−	0.818242i	$-0.305051\pi$
$449$	24.3627			1.14975			0.574874	+	0.818242i	$0.305051\pi$
$450$		0			0
$451$	−30.9446			−1.45712
$452$	1.53568	−	5.73124i	0.0722324	−	0.269575i
$453$		0			0
$454$	−5.15716	−	2.97749i	−0.242037	−	0.139740i
$455$		0			0
$456$		0			0
$457$	12.6705	+	3.39506i	0.592702	+	0.158814i	0.542688	−	0.839935i	$-0.317407\pi$
$457$	12.6705	+	3.39506i	0.592702	+	0.158814i	0.0500141	+	0.998749i	$0.484073\pi$
$458$	8.31377	−	8.31377i	0.388477	−	0.388477i
$459$		0			0
$460$		0			0
$461$	−34.7684	+	20.0736i	−1.61933	+	0.934919i	−0.632233	+	0.774778i	$0.717861\pi$
$461$	−34.7684	+	20.0736i	−1.61933	+	0.934919i	−0.987094	+	0.160141i	$0.948805\pi$
$462$		0			0
$463$	11.5688	−	3.09986i	0.537649	−	0.144063i	0.0202307	−	0.999795i	$-0.493560\pi$
$463$	11.5688	−	3.09986i	0.537649	−	0.144063i	0.517418	+	0.855733i	$0.326893\pi$
$464$	−0.920201	+	1.59383i	−0.0427192	+	0.0739919i
$465$		0			0
$466$	−9.49800	−	16.4510i	−0.439986	−	0.762079i
$467$	8.63124	+	8.63124i	0.399406	+	0.399406i	0.878024	−	0.478617i	$-0.158862\pi$
$467$	8.63124	+	8.63124i	0.399406	+	0.399406i	−0.478617	+	0.878024i	$0.658862\pi$
$468$		0			0
$469$		−	29.2855i		−	1.35228i
$470$		0			0
$471$		0			0
$472$	0.0334121	+	0.124696i	0.00153792	+	0.00573959i
$473$	3.09188	+	11.5390i	0.142165	+	0.530565i
$474$		0			0
$475$		0			0
$476$		−	16.5362i		−	0.757935i
$477$		0			0
$478$	−3.22360	−	3.22360i	−0.147444	−	0.147444i
$479$	−5.13488	−	8.89388i	−0.234619	−	0.406372i	0.724543	−	0.689230i	$-0.242051\pi$
$479$	−5.13488	−	8.89388i	−0.234619	−	0.406372i	−0.959162	+	0.282858i	$0.908718\pi$
$480$		0			0
$481$	0.269215	−	0.466295i	0.0122752	−	0.0212612i
$482$	15.5148	−	4.15717i	0.706678	−	0.189354i
$483$		0			0
$484$	−10.4097	+	6.01003i	−0.473167	+	0.273183i
$485$		0			0
$486$		0			0
$487$	−17.5218	+	17.5218i	−0.793987	+	0.793987i	−0.982140	−	0.188153i	$-0.939750\pi$
$487$	−17.5218	+	17.5218i	−0.793987	+	0.793987i	0.188153	+	0.982140i	$0.439750\pi$
$488$	−12.1176	−	3.24689i	−0.548536	−	0.146980i
$489$		0			0
$490$		0			0
$491$	7.70100	+	4.44617i	0.347541	+	0.200653i	0.663602	−	0.748086i	$-0.269027\pi$
$491$	7.70100	+	4.44617i	0.347541	+	0.200653i	−0.316061	+	0.948739i	$0.602360\pi$
$492$		0			0
$493$	−2.96982	+	11.0835i	−0.133754	+	0.499176i
$494$	−3.12714			−0.140697
$495$		0			0
$496$	−4.07776			−0.183097
$497$	−7.15302	+	26.6954i	−0.320857	+	1.19745i
$498$		0			0
$499$	25.4186	+	14.6754i	1.13789	+	0.656963i	0.945908	−	0.324435i	$-0.105174\pi$
$499$	25.4186	+	14.6754i	1.13789	+	0.656963i	0.191985	+	0.981398i	$0.438507\pi$
$500$		0			0
$501$		0			0
$502$	18.3507	+	4.91707i	0.819034	+	0.219459i
$503$	10.0766	−	10.0766i	0.449293	−	0.449293i	−0.445826	−	0.895120i	$-0.647090\pi$
$503$	10.0766	−	10.0766i	0.449293	−	0.449293i	0.895120	+	0.445826i	$0.147090\pi$
$504$		0			0
$505$		0			0
$506$	10.9365	−	6.31420i	0.486188	−	0.280701i
$507$		0			0
$508$	3.44015	−	0.921786i	0.152632	−	0.0408976i
$509$	15.0024	−	25.9849i	0.664970	−	1.15176i	−0.314323	−	0.949316i	$-0.601777\pi$
$509$	15.0024	−	25.9849i	0.664970	−	1.15176i	0.979293	−	0.202446i	$-0.0648892\pi$
$510$		0			0
$511$	−6.18930	−	10.7202i	−0.273799	−	0.474233i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$		−	3.35128i		−	0.147819i
$515$		0			0
$516$		0			0
$517$	−4.91971	−	18.3606i	−0.216369	−	0.807499i
$518$	0.613596	+	2.28997i	0.0269598	+	0.100615i
$519$		0			0
$520$		0			0
$521$		−	6.40485i		−	0.280602i	−0.990109	−	0.140301i	$-0.955193\pi$
$521$		−	6.40485i		−	0.280602i	0.990109	−	0.140301i	$-0.0448070\pi$
$522$		0			0
$523$	−16.0596	−	16.0596i	−0.702237	−	0.702237i	0.262653	−	0.964890i	$-0.415403\pi$
$523$	−16.0596	−	16.0596i	−0.702237	−	0.702237i	−0.964890	+	0.262653i	$0.915403\pi$
