LMFDB - Embedded newform 115.3.h.a.11.2

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			11.2
Character	$\chi$	$=$	115.11
Dual form			115.3.h.a.21.2

$q$-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 $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{9}{22}\right)$

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	−0.487984	+	0.872853i	$0.662268\pi$
$2$	−2.96935	+	1.90828i	−1.48467	+	0.954142i	−0.996691	+	0.0812899i	$0.974096\pi$
$3$	0.852548	−	5.92960i	0.284183	−	1.97653i	0.0866400	−	0.996240i	$-0.472387\pi$
$3$	0.852548	−	5.92960i	0.284183	−	1.97653i	0.197543	−	0.980294i	$-0.436704\pi$
$4$	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	−0.274459	−	0.961599i	$-0.588499\pi$
$7$	4.46805	−	3.87159i	0.638293	−	0.553084i	0.912752	+	0.408515i	$0.133953\pi$
$8$	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	0.390982	+	0.920398i	$0.372136\pi$
$11$	−6.69528	+	10.4181i	−0.608662	+	0.947096i	−0.999644	+	0.0266977i	$0.991501\pi$
$12$	−42.6278	−	27.3952i	−3.55232	−	2.28294i
$13$	3.31427	−	3.82487i	0.254944	−	0.294220i	−0.613822	−	0.789445i	$-0.710369\pi$
$13$	3.31427	−	3.82487i	0.254944	−	0.294220i	0.868765	+	0.495224i	$0.164914\pi$
$14$	−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	−0.0381832	−	0.999271i	$-0.512157\pi$
$17$	11.7642	−	5.37252i	0.692011	−	0.316031i	0.730194	+	0.683240i	$0.239430\pi$
$18$	91.0581	−	26.7371i	5.05879	−	1.48539i
$19$	−1.34372	−	0.613655i	−0.0707220	−	0.0322977i	0.379740	−	0.925093i	$-0.376013\pi$
$19$	−1.34372	−	0.613655i	−0.0707220	−	0.0322977i	−0.450462	+	0.892796i	$0.648741\pi$
$20$	−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	0.965557	−	0.260191i	$-0.0837855\pi$
$29$	3.96176	+	8.67505i	0.136613	+	0.299140i	−0.828945	+	0.559331i	$0.811058\pi$
$30$	35.7327	−	30.9626i	1.19109	−	1.03209i
$31$	−2.32142	−	16.1459i	−0.0748846	−	0.520834i	−0.992392	−	0.123116i	$-0.960711\pi$
$31$	−2.32142	−	16.1459i	−0.0748846	−	0.520834i	0.917508	−	0.397718i	$-0.130198\pi$
$32$	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	−0.595200	−	0.803577i	$-0.702927\pi$
$37$	12.5785	−	42.8386i	0.339961	−	1.15780i	0.935161	−	0.354223i	$-0.115255\pi$
$38$	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	−0.294951	−	0.955512i	$-0.595303\pi$
$41$	−1.08614	+	0.318919i	−0.0264911	+	0.00777850i	0.268460	+	0.963291i	$0.413485\pi$
$42$	113.713	+	51.9308i	2.70744	+	1.23645i
$43$	−16.5332	−	2.37712i	−0.384494	−	0.0552819i	−0.0526421	−	0.998613i	$-0.516764\pi$
$43$	−16.5332	−	2.37712i	−0.384494	−	0.0552819i	−0.331852	+	0.943332i	$0.607673\pi$
$44$	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	−0.589361	−	0.807870i	$-0.700620\pi$
$53$	6.69979	−	5.80540i	0.126411	−	0.109536i	0.715772	+	0.698334i	$0.246075\pi$
$54$	−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	−0.535241	−	0.844700i	$-0.679779\pi$
$59$	22.2450	−	25.6721i	0.377034	−	0.435120i	0.912275	+	0.409579i	$0.134324\pi$
$60$	−31.9219	+	108.716i	−0.532031	+	1.81193i
$61$	75.8579	−	10.9067i	1.24357	−	0.178799i	0.511056	−	0.859548i	$-0.329255\pi$
$61$	75.8579	−	10.9067i	1.24357	−	0.178799i	0.732517	+	0.680749i	$0.238346\pi$
$62$	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	0.513822	−	0.857897i	$-0.328229\pi$
$67$	−32.1599	−	50.0417i	−0.479998	−	0.746892i	−0.993820	+	0.111005i	$0.964593\pi$
$68$		−	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	−0.363074	−	0.931760i	$-0.618273\pi$
$71$	23.6897	−	15.2245i	0.333658	−	0.214429i	0.696732	+	0.717331i	$0.254637\pi$
$72$	60.2177	−	418.823i	0.836357	−	5.81699i
$73$	35.2466	−	77.1794i	0.482831	−	1.05725i	−0.498845	−	0.866691i	$-0.666242\pi$
$73$	35.2466	−	77.1794i	0.482831	−	1.05725i	0.981675	−	0.190560i	$-0.0610305\pi$
$74$	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	0.461694	−	0.887039i	$-0.347242\pi$
