LMFDB - Embedded newform 912.3.be.f.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,3,Mod(145,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("912.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	912.be (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.8502001097$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.92607408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 94x^{2} - 77x + 43 $ x^6 - 3x^5 + 20x^4 - 35x^3 + 94x^2 - 77*x + 43
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.1
Root			$0.500000 + 2.93068i$ of defining polynomial
Character	$\chi$	$=$	912.145
Dual form			912.3.be.f.673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{3} +(-3.20750 - 5.55555i) q^{5} +2.26281 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{3} +(-3.20750 - 5.55555i) q^{5} +2.26281 q^{7} +(1.50000 - 2.59808i) q^{9} +20.0928 q^{11} +(-0.135471 - 0.0782143i) q^{13} +(-9.62250 - 5.55555i) q^{15} +(12.3133 + 21.3272i) q^{17} +(18.9317 + 1.60945i) q^{19} +(3.39422 - 1.95965i) q^{21} +(2.62250 - 4.54230i) q^{23} +(-8.07609 + 13.9882i) q^{25} -5.19615i q^{27} +(-31.4573 - 18.1619i) q^{29} +17.1105i q^{31} +(30.1392 - 17.4009i) q^{33} +(-7.25797 - 12.5712i) q^{35} -42.7124i q^{37} -0.270942 q^{39} +(30.0928 - 17.3741i) q^{41} +(-12.5553 - 21.7464i) q^{43} -19.2450 q^{45} +(14.6778 - 25.4227i) q^{47} -43.8797 q^{49} +(36.9398 + 21.3272i) q^{51} +(48.4176 + 27.9539i) q^{53} +(-64.4476 - 111.627i) q^{55} +(29.7914 - 13.9812i) q^{57} +(29.9269 - 17.2783i) q^{59} +(27.3805 - 47.4244i) q^{61} +(3.39422 - 5.87896i) q^{63} +1.00349i q^{65} +(-66.0698 - 38.1454i) q^{67} -9.08459i q^{69} +(-63.6080 + 36.7241i) q^{71} +(-45.9053 - 79.5103i) q^{73} +27.9764i q^{75} +45.4662 q^{77} +(53.1300 - 30.6746i) q^{79} +(-4.50000 - 7.79423i) q^{81} +148.793 q^{83} +(78.9897 - 136.814i) q^{85} -62.9147 q^{87} +(-62.7829 - 36.2477i) q^{89} +(-0.306546 - 0.176984i) q^{91} +(14.8181 + 25.6657i) q^{93} +(-51.7820 - 110.338i) q^{95} +(-70.0326 + 40.4334i) q^{97} +(30.1392 - 52.2026i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{3} + 4 q^{5} + 22 q^{7} + 9 q^{9}+O(q^{10}) $ 6 * q + 9 * q^3 + 4 * q^5 + 22 * q^7 + 9 * q^9	$ 6 q + 9 q^{3} + 4 q^{5} + 22 q^{7} + 9 q^{9} + 36 q^{11} - 3 q^{13} + 12 q^{15} + 38 q^{17} + 10 q^{19} + 33 q^{21} - 54 q^{23} - 21 q^{25} - 102 q^{29} + 54 q^{33} + 24 q^{35} - 6 q^{39} + 96 q^{41} - 107 q^{43} + 24 q^{45} + 50 q^{47} - 48 q^{49} + 114 q^{51} - 90 q^{53} - 148 q^{55} - 3 q^{57} + 27 q^{61} + 33 q^{63} + 39 q^{67} - 84 q^{71} - 77 q^{73} + 260 q^{77} - 9 q^{79} - 27 q^{81} + 348 q^{83} + 68 q^{85} - 204 q^{87} - 72 q^{89} + 393 q^{91} + 129 q^{93} - 104 q^{95} - 228 q^{97} + 54 q^{99}+O(q^{100}) $ 6 * q + 9 * q^3 + 4 * q^5 + 22 * q^7 + 9 * q^9 + 36 * q^11 - 3 * q^13 + 12 * q^15 + 38 * q^17 + 10 * q^19 + 33 * q^21 - 54 * q^23 - 21 * q^25 - 102 * q^29 + 54 * q^33 + 24 * q^35 - 6 * q^39 + 96 * q^41 - 107 * q^43 + 24 * q^45 + 50 * q^47 - 48 * q^49 + 114 * q^51 - 90 * q^53 - 148 * q^55 - 3 * q^57 + 27 * q^61 + 33 * q^63 + 39 * q^67 - 84 * q^71 - 77 * q^73 + 260 * q^77 - 9 * q^79 - 27 * q^81 + 348 * q^83 + 68 * q^85 - 204 * q^87 - 72 * q^89 + 393 * q^91 + 129 * q^93 - 104 * q^95 - 228 * q^97 + 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$		0			0
$5$	−3.20750	−	5.55555i	−0.641500	−	1.11111i	−0.985098	−	0.171993i	$-0.944979\pi$
$5$	−3.20750	−	5.55555i	−0.641500	−	1.11111i	0.343598	−	0.939117i	$-0.388354\pi$
$6$		0			0
$7$	2.26281			0.323259			0.161629	−	0.986852i	$-0.448325\pi$
$7$	2.26281			0.323259			0.161629	+	0.986852i	$0.448325\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	20.0928			1.82662			0.913309	−	0.407267i	$-0.133518\pi$
$11$	20.0928			1.82662			0.913309	+	0.407267i	$0.133518\pi$
$12$		0			0
$13$	−0.135471	−	0.0782143i	−0.0104209	−	0.00601649i	0.494781	−	0.869018i	$-0.335248\pi$
$13$	−0.135471	−	0.0782143i	−0.0104209	−	0.00601649i	−0.505201	+	0.863001i	$0.668582\pi$
$14$		0			0
$15$	−9.62250	−	5.55555i	−0.641500	−	0.370370i
$16$		0			0
$17$	12.3133	+	21.3272i	0.724311	+	1.25454i	0.959257	+	0.282534i	$0.0911752\pi$
$17$	12.3133	+	21.3272i	0.724311	+	1.25454i	−0.234947	+	0.972008i	$0.575492\pi$
$18$		0			0
$19$	18.9317	+	1.60945i	0.996406	+	0.0847081i
$19$	18.9317	+	1.60945i	0.996406	+	0.0847081i
$20$		0			0
$21$	3.39422	−	1.95965i	0.161629	−	0.0933168i
$22$		0			0
$23$	2.62250	−	4.54230i	0.114022	−	0.197491i	−0.803367	−	0.595485i	$-0.796960\pi$
$23$	2.62250	−	4.54230i	0.114022	−	0.197491i	0.917388	+	0.397994i	$0.130293\pi$
$24$		0			0
$25$	−8.07609	+	13.9882i	−0.323044	+	0.559528i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	−31.4573	−	18.1619i	−1.08474	−	0.626272i	−0.152566	−	0.988293i	$-0.548754\pi$
$29$	−31.4573	−	18.1619i	−1.08474	−	0.626272i	−0.932170	+	0.362021i	$0.882087\pi$
$30$		0			0
$31$			17.1105i			0.551952i	0.961165	+	0.275976i	$0.0890010\pi$
$31$			17.1105i			0.551952i	−0.961165	+	0.275976i	$0.910999\pi$
$32$		0			0
$33$	30.1392	−	17.4009i	0.913309	−	0.527299i
$34$		0			0
$35$	−7.25797	−	12.5712i	−0.207370	−	0.359176i
$36$		0			0
$37$		−	42.7124i		−	1.15439i	−0.816607	−	0.577194i	$-0.804148\pi$
$37$		−	42.7124i		−	1.15439i	0.816607	−	0.577194i	$-0.195852\pi$
$38$		0			0
$39$	−0.270942			−0.00694724
$40$		0			0
$41$	30.0928	−	17.3741i	0.733971	−	0.423758i	−0.0859022	−	0.996304i	$-0.527377\pi$
$41$	30.0928	−	17.3741i	0.733971	−	0.423758i	0.819873	+	0.572545i	$0.194044\pi$
$42$		0			0
$43$	−12.5553	−	21.7464i	−0.291984	−	0.505731i	0.682295	−	0.731077i	$-0.260982\pi$
$43$	−12.5553	−	21.7464i	−0.291984	−	0.505731i	−0.974279	+	0.225346i	$0.927649\pi$
$44$		0			0
$45$	−19.2450			−0.427666
$46$		0			0
$47$	14.6778	−	25.4227i	0.312294	−	0.540909i	−0.666565	−	0.745447i	$-0.732236\pi$
$47$	14.6778	−	25.4227i	0.312294	−	0.540909i	0.978859	+	0.204538i	$0.0655693\pi$
$48$		0			0
$49$	−43.8797			−0.895504
$50$		0			0
$51$	36.9398	+	21.3272i	0.724311	+	0.418181i
$52$		0			0
$53$	48.4176	+	27.9539i	0.913540	+	0.527433i	0.881568	−	0.472056i	$-0.156488\pi$
$53$	48.4176	+	27.9539i	0.913540	+	0.527433i	0.0319716	+	0.999489i	$0.489821\pi$
$54$		0			0
$55$	−64.4476	−	111.627i	−1.17178	−	2.02957i
$56$		0			0
$57$	29.7914	−	13.9812i	0.522656	−	0.245284i
$58$		0			0
$59$	29.9269	−	17.2783i	0.507235	−	0.292852i	−0.224461	−	0.974483i	$-0.572062\pi$
$59$	29.9269	−	17.2783i	0.507235	−	0.292852i	0.731696	+	0.681631i	$0.238729\pi$
$60$		0			0
$61$	27.3805	−	47.4244i	0.448860	−	0.777448i	−0.549452	−	0.835525i	$-0.685164\pi$
$61$	27.3805	−	47.4244i	0.448860	−	0.777448i	0.998312	+	0.0580769i	$0.0184968\pi$
$62$		0			0
