LMFDB - Embedded newform 117.3.k.a.29.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(29,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("117.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.10
Character	$\chi$	$=$	117.29
Dual form			117.3.k.a.113.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.67065i q^{2} +(0.0978207 - 2.99840i) q^{3} +1.20892 q^{4} +(-8.08978 + 4.67064i) q^{5} +(-5.00930 - 0.163425i) q^{6} +(-4.17857 - 7.23749i) q^{7} -8.70230i q^{8} +(-8.98086 - 0.586612i) q^{9} +(7.80302 + 13.5152i) q^{10} +2.35846i q^{11} +(0.118257 - 3.62482i) q^{12} +(6.74084 - 11.1158i) q^{13} +(-12.0913 + 6.98094i) q^{14} +(13.2131 + 24.7133i) q^{15} -9.70286 q^{16} +(5.30206 + 3.06114i) q^{17} +(-0.980026 + 15.0039i) q^{18} +(3.19129 - 5.52747i) q^{19} +(-9.77986 + 5.64641i) q^{20} +(-22.1097 + 11.8211i) q^{21} +3.94017 q^{22} +(18.1610 + 10.4852i) q^{23} +(-26.0930 - 0.851265i) q^{24} +(31.1297 - 53.9182i) q^{25} +(-18.5707 - 11.2616i) q^{26} +(-2.63742 + 26.8709i) q^{27} +(-5.05153 - 8.74951i) q^{28} -32.8392i q^{29} +(41.2874 - 22.0745i) q^{30} +(-10.3041 - 17.8473i) q^{31} -18.5991i q^{32} +(7.07162 + 0.230707i) q^{33} +(5.11411 - 8.85790i) q^{34} +(67.6074 + 39.0331i) q^{35} +(-10.8571 - 0.709165i) q^{36} +(14.1201 + 24.4568i) q^{37} +(-9.23450 - 5.33154i) q^{38} +(-32.6703 - 21.2991i) q^{39} +(40.6453 + 70.3997i) q^{40} +(-23.6843 - 13.6741i) q^{41} +(19.7489 + 36.9376i) q^{42} +(37.1380 + 64.3249i) q^{43} +2.85118i q^{44} +(75.3931 - 37.2008i) q^{45} +(17.5172 - 30.3407i) q^{46} +(-20.4110 - 11.7843i) q^{47} +(-0.949141 + 29.0931i) q^{48} +(-10.4208 + 18.0494i) q^{49} +(-90.0787 - 52.0069i) q^{50} +(9.69720 - 15.5983i) q^{51} +(8.14910 - 13.4381i) q^{52} -97.2822i q^{53} +(44.8919 + 4.40621i) q^{54} +(-11.0155 - 19.0794i) q^{55} +(-62.9828 + 36.3631i) q^{56} +(-16.2614 - 10.1095i) q^{57} -54.8629 q^{58} -8.91451i q^{59} +(15.9735 + 29.8763i) q^{60} +(8.35559 + 14.4723i) q^{61} +(-29.8167 + 17.2147i) q^{62} +(33.2815 + 67.4501i) q^{63} -69.8840 q^{64} +(-2.61400 + 121.408i) q^{65} +(0.385431 - 11.8142i) q^{66} +(2.20817 - 3.82466i) q^{67} +(6.40974 + 3.70067i) q^{68} +(33.2155 - 53.4283i) q^{69} +(65.2108 - 112.948i) q^{70} +(12.9685 + 7.48739i) q^{71} +(-5.10487 + 78.1541i) q^{72} -42.4558 q^{73} +(40.8589 - 23.5899i) q^{74} +(-158.623 - 98.6137i) q^{75} +(3.85800 - 6.68225i) q^{76} +(17.0693 - 9.85499i) q^{77} +(-35.5834 + 54.5807i) q^{78} +(-44.1406 + 76.4538i) q^{79} +(78.4940 - 45.3185i) q^{80} +(80.3118 + 10.5366i) q^{81} +(-22.8447 + 39.5682i) q^{82} +(55.1815 + 31.8591i) q^{83} +(-26.7287 + 14.2907i) q^{84} -57.1900 q^{85} +(107.465 - 62.0447i) q^{86} +(-98.4651 - 3.21235i) q^{87} +20.5240 q^{88} +(-72.0627 + 41.6054i) q^{89} +(-62.1496 - 125.956i) q^{90} +(-108.618 - 2.33861i) q^{91} +(21.9551 + 12.6758i) q^{92} +(-54.5214 + 29.1502i) q^{93} +(-19.6875 + 34.0997i) q^{94} +59.6214i q^{95} +(-55.7675 - 1.81937i) q^{96} +(55.6874 + 96.4534i) q^{97} +(30.1543 + 17.4096i) q^{98} +(1.38350 - 21.1810i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) $ 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.67065i		−	0.835327i	−0.908602	−	0.417663i	$-0.862849\pi$
$2$		−	1.67065i		−	0.835327i	0.908602	−	0.417663i	$-0.137151\pi$
$3$	0.0978207	−	2.99840i	0.0326069	−	0.999468i
$3$	0.0978207	−	2.99840i	0.0326069	−	0.999468i
$4$	1.20892			0.302229
$5$	−8.08978	+	4.67064i	−1.61796	+	0.934127i	−0.630508	+	0.776183i	$0.717153\pi$
$5$	−8.08978	+	4.67064i	−1.61796	+	0.934127i	−0.987448	+	0.157945i	$0.949513\pi$
$6$	−5.00930	−	0.163425i	−0.834883	−	0.0272374i
$7$	−4.17857	−	7.23749i	−0.596938	−	1.03393i	−0.993270	−	0.115820i	$-0.963051\pi$
$7$	−4.17857	−	7.23749i	−0.596938	−	1.03393i	0.396332	−	0.918107i	$-0.370283\pi$
$8$		−	8.70230i		−	1.08779i
$9$	−8.98086	−	0.586612i	−0.997874	−	0.0651791i
$10$	7.80302	+	13.5152i	0.780302	+	1.35152i
$11$			2.35846i			0.214406i	0.994237	+	0.107203i	$0.0341894\pi$
$11$			2.35846i			0.214406i	−0.994237	+	0.107203i	$0.965811\pi$
$12$	0.118257	−	3.62482i	0.00985475	−	0.302068i
$13$	6.74084	−	11.1158i	0.518526	−	0.855062i
$13$	6.74084	−	11.1158i	0.518526	−	0.855062i
$14$	−12.0913	+	6.98094i	−0.863667	+	0.498638i
$15$	13.2131	+	24.7133i	0.880874	+	1.64755i
$16$	−9.70286			−0.606429
$17$	5.30206	+	3.06114i	0.311886	+	0.180067i	0.647770	−	0.761836i	$-0.275702\pi$
$17$	5.30206	+	3.06114i	0.311886	+	0.180067i	−0.335884	+	0.941903i	$0.609035\pi$
$18$	−0.980026	+	15.0039i	−0.0544459	+	0.833551i
$19$	3.19129	−	5.52747i	0.167963	−	0.290920i	−0.769741	−	0.638357i	$-0.779615\pi$
$19$	3.19129	−	5.52747i	0.167963	−	0.290920i	0.937703	+	0.347437i	$0.112948\pi$
$20$	−9.77986	+	5.64641i	−0.488993	+	0.282320i
$21$	−22.1097	+	11.8211i	−1.05284	+	0.562907i
$22$	3.94017			0.179099
$23$	18.1610	+	10.4852i	0.789607	+	0.455880i	0.839824	−	0.542858i	$-0.182658\pi$
$23$	18.1610	+	10.4852i	0.789607	+	0.455880i	−0.0502170	+	0.998738i	$0.515991\pi$
$24$	−26.0930	−	0.851265i	−1.08721	−	0.0354694i
$25$	31.1297	−	53.9182i	1.24519	−	2.15673i
$26$	−18.5707	−	11.2616i	−0.714256	−	0.433139i
$27$	−2.63742	+	26.8709i	−0.0976821	+	0.995218i
$28$	−5.05153	−	8.74951i	−0.180412	−	0.312483i
$29$		−	32.8392i		−	1.13239i	−0.824273	−	0.566193i	$-0.808416\pi$
$29$		−	32.8392i		−	1.13239i	0.824273	−	0.566193i	$-0.191584\pi$
$30$	41.2874	−	22.0745i	1.37625	−	0.735818i
$31$	−10.3041	−	17.8473i	−0.332392	−	0.575720i	0.650588	−	0.759431i	$-0.274522\pi$
$31$	−10.3041	−	17.8473i	−0.332392	−	0.575720i	−0.982980	+	0.183711i	$0.941189\pi$
$32$		−	18.5991i		−	0.581221i
$33$	7.07162	+	0.230707i	0.214292	+	0.00699111i
$34$	5.11411	−	8.85790i	0.150415	−	0.260527i
$35$	67.6074	+	39.0331i	1.93164	+	1.11523i
$36$	−10.8571	−	0.709165i	−0.301586	−	0.0196990i
$37$	14.1201	+	24.4568i	0.381626	+	0.660995i	0.991295	−	0.131661i	$-0.0420311\pi$
$37$	14.1201	+	24.4568i	0.381626	+	0.660995i	−0.609669	+	0.792656i	$0.708698\pi$
$38$	−9.23450	−	5.33154i	−0.243013	−	0.140304i
$39$	−32.6703	−	21.2991i	−0.837700	−	0.546131i
$40$	40.6453	+	70.3997i	1.01613	+	1.75999i
$41$	−23.6843	−	13.6741i	−0.577665	−	0.333515i	0.182540	−	0.983198i	$-0.441568\pi$
$41$	−23.6843	−	13.6741i	−0.577665	−	0.333515i	−0.760205	+	0.649683i	$0.774901\pi$
$42$	19.7489	+	36.9376i	0.470212	+	0.879467i
$43$	37.1380	+	64.3249i	0.863674	+	1.49593i	0.868357	+	0.495939i	$0.165176\pi$
$43$	37.1380	+	64.3249i	0.863674	+	1.49593i	−0.00468301	+	0.999989i	$0.501491\pi$
$44$			2.85118i			0.0647996i
$45$	75.3931	−	37.2008i	1.67540	−	0.826684i
$46$	17.5172	−	30.3407i	0.380809	−	0.659580i
$47$	−20.4110	−	11.7843i	−0.434277	−	0.250730i	0.266890	−	0.963727i	$-0.414004\pi$
$47$	−20.4110	−	11.7843i	−0.434277	−	0.250730i	−0.701167	+	0.712997i	$0.747337\pi$
$48$	−0.949141	+	29.0931i	−0.0197738	+	0.606106i
$49$	−10.4208	+	18.0494i	−0.212670	+	0.368355i
$50$	−90.0787	−	52.0069i	−1.80157	−	1.04014i
$51$	9.69720	−	15.5983i	0.190141	−	0.305848i
