LMFDB - Embedded newform 184.3.g.a.139.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [184,3,Mod(139,184)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			139.1
Character	$\chi$	$=$	184.139
Dual form			184.3.g.a.139.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.97298 - 0.327653i) q^{2} +2.30854 q^{3} +(3.78529 + 1.29291i) q^{4} -6.63468i q^{5} +(-4.55469 - 0.756400i) q^{6} -5.68430i q^{7} +(-7.04466 - 3.79114i) q^{8} -3.67066 q^{9} +(-2.17387 + 13.0901i) q^{10} -6.58413 q^{11} +(8.73847 + 2.98472i) q^{12} -1.70195i q^{13} +(-1.86248 + 11.2150i) q^{14} -15.3164i q^{15} +(12.6568 + 9.78804i) q^{16} -15.6775 q^{17} +(7.24213 + 1.20270i) q^{18} +17.3471 q^{19} +(8.57802 - 25.1142i) q^{20} -13.1224i q^{21} +(12.9903 + 2.15731i) q^{22} +4.79583i q^{23} +(-16.2629 - 8.75198i) q^{24} -19.0190 q^{25} +(-0.557651 + 3.35792i) q^{26} -29.2507 q^{27} +(7.34926 - 21.5167i) q^{28} -28.8048i q^{29} +(-5.01847 + 30.2189i) q^{30} -42.9453i q^{31} +(-21.7645 - 23.4586i) q^{32} -15.1997 q^{33} +(30.9315 + 5.13680i) q^{34} -37.7135 q^{35} +(-13.8945 - 4.74582i) q^{36} +21.2861i q^{37} +(-34.2254 - 5.68383i) q^{38} -3.92902i q^{39} +(-25.1530 + 46.7391i) q^{40} +67.2750 q^{41} +(-4.29960 + 25.8902i) q^{42} +45.7078 q^{43} +(-24.9228 - 8.51266i) q^{44} +24.3536i q^{45} +(1.57137 - 9.46207i) q^{46} -81.7755i q^{47} +(29.2187 + 22.5960i) q^{48} +16.6888 q^{49} +(37.5240 + 6.23163i) q^{50} -36.1922 q^{51} +(2.20046 - 6.44238i) q^{52} +66.7853i q^{53} +(57.7110 + 9.58408i) q^{54} +43.6836i q^{55} +(-21.5500 + 40.0440i) q^{56} +40.0464 q^{57} +(-9.43798 + 56.8312i) q^{58} +34.9065 q^{59} +(19.8027 - 57.9770i) q^{60} +61.7559i q^{61} +(-14.0712 + 84.7301i) q^{62} +20.8651i q^{63} +(35.2546 + 53.4146i) q^{64} -11.2919 q^{65} +(29.9887 + 4.98023i) q^{66} +8.27021 q^{67} +(-59.3440 - 20.2696i) q^{68} +11.0714i q^{69} +(74.4079 + 12.3570i) q^{70} -53.7902i q^{71} +(25.8586 + 13.9160i) q^{72} +59.7633 q^{73} +(6.97446 - 41.9970i) q^{74} -43.9060 q^{75} +(65.6637 + 22.4282i) q^{76} +37.4261i q^{77} +(-1.28736 + 7.75187i) q^{78} +44.7927i q^{79} +(64.9405 - 83.9737i) q^{80} -34.4903 q^{81} +(-132.732 - 22.0429i) q^{82} -48.5204 q^{83} +(16.9660 - 49.6721i) q^{84} +104.015i q^{85} +(-90.1804 - 14.9763i) q^{86} -66.4968i q^{87} +(46.3830 + 24.9613i) q^{88} +32.7845 q^{89} +(7.97956 - 48.0492i) q^{90} -9.67441 q^{91} +(-6.20056 + 18.1536i) q^{92} -99.1408i q^{93} +(-26.7940 + 161.341i) q^{94} -115.092i q^{95} +(-50.2441 - 54.1551i) q^{96} -132.916 q^{97} +(-32.9265 - 5.46813i) q^{98} +24.1681 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

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 $

$2$	−1.97298	−	0.327653i	−0.986489	−	0.163827i
$2$	−1.97298	−	0.327653i	−0.986489	−	0.163827i
$3$	2.30854			0.769512			0.384756	−	0.923018i	$-0.374286\pi$
$3$	2.30854			0.769512			0.384756	+	0.923018i	$0.374286\pi$
$4$	3.78529	+	1.29291i	0.946322	+	0.323227i
$5$		−	6.63468i		−	1.32694i	−0.748205	−	0.663468i	$-0.769084\pi$
$5$		−	6.63468i		−	1.32694i	0.748205	−	0.663468i	$-0.230916\pi$
$6$	−4.55469	−	0.756400i	−0.759115	−	0.126067i
$7$		−	5.68430i		−	0.812043i	−0.913864	−	0.406021i	$-0.866916\pi$
$7$		−	5.68430i		−	0.812043i	0.913864	−	0.406021i	$-0.133084\pi$
$8$	−7.04466	−	3.79114i	−0.880583	−	0.473892i
$9$	−3.67066			−0.407851
$10$	−2.17387	+	13.0901i	−0.217387	+	1.30901i
$11$	−6.58413			−0.598557			−0.299278	−	0.954166i	$-0.596746\pi$
$11$	−6.58413			−0.598557			−0.299278	+	0.954166i	$0.596746\pi$
$12$	8.73847	+	2.98472i	0.728206	+	0.248727i
$13$		−	1.70195i		−	0.130919i	−0.997855	−	0.0654597i	$-0.979149\pi$
$13$		−	1.70195i		−	0.130919i	0.997855	−	0.0654597i	$-0.0208514\pi$
$14$	−1.86248	+	11.2150i	−0.133034	+	0.801071i
$15$		−	15.3164i		−	1.02109i
$16$	12.6568	+	9.78804i	0.791049	+	0.611752i
$17$	−15.6775			−0.922209			−0.461104	−	0.887346i	$-0.652547\pi$
$17$	−15.6775			−0.922209			−0.461104	+	0.887346i	$0.652547\pi$
$18$	7.24213	+	1.20270i	0.402341	+	0.0668169i
$19$	17.3471			0.913004			0.456502	−	0.889722i	$-0.349102\pi$
$19$	17.3471			0.913004			0.456502	+	0.889722i	$0.349102\pi$
$20$	8.57802	−	25.1142i	0.428901	−	1.25571i
$21$		−	13.1224i		−	0.624877i
$22$	12.9903	+	2.15731i	0.590470	+	0.0980596i
$23$			4.79583i			0.208514i
$23$			4.79583i			0.208514i
$24$	−16.2629	−	8.75198i	−0.677619	−	0.364666i
$25$	−19.0190			−0.760758
$26$	−0.557651	+	3.35792i	−0.0214481	+	0.129151i
$27$	−29.2507			−1.08336
$28$	7.34926	−	21.5167i	0.262474	−	0.768454i
$29$		−	28.8048i		−	0.993268i	−0.867960	−	0.496634i	$-0.834569\pi$
$29$		−	28.8048i		−	0.993268i	0.867960	−	0.496634i	$-0.165431\pi$
$30$	−5.01847	+	30.2189i	−0.167282	+	1.00730i
$31$		−	42.9453i		−	1.38533i	−0.721259	−	0.692666i	$-0.756436\pi$
$31$		−	42.9453i		−	1.38533i	0.721259	−	0.692666i	$-0.243564\pi$
$32$	−21.7645	−	23.4586i	−0.680140	−	0.733082i
$33$	−15.1997			−0.460597
$34$	30.9315	+	5.13680i	0.909749	+	0.151082i
$35$	−37.7135			−1.07753
$36$	−13.8945	−	4.74582i	−0.385958	−	0.131828i
$37$			21.2861i			0.575299i	0.957736	+	0.287650i	$0.0928739\pi$
$37$			21.2861i			0.575299i	−0.957736	+	0.287650i	$0.907126\pi$
$38$	−34.2254	−	5.68383i	−0.900669	−	0.149575i
$39$		−	3.92902i		−	0.100744i
$40$	−25.1530	+	46.7391i	−0.628824	+	1.16848i
$41$	67.2750			1.64085			0.820427	−	0.571752i	$-0.193736\pi$
$41$	67.2750			1.64085			0.820427	+	0.571752i	$0.193736\pi$
$42$	−4.29960	+	25.8902i	−0.102371	+	0.616434i
$43$	45.7078			1.06297			0.531486	−	0.847067i	$-0.321634\pi$
$43$	45.7078			1.06297			0.531486	+	0.847067i	$0.321634\pi$
$44$	−24.9228	−	8.51266i	−0.566427	−	0.193469i
$45$			24.3536i			0.541192i
$46$	1.57137	−	9.46207i	0.0341602	−	0.205697i
$47$		−	81.7755i		−	1.73991i	−0.493135	−	0.869953i	$-0.664149\pi$
$47$		−	81.7755i		−	1.73991i	0.493135	−	0.869953i	$-0.335851\pi$
$48$	29.2187	+	22.5960i	0.608722	+	0.470751i
$49$	16.6888			0.340587
$50$	37.5240	+	6.23163i	0.750480	+	0.124633i
$51$	−36.1922			−0.709651
$52$	2.20046	−	6.44238i	0.0423166	−	0.123892i
$53$			66.7853i			1.26010i	0.776555	+	0.630050i	$0.216965\pi$
$53$			66.7853i			1.26010i	−0.776555	+	0.630050i	$0.783035\pi$
$54$	57.7110	+	9.58408i	1.06872	+	0.177483i
$55$			43.6836i			0.794247i
$56$	−21.5500	+	40.0440i	−0.384821	+	0.715071i
$57$	40.0464			0.702568
$58$	−9.43798	+	56.8312i	−0.162724	+	0.979848i
$59$	34.9065			0.591636			0.295818	−	0.955244i	$-0.404408\pi$
$59$	34.9065			0.591636			0.295818	+	0.955244i	$0.404408\pi$
$60$	19.8027	−	57.9770i	0.330044	−	0.966283i
$61$			61.7559i			1.01239i	0.862419	+	0.506196i	$0.168949\pi$
$61$			61.7559i			1.01239i	−0.862419	+	0.506196i	$0.831051\pi$
$62$	−14.0712	+	84.7301i	−0.226954	+	1.36661i
$63$			20.8651i			0.331192i
$64$	35.2546	+	53.4146i	0.550852	+	0.834603i
$65$	−11.2919			−0.173722
$66$	29.9887	+	4.98023i	0.454374	+	0.0754581i
$67$	8.27021			0.123436			0.0617180	−	0.998094i	$-0.480342\pi$
$67$	8.27021			0.123436			0.0617180	+	0.998094i	$0.480342\pi$
$68$	−59.3440	−	20.2696i	−0.872706	−	0.298082i
$69$			11.0714i			0.160454i
$70$	74.4079	+	12.3570i	1.06297	+	0.176528i
$71$		−	53.7902i		−	0.757609i	−0.925477	−	0.378804i	$-0.876335\pi$
$71$		−	53.7902i		−	0.757609i	0.925477	−	0.378804i	$-0.123665\pi$
$72$	25.8586	+	13.9160i	0.359147	+	0.193277i
$73$	59.7633			0.818676			0.409338	−	0.912383i	$-0.365760\pi$
$73$	59.7633			0.818676			0.409338	+	0.912383i	$0.365760\pi$
$74$	6.97446	−	41.9970i	0.0942494	−	0.567527i
$75$	−43.9060			−0.585413
$76$	65.6637	+	22.4282i	0.863996	+	0.295107i
$77$			37.4261i			0.486054i
$78$	−1.28736	+	7.75187i	−0.0165046	+	0.0993830i
$79$			44.7927i			0.566996i	0.958973	+	0.283498i	$0.0914949\pi$