$524$	6.52997	+	11.3102i	0.285263	+	0.494090i
$525$		0			0
$526$	−8.37268	+	14.5019i	−0.365066	+	0.632313i
$527$	−24.5576	+	6.58020i	−1.06975	+	0.286638i
$528$		0			0
$529$	13.9190	−	8.03614i	0.605174	−	0.349397i
$530$		0			0
$531$		0			0
$532$	9.73618	−	9.73618i	0.422117	−	0.422117i
$533$	−3.75261	−	1.00551i	−0.162544	−	0.0435535i
$534$		0			0
$535$		0			0
$536$	9.56244	+	5.52087i	0.413034	+	0.238465i
$537$		0			0
$538$	−0.138660	+	0.517486i	−0.00597806	+	0.0223104i
$539$	−0.165230			−0.00711696
$540$		0			0
$541$	44.6389			1.91917			0.959587	−	0.281412i	$-0.0908026\pi$
$541$	44.6389			1.91917			0.959587	+	0.281412i	$0.0908026\pi$
$542$	−4.02237	+	15.0117i	−0.172776	+	0.644807i
$543$		0			0
$544$	5.39948	+	3.11739i	0.231501	+	0.133657i
$545$		0			0
$546$		0			0
$547$	−5.15053	−	1.38008i	−0.220221	−	0.0590080i	0.147022	−	0.989133i	$-0.453031\pi$
$547$	−5.15053	−	1.38008i	−0.220221	−	0.0590080i	−0.367242	+	0.930125i	$0.619698\pi$
$548$	−2.29750	+	2.29750i	−0.0981442	+	0.0981442i
$549$		0			0
$550$		0			0
$551$	−8.27432	+	4.77718i	−0.352498	+	0.203515i
$552$		0			0
$553$	10.7321	−	2.87566i	0.456376	−	0.122286i
$554$	−8.65490	+	14.9907i	−0.367712	+	0.636895i
$555$		0			0
$556$	10.9973	+	19.0478i	0.466388	+	0.807807i
$557$	4.10329	+	4.10329i	0.173862	+	0.173862i	0.788674	−	0.614812i	$-0.210768\pi$
$557$	4.10329	+	4.10329i	0.173862	+	0.173862i	−0.614812	+	0.788674i	$0.710768\pi$
$558$		0			0
$559$			1.49979i			0.0634344i
$560$		0			0
$561$		0			0
$562$	−6.24341	−	23.3007i	−0.263362	−	0.982882i
$563$	1.53547	+	5.73047i	0.0647125	+	0.241510i	0.990704	−	0.136033i	$-0.0434354\pi$
$563$	1.53547	+	5.73047i	0.0647125	+	0.241510i	−0.925992	+	0.377544i	$0.876769\pi$
$564$		0			0
$565$		0			0
$566$			16.5516i			0.695715i
$567$		0			0
$568$	−7.36824	−	7.36824i	−0.309164	−	0.309164i
$569$	−17.6714	−	30.6077i	−0.740822	−	1.28314i	−0.952122	−	0.305720i	$-0.901103\pi$
$569$	−17.6714	−	30.6077i	−0.740822	−	1.28314i	0.211300	−	0.977421i	$-0.432230\pi$
$570$		0			0
$571$	1.50529	−	2.60725i	0.0629946	−	0.109110i	−0.832808	−	0.553562i	$-0.813268\pi$
$571$	1.50529	−	2.60725i	0.0629946	−	0.109110i	0.895803	+	0.444452i	$0.146602\pi$
$572$	−2.79162	+	0.748011i	−0.116723	+	0.0312759i
$573$		0			0
$574$	14.8142	−	8.55296i	0.618331	−	0.356993i
$575$		0			0
$576$		0			0
$577$	11.5350	−	11.5350i	0.480208	−	0.480208i	−0.424990	−	0.905198i	$-0.639722\pi$
$577$	11.5350	−	11.5350i	0.480208	−	0.480208i	0.905198	+	0.424990i	$0.139722\pi$
$578$	21.1272	+	5.66101i	0.878774	+	0.235467i
$579$		0			0
$580$		0			0
$581$	26.4185	+	15.2527i	1.09602	+	0.632789i
$582$		0			0
$583$	2.30434	−	8.59992i	0.0954361	−	0.356172i
$584$	4.66721			0.193130
$585$		0			0
$586$	16.1515			0.667214
$587$	−2.95165	+	11.0157i	−0.121828	+	0.454666i	−0.999707	−	0.0242156i	$-0.992291\pi$
$587$	−2.95165	+	11.0157i	−0.121828	+	0.454666i	0.877879	+	0.478882i	$0.158958\pi$
$588$		0			0
$589$	−18.3333	−	10.5848i	−0.755412	−	0.436137i
$590$		0			0
$591$		0			0
$592$	−0.863406	−	0.231349i	−0.0354858	−	0.00950838i
$593$	23.4664	−	23.4664i	0.963651	−	0.963651i	−0.0357109	−	0.999362i	$-0.511370\pi$
$593$	23.4664	−	23.4664i	0.963651	−	0.963651i	0.999362	+	0.0357109i	$0.0113696\pi$
$594$		0			0
$595$		0			0
$596$	11.3738	−	6.56668i	0.465890	−	0.268982i
$597$		0			0
$598$	1.53143	−	0.410346i	0.0626249	−	0.0167803i
$599$	17.2683	−	29.9097i	0.705566	−	1.22208i	−0.260922	−	0.965360i	$-0.584026\pi$
$599$	17.2683	−	29.9097i	0.705566	−	1.22208i	0.966487	−	0.256715i	$-0.0826403\pi$
$600$		0			0
$601$	−1.57759	−	2.73247i	−0.0643513	−	0.111460i	0.832055	−	0.554694i	$-0.187164\pi$
$601$	−1.57759	−	2.73247i	−0.0643513	−	0.111460i	−0.896406	+	0.443234i	$0.853831\pi$
$602$	−4.66952	−	4.66952i	−0.190315	−	0.190315i
