LMFDB - Embedded newform 405.4.e.h.136.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,4,Mod(136,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("405.136");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	405.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$23.8957735523$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			136.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	405.136
Dual form			405.4.e.h.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(3.50000 + 6.06218i) q^{4} +(2.50000 + 4.33013i) q^{5} +(3.00000 - 5.19615i) q^{7} +15.0000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(3.50000 + 6.06218i) q^{4} +(2.50000 + 4.33013i) q^{5} +(3.00000 - 5.19615i) q^{7} +15.0000 q^{8} +5.00000 q^{10} +(-23.5000 + 40.7032i) q^{11} +(2.50000 + 4.33013i) q^{13} +(-3.00000 - 5.19615i) q^{14} +(-20.5000 + 35.5070i) q^{16} +131.000 q^{17} -56.0000 q^{19} +(-17.5000 + 30.3109i) q^{20} +(23.5000 + 40.7032i) q^{22} +(1.50000 + 2.59808i) q^{23} +(-12.5000 + 21.6506i) q^{25} +5.00000 q^{26} +42.0000 q^{28} +(-78.5000 + 135.966i) q^{29} +(-112.500 - 194.856i) q^{31} +(80.5000 + 139.430i) q^{32} +(65.5000 - 113.449i) q^{34} +30.0000 q^{35} -70.0000 q^{37} +(-28.0000 + 48.4974i) q^{38} +(37.5000 + 64.9519i) q^{40} +(70.0000 + 121.244i) q^{41} +(-198.500 + 343.812i) q^{43} -329.000 q^{44} +3.00000 q^{46} +(-173.500 + 300.511i) q^{47} +(153.500 + 265.870i) q^{49} +(12.5000 + 21.6506i) q^{50} +(-17.5000 + 30.3109i) q^{52} -4.00000 q^{53} -235.000 q^{55} +(45.0000 - 77.9423i) q^{56} +(78.5000 + 135.966i) q^{58} +(374.000 + 647.787i) q^{59} +(169.000 - 292.717i) q^{61} -225.000 q^{62} -167.000 q^{64} +(-12.5000 + 21.6506i) q^{65} +(-246.000 - 426.084i) q^{67} +(458.500 + 794.145i) q^{68} +(15.0000 - 25.9808i) q^{70} -32.0000 q^{71} +970.000 q^{73} +(-35.0000 + 60.6218i) q^{74} +(-196.000 - 339.482i) q^{76} +(141.000 + 244.219i) q^{77} +(628.500 - 1088.59i) q^{79} -205.000 q^{80} +140.000 q^{82} +(-51.0000 + 88.3346i) q^{83} +(327.500 + 567.247i) q^{85} +(198.500 + 343.812i) q^{86} +(-352.500 + 610.548i) q^{88} +1488.00 q^{89} +30.0000 q^{91} +(-10.5000 + 18.1865i) q^{92} +(173.500 + 300.511i) q^{94} +(-140.000 - 242.487i) q^{95} +(-487.000 + 843.509i) q^{97} +307.000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 7 q^{4} + 5 q^{5} + 6 q^{7} + 30 q^{8}+O(q^{10}) $ 2 * q + q^2 + 7 * q^4 + 5 * q^5 + 6 * q^7 + 30 * q^8	$ 2 q + q^{2} + 7 q^{4} + 5 q^{5} + 6 q^{7} + 30 q^{8} + 10 q^{10} - 47 q^{11} + 5 q^{13} - 6 q^{14} - 41 q^{16} + 262 q^{17} - 112 q^{19} - 35 q^{20} + 47 q^{22} + 3 q^{23} - 25 q^{25} + 10 q^{26} + 84 q^{28} - 157 q^{29} - 225 q^{31} + 161 q^{32} + 131 q^{34} + 60 q^{35} - 140 q^{37} - 56 q^{38} + 75 q^{40} + 140 q^{41} - 397 q^{43} - 658 q^{44} + 6 q^{46} - 347 q^{47} + 307 q^{49} + 25 q^{50} - 35 q^{52} - 8 q^{53} - 470 q^{55} + 90 q^{56} + 157 q^{58} + 748 q^{59} + 338 q^{61} - 450 q^{62} - 334 q^{64} - 25 q^{65} - 492 q^{67} + 917 q^{68} + 30 q^{70} - 64 q^{71} + 1940 q^{73} - 70 q^{74} - 392 q^{76} + 282 q^{77} + 1257 q^{79} - 410 q^{80} + 280 q^{82} - 102 q^{83} + 655 q^{85} + 397 q^{86} - 705 q^{88} + 2976 q^{89} + 60 q^{91} - 21 q^{92} + 347 q^{94} - 280 q^{95} - 974 q^{97} + 614 q^{98}+O(q^{100}) $ 2 * q + q^2 + 7 * q^4 + 5 * q^5 + 6 * q^7 + 30 * q^8 + 10 * q^10 - 47 * q^11 + 5 * q^13 - 6 * q^14 - 41 * q^16 + 262 * q^17 - 112 * q^19 - 35 * q^20 + 47 * q^22 + 3 * q^23 - 25 * q^25 + 10 * q^26 + 84 * q^28 - 157 * q^29 - 225 * q^31 + 161 * q^32 + 131 * q^34 + 60 * q^35 - 140 * q^37 - 56 * q^38 + 75 * q^40 + 140 * q^41 - 397 * q^43 - 658 * q^44 + 6 * q^46 - 347 * q^47 + 307 * q^49 + 25 * q^50 - 35 * q^52 - 8 * q^53 - 470 * q^55 + 90 * q^56 + 157 * q^58 + 748 * q^59 + 338 * q^61 - 450 * q^62 - 334 * q^64 - 25 * q^65 - 492 * q^67 + 917 * q^68 + 30 * q^70 - 64 * q^71 + 1940 * q^73 - 70 * q^74 - 392 * q^76 + 282 * q^77 + 1257 * q^79 - 410 * q^80 + 280 * q^82 - 102 * q^83 + 655 * q^85 + 397 * q^86 - 705 * q^88 + 2976 * q^89 + 60 * q^91 - 21 * q^92 + 347 * q^94 - 280 * q^95 - 974 * q^97 + 614 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.176777	−	0.306186i	−0.763998	−	0.645219i	$-0.776766\pi$
$2$	0.500000	−	0.866025i	0.176777	−	0.306186i	0.940775	+	0.339032i	$0.110100\pi$
$3$		0			0
$3$		0			0
$4$	3.50000	+	6.06218i	0.437500	+	0.757772i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$		0			0
$7$	3.00000	−	5.19615i	0.161985	−	0.280566i	−0.773596	−	0.633680i	$-0.781544\pi$
$7$	3.00000	−	5.19615i	0.161985	−	0.280566i	0.935580	+	0.353114i	$0.114877\pi$
$8$	15.0000			0.662913
$9$		0			0
$10$	5.00000			0.158114
$11$	−23.5000	+	40.7032i	−0.644138	+	1.11568i	0.340362	+	0.940294i	$0.389450\pi$
$11$	−23.5000	+	40.7032i	−0.644138	+	1.11568i	−0.984500	+	0.175385i	$0.943883\pi$
$12$		0			0
$13$	2.50000	+	4.33013i	0.0533366	+	0.0923816i	0.891461	−	0.453097i	$-0.149681\pi$
$13$	2.50000	+	4.33013i	0.0533366	+	0.0923816i	−0.838124	+	0.545479i	$0.816348\pi$
$14$	−3.00000	−	5.19615i	−0.0572703	−	0.0991950i
$15$		0			0
$16$	−20.5000	+	35.5070i	−0.320312	+	0.554798i
$17$	131.000			1.86895			0.934475	−	0.356027i	$-0.115869\pi$
$17$	131.000			1.86895			0.934475	+	0.356027i	$0.115869\pi$
$18$		0			0
$19$	−56.0000			−0.676173			−0.338086	−	0.941115i	$-0.609780\pi$
$19$	−56.0000			−0.676173			−0.338086	+	0.941115i	$0.609780\pi$
$20$	−17.5000	+	30.3109i	−0.195656	+	0.338886i
$21$		0			0
$22$	23.5000	+	40.7032i	0.227737	+	0.394452i
$23$	1.50000	+	2.59808i	0.0135988	+	0.0235538i	0.872745	−	0.488177i	$-0.162338\pi$
$23$	1.50000	+	2.59808i	0.0135988	+	0.0235538i	−0.859146	+	0.511731i	$0.829005\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	5.00000			0.0377146
$27$		0			0
$28$	42.0000			0.283473
$29$	−78.5000	+	135.966i	−0.502658	+	0.870629i	0.497337	+	0.867557i	$0.334311\pi$
$29$	−78.5000	+	135.966i	−0.502658	+	0.870629i	−0.999995	+	0.00307200i	$0.999022\pi$
$30$		0			0
$31$	−112.500	−	194.856i	−0.651793	−	1.12894i	−0.982687	−	0.185271i	$-0.940684\pi$
$31$	−112.500	−	194.856i	−0.651793	−	1.12894i	0.330894	−	0.943668i	$-0.392650\pi$
$32$	80.5000	+	139.430i	0.444704	+	0.770250i
$33$		0			0
$34$	65.5000	−	113.449i	0.330387	−	0.572247i
$35$	30.0000			0.144884
$36$		0			0
$37$	−70.0000			−0.311025			−0.155513	−	0.987834i	$-0.549703\pi$
$37$	−70.0000			−0.311025			−0.155513	+	0.987834i	$0.549703\pi$
$38$	−28.0000	+	48.4974i	−0.119532	+	0.207035i
$39$		0			0
$40$	37.5000	+	64.9519i	0.148232	+	0.256745i
$41$	70.0000	+	121.244i	0.266638	+	0.461831i	0.967992	−	0.250983i	$-0.0807538\pi$
$41$	70.0000	+	121.244i	0.266638	+	0.461831i	−0.701353	+	0.712814i	$0.747420\pi$
$42$		0			0
$43$	−198.500	+	343.812i	−0.703976	+	1.21932i	0.263084	+	0.964773i	$0.415260\pi$
$43$	−198.500	+	343.812i	−0.703976	+	1.21932i	−0.967060	+	0.254549i	$0.918073\pi$
$44$	−329.000			−1.12724
$45$		0			0
$46$	3.00000			0.00961578
$47$	−173.500	+	300.511i	−0.538459	+	0.932638i	0.460528	+	0.887645i	$0.347660\pi$
$47$	−173.500	+	300.511i	−0.538459	+	0.932638i	−0.998987	+	0.0449934i	$0.985673\pi$
$48$		0			0
$49$	153.500	+	265.870i	0.447522	+	0.775131i
$50$	12.5000	+	21.6506i	0.0353553	+	0.0612372i
$51$		0			0
$52$	−17.5000	+	30.3109i	−0.0466695	+	0.0808339i
$53$	−4.00000			−0.0103668			−0.00518342	−	0.999987i	$-0.501650\pi$
$53$	−4.00000			−0.0103668			−0.00518342	+	0.999987i	$0.501650\pi$
$54$		0			0
$55$	−235.000			−0.576134
$56$	45.0000	−	77.9423i	0.107382	−	0.185991i
$57$		0			0