$52$	8.14910	−	13.4381i	0.156714	−	0.258424i
$53$		−	97.2822i		−	1.83551i	−0.397143	−	0.917757i	$-0.629998\pi$
$53$		−	97.2822i		−	1.83551i	0.397143	−	0.917757i	$-0.370002\pi$
$54$	44.8919	+	4.40621i	0.831332	+	0.0815964i
$55$	−11.0155	−	19.0794i	−0.200282	−	0.346899i
$56$	−62.9828	+	36.3631i	−1.12469	+	0.649341i
$57$	−16.2614	−	10.1095i	−0.285288	−	0.177359i
$58$	−54.8629			−0.945912
$59$		−	8.91451i		−	0.151093i	−0.997142	−	0.0755467i	$-0.975930\pi$
$59$		−	8.91451i		−	0.151093i	0.997142	−	0.0755467i	$-0.0240702\pi$
$60$	15.9735	+	29.8763i	0.266226	+	0.497939i
$61$	8.35559	+	14.4723i	0.136977	+	0.237251i	0.926351	−	0.376662i	$-0.122928\pi$
$61$	8.35559	+	14.4723i	0.136977	+	0.237251i	−0.789374	+	0.613913i	$0.789595\pi$
$62$	−29.8167	+	17.2147i	−0.480914	+	0.277656i
$63$	33.2815	+	67.4501i	0.528278	+	1.07064i
$64$	−69.8840			−1.09194
$65$	−2.61400	+	121.408i	−0.0402154	+	1.86782i
$66$	0.385431	−	11.8142i	0.00583986	−	0.179004i
$67$	2.20817	−	3.82466i	0.0329578	−	0.0570845i	−0.849076	−	0.528271i	$-0.822841\pi$
$67$	2.20817	−	3.82466i	0.0329578	−	0.0570845i	0.882034	+	0.471186i	$0.156174\pi$
$68$	6.40974	+	3.70067i	0.0942609	+	0.0544215i
$69$	33.2155	−	53.4283i	0.481384	−	0.774323i
$70$	65.2108	−	112.948i	0.931583	−	1.61355i
$71$	12.9685	+	7.48739i	0.182656	+	0.105456i	0.588540	−	0.808468i	$-0.299703\pi$
$71$	12.9685	+	7.48739i	0.182656	+	0.105456i	−0.405884	+	0.913925i	$0.633036\pi$
$72$	−5.10487	+	78.1541i	−0.0709010	+	1.08547i
$73$	−42.4558			−0.581586			−0.290793	−	0.956786i	$-0.593919\pi$
$73$	−42.4558			−0.581586			−0.290793	+	0.956786i	$0.593919\pi$
$74$	40.8589	−	23.5899i	0.552147	−	0.318782i
$75$	−158.623	−	98.6137i	−2.11498	−	1.31485i
$76$	3.85800	−	6.68225i	0.0507632	−	0.0879244i
$77$	17.0693	−	9.85499i	0.221680	−	0.127987i
$78$	−35.5834	+	54.5807i	−0.456198	+	0.699753i
$79$	−44.1406	+	76.4538i	−0.558742	+	0.967769i	0.438860	+	0.898555i	$0.355382\pi$
$79$	−44.1406	+	76.4538i	−0.558742	+	0.967769i	−0.997602	+	0.0692138i	$0.977951\pi$
$80$	78.4940	−	45.3185i	0.981175	−	0.566482i
$81$	80.3118	+	10.5366i	0.991503	+	0.130081i
$82$	−22.8447	+	39.5682i	−0.278594	+	0.482539i
$83$	55.1815	+	31.8591i	0.664838	+	0.383844i	0.794118	−	0.607764i	$-0.207933\pi$
$83$	55.1815	+	31.8591i	0.664838	+	0.383844i	−0.129280	+	0.991608i	$0.541267\pi$
$84$	−26.7287	+	14.2907i	−0.318199	+	0.170127i
$85$	−57.1900			−0.672823
$86$	107.465	−	62.0447i	1.24959	−	0.721450i
$87$	−98.4651	−	3.21235i	−1.13178	−	0.0369236i
$88$	20.5240			0.233228
$89$	−72.0627	+	41.6054i	−0.809693	+	0.467477i	−0.846849	−	0.531833i	$-0.821503\pi$
$89$	−72.0627	+	41.6054i	−0.809693	+	0.467477i	0.0371560	+	0.999309i	$0.488170\pi$
$90$	−62.1496	−	125.956i	−0.690551	−	1.39951i
$91$	−108.618	−	2.33861i	−1.19360	−	0.0256990i
$92$	21.9551	+	12.6758i	0.238642	+	0.137780i
$93$	−54.5214	+	29.1502i	−0.586252	+	0.313443i
$94$	−19.6875	+	34.0997i	−0.209441	+	0.362763i
$95$			59.6214i			0.627594i
$96$	−55.7675	−	1.81937i	−0.580912	−	0.0189518i
$97$	55.6874	+	96.4534i	0.574097	+	0.994365i	0.996139	+	0.0877889i	$0.0279801\pi$
$97$	55.6874	+	96.4534i	0.574097	+	0.994365i	−0.422042	+	0.906576i	$0.638687\pi$
$98$	30.1543	+	17.4096i	0.307697	+	0.177649i
$99$	1.38350	−	21.1810i	0.0139748	−	0.213950i
$100$	37.6332	−	65.1826i	0.376332	−	0.651826i
$101$			120.981i			1.19783i	0.800813	+	0.598915i	$0.204401\pi$
$101$			120.981i			1.19783i	−0.800813	+	0.598915i	$0.795599\pi$
$102$	−26.0593	−	16.2007i	−0.255483	−	0.158830i
$103$	−48.3172	−	83.6878i	−0.469099	−	0.812503i	0.530277	−	0.847824i	$-0.322088\pi$
$103$	−48.3172	−	83.6878i	−0.469099	−	0.812503i	−0.999376	+	0.0353213i	$0.988755\pi$
$104$	−96.7330	−	58.6608i	−0.930125	−	0.564046i
$105$	123.651	−	198.896i	1.17762	−	1.89425i
$106$	−162.525			−1.53325
$107$	160.718	−	92.7908i	1.50204	−	0.867204i	0.502044	−	0.864842i	$-0.332582\pi$
$107$	160.718	−	92.7908i	1.50204	−	0.867204i	0.999997	−	0.00236190i	$-0.000751816\pi$
$108$	−3.18841	+	32.4846i	−0.0295223	+	0.300784i
$109$	164.763			1.51158			0.755792	−	0.654812i	$-0.227252\pi$
$109$	164.763			1.51158			0.755792	+	0.654812i	$0.227252\pi$
$110$	−31.8751	+	18.4031i	−0.289774	+	0.167301i
$111$	74.7127	−	39.9455i	0.673087	−	0.359870i
$112$	40.5440	+	70.2243i	0.362000	+	0.627003i
$113$			20.9389i			0.185300i	0.995699	+	0.0926501i	$0.0295338\pi$
$113$			20.9389i			0.185300i	−0.995699	+	0.0926501i	$0.970466\pi$
$114$	−16.8894	+	27.1672i	−0.148153	+	0.238309i
$115$	−195.891			−1.70340
$116$		−	39.6998i		−	0.342240i
$117$	−67.0592	+	95.8753i	−0.573156	+	0.819447i
$118$	−14.8931			−0.126212
$119$		−	51.1648i		−	0.429956i
$120$	215.063	−	114.984i	1.79219	−	0.958203i
$121$	115.438			0.954030
$122$	24.1782	−	13.9593i	0.198182	−	0.114420i
$123$	−43.3174	+	69.6774i	−0.352174	+	0.566483i
$124$	−12.4568	−	21.5759i	−0.100458	−	0.173999i
$125$			348.050i			2.78440i
$126$	112.686	−	55.6019i	0.894331	−	0.441285i
$127$	−52.3042	−	90.5936i	−0.411844	−	0.713335i	0.583247	−	0.812295i	$-0.301782\pi$
$127$	−52.3042	−	90.5936i	−0.411844	−	0.713335i	−0.995091	+	0.0989596i	$0.968449\pi$
$128$			42.3558i			0.330905i
$129$	196.505	−	105.062i	1.52329	−	0.814438i
$130$	202.831	+	4.36709i	1.56024	+	0.0335930i
$131$	−147.300	+	85.0439i	−1.12443	+	0.649190i	−0.942528	−	0.334127i	$-0.891559\pi$
$131$	−147.300	+	85.0439i	−1.12443	+	0.649190i	−0.181902	+	0.983317i	$0.558225\pi$
$132$	8.54900	+	0.278905i	0.0647651	+	0.00211291i
$133$	−53.3400			−0.401053
$134$	−6.38969	−	3.68909i	−0.0476842	−	0.0275305i
$135$	−104.168	−	229.698i	−0.771615	−	1.70147i
$136$	26.6390	−	46.1401i	0.195875	−	0.339265i
$137$	125.698	−	72.5715i	0.917500	−	0.529719i	0.0346634	−	0.999399i	$-0.488964\pi$
$137$	125.698	−	72.5715i	0.917500	−	0.529719i	0.882837	+	0.469680i	$0.155631\pi$
$138$	−89.2601	−	55.4916i	−0.646812	−	0.402113i
$139$	78.9427			0.567933			0.283966	−	0.958834i	$-0.408350\pi$
$139$	78.9427			0.567933			0.283966	+	0.958834i	$0.408350\pi$
$140$	81.7316	+	47.1878i	0.583797	+	0.337055i
$141$	−37.3307	+	60.0477i	−0.264757	+	0.425870i
$142$	12.5088	−	21.6659i	0.0880904	−	0.152577i
$143$	26.2162	+	15.8980i	0.183330	+	0.111175i
$144$	87.1400	+	5.69182i	0.605139	+	0.0395265i
$145$	153.380	+	265.662i	1.05779	+	1.83215i
$146$			70.9289i			0.485815i
$147$	53.1000	+	33.0114i	0.361225	+	0.224568i
$148$	17.0701	+	29.5662i	0.115338	+	0.199772i
$149$		−	255.625i		−	1.71561i	−0.513978	−	0.857804i	$-0.671829\pi$
$149$		−	255.625i		−	1.71561i	0.513978	−	0.857804i	$-0.328171\pi$
$150$	−164.749	+	265.005i	−1.09833	+	1.76670i
$151$	−44.7204	+	77.4580i	−0.296161	+	0.512967i	−0.975254	−	0.221086i	$-0.929040\pi$
$151$	−44.7204	+	77.4580i	−0.296161	+	0.512967i	0.679093	+	0.734052i	$0.262373\pi$
$152$	−48.1017	−	27.7715i	−0.316459	−	0.182707i
$153$	−45.8213	−	30.6020i	−0.299486	−	0.200013i
$154$	−16.4643	−	28.5170i	−0.106911	−	0.185175i
$155$	166.717	+	96.2539i	1.07559	+	0.620993i
$156$	−39.4956	−	25.7488i	−0.253177	−	0.165057i
