LMFDB - Embedded newform 115.3.h.a.21.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [115,3,Mod(11,115)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(115, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 9])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("115.11"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	115.h (of order $22$, degree $10$, 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:	$3.13352304014$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			21.2
Character	$\chi$	$=$	115.21
Dual form			115.3.h.a.11.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.96935 - 1.90828i) q^{2} +(0.852548 + 5.92960i) q^{3} +(3.51382 + 7.69420i) q^{4} +(-0.629973 + 2.14549i) q^{5} +(8.78386 - 19.2340i) q^{6} +(4.46805 + 3.87159i) q^{7} +(2.23966 - 15.5772i) q^{8} +(-25.7979 + 7.57495i) q^{9} +(5.96482 - 5.16855i) q^{10} +(-6.69528 - 10.4181i) q^{11} +(-42.6278 + 27.3952i) q^{12} +(3.31427 + 3.82487i) q^{13} +(-5.87911 - 20.0224i) q^{14} +(-13.2590 - 1.90636i) q^{15} +(-14.2192 + 16.4098i) q^{16} +(11.7642 + 5.37252i) q^{17} +(91.0581 + 26.7371i) q^{18} +(-1.34372 + 0.613655i) q^{19} +(-18.7215 + 2.69174i) q^{20} +(-19.1477 + 29.7945i) q^{21} +43.7113i q^{22} +(-19.5514 + 12.1137i) q^{23} +94.2758 q^{24} +(-4.20627 - 2.70320i) q^{25} +(-2.54228 - 17.6819i) q^{26} +(-44.5132 - 97.4703i) q^{27} +(-14.0888 + 47.9821i) q^{28} +(3.96176 - 8.67505i) q^{29} +(35.7327 + 30.9626i) q^{30} +(-2.32142 + 16.1459i) q^{31} +(13.1369 - 3.85735i) q^{32} +(56.0669 - 48.5822i) q^{33} +(-24.6797 - 38.4023i) q^{34} +(-11.1212 + 7.14717i) q^{35} +(-148.932 - 171.877i) q^{36} +(12.5785 + 42.8386i) q^{37} +(5.16100 + 0.742039i) q^{38} +(-19.8544 + 22.9132i) q^{39} +(32.0097 + 14.6184i) q^{40} +(-1.08614 - 0.318919i) q^{41} +(113.713 - 51.9308i) q^{42} +(-16.5332 + 2.37712i) q^{43} +(56.6326 - 88.1220i) q^{44} -60.1212i q^{45} +(81.1714 + 1.34004i) q^{46} +41.3808 q^{47} +(-109.426 - 70.3240i) q^{48} +(-1.99915 - 13.9044i) q^{49} +(7.33139 + 16.0535i) q^{50} +(-21.8274 + 74.3372i) q^{51} +(-17.7835 + 38.9405i) q^{52} +(6.69979 + 5.80540i) q^{53} +(-53.8259 + 374.367i) q^{54} +(26.5697 - 7.80157i) q^{55} +(70.3152 - 60.9285i) q^{56} +(-4.78432 - 7.44454i) q^{57} +(-28.3183 + 18.1991i) q^{58} +(22.2450 + 25.6721i) q^{59} +(-31.9219 - 108.716i) q^{60} +(75.8579 + 10.9067i) q^{61} +(37.7040 - 43.5127i) q^{62} +(-144.593 - 66.0336i) q^{63} +(36.9661 + 10.8542i) q^{64} +(-10.2941 + 4.70117i) q^{65} +(-259.191 + 37.2660i) q^{66} +(-32.1599 + 50.0417i) q^{67} +109.394i q^{68} +(-88.4977 - 105.605i) q^{69} +46.6616 q^{70} +(23.6897 + 15.2245i) q^{71} +(60.2177 + 418.823i) q^{72} +(35.2466 + 77.1794i) q^{73} +(44.3982 - 151.206i) q^{74} +(12.4429 - 27.2461i) q^{75} +(-9.44318 - 8.18256i) q^{76} +(10.4196 - 72.4697i) q^{77} +(102.679 - 30.1494i) q^{78} +(-27.6983 + 24.0007i) q^{79} +(-26.2494 - 40.8449i) q^{80} +(336.441 - 216.218i) q^{81} +(2.61653 + 3.01964i) q^{82} +(33.5400 + 114.227i) q^{83} +(-296.526 - 42.6341i) q^{84} +(-18.9378 + 21.8554i) q^{85} +(53.6292 + 24.4916i) q^{86} +(54.8172 + 16.0958i) q^{87} +(-177.279 + 80.9606i) q^{88} +(45.4904 - 6.54053i) q^{89} +(-114.728 + 178.521i) q^{90} +29.9212i q^{91} +(-161.905 - 107.867i) q^{92} -97.7176 q^{93} +(-122.874 - 78.9663i) q^{94} +(-0.470086 - 3.26952i) q^{95} +(34.0724 + 74.6082i) q^{96} +(22.5360 - 76.7506i) q^{97} +(-20.5973 + 45.1019i) q^{98} +(251.640 + 218.048i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 4 q^{2} - 16 q^{4} - 26 q^{6} - 22 q^{8} - 32 q^{9} + 30 q^{12} + 12 q^{13} - 256 q^{16} - 110 q^{17} + 70 q^{18} - 66 q^{19} - 66 q^{21} - 34 q^{23} + 180 q^{24} + 80 q^{25} + 238 q^{26} + 234 q^{27}+ \cdots + 2112 q^{99}+O(q^{100}) $ 160 * q + 4 * q^2 - 16 * q^4 - 26 * q^6 - 22 * q^8 - 32 * q^9 + 30 * q^12 + 12 * q^13 - 256 * q^16 - 110 * q^17 + 70 * q^18 - 66 * q^19 - 66 * q^21 - 34 * q^23 + 180 * q^24 + 80 * q^25 + 238 * q^26 + 234 * q^27 + 128 * q^29 + 188 * q^31 + 496 * q^32 - 242 * q^34 - 170 * q^35 - 736 * q^36 - 770 * q^38 - 188 * q^39 - 440 * q^40 - 234 * q^41 - 176 * q^43 - 22 * q^44 + 80 * q^46 - 224 * q^47 + 754 * q^48 + 518 * q^49 + 90 * q^50 + 528 * q^51 - 82 * q^52 + 352 * q^53 + 510 * q^54 + 400 * q^55 + 418 * q^56 - 726 * q^57 + 376 * q^58 - 62 * q^59 + 330 * q^60 - 308 * q^61 - 662 * q^62 - 550 * q^63 - 206 * q^64 - 176 * q^66 - 44 * q^67 - 280 * q^69 - 120 * q^70 - 18 * q^71 + 1126 * q^72 + 52 * q^73 + 154 * q^74 + 704 * q^76 - 726 * q^77 - 1434 * q^78 - 572 * q^79 + 476 * q^81 + 46 * q^82 + 286 * q^83 - 1100 * q^84 - 130 * q^85 + 396 * q^86 - 1012 * q^87 - 528 * q^88 - 264 * q^89 + 350 * q^92 + 604 * q^93 + 444 * q^94 - 80 * q^95 - 394 * q^96 + 792 * q^97 + 540 * q^98 + 2112 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−2.96935	−	1.90828i	−1.48467	−	0.954142i	−0.996691	−	0.0812899i	$-0.974096\pi$
$2$	−2.96935	−	1.90828i	−1.48467	−	0.954142i	−0.487984	−	0.872853i	$-0.662268\pi$
$3$	0.852548	+	5.92960i	0.284183	+	1.97653i	0.197543	+	0.980294i	$0.436704\pi$
$3$	0.852548	+	5.92960i	0.284183	+	1.97653i	0.0866400	+	0.996240i	$0.472387\pi$
$4$	3.51382	+	7.69420i	0.878456	+	1.92355i
$5$	−0.629973	+	2.14549i	−0.125995	+	0.429098i
$5$	−0.629973	+	2.14549i	−0.125995	+	0.429098i
$6$	8.78386	−	19.2340i	1.46398	−	3.20566i
$7$	4.46805	+	3.87159i	0.638293	+	0.553084i	0.912752	−	0.408515i	$-0.133953\pi$
$7$	4.46805	+	3.87159i	0.638293	+	0.553084i	−0.274459	+	0.961599i	$0.588499\pi$
$8$	2.23966	−	15.5772i	0.279957	−	1.94715i
$9$	−25.7979	+	7.57495i	−2.86643	+	0.841661i
$10$	5.96482	−	5.16855i	0.596482	−	0.516855i
$11$	−6.69528	−	10.4181i	−0.608662	−	0.947096i	−0.999644	−	0.0266977i	$-0.991501\pi$
$11$	−6.69528	−	10.4181i	−0.608662	−	0.947096i	0.390982	−	0.920398i	$-0.372136\pi$
$12$	−42.6278	+	27.3952i	−3.55232	+	2.28294i
$13$	3.31427	+	3.82487i	0.254944	+	0.294220i	0.868765	−	0.495224i	$-0.164914\pi$
$13$	3.31427	+	3.82487i	0.254944	+	0.294220i	−0.613822	+	0.789445i	$0.710369\pi$
$14$	−5.87911	−	20.0224i	−0.419936	−	1.43017i
$15$	−13.2590	−	1.90636i	−0.883933	−	0.127090i
$16$	−14.2192	+	16.4098i	−0.888700	+	1.02561i
$17$	11.7642	+	5.37252i	0.692011	+	0.316031i	0.730194	−	0.683240i	$-0.239430\pi$
$17$	11.7642	+	5.37252i	0.692011	+	0.316031i	−0.0381832	+	0.999271i	$0.512157\pi$
$18$	91.0581	+	26.7371i	5.05879	+	1.48539i
$19$	−1.34372	+	0.613655i	−0.0707220	+	0.0322977i	−0.450462	−	0.892796i	$-0.648741\pi$
$19$	−1.34372	+	0.613655i	−0.0707220	+	0.0322977i	0.379740	+	0.925093i	$0.376013\pi$
$20$	−18.7215	+	2.69174i	−0.936073	+	0.134587i
$21$	−19.1477	+	29.7945i	−0.911797	+	1.41878i
$22$			43.7113i			1.98688i
$23$	−19.5514	+	12.1137i	−0.850063	+	0.526681i
$23$	−19.5514	+	12.1137i	−0.850063	+	0.526681i
$24$	94.2758			3.92816
$25$	−4.20627	−	2.70320i	−0.168251	−	0.108128i
$26$	−2.54228	−	17.6819i	−0.0977799	−	0.680074i
$27$	−44.5132	−	97.4703i	−1.64864	−	3.61001i
$28$	−14.0888	+	47.9821i	−0.503172	+	1.71365i
$29$	3.96176	−	8.67505i	0.136613	−	0.299140i	−0.828945	−	0.559331i	$-0.811058\pi$
$29$	3.96176	−	8.67505i	0.136613	−	0.299140i	0.965557	+	0.260191i	$0.0837855\pi$
$30$	35.7327	+	30.9626i	1.19109	+	1.03209i
$31$	−2.32142	+	16.1459i	−0.0748846	+	0.520834i	0.917508	+	0.397718i	$0.130198\pi$
$31$	−2.32142	+	16.1459i	−0.0748846	+	0.520834i	−0.992392	+	0.123116i	$0.960711\pi$
$32$	13.1369	−	3.85735i	0.410529	−	0.120542i
$33$	56.0669	−	48.5822i	1.69900	−	1.47219i
$34$	−24.6797	−	38.4023i	−0.725872	−	1.12948i
$35$	−11.1212	+	7.14717i	−0.317749	+	0.204205i
$36$	−148.932	−	171.877i	−4.13701	−	4.77437i
$37$	12.5785	+	42.8386i	0.339961	+	1.15780i	0.935161	+	0.354223i	$0.115255\pi$
$37$	12.5785	+	42.8386i	0.339961	+	1.15780i	−0.595200	+	0.803577i	$0.702927\pi$
$38$	5.16100	+	0.742039i	0.135816	+	0.0195274i
$39$	−19.8544	+	22.9132i	−0.509086	+	0.587517i
$40$	32.0097	+	14.6184i	0.800244	+	0.365459i
$41$	−1.08614	−	0.318919i	−0.0264911	−	0.00777850i	0.268460	−	0.963291i	$-0.413485\pi$
$41$	−1.08614	−	0.318919i	−0.0264911	−	0.00777850i	−0.294951	+	0.955512i	$0.595303\pi$
$42$	113.713	−	51.9308i	2.70744	−	1.23645i
$43$	−16.5332	+	2.37712i	−0.384494	+	0.0552819i	−0.331852	−	0.943332i	$-0.607673\pi$
$43$	−16.5332	+	2.37712i	−0.384494	+	0.0552819i	−0.0526421	+	0.998613i	$0.516764\pi$
$44$	56.6326	−	88.1220i	1.28710	−	2.00277i
$45$		−	60.1212i		−	1.33603i
$46$	81.1714	+	1.34004i	1.76460	+	0.0291314i
$47$	41.3808			0.880442			0.440221	−	0.897889i	$-0.354900\pi$
$47$	41.3808			0.880442			0.440221	+	0.897889i	$0.354900\pi$
$48$	−109.426	−	70.3240i	−2.27972	−	1.46508i
$49$	−1.99915	−	13.9044i	−0.0407989	−	0.283763i
$50$	7.33139	+	16.0535i	0.146628	+	0.321070i
$51$	−21.8274	+	74.3372i	−0.427988	+	1.45759i
$52$	−17.7835	+	38.9405i	−0.341991	+	0.748856i
$53$	6.69979	+	5.80540i	0.126411	+	0.109536i	0.715772	−	0.698334i	$-0.246075\pi$
$53$	6.69979	+	5.80540i	0.126411	+	0.109536i	−0.589361	+	0.807870i	$0.700620\pi$
$54$	−53.8259	+	374.367i	−0.996776	+	6.93273i
$55$	26.5697	−	7.80157i	0.483085	−	0.141847i
$56$	70.3152	−	60.9285i	1.25563	−	1.08801i
$57$	−4.78432	−	7.44454i	−0.0839354	−	0.130606i
$58$	−28.3183	+	18.1991i	−0.488247	+	0.313777i
$59$	22.2450	+	25.6721i	0.377034	+	0.435120i	0.912275	−	0.409579i	$-0.134324\pi$
$59$	22.2450	+	25.6721i	0.377034	+	0.435120i	−0.535241	+	0.844700i	$0.679779\pi$
$60$	−31.9219	−	108.716i	−0.532031	−	1.81193i
$61$	75.8579	+	10.9067i	1.24357	+	0.178799i	0.732517	−	0.680749i	$-0.238346\pi$
