LMFDB - Embedded newform 405.3.g.d.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(82,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("405.82");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.g (of order $4$, degree $2$, 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:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.49787136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.1
Root			$1.09445 + 0.895644i$ of defining polynomial
Character	$\chi$	$=$	405.163
Dual form			405.3.g.d.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.18890 + 2.18890i) q^{2} -5.58258i q^{4} +(1.27520 - 4.83465i) q^{5} +(-8.79129 + 8.79129i) q^{7} +(3.46410 + 3.46410i) q^{8} +(7.79129 + 13.3739i) q^{10} +10.4877 q^{11} +(11.5826 + 11.5826i) q^{13} -38.4865i q^{14} +7.16515 q^{16} +(-1.17985 + 1.17985i) q^{17} +1.74773i q^{19} +(-26.9898 - 7.11890i) q^{20} +(-22.9564 + 22.9564i) q^{22} +(-13.9518 - 13.9518i) q^{23} +(-21.7477 - 12.3303i) q^{25} -50.7062 q^{26} +(49.0780 + 49.0780i) q^{28} -6.49125i q^{29} -37.0000 q^{31} +(-29.5402 + 29.5402i) q^{32} -5.16515i q^{34} +(31.2922 + 53.7135i) q^{35} +(-45.6170 + 45.6170i) q^{37} +(-3.82560 - 3.82560i) q^{38} +(21.1652 - 12.3303i) q^{40} -39.3049 q^{41} +(-25.7042 - 25.7042i) q^{43} -58.5481i q^{44} +61.0780 q^{46} +(-18.0634 + 18.0634i) q^{47} -105.573i q^{49} +(74.5934 - 20.6138i) q^{50} +(64.6606 - 64.6606i) q^{52} +(-64.6779 - 64.6779i) q^{53} +(13.3739 - 50.7042i) q^{55} -60.9078 q^{56} +(14.2087 + 14.2087i) q^{58} +52.3985i q^{59} -0.504546 q^{61} +(80.9893 - 80.9893i) q^{62} -100.661i q^{64} +(70.7678 - 41.2276i) q^{65} +(0.669697 - 0.669697i) q^{67} +(6.58660 + 6.58660i) q^{68} +(-186.069 - 49.0780i) q^{70} -60.6616 q^{71} +(25.6261 + 25.6261i) q^{73} -199.702i q^{74} +9.75682 q^{76} +(-92.2000 + 92.2000i) q^{77} +114.069i q^{79} +(9.13701 - 34.6410i) q^{80} +(86.0345 - 86.0345i) q^{82} +(90.6188 + 90.6188i) q^{83} +(4.19962 + 7.20871i) q^{85} +112.528 q^{86} +(36.3303 + 36.3303i) q^{88} -83.4245i q^{89} -203.652 q^{91} +(-77.8867 + 77.8867i) q^{92} -79.0780i q^{94} +(8.44965 + 2.22870i) q^{95} +(66.2087 - 66.2087i) q^{97} +(231.090 + 231.090i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 52 q^{7} + 44 q^{10} + 56 q^{13} - 16 q^{16} - 92 q^{22} - 64 q^{25} + 136 q^{28} - 296 q^{31} + 20 q^{37} + 96 q^{40} - 4 q^{43} + 232 q^{46} + 224 q^{52} + 52 q^{55} + 132 q^{58} - 224 q^{61} + 152 q^{67}+ \cdots + 548 q^{97}+O(q^{100}) $ 8 * q - 52 * q^7 + 44 * q^10 + 56 * q^13 - 16 * q^16 - 92 * q^22 - 64 * q^25 + 136 * q^28 - 296 * q^31 + 20 * q^37 + 96 * q^40 - 4 * q^43 + 232 * q^46 + 224 * q^52 + 52 * q^55 + 132 * q^58 - 224 * q^61 + 152 * q^67 - 792 * q^70 + 260 * q^73 + 408 * q^76 + 340 * q^82 - 388 * q^85 + 144 * q^88 - 896 * q^91 + 548 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.18890	+	2.18890i	−1.09445	+	1.09445i	−0.0994033	+	0.995047i	$0.531693\pi$
$2$	−2.18890	+	2.18890i	−1.09445	+	1.09445i	−0.995047	+	0.0994033i	$0.968307\pi$
$3$		0			0
$3$		0			0
$4$		−	5.58258i		−	1.39564i
$5$	1.27520	−	4.83465i	0.255040	−	0.966930i
$5$	1.27520	−	4.83465i	0.255040	−	0.966930i
$6$		0			0
$7$	−8.79129	+	8.79129i	−1.25590	+	1.25590i	−0.302865	+	0.953034i	$0.597943\pi$
$7$	−8.79129	+	8.79129i	−1.25590	+	1.25590i	−0.953034	+	0.302865i	$0.902057\pi$
$8$	3.46410	+	3.46410i	0.433013	+	0.433013i
$9$		0			0
$10$	7.79129	+	13.3739i	0.779129	+	1.33739i
$11$	10.4877			0.953423			0.476712	−	0.879060i	$-0.341829\pi$
$11$	10.4877			0.953423			0.476712	+	0.879060i	$0.341829\pi$
$12$		0			0
$13$	11.5826	+	11.5826i	0.890967	+	0.890967i	0.994614	−	0.103647i	$-0.0330512\pi$
$13$	11.5826	+	11.5826i	0.890967	+	0.890967i	−0.103647	+	0.994614i	$0.533051\pi$
$14$		−	38.4865i		−	2.74904i
$15$		0			0
$16$	7.16515			0.447822
$17$	−1.17985	+	1.17985i	−0.0694030	+	0.0694030i	−0.740956	−	0.671553i	$-0.765627\pi$
$17$	−1.17985	+	1.17985i	−0.0694030	+	0.0694030i	0.671553	+	0.740956i	$0.265627\pi$
$18$		0			0
$19$			1.74773i			0.0919856i	0.998942	+	0.0459928i	$0.0146451\pi$
$19$			1.74773i			0.0919856i	−0.998942	+	0.0459928i	$0.985355\pi$
$20$	−26.9898	−	7.11890i	−1.34949	−	0.355945i
$21$		0			0
$22$	−22.9564	+	22.9564i	−1.04347	+	1.04347i
$23$	−13.9518	−	13.9518i	−0.606598	−	0.606598i	0.335457	−	0.942055i	$-0.391109\pi$
$23$	−13.9518	−	13.9518i	−0.606598	−	0.606598i	−0.942055	+	0.335457i	$0.891109\pi$
$24$		0			0
$25$	−21.7477	−	12.3303i	−0.869909	−	0.493212i
$26$	−50.7062			−1.95024
$27$		0			0
$28$	49.0780	+	49.0780i	1.75279	+	1.75279i
$29$		−	6.49125i		−	0.223836i	−0.993717	−	0.111918i	$-0.964301\pi$
$29$		−	6.49125i		−	0.223836i	0.993717	−	0.111918i	$-0.0356995\pi$
$30$		0			0
$31$	−37.0000			−1.19355			−0.596774	−	0.802409i	$-0.703551\pi$
$31$	−37.0000			−1.19355			−0.596774	+	0.802409i	$0.703551\pi$
$32$	−29.5402	+	29.5402i	−0.923132	+	0.923132i
$33$		0			0
$34$		−	5.16515i		−	0.151916i
$35$	31.2922	+	53.7135i	0.894062	+	1.53467i
$36$		0			0
$37$	−45.6170	+	45.6170i	−1.23289	+	1.23289i	−0.270046	+	0.962848i	$0.587039\pi$
$37$	−45.6170	+	45.6170i	−1.23289	+	1.23289i	−0.962848	+	0.270046i	$0.912961\pi$
$38$	−3.82560	−	3.82560i	−0.100674	−	0.100674i
$39$		0			0
$40$	21.1652	−	12.3303i	0.529129	−	0.308258i
$41$	−39.3049			−0.958655			−0.479328	−	0.877636i	$-0.659119\pi$
$41$	−39.3049			−0.958655			−0.479328	+	0.877636i	$0.659119\pi$
$42$		0			0
$43$	−25.7042	−	25.7042i	−0.597771	−	0.597771i	0.341948	−	0.939719i	$-0.388913\pi$
$43$	−25.7042	−	25.7042i	−0.597771	−	0.597771i	−0.939719	+	0.341948i	$0.888913\pi$
$44$		−	58.5481i		−	1.33064i
$45$		0			0
$46$	61.0780			1.32778
$47$	−18.0634	+	18.0634i	−0.384328	+	0.384328i	−0.872659	−	0.488331i	$-0.837606\pi$
$47$	−18.0634	+	18.0634i	−0.384328	+	0.384328i	0.488331	+	0.872659i	$0.337606\pi$
$48$		0			0
$49$		−	105.573i		−	2.15456i
$50$	74.5934	−	20.6138i	1.49187	−	0.412276i
$51$		0			0
$52$	64.6606	−	64.6606i	1.24347	−	1.24347i
$53$	−64.6779	−	64.6779i	−1.22034	−	1.22034i	−0.967512	−	0.252825i	$-0.918640\pi$
$53$	−64.6779	−	64.6779i	−1.22034	−	1.22034i	−0.252825	−	0.967512i	$-0.581360\pi$
$54$		0			0
$55$	13.3739	−	50.7042i	0.243161	−	0.921894i
$56$	−60.9078			−1.08764
$57$		0			0
$58$	14.2087	+	14.2087i	0.244978	+	0.244978i
$59$			52.3985i			0.888110i	0.896000	+	0.444055i	$0.146460\pi$
$59$			52.3985i			0.888110i	−0.896000	+	0.444055i	$0.853540\pi$
$60$		0			0
$61$	−0.504546			−0.00827124			−0.00413562	−	0.999991i	$-0.501316\pi$
$61$	−0.504546			−0.00827124			−0.00413562	+	0.999991i	$0.501316\pi$
$62$	80.9893	−	80.9893i	1.30628	−	1.30628i
$63$		0			0
$64$		−	100.661i		−	1.57282i
$65$	70.7678	−	41.2276i	1.08874	−	0.634271i
$66$		0			0
$67$	0.669697	−	0.669697i	0.00999548	−	0.00999548i	−0.702091	−	0.712087i	$-0.747750\pi$
$67$	0.669697	−	0.669697i	0.00999548	−	0.00999548i	0.712087	+	0.702091i	$0.247750\pi$
$68$	6.58660	+	6.58660i	0.0968618	+	0.0968618i
$69$		0			0
$70$	−186.069	−	49.0780i	−2.65813	−	0.701115i
$71$	−60.6616			−0.854388			−0.427194	−	0.904160i	$-0.640498\pi$
