LMFDB - Embedded newform 184.3.g.a.139.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [184,3,Mod(139,184)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(184, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("184.139");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 184 = 2^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	184.g (of order $2$, degree $1$, 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:	$5.01363686423$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.12
Character	$\chi$	$=$	184.139
Dual form			184.3.g.a.139.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54512 + 1.26989i) q^{2} +0.245976 q^{3} +(0.774772 - 3.92425i) q^{4} -4.88516i q^{5} +(-0.380062 + 0.312362i) q^{6} -0.635668i q^{7} +(3.78624 + 7.04730i) q^{8} -8.93950 q^{9} +O(q^{10})$	\(q+(-1.54512 + 1.26989i) q^{2} +0.245976 q^{3} +(0.774772 - 3.92425i) q^{4} -4.88516i q^{5} +(-0.380062 + 0.312362i) q^{6} -0.635668i q^{7} +(3.78624 + 7.04730i) q^{8} -8.93950 q^{9} +(6.20360 + 7.54814i) q^{10} -16.7594 q^{11} +(0.190576 - 0.965273i) q^{12} +18.0005i q^{13} +(0.807227 + 0.982182i) q^{14} -1.20163i q^{15} +(-14.7995 - 6.08080i) q^{16} -0.253600 q^{17} +(13.8126 - 11.3522i) q^{18} -24.4492 q^{19} +(-19.1706 - 3.78488i) q^{20} -0.156359i q^{21} +(25.8953 - 21.2826i) q^{22} -4.79583i q^{23} +(0.931326 + 1.73347i) q^{24} +1.13525 q^{25} +(-22.8586 - 27.8128i) q^{26} -4.41269 q^{27} +(-2.49452 - 0.492498i) q^{28} -52.8309i q^{29} +(1.52594 + 1.85666i) q^{30} +29.9736i q^{31} +(30.5888 - 9.39810i) q^{32} -4.12243 q^{33} +(0.391842 - 0.322044i) q^{34} -3.10534 q^{35} +(-6.92607 + 35.0808i) q^{36} -28.6474i q^{37} +(37.7769 - 31.0478i) q^{38} +4.42769i q^{39} +(34.4271 - 18.4964i) q^{40} -51.8018 q^{41} +(0.198559 + 0.241594i) q^{42} -63.6733 q^{43} +(-12.9848 + 65.7682i) q^{44} +43.6708i q^{45} +(6.09017 + 7.41012i) q^{46} +39.3858i q^{47} +(-3.64032 - 1.49573i) q^{48} +48.5959 q^{49} +(-1.75409 + 1.44164i) q^{50} -0.0623797 q^{51} +(70.6384 + 13.9463i) q^{52} -58.7879i q^{53} +(6.81813 - 5.60362i) q^{54} +81.8725i q^{55} +(4.47974 - 2.40679i) q^{56} -6.01394 q^{57} +(67.0893 + 81.6299i) q^{58} +84.9337 q^{59} +(-4.71551 - 0.930992i) q^{60} +14.4107i q^{61} +(-38.0630 - 46.3127i) q^{62} +5.68255i q^{63} +(-35.3288 + 53.3655i) q^{64} +87.9351 q^{65} +(6.36964 - 5.23502i) q^{66} -2.53300 q^{67} +(-0.196482 + 0.995191i) q^{68} -1.17966i q^{69} +(4.79811 - 3.94343i) q^{70} -65.9084i q^{71} +(-33.8471 - 62.9993i) q^{72} +38.9503 q^{73} +(36.3790 + 44.2636i) q^{74} +0.279244 q^{75} +(-18.9426 + 95.9449i) q^{76} +10.6534i q^{77} +(-5.62267 - 6.84130i) q^{78} +62.9371i q^{79} +(-29.7056 + 72.2977i) q^{80} +79.3700 q^{81} +(80.0399 - 65.7825i) q^{82} -129.115 q^{83} +(-0.613593 - 0.121143i) q^{84} +1.23888i q^{85} +(98.3828 - 80.8580i) q^{86} -12.9952i q^{87} +(-63.4553 - 118.109i) q^{88} -103.719 q^{89} +(-55.4570 - 67.4765i) q^{90} +11.4423 q^{91} +(-18.8200 - 3.71568i) q^{92} +7.37279i q^{93} +(-50.0155 - 60.8557i) q^{94} +119.438i q^{95} +(7.52413 - 2.31171i) q^{96} +118.786 q^{97} +(-75.0864 + 61.7114i) q^{98} +149.821 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 3 q^{6} + 15 q^{8} + 132 q^{9}+O(q^{10}) $ 44 * q - 3 * q^6 + 15 * q^8 + 132 * q^9	$ 44 q - 3 q^{6} + 15 q^{8} + 132 q^{9} + 26 q^{10} - 19 q^{12} - 8 q^{14} - 16 q^{16} - 8 q^{17} - 57 q^{18} + 40 q^{20} + 44 q^{22} - 88 q^{24} - 244 q^{25} + 19 q^{26} - 48 q^{27} + 6 q^{28} + 86 q^{30} + 160 q^{32} + 16 q^{33} + 18 q^{34} + 96 q^{35} + 179 q^{36} - 156 q^{38} + 130 q^{40} + 88 q^{41} + 100 q^{42} - 128 q^{43} - 158 q^{44} + 5 q^{48} - 340 q^{49} + 4 q^{50} + 160 q^{51} - 127 q^{52} + 53 q^{54} - 6 q^{56} - 176 q^{57} + 147 q^{58} + 16 q^{59} - 283 q^{62} - 405 q^{64} + 96 q^{65} - 602 q^{66} - 288 q^{67} + 72 q^{68} + 312 q^{70} - 57 q^{72} + 280 q^{73} - 198 q^{74} + 160 q^{75} + 172 q^{76} - 185 q^{78} - 90 q^{80} + 284 q^{81} - 75 q^{82} - 480 q^{83} - 254 q^{84} - 98 q^{86} + 204 q^{88} - 200 q^{89} + 488 q^{90} + 192 q^{91} + 19 q^{94} - 107 q^{96} + 184 q^{97} + 200 q^{98} + 256 q^{99}+O(q^{100}) $ 44 * q - 3 * q^6 + 15 * q^8 + 132 * q^9 + 26 * q^10 - 19 * q^12 - 8 * q^14 - 16 * q^16 - 8 * q^17 - 57 * q^18 + 40 * q^20 + 44 * q^22 - 88 * q^24 - 244 * q^25 + 19 * q^26 - 48 * q^27 + 6 * q^28 + 86 * q^30 + 160 * q^32 + 16 * q^33 + 18 * q^34 + 96 * q^35 + 179 * q^36 - 156 * q^38 + 130 * q^40 + 88 * q^41 + 100 * q^42 - 128 * q^43 - 158 * q^44 + 5 * q^48 - 340 * q^49 + 4 * q^50 + 160 * q^51 - 127 * q^52 + 53 * q^54 - 6 * q^56 - 176 * q^57 + 147 * q^58 + 16 * q^59 - 283 * q^62 - 405 * q^64 + 96 * q^65 - 602 * q^66 - 288 * q^67 + 72 * q^68 + 312 * q^70 - 57 * q^72 + 280 * q^73 - 198 * q^74 + 160 * q^75 + 172 * q^76 - 185 * q^78 - 90 * q^80 + 284 * q^81 - 75 * q^82 - 480 * q^83 - 254 * q^84 - 98 * q^86 + 204 * q^88 - 200 * q^89 + 488 * q^90 + 192 * q^91 + 19 * q^94 - 107 * q^96 + 184 * q^97 + 200 * q^98 + 256 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/184\mathbb{Z}\right)^\times$.

$n$	$47$	$93$	$97$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.54512	+	1.26989i	−0.772558	+	0.634944i
$2$	−1.54512	+	1.26989i	−0.772558	+	0.634944i
$3$	0.245976			0.0819922			0.0409961	−	0.999159i	$-0.486947\pi$
$3$	0.245976			0.0819922			0.0409961	+	0.999159i	$0.486947\pi$
$4$	0.774772	−	3.92425i	0.193693	−	0.981062i
$5$		−	4.88516i		−	0.977031i	−0.872555	−	0.488516i	$-0.837539\pi$
$5$		−	4.88516i		−	0.977031i	0.872555	−	0.488516i	$-0.162461\pi$
$6$	−0.380062	+	0.312362i	−0.0633437	+	0.0520604i
$7$		−	0.635668i		−	0.0908097i	−0.998969	−	0.0454049i	$-0.985542\pi$
$7$		−	0.635668i		−	0.0908097i	0.998969	−	0.0454049i	$-0.0144578\pi$
$8$	3.78624	+	7.04730i	0.473280	+	0.880912i
$9$	−8.93950			−0.993277
$10$	6.20360	+	7.54814i	0.620360	+	0.754814i
$11$	−16.7594			−1.52359			−0.761793	−	0.647820i	$-0.775681\pi$
$11$	−16.7594			−1.52359			−0.761793	+	0.647820i	$0.775681\pi$
$12$	0.190576	−	0.965273i	0.0158813	−	0.0804394i
$13$			18.0005i			1.38465i	0.721585	+	0.692326i	$0.243414\pi$
$13$			18.0005i			1.38465i	−0.721585	+	0.692326i	$0.756586\pi$
$14$	0.807227	+	0.982182i	0.0576591	+	0.0701558i
$15$		−	1.20163i		−	0.0801089i
$16$	−14.7995	−	6.08080i	−0.924966	−	0.380050i
$17$	−0.253600			−0.0149177			−0.00745884	−	0.999972i	$-0.502374\pi$
$17$	−0.253600			−0.0149177			−0.00745884	+	0.999972i	$0.502374\pi$
$18$	13.8126	−	11.3522i	0.767365	−	0.630675i
$19$	−24.4492			−1.28680			−0.643401	−	0.765529i	$-0.722477\pi$
$19$	−24.4492			−1.28680			−0.643401	+	0.765529i	$0.722477\pi$
$20$	−19.1706	−	3.78488i	−0.958528	−	0.189244i
$21$		−	0.156359i		−	0.00744569i
$22$	25.8953	−	21.2826i	1.17706	−	0.967391i
$23$		−	4.79583i		−	0.208514i
$23$		−	4.79583i		−	0.208514i
$24$	0.931326	+	1.73347i	0.0388053	+	0.0722279i
$25$	1.13525			0.0454099
$26$	−22.8586	−	27.8128i	−0.879176	−	1.06972i
$27$	−4.41269			−0.163433
$28$	−2.49452	−	0.492498i	−0.0890900	−	0.0175892i
$29$		−	52.8309i		−	1.82176i	−0.412677	−	0.910878i	$-0.635406\pi$
$29$		−	52.8309i		−	1.82176i	0.412677	−	0.910878i	$-0.364594\pi$
$30$	1.52594	+	1.85666i	0.0508646	+	0.0618888i
$31$			29.9736i			0.966889i	0.875375	+	0.483445i	$0.160615\pi$
$31$			29.9736i			0.966889i	−0.875375	+	0.483445i	$0.839385\pi$
$32$	30.5888	−	9.39810i	0.955900	−	0.293691i
$33$	−4.12243			−0.124922
$34$	0.391842	−	0.322044i	0.0115248	−	0.00947188i
$35$	−3.10534			−0.0887239
$36$	−6.92607	+	35.0808i	−0.192391	+	0.974467i
$37$		−	28.6474i		−	0.774254i	−0.922026	−	0.387127i	$-0.873467\pi$
$37$		−	28.6474i		−	0.774254i	0.922026	−	0.387127i	$-0.126533\pi$
$38$	37.7769	−	31.0478i	0.994130	−	0.817047i
$39$			4.42769i			0.113531i
$40$	34.4271	−	18.4964i	0.860679	−	0.462409i
$41$	−51.8018			−1.26346			−0.631730	−	0.775189i	$-0.717655\pi$
$41$	−51.8018			−1.26346			−0.631730	+	0.775189i	$0.717655\pi$
$42$	0.198559	+	0.241594i	0.00472759	+	0.00575223i
$43$	−63.6733			−1.48078			−0.740388	−	0.672180i	$-0.765358\pi$
$43$	−63.6733			−1.48078			−0.740388	+	0.672180i	$0.765358\pi$
$44$	−12.9848	+	65.7682i	−0.295108	+	1.49473i
$45$			43.6708i			0.970463i
$46$	6.09017	+	7.41012i	0.132395	+	0.161090i
$47$			39.3858i			0.837996i	0.907987	+	0.418998i	$0.137619\pi$