$61$	75.8579	+	10.9067i	1.24357	+	0.178799i	0.511056	+	0.859548i	$0.329255\pi$
$62$	37.7040	−	43.5127i	0.608129	−	0.701818i
$63$	−144.593	−	66.0336i	−2.29513	−	1.04815i
$64$	36.9661	+	10.8542i	0.577595	+	0.169597i
$65$	−10.2941	+	4.70117i	−0.158371	+	0.0723256i
$66$	−259.191	+	37.2660i	−3.92713	+	0.564637i
$67$	−32.1599	+	50.0417i	−0.479998	+	0.746892i	−0.993820	−	0.111005i	$-0.964593\pi$
$67$	−32.1599	+	50.0417i	−0.479998	+	0.746892i	0.513822	+	0.857897i	$0.328229\pi$
$68$			109.394i			1.60874i
$69$	−88.4977	−	105.605i	−1.28258	−	1.53050i
$70$	46.6616			0.666594
$71$	23.6897	+	15.2245i	0.333658	+	0.214429i	0.696732	−	0.717331i	$-0.254637\pi$
$71$	23.6897	+	15.2245i	0.333658	+	0.214429i	−0.363074	+	0.931760i	$0.618273\pi$
$72$	60.2177	+	418.823i	0.836357	+	5.81699i
$73$	35.2466	+	77.1794i	0.482831	+	1.05725i	0.981675	+	0.190560i	$0.0610305\pi$
$73$	35.2466	+	77.1794i	0.482831	+	1.05725i	−0.498845	+	0.866691i	$0.666242\pi$
$74$	44.3982	−	151.206i	0.599975	−	2.04333i
$75$	12.4429	−	27.2461i	0.165905	−	0.363281i
$76$	−9.44318	−	8.18256i	−0.124252	−	0.107665i
$77$	10.4196	−	72.4697i	0.135319	−	0.941165i
$78$	102.679	−	30.1494i	1.31640	−	0.386531i
$79$	−27.6983	+	24.0007i	−0.350611	+	0.303806i	−0.812305	−	0.583233i	$-0.801787\pi$
$79$	−27.6983	+	24.0007i	−0.350611	+	0.303806i	0.461694	+	0.887039i	$0.347242\pi$
$80$	−26.2494	−	40.8449i	−0.328118	−	0.510562i
$81$	336.441	−	216.218i	4.15360	−	2.66935i
$82$	2.61653	+	3.01964i	0.0319089	+	0.0368249i
$83$	33.5400	+	114.227i	0.404096	+	1.37622i	0.870724	+	0.491771i	$0.163650\pi$
$83$	33.5400	+	114.227i	0.404096	+	1.37622i	−0.466628	+	0.884454i	$0.654531\pi$
$84$	−296.526	−	42.6341i	−3.53008	−	0.507548i
$85$	−18.9378	+	21.8554i	−0.222798	+	0.257122i
$86$	53.6292	+	24.4916i	0.623595	+	0.284786i
$87$	54.8172	+	16.0958i	0.630083	+	0.185009i
$88$	−177.279	+	80.9606i	−2.01453	+	0.920006i
$89$	45.4904	−	6.54053i	0.511128	−	0.0734891i	0.118075	−	0.993005i	$-0.462328\pi$
$89$	45.4904	−	6.54053i	0.511128	−	0.0734891i	0.393053	+	0.919516i	$0.371419\pi$
$90$	−114.728	+	178.521i	−1.27476	+	1.98356i
$91$			29.9212i			0.328804i
$92$	−161.905	−	107.867i	−1.75984	−	1.17247i
$93$	−97.7176			−1.05073
$94$	−122.874	−	78.9663i	−1.30717	−	0.840067i
$95$	−0.470086	−	3.26952i	−0.00494828	−	0.0344160i
$96$	34.0724	+	74.6082i	0.354921	+	0.777169i
$97$	22.5360	−	76.7506i	0.232330	−	0.791243i	−0.757969	−	0.652291i	$-0.773808\pi$
$97$	22.5360	−	76.7506i	0.232330	−	0.791243i	0.990299	−	0.138953i	$-0.0443736\pi$
$98$	−20.5973	+	45.1019i	−0.210177	+	0.460223i
$99$	251.640	+	218.048i	2.54182	+	2.20250i
$100$	6.01891	−	41.8624i	0.0601891	−	0.418624i
$101$	−113.363	+	33.2865i	−1.12241	+	0.329570i	−0.789721	−	0.613467i	$-0.789774\pi$
$101$	−113.363	+	33.2865i	−1.12241	+	0.329570i	−0.332690	+	0.943036i	$0.607956\pi$
$102$	206.670	−	179.080i	2.02617	−	1.75569i
$103$	−95.6429	−	148.823i	−0.928571	−	1.44489i	−0.895312	−	0.445439i	$-0.853048\pi$
$103$	−95.6429	−	148.823i	−0.928571	−	1.44489i	−0.0332590	−	0.999447i	$-0.510589\pi$
$104$	67.0034	−	43.0605i	0.644263	−	0.414043i
$105$	−51.8612	−	59.8510i	−0.493916	−	0.570010i
$106$	−8.81566	−	30.0234i	−0.0831666	−	0.283239i
$107$	−11.9846	−	1.72312i	−0.112005	−	0.0161039i	0.0860843	−	0.996288i	$-0.472565\pi$
$107$	−11.9846	−	1.72312i	−0.112005	−	0.0161039i	−0.198089	+	0.980184i	$0.563474\pi$
$108$	593.544	−	684.987i	5.49578	−	6.34247i
$109$	37.5261	+	17.1376i	0.344276	+	0.157226i	0.580047	−	0.814583i	$-0.303034\pi$
$109$	37.5261	+	17.1376i	0.344276	+	0.157226i	−0.235771	+	0.971809i	$0.575761\pi$
$110$	−93.7823	−	27.5370i	−0.852567	−	0.250336i
$111$	−243.292	+	111.108i	−2.19182	+	1.00097i
$112$	−127.064	+	18.2691i	−1.13450	+	0.163117i
$113$	−85.6768	+	133.316i	−0.758202	+	1.17979i	0.220678	+	0.975347i	$0.429173\pi$
$113$	−85.6768	+	133.316i	−0.758202	+	1.17979i	−0.978879	+	0.204438i	$0.934463\pi$
$114$			31.2353i			0.273994i
$115$	−13.6729	−	49.5788i	−0.118895	−	0.431120i
$116$	80.6685			0.695418
$117$	−114.474	−	73.5681i	−0.978413	−	0.628788i
$118$	−17.0635	−	118.679i	−0.144606	−	1.00576i
$119$	31.7628	+	69.5507i	0.266914	+	0.584460i
$120$	−59.3912	+	202.268i	−0.494927	+	1.68557i
$121$	−13.4439	+	29.4381i	−0.111107	+	0.243290i
$122$	−204.436	−	177.144i	−1.67570	−	1.45200i
$123$	0.965076	−	6.71225i	0.00784615	−	0.0545712i
$124$	−132.386	+	38.8722i	−1.06763	+	0.313485i
$125$	8.44954	−	7.32157i	0.0675963	−	0.0585725i
$126$	303.337	+	472.002i	2.40744	+	3.74605i
$127$	53.1099	−	34.1316i	0.418188	−	0.268753i	−0.314581	−	0.949231i	$-0.601864\pi$
$127$	53.1099	−	34.1316i	0.418188	−	0.268753i	0.732769	+	0.680478i	$0.238228\pi$
$128$	−124.916	−	144.161i	−0.975909	−	1.12626i
$129$	−28.1907	−	96.0089i	−0.218533	−	0.744255i
$130$	39.5380	+	5.68470i	0.304138	+	0.0437285i
$131$	−60.9317	+	70.3190i	−0.465128	+	0.536786i	−0.939050	−	0.343781i	$-0.888292\pi$
$131$	−60.9317	+	70.3190i	−0.465128	+	0.536786i	0.473922	+	0.880567i	$0.342838\pi$
$132$	570.811	+	260.680i	4.32432	+	1.97485i
$133$	−8.37962	−	2.46048i	−0.0630046	−	0.0184998i
$134$	190.988	−	87.2212i	1.42528	−	0.650905i
$135$	237.164	−	34.0990i	1.75677	−	0.252585i
$136$	110.036	−	171.220i	0.809091	−	1.25897i
$137$			231.740i			1.69153i	0.533556	+	0.845765i	$0.320855\pi$
$137$			231.740i			1.69153i	−0.533556	+	0.845765i	$0.679145\pi$
$138$	61.2566	+	482.457i	0.443888	+	3.49606i
$139$	93.1621			0.670231			0.335115	−	0.942177i	$-0.391225\pi$
$139$	93.1621			0.670231			0.335115	+	0.942177i	$0.391225\pi$
$140$	−94.0697	−	60.4549i	−0.671926	−	0.431821i
$141$	35.2791	+	245.371i	0.250206	+	1.74022i
$142$	−41.2905	−	90.4135i	−0.290778	−	0.636715i
$143$	17.6577	−	60.1368i	0.123481	−	0.420537i
$144$	242.522	−	531.049i	1.68418	−	3.68784i
$145$	16.1164	+	13.9650i	0.111148	+	0.0963102i
$146$	42.6206	−	296.433i	0.291922	−	2.03036i
$147$	80.7430	−	23.7083i	0.549272	−	0.161281i
$148$	−285.410	+	247.309i	−1.92845	+	1.67101i
$149$	98.2658	+	152.905i	0.659502	+	1.02621i	0.996409	+	0.0846676i	$0.0269828\pi$
$149$	98.2658	+	152.905i	0.659502	+	1.02621i	−0.336907	+	0.941538i	$0.609381\pi$
$150$	−88.9406	+	57.1586i	−0.592937	+	0.381058i
$151$	−50.2711	−	58.0159i	−0.332921	−	0.384212i	0.564465	−	0.825457i	$-0.309082\pi$
$151$	−50.2711	−	58.0159i	−0.332921	−	0.384212i	−0.897387	+	0.441245i	$0.854537\pi$
$152$	6.54954	+	22.3057i	0.0430891	+	0.146748i
$153$	−344.188	−	49.4867i	−2.24959	−	0.323443i
$154$	−169.232	+	195.304i	−1.09891	+	1.26821i
$155$	−33.1784	−	15.1520i	−0.214054	−	0.0977551i
$156$	−246.063	−	72.2507i	−1.57733	−	0.463145i
$157$	71.8968	−	32.8342i	0.457942	−	0.209135i	−0.173068	−	0.984910i	$-0.555368\pi$
$157$	71.8968	−	32.8342i	0.457942	−	0.209135i	0.631010	+	0.775775i	$0.282641\pi$
$158$	128.046	−	18.4102i	0.810417	−	0.116520i
$159$	−28.7118	+	44.6765i	−0.180578	+	0.280984i
$160$			30.6152i			0.191345i
$161$	−134.256	−	21.5707i	−0.833888	−	0.133979i
$162$	−1411.62			−8.71368
$163$	54.1691	+	34.8123i	0.332326	+	0.213573i	0.696153	−	0.717894i	$-0.254894\pi$
$163$	54.1691	+	34.8123i	0.332326	+	0.213573i	−0.363827	+	0.931467i	$0.618530\pi$
$164$	−1.36267	−	9.47758i	−0.00830896	−	0.0577901i
$165$	68.9121	+	150.897i	0.417649	+	0.914524i
$166$	118.385	−	403.183i	0.713163	−	2.42881i
$167$	18.0076	−	39.4310i	0.107830	−	0.236114i	−0.848024	−	0.529959i	$-0.822207\pi$
$167$	18.0076	−	39.4310i	0.107830	−	0.236114i	0.955853	+	0.293844i	$0.0949348\pi$
$168$	421.229	+	364.997i	2.50731	+	2.17260i
$169$	20.4060	−	141.927i	0.120745	−	0.839802i
$170$	97.9393	−	28.7576i	0.576114	−	0.169162i
$171$	30.0167	−	26.0096i	0.175536	−	0.152103i
$172$	−76.3849	−	118.857i	−0.444098	−	0.691030i
$173$	191.841	−	123.289i	1.10891	−	0.712651i	0.147852	−	0.989010i	$-0.452764\pi$
$173$	191.841	−	123.289i	1.10891	−	0.712651i	0.961055	+	0.276359i	$0.0891278\pi$
$174$	−132.056	−	152.401i	−0.758943	−	0.875867i
$175$	−8.32812	−	28.3630i	−0.0475893	−	0.162074i
$176$	266.160	+	38.2680i	1.51227	+	0.217432i
$177$	−133.260	+	153.791i	−0.752884	+	0.868874i
$178$	−147.558	−	67.3875i	−0.828978	−	0.378582i
$179$	225.983	+	66.3545i	1.26247	+	0.370696i	0.843414	−	0.537264i	$-0.180542\pi$
$179$	225.983	+	66.3545i	1.26247	+	0.370696i	0.419059	+	0.907959i	$0.362360\pi$
$180$	462.585	−	211.255i	2.56991	−	1.17364i
$181$	129.749	−	18.6550i	0.716843	−	0.103066i	0.225765	−	0.974182i	$-0.427512\pi$
$181$	129.749	−	18.6550i	0.716843	−	0.103066i	0.491078	+	0.871115i	$0.336603\pi$
$182$	57.0981	−	88.8464i	0.313726	−	0.488167i
$183$			459.106i			2.50877i
$184$	144.908	+	331.687i	0.787543	+	1.80264i
$185$	−99.8340			−0.539643
$186$	290.158	+	186.473i	1.55999	+	1.00254i
$187$	−22.7932	−	158.530i	−0.121889	−	0.847756i
$188$	145.405	+	318.392i	0.773429	+	1.69357i
$189$	178.478	−	607.839i	0.944326	−	3.21608i
$190$	−4.84333	+	10.6054i	−0.0254912	+	0.0558180i
$191$	−230.892	−	200.069i	−1.20886	−	1.04748i	−0.997543	−	0.0700625i	$-0.977680\pi$
$191$	−230.892	−	200.069i	−1.20886	−	1.04748i	−0.211314	−	0.977418i	$-0.567774\pi$
$192$	−32.8458	+	228.448i	−0.171072	+	1.18983i
$193$	276.255	−	81.1157i	1.43137	−	0.420289i	0.528036	−	0.849222i	$-0.322929\pi$
$193$	276.255	−	81.1157i	1.43137	−	0.420289i	0.903336	+	0.428934i	$0.141111\pi$
$194$	−213.379	+	184.894i	−1.09989	+	0.953063i
$195$	−36.6523	−	57.0320i	−0.187960	−	0.292472i
$196$	99.9584	−	64.2393i	0.509992	−	0.327752i