$79$			44.7927i			0.566996i	−0.958973	+	0.283498i	$0.908505\pi$
$80$	64.9405	−	83.9737i	0.811756	−	1.04967i
$81$	−34.4903			−0.425806
$82$	−132.732	−	22.0429i	−1.61868	−	0.268816i
$83$	−48.5204			−0.584583			−0.292291	−	0.956329i	$-0.594418\pi$
$83$	−48.5204			−0.584583			−0.292291	+	0.956329i	$0.594418\pi$
$84$	16.9660	−	49.6721i	0.201977	−	0.591334i
$85$			104.015i			1.22371i
$86$	−90.1804	−	14.9763i	−1.04861	−	0.174143i
$87$		−	66.4968i		−	0.764331i
$88$	46.3830	+	24.9613i	0.527079	+	0.283651i
$89$	32.7845			0.368365			0.184183	−	0.982892i	$-0.441036\pi$
$89$	32.7845			0.368365			0.184183	+	0.982892i	$0.441036\pi$
$90$	7.97956	−	48.0492i	0.0886617	−	0.533880i
$91$	−9.67441			−0.106312
$92$	−6.20056	+	18.1536i	−0.0673974	+	0.197322i
$93$		−	99.1408i		−	1.06603i
$94$	−26.7940	+	161.341i	−0.285043	+	1.71640i
$95$		−	115.092i		−	1.21150i
$96$	−50.2441	−	54.1551i	−0.523376	−	0.564116i
$97$	−132.916			−1.37027			−0.685136	−	0.728415i	$-0.740257\pi$
$97$	−132.916			−1.37027			−0.685136	+	0.728415i	$0.740257\pi$
$98$	−32.9265	−	5.46813i	−0.335985	−	0.0557972i
$99$	24.1681			0.244122
$100$	−71.9922	−	24.5897i	−0.719922	−	0.245897i
$101$			77.2794i			0.765142i	0.923926	+	0.382571i	$0.124961\pi$
$101$			77.2794i			0.765142i	−0.923926	+	0.382571i	$0.875039\pi$
$102$	71.4064	+	11.8585i	0.700063	+	0.116260i
$103$		−	134.485i		−	1.30568i	−0.757494	−	0.652842i	$-0.773577\pi$
$103$		−	134.485i		−	1.30568i	0.757494	−	0.652842i	$-0.226423\pi$
$104$	−6.45234	+	11.9897i	−0.0620417	+	0.115285i
$105$	−87.0630			−0.829171
$106$	21.8824	−	131.766i	0.206438	−	1.24307i
$107$	45.2694			0.423079			0.211539	−	0.977369i	$-0.432152\pi$
$107$	45.2694			0.423079			0.211539	+	0.977369i	$0.432152\pi$
$108$	−110.722	−	37.8184i	−1.02521	−	0.350170i
$109$			168.137i			1.54254i	0.636509	+	0.771270i	$0.280378\pi$
$109$			168.137i			1.54254i	−0.636509	+	0.771270i	$0.719622\pi$
$110$	14.3131	−	86.1867i	0.130119	−	0.783516i
$111$			49.1397i			0.442700i
$112$	55.6381	−	71.9450i	0.496769	−	0.642366i
$113$	27.6380			0.244584			0.122292	−	0.992494i	$-0.460976\pi$
$113$	27.6380			0.244584			0.122292	+	0.992494i	$0.460976\pi$
$114$	−79.0106	−	13.1213i	−0.693076	−	0.115099i
$115$	31.8188			0.276685
$116$	37.2418	−	109.034i	0.321050	−	0.939951i
$117$			6.24729i			0.0533956i
$118$	−68.8698	−	11.4372i	−0.583642	−	0.0969258i
$119$			89.1158i			0.748873i
$120$	−58.0666	+	107.899i	−0.483888	+	0.899157i
$121$	−77.6493			−0.641730
$122$	20.2345	−	121.843i	0.165857	−	0.998713i
$123$	155.307			1.26266
$124$	55.5242	−	162.560i	0.447776	−	1.31097i
$125$		−	39.6823i		−	0.317458i
$126$	6.83653	−	41.1664i	0.0542582	−	0.326718i
$127$		−	92.6854i		−	0.729806i	−0.931046	−	0.364903i	$-0.881102\pi$
$127$		−	92.6854i		−	0.729806i	0.931046	−	0.364903i	$-0.118898\pi$
$128$	−52.0550	−	116.937i	−0.406680	−	0.913571i
$129$	105.518			0.817969
$130$	22.2787	+	3.69983i	0.171375	+	0.0284602i
$131$	−66.9005			−0.510691			−0.255346	−	0.966850i	$-0.582189\pi$
$131$	−66.9005			−0.510691			−0.255346	+	0.966850i	$0.582189\pi$
$132$	−57.5352	−	19.6518i	−0.435873	−	0.148877i
$133$		−	98.6060i		−	0.741399i
$134$	−16.3170	−	2.70976i	−0.121768	−	0.0202221i
$135$			194.069i			1.43755i
$136$	110.443	+	59.4357i	0.812081	+	0.437027i
$137$	156.575			1.14289			0.571443	−	0.820642i	$-0.306384\pi$
$137$	156.575			1.14289			0.571443	+	0.820642i	$0.306384\pi$
$138$	3.62757	−	21.8435i	0.0262867	−	0.158286i
$139$	178.127			1.28149			0.640744	−	0.767754i	$-0.278626\pi$
$139$	178.127			1.28149			0.640744	+	0.767754i	$0.278626\pi$
$140$	−142.756	−	48.7600i	−1.01969	−	0.348286i
$141$		−	188.782i		−	1.33888i
$142$	−17.6246	+	106.127i	−0.124117	+	0.747373i
$143$			11.2059i			0.0783627i
$144$	−46.4588	−	35.9286i	−0.322630	−	0.249504i
$145$	−191.110			−1.31800
$146$	−117.912	−	19.5817i	−0.807615	−	0.134121i
$147$	38.5266			0.262086
$148$	−27.5209	+	80.5739i	−0.185952	+	0.544418i
$149$			187.761i			1.26014i	0.776538	+	0.630070i	$0.216974\pi$
$149$			187.761i			1.26014i	−0.776538	+	0.630070i	$0.783026\pi$
$150$	86.6255	+	14.3859i	0.577503	+	0.0959062i
$151$			95.8596i			0.634831i	0.948286	+	0.317416i	$0.102815\pi$
$151$			95.8596i			0.634831i	−0.948286	+	0.317416i	$0.897185\pi$
$152$	−122.204	−	65.7652i	−0.803976	−	0.432666i
$153$	57.5469			0.376124
$154$	12.2628	−	73.8410i	0.0796286	−	0.479487i
$155$	−284.928			−1.83825
$156$	5.07985	−	14.8725i	0.0325632	−	0.0953363i
$157$		−	13.5115i		−	0.0860605i	−0.999074	−	0.0430302i	$-0.986299\pi$
$157$		−	13.5115i		−	0.0860605i	0.999074	−	0.0430302i	$-0.0137012\pi$
$158$	14.6765	−	88.3750i	0.0928891	−	0.559335i
$159$			154.176i			0.969662i
$160$	−155.640	+	144.400i	−0.972753	+	0.902502i
$161$	27.2609			0.169323
$162$	68.0487	+	11.3009i	0.420053	+	0.0697585i
$163$	−140.385			−0.861256			−0.430628	−	0.902529i	$-0.641708\pi$
$163$	−140.385			−0.861256			−0.430628	+	0.902529i	$0.641708\pi$
$164$	254.655	+	86.9802i	1.55278	+	0.530367i
$165$			100.845i			0.611182i
$166$	95.7296	+	15.8979i	0.576685	+	0.0957703i
$167$			208.303i			1.24732i	0.781695	+	0.623661i	$0.214355\pi$
$167$			208.303i			1.24732i	−0.781695	+	0.623661i	$0.785645\pi$
$168$	−49.7489	+	92.4430i	−0.296124	+	0.550256i
$169$	166.103			0.982860
$170$	34.0810	−	205.220i	0.200477	−	1.20718i
$171$	−63.6752			−0.372370
$172$	173.017	+	59.0958i	1.00591	+	0.343581i
$173$		−	284.507i		−	1.64455i	−0.569091	−	0.822274i	$-0.692705\pi$
$173$		−	284.507i		−	1.64455i	0.569091	−	0.822274i	$-0.307295\pi$
$174$	−21.7879	+	131.197i	−0.125218	+	0.754005i
$175$			108.109i			0.617768i
$176$	−83.3339	−	64.4457i	−0.473488	−	0.366169i
$177$	80.5830			0.455271
$178$	−64.6831	−	10.7419i	−0.363388	−	0.0603480i
$179$	43.1219			0.240904			0.120452	−	0.992719i	$-0.461566\pi$
$179$	43.1219			0.240904			0.120452	+	0.992719i	$0.461566\pi$
$180$	−31.4870	+	92.1855i	−0.174928	+	0.512142i
$181$		−	175.849i		−	0.971541i	−0.874086	−	0.485770i	$-0.838539\pi$
$181$		−	175.849i		−	0.971541i	0.874086	−	0.485770i	$-0.161461\pi$
$182$	19.0874	+	3.16985i	0.104876	+	0.0174168i
$183$			142.566i			0.779048i
$184$	18.1817	−	33.7850i	0.0988134	−	0.183614i
$185$	141.226			0.763385
$186$	−32.4838	+	195.603i	−0.174644	+	1.05163i
$187$	103.223			0.551994
$188$	105.728	−	309.544i	0.562383	−	1.64651i
$189$			166.270i			0.879733i
$190$	−37.7104	+	227.075i	−0.198476	+	1.19513i
$191$		−	174.764i		−	0.914995i	−0.889211	−	0.457497i	$-0.848746\pi$
$191$		−	174.764i		−	0.914995i	0.889211	−	0.457497i	$-0.151254\pi$
$192$	81.3864	+	123.309i	0.423888	+	0.642237i
$193$	−83.6805			−0.433578			−0.216789	−	0.976219i	$-0.569558\pi$
$193$	−83.6805			−0.433578			−0.216789	+	0.976219i	$0.569558\pi$
$194$	262.241	+	43.5505i	1.35176	+	0.224487i
$195$	−26.0678			−0.133681
$196$	63.1717	+	21.5770i	0.322305	+	0.110087i
$197$			156.944i			0.796669i	0.917240	+	0.398334i	$0.130412\pi$
$197$			156.944i			0.796669i	−0.917240	+	0.398334i	$0.869588\pi$
$198$	−47.6831	−	7.91876i	−0.240824	−	0.0399937i
$199$			219.491i			1.10297i	0.834184	+	0.551486i	$0.185939\pi$
$199$			219.491i			1.10297i	−0.834184	+	0.551486i	$0.814061\pi$
$200$	133.982	+	72.1035i	0.669911	+	0.360517i
$201$	19.0921			0.0949855
$202$	25.3208	−	152.470i	0.125351	−	0.754804i
$203$	−163.735			−0.806576
$204$	−136.998	−	46.7931i	−0.671558	−	0.229378i
$205$		−	446.348i		−	2.17731i
$206$	−44.0646	+	265.337i	−0.213906	+	1.28804i
$207$		−	17.6039i		−	0.0850428i
$208$	16.6588	−	21.5413i	0.0800903	−	0.103564i
$209$	−114.215			−0.546485
$210$	171.773	+	28.5265i	0.817968	+	0.135840i
$211$	138.858			0.658094			0.329047	−	0.944314i	$-0.393273\pi$
$211$	138.858			0.658094			0.329047	+	0.944314i	$0.393273\pi$