$47$			39.3858i			0.837996i	−0.907987	+	0.418998i	$0.862381\pi$
$48$	−3.64032	−	1.49573i	−0.0758400	−	0.0311611i
$49$	48.5959			0.991754
$50$	−1.75409	+	1.44164i	−0.0350818	+	0.0288328i
$51$	−0.0623797			−0.00122313
$52$	70.6384	+	13.9463i	1.35843	+	0.268197i
$53$		−	58.7879i		−	1.10921i	−0.832115	−	0.554603i	$-0.812870\pi$
$53$		−	58.7879i		−	1.10921i	0.832115	−	0.554603i	$-0.187130\pi$
$54$	6.81813	−	5.60362i	0.126262	−	0.103771i
$55$			81.8725i			1.48859i
$56$	4.47974	−	2.40679i	0.0799954	−	0.0429784i
$57$	−6.01394			−0.105508
$58$	67.0893	+	81.6299i	1.15671	+	1.40741i
$59$	84.9337			1.43955			0.719777	−	0.694205i	$-0.244244\pi$
$59$	84.9337			1.43955			0.719777	+	0.694205i	$0.244244\pi$
$60$	−4.71551	−	0.930992i	−0.0785918	−	0.0155165i
$61$			14.4107i			0.236241i	0.992999	+	0.118121i	$0.0376870\pi$
$61$			14.4107i			0.236241i	−0.992999	+	0.118121i	$0.962313\pi$
$62$	−38.0630	−	46.3127i	−0.613920	−	0.746978i
$63$			5.68255i			0.0901992i
$64$	−35.3288	+	53.3655i	−0.552012	+	0.833836i
$65$	87.9351			1.35285
$66$	6.36964	−	5.23502i	0.0965096	−	0.0793185i
$67$	−2.53300			−0.0378060			−0.0189030	−	0.999821i	$-0.506017\pi$
$67$	−2.53300			−0.0378060			−0.0189030	+	0.999821i	$0.506017\pi$
$68$	−0.196482	+	0.995191i	−0.00288945	+	0.0146352i
$69$		−	1.17966i		−	0.0170965i
$70$	4.79811	−	3.94343i	0.0685444	−	0.0563347i
$71$		−	65.9084i		−	0.928287i	−0.885760	−	0.464144i	$-0.846362\pi$
$71$		−	65.9084i		−	0.928287i	0.885760	−	0.464144i	$-0.153638\pi$
$72$	−33.8471	−	62.9993i	−0.470098	−	0.874990i
$73$	38.9503			0.533566			0.266783	−	0.963757i	$-0.414039\pi$
$73$	38.9503			0.533566			0.266783	+	0.963757i	$0.414039\pi$
$74$	36.3790	+	44.2636i	0.491608	+	0.598157i
$75$	0.279244			0.00372326
$76$	−18.9426	+	95.9449i	−0.249245	+	1.26243i
$77$			10.6534i			0.138356i
$78$	−5.62267	−	6.84130i	−0.0720855	−	0.0877090i
$79$			62.9371i			0.796672i	0.917240	+	0.398336i	$0.130412\pi$
$79$			62.9371i			0.796672i	−0.917240	+	0.398336i	$0.869588\pi$
$80$	−29.7056	+	72.2977i	−0.371320	+	0.903721i
$81$	79.3700			0.979877
$82$	80.0399	−	65.7825i	0.976096	−	0.802226i
$83$	−129.115			−1.55561			−0.777803	−	0.628508i	$-0.783666\pi$
$83$	−129.115			−1.55561			−0.777803	+	0.628508i	$0.783666\pi$
$84$	−0.613593	−	0.121143i	−0.00730468	−	0.00144218i
$85$			1.23888i			0.0145750i
$86$	98.3828	−	80.8580i	1.14399	−	0.940209i
$87$		−	12.9952i		−	0.149370i
$88$	−63.4553	−	118.109i	−0.721083	−	1.34215i
$89$	−103.719			−1.16539			−0.582693	−	0.812692i	$-0.698001\pi$
$89$	−103.719			−1.16539			−0.582693	+	0.812692i	$0.698001\pi$
$90$	−55.4570	−	67.4765i	−0.616189	−	0.749739i
$91$	11.4423			0.125740
$92$	−18.8200	−	3.71568i	−0.204566	−	0.0403878i
$93$			7.37279i			0.0792773i
$94$	−50.0155	−	60.8557i	−0.532080	−	0.647401i
$95$			119.438i			1.25725i
$96$	7.52413	−	2.31171i	0.0783763	−	0.0240803i
$97$	118.786			1.22460			0.612301	−	0.790625i	$-0.290244\pi$
$97$	118.786			1.22460			0.612301	+	0.790625i	$0.290244\pi$
$98$	−75.0864	+	61.7114i	−0.766188	+	0.629708i
$99$	149.821			1.51334
$100$	0.879559	−	4.45500i	0.00879559	−	0.0445500i
$101$		−	135.565i		−	1.34223i	−0.741355	−	0.671114i	$-0.765816\pi$
$101$		−	135.565i		−	1.34223i	0.741355	−	0.671114i	$-0.234184\pi$
$102$	0.0963840	−	0.0792152i	0.000944941	−	0.000776620i
$103$		−	95.2288i		−	0.924551i	−0.886736	−	0.462276i	$-0.847033\pi$
$103$		−	95.2288i		−	0.924551i	0.886736	−	0.462276i	$-0.152967\pi$
$104$	−126.855	+	68.1541i	−1.21976	+	0.655328i
$105$	−0.763840			−0.00727467
$106$	74.6540	+	90.8342i	0.704283	+	0.856926i
$107$	−142.223			−1.32919			−0.664595	−	0.747204i	$-0.731396\pi$
$107$	−142.223			−1.32919			−0.664595	+	0.747204i	$0.731396\pi$
$108$	−3.41883	+	17.3165i	−0.0316558	+	0.160338i
$109$			72.4948i			0.665090i	0.943087	+	0.332545i	$0.107907\pi$
$109$			72.4948i			0.665090i	−0.943087	+	0.332545i	$0.892093\pi$
$110$	−103.969	−	126.503i	−0.945172	−	1.15002i
$111$		−	7.04659i		−	0.0634828i
$112$	−3.86537	+	9.40754i	−0.0345122	+	0.0839959i
$113$	−46.3232			−0.409940			−0.204970	−	0.978768i	$-0.565710\pi$
$113$	−46.3232			−0.409940			−0.204970	+	0.978768i	$0.565710\pi$
$114$	9.29224	−	7.63702i	0.0815108	−	0.0669914i
$115$	−23.4284			−0.203725
$116$	−207.322	−	40.9319i	−1.78726	−	0.352861i
$117$		−	160.915i		−	1.37534i
$118$	−131.233	+	107.856i	−1.11214	+	0.914036i
$119$			0.161206i			0.00135467i
$120$	8.46827	−	4.54967i	0.0705689	−	0.0379139i
$121$	159.879			1.32131
$122$	−18.3000	−	22.2663i	−0.150000	−	0.182510i
$123$	−12.7420			−0.103594
$124$	117.624	+	23.2227i	0.948578	+	0.187280i
$125$		−	127.675i		−	1.02140i
$126$	−7.21620	−	8.78021i	−0.0572714	−	0.0696842i
$127$		−	54.1583i		−	0.426443i	−0.977004	−	0.213222i	$-0.931604\pi$
$127$		−	54.1583i		−	0.426443i	0.977004	−	0.213222i	$-0.0683957\pi$
$128$	−13.1811	−	127.320i	−0.102978	−	0.994684i
$129$	−15.6621			−0.121412
$130$	−135.870	+	111.668i	−1.04515	+	0.858983i
$131$	7.38200			0.0563511			0.0281756	−	0.999603i	$-0.491030\pi$
$131$	7.38200			0.0563511			0.0281756	+	0.999603i	$0.491030\pi$
$132$	−3.19394	+	16.1774i	−0.0241965	+	0.122556i
$133$			15.5416i			0.116854i
$134$	3.91379	−	3.21663i	0.0292074	−	0.0240047i
$135$			21.5567i			0.159679i
$136$	−0.960192	−	1.78720i	−0.00706024	−	0.0131412i
$137$	176.884			1.29112			0.645561	−	0.763709i	$-0.276624\pi$
$137$	176.884			1.29112			0.645561	+	0.763709i	$0.276624\pi$
$138$	1.49804	+	1.82272i	0.0108553	+	0.0132081i
$139$	−37.7629			−0.271676			−0.135838	−	0.990731i	$-0.543373\pi$
$139$	−37.7629			−0.271676			−0.135838	+	0.990731i	$0.543373\pi$
$140$	−2.40593	+	12.1861i	−0.0171852	+	0.0870437i
$141$			9.68798i			0.0687091i
$142$	83.6962	+	101.836i	0.589410	+	0.717156i
$143$		−	301.678i		−	2.10964i
$144$	132.300	+	54.3592i	0.918748	+	0.377495i
$145$	−258.087			−1.77991
$146$	−60.1828	+	49.4625i	−0.412211	+	0.338784i
$147$	11.9535			0.0813160
$148$	−112.420	−	22.1952i	−0.759592	−	0.149968i
$149$			260.886i			1.75092i	0.483294	+	0.875458i	$0.339440\pi$
$149$			260.886i			1.75092i	−0.483294	+	0.875458i	$0.660560\pi$
$150$	−0.431465	+	0.354609i	−0.00287643	+	0.00236406i
$151$			40.7112i			0.269611i	0.990872	+	0.134805i	$0.0430409\pi$
$151$			40.7112i			0.269611i	−0.990872	+	0.134805i	$0.956959\pi$
$152$	−92.5707	−	172.301i	−0.609018	−	1.13356i
$153$	2.26706			0.0148174
$154$	−13.5287	−	16.4608i	−0.0878486	−	0.106888i
$155$	146.426			0.944681
$156$	17.3754	+	3.43045i	0.111381	+	0.0219901i
$157$			26.8871i			0.171255i	0.996327	+	0.0856275i	$0.0272895\pi$
$157$			26.8871i			0.171255i	−0.996327	+	0.0856275i	$0.972710\pi$
$158$	−79.9230	−	97.2451i	−0.505842	−	0.615475i
$159$		−	14.4604i		−	0.0909462i
$160$	−45.9112	−	149.431i	−0.286945	−	0.933945i
$161$	−3.04856			−0.0189351
$162$	−122.636	+	100.791i	−0.757012	+	0.622167i
$163$	135.994			0.834317			0.417158	−	0.908834i	$-0.363026\pi$
$163$	135.994			0.834317			0.417158	+	0.908834i	$0.363026\pi$
$164$	−40.1346	+	203.283i	−0.244723	+	1.23953i
$165$			20.1387i			0.122053i
$166$	199.498	−	163.962i	1.20180	−	0.987722i
$167$			229.215i			1.37254i	0.727346	+	0.686271i	$0.240754\pi$
$167$			229.215i			1.37254i	−0.727346	+	0.686271i	$0.759246\pi$
$168$	1.10191	−	0.592014i	0.00655899	−	0.00352389i
$169$	−155.017			−0.917261
$170$	−1.57324	−	1.91421i	−0.00925432	−	0.0112601i
$171$	218.564			1.27815
$172$	−49.3323	+	249.870i	−0.286816	+	1.45273i
$173$			87.0344i			0.503089i	0.967846	+	0.251545i	$0.0809385\pi$
$173$			87.0344i			0.503089i	−0.967846	+	0.251545i	$0.919061\pi$
$174$	16.5024	+	20.0790i	0.0948413	+	0.115397i
$175$		−	0.721641i		−	0.00412366i
$176$	248.031	+	101.911i	1.40927	+	0.579039i
$177$	20.8917			0.118032
$178$	160.258	−	131.712i	0.900329	−	0.739954i
$179$	136.339			0.761668			0.380834	−	0.924643i	$-0.375637\pi$
$179$	136.339			0.761668			0.380834	+	0.924643i	$0.375637\pi$
$180$	171.375	+	33.8349i	0.952085	+	0.187972i
$181$			101.555i			0.561075i	0.959843	+	0.280538i	$0.0905127\pi$
$181$			101.555i			0.561075i	−0.959843	+	0.280538i	$0.909487\pi$
$182$	−17.6797	+	14.5305i	−0.0971414	+	0.0798377i
$183$			3.54470i			0.0193699i
$184$	33.7976	−	18.1582i	0.183683	−	0.0986857i
$185$	−139.947			−0.756471
$186$	−9.36261	−	11.3918i	−0.0503366	−	0.0612464i
$187$	4.25020			0.0227284
$188$	154.560	+	30.5150i	0.822126	+	0.162314i
