LMFDB - Embedded newform 70.3.l.a.23.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [70,3,Mod(23,70)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(70, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 4])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("70.23"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	70.l (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,4,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.90736185052$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.3317760000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 25x^{4} + 625 $ x^8 - 25*x^4 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.2
Root			$-0.578737 + 2.15988i$ of defining polynomial
Character	$\chi$	$=$	70.23
Dual form			70.3.l.a.67.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.366025 - 1.36603i) q^{2} +(1.36843 - 5.10704i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(4.96410 - 0.598076i) q^{5} -7.47723 q^{6} +(-2.80041 + 6.41543i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-16.4150 - 9.47723i) q^{9} +(-2.63397 - 6.56218i) q^{10} +(-1.73861 - 3.01137i) q^{11} +(2.73685 + 10.2141i) q^{12} +(10.9545 + 10.9545i) q^{13} +(9.78866 + 1.47723i) q^{14} +(3.73861 - 26.1703i) q^{15} +(2.00000 - 3.46410i) q^{16} +(9.49996 + 2.54551i) q^{17} +(-6.93781 + 25.8923i) q^{18} +(-15.9623 - 9.21584i) q^{19} +(-8.00000 + 6.00000i) q^{20} +(28.9317 + 23.0809i) q^{21} +(-3.47723 + 3.47723i) q^{22} +(17.3390 - 4.64598i) q^{23} +(12.9509 - 7.47723i) q^{24} +(24.2846 - 5.93782i) q^{25} +(10.9545 - 18.9737i) q^{26} +(-37.2158 + 37.2158i) q^{27} +(-1.56497 - 13.9123i) q^{28} +49.8634i q^{29} +(-37.1177 + 4.47195i) q^{30} +(-8.00000 - 13.8564i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-17.7583 + 4.75833i) q^{33} -13.9089i q^{34} +(-10.0646 + 33.5217i) q^{35} +37.9089 q^{36} +(-9.16731 - 34.2129i) q^{37} +(-6.74646 + 25.1781i) q^{38} +(70.9352 - 40.9545i) q^{39} +(11.1244 + 8.73205i) q^{40} -6.04555 q^{41} +(20.9393 - 47.9696i) q^{42} +(-9.64752 - 9.64752i) q^{43} +(6.02273 + 3.47723i) q^{44} +(-87.1540 - 37.2285i) q^{45} +(-12.6931 - 21.9850i) q^{46} +(5.44036 + 20.3037i) q^{47} +(-14.9545 - 14.9545i) q^{48} +(-33.3154 - 35.9317i) q^{49} +(-17.0000 - 31.0000i) q^{50} +(26.0000 - 45.0333i) q^{51} +(-29.9281 - 8.01921i) q^{52} +(-2.94488 + 10.9904i) q^{53} +(64.4597 + 37.2158i) q^{54} +(-10.4317 - 13.9089i) q^{55} +(-18.4317 + 7.23003i) q^{56} +(-68.9089 + 68.9089i) q^{57} +(68.1146 - 18.2513i) q^{58} +(-65.3652 + 37.7386i) q^{59} +(19.6948 + 49.0669i) q^{60} +(-51.4545 + 89.1217i) q^{61} +(-16.0000 + 16.0000i) q^{62} +(106.769 - 78.7693i) q^{63} +8.00000i q^{64} +(60.9306 + 47.8274i) q^{65} +(13.0000 + 22.5167i) q^{66} +(31.1237 + 8.33958i) q^{67} +(-18.9999 + 5.09101i) q^{68} -94.9089i q^{69} +(49.4754 + 1.47874i) q^{70} +40.3406 q^{71} +(-13.8756 - 51.7845i) q^{72} +(-22.9762 + 85.7485i) q^{73} +(-43.3802 + 25.0455i) q^{74} +(2.90703 - 132.148i) q^{75} +36.8634 q^{76} +(24.1880 - 2.72088i) q^{77} +(-81.9089 - 81.9089i) q^{78} +(-87.6452 - 50.6020i) q^{79} +(7.85641 - 18.3923i) q^{80} +(53.8406 + 93.2546i) q^{81} +(2.21282 + 8.25837i) q^{82} +(51.1247 + 51.1247i) q^{83} +(-73.1920 - 11.0455i) q^{84} +(48.6812 + 6.95445i) q^{85} +(-9.64752 + 16.7100i) q^{86} +(254.654 + 68.2344i) q^{87} +(2.54551 - 9.49996i) q^{88} +(71.6434 + 41.3634i) q^{89} +(-18.9545 + 132.681i) q^{90} +(-100.954 + 39.6005i) q^{91} +(-25.3861 + 25.3861i) q^{92} +(-81.7126 + 21.8948i) q^{93} +(25.7441 - 14.8634i) q^{94} +(-84.7503 - 36.2017i) q^{95} +(-14.9545 + 25.9019i) q^{96} +(45.7723 - 45.7723i) q^{97} +(-36.8893 + 58.6616i) q^{98} +65.9089i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{3} + 12 q^{5} - 16 q^{6} - 4 q^{7} + 16 q^{8} - 28 q^{10} + 8 q^{11} - 8 q^{12} + 8 q^{15} + 16 q^{16} - 16 q^{17} + 32 q^{18} - 64 q^{20} + 100 q^{21} + 16 q^{22} - 4 q^{23} + 28 q^{25}+ \cdots - 132 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^3 + 12 * q^5 - 16 * q^6 - 4 * q^7 + 16 * q^8 - 28 * q^10 + 8 * q^11 - 8 * q^12 + 8 * q^15 + 16 * q^16 - 16 * q^17 + 32 * q^18 - 64 * q^20 + 100 * q^21 + 16 * q^22 - 4 * q^23 + 28 * q^25 - 232 * q^27 - 40 * q^28 - 24 * q^30 - 64 * q^31 - 16 * q^32 - 52 * q^33 + 112 * q^35 + 128 * q^36 + 144 * q^37 + 8 * q^38 - 8 * q^40 - 136 * q^41 + 188 * q^42 + 120 * q^43 - 128 * q^45 + 8 * q^46 + 72 * q^47 - 32 * q^48 - 136 * q^50 + 208 * q^51 + 76 * q^53 + 48 * q^55 - 16 * q^56 - 376 * q^57 + 68 * q^58 + 56 * q^60 - 324 * q^61 - 128 * q^62 + 112 * q^63 + 104 * q^66 + 124 * q^67 + 32 * q^68 + 160 * q^70 + 16 * q^71 + 64 * q^72 + 32 * q^73 + 124 * q^75 + 32 * q^76 + 20 * q^77 - 480 * q^78 - 48 * q^80 + 124 * q^81 - 68 * q^82 + 168 * q^83 - 224 * q^85 + 120 * q^86 + 428 * q^87 + 16 * q^88 - 64 * q^90 - 720 * q^91 + 16 * q^92 - 64 * q^93 - 32 * q^95 - 32 * q^96 - 72 * q^97 - 132 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$3$	1.36843	−	5.10704i	0.456142	−	1.70235i	−0.228565	−	0.973529i	$-0.573403\pi$
$3$	1.36843	−	5.10704i	0.456142	−	1.70235i	0.684707	−	0.728818i	$-0.259930\pi$
$4$	−1.73205	+	1.00000i	−0.433013	+	0.250000i
$5$	4.96410	−	0.598076i	0.992820	−	0.119615i
$5$	4.96410	−	0.598076i	0.992820	−	0.119615i
$6$	−7.47723			−1.24620
$7$	−2.80041	+	6.41543i	−0.400059	+	0.916489i
$7$	−2.80041	+	6.41543i	−0.400059	+	0.916489i
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	−16.4150	−	9.47723i	−1.82389	−	1.05303i
$10$	−2.63397	−	6.56218i	−0.263397	−	0.656218i
$11$	−1.73861	−	3.01137i	−0.158056	−	0.273761i	0.776112	−	0.630595i	$-0.217189\pi$
$11$	−1.73861	−	3.01137i	−0.158056	−	0.273761i	−0.934167	+	0.356835i	$0.883856\pi$
$12$	2.73685	+	10.2141i	0.228071	+	0.851173i
$13$	10.9545	+	10.9545i	0.842650	+	0.842650i	0.989203	−	0.146553i	$-0.0468178\pi$
$13$	10.9545	+	10.9545i	0.842650	+	0.842650i	−0.146553	+	0.989203i	$0.546818\pi$
$14$	9.78866	+	1.47723i	0.699190	+	0.105516i
$15$	3.73861	−	26.1703i	0.249241	−	1.74469i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	9.49996	+	2.54551i	0.558821	+	0.149736i	0.527165	−	0.849763i	$-0.323255\pi$
$17$	9.49996	+	2.54551i	0.558821	+	0.149736i	0.0316564	+	0.999499i	$0.489922\pi$
$18$	−6.93781	+	25.8923i	−0.385434	+	1.43846i
$19$	−15.9623	−	9.21584i	−0.840121	−	0.485044i	0.0171843	−	0.999852i	$-0.494530\pi$
$19$	−15.9623	−	9.21584i	−0.840121	−	0.485044i	−0.857305	+	0.514808i	$0.827863\pi$
$20$	−8.00000	+	6.00000i	−0.400000	+	0.300000i
$21$	28.9317	+	23.0809i	1.37770	+	1.09909i
$22$	−3.47723	+	3.47723i	−0.158056	+	0.158056i
$23$	17.3390	−	4.64598i	0.753872	−	0.201999i	0.138637	−	0.990343i	$-0.455728\pi$
$23$	17.3390	−	4.64598i	0.753872	−	0.201999i	0.615235	+	0.788344i	$0.289061\pi$
$24$	12.9509	−	7.47723i	0.539622	−	0.311551i
$25$	24.2846	−	5.93782i	0.971384	−	0.237513i
$26$	10.9545	−	18.9737i	0.421325	−	0.729756i
$27$	−37.2158	+	37.2158i	−1.37836	+	1.37836i
$28$	−1.56497	−	13.9123i	−0.0558918	−	0.496866i
$29$			49.8634i			1.71943i	0.510777	+	0.859713i	$0.329358\pi$
$29$			49.8634i			1.71943i	−0.510777	+	0.859713i	$0.670642\pi$
$30$	−37.1177	+	4.47195i	−1.23726	+	0.149065i
$31$	−8.00000	−	13.8564i	−0.258065	−	0.446981i	0.707659	−	0.706554i	$-0.249751\pi$
$31$	−8.00000	−	13.8564i	−0.258065	−	0.446981i	−0.965723	+	0.259573i	$0.916418\pi$
$32$	−5.46410	−	1.46410i	−0.170753	−	0.0457532i
$33$	−17.7583	+	4.75833i	−0.538131	+	0.144192i
$34$		−	13.9089i		−	0.409085i
$35$	−10.0646	+	33.5217i	−0.287561	+	0.957762i
$36$	37.9089			1.05303
$37$	−9.16731	−	34.2129i	−0.247765	−	0.924672i	−0.971973	−	0.235091i	$-0.924461\pi$
$37$	−9.16731	−	34.2129i	−0.247765	−	0.924672i	0.724208	−	0.689581i	$-0.242205\pi$
$38$	−6.74646	+	25.1781i	−0.177538	+	0.662583i
$39$	70.9352	−	40.9545i	1.81885	−	1.05011i
$40$	11.1244	+	8.73205i	0.278109	+	0.218301i
$41$	−6.04555			−0.147452			−0.0737262	−	0.997279i	$-0.523489\pi$
$41$	−6.04555			−0.147452			−0.0737262	+	0.997279i	$0.523489\pi$
$42$	20.9393	−	47.9696i	0.498555	−	1.14213i
$43$	−9.64752	−	9.64752i	−0.224361	−	0.224361i	0.585971	−	0.810332i	$-0.300713\pi$
$43$	−9.64752	−	9.64752i	−0.224361	−	0.224361i	−0.810332	+	0.585971i	$0.800713\pi$
$44$	6.02273	+	3.47723i	0.136880	+	0.0790279i
$45$	−87.1540	−	37.2285i	−1.93676	−	0.827299i
$46$	−12.6931	−	21.9850i	−0.275936	−	0.477935i
