LMFDB - Embedded newform 177.4.e.a.4.10

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.e (of order $29$, degree $28$, minimal)

Newform invariants

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			4.10
Character	$\chi$	$=$	177.4
Dual form			177.4.e.a.133.10

$q$-expansion

$f(q)$	$=$	$q+(1.07661 + 0.117088i) q^{2} +(-1.94216 + 2.28649i) q^{3} +(-6.66759 - 1.46765i) q^{4} +(6.87670 + 5.22753i) q^{5} +(-2.35866 + 2.23424i) q^{6} +(7.63111 - 19.1526i) q^{7} +(-15.2167 - 5.12709i) q^{8} +(-1.45604 - 8.88144i) q^{9} +O(q^{10})$	\(q+(1.07661 + 0.117088i) q^{2} +(-1.94216 + 2.28649i) q^{3} +(-6.66759 - 1.46765i) q^{4} +(6.87670 + 5.22753i) q^{5} +(-2.35866 + 2.23424i) q^{6} +(7.63111 - 19.1526i) q^{7} +(-15.2167 - 5.12709i) q^{8} +(-1.45604 - 8.88144i) q^{9} +(6.79142 + 6.43318i) q^{10} +(58.4670 - 27.0497i) q^{11} +(16.3053 - 12.3949i) q^{12} +(-12.7082 + 77.5166i) q^{13} +(10.4583 - 19.7264i) q^{14} +(-25.3083 + 5.57078i) q^{15} +(33.7876 + 15.6318i) q^{16} +(17.0727 + 42.8492i) q^{17} +(-0.527670 - 9.73231i) q^{18} +(72.8150 + 107.394i) q^{19} +(-38.1788 - 44.9476i) q^{20} +(28.9714 + 54.6459i) q^{21} +(66.1132 - 22.2761i) q^{22} +(-0.752907 + 13.8865i) q^{23} +(41.2762 - 24.8351i) q^{24} +(-13.4791 - 48.5474i) q^{25} +(-22.7580 + 81.9670i) q^{26} +(23.1351 + 13.9200i) q^{27} +(-78.9904 + 116.502i) q^{28} +(212.803 - 23.1437i) q^{29} +(-27.8994 + 3.03424i) q^{30} +(162.441 - 239.582i) q^{31} +(144.616 + 87.0123i) q^{32} +(-51.7034 + 186.219i) q^{33} +(13.3634 + 48.1308i) q^{34} +(152.598 - 91.8151i) q^{35} +(-3.32656 + 61.3548i) q^{36} +(-78.4246 + 26.4243i) q^{37} +(65.8186 + 124.147i) q^{38} +(-152.559 - 179.607i) q^{39} +(-77.8384 - 114.803i) q^{40} +(-7.91340 - 145.954i) q^{41} +(24.7925 + 62.2244i) q^{42} +(-127.758 - 59.1072i) q^{43} +(-429.534 + 94.5475i) q^{44} +(36.4153 - 68.6865i) q^{45} +(-2.43653 + 14.8622i) q^{46} +(-78.6113 + 59.7588i) q^{47} +(-101.363 + 46.8954i) q^{48} +(-59.5733 - 56.4308i) q^{49} +(-8.82740 - 53.8448i) q^{50} +(-131.132 - 44.1835i) q^{51} +(198.500 - 498.198i) q^{52} +(-389.201 + 368.670i) q^{53} +(23.2776 + 17.6952i) q^{54} +(543.463 + 119.625i) q^{55} +(-214.317 + 252.314i) q^{56} +(-386.973 - 42.0859i) q^{57} +231.815 q^{58} +(36.3787 - 451.725i) q^{59} +176.921 q^{60} +(629.215 + 68.4312i) q^{61} +(202.937 - 238.916i) q^{62} +(-181.214 - 39.8883i) q^{63} +(-91.5923 - 69.6266i) q^{64} +(-492.611 + 466.626i) q^{65} +(-77.4683 + 194.431i) q^{66} +(800.730 + 269.797i) q^{67} +(-50.9461 - 310.758i) q^{68} +(-30.2891 - 28.6914i) q^{69} +(175.038 - 80.9814i) q^{70} +(-472.947 + 359.525i) q^{71} +(-23.3799 + 142.611i) q^{72} +(-57.3315 + 108.139i) q^{73} +(-87.5265 + 19.2660i) q^{74} +(137.182 + 63.4670i) q^{75} +(-327.884 - 822.926i) q^{76} +(-71.9054 - 1326.22i) q^{77} +(-143.217 - 211.229i) q^{78} +(-302.167 - 355.738i) q^{79} +(150.631 + 284.121i) q^{80} +(-76.7599 + 25.8634i) q^{81} +(8.56986 - 158.062i) q^{82} +(-239.007 + 143.806i) q^{83} +(-112.969 - 406.876i) q^{84} +(-106.592 + 383.909i) q^{85} +(-130.625 - 78.5943i) q^{86} +(-360.379 + 531.519i) q^{87} +(-1028.36 + 111.841i) q^{88} +(-151.998 + 16.5308i) q^{89} +(47.2473 - 69.6846i) q^{90} +(1387.67 + 834.934i) q^{91} +(25.4006 - 91.4848i) q^{92} +(232.316 + 836.725i) q^{93} +(-91.6305 + 55.1323i) q^{94} +(-60.6790 + 1119.16i) q^{95} +(-479.819 + 161.670i) q^{96} +(-818.511 - 1543.88i) q^{97} +(-57.5296 - 67.7291i) q^{98} +(-325.371 - 479.886i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 420q - 2q^{2} + 45q^{3} - 64q^{4} + 14q^{5} + 6q^{6} + 6q^{7} + 18q^{8} - 135q^{9} + O(q^{10}) $	\( 420q - 2q^{2} + 45q^{3} - 64q^{4} + 14q^{5} + 6q^{6} + 6q^{7} + 18q^{8} - 135q^{9} + 854q^{10} + 32q^{11} + 192q^{12} - 22q^{13} - 884q^{14} - 42q^{15} - 268q^{16} - 56q^{17} - 18q^{18} - 112q^{19} - 250q^{20} + 243q^{21} + 108q^{22} + 16q^{23} - 54q^{24} - 197q^{25} - 328q^{26} + 405q^{27} + 236q^{28} - 54q^{29} - 126q^{30} + 66q^{31} + 857q^{32} - 96q^{33} + 112q^{34} + 532q^{35} - 576q^{36} + 110q^{37} + 56q^{38} + 66q^{39} - 6044q^{40} + 304q^{41} - 306q^{42} - 324q^{43} - 568q^{44} + 126q^{45} + 5842q^{46} + 4082q^{47} + 804q^{48} + 739q^{49} + 576q^{50} + 168q^{51} - 1372q^{52} - 1498q^{53} + 54q^{54} - 4422q^{55} - 12036q^{56} + 336q^{57} + 6298q^{58} - 3305q^{59} + 750q^{60} - 1718q^{61} - 4333q^{62} + 54q^{63} - 6250q^{64} - 5884q^{65} - 324q^{66} + 382q^{67} + 734q^{68} + 3780q^{69} + 8082q^{70} + 8638q^{71} + 162q^{72} + 8894q^{73} + 12428q^{74} + 243q^{75} - 15468q^{76} - 9916q^{77} + 984q^{78} - 578q^{79} + 24570q^{80} - 1215q^{81} - 1382q^{82} - 32q^{83} + 7557q^{84} + 708q^{85} + 2296q^{86} - 5928q^{87} - 17646q^{88} - 2284q^{89} + 378q^{90} + 11124q^{91} + 762q^{92} - 198q^{93} - 1232q^{94} + 24184q^{95} - 396q^{96} - 658q^{97} - 4356q^{98} + 288q^{99} + O(q^{100}) \)

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 $

$2$	1.07661	+	0.117088i	0.380638	+	0.0413969i	0.296438	−	0.955052i	$-0.404201\pi$
$2$	1.07661	+	0.117088i	0.380638	+	0.0413969i	0.0841998	+	0.996449i	$0.473167\pi$
$3$	−1.94216	+	2.28649i	−0.373769	+	0.440034i
$3$	−1.94216	+	2.28649i	−0.373769	+	0.440034i
$4$	−6.66759	−	1.46765i	−0.833449	−	0.183456i
$5$	6.87670	+	5.22753i	0.615071	+	0.467565i	0.865730	−	0.500511i	$-0.166854\pi$
$5$	6.87670	+	5.22753i	0.615071	+	0.467565i	−0.250660	+	0.968075i	$0.580648\pi$
$6$	−2.35866	+	2.23424i	−0.160487	+	0.152021i
$7$	7.63111	−	19.1526i	0.412041	−	1.03415i	−0.565752	−	0.824575i	$-0.691414\pi$
$7$	7.63111	−	19.1526i	0.412041	−	1.03415i	0.977794	−	0.209570i	$-0.0672065\pi$
$8$	−15.2167	−	5.12709i	−0.672488	−	0.226588i
$9$	−1.45604	−	8.88144i	−0.0539273	−	0.328942i
$10$	6.79142	+	6.43318i	0.214764	+	0.203435i
$11$	58.4670	−	27.0497i	1.60259	−	0.741436i	0.604127	−	0.796888i	$-0.293522\pi$
$11$	58.4670	−	27.0497i	1.60259	−	0.741436i	0.998461	+	0.0554521i	$0.0176600\pi$
$12$	16.3053	−	12.3949i	0.392244	−	0.298176i
$13$	−12.7082	+	77.5166i	−0.271125	+	1.65379i	0.403021	+	0.915191i	$0.367960\pi$
$13$	−12.7082	+	77.5166i	−0.271125	+	1.65379i	−0.674146	+	0.738598i	$0.735488\pi$
$14$	10.4583	−	19.7264i	0.199649	−	0.376578i
$15$	−25.3083	+	5.57078i	−0.435639	+	0.0958913i
$16$	33.7876	+	15.6318i	0.527931	+	0.244247i
$17$	17.0727	+	42.8492i	0.243573	+	0.611321i	0.999037	−	0.0438682i	$-0.0139682\pi$
$17$	17.0727	+	42.8492i	0.243573	+	0.611321i	−0.755465	+	0.655189i	$0.772589\pi$
$18$	−0.527670	−	9.73231i	−0.00690962	−	0.127440i
$19$	72.8150	+	107.394i	0.879205	+	1.29673i	0.954084	+	0.299538i	$0.0968326\pi$
$19$	72.8150	+	107.394i	0.879205	+	1.29673i	−0.0748790	+	0.997193i	$0.523857\pi$
$20$	−38.1788	−	44.9476i	−0.426852	−	0.502530i
$21$	28.9714	+	54.6459i	0.301051	+	0.567843i
$22$	66.1132	−	22.2761i	0.640699	−	0.215877i
$23$	−0.752907	+	13.8865i	−0.00682573	+	0.125893i	0.993135	+	0.116978i	$0.0373207\pi$
$23$	−0.752907	+	13.8865i	−0.00682573	+	0.125893i	−0.999960	+	0.00891540i	$0.997162\pi$
$24$	41.2762	−	24.8351i	0.351061	−	0.211227i
$25$	−13.4791	−	48.5474i	−0.107833	−	0.388380i
$26$	−22.7580	+	81.9670i	−0.171662	+	0.618271i
$27$	23.1351	+	13.9200i	0.164902	+	0.0992184i
$28$	−78.9904	+	116.502i	−0.533135	+	0.786316i
$29$	212.803	−	23.1437i	1.36264	−	0.148196i	0.602583	−	0.798056i	$-0.294138\pi$
$29$	212.803	−	23.1437i	1.36264	−	0.148196i	0.760053	+	0.649861i	$0.225173\pi$
$30$	−27.8994	+	3.03424i	−0.169790	+	0.0184658i
$31$	162.441	−	239.582i	0.941136	−	1.38807i	0.0195879	−	0.999808i	$-0.493765\pi$
$31$	162.441	−	239.582i	0.941136	−	1.38807i	0.921548	−	0.388264i	$-0.126925\pi$
$32$	144.616	+	87.0123i	0.798896	+	0.480679i
$33$	−51.7034	+	186.219i	−0.272740	+	0.982320i
$34$	13.3634	+	48.1308i	0.0674062	+	0.242775i
$35$	152.598	−	91.8151i	0.736964	−	0.443417i
$36$	−3.32656	+	61.3548i	−0.0154007	+	0.284050i