$189$			2.80501i			0.0148413i
$190$	−151.673	−	184.546i	−0.798280	−	0.971296i
$191$		−	44.7448i		−	0.234266i	−0.993116	−	0.117133i	$-0.962630\pi$
$191$		−	44.7448i		−	0.234266i	0.993116	−	0.117133i	$-0.0373704\pi$
$192$	−8.69004	+	13.1267i	−0.0452606	+	0.0683680i
$193$	−255.698			−1.32486			−0.662431	−	0.749123i	$-0.730475\pi$
$193$	−255.698			−1.32486			−0.662431	+	0.749123i	$0.730475\pi$
$194$	−183.539	+	150.845i	−0.946077	+	0.777554i
$195$	21.6300			0.110923
$196$	37.6508	−	190.703i	0.192096	−	0.972972i
$197$		−	222.634i		−	1.13012i	−0.825049	−	0.565061i	$-0.808853\pi$
$197$		−	222.634i		−	1.13012i	0.825049	−	0.565061i	$-0.191147\pi$
$198$	−231.491	+	190.256i	−1.16915	+	0.960888i
$199$		−	74.3564i		−	0.373650i	−0.982393	−	0.186825i	$-0.940180\pi$
$199$		−	74.3564i		−	0.373650i	0.982393	−	0.186825i	$-0.0598198\pi$
$200$	4.29832	+	8.00043i	0.0214916	+	0.0400022i
$201$	−0.623059			−0.00309980
$202$	172.152	+	209.464i	0.852239	+	1.03695i
$203$	−33.5829			−0.165433
$204$	−0.0483301	+	0.244794i	−0.000236912	+	0.00119997i
$205$			253.060i			1.23444i
$206$	120.930	+	147.140i	0.587038	+	0.714270i
$207$			42.8723i			0.207113i
$208$	109.457	−	266.397i	0.526237	−	1.28076i
$209$	409.756			1.96055
$210$	1.18022	−	0.969991i	0.00562011	−	0.00461900i
$211$	−307.307			−1.45643			−0.728215	−	0.685348i	$-0.759650\pi$
$211$	−307.307			−1.45643			−0.728215	+	0.685348i	$0.759650\pi$
$212$	−230.698	−	45.5472i	−1.08820	−	0.214845i
$213$		−	16.2119i		−	0.0761123i
$214$	219.752	−	180.608i	1.02688	−	0.843961i
$215$			311.054i			1.44676i
$216$	−16.7075	−	31.0976i	−0.0773496	−	0.143970i
$217$	19.0532			0.0878029
$218$	−92.0603	−	112.013i	−0.422295	−	0.513821i
$219$	9.58086			0.0437482
$220$	321.288	+	63.4325i	1.46040	+	0.288330i
$221$		−	4.56493i		−	0.0206558i
$222$	8.94837	+	10.8878i	0.0403080	+	0.0490441i
$223$		−	176.917i		−	0.793351i	−0.917959	−	0.396676i	$-0.870164\pi$
$223$		−	176.917i		−	0.793351i	0.917959	−	0.396676i	$-0.129836\pi$
$224$	−5.97407	−	19.4443i	−0.0266700	−	0.0868051i
$225$	−10.1485			−0.0451047
$226$	71.5748	−	58.8253i	0.316702	−	0.260289i
$227$	−9.52657			−0.0419673			−0.0209836	−	0.999780i	$-0.506680\pi$
$227$	−9.52657			−0.0419673			−0.0209836	+	0.999780i	$0.506680\pi$
$228$	−4.65943	+	23.6002i	−0.0204361	+	0.103510i
$229$			63.9221i			0.279136i	0.990213	+	0.139568i	$0.0445713\pi$
$229$			63.9221i			0.279136i	−0.990213	+	0.139568i	$0.955429\pi$
$230$	36.1996	−	29.7514i	0.157390	−	0.129354i
$231$			2.62050i			0.0113441i
$232$	372.315	−	200.031i	1.60481	−	0.862201i
$233$	−177.826			−0.763202			−0.381601	−	0.924327i	$-0.624627\pi$
$233$	−177.826			−0.763202			−0.381601	+	0.924327i	$0.624627\pi$
$234$	204.344	+	248.633i	0.873266	+	1.06253i
$235$	192.406			0.818748
$236$	65.8043	−	333.301i	0.278832	−	1.41229i
$237$			15.4810i			0.0653208i
$238$	−0.204713	−	0.249082i	−0.000860139	−	0.00104656i
$239$		−	118.872i		−	0.497374i	−0.968584	−	0.248687i	$-0.920001\pi$
$239$		−	118.872i		−	0.497374i	0.968584	−	0.248687i	$-0.0799991\pi$
$240$	−7.30689	+	17.7835i	−0.0304454	+	0.0740980i
$241$	−207.839			−0.862403			−0.431202	−	0.902256i	$-0.641910\pi$
$241$	−207.839			−0.862403			−0.431202	+	0.902256i	$0.641910\pi$
$242$	−247.032	+	203.028i	−1.02079	+	0.838960i
$243$	59.2374			0.243775
$244$	56.5513	+	11.1650i	0.231768	+	0.0457583i
$245$		−	237.399i		−	0.968974i
$246$	19.6879	−	16.1810i	0.0800323	−	0.0657762i
$247$		−	440.098i		−	1.78177i
$248$	−211.233	+	113.487i	−0.851744	+	0.457609i
$249$	−31.7593			−0.127548
$250$	162.133	+	197.272i	0.648530	+	0.789090i
$251$	−451.091			−1.79717			−0.898587	−	0.438796i	$-0.855405\pi$
$251$	−451.091			−1.79717			−0.898587	+	0.438796i	$0.855405\pi$
$252$	22.2997	+	4.40268i	0.0884911	+	0.0174710i
$253$			80.3755i			0.317690i
$254$	68.7750	+	83.6809i	0.270768	+	0.329452i
$255$			0.304735i			0.00119504i
$256$	182.048	+	179.985i	0.711124	+	0.703066i
$257$	105.943			0.412230			0.206115	−	0.978528i	$-0.433918\pi$
$257$	105.943			0.412230			0.206115	+	0.978528i	$0.433918\pi$
$258$	24.1998	−	19.8892i	0.0937978	−	0.0770898i
$259$	−18.2102			−0.0703098
$260$	68.1297	−	345.079i	0.262037	−	1.32723i
$261$			472.282i			1.80951i
$262$	−11.4060	+	9.37431i	−0.0435345	+	0.0357798i
$263$		−	48.5726i		−	0.184687i	−0.995727	−	0.0923433i	$-0.970564\pi$
$263$		−	48.5726i		−	0.184687i	0.995727	−	0.0923433i	$-0.0294357\pi$
$264$	−15.6085	−	29.0520i	−0.0591231	−	0.110045i
$265$	−287.188			−1.08373
$266$	−19.7361	−	24.0136i	−0.0741958	−	0.0902767i
$267$	−25.5125			−0.0955525
$268$	−1.96250	+	9.94014i	−0.00732276	+	0.0370901i
$269$			447.913i			1.66510i	0.553947	+	0.832552i	$0.313121\pi$
$269$			447.913i			1.66510i	−0.553947	+	0.832552i	$0.686879\pi$
$270$	−27.3746	−	33.3076i	−0.101387	−	0.123362i
$271$		−	254.776i		−	0.940134i	−0.882631	−	0.470067i	$-0.844230\pi$
$271$		−	254.776i		−	0.940134i	0.882631	−	0.470067i	$-0.155770\pi$
$272$	3.75315	+	1.54209i	0.0137983	+	0.00566946i
$273$	2.81454			0.0103097
$274$	−273.306	+	224.622i	−0.997467	+	0.819790i
$275$	−19.0261			−0.0691860
$276$	−4.62929	−	0.913969i	−0.0167728	−	0.00331148i
$277$		−	134.568i		−	0.485805i	−0.970051	−	0.242903i	$-0.921900\pi$
$277$		−	134.568i		−	0.485805i	0.970051	−	0.242903i	$-0.0780995\pi$
$278$	58.3481	−	47.9546i	0.209885	−	0.172499i
$279$		−	267.949i		−	0.960389i
$280$	−11.7576	−	21.8842i	−0.0419913	−	0.0781580i
$281$	−138.880			−0.494236			−0.247118	−	0.968985i	$-0.579484\pi$
$281$	−138.880			−0.494236			−0.247118	+	0.968985i	$0.579484\pi$
$282$	−12.3026	−	14.9691i	−0.0436264	−	0.0530818i
$283$	154.457			0.545785			0.272893	−	0.962044i	$-0.412020\pi$
$283$	154.457			0.545785			0.272893	+	0.962044i	$0.412020\pi$
$284$	−258.641	−	51.0640i	−0.910707	−	0.179803i
$285$			29.3790i			0.103084i
$286$	383.097	+	466.128i	1.33950	+	1.62982i
$287$			32.9288i			0.114734i
$288$	−273.449	+	84.0143i	−0.949474	+	0.291716i
$289$	−288.936			−0.999777
$290$	398.775	−	327.742i	1.37509	−	1.13014i
$291$	29.2187			0.100408
$292$	30.1776	−	152.851i	0.103348	−	0.523461i
$293$		−	31.2735i		−	0.106735i	−0.998575	−	0.0533677i	$-0.983004\pi$
$293$		−	31.2735i		−	0.106735i	0.998575	−	0.0533677i	$-0.0169956\pi$
$294$	−18.4695	+	15.1795i	−0.0628214	+	0.0516311i
$295$		−	414.914i		−	1.40649i
$296$	201.887	−	108.466i	0.682050	−	0.366439i
$297$	73.9543			0.249004
$298$	−331.296	−	403.100i	−1.11173	−	1.35268i
$299$	86.3273			0.288720
$300$	0.216351	−	1.09582i	0.000721169	−	0.00365275i
$301$			40.4751i			0.134469i
$302$	−51.6987	−	62.9036i	−0.171188	−	0.208290i
$303$		−	33.3458i		−	0.110052i
$304$	361.835	+	148.671i	1.19025	+	0.489049i
$305$	70.3987			0.230815
$306$	−3.50287	+	2.87891i	−0.0114473	+	0.00940820i
$307$	50.7041			0.165160			0.0825799	−	0.996584i	$-0.473684\pi$
$307$	50.7041			0.165160			0.0825799	+	0.996584i	$0.473684\pi$
$308$	41.8068	+	8.25399i	0.135736	+	0.0267987i
$309$		−	23.4240i		−	0.0758059i
$310$	−226.245	+	185.944i	−0.729821	+	0.599819i
$311$			582.285i			1.87230i	0.351603	+	0.936149i	$0.385637\pi$
$311$			582.285i			1.87230i	−0.351603	+	0.936149i	$0.614363\pi$
$312$	−31.2033	+	16.7643i	−0.100010	+	0.0537318i
$313$	−123.468			−0.394465			−0.197232	−	0.980357i	$-0.563195\pi$
$313$	−123.468			−0.394465			−0.197232	+	0.980357i	$0.563195\pi$
$314$	−34.1435	−	41.5436i	−0.108737	−	0.132305i
$315$	27.7602			0.0881275
$316$	246.981	+	48.7619i	0.781585	+	0.154310i
$317$			208.509i			0.657758i	0.944372	+	0.328879i	$0.106671\pi$
$317$			208.509i			0.657758i	−0.944372	+	0.328879i	$0.893329\pi$
$318$	18.3631	+	22.3431i	0.0577457	+	0.0702612i
$319$			885.417i			2.77560i
$320$	260.699	+	172.587i	0.814684	+	0.539333i
$321$	−34.9836			−0.108983
$322$	4.71038	−	3.87132i	0.0146285	−	0.0120227i
$323$	6.20034			0.0191961
$324$	61.4937	−	311.468i	0.189795	−	0.961320i
$325$			20.4350i			0.0628770i
$326$	−210.126	+	172.697i	−0.644558	+	0.529744i
$327$			17.8320i			0.0545322i
$328$	−196.134	−	365.063i	−0.597970	−	1.11300i
$329$	25.0363			0.0760982
$330$	−25.5739	−	31.1167i	−0.0774967	−	0.0942929i
$331$	−199.703			−0.603331			−0.301665	−	0.953414i	$-0.597543\pi$
$331$	−199.703			−0.603331			−0.301665	+	0.953414i	$0.597543\pi$
$332$	−100.035	+	506.681i	−0.301310	+	1.52615i
$333$			256.093i			0.769049i
