LMFDB - Embedded newform 150.3.b.b.149.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,3,Mod(149,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("150.149");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	150.b (of order $2$, degree $1$, 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:	$4.08720396540$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.40960000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{4} + 1 $ x^8 + 7*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.7
Root			$0.437016 - 0.437016i$ of defining polynomial
Character	$\chi$	$=$	150.149
Dual form			150.3.b.b.149.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +(1.52896 - 2.58114i) q^{3} +2.00000 q^{4} +(2.16228 - 3.65028i) q^{6} -7.48683i q^{7} +2.82843 q^{8} +(-4.32456 - 7.89292i) q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +(1.52896 - 2.58114i) q^{3} +2.00000 q^{4} +(2.16228 - 3.65028i) q^{6} -7.48683i q^{7} +2.82843 q^{8} +(-4.32456 - 7.89292i) q^{9} +8.48528i q^{11} +(3.05792 - 5.16228i) q^{12} +10.0000i q^{13} -10.5880i q^{14} +4.00000 q^{16} +30.3870 q^{17} +(-6.11584 - 11.1623i) q^{18} -26.9737 q^{19} +(-19.3246 - 11.4471i) q^{21} +12.0000i q^{22} +9.17377 q^{23} +(4.32456 - 7.30056i) q^{24} +14.1421i q^{26} +(-26.9848 - 0.905694i) q^{27} -14.9737i q^{28} +26.8328i q^{29} +8.00000 q^{31} +5.65685 q^{32} +(21.9017 + 12.9737i) q^{33} +42.9737 q^{34} +(-8.64911 - 15.7858i) q^{36} +15.9473i q^{37} -38.1465 q^{38} +(25.8114 + 15.2896i) q^{39} +47.3575i q^{41} +(-27.3290 - 16.1886i) q^{42} +14.4605i q^{43} +16.9706i q^{44} +12.9737 q^{46} -45.8688 q^{47} +(6.11584 - 10.3246i) q^{48} -7.05267 q^{49} +(46.4605 - 78.4330i) q^{51} +20.0000i q^{52} -30.3870 q^{53} +(-38.1623 - 1.28084i) q^{54} -21.1760i q^{56} +(-41.2417 + 69.6228i) q^{57} +37.9473i q^{58} +24.0789i q^{59} -53.9473 q^{61} +11.3137 q^{62} +(-59.0930 + 32.3772i) q^{63} +8.00000 q^{64} +(30.9737 + 18.3475i) q^{66} -110.460i q^{67} +60.7739 q^{68} +(14.0263 - 23.6788i) q^{69} +15.5936i q^{71} +(-12.2317 - 22.3246i) q^{72} -87.9473i q^{73} +22.5529i q^{74} -53.9473 q^{76} +63.5279 q^{77} +(36.5028 + 21.6228i) q^{78} +46.9737 q^{79} +(-43.5964 + 68.2668i) q^{81} +66.9737i q^{82} +26.1443 q^{83} +(-38.6491 - 22.8942i) q^{84} +20.4502i q^{86} +(69.2592 + 41.0263i) q^{87} +24.0000i q^{88} -60.7739i q^{89} +74.8683 q^{91} +18.3475 q^{92} +(12.2317 - 20.6491i) q^{93} -64.8683 q^{94} +(8.64911 - 14.6011i) q^{96} +36.0527i q^{97} -9.97398 q^{98} +(66.9737 - 36.6951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{4} - 8 q^{6} + 16 q^{9}+O(q^{10}) $ 8 * q + 16 * q^4 - 8 * q^6 + 16 * q^9	$ 8 q + 16 q^{4} - 8 q^{6} + 16 q^{9} + 32 q^{16} - 64 q^{19} - 104 q^{21} - 16 q^{24} + 64 q^{31} + 192 q^{34} + 32 q^{36} + 80 q^{39} - 48 q^{46} - 360 q^{49} + 144 q^{51} - 280 q^{54} - 128 q^{61} + 64 q^{64} + 96 q^{66} + 264 q^{69} - 128 q^{76} + 224 q^{79} + 56 q^{81} - 208 q^{84} - 160 q^{91} + 240 q^{94} - 32 q^{96} + 384 q^{99}+O(q^{100}) $ 8 * q + 16 * q^4 - 8 * q^6 + 16 * q^9 + 32 * q^16 - 64 * q^19 - 104 * q^21 - 16 * q^24 + 64 * q^31 + 192 * q^34 + 32 * q^36 + 80 * q^39 - 48 * q^46 - 360 * q^49 + 144 * q^51 - 280 * q^54 - 128 * q^61 + 64 * q^64 + 96 * q^66 + 264 * q^69 - 128 * q^76 + 224 * q^79 + 56 * q^81 - 208 * q^84 - 160 * q^91 + 240 * q^94 - 32 * q^96 + 384 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.41421			0.707107
$2$	1.41421			0.707107
$3$	1.52896	−	2.58114i	0.509654	−	0.860380i
$3$	1.52896	−	2.58114i	0.509654	−	0.860380i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	2.16228	−	3.65028i	0.360380	−	0.608380i
$7$		−	7.48683i		−	1.06955i	−0.844995	−	0.534774i	$-0.820397\pi$
$7$		−	7.48683i		−	1.06955i	0.844995	−	0.534774i	$-0.179603\pi$
$8$	2.82843			0.353553
$9$	−4.32456	−	7.89292i	−0.480506	−	0.876991i
$10$		0			0
$11$			8.48528i			0.771389i	0.922627	+	0.385695i	$0.126038\pi$
$11$			8.48528i			0.771389i	−0.922627	+	0.385695i	$0.873962\pi$
$12$	3.05792	−	5.16228i	0.254827	−	0.430190i
$13$			10.0000i			0.769231i	0.923077	+	0.384615i	$0.125666\pi$
$13$			10.0000i			0.769231i	−0.923077	+	0.384615i	$0.874334\pi$
$14$		−	10.5880i		−	0.756284i
$15$		0			0
$16$	4.00000			0.250000
$17$	30.3870			1.78747			0.893734	−	0.448596i	$-0.148076\pi$
$17$	30.3870			1.78747			0.893734	+	0.448596i	$0.148076\pi$
$18$	−6.11584	−	11.1623i	−0.339769	−	0.620127i
$19$	−26.9737			−1.41967			−0.709833	−	0.704370i	$-0.751230\pi$
$19$	−26.9737			−1.41967			−0.709833	+	0.704370i	$0.751230\pi$
$20$		0			0
$21$	−19.3246	−	11.4471i	−0.920217	−	0.545099i
$22$			12.0000i			0.545455i
$23$	9.17377			0.398859			0.199430	−	0.979912i	$-0.436091\pi$
$23$	9.17377			0.398859			0.199430	+	0.979912i	$0.436091\pi$
$24$	4.32456	−	7.30056i	0.180190	−	0.304190i
$25$		0			0
$26$			14.1421i			0.543928i
$27$	−26.9848	−	0.905694i	−0.999437	−	0.0335442i
$28$		−	14.9737i		−	0.534774i
$29$			26.8328i			0.925270i	0.886549	+	0.462635i	$0.153096\pi$
$29$			26.8328i			0.925270i	−0.886549	+	0.462635i	$0.846904\pi$
$30$		0			0
$31$	8.00000			0.258065			0.129032	−	0.991640i	$-0.458813\pi$
$31$	8.00000			0.258065			0.129032	+	0.991640i	$0.458813\pi$
$32$	5.65685			0.176777
$33$	21.9017	+	12.9737i	0.663688	+	0.393141i
$34$	42.9737			1.26393
$35$		0			0
$36$	−8.64911	−	15.7858i	−0.240253	−	0.438496i
$37$			15.9473i			0.431009i	0.976503	+	0.215504i	$0.0691396\pi$
$37$			15.9473i			0.431009i	−0.976503	+	0.215504i	$0.930860\pi$
$38$	−38.1465			−1.00386
$39$	25.8114	+	15.2896i	0.661830	+	0.392041i
$40$		0			0
$41$			47.3575i			1.15506i	0.816369	+	0.577531i	$0.195984\pi$
$41$			47.3575i			1.15506i	−0.816369	+	0.577531i	$0.804016\pi$
$42$	−27.3290	−	16.1886i	−0.650692	−	0.385443i
$43$			14.4605i			0.336291i	0.985762	+	0.168145i	$0.0537778\pi$
$43$			14.4605i			0.336291i	−0.985762	+	0.168145i	$0.946222\pi$
$44$			16.9706i			0.385695i
$45$		0			0
$46$	12.9737			0.282036
$47$	−45.8688			−0.975933			−0.487966	−	0.872862i	$-0.662261\pi$
$47$	−45.8688			−0.975933			−0.487966	+	0.872862i	$0.662261\pi$
$48$	6.11584	−	10.3246i	0.127413	−	0.215095i
$49$	−7.05267			−0.143932
$50$		0			0
$51$	46.4605	−	78.4330i	0.910990	−	1.53790i
$52$			20.0000i			0.384615i
$53$	−30.3870			−0.573339			−0.286670	−	0.958030i	$-0.592548\pi$
$53$	−30.3870			−0.573339			−0.286670	+	0.958030i	$0.592548\pi$
$54$	−38.1623	−	1.28084i	−0.706709	−	0.0237194i
$55$		0			0
$56$		−	21.1760i		−	0.378142i
$57$	−41.2417	+	69.6228i	−0.723538	+	1.22145i
$58$			37.9473i			0.654264i
$59$			24.0789i			0.408116i	0.978959	+	0.204058i	$0.0654132\pi$
$59$			24.0789i			0.408116i	−0.978959	+	0.204058i	$0.934587\pi$
$60$		0			0
$61$	−53.9473			−0.884382			−0.442191	−	0.896921i	$-0.645799\pi$
$61$	−53.9473			−0.884382			−0.442191	+	0.896921i	$0.645799\pi$
$62$	11.3137			0.182479
$63$	−59.0930	+	32.3772i	−0.937984	+	0.513924i
$64$	8.00000			0.125000
$65$		0			0
$66$	30.9737	+	18.3475i	0.469298	+	0.277993i