$37$	−78.4246	+	26.4243i	−0.348457	+	0.117409i	−0.488087	−	0.872795i	$-0.662305\pi$
$37$	−78.4246	+	26.4243i	−0.348457	+	0.117409i	0.139630	+	0.990204i	$0.455409\pi$
$38$	65.8186	+	124.147i	0.280978	+	0.529982i
$39$	−152.559	−	179.607i	−0.626386	−	0.737438i
$40$	−77.8384	−	114.803i	−0.307683	−	0.453799i
$41$	−7.91340	−	145.954i	−0.0301431	−	0.555956i	−0.974132	−	0.225979i	$-0.927442\pi$
$41$	−7.91340	−	145.954i	−0.0301431	−	0.555956i	0.943989	−	0.329977i	$-0.107041\pi$
$42$	24.7925	+	62.2244i	0.0910847	+	0.228605i
$43$	−127.758	−	59.1072i	−0.453092	−	0.209623i	0.180052	−	0.983657i	$-0.442374\pi$
$43$	−127.758	−	59.1072i	−0.453092	−	0.209623i	−0.633143	+	0.774035i	$0.718236\pi$
$44$	−429.534	+	94.5475i	−1.47170	+	0.323945i
$45$	36.4153	−	68.6865i	0.120633	−	0.227537i
$46$	−2.43653	+	14.8622i	−0.00780972	+	0.0476372i
$47$	−78.6113	+	59.7588i	−0.243971	+	0.185462i	−0.720013	−	0.693961i	$-0.755864\pi$
$47$	−78.6113	+	59.7588i	−0.243971	+	0.185462i	0.476042	+	0.879423i	$0.342071\pi$
$48$	−101.363	+	46.8954i	−0.304801	+	0.141016i
$49$	−59.5733	−	56.4308i	−0.173683	−	0.164521i
$50$	−8.82740	−	53.8448i	−0.0249677	−	0.152296i
$51$	−131.132	−	44.1835i	−0.360042	−	0.121312i
$52$	198.500	−	498.198i	0.529366	−	1.32861i
$53$	−389.201	+	368.670i	−1.00869	+	0.955486i	−0.999011	−	0.0444670i	$-0.985841\pi$
$53$	−389.201	+	368.670i	−1.00869	+	0.955486i	−0.00968357	+	0.999953i	$0.503082\pi$
$54$	23.2776	+	17.6952i	0.0586607	+	0.0445927i
$55$	543.463	+	119.625i	1.33237	+	0.293278i
$56$	−214.317	+	252.314i	−0.511417	+	0.602087i
$57$	−386.973	−	42.0859i	−0.899226	−	0.0977967i
$58$	231.815			0.524806
$59$	36.3787	−	451.725i	0.0802730	−	0.996773i
$59$	36.3787	−	451.725i	0.0802730	−	0.996773i
$60$	176.921			0.380674
$61$	629.215	+	68.4312i	1.32070	+	0.143635i	0.741171	−	0.671317i	$-0.234271\pi$
$61$	629.215	+	68.4312i	1.32070	+	0.143635i	0.579529	+	0.814952i	$0.303237\pi$
$62$	202.937	−	238.916i	0.415694	−	0.489393i
$63$	−181.214	−	39.8883i	−0.362394	−	0.0797690i
$64$	−91.5923	−	69.6266i	−0.178891	−	0.135989i
$65$	−492.611	+	466.626i	−0.940014	+	0.890428i
$66$	−77.4683	+	194.431i	−0.144480	+	0.362618i
$67$	800.730	+	269.797i	1.46007	+	0.491955i	0.933625	−	0.358253i	$-0.116627\pi$
$67$	800.730	+	269.797i	1.46007	+	0.491955i	0.526447	+	0.850208i	$0.323524\pi$
$68$	−50.9461	−	310.758i	−0.0908548	−	0.554190i
$69$	−30.2891	−	28.6914i	−0.0528461	−	0.0500585i
$70$	175.038	−	80.9814i	0.298873	−	0.138273i
$71$	−472.947	+	359.525i	−0.790543	+	0.600955i	−0.920580	−	0.390554i	$-0.872283\pi$
$71$	−472.947	+	359.525i	−0.790543	+	0.600955i	0.130037	+	0.991509i	$0.458490\pi$
$72$	−23.3799	+	142.611i	−0.0382687	+	0.233429i
$73$	−57.3315	+	108.139i	−0.0919197	+	0.173379i	−0.925209	−	0.379459i	$-0.876110\pi$
$73$	−57.3315	+	108.139i	−0.0919197	+	0.173379i	0.833289	+	0.552838i	$0.186455\pi$
$74$	−87.5265	+	19.2660i	−0.137497	+	0.0302653i
$75$	137.182	+	63.4670i	0.211205	+	0.0977138i
$76$	−327.884	−	822.926i	−0.494880	−	1.24205i
$77$	−71.9054	−	1326.22i	−0.106421	−	1.96281i
$78$	−143.217	−	211.229i	−0.207899	−	0.306628i
$79$	−302.167	−	355.738i	−0.430334	−	0.506629i	0.503667	−	0.863898i	$-0.331984\pi$
$79$	−302.167	−	355.738i	−0.430334	−	0.506629i	−0.934002	+	0.357269i	$0.883708\pi$
$80$	150.631	+	284.121i	0.210514	+	0.397071i
$81$	−76.7599	+	25.8634i	−0.105295	+	0.0354779i
$82$	8.56986	−	158.062i	0.0115413	−	0.212866i
$83$	−239.007	+	143.806i	−0.316078	+	0.190178i	−0.664748	−	0.747068i	$-0.731461\pi$
$83$	−239.007	+	143.806i	−0.316078	+	0.190178i	0.348670	+	0.937246i	$0.386633\pi$
$84$	−112.969	−	406.876i	−0.146737	−	0.528498i
$85$	−106.592	+	383.909i	−0.136018	+	0.489892i
$86$	−130.625	−	78.5943i	−0.163786	−	0.0985469i
$87$	−360.379	+	531.519i	−0.444099	+	0.654998i
$88$	−1028.36	+	111.841i	−1.24572	+	0.135480i
$89$	−151.998	+	16.5308i	−0.181031	+	0.0196883i	−0.198185	−	0.980165i	$-0.563505\pi$
$89$	−151.998	+	16.5308i	−0.181031	+	0.0196883i	0.0171544	+	0.999853i	$0.494539\pi$
$90$	47.2473	−	69.6846i	0.0553367	−	0.0816155i
$91$	1387.67	+	834.934i	1.59854	+	0.961811i
$92$	25.4006	−	91.4848i	0.0287848	−	0.103673i
$93$	232.316	+	836.725i	0.259032	+	0.932950i
$94$	−91.6305	+	55.1323i	−0.100542	+	0.0604942i
$95$	−60.6790	+	1119.16i	−0.0655320	+	1.20867i
$96$	−479.819	+	161.670i	−0.510118	+	0.171879i
$97$	−818.511	−	1543.88i	−0.856776	−	1.61605i	−0.785723	−	0.618578i	$-0.787709\pi$
$97$	−818.511	−	1543.88i	−0.856776	−	1.61605i	−0.0710523	−	0.997473i	$-0.522636\pi$
$98$	−57.5296	−	67.7291i	−0.0592997	−	0.0698130i
$99$	−325.371	−	479.886i	−0.330313	−	0.487175i
$100$	18.6228	+	343.477i	0.0186228	+	0.343477i
$101$	423.811	+	1063.68i	0.417532	+	1.04793i	0.975878	+	0.218318i	$0.0700570\pi$
$101$	423.811	+	1063.68i	0.417532	+	1.04793i	−0.558346	+	0.829608i	$0.688564\pi$
$102$	−136.004	−	62.9223i	−0.132024	−	0.0610807i
$103$	−678.236	+	149.291i	−0.648821	+	0.142816i	−0.527174	−	0.849757i	$-0.676749\pi$
$103$	−678.236	+	149.291i	−0.648821	+	0.142816i	−0.121647	+	0.992573i	$0.538817\pi$
$104$	590.811	−	1114.39i	0.557056	−	1.05072i
$105$	−86.4353	+	527.232i	−0.0803355	+	0.490025i
$106$	−462.183	+	351.342i	−0.423502	+	0.321938i
$107$	−92.7714	+	42.9206i	−0.0838182	+	0.0387784i	−0.461350	−	0.887218i	$-0.652635\pi$
$107$	−92.7714	+	42.9206i	−0.0838182	+	0.0387784i	0.377532	+	0.925997i	$0.376773\pi$
$108$	−133.826	−	126.767i	−0.119235	−	0.112946i
$109$	−50.2986	−	306.808i	−0.0441994	−	0.269604i	0.955476	−	0.295068i	$-0.0953422\pi$
$109$	−50.2986	−	306.808i	−0.0441994	−	0.269604i	−0.999676	+	0.0254632i	$0.991894\pi$
$110$	571.090	+	192.423i	0.495012	+	0.166789i
$111$	91.8942	−	230.637i	0.0785785	−	0.197217i
$112$	557.227	−	527.834i	0.470116	−	0.445318i
$113$	−1373.97	−	1044.46i	−1.14382	−	0.869512i	−0.150934	−	0.988544i	$-0.548228\pi$
$113$	−1373.97	−	1044.46i	−1.14382	−	0.869512i	−0.992890	+	0.119031i	$0.962021\pi$
$114$	−411.690	−	90.6199i	−0.338231	−	0.0744503i
$115$	−77.7699	+	91.5577i	−0.0630615	+	0.0742418i
$116$	−1452.85	−	158.007i	−1.16287	−	0.126470i
$117$	706.963			0.558622
$118$	92.0572	−	482.071i	0.0718183	−	0.376087i
$119$	950.959			0.732557
$120$	413.670	+	44.9893i	0.314689	+	0.0342245i
$121$	1825.03	−	2148.60i	1.37117	−	1.61427i
$122$	669.405	+	147.347i	0.496763	+	0.109346i
$123$	349.091	+	265.372i	0.255906	+	0.194535i
$124$	−1434.71	+	1359.03i	−1.03904	+	0.984230i
$125$	560.751	−	1407.38i	0.401241	−	1.00704i
$126$	−190.426	−	64.1620i	−0.134639	−	0.0453651i
$127$	155.894	+	950.910i	0.108924	+	0.664406i	0.983692	+	0.179864i	$0.0575657\pi$
$127$	155.894	+	950.910i	0.108924	+	0.664406i	−0.874768	+	0.484543i	$0.838986\pi$
$128$	−1070.69	−	1014.21i	−0.739349	−	0.700349i
$129$	383.275	−	177.322i	0.261593	−	0.121026i
$130$	−584.985	+	444.694i	−0.394666	+	0.300017i
$131$	−221.394	+	1350.45i	−0.147659	+	0.900680i	0.804248	+	0.594293i	$0.202568\pi$
$131$	−221.394	+	1350.45i	−0.147659	+	0.900680i	−0.951907	+	0.306386i	$0.900880\pi$
$132$	618.041	−	1165.75i	0.407527	−	0.768677i
$133$	2612.54	−	575.063i	1.70328	−	0.374920i
$134$	830.482	+	384.222i	0.535393	+	0.247699i
$135$	86.3264	+	216.663i	0.0550355	+	0.138129i
$136$	−40.0975	−	739.555i	−0.0252819	−	0.466297i
$137$	−733.190	−	1081.37i	−0.457231	−	0.674365i	0.527279	−	0.849692i	$-0.323212\pi$
$137$	−733.190	−	1081.37i	−0.457231	−	0.674365i	−0.984510	+	0.175327i	$0.943902\pi$
$138$	−29.2501	−	34.4359i	−0.0180430	−	0.0212418i
$139$	1214.08	+	2289.99i	0.740838	+	1.39737i	0.911190	+	0.411986i	$0.135165\pi$
$139$	1214.08	+	2289.99i	0.740838	+	1.39737i	−0.170352	+	0.985383i	$0.554490\pi$
$140$	−1152.21	+	388.225i	−0.695569	+	0.234365i
$141$	16.0381	−	295.805i	0.00957907	−	0.176676i
$142$	−551.275	+	331.691i	−0.325788	+	0.196020i
$143$	1353.79	+	4875.92i	0.791677	+	2.85136i
$144$	89.6369	−	322.843i	0.0518732	−	0.186830i