$71$	−60.6616			−0.854388			−0.427194	+	0.904160i	$0.640498\pi$
$72$		0			0
$73$	25.6261	+	25.6261i	0.351043	+	0.351043i	0.860498	−	0.509455i	$-0.170153\pi$
$73$	25.6261	+	25.6261i	0.351043	+	0.351043i	−0.509455	+	0.860498i	$0.670153\pi$
$74$		−	199.702i		−	2.69868i
$75$		0			0
$76$	9.75682			0.128379
$77$	−92.2000	+	92.2000i	−1.19740	+	1.19740i
$78$		0			0
$79$			114.069i			1.44391i	0.691940	+	0.721955i	$0.256756\pi$
$79$			114.069i			1.44391i	−0.691940	+	0.721955i	$0.743244\pi$
$80$	9.13701	−	34.6410i	0.114213	−	0.433013i
$81$		0			0
$82$	86.0345	−	86.0345i	1.04920	−	1.04920i
$83$	90.6188	+	90.6188i	1.09179	+	1.09179i	0.995337	+	0.0964560i	$0.0307507\pi$
$83$	90.6188	+	90.6188i	1.09179	+	1.09179i	0.0964560	+	0.995337i	$0.469249\pi$
$84$		0			0
$85$	4.19962	+	7.20871i	0.0494073	+	0.0848084i
$86$	112.528			1.30846
$87$		0			0
$88$	36.3303	+	36.3303i	0.412844	+	0.412844i
$89$		−	83.4245i		−	0.937354i	−0.883370	−	0.468677i	$-0.844731\pi$
$89$		−	83.4245i		−	0.937354i	0.883370	−	0.468677i	$-0.155269\pi$
$90$		0			0
$91$	−203.652			−2.23793
$92$	−77.8867	+	77.8867i	−0.846595	+	0.846595i
$93$		0			0
$94$		−	79.0780i		−	0.841256i
$95$	8.44965	+	2.22870i	0.0889437	+	0.0234600i
$96$		0			0
$97$	66.2087	−	66.2087i	0.682564	−	0.682564i	−0.278013	−	0.960577i	$-0.589676\pi$
$97$	66.2087	−	66.2087i	0.682564	−	0.682564i	0.960577	+	0.278013i	$0.0896759\pi$
$98$	231.090	+	231.090i	2.35806	+	2.35806i
$99$		0			0
$100$	−68.8348	+	121.408i	−0.688348	+	1.21408i
$101$	−23.4304			−0.231984			−0.115992	−	0.993250i	$-0.537005\pi$
$101$	−23.4304			−0.231984			−0.115992	+	0.993250i	$0.537005\pi$
$102$		0			0
$103$	46.8258	+	46.8258i	0.454619	+	0.454619i	0.896884	−	0.442265i	$-0.145825\pi$
$103$	46.8258	+	46.8258i	0.454619	+	0.454619i	−0.442265	+	0.896884i	$0.645825\pi$
$104$			80.2464i			0.771600i
$105$		0			0
$106$	283.147			2.67120
$107$	−129.833	+	129.833i	−1.21339	+	1.21339i	−0.243483	+	0.969905i	$0.578290\pi$
$107$	−129.833	+	129.833i	−1.21339	+	1.21339i	−0.969905	+	0.243483i	$0.921710\pi$
$108$		0			0
$109$			71.5045i			0.656005i	0.944677	+	0.328003i	$0.106375\pi$
$109$			71.5045i			0.656005i	−0.944677	+	0.328003i	$0.893625\pi$
$110$	81.7123	+	140.260i	0.742839	+	1.27510i
$111$		0			0
$112$	−62.9909	+	62.9909i	−0.562419	+	0.562419i
$113$	−56.0334	−	56.0334i	−0.495871	−	0.495871i	0.414279	−	0.910150i	$-0.364034\pi$
$113$	−56.0334	−	56.0334i	−0.495871	−	0.495871i	−0.910150	+	0.414279i	$0.864034\pi$
$114$		0			0
$115$	−85.2432	+	49.6606i	−0.741245	+	0.431831i
$116$	−36.2379			−0.312396
$117$		0			0
$118$	−114.695	−	114.695i	−0.971992	−	0.971992i
$119$		−	20.7448i		−	0.174326i
$120$		0			0
$121$	−11.0091			−0.0909842
$122$	1.10440	−	1.10440i	0.00905247	−	0.00905247i
$123$		0			0
$124$			206.555i			1.66577i
$125$	−87.3454	+	89.4191i	−0.698764	+	0.715353i
$126$		0			0
$127$	9.86932	−	9.86932i	0.0777112	−	0.0777112i	−0.667183	−	0.744894i	$-0.732500\pi$
$127$	9.86932	−	9.86932i	0.0777112	−	0.0777112i	0.744894	+	0.667183i	$0.232500\pi$
$128$	102.175	+	102.175i	0.798244	+	0.798244i
$129$		0			0
$130$	−64.6606	+	245.147i	−0.497389	+	1.88575i
$131$	−38.8522			−0.296581			−0.148291	−	0.988944i	$-0.547377\pi$
$131$	−38.8522			−0.296581			−0.148291	+	0.988944i	$0.547377\pi$
$132$		0			0
$133$	−15.3648	−	15.3648i	−0.115525	−	0.115525i
$134$			2.93180i			0.0218791i
$135$		0			0
$136$	−8.17424			−0.0601047
$137$	−6.58660	+	6.58660i	−0.0480774	+	0.0480774i	−0.730737	−	0.682659i	$-0.760823\pi$
$137$	−6.58660	+	6.58660i	−0.0480774	+	0.0480774i	0.682659	+	0.730737i	$0.260823\pi$
$138$		0			0
$139$			51.3992i			0.369779i	0.982759	+	0.184889i	$0.0591927\pi$
$139$			51.3992i			0.369779i	−0.982759	+	0.184889i	$0.940807\pi$
$140$	299.860	−	174.691i	2.14185	−	1.24779i
$141$		0			0
$142$	132.782	−	132.782i	0.935086	−	0.935086i
$143$	121.474	+	121.474i	0.849469	+	0.849469i
$144$		0			0
$145$	−31.3830	−	8.27765i	−0.216434	−	0.0570872i
$146$	−112.186			−0.768398
$147$		0			0
$148$	254.661	+	254.661i	1.72068	+	1.72068i
$149$		−	138.834i		−	0.931774i	−0.884844	−	0.465887i	$-0.845735\pi$
$149$		−	138.834i		−	0.931774i	0.884844	−	0.465887i	$-0.154265\pi$
$150$		0			0
$151$	−117.243			−0.776445			−0.388222	−	0.921566i	$-0.626911\pi$
$151$	−117.243			−0.776445			−0.388222	+	0.921566i	$0.626911\pi$
$152$	−6.05430	+	6.05430i	−0.0398309	+	0.0398309i
$153$		0			0
$154$		−	403.633i		−	2.62100i
$155$	−47.1824	+	178.882i	−0.304403	+	1.15408i
$156$		0			0
$157$	174.278	−	174.278i	1.11005	−	1.11005i	0.116906	−	0.993143i	$-0.462702\pi$
$157$	174.278	−	174.278i	1.11005	−	1.11005i	0.993143	−	0.116906i	$-0.0372975\pi$
$158$	−249.686	−	249.686i	−1.58029	−	1.58029i
$159$		0			0
$160$	105.147	+	180.486i	0.657169	+	1.12804i
$161$	245.308			1.52365
$162$		0			0
$163$	157.626	+	157.626i	0.967032	+	0.967032i	0.999474	−	0.0324421i	$-0.0103285\pi$
$163$	157.626	+	157.626i	0.967032	+	0.967032i	−0.0324421	+	0.999474i	$0.510328\pi$
$164$			219.422i			1.33794i
$165$		0			0
$166$	−396.711			−2.38983
$167$	86.5669	−	86.5669i	0.518365	−	0.518365i	−0.398712	−	0.917076i	$-0.630543\pi$
$167$	86.5669	−	86.5669i	0.518365	−	0.518365i	0.917076	+	0.398712i	$0.130543\pi$
$168$		0			0
$169$			99.3121i			0.587646i
$170$	−24.9717	−	6.58660i	−0.146892	−	0.0387447i
$171$		0			0
$172$	−143.495	+	143.495i	−0.834276	+	0.834276i
$173$	−37.1757	−	37.1757i	−0.214888	−	0.214888i	0.591452	−	0.806340i	$-0.298555\pi$
$173$	−37.1757	−	37.1757i	−0.214888	−	0.214888i	−0.806340	+	0.591452i	$0.798555\pi$
$174$		0			0
$175$	299.590	−	82.7913i	1.71194	−	0.473093i
$176$	75.1456			0.426964
$177$		0			0
$178$	182.608	+	182.608i	1.02589	+	1.02589i
$179$		−	140.296i		−	0.783777i	−0.920013	−	0.391889i	$-0.871822\pi$
$179$		−	140.296i		−	0.783777i	0.920013	−	0.391889i	$-0.128178\pi$
$180$		0			0
$181$	−242.720			−1.34100			−0.670498	−	0.741911i	$-0.733920\pi$
$181$	−242.720			−1.34100			−0.670498	+	0.741911i	$0.733920\pi$
$182$	445.773	−	445.773i	2.44930	−	2.44930i
$183$		0			0
$184$		−	96.6606i		−	0.525329i
$185$	162.372	+	278.713i	0.877685	+	1.50656i
$186$		0			0
$187$	−12.3739	+	12.3739i	−0.0661704	+	0.0661704i
$188$	100.840	+	100.840i	0.536385	+	0.536385i
$189$		0			0
$190$	−23.3739	+	13.6170i	−0.123020	+	0.0716687i
$191$	−18.0676			−0.0945946			−0.0472973	−	0.998881i	$-0.515061\pi$
$191$	−18.0676			−0.0945946			−0.0472973	+	0.998881i	$0.515061\pi$
$192$		0			0
$193$	−191.269	−	191.269i	−0.991029	−	0.991029i	0.00893131	−	0.999960i	$-0.497157\pi$
$193$	−191.269	−	191.269i	−0.991029	−	0.991029i	−0.999960	+	0.00893131i	$0.997157\pi$
$194$			289.849i			1.49407i
$195$		0			0
$196$	−589.372			−3.00700
$197$	−13.5148	+	13.5148i	−0.0686031	+	0.0686031i	−0.740576	−	0.671973i	$-0.765447\pi$
$197$	−13.5148	+	13.5148i	−0.0686031	+	0.0686031i	0.671973	+	0.740576i	$0.265447\pi$
$198$		0			0
$199$			141.964i			0.713385i	0.934222	+	0.356693i	$0.116096\pi$
$199$			141.964i			0.713385i	−0.934222	+	0.356693i	$0.883904\pi$