$58$	78.5000	+	135.966i	0.177716	+	0.307814i
$59$	374.000	+	647.787i	0.825265	+	1.42940i	0.901716	+	0.432328i	$0.142308\pi$
$59$	374.000	+	647.787i	0.825265	+	1.42940i	−0.0764511	+	0.997073i	$0.524359\pi$
$60$		0			0
$61$	169.000	−	292.717i	0.354725	−	0.614402i	−0.632346	−	0.774686i	$-0.717908\pi$
$61$	169.000	−	292.717i	0.354725	−	0.614402i	0.987071	+	0.160284i	$0.0512411\pi$
$62$	−225.000			−0.460888
$63$		0			0
$64$	−167.000			−0.326172
$65$	−12.5000	+	21.6506i	−0.0238528	+	0.0413143i
$66$		0			0
$67$	−246.000	−	426.084i	−0.448562	−	0.776933i	0.549730	−	0.835342i	$-0.314730\pi$
$67$	−246.000	−	426.084i	−0.448562	−	0.776933i	−0.998293	+	0.0584093i	$0.981397\pi$
$68$	458.500	+	794.145i	0.817666	+	1.41624i
$69$		0			0
$70$	15.0000	−	25.9808i	0.0256120	−	0.0443614i
$71$	−32.0000			−0.0534888			−0.0267444	−	0.999642i	$-0.508514\pi$
$71$	−32.0000			−0.0534888			−0.0267444	+	0.999642i	$0.508514\pi$
$72$		0			0
$73$	970.000			1.55520			0.777602	−	0.628757i	$-0.216436\pi$
$73$	970.000			1.55520			0.777602	+	0.628757i	$0.216436\pi$
$74$	−35.0000	+	60.6218i	−0.0549820	+	0.0952316i
$75$		0			0
$76$	−196.000	−	339.482i	−0.295826	−	0.512385i
$77$	141.000	+	244.219i	0.208681	+	0.361446i
$78$		0			0
$79$	628.500	−	1088.59i	0.895086	−	1.55033i	0.0613873	−	0.998114i	$-0.480448\pi$
$79$	628.500	−	1088.59i	0.895086	−	1.55033i	0.833698	−	0.552220i	$-0.186219\pi$
$80$	−205.000			−0.286496
$81$		0			0
$82$	140.000			0.188542
$83$	−51.0000	+	88.3346i	−0.0674455	+	0.116819i	−0.897776	−	0.440452i	$-0.854818\pi$
$83$	−51.0000	+	88.3346i	−0.0674455	+	0.116819i	0.830331	+	0.557271i	$0.188152\pi$
$84$		0			0
$85$	327.500	+	567.247i	0.417910	+	0.723842i
$86$	198.500	+	343.812i	0.248893	+	0.431095i
$87$		0			0
$88$	−352.500	+	610.548i	−0.427007	+	0.739598i
$89$	1488.00			1.77222			0.886111	−	0.463474i	$-0.153397\pi$
$89$	1488.00			1.77222			0.886111	+	0.463474i	$0.153397\pi$
$90$		0			0
$91$	30.0000			0.0345588
$92$	−10.5000	+	18.1865i	−0.0118989	+	0.0206095i
$93$		0			0
$94$	173.500	+	300.511i	0.190374	+	0.329737i
$95$	−140.000	−	242.487i	−0.151197	−	0.261881i
$96$		0			0
$97$	−487.000	+	843.509i	−0.509767	+	0.882942i	0.490169	+	0.871627i	$0.336935\pi$
$97$	−487.000	+	843.509i	−0.509767	+	0.882942i	−0.999936	+	0.0113144i	$0.996398\pi$
$98$	307.000			0.316446
$99$		0			0
$100$	−175.000			−0.175000
$101$	−667.500	+	1156.14i	−0.657611	+	1.13902i	0.323621	+	0.946187i	$0.395100\pi$
$101$	−667.500	+	1156.14i	−0.657611	+	1.13902i	−0.981232	+	0.192829i	$0.938234\pi$
$102$		0			0
$103$	−343.000	−	594.093i	−0.328124	−	0.568328i	0.654015	−	0.756481i	$-0.273083\pi$
$103$	−343.000	−	594.093i	−0.328124	−	0.568328i	−0.982140	+	0.188153i	$0.939750\pi$
$104$	37.5000	+	64.9519i	0.0353575	+	0.0612409i
$105$		0			0
$106$	−2.00000	+	3.46410i	−0.00183261	+	0.00317418i
$107$	1098.00			0.992034			0.496017	−	0.868313i	$-0.334795\pi$
$107$	1098.00			0.992034			0.496017	+	0.868313i	$0.334795\pi$
$108$		0			0
$109$	−700.000			−0.615118			−0.307559	−	0.951529i	$-0.599512\pi$
$109$	−700.000			−0.615118			−0.307559	+	0.951529i	$0.599512\pi$
$110$	−117.500	+	203.516i	−0.101847	+	0.176404i
$111$		0			0
$112$	123.000	+	213.042i	0.103771	+	0.179738i
$113$	−527.500	−	913.657i	−0.439142	−	0.760616i	0.558482	−	0.829517i	$-0.311384\pi$
$113$	−527.500	−	913.657i	−0.439142	−	0.760616i	−0.997624	+	0.0689009i	$0.978051\pi$
$114$		0			0
$115$	−7.50000	+	12.9904i	−0.00608155	+	0.0105336i
$116$	−1099.00			−0.879652
$117$		0			0
$118$	748.000			0.583551
$119$	393.000	−	680.696i	0.302742	−	0.524364i
$120$		0			0
$121$	−439.000	−	760.370i	−0.329827	−	0.571277i
$122$	−169.000	−	292.717i	−0.125414	−	0.217224i
$123$		0			0
$124$	787.500	−	1363.99i	0.570319	−	0.987822i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−1646.00			−1.15007			−0.575035	−	0.818129i	$-0.695012\pi$
$127$	−1646.00			−1.15007			−0.575035	+	0.818129i	$0.695012\pi$
$128$	−727.500	+	1260.07i	−0.502363	+	0.870119i
$129$		0			0
$130$	12.5000	+	21.6506i	0.00843325	+	0.0146068i
$131$	−916.500	−	1587.42i	−0.611259	−	1.05873i	−0.991028	−	0.133651i	$-0.957330\pi$
$131$	−916.500	−	1587.42i	−0.611259	−	1.05873i	0.379769	−	0.925081i	$-0.376003\pi$
$132$		0			0
$133$	−168.000	+	290.985i	−0.109530	+	0.189711i
$134$	−492.000			−0.317182
$135$		0			0
$136$	1965.00			1.23895
$137$	549.000	−	950.896i	0.342367	−	0.592996i	−0.642505	−	0.766281i	$-0.722105\pi$
$137$	549.000	−	950.896i	0.342367	−	0.592996i	0.984872	+	0.173285i	$0.0554382\pi$
$138$		0			0
$139$	521.000	+	902.398i	0.317918	+	0.550651i	0.980054	−	0.198734i	$-0.0636829\pi$
$139$	521.000	+	902.398i	0.317918	+	0.550651i	−0.662135	+	0.749384i	$0.730350\pi$
$140$	105.000	+	181.865i	0.0633866	+	0.109789i
$141$		0			0
$142$	−16.0000	+	27.7128i	−0.00945556	+	0.0163775i
$143$	−235.000			−0.137424
$144$		0			0
$145$	−785.000			−0.449591
$146$	485.000	−	840.045i	0.274924	−	0.476182i
$147$		0			0
$148$	−245.000	−	424.352i	−0.136073	−	0.235686i
$149$	−1470.50	−	2546.98i	−0.808510	−	1.40038i	−0.913895	−	0.405950i	$-0.866941\pi$
$149$	−1470.50	−	2546.98i	−0.808510	−	1.40038i	0.105385	−	0.994431i	$-0.466393\pi$
$150$		0			0
$151$	−255.500	+	442.539i	−0.137697	+	0.238499i	−0.926625	−	0.375988i	$-0.877303\pi$
$151$	−255.500	+	442.539i	−0.137697	+	0.238499i	0.788927	+	0.614487i	$0.210637\pi$
$152$	−840.000			−0.448243
$153$		0			0
$154$	282.000			0.147560
$155$	562.500	−	974.279i	0.291491	−	0.504877i
$156$		0			0
$157$	285.500	+	494.501i	0.145130	+	0.251372i	0.929421	−	0.369020i	$-0.120307\pi$
$157$	285.500	+	494.501i	0.145130	+	0.251372i	−0.784292	+	0.620392i	$0.786973\pi$
$158$	−628.500	−	1088.59i	−0.316461	−	0.548126i
$159$		0			0
$160$	−402.500	+	697.150i	−0.198878	+	0.344466i
$161$	18.0000			0.00881117
$162$		0			0
$163$	713.000			0.342616			0.171308	−	0.985217i	$-0.445201\pi$
$163$	713.000			0.342616			0.171308	+	0.985217i	$0.445201\pi$
$164$	−490.000	+	848.705i	−0.233308	+	0.404102i
$165$		0			0
$166$	51.0000	+	88.3346i	0.0238456	+	0.0413018i
$167$	798.000	+	1382.18i	0.369767	+	0.640455i	0.989529	−	0.144335i	$-0.0461042\pi$
$167$	798.000	+	1382.18i	0.369767	+	0.640455i	−0.619762	+	0.784790i	$0.712771\pi$
$168$		0			0
$169$	1086.00	−	1881.01i	0.494310	−	0.856171i
$170$	655.000			0.295507
$171$		0			0
$172$	−2779.00			−1.23196
$173$	2067.00	−	3580.15i	0.908388	−	1.57337i	0.0920840	−	0.995751i	$-0.470647\pi$
$173$	2067.00	−	3580.15i	0.908388	−	1.57337i	0.816304	−	0.577623i	$-0.196019\pi$
$174$		0			0
$175$	75.0000	+	129.904i	0.0323970	+	0.0561132i
$176$	−963.500	−	1668.83i	−0.412651	−	0.714732i
$177$		0			0
$178$	744.000	−	1288.65i	0.313287	−	0.542630i
$179$	−1828.00			−0.763302			−0.381651	−	0.924306i	$-0.624644\pi$
$179$	−1828.00			−0.763302			−0.381651	+	0.924306i	$0.624644\pi$
$180$		0			0
$181$	−520.000			−0.213543			−0.106772	−	0.994284i	$-0.534051\pi$
$181$	−520.000			−0.213543			−0.106772	+	0.994284i	$0.534051\pi$
$182$	15.0000	−	25.9808i	0.00610920	−	0.0105814i
$183$		0			0
$184$	22.5000	+	38.9711i	0.00901479	+	0.0156141i
$185$	−175.000	−	303.109i	−0.0695473	−	0.120460i
$186$		0			0
$187$	−3078.50	+	5332.12i	−1.20386	+	2.08515i
$188$	−2429.00			−0.942303
$189$		0			0
$190$	−280.000			−0.106912
$191$	2413.00	−	4179.44i	0.914129	−	1.58332i	0.105956	−	0.994371i	$-0.466210\pi$
$191$	2413.00	−	4179.44i	0.914129	−	1.58332i	0.808172	−	0.588946i	$-0.200457\pi$
$192$		0			0
$193$	−835.000	−	1446.26i	−0.311423	−	0.539400i	0.667248	−	0.744836i	$-0.267472\pi$