$334$	−291.077	−	354.163i	−0.871487	−	1.06037i
$335$			12.3741i			0.0369377i
$336$	−0.950790	+	2.31403i	−0.00282973	+	0.00688701i
$337$	−335.306			−0.994974			−0.497487	−	0.867472i	$-0.665744\pi$
$337$	−335.306			−0.994974			−0.497487	+	0.867472i	$0.665744\pi$
$338$	239.520	−	196.854i	0.708638	−	0.582409i
$339$	−11.3944			−0.0336119
$340$	4.86166	+	0.959848i	0.0142990	+	0.00282308i
$341$		−	502.340i		−	1.47314i
$342$	−337.707	+	277.551i	−0.987446	+	0.811554i
$343$		−	62.0386i		−	0.180871i
$344$	−241.083	−	448.725i	−0.700822	−	1.30443i
$345$	−5.76283			−0.0167039
$346$	−110.524	−	134.478i	−0.319433	−	0.388666i
$347$	150.724			0.434362			0.217181	−	0.976131i	$-0.430314\pi$
$347$	150.724			0.434362			0.217181	+	0.976131i	$0.430314\pi$
$348$	−50.9962	−	10.0683i	−0.146541	−	0.0289319i
$349$		−	190.653i		−	0.546284i	−0.961974	−	0.273142i	$-0.911937\pi$
$349$		−	190.653i		−	0.546284i	0.961974	−	0.273142i	$-0.0880629\pi$
$350$	0.916403	+	1.11502i	0.00261829	+	0.00318577i
$351$		−	79.4306i		−	0.226298i
$352$	−512.652	+	157.507i	−1.45640	+	0.447463i
$353$	−390.652			−1.10666			−0.553332	−	0.832961i	$-0.686644\pi$
$353$	−390.652			−1.10666			−0.553332	+	0.832961i	$0.686644\pi$
$354$	−32.2801	+	26.5301i	−0.0911868	+	0.0749438i
$355$	−321.973			−0.906966
$356$	−80.3588	+	407.020i	−0.225727	+	1.14332i
$357$			0.0396528i			0.000111072i
$358$	−210.659	+	173.135i	−0.588433	+	0.483616i
$359$		−	436.136i		−	1.21486i	−0.794372	−	0.607432i	$-0.792200\pi$
$359$		−	436.136i		−	1.21486i	0.794372	−	0.607432i	$-0.207800\pi$
$360$	−307.761	+	165.348i	−0.854892	+	0.459301i
$361$	236.765			0.655859
$362$	−128.963	−	156.914i	−0.356251	−	0.433463i
$363$	39.3265			0.108337
$364$	8.86520	−	44.9025i	0.0243549	−	0.123359i
$365$		−	190.278i		−	0.521310i
$366$	−4.50137	−	5.47698i	−0.0122988	−	0.0149644i
$367$			230.803i			0.628891i	0.949276	+	0.314445i	$0.101819\pi$
$367$			230.803i			0.628891i	−0.949276	+	0.314445i	$0.898181\pi$
$368$	−29.1625	+	70.9757i	−0.0792459	+	0.192869i
$369$	463.082			1.25497
$370$	216.235	−	177.717i	0.584418	−	0.480316i
$371$	−37.3696			−0.100727
$372$	28.9327	+	5.71223i	0.0777760	+	0.0153555i
$373$		−	508.922i		−	1.36440i	−0.731165	−	0.682201i	$-0.761023\pi$
$373$		−	508.922i		−	1.36440i	0.731165	−	0.682201i	$-0.238977\pi$
$374$	−6.56706	+	5.39728i	−0.0175590	+	0.0144312i
$375$		−	31.4050i		−	0.0837466i
$376$	−277.563	+	149.124i	−0.738201	+	0.396607i
$377$	950.981			2.52250
$378$	−3.56205	−	4.33407i	−0.00942340	−	0.0114658i
$379$	−208.036			−0.548909			−0.274454	−	0.961600i	$-0.588497\pi$
$379$	−208.036			−0.548909			−0.274454	+	0.961600i	$0.588497\pi$
$380$	468.706	+	92.5375i	1.23344	+	0.243520i
$381$		−	13.3217i		−	0.0349650i
$382$	56.8209	+	69.1360i	0.148746	+	0.180984i
$383$		−	552.136i		−	1.44161i	−0.693139	−	0.720804i	$-0.743773\pi$
$383$		−	552.136i		−	1.44161i	0.693139	−	0.720804i	$-0.256227\pi$
$384$	−3.24225	−	31.3176i	−0.00844336	−	0.0815563i
$385$	52.0438			0.135179
$386$	395.084	−	324.708i	1.02353	−	0.841213i
$387$	569.208			1.47082
$388$	92.0324	−	466.147i	0.237197	−	1.20141i
$389$		−	422.016i		−	1.08487i	−0.840097	−	0.542437i	$-0.817502\pi$
$389$		−	422.016i		−	1.08487i	0.840097	−	0.542437i	$-0.182498\pi$
$390$	−33.4208	+	27.4676i	−0.0856945	+	0.0704298i
$391$			1.21622i			0.00311055i
$392$	183.996	+	342.470i	0.469377	+	0.873648i
$393$	1.81580			0.00462035
$394$	282.720	+	343.996i	0.717564	+	0.873085i
$395$	307.457			0.778373
$396$	116.077	−	587.935i	0.293124	−	1.48468i
$397$			439.410i			1.10683i	0.832907	+	0.553413i	$0.186675\pi$
$397$			439.410i			1.10683i	−0.832907	+	0.553413i	$0.813325\pi$
$398$	94.4242	+	114.889i	0.237247	+	0.288667i
$399$			3.82287i			0.00958112i
$400$	−16.8011	−	6.90321i	−0.0420027	−	0.0172580i
$401$	−202.853			−0.505869			−0.252934	−	0.967483i	$-0.581396\pi$
$401$	−202.853			−0.505869			−0.252934	+	0.967483i	$0.581396\pi$
$402$	0.962700	−	0.791215i	0.00239478	−	0.00196820i
$403$	−539.538			−1.33881
$404$	−531.991	−	105.032i	−1.31681	−	0.259980i
$405$		−	387.735i		−	0.957371i
$406$	51.8895	−	42.6465i	0.127807	−	0.105041i
$407$			480.115i			1.17964i
$408$	−0.236185	−	0.439608i	−0.000578884	−	0.00107747i
$409$	−96.8387			−0.236769			−0.118385	−	0.992968i	$-0.537772\pi$
$409$	−96.8387			−0.236769			−0.118385	+	0.992968i	$0.537772\pi$
$410$	−321.358	−	391.007i	−0.783800	−	0.953677i
$411$	43.5092			0.105862
$412$	−373.701	−	73.7806i	−0.907042	−	0.179079i
$413$		−	53.9897i		−	0.130726i
$414$	−54.4430	−	66.2427i	−0.131505	−	0.160007i
$415$			630.748i			1.51988i
$416$	169.170	+	550.613i	0.406659	+	1.32359i
$417$	−9.28879			−0.0222753
$418$	−633.120	+	520.344i	−1.51464	+	1.24484i
$419$	342.596			0.817651			0.408825	−	0.912613i	$-0.365939\pi$
$419$	342.596			0.817651			0.408825	+	0.912613i	$0.365939\pi$
$420$	−0.591802	+	2.99750i	−0.00140905	+	0.00713690i
$421$		−	296.426i		−	0.704101i	−0.935981	−	0.352050i	$-0.885485\pi$
$421$		−	296.426i		−	0.704101i	0.935981	−	0.352050i	$-0.114515\pi$
$422$	474.825	−	390.245i	1.12518	−	0.924751i
$423$		−	352.089i		−	0.832362i
$424$	414.296	−	222.585i	0.977113	−	0.524965i
$425$	−0.287899			−0.000677411
$426$	20.5873	+	25.0493i	0.0483270	+	0.0588012i
$427$	9.16044			0.0214530
$428$	−110.191	+	558.120i	−0.257455	+	1.30402i
$429$		−	74.2057i		−	0.172974i
$430$	−395.004	−	480.615i	−0.918614	−	1.11771i
$431$			211.905i			0.491660i	0.969313	+	0.245830i	$0.0790604\pi$
$431$			211.905i			0.491660i	−0.969313	+	0.245830i	$0.920940\pi$
$432$	65.3055	+	26.8327i	0.151170	+	0.0621127i
$433$	−156.430			−0.361271			−0.180635	−	0.983550i	$-0.557815\pi$
$433$	−156.430			−0.361271			−0.180635	+	0.983550i	$0.557815\pi$
$434$	−29.4395	+	24.1955i	−0.0678329	+	0.0557499i
$435$	−63.4834			−0.145939
$436$	284.488	+	56.1670i	0.652495	+	0.128823i
$437$			117.254i			0.268317i
$438$	−14.8035	+	12.1666i	−0.0337980	+	0.0277776i
$439$		−	783.786i		−	1.78539i	−0.450661	−	0.892695i	$-0.648812\pi$
$439$		−	783.786i		−	1.78539i	0.450661	−	0.892695i	$-0.351188\pi$
$440$	−576.980	+	309.989i	−1.31132	+	0.704521i
$441$	−434.423			−0.985086
$442$	5.79695	+	7.05335i	0.0131153	+	0.0159578i
$443$	−212.023			−0.478607			−0.239304	−	0.970945i	$-0.576919\pi$
$443$	−212.023			−0.478607			−0.239304	+	0.970945i	$0.576919\pi$
$444$	−27.6526	−	5.45950i	−0.0622805	−	0.0122962i
$445$			506.685i			1.13862i
$446$	224.665	+	273.358i	0.503734	+	0.612910i
$447$			64.1719i			0.143561i
$448$	33.9228	+	22.4574i	0.0757204	+	0.0501281i
$449$	426.299			0.949440			0.474720	−	0.880137i	$-0.342549\pi$
$449$	426.299			0.949440			0.474720	+	0.880137i	$0.342549\pi$
$450$	15.6807	−	12.8875i	0.0348460	−	0.0286389i
$451$	868.170			1.92499
$452$	−35.8899	+	181.784i	−0.0794025	+	0.402176i
$453$			10.0140i			0.0221060i
$454$	14.7197	−	12.0977i	0.0324222	−	0.0266468i
$455$		−	55.8976i		−	0.122852i
$456$	−22.7702	−	42.3820i	−0.0499347	−	0.0929430i
$457$	787.075			1.72226			0.861132	−	0.508381i	$-0.169756\pi$
$457$	787.075			1.72226			0.861132	+	0.508381i	$0.169756\pi$
$458$	−81.1738	−	98.7671i	−0.177235	−	0.215649i
$459$	1.11906			0.00243804
$460$	−18.1517	+	91.9388i	−0.0394601	+	0.199867i
$461$			179.041i			0.388375i	0.980964	+	0.194188i	$0.0622071\pi$
$461$			179.041i			0.388375i	−0.980964	+	0.194188i	$0.937793\pi$
$462$	−3.32774	−	4.04897i	−0.00720289	−	0.00876401i
$463$			582.563i			1.25824i	0.777310	+	0.629118i	$0.216584\pi$
$463$			582.563i			1.25824i	−0.777310	+	0.629118i	$0.783416\pi$
$464$	−321.254	+	781.869i	−0.692358	+	1.68506i
$465$	36.0172			0.0774564
$466$	274.762	−	225.819i	0.589618	−	0.484590i
$467$	48.2342			0.103285			0.0516426	−	0.998666i	$-0.483554\pi$
$467$	48.2342			0.103285			0.0516426	+	0.998666i	$0.483554\pi$
$468$	−631.471	−	124.673i	−1.34930	−	0.266394i
$469$			1.61015i			0.00343316i
$470$	−297.290	+	244.334i	−0.632531	+	0.519859i
$471$			6.61358i			0.0140416i
$472$	321.580	+	598.553i	0.681313	+	1.26812i
$473$	1067.13			2.25609
$474$	−19.6592	−	23.9200i	−0.0414751	−	0.0504642i
$475$	−27.7560			−0.0584336
$476$	0.632611	+	0.124898i	0.00132902	+	0.000262390i
$477$			525.534i			1.10175i
$478$	150.955	+	183.672i	0.315805	+	0.384251i
$479$			416.452i			0.869420i	0.900570	+	0.434710i	$0.143149\pi$
$479$			416.452i			0.869420i	−0.900570	+	0.434710i	$0.856851\pi$