$200$	−32.6229	−	118.050i	−0.163115	−	0.590249i
$201$		0			0
$202$	51.2867	−	51.2867i	0.253895	−	0.253895i
$203$	57.0665	+	57.0665i	0.281116	+	0.281116i
$204$		0			0
$205$	−50.1216	+	190.025i	−0.244496	+	0.926953i
$206$	−204.994			−0.995116
$207$		0			0
$208$	82.9909	+	82.9909i	0.398995	+	0.398995i
$209$			18.3296i			0.0877012i
$210$		0			0
$211$	193.973			0.919302			0.459651	−	0.888100i	$-0.347975\pi$
$211$	193.973			0.919302			0.459651	+	0.888100i	$0.347975\pi$
$212$	−361.069	+	361.069i	−1.70316	+	1.70316i
$213$		0			0
$214$		−	568.381i		−	2.65599i
$215$	−157.049	+	91.4927i	−0.730459	+	0.425548i
$216$		0			0
$217$	325.278	−	325.278i	1.49898	−	1.49898i
$218$	−156.516	−	156.516i	−0.717965	−	0.717965i
$219$		0			0
$220$	−283.060	−	74.6606i	−1.28664	−	0.339366i
$221$	−27.3314			−0.123672
$222$		0			0
$223$	−14.0689	−	14.0689i	−0.0630894	−	0.0630894i	0.674858	−	0.737948i	$-0.264205\pi$
$223$	−14.0689	−	14.0689i	−0.0630894	−	0.0630894i	−0.737948	+	0.674858i	$0.764205\pi$
$224$		−	519.393i		−	2.31872i
$225$		0			0
$226$	245.303			1.08541
$227$	−148.539	+	148.539i	−0.654358	+	0.654358i	−0.954039	−	0.299681i	$-0.903120\pi$
$227$	−148.539	+	148.539i	−0.654358	+	0.654358i	0.299681	+	0.954039i	$0.403120\pi$
$228$		0			0
$229$		−	72.3303i		−	0.315853i	−0.987451	−	0.157926i	$-0.949519\pi$
$229$		−	72.3303i		−	0.315853i	0.987451	−	0.157926i	$-0.0504809\pi$
$230$	77.8867	−	295.291i	0.338638	−	1.28387i
$231$		0			0
$232$	22.4864	−	22.4864i	0.0969240	−	0.0969240i
$233$	−113.160	−	113.160i	−0.485663	−	0.485663i	0.421271	−	0.906935i	$-0.361584\pi$
$233$	−113.160	−	113.160i	−0.485663	−	0.485663i	−0.906935	+	0.421271i	$0.861584\pi$
$234$		0			0
$235$	64.2958	+	110.365i	0.273599	+	0.469637i
$236$	292.518			1.23948
$237$		0			0
$238$	45.4083	+	45.4083i	0.190791	+	0.190791i
$239$			283.484i			1.18613i	0.805156	+	0.593063i	$0.202082\pi$
$239$			283.484i			1.18613i	−0.805156	+	0.593063i	$0.797918\pi$
$240$		0			0
$241$	481.711			1.99880			0.999401	−	0.0346023i	$-0.0110164\pi$
$241$	481.711			1.99880			0.999401	+	0.0346023i	$0.0110164\pi$
$242$	24.0978	−	24.0978i	0.0995777	−	0.0995777i
$243$		0			0
$244$			2.81667i			0.0115437i
$245$	−510.411	−	134.627i	−2.08331	−	0.549499i
$246$		0			0
$247$	−20.2432	+	20.2432i	−0.0819562	+	0.0819562i
$248$	−128.172	−	128.172i	−0.516822	−	0.516822i
$249$		0			0
$250$	−4.53901	−	386.920i	−0.0181561	−	1.54768i
$251$	87.5245			0.348703			0.174352	−	0.984683i	$-0.444217\pi$
$251$	87.5245			0.348703			0.174352	+	0.984683i	$0.444217\pi$
$252$		0			0
$253$	−146.321	−	146.321i	−0.578345	−	0.578345i
$254$			43.2059i			0.170102i
$255$		0			0
$256$	−44.6606			−0.174455
$257$	−130.587	+	130.587i	−0.508121	+	0.508121i	−0.913949	−	0.405829i	$-0.866983\pi$
$257$	−130.587	+	130.587i	−0.508121	+	0.508121i	0.405829	+	0.913949i	$0.366983\pi$
$258$		0			0
$259$		−	802.065i		−	3.09678i
$260$	−230.156	−	395.067i	−0.885217	−	1.51949i
$261$		0			0
$262$	85.0436	−	85.0436i	0.324594	−	0.324594i
$263$	−216.586	−	216.586i	−0.823521	−	0.823521i	0.163090	−	0.986611i	$-0.447854\pi$
$263$	−216.586	−	216.586i	−0.823521	−	0.823521i	−0.986611	+	0.163090i	$0.947854\pi$
$264$		0			0
$265$	−395.172	+	230.218i	−1.49122	+	0.868746i
$266$	67.2639			0.252872
$267$		0			0
$268$	−3.73864	−	3.73864i	−0.0139501	−	0.0139501i
$269$			283.047i			1.05222i	0.850416	+	0.526110i	$0.176350\pi$
$269$			283.047i			1.05222i	−0.850416	+	0.526110i	$0.823650\pi$
$270$		0			0
$271$	−130.991			−0.483361			−0.241681	−	0.970356i	$-0.577699\pi$
$271$	−130.991			−0.483361			−0.241681	+	0.970356i	$0.577699\pi$
$272$	−8.45381	+	8.45381i	−0.0310802	+	0.0310802i
$273$		0			0
$274$		−	28.8348i		−	0.105237i
$275$	−228.083	−	129.316i	−0.829391	−	0.470240i
$276$		0			0
$277$	−114.259	+	114.259i	−0.412489	+	0.412489i	−0.882605	−	0.470116i	$-0.844212\pi$
$277$	−114.259	+	114.259i	−0.412489	+	0.412489i	0.470116	+	0.882605i	$0.344212\pi$
$278$	−112.508	−	112.508i	−0.404705	−	0.404705i
$279$		0			0
$280$	−77.6697	+	294.468i	−0.277392	+	1.05167i
$281$	−24.7412			−0.0880470			−0.0440235	−	0.999030i	$-0.514018\pi$
$281$	−24.7412			−0.0880470			−0.0440235	+	0.999030i	$0.514018\pi$
$282$		0			0
$283$	−83.3992	−	83.3992i	−0.294697	−	0.294697i	0.544236	−	0.838932i	$-0.316820\pi$
$283$	−83.3992	−	83.3992i	−0.294697	−	0.294697i	−0.838932	+	0.544236i	$0.816820\pi$
$284$			338.648i			1.19242i
$285$		0			0
$286$	−531.789			−1.85940
$287$	345.540	−	345.540i	1.20397	−	1.20397i
$288$		0			0
$289$			286.216i			0.990366i
$290$	86.8131	−	50.5752i	0.299356	−	0.174397i
$291$		0			0
$292$	143.060	−	143.060i	0.489931	−	0.489931i
$293$	−205.816	−	205.816i	−0.702445	−	0.702445i	0.262490	−	0.964935i	$-0.415456\pi$
$293$	−205.816	−	205.816i	−0.702445	−	0.702445i	−0.964935	+	0.262490i	$0.915456\pi$
$294$		0			0
$295$	253.328	+	66.8186i	0.858740	+	0.226504i
$296$	−316.044			−1.06772
$297$		0			0
$298$	303.895	+	303.895i	1.01978	+	1.01978i
$299$		−	323.195i		−	1.08092i
$300$		0			0
$301$	451.945			1.50148
$302$	256.634	−	256.634i	0.849781	−	0.849781i
$303$		0			0
$304$			12.5227i			0.0411932i
$305$	−0.643397	+	2.43930i	−0.00210950	+	0.00799772i
$306$		0			0
$307$	61.6534	−	61.6534i	0.200825	−	0.200825i	−0.599528	−	0.800354i	$-0.704645\pi$
$307$	61.6534	−	61.6534i	0.200825	−	0.200825i	0.800354	+	0.599528i	$0.204645\pi$
$308$	514.713	+	514.713i	1.67115	+	1.67115i
$309$		0			0
$310$	−288.278	−	494.833i	−0.929928	−	1.59624i
$311$	612.455			1.96931			0.984655	−	0.174513i	$-0.0558351\pi$
$311$	612.455			1.96931			0.984655	+	0.174513i	$0.0558351\pi$
$312$		0			0
$313$	73.8947	+	73.8947i	0.236085	+	0.236085i	0.815227	−	0.579142i	$-0.196612\pi$
$313$	73.8947	+	73.8947i	0.236085	+	0.236085i	−0.579142	+	0.815227i	$0.696612\pi$
$314$			762.953i			2.42979i
$315$		0			0
$316$	636.798			2.01519
$317$	−295.915	+	295.915i	−0.933484	+	0.933484i	−0.997922	−	0.0644374i	$-0.979475\pi$
$317$	−295.915	+	295.915i	−0.933484	+	0.933484i	0.0644374	+	0.997922i	$0.479475\pi$
$318$		0			0
$319$		−	68.0780i		−	0.213411i
$320$	−486.659	−	128.362i	−1.52081	−	0.401133i
$321$		0			0
$322$	−536.955	+	536.955i	−1.66756	+	1.66756i
$323$	−2.06206	−	2.06206i	−0.00638408	−	0.00638408i
$324$		0			0
$325$	−109.078	−	394.711i	−0.335625	−	1.21450i
$326$	−690.056			−2.11674
$327$		0			0
$328$	−136.156	−	136.156i	−0.415110	−	0.415110i
$329$		−	317.601i		−	0.965353i
$330$		0			0
$331$	−220.757			−0.666939			−0.333470	−	0.942761i	$-0.608219\pi$
$331$	−220.757			−0.666939			−0.333470	+	0.942761i	$0.608219\pi$
$332$	505.887	−	505.887i	1.52375	−	1.52375i
$333$		0			0
$334$			378.973i			1.13465i
$335$	−2.38375	−	4.09175i	−0.00711569	−	0.0122142i
$336$		0			0
$337$	61.1652	−	61.1652i	0.181499	−	0.181499i	−0.610510	−	0.792009i	$-0.709035\pi$
$337$	61.1652	−	61.1652i	0.181499	−	0.181499i	0.792009	+	0.610510i	$0.209035\pi$
$338$	−217.384	−	217.384i	−0.643149	−	0.643149i
$339$		0			0
$340$	40.2432	−	23.4447i	0.118362	−	0.0689550i
$341$	−388.043			−1.13796
$342$		0			0
$343$	497.354	+	497.354i	1.45001	+	1.45001i
