LMFDB - Embedded newform 171.3.p.c.46.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,3,Mod(46,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("171.46");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	171.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.65941252056$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			46.3
Root			$0.500000 - 2.93068i$ of defining polynomial
Character	$\chi$	$=$	171.46
Dual form			171.3.p.c.145.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.78805 + 1.03233i) q^{2} +(0.131406 + 0.227602i) q^{4} +(3.20750 - 5.55555i) q^{5} -2.26281 q^{7} -7.71601i q^{8} +O(q^{10})$	\(q+(1.78805 + 1.03233i) q^{2} +(0.131406 + 0.227602i) q^{4} +(3.20750 - 5.55555i) q^{5} -2.26281 q^{7} -7.71601i q^{8} +(11.4703 - 6.62239i) q^{10} +20.0928 q^{11} +(-0.135471 + 0.0782143i) q^{13} +(-4.04601 - 2.33597i) q^{14} +(8.49109 - 14.7070i) q^{16} +(-12.3133 + 21.3272i) q^{17} +(-18.9317 + 1.60945i) q^{19} +1.68594 q^{20} +(35.9269 + 20.7424i) q^{22} +(2.62250 + 4.54230i) q^{23} +(-8.07609 - 13.9882i) q^{25} -0.322972 q^{26} +(-0.297347 - 0.515021i) q^{28} +(31.4573 - 18.1619i) q^{29} +17.1105i q^{31} +(3.63586 - 2.09917i) q^{32} +(-44.0334 + 25.4227i) q^{34} +(-7.25797 + 12.5712i) q^{35} +42.7124i q^{37} +(-35.5123 - 16.6660i) q^{38} +(-42.8667 - 24.7491i) q^{40} +(-30.0928 - 17.3741i) q^{41} +(12.5553 - 21.7464i) q^{43} +(2.64032 + 4.57316i) q^{44} +10.8291i q^{46} +(14.6778 + 25.4227i) q^{47} -43.8797 q^{49} -33.3487i q^{50} +(-0.0356035 - 0.0205557i) q^{52} +(-48.4176 + 27.9539i) q^{53} +(64.4476 - 111.627i) q^{55} +17.4599i q^{56} +74.9962 q^{58} +(29.9269 + 17.2783i) q^{59} +(27.3805 + 47.4244i) q^{61} +(-17.6637 + 30.5944i) q^{62} -59.2606 q^{64} +1.00349i q^{65} +(66.0698 - 38.1454i) q^{67} -6.47216 q^{68} +(-25.9552 + 14.9852i) q^{70} +(-63.6080 - 36.7241i) q^{71} +(-45.9053 + 79.5103i) q^{73} +(-44.0932 + 76.3717i) q^{74} +(-2.85406 - 4.09740i) q^{76} -45.4662 q^{77} +(-53.1300 - 30.6746i) q^{79} +(-54.4703 - 94.3453i) q^{80} +(-35.8716 - 62.1313i) q^{82} +148.793 q^{83} +(78.9897 + 136.814i) q^{85} +(44.8990 - 25.9224i) q^{86} -155.036i q^{88} +(62.7829 - 36.2477i) q^{89} +(0.306546 - 0.176984i) q^{91} +(-0.689224 + 1.19377i) q^{92} +60.6093i q^{94} +(-51.7820 + 110.338i) q^{95} +(-70.0326 - 40.4334i) q^{97} +(-78.4589 - 45.2983i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7}+O(q^{10}) $ 6 * q - 3 * q^2 + 5 * q^4 - 4 * q^5 - 22 * q^7	$ 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7} + 54 q^{10} + 36 q^{11} - 3 q^{13} + 57 q^{14} - 23 q^{16} - 38 q^{17} - 10 q^{19} - 32 q^{20} + 36 q^{22} - 54 q^{23} - 21 q^{25} - 118 q^{26} - 101 q^{28} + 102 q^{29} + 63 q^{32} - 150 q^{34} + 24 q^{35} - 119 q^{38} + 30 q^{40} - 96 q^{41} + 107 q^{43} + 94 q^{44} + 50 q^{47} - 48 q^{49} + 399 q^{52} + 90 q^{53} + 148 q^{55} - 116 q^{58} + 27 q^{61} + 121 q^{62} + 46 q^{64} - 39 q^{67} + 388 q^{68} - 354 q^{70} - 84 q^{71} - 77 q^{73} - 219 q^{74} + 215 q^{76} - 260 q^{77} + 9 q^{79} - 312 q^{80} - 4 q^{82} + 348 q^{83} + 68 q^{85} - 249 q^{86} + 72 q^{89} - 393 q^{91} + 118 q^{92} - 104 q^{95} - 228 q^{97} - 540 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 + 5 * q^4 - 4 * q^5 - 22 * q^7 + 54 * q^10 + 36 * q^11 - 3 * q^13 + 57 * q^14 - 23 * q^16 - 38 * q^17 - 10 * q^19 - 32 * q^20 + 36 * q^22 - 54 * q^23 - 21 * q^25 - 118 * q^26 - 101 * q^28 + 102 * q^29 + 63 * q^32 - 150 * q^34 + 24 * q^35 - 119 * q^38 + 30 * q^40 - 96 * q^41 + 107 * q^43 + 94 * q^44 + 50 * q^47 - 48 * q^49 + 399 * q^52 + 90 * q^53 + 148 * q^55 - 116 * q^58 + 27 * q^61 + 121 * q^62 + 46 * q^64 - 39 * q^67 + 388 * q^68 - 354 * q^70 - 84 * q^71 - 77 * q^73 - 219 * q^74 + 215 * q^76 - 260 * q^77 + 9 * q^79 - 312 * q^80 - 4 * q^82 + 348 * q^83 + 68 * q^85 - 249 * q^86 + 72 * q^89 - 393 * q^91 + 118 * q^92 - 104 * q^95 - 228 * q^97 - 540 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.78805	+	1.03233i	0.894023	+	0.516164i	0.875256	−	0.483659i	$-0.160693\pi$
$2$	1.78805	+	1.03233i	0.894023	+	0.516164i	0.0187668	+	0.999824i	$0.494026\pi$
$3$		0			0
$3$		0			0
$4$	0.131406	+	0.227602i	0.0328515	+	0.0569005i
$5$	3.20750	−	5.55555i	0.641500	−	1.11111i	−0.343598	−	0.939117i	$-0.611646\pi$
$5$	3.20750	−	5.55555i	0.641500	−	1.11111i	0.985098	−	0.171993i	$-0.0550208\pi$
$6$		0			0
$7$	−2.26281			−0.323259			−0.161629	−	0.986852i	$-0.551675\pi$
$7$	−2.26281			−0.323259			−0.161629	+	0.986852i	$0.551675\pi$
$8$		−	7.71601i		−	0.964502i
$9$		0			0
$10$	11.4703	−	6.62239i	1.14703	−	0.662239i
$11$	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	−0.505201	−	0.863001i	$-0.668582\pi$
$13$	−0.135471	+	0.0782143i	−0.0104209	+	0.00601649i	0.494781	+	0.869018i	$0.335248\pi$
$14$	−4.04601	−	2.33597i	−0.289001	−	0.166855i
$15$		0			0
$16$	8.49109	−	14.7070i	0.530693	−	0.919187i
$17$	−12.3133	+	21.3272i	−0.724311	+	1.25454i	0.234947	+	0.972008i	$0.424508\pi$
$17$	−12.3133	+	21.3272i	−0.724311	+	1.25454i	−0.959257	+	0.282534i	$0.908825\pi$
$18$		0			0
$19$	−18.9317	+	1.60945i	−0.996406	+	0.0847081i
$19$	−18.9317	+	1.60945i	−0.996406	+	0.0847081i
$20$	1.68594			0.0842970
$21$		0			0
$22$	35.9269	+	20.7424i	1.63304	+	0.942836i
$23$	2.62250	+	4.54230i	0.114022	+	0.197491i	0.917388	−	0.397994i	$-0.130293\pi$
$23$	2.62250	+	4.54230i	0.114022	+	0.197491i	−0.803367	+	0.595485i	$0.796960\pi$
$24$		0			0
$25$	−8.07609	−	13.9882i	−0.323044	−	0.559528i
$26$	−0.322972			−0.0124220
$27$		0			0
$28$	−0.297347	−	0.515021i	−0.0106195	−	0.0183936i
$29$	31.4573	−	18.1619i	1.08474	−	0.626272i	0.152566	−	0.988293i	$-0.451246\pi$
$29$	31.4573	−	18.1619i	1.08474	−	0.626272i	0.932170	+	0.362021i	$0.117913\pi$
$30$		0			0
$31$			17.1105i			0.551952i	0.961165	+	0.275976i	$0.0890010\pi$
$31$			17.1105i			0.551952i	−0.961165	+	0.275976i	$0.910999\pi$
$32$	3.63586	−	2.09917i	0.113621	−	0.0655989i
$33$		0			0
$34$	−44.0334	+	25.4227i	−1.29510	+	0.747727i
$35$	−7.25797	+	12.5712i	−0.207370	+	0.359176i
$36$		0			0
$37$			42.7124i			1.15439i	0.816607	+	0.577194i	$0.195852\pi$
$37$			42.7124i			1.15439i	−0.816607	+	0.577194i	$0.804148\pi$
$38$	−35.5123	−	16.6660i	−0.934533	−	0.438578i
$39$		0			0
$40$	−42.8667	−	24.7491i	−1.07167	−	0.618728i
$41$	−30.0928	−	17.3741i	−0.733971	−	0.423758i	0.0859022	−	0.996304i	$-0.472623\pi$
$41$	−30.0928	−	17.3741i	−0.733971	−	0.423758i	−0.819873	+	0.572545i	$0.805956\pi$
$42$		0			0
$43$	12.5553	−	21.7464i	0.291984	−	0.505731i	−0.682295	−	0.731077i	$-0.739018\pi$
$43$	12.5553	−	21.7464i	0.291984	−	0.505731i	0.974279	+	0.225346i	$0.0723512\pi$
$44$	2.64032	+	4.57316i	0.0600072	+	0.103936i
$45$		0			0
$46$			10.8291i			0.235415i
$47$	14.6778	+	25.4227i	0.312294	+	0.540909i	0.978859	−	0.204538i	$-0.0655693\pi$
$47$	14.6778	+	25.4227i	0.312294	+	0.540909i	−0.666565	+	0.745447i	$0.732236\pi$
$48$		0			0
$49$	−43.8797			−0.895504
$50$		−	33.3487i		−	0.666975i
$51$		0			0
$52$	−0.0356035	−	0.0205557i	−0.000684682	−	0.000395301i
$53$	−48.4176	+	27.9539i	−0.913540	+	0.527433i	−0.881568	−	0.472056i	$-0.843512\pi$