$47$	5.44036	+	20.3037i	0.115752	+	0.431994i	0.999342	−	0.0362680i	$-0.0115470\pi$
$47$	5.44036	+	20.3037i	0.115752	+	0.431994i	−0.883590	+	0.468262i	$0.844880\pi$
$48$	−14.9545	−	14.9545i	−0.311551	−	0.311551i
$49$	−33.3154	−	35.9317i	−0.679906	−	0.733300i
$50$	−17.0000	−	31.0000i	−0.340000	−	0.620000i
$51$	26.0000	−	45.0333i	0.509804	−	0.883006i
$52$	−29.9281	−	8.01921i	−0.575541	−	0.154216i
$53$	−2.94488	+	10.9904i	−0.0555637	+	0.207366i	−0.988127	−	0.153640i	$-0.950900\pi$
$53$	−2.94488	+	10.9904i	−0.0555637	+	0.207366i	0.932563	+	0.361007i	$0.117567\pi$
$54$	64.4597	+	37.2158i	1.19370	+	0.689182i
$55$	−10.4317	−	13.9089i	−0.189667	−	0.252889i
$56$	−18.4317	+	7.23003i	−0.329137	+	0.129108i
$57$	−68.9089	+	68.9089i	−1.20893	+	1.20893i
$58$	68.1146	−	18.2513i	1.17439	−	0.314677i
$59$	−65.3652	+	37.7386i	−1.10788	+	0.639638i	−0.938281	−	0.345875i	$-0.887582\pi$
$59$	−65.3652	+	37.7386i	−1.10788	+	0.639638i	−0.169604	+	0.985512i	$0.554249\pi$
$60$	19.6948	+	49.0669i	0.328247	+	0.817781i
$61$	−51.4545	+	89.1217i	−0.843516	+	1.46101i	0.0433885	+	0.999058i	$0.486185\pi$
$61$	−51.4545	+	89.1217i	−0.843516	+	1.46101i	−0.886904	+	0.461954i	$0.847149\pi$
$62$	−16.0000	+	16.0000i	−0.258065	+	0.258065i
$63$	106.769	−	78.7693i	1.69475	−	1.25031i
$64$			8.00000i			0.125000i
$65$	60.9306	+	47.8274i	0.937394	+	0.735806i
$66$	13.0000	+	22.5167i	0.196970	+	0.341162i
$67$	31.1237	+	8.33958i	0.464533	+	0.124471i	0.483492	−	0.875349i	$-0.339368\pi$
$67$	31.1237	+	8.33958i	0.464533	+	0.124471i	−0.0189583	+	0.999820i	$0.506035\pi$
$68$	−18.9999	+	5.09101i	−0.279410	+	0.0748678i
$69$		−	94.9089i		−	1.37549i
$70$	49.4754	+	1.47874i	0.706791	+	0.0211248i
$71$	40.3406			0.568177			0.284089	−	0.958798i	$-0.408309\pi$
$71$	40.3406			0.568177			0.284089	+	0.958798i	$0.408309\pi$
$72$	−13.8756	−	51.7845i	−0.192717	−	0.719229i
$73$	−22.9762	+	85.7485i	−0.314743	+	1.17464i	0.609486	+	0.792797i	$0.291376\pi$
$73$	−22.9762	+	85.7485i	−0.314743	+	1.17464i	−0.924229	+	0.381840i	$0.875291\pi$
$74$	−43.3802	+	25.0455i	−0.586218	+	0.338453i
$75$	2.90703	−	132.148i	0.0387603	−	1.76197i
$76$	36.8634			0.485044
$77$	24.1880	−	2.72088i	0.314130	−	0.0353361i
$78$	−81.9089	−	81.9089i	−1.05011	−	1.05011i
$79$	−87.6452	−	50.6020i	−1.10943	−	0.640531i	−0.170750	−	0.985314i	$-0.554619\pi$
$79$	−87.6452	−	50.6020i	−1.10943	−	0.640531i	−0.938682	+	0.344783i	$0.887952\pi$
$80$	7.85641	−	18.3923i	0.0982051	−	0.229904i
$81$	53.8406	+	93.2546i	0.664699	+	1.15129i
$82$	2.21282	+	8.25837i	0.0269857	+	0.100712i
$83$	51.1247	+	51.1247i	0.615961	+	0.615961i	0.944493	−	0.328532i	$-0.106554\pi$
$83$	51.1247	+	51.1247i	0.615961	+	0.615961i	−0.328532	+	0.944493i	$0.606554\pi$
$84$	−73.1920	−	11.0455i	−0.871333	−	0.131495i
$85$	48.6812	+	6.95445i	0.572720	+	0.0818171i
$86$	−9.64752	+	16.7100i	−0.112180	+	0.194302i
$87$	254.654	+	68.2344i	2.92706	+	0.784303i
$88$	2.54551	−	9.49996i	0.0289262	−	0.107954i
$89$	71.6434	+	41.3634i	0.804982	+	0.464757i	0.845210	−	0.534434i	$-0.179475\pi$
$89$	71.6434	+	41.3634i	0.804982	+	0.464757i	−0.0402280	+	0.999191i	$0.512808\pi$
$90$	−18.9545	+	132.681i	−0.210605	+	1.47424i
$91$	−100.954	+	39.6005i	−1.10939	+	0.435170i
$92$	−25.3861	+	25.3861i	−0.275936	+	0.275936i
$93$	−81.7126	+	21.8948i	−0.878631	+	0.235428i
$94$	25.7441	−	14.8634i	0.273873	−	0.158121i
$95$	−84.7503	−	36.2017i	−0.892108	−	0.381070i
$96$	−14.9545	+	25.9019i	−0.155776	+	0.269811i
$97$	45.7723	−	45.7723i	0.471879	−	0.471879i	−0.430643	−	0.902522i	$-0.641713\pi$
$97$	45.7723	−	45.7723i	0.471879	−	0.471879i	0.902522	+	0.430643i	$0.141713\pi$
$98$	−36.8893	+	58.6616i	−0.376422	+	0.598587i
$99$			65.9089i			0.665746i
$100$	−36.1244	+	34.5692i	−0.361244	+	0.345692i
$101$	−71.7495	−	124.274i	−0.710391	−	1.23043i	−0.964710	−	0.263313i	$-0.915185\pi$
$101$	−71.7495	−	124.274i	−0.710391	−	1.23043i	0.254320	−	0.967120i	$-0.418148\pi$
$102$	−71.0333	−	19.0333i	−0.696405	−	0.186601i
$103$	−54.2840	+	14.5453i	−0.527029	+	0.141217i	−0.512516	−	0.858678i	$-0.671286\pi$
$103$	−54.2840	+	14.5453i	−0.527029	+	0.141217i	−0.0145128	+	0.999895i	$0.504620\pi$
$104$			43.8178i			0.421325i