$63$	3.39422	−	5.87896i	0.0538765	−	0.0933168i
$64$		0			0
$65$			1.00349i			0.0154383i
$66$		0			0
$67$	−66.0698	−	38.1454i	−0.986117	−	0.569335i	−0.0820054	−	0.996632i	$-0.526132\pi$
$67$	−66.0698	−	38.1454i	−0.986117	−	0.569335i	−0.904111	+	0.427297i	$0.859466\pi$
$68$		0			0
$69$		−	9.08459i		−	0.131661i
$70$		0			0
$71$	−63.6080	+	36.7241i	−0.895887	+	0.517240i	−0.875863	−	0.482559i	$-0.839707\pi$
$71$	−63.6080	+	36.7241i	−0.895887	+	0.517240i	−0.0200233	+	0.999800i	$0.506374\pi$
$72$		0			0
$73$	−45.9053	−	79.5103i	−0.628840	−	1.08918i	−0.987785	−	0.155824i	$-0.950197\pi$
$73$	−45.9053	−	79.5103i	−0.628840	−	1.08918i	0.358945	−	0.933359i	$-0.383137\pi$
$74$		0			0
$75$			27.9764i			0.373019i
$76$		0			0
$77$	45.4662			0.590471
$78$		0			0
$79$	53.1300	−	30.6746i	0.672531	−	0.388286i	−0.124504	−	0.992219i	$-0.539734\pi$
$79$	53.1300	−	30.6746i	0.672531	−	0.388286i	0.797035	+	0.603933i	$0.206401\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	148.793			1.79268			0.896342	−	0.443363i	$-0.146215\pi$
$83$	148.793			1.79268			0.896342	+	0.443363i	$0.146215\pi$
$84$		0			0
$85$	78.9897	−	136.814i	0.929290	−	1.60958i
$86$		0			0
$87$	−62.9147			−0.723157
$88$		0			0
$89$	−62.7829	−	36.2477i	−0.705426	−	0.407278i	0.103939	−	0.994584i	$-0.466855\pi$
$89$	−62.7829	−	36.2477i	−0.705426	−	0.407278i	−0.809365	+	0.587306i	$0.800189\pi$
$90$		0			0
$91$	−0.306546	−	0.176984i	−0.00336864	−	0.00194488i
$92$		0			0
$93$	14.8181	+	25.6657i	0.159335	+	0.275976i
$94$		0			0
$95$	−51.7820	−	110.338i	−0.545074	−	1.16146i
$96$		0			0
$97$	−70.0326	+	40.4334i	−0.721986	+	0.416839i	−0.815483	−	0.578781i	$-0.803529\pi$
$97$	−70.0326	+	40.4334i	−0.721986	+	0.416839i	0.0934972	+	0.995620i	$0.470195\pi$
$98$		0			0
$99$	30.1392	−	52.2026i	0.304436	−	0.527299i
$100$		0			0
$101$	−76.6770	+	132.809i	−0.759178	+	1.31494i	0.184092	+	0.982909i	$0.441066\pi$
$101$	−76.6770	+	132.809i	−0.759178	+	1.31494i	−0.943270	+	0.332027i	$0.892268\pi$
$102$		0			0
$103$			168.948i			1.64027i	0.572169	+	0.820136i	$0.306102\pi$
$103$			168.948i			1.64027i	−0.572169	+	0.820136i	$0.693898\pi$
$104$		0			0
$105$	−21.7739	−	12.5712i	−0.207370	−	0.119725i
$106$		0			0
$107$			139.060i			1.29963i	0.760093	+	0.649815i	$0.225154\pi$
$107$			139.060i			1.29963i	−0.760093	+	0.649815i	$0.774846\pi$
$108$		0			0
$109$	−9.15888	+	5.28788i	−0.0840264	+	0.0485127i	−0.541424	−	0.840749i	$-0.682115\pi$
$109$	−9.15888	+	5.28788i	−0.0840264	+	0.0485127i	0.457398	+	0.889262i	$0.348781\pi$
$110$		0			0
$111$	−36.9900	−	64.0685i	−0.333243	−	0.577194i
$112$		0			0
$113$			69.1581i			0.612018i	0.952029	+	0.306009i	$0.0989938\pi$
$113$			69.1581i			0.612018i	−0.952029	+	0.306009i	$0.901006\pi$
$114$		0			0
$115$	−33.6466			−0.292579
$116$		0			0
$117$	−0.406413	+	0.234643i	−0.00347362	+	0.00200550i
$118$		0			0
$119$	27.8626	+	48.2595i	0.234140	+	0.405542i
$120$		0			0
$121$	282.721			2.33654
$122$		0			0
$123$	30.0928	−	52.1223i	0.244657	−	0.423758i
$124$		0			0
$125$	−56.7587			−0.454070
$126$		0			0
$127$	25.6547	+	14.8118i	0.202006	+	0.116628i	0.597591	−	0.801801i	$-0.296125\pi$
$127$	25.6547	+	14.8118i	0.202006	+	0.116628i	−0.395585	+	0.918429i	$0.629458\pi$
$128$		0			0
$129$	−37.6659	−	21.7464i	−0.291984	−	0.168577i
$130$		0			0
$131$	28.6526	+	49.6278i	0.218722	+	0.378838i	0.954418	−	0.298474i	$-0.0964777\pi$
$131$	28.6526	+	49.6278i	0.218722	+	0.378838i	−0.735695	+	0.677313i	$0.763144\pi$
$132$		0			0
$133$	42.8389	+	3.64189i	0.322097	+	0.0273826i
$134$		0			0
$135$	−28.8675	+	16.6667i	−0.213833	+	0.123457i
$136$		0			0
$137$	47.4499	−	82.1856i	0.346349	−	0.599895i	−0.639249	−	0.769000i	$-0.720755\pi$
$137$	47.4499	−	82.1856i	0.346349	−	0.599895i	0.985598	+	0.169105i	$0.0540879\pi$
$138$		0			0
$139$	91.2747	−	158.092i	0.656652	−	1.13736i	−0.324824	−	0.945774i	$-0.605305\pi$
$139$	91.2747	−	158.092i	0.656652	−	1.13736i	0.981477	−	0.191581i	$-0.0613614\pi$
$140$		0			0
$141$		−	50.8454i		−	0.360606i
$142$		0			0
$143$	−2.72200	−	1.57155i	−0.0190349	−	0.0109898i
$144$		0			0
$145$			233.017i			1.60701i
$146$		0			0
$147$	−65.8195	+	38.0009i	−0.447752	+	0.258510i
$148$		0			0
$149$	−5.50439	−	9.53389i	−0.0369422	−	0.0639858i	0.846963	−	0.531652i	$-0.178428\pi$
$149$	−5.50439	−	9.53389i	−0.0369422	−	0.0639858i	−0.883905	+	0.467666i	$0.845095\pi$
$150$		0			0
$151$		−	238.846i		−	1.58176i	−0.611968	−	0.790882i	$-0.709622\pi$
$151$		−	238.846i		−	1.58176i	0.611968	−	0.790882i	$-0.290378\pi$
$152$		0			0
$153$	73.8797			0.482874
$154$		0			0
$155$	95.0582	−	54.8819i	0.613279	−	0.354077i
$156$		0			0
$157$	22.8125	+	39.5124i	0.145303	+	0.251671i	0.929486	−	0.368858i	$-0.120251\pi$
$157$	22.8125	+	39.5124i	0.145303	+	0.251671i	−0.784183	+	0.620529i	$0.786918\pi$
$158$		0			0
$159$	96.8353			0.609027
$160$		0			0
$161$	5.93421	−	10.2784i	0.0368585	−	0.0638407i
$162$		0			0
$163$	−5.89159			−0.0361447			−0.0180724	−	0.999837i	$-0.505753\pi$
$163$	−5.89159			−0.0361447			−0.0180724	+	0.999837i	$0.505753\pi$
$164$		0			0
$165$	−193.343	−	111.627i	−1.17178	−	0.676525i
$166$		0			0
$167$	−142.140	−	82.0646i	−0.851138	−	0.491405i	0.00989689	−	0.999951i	$-0.496850\pi$
$167$	−142.140	−	82.0646i	−0.851138	−	0.491405i	−0.861035	+	0.508546i	$0.830183\pi$
$168$		0			0
$169$	−84.4878	−	146.337i	−0.499928	−	0.865900i
$170$		0			0
$171$	32.5790	−	46.7718i	0.190521	−	0.273520i
$172$		0			0
$173$	234.355	−	135.305i	1.35465	−	0.782109i	0.365755	−	0.930711i	$-0.380811\pi$
$173$	234.355	−	135.305i	1.35465	−	0.782109i	0.988897	+	0.148603i	$0.0474775\pi$
$174$		0			0
$175$	−18.2747	+	31.6527i	−0.104427	+	0.180872i
$176$		0			0
$177$	29.9269	−	51.8349i	0.169078	−	0.292852i
$178$		0			0
$179$			186.439i			1.04156i	0.853691	+	0.520779i	$0.174359\pi$
$179$			186.439i			1.04156i	−0.853691	+	0.520779i	$0.825641\pi$
$180$		0			0
$181$	−40.1939	−	23.2059i	−0.222066	−	0.128210i	0.384841	−	0.922983i	$-0.374256\pi$
$181$	−40.1939	−	23.2059i	−0.222066	−	0.128210i	−0.606906	+	0.794773i	$0.707590\pi$
$182$		0			0
$183$		−	94.8487i		−	0.518299i
$184$		0			0
$185$	−237.291	+	137.000i	−1.28265	+	0.740539i
$186$		0			0
$187$	247.408	+	428.524i	1.32304	+	2.29157i
$188$		0			0
$189$		−	11.7579i		−	0.0622112i
$190$		0			0
$191$	36.7222			0.192263			0.0961315	−	0.995369i	$-0.469353\pi$
$191$	36.7222			0.192263			0.0961315	+	0.995369i	$0.469353\pi$
$192$		0			0
$193$	−173.472	+	100.154i	−0.898817	+	0.518932i	−0.876816	−	0.480826i	$-0.840337\pi$
$193$	−173.472	+	100.154i	−0.898817	+	0.518932i	−0.0220009	+	0.999758i	$0.507004\pi$
$194$		0			0
$195$	0.869047	+	1.50523i	0.00445665	+	0.00771915i
$196$		0			0