$480$	−11.2931	−	36.7565i	−0.0235272	−	0.0765761i
$481$	515.667			1.07207
$482$	321.136	−	263.932i	0.666257	−	0.547578i
$483$	−0.749873			−0.00155253
$484$	123.870	−	627.405i	0.255929	−	1.29629i
$485$		−	580.290i		−	1.19647i
$486$	−91.5287	+	75.2248i	−0.188331	+	0.154784i
$487$			646.073i			1.32664i	0.748336	+	0.663320i	$0.230853\pi$
$487$			646.073i			1.32664i	−0.748336	+	0.663320i	$0.769147\pi$
$488$	−101.557	+	54.5625i	−0.208108	+	0.111808i
$489$	33.4512			0.0684074
$490$	301.470	+	366.809i	0.615244	+	0.748589i
$491$	585.821			1.19312			0.596560	−	0.802569i	$-0.296534\pi$
$491$	585.821			1.19312			0.596560	+	0.802569i	$0.296534\pi$
$492$	−9.87217	+	50.0029i	−0.0200654	+	0.101632i
$493$			13.3979i			0.0271763i
$494$	558.875	+	680.003i	1.13133	+	1.37652i
$495$		−	731.899i		−	1.47858i
$496$	182.263	−	443.592i	0.367466	−	0.894340i
$497$	−41.8959			−0.0842975
$498$	49.0719	−	40.3308i	0.0985379	−	0.0809855i
$499$	1.38299			0.00277153			0.00138576	−	0.999999i	$-0.499559\pi$
$499$	1.38299			0.00277153			0.00138576	+	0.999999i	$0.499559\pi$
$500$	−501.028	−	98.9188i	−1.00206	−	0.197838i
$501$			56.3814i			0.112538i
$502$	696.988	−	572.834i	1.38842	−	1.14110i
$503$			213.583i			0.424619i	0.977202	+	0.212309i	$0.0680985\pi$
$503$			213.583i			0.424619i	−0.977202	+	0.212309i	$0.931902\pi$
$504$	−40.0466	+	21.5155i	−0.0794576	+	0.0426895i
$505$	−662.256			−1.31140
$506$	−102.068	−	124.190i	−0.201715	−	0.245434i
$507$	−38.1306			−0.0752082
$508$	−212.531	−	41.9603i	−0.418368	−	0.0825991i
$509$			847.860i			1.66574i	0.553472	+	0.832868i	$0.313303\pi$
$509$			847.860i			1.66574i	−0.553472	+	0.832868i	$0.686697\pi$
$510$	−0.386979	−	0.470851i	−0.000758782	−	0.000923237i
$511$		−	24.7595i		−	0.0484530i
$512$	−509.846	−	46.9175i	−0.995793	−	0.0916358i
$513$	107.887			0.210306
$514$	−163.695	+	134.536i	−0.318472	+	0.261743i
$515$	−465.207			−0.903315
$516$	−12.1346	+	61.4622i	−0.0235166	+	0.119113i
$517$		−	660.084i		−	1.27676i
$518$	28.1370	−	23.1250i	0.0543184	−	0.0446428i
$519$			21.4084i			0.0412494i
$520$	332.944	+	619.705i	0.640276	+	1.19174i
$521$	808.045			1.55095			0.775475	−	0.631379i	$-0.217511\pi$
$521$	808.045			1.55095			0.775475	+	0.631379i	$0.217511\pi$
$522$	−599.744	−	729.730i	−1.14894	−	1.39795i
$523$	−136.554			−0.261097			−0.130548	−	0.991442i	$-0.541674\pi$
$523$	−136.554			−0.261097			−0.130548	+	0.991442i	$0.541674\pi$
$524$	5.71937	−	28.9688i	0.0109148	−	0.0552840i
$525$		−	0.177507i		−	0.000338108i
$526$	61.6817	+	75.0503i	0.117266	+	0.142681i
$527$		−	7.60131i		−	0.0144237i
$528$	61.0097	+	25.0677i	0.115549	+	0.0474766i
$529$	−23.0000			−0.0434783
$530$	443.739	−	364.696i	0.837244	−	0.688107i
$531$	−759.265			−1.42988
$532$	60.9891	+	12.0412i	0.114641	+	0.0226338i
$533$		−	932.458i		−	1.74945i
$534$	39.4198	−	32.3980i	0.0738199	−	0.0606705i
$535$			694.783i			1.29866i
$536$	−9.59057	−	17.8508i	−0.0178928	−	0.0333038i
$537$	33.5361			0.0624508
$538$	−568.799	−	692.078i	−1.05725	−	1.28639i
$539$	−814.441			−1.51102
$540$	84.5938	+	16.7015i	0.156655	+	0.0309288i
$541$			425.750i			0.786968i	0.919331	+	0.393484i	$0.128730\pi$
$541$			425.750i			0.786968i	−0.919331	+	0.393484i	$0.871270\pi$
$542$	323.537	+	393.659i	0.596932	+	0.726309i
$543$			24.9800i			0.0460038i
$544$	−7.75734	+	2.38336i	−0.0142598	+	0.00438118i
$545$	354.149			0.649814
$546$	−4.34880	+	3.57415i	−0.00796483	+	0.00654607i
$547$	−97.7525			−0.178707			−0.0893533	−	0.996000i	$-0.528480\pi$
$547$	−97.7525			−0.178707			−0.0893533	+	0.996000i	$0.528480\pi$
$548$	137.045	−	694.136i	0.250081	−	1.26667i
$549$		−	128.825i		−	0.234653i
$550$	29.3976	−	24.1611i	0.0534502	−	0.0439292i
$551$			1291.68i			2.34424i
$552$	8.31343	−	4.46648i	0.0150606	−	0.00809146i
$553$	40.0071			0.0723455
$554$	170.886	+	207.923i	0.308459	+	0.375313i
$555$	−34.4237			−0.0620246
$556$	−29.2576	+	148.191i	−0.0526217	+	0.266531i
$557$		−	696.625i		−	1.25067i	−0.780355	−	0.625337i	$-0.784962\pi$
$557$		−	696.625i		−	1.25067i	0.780355	−	0.625337i	$-0.215038\pi$
$558$	340.264	+	414.012i	0.609793	+	0.741957i
$559$		−	1146.15i		−	2.05036i
$560$	45.9573	+	18.8829i	0.0820666	+	0.0337195i
$561$	1.04545			0.00186355
$562$	214.586	−	176.362i	0.381826	−	0.313812i
$563$	−534.873			−0.950042			−0.475021	−	0.879975i	$-0.657559\pi$
$563$	−534.873			−0.950042			−0.475021	+	0.879975i	$0.657559\pi$
$564$	38.0181	+	7.50598i	0.0674079	+	0.0133085i
$565$			226.296i			0.400524i
$566$	−238.654	+	196.143i	−0.421651	+	0.346543i
$567$		−	50.4530i		−	0.0889824i
$568$	464.476	−	249.545i	0.817739	−	0.439340i
$569$	612.178			1.07588			0.537942	−	0.842982i	$-0.319202\pi$
$569$	612.178			1.07588			0.537942	+	0.842982i	$0.319202\pi$
$570$	−37.3081	−	45.3940i	−0.0654527	−	0.0796386i
$571$	−10.7791			−0.0188776			−0.00943880	−	0.999955i	$-0.503005\pi$
$571$	−10.7791			−0.0188776			−0.00943880	+	0.999955i	$0.503005\pi$
$572$	−1183.86	−	233.732i	−2.06968	−	0.408622i
$573$		−	11.0062i		−	0.0192080i
$574$	−41.8158	−	50.8788i	−0.0728499	−	0.0886391i
$575$		−	5.44446i		−	0.00946863i
$576$	315.821	−	477.061i	0.548301	−	0.828231i
$577$	−200.659			−0.347763			−0.173882	−	0.984767i	$-0.555631\pi$
$577$	−200.659			−0.347763			−0.173882	+	0.984767i	$0.555631\pi$
$578$	446.439	−	366.916i	0.772386	−	0.634802i
$579$	−62.8958			−0.108628
$580$	−199.959	+	1012.80i	−0.344756	+	1.74620i
$581$			82.0745i			0.141264i
$582$	−45.1463	+	37.1044i	−0.0775709	+	0.0637533i
$583$			985.253i			1.68997i
$584$	147.475	+	274.494i	0.252526	+	0.470024i
$585$	−786.096			−1.34375
$586$	39.7138	+	48.3212i	0.0677710	+	0.0824594i
$587$	−354.828			−0.604477			−0.302238	−	0.953232i	$-0.597734\pi$
$587$	−354.828			−0.604477			−0.302238	+	0.953232i	$0.597734\pi$
$588$	9.26120	−	46.9083i	0.0157503	−	0.0797761i
$589$		−	732.831i		−	1.24419i
$590$	526.895	+	641.091i	0.893042	+	1.08660i
$591$		−	54.7627i		−	0.0926611i
$592$	−174.199	+	423.966i	−0.294255	+	0.716159i
$593$	−260.011			−0.438467			−0.219233	−	0.975672i	$-0.570356\pi$
$593$	−260.011			−0.438467			−0.219233	+	0.975672i	$0.570356\pi$
$594$	−114.268	+	93.9136i	−0.192370	+	0.158104i
$595$	0.787515			0.00132355
$596$	1023.78	+	202.128i	1.71776	+	0.339140i
$597$		−	18.2899i		−	0.0306364i
$598$	−133.386	+	109.626i	−0.223053	+	0.183321i
$599$		−	409.205i		−	0.683147i	−0.939855	−	0.341573i	$-0.889040\pi$
$599$		−	409.205i		−	0.683147i	0.939855	−	0.341573i	$-0.110960\pi$
$600$	1.05729	+	1.96792i	0.00176214	+	0.00327986i
$601$	−499.713			−0.831470			−0.415735	−	0.909486i	$-0.636476\pi$
$601$	−499.713			−0.831470			−0.415735	+	0.909486i	$0.636476\pi$
$602$	−51.3988	−	62.5388i	−0.0853801	−	0.103885i
$603$	22.6438			0.0375519
$604$	159.761	+	31.5419i	0.264505	+	0.0522217i
$605$		−	781.034i		−	1.29097i
$606$	42.3454	+	51.5231i	0.0698769	+	0.0850217i
$607$		−	1053.33i		−	1.73530i	−0.497178	−	0.867648i	$-0.665631\pi$
$607$		−	1053.33i		−	1.73530i	0.497178	−	0.867648i	$-0.334369\pi$
$608$	−747.873	+	229.776i	−1.23005	+	0.377922i
$609$	−8.26061			−0.0135642
$610$	−108.774	+	89.3984i	−0.178318	+	0.146555i
$611$	−708.963			−1.16033
$612$	1.75645	−	8.89651i	0.00287002	−	0.0145368i
$613$		−	651.709i		−	1.06315i	−0.847012	−	0.531573i	$-0.821601\pi$
$613$		−	651.709i		−	1.06315i	0.847012	−	0.531573i	$-0.178399\pi$
$614$	−78.3437	+	64.3885i	−0.127596	+	0.104867i
$615$			62.2468i			0.101214i
$616$	−75.0780	+	40.3365i	−0.121880	+	0.0654814i
$617$	−130.834			−0.212049			−0.106024	−	0.994364i	$-0.533812\pi$
$617$	−130.834			−0.212049			−0.106024	+	0.994364i	$0.533812\pi$
$618$	29.7459	+	36.1929i	0.0481325	+	0.0585645i
$619$	551.414			0.890814			0.445407	−	0.895328i	$-0.353059\pi$
$619$	551.414			0.890814			0.445407	+	0.895328i	$0.353059\pi$
$620$	113.446	−	574.610i	0.182978	−	0.926791i
$621$			21.1625i			0.0340782i
$622$	−739.436	−	899.698i	−1.18880	−	1.44646i
$623$			65.9311i			0.105828i
$624$	26.9239	−	65.5275i	0.0431473	−	0.105012i
$625$	−595.330			−0.952528
$626$	190.772	−	156.790i	0.304747	−	0.250463i
$627$	100.790			0.160750
$628$	105.511	+	20.8313i	0.168012	+	0.0331709i
$629$			7.26499i			0.0115501i
$630$	−42.8927	+	35.2523i	−0.0680836	+	0.0559560i
$631$		−	388.007i		−	0.614908i	−0.951563	−	0.307454i	$-0.900523\pi$