$212$	−86.3471	+	252.801i	−0.407297	+	1.19246i
$213$		−	124.177i		−	0.582989i
$214$	−89.3156	−	14.8327i	−0.417363	−	0.0693116i
$215$		−	303.256i		−	1.41049i
$216$	206.061	+	110.893i	0.953987	+	0.513395i
$217$	−244.114			−1.12495
$218$	55.0906	−	331.730i	0.252709	−	1.52170i
$219$	137.966			0.629981
$220$	−56.4787	+	165.355i	−0.256722	+	0.751613i
$221$			26.6824i			0.120735i
$222$	16.1008	−	96.9515i	0.0725261	−	0.436719i
$223$		−	291.890i		−	1.30892i	−0.756096	−	0.654461i	$-0.772896\pi$
$223$		−	291.890i		−	1.30892i	0.756096	−	0.654461i	$-0.227104\pi$
$224$	−133.346	+	123.716i	−0.595294	+	0.552303i
$225$	69.8121			0.310276
$226$	−54.5291	−	9.05567i	−0.241279	−	0.0400693i
$227$	94.3305			0.415553			0.207776	−	0.978176i	$-0.433377\pi$
$227$	94.3305			0.415553			0.207776	+	0.978176i	$0.433377\pi$
$228$	151.587	+	51.7762i	0.664855	+	0.227089i
$229$		−	399.749i		−	1.74563i	−0.488051	−	0.872815i	$-0.662292\pi$
$229$		−	399.749i		−	1.74563i	0.488051	−	0.872815i	$-0.337708\pi$
$230$	−62.7778	−	10.4255i	−0.272947	−	0.0453284i
$231$			86.3996i			0.374024i
$232$	−109.203	+	202.920i	−0.470702	+	0.874654i
$233$	−280.560			−1.20412			−0.602060	−	0.798450i	$-0.705653\pi$
$233$	−280.560			−1.20412			−0.602060	+	0.798450i	$0.705653\pi$
$234$	2.04695	−	12.3258i	0.00874763	−	0.0526742i
$235$	−542.554			−2.30874
$236$	132.131	+	45.1309i	0.559878	+	0.191232i
$237$			103.406i			0.436310i
$238$	29.1991	−	175.824i	0.122685	−	0.738755i
$239$			333.128i			1.39384i	0.717148	+	0.696921i	$0.245447\pi$
$239$			333.128i			1.39384i	−0.717148	+	0.696921i	$0.754553\pi$
$240$	149.918	−	193.856i	0.624656	−	0.807735i
$241$	209.486			0.869237			0.434619	−	0.900615i	$-0.356883\pi$
$241$	209.486			0.869237			0.434619	+	0.900615i	$0.356883\pi$
$242$	153.200	+	25.4421i	0.633059	+	0.105132i
$243$	183.634			0.755695
$244$	−79.8446	+	233.764i	−0.327232	+	0.958048i
$245$		−	110.725i		−	0.451937i
$246$	−306.417	−	50.8868i	−1.24560	−	0.206857i
$247$		−	29.5239i		−	0.119530i
$248$	−162.812	+	302.535i	−0.656498	+	1.21990i
$249$	−112.011			−0.449844
$250$	−13.0020	+	78.2923i	−0.0520081	+	0.313169i
$251$	306.286			1.22026			0.610131	−	0.792300i	$-0.291117\pi$
$251$	306.286			1.22026			0.610131	+	0.792300i	$0.291117\pi$
$252$	−26.9766	+	78.9805i	−0.107050	+	0.313415i
$253$		−	31.5764i		−	0.124808i
$254$	−30.3687	+	182.866i	−0.119562	+	0.719946i
$255$			240.123i			0.941661i
$256$	64.3886	+	247.770i	0.251518	+	0.967853i
$257$	−473.033			−1.84059			−0.920297	−	0.391221i	$-0.872053\pi$
$257$	−473.033			−1.84059			−0.920297	+	0.391221i	$0.872053\pi$
$258$	−208.185	−	34.5733i	−0.806918	−	0.134005i
$259$	120.996			0.467168
$260$	−42.7431	−	14.5994i	−0.164397	−	0.0561515i
$261$			105.732i			0.405105i
$262$	131.993	+	21.9202i	0.503791	+	0.0836648i
$263$		−	171.819i		−	0.653304i	−0.945145	−	0.326652i	$-0.894080\pi$
$263$		−	171.819i		−	0.653304i	0.945145	−	0.326652i	$-0.105920\pi$
$264$	107.077	+	57.6241i	0.405594	+	0.218273i
$265$	443.099			1.67207
$266$	−32.3086	+	194.547i	−0.121461	+	0.731382i
$267$	75.6842			0.283461
$268$	31.3051	+	10.6926i	0.116810	+	0.0398978i
$269$		−	135.873i		−	0.505105i	−0.967583	−	0.252553i	$-0.918730\pi$
$269$		−	135.873i		−	0.505105i	0.967583	−	0.252553i	$-0.0812701\pi$
$270$	63.5873	−	382.894i	0.235509	−	1.41812i
$271$		−	272.728i		−	1.00638i	−0.864177	−	0.503188i	$-0.832160\pi$
$271$		−	272.728i		−	1.00638i	0.864177	−	0.503188i	$-0.167840\pi$
$272$	−198.427	−	153.452i	−0.729512	−	0.564163i
$273$	−22.3337			−0.0818085
$274$	−308.920	−	51.3024i	−1.12744	−	0.187235i
$275$	125.223			0.455357
$276$	−14.3142	+	41.9082i	−0.0518631	+	0.151841i
$277$		−	69.0908i		−	0.249425i	−0.992193	−	0.124713i	$-0.960199\pi$
$277$		−	69.0908i		−	0.249425i	0.992193	−	0.124713i	$-0.0398009\pi$
$278$	−351.441	−	58.3639i	−1.26417	−	0.209942i
$279$			157.638i			0.565009i
$280$	265.679	+	142.977i	0.948853	+	0.510632i
$281$	−345.907			−1.23099			−0.615493	−	0.788142i	$-0.711043\pi$
$281$	−345.907			−1.23099			−0.615493	+	0.788142i	$0.711043\pi$
$282$	−61.8550	+	372.462i	−0.219344	+	1.32079i
$283$	158.112			0.558698			0.279349	−	0.960190i	$-0.409881\pi$
$283$	158.112			0.558698			0.279349	+	0.960190i	$0.409881\pi$
$284$	69.5457	−	203.611i	0.244879	−	0.716942i
$285$		−	265.695i		−	0.932263i
$286$	3.67164	−	22.1089i	0.0128379	−	0.0773040i
$287$		−	382.411i		−	1.33244i
$288$	79.8900	+	86.1086i	0.277396	+	0.298988i
$289$	−43.2146			−0.149531
$290$	377.056	+	62.6179i	1.30019	+	0.215924i
$291$	−306.842			−1.05444
$292$	226.221	+	77.2684i	0.774731	+	0.264618i
$293$			424.612i			1.44919i	0.689176	+	0.724594i	$0.257973\pi$
$293$			424.612i			1.44919i	−0.689176	+	0.724594i	$0.742027\pi$
$294$	−76.0121	−	12.6234i	−0.258545	−	0.0429366i
$295$		−	231.594i		−	0.785063i
$296$	80.6985	−	149.953i	0.272630	−	0.506599i
$297$	192.590			0.648452
$298$	61.5205	−	370.448i	0.206445	−	1.24312i
$299$	8.16228			0.0272986
$300$	−166.197	−	56.7663i	−0.553989	−	0.189221i
$301$		−	259.817i		−	0.863178i
$302$	31.4087	−	189.129i	0.104002	−	0.626254i
$303$			178.402i			0.588786i
$304$	219.558	+	169.794i	0.722231	+	0.558533i
$305$	409.731			1.34338
$306$	−113.539	−	18.8554i	−0.371042	−	0.0616191i
$307$	460.273			1.49926			0.749630	−	0.661857i	$-0.230232\pi$
$307$	460.273			1.49926			0.749630	+	0.661857i	$0.230232\pi$
$308$	−48.3885	+	141.669i	−0.157105	+	0.459963i
$309$		−	310.464i		−	1.00474i
$310$	562.157	+	93.3577i	1.81341	+	0.301154i
$311$			256.687i			0.825359i	0.910876	+	0.412680i	$0.135407\pi$
$311$			256.687i			0.825359i	−0.910876	+	0.412680i	$0.864593\pi$
$312$	−14.8955	+	27.6786i	−0.0477418	+	0.0887135i
$313$	−491.032			−1.56879			−0.784396	−	0.620261i	$-0.787027\pi$
$313$	−491.032			−1.56879			−0.784396	+	0.620261i	$0.787027\pi$
$314$	−4.42709	+	26.6579i	−0.0140990	+	0.0848977i
$315$	138.433			0.439471
$316$	−57.9127	+	169.553i	−0.183268	+	0.536561i
$317$			533.919i			1.68429i	0.539253	+	0.842144i	$0.318707\pi$
$317$			533.919i			1.68429i	−0.539253	+	0.842144i	$0.681293\pi$
$318$	50.5164	−	304.186i	0.158856	−	0.956561i
$319$			189.654i			0.594527i
$320$	354.389	−	233.903i	1.10746	−	0.730946i
$321$	104.506			0.325564
$322$	−53.7852	−	8.93214i	−0.167035	−	0.0277396i
$323$	−271.960			−0.841980
$324$	−130.556	−	44.5927i	−0.402950	−	0.137632i
$325$			32.3694i			0.0995981i
$326$	276.976	+	45.9975i	0.849620	+	0.141097i
$327$			388.150i			1.18700i
$328$	−473.930	−	255.049i	−1.44491	−	0.777588i
$329$	−464.837			−1.41288
$330$	33.0422	−	198.965i	0.100128	−	0.602925i
$331$	−558.000			−1.68580			−0.842900	−	0.538070i	$-0.819154\pi$
$331$	−558.000			−1.68580			−0.842900	+	0.538070i	$0.819154\pi$
$332$	−183.664	−	62.7323i	−0.553203	−	0.188953i
$333$		−	78.1340i		−	0.234636i
$334$	68.2511	−	410.977i	0.204345	−	1.23047i
$335$		−	54.8702i		−	0.163792i
$336$	128.443	−	166.088i	0.382270	−	0.494308i
$337$	208.304			0.618114			0.309057	−	0.951043i	$-0.399987\pi$
$337$	208.304			0.618114			0.309057	+	0.951043i	$0.399987\pi$
$338$	−327.718	−	54.4243i	−0.969581	−	0.161019i
$339$	63.8032			0.188210
$340$	−134.482	+	393.728i	−0.395536	+	1.15802i
$341$			282.757i			0.829200i
$342$	125.630	+	20.8634i	0.367339	+	0.0610041i
$343$		−	373.394i		−	1.08861i
$344$	−321.996	−	173.284i	−0.936034	−	0.503734i
$345$	73.4549			0.212913
$346$	−93.2197	+	561.326i	−0.269421	+	1.62233i
$347$	−440.715			−1.27007			−0.635036	−	0.772482i	$-0.719015\pi$
$347$	−440.715			−1.27007			−0.635036	+	0.772482i	$0.719015\pi$
$348$	85.9742	−	251.710i	0.247052	−	0.723303i
$349$		−	445.460i		−	1.27639i	−0.769875	−	0.638195i	$-0.779681\pi$
$349$		−	445.460i		−	1.27639i	0.769875	−	0.638195i	$-0.220319\pi$