$193$	−835.000	−	1446.26i	−0.311423	−	0.539400i	−0.978671	+	0.205436i	$0.934139\pi$
$194$	487.000	+	843.509i	0.180230	+	0.312167i
$195$		0			0
$196$	−1074.50	+	1861.09i	−0.391582	+	0.678239i
$197$	1380.00			0.499091			0.249546	−	0.968363i	$-0.419719\pi$
$197$	1380.00			0.499091			0.249546	+	0.968363i	$0.419719\pi$
$198$		0			0
$199$	4357.00			1.55206			0.776029	−	0.630697i	$-0.217231\pi$
$199$	4357.00			1.55206			0.776029	+	0.630697i	$0.217231\pi$
$200$	−187.500	+	324.760i	−0.0662913	+	0.114820i
$201$		0			0
$202$	667.500	+	1156.14i	0.232501	+	0.402703i
$203$	471.000	+	815.796i	0.162846	+	0.282057i
$204$		0			0
$205$	−350.000	+	606.218i	−0.119244	+	0.206537i
$206$	−686.000			−0.232019
$207$		0			0
$208$	−205.000			−0.0683375
$209$	1316.00	−	2279.38i	0.435548	−	0.754392i
$210$		0			0
$211$	2081.00	+	3604.40i	0.678967	+	1.17600i	0.975292	+	0.220918i	$0.0709052\pi$
$211$	2081.00	+	3604.40i	0.678967	+	1.17600i	−0.296326	+	0.955087i	$0.595761\pi$
$212$	−14.0000	−	24.2487i	−0.00453549	−	0.00785570i
$213$		0			0
$214$	549.000	−	950.896i	0.175369	−	0.303747i
$215$	−1985.00			−0.629655
$216$		0			0
$217$	−1350.00			−0.422322
$218$	−350.000	+	606.218i	−0.108738	+	0.188341i
$219$		0			0
$220$	−822.500	−	1424.61i	−0.252059	−	0.436579i
$221$	327.500	+	567.247i	0.0996834	+	0.172657i
$222$		0			0
$223$	2978.00	−	5158.05i	0.894267	−	1.54892i	0.0595587	−	0.998225i	$-0.481031\pi$
$223$	2978.00	−	5158.05i	0.894267	−	1.54892i	0.834709	−	0.550692i	$-0.185636\pi$
$224$	966.000			0.288141
$225$		0			0
$226$	−1055.00			−0.310520
$227$	2470.00	−	4278.17i	0.722201	−	1.25089i	−0.237915	−	0.971286i	$-0.576464\pi$
$227$	2470.00	−	4278.17i	0.722201	−	1.25089i	0.960116	−	0.279603i	$-0.0902028\pi$
$228$		0			0
$229$	−2172.00	−	3762.01i	−0.626768	−	1.08559i	−0.988196	−	0.153194i	$-0.951044\pi$
$229$	−2172.00	−	3762.01i	−0.626768	−	1.08559i	0.361429	−	0.932400i	$-0.382289\pi$
$230$	7.50000	+	12.9904i	0.00215015	+	0.00372418i
$231$		0			0
$232$	−1177.50	+	2039.49i	−0.333218	+	0.577151i
$233$	5202.00			1.46264			0.731318	−	0.682036i	$-0.238905\pi$
$233$	5202.00			1.46264			0.731318	+	0.682036i	$0.238905\pi$
$234$		0			0
$235$	−1735.00			−0.481612
$236$	−2618.00	+	4534.51i	−0.722107	+	1.25073i
$237$		0			0
$238$	−393.000	−	680.696i	−0.107035	−	0.185391i
$239$	773.000	+	1338.88i	0.209210	+	0.362363i	0.951466	−	0.307754i	$-0.0995774\pi$
$239$	773.000	+	1338.88i	0.209210	+	0.362363i	−0.742256	+	0.670117i	$0.766244\pi$
$240$		0			0
$241$	1829.50	−	3168.79i	0.488998	−	0.846969i	−0.510922	−	0.859627i	$-0.670696\pi$
$241$	1829.50	−	3168.79i	0.488998	−	0.846969i	0.999920	+	0.0126581i	$0.00402929\pi$
$242$	−878.000			−0.233223
$243$		0			0
$244$	2366.00			0.620769
$245$	−767.500	+	1329.35i	−0.200138	+	0.346649i
$246$		0			0
$247$	−140.000	−	242.487i	−0.0360647	−	0.0624659i
$248$	−1687.50	−	2922.84i	−0.432082	−	0.748388i
$249$		0			0
$250$	−62.5000	+	108.253i	−0.0158114	+	0.0273861i
$251$	−1221.00			−0.307047			−0.153524	−	0.988145i	$-0.549062\pi$
$251$	−1221.00			−0.307047			−0.153524	+	0.988145i	$0.549062\pi$
$252$		0			0
$253$	−141.000			−0.0350379
$254$	−823.000	+	1425.48i	−0.203306	+	0.352136i
$255$		0			0
$256$	59.5000	+	103.057i	0.0145264	+	0.0251604i
$257$	−3127.50	−	5416.99i	−0.759098	−	1.31480i	−0.943311	−	0.331909i	$-0.892307\pi$
$257$	−3127.50	−	5416.99i	−0.759098	−	1.31480i	0.184214	−	0.982886i	$-0.441026\pi$
$258$		0			0
$259$	−210.000	+	363.731i	−0.0503813	+	0.0872630i
$260$	−175.000			−0.0417425
$261$		0			0
$262$	−1833.00			−0.432226
$263$	418.000	−	723.997i	0.0980037	−	0.169747i	−0.812855	−	0.582467i	$-0.802088\pi$
$263$	418.000	−	723.997i	0.0980037	−	0.169747i	0.910858	+	0.412719i	$0.135421\pi$
$264$		0			0
$265$	−10.0000	−	17.3205i	−0.00231809	−	0.00401506i
$266$	168.000	+	290.985i	0.0387246	+	0.0670730i
$267$		0			0
$268$	1722.00	−	2982.59i	0.392492	−	0.679816i
$269$	2231.00			0.505675			0.252837	−	0.967509i	$-0.418636\pi$
$269$	2231.00			0.505675			0.252837	+	0.967509i	$0.418636\pi$
$270$		0			0
$271$	−4832.00			−1.08311			−0.541556	−	0.840665i	$-0.682164\pi$
$271$	−4832.00			−1.08311			−0.541556	+	0.840665i	$0.682164\pi$
$272$	−2685.50	+	4651.42i	−0.598648	+	1.03689i
$273$		0			0
$274$	−549.000	−	950.896i	−0.121045	−	0.209656i
$275$	−587.500	−	1017.58i	−0.128828	−	0.223136i
$276$		0			0
$277$	−3225.00	+	5585.86i	−0.699536	+	1.21163i	0.269091	+	0.963115i	$0.413277\pi$
$277$	−3225.00	+	5585.86i	−0.699536	+	1.21163i	−0.968627	+	0.248517i	$0.920057\pi$
$278$	1042.00			0.224802
$279$		0			0
$280$	450.000			0.0960452
$281$	−525.000	+	909.327i	−0.111455	+	0.193046i	−0.916357	−	0.400362i	$-0.868884\pi$
$281$	−525.000	+	909.327i	−0.111455	+	0.193046i	0.804902	+	0.593408i	$0.202218\pi$
$282$		0			0
$283$	792.000	+	1371.78i	0.166359	+	0.288142i	0.937137	−	0.348962i	$-0.113466\pi$
$283$	792.000	+	1371.78i	0.166359	+	0.288142i	−0.770778	+	0.637104i	$0.780132\pi$
$284$	−112.000	−	193.990i	−0.0234013	−	0.0405323i
$285$		0			0
$286$	−117.500	+	203.516i	−0.0242934	+	0.0420775i
$287$	840.000			0.172765
$288$		0			0
$289$	12248.0			2.49298
$290$	−392.500	+	679.830i	−0.0794772	+	0.137659i
$291$		0			0
$292$	3395.00	+	5880.31i	0.680402	+	1.17849i
$293$	3297.00	+	5710.57i	0.657382	+	1.13862i	0.981291	+	0.192530i	$0.0616693\pi$
$293$	3297.00	+	5710.57i	0.657382	+	1.13862i	−0.323909	+	0.946088i	$0.604997\pi$
$294$		0			0
$295$	−1870.00	+	3238.94i	−0.369070	+	0.639248i
$296$	−1050.00			−0.206182
$297$		0			0
$298$	−2941.00			−0.571703
$299$	−7.50000	+	12.9904i	−0.00145062	+	0.00251255i
$300$		0			0
$301$	1191.00	+	2062.87i	0.228067	+	0.395023i
$302$	255.500	+	442.539i	0.0486834	+	0.0843220i
$303$		0			0
$304$	1148.00	−	1988.39i	0.216587	−	0.375139i
$305$	1690.00			0.317276
$306$		0			0
$307$	−4343.00			−0.807388			−0.403694	−	0.914894i	$-0.632274\pi$
$307$	−4343.00			−0.807388			−0.403694	+	0.914894i	$0.632274\pi$
$308$	−987.000	+	1709.53i	−0.182596	+	0.316265i
$309$		0			0
$310$	−562.500	−	974.279i	−0.103058	−	0.178501i
$311$	−1062.00	−	1839.44i	−0.193635	−	0.335386i	0.752817	−	0.658230i	$-0.228694\pi$
$311$	−1062.00	−	1839.44i	−0.193635	−	0.335386i	−0.946452	+	0.322844i	$0.895361\pi$
$312$		0			0
$313$	3758.00	−	6509.05i	0.678641	−	1.17544i	−0.296749	−	0.954956i	$-0.595902\pi$
$313$	3758.00	−	6509.05i	0.678641	−	1.17544i	0.975390	−	0.220486i	$-0.0707642\pi$
$314$	571.000			0.102622
$315$		0			0
$316$	8799.00			1.56640
$317$	−3440.00	+	5958.25i	−0.609494	+	1.05567i	0.381830	+	0.924233i	$0.375294\pi$
$317$	−3440.00	+	5958.25i	−0.609494	+	1.05567i	−0.991324	+	0.131442i	$0.958039\pi$
$318$		0			0
$319$	−3689.50	−	6390.40i	−0.647562	−	1.12161i
$320$	−417.500	−	723.131i	−0.0729342	−	0.126326i
$321$		0			0
$322$	9.00000	−	15.5885i	0.00155761	−	0.00269786i
$323$	−7336.00			−1.26373
$324$		0			0
$325$	−125.000			−0.0213346
$326$	356.500	−	617.476i	0.0605666	−	0.104904i
$327$		0			0
$328$	1050.00	+	1818.65i	0.176758	+	0.306153i
$329$	1041.00	+	1803.06i	0.174444	+	0.302146i
$330$		0			0
$331$	2493.00	−	4318.00i	0.413981	−	0.717036i	−0.581340	−	0.813661i	$-0.697471\pi$
$331$	2493.00	−	4318.00i	0.413981	−	0.717036i	0.995321	+	0.0966248i	$0.0308047\pi$
$332$	−714.000			−0.118030
$333$		0			0
$334$	1596.00			0.261465
$335$	1230.00	−	2130.42i	0.200603	−	0.347455i
$336$		0			0
$337$	−452.000	−	782.887i	−0.0730623	−	0.126548i	0.827180	−	0.561938i	$-0.189944\pi$
$337$	−452.000	−	782.887i	−0.0730623	−	0.126548i	−0.900242	+	0.435390i	$0.856611\pi$