$631$		−	388.007i		−	0.614908i	0.951563	−	0.307454i	$-0.0994770\pi$
$632$	−443.536	+	238.295i	−0.701798	+	0.377049i
$633$	−75.5903			−0.119416
$634$	−264.783	−	322.171i	−0.417639	−	0.508157i
$635$	−264.572			−0.416649
$636$	−56.7464	−	11.2035i	−0.0892238	−	0.0176156i
$637$			874.750i			1.37323i
$638$	−1124.38	−	1368.07i	−1.76235	−	2.14431i
$639$			589.188i			0.922047i
$640$	−621.976	+	64.3919i	−0.971837	+	0.100612i
$641$	−1128.01			−1.75976			−0.879882	−	0.475192i	$-0.842379\pi$
$641$	−1128.01			−1.75976			−0.879882	+	0.475192i	$0.842379\pi$
$642$	54.0537	−	44.4252i	0.0841958	−	0.0691981i
$643$	872.385			1.35674			0.678371	−	0.734719i	$-0.262686\pi$
$643$	872.385			1.35674			0.678371	+	0.734719i	$0.262686\pi$
$644$	−2.36194	+	11.9633i	−0.00366760	+	0.0185765i
$645$			76.5120i			0.118623i
$646$	−9.58024	+	7.87373i	−0.0148301	+	0.0121884i
$647$		−	184.431i		−	0.285056i	−0.989791	−	0.142528i	$-0.954477\pi$
$647$		−	184.431i		−	0.285056i	0.989791	−	0.142528i	$-0.0455231\pi$
$648$	300.514	+	559.344i	0.463756	+	0.863185i
$649$	−1423.44			−2.19329
$650$	−25.9502	−	31.5745i	−0.0399233	−	0.0485761i
$651$	4.68665			0.00719915
$652$	105.364	−	533.673i	0.161601	−	0.818517i
$653$			867.243i			1.32809i	0.747693	+	0.664045i	$0.231162\pi$
$653$			867.243i			1.32809i	−0.747693	+	0.664045i	$0.768838\pi$
$654$	−22.6447	−	27.5526i	−0.0346249	−	0.0421293i
$655$		−	36.0622i		−	0.0550568i
$656$	766.639	+	314.996i	1.16866	+	0.480178i
$657$	−348.196			−0.529979
$658$	−38.6840	+	31.7933i	−0.0587903	+	0.0483181i
$659$	447.686			0.679342			0.339671	−	0.940544i	$-0.389684\pi$
$659$	447.686			0.679342			0.339671	+	0.940544i	$0.389684\pi$
$660$	79.0293	+	15.6029i	0.119741	+	0.0236408i
$661$			319.213i			0.482925i	0.970410	+	0.241463i	$0.0776271\pi$
$661$			319.213i			0.482925i	−0.970410	+	0.241463i	$0.922373\pi$
$662$	308.564	−	253.600i	0.466108	−	0.383081i
$663$		−	1.12286i		−	0.00169361i
$664$	−488.862	−	909.914i	−0.736237	−	1.37035i
$665$	75.9232			0.114170
$666$	−325.210	−	395.694i	−0.488303	−	0.594135i
$667$	−253.368			−0.379862
$668$	899.495	+	177.589i	1.34655	+	0.265852i
$669$		−	43.5175i		−	0.0650486i
$670$	−15.7137	−	19.1195i	−0.0234533	−	0.0285365i
$671$		−	241.516i		−	0.359934i
$672$	−1.46948	−	4.78285i	−0.00218673	−	0.00711733i
$673$	−340.474			−0.505905			−0.252952	−	0.967479i	$-0.581402\pi$
$673$	−340.474			−0.505905			−0.252952	+	0.967479i	$0.581402\pi$
$674$	518.087	−	425.801i	0.768675	−	0.631752i
$675$	−5.00950			−0.00742149
$676$	−120.103	+	608.326i	−0.177667	+	0.899890i
$677$		−	454.189i		−	0.670885i	−0.942061	−	0.335443i	$-0.891114\pi$
$677$		−	454.189i		−	0.670885i	0.942061	−	0.335443i	$-0.108886\pi$
$678$	17.6057	−	14.4696i	0.0259671	−	0.0213416i
$679$		−	75.5087i		−	0.111206i
$680$	−8.73074	+	4.69069i	−0.0128393	+	0.00689807i
$681$	−2.34331			−0.00344099
$682$	637.916	+	776.175i	0.935360	+	1.13809i
$683$	−588.505			−0.861648			−0.430824	−	0.902436i	$-0.641777\pi$
$683$	−588.505			−0.861648			−0.430824	+	0.902436i	$0.641777\pi$
$684$	169.337	−	857.699i	0.247569	−	1.25395i
$685$		−	864.105i		−	1.26147i
$686$	78.7821	+	95.8569i	0.114843	+	0.139733i
$687$			15.7233i			0.0228869i
$688$	942.331	+	387.185i	1.36967	+	0.562768i
$689$	1058.21			1.53586
$690$	8.90425	−	7.31815i	0.0129047	−	0.0106060i
$691$	411.419			0.595397			0.297698	−	0.954660i	$-0.403781\pi$
$691$	411.419			0.595397			0.297698	+	0.954660i	$0.403781\pi$
$692$	341.545	+	67.4319i	0.493562	+	0.0974449i
$693$		−	95.2364i		−	0.137426i
$694$	−232.885	+	191.402i	−0.335570	+	0.275795i
$695$			184.478i			0.265436i
$696$	91.5807	−	49.2028i	0.131582	−	0.0706937i
$697$	13.1370			0.0188479
$698$	242.108	+	294.581i	0.346859	+	0.422036i
$699$	−43.7410			−0.0625766
$700$	−2.83190	−	0.559107i	−0.00404557	−	0.000798725i
$701$			848.269i			1.21008i	0.796194	+	0.605042i	$0.206844\pi$
$701$			848.269i			1.21008i	−0.796194	+	0.605042i	$0.793156\pi$
$702$	100.868	+	122.730i	0.143686	+	0.174828i
$703$			700.407i			0.996312i
$704$	592.091	−	894.377i	0.841038	−	1.27042i
$705$	47.3273			0.0671309
$706$	603.603	−	496.084i	0.854962	−	0.702669i
$707$	−86.1743			−0.121887
$708$	16.1863	−	81.9842i	0.0228620	−	0.115797i
$709$			592.826i			0.836144i	0.908414	+	0.418072i	$0.137294\pi$
$709$			592.826i			0.836144i	−0.908414	+	0.418072i	$0.862706\pi$
$710$	497.486	−	408.869i	0.700684	−	0.575872i
$711$		−	562.626i		−	0.791316i
$712$	−392.706	−	730.941i	−0.551554	−	1.02660i
$713$	143.748			0.201610
$714$	−0.0503546	−	0.0612682i	−7.05247e−5	−	8.58098e-5i
$715$	−1473.74			−2.06118
$716$	105.631	−	535.027i	0.147530	−	0.747244i
$717$		−	29.2398i		−	0.0407808i
$718$	553.844	+	673.881i	0.771370	+	0.938553i
$719$			389.239i			0.541361i	0.962669	+	0.270681i	$0.0872488\pi$
$719$			389.239i			0.541361i	−0.962669	+	0.270681i	$0.912751\pi$
$720$	265.553	−	646.305i	0.368824	−	0.897645i
$721$	−60.5339			−0.0839582
$722$	−365.830	+	300.665i	−0.506690	+	0.416434i
$723$	−51.1236			−0.0707103
$724$	398.526	+	78.6817i	0.550450	+	0.108676i
$725$		−	59.9762i		−	0.0827258i
$726$	−60.7640	+	49.9402i	−0.0836970	+	0.0687882i
$727$		−	757.781i		−	1.04234i	−0.853453	−	0.521170i	$-0.825496\pi$
$727$		−	757.781i		−	1.04234i	0.853453	−	0.521170i	$-0.174504\pi$
$728$	43.3234	+	80.6375i	0.0595102	+	0.110766i
$729$	−699.759			−0.959889
$730$	241.632	+	294.002i	0.331003	+	0.402743i
$731$	16.1476			0.0220897
$732$	13.9103	+	2.74633i	0.0190031	+	0.00375182i
$733$			925.330i			1.26239i	0.775625	+	0.631194i	$0.217435\pi$
$733$			925.330i			1.26239i	−0.775625	+	0.631194i	$0.782565\pi$
$734$	−293.094	−	356.617i	−0.399310	−	0.485855i
$735$		−	58.3945i		−	0.0794483i
$736$	−45.0717	−	146.699i	−0.0612388	−	0.199319i
$737$	42.4518			0.0576008
$738$	−715.516	+	588.063i	−0.969534	+	0.796833i
$739$	−1066.02			−1.44252			−0.721261	−	0.692663i	$-0.756437\pi$
$739$	−1066.02			−1.44252			−0.721261	+	0.692663i	$0.756437\pi$
$740$	−108.427	+	549.187i	−0.146523	+	0.742145i
$741$		−	108.254i		−	0.146091i
$742$	57.7404	−	47.4552i	0.0778172	−	0.0639558i
$743$			1178.68i			1.58638i	0.608975	+	0.793190i	$0.291581\pi$
$743$			1178.68i			1.58638i	−0.608975	+	0.793190i	$0.708419\pi$
$744$	−51.9582	+	27.9152i	−0.0698363	+	0.0375204i
$745$	1274.47			1.71070
$746$	646.273	+	786.343i	0.866318	+	1.05408i
$747$	1154.23			1.54515
$748$	3.29294	−	16.6789i	0.00440232	−	0.0222979i
$749$			90.4068i			0.120703i
$750$	39.8808	+	48.5244i	0.0531744	+	0.0646992i
$751$		−	1318.16i		−	1.75521i	−0.479385	−	0.877604i	$-0.659140\pi$
$751$		−	1318.16i		−	1.75521i	0.479385	−	0.877604i	$-0.340860\pi$
$752$	239.497	−	582.889i	0.318480	−	0.775118i
$753$	−110.958			−0.147354
$754$	−1469.38	+	1207.64i	−1.94878	+	1.60164i
$755$	198.881			0.263418
$756$	11.0076	+	2.17324i	0.0145603	+	0.00287466i
$757$			545.745i			0.720932i	0.932772	+	0.360466i	$0.117382\pi$
$757$			545.745i			0.720932i	−0.932772	+	0.360466i	$0.882618\pi$
$758$	321.441	−	264.183i	0.424064	−	0.348526i
$759$			19.7705i			0.0260481i
$760$	−841.717	+	452.222i	−1.10752	+	0.595029i
$761$	−170.477			−0.224017			−0.112009	−	0.993707i	$-0.535728\pi$
$761$	−170.477			−0.224017			−0.112009	+	0.993707i	$0.535728\pi$
$762$	16.9170	+	20.5835i	0.0222008	+	0.0270125i
$763$	46.0827			0.0603967
$764$	−175.590	−	34.6670i	−0.229830	−	0.0453757i
$765$		−	11.0749i		−	0.0144770i
$766$	701.150	+	853.114i	0.915339	+	1.11373i
$767$			1528.85i			1.99328i
$768$	44.7795	+	44.2721i	0.0583066	+	0.0576459i
$769$	953.372			1.23976			0.619878	−	0.784698i	$-0.287182\pi$
$769$	953.372			1.23976			0.619878	+	0.784698i	$0.287182\pi$
$770$	−80.4137	+	66.0897i	−0.104433	+	0.0858308i
$771$	26.0595			0.0337996
$772$	−198.108	+	1003.42i	−0.256616	+	1.29977i
$773$		−	407.134i		−	0.526694i	−0.964701	−	0.263347i	$-0.915174\pi$
$773$		−	407.134i		−	0.526694i	0.964701	−	0.263347i	$-0.0848263\pi$
$774$	−879.492	+	722.830i	−1.13629	+	0.933888i
$775$			34.0274i			0.0439064i
$776$	449.754	+	837.123i	0.579580	+	1.07877i
$777$	−4.47929			−0.00576485
$778$	535.912	+	652.064i	0.688834	+	0.838128i
$779$	1266.52			1.62582
$780$	16.7583	−	84.8814i	0.0214850	−	0.108822i
$781$			1104.59i			1.41433i
$782$	−1.54447	−	1.87921i	−0.00197502	−	0.00240308i
$783$			233.127i			0.297735i
$784$	−719.193	−	295.502i	−0.917338	−	0.376916i