$350$	35.4224	−	213.298i	0.101207	−	0.609422i
$351$			49.7833i			0.141833i
$352$	143.300	+	154.455i	0.407103	+	0.438791i
$353$	591.364			1.67525			0.837626	−	0.546245i	$-0.183943\pi$
$353$	591.364			1.67525			0.837626	+	0.546245i	$0.183943\pi$
$354$	−158.988	−	26.4033i	−0.449120	−	0.0745856i
$355$	−356.881			−1.00530
$356$	124.099	+	42.3873i	0.348592	+	0.119065i
$357$			205.727i			0.576267i
$358$	−85.0785	−	14.1290i	−0.237650	−	0.0394666i
$359$		−	33.1276i		−	0.0922774i	−0.998935	−	0.0461387i	$-0.985308\pi$
$359$		−	33.1276i		−	0.0922774i	0.998935	−	0.0461387i	$-0.0146916\pi$
$360$	92.3280	−	171.563i	0.256467	−	0.476565i
$361$	−60.0787			−0.166423
$362$	−57.6175	+	346.946i	−0.159164	+	0.958414i
$363$	−179.256			−0.493819
$364$	−36.6204	−	12.5081i	−0.100605	−	0.0343629i
$365$		−	396.510i		−	1.08633i
$366$	46.7121	−	281.279i	0.127629	−	0.768522i
$367$			52.5165i			0.143097i	0.997437	+	0.0715483i	$0.0227940\pi$
$367$			52.5165i			0.143097i	−0.997437	+	0.0715483i	$0.977206\pi$
$368$	−46.9418	+	60.6998i	−0.127559	+	0.164945i
$369$	−246.944			−0.669224
$370$	−278.636	−	46.2733i	−0.753071	−	0.125063i
$371$	379.627			1.02325
$372$	128.180	−	375.276i	0.344569	−	1.00881i
$373$			335.552i			0.899602i	0.893129	+	0.449801i	$0.148505\pi$
$373$			335.552i			0.899602i	−0.893129	+	0.449801i	$0.851495\pi$
$374$	−203.657	−	33.8213i	−0.544536	−	0.0904314i
$375$		−	91.6080i		−	0.244288i
$376$	−310.022	+	576.081i	−0.824527	+	1.53213i
$377$	−49.0243			−0.130038
$378$	54.4788	−	328.046i	0.144124	−	0.867847i
$379$	−447.090			−1.17966			−0.589829	−	0.807528i	$-0.700805\pi$
$379$	−447.090			−1.17966			−0.589829	+	0.807528i	$0.700805\pi$
$380$	148.804	−	435.657i	0.391588	−	1.14647i
$381$		−	213.968i		−	0.561595i
$382$	−57.2620	+	344.806i	−0.149901	+	0.902632i
$383$		−	335.690i		−	0.876475i	−0.898859	−	0.438237i	$-0.855603\pi$
$383$		−	335.690i		−	0.876475i	0.898859	−	0.438237i	$-0.144397\pi$
$384$	−120.171	−	269.953i	−0.312945	−	0.703004i
$385$	248.310			0.644962
$386$	165.100	+	27.4182i	0.427720	+	0.0710316i
$387$	−167.778			−0.433534
$388$	−503.127	−	171.848i	−1.29672	−	0.442908i
$389$			680.719i			1.74992i	0.484195	+	0.874960i	$0.339112\pi$
$389$			680.719i			1.74992i	−0.484195	+	0.874960i	$0.660888\pi$
$390$	51.4312	+	8.54120i	0.131875	+	0.0219005i
$391$		−	75.1869i		−	0.192294i
$392$	−117.567	−	63.2694i	−0.299915	−	0.161401i
$393$	−154.442			−0.392983
$394$	51.4231	−	309.647i	0.130516	−	0.785905i
$395$	297.185			0.752367
$396$	91.4831	+	31.2471i	0.231018	+	0.0789067i
$397$		−	436.464i		−	1.09941i	−0.835360	−	0.549703i	$-0.814741\pi$
$397$		−	436.464i		−	1.09941i	0.835360	−	0.549703i	$-0.185259\pi$
$398$	71.9171	−	433.052i	0.180696	−	1.08807i
$399$		−	227.636i		−	0.570515i
$400$	−240.719	−	186.158i	−0.601797	−	0.465396i
$401$	725.449			1.80910			0.904550	−	0.426368i	$-0.140207\pi$
$401$	725.449			1.80910			0.904550	+	0.426368i	$0.140207\pi$
$402$	−37.6683	−	6.25559i	−0.0937022	−	0.0155612i
$403$	−73.0909			−0.181367
$404$	−99.9150	+	292.525i	−0.247314	+	0.724071i
$405$			228.832i			0.565018i
$406$	323.045	+	53.6483i	0.795678	+	0.132139i
$407$		−	140.150i		−	0.344349i
$408$	254.962	+	137.210i	0.624906	+	0.336298i
$409$	168.291			0.411469			0.205735	−	0.978608i	$-0.434042\pi$
$409$	168.291			0.411469			0.205735	+	0.978608i	$0.434042\pi$
$410$	−146.247	+	880.635i	−0.356701	+	2.14789i
$411$	361.460			0.879464
$412$	173.877	−	509.066i	0.422031	−	1.23560i
$413$		−	198.419i		−	0.480434i
$414$	−5.76797	+	34.7320i	−0.0139323	+	0.0838938i
$415$			321.917i			0.775704i
$416$	−39.9255	+	37.0421i	−0.0959747	+	0.0890436i
$417$	411.213			0.986121
$418$	225.344	+	37.4231i	0.539102	+	0.0895289i
$419$	512.274			1.22261			0.611306	−	0.791395i	$-0.290645\pi$
$419$	512.274			1.22261			0.611306	+	0.791395i	$0.290645\pi$
$420$	−329.558	−	112.564i	−0.784663	−	0.268010i
$421$			468.183i			1.11207i	0.831158	+	0.556036i	$0.187678\pi$
$421$			468.183i			1.11207i	−0.831158	+	0.556036i	$0.812322\pi$
$422$	−273.964	−	45.4973i	−0.649203	−	0.107813i
$423$			300.170i			0.709622i
$424$	253.192	−	470.480i	0.597151	−	1.10962i
$425$	298.171			0.701578
$426$	−40.6869	+	244.998i	−0.0955092	+	0.575113i
$427$	351.039			0.822105
$428$	171.358	+	58.5291i	0.400369	+	0.136750i
$429$			25.8692i			0.0603011i
$430$	−99.3630	+	598.318i	−0.231077	+	1.39144i
$431$		−	272.969i		−	0.633340i	−0.948536	−	0.316670i	$-0.897435\pi$
$431$		−	272.969i		−	0.633340i	0.948536	−	0.316670i	$-0.102565\pi$
$432$	−370.220	−	286.307i	−0.856990	−	0.662747i
$433$	−703.918			−1.62568			−0.812838	−	0.582490i	$-0.802079\pi$
$433$	−703.918			−1.62568			−0.812838	+	0.582490i	$0.802079\pi$
$434$	481.631	+	79.9847i	1.10975	+	0.184297i
$435$	−441.185			−1.01422
$436$	−217.385	+	636.446i	−0.498590	+	1.45974i
$437$			83.1937i			0.190375i
$438$	−272.204	−	45.2050i	−0.621469	−	0.103208i
$439$			692.678i			1.57785i	0.614486	+	0.788927i	$0.289363\pi$
$439$			692.678i			1.57785i	−0.614486	+	0.788927i	$0.710637\pi$
$440$	165.610	−	307.736i	0.376387	−	0.699400i
$441$	−61.2587			−0.138909
$442$	8.74259	−	52.6439i	0.0197796	−	0.119104i
$443$	434.796			0.981481			0.490741	−	0.871306i	$-0.336726\pi$
$443$	434.796			0.981481			0.490741	+	0.871306i	$0.336726\pi$
$444$	−63.5330	+	186.008i	−0.143092	+	0.418936i
$445$		−	217.515i		−	0.488797i
$446$	−95.6386	+	575.892i	−0.214436	+	1.29124i
$447$			433.453i			0.969694i
$448$	303.624	−	200.397i	0.677733	−	0.447316i
$449$	114.638			0.255319			0.127660	−	0.991818i	$-0.459253\pi$
$449$	114.638			0.255319			0.127660	+	0.991818i	$0.459253\pi$
$450$	−137.738	−	22.8742i	−0.306084	−	0.0508315i
$451$	−442.947			−0.982144
$452$	104.618	+	35.7333i	0.231455	+	0.0790559i
$453$			221.295i			0.488511i
$454$	−186.112	−	30.9077i	−0.409938	−	0.0680786i
$455$			64.1866i			0.141069i
$456$	−282.113	−	151.821i	−0.618669	−	0.332941i
$457$	178.593			0.390795			0.195397	−	0.980724i	$-0.437400\pi$
$457$	178.593			0.390795			0.195397	+	0.980724i	$0.437400\pi$
$458$	−130.979	+	788.697i	−0.285981	+	1.72205i
$459$	458.579			0.999082
$460$	120.443	+	41.1387i	0.261833	+	0.0894320i
$461$			429.496i			0.931662i	0.884874	+	0.465831i	$0.154244\pi$
$461$			429.496i			0.931662i	−0.884874	+	0.465831i	$0.845756\pi$
$462$	28.3091	−	170.465i	0.0612752	−	0.368971i
$463$			115.307i			0.249044i	0.992217	+	0.124522i	$0.0397397\pi$
$463$			115.307i			0.249044i	−0.992217	+	0.124522i	$0.960260\pi$
$464$	281.942	−	364.576i	0.607634	−	0.785724i
$465$	−657.767			−1.41455
$466$	553.539	+	91.9265i	1.18785	+	0.197267i
$467$	274.914			0.588681			0.294340	−	0.955701i	$-0.404900\pi$
$467$	274.914			0.588681			0.294340	+	0.955701i	$0.404900\pi$
$468$	−8.07716	+	23.6478i	−0.0172589	+	0.0505294i
$469$		−	47.0104i		−	0.100235i
$470$	1070.45	+	177.770i	2.27755	+	0.378234i
$471$		−	31.1918i		−	0.0662246i
$472$	−245.905	−	132.335i	−0.520984	−	0.280372i
$473$	−300.946			−0.636249
$474$	33.8812	−	204.017i	0.0714793	−	0.430415i
$475$	−329.923			−0.694576
$476$	−115.218	+	337.329i	−0.242055	+	0.708674i
$477$		−	245.146i		−	0.513933i
$478$	109.151	−	657.255i	0.228349	−	1.37501i
$479$			483.354i			1.00909i	0.863385	+	0.504545i	$0.168340\pi$
$479$			483.354i			1.00909i	−0.863385	+	0.504545i	$0.831660\pi$
$480$	−359.302	+	333.353i	−0.748545	+	0.694486i
$481$	36.2279			0.0753179
$482$	−413.312	−	68.6388i	−0.857493	−	0.142404i
$483$	62.9329			0.130296
$484$	−293.925	−	100.393i	−0.607283	−	0.207424i
$485$			881.858i			1.81826i
$486$	−362.306	−	60.1683i	−0.745485	−	0.123803i
$487$		−	182.966i		−	0.375699i	−0.982198	−	0.187850i	$-0.939848\pi$