$79$	−27.6983	−	24.0007i	−0.350611	−	0.303806i	−0.812305	+	0.583233i	$0.801787\pi$
$80$	−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	−0.466628	−	0.884454i	$-0.654531\pi$
$83$	33.5400	−	114.227i	0.404096	−	1.37622i	0.870724	−	0.491771i	$-0.163650\pi$
$84$	−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	0.393053	−	0.919516i	$-0.371419\pi$
$89$	45.4904	+	6.54053i	0.511128	+	0.0734891i	0.118075	+	0.993005i	$0.462328\pi$
$90$	−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	0.990299	+	0.138953i	$0.0443736\pi$
$97$	22.5360	+	76.7506i	0.232330	+	0.791243i	−0.757969	+	0.652291i	$0.773808\pi$
$98$	−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	−0.332690	−	0.943036i	$-0.607956\pi$
$101$	−113.363	−	33.2865i	−1.12241	−	0.329570i	−0.789721	+	0.613467i	$0.789774\pi$
$102$	206.670	+	179.080i	2.02617	+	1.75569i
$103$	−95.6429	+	148.823i	−0.928571	+	1.44489i	−0.0332590	+	0.999447i	$0.510589\pi$
$103$	−95.6429	+	148.823i	−0.928571	+	1.44489i	−0.895312	+	0.445439i	$0.853048\pi$
$104$	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	−0.198089	−	0.980184i	$-0.563474\pi$
$107$	−11.9846	+	1.72312i	−0.112005	+	0.0161039i	0.0860843	+	0.996288i	$0.472565\pi$
$108$	593.544	+	684.987i	5.49578	+	6.34247i
$109$	37.5261	−	17.1376i	0.344276	−	0.157226i	−0.235771	−	0.971809i	$-0.575761\pi$
$109$	37.5261	−	17.1376i	0.344276	−	0.157226i	0.580047	+	0.814583i	$0.303034\pi$
$110$	−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	−0.978879	−	0.204438i	$-0.934463\pi$
$113$	−85.6768	−	133.316i	−0.758202	−	1.17979i	0.220678	−	0.975347i	$-0.429173\pi$
$114$		−	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	0.732769	−	0.680478i	$-0.238228\pi$
$127$	53.1099	+	34.1316i	0.418188	+	0.268753i	−0.314581	+	0.949231i	$0.601864\pi$
$128$	−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	0.473922	−	0.880567i	$-0.342838\pi$
$131$	−60.9317	−	70.3190i	−0.465128	−	0.536786i	−0.939050	+	0.343781i	$0.888292\pi$
$132$	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	$-0.679145\pi$
$137$		−	231.740i		−	1.69153i	0.533556	−	0.845765i	$-0.320855\pi$
$138$	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	−0.336907	−	0.941538i	$-0.609381\pi$
$149$	98.2658	−	152.905i	0.659502	−	1.02621i	0.996409	−	0.0846676i	$-0.0269828\pi$
$150$	−88.9406	−	57.1586i	−0.592937	−	0.381058i
$151$	−50.2711	+	58.0159i	−0.332921	+	0.384212i	−0.897387	−	0.441245i	$-0.854537\pi$
$151$	−50.2711	+	58.0159i	−0.332921	+	0.384212i	0.564465	+	0.825457i	$0.309082\pi$
$152$	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	0.631010	−	0.775775i	$-0.282641\pi$
$157$	71.8968	+	32.8342i	0.457942	+	0.209135i	−0.173068	+	0.984910i	$0.555368\pi$
$158$	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	−0.363827	−	0.931467i	$-0.618530\pi$
$163$	54.1691	−	34.8123i	0.332326	−	0.213573i	0.696153	+	0.717894i	$0.254894\pi$
$164$	−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	0.955853	−	0.293844i	$-0.0949348\pi$
$167$	18.0076	+	39.4310i	0.107830	+	0.236114i	−0.848024	+	0.529959i	$0.822207\pi$
$168$	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	0.961055	−	0.276359i	$-0.0891278\pi$
$173$	191.841	+	123.289i	1.10891	+	0.712651i	0.147852	+	0.989010i	$0.452764\pi$
$174$	−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	0.419059	−	0.907959i	$-0.362360\pi$
$179$	225.983	−	66.3545i	1.26247	−	0.370696i	0.843414	+	0.537264i	$0.180542\pi$
$180$	462.585	+	211.255i	2.56991	+	1.17364i
$181$	129.749	+	18.6550i	0.716843	+	0.103066i	0.491078	−	0.871115i	$-0.336603\pi$
$181$	129.749	+	18.6550i	0.716843	+	0.103066i	0.225765	+	0.974182i	$0.427512\pi$
$182$	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	−0.211314	+	0.977418i	$0.567774\pi$