$157$	−99.5128	−	172.361i	−0.633839	−	1.09784i	−0.986760	−	0.162189i	$-0.948145\pi$
$157$	−99.5128	−	172.361i	−0.633839	−	1.09784i	0.352920	−	0.935653i	$-0.385189\pi$
$158$	127.728	+	73.7437i	0.808404	+	0.466732i
$159$	−291.691	−	9.51622i	−1.83454	−	0.0598504i
$160$	86.8695	+	150.462i	0.542934	+	0.940389i
$161$		−	175.253i		−	1.08853i
$162$	17.6030	−	134.173i	0.108660	−	0.828229i
$163$	−5.14052	+	8.90365i	−0.0315369	+	0.0546236i	−0.881363	−	0.472439i	$-0.843374\pi$
$163$	−5.14052	+	8.90365i	−0.0315369	+	0.0546236i	0.849826	+	0.527063i	$0.176707\pi$
$164$	−28.6323	−	16.5309i	−0.174587	−	0.100798i
$165$	−58.2854	+	31.1626i	−0.353245	+	0.188864i
$166$	53.2255	−	92.1892i	0.320635	−	0.555357i
$167$	58.7250	+	33.9049i	0.351647	+	0.203023i	0.665410	−	0.746478i	$-0.268257\pi$
$167$	58.7250	+	33.9049i	0.351647	+	0.203023i	−0.313764	+	0.949501i	$0.601590\pi$
$168$	102.870	+	192.405i	0.612323	+	1.14527i
$169$	−78.1222	−	149.860i	−0.462262	−	0.886744i
$170$			95.5446i			0.562027i
$171$	−31.9030	+	47.7694i	−0.186567	+	0.279353i
$172$	44.8967	+	77.7634i	0.261027	+	0.452113i
$173$	−22.5261	+	13.0054i	−0.130209	+	0.0751760i	−0.563689	−	0.825987i	$-0.690619\pi$
$173$	−22.5261	+	13.0054i	−0.130209	+	0.0751760i	0.433481	+	0.901163i	$0.357285\pi$
$174$	−5.36673	+	164.501i	−0.0308433	+	0.945409i
$175$	−520.310			−2.97320
$176$		−	22.8838i		−	0.130022i
$177$	−26.7293	−	0.872024i	−0.151013	−	0.00492669i
$178$	69.5083	+	120.392i	0.390496	+	0.676359i
$179$	218.650	−	126.238i	1.22151	−	0.705238i	0.256269	−	0.966605i	$-0.417507\pi$
$179$	218.650	−	126.238i	1.22151	−	0.705238i	0.965239	+	0.261367i	$0.0841733\pi$
$180$	91.1438	−	44.9726i	0.506355	−	0.249848i
$181$	−237.385			−1.31152			−0.655759	−	0.754970i	$-0.727651\pi$
$181$	−237.385			−1.31152			−0.655759	+	0.754970i	$0.727651\pi$
$182$	−3.90700	+	181.462i	−0.0214670	+	0.997046i
$183$	44.2112	−	23.6377i	0.241591	−	0.129168i
$184$	91.2456	−	158.042i	0.495900	−	0.858924i
$185$	−228.458	−	131.900i	−1.23491	−	0.712974i
$186$	48.6998	+	91.0864i	0.261827	+	0.489712i
$187$	−7.21959	+	12.5047i	−0.0386075	+	0.0668701i
$188$	−24.6752	−	14.2462i	−0.131251	−	0.0757778i
$189$	205.498	−	93.1935i	1.08729	−	0.493087i
$190$	99.6067			0.524246
$191$	−127.503	+	73.6137i	−0.667554	+	0.385412i	−0.795149	−	0.606414i	$-0.792607\pi$
$191$	−127.503	+	73.6137i	−0.667554	+	0.385412i	0.127595	+	0.991826i	$0.459274\pi$
$192$	−6.83611	+	209.541i	−0.0356047	+	1.09136i
$193$	7.30490	−	12.6525i	0.0378492	−	0.0655568i	−0.846480	−	0.532420i	$-0.821283\pi$
$193$	7.30490	−	12.6525i	0.0378492	−	0.0655568i	0.884329	+	0.466863i	$0.154616\pi$
$194$	161.140	−	93.0344i	0.830620	−	0.479559i
$195$	363.776	+	19.7141i	1.86552	+	0.101098i
$196$	−12.5979	+	21.8202i	−0.0642750	+	0.111328i
$197$	218.207	−	125.982i	1.10765	−	0.639503i	0.169431	−	0.985542i	$-0.445807\pi$
$197$	218.207	−	125.982i	1.10765	−	0.639503i	0.938220	+	0.346039i	$0.112474\pi$
$198$	−35.3862	−	2.31135i	−0.178718	−	0.0116735i
$199$	134.225	−	232.484i	0.674497	−	1.16826i	−0.302119	−	0.953270i	$-0.597694\pi$
$199$	134.225	−	232.484i	0.674497	−	1.16826i	0.976616	−	0.214993i	$-0.0689727\pi$
$200$	−469.212	−	270.900i	−2.34606	−	1.35450i
$201$	−11.2519	−	6.99512i	−0.0559795	−	0.0348016i
$202$	202.117			1.00058
$203$	−237.673	+	137.221i	−1.17080	+	0.675964i
$204$	11.7231	−	18.8570i	0.0574662	−	0.0924362i
$205$	255.467			1.24618
$206$	−139.813	+	80.7213i	−0.678706	+	0.391851i
$207$	−156.950	−	104.820i	−0.758214	−	0.506376i
$208$	−65.4054	+	107.855i	−0.314449	+	0.518534i
$209$	13.0363	+	7.52654i	0.0623748	+	0.0360121i
$210$	−332.286	−	206.577i	−1.58232	−	0.983701i
$211$	−113.858	+	197.208i	−0.539611	+	0.934634i	0.459314	+	0.888274i	$0.348095\pi$
$211$	−113.858	+	197.208i	−0.539611	+	0.934634i	−0.998925	+	0.0463599i	$0.985238\pi$
$212$		−	117.606i		−	0.554745i
$213$	23.7188	−	38.1525i	0.111356	−	0.179120i
$214$	−155.021	−	268.505i	−0.724399	−	1.25470i
$215$	−600.876	−	346.916i	−2.79477	−	1.61356i
$216$	233.838	+	22.9516i	1.08258	+	0.106257i
$217$	−86.1131	+	149.152i	−0.396835	+	0.687338i
$218$		−	275.261i		−	1.26267i
$219$	−4.15306	+	127.300i	−0.0189637	+	0.581277i
$220$	−13.3168	−	23.0654i	−0.0605311	−	0.104843i
$221$	69.7674	−	38.3020i	0.315690	−	0.173312i
$222$	−66.7351	−	124.819i	−0.300609	−	0.562248i
$223$	49.8543			0.223562			0.111781	−	0.993733i	$-0.464344\pi$
$223$	49.8543			0.223562			0.111781	+	0.993733i	$0.464344\pi$
$224$	−134.610	+	77.7174i	−0.600940	+	0.346953i
$225$	−311.201	+	465.971i	−1.38311	+	2.07098i
$226$	34.9817			0.154786
$227$	191.094	−	110.328i	0.841823	−	0.486027i	−0.0160605	−	0.999871i	$-0.505112\pi$
$227$	191.094	−	110.328i	0.841823	−	0.486027i	0.857883	+	0.513844i	$0.171779\pi$
$228$	−19.6587	−	12.2215i	−0.0862224	−	0.0536031i
$229$	−76.4745	−	132.458i	−0.333950	−	0.578418i	0.649333	−	0.760504i	$-0.275048\pi$
$229$	−76.4745	−	132.458i	−0.333950	−	0.578418i	−0.983283	+	0.182087i	$0.941715\pi$
$230$			327.266i			1.42290i
$231$	−27.8795	−	52.1448i	−0.120691	−	0.225735i
$232$	−285.776			−1.23179
$233$			236.849i			1.01652i	0.861204	+	0.508260i	$0.169711\pi$
$233$			236.849i			1.01652i	−0.861204	+	0.508260i	$0.830289\pi$
$234$	160.174	+	112.033i	0.684506	+	0.478772i
$235$	220.161			0.936854
$236$		−	10.7769i		−	0.0456648i
$237$	224.921	+	139.830i	0.949036	+	0.590001i
$238$	−85.4786			−0.359154
$239$	−102.735	+	59.3143i	−0.429855	+	0.248177i	−0.699285	−	0.714843i	$-0.746498\pi$
$239$	−102.735	+	59.3143i	−0.429855	+	0.248177i	0.269430	+	0.963020i	$0.413165\pi$
$240$	−128.205	−	239.790i	−0.534187	−	0.999125i
$241$	141.762	+	245.539i	0.588225	+	1.01884i	0.994465	+	0.105069i	$0.0335063\pi$
$241$	141.762	+	245.539i	0.588225	+	1.01884i	−0.406240	+	0.913766i	$0.633160\pi$
$242$		−	192.856i		−	0.796927i
$243$	39.4491	−	239.777i	0.162342	−	0.986735i
$244$	10.1012	+	17.4958i	0.0413984	+	0.0717041i
$245$		−	194.687i		−	0.794643i
$246$	116.407	+	72.3683i	0.473199	+	0.294180i
$247$	−39.9304	−	72.7336i	−0.161661	−	0.294468i
$248$	−155.313	+	89.6697i	−0.626260	+	0.361572i
$249$	100.924	−	162.340i	0.405318	−	0.651968i
$250$	581.471			2.32589
$251$	151.189	+	87.2892i	0.602348	+	0.347766i	0.769965	−	0.638087i	$-0.220274\pi$
$251$	151.189	+	87.2892i	0.602348	+	0.347766i	−0.167617	+	0.985852i	$0.553607\pi$
$252$	40.2346	+	81.5415i	0.159661	+	0.323577i
$253$	−24.7290	+	42.8320i	−0.0977433	+	0.169296i
$254$	−151.350	+	87.3822i	−0.595868	+	0.344025i
$255$	−5.59436	+	171.479i	−0.0219387	+	0.672465i
$256$	−208.774			−0.815524
$257$	99.7520	+	57.5918i	0.388140	+	0.224093i	0.681354	−	0.731954i	$-0.261391\pi$
$257$	99.7520	+	57.5918i	0.388140	+	0.224093i	−0.293214	+	0.956047i	$0.594725\pi$
$258$	−175.523	−	328.292i	−0.680322	−	1.27245i
$259$	118.004	−	204.389i	0.455614	−	0.789146i
$260$	−3.16011	+	146.773i	−0.0121543	+	0.564510i
$261$	−19.2639	+	294.924i	−0.0738079	+	1.12998i
$262$	142.079	+	246.088i	0.542286	+	0.939266i
