LMFDB - Embedded newform 177.4.e.a.4.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,4,Mod(4,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("177.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.e (of order $29$, degree $28$, 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:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$420$
Relative dimension:	$15$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			4.8
Character	$\chi$	$=$	177.4
Dual form			177.4.e.a.133.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.115030 + 0.0125102i) q^{2} +(-1.94216 + 2.28649i) q^{3} +(-7.79989 - 1.71689i) q^{4} +(-3.58691 - 2.72670i) q^{5} +(-0.252010 + 0.238717i) q^{6} +(-13.1064 + 32.8946i) q^{7} +(-1.75295 - 0.590637i) q^{8} +(-1.45604 - 8.88144i) q^{9} +O(q^{10})$	\(q+(0.115030 + 0.0125102i) q^{2} +(-1.94216 + 2.28649i) q^{3} +(-7.79989 - 1.71689i) q^{4} +(-3.58691 - 2.72670i) q^{5} +(-0.252010 + 0.238717i) q^{6} +(-13.1064 + 32.8946i) q^{7} +(-1.75295 - 0.590637i) q^{8} +(-1.45604 - 8.88144i) q^{9} +(-0.378490 - 0.358525i) q^{10} +(54.4941 - 25.2117i) q^{11} +(19.0743 - 14.4999i) q^{12} +(5.23084 - 31.9067i) q^{13} +(-1.91914 + 3.61989i) q^{14} +(13.2009 - 2.90574i) q^{15} +(57.7934 + 26.7381i) q^{16} +(-43.9106 - 110.207i) q^{17} +(-0.0563787 - 1.03984i) q^{18} +(-24.7078 - 36.4412i) q^{19} +(23.2961 + 27.4263i) q^{20} +(-49.7583 - 93.8541i) q^{21} +(6.58384 - 2.21836i) q^{22} +(-3.13883 + 57.8923i) q^{23} +(4.75498 - 2.86098i) q^{24} +(-28.0100 - 100.883i) q^{25} +(1.00086 - 3.60478i) q^{26} +(23.1351 + 13.9200i) q^{27} +(158.705 - 234.072i) q^{28} +(136.883 - 14.8869i) q^{29} +(1.55485 - 0.169100i) q^{30} +(-55.2317 + 81.4606i) q^{31} +(18.9934 + 11.4280i) q^{32} +(-48.1901 + 173.565i) q^{33} +(-3.67230 - 13.2264i) q^{34} +(136.705 - 82.2529i) q^{35} +(-3.89148 + 71.7741i) q^{36} +(366.476 - 123.480i) q^{37} +(-2.38624 - 4.50092i) q^{38} +(62.7951 + 73.9281i) q^{39} +(4.67718 + 6.89833i) q^{40} +(-1.09664 - 20.2263i) q^{41} +(-4.54954 - 11.4185i) q^{42} +(119.384 + 55.2328i) q^{43} +(-468.334 + 103.088i) q^{44} +(-18.9944 + 35.8271i) q^{45} +(-1.08530 + 6.62006i) q^{46} +(-297.381 + 226.063i) q^{47} +(-173.380 + 80.2142i) q^{48} +(-661.260 - 626.379i) q^{49} +(-1.95991 - 11.9549i) q^{50} +(337.269 + 113.639i) q^{51} +(-95.5801 + 239.888i) q^{52} +(190.286 - 180.248i) q^{53} +(2.48708 + 1.89063i) q^{54} +(-264.211 - 58.1571i) q^{55} +(42.4036 - 49.9214i) q^{56} +(131.309 + 14.2807i) q^{57} +15.9318 q^{58} +(453.173 - 3.65433i) q^{59} -107.955 q^{60} +(-156.618 - 17.0332i) q^{61} +(-7.37237 + 8.67942i) q^{62} +(311.235 + 68.5079i) q^{63} +(-403.513 - 306.742i) q^{64} +(-105.763 + 100.184i) q^{65} +(-7.71463 + 19.3623i) q^{66} +(-374.132 - 126.060i) q^{67} +(153.284 + 934.994i) q^{68} +(-126.274 - 119.613i) q^{69} +(16.7542 - 7.75130i) q^{70} +(616.021 - 468.287i) q^{71} +(-2.69335 + 16.4287i) q^{72} +(186.869 - 352.472i) q^{73} +(43.7004 - 9.61918i) q^{74} +(285.067 + 131.886i) q^{75} +(130.152 + 326.658i) q^{76} +(115.106 + 2123.00i) q^{77} +(6.29844 + 9.28950i) q^{78} +(-529.258 - 623.091i) q^{79} +(-134.393 - 253.492i) q^{80} +(-76.7599 + 25.8634i) q^{81} +(0.126890 - 2.34034i) q^{82} +(-98.8592 + 59.4816i) q^{83} +(226.973 + 817.481i) q^{84} +(-142.999 + 515.035i) q^{85} +(13.0417 + 7.84692i) q^{86} +(-231.810 + 341.894i) q^{87} +(-110.416 + 12.0085i) q^{88} +(-1183.81 + 128.747i) q^{89} +(-2.63312 + 3.88356i) q^{90} +(981.000 + 590.248i) q^{91} +(123.877 - 446.164i) q^{92} +(-78.9899 - 284.496i) q^{93} +(-37.0357 + 22.2836i) q^{94} +(-10.7397 + 198.082i) q^{95} +(-63.0181 + 21.2333i) q^{96} +(-633.234 - 1194.41i) q^{97} +(-68.2283 - 80.3246i) q^{98} +(-303.261 - 447.277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9}+O(q^{10}) $ 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9	\( 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9} + 854 q^{10} + 32 q^{11} + 192 q^{12} - 22 q^{13} - 884 q^{14} - 42 q^{15} - 268 q^{16} - 56 q^{17} - 18 q^{18} - 112 q^{19} - 250 q^{20} + 243 q^{21} + 108 q^{22} + 16 q^{23} - 54 q^{24} - 197 q^{25} - 328 q^{26} + 405 q^{27} + 236 q^{28} - 54 q^{29} - 126 q^{30} + 66 q^{31} + 857 q^{32} - 96 q^{33} + 112 q^{34} + 532 q^{35} - 576 q^{36} + 110 q^{37} + 56 q^{38} + 66 q^{39} - 6044 q^{40} + 304 q^{41} - 306 q^{42} - 324 q^{43} - 568 q^{44} + 126 q^{45} + 5842 q^{46} + 4082 q^{47} + 804 q^{48} + 739 q^{49} + 576 q^{50} + 168 q^{51} - 1372 q^{52} - 1498 q^{53} + 54 q^{54} - 4422 q^{55} - 12036 q^{56} + 336 q^{57} + 6298 q^{58} - 3305 q^{59} + 750 q^{60} - 1718 q^{61} - 4333 q^{62} + 54 q^{63} - 6250 q^{64} - 5884 q^{65} - 324 q^{66} + 382 q^{67} + 734 q^{68} + 3780 q^{69} + 8082 q^{70} + 8638 q^{71} + 162 q^{72} + 8894 q^{73} + 12428 q^{74} + 243 q^{75} - 15468 q^{76} - 9916 q^{77} + 984 q^{78} - 578 q^{79} + 24570 q^{80} - 1215 q^{81} - 1382 q^{82} - 32 q^{83} + 7557 q^{84} + 708 q^{85} + 2296 q^{86} - 5928 q^{87} - 17646 q^{88} - 2284 q^{89} + 378 q^{90} + 11124 q^{91} + 762 q^{92} - 198 q^{93} - 1232 q^{94} + 24184 q^{95} - 396 q^{96} - 658 q^{97} - 4356 q^{98} + 288 q^{99}+O(q^{100}) \) 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9 + 854 * q^10 + 32 * q^11 + 192 * q^12 - 22 * q^13 - 884 * q^14 - 42 * q^15 - 268 * q^16 - 56 * q^17 - 18 * q^18 - 112 * q^19 - 250 * q^20 + 243 * q^21 + 108 * q^22 + 16 * q^23 - 54 * q^24 - 197 * q^25 - 328 * q^26 + 405 * q^27 + 236 * q^28 - 54 * q^29 - 126 * q^30 + 66 * q^31 + 857 * q^32 - 96 * q^33 + 112 * q^34 + 532 * q^35 - 576 * q^36 + 110 * q^37 + 56 * q^38 + 66 * q^39 - 6044 * q^40 + 304 * q^41 - 306 * q^42 - 324 * q^43 - 568 * q^44 + 126 * q^45 + 5842 * q^46 + 4082 * q^47 + 804 * q^48 + 739 * q^49 + 576 * q^50 + 168 * q^51 - 1372 * q^52 - 1498 * q^53 + 54 * q^54 - 4422 * q^55 - 12036 * q^56 + 336 * q^57 + 6298 * q^58 - 3305 * q^59 + 750 * q^60 - 1718 * q^61 - 4333 * q^62 + 54 * q^63 - 6250 * q^64 - 5884 * q^65 - 324 * q^66 + 382 * q^67 + 734 * q^68 + 3780 * q^69 + 8082 * q^70 + 8638 * q^71 + 162 * q^72 + 8894 * q^73 + 12428 * q^74 + 243 * q^75 - 15468 * q^76 - 9916 * q^77 + 984 * q^78 - 578 * q^79 + 24570 * q^80 - 1215 * q^81 - 1382 * q^82 - 32 * q^83 + 7557 * q^84 + 708 * q^85 + 2296 * q^86 - 5928 * q^87 - 17646 * q^88 - 2284 * q^89 + 378 * q^90 + 11124 * q^91 + 762 * q^92 - 198 * q^93 - 1232 * q^94 + 24184 * q^95 - 396 * q^96 - 658 * q^97 - 4356 * q^98 + 288 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{1}{29}\right)$	$1$

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 $

$2$	0.115030	+	0.0125102i	0.0406691	+	0.00442303i	0.128431	−	0.991718i	$-0.459006\pi$
$2$	0.115030	+	0.0125102i	0.0406691	+	0.00442303i	−0.0877618	+	0.996141i	$0.527971\pi$
$3$	−1.94216	+	2.28649i	−0.373769	+	0.440034i
$3$	−1.94216	+	2.28649i	−0.373769	+	0.440034i
$4$	−7.79989	−	1.71689i	−0.974986	−	0.214611i
$5$	−3.58691	−	2.72670i	−0.320823	−	0.243884i	0.432350	−	0.901706i	$-0.357685\pi$
$5$	−3.58691	−	2.72670i	−0.320823	−	0.243884i	−0.753173	+	0.657822i	$0.771478\pi$
$6$	−0.252010	+	0.238717i	−0.0171471	+	0.0162426i
$7$	−13.1064	+	32.8946i	−0.707679	+	1.77614i	−0.0812072	+	0.996697i	$0.525878\pi$
$7$	−13.1064	+	32.8946i	−0.707679	+	1.77614i	−0.626472	+	0.779444i	$0.715502\pi$
$8$	−1.75295	−	0.590637i	−0.0774701	−	0.0261027i
$9$	−1.45604	−	8.88144i	−0.0539273	−	0.328942i
$10$	−0.378490	−	0.358525i	−0.0119689	−	0.0113375i
$11$	54.4941	−	25.2117i	1.49369	−	0.691055i	0.508271	−	0.861197i	$-0.330285\pi$
$11$	54.4941	−	25.2117i	1.49369	−	0.691055i	0.985420	+	0.170142i	$0.0544226\pi$
$12$	19.0743	−	14.4999i	0.458855	−	0.348813i
$13$	5.23084	−	31.9067i	0.111598	−	0.680717i	−0.870475	−	0.492213i	$-0.836188\pi$
$13$	5.23084	−	31.9067i	0.111598	−	0.680717i	0.982072	−	0.188504i	$-0.0603638\pi$
$14$	−1.91914	+	3.61989i	−0.0366366	+	0.0691040i
$15$	13.2009	−	2.90574i	0.227231	−	0.0500173i
$16$	57.7934	+	26.7381i	0.903021	+	0.417782i
$17$	−43.9106	−	110.207i	−0.626464	−	1.57230i	−0.808168	−	0.588952i	$-0.799541\pi$
$17$	−43.9106	−	110.207i	−0.626464	−	1.57230i	0.181705	−	0.983353i	$-0.441838\pi$
$18$	−0.0563787	−	1.03984i	−0.000738255	−	0.0136163i
$19$	−24.7078	−	36.4412i	−0.298334	−	0.440010i	0.648747	−	0.761004i	$-0.275293\pi$
$19$	−24.7078	−	36.4412i	−0.298334	−	0.440010i	−0.947081	+	0.320994i	$0.895983\pi$
$20$	23.2961	+	27.4263i	0.260458	+	0.306635i
$21$	−49.7583	−	93.8541i	−0.517055	−	0.975269i
$22$	6.58384	−	2.21836i	0.0638036	−	0.0214980i
$23$	−3.13883	+	57.8923i	−0.0284561	+	0.524842i	0.949205	+	0.314657i	$0.101889\pi$
$23$	−3.13883	+	57.8923i	−0.0284561	+	0.524842i	−0.977662	+	0.210185i	$0.932593\pi$
$24$	4.75498	−	2.86098i	0.0404420	−	0.0243331i
$25$	−28.0100	−	100.883i	−0.224080	−	0.807063i
$26$	1.00086	−	3.60478i	0.00754942	−	0.0271906i
$27$	23.1351	+	13.9200i	0.164902	+	0.0992184i
$28$	158.705	−	234.072i	1.07116	−	1.57984i
$29$	136.883	−	14.8869i	0.876501	−	0.0953253i	0.341204	−	0.939989i	$-0.389165\pi$
$29$	136.883	−	14.8869i	0.876501	−	0.0953253i	0.535297	+	0.844664i	$0.320200\pi$
$30$	1.55485	−	0.169100i	0.00946251	−	0.00102911i
$31$	−55.2317	+	81.4606i	−0.319997	+	0.471960i	−0.953335	−	0.301915i	$-0.902374\pi$
$31$	−55.2317	+	81.4606i	−0.319997	+	0.471960i	0.633338	+	0.773875i	$0.281684\pi$
$32$	18.9934	+	11.4280i	0.104925	+	0.0631311i
$33$	−48.1901	+	173.565i	−0.254207	+	0.915570i
$34$	−3.67230	−	13.2264i	−0.0185234	−	0.0667151i
$35$	136.705	−	82.2529i	0.660212	−	0.397236i
$36$	−3.89148	+	71.7741i	−0.0180161	+	0.332287i
$37$	366.476	−	123.480i	1.62833	−	0.548649i	0.650767	−	0.759278i	$-0.274448\pi$
$37$	366.476	−	123.480i	1.62833	−	0.548649i	0.977566	+	0.210629i	$0.0675511\pi$
$38$	−2.38624	−	4.50092i	−0.0101868	−	0.0192144i
$39$	62.7951	+	73.9281i	0.257827	+	0.303538i
$40$	4.67718	+	6.89833i	0.0184882	+	0.0272680i
$41$	−1.09664	−	20.2263i	−0.00417722	−	0.0770443i	0.995701	−	0.0926208i	$-0.0295244\pi$
$41$	−1.09664	−	20.2263i	−0.00417722	−	0.0770443i	−0.999879	+	0.0155765i	$0.995042\pi$
$42$	−4.54954	−	11.4185i	−0.0167145	−	0.0419503i
$43$	119.384	+	55.2328i	0.423392	+	0.195882i	0.620003	−	0.784600i	$-0.287132\pi$