$67$		−	110.460i		−	1.64866i	−0.566107	−	0.824332i	$-0.691551\pi$
$67$		−	110.460i		−	1.64866i	0.566107	−	0.824332i	$-0.308449\pi$
$68$	60.7739			0.893734
$69$	14.0263	−	23.6788i	0.203280	−	0.343171i
$70$		0			0
$71$			15.5936i			0.219628i	0.993952	+	0.109814i	$0.0350255\pi$
$71$			15.5936i			0.219628i	−0.993952	+	0.109814i	$0.964974\pi$
$72$	−12.2317	−	22.3246i	−0.169885	−	0.310063i
$73$		−	87.9473i		−	1.20476i	−0.798210	−	0.602379i	$-0.794220\pi$
$73$		−	87.9473i		−	1.20476i	0.798210	−	0.602379i	$-0.205780\pi$
$74$			22.5529i			0.304769i
$75$		0			0
$76$	−53.9473			−0.709833
$77$	63.5279			0.825037
$78$	36.5028	+	21.6228i	0.467985	+	0.277215i
$79$	46.9737			0.594603			0.297302	−	0.954784i	$-0.403913\pi$
$79$	46.9737			0.594603			0.297302	+	0.954784i	$0.403913\pi$
$80$		0			0
$81$	−43.5964	+	68.2668i	−0.538228	+	0.842799i
$82$			66.9737i			0.816752i
$83$	26.1443			0.314992			0.157496	−	0.987520i	$-0.449658\pi$
$83$	26.1443			0.314992			0.157496	+	0.987520i	$0.449658\pi$
$84$	−38.6491	−	22.8942i	−0.460108	−	0.272549i
$85$		0			0
$86$			20.4502i			0.237793i
$87$	69.2592	+	41.0263i	0.796083	+	0.471567i
$88$			24.0000i			0.272727i
$89$		−	60.7739i		−	0.682853i	−0.939908	−	0.341427i	$-0.889090\pi$
$89$		−	60.7739i		−	0.682853i	0.939908	−	0.341427i	$-0.110910\pi$
$90$		0			0
$91$	74.8683			0.822729
$92$	18.3475			0.199430
$93$	12.2317	−	20.6491i	0.131524	−	0.222033i
$94$	−64.8683			−0.690089
$95$		0			0
$96$	8.64911	−	14.6011i	0.0900949	−	0.152095i
$97$			36.0527i			0.371677i	0.982580	+	0.185838i	$0.0595001\pi$
$97$			36.0527i			0.371677i	−0.982580	+	0.185838i	$0.940500\pi$
$98$	−9.97398			−0.101775
$99$	66.9737	−	36.6951i	0.676502	−	0.370657i
$100$		0			0
$101$		−	48.1577i		−	0.476809i	−0.971166	−	0.238405i	$-0.923376\pi$
$101$		−	48.1577i		−	0.476809i	0.971166	−	0.238405i	$-0.0766245\pi$
$102$	65.7051	−	110.921i	0.644167	−	1.08746i
$103$		−	140.408i		−	1.36318i	−0.731733	−	0.681591i	$-0.761288\pi$
$103$		−	140.408i		−	1.36318i	0.731733	−	0.681591i	$-0.238712\pi$
$104$			28.2843i			0.271964i
$105$		0			0
$106$	−42.9737			−0.405412
$107$	43.1149			0.402943			0.201471	−	0.979494i	$-0.435428\pi$
$107$	43.1149			0.402943			0.201471	+	0.979494i	$0.435428\pi$
$108$	−53.9696	−	1.81139i	−0.499719	−	0.0167721i
$109$	−133.842			−1.22791			−0.613954	−	0.789342i	$-0.710422\pi$
$109$	−133.842			−1.22791			−0.613954	+	0.789342i	$0.710422\pi$
$110$		0			0
$111$	41.1623	+	24.3829i	0.370831	+	0.219665i
$112$		−	29.9473i		−	0.267387i
$113$	7.90852			0.0699869			0.0349935	−	0.999388i	$-0.488859\pi$
$113$	7.90852			0.0699869			0.0349935	+	0.999388i	$0.488859\pi$
$114$	−58.3246	+	98.4615i	−0.511619	+	0.863697i
$115$		0			0
$116$			53.6656i			0.462635i
$117$	78.9292	−	43.2456i	0.674609	−	0.369620i
$118$			34.0527i			0.288582i
$119$		−	227.502i		−	1.91178i
$120$		0			0
$121$	49.0000			0.404959
$122$	−76.2930			−0.625353
$123$	122.236	+	72.4078i	0.993792	+	0.588682i
$124$	16.0000			0.129032
$125$		0			0
$126$	−83.5701	+	45.7883i	−0.663255	+	0.363399i
$127$		−	134.460i		−	1.05874i	−0.848390	−	0.529372i	$-0.822428\pi$
$127$		−	134.460i		−	1.05874i	0.848390	−	0.529372i	$-0.177572\pi$
$128$	11.3137			0.0883883
$129$	37.3246	+	22.1095i	0.289338	+	0.171392i
$130$		0			0
$131$		−	220.394i		−	1.68240i	−0.540727	−	0.841198i	$-0.681851\pi$
$131$		−	220.394i		−	1.68240i	0.540727	−	0.841198i	$-0.318149\pi$
$132$	43.8034	+	25.9473i	0.331844	+	0.196571i
$133$			201.947i			1.51840i
$134$		−	156.215i		−	1.16578i
$135$		0			0
$136$	85.9473			0.631966
$137$	−95.5153			−0.697192			−0.348596	−	0.937273i	$-0.613341\pi$
$137$	−95.5153			−0.697192			−0.348596	+	0.937273i	$0.613341\pi$
$138$	19.8362	−	33.4868i	0.143741	−	0.242658i
$139$	76.8157			0.552631			0.276315	−	0.961067i	$-0.410887\pi$
$139$	76.8157			0.552631			0.276315	+	0.961067i	$0.410887\pi$
$140$		0			0
$141$	−70.1317	+	118.394i	−0.497388	+	0.839673i
$142$			22.0527i			0.155300i
$143$	−84.8528			−0.593376
$144$	−17.2982	−	31.5717i	−0.120127	−	0.219248i
$145$		0			0
$146$		−	124.376i		−	0.851893i
$147$	−10.7833	+	18.2039i	−0.0733555	+	0.123836i
$148$			31.8947i			0.215504i
$149$			276.237i			1.85394i	0.375139	+	0.926969i	$0.377595\pi$
$149$			276.237i			1.85394i	−0.375139	+	0.926969i	$0.622405\pi$
$150$		0			0
$151$	18.0527			0.119554			0.0597770	−	0.998212i	$-0.480961\pi$
$151$	18.0527			0.119554			0.0597770	+	0.998212i	$0.480961\pi$
$152$	−76.2930			−0.501928
$153$	−131.410	−	239.842i	−0.858890	−	1.56759i
$154$	89.8420			0.583390
$155$		0			0
$156$	51.6228	+	30.5792i	0.330915	+	0.196021i
$157$			103.842i			0.661414i	0.943733	+	0.330707i	$0.107287\pi$
$157$			103.842i			0.661414i	−0.943733	+	0.330707i	$0.892713\pi$
$158$	66.4308			0.420448
$159$	−46.4605	+	78.4330i	−0.292204	+	0.493289i
$160$		0			0
$161$		−	68.6825i		−	0.426599i
$162$	−61.6547	+	96.5438i	−0.380584	+	0.595949i
$163$			11.3815i			0.0698251i	0.999390	+	0.0349126i	$0.0111153\pi$
$163$			11.3815i			0.0698251i	−0.999390	+	0.0349126i	$0.988885\pi$
$164$			94.7151i			0.577531i
$165$		0			0
$166$	36.9737			0.222733
$167$	−252.270			−1.51060			−0.755298	−	0.655382i	$-0.772508\pi$
$167$	−252.270			−1.51060			−0.755298	+	0.655382i	$0.772508\pi$
$168$	−54.6581	−	32.3772i	−0.325346	−	0.192722i
$169$	69.0000			0.408284
$170$		0			0
$171$	116.649	+	212.901i	0.682159	+	1.24504i
$172$			28.9210i			0.168145i
$173$	11.8160			0.0683005			0.0341502	−	0.999417i	$-0.489128\pi$
$173$	11.8160			0.0683005			0.0341502	+	0.999417i	$0.489128\pi$
$174$	97.9473	+	58.0200i	0.562916	+	0.333448i
$175$		0			0
$176$			33.9411i			0.192847i
$177$	62.1509	+	36.8157i	0.351135	+	0.207998i
$178$		−	85.9473i		−	0.482850i
$179$			69.0358i			0.385675i	0.981231	+	0.192837i	$0.0617690\pi$
$179$			69.0358i			0.385675i	−0.981231	+	0.192837i	$0.938231\pi$
$180$		0			0
$181$	−189.684			−1.04798			−0.523989	−	0.851725i	$-0.675557\pi$
$181$	−189.684			−1.04798			−0.523989	+	0.851725i	$0.675557\pi$
$182$	105.880			0.581757
$183$	−82.4834	+	139.246i	−0.450729	+	0.760905i
$184$	25.9473			0.141018
$185$		0			0
$186$	17.2982	−	29.2023i	0.0930012	−	0.157001i
$187$			257.842i			1.37883i
$188$	−91.7377			−0.487966
$189$	−6.78078	+	202.031i	−0.0358771	+	1.06895i
$190$		0			0
$191$			108.708i			0.569153i	0.958653	+	0.284577i	$0.0918530\pi$
$191$			108.708i			0.569153i	−0.958653	+	0.284577i	$0.908147\pi$
$192$	12.2317	−	20.6491i	0.0637067	−	0.107547i
$193$			167.947i			0.870193i	0.900384	+	0.435097i	$0.143286\pi$
$193$			167.947i			0.870193i	−0.900384	+	0.435097i	$0.856714\pi$
$194$			50.9862i			0.262815i
$195$		0			0
$196$	−14.1053			−0.0719660
$197$	−171.659			−0.871367			−0.435684	−	0.900100i	$-0.643493\pi$
$197$	−171.659			−0.871367			−0.435684	+	0.900100i	$0.643493\pi$
$198$	94.7151	−	51.8947i	0.478359	−	0.262094i
$199$	−35.0790			−0.176276			−0.0881382	−	0.996108i	$-0.528092\pi$
$199$	−35.0790			−0.176276			−0.0881382	+	0.996108i	$0.528092\pi$
$200$		0			0
$201$	−285.114	−	168.890i	−1.41848	−	0.840248i