$145$	1584.36	+	953.280i	0.907408	+	0.545970i
$146$	−74.3852	+	109.710i	−0.0421655	+	0.0621895i
$147$	244.729	−	26.6159i	0.137312	−	0.0149336i
$148$	561.685	−	61.0869i	0.311961	−	0.0339278i
$149$	−1734.72	+	2558.53i	−0.953786	+	1.40673i	−0.0406048	+	0.999175i	$0.512928\pi$
$149$	−1734.72	+	2558.53i	−0.953786	+	1.40673i	−0.913181	+	0.407554i	$0.866382\pi$
$150$	140.260	+	84.3914i	0.0763476	+	0.0459368i
$151$	222.012	−	799.615i	0.119650	−	0.430939i	−0.879325	−	0.476223i	$-0.842006\pi$
$151$	222.012	−	799.615i	0.119650	−	0.430939i	0.998974	+	0.0452842i	$0.0144193\pi$
$152$	−557.382	−	2007.51i	−0.297432	−	1.07125i
$153$	355.704	−	214.020i	0.187954	−	0.113088i
$154$	77.8703	−	1436.23i	0.0407466	−	0.751526i
$155$	2369.48	−	798.371i	1.22788	−	0.413720i
$156$	753.604	+	1421.45i	0.386773	+	0.729532i
$157$	572.259	+	673.715i	0.290900	+	0.342473i	0.888127	−	0.459599i	$-0.152007\pi$
$157$	572.259	+	673.715i	0.290900	+	0.342473i	−0.597227	+	0.802072i	$0.703731\pi$
$158$	−283.662	−	418.370i	−0.142829	−	0.210657i
$159$	−87.0703	−	1605.92i	−0.0434285	−	0.800991i
$160$	539.618	+	1354.34i	0.266628	+	0.669187i
$161$	260.218	+	120.390i	0.127379	+	0.0589320i
$162$	−85.6686	+	18.8571i	−0.0415479	+	0.00914538i
$163$	479.698	−	904.807i	0.230508	−	0.434785i	−0.741095	−	0.671400i	$-0.765693\pi$
$163$	479.698	−	904.807i	0.230508	−	0.434785i	0.971603	+	0.236615i	$0.0760380\pi$
$164$	−161.446	+	984.776i	−0.0768708	+	0.468891i
$165$	−1329.01	+	1010.29i	−0.627052	+	0.476673i
$166$	−274.155	+	126.838i	−0.128184	+	0.0593043i
$167$	15.4198	+	14.6064i	0.00714503	+	0.00676813i	0.691264	−	0.722603i	$-0.257054\pi$
$167$	15.4198	+	14.6064i	0.00714503	+	0.00676813i	−0.684119	+	0.729371i	$0.739813\pi$
$168$	−160.674	−	980.067i	−0.0737872	−	0.450082i
$169$	−3765.34	−	1268.69i	−1.71385	−	0.577465i
$170$	−159.709	+	400.839i	−0.0720535	+	0.180841i
$171$	847.792	−	803.072i	0.379136	−	0.359137i
$172$	765.091	+	581.607i	0.339172	+	0.257832i
$173$	2147.30	+	472.656i	0.943676	+	0.207719i	0.660054	−	0.751218i	$-0.270533\pi$
$173$	2147.30	+	472.656i	0.943676	+	0.207719i	0.283621	+	0.958936i	$0.408464\pi$
$174$	−450.221	+	530.041i	−0.196156	+	0.230933i
$175$	−1032.67	−	112.310i	−0.446072	−	0.0485133i
$176$	2398.30			1.02715
$177$	962.210	+	960.501i	0.408611	+	0.407885i
$178$	−165.578			−0.0697223
$179$	−1359.14	−	147.815i	−0.567525	−	0.0617220i	−0.180141	−	0.983641i	$-0.557655\pi$
$179$	−1359.14	−	147.815i	−0.567525	−	0.0617220i	−0.387383	+	0.921919i	$0.626621\pi$
$180$	−343.610	+	404.528i	−0.142284	+	0.167510i
$181$	−2722.06	−	599.171i	−1.11784	−	0.246055i	−0.382636	−	0.923899i	$-0.624983\pi$
$181$	−2722.06	−	599.171i	−1.11784	−	0.246055i	−0.735206	+	0.677844i	$0.762915\pi$
$182$	1396.22	+	1061.38i	0.568650	+	0.432277i
$183$	−1378.50	+	1305.79i	−0.556840	+	0.527467i
$184$	82.6543	−	207.447i	0.0331161	−	0.0831151i
$185$	−677.436	−	228.255i	−0.269222	−	0.0907115i
$186$	152.142	+	928.026i	0.0599763	+	0.365840i
$187$	2157.25	+	2043.45i	0.843602	+	0.799102i
$188$	611.853	−	283.073i	0.237361	−	0.109815i
$189$	443.151	−	336.874i	0.170553	−	0.129651i
$190$	−196.368	+	1197.79i	−0.0749790	+	0.457352i
$191$	539.237	−	1017.11i	0.204282	−	0.385317i	−0.760110	−	0.649795i	$-0.774855\pi$
$191$	539.237	−	1017.11i	0.204282	−	0.385317i	0.964392	+	0.264478i	$0.0851997\pi$
$192$	337.087	−	74.1985i	0.126704	−	0.0278896i
$193$	2889.04	+	1336.61i	1.07750	+	0.498505i	0.876656	−	0.481118i	$-0.159769\pi$
$193$	2889.04	+	1336.61i	1.07750	+	0.498505i	0.200845	+	0.979623i	$0.435631\pi$
$194$	−700.446	−	1757.99i	−0.259222	−	0.650598i
$195$	−110.205	−	2032.61i	−0.0404715	−	0.746453i
$196$	314.390	+	463.690i	0.114573	+	0.168983i
$197$	−2046.92	−	2409.83i	−0.740291	−	0.871538i	0.255152	−	0.966901i	$-0.417875\pi$
$197$	−2046.92	−	2409.83i	−0.740291	−	0.871538i	−0.995443	+	0.0953633i	$0.969599\pi$
$198$	−294.107	−	554.746i	−0.105562	−	0.199111i
$199$	−290.018	+	97.7184i	−0.103311	+	0.0348094i	−0.370482	−	0.928840i	$-0.620808\pi$
$199$	−290.018	+	97.7184i	−0.103311	+	0.0348094i	0.267172	+	0.963649i	$0.413911\pi$
$200$	−43.7997	+	807.839i	−0.0154855	+	0.285614i
$201$	−2172.03	+	1306.87i	−0.762206	+	0.458604i
$202$	331.733	+	1194.79i	0.115548	+	0.416165i
$203$	1180.66	−	4252.34i	0.408206	−	1.47023i
$204$	809.489	+	487.053i	0.277821	+	0.167160i
$205$	708.561	−	1045.05i	0.241405	−	0.356046i
$206$	−747.674	+	81.3144i	−0.252878	+	0.0275022i
$207$	124.429	−	13.5324i	0.0417797	−	0.00454382i
$208$	−1641.10	+	2420.45i	−0.547068	+	0.806865i
$209$	7162.25	+	4309.39i	2.37045	+	1.42625i
$210$	−154.790	+	557.502i	−0.0508643	+	0.183196i
$211$	759.854	+	2736.75i	0.247917	+	0.892917i	0.977834	+	0.209381i	$0.0671449\pi$
$211$	759.854	+	2736.75i	0.247917	+	0.892917i	−0.729917	+	0.683536i	$0.760441\pi$
$212$	3136.11	−	1886.93i	1.01598	−	0.611298i
$213$	96.4894	−	1779.64i	0.0310392	−	0.572484i
$214$	−104.904	+	35.3462i	−0.0335097	+	0.0112907i
$215$	−569.570	−	1074.32i	−0.180671	−	0.340782i
$216$	−280.671	−	330.431i	−0.0884131	−	0.104088i
$217$	−3349.03	−	4939.45i	−1.04768	−	1.54521i
$218$	−18.2283	−	336.201i	−0.00566319	−	0.104451i
$219$	−135.911	−	341.110i	−0.0419360	−	0.105251i
$220$	−3448.02	−	1595.23i	−1.05666	−	0.488864i
$221$	−3538.49	+	778.880i	−1.07703	+	0.237073i
$222$	125.939	−	237.546i	0.0380741	−	0.0718154i
$223$	28.1627	−	171.785i	0.00845700	−	0.0515854i	−0.982261	−	0.187519i	$-0.939955\pi$
$223$	28.1627	−	171.785i	0.00845700	−	0.0515854i	0.990718	+	0.135934i	$0.0434035\pi$
$224$	2770.09	−	2105.77i	0.826270	−	0.628114i
$225$	−411.545	+	190.401i	−0.121939	+	0.0564151i
$226$	−1356.93	−	1285.35i	−0.399388	−	0.378320i
$227$	−287.625	−	1754.43i	−0.0840983	−	0.512977i	−0.994961	−	0.100267i	$-0.968030\pi$
$227$	−287.625	−	1754.43i	−0.0840983	−	0.512977i	0.910862	−	0.412710i	$-0.135418\pi$
$228$	2518.41	+	848.552i	0.731517	+	0.246477i
$229$	944.302	−	2370.02i	0.272495	−	0.683910i	−0.727503	−	0.686104i	$-0.759319\pi$
$229$	944.302	−	2370.02i	0.272495	−	0.683910i	0.999998	+	0.00219469i	$0.000698592\pi$
$230$	−94.4479	+	89.4658i	−0.0270770	+	0.0256487i
$231$	3172.03	+	2411.31i	0.903481	+	0.686809i
$232$	−3356.80	−	738.889i	−0.949935	−	0.209097i
$233$	−635.030	+	747.616i	−0.178550	+	0.210206i	−0.844156	−	0.536098i	$-0.819898\pi$
$233$	−635.030	+	747.616i	−0.178550	+	0.210206i	0.665605	+	0.746304i	$0.268173\pi$
$234$	761.121	+	82.7769i	0.212633	+	0.0231252i
$235$	−852.977			−0.236775
$236$	−905.532	+	2958.53i	−0.249767	+	0.816033i
$237$	1400.25			0.383780
$238$	1023.81	+	111.346i	0.278839	+	0.0303256i
$239$	−3281.17	+	3862.89i	−0.888038	+	1.04548i	0.110629	+	0.993862i	$0.464714\pi$
$239$	−3281.17	+	3862.89i	−0.888038	+	1.04548i	−0.998667	+	0.0516176i	$0.983562\pi$
$240$	−942.189	−	207.391i	−0.253408	−	0.0557794i
$241$	−536.710	−	407.996i	−0.143454	−	0.109051i	0.530986	−	0.847381i	$-0.321822\pi$
$241$	−536.710	−	407.996i	−0.143454	−	0.109051i	−0.674440	+	0.738330i	$0.735615\pi$
$242$	2216.42	−	2099.50i	0.588747	−	0.557691i
$243$	89.9436	−	225.741i	0.0237444	−	0.0595939i
$244$	−4094.91	−	1379.74i	−1.07438	−	0.362002i
$245$	−114.674	−	699.479i	−0.0299030	−	0.182400i
$246$	344.762	+	326.576i	0.0893546	+	0.0846412i
$247$	−9250.17	+	4279.59i	−2.38289	+	1.10244i
$248$	−3700.17	+	2812.79i	−0.947422	+	0.720212i
$249$	135.380	−	825.781i	0.0344553	−	0.210168i
$250$	768.496	−	1449.54i	0.194416	−	0.366707i
$251$	−2942.30	+	647.649i	−0.739906	+	0.162866i	−0.568903	−	0.822405i	$-0.692632\pi$
$251$	−2942.30	+	647.649i	−0.739906	+	0.162866i	−0.171003	+	0.985270i	$0.554701\pi$
$252$	1149.72	+	531.917i	0.287403	+	0.132967i
$253$	331.607	+	832.271i	0.0824030	+	0.206816i
$254$	56.4961	+	1042.01i	0.0139562	+	0.257408i
$255$	−670.785	−	989.333i	−0.164730	−	0.242959i
$256$	−438.097	−	515.767i	−0.106957	−	0.125920i
$257$	−3155.61	−	5952.12i	−0.765921	−	1.44468i	−0.891702	−	0.452622i	$-0.850489\pi$