$43$	119.384	+	55.2328i	0.423392	+	0.195882i	−0.196611	+	0.980482i	$0.562994\pi$
$44$	−468.334	+	103.088i	−1.60464	+	0.353207i
$45$	−18.9944	+	35.8271i	−0.0629225	+	0.118684i
$46$	−1.08530	+	6.62006i	−0.00347868	+	0.0212190i
$47$	−297.381	+	226.063i	−0.922924	+	0.701589i	−0.954594	−	0.297909i	$-0.903711\pi$
$47$	−297.381	+	226.063i	−0.922924	+	0.701589i	0.0316697	+	0.999498i	$0.489918\pi$
$48$	−173.380	+	80.2142i	−0.521360	+	0.241207i
$49$	−661.260	−	626.379i	−1.92787	−	1.82618i
$50$	−1.95991	−	11.9549i	−0.00554346	−	0.0338136i
$51$	337.269	+	113.639i	0.926021	+	0.312013i
$52$	−95.5801	+	239.888i	−0.254896	+	0.639740i
$53$	190.286	−	180.248i	0.493165	−	0.467151i	−0.400235	−	0.916412i	$-0.631072\pi$
$53$	190.286	−	180.248i	0.493165	−	0.467151i	0.893400	+	0.449262i	$0.148313\pi$
$54$	2.48708	+	1.89063i	0.00626758	+	0.00476449i
$55$	−264.211	−	58.1571i	−0.647748	−	0.142580i
$56$	42.4036	−	49.9214i	0.101186	−	0.119125i
$57$	131.309	+	14.2807i	0.305128	+	0.0331846i
$58$	15.9318			0.0360682
$59$	453.173	−	3.65433i	0.999967	−	0.00806362i
$59$	453.173	−	3.65433i	0.999967	−	0.00806362i
$60$	−107.955			−0.232281
$61$	−156.618	−	17.0332i	−0.328736	−	0.0357522i	−0.0577368	−	0.998332i	$-0.518388\pi$
$61$	−156.618	−	17.0332i	−0.328736	−	0.0357522i	−0.270999	+	0.962580i	$0.587354\pi$
$62$	−7.37237	+	8.67942i	−0.0151015	+	0.0177788i
$63$	311.235	+	68.5079i	0.622411	+	0.137003i
$64$	−403.513	−	306.742i	−0.788110	−	0.599106i
$65$	−105.763	+	100.184i	−0.201819	+	0.191173i
$66$	−7.71463	+	19.3623i	−0.0143880	+	0.0361111i
$67$	−374.132	−	126.060i	−0.682201	−	0.229860i	−0.0432004	−	0.999066i	$-0.513755\pi$
$67$	−374.132	−	126.060i	−0.682201	−	0.229860i	−0.639001	+	0.769206i	$0.720652\pi$
$68$	153.284	+	934.994i	0.273360	+	1.66742i
$69$	−126.274	−	119.613i	−0.220313	−	0.208691i
$70$	16.7542	−	7.75130i	0.0286072	−	0.0132351i
$71$	616.021	−	468.287i	1.02969	−	0.782753i	0.0532622	−	0.998581i	$-0.483038\pi$
$71$	616.021	−	468.287i	1.02969	−	0.782753i	0.976431	+	0.215828i	$0.0692450\pi$
$72$	−2.69335	+	16.4287i	−0.00440853	+	0.0268908i
$73$	186.869	−	352.472i	0.299607	−	0.565120i	−0.687307	−	0.726368i	$-0.741207\pi$
$73$	186.869	−	352.472i	0.299607	−	0.565120i	0.986914	+	0.161248i	$0.0515519\pi$
$74$	43.7004	−	9.61918i	0.0686495	−	0.0151109i
$75$	285.067	+	131.886i	0.438890	+	0.203052i
$76$	130.152	+	326.658i	0.196441	+	0.493030i
$77$	115.106	+	2123.00i	0.170357	+	3.14205i
$78$	6.29844	+	9.28950i	0.00914305	+	0.0134850i
$79$	−529.258	−	623.091i	−0.753749	−	0.887382i	0.242827	−	0.970070i	$-0.421925\pi$
$79$	−529.258	−	623.091i	−0.753749	−	0.887382i	−0.996575	+	0.0826878i	$0.973650\pi$
$80$	−134.393	−	253.492i	−0.187820	−	0.354266i
$81$	−76.7599	+	25.8634i	−0.105295	+	0.0354779i
$82$	0.126890	−	2.34034i	0.000170886	−	0.00315180i
$83$	−98.8592	+	59.4816i	−0.130737	+	0.0786621i	−0.579420	−	0.815029i	$-0.696721\pi$
$83$	−98.8592	+	59.4816i	−0.130737	+	0.0786621i	0.448683	+	0.893691i	$0.351893\pi$
$84$	226.973	+	817.481i	0.294818	+	1.06184i
$85$	−142.999	+	515.035i	−0.182475	+	0.657216i
$86$	13.0417	+	7.84692i	0.0163526	+	0.00983902i
$87$	−231.810	+	341.894i	−0.285662	+	0.421320i
$88$	−110.416	+	12.0085i	−0.133755	+	0.0145467i
$89$	−1183.81	+	128.747i	−1.40992	+	0.153338i	−0.781195	−	0.624287i	$-0.785390\pi$
$89$	−1183.81	+	128.747i	−1.40992	+	0.153338i	−0.628728	+	0.777625i	$0.716424\pi$
$90$	−2.63312	+	3.88356i	−0.00308395	+	0.00454848i
$91$	981.000	+	590.248i	1.13007	+	0.679943i
$92$	123.877	−	446.164i	0.140381	−	0.505607i
$93$	−78.9899	−	284.496i	−0.0880739	−	0.317213i
$94$	−37.0357	+	22.2836i	−0.0406377	+	0.0244509i
$95$	−10.7397	+	198.082i	−0.0115986	+	0.213924i
$96$	−63.0181	+	21.2333i	−0.0669975	+	0.0225741i
$97$	−633.234	−	1194.41i	−0.662836	−	1.25024i	−0.955772	−	0.294110i	$-0.904977\pi$
$97$	−633.234	−	1194.41i	−0.662836	−	1.25024i	0.292935	−	0.956132i	$-0.405368\pi$
$98$	−68.2283	−	80.3246i	−0.0703276	−	0.0827960i
$99$	−303.261	−	447.277i	−0.307868	−	0.454071i
$100$	45.2705	+	834.965i	0.0452705	+	0.834965i
$101$	−237.752	−	596.712i	−0.234229	−	0.587871i	0.764134	−	0.645057i	$-0.223167\pi$
$101$	−237.752	−	596.712i	−0.234229	−	0.587871i	−0.998364	+	0.0571859i	$0.981787\pi$
$102$	37.3742	+	17.2912i	0.0362804	+	0.0167851i
$103$	1042.27	−	229.421i	0.997066	−	0.219471i	0.313680	−	0.949529i	$-0.398438\pi$
$103$	1042.27	−	229.421i	0.997066	−	0.219471i	0.683385	+	0.730058i	$0.260507\pi$
$104$	−28.0146	+	52.8412i	−0.0264141	+	0.0498222i
$105$	−77.4334	+	472.323i	−0.0719688	+	0.438990i
$106$	24.1434	−	18.3534i	0.0221228	−	0.0168173i
$107$	−892.884	+	413.092i	−0.806713	+	0.373225i	−0.779498	−	0.626404i	$-0.784526\pi$
$107$	−892.884	+	413.092i	−0.806713	+	0.373225i	−0.0272149	+	0.999630i	$0.508664\pi$
$108$	−156.553	−	148.294i	−0.139484	−	0.132126i
$109$	−219.289	−	1337.60i	−0.192698	−	1.17541i	−0.889086	−	0.457740i	$-0.848659\pi$
$109$	−219.289	−	1337.60i	−0.192698	−	1.17541i	0.696388	−	0.717666i	$-0.254789\pi$
$110$	−29.6645	−	9.99513i	−0.0257127	−	0.00866362i
$111$	−429.419	+	1077.76i	−0.367195	+	0.921590i
$112$	−1637.00	+	1550.65i	−1.38109	+	1.30824i
$113$	−16.5012	−	12.5439i	−0.0137372	−	0.0104428i	0.598283	−	0.801285i	$-0.295850\pi$
$113$	−16.5012	−	12.5439i	−0.0137372	−	0.0104428i	−0.612020	+	0.790842i	$0.709643\pi$
$114$	14.9258	+	3.28541i	0.0122625	+	0.00269918i
$115$	169.114	−	199.096i	0.137130	−	0.161442i
$116$	−1093.23	−	118.896i	−0.875035	−	0.0951657i
$117$	−290.994			−0.229935
$118$	52.1740	+	5.24894i	0.0407035	+	0.00409495i
$119$	4200.73			3.23597
$120$	−24.8568	−	2.70334i	−0.0189092	−	0.00205650i
$121$	1472.31	−	1733.34i	1.10617	−	1.30228i
$122$	−17.8026	−	3.91865i	−0.0132113	−	0.00290802i
$123$	48.3770	+	36.7752i	0.0354635	+	0.0269586i
$124$	570.659	−	540.557i	0.413280	−	0.391480i
$125$	−383.072	+	961.438i	−0.274104	+	0.687949i
$126$	34.9442	+	11.7741i	0.0247069	+	0.00832473i
$127$	145.127	+	885.236i	0.101401	+	0.618520i	0.987816	+	0.155628i	$0.0497400\pi$
$127$	145.127	+	885.236i	0.101401	+	0.618520i	−0.886415	+	0.462892i	$0.846812\pi$
$128$	−171.320	−	162.283i	−0.118302	−	0.112062i
$129$	−358.151	+	165.698i	−0.244445	+	0.113092i
$130$	−13.4192	+	10.2010i	−0.00905337	+	0.00688219i
$131$	160.845	−	981.111i	0.107275	−	0.654352i	−0.877374	−	0.479807i	$-0.840707\pi$
$131$	160.845	−	981.111i	0.107275	−	0.654352i	0.984649	−	0.174544i	$-0.0558452\pi$
$132$	673.869	−	1271.05i	0.444339	−	0.838113i
$133$	1522.55	−	335.139i	0.992645	−	0.218498i
$134$	−41.4592	−	19.1811i	−0.0267278	−	0.0123656i
$135$	−45.0282	−	113.012i	−0.0287068	−	0.0720485i
$136$	11.8805	+	219.123i	0.00749076	+	0.138159i
$137$	464.423	+	684.973i	0.289623	+	0.427162i	0.944469	−	0.328600i	$-0.106577\pi$
$137$	464.423	+	684.973i	0.289623	+	0.427162i	−0.654846	+	0.755762i	$0.727267\pi$
$138$	−13.0288	−	15.3387i	−0.00803687	−	0.00946174i
$139$	−1047.35	−	1975.51i	−0.639100	−	1.20547i	−0.965541	−	0.260252i	$-0.916194\pi$
$139$	−1047.35	−	1975.51i	−0.639100	−	1.20547i	0.326441	−	0.945218i	$-0.394151\pi$
$140$	−1207.50	+	406.856i	−0.728949	+	0.245611i
$141$	60.6708	−	1119.01i	0.0362369	−	0.668351i
$142$	76.7190	−	46.1603i	0.0453389	−	0.0272795i
$143$	−519.371	−	1870.61i	−0.303720	−	1.09390i
$144$	153.323	−	552.220i	0.0887286	−	0.319572i
$145$	−531.580	−	319.841i	−0.304450	−	0.183182i
$146$	25.9050	−	38.2069i	0.0146843	−	0.0216577i
$147$	2716.48	−	295.435i	1.52416	−	0.165762i
$148$	−3070.48	+	333.934i	−1.70535	+	0.185468i
$149$	452.695	−	667.676i	0.248901	−	0.367101i	−0.682630	−	0.730765i	$-0.739164\pi$
$149$	452.695	−	667.676i	0.248901	−	0.367101i	0.931531	+	0.363663i	$0.118474\pi$
$150$	31.1412	+	18.7371i	0.0169511	+	0.0101992i
$151$	102.891	−	370.580i	0.0554513	−	0.199717i	−0.930636	−	0.365946i	$-0.880745\pi$
$151$	102.891	−	370.580i	0.0554513	−	0.199717i	0.986087	+	0.166229i	$0.0531591\pi$
$152$	21.7879	+	78.4729i	0.0116265	+	0.0418750i
$153$	−914.863	+	550.455i	−0.483414	+	0.290860i
$154$	−13.3186	+	245.648i	−0.00696912	+	0.128538i
$155$	420.230	−	141.592i	0.217766	−	0.0733738i
$156$	−362.869	−	684.443i	−0.186236	−	0.351278i
$157$	2324.32	+	2736.41i	1.18154	+	1.39101i	0.902477	+	0.430738i	$0.141747\pi$
$157$	2324.32	+	2736.41i	1.18154	+	1.39101i	0.279060	+	0.960274i	$0.409977\pi$
$158$	−53.0853	−	78.2950i	−0.0267294	−	0.0394229i
$159$	42.5699	+	785.156i	0.0212328	+	0.391616i
$160$	−36.9671	−	92.7805i	−0.0182657	−	0.0458434i
$161$	−1863.20	−	862.010i	−0.912056	−	0.421962i
$162$	−9.15322	+	2.01478i	−0.00443917	+	0.000977134i
$163$	−322.619	+	608.524i	−0.155027	+	0.292413i	−0.948844	−	0.315744i	$-0.897746\pi$
$163$	−322.619	+	608.524i	−0.155027	+	0.292413i	0.793817	+	0.608157i	$0.208091\pi$
$164$	−26.1726	+	159.646i	−0.0124618	+	0.0760136i
$165$	646.114	−	491.163i	0.304848	−	0.231740i
$166$	−12.1159	+	5.60540i	−0.00566490	+	0.00262086i
$167$	−1706.25	−	1616.25i	−0.790620	−	0.748915i	0.181502	−	0.983391i	$-0.441904\pi$
$167$	−1706.25	−	1616.25i	−0.790620	−	0.748915i	−0.972122	+	0.234475i	$0.924663\pi$
$168$	31.7900	+	193.910i	0.0145991	+	0.0890507i
$169$	1091.32	+	367.708i	0.496731	+	0.167368i
$170$	−22.8923	+	57.4553i	−0.0103280	+	0.0259213i
$171$	−287.675	+	272.500i	−0.128650	+	0.121863i
$172$	−836.351	−	635.778i	−0.370763	−	0.281847i
$173$	1640.98	+	361.207i	0.721165	+	0.158740i	0.560364	−	0.828247i	$-0.310661\pi$
$173$	1640.98	+	361.207i	0.721165	+	0.158740i	0.160801	+	0.986987i	$0.448592\pi$
$174$	−30.9422	+	36.4279i	−0.0134811	+	0.0158712i
$175$	3685.61	+	400.834i	1.59203	+	0.173144i
$176$	3823.51			1.63755
$177$	−871.778	+	1043.27i	−0.370208	+	0.443034i
$178$	−137.783			−0.0580185
$179$	1008.74	+	109.708i	0.421213	+	0.0458096i	0.316271	−	0.948669i	$-0.397569\pi$
$179$	1008.74	+	109.708i	0.421213	+	0.0458096i	0.104941	+	0.994478i	$0.466535\pi$
$180$	209.665	−	246.837i	0.0868195	−	0.102212i
$181$	835.129	+	183.826i	0.342954	+	0.0754899i	0.383108	−	0.923704i	$-0.374854\pi$
$181$	835.129	+	183.826i	0.342954	+	0.0754899i	−0.0401538	+	0.999194i	$0.512785\pi$
$182$	105.460	+	80.1686i	0.0429517	+	0.0326510i
$183$	343.123	−	325.024i	0.138603	−	0.131292i
$184$	39.6955	−	99.6282i	0.0159043	−	0.0399168i
$185$	−1651.21	−	556.358i	−0.656214	−	0.221104i