$197$	−194.899	−	224.925i	−0.989335	−	1.14175i	−0.989902	−	0.141753i	$-0.954726\pi$
$197$	−194.899	−	224.925i	−0.989335	−	1.14175i	0.000567304	−	1.00000i	$-0.499819\pi$
$198$	−331.111	−	1127.66i	−1.67228	−	5.69526i
$199$	−57.1585	−	8.21815i	−0.287229	−	0.0412973i	−0.00280545	−	0.999996i	$-0.500893\pi$
$199$	−57.1585	−	8.21815i	−0.287229	−	0.0412973i	−0.284423	+	0.958699i	$0.591802\pi$
$200$	−51.5288	+	59.4675i	−0.257644	+	0.297337i
$201$	−324.145	−	148.032i	−1.61266	−	0.736479i
$202$	400.136	+	117.491i	1.98087	+	0.581636i
$203$	51.2876	−	23.4223i	0.252648	−	0.115381i
$204$	−648.663	+	93.2637i	−3.17972	+	0.457175i
$205$	1.36847	−	2.12939i	0.00667548	−	0.0103873i
$206$			624.422i			3.03117i
$207$	412.626	−	460.608i	1.99336	−	2.22516i
$208$	−109.892			−0.528325
$209$	15.3897	+	9.89034i	0.0736348	+	0.0473222i
$210$	39.7812	+	276.685i	0.189434	+	1.31755i
$211$	43.4814	+	95.2109i	0.206073	+	0.451237i	0.984244	−	0.176816i	$-0.0565797\pi$
$211$	43.4814	+	95.2109i	0.206073	+	0.451237i	−0.778171	+	0.628052i	$0.783852\pi$
$212$	−21.1260	+	71.9487i	−0.0996512	+	0.339381i
$213$	−70.0784	+	153.450i	−0.329006	+	0.720424i
$214$	32.2981	+	27.9865i	0.150926	+	0.130778i
$215$	5.31540	−	36.9694i	0.0247228	−	0.171951i
$216$	−1618.00	+	475.089i	−7.49076	+	2.19949i
$217$	−72.8823	+	63.1529i	−0.335863	+	0.291027i
$218$	−78.7247	−	122.498i	−0.361123	−	0.561918i
$219$	−427.593	+	274.798i	−1.95248	+	1.25478i
$220$	153.388	+	177.019i	0.697218	+	0.804633i
$221$	18.4404	+	62.8024i	0.0834409	+	0.284174i
$222$	934.444	+	134.353i	4.20921	+	0.605193i
$223$	−161.365	+	186.225i	−0.723610	+	0.835090i	−0.991736	−	0.128294i	$-0.959050\pi$
$223$	−161.365	+	186.225i	−0.723610	+	0.835090i	0.268127	+	0.963384i	$0.413595\pi$
$224$	73.6305	+	33.6259i	0.328708	+	0.150116i
$225$	128.990	+	37.8747i	0.573287	+	0.168332i
$226$	508.809	−	232.365i	2.25137	−	1.02816i
$227$	−128.219	+	18.4351i	−0.564842	+	0.0812121i	−0.418820	−	0.908069i	$-0.637556\pi$
$227$	−128.219	+	18.4351i	−0.564842	+	0.0812121i	−0.146022	+	0.989281i	$0.546647\pi$
$228$	40.4686	−	62.9703i	0.177494	−	0.276186i
$229$		−	377.761i		−	1.64961i	−0.565415	−	0.824806i	$-0.691284\pi$
$229$		−	377.761i		−	1.64961i	0.565415	−	0.824806i	$-0.308716\pi$
$230$	−54.0109	+	173.308i	−0.234830	+	0.753515i
$231$	438.600			1.89870
$232$	−126.260	−	81.1422i	−0.544223	−	0.349751i
$233$	−44.7711	−	311.390i	−0.192151	−	1.33644i	−0.826302	−	0.563227i	$-0.809559\pi$
$233$	−44.7711	−	311.390i	−0.192151	−	1.33644i	0.634151	−	0.773209i	$-0.281350\pi$
$234$	199.525	+	436.899i	0.852671	+	1.86709i
$235$	−26.0688	+	88.7821i	−0.110931	+	0.377796i
$236$	−119.361	+	261.365i	−0.505768	+	1.10748i
$237$	−165.929	−	143.778i	−0.700120	−	0.606658i
$238$	38.4079	−	267.133i	0.161378	−	1.12241i
$239$	162.269	−	47.6464i	0.678949	−	0.199357i	0.0759648	−	0.997110i	$-0.475796\pi$
$239$	162.269	−	47.6464i	0.678949	−	0.199357i	0.602984	+	0.797753i	$0.293978\pi$
$240$	219.815	−	190.471i	0.915897	−	0.793629i
$241$	−178.481	−	277.721i	−0.740583	−	1.15237i	−0.983250	−	0.182260i	$-0.941659\pi$
$241$	−178.481	−	277.721i	−0.740583	−	1.15237i	0.242667	−	0.970110i	$-0.421978\pi$
$242$	96.0961	−	61.7572i	0.397091	−	0.255195i
$243$	937.381	+	1081.80i	3.85754	+	4.45183i
$244$	182.633	+	621.990i	0.748495	+	2.54914i
$245$	31.0911	+	4.47023i	0.126903	+	0.0182458i
$246$	−15.6745	+	18.0894i	−0.0637176	+	0.0735341i
$247$	−6.80059	−	3.10572i	−0.0275327	−	0.0125738i
$248$	246.307	+	72.3224i	0.993175	+	0.291622i
$249$	−648.724	+	296.262i	−2.60532	+	1.18981i
$250$	−39.0613	+	5.61616i	−0.156245	+	0.0224646i
$251$	−72.3564	+	112.589i	−0.288272	+	0.448561i	−0.954942	−	0.296793i	$-0.904083\pi$
$251$	−72.3564	+	112.589i	−0.288272	+	0.448561i	0.666669	+	0.745353i	$0.267719\pi$
$252$		−	1344.56i		−	5.33556i
$253$	257.103	+	122.584i	1.01622	+	0.484521i
$254$	−222.835			−0.877302
$255$	−145.739	−	93.6609i	−0.571526	−	0.367298i
$256$	73.8881	+	513.903i	0.288625	+	2.00743i
$257$	49.0716	+	107.452i	0.190940	+	0.418101i	0.980754	−	0.195245i	$-0.0625504\pi$
$257$	49.0716	+	107.452i	0.190940	+	0.418101i	−0.789814	+	0.613346i	$0.789823\pi$
$258$	−99.5041	+	338.880i	−0.385675	+	1.31349i
$259$	−109.652	+	240.104i	−0.423366	+	0.927042i
$260$	−72.3434	−	62.6859i	−0.278244	−	0.241100i
$261$	−36.4921	+	253.808i	−0.139817	+	0.972446i
$262$	315.116	−	92.5265i	1.20273	−	0.353154i
$263$	−92.0439	+	79.7565i	−0.349977	+	0.303257i	−0.812053	−	0.583584i	$-0.801650\pi$
$263$	−92.0439	+	79.7565i	−0.349977	+	0.303257i	0.462076	+	0.886840i	$0.347105\pi$
$264$	−631.203	−	982.170i	−2.39092	−	3.72034i
$265$	−16.6761	+	10.7171i	−0.0629288	+	0.0404419i
$266$	20.1867	+	23.2967i	0.0758899	+	0.0875816i
$267$	77.5655	+	264.164i	0.290507	+	0.989378i
$268$	−498.035	−	71.6067i	−1.85834	−	0.267189i
$269$	−4.38250	+	5.05767i	−0.0162918	+	0.0188018i	−0.763837	−	0.645409i	$-0.776687\pi$
$269$	−4.38250	+	5.05767i	−0.0162918	+	0.0188018i	0.747545	+	0.664211i	$0.231232\pi$
$270$	−769.293	−	351.324i	−2.84923	−	1.30120i
$271$	−68.2929	−	20.0526i	−0.252003	−	0.0739948i	0.153291	−	0.988181i	$-0.451013\pi$
$271$	−68.2929	−	20.0526i	−0.252003	−	0.0739948i	−0.405294	+	0.914186i	$0.632831\pi$
$272$	−255.439	+	116.655i	−0.939116	+	0.428880i
$273$	−177.421	+	25.5092i	−0.649892	+	0.0934404i
$274$	442.225	−	688.116i	1.61396	−	2.51137i
$275$			61.9198i			0.225163i
$276$	501.579	−	1052.00i	1.81732	−	3.81158i
$277$	388.320			1.40188			0.700938	−	0.713222i	$-0.252765\pi$
$277$	388.320			1.40188			0.700938	+	0.713222i	$0.252765\pi$
$278$	−276.631	−	177.780i	−0.995075	−	0.639496i
$279$	−62.4161	−	434.114i	−0.223714	−	1.55596i
$280$	86.4249	+	189.244i	0.308660	+	0.675872i
$281$	108.034	−	367.929i	0.384462	−	1.30936i	−0.509213	−	0.860641i	$-0.670063\pi$
$281$	108.034	−	367.929i	0.384462	−	1.30936i	0.893675	−	0.448716i	$-0.148118\pi$
$282$	363.483	−	795.916i	1.28895	−	2.82240i
$283$	17.8724	+	15.4865i	0.0631534	+	0.0547227i	0.685866	−	0.727728i	$-0.259424\pi$
$283$	17.8724	+	15.4865i	0.0631534	+	0.0547227i	−0.622712	+	0.782451i	$0.713969\pi$
$284$	−33.8985	+	235.770i	−0.119361	+	0.830174i
$285$	18.9862	−	5.57485i	0.0666182	−	0.0195609i
$286$	−167.190	+	144.871i	−0.584581	+	0.506542i
$287$	−3.61819	−	5.63002i	−0.0126069	−	0.0196168i
$288$	−309.686	+	199.023i	−1.07530	+	0.691053i
$289$	−79.7228	−	92.0050i	−0.275857	−	0.318356i
$290$	−21.2062	−	72.2217i	−0.0731248	−	0.249040i
$291$	474.314	+	68.1960i	1.62994	+	0.234351i
$292$	−469.983	+	542.389i	−1.60953	+	1.85750i
$293$	453.214	+	206.976i	1.54681	+	0.706402i	0.992077	−	0.125629i	$-0.0400949\pi$
$293$	453.214	+	206.976i	1.54681	+	0.706402i	0.554728	+	0.832032i	$0.312822\pi$
$294$	−284.996	−	83.6825i	−0.969376	−	0.284634i
$295$	−69.0930	+	31.5537i	−0.234214	+	0.106962i
$296$	695.475	−	99.9943i	2.34958	−	0.337818i
$297$	−717.423	+	1116.33i	−2.41557	+	3.75869i
$298$		−	641.546i		−	2.15284i
$299$	−111.132	−	34.6338i	−0.371678	−	0.115832i
$300$	253.359			0.844530
$301$	−83.0745	−	53.3887i	−0.275995	−	0.177371i
$302$	38.5615	+	268.201i	0.127687	+	0.888083i
$303$	−294.024	−	643.822i	−0.970375	−	2.12482i
$304$	9.03661	−	30.7759i	0.0297257	−	0.101236i
$305$	−71.1887	+	155.882i	−0.233406	+	0.511087i
$306$	927.579	+	803.752i	3.03130	+	2.62664i
$307$	−15.7113	+	109.274i	−0.0511768	+	0.355942i	0.948102	+	0.317967i	$0.103000\pi$
$307$	−15.7113	+	109.274i	−0.0511768	+	0.355942i	−0.999279	+	0.0379756i	$0.987909\pi$
$308$	594.209	−	174.476i	1.92925	−	0.566479i
$309$	800.922	−	694.003i	2.59198	−	2.24596i
$310$	69.6037	+	108.305i	0.224528	+	0.349372i
$311$	13.6590	−	8.77809i	0.0439196	−	0.0282254i	−0.518497	−	0.855080i	$-0.673508\pi$
$311$	13.6590	−	8.77809i	0.0439196	−	0.0282254i	0.562416	+	0.826854i	$0.309872\pi$
$312$	312.455	+	360.592i	1.00146	+	1.15574i
$313$	−96.2499	−	327.797i	−0.307508	−	1.04727i	−0.957763	−	0.287559i	$-0.907156\pi$
$313$	−96.2499	−	327.797i	−0.307508	−	1.04727i	0.650255	−	0.759716i	$-0.274662\pi$
$314$	−276.144	−	39.7035i	−0.879439	−	0.126444i
$315$	232.764	−	268.624i	0.738935	−	0.852776i
$316$	−281.993	−	128.782i	−0.892382	−	0.407537i
$317$	83.4009	+	24.4887i	0.263094	+	0.0772514i	0.410619	−	0.911807i	$-0.365313\pi$
$317$	83.4009	+	24.4887i	0.263094	+	0.0772514i	−0.147525	+	0.989058i	$0.547131\pi$
$318$	170.511	−	77.8697i	0.536198	−	0.244873i
$319$	−116.902	+	16.8080i	−0.366465	+	0.0526897i
$320$	−46.5753	+	72.4725i	−0.145548	+	0.226477i
$321$		−	72.5327i		−	0.225958i
$322$	357.490	+	320.249i	1.11022	+	0.994564i
$323$	−19.1046			−0.0591474
$324$	2845.82	+	1828.90i	8.78339	+	5.64474i
$325$	−3.60129	−	25.0475i	−0.0110809	−	0.0770694i
$326$	−94.4150	−	206.740i	−0.289617	−	0.634172i
$327$	−69.6264	+	237.126i	−0.212925	+	0.725155i
$328$	−7.40042	+	16.2047i	−0.0225623	+	0.0494045i
$329$	184.891	+	160.209i	0.561980	+	0.486958i
$330$	83.3294	−	579.568i	0.252513	−	1.75627i
$331$	−324.764	+	95.3592i	−0.981159	+	0.288094i	−0.732703	−	0.680549i	$-0.761741\pi$
$331$	−324.764	+	95.3592i	−0.981159	+	0.288094i	−0.248456	+	0.968643i	$0.579923\pi$
$332$	−761.029	+	659.436i	−2.29226	+	1.98625i
$333$	−649.000	−	1009.86i	−1.94895	−	3.03263i
$334$	−128.716	+	82.7210i	−0.385378	+	0.247668i
$335$	−87.1043	−	100.524i	−0.260013	−	0.300071i
$336$	−216.657	−	737.865i	−0.644811	−	2.19603i
$337$	−326.367	−	46.9245i	−0.968449	−	0.139242i	−0.360102	−	0.932913i	$-0.617258\pi$
$337$	−326.367	−	46.9245i	−0.968449	−	0.139242i	−0.608347	+	0.793671i	$0.708167\pi$
