LMFDB - Embedded newform 150.4.e.a.143.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,4,Mod(107,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("150.107");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	150.e (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:	$8.85028650086$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			143.2
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	150.143
Dual form			150.4.e.a.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41421 + 1.41421i) q^{2} +(-5.12132 - 0.878680i) q^{3} +4.00000i q^{4} +(-6.00000 - 8.48528i) q^{6} +(18.0000 - 18.0000i) q^{7} +(-5.65685 + 5.65685i) q^{8} +(25.4558 + 9.00000i) q^{9} +O(q^{10})$	\(q+(1.41421 + 1.41421i) q^{2} +(-5.12132 - 0.878680i) q^{3} +4.00000i q^{4} +(-6.00000 - 8.48528i) q^{6} +(18.0000 - 18.0000i) q^{7} +(-5.65685 + 5.65685i) q^{8} +(25.4558 + 9.00000i) q^{9} +50.9117i q^{11} +(3.51472 - 20.4853i) q^{12} +50.9117 q^{14} -16.0000 q^{16} +(59.3970 + 59.3970i) q^{17} +(23.2721 + 48.7279i) q^{18} +124.000i q^{19} +(-108.000 + 76.3675i) q^{21} +(-72.0000 + 72.0000i) q^{22} +(29.6985 - 29.6985i) q^{23} +(33.9411 - 24.0000i) q^{24} +(-122.459 - 68.4594i) q^{27} +(72.0000 + 72.0000i) q^{28} +254.558 q^{29} +88.0000 q^{31} +(-22.6274 - 22.6274i) q^{32} +(44.7351 - 260.735i) q^{33} +168.000i q^{34} +(-36.0000 + 101.823i) q^{36} +(72.0000 - 72.0000i) q^{37} +(-175.362 + 175.362i) q^{38} -50.9117i q^{41} +(-260.735 - 44.7351i) q^{42} +(-342.000 - 342.000i) q^{43} -203.647 q^{44} +84.0000 q^{46} +(318.198 + 318.198i) q^{47} +(81.9411 + 14.0589i) q^{48} -305.000i q^{49} +(-252.000 - 356.382i) q^{51} +(-220.617 + 220.617i) q^{53} +(-76.3675 - 270.000i) q^{54} +203.647i q^{56} +(108.956 - 635.044i) q^{57} +(360.000 + 360.000i) q^{58} -865.499 q^{59} +434.000 q^{61} +(124.451 + 124.451i) q^{62} +(620.205 - 296.205i) q^{63} -64.0000i q^{64} +(432.000 - 305.470i) q^{66} +(-18.0000 + 18.0000i) q^{67} +(-237.588 + 237.588i) q^{68} +(-178.191 + 126.000i) q^{69} -509.117i q^{71} +(-194.912 + 93.0883i) q^{72} +(360.000 + 360.000i) q^{73} +203.647 q^{74} -496.000 q^{76} +(916.410 + 916.410i) q^{77} -1024.00i q^{79} +(567.000 + 458.205i) q^{81} +(72.0000 - 72.0000i) q^{82} +(-173.948 + 173.948i) q^{83} +(-305.470 - 432.000i) q^{84} -967.322i q^{86} +(-1303.68 - 223.675i) q^{87} +(-288.000 - 288.000i) q^{88} -101.823 q^{89} +(118.794 + 118.794i) q^{92} +(-450.676 - 77.3238i) q^{93} +900.000i q^{94} +(96.0000 + 135.765i) q^{96} +(216.000 - 216.000i) q^{97} +(431.335 - 431.335i) q^{98} +(-458.205 + 1296.00i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 12 q^{3} - 24 q^{6} + 72 q^{7}+O(q^{10}) $ 4 * q - 12 * q^3 - 24 * q^6 + 72 * q^7	$ 4 q - 12 q^{3} - 24 q^{6} + 72 q^{7} + 48 q^{12} - 64 q^{16} + 144 q^{18} - 432 q^{21} - 288 q^{22} - 108 q^{27} + 288 q^{28} + 352 q^{31} - 432 q^{33} - 144 q^{36} + 288 q^{37} - 432 q^{42} - 1368 q^{43} + 336 q^{46} + 192 q^{48} - 1008 q^{51} + 1488 q^{57} + 1440 q^{58} + 1736 q^{61} + 648 q^{63} + 1728 q^{66} - 72 q^{67} - 576 q^{72} + 1440 q^{73} - 1984 q^{76} + 2268 q^{81} + 288 q^{82} - 2160 q^{87} - 1152 q^{88} - 1056 q^{93} + 384 q^{96} + 864 q^{97}+O(q^{100}) $ 4 * q - 12 * q^3 - 24 * q^6 + 72 * q^7 + 48 * q^12 - 64 * q^16 + 144 * q^18 - 432 * q^21 - 288 * q^22 - 108 * q^27 + 288 * q^28 + 352 * q^31 - 432 * q^33 - 144 * q^36 + 288 * q^37 - 432 * q^42 - 1368 * q^43 + 336 * q^46 + 192 * q^48 - 1008 * q^51 + 1488 * q^57 + 1440 * q^58 + 1736 * q^61 + 648 * q^63 + 1728 * q^66 - 72 * q^67 - 576 * q^72 + 1440 * q^73 - 1984 * q^76 + 2268 * q^81 + 288 * q^82 - 2160 * q^87 - 1152 * q^88 - 1056 * q^93 + 384 * q^96 + 864 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.41421	+	1.41421i	0.500000	+	0.500000i
$2$	1.41421	+	1.41421i	0.500000	+	0.500000i
$3$	−5.12132	−	0.878680i	−0.985599	−	0.169102i
$3$	−5.12132	−	0.878680i	−0.985599	−	0.169102i
$4$			4.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	−6.00000	−	8.48528i	−0.408248	−	0.577350i
$7$	18.0000	−	18.0000i	0.971909	−	0.971909i	−0.0277074	−	0.999616i	$-0.508821\pi$
$7$	18.0000	−	18.0000i	0.971909	−	0.971909i	0.999616	+	0.0277074i	$0.00882068\pi$
$8$	−5.65685	+	5.65685i	−0.250000	+	0.250000i
$9$	25.4558	+	9.00000i	0.942809	+	0.333333i
$10$		0			0
$11$			50.9117i			1.39550i	0.716343	+	0.697748i	$0.245814\pi$
$11$			50.9117i			1.39550i	−0.716343	+	0.697748i	$0.754186\pi$
$12$	3.51472	−	20.4853i	0.0845510	−	0.492799i
$13$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$13$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$14$	50.9117			0.971909
$15$		0			0
$16$	−16.0000			−0.250000
$17$	59.3970	+	59.3970i	0.847405	+	0.847405i	0.989809	−	0.142404i	$-0.0454832\pi$
$17$	59.3970	+	59.3970i	0.847405	+	0.847405i	−0.142404	+	0.989809i	$0.545483\pi$
$18$	23.2721	+	48.7279i	0.304738	+	0.638071i
$19$			124.000i			1.49724i	0.663000	+	0.748620i	$0.269283\pi$
$19$			124.000i			1.49724i	−0.663000	+	0.748620i	$0.730717\pi$
$20$		0			0
$21$	−108.000	+	76.3675i	−1.12226	+	0.793560i
$22$	−72.0000	+	72.0000i	−0.697748	+	0.697748i
$23$	29.6985	−	29.6985i	0.269242	−	0.269242i	−0.559553	−	0.828795i	$-0.689027\pi$
$23$	29.6985	−	29.6985i	0.269242	−	0.269242i	0.828795	+	0.559553i	$0.189027\pi$
$24$	33.9411	−	24.0000i	0.288675	−	0.204124i
$25$		0			0
$26$		0			0
$27$	−122.459	−	68.4594i	−0.872864	−	0.487964i
$28$	72.0000	+	72.0000i	0.485954	+	0.485954i
$29$	254.558			1.63001			0.815005	−	0.579453i	$-0.196734\pi$
$29$	254.558			1.63001			0.815005	+	0.579453i	$0.196734\pi$
$30$		0			0
$31$	88.0000			0.509847			0.254924	−	0.966961i	$-0.417950\pi$
$31$	88.0000			0.509847			0.254924	+	0.966961i	$0.417950\pi$
$32$	−22.6274	−	22.6274i	−0.125000	−	0.125000i
$33$	44.7351	−	260.735i	0.235981	−	1.37540i
$34$			168.000i			0.847405i
$35$		0			0
$36$	−36.0000	+	101.823i	−0.166667	+	0.471405i
$37$	72.0000	−	72.0000i	0.319912	−	0.319912i	−0.528822	−	0.848733i	$-0.677366\pi$
$37$	72.0000	−	72.0000i	0.319912	−	0.319912i	0.848733	+	0.528822i	$0.177366\pi$
$38$	−175.362	+	175.362i	−0.748620	+	0.748620i
$39$		0			0
$40$		0			0
$41$		−	50.9117i		−	0.193929i	−0.995288	−	0.0969643i	$-0.969087\pi$
$41$		−	50.9117i		−	0.193929i	0.995288	−	0.0969643i	$-0.0309133\pi$
$42$	−260.735	−	44.7351i	−0.957912	−	0.164352i
$43$	−342.000	−	342.000i	−1.21290	−	1.21290i	−0.970070	−	0.242826i	$-0.921926\pi$
$43$	−342.000	−	342.000i	−1.21290	−	1.21290i	−0.242826	−	0.970070i	$-0.578074\pi$
$44$	−203.647			−0.697748
$45$		0			0
$46$	84.0000			0.269242
$47$	318.198	+	318.198i	0.987531	+	0.987531i	0.999923	−	0.0123922i	$-0.00394467\pi$
$47$	318.198	+	318.198i	0.987531	+	0.987531i	−0.0123922	+	0.999923i	$0.503945\pi$
$48$	81.9411	+	14.0589i	0.246400	+	0.0422755i
$49$		−	305.000i		−	0.889213i
$50$		0			0
$51$	−252.000	−	356.382i	−0.691903	−	0.978499i
$52$		0			0
$53$	−220.617	+	220.617i	−0.571776	+	0.571776i	−0.932624	−	0.360849i	$-0.882487\pi$
$53$	−220.617	+	220.617i	−0.571776	+	0.571776i	0.360849	+	0.932624i	$0.382487\pi$
$54$	−76.3675	−	270.000i	−0.192450	−	0.680414i
$55$		0			0
$56$			203.647i			0.485954i
$57$	108.956	−	635.044i	0.253186	−	1.47568i
$58$	360.000	+	360.000i	0.815005	+	0.815005i
$59$	−865.499			−1.90980			−0.954901	−	0.296924i	$-0.904039\pi$
$59$	−865.499			−1.90980			−0.954901	+	0.296924i	$0.904039\pi$
$60$		0			0
$61$	434.000			0.910951			0.455475	−	0.890248i	$-0.349469\pi$
$61$	434.000			0.910951			0.455475	+	0.890248i	$0.349469\pi$
$62$	124.451	+	124.451i	0.254924	+	0.254924i
$63$	620.205	−	296.205i	1.24029	−	0.592355i
$64$		−	64.0000i		−	0.125000i