$197$	−171.512			−0.870620			−0.435310	−	0.900281i	$-0.643361\pi$
$197$	−171.512			−0.870620			−0.435310	+	0.900281i	$0.643361\pi$
$198$		0			0
$199$	43.7500	−	75.7772i	0.219849	−	0.380790i	−0.734913	−	0.678162i	$-0.762777\pi$
$199$	43.7500	−	75.7772i	0.219849	−	0.380790i	0.954762	+	0.297372i	$0.0961102\pi$
$200$		0			0
$201$	−132.140			−0.657411
$202$		0			0
$203$	−71.1820	−	41.0970i	−0.350650	−	0.202448i
$204$		0			0
$205$	−193.045	−	111.455i	−0.941684	−	0.543682i
$206$		0			0
$207$	−7.86749	−	13.6269i	−0.0380072	−	0.0658304i
$208$		0			0
$209$	380.391	+	32.3384i	1.82005	+	0.154729i
$210$		0			0
$211$	−16.3950	+	9.46566i	−0.0777014	+	0.0448609i	−0.538347	−	0.842723i	$-0.680951\pi$
$211$	−16.3950	+	9.46566i	−0.0777014	+	0.0448609i	0.460646	+	0.887584i	$0.347618\pi$
$212$		0			0
$213$	−63.6080	+	110.172i	−0.298629	+	0.517240i
$214$		0			0
$215$	−80.5423	+	139.503i	−0.374615	+	0.648853i
$216$		0			0
$217$			38.7178i			0.178423i
$218$		0			0
$219$	−137.716	−	79.5103i	−0.628840	−	0.363061i
$220$		0			0
$221$		−	3.85230i		−	0.0174312i
$222$		0			0
$223$	224.162	−	129.420i	1.00521	−	0.580358i	0.0954244	−	0.995437i	$-0.469579\pi$
$223$	224.162	−	129.420i	1.00521	−	0.580358i	0.909786	+	0.415078i	$0.136246\pi$
$224$		0			0
$225$	24.2283	+	41.9646i	0.107681	+	0.186509i
$226$		0			0
$227$			129.054i			0.568522i	0.958747	+	0.284261i	$0.0917482\pi$
$227$			129.054i			0.568522i	−0.958747	+	0.284261i	$0.908252\pi$
$228$		0			0
$229$	−98.8946			−0.431854			−0.215927	−	0.976409i	$-0.569277\pi$
$229$	−98.8946			−0.431854			−0.215927	+	0.976409i	$0.569277\pi$
$230$		0			0
$231$	68.1994	−	39.3749i	0.295235	−	0.170454i
$232$		0			0
$233$	174.731	+	302.644i	0.749920	+	1.29890i	0.947861	+	0.318685i	$0.103241\pi$
$233$	174.731	+	302.644i	0.749920	+	1.29890i	−0.197941	+	0.980214i	$0.563425\pi$
$234$		0			0
$235$	−188.316			−0.801346
$236$		0			0
$237$	53.1300	−	92.0238i	0.224177	−	0.388286i
$238$		0			0
$239$	−301.091			−1.25979			−0.629897	−	0.776679i	$-0.716903\pi$
$239$	−301.091			−1.25979			−0.629897	+	0.776679i	$0.716903\pi$
$240$		0			0
$241$	110.242	+	63.6485i	0.457438	+	0.264102i	0.710966	−	0.703226i	$-0.248258\pi$
$241$	110.242	+	63.6485i	0.457438	+	0.264102i	−0.253529	+	0.967328i	$0.581591\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	140.744	+	243.776i	0.574465	+	0.995003i
$246$		0			0
$247$	−2.43882	−	1.69877i	−0.00987376	−	0.00687759i
$248$		0			0
$249$	223.189	−	128.858i	0.896342	−	0.517503i
$250$		0			0
$251$	−177.023	+	306.613i	−0.705271	+	1.22157i	0.261322	+	0.965252i	$0.415841\pi$
$251$	−177.023	+	306.613i	−0.705271	+	1.22157i	−0.966594	+	0.256314i	$0.917492\pi$
$252$		0			0
$253$	52.6933	−	91.2675i	0.208274	−	0.360741i
$254$		0			0
$255$		−	273.628i		−	1.07305i
$256$		0			0
$257$	−236.669	−	136.641i	−0.920889	−	0.531676i	−0.0369706	−	0.999316i	$-0.511771\pi$
$257$	−236.669	−	136.641i	−0.920889	−	0.531676i	−0.883919	+	0.467641i	$0.845104\pi$
$258$		0			0
$259$		−	96.6500i		−	0.373166i
$260$		0			0
$261$	−94.3720	+	54.4857i	−0.361579	+	0.208757i
$262$		0			0
$263$	75.5642	+	130.881i	0.287316	+	0.497646i	0.973168	−	0.230095i	$-0.0739036\pi$
$263$	75.5642	+	130.881i	0.287316	+	0.497646i	−0.685852	+	0.727741i	$0.740570\pi$
$264$		0			0
$265$		−	358.649i		−	1.35339i
$266$		0			0
$267$	−125.566			−0.470284
$268$		0			0
$269$	58.9364	−	34.0269i	0.219094	−	0.126494i	−0.386437	−	0.922316i	$-0.626294\pi$
$269$	58.9364	−	34.0269i	0.219094	−	0.126494i	0.605531	+	0.795822i	$0.292961\pi$
$270$		0			0
$271$	−56.8991	−	98.5521i	−0.209960	−	0.363661i	0.741742	−	0.670685i	$-0.234000\pi$
$271$	−56.8991	−	98.5521i	−0.209960	−	0.363661i	−0.951702	+	0.307025i	$0.900667\pi$
$272$		0			0
$273$	−0.613092			−0.00224576
$274$		0			0
$275$	−162.271	+	281.062i	−0.590078	+	1.02204i
$276$		0			0
$277$	440.910			1.59173			0.795867	−	0.605472i	$-0.207016\pi$
$277$	440.910			1.59173			0.795867	+	0.605472i	$0.207016\pi$
$278$		0			0
$279$	44.4544	+	25.6657i	0.159335	+	0.0919919i
$280$		0			0
$281$	78.0928	+	45.0869i	0.277910	+	0.160452i	0.632477	−	0.774579i	$-0.282038\pi$
$281$	78.0928	+	45.0869i	0.277910	+	0.160452i	−0.354567	+	0.935031i	$0.615372\pi$
$282$		0			0
$283$	−34.5331	−	59.8131i	−0.122025	−	0.211354i	0.798541	−	0.601940i	$-0.205606\pi$
$283$	−34.5331	−	59.8131i	−0.122025	−	0.211354i	−0.920566	+	0.390587i	$0.872272\pi$
$284$		0			0
$285$	−173.229	−	120.663i	−0.607821	−	0.423379i
$286$		0			0
$287$	68.0944	−	39.3143i	0.237263	−	0.136984i
$288$		0			0
$289$	−158.734	+	274.935i	−0.549252	+	0.951332i
$290$		0			0
$291$	−70.0326	+	121.300i	−0.240662	+	0.416839i
$292$		0			0
$293$			410.238i			1.40013i	0.714079	+	0.700065i	$0.246846\pi$
$293$			410.238i			1.40013i	−0.714079	+	0.700065i	$0.753154\pi$
$294$		0			0
$295$	−191.981	−	110.840i	−0.650782	−	0.375729i
$296$		0			0
$297$		−	104.405i		−	0.351533i
$298$		0			0
$299$	−0.710545	+	0.410233i	−0.00237640	+	0.00137202i
$300$		0			0
$301$	−28.4103	−	49.2081i	−0.0943864	−	0.163482i
$302$		0			0
$303$			265.617i			0.876624i
$304$		0			0
$305$	−351.291			−1.15177
$306$		0			0
$307$	201.882	−	116.556i	0.657595	−	0.379663i	−0.133765	−	0.991013i	$-0.542707\pi$
$307$	201.882	−	116.556i	0.657595	−	0.379663i	0.791360	+	0.611350i	$0.209373\pi$
$308$		0			0
$309$	146.313	+	253.422i	0.473506	+	0.820136i
$310$		0			0
$311$	441.280			1.41891			0.709454	−	0.704752i	$-0.248942\pi$
$311$	441.280			1.41891			0.709454	+	0.704752i	$0.248942\pi$
$312$		0			0
$313$	−60.6339	+	105.021i	−0.193719	+	0.335530i	−0.946480	−	0.322763i	$-0.895388\pi$
$313$	−60.6339	+	105.021i	−0.193719	+	0.335530i	0.752761	+	0.658294i	$0.228722\pi$
$314$		0			0
$315$	−43.5478			−0.138247
$316$		0			0
$317$	286.409	+	165.358i	0.903499	+	0.521635i	0.878334	−	0.478048i	$-0.158656\pi$
$317$	286.409	+	165.358i	0.903499	+	0.521635i	0.0251649	+	0.999683i	$0.491989\pi$
$318$		0			0
$319$	−632.066	−	364.924i	−1.98140	−	1.14396i
$320$		0			0
$321$	120.430	+	208.591i	0.375171	+	0.649815i
$322$		0			0
$323$	198.786	+	423.579i	0.615437	+	1.31139i
$324$		0			0
$325$	2.18816	−	1.26333i	0.00673279	−	0.00388718i
$326$		0			0
$327$	−9.15888	+	15.8636i	−0.0280088	+	0.0485127i
$328$		0			0
$329$	33.2131	−	57.5268i	0.100952	−	0.174854i
$330$		0			0
$331$			436.308i			1.31815i	0.752077	+	0.659075i	$0.229052\pi$
$331$			436.308i			1.31815i	−0.752077	+	0.659075i	$0.770948\pi$
$332$		0			0
$333$	−110.970	−	64.0685i	−0.333243	−	0.192398i
$334$		0			0
$335$			489.406i			1.46091i
$336$		0			0
$337$	−217.027	+	125.301i	−0.643997	+	0.371812i	−0.786153	−	0.618033i	$-0.787930\pi$
$337$	−217.027	+	125.301i	−0.643997	+	0.371812i	0.142156	+	0.989844i	$0.454597\pi$