$603$		0			0
$604$			0.335798i			0.0136634i
$605$		0			0
$606$		0			0
$607$	−1.32070	−	4.92890i	−0.0536054	−	0.200058i	0.933930	−	0.357456i	$-0.116356\pi$
$607$	−1.32070	−	4.92890i	−0.0536054	−	0.200058i	−0.987535	+	0.157399i	$0.949689\pi$
$608$	1.34365	+	5.01456i	0.0544921	+	0.203367i
$609$		0			0
$610$		0			0
$611$		−	2.38643i		−	0.0965446i
$612$		0			0
$613$	9.09622	+	9.09622i	0.367393	+	0.367393i	0.866525	−	0.499133i	$-0.166348\pi$
$613$	9.09622	+	9.09622i	0.367393	+	0.367393i	−0.499133	+	0.866525i	$0.666348\pi$
$614$	−1.02984	−	1.78374i	−0.0415611	−	0.0719859i
$615$		0			0
$616$	6.36265	−	11.0204i	0.256358	−	0.444026i
$617$	23.2998	−	6.24315i	0.938013	−	0.251340i	0.242745	−	0.970090i	$-0.421952\pi$
$617$	23.2998	−	6.24315i	0.938013	−	0.251340i	0.695268	+	0.718751i	$0.255286\pi$
$618$		0			0
$619$	26.9280	−	15.5469i	1.08233	−	0.624883i	0.150806	−	0.988563i	$-0.451813\pi$
$619$	26.9280	−	15.5469i	1.08233	−	0.624883i	0.931524	+	0.363680i	$0.118480\pi$
$620$		0			0
$621$		0			0
$622$	1.48163	−	1.48163i	0.0594081	−	0.0594081i
$623$	−5.25156	−	1.40715i	−0.210399	−	0.0563764i
$624$		0			0
$625$		0			0
$626$	−17.1057	−	9.87595i	−0.683679	−	0.394723i
$627$		0			0
$628$	1.17992	−	4.40352i	0.0470839	−	0.175719i
$629$	−5.57304			−0.222212
$630$		0			0
$631$	46.1604			1.83762			0.918809	−	0.394703i	$-0.129153\pi$
$631$	46.1604			1.83762			0.918809	+	0.394703i	$0.129153\pi$
$632$	−1.08423	+	4.04642i	−0.0431285	+	0.160958i
$633$		0			0
$634$	−29.5196	−	17.0431i	−1.17237	−	0.676869i
$635$		0			0
$636$		0			0
$637$	−0.0200372	−	0.00536896i	−0.000793905	−	0.000212726i
$638$	−6.24383	+	6.24383i	−0.247195	+	0.247195i
$639$		0			0
$640$		0			0
$641$	3.41084	−	1.96925i	0.134720	−	0.0777808i	−0.431125	−	0.902292i	$-0.641883\pi$
$641$	3.41084	−	1.96925i	0.134720	−	0.0777808i	0.565845	+	0.824511i	$0.308550\pi$
$642$		0			0
$643$	29.9917	−	8.03625i	1.18276	−	0.316919i	0.386737	−	0.922190i	$-0.373602\pi$
$643$	29.9917	−	8.03625i	1.18276	−	0.316919i	0.796019	+	0.605271i	$0.206935\pi$
$644$	−3.49044	+	6.04562i	−0.137543	+	0.238231i
$645$		0			0
$646$	16.1838	+	28.0311i	0.636742	+	1.10287i
$647$	−18.0986	−	18.0986i	−0.711531	−	0.711531i	0.255325	−	0.966855i	$-0.417818\pi$
$647$	−18.0986	−	18.0986i	−0.711531	−	0.711531i	−0.966855	+	0.255325i	$0.917818\pi$
$648$		0			0
$649$			0.619386i			0.0243130i
$650$		0			0
$651$		0			0
$652$	3.29971	+	12.3147i	0.129226	+	0.482280i
$653$	3.63685	+	13.5729i	0.142321	+	0.531148i	0.999860	+	0.0167299i	$0.00532554\pi$
$653$	3.63685	+	13.5729i	0.142321	+	0.531148i	−0.857539	+	0.514419i	$0.828008\pi$
$654$		0			0
$655$		0			0
$656$			6.44958i			0.251814i
$657$		0			0
$658$	7.43002	+	7.43002i	0.289652	+	0.289652i
$659$	18.2709	+	31.6462i	0.711734	+	1.23276i	0.964206	+	0.265155i	$0.0854233\pi$
$659$	18.2709	+	31.6462i	0.711734	+	1.23276i	−0.252471	+	0.967604i	$0.581243\pi$
$660$		0			0
$661$	−17.9365	+	31.0670i	−0.697650	+	1.20836i	0.271629	+	0.962402i	$0.412438\pi$
$661$	−17.9365	+	31.0670i	−0.697650	+	1.20836i	−0.969279	+	0.245963i	$0.920896\pi$
$662$	−23.2092	+	6.21890i	−0.902053	+	0.241704i
$663$		0			0
$664$	−9.96076	+	5.75085i	−0.386553	+	0.223176i
$665$		0			0
$666$		0			0
$667$	3.42525	−	3.42525i	0.132626	−	0.132626i
$668$	0.00858342	+	0.00229992i	0.000332102	+	8.89866e-5i
$669$		0			0
$670$		0			0
$671$	−52.1261	−	30.0950i	−2.01231	−	1.16181i
$672$		0			0
$673$	6.49200	−	24.2285i	0.250248	−	0.933939i	−0.720424	−	0.693534i	$-0.756053\pi$
$673$	6.49200	−	24.2285i	0.250248	−	0.933939i	0.970673	−	0.240406i	$-0.0772804\pi$
$674$	−12.2514			−0.471907
$675$		0			0
$676$	12.6372			0.486045
$677$	1.40152	−	5.23054i	0.0538647	−	0.201026i	−0.933750	−	0.357927i	$-0.883484\pi$