$487$		−	182.966i		−	0.375699i	0.982198	−	0.187850i	$-0.0601518\pi$
$488$	234.125	−	435.049i	0.479765	−	0.891495i
$489$	−324.083			−0.662747
$490$	−36.2793	+	218.457i	−0.0740393	+	0.445831i
$491$	881.931			1.79619			0.898097	−	0.439798i	$-0.144950\pi$
$491$	881.931			1.79619			0.898097	+	0.439798i	$0.144950\pi$
$492$	587.881	+	200.797i	1.19488	+	0.408124i
$493$			451.588i			0.916000i
$494$	−9.67361	+	58.2500i	−0.0195822	+	0.117915i
$495$		−	160.347i		−	0.323934i
$496$	420.350	−	543.549i	0.847480	−	1.09587i
$497$	−305.760			−0.615211
$498$	220.995	+	36.7008i	0.443766	+	0.0736964i
$499$	493.337			0.988652			0.494326	−	0.869277i	$-0.335415\pi$
$499$	493.337			0.988652			0.494326	+	0.869277i	$0.335415\pi$
$500$	51.3055	−	150.209i	0.102611	−	0.300418i
$501$			480.874i			0.959829i
$502$	−604.295	−	100.356i	−1.20378	−	0.199912i
$503$		−	349.547i		−	0.694925i	−0.937694	−	0.347462i	$-0.887043\pi$
$503$		−	349.547i		−	0.694925i	0.937694	−	0.347462i	$-0.112957\pi$
$504$	79.1026	−	146.988i	0.156950	−	0.291642i
$505$	512.724			1.01529
$506$	−10.3461	+	62.2995i	−0.0204468	+	0.123121i
$507$	383.456			0.756323
$508$	119.833	−	350.841i	0.235893	−	0.690631i
$509$			477.957i			0.939011i	0.882929	+	0.469506i	$0.155568\pi$
$509$			477.957i			0.939011i	−0.882929	+	0.469506i	$0.844432\pi$
$510$	78.6773	−	473.758i	0.154269	−	0.928938i
$511$		−	339.713i		−	0.664800i
$512$	−45.8544	−	509.943i	−0.0895594	−	0.995981i
$513$	−507.414			−0.989111
$514$	933.283	+	154.991i	1.81573	+	0.301538i
$515$	−892.267			−1.73256
$516$	399.416	+	136.425i	0.774062	+	0.264389i
$517$			538.420i			1.04143i
$518$	−238.723	−	39.6449i	−0.460856	−	0.0765345i
$519$		−	656.795i		−	1.26550i
$520$	79.5477	+	42.8092i	0.152976	+	0.0823253i
$521$	−714.138			−1.37071			−0.685353	−	0.728211i	$-0.740352\pi$
$521$	−714.138			−1.37071			−0.685353	+	0.728211i	$0.740352\pi$
$522$	34.6436	−	208.608i	0.0663671	−	0.399632i
$523$	−768.507			−1.46942			−0.734710	−	0.678381i	$-0.762682\pi$
$523$	−768.507			−1.46942			−0.734710	+	0.678381i	$0.762682\pi$
$524$	−253.238	−	86.4961i	−0.483278	−	0.165069i
$525$			249.575i			0.475380i
$526$	−56.2970	+	338.995i	−0.107029	+	0.644477i
$527$			673.277i			1.27756i
$528$	−192.379	−	148.775i	−0.364355	−	0.281771i
$529$	−23.0000			−0.0434783
$530$	−874.224	−	145.183i	−1.64948	−	0.273930i
$531$	−128.130			−0.241299
$532$	127.488	−	373.252i	0.239640	−	0.701601i
$533$		−	114.499i		−	0.214820i
$534$	−149.323	−	24.7982i	−0.279632	−	0.0464385i
$535$		−	300.348i		−	0.561398i
$536$	−58.2609	−	31.3535i	−0.108696	−	0.0584954i
$537$	99.5484			0.185379
$538$	−44.5194	+	268.075i	−0.0827497	+	0.498281i
$539$	−109.881			−0.203861
$540$	−250.913	+	734.606i	−0.464653	+	1.36038i
$541$		−	266.158i		−	0.491975i	−0.969273	−	0.245987i	$-0.920888\pi$
$541$		−	266.158i		−	0.491975i	0.969273	−	0.245987i	$-0.0791121\pi$
$542$	−89.3603	+	538.087i	−0.164871	+	0.992780i
$543$		−	405.954i		−	0.747612i
$544$	341.214	+	367.774i	0.627231	+	0.676055i
$545$	1115.53			2.04685
$546$	44.0639	+	7.31772i	0.0807032	+	0.0134024i
$547$	−521.270			−0.952962			−0.476481	−	0.879185i	$-0.658088\pi$
$547$	−521.270			−0.952962			−0.476481	+	0.879185i	$0.658088\pi$
$548$	592.682	+	202.437i	1.08154	+	0.369411i
$549$		−	226.685i		−	0.412905i
$550$	−247.063	−	41.0298i	−0.449205	−	0.0745997i
$551$		−	499.679i		−	0.906858i
$552$	41.9730	−	77.9939i	0.0760381	−	0.141293i
$553$	254.615			0.460425
$554$	−22.6378	+	136.315i	−0.0408625	+	0.246055i
$555$	326.026			0.587434
$556$	674.261	+	230.301i	1.21270	+	0.414211i
$557$			198.144i			0.355735i	0.984054	+	0.177867i	$0.0569198\pi$
$557$			198.144i			0.355735i	−0.984054	+	0.177867i	$0.943080\pi$
$558$	51.6505	−	311.015i	0.0925636	−	0.557375i
$559$		−	77.7925i		−	0.139164i
$560$	−477.332	−	369.141i	−0.852378	−	0.659181i
$561$	238.294			0.424766
$562$	682.467	+	113.338i	1.21435	+	0.201668i
$563$	−49.7822			−0.0884231			−0.0442115	−	0.999022i	$-0.514078\pi$
$563$	−49.7822			−0.0884231			−0.0442115	+	0.999022i	$0.514078\pi$
$564$	244.077	−	714.593i	0.432761	−	1.26701i
$565$		−	183.369i		−	0.324547i
$566$	−311.951	−	51.8058i	−0.551150	−	0.0915297i
$567$			196.053i			0.345773i
$568$	−203.926	+	378.934i	−0.359025	+	0.667137i
$569$	1047.92			1.84169			0.920844	−	0.389932i	$-0.127501\pi$
$569$	1047.92			1.84169			0.920844	+	0.389932i	$0.127501\pi$
$570$	−87.0558	+	524.210i	−0.152729	+	0.919667i
$571$	613.654			1.07470			0.537350	−	0.843359i	$-0.319425\pi$
$571$	613.654			1.07470			0.537350	+	0.843359i	$0.319425\pi$
$572$	−14.4881	+	42.4174i	−0.0253289	+	0.0741563i
$573$		−	403.449i		−	0.704100i
$574$	−125.298	+	754.489i	−0.218290	+	1.31444i
$575$		−	91.2117i		−	0.158629i
$576$	−129.407	−	196.067i	−0.224666	−	0.340394i
$577$	432.629			0.749790			0.374895	−	0.927067i	$-0.377679\pi$
$577$	432.629			0.749790			0.374895	+	0.927067i	$0.377679\pi$
$578$	85.2615	+	14.1594i	0.147511	+	0.0244972i
$579$	−193.179			−0.333643
$580$	−723.407	−	247.088i	−1.24725	−	0.426013i
$581$			275.804i			0.474706i
$582$	605.393	+	100.538i	1.04019	+	0.172746i
$583$		−	439.723i		−	0.754241i
$584$	−421.013	−	226.571i	−0.720912	−	0.387964i
$585$	41.4488			0.0708526
$586$	139.126	−	837.750i	0.237416	−	1.42961i
$587$	−318.340			−0.542317			−0.271158	−	0.962535i	$-0.587407\pi$
$587$	−318.340			−0.542317			−0.271158	+	0.962535i	$0.587407\pi$
$588$	145.834	+	49.8113i	0.248017	+	0.0847130i
$589$		−	744.976i		−	1.26481i
$590$	−75.8824	+	456.929i	−0.128614	+	0.774456i
$591$			362.310i			0.613046i
$592$	−208.349	+	269.413i	−0.351941	+	0.455090i
$593$	−131.119			−0.221111			−0.110556	−	0.993870i	$-0.535263\pi$
$593$	−131.119			−0.221111			−0.110556	+	0.993870i	$0.535263\pi$
$594$	−379.976	−	63.1028i	−0.639691	−	0.106234i
$595$	591.255			0.993706
$596$	−242.757	+	710.729i	−0.407311	+	1.19250i
$597$			506.704i			0.848750i
$598$	−16.1040	−	2.67440i	−0.0269298	−	0.00447224i
$599$		−	304.644i		−	0.508588i	−0.967127	−	0.254294i	$-0.918157\pi$
$599$		−	304.644i		−	0.508588i	0.967127	−	0.254294i	$-0.0818431\pi$
$600$	309.303	+	166.454i	0.515504	+	0.277423i
$601$	−262.821			−0.437306			−0.218653	−	0.975803i	$-0.570166\pi$
$601$	−262.821			−0.437306			−0.218653	+	0.975803i	$0.570166\pi$
$602$	−85.1298	+	512.612i	−0.141412	+	0.851516i
$603$	−30.3571			−0.0503435
$604$	−123.937	+	362.856i	−0.205194	+	0.600755i
$605$			515.178i			0.851534i
$606$	58.4541	−	351.984i	0.0964589	−	0.580831i
$607$		−	884.937i		−	1.45789i	−0.684574	−	0.728943i	$-0.740012\pi$
$607$		−	884.937i		−	1.45789i	0.684574	−	0.728943i	$-0.259988\pi$
$608$	−377.550	−	406.939i	−0.620971	−	0.669307i
$609$	−377.988			−0.620670
$610$	−808.389	−	134.250i	−1.32523	−	0.220081i
$611$	−139.178			−0.227787
$612$	217.832	+	74.4028i	0.355934	+	0.121573i
$613$			78.9790i			0.128840i	0.997923	+	0.0644200i	$0.0205197\pi$
$613$			78.9790i			0.128840i	−0.997923	+	0.0644200i	$0.979480\pi$
$614$	−908.108	−	150.810i	−1.47900	−	0.245619i
$615$		−	1030.41i		−	1.67546i
$616$	141.888	−	263.655i	0.230337	−	0.428011i
$617$	−152.392			−0.246989			−0.123494	−	0.992345i	$-0.539410\pi$
$617$	−152.392			−0.246989			−0.123494	+	0.992345i	$0.539410\pi$
$618$	−101.725	+	612.540i	−0.164603	+	0.991164i
$619$	−582.058			−0.940320			−0.470160	−	0.882581i	$-0.655804\pi$
$619$	−582.058			−0.940320			−0.470160	+	0.882581i	$0.655804\pi$
$620$	−1078.53	−	368.385i	−1.73957	−	0.594170i
$621$		−	140.281i		−	0.225896i
$622$	84.1043	−	506.437i	0.135216	−	0.814208i
$623$		−	186.357i		−	0.299128i
$624$	38.4574	−	49.7288i	0.0616304	−	0.0796935i
$625$	−738.753			−1.18201
$626$	968.795	+	160.888i	1.54760	+	0.257010i
$627$	−263.670			−0.420527