$105$	157.424	+	97.2724i	1.49928	+	0.926404i
$106$	16.0911			0.151803
$107$	−15.5267	−	57.9465i	−0.145109	−	0.541556i	−0.999751	−	0.0223366i	$-0.992889\pi$
$107$	−15.5267	−	57.9465i	−0.145109	−	0.541556i	0.854641	−	0.519219i	$-0.173777\pi$
$108$	27.2439	−	101.676i	0.252258	−	0.941440i
$109$	32.2796	−	18.6366i	0.296143	−	0.170978i	−0.344566	−	0.938762i	$-0.611974\pi$
$109$	32.2796	−	18.6366i	0.296143	−	0.170978i	0.640709	+	0.767784i	$0.278640\pi$
$110$	−15.1817	+	19.3409i	−0.138015	+	0.175827i
$111$	−187.271			−1.68713
$112$	16.6229	+	22.5318i	0.148418	+	0.201176i
$113$	−118.636	−	118.636i	−1.04987	−	1.04987i	−0.998689	−	0.0511834i	$-0.983701\pi$
$113$	−118.636	−	118.636i	−1.04987	−	1.04987i	−0.0511834	−	0.998689i	$-0.516299\pi$
$114$	119.354	+	68.9089i	1.04696	+	0.604464i
$115$	83.2941	−	33.4332i	0.724297	−	0.290724i
$116$	−49.8634	−	86.3659i	−0.429856	−	0.744533i
$117$	−75.9999	−	283.636i	−0.649572	−	2.42424i
$118$	75.4772	+	75.4772i	0.639638	+	0.639638i
$119$	−42.9343	+	53.8178i	−0.360792	+	0.452250i
$120$	59.8178	−	44.8634i	0.498482	−	0.373861i
$121$	54.4545	−	94.3179i	0.450037	−	0.779487i
$122$	140.576	+	37.6673i	1.15226	+	0.308748i
$123$	−8.27289	+	30.8749i	−0.0672593	+	0.251015i
$124$	27.7128	+	16.0000i	0.223490	+	0.129032i
$125$	117.000	−	44.0000i	0.936000	−	0.352000i
$126$	−146.681	−	117.018i	−1.16414	−	0.928714i
$127$	24.9545	−	24.9545i	0.196492	−	0.196492i	−0.602002	−	0.798494i	$-0.705630\pi$
$127$	24.9545	−	24.9545i	0.196492	−	0.196492i	0.798494	+	0.602002i	$0.205630\pi$
$128$	10.9282	−	2.92820i	0.0853766	−	0.0228766i
$129$	−62.4722	+	36.0683i	−0.484280	+	0.279599i
$130$	43.0313	−	100.739i	0.331010	−	0.774914i
$131$	35.0455	−	60.7007i	0.267523	−	0.463364i	−0.700698	−	0.713458i	$-0.747128\pi$
$131$	35.0455	−	60.7007i	0.267523	−	0.463364i	0.968222	+	0.250094i	$0.0804614\pi$
$132$	26.0000	−	26.0000i	0.196970	−	0.196970i
$133$	103.825	−	76.5968i	0.780636	−	0.575916i
$134$		−	45.5683i		−	0.340062i
$135$	−162.485	+	207.001i	−1.20359	+	1.53334i
$136$	13.9089	+	24.0909i	0.102271	+	0.177139i
$137$	9.25107	+	2.47882i	0.0675261	+	0.0180936i	0.292424	−	0.956289i	$-0.405538\pi$
$137$	9.25107	+	2.47882i	0.0675261	+	0.0180936i	−0.224898	+	0.974382i	$0.572205\pi$
$138$	−129.648	+	34.7391i	−0.939478	+	0.251732i
$139$			53.0217i			0.381451i	0.981643	+	0.190726i	$0.0610841\pi$
$139$			53.0217i			0.381451i	−0.981643	+	0.190726i	$0.938916\pi$
$140$	−16.0893	−	68.1259i	−0.114923	−	0.486613i
$141$	111.137			0.788203
$142$	−14.7657	−	55.1063i	−0.103984	−	0.388072i
$143$	13.9423	−	52.0334i	0.0974987	−	0.363870i
$144$	−65.6601	+	37.9089i	−0.455973	+	0.263256i
$145$	29.8221	+	247.527i	0.205670	+	1.70708i
$146$	125.545			0.859894
$147$	−229.094	+	120.973i	−1.55846	+	0.822946i
$148$	50.0911	+	50.0911i	0.338453	+	0.338453i
$149$	181.078	+	104.546i	1.21529	+	0.701648i	0.963907	−	0.266240i	$-0.0857813\pi$
$149$	181.078	+	104.546i	1.21529	+	0.701648i	0.251383	+	0.967888i	$0.419115\pi$
$150$	−181.582	+	44.3984i	−1.21054	+	0.295990i
$151$	−81.0455	−	140.375i	−0.536725	−	0.929636i	−0.999078	−	0.0429394i	$-0.986328\pi$
$151$	−81.0455	−	140.375i	−0.536725	−	0.929636i	0.462352	−	0.886696i	$-0.347006\pi$
$152$	−13.4929	−	50.3563i	−0.0887692	−	0.331291i
$153$	−131.818	−	131.818i	−0.861554	−	0.861554i
$154$	−12.5702	−	32.0455i	−0.0816248	−	0.208088i
$155$	−48.0000	−	64.0000i	−0.309677	−	0.412903i
$156$	−81.9089	+	141.870i	−0.525057	+	0.909426i
$157$	−133.062	−	35.6538i	−0.847526	−	0.227094i	−0.191181	−	0.981555i	$-0.561232\pi$
$157$	−133.062	−	35.6538i	−0.847526	−	0.227094i	−0.656345	+	0.754461i	$0.727898\pi$
$158$	−37.0432	+	138.247i	−0.234451	+	0.874982i
$159$	52.0987	+	30.0792i	0.327665	+	0.189177i
$160$	−28.0000	−	4.00000i	−0.175000	−	0.0250000i
$161$	−18.7505	+	124.248i	−0.116463	+	0.771727i
$162$	107.681	−	107.681i	0.664699	−	0.664699i
$163$	−91.8348	+	24.6071i	−0.563404	+	0.150964i	−0.529270	−	0.848454i	$-0.677534\pi$
$163$	−91.8348	+	24.6071i	−0.563404	+	0.150964i	−0.0341341	+	0.999417i	$0.510867\pi$
$164$	10.4712	−	6.04555i	0.0638488	−	0.0368631i
$165$	−85.3083	+	34.2417i	−0.517020	+	0.207525i