$202$		−	68.1053i		−	0.337155i
$203$	200.893			0.989620
$204$	92.9210	−	156.866i	0.455495	−	0.768951i
$205$		0			0
$206$		−	198.567i		−	0.963916i
$207$	−39.6725	−	72.4078i	−0.191654	−	0.349796i
$208$			40.0000i			0.192308i
$209$		−	228.879i		−	1.09512i
$210$		0			0
$211$	−58.1580			−0.275630			−0.137815	−	0.990458i	$-0.544008\pi$
$211$	−58.1580			−0.275630			−0.137815	+	0.990458i	$0.544008\pi$
$212$	−60.7739			−0.286670
$213$	40.2492	+	23.8420i	0.188963	+	0.111934i
$214$	60.9737			0.284924
$215$		0			0
$216$	−76.3246	−	2.56169i	−0.353354	−	0.0118597i
$217$		−	59.8947i		−	0.276012i
$218$	−189.281			−0.868262
$219$	−227.004	−	134.468i	−1.03655	−	0.614009i
$220$		0			0
$221$			303.870i			1.37498i
$222$	58.2123	+	34.4826i	0.262217	+	0.155327i
$223$		−	99.3815i		−	0.445657i	−0.974858	−	0.222828i	$-0.928471\pi$
$223$		−	99.3815i		−	0.445657i	0.974858	−	0.222828i	$-0.0715290\pi$
$224$		−	42.3519i		−	0.189071i
$225$		0			0
$226$	11.1843			0.0494882
$227$	216.951			0.955733			0.477867	−	0.878432i	$-0.341410\pi$
$227$	216.951			0.955733			0.477867	+	0.878432i	$0.341410\pi$
$228$	−82.4834	+	139.246i	−0.361769	+	0.610726i
$229$	−325.684			−1.42220			−0.711100	−	0.703090i	$-0.751803\pi$
$229$	−325.684			−1.42220			−0.711100	+	0.703090i	$0.751803\pi$
$230$		0			0
$231$	97.1317	−	163.974i	0.420483	−	0.709845i
$232$			75.8947i			0.327132i
$233$	−51.7119			−0.221939			−0.110970	−	0.993824i	$-0.535396\pi$
$233$	−51.7119			−0.221939			−0.110970	+	0.993824i	$0.535396\pi$
$234$	111.623	−	61.1584i	0.477020	−	0.261361i
$235$		0			0
$236$			48.1577i			0.204058i
$237$	71.8209	−	121.246i	0.303042	−	0.511585i
$238$		−	321.737i		−	1.35183i
$239$			410.047i			1.71568i	0.513917	+	0.857840i	$0.328194\pi$
$239$			410.047i			1.71568i	−0.513917	+	0.857840i	$0.671806\pi$
$240$		0			0
$241$	445.526			1.84866			0.924328	−	0.381599i	$-0.124627\pi$
$241$	445.526			1.84866			0.924328	+	0.381599i	$0.124627\pi$
$242$	69.2965			0.286349
$243$	109.549	+	216.906i	0.450818	+	0.892616i
$244$	−107.895			−0.442191
$245$		0			0
$246$	172.868	+	102.400i	0.702717	+	0.416261i
$247$		−	269.737i		−	1.09205i
$248$	22.6274			0.0912396
$249$	39.9737	−	67.4821i	0.160537	−	0.271013i
$250$		0			0
$251$		−	237.364i		−	0.945675i	−0.881150	−	0.472838i	$-0.843230\pi$
$251$		−	237.364i		−	0.945675i	0.881150	−	0.472838i	$-0.156770\pi$
$252$	−118.186	+	64.7544i	−0.468992	+	0.256962i
$253$			77.8420i			0.307676i
$254$		−	190.156i		−	0.748645i
$255$		0			0
$256$	16.0000			0.0625000
$257$	318.887			1.24080			0.620402	−	0.784284i	$-0.286970\pi$
$257$	318.887			1.24080			0.620402	+	0.784284i	$0.286970\pi$
$258$	52.7849	+	31.2676i	0.204593	+	0.121192i
$259$	119.395			0.460985
$260$		0			0
$261$	211.789	−	116.040i	0.811453	−	0.444598i
$262$		−	311.684i		−	1.18963i
$263$	−36.2300			−0.137757			−0.0688784	−	0.997625i	$-0.521942\pi$
$263$	−36.2300			−0.137757			−0.0688784	+	0.997625i	$0.521942\pi$
$264$	61.9473	+	36.6951i	0.234649	+	0.138996i
$265$		0			0
$266$			285.597i			1.07367i
$267$	−156.866	−	92.9210i	−0.587513	−	0.348019i
$268$		−	220.921i		−	0.824332i
$269$		−	528.041i		−	1.96298i	−0.191518	−	0.981489i	$-0.561341\pi$
$269$		−	528.041i		−	1.96298i	0.191518	−	0.981489i	$-0.438659\pi$
$270$		0			0
$271$	−475.895			−1.75607			−0.878034	−	0.478597i	$-0.841145\pi$
$271$	−475.895			−1.75607			−0.878034	+	0.478597i	$0.841145\pi$
$272$	121.548			0.446867
$273$	114.471	−	193.246i	0.419307	−	0.707859i
$274$	−135.079			−0.492989
$275$		0			0
$276$	28.0527	−	47.3575i	0.101640	−	0.171585i
$277$			188.158i			0.679271i	0.940557	+	0.339635i	$0.110304\pi$
$277$			188.158i			0.679271i	−0.940557	+	0.339635i	$0.889696\pi$
$278$	108.634			0.390769
$279$	−34.5964	−	63.1434i	−0.124002	−	0.226320i
$280$		0			0
$281$		−	24.4322i		−	0.0869473i	−0.999055	−	0.0434736i	$-0.986158\pi$
$281$		−	24.4322i		−	0.0869473i	0.999055	−	0.0434736i	$-0.0138424\pi$
$282$	−99.1812	+	167.434i	−0.351706	+	0.593738i
$283$		−	198.460i		−	0.701274i	−0.936511	−	0.350637i	$-0.885965\pi$
$283$		−	198.460i		−	0.701274i	0.936511	−	0.350637i	$-0.114035\pi$
$284$			31.1872i			0.109814i
$285$		0			0
$286$	−120.000			−0.419580
$287$	354.558			1.23539
$288$	−24.4634	−	44.6491i	−0.0849423	−	0.155032i
$289$	634.368			2.19504
$290$		0			0
$291$	93.0569	+	55.1231i	0.319783	+	0.189427i
$292$		−	175.895i		−	0.602379i
$293$	513.825			1.75367			0.876834	−	0.480794i	$-0.159651\pi$
$293$	513.825			1.75367			0.876834	+	0.480794i	$0.159651\pi$
$294$	−15.2498	+	25.7442i	−0.0518702	+	0.0875654i
$295$		0			0
$296$			45.1059i			0.152385i
$297$	7.68507	−	228.974i	0.0258757	−	0.770955i
$298$			390.658i			1.31093i
$299$			91.7377i			0.306815i
$300$		0			0
$301$	108.263			0.359679
$302$	25.5303			0.0845375
$303$	−124.302	−	73.6313i	−0.410237	−	0.243008i
$304$	−107.895			−0.354917
$305$		0			0
$306$	−185.842	−	339.188i	−0.607327	−	1.10846i
$307$		−	11.3815i		−	0.0370733i	−0.999828	−	0.0185366i	$-0.994099\pi$
$307$		−	11.3815i		−	0.0370733i	0.999828	−	0.0185366i	$-0.00590073\pi$
$308$	127.056			0.412519
$309$	−362.412	−	214.678i	−1.17285	−	0.694751i
$310$		0			0
$311$			518.756i			1.66802i	0.551746	+	0.834012i	$0.313962\pi$
$311$			518.756i			1.66802i	−0.551746	+	0.834012i	$0.686038\pi$
$312$	73.0056	+	43.2456i	0.233992	+	0.138608i
$313$			46.3160i			0.147974i	0.997259	+	0.0739872i	$0.0235724\pi$
$313$			46.3160i			0.147974i	−0.997259	+	0.0739872i	$0.976428\pi$
$314$			146.855i			0.467690i
$315$		0			0
$316$	93.9473			0.297302
$317$	39.0957			0.123330			0.0616651	−	0.998097i	$-0.480359\pi$
$317$	39.0957			0.123330			0.0616651	+	0.998097i	$0.480359\pi$
$318$	−65.7051	+	110.921i	−0.206620	+	0.348808i
$319$	−227.684			−0.713743
$320$		0			0
$321$	65.9210	−	111.286i	0.205361	−	0.346684i
$322$		−	97.1317i		−	0.301651i
$323$	−819.648			−2.53761
$324$	−87.1929	+	136.534i	−0.269114	+	0.421400i
$325$		0			0
$326$			16.0959i			0.0493738i
$327$	−204.639	+	345.465i	−0.625808	+	1.05647i
$328$			133.947i			0.408376i
$329$			343.412i			1.04381i
$330$		0			0
$331$	−445.421			−1.34568			−0.672841	−	0.739787i	$-0.734926\pi$
$331$	−445.421			−1.34568			−0.672841	+	0.739787i	$0.734926\pi$
$332$	52.2887			0.157496
$333$	125.871	−	68.9651i	0.377991	−	0.207102i
$334$	−356.763			−1.06815
$335$		0			0
$336$	−77.2982	−	45.7883i	−0.230054	−	0.136275i
$337$			325.684i			0.966421i	0.875504	+	0.483211i	$0.160529\pi$
$337$			325.684i			0.966421i	−0.875504	+	0.483211i	$0.839471\pi$
$338$	97.5807			0.288700
$339$	12.0918	−	20.4130i	0.0356691	−	0.0602153i
$340$		0			0
$341$			67.8823i			0.199068i
$342$	164.967	+	301.088i	0.482359	+	0.880373i
$343$		−	314.053i		−	0.915605i
$344$			40.9005i			0.118897i
$345$		0			0
$346$	16.7103			0.0482957
$347$	−51.8236			−0.149348			−0.0746738	−	0.997208i	$-0.523792\pi$
$347$	−51.8236			−0.149348			−0.0746738	+	0.997208i	$0.523792\pi$
$348$	138.518	+	82.0527i	0.398042	+	0.235784i
$349$	97.5787			0.279595			0.139798	−	0.990180i	$-0.455355\pi$