$677$	1.40152	−	5.23054i	0.0538647	−	0.201026i	0.987614	+	0.156901i	$0.0501504\pi$
$678$		0			0
$679$	39.7389	+	22.9433i	1.52504	+	0.880481i
$680$		0			0
$681$		0			0
$682$	−18.8981	−	5.06374i	−0.723647	−	0.193901i
$683$	14.3302	−	14.3302i	0.548331	−	0.548331i	−0.377627	−	0.925958i	$-0.623260\pi$
$683$	14.3302	−	14.3302i	0.548331	−	0.548331i	0.925958	+	0.377627i	$0.123260\pi$
$684$		0			0
$685$		0			0
$686$	−15.9993	+	9.23721i	−0.610857	+	0.352678i
$687$		0			0
$688$	2.40501	−	0.644420i	0.0916900	−	0.0245683i
$689$	0.558889	−	0.968025i	0.0212920	−	0.0368788i
$690$		0			0
$691$	−5.85991	−	10.1497i	−0.222921	−	0.386111i	0.732772	−	0.680474i	$-0.238226\pi$
$691$	−5.85991	−	10.1497i	−0.222921	−	0.386111i	−0.955694	+	0.294363i	$0.904893\pi$
$692$	7.34182	+	7.34182i	0.279094	+	0.279094i
$693$		0			0
$694$			18.5893i			0.705641i
$695$		0			0
$696$		0			0
$697$	10.4076	+	38.8415i	0.394214	+	1.47123i
$698$	−8.13805	−	30.3716i	−0.308030	−	1.14958i
$699$		0			0
$700$		0			0
$701$			30.7235i			1.16041i	0.814471	+	0.580205i	$0.197028\pi$
$701$			30.7235i			1.16041i	−0.814471	+	0.580205i	$0.802972\pi$
$702$		0			0
$703$	−3.28129	−	3.28129i	−0.123756	−	0.123756i
$704$	2.39896	+	4.15512i	0.0904143	+	0.156602i
$705$		0			0
$706$	6.07917	−	10.5294i	0.228792	−	0.396280i
$707$	30.6451	−	8.21132i	1.15253	−	0.308818i
$708$		0			0
$709$	−27.4879	+	15.8701i	−1.03233	+	0.596015i	−0.917651	−	0.397387i	$-0.869917\pi$
$709$	−27.4879	+	15.8701i	−1.03233	+	0.596015i	−0.114678	+	0.993403i	$0.536584\pi$
$710$		0			0
$711$		0			0
$712$	1.44949	−	1.44949i	0.0543219	−	0.0543219i
$713$	10.3672	+	2.77788i	0.388254	+	0.104032i
$714$		0			0
$715$		0			0
$716$	1.26692	+	0.731458i	0.0473471	+	0.0273359i
$717$		0			0
$718$	1.11708	−	4.16899i	0.0416890	−	0.155585i
$719$	7.79879			0.290846			0.145423	−	0.989370i	$-0.453546\pi$
$719$	7.79879			0.290846			0.145423	+	0.989370i	$0.453546\pi$
$720$		0			0
$721$	28.5717			1.06407
$722$	−2.05792	+	7.68026i	−0.0765878	+	0.285830i
$723$		0			0
$724$	7.52209	+	4.34288i	0.279556	+	0.161402i
$725$		0			0
$726$		0			0
$727$	42.7863	+	11.4645i	1.58685	+	0.425196i	0.941039	−	0.338297i	$-0.109851\pi$
$727$	42.7863	+	11.4645i	1.58685	+	0.425196i	0.645815	+	0.763494i	$0.276518\pi$
$728$	1.12969	−	1.12969i	0.0418690	−	0.0418690i
$729$		0			0
$730$		0			0
$731$	13.4439	−	7.76182i	0.497239	−	0.287081i
$732$		0			0
$733$	−26.9304	+	7.21598i	−0.994697	+	0.266528i	−0.719222	−	0.694780i	$-0.755502\pi$
$733$	−26.9304	+	7.21598i	−0.994697	+	0.266528i	−0.275475	+	0.961308i	$0.588835\pi$
$734$	9.93909	−	17.2150i	0.366858	−	0.635418i
$735$		0			0
$736$	−1.31603	−	2.27943i	−0.0485095	−	0.0840208i
$737$	37.4607	+	37.4607i	1.37988	+	1.37988i
$738$		0			0
$739$		−	10.8068i		−	0.397536i	−0.980047	−	0.198768i	$-0.936306\pi$
$739$		−	10.8068i		−	0.397536i	0.980047	−	0.198768i	$-0.0636941\pi$
$740$		0			0
$741$		0			0
$742$	1.27382	+	4.75396i	0.0467634	+	0.174523i
$743$	−5.75762	−	21.4877i	−0.211227	−	0.788309i	−0.987461	−	0.157864i	$-0.949539\pi$
$743$	−5.75762	−	21.4877i	−0.211227	−	0.788309i	0.776234	−	0.630445i	$-0.217127\pi$
$744$		0			0
$745$		0			0
$746$			2.62754i			0.0962009i
$747$		0			0
$748$	21.1524	+	21.1524i	0.773408	+	0.773408i
$749$	8.16498	+	14.1422i	0.298342	+	0.516743i
$750$		0			0
$751$	−20.6235	+	35.7209i	−0.752561	+	1.30347i	0.194017	+	0.980998i	$0.437848\pi$
$751$	−20.6235	+	35.7209i	−0.752561	+	1.30347i	−0.946578	+	0.322476i	$0.895485\pi$
$752$	−3.82678	+	1.02538i	−0.139548	+	0.0373919i
$753$		0			0
$754$	−0.960067	+	0.554295i	−0.0349636	+	0.0201862i
$755$		0			0
$756$		0			0
$757$	20.5246	−	20.5246i	0.745978	−	0.745978i	−0.227743	−	0.973721i	$-0.573135\pi$
$757$	20.5246	−	20.5246i	0.745978	−	0.745978i	0.973721	+	0.227743i	$0.0731346\pi$
