LMFDB - Embedded newform 150.3.b.b.149.8

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

$q$-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	$0.179603\pi$
$7$			7.48683i			1.06955i	−0.844995	+	0.534774i	$0.820397\pi$
$8$	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	$-0.873962\pi$
$11$		−	8.48528i		−	0.771389i	0.922627	−	0.385695i	$-0.126038\pi$
$12$	3.05792	+	5.16228i	0.254827	+	0.430190i
$13$		−	10.0000i		−	0.769231i	−0.923077	−	0.384615i	$-0.874334\pi$
$13$		−	10.0000i		−	0.769231i	0.923077	−	0.384615i	$-0.125666\pi$
$14$			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	$-0.846904\pi$
$29$		−	26.8328i		−	0.925270i	0.886549	−	0.462635i	$-0.153096\pi$
$30$		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	$-0.930860\pi$
$37$		−	15.9473i		−	0.431009i	0.976503	−	0.215504i	$-0.0691396\pi$
$38$	−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	$-0.804016\pi$
$41$		−	47.3575i		−	1.15506i	0.816369	−	0.577531i	$-0.195984\pi$
$42$	−27.3290	+	16.1886i	−0.650692	+	0.385443i
$43$		−	14.4605i		−	0.336291i	−0.985762	−	0.168145i	$-0.946222\pi$
$43$		−	14.4605i		−	0.336291i	0.985762	−	0.168145i	$-0.0537778\pi$
$44$		−	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	$-0.934587\pi$
$59$		−	24.0789i		−	0.408116i	0.978959	−	0.204058i	$-0.0654132\pi$
$60$		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	$0.308449\pi$
$67$			110.460i			1.64866i	−0.566107	+	0.824332i	$0.691551\pi$
$68$	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	$-0.964974\pi$
$71$		−	15.5936i		−	0.219628i	0.993952	−	0.109814i	$-0.0350255\pi$
$72$	−12.2317	+	22.3246i	−0.169885	+	0.310063i
$73$			87.9473i			1.20476i	0.798210	+	0.602379i	$0.205780\pi$
$73$			87.9473i			1.20476i	−0.798210	+	0.602379i	$0.794220\pi$
$74$		−	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	$0.110910\pi$
$89$			60.7739i			0.682853i	−0.939908	+	0.341427i	$0.889090\pi$
$90$		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	$-0.940500\pi$
$97$		−	36.0527i		−	0.371677i	0.982580	−	0.185838i	$-0.0595001\pi$
$98$	−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	$0.0766245\pi$
$101$			48.1577i			0.476809i	−0.971166	+	0.238405i	$0.923376\pi$
$102$	65.7051	+	110.921i	0.644167	+	1.08746i
$103$			140.408i			1.36318i	0.731733	+	0.681591i	$0.238712\pi$
$103$			140.408i			1.36318i	−0.731733	+	0.681591i	$0.761288\pi$
$104$		−	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	$0.177572\pi$
$127$			134.460i			1.05874i	−0.848390	+	0.529372i	$0.822428\pi$
$128$	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	$0.318149\pi$
$131$			220.394i			1.68240i	−0.540727	+	0.841198i	$0.681851\pi$
$132$	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	$-0.622405\pi$
$149$		−	276.237i		−	1.85394i	0.375139	−	0.926969i	$-0.377595\pi$
$150$		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	$-0.892713\pi$
$157$		−	103.842i		−	0.661414i	0.943733	−	0.330707i	$-0.107287\pi$
$158$	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	$-0.988885\pi$
$163$		−	11.3815i		−	0.0698251i	0.999390	−	0.0349126i	$-0.0111153\pi$
$164$		−	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	$-0.938231\pi$
$179$		−	69.0358i		−	0.385675i	0.981231	−	0.192837i	$-0.0617690\pi$
$180$		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	$-0.908147\pi$
$191$		−	108.708i		−	0.569153i	0.958653	−	0.284577i	$-0.0918530\pi$
$192$	12.2317	+	20.6491i	0.0637067	+	0.107547i
$193$		−	167.947i		−	0.870193i	−0.900384	−	0.435097i	$-0.856714\pi$
$193$		−	167.947i		−	0.870193i	0.900384	−	0.435097i	$-0.143286\pi$
$194$		−	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	$0.0715290\pi$
$223$			99.3815i			0.445657i	−0.974858	+	0.222828i	$0.928471\pi$