$263$			36.9549i			0.140513i	0.997529	+	0.0702565i	$0.0223818\pi$
$263$			36.9549i			0.140513i	−0.997529	+	0.0702565i	$0.977618\pi$
$264$	2.00768	−	61.5394i	0.00760483	−	0.233104i
$265$	454.370	+	786.992i	1.71460	+	2.96978i
$266$			89.1128i			0.335010i
$267$	117.701	+	220.143i	0.440827	+	0.824506i
$268$	2.66949	−	4.62369i	0.00996079	−	0.0172526i
$269$	51.7619	+	29.8847i	0.192423	+	0.111096i	0.593117	−	0.805117i	$-0.297897\pi$
$269$	51.7619	+	29.8847i	0.192423	+	0.111096i	−0.400693	+	0.916212i	$0.631231\pi$
$270$	−383.746	+	174.029i	−1.42128	+	0.644551i
$271$	86.1985	+	149.300i	0.318076	+	0.550923i	0.980086	−	0.198571i	$-0.0636301\pi$
$271$	86.1985	+	149.300i	0.318076	+	0.550923i	−0.662011	+	0.749494i	$0.730297\pi$
$272$	−51.4451	−	29.7019i	−0.189136	−	0.109198i
$273$	−17.6371	+	325.451i	−0.0646049	+	1.19213i
$274$	−121.242	−	209.997i	−0.442488	−	0.766413i
$275$	127.164	+	73.4182i	0.462415	+	0.266975i
$276$	40.1548	−	64.5903i	0.145488	−	0.234023i
$277$	−157.899	−	273.489i	−0.570032	−	0.987325i	−0.996562	−	0.0828513i	$-0.973597\pi$
$277$	−157.899	−	273.489i	−0.570032	−	0.987325i	0.426530	−	0.904474i	$-0.359736\pi$
$278$		−	131.886i		−	0.474410i
$279$	82.0707	+	166.329i	0.294160	+	0.596160i
$280$	339.678	−	588.339i	1.21313	−	2.10121i
$281$	−329.999	−	190.525i	−1.17437	−	0.678025i	−0.219668	−	0.975575i	$-0.570497\pi$
$281$	−329.999	−	190.525i	−1.17437	−	0.678025i	−0.954706	+	0.297549i	$0.903831\pi$
$282$	100.319	+	62.3667i	0.355741	+	0.221159i
$283$	−118.081	+	204.523i	−0.417249	+	0.722696i	−0.995662	−	0.0930482i	$-0.970339\pi$
$283$	−118.081	+	204.523i	−0.417249	+	0.722696i	0.578413	+	0.815744i	$0.303672\pi$
$284$	15.6779	+	9.05163i	0.0552038	+	0.0318719i
$285$	178.769	+	5.83221i	0.627260	+	0.0204639i
$286$	26.5601	−	43.7982i	0.0928674	−	0.153141i
$287$			228.553i			0.796351i
$288$	−10.9104	+	167.036i	−0.0378835	+	0.579985i
$289$	−125.759	−	217.821i	−0.435152	−	0.753705i
$290$	443.829	−	256.245i	1.53044	−	0.883602i
$291$	294.654	−	157.538i	1.01256	−	0.541369i
$292$	−51.3255			−0.175772
$293$		−	44.4854i		−	0.151827i	−0.997114	−	0.0759137i	$-0.975813\pi$
$293$		−	44.4854i		−	0.151827i	0.997114	−	0.0759137i	$-0.0241873\pi$
$294$	55.1507	−	88.7117i	0.187587	−	0.301741i
$295$	41.6364	+	72.1164i	0.141140	+	0.244462i
$296$	212.830	−	122.878i	0.719021	−	0.415127i
$297$	−63.3740	−	6.22025i	−0.213380	−	0.0209436i
$298$	−427.062			−1.43309
$299$	238.972	−	131.194i	0.799237	−	0.438778i
$300$	−191.762	−	119.216i	−0.639208	−	0.397386i
$301$	310.367	−	537.572i	1.03112	−	1.78595i
$302$	129.405	+	74.7123i	0.428495	+	0.247392i
$303$	362.749	+	11.8344i	1.19719	+	0.0390575i
$304$	−30.9646	+	53.6323i	−0.101857	+	0.176422i
$305$	−135.190	−	78.0518i	−0.443245	−	0.255908i
$306$	−51.1253	+	76.5516i	−0.167076	+	0.250169i
$307$	259.871			0.846485			0.423243	−	0.906016i	$-0.360892\pi$
$307$	259.871			0.846485			0.423243	+	0.906016i	$0.360892\pi$
$308$	20.6354	−	11.9139i	0.0669980	−	0.0386813i
$309$	−255.656	+	136.688i	−0.827367	+	0.442356i
$310$	160.807	−	278.526i	0.518732	−	0.898470i
$311$	−113.035	+	65.2607i	−0.363456	+	0.209841i	−0.670596	−	0.741823i	$-0.733961\pi$
$311$	−113.035	+	65.2607i	−0.363456	+	0.209841i	0.307140	+	0.951664i	$0.400628\pi$
$312$	−185.351	+	284.306i	−0.594074	+	0.911239i
$313$	211.785	−	366.822i	0.676628	−	1.17195i	−0.299362	−	0.954140i	$-0.596774\pi$
$313$	211.785	−	366.822i	0.676628	−	1.17195i	0.975990	−	0.217815i	$-0.0698928\pi$
$314$	−287.956	+	166.251i	−0.917057	+	0.529463i
$315$	−584.275	−	390.210i	−1.85484	−	1.23876i
$316$	−53.3623	+	92.4262i	−0.168868	+	0.292488i
$317$	108.455	+	62.6168i	0.342131	+	0.197529i	0.661214	−	0.750197i	$-0.270042\pi$
$317$	108.455	+	62.6168i	0.342131	+	0.197529i	−0.319083	+	0.947727i	$0.603375\pi$
$318$	−15.8983	+	487.316i	−0.0499947	+	1.53244i
$319$	77.4500			0.242790
$320$	565.346	−	326.403i	1.76671	−	1.02001i
$321$	−262.503	−	490.976i	−0.817766	−	1.52952i
$322$	−292.787			−0.909277
$323$	33.8408	−	19.5380i	0.104770	−	0.0604891i
$324$	97.0902	+	12.7378i	0.299661	+	0.0393143i
$325$	−389.504	−	709.485i	−1.19847	−	2.18303i
$326$	14.8749	+	8.58803i	0.0456286	+	0.0263437i
$327$	16.1172	−	494.025i	0.0492881	−	1.51078i
$328$	−118.996	+	206.107i	−0.362793	+	0.628377i
$329$			196.966i			0.598680i
$330$	52.0620	+	97.3748i	0.157764	+	0.295075i
$331$	262.960	+	455.459i	0.794440	+	1.37601i	0.923194	+	0.384333i	$0.125569\pi$
$331$	262.960	+	455.459i	0.794440	+	1.37601i	−0.128755	+	0.991676i	$0.541098\pi$
$332$	66.7098	+	38.5149i	0.200933	+	0.116009i
$333$	−112.464	−	227.926i	−0.337731	−	0.684463i
$334$	56.6433	−	98.1091i	0.169591	−	0.293740i
$335$			41.2542i			0.123147i
$336$	214.527	−	114.698i	0.638473	−	0.341363i
$337$	118.122	+	204.594i	0.350511	+	0.607103i	0.986339	−	0.164728i	$-0.0526746\pi$
$337$	118.122	+	204.594i	0.350511	+	0.607103i	−0.635828	+	0.771831i	$0.719341\pi$
$338$	−250.364	+	130.515i	−0.740721	+	0.386140i
$339$	62.7834	+	2.04826i	0.185202	+	0.00604207i
$340$	−69.1379			−0.203347
$341$	42.0922	−	24.3019i	0.123438	−	0.0712667i
$342$	79.8062	+	53.2989i	0.233351	+	0.155845i
$343$	−235.323			−0.686073
$344$	559.774	−	323.186i	1.62725	−	0.939494i
$345$	−19.1622	+	587.360i	−0.0555426	+	1.70249i
$346$	21.7276	+	37.6333i	0.0627965	+	0.108767i
$347$		−	4.21494i		−	0.0121468i	−0.999982	−	0.00607340i	$-0.998067\pi$
$347$		−	4.21494i		−	0.0121468i	0.999982	−	0.00607340i	$-0.00193323\pi$
$348$	−119.036	−	3.88346i	−0.342058	−	0.0111594i
$349$	325.320			0.932150			0.466075	−	0.884745i	$-0.345668\pi$
$349$	325.320			0.932150			0.466075	+	0.884745i	$0.345668\pi$
$350$			869.258i			2.48359i
$351$	280.913	+	210.449i	0.800322	+	0.599570i
$352$	43.8652			0.124617
$353$		−	59.4194i		−	0.168327i	−0.996452	−	0.0841635i	$-0.973178\pi$
$353$		−	59.4194i		−	0.168327i	0.996452	−	0.0841635i	$-0.0268218\pi$
$354$	−1.45685	+	44.6554i	−0.00411539	+	0.126145i
$355$	−139.884			−0.394038
$356$	−87.1177	+	50.2975i	−0.244713	+	0.141285i
$357$	−153.413	−	5.00497i	−0.429727	−	0.0140195i
$358$	−210.899	−	365.289i	−0.589105	−	1.02036i
$359$			33.7016i			0.0938763i	0.998898	+	0.0469381i	$0.0149464\pi$
$359$			33.7016i			0.0938763i	−0.998898	+	0.0469381i	$0.985054\pi$
$360$	−323.732	−	656.093i	−0.899256	−	1.82248i
$361$	160.131	+	277.356i	0.443577	+	0.768298i
$362$			396.588i			1.09555i
$363$	11.2922	−	346.129i	0.0311080	−	0.953523i
$364$	−131.309	−	2.82718i	−0.360740	−	0.00776697i
$365$	343.458	−	198.296i	0.940981	−	0.543276i
$366$	−39.4905	−	73.8615i	−0.107897	−	0.201808i
$367$	−475.188			−1.29479			−0.647395	−	0.762154i	$-0.724142\pi$
$367$	−475.188			−1.29479			−0.647395	+	0.762154i	$0.724142\pi$
$368$	−176.213	−	101.737i	−0.478841	−	0.276459i
$369$	204.684	+	136.699i	0.554698	+	0.370458i
$370$	−220.359	+	381.674i	−0.595566	+	1.03155i
$371$	−704.079	+	406.500i	−1.89779	+	1.09569i
$372$	−65.9118	+	35.2401i	−0.177182	+	0.0947315i