$338$	−1086.00	−	1881.01i	−0.174765	−	0.302702i
$339$		0			0
$340$	−2292.50	+	3970.73i	−0.365671	+	0.633361i
$341$	10575.0			1.67938
$342$		0			0
$343$	3900.00			0.613936
$344$	−2977.50	+	5157.18i	−0.466675	+	0.808304i
$345$		0			0
$346$	−2067.00	−	3580.15i	−0.321164	−	0.556272i
$347$	4430.00	+	7672.99i	0.685345	+	1.18705i	0.973328	+	0.229417i	$0.0736821\pi$
$347$	4430.00	+	7672.99i	0.685345	+	1.18705i	−0.287983	+	0.957636i	$0.592985\pi$
$348$		0			0
$349$	2227.00	−	3857.28i	0.341572	−	0.591620i	−0.643153	−	0.765738i	$-0.722374\pi$
$349$	2227.00	−	3857.28i	0.341572	−	0.591620i	0.984725	+	0.174118i	$0.0557074\pi$
$350$	150.000			0.0229081
$351$		0			0
$352$	−7567.00			−1.14580
$353$	−4390.50	+	7604.57i	−0.661991	+	1.14660i	0.318101	+	0.948057i	$0.396955\pi$
$353$	−4390.50	+	7604.57i	−0.661991	+	1.14660i	−0.980092	+	0.198545i	$0.936378\pi$
$354$		0			0
$355$	−80.0000	−	138.564i	−0.0119604	−	0.0207161i
$356$	5208.00	+	9020.52i	0.775347	+	1.34294i
$357$		0			0
$358$	−914.000	+	1583.09i	−0.134934	+	0.233713i
$359$	−2928.00			−0.430457			−0.215228	−	0.976564i	$-0.569050\pi$
$359$	−2928.00			−0.430457			−0.215228	+	0.976564i	$0.569050\pi$
$360$		0			0
$361$	−3723.00			−0.542790
$362$	−260.000	+	450.333i	−0.0377494	+	0.0653839i
$363$		0			0
$364$	105.000	+	181.865i	0.0151195	+	0.0261877i
$365$	2425.00	+	4200.22i	0.347754	+	0.602328i
$366$		0			0
$367$	−4551.00	+	7882.56i	−0.647303	+	1.12116i	0.336461	+	0.941697i	$0.390770\pi$
$367$	−4551.00	+	7882.56i	−0.647303	+	1.12116i	−0.983764	+	0.179465i	$0.942563\pi$
$368$	−123.000			−0.0174234
$369$		0			0
$370$	−350.000			−0.0491774
$371$	−12.0000	+	20.7846i	−0.00167927	+	0.00290858i
$372$		0			0
$373$	4091.50	+	7086.69i	0.567962	+	0.983739i	0.996767	+	0.0803422i	$0.0256013\pi$
$373$	4091.50	+	7086.69i	0.567962	+	0.983739i	−0.428805	+	0.903397i	$0.641065\pi$
$374$	3078.50	+	5332.12i	0.425630	+	0.737212i
$375$		0			0
$376$	−2602.50	+	4507.66i	−0.356951	+	0.618258i
$377$	−785.000			−0.107240
$378$		0			0
$379$	6136.00			0.831623			0.415812	−	0.909451i	$-0.363498\pi$
$379$	6136.00			0.831623			0.415812	+	0.909451i	$0.363498\pi$
$380$	980.000	−	1697.41i	0.132297	−	0.229145i
$381$		0			0
$382$	−2413.00	−	4179.44i	−0.323193	−	0.559787i
$383$	2821.50	+	4886.98i	0.376428	+	0.651992i	0.990540	−	0.137227i	$-0.0438189\pi$
$383$	2821.50	+	4886.98i	0.376428	+	0.651992i	−0.614112	+	0.789219i	$0.710486\pi$
$384$		0			0
$385$	−705.000	+	1221.10i	−0.0933250	+	0.161644i
$386$	−1670.00			−0.220209
$387$		0			0
$388$	−6818.00			−0.892092
$389$	4495.50	−	7786.43i	0.585941	−	1.01488i	−0.408817	−	0.912616i	$-0.634059\pi$
$389$	4495.50	−	7786.43i	0.585941	−	1.01488i	0.994757	−	0.102262i	$-0.0326082\pi$
$390$		0			0
$391$	196.500	+	340.348i	0.0254154	+	0.0440208i
$392$	2302.50	+	3988.05i	0.296668	+	0.513844i
$393$		0			0
$394$	690.000	−	1195.12i	0.0882277	−	0.152815i
$395$	6285.00			0.800589
$396$		0			0
$397$	−12449.0			−1.57380			−0.786898	−	0.617082i	$-0.788314\pi$
$397$	−12449.0			−1.57380			−0.786898	+	0.617082i	$0.788314\pi$
$398$	2178.50	−	3773.27i	0.274368	−	0.475219i
$399$		0			0
$400$	−512.500	−	887.676i	−0.0640625	−	0.110960i
$401$	4038.00	+	6994.02i	0.502863	+	0.870984i	0.999995	+	0.00330917i	$0.00105334\pi$
$401$	4038.00	+	6994.02i	0.502863	+	0.870984i	−0.497131	+	0.867675i	$0.665613\pi$
$402$		0			0
$403$	562.500	−	974.279i	0.0695288	−	0.120427i
$404$	−9345.00			−1.15082
$405$		0			0
$406$	942.000			0.115149
$407$	1645.00	−	2849.22i	0.200343	−	0.347004i
$408$		0			0
$409$	1416.50	+	2453.45i	0.171250	+	0.296614i	0.938857	−	0.344307i	$-0.111886\pi$
$409$	1416.50	+	2453.45i	0.171250	+	0.296614i	−0.767607	+	0.640921i	$0.778553\pi$
$410$	350.000	+	606.218i	0.0421592	+	0.0730219i
$411$		0			0
$412$	2401.00	−	4158.65i	0.287109	−	0.497287i
$413$	4488.00			0.534722
$414$		0			0
$415$	−510.000			−0.0603251
$416$	−402.500	+	697.150i	−0.0474379	+	0.0821649i
$417$		0			0
$418$	−1316.00	−	2279.38i	−0.153990	−	0.266718i
$419$	−2388.50	−	4137.00i	−0.278487	−	0.482353i	0.692522	−	0.721396i	$-0.256499\pi$
$419$	−2388.50	−	4137.00i	−0.278487	−	0.482353i	−0.971009	+	0.239044i	$0.923166\pi$
$420$		0			0
$421$	3232.00	−	5597.99i	0.374152	−	0.648050i	−0.616048	−	0.787709i	$-0.711267\pi$
$421$	3232.00	−	5597.99i	0.374152	−	0.648050i	0.990200	+	0.139658i	$0.0446005\pi$
$422$	4162.00			0.480102
$423$		0			0
$424$	−60.0000			−0.00687231
$425$	−1637.50	+	2836.23i	−0.186895	+	0.323712i
$426$		0			0
$427$	−1014.00	−	1756.30i	−0.114920	−	0.199048i
$428$	3843.00	+	6656.27i	0.434015	+	0.751736i
$429$		0			0
$430$	−992.500	+	1719.06i	−0.111308	+	0.192792i
$431$	−10680.0			−1.19359			−0.596795	−	0.802394i	$-0.703560\pi$
$431$	−10680.0			−1.19359			−0.596795	+	0.802394i	$0.703560\pi$
$432$		0			0
$433$	11566.0			1.28366			0.641832	−	0.766845i	$-0.278175\pi$
$433$	11566.0			1.28366			0.641832	+	0.766845i	$0.278175\pi$
$434$	−675.000	+	1169.13i	−0.0746568	+	0.129309i
$435$		0			0
$436$	−2450.00	−	4243.52i	−0.269114	−	0.466119i
$437$	−84.0000	−	145.492i	−0.00919511	−	0.0159264i
$438$		0			0
$439$	724.000	−	1254.00i	0.0787122	−	0.136333i	−0.823982	−	0.566615i	$-0.808253\pi$
$439$	724.000	−	1254.00i	0.0787122	−	0.136333i	0.902695	+	0.430282i	$0.141586\pi$
$440$	−3525.00			−0.381927
$441$		0			0
$442$	655.000			0.0704868
$443$	−1188.00	+	2057.68i	−0.127412	+	0.220684i	−0.922673	−	0.385583i	$-0.874000\pi$
$443$	−1188.00	+	2057.68i	−0.127412	+	0.220684i	0.795261	+	0.606267i	$0.207334\pi$
$444$		0			0
$445$	3720.00	+	6443.23i	0.396281	+	0.686378i
$446$	−2978.00	−	5158.05i	−0.316171	−	0.547625i
$447$		0			0
$448$	−501.000	+	867.757i	−0.0528349	+	0.0915127i
$449$	14894.0			1.56546			0.782730	−	0.622362i	$-0.213827\pi$
$449$	14894.0			1.56546			0.782730	+	0.622362i	$0.213827\pi$
$450$		0			0
$451$	−6580.00			−0.687007
$452$	3692.50	−	6395.60i	0.384249	−	0.665539i
$453$		0			0
$454$	−2470.00	−	4278.17i	−0.255337	−	0.442256i
$455$	75.0000	+	129.904i	0.00772759	+	0.0133846i
$456$		0			0
$457$	−8102.00	+	14033.1i	−0.829312	+	1.43641i	0.0692668	+	0.997598i	$0.477934\pi$
$457$	−8102.00	+	14033.1i	−0.829312	+	1.43641i	−0.898579	+	0.438812i	$0.855399\pi$
$458$	−4344.00			−0.443192
$459$		0			0
$460$	−105.000			−0.0106427
$461$	−2541.00	+	4401.14i	−0.256716	+	0.444646i	−0.965360	−	0.260921i	$-0.915974\pi$
$461$	−2541.00	+	4401.14i	−0.256716	+	0.444646i	0.708644	+	0.705566i	$0.249307\pi$
$462$		0			0
$463$	5163.00	+	8942.58i	0.518240	+	0.897617i	0.999775	+	0.0211910i	$0.00674580\pi$
$463$	5163.00	+	8942.58i	0.518240	+	0.897617i	−0.481536	+	0.876426i	$0.659921\pi$
$464$	−3218.50	−	5574.61i	−0.322015	−	0.557747i
$465$		0			0
$466$	2601.00	−	4505.06i	0.258560	−	0.447839i
$467$	−4184.00			−0.414588			−0.207294	−	0.978279i	$-0.566466\pi$
$467$	−4184.00			−0.414588			−0.207294	+	0.978279i	$0.566466\pi$
$468$		0			0
$469$	−2952.00			−0.290641
$470$	−867.500	+	1502.55i	−0.0851379	+	0.147463i
$471$		0			0
$472$	5610.00	+	9716.81i	0.547079	+	0.947568i
$473$	−9329.50	−	16159.2i	−0.906915	−	1.57082i
$474$		0			0
$475$	700.000	−	1212.44i	0.0676173	−	0.117117i
$476$	5502.00			0.529798
$477$		0			0
$478$	1546.00			0.147934
$479$	−7788.00	+	13489.2i	−0.742887	+	1.28672i	0.208289	+	0.978067i	$0.433211\pi$
$479$	−7788.00	+	13489.2i	−0.742887	+	1.28672i	−0.951176	+	0.308650i	$0.900123\pi$
$480$		0			0
$481$	−175.000	−	303.109i	−0.0165890	−	0.0287330i
$482$	−1829.50	−	3168.79i	−0.172887	−	0.299449i
$483$		0			0
$484$	3073.00	−	5322.59i	0.288599	−	0.499868i