$191$	−230.892	+	200.069i	−1.20886	+	1.04748i	−0.997543	+	0.0700625i	$0.977680\pi$
$192$	−32.8458	−	228.448i	−0.171072	−	1.18983i
$193$	276.255	+	81.1157i	1.43137	+	0.420289i	0.903336	−	0.428934i	$-0.141111\pi$
$193$	276.255	+	81.1157i	1.43137	+	0.420289i	0.528036	+	0.849222i	$0.322929\pi$
$194$	−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	0.000567304		1.00000i	$0.499819\pi$
$197$	−194.899	+	224.925i	−0.989335	+	1.14175i	−0.989902	+	0.141753i	$0.954726\pi$
$198$	−331.111	+	1127.66i	−1.67228	+	5.69526i
$199$	−57.1585	+	8.21815i	−0.287229	+	0.0412973i	−0.284423	−	0.958699i	$-0.591802\pi$
$199$	−57.1585	+	8.21815i	−0.287229	+	0.0412973i	−0.00280545	+	0.999996i	$0.500893\pi$
$200$	−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	−0.778171	−	0.628052i	$-0.783852\pi$
$211$	43.4814	−	95.2109i	0.206073	−	0.451237i	0.984244	+	0.176816i	$0.0565797\pi$
$212$	−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	0.268127	−	0.963384i	$-0.413595\pi$
$223$	−161.365	−	186.225i	−0.723610	−	0.835090i	−0.991736	+	0.128294i	$0.959050\pi$
$224$	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	−0.146022	−	0.989281i	$-0.546647\pi$
$227$	−128.219	−	18.4351i	−0.564842	−	0.0812121i	−0.418820	+	0.908069i	$0.637556\pi$
$228$	40.4686	+	62.9703i	0.177494	+	0.276186i
$229$			377.761i			1.64961i	0.565415	+	0.824806i	$0.308716\pi$
$229$			377.761i			1.64961i	−0.565415	+	0.824806i	$0.691284\pi$
$230$	−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	0.634151	+	0.773209i	$0.281350\pi$
$233$	−44.7711	+	311.390i	−0.192151	+	1.33644i	−0.826302	+	0.563227i	$0.809559\pi$
$234$	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	0.602984	−	0.797753i	$-0.293978\pi$
$239$	162.269	+	47.6464i	0.678949	+	0.199357i	0.0759648	+	0.997110i	$0.475796\pi$
$240$	219.815	+	190.471i	0.915897	+	0.793629i
$241$	−178.481	+	277.721i	−0.740583	+	1.15237i	0.242667	+	0.970110i	$0.421978\pi$
$241$	−178.481	+	277.721i	−0.740583	+	1.15237i	−0.983250	+	0.182260i	$0.941659\pi$
$242$	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	0.666669	−	0.745353i	$-0.267719\pi$
$251$	−72.3564	−	112.589i	−0.288272	−	0.448561i	−0.954942	+	0.296793i	$0.904083\pi$
$252$			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	−0.789814	−	0.613346i	$-0.789823\pi$
$257$	49.0716	−	107.452i	0.190940	−	0.418101i	0.980754	+	0.195245i	$0.0625504\pi$
$258$	−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	0.462076	−	0.886840i	$-0.347105\pi$
$263$	−92.0439	−	79.7565i	−0.349977	−	0.303257i	−0.812053	+	0.583584i	$0.801650\pi$
$264$	−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	0.747545	−	0.664211i	$-0.231232\pi$
$269$	−4.38250	−	5.05767i	−0.0162918	−	0.0188018i	−0.763837	+	0.645409i	$0.776687\pi$
$270$	−769.293	+	351.324i	−2.84923	+	1.30120i
$271$	−68.2929	+	20.0526i	−0.252003	+	0.0739948i	−0.405294	−	0.914186i	$-0.632831\pi$
$271$	−68.2929	+	20.0526i	−0.252003	+	0.0739948i	0.153291	+	0.988181i	$0.451013\pi$
$272$	−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	0.893675	+	0.448716i	$0.148118\pi$
$281$	108.034	+	367.929i	0.384462	+	1.30936i	−0.509213	+	0.860641i	$0.670063\pi$
$282$	363.483	+	795.916i	1.28895	+	2.82240i
$283$	17.8724	−	15.4865i	0.0631534	−	0.0547227i	−0.622712	−	0.782451i	$-0.713969\pi$
$283$	17.8724	−	15.4865i	0.0631534	−	0.0547227i	0.685866	+	0.727728i	$0.259424\pi$
$284$	−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	0.554728	−	0.832032i	$-0.312822\pi$
$293$	453.214	−	206.976i	1.54681	−	0.706402i	0.992077	+	0.125629i	$0.0400949\pi$
$294$	−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	−0.999279	−	0.0379756i	$-0.987909\pi$
$307$	−15.7113	−	109.274i	−0.0511768	−	0.355942i	0.948102	−	0.317967i	$-0.103000\pi$
$308$	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	0.562416	−	0.826854i	$-0.309872\pi$