$338$	−331.429	+	382.489i	−0.980558	+	1.13162i
$339$	−863.553	−	394.371i	−2.54735	−	1.16334i
$340$	−234.704	−	68.9153i	−0.690306	−	0.202692i
$341$	183.751	−	83.9163i	0.538859	−	0.246089i
$342$	−138.764	+	19.9512i	−0.405742	+	0.0583369i
$343$	201.519	−	313.569i	0.587519	−	0.914197i
$344$			262.865i			0.764142i
$345$	282.325	−	123.343i	0.818335	−	0.357516i
$346$	−804.912			−2.32633
$347$	79.1367	+	50.8580i	0.228060	+	0.146565i	0.649681	−	0.760207i	$-0.274903\pi$
$347$	79.1367	+	50.8580i	0.228060	+	0.146565i	−0.421621	+	0.906772i	$0.638539\pi$
$348$	68.7738	+	478.332i	0.197626	+	1.37452i
$349$	131.562	+	288.080i	0.376967	+	0.825444i	0.999095	+	0.0425279i	$0.0135411\pi$
$349$	131.562	+	288.080i	0.376967	+	0.825444i	−0.622128	+	0.782916i	$0.713732\pi$
$350$	−29.3955	+	100.112i	−0.0839873	+	0.286034i
$351$	225.282	−	493.300i	0.641830	−	1.40541i
$352$	−128.142	−	111.035i	−0.364038	−	0.315441i
$353$	−50.8817	+	353.890i	−0.144141	+	1.00252i	0.781442	+	0.623977i	$0.214484\pi$
$353$	−50.8817	+	353.890i	−0.144141	+	1.00252i	−0.925583	+	0.378544i	$0.876425\pi$
$354$	689.173	−	202.360i	1.94682	−	0.571637i
$355$	−47.5878	+	41.2351i	−0.134050	+	0.116155i
$356$	210.169	+	327.030i	0.590363	+	0.918623i
$357$	−385.329	+	247.636i	−1.07935	+	0.693658i
$358$	−544.398	−	628.269i	−1.52067	−	1.75494i
$359$	−61.6795	−	210.061i	−0.171809	−	0.585128i	−0.999706	−	0.0242478i	$-0.992281\pi$
$359$	−61.6795	−	210.061i	−0.171809	−	0.585128i	0.827897	−	0.560880i	$-0.189537\pi$
$360$	−936.518	−	134.651i	−2.60144	−	0.374030i
$361$	−234.976	+	271.176i	−0.650902	+	0.751181i
$362$	−420.868	−	192.204i	−1.16262	−	0.530950i
$363$	−186.018	−	54.6198i	−0.512446	−	0.150468i
$364$	−230.219	+	105.138i	−0.632471	+	0.288840i
$365$	−187.792	+	27.0004i	−0.514499	+	0.0739738i
$366$	876.105	−	1363.25i	2.39373	−	3.72471i
$367$		−	424.319i		−	1.15618i	−0.815972	−	0.578091i	$-0.803798\pi$
$367$		−	424.319i		−	1.15618i	0.815972	−	0.578091i	$-0.196202\pi$
$368$	79.2228	−	493.083i	0.215279	−	1.33990i
$369$	30.4358			0.0824820
$370$	296.442	+	190.512i	0.801195	+	0.514897i
$371$	7.45888	+	51.8776i	0.0201048	+	0.139832i
$372$	−343.362	−	751.859i	−0.923017	−	2.02113i
$373$	−165.617	+	564.039i	−0.444013	+	1.51217i	0.368724	+	0.929539i	$0.379795\pi$
$373$	−165.617	+	564.039i	−0.444013	+	1.51217i	−0.812737	+	0.582630i	$0.802024\pi$
$374$	−234.840	+	514.228i	−0.627915	+	1.37494i
$375$	50.6176	+	43.8604i	0.134980	+	0.116961i
$376$	92.6787	−	644.595i	0.246486	−	1.71435i
$377$	46.3113	−	13.5982i	0.122842	−	0.0360695i
$378$	−1689.89	+	1464.30i	−4.47061	+	3.87381i
$379$	173.219	+	269.534i	0.457042	+	0.711171i	0.990929	−	0.134385i	$-0.0429058\pi$
$379$	173.219	+	269.534i	0.457042	+	0.711171i	−0.533888	+	0.845555i	$0.679269\pi$
$380$	23.5046	−	15.1055i	0.0618541	−	0.0397512i
$381$	247.666	+	285.822i	0.650041	+	0.750188i
$382$	303.810	+	1034.68i	0.795314	+	2.70859i
$383$	194.046	+	27.8996i	0.506647	+	0.0728448i	0.390899	−	0.920434i	$-0.372164\pi$
$383$	194.046	+	27.8996i	0.506647	+	0.0728448i	0.115748	+	0.993279i	$0.463073\pi$
$384$	748.321	−	863.609i	1.94875	−	2.24898i
$385$	148.919	+	68.0091i	0.386803	+	0.176647i
$386$	−975.089	−	286.312i	−2.52614	−	0.741741i
$387$	408.516	−	186.563i	1.05560	−	0.482075i
$388$	669.722	−	96.2915i	1.72609	−	0.248174i
$389$	266.006	−	413.913i	0.683819	−	1.06404i	−0.309751	−	0.950818i	$-0.600246\pi$
$389$	266.006	−	413.913i	0.683819	−	1.06404i	0.993569	−	0.113225i	$-0.0361181\pi$
$390$			239.291i			0.613567i
$391$	−295.088	+	37.4667i	−0.754700	+	0.0958228i
$392$	−221.068			−0.563949
$393$	−468.911	−	301.351i	−1.19316	−	0.766795i
$394$	149.501	+	1039.80i	0.379445	+	2.63910i
$395$	−34.0441	−	74.5462i	−0.0861876	−	0.188724i
$396$	−793.482	+	2702.35i	−2.00374	+	6.82412i
$397$	133.586	−	292.512i	0.336488	−	0.736805i	−0.663447	−	0.748223i	$-0.730907\pi$
$397$	133.586	−	292.512i	0.336488	−	0.736805i	0.999935	+	0.0114179i	$0.00363451\pi$
$398$	154.041	+	133.477i	0.387038	+	0.335370i
$399$	7.44563	−	51.7855i	0.0186607	−	0.129788i
$400$	104.169	−	30.5868i	0.260422	−	0.0764669i
$401$	303.403	−	262.900i	0.756617	−	0.655612i	−0.188601	−	0.982054i	$-0.560395\pi$
$401$	303.403	−	262.900i	0.756617	−	0.655612i	0.945217	+	0.326442i	$0.105850\pi$
$402$	680.013	+	1058.12i	1.69158	+	2.63214i
$403$	−69.4495	+	44.6325i	−0.172331	+	0.110751i
$404$	−654.452	−	755.278i	−1.61993	−	1.86950i
$405$	251.944	+	858.043i	0.622085	+	2.11863i
$406$	−196.987	−	28.3225i	−0.485190	−	0.0697598i
$407$	362.078	−	417.860i	0.889627	−	1.02668i
$408$	1109.08	+	506.499i	2.71833	+	1.24142i
$409$	511.845	+	150.291i	1.25146	+	0.367461i	0.839308	−	0.543656i	$-0.182960\pi$
$409$	511.845	+	150.291i	1.25146	+	0.367461i	0.412148	+	0.911117i	$0.364779\pi$
$410$	−8.12696	+	3.71146i	−0.0198218	+	0.00905233i
$411$	−1374.12	+	197.569i	−3.34337	+	0.480703i
$412$	809.003	−	1258.83i	1.96360	−	3.05542i
$413$			200.828i			0.486266i
$414$	−2104.20	+	580.299i	−5.08262	+	1.40169i
$415$	−266.202			−0.641450
$416$	58.2931	+	37.4627i	0.140128	+	0.0900546i
$417$	79.4251	+	552.414i	0.190468	+	1.32473i
$418$	−26.8237	−	58.7357i	−0.0641715	−	0.140516i
$419$	−83.3863	+	283.988i	−0.199013	+	0.677775i	0.798147	+	0.602462i	$0.205814\pi$
$419$	−83.3863	+	283.988i	−0.199013	+	0.677775i	−0.997160	+	0.0753126i	$0.976005\pi$
$420$	278.275	−	609.336i	0.662559	−	1.45080i
$421$	−108.092	−	93.6623i	−0.256751	−	0.222476i	0.516969	−	0.856004i	$-0.327060\pi$
$421$	−108.092	−	93.6623i	−0.256751	−	0.222476i	−0.773719	+	0.633529i	$0.781606\pi$
$422$	52.5782	−	365.689i	0.124593	−	0.866562i
$423$	−1067.54	+	313.457i	−2.52373	+	0.741033i
$424$	105.437	−	91.3616i	0.248672	−	0.215476i
$425$	−34.9603	−	54.3992i	−0.0822595	−	0.127998i
$426$	500.914	−	321.918i	1.17585	−	0.755676i
$427$	296.711	+	342.422i	0.694873	+	0.801926i
$428$	−28.8536	−	98.2663i	−0.0674149	−	0.229594i
$429$	371.641	+	53.4339i	0.866296	+	0.124555i
$430$	−86.3315	+	99.6318i	−0.200771	+	0.231702i
$431$	88.7576	+	40.5342i	0.205934	+	0.0940469i	0.515712	−	0.856762i	$-0.327527\pi$
$431$	88.7576	+	40.5342i	0.205934	+	0.0940469i	−0.309778	+	0.950809i	$0.600255\pi$
$432$	2232.41	+	655.496i	5.16762	+	1.51735i
$433$	175.599	−	80.1936i	0.405541	−	0.185205i	−0.202192	−	0.979346i	$-0.564806\pi$
$433$	175.599	−	80.1936i	0.405541	−	0.185205i	0.607733	+	0.794141i	$0.292079\pi$
$434$	336.927	−	48.4427i	0.776329	−	0.111619i
$435$	−69.0667	+	107.470i	−0.158774	+	0.247057i
$436$			348.952i			0.800349i
$437$	18.8380	−	28.2752i	0.0431076	−	0.0647030i
$438$	1794.07			4.09604
$439$	343.091	+	220.491i	0.781528	+	0.502257i	0.869540	−	0.493862i	$-0.164415\pi$
$439$	343.091	+	220.491i	0.781528	+	0.502257i	−0.0880126	+	0.996119i	$0.528052\pi$
$440$	−62.0192	−	431.353i	−0.140953	−	0.980348i
$441$	156.899	+	343.560i	0.355779	+	0.779048i
$442$	65.0887	−	221.672i	0.147260	−	0.501520i
$443$	14.5857	−	31.9381i	0.0329247	−	0.0720951i	−0.892455	−	0.451136i	$-0.851019\pi$
$443$	14.5857	−	31.9381i	0.0329247	−	0.0720951i	0.925380	+	0.379041i	$0.123746\pi$
$444$	−1709.77	−	1481.52i	−3.85083	−	3.33677i
$445$	−14.6251	+	101.720i	−0.0328653	+	0.228583i
$446$	834.519	−	245.037i	1.87112	−	0.549410i
$447$	−822.887	+	713.036i	−1.84091	+	1.59516i
$448$	123.143	+	191.614i	0.274873	+	0.427711i
$449$	349.262	−	224.457i	0.777867	−	0.499905i	−0.0904582	−	0.995900i	$-0.528833\pi$
$449$	349.262	−	224.457i	0.777867	−	0.499905i	0.868325	+	0.495996i	$0.165197\pi$
$450$	−310.739	−	358.612i	−0.690531	−	0.796916i
$451$	3.94948	+	13.4507i	0.00875716	+	0.0298241i
$452$	−1326.81	−	190.767i	−2.93542	−	0.422050i
$453$	301.153	−	347.549i	0.664797	−	0.767216i
$454$	415.907	+	189.938i	0.916095	+	0.418367i
$455$	−64.1956	−	18.8495i	−0.141089	−	0.0414275i
$456$	−126.680	+	57.8528i	−0.277807	+	0.126870i
$457$	673.622	−	96.8522i	1.47401	−	0.211931i	0.642005	−	0.766700i	$-0.278103\pi$
$457$	673.622	−	96.8522i	1.47401	−	0.211931i	0.832004	+	0.554770i	$0.187194\pi$
$458$	−720.876	+	1121.71i	−1.57397	+	2.44914i
$459$		−	1385.81i		−	3.01919i
$460$	333.425	−	279.413i	0.724836	−	0.607419i
$461$	467.274			1.01361			0.506805	−	0.862061i	$-0.330826\pi$
$461$	467.274			1.01361			0.506805	+	0.862061i	$0.330826\pi$
$462$	−1302.36	−	836.974i	−2.81895	−	1.81163i
$463$	−48.3113	−	336.013i	−0.104344	−	0.725729i	−0.973082	−	0.230458i	$-0.925978\pi$
$463$	−48.3113	−	336.013i	−0.104344	−	0.725729i	0.868738	−	0.495271i	$-0.164931\pi$
$464$	86.0231	+	188.364i	0.185395	+	0.405957i
$465$	61.5595	−	209.652i	0.132386	−	0.450865i
$466$	−461.279	+	1010.06i	−0.989870	+	2.16751i
$467$	−611.614	−	529.966i	−1.30967	−	1.13483i	−0.981761	−	0.190121i	$-0.939112\pi$
$467$	−611.614	−	529.966i	−1.30967	−	1.13483i	−0.327905	−	0.944711i	$-0.606343\pi$
$468$	163.806	−	1139.29i	0.350012	−	2.43439i
$469$	−337.433	+	99.0792i	−0.719473	+	0.211256i
$470$	246.829	−	213.878i	0.525168	−	0.455060i
$471$	255.989	+	398.327i	0.543501	+	0.845704i
$472$	449.720	−	289.017i	0.952796	−	0.612325i
$473$	135.460	+	156.329i	0.286384	+	0.330505i
$474$	218.331	+	743.566i	0.460613	+	1.56870i
$475$	7.31087	+	1.05114i	0.0153913	+	0.00221294i
$476$	−423.529	+	488.778i	−0.889766	+	1.02684i
$477$	−216.816	−	99.0166i	−0.454541	−	0.207582i
$478$	−572.756	−	168.176i	−1.19823	−	0.351833i
$479$	−41.7167	+	19.0514i	−0.0870912	+	0.0397732i	−0.458484	−	0.888702i	$-0.651607\pi$
$479$	−41.7167	+	19.0514i	−0.0870912	+	0.0397732i	0.371393	+	0.928476i	$0.378880\pi$