$53$	−48.4176	+	27.9539i	−0.913540	+	0.527433i	−0.0319716	+	0.999489i	$0.510179\pi$
$54$		0			0
$55$	64.4476	−	111.627i	1.17178	−	2.02957i
$56$			17.4599i			0.311784i
$57$		0			0
$58$	74.9962			1.29304
$59$	29.9269	+	17.2783i	0.507235	+	0.292852i	0.731696	−	0.681631i	$-0.238729\pi$
$59$	29.9269	+	17.2783i	0.507235	+	0.292852i	−0.224461	+	0.974483i	$0.572062\pi$
$60$		0			0
$61$	27.3805	+	47.4244i	0.448860	+	0.777448i	0.998312	−	0.0580769i	$-0.0184968\pi$
$61$	27.3805	+	47.4244i	0.448860	+	0.777448i	−0.549452	+	0.835525i	$0.685164\pi$
$62$	−17.6637	+	30.5944i	−0.284898	+	0.493457i
$63$		0			0
$64$	−59.2606			−0.925947
$65$			1.00349i			0.0154383i
$66$		0			0
$67$	66.0698	−	38.1454i	0.986117	−	0.569335i	0.0820054	−	0.996632i	$-0.473868\pi$
$67$	66.0698	−	38.1454i	0.986117	−	0.569335i	0.904111	+	0.427297i	$0.140534\pi$
$68$	−6.47216			−0.0951788
$69$		0			0
$70$	−25.9552	+	14.9852i	−0.370788	+	0.214075i
$71$	−63.6080	−	36.7241i	−0.895887	−	0.517240i	−0.0200233	−	0.999800i	$-0.506374\pi$
$71$	−63.6080	−	36.7241i	−0.895887	−	0.517240i	−0.875863	+	0.482559i	$0.839707\pi$
$72$		0			0
$73$	−45.9053	+	79.5103i	−0.628840	+	1.08918i	0.358945	+	0.933359i	$0.383137\pi$
$73$	−45.9053	+	79.5103i	−0.628840	+	1.08918i	−0.987785	+	0.155824i	$0.950197\pi$
$74$	−44.0932	+	76.3717i	−0.595854	+	1.03205i
$75$		0			0
$76$	−2.85406	−	4.09740i	−0.0375534	−	0.0539132i
$77$	−45.4662			−0.590471
$78$		0			0
$79$	−53.1300	−	30.6746i	−0.672531	−	0.388286i	0.124504	−	0.992219i	$-0.460266\pi$
$79$	−53.1300	−	30.6746i	−0.672531	−	0.388286i	−0.797035	+	0.603933i	$0.793599\pi$
$80$	−54.4703	−	94.3453i	−0.680879	−	1.17932i
$81$		0			0
$82$	−35.8716	−	62.1313i	−0.437458	−	0.757699i
$83$	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
$86$	44.8990	−	25.9224i	0.522081	−	0.301424i
$87$		0			0
$88$		−	155.036i		−	1.76178i
$89$	62.7829	−	36.2477i	0.705426	−	0.407278i	−0.103939	−	0.994584i	$-0.533145\pi$
$89$	62.7829	−	36.2477i	0.705426	−	0.407278i	0.809365	+	0.587306i	$0.199811\pi$
$90$		0			0
$91$	0.306546	−	0.176984i	0.00336864	−	0.00194488i
$92$	−0.689224	+	1.19377i	−0.00749156	+	0.0129758i
$93$		0			0
$94$			60.6093i			0.644780i
$95$	−51.7820	+	110.338i	−0.545074	+	1.16146i
$96$		0			0
$97$	−70.0326	−	40.4334i	−0.721986	−	0.416839i	0.0934972	−	0.995620i	$-0.470195\pi$
$97$	−70.0326	−	40.4334i	−0.721986	−	0.416839i	−0.815483	+	0.578781i	$0.803529\pi$
$98$	−78.4589	−	45.2983i	−0.800601	−	0.462227i
$99$		0			0
$100$	2.12250	−	3.67627i	0.0212250	−	0.0367627i
$101$	76.6770	+	132.809i	0.759178	+	1.31494i	0.943270	+	0.332027i	$0.107732\pi$
$101$	76.6770	+	132.809i	0.759178	+	1.31494i	−0.184092	+	0.982909i	$0.558934\pi$
$102$		0			0
$103$			168.948i			1.64027i	0.572169	+	0.820136i	$0.306102\pi$
$103$			168.948i			1.64027i	−0.572169	+	0.820136i	$0.693898\pi$
$104$	0.603503	+	1.04530i	0.00580291	+	0.0100509i
$105$		0			0
$106$	−115.431			−1.08897
$107$		−	139.060i		−	1.29963i	−0.760093	−	0.649815i	$-0.774846\pi$
$107$		−	139.060i		−	1.29963i	0.760093	−	0.649815i	$-0.225154\pi$
$108$		0			0
$109$	−9.15888	−	5.28788i	−0.0840264	−	0.0485127i	0.457398	−	0.889262i	$-0.348781\pi$
$109$	−9.15888	−	5.28788i	−0.0840264	−	0.0485127i	−0.541424	+	0.840749i	$0.682115\pi$
$110$	230.471	−	133.062i	2.09519	−	1.20966i
$111$		0			0
$112$	−19.2137	+	33.2792i	−0.171551	+	0.297135i
$113$			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
$116$	8.26737	+	4.77317i	0.0712704	+	0.0411480i
$117$		0			0
$118$	35.6737	+	61.7887i	0.302320	+	0.523633i
$119$	27.8626	−	48.2595i	0.234140	−	0.405542i
$120$		0			0
$121$	282.721			2.33654
$122$			113.063i			0.926742i
$123$		0			0
$124$	−3.89438	+	2.24842i	−0.0314063	+	0.0181324i
$125$	56.7587			0.454070
$126$		0			0
$127$	−25.6547	+	14.8118i	−0.202006	+	0.116628i	−0.597591	−	0.801801i	$-0.703875\pi$
$127$	−25.6547	+	14.8118i	−0.202006	+	0.116628i	0.395585	+	0.918429i	$0.370542\pi$
$128$	−120.504	−	69.5731i	−0.941438	−	0.543540i
$129$		0			0
$130$	−1.03593	+	1.79428i	−0.00796870	+	0.0138022i
$131$	28.6526	−	49.6278i	0.218722	−	0.378838i	−0.735695	−	0.677313i	$-0.763144\pi$
$131$	28.6526	−	49.6278i	0.218722	−	0.378838i	0.954418	+	0.298474i	$0.0964777\pi$
$132$		0			0
$133$	42.8389	−	3.64189i	0.322097	−	0.0273826i
$134$	157.514			1.17548
$135$		0			0
$136$	164.561	+	95.0094i	1.21001	+	0.698599i
$137$	−47.4499	−	82.1856i	−0.346349	−	0.599895i	0.639249	−	0.769000i	$-0.279245\pi$
$137$	−47.4499	−	82.1856i	−0.346349	−	0.599895i	−0.985598	+	0.169105i	$0.945912\pi$
$138$		0			0
$139$	−91.2747	−	158.092i	−0.656652	−	1.13736i	−0.981477	−	0.191581i	$-0.938639\pi$
$139$	−91.2747	−	158.092i	−0.656652	−	1.13736i	0.324824	−	0.945774i	$-0.394695\pi$
$140$	−3.81496			−0.0272497
$141$		0			0
$142$	−75.8226	−	131.329i	−0.533962	−	0.924850i
$143$	−2.72200	+	1.57155i	−0.0190349	+	0.0109898i
$144$		0			0
$145$		−	233.017i		−	1.60701i
$146$	−164.162	+	94.7788i	−1.12439	+	0.649170i
$147$		0			0
$148$	−9.72142	+	5.61266i	−0.0656852	+	0.0379234i
$149$	5.50439	−	9.53389i	0.0369422	−	0.0639858i	−0.846963	−	0.531652i	$-0.821572\pi$
$149$	5.50439	−	9.53389i	0.0369422	−	0.0639858i	0.883905	+	0.467666i	$0.154905\pi$
$150$		0			0
$151$		−	238.846i		−	1.58176i	−0.611968	−	0.790882i	$-0.709622\pi$
$151$		−	238.846i		−	1.58176i	0.611968	−	0.790882i	$-0.290378\pi$
$152$	12.4186	+	146.077i	0.0817011	+	0.961035i
$153$		0			0
$154$	−81.2957	−	46.9361i	−0.527894	−	0.304780i
$155$	95.0582	+	54.8819i	0.613279	+	0.354077i
$156$		0			0
$157$	22.8125	−	39.5124i	0.145303	−	0.251671i	−0.784183	−	0.620529i	$-0.786918\pi$
$157$	22.8125	−	39.5124i	0.145303	−	0.251671i	0.929486	+	0.368858i	$0.120251\pi$
$158$	−63.3326	−	109.695i	−0.400839	−	0.694273i
$159$		0			0
$160$		−	26.9323i		−	0.168327i
$161$	−5.93421	−	10.2784i	−0.0368585	−	0.0638407i
$162$		0			0
$163$	5.89159			0.0361447			0.0180724	−	0.999837i	$-0.494247\pi$
$163$	5.89159			0.0361447			0.0180724	+	0.999837i	$0.494247\pi$
$164$		−	9.13224i		−	0.0556844i
$165$		0			0
$166$	266.048	+	153.603i	1.60270	+	0.925320i
$167$	−142.140	+	82.0646i	−0.851138	+	0.491405i	−0.861035	−	0.508546i	$-0.830183\pi$
$167$	−142.140	+	82.0646i	−0.851138	+	0.491405i	0.00989689	+	0.999951i	$0.496850\pi$
$168$		0			0
$169$	−84.4878	+	146.337i	−0.499928	+	0.865900i
$170$			326.173i			1.91867i
$171$		0			0
$172$	6.59938			0.0383685
$173$	−234.355	−	135.305i	−1.35465	−	0.782109i	−0.365755	−	0.930711i	$-0.619189\pi$
$173$	−234.355	−	135.305i	−1.35465	−	0.782109i	−0.988897	+	0.148603i	$0.952522\pi$
$174$		0			0
$175$	18.2747	+	31.6527i	0.104427	+	0.180872i
$176$	170.610	−	295.505i	0.969374	−	1.67900i
$177$		0			0
$178$	149.678			0.840890
$179$		−	186.439i		−	1.04156i	−0.853691	−	0.520779i	$-0.825641\pi$
$179$		−	186.439i		−	1.04156i	0.853691	−	0.520779i	$-0.174359\pi$
$180$		0			0
$181$	−40.1939	+	23.2059i	−0.222066	+	0.128210i	−0.606906	−	0.794773i	$-0.707590\pi$
$181$	−40.1939	+	23.2059i	−0.222066	+	0.128210i	0.384841	+	0.922983i	$0.374256\pi$
$182$	0.730824			0.00401552