$785$	131.347			0.167322
$786$	−2.80562	+	2.30586i	−0.00356949	+	0.00293366i
$787$	713.833			0.907031			0.453515	−	0.891249i	$-0.350170\pi$
$787$	713.833			0.907031			0.453515	+	0.891249i	$0.350170\pi$
$788$	−873.671	−	172.491i	−1.10872	−	0.218897i
$789$		−	11.9477i		−	0.0151428i
$790$	−475.058	+	390.436i	−0.601339	+	0.494223i
$791$			29.4462i			0.0372265i
$792$	567.258	+	1055.83i	0.716235	+	1.33312i
$793$	−259.400			−0.327112
$794$	−558.001	−	678.939i	−0.702772	−	0.855087i
$795$	−70.6415			−0.0888572
$796$	−291.793	−	57.6092i	−0.366574	−	0.0723734i
$797$		−	919.878i		−	1.15418i	−0.816682	−	0.577088i	$-0.804189\pi$
$797$		−	919.878i		−	1.15418i	0.816682	−	0.577088i	$-0.195811\pi$
$798$	−4.85461	−	5.90678i	−0.00608347	−	0.00740198i
$799$		−	9.98826i		−	0.0125009i
$800$	34.7259	−	10.6692i	0.0434074	−	0.0133365i
$801$	927.199			1.15755
$802$	313.432	−	257.601i	0.390813	−	0.321198i
$803$	−652.785			−0.812933
$804$	−0.482729	+	2.44504i	−0.000600409	+	0.00304110i
$805$			14.8927i			0.0185002i
$806$	833.650	−	685.153i	1.03431	−	0.850066i
$807$			110.176i			0.136525i
$808$	955.366	−	513.282i	1.18238	−	0.635249i
$809$	−684.005			−0.845494			−0.422747	−	0.906248i	$-0.638934\pi$
$809$	−684.005			−0.845494			−0.422747	+	0.906248i	$0.638934\pi$
$810$	492.380	+	599.096i	0.607876	+	0.739625i
$811$	857.285			1.05707			0.528536	−	0.848911i	$-0.322741\pi$
$811$	857.285			1.05707			0.528536	+	0.848911i	$0.322741\pi$
$812$	−26.0191	+	131.788i	−0.0320432	+	0.162300i
$813$		−	62.6690i		−	0.0770836i
$814$	−609.692	−	741.833i	−0.749007	−	0.911343i
$815$		−	664.350i		−	0.815154i
$816$	0.923186	+	0.379318i	0.00113136	+	0.000464851i
$817$	1556.76			1.90546
$818$	149.627	−	122.974i	0.182918	−	0.150335i
$819$	−102.289			−0.124895
$820$	993.071	+	196.064i	1.21106	+	0.239102i
$821$			623.027i			0.758863i	0.925220	+	0.379432i	$0.123880\pi$
$821$			623.027i			0.758863i	−0.925220	+	0.379432i	$0.876120\pi$
$822$	−67.2269	+	55.2518i	−0.0817845	+	0.0672163i
$823$		−	1479.00i		−	1.79709i	−0.438884	−	0.898544i	$-0.644626\pi$
$823$		−	1479.00i		−	1.79709i	0.438884	−	0.898544i	$-0.355374\pi$
$824$	671.105	−	360.559i	0.814448	−	0.437572i
$825$	−4.67998			−0.00567271
$826$	68.5608	+	83.4203i	0.0830034	+	0.100993i
$827$	285.203			0.344865			0.172432	−	0.985021i	$-0.444837\pi$
$827$	285.203			0.344865			0.172432	+	0.985021i	$0.444837\pi$
$828$	168.242	+	33.2163i	0.203190	+	0.0401163i
$829$			769.997i			0.928826i	0.885619	+	0.464413i	$0.153735\pi$
$829$			769.997i			0.928826i	−0.885619	+	0.464413i	$0.846265\pi$
$830$	−800.980	−	974.580i	−0.965036	−	1.17419i
$831$		−	33.1006i		−	0.0398322i
$832$	−960.605	−	635.935i	−1.15457	−	0.764344i
$833$	−12.3239			−0.0147947
$834$	14.3523	−	11.7957i	0.0172089	−	0.0141435i
$835$	1119.75			1.34102
$836$	317.467	−	1607.98i	0.379746	−	1.92343i
$837$		−	132.264i		−	0.158022i
$838$	−529.350	+	435.058i	−0.631683	+	0.519162i
$839$		−	583.444i		−	0.695404i	−0.937605	−	0.347702i	$-0.886962\pi$
$839$		−	583.444i		−	0.695404i	0.937605	−	0.347702i	$-0.113038\pi$
$840$	−2.89208	−	5.38301i	−0.00344296	−	0.00640834i
$841$	−1950.10			−2.31879
$842$	376.428	+	458.013i	0.447064	+	0.543959i
$843$	−34.1613			−0.0405235
$844$	−238.093	+	1205.95i	−0.282100	+	1.42885i
$845$			757.283i			0.896193i
$846$	447.114	+	544.019i	0.528503	+	0.643049i
$847$		−	101.630i		−	0.119988i
$848$	−357.477	+	870.029i	−0.421553	+	1.02598i
$849$	37.9928			0.0447501
$850$	0.444838	−	0.365600i	0.000523339	−	0.000430118i
$851$	−137.388			−0.161443
$852$	−63.6196	−	12.5605i	−0.0746709	−	0.0147424i
$853$			1468.52i			1.72159i	0.508948	+	0.860797i	$0.330035\pi$
$853$			1468.52i			1.72159i	−0.508948	+	0.860797i	$0.669965\pi$
$854$	−14.1540	+	11.6327i	−0.0165737	+	0.0136215i
$855$		−	1067.72i		−	1.24879i
$856$	−538.492	−	1002.29i	−0.629079	−	1.17090i
$857$	−303.344			−0.353960			−0.176980	−	0.984214i	$-0.556633\pi$
$857$	−303.344			−0.353960			−0.176980	+	0.984214i	$0.556633\pi$
$858$	94.2329	+	114.656i	0.109829	+	0.133632i
$859$	966.200			1.12480			0.562398	−	0.826867i	$-0.309879\pi$
$859$	966.200			1.12480			0.562398	+	0.826867i	$0.309879\pi$
$860$	1220.65	+	240.996i	1.41937	+	0.280228i
$861$			8.09971i			0.00940732i
$862$	−269.096	−	327.418i	−0.312176	−	0.379836i
$863$		−	1002.53i		−	1.16168i	−0.814019	−	0.580838i	$-0.802725\pi$
$863$		−	1002.53i		−	1.16168i	0.814019	−	0.580838i	$-0.197275\pi$
$864$	−134.979	+	41.4710i	−0.156226	+	0.0479988i
$865$	425.177			0.491534
$866$	241.703	−	198.649i	0.279103	−	0.229387i
$867$	−71.0714			−0.0819739
$868$	14.7619	−	74.7696i	0.0170068	−	0.0861401i
$869$		−	1054.79i		−	1.21380i
$870$	98.0892	−	80.6167i	0.112746	−	0.0926629i
$871$		−	45.5953i		−	0.0523482i
$872$	−510.893	+	274.483i	−0.585886	+	0.314774i
$873$	−1061.89			−1.21637
$874$	−148.900	−	181.172i	−0.170366	−	0.207290i
$875$	−81.1588			−0.0927529
$876$	7.42298	−	37.5977i	0.00847372	−	0.0429197i
$877$		−	1356.02i		−	1.54620i	−0.634284	−	0.773100i	$-0.718705\pi$
$877$		−	1356.02i		−	1.54620i	0.634284	−	0.773100i	$-0.281295\pi$
$878$	995.320	+	1211.04i	1.13362	+	1.37932i
$879$		−	7.69254i		−	0.00875147i
$880$	497.850	−	1211.67i	0.565739	−	1.37690i
$881$	−1343.85			−1.52536			−0.762682	−	0.646773i	$-0.776118\pi$
$881$	−1343.85			−1.52536			−0.762682	+	0.646773i	$0.776118\pi$
$882$	671.234	−	551.668i	0.761037	−	0.625474i
$883$	−17.2505			−0.0195363			−0.00976815	−	0.999952i	$-0.503109\pi$
$883$	−17.2505			−0.0195363			−0.00976815	+	0.999952i	$0.503109\pi$
$884$	−17.9139	−	3.53678i	−0.0202646	−	0.00400088i
$885$		−	102.059i		−	0.115321i
$886$	327.600	−	269.245i	0.369752	−	0.303889i
$887$		−	1374.52i		−	1.54962i	−0.632192	−	0.774811i	$-0.717845\pi$
$887$		−	1374.52i		−	1.54962i	0.632192	−	0.774811i	$-0.282155\pi$
$888$	49.6594	−	26.6801i	0.0559227	−	0.0300451i
$889$	−34.4267			−0.0387252
$890$	−643.433	−	782.888i	−0.722959	−	0.879649i
$891$	−1330.20			−1.49293
$892$	−694.268	−	137.071i	−0.778327	−	0.153667i
$893$		−	962.953i		−	1.07833i
$894$	−81.4911	−	99.1531i	−0.0911534	−	0.110910i
$895$		−	666.035i		−	0.744174i
$896$	−80.9330	+	8.37883i	−0.0903270	+	0.00935137i
$897$	21.2345			0.0236728
$898$	−658.681	+	541.351i	−0.733498	+	0.602841i
$899$	1583.53			1.76144
$900$	−7.86281	+	39.8254i	−0.00873646	+	0.0442505i
$901$			14.9086i			0.0165468i
$902$	−1341.42	+	1102.48i	−1.48717	+	1.22226i
$903$			9.95593i			0.0110254i
$904$	−175.391	−	326.453i	−0.194016	−	0.361121i
$905$	496.110			0.548188
$906$	−12.7167	−	15.4728i	−0.0140361	−	0.0170782i
$907$	1602.33			1.76662			0.883310	−	0.468789i	$-0.155309\pi$
$907$	1602.33			1.76662			0.883310	+	0.468789i	$0.155309\pi$
$908$	−7.38092	+	37.3846i	−0.00812877	+	0.0411725i
$909$			1211.88i			1.33320i
$910$	70.9836	+	86.3683i	0.0780040	+	0.0949102i
$911$			518.387i			0.569030i	0.958672	+	0.284515i	$0.0918326\pi$
$911$			518.387i			0.569030i	−0.958672	+	0.284515i	$0.908167\pi$
$912$	89.0030	+	36.5695i	0.0975910	+	0.0400982i
$913$	2163.90			2.37010
$914$	−1216.12	+	999.496i	−1.33055	+	1.09354i
$915$	17.3164			0.0189250
$916$	250.846	+	49.5250i	0.273849	+	0.0540666i
$917$		−	4.69250i		−	0.00511723i
$918$	−1.72908	+	1.42108i	−0.00188353	+	0.00154802i
$919$			821.823i			0.894258i	0.894470	+	0.447129i	$0.147554\pi$
$919$			821.823i			0.894258i	−0.894470	+	0.447129i	$0.852446\pi$
$920$	−88.7055	−	165.107i	−0.0964190	−	0.179464i
$921$	12.4720			0.0135418
$922$	−227.362	−	276.639i	−0.246596	−	0.300043i
$923$	1186.38			1.28535
$924$	10.2835	+	2.03029i	0.0111293	+	0.00219728i
$925$		−	32.5219i		−	0.0351588i
$926$	−739.789	−	900.128i	−0.798909	−	0.972060i
$927$			851.297i			0.918336i
$928$	−496.510	−	1616.03i	−0.535033	−	1.74142i
$929$	−940.145			−1.01200			−0.505998	−	0.862535i	$-0.668876\pi$
$929$	−940.145			−1.01200			−0.505998	+	0.862535i	$0.668876\pi$
$930$	−55.6508	+	45.7378i	−0.0598396	+	0.0491805i
$931$	−1188.13			−1.27619
$932$	−137.775	+	697.834i	−0.147827	+	0.748748i
$933$			143.228i			0.153514i
$934$	−74.5275	+	61.2520i	−0.0797939	+	0.0655803i
$935$		−	20.7629i		−	0.0222063i
$936$	1134.02	−	609.264i	1.21156	−	0.650923i
$937$	1362.55			1.45416			0.727080	−	0.686553i	$-0.240877\pi$
$937$	1362.55			1.45416			0.727080	+	0.686553i	$0.240877\pi$
$938$	−2.04471	−	2.48787i	−0.00217986	−	0.00265231i