$338$		0			0
$339$	59.8927	+	103.737i	0.176675	+	0.306009i
$340$		0			0
$341$			343.798i			1.00821i
$342$		0			0
$343$	−210.169			−0.612738
$344$		0			0
$345$	−50.4699	+	29.1388i	−0.146290	+	0.0844603i
$346$		0			0
$347$	83.6670	+	144.915i	0.241115	+	0.417624i	0.961032	−	0.276436i	$-0.0891535\pi$
$347$	83.6670	+	144.915i	0.241115	+	0.417624i	−0.719917	+	0.694060i	$0.755820\pi$
$348$		0			0
$349$	−486.776			−1.39477			−0.697387	−	0.716695i	$-0.745654\pi$
$349$	−486.776			−1.39477			−0.697387	+	0.716695i	$0.745654\pi$
$350$		0			0
$351$	−0.406413	+	0.703929i	−0.00115787	+	0.00200550i
$352$		0			0
$353$	30.1507			0.0854128			0.0427064	−	0.999088i	$-0.486402\pi$
$353$	30.1507			0.0854128			0.0427064	+	0.999088i	$0.486402\pi$
$354$		0			0
$355$	408.045	+	235.585i	1.14942	+	0.663619i
$356$		0			0
$357$	83.5879	+	48.2595i	0.234140	+	0.135181i
$358$		0			0
$359$	75.0088	+	129.919i	0.208938	+	0.361891i	0.951380	−	0.308019i	$-0.0996659\pi$
$359$	75.0088	+	129.919i	0.208938	+	0.361891i	−0.742442	+	0.669910i	$0.766333\pi$
$360$		0			0
$361$	355.819	+	60.9394i	0.985649	+	0.168807i
$362$		0			0
$363$	424.081	−	244.843i	1.16827	−	0.674500i
$364$		0			0
$365$	−294.482	+	510.058i	−0.806801	+	1.39742i
$366$		0			0
$367$	−248.090	+	429.704i	−0.675994	+	1.17086i	0.300183	+	0.953882i	$0.402952\pi$
$367$	−248.090	+	429.704i	−0.675994	+	1.17086i	−0.976177	+	0.216975i	$0.930381\pi$
$368$		0			0
$369$		−	104.245i		−	0.282506i
$370$		0			0
$371$	109.560	+	63.2545i	0.295310	+	0.170497i
$372$		0			0
$373$			449.613i			1.20540i	0.797969	+	0.602698i	$0.205908\pi$
$373$			449.613i			1.20540i	−0.797969	+	0.602698i	$0.794092\pi$
$374$		0			0
$375$	−85.1381	+	49.1545i	−0.227035	+	0.131079i
$376$		0			0
$377$	2.84104	+	4.92083i	0.00753592	+	0.0130526i
$378$		0			0
$379$			471.336i			1.24363i	0.783163	+	0.621816i	$0.213605\pi$
$379$			471.336i			1.24363i	−0.783163	+	0.621816i	$0.786395\pi$
$380$		0			0
$381$	51.3095			0.134670
$382$		0			0
$383$	23.4258	−	13.5249i	0.0611641	−	0.0353131i	−0.469106	−	0.883142i	$-0.655424\pi$
$383$	23.4258	−	13.5249i	0.0611641	−	0.0353131i	0.530270	+	0.847829i	$0.322090\pi$
$384$		0			0
$385$	−145.833	−	252.590i	−0.378787	−	0.656078i
$386$		0			0
$387$	−75.3319			−0.194656
$388$		0			0
$389$	177.144	−	306.822i	0.455382	−	0.788745i	−0.543328	−	0.839520i	$-0.682836\pi$
$389$	177.144	−	306.822i	0.455382	−	0.788745i	0.998710	+	0.0507758i	$0.0161694\pi$
$390$		0			0
$391$	129.166			0.330348
$392$		0			0
$393$	85.9579	+	49.6278i	0.218722	+	0.126279i
$394$		0			0
$395$	−340.829	−	196.777i	−0.862857	−	0.498171i
$396$		0			0
$397$	−79.5105	−	137.716i	−0.200278	−	0.346892i	0.748340	−	0.663316i	$-0.230851\pi$
$397$	−79.5105	−	137.716i	−0.200278	−	0.346892i	−0.948618	+	0.316423i	$0.897518\pi$
$398$		0			0
$399$	67.4123	−	31.6367i	0.168953	−	0.0792901i
$400$		0			0
$401$	−277.534	+	160.234i	−0.692105	+	0.399587i	−0.804400	−	0.594088i	$-0.797513\pi$
$401$	−277.534	+	160.234i	−0.692105	+	0.399587i	0.112295	+	0.993675i	$0.464180\pi$
$402$		0			0
$403$	1.33829	−	2.31798i	0.00332081	−	0.00575181i
$404$		0			0
$405$	−28.8675	+	50.0000i	−0.0712777	+	0.123457i
$406$		0			0
$407$		−	858.211i		−	2.10863i
$408$		0			0
$409$	−251.776	−	145.363i	−0.615590	−	0.355411i	0.159560	−	0.987188i	$-0.448992\pi$
$409$	−251.776	−	145.363i	−0.615590	−	0.355411i	−0.775150	+	0.631777i	$0.782326\pi$
$410$		0			0
$411$		−	164.371i		−	0.399930i
$412$		0			0
$413$	67.7189	−	39.0975i	0.163968	−	0.0946671i
$414$		0			0
$415$	−477.253	−	826.626i	−1.15001	−	1.99187i
$416$		0			0
$417$		−	316.185i		−	0.758237i
$418$		0			0
$419$	141.846			0.338535			0.169267	−	0.985570i	$-0.445860\pi$
$419$	141.846			0.338535			0.169267	+	0.985570i	$0.445860\pi$
$420$		0			0
$421$	98.6666	−	56.9652i	0.234362	−	0.135309i	−0.378220	−	0.925716i	$-0.623464\pi$
$421$	98.6666	−	56.9652i	0.234362	−	0.135309i	0.612583	+	0.790406i	$0.290131\pi$
$422$		0			0
$423$	−44.0334	−	76.2681i	−0.104098	−	0.180303i
$424$		0			0
$425$	−397.773			−0.935936
$426$		0			0
$427$	61.9568	−	107.312i	0.145098	−	0.251317i
$428$		0			0
$429$	−5.44399			−0.0126900
$430$		0			0
$431$	−229.263	−	132.365i	−0.531932	−	0.307111i	0.209871	−	0.977729i	$-0.432696\pi$
$431$	−229.263	−	132.365i	−0.531932	−	0.307111i	−0.741803	+	0.670618i	$0.766029\pi$
$432$		0			0
$433$	−631.333	−	364.500i	−1.45804	−	0.841802i	−0.459129	−	0.888369i	$-0.651839\pi$
$433$	−631.333	−	364.500i	−1.45804	−	0.841802i	−0.998915	+	0.0465669i	$0.985172\pi$
$434$		0			0
$435$	201.799	+	349.526i	0.463905	+	0.803507i
$436$		0			0
$437$	56.9589	−	81.7726i	0.130341	−	0.187123i
$438$		0			0
$439$	−319.591	+	184.516i	−0.727998	+	0.420310i	−0.817689	−	0.575660i	$-0.804745\pi$
$439$	−319.591	+	184.516i	−0.727998	+	0.420310i	0.0896911	+	0.995970i	$0.471412\pi$
$440$		0			0
$441$	−65.8195	+	114.003i	−0.149251	+	0.258510i
$442$		0			0
$443$	291.547	−	504.975i	0.658120	−	1.13990i	−0.322982	−	0.946405i	$-0.604685\pi$
$443$	291.547	−	504.975i	0.658120	−	1.13990i	0.981102	−	0.193492i	$-0.0619815\pi$
$444$		0			0
$445$			465.058i			1.04507i
$446$		0			0
$447$	−16.5132	−	9.53389i	−0.0369422	−	0.0213286i
$448$		0			0
$449$		−	314.423i		−	0.700273i	−0.936699	−	0.350137i	$-0.886135\pi$
$449$		−	314.423i		−	0.700273i	0.936699	−	0.350137i	$-0.113865\pi$
$450$		0			0
$451$	604.649	−	349.094i	1.34068	−	0.774045i
$452$		0			0
$453$	−206.847	−	358.270i	−0.456616	−	0.790882i
$454$		0			0
$455$			2.27071i			0.00499057i
$456$		0			0
$457$	505.253			1.10559			0.552793	−	0.833319i	$-0.313562\pi$
$457$	505.253			1.10559			0.552793	+	0.833319i	$0.313562\pi$
$458$		0			0
$459$	110.820	−	63.9817i	0.241437	−	0.139394i
$460$		0			0
$461$	136.902	+	237.122i	0.296968	+	0.514364i	0.975441	−	0.220262i	$-0.0706912\pi$
$461$	136.902	+	237.122i	0.296968	+	0.514364i	−0.678473	+	0.734626i	$0.737358\pi$
$462$		0			0
$463$	−319.780			−0.690669			−0.345334	−	0.938480i	$-0.612235\pi$
$463$	−319.780			−0.690669			−0.345334	+	0.938480i	$0.612235\pi$
$464$		0			0
$465$	95.0582	−	164.646i	0.204426	−	0.354077i
$466$		0			0
$467$	295.510			0.632785			0.316392	−	0.948628i	$-0.397528\pi$
$467$	295.510			0.632785			0.316392	+	0.948628i	$0.397528\pi$
$468$		0			0
$469$	−149.504	−	86.3159i	−0.318771	−	0.184042i
$470$		0			0
$471$	68.4375	+	39.5124i	0.145303	+	0.0838905i
$472$		0			0
$473$	−252.271	−	436.947i	−0.533344	−	0.923778i
$474$		0			0
$475$	−175.408	+	251.822i	−0.369279	+	0.530153i
$476$		0			0
$477$	145.253	−	83.8618i	0.304513	−	0.175811i
$478$		0			0
$479$	−204.559	+	354.306i	−0.427054	+	0.739679i	−0.996610	−	0.0822735i	$-0.973782\pi$