$183$		0			0
$184$	35.0484	−	20.2352i	0.190481	−	0.109974i
$185$	237.291	+	137.000i	1.28265	+	0.740539i
$186$		0			0
$187$	−247.408	+	428.524i	−1.32304	+	2.29157i
$188$	−3.85751	+	6.68140i	−0.0205187	+	0.0355393i
$189$		0			0
$190$	−206.494	+	143.834i	−1.08681	+	0.757021i
$191$	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	−0.0220009	−	0.999758i	$-0.507004\pi$
$193$	−173.472	−	100.154i	−0.898817	−	0.518932i	−0.876816	+	0.480826i	$0.840337\pi$
$194$	−83.4811	−	144.593i	−0.430315	−	0.745327i
$195$		0			0
$196$	−5.76606	−	9.98710i	−0.0294187	−	0.0509546i
$197$	171.512			0.870620			0.435310	−	0.900281i	$-0.356639\pi$
$197$	171.512			0.870620			0.435310	+	0.900281i	$0.356639\pi$
$198$		0			0
$199$	−43.7500	−	75.7772i	−0.219849	−	0.380790i	0.734913	−	0.678162i	$-0.237223\pi$
$199$	−43.7500	−	75.7772i	−0.219849	−	0.380790i	−0.954762	+	0.297372i	$0.903890\pi$
$200$	−107.933	+	62.3152i	−0.539666	+	0.311576i
$201$		0			0
$202$			316.624i			1.56744i
$203$	−71.1820	+	41.0970i	−0.350650	+	0.202448i
$204$		0			0
$205$	−193.045	+	111.455i	−0.941684	+	0.543682i
$206$	−174.410	+	302.087i	−0.846650	+	1.46644i
$207$		0			0
$208$			2.65650i			0.0127716i
$209$	−380.391	+	32.3384i	−1.82005	+	0.154729i
$210$		0			0
$211$	16.3950	+	9.46566i	0.0777014	+	0.0448609i	0.538347	−	0.842723i	$-0.319049\pi$
$211$	16.3950	+	9.46566i	0.0777014	+	0.0448609i	−0.460646	+	0.887584i	$0.652382\pi$
$212$	−12.7247	−	7.34663i	−0.0600224	−	0.0346539i
$213$		0			0
$214$	143.556	−	248.646i	0.670823	−	1.16190i
$215$	−80.5423	−	139.503i	−0.374615	−	0.648853i
$216$		0			0
$217$		−	38.7178i		−	0.178423i
$218$	−10.9177	−	18.9100i	−0.0500810	−	0.0867429i
$219$		0			0
$220$	33.8752			0.153978
$221$		−	3.85230i		−	0.0174312i
$222$		0			0
$223$	−224.162	−	129.420i	−1.00521	−	0.580358i	−0.0954244	−	0.995437i	$-0.530421\pi$
$223$	−224.162	−	129.420i	−1.00521	−	0.580358i	−0.909786	+	0.415078i	$0.863754\pi$
$224$	−8.22727	+	4.75002i	−0.0367289	+	0.0212054i
$225$		0			0
$226$	−71.3939	+	123.658i	−0.315902	+	0.547159i
$227$		−	129.054i		−	0.568522i	−0.958747	−	0.284261i	$-0.908252\pi$
$227$		−	129.054i		−	0.568522i	0.958747	−	0.284261i	$-0.0917482\pi$
$228$		0			0
$229$	−98.8946			−0.431854			−0.215927	−	0.976409i	$-0.569277\pi$
$229$	−98.8946			−0.431854			−0.215927	+	0.976409i	$0.569277\pi$
$230$	60.1617	+	34.7344i	0.261572	+	0.151019i
$231$		0			0
$232$	−140.137	−	242.725i	−0.604041	−	1.04623i
$233$	−174.731	+	302.644i	−0.749920	+	1.29890i	0.197941	+	0.980214i	$0.436575\pi$
$233$	−174.731	+	302.644i	−0.749920	+	1.29890i	−0.947861	+	0.318685i	$0.896759\pi$
$234$		0			0
$235$	188.316			0.801346
$236$			9.08189i			0.0384826i
$237$		0			0
$238$	99.6394	−	57.5268i	0.418653	−	0.241709i
$239$	−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	−0.253529	−	0.967328i	$-0.581591\pi$
$241$	110.242	−	63.6485i	0.457438	−	0.264102i	0.710966	+	0.703226i	$0.248258\pi$
$242$	505.518	+	291.861i	2.08892	+	1.20604i
$243$		0			0
$244$	−7.19592	+	12.4637i	−0.0294915	+	0.0510807i
$245$	−140.744	+	243.776i	−0.574465	+	0.995003i
$246$		0			0
$247$	2.43882	−	1.69877i	0.00987376	−	0.00687759i
$248$	132.025			0.532358
$249$		0			0
$250$	101.487	+	58.5937i	0.405949	+	0.234375i
$251$	−177.023	−	306.613i	−0.705271	−	1.22157i	−0.966594	−	0.256314i	$-0.917492\pi$
$251$	−177.023	−	306.613i	−0.705271	−	1.22157i	0.261322	−	0.965252i	$-0.415841\pi$
$252$		0			0
$253$	52.6933	+	91.2675i	0.208274	+	0.360741i
$254$	−61.1625			−0.240797
$255$		0			0
$256$	−25.1234	−	43.5151i	−0.0981384	−	0.169981i
$257$	236.669	−	136.641i	0.920889	−	0.531676i	0.0369706	−	0.999316i	$-0.488229\pi$
$257$	236.669	−	136.641i	0.920889	−	0.531676i	0.883919	+	0.467641i	$0.154896\pi$
$258$		0			0
$259$		−	96.6500i		−	0.373166i
$260$	−0.228396	+	0.131865i	−0.000878447	+	0.000507171i
$261$		0			0
$262$	102.464	−	59.1579i	0.391086	−	0.225793i
$263$	75.5642	−	130.881i	0.287316	−	0.497646i	−0.685852	−	0.727741i	$-0.740570\pi$
$263$	75.5642	−	130.881i	0.287316	−	0.497646i	0.973168	+	0.230095i	$0.0739036\pi$
$264$		0			0
$265$			358.649i			1.35339i
$266$	80.3576	+	37.7120i	0.302096	+	0.141774i
$267$		0			0
$268$	17.3639	+	10.0251i	0.0647909	+	0.0374070i
$269$	−58.9364	−	34.0269i	−0.219094	−	0.126494i	0.386437	−	0.922316i	$-0.373706\pi$
$269$	−58.9364	−	34.0269i	−0.219094	−	0.126494i	−0.605531	+	0.795822i	$0.707039\pi$
$270$		0			0
$271$	56.8991	−	98.5521i	0.209960	−	0.363661i	−0.741742	−	0.670685i	$-0.766000\pi$
$271$	56.8991	−	98.5521i	0.209960	−	0.363661i	0.951702	+	0.307025i	$0.0993334\pi$
$272$	209.106	+	362.183i	0.768773	+	1.33155i
$273$		0			0
$274$		−	195.935i		−	0.715093i
$275$	−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	$0.207016\pi$
$278$		−	376.902i		−	1.35576i
$279$		0			0
$280$	96.9993	+	56.0026i	0.346426	+	0.200009i
$281$	−78.0928	+	45.0869i	−0.277910	+	0.160452i	−0.632477	−	0.774579i	$-0.717962\pi$
$281$	−78.0928	+	45.0869i	−0.277910	+	0.160452i	0.354567	+	0.935031i	$0.384628\pi$
$282$		0			0
$283$	34.5331	−	59.8131i	0.122025	−	0.211354i	−0.798541	−	0.601940i	$-0.794394\pi$
$283$	34.5331	−	59.8131i	0.122025	−	0.211354i	0.920566	+	0.390587i	$0.127728\pi$
$284$		−	19.3031i		−	0.0679685i
$285$		0			0
$286$	−6.48941			−0.0226902
$287$	68.0944	+	39.3143i	0.237263	+	0.136984i
$288$		0			0
$289$	−158.734	−	274.935i	−0.549252	−	0.951332i
$290$	240.550	−	416.645i	0.829484	−	1.43671i
$291$		0			0
$292$	−24.1289			−0.0826334
$293$			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
$296$	329.569			1.11341
$297$		0			0
$298$	19.6842	−	11.3647i	0.0660544	−	0.0381365i
$299$	−0.710545	−	0.410233i	−0.00237640	−	0.00137202i
$300$		0			0
$301$	−28.4103	+	49.2081i	−0.0943864	+	0.163482i
$302$	246.568	−	427.068i	0.816451	−	1.41413i
$303$		0			0
$304$	−137.081	+	292.095i	−0.450923	+	0.960838i
$305$	351.291			1.15177
$306$		0			0
$307$	−201.882	−	116.556i	−0.657595	−	0.379663i	0.133765	−	0.991013i	$-0.457293\pi$
$307$	−201.882	−	116.556i	−0.657595	−	0.379663i	−0.791360	+	0.611350i	$0.790627\pi$
$308$	−5.97454	−	10.3482i	−0.0193979	−	0.0335981i
$309$		0			0
$310$	113.312	+	196.263i	0.365524	+	0.633106i
$311$	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	0.752761	−	0.658294i	$-0.228722\pi$
$313$	−60.6339	−	105.021i	−0.193719	−	0.335530i	−0.946480	+	0.322763i	$0.895388\pi$
$314$	81.5796	−	47.1000i	0.259808	−	0.150000i
$315$		0			0
$316$		−	16.1233i		−	0.0510232i
$317$	−286.409	+	165.358i	−0.903499	+	0.521635i	−0.878334	−	0.478048i	$-0.841344\pi$
$317$	−286.409	+	165.358i	−0.903499	+	0.521635i	−0.0251649	+	0.999683i	$0.508011\pi$
$318$		0			0
$319$	632.066	−	364.924i	1.98140	−	1.14396i
$320$	−190.078	+	329.225i	−0.593995	+	1.02883i
$321$		0			0
$322$		−	24.5042i		−	0.0761001i
$323$	198.786	−	423.579i	0.615437	−	1.31139i
$324$		0			0
$325$	2.18816	+	1.26333i	0.00673279	+	0.00388718i
$326$	10.5344	+	6.08206i	0.0323142	+	0.0186566i
$327$		0			0
$328$	−134.059	+	232.197i	−0.408716	+	0.707916i
$329$	−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	$0.770948\pi$