$65$		0			0
$66$	432.000	−	305.470i	0.805690	−	0.569709i
$67$	−18.0000	+	18.0000i	−0.0328216	+	0.0328216i	−0.723327	−	0.690506i	$-0.757388\pi$
$67$	−18.0000	+	18.0000i	−0.0328216	+	0.0328216i	0.690506	+	0.723327i	$0.257388\pi$
$68$	−237.588	+	237.588i	−0.423702	+	0.423702i
$69$	−178.191	+	126.000i	−0.310894	+	0.219835i
$70$		0			0
$71$		−	509.117i		−	0.851001i	−0.904958	−	0.425500i	$-0.860098\pi$
$71$		−	509.117i		−	0.851001i	0.904958	−	0.425500i	$-0.139902\pi$
$72$	−194.912	+	93.0883i	−0.319036	+	0.152369i
$73$	360.000	+	360.000i	0.577189	+	0.577189i	0.934128	−	0.356939i	$-0.116179\pi$
$73$	360.000	+	360.000i	0.577189	+	0.577189i	−0.356939	+	0.934128i	$0.616179\pi$
$74$	203.647			0.319912
$75$		0			0
$76$	−496.000			−0.748620
$77$	916.410	+	916.410i	1.35629	+	1.35629i
$78$		0			0
$79$		−	1024.00i		−	1.45834i	−0.684332	−	0.729171i	$-0.739906\pi$
$79$		−	1024.00i		−	1.45834i	0.684332	−	0.729171i	$-0.260094\pi$
$80$		0			0
$81$	567.000	+	458.205i	0.777778	+	0.628539i
$82$	72.0000	−	72.0000i	0.0969643	−	0.0969643i
$83$	−173.948	+	173.948i	−0.230040	+	0.230040i	−0.812709	−	0.582669i	$-0.802008\pi$
$83$	−173.948	+	173.948i	−0.230040	+	0.230040i	0.582669	+	0.812709i	$0.302008\pi$
$84$	−305.470	−	432.000i	−0.396780	−	0.561132i
$85$		0			0
$86$		−	967.322i		−	1.21290i
$87$	−1303.68	−	223.675i	−1.60654	−	0.275638i
$88$	−288.000	−	288.000i	−0.348874	−	0.348874i
$89$	−101.823			−0.121273			−0.0606363	−	0.998160i	$-0.519313\pi$
$89$	−101.823			−0.121273			−0.0606363	+	0.998160i	$0.519313\pi$
$90$		0			0
$91$		0			0
$92$	118.794	+	118.794i	0.134621	+	0.134621i
$93$	−450.676	−	77.3238i	−0.502505	−	0.0862162i
$94$			900.000i			0.987531i
$95$		0			0
$96$	96.0000	+	135.765i	0.102062	+	0.144338i
$97$	216.000	−	216.000i	0.226098	−	0.226098i	−0.584963	−	0.811060i	$-0.698891\pi$
$97$	216.000	−	216.000i	0.226098	−	0.226098i	0.811060	+	0.584963i	$0.198891\pi$
$98$	431.335	−	431.335i	0.444606	−	0.444606i
$99$	−458.205	+	1296.00i	−0.465165	+	1.31569i
$100$		0			0
$101$			661.852i			0.652047i	0.945362	+	0.326023i	$0.105709\pi$
$101$			661.852i			0.652047i	−0.945362	+	0.326023i	$0.894291\pi$
$102$	147.618	−	860.382i	0.143298	−	0.835201i
$103$	−522.000	−	522.000i	−0.499361	−	0.499361i	0.411878	−	0.911239i	$-0.364873\pi$
$103$	−522.000	−	522.000i	−0.499361	−	0.499361i	−0.911239	+	0.411878i	$0.864873\pi$
$104$		0			0
$105$		0			0
$106$	−624.000			−0.571776
$107$	−903.682	−	903.682i	−0.816470	−	0.816470i	0.169125	−	0.985595i	$-0.445906\pi$
$107$	−903.682	−	903.682i	−0.816470	−	0.816470i	−0.985595	+	0.169125i	$0.945906\pi$
$108$	273.838	−	489.838i	0.243982	−	0.436432i
$109$		−	610.000i		−	0.536031i	−0.963415	−	0.268016i	$-0.913632\pi$
$109$		−	610.000i		−	0.536031i	0.963415	−	0.268016i	$-0.0863679\pi$
$110$		0			0
$111$	−432.000	+	305.470i	−0.369402	+	0.261207i
$112$	−288.000	+	288.000i	−0.242977	+	0.242977i
$113$	−330.926	+	330.926i	−0.275495	+	0.275495i	−0.831307	−	0.555813i	$-0.812407\pi$
$113$	−330.926	+	330.926i	−0.275495	+	0.275495i	0.555813	+	0.831307i	$0.312407\pi$
$114$	1052.17	−	744.000i	0.864432	−	0.611245i
$115$		0			0
$116$			1018.23i			0.815005i
$117$		0			0
$118$	−1224.00	−	1224.00i	−0.954901	−	0.954901i
$119$	2138.29			1.64720
$120$		0			0
$121$	−1261.00			−0.947408
$122$	613.769	+	613.769i	0.455475	+	0.455475i
$123$	−44.7351	+	260.735i	−0.0327937	+	0.191136i
$124$			352.000i			0.254924i
$125$		0			0
$126$	1296.00	+	458.205i	0.916324	+	0.323970i
$127$	−1314.00	+	1314.00i	−0.918100	+	0.918100i	−0.996891	−	0.0787915i	$-0.974894\pi$
$127$	−1314.00	+	1314.00i	−0.918100	+	0.918100i	0.0787915	+	0.996891i	$0.474894\pi$
$128$	90.5097	−	90.5097i	0.0625000	−	0.0625000i
$129$	1450.98	+	2052.00i	0.990325	+	1.40053i
$130$		0			0
$131$			1170.97i			0.780977i	0.920608	+	0.390489i	$0.127694\pi$
$131$			1170.97i			0.780977i	−0.920608	+	0.390489i	$0.872306\pi$
$132$	1042.94	+	178.940i	0.687699	+	0.117991i
$133$	2232.00	+	2232.00i	1.45518	+	1.45518i
$134$	−50.9117			−0.0328216
$135$		0			0
$136$	−672.000			−0.423702
$137$	161.220	+	161.220i	0.100540	+	0.100540i	0.755588	−	0.655048i	$-0.227351\pi$
$137$	161.220	+	161.220i	0.100540	+	0.100540i	−0.655048	+	0.755588i	$0.727351\pi$
$138$	−430.191	−	73.8091i	−0.265364	−	0.0455293i
$139$			988.000i			0.602885i	0.953484	+	0.301443i	$0.0974682\pi$
$139$			988.000i			0.602885i	−0.953484	+	0.301443i	$0.902532\pi$
$140$		0			0
$141$	−1350.00	−	1909.19i	−0.806316	−	1.14030i
$142$	720.000	−	720.000i	0.425500	−	0.425500i
$143$		0			0
$144$	−407.294	−	144.000i	−0.235702	−	0.0833333i
$145$		0			0
$146$			1018.23i			0.577189i
$147$	−267.997	+	1562.00i	−0.150368	+	0.876407i
$148$	288.000	+	288.000i	0.159956	+	0.159956i
$149$	305.470			0.167954			0.0839768	−	0.996468i	$-0.473238\pi$
$149$	305.470			0.167954			0.0839768	+	0.996468i	$0.473238\pi$
$150$		0			0
$151$	1816.00			0.978702			0.489351	−	0.872087i	$-0.337234\pi$
$151$	1816.00			0.978702			0.489351	+	0.872087i	$0.337234\pi$
$152$	−701.450	−	701.450i	−0.374310	−	0.374310i
$153$	977.427	+	2046.57i	0.516473	+	1.08141i
$154$			2592.00i			1.35629i
$155$		0			0
$156$		0			0
$157$	1800.00	−	1800.00i	0.915004	−	0.915004i	−0.0816565	−	0.996661i	$-0.526021\pi$
$157$	1800.00	−	1800.00i	0.915004	−	0.915004i	0.996661	+	0.0816565i	$0.0260210\pi$
$158$	1448.15	−	1448.15i	0.729171	−	0.729171i
$159$	1323.70	−	936.000i	0.660230	−	0.466853i
$160$		0			0
$161$		−	1069.15i		−	0.523357i
$162$	153.859	+	1449.86i	0.0746192	+	0.703159i
$163$	198.000	+	198.000i	0.0951445	+	0.0951445i	0.753077	−	0.657932i	$-0.228569\pi$
$163$	198.000	+	198.000i	0.0951445	+	0.0951445i	−0.657932	+	0.753077i	$0.728569\pi$
$164$	203.647			0.0969643
$165$		0			0
$166$	−492.000			−0.230040
$167$	−1828.58	−	1828.58i	−0.847303	−	0.847303i	0.142493	−	0.989796i	$-0.454488\pi$
$167$	−1828.58	−	1828.58i	−0.847303	−	0.847303i	−0.989796	+	0.142493i	$0.954488\pi$
$168$	178.940	−	1042.94i	0.0821758	−	0.478956i
$169$		−	2197.00i		−	1.00000i
$170$		0			0
$171$	−1116.00	+	3156.52i	−0.499080	+	1.41161i
$172$	1368.00	−	1368.00i	0.606448	−	0.606448i
$173$	−1340.67	+	1340.67i	−0.589188	+	0.589188i	−0.937412	−	0.348223i	$-0.886785\pi$
$173$	−1340.67	+	1340.67i	−0.589188	+	0.589188i	0.348223	+	0.937412i	$0.386785\pi$
$174$	−1527.35	−	2160.00i	−0.665449	−	0.941087i
$175$		0			0
$176$		−	814.587i		−	0.348874i
$177$	4432.50	+	760.496i	1.88230	+	0.322951i
$178$	−144.000	−	144.000i	−0.0606363	−	0.0606363i
$179$	−356.382			−0.148811			−0.0744057	−	0.997228i	$-0.523706\pi$
$179$	−356.382			−0.148811			−0.0744057	+	0.997228i	$0.523706\pi$
$180$		0			0
$181$	718.000			0.294854			0.147427	−	0.989073i	$-0.452901\pi$
$181$	718.000			0.294854			0.147427	+	0.989073i	$0.452901\pi$
$182$		0			0
$183$	−2222.65	−	381.347i	−0.897832	−	0.154044i
$184$			336.000i			0.134621i
$185$		0			0
$186$	−528.000	−	746.705i	−0.208144	−	0.294360i
$187$	−3024.00	+	3024.00i	−1.18255	+	1.18255i
$188$	−1272.79	+	1272.79i	−0.493765	+	0.493765i
$189$	−3436.54	+	972.000i	−1.32260	+	0.374088i
$190$		0			0
$191$		−	1934.64i		−	0.732911i	−0.930436	−	0.366455i	$-0.880571\pi$
$191$		−	1934.64i		−	0.732911i	0.930436	−	0.366455i	$-0.119429\pi$
$192$	−56.2355	+	327.765i	−0.0211377	+	0.123200i
$193$	−2520.00	−	2520.00i	−0.939863	−	0.939863i	0.0584285	−	0.998292i	$-0.481391\pi$
$193$	−2520.00	−	2520.00i	−0.939863	−	0.939863i	−0.998292	+	0.0584285i	$0.981391\pi$
$194$	610.940			0.226098
$195$		0			0
$196$	1220.00			0.444606
$197$	−2172.23	−	2172.23i	−0.785610	−	0.785610i	0.195161	−	0.980771i	$-0.437477\pi$