$186$	−5.52707	−	33.7136i	−0.00217884	−	0.0132903i
$187$	−5171.38	−	4898.59i	−2.02229	−	1.91562i
$188$	2707.66	−	1252.70i	1.05041	−	0.485970i
$189$	−761.110	+	578.581i	−0.292924	+	0.222675i
$190$	−3.71344	+	22.6510i	−0.00141790	+	0.00864882i
$191$	2356.65	−	4445.12i	0.892782	−	1.68397i	0.178701	−	0.983903i	$-0.442810\pi$
$191$	2356.65	−	4445.12i	0.892782	−	1.68397i	0.714081	−	0.700063i	$-0.246845\pi$
$192$	1485.05	−	326.884i	0.558198	−	0.122869i
$193$	332.413	+	153.791i	0.123977	+	0.0573580i	0.480897	−	0.876777i	$-0.340311\pi$
$193$	332.413	+	153.791i	0.123977	+	0.0573580i	−0.356920	+	0.934135i	$0.616173\pi$
$194$	−57.8983	−	145.314i	−0.0214271	−	0.0537780i
$195$	−23.6608	−	436.397i	−0.00868915	−	0.160262i
$196$	4082.33	+	6020.99i	1.48773	+	2.19424i
$197$	1189.09	+	1399.90i	0.430045	+	0.506288i	0.933917	−	0.357490i	$-0.116367\pi$
$197$	1189.09	+	1399.90i	0.430045	+	0.506288i	−0.503872	+	0.863778i	$0.668092\pi$
$198$	−29.2885	−	55.2440i	−0.0105123	−	0.0198284i
$199$	−4241.22	+	1429.03i	−1.51081	+	0.509053i	−0.948202	−	0.317668i	$-0.897100\pi$
$199$	−4241.22	+	1429.03i	−1.51081	+	0.509053i	−0.562612	+	0.826721i	$0.690204\pi$
$200$	−10.4851	+	193.386i	−0.00370704	+	0.0683723i
$201$	1014.86	−	610.619i	0.356132	−	0.214277i
$202$	−19.8835	−	71.6138i	−0.00692573	−	0.0249442i
$203$	−1304.34	+	4697.83i	−0.450971	+	1.62425i
$204$	−2435.55	−	1465.42i	−0.835896	−	0.502942i
$205$	−51.2175	+	75.5402i	−0.0174497	+	0.0257364i
$206$	122.762	−	13.3512i	0.0415205	−	0.00451563i
$207$	518.737	−	56.4160i	0.174177	−	0.0189429i
$208$	1155.43	−	1704.13i	0.385167	−	0.568079i
$209$	−2265.17	−	1362.91i	−0.749691	−	0.451074i
$210$	−14.8160	+	53.3624i	−0.00486858	+	0.0175350i
$211$	88.6503	+	319.289i	0.0289239	+	0.104174i	0.976603	−	0.215050i	$-0.0689914\pi$
$211$	88.6503	+	319.289i	0.0289239	+	0.104174i	−0.947679	+	0.319224i	$0.896578\pi$
$212$	−1793.67	+	1079.22i	−0.581084	+	0.349627i
$213$	−125.679	+	2318.01i	−0.0404290	+	0.745669i
$214$	−107.876	+	36.3476i	−0.0344591	+	0.0116106i
$215$	−277.616	−	523.639i	−0.0880616	−	0.166102i
$216$	−32.3331	−	38.0654i	−0.0101851	−	0.0119908i
$217$	−1955.73	−	2884.48i	−0.611812	−	0.902356i
$218$	−8.49101	−	156.607i	−0.00263800	−	0.0486550i
$219$	442.993	+	1111.83i	0.136688	+	0.343062i
$220$	1960.96	+	907.239i	0.600946	+	0.278027i
$221$	−3746.04	+	824.565i	−1.14021	+	0.250979i
$222$	−62.8790	+	118.602i	−0.0190097	+	0.0358561i
$223$	−65.6135	+	400.225i	−0.0197032	+	0.120184i	−0.994847	−	0.101390i	$-0.967671\pi$
$223$	−65.6135	+	400.225i	−0.0197032	+	0.120184i	0.975144	+	0.221574i	$0.0711194\pi$
$224$	−624.853	+	475.001i	−0.186383	+	0.141685i
$225$	−855.201	+	395.658i	−0.253393	+	0.117232i
$226$	−1.74120	−	1.64936i	−0.000512492	−	0.000485458i
$227$	−479.034	−	2921.98i	−0.140064	−	0.854354i	−0.959609	−	0.281338i	$-0.909222\pi$
$227$	−479.034	−	2921.98i	−0.140064	−	0.854354i	0.819544	−	0.573016i	$-0.194227\pi$
$228$	−999.676	−	336.830i	−0.290374	−	0.0978382i
$229$	156.754	−	393.422i	0.0452340	−	0.113529i	−0.904624	−	0.426211i	$-0.859848\pi$
$229$	156.754	−	393.422i	0.0452340	−	0.113529i	0.949858	+	0.312682i	$0.101227\pi$
$230$	21.9438	−	20.7863i	0.00629101	−	0.00595916i
$231$	−5077.76	−	3860.01i	−1.44629	−	1.09944i
$232$	−248.742	−	54.7521i	−0.0703909	−	0.0154942i
$233$	−4043.01	+	4759.80i	−1.13676	+	1.33830i	−0.203516	+	0.979072i	$0.565237\pi$
$233$	−4043.01	+	4759.80i	−1.13676	+	1.33830i	−0.933249	+	0.359231i	$0.883039\pi$
$234$	−33.4729	−	3.64040i	−0.00935124	−	0.00101701i
$235$	1683.09			0.467202
$236$	−3540.97	−	749.542i	−0.976685	−	0.206742i
$237$	2452.59			0.672206
$238$	483.209	+	52.5521i	0.131604	+	0.0143128i
$239$	−2289.37	+	2695.25i	−0.619610	+	0.729461i	−0.979030	−	0.203715i	$-0.934699\pi$
$239$	−2289.37	+	2695.25i	−0.619610	+	0.729461i	0.359420	+	0.933176i	$0.382974\pi$
$240$	840.620	+	185.034i	0.226091	+	0.0497663i
$241$	2355.52	+	1790.62i	0.629594	+	0.478605i	0.870648	−	0.491907i	$-0.163700\pi$
$241$	2355.52	+	1790.62i	0.629594	+	0.478605i	−0.241054	+	0.970512i	$0.577493\pi$
$242$	191.044	−	180.966i	0.0507470	−	0.0480701i
$243$	89.9436	−	225.741i	0.0237444	−	0.0595939i
$244$	1192.36	+	401.752i	0.312840	+	0.105408i
$245$	663.935	+	4049.83i	0.173132	+	1.05606i
$246$	5.10472	+	4.83545i	0.00132303	+	0.00125324i
$247$	−1291.96	+	597.725i	−0.332816	+	0.153977i
$248$	144.932	−	110.174i	0.0371096	−	0.0282100i
$249$	55.9964	−	341.563i	0.0142515	−	0.0869304i
$250$	−56.0924	+	105.802i	−0.0141904	+	0.0267659i
$251$	5457.01	−	1201.18i	1.37228	−	0.302062i	0.533165	−	0.846011i	$-0.321002\pi$
$251$	5457.01	−	1201.18i	1.37228	−	0.302062i	0.839118	+	0.543949i	$0.183071\pi$
$252$	−2309.98	−	1068.71i	−0.577440	−	0.267152i
$253$	1288.51	+	3233.92i	0.320190	+	0.803617i
$254$	5.61941	+	103.644i	0.00138816	+	0.0256031i
$255$	−899.894	−	1327.24i	−0.220994	−	0.325942i
$256$	2607.43	+	3069.70i	0.636579	+	0.749439i
$257$	−1802.34	−	3399.57i	−0.437459	−	0.825135i	0.562540	−	0.826770i	$-0.309824\pi$
$257$	−1802.34	−	3399.57i	−0.437459	−	0.825135i	−0.999999	+	0.00163536i	$0.999479\pi$
$258$	−43.2709	+	14.5797i	−0.0104416	+	0.00351818i
$259$	−741.354	+	13673.5i	−0.177859	+	3.28042i
$260$	996.941	−	599.839i	0.237799	−	0.143079i
$261$	−331.524	−	1194.04i	−0.0786239	−	0.283178i
$262$	30.7759	−	110.845i	0.00725702	−	0.0261374i
$263$	6900.37	+	4151.81i	1.61785	+	0.973429i	0.978940	+	0.204149i	$0.0654427\pi$
$263$	6900.37	+	4151.81i	1.61785	+	0.973429i	0.638912	+	0.769280i	$0.279385\pi$
$264$	186.989	−	275.788i	0.0435923	−	0.0642938i
$265$	−1174.02	+	127.682i	−0.272149	+	0.0295980i
$266$	179.331	−	19.5034i	0.0413364	−	0.00449561i
$267$	2004.76	−	2956.80i	0.459511	−	0.677728i
$268$	2701.76	+	1625.59i	0.615806	+	0.370518i
$269$	115.622	−	416.431i	0.0262066	−	0.0943876i	−0.949290	−	0.314401i	$-0.898196\pi$
$269$	115.622	−	416.431i	0.0262066	−	0.0943876i	0.975497	+	0.220013i	$0.0706101\pi$
$270$	−3.76577	−	13.5631i	−0.000848805	−	0.00305712i
$271$	−3345.00	+	2012.62i	−0.749794	+	0.451136i	−0.838486	−	0.544923i	$-0.816559\pi$
$271$	−3345.00	+	2012.62i	−0.749794	+	0.451136i	0.0886923	+	0.996059i	$0.471731\pi$
$272$	408.988	−	7543.33i	0.0911710	−	1.68155i
$273$	−3254.85	+	1096.69i	−0.721585	+	0.243130i
$274$	44.8533	+	84.6022i	0.00988936	+	0.0186533i
$275$	−4069.81	−	4791.35i	−0.892431	−	1.05065i
$276$	779.560	+	1149.76i	0.170014	+	0.250752i
$277$	−151.853	−	2800.77i	−0.0329385	−	0.607515i	−0.967679	−	0.252185i	$-0.918851\pi$
$277$	−151.853	−	2800.77i	−0.0329385	−	0.607515i	0.934741	−	0.355331i	$-0.115632\pi$
$278$	−95.7619	−	240.344i	−0.0206598	−	0.0518521i
$279$	803.907	+	371.927i	0.172504	+	0.0798089i
$280$	−288.219	+	63.4417i	−0.0615156	+	0.0135406i
$281$	−2034.77	+	3837.98i	−0.431972	+	0.814786i	−0.999966	−	0.00824669i	$-0.997375\pi$
$281$	−2034.77	+	3837.98i	−0.431972	+	0.814786i	0.567994	+	0.823033i	$0.307720\pi$
$282$	20.9780	−	127.960i	0.00442986	−	0.0270209i
$283$	−1919.88	+	1459.46i	−0.403270	+	0.306558i	−0.787076	−	0.616856i	$-0.788406\pi$
$283$	−1919.88	+	1459.46i	−0.403270	+	0.306558i	0.383806	+	0.923414i	$0.374613\pi$
$284$	−5608.89	+	2594.95i	−1.17192	+	0.542190i
$285$	−432.054	−	409.264i	−0.0897989	−	0.0850621i
$286$	−36.3414	−	221.673i	−0.00751367	−	0.0458314i
$287$	679.709	+	229.020i	0.139798	+	0.0471033i
$288$	73.8416	−	185.328i	0.0151082	−	0.0379187i
$289$	−6650.68	+	6299.86i	−1.35369	+	1.28228i
$290$	−57.1462	−	43.4414i	−0.0115715	−	0.00879643i
$291$	3960.83	+	871.845i	0.797897	+	0.175630i
$292$	−2062.71	+	2428.41i	−0.413394	+	0.486685i
$293$	8493.34	+	923.706i	1.69347	+	0.184176i	0.903387	−	0.428827i	$-0.141073\pi$
$293$	8493.34	+	923.706i	1.69347	+	0.184176i	0.790081	+	0.613002i	$0.210038\pi$
$294$	316.171			0.0627194
$295$	−1635.46	−	1222.56i	−0.322780	−	0.241289i
$296$	−715.345			−0.140468
$297$	1611.68	+	175.280i	0.314878	+	0.0342451i
$298$	60.4261	−	71.1391i	0.0117463	−	0.0138288i
$299$	1830.73	+	402.975i	0.354093	+	0.0779419i
$300$	−1997.06	−	1518.12i	−0.384334	−	0.292163i
$301$	−3381.55	+	3203.18i	−0.647539	+	0.613382i
$302$	16.4715	−	41.3404i	0.00313851	−	0.00787707i
$303$	1826.12	+	615.293i	0.346231	+	0.116659i
$304$	−453.578	−	2766.70i	−0.0855739	−	0.521977i
$305$	515.331	+	488.147i	0.0967467	+	0.0916434i
$306$	−112.123	+	51.8735i	−0.0209465	+	0.00969088i
$307$	5436.42	−	4132.66i	1.01066	−	0.768284i	0.0377080	−	0.999289i	$-0.487994\pi$
$307$	5436.42	−	4132.66i	1.01066	−	0.768284i	0.972953	+	0.231005i	$0.0742012\pi$
$308$	2747.13	−	16756.8i	0.508222	−	3.10002i
$309$	−1499.68	+	2828.70i	−0.276097	+	0.520775i
$310$	50.1103	−	11.0301i	0.00918088	−	0.00202086i
$311$	−5120.42	−	2368.96i	−0.933610	−	0.431934i	−0.106714	−	0.994290i	$-0.534033\pi$
$311$	−5120.42	−	2368.96i	−0.933610	−	0.431934i	−0.826895	+	0.562356i	$0.809895\pi$
$312$	−66.4118	−	166.681i	−0.0120507	−	0.0302451i
$313$	295.925	+	5458.01i	0.0534398	+	0.985639i	0.895166	+	0.445734i	$0.147057\pi$
$313$	295.925	+	5458.01i	0.0534398	+	0.985639i	−0.841726	+	0.539905i	$0.818460\pi$
$314$	233.133	+	343.845i	0.0418995	+	0.0617972i
$315$	−929.572	−	1094.38i	−0.166271	−	0.195750i
$316$	3058.38	+	5768.71i	0.544453	+	1.02695i
$317$	−2740.71	+	923.453i	−0.485595	+	0.163616i	−0.551441	−	0.834214i	$-0.685922\pi$
$317$	−2740.71	+	923.453i	−0.485595	+	0.163616i	0.0658462	+	0.997830i	$0.479025\pi$
$318$	−4.92567	+	90.8487i	−0.000868610	+	0.0160206i
$319$	7084.00	−	4262.30i	1.24335	−	0.748097i
$320$	610.970	+	2200.52i	0.106732	+	0.384414i
$321$	789.593	−	2843.86i	0.137292	−	0.494482i
$322$	−203.540	−	122.466i	−0.0352261	−	0.0211949i
$323$	−2931.16	+	4323.13i	−0.504935	+	0.744723i
$324$	643.123	−	69.9439i	0.110275	−	0.0119931i
$325$	−3365.35	+	366.004i	−0.574388	+	0.0624685i
$326$	−44.7235	+	65.9622i	−0.00759817	+	0.0112065i
$327$	3484.31	+	2096.44i	0.589244	+	0.354536i
$328$	−10.0240	+	36.1033i	−0.00168745	+	0.00607766i
$329$	−3538.66	−	12745.1i	−0.592986	−	2.13574i
$330$	80.4669	−	48.4153i	0.0134229	−	0.00807629i
$331$	369.391	−	6813.01i	0.0613400	−	1.13135i	−0.792179	−	0.610289i	$-0.791053\pi$
$331$	369.391	−	6813.01i	0.0613400	−	1.13135i	0.853519	−	0.521061i	$-0.174464\pi$
$332$	873.214	−	294.220i	0.144349	−	0.0486368i