$758$	2.92796	+	0.784544i	0.106348	+	0.0284959i
$759$		0			0
$760$		0			0
$761$	−39.8188	−	22.9894i	−1.44343	−	0.833365i	−0.445353	−	0.895355i	$-0.646922\pi$
$761$	−39.8188	−	22.9894i	−1.44343	−	0.833365i	−0.998077	+	0.0619904i	$0.980255\pi$
$762$		0			0
$763$	10.6089	−	39.5928i	0.384066	−	1.43335i
$764$	−5.00903			−0.181220
$765$		0			0
$766$	−23.7508			−0.858153
$767$	−0.0201262	+	0.0751122i	−0.000726717	+	0.00271214i
$768$		0			0
$769$	26.6702	+	15.3980i	0.961752	+	0.555268i	0.896712	−	0.442615i	$-0.145949\pi$
$769$	26.6702	+	15.3980i	0.961752	+	0.555268i	0.0650399	+	0.997883i	$0.479283\pi$
$770$		0			0
$771$		0			0
$772$	−3.25355	−	0.871785i	−0.117098	−	0.0313762i
$773$	29.6376	−	29.6376i	1.06599	−	1.06599i	0.0683287	−	0.997663i	$-0.478233\pi$
$773$	29.6376	−	29.6376i	1.06599	−	1.06599i	0.997663	−	0.0683287i	$-0.0217667\pi$
$774$		0			0
$775$		0			0
$776$	−14.9831	+	8.65048i	−0.537861	+	0.310534i
$777$		0			0
$778$	−6.43797	+	1.72505i	−0.230813	+	0.0618460i
$779$	−16.7414	+	28.9969i	−0.599821	+	1.03892i
$780$		0			0
$781$	−24.9978	−	43.2975i	−0.894492	−	1.54931i
$782$	−11.6038	−	11.6038i	−0.414952	−	0.414952i
$783$		0			0
$784$			0.0344378i			0.00122992i
$785$		0			0
$786$		0			0
$787$	6.98316	+	26.0615i	0.248923	+	0.928993i	0.971371	+	0.237568i	$0.0763501\pi$
$787$	6.98316	+	26.0615i	0.248923	+	0.928993i	−0.722448	+	0.691425i	$0.756983\pi$
$788$	5.67439	+	21.1771i	0.202142	+	0.754403i
$789$		0			0
$790$		0			0
$791$			15.7369i			0.559540i
$792$		0			0
$793$	−5.34337	−	5.34337i	−0.189749	−	0.189749i
$794$	−9.35091	−	16.1963i	−0.331852	−	0.574784i
$795$		0			0
$796$	9.23033	−	15.9874i	0.327161	−	0.566659i
$797$	6.28188	−	1.68322i	0.222515	−	0.0596228i	−0.145839	−	0.989308i	$-0.546588\pi$
$797$	6.28188	−	1.68322i	0.222515	−	0.0596228i	0.368354	+	0.929686i	$0.379921\pi$
$798$		0			0
$799$	−21.3915	+	12.3504i	−0.756778	+	0.436926i
$800$		0			0
$801$		0			0
$802$	−3.81250	+	3.81250i	−0.134624	+	0.134624i
$803$	21.6299	+	5.79571i	0.763302	+	0.204526i
$804$		0			0
$805$		0			0
$806$	−2.12721	−	1.22815i	−0.0749279	−	0.0432596i
$807$		0			0
$808$	−3.09598	+	11.5544i	−0.108916	+	0.406481i
$809$	5.79431			0.203717			0.101859	−	0.994799i	$-0.467521\pi$
$809$	5.79431			0.203717			0.101859	+	0.994799i	$0.467521\pi$
$810$		0			0
$811$	1.90498			0.0668929			0.0334465	−	0.999441i	$-0.489352\pi$
$811$	1.90498			0.0668929			0.0334465	+	0.999441i	$0.489352\pi$
$812$	1.26335	−	4.71488i	0.0443349	−	0.165460i
$813$		0			0
$814$	−3.71411	−	2.14434i	−0.130180	−	0.0751592i
$815$		0			0
$816$		0			0
$817$	12.4855	+	3.34547i	0.436812	+	0.117043i
$818$	−6.07126	+	6.07126i	−0.212277	+	0.212277i
$819$		0			0
$820$		0			0
$821$	33.4503	−	19.3125i	1.16742	−	0.674012i	0.214351	−	0.976757i	$-0.431236\pi$
$821$	33.4503	−	19.3125i	1.16742	−	0.674012i	0.953072	+	0.302745i	$0.0979030\pi$
$822$		0			0
$823$	−20.6711	+	5.53879i	−0.720548	+	0.193070i	−0.600416	−	0.799688i	$-0.704998\pi$
$823$	−20.6711	+	5.53879i	−0.720548	+	0.193070i	−0.120132	+	0.992758i	$0.538332\pi$
$824$	−5.38631	+	9.32936i	−0.187641	+	0.325004i
$825$		0			0
$826$	−0.171196	−	0.296520i	−0.00595666	−	0.0103172i
$827$	23.1603	+	23.1603i	0.805364	+	0.805364i	0.983928	−	0.178564i	$-0.0571453\pi$
$827$	23.1603	+	23.1603i	0.805364	+	0.805364i	−0.178564	+	0.983928i	$0.557145\pi$
$828$		0			0
$829$		−	34.1116i		−	1.18475i	−0.805664	−	0.592373i	$-0.798191\pi$
$829$		−	34.1116i		−	1.18475i	0.805664	−	0.592373i	$-0.201809\pi$
$830$		0			0
$831$		0			0
$832$	0.155903	+	0.581838i	0.00540497	+	0.0201716i
$833$	0.0555716	+	0.207396i	0.00192544	+	0.00718585i
$834$		0			0
$835$		0			0
$836$			24.9082i			0.861468i
$837$		0			0
$838$	10.9283	+	10.9283i	0.377512	+	0.377512i