$479$	−204.559	+	354.306i	−0.427054	+	0.739679i	0.569556	+	0.821953i	$0.307115\pi$
$480$		0			0
$481$	−3.34072	+	5.78629i	−0.00694536	+	0.0120297i
$482$		0			0
$483$		−	20.5567i		−	0.0425605i
$484$		0			0
$485$	449.259	+	259.380i	0.926308	+	0.534804i
$486$		0			0
$487$			638.208i			1.31049i	0.755417	+	0.655244i	$0.227434\pi$
$487$			638.208i			1.31049i	−0.755417	+	0.655244i	$0.772566\pi$
$488$		0			0
$489$	−8.83738	+	5.10227i	−0.0180724	+	0.0104341i
$490$		0			0
$491$	173.278	+	300.126i	0.352908	+	0.611255i	0.986758	−	0.162202i	$-0.0518595\pi$
$491$	173.278	+	300.126i	0.352908	+	0.611255i	−0.633850	+	0.773456i	$0.718526\pi$
$492$		0			0
$493$		−	894.530i		−	1.81446i
$494$		0			0
$495$	−386.686			−0.781184
$496$		0			0
$497$	−143.933	+	83.0997i	−0.289603	+	0.167203i
$498$		0			0
$499$	40.3510	+	69.8900i	0.0808638	+	0.140060i	0.903621	−	0.428333i	$-0.140899\pi$
$499$	40.3510	+	69.8900i	0.0808638	+	0.140060i	−0.822757	+	0.568393i	$0.807565\pi$
$500$		0			0
$501$	−284.280			−0.567425
$502$		0			0
$503$	247.050	−	427.903i	0.491153	−	0.850701i	−0.508796	−	0.860887i	$-0.669909\pi$
$503$	247.050	−	427.903i	0.491153	−	0.850701i	0.999948	+	0.0101862i	$0.00324242\pi$
$504$		0			0
$505$	983.766			1.94805
$506$		0			0
$507$	−253.463	−	146.337i	−0.499928	−	0.288633i
$508$		0			0
$509$	63.9084	+	36.8975i	0.125557	+	0.0724902i	0.561463	−	0.827502i	$-0.310239\pi$
$509$	63.9084	+	36.8975i	0.125557	+	0.0724902i	−0.435906	+	0.899992i	$0.643572\pi$
$510$		0			0
$511$	−103.875	−	179.917i	−0.203278	−	0.352088i
$512$		0			0
$513$	8.36297	−	98.3721i	0.0163021	−	0.191758i
$514$		0			0
$515$	938.599	−	541.900i	1.82252	−	1.05223i
$516$		0			0
$517$	294.918	−	510.814i	0.570442	−	0.988034i
$518$		0			0
$519$	234.355	−	405.914i	0.451551	−	0.782109i
$520$		0			0
$521$		−	357.582i		−	0.686337i	−0.939274	−	0.343169i	$-0.888500\pi$
$521$		−	357.582i		−	0.686337i	0.939274	−	0.343169i	$-0.111500\pi$
$522$		0			0
$523$	−382.935	−	221.088i	−0.732190	−	0.422730i	0.0870328	−	0.996205i	$-0.472261\pi$
$523$	−382.935	−	221.088i	−0.732190	−	0.422730i	−0.819223	+	0.573475i	$0.805595\pi$
$524$		0			0
$525$			63.3053i			0.120582i
$526$		0			0
$527$	−364.919	+	210.686i	−0.692447	+	0.399784i
$528$		0			0
$529$	250.745	+	434.303i	0.473998	+	0.820989i
$530$		0			0
$531$		−	103.670i		−	0.195235i
$532$		0			0
$533$	−5.43561			−0.0101981
$534$		0			0
$535$	772.557	−	446.036i	1.44403	−	0.833712i
$536$		0			0
$537$	161.461	+	279.658i	0.300672	+	0.520779i
$538$		0			0
$539$	−881.666			−1.63574
$540$		0			0
$541$	−487.737	+	844.785i	−0.901547	+	1.56152i	−0.0760596	+	0.997103i	$0.524234\pi$
$541$	−487.737	+	844.785i	−0.901547	+	1.56152i	−0.825487	+	0.564421i	$0.809099\pi$
$542$		0			0
$543$	−80.3877			−0.148044
$544$		0			0
$545$	58.7542	+	33.9217i	0.107806	+	0.0622417i
$546$		0			0
$547$	−350.050	−	202.102i	−0.639945	−	0.369473i	0.144648	−	0.989483i	$-0.453795\pi$
$547$	−350.050	−	202.102i	−0.639945	−	0.369473i	−0.784594	+	0.620010i	$0.787128\pi$
$548$		0			0
$549$	−82.1414	−	142.273i	−0.149620	−	0.259149i
$550$		0			0
$551$	−566.310	−	394.465i	−1.02779	−	0.715907i
$552$		0			0
$553$	120.223	−	69.4109i	0.217402	−	0.125517i
$554$		0			0
$555$	−237.291	+	410.999i	−0.427551	+	0.740539i
$556$		0			0
$557$	−29.9352	+	51.8492i	−0.0537435	+	0.0930866i	−0.891646	−	0.452734i	$-0.850449\pi$
$557$	−29.9352	+	51.8492i	−0.0537435	+	0.0930866i	0.837902	+	0.545821i	$0.183782\pi$
$558$		0			0
$559$			3.92802i			0.00702687i
$560$		0			0
$561$	742.225	+	428.524i	1.32304	+	0.763857i
$562$		0			0
$563$		−	247.579i		−	0.439749i	−0.975528	−	0.219874i	$-0.929435\pi$
$563$		−	247.579i		−	0.439749i	0.975528	−	0.219874i	$-0.0705648\pi$
$564$		0			0
$565$	384.211	−	221.824i	0.680020	−	0.392610i
$566$		0			0
$567$	−10.1827	−	17.6369i	−0.0179588	−	0.0311056i
$568$		0			0
$569$		−	76.4991i		−	0.134445i	−0.997738	−	0.0672224i	$-0.978586\pi$
$569$		−	76.4991i		−	0.134445i	0.997738	−	0.0672224i	$-0.0214137\pi$
$570$		0			0
$571$	624.523			1.09373			0.546867	−	0.837219i	$-0.315820\pi$
$571$	624.523			1.09373			0.546867	+	0.837219i	$0.315820\pi$
$572$		0			0
$573$	55.0834	−	31.8024i	0.0961315	−	0.0555016i
$574$		0			0
$575$	42.3590	+	73.3680i	0.0736679	+	0.127597i
$576$		0			0
$577$	185.550			0.321577			0.160789	−	0.986989i	$-0.448596\pi$
$577$	185.550			0.321577			0.160789	+	0.986989i	$0.448596\pi$
$578$		0			0
$579$	−173.472	+	300.462i	−0.299606	+	0.518932i
$580$		0			0
$581$	336.690			0.579501
$582$		0			0
$583$	972.846	+	561.673i	1.66869	+	0.963418i
$584$		0			0
$585$	2.60714	+	1.50523i	0.00445665	+	0.00257305i
$586$		0			0
$587$	130.891	+	226.710i	0.222983	+	0.386218i	0.955712	−	0.294302i	$-0.0950872\pi$
$587$	130.891	+	226.710i	0.222983	+	0.386218i	−0.732729	+	0.680520i	$0.761754\pi$
$588$		0			0
$589$	−27.5386	+	323.931i	−0.0467548	+	0.549968i
$590$		0			0
$591$	−257.268	+	148.534i	−0.435310	+	0.251326i
$592$		0			0
$593$	−124.254	+	215.215i	−0.209535	+	0.362925i	−0.951568	−	0.307438i	$-0.900528\pi$
$593$	−124.254	+	215.215i	−0.209535	+	0.362925i	0.742033	+	0.670363i	$0.233862\pi$
$594$		0			0
$595$	178.739	−	309.585i	0.300401	−	0.520310i
$596$		0			0
$597$		−	151.554i		−	0.253860i
$598$		0			0
$599$	167.646	+	96.7905i	0.279877	+	0.161587i	0.633368	−	0.773851i	$-0.281672\pi$
$599$	167.646	+	96.7905i	0.279877	+	0.161587i	−0.353491	+	0.935438i	$0.615005\pi$
$600$		0			0
$601$		−	675.975i		−	1.12475i	−0.826882	−	0.562375i	$-0.809888\pi$
$601$		−	675.975i		−	1.12475i	0.826882	−	0.562375i	$-0.190112\pi$
$602$		0			0
$603$	−198.209	+	114.436i	−0.328706	+	0.189778i
$604$		0			0
$605$	−906.827	−	1570.67i	−1.49889	−	2.59615i
$606$		0			0
$607$		−	383.052i		−	0.631057i	−0.948916	−	0.315528i	$-0.897818\pi$
$607$		−	383.052i		−	0.631057i	0.948916	−	0.315528i	$-0.102182\pi$
$608$		0			0
$609$	−142.364			−0.233767
$610$		0			0
$611$	−3.97684	+	2.29603i	−0.00650874	+	0.00375782i
$612$		0			0
$613$	−27.5410	−	47.7025i	−0.0449283	−	0.0778180i	0.842687	−	0.538404i	$-0.180973\pi$
$613$	−27.5410	−	47.7025i	−0.0449283	−	0.0778180i	−0.887615	+	0.460586i	$0.847639\pi$
$614$		0			0
$615$	−386.091			−0.627789
$616$		0			0
$617$	−51.7851	+	89.6944i	−0.0839305	+	0.145372i	−0.904935	−	0.425550i	$-0.860081\pi$
$617$	−51.7851	+	89.6944i	−0.0839305	+	0.145372i	0.821004	+	0.570922i	$0.193414\pi$
$618$		0			0
$619$	263.102			0.425043			0.212521	−	0.977156i	$-0.431832\pi$
$619$	263.102			0.425043			0.212521	+	0.977156i	$0.431832\pi$
$620$		0			0
$621$	−23.6025	−	13.6269i	−0.0380072	−	0.0219435i
$622$		0			0
$623$	−142.066	−	82.0218i	−0.228035	−	0.131656i
$624$		0			0
$625$	383.956	+	665.031i	0.614329	+	1.06405i