$349$	97.5787			0.279595			0.139798	+	0.990180i	$0.455355\pi$
$350$		0			0
$351$	9.05694	−	269.848i	0.0258033	−	0.768798i
$352$			48.0000i			0.136364i
$353$	−569.797			−1.61416			−0.807078	−	0.590445i	$-0.798952\pi$
$353$	−569.797			−1.61416			−0.807078	+	0.590445i	$0.798952\pi$
$354$	87.8947	+	52.0652i	0.248290	+	0.147077i
$355$		0			0
$356$		−	121.548i		−	0.341427i
$357$	−587.215	−	347.842i	−1.64486	−	0.974347i
$358$			97.6313i			0.272713i
$359$		−	274.283i		−	0.764019i	−0.924158	−	0.382010i	$-0.875232\pi$
$359$		−	274.283i		−	0.764019i	0.924158	−	0.382010i	$-0.124768\pi$
$360$		0			0
$361$	366.579			1.01545
$362$	−268.254			−0.741032
$363$	74.9191	−	126.476i	0.206389	−	0.348418i
$364$	149.737			0.411364
$365$		0			0
$366$	−116.649	+	196.923i	−0.318713	+	0.538041i
$367$			461.828i			1.25839i	0.777248	+	0.629194i	$0.216615\pi$
$367$			461.828i			1.25839i	−0.777248	+	0.629194i	$0.783385\pi$
$368$	36.6951			0.0997149
$369$	373.789	−	204.800i	1.01298	−	0.555014i
$370$		0			0
$371$			227.502i			0.613213i
$372$	24.4634	−	41.2982i	0.0657618	−	0.111017i
$373$			491.947i			1.31889i	0.751751	+	0.659447i	$0.229209\pi$
$373$			491.947i			1.31889i	−0.751751	+	0.659447i	$0.770791\pi$
$374$			364.644i			0.974983i
$375$		0			0
$376$	−129.737			−0.345044
$377$	−268.328			−0.711746
$378$	−9.58947	+	285.715i	−0.0253690	+	0.755859i
$379$	258.763			0.682752			0.341376	−	0.939927i	$-0.389107\pi$
$379$	258.763			0.682752			0.341376	+	0.939927i	$0.389107\pi$
$380$		0			0
$381$	−347.061	−	205.585i	−0.910922	−	0.539593i
$382$			153.737i			0.402452i
$383$	522.422			1.36402			0.682012	−	0.731341i	$-0.261105\pi$
$383$	522.422			1.36402			0.682012	+	0.731341i	$0.261105\pi$
$384$	17.2982	−	29.2023i	0.0450475	−	0.0760475i
$385$		0			0
$386$			237.513i			0.615320i
$387$	114.136	−	62.5352i	0.294924	−	0.161590i
$388$			72.1053i			0.185838i
$389$			610.847i			1.57030i	0.619306	+	0.785150i	$0.287414\pi$
$389$			610.847i			1.57030i	−0.619306	+	0.785150i	$0.712586\pi$
$390$		0			0
$391$	278.763			0.712949
$392$	−19.9480			−0.0508876
$393$	−568.867	−	336.974i	−1.44750	−	0.857439i
$394$	−242.763			−0.616150
$395$		0			0
$396$	133.947	−	73.3901i	0.338251	−	0.185329i
$397$		−	214.000i		−	0.539043i	−0.962994	−	0.269521i	$-0.913135\pi$
$397$		−	214.000i		−	0.539043i	0.962994	−	0.269521i	$-0.0868655\pi$
$398$	−49.6092			−0.124646
$399$	521.254	+	308.770i	1.30640	+	0.773859i
$400$		0			0
$401$		−	454.557i		−	1.13356i	−0.823869	−	0.566780i	$-0.808189\pi$
$401$		−	454.557i		−	1.13356i	0.823869	−	0.566780i	$-0.191811\pi$
$402$	−403.212	−	238.846i	−1.00301	−	0.594145i
$403$			80.0000i			0.198511i
$404$		−	96.3155i		−	0.238405i
$405$		0			0
$406$	284.105			0.699767
$407$	−135.318			−0.332476
$408$	131.410	−	221.842i	0.322084	−	0.543730i
$409$	573.842			1.40304			0.701518	−	0.712651i	$-0.252506\pi$
$409$	573.842			1.40304			0.701518	+	0.712651i	$0.252506\pi$
$410$		0			0
$411$	−146.039	+	246.538i	−0.355326	+	0.599850i
$412$		−	280.816i		−	0.681591i
$413$	180.274			0.436500
$414$	−56.1053	−	102.400i	−0.135520	−	0.247343i
$415$		0			0
$416$			56.5685i			0.135982i
$417$	117.448	−	198.272i	0.281650	−	0.475472i
$418$		−	323.684i		−	0.774364i
$419$			97.9159i			0.233690i	0.993150	+	0.116845i	$0.0372780\pi$
$419$			97.9159i			0.233690i	−0.993150	+	0.116845i	$0.962722\pi$
$420$		0			0
$421$	717.315			1.70384			0.851918	−	0.523675i	$-0.175439\pi$
$421$	717.315			1.70384			0.851918	+	0.523675i	$0.175439\pi$
$422$	−82.2478			−0.194900
$423$	198.362	+	362.039i	0.468942	+	0.855885i
$424$	−85.9473			−0.202706
$425$		0			0
$426$	56.9210	+	33.7177i	0.133617	+	0.0791495i
$427$			403.895i			0.945889i
$428$	86.2298			0.201471
$429$	−129.737	+	219.017i	−0.302416	+	0.510529i
$430$		0			0
$431$		−	293.077i		−	0.679994i	−0.940427	−	0.339997i	$-0.889574\pi$
$431$		−	293.077i		−	0.679994i	0.940427	−	0.339997i	$-0.110426\pi$
$432$	−107.939	−	3.62278i	−0.249859	−	0.00838606i
$433$		−	487.526i		−	1.12593i	−0.826482	−	0.562963i	$-0.809661\pi$
$433$		−	487.526i		−	1.12593i	0.826482	−	0.562963i	$-0.190339\pi$
$434$		−	84.7038i		−	0.195170i
$435$		0			0
$436$	−267.684			−0.613954
$437$	−247.450			−0.566247
$438$	−321.033	−	190.167i	−0.732951	−	0.434170i
$439$	−257.237			−0.585961			−0.292981	−	0.956118i	$-0.594647\pi$
$439$	−257.237			−0.585961			−0.292981	+	0.956118i	$0.594647\pi$
$440$		0			0
$441$	30.4997	+	55.6662i	0.0691602	+	0.126227i
$442$			429.737i			0.972255i
$443$	293.096			0.661615			0.330808	−	0.943698i	$-0.392679\pi$
$443$	293.096			0.661615			0.330808	+	0.943698i	$0.392679\pi$
$444$	82.3246	+	48.7657i	0.185416	+	0.109833i
$445$		0			0
$446$		−	140.547i		−	0.315127i
$447$	713.005	+	422.355i	1.59509	+	0.944866i
$448$		−	59.8947i		−	0.133693i
$449$		−	585.614i		−	1.30426i	−0.758106	−	0.652132i	$-0.773875\pi$
$449$		−	585.614i		−	1.30426i	0.758106	−	0.652132i	$-0.226125\pi$
$450$		0			0
$451$	−401.842			−0.891002
$452$	15.8170			0.0349935
$453$	27.6018	−	46.5964i	0.0609312	−	0.102862i
$454$	306.816			0.675805
$455$		0			0
$456$	−116.649	+	196.923i	−0.255809	+	0.431849i
$457$		−	813.052i		−	1.77911i	−0.456831	−	0.889554i	$-0.651016\pi$
$457$		−	813.052i		−	1.77911i	0.456831	−	0.889554i	$-0.348984\pi$
$458$	−460.587			−1.00565
$459$	−819.986	−	27.5213i	−1.78646	−	0.0599593i
$460$		0			0
$461$		−	554.074i		−	1.20190i	−0.799288	−	0.600948i	$-0.794790\pi$
$461$		−	554.074i		−	1.20190i	0.799288	−	0.600948i	$-0.205210\pi$
$462$	137.365	−	231.895i	0.297327	−	0.501937i
$463$			449.723i			0.971324i	0.874147	+	0.485662i	$0.161421\pi$
$463$			449.723i			0.971324i	−0.874147	+	0.485662i	$0.838579\pi$
$464$			107.331i			0.231317i
$465$		0			0
$466$	−73.1317			−0.156935
$467$	−30.7221			−0.0657862			−0.0328931	−	0.999459i	$-0.510472\pi$
$467$	−30.7221			−0.0657862			−0.0328931	+	0.999459i	$0.510472\pi$
$468$	157.858	−	86.4911i	0.337304	−	0.184810i
$469$	−826.999			−1.76332
$470$		0			0
$471$	268.031	+	158.770i	0.569067	+	0.337092i
$472$			68.1053i			0.144291i
$473$	−122.701			−0.259411
$474$	101.570	−	171.467i	0.214283	−	0.361745i
$475$		0			0
$476$		−	455.004i		−	0.955891i
$477$	131.410	+	239.842i	0.275493	+	0.502813i
$478$			579.895i			1.21317i
$479$		−	735.242i		−	1.53495i	−0.641078	−	0.767476i	$-0.721512\pi$
$479$		−	735.242i		−	1.53495i	0.641078	−	0.767476i	$-0.278488\pi$
$480$		0			0
$481$	−159.473			−0.331545
$482$	630.069			1.30720
$483$	−177.279	−	105.013i	−0.367037	−	0.217418i
$484$	98.0000			0.202479
$485$		0			0
$486$	154.925	+	306.751i	0.318776	+	0.631175i
$487$		−	92.6185i		−	0.190182i	−0.995469	−	0.0950909i	$-0.969686\pi$
$487$		−	92.6185i		−	0.190182i	0.995469	−	0.0950909i	$-0.0303142\pi$
$488$	−152.586			−0.312676
$489$	29.3772	+	17.4019i	0.0600761	+	0.0355866i
$490$		0			0
$491$			898.323i			1.82958i	0.403933	+	0.914789i	$0.367643\pi$
$491$			898.323i			1.82958i	−0.403933	+	0.914789i	$0.632357\pi$
$492$	244.473	+	144.816i	0.496896	+	0.294341i