$311$	13.6590	+	8.77809i	0.0439196	+	0.0282254i	−0.518497	+	0.855080i	$0.673508\pi$
$312$	312.455	−	360.592i	1.00146	−	1.15574i
$313$	−96.2499	+	327.797i	−0.307508	+	1.04727i	0.650255	+	0.759716i	$0.274662\pi$
$313$	−96.2499	+	327.797i	−0.307508	+	1.04727i	−0.957763	+	0.287559i	$0.907156\pi$
$314$	−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	−0.147525	−	0.989058i	$-0.547131\pi$
$317$	83.4009	−	24.4887i	0.263094	−	0.0772514i	0.410619	+	0.911807i	$0.365313\pi$
$318$	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	−0.248456	−	0.968643i	$-0.579923\pi$
$331$	−324.764	−	95.3592i	−0.981159	−	0.288094i	−0.732703	+	0.680549i	$0.761741\pi$
$332$	−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	−0.608347	−	0.793671i	$-0.708167\pi$
$337$	−326.367	+	46.9245i	−0.968449	+	0.139242i	−0.360102	+	0.932913i	$0.617258\pi$
$338$	−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	−0.421621	−	0.906772i	$-0.638539\pi$
$347$	79.1367	−	50.8580i	0.228060	−	0.146565i	0.649681	+	0.760207i	$0.274903\pi$
$348$	68.7738	−	478.332i	0.197626	−	1.37452i
$349$	131.562	−	288.080i	0.376967	−	0.825444i	−0.622128	−	0.782916i	$-0.713732\pi$
$349$	131.562	−	288.080i	0.376967	−	0.825444i	0.999095	−	0.0425279i	$-0.0135411\pi$
$350$	−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	−0.925583	−	0.378544i	$-0.876425\pi$
$353$	−50.8817	−	353.890i	−0.144141	−	1.00252i	0.781442	−	0.623977i	$-0.214484\pi$
$354$	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	0.827897	+	0.560880i	$0.189537\pi$
$359$	−61.6795	+	210.061i	−0.171809	+	0.585128i	−0.999706	+	0.0242478i	$0.992281\pi$
$360$	−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	$0.196202\pi$
$367$			424.319i			1.15618i	−0.815972	+	0.578091i	$0.803798\pi$
$368$	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	−0.812737	−	0.582630i	$-0.802024\pi$
$373$	−165.617	−	564.039i	−0.444013	−	1.51217i	0.368724	−	0.929539i	$-0.379795\pi$
$374$	−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	−0.533888	−	0.845555i	$-0.679269\pi$
$379$	173.219	−	269.534i	0.457042	−	0.711171i	0.990929	+	0.134385i	$0.0429058\pi$
$380$	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	0.115748	−	0.993279i	$-0.463073\pi$
$383$	194.046	−	27.8996i	0.506647	−	0.0728448i	0.390899	+	0.920434i	$0.372164\pi$
$384$	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	0.993569	+	0.113225i	$0.0361181\pi$
$389$	266.006	+	413.913i	0.683819	+	1.06404i	−0.309751	+	0.950818i	$0.600246\pi$
$390$		−	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	0.999935	−	0.0114179i	$-0.00363451\pi$
$397$	133.586	+	292.512i	0.336488	+	0.736805i	−0.663447	+	0.748223i	$0.730907\pi$
$398$	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	0.945217	−	0.326442i	$-0.105850\pi$
$401$	303.403	+	262.900i	0.756617	+	0.655612i	−0.188601	+	0.982054i	$0.560395\pi$
$402$	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	0.412148	−	0.911117i	$-0.364779\pi$
$409$	511.845	−	150.291i	1.25146	−	0.367461i	0.839308	+	0.543656i	$0.182960\pi$
$410$	−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	−0.997160	−	0.0753126i	$-0.976005\pi$
$419$	−83.3863	−	283.988i	−0.199013	−	0.677775i	0.798147	−	0.602462i	$-0.205814\pi$
$420$	278.275	+	609.336i	0.662559	+	1.45080i
$421$	−108.092	+	93.6623i	−0.256751	+	0.222476i	−0.773719	−	0.633529i	$-0.781606\pi$
$421$	−108.092	+	93.6623i	−0.256751	+	0.222476i	0.516969	+	0.856004i	$0.327060\pi$
$422$	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	−0.309778	−	0.950809i	$-0.600255\pi$
$431$	88.7576	−	40.5342i	0.205934	−	0.0940469i	0.515712	+	0.856762i	$0.327527\pi$
$432$	2232.41	−	655.496i	5.16762	−	1.51735i
$433$	175.599	+	80.1936i	0.405541	+	0.185205i	0.607733	−	0.794141i	$-0.292079\pi$