$224$			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	$-0.671806\pi$
$239$		−	410.047i		−	1.71568i	0.513917	−	0.857840i	$-0.328194\pi$
$240$		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	$0.156770\pi$
$251$			237.364i			0.945675i	−0.881150	+	0.472838i	$0.843230\pi$
$252$	−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	$0.438659\pi$
$269$			528.041i			1.96298i	−0.191518	+	0.981489i	$0.561341\pi$
$270$		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	$-0.889696\pi$
$277$		−	188.158i		−	0.679271i	0.940557	−	0.339635i	$-0.110304\pi$
$278$	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	$0.0138424\pi$
$281$			24.4322i			0.0869473i	−0.999055	+	0.0434736i	$0.986158\pi$
$282$	−99.1812	−	167.434i	−0.351706	−	0.593738i
$283$			198.460i			0.701274i	0.936511	+	0.350637i	$0.114035\pi$
$283$			198.460i			0.701274i	−0.936511	+	0.350637i	$0.885965\pi$
$284$		−	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	$0.00590073\pi$
$307$			11.3815i			0.0370733i	−0.999828	+	0.0185366i	$0.994099\pi$
$308$	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	$-0.686038\pi$
$311$		−	518.756i		−	1.66802i	0.551746	−	0.834012i	$-0.313962\pi$
$312$	73.0056	−	43.2456i	0.233992	−	0.138608i
$313$		−	46.3160i		−	0.147974i	−0.997259	−	0.0739872i	$-0.976428\pi$
$313$		−	46.3160i		−	0.147974i	0.997259	−	0.0739872i	$-0.0235724\pi$
$314$		−	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	$-0.839471\pi$
$337$		−	325.684i		−	0.966421i	0.875504	−	0.483211i	$-0.160529\pi$
$338$	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	$0.124768\pi$
$359$			274.283i			0.764019i	−0.924158	+	0.382010i	$0.875232\pi$
$360$		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	$-0.783385\pi$
$367$		−	461.828i		−	1.25839i	0.777248	−	0.629194i	$-0.216615\pi$
$368$	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	$-0.770791\pi$
$373$		−	491.947i		−	1.31889i	0.751751	−	0.659447i	$-0.229209\pi$
$374$		−	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	$-0.712586\pi$
$389$		−	610.847i		−	1.57030i	0.619306	−	0.785150i	$-0.287414\pi$
$390$		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	$0.0868655\pi$
$397$			214.000i			0.539043i	−0.962994	+	0.269521i	$0.913135\pi$
$398$	−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	$0.191811\pi$
$401$			454.557i			1.13356i	−0.823869	+	0.566780i	$0.808189\pi$
$402$	−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	$-0.962722\pi$
$419$		−	97.9159i		−	0.233690i	0.993150	−	0.116845i	$-0.0372780\pi$
$420$		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	$0.110426\pi$
$431$			293.077i			0.679994i	−0.940427	+	0.339997i	$0.889574\pi$
$432$	−107.939	+	3.62278i	−0.249859	+	0.00838606i
$433$			487.526i			1.12593i	0.826482	+	0.562963i	$0.190339\pi$
$433$			487.526i			1.12593i	−0.826482	+	0.562963i	$0.809661\pi$
$434$			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	$0.226125\pi$
$449$			585.614i			1.30426i	−0.758106	+	0.652132i	$0.773875\pi$
$450$		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	$0.348984\pi$
$457$			813.052i			1.77911i	−0.456831	+	0.889554i	$0.651016\pi$
$458$	−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	$0.205210\pi$
$461$			554.074i			1.20190i	−0.799288	+	0.600948i	$0.794790\pi$
$462$	137.365	+	231.895i	0.297327	+	0.501937i
$463$		−	449.723i		−	0.971324i	−0.874147	−	0.485662i	$-0.838579\pi$
$463$		−	449.723i		−	0.971324i	0.874147	−	0.485662i	$-0.161421\pi$
$464$		−	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	$0.278488\pi$
$479$			735.242i			1.53495i	−0.641078	+	0.767476i	$0.721512\pi$
$480$		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	$0.0303142\pi$