$333$	−1630.29	−	3075.04i	−0.268286	−	0.506040i
$334$	−176.050	−	207.262i	−0.0288413	−	0.0339546i
$335$	998.252	+	1472.31i	0.162807	+	0.240122i
$336$	−366.223	−	6754.59i	−0.0594616	−	1.09671i
$337$	1078.76	+	2707.47i	0.174373	+	0.437643i	0.990024	−	0.140902i	$-0.0450002\pi$
$337$	1078.76	+	2707.47i	0.174373	+	0.437643i	−0.815651	+	0.578544i	$0.803621\pi$
$338$	120.934	+	55.9500i	0.0194613	+	0.00900378i
$339$	60.7295	−	13.3676i	0.00972971	−	0.00214167i
$340$	1999.63	−	3771.70i	0.318956	−	0.601616i
$341$	−956.044	+	5831.61i	−0.151826	+	0.926098i
$342$	−36.5002	+	27.7467i	−0.00577107	+	0.00438705i
$343$	18248.3	−	8442.56i	2.87264	−	1.32902i
$344$	−176.651	−	167.333i	−0.0276871	−	0.0262266i
$345$	126.785	+	773.352i	0.0197851	+	0.120684i
$346$	184.243	+	62.0786i	0.0286270	+	0.00964556i
$347$	−2958.12	+	7424.32i	−0.457637	+	1.14858i	0.501378	+	0.865228i	$0.332827\pi$
$347$	−2958.12	+	7424.32i	−0.457637	+	1.14858i	−0.959015	+	0.283354i	$0.908553\pi$
$348$	2395.08	−	2268.74i	0.368937	−	0.349475i
$349$	−5182.76	−	3939.83i	−0.794918	−	0.604281i	0.126895	−	0.991916i	$-0.459499\pi$
$349$	−5182.76	−	3939.83i	−0.794918	−	0.604281i	−0.921813	+	0.387635i	$0.873292\pi$
$350$	418.940	+	92.2156i	0.0639808	+	0.0140832i
$351$	565.156	−	665.353i	0.0859424	−	0.101179i
$352$	1323.15	+	143.901i	0.200352	+	0.0217896i
$353$	5284.54			0.796793			0.398396	−	0.917213i	$-0.369567\pi$
$353$	5284.54			0.796793			0.398396	+	0.917213i	$0.369567\pi$
$354$	−113.332	+	109.101i	−0.0170156	+	0.0163804i
$355$	−3486.49			−0.521250
$356$	9454.60	+	1028.25i	1.40756	+	0.153082i
$357$	−8158.49	+	9604.92i	−1.20950	+	1.42394i
$358$	114.663	+	25.2392i	0.0169277	+	0.00372607i
$359$	130.402	+	99.1291i	0.0191709	+	0.0145734i	0.614716	−	0.788749i	$-0.289271\pi$
$359$	130.402	+	99.1291i	0.0191709	+	0.0145734i	−0.595545	+	0.803322i	$0.703064\pi$
$360$	54.4569	−	51.5843i	0.00797259	−	0.00755204i
$361$	1821.29	−	4571.09i	0.265533	−	0.666436i
$362$	93.7649	+	31.5931i	0.0136137	+	0.00458700i
$363$	1103.79	+	6732.84i	0.159598	+	0.973506i
$364$	−6638.30	−	6288.14i	−0.955884	−	0.905461i
$365$	−1631.37	+	754.751i	−0.233944	+	0.108234i
$366$	43.5354	−	33.0948i	0.00621758	−	0.00472648i
$367$	57.8356	−	352.782i	0.00822615	−	0.0501773i	−0.982394	−	0.186818i	$-0.940182\pi$
$367$	57.8356	−	352.782i	0.00822615	−	0.0501773i	0.990621	+	0.136641i	$0.0436307\pi$
$368$	−1729.33	+	3261.86i	−0.244966	+	0.462055i
$369$	−178.042	+	39.1900i	−0.0251179	+	0.00552886i
$370$	−182.978	−	84.6547i	−0.0257097	−	0.0118946i
$371$	3435.23	+	8621.77i	0.480723	+	1.20652i
$372$	127.666	+	2354.65i	0.0177934	+	0.328180i
$373$	−7311.70	−	10784.0i	−1.01497	−	1.49698i	−0.860808	−	0.508931i	$-0.830041\pi$
$373$	−7311.70	−	10784.0i	−1.01497	−	1.49698i	−0.154167	−	0.988045i	$-0.549269\pi$
$374$	−533.579	−	628.178i	−0.0737720	−	0.0868511i
$375$	−1454.33	−	2743.15i	−0.200270	−	0.377749i
$376$	654.814	−	220.633i	0.0898124	−	0.0302613i
$377$	241.020	−	4445.36i	0.0329262	−	0.607288i
$378$	−94.7883	+	57.0322i	−0.0128978	+	0.00776038i
$379$	−2467.05	−	8885.52i	−0.334364	−	1.20427i	−0.919420	−	0.393278i	$-0.871341\pi$
$379$	−2467.05	−	8885.52i	−0.334364	−	1.20427i	0.585056	−	0.810993i	$-0.301073\pi$
$380$	423.853	−	1526.58i	0.0572190	−	0.206084i
$381$	−2305.94	−	1387.44i	−0.310071	−	0.186563i
$382$	326.694	−	481.838i	0.0437569	−	0.0645366i
$383$	−9429.12	+	1025.48i	−1.25798	+	0.136813i	−0.712716	−	0.701453i	$-0.752535\pi$
$383$	−9429.12	+	1025.48i	−1.25798	+	0.136813i	−0.545261	+	0.838266i	$0.683570\pi$
$384$	703.788	−	76.5416i	0.0935287	−	0.0101719i
$385$	5375.91	−	7928.87i	0.711640	−	1.04959i
$386$	36.3134	+	21.8491i	0.00478835	+	0.00288106i
$387$	316.719	−	1140.72i	0.0416014	−	0.149835i
$388$	2888.49	+	10403.4i	0.377941	+	1.36122i
$389$	2172.29	−	1307.02i	0.283135	−	0.170356i	−0.366901	−	0.930260i	$-0.619581\pi$
$389$	2172.29	−	1307.02i	0.283135	−	0.170356i	0.650036	+	0.759903i	$0.274754\pi$
$390$	2.73774	−	50.4946i	0.000355464	−	0.00655614i
$391$	6517.97	−	2196.16i	0.843039	−	0.284053i
$392$	789.192	+	1488.57i	0.101684	+	0.191797i
$393$	1930.91	+	2273.24i	0.247841	+	0.291781i
$394$	119.267	+	175.906i	0.0152502	+	0.0224924i
$395$	199.421	+	3678.10i	0.0254024	+	0.468520i
$396$	1597.48	+	4009.38i	0.202718	+	0.508785i
$397$	−6712.92	−	3105.73i	−0.848644	−	0.392625i	−0.0531505	−	0.998587i	$-0.516926\pi$
$397$	−6712.92	−	3105.73i	−0.848644	−	0.392625i	−0.795494	+	0.605962i	$0.792788\pi$
$398$	−505.743	+	111.322i	−0.0636950	+	0.0140203i
$399$	−2190.74	+	4132.18i	−0.274873	+	0.518466i
$400$	1078.62	−	6579.29i	0.134828	−	0.822412i
$401$	2062.60	−	1567.95i	0.256861	−	0.195260i	−0.468817	−	0.883295i	$-0.655320\pi$
$401$	2062.60	−	1567.95i	0.256861	−	0.195260i	0.725678	+	0.688035i	$0.241526\pi$
$402$	124.378	−	57.5432i	0.0154313	−	0.00713929i
$403$	2310.23	+	2188.37i	0.285560	+	0.270497i
$404$	829.951	+	5062.48i	0.102207	+	0.623435i
$405$	345.853	+	116.531i	0.0424335	+	0.0142975i
$406$	−208.809	+	524.071i	−0.0255247	+	0.0640621i
$407$	16857.7	−	15968.4i	2.05308	−	1.94478i
$408$	−524.095	−	398.406i	−0.0635945	−	0.0483433i
$409$	−9956.40	−	2191.57i	−1.20370	−	0.264954i	−0.432550	−	0.901610i	$-0.642386\pi$
$409$	−9956.40	−	2191.57i	−1.20370	−	0.264954i	−0.771148	+	0.636656i	$0.780317\pi$
$410$	−6.83656	+	8.04862i	−0.000823496	+	0.000969495i
$411$	−2468.17	−	268.429i	−0.296218	−	0.0322157i
$412$	−8523.47			−1.01923
$413$	−5819.26	+	14954.8i	−0.693334	+	1.78179i
$414$	60.3759			0.00716742
$415$	516.788	+	56.2041i	0.0611281	+	0.00664808i
$416$	463.980	−	546.239i	0.0546838	−	0.0643788i
$417$	6551.08	+	1442.00i	0.769324	+	0.169341i
$418$	−243.512	−	185.113i	−0.0284941	−	0.0216607i
$419$	7134.74	−	6758.38i	0.831873	−	0.787992i	−0.147711	−	0.989031i	$-0.547190\pi$
$419$	7134.74	−	6758.38i	0.831873	−	0.787992i	0.979583	+	0.201039i	$0.0644318\pi$
$420$	1414.90	−	3551.12i	0.164381	−	0.412564i
$421$	−11866.5	−	3998.30i	−1.37373	−	0.462862i	−0.466879	−	0.884321i	$-0.654622\pi$
$421$	−11866.5	−	3998.30i	−1.37373	−	0.462862i	−0.906847	+	0.421459i	$0.861518\pi$
$422$	6.20303	+	37.8368i	0.000715542	+	0.00436461i
$423$	2440.76	+	2312.01i	0.280553	+	0.265754i
$424$	−440.022	+	203.576i	−0.0503994	+	0.0233172i
$425$	−9888.09	+	7516.73i	−1.12857	+	0.857917i
$426$	−43.4556	+	265.068i	−0.00494233	+	0.0301469i
$427$	2613.00	−	4928.64i	0.296140	−	0.558580i
$428$	7673.63	−	1689.09i	0.866632	−	0.190760i
$429$	5285.82	+	2445.48i	0.594876	+	0.275219i
$430$	−25.3832	−	63.7070i	−0.00284671	−	0.00714471i
$431$	−318.026	−	5865.65i	−0.0355424	−	0.655542i	−0.960976	−	0.276632i	$-0.910782\pi$
$431$	−318.026	−	5865.65i	−0.0355424	−	0.655542i	0.925434	−	0.378910i	$-0.123701\pi$
$432$	964.865	+	1423.07i	0.107459	+	0.158490i
$433$	7161.21	+	8430.83i	0.794794	+	0.935704i	0.999066	−	0.0432099i	$-0.0137584\pi$
$433$	7161.21	+	8430.83i	0.794794	+	0.935704i	−0.204272	+	0.978914i	$0.565483\pi$
$434$	−188.881	−	356.267i	−0.0208907	−	0.0394041i
$435$	1763.73	−	594.268i	0.194400	−	0.0655011i
$436$	−586.083	+	10809.7i	−0.0643768	+	1.18736i
$437$	2187.22	−	1316.01i	0.239425	−	0.144057i
$438$	37.0481	+	133.435i	0.00404162	+	0.0145566i
$439$	−75.0327	+	270.243i	−0.00815744	+	0.0293804i	−0.967517	−	0.252807i	$-0.918646\pi$
$439$	−75.0327	+	270.243i	−0.00815744	+	0.0293804i	0.959359	+	0.282187i	$0.0910600\pi$
$440$	428.797	+	257.999i	0.0464594	+	0.0279537i
$441$	−4600.32	+	6784.97i	−0.496742	+	0.732639i
$442$	−441.221	+	47.9857i	−0.0474813	+	0.00516390i
$443$	−13830.6	+	1504.17i	−1.48332	+	0.161321i	−0.813658	−	0.581343i	$-0.802527\pi$
$443$	−13830.6	+	1504.17i	−1.48332	+	0.161321i	−0.669664	+	0.742664i	$0.733562\pi$
$444$	5199.81	−	7669.15i	0.555793	−	0.819734i
$445$	4597.26	+	2766.08i	0.489733	+	0.294663i
$446$	−12.5544	+	45.2169i	−0.00133289	+	0.00480063i
$447$	647.425	+	2331.81i	0.0685059	+	0.246736i
$448$	15378.8	−	9253.09i	1.62183	−	0.975820i
$449$	37.4214	−	690.197i	0.00393324	−	0.0725443i	−0.995908	−	0.0903753i	$-0.971193\pi$
$449$	37.4214	−	690.197i	0.00393324	−	0.0725443i	0.999841	+	0.0178310i	$0.00567609\pi$
$450$	−103.323	+	34.8137i	−0.0108238	+	0.00364696i
$451$	−569.699	−	1074.57i	−0.0594813	−	0.112194i
$452$	107.171	+	126.172i	0.0111525	+	0.0131297i
$453$	647.495	+	954.983i	0.0671566	+	0.0990486i
$454$	−18.5485	−	342.107i	−0.00191745	−	0.0353653i
$455$	−1909.33	−	4792.07i	−0.196727	−	0.493748i
$456$	−221.743	−	102.589i	−0.0227721	−	0.0105355i
$457$	−10903.7	+	2400.08i	−1.11609	+	0.245670i	−0.734464	−	0.678648i	$-0.762566\pi$
$457$	−10903.7	+	2400.08i	−1.11609	+	0.245670i	−0.381625	+	0.924317i	$0.624635\pi$
$458$	22.9531	−	43.2942i	0.00234177	−	0.00441704i
$459$	518.202	−	3160.89i	0.0526963	−	0.321433i
$460$	−1660.89	+	1262.58i	−0.168347	+	0.127974i
$461$	16860.5	−	7800.49i	1.70341	−	0.788081i	0.706656	−	0.707557i	$-0.250203\pi$
$461$	16860.5	−	7800.49i	1.70341	−	0.788081i	0.996753	−	0.0805234i	$-0.0256592\pi$
$462$	−535.803	−	507.539i	−0.0539563	−	0.0511101i
$463$	1191.31	+	7266.69i	0.119579	+	0.729399i	0.976752	+	0.214371i	$0.0687702\pi$
$463$	1191.31	+	7266.69i	0.119579	+	0.729399i	−0.857173	+	0.515028i	$0.827782\pi$
$464$	8308.98	+	2799.62i	0.831325	+	0.280106i
$465$	−492.405	+	1235.84i	−0.0491070	+	0.123249i
$466$	−524.612	+	496.939i	−0.0521506	+	0.0493996i
$467$	12504.5	+	9505.71i	1.23906	+	0.941909i	0.999580	−	0.0289917i	$-0.00922963\pi$
$467$	12504.5	+	9505.71i	1.23906	+	0.941909i	0.239481	+	0.970901i	$0.423023\pi$
$468$	2269.72	+	499.603i	0.224183	+	0.0493465i
$469$	9050.20	−	10654.7i	0.891044	−	1.04902i
$470$	193.605	+	21.0558i	0.0190007	+	0.00206645i
$471$	−10771.0			−1.05371
$472$	−796.547	−	261.255i	−0.0776780	−	0.0254772i
$473$	7898.22			0.767782
$474$	282.121	+	30.6825i	0.0273380	+	0.00297319i
$475$	−2984.23	+	3513.31i	−0.288265	+	0.339372i
$476$	−32765.2	−	7212.18i	−3.15503	−	0.694474i
$477$	−1877.93	−	1427.56i	−0.180261	−	0.137031i
$478$	−297.063	+	281.393i	−0.0284254	+	0.0269260i
$479$	−1170.86	+	2938.63i	−0.111686	+	0.280312i	−0.974186	−	0.225746i	$-0.927518\pi$
$479$	−1170.86	+	2938.63i	−0.111686	+	0.280312i	0.862500	+	0.506057i	$0.168898\pi$
$480$	283.937	+	95.6696i	0.0269998	+	0.00909729i