$166$	51.1247	−	88.5506i	0.307980	−	0.533438i
$167$	133.988	−	133.988i	0.802324	−	0.802324i	−0.181134	−	0.983458i	$-0.557977\pi$
$167$	133.988	−	133.988i	0.802324	−	0.802324i	0.983458	+	0.181134i	$0.0579769\pi$
$168$	11.7016	+	104.025i	0.0696526	+	0.619197i
$169$			71.0000i			0.420118i
$170$	−8.31858	−	69.0452i	−0.0489328	−	0.406148i
$171$	174.681	+	302.557i	1.02153	+	1.76934i
$172$	26.3575	+	7.06247i	0.153241	+	0.0410609i
$173$	0.248884	−	0.0666881i	0.00143863	−	0.000385481i	−0.258100	−	0.966118i	$-0.583096\pi$
$173$	0.248884	−	0.0666881i	0.00143863	−	0.000385481i	0.259538	+	0.965733i	$0.416430\pi$
$174$		−	372.840i		−	2.14276i
$175$	−29.9133	+	172.424i	−0.170933	+	0.985283i
$176$	−13.9089			−0.0790279
$177$	103.285	+	385.465i	0.583532	+	2.17777i
$178$	30.2801	−	113.007i	0.170113	−	0.634870i
$179$	37.7895	−	21.8178i	0.211115	−	0.121887i	−0.390715	−	0.920512i	$-0.627772\pi$
$179$	37.7895	−	21.8178i	0.211115	−	0.121887i	0.601829	+	0.798625i	$0.294439\pi$
$180$	188.184	−	22.6724i	1.04546	−	0.125958i
$181$	3.68116			0.0203379			0.0101689	−	0.999948i	$-0.496763\pi$
$181$	3.68116			0.0203379			0.0101689	+	0.999948i	$0.496763\pi$
$182$	91.0472	+	123.412i	0.500259	+	0.678085i
$183$	384.737	+	384.737i	2.10239	+	2.10239i
$184$	43.9701	+	25.3861i	0.238968	+	0.137968i
$185$	−65.9693	−	164.353i	−0.356591	−	0.888396i
$186$	59.8178	+	103.607i	0.321601	+	0.557029i
$187$	−8.85130	−	33.0335i	−0.0473331	−	0.176650i
$188$	−29.7267	−	29.7267i	−0.158121	−	0.158121i
$189$	−134.536	−	342.975i	−0.711829	−	1.81468i
$190$	−18.4317	+	129.022i	−0.0970088	+	0.679062i
$191$	−8.96636	+	15.5302i	−0.0469443	+	0.0813099i	−0.888543	−	0.458794i	$-0.848282\pi$
$191$	−8.96636	+	15.5302i	−0.0469443	+	0.0813099i	0.841598	+	0.540104i	$0.181615\pi$
$192$	40.8563	+	10.9474i	0.212793	+	0.0570178i
$193$	55.0364	−	205.399i	0.285163	−	1.06424i	−0.663557	−	0.748125i	$-0.730954\pi$
$193$	55.0364	−	205.399i	0.285163	−	1.06424i	0.948720	−	0.316117i	$-0.102379\pi$
$194$	−79.2799	−	45.7723i	−0.408659	−	0.235939i
$195$	327.636	−	245.727i	1.68018	−	1.26014i
$196$	93.6356	+	28.9201i	0.477733	+	0.147552i
$197$	41.0911	−	41.0911i	0.208584	−	0.208584i	−0.595081	−	0.803666i	$-0.702880\pi$
$197$	41.0911	−	41.0911i	0.208584	−	0.208584i	0.803666	+	0.595081i	$0.202880\pi$
$198$	90.0332	−	24.1243i	0.454713	−	0.121840i
$199$	−261.145	+	150.772i	−1.31229	+	0.757650i	−0.982475	−	0.186397i	$-0.940319\pi$
$199$	−261.145	+	150.772i	−1.31229	+	0.757650i	−0.329813	+	0.944046i	$0.606986\pi$
$200$	60.4449	+	36.6936i	0.302224	+	0.183468i
$201$	85.1812	−	147.538i	0.423787	−	0.734020i
$202$	−143.499	+	143.499i	−0.710391	+	0.710391i
$203$	−319.895	−	139.638i	−1.57584	−	0.687872i
$204$			104.000i			0.509804i
$205$	−30.0107	+	3.61570i	−0.146394	+	0.0176376i
$206$	39.7386	+	68.8293i	0.192906	+	0.334123i
$207$	−328.652	−	88.0621i	−1.58769	−	0.425421i
$208$	59.8562	−	16.0384i	0.287770	−	0.0771078i
$209$			64.0911i			0.306656i
$210$	75.2554	−	250.649i	0.358359	−	1.19357i
$211$	−177.703			−0.842194			−0.421097	−	0.907016i	$-0.638355\pi$
$211$	−177.703			−0.842194			−0.421097	+	0.907016i	$0.638355\pi$
$212$	−5.88975	−	21.9808i	−0.0277818	−	0.103683i
$213$	55.2031	−	206.021i	0.259170	−	0.967235i
$214$	−73.4732	+	42.4198i	−0.343333	+	0.198223i
$215$	−53.6612	−	42.1213i	−0.249587	−	0.195913i
$216$	−148.863			−0.689182
$217$	111.298	−	12.5198i	0.512894	−	0.0576947i
$218$	−37.2733	−	37.2733i	−0.170978	−	0.170978i
$219$	406.480	+	234.681i	1.85607	+	1.07160i
$220$	31.9771	+	13.6592i	0.145350	+	0.0620875i
$221$	76.1822	+	131.951i	0.344716	+	0.597065i
$222$	68.5460	+	255.817i	0.308766	+	1.15233i
$223$	249.113	+	249.113i	1.11710	+	1.11710i	0.992165	+	0.124933i	$0.0398715\pi$
$223$	249.113	+	249.113i	1.11710	+	1.11710i	0.124933	+	0.992165i	$0.460129\pi$
$224$	24.6946	−	30.9545i	0.110244	−	0.138190i
$225$	−454.907	−	132.681i	−2.02181	−	0.589694i
$226$	−118.636	+	205.483i	−0.524936	+	0.909216i
$227$	40.0503	+	10.7314i	0.176433	+	0.0472751i	0.345954	−	0.938252i	$-0.387555\pi$
$227$	40.0503	+	10.7314i	0.176433	+	0.0472751i	−0.169521	+	0.985527i	$0.554222\pi$
$228$	50.4448	−	188.263i	0.221249	−	0.825713i