$493$			815.368i			1.65389i
$494$		−	381.465i		−	0.772197i
$495$		0			0
$496$	32.0000			0.0645161
$497$	116.747			0.234903
$498$	56.5313	−	95.4342i	0.113517	−	0.191635i
$499$	−136.921			−0.274391			−0.137195	−	0.990544i	$-0.543809\pi$
$499$	−136.921			−0.274391			−0.137195	+	0.990544i	$0.543809\pi$
$500$		0			0
$501$	−385.710	+	651.143i	−0.769881	+	1.29969i
$502$		−	335.684i		−	0.668693i
$503$	443.077			0.880868			0.440434	−	0.897785i	$-0.354825\pi$
$503$	443.077			0.880868			0.440434	+	0.897785i	$0.354825\pi$
$504$	−167.140	+	91.5766i	−0.331627	+	0.181700i
$505$		0			0
$506$			110.085i			0.217560i
$507$	105.498	−	178.099i	0.208083	−	0.351279i
$508$		−	268.921i		−	0.529372i
$509$			213.062i			0.418590i	0.977853	+	0.209295i	$0.0671168\pi$
$509$			213.062i			0.418590i	−0.977853	+	0.209295i	$0.932883\pi$
$510$		0			0
$511$	−658.447			−1.28855
$512$	22.6274			0.0441942
$513$	727.879	+	24.4299i	1.41887	+	0.0476216i
$514$	450.974			0.877381
$515$		0			0
$516$	74.6491	+	44.2191i	0.144669	+	0.0856959i
$517$		−	389.210i		−	0.752824i
$518$	168.850			0.325965
$519$	18.0662	−	30.4987i	0.0348096	−	0.0587643i
$520$		0			0
$521$		−	3.20085i		−	0.00614366i	−0.999995	−	0.00307183i	$-0.999022\pi$
$521$		−	3.20085i		−	0.00614366i	0.999995	−	0.00307183i	$-0.000977795\pi$
$522$	299.515	−	164.105i	0.573784	−	0.314378i
$523$		−	966.644i		−	1.84827i	−0.382069	−	0.924134i	$-0.624788\pi$
$523$		−	966.644i		−	1.84827i	0.382069	−	0.924134i	$-0.375212\pi$
$524$		−	440.788i		−	0.841198i
$525$		0			0
$526$	−51.2370			−0.0974088
$527$	243.096			0.461282
$528$	87.6068	+	51.8947i	0.165922	+	0.0982853i
$529$	−444.842			−0.840911
$530$		0			0
$531$	190.053	−	104.130i	0.357915	−	0.196102i
$532$			403.895i			0.759200i
$533$	−473.575			−0.888509
$534$	−221.842	−	131.410i	−0.415434	−	0.246086i
$535$		0			0
$536$		−	312.429i		−	0.582891i
$537$	178.191	+	105.553i	0.331827	+	0.196561i
$538$		−	746.763i		−	1.38804i
$539$		−	59.8439i		−	0.111028i
$540$		0			0
$541$	−186.105			−0.344002			−0.172001	−	0.985097i	$-0.555023\pi$
$541$	−186.105			−0.344002			−0.172001	+	0.985097i	$0.555023\pi$
$542$	−673.017			−1.24173
$543$	−290.019	+	489.601i	−0.534106	+	0.901659i
$544$	171.895			0.315983
$545$		0			0
$546$	161.886	−	273.290i	0.296495	−	0.500532i
$547$		−	309.434i		−	0.565693i	−0.959165	−	0.282847i	$-0.908721\pi$
$547$		−	309.434i		−	0.565693i	0.959165	−	0.282847i	$-0.0912787\pi$
$548$	−191.031			−0.348596
$549$	233.298	+	425.802i	0.424951	+	0.775596i
$550$		0			0
$551$		−	723.779i		−	1.31357i
$552$	39.6725	−	66.9737i	0.0718704	−	0.121329i
$553$		−	351.684i		−	0.635957i
$554$			266.096i			0.480317i
$555$		0			0
$556$	153.631			0.276315
$557$	4.00106			0.00718323			0.00359161	−	0.999994i	$-0.498857\pi$
$557$	4.00106			0.00718323			0.00359161	+	0.999994i	$0.498857\pi$
$558$	−48.9268	−	89.2982i	−0.0876824	−	0.160033i
$559$	−144.605			−0.258685
$560$		0			0
$561$	665.526	+	394.230i	1.18632	+	0.702728i
$562$		−	34.5523i		−	0.0614810i
$563$	166.970			0.296572			0.148286	−	0.988945i	$-0.452624\pi$
$563$	166.970			0.296572			0.148286	+	0.988945i	$0.452624\pi$
$564$	−140.263	+	236.788i	−0.248694	+	0.419836i
$565$		0			0
$566$		−	280.666i		−	0.495875i
$567$	511.102	+	326.399i	0.901414	+	0.575660i
$568$			44.1053i			0.0776502i
$569$		−	156.289i		−	0.274673i	−0.990524	−	0.137337i	$-0.956146\pi$
$569$		−	156.289i		−	0.274673i	0.990524	−	0.137337i	$-0.0438542\pi$
$570$		0			0
$571$	−144.105			−0.252374			−0.126187	−	0.992006i	$-0.540274\pi$
$571$	−144.105			−0.252374			−0.126187	+	0.992006i	$0.540274\pi$
$572$	−169.706			−0.296688
$573$	280.591	+	166.211i	0.489688	+	0.290071i
$574$	501.421			0.873555
$575$		0			0
$576$	−34.5964	−	63.1434i	−0.0600633	−	0.109624i
$577$			532.947i			0.923651i	0.886971	+	0.461826i	$0.152805\pi$
$577$			532.947i			0.923651i	−0.886971	+	0.461826i	$0.847195\pi$
$578$	897.132			1.55213
$579$	433.495	+	256.785i	0.748697	+	0.443497i
$580$		0			0
$581$		−	195.738i		−	0.336899i
$582$	131.602	+	77.9559i	0.226121	+	0.133945i
$583$		−	257.842i		−	0.442268i
$584$		−	248.753i		−	0.425946i
$585$		0			0
$586$	726.658			1.24003
$587$	−190.342			−0.324262			−0.162131	−	0.986769i	$-0.551837\pi$
$587$	−190.342			−0.324262			−0.162131	+	0.986769i	$0.551837\pi$
$588$	−21.5665	+	36.4078i	−0.0366777	+	0.0619181i
$589$	−215.789			−0.366366
$590$		0			0
$591$	−262.460	+	443.077i	−0.444096	+	0.749707i
$592$			63.7893i			0.107752i
$593$	345.719			0.583001			0.291500	−	0.956571i	$-0.405846\pi$
$593$	345.719			0.583001			0.291500	+	0.956571i	$0.405846\pi$
$594$	10.8683	−	323.818i	0.0182969	−	0.545148i
$595$		0			0
$596$			552.473i			0.926969i
$597$	−53.6344	+	90.5438i	−0.0898399	+	0.151665i
$598$			129.737i			0.216951i
$599$			704.055i			1.17538i	0.809085	+	0.587692i	$0.199963\pi$
$599$			704.055i			1.17538i	−0.809085	+	0.587692i	$0.800037\pi$
$600$		0			0
$601$	338.474			0.563185			0.281592	−	0.959534i	$-0.409137\pi$
$601$	338.474			0.563185			0.281592	+	0.959534i	$0.409137\pi$
$602$	153.107			0.254331
$603$	−871.856	+	477.693i	−1.44586	+	0.792193i
$604$	36.1053			0.0597770
$605$		0			0
$606$	−175.789	−	104.130i	−0.290081	−	0.171832i
$607$		−	816.513i		−	1.34516i	−0.740024	−	0.672581i	$-0.765186\pi$
$607$		−	816.513i		−	1.34516i	0.740024	−	0.672581i	$-0.234814\pi$
$608$	−152.586			−0.250964
$609$	307.157	−	518.532i	0.504363	−	0.851449i
$610$		0			0
$611$		−	458.688i		−	0.750717i
$612$	−262.820	−	479.684i	−0.429445	−	0.783797i
$613$			229.263i			0.374001i	0.982360	+	0.187001i	$0.0598766\pi$
$613$			229.263i			0.374001i	−0.982360	+	0.187001i	$0.940123\pi$
$614$		−	16.0959i		−	0.0262148i
$615$		0			0
$616$	179.684			0.291695
$617$	−1072.25			−1.73785			−0.868924	−	0.494945i	$-0.835188\pi$
$617$	−1072.25			−1.73785			−0.868924	+	0.494945i	$0.835188\pi$
$618$	−512.528	−	303.601i	−0.829334	−	0.491263i
$619$	80.7103			0.130388			0.0651941	−	0.997873i	$-0.479233\pi$
$619$	80.7103			0.130388			0.0651941	+	0.997873i	$0.479233\pi$
$620$		0			0
$621$	−247.552	−	8.30863i	−0.398635	−	0.0133794i
$622$			733.631i			1.17947i
$623$	−455.004			−0.730344
$624$	103.246	+	61.1584i	0.165458	+	0.0980103i
$625$		0			0
$626$			65.5007i			0.104634i
$627$	−590.769	−	349.947i	−0.942215	−	0.558130i
$628$			207.684i			0.330707i
$629$			484.591i			0.770415i
$630$		0			0
$631$	492.894			0.781131			0.390566	−	0.920575i	$-0.372279\pi$
$631$	492.894			0.781131			0.390566	+	0.920575i	$0.372279\pi$
$632$	132.862			0.210224
$633$	−88.9213	+	150.114i	−0.140476	+	0.237147i
$634$	55.2897			0.0872077
$635$		0			0
$636$	−92.9210	+	156.866i	−0.146102	+	0.246645i
$637$		−	70.5267i		−	0.110717i
$638$	−321.994			−0.504692
$639$	123.079	−	67.4353i	0.192612	−	0.105533i
$640$		0			0
$641$		−	65.4816i		−	0.102155i	−0.998695	−	0.0510777i	$-0.983734\pi$
$641$		−	65.4816i		−	0.102155i	0.998695	−	0.0510777i	$-0.0162656\pi$
$642$	93.2264	−	157.381i	0.145212	−	0.245143i
$643$			428.619i			0.666592i	0.942822	+	0.333296i	$0.108161\pi$