$433$	175.599	+	80.1936i	0.405541	+	0.185205i	−0.202192	+	0.979346i	$0.564806\pi$
$434$	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	−0.0880126	−	0.996119i	$-0.528052\pi$
$439$	343.091	−	220.491i	0.781528	−	0.502257i	0.869540	+	0.493862i	$0.164415\pi$
$440$	−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	0.925380	−	0.379041i	$-0.123746\pi$
$443$	14.5857	+	31.9381i	0.0329247	+	0.0720951i	−0.892455	+	0.451136i	$0.851019\pi$
$444$	−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	0.868325	−	0.495996i	$-0.165197\pi$
$449$	349.262	+	224.457i	0.777867	+	0.499905i	−0.0904582	+	0.995900i	$0.528833\pi$
$450$	−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	0.832004	−	0.554770i	$-0.187194\pi$
$457$	673.622	+	96.8522i	1.47401	+	0.211931i	0.642005	+	0.766700i	$0.278103\pi$
$458$	−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	0.868738	+	0.495271i	$0.164931\pi$
$463$	−48.3113	+	336.013i	−0.104344	+	0.725729i	−0.973082	+	0.230458i	$0.925978\pi$
$464$	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	−0.327905	+	0.944711i	$0.606343\pi$
$467$	−611.614	+	529.966i	−1.30967	+	1.13483i	−0.981761	+	0.190121i	$0.939112\pi$
$468$	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	0.371393	−	0.928476i	$-0.378880\pi$
$479$	−41.7167	−	19.0514i	−0.0870912	−	0.0397732i	−0.458484	+	0.888702i	$0.651607\pi$
$480$	−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	−0.945495	−	0.325636i	$-0.894421\pi$
$487$	−39.0710	+	85.5536i	−0.0802279	+	0.175675i	0.865267	+	0.501311i	$0.167149\pi$
$488$	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	0.933748	+	0.357931i	$0.116518\pi$
$491$	68.0841	+	473.535i	0.138664	+	0.964430i	−0.795084	+	0.606499i	$0.792573\pi$
$492$	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	0.892633	−	0.450783i	$-0.148855\pi$
$499$	159.382	+	183.937i	0.319403	+	0.368611i	−0.573230	+	0.819394i	$0.694310\pi$
$500$	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	−0.539786	−	0.841802i	$-0.681495\pi$
$503$	−651.320	−	93.6456i	−1.29487	−	0.186174i	−0.755084	+	0.655628i	$0.772404\pi$
$504$	−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	−0.937540	−	0.347879i	$-0.886902\pi$
$509$	30.5562	−	212.523i	0.0600318	−	0.417531i	0.997571	−	0.0696518i	$-0.0221888\pi$
$510$	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	−0.0863976	−	0.996261i	$-0.527536\pi$
$521$	58.0308	−	8.34357i	0.111384	−	0.0160145i	0.197781	+	0.980246i	$0.436626\pi$
$522$	592.697	+	684.008i	1.13543	+	1.31036i
$523$	−30.9784	+	14.1473i	−0.0592321	+	0.0270504i	−0.444811	−	0.895625i	$-0.646729\pi$
$523$	−30.9784	+	14.1473i	−0.0592321	+	0.0270504i	0.385579	+	0.922675i	$0.374002\pi$
$524$	−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	0.230125	−	0.973161i	$-0.426086\pi$
$541$	−302.687	−	194.525i	−0.559496	−	0.359566i	−0.789621	+	0.613595i	$0.789723\pi$
$542$	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	−0.610171	−	0.792270i	$-0.708899\pi$
$547$	−380.245	+	111.650i	−0.695146	+	0.204113i	−0.0849751	+	0.996383i	$0.527081\pi$
$548$	−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	0.936370	−	0.351014i	$-0.114163\pi$
$557$	−22.9077	−	78.0166i	−0.0411270	−	0.140066i	−0.977497	+	0.210948i	$0.932345\pi$
$558$	−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	−0.124642	−	0.992202i	$-0.539778\pi$
$563$	467.107	−	726.833i	0.829675	−	1.29100i	0.954317	−	0.298798i	$-0.0965855\pi$
$564$	−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	−0.339413	−	0.940638i	$-0.610228\pi$
$569$	84.8981	−	38.7717i	0.149206	−	0.0681400i	0.488618	+	0.872498i	$0.337501\pi$
$570$	−67.0150	+	19.6774i	−0.117570	+	0.0345217i
$571$	−248.296	−	113.393i	−0.434845	−	0.198587i	0.185951	−	0.982559i	$-0.440463\pi$