$485$	−4870.00			−0.455949
$486$		0			0
$487$	10220.0			0.950949			0.475475	−	0.879729i	$-0.342276\pi$
$487$	10220.0			0.950949			0.475475	+	0.879729i	$0.342276\pi$
$488$	2535.00	−	4390.75i	0.235152	−	0.407295i
$489$		0			0
$490$	767.500	+	1329.35i	0.0707594	+	0.122559i
$491$	−1346.00	−	2331.34i	−0.123715	−	0.214281i	0.797515	−	0.603299i	$-0.206148\pi$
$491$	−1346.00	−	2331.34i	−0.123715	−	0.214281i	−0.921230	+	0.389018i	$0.872814\pi$
$492$		0			0
$493$	−10283.5	+	17811.5i	−0.939443	+	1.62716i
$494$	−280.000			−0.0255016
$495$		0			0
$496$	9225.00			0.835110
$497$	−96.0000	+	166.277i	−0.00866436	+	0.0150071i
$498$		0			0
$499$	−2882.00	−	4991.77i	−0.258549	−	0.447820i	0.707304	−	0.706909i	$-0.249911\pi$
$499$	−2882.00	−	4991.77i	−0.258549	−	0.447820i	−0.965853	+	0.259089i	$0.916578\pi$
$500$	−437.500	−	757.772i	−0.0391312	−	0.0677772i
$501$		0			0
$502$	−610.500	+	1057.42i	−0.0542788	+	0.0940136i
$503$	2437.00			0.216025			0.108012	−	0.994150i	$-0.465551\pi$
$503$	2437.00			0.216025			0.108012	+	0.994150i	$0.465551\pi$
$504$		0			0
$505$	−6675.00			−0.588185
$506$	−70.5000	+	122.110i	−0.00619389	+	0.0107281i
$507$		0			0
$508$	−5761.00	−	9978.34i	−0.503156	−	0.871491i
$509$	−2924.50	−	5065.38i	−0.254668	−	0.441098i	0.710137	−	0.704063i	$-0.248633\pi$
$509$	−2924.50	−	5065.38i	−0.254668	−	0.441098i	−0.964805	+	0.262965i	$0.915300\pi$
$510$		0			0
$511$	2910.00	−	5040.27i	0.251919	−	0.436337i
$512$	−11521.0			−0.994455
$513$		0			0
$514$	−6255.00			−0.536763
$515$	1715.00	−	2970.47i	0.146742	−	0.254164i
$516$		0			0
$517$	−8154.50	−	14124.0i	−0.693684	−	1.20150i
$518$	210.000	+	363.731i	0.0178125	+	0.0308521i
$519$		0			0
$520$	−187.500	+	324.760i	−0.0158123	+	0.0273878i
$521$	17032.0			1.43222			0.716109	−	0.697989i	$-0.245921\pi$
$521$	17032.0			1.43222			0.716109	+	0.697989i	$0.245921\pi$
$522$		0			0
$523$	4147.00			0.346722			0.173361	−	0.984858i	$-0.444537\pi$
$523$	4147.00			0.346722			0.173361	+	0.984858i	$0.444537\pi$
$524$	6415.50	−	11112.0i	0.534852	−	0.926391i
$525$		0			0
$526$	−418.000	−	723.997i	−0.0346496	−	0.0600148i
$527$	−14737.5	−	25526.1i	−1.21817	−	2.10993i
$528$		0			0
$529$	6079.00	−	10529.1i	0.499630	−	0.865385i
$530$	−20.0000			−0.00163914
$531$		0			0
$532$	−2352.00			−0.191677
$533$	−350.000	+	606.218i	−0.0284431	+	0.0492649i
$534$		0			0
$535$	2745.00	+	4754.48i	0.221826	+	0.384213i
$536$	−3690.00	−	6391.27i	−0.297358	−	0.515039i
$537$		0			0
$538$	1115.50	−	1932.10i	0.0893915	−	0.154831i
$539$	−14429.0			−1.15306
$540$		0			0
$541$	−3942.00			−0.313271			−0.156636	−	0.987656i	$-0.550065\pi$
$541$	−3942.00			−0.313271			−0.156636	+	0.987656i	$0.550065\pi$
$542$	−2416.00	+	4184.63i	−0.191469	+	0.331634i
$543$		0			0
$544$	10545.5	+	18265.3i	0.831130	+	1.43956i
$545$	−1750.00	−	3031.09i	−0.137545	−	0.238234i
$546$		0			0
$547$	6875.50	−	11908.7i	0.537432	−	0.930859i	−0.461610	−	0.887083i	$-0.652728\pi$
$547$	6875.50	−	11908.7i	0.537432	−	0.930859i	0.999041	−	0.0437759i	$-0.0139388\pi$
$548$	7686.00			0.599142
$549$		0			0
$550$	−1175.00			−0.0910949
$551$	4396.00	−	7614.10i	0.339884	−	0.588696i
$552$		0			0
$553$	−3771.00	−	6531.56i	−0.289981	−	0.502261i
$554$	3225.00	+	5585.86i	0.247323	+	0.428377i
$555$		0			0
$556$	−3647.00	+	6316.79i	−0.278179	+	0.481819i
$557$	−7944.00			−0.604305			−0.302153	−	0.953260i	$-0.597705\pi$
$557$	−7944.00			−0.604305			−0.302153	+	0.953260i	$0.597705\pi$
$558$		0			0
$559$	−1985.00			−0.150191
$560$	−615.000	+	1065.21i	−0.0464080	+	0.0803811i
$561$		0			0
$562$	525.000	+	909.327i	0.0394053	+	0.0682520i
$563$	−3351.00	−	5804.10i	−0.250849	−	0.434483i	0.712911	−	0.701254i	$-0.247376\pi$
$563$	−3351.00	−	5804.10i	−0.250849	−	0.434483i	−0.963760	+	0.266772i	$0.914043\pi$
$564$		0			0
$565$	2637.50	−	4568.28i	0.196390	−	0.340158i
$566$	1584.00			0.117633
$567$		0			0
$568$	−480.000			−0.0354584
$569$	−1380.00	+	2390.23i	−0.101674	+	0.176105i	−0.912375	−	0.409356i	$-0.865753\pi$
$569$	−1380.00	+	2390.23i	−0.101674	+	0.176105i	0.810700	+	0.585461i	$0.199087\pi$
$570$		0			0
$571$	−4465.00	−	7733.61i	−0.327241	−	0.566798i	0.654723	−	0.755869i	$-0.272785\pi$
$571$	−4465.00	−	7733.61i	−0.327241	−	0.566798i	−0.981963	+	0.189072i	$0.939452\pi$
$572$	−822.500	−	1424.61i	−0.0601232	−	0.104136i
$573$		0			0
$574$	420.000	−	727.461i	0.0305409	−	0.0528983i
$575$	−75.0000			−0.00543951
$576$		0			0
$577$	6944.00			0.501010			0.250505	−	0.968115i	$-0.419403\pi$
$577$	6944.00			0.501010			0.250505	+	0.968115i	$0.419403\pi$
$578$	6124.00	−	10607.1i	0.440700	−	0.763315i
$579$		0			0
$580$	−2747.50	−	4758.81i	−0.196696	−	0.340688i
$581$	306.000	+	530.008i	0.0218503	+	0.0378458i
$582$		0			0
$583$	94.0000	−	162.813i	0.00667767	−	0.0115661i
$584$	14550.0			1.03096
$585$		0			0
$586$	6594.00			0.464839
$587$	−2103.00	+	3642.50i	−0.147871	+	0.256120i	−0.930440	−	0.366444i	$-0.880575\pi$
$587$	−2103.00	+	3642.50i	−0.147871	+	0.256120i	0.782570	+	0.622563i	$0.213909\pi$
$588$		0			0
$589$	6300.00	+	10911.9i	0.440725	+	0.763358i
$590$	1870.00	+	3238.94i	0.130486	+	0.226008i
$591$		0			0
$592$	1435.00	−	2485.49i	0.0996252	−	0.172556i
$593$	6571.00			0.455040			0.227520	−	0.973773i	$-0.426938\pi$
$593$	6571.00			0.455040			0.227520	+	0.973773i	$0.426938\pi$
$594$		0			0
$595$	3930.00			0.270780
$596$	10293.5	−	17828.9i	0.707447	−	1.22533i
$597$		0			0
$598$	7.50000	+	12.9904i	0.000512873	+	0.000888321i
$599$	−4745.00	−	8218.58i	−0.323665	−	0.560605i	0.657576	−	0.753388i	$-0.271582\pi$
$599$	−4745.00	−	8218.58i	−0.323665	−	0.560605i	−0.981241	+	0.192784i	$0.938248\pi$
$600$		0			0
$601$	−5930.50	+	10271.9i	−0.402513	+	0.697172i	−0.994028	−	0.109121i	$-0.965196\pi$
$601$	−5930.50	+	10271.9i	−0.402513	+	0.697172i	0.591516	+	0.806293i	$0.298530\pi$
$602$	2382.00			0.161268
$603$		0			0
$604$	−3577.00			−0.240970
$605$	2195.00	−	3801.85i	0.147503	−	0.255483i
$606$		0			0
$607$	259.000	+	448.601i	0.0173188	+	0.0299970i	0.874555	−	0.484927i	$-0.161154\pi$
$607$	259.000	+	448.601i	0.0173188	+	0.0299970i	−0.857236	+	0.514923i	$0.827820\pi$
$608$	−4508.00	−	7808.09i	−0.300697	−	0.520822i
$609$		0			0
$610$	845.000	−	1463.58i	0.0560870	−	0.0971455i
$611$	−1735.00			−0.114878
$612$		0			0
$613$	15163.0			0.999067			0.499533	−	0.866295i	$-0.333505\pi$
$613$	15163.0			0.999067			0.499533	+	0.866295i	$0.333505\pi$
$614$	−2171.50	+	3761.15i	−0.142727	+	0.247211i
$615$		0			0
$616$	2115.00	+	3663.29i	0.138337	+	0.239607i
$617$	9505.50	+	16464.0i	0.620222	+	1.07426i	0.989444	+	0.144915i	$0.0462909\pi$
$617$	9505.50	+	16464.0i	0.620222	+	1.07426i	−0.369222	+	0.929341i	$0.620376\pi$
$618$		0			0
$619$	3953.00	−	6846.80i	0.256679	−	0.444582i	−0.708671	−	0.705539i	$-0.750705\pi$
$619$	3953.00	−	6846.80i	0.256679	−	0.444582i	0.965350	+	0.260958i	$0.0840383\pi$
$620$	7875.00			0.510109
$621$		0			0
$622$	−2124.00			−0.136921
$623$	4464.00	−	7731.87i	0.287073	−	0.497225i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−3758.00	−	6509.05i	−0.239936	−	0.415581i
$627$		0			0
$628$	−1998.50	+	3461.50i	−0.126989	+	0.219951i
$629$	−9170.00			−0.581291
$630$		0			0
$631$	−3416.00			−0.215513			−0.107757	−	0.994177i	$-0.534367\pi$
$631$	−3416.00			−0.215513			−0.107757	+	0.994177i	$0.534367\pi$
$632$	9427.50	−	16328.9i	0.593364	−	1.02774i
$633$		0			0
$634$	3440.00	+	5958.25i	0.215489	+	0.373237i
$635$	−4115.00	−	7127.39i	−0.257163	−	0.445420i
$636$		0			0
$637$	−767.500	+	1329.35i	−0.0477386	+	0.0826856i