$480$	−181.536	+	26.1009i	−0.378200	+	0.0543769i
$481$	−122.163	+	190.090i	−0.253978	+	0.395197i
$482$			1165.24i			2.41752i
$483$	13.4460	−	814.474i	0.0278385	−	1.68628i
$484$	−273.742			−0.565584
$485$	150.471	+	96.7017i	0.310249	+	0.199385i
$486$	−719.038	−	5001.02i	−1.47950	−	10.2902i
$487$	−39.0710	−	85.5536i	−0.0802279	−	0.175675i	0.865267	−	0.501311i	$-0.167149\pi$
$487$	−39.0710	−	85.5536i	−0.0802279	−	0.175675i	−0.945495	+	0.325636i	$0.894421\pi$
$488$	339.792	−	1157.22i	0.696294	−	2.37136i
$489$	−160.242	+	350.880i	−0.327692	+	0.717546i
$490$	−83.7899	−	72.6044i	−0.171000	−	0.148172i
$491$	68.0841	−	473.535i	0.138664	−	0.964430i	−0.795084	−	0.606499i	$-0.792573\pi$
$491$	68.0841	−	473.535i	0.138664	−	0.964430i	0.933748	−	0.357931i	$-0.116518\pi$
$492$	55.0365	−	16.1602i	0.111863	−	0.0328459i
$493$	93.2138	−	80.7702i	0.189075	−	0.163834i
$494$	14.2667	+	22.1994i	0.0288800	+	0.0449381i
$495$	−626.346	+	402.528i	−1.26535	+	0.813188i
$496$	−231.942	−	267.675i	−0.467625	−	0.539668i
$497$	46.9040	+	159.740i	0.0943743	+	0.321409i
$498$	2491.64	+	358.244i	5.00330	+	0.719365i
$499$	159.382	−	183.937i	0.319403	−	0.368611i	−0.573230	−	0.819394i	$-0.694310\pi$
$499$	159.382	−	183.937i	0.319403	−	0.368611i	0.892633	+	0.450783i	$0.148855\pi$
$500$	86.0238	+	39.2857i	0.172048	+	0.0785715i
$501$	249.163	+	73.1608i	0.497331	+	0.146029i
$502$	429.703	−	196.239i	0.855981	−	0.390914i
$503$	−651.320	+	93.6456i	−1.29487	+	0.186174i	−0.755084	−	0.655628i	$-0.772404\pi$
$503$	−651.320	+	93.6456i	−1.29487	+	0.186174i	−0.539786	+	0.841802i	$0.681495\pi$
$504$	−1352.46	+	2104.46i	−2.68344	+	4.17552i
$505$		−	264.190i		−	0.523149i
$506$	−529.504	−	854.620i	−1.04645	−	1.68897i
$507$	858.965			1.69421
$508$	449.234	+	288.705i	0.884320	+	0.568318i
$509$	30.5562	+	212.523i	0.0600318	+	0.417531i	0.997571	+	0.0696518i	$0.0221888\pi$
$509$	30.5562	+	212.523i	0.0600318	+	0.417531i	−0.937540	+	0.347879i	$0.886902\pi$
$510$	254.019	+	556.224i	0.498076	+	1.09064i
$511$	−141.323	+	481.302i	−0.276561	+	0.941882i
$512$	444.308	−	972.898i	0.867788	−	1.90019i
$513$	119.626	+	103.657i	0.233190	+	0.202060i
$514$	59.3380	−	412.705i	0.115444	−	0.802927i
$515$	379.551	−	111.446i	0.736993	−	0.216401i
$516$	639.654	−	554.263i	1.23964	−	1.07415i
$517$	−277.056	−	431.107i	−0.535891	−	0.833863i
$518$	783.781	−	503.706i	1.51309	−	0.972404i
$519$	894.606	+	1032.43i	1.72371	+	1.98927i
$520$	50.1755	+	170.882i	0.0964914	+	0.328619i
$521$	58.0308	+	8.34357i	0.111384	+	0.0160145i	0.197781	−	0.980246i	$-0.436626\pi$
$521$	58.0308	+	8.34357i	0.111384	+	0.0160145i	−0.0863976	+	0.996261i	$0.527536\pi$
$522$	592.697	−	684.008i	1.13543	−	1.31036i
$523$	−30.9784	−	14.1473i	−0.0592321	−	0.0270504i	0.385579	−	0.922675i	$-0.374002\pi$
$523$	−30.9784	−	14.1473i	−0.0592321	−	0.0270504i	−0.444811	+	0.895625i	$0.646729\pi$
$524$	−755.151	−	221.732i	−1.44113	−	0.423154i
$525$	161.081	−	73.5632i	0.306821	−	0.140120i
$526$	425.508	−	61.1789i	0.808951	−	0.116310i
$527$	−114.054	+	177.471i	−0.216420	+	0.336757i
$528$			1610.85i			3.05085i
$529$	235.518	−	473.679i	0.445214	−	0.895424i
$530$	69.9685			0.132016
$531$	−768.339	−	493.782i	−1.44697	−	0.929909i
$532$	−10.5131	−	73.1201i	−0.0197614	−	0.137444i
$533$	−2.37993	−	5.21131i	−0.00446515	−	0.00977732i
$534$	273.781	−	932.412i	0.512698	−	1.74609i
$535$	11.2469	−	24.6272i	0.0210222	−	0.0460322i
$536$	707.481	+	613.036i	1.31993	+	1.14372i
$537$	−200.795	+	1396.56i	−0.373919	+	2.60067i
$538$	22.6646	−	6.65494i	0.0421276	−	0.0123698i
$539$	−131.472	+	113.921i	−0.243918	+	0.211356i
$540$	1095.72	+	1704.97i	2.02910	+	3.15735i
$541$	−302.687	+	194.525i	−0.559496	+	0.359566i	−0.789621	−	0.613595i	$-0.789723\pi$
$541$	−302.687	+	194.525i	−0.559496	+	0.359566i	0.230125	+	0.973161i	$0.426086\pi$
$542$	164.519	+	189.865i	0.303541	+	0.350305i
$543$	221.234	+	753.453i	0.407429	+	1.38757i
$544$	175.269	+	25.1999i	0.322186	+	0.0463233i
$545$	−60.4090	+	69.7157i	−0.110842	+	0.127919i
$546$	575.502	+	262.823i	1.05403	+	0.481361i
$547$	−380.245	−	111.650i	−0.695146	−	0.204113i	−0.0849751	−	0.996383i	$-0.527081\pi$
$547$	−380.245	−	111.650i	−0.695146	−	0.204113i	−0.610171	+	0.792270i	$0.708899\pi$
$548$	−1783.05	+	814.292i	−3.25374	+	1.48593i
$549$	−2039.59	+	293.249i	−3.71511	+	0.534152i
$550$	118.161	−	183.862i	0.214838	−	0.334294i
$551$			14.0880i			0.0255680i
$552$	−1843.23	+	1142.02i	−3.33918	+	2.06889i
$553$	−216.678			−0.391823
$554$	−1153.06	−	741.024i	−2.08133	−	1.33759i
$555$	−85.1133	−	591.976i	−0.153357	−	1.06662i
$556$	327.355	+	716.808i	0.588768	+	1.28922i
$557$	−22.9077	+	78.0166i	−0.0411270	+	0.140066i	−0.977497	−	0.210948i	$-0.932345\pi$
$557$	−22.9077	+	78.0166i	−0.0411270	+	0.140066i	0.936370	+	0.351014i	$0.114163\pi$
$558$	−643.077	+	1408.14i	−1.15247	+	2.52355i
$559$	−63.8877	−	55.3590i	−0.114289	−	0.0990322i
$560$	40.8509	−	284.124i	0.0729480	−	0.507365i
$561$	920.590	−	270.310i	1.64098	−	0.481835i
$562$	−1022.90	+	886.351i	−1.82011	+	1.57714i
$563$	467.107	+	726.833i	0.829675	+	1.29100i	0.954317	+	0.298798i	$0.0965855\pi$
$563$	467.107	+	726.833i	0.829675	+	1.29100i	−0.124642	+	0.992202i	$0.539778\pi$
$564$	−1763.97	+	1133.64i	−3.12761	+	2.00999i
$565$	−232.054	−	267.804i	−0.410714	−	0.473990i
$566$	−23.5167	−	80.0906i	−0.0415490	−	0.141503i
$567$	2340.34	+	336.490i	4.12759	+	0.593457i
$568$	290.211	−	334.921i	0.510934	−	0.589650i
$569$	84.8981	+	38.7717i	0.149206	+	0.0681400i	0.488618	−	0.872498i	$-0.337501\pi$
$569$	84.8981	+	38.7717i	0.149206	+	0.0681400i	−0.339413	+	0.940638i	$0.610228\pi$
$570$	−67.0150	−	19.6774i	−0.117570	−	0.0345217i
$571$	−248.296	+	113.393i	−0.434845	+	0.198587i	−0.620796	−	0.783972i	$-0.713191\pi$
$571$	−248.296	+	113.393i	−0.434845	+	0.198587i	0.185951	+	0.982559i	$0.440463\pi$
$572$	524.750	−	75.4477i	0.917396	−	0.131902i
$573$	989.482	−	1539.66i	1.72684	−	2.68702i
$574$			23.6220i			0.0411534i
$575$	114.984	+	1.89825i	0.199973	+	0.00330131i
$576$	−1035.87			−1.79838
$577$	−130.599	−	83.9307i	−0.226341	−	0.145460i	0.422556	−	0.906337i	$-0.361133\pi$
$577$	−130.599	−	83.9307i	−0.226341	−	0.145460i	−0.648897	+	0.760876i	$0.724769\pi$
$578$	61.1531	+	425.329i	0.105801	+	0.735863i
$579$	716.504	+	1568.93i	1.23749	+	2.70972i
$580$	−50.8190	+	173.074i	−0.0876190	+	0.298403i
$581$	−292.380	+	640.223i	−0.503236	+	1.10193i
$582$	−1278.27	−	1107.62i	−2.19633	−	1.90313i
$583$	15.6240	−	108.668i	0.0267994	−	0.186394i
$584$	1281.18	−	376.187i	2.19379	−	0.644156i
$585$	229.956	−	199.258i	0.393086	−	0.340611i
$586$	−950.782	−	1479.45i	−1.62249	−	2.52465i
$587$	802.392	−	515.666i	1.36694	−	0.878477i	0.368251	−	0.929726i	$-0.379957\pi$
$587$	802.392	−	515.666i	1.36694	−	0.878477i	0.998686	+	0.0512496i	$0.0163204\pi$
$588$	466.133	+	537.946i	0.792743	+	0.914875i
$589$	−6.78865	−	23.1200i	−0.0115257	−	0.0392530i
$590$	265.375	+	38.1551i	0.449788	+	0.0646697i
$591$	1167.56	−	1347.43i	1.97556	−	2.27992i
$592$	−881.831	−	402.719i	−1.48958	−	0.680268i
$593$	1013.85	+	297.693i	1.70970	+	0.502012i	0.982791	−	0.184724i	$-0.0591390\pi$
$593$	1013.85	+	297.693i	1.70970	+	0.502012i	0.726907	+	0.686736i	$0.240957\pi$
$594$	4260.56	−	1945.73i	7.17266	−	3.27564i
$595$	−169.230	+	24.3316i	−0.284420	+	0.0408935i
$596$	−831.190	+	1293.36i	−1.39461	+	2.17006i
$597$		−	345.934i		−	0.579453i
$598$	263.898	+	314.911i	0.441301	+	0.526607i
$599$	415.407			0.693501			0.346750	−	0.937957i	$-0.387285\pi$
$599$	415.407			0.693501			0.346750	+	0.937957i	$0.387285\pi$
$600$	−396.549	−	254.847i	−0.660915	−	0.424744i
$601$	88.0307	+	612.267i	0.146474	+	1.01875i	0.921933	+	0.387349i	$0.126609\pi$
$601$	88.0307	+	612.267i	0.146474	+	1.01875i	−0.775459	+	0.631398i	$0.782482\pi$
$602$	144.796	+	317.060i	0.240525	+	0.526677i
$603$	450.594	−	1534.58i	0.747253	−	2.54491i
$604$	269.742	−	590.654i	0.446594	−	0.977903i
$605$	−54.6899	−	47.3891i	−0.0903966	−	0.0783291i
$606$	−355.537	+	2472.81i	−0.586694	+	4.08055i
$607$	−1122.54	+	329.608i	−1.84933	+	0.543012i	−0.849447	+	0.527674i	$0.823064\pi$
$607$	−1122.54	+	329.608i	−1.84933	+	0.543012i	−0.999882	+	0.0153381i	$0.995118\pi$
$608$	−15.2852	+	13.2447i	−0.0251402	+	0.0217841i
$609$	182.610	+	284.146i	0.299852	+	0.466579i
$610$	508.851	−	327.018i	0.834181	−	0.536096i
$611$	137.147	+	158.276i	0.224463	+	0.259044i
$612$	−828.654	−	2822.14i	−1.35401	−	4.61133i
$613$	−994.081	−	142.927i	−1.62167	−	0.233160i	−0.729208	−	0.684292i	$-0.760111\pi$
$613$	−994.081	−	142.927i	−1.62167	−	0.233160i	−0.892457	+	0.451132i	$0.851020\pi$
$614$	255.179	−	294.492i	0.415600	−	0.479628i
$615$	13.7931	+	6.29910i	0.0224278	+	0.0102424i
$616$	−1105.54	−	324.615i	−1.79470	−	0.526972i
$617$	−422.865	+	193.116i	−0.685357	+	0.312992i	−0.727488	−	0.686120i	$-0.759312\pi$
$617$	−422.865	+	193.116i	−0.685357	+	0.312992i	0.0421315	+	0.999112i	$0.486585\pi$
$618$	−3702.57	+	532.350i	−5.99122	+	0.861407i
$619$	75.9907	−	118.244i	0.122764	−	0.191024i	−0.774432	−	0.632657i	$-0.781964\pi$
$619$	75.9907	−	118.244i	0.122764	−	0.191024i	0.897196	+	0.441633i	$0.145601\pi$
$620$		−	308.522i		−	0.497617i
$621$	2051.02	+	1366.47i	3.30277	+	2.20043i
$622$	−57.3094			−0.0921373
$623$	228.576	+	146.897i	0.366895	+	0.235789i
$624$	−93.6879	−	651.614i	−0.150141	−	1.04425i
$625$	10.3854	+	22.7408i	0.0166166	+	0.0363853i
$626$	−339.731	+	1157.02i	−0.542701	+	1.84827i