$373$	257.358			0.689969			0.344984	−	0.938608i	$-0.387884\pi$
$373$	257.358			0.689969			0.344984	+	0.938608i	$0.387884\pi$
$374$	20.8910	+	12.0614i	0.0558584	+	0.0322498i
$375$	1043.60	+	34.0465i	2.78292	+	0.0907907i
$376$	−102.550	+	177.623i	−0.272741	+	0.472400i
$377$	−365.034	−	221.364i	−0.968260	−	0.587171i
$378$	−155.694	−	343.316i	−0.411889	−	0.908245i
$379$	209.859	+	363.487i	0.553718	+	0.959068i	0.998002	+	0.0631817i	$0.0201248\pi$
$379$	209.859	+	363.487i	0.553718	+	0.959068i	−0.444284	+	0.895886i	$0.646542\pi$
$380$			72.0773i			0.189677i
$381$	−276.753	+	147.967i	−0.726385	+	0.388366i
$382$	122.983	+	213.013i	0.321945	+	0.557626i
$383$			665.575i			1.73779i	0.494993	+	0.868897i	$0.335171\pi$
$383$			665.575i			1.73779i	−0.494993	+	0.868897i	$0.664829\pi$
$384$	127.000	+	4.14327i	0.330729	+	0.0107898i
$385$	−92.0582	+	159.449i	−0.239112	+	0.414154i
$386$	−21.1379	−	12.2040i	−0.0547613	−	0.0316165i
$387$	−295.797	−	599.479i	−0.764335	−	1.54904i
$388$	67.3214	+	116.604i	0.173509	+	0.300526i
$389$	92.2928	+	53.2853i	0.237256	+	0.136980i	0.613915	−	0.789372i	$-0.289594\pi$
$389$	92.2928	+	53.2853i	0.237256	+	0.136980i	−0.376659	+	0.926352i	$0.622927\pi$
$390$	32.9354	−	607.744i	0.0844498	−	1.55832i
$391$	64.1937	+	111.187i	0.164178	+	0.284365i
$392$	157.071	+	90.6851i	0.400692	+	0.231339i
$393$	240.587	+	449.985i	0.612180	+	1.14500i
$394$	−210.472	−	364.549i	−0.534194	−	0.925251i
$395$		−	824.659i		−	2.08774i
$396$	1.67254	−	25.6061i	0.00422358	−	0.0646618i
$397$	−116.806	+	202.314i	−0.294222	+	0.509607i	−0.974804	−	0.223065i	$-0.928394\pi$
$397$	−116.806	+	202.314i	−0.294222	+	0.509607i	0.680582	+	0.732672i	$0.261727\pi$
$398$	−388.401	−	224.243i	−0.975881	−	0.563425i
$399$	−5.21776	+	159.935i	−0.0130771	+	0.400840i
$400$	−302.047	+	523.161i	−0.755118	+	1.30790i
$401$	−101.782	−	58.7638i	−0.253820	−	0.146543i	0.367692	−	0.929948i	$-0.380148\pi$
$401$	−101.782	−	58.7638i	−0.253820	−	0.146543i	−0.621512	+	0.783405i	$0.713481\pi$
$402$	−11.6864	+	18.7980i	−0.0290707	+	0.0467612i
$403$	−267.846	−	5.76689i	−0.664630	−	0.0143099i
$404$			146.256i			0.362019i
$405$	−698.917	+	289.869i	−1.72572	+	0.715725i
$406$	229.248	+	397.070i	0.564651	+	0.978004i
$407$	−57.6805	+	33.3018i	−0.141721	+	0.0818227i
$408$	−135.741	−	84.3879i	−0.332698	−	0.206833i
$409$	−224.762			−0.549541			−0.274770	−	0.961510i	$-0.588602\pi$
$409$	−224.762			−0.549541			−0.274770	+	0.961510i	$0.588602\pi$
$410$		−	426.798i		−	1.04097i
$411$	−205.303	−	383.991i	−0.499520	−	0.934285i
$412$	−58.4114	−	101.172i	−0.141775	−	0.245562i
$413$	−64.5186	+	37.2499i	−0.156219	+	0.0901934i
$414$	−175.118	+	262.210i	−0.422990	+	0.633357i
$415$	−595.209			−1.43424
$416$	−206.744	−	125.373i	−0.496980	−	0.301378i
$417$	7.72223	−	236.702i	0.0185185	−	0.567631i
$418$	12.5742	−	21.7792i	0.0300819	−	0.0521034i
$419$	−33.5256	−	19.3560i	−0.0800134	−	0.0461957i	0.459460	−	0.888199i	$-0.348043\pi$
$419$	−33.5256	−	19.3560i	−0.0800134	−	0.0461957i	−0.539473	+	0.842003i	$0.681376\pi$
$420$	149.483	−	240.448i	0.355912	−	0.572496i
$421$	87.7948	−	152.065i	0.208539	−	0.361200i	−0.742716	−	0.669607i	$-0.766463\pi$
$421$	87.7948	−	152.065i	0.208539	−	0.361200i	0.951254	+	0.308407i	$0.0997959\pi$
$422$	329.466	+	190.217i	0.780725	+	0.450752i
$423$	176.396	+	117.806i	0.417011	+	0.278502i
$424$	−846.579			−1.99665
$425$	330.103	−	190.585i	0.776713	−	0.448435i
$426$	−63.7397	−	39.6259i	−0.149624	−	0.0930186i
$427$	69.8287	−	120.947i	0.163533	−	0.283248i
$428$	194.295	−	112.176i	0.453960	−	0.262094i
$429$	50.2332	−	77.0516i	0.117094	−	0.179608i
$430$	−579.577	+	1003.86i	−1.34785	+	2.33455i
$431$	−208.258	+	120.238i	−0.483197	+	0.278974i	−0.721748	−	0.692156i	$-0.756661\pi$
$431$	−208.258	+	120.238i	−0.483197	+	0.278974i	0.238551	+	0.971130i	$0.423328\pi$
$432$	25.5905	−	260.724i	0.0592372	−	0.603529i
$433$	79.6023	−	137.875i	0.183839	−	0.318419i	−0.759346	−	0.650687i	$-0.774481\pi$
$433$	79.6023	−	137.875i	0.183839	−	0.318419i	0.943185	+	0.332269i	$0.107814\pi$
$434$	249.182	+	143.865i	0.574152	+	0.331487i
$435$	811.565	−	433.908i	1.86567	−	0.997489i
$436$	199.184			0.456845
$437$	115.914	−	66.9229i	0.265249	−	0.153142i
$438$	212.674	+	6.93832i	0.485556	+	0.0158409i
$439$	410.962			0.936133			0.468067	−	0.883693i	$-0.344951\pi$
$439$	410.962			0.936133			0.468067	+	0.883693i	$0.344951\pi$
$440$	−166.035	+	95.8603i	−0.377352	+	0.217864i
$441$	104.176	−	155.986i	0.236227	−	0.353710i
$442$	−63.9893	−	116.557i	−0.144772	−	0.263704i
$443$	410.331	+	236.905i	0.926254	+	0.534773i	0.885625	−	0.464401i	$-0.153730\pi$
$443$	410.331	+	236.905i	0.926254	+	0.534773i	0.0406294	+	0.999174i	$0.487064\pi$
$444$	90.3213	−	48.2908i	0.203426	−	0.108763i
$445$	388.648	−	673.157i	0.873366	−	1.51271i
$446$		−	83.2893i		−	0.186747i
$447$	−766.469	−	25.0055i	−1.71469	−	0.0559406i
$448$	292.015	+	505.785i	0.651819	+	1.12898i
$449$	52.5806	+	30.3574i	0.117106	+	0.0676112i	0.557409	−	0.830238i	$-0.311796\pi$
$449$	52.5806	+	30.3574i	0.117106	+	0.0676112i	−0.440303	+	0.897849i	$0.645129\pi$
$450$	778.476	+	519.908i	1.72995	+	1.15535i
$451$	32.2499	−	55.8585i	0.0715075	−	0.123855i
$452$			25.3134i			0.0560031i
$453$	227.876	+	141.667i	0.503037	+	0.312730i
$454$	−184.320	−	319.252i	−0.405991	−	0.703197i
$455$	889.615	−	488.394i	1.95520	−	1.07339i
$456$	−87.9757	+	141.512i	−0.192929	+	0.310333i
$457$	−624.595			−1.36673			−0.683364	−	0.730078i	$-0.739484\pi$
$457$	−624.595			−1.36673			−0.683364	+	0.730078i	$0.739484\pi$
$458$	−221.291	+	127.762i	−0.483168	+	0.278957i
$459$	−96.2394	+	134.397i	−0.209672	+	0.292805i
$460$	−236.816			−0.514817
$461$	373.689	−	215.749i	0.810605	−	0.468003i	−0.0365608	−	0.999331i	$-0.511640\pi$
$461$	373.689	−	215.749i	0.810605	−	0.468003i	0.847166	+	0.531328i	$0.178307\pi$
$462$	−87.1159	+	46.5770i	−0.188563	+	0.100816i
$463$	−68.5486	−	118.730i	−0.148053	−	0.256435i	0.782455	−	0.622707i	$-0.213967\pi$
$463$	−68.5486	−	118.730i	−0.148053	−	0.256435i	−0.930508	+	0.366272i	$0.880634\pi$
$464$			318.634i			0.686711i
$465$	304.916	−	490.468i	0.655734	−	1.05477i
$466$	395.693			0.849126
$467$			158.770i			0.339978i	0.985446	+	0.169989i	$0.0543733\pi$
$467$			158.770i			0.339978i	−0.985446	+	0.169989i	$0.945627\pi$
$468$	−81.0689	+	115.905i	−0.173224	+	0.247660i
$469$	−36.9079			−0.0786949
$470$		−	367.812i		−	0.782579i
$471$	−526.543	+	281.519i	−1.11793	+	0.597705i
$472$	−77.5767			−0.164357
$473$	−151.708	+	87.5886i	−0.320735	+	0.185177i
$474$	233.608	−	375.766i	0.492843	−	0.792755i
$475$	−198.688	−	344.137i	−0.418290	−	0.724499i
$476$		−	61.8539i		−	0.129945i
$477$	−57.0669	+	873.678i	−0.119637	+	1.83161i
$478$	99.0936	+	171.635i	0.207309	+	0.359069i
$479$			279.391i			0.583280i	0.956528	+	0.291640i	$0.0942008\pi$
$479$			279.391i			0.583280i	−0.956528	+	0.291640i	$0.905799\pi$
$480$	459.645	−	245.751i	0.957593	−	0.511982i
$481$	367.039	+	7.90258i	0.763074	+	0.0164295i