$197$	−2172.23	−	2172.23i	−0.785610	−	0.785610i	−0.980771	+	0.195161i	$0.937477\pi$
$198$	−2480.82	+	1184.82i	−0.890426	+	0.425260i
$199$		−	1024.00i		−	0.364771i	−0.983227	−	0.182386i	$-0.941618\pi$
$199$		−	1024.00i		−	0.364771i	0.983227	−	0.182386i	$-0.0583819\pi$
$200$		0			0
$201$	108.000	−	76.3675i	0.0378992	−	0.0267988i
$202$	−936.000	+	936.000i	−0.326023	+	0.326023i
$203$	4582.05	−	4582.05i	1.58422	−	1.58422i
$204$	1425.53	−	1008.00i	0.489249	−	0.345952i
$205$		0			0
$206$		−	1476.44i		−	0.499361i
$207$	1023.29	−	488.714i	0.343591	−	0.164096i
$208$		0			0
$209$	−6313.05			−2.08939
$210$		0			0
$211$	4988.00			1.62743			0.813716	−	0.581263i	$-0.197441\pi$
$211$	4988.00			1.62743			0.813716	+	0.581263i	$0.197441\pi$
$212$	−882.469	−	882.469i	−0.285888	−	0.285888i
$213$	−447.351	+	2607.35i	−0.143906	+	0.838745i
$214$		−	2556.00i		−	0.816470i
$215$		0			0
$216$	1080.00	−	305.470i	0.340207	−	0.0962250i
$217$	1584.00	−	1584.00i	0.495525	−	0.495525i
$218$	862.670	−	862.670i	0.268016	−	0.268016i
$219$	−1527.35	−	2160.00i	−0.471273	−	0.666481i
$220$		0			0
$221$		0			0
$222$	−1042.94	−	178.940i	−0.315304	−	0.0540977i
$223$	−882.000	−	882.000i	−0.264857	−	0.264857i	0.562167	−	0.827024i	$-0.309968\pi$
$223$	−882.000	−	882.000i	−0.264857	−	0.264857i	−0.827024	+	0.562167i	$0.809968\pi$
$224$	−814.587			−0.242977
$225$		0			0
$226$	−936.000			−0.275495
$227$	−2337.70	−	2337.70i	−0.683517	−	0.683517i	0.277274	−	0.960791i	$-0.410569\pi$
$227$	−2337.70	−	2337.70i	−0.683517	−	0.683517i	−0.960791	+	0.277274i	$0.910569\pi$
$228$	2540.17	+	435.825i	0.737839	+	0.126593i
$229$			574.000i			0.165638i	0.996565	+	0.0828188i	$0.0263923\pi$
$229$			574.000i			0.165638i	−0.996565	+	0.0828188i	$0.973608\pi$
$230$		0			0
$231$	−3888.00	−	5498.46i	−1.10741	−	1.56611i
$232$	−1440.00	+	1440.00i	−0.407503	+	0.407503i
$233$	1807.36	−	1807.36i	0.508173	−	0.508173i	−0.405792	−	0.913965i	$-0.633004\pi$
$233$	1807.36	−	1807.36i	0.508173	−	0.508173i	0.913965	+	0.405792i	$0.133004\pi$
$234$		0			0
$235$		0			0
$236$		−	3461.99i		−	0.954901i
$237$	−899.768	+	5244.23i	−0.246608	+	1.43734i
$238$	3024.00	+	3024.00i	0.823600	+	0.823600i
$239$	305.470			0.0826746			0.0413373	−	0.999145i	$-0.486838\pi$
$239$	305.470			0.0826746			0.0413373	+	0.999145i	$0.486838\pi$
$240$		0			0
$241$	1514.00			0.404669			0.202335	−	0.979316i	$-0.435147\pi$
$241$	1514.00			0.404669			0.202335	+	0.979316i	$0.435147\pi$
$242$	−1783.32	−	1783.32i	−0.473704	−	0.473704i
$243$	−2501.17	−	2844.83i	−0.660289	−	0.751011i
$244$			1736.00i			0.455475i
$245$		0			0
$246$	−432.000	+	305.470i	−0.111965	+	0.0791710i
$247$		0			0
$248$	−497.803	+	497.803i	−0.127462	+	0.127462i
$249$	1043.69	−	738.000i	0.265627	−	0.187827i
$250$		0			0
$251$			4123.85i			1.03703i	0.855068	+	0.518516i	$0.173515\pi$
$251$			4123.85i			1.03703i	−0.855068	+	0.518516i	$0.826485\pi$
$252$	1184.82	+	2480.82i	0.296177	+	0.620147i
$253$	1512.00	+	1512.00i	0.375726	+	0.375726i
$254$	−3716.55			−0.918100
$255$		0			0
$256$	256.000			0.0625000
$257$	4845.10	+	4845.10i	1.17599	+	1.17599i	0.980758	+	0.195230i	$0.0625453\pi$
$257$	4845.10	+	4845.10i	1.17599	+	1.17599i	0.195230	+	0.980758i	$0.437455\pi$
$258$	−849.966	+	4953.97i	−0.205103	+	1.19543i
$259$		−	2592.00i		−	0.621850i
$260$		0			0
$261$	6480.00	+	2291.03i	1.53679	+	0.543337i
$262$	−1656.00	+	1656.00i	−0.390489	+	0.390489i
$263$	38.1838	−	38.1838i	0.00895252	−	0.00895252i	−0.702616	−	0.711569i	$-0.747985\pi$
$263$	38.1838	−	38.1838i	0.00895252	−	0.00895252i	0.711569	+	0.702616i	$0.247985\pi$
$264$	1221.88	+	1728.00i	0.284854	+	0.402845i
$265$		0			0
$266$			6313.05i			1.45518i
$267$	521.470	+	89.4701i	0.119526	+	0.0205074i
$268$	−72.0000	−	72.0000i	−0.0164108	−	0.0164108i
$269$	5396.64			1.22319			0.611596	−	0.791170i	$-0.290528\pi$
$269$	5396.64			1.22319			0.611596	+	0.791170i	$0.290528\pi$
$270$		0			0
$271$	−5200.00			−1.16560			−0.582800	−	0.812616i	$-0.698043\pi$
$271$	−5200.00			−1.16560			−0.582800	+	0.812616i	$0.698043\pi$
$272$	−950.352	−	950.352i	−0.211851	−	0.211851i
$273$		0			0
$274$			456.000i			0.100540i
$275$		0			0
$276$	−504.000	−	712.764i	−0.109918	−	0.155447i
$277$	5688.00	−	5688.00i	1.23379	−	1.23379i	0.271288	−	0.962498i	$-0.412550\pi$
$277$	5688.00	−	5688.00i	1.23379	−	1.23379i	0.962498	−	0.271288i	$-0.0874496\pi$
$278$	−1397.24	+	1397.24i	−0.301443	+	0.301443i
$279$	2240.11	+	792.000i	0.480689	+	0.169949i
$280$		0			0
$281$		−	2596.50i		−	0.551224i	−0.961269	−	0.275612i	$-0.911119\pi$
$281$		−	2596.50i		−	0.551224i	0.961269	−	0.275612i	$-0.0888805\pi$
$282$	790.812	−	4609.19i	0.166993	−	0.973309i
$283$	−990.000	−	990.000i	−0.207948	−	0.207948i	0.595447	−	0.803395i	$-0.296975\pi$
$283$	−990.000	−	990.000i	−0.207948	−	0.207948i	−0.803395	+	0.595447i	$0.796975\pi$
$284$	2036.47			0.425500
$285$		0			0
$286$		0			0
$287$	−916.410	−	916.410i	−0.188481	−	0.188481i
$288$	−372.353	−	779.647i	−0.0761845	−	0.159518i
$289$			2143.00i			0.436190i
$290$		0			0
$291$	−1296.00	+	916.410i	−0.261075	+	0.184608i
$292$	−1440.00	+	1440.00i	−0.288595	+	0.288595i
$293$	2121.32	−	2121.32i	0.422965	−	0.422965i	−0.463258	−	0.886223i	$-0.653320\pi$
$293$	2121.32	−	2121.32i	0.422965	−	0.422965i	0.886223	+	0.463258i	$0.153320\pi$
$294$	−2588.01	+	1830.00i	−0.513387	+	0.363020i
$295$		0			0
$296$			814.587i			0.159956i
$297$	3485.38	−	6234.62i	0.680951	−	1.21808i
$298$	432.000	+	432.000i	0.0839768	+	0.0839768i
$299$		0			0
$300$		0			0
$301$	−12312.0			−2.35765
$302$	2568.21	+	2568.21i	0.489351	+	0.489351i
$303$	581.556	−	3389.56i	0.110262	−	0.642656i
$304$		−	1984.00i		−	0.374310i
$305$		0			0
$306$	−1512.00	+	4276.58i	−0.282468	+	0.798941i
$307$	1026.00	−	1026.00i	0.190739	−	0.190739i	−0.605276	−	0.796015i	$-0.706937\pi$
$307$	1026.00	−	1026.00i	0.190739	−	0.190739i	0.796015	+	0.605276i	$0.206937\pi$
$308$	−3665.64	+	3665.64i	−0.678147	+	0.678147i
$309$	2214.66	+	3132.00i	0.407727	+	0.576612i
$310$		0			0
$311$		−	4378.41i		−	0.798317i	−0.916882	−	0.399158i	$-0.869302\pi$
$311$		−	4378.41i		−	0.798317i	0.916882	−	0.399158i	$-0.130698\pi$
$312$		0			0
$313$	−4608.00	−	4608.00i	−0.832139	−	0.832139i	0.155670	−	0.987809i	$-0.450246\pi$
$313$	−4608.00	−	4608.00i	−0.832139	−	0.832139i	−0.987809	+	0.155670i	$0.950246\pi$
$314$	5091.17			0.915004
$315$		0			0
$316$	4096.00			0.729171
$317$	−746.705	−	746.705i	−0.132300	−	0.132300i	0.637856	−	0.770156i	$-0.279822\pi$
$317$	−746.705	−	746.705i	−0.132300	−	0.132300i	−0.770156	+	0.637856i	$0.779822\pi$
$318$	3195.70	+	548.296i	0.563541	+	0.0966884i
$319$			12960.0i			2.27467i
$320$		0			0
$321$	3834.00	+	5422.09i	0.666645	+	0.942778i
$322$	1512.00	−	1512.00i	0.261678	−	0.261678i
$323$	−7365.22	+	7365.22i	−1.26877	+	1.26877i
$324$	−1832.82	+	2268.00i	−0.314270	+	0.388889i
$325$		0			0
$326$			560.029i			0.0951445i
$327$	−535.995	+	3124.01i	−0.0906439	+	0.528312i
$328$	288.000	+	288.000i	0.0484821	+	0.0484821i
$329$	11455.1			1.91958
$330$		0			0
$331$	5852.00			0.971767			0.485884	−	0.874023i	$-0.338498\pi$
$331$	5852.00			0.971767			0.485884	+	0.874023i	$0.338498\pi$
$332$	−695.793	−	695.793i	−0.115020	−	0.115020i
$333$	2480.82	−	1184.82i	0.408253	−	0.194978i
$334$		−	5172.00i		−	0.847303i
$335$		0			0
$336$	1728.00	−	1221.88i	0.280566	−	0.198390i
$337$	−4608.00	+	4608.00i	−0.744848	+	0.744848i	−0.973507	−	0.228659i	$-0.926566\pi$
$337$	−4608.00	+	4608.00i	−0.744848	+	0.744848i	0.228659	+	0.973507i	$0.426566\pi$
$338$	3107.03	−	3107.03i	0.500000	−	0.500000i
$339$	1985.56	−	1404.00i	0.318114	−	0.224940i
$340$		0			0