$332$	19.5523	+	33.8655i	0.0588924	+	0.102005i
$333$		0			0
$334$	−338.870			−1.01458
$335$		−	489.406i		−	1.46091i
$336$		0			0
$337$	−217.027	−	125.301i	−0.643997	−	0.371812i	0.142156	−	0.989844i	$-0.454597\pi$
$337$	−217.027	−	125.301i	−0.643997	−	0.371812i	−0.786153	+	0.618033i	$0.787930\pi$
$338$	−302.136	+	174.438i	−0.893894	+	0.516090i
$339$		0			0
$340$	−20.7594	+	35.9564i	−0.0610572	+	0.105754i
$341$			343.798i			1.00821i
$342$		0			0
$343$	210.169			0.612738
$344$	−167.796	−	96.8770i	−0.487779	−	0.281619i
$345$		0			0
$346$	−279.358	−	483.862i	−0.807393	−	1.39845i
$347$	83.6670	−	144.915i	0.241115	−	0.417624i	−0.719917	−	0.694060i	$-0.755820\pi$
$347$	83.6670	−	144.915i	0.241115	−	0.417624i	0.961032	+	0.276436i	$0.0891535\pi$
$348$		0			0
$349$	−486.776			−1.39477			−0.697387	−	0.716695i	$-0.745654\pi$
$349$	−486.776			−1.39477			−0.697387	+	0.716695i	$0.745654\pi$
$350$			75.4619i			0.215605i
$351$		0			0
$352$	73.0547	−	42.1781i	0.207542	−	0.119824i
$353$	−30.1507			−0.0854128			−0.0427064	−	0.999088i	$-0.513598\pi$
$353$	−30.1507			−0.0854128			−0.0427064	+	0.999088i	$0.513598\pi$
$354$		0			0
$355$	−408.045	+	235.585i	−1.14942	+	0.663619i
$356$	16.5001	+	9.52635i	0.0463486	+	0.0267594i
$357$		0			0
$358$	192.466	−	333.361i	0.537615	−	0.931177i
$359$	75.0088	−	129.919i	0.208938	−	0.361891i	−0.742442	−	0.669910i	$-0.766333\pi$
$359$	75.0088	−	129.919i	0.208938	−	0.361891i	0.951380	+	0.308019i	$0.0996659\pi$
$360$		0			0
$361$	355.819	−	60.9394i	0.985649	−	0.168807i
$362$	−95.8247			−0.264709
$363$		0			0
$364$	0.0805640	+	0.0465136i	0.000221330	+	0.000127785i
$365$	294.482	+	510.058i	0.806801	+	1.39742i
$366$		0			0
$367$	248.090	+	429.704i	0.675994	+	1.17086i	0.976177	+	0.216975i	$0.0696189\pi$
$367$	248.090	+	429.704i	0.675994	+	1.17086i	−0.300183	+	0.953882i	$0.597048\pi$
$368$	89.0714			0.242042
$369$		0			0
$370$	282.858	+	489.924i	0.764480	+	1.32412i
$371$	109.560	−	63.2545i	0.295310	−	0.170497i
$372$		0			0
$373$		−	449.613i		−	1.20540i	−0.797969	−	0.602698i	$-0.794092\pi$
$373$		−	449.613i		−	1.20540i	0.797969	−	0.602698i	$-0.205908\pi$
$374$	−884.755	+	510.814i	−2.36566	+	1.36581i
$375$		0			0
$376$	196.162	−	113.254i	0.521707	−	0.301208i
$377$	−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	$0.786395\pi$
$380$	−31.9177	+	2.71344i	−0.0839940	+	0.00714064i
$381$		0			0
$382$	65.6611	+	37.9094i	0.171888	+	0.0992393i
$383$	23.4258	+	13.5249i	0.0611641	+	0.0353131i	0.530270	−	0.847829i	$-0.322090\pi$
$383$	23.4258	+	13.5249i	0.0611641	+	0.0353131i	−0.469106	+	0.883142i	$0.655424\pi$
$384$		0			0
$385$	−145.833	+	252.590i	−0.378787	+	0.656078i
$386$	−206.784	−	358.160i	−0.535709	−	0.927875i
$387$		0			0
$388$		−	21.2528i		−	0.0547752i
$389$	−177.144	−	306.822i	−0.455382	−	0.788745i	0.543328	−	0.839520i	$-0.317164\pi$
$389$	−177.144	−	306.822i	−0.455382	−	0.788745i	−0.998710	+	0.0507758i	$0.983831\pi$
$390$		0			0
$391$	−129.166			−0.330348
$392$			338.576i			0.863715i
$393$		0			0
$394$	306.672	+	177.057i	0.778354	+	0.449383i
$395$	−340.829	+	196.777i	−0.862857	+	0.498171i
$396$		0			0
$397$	−79.5105	+	137.716i	−0.200278	+	0.346892i	−0.948618	−	0.316423i	$-0.897518\pi$
$397$	−79.5105	+	137.716i	−0.200278	+	0.346892i	0.748340	+	0.663316i	$0.230851\pi$
$398$		−	180.657i		−	0.453913i
$399$		0			0
$400$	−274.299			−0.685748
$401$	277.534	+	160.234i	0.692105	+	0.399587i	0.804400	−	0.594088i	$-0.202487\pi$
$401$	277.534	+	160.234i	0.692105	+	0.399587i	−0.112295	+	0.993675i	$0.535820\pi$
$402$		0			0
$403$	−1.33829	−	2.31798i	−0.00332081	−	0.00575181i
$404$	−20.1517	+	34.9037i	−0.0498803	+	0.0863953i
$405$		0			0
$406$	−169.702			−0.417986
$407$			858.211i			2.10863i
$408$		0			0
$409$	−251.776	+	145.363i	−0.615590	+	0.355411i	−0.775150	−	0.631777i	$-0.782326\pi$
$409$	−251.776	+	145.363i	−0.615590	+	0.355411i	0.159560	+	0.987188i	$0.448992\pi$
$410$	−460.232			−1.12252
$411$		0			0
$412$	−38.4529	+	22.2008i	−0.0933323	+	0.0538854i
$413$	−67.7189	−	39.0975i	−0.163968	−	0.0946671i
$414$		0			0
$415$	477.253	−	826.626i	1.15001	−	1.99187i
$416$	−0.328370	+	0.568753i	−0.000789350	+	0.00136719i
$417$		0			0
$418$	−713.541	−	334.866i	−1.70704	−	0.801115i
$419$	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	0.612583	−	0.790406i	$-0.290131\pi$
$421$	98.6666	+	56.9652i	0.234362	+	0.135309i	−0.378220	+	0.925716i	$0.623464\pi$
$422$	19.5433	+	33.8501i	0.0463112	+	0.0802134i
$423$		0			0
$424$	215.693	+	373.591i	0.508710	+	0.881111i
$425$	397.773			0.935936
$426$		0			0
$427$	−61.9568	−	107.312i	−0.145098	−	0.251317i
$428$	31.6504	−	18.2734i	0.0739496	−	0.0426948i
$429$		0			0
$430$		−	332.585i		−	0.773453i
$431$	−229.263	+	132.365i	−0.531932	+	0.307111i	−0.741803	−	0.670618i	$-0.766029\pi$
$431$	−229.263	+	132.365i	−0.531932	+	0.307111i	0.209871	+	0.977729i	$0.432696\pi$
$432$		0			0
$433$	−631.333	+	364.500i	−1.45804	+	0.841802i	−0.998915	−	0.0465669i	$-0.985172\pi$
$433$	−631.333	+	364.500i	−1.45804	+	0.841802i	−0.459129	+	0.888369i	$0.651839\pi$
$434$	39.9695	−	69.2293i	0.0920957	−	0.159514i
$435$		0			0
$436$		−	2.77944i		−	0.00637486i
$437$	−56.9589	−	81.7726i	−0.130341	−	0.187123i
$438$		0			0
$439$	319.591	+	184.516i	0.727998	+	0.420310i	0.817689	−	0.575660i	$-0.195255\pi$
$439$	319.591	+	184.516i	0.727998	+	0.420310i	−0.0896911	+	0.995970i	$0.528588\pi$
$440$	−861.312	−	497.279i	−1.95753	−	1.13018i
$441$		0			0
$442$	3.97684	−	6.88809i	0.00899738	−	0.0155839i
$443$	291.547	+	504.975i	0.658120	+	1.13990i	0.981102	+	0.193492i	$0.0619815\pi$
$443$	291.547	+	504.975i	0.658120	+	1.13990i	−0.322982	+	0.946405i	$0.604685\pi$
$444$		0			0
$445$		−	465.058i		−	1.04507i
$446$	−267.208	−	462.818i	−0.599121	−	1.03771i
$447$		0			0
$448$	134.096			0.299321
$449$		−	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
$452$	−15.7405	+	9.08779i	−0.0348242	+	0.0201057i
$453$		0			0
$454$	133.227	−	230.755i	0.293451	−	0.508272i
$455$		−	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	$0.313562\pi$
$458$	−176.828	−	102.092i	−0.386088	−	0.222908i
$459$		0			0
$460$	4.42137	+	7.65803i	0.00961167	+	0.0166479i
$461$	−136.902	+	237.122i	−0.296968	+	0.514364i	−0.975441	−	0.220262i	$-0.929309\pi$
$461$	−136.902	+	237.122i	−0.296968	+	0.514364i	0.678473	+	0.734626i	$0.262642\pi$
$462$		0			0
$463$	319.780			0.690669			0.345334	−	0.938480i	$-0.387765\pi$
$463$	319.780			0.690669			0.345334	+	0.938480i	$0.387765\pi$
$464$		−	616.857i		−	1.32943i
$465$		0			0
$466$	−624.855	+	360.760i	−1.34089	+	0.774164i
$467$	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
$470$	336.718	+	194.404i	0.716421	+	0.413626i
$471$		0			0
$472$	133.319	−	230.916i	0.282457	−	0.489229i
$473$	252.271	−	436.947i	0.533344	−	0.923778i
$474$		0			0
$475$	175.408	+	251.822i	0.369279	+	0.530153i
$476$	14.6453			0.0307674
$477$		0			0
$478$	−538.364	−	310.825i	−1.12629	−	0.650261i
$479$	−204.559	−	354.306i	−0.427054	−	0.739679i	0.569556	−	0.821953i	$-0.307115\pi$
$479$	−204.559	−	354.306i	−0.427054	−	0.739679i	−0.996610	+	0.0822735i	$0.973782\pi$