$628$	17.4691	−	51.1449i	0.0278170	−	0.0814409i
$629$		−	333.713i		−	0.530546i
$630$	−273.126	−	45.3582i	−0.433533	−	0.0719971i
$631$		−	98.8684i		−	0.156685i	−0.996926	−	0.0783426i	$-0.975037\pi$
$631$		−	98.8684i		−	0.156685i	0.996926	−	0.0783426i	$-0.0249628\pi$
$632$	169.815	−	315.549i	0.268695	−	0.499287i
$633$	320.558			0.506411
$634$	174.940	−	1053.41i	0.275931	−	1.66153i
$635$	−614.938			−0.968406
$636$	−199.335	+	583.601i	−0.313420	+	0.917612i
$637$		−	28.4035i		−	0.0445894i
$638$	62.1408	−	374.184i	0.0973994	−	0.586495i
$639$			197.446i			0.308992i
$640$	−775.840	+	345.368i	−1.21225	+	0.539638i
$641$	−38.9478			−0.0607611			−0.0303805	−	0.999538i	$-0.509672\pi$
$641$	−38.9478			−0.0607611			−0.0303805	+	0.999538i	$0.509672\pi$
$642$	−206.188	−	34.2418i	−0.321166	−	0.0533361i
$643$	224.528			0.349188			0.174594	−	0.984640i	$-0.444139\pi$
$643$	224.528			0.349188			0.174594	+	0.984640i	$0.444139\pi$
$644$	103.190	+	35.2458i	0.160234	+	0.0547296i
$645$		−	700.078i		−	1.08539i
$646$	536.571	+	89.1085i	0.830605	+	0.137939i
$647$		−	773.141i		−	1.19496i	−0.801883	−	0.597481i	$-0.796168\pi$
$647$		−	773.141i		−	1.19496i	0.801883	−	0.597481i	$-0.203832\pi$
$648$	242.973	+	130.758i	0.374958	+	0.201786i
$649$	−229.829			−0.354128
$650$	10.6059	−	63.8641i	0.0163168	−	0.0982524i
$651$	−563.546			−0.865662
$652$	−531.397	−	181.504i	−0.815025	−	0.278381i
$653$		−	582.457i		−	0.891972i	−0.895040	−	0.445986i	$-0.852853\pi$
$653$		−	582.457i		−	0.891972i	0.895040	−	0.445986i	$-0.147147\pi$
$654$	127.179	−	765.811i	0.194463	−	1.17097i
$655$			443.863i			0.677654i
$656$	851.485	+	658.490i	1.29800	+	1.00380i
$657$	−219.371			−0.333898
$658$	917.112	+	152.305i	1.39379	+	0.231467i
$659$	−1221.95			−1.85425			−0.927125	−	0.374752i	$-0.877728\pi$
$659$	−1221.95			−1.85425			−0.927125	+	0.374752i	$0.877728\pi$
$660$	−130.383	+	381.728i	−0.197550	+	0.578375i
$661$		−	869.718i		−	1.31576i	−0.753122	−	0.657881i	$-0.771453\pi$
$661$		−	869.718i		−	1.31576i	0.753122	−	0.657881i	$-0.228547\pi$
$662$	1100.92	+	182.831i	1.66302	+	0.276179i
$663$			61.5974i			0.0929071i
$664$	341.810	+	183.947i	0.514774	+	0.277029i
$665$	−654.219			−0.983788
$666$	−25.6009	+	154.157i	−0.0384397	+	0.231466i
$667$	138.143			0.207111
$668$	−269.316	+	788.486i	−0.403168	+	1.18037i
$669$		−	673.838i		−	1.00723i
$670$	−17.9784	+	108.258i	−0.0268334	+	0.161579i
$671$		−	406.609i		−	0.605974i
$672$	−307.834	+	285.602i	−0.458086	+	0.425004i
$673$	1183.23			1.75815			0.879075	−	0.476684i	$-0.158161\pi$
$673$	1183.23			1.75815			0.879075	+	0.476684i	$0.158161\pi$
$674$	−410.980	−	68.2517i	−0.609763	−	0.101264i
$675$	556.317			0.824174
$676$	628.749	+	214.756i	0.930102	+	0.317686i
$677$			525.477i			0.776185i	0.921620	+	0.388093i	$0.126866\pi$
$677$			525.477i			0.776185i	−0.921620	+	0.388093i	$0.873134\pi$
$678$	−125.882	−	20.9053i	−0.185667	−	0.0308338i
$679$			755.537i			1.11272i
$680$	394.337	−	732.754i	0.579907	−	1.07758i
$681$	217.765			0.319773
$682$	92.6464	−	557.874i	0.135845	−	0.817997i
$683$	−333.863			−0.488819			−0.244409	−	0.969672i	$-0.578594\pi$
$683$	−333.863			−0.488819			−0.244409	+	0.969672i	$0.578594\pi$
$684$	−241.029	−	82.3261i	−0.352382	−	0.120360i
$685$		−	1038.83i		−	1.51654i
$686$	−122.344	+	736.699i	−0.178344	+	1.07391i
$687$		−	922.836i		−	1.34328i
$688$	578.513	+	447.389i	0.840863	+	0.650275i
$689$	113.665			0.164971
$690$	−144.925	−	24.0677i	−0.210036	−	0.0348808i
$691$	160.462			0.232217			0.116108	−	0.993237i	$-0.462958\pi$
$691$	160.462			0.232217			0.116108	+	0.993237i	$0.462958\pi$
$692$	367.841	−	1076.94i	0.531562	−	1.55627i
$693$		−	137.379i		−	0.198238i
$694$	869.522	+	144.402i	1.25291	+	0.208072i
$695$		−	1181.81i		−	1.70045i
$696$	−252.099	+	468.448i	−0.362211	+	0.673057i
$697$	−1054.71			−1.51321
$698$	−145.956	+	878.883i	−0.209107	+	1.25914i
$699$	−647.683			−0.926586
$700$	−139.775	+	409.225i	−0.199679	+	0.584607i
$701$		−	767.973i		−	1.09554i	−0.836629	−	0.547770i	$-0.815477\pi$
$701$		−	767.973i		−	1.09554i	0.836629	−	0.547770i	$-0.184523\pi$
$702$	16.3117	−	98.2213i	0.0232360	−	0.139916i
$703$			369.251i			0.525251i
$704$	−232.120	−	351.688i	−0.329717	−	0.499557i
$705$	−1252.51			−1.77661
$706$	−1166.75	−	193.762i	−1.65262	−	0.274451i
$707$	439.279			0.621328
$708$	305.030	+	104.186i	0.430833	+	0.147156i
$709$			147.850i			0.208533i	0.994549	+	0.104266i	$0.0332494\pi$
$709$			147.850i			0.208533i	−0.994549	+	0.104266i	$0.966751\pi$
$710$	704.118	+	116.933i	0.991716	+	0.164695i
$711$		−	164.419i		−	0.231250i
$712$	−230.956	−	124.291i	−0.324376	−	0.174565i
$713$	205.958			0.288862
$714$	67.4072	−	405.895i	0.0944079	−	0.568481i
$715$	74.3474			0.103982
$716$	163.229	+	55.7525i	0.227973	+	0.0778667i
$717$			769.039i			1.07258i
$718$	−10.8544	+	65.3600i	−0.0151175	+	0.0910307i
$719$			360.341i			0.501169i	0.968095	+	0.250585i	$0.0806229\pi$
$719$			360.341i			0.501169i	−0.968095	+	0.250585i	$0.919377\pi$
$720$	−238.374	+	308.239i	−0.331076	+	0.428110i
$721$	−764.455			−1.06027
$722$	118.534	+	19.6850i	0.164174	+	0.0272645i
$723$	483.606			0.668888
$724$	227.356	−	665.638i	0.314028	−	0.919390i
$725$			547.837i			0.755637i
$726$	353.669	+	58.7339i	0.487147	+	0.0809007i
$727$			1008.39i			1.38706i	0.720427	+	0.693531i	$0.243946\pi$
$727$			1008.39i			1.38706i	−0.720427	+	0.693531i	$0.756054\pi$
$728$	68.1529	+	36.6770i	0.0936167	+	0.0503805i
$729$	734.339			1.00732
$730$	−129.918	+	782.307i	−0.177970	+	1.07165i
$731$	−716.586			−0.980281
$732$	−184.324	+	539.652i	−0.251809	+	0.737230i
$733$			514.256i			0.701577i	0.936455	+	0.350789i	$0.114086\pi$
$733$			514.256i			0.701577i	−0.936455	+	0.350789i	$0.885914\pi$
$734$	17.2072	−	103.614i	0.0234430	−	0.141163i
$735$		−	255.612i		−	0.347771i
$736$	112.504	−	104.379i	0.152858	−	0.141819i
$737$	−54.4521			−0.0738835
$738$	487.214	+	80.9119i	0.660182	+	0.109637i
$739$	360.794			0.488220			0.244110	−	0.969748i	$-0.421504\pi$
$739$	360.794			0.488220			0.244110	+	0.969748i	$0.421504\pi$
$740$	534.582	+	182.592i	0.722408	+	0.246746i
$741$		−	68.1570i		−	0.0919798i
$742$	−748.996	−	124.386i	−1.00943	−	0.167636i
$743$			515.070i			0.693230i	0.938007	+	0.346615i	$0.112669\pi$
$743$			515.070i			0.693230i	−0.938007	+	0.346615i	$0.887331\pi$
$744$	−375.856	+	698.413i	−0.505183	+	0.938728i
$745$	1245.73			1.67213
$746$	109.945	−	662.036i	0.147379	−	0.887448i
$747$	178.102			0.238423
$748$	390.728	+	133.458i	0.522364	+	0.178419i
$749$		−	257.325i		−	0.343558i
$750$	−30.0157	+	180.741i	−0.0400209	+	0.240987i
$751$			1155.50i			1.53861i	0.638881	+	0.769306i	$0.279398\pi$
$751$			1155.50i			1.53861i	−0.638881	+	0.769306i	$0.720602\pi$
$752$	800.422	−	1035.02i	1.06439	−	1.37635i
$753$	707.072			0.939007
$754$	96.7239	+	16.0630i	0.128281	+	0.0213037i
$755$	635.997			0.842381
$756$	−214.971	+	629.378i	−0.284353	+	0.832511i
$757$			67.7308i			0.0894726i	0.998999	+	0.0447363i	$0.0142448\pi$
$757$			67.7308i			0.0894726i	−0.998999	+	0.0447363i	$0.985755\pi$
$758$	882.100	+	146.491i	1.16372	+	0.193259i
$759$		−	72.8952i		−	0.0960411i
$760$	−436.331	+	810.787i	−0.574120	+	1.06682i
$761$	−80.8701			−0.106268			−0.0531341	−	0.998587i	$-0.516921\pi$
$761$	−80.8701			−0.106268			−0.0531341	+	0.998587i	$0.516921\pi$
$762$	−70.1072	+	422.153i	−0.0920042	+	0.554007i
$763$	955.740			1.25261
$764$	225.953	−	661.532i	0.295751	−	0.865879i
$765$		−	381.805i		−	0.499092i
$766$	−109.990	+	662.309i	−0.143590	+	0.864633i
$767$		−	59.4092i		−	0.0774566i
$768$	148.643	+	571.987i	0.193546	+	0.744774i
$769$	−1175.57			−1.52870			−0.764352	−	0.644799i	$-0.776941\pi$