$626$		0			0
$627$	598.593	−	280.921i	0.954693	−	0.448039i
$628$		0			0
$629$	910.936	−	525.929i	1.44823	−	0.836135i
$630$		0			0
$631$	−72.5474	+	125.656i	−0.114972	+	0.199137i	−0.917769	−	0.397116i	$-0.870011\pi$
$631$	−72.5474	+	125.656i	−0.114972	+	0.199137i	0.802797	+	0.596253i	$0.203345\pi$
$632$		0			0
$633$	−16.3950	+	28.3970i	−0.0259005	+	0.0448609i
$634$		0			0
$635$		−	190.035i		−	0.299267i
$636$		0			0
$637$	5.94443	+	3.43202i	0.00933192	+	0.00538779i
$638$		0			0
$639$			220.344i			0.344827i
$640$		0			0
$641$	−583.796	+	337.055i	−0.910758	+	0.525826i	−0.880675	−	0.473721i	$-0.842911\pi$
$641$	−583.796	+	337.055i	−0.910758	+	0.525826i	−0.0300832	+	0.999547i	$0.509577\pi$
$642$		0			0
$643$	−0.719856	−	1.24683i	−0.00111953	−	0.00193908i	0.865465	−	0.500969i	$-0.167023\pi$
$643$	−0.719856	−	1.24683i	−0.00111953	−	0.00193908i	−0.866585	+	0.499030i	$0.833690\pi$
$644$		0			0
$645$			279.007i			0.432569i
$646$		0			0
$647$	614.044			0.949063			0.474532	−	0.880239i	$-0.342617\pi$
$647$	614.044			0.949063			0.474532	+	0.880239i	$0.342617\pi$
$648$		0			0
$649$	601.315	−	347.169i	0.926525	−	0.534929i
$650$		0			0
$651$	33.5306	+	58.0768i	0.0515064	+	0.0892116i
$652$		0			0
$653$	822.374			1.25938			0.629689	−	0.776847i	$-0.283182\pi$
$653$	822.374			1.25938			0.629689	+	0.776847i	$0.283182\pi$
$654$		0			0
$655$	183.807	−	318.362i	0.280621	−	0.486049i
$656$		0			0
$657$	−275.432			−0.419227
$658$		0			0
$659$	549.386	+	317.188i	0.833666	+	0.481317i	0.855106	−	0.518453i	$-0.173492\pi$
$659$	549.386	+	317.188i	0.833666	+	0.481317i	−0.0214404	+	0.999770i	$0.506825\pi$
$660$		0			0
$661$	−818.470	−	472.544i	−1.23823	−	0.714893i	−0.269498	−	0.963001i	$-0.586858\pi$
$661$	−818.470	−	472.544i	−1.23823	−	0.714893i	−0.968732	+	0.248108i	$0.920191\pi$
$662$		0			0
$663$	−3.33619	−	5.77845i	−0.00503196	−	0.00871561i
$664$		0			0
$665$	−117.173	−	249.675i	−0.176200	−	0.375451i
$666$		0			0
$667$	−164.993	+	95.2590i	−0.247366	+	0.142817i
$668$		0			0
$669$	224.162	−	388.260i	0.335070	−	0.580358i
$670$		0			0
$671$	550.150	−	952.888i	0.819896	−	1.42010i
$672$		0			0
$673$		−	570.803i		−	0.848147i	−0.905628	−	0.424074i	$-0.860600\pi$
$673$		−	570.803i		−	0.848147i	0.905628	−	0.424074i	$-0.139400\pi$
$674$		0			0
$675$	72.6848	+	41.9646i	0.107681	+	0.0621698i
$676$		0			0
$677$		−	275.976i		−	0.407646i	−0.979008	−	0.203823i	$-0.934663\pi$
$677$		−	275.976i		−	0.407646i	0.979008	−	0.203823i	$-0.0653367\pi$
$678$		0			0
$679$	−158.471	+	91.4931i	−0.233388	+	0.134747i
$680$		0			0
$681$	111.764	+	193.582i	0.164118	+	0.284261i
$682$		0			0
$683$		−	106.224i		−	0.155525i	−0.996972	−	0.0777627i	$-0.975222\pi$
$683$		−	106.224i		−	0.155525i	0.996972	−	0.0777627i	$-0.0247776\pi$
$684$		0			0
$685$	−608.781			−0.888732
$686$		0			0
$687$	−148.342	+	85.6453i	−0.215927	+	0.124666i
$688$		0			0
$689$	−4.37279	−	7.57390i	−0.00634658	−	0.0109926i
$690$		0			0
$691$	−244.177			−0.353367			−0.176684	−	0.984268i	$-0.556537\pi$
$691$	−244.177			−0.353367			−0.176684	+	0.984268i	$0.556537\pi$
$692$		0			0
$693$	68.1994	−	118.125i	0.0984118	−	0.170454i
$694$		0			0
$695$	−1171.05			−1.68497
$696$		0			0
$697$	741.082	+	427.864i	1.06325	+	0.613865i
$698$		0			0
$699$	524.194	+	302.644i	0.749920	+	0.432966i
$700$		0			0
$701$	143.276	+	248.161i	0.204388	+	0.354010i	0.949938	−	0.312440i	$-0.101146\pi$
$701$	143.276	+	248.161i	0.204388	+	0.354010i	−0.745550	+	0.666450i	$0.767813\pi$
$702$		0			0
$703$	68.7436	−	808.618i	0.0977860	−	1.15024i
$704$		0			0
$705$	−282.474	+	163.087i	−0.400673	+	0.231329i
$706$		0			0
$707$	−173.506	+	300.521i	−0.245411	+	0.425065i
$708$		0			0
$709$	−5.70585	+	9.88282i	−0.00804774	+	0.0139391i	−0.870021	−	0.493014i	$-0.835895\pi$
$709$	−5.70585	+	9.88282i	−0.00804774	+	0.0139391i	0.861973	+	0.506953i	$0.169228\pi$
$710$		0			0
$711$		−	184.048i		−	0.258857i
$712$		0			0
$713$	77.7209	+	44.8722i	0.109006	+	0.0629344i
$714$		0			0
$715$			20.1629i			0.0281999i
$716$		0			0
$717$	−451.636	+	260.752i	−0.629897	+	0.363671i
$718$		0			0
$719$	−438.491	−	759.488i	−0.609862	−	1.05631i	−0.991263	−	0.131902i	$-0.957892\pi$
$719$	−438.491	−	759.488i	−0.609862	−	1.05631i	0.381401	−	0.924410i	$-0.375442\pi$
$720$		0			0
$721$			382.298i			0.530232i
$722$		0			0
$723$	220.485			0.304958
$724$		0			0
$725$	508.105	−	293.354i	0.700834	−	0.404627i
$726$		0			0
$727$	360.167	+	623.827i	0.495415	+	0.858084i	0.999986	−	0.00528653i	$-0.00168276\pi$
$727$	360.167	+	623.827i	0.495415	+	0.858084i	−0.504571	+	0.863370i	$0.668349\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	309.194	−	535.540i	0.422974	−	0.732613i
$732$		0			0
$733$	−170.651			−0.232812			−0.116406	−	0.993202i	$-0.537137\pi$
$733$	−170.651			−0.232812			−0.116406	+	0.993202i	$0.537137\pi$
$734$		0			0
$735$	422.232	+	243.776i	0.574465	+	0.331668i
$736$		0			0
$737$	−1327.53	−	766.449i	−1.80126	−	1.03996i
$738$		0			0
$739$	−530.334	−	918.566i	−0.717637	−	1.24298i	−0.961933	−	0.273284i	$-0.911890\pi$
$739$	−530.334	−	918.566i	−0.717637	−	1.24298i	0.244296	−	0.969701i	$-0.421443\pi$
$740$		0			0
$741$	−5.12940	−	0.436069i	−0.00692227	−	0.000588487i
$742$		0			0
$743$	−290.537	+	167.742i	−0.391033	+	0.225763i	−0.682607	−	0.730785i	$-0.739154\pi$
$743$	−290.537	+	167.742i	−0.391033	+	0.225763i	0.291575	+	0.956548i	$0.405821\pi$
$744$		0			0
$745$	−35.3107	+	61.1599i	−0.0473969	+	0.0820938i
$746$		0			0
$747$	223.189	−	386.575i	0.298781	−	0.517503i
$748$		0			0
$749$			314.668i			0.420117i
$750$		0			0
$751$	1128.41	+	651.490i	1.50255	+	0.867497i	0.999996	+	0.00295120i	$0.000939399\pi$
$751$	1128.41	+	651.490i	1.50255	+	0.867497i	0.502554	+	0.864546i	$0.332394\pi$
$752$		0			0
$753$			613.226i			0.814377i
$754$		0			0
$755$	−1326.92	+	766.100i	−1.75751	+	1.01470i
$756$		0			0
$757$	−60.1511	−	104.185i	−0.0794598	−	0.137628i	0.823557	−	0.567233i	$-0.191986\pi$
$757$	−60.1511	−	104.185i	−0.0794598	−	0.137628i	−0.903017	+	0.429605i	$0.858653\pi$
$758$		0			0
$759$		−	182.535i		−	0.240494i
$760$		0			0
$761$	1346.45			1.76932			0.884658	−	0.466240i	$-0.154392\pi$
$761$	1346.45			1.76932			0.884658	+	0.466240i	$0.154392\pi$
$762$		0			0
$763$	−20.7248	+	11.9655i	−0.0271623	+	0.0156822i
$764$		0			0
$765$	−236.969	−	410.442i	−0.309763	−	0.536526i
$766$		0			0
$767$	−5.40564			−0.00704777
$768$		0			0
$769$	109.016	−	188.821i	0.141763	−	0.245541i	−0.786398	−	0.617721i	$-0.788056\pi$
$769$	109.016	−	188.821i	0.141763	−	0.245541i	0.928161	+	0.372180i	$0.121390\pi$
$770$		0			0
$771$	−473.337			−0.613926
$772$		0			0