$229$	−272.875	−	157.545i	−1.19159	−	0.687967i	−0.232926	−	0.972494i	$-0.574830\pi$
$229$	−272.875	−	157.545i	−1.19159	−	0.687967i	−0.958668	+	0.284527i	$0.908163\pi$
$230$	−76.1584	−	101.545i	−0.331123	−	0.441498i
$231$	19.2039	−	127.253i	0.0831339	−	0.550877i
$232$	−99.7267	+	99.7267i	−0.429856	+	0.429856i
$233$	−111.143	+	29.7807i	−0.477009	+	0.127814i	−0.489309	−	0.872110i	$-0.662751\pi$
$233$	−111.143	+	29.7807i	−0.477009	+	0.127814i	0.0123008	+	0.999924i	$0.496084\pi$
$234$	−359.635	+	207.636i	−1.53690	+	0.887332i
$235$	39.1497	+	97.5360i	0.166594	+	0.415047i
$236$	75.4772	−	130.730i	0.319819	−	0.553942i
$237$	−378.362	+	378.362i	−1.59647	+	1.59647i
$238$	89.2315	+	38.9507i	0.374922	+	0.163658i
$239$		−	438.725i		−	1.83567i	−0.396965	−	0.917834i	$-0.629936\pi$
$239$		−	438.725i		−	1.83567i	0.396965	−	0.917834i	$-0.370064\pi$
$240$	−83.1793	−	65.2915i	−0.346580	−	0.272048i
$241$	78.0911	+	135.258i	0.324029	+	0.561235i	0.981315	−	0.192406i	$-0.0616290\pi$
$241$	78.0911	+	135.258i	0.324029	+	0.561235i	−0.657286	+	0.753641i	$0.728296\pi$
$242$	−148.772	−	39.8634i	−0.614762	−	0.164725i
$243$	92.3920	−	24.7564i	0.380214	−	0.101878i
$244$		−	205.818i		−	0.843516i
$245$	−186.871	−	158.443i	−0.762738	−	0.646708i
$246$	45.2039			0.183756
$247$	−73.9038	−	275.813i	−0.299206	−	1.11665i
$248$	11.7128	−	43.7128i	0.0472291	−	0.176261i
$249$	331.057	−	191.136i	1.32954	−	0.767613i
$250$	−102.930	−	143.720i	−0.411720	−	0.574879i
$251$	185.727			0.739947			0.369974	−	0.929042i	$-0.379367\pi$
$251$	185.727			0.739947			0.369974	+	0.929042i	$0.379367\pi$
$252$	−106.161	+	243.202i	−0.421272	+	0.965086i
$253$	−44.1366	−	44.1366i	−0.174453	−	0.174453i
$254$	−43.2224	−	24.9545i	−0.170167	−	0.0982459i
$255$	102.133	−	239.100i	0.400523	−	0.937647i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	61.7416	+	230.423i	0.240240	+	0.896587i	0.975717	+	0.219037i	$0.0702915\pi$
$257$	61.7416	+	230.423i	0.240240	+	0.896587i	−0.735477	+	0.677550i	$0.763042\pi$
$258$	72.1366	+	72.1366i	0.279599	+	0.279599i
$259$	245.162	+	36.9979i	0.946573	+	0.142849i
$260$	−153.362	−	21.9089i	−0.589855	−	0.0842650i
$261$	472.566	−	818.509i	1.81060	−	3.13605i
$262$	−95.7462	−	25.6551i	−0.365444	−	0.0979203i
$263$	−85.0136	+	317.275i	−0.323246	+	1.20637i	0.592818	+	0.805336i	$0.298015\pi$
$263$	−85.0136	+	317.275i	−0.323246	+	1.20637i	−0.916064	+	0.401032i	$0.868651\pi$
$264$	−45.0333	−	26.0000i	−0.170581	−	0.0984848i
$265$	−8.04555	+	56.3188i	−0.0303606	+	0.212524i
$266$	−142.636	−	113.791i	−0.536224	−	0.427784i
$267$	309.283	−	309.283i	1.15836	−	1.15836i
$268$	−62.2475	+	16.6792i	−0.232267	+	0.0622357i
$269$	247.839	−	143.090i	0.921336	−	0.531933i	0.0372746	−	0.999305i	$-0.488132\pi$
$269$	247.839	−	143.090i	0.921336	−	0.531933i	0.884061	+	0.467372i	$0.154799\pi$
$270$	342.243	+	146.191i	1.26756	+	0.541450i
$271$	−204.760	+	354.655i	−0.755573	+	1.30869i	0.189516	+	0.981878i	$0.439308\pi$
$271$	−204.760	+	354.655i	−0.755573	+	1.30869i	−0.945089	+	0.326814i	$0.894025\pi$
$272$	27.8178	−	27.8178i	0.102271	−	0.102271i
$273$	64.0925	+	569.769i	0.234771	+	2.08707i
$274$		−	13.5445i		−	0.0494325i
$275$	−60.1025	−	62.8063i	−0.218554	−	0.228386i
$276$	94.9089	+	164.387i	0.343873	+	0.595605i
$277$	15.7107	+	4.20967i	0.0567174	+	0.0151974i	0.287066	−	0.957911i	$-0.407320\pi$
$277$	15.7107	+	4.20967i	0.0567174	+	0.0151974i	−0.230349	+	0.973108i	$0.573987\pi$
$278$	72.4290	−	19.4073i	0.260536	−	0.0698104i
$279$			303.271i			1.08699i
$280$	−87.1726	+	46.9141i	−0.311331	+	0.167550i
$281$	302.542			1.07666			0.538332	−	0.842733i	$-0.319055\pi$
$281$	302.542			1.07666			0.538332	+	0.842733i	$0.319055\pi$
$282$	−40.6788	−	151.815i	−0.144251	−	0.538353i
$283$	41.0108	−	153.054i	0.144914	−	0.540828i	−0.854845	−	0.518884i	$-0.826348\pi$
$283$	41.0108	−	153.054i	0.144914	−	0.540828i	0.999759	−	0.0219440i	$-0.00698556\pi$
$284$	−69.8719	+	40.3406i	−0.246028	+	0.142044i
$285$	−300.858	+	383.284i	−1.05564	+	1.34485i
$286$	−76.1822			−0.266371
$287$	16.9300	−	38.7848i	0.0589897	−	0.135139i
$288$	75.8178	+	75.8178i	0.263256	+	0.263256i
$289$	−166.512	−	96.1356i	−0.576165	−	0.332649i