$257$	−3155.61	−	5952.12i	−0.765921	−	1.44468i	0.125782	−	0.992058i	$-0.459856\pi$
$258$	433.399	−	146.029i	0.104582	−	0.0352379i
$259$	−92.3711	+	1703.68i	−0.0221609	+	0.408733i
$260$	3969.37	−	2388.29i	0.946808	−	0.569675i
$261$	−515.398	−	1856.29i	−0.122231	−	0.440237i
$262$	−396.476	+	1427.98i	−0.0934900	+	0.336720i
$263$	−5139.87	−	3092.56i	−1.20509	−	0.725077i	−0.235991	−	0.971755i	$-0.575833\pi$
$263$	−5139.87	−	3092.56i	−1.20509	−	0.725077i	−0.969098	+	0.246678i	$0.920661\pi$
$264$	1741.51	−	2568.54i	0.405995	−	0.598799i
$265$	−4603.65	+	500.677i	−1.06717	+	0.116062i
$266$	2880.01	−	313.220i	0.663853	−	0.0721983i
$267$	257.407	−	379.647i	0.0590002	−	0.0870188i
$268$	−4942.97	−	2974.09i	−1.12664	−	0.677878i
$269$	2189.00	−	7884.06i	0.496155	−	1.78699i	−0.112613	−	0.993639i	$-0.535922\pi$
$269$	2189.00	−	7884.06i	0.496155	−	1.78699i	0.608767	−	0.793349i	$-0.291664\pi$
$270$	67.5710	+	243.369i	0.0152305	+	0.0548554i
$271$	4625.83	−	2783.27i	1.03690	−	0.623881i	0.107975	−	0.994154i	$-0.465563\pi$
$271$	4625.83	−	2783.27i	1.03690	−	0.623881i	0.928923	+	0.370273i	$0.120736\pi$
$272$	−92.9655	+	1714.65i	−0.0207238	+	0.382227i
$273$	−4604.14	+	1551.32i	−1.02072	+	0.343919i
$274$	−662.741	−	1250.06i	−0.146123	−	0.275617i
$275$	−2101.28	−	2473.82i	−0.460771	−	0.542461i
$276$	159.847	+	235.756i	0.0348610	+	0.0514161i
$277$	344.413	+	6352.32i	0.0747068	+	1.37788i	0.760145	+	0.649754i	$0.225128\pi$
$277$	344.413	+	6352.32i	0.0747068	+	1.37788i	−0.685438	+	0.728131i	$0.740389\pi$
$278$	1038.95	+	2607.57i	0.224145	+	0.562560i
$279$	−2364.35	−	1093.87i	−0.507348	−	0.234724i
$280$	−2792.77	+	614.736i	−0.596072	+	0.131205i
$281$	−707.102	+	1333.74i	−0.150114	+	0.283146i	−0.947153	−	0.320783i	$-0.896054\pi$
$281$	−707.102	+	1333.74i	−0.150114	+	0.283146i	0.797038	+	0.603929i	$0.206399\pi$
$282$	51.9019	−	316.588i	0.0109600	−	0.0668529i
$283$	−3178.51	+	2416.24i	−0.667643	+	0.507529i	−0.883221	−	0.468958i	$-0.844630\pi$
$283$	−3178.51	+	2416.24i	−0.667643	+	0.507529i	0.215578	+	0.976487i	$0.430837\pi$
$284$	3681.08	−	1703.05i	0.769126	−	0.355835i
$285$	−2441.09	−	2312.33i	−0.507361	−	0.480598i
$286$	886.591	+	5407.96i	0.183305	+	1.11811i
$287$	−2855.79	−	962.229i	−0.587360	−	0.197904i
$288$	562.229	−	1411.09i	0.115033	−	0.288712i
$289$	2022.24	−	1915.57i	0.411610	−	0.389897i
$290$	1594.12	+	1211.82i	0.322793	+	0.245381i
$291$	5119.73	+	1126.94i	1.03135	+	0.227018i
$292$	540.972	−	636.882i	0.108418	−	0.127639i
$293$	−1480.42	−	161.005i	−0.295178	−	0.0321025i	−0.0406680	−	0.999173i	$-0.512949\pi$
$293$	−1480.42	−	161.005i	−0.295178	−	0.0321025i	−0.254510	+	0.967070i	$0.581914\pi$
$294$	266.593			0.0528845
$295$	2611.57	−	2916.21i	0.515429	−	0.575553i
$296$	1328.84			0.260937
$297$	1729.17	+	188.059i	0.337834	+	0.0367417i
$298$	−2167.19	+	2551.41i	−0.421282	+	0.495971i
$299$	−1066.87	−	234.836i	−0.206350	−	0.0454211i
$300$	−821.524	−	624.506i	−0.158102	−	0.120186i
$301$	−2107.00	+	1995.85i	−0.403473	+	0.382190i
$302$	332.645	−	834.876i	0.0633827	−	0.159079i
$303$	−3255.21	−	1096.81i	−0.617184	−	0.207954i
$304$	781.480	+	4766.82i	0.147437	+	0.899328i
$305$	3969.19	+	3759.82i	0.745165	+	0.705858i
$306$	408.013	−	188.767i	0.0762240	−	0.0352650i
$307$	−4183.02	+	3179.85i	−0.777647	+	0.591152i	−0.916906	−	0.399104i	$-0.869321\pi$
$307$	−4183.02	+	3179.85i	−0.777647	+	0.591152i	0.139258	+	0.990256i	$0.455528\pi$
$308$	−1466.98	+	8948.20i	−0.271393	+	1.65543i
$309$	975.890	−	1840.72i	0.179665	−	0.338884i
$310$	2644.48	−	582.094i	0.484504	−	0.106647i
$311$	6612.53	+	3059.28i	1.20567	+	0.557800i	0.916714	−	0.399543i	$-0.130831\pi$
$311$	6612.53	+	3059.28i	1.20567	+	0.557800i	0.288952	+	0.957344i	$0.406693\pi$
$312$	1400.58	+	3515.20i	0.254143	+	0.637850i
$313$	347.502	+	6409.29i	0.0627538	+	1.15743i	0.845109	+	0.534594i	$0.179535\pi$
$313$	347.502	+	6409.29i	0.0627538	+	1.15743i	−0.782355	+	0.622833i	$0.785982\pi$
$314$	537.214	+	792.331i	0.0965501	+	0.142401i
$315$	−1037.64	−	1221.60i	−0.185601	−	0.218506i
$316$	1492.63	+	2815.39i	0.265718	+	0.501197i
$317$	4955.70	−	1669.77i	0.878043	−	0.295847i	0.156052	−	0.987749i	$-0.450123\pi$
$317$	4955.70	−	1669.77i	0.878043	−	0.295847i	0.721992	+	0.691902i	$0.243227\pi$
$318$	94.2933	−	1739.14i	0.0166280	−	0.306686i
$319$	11815.9	−	7109.39i	2.07387	−	1.24780i
$320$	−265.877	−	957.603i	−0.0464468	−	0.167286i
$321$	82.0394	−	295.479i	0.0142648	−	0.0513771i
$322$	266.057	+	160.081i	0.0460459	+	0.0277049i
$323$	−3358.60	+	4953.57i	−0.578569	+	0.853325i
$324$	549.762	−	59.7902i	0.0942665	−	0.0102521i
$325$	3934.53	−	427.906i	0.671534	−	0.0730337i
$326$	622.389	−	917.955i	0.105739	−	0.155953i
$327$	799.201	+	480.863i	0.135156	+	0.0813204i
$328$	−627.904	+	2261.51i	−0.105702	+	0.380704i
$329$	544.646	+	1961.64i	0.0912685	+	0.328719i
$330$	−1549.12	+	932.074i	−0.258413	+	0.155482i
$331$	448.629	−	8274.48i	0.0744982	−	1.37404i	−0.687371	−	0.726307i	$-0.741235\pi$
$331$	448.629	−	8274.48i	0.0744982	−	1.37404i	0.761869	−	0.647731i	$-0.224282\pi$
$332$	1804.66	−	608.061i	0.298324	−	0.100517i
$333$	348.875	+	658.048i	0.0574121	+	0.108291i
$334$	14.8908	+	17.5308i	0.00243949	+	0.00287199i
$335$	4096.01	+	6041.16i	0.668026	+	0.985265i
$336$	124.661	+	2299.23i	0.0202405	+	0.373313i
$337$	−3538.08	−	8879.92i	−0.571904	−	1.43537i	−0.875804	−	0.482667i	$-0.839668\pi$
$337$	−3538.08	−	8879.92i	−0.571904	−	1.43537i	0.303900	−	0.952704i	$-0.401711\pi$
$338$	−3905.24	−	1806.76i	−0.628453	−	0.290753i
$339$	5056.62	−	1113.05i	0.810141	−	0.178326i
$340$	1274.15	−	2403.31i	0.203237	−	0.383346i
$341$	3016.79	−	18401.6i	0.479087	−	2.92230i
$342$	1006.77	−	765.326i	0.159181	−	0.121006i
$343$	4882.60	−	2258.93i	0.768618	−	0.355600i
$344$	1641.01	+	1554.44i	0.257201	+	0.243634i
$345$	−58.3041	−	355.639i	−0.00909852	−	0.0554985i
$346$	2256.45	+	760.287i	0.350600	+	0.118131i
$347$	−1719.82	+	4316.43i	−0.266066	+	0.667776i	−0.999934	−	0.0115167i	$-0.996334\pi$
$347$	−1719.82	+	4316.43i	−0.266066	+	0.667776i	0.733867	+	0.679293i	$0.237713\pi$
$348$	3182.94	−	3015.04i	0.490297	−	0.464434i
$349$	978.887	+	744.131i	0.150139	+	0.114133i	0.677547	−	0.735479i	$-0.263043\pi$
$349$	978.887	+	744.131i	0.150139	+	0.114133i	−0.527408	+	0.849612i	$0.676836\pi$
$350$	−1098.63	−	241.827i	−0.167784	−	0.0369320i
$351$	−1373.03	+	1616.46i	−0.208795	+	0.245813i
$352$	10808.9	+	1175.54i	1.63669	+	0.178001i
$353$	−9846.19			−1.48459			−0.742295	−	0.670074i	$-0.766262\pi$
$353$	−9846.19			−1.48459			−0.742295	+	0.670074i	$0.766262\pi$
$354$	923.459	+	1146.75i	0.138648	+	0.172172i
$355$	−5131.75			−0.767225
$356$	1037.72	+	112.859i	0.154492	+	0.0168020i
$357$	−1846.91	+	2174.35i	−0.273807	+	0.322350i
$358$	−1445.95	−	318.278i	−0.213466	−	0.0469875i
$359$	−7093.38	−	5392.25i	−1.04283	−	0.792736i	−0.0641073	−	0.997943i	$-0.520420\pi$
$359$	−7093.38	−	5392.25i	−1.04283	−	0.792736i	−0.978719	+	0.205207i	$0.934213\pi$
$360$	−906.280	+	858.474i	−0.132681	+	0.125682i
$361$	−3692.68	+	9267.94i	−0.538371	+	1.35121i
$362$	−2860.44	−	963.793i	−0.415307	−	0.139933i
$363$	1368.23	+	8345.83i	0.197833	+	1.20673i
$364$	−8027.03	−	7603.61i	−1.15585	−	1.09488i
$365$	−959.549	+	443.935i	−0.137603	+	0.0636619i
$366$	−1637.00	+	1244.41i	−0.233790	+	0.177723i
$367$	1994.85	−	12168.0i	0.283734	−	1.73070i	−0.332471	−	0.943114i	$-0.607882\pi$
$367$	1994.85	−	12168.0i	0.283734	−	1.73070i	0.616205	−	0.787586i	$-0.288669\pi$
$368$	−242.511	+	457.424i	−0.0343526	+	0.0647958i
$369$	−1284.76	+	282.797i	−0.181252	+	0.0398966i
$370$	−702.607	−	325.061i	−0.0987211	−	0.0456732i
$371$	4090.98	+	10267.6i	0.572488	+	1.43684i
$372$	−320.968	−	5919.90i	−0.0447349	−	0.825087i
$373$	−3304.73	−	4874.11i	−0.458746	−	0.676600i	0.526023	−	0.850471i	$-0.323683\pi$