$487$			92.6185i			0.190182i	−0.995469	+	0.0950909i	$0.969686\pi$
$488$	−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	$-0.632357\pi$
$491$		−	898.323i		−	1.82958i	0.403933	−	0.914789i	$-0.367643\pi$
$492$	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	$-0.932883\pi$
$509$		−	213.062i		−	0.418590i	0.977853	−	0.209295i	$-0.0671168\pi$
$510$		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	$0.000977795\pi$
$521$			3.20085i			0.00614366i	−0.999995	+	0.00307183i	$0.999022\pi$
$522$	299.515	+	164.105i	0.573784	+	0.314378i
$523$			966.644i			1.84827i	0.382069	+	0.924134i	$0.375212\pi$
$523$			966.644i			1.84827i	−0.382069	+	0.924134i	$0.624788\pi$
$524$			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	$0.0912787\pi$
$547$			309.434i			0.565693i	−0.959165	+	0.282847i	$0.908721\pi$
$548$	−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	$0.0438542\pi$
$569$			156.289i			0.274673i	−0.990524	+	0.137337i	$0.956146\pi$
$570$		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	$-0.847195\pi$
$577$		−	532.947i		−	0.923651i	0.886971	−	0.461826i	$-0.152805\pi$
$578$	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	$-0.800037\pi$
$599$		−	704.055i		−	1.17538i	0.809085	−	0.587692i	$-0.199963\pi$
$600$		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	$0.234814\pi$
$607$			816.513i			1.34516i	−0.740024	+	0.672581i	$0.765186\pi$
$608$	−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	$-0.940123\pi$
$613$		−	229.263i		−	0.374001i	0.982360	−	0.187001i	$-0.0598766\pi$
$614$			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	$0.0162656\pi$
$641$			65.4816i			0.102155i	−0.998695	+	0.0510777i	$0.983734\pi$
$642$	93.2264	+	157.381i	0.145212	+	0.245143i
$643$		−	428.619i		−	0.666592i	−0.942822	−	0.333296i	$-0.891839\pi$
$643$		−	428.619i		−	0.666592i	0.942822	−	0.333296i	$-0.108161\pi$
$644$			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	$-0.955717\pi$
$659$		−	182.769i		−	0.277343i	0.990338	−	0.138671i	$-0.0442831\pi$
$660$		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	$0.0437884\pi$
$673$			184.579i			0.274264i	−0.990553	+	0.137132i	$0.956212\pi$
$674$		−	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	$-0.584620\pi$
$701$		−	1352.75i		−	1.92974i	0.262721	−	0.964872i	$-0.415380\pi$
$702$	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	$-0.878155\pi$
$719$		−	537.103i		−	0.747014i	0.927627	−	0.373507i	$-0.121845\pi$
$720$		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	$0.279144\pi$
$727$			1117.83i			1.53759i	−0.639495	+	0.768795i	$0.720856\pi$
$728$	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	$0.00163411\pi$
$733$			7.52599i			0.0102674i	−0.999987	+	0.00513369i	$0.998366\pi$
$734$		−	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	$0.193143\pi$
$757$			863.315i			1.14044i	−0.821491	+	0.570221i	$0.806857\pi$
$758$	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	$-0.877677\pi$
$761$		−	570.597i		−	0.749800i	0.927065	−	0.374900i	$-0.122323\pi$
$762$	−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	$-0.931668\pi$
$787$		−	335.303i		−	0.426052i	0.977046	−	0.213026i	$-0.0683320\pi$
$788$	−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	$0.112557\pi$
$809$			560.288i			0.692569i	−0.938130	+	0.346284i	$0.887443\pi$
$810$		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	$0.0126973\pi$
$821$			65.4816i			0.0797584i	−0.999205	+	0.0398792i	$0.987303\pi$
$822$	−206.531	−	348.658i	−0.251254	−	0.424158i
$823$			521.512i			0.633673i	0.948480	+	0.316836i	$0.102621\pi$
$823$			521.512i			0.633673i	−0.948480	+	0.316836i	$0.897379\pi$
$824$			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	$0.0245640\pi$