$839$	−18.8058	−	32.5726i	−0.649249	−	1.12453i	−0.983303	−	0.181978i	$-0.941750\pi$
$839$	−18.8058	−	32.5726i	−0.649249	−	1.12453i	0.334054	−	0.942554i	$-0.391583\pi$
$840$		0			0
$841$	12.8065	−	22.1814i	0.441602	−	0.764877i
$842$	18.2585	−	4.89235i	0.629229	−	0.168602i
$843$		0			0
$844$	−1.13357	+	0.654465i	−0.0390190	+	0.0225276i
$845$		0			0
$846$		0			0
$847$	22.5427	−	22.5427i	0.774577	−	0.774577i
$848$	−1.79243	−	0.480279i	−0.0615521	−	0.0164928i
$849$		0			0
$850$		0			0
$851$	2.03750	+	1.17635i	0.0698445	+	0.0403248i
$852$		0			0
$853$	1.98742	−	7.41714i	0.0680478	−	0.253958i	−0.923519	−	0.383552i	$-0.874701\pi$
$853$	1.98742	−	7.41714i	0.0680478	−	0.253958i	0.991567	+	0.129594i	$0.0413674\pi$
$854$	33.2726			1.13856
$855$		0			0
$856$	−6.15702			−0.210442
$857$	1.87635	−	7.00264i	0.0640949	−	0.239206i	−0.926445	−	0.376430i	$-0.877152\pi$
$857$	1.87635	−	7.00264i	0.0640949	−	0.239206i	0.990540	+	0.137224i	$0.0438182\pi$
$858$		0			0
$859$	−1.50446	−	0.868601i	−0.0513316	−	0.0296363i	0.474115	−	0.880463i	$-0.342768\pi$
$859$	−1.50446	−	0.868601i	−0.0513316	−	0.0296363i	−0.525446	+	0.850827i	$0.676102\pi$
$860$		0			0
$861$		0			0
$862$	−3.78090	−	1.01309i	−0.128778	−	0.0345060i
$863$	−36.4612	+	36.4612i	−1.24115	+	1.24115i	−0.281630	+	0.959523i	$0.590875\pi$
$863$	−36.4612	+	36.4612i	−1.24115	+	1.24115i	−0.959523	+	0.281630i	$0.909125\pi$
$864$		0			0
$865$		0			0
$866$	33.3190	−	19.2368i	1.13223	−	0.653692i
$867$		0			0
$868$	10.4467	−	2.79919i	0.354585	−	0.0950108i
$869$	−10.0496	+	17.4065i	−0.340911	+	0.590474i
$870$		0			0
$871$	3.32557	+	5.76006i	0.112683	+	0.195172i
$872$	10.9280	+	10.9280i	0.370070	+	0.370070i
$873$		0			0
$874$		−	13.6642i		−	0.462199i
$875$		0			0
$876$		0			0
$877$	−2.68194	−	10.0092i	−0.0905628	−	0.337985i	0.905747	−	0.423820i	$-0.139311\pi$
$877$	−2.68194	−	10.0092i	−0.0905628	−	0.337985i	−0.996309	+	0.0858347i	$0.972644\pi$
$878$	3.96659	+	14.8035i	0.133866	+	0.499594i
$879$		0			0
$880$		0			0
$881$		−	1.17719i		−	0.0396604i	−0.999803	−	0.0198302i	$-0.993687\pi$
$881$		−	1.17719i		−	0.0396604i	0.999803	−	0.0198302i	$-0.00631257\pi$
$882$		0			0
$883$	22.1929	+	22.1929i	0.746850	+	0.746850i	0.973886	−	0.227036i	$-0.0729035\pi$
$883$	22.1929	+	22.1929i	0.746850	+	0.746850i	−0.227036	+	0.973886i	$0.572903\pi$
$884$	1.87780	+	3.25245i	0.0631573	+	0.109392i
$885$		0			0
$886$	−13.9099	+	24.0927i	−0.467313	+	0.809410i
$887$	8.80492	−	2.35927i	0.295640	−	0.0792166i	−0.107950	−	0.994156i	$-0.534429\pi$
$887$	8.80492	−	2.35927i	0.295640	−	0.0792166i	0.403590	+	0.914940i	$0.367762\pi$
$888$		0			0
$889$	−8.18049	+	4.72301i	−0.274365	+	0.158405i
$890$		0			0
$891$		0			0
$892$	14.8324	−	14.8324i	0.496625	−	0.496625i
$893$	−19.8666	−	5.32323i	−0.664809	−	0.178135i
$894$		0			0
$895$		0			0
$896$	−2.29692	−	1.32613i	−0.0767346	−	0.0443028i
$897$		0			0
$898$	6.30553	−	23.5326i	0.210418	−	0.785292i
$899$	−7.50472			−0.250296
$900$		0			0
$901$	−11.5696			−0.385439
$902$	−8.00905	+	29.8902i	−0.266672	+	0.995234i
$903$		0			0
$904$	−5.13849	−	2.96671i	−0.170904	−	0.0986713i
$905$		0			0
$906$		0			0
$907$	−7.35203	−	1.96997i	−0.244120	−	0.0654118i	0.134684	−	0.990889i	$-0.456998\pi$
$907$	−7.35203	−	1.96997i	−0.244120	−	0.0654118i	−0.378804	+	0.925477i	$0.623665\pi$
$908$	−4.21080	+	4.21080i	−0.139740	+	0.139740i
$909$		0			0
$910$		0			0
$911$	−39.2522	+	22.6623i	−1.30048	+	0.750835i	−0.980487	−	0.196583i	$-0.937015\pi$
$911$	−39.2522	+	22.6623i	−1.30048	+	0.750835i	−0.319997	+	0.947418i	$0.603682\pi$
$912$		0			0
$913$	−53.3039	+	14.2827i	−1.76410	+	0.472690i
$914$	6.55874	−	11.3601i	0.216944	−	0.375758i
$915$		0			0
$916$	−5.87872	−	10.1822i	−0.194238	−	0.336431i
$917$	−24.4930	−	24.4930i	−0.808829	−	0.808829i