$571$	−248.296	−	113.393i	−0.434845	−	0.198587i	−0.620796	+	0.783972i	$0.713191\pi$
$572$	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	−0.648897	−	0.760876i	$-0.724769\pi$
$577$	−130.599	+	83.9307i	−0.226341	+	0.145460i	0.422556	+	0.906337i	$0.361133\pi$
$578$	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	0.998686	−	0.0512496i	$-0.0163204\pi$
$587$	802.392	+	515.666i	1.36694	+	0.878477i	0.368251	+	0.929726i	$0.379957\pi$
$588$	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	0.726907	−	0.686736i	$-0.240957\pi$
$593$	1013.85	−	297.693i	1.70970	−	0.502012i	0.982791	+	0.184724i	$0.0591390\pi$
$594$	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	−0.775459	−	0.631398i	$-0.782482\pi$
$601$	88.0307	−	612.267i	0.146474	−	1.01875i	0.921933	−	0.387349i	$-0.126609\pi$
$602$	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	−0.999882	−	0.0153381i	$-0.995118\pi$
$607$	−1122.54	−	329.608i	−1.84933	−	0.543012i	−0.849447	−	0.527674i	$-0.823064\pi$
$608$	−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	−0.892457	−	0.451132i	$-0.851020\pi$
$613$	−994.081	+	142.927i	−1.62167	+	0.233160i	−0.729208	+	0.684292i	$0.760111\pi$
$614$	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	0.0421315	−	0.999112i	$-0.486585\pi$
$617$	−422.865	−	193.116i	−0.685357	−	0.312992i	−0.727488	+	0.686120i	$0.759312\pi$
$618$	−3702.57	−	532.350i	−5.99122	−	0.861407i
$619$	75.9907	+	118.244i	0.122764	+	0.191024i	0.897196	−	0.441633i	$-0.145601\pi$
$619$	75.9907	+	118.244i	0.122764	+	0.191024i	−0.774432	+	0.632657i	$0.781964\pi$
$620$			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	0.240288	−	0.970702i	$-0.422758\pi$
$631$	−433.078	−	375.265i	−0.686337	−	0.594714i	−0.926625	+	0.375987i	$0.877304\pi$
$632$	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	0.450347	−	0.892854i	$-0.351300\pi$
$641$	404.411	+	58.1455i	0.630906	+	0.0907106i	0.180559	+	0.983564i	$0.442209\pi$
$642$	−138.413	−	215.375i	−0.215597	−	0.335475i
$643$			1082.69i			1.68381i	0.539628	+	0.841904i	$0.318565\pi$
$643$			1082.69i			1.68381i	−0.539628	+	0.841904i	$0.681435\pi$
$644$	−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	0.950460	+	0.310847i	$0.100613\pi$
$647$	−31.7518	+	220.838i	−0.0490754	+	0.341327i	−0.999535	+	0.0304799i	$0.990296\pi$
$648$	−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	0.699701	−	0.714435i	$-0.253316\pi$
$653$	589.055	+	172.962i	0.902075	+	0.264873i	0.202373	+	0.979308i	$0.435135\pi$
$654$	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	−0.789232	−	0.614096i	$-0.789521\pi$
$659$	−905.125	+	130.137i	−1.37348	+	0.197477i	−0.584252	+	0.811573i	$0.698612\pi$
$660$	−918.883	−	1060.45i	−1.39225	−	1.60674i
$661$	378.304	−	172.766i	0.572321	−	0.261370i	−0.108163	−	0.994133i	$-0.534497\pi$
$661$	378.304	−	172.766i	0.572321	−	0.261370i	0.680484	+	0.732763i	$0.261770\pi$
$662$	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	−0.785508	−	0.618851i	$-0.787598\pi$
$673$	−497.217	−	1088.75i	−0.738806	−	1.61776i	0.0467018	−	0.998909i	$-0.485129\pi$
$674$	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	0.759338	−	0.650696i	$-0.225523\pi$
$677$	151.195	+	131.011i	0.223330	+	0.193517i	−0.536008	+	0.844213i	$0.680068\pi$
$678$	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	0.177799	−	0.984067i	$-0.443102\pi$
$683$	−561.122	−	647.569i	−0.821554	−	0.948124i	−0.999354	+	0.0359425i	$0.988557\pi$
$684$	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	−0.996259	−	0.0864191i	$-0.972458\pi$
$701$	−353.156	+	549.521i	−0.503788	+	0.783910i	0.492470	+	0.870329i	$0.336094\pi$
$702$	−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	−0.0822222	−	0.996614i	$-0.526202\pi$
$709$	−630.483	−	287.932i	−0.889257	−	0.406110i	−0.807035	+	0.590504i	$0.798929\pi$