$290$	327.212	−	131.339i	1.12832	−	0.452892i
$291$	−171.125	−	296.397i	−0.588058	−	1.01855i
$292$	−45.9525	−	171.497i	−0.157372	−	0.587318i
$293$	−100.182	−	100.182i	−0.341919	−	0.341919i	0.515170	−	0.857088i	$-0.327729\pi$
$293$	−100.182	−	100.182i	−0.341919	−	0.341919i	−0.857088	+	0.515170i	$0.827729\pi$
$294$	249.107	+	268.669i	0.847301	+	0.913841i
$295$	−301.909	+	226.432i	−1.02342	+	0.767565i
$296$	50.0911	−	86.7603i	0.169227	−	0.293109i
$297$	176.774	+	47.3666i	0.595200	+	0.159483i
$298$	76.5327	−	285.624i	0.256821	−	0.958469i
$299$	240.834	+	139.046i	0.805465	+	0.465035i
$300$	127.113	+	231.794i	0.423709	+	0.772647i
$301$	88.9099	−	34.8759i	0.295382	−	0.115867i
$302$	−162.091	+	162.091i	−0.536725	+	0.536725i
$303$	−732.855	+	196.368i	−2.41866	+	0.648079i
$304$	−63.8492	+	36.8634i	−0.210030	+	0.121261i
$305$	−202.124	+	473.183i	−0.662700	+	1.55142i
$306$	−131.818	+	228.315i	−0.430777	+	0.746128i
$307$	−242.602	+	242.602i	−0.790234	+	0.790234i	−0.981532	−	0.191298i	$-0.938730\pi$
$307$	−242.602	+	242.602i	−0.790234	+	0.790234i	0.191298	+	0.981532i	$0.438730\pi$
$308$	−39.1740	+	28.9007i	−0.127188	+	0.0938335i
$309$			297.135i			0.961601i
$310$	−69.8564	+	88.9948i	−0.225343	+	0.287080i
$311$	−3.73861	−	6.47547i	−0.0120213	−	0.0208214i	0.859952	−	0.510375i	$-0.170493\pi$
$311$	−3.73861	−	6.47547i	−0.0120213	−	0.0208214i	−0.871973	+	0.489553i	$0.837160\pi$
$312$	223.779	+	59.9615i	0.717241	+	0.192184i
$313$	577.950	−	154.861i	1.84649	−	0.494765i	0.847156	−	0.531344i	$-0.178313\pi$
$313$	577.950	−	154.861i	1.84649	−	0.494765i	0.999331	+	0.0365796i	$0.0116462\pi$
$314$			194.816i			0.620432i
$315$	482.904	−	454.875i	1.53303	−	1.44405i
$316$	202.408			0.640531
$317$	−105.415	−	393.415i	−0.332540	−	1.24106i	−0.906511	−	0.422182i	$-0.861264\pi$
$317$	−105.415	−	393.415i	−0.332540	−	1.24106i	0.573971	−	0.818876i	$-0.305402\pi$
$318$	22.0195	−	82.1779i	0.0692437	−	0.258421i
$319$	150.157	−	86.6931i	0.470711	−	0.271765i
$320$	4.78461	+	39.7128i	0.0149519	+	0.124103i
$321$	−317.182			−0.988107
$322$	176.589	−	19.8643i	0.548414	−	0.0616902i
$323$	−128.182	−	128.182i	−0.396849	−	0.396849i
$324$	−186.509	−	107.681i	−0.575646	−	0.332349i
$325$	331.070	+	200.979i	1.01868	+	0.618397i
$326$	67.2277	+	116.442i	0.206220	+	0.357184i
$327$	−51.0058	−	190.356i	−0.155981	−	0.582129i
$328$	−12.0911	−	12.0911i	−0.0368631	−	0.0368631i
$329$	−145.492	−	21.9565i	−0.442226	−	0.0667372i
$330$	78.0000	+	104.000i	0.236364	+	0.315152i
$331$	−118.317	+	204.931i	−0.357452	+	0.619126i	−0.987534	−	0.157403i	$-0.949688\pi$
$331$	−118.317	+	204.931i	−0.357452	+	0.619126i	0.630082	+	0.776529i	$0.283021\pi$
$332$	−139.675	−	37.4259i	−0.420709	−	0.112729i
$333$	−173.761	+	648.486i	−0.521806	+	1.94741i
$334$	−232.074	−	133.988i	−0.694833	−	0.401162i
$335$	159.489	+	22.7842i	0.476087	+	0.0680124i
$336$	137.818	−	54.0605i	0.410172	−	0.160894i
$337$	316.271	−	316.271i	0.938490	−	0.938490i	−0.0597246	−	0.998215i	$-0.519022\pi$
$337$	316.271	−	316.271i	0.938490	−	0.938490i	0.998215	+	0.0597246i	$0.0190223\pi$
$338$	96.9878	−	25.9878i	0.286946	−	0.0768870i
$339$	−768.221	+	443.533i	−2.26614	+	1.30836i
$340$	−91.2727	+	36.6357i	−0.268449	+	0.107752i
$341$	−27.8178	+	48.1819i	−0.0815771	+	0.141296i
$342$	349.362	−	349.362i	1.02153	−	1.02153i
$343$	323.814	−	113.109i	0.944064	−	0.329763i
$344$		−	38.5901i		−	0.112180i
$345$	−56.7628	−	471.137i	−0.164530	−	1.36562i
$346$	−0.182195	−	0.315572i	−0.000526576	−	0.000912057i
$347$	137.052	+	36.7228i	0.394961	+	0.105830i	0.450833	−	0.892608i	$-0.351127\pi$
$347$	137.052	+	36.7228i	0.394961	+	0.105830i	−0.0558716	+	0.998438i	$0.517794\pi$
$348$	−509.308	+	136.469i	−1.46353	+	0.392152i
$349$		−	298.861i		−	0.856336i	−0.903699	−	0.428168i	$-0.859159\pi$
$349$		−	298.861i		−	0.856336i	0.903699	−	0.428168i	$-0.140841\pi$
$350$	246.485	−	22.2495i	0.704243	−	0.0635699i
$351$	−815.358			−2.32296
$352$	5.09101	+	18.9999i	0.0144631	+	0.0539770i
$353$	−8.91723	+	33.2795i	−0.0252613	+	0.0942763i	−0.977406	−	0.211373i	$-0.932207\pi$
$353$	−8.91723	+	33.2795i	−0.0252613	+	0.0942763i	0.952144	+	0.305649i	$0.0988734\pi$