$638$	−7379.00			−0.457896
$639$		0			0
$640$	−7275.00			−0.449328
$641$	2415.00	−	4182.90i	0.148809	−	0.257745i	−0.781978	−	0.623306i	$-0.785789\pi$
$641$	2415.00	−	4182.90i	0.148809	−	0.257745i	0.930788	+	0.365560i	$0.119123\pi$
$642$		0			0
$643$	−6274.50	−	10867.8i	−0.384824	−	0.666536i	0.606920	−	0.794763i	$-0.292405\pi$
$643$	−6274.50	−	10867.8i	−0.384824	−	0.666536i	−0.991745	+	0.128227i	$0.959071\pi$
$644$	63.0000	+	109.119i	0.00385489	+	0.00667686i
$645$		0			0
$646$	−3668.00	+	6353.16i	−0.223399	+	0.386938i
$647$	−8164.00			−0.496074			−0.248037	−	0.968751i	$-0.579785\pi$
$647$	−8164.00			−0.496074			−0.248037	+	0.968751i	$0.579785\pi$
$648$		0			0
$649$	−35156.0			−2.12634
$650$	−62.5000	+	108.253i	−0.00377146	+	0.00653237i
$651$		0			0
$652$	2495.50	+	4322.33i	0.149895	+	0.259625i
$653$	11884.0	+	20583.7i	0.712185	+	1.23354i	0.964035	+	0.265774i	$0.0856277\pi$
$653$	11884.0	+	20583.7i	0.712185	+	1.23354i	−0.251850	+	0.967766i	$0.581039\pi$
$654$		0			0
$655$	4582.50	−	7937.12i	0.273363	−	0.473479i
$656$	−5740.00			−0.341630
$657$		0			0
$658$	2082.00			0.123351
$659$	10736.0	−	18595.3i	0.634621	−	1.09920i	−0.351974	−	0.936010i	$-0.614490\pi$
$659$	10736.0	−	18595.3i	0.634621	−	1.09920i	0.986595	−	0.163186i	$-0.0521771\pi$
$660$		0			0
$661$	−6491.00	−	11242.7i	−0.381953	−	0.661561i	0.609389	−	0.792872i	$-0.291415\pi$
$661$	−6491.00	−	11242.7i	−0.381953	−	0.661561i	−0.991341	+	0.131310i	$0.958082\pi$
$662$	−2493.00	−	4318.00i	−0.146364	−	0.253510i
$663$		0			0
$664$	−765.000	+	1325.02i	−0.0447105	+	0.0774408i
$665$	−1680.00			−0.0979663
$666$		0			0
$667$	−471.000			−0.0273421
$668$	−5586.00	+	9675.24i	−0.323546	+	0.560398i
$669$		0			0
$670$	−1230.00	−	2130.42i	−0.0709239	−	0.122844i
$671$	7943.00	+	13757.7i	0.456984	+	0.791519i
$672$		0			0
$673$	3003.00	−	5201.35i	0.172002	−	0.297916i	−0.767118	−	0.641506i	$-0.778310\pi$
$673$	3003.00	−	5201.35i	0.172002	−	0.297916i	0.939120	+	0.343590i	$0.111643\pi$
$674$	−904.000			−0.0516629
$675$		0			0
$676$	15204.0			0.865043
$677$	582.000	−	1008.05i	0.0330400	−	0.0572270i	−0.849033	−	0.528340i	$-0.822814\pi$
$677$	582.000	−	1008.05i	0.0330400	−	0.0572270i	0.882073	+	0.471114i	$0.156148\pi$
$678$		0			0
$679$	2922.00	+	5061.05i	0.165149	+	0.286046i
$680$	4912.50	+	8508.70i	0.277038	+	0.479844i
$681$		0			0
$682$	5287.50	−	9158.22i	0.296875	−	0.514203i
$683$	−26496.0			−1.48439			−0.742197	−	0.670182i	$-0.766216\pi$
$683$	−26496.0			−1.48439			−0.742197	+	0.670182i	$0.766216\pi$
$684$		0			0
$685$	5490.00			0.306222
$686$	1950.00	−	3377.50i	0.108530	−	0.187979i
$687$		0			0
$688$	−8138.50	−	14096.3i	−0.450985	−	0.781128i
$689$	−10.0000	−	17.3205i	−0.000552931	−	0.000957705i
$690$		0			0
$691$	−8555.00	+	14817.7i	−0.470981	+	0.815762i	−0.999449	−	0.0331907i	$-0.989433\pi$
$691$	−8555.00	+	14817.7i	−0.470981	+	0.815762i	0.528469	+	0.848953i	$0.322766\pi$
$692$	28938.0			1.58968
$693$		0			0
$694$	8860.00			0.484612
$695$	−2605.00	+	4511.99i	−0.142177	+	0.246258i
$696$		0			0
$697$	9170.00	+	15882.9i	0.498334	+	0.863139i
$698$	−2227.00	−	3857.28i	−0.120764	−	0.209169i
$699$		0			0
$700$	−525.000	+	909.327i	−0.0283473	+	0.0490990i
$701$	−30251.0			−1.62991			−0.814953	−	0.579527i	$-0.803237\pi$
$701$	−30251.0			−1.62991			−0.814953	+	0.579527i	$0.803237\pi$
$702$		0			0
$703$	3920.00			0.210307
$704$	3924.50	−	6797.43i	0.210100	−	0.363903i
$705$		0			0
$706$	4390.50	+	7604.57i	0.234049	+	0.405385i
$707$	4005.00	+	6936.86i	0.213046	+	0.369007i
$708$		0			0
$709$	−9410.00	+	16298.6i	−0.498448	+	0.863338i	−0.999998	−	0.00179062i	$-0.999430\pi$
$709$	−9410.00	+	16298.6i	−0.498448	+	0.863338i	0.501550	+	0.865129i	$0.332763\pi$
$710$	−160.000			−0.00845731
$711$		0			0
$712$	22320.0			1.17483
$713$	337.500	−	584.567i	0.0177272	−	0.0307044i
$714$		0			0
$715$	−587.500	−	1017.58i	−0.0307290	−	0.0532242i
$716$	−6398.00	−	11081.7i	−0.333945	−	0.578409i
$717$		0			0
$718$	−1464.00	+	2535.72i	−0.0760947	+	0.131800i
$719$	−31890.0			−1.65410			−0.827049	−	0.562130i	$-0.809982\pi$
$719$	−31890.0			−1.65410			−0.827049	+	0.562130i	$0.809982\pi$
$720$		0			0
$721$	−4116.00			−0.212605
$722$	−1861.50	+	3224.21i	−0.0959527	+	0.166195i
$723$		0			0
$724$	−1820.00	−	3152.33i	−0.0934251	−	0.161817i
$725$	−1962.50	−	3399.15i	−0.100532	−	0.174126i
$726$		0			0
$727$	5726.00	−	9917.72i	0.292112	−	0.505953i	−0.682197	−	0.731169i	$-0.738975\pi$
$727$	5726.00	−	9917.72i	0.292112	−	0.505953i	0.974309	+	0.225215i	$0.0723086\pi$
$728$	450.000			0.0229095
$729$		0			0
$730$	4850.00			0.245899
$731$	−26003.5	+	45039.4i	−1.31570	+	2.27885i
$732$		0			0
$733$	−3547.00	−	6143.58i	−0.178733	−	0.309575i	0.762714	−	0.646736i	$-0.223867\pi$
$733$	−3547.00	−	6143.58i	−0.178733	−	0.309575i	−0.941447	+	0.337161i	$0.890533\pi$
$734$	4551.00	+	7882.56i	0.228856	+	0.396391i
$735$		0			0
$736$	−241.500	+	418.290i	−0.0120948	+	0.0209489i
$737$	23124.0			1.15574
$738$		0			0
$739$	−3200.00			−0.159288			−0.0796440	−	0.996823i	$-0.525378\pi$
$739$	−3200.00			−0.159288			−0.0796440	+	0.996823i	$0.525378\pi$
$740$	1225.00	−	2121.76i	0.0608539	−	0.105402i
$741$		0			0
$742$	12.0000	+	20.7846i	0.000593711	+	0.00102834i
$743$	−10415.5	−	18040.2i	−0.514277	−	0.890753i	−0.999863	−	0.0165646i	$-0.994727\pi$
$743$	−10415.5	−	18040.2i	−0.514277	−	0.890753i	0.485586	−	0.874189i	$-0.338606\pi$
$744$		0			0
$745$	7352.50	−	12734.9i	0.361577	−	0.626269i
$746$	8183.00			0.401610
$747$		0			0
$748$	−43099.0			−2.10676
$749$	3294.00	−	5705.38i	0.160694	−	0.278331i
$750$		0			0
$751$	7802.50	+	13514.3i	0.379118	+	0.656651i	0.990934	−	0.134349i	$-0.0428943\pi$
$751$	7802.50	+	13514.3i	0.379118	+	0.656651i	−0.611817	+	0.791000i	$0.709561\pi$
$752$	−7113.50	−	12320.9i	−0.344950	−	0.597472i
$753$		0			0
$754$	−392.500	+	679.830i	−0.0189576	+	0.0328355i
$755$	−2555.00			−0.123160
$756$		0			0
$757$	21349.0			1.02502			0.512512	−	0.858680i	$-0.328715\pi$
$757$	21349.0			1.02502			0.512512	+	0.858680i	$0.328715\pi$
$758$	3068.00	−	5313.93i	0.147012	−	0.254632i
$759$		0			0
$760$	−2100.00	−	3637.31i	−0.100230	−	0.173604i
$761$	1851.00	+	3206.03i	0.0881717	+	0.152718i	0.906738	−	0.421694i	$-0.138564\pi$
$761$	1851.00	+	3206.03i	0.0881717	+	0.152718i	−0.818567	+	0.574412i	$0.805231\pi$
$762$		0			0
$763$	−2100.00	+	3637.31i	−0.0996397	+	0.172581i
$764$	33782.0			1.59972
$765$		0			0
$766$	5643.00			0.266175
$767$	−1870.00	+	3238.94i	−0.0880336	+	0.152479i
$768$		0			0
$769$	696.500	+	1206.37i	0.0326612	+	0.0565708i	0.881894	−	0.471448i	$-0.156268\pi$
$769$	696.500	+	1206.37i	0.0326612	+	0.0565708i	−0.849233	+	0.528019i	$0.822935\pi$
$770$	705.000	+	1221.10i	0.0329954	+	0.0571497i
$771$		0			0
$772$	5845.00	−	10123.8i	0.272495	−	0.471975i
$773$	6906.00			0.321334			0.160667	−	0.987009i	$-0.448635\pi$
$773$	6906.00			0.321334			0.160667	+	0.987009i	$0.448635\pi$
$774$		0			0
$775$	5625.00			0.260717
$776$	−7305.00	+	12652.6i	−0.337931	+	0.585313i
$777$		0			0
$778$	−4495.50	−	7786.43i	−0.207161	−	0.358814i
$779$	−3920.00	−	6789.64i	−0.180293	−	0.312277i
$780$		0			0
$781$	752.000	−	1302.50i	0.0344541	−	0.0596763i
$782$	393.000			0.0179714
$783$		0			0
$784$	−12587.0			−0.573387
$785$	−1427.50	+	2472.50i	−0.0649040	+	0.112417i
$786$		0			0
$787$	−15246.5	−	26407.7i	−0.690571	−	1.19610i	−0.971651	−	0.236419i	$-0.924026\pi$
$787$	−15246.5	−	26407.7i	−0.690571	−	1.19610i	0.281081	−	0.959684i	$-0.409307\pi$