$710$	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	0.751427	+	0.659816i	$0.229366\pi$
$719$	545.004	+	1193.39i	0.758003	+	1.65979i	0.00657577	+	0.999978i	$0.497907\pi$
$720$	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	−0.924430	−	0.381352i	$-0.875459\pi$
$727$	43.2016	−	147.131i	0.0594245	−	0.202381i	0.983854	+	0.178971i	$0.0572768\pi$
$728$	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	0.573677	−	0.819082i	$-0.305517\pi$
$733$	654.828	+	94.1501i	0.893353	+	0.128445i	0.319677	+	0.947527i	$0.396426\pi$
$734$	−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	−0.965469	−	0.260518i	$-0.916107\pi$
$739$	25.3389	−	176.236i	0.0342881	−	0.238479i	0.999757	+	0.0220390i	$0.00701581\pi$
$740$	−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	−0.748076	−	0.663613i	$-0.769022\pi$
$743$	−146.876	+	127.269i	−0.197680	+	0.171290i	0.550396	+	0.834904i	$0.314477\pi$
$744$	−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	0.398329	−	0.917242i	$-0.369590\pi$
$751$	780.244	−	112.182i	1.03894	−	0.149377i	0.640611	+	0.767865i	$0.278681\pi$
$752$	−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	0.937805	−	0.347162i	$-0.112854\pi$
$757$	175.955	+	273.792i	0.232438	+	0.361680i	−0.705368	+	0.708842i	$0.749218\pi$
$758$			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	−0.544522	−	0.838747i	$-0.683289\pi$
$761$	−5.91604	+	3.80201i	−0.00777403	+	0.00499607i	0.536748	+	0.843743i	$0.319653\pi$
$762$	−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	0.368617	−	0.929581i	$-0.379831\pi$
$769$	−383.764	−	332.533i	−0.499043	−	0.432423i	−0.867660	+	0.497158i	$0.834377\pi$
$770$	−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	−0.424821	−	0.905277i	$-0.639663\pi$
$773$	326.199	−	1110.93i	0.421991	−	1.43717i	0.846812	−	0.531892i	$-0.178519\pi$
$774$	−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	−0.832743	−	0.553659i	$-0.813231\pi$
$787$	−339.611	−	1156.61i	−0.431526	−	1.46964i	0.401217	−	0.915983i	$-0.368587\pi$
$788$	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	−0.447851	−	0.894108i	$-0.647811\pi$
$797$	−498.653	+	71.6954i	−0.625662	+	0.0899566i	−0.177811	+	0.984065i	$0.556901\pi$
$798$	−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	−0.936536	−	0.350572i	$-0.885987\pi$
$809$	−47.1570	+	103.260i	−0.0582905	+	0.127638i	0.878245	+	0.478211i	$0.158714\pi$
$810$	889.281	+	3028.61i	1.09788	+	3.73903i
$811$	−575.873	−	1260.99i	−0.710078	−	1.55485i	−0.827308	−	0.561749i	$-0.810129\pi$
$811$	−575.873	−	1260.99i	−0.710078	−	1.55485i	0.117230	−	0.993105i	$-0.462599\pi$
$812$	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	0.971602	−	0.236620i	$-0.0760396\pi$
$821$	491.875	+	567.654i	0.599117	+	0.691418i	−0.372485	+	0.928038i	$0.621494\pi$
$822$	4457.27	−	2035.57i	5.42247	−	2.47636i
$823$	−699.042	+	205.257i	−0.849383	+	0.249401i	−0.677324	−	0.735685i	$-0.736860\pi$
$823$	−699.042	+	205.257i	−0.849383	+	0.249401i	−0.172060	+	0.985087i	$0.555042\pi$
$824$	−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	$-0.666124\pi$
$827$		−	1433.81i		−	1.73375i	0.498523	−	0.866876i	$-0.333876\pi$
$828$	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	0.148975	+	0.988841i	$0.452403\pi$
$839$	−681.597	+	1060.59i	−0.812393	+	1.26411i	−0.961368	+	0.275267i	$0.911234\pi$
$840$	−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	−0.942194	−	0.335067i	$-0.891241\pi$
$853$	−877.573	+	563.982i	−1.02881	+	0.661175i	−0.0866137	+	0.996242i	$0.527605\pi$
$854$	−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	0.975034	+	0.222056i	$0.0712767\pi$
$857$	432.220	+	946.430i	0.504341	+	1.10435i	−0.470693	+	0.882297i	$0.655996\pi$
$858$	−1001.57	+	867.861i	−1.16733	+	1.01149i
$859$	−105.798	−	735.843i	−0.123164	−	0.856628i	−0.953935	−	0.300013i	$-0.903009\pi$