$643$			428.619i			0.666592i	−0.942822	+	0.333296i	$0.891839\pi$
$644$		−	137.365i		−	0.213300i
$645$		0			0
$646$	−1159.16			−1.79436
$647$	−462.801			−0.715303			−0.357652	−	0.933855i	$-0.616422\pi$
$647$	−462.801			−0.715303			−0.357652	+	0.933855i	$0.616422\pi$
$648$	−123.309	+	193.088i	−0.190292	+	0.297975i
$649$	−204.316			−0.314817
$650$		0			0
$651$	−154.596	−	91.5766i	−0.237475	−	0.140671i
$652$			22.7630i			0.0349126i
$653$	425.064			0.650941			0.325470	−	0.945552i	$-0.394477\pi$
$653$	425.064			0.650941			0.325470	+	0.945552i	$0.394477\pi$
$654$	−289.404	+	488.561i	−0.442513	+	0.747035i
$655$		0			0
$656$			189.430i			0.288765i
$657$	−694.161	+	380.333i	−1.05656	+	0.578894i
$658$			485.658i			0.738083i
$659$			182.769i			0.277343i	0.990338	+	0.138671i	$0.0442831\pi$
$659$			182.769i			0.277343i	−0.990338	+	0.138671i	$0.955717\pi$
$660$		0			0
$661$	−482.053			−0.729278			−0.364639	−	0.931149i	$-0.618808\pi$
$661$	−482.053			−0.729278			−0.364639	+	0.931149i	$0.618808\pi$
$662$	−629.920			−0.951541
$663$	784.330	+	464.605i	1.18300	+	0.700762i
$664$	73.9473			0.111366
$665$		0			0
$666$	178.009	−	97.5314i	0.267280	−	0.146444i
$667$			246.158i			0.369052i
$668$	−504.539			−0.755298
$669$	−256.517	−	151.950i	−0.383434	−	0.227131i
$670$		0			0
$671$		−	457.758i		−	0.682203i
$672$	−109.316	−	64.7544i	−0.162673	−	0.0963608i
$673$		−	184.579i		−	0.274264i	−0.990553	−	0.137132i	$-0.956212\pi$
$673$		−	184.579i		−	0.274264i	0.990553	−	0.137132i	$-0.0437884\pi$
$674$			460.587i			0.683363i
$675$		0			0
$676$	138.000			0.204142
$677$	1065.85			1.57437			0.787187	−	0.616715i	$-0.211537\pi$
$677$	1065.85			1.57437			0.787187	+	0.616715i	$0.211537\pi$
$678$	17.1004	−	28.8683i	0.0252219	−	0.0425787i
$679$	269.920			0.397526
$680$		0			0
$681$	331.710	−	559.982i	0.487093	−	0.822293i
$682$			96.0000i			0.140762i
$683$	−788.926			−1.15509			−0.577545	−	0.816359i	$-0.695989\pi$
$683$	−788.926			−1.15509			−0.577545	+	0.816359i	$0.695989\pi$
$684$	233.298	+	425.802i	0.341079	+	0.622518i
$685$		0			0
$686$		−	444.138i		−	0.647431i
$687$	−497.958	+	840.636i	−0.724830	+	1.22363i
$688$			57.8420i			0.0840727i
$689$		−	303.870i		−	0.441030i
$690$		0			0
$691$	932.000			1.34877			0.674385	−	0.738380i	$-0.264409\pi$
$691$	932.000			1.34877			0.674385	+	0.738380i	$0.264409\pi$
$692$	23.6320			0.0341502
$693$	−274.730	−	501.421i	−0.396436	−	0.723551i
$694$	−73.2897			−0.105605
$695$		0			0
$696$	195.895	+	116.040i	0.281458	+	0.166724i
$697$			1439.05i			2.06464i
$698$	137.997			0.197704
$699$	−79.0655	+	133.476i	−0.113112	+	0.190952i
$700$		0			0
$701$			1352.75i			1.92974i	0.262721	+	0.964872i	$0.415380\pi$
$701$			1352.75i			1.92974i	−0.262721	+	0.964872i	$0.584620\pi$
$702$	12.8084	−	381.623i	0.0182457	−	0.543622i
$703$		−	430.158i		−	0.611889i
$704$			67.8823i			0.0964237i
$705$		0			0
$706$	−805.815			−1.14138
$707$	−360.549			−0.509970
$708$	124.302	+	73.6313i	0.175568	+	0.103999i
$709$	269.473			0.380075			0.190038	−	0.981777i	$-0.439139\pi$
$709$	269.473			0.380075			0.190038	+	0.981777i	$0.439139\pi$
$710$		0			0
$711$	−203.140	−	370.759i	−0.285711	−	0.521462i
$712$		−	171.895i		−	0.241425i
$713$	73.3901			0.102931
$714$	−830.447	−	491.923i	−1.16309	−	0.688968i
$715$		0			0
$716$			138.072i			0.192837i
$717$	1058.39	+	626.947i	1.47614	+	0.874403i
$718$		−	387.895i		−	0.540243i
$719$			537.103i			0.747014i	0.927627	+	0.373507i	$0.121845\pi$
$719$			537.103i			0.747014i	−0.927627	+	0.373507i	$0.878155\pi$
$720$		0			0
$721$	−1051.21			−1.45799
$722$	518.421			0.718034
$723$	681.192	−	1149.96i	0.942174	−	1.59055i
$724$	−379.368			−0.523989
$725$		0			0
$726$	105.952	−	178.864i	0.145939	−	0.246369i
$727$		−	1117.83i		−	1.53759i	−0.639495	−	0.768795i	$-0.720856\pi$
$727$		−	1117.83i		−	1.53759i	0.639495	−	0.768795i	$-0.279144\pi$
$728$	211.760			0.290879
$729$	727.359	+	48.8800i	0.997750	+	0.0670507i
$730$		0			0
$731$			439.411i			0.601109i
$732$	−164.967	+	278.491i	−0.225364	+	0.380452i
$733$		−	7.52599i		−	0.0102674i	−0.999987	−	0.00513369i	$-0.998366\pi$
$733$		−	7.52599i		−	0.0102674i	0.999987	−	0.00513369i	$-0.00163411\pi$
$734$			653.124i			0.889815i
$735$		0			0
$736$	51.8947			0.0705091
$737$	937.288			1.27176
$738$	528.618	−	289.631i	0.716284	−	0.392454i
$739$	823.079			1.11377			0.556887	−	0.830588i	$-0.311996\pi$
$739$	823.079			1.11377			0.556887	+	0.830588i	$0.311996\pi$
$740$		0			0
$741$	−696.228	−	412.417i	−0.939579	−	0.556568i
$742$			321.737i			0.433607i
$743$	−3.21898			−0.00433241			−0.00216620	−	0.999998i	$-0.500690\pi$
$743$	−3.21898			−0.00433241			−0.00216620	+	0.999998i	$0.500690\pi$
$744$	34.5964	−	58.4045i	0.0465006	−	0.0785007i
$745$		0			0
$746$			695.719i			0.932599i
$747$	−113.063	−	206.355i	−0.151356	−	0.276245i
$748$			515.684i			0.689417i
$749$		−	322.794i		−	0.430967i
$750$		0			0
$751$	1185.63			1.57874			0.789368	−	0.613920i	$-0.210408\pi$
$751$	1185.63			1.57874			0.789368	+	0.613920i	$0.210408\pi$
$752$	−183.475			−0.243983
$753$	−612.671	−	362.921i	−0.813639	−	0.481967i
$754$	−379.473			−0.503280
$755$		0			0
$756$	−13.5616	+	404.061i	−0.0179386	+	0.534473i
$757$		−	863.315i		−	1.14044i	−0.821491	−	0.570221i	$-0.806857\pi$
$757$		−	863.315i		−	1.14044i	0.821491	−	0.570221i	$-0.193143\pi$
$758$	365.946			0.482779
$759$	200.921	+	119.017i	0.264718	+	0.156808i
$760$		0			0
$761$			570.597i			0.749800i	0.927065	+	0.374900i	$0.122323\pi$
$761$			570.597i			0.749800i	−0.927065	+	0.374900i	$0.877677\pi$
$762$	−490.819	−	290.741i	−0.644119	−	0.381550i
$763$			1002.05i			1.31331i
$764$			217.416i			0.284577i
$765$		0			0
$766$	738.816			0.964511
$767$	−240.789			−0.313936
$768$	24.4634	−	41.2982i	0.0318534	−	0.0537737i
$769$	741.684			0.964479			0.482239	−	0.876040i	$-0.339824\pi$
$769$	741.684			0.964479			0.482239	+	0.876040i	$0.339824\pi$
$770$		0			0
$771$	487.565	−	823.090i	0.632380	−	1.06756i
$772$			335.895i			0.435097i
$773$	−623.203			−0.806214			−0.403107	−	0.915153i	$-0.632070\pi$
$773$	−623.203			−0.806214			−0.403107	+	0.915153i	$0.632070\pi$
$774$	161.412	−	88.4382i	0.208543	−	0.114261i
$775$		0			0
$776$			101.972i			0.131408i
$777$	182.550	−	308.175i	0.234943	−	0.396622i
$778$			863.868i			1.11037i
$779$		−	1277.41i		−	1.63980i
$780$		0			0
$781$	−132.316			−0.169419
$782$	394.230			0.504131
$783$	24.3023	−	724.078i	0.0310375	−	0.924749i
$784$	−28.2107			−0.0359830
$785$		0			0
$786$	−804.500	−	476.553i	−1.02354	−	0.606301i
$787$			335.303i			0.426052i	0.977046	+	0.213026i	$0.0683320\pi$
$787$			335.303i			0.426052i	−0.977046	+	0.213026i	$0.931668\pi$
$788$	−343.319			−0.435684
$789$	−55.3943	+	93.5147i	−0.0702083	+	0.118523i
$790$		0			0
$791$		−	59.2098i		−	0.0748543i
$792$	189.430	−	103.789i	0.239179	−	0.131047i
$793$		−	539.473i		−	0.680294i
$794$		−	302.642i		−	0.381161i
$795$		0			0
$796$	−70.1580			−0.0881382