$839$			129.363i			0.154187i	−0.997024	+	0.0770934i	$0.975436\pi$
$840$		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	$0.218303\pi$
$853$			1080.42i			1.26661i	−0.773902	+	0.633306i	$0.781697\pi$
$854$		−	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	$-0.788992\pi$
$877$		−	1079.42i		−	1.23081i	0.788211	−	0.615405i	$-0.211008\pi$
$878$	−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	$-0.860401\pi$
$881$		−	748.212i		−	0.849275i	0.905363	−	0.424638i	$-0.139599\pi$
$882$	43.1330	−	78.7238i	0.0489037	−	0.0892561i
$883$		−	875.749i		−	0.991788i	−0.868383	−	0.495894i	$-0.834840\pi$
$883$		−	875.749i		−	0.991788i	0.868383	−	0.495894i	$-0.165160\pi$
$884$		−	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	$-0.688631\pi$
$907$		−	1504.70i		−	1.65898i	0.558520	−	0.829491i	$-0.311369\pi$
$908$	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	$-0.814608\pi$
$911$		−	1002.19i		−	1.10010i	0.835131	−	0.550051i	$-0.185392\pi$
$912$	−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	$-0.799633\pi$
$929$		−	1093.84i		−	1.17744i	0.808339	−	0.588718i	$-0.200367\pi$
$930$		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	$0.0698515\pi$
$937$			407.947i			0.435376i	−0.976018	+	0.217688i	$0.930148\pi$
$938$	−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	$0.116044\pi$
$941$			671.008i			0.713079i	−0.934280	+	0.356540i	$0.883956\pi$
$942$	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	$0.178788\pi$
$967$			1030.07i			1.06522i	−0.846361	+	0.532609i	$0.821212\pi$
$968$	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	$0.204840\pi$
$971$			1165.24i			1.20004i	−0.799986	+	0.600019i	$0.795160\pi$
$972$	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	$-0.850696\pi$
$997$		−	901.368i		−	0.904080i	0.891998	−	0.452040i	$-0.149304\pi$
$998$	−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.149.8		8
3.2	odd	2	inner	150.3.b.b.149.2		8
4.3	odd	2		1200.3.c.k.449.3		8
5.2	odd	4		30.3.d.a.11.4	yes	4
5.3	odd	4		150.3.d.c.101.1		4
5.4	even	2	inner	150.3.b.b.149.1		8
12.11	even	2		1200.3.c.k.449.5		8
15.2	even	4		30.3.d.a.11.2	✓	4
15.8	even	4		150.3.d.c.101.3		4
15.14	odd	2	inner	150.3.b.b.149.7		8
20.3	even	4		1200.3.l.u.401.3		4
20.7	even	4		240.3.l.c.161.2		4
20.19	odd	2		1200.3.c.k.449.6		8
40.27	even	4		960.3.l.f.641.3		4
40.37	odd	4		960.3.l.e.641.2		4
45.2	even	12		810.3.h.a.701.2		8
45.7	odd	12		810.3.h.a.701.3		8
45.22	odd	12		810.3.h.a.431.2		8
45.32	even	12		810.3.h.a.431.3		8
60.23	odd	4		1200.3.l.u.401.4		4
60.47	odd	4		240.3.l.c.161.1		4
60.59	even	2		1200.3.c.k.449.4		8
120.77	even	4		960.3.l.e.641.1		4
120.107	odd	4		960.3.l.f.641.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.d.a.11.2	✓	4	15.2	even	4
30.3.d.a.11.4	yes	4	5.2	odd	4
150.3.b.b.149.1		8	5.4	even	2	inner
150.3.b.b.149.2		8	3.2	odd	2	inner
150.3.b.b.149.7		8	15.14	odd	2	inner
150.3.b.b.149.8		8	1.1	even	1	trivial
150.3.d.c.101.1		4	5.3	odd	4
150.3.d.c.101.3		4	15.8	even	4
240.3.l.c.161.1		4	60.47	odd	4
240.3.l.c.161.2		4	20.7	even	4
810.3.h.a.431.2		8	45.22	odd	12
810.3.h.a.431.3		8	45.32	even	12
810.3.h.a.701.2		8	45.2	even	12
810.3.h.a.701.3		8	45.7	odd	12
960.3.l.e.641.1		4	120.77	even	4
960.3.l.e.641.2		4	40.37	odd	4
960.3.l.f.641.3		4	40.27	even	4
960.3.l.f.641.4		4	120.107	odd	4
1200.3.c.k.449.3		8	4.3	odd	2
1200.3.c.k.449.4		8	60.59	even	2
1200.3.c.k.449.5		8	12.11	even	2
1200.3.c.k.449.6		8	20.19	odd	2
1200.3.l.u.401.3		4	20.3	even	4
1200.3.l.u.401.4		4	60.23	odd	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

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Representations

Groups

Database

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