$769$	−1175.57			−1.52870			−0.764352	+	0.644799i	$0.776941\pi$
$770$	−489.911	−	81.3597i	−0.636248	−	0.105662i
$771$	−1092.01			−1.41636
$772$	−316.755	−	108.191i	−0.410304	−	0.140144i
$773$			1046.97i			1.35442i	0.735790	+	0.677209i	$0.236811\pi$
$773$			1046.97i			1.35442i	−0.735790	+	0.677209i	$0.763189\pi$
$774$	331.022	+	54.9729i	0.427677	+	0.0710244i
$775$			816.775i			1.05390i
$776$	936.351	+	503.904i	1.20664	+	0.649361i
$777$	279.325			0.359491
$778$	223.040	−	1343.04i	0.286684	−	1.72628i
$779$	1167.02			1.49811
$780$	−98.6740	−	33.7032i	−0.126505	−	0.0432092i
$781$			354.162i			0.453472i
$782$	−24.6352	+	148.342i	−0.0315029	+	0.189696i
$783$			842.559i			1.07606i
$784$	211.226	+	163.350i	0.269421	+	0.208355i
$785$	−89.6444			−0.114197
$786$	304.711	+	50.6035i	0.387673	+	0.0643811i
$787$	467.379			0.593874			0.296937	−	0.954897i	$-0.404035\pi$
$787$	467.379			0.593874			0.296937	+	0.954897i	$0.404035\pi$
$788$	−202.913	+	594.077i	−0.257504	+	0.753905i
$789$		−	396.650i		−	0.502725i
$790$	−586.340	−	97.3737i	−0.742202	−	0.123258i
$791$		−	157.102i		−	0.198612i
$792$	−170.256	−	91.6245i	−0.214970	−	0.115688i
$793$	105.106			0.132542
$794$	−143.009	+	861.135i	−0.180112	+	1.08455i
$795$	1022.91			1.28668
$796$	−283.782	+	830.838i	−0.356510	+	1.04377i
$797$			730.259i			0.916260i	0.888885	+	0.458130i	$0.151481\pi$
$797$			730.259i			0.916260i	−0.888885	+	0.458130i	$0.848519\pi$
$798$	−74.5856	+	449.120i	−0.0934656	+	0.562807i
$799$			1282.04i			1.60456i
$800$	413.938	+	446.159i	0.517422	+	0.557698i
$801$	−120.341			−0.150238
$802$	−1431.29	−	237.696i	−1.78466	−	0.296379i
$803$	−393.489			−0.490024
$804$	72.2690	+	24.6843i	0.0898868	+	0.0307018i
$805$		−	180.868i		−	0.224680i
$806$	144.207	+	23.9485i	0.178916	+	0.0297127i
$807$		−	313.669i		−	0.388685i
$808$	292.977	−	544.407i	0.362595	−	0.673771i
$809$	−318.542			−0.393748			−0.196874	−	0.980429i	$-0.563079\pi$
$809$	−318.542			−0.393748			−0.196874	+	0.980429i	$0.563079\pi$
$810$	74.9776	−	451.481i	0.0925650	−	0.557384i
$811$	945.135			1.16539			0.582697	−	0.812689i	$-0.301997\pi$
$811$	945.135			1.16539			0.582697	+	0.812689i	$0.301997\pi$
$812$	−619.783	−	211.694i	−0.763280	−	0.260707i
$813$		−	629.603i		−	0.774419i
$814$	−45.9207	+	276.513i	−0.0564136	+	0.339697i
$815$			931.408i			1.14283i
$816$	−458.077	−	354.251i	−0.561369	−	0.434131i
$817$	792.896			0.970497
$818$	−332.035	−	55.1411i	−0.405910	−	0.0674097i
$819$	35.5115			0.0433595
$820$	577.086	−	1689.55i	0.703763	−	2.06043i
$821$		−	1044.28i		−	1.27196i	−0.771706	−	0.635980i	$-0.780596\pi$
$821$		−	1044.28i		−	1.27196i	0.771706	−	0.635980i	$-0.219404\pi$
$822$	−713.152	−	118.434i	−0.867582	−	0.144080i
$823$			282.350i			0.343075i	0.985178	+	0.171537i	$0.0548734\pi$
$823$			282.350i			0.343075i	−0.985178	+	0.171537i	$0.945127\pi$
$824$	−509.853	+	947.404i	−0.618753	+	1.14976i
$825$	289.082			0.350403
$826$	−65.0127	+	391.477i	−0.0787079	+	0.473943i
$827$	−149.759			−0.181087			−0.0905436	−	0.995892i	$-0.528860\pi$
$827$	−149.759			−0.181087			−0.0905436	+	0.995892i	$0.528860\pi$
$828$	22.7601	−	66.6357i	0.0274881	−	0.0804779i
$829$		−	326.779i		−	0.394184i	−0.980385	−	0.197092i	$-0.936850\pi$
$829$		−	326.779i		−	0.394184i	0.980385	−	0.197092i	$-0.0631498\pi$
$830$	105.477	−	635.135i	0.127081	−	0.765223i
$831$		−	159.499i		−	0.191936i
$832$	90.9091	−	60.0016i	0.109266	−	0.0721173i
$833$	−261.639			−0.314092
$834$	−811.313	−	134.735i	−0.972798	−	0.161553i
$835$	1382.02			1.65512
$836$	−432.338	−	147.670i	−0.517151	−	0.176638i
$837$			1256.18i			1.50081i
$838$	−1010.71	−	167.848i	−1.20609	−	0.200296i
$839$			943.371i			1.12440i	0.827001	+	0.562200i	$0.190045\pi$
$839$			943.371i			1.12440i	−0.827001	+	0.562200i	$0.809955\pi$
$840$	613.329	+	330.068i	0.730154	+	0.392938i
$841$	11.2859			0.0134196
$842$	153.402	−	923.714i	0.182187	−	1.09705i
$843$	−798.539			−0.947259
$844$	525.617	+	179.530i	0.622769	+	0.212713i
$845$		−	1102.04i		−	1.30419i
$846$	98.3518	−	592.229i	0.116255	−	0.700035i
$847$			441.382i			0.521112i
$848$	−653.697	+	845.287i	−0.770869	+	0.996800i
$849$	365.006			0.429925
$850$	−588.284	−	97.6966i	−0.692099	−	0.114937i
$851$	−102.084			−0.119958
$852$	160.549	−	470.044i	0.188438	−	0.551695i
$853$			341.998i			0.400935i	0.979700	+	0.200468i	$0.0642461\pi$
$853$			341.998i			0.400935i	−0.979700	+	0.200468i	$0.935754\pi$
$854$	−692.592	−	115.019i	−0.810998	−	0.134683i
$855$			422.465i			0.494111i
$856$	−318.908	−	171.623i	−0.372556	−	0.200494i
$857$	938.470			1.09506			0.547532	−	0.836785i	$-0.315567\pi$
$857$	938.470			1.09506			0.547532	+	0.836785i	$0.315567\pi$
$858$	8.47612	−	51.0393i	0.00987893	−	0.0594864i
$859$	462.762			0.538722			0.269361	−	0.963039i	$-0.413187\pi$
$859$	462.762			0.538722			0.269361	+	0.963039i	$0.413187\pi$
$860$	392.082	−	1147.91i	0.455909	−	1.33478i
$861$		−	882.810i		−	1.02533i
$862$	−89.4394	+	538.563i	−0.103758	+	0.624783i
$863$		−	625.664i		−	0.724988i	−0.931986	−	0.362494i	$-0.881925\pi$
$863$		−	625.664i		−	0.724988i	0.931986	−	0.362494i	$-0.118075\pi$
$864$	636.626	+	686.181i	0.736836	+	0.794191i
$865$	−1887.61			−2.18221
$866$	1388.81	+	230.641i	1.60371	+	0.266329i
$867$	−99.7625			−0.115066
$868$	−924.041	−	315.616i	−1.06456	−	0.363613i
$869$		−	294.921i		−	0.339379i
$870$	870.449	+	144.556i	1.00052	+	0.166156i
$871$		−	14.0755i		−	0.0161602i
$872$	637.430	−	1184.47i	0.730997	−	1.35833i
$873$	487.891			0.558867
$874$	27.2587	−	164.139i	0.0311884	−	0.187802i
$875$	−225.566			−0.257790
$876$	522.240	+	178.377i	0.596165	+	0.203627i
$877$			995.782i			1.13544i	0.823221	+	0.567721i	$0.192175\pi$
$877$			995.782i			1.13544i	−0.823221	+	0.567721i	$0.807825\pi$
$878$	226.958	−	1366.64i	0.258495	−	1.55654i
$879$			980.232i			1.11517i
$880$	−427.576	+	552.894i	−0.485882	+	0.628288i
$881$	−816.257			−0.926512			−0.463256	−	0.886225i	$-0.653319\pi$
$881$	−816.257			−0.926512			−0.463256	+	0.886225i	$0.653319\pi$
$882$	120.862	+	20.0716i	0.137032	+	0.0227570i
$883$	59.1142			0.0669470			0.0334735	−	0.999440i	$-0.489343\pi$
$883$	59.1142			0.0669470			0.0334735	+	0.999440i	$0.489343\pi$
$884$	−34.4979	+	101.001i	−0.0390248	+	0.114254i
$885$		−	534.642i		−	0.604115i
$886$	−857.843	−	142.462i	−0.968220	−	0.160793i
$887$			1156.85i			1.30423i	0.758120	+	0.652115i	$0.226118\pi$
$887$			1156.85i			1.30423i	−0.758120	+	0.652115i	$0.773882\pi$
$888$	186.295	−	346.173i	0.209792	−	0.389834i
$889$	−526.851			−0.592634
$890$	−71.2694	+	429.151i	−0.0800780	+	0.482193i
$891$	227.089			0.254869
$892$	377.386	−	1104.89i	0.423078	−	1.23866i
$893$		−	1418.57i		−	1.58854i
$894$	142.022	−	855.194i	0.158862	−	0.956592i
$895$		−	286.100i		−	0.319665i
$896$	−664.705	+	295.896i	−0.741858	+	0.330241i
$897$	18.8429			0.0210066
$898$	−226.179	−	37.5617i	−0.251870	−	0.0418281i
$899$	−1237.03			−1.37601
$900$	264.259	+	90.2605i	0.293621	+	0.100289i
$901$		−	1047.03i		−	1.16207i
$902$	873.925	+	145.133i	0.968875	+	0.160901i
$903$		−	599.796i		−	0.664226i
$904$	−194.700	−	104.779i	−0.215376	−	0.115906i
$905$	−1166.70			−1.28917
$906$	72.5081	−	436.611i	0.0800311	−	0.481910i
$907$	−714.420			−0.787673			−0.393837	−	0.919180i	$-0.628852\pi$
$907$	−714.420			−0.787673			−0.393837	+	0.919180i	$0.628852\pi$
$908$	357.068	+	121.960i	0.393246	+	0.134318i
$909$		−	283.666i		−	0.312064i
$910$	21.0310	−	126.639i	0.0231109	−	0.139163i
$911$			550.158i			0.603906i	0.953323	+	0.301953i	$0.0976385\pi$
$911$			550.158i			0.603906i	−0.953323	+	0.301953i	$0.902361\pi$
$912$	506.858	+	391.976i	0.555766	+	0.429798i
$913$	319.464			0.349906
$914$	−352.360	−	58.5166i	−0.385515	−	0.0640226i