$341$			4480.23i			0.711490i
$342$	−6042.26	+	2885.74i	−0.955345	+	0.456266i
$343$	684.000	+	684.000i	0.107675	+	0.107675i
$344$	3869.29			0.606448
$345$		0			0
$346$	−3792.00			−0.589188
$347$	6122.13	+	6122.13i	0.947127	+	0.947127i	0.998671	−	0.0515434i	$-0.0164141\pi$
$347$	6122.13	+	6122.13i	0.947127	+	0.947127i	−0.0515434	+	0.998671i	$0.516414\pi$
$348$	894.701	−	5214.70i	0.137819	−	0.803268i
$349$		−	8102.00i		−	1.24267i	−0.783547	−	0.621333i	$-0.786592\pi$
$349$		−	8102.00i		−	1.24267i	0.783547	−	0.621333i	$-0.213408\pi$
$350$		0			0
$351$		0			0
$352$	1152.00	−	1152.00i	0.174437	−	0.174437i
$353$	−1552.81	+	1552.81i	−0.234129	+	0.234129i	−0.814414	−	0.580285i	$-0.802941\pi$
$353$	−1552.81	+	1552.81i	−0.234129	+	0.234129i	0.580285	+	0.814414i	$0.302941\pi$
$354$	5192.99	+	7344.00i	0.779674	+	1.10262i
$355$		0			0
$356$		−	407.294i		−	0.0606363i
$357$	−10950.9	−	1878.87i	−1.62348	−	0.278545i
$358$	−504.000	−	504.000i	−0.0744057	−	0.0744057i
$359$	−7534.93			−1.10774			−0.553870	−	0.832603i	$-0.686849\pi$
$359$	−7534.93			−1.10774			−0.553870	+	0.832603i	$0.686849\pi$
$360$		0			0
$361$	−8517.00			−1.24173
$362$	1015.41	+	1015.41i	0.147427	+	0.147427i
$363$	6457.98	+	1108.02i	0.933764	+	0.160209i
$364$		0			0
$365$		0			0
$366$	−2604.00	−	3682.61i	−0.371894	−	0.525938i
$367$	−2898.00	+	2898.00i	−0.412192	+	0.412192i	−0.882501	−	0.470310i	$-0.844142\pi$
$367$	−2898.00	+	2898.00i	−0.412192	+	0.412192i	0.470310	+	0.882501i	$0.344142\pi$
$368$	−475.176	+	475.176i	−0.0673105	+	0.0673105i
$369$	458.205	−	1296.00i	0.0646428	−	0.182838i
$370$		0			0
$371$			7942.22i			1.11143i
$372$	309.295	−	1802.70i	0.0431081	−	0.251252i
$373$	7992.00	+	7992.00i	1.10941	+	1.10941i	0.993228	+	0.116183i	$0.0370657\pi$
$373$	7992.00	+	7992.00i	1.10941	+	1.10941i	0.116183	+	0.993228i	$0.462934\pi$
$374$	−8553.16			−1.18255
$375$		0			0
$376$	−3600.00			−0.493765
$377$		0			0
$378$	−6234.62	−	3485.38i	−0.848344	−	0.474256i
$379$			7036.00i			0.953602i	0.879011	+	0.476801i	$0.158204\pi$
$379$			7036.00i			0.953602i	−0.879011	+	0.476801i	$0.841796\pi$
$380$		0			0
$381$	7884.00	−	5574.83i	1.06013	−	0.749625i
$382$	2736.00	−	2736.00i	0.366455	−	0.366455i
$383$	6334.26	−	6334.26i	0.845080	−	0.845080i	−0.144434	−	0.989514i	$-0.546136\pi$
$383$	6334.26	−	6334.26i	0.845080	−	0.845080i	0.989514	+	0.144434i	$0.0461362\pi$
$384$	−543.058	+	384.000i	−0.0721688	+	0.0510310i
$385$		0			0
$386$		−	7127.64i		−	0.939863i
$387$	−5627.90	−	11783.9i	−0.739230	−	1.54783i
$388$	864.000	+	864.000i	0.113049	+	0.113049i
$389$	−3971.11			−0.517592			−0.258796	−	0.965932i	$-0.583326\pi$
$389$	−3971.11			−0.517592			−0.258796	+	0.965932i	$0.583326\pi$
$390$		0			0
$391$	3528.00			0.456314
$392$	1725.34	+	1725.34i	0.222303	+	0.222303i
$393$	1028.91	−	5996.91i	0.132065	−	0.769730i
$394$		−	6144.00i		−	0.785610i
$395$		0			0
$396$	−5184.00	−	1832.82i	−0.657843	−	0.232583i
$397$	−9216.00	+	9216.00i	−1.16508	+	1.16508i	−0.181735	+	0.983348i	$0.558171\pi$
$397$	−9216.00	+	9216.00i	−1.16508	+	1.16508i	−0.983348	+	0.181735i	$0.941829\pi$
$398$	1448.15	−	1448.15i	0.182386	−	0.182386i
$399$	−9469.57	−	13392.0i	−1.18815	−	1.68030i
$400$		0			0
$401$			4887.52i			0.608656i	0.952567	+	0.304328i	$0.0984319\pi$
$401$			4887.52i			0.608656i	−0.952567	+	0.304328i	$0.901568\pi$
$402$	260.735	+	44.7351i	0.0323490	+	0.00555020i
$403$		0			0
$404$	−2647.41			−0.326023
$405$		0			0
$406$	12960.0			1.58422
$407$	3665.64	+	3665.64i	0.446435	+	0.446435i
$408$	3441.53	+	590.473i	0.417600	+	0.0716489i
$409$		−	2450.00i		−	0.296197i	−0.988973	−	0.148099i	$-0.952685\pi$
$409$		−	2450.00i		−	0.296197i	0.988973	−	0.148099i	$-0.0473153\pi$
$410$		0			0
$411$	−684.000	−	967.322i	−0.0820906	−	0.116094i
$412$	2088.00	−	2088.00i	0.249681	−	0.249681i
$413$	−15579.0	+	15579.0i	−1.85615	+	1.85615i
$414$	2138.29	+	756.000i	0.253844	+	0.0897473i
$415$		0			0
$416$		0			0
$417$	868.136	−	5059.86i	0.101949	−	0.594203i
$418$	−8928.00	−	8928.00i	−1.04470	−	1.04470i
$419$	−8400.43			−0.979446			−0.489723	−	0.871878i	$-0.662902\pi$
$419$	−8400.43			−0.979446			−0.489723	+	0.871878i	$0.662902\pi$
$420$		0			0
$421$	3994.00			0.462365			0.231182	−	0.972910i	$-0.425741\pi$
$421$	3994.00			0.462365			0.231182	+	0.972910i	$0.425741\pi$
$422$	7054.10	+	7054.10i	0.813716	+	0.813716i
$423$	5236.22	+	10963.8i	0.601876	+	1.26023i
$424$		−	2496.00i		−	0.285888i
$425$		0			0
$426$	−4320.00	+	3054.70i	−0.491326	+	0.347420i
$427$	7812.00	−	7812.00i	0.885361	−	0.885361i
$428$	3614.73	−	3614.73i	0.408235	−	0.408235i
$429$		0			0
$430$		0			0
$431$		−	13644.3i		−	1.52488i	−0.647057	−	0.762441i	$-0.724001\pi$
$431$		−	13644.3i		−	1.52488i	0.647057	−	0.762441i	$-0.275999\pi$
$432$	1959.35	+	1095.35i	0.218216	+	0.121991i
$433$	−6408.00	−	6408.00i	−0.711198	−	0.711198i	0.255588	−	0.966786i	$-0.417731\pi$
$433$	−6408.00	−	6408.00i	−0.711198	−	0.711198i	−0.966786	+	0.255588i	$0.917731\pi$
$434$	4480.23			0.495525
$435$		0			0
$436$	2440.00			0.268016
$437$	3682.61	+	3682.61i	0.403120	+	0.403120i
$438$	894.701	−	5214.70i	0.0976038	−	0.568877i
$439$			5024.00i			0.546201i	0.961985	+	0.273101i	$0.0880492\pi$
$439$			5024.00i			0.546201i	−0.961985	+	0.273101i	$0.911951\pi$
$440$		0			0
$441$	2745.00	−	7764.03i	0.296404	−	0.838358i
$442$		0			0
$443$	−7819.19	+	7819.19i	−0.838602	+	0.838602i	−0.988675	−	0.150073i	$-0.952049\pi$
$443$	−7819.19	+	7819.19i	−0.838602	+	0.838602i	0.150073	+	0.988675i	$0.452049\pi$
$444$	−1221.88	−	1728.00i	−0.130603	−	0.184701i
$445$		0			0
$446$		−	2494.67i		−	0.264857i
$447$	−1564.41	−	268.410i	−0.165535	−	0.0284013i
$448$	−1152.00	−	1152.00i	−0.121489	−	0.121489i
$449$	−9418.66			−0.989965			−0.494982	−	0.868903i	$-0.664825\pi$
$449$	−9418.66			−0.989965			−0.494982	+	0.868903i	$0.664825\pi$
$450$		0			0
$451$	2592.00			0.270626
$452$	−1323.70	−	1323.70i	−0.137747	−	0.137747i
$453$	−9300.32	−	1595.68i	−0.964607	−	0.165500i
$454$		−	6612.00i		−	0.683517i
$455$		0			0
$456$	2976.00	+	4208.70i	0.305623	+	0.432216i
$457$	720.000	−	720.000i	0.0736984	−	0.0736984i	−0.669297	−	0.742995i	$-0.733405\pi$
$457$	720.000	−	720.000i	0.0736984	−	0.0736984i	0.742995	+	0.669297i	$0.233405\pi$
$458$	−811.759	+	811.759i	−0.0828188	+	0.0828188i
$459$	−3207.44	−	11340.0i	−0.326166	−	1.15317i
$460$		0			0
$461$		−	10436.9i		−	1.05444i	−0.849730	−	0.527218i	$-0.823235\pi$
$461$		−	10436.9i		−	1.05444i	0.849730	−	0.527218i	$-0.176765\pi$
$462$	2277.54	−	13274.5i	0.229352	−	1.33676i
$463$	7290.00	+	7290.00i	0.731739	+	0.731739i	0.970964	−	0.239225i	$-0.0768935\pi$
$463$	7290.00	+	7290.00i	0.731739	+	0.731739i	−0.239225	+	0.970964i	$0.576893\pi$
$464$	−4072.94			−0.407503
$465$		0			0
$466$	5112.00			0.508173
$467$	4789.94	+	4789.94i	0.474630	+	0.474630i	0.903409	−	0.428780i	$-0.141056\pi$
$467$	4789.94	+	4789.94i	0.474630	+	0.474630i	−0.428780	+	0.903409i	$0.641056\pi$
$468$		0			0
$469$			648.000i			0.0637993i
$470$		0			0
$471$	−10800.0	+	7636.75i	−1.05656	+	0.747098i
$472$	4896.00	−	4896.00i	0.477451	−	0.477451i
$473$	17411.8	−	17411.8i	1.69259	−	1.69259i
$474$	−8688.93	+	6144.00i	−0.841974	+	0.595366i
$475$		0			0
$476$			8553.16i			0.823600i
$477$	−7601.56	+	3630.44i	−0.729667	+	0.348483i
$478$	432.000	+	432.000i	0.0413373	+	0.0413373i
$479$	18226.4			1.73859			0.869295	−	0.494293i	$-0.164573\pi$
$479$	18226.4			1.73859			0.869295	+	0.494293i	$0.164573\pi$
$480$		0			0
$481$		0			0
$482$	2141.12	+	2141.12i	0.202335	+	0.202335i
$483$	−939.436	+	5475.44i	−0.0885007	+	0.515820i