$344$		−	178.084i		−	0.517685i
$345$		0			0
$346$	162.748			0.470369
$347$	307.427	−	307.427i	0.885957	−	0.885957i	−0.108175	−	0.994132i	$-0.534501\pi$
$347$	307.427	−	307.427i	0.885957	−	0.885957i	0.994132	+	0.108175i	$0.0345007\pi$
$348$		0			0
$349$			388.789i			1.11401i	0.830509	+	0.557005i	$0.188050\pi$
$349$			388.789i			1.11401i	−0.830509	+	0.557005i	$0.811950\pi$
$350$	−474.550	+	836.994i	−1.35586	+	2.39141i
$351$		0			0
$352$	−309.808	+	309.808i	−0.880135	+	0.880135i
$353$	16.1564	+	16.1564i	0.0457689	+	0.0457689i	0.729621	−	0.683852i	$-0.239697\pi$
$353$	16.1564	+	16.1564i	0.0457689	+	0.0457689i	−0.683852	+	0.729621i	$0.739697\pi$
$354$		0			0
$355$	−77.3557	+	293.278i	−0.217903	+	0.826134i
$356$	−465.724			−1.30821
$357$		0			0
$358$	307.094	+	307.094i	0.857805	+	0.857805i
$359$			105.473i			0.293796i	0.989152	+	0.146898i	$0.0469289\pi$
$359$			105.473i			0.293796i	−0.989152	+	0.146898i	$0.953071\pi$
$360$		0			0
$361$	357.945			0.991539
$362$	531.291	−	531.291i	1.46765	−	1.46765i
$363$		0			0
$364$			1136.90i			3.12335i
$365$	156.572	−	91.2150i	0.428964	−	0.249904i
$366$		0			0
$367$	−130.670	+	130.670i	−0.356048	+	0.356048i	−0.862354	−	0.506306i	$-0.831011\pi$
$367$	−130.670	+	130.670i	−0.356048	+	0.356048i	0.506306	+	0.862354i	$0.331011\pi$
$368$	−99.9664	−	99.9664i	−0.271648	−	0.271648i
$369$		0			0
$370$	−965.492	−	254.661i	−2.60944	−	0.688272i
$371$	1137.20			3.06524
$372$		0			0
$373$	213.677	+	213.677i	0.572860	+	0.572860i	0.932927	−	0.360066i	$-0.117246\pi$
$373$	213.677	+	213.677i	0.572860	+	0.572860i	−0.360066	+	0.932927i	$0.617246\pi$
$374$		−	54.1703i		−	0.144840i
$375$		0			0
$376$	−125.147			−0.332838
$377$	75.1854	−	75.1854i	0.199431	−	0.199431i
$378$		0			0
$379$			142.748i			0.376643i	0.982107	+	0.188322i	$0.0603047\pi$
$379$			142.748i			0.376643i	−0.982107	+	0.188322i	$0.939695\pi$
$380$	12.4419	−	47.1708i	0.0327418	−	0.124134i
$381$		0			0
$382$	39.5481	−	39.5481i	0.103529	−	0.103529i
$383$	−225.850	−	225.850i	−0.589686	−	0.589686i	0.347860	−	0.937546i	$-0.386908\pi$
$383$	−225.850	−	225.850i	−0.589686	−	0.589686i	−0.937546	+	0.347860i	$0.886908\pi$
$384$		0			0
$385$	328.181	+	563.328i	0.852419	+	1.46319i
$386$	837.336			2.16926
$387$		0			0
$388$	−369.615	−	369.615i	−0.952616	−	0.952616i
$389$			78.1968i			0.201020i	0.994936	+	0.100510i	$0.0320475\pi$
$389$			78.1968i			0.201020i	−0.994936	+	0.100510i	$0.967953\pi$
$390$		0			0
$391$	32.9220			0.0841994
$392$	365.717	−	365.717i	0.932952	−	0.932952i
$393$		0			0
$394$		−	59.1652i		−	0.150165i
$395$	551.484	+	145.461i	1.39616	+	0.368255i
$396$		0			0
$397$	−140.027	+	140.027i	−0.352714	+	0.352714i	−0.861118	−	0.508405i	$-0.830235\pi$
$397$	−140.027	+	140.027i	−0.352714	+	0.352714i	0.508405	+	0.861118i	$0.330235\pi$
$398$	−310.744	−	310.744i	−0.780765	−	0.780765i
$399$		0			0
$400$	−155.826	−	88.3485i	−0.389564	−	0.220871i
$401$	345.163			0.860756			0.430378	−	0.902649i	$-0.358380\pi$
$401$	345.163			0.860756			0.430378	+	0.902649i	$0.358380\pi$
$402$		0			0
$403$	−428.555	−	428.555i	−1.06341	−	1.06341i
$404$			130.802i			0.323767i
$405$		0			0
$406$	−249.826			−0.615334
$407$	−478.416	+	478.416i	−1.17547	+	1.17547i
$408$		0			0
$409$			280.679i			0.686256i	0.939289	+	0.343128i	$0.111487\pi$
$409$			280.679i			0.686256i	−0.939289	+	0.343128i	$0.888513\pi$
$410$	−306.236	−	525.658i	−0.746916	−	1.28209i
$411$		0			0
$412$	261.408	−	261.408i	0.634486	−	0.634486i
$413$	−460.650	−	460.650i	−1.11538	−	1.11538i
$414$		0			0
$415$	553.668	−	322.553i	1.33414	−	0.777237i
$416$	−684.304			−1.64496
$417$		0			0
$418$	−40.1216	−	40.1216i	−0.0959847	−	0.0959847i
$419$			493.405i			1.17758i	0.808287	+	0.588789i	$0.200395\pi$
$419$			493.405i			1.17758i	−0.808287	+	0.588789i	$0.799605\pi$
$420$		0			0
$421$	395.000			0.938242			0.469121	−	0.883134i	$-0.344571\pi$
$421$	395.000			0.938242			0.469121	+	0.883134i	$0.344571\pi$
$422$	−424.587	+	424.587i	−1.00613	+	1.00613i
$423$		0			0
$424$		−	448.102i		−	1.05684i
$425$	40.2070	−	11.1112i	0.0946046	−	0.0261439i
$426$		0			0
$427$	4.43561	−	4.43561i	0.0103878	−	0.0103878i
$428$	724.800	+	724.800i	1.69346	+	1.69346i
$429$		0			0
$430$	143.495	−	544.033i	0.333710	−	1.26519i
$431$	23.0490			0.0534779			0.0267389	−	0.999642i	$-0.491488\pi$
$431$	23.0490			0.0534779			0.0267389	+	0.999642i	$0.491488\pi$
$432$		0			0
$433$	−357.486	−	357.486i	−0.825604	−	0.825604i	0.161302	−	0.986905i	$-0.448431\pi$
$433$	−357.486	−	357.486i	−0.825604	−	0.825604i	−0.986905	+	0.161302i	$0.948431\pi$
$434$			1424.00i			3.28111i
$435$		0			0
$436$	399.180			0.915549
$437$	24.3839	−	24.3839i	0.0557983	−	0.0557983i
$438$		0			0
$439$		−	688.336i		−	1.56796i	−0.620784	−	0.783981i	$-0.713186\pi$
$439$		−	688.336i		−	1.56796i	0.620784	−	0.783981i	$-0.286814\pi$
$440$	221.973	−	129.316i	0.504484	−	0.293900i
$441$		0			0
$442$	59.8258	−	59.8258i	0.135352	−	0.135352i
$443$	237.947	+	237.947i	0.537126	+	0.537126i	0.922684	−	0.385558i	$-0.125991\pi$
$443$	237.947	+	237.947i	0.537126	+	0.537126i	−0.385558	+	0.922684i	$0.625991\pi$
$444$		0			0
$445$	−403.328	−	106.383i	−0.906356	−	0.239063i
$446$	61.5910			0.138096
$447$		0			0
$448$	884.936	+	884.936i	1.97530	+	1.97530i
$449$			387.090i			0.862115i	0.902324	+	0.431058i	$0.141859\pi$
$449$			387.090i			0.862115i	−0.902324	+	0.431058i	$0.858141\pi$
$450$		0			0
$451$	−412.216			−0.914004
$452$	−312.811	+	312.811i	−0.692059	+	0.692059i
$453$		0			0
$454$		−	650.276i		−	1.43233i
$455$	−259.697	+	984.584i	−0.570762	+	2.16392i
$456$		0			0
$457$	−141.494	+	141.494i	−0.309614	+	0.309614i	−0.844760	−	0.535146i	$-0.820257\pi$
$457$	−141.494	+	141.494i	−0.309614	+	0.309614i	0.535146	+	0.844760i	$0.320257\pi$
$458$	158.324	+	158.324i	0.345685	+	0.345685i
$459$		0			0
$460$	277.234	+	475.877i	0.602683	+	1.03451i
$461$	705.175			1.52966			0.764832	−	0.644230i	$-0.222822\pi$
$461$	705.175			1.52966			0.764832	+	0.644230i	$0.222822\pi$
$462$		0			0
$463$	119.817	+	119.817i	0.258783	+	0.258783i	0.824559	−	0.565776i	$-0.191423\pi$
$463$	119.817	+	119.817i	0.258783	+	0.258783i	−0.565776	+	0.824559i	$0.691423\pi$
$464$		−	46.5108i		−	0.100239i
$465$		0			0
$466$	495.390			1.06307
$467$	−47.2065	+	47.2065i	−0.101085	+	0.101085i	−0.755840	−	0.654756i	$-0.772771\pi$
$467$	−47.2065	+	47.2065i	−0.101085	+	0.101085i	0.654756	+	0.755840i	$0.272771\pi$
$468$		0			0
$469$			11.7750i			0.0251066i
$470$	−382.315	−	100.840i	−0.813436	−	0.214554i
$471$		0			0
$472$	−181.514	+	181.514i	−0.384563	+	0.384563i
$473$	−269.576	−	269.576i	−0.569929	−	0.569929i
$474$		0			0
$475$	21.5500	−	38.0091i	0.0453684	−	0.0800191i
$476$	−115.809			−0.243297
$477$		0			0
$478$	−620.519	−	620.519i	−1.29816	−	1.29816i
$479$		−	534.902i		−	1.11671i	−0.829604	−	0.558353i	$-0.811434\pi$
$479$		−	534.902i		−	1.11671i	0.829604	−	0.558353i	$-0.188566\pi$
$480$		0			0
$481$	−1056.73			−2.19694
$482$	−1054.42	+	1054.42i	−2.18759	+	2.18759i
$483$		0			0