$788$	4830.00	+	8365.81i	0.218352	+	0.378197i
$789$		0			0
$790$	3142.50	−	5442.97i	0.141525	−	0.245129i
$791$	−6330.00			−0.284537
$792$		0			0
$793$	1690.00			0.0756793
$794$	−6224.50	+	10781.2i	−0.278211	+	0.481875i
$795$		0			0
$796$	15249.5	+	26412.9i	0.679025	+	1.17611i
$797$	16744.0	+	29001.5i	0.744169	+	1.28894i	0.950582	+	0.310474i	$0.100488\pi$
$797$	16744.0	+	29001.5i	0.744169	+	1.28894i	−0.206413	+	0.978465i	$0.566179\pi$
$798$		0			0
$799$	−22728.5	+	39366.9i	−1.00635	+	1.74306i
$800$	−4025.00			−0.177882
$801$		0			0
$802$	8076.00			0.355578
$803$	−22795.0	+	39482.1i	−1.00177	+	1.73511i
$804$		0			0
$805$	45.0000	+	77.9423i	0.00197024	+	0.00341255i
$806$	−562.500	−	974.279i	−0.0245822	−	0.0425775i
$807$		0			0
$808$	−10012.5	+	17342.2i	−0.435939	+	0.755068i
$809$	15304.0			0.665093			0.332546	−	0.943087i	$-0.392092\pi$
$809$	15304.0			0.665093			0.332546	+	0.943087i	$0.392092\pi$
$810$		0			0
$811$	−40122.0			−1.73721			−0.868603	−	0.495509i	$-0.834982\pi$
$811$	−40122.0			−1.73721			−0.868603	+	0.495509i	$0.834982\pi$
$812$	−3297.00	+	5710.57i	−0.142490	+	0.246800i
$813$		0			0
$814$	−1645.00	−	2849.22i	−0.0708320	−	0.122685i
$815$	1782.50	+	3087.38i	0.0766114	+	0.132695i
$816$		0			0
$817$	11116.0	−	19253.5i	0.476009	−	0.824472i
$818$	2833.00			0.121092
$819$		0			0
$820$	−4900.00			−0.208677
$821$	12549.0	−	21735.5i	0.533451	−	0.923964i	−0.465786	−	0.884898i	$-0.654228\pi$
$821$	12549.0	−	21735.5i	0.533451	−	0.923964i	0.999237	−	0.0390664i	$-0.0124384\pi$
$822$		0			0
$823$	21746.0	+	37665.2i	0.921042	+	1.59529i	0.797805	+	0.602915i	$0.205994\pi$
$823$	21746.0	+	37665.2i	0.921042	+	1.59529i	0.123237	+	0.992377i	$0.460672\pi$
$824$	−5145.00	−	8911.40i	−0.217518	−	0.376752i
$825$		0			0
$826$	2244.00	−	3886.72i	0.0945263	−	0.163724i
$827$	−11206.0			−0.471186			−0.235593	−	0.971852i	$-0.575703\pi$
$827$	−11206.0			−0.471186			−0.235593	+	0.971852i	$0.575703\pi$
$828$		0			0
$829$	−23964.0			−1.00399			−0.501993	−	0.864872i	$-0.667400\pi$
$829$	−23964.0			−1.00399			−0.501993	+	0.864872i	$0.667400\pi$
$830$	−255.000	+	441.673i	−0.0106641	+	0.0184707i
$831$		0			0
$832$	−417.500	−	723.131i	−0.0173969	−	0.0301323i
$833$	20108.5	+	34828.9i	0.836396	+	1.44868i
$834$		0			0
$835$	−3990.00	+	6910.88i	−0.165365	+	0.286420i
$836$	18424.0			0.762210
$837$		0			0
$838$	−4777.00			−0.196920
$839$	−17303.0	+	29969.7i	−0.711997	+	1.23322i	0.252109	+	0.967699i	$0.418876\pi$
$839$	−17303.0	+	29969.7i	−0.711997	+	1.23322i	−0.964106	+	0.265517i	$0.914457\pi$
$840$		0			0
$841$	−130.000	−	225.167i	−0.00533027	−	0.00923230i
$842$	−3232.00	−	5597.99i	−0.132283	−	0.229120i
$843$		0			0
$844$	−14567.0	+	25230.8i	−0.594096	+	1.02900i
$845$	10860.0			0.442125
$846$		0			0
$847$	−5268.00			−0.213708
$848$	82.0000	−	142.028i	0.00332063	−	0.00575149i
$849$		0			0
$850$	1637.50	+	2836.23i	0.0660774	+	0.114449i
$851$	−105.000	−	181.865i	−0.00422956	−	0.00732581i
$852$		0			0
$853$	9238.50	−	16001.6i	0.370833	−	0.642301i	−0.618861	−	0.785500i	$-0.712406\pi$
$853$	9238.50	−	16001.6i	0.370833	−	0.642301i	0.989694	+	0.143199i	$0.0457390\pi$
$854$	−2028.00			−0.0812608
$855$		0			0
$856$	16470.0			0.657632
$857$	−20671.0	+	35803.2i	−0.823930	+	1.42709i	0.0788045	+	0.996890i	$0.474890\pi$
$857$	−20671.0	+	35803.2i	−0.823930	+	1.42709i	−0.902734	+	0.430198i	$0.858444\pi$
$858$		0			0
$859$	−10949.0	−	18964.2i	−0.434895	−	0.753261i	0.562392	−	0.826871i	$-0.309881\pi$
$859$	−10949.0	−	18964.2i	−0.434895	−	0.753261i	−0.997287	+	0.0736101i	$0.976548\pi$
$860$	−6947.50	−	12033.4i	−0.275474	−	0.477135i
$861$		0			0
$862$	−5340.00	+	9249.15i	−0.210999	+	0.365461i
$863$	18487.0			0.729206			0.364603	−	0.931163i	$-0.381205\pi$
$863$	18487.0			0.729206			0.364603	+	0.931163i	$0.381205\pi$
$864$		0			0
$865$	20670.0			0.812487
$866$	5783.00	−	10016.4i	0.226922	−	0.393040i
$867$		0			0
$868$	−4725.00	−	8183.94i	−0.184766	−	0.320024i
$869$	29539.5	+	51163.9i	1.15312	+	1.99726i
$870$		0			0
$871$	1230.00	−	2130.42i	0.0478496	−	0.0828779i
$872$	−10500.0			−0.407769
$873$		0			0
$874$	−168.000			−0.00650193
$875$	−375.000	+	649.519i	−0.0144884	+	0.0250946i
$876$		0			0
$877$	−3796.50	−	6575.73i	−0.146179	−	0.253189i	0.783633	−	0.621224i	$-0.213364\pi$
$877$	−3796.50	−	6575.73i	−0.146179	−	0.253189i	−0.929812	+	0.368035i	$0.880031\pi$
$878$	−724.000	−	1254.00i	−0.0278289	−	0.0482012i
$879$		0			0
$880$	4817.50	−	8344.15i	0.184543	−	0.319638i
$881$	3038.00			0.116178			0.0580890	−	0.998311i	$-0.481499\pi$
$881$	3038.00			0.116178			0.0580890	+	0.998311i	$0.481499\pi$
$882$		0			0
$883$	−16732.0			−0.637686			−0.318843	−	0.947808i	$-0.603294\pi$
$883$	−16732.0			−0.637686			−0.318843	+	0.947808i	$0.603294\pi$
$884$	−2292.50	+	3970.73i	−0.0872230	+	0.151075i
$885$		0			0
$886$	1188.00	+	2057.68i	0.0450470	+	0.0780237i
$887$	−4015.50	−	6955.05i	−0.152004	−	0.263278i	0.779960	−	0.625829i	$-0.215239\pi$
$887$	−4015.50	−	6955.05i	−0.152004	−	0.263278i	−0.931964	+	0.362551i	$0.881906\pi$
$888$		0			0
$889$	−4938.00	+	8552.87i	−0.186294	+	0.322670i
$890$	7440.00			0.280213
$891$		0			0
$892$	41692.0			1.56497
$893$	9716.00	−	16828.6i	0.364091	−	0.630625i
$894$		0			0
$895$	−4570.00	−	7915.47i	−0.170680	−	0.295626i
$896$	4365.00	+	7560.40i	0.162750	+	0.281892i
$897$		0			0
$898$	7447.00	−	12898.6i	0.276737	−	0.479322i
$899$	35325.0			1.31052
$900$		0			0
$901$	−524.000			−0.0193751
$902$	−3290.00	+	5698.45i	−0.121447	+	0.210352i
$903$		0			0
$904$	−7912.50	−	13704.9i	−0.291113	−	0.504222i
$905$	−1300.00	−	2251.67i	−0.0477497	−	0.0827049i
$906$		0			0
$907$	19243.5	−	33330.7i	0.704487	−	1.22021i	−0.262389	−	0.964962i	$-0.584510\pi$
$907$	19243.5	−	33330.7i	0.704487	−	1.22021i	0.966876	−	0.255246i	$-0.0821563\pi$
$908$	34580.0			1.26385
$909$		0			0
$910$	150.000			0.00546423
$911$	−2560.00	+	4434.05i	−0.0931027	+	0.161259i	−0.908815	−	0.417199i	$-0.863012\pi$
$911$	−2560.00	+	4434.05i	−0.0931027	+	0.161259i	0.815712	+	0.578458i	$0.196345\pi$
$912$		0			0
$913$	−2397.00	−	4151.73i	−0.0868884	−	0.150495i
$914$	8102.00	+	14033.1i	0.293206	+	0.507848i
$915$		0			0
$916$	15204.0	−	26334.1i	0.548422	−	0.949894i
$917$	−10998.0			−0.396059
$918$		0			0
$919$	28075.0			1.00774			0.503868	−	0.863781i	$-0.331910\pi$
$919$	28075.0			1.00774			0.503868	+	0.863781i	$0.331910\pi$
$920$	−112.500	+	194.856i	−0.00403154	+	0.00698283i
$921$		0			0
$922$	2541.00	+	4401.14i	0.0907629	+	0.157206i
$923$	−80.0000	−	138.564i	−0.00285291	−	0.00494138i
$924$		0			0
$925$	875.000	−	1515.54i	0.0311025	−	0.0538711i
$926$	10326.0			0.366451
$927$		0			0
$928$	−25277.0			−0.894136
$929$	−6428.00	+	11133.6i	−0.227014	+	0.393199i	−0.956922	−	0.290346i	$-0.906230\pi$
$929$	−6428.00	+	11133.6i	−0.227014	+	0.393199i	0.729908	+	0.683546i	$0.239563\pi$
$930$		0			0
$931$	−8596.00	−	14888.7i	−0.302602	−	0.524122i
$932$	18207.0	+	31535.4i	0.639904	+	1.10835i
$933$		0			0
$934$	−2092.00	+	3623.45i	−0.0732894	+	0.126941i
$935$	−30785.0			−1.07677
$936$		0			0
$937$	−1374.00			−0.0479046			−0.0239523	−	0.999713i	$-0.507625\pi$
$937$	−1374.00			−0.0479046			−0.0239523	+	0.999713i	$0.507625\pi$
$938$	−1476.00	+	2556.51i	−0.0513786	+	0.0889903i
$939$		0			0
$940$	−6072.50	−	10517.9i	−0.210705	−	0.364953i
$941$	4271.50	+	7398.46i	0.147978	+	0.256305i	0.930480	−	0.366343i	$-0.119390\pi$
$941$	4271.50	+	7398.46i	0.147978	+	0.256305i	−0.782502	+	0.622648i	$0.786057\pi$