$480$		0			0
$481$	−3.34072	−	5.78629i	−0.00694536	−	0.0120297i
$482$	262.825			0.545280
$483$		0			0
$484$	37.1512	+	64.3478i	0.0767588	+	0.132950i
$485$	−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	$0.772566\pi$
$488$	365.927	−	211.268i	0.749850	−	0.432926i
$489$		0			0
$490$	−503.314	+	290.588i	−1.02717	+	0.593037i
$491$	173.278	−	300.126i	0.352908	−	0.611255i	−0.633850	−	0.773456i	$-0.718526\pi$
$491$	173.278	−	300.126i	0.352908	−	0.611255i	0.986758	+	0.162202i	$0.0518595\pi$
$492$		0			0
$493$			894.530i			1.81446i
$494$	6.11440	−	0.519808i	0.0123773	−	0.00105224i
$495$		0			0
$496$	251.644	+	145.287i	0.507347	+	0.292917i
$497$	143.933	+	83.0997i	0.289603	+	0.167203i
$498$		0			0
$499$	−40.3510	+	69.8900i	−0.0808638	+	0.140060i	−0.903621	−	0.428333i	$-0.859101\pi$
$499$	−40.3510	+	69.8900i	−0.0808638	+	0.140060i	0.822757	+	0.568393i	$0.192435\pi$
$500$	7.45844	+	12.9184i	0.0149169	+	0.0258368i
$501$		0			0
$502$		−	730.984i		−	1.45614i
$503$	247.050	+	427.903i	0.491153	+	0.850701i	0.999948	−	0.0101862i	$-0.00324242\pi$
$503$	247.050	+	427.903i	0.491153	+	0.850701i	−0.508796	+	0.860887i	$0.669909\pi$
$504$		0			0
$505$	983.766			1.94805
$506$			217.587i			0.430014i
$507$		0			0
$508$	−6.74237	−	3.89271i	−0.0132724	−	0.00766282i
$509$	−63.9084	+	36.8975i	−0.125557	+	0.0724902i	−0.561463	−	0.827502i	$-0.689761\pi$
$509$	−63.9084	+	36.8975i	−0.125557	+	0.0724902i	0.435906	+	0.899992i	$0.356428\pi$
$510$		0			0
$511$	103.875	−	179.917i	0.203278	−	0.352088i
$512$			452.842i			0.884457i
$513$		0			0
$514$	564.232			1.09773
$515$	938.599	+	541.900i	1.82252	+	1.05223i
$516$		0			0
$517$	294.918	+	510.814i	0.570442	+	0.988034i
$518$	99.7746	−	172.815i	0.192615	−	0.333619i
$519$		0			0
$520$	7.74294			0.0148903
$521$		−	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	$-0.527739\pi$
$523$	382.935	−	221.088i	0.732190	−	0.422730i	0.819223	+	0.573475i	$0.194405\pi$
$524$	15.0605			0.0287415
$525$		0			0
$526$	270.225	−	156.014i	0.513735	−	0.296605i
$527$	−364.919	−	210.686i	−0.692447	−	0.399784i
$528$		0			0
$529$	250.745	−	434.303i	0.473998	−	0.820989i
$530$	−370.243	+	641.281i	−0.698573	+	1.20996i
$531$		0			0
$532$	6.45819	+	9.27165i	0.0121395	+	0.0174279i
$533$	5.43561			0.0101981
$534$		0			0
$535$	−772.557	−	446.036i	−1.44403	−	0.833712i
$536$	−294.331	−	509.796i	−0.549124	−	0.951111i
$537$		0			0
$538$	−70.2539	−	121.683i	−0.130584	−	0.226177i
$539$	−881.666			−1.63574
$540$		0			0
$541$	−487.737	−	844.785i	−0.901547	−	1.56152i	−0.825487	−	0.564421i	$-0.809099\pi$
$541$	−487.737	−	844.785i	−0.901547	−	1.56152i	−0.0760596	−	0.997103i	$-0.524234\pi$
$542$	203.476	−	117.477i	0.375418	−	0.216747i
$543$		0			0
$544$			103.390i			0.190056i
$545$	−58.7542	+	33.9217i	−0.107806	+	0.0622417i
$546$		0			0
$547$	350.050	−	202.102i	0.639945	−	0.369473i	−0.144648	−	0.989483i	$-0.546205\pi$
$547$	350.050	−	202.102i	0.639945	−	0.369473i	0.784594	+	0.620010i	$0.212872\pi$
$548$	12.4704	−	21.5994i	0.0227562	−	0.0394149i
$549$		0			0
$550$		−	670.070i		−	1.21831i
$551$	−566.310	+	394.465i	−1.02779	+	0.715907i
$552$		0			0
$553$	120.223	+	69.4109i	0.217402	+	0.125517i
$554$	788.368	+	455.164i	1.42305	+	0.821596i
$555$		0			0
$556$	23.9881	−	41.5486i	0.0431441	−	0.0747277i
$557$	29.9352	+	51.8492i	0.0537435	+	0.0930866i	0.891646	−	0.452734i	$-0.149551\pi$
$557$	29.9352	+	51.8492i	0.0537435	+	0.0930866i	−0.837902	+	0.545821i	$0.816218\pi$
$558$		0			0
$559$			3.92802i			0.00702687i
$560$	123.256	+	213.486i	0.220100	+	0.381225i
$561$		0			0
$562$	−186.178			−0.331278
$563$			247.579i			0.439749i	0.975528	+	0.219874i	$0.0705648\pi$
$563$			247.579i			0.439749i	−0.975528	+	0.219874i	$0.929435\pi$
$564$		0			0
$565$	384.211	+	221.824i	0.680020	+	0.392610i
$566$	123.494	−	71.2990i	0.218186	−	0.125970i
$567$		0			0
$568$	−283.363	+	490.800i	−0.498879	+	0.864084i
$569$		−	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	$-0.684180\pi$
$571$	−624.523			−1.09373			−0.546867	+	0.837219i	$0.684180\pi$
$572$	−0.715374	−	0.413021i	−0.00125065	−	0.000722065i
$573$		0			0
$574$	81.1706	+	140.592i	0.141412	+	0.244933i
$575$	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	$0.448596\pi$
$578$		−	655.462i		−	1.13402i
$579$		0			0
$580$	53.0352	−	30.6199i	0.0914399	−	0.0527929i
$581$	−336.690			−0.579501
$582$		0			0
$583$	−972.846	+	561.673i	−1.66869	+	0.963418i
$584$	613.503	+	354.206i	1.05052	+	0.606517i
$585$		0			0
$586$	−423.501	+	733.525i	−0.722698	+	1.25175i
$587$	130.891	−	226.710i	0.222983	−	0.386218i	−0.732729	−	0.680520i	$-0.761754\pi$
$587$	130.891	−	226.710i	0.222983	−	0.386218i	0.955712	+	0.294302i	$0.0950872\pi$
$588$		0			0
$589$	−27.5386	−	323.931i	−0.0467548	−	0.549968i
$590$	457.694			0.775752
$591$		0			0
$592$	628.170	+	362.674i	1.06110	+	0.612626i
$593$	124.254	+	215.215i	0.209535	+	0.362925i	0.951568	−	0.307438i	$-0.0994717\pi$
$593$	124.254	+	215.215i	0.209535	+	0.362925i	−0.742033	+	0.670363i	$0.766138\pi$
$594$		0			0
$595$	−178.739	−	309.585i	−0.300401	−	0.520310i
$596$	2.89324			0.00485443
$597$		0			0
$598$	−0.846992	−	1.46703i	−0.00141637	−	0.00245323i
$599$	167.646	−	96.7905i	0.279877	−	0.161587i	−0.353491	−	0.935438i	$-0.615005\pi$
$599$	167.646	−	96.7905i	0.279877	−	0.161587i	0.633368	+	0.773851i	$0.281672\pi$
$600$		0			0
$601$			675.975i			1.12475i	0.826882	+	0.562375i	$0.190112\pi$
$601$			675.975i			1.12475i	−0.826882	+	0.562375i	$0.809888\pi$
$602$	−101.598	+	58.6576i	−0.168767	+	0.0974378i
$603$		0			0
$604$	54.3619	−	31.3859i	0.0900032	−	0.0519634i
$605$	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	$-0.102182\pi$
$608$	−65.4546	+	45.5925i	−0.107656	+	0.0749877i
$609$		0			0
$610$	628.125	+	362.648i	1.02971	+	0.594505i
$611$	−3.97684	−	2.29603i	−0.00650874	−	0.00375782i
$612$		0			0
$613$	−27.5410	+	47.7025i	−0.0449283	+	0.0778180i	−0.887615	−	0.460586i	$-0.847639\pi$
$613$	−27.5410	+	47.7025i	−0.0449283	+	0.0778180i	0.842687	+	0.538404i	$0.180973\pi$
$614$	−240.649	−	416.817i	−0.391937	−	0.678854i
$615$		0			0
$616$			350.818i			0.569510i
$617$	51.7851	+	89.6944i	0.0839305	+	0.145372i	0.904935	−	0.425550i	$-0.139919\pi$
$617$	51.7851	+	89.6944i	0.0839305	+	0.145372i	−0.821004	+	0.570922i	$0.806586\pi$
$618$		0			0
$619$	−263.102			−0.425043			−0.212521	−	0.977156i	$-0.568168\pi$
$619$	−263.102			−0.425043			−0.212521	+	0.977156i	$0.568168\pi$
$620$			28.8473i			0.0465278i
$621$		0			0
$622$	789.030	+	455.547i	1.26854	+	0.732390i
$623$	−142.066	+	82.0218i	−0.228035	+	0.131656i
$624$		0			0
$625$	383.956	−	665.031i	0.614329	−	1.06405i
$626$		−	250.377i		−	0.399963i
$627$		0			0
$628$	11.9908			0.0190936
$629$	−910.936	−	525.929i	−1.44823	−	0.836135i
$630$		0			0
$631$	72.5474	+	125.656i	0.114972	+	0.199137i	0.917769	−	0.397116i	$-0.129989\pi$
$631$	72.5474	+	125.656i	0.114972	+	0.199137i	−0.802797	+	0.596253i	$0.796655\pi$
$632$	−236.686	+	409.952i	−0.374503	+	0.648658i
$633$		0			0