$484$		−	5044.00i		−	0.473704i
$485$		0			0
$486$	486.000	−	7560.39i	0.0453609	−	0.705650i
$487$	12258.0	−	12258.0i	1.14058	−	1.14058i	0.152237	−	0.988344i	$-0.451352\pi$
$487$	12258.0	−	12258.0i	1.14058	−	1.14058i	0.988344	−	0.152237i	$-0.0486477\pi$
$488$	−2455.07	+	2455.07i	−0.227738	+	0.227738i
$489$	−840.043	−	1188.00i	−0.0776852	−	0.109863i
$490$		0			0
$491$		−	14713.5i		−	1.35236i	−0.736735	−	0.676181i	$-0.763634\pi$
$491$		−	14713.5i		−	1.35236i	0.736735	−	0.676181i	$-0.236366\pi$
$492$	−1042.94	−	178.940i	−0.0955678	−	0.0163968i
$493$	15120.0	+	15120.0i	1.38128	+	1.38128i
$494$		0			0
$495$		0			0
$496$	−1408.00			−0.127462
$497$	−9164.10	−	9164.10i	−0.827095	−	0.827095i
$498$	2519.69	+	432.310i	0.226727	+	0.0389002i
$499$			20.0000i			0.00179423i	1.00000		0.000897117i	$0.000285561\pi$
$499$			20.0000i			0.00179423i	−1.00000		0.000897117i	$0.999714\pi$
$500$		0			0
$501$	7758.00	+	10971.5i	0.691820	+	0.978381i
$502$	−5832.00	+	5832.00i	−0.518516	+	0.518516i
$503$	−12596.4	+	12596.4i	−1.11659	+	1.11659i	−0.124354	+	0.992238i	$0.539686\pi$
$503$	−12596.4	+	12596.4i	−1.11659	+	1.11659i	−0.992238	+	0.124354i	$0.960314\pi$
$504$	−1832.82	+	5184.00i	−0.161985	+	0.458162i
$505$		0			0
$506$			4276.58i			0.375726i
$507$	−1930.46	+	11251.5i	−0.169102	+	0.985599i
$508$	−5256.00	−	5256.00i	−0.459050	−	0.459050i
$509$	−13898.9			−1.21033			−0.605165	−	0.796100i	$-0.706893\pi$
$509$	−13898.9			−1.21033			−0.605165	+	0.796100i	$0.706893\pi$
$510$		0			0
$511$	12960.0			1.12195
$512$	362.039	+	362.039i	0.0312500	+	0.0312500i
$513$	8488.97	−	15185.0i	0.730599	−	1.30689i
$514$			13704.0i			1.17599i
$515$		0			0
$516$	−8208.00	+	5803.93i	−0.700266	+	0.495163i
$517$	−16200.0	+	16200.0i	−1.37810	+	1.37810i
$518$	3665.64	−	3665.64i	0.310925	−	0.310925i
$519$	8044.05	−	5688.00i	0.680336	−	0.481070i
$520$		0			0
$521$			10080.5i			0.847669i	0.905740	+	0.423834i	$0.139316\pi$
$521$			10080.5i			0.847669i	−0.905740	+	0.423834i	$0.860684\pi$
$522$	5924.10	+	12404.1i	0.496726	+	1.04006i
$523$	−450.000	−	450.000i	−0.0376236	−	0.0376236i	0.688045	−	0.725668i	$-0.258469\pi$
$523$	−450.000	−	450.000i	−0.0376236	−	0.0376236i	−0.725668	+	0.688045i	$0.758469\pi$
$524$	−4683.88			−0.390489
$525$		0			0
$526$	108.000			0.00895252
$527$	5226.93	+	5226.93i	0.432047	+	0.432047i
$528$	−715.761	+	4171.76i	−0.0589953	+	0.343850i
$529$			10403.0i			0.855018i
$530$		0			0
$531$	−22032.0	−	7789.49i	−1.80058	−	0.636601i
$532$	−8928.00	+	8928.00i	−0.727590	+	0.727590i
$533$		0			0
$534$	610.940	+	864.000i	0.0495093	+	0.0700167i
$535$		0			0
$536$		−	203.647i		−	0.0164108i
$537$	1825.15	+	313.145i	0.146668	+	0.0251643i
$538$	7632.00	+	7632.00i	0.611596	+	0.611596i
$539$	15528.1			1.24089
$540$		0			0
$541$	−21382.0			−1.69923			−0.849616	−	0.527403i	$-0.823166\pi$
$541$	−21382.0			−1.69923			−0.849616	+	0.527403i	$0.823166\pi$
$542$	−7353.91	−	7353.91i	−0.582800	−	0.582800i
$543$	−3677.11	−	630.892i	−0.290607	−	0.0498603i
$544$		−	2688.00i		−	0.211851i
$545$		0			0
$546$		0			0
$547$	−1818.00	+	1818.00i	−0.142106	+	0.142106i	−0.774581	−	0.632475i	$-0.782039\pi$
$547$	−1818.00	+	1818.00i	−0.142106	+	0.142106i	0.632475	+	0.774581i	$0.282039\pi$
$548$	−644.881	+	644.881i	−0.0502700	+	0.0502700i
$549$	11047.8	+	3906.00i	0.858853	+	0.303650i
$550$		0			0
$551$			31565.2i			2.44052i
$552$	295.236	−	1720.76i	0.0227647	−	0.132682i
$553$	−18432.0	−	18432.0i	−1.41737	−	1.41737i
$554$	16088.1			1.23379
$555$		0			0
$556$	−3952.00			−0.301443
$557$	−16546.3	−	16546.3i	−1.25869	−	1.25869i	−0.951720	−	0.306968i	$-0.900685\pi$
$557$	−16546.3	−	16546.3i	−1.25869	−	1.25869i	−0.306968	−	0.951720i	$-0.599315\pi$
$558$	2047.94	+	4288.06i	0.155370	+	0.325319i
$559$		0			0
$560$		0			0
$561$	18144.0	−	12829.7i	1.36549	−	0.965548i
$562$	3672.00	−	3672.00i	0.275612	−	0.275612i
$563$	14700.7	−	14700.7i	1.10047	−	1.10047i	0.106113	−	0.994354i	$-0.466160\pi$
$563$	14700.7	−	14700.7i	1.10047	−	1.10047i	0.994354	−	0.106113i	$-0.0338404\pi$
$564$	7636.75	−	5400.00i	0.570151	−	0.403158i
$565$		0			0
$566$		−	2800.14i		−	0.207948i
$567$	18453.7	−	1958.31i	1.36681	−	0.145046i
$568$	2880.00	+	2880.00i	0.212750	+	0.212750i
$569$	11964.2			0.881489			0.440745	−	0.897633i	$-0.354714\pi$
$569$	11964.2			0.881489			0.440745	+	0.897633i	$0.354714\pi$
$570$		0			0
$571$	3260.00			0.238926			0.119463	−	0.992839i	$-0.461883\pi$
$571$	3260.00			0.238926			0.119463	+	0.992839i	$0.461883\pi$
$572$		0			0
$573$	−1699.93	+	9907.93i	−0.123937	+	0.722356i
$574$		−	2592.00i		−	0.188481i
$575$		0			0
$576$	576.000	−	1629.17i	0.0416667	−	0.117851i
$577$	4176.00	−	4176.00i	0.301298	−	0.301298i	−0.540223	−	0.841522i	$-0.681660\pi$
$577$	4176.00	−	4176.00i	0.301298	−	0.301298i	0.841522	+	0.540223i	$0.181660\pi$
$578$	−3030.66	+	3030.66i	−0.218095	+	0.218095i
$579$	10691.5	+	15120.0i	0.767395	+	1.08526i
$580$		0			0
$581$			6262.14i			0.447155i
$582$	−3128.82	−	536.821i	−0.222842	−	0.0382336i
$583$	−11232.0	−	11232.0i	−0.797911	−	0.797911i
$584$	−4072.94			−0.288595
$585$		0			0
$586$	6000.00			0.422965
$587$	−7411.89	−	7411.89i	−0.521161	−	0.521161i	0.396761	−	0.917922i	$-0.370134\pi$
$587$	−7411.89	−	7411.89i	−0.521161	−	0.521161i	−0.917922	+	0.396761i	$0.870134\pi$
$588$	−6248.01	−	1071.99i	−0.438203	−	0.0751838i
$589$			10912.0i			0.763364i
$590$		0			0
$591$	9216.00	+	13033.4i	0.641448	+	0.907144i
$592$	−1152.00	+	1152.00i	−0.0799779	+	0.0799779i
$593$	5795.45	−	5795.45i	0.401333	−	0.401333i	−0.477370	−	0.878703i	$-0.658410\pi$
$593$	5795.45	−	5795.45i	0.401333	−	0.401333i	0.878703	+	0.477370i	$0.158410\pi$
$594$	13746.2	−	3888.00i	0.949514	−	0.268563i
$595$		0			0
$596$			1221.88i			0.0839768i
$597$	−899.768	+	5244.23i	−0.0616835	+	0.359518i
$598$		0			0
$599$	−4480.23			−0.305605			−0.152802	−	0.988257i	$-0.548830\pi$
$599$	−4480.23			−0.305605			−0.152802	+	0.988257i	$0.548830\pi$
$600$		0			0
$601$	−21710.0			−1.47349			−0.736747	−	0.676169i	$-0.763639\pi$
$601$	−21710.0			−1.47349			−0.736747	+	0.676169i	$0.763639\pi$
$602$	−17411.8	−	17411.8i	−1.17882	−	1.17882i
$603$	−620.205	+	296.205i	−0.0418851	+	0.0200040i
$604$			7264.00i			0.489351i
$605$		0			0
$606$	5616.00	−	3971.11i	0.376459	−	0.266197i
$607$	7146.00	−	7146.00i	0.477837	−	0.477837i	−0.426602	−	0.904439i	$-0.640290\pi$
$607$	7146.00	−	7146.00i	0.477837	−	0.477837i	0.904439	+	0.426602i	$0.140290\pi$
$608$	2805.80	−	2805.80i	0.187155	−	0.187155i
$609$	−27492.3	+	19440.0i	−1.82930	+	1.29351i
$610$		0			0
$611$		0			0
$612$	−8186.29	+	3909.71i	−0.540705	+	0.258236i
$613$	−9216.00	−	9216.00i	−0.607228	−	0.607228i	0.334993	−	0.942221i	$-0.391266\pi$
$613$	−9216.00	−	9216.00i	−0.607228	−	0.607228i	−0.942221	+	0.334993i	$0.891266\pi$
$614$	2901.97			0.190739
$615$		0			0
$616$	−10368.0			−0.678147
$617$	10649.0	+	10649.0i	0.694836	+	0.694836i	0.963292	−	0.268456i	$-0.0865134\pi$
$617$	10649.0	+	10649.0i	0.694836	+	0.694836i	−0.268456	+	0.963292i	$0.586513\pi$
$618$	−1297.32	+	7561.32i	−0.0844429	+	0.492170i
$619$			13844.0i			0.898929i	0.893298	+	0.449465i	$0.148385\pi$
$619$			13844.0i			0.898929i	−0.893298	+	0.449465i	$0.851615\pi$
$620$		0			0
$621$	−5670.00	+	1603.72i	−0.366392	+	0.103631i
$622$	6192.00	−	6192.00i	0.399158	−	0.399158i
$623$	−1832.82	+	1832.82i	−0.117866	+	0.117866i
$624$		0			0
$625$		0			0
$626$		−	13033.4i		−	0.832139i
$627$	32331.1	+	5547.15i	2.05930	+	0.353320i
$628$	7200.00	+	7200.00i	0.457502	+	0.457502i
$629$	8553.16			0.542189
$630$		0			0
$631$	11216.0			0.707610			0.353805	−	0.935319i	$-0.384888\pi$