$373$	−3304.73	−	4874.11i	−0.458746	−	0.676600i	−0.984768	+	0.173871i	$0.944372\pi$
$374$	2083.24	+	2452.59i	0.288027	+	0.339091i
$375$	2128.88	+	4015.50i	0.293160	+	0.552959i
$376$	1502.59	−	506.282i	0.206091	−	0.0694401i
$377$	−910.320	+	16789.9i	−0.124360	+	2.29369i
$378$	516.543	−	310.794i	0.0702860	−	0.0422897i
$379$	3324.18	+	11972.6i	0.450533	+	1.62267i	0.745038	+	0.667022i	$0.232431\pi$
$379$	3324.18	+	11972.6i	0.450533	+	1.62267i	−0.294505	+	0.955650i	$0.595155\pi$
$380$	2047.11	−	7373.04i	0.276355	−	0.995339i
$381$	−2477.01	−	1490.37i	−0.333074	−	0.200404i
$382$	699.638	−	1031.89i	0.0937084	−	0.138210i
$383$	5421.15	−	589.585i	0.723258	−	0.0786590i	0.260917	−	0.965361i	$-0.415975\pi$
$383$	5421.15	−	589.585i	0.723258	−	0.0786590i	0.462341	+	0.886702i	$0.347010\pi$
$384$	4398.44	−	478.359i	0.584523	−	0.0635707i
$385$	6438.37	−	9495.88i	0.852285	−	1.25703i
$386$	2953.86	+	1777.28i	0.389501	+	0.234355i
$387$	−338.937	+	1220.74i	−0.0445197	+	0.160345i
$388$	3191.63	+	11495.2i	0.417605	+	1.50408i
$389$	1063.88	−	640.118i	0.138666	−	0.0834326i	−0.444530	−	0.895764i	$-0.646629\pi$
$389$	1063.88	−	640.118i	0.138666	−	0.0834326i	0.583196	+	0.812331i	$0.301802\pi$
$390$	119.347	−	2201.23i	0.0154958	−	0.285804i
$391$	−607.882	+	204.819i	−0.0786238	+	0.0264914i
$392$	617.181	+	1164.13i	0.0795212	+	0.149993i
$393$	−2657.79	−	3129.00i	−0.341140	−	0.401621i
$394$	−1921.57	−	2834.11i	−0.245704	−	0.362386i
$395$	−218.277	−	4025.89i	−0.0278044	−	0.512822i
$396$	1465.14	+	3677.21i	0.185924	+	0.466633i
$397$	2929.06	+	1355.13i	0.370290	+	0.171315i	0.596204	−	0.802833i	$-0.296675\pi$
$397$	2929.06	+	1355.13i	0.370290	+	0.171315i	−0.225914	+	0.974147i	$0.572537\pi$
$398$	−323.677	+	71.2467i	−0.0407650	+	0.00897305i
$399$	−3759.09	+	7090.40i	−0.471654	+	0.889634i
$400$	303.457	−	1851.00i	0.0379321	−	0.231376i
$401$	−4084.22	+	3104.74i	−0.508619	+	0.386642i	−0.827775	−	0.561060i	$-0.810394\pi$
$401$	−4084.22	+	3104.74i	−0.508619	+	0.386642i	0.319156	+	0.947702i	$0.396601\pi$
$402$	−2491.45	+	1152.67i	−0.309110	+	0.143009i
$403$	16507.3	+	15636.5i	2.04041	+	1.93278i
$404$	−1264.68	−	7714.22i	−0.155743	−	0.949992i
$405$	−663.057	−	223.410i	−0.0813520	−	0.0274107i
$406$	1769.00	−	4439.86i	0.216242	−	0.542726i
$407$	−3870.48	+	3666.31i	−0.471382	+	0.446517i
$408$	1768.86	+	1344.65i	0.214636	+	0.163162i
$409$	384.159	+	84.5598i	0.0464436	+	0.0102230i	0.238131	−	0.971233i	$-0.423465\pi$
$409$	384.159	+	84.5598i	0.0464436	+	0.0102230i	−0.191688	+	0.981456i	$0.561396\pi$
$410$	885.205	−	1042.14i	0.106627	−	0.125531i
$411$	3896.52	+	423.772i	0.467642	+	0.0508592i
$412$	4741.31			0.566960
$413$	−8374.12	−	4143.91i	−0.997732	−	0.493725i
$414$	135.545			0.0160910
$415$	−2395.33	−	260.508i	−0.283331	−	0.0308141i
$416$	−8582.70	+	10104.3i	−1.01154	+	1.19088i
$417$	−7593.95	−	1671.56i	−0.891793	−	0.196298i
$418$	7206.36	+	5478.13i	0.843240	+	0.641015i
$419$	6606.84	−	6258.33i	0.770323	−	0.729689i	−0.197779	−	0.980247i	$-0.563373\pi$
$419$	6606.84	−	6258.33i	0.770323	−	0.729689i	0.968102	+	0.250558i	$0.0806141\pi$
$420$	1350.11	−	3388.51i	0.156853	−	0.393673i
$421$	−12029.5	−	4053.22i	−1.39260	−	0.469220i	−0.479707	−	0.877429i	$-0.659257\pi$
$421$	−12029.5	−	4053.22i	−1.39260	−	0.469220i	−0.912889	+	0.408209i	$0.866154\pi$
$422$	497.624	+	3035.37i	0.0574027	+	0.350141i
$423$	645.205	+	611.170i	0.0741630	+	0.0702509i
$424$	7812.54	−	3614.47i	0.894836	−	0.413995i
$425$	1850.09	−	1406.41i	0.211159	−	0.160519i
$426$	312.256	−	1904.68i	0.0355138	−	0.216624i
$427$	6112.24	−	11528.9i	0.692722	−	1.30661i
$428$	681.554	−	150.021i	0.0769723	−	0.0169429i
$429$	−13778.0	−	6374.38i	−1.55060	−	0.717385i
$430$	−487.413	−	1223.31i	−0.0546631	−	0.137194i
$431$	199.787	+	3684.86i	0.0223281	+	0.411818i	0.988236	+	0.152934i	$0.0488721\pi$
$431$	199.787	+	3684.86i	0.0223281	+	0.411818i	−0.965908	+	0.258884i	$0.916645\pi$
$432$	564.087	+	831.966i	0.0628232	+	0.0926574i
$433$	8263.19	+	9728.18i	0.917099	+	1.07969i	0.996562	+	0.0828544i	$0.0264036\pi$
$433$	8263.19	+	9728.18i	0.917099	+	1.07969i	−0.0794628	+	0.996838i	$0.525320\pi$
$434$	−3027.24	−	5709.98i	−0.334820	−	0.631538i
$435$	−5256.75	+	1771.20i	−0.579406	+	0.195225i
$436$	−114.916	+	2119.49i	−0.0126226	+	0.232810i
$437$	−1546.16	+	930.291i	−0.169251	+	0.101835i
$438$	−106.382	−	383.155i	−0.0116054	−	0.0417987i
$439$	−506.865	+	1825.56i	−0.0551056	+	0.198472i	−0.985979	−	0.166870i	$-0.946634\pi$
$439$	−506.865	+	1825.56i	−0.0551056	+	0.198472i	0.930873	+	0.365342i	$0.119048\pi$
$440$	−7656.37	−	4606.68i	−0.829552	−	0.499125i
$441$	−414.446	+	611.262i	−0.0447517	+	0.0660039i
$442$	−3900.76	+	424.233i	−0.419774	+	0.0456532i
$443$	12698.3	−	1381.02i	1.36188	−	0.148114i	0.602169	−	0.798369i	$-0.294303\pi$
$443$	12698.3	−	1381.02i	1.36188	−	0.148114i	0.759716	+	0.650255i	$0.225338\pi$
$444$	−951.207	+	1402.92i	−0.101672	+	0.149955i
$445$	−1131.66	−	680.897i	−0.120552	−	0.0725340i
$446$	50.4341	−	181.647i	0.00535453	−	0.0192853i
$447$	−2480.93	−	8935.49i	−0.262514	−	0.945490i
$448$	−2032.48	+	1222.90i	−0.214343	+	0.128966i
$449$	114.244	−	2107.10i	0.0120078	−	0.221471i	−0.986370	−	0.164540i	$-0.947386\pi$
$449$	114.244	−	2107.10i	0.0120078	−	0.221471i	0.998378	−	0.0569304i	$-0.0181313\pi$
$450$	−465.366	+	156.800i	−0.0487501	+	0.0164258i
$451$	−4410.69	−	8319.44i	−0.460513	−	0.868619i
$452$	7628.16	+	8980.56i	0.793802	+	0.934535i
$453$	1397.13	+	2060.61i	0.144907	+	0.213721i
$454$	−104.236	−	1922.51i	−0.0107754	−	0.198740i
$455$	5177.95	+	12995.7i	0.533508	+	1.33900i
$456$	5672.66	+	2624.45i	0.582559	+	0.269520i
$457$	−309.362	+	68.0956i	−0.0316659	+	0.00697019i	−0.230775	−	0.973007i	$-0.574126\pi$
$457$	−309.362	+	68.0956i	−0.0316659	+	0.00697019i	0.199109	+	0.979977i	$0.436195\pi$
$458$	1294.14	−	2441.01i	0.132034	−	0.249042i
$459$	−201.480	+	1228.97i	−0.0204886	+	0.124975i
$460$	652.912	−	496.331i	0.0661787	−	0.0503077i
$461$	−943.627	+	436.568i	−0.0953343	+	0.0441063i	−0.466977	−	0.884270i	$-0.654657\pi$
$461$	−943.627	+	436.568i	−0.0953343	+	0.0441063i	0.371642	+	0.928376i	$0.378795\pi$
$462$	3132.69	+	2967.44i	0.315468	+	0.298827i
$463$	−348.411	−	2125.22i	−0.0349720	−	0.213320i	0.963559	−	0.267494i	$-0.0861956\pi$
$463$	−348.411	−	2125.22i	−0.0349720	−	0.213320i	−0.998531	+	0.0541743i	$0.982747\pi$
$464$	7551.86	+	2544.52i	0.755574	+	0.254583i
$465$	−2776.44	+	6968.34i	−0.276891	+	0.694945i
$466$	−771.215	+	730.534i	−0.0766649	+	0.0726209i
$467$	−8553.48	−	6502.19i	−0.847554	−	0.644294i	0.0885286	−	0.996074i	$-0.471784\pi$
$467$	−8553.48	−	6502.19i	−0.847554	−	0.644294i	−0.936083	+	0.351780i	$0.885577\pi$
$468$	−4713.74	−	1037.57i	−0.465583	−	0.102482i
$469$	11277.8	−	13277.2i	1.11036	−	1.30722i
$470$	−918.321	−	99.8735i	−0.0901255	−	0.00980174i
$471$	−2651.86			−0.259429
$472$	−2869.60	+	6687.23i	−0.279839	+	0.652129i
$473$	−9068.48			−0.881541
$474$	1507.52	+	163.952i	0.146081	+	0.0158873i
$475$	4232.22	−	4982.56i	0.408816	−	0.481296i
$476$	−6340.60	−	1395.67i	−0.610549	−	0.134392i
$477$	3841.01	+	2919.86i	0.368696	+	0.280275i
$478$	−3984.83	+	3774.63i	−0.381301	+	0.361187i
$479$	1890.90	−	4745.80i	0.180370	−	0.452695i	−0.810795	−	0.585331i	$-0.800965\pi$
$479$	1890.90	−	4745.80i	0.180370	−	0.452695i	0.991165	+	0.132636i	$0.0423440\pi$
$480$	−4144.70	−	1396.51i	−0.394123	−	0.132795i
$481$	−1051.69	−	6415.02i	−0.0996941	−	0.608107i
$482$	−530.054	−	502.094i	−0.0500899	−	0.0474476i
$483$	−780.655	+	361.170i	−0.0735425	+	0.0340244i
$484$	−15322.0	+	11647.4i	−1.43895	+	1.09386i
$485$	2442.00	−	14895.6i	0.228630	−	1.39458i
$486$	123.266	−	232.503i	0.0115050	−	0.0217008i
$487$	1706.13	−	375.548i	0.158752	−	0.0349439i	−0.134883	−	0.990861i	$-0.543066\pi$
$487$	1706.13	−	375.548i	0.158752	−	0.0349439i	0.293635	+	0.955918i	$0.405135\pi$