$627$	−45.5253	+	99.6866i	−0.0726082	+	0.158990i
$628$	505.265	+	437.815i	0.804563	+	0.697158i
$629$	−82.1750	+	571.540i	−0.130644	+	0.908648i
$630$	−1203.77	+	353.459i	−1.91075	+	0.561046i
$631$	−433.078	+	375.265i	−0.686337	+	0.594714i	−0.926625	−	0.375987i	$-0.877304\pi$
$631$	−433.078	+	375.265i	−0.686337	+	0.594714i	0.240288	+	0.970702i	$0.422758\pi$
$632$	311.828	+	485.214i	0.493398	+	0.767743i
$633$	−527.493	+	338.999i	−0.833322	+	0.535544i
$634$	−200.915	−	231.868i	−0.316900	−	0.365723i
$635$	39.7714	+	135.449i	0.0626321	+	0.213305i
$636$	−444.638	−	63.9293i	−0.699117	−	0.100518i
$637$	46.5567	−	53.7293i	0.0730874	−	0.0843473i
$638$	379.198	+	173.174i	0.594355	+	0.271433i
$639$	−726.470	−	213.311i	−1.13689	−	0.333820i
$640$	387.991	−	177.189i	0.606235	−	0.276858i
$641$	404.411	−	58.1455i	0.630906	−	0.0907106i	0.180559	−	0.983564i	$-0.442209\pi$
$641$	404.411	−	58.1455i	0.630906	−	0.0907106i	0.450347	+	0.892854i	$0.351300\pi$
$642$	−138.413	+	215.375i	−0.215597	+	0.335475i
$643$		−	1082.69i		−	1.68381i	−0.539628	−	0.841904i	$-0.681435\pi$
$643$		−	1082.69i		−	1.68381i	0.539628	−	0.841904i	$-0.318565\pi$
$644$	−305.782	−	1108.79i	−0.474817	−	1.72172i
$645$	223.746			0.346892
$646$	56.7283	+	36.4571i	0.0878147	+	0.0564351i
$647$	−31.7518	−	220.838i	−0.0490754	−	0.341327i	−0.999535	−	0.0304799i	$-0.990296\pi$
$647$	−31.7518	−	220.838i	−0.0490754	−	0.341327i	0.950460	−	0.310847i	$-0.100613\pi$
$648$	−2614.54	−	5725.05i	−4.03479	−	8.83496i
$649$	118.517	−	403.632i	0.182615	−	0.621929i
$650$	−37.1044	+	81.2472i	−0.0570836	+	0.124996i
$651$	−436.607	−	378.322i	−0.670671	−	0.581140i
$652$	−77.5126	+	539.112i	−0.118884	+	0.826859i
$653$	589.055	−	172.962i	0.902075	−	0.264873i	0.202373	−	0.979308i	$-0.435135\pi$
$653$	589.055	−	172.962i	0.902075	−	0.264873i	0.699701	+	0.714435i	$0.253316\pi$
$654$	659.248	−	571.242i	1.00802	−	0.873458i
$655$	−112.483	−	175.028i	−0.171730	−	0.267218i
$656$	20.6774	−	13.2886i	0.0315204	−	0.0202570i
$657$	−1493.92	−	1724.07i	−2.27385	−	2.62416i
$658$	−243.282	−	828.542i	−0.369729	−	1.25918i
$659$	−905.125	−	130.137i	−1.37348	−	0.197477i	−0.584252	−	0.811573i	$-0.698612\pi$
$659$	−905.125	−	130.137i	−1.37348	−	0.197477i	−0.789232	+	0.614096i	$0.789521\pi$
$660$	−918.883	+	1060.45i	−1.39225	+	1.60674i
$661$	378.304	+	172.766i	0.572321	+	0.261370i	0.680484	−	0.732763i	$-0.261770\pi$
$661$	378.304	+	172.766i	0.572321	+	0.261370i	−0.108163	+	0.994133i	$0.534497\pi$
$662$	1146.31	+	336.587i	1.73158	+	0.508439i
$663$	−356.672	+	162.887i	−0.537966	+	0.245681i
$664$	1854.45	−	266.629i	2.79284	−	0.401550i
$665$	10.5579	−	16.4284i	0.0158765	−	0.0247043i
$666$			4237.12i			6.36204i
$667$	27.6284	+	217.601i	0.0414219	+	0.326239i
$668$	366.666			0.548901
$669$	−1241.81	−	798.064i	−1.85622	−	1.19292i
$670$	66.8152	+	464.710i	0.0997241	+	0.693597i
$671$	−394.263	−	863.316i	−0.587575	−	1.28661i
$672$	−136.615	+	465.267i	−0.203296	+	0.692362i
$673$	−497.217	+	1088.75i	−0.738806	+	1.61776i	0.0467018	+	0.998909i	$0.485129\pi$
$673$	−497.217	+	1088.75i	−0.738806	+	1.61776i	−0.785508	+	0.618851i	$0.787598\pi$
$674$	879.553	+	762.137i	1.30498	+	1.13077i
$675$	−76.2477	+	530.314i	−0.112960	+	0.785651i
$676$	1163.71	−	341.697i	1.72147	−	0.505469i
$677$	151.195	−	131.011i	0.223330	−	0.193517i	−0.536008	−	0.844213i	$-0.680068\pi$
$677$	151.195	−	131.011i	0.223330	−	0.193517i	0.759338	+	0.650696i	$0.225523\pi$
$678$	1811.62	+	2818.93i	2.67200	+	4.15771i
$679$	397.839	−	255.675i	0.585919	−	0.376547i
$680$	298.031	+	343.946i	0.438281	+	0.505803i
$681$	−218.626	−	744.572i	−0.321037	−	1.09335i
$682$	−705.757	−	101.473i	−1.03483	−	0.148787i
$683$	−561.122	+	647.569i	−0.821554	+	0.948124i	−0.999354	−	0.0359425i	$-0.988557\pi$
$683$	−561.122	+	647.569i	−0.821554	+	0.948124i	0.177799	+	0.984067i	$0.443102\pi$
$684$	305.597	+	139.561i	0.446779	+	0.204037i
$685$	−497.195	−	145.990i	−0.725832	−	0.213124i
$686$	−1196.76	+	546.542i	−1.74455	+	0.796708i
$687$	2239.97	−	322.060i	3.26052	−	0.468791i
$688$	196.081	−	305.108i	0.285002	−	0.443471i
$689$			44.8665i			0.0651182i
$690$	−1073.70	−	172.509i	−1.55608	−	0.250013i
$691$	751.065			1.08692			0.543462	−	0.839434i	$-0.317113\pi$
$691$	751.065			1.08692			0.543462	+	0.839434i	$0.317113\pi$
$692$	1622.70	+	1042.85i	2.34494	+	1.50700i
$693$	280.151	+	1948.50i	0.404259	+	2.81168i
$694$	−137.933	−	302.031i	−0.198750	−	0.435203i
$695$	−58.6896	+	199.878i	−0.0844455	+	0.287595i
$696$	373.498	−	817.847i	0.536636	−	1.17507i
$697$	−11.0641	−	9.58711i	−0.0158739	−	0.0137548i
$698$	159.086	−	1106.47i	0.227917	−	1.58520i
$699$	1808.25	−	530.949i	2.58691	−	0.759584i
$700$	188.967	−	163.741i	0.269953	−	0.233915i
$701$	−353.156	−	549.521i	−0.503788	−	0.783910i	0.492470	−	0.870329i	$-0.336094\pi$
$701$	−353.156	−	549.521i	−0.503788	−	0.783910i	−0.996259	+	0.0864191i	$0.972458\pi$
$702$	−1610.30	+	1034.88i	−2.29387	+	1.47418i
$703$	−43.1902	−	49.8441i	−0.0614369	−	0.0709020i
$704$	−134.418	−	457.787i	−0.190935	−	0.650265i
$705$	−548.667	−	78.8864i	−0.778251	−	0.111896i
$706$	826.409	−	953.726i	1.17055	−	1.35089i
$707$	−635.385	−	290.171i	−0.898706	−	0.410425i
$708$	−1651.55	−	484.939i	−2.33270	−	0.684942i
$709$	−630.483	+	287.932i	−0.889257	+	0.406110i	−0.807035	−	0.590504i	$-0.798929\pi$
$709$	−630.483	+	287.932i	−0.889257	+	0.406110i	−0.0822222	+	0.996614i	$0.526202\pi$
$710$	219.993	−	31.6303i	0.309850	−	0.0445497i
$711$	532.753	−	828.980i	0.749301	−	1.16594i
$712$		−	723.260i		−	1.01581i
$713$	−150.198	−	343.796i	−0.210657	−	0.482182i
$714$	1616.74			2.26434
$715$	117.899	+	75.7691i	0.164894	+	0.105971i
$716$	283.518	+	1971.91i	0.395975	+	2.75407i
$717$	420.866	+	921.569i	0.586982	+	1.28531i
$718$	−217.708	+	741.447i	−0.303215	+	1.03266i
$719$	545.004	−	1193.39i	0.758003	−	1.65979i	0.00657577	−	0.999978i	$-0.497907\pi$
$719$	545.004	−	1193.39i	0.758003	−	1.65979i	0.751427	−	0.659816i	$-0.229366\pi$
$720$	986.579	+	854.875i	1.37025	+	1.18733i
$721$	148.845	−	1035.24i	0.206442	−	1.43584i
$722$	1215.21	−	356.817i	1.68311	−	0.494206i
$723$	1494.61	−	1295.09i	2.06724	−	1.79127i
$724$	599.449	+	932.761i	0.827968	+	1.28834i
$725$	−40.1147	+	25.7801i	−0.0553306	+	0.0355588i
$726$	448.122	+	517.160i	0.617248	+	0.712342i
$727$	43.2016	+	147.131i	0.0594245	+	0.202381i	0.983854	−	0.178971i	$-0.0572768\pi$
$727$	43.2016	+	147.131i	0.0594245	+	0.202381i	−0.924430	+	0.381352i	$0.875459\pi$
$728$	466.087	+	67.0131i	0.640229	+	0.0920510i
$729$	−3258.38	+	3760.37i	−4.46965	+	5.15826i
$730$	609.145	+	278.187i	0.834445	+	0.381078i
$731$	−207.271	−	60.8603i	−0.283545	−	0.0832562i
$732$	−3532.45	+	1613.22i	−4.82575	+	2.20385i
$733$	654.828	−	94.1501i	0.893353	−	0.128445i	0.319677	−	0.947527i	$-0.396426\pi$
$733$	654.828	−	94.1501i	0.893353	−	0.128445i	0.573677	+	0.819082i	$0.305517\pi$
$734$	−809.722	+	1259.95i	−1.10316	+	1.71656i
$735$			188.169i			0.256012i
$736$	−210.119	+	234.553i	−0.285488	+	0.318686i
$737$	736.657			0.999535
$738$	−90.3747	−	58.0803i	−0.122459	−	0.0786995i
$739$	25.3389	+	176.236i	0.0342881	+	0.238479i	0.999757	−	0.0220390i	$-0.00701581\pi$
$739$	25.3389	+	176.236i	0.0342881	+	0.238479i	−0.965469	+	0.260518i	$0.916107\pi$
$740$	−350.799	−	768.143i	−0.474053	−	1.03803i
$741$	12.6179	−	42.9726i	0.0170282	−	0.0579927i
$742$	76.8493	−	168.277i	0.103571	−	0.226788i
$743$	−146.876	−	127.269i	−0.197680	−	0.171290i	0.550396	−	0.834904i	$-0.314477\pi$
$743$	−146.876	−	127.269i	−0.197680	−	0.171290i	−0.748076	+	0.663613i	$0.769022\pi$
$744$	−218.854	+	1522.16i	−0.294159	+	2.04592i
$745$	−389.960	+	114.503i	−0.523437	+	0.153695i
$746$	1568.12	−	1358.78i	2.10204	−	1.82143i
$747$	−1730.52	−	2692.74i	−2.31663	−	3.60475i
$748$	1139.67	−	732.424i	1.52363	−	0.979176i
$749$	−46.8764	−	54.0982i	−0.0625853	−	0.0722273i
$750$	−66.6032	−	226.830i	−0.0888043	−	0.302440i
$751$	780.244	+	112.182i	1.03894	+	0.149377i	0.640611	−	0.767865i	$-0.278681\pi$
$751$	780.244	+	112.182i	1.03894	+	0.149377i	0.398329	+	0.917242i	$0.369590\pi$
$752$	−588.402	+	679.052i	−0.782449	+	0.902994i
$753$	−729.294	−	333.057i	−0.968517	−	0.442307i
$754$	−163.464	−	47.9972i	−0.216795	−	0.0636568i
$755$	156.142	−	71.3077i	0.206811	−	0.0944473i
$756$	5303.97	−	762.596i	7.01584	−	1.00872i
$757$	175.955	−	273.792i	0.232438	−	0.361680i	−0.705368	−	0.708842i	$-0.749218\pi$
$757$	175.955	−	273.792i	0.232438	−	0.361680i	0.937805	+	0.347162i	$0.112854\pi$
$758$		−	1130.89i		−	1.49194i
$759$	−507.680	+	1629.03i	−0.668880	+	2.14628i
$760$	−51.9827			−0.0683983
$761$	−5.91604	−	3.80201i	−0.00777403	−	0.00499607i	0.536748	−	0.843743i	$-0.319653\pi$
$761$	−5.91604	−	3.80201i	−0.00777403	−	0.00499607i	−0.544522	+	0.838747i	$0.683289\pi$
$762$	−189.977	−	1321.32i	−0.249314	−	1.73402i
$763$	101.319	+	221.857i	0.132790	+	0.290770i
$764$	728.057	−	2479.53i	0.952954	−	3.24546i
$765$	323.002	−	707.277i	0.422225	−	0.924545i
$766$	−522.949	−	453.138i	−0.682702	−	0.591564i
$767$	−24.4665	+	170.168i	−0.0318990	+	0.221862i
$768$	−2984.25	+	876.254i	−3.88574	+	1.14096i
$769$	−383.764	+	332.533i	−0.499043	+	0.432423i	−0.867660	−	0.497158i	$-0.834377\pi$
$769$	−383.764	+	332.533i	−0.499043	+	0.432423i	0.368617	+	0.929581i	$0.379831\pi$
$770$	−312.412	−	486.123i	−0.405730	−	0.631329i
$771$	−595.311	+	382.583i	−0.772128	+	0.496217i
$772$	1594.83	+	1840.53i	2.06584	+	2.38411i