$482$	410.211	−	236.836i	0.851061	−	0.491360i
$483$	−525.480	−	17.1434i	−1.08795	−	0.0354935i
$484$	139.554			0.288336
$485$	−900.998	−	520.191i	−1.85773	−	1.07256i
$486$	−400.584	−	65.9057i	−0.824246	−	0.135608i
$487$	294.379	−	509.879i	0.604474	−	1.04698i	−0.387661	−	0.921802i	$-0.626717\pi$
$487$	294.379	−	509.879i	0.604474	−	1.04698i	0.992134	−	0.125177i	$-0.0399499\pi$
$488$	125.942	−	72.7128i	0.258078	−	0.149002i
$489$	26.1939	+	16.2843i	0.0535662	+	0.0333013i
$490$	−325.255			−0.663787
$491$	−104.766	−	60.4867i	−0.213373	−	0.123191i	0.389505	−	0.921024i	$-0.372646\pi$
$491$	−104.766	−	60.4867i	−0.213373	−	0.123191i	−0.602878	+	0.797833i	$0.705979\pi$
$492$	−52.3670	+	84.2341i	−0.106437	+	0.171208i
$493$	100.525	−	174.115i	0.203906	−	0.353175i
$494$	−121.513	+	66.7098i	−0.245977	+	0.135040i
$495$	87.7366	+	177.812i	0.177246	+	0.359216i
$496$	99.9797	+	173.170i	0.201572	+	0.349133i
$497$		−	125.146i		−	0.251803i
$498$	−271.214	−	168.610i	−0.544607	−	0.338573i
$499$	24.9704	+	43.2501i	0.0500409	+	0.0866734i	0.889961	−	0.456037i	$-0.150731\pi$
$499$	24.9704	+	43.2501i	0.0500409	+	0.0866734i	−0.839920	+	0.542710i	$0.817398\pi$
$500$			420.763i			0.841527i
$501$	107.405	−	172.765i	0.214381	−	0.344840i
$502$	145.830	−	252.585i	0.290498	−	0.503157i
$503$	−215.845	−	124.618i	−0.429115	−	0.247750i	0.269855	−	0.962901i	$-0.413024\pi$
$503$	−215.845	−	124.618i	−0.429115	−	0.247750i	−0.698970	+	0.715151i	$0.746358\pi$
$504$	586.971	−	289.626i	1.16462	−	0.574654i
$505$	−565.057	−	978.708i	−1.11893	−	1.93804i
$506$	71.5574	+	41.3137i	0.141418	+	0.0816476i
$507$	−456.982	+	219.583i	−0.901345	+	0.433102i
$508$	−63.2314	−	109.520i	−0.124471	−	0.215590i
$509$	178.670	+	103.155i	0.351021	+	0.202662i	0.665135	−	0.746723i	$-0.268374\pi$
$509$	178.670	+	103.155i	0.351021	+	0.202662i	−0.314114	+	0.949385i	$0.601707\pi$
$510$	286.482	+	9.34625i	0.561728	+	0.0183260i
$511$	177.404	+	307.273i	0.347171	+	0.601318i
$512$			518.213i			1.01213i
$513$	140.111	+	100.331i	0.273122	+	0.195577i
$514$	96.2160	−	166.651i	0.187191	−	0.324224i
$515$	781.751	+	451.344i	1.51796	+	0.876396i
$516$	237.558	−	127.012i	0.460384	−	0.246147i
$517$	27.7928	−	48.1386i	0.0537579	−	0.0931114i
$518$	−341.463	−	197.144i	−0.659195	−	0.380586i
$519$	36.7921	+	68.8145i	0.0708903	+	0.132591i
$520$	1056.53	+	22.7478i	2.03179	+	0.0437458i
$521$			437.553i			0.839832i	0.907563	+	0.419916i	$0.137941\pi$
$521$			437.553i			0.839832i	−0.907563	+	0.419916i	$0.862059\pi$
$522$	492.716	+	32.1832i	0.943901	+	0.0616537i
$523$	61.7422	+	106.941i	0.118054	+	0.204475i	0.918996	−	0.394266i	$-0.129001\pi$
$523$	61.7422	+	106.941i	0.118054	+	0.204475i	−0.800942	+	0.598741i	$0.795668\pi$
$524$	−178.074	+	102.811i	−0.339835	+	0.196204i
$525$	−50.8971	+	1560.10i	−0.0969468	+	2.97162i
$526$	61.7389			0.117374
$527$		−	126.170i		−	0.239412i
$528$	−68.6150	−	2.23851i	−0.129953	−	0.00423961i
$529$	−44.6195	−	77.2833i	−0.0843469	−	0.146093i
$530$	1314.79	−	759.095i	2.48074	−	1.43225i
$531$	−5.22936	+	80.0600i	−0.00984814	+	0.150772i
$532$	−64.4836			−0.121210
$533$	−311.651	+	171.095i	−0.584710	+	0.321003i
$534$	367.783	−	196.637i	0.688732	−	0.368234i
$535$	−866.784	+	1501.31i	−1.62016	+	2.80620i
$536$	−33.2833	−	19.2161i	−0.0620958	−	0.0358510i
$537$	−357.123	−	667.950i	−0.665034	−	1.24385i
$538$	49.9271	−	86.4762i	0.0928012	−	0.160736i
$539$	−42.5688	−	24.5771i	−0.0789774	−	0.0455976i
$540$	−125.930	−	277.685i	−0.233204	−	0.514232i
$541$	599.652			1.10841			0.554207	−	0.832379i	$-0.313021\pi$
$541$	599.652			1.10841			0.554207	+	0.832379i	$0.313021\pi$
$542$	249.429	−	144.008i	0.460201	−	0.265697i
$543$	−23.2212	+	711.776i	−0.0427646	+	1.31082i
$544$	56.9344	−	98.6133i	0.104659	−	0.181274i
$545$	−1332.89	+	769.547i	−2.44568	+	1.41201i
$546$	543.715	+	29.4655i	0.995815	+	0.0539662i
$547$	−349.541	+	605.422i	−0.639014	+	1.10680i	0.346635	+	0.938000i	$0.387324\pi$
$547$	−349.541	+	605.422i	−0.639014	+	1.10680i	−0.985649	+	0.168805i	$0.946009\pi$
$548$	151.958	−	87.7328i	0.277295	−	0.160096i
$549$	−66.5507	−	134.875i	−0.121222	−	0.245674i
$550$	122.656	−	212.447i	0.223012	−	0.386268i
$551$	−181.518	−	104.799i	−0.329433	−	0.190198i
$552$	−464.948	−	289.051i	−0.842298	−	0.523643i
$553$	737.778			1.33414
$554$	−456.905	+	263.794i	−0.824739	+	0.476163i
$555$	−417.838	+	672.106i	−0.752861	+	1.21100i
$556$	95.4350			0.171646
$557$	161.349	−	93.1547i	0.289674	−	0.167244i	−0.348121	−	0.937450i	$-0.613180\pi$
$557$	161.349	−	93.1547i	0.289674	−	0.167244i	0.637795	+	0.770206i	$0.279847\pi$
$558$	277.878	−	137.112i	0.497989	−	0.245720i
$559$	965.364	+	20.7849i	1.72695	+	0.0371823i
$560$	−655.985	−	378.733i	−1.17140	−	0.676309i
$561$	36.7879	+	22.8705i	0.0655756	+	0.0407673i
$562$	−318.302	+	551.314i	−0.566373	+	0.980987i
$563$			100.412i			0.178352i	0.996016	+	0.0891762i	$0.0284234\pi$
$563$			100.412i			0.178352i	−0.996016	+	0.0891762i	$0.971577\pi$
$564$	−45.1297	+	72.5926i	−0.0800172	+	0.128710i
$565$	−97.7981	−	169.391i	−0.173094	−	0.299808i
$566$	341.687	+	197.273i	0.603687	+	0.348539i
$567$	−259.330	−	625.283i	−0.457372	−	1.10279i
$568$	65.1575	−	112.856i	0.114714	−	0.198690i
$569$			33.2119i			0.0583690i	0.999574	+	0.0291845i	$0.00929103\pi$
$569$			33.2119i			0.0583690i	−0.999574	+	0.0291845i	$0.990709\pi$
$570$	9.74360	−	298.661i	0.0170940	−	0.523967i
$571$	−133.349	−	230.967i	−0.233536	−	0.404496i	0.725310	−	0.688422i	$-0.241696\pi$
$571$	−133.349	−	230.967i	−0.233536	−	0.404496i	−0.958846	+	0.283926i	$0.908363\pi$
$572$	31.6932	+	19.2194i	0.0554077	+	0.0336003i
$573$	208.251	+	389.506i	0.363440	+	0.679766i
$574$	381.833			0.665214
$575$	1130.69	−	652.805i	1.96642	−	1.13531i
$576$	627.619	+	40.9948i	1.08962	+	0.0711716i
$577$	594.972			1.03115			0.515573	−	0.856845i	$-0.327579\pi$
$577$	594.972			1.03115			0.515573	+	0.856845i	$0.327579\pi$
$578$	−363.903	+	210.099i	−0.629590	+	0.363494i
$579$	−37.2226	−	23.1407i	−0.0642878	−	0.0399667i
$580$	185.423	+	321.163i	0.319695	+	0.553729i
$581$		−	532.501i		−	0.916525i
$582$	−263.192	−	492.264i	−0.452220	−	0.845815i
$583$	229.436			0.393545
$584$			369.463i			0.632642i
$585$	94.6957	−	1088.82i	0.161873	−	1.86123i
$586$	−74.3197			−0.126825
$587$		−	1036.55i		−	1.76584i	−0.469525	−	0.882919i	$-0.655575\pi$
$587$		−	1036.55i		−	1.76584i	0.469525	−	0.882919i	$-0.344425\pi$
$588$	64.1934	+	39.9081i	0.109173	+	0.0678708i
$589$	−131.534			−0.223318
$590$	120.482	−	69.5601i	0.204206	−	0.117898i
$591$	−356.400	−	666.598i	−0.603046	−	1.12791i
$592$	−137.006	−	237.301i	−0.231429	−	0.400846i
$593$			332.831i			0.561266i	0.959815	+	0.280633i	$0.0905444\pi$
$593$			332.831i			0.561266i	−0.959815	+	0.280633i	$0.909456\pi$
$594$	−10.3919	+	105.876i	−0.0174947	+	0.178242i
$595$	238.972	+	413.912i	0.401634	+	0.695650i
$596$		−	309.030i		−	0.518506i
$597$	−683.952	−	425.202i	−1.14565	−	0.712232i