$631$	11216.0			0.707610			0.353805	+	0.935319i	$0.384888\pi$
$632$	5792.62	+	5792.62i	0.364585	+	0.364585i
$633$	−25545.1	−	4382.85i	−1.60399	−	0.275202i
$634$		−	2112.00i		−	0.132300i
$635$		0			0
$636$	3744.00	+	5294.82i	0.233427	+	0.330115i
$637$		0			0
$638$	−18328.2	+	18328.2i	−1.13734	+	1.13734i
$639$	4582.05	−	12960.0i	0.283667	−	0.802331i
$640$		0			0
$641$		−	17768.2i		−	1.09485i	−0.836854	−	0.547427i	$-0.815608\pi$
$641$		−	17768.2i		−	1.09485i	0.836854	−	0.547427i	$-0.184392\pi$
$642$	−2245.91	+	13090.1i	−0.138067	+	0.804712i
$643$	17982.0	+	17982.0i	1.10286	+	1.10286i	0.994064	+	0.108799i	$0.0347005\pi$
$643$	17982.0	+	17982.0i	1.10286	+	1.10286i	0.108799	+	0.994064i	$0.465299\pi$
$644$	4276.58			0.261678
$645$		0			0
$646$	−20832.0			−1.26877
$647$	−8650.74	−	8650.74i	−0.525650	−	0.525650i	0.393622	−	0.919272i	$-0.371222\pi$
$647$	−8650.74	−	8650.74i	−0.525650	−	0.525650i	−0.919272	+	0.393622i	$0.871222\pi$
$648$	−5799.44	+	615.436i	−0.351579	+	0.0373096i
$649$		−	44064.0i		−	2.66512i
$650$		0			0
$651$	−9504.00	+	6720.34i	−0.572183	+	0.404594i
$652$	−792.000	+	792.000i	−0.0475723	+	0.0475723i
$653$	17089.4	−	17089.4i	1.02413	−	1.02413i	0.0244305	−	0.999702i	$-0.492223\pi$
$653$	17089.4	−	17089.4i	1.02413	−	1.02413i	0.999702	−	0.0244305i	$-0.00777724\pi$
$654$	−5176.02	+	3660.00i	−0.309478	+	0.218834i
$655$		0			0
$656$			814.587i			0.0484821i
$657$	5924.10	+	12404.1i	0.351783	+	0.736576i
$658$	16200.0	+	16200.0i	0.959790	+	0.959790i
$659$	−3818.38			−0.225710			−0.112855	−	0.993611i	$-0.536000\pi$
$659$	−3818.38			−0.225710			−0.112855	+	0.993611i	$0.536000\pi$
$660$		0			0
$661$	6550.00			0.385424			0.192712	−	0.981255i	$-0.438272\pi$
$661$	6550.00			0.385424			0.192712	+	0.981255i	$0.438272\pi$
$662$	8275.98	+	8275.98i	0.485884	+	0.485884i
$663$		0			0
$664$		−	1968.00i		−	0.115020i
$665$		0			0
$666$	5184.00	+	1832.82i	0.301615	+	0.106637i
$667$	7560.00	−	7560.00i	0.438867	−	0.438867i
$668$	7314.31	−	7314.31i	0.423652	−	0.423652i
$669$	3742.01	+	5292.00i	0.216255	+	0.305830i
$670$		0			0
$671$			22095.7i			1.27123i
$672$	4171.76	+	715.761i	0.239478	+	0.0410879i
$673$	−13176.0	−	13176.0i	−0.754677	−	0.754677i	0.220671	−	0.975348i	$-0.429175\pi$
$673$	−13176.0	−	13176.0i	−0.754677	−	0.754677i	−0.975348	+	0.220671i	$0.929175\pi$
$674$	−13033.4			−0.744848
$675$		0			0
$676$	8788.00			0.500000
$677$	−13186.1	−	13186.1i	−0.748573	−	0.748573i	0.225638	−	0.974211i	$-0.427553\pi$
$677$	−13186.1	−	13186.1i	−0.748573	−	0.748573i	−0.974211	+	0.225638i	$0.927553\pi$
$678$	4793.56	+	822.444i	0.271527	+	0.0465867i
$679$		−	7776.00i		−	0.439493i
$680$		0			0
$681$	9918.00	+	14026.2i	0.558089	+	0.789257i
$682$	−6336.00	+	6336.00i	−0.355745	+	0.355745i
$683$	7963.44	−	7963.44i	0.446138	−	0.446138i	−0.447930	−	0.894069i	$-0.647839\pi$
$683$	7963.44	−	7963.44i	0.446138	−	0.446138i	0.894069	+	0.447930i	$0.147839\pi$
$684$	−12626.1	−	4464.00i	−0.705805	−	0.249540i
$685$		0			0
$686$			1934.64i			0.107675i
$687$	504.362	−	2939.64i	0.0280096	−	0.163252i
$688$	5472.00	+	5472.00i	0.303224	+	0.303224i
$689$		0			0
$690$		0			0
$691$	14092.0			0.775810			0.387905	−	0.921699i	$-0.373199\pi$
$691$	14092.0			0.775810			0.387905	+	0.921699i	$0.373199\pi$
$692$	−5362.70	−	5362.70i	−0.294594	−	0.294594i
$693$	15080.3	+	31575.7i	0.826628	+	1.73082i
$694$			17316.0i			0.947127i
$695$		0			0
$696$	8640.00	−	6109.40i	0.470544	−	0.332725i
$697$	3024.00	−	3024.00i	0.164336	−	0.164336i
$698$	11458.0	−	11458.0i	0.621333	−	0.621333i
$699$	−10844.2	+	7668.00i	−0.586788	+	0.414922i
$700$		0			0
$701$		−	30343.4i		−	1.63488i	−0.576011	−	0.817442i	$-0.695392\pi$
$701$		−	30343.4i		−	1.63488i	0.576011	−	0.817442i	$-0.304608\pi$
$702$		0			0
$703$	8928.00	+	8928.00i	0.478984	+	0.478984i
$704$	3258.35			0.174437
$705$		0			0
$706$	−4392.00			−0.234129
$707$	11913.3	+	11913.3i	0.633730	+	0.633730i
$708$	−3041.98	+	17730.0i	−0.161476	+	0.941149i
$709$		−	21890.0i		−	1.15952i	−0.814789	−	0.579758i	$-0.803147\pi$
$709$		−	21890.0i		−	1.15952i	0.814789	−	0.579758i	$-0.196853\pi$
$710$		0			0
$711$	9216.00	−	26066.8i	0.486114	−	1.37494i
$712$	576.000	−	576.000i	0.0303181	−	0.0303181i
$713$	2613.47	−	2613.47i	0.137272	−	0.137272i
$714$	−12829.7	−	18144.0i	−0.672467	−	0.951011i
$715$		0			0
$716$		−	1425.53i		−	0.0744057i
$717$	−1564.41	−	268.410i	−0.0814839	−	0.0139804i
$718$	−10656.0	−	10656.0i	−0.553870	−	0.553870i
$719$	−27288.7			−1.41543			−0.707716	−	0.706497i	$-0.750274\pi$
$719$	−27288.7			−1.41543			−0.707716	+	0.706497i	$0.750274\pi$
$720$		0			0
$721$	−18792.0			−0.970667
$722$	−12044.9	−	12044.9i	−0.620863	−	0.620863i
$723$	−7753.68	−	1330.32i	−0.398842	−	0.0684304i
$724$			2872.00i			0.147427i
$725$		0			0
$726$	7566.00	+	10699.9i	0.386778	+	0.546986i
$727$	−7506.00	+	7506.00i	−0.382919	+	0.382919i	−0.872153	−	0.489234i	$-0.837277\pi$
$727$	−7506.00	+	7506.00i	−0.382919	+	0.382919i	0.489234	+	0.872153i	$0.337277\pi$
$728$		0			0
$729$	10309.6	+	16767.0i	0.523783	+	0.851852i
$730$		0			0
$731$		−	40627.5i		−	2.05563i
$732$	1525.39	−	8890.61i	0.0770218	−	0.448916i
$733$	792.000	+	792.000i	0.0399089	+	0.0399089i	0.726780	−	0.686871i	$-0.241016\pi$
$733$	792.000	+	792.000i	0.0399089	+	0.0399089i	−0.686871	+	0.726780i	$0.741016\pi$
$734$	−8196.78			−0.412192
$735$		0			0
$736$	−1344.00			−0.0673105
$737$	−916.410	−	916.410i	−0.0458025	−	0.0458025i
$738$	2480.82	−	1184.82i	0.123740	−	0.0590974i
$739$		−	22340.0i		−	1.11203i	−0.831172	−	0.556015i	$-0.812330\pi$
$739$		−	22340.0i		−	1.11203i	0.831172	−	0.556015i	$-0.187670\pi$
$740$		0			0
$741$		0			0
$742$	−11232.0	+	11232.0i	−0.555714	+	0.555714i
$743$	9202.29	−	9202.29i	0.454373	−	0.454373i	−0.442430	−	0.896803i	$-0.645883\pi$
$743$	9202.29	−	9202.29i	0.454373	−	0.454373i	0.896803	+	0.442430i	$0.145883\pi$
$744$	2986.82	−	2112.00i	0.147180	−	0.104072i
$745$		0			0
$746$			22604.8i			1.10941i
$747$	−5993.53	+	2862.47i	−0.293564	+	0.140204i
$748$	−12096.0	−	12096.0i	−0.591275	−	0.591275i
$749$	−32532.6			−1.58707
$750$		0			0
$751$	11320.0			0.550030			0.275015	−	0.961440i	$-0.411317\pi$
$751$	11320.0			0.550030			0.275015	+	0.961440i	$0.411317\pi$
$752$	−5091.17	−	5091.17i	−0.246883	−	0.246883i
$753$	3623.54	−	21119.5i	0.175364	−	1.02210i
$754$		0			0
$755$		0			0
$756$	−3888.00	−	13746.2i	−0.187044	−	0.661300i
$757$	−14760.0	+	14760.0i	−0.708668	+	0.708668i	−0.966255	−	0.257587i	$-0.917072\pi$
$757$	−14760.0	+	14760.0i	−0.708668	+	0.708668i	0.257587	+	0.966255i	$0.417072\pi$
$758$	−9950.41	+	9950.41i	−0.476801	+	0.476801i
$759$	−6414.87	−	9072.00i	−0.306779	−	0.433851i
$760$		0			0
$761$			6313.05i			0.300720i	0.988631	+	0.150360i	$0.0480433\pi$
$761$			6313.05i			0.300720i	−0.988631	+	0.150360i	$0.951957\pi$
$762$	19033.7	+	3265.66i	0.904878	+	0.155252i
$763$	−10980.0	−	10980.0i	−0.520973	−	0.520973i
$764$	7738.58			0.366455
$765$		0			0
$766$	17916.0			0.845080
$767$		0			0
$768$	−1311.06	−	224.942i	−0.0615999	−	0.0105689i
$769$		−	8782.00i		−	0.411817i	−0.978571	−	0.205908i	$-0.933985\pi$
$769$		−	8782.00i		−	0.411817i	0.978571	−	0.205908i	$-0.0660149\pi$
$770$		0			0
$771$	−20556.0	−	29070.6i	−0.960190	−	1.35791i
$772$	10080.0	−	10080.0i	0.469932	−	0.469932i
$773$	−24878.8	+	24878.8i	−1.15761	+	1.15761i	−0.172618	+	0.984989i	$0.555222\pi$
$773$	−24878.8	+	24878.8i	−1.15761	+	1.15761i	−0.984989	+	0.172618i	$0.944778\pi$
$774$	8705.90	−	24624.0i	0.404299	−	1.14353i
$775$		0			0
$776$			2443.76i			0.113049i
$777$	−2277.54	+	13274.5i	−0.105156	+	0.612894i