$773$	326.199	+	1110.93i	0.421991	+	1.43717i	0.846812	+	0.531892i	$0.178519\pi$
$773$	326.199	+	1110.93i	0.421991	+	1.43717i	−0.424821	+	0.905277i	$0.639663\pi$
$774$	−1569.04	−	225.594i	−2.02719	−	0.291465i
$775$	53.4101	−	61.6385i	0.0689162	−	0.0795335i
$776$	−1145.08	−	522.942i	−1.47562	−	0.673895i
$777$	−1517.20	−	445.491i	−1.95264	−	0.573348i
$778$	−1579.73	+	721.437i	−2.03050	+	0.927297i
$779$	1.65517	−	0.237977i	0.00212473	−	0.000305491i
$780$	310.026	−	482.410i	0.397470	−	0.618475i
$781$		−	348.733i		−	0.446521i
$782$	947.716	+	451.860i	1.21191	+	0.577826i
$783$	−1021.91			−1.30512
$784$	256.595	+	164.903i	0.327289	+	0.210336i
$785$	25.1524	+	174.939i	0.0320413	+	0.222852i
$786$	817.297	+	1789.63i	1.03982	+	2.27688i
$787$	−339.611	+	1156.61i	−0.431526	+	1.46964i	0.401217	+	0.915983i	$0.368587\pi$
$787$	−339.611	+	1156.61i	−0.431526	+	1.46964i	−0.832743	+	0.553659i	$0.813231\pi$
$788$	1045.78	−	2289.94i	1.32713	−	2.90601i
$789$	−551.396	−	477.787i	−0.698854	−	0.605561i
$790$	−41.1665	+	286.319i	−0.0521095	+	0.362430i
$791$	−898.951	+	263.956i	−1.13647	+	0.333699i
$792$	3960.15	−	3431.49i	5.00019	−	4.33269i
$793$	209.697	+	326.294i	0.264434	+	0.411468i
$794$	−954.858	+	613.650i	−1.20259	+	0.772859i
$795$	−77.7653	−	89.7460i	−0.0978180	−	0.112888i
$796$	−137.613	−	468.666i	−0.172880	−	0.588777i
$797$	−498.653	−	71.6954i	−0.625662	−	0.0899566i	−0.177811	−	0.984065i	$-0.556901\pi$
$797$	−498.653	−	71.6954i	−0.625662	−	0.0899566i	−0.447851	+	0.894108i	$0.647811\pi$
$798$	−120.930	+	139.561i	−0.151541	+	0.174888i
$799$	486.811	+	222.319i	0.609275	+	0.278247i
$800$	−65.6847	−	19.2868i	−0.0821058	−	0.0241084i
$801$	−1124.01	+	513.319i	−1.40326	+	0.640848i
$802$	−1402.60	+	201.663i	−1.74888	+	0.251451i
$803$	568.073	−	883.939i	0.707438	−	1.10080i
$804$		−	3014.20i		−	3.74900i
$805$	130.857	−	274.456i	0.162556	−	0.340939i
$806$	291.391			0.361528
$807$	−33.7263	−	21.6746i	−0.0417922	−	0.0268582i
$808$	264.614	+	1840.43i	0.327493	+	2.27776i
$809$	−47.1570	−	103.260i	−0.0582905	−	0.127638i	0.878245	−	0.478211i	$-0.158714\pi$
$809$	−47.1570	−	103.260i	−0.0582905	−	0.127638i	−0.936536	+	0.350572i	$0.885987\pi$
$810$	889.281	−	3028.61i	1.09788	−	3.73903i
$811$	−575.873	+	1260.99i	−0.710078	+	1.55485i	0.117230	+	0.993105i	$0.462599\pi$
$811$	−575.873	+	1260.99i	−0.710078	+	1.55485i	−0.827308	+	0.561749i	$0.810129\pi$
$812$	360.431	+	312.315i	0.443881	+	0.384625i
$813$	60.6809	−	422.045i	0.0746383	−	0.519121i
$814$	−1872.53	+	549.825i	−2.30041	+	0.675461i
$815$	−108.815	+	94.2884i	−0.133515	+	0.115691i
$816$	−909.494	−	1415.20i	−1.11458	−	1.73431i
$817$	20.7573	−	13.3399i	0.0254067	−	0.0163279i
$818$	−1233.05	−	1423.01i	−1.50740	−	1.73963i
$819$	−226.651	−	771.903i	−0.276741	−	0.942495i
$820$	21.1925	+	3.04702i	0.0258445	+	0.00371588i
$821$	491.875	−	567.654i	0.599117	−	0.691418i	−0.372485	−	0.928038i	$-0.621494\pi$
$821$	491.875	−	567.654i	0.599117	−	0.691418i	0.971602	+	0.236620i	$0.0760396\pi$
$822$	4457.27	+	2035.57i	5.42247	+	2.47636i
$823$	−699.042	−	205.257i	−0.849383	−	0.249401i	−0.172060	−	0.985087i	$-0.555042\pi$
$823$	−699.042	−	205.257i	−0.849383	−	0.249401i	−0.677324	+	0.735685i	$0.736860\pi$
$824$	−2532.45	+	1156.53i	−3.07336	+	1.40356i
$825$	−367.160	+	52.7896i	−0.445042	+	0.0639874i
$826$	383.236	−	596.328i	0.463967	−	0.721946i
$827$			1433.81i			1.73375i	0.498523	+	0.866876i	$0.333876\pi$
$827$			1433.81i			1.73375i	−0.498523	+	0.866876i	$0.666124\pi$
$828$	4993.91	+	1556.33i	6.03129	+	1.87963i
$829$	−342.425			−0.413058			−0.206529	−	0.978440i	$-0.566217\pi$
$829$	−342.425			−0.413058			−0.206529	+	0.978440i	$0.566217\pi$
$830$	790.446	+	507.989i	0.952344	+	0.612034i
$831$	331.061	+	2302.58i	0.398389	+	2.77085i
$832$	80.9994	+	177.364i	0.0973551	+	0.213178i
$833$	51.1832	−	174.314i	0.0614444	−	0.209261i
$834$	818.322	−	1791.88i	0.981202	−	2.14853i
$835$	73.2547	+	63.4756i	0.0877302	+	0.0760186i
$836$	−22.0217	+	153.164i	−0.0263417	+	0.183211i
$837$	1677.07	−	492.434i	2.00367	−	0.588332i
$838$	789.533	−	684.134i	0.942163	−	0.816389i
$839$	−681.597	−	1060.59i	−0.812393	−	1.26411i	−0.961368	−	0.275267i	$-0.911234\pi$
$839$	−681.597	−	1060.59i	−0.812393	−	1.26411i	0.148975	−	0.988841i	$-0.452403\pi$
$840$	−1048.46	+	673.805i	−1.24817	+	0.802148i
$841$	491.177	+	566.848i	0.584039	+	0.674017i
$842$	142.229	+	484.386i	0.168918	+	0.575281i
$843$	2273.78	+	326.920i	2.69724	+	0.387805i
$844$	−579.786	+	669.109i	−0.686950	+	0.792783i
$845$	291.647	+	133.191i	0.345144	+	0.157622i
$846$	3768.06	+	1106.40i	4.45397	+	1.30780i
$847$	−174.040	+	79.4816i	−0.205479	+	0.0938390i
$848$	−190.531	+	27.3943i	−0.224683	+	0.0323046i
$849$	−76.5919	+	119.179i	−0.0902142	+	0.140376i
$850$			228.244i			0.268523i
$851$	−764.861	−	685.184i	−0.898779	−	0.805152i
$852$	−1426.92			−1.67479
$853$	−877.573	−	563.982i	−1.02881	−	0.661175i	−0.0866137	−	0.996242i	$-0.527605\pi$
$853$	−877.573	−	563.982i	−1.02881	−	0.661175i	−0.942194	+	0.335067i	$0.891241\pi$
$854$	−227.598	−	1582.98i	−0.266508	−	1.85361i
$855$	36.8937	+	80.7859i	0.0431505	+	0.0944865i
$856$	−53.6826	+	182.826i	−0.0627133	+	0.213582i
$857$	432.220	−	946.430i	0.504341	−	1.10435i	−0.470693	−	0.882297i	$-0.655996\pi$
$857$	432.220	−	946.430i	0.504341	−	1.10435i	0.975034	−	0.222056i	$-0.0712767\pi$
$858$	−1001.57	−	867.861i	−1.16733	−	1.01149i
$859$	−105.798	+	735.843i	−0.123164	+	0.856628i	0.830771	+	0.556615i	$0.187900\pi$
$859$	−105.798	+	735.843i	−0.123164	+	0.856628i	−0.953935	+	0.300013i	$0.903009\pi$
$860$	303.128	−	89.0063i	0.352474	−	0.103496i
$861$	30.2991	−	26.2543i	0.0351906	−	0.0304928i
$862$	−186.201	−	289.735i	−0.216011	−	0.336120i
$863$	−444.101	+	285.406i	−0.514601	+	0.330714i	−0.772033	−	0.635582i	$-0.780760\pi$
$863$	−444.101	+	285.406i	−0.514601	+	0.330714i	0.257432	+	0.966296i	$0.417124\pi$
$864$	−960.744	−	1108.76i	−1.11197	−	1.28328i
$865$	143.660	+	489.261i	0.166081	+	0.565620i
$866$	−674.448	−	96.9710i	−0.778809	−	0.111976i
$867$	477.586	−	551.163i	0.550848	−	0.635713i
$868$	−742.006	−	338.863i	−0.854846	−	0.390395i
$869$	435.488	+	127.871i	0.501137	+	0.147147i
$870$	410.167	−	187.317i	0.471456	−	0.215307i
$871$	−297.989	+	42.8444i	−0.342123	+	0.0491899i
$872$	351.001	−	546.168i	0.402524	−	0.626339i
$873$			2150.71i			2.46359i
$874$	−109.894	+	48.0106i	−0.125737	+	0.0549321i
$875$	66.0990			0.0755417
$876$	−3616.84	−	2324.40i	−4.12881	−	2.65342i
$877$	−145.745	−	1013.68i	−0.166186	−	1.15585i	−0.886678	−	0.462388i	$-0.846993\pi$
$877$	−145.745	−	1013.68i	−0.166186	−	1.15585i	0.720492	−	0.693464i	$-0.243916\pi$
$878$	−597.996	−	1309.43i	−0.681089	−	1.49138i
$879$	−840.898	+	2863.84i	−0.956653	+	3.25806i
$880$	−249.778	+	546.936i	−0.283838	+	0.621519i
$881$	78.8212	+	68.2990i	0.0894679	+	0.0775244i	0.698446	−	0.715662i	$-0.253875\pi$
$881$	78.8212	+	68.2990i	0.0894679	+	0.0775244i	−0.608979	+	0.793187i	$0.708420\pi$
$882$	189.724	−	1319.56i	0.215106	−	1.49610i
$883$	270.329	−	79.3756i	0.306148	−	0.0898931i	−0.125050	−	0.992150i	$-0.539909\pi$
$883$	270.329	−	79.3756i	0.306148	−	0.0898931i	0.431198	+	0.902257i	$0.358091\pi$
$884$	−418.418	+	362.561i	−0.473323	+	0.410137i
$885$	−246.006	−	382.793i	−0.277973	−	0.432535i
$886$	−104.257	+	67.0019i	−0.117672	+	0.0756229i
$887$	−392.256	−	452.688i	−0.442228	−	0.510358i	0.490252	−	0.871581i	$-0.336905\pi$
$887$	−392.256	−	452.688i	−0.442228	−	0.510358i	−0.932480	+	0.361223i	$0.882359\pi$
$888$	1185.85	+	4038.64i	1.33542	+	4.54802i
$889$	369.441	+	53.1176i	0.415569	+	0.0597499i
$890$	237.537	−	274.132i	0.266895	−	0.308014i
$891$	−4505.14	−	2057.43i	−5.05627	−	2.30912i
$892$	−1999.86	−	587.212i	−2.24200	−	0.658309i
$893$	−55.6041	+	25.3935i	−0.0622666	+	0.0284362i
$894$	3804.11	−	546.949i	4.25516	−	0.611800i
$895$	−284.726	+	443.042i	−0.318130	+	0.495019i
$896$		−	1127.74i		−	1.25864i
$897$	110.619	−	688.495i	0.123321	−	0.767552i
$898$	−1465.41			−1.63186
$899$	130.869	+	84.1045i	0.145572	+	0.0935534i
$900$	161.831	+	1125.56i	0.179812	+	1.25062i
$901$	47.6279	+	104.291i	0.0528612	+	0.115750i
$902$	13.9404	−	47.4765i	0.0154549	−	0.0526347i
$903$	245.749	−	538.115i	0.272147	−	0.595919i
$904$	1884.79	+	1633.18i	2.08495	+	1.80662i
$905$	−41.7139	+	290.127i	−0.0460927	+	0.320582i
$906$	−1557.45	+	457.309i	−1.71904	+	0.504756i
$907$	−837.816	+	725.972i	−0.923722	+	0.800410i	−0.980203	−	0.197994i	$-0.936557\pi$
$907$	−837.816	+	725.972i	−0.923722	+	0.800410i	0.0564813	+	0.998404i	$0.482012\pi$
$908$	−592.383	−	921.767i	−0.652405	−	1.01516i
$909$	2672.40	−	1717.44i	2.93993	−	1.88938i
$910$	154.649	+	178.474i	0.169944	+	0.196126i
$911$	−79.7054	−	271.452i	−0.0874922	−	0.297971i	0.904109	−	0.427301i	$-0.140536\pi$
$911$	−79.7054	−	271.452i	−0.0874922	−	0.297971i	−0.991602	+	0.129330i	$0.958717\pi$
$912$	190.193	+	27.3456i	0.208545	+	0.0299842i
$913$	965.460	−	1114.20i	1.05746	−	1.22037i
$914$	−2185.04	−	997.875i	−2.39064	−	1.09177i
$915$	−985.008	−	289.224i	−1.07651	−	0.316092i
$916$	2906.57	−	1327.39i	3.17311	−	1.44911i
$917$	−544.492	+	78.2861i	−0.593775	+	0.0853720i
$918$	−2644.51	+	4114.94i	−2.88073	+	4.48251i
$919$		−	336.342i		−	0.365987i	−0.983114	−	0.182993i	$-0.941421\pi$
$919$		−	336.342i		−	0.365987i	0.983114	−	0.182993i	$-0.0585787\pi$
$920$	−802.919	+	101.945i	−0.872738	+	0.110810i
$921$	−661.348			−0.718075
$922$	−1387.50	−	891.692i	−1.50488	−	0.967128i