$918$		0			0
$919$		−	19.9726i		−	0.658836i	−0.944184	−	0.329418i	$-0.893148\pi$
$919$		−	19.9726i		−	0.658836i	0.944184	−	0.329418i	$-0.106852\pi$
$920$		0			0
$921$		0			0
$922$	10.3908	+	38.7791i	0.342204	+	1.27712i
$923$	−1.62455	−	6.06291i	−0.0534728	−	0.199563i
$924$		0			0
$925$		0			0
$926$		−	11.9769i		−	0.393586i
$927$		0			0
$928$	1.30136	+	1.30136i	0.0427192	+	0.0427192i
$929$	24.8920	+	43.1142i	0.816681	+	1.41453i	0.908115	+	0.418721i	$0.137522\pi$
$929$	24.8920	+	43.1142i	0.816681	+	1.41453i	−0.0914341	+	0.995811i	$0.529145\pi$
$930$		0			0
$931$	−0.0893912	+	0.154830i	−0.00292968	+	0.00507435i
$932$	−18.3487	+	4.91653i	−0.601033	+	0.161046i
$933$		0			0
$934$	10.5711	−	6.10321i	0.345896	−	0.199703i
$935$		0			0
$936$		0			0
$937$	−28.6750	+	28.6750i	−0.936771	+	0.936771i	−0.998117	−	0.0613453i	$-0.980461\pi$
$937$	−28.6750	+	28.6750i	−0.936771	+	0.936771i	0.0613453	+	0.998117i	$0.480461\pi$
$938$	−28.2876	−	7.57964i	−0.923623	−	0.247484i
$939$		0			0
$940$		0			0
$941$	42.4585	+	24.5134i	1.38411	+	0.799115i	0.992643	−	0.121078i	$-0.0386353\pi$
$941$	42.4585	+	24.5134i	1.38411	+	0.799115i	0.391464	+	0.920193i	$0.371969\pi$
$942$		0			0
$943$	4.39363	−	16.3972i	0.143076	−	0.533967i
$944$	0.129095			0.00420167
$945$		0			0
$946$	11.9461			0.388401
$947$	11.6667	−	43.5407i	0.379117	−	1.41488i	−0.468119	−	0.883665i	$-0.655068\pi$
$947$	11.6667	−	43.5407i	0.379117	−	1.41488i	0.847236	−	0.531217i	$-0.178265\pi$
$948$		0			0
$949$	2.43470	+	1.40568i	0.0790339	+	0.0456302i
$950$		0			0
$951$		0			0
$952$	−15.9727	−	4.27988i	−0.517679	−	0.138712i
$953$	−2.71971	+	2.71971i	−0.0881001	+	0.0881001i	−0.749783	−	0.661683i	$-0.769842\pi$
$953$	−2.71971	+	2.71971i	−0.0881001	+	0.0881001i	0.661683	+	0.749783i	$0.269842\pi$
$954$		0			0
$955$		0			0
$956$	−3.94809	+	2.27943i	−0.127690	+	0.0737220i
$957$		0			0
$958$	−9.91983	+	2.65801i	−0.320495	+	0.0858764i
$959$	4.30878	−	7.46303i	0.139138	−	0.240994i
$960$		0			0
$961$	7.18593	+	12.4464i	0.231804	+	0.401497i
$962$	−0.380728	−	0.380728i	−0.0122752	−	0.0122752i
$963$		0			0
$964$		−	16.0621i		−	0.517325i
$965$		0			0
$966$		0			0
$967$	−8.10886	−	30.2627i	−0.260763	−	0.973182i	−0.964793	−	0.263011i	$-0.915284\pi$
$967$	−8.10886	−	30.2627i	−0.260763	−	0.973182i	0.704029	−	0.710171i	$-0.251382\pi$
$968$	3.11102	+	11.6105i	0.0999920	+	0.373175i
$969$		0			0
$970$		0			0
$971$			31.9680i			1.02590i	0.858418	+	0.512951i	$0.171448\pi$
$971$			31.9680i			1.02590i	−0.858418	+	0.512951i	$0.828552\pi$
$972$		0			0
$973$	−41.2491	−	41.2491i	−1.32238	−	1.32238i
$974$	12.3898	+	21.4597i	0.396993	+	0.687613i
$975$		0			0
$976$	−6.27251	+	10.8643i	−0.200778	+	0.347758i
$977$	−8.45932	+	2.26667i	−0.270638	+	0.0725171i	−0.391585	−	0.920142i	$-0.628073\pi$
$977$	−8.45932	+	2.26667i	−0.270638	+	0.0725171i	0.120948	+	0.992659i	$0.461407\pi$
$978$		0			0
$979$	8.51754	−	4.91760i	0.272222	−	0.157167i
$980$		0			0
$981$		0			0
$982$	6.28784	−	6.28784i	0.200653	−	0.200653i
$983$	40.7397	+	10.9162i	1.29940	+	0.348172i	0.841222	−	0.540691i	$-0.181837\pi$
$983$	40.7397	+	10.9162i	1.29940	+	0.348172i	0.458174	+	0.888863i	$0.348504\pi$
$984$		0			0
$985$		0			0
$986$	9.93720	+	5.73725i	0.316465	+	0.182711i
$987$		0			0
$988$	−0.809364	+	3.02059i	−0.0257493	+	0.0960977i
$989$	−6.55342			−0.208387
$990$		0			0
$991$	−13.9120			−0.441929			−0.220964	−	0.975282i	$-0.570920\pi$
$991$	−13.9120			−0.441929			−0.220964	+	0.975282i	$0.570920\pi$
$992$	−1.05540	+	3.93882i	−0.0335091	+	0.125058i
$993$		0			0
$994$	23.9345	+	13.8186i	0.759156	+	0.438299i
$995$		0			0
$996$		0			0
$997$	−29.2374	−	7.83414i	−0.925958	−	0.248110i	−0.235828	−	0.971795i	$-0.575780\pi$