$481$	−2022.87	−	12338.9i	−0.191756	−	1.16966i
$482$	248.553	+	235.442i	0.0234882	+	0.0222492i
$483$	5589.61	−	2586.03i	0.526576	−	0.243620i
$484$	−14459.8	+	10992.1i	−1.35798	+	1.03231i
$485$	−985.432	+	6010.87i	−0.0922601	+	0.562762i
$486$	13.1702	−	24.8417i	0.00122925	−	0.00231861i
$487$	−934.095	+	205.610i	−0.0869155	+	0.0191316i	−0.258215	−	0.966087i	$-0.583134\pi$
$487$	−934.095	+	205.610i	−0.0869155	+	0.0191316i	0.171300	+	0.985219i	$0.445203\pi$
$488$	264.483	+	122.363i	0.0245339	+	0.0113506i
$489$	−764.804	−	1919.51i	−0.0707273	−	0.177512i
$490$	25.7080	+	474.156i	0.00237014	+	0.0437147i
$491$	−2716.46	−	4006.49i	−0.249679	−	0.368249i	0.682110	−	0.731250i	$-0.261063\pi$
$491$	−2716.46	−	4006.49i	−0.249679	−	0.368249i	−0.931789	+	0.363001i	$0.881752\pi$
$492$	−314.196	−	369.900i	−0.0287908	−	0.0338951i
$493$	−7651.26	−	14431.8i	−0.698977	−	1.31841i
$494$	−156.092	+	52.5934i	−0.0142164	+	0.00479006i
$495$	−131.818	+	2431.25i	−0.0119693	+	0.220761i
$496$	−5370.12	+	3231.10i	−0.486140	+	0.292501i
$497$	7330.29	+	26401.3i	0.661586	+	2.38282i
$498$	10.7143	−	38.5893i	0.000964093	−	0.00347235i
$499$	−4025.28	−	2421.93i	−0.361115	−	0.217276i	0.323420	−	0.946255i	$-0.395167\pi$
$499$	−4025.28	−	2421.93i	−0.361115	−	0.217276i	−0.684535	+	0.728980i	$0.739995\pi$
$500$	4638.60	−	6841.42i	0.414889	−	0.611915i
$501$	7009.33	−	762.311i	0.625057	−	0.0679791i
$502$	642.744	−	69.9027i	0.0571456	−	0.00621496i
$503$	−7576.96	+	11175.2i	−0.671650	+	0.990609i	0.327306	+	0.944918i	$0.393859\pi$
$503$	−7576.96	+	11175.2i	−0.671650	+	0.990609i	−0.998956	+	0.0456907i	$0.985451\pi$
$504$	−505.115	−	303.917i	−0.0446421	−	0.0268602i
$505$	−774.260	+	2788.63i	−0.0682259	+	0.245728i
$506$	107.760	+	388.117i	0.00946743	+	0.0340986i
$507$	−2960.27	+	1781.14i	−0.259310	+	0.156022i
$508$	387.874	−	7153.91i	0.0338762	−	0.624810i
$509$	−19422.0	+	6544.04i	−1.69129	+	0.569862i	−0.989755	−	0.142774i	$-0.954398\pi$
$509$	−19422.0	+	6544.04i	−1.69129	+	0.569862i	−0.701534	+	0.712636i	$0.747501\pi$
$510$	−86.9104	−	163.930i	−0.00754599	−	0.0142332i
$511$	9145.24	+	10766.6i	0.791706	+	0.932068i
$512$	1320.96	+	1948.27i	0.114021	+	0.168168i
$513$	−64.3575	−	1187.00i	−0.00553890	−	0.102159i
$514$	−164.793	−	413.599i	−0.0141415	−	0.0354924i
$515$	−4364.09	−	2019.04i	−0.373407	−	0.172757i
$516$	3078.02	−	677.524i	0.262602	−	0.0578030i
$517$	−10506.1	+	19816.6i	−0.893727	+	1.68575i
$518$	−256.336	+	1563.58i	−0.0217428	+	0.132625i
$519$	−4012.94	+	3050.56i	−0.339400	+	0.258005i
$520$	244.568	−	113.149i	0.0206251	−	0.00954217i
$521$	6832.80	+	6472.38i	0.574569	+	0.544261i	0.918851	−	0.394606i	$-0.129119\pi$
$521$	6832.80	+	6472.38i	0.574569	+	0.544261i	−0.344281	+	0.938867i	$0.611877\pi$
$522$	−23.1974	−	141.498i	−0.00194506	−	0.0118643i
$523$	−14337.5	−	4830.87i	−1.19873	−	0.403899i	−0.352039	−	0.935985i	$-0.614512\pi$
$523$	−14337.5	−	4830.87i	−1.19873	−	0.403899i	−0.846690	+	0.532086i	$0.821408\pi$
$524$	−2939.03	+	7376.40i	−0.245023	+	0.614961i
$525$	−8074.54	+	7648.61i	−0.671242	+	0.635834i
$526$	741.807	+	563.907i	0.0614911	+	0.0467443i
$527$	11402.8	+	2509.95i	0.942531	+	0.207467i
$528$	−7425.87	+	8742.41i	−0.612063	+	0.720576i
$529$	8754.02	+	952.057i	0.719488	+	0.0782491i
$530$	−136.645			−0.0111990
$531$	−692.293	−	4019.51i	−0.0565780	−	0.328497i
$532$	−12451.1			−1.01471
$533$	−651.090	−	70.8104i	−0.0529116	−	0.00575448i
$534$	267.597	−	315.040i	0.0216855	−	0.0255302i
$535$	4329.08	+	952.902i	0.349836	+	0.0770047i
$536$	581.378	+	441.952i	0.0468502	+	0.0356146i
$537$	−2209.99	+	2093.41i	−0.177594	+	0.168226i
$538$	18.5096	−	46.4555i	0.00148328	−	0.00372275i
$539$	−51826.9	−	17462.5i	−4.14163	−	1.39548i
$540$	157.186	+	958.792i	0.0125263	+	0.0764071i
$541$	−1885.63	−	1786.17i	−0.149852	−	0.141947i	0.609101	−	0.793092i	$-0.291530\pi$
$541$	−1885.63	−	1786.17i	−0.149852	−	0.141947i	−0.758953	+	0.651145i	$0.774289\pi$
$542$	−409.952	+	189.664i	−0.0324888	+	0.0150309i
$543$	−2042.27	+	1552.49i	−0.161404	+	0.122696i
$544$	425.432	−	2595.02i	0.0335299	−	0.204523i
$545$	−2860.68	+	5395.81i	−0.224840	+	0.424094i
$546$	−388.124	+	85.4326i	−0.0304216	+	0.00669630i
$547$	18709.1	+	8655.74i	1.46242	+	0.676586i	0.979935	−	0.199319i	$-0.0638731\pi$
$547$	18709.1	+	8655.74i	1.46242	+	0.676586i	0.482483	+	0.875906i	$0.339735\pi$
$548$	−2446.43	−	6140.08i	−0.190705	−	0.478633i
$549$	76.7621	+	1415.79i	0.00596744	+	0.110063i
$550$	−408.207	−	602.061i	−0.0316473	−	0.0466763i
$551$	−3924.57	−	4620.37i	−0.303435	−	0.357231i
$552$	150.703	+	284.257i	0.0116202	+	0.0219181i
$553$	27433.0	−	9243.25i	2.10953	−	0.710783i
$554$	17.5706	−	324.071i	0.00134748	−	0.0248528i
$555$	4479.02	−	2694.94i	0.342566	−	0.206115i
$556$	4777.47	+	17206.9i	0.364407	+	1.31247i
$557$	1485.37	−	5349.83i	0.112993	−	0.406965i	−0.885322	−	0.464978i	$-0.846062\pi$
$557$	1485.37	−	5349.83i	0.112993	−	0.406965i	0.998316	+	0.0580121i	$0.0184762\pi$
$558$	87.8202	+	52.8397i	0.00666259	+	0.00400875i
$559$	2386.77	−	3520.23i	0.180590	−	0.266350i
$560$	10099.9	−	1098.43i	0.762144	−	0.0828881i
$561$	21244.2	−	2310.45i	1.59881	−	0.173881i
$562$	−282.073	+	416.026i	−0.0211718	+	0.0312260i
$563$	13716.5	+	8252.97i	1.02679	+	0.617800i	0.926163	−	0.377124i	$-0.123087\pi$
$563$	13716.5	+	8252.97i	1.02679	+	0.617800i	0.100628	+	0.994924i	$0.467915\pi$
$564$	−2394.43	+	8623.97i	−0.178766	+	0.643856i
$565$	24.9850	+	89.9879i	0.00186040	+	0.00670056i
$566$	−239.102	+	143.863i	−0.0177565	+	0.0106837i
$567$	155.280	−	2863.96i	0.0115011	−	0.212125i
$568$	−1356.44	+	457.038i	−0.100202	+	0.0337621i
$569$	6062.60	+	11435.3i	0.446674	+	0.842516i	0.999955	+	0.00952111i	$0.00303071\pi$
$569$	6062.60	+	11435.3i	0.446674	+	0.842516i	−0.553281	+	0.832995i	$0.686624\pi$
$570$	−44.5791	−	52.4825i	−0.00327581	−	0.00385658i
$571$	−8126.17	−	11985.2i	−0.595569	−	0.878398i	0.403766	−	0.914862i	$-0.367701\pi$
$571$	−8126.17	−	11985.2i	−0.595569	−	0.878398i	−0.999335	+	0.0364641i	$0.988391\pi$
$572$	839.422	+	15482.2i	0.0613601	+	1.13172i
$573$	5586.71	+	14021.6i	0.407309	+	1.02227i
$574$	75.3215	+	34.8474i	0.00547711	+	0.00253398i
$575$	5928.25	−	1304.91i	0.429957	−	0.0946407i
$576$	−2136.78	+	4030.40i	−0.154571	+	0.291551i
$577$	−881.826	+	5378.90i	−0.0636238	+	0.388088i	0.935749	+	0.352667i	$0.114725\pi$
$577$	−881.826	+	5378.90i	−0.0636238	+	0.388088i	−0.999373	+	0.0354204i	$0.988723\pi$
$578$	−843.838	+	641.469i	−0.0607250	+	0.0461619i
$579$	−997.240	+	461.372i	−0.0715784	+	0.0331157i
$580$	3597.13	+	3407.39i	0.257522	+	0.243938i
$581$	−660.935	−	4031.52i	−0.0471948	−	0.287876i
$582$	444.706	+	149.839i	0.0316729	+	0.0106719i
$583$	5825.09	−	14619.9i	0.413809	−	1.03858i
$584$	−535.754	+	507.493i	−0.0379617	+	0.0359593i
$585$	1043.77	+	793.453i	0.0737685	+	0.0560773i
$586$	965.429	+	212.507i	0.0680572	+	0.0149805i
$587$	17569.5	−	20684.4i	1.23538	−	1.45441i	0.389509	−	0.921023i	$-0.372645\pi$
$587$	17569.5	−	20684.4i	1.23538	−	1.45441i	0.845874	−	0.533383i	$-0.179079\pi$
$588$	−21695.5	−	2359.52i	−1.52161	−	0.165485i
$589$	4333.18			0.303133
$590$	−172.831	−	161.090i	−0.0120599	−	0.0112407i
$591$	−5510.25			−0.383522
$592$	24481.5	+	2662.53i	1.69964	+	0.184846i
$593$	6776.96	−	7978.45i	0.469303	−	0.552506i	−0.475683	−	0.879617i	$-0.657799\pi$
$593$	6776.96	−	7978.45i	0.469303	−	0.552506i	0.944986	+	0.327111i	$0.106075\pi$
$594$	183.198	+	40.3248i	0.0126544	+	0.00278543i
$595$	−15067.7	−	11454.1i	−1.03818	−	0.789200i
$596$	−4677.30	+	4430.57i	−0.321459	+	0.304502i
$597$	4969.66	−	12472.9i	0.340694	−	0.855078i
$598$	205.547	+	69.2569i	0.0140559	+	0.00473599i
$599$	151.555	+	924.444i	0.0103378	+	0.0630580i	0.991492	−	0.130170i	$-0.0415524\pi$
$599$	151.555	+	924.444i	0.0103378	+	0.0630580i	−0.981154	+	0.193228i	$0.938104\pi$
$600$	−421.811	−	399.560i	−0.0287006	−	0.0271866i
$601$	−6720.48	+	3109.23i	−0.456130	+	0.211028i	−0.634481	−	0.772939i	$-0.718786\pi$
$601$	−6720.48	+	3109.23i	−0.456130	+	0.211028i	0.178351	+	0.983967i	$0.442924\pi$
$602$	−429.051	+	326.156i	−0.0290479	+	0.0220816i
$603$	−574.841	+	3506.38i	−0.0388215	+	0.236800i
$604$	−1438.78	+	2713.83i	−0.0969257	+	0.182821i
$605$	−10007.4	+	2202.79i	−0.672491	+	0.148026i
$606$	202.361	+	93.6221i	0.0135649	+	0.00627581i
$607$	1879.98	+	4718.40i	0.125710	+	0.315509i	0.978339	−	0.207008i	$-0.0663725\pi$
$607$	1879.98	+	4718.40i	0.125710	+	0.315509i	−0.852629	+	0.522517i	$0.824993\pi$
$608$	−52.8360	−	974.503i	−0.00352431	−	0.0650022i
$609$	−8208.27	−	12106.3i	−0.546167	−	0.805536i
$610$	53.1715	+	62.5983i	0.00352926	+	0.00415497i
$611$	5657.37	+	10670.9i	0.374587	+	0.706547i
$612$	8080.90	−	2722.77i	0.533744	−	0.179839i
$613$	867.929	−	16008.0i	0.0571865	−	1.05474i	−0.819315	−	0.573344i	$-0.805646\pi$
$613$	867.929	−	16008.0i	0.0571865	−	1.05474i	0.876501	−	0.481399i	$-0.159871\pi$
$614$	677.050	−	407.367i	0.0445008	−	0.0267753i
$615$	−73.2490	−	263.819i	−0.00480274	−	0.0172979i
$616$	1052.15	−	3789.49i	0.0688185	−	0.247862i
$617$	9356.47	+	5629.60i	0.610498	+	0.367324i	0.786979	−	0.616980i	$-0.211644\pi$
$617$	9356.47	+	5629.60i	0.610498	+	0.367324i	−0.176481	+	0.984304i	$0.556472\pi$
$618$	−207.896	+	306.623i	−0.0135320	+	0.0199583i
$619$	−22002.5	+	2392.91i	−1.42868	+	0.155378i	−0.789534	−	0.613706i	$-0.789678\pi$
$619$	−22002.5	+	2392.91i	−1.42868	+	0.155378i	−0.639147	+	0.769085i	$0.720712\pi$
$620$	−3520.85	+	382.915i	−0.228065	+	0.0248036i
$621$	−878.475	+	1295.65i	−0.0567665	+	0.0837243i
$622$	−559.364	−	336.558i	−0.0360586	−	0.0216957i
$623$	11280.4	−	40628.2i	0.725423	−	2.61274i
$624$	1652.45	+	5951.57i	0.106011	+	0.381817i
$625$	−7218.42	+	4343.18i	−0.461979	+	0.277964i
$626$	−34.2408	+	631.535i	−0.00218616	+	0.0403214i
$627$	7515.60	−	2532.30i	0.478699	−	0.161292i
$628$	−13431.4	−	25334.3i	−0.853456	−	1.60979i
$629$	−29700.6	−	34966.2i	−1.88273	−	2.21653i
$630$	−93.2374	−	137.515i	−0.00589630	−	0.00869639i
$631$	−53.7262	−	990.922i	−0.00338955	−	0.0625166i	0.996349	−	0.0853707i	$-0.0272074\pi$
$631$	−53.7262	−	990.922i	−0.00338955	−	0.0625166i	−0.999739	+	0.0228541i	$0.992725\pi$