$484$			61.4591i			0.126982i
$485$	−235.667	−	404.525i	−0.485911	−	0.834073i
$486$		0			0
$487$	284.693	−	284.693i	0.584586	−	0.584586i	−0.351574	−	0.936160i	$-0.614354\pi$
$487$	284.693	−	284.693i	0.584586	−	0.584586i	0.936160	+	0.351574i	$0.114354\pi$
$488$	−1.74780	−	1.74780i	−0.00358155	−	0.00358155i
$489$		0			0
$490$	1411.93	−	822.553i	2.88148	−	1.67868i
$491$	58.2306			0.118596			0.0592979	−	0.998240i	$-0.481114\pi$
$491$	58.2306			0.118596			0.0592979	+	0.998240i	$0.481114\pi$
$492$		0			0
$493$	7.65871	+	7.65871i	0.0155349	+	0.0155349i
$494$		−	88.6206i		−	0.179394i
$495$		0			0
$496$	−265.111			−0.534497
$497$	533.293	−	533.293i	1.07302	−	1.07302i
$498$		0			0
$499$			6.37197i			0.0127695i	0.999980	+	0.00638474i	$0.00203234\pi$
$499$			6.37197i			0.0127695i	−0.999980	+	0.00638474i	$0.997968\pi$
$500$	499.189	+	487.613i	0.998378	+	0.975225i
$501$		0			0
$502$	−191.583	+	191.583i	−0.381639	+	0.381639i
$503$	452.328	+	452.328i	0.899261	+	0.899261i	0.995371	−	0.0961100i	$-0.0306401\pi$
$503$	452.328	+	452.328i	0.899261	+	0.899261i	−0.0961100	+	0.995371i	$0.530640\pi$
$504$		0			0
$505$	−29.8784	+	113.278i	−0.0591652	+	0.224312i
$506$	640.565			1.26594
$507$		0			0
$508$	−55.0962	−	55.0962i	−0.108457	−	0.108457i
$509$		−	584.107i		−	1.14756i	−0.819010	−	0.573779i	$-0.805477\pi$
$509$		−	584.107i		−	1.14756i	0.819010	−	0.573779i	$-0.194523\pi$
$510$		0			0
$511$	−450.573			−0.881749
$512$	−310.943	+	310.943i	−0.607311	+	0.607311i
$513$		0			0
$514$		−	571.684i		−	1.11223i
$515$	286.098	−	166.674i	0.555531	−	0.323639i
$516$		0			0
$517$	−189.443	+	189.443i	−0.366427	+	0.366427i
$518$	1755.64	+	1755.64i	3.38927	+	3.38927i
$519$		0			0
$520$	387.964	+	102.330i	0.746084	+	0.196789i
$521$	512.704			0.984076			0.492038	−	0.870574i	$-0.336252\pi$
$521$	512.704			0.984076			0.492038	+	0.870574i	$0.336252\pi$
$522$		0			0
$523$	−562.973	−	562.973i	−1.07643	−	1.07643i	−0.996827	−	0.0796030i	$-0.974635\pi$
$523$	−562.973	−	562.973i	−1.07643	−	1.07643i	−0.0796030	−	0.996827i	$-0.525365\pi$
$524$			216.895i			0.413922i
$525$		0			0
$526$	948.170			1.80261
$527$	43.6545	−	43.6545i	0.0828358	−	0.0828358i
$528$		0			0
$529$		−	139.697i		−	0.264077i
$530$	361.069	−	1368.92i	0.681263	−	2.58286i
$531$		0			0
$532$	−85.7750	+	85.7750i	−0.161231	+	0.161231i
$533$	−455.252	−	455.252i	−0.854131	−	0.854131i
$534$		0			0
$535$	462.133	+	793.258i	0.863799	+	1.48272i
$536$	4.63980			0.00865634
$537$		0			0
$538$	−619.562	−	619.562i	−1.15160	−	1.15160i
$539$		−	1107.22i		−	2.05421i
$540$		0			0
$541$	−943.675			−1.74432			−0.872158	−	0.489224i	$-0.837280\pi$
$541$	−943.675			−1.74432			−0.872158	+	0.489224i	$0.837280\pi$
$542$	286.726	−	286.726i	0.529015	−	0.529015i
$543$		0			0
$544$		−	69.7061i		−	0.128136i
$545$	345.700	+	91.1826i	0.634311	+	0.167308i
$546$		0			0
$547$	208.537	−	208.537i	0.381238	−	0.381238i	−0.490310	−	0.871548i	$-0.663116\pi$
$547$	208.537	−	208.537i	0.381238	−	0.381238i	0.871548	+	0.490310i	$0.163116\pi$
$548$	36.7702	+	36.7702i	0.0670989	+	0.0670989i
$549$		0			0
$550$	782.310	−	216.191i	1.42238	−	0.393074i
$551$	11.3449			0.0205897
$552$		0			0
$553$	−1002.81	−	1002.81i	−1.81340	−	1.81340i
$554$		−	500.205i		−	0.902898i
$555$		0			0
$556$	286.940			0.516079
$557$	154.478	−	154.478i	0.277340	−	0.277340i	−0.554706	−	0.832046i	$-0.687169\pi$
$557$	154.478	−	154.478i	0.277340	−	0.277340i	0.832046	+	0.554706i	$0.187169\pi$
$558$		0			0
$559$		−	595.441i		−	1.06519i
$560$	224.213	+	384.865i	0.400381	+	0.687259i
$561$		0			0
$562$	54.1561	−	54.1561i	0.0963631	−	0.0963631i
$563$	−326.186	−	326.186i	−0.579371	−	0.579371i	0.355359	−	0.934730i	$-0.384359\pi$
$563$	−326.186	−	326.186i	−0.579371	−	0.579371i	−0.934730	+	0.355359i	$0.884359\pi$
$564$		0			0
$565$	−342.356	+	199.448i	−0.605939	+	0.353005i
$566$	365.105			0.645062
$567$		0			0
$568$	−210.138	−	210.138i	−0.369961	−	0.369961i
$569$		−	533.091i		−	0.936891i	−0.883492	−	0.468446i	$-0.844814\pi$
$569$		−	533.091i		−	0.936891i	0.883492	−	0.468446i	$-0.155186\pi$
$570$		0			0
$571$	−59.4318			−0.104084			−0.0520419	−	0.998645i	$-0.516573\pi$
$571$	−59.4318			−0.104084			−0.0520419	+	0.998645i	$0.516573\pi$
$572$	678.138	−	678.138i	1.18556	−	1.18556i
$573$		0			0
$574$			1512.71i			2.63538i
$575$	131.390	+	475.448i	0.228504	+	0.826867i
$576$		0			0
$577$	410.356	−	410.356i	0.711188	−	0.711188i	−0.255595	−	0.966784i	$-0.582272\pi$
$577$	410.356	−	410.356i	0.711188	−	0.711188i	0.966784	+	0.255595i	$0.0822715\pi$
$578$	−626.498	−	626.498i	−1.08391	−	1.08391i
$579$		0			0
$580$	−46.2106	+	175.198i	−0.0796735	+	0.302065i
$581$	−1593.31			−2.74236
$582$		0			0
$583$	−678.319	−	678.319i	−1.16350	−	1.16350i
$584$			177.543i			0.304012i
$585$		0			0
$586$	901.023			1.53758
$587$	405.066	−	405.066i	0.690061	−	0.690061i	−0.272184	−	0.962245i	$-0.587746\pi$
$587$	405.066	−	405.066i	0.690061	−	0.690061i	0.962245	+	0.272184i	$0.0877459\pi$
$588$		0			0
$589$		−	64.6659i		−	0.109789i
$590$	−700.770	+	408.252i	−1.18775	+	0.691952i
$591$		0			0
$592$	−326.853	+	326.853i	−0.552117	+	0.552117i
$593$	−526.790	−	526.790i	−0.888347	−	0.888347i	0.106017	−	0.994364i	$-0.466190\pi$
$593$	−526.790	−	526.790i	−0.888347	−	0.888347i	−0.994364	+	0.106017i	$0.966190\pi$
$594$		0			0
$595$	−100.294	−	26.4538i	−0.168561	−	0.0444602i
$596$	−775.053			−1.30043
$597$		0			0
$598$	707.441	+	707.441i	1.18301	+	1.18301i
$599$			429.621i			0.717230i	0.933486	+	0.358615i	$0.116751\pi$
$599$			429.621i			0.717230i	−0.933486	+	0.358615i	$0.883249\pi$
$600$		0			0
$601$	415.189			0.690830			0.345415	−	0.938450i	$-0.387738\pi$
$601$	415.189			0.690830			0.345415	+	0.938450i	$0.387738\pi$
$602$	−989.264	+	989.264i	−1.64330	+	1.64330i
$603$		0			0
$604$			654.519i			1.08364i
$605$	−14.0388	+	53.2251i	−0.0232046	+	0.0879754i
$606$		0			0
$607$	−525.425	+	525.425i	−0.865609	+	0.865609i	−0.991983	−	0.126374i	$-0.959666\pi$
$607$	−525.425	+	525.425i	−0.865609	+	0.865609i	0.126374	+	0.991983i	$0.459666\pi$
$608$	−51.6282	−	51.6282i	−0.0849149	−	0.0849149i
$609$		0			0
$610$	−3.93106	−	6.74773i	−0.00644436	−	0.0110618i
$611$	−418.442			−0.684847
$612$		0			0
$613$	764.432	+	764.432i	1.24703	+	1.24703i	0.957023	+	0.290010i	$0.0936588\pi$
$613$	764.432	+	764.432i	1.24703	+	1.24703i	0.290010	+	0.957023i	$0.406341\pi$
$614$			269.906i			0.439587i
$615$		0			0
$616$	−638.780			−1.03698
$617$	530.469	−	530.469i	0.859755	−	0.859755i	−0.131554	−	0.991309i	$-0.541997\pi$
$617$	530.469	−	530.469i	0.859755	−	0.859755i	0.991309	+	0.131554i	$0.0419968\pi$
$618$		0			0
$619$			1203.77i			1.94470i	0.233522	+	0.972352i	$0.424975\pi$
$619$			1203.77i			1.94470i	−0.233522	+	0.972352i	$0.575025\pi$
$620$	998.623	+	263.399i	1.61068	+	0.424838i
$621$		0			0
$622$	−1340.60	+	1340.60i	−2.15531	+	2.15531i
$623$	733.409	+	733.409i	1.17722	+	1.17722i
$624$		0			0
$625$	320.927	+	536.312i	0.513484	+	0.858099i
$626$	−323.496			−0.516767
$627$		0			0