$598$	−219.181	−	399.239i	−0.366523	−	0.667625i
$599$	−778.713	+	449.590i	−1.30002	+	0.750568i	−0.980408	−	0.196980i	$-0.936887\pi$
$599$	−778.713	+	449.590i	−1.30002	+	0.750568i	−0.319614	+	0.947548i	$0.603553\pi$
$600$	−858.166	+	1380.39i	−1.43028	+	2.30065i
$601$	−926.787			−1.54207			−0.771037	−	0.636790i	$-0.780262\pi$
$601$	−926.787			−1.54207			−0.771037	+	0.636790i	$0.780262\pi$
$602$	−898.096	−	518.516i	−1.49185	−	0.861322i
$603$	−22.0749	+	33.0534i	−0.0366084	+	0.0548150i
$604$	−54.0632	+	93.6401i	−0.0895085	+	0.155033i
$605$	−933.865	+	539.167i	−1.54358	+	0.891186i
$606$	19.7712	−	606.029i	0.0326258	−	1.00005i
$607$	−236.251			−0.389210			−0.194605	−	0.980882i	$-0.562343\pi$
$607$	−236.251			−0.389210			−0.194605	+	0.980882i	$0.562343\pi$
$608$	−102.806	−	59.3550i	−0.169089	−	0.0976233i
$609$	388.194	+	726.063i	0.637428	+	1.19222i
$610$	−130.398	+	225.855i	−0.213766	+	0.370254i
$611$	−268.579	+	147.449i	−0.439573	+	0.241324i
$612$	−55.3941	−	36.9952i	−0.0905133	−	0.0604497i
$613$	144.036	+	249.478i	0.234970	+	0.406979i	0.959264	−	0.282512i	$-0.0911676\pi$
$613$	144.036	+	249.478i	0.234970	+	0.406979i	−0.724294	+	0.689491i	$0.757834\pi$
$614$		−	434.155i		−	0.707092i
$615$	24.9900	−	765.995i	0.0406342	−	1.24552i
$616$	−85.7610	−	148.542i	−0.139222	−	0.241140i
$617$		−	172.269i		−	0.279205i	−0.990208	−	0.139602i	$-0.955418\pi$
$617$		−	172.269i		−	0.279205i	0.990208	−	0.139602i	$-0.0445824\pi$
$618$	228.358	+	427.113i	0.369512	+	0.691122i
$619$	247.022	−	427.854i	0.399066	−	0.691202i	−0.594545	−	0.804062i	$-0.702668\pi$
$619$	247.022	−	427.854i	0.399066	−	0.691202i	0.993611	+	0.112860i	$0.0360012\pi$
$620$	201.546	+	116.363i	0.325075	+	0.187682i
$621$	−329.646	+	460.347i	−0.530830	+	0.741300i
$622$	109.028	+	188.842i	0.175286	+	0.303605i
$623$	602.238	+	347.702i	0.966673	+	0.558109i
$624$	316.995	+	206.662i	0.508005	+	0.331190i
$625$	−847.373	−	1467.69i	−1.35580	−	2.34831i
$626$	−612.832	−	353.819i	−0.978965	−	0.565206i
$627$	23.8428	−	38.3520i	0.0380268	−	0.0611674i
$628$	−120.303	−	208.370i	−0.191565	−	0.331800i
$629$			172.895i			0.274873i
$630$	−651.907	+	976.121i	−1.03477	+	1.54940i
$631$	−17.1478	+	29.7009i	−0.0271756	+	0.0470696i	−0.879293	−	0.476281i	$-0.841985\pi$
$631$	−17.1478	+	29.7009i	−0.0271756	+	0.0470696i	0.852118	+	0.523350i	$0.175318\pi$
$632$	665.323	+	384.125i	1.05273	+	0.607792i
$633$	580.171	+	360.683i	0.916542	+	0.569800i
$634$	104.611	−	181.192i	0.165002	−	0.285791i
$635$	846.259	+	488.588i	1.33269	+	0.769430i
$636$	−352.630	−	11.5043i	−0.554450	−	0.0180885i
$637$	130.388	+	237.504i	0.204691	+	0.372847i
$638$		−	129.392i		−	0.202809i
$639$	−112.076	−	74.8507i	−0.175394	−	0.117137i
$640$	−197.828	−	342.649i	−0.309107	−	0.535389i
$641$	−949.249	+	548.049i	−1.48089	+	0.854991i	−0.999765	−	0.0216626i	$-0.993104\pi$
$641$	−949.249	+	548.049i	−1.48089	+	0.854991i	−0.481122	+	0.876653i	$0.659771\pi$
$642$	−820.251	+	438.551i	−1.27765	+	0.683102i
$643$	1056.58			1.64321			0.821603	−	0.570060i	$-0.193080\pi$
$643$	1056.58			1.64321			0.821603	+	0.570060i	$0.193080\pi$
$644$		−	211.866i		−	0.328985i
$645$	−1098.97	+	1767.74i	−1.70383	+	2.74067i
$646$	−32.6412	−	56.5363i	−0.0505282	−	0.0875174i
$647$	119.357	−	68.9110i	0.184478	−	0.106509i	−0.404917	−	0.914354i	$-0.632700\pi$
$647$	119.357	−	68.9110i	0.184478	−	0.106509i	0.589395	+	0.807845i	$0.299366\pi$
$648$	91.6923	−	698.897i	0.141500	−	1.07854i
$649$	21.0245			0.0323953
$650$	−1185.30	+	650.727i	−1.82355	+	1.00112i
$651$	438.795	+	272.792i	0.674033	+	0.419036i
$652$	−6.21446	+	10.7638i	−0.00953138	+	0.0165088i
$653$	−439.702	−	253.862i	−0.673357	−	0.388763i	0.123990	−	0.992283i	$-0.460431\pi$
$653$	−439.702	−	253.862i	−0.673357	−	0.388763i	−0.797347	+	0.603521i	$0.793764\pi$
$654$	−825.345	−	26.9263i	−1.26200	−	0.0411717i
$655$	794.418	−	1375.97i	1.21285	−	2.10072i
$656$	229.805	+	132.678i	0.350313	+	0.202253i
$657$	381.290	+	24.9051i	0.580350	+	0.0379073i
$658$	329.062			0.500094
$659$	7.47529	−	4.31586i	0.0113434	−	0.00654911i	−0.494318	−	0.869281i	$-0.664582\pi$
$659$	7.47529	−	4.31586i	0.0113434	−	0.00654911i	0.505661	+	0.862732i	$0.331249\pi$
$660$	−70.4622	+	37.6730i	−0.106761	+	0.0570803i
$661$	114.006	−	197.464i	0.172475	−	0.298735i	−0.766810	−	0.641874i	$-0.778157\pi$
$661$	114.006	−	197.464i	0.172475	−	0.298735i	0.939284	+	0.343140i	$0.111490\pi$
$662$	760.915	−	439.314i	1.14942	−	0.663617i
$663$	−108.020	−	212.938i	−0.162926	−	0.321173i
$664$	277.247	−	480.206i	0.417541	−	0.723202i
$665$	431.509	−	249.132i	0.648886	−	0.374635i
$666$	−380.786	+	187.889i	−0.571751	+	0.282116i
$667$	344.327	−	596.391i	0.516232	−	0.894140i
$668$	70.9936	+	40.9882i	0.106278	+	0.0613595i
$669$	4.87679	−	149.483i	0.00728966	−	0.223443i
$670$	68.9215			0.102868
$671$	−34.1324	+	19.7063i	−0.0508679	+	0.0293686i
$672$	219.861	+	411.219i	0.327173	+	0.611933i
$673$	328.551			0.488188			0.244094	−	0.969752i	$-0.421509\pi$
$673$	328.551			0.488188			0.244094	+	0.969752i	$0.421509\pi$
$674$	341.805	−	197.341i	0.507129	−	0.292791i
$675$	1366.73	+	978.687i	2.02478	+	1.44991i
$676$	−94.4432	−	181.168i	−0.139709	−	0.268000i
$677$	28.7642	+	16.6070i	0.0424878	+	0.0245303i	0.521093	−	0.853500i	$-0.325524\pi$
$677$	28.7642	+	16.6070i	0.0424878	+	0.0245303i	−0.478606	+	0.878030i	$0.658858\pi$
$678$	3.42193	−	104.889i	0.00504710	−	0.154704i
$679$	465.387	−	806.074i	0.685401	−	1.18715i
$680$			497.684i			0.731888i
$681$	−312.115	−	583.769i	−0.458319	−	0.857223i
$682$	−40.6001	−	70.3215i	−0.0595310	−	0.103111i
$683$	342.607	+	197.804i	0.501621	+	0.289611i	0.729383	−	0.684106i	$-0.239807\pi$
$683$	342.607	+	197.804i	0.501621	+	0.289611i	−0.227762	+	0.973717i	$0.573141\pi$
$684$	−38.5681	+	57.7492i	−0.0563860	+	0.0844287i
$685$	−677.910	+	1174.17i	−0.989650	+	1.71412i
$686$			393.143i			0.573095i
$687$	−404.643	+	216.344i	−0.588999	+	0.314912i
$688$	−360.345	−	624.136i	−0.523757	−	0.907174i
$689$	−1081.37	−	655.764i	−1.56948	−	0.951761i
$690$	981.276	+	32.0134i	1.42214	+	0.0463962i
$691$	−1335.64			−1.93291			−0.966455	−	0.256837i	$-0.917320\pi$
$691$	−1335.64			−1.93291			−0.966455	+	0.256837i	$0.917320\pi$
$692$	−27.2321	+	15.7225i	−0.0393528	+	0.0227204i
$693$	−159.078	+	78.4932i	−0.229550	+	0.113266i
$694$	−7.04170			−0.0101465
$695$	−638.629	+	368.713i	−0.918890	+	0.530522i
$696$	−27.9548	+	856.873i	−0.0401650	+	1.23114i
$697$	−83.7169	−	145.002i	−0.120110	−	0.208037i
$698$		−	543.498i		−	0.778650i
$699$	710.169	+	23.1687i	1.01598	+	0.0331455i
$700$	−629.011			−0.898587
$701$		−	796.387i		−	1.13607i	−0.823004	−	0.568036i	$-0.807703\pi$
$701$		−	796.387i		−	1.13607i	0.823004	−	0.568036i	$-0.192297\pi$
$702$	351.588	−	469.308i	0.500837	−	0.668531i
$703$	180.246			0.256395
$704$		−	164.819i		−	0.234118i
$705$	21.5363	−	660.131i	0.0305479	−	0.936356i
$706$	−99.2693			−0.140608
$707$	875.597	−	505.526i	1.23847	−	0.715030i