$632$	559.741	+	1404.84i	0.0352299	+	0.0884204i
$633$	−902.224	−	417.413i	−0.0566512	−	0.0262096i
$634$	−326.815	+	71.9375i	−0.0204724	+	0.00450631i
$635$	1893.22	−	3570.99i	0.118315	−	0.223166i
$636$	1015.98	−	6197.22i	0.0633432	−	0.386377i
$637$	−23444.6	+	17822.1i	−1.45826	+	1.10854i
$638$	868.192	−	401.668i	0.0538747	−	0.0249251i
$639$	−5056.01	−	4789.31i	−0.313009	−	0.296498i
$640$	172.013	+	1049.23i	0.0106241	+	0.0648040i
$641$	27382.2	+	9226.12i	1.68725	+	0.568502i	0.989074	−	0.147420i	$-0.0470968\pi$
$641$	27382.2	+	9226.12i	1.68725	+	0.568502i	0.698180	+	0.715922i	$0.253993\pi$
$642$	126.404	−	317.250i	0.00777066	−	0.0195029i
$643$	21.7037	−	20.5588i	0.00133112	−	0.00126090i	−0.687034	−	0.726626i	$-0.741087\pi$
$643$	21.7037	−	20.5588i	0.00133112	−	0.00126090i	0.688365	+	0.725365i	$0.258329\pi$
$644$	13052.8	+	9922.49i	0.798684	+	0.607144i
$645$	1736.47	+	382.225i	0.106005	+	0.0233335i
$646$	−391.253	+	460.619i	−0.0238292	+	0.0280539i
$647$	−3695.99	−	401.963i	−0.224581	−	0.0244247i	−0.00486363	−	0.999988i	$-0.501548\pi$
$647$	−3695.99	−	401.963i	−0.224581	−	0.0244247i	−0.219718	+	0.975563i	$0.570514\pi$
$648$	149.832			0.00908326
$649$	24603.1	−	11624.4i	1.48807	−	0.703077i
$650$	−391.694			−0.0236362
$651$	10393.7	+	1130.38i	0.625744	+	0.0680538i
$652$	3561.16	−	4192.52i	0.213904	−	0.251828i
$653$	−6673.74	−	1469.00i	−0.399944	−	0.0880343i	0.0104437	−	0.999945i	$-0.496676\pi$
$653$	−6673.74	−	1469.00i	−0.399944	−	0.0880343i	−0.410388	+	0.911911i	$0.634607\pi$
$654$	374.572	+	284.742i	0.0223959	+	0.0170249i
$655$	−3252.13	+	3080.59i	−0.194002	+	0.183769i
$656$	477.433	−	1198.27i	0.0284156	−	0.0713178i
$657$	−3402.55	−	1146.45i	−0.202049	−	0.0680781i
$658$	−247.606	−	1510.33i	−0.0146698	−	0.0894816i
$659$	21661.6	+	20518.9i	1.28045	+	1.21290i	0.964487	+	0.264131i	$0.0850852\pi$
$659$	21661.6	+	20518.9i	1.28045	+	1.21290i	0.315960	+	0.948772i	$0.397673\pi$
$660$	−5882.89	+	2721.72i	−0.346956	+	0.160519i
$661$	−13758.7	+	10459.1i	−0.809607	+	0.615447i	−0.925900	−	0.377768i	$-0.876692\pi$
$661$	−13758.7	+	10459.1i	−0.809607	+	0.615447i	0.116293	+	0.993215i	$0.462899\pi$
$662$	127.723	−	779.077i	0.00749864	−	0.0457397i
$663$	5390.04	−	10166.7i	0.315734	−	0.595538i
$664$	208.427	−	45.8783i	0.0121815	−	0.00268136i
$665$	−6375.08	−	2949.43i	−0.371752	−	0.171991i
$666$	−149.062	−	374.116i	−0.00867270	−	0.0217668i
$667$	432.186	+	7971.20i	0.0250889	+	0.462738i
$668$	10533.6	+	15536.0i	0.610118	+	0.899857i
$669$	−787.677	−	927.325i	−0.0455207	−	0.0535911i
$670$	96.4096	+	181.848i	0.00555914	+	0.0104857i
$671$	−8964.20	+	3020.39i	−0.515736	+	0.173772i
$672$	127.481	−	2351.25i	0.00731798	−	0.134972i
$673$	17526.1	−	10545.1i	1.00384	−	0.603989i	0.0840736	−	0.996460i	$-0.473207\pi$
$673$	17526.1	−	10545.1i	1.00384	−	0.603989i	0.919765	+	0.392470i	$0.128379\pi$
$674$	90.2178	+	324.935i	0.00515588	+	0.0185698i
$675$	756.270	−	2723.84i	0.0431242	−	0.155319i
$676$	−7880.85	−	4741.75i	−0.448387	−	0.269786i
$677$	7568.90	−	11163.3i	0.429685	−	0.633738i	−0.549790	−	0.835303i	$-0.685292\pi$
$677$	7568.90	−	11163.3i	0.429685	−	0.633738i	0.979475	+	0.201565i	$0.0646027\pi$
$678$	7.15292	−	0.777927i	0.000405171	−	4.40651e-5i
$679$	47588.9	−	5175.60i	2.68968	−	0.292521i
$680$	554.868	−	818.369i	0.0312915	−	0.0461515i
$681$	7611.42	+	4579.64i	0.428297	+	0.257698i
$682$	−182.928	+	658.847i	−0.0102708	+	0.0369920i
$683$	3339.23	+	12026.8i	0.187075	+	0.673784i	0.996274	+	0.0862483i	$0.0274878\pi$
$683$	3339.23	+	12026.8i	0.187075	+	0.673784i	−0.809199	+	0.587535i	$0.800098\pi$
$684$	2711.69	−	1631.57i	0.151585	−	0.0912055i
$685$	201.871	−	3723.28i	0.0112600	−	0.207678i
$686$	2204.71	−	742.854i	0.122706	−	0.0413445i
$687$	595.114	+	1122.50i	0.0330495	+	0.0623380i
$688$	5422.77	+	6384.18i	0.300496	+	0.353771i
$689$	−4755.77	−	7014.23i	−0.262961	−	0.387839i
$690$	4.90918	+	90.5445i	0.000270854	+	0.00499561i
$691$	9353.47	+	23475.4i	0.514939	+	1.29240i	0.924870	+	0.380283i	$0.124173\pi$
$691$	9353.47	+	23475.4i	0.514939	+	1.29240i	−0.409932	+	0.912116i	$0.634447\pi$
$692$	−12179.3	−	5634.75i	−0.669058	−	0.309539i
$693$	18687.7	−	4113.47i	1.02437	−	0.225480i
$694$	−433.151	+	817.009i	−0.0236919	+	0.0446877i
$695$	−1629.87	+	9941.78i	−0.0889562	+	0.542609i
$696$	608.286	−	462.407i	0.0331279	−	0.0251832i
$697$	−2180.93	+	1009.01i	−0.118520	+	0.0548333i
$698$	−546.882	−	518.034i	−0.0296559	−	0.0280915i
$699$	−3031.05	−	18488.6i	−0.164012	−	1.00043i
$700$	−28059.2	−	9454.23i	−1.51505	−	0.510481i
$701$	117.349	−	294.525i	0.00632272	−	0.0158688i	−0.925781	−	0.378059i	$-0.876592\pi$
$701$	117.349	−	294.525i	0.00632272	−	0.0158688i	0.932104	+	0.362190i	$0.117971\pi$
$702$	73.3334	−	69.4651i	0.00394272	−	0.00373474i
$703$	−13554.6	−	10303.9i	−0.727199	−	0.552802i
$704$	−29722.6	−	6542.43i	−1.59121	−	0.350252i
$705$	−3268.82	+	3848.35i	−0.174625	+	0.205585i
$706$	607.879	+	66.1108i	0.0324048	+	0.00352424i
$707$	22744.7			1.20990
$708$	8590.95	−	6640.65i	0.456028	−	0.352501i
$709$	6329.69			0.335284			0.167642	−	0.985848i	$-0.446385\pi$
$709$	6329.69			0.335284			0.167642	+	0.985848i	$0.446385\pi$
$710$	−401.050	−	43.6168i	−0.0211988	−	0.00230551i
$711$	−4763.32	+	5607.82i	−0.251250	+	0.295794i
$712$	2151.19	+	473.513i	0.113229	+	0.0249237i
$713$	−4542.58	−	3453.18i	−0.238599	−	0.181378i
$714$	−1058.63	+	1002.79i	−0.0554876	+	0.0525606i
$715$	−3237.64	+	8125.88i	−0.169344	+	0.425022i
$716$	−7679.74	−	2587.60i	−0.400845	−	0.135060i
$717$	−1716.34	−	10469.2i	−0.0893973	−	0.545299i
$718$	13.7600	+	13.0341i	0.000715206	+	0.000677479i
$719$	9088.10	−	4204.61i	0.471390	−	0.218088i	−0.169788	−	0.985481i	$-0.554308\pi$
$719$	9088.10	−	4204.61i	0.471390	−	0.218088i	0.641178	+	0.767393i	$0.278446\pi$
$720$	−2055.70	+	1562.70i	−0.106405	+	0.0808866i
$721$	−6113.69	+	37291.9i	−0.315792	+	1.92624i
$722$	266.687	−	503.026i	0.0137466	−	0.0259289i
$723$	−8669.01	+	1908.19i	−0.445925	+	0.0981556i
$724$	−6198.31	−	2867.64i	−0.318174	−	0.147203i
$725$	−5335.93	−	13392.2i	−0.273340	−	0.686031i
$726$	42.7396	+	788.285i	0.00218487	+	0.0402975i
$727$	−3288.46	−	4850.11i	−0.167761	−	0.247429i	0.734511	−	0.678597i	$-0.237412\pi$
$727$	−3288.46	−	4850.11i	−0.167761	−	0.247429i	−0.902271	+	0.431168i	$0.858101\pi$
$728$	−1371.02	−	1614.09i	−0.0697986	−	0.0821732i
$729$	341.470	+	644.080i	0.0173485	+	0.0327227i
$730$	−197.098	+	66.4100i	−0.00999304	+	0.00336705i
$731$	844.845	−	15582.3i	0.0427466	−	0.788414i
$732$	−3234.35	+	1946.04i	−0.163313	+	0.0982621i
$733$	3833.43	+	13806.8i	0.193166	+	0.695722i	0.995149	+	0.0983752i	$0.0313645\pi$
$733$	3833.43	+	13806.8i	0.193166	+	0.695722i	−0.801983	+	0.597347i	$0.796222\pi$
$734$	11.0662	−	39.8568i	0.000556486	−	0.00200428i
$735$	−10549.3	−	6347.33i	−0.529413	−	0.318537i
$736$	−721.207	+	1063.70i	−0.0361196	+	0.0532725i
$737$	−23566.2	+	2562.98i	−1.17784	+	0.128098i
$738$	−20.9704	+	2.28066i	−0.00104597	+	0.000113757i
$739$	−10723.4	+	15815.9i	−0.533787	+	0.787276i	−0.994985	−	0.100020i	$-0.968109\pi$
$739$	−10723.4	+	15815.9i	−0.533787	+	0.787276i	0.461199	+	0.887297i	$0.347420\pi$
$740$	11924.1	+	7174.48i	0.592348	+	0.356404i
$741$	1142.50	−	4114.93i	0.0566410	−	0.204002i
$742$	287.293	+	1034.73i	0.0142141	+	0.0511945i
$743$	30151.0	−	18141.3i	1.48874	−	0.895745i	0.489016	−	0.872275i	$-0.337356\pi$
$743$	30151.0	−	18141.3i	1.48874	−	0.895745i	0.999725	−	0.0234706i	$-0.00747162\pi$
$744$	−29.5686	+	545.361i	−0.00145704	+	0.0268735i
$745$	−3444.33	+	1160.53i	−0.169383	+	0.0570719i
$746$	−706.152	−	1331.94i	−0.0346569	−	0.0653699i
$747$	672.225	+	791.405i	0.0329256	+	0.0387630i
$748$	31925.9	+	47087.1i	1.56060	+	2.30171i
$749$	−1886.00	−	34785.2i	−0.0920065	−	1.69696i
$750$	−132.973	−	333.738i	−0.00647400	−	0.0162485i
$751$	−28945.7	−	13391.7i	−1.40645	−	0.650692i	−0.437787	−	0.899079i	$-0.644238\pi$
$751$	−28945.7	−	13391.7i	−1.40645	−	0.650692i	−0.968661	+	0.248387i	$0.920100\pi$
$752$	−23231.1	+	5113.56i	−1.12653	+	0.247968i
$753$	−7851.90	+	14810.2i	−0.379999	+	0.716754i
$754$	83.3369	−	508.332i	0.00402513	−	0.0245522i
$755$	−1379.52	+	1048.68i	−0.0664979	+	0.0505504i
$756$	6929.93	−	3206.13i	0.333385	−	0.154240i
$757$	14275.8	+	13522.8i	0.685420	+	0.649264i	0.948964	−	0.315383i	$-0.102133\pi$
$757$	14275.8	+	13522.8i	0.685420	+	0.649264i	−0.263545	+	0.964647i	$0.584892\pi$
$758$	−172.624	−	1052.96i	−0.00827176	−	0.0504555i
$759$	−9896.82	−	3334.63i	−0.473296	−	0.159472i
$760$	135.821	−	340.885i	0.00648255	−	0.0162700i
$761$	25655.7	−	24302.4i	1.22210	−	1.15764i	0.239703	−	0.970846i	$-0.422950\pi$
$761$	25655.7	−	24302.4i	1.22210	−	1.15764i	0.982400	−	0.186791i	$-0.0598086\pi$
$762$	−247.894	−	188.444i	−0.0117851	−	0.00895881i
$763$	46874.0	+	10317.8i	2.22406	+	0.489552i
$764$	−26013.4	+	30625.3i	−1.23185	+	1.45024i
$765$	4782.46	+	520.124i	0.226027	+	0.0245819i
$766$	−1097.46			−0.0517659
$767$	2253.88	−	14478.4i	0.106105	−	0.681595i
$768$	−12082.9			−0.567712
$769$	−12256.3	−	1332.95i	−0.574736	−	0.0625064i	−0.183865	−	0.982952i	$-0.558861\pi$
$769$	−12256.3	−	1332.95i	−0.574736	−	0.0625064i	−0.390872	+	0.920445i	$0.627826\pi$
$770$	717.580	−	844.801i	0.0335842	−	0.0395383i
$771$	11273.5	+	2481.49i	0.526596	+	0.115913i
$772$	−2328.75	−	1770.27i	−0.108567	−	0.0825301i
$773$	−19391.8	+	18368.9i	−0.902298	+	0.854702i	−0.989945	−	0.141450i	$-0.954824\pi$
$773$	−19391.8	+	18368.9i	−0.902298	+	0.854702i	0.0876477	+	0.996152i	$0.472065\pi$
$774$	50.7028	−	127.254i	0.00235462	−	0.00590964i
$775$	9765.02	+	3290.22i	0.452606	+	0.152501i
$776$	404.566	+	2467.74i	0.0187153	+	0.114158i
$777$	−29824.4	−	28251.1i	−1.37702	−	1.30438i
$778$	266.229	−	123.170i	0.0122683	−	0.00567593i
$779$	−709.976	+	539.710i	−0.0326541	+	0.0248230i
$780$	−564.693	+	3444.47i	−0.0259221	+	0.158118i
$781$	21763.2	−	41049.8i	0.997119	−	1.88077i
$782$	777.234	−	171.082i	0.0355420	−	0.00782339i
$783$	3374.03	+	1560.99i	0.153995	+	0.0712457i
$784$	−21468.3	−	53881.3i	−0.977965	−	2.45451i
$785$	−875.790	−	16153.0i	−0.0398195	−	0.734427i
$786$	193.673	+	285.646i	0.00878892	+	0.0129627i
$787$	−932.801	−	1098.18i	−0.0422500	−	0.0497405i	0.740631	−	0.671912i	$-0.234527\pi$