$997$	−29.2374	−	7.83414i	−0.925958	−	0.248110i	−0.690130	+	0.723685i	$0.742447\pi$
$998$	20.7542	−	20.7542i	0.656963	−	0.656963i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.2.q.h.1043.4		16
3.2	odd	2		450.2.p.h.293.2		16
5.2	odd	4	inner	1350.2.q.h.557.3		16
5.3	odd	4		270.2.m.b.17.1		16
5.4	even	2		270.2.m.b.233.1		16
9.2	odd	6	inner	1350.2.q.h.143.3		16
9.7	even	3		450.2.p.h.443.2		16
15.2	even	4		450.2.p.h.257.2		16
15.8	even	4		90.2.l.b.77.3	yes	16
15.14	odd	2		90.2.l.b.23.3	✓	16
45.2	even	12	inner	1350.2.q.h.1007.4		16
45.4	even	6		810.2.f.c.323.4		16
45.7	odd	12		450.2.p.h.407.2		16
45.13	odd	12		810.2.f.c.647.5		16
45.14	odd	6		810.2.f.c.323.5		16
45.23	even	12		810.2.f.c.647.4		16
45.29	odd	6		270.2.m.b.143.1		16
45.34	even	6		90.2.l.b.83.3	yes	16
45.38	even	12		270.2.m.b.197.1		16
45.43	odd	12		90.2.l.b.47.3	yes	16
60.23	odd	4		720.2.cu.b.257.3		16
60.59	even	2		720.2.cu.b.113.4		16
180.43	even	12		720.2.cu.b.497.4		16
180.79	odd	6		720.2.cu.b.353.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.3	✓	16	15.14	odd	2
90.2.l.b.47.3	yes	16	45.43	odd	12
90.2.l.b.77.3	yes	16	15.8	even	4
90.2.l.b.83.3	yes	16	45.34	even	6
270.2.m.b.17.1		16	5.3	odd	4
270.2.m.b.143.1		16	45.29	odd	6
270.2.m.b.197.1		16	45.38	even	12
270.2.m.b.233.1		16	5.4	even	2
450.2.p.h.257.2		16	15.2	even	4
450.2.p.h.293.2		16	3.2	odd	2
450.2.p.h.407.2		16	45.7	odd	12
450.2.p.h.443.2		16	9.7	even	3
720.2.cu.b.113.4		16	60.59	even	2
720.2.cu.b.257.3		16	60.23	odd	4
720.2.cu.b.353.3		16	180.79	odd	6
720.2.cu.b.497.4		16	180.43	even	12
810.2.f.c.323.4		16	45.4	even	6
810.2.f.c.323.5		16	45.14	odd	6
810.2.f.c.647.4		16	45.23	even	12
810.2.f.c.647.5		16	45.13	odd	12
1350.2.q.h.143.3		16	9.2	odd	6	inner
1350.2.q.h.557.3		16	5.2	odd	4	inner
1350.2.q.h.1007.4		16	45.2	even	12	inner
1350.2.q.h.1043.4		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)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(2.56188 + 0.686453i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-4.15512 + 2.39896i) q^{11} +(-0.581838 + 0.155903i) q^{13} +(1.32613 - 2.29692i) q^{14} +(0.500000 + 0.866025i) q^{16} +(4.40865 + 4.40865i) q^{17} +5.19145i q^{19} +(1.24179 + 4.63444i) q^{22} +(-0.681226 - 2.54237i) q^{23} +0.602363i q^{26} +(-1.87542 - 1.87542i) q^{28} +(0.920201 + 1.59383i) q^{29} +(-2.03888 + 3.53145i) q^{31} +(0.965926 - 0.258819i) q^{32} +(5.39948 - 3.11739i) q^{34} +(-0.632057 + 0.632057i) q^{37} +(5.01456 + 1.34365i) q^{38} +(5.58550 + 3.22479i) q^{41} +(0.644420 - 2.40501i) q^{43} +4.79792 q^{44} -2.63206 q^{46} +(-1.02538 + 3.82678i) q^{47} +(0.0298240 + 0.0172189i) q^{49} +(0.581838 + 0.155903i) q^{52} +(-1.31215 + 1.31215i) q^{53} +(-2.29692 + 1.32613i) q^{56} +(1.77769 - 0.476331i) q^{58} +(0.0645473 - 0.111799i) q^{59} +(6.27251 + 10.8643i) q^{61} +(2.88341 + 2.88341i) q^{62} -1.00000i q^{64} +(-2.85782 - 10.6655i) q^{67} +(-1.61368 - 6.02233i) q^{68} +10.4203i q^{71} +(-3.30021 - 3.30021i) q^{73} +(0.446932 + 0.774109i) q^{74} +(2.59573 - 4.49593i) q^{76} +(-12.2917 + 3.29355i) q^{77} +(3.62792 - 2.09458i) q^{79} +(4.56054 - 4.56054i) q^{82} +(11.1098 + 2.97686i) q^{83} +(-2.15627 - 1.24492i) q^{86} +(1.24179 - 4.63444i) q^{88} -2.04989 q^{89} -1.59762 q^{91} +(-0.681226 + 2.54237i) q^{92} +(3.43100 + 1.98089i) q^{94} +(16.7115 + 4.47782i) q^{97} +(0.0243512 - 0.0243512i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} + 8 q^{16} - 8 q^{22} - 24 q^{23} + 16 q^{28} - 8 q^{31} + 24 q^{38} - 24 q^{41} - 32 q^{46} + 48 q^{47} - 24 q^{56} - 16 q^{58} - 24 q^{61} + 16 q^{67} - 24 q^{68} - 16 q^{73} + 16 q^{76}+ \cdots + 48 q^{97}+O(q^{100}) \) 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

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