$773$	−48.6422	−	28.0836i	−0.0629266	−	0.0363307i	0.468207	−	0.883619i	$-0.344900\pi$
$773$	−48.6422	−	28.0836i	−0.0629266	−	0.0363307i	−0.531133	+	0.847288i	$0.678234\pi$
$774$		0			0
$775$	−239.345	−	138.186i	−0.308832	−	0.178304i
$776$		0			0
$777$	−83.7014	−	144.975i	−0.107724	−	0.186583i
$778$		0			0
$779$	597.671	−	280.488i	0.767229	−	0.360062i
$780$		0			0
$781$	−1278.06	+	737.890i	−1.63644	+	0.944801i
$782$		0			0
$783$	−94.3720	+	163.457i	−0.120526	+	0.208757i
$784$		0			0
$785$	146.342	−	253.472i	0.186423	−	0.322894i
$786$		0			0
$787$			170.104i			0.216142i	0.994143	+	0.108071i	$0.0344674\pi$
$787$			170.104i			0.216142i	−0.994143	+	0.108071i	$0.965533\pi$
$788$		0			0
$789$	226.693	+	130.881i	0.287316	+	0.165882i
$790$		0			0
$791$			156.492i			0.197840i
$792$		0			0
$793$	−7.41853	+	4.28309i	−0.00935501	+	0.00540112i
$794$		0			0
$795$	−310.599	−	537.973i	−0.390690	−	0.676696i
$796$		0			0
$797$			740.226i			0.928765i	0.885635	+	0.464383i	$0.153724\pi$
$797$			740.226i			0.928765i	−0.885635	+	0.464383i	$0.846276\pi$
$798$		0			0
$799$	722.928			0.904791
$800$		0			0
$801$	−188.349	+	108.743i	−0.235142	+	0.135759i
$802$		0			0
$803$	−922.366	−	1597.59i	−1.14865	−	1.98952i
$804$		0			0
$805$	−76.1359			−0.0945788
$806$		0			0
$807$	58.9364	−	102.081i	0.0730314	−	0.126494i
$808$		0			0
$809$	−1489.01			−1.84056			−0.920280	−	0.391260i	$-0.872039\pi$
$809$	−1489.01			−1.84056			−0.920280	+	0.391260i	$0.872039\pi$
$810$		0			0
$811$	−823.672	−	475.547i	−1.01563	−	0.586372i	−0.102792	−	0.994703i	$-0.532777\pi$
$811$	−823.672	−	475.547i	−1.01563	−	0.586372i	−0.912834	+	0.408331i	$0.866111\pi$
$812$		0			0
$813$	−170.697	−	98.5521i	−0.209960	−	0.121220i
$814$		0			0
$815$	18.8973	+	32.7310i	0.0231868	+	0.0401608i
$816$		0			0
$817$	−202.694	−	431.905i	−0.248095	−	0.528647i
$818$		0			0
$819$	−0.919637	+	0.530953i	−0.00112288	+	0.000648294i
$820$		0			0
$821$	790.459	−	1369.12i	0.962801	−	1.66762i	0.247390	−	0.968916i	$-0.420427\pi$
$821$	790.459	−	1369.12i	0.962801	−	1.66762i	0.715411	−	0.698704i	$-0.246240\pi$
$822$		0			0
$823$	−734.523	+	1272.23i	−0.892494	+	1.54585i	−0.0556192	+	0.998452i	$0.517713\pi$
$823$	−734.523	+	1272.23i	−0.892494	+	1.54585i	−0.836875	+	0.547394i	$0.815620\pi$
$824$		0			0
$825$			562.124i			0.681363i
$826$		0			0
$827$	13.7499	+	7.93854i	0.0166263	+	0.00959920i	0.508290	−	0.861186i	$-0.330278\pi$
$827$	13.7499	+	7.93854i	0.0166263	+	0.00959920i	−0.491664	+	0.870785i	$0.663611\pi$
$828$		0			0
$829$			460.891i			0.555960i	0.960587	+	0.277980i	$0.0896649\pi$
$829$			460.891i			0.555960i	−0.960587	+	0.277980i	$0.910335\pi$
$830$		0			0
$831$	661.365	−	381.839i	0.795867	−	0.459494i
$832$		0			0
$833$	−540.303	−	935.832i	−0.648623	−	1.12345i
$834$		0			0
$835$			1052.89i			1.26094i
$836$		0			0
$837$	88.9088			0.106223
$838$		0			0
$839$	11.1163	−	6.41800i	0.0132495	−	0.00764959i	−0.493361	−	0.869825i	$-0.664232\pi$
$839$	11.1163	−	6.41800i	0.0132495	−	0.00764959i	0.506610	+	0.862175i	$0.330898\pi$
$840$		0			0
$841$	239.209	+	414.323i	0.284434	+	0.492655i
$842$		0			0
$843$	156.186			0.185274
$844$		0			0
$845$	−541.989	+	938.752i	−0.641407	+	1.11095i
$846$		0			0
$847$	639.744			0.755306
$848$		0			0
$849$	−103.599	−	59.8131i	−0.122025	−	0.0704512i
$850$		0			0
$851$	−194.012	−	112.013i	−0.227981	−	0.131625i
$852$		0			0
$853$	321.717	+	557.231i	0.377160	+	0.653260i	0.990648	−	0.136444i	$-0.0435674\pi$
$853$	321.717	+	557.231i	0.377160	+	0.653260i	−0.613488	+	0.789704i	$0.710234\pi$
$854$		0			0
$855$	−364.341	−	30.9739i	−0.426129	−	0.0362268i
$856$		0			0
$857$	−115.805	+	66.8603i	−0.135129	+	0.0780167i	−0.566040	−	0.824377i	$-0.691525\pi$
$857$	−115.805	+	66.8603i	−0.135129	+	0.0780167i	0.430912	+	0.902394i	$0.358192\pi$
$858$		0			0
$859$	49.3229	−	85.4297i	0.0574189	−	0.0994525i	−0.835887	−	0.548901i	$-0.815046\pi$
$859$	49.3229	−	85.4297i	0.0574189	−	0.0994525i	0.893306	+	0.449449i	$0.148380\pi$
$860$		0			0
$861$	68.0944	−	117.943i	0.0790875	−	0.136984i
$862$		0			0
$863$			829.585i			0.961280i	0.876918	+	0.480640i	$0.159596\pi$
$863$			829.585i			0.961280i	−0.876918	+	0.480640i	$0.840404\pi$
$864$		0			0
$865$	−1503.39	−	867.980i	−1.73802	−	1.00344i
$866$		0			0
$867$			549.870i			0.634221i
$868$		0			0
$869$	1067.53	−	616.339i	1.22846	−	0.709251i
$870$		0			0
$871$	5.96704	+	10.3352i	0.00685079	+	0.0118659i
$872$		0			0
$873$			242.600i			0.277893i
$874$		0			0
$875$	−128.434			−0.146782
$876$		0			0
$877$	157.383	−	90.8649i	0.179456	−	0.103609i	−0.407581	−	0.913169i	$-0.633628\pi$
$877$	157.383	−	90.8649i	0.179456	−	0.103609i	0.587037	+	0.809560i	$0.300294\pi$
$878$		0			0
$879$	355.277	+	615.358i	0.404183	+	0.700065i
$880$		0			0
$881$	−517.816			−0.587759			−0.293880	−	0.955842i	$-0.594946\pi$
$881$	−517.816			−0.587759			−0.293880	+	0.955842i	$0.594946\pi$
$882$		0			0
$883$	−782.367	+	1355.10i	−0.886033	+	1.53465i	−0.0415084	+	0.999138i	$0.513216\pi$
$883$	−782.367	+	1355.10i	−0.886033	+	1.53465i	−0.844525	+	0.535516i	$0.820117\pi$
$884$		0			0
$885$	−383.961			−0.433855
$886$		0			0
$887$	620.266	+	358.111i	0.699285	+	0.403732i	0.807081	−	0.590441i	$-0.201046\pi$
$887$	620.266	+	358.111i	0.699285	+	0.403732i	−0.107796	+	0.994173i	$0.534379\pi$
$888$		0			0
$889$	58.0518	+	33.5162i	0.0653001	+	0.0377011i
$890$		0			0
$891$	−90.4176	−	156.608i	−0.101479	−	0.175766i
$892$		0			0
$893$	318.793	−	457.672i	0.356991	−	0.512511i
$894$		0			0
$895$	1035.77	−	598.003i	1.15729	−	0.668159i
$896$		0			0
$897$	−0.710545	+	1.23070i	−0.000792135	+	0.00137202i
$898$		0			0
$899$	310.759	−	538.251i	0.345672	−	0.598722i
$900$		0			0
$901$			1376.82i			1.52810i
$902$		0			0
$903$	−85.2309	−	49.2081i	−0.0943864	−	0.0544940i
$904$		0			0
$905$			297.732i			0.328986i
$906$		0			0
$907$	−240.379	+	138.783i	−0.265026	+	0.153013i	−0.626625	−	0.779321i	$-0.715564\pi$
$907$	−240.379	+	138.783i	−0.265026	+	0.153013i	0.361599	+	0.932334i	$0.382231\pi$
$908$		0			0
$909$	230.031	+	398.426i	0.253059	+	0.438312i
$910$		0			0
$911$			1630.56i			1.78986i	0.446207	+	0.894930i	$0.352774\pi$
$911$			1630.56i			1.78986i	−0.446207	+	0.894930i	$0.647226\pi$
$912$		0			0
$913$	2989.66			3.27455
$914$		0			0
$915$	−526.937	+	304.227i	−0.575887	+	0.332489i
$916$		0			0
$917$	64.8355	+	112.298i	0.0707040	+	0.122463i
$918$		0			0
$919$	48.0409			0.0522752			0.0261376	−	0.999658i	$-0.491679\pi$
$919$	48.0409			0.0522752			0.0261376	+	0.999658i	$0.491679\pi$
$920$		0			0
$921$	201.882	−	349.669i	0.219198	−	0.379663i
$922$		0			0
$923$	11.4894			0.0124479
$924$		0			0
$925$	597.469	+	344.949i	0.645912	+	0.372918i