$787$	−932.801	−	1098.18i	−0.0422500	−	0.0497405i	−0.782881	+	0.622171i	$0.786251\pi$
$788$	−6871.27	−	12960.6i	−0.310633	−	0.585916i
$789$	−22894.7	+	7714.12i	−1.03304	+	0.348073i
$790$	−23.0746	+	425.585i	−0.00103919	+	0.0191666i
$791$	628.899	−	378.396i	0.0282694	−	0.0170091i
$792$	267.423	+	963.171i	0.0119981	+	0.0432131i
$793$	−1362.72	+	4908.06i	−0.0610233	+	0.219786i
$794$	−733.331	−	441.231i	−0.0327770	−	0.0197213i
$795$	1988.19	−	2932.36i	0.0886967	−	0.130818i
$796$	35534.5	−	3864.61i	1.58227	−	0.172082i
$797$	−15463.1	+	1681.71i	−0.687239	+	0.0747418i	−0.445075	−	0.895493i	$-0.646823\pi$
$797$	−15463.1	+	1681.71i	−0.687239	+	0.0747418i	−0.242165	+	0.970235i	$0.577857\pi$
$798$	−303.695	+	447.917i	−0.0134720	+	0.0198698i
$799$	37971.9	+	22847.0i	1.68129	+	1.01160i
$800$	620.880	−	2236.21i	0.0274393	−	0.0988273i
$801$	2867.12	+	10326.4i	0.126473	+	0.455514i
$802$	256.875	−	154.557i	0.0113099	−	0.00680497i
$803$	1296.85	−	23918.9i	0.0569922	−	1.05116i
$804$	−8964.14	+	3020.37i	−0.393210	+	0.132488i
$805$	4332.71	+	8172.36i	0.189699	+	0.357811i
$806$	238.368	+	280.629i	0.0104171	+	0.0122639i
$807$	727.609	+	1073.14i	0.0317386	+	0.0468109i
$808$	64.3263	+	1186.43i	0.00280073	+	0.0516565i
$809$	8203.87	+	20590.2i	0.356530	+	0.894822i	0.992403	+	0.123029i	$0.0392607\pi$
$809$	8203.87	+	20590.2i	0.356530	+	0.894822i	−0.635873	+	0.771793i	$0.719360\pi$
$810$	38.3255	+	17.7313i	0.00166250	+	0.000769152i
$811$	4342.48	−	955.853i	0.188021	−	0.0413866i	−0.119962	−	0.992779i	$-0.538277\pi$
$811$	4342.48	−	955.853i	0.188021	−	0.0413866i	0.307983	+	0.951392i	$0.400346\pi$
$812$	18239.4	−	34403.1i	0.788272	−	1.48684i
$813$	1894.69	−	11557.1i	0.0817340	−	0.498556i
$814$	2138.90	−	1625.95i	0.0920987	−	0.0700116i
$815$	2816.47	−	1303.04i	0.121051	−	0.0560042i
$816$	16453.4	+	15585.5i	0.705863	+	0.668629i
$817$	−936.955	−	5715.17i	−0.0401223	−	0.244735i
$818$	−1117.86	−	376.652i	−0.0477814	−	0.0160994i
$819$	3813.88	−	9572.12i	0.162720	−	0.408397i
$820$	529.185	−	501.270i	0.0225365	−	0.0213477i
$821$	16674.9	+	12675.9i	0.708840	+	0.538846i	0.896312	−	0.443424i	$-0.146236\pi$
$821$	16674.9	+	12675.9i	0.708840	+	0.538846i	−0.187472	+	0.982270i	$0.560030\pi$
$822$	−280.554	−	61.7546i	−0.0119044	−	0.00262036i
$823$	−18655.0	+	21962.4i	−0.790124	+	0.930206i	−0.998859	−	0.0477661i	$-0.984790\pi$
$823$	−18655.0	+	21962.4i	−0.790124	+	0.930206i	0.208734	+	0.977972i	$0.433066\pi$
$824$	−1962.55	−	213.440i	−0.0829715	−	0.00902370i
$825$	18859.6			0.795885
$826$	−856.475	+	1647.45i	−0.0360782	+	0.0693972i
$827$	−20386.4			−0.857202			−0.428601	−	0.903494i	$-0.640993\pi$
$827$	−20386.4			−0.857202			−0.428601	+	0.903494i	$0.640993\pi$
$828$	−4142.95	−	450.573i	−0.173886	−	0.0189112i
$829$	−5601.44	+	6594.53i	−0.234676	+	0.276282i	−0.866876	−	0.498523i	$-0.833876\pi$
$829$	−5601.44	+	6594.53i	−0.234676	+	0.276282i	0.632201	+	0.774805i	$0.282152\pi$
$830$	58.7428	+	12.9303i	0.00245662	+	0.000540743i
$831$	6698.84	+	5092.32i	0.279639	+	0.212576i
$832$	−11897.8	+	11270.2i	−0.495773	+	0.469621i
$833$	−39995.2	+	100380.i	−1.66357	+	4.17524i
$834$	735.529	+	247.829i	0.0305387	+	0.0102897i
$835$	1713.15	+	10449.8i	0.0710013	+	0.433089i
$836$	15328.1	+	14519.6i	0.634133	+	0.600682i
$837$	−2411.72	+	1115.78i	−0.0995953	+	0.0460777i
$838$	905.255	−	688.157i	0.0373168	−	0.0283675i
$839$	99.6025	−	607.548i	0.00409852	−	0.0249999i	−0.984698	−	0.174269i	$-0.944244\pi$
$839$	99.6025	−	607.548i	0.00409852	−	0.0249999i	0.988797	+	0.149269i	$0.0476921\pi$
$840$	414.708	−	782.222i	0.0170343	−	0.0321300i
$841$	−5303.45	+	1167.38i	−0.217453	+	0.0478649i
$842$	−1314.98	−	608.375i	−0.0538210	−	0.0249002i
$843$	−4823.65	−	12106.4i	−0.197076	−	0.494624i
$844$	−143.279	−	2642.63i	−0.00584344	−	0.107776i
$845$	−2911.84	−	4294.64i	−0.118545	−	0.174840i
$846$	251.836	+	296.484i	0.0102344	+	0.0120489i
$847$	37720.8	+	71148.9i	1.53023	+	2.88631i
$848$	15816.7	−	5329.28i	0.640506	−	0.215811i
$849$	391.690	−	7224.29i	0.0158336	−	0.292034i
$850$	−1231.46	+	740.944i	−0.0496926	+	0.0298990i
$851$	5998.24	+	21603.7i	0.241618	+	0.870230i
$852$	4960.04	−	17864.5i	0.199446	−	0.718341i
$853$	2257.11	+	1358.06i	0.0906003	+	0.0545124i	0.560133	−	0.828403i	$-0.310750\pi$
$853$	2257.11	+	1358.06i	0.0906003	+	0.0545124i	−0.469533	+	0.882915i	$0.655578\pi$
$854$	362.231	−	534.250i	0.0145144	−	0.0214071i
$855$	1774.89	−	193.031i	0.0709943	−	0.00772109i
$856$	1809.17	−	196.759i	0.0722383	−	0.00785639i
$857$	−11174.0	+	16480.4i	−0.445386	+	0.656895i	−0.982424	−	0.186663i	$-0.940233\pi$
$857$	−11174.0	+	16480.4i	−0.445386	+	0.656895i	0.537038	+	0.843558i	$0.319543\pi$
$858$	577.432	+	347.429i	0.0229758	+	0.0138241i
$859$	−7183.92	+	25874.1i	−0.285346	+	1.02772i	0.672419	+	0.740171i	$0.265255\pi$
$859$	−7183.92	+	25874.1i	−0.285346	+	1.02772i	−0.957765	+	0.287552i	$0.907158\pi$
$860$	1266.34	+	4560.96i	0.0502116	+	0.180846i
$861$	−1843.75	+	1109.35i	−0.0729791	+	0.0439100i
$862$	36.7982	−	678.702i	0.00145400	−	0.0268175i
$863$	27292.0	−	9195.73i	1.07651	−	0.362719i	0.275459	−	0.961313i	$-0.411170\pi$
$863$	27292.0	−	9195.73i	1.07651	−	0.362719i	0.801052	+	0.598594i	$0.204274\pi$
$864$	280.339	+	528.775i	0.0110386	+	0.0208209i
$865$	−4901.16	−	5770.09i	−0.192652	−	0.226808i
$866$	718.280	+	1059.38i	0.0281849	+	0.0415697i
$867$	−1487.86	−	27442.0i	−0.0582820	−	1.07495i
$868$	10302.1	+	25856.4i	0.402853	+	1.01109i
$869$	−44550.6	−	20611.3i	−1.73910	−	0.804592i
$870$	210.315	−	46.2938i	0.00819580	−	0.00180403i
$871$	−5979.17	+	11277.9i	−0.232602	+	0.438734i
$872$	−405.636	+	2474.27i	−0.0157529	+	0.0960887i
$873$	−9686.03	+	7363.13i	−0.375512	+	0.285457i
$874$	268.059	−	124.017i	0.0103744	−	0.00479970i
$875$	−26605.4	−	25202.0i	−1.02792	−	0.973695i
$876$	−1546.42	−	9432.72i	−0.0596444	−	0.363815i
$877$	−18643.0	−	6281.56i	−0.717822	−	0.241862i	−0.0633958	−	0.997988i	$-0.520193\pi$
$877$	−18643.0	−	6281.56i	−0.717822	−	0.241862i	−0.654426	+	0.756126i	$0.727090\pi$
$878$	−12.0118	+	30.1473i	−0.000461706	+	0.00115880i
$879$	−18607.5	+	17625.9i	−0.714009	+	0.676345i
$880$	−13714.6	−	10425.6i	−0.525363	−	0.399371i
$881$	−23459.6	−	5163.84i	−0.897131	−	0.197474i	−0.257612	−	0.966248i	$-0.582936\pi$
$881$	−23459.6	−	5163.84i	−0.897131	−	0.197474i	−0.639519	+	0.768775i	$0.720867\pi$
$882$	−614.055	+	722.922i	−0.0234425	+	0.0275987i
$883$	−15599.3	−	1696.53i	−0.594518	−	0.0646577i	−0.194086	−	0.980984i	$-0.562174\pi$
$883$	−15599.3	−	1696.53i	−0.594518	−	0.0646577i	−0.400432	+	0.916327i	$0.631140\pi$
$884$	30634.4			1.16555
$885$	5971.68	−	1365.04i	0.226820	−	0.0518480i
$886$	−1609.75			−0.0610389
$887$	−27305.8	−	2969.69i	−1.03364	−	0.112415i	−0.424460	−	0.905447i	$-0.639536\pi$
$887$	−27305.8	−	2969.69i	−1.03364	−	0.112415i	−0.609181	+	0.793031i	$0.708502\pi$
$888$	1389.31	−	1635.63i	0.0525026	−	0.0618109i
$889$	−31021.6	−	6828.37i	−1.17034	−	0.257611i
$890$	494.217	+	375.694i	0.0186137	+	0.0141498i
$891$	−3530.90	+	3344.65i	−0.132761	+	0.125758i
$892$	1198.92	−	3009.06i	0.0450031	−	0.112949i
$893$	15585.6	+	5251.41i	0.584046	+	0.196788i
$894$	45.3015	+	276.327i	0.00169475	+	0.0103375i
$895$	−3319.14	−	3144.06i	−0.123963	−	0.117424i
$896$	7583.62	−	3508.55i	0.282758	−	0.130818i
$897$	−4476.97	+	3403.30i	−0.166646	+	0.126681i
$898$	12.9391	−	78.9249i	0.000480827	−	0.00293292i
$899$	−6347.58	+	11972.8i	−0.235488	+	0.444177i
$900$	7349.78	−	1617.81i	0.272214	−	0.0599188i
$901$	−28220.2	−	13056.1i	−1.04345	−	0.482753i
$902$	−52.0892	−	130.734i	−0.00192282	−	0.00482590i
$903$	−756.507	−	13952.9i	−0.0278793	−	0.514203i
$904$	21.5169	+	31.7350i	0.000791639	+	0.00116758i
$905$	−2494.30	−	2936.52i	−0.0916169	−	0.107860i
$906$	62.5340	+	117.952i	0.00229310	+	0.00432525i
$907$	−31078.0	+	10471.4i	−1.13774	+	0.383349i	−0.824240	−	0.566240i	$-0.808397\pi$
$907$	−31078.0	+	10471.4i	−1.13774	+	0.383349i	−0.313498	+	0.949589i	$0.601501\pi$
$908$	−1280.29	+	23613.5i	−0.0467928	+	0.863042i
$909$	−4953.48	+	2980.41i	−0.180744	+	0.108750i
$910$	−159.680	−	575.116i	−0.00581686	−	0.0209504i
$911$	−5298.01	+	19081.7i	−0.192679	+	0.693968i	0.802566	+	0.596564i	$0.203468\pi$
$911$	−5298.01	+	19081.7i	−0.192679	+	0.693968i	−0.995245	+	0.0974041i	$0.968946\pi$
$912$	7206.94	+	4336.27i	0.261673	+	0.157443i
$913$	−3887.62	+	5733.81i	−0.140922	+	0.207844i
$914$	−1284.27	+	139.673i	−0.0464769	+	0.00505467i
$915$	−2117.00	+	230.237i	−0.0764871	+	0.00831848i
$916$	−1898.12	+	2799.52i	−0.0684670	+	0.100981i
$917$	30165.1	+	18149.8i	1.08630	+	0.653607i
$918$	99.1521	−	357.114i	0.00356482	−	0.0128393i
$919$	5169.58	+	18619.2i	0.185559	+	0.668323i	0.996530	+	0.0832366i	$0.0265257\pi$
$919$	5169.58	+	18619.2i	0.185559	+	0.668323i	−0.810971	+	0.585087i	$0.801060\pi$
$920$	−414.041	+	249.120i	−0.0148375	+	0.00892744i
$921$	−1109.12	+	20456.6i	−0.0396817	+	0.731886i
$922$	2037.04	−	686.359i	0.0727618	−	0.0245163i
$923$	−11719.2	−	22104.7i	−0.417922	−	0.788284i
$924$	32978.7	+	38825.6i	1.17416	+	1.38232i
$925$	−22722.0	−	33512.5i	−0.807671	−	1.19123i
$926$	46.1284	+	850.788i	0.00163701	+	0.0301929i
$927$	−3555.17	−	8922.80i	−0.125962	−	0.316142i
$928$	2770.00	+	1281.54i	0.0979847	+	0.0453325i
$929$	−11195.8	+	2464.39i	−0.395397	+	0.0870335i	−0.408218	−	0.912884i	$-0.633850\pi$
$929$	−11195.8	+	2464.39i	−0.395397	+	0.0870335i	0.0128213	+	0.999918i	$0.495919\pi$
$930$	−72.1019	+	135.999i	−0.00254227	+	0.00479524i
$931$	−6487.76	+	39573.6i	−0.228386	+	1.39309i
$932$	39707.0	−	30184.5i	1.39554	−	1.06087i
$933$	15361.3	−	7106.88i	0.539020	−	0.249377i
$934$	1319.47	+	1249.87i	0.0462254	+	0.0437870i
$935$	5192.30	+	31671.6i	0.181611	+	1.10778i
$936$	510.097	+	171.872i	0.0178131	+	0.00600192i
$937$	5706.71	−	14322.8i	0.198965	−	0.499365i	−0.795312	−	0.606201i	$-0.792693\pi$
$937$	5706.71	−	14322.8i	0.198965	−	0.499365i	0.994277	+	0.106836i	$0.0340721\pi$
$938$	1174.33	−	1112.39i	0.0408778	−	0.0387215i
$939$	−13054.4	−	9923.69i	−0.453689	−	0.344886i
$940$	−13127.9	−	2889.67i	−0.455515	−	0.100267i
$941$	1236.73	−	1455.99i	0.0428441	−	0.0504400i	−0.740323	−	0.672252i	$-0.765327\pi$