$628$	−972.918	−	972.918i	−1.54923	−	1.54923i
$629$		−	107.643i		−	0.171133i
$630$		0			0
$631$	133.973			0.212318			0.106159	−	0.994349i	$-0.466145\pi$
$631$	133.973			0.212318			0.106159	+	0.994349i	$0.466145\pi$
$632$	−395.146	+	395.146i	−0.625232	+	0.625232i
$633$		0			0
$634$		−	1295.46i		−	2.04330i
$635$	−35.1294	−	60.3001i	−0.0553218	−	0.0949608i
$636$		0			0
$637$	1222.81	−	1222.81i	1.91964	−	1.91964i
$638$	149.016	+	149.016i	0.233568	+	0.233568i
$639$		0			0
$640$	624.276	−	363.688i	0.975431	−	0.568262i
$641$	−362.038			−0.564803			−0.282401	−	0.959296i	$-0.591131\pi$
$641$	−362.038			−0.564803			−0.282401	+	0.959296i	$0.591131\pi$
$642$		0			0
$643$	−243.080	−	243.080i	−0.378040	−	0.378040i	0.492354	−	0.870395i	$-0.336136\pi$
$643$	−243.080	−	243.080i	−0.378040	−	0.378040i	−0.870395	+	0.492354i	$0.836136\pi$
$644$		−	1369.45i		−	2.12647i
$645$		0			0
$646$	9.02727			0.0139741
$647$	−627.638	+	627.638i	−0.970075	+	0.970075i	−0.999565	−	0.0294903i	$-0.990612\pi$
$647$	−627.638	+	627.638i	−0.970075	+	0.970075i	0.0294903	+	0.999565i	$0.490612\pi$
$648$		0			0
$649$			549.537i			0.846744i
$650$	1102.75	+	625.223i	1.69653	+	0.961882i
$651$		0			0
$652$	879.960	−	879.960i	1.34963	−	1.34963i
$653$	343.319	+	343.319i	0.525757	+	0.525757i	0.919304	−	0.393548i	$-0.128752\pi$
$653$	343.319	+	343.319i	0.525757	+	0.525757i	−0.393548	+	0.919304i	$0.628752\pi$
$654$		0			0
$655$	−49.5443	+	187.837i	−0.0756402	+	0.286774i
$656$	−281.625			−0.429307
$657$		0			0
$658$	695.198	+	695.198i	1.05653	+	1.05653i
$659$			1203.78i			1.82668i	0.407194	+	0.913342i	$0.366507\pi$
$659$			1203.78i			1.82668i	−0.407194	+	0.913342i	$0.633493\pi$
$660$		0			0
$661$	−788.143			−1.19235			−0.596175	−	0.802855i	$-0.703314\pi$
$661$	−788.143			−1.19235			−0.596175	+	0.802855i	$0.703314\pi$
$662$	483.215	−	483.215i	0.729932	−	0.729932i
$663$		0			0
$664$			627.826i			0.945521i
$665$	−93.8765	+	54.6902i	−0.141168	+	0.0822408i
$666$		0			0
$667$	−90.5644	+	90.5644i	−0.135779	+	0.135779i
$668$	−483.266	−	483.266i	−0.723452	−	0.723452i
$669$		0			0
$670$	14.1742	+	3.73864i	0.0211556	+	0.00558005i
$671$	−5.29150			−0.00788599
$672$		0			0
$673$	199.922	+	199.922i	0.297061	+	0.297061i	0.839862	−	0.542801i	$-0.182636\pi$
$673$	199.922	+	199.922i	0.297061	+	0.297061i	−0.542801	+	0.839862i	$0.682636\pi$
$674$			267.769i			0.397283i
$675$		0			0
$676$	554.417			0.820144
$677$	−496.788	+	496.788i	−0.733809	+	0.733809i	−0.971372	−	0.237563i	$-0.923651\pi$
$677$	−496.788	+	496.788i	−0.733809	+	0.733809i	0.237563	+	0.971372i	$0.423651\pi$
$678$		0			0
$679$			1164.12i			1.71446i
$680$	−10.4238	+	39.5196i	−0.0153291	+	0.0581171i
$681$		0			0
$682$	849.388	−	849.388i	1.24544	−	1.24544i
$683$	328.645	+	328.645i	0.481179	+	0.481179i	0.905508	−	0.424329i	$-0.139490\pi$
$683$	328.645	+	328.645i	0.481179	+	0.481179i	−0.424329	+	0.905508i	$0.639490\pi$
$684$		0			0
$685$	23.4447	+	40.2432i	0.0342258	+	0.0587492i
$686$	−2177.32			−3.17393
$687$		0			0
$688$	−184.174	−	184.174i	−0.267695	−	0.267695i
$689$		−	1498.27i		−	2.17456i
$690$		0			0
$691$	−27.5318			−0.0398434			−0.0199217	−	0.999802i	$-0.506342\pi$
$691$	−27.5318			−0.0398434			−0.0199217	+	0.999802i	$0.506342\pi$
$692$	−207.536	+	207.536i	−0.299908	+	0.299908i
$693$		0			0
$694$			1345.85i			1.93927i
$695$	248.497	+	65.5443i	0.357550	+	0.0943084i
$696$		0			0
$697$	46.3739	−	46.3739i	0.0665335	−	0.0665335i
$698$	−851.022	−	851.022i	−1.21923	−	1.21923i
$699$		0			0
$700$	−462.189	−	1672.48i	−0.660269	−	2.38926i
$701$	520.641			0.742712			0.371356	−	0.928491i	$-0.378893\pi$
$701$	520.641			0.742712			0.371356	+	0.928491i	$0.378893\pi$
$702$		0			0
$703$	−79.7261	−	79.7261i	−0.113408	−	0.113408i
$704$		−	1055.69i		−	1.49956i
$705$		0			0
$706$	−70.7295			−0.100183
$707$	205.983	−	205.983i	0.291348	−	0.291348i
$708$		0			0
$709$			931.060i			1.31320i	0.754238	+	0.656601i	$0.228006\pi$
$709$			931.060i			1.31320i	−0.754238	+	0.656601i	$0.771994\pi$
$710$	−472.632	−	811.280i	−0.665679	−	1.14265i
$711$		0			0
$712$	288.991	−	288.991i	0.405886	−	0.405886i
$713$	516.215	+	516.215i	0.724004	+	0.724004i
$714$		0			0
$715$	742.189	−	432.381i	1.03803	−	0.604729i
$716$	−783.214			−1.09387
$717$		0			0
$718$	−230.869	−	230.869i	−0.321545	−	0.321545i
$719$			441.340i			0.613824i	0.951738	+	0.306912i	$0.0992958\pi$
$719$			441.340i			0.613824i	−0.951738	+	0.306912i	$0.900704\pi$
$720$		0			0
$721$	−823.317			−1.14191
$722$	−783.507	+	783.507i	−1.08519	+	1.08519i
$723$		0			0
$724$			1355.01i			1.87155i
$725$	−80.0391	+	141.170i	−0.110399	+	0.194717i
$726$		0			0
$727$	−187.463	+	187.463i	−0.257858	+	0.257858i	−0.824182	−	0.566324i	$-0.808365\pi$
$727$	−187.463	+	187.463i	−0.257858	+	0.257858i	0.566324	+	0.824182i	$0.308365\pi$
$728$	−705.470	−	705.470i	−0.969052	−	0.969052i
$729$		0			0
$730$	−143.060	+	542.381i	−0.195972	+	0.742988i
$731$	60.6541			0.0829742
$732$		0			0
$733$	−211.642	−	211.642i	−0.288735	−	0.288735i	0.547845	−	0.836580i	$-0.315448\pi$
$733$	−211.642	−	211.642i	−0.288735	−	0.288735i	−0.836580	+	0.547845i	$0.815448\pi$
$734$		−	572.046i		−	0.779354i
$735$		0			0
$736$	824.276			1.11994
$737$	7.02355	−	7.02355i	0.00952992	−	0.00952992i
$738$		0			0
$739$			784.720i			1.06187i	0.847413	+	0.530934i	$0.178159\pi$
$739$			784.720i			1.06187i	−0.847413	+	0.530934i	$0.821841\pi$
$740$	1555.94	−	906.452i	2.10262	−	1.22494i
$741$		0			0
$742$	−2489.23	+	2489.23i	−3.35475	+	3.35475i
$743$	858.156	+	858.156i	1.15499	+	1.15499i	0.985539	+	0.169449i	$0.0541989\pi$
$743$	858.156	+	858.156i	1.15499	+	1.15499i	0.169449	+	0.985539i	$0.445801\pi$
$744$		0			0
$745$	−671.216	−	177.042i	−0.900961	−	0.237640i
$746$	−935.435			−1.25393
$747$		0			0
$748$	69.0780	+	69.0780i	0.0923503	+	0.0923503i
$749$		−	2282.79i		−	3.04778i
$750$		0			0
$751$	111.405			0.148342			0.0741708	−	0.997246i	$-0.476369\pi$
$751$	111.405			0.148342			0.0741708	+	0.997246i	$0.476369\pi$
$752$	−129.427	+	129.427i	−0.172110	+	0.172110i
$753$		0			0
$754$			329.147i			0.436534i
$755$	−149.509	+	566.830i	−0.198025	+	0.750768i
$756$		0			0
$757$	668.748	−	668.748i	0.883418	−	0.883418i	−0.110462	−	0.993880i	$-0.535233\pi$
$757$	668.748	−	668.748i	0.883418	−	0.883418i	0.993880	+	0.110462i	$0.0352330\pi$
$758$	−312.461	−	312.461i	−0.412217	−	0.412217i
$759$		0			0
$760$	21.5500	+	36.9909i	0.0283553	+	0.0486722i
$761$	−1255.44			−1.64973			−0.824864	−	0.565331i	$-0.808748\pi$
$761$	−1255.44			−1.64973			−0.824864	+	0.565331i	$0.808748\pi$
$762$		0			0
$763$	−628.617	−	628.617i	−0.823876	−	0.823876i
$764$			100.864i			0.132020i
$765$		0			0
$766$	988.726			1.29076
$767$	−606.909	+	606.909i	−0.791277	+	0.791277i
$768$		0			0
$769$		−	527.519i		−	0.685980i	−0.939339	−	0.342990i	$-0.888560\pi$
$769$		−	527.519i		−	0.685980i	0.939339	−	0.342990i	$-0.111440\pi$
$770$	−1951.43	−	514.713i	−2.53432	−	0.668459i
$771$		0			0
$772$	−1067.77	+	1067.77i	−1.38312	+	1.38312i