$797$	550.520			0.690740			0.345370	−	0.938467i	$-0.387753\pi$
$797$	550.520			0.690740			0.345370	+	0.938467i	$0.387753\pi$
$798$	737.165	+	436.666i	0.923765	+	0.547201i
$799$	−1393.81			−1.74445
$800$		0			0
$801$	−479.684	+	262.820i	−0.598856	+	0.328115i
$802$		−	642.841i		−	0.801548i
$803$	746.258			0.929337
$804$	−570.228	−	337.780i	−0.709239	−	0.420124i
$805$		0			0
$806$			113.137i			0.140369i
$807$	−1362.95	−	807.354i	−1.68891	−	1.00044i
$808$		−	136.211i		−	0.168578i
$809$		−	560.288i		−	0.692569i	−0.938130	−	0.346284i	$-0.887443\pi$
$809$		−	560.288i		−	0.692569i	0.938130	−	0.346284i	$-0.112557\pi$
$810$		0			0
$811$	−237.842			−0.293270			−0.146635	−	0.989191i	$-0.546844\pi$
$811$	−237.842			−0.293270			−0.146635	+	0.989191i	$0.546844\pi$
$812$	401.786			0.494810
$813$	−727.624	+	1228.35i	−0.894987	+	1.51089i
$814$	−191.368			−0.235096
$815$		0			0
$816$	185.842	−	313.732i	0.227748	−	0.384475i
$817$		−	390.053i		−	0.477421i
$818$	811.535			0.992097
$819$	−323.772	−	590.930i	−0.395326	−	0.721526i
$820$		0			0
$821$		−	65.4816i		−	0.0797584i	−0.999205	−	0.0398792i	$-0.987303\pi$
$821$		−	65.4816i		−	0.0797584i	0.999205	−	0.0398792i	$-0.0126973\pi$
$822$	−206.531	+	348.658i	−0.251254	+	0.424158i
$823$		−	521.512i		−	0.633673i	−0.948480	−	0.316836i	$-0.897379\pi$
$823$		−	521.512i		−	0.633673i	0.948480	−	0.316836i	$-0.102621\pi$
$824$		−	397.133i		−	0.481958i
$825$		0			0
$826$	254.947			0.308652
$827$	987.512			1.19409			0.597045	−	0.802208i	$-0.296342\pi$
$827$	987.512			1.19409			0.597045	+	0.802208i	$0.296342\pi$
$828$	−79.3449	−	144.816i	−0.0958272	−	0.174898i
$829$	−333.631			−0.402450			−0.201225	−	0.979545i	$-0.564492\pi$
$829$	−333.631			−0.402450			−0.201225	+	0.979545i	$0.564492\pi$
$830$		0			0
$831$	485.662	+	287.686i	0.584431	+	0.346193i
$832$			80.0000i			0.0961538i
$833$	−214.309			−0.257274
$834$	166.097	−	280.399i	0.199157	−	0.336210i
$835$		0			0
$836$		−	457.758i		−	0.547558i
$837$	−215.878	−	7.24555i	−0.257919	−	0.00865657i
$838$			138.474i			0.165243i
$839$		−	129.363i		−	0.154187i	−0.997024	−	0.0770934i	$-0.975436\pi$
$839$		−	129.363i		−	0.154187i	0.997024	−	0.0770934i	$-0.0245640\pi$
$840$		0			0
$841$	121.000			0.143876
$842$	1014.44			1.20479
$843$	−63.0629	−	37.3559i	−0.0748077	−	0.0443130i
$844$	−116.316			−0.137815
$845$		0			0
$846$	280.527	+	512.001i	0.331592	+	0.605202i
$847$		−	366.855i		−	0.433123i
$848$	−121.548			−0.143335
$849$	−512.254	−	303.438i	−0.603362	−	0.357407i
$850$		0			0
$851$			146.297i			0.171912i
$852$	80.4984	+	47.6840i	0.0944817	+	0.0559671i
$853$		−	1080.42i		−	1.26661i	−0.773902	−	0.633306i	$-0.781697\pi$
$853$		−	1080.42i		−	1.26661i	0.773902	−	0.633306i	$-0.218303\pi$
$854$			571.193i			0.668845i
$855$		0			0
$856$	121.947			0.142462
$857$	702.548			0.819776			0.409888	−	0.912136i	$-0.365568\pi$
$857$	702.548			0.819776			0.409888	+	0.912136i	$0.365568\pi$
$858$	−183.475	+	309.737i	−0.213841	+	0.360998i
$859$	281.132			0.327278			0.163639	−	0.986520i	$-0.447677\pi$
$859$	281.132			0.327278			0.163639	+	0.986520i	$0.447677\pi$
$860$		0			0
$861$	542.105	−	915.163i	0.629623	−	1.06291i
$862$		−	414.474i		−	0.480828i
$863$	−419.221			−0.485772			−0.242886	−	0.970055i	$-0.578094\pi$
$863$	−419.221			−0.485772			−0.242886	+	0.970055i	$0.578094\pi$
$864$	−152.649	−	5.12338i	−0.176677	−	0.00592984i
$865$		0			0
$866$		−	689.466i		−	0.796150i
$867$	969.924	−	1637.39i	1.11871	−	1.88857i
$868$		−	119.789i		−	0.138006i
$869$			398.585i			0.458671i
$870$		0			0
$871$	1104.60			1.26820
$872$	−378.562			−0.434131
$873$	284.561	−	155.912i	0.325958	−	0.178593i
$874$	−349.947			−0.400397
$875$		0			0
$876$	−454.009	−	268.936i	−0.518275	−	0.307005i
$877$			1079.42i			1.23081i	0.788211	+	0.615405i	$0.211008\pi$
$877$			1079.42i			1.23081i	−0.788211	+	0.615405i	$0.788992\pi$
$878$	−363.788			−0.414337
$879$	785.618	−	1326.25i	0.893763	−	1.50882i
$880$		0			0
$881$			748.212i			0.849275i	0.905363	+	0.424638i	$0.139599\pi$
$881$			748.212i			0.849275i	−0.905363	+	0.424638i	$0.860401\pi$
$882$	43.1330	+	78.7238i	0.0489037	+	0.0892561i
$883$			875.749i			0.991788i	0.868383	+	0.495894i	$0.165160\pi$
$883$			875.749i			0.991788i	−0.868383	+	0.495894i	$0.834840\pi$
$884$			607.739i			0.687488i
$885$		0			0
$886$	414.500			0.467833
$887$	1015.05			1.14436			0.572182	−	0.820127i	$-0.306097\pi$
$887$	1015.05			1.14436			0.572182	+	0.820127i	$0.306097\pi$
$888$	116.425	+	68.9651i	0.131109	+	0.0776634i
$889$	−1006.68			−1.13238
$890$		0			0
$891$	−579.263	−	369.928i	−0.650126	−	0.415183i
$892$		−	198.763i		−	0.222828i
$893$	1237.25			1.38550
$894$	1008.34	+	597.300i	1.12790	+	0.668121i
$895$		0			0
$896$		−	84.7038i		−	0.0945355i
$897$	236.788	+	140.263i	0.263977	+	0.156369i
$898$		−	828.184i		−	0.922254i
$899$			214.663i			0.238779i
$900$		0			0
$901$	−923.368			−1.02483
$902$	−568.290			−0.630034
$903$	165.530	−	279.443i	0.183312	−	0.309460i
$904$	22.3687			0.0247441
$905$		0			0
$906$	39.0349	−	65.8973i	0.0430849	−	0.0727343i
$907$			1504.70i			1.65898i	0.558520	+	0.829491i	$0.311369\pi$
$907$			1504.70i			1.65898i	−0.558520	+	0.829491i	$0.688631\pi$
$908$	433.903			0.477867
$909$	−380.105	+	208.261i	−0.418158	+	0.229110i
$910$		0			0
$911$			1002.19i			1.10010i	0.835131	+	0.550051i	$0.185392\pi$
$911$			1002.19i			1.10010i	−0.835131	+	0.550051i	$0.814608\pi$
$912$	−164.967	+	278.491i	−0.180885	+	0.305363i
$913$			221.842i			0.242981i
$914$		−	1149.83i		−	1.25802i
$915$		0			0
$916$	−651.368			−0.711100
$917$	−1650.05			−1.79940
$918$	−1159.64	−	38.9210i	−1.26322	−	0.0423976i
$919$	780.289			0.849063			0.424532	−	0.905413i	$-0.360439\pi$
$919$	780.289			0.849063			0.424532	+	0.905413i	$0.360439\pi$
$920$		0			0
$921$	−29.3772	−	17.4019i	−0.0318971	−	0.0188945i
$922$		−	783.579i		−	0.849868i
$923$	−155.936			−0.168945
$924$	194.263	−	327.949i	0.210242	−	0.354923i
$925$		0			0
$926$			636.005i			0.686830i
$927$	−1108.23	+	607.201i	−1.19550	+	0.655018i
$928$			151.789i			0.163566i
$929$			1093.84i			1.17744i	0.808339	+	0.588718i	$0.200367\pi$
$929$			1093.84i			1.17744i	−0.808339	+	0.588718i	$0.799633\pi$
$930$		0			0
$931$	190.236			0.204335
$932$	−103.424			−0.110970
$933$	1338.98	+	793.157i	1.43513	+	0.850115i
$934$	−43.4477			−0.0465179
$935$		0			0
$936$	223.246	−	122.317i	0.238510	−	0.130680i
$937$		−	407.947i		−	0.435376i	−0.976018	−	0.217688i	$-0.930148\pi$
$937$		−	407.947i		−	0.435376i	0.976018	−	0.217688i	$-0.0698515\pi$
$938$	−1169.55			−1.24686
$939$	119.548	+	70.8154i	0.127314	+	0.0754157i
$940$		0			0
$941$		−	671.008i		−	0.713079i	−0.934280	−	0.356540i	$-0.883956\pi$
$941$		−	671.008i		−	0.713079i	0.934280	−	0.356540i	$-0.116044\pi$
$942$	379.053	+	224.535i	0.402391	+	0.238360i
$943$			434.447i			0.460707i
$944$			96.3155i			0.102029i
$945$		0			0
$946$	−173.526			−0.183431
$947$	−1608.13			−1.69813			−0.849064	−	0.528290i	$-0.822833\pi$