$859$	−105.798	−	735.843i	−0.123164	−	0.856628i	0.830771	−	0.556615i	$-0.187900\pi$
$860$	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	0.257432	−	0.966296i	$-0.417124\pi$
$863$	−444.101	−	285.406i	−0.514601	−	0.330714i	−0.772033	+	0.635582i	$0.780760\pi$
$864$	−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	0.720492	+	0.693464i	$0.243916\pi$
$877$	−145.745	+	1013.68i	−0.166186	+	1.15585i	−0.886678	+	0.462388i	$0.846993\pi$
$878$	−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	−0.608979	−	0.793187i	$-0.708420\pi$
$881$	78.8212	−	68.2990i	0.0894679	−	0.0775244i	0.698446	+	0.715662i	$0.253875\pi$
$882$	189.724	+	1319.56i	0.215106	+	1.49610i
$883$	270.329	+	79.3756i	0.306148	+	0.0898931i	0.431198	−	0.902257i	$-0.358091\pi$
$883$	270.329	+	79.3756i	0.306148	+	0.0898931i	−0.125050	+	0.992150i	$0.539909\pi$
$884$	−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	−0.932480	−	0.361223i	$-0.882359\pi$
$887$	−392.256	+	452.688i	−0.442228	+	0.510358i	0.490252	+	0.871581i	$0.336905\pi$
$888$	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	0.0564813	−	0.998404i	$-0.482012\pi$
$907$	−837.816	−	725.972i	−0.923722	−	0.800410i	−0.980203	+	0.197994i	$0.936557\pi$
$908$	−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	−0.991602	−	0.129330i	$-0.958717\pi$
$911$	−79.7054	+	271.452i	−0.0874922	+	0.297971i	0.904109	+	0.427301i	$0.140536\pi$
$912$	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	$0.0585787\pi$
$919$			336.342i			0.365987i	−0.983114	+	0.182993i	$0.941421\pi$
$920$	−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	0.268874	−	0.963175i	$-0.413349\pi$
$929$	−23.8449	−	7.00150i	−0.0256673	−	0.00753660i	−0.294541	+	0.955639i	$0.595167\pi$
$930$	−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	−0.843504	−	0.537122i	$-0.819511\pi$
$937$	−927.586	+	423.614i	−0.989953	+	0.452096i	−0.146448	+	0.989218i	$0.546784\pi$
$938$	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	0.901519	−	0.432740i	$-0.142453\pi$
$941$	125.510	+	195.298i	0.133380	+	0.207543i	−0.768139	+	0.640283i	$0.778817\pi$
$942$			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	−0.135538	+	0.990772i	$0.543276\pi$
$947$	−753.391	+	1649.70i	−0.795555	+	1.74202i	−0.660017	+	0.751250i	$0.729451\pi$
$948$	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	−0.923557	−	0.383460i	$-0.874732\pi$
$953$	−1367.13	−	1184.62i	−1.43455	−	1.24305i	−0.510993	−	0.859585i	$-0.670722\pi$
$954$	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	0.979853	−	0.199721i	$-0.0640037\pi$
$971$	46.1912	+	157.313i	0.0475707	+	0.162011i	−0.932282	+	0.361732i	$0.882185\pi$
$972$	−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	−0.923857	−	0.382737i	$-0.874982\pi$
$977$	−187.509	+	291.770i	−0.191923	+	0.298639i	0.731934	+	0.681376i	$0.238618\pi$
$978$	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	−0.622307	−	0.782773i	$-0.713804\pi$
$983$	−430.800	+	196.740i	−0.438251	+	0.200142i	0.184056	+	0.982916i	$0.441077\pi$
$984$	−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	−0.103369	−	0.994643i	$-0.532962\pi$
$991$	751.623	−	483.039i	0.758449	−	0.487425i	0.861818	+	0.507218i	$0.169326\pi$
$992$	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	−0.999906	−	0.0137440i	$-0.995625\pi$
$997$	−44.2422	−	307.711i	−0.0443753	−	0.308637i	0.955530	−	0.294893i	$-0.0952841\pi$
$998$	−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.11.2	✓	160
23.21	odd	22	inner	115.3.h.a.21.2	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.3.h.a.11.2	✓	160	1.1	even	1	trivial
115.3.h.a.21.2	yes	160	23.21	odd	22	inner

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

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