$773$	−97.6183	−	97.6183i	−0.126285	−	0.126285i	0.641139	−	0.767424i	$-0.278462\pi$
$773$	−97.6183	−	97.6183i	−0.126285	−	0.126285i	−0.767424	+	0.641139i	$0.778462\pi$
$774$		0			0
$775$	804.666	+	456.221i	1.03828	+	0.588673i
$776$	458.707			0.591118
$777$		0			0
$778$	−171.165	−	171.165i	−0.220007	−	0.220007i
$779$		−	68.6942i		−	0.0881825i
$780$		0			0
$781$	−636.198			−0.814594
$782$	−72.0629	+	72.0629i	−0.0921521	+	0.0921521i
$783$		0			0
$784$		−	756.450i		−	0.964860i
$785$	−620.333	−	1064.81i	−0.790233	−	1.35645i
$786$		0			0
$787$	−17.9019	+	17.9019i	−0.0227470	+	0.0227470i	−0.718389	−	0.695642i	$-0.755120\pi$
$787$	−17.9019	+	17.9019i	−0.0227470	+	0.0227470i	0.695642	+	0.718389i	$0.255120\pi$
$788$	75.4474	+	75.4474i	0.0957455	+	0.0957455i
$789$		0			0
$790$	−1525.54	+	888.744i	−1.93107	+	1.12499i
$791$	985.211			1.24553
$792$		0			0
$793$	−5.84394	−	5.84394i	−0.00736941	−	0.00736941i
$794$		−	613.012i		−	0.772055i
$795$		0			0
$796$	792.523			0.995632
$797$	−108.850	+	108.850i	−0.136574	+	0.136574i	−0.772089	−	0.635515i	$-0.780788\pi$
$797$	−108.850	+	108.850i	−0.136574	+	0.136574i	0.635515	+	0.772089i	$0.280788\pi$
$798$		0			0
$799$		−	42.6242i		−	0.0533470i
$800$	1006.67	−	278.193i	1.25834	−	0.347741i
$801$		0			0
$802$	−755.528	+	755.528i	−0.942055	+	0.942055i
$803$	268.758	+	268.758i	0.334693	+	0.334693i
$804$		0			0
$805$	312.817	−	1185.98i	0.388592	−	1.47326i
$806$	1876.13			2.32771
$807$		0			0
$808$	−81.1652	−	81.1652i	−0.100452	−	0.100452i
$809$		−	992.609i		−	1.22696i	−0.789711	−	0.613479i	$-0.789769\pi$
$809$		−	992.609i		−	1.22696i	0.789711	−	0.613479i	$-0.210231\pi$
$810$		0			0
$811$	815.730			1.00583			0.502916	−	0.864335i	$-0.332261\pi$
$811$	815.730			1.00583			0.502916	+	0.864335i	$0.332261\pi$
$812$	318.578	−	318.578i	0.392337	−	0.392337i
$813$		0			0
$814$		−	2094.41i		−	2.57299i
$815$	963.073	−	561.063i	1.18168	−	0.688420i
$816$		0			0
$817$	44.9239	−	44.9239i	0.0549864	−	0.0549864i
$818$	−614.378	−	614.378i	−0.751073	−	0.751073i
$819$		0			0
$820$	1060.83	+	279.808i	1.29370	+	0.341229i
$821$	1179.57			1.43675			0.718377	−	0.695654i	$-0.244885\pi$
$821$	1179.57			1.43675			0.718377	+	0.695654i	$0.244885\pi$
$822$		0			0
$823$	878.005	+	878.005i	1.06684	+	1.06684i	0.997600	+	0.0692347i	$0.0220557\pi$
$823$	878.005	+	878.005i	1.06684	+	1.06684i	0.0692347	+	0.997600i	$0.477944\pi$
$824$			324.418i			0.393712i
$825$		0			0
$826$	2016.63			2.44145
$827$	537.516	−	537.516i	0.649959	−	0.649959i	−0.303024	−	0.952983i	$-0.597996\pi$
$827$	537.516	−	537.516i	0.649959	−	0.649959i	0.952983	+	0.303024i	$0.0979962\pi$
$828$		0			0
$829$		−	600.964i		−	0.724926i	−0.931998	−	0.362463i	$-0.881936\pi$
$829$		−	600.964i		−	0.724926i	0.931998	−	0.362463i	$-0.118064\pi$
$830$	−505.887	+	1917.96i	−0.609502	+	2.31080i
$831$		0			0
$832$	1165.91	−	1165.91i	1.40133	−	1.40133i
$833$	124.561	+	124.561i	0.149533	+	0.149533i
$834$		0			0
$835$	−308.131	−	528.911i	−0.369019	−	0.633426i
$836$	102.326			0.122400
$837$		0			0
$838$	−1080.01	−	1080.01i	−1.28880	−	1.28880i
$839$			96.9791i			0.115589i	0.998329	+	0.0577945i	$0.0184068\pi$
$839$			96.9791i			0.115589i	−0.998329	+	0.0577945i	$0.981593\pi$
$840$		0			0
$841$	798.864			0.949897
$842$	−864.616	+	864.616i	−1.02686	+	1.02686i
$843$		0			0
$844$		−	1082.87i		−	1.28302i
$845$	480.140	+	126.643i	0.568213	+	0.149873i
$846$		0			0
$847$	96.7841	−	96.7841i	0.114267	−	0.114267i
$848$	−463.427	−	463.427i	−0.546494	−	0.546494i
$849$		0			0
$850$	−63.6879	+	112.330i	−0.0749269	+	0.132153i
$851$	1272.88			1.49574
$852$		0			0
$853$	608.232	+	608.232i	0.713051	+	0.713051i	0.967172	−	0.254122i	$-0.0817864\pi$
$853$	608.232	+	608.232i	0.713051	+	0.713051i	−0.254122	+	0.967172i	$0.581786\pi$
$854$			19.4182i			0.0227380i
$855$		0			0
$856$	−899.506			−1.05082
$857$	−953.217	+	953.217i	−1.11227	+	1.11227i	−0.119429	+	0.992843i	$0.538106\pi$
$857$	−953.217	+	953.217i	−1.11227	+	1.11227i	−0.992843	+	0.119429i	$0.961894\pi$
$858$		0			0
$859$		−	143.780i		−	0.167381i	−0.996492	−	0.0836905i	$-0.973329\pi$
$859$		−	143.780i		−	0.167381i	0.996492	−	0.0836905i	$-0.0266707\pi$
$860$	510.765	+	876.736i	0.593913	+	1.01946i
$861$		0			0
$862$	−50.4519	+	50.4519i	−0.0585289	+	0.0585289i
$863$	−945.308	−	945.308i	−1.09537	−	1.09537i	−0.994944	−	0.100430i	$-0.967978\pi$
$863$	−945.308	−	945.308i	−1.09537	−	1.09537i	−0.100430	−	0.994944i	$-0.532022\pi$
$864$		0			0
$865$	−227.138	+	132.325i	−0.262587	+	0.152977i
$866$	1565.00			1.80716
$867$		0			0
$868$	−1815.89	−	1815.89i	−2.09204	−	2.09204i
$869$			1196.32i			1.37666i
$870$		0			0
$871$	15.5136			0.0178113
$872$	−247.699	+	247.699i	−0.284059	+	0.284059i
$873$		0			0
$874$			106.748i			0.122137i
$875$	−18.2301	−	1553.99i	−0.0208343	−	1.77599i
$876$		0			0
$877$	818.047	−	818.047i	0.932779	−	0.932779i	−0.0651000	−	0.997879i	$-0.520737\pi$
$877$	818.047	−	818.047i	0.932779	−	0.932779i	0.997879	+	0.0651000i	$0.0207366\pi$
$878$	1506.70	+	1506.70i	1.71606	+	1.71606i
$879$		0			0
$880$	95.8258	−	363.303i	0.108893	−	0.412844i
$881$	−1608.71			−1.82601			−0.913003	−	0.407952i	$-0.866243\pi$
$881$	−1608.71			−1.82601			−0.913003	+	0.407952i	$0.866243\pi$
$882$		0			0
$883$	−12.3011	−	12.3011i	−0.0139311	−	0.0139311i	0.700107	−	0.714038i	$-0.253136\pi$
$883$	−12.3011	−	12.3011i	−0.0139311	−	0.0139311i	−0.714038	+	0.700107i	$0.753136\pi$
$884$			152.580i			0.172601i
$885$		0			0
$886$	−1041.68			−1.17572
$887$	−236.119	+	236.119i	−0.266200	+	0.266200i	−0.827567	−	0.561367i	$-0.810276\pi$
$887$	−236.119	+	236.119i	−0.266200	+	0.266200i	0.561367	+	0.827567i	$0.310276\pi$
$888$		0			0
$889$			173.528i			0.195195i
$890$	1115.71	−	649.984i	1.25360	−	0.730319i
$891$		0			0
$892$	−78.5409	+	78.5409i	−0.0880504	+	0.0880504i
$893$	−31.5699	−	31.5699i	−0.0353526	−	0.0353526i
$894$		0			0
$895$	−678.283	−	178.906i	−0.757858	−	0.199895i
$896$	−1796.50			−2.00503
$897$		0			0
$898$	−847.301	−	847.301i	−0.943542	−	0.943542i
$899$			240.176i			0.267159i
$900$		0			0
$901$	152.620			0.169390
$902$	902.300	−	902.300i	1.00033	−	1.00033i
$903$		0			0
$904$		−	388.211i		−	0.429437i
$905$	−309.517	+	1173.47i	−0.342008	+	1.29665i
$906$		0			0
$907$	125.817	−	125.817i	0.138717	−	0.138717i	−0.634338	−	0.773056i	$-0.718727\pi$
$907$	125.817	−	125.817i	0.138717	−	0.138717i	0.773056	+	0.634338i	$0.218727\pi$
$908$	829.232	+	829.232i	0.913251	+	0.913251i
$909$		0			0
$910$	−1586.71	−	2723.61i	−1.74363	−	2.99298i
$911$	−1208.42			−1.32647			−0.663236	−	0.748410i	$-0.730818\pi$
$911$	−1208.42			−1.32647			−0.663236	+	0.748410i	$0.730818\pi$
$912$		0			0
$913$	950.379	+	950.379i	1.04094	+	1.04094i
$914$		−	619.431i		−	0.677714i
$915$		0			0
$916$	−403.789			−0.440818
$917$	341.561	−	341.561i	0.372476	−	0.372476i
$918$		0			0
$919$		−	58.7205i		−	0.0638960i	−0.999490	−	0.0319480i	$-0.989829\pi$
$919$		−	58.7205i		−	0.0638960i	0.999490	−	0.0319480i	$-0.0101711\pi$
$920$	−467.320	−	123.262i	−0.507957	−	0.133980i