$488$	−9223.69	−	4267.33i	−0.855609	−	0.395847i
$489$	1137.18	+	2854.10i	0.105164	+	0.263941i
$490$	−41.5579	−	766.491i	−0.00383142	−	0.0706664i
$491$	−8212.37	−	12112.3i	−0.754825	−	1.11328i	−0.989964	−	0.141322i	$-0.954865\pi$
$491$	−8212.37	−	12112.3i	−0.754825	−	1.11328i	0.235139	−	0.971962i	$-0.424446\pi$
$492$	−1938.12	−	2281.74i	−0.177596	−	0.209082i
$493$	4624.80	+	8723.30i	0.422496	+	0.796912i
$494$	−10459.9	+	3524.35i	−0.952658	+	0.320988i
$495$	271.142	−	5000.92i	0.0246200	−	0.454090i
$496$	9233.59	−	5555.66i	0.835888	−	0.502937i
$497$	3276.74	+	11801.8i	0.295739	+	1.06515i
$498$	242.440	−	873.191i	0.0218153	−	0.0785715i
$499$	−538.396	−	323.942i	−0.0483004	−	0.0290614i	0.491199	−	0.871047i	$-0.336559\pi$
$499$	−538.396	−	323.942i	−0.0483004	−	0.0290614i	−0.539499	+	0.841986i	$0.681386\pi$
$500$	−5804.39	+	8560.84i	−0.519161	+	0.765705i
$501$	−63.3451	+	6.88919i	−0.00564880	+	0.000614344i
$502$	−3243.53	+	352.756i	−0.288378	+	0.0313631i
$503$	2821.06	−	4160.75i	0.250069	−	0.368825i	−0.681849	−	0.731493i	$-0.738824\pi$
$503$	2821.06	−	4160.75i	0.250069	−	0.368825i	0.931918	+	0.362668i	$0.118134\pi$
$504$	2552.96	+	1536.07i	0.225631	+	0.135758i
$505$	−2646.03	+	9530.12i	−0.233162	+	0.839772i
$506$	259.561	+	934.856i	0.0228042	+	0.0821332i
$507$	10213.7	−	6145.39i	0.894689	−	0.538317i
$508$	356.165	−	6569.08i	0.0311068	−	0.573731i
$509$	−18520.9	+	6240.42i	−1.61282	+	0.543422i	−0.974119	−	0.226035i	$-0.927424\pi$
$509$	−18520.9	+	6240.42i	−1.61282	+	0.543422i	−0.638699	+	0.769457i	$0.720527\pi$
$510$	−606.332	−	1143.66i	−0.0526448	−	0.0992986i
$511$	1633.64	+	1923.27i	0.141424	+	0.166498i
$512$	6209.80	+	9158.77i	0.536010	+	0.790556i
$513$	189.665	+	3498.16i	0.0163234	+	0.301067i
$514$	−2700.43	−	6777.58i	−0.231733	−	0.581607i
$515$	−5444.45	−	2518.87i	−0.465847	−	0.215524i
$516$	−2815.76	+	619.797i	−0.240227	+	0.0528780i
$517$	−2979.71	+	5620.33i	−0.253477	+	0.478108i
$518$	−298.929	+	1823.38i	−0.0253555	+	0.154662i
$519$	−5251.11	+	3991.79i	−0.444120	+	0.337611i
$520$	9888.33	−	4574.83i	0.833908	−	0.385807i
$521$	−16548.6	−	15675.7i	−1.39157	−	1.31816i	−0.892104	−	0.451831i	$-0.850771\pi$
$521$	−16548.6	−	15675.7i	−1.39157	−	1.31816i	−0.499466	−	0.866334i	$-0.666470\pi$
$522$	−337.531	−	2058.85i	−0.0283014	−	0.172631i
$523$	−4744.56	−	1598.63i	−0.396683	−	0.133658i	0.113888	−	0.993494i	$-0.463669\pi$
$523$	−4744.56	−	1598.63i	−0.396683	−	0.133658i	−0.510571	+	0.859836i	$0.670566\pi$
$524$	3458.15	−	8679.30i	0.288301	−	0.723582i
$525$	2262.41	−	2143.07i	0.188075	−	0.178155i
$526$	−5171.52	−	3931.29i	−0.428687	−	0.325879i
$527$	13039.2	+	2870.15i	1.07779	+	0.237240i
$528$	−4657.87	+	5483.67i	−0.383916	+	0.451981i
$529$	11903.4	+	1294.57i	0.978335	+	0.106400i
$530$	−5014.95			−0.411010
$531$	−4064.94	+	334.633i	−0.332210	+	0.0273481i
$532$	−18263.3			−1.48838
$533$	11414.4	+	1241.39i	0.927606	+	0.100883i
$534$	321.578	−	378.591i	0.0260600	−	0.0306802i
$535$	−862.330	−	189.813i	−0.0696855	−	0.0153389i
$536$	−10801.2	−	8210.83i	−0.870409	−	0.661668i
$537$	2977.64	−	2820.57i	0.239283	−	0.226661i
$538$	3279.82	−	8231.73i	0.262831	−	0.659656i
$539$	−5009.51	−	1687.90i	−0.400324	−	0.134885i
$540$	−257.604	−	1571.32i	−0.0205288	−	0.125220i
$541$	−8200.32	−	7767.76i	−0.651681	−	0.617305i	0.288703	−	0.957419i	$-0.406776\pi$
$541$	−8200.32	−	7767.76i	−0.651681	−	0.617305i	−0.940384	+	0.340114i	$0.889535\pi$
$542$	5306.09	−	2454.86i	0.420510	−	0.194548i
$543$	6656.67	−	5060.27i	0.526087	−	0.399921i
$544$	−1259.43	+	7682.19i	−0.0992605	+	0.605462i
$545$	1257.96	−	2372.76i	0.0988717	−	0.186492i
$546$	−5138.49	+	1131.07i	−0.402760	+	0.0886543i
$547$	−3170.79	−	1466.97i	−0.247849	−	0.114667i	0.292032	−	0.956409i	$-0.405669\pi$
$547$	−3170.79	−	1466.97i	−0.247849	−	0.114667i	−0.539881	+	0.841741i	$0.681531\pi$
$548$	3301.53	+	8286.22i	0.257362	+	0.645930i
$549$	−308.393	−	5687.97i	−0.0239743	−	0.442180i
$550$	−1972.60	−	2909.36i	−0.152931	−	0.225556i
$551$	17980.7	+	21168.5i	1.39021	+	1.63668i
$552$	313.796	+	591.882i	0.0241957	+	0.0456380i
$553$	−9119.19	+	3072.61i	−0.701243	+	0.236276i
$554$	−372.984	+	6879.28i	−0.0286039	+	0.527568i
$555$	1837.59	−	1105.64i	0.140543	−	0.0845619i
$556$	−4734.06	−	17050.5i	−0.361095	−	1.30055i
$557$	−2782.43	+	10021.4i	−0.211661	+	0.762336i	0.779121	+	0.626874i	$0.215666\pi$
$557$	−2782.43	+	10021.4i	−0.211661	+	0.762336i	−0.990783	+	0.135462i	$0.956748\pi$
$558$	−2417.40	−	1454.50i	−0.183399	−	0.110348i
$559$	6205.37	−	9152.24i	0.469516	−	0.692484i
$560$	6591.15	−	716.831i	0.497369	−	0.0540922i
$561$	−8862.05	+	963.806i	−0.666945	+	0.0725346i
$562$	−917.435	+	1353.12i	−0.0688606	+	0.101562i
$563$	10217.3	+	6147.54i	0.764844	+	0.460192i	0.843781	−	0.536688i	$-0.180325\pi$
$563$	10217.3	+	6147.54i	0.764844	+	0.460192i	−0.0789364	+	0.996880i	$0.525152\pi$
$564$	−541.072	+	1948.77i	−0.0403958	+	0.145493i
$565$	−3988.40	−	14364.9i	−0.296979	−	1.06962i
$566$	−3704.92	+	2229.18i	−0.275140	+	0.165547i
$567$	−90.4104	+	1667.52i	−0.00669644	+	0.123508i
$568$	9040.00	−	3045.93i	0.667799	−	0.225008i
$569$	−4776.28	−	9009.03i	−0.351902	−	0.663758i	0.642859	−	0.765984i	$-0.277748\pi$
$569$	−4776.28	−	9009.03i	−0.351902	−	0.663758i	−0.994761	+	0.102227i	$0.967403\pi$
$570$	−2357.35	−	2775.29i	−0.173226	−	0.203937i
$571$	7118.50	+	10499.0i	0.521716	+	0.769474i	0.993693	−	0.112137i	$-0.0357696\pi$
$571$	7118.50	+	10499.0i	0.521716	+	0.769474i	−0.471977	+	0.881611i	$0.656459\pi$
$572$	−1870.40	−	34497.5i	−0.136723	−	2.52170i
$573$	1278.32	+	3208.35i	0.0931984	+	0.233910i
$574$	−2961.90	−	1370.32i	−0.215379	−	0.0996448i
$575$	684.305	−	150.627i	0.0496304	−	0.0109245i
$576$	−485.023	+	914.850i	−0.0350856	+	0.0661784i
$577$	193.590	−	1180.84i	0.0139675	−	0.0851979i	−0.978923	−	0.204230i	$-0.934531\pi$
$577$	193.590	−	1180.84i	0.0139675	−	0.0851979i	0.992890	+	0.119032i	$0.0379792\pi$
$578$	2401.45	−	1825.53i	0.172815	−	0.131370i
$579$	−8667.12	+	4009.83i	−0.622095	+	0.287812i
$580$	−9164.81	−	8681.37i	−0.656117	−	0.621507i
$581$	930.373	+	5675.02i	0.0664344	+	0.405232i
$582$	5379.99	+	1812.73i	0.383175	+	0.129107i
$583$	−12783.0	+	32082.8i	−0.908090	+	2.27913i
$584$	1426.83	−	1351.57i	0.101100	−	0.0957674i
$585$	4861.57	+	3695.67i	0.343592	+	0.261192i
$586$	−1574.98	−	346.679i	−0.111027	−	0.0244389i
$587$	−8888.51	+	10464.4i	−0.624988	+	0.735793i	−0.979984	−	0.199075i	$-0.936206\pi$
$587$	−8888.51	+	10464.4i	−0.624988	+	0.735793i	0.354996	+	0.934868i	$0.384482\pi$
$588$	−1670.82	−	181.712i	−0.117182	−	0.0127444i
$589$	37557.8			2.62741
$590$	3153.09	−	2833.83i	0.220018	−	0.197740i
$591$	9485.48			0.660204
$592$	−3062.84	−	333.104i	−0.212638	−	0.0231258i
$593$	2653.67	−	3124.14i	0.183766	−	0.216346i	−0.662564	−	0.749006i	$-0.730532\pi$
$593$	2653.67	−	3124.14i	0.183766	−	0.216346i	0.846329	+	0.532660i	$0.178807\pi$
$594$	1839.62	+	404.931i	0.127072	+	0.0279706i
$595$	6539.46	+	4971.17i	0.450574	+	0.342518i
$596$	15321.4	−	14513.2i	1.05300	−	0.997459i
$597$	339.829	−	852.906i	0.0232969	−	0.0584709i
$598$	−1121.10	−	377.744i	−0.0766644	−	0.0258313i
$599$	730.751	+	4457.39i	0.0498459	+	0.304046i	0.999969	−	0.00782751i	$-0.00249160\pi$
$599$	730.751	+	4457.39i	0.0498459	+	0.304046i	−0.950123	+	0.311874i	$0.899043\pi$
$600$	−1762.05	−	1669.10i	−0.119892	−	0.113568i
$601$	7536.81	−	3486.90i	0.511536	−	0.236662i	−0.147103	−	0.989121i	$-0.546995\pi$
$601$	7536.81	−	3486.90i	0.511536	−	0.236662i	0.658638	+	0.752460i	$0.271133\pi$
$602$	−2502.10	+	1902.05i	−0.169399	+	0.128773i
$603$	1230.30	−	7504.47i	0.0830871	−	0.506809i
$604$	−2653.84	+	5005.67i	−0.178780	+	0.337215i
$605$	23782.1	−	5234.83i	1.59815	−	0.351778i
$606$	−3376.16	−	1561.98i	−0.226315	−	0.104705i