$926$		0			0
$927$	438.940	+	253.422i	0.473506	+	0.273379i
$928$		0			0
$929$	−641.727	−	1111.50i	−0.690772	−	1.19645i	−0.971585	−	0.236690i	$-0.923937\pi$
$929$	−641.727	−	1111.50i	−0.690772	−	1.19645i	0.280813	−	0.959763i	$-0.409396\pi$
$930$		0			0
$931$	−830.717	−	70.6223i	−0.892285	−	0.0758564i
$932$		0			0
$933$	661.921	−	382.160i	0.709454	−	0.409604i
$934$		0			0
$935$	1587.12	−	2748.98i	1.69746	−	2.94008i
$936$		0			0
$937$	−769.568	+	1332.93i	−0.821311	+	1.42255i	0.0833953	+	0.996517i	$0.473424\pi$
$937$	−769.568	+	1332.93i	−0.821311	+	1.42255i	−0.904706	+	0.426036i	$0.859910\pi$
$938$		0			0
$939$			210.042i			0.223687i
$940$		0			0
$941$	−1281.05	−	739.617i	−1.36138	−	0.785990i	−0.371568	−	0.928406i	$-0.621180\pi$
$941$	−1281.05	−	739.617i	−1.36138	−	0.785990i	−0.989807	+	0.142415i	$0.954513\pi$
$942$		0			0
$943$		−	182.254i		−	0.193270i
$944$		0			0
$945$	−65.3217	+	37.7135i	−0.0691235	+	0.0399085i
$946$		0			0
$947$	−349.924	−	606.086i	−0.369508	−	0.640006i	0.619981	−	0.784617i	$-0.287140\pi$
$947$	−349.924	−	606.086i	−0.369508	−	0.640006i	−0.989489	+	0.144611i	$0.953807\pi$
$948$		0			0
$949$			14.3618i			0.0151336i
$950$		0			0
$951$	572.818			0.602332
$952$		0			0
$953$	−354.907	+	204.906i	−0.372411	+	0.215011i	−0.674511	−	0.738265i	$-0.735646\pi$
$953$	−354.907	+	204.906i	−0.372411	+	0.215011i	0.302100	+	0.953276i	$0.402312\pi$
$954$		0			0
$955$	−117.787	−	204.012i	−0.123337	−	0.213625i
$956$		0			0
$957$	−1264.13			−1.32093
$958$		0			0
$959$	107.370	−	185.971i	0.111960	−	0.193921i
$960$		0			0
$961$	668.231			0.695349
$962$		0			0
$963$	361.289	+	208.591i	0.375171	+	0.216605i
$964$		0			0
$965$	1112.82	+	642.487i	1.15318	+	0.665790i
$966$		0			0
$967$	−92.4602	−	160.146i	−0.0956155	−	0.165611i	0.814250	−	0.580515i	$-0.197149\pi$
$967$	−92.4602	−	160.146i	−0.0956155	−	0.165611i	−0.909865	+	0.414904i	$0.863815\pi$
$968$		0			0
$969$	665.009	+	463.214i	0.686284	+	0.478033i
$970$		0			0
$971$	−218.148	+	125.948i	−0.224663	+	0.129709i	−0.608107	−	0.793855i	$-0.708071\pi$
$971$	−218.148	+	125.948i	−0.224663	+	0.129709i	0.383445	+	0.923564i	$0.374738\pi$
$972$		0			0
$973$	206.537	−	357.733i	0.212269	−	0.367660i
$974$		0			0
$975$	2.18816	−	3.79000i	0.00224426	−	0.00388718i
$976$		0			0
$977$		−	372.639i		−	0.381411i	−0.981647	−	0.190706i	$-0.938922\pi$
$977$		−	372.639i		−	0.381411i	0.981647	−	0.190706i	$-0.0610776\pi$
$978$		0			0
$979$	−1261.49	−	728.319i	−1.28854	−	0.743942i
$980$		0			0
$981$			31.7273i			0.0323418i
$982$		0			0
$983$	−137.328	+	79.2861i	−0.139702	+	0.0806573i	−0.568222	−	0.822875i	$-0.692369\pi$
$983$	−137.328	+	79.2861i	−0.139702	+	0.0806573i	0.428520	+	0.903532i	$0.359035\pi$
$984$		0			0
$985$	550.125	+	952.844i	0.558503	+	0.967355i
$986$		0			0
$987$		−	115.054i		−	0.116569i
$988$		0			0
$989$	−131.705			−0.133170
$990$		0			0
$991$	−1489.96	+	860.227i	−1.50349	+	0.868039i	−0.503496	+	0.863998i	$0.667953\pi$
$991$	−1489.96	+	860.227i	−1.50349	+	0.868039i	−0.999992	+	0.00404127i	$0.998714\pi$
$992$		0			0
$993$	377.854	+	654.462i	0.380517	+	0.659075i
$994$		0			0
$995$	−561.312			−0.564132
$996$		0			0
$997$	−261.532	+	452.987i	−0.262319	+	0.454350i	−0.966858	−	0.255316i	$-0.917821\pi$
$997$	−261.532	+	452.987i	−0.262319	+	0.454350i	0.704539	+	0.709666i	$0.251154\pi$
$998$		0			0
$999$	−221.940			−0.222162

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.f.145.1		6
4.3	odd	2		57.3.g.b.31.1	✓	6
12.11	even	2		171.3.p.c.145.3		6
19.8	odd	6	inner	912.3.be.f.673.1		6
76.27	even	6		57.3.g.b.46.1	yes	6
228.179	odd	6		171.3.p.c.46.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.3.g.b.31.1	✓	6	4.3	odd	2
57.3.g.b.46.1	yes	6	76.27	even	6
171.3.p.c.46.3		6	228.179	odd	6
171.3.p.c.145.3		6	12.11	even	2
912.3.be.f.145.1		6	1.1	even	1	trivial
912.3.be.f.673.1		6	19.8	odd	6	inner

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	912.be (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(-3.20750 - 5.55555i) q^{5} +2.26281 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{3} +(-3.20750 - 5.55555i) q^{5} +2.26281 q^{7} +(1.50000 - 2.59808i) q^{9} +20.0928 q^{11} +(-0.135471 - 0.0782143i) q^{13} +(-9.62250 - 5.55555i) q^{15} +(12.3133 + 21.3272i) q^{17} +(18.9317 + 1.60945i) q^{19} +(3.39422 - 1.95965i) q^{21} +(2.62250 - 4.54230i) q^{23} +(-8.07609 + 13.9882i) q^{25} -5.19615i q^{27} +(-31.4573 - 18.1619i) q^{29} +17.1105i q^{31} +(30.1392 - 17.4009i) q^{33} +(-7.25797 - 12.5712i) q^{35} -42.7124i q^{37} -0.270942 q^{39} +(30.0928 - 17.3741i) q^{41} +(-12.5553 - 21.7464i) q^{43} -19.2450 q^{45} +(14.6778 - 25.4227i) q^{47} -43.8797 q^{49} +(36.9398 + 21.3272i) q^{51} +(48.4176 + 27.9539i) q^{53} +(-64.4476 - 111.627i) q^{55} +(29.7914 - 13.9812i) q^{57} +(29.9269 - 17.2783i) q^{59} +(27.3805 - 47.4244i) q^{61} +(3.39422 - 5.87896i) q^{63} +1.00349i q^{65} +(-66.0698 - 38.1454i) q^{67} -9.08459i q^{69} +(-63.6080 + 36.7241i) q^{71} +(-45.9053 - 79.5103i) q^{73} +27.9764i q^{75} +45.4662 q^{77} +(53.1300 - 30.6746i) q^{79} +(-4.50000 - 7.79423i) q^{81} +148.793 q^{83} +(78.9897 - 136.814i) q^{85} -62.9147 q^{87} +(-62.7829 - 36.2477i) q^{89} +(-0.306546 - 0.176984i) q^{91} +(14.8181 + 25.6657i) q^{93} +(-51.7820 - 110.338i) q^{95} +(-70.0326 + 40.4334i) q^{97} +(30.1392 - 52.2026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{3} + 4 q^{5} + 22 q^{7} + 9 q^{9}+O(q^{10}) \) 6 * q + 9 * q^3 + 4 * q^5 + 22 * q^7 + 9 * q^9	\( 6 q + 9 q^{3} + 4 q^{5} + 22 q^{7} + 9 q^{9} + 36 q^{11} - 3 q^{13} + 12 q^{15} + 38 q^{17} + 10 q^{19} + 33 q^{21} - 54 q^{23} - 21 q^{25} - 102 q^{29} + 54 q^{33} + 24 q^{35} - 6 q^{39} + 96 q^{41} - 107 q^{43} + 24 q^{45} + 50 q^{47} - 48 q^{49} + 114 q^{51} - 90 q^{53} - 148 q^{55} - 3 q^{57} + 27 q^{61} + 33 q^{63} + 39 q^{67} - 84 q^{71} - 77 q^{73} + 260 q^{77} - 9 q^{79} - 27 q^{81} + 348 q^{83} + 68 q^{85} - 204 q^{87} - 72 q^{89} + 393 q^{91} + 129 q^{93} - 104 q^{95} - 228 q^{97} + 54 q^{99}+O(q^{100}) \) 6 * q + 9 * q^3 + 4 * q^5 + 22 * q^7 + 9 * q^9 + 36 * q^11 - 3 * q^13 + 12 * q^15 + 38 * q^17 + 10 * q^19 + 33 * q^21 - 54 * q^23 - 21 * q^25 - 102 * q^29 + 54 * q^33 + 24 * q^35 - 6 * q^39 + 96 * q^41 - 107 * q^43 + 24 * q^45 + 50 * q^47 - 48 * q^49 + 114 * q^51 - 90 * q^53 - 148 * q^55 - 3 * q^57 + 27 * q^61 + 33 * q^63 + 39 * q^67 - 84 * q^71 - 77 * q^73 + 260 * q^77 - 9 * q^79 - 27 * q^81 + 348 * q^83 + 68 * q^85 - 204 * q^87 - 72 * q^89 + 393 * q^91 + 129 * q^93 - 104 * q^95 - 228 * q^97 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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