$921$		0			0
$922$	−1543.56	+	1543.56i	−1.67414	+	1.67414i
$923$	−702.617	−	702.617i	−0.761232	−	0.761232i
$924$		0			0
$925$	1554.54	−	429.595i	1.68058	−	0.464427i
$926$	−524.534			−0.566451
$927$		0			0
$928$	191.753	+	191.753i	0.206630	+	0.206630i
$929$			1527.16i			1.64388i	0.569576	+	0.821939i	$0.307107\pi$
$929$			1527.16i			1.64388i	−0.569576	+	0.821939i	$0.692893\pi$
$930$		0			0
$931$	184.514			0.198189
$932$	−631.722	+	631.722i	−0.677813	+	0.677813i
$933$		0			0
$934$		−	206.661i		−	0.221264i
$935$	44.0442	+	75.6025i	0.0471061	+	0.0808583i
$936$		0			0
$937$	−566.027	+	566.027i	−0.604085	+	0.604085i	−0.941394	−	0.337309i	$-0.890483\pi$
$937$	−566.027	+	566.027i	−0.604085	+	0.604085i	0.337309	+	0.941394i	$0.390483\pi$
$938$	−25.7743	−	25.7743i	−0.0274779	−	0.0274779i
$939$		0			0
$940$	616.120	−	358.936i	0.655446	−	0.381847i
$941$	1065.69			1.13251			0.566254	−	0.824231i	$-0.308392\pi$
$941$	1065.69			1.13251			0.566254	+	0.824231i	$0.308392\pi$
$942$		0			0
$943$	548.372	+	548.372i	0.581519	+	0.581519i
$944$			375.443i			0.397715i
$945$		0			0
$946$	1180.15			1.24752
$947$	−361.475	+	361.475i	−0.381705	+	0.381705i	−0.871716	−	0.490011i	$-0.836993\pi$
$947$	−361.475	+	361.475i	−0.381705	+	0.381705i	0.490011	+	0.871716i	$0.336993\pi$
$948$		0			0
$949$			593.633i			0.625536i
$950$	36.0273	+	130.369i	0.0379235	+	0.137230i
$951$		0			0
$952$	71.8621	−	71.8621i	0.0754854	−	0.0754854i
$953$	−477.641	−	477.641i	−0.501198	−	0.501198i	0.410612	−	0.911810i	$-0.365315\pi$
$953$	−477.641	−	477.641i	−0.501198	−	0.501198i	−0.911810	+	0.410612i	$0.865315\pi$
$954$		0			0
$955$	−23.0398	+	87.3504i	−0.0241254	+	0.0914664i
$956$	1582.57			1.65541
$957$		0			0
$958$	1170.85	+	1170.85i	1.22218	+	1.22218i
$959$		−	115.809i		−	0.120761i
$960$		0			0
$961$	408.000			0.424558
$962$	2313.07	−	2313.07i	2.40444	−	2.40444i
$963$		0			0
$964$		−	2689.19i		−	2.78962i
$965$	−1168.62	+	680.811i	−1.21101	+	0.705504i
$966$		0			0
$967$	339.332	−	339.332i	0.350912	−	0.350912i	−0.509537	−	0.860449i	$-0.670183\pi$
$967$	339.332	−	339.332i	0.350912	−	0.350912i	0.860449	+	0.509537i	$0.170183\pi$
$968$	−38.1366	−	38.1366i	−0.0393973	−	0.0393973i
$969$		0			0
$970$	1401.32	+	369.615i	1.44466	+	0.381047i
$971$	−364.302			−0.375182			−0.187591	−	0.982247i	$-0.560068\pi$
$971$	−364.302			−0.375182			−0.187591	+	0.982247i	$0.560068\pi$
$972$		0			0
$973$	−451.866	−	451.866i	−0.464404	−	0.464404i
$974$			1246.33i			1.27960i
$975$		0			0
$976$	−3.61515			−0.00370404
$977$	−59.2711	+	59.2711i	−0.0606665	+	0.0606665i	−0.736789	−	0.676123i	$-0.763659\pi$
$977$	−59.2711	+	59.2711i	−0.0606665	+	0.0606665i	0.676123	+	0.736789i	$0.263659\pi$
$978$		0			0
$979$		−	874.927i		−	0.893695i
$980$	−751.567	+	2849.41i	−0.766906	+	2.90756i
$981$		0			0
$982$	−127.461	+	127.461i	−0.129797	+	0.129797i
$983$	−13.4709	−	13.4709i	−0.0137038	−	0.0137038i	0.700222	−	0.713925i	$-0.253084\pi$
$983$	−13.4709	−	13.4709i	−0.0137038	−	0.0137038i	−0.713925	+	0.700222i	$0.753084\pi$
$984$		0			0
$985$	48.1053	+	82.5735i	0.0488379	+	0.0838309i
$986$	−33.5283			−0.0340044
$987$		0			0
$988$	113.009	+	113.009i	0.114382	+	0.114382i
$989$			717.237i			0.725214i
$990$		0			0
$991$	522.405			0.527149			0.263574	−	0.964639i	$-0.415099\pi$
$991$	522.405			0.527149			0.263574	+	0.964639i	$0.415099\pi$
$992$	1092.99	−	1092.99i	1.10180	−	1.10180i
$993$		0			0
$994$			2334.65i			2.34875i
$995$	686.345	+	181.032i	0.689794	+	0.181942i
$996$		0			0
$997$	419.975	−	419.975i	0.421238	−	0.421238i	−0.464392	−	0.885630i	$-0.653727\pi$
$997$	419.975	−	419.975i	0.421238	−	0.421238i	0.885630	+	0.464392i	$0.153727\pi$
$998$	−13.9476	−	13.9476i	−0.0139756	−	0.0139756i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.g.d.163.1	yes	8
3.2	odd	2	inner	405.3.g.d.163.4	yes	8
5.2	odd	4	inner	405.3.g.d.82.1	✓	8
9.2	odd	6		405.3.l.e.28.1		8
9.4	even	3		405.3.l.e.298.1		8
9.5	odd	6		405.3.l.i.298.2		8
9.7	even	3		405.3.l.i.28.2		8
15.2	even	4	inner	405.3.g.d.82.4	yes	8
45.2	even	12		405.3.l.i.352.2		8
45.7	odd	12		405.3.l.e.352.1		8
45.22	odd	12		405.3.l.i.217.2		8
45.32	even	12		405.3.l.e.217.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.3.g.d.82.1	✓	8	5.2	odd	4	inner
405.3.g.d.82.4	yes	8	15.2	even	4	inner
405.3.g.d.163.1	yes	8	1.1	even	1	trivial
405.3.g.d.163.4	yes	8	3.2	odd	2	inner
405.3.l.e.28.1		8	9.2	odd	6
405.3.l.e.217.1		8	45.32	even	12
405.3.l.e.298.1		8	9.4	even	3
405.3.l.e.352.1		8	45.7	odd	12
405.3.l.i.28.2		8	9.7	even	3
405.3.l.i.217.2		8	45.22	odd	12
405.3.l.i.298.2		8	9.5	odd	6
405.3.l.i.352.2		8	45.2	even	12

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.18890 + 2.18890i) q^{2} -5.58258i q^{4} +(1.27520 - 4.83465i) q^{5} +(-8.79129 + 8.79129i) q^{7} +(3.46410 + 3.46410i) q^{8} +(7.79129 + 13.3739i) q^{10} +10.4877 q^{11} +(11.5826 + 11.5826i) q^{13} -38.4865i q^{14} +7.16515 q^{16} +(-1.17985 + 1.17985i) q^{17} +1.74773i q^{19} +(-26.9898 - 7.11890i) q^{20} +(-22.9564 + 22.9564i) q^{22} +(-13.9518 - 13.9518i) q^{23} +(-21.7477 - 12.3303i) q^{25} -50.7062 q^{26} +(49.0780 + 49.0780i) q^{28} -6.49125i q^{29} -37.0000 q^{31} +(-29.5402 + 29.5402i) q^{32} -5.16515i q^{34} +(31.2922 + 53.7135i) q^{35} +(-45.6170 + 45.6170i) q^{37} +(-3.82560 - 3.82560i) q^{38} +(21.1652 - 12.3303i) q^{40} -39.3049 q^{41} +(-25.7042 - 25.7042i) q^{43} -58.5481i q^{44} +61.0780 q^{46} +(-18.0634 + 18.0634i) q^{47} -105.573i q^{49} +(74.5934 - 20.6138i) q^{50} +(64.6606 - 64.6606i) q^{52} +(-64.6779 - 64.6779i) q^{53} +(13.3739 - 50.7042i) q^{55} -60.9078 q^{56} +(14.2087 + 14.2087i) q^{58} +52.3985i q^{59} -0.504546 q^{61} +(80.9893 - 80.9893i) q^{62} -100.661i q^{64} +(70.7678 - 41.2276i) q^{65} +(0.669697 - 0.669697i) q^{67} +(6.58660 + 6.58660i) q^{68} +(-186.069 - 49.0780i) q^{70} -60.6616 q^{71} +(25.6261 + 25.6261i) q^{73} -199.702i q^{74} +9.75682 q^{76} +(-92.2000 + 92.2000i) q^{77} +114.069i q^{79} +(9.13701 - 34.6410i) q^{80} +(86.0345 - 86.0345i) q^{82} +(90.6188 + 90.6188i) q^{83} +(4.19962 + 7.20871i) q^{85} +112.528 q^{86} +(36.3303 + 36.3303i) q^{88} -83.4245i q^{89} -203.652 q^{91} +(-77.8867 + 77.8867i) q^{92} -79.0780i q^{94} +(8.44965 + 2.22870i) q^{95} +(66.2087 - 66.2087i) q^{97} +(231.090 + 231.090i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 52 q^{7} + 44 q^{10} + 56 q^{13} - 16 q^{16} - 92 q^{22} - 64 q^{25} + 136 q^{28} - 296 q^{31} + 20 q^{37} + 96 q^{40} - 4 q^{43} + 232 q^{46} + 224 q^{52} + 52 q^{55} + 132 q^{58} - 224 q^{61} + 152 q^{67}+ \cdots + 548 q^{97}+O(q^{100}) \) 8 * q - 52 * q^7 + 44 * q^10 + 56 * q^13 - 16 * q^16 - 92 * q^22 - 64 * q^25 + 136 * q^28 - 296 * q^31 + 20 * q^37 + 96 * q^40 - 4 * q^43 + 232 * q^46 + 224 * q^52 + 52 * q^55 + 132 * q^58 - 224 * q^61 + 152 * q^67 - 792 * q^70 + 260 * q^73 + 408 * q^76 + 340 * q^82 - 388 * q^85 + 144 * q^88 - 896 * q^91 + 548 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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