$708$	−32.3135	−	1.05420i	−0.0456405	−	0.00148899i
$709$	76.0541	+	131.730i	0.107270	+	0.185796i	0.914663	−	0.404217i	$-0.132456\pi$
$709$	76.0541	+	131.730i	0.107270	+	0.185796i	−0.807394	+	0.590013i	$0.799123\pi$
$710$			233.697i			0.329151i
$711$	441.269	−	660.727i	0.620632	−	0.929293i
$712$	362.063	+	627.111i	0.508515	+	0.880774i
$713$		−	432.166i		−	0.606123i
$714$	−8.36158	+	256.299i	−0.0117109	+	0.358963i
$715$	−286.337	−	6.16503i	−0.400472	−	0.00862241i
$716$	264.329	−	152.611i	0.369175	−	0.213143i
$717$	167.799	+	313.844i	0.234029	+	0.437719i
$718$	56.3037			0.0784174
$719$	216.473	+	124.981i	0.301075	+	0.173825i	0.642926	−	0.765929i	$-0.277720\pi$
$719$	216.473	+	124.981i	0.301075	+	0.173825i	−0.341851	+	0.939754i	$0.611054\pi$
$720$	−731.528	+	360.954i	−1.01601	+	0.501325i
$721$	−403.793	+	699.390i	−0.560046	+	0.970028i
$722$	463.365	−	267.524i	0.641780	−	0.370532i
$723$	750.093	−	401.042i	1.03747	−	0.554691i
$724$	−286.978			−0.396379
$725$	−1770.63	−	1022.27i	−2.44225	−	1.41003i
$726$	−578.261	−	18.8653i	−0.796503	−	0.0259853i
$727$	−617.631	+	1069.77i	−0.849561	+	1.47148i	0.0320404	+	0.999487i	$0.489799\pi$
$727$	−617.631	+	1069.77i	−0.849561	+	1.47148i	−0.881601	+	0.471996i	$0.843534\pi$
$728$	−20.3512	+	945.222i	−0.0279550	+	1.29838i
$729$	−715.088	−	141.739i	−0.980916	−	0.194430i
$730$	−331.283	−	573.800i	−0.453813	−	0.786027i
$731$			454.739i			0.622078i
$732$	53.4476	−	28.5760i	0.0730158	−	0.0390383i
$733$	−106.738	−	184.876i	−0.145619	−	0.252219i	0.783985	−	0.620780i	$-0.213184\pi$
$733$	−106.738	−	184.876i	−0.145619	−	0.252219i	−0.929604	+	0.368561i	$0.879851\pi$
$734$			793.875i			1.08157i
$735$	−583.752	−	19.0445i	−0.794220	−	0.0259108i
$736$	195.016	−	337.777i	0.264967	−	0.458936i
$737$	9.02032	+	5.20788i	0.0122392	+	0.00706633i
$738$	228.376	−	341.956i	0.309453	−	0.463355i
$739$	410.342	+	710.734i	0.555267	+	0.961751i	0.997883	+	0.0650392i	$0.0207172\pi$
$739$	410.342	+	710.734i	0.555267	+	0.961751i	−0.442616	+	0.896711i	$0.645949\pi$
$740$	−276.186	−	159.456i	−0.373225	−	0.215481i
$741$	−221.991	+	112.613i	−0.299583	+	0.151974i
$742$	679.121	+	1176.27i	0.915258	+	1.58527i
$743$	689.188	+	397.903i	0.927575	+	0.535536i	0.886044	−	0.463601i	$-0.153443\pi$
$743$	689.188	+	397.903i	0.927575	+	0.535536i	0.0415314	+	0.999137i	$0.486776\pi$
$744$	253.673	+	474.461i	0.340959	+	0.637717i
$745$	1193.93	+	2067.95i	1.60260	+	2.77578i
$746$		−	429.957i		−	0.576349i
$747$	−476.889	−	318.492i	−0.638405	−	0.426362i
$748$	−8.72788	+	15.1171i	−0.0116683	+	0.0202101i
$749$	−1343.14	−	775.465i	−1.79325	−	1.03533i
$750$	56.8799	−	1743.49i	0.0758399	−	2.32465i
$751$	−2.18705	+	3.78808i	−0.00291219	+	0.00504405i	−0.867478	−	0.497476i	$-0.834260\pi$
$751$	−2.18705	+	3.78808i	−0.00291219	+	0.00504405i	0.864566	+	0.502520i	$0.167594\pi$
$752$	198.045	+	114.341i	0.263358	+	0.152050i
$753$	276.518	−	444.788i	0.367221	−	0.590688i
$754$	−369.822	+	609.845i	−0.490480	+	0.808813i
$755$		−	835.490i		−	1.10661i
$756$	248.430	−	112.663i	0.328611	−	0.149025i
$757$	501.201	+	868.106i	0.662089	+	1.14677i	0.980066	+	0.198673i	$0.0636631\pi$
$757$	501.201	+	868.106i	0.662089	+	1.14677i	−0.317977	+	0.948098i	$0.603004\pi$
$758$	607.260	−	350.602i	0.801135	−	0.462536i
$759$	126.009	+	78.3375i	0.166019	+	0.103212i
$760$	518.843			0.682688
$761$		−	937.723i		−	1.23222i	−0.787658	−	0.616112i	$-0.788707\pi$
$761$		−	937.723i		−	1.23222i	0.787658	−	0.616112i	$-0.211293\pi$
$762$	247.202	+	462.358i	0.324412	+	0.606769i
$763$	−688.472	−	1192.47i	−0.902322	−	1.56287i
$764$	−154.140	+	88.9928i	−0.201754	+	0.116483i
$765$	513.615	+	33.5483i	0.671392	+	0.0438540i
$766$	1111.95			1.45163
$767$	−99.0919	−	60.0912i	−0.129194	−	0.0783458i
$768$	−20.4225	+	625.990i	−0.0265917	+	0.815091i
$769$	−54.3840	+	94.1959i	−0.0707205	+	0.122491i	−0.899217	−	0.437502i	$-0.855863\pi$
$769$	−54.3840	+	94.1959i	−0.0707205	+	0.122491i	0.828497	+	0.559994i	$0.189196\pi$
$770$

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.67065i q^{2} +(0.0978207 - 2.99840i) q^{3} +1.20892 q^{4} +(-8.08978 + 4.67064i) q^{5} +(-5.00930 - 0.163425i) q^{6} +(-4.17857 - 7.23749i) q^{7} -8.70230i q^{8} +(-8.98086 - 0.586612i) q^{9} +(7.80302 + 13.5152i) q^{10} +2.35846i q^{11} +(0.118257 - 3.62482i) q^{12} +(6.74084 - 11.1158i) q^{13} +(-12.0913 + 6.98094i) q^{14} +(13.2131 + 24.7133i) q^{15} -9.70286 q^{16} +(5.30206 + 3.06114i) q^{17} +(-0.980026 + 15.0039i) q^{18} +(3.19129 - 5.52747i) q^{19} +(-9.77986 + 5.64641i) q^{20} +(-22.1097 + 11.8211i) q^{21} +3.94017 q^{22} +(18.1610 + 10.4852i) q^{23} +(-26.0930 - 0.851265i) q^{24} +(31.1297 - 53.9182i) q^{25} +(-18.5707 - 11.2616i) q^{26} +(-2.63742 + 26.8709i) q^{27} +(-5.05153 - 8.74951i) q^{28} -32.8392i q^{29} +(41.2874 - 22.0745i) q^{30} +(-10.3041 - 17.8473i) q^{31} -18.5991i q^{32} +(7.07162 + 0.230707i) q^{33} +(5.11411 - 8.85790i) q^{34} +(67.6074 + 39.0331i) q^{35} +(-10.8571 - 0.709165i) q^{36} +(14.1201 + 24.4568i) q^{37} +(-9.23450 - 5.33154i) q^{38} +(-32.6703 - 21.2991i) q^{39} +(40.6453 + 70.3997i) q^{40} +(-23.6843 - 13.6741i) q^{41} +(19.7489 + 36.9376i) q^{42} +(37.1380 + 64.3249i) q^{43} +2.85118i q^{44} +(75.3931 - 37.2008i) q^{45} +(17.5172 - 30.3407i) q^{46} +(-20.4110 - 11.7843i) q^{47} +(-0.949141 + 29.0931i) q^{48} +(-10.4208 + 18.0494i) q^{49} +(-90.0787 - 52.0069i) q^{50} +(9.69720 - 15.5983i) q^{51} +(8.14910 - 13.4381i) q^{52} -97.2822i q^{53} +(44.8919 + 4.40621i) q^{54} +(-11.0155 - 19.0794i) q^{55} +(-62.9828 + 36.3631i) q^{56} +(-16.2614 - 10.1095i) q^{57} -54.8629 q^{58} -8.91451i q^{59} +(15.9735 + 29.8763i) q^{60} +(8.35559 + 14.4723i) q^{61} +(-29.8167 + 17.2147i) q^{62} +(33.2815 + 67.4501i) q^{63} -69.8840 q^{64} +(-2.61400 + 121.408i) q^{65} +(0.385431 - 11.8142i) q^{66} +(2.20817 - 3.82466i) q^{67} +(6.40974 + 3.70067i) q^{68} +(33.2155 - 53.4283i) q^{69} +(65.2108 - 112.948i) q^{70} +(12.9685 + 7.48739i) q^{71} +(-5.10487 + 78.1541i) q^{72} -42.4558 q^{73} +(40.8589 - 23.5899i) q^{74} +(-158.623 - 98.6137i) q^{75} +(3.85800 - 6.68225i) q^{76} +(17.0693 - 9.85499i) q^{77} +(-35.5834 + 54.5807i) q^{78} +(-44.1406 + 76.4538i) q^{79} +(78.4940 - 45.3185i) q^{80} +(80.3118 + 10.5366i) q^{81} +(-22.8447 + 39.5682i) q^{82} +(55.1815 + 31.8591i) q^{83} +(-26.7287 + 14.2907i) q^{84} -57.1900 q^{85} +(107.465 - 62.0447i) q^{86} +(-98.4651 - 3.21235i) q^{87} +20.5240 q^{88} +(-72.0627 + 41.6054i) q^{89} +(-62.1496 - 125.956i) q^{90} +(-108.618 - 2.33861i) q^{91} +(21.9551 + 12.6758i) q^{92} +(-54.5214 + 29.1502i) q^{93} +(-19.6875 + 34.0997i) q^{94} +59.6214i q^{95} +(-55.7675 - 1.81937i) q^{96} +(55.6874 + 96.4534i) q^{97} +(30.1543 + 17.4096i) q^{98} +(1.38350 - 21.1810i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) \) 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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