$947$	−1608.13			−1.69813			−0.849064	+	0.528290i	$0.822833\pi$
$948$	143.642	−	242.491i	0.151521	−	0.255792i
$949$	879.473			0.926737
$950$		0			0
$951$	59.7758	−	100.911i	0.0628557	−	0.106111i
$952$		−	643.473i		−	0.675917i
$953$	695.440			0.729737			0.364869	−	0.931059i	$-0.381114\pi$
$953$	695.440			0.729737			0.364869	+	0.931059i	$0.381114\pi$
$954$	185.842	+	339.188i	0.194803	+	0.355543i
$955$		0			0
$956$			820.095i			0.857840i
$957$	−348.120	+	587.684i	−0.363762	+	0.614090i
$958$		−	1039.79i		−	1.08538i
$959$			715.107i			0.745680i
$960$		0			0
$961$	−897.000			−0.933403
$962$	−225.529			−0.234438
$963$	−186.453	−	340.302i	−0.193617	−	0.353377i
$964$	891.052			0.924328
$965$		0			0
$966$	−250.710	−	148.511i	−0.259534	−	0.153738i
$967$		−	1030.07i		−	1.06522i	−0.846361	−	0.532609i	$-0.821212\pi$
$967$		−	1030.07i		−	1.06522i	0.846361	−	0.532609i	$-0.178788\pi$
$968$	138.593			0.143175
$969$	−1253.21	+	2115.63i	−1.29330	+	2.18331i
$970$		0			0
$971$		−	1165.24i		−	1.20004i	−0.799986	−	0.600019i	$-0.795160\pi$
$971$		−	1165.24i		−	1.20004i	0.799986	−	0.600019i	$-0.204840\pi$
$972$	219.097	+	433.811i	0.225409	+	0.446308i
$973$		−	575.106i		−	0.591065i
$974$		−	130.982i		−	0.134479i
$975$		0			0
$976$	−215.789			−0.221096
$977$	726.440			0.743541			0.371771	−	0.928325i	$-0.378751\pi$
$977$	726.440			0.743541			0.371771	+	0.928325i	$0.378751\pi$
$978$	41.5457	+	24.6100i	0.0424802	+	0.0251636i
$979$	515.684			0.526746
$980$		0			0
$981$	578.807	+	1056.40i	0.590017	+	1.07686i
$982$			1270.42i			1.29371i
$983$	−1024.21			−1.04192			−0.520960	−	0.853581i	$-0.674426\pi$
$983$	−1024.21			−1.04192			−0.520960	+	0.853581i	$0.674426\pi$
$984$	345.737	+	204.800i	0.351358	+	0.208130i
$985$		0			0
$986$			1153.10i			1.16948i
$987$	886.395	+	525.064i	0.898070	+	0.531980i
$988$		−	539.473i		−	0.546026i
$989$			132.657i			0.134133i
$990$		0			0
$991$	−1797.89			−1.81422			−0.907111	−	0.420892i	$-0.861717\pi$
$991$	−1797.89			−1.81422			−0.907111	+	0.420892i	$0.861717\pi$
$992$	45.2548			0.0456198
$993$	−681.031	+	1149.69i	−0.685832	+	1.15780i
$994$	165.105			0.166101
$995$		0			0
$996$	79.9473	−	134.964i	0.0802684	−	0.135506i
$997$			901.368i			0.904080i	0.891998	+	0.452040i	$0.149304\pi$
$997$			901.368i			0.904080i	−0.891998	+	0.452040i	$0.850696\pi$
$998$	−193.636			−0.194024
$999$	14.4434	−	430.336i	0.0144579	−	0.430766i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.3.b.b.149.7		8
3.2	odd	2	inner	150.3.b.b.149.1		8
4.3	odd	2		1200.3.c.k.449.4		8
5.2	odd	4		150.3.d.c.101.3		4
5.3	odd	4		30.3.d.a.11.2	✓	4
5.4	even	2	inner	150.3.b.b.149.2		8
12.11	even	2		1200.3.c.k.449.6		8
15.2	even	4		150.3.d.c.101.1		4
15.8	even	4		30.3.d.a.11.4	yes	4
15.14	odd	2	inner	150.3.b.b.149.8		8
20.3	even	4		240.3.l.c.161.1		4
20.7	even	4		1200.3.l.u.401.4		4
20.19	odd	2		1200.3.c.k.449.5		8
40.3	even	4		960.3.l.f.641.4		4
40.13	odd	4		960.3.l.e.641.1		4
45.13	odd	12		810.3.h.a.431.3		8
45.23	even	12		810.3.h.a.431.2		8
45.38	even	12		810.3.h.a.701.3		8
45.43	odd	12		810.3.h.a.701.2		8
60.23	odd	4		240.3.l.c.161.2		4
60.47	odd	4		1200.3.l.u.401.3		4
60.59	even	2		1200.3.c.k.449.3		8
120.53	even	4		960.3.l.e.641.2		4
120.83	odd	4		960.3.l.f.641.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.d.a.11.2	✓	4	5.3	odd	4
30.3.d.a.11.4	yes	4	15.8	even	4
150.3.b.b.149.1		8	3.2	odd	2	inner
150.3.b.b.149.2		8	5.4	even	2	inner
150.3.b.b.149.7		8	1.1	even	1	trivial
150.3.b.b.149.8		8	15.14	odd	2	inner
150.3.d.c.101.1		4	15.2	even	4
150.3.d.c.101.3		4	5.2	odd	4
240.3.l.c.161.1		4	20.3	even	4
240.3.l.c.161.2		4	60.23	odd	4
810.3.h.a.431.2		8	45.23	even	12
810.3.h.a.431.3		8	45.13	odd	12
810.3.h.a.701.2		8	45.43	odd	12
810.3.h.a.701.3		8	45.38	even	12
960.3.l.e.641.1		4	40.13	odd	4
960.3.l.e.641.2		4	120.53	even	4
960.3.l.f.641.3		4	120.83	odd	4
960.3.l.f.641.4		4	40.3	even	4
1200.3.c.k.449.3		8	60.59	even	2
1200.3.c.k.449.4		8	4.3	odd	2
1200.3.c.k.449.5		8	20.19	odd	2
1200.3.c.k.449.6		8	12.11	even	2
1200.3.l.u.401.3		4	60.47	odd	4
1200.3.l.u.401.4		4	20.7	even	4

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	150.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +(1.52896 - 2.58114i) q^{3} +2.00000 q^{4} +(2.16228 - 3.65028i) q^{6} -7.48683i q^{7} +2.82843 q^{8} +(-4.32456 - 7.89292i) q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +(1.52896 - 2.58114i) q^{3} +2.00000 q^{4} +(2.16228 - 3.65028i) q^{6} -7.48683i q^{7} +2.82843 q^{8} +(-4.32456 - 7.89292i) q^{9} +8.48528i q^{11} +(3.05792 - 5.16228i) q^{12} +10.0000i q^{13} -10.5880i q^{14} +4.00000 q^{16} +30.3870 q^{17} +(-6.11584 - 11.1623i) q^{18} -26.9737 q^{19} +(-19.3246 - 11.4471i) q^{21} +12.0000i q^{22} +9.17377 q^{23} +(4.32456 - 7.30056i) q^{24} +14.1421i q^{26} +(-26.9848 - 0.905694i) q^{27} -14.9737i q^{28} +26.8328i q^{29} +8.00000 q^{31} +5.65685 q^{32} +(21.9017 + 12.9737i) q^{33} +42.9737 q^{34} +(-8.64911 - 15.7858i) q^{36} +15.9473i q^{37} -38.1465 q^{38} +(25.8114 + 15.2896i) q^{39} +47.3575i q^{41} +(-27.3290 - 16.1886i) q^{42} +14.4605i q^{43} +16.9706i q^{44} +12.9737 q^{46} -45.8688 q^{47} +(6.11584 - 10.3246i) q^{48} -7.05267 q^{49} +(46.4605 - 78.4330i) q^{51} +20.0000i q^{52} -30.3870 q^{53} +(-38.1623 - 1.28084i) q^{54} -21.1760i q^{56} +(-41.2417 + 69.6228i) q^{57} +37.9473i q^{58} +24.0789i q^{59} -53.9473 q^{61} +11.3137 q^{62} +(-59.0930 + 32.3772i) q^{63} +8.00000 q^{64} +(30.9737 + 18.3475i) q^{66} -110.460i q^{67} +60.7739 q^{68} +(14.0263 - 23.6788i) q^{69} +15.5936i q^{71} +(-12.2317 - 22.3246i) q^{72} -87.9473i q^{73} +22.5529i q^{74} -53.9473 q^{76} +63.5279 q^{77} +(36.5028 + 21.6228i) q^{78} +46.9737 q^{79} +(-43.5964 + 68.2668i) q^{81} +66.9737i q^{82} +26.1443 q^{83} +(-38.6491 - 22.8942i) q^{84} +20.4502i q^{86} +(69.2592 + 41.0263i) q^{87} +24.0000i q^{88} -60.7739i q^{89} +74.8683 q^{91} +18.3475 q^{92} +(12.2317 - 20.6491i) q^{93} -64.8683 q^{94} +(8.64911 - 14.6011i) q^{96} +36.0527i q^{97} -9.97398 q^{98} +(66.9737 - 36.6951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{4} - 8 q^{6} + 16 q^{9}+O(q^{10}) \) 8 * q + 16 * q^4 - 8 * q^6 + 16 * q^9	\( 8 q + 16 q^{4} - 8 q^{6} + 16 q^{9} + 32 q^{16} - 64 q^{19} - 104 q^{21} - 16 q^{24} + 64 q^{31} + 192 q^{34} + 32 q^{36} + 80 q^{39} - 48 q^{46} - 360 q^{49} + 144 q^{51} - 280 q^{54} - 128 q^{61} + 64 q^{64} + 96 q^{66} + 264 q^{69} - 128 q^{76} + 224 q^{79} + 56 q^{81} - 208 q^{84} - 160 q^{91} + 240 q^{94} - 32 q^{96} + 384 q^{99}+O(q^{100}) \) 8 * q + 16 * q^4 - 8 * q^6 + 16 * q^9 + 32 * q^16 - 64 * q^19 - 104 * q^21 - 16 * q^24 + 64 * q^31 + 192 * q^34 + 32 * q^36 + 80 * q^39 - 48 * q^46 - 360 * q^49 + 144 * q^51 - 280 * q^54 - 128 * q^61 + 64 * q^64 + 96 * q^66 + 264 * q^69 - 128 * q^76 + 224 * q^79 + 56 * q^81 - 208 * q^84 - 160 * q^91 + 240 * q^94 - 32 * q^96 + 384 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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