$634$	−682.817			−1.07700
$635$			190.035i			0.299267i
$636$		0			0
$637$	5.94443	−	3.43202i	0.00933192	−	0.00538779i
$638$	1506.88			2.36189
$639$		0			0
$640$	−773.034	+	446.311i	−1.20787	+	0.697361i
$641$	583.796	+	337.055i	0.910758	+	0.525826i	0.880675	−	0.473721i	$-0.157089\pi$
$641$	583.796	+	337.055i	0.910758	+	0.525826i	0.0300832	+	0.999547i	$0.490423\pi$
$642$		0			0
$643$	0.719856	−	1.24683i	0.00111953	−	0.00193908i	−0.865465	−	0.500969i	$-0.832977\pi$
$643$	0.719856	−	1.24683i	0.00111953	−	0.00193908i	0.866585	+	0.499030i	$0.166310\pi$
$644$	1.55958	−	2.70128i	0.00242171	−	0.00419453i
$645$		0			0
$646$	792.711	−	552.165i	1.22711	−	0.854745i
$647$	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
$650$	2.60835	+	4.51779i	0.00401284	+	0.00695045i
$651$		0			0
$652$	0.774191	+	1.34094i	0.00118741	+	0.00205665i
$653$	−822.374			−1.25938			−0.629689	−	0.776847i	$-0.716818\pi$
$653$	−822.374			−1.25938			−0.629689	+	0.776847i	$0.716818\pi$
$654$		0			0
$655$	−183.807	−	318.362i	−0.280621	−	0.486049i
$656$	−511.041	+	295.050i	−0.779027	+	0.449771i
$657$		0			0
$658$		−	137.147i		−	0.208431i
$659$	549.386	−	317.188i	0.833666	−	0.481317i	−0.0214404	−	0.999770i	$-0.506825\pi$
$659$	549.386	−	317.188i	0.833666	−	0.481317i	0.855106	+	0.518453i	$0.173492\pi$
$660$		0			0
$661$	−818.470	+	472.544i	−1.23823	+	0.714893i	−0.968732	−	0.248108i	$-0.920191\pi$
$661$	−818.470	+	472.544i	−1.23823	+	0.714893i	−0.269498	+	0.963001i	$0.586858\pi$
$662$	−450.413	+	780.138i	−0.680382	+	1.17846i
$663$		0			0
$664$		−	1148.09i		−	1.72905i
$665$	117.173	−	249.675i	0.176200	−	0.375451i
$666$		0			0
$667$	164.993	+	95.2590i	0.247366	+	0.142817i
$668$	−37.3561	−	21.5676i	−0.0559223	−	0.0322868i
$669$		0			0
$670$	505.228	−	875.080i	0.754071	−	1.30609i
$671$	550.150	+	952.888i	0.819896	+	1.42010i
$672$		0			0
$673$			570.803i			0.848147i	0.905628	+	0.424074i	$0.139400\pi$
$673$			570.803i			0.848147i	−0.905628	+	0.424074i	$0.860600\pi$
$674$	−258.703	−	448.086i	−0.383832	−	0.664817i
$675$		0			0
$676$	−44.4088			−0.0656935
$677$		−	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
$680$	1055.66	−	609.485i	1.55244	−	0.896302i
$681$		0			0
$682$	−354.913	+	614.727i	−0.520400	+	0.901359i
$683$			106.224i			0.155525i	0.996972	+	0.0777627i	$0.0247776\pi$
$683$			106.224i			0.155525i	−0.996972	+	0.0777627i	$0.975222\pi$
$684$		0			0
$685$	−608.781			−0.888732
$686$	375.792	+	216.964i	0.547802	+	0.316274i
$687$		0			0
$688$	−213.217	−	369.302i	−0.309908	−	0.536776i
$689$	4.37279	−	7.57390i	0.00634658	−	0.0109926i
$690$		0			0
$691$	244.177			0.353367			0.176684	−	0.984268i	$-0.443463\pi$
$691$	244.177			0.353367			0.176684	+	0.984268i	$0.443463\pi$
$692$		−	71.1195i		−	0.102774i
$693$		0			0
$694$	299.201	−	172.744i	0.431125	−	0.248910i
$695$	−1171.05			−1.68497
$696$		0			0
$697$	741.082	−	427.864i	1.06325	−	0.613865i
$698$	−870.378	−	502.513i	−1.24696	−	0.719932i
$699$		0			0
$700$	−4.80281	+	8.31871i	−0.00686115	+	0.0118839i
$701$	−143.276	+	248.161i	−0.204388	+	0.354010i	−0.949938	−	0.312440i	$-0.898854\pi$
$701$	−143.276	+	248.161i	−0.204388	+	0.354010i	0.745550	+	0.666450i	$0.232187\pi$
$702$		0			0
$703$	−68.7436	−	808.618i	−0.0977860	−	1.15024i
$704$	−1190.71			−1.69135
$705$		0			0
$706$	−53.9108	−	31.1254i	−0.0763610	−	0.0440870i
$707$	−173.506	−	300.521i	−0.245411	−	0.425065i
$708$		0			0
$709$	−5.70585	−	9.88282i	−0.00804774	−	0.0139391i	0.861973	−	0.506953i	$-0.169228\pi$
$709$	−5.70585	−	9.88282i	−0.00804774	−	0.0139391i	−0.870021	+	0.493014i	$0.835895\pi$
$710$	−972.804			−1.37015
$711$		0			0
$712$	−279.688	−	484.434i	−0.392820	−	0.680385i
$713$	−77.7209	+	44.8722i	−0.109006	+	0.0629344i
$714$		0			0
$715$			20.1629i			0.0281999i
$716$	42.4339	−	24.4992i	0.0592652	−	0.0342168i
$717$		0			0
$718$	268.238	−	154.867i	0.373591	−	0.215693i
$719$	−438.491	+	759.488i	−0.609862	+	1.05631i	0.381401	+	0.924410i	$0.375442\pi$
$719$	−438.491	+	759.488i	−0.609862	+	1.05631i	−0.991263	+	0.131902i	$0.957892\pi$
$720$		0			0
$721$		−	382.298i		−	0.530232i
$722$	699.131	+	258.360i	0.968325	+	0.357839i
$723$		0			0
$724$	−10.5634	−	6.09880i	−0.0145904	−	0.00842376i
$725$	−508.105	−	293.354i	−0.700834	−	0.404627i
$726$		0			0
$727$	−360.167	+	623.827i	−0.495415	+	0.858084i	−0.999986	−	0.00528653i	$-0.998317\pi$
$727$	−360.167	+	623.827i	−0.495415	+	0.858084i	0.504571	+	0.863370i	$0.331651\pi$
$728$	−1.36561	−	2.36531i	−0.00187584	−	0.00324905i
$729$		0			0
$730$			1216.01i			1.66577i
$731$	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	$0.537137\pi$
$734$			1024.44i			1.39570i
$735$		0			0
$736$	19.0701	+	11.0101i	0.0259104	+	0.0149594i
$737$	1327.53	−	766.449i	1.80126	−	1.03996i
$738$		0			0
$739$	530.334	−	918.566i	0.717637	−	1.24298i	−0.244296	−	0.969701i	$-0.578557\pi$
$739$	530.334	−	918.566i	0.717637	−	1.24298i	0.961933	−	0.273284i	$-0.0881098\pi$
$740$			72.0104i			0.0973114i
$741$		0			0
$742$	261.198			0.352019
$743$	−290.537	−	167.742i	−0.391033	−	0.225763i	0.291575	−	0.956548i	$-0.405821\pi$
$743$	−290.537	−	167.742i	−0.391033	−	0.225763i	−0.682607	+	0.730785i	$0.739154\pi$
$744$		0			0
$745$	−35.3107	−	61.1599i	−0.0473969	−	0.0820938i
$746$	464.148	−	803.928i	0.622182	−	1.07765i
$747$		0			0
$748$	−130.044			−0.173855
$749$			314.668i			0.420117i
$750$		0			0
$751$	−1128.41	+	651.490i	−1.50255	+	0.867497i	−0.502554	+	0.864546i	$0.667606\pi$
$751$	−1128.41	+	651.490i	−1.50255	+	0.867497i	−0.999996	+	0.00295120i	$0.999061\pi$
$752$	498.522			0.662929
$753$		0			0
$754$	−10.1598	+	5.86578i	−0.0134746	+	0.00777955i
$755$	−1326.92	−	766.100i	−1.75751	−	1.01470i
$756$		0			0
$757$	−60.1511	+	104.185i	−0.0794598	+	0.137628i	−0.903017	−	0.429605i	$-0.858653\pi$
$757$	−60.1511	+	104.185i	−0.0794598	+	0.137628i	0.823557	+	0.567233i	$0.191986\pi$
$758$	−486.574	+	842.771i	−0.641919	+	1.11184i
$759$		0			0
$760$	851.373	+	399.551i	1.12023	+	0.525725i
$761$	−1346.45			−1.76932			−0.884658	−	0.466240i	$-0.845608\pi$
$761$	−1346.45			−1.76932			−0.884658	+	0.466240i	$0.845608\pi$
$762$		0			0
$763$	20.7248	+	11.9655i	0.0271623	+	0.0156822i
$764$	4.82553	+	8.35805i	0.00631613	+	0.0109399i
$765$		0			0
$766$	27.9243	+	48.3663i	0.0364547	+	0.0631414i
$767$	−5.40564			−0.00704777
$768$		0			0
$769$	109.016	+	188.821i	0.141763	+	0.245541i	0.928161	−	0.372180i	$-0.121390\pi$
$769$	109.016	+	188.821i	0.141763	+	0.245541i	−0.786398	+	0.617721i	$0.788056\pi$
$770$	−521.512	+	301.095i	−0.677288	+	0.391033i
$771$		0			0
$772$		−	52.6433i		−	0.0681909i
$773$	48.6422	−	28.0836i	0.0629266	−	0.0363307i	−0.468207	−	0.883619i	$-0.655100\pi$
$773$	48.6422	−	28.0836i	0.0629266	−	0.0363307i	0.531133	+	0.847288i	$0.321766\pi$
$774$		0			0
$775$	239.345	−	138.186i	0.308832	−	0.178304i
$776$	−311.984	+	540.373i	−0.402042	+	0.696357i
$777$		0			0
$778$		−	731.482i		−	0.940208i
$779$	597.671	+	280.488i	0.767229	+	0.360062i
$780$		0			0
$781$	−1278.06	−	737.890i	−1.63644	−	0.944801i
$782$	−230.955	−	133.342i	−0.295339	−	0.170514i