$778$	−5616.00	−	5616.00i	−0.258796	−	0.258796i
$779$	6313.05			0.290357
$780$		0			0
$781$	25920.0			1.18757
$782$	4989.35	+	4989.35i	0.228157	+	0.228157i
$783$	−31173.1	−	17426.9i	−1.42278	−	0.795386i
$784$			4880.00i			0.222303i
$785$		0			0
$786$	9936.00	−	7025.81i	0.450897	−	0.318833i
$787$	−1314.00	+	1314.00i	−0.0595159	+	0.0595159i	−0.736238	−	0.676722i	$-0.763400\pi$
$787$	−1314.00	+	1314.00i	−0.0595159	+	0.0595159i	0.676722	+	0.736238i	$0.263400\pi$
$788$	8688.93	−	8688.93i	0.392805	−	0.392805i
$789$	−229.103	+	162.000i	−0.0103375	+	0.00730970i
$790$		0			0
$791$			11913.3i			0.535511i
$792$	−4739.28	−	9923.28i	−0.212630	−	0.445213i
$793$		0			0
$794$	−26066.8			−1.16508
$795$		0			0
$796$	4096.00			0.182386
$797$	−15205.6	−	15205.6i	−0.675798	−	0.675798i	0.283249	−	0.959046i	$-0.408588\pi$
$797$	−15205.6	−	15205.6i	−0.675798	−	0.675798i	−0.959046	+	0.283249i	$0.908588\pi$
$798$	5547.15	−	32331.1i	0.246074	−	1.43422i
$799$			37800.0i			1.67368i
$800$		0			0
$801$	−2592.00	−	916.410i	−0.114337	−	0.0404242i
$802$	−6912.00	+	6912.00i	−0.304328	+	0.304328i
$803$	−18328.2	+	18328.2i	−0.805465	+	0.805465i
$804$	305.470	+	432.000i	0.0133994	+	0.0189496i
$805$		0			0
$806$		0			0
$807$	−27637.9	−	4741.92i	−1.20558	−	0.206844i
$808$	−3744.00	−	3744.00i	−0.163012	−	0.163012i
$809$	22706.6			0.986801			0.493400	−	0.869802i	$-0.335754\pi$
$809$	22706.6			0.986801			0.493400	+	0.869802i	$0.335754\pi$
$810$		0			0
$811$	−6644.00			−0.287672			−0.143836	−	0.989602i	$-0.545944\pi$
$811$	−6644.00			−0.287672			−0.143836	+	0.989602i	$0.545944\pi$
$812$	18328.2	+	18328.2i	0.792111	+	0.792111i
$813$	26630.9	+	4569.13i	1.14881	+	0.197105i
$814$			10368.0i			0.446435i
$815$		0			0
$816$	4032.00	+	5702.11i	0.172976	+	0.244625i
$817$	42408.0	−	42408.0i	1.81600	−	1.81600i
$818$	3464.82	−	3464.82i	0.148099	−	0.148099i
$819$		0			0
$820$		0			0
$821$			36452.8i			1.54959i	0.632215	+	0.774793i	$0.282146\pi$
$821$			36452.8i			1.54959i	−0.632215	+	0.774793i	$0.717854\pi$
$822$	400.678	−	2335.32i	0.0170015	−	0.0990921i
$823$	9450.00	+	9450.00i	0.400251	+	0.400251i	0.878321	−	0.478071i	$-0.158664\pi$
$823$	9450.00	+	9450.00i	0.400251	+	0.400251i	−0.478071	+	0.878321i	$0.658664\pi$
$824$	5905.76			0.249681
$825$		0			0
$826$	−44064.0			−1.85615
$827$	−24314.6	−	24314.6i	−1.02237	−	1.02237i	−0.999744	−	0.0226267i	$-0.992797\pi$
$827$	−24314.6	−	24314.6i	−1.02237	−	1.02237i	−0.0226267	−	0.999744i	$-0.507203\pi$
$828$	1954.85	+	4093.15i	0.0820482	+	0.171795i
$829$		−	12206.0i		−	0.511377i	−0.966759	−	0.255689i	$-0.917698\pi$
$829$		−	12206.0i		−	0.511377i	0.966759	−	0.255689i	$-0.0823022\pi$
$830$		0			0
$831$	−34128.0	+	24132.1i	−1.42465	+	1.00738i
$832$		0			0
$833$	18116.1	−	18116.1i	0.753523	−	0.753523i
$834$	8383.46	−	5928.00i	0.348076	−	0.246127i
$835$		0			0
$836$		−	25252.2i		−	1.04470i
$837$	−10776.4	−	6024.43i	−0.445027	−	0.248787i
$838$	−11880.0	−	11880.0i	−0.489723	−	0.489723i
$839$	−15069.9			−0.620106			−0.310053	−	0.950719i	$-0.600347\pi$
$839$	−15069.9			−0.620106			−0.310053	+	0.950719i	$0.600347\pi$
$840$		0			0
$841$	40411.0			1.65694
$842$	5648.37	+	5648.37i	0.231182	+	0.231182i
$843$	−2281.49	+	13297.5i	−0.0932131	+	0.543286i
$844$			19952.0i			0.813716i
$845$		0			0
$846$	−8100.00	+	22910.3i	−0.329177	+	0.931053i
$847$	−22698.0	+	22698.0i	−0.920794	+	0.920794i
$848$	3529.88	−	3529.88i	0.142944	−	0.142944i
$849$	4200.21	+	5940.00i	0.169789	+	0.240118i
$850$		0			0
$851$		−	4276.58i		−	0.172267i
$852$	−10429.4	−	1789.40i	−0.419373	−	0.0719530i
$853$	32544.0	+	32544.0i	1.30631	+	1.30631i	0.924056	+	0.382258i	$0.124853\pi$
$853$	32544.0	+	32544.0i	1.30631	+	1.30631i	0.382258	+	0.924056i	$0.375147\pi$
$854$	22095.7			0.885361
$855$		0			0
$856$	10224.0			0.408235
$857$	28264.5	+	28264.5i	1.12660	+	1.12660i	0.990726	+	0.135874i	$0.0433841\pi$
$857$	28264.5	+	28264.5i	1.12660	+	1.12660i	0.135874	+	0.990726i	$0.456616\pi$
$858$		0			0
$859$		−	40588.0i		−	1.61216i	−0.591807	−	0.806080i	$-0.701585\pi$
$859$		−	40588.0i		−	1.61216i	0.591807	−	0.806080i	$-0.298415\pi$
$860$		0			0
$861$	3888.00	+	5498.46i	0.153894	+	0.217639i
$862$	19296.0	−	19296.0i	0.762441	−	0.762441i
$863$	−14335.9	+	14335.9i	−0.565468	+	0.565468i	−0.930856	−	0.365387i	$-0.880937\pi$
$863$	−14335.9	+	14335.9i	−0.565468	+	0.565468i	0.365387	+	0.930856i	$0.380937\pi$
$864$	1221.88	+	4320.00i	0.0481125	+	0.170103i
$865$		0			0
$866$		−	18124.6i		−	0.711198i
$867$	1883.01	−	10975.0i	0.0737605	−	0.429908i
$868$	6336.00	+	6336.00i	0.247763	+	0.247763i
$869$	52133.6			2.03511
$870$		0			0
$871$		0			0
$872$	3450.68	+	3450.68i	0.134008	+	0.134008i
$873$	7442.46	−	3554.46i	0.288533	−	0.137801i
$874$			10416.0i			0.403120i
$875$		0			0
$876$	8640.00	−	6109.40i	0.333240	−	0.235637i
$877$	−18072.0	+	18072.0i	−0.695836	+	0.695836i	−0.963510	−	0.267674i	$-0.913745\pi$
$877$	−18072.0	+	18072.0i	−0.695836	+	0.695836i	0.267674	+	0.963510i	$0.413745\pi$
$878$	−7105.01	+	7105.01i	−0.273101	+	0.273101i
$879$	−12727.9	+	9000.00i	−0.488398	+	0.345350i
$880$		0			0
$881$			32125.3i			1.22852i	0.789103	+	0.614261i	$0.210546\pi$
$881$			32125.3i			1.22852i	−0.789103	+	0.614261i	$0.789454\pi$
$882$	14862.0	−	7097.98i	0.567381	−	0.270977i
$883$	9882.00	+	9882.00i	0.376620	+	0.376620i	0.869881	−	0.493261i	$-0.164195\pi$
$883$	9882.00	+	9882.00i	0.376620	+	0.376620i	−0.493261	+	0.869881i	$0.664195\pi$
$884$		0			0
$885$		0			0
$886$	−22116.0			−0.838602
$887$	35633.9	+	35633.9i	1.34890	+	1.34890i	0.886863	+	0.462033i	$0.152880\pi$
$887$	35633.9	+	35633.9i	1.34890	+	1.34890i	0.462033	+	0.886863i	$0.347120\pi$
$888$	715.761	−	4171.76i	0.0270488	−	0.157652i
$889$			47304.0i			1.78462i
$890$		0			0
$891$	−23328.0	+	28866.9i	−0.877124	+	1.08539i
$892$	3528.00	−	3528.00i	0.132428	−	0.132428i
$893$	−39456.6	+	39456.6i	−1.47857	+	1.47857i
$894$	−1832.82	−	2592.00i	−0.0685668	−	0.0969681i
$895$		0			0
$896$		−	3258.35i		−	0.121489i
$897$		0			0
$898$	−13320.0	−	13320.0i	−0.494982	−	0.494982i
$899$	22401.1			0.831057
$900$		0			0
$901$	−26208.0			−0.969051
$902$	3665.64	+	3665.64i	0.135313	+	0.135313i
$903$	63053.7	+	10818.3i	2.32369	+	0.398683i
$904$		−	3744.00i		−	0.137747i
$905$		0			0
$906$	−10896.0	−	15409.3i	−0.399553	−	0.565054i
$907$	−26946.0	+	26946.0i	−0.986469	+	0.986469i	−0.999910	−	0.0134408i	$-0.995722\pi$
$907$	−26946.0	+	26946.0i	−0.986469	+	0.986469i	0.0134408	+	0.999910i	$0.495722\pi$
$908$	9350.78	−	9350.78i	0.341758	−	0.341758i
$909$	−5956.67	+	16848.0i	−0.217349	+	0.614756i
$910$		0			0
$911$		−	31972.5i		−	1.16279i	−0.813623	−	0.581393i	$-0.802508\pi$
$911$		−	31972.5i		−	1.16279i	0.813623	−	0.581393i	$-0.197492\pi$
$912$	−1743.30	+	10160.7i	−0.0632965	+	0.368919i
$913$	−8856.00	−	8856.00i	−0.321020	−	0.321020i
$914$	2036.47			0.0736984
$915$		0			0
$916$	−2296.00			−0.0828188
$917$	21077.4	+	21077.4i	0.759039	+	0.759039i
$918$	11501.2	−	20573.2i	0.413503	−	0.739669i
$919$			37096.0i			1.33154i	0.746158	+	0.665769i	$0.231897\pi$
$919$			37096.0i			1.33154i	−0.746158	+	0.665769i	$0.768103\pi$
$920$		0			0
$921$	−6156.00	+	4352.95i	−0.220247	+	0.155738i
$922$	14760.0	−	14760.0i	0.527218	−	0.527218i
$923$		0			0
$924$	21993.8	−	15552.0i	0.783057	−	0.553705i
$925$		0			0
$926$			20619.2i			0.731739i
$927$	−8589.95	−	17986.0i	−0.304348	−	0.637256i
$928$	−5760.00	−	5760.00i	−0.203751	−	0.203751i
$929$	−5243.90			−0.185196			−0.0925979	−	0.995704i	$-0.529517\pi$
$929$	−5243.90			−0.185196			−0.0925979	+	0.995704i	$0.529517\pi$
$930$		0			0