$939$	−30.3701			−0.0323430
$940$	149.071	−	755.048i	0.158586	−	0.803243i
$941$			549.207i			0.583642i	0.956473	+	0.291821i	$0.0942612\pi$
$941$			549.207i			0.583642i	−0.956473	+	0.291821i	$0.905739\pi$
$942$	−8.39850	−	10.2188i	−0.00891561	−	0.0108479i
$943$			248.433i			0.263450i
$944$	−1256.97	−	516.465i	−1.33154	−	0.547102i
$945$	13.7029			0.0145004
$946$	−1648.84	+	1355.14i	−1.74296	+	1.43249i
$947$	−248.617			−0.262531			−0.131265	−	0.991347i	$-0.541904\pi$
$947$	−248.617			−0.262531			−0.131265	+	0.991347i	$0.541904\pi$
$948$	60.7514	+	11.9943i	0.0640838	+	0.0126522i
$949$			701.124i			0.738803i
$950$	42.8862	−	35.2469i	0.0451434	−	0.0371020i
$951$			51.2884i			0.0539310i
$952$	−1.13606	+	0.610364i	−0.00119334	+	0.000641138i
$953$	−1061.89			−1.11426			−0.557130	−	0.830425i	$-0.688097\pi$
$953$	−1061.89			−1.11426			−0.557130	+	0.830425i	$0.688097\pi$
$954$	−667.369	−	812.012i	−0.699548	−	0.851165i
$955$	−218.585			−0.228885
$956$	−466.485	−	92.0991i	−0.487955	−	0.0963379i
$957$			217.792i			0.227578i
$958$	−528.848	−	643.468i	−0.552033	−	0.671678i
$959$		−	112.439i		−	0.117246i
$960$	64.1258	+	42.4522i	0.0667977	+	0.0442211i
$961$	62.5855			0.0651254
$962$	−796.766	+	654.839i	−0.828239	+	0.680706i
$963$	1271.40			1.32025
$964$	−161.028	+	815.613i	−0.167041	+	0.846071i
$965$			1249.13i			1.29443i
$966$	1.15864	−	0.952255i	0.00119942	−	0.000985771i
$967$		−	560.022i		−	0.579133i	−0.957158	−	0.289567i	$-0.906489\pi$
$967$		−	560.022i		−	0.579133i	0.957158	−	0.289567i	$-0.0935112\pi$
$968$	605.341	+	1126.72i	0.625352	+	1.16396i
$969$	1.52514			0.00157393
$970$	736.903	+	896.616i	0.759694	+	0.924347i
$971$	−1684.93			−1.73525			−0.867627	−	0.497216i	$-0.834356\pi$
$971$	−1684.93			−1.73525			−0.867627	+	0.497216i	$0.834356\pi$
$972$	45.8955	−	232.462i	0.0472176	−	0.239159i
$973$			24.0047i			0.0246708i
$974$	−820.441	−	998.259i	−0.842341	−	1.02491i
$975$			5.02653i			0.00515542i
$976$	87.6287	−	213.271i	0.0897835	−	0.218515i
$977$	1267.22			1.29705			0.648524	−	0.761194i	$-0.275387\pi$
$977$	1267.22			1.29705			0.648524	+	0.761194i	$0.275387\pi$
$978$	−51.6861	+	42.4793i	−0.0528487	+	0.0434349i
$979$	1738.28			1.77557
$980$	−931.612	−	183.930i	−0.950624	−	0.187684i
$981$		−	648.067i		−	0.660619i
$982$	−905.163	+	743.927i	−0.921754	+	0.757563i
$983$			368.352i			0.374722i	0.982291	+	0.187361i	$0.0599934\pi$
$983$			368.352i			0.374722i	−0.982291	+	0.187361i	$0.940007\pi$
$984$	−48.2444	−	89.7969i	−0.0490289	−	0.0912570i
$985$	−1087.60			−1.10416
$986$	−17.0139	−	20.7014i	−0.0172554	−	0.0209953i
$987$	6.15834			0.00623945
$988$	−1727.05	−	340.976i	−1.74803	−	0.345117i
$989$			305.367i			0.308763i
$990$	929.429	+	1130.87i	0.938818	+	1.14229i
$991$		−	883.011i		−	0.891030i	−0.895274	−	0.445515i	$-0.853021\pi$
$991$		−	883.011i		−	0.891030i	0.895274	−	0.445515i	$-0.146979\pi$
$992$	281.695	+	916.856i	0.283966	+	0.924250i
$993$	−49.1221			−0.0494684
$994$	64.7340	−	53.2030i	0.0651247	−	0.0535242i
$995$	−363.243			−0.365068
$996$	−24.6062	+	124.632i	−0.0247051	+	0.125132i
$997$		−	1504.81i		−	1.50934i	−0.656107	−	0.754668i	$-0.727798\pi$
$997$		−	1504.81i		−	1.50934i	0.656107	−	0.754668i	$-0.272202\pi$
$998$	−2.13688	+	1.75624i	−0.00214117	+	0.00175976i
$999$			126.412i			0.126539i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	184.3.g.a.139.12	yes	44
4.3	odd	2		736.3.g.a.47.21		44
8.3	odd	2	inner	184.3.g.a.139.11	✓	44
8.5	even	2		736.3.g.a.47.22		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.3.g.a.139.11	✓	44	8.3	odd	2	inner
184.3.g.a.139.12	yes	44	1.1	even	1	trivial
736.3.g.a.47.21		44	4.3	odd	2
736.3.g.a.47.22		44	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 184 = 2^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	184.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.54512 + 1.26989i) q^{2} +0.245976 q^{3} +(0.774772 - 3.92425i) q^{4} -4.88516i q^{5} +(-0.380062 + 0.312362i) q^{6} -0.635668i q^{7} +(3.78624 + 7.04730i) q^{8} -8.93950 q^{9} +O(q^{10})\)	\(q+(-1.54512 + 1.26989i) q^{2} +0.245976 q^{3} +(0.774772 - 3.92425i) q^{4} -4.88516i q^{5} +(-0.380062 + 0.312362i) q^{6} -0.635668i q^{7} +(3.78624 + 7.04730i) q^{8} -8.93950 q^{9} +(6.20360 + 7.54814i) q^{10} -16.7594 q^{11} +(0.190576 - 0.965273i) q^{12} +18.0005i q^{13} +(0.807227 + 0.982182i) q^{14} -1.20163i q^{15} +(-14.7995 - 6.08080i) q^{16} -0.253600 q^{17} +(13.8126 - 11.3522i) q^{18} -24.4492 q^{19} +(-19.1706 - 3.78488i) q^{20} -0.156359i q^{21} +(25.8953 - 21.2826i) q^{22} -4.79583i q^{23} +(0.931326 + 1.73347i) q^{24} +1.13525 q^{25} +(-22.8586 - 27.8128i) q^{26} -4.41269 q^{27} +(-2.49452 - 0.492498i) q^{28} -52.8309i q^{29} +(1.52594 + 1.85666i) q^{30} +29.9736i q^{31} +(30.5888 - 9.39810i) q^{32} -4.12243 q^{33} +(0.391842 - 0.322044i) q^{34} -3.10534 q^{35} +(-6.92607 + 35.0808i) q^{36} -28.6474i q^{37} +(37.7769 - 31.0478i) q^{38} +4.42769i q^{39} +(34.4271 - 18.4964i) q^{40} -51.8018 q^{41} +(0.198559 + 0.241594i) q^{42} -63.6733 q^{43} +(-12.9848 + 65.7682i) q^{44} +43.6708i q^{45} +(6.09017 + 7.41012i) q^{46} +39.3858i q^{47} +(-3.64032 - 1.49573i) q^{48} +48.5959 q^{49} +(-1.75409 + 1.44164i) q^{50} -0.0623797 q^{51} +(70.6384 + 13.9463i) q^{52} -58.7879i q^{53} +(6.81813 - 5.60362i) q^{54} +81.8725i q^{55} +(4.47974 - 2.40679i) q^{56} -6.01394 q^{57} +(67.0893 + 81.6299i) q^{58} +84.9337 q^{59} +(-4.71551 - 0.930992i) q^{60} +14.4107i q^{61} +(-38.0630 - 46.3127i) q^{62} +5.68255i q^{63} +(-35.3288 + 53.3655i) q^{64} +87.9351 q^{65} +(6.36964 - 5.23502i) q^{66} -2.53300 q^{67} +(-0.196482 + 0.995191i) q^{68} -1.17966i q^{69} +(4.79811 - 3.94343i) q^{70} -65.9084i q^{71} +(-33.8471 - 62.9993i) q^{72} +38.9503 q^{73} +(36.3790 + 44.2636i) q^{74} +0.279244 q^{75} +(-18.9426 + 95.9449i) q^{76} +10.6534i q^{77} +(-5.62267 - 6.84130i) q^{78} +62.9371i q^{79} +(-29.7056 + 72.2977i) q^{80} +79.3700 q^{81} +(80.0399 - 65.7825i) q^{82} -129.115 q^{83} +(-0.613593 - 0.121143i) q^{84} +1.23888i q^{85} +(98.3828 - 80.8580i) q^{86} -12.9952i q^{87} +(-63.4553 - 118.109i) q^{88} -103.719 q^{89} +(-55.4570 - 67.4765i) q^{90} +11.4423 q^{91} +(-18.8200 - 3.71568i) q^{92} +7.37279i q^{93} +(-50.0155 - 60.8557i) q^{94} +119.438i q^{95} +(7.52413 - 2.31171i) q^{96} +118.786 q^{97} +(-75.0864 + 61.7114i) q^{98} +149.821 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 3 q^{6} + 15 q^{8} + 132 q^{9}+O(q^{10}) \) 44 * q - 3 * q^6 + 15 * q^8 + 132 * q^9	\( 44 q - 3 q^{6} + 15 q^{8} + 132 q^{9} + 26 q^{10} - 19 q^{12} - 8 q^{14} - 16 q^{16} - 8 q^{17} - 57 q^{18} + 40 q^{20} + 44 q^{22} - 88 q^{24} - 244 q^{25} + 19 q^{26} - 48 q^{27} + 6 q^{28} + 86 q^{30} + 160 q^{32} + 16 q^{33} + 18 q^{34} + 96 q^{35} + 179 q^{36} - 156 q^{38} + 130 q^{40} + 88 q^{41} + 100 q^{42} - 128 q^{43} - 158 q^{44} + 5 q^{48} - 340 q^{49} + 4 q^{50} + 160 q^{51} - 127 q^{52} + 53 q^{54} - 6 q^{56} - 176 q^{57} + 147 q^{58} + 16 q^{59} - 283 q^{62} - 405 q^{64} + 96 q^{65} - 602 q^{66} - 288 q^{67} + 72 q^{68} + 312 q^{70} - 57 q^{72} + 280 q^{73} - 198 q^{74} + 160 q^{75} + 172 q^{76} - 185 q^{78} - 90 q^{80} + 284 q^{81} - 75 q^{82} - 480 q^{83} - 254 q^{84} - 98 q^{86} + 204 q^{88} - 200 q^{89} + 488 q^{90} + 192 q^{91} + 19 q^{94} - 107 q^{96} + 184 q^{97} + 200 q^{98} + 256 q^{99}+O(q^{100}) \) 44 * q - 3 * q^6 + 15 * q^8 + 132 * q^9 + 26 * q^10 - 19 * q^12 - 8 * q^14 - 16 * q^16 - 8 * q^17 - 57 * q^18 + 40 * q^20 + 44 * q^22 - 88 * q^24 - 244 * q^25 + 19 * q^26 - 48 * q^27 + 6 * q^28 + 86 * q^30 + 160 * q^32 + 16 * q^33 + 18 * q^34 + 96 * q^35 + 179 * q^36 - 156 * q^38 + 130 * q^40 + 88 * q^41 + 100 * q^42 - 128 * q^43 - 158 * q^44 + 5 * q^48 - 340 * q^49 + 4 * q^50 + 160 * q^51 - 127 * q^52 + 53 * q^54 - 6 * q^56 - 176 * q^57 + 147 * q^58 + 16 * q^59 - 283 * q^62 - 405 * q^64 + 96 * q^65 - 602 * q^66 - 288 * q^67 + 72 * q^68 + 312 * q^70 - 57 * q^72 + 280 * q^73 - 198 * q^74 + 160 * q^75 + 172 * q^76 - 185 * q^78 - 90 * q^80 + 284 * q^81 - 75 * q^82 - 480 * q^83 - 254 * q^84 - 98 * q^86 + 204 * q^88 - 200 * q^89 + 488 * q^90 + 192 * q^91 + 19 * q^94 - 107 * q^96 + 184 * q^97 + 200 * q^98 + 256 * q^99

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