$783$		0			0
$784$	−372.586	+	645.338i	−0.475238	+	0.823136i
$785$	−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	$0.965533\pi$
$788$	22.5377	+	39.0365i	0.0286012	+	0.0495387i
$789$		0			0
$790$	−812.556			−1.02855
$791$		−	156.492i		−	0.197840i
$792$		0			0
$793$	−7.41853	−	4.28309i	−0.00935501	−	0.00540112i
$794$	−284.337	+	164.162i	−0.358107	+	0.206753i
$795$		0			0
$796$	11.4980	−	19.9152i	0.0144448	−	0.0250190i
$797$			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
$800$	−58.7271	−	33.9061i	−0.0734089	−	0.0423826i
$801$		0			0
$802$	330.829	+	573.013i	0.412505	+	0.714480i
$803$	−922.366	+	1597.59i	−1.14865	+	1.98952i
$804$		0			0
$805$	−76.1359			−0.0945788
$806$		−	5.52620i		−	0.00685633i
$807$		0			0
$808$	1024.75	−	591.641i	1.26826	−	0.732229i
$809$	1489.01			1.84056			0.920280	−	0.391260i	$-0.127961\pi$
$809$	1489.01			1.84056			0.920280	+	0.391260i	$0.127961\pi$
$810$		0			0
$811$	823.672	−	475.547i	1.01563	−	0.586372i	0.102792	−	0.994703i	$-0.467223\pi$
$811$	823.672	−	475.547i	1.01563	−	0.586372i	0.912834	+	0.408331i	$0.133889\pi$
$812$	−18.7075	−	10.8008i	−0.0230388	−	0.0133015i
$813$		0			0
$814$	−885.956	+	1534.52i	−1.08840	+	1.88516i
$815$	18.8973	−	32.7310i	0.0231868	−	0.0401608i
$816$		0			0
$817$	−202.694	+	431.905i	−0.248095	+	0.528647i
$818$	−600.250			−0.733802
$819$		0			0
$820$	−50.7346	−	29.2917i	−0.0618715	−	0.0357215i
$821$	−790.459	−	1369.12i	−0.962801	−	1.66762i	−0.715411	−	0.698704i	$-0.753760\pi$
$821$	−790.459	−	1369.12i	−0.962801	−	1.66762i	−0.247390	−	0.968916i	$-0.579573\pi$
$822$		0			0
$823$	734.523	+	1272.23i	0.892494	+	1.54585i	0.836875	+	0.547394i	$0.184380\pi$
$823$	734.523	+	1272.23i	0.892494	+	1.54585i	0.0556192	+	0.998452i	$0.482287\pi$
$824$	1303.61			1.58204
$825$		0			0
$826$	−80.7230	−	139.816i	−0.0977276	−	0.169269i
$827$	13.7499	−	7.93854i	0.0166263	−	0.00959920i	−0.491664	−	0.870785i	$-0.663611\pi$
$827$	13.7499	−	7.93854i	0.0166263	−	0.00959920i	0.508290	+	0.861186i	$0.330278\pi$
$828$		0			0
$829$		−	460.891i		−	0.555960i	−0.960587	−	0.277980i	$-0.910335\pi$
$829$		−	460.891i		−	0.555960i	0.960587	−	0.277980i	$-0.0896649\pi$
$830$	1706.70	−	985.363i	2.05626	−	1.18718i
$831$		0			0
$832$	8.02810	−	4.63503i	0.00964916	−	0.00557095i
$833$	540.303	−	935.832i	0.648623	−	1.12345i
$834$		0			0
$835$			1052.89i			1.26094i
$836$	−57.3460	−	82.3283i	−0.0685957	−	0.0984789i
$837$		0			0
$838$	253.627	+	146.432i	0.302658	+	0.174740i
$839$	11.1163	+	6.41800i	0.0132495	+	0.00764959i	0.506610	−	0.862175i	$-0.330898\pi$
$839$	11.1163	+	6.41800i	0.0132495	+	0.00764959i	−0.493361	+	0.869825i	$0.664232\pi$
$840$		0			0
$841$	239.209	−	414.323i	0.284434	−	0.492655i
$842$	117.614	+	203.713i	0.139684	+	0.241939i
$843$		0			0
$844$			4.97538i			0.00589500i
$845$	541.989	+	938.752i	0.641407	+	1.11095i
$846$		0			0
$847$	−639.744			−0.755306
$848$			949.437i			1.11962i
$849$		0			0
$850$	711.236	+	410.632i	0.836748	+	0.483097i
$851$	−194.012	+	112.013i	−0.227981	+	0.131625i
$852$		0			0
$853$	321.717	−	557.231i	0.377160	−	0.653260i	−0.613488	−	0.789704i	$-0.710234\pi$
$853$	321.717	−	557.231i	0.377160	−	0.653260i	0.990648	+	0.136444i	$0.0435674\pi$
$854$		−	255.839i		−	0.299578i
$855$		0			0
$856$	−1072.99			−1.25350
$857$	115.805	+	66.8603i	0.135129	+	0.0780167i	0.566040	−	0.824377i	$-0.308475\pi$
$857$	115.805	+	66.8603i	0.135129	+	0.0780167i	−0.430912	+	0.902394i	$0.641808\pi$
$858$		0			0
$859$	−49.3229	−	85.4297i	−0.0574189	−	0.0994525i	0.835887	−	0.548901i	$-0.184954\pi$
$859$	−49.3229	−	85.4297i	−0.0574189	−	0.0994525i	−0.893306	+	0.449449i	$0.851620\pi$
$860$	21.1675	−	36.6632i	0.0246134	−	0.0426316i
$861$		0			0
$862$	−546.576			−0.634079
$863$		−	829.585i		−	0.961280i	−0.876918	−	0.480640i	$-0.840404\pi$
$863$		−	829.585i		−	0.961280i	0.876918	−	0.480640i	$-0.159596\pi$
$864$		0			0
$865$	−1503.39	+	867.980i	−1.73802	+	1.00344i
$866$	−1505.14			−1.73803
$867$		0			0
$868$	8.81226	−	5.08776i	0.0101524	−	0.00586147i
$869$	−1067.53	−	616.339i	−1.22846	−	0.709251i
$870$		0			0
$871$	−5.96704	+	10.3352i	−0.00685079	+	0.0118659i
$872$	−40.8014	+	70.6700i	−0.0467906	+	0.0810436i
$873$		0			0
$874$	−17.4290	−	205.014i	−0.0199416	−	0.234569i
$875$	−128.434			−0.146782
$876$		0			0
$877$	157.383	+	90.8649i	0.179456	+	0.103609i	0.587037	−	0.809560i	$-0.300294\pi$
$877$	157.383	+	90.8649i	0.179456	+	0.103609i	−0.407581	+	0.913169i	$0.633628\pi$
$878$	380.963	+	659.847i	0.433898	+	0.751534i
$879$		0			0
$880$	−1094.46	−	1895.66i	−1.24371	−	2.15416i
$881$	517.816			0.587759			0.293880	−	0.955842i	$-0.405054\pi$
$881$	517.816			0.587759			0.293880	+	0.955842i	$0.405054\pi$
$882$		0			0
$883$	782.367	+	1355.10i	0.886033	+	1.53465i	0.844525	+	0.535516i	$0.179883\pi$
$883$	782.367	+	1355.10i	0.886033	+	1.53465i	0.0415084	+	0.999138i	$0.486784\pi$
$884$	0.876791	−	0.506216i	0.000991845	−	0.000572642i
$885$		0			0
$886$			1203.89i			1.35879i
$887$	620.266	−	358.111i	0.699285	−	0.403732i	−0.107796	−	0.994173i	$-0.534379\pi$
$887$	620.266	−	358.111i	0.699285	−	0.403732i	0.807081	+	0.590441i	$0.201046\pi$
$888$		0			0
$889$	58.0518	−	33.5162i	0.0653001	−	0.0377011i
$890$	480.093	−	831.546i	0.539431	−	0.934321i
$891$		0			0
$892$		−	68.0262i		−	0.0762626i
$893$	−318.793	−	457.672i	−0.356991	−	0.512511i
$894$		0			0
$895$	−1035.77	−	598.003i	−1.15729	−	0.668159i
$896$	272.678	+	157.431i	0.304328	+	0.175704i
$897$		0			0
$898$	324.588	−	562.202i	0.361456	−	0.626061i
$899$	310.759	+	538.251i	0.345672	+	0.598722i
$900$		0			0
$901$		−	1376.82i		−	1.52810i
$902$	−720.760	−	1248.39i	−0.799069	−	1.38403i
$903$		0			0
$904$	533.625			0.590293
$905$			297.732i			0.328986i
$906$		0			0
$907$	240.379	+	138.783i	0.265026	+	0.153013i	0.626625	−	0.779321i	$-0.284436\pi$
$907$	240.379	+	138.783i	0.265026	+	0.153013i	−0.361599	+	0.932334i	$0.617769\pi$
$908$	29.3731	−	16.9585i	0.0323492	−	0.0186768i
$909$		0			0
$910$	2.34412	−	4.06013i	0.00257595	−	0.00446168i
$911$		−	1630.56i		−	1.78986i	−0.446207	−	0.894930i	$-0.647226\pi$
$911$		−	1630.56i		−	1.78986i	0.446207	−	0.894930i	$-0.352774\pi$
$912$		0			0
$913$	2989.66			3.27455
$914$	903.415	+	521.587i	0.988419	+	0.570664i
$915$		0			0
$916$	−12.9954	−	22.5086i	−0.0141871	−	0.0245727i
$917$	−64.8355	+	112.298i	−0.0707040	+	0.122463i
$918$		0			0
$919$	−48.0409			−0.0522752			−0.0261376	−	0.999658i	$-0.508321\pi$
$919$	−48.0409			−0.0522752			−0.0261376	+	0.999658i	$0.508321\pi$
$920$		−	259.618i		−	0.282193i
$921$		0			0
$922$	−489.575	+	282.656i	−0.530993	+	0.306569i
$923$	11.4894			0.0124479
$924$		0			0
$925$	597.469	−	344.949i	0.645912	−	0.372918i
$926$	571.781	+	330.118i	0.617474	+	0.356499i
$927$		0			0
$928$	76.2497	−	132.068i	0.0821656	−	0.142315i
$929$	641.727	−	1111.50i	0.690772	−	1.19645i	−0.280813	−	0.959763i	$-0.590604\pi$
$929$	641.727	−	1111.50i	0.690772	−	1.19645i	0.971585	−	0.236690i	$-0.0760626\pi$
$930$		0			0
$931$	830.717	−	70.6223i	0.892285	−	0.0758564i
$932$	−91.8430			−0.0985440