$942$		0			0
$943$	−210.000	+	363.731i	−0.00725190	+	0.0125607i
$944$	−30668.0			−1.05737
$945$		0			0
$946$	−18659.0			−0.641286
$947$	6753.00	−	11696.5i	0.231724	−	0.401358i	−0.726591	−	0.687070i	$-0.758897\pi$
$947$	6753.00	−	11696.5i	0.231724	−	0.401358i	0.958316	+	0.285712i	$0.0922299\pi$
$948$		0			0
$949$	2425.00	+	4200.22i	0.0829492	+	0.143672i
$950$	−700.000	−	1212.44i	−0.0239063	−	0.0414070i
$951$		0			0
$952$	5895.00	−	10210.4i	0.200691	−	0.347607i
$953$	−21775.0			−0.740148			−0.370074	−	0.929002i	$-0.620668\pi$
$953$	−21775.0			−0.740148			−0.370074	+	0.929002i	$0.620668\pi$
$954$		0			0
$955$	24130.0			0.817621
$956$	−5411.00	+	9372.13i	−0.183059	+	0.317067i
$957$		0			0
$958$	7788.00	+	13489.2i	0.262650	+	0.454923i
$959$	−3294.00	−	5705.38i	−0.110916	−	0.192113i
$960$		0			0
$961$	−10417.0	+	18042.8i	−0.349669	+	0.605645i
$962$	−350.000			−0.0117302
$963$		0			0
$964$	25613.0			0.855746
$965$	4175.00	−	7231.31i	0.139273	−	0.241227i
$966$		0			0
$967$	−1927.00	−	3337.66i	−0.0640829	−	0.110995i	0.832204	−	0.554470i	$-0.187079\pi$
$967$	−1927.00	−	3337.66i	−0.0640829	−	0.110995i	−0.896287	+	0.443475i	$0.853746\pi$
$968$	−6585.00	−	11405.6i	−0.218647	−	0.378707i
$969$		0			0
$970$	−2435.00	+	4217.54i	−0.0806012	+	0.139605i
$971$	−12933.0			−0.427435			−0.213718	−	0.976895i	$-0.568557\pi$
$971$	−12933.0			−0.427435			−0.213718	+	0.976895i	$0.568557\pi$
$972$		0			0
$973$	6252.00			0.205992
$974$	5110.00	−	8850.78i	0.168106	−	0.291168i
$975$		0			0
$976$	6929.00	+	12001.4i	0.227246	+	0.393601i
$977$	8760.50	+	15173.6i	0.286871	+	0.496876i	0.973061	−	0.230547i	$-0.0740515\pi$
$977$	8760.50	+	15173.6i	0.286871	+	0.496876i	−0.686190	+	0.727422i	$0.740718\pi$
$978$		0			0
$979$	−34968.0	+	60566.4i	−1.14155	+	1.97723i
$980$	−10745.0			−0.350241
$981$		0			0
$982$	−2692.00			−0.0874798
$983$	−6286.50	+	10888.5i	−0.203976	+	0.353296i	−0.949806	−	0.312840i	$-0.898720\pi$
$983$	−6286.50	+	10888.5i	−0.203976	+	0.353296i	0.745830	+	0.666136i	$0.232053\pi$
$984$		0			0
$985$	3450.00	+	5975.58i	0.111600	+	0.193297i
$986$	10283.5	+	17811.5i	0.332143	+	0.575289i
$987$		0			0
$988$	980.000	−	1697.41i	0.0315566	−	0.0546577i
$989$	−1191.00			−0.0382928
$990$		0			0
$991$	8945.00			0.286728			0.143364	−	0.989670i	$-0.454208\pi$
$991$	8945.00			0.286728			0.143364	+	0.989670i	$0.454208\pi$
$992$	18112.5	−	31371.8i	0.579710	−	1.00409i
$993$		0			0
$994$	96.0000	+	166.277i	0.00306331	+	0.00530582i
$995$	10892.5	+	18866.4i	0.347051	+	0.601109i
$996$		0			0
$997$	29089.5	−	50384.5i	0.924046	−	1.60049i	0.130957	−	0.991388i	$-0.458195\pi$
$997$	29089.5	−	50384.5i	0.924046	−	1.60049i	0.793089	−	0.609106i	$-0.208472\pi$
$998$	−5764.00			−0.182822
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.4.e.h.136.1		2
3.2	odd	2		405.4.e.f.136.1		2
9.2	odd	6		135.4.a.c.1.1	yes	1
9.4	even	3	inner	405.4.e.h.271.1		2
9.5	odd	6		405.4.e.f.271.1		2
9.7	even	3		135.4.a.b.1.1	✓	1
36.7	odd	6		2160.4.a.f.1.1		1
36.11	even	6		2160.4.a.p.1.1		1
45.2	even	12		675.4.b.e.649.2		2
45.7	odd	12		675.4.b.f.649.1		2
45.29	odd	6		675.4.a.c.1.1		1
45.34	even	6		675.4.a.h.1.1		1
45.38	even	12		675.4.b.e.649.1		2
45.43	odd	12		675.4.b.f.649.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.4.a.b.1.1	✓	1	9.7	even	3
135.4.a.c.1.1	yes	1	9.2	odd	6
405.4.e.f.136.1		2	3.2	odd	2
405.4.e.f.271.1		2	9.5	odd	6
405.4.e.h.136.1		2	1.1	even	1	trivial
405.4.e.h.271.1		2	9.4	even	3	inner
675.4.a.c.1.1		1	45.29	odd	6
675.4.a.h.1.1		1	45.34	even	6
675.4.b.e.649.1		2	45.38	even	12
675.4.b.e.649.2		2	45.2	even	12
675.4.b.f.649.1		2	45.7	odd	12
675.4.b.f.649.2		2	45.43	odd	12
2160.4.a.f.1.1		1	36.7	odd	6
2160.4.a.p.1.1		1	36.11	even	6

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	405.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(3.50000 + 6.06218i) q^{4} +(2.50000 + 4.33013i) q^{5} +(3.00000 - 5.19615i) q^{7} +15.0000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(3.50000 + 6.06218i) q^{4} +(2.50000 + 4.33013i) q^{5} +(3.00000 - 5.19615i) q^{7} +15.0000 q^{8} +5.00000 q^{10} +(-23.5000 + 40.7032i) q^{11} +(2.50000 + 4.33013i) q^{13} +(-3.00000 - 5.19615i) q^{14} +(-20.5000 + 35.5070i) q^{16} +131.000 q^{17} -56.0000 q^{19} +(-17.5000 + 30.3109i) q^{20} +(23.5000 + 40.7032i) q^{22} +(1.50000 + 2.59808i) q^{23} +(-12.5000 + 21.6506i) q^{25} +5.00000 q^{26} +42.0000 q^{28} +(-78.5000 + 135.966i) q^{29} +(-112.500 - 194.856i) q^{31} +(80.5000 + 139.430i) q^{32} +(65.5000 - 113.449i) q^{34} +30.0000 q^{35} -70.0000 q^{37} +(-28.0000 + 48.4974i) q^{38} +(37.5000 + 64.9519i) q^{40} +(70.0000 + 121.244i) q^{41} +(-198.500 + 343.812i) q^{43} -329.000 q^{44} +3.00000 q^{46} +(-173.500 + 300.511i) q^{47} +(153.500 + 265.870i) q^{49} +(12.5000 + 21.6506i) q^{50} +(-17.5000 + 30.3109i) q^{52} -4.00000 q^{53} -235.000 q^{55} +(45.0000 - 77.9423i) q^{56} +(78.5000 + 135.966i) q^{58} +(374.000 + 647.787i) q^{59} +(169.000 - 292.717i) q^{61} -225.000 q^{62} -167.000 q^{64} +(-12.5000 + 21.6506i) q^{65} +(-246.000 - 426.084i) q^{67} +(458.500 + 794.145i) q^{68} +(15.0000 - 25.9808i) q^{70} -32.0000 q^{71} +970.000 q^{73} +(-35.0000 + 60.6218i) q^{74} +(-196.000 - 339.482i) q^{76} +(141.000 + 244.219i) q^{77} +(628.500 - 1088.59i) q^{79} -205.000 q^{80} +140.000 q^{82} +(-51.0000 + 88.3346i) q^{83} +(327.500 + 567.247i) q^{85} +(198.500 + 343.812i) q^{86} +(-352.500 + 610.548i) q^{88} +1488.00 q^{89} +30.0000 q^{91} +(-10.5000 + 18.1865i) q^{92} +(173.500 + 300.511i) q^{94} +(-140.000 - 242.487i) q^{95} +(-487.000 + 843.509i) q^{97} +307.000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 7 q^{4} + 5 q^{5} + 6 q^{7} + 30 q^{8}+O(q^{10}) \) 2 * q + q^2 + 7 * q^4 + 5 * q^5 + 6 * q^7 + 30 * q^8	\( 2 q + q^{2} + 7 q^{4} + 5 q^{5} + 6 q^{7} + 30 q^{8} + 10 q^{10} - 47 q^{11} + 5 q^{13} - 6 q^{14} - 41 q^{16} + 262 q^{17} - 112 q^{19} - 35 q^{20} + 47 q^{22} + 3 q^{23} - 25 q^{25} + 10 q^{26} + 84 q^{28} - 157 q^{29} - 225 q^{31} + 161 q^{32} + 131 q^{34} + 60 q^{35} - 140 q^{37} - 56 q^{38} + 75 q^{40} + 140 q^{41} - 397 q^{43} - 658 q^{44} + 6 q^{46} - 347 q^{47} + 307 q^{49} + 25 q^{50} - 35 q^{52} - 8 q^{53} - 470 q^{55} + 90 q^{56} + 157 q^{58} + 748 q^{59} + 338 q^{61} - 450 q^{62} - 334 q^{64} - 25 q^{65} - 492 q^{67} + 917 q^{68} + 30 q^{70} - 64 q^{71} + 1940 q^{73} - 70 q^{74} - 392 q^{76} + 282 q^{77} + 1257 q^{79} - 410 q^{80} + 280 q^{82} - 102 q^{83} + 655 q^{85} + 397 q^{86} - 705 q^{88} + 2976 q^{89} + 60 q^{91} - 21 q^{92} + 347 q^{94} - 280 q^{95} - 974 q^{97} + 614 q^{98}+O(q^{100}) \) 2 * q + q^2 + 7 * q^4 + 5 * q^5 + 6 * q^7 + 30 * q^8 + 10 * q^10 - 47 * q^11 + 5 * q^13 - 6 * q^14 - 41 * q^16 + 262 * q^17 - 112 * q^19 - 35 * q^20 + 47 * q^22 + 3 * q^23 - 25 * q^25 + 10 * q^26 + 84 * q^28 - 157 * q^29 - 225 * q^31 + 161 * q^32 + 131 * q^34 + 60 * q^35 - 140 * q^37 - 56 * q^38 + 75 * q^40 + 140 * q^41 - 397 * q^43 - 658 * q^44 + 6 * q^46 - 347 * q^47 + 307 * q^49 + 25 * q^50 - 35 * q^52 - 8 * q^53 - 470 * q^55 + 90 * q^56 + 157 * q^58 + 748 * q^59 + 338 * q^61 - 450 * q^62 - 334 * q^64 - 25 * q^65 - 492 * q^67 + 917 * q^68 + 30 * q^70 - 64 * q^71 + 1940 * q^73 - 70 * q^74 - 392 * q^76 + 282 * q^77 + 1257 * q^79 - 410 * q^80 + 280 * q^82 - 102 * q^83 + 655 * q^85 + 397 * q^86 - 705 * q^88 + 2976 * q^89 + 60 * q^91 - 21 * q^92 + 347 * q^94 - 280 * q^95 - 974 * q^97 + 614 * q^98

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