$923$	20.2825	+	141.068i	0.0219745	+	0.152836i
$924$	1541.16	+	3374.68i	1.66792	+	3.65225i
$925$	62.8927	−	214.193i	0.0679922	−	0.231560i
$926$	−497.755	+	1089.93i	−0.537532	+	1.17703i
$927$	3594.71	+	3114.84i	3.87779	+	3.36013i
$928$	18.5827	−	129.246i	0.0200245	−	0.139273i
$929$	−23.8449	+	7.00150i	−0.0256673	+	0.00753660i	−0.294541	−	0.955639i	$-0.595167\pi$
$929$	−23.8449	+	7.00150i	−0.0256673	+	0.00753660i	0.268874	+	0.963175i	$0.413349\pi$
$930$	−582.868	+	505.058i	−0.626740	+	0.543073i
$931$	11.2188	+	17.4568i	0.0120503	+	0.0187506i
$932$	2238.58	−	1438.65i	2.40191	−	1.54361i
$933$	63.6955	+	73.5086i	0.0682696	+	0.0787873i
$934$	804.768	+	2740.79i	0.861636	+	2.93446i
$935$	354.485	+	50.9672i	0.379128	+	0.0545104i
$936$	−1402.37	+	1618.42i	−1.49825	+	1.72908i
$937$	−927.586	−	423.614i	−0.989953	−	0.452096i	−0.146448	−	0.989218i	$-0.546784\pi$
$937$	−927.586	−	423.614i	−0.989953	−	0.452096i	−0.843504	+	0.537122i	$0.819511\pi$
$938$	1191.03	+	349.717i	1.26975	+	0.372833i
$939$	1861.65	−	850.186i	1.98259	−	0.905417i
$940$	−774.708	+	111.386i	−0.824158	+	0.118496i
$941$	125.510	−	195.298i	0.133380	−	0.207543i	−0.768139	−	0.640283i	$-0.778817\pi$
$941$	125.510	−	195.298i	0.133380	−	0.207543i	0.901519	+	0.432740i	$0.142453\pi$
$942$		−	1671.27i		−	1.77417i
$943$	25.0988	−	6.92178i	0.0266159	−	0.00734016i
$944$	−737.581			−0.781336
$945$	1191.68	+	765.844i	1.26103	+	0.810417i
$946$	−103.907	−	722.690i	−0.109838	−	0.763943i
$947$	−753.391	−	1649.70i	−0.795555	−	1.74202i	−0.660017	−	0.751250i	$-0.729451\pi$
$947$	−753.391	−	1649.70i	−0.795555	−	1.74202i	−0.135538	−	0.990772i	$-0.543276\pi$
$948$	523.212	−	1781.90i	0.551912	−	1.87964i
$949$	−178.384	+	390.607i	−0.187971	+	0.411598i
$950$	−19.7027	−	17.0724i	−0.0207396	−	0.0179710i
$951$	−74.1050	+	515.412i	−0.0779233	+	0.541968i
$952$	1154.54	−	339.004i	1.21275	−	0.356096i
$953$	−1367.13	+	1184.62i	−1.43455	+	1.24305i	−0.510993	+	0.859585i	$0.670722\pi$
$953$	−1367.13	+	1184.62i	−1.43455	+	1.24305i	−0.923557	+	0.383460i	$0.874732\pi$
$954$	454.851	+	707.762i	0.476783	+	0.741889i
$955$	574.701	−	369.338i	0.601782	−	0.386742i
$956$	936.785	+	1081.11i	0.979901	+	1.13087i
$957$	−199.330	−	678.855i	−0.208286	−	0.709357i
$958$	160.227	+	23.0371i	0.167251	+	0.0240471i
$959$	−897.200	+	1035.42i	−0.935557	+	1.07969i
$960$	−469.441	−	214.386i	−0.489001	−	0.223319i
$961$	666.773	+	195.782i	0.693833	+	0.203728i
$962$	725.491	−	331.321i	0.754148	−	0.344408i
$963$	322.229	−	46.3295i	0.334609	−	0.0481096i
$964$	1509.69	−	2349.13i	1.56607	−	2.43685i
$965$			643.803i			0.667153i
$966$	−1594.17	+	2392.80i	−1.65028	+	2.47702i
$967$	−496.744			−0.513696			−0.256848	−	0.966452i	$-0.582684\pi$
$967$	−496.744			−0.513696			−0.256848	+	0.966452i	$0.582684\pi$
$968$	428.453	+	275.350i	0.442616	+	0.284452i
$969$	−16.2876	−	113.283i	−0.0168087	−	0.116907i
$970$	−262.266	−	574.282i	−0.270377	−	0.592043i
$971$	46.1912	−	157.313i	0.0475707	−	0.162011i	−0.932282	−	0.361732i	$-0.882185\pi$
$971$	46.1912	−	157.313i	0.0475707	−	0.162011i	0.979853	+	0.199721i	$0.0640037\pi$
$972$	−5029.76	+	11013.6i	−5.17465	+	11.3309i
$973$	416.253	+	360.685i	0.427803	+	0.370694i
$974$	−47.2451	+	328.597i	−0.0485063	+	0.337369i
$975$	145.452	−	42.7085i	0.149181	−	0.0438036i
$976$	−1257.62	+	1089.73i	−1.28854	+	1.11653i
$977$	−187.509	−	291.770i	−0.191923	−	0.298639i	0.731934	−	0.681376i	$-0.238618\pi$
$977$	−187.509	−	291.770i	−0.191923	−	0.298639i	−0.923857	+	0.382737i	$0.874982\pi$
$978$	1145.39	−	736.099i	1.17116	−	0.752658i
$979$	−372.711	−	430.131i	−0.380705	−	0.439357i
$980$	74.8539	+	254.929i	0.0763815	+	0.260132i
$981$	−1097.91	−	157.856i	−1.11918	−	0.160913i
$982$	−1105.81	+	1276.17i	−1.12607	+	1.29956i
$983$	−430.800	−	196.740i	−0.438251	−	0.200142i	0.184056	−	0.982916i	$-0.441077\pi$
$983$	−430.800	−	196.740i	−0.438251	−	0.200142i	−0.622307	+	0.782773i	$0.713804\pi$
$984$	−102.396	−	30.0663i	−0.104061	−	0.0305552i
$985$	605.357	−	276.457i	0.614575	−	0.280667i
$986$	−430.917	+	61.9565i	−0.437035	+	0.0628362i
$987$	−792.348	+	1232.92i	−0.802784	+	1.24916i
$988$		−	63.2381i		−	0.0640061i
$989$	294.453	−	246.754i	0.297728	−	0.249499i
$990$	2627.98			2.65452
$991$	751.623	+	483.039i	0.758449	+	0.487425i	0.861818	−	0.507218i	$-0.169326\pi$
$991$	751.623	+	483.039i	0.758449	+	0.487425i	−0.103369	+	0.994643i	$0.532962\pi$
$992$	31.7838	+	221.061i	0.0320402	+	0.222844i
$993$	−842.319	−	1844.42i	−0.848256	−	1.85742i
$994$	165.556	−	563.831i	0.166555	−	0.567235i
$995$	53.6403	−	117.456i	0.0539099	−	0.118046i
$996$	−4559.00	−	3950.40i	−4.57731	−	3.96626i
$997$	−44.2422	+	307.711i	−0.0443753	+	0.308637i	0.955530	+	0.294893i	$0.0952841\pi$
$997$	−44.2422	+	307.711i	−0.0443753	+	0.308637i	−0.999906	+	0.0137440i	$0.995625\pi$
$998$	−824.266	+	242.026i	−0.825918	+	0.242511i
$999$	3615.58	−	3132.92i	3.61920	−	3.13605i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.3.h.a.21.2	yes	160
23.11	odd	22	inner	115.3.h.a.11.2	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.3.h.a.11.2	✓	160	23.11	odd	22	inner
115.3.h.a.21.2	yes	160	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	115.h (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.96935 - 1.90828i) q^{2} +(0.852548 + 5.92960i) q^{3} +(3.51382 + 7.69420i) q^{4} +(-0.629973 + 2.14549i) q^{5} +(8.78386 - 19.2340i) q^{6} +(4.46805 + 3.87159i) q^{7} +(2.23966 - 15.5772i) q^{8} +(-25.7979 + 7.57495i) q^{9} +(5.96482 - 5.16855i) q^{10} +(-6.69528 - 10.4181i) q^{11} +(-42.6278 + 27.3952i) q^{12} +(3.31427 + 3.82487i) q^{13} +(-5.87911 - 20.0224i) q^{14} +(-13.2590 - 1.90636i) q^{15} +(-14.2192 + 16.4098i) q^{16} +(11.7642 + 5.37252i) q^{17} +(91.0581 + 26.7371i) q^{18} +(-1.34372 + 0.613655i) q^{19} +(-18.7215 + 2.69174i) q^{20} +(-19.1477 + 29.7945i) q^{21} +43.7113i q^{22} +(-19.5514 + 12.1137i) q^{23} +94.2758 q^{24} +(-4.20627 - 2.70320i) q^{25} +(-2.54228 - 17.6819i) q^{26} +(-44.5132 - 97.4703i) q^{27} +(-14.0888 + 47.9821i) q^{28} +(3.96176 - 8.67505i) q^{29} +(35.7327 + 30.9626i) q^{30} +(-2.32142 + 16.1459i) q^{31} +(13.1369 - 3.85735i) q^{32} +(56.0669 - 48.5822i) q^{33} +(-24.6797 - 38.4023i) q^{34} +(-11.1212 + 7.14717i) q^{35} +(-148.932 - 171.877i) q^{36} +(12.5785 + 42.8386i) q^{37} +(5.16100 + 0.742039i) q^{38} +(-19.8544 + 22.9132i) q^{39} +(32.0097 + 14.6184i) q^{40} +(-1.08614 - 0.318919i) q^{41} +(113.713 - 51.9308i) q^{42} +(-16.5332 + 2.37712i) q^{43} +(56.6326 - 88.1220i) q^{44} -60.1212i q^{45} +(81.1714 + 1.34004i) q^{46} +41.3808 q^{47} +(-109.426 - 70.3240i) q^{48} +(-1.99915 - 13.9044i) q^{49} +(7.33139 + 16.0535i) q^{50} +(-21.8274 + 74.3372i) q^{51} +(-17.7835 + 38.9405i) q^{52} +(6.69979 + 5.80540i) q^{53} +(-53.8259 + 374.367i) q^{54} +(26.5697 - 7.80157i) q^{55} +(70.3152 - 60.9285i) q^{56} +(-4.78432 - 7.44454i) q^{57} +(-28.3183 + 18.1991i) q^{58} +(22.2450 + 25.6721i) q^{59} +(-31.9219 - 108.716i) q^{60} +(75.8579 + 10.9067i) q^{61} +(37.7040 - 43.5127i) q^{62} +(-144.593 - 66.0336i) q^{63} +(36.9661 + 10.8542i) q^{64} +(-10.2941 + 4.70117i) q^{65} +(-259.191 + 37.2660i) q^{66} +(-32.1599 + 50.0417i) q^{67} +109.394i q^{68} +(-88.4977 - 105.605i) q^{69} +46.6616 q^{70} +(23.6897 + 15.2245i) q^{71} +(60.2177 + 418.823i) q^{72} +(35.2466 + 77.1794i) q^{73} +(44.3982 - 151.206i) q^{74} +(12.4429 - 27.2461i) q^{75} +(-9.44318 - 8.18256i) q^{76} +(10.4196 - 72.4697i) q^{77} +(102.679 - 30.1494i) q^{78} +(-27.6983 + 24.0007i) q^{79} +(-26.2494 - 40.8449i) q^{80} +(336.441 - 216.218i) q^{81} +(2.61653 + 3.01964i) q^{82} +(33.5400 + 114.227i) q^{83} +(-296.526 - 42.6341i) q^{84} +(-18.9378 + 21.8554i) q^{85} +(53.6292 + 24.4916i) q^{86} +(54.8172 + 16.0958i) q^{87} +(-177.279 + 80.9606i) q^{88} +(45.4904 - 6.54053i) q^{89} +(-114.728 + 178.521i) q^{90} +29.9212i q^{91} +(-161.905 - 107.867i) q^{92} -97.7176 q^{93} +(-122.874 - 78.9663i) q^{94} +(-0.470086 - 3.26952i) q^{95} +(34.0724 + 74.6082i) q^{96} +(22.5360 - 76.7506i) q^{97} +(-20.5973 + 45.1019i) q^{98} +(251.640 + 218.048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 4 q^{2} - 16 q^{4} - 26 q^{6} - 22 q^{8} - 32 q^{9} + 30 q^{12} + 12 q^{13} - 256 q^{16} - 110 q^{17} + 70 q^{18} - 66 q^{19} - 66 q^{21} - 34 q^{23} + 180 q^{24} + 80 q^{25} + 238 q^{26} + 234 q^{27}+ \cdots + 2112 q^{99}+O(q^{100}) \) 160 * q + 4 * q^2 - 16 * q^4 - 26 * q^6 - 22 * q^8 - 32 * q^9 + 30 * q^12 + 12 * q^13 - 256 * q^16 - 110 * q^17 + 70 * q^18 - 66 * q^19 - 66 * q^21 - 34 * q^23 + 180 * q^24 + 80 * q^25 + 238 * q^26 + 234 * q^27 + 128 * q^29 + 188 * q^31 + 496 * q^32 - 242 * q^34 - 170 * q^35 - 736 * q^36 - 770 * q^38 - 188 * q^39 - 440 * q^40 - 234 * q^41 - 176 * q^43 - 22 * q^44 + 80 * q^46 - 224 * q^47 + 754 * q^48 + 518 * q^49 + 90 * q^50 + 528 * q^51 - 82 * q^52 + 352 * q^53 + 510 * q^54 + 400 * q^55 + 418 * q^56 - 726 * q^57 + 376 * q^58 - 62 * q^59 + 330 * q^60 - 308 * q^61 - 662 * q^62 - 550 * q^63 - 206 * q^64 - 176 * q^66 - 44 * q^67 - 280 * q^69 - 120 * q^70 - 18 * q^71 + 1126 * q^72 + 52 * q^73 + 154 * q^74 + 704 * q^76 - 726 * q^77 - 1434 * q^78 - 572 * q^79 + 476 * q^81 + 46 * q^82 + 286 * q^83 - 1100 * q^84 - 130 * q^85 + 396 * q^86 - 1012 * q^87 - 528 * q^88 - 264 * q^89 + 350 * q^92 + 604 * q^93 + 444 * q^94 - 80 * q^95 - 394 * q^96 + 792 * q^97 + 540 * q^98 + 2112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more