$941$	1236.73	−	1455.99i	0.0428441	−	0.0504400i	0.783167	+	0.621812i	$0.213603\pi$
$942$	−1238.98	−	134.747i	−0.0428536	−	0.00466061i
$943$	1174.39			0.0405550
$944$	26288.1	+	11905.8i	0.906361	+	0.410487i
$945$	4307.65			0.148284
$946$	908.530	+	98.8086i	0.0312250	+	0.00339592i
$947$	−935.841	+	1101.76i	−0.0321127	+	0.0378060i	−0.777984	−	0.628284i	$-0.783758\pi$
$947$	−935.841	+	1101.76i	−0.0321127	+	0.0378060i	0.745871	+	0.666090i	$0.232033\pi$
$948$	−19129.9	−	4210.82i	−0.655392	−	0.144263i
$949$	−10268.7	−	7806.09i	−0.351251	−	0.267014i
$950$	−387.227	+	366.801i	−0.0132245	+	0.0125270i
$951$	3211.43	−	8060.09i	0.109503	−	0.274833i
$952$	−7363.66	−	2481.11i	−0.250691	−	0.0844676i
$953$	−2185.26	−	13329.5i	−0.0742786	−	0.453079i	−0.997611	−	0.0690783i	$-0.977994\pi$
$953$	−2185.26	−	13329.5i	−0.0742786	−	0.453079i	0.923333	−	0.384001i	$-0.125454\pi$
$954$	−198.158	−	187.705i	−0.00672495	−	0.00637021i
$955$	−20573.6	+	9518.38i	−0.697117	+	0.322521i
$956$	22484.2	−	17092.1i	0.760661	−	0.578240i
$957$	−4012.56	+	24475.5i	−0.135536	+	0.826731i
$958$	−171.446	+	323.381i	−0.00578201	+	0.0109060i
$959$	−28618.8	+	6299.48i	−0.963660	+	0.212118i
$960$	−6218.05	−	2876.78i	−0.209049	−	0.0967162i
$961$	7441.49	+	18676.7i	0.249790	+	0.626925i
$962$	−78.3267	−	1444.65i	−0.00262511	−	0.0484173i
$963$	4968.92	+	7328.61i	0.166273	+	0.245235i
$964$	−15298.5	−	18010.8i	−0.511132	−	0.601751i
$965$	−772.996	−	1458.03i	−0.0257862	−	0.0486378i
$966$	675.322	−	227.543i	0.0224929	−	0.00757874i
$967$	2506.70	−	46233.4i	0.0833611	−	1.53750i	−0.595570	−	0.803303i	$-0.703074\pi$
$967$	2506.70	−	46233.4i	0.0833611	−	1.53750i	0.678931	−	0.734202i	$-0.262443\pi$
$968$	−3604.66	+	2168.85i	−0.119688	+	0.0720140i
$969$	−4192.01	−	15098.3i	−0.138975	−	0.500543i
$970$	−188.551	+	679.100i	−0.00624125	+	0.0224790i
$971$	26812.7	+	16132.7i	0.886161	+	0.533185i	0.884356	−	0.466813i	$-0.154598\pi$
$971$	26812.7	+	16132.7i	0.886161	+	0.533185i	0.00180470	+	0.999998i	$0.499426\pi$
$972$	−1089.12	+	1606.33i	−0.0359399	+	0.0530074i
$973$	78710.4	−	8560.28i	2.59336	−	0.282045i
$974$	−110.021	+	11.9655i	−0.00361940	+	0.000393633i
$975$	5699.19	−	8405.67i	0.187200	−	0.276100i
$976$	−8596.04	−	5172.07i	−0.281919	−	0.169625i
$977$	13142.8	−	47336.1i	0.430374	−	1.55007i	−0.357309	−	0.933986i	$-0.616306\pi$
$977$	13142.8	−	47336.1i	0.430374	−	1.55007i	0.787683	−	0.616080i	$-0.211280\pi$
$978$	−63.9616	−	230.369i	−0.00209127	−	0.00753208i
$979$	−61264.6	+	36861.7i	−2.00002	+	1.20337i
$980$	1774.47	−	32728.1i	0.0578400	−	1.06680i
$981$	−11560.6	+	3895.21i	−0.376249	+	0.126773i
$982$	−262.352	−	494.848i	−0.00852544	−	0.0160807i
$983$	−13055.9	−	15370.6i	−0.423620	−	0.498725i	0.508405	−	0.861118i	$-0.330235\pi$
$983$	−13055.9	−	15370.6i	−0.423620	−	0.498725i	−0.932025	+	0.362394i	$0.881960\pi$
$984$	−63.0815	−	93.0382i	−0.00204366	−	0.00301418i
$985$	−448.040	−	8263.61i	−0.0144931	−	0.267310i
$986$	−699.576	−	1755.80i	−0.0225954	−	0.0567101i
$987$	36014.1	+	16661.9i	1.16144	+	0.537340i
$988$	11103.4	−	2444.04i	0.357536	−	0.0786997i
$989$	−3572.28	+	6738.03i	−0.114855	+	0.216640i
$990$	−45.5785	+	278.017i	−0.00146321	+	0.00892520i
$991$	43568.8	−	33120.2i	1.39658	−	1.06165i	0.407669	−	0.913130i	$-0.366342\pi$
$991$	43568.8	−	33120.2i	1.39658	−	1.06165i	0.988909	−	0.148522i	$-0.0474515\pi$
$992$	−1979.97	+	916.030i	−0.0633710	+	0.0293185i
$993$	14860.4	+	14076.6i	0.474906	+	0.449855i
$994$	512.914	+	3128.64i	0.0163668	+	0.0998333i
$995$	19109.4	+	6438.72i	0.608854	+	0.205147i
$996$	−1023.19	+	2568.01i	−0.0325512	+	0.0816974i
$997$	29949.8	−	28370.0i	0.951374	−	0.901189i	−0.0438275	−	0.999039i	$-0.513955\pi$
$997$	29949.8	−	28370.0i	0.951374	−	0.901189i	0.995201	+	0.0978501i	$0.0311966\pi$
$998$	−432.728	−	328.951i	−0.0137252	−	0.0104336i
$999$	10197.3	+	2244.60i	0.322952	+	0.0710871i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.e.a.4.8	✓	420
59.15	even	29	inner	177.4.e.a.133.8	yes	420

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.e.a.4.8	✓	420	1.1	even	1	trivial
177.4.e.a.133.8	yes	420	59.15	even	29	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.115030 + 0.0125102i) q^{2} +(-1.94216 + 2.28649i) q^{3} +(-7.79989 - 1.71689i) q^{4} +(-3.58691 - 2.72670i) q^{5} +(-0.252010 + 0.238717i) q^{6} +(-13.1064 + 32.8946i) q^{7} +(-1.75295 - 0.590637i) q^{8} +(-1.45604 - 8.88144i) q^{9} +O(q^{10})\)	\(q+(0.115030 + 0.0125102i) q^{2} +(-1.94216 + 2.28649i) q^{3} +(-7.79989 - 1.71689i) q^{4} +(-3.58691 - 2.72670i) q^{5} +(-0.252010 + 0.238717i) q^{6} +(-13.1064 + 32.8946i) q^{7} +(-1.75295 - 0.590637i) q^{8} +(-1.45604 - 8.88144i) q^{9} +(-0.378490 - 0.358525i) q^{10} +(54.4941 - 25.2117i) q^{11} +(19.0743 - 14.4999i) q^{12} +(5.23084 - 31.9067i) q^{13} +(-1.91914 + 3.61989i) q^{14} +(13.2009 - 2.90574i) q^{15} +(57.7934 + 26.7381i) q^{16} +(-43.9106 - 110.207i) q^{17} +(-0.0563787 - 1.03984i) q^{18} +(-24.7078 - 36.4412i) q^{19} +(23.2961 + 27.4263i) q^{20} +(-49.7583 - 93.8541i) q^{21} +(6.58384 - 2.21836i) q^{22} +(-3.13883 + 57.8923i) q^{23} +(4.75498 - 2.86098i) q^{24} +(-28.0100 - 100.883i) q^{25} +(1.00086 - 3.60478i) q^{26} +(23.1351 + 13.9200i) q^{27} +(158.705 - 234.072i) q^{28} +(136.883 - 14.8869i) q^{29} +(1.55485 - 0.169100i) q^{30} +(-55.2317 + 81.4606i) q^{31} +(18.9934 + 11.4280i) q^{32} +(-48.1901 + 173.565i) q^{33} +(-3.67230 - 13.2264i) q^{34} +(136.705 - 82.2529i) q^{35} +(-3.89148 + 71.7741i) q^{36} +(366.476 - 123.480i) q^{37} +(-2.38624 - 4.50092i) q^{38} +(62.7951 + 73.9281i) q^{39} +(4.67718 + 6.89833i) q^{40} +(-1.09664 - 20.2263i) q^{41} +(-4.54954 - 11.4185i) q^{42} +(119.384 + 55.2328i) q^{43} +(-468.334 + 103.088i) q^{44} +(-18.9944 + 35.8271i) q^{45} +(-1.08530 + 6.62006i) q^{46} +(-297.381 + 226.063i) q^{47} +(-173.380 + 80.2142i) q^{48} +(-661.260 - 626.379i) q^{49} +(-1.95991 - 11.9549i) q^{50} +(337.269 + 113.639i) q^{51} +(-95.5801 + 239.888i) q^{52} +(190.286 - 180.248i) q^{53} +(2.48708 + 1.89063i) q^{54} +(-264.211 - 58.1571i) q^{55} +(42.4036 - 49.9214i) q^{56} +(131.309 + 14.2807i) q^{57} +15.9318 q^{58} +(453.173 - 3.65433i) q^{59} -107.955 q^{60} +(-156.618 - 17.0332i) q^{61} +(-7.37237 + 8.67942i) q^{62} +(311.235 + 68.5079i) q^{63} +(-403.513 - 306.742i) q^{64} +(-105.763 + 100.184i) q^{65} +(-7.71463 + 19.3623i) q^{66} +(-374.132 - 126.060i) q^{67} +(153.284 + 934.994i) q^{68} +(-126.274 - 119.613i) q^{69} +(16.7542 - 7.75130i) q^{70} +(616.021 - 468.287i) q^{71} +(-2.69335 + 16.4287i) q^{72} +(186.869 - 352.472i) q^{73} +(43.7004 - 9.61918i) q^{74} +(285.067 + 131.886i) q^{75} +(130.152 + 326.658i) q^{76} +(115.106 + 2123.00i) q^{77} +(6.29844 + 9.28950i) q^{78} +(-529.258 - 623.091i) q^{79} +(-134.393 - 253.492i) q^{80} +(-76.7599 + 25.8634i) q^{81} +(0.126890 - 2.34034i) q^{82} +(-98.8592 + 59.4816i) q^{83} +(226.973 + 817.481i) q^{84} +(-142.999 + 515.035i) q^{85} +(13.0417 + 7.84692i) q^{86} +(-231.810 + 341.894i) q^{87} +(-110.416 + 12.0085i) q^{88} +(-1183.81 + 128.747i) q^{89} +(-2.63312 + 3.88356i) q^{90} +(981.000 + 590.248i) q^{91} +(123.877 - 446.164i) q^{92} +(-78.9899 - 284.496i) q^{93} +(-37.0357 + 22.2836i) q^{94} +(-10.7397 + 198.082i) q^{95} +(-63.0181 + 21.2333i) q^{96} +(-633.234 - 1194.41i) q^{97} +(-68.2283 - 80.3246i) q^{98} +(-303.261 - 447.277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9}+O(q^{10}) \) 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9	\( 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9} + 854 q^{10} + 32 q^{11} + 192 q^{12} - 22 q^{13} - 884 q^{14} - 42 q^{15} - 268 q^{16} - 56 q^{17} - 18 q^{18} - 112 q^{19} - 250 q^{20} + 243 q^{21} + 108 q^{22} + 16 q^{23} - 54 q^{24} - 197 q^{25} - 328 q^{26} + 405 q^{27} + 236 q^{28} - 54 q^{29} - 126 q^{30} + 66 q^{31} + 857 q^{32} - 96 q^{33} + 112 q^{34} + 532 q^{35} - 576 q^{36} + 110 q^{37} + 56 q^{38} + 66 q^{39} - 6044 q^{40} + 304 q^{41} - 306 q^{42} - 324 q^{43} - 568 q^{44} + 126 q^{45} + 5842 q^{46} + 4082 q^{47} + 804 q^{48} + 739 q^{49} + 576 q^{50} + 168 q^{51} - 1372 q^{52} - 1498 q^{53} + 54 q^{54} - 4422 q^{55} - 12036 q^{56} + 336 q^{57} + 6298 q^{58} - 3305 q^{59} + 750 q^{60} - 1718 q^{61} - 4333 q^{62} + 54 q^{63} - 6250 q^{64} - 5884 q^{65} - 324 q^{66} + 382 q^{67} + 734 q^{68} + 3780 q^{69} + 8082 q^{70} + 8638 q^{71} + 162 q^{72} + 8894 q^{73} + 12428 q^{74} + 243 q^{75} - 15468 q^{76} - 9916 q^{77} + 984 q^{78} - 578 q^{79} + 24570 q^{80} - 1215 q^{81} - 1382 q^{82} - 32 q^{83} + 7557 q^{84} + 708 q^{85} + 2296 q^{86} - 5928 q^{87} - 17646 q^{88} - 2284 q^{89} + 378 q^{90} + 11124 q^{91} + 762 q^{92} - 198 q^{93} - 1232 q^{94} + 24184 q^{95} - 396 q^{96} - 658 q^{97} - 4356 q^{98} + 288 q^{99}+O(q^{100}) \) 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9 + 854 * q^10 + 32 * q^11 + 192 * q^12 - 22 * q^13 - 884 * q^14 - 42 * q^15 - 268 * q^16 - 56 * q^17 - 18 * q^18 - 112 * q^19 - 250 * q^20 + 243 * q^21 + 108 * q^22 + 16 * q^23 - 54 * q^24 - 197 * q^25 - 328 * q^26 + 405 * q^27 + 236 * q^28 - 54 * q^29 - 126 * q^30 + 66 * q^31 + 857 * q^32 - 96 * q^33 + 112 * q^34 + 532 * q^35 - 576 * q^36 + 110 * q^37 + 56 * q^38 + 66 * q^39 - 6044 * q^40 + 304 * q^41 - 306 * q^42 - 324 * q^43 - 568 * q^44 + 126 * q^45 + 5842 * q^46 + 4082 * q^47 + 804 * q^48 + 739 * q^49 + 576 * q^50 + 168 * q^51 - 1372 * q^52 - 1498 * q^53 + 54 * q^54 - 4422 * q^55 - 12036 * q^56 + 336 * q^57 + 6298 * q^58 - 3305 * q^59 + 750 * q^60 - 1718 * q^61 - 4333 * q^62 + 54 * q^63 - 6250 * q^64 - 5884 * q^65 - 324 * q^66 + 382 * q^67 + 734 * q^68 + 3780 * q^69 + 8082 * q^70 + 8638 * q^71 + 162 * q^72 + 8894 * q^73 + 12428 * q^74 + 243 * q^75 - 15468 * q^76 - 9916 * q^77 + 984 * q^78 - 578 * q^79 + 24570 * q^80 - 1215 * q^81 - 1382 * q^82 - 32 * q^83 + 7557 * q^84 + 708 * q^85 + 2296 * q^86 - 5928 * q^87 - 17646 * q^88 - 2284 * q^89 + 378 * q^90 + 11124 * q^91 + 762 * q^92 - 198 * q^93 - 1232 * q^94 + 24184 * q^95 - 396 * q^96 - 658 * q^97 - 4356 * q^98 + 288 * q^99

Introduction

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