$607$	−625.832	−	1570.72i	−0.0418480	−	0.105031i	0.906567	−	0.422062i	$-0.138693\pi$
$607$	−625.832	−	1570.72i	−0.0418480	−	0.105031i	−0.948415	+	0.317031i	$0.897314\pi$
$608$	1185.58	+	21866.6i	0.0790813	+	1.45857i
$609$	7429.90	+	10958.3i	0.494376	+	0.729149i
$610$	3833.03	+	4512.59i	0.254418	+	0.299524i
$611$	−3633.29	−	6853.11i	−0.240568	−	0.453760i
$612$	−2685.80	+	904.950i	−0.177397	+	0.0597719i
$613$	−865.187	+	15957.4i	−0.0570059	+	1.05141i	0.820439	+	0.571734i	$0.193729\pi$
$613$	−865.187	+	15957.4i	−0.0570059	+	1.05141i	−0.877445	+	0.479677i	$0.840754\pi$
$614$	−4875.80	+	2933.67i	−0.320474	+	0.192823i
$615$	1013.35	+	3649.77i	0.0664428	+	0.239305i
$616$	−5705.47	+	20549.3i	−0.373182	+	1.34408i
$617$	11567.7	+	6960.08i	0.754781	+	0.454137i	0.840247	−	0.542204i	$-0.182410\pi$
$617$	11567.7	+	6960.08i	0.754781	+	0.454137i	−0.0854655	+	0.996341i	$0.527238\pi$
$618$	1266.18	−	1867.47i	0.0824160	−	0.121555i
$619$	−14143.3	+	1538.18i	−0.918363	+	0.0998780i	−0.555076	−	0.831799i	$-0.687311\pi$
$619$	−14143.3	+	1538.18i	−0.918363	+	0.0998780i	−0.363287	+	0.931677i	$0.618345\pi$
$620$	−16970.4	+	1845.65i	−1.09927	+	0.119553i
$621$	−210.719	+	310.787i	−0.0136165	+	0.0200828i
$622$	6760.89	+	4067.89i	0.435831	+	0.262231i
$623$	−843.305	+	3037.31i	−0.0542316	+	0.195325i
$624$	−2347.04	−	8453.26i	−0.150572	−	0.542310i
$625$	5816.75	−	3499.82i	0.372272	−	0.223989i
$626$	−376.329	+	6940.98i	−0.0240274	+	0.443158i
$627$	−23763.6	+	8006.88i	−1.51360	+	0.509991i
$628$	−2826.81	−	5331.93i	−0.179621	−	0.338801i
$629$	−2471.18	−	2909.30i	−0.156649	−	0.184422i
$630$	−974.094	−	1436.68i	−0.0616013	−	0.0908551i
$631$	945.711	+	17442.6i	0.0596643	+	1.10044i	0.863094	+	0.505044i	$0.168524\pi$
$631$	945.711	+	17442.6i	0.0596643	+	1.10044i	−0.803430	+	0.595400i	$0.796994\pi$
$632$	2774.07	+	6962.38i	0.174599	+	0.438210i
$633$	−7733.29	−	3577.80i	−0.485578	−	0.224652i
$634$	5530.85	−	1217.43i	0.346464	−	0.0762625i
$635$	−3898.88	+	7354.06i	−0.243657	+	0.459586i
$636$	−1776.37	+	10835.4i	−0.110751	+	0.675552i
$637$	5131.40	−	3900.79i	0.319173	−	0.242629i
$638$	13553.5	−	6270.52i	0.841048	−	0.389110i
$639$	3881.73	+	3676.97i	0.240311	+	0.227635i
$640$	−2061.00	−	12571.5i	−0.127294	−	0.776457i
$641$	−24688.2	−	8318.43i	−1.52126	−	0.512571i	−0.570179	−	0.821521i	$-0.693126\pi$
$641$	−24688.2	−	8318.43i	−1.52126	−	0.512571i	−0.951078	+	0.308950i	$0.900023\pi$
$642$	122.921	−	308.509i	0.00755657	−	0.0189656i
$643$	5256.80	−	4979.51i	0.322408	−	0.305401i	−0.509328	−	0.860572i	$-0.670106\pi$
$643$	5256.80	−	4979.51i	0.322408	−	0.305401i	0.831736	+	0.555172i	$0.187347\pi$
$644$	−1558.34	−	1184.62i	−0.0953528	−	0.0724853i
$645$	3562.62	+	784.192i	0.217485	+	0.0478721i
$646$	−4195.90	+	4939.80i	−0.255550	+	0.300857i
$647$	2243.54	+	244.000i	0.136326	+	0.0148263i	0.176027	−	0.984385i	$-0.443675\pi$
$647$	2243.54	+	244.000i	0.136326	+	0.0148263i	−0.0397018	+	0.999212i	$0.512641\pi$
$648$	1300.63			0.0788483
$649$	−10092.1	−	27395.1i	−0.610399	−	1.65693i
$650$	4286.05			0.258635
$651$	17798.3	+	1935.68i	1.07154	+	0.116537i
$652$	−4526.37	+	5328.86i	−0.271881	+	0.320083i
$653$	−9138.46	−	2011.53i	−0.547650	−	0.120547i	−0.0674774	−	0.997721i	$-0.521495\pi$
$653$	−9138.46	−	2011.53i	−0.547650	−	0.120547i	−0.480173	+	0.877174i	$0.659426\pi$
$654$	804.122	+	611.277i	0.0480790	+	0.0365487i
$655$	−8581.96	+	8129.27i	−0.511947	+	0.484942i
$656$	2014.15	−	5055.14i	0.119877	−	0.300869i
$657$	1043.90	+	351.732i	0.0619887	+	0.0208864i
$658$	356.686	+	2175.69i	0.0211323	+	0.128901i
$659$	−2037.50	−	1930.03i	−0.120440	−	0.114087i	0.625110	−	0.780537i	$-0.285054\pi$
$659$	−2037.50	−	1930.03i	−0.120440	−	0.114087i	−0.745550	+	0.666450i	$0.767813\pi$
$660$	10344.1	−	4785.68i	0.610064	−	0.282246i
$661$	4300.06	−	3268.82i	0.253030	−	0.192349i	−0.470968	−	0.882150i	$-0.656095\pi$
$661$	4300.06	−	3268.82i	0.253030	−	0.192349i	0.723998	+	0.689802i	$0.242302\pi$
$662$	1451.84	−	8855.84i	0.0852378	−	0.519927i
$663$	5091.41	−	9603.42i	0.298241	−	0.562543i
$664$	4374.20	−	962.835i	0.255651	−	0.0562729i
$665$	20971.8	+	9702.59i	1.22293	+	0.565790i
$666$	298.552	+	749.309i	0.0173703	+	0.0435963i
$667$	161.165	+	2972.52i	0.00935584	+	0.172558i
$668$	−81.3759	−	120.020i	−0.00471336	−	0.00695169i
$669$	338.087	+	398.027i	0.0195384	+	0.0230024i
$670$	3702.44	+	6983.55i	0.213489	+	0.402684i
$671$	38639.3	−	13019.1i	2.22303	−	0.749027i
$672$	−565.146	+	10423.5i	−0.0324420	+	0.598357i
$673$	18896.6	−	11369.7i	1.08233	−	0.651217i	0.141448	−	0.989946i	$-0.454824\pi$
$673$	18896.6	−	11369.7i	1.08233	−	0.651217i	0.940884	+	0.338728i	$0.109997\pi$
$674$	−2769.39	−	9974.45i	−0.158269	−	0.570032i
$675$	363.937	−	1310.78i	0.0207525	−	0.0747437i
$676$	23243.7	+	13985.3i	1.32247	+	0.795704i
$677$	−15977.8	+	23565.5i	−0.907056	+	1.33781i	0.0339526	+	0.999423i	$0.489190\pi$
$677$	−15977.8	+	23565.5i	−0.907056	+	1.33781i	−0.941008	+	0.338384i	$0.890120\pi$
$678$	5574.32	−	606.243i	0.315753	−	0.0343402i
$679$	−35815.5	+	3895.17i	−2.02426	+	0.220151i
$680$	3590.31	−	5295.31i	0.202474	−	0.298626i
$681$	4570.10	+	2749.74i	0.257161	+	0.154729i
$682$	5402.52	−	19458.1i	0.303333	−	1.09251i
$683$	−683.053	−	2460.14i	−0.0382669	−	0.137825i	0.941949	−	0.335756i	$-0.108992\pi$
$683$	−683.053	−	2460.14i	−0.0382669	−	0.137825i	−0.980216	+	0.197931i	$0.936578\pi$
$684$	−6831.36	+	4110.29i	−0.381877	+	0.229767i
$685$	610.990	−	11269.1i	0.0340799	−	0.628567i
$686$	5521.14	−	1860.29i	0.307286	−	0.103537i
$687$	3585.03	+	6762.09i	0.199094	+	0.375531i
$688$	−3392.69	−	3994.18i	−0.188002	−	0.221333i
$689$	−23632.0	−	34854.7i	−1.30669	−	1.92722i
$690$	−21.1295	−	389.711i	−0.00116578	−	0.0215015i
$691$	1714.94	+	4304.18i	0.0944131	+	0.236959i	0.968597	−	0.248636i	$-0.0799823\pi$
$691$	1714.94	+	4304.18i	0.0944131	+	0.236959i	−0.874184	+	0.485595i	$0.838603\pi$
$692$	−13623.6	−	6302.95i	−0.748398	−	0.346246i
$693$	−11674.0	+	2569.65i	−0.639912	+	0.140855i
$694$	−2356.98	+	4445.73i	−0.128919	+	0.243167i
$695$	−3622.16	+	22094.2i	−0.197692	+	1.20587i
$696$	8208.91	−	6240.25i	0.447066	−	0.339851i
$697$	6118.91	−	2830.91i	0.332526	−	0.153843i
$698$	966.748	+	915.753i	0.0524240	+	0.0496587i
$699$	−476.083	−	2903.98i	−0.0257612	−	0.157137i
$700$	6720.60	+	2264.44i	0.362879	+	0.122268i
$701$	−11470.0	+	28787.5i	−0.617996	+	1.55105i	0.202428	+	0.979297i	$0.435117\pi$
$701$	−11470.0	+	28787.5i	−0.617996	+	1.55105i	−0.820424	+	0.571756i	$0.806262\pi$
$702$	−1667.49	+	1579.53i	−0.0896513	+	0.0849223i
$703$	−8548.30	−	6498.25i	−0.458613	−	0.348629i
$704$	−7238.51	−	1593.32i	−0.387516	−	0.0852988i
$705$	1656.62	−	1950.32i	0.0884990	−	0.104189i
$706$	−10600.5	−	1152.87i	−0.565091	−	0.0614574i
$707$	23606.5			1.25575
$708$	−5005.94	−	7816.42i	−0.265727	−	0.414914i
$709$	20736.2			1.09840			0.549200	−	0.835691i	$-0.314933\pi$
$709$	20736.2			1.09840			0.549200	+	0.835691i	$0.314933\pi$
$710$	−5524.87	−	600.866i	−0.292035	−	0.0317607i
$711$	−2719.50	+	3201.64i	−0.143445	+	0.168876i
$712$	2397.66	+	527.764i	0.126202	+	0.0277792i
$713$	3204.67	+	2436.12i	0.168325	+	0.127957i
$714$	−2242.99	+	2124.67i	−0.117566	+	0.111364i
$715$	−16179.4	+	40607.2i	−0.846259	+	2.12395i
$716$	8845.25	+	2980.31i	0.461679	+	0.155558i
$717$	−2459.89	−	15004.7i	−0.128126	−	0.781535i
$718$	−7005.42	−	6635.89i	−0.364122	−	0.344915i
$719$	10808.8	−	5000.69i	0.560641	−	0.259380i	−0.119038	−	0.992890i	$-0.537981\pi$
$719$	10808.8	−	5000.69i	0.560641	−	0.259380i	0.679679	+	0.733510i	$0.262119\pi$
$720$	2304.08	−	1751.51i	0.119261	−	0.0906598i
$721$	−2316.37	+	14129.3i	−0.119648	+	0.729821i
$722$	−5060.74	+	9545.56i	−0.260860	+	0.492035i
$723$	1975.25	−	434.786i	0.101605	−	0.0223650i
$724$	17270.2	+	7990.06i	0.886523	+	0.410149i
$725$	−3991.96	−	10019.1i	−0.204493	−	0.513240i
$726$	495.848	+	9145.38i	0.0253480	+	0.467516i