$915$	945.878			1.03375
$916$	516.838	−	1513.17i	0.564234	−	1.65193i
$917$			380.283i			0.414703i
$918$	−904.766	−	150.255i	−0.985584	−	0.163676i
$919$			644.500i			0.701305i	0.936506	+	0.350653i	$0.114040\pi$
$919$			644.500i			0.701305i	−0.936506	+	0.350653i	$0.885960\pi$
$920$	−224.153	−	120.629i	−0.243644	−	0.131119i
$921$	1062.56			1.15370
$922$	140.726	−	847.386i	0.152631	−	0.919074i
$923$	−91.5484			−0.0991857
$924$	−111.707	+	327.047i	−0.120895	+	0.353947i
$925$		−	404.839i		−	0.437664i
$926$	37.7808	−	227.499i	0.0408000	−	0.245679i
$927$			493.650i			0.532524i
$928$	−675.720	+	626.921i	−0.728147	+	0.675561i
$929$	818.122			0.880648			0.440324	−	0.897839i	$-0.354864\pi$
$929$	818.122			0.880648			0.440324	+	0.897839i	$0.354864\pi$
$930$	1297.76	+	215.520i	1.39544	+	0.231742i
$931$	289.501			0.310957
$932$	−1062.00	−	362.738i	−1.13949	−	0.389204i
$933$			592.570i			0.635124i
$934$	−542.399	−	90.0765i	−0.580727	−	0.0964416i
$935$		−	684.851i		−	0.732461i
$936$	23.6843	−	44.0100i	0.0253038	−	0.0470193i
$937$	371.060			0.396009			0.198004	−	0.980201i	$-0.436554\pi$
$937$	371.060			0.396009			0.198004	+	0.980201i	$0.436554\pi$
$938$	−15.4031	+	92.7504i	−0.0164212	+	0.0988810i
$939$	−1133.56			−1.20720
$940$	−2053.72	−	701.472i	−2.18481	−	0.746247i
$941$			1075.23i			1.14265i	0.820725	+	0.571323i	$0.193570\pi$
$941$			1075.23i			1.14265i	−0.820725	+	0.571323i	$0.806430\pi$
$942$	−10.2201	+	61.5407i	−0.0108494	+	0.0653298i
$943$			322.640i			0.342142i
$944$	441.804	+	341.666i	0.468013	+	0.361935i
$945$	1103.15			1.16735
$946$	593.759	+	98.6059i	0.627653	+	0.104235i
$947$	−1716.50			−1.81257			−0.906286	−	0.422666i	$-0.861094\pi$
$947$	−1716.50			−1.81257			−0.906286	+	0.422666i	$0.861094\pi$
$948$	−133.694	+	391.420i	−0.141027	+	0.412890i
$949$		−	101.714i		−	0.107181i
$950$	650.932	+	108.101i	0.685191	+	0.113790i
$951$			1232.57i			1.29608i
$952$	337.850	−	627.791i	0.354885	−	0.659444i
$953$	−743.732			−0.780411			−0.390206	−	0.920728i	$-0.627596\pi$
$953$	−743.732			−0.780411			−0.390206	+	0.920728i	$0.627596\pi$
$954$	−80.3229	+	483.668i	−0.0841959	+	0.506989i
$955$	−1159.50			−1.21414
$956$	−430.704	+	1260.99i	−0.450527	+	1.31902i
$957$			437.824i			0.457496i
$958$	158.373	−	953.647i	0.165316	−	0.995457i
$959$		−	890.021i		−	0.928071i
$960$	818.119	−	539.973i	0.852207	−	0.562472i
$961$	−883.298			−0.919145
$962$	−71.4769	−	11.8702i	−0.0743003	−	0.0123391i
$963$	−166.169			−0.172553
$964$	792.965	+	270.846i	0.822578	+	0.280960i
$965$			555.193i			0.575330i
$966$	−124.165	−	20.6202i	−0.128535	−	0.0213459i
$967$		−	599.519i		−	0.619978i	−0.950740	−	0.309989i	$-0.899675\pi$
$967$		−	599.519i		−	0.619978i	0.950740	−	0.309989i	$-0.100325\pi$
$968$	547.013	+	294.379i	0.565096	+	0.304111i
$969$	−627.829			−0.647914
$970$	288.944	−	1739.89i	0.297880	−	1.79370i
$971$	1245.45			1.28265			0.641326	−	0.767269i	$-0.278385\pi$
$971$	1245.45			1.28265			0.641326	+	0.767269i	$0.278385\pi$
$972$	695.107	+	237.421i	0.715131	+	0.244261i
$973$		−	1012.53i		−	1.04062i
$974$	−59.9493	+	360.987i	−0.0615496	+	0.370623i
$975$			74.7259i			0.0766419i
$976$	−604.469	+	781.631i	−0.619333	+	0.800852i
$977$	1746.19			1.78729			0.893647	−	0.448771i	$-0.148138\pi$
$977$	1746.19			1.78729			0.893647	+	0.448771i	$0.148138\pi$
$978$	639.409	+	106.187i	0.653793	+	0.108576i
$979$	−215.857			−0.220487
$980$	143.156	−	419.124i	0.146078	−	0.427678i
$981$		−	617.173i		−	0.629126i
$982$	−1740.03	−	288.968i	−1.77193	−	0.294264i
$983$			914.558i			0.930375i	0.885212	+	0.465187i	$0.154013\pi$
$983$			914.558i			0.930375i	−0.885212	+	0.465187i	$0.845987\pi$
$984$	−1094.08	−	588.789i	−1.11187	−	0.598363i
$985$	1041.27			1.05713
$986$	147.964	−	890.973i	0.150065	−	0.903624i
$987$	−1073.09			−1.08723
$988$	38.1716	−	111.756i	0.0386353	−	0.113114i
$989$			219.207i			0.221645i
$990$	−52.5384	+	316.362i	−0.0530691	+	0.319558i
$991$		−	1808.51i		−	1.82493i	−0.409151	−	0.912467i	$-0.634175\pi$
$991$		−	1808.51i		−	1.82493i	0.409151	−	0.912467i	$-0.365825\pi$
$992$	−1007.44	+	934.682i	−1.01556	+	0.942220i
$993$	−1288.16			−1.29724
$994$	603.257	+	100.183i	0.606899	+	0.100788i
$995$	1456.25			1.46357
$996$	−423.994	−	144.820i	−0.425697	−	0.145401i
$997$			1450.57i			1.45494i	0.686141	+	0.727468i	$0.259303\pi$
$997$			1450.57i			1.45494i	−0.686141	+	0.727468i	$0.740697\pi$
$998$	−973.343	−	161.644i	−0.975294	−	0.161968i
$999$		−	622.632i		−	0.623256i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	184.3.g.a.139.1	✓	44
4.3	odd	2		736.3.g.a.47.15		44
8.3	odd	2	inner	184.3.g.a.139.2	yes	44
8.5	even	2		736.3.g.a.47.16		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.3.g.a.139.1	✓	44	1.1	even	1	trivial
184.3.g.a.139.2	yes	44	8.3	odd	2	inner
736.3.g.a.47.15		44	4.3	odd	2
736.3.g.a.47.16		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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.97298 - 0.327653i) q^{2} +2.30854 q^{3} +(3.78529 + 1.29291i) q^{4} -6.63468i q^{5} +(-4.55469 - 0.756400i) q^{6} -5.68430i q^{7} +(-7.04466 - 3.79114i) q^{8} -3.67066 q^{9} +(-2.17387 + 13.0901i) q^{10} -6.58413 q^{11} +(8.73847 + 2.98472i) q^{12} -1.70195i q^{13} +(-1.86248 + 11.2150i) q^{14} -15.3164i q^{15} +(12.6568 + 9.78804i) q^{16} -15.6775 q^{17} +(7.24213 + 1.20270i) q^{18} +17.3471 q^{19} +(8.57802 - 25.1142i) q^{20} -13.1224i q^{21} +(12.9903 + 2.15731i) q^{22} +4.79583i q^{23} +(-16.2629 - 8.75198i) q^{24} -19.0190 q^{25} +(-0.557651 + 3.35792i) q^{26} -29.2507 q^{27} +(7.34926 - 21.5167i) q^{28} -28.8048i q^{29} +(-5.01847 + 30.2189i) q^{30} -42.9453i q^{31} +(-21.7645 - 23.4586i) q^{32} -15.1997 q^{33} +(30.9315 + 5.13680i) q^{34} -37.7135 q^{35} +(-13.8945 - 4.74582i) q^{36} +21.2861i q^{37} +(-34.2254 - 5.68383i) q^{38} -3.92902i q^{39} +(-25.1530 + 46.7391i) q^{40} +67.2750 q^{41} +(-4.29960 + 25.8902i) q^{42} +45.7078 q^{43} +(-24.9228 - 8.51266i) q^{44} +24.3536i q^{45} +(1.57137 - 9.46207i) q^{46} -81.7755i q^{47} +(29.2187 + 22.5960i) q^{48} +16.6888 q^{49} +(37.5240 + 6.23163i) q^{50} -36.1922 q^{51} +(2.20046 - 6.44238i) q^{52} +66.7853i q^{53} +(57.7110 + 9.58408i) q^{54} +43.6836i q^{55} +(-21.5500 + 40.0440i) q^{56} +40.0464 q^{57} +(-9.43798 + 56.8312i) q^{58} +34.9065 q^{59} +(19.8027 - 57.9770i) q^{60} +61.7559i q^{61} +(-14.0712 + 84.7301i) q^{62} +20.8651i q^{63} +(35.2546 + 53.4146i) q^{64} -11.2919 q^{65} +(29.9887 + 4.98023i) q^{66} +8.27021 q^{67} +(-59.3440 - 20.2696i) q^{68} +11.0714i q^{69} +(74.4079 + 12.3570i) q^{70} -53.7902i q^{71} +(25.8586 + 13.9160i) q^{72} +59.7633 q^{73} +(6.97446 - 41.9970i) q^{74} -43.9060 q^{75} +(65.6637 + 22.4282i) q^{76} +37.4261i q^{77} +(-1.28736 + 7.75187i) q^{78} +44.7927i q^{79} +(64.9405 - 83.9737i) q^{80} -34.4903 q^{81} +(-132.732 - 22.0429i) q^{82} -48.5204 q^{83} +(16.9660 - 49.6721i) q^{84} +104.015i q^{85} +(-90.1804 - 14.9763i) q^{86} -66.4968i q^{87} +(46.3830 + 24.9613i) q^{88} +32.7845 q^{89} +(7.97956 - 48.0492i) q^{90} -9.67441 q^{91} +(-6.20056 + 18.1536i) q^{92} -99.1408i q^{93} +(-26.7940 + 161.341i) q^{94} -115.092i q^{95} +(-50.2441 - 54.1551i) q^{96} -132.916 q^{97} +(-32.9265 - 5.46813i) q^{98} +24.1681 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 3 q^{6} + 15 q^{8} + 132 q^{9} + 26 q^{10} - 19 q^{12} - 8 q^{14} - 16 q^{16} - 8 q^{17} - 57 q^{18} + 40 q^{20} + 44 q^{22} - 88 q^{24} - 244 q^{25} + 19 q^{26} - 48 q^{27} + 6 q^{28} + 86 q^{30}+ \cdots + 256 q^{99}+O(q^{100}) \) 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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