$933$		0			0
$934$	528.386	+	305.064i	0.565724	+	0.326621i
$935$	1587.12	+	2748.98i	1.69746	+	2.94008i
$936$		0			0
$937$	−769.568	−	1332.93i	−0.821311	−	1.42255i	−0.904706	−	0.426036i	$-0.859910\pi$
$937$	−769.568	−	1332.93i	−0.821311	−	1.42255i	0.0833953	−	0.996517i	$-0.473424\pi$
$938$	−356.426			−0.379985
$939$		0			0
$940$	24.7459	+	42.8611i	0.0263254	+	0.0455970i
$941$	1281.05	−	739.617i	1.36138	−	0.785990i	0.371568	−	0.928406i	$-0.378820\pi$
$941$	1281.05	−	739.617i	1.36138	−	0.785990i	0.989807	+	0.142415i	$0.0454869\pi$
$942$		0			0
$943$		−	182.254i		−	0.193270i
$944$	508.223	−	293.423i	0.538372	−	0.310829i
$945$		0			0
$946$	902.146	−	520.854i	0.953643	−	0.550586i
$947$	−349.924	+	606.086i	−0.369508	+	0.640006i	−0.989489	−	0.144611i	$-0.953807\pi$
$947$	−349.924	+	606.086i	−0.369508	+	0.640006i	0.619981	+	0.784617i	$0.287140\pi$
$948$		0			0
$949$		−	14.3618i		−	0.0151336i
$950$	53.6733	+	631.349i	0.0564982	+	0.664577i
$951$		0			0
$952$	−372.371	−	214.989i	−0.391146	−	0.225828i
$953$	354.907	+	204.906i	0.372411	+	0.215011i	0.674511	−	0.738265i	$-0.264354\pi$
$953$	354.907	+	204.906i	0.372411	+	0.215011i	−0.302100	+	0.953276i	$0.597688\pi$
$954$		0			0
$955$	117.787	−	204.012i	0.123337	−	0.213625i
$956$	−39.5652	−	68.5289i	−0.0413862	−	0.0716829i
$957$		0			0
$958$		−	844.688i		−	0.881720i
$959$	107.370	+	185.971i	0.111960	+	0.193921i
$960$		0			0
$961$	668.231			0.695349
$962$		−	13.7949i		−	0.0143398i
$963$		0			0
$964$	28.9731	+	16.7276i	0.0300550	+	0.0173523i
$965$	−1112.82	+	642.487i	−1.15318	+	0.665790i
$966$		0			0
$967$	92.4602	−	160.146i	0.0956155	−	0.165611i	−0.814250	−	0.580515i	$-0.802851\pi$
$967$	92.4602	−	160.146i	0.0956155	−	0.165611i	0.909865	+	0.414904i	$0.136185\pi$
$968$		−	2181.48i		−	2.25359i
$969$		0			0
$970$	−1071.06			−1.10419
$971$	−218.148	−	125.948i	−0.224663	−	0.129709i	0.383445	−	0.923564i	$-0.374738\pi$
$971$	−218.148	−	125.948i	−0.224663	−	0.129709i	−0.608107	+	0.793855i	$0.708071\pi$
$972$		0			0
$973$	206.537	+	357.733i	0.212269	+	0.367660i
$974$	−658.840	+	1141.14i	−0.676427	+	1.17161i
$975$		0			0
$976$	929.960			0.952828
$977$		−	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
$980$	−73.9785			−0.0754882
$981$		0			0
$982$	619.658	−	357.760i	0.631016	−	0.364317i
$983$	−137.328	−	79.2861i	−0.139702	−	0.0806573i	0.428520	−	0.903532i	$-0.359035\pi$
$983$	−137.328	−	79.2861i	−0.139702	−	0.0806573i	−0.568222	+	0.822875i	$0.692369\pi$
$984$		0			0
$985$	550.125	−	952.844i	0.558503	−	0.967355i
$986$	−923.450	+	1599.46i	−0.936561	+	1.62217i
$987$		0			0
$988$	0.707118	+	0.331852i	0.000715706	+	0.000335882i
$989$	131.705			0.133170
$990$		0			0
$991$	1489.96	+	860.227i	1.50349	+	0.868039i	0.999992	+	0.00404127i	$0.00128638\pi$
$991$	1489.96	+	860.227i	1.50349	+	0.868039i	0.503496	+	0.863998i	$0.332047\pi$
$992$	35.9178	+	62.2114i	0.0362074	+	0.0627131i
$993$		0			0
$994$	171.572	+	297.172i	0.172608	+	0.298966i
$995$	−561.312			−0.564132
$996$		0			0
$997$	−261.532	−	452.987i	−0.262319	−	0.454350i	0.704539	−	0.709666i	$-0.251154\pi$
$997$	−261.532	−	452.987i	−0.262319	−	0.454350i	−0.966858	+	0.255316i	$0.917821\pi$
$998$	−144.299	+	83.3111i	−0.144588	+	0.0834780i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.3.g.b.31.1	✓	6	57.50	even	6
57.3.g.b.46.1	yes	6	3.2	odd	2
171.3.p.c.46.3		6	1.1	even	1	trivial
171.3.p.c.145.3		6	19.12	odd	6	inner
912.3.be.f.145.1		6	228.107	odd	6
912.3.be.f.673.1		6	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	171.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.78805 + 1.03233i) q^{2} +(0.131406 + 0.227602i) q^{4} +(3.20750 - 5.55555i) q^{5} -2.26281 q^{7} -7.71601i q^{8} +O(q^{10})\)	\(q+(1.78805 + 1.03233i) q^{2} +(0.131406 + 0.227602i) q^{4} +(3.20750 - 5.55555i) q^{5} -2.26281 q^{7} -7.71601i q^{8} +(11.4703 - 6.62239i) q^{10} +20.0928 q^{11} +(-0.135471 + 0.0782143i) q^{13} +(-4.04601 - 2.33597i) q^{14} +(8.49109 - 14.7070i) q^{16} +(-12.3133 + 21.3272i) q^{17} +(-18.9317 + 1.60945i) q^{19} +1.68594 q^{20} +(35.9269 + 20.7424i) q^{22} +(2.62250 + 4.54230i) q^{23} +(-8.07609 - 13.9882i) q^{25} -0.322972 q^{26} +(-0.297347 - 0.515021i) q^{28} +(31.4573 - 18.1619i) q^{29} +17.1105i q^{31} +(3.63586 - 2.09917i) q^{32} +(-44.0334 + 25.4227i) q^{34} +(-7.25797 + 12.5712i) q^{35} +42.7124i q^{37} +(-35.5123 - 16.6660i) q^{38} +(-42.8667 - 24.7491i) q^{40} +(-30.0928 - 17.3741i) q^{41} +(12.5553 - 21.7464i) q^{43} +(2.64032 + 4.57316i) q^{44} +10.8291i q^{46} +(14.6778 + 25.4227i) q^{47} -43.8797 q^{49} -33.3487i q^{50} +(-0.0356035 - 0.0205557i) q^{52} +(-48.4176 + 27.9539i) q^{53} +(64.4476 - 111.627i) q^{55} +17.4599i q^{56} +74.9962 q^{58} +(29.9269 + 17.2783i) q^{59} +(27.3805 + 47.4244i) q^{61} +(-17.6637 + 30.5944i) q^{62} -59.2606 q^{64} +1.00349i q^{65} +(66.0698 - 38.1454i) q^{67} -6.47216 q^{68} +(-25.9552 + 14.9852i) q^{70} +(-63.6080 - 36.7241i) q^{71} +(-45.9053 + 79.5103i) q^{73} +(-44.0932 + 76.3717i) q^{74} +(-2.85406 - 4.09740i) q^{76} -45.4662 q^{77} +(-53.1300 - 30.6746i) q^{79} +(-54.4703 - 94.3453i) q^{80} +(-35.8716 - 62.1313i) q^{82} +148.793 q^{83} +(78.9897 + 136.814i) q^{85} +(44.8990 - 25.9224i) q^{86} -155.036i q^{88} +(62.7829 - 36.2477i) q^{89} +(0.306546 - 0.176984i) q^{91} +(-0.689224 + 1.19377i) q^{92} +60.6093i q^{94} +(-51.7820 + 110.338i) q^{95} +(-70.0326 - 40.4334i) q^{97} +(-78.4589 - 45.2983i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7}+O(q^{10}) \) 6 * q - 3 * q^2 + 5 * q^4 - 4 * q^5 - 22 * q^7	\( 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7} + 54 q^{10} + 36 q^{11} - 3 q^{13} + 57 q^{14} - 23 q^{16} - 38 q^{17} - 10 q^{19} - 32 q^{20} + 36 q^{22} - 54 q^{23} - 21 q^{25} - 118 q^{26} - 101 q^{28} + 102 q^{29} + 63 q^{32} - 150 q^{34} + 24 q^{35} - 119 q^{38} + 30 q^{40} - 96 q^{41} + 107 q^{43} + 94 q^{44} + 50 q^{47} - 48 q^{49} + 399 q^{52} + 90 q^{53} + 148 q^{55} - 116 q^{58} + 27 q^{61} + 121 q^{62} + 46 q^{64} - 39 q^{67} + 388 q^{68} - 354 q^{70} - 84 q^{71} - 77 q^{73} - 219 q^{74} + 215 q^{76} - 260 q^{77} + 9 q^{79} - 312 q^{80} - 4 q^{82} + 348 q^{83} + 68 q^{85} - 249 q^{86} + 72 q^{89} - 393 q^{91} + 118 q^{92} - 104 q^{95} - 228 q^{97} - 540 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 + 5 * q^4 - 4 * q^5 - 22 * q^7 + 54 * q^10 + 36 * q^11 - 3 * q^13 + 57 * q^14 - 23 * q^16 - 38 * q^17 - 10 * q^19 - 32 * q^20 + 36 * q^22 - 54 * q^23 - 21 * q^25 - 118 * q^26 - 101 * q^28 + 102 * q^29 + 63 * q^32 - 150 * q^34 + 24 * q^35 - 119 * q^38 + 30 * q^40 - 96 * q^41 + 107 * q^43 + 94 * q^44 + 50 * q^47 - 48 * q^49 + 399 * q^52 + 90 * q^53 + 148 * q^55 - 116 * q^58 + 27 * q^61 + 121 * q^62 + 46 * q^64 - 39 * q^67 + 388 * q^68 - 354 * q^70 - 84 * q^71 - 77 * q^73 - 219 * q^74 + 215 * q^76 - 260 * q^77 + 9 * q^79 - 312 * q^80 - 4 * q^82 + 348 * q^83 + 68 * q^85 - 249 * q^86 + 72 * q^89 - 393 * q^91 + 118 * q^92 - 104 * q^95 - 228 * q^97 - 540 * q^98

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