$727$	8481.49	+	12509.3i	0.432684	+	0.638161i	0.980054	−	0.198729i	$-0.0636815\pi$
$727$	8481.49	+	12509.3i	0.432684	+	0.638161i	−0.547370	+	0.836890i	$0.684371\pi$
$728$	−16834.9	−	19819.6i	−0.857066	−	1.00902i
$729$	341.470	+	644.080i	0.0173485	+	0.0327227i
$730$	−1085.04	+	365.592i	−0.0550124	+	0.0185358i
$731$	351.523	−	6483.46i	0.0177860	−	0.328043i
$732$	11107.7	−	6683.29i	0.560865	−	0.337461i
$733$	4303.75	+	15500.7i	0.216866	+	0.781079i	0.989289	+	0.145971i	$0.0466307\pi$
$733$	4303.75	+	15500.7i	0.216866	+	0.781079i	−0.772423	+	0.635108i	$0.780956\pi$
$734$	3572.40	−	12866.6i	0.179645	−	0.647025i
$735$	1822.06	+	1096.30i	0.0914392	+	0.0550171i
$736$	−1317.18	+	1942.70i	−0.0659673	+	0.0972946i
$737$	54114.3	−	5885.28i	2.70465	−	0.294148i
$738$	−1416.29	+	154.031i	−0.0706430	+	0.00768289i
$739$	8797.60	−	12975.5i	0.437923	−	0.645888i	−0.543125	−	0.839652i	$-0.682759\pi$
$739$	8797.60	−	12975.5i	0.437923	−	0.645888i	0.981048	+	0.193764i	$0.0620695\pi$
$740$	4181.87	+	2516.15i	0.207741	+	0.124994i
$741$	8180.09	−	29462.0i	0.405537	−	1.46061i
$742$	3202.16	+	11533.2i	0.158430	+	0.570614i
$743$	−2365.91	+	1423.52i	−0.116820	+	0.0702880i	−0.572764	−	0.819720i	$-0.694129\pi$
$743$	−2365.91	+	1423.52i	−0.116820	+	0.0702880i	0.455945	+	0.890008i	$0.349301\pi$
$744$	754.898	−	13923.3i	0.0371988	−	0.686091i
$745$	−25303.9	+	8525.89i	−1.24438	+	0.419281i
$746$	−2987.19	−	5634.44i	−0.146607	−	0.276530i
$747$	1625.21	+	1913.34i	0.0796028	+	0.0937156i
$748$	−11384.6	−	16791.0i	−0.556499	−	0.820775i
$749$	114.094	+	2104.35i	0.00556598	+	0.102659i
$750$	1821.80	+	4572.38i	0.0886972	+	0.222613i
$751$	−8886.63	−	4111.39i	−0.431794	−	0.199769i	0.191938	−	0.981407i	$-0.438523\pi$
$751$	−8886.63	−	4111.39i	−0.431794	−	0.199769i	−0.623733	+	0.781638i	$0.714385\pi$
$752$	−3590.22	+	790.268i	−0.174098	+	0.0383220i
$753$	4233.57	−	7985.37i	0.204887	−	0.386458i
$754$	−2945.95	+	17969.5i	−0.142288	+	0.867918i
$755$	5706.72	−	4338.14i	0.275085	−	0.209114i
$756$	−3449.16	+	1595.75i	−0.165932	+	0.0767684i
$757$	−13978.8	−	13241.4i	−0.671159	−	0.635756i	0.274243	−	0.961660i	$-0.411573\pi$
$757$	−13978.8	−	13241.4i	−0.671159	−	0.635756i	−0.945403	+	0.325904i	$0.894331\pi$
$758$	2176.99	+	13279.0i	0.104316	+	0.636301i
$759$	−2547.01	−	858.187i	−0.121806	−	0.0410411i
$760$	6661.36	−	16718.8i	0.317938	−	0.797965i
$761$	5420.01	−	5134.10i	0.258180	−	0.244561i	−0.547651	−	0.836707i	$-0.684478\pi$
$761$	5420.01	−	5134.10i	0.258180	−	0.244561i	0.805831	+	0.592146i	$0.201719\pi$
$762$	−2492.27	−	1894.57i	−0.118485	−	0.0900696i
$763$	−6260.02	−	1377.93i	−0.297022	−	0.0653795i
$764$	−5088.17	+	5990.26i	−0.240947	+	0.283665i
$765$	3564.87	+	387.703i	0.168481	+	0.0183234i
$766$	5905.48			0.278556
$767$	34553.9	+	8560.57i	1.62669	+	0.403004i
$768$	2030.15			0.0953863
$769$	−6192.45	−	673.470i	−0.290384	−	0.0315812i	−0.0382325	−	0.999269i	$-0.512173\pi$
$769$	−6192.45	−	673.470i	−0.290384	−	0.0315812i	−0.252152	+	0.967688i	$0.581138\pi$
$770$	8043.45	−	9469.48i	0.376449	−	0.443190i
$771$	19738.1	+	4344.69i	0.921986	+	0.202945i

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)

\(f(q)\)	\(=\)	\(q+(1.07661 + 0.117088i) q^{2} +(-1.94216 + 2.28649i) q^{3} +(-6.66759 - 1.46765i) q^{4} +(6.87670 + 5.22753i) q^{5} +(-2.35866 + 2.23424i) q^{6} +(7.63111 - 19.1526i) q^{7} +(-15.2167 - 5.12709i) q^{8} +(-1.45604 - 8.88144i) q^{9} +O(q^{10})\)	\(q+(1.07661 + 0.117088i) q^{2} +(-1.94216 + 2.28649i) q^{3} +(-6.66759 - 1.46765i) q^{4} +(6.87670 + 5.22753i) q^{5} +(-2.35866 + 2.23424i) q^{6} +(7.63111 - 19.1526i) q^{7} +(-15.2167 - 5.12709i) q^{8} +(-1.45604 - 8.88144i) q^{9} +(6.79142 + 6.43318i) q^{10} +(58.4670 - 27.0497i) q^{11} +(16.3053 - 12.3949i) q^{12} +(-12.7082 + 77.5166i) q^{13} +(10.4583 - 19.7264i) q^{14} +(-25.3083 + 5.57078i) q^{15} +(33.7876 + 15.6318i) q^{16} +(17.0727 + 42.8492i) q^{17} +(-0.527670 - 9.73231i) q^{18} +(72.8150 + 107.394i) q^{19} +(-38.1788 - 44.9476i) q^{20} +(28.9714 + 54.6459i) q^{21} +(66.1132 - 22.2761i) q^{22} +(-0.752907 + 13.8865i) q^{23} +(41.2762 - 24.8351i) q^{24} +(-13.4791 - 48.5474i) q^{25} +(-22.7580 + 81.9670i) q^{26} +(23.1351 + 13.9200i) q^{27} +(-78.9904 + 116.502i) q^{28} +(212.803 - 23.1437i) q^{29} +(-27.8994 + 3.03424i) q^{30} +(162.441 - 239.582i) q^{31} +(144.616 + 87.0123i) q^{32} +(-51.7034 + 186.219i) q^{33} +(13.3634 + 48.1308i) q^{34} +(152.598 - 91.8151i) q^{35} +(-3.32656 + 61.3548i) q^{36} +(-78.4246 + 26.4243i) q^{37} +(65.8186 + 124.147i) q^{38} +(-152.559 - 179.607i) q^{39} +(-77.8384 - 114.803i) q^{40} +(-7.91340 - 145.954i) q^{41} +(24.7925 + 62.2244i) q^{42} +(-127.758 - 59.1072i) q^{43} +(-429.534 + 94.5475i) q^{44} +(36.4153 - 68.6865i) q^{45} +(-2.43653 + 14.8622i) q^{46} +(-78.6113 + 59.7588i) q^{47} +(-101.363 + 46.8954i) q^{48} +(-59.5733 - 56.4308i) q^{49} +(-8.82740 - 53.8448i) q^{50} +(-131.132 - 44.1835i) q^{51} +(198.500 - 498.198i) q^{52} +(-389.201 + 368.670i) q^{53} +(23.2776 + 17.6952i) q^{54} +(543.463 + 119.625i) q^{55} +(-214.317 + 252.314i) q^{56} +(-386.973 - 42.0859i) q^{57} +231.815 q^{58} +(36.3787 - 451.725i) q^{59} +176.921 q^{60} +(629.215 + 68.4312i) q^{61} +(202.937 - 238.916i) q^{62} +(-181.214 - 39.8883i) q^{63} +(-91.5923 - 69.6266i) q^{64} +(-492.611 + 466.626i) q^{65} +(-77.4683 + 194.431i) q^{66} +(800.730 + 269.797i) q^{67} +(-50.9461 - 310.758i) q^{68} +(-30.2891 - 28.6914i) q^{69} +(175.038 - 80.9814i) q^{70} +(-472.947 + 359.525i) q^{71} +(-23.3799 + 142.611i) q^{72} +(-57.3315 + 108.139i) q^{73} +(-87.5265 + 19.2660i) q^{74} +(137.182 + 63.4670i) q^{75} +(-327.884 - 822.926i) q^{76} +(-71.9054 - 1326.22i) q^{77} +(-143.217 - 211.229i) q^{78} +(-302.167 - 355.738i) q^{79} +(150.631 + 284.121i) q^{80} +(-76.7599 + 25.8634i) q^{81} +(8.56986 - 158.062i) q^{82} +(-239.007 + 143.806i) q^{83} +(-112.969 - 406.876i) q^{84} +(-106.592 + 383.909i) q^{85} +(-130.625 - 78.5943i) q^{86} +(-360.379 + 531.519i) q^{87} +(-1028.36 + 111.841i) q^{88} +(-151.998 + 16.5308i) q^{89} +(47.2473 - 69.6846i) q^{90} +(1387.67 + 834.934i) q^{91} +(25.4006 - 91.4848i) q^{92} +(232.316 + 836.725i) q^{93} +(-91.6305 + 55.1323i) q^{94} +(-60.6790 + 1119.16i) q^{95} +(-479.819 + 161.670i) q^{96} +(-818.511 - 1543.88i) q^{97} +(-57.5296 - 67.7291i) q^{98} +(-325.371 - 479.886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 420q - 2q^{2} + 45q^{3} - 64q^{4} + 14q^{5} + 6q^{6} + 6q^{7} + 18q^{8} - 135q^{9} + O(q^{10}) \)	\( 420q - 2q^{2} + 45q^{3} - 64q^{4} + 14q^{5} + 6q^{6} + 6q^{7} + 18q^{8} - 135q^{9} + 854q^{10} + 32q^{11} + 192q^{12} - 22q^{13} - 884q^{14} - 42q^{15} - 268q^{16} - 56q^{17} - 18q^{18} - 112q^{19} - 250q^{20} + 243q^{21} + 108q^{22} + 16q^{23} - 54q^{24} - 197q^{25} - 328q^{26} + 405q^{27} + 236q^{28} - 54q^{29} - 126q^{30} + 66q^{31} + 857q^{32} - 96q^{33} + 112q^{34} + 532q^{35} - 576q^{36} + 110q^{37} + 56q^{38} + 66q^{39} - 6044q^{40} + 304q^{41} - 306q^{42} - 324q^{43} - 568q^{44} + 126q^{45} + 5842q^{46} + 4082q^{47} + 804q^{48} + 739q^{49} + 576q^{50} + 168q^{51} - 1372q^{52} - 1498q^{53} + 54q^{54} - 4422q^{55} - 12036q^{56} + 336q^{57} + 6298q^{58} - 3305q^{59} + 750q^{60} - 1718q^{61} - 4333q^{62} + 54q^{63} - 6250q^{64} - 5884q^{65} - 324q^{66} + 382q^{67} + 734q^{68} + 3780q^{69} + 8082q^{70} + 8638q^{71} + 162q^{72} + 8894q^{73} + 12428q^{74} + 243q^{75} - 15468q^{76} - 9916q^{77} + 984q^{78} - 578q^{79} + 24570q^{80} - 1215q^{81} - 1382q^{82} - 32q^{83} + 7557q^{84} + 708q^{85} + 2296q^{86} - 5928q^{87} - 17646q^{88} - 2284q^{89} + 378q^{90} + 11124q^{91} + 762q^{92} - 198q^{93} - 1232q^{94} + 24184q^{95} - 396q^{96} - 658q^{97} - 4356q^{98} + 288q^{99} + O(q^{100}) \)

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