$931$	37820.0			1.33136
$932$	7229.46	+	7229.46i	0.254087	+	0.254087i
$933$	−3847.22	+	22423.2i	−0.134997	+	0.786820i
$934$			13548.0i			0.474630i
$935$		0			0
$936$		0			0
$937$	10440.0	−	10440.0i	0.363991	−	0.363991i	−0.501289	−	0.865280i	$-0.667141\pi$
$937$	10440.0	−	10440.0i	0.363991	−	0.363991i	0.865280	+	0.501289i	$0.167141\pi$
$938$	−916.410	+	916.410i	−0.0318996	+	0.0318996i
$939$	19550.1	+	27648.0i	0.679439	+	0.960872i
$940$		0			0
$941$			6567.61i			0.227522i	0.993508	+	0.113761i	$0.0362898\pi$
$941$			6567.61i			0.227522i	−0.993508	+	0.113761i	$0.963710\pi$
$942$	−26073.5	−	4473.51i	−0.901827	−	0.154729i
$943$	−1512.00	−	1512.00i	−0.0522137	−	0.0522137i
$944$	13848.0			0.477451
$945$		0			0
$946$	49248.0			1.69259
$947$	−9066.52	−	9066.52i	−0.311111	−	0.311111i	0.534229	−	0.845340i	$-0.320602\pi$
$947$	−9066.52	−	9066.52i	−0.311111	−	0.311111i	−0.845340	+	0.534229i	$0.820602\pi$
$948$	−20976.9	−	3599.07i	−0.718670	−	0.123304i
$949$		0			0
$950$		0			0
$951$	3168.00	+	4480.23i	0.108023	+	0.152767i
$952$	−12096.0	+	12096.0i	−0.411800	+	0.411800i
$953$	−15604.4	+	15604.4i	−0.530406	+	0.530406i	−0.920693	−	0.390287i	$-0.872376\pi$
$953$	−15604.4	+	15604.4i	−0.530406	+	0.530406i	0.390287	+	0.920693i	$0.372376\pi$
$954$	−15884.4	−	5616.00i	−0.539075	−	0.190592i
$955$		0			0
$956$			1221.88i			0.0413373i
$957$	11387.7	−	66372.3i	0.384652	−	2.24191i
$958$	25776.0	+	25776.0i	0.869295	+	0.869295i
$959$	5803.93			0.195431
$960$		0			0
$961$	−22047.0			−0.740056
$962$		0			0
$963$	−14870.9	−	31137.1i	−0.497619	−	1.04193i
$964$			6056.00i			0.202335i
$965$		0			0
$966$	−9072.00	+	6414.87i	−0.302160	+	0.213660i
$967$	21798.0	−	21798.0i	0.724898	−	0.724898i	−0.244701	−	0.969599i	$-0.578690\pi$
$967$	21798.0	−	21798.0i	0.724898	−	0.724898i	0.969599	+	0.244701i	$0.0786897\pi$
$968$	7133.29	−	7133.29i	0.236852	−	0.236852i
$969$	44191.3	−	31248.0i	1.46505	−	1.03594i
$970$		0			0
$971$			16240.8i			0.536759i	0.963313	+	0.268380i	$0.0864881\pi$
$971$			16240.8i			0.536759i	−0.963313	+	0.268380i	$0.913512\pi$
$972$	11379.3	−	10004.7i	0.375506	−	0.330145i
$973$	17784.0	+	17784.0i	0.585950	+	0.585950i
$974$	34670.9			1.14058
$975$		0			0
$976$	−6944.00			−0.227738
$977$	22070.2	+	22070.2i	0.722711	+	0.722711i	0.969157	−	0.246446i	$-0.0792626\pi$
$977$	22070.2	+	22070.2i	0.722711	+	0.722711i	−0.246446	+	0.969157i	$0.579263\pi$
$978$	492.086	−	2868.09i	0.0160891	−	0.0937743i
$979$		−	5184.00i		−	0.169235i
$980$		0			0
$981$	5490.00	−	15528.1i	0.178677	−	0.505375i
$982$	20808.0	−	20808.0i	0.676181	−	0.676181i
$983$	25180.1	−	25180.1i	0.817009	−	0.817009i	−0.168665	−	0.985673i	$-0.553946\pi$
$983$	25180.1	−	25180.1i	0.817009	−	0.817009i	0.985673	+	0.168665i	$0.0539455\pi$
$984$	−1221.88	−	1728.00i	−0.0395855	−	0.0559823i
$985$		0			0
$986$			42765.8i			1.38128i
$987$	−58665.4	−	10065.4i	−1.89194	−	0.324605i
$988$		0			0
$989$	−20313.8			−0.653124
$990$		0			0
$991$	−39760.0			−1.27449			−0.637244	−	0.770662i	$-0.719926\pi$
$991$	−39760.0			−1.27449			−0.637244	+	0.770662i	$0.719926\pi$
$992$	−1991.21	−	1991.21i	−0.0637309	−	0.0637309i
$993$	−29970.0	−	5142.03i	−0.957773	−	0.164328i
$994$		−	25920.0i		−	0.827095i
$995$		0			0
$996$	2952.00	+	4174.76i	0.0939134	+	0.132814i
$997$	−18576.0	+	18576.0i	−0.590078	+	0.590078i	−0.937652	−	0.347574i	$-0.887005\pi$
$997$	−18576.0	+	18576.0i	−0.590078	+	0.590078i	0.347574	+	0.937652i	$0.387005\pi$
$998$	−28.2843	+	28.2843i	−0.000897117	+	0.000897117i
$999$	−13746.2	+	3888.00i	−0.435344	+	0.123134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.4.e.a.143.2	yes	4
3.2	odd	2	inner	150.4.e.a.143.1	yes	4
5.2	odd	4	inner	150.4.e.a.107.1	✓	4
5.3	odd	4		150.4.e.b.107.2	yes	4
5.4	even	2		150.4.e.b.143.1	yes	4
15.2	even	4	inner	150.4.e.a.107.2	yes	4
15.8	even	4		150.4.e.b.107.1	yes	4
15.14	odd	2		150.4.e.b.143.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.4.e.a.107.1	✓	4	5.2	odd	4	inner
150.4.e.a.107.2	yes	4	15.2	even	4	inner
150.4.e.a.143.1	yes	4	3.2	odd	2	inner
150.4.e.a.143.2	yes	4	1.1	even	1	trivial
150.4.e.b.107.1	yes	4	15.8	even	4
150.4.e.b.107.2	yes	4	5.3	odd	4
150.4.e.b.143.1	yes	4	5.4	even	2
150.4.e.b.143.2	yes	4	15.14	odd	2

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	150.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41421 + 1.41421i) q^{2} +(-5.12132 - 0.878680i) q^{3} +4.00000i q^{4} +(-6.00000 - 8.48528i) q^{6} +(18.0000 - 18.0000i) q^{7} +(-5.65685 + 5.65685i) q^{8} +(25.4558 + 9.00000i) q^{9} +O(q^{10})\)	\(q+(1.41421 + 1.41421i) q^{2} +(-5.12132 - 0.878680i) q^{3} +4.00000i q^{4} +(-6.00000 - 8.48528i) q^{6} +(18.0000 - 18.0000i) q^{7} +(-5.65685 + 5.65685i) q^{8} +(25.4558 + 9.00000i) q^{9} +50.9117i q^{11} +(3.51472 - 20.4853i) q^{12} +50.9117 q^{14} -16.0000 q^{16} +(59.3970 + 59.3970i) q^{17} +(23.2721 + 48.7279i) q^{18} +124.000i q^{19} +(-108.000 + 76.3675i) q^{21} +(-72.0000 + 72.0000i) q^{22} +(29.6985 - 29.6985i) q^{23} +(33.9411 - 24.0000i) q^{24} +(-122.459 - 68.4594i) q^{27} +(72.0000 + 72.0000i) q^{28} +254.558 q^{29} +88.0000 q^{31} +(-22.6274 - 22.6274i) q^{32} +(44.7351 - 260.735i) q^{33} +168.000i q^{34} +(-36.0000 + 101.823i) q^{36} +(72.0000 - 72.0000i) q^{37} +(-175.362 + 175.362i) q^{38} -50.9117i q^{41} +(-260.735 - 44.7351i) q^{42} +(-342.000 - 342.000i) q^{43} -203.647 q^{44} +84.0000 q^{46} +(318.198 + 318.198i) q^{47} +(81.9411 + 14.0589i) q^{48} -305.000i q^{49} +(-252.000 - 356.382i) q^{51} +(-220.617 + 220.617i) q^{53} +(-76.3675 - 270.000i) q^{54} +203.647i q^{56} +(108.956 - 635.044i) q^{57} +(360.000 + 360.000i) q^{58} -865.499 q^{59} +434.000 q^{61} +(124.451 + 124.451i) q^{62} +(620.205 - 296.205i) q^{63} -64.0000i q^{64} +(432.000 - 305.470i) q^{66} +(-18.0000 + 18.0000i) q^{67} +(-237.588 + 237.588i) q^{68} +(-178.191 + 126.000i) q^{69} -509.117i q^{71} +(-194.912 + 93.0883i) q^{72} +(360.000 + 360.000i) q^{73} +203.647 q^{74} -496.000 q^{76} +(916.410 + 916.410i) q^{77} -1024.00i q^{79} +(567.000 + 458.205i) q^{81} +(72.0000 - 72.0000i) q^{82} +(-173.948 + 173.948i) q^{83} +(-305.470 - 432.000i) q^{84} -967.322i q^{86} +(-1303.68 - 223.675i) q^{87} +(-288.000 - 288.000i) q^{88} -101.823 q^{89} +(118.794 + 118.794i) q^{92} +(-450.676 - 77.3238i) q^{93} +900.000i q^{94} +(96.0000 + 135.765i) q^{96} +(216.000 - 216.000i) q^{97} +(431.335 - 431.335i) q^{98} +(-458.205 + 1296.00i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 12 q^{3} - 24 q^{6} + 72 q^{7}+O(q^{10}) \) 4 * q - 12 * q^3 - 24 * q^6 + 72 * q^7	\( 4 q - 12 q^{3} - 24 q^{6} + 72 q^{7} + 48 q^{12} - 64 q^{16} + 144 q^{18} - 432 q^{21} - 288 q^{22} - 108 q^{27} + 288 q^{28} + 352 q^{31} - 432 q^{33} - 144 q^{36} + 288 q^{37} - 432 q^{42} - 1368 q^{43} + 336 q^{46} + 192 q^{48} - 1008 q^{51} + 1488 q^{57} + 1440 q^{58} + 1736 q^{61} + 648 q^{63} + 1728 q^{66} - 72 q^{67} - 576 q^{72} + 1440 q^{73} - 1984 q^{76} + 2268 q^{81} + 288 q^{82} - 2160 q^{87} - 1152 q^{88} - 1056 q^{93} + 384 q^{96} + 864 q^{97}+O(q^{100}) \) 4 * q - 12 * q^3 - 24 * q^6 + 72 * q^7 + 48 * q^12 - 64 * q^16 + 144 * q^18 - 432 * q^21 - 288 * q^22 - 108 * q^27 + 288 * q^28 + 352 * q^31 - 432 * q^33 - 144 * q^36 + 288 * q^37 - 432 * q^42 - 1368 * q^43 + 336 * q^46 + 192 * q^48 - 1008 * q^51 + 1488 * q^57 + 1440 * q^58 + 1736 * q^61 + 648 * q^63 + 1728 * q^66 - 72 * q^67 - 576 * q^72 + 1440 * q^73 - 1984 * q^76 + 2268 * q^81 + 288 * q^82 - 2160 * q^87 - 1152 * q^88 - 1056 * q^93 + 384 * q^96 + 864 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more