$354$	488.750	−	282.180i	1.38065	−	0.797119i
$355$	200.255	−	24.1267i	0.564098	−	0.0679626i
$356$	−165.453			−0.464757
$357$	216.097	+	292.913i	0.605314	+	0.820484i
$358$	−43.6356	−	43.6356i	−0.121887	−	0.121887i
$359$	426.160	+	246.043i	1.18707	+	0.685358i	0.957641	−	0.287966i	$-0.0929791\pi$
$359$	426.160	+	246.043i	1.18707	+	0.685358i	0.229434	+	0.973324i	$0.426312\pi$
$360$	−99.8511	−	248.765i	−0.277364	−	0.691014i
$361$	−10.6366	−	18.4232i	−0.0294644	−	0.0510338i
$362$	−1.34740	−	5.02856i	−0.00372209	−	0.0138910i
$363$	−407.168	−	407.168i	−1.12168	−	1.12168i
$364$	135.258	−	169.545i	0.371587	−	0.465782i
$365$	−62.7723	+	439.406i	−0.171979	+	1.20385i
$366$	384.737	−	666.383i	1.05119	−	1.82072i
$367$	70.3355	+	18.8463i	0.191650	+	0.0513524i	0.353367	−	0.935485i	$-0.385037\pi$
$367$	70.3355	+	18.8463i	0.191650	+	0.0513524i	−0.161717	+	0.986837i	$0.551703\pi$
$368$	18.5839	−	69.3562i	0.0504998	−	0.188468i
$369$	99.2379	+	57.2950i	0.268937	+	0.155271i
$370$	−200.364	+	150.273i	−0.541525	+	0.406144i
$371$	−62.2614	−	49.6703i	−0.167820	−	0.133882i
$372$	119.636	−	119.636i	0.321601	−	0.321601i
$373$	332.315	−	89.0434i	0.890924	−	0.238722i	0.215810	−	0.976435i	$-0.430761\pi$
$373$	332.315	−	89.0434i	0.890924	−	0.238722i	0.675114	+	0.737713i	$0.264094\pi$
$374$	−41.8848	+	24.1822i	−0.111991	+	0.0646583i
$375$	−64.6038	−	657.734i	−0.172277	−	1.75396i
$376$	−29.7267	+	51.4882i	−0.0790604	+	0.136937i
$377$	−546.226	+	546.226i	−1.44887	+	1.44887i
$378$	−419.269	+	309.317i	−1.10918	+	0.818299i
$379$			33.5683i			0.0885708i	0.999019	+	0.0442854i	$0.0141011\pi$
$379$			33.5683i			0.0885708i	−0.999019	+	0.0442854i	$0.985899\pi$
$380$	182.993	−	22.0471i	0.481562	−	0.0580187i
$381$	−93.2950	−	161.592i	−0.244869	−	0.424125i
$382$	24.4965	+	6.56383i	0.0641271	+	0.0171828i
$383$	694.888	−	186.195i	1.81433	−	0.486148i	0.818269	−	0.574836i	$-0.194934\pi$
$383$	694.888	−	186.195i	1.81433	−	0.486148i	0.996059	+	0.0886883i	$0.0282675\pi$
$384$		−	59.8178i		−	0.155776i
$385$	118.445	−	27.9730i	0.307648	−	0.0726571i
$386$	−300.725			−0.779079
$387$	66.9326	+	249.796i	0.172953	+	0.645468i
$388$	−33.5076	+	125.052i	−0.0863598	+	0.322299i
$389$	−459.937	+	265.545i	−1.18236	+	0.682634i	−0.956558	−	0.291540i	$-0.905832\pi$
$389$	−459.937	+	265.545i	−1.18236	+	0.682634i	−0.225798	+	0.974174i	$0.572499\pi$
$390$	−455.592	−	357.616i	−1.16818	−	0.916965i
$391$	176.547			0.451526
$392$	5.23259	−	138.494i	0.0133484	−	0.353301i
$393$	−262.043	−	262.043i	−0.666777	−	0.666777i
$394$	−71.1719	−	41.0911i	−0.180639	−	0.104292i
$395$	−465.343	−	198.775i	−1.17808	−	0.503227i
$396$	−65.9089	−	114.158i	−0.166437	−	0.288277i
$397$	69.5948	+	259.731i	0.175302	+	0.654235i	0.996500	+	0.0835924i	$0.0266394\pi$
$397$	69.5948	+	259.731i	0.175302	+	0.654235i	−0.821198	+	0.570643i	$0.806694\pi$
$398$	301.545	+	301.545i	0.757650	+	0.757650i
$399$	−249.107	−	635.053i	−0.624327	−	1.59161i
$400$	28.0000	−	96.0000i	0.0700000	−	0.240000i
$401$	−276.270	+	478.514i	−0.688953	+	1.19330i	0.283224	+	0.959054i	$0.408596\pi$
$401$	−276.270	+	478.514i	−0.688953	+	1.19330i	−0.972177	+	0.234248i	$0.924737\pi$
$402$	−232.719	−	62.3569i	−0.578904	−	0.155117i
$403$	64.1537	−	239.425i	0.159190	−	0.594107i
$404$	248.547	+	143.499i	0.615217	+	0.355195i
$405$	323.043	+	430.725i	0.797638	+	1.06352i
$406$	−73.6594	+	488.095i	−0.181427	+	1.20221i
$407$	−87.0890	+	87.0890i	−0.213978	+	0.213978i
$408$	142.067	−	38.0666i	0.348203	−	0.0933006i
$409$	−108.528	+	62.6584i	−0.265348	+	0.153199i	−0.626772	−	0.779203i	$-0.715624\pi$
$409$	−108.528	+	62.6584i	−0.265348	+	0.153199i	0.361423	+	0.932402i	$0.382291\pi$
$410$	15.9238	+	39.6720i	0.0388386	+	0.0967609i
$411$	25.3188	−	43.8535i	0.0616030	−	0.106700i
$412$	79.4772	−	79.4772i	0.192906	−	0.192906i
$413$	−59.0598	−	525.029i	−0.143002	−	1.27126i
$414$			481.180i			1.16227i
$415$	284.365	+	223.212i	0.685217	+	0.537860i
$416$	−43.8178	−	75.8947i	−0.105331	−	0.182439i
$417$	270.784	+	72.5564i	0.649362	+	0.173996i
$418$	87.5501	−	23.4590i	0.209450	−	0.0561219i
$419$		−	116.269i		−	0.277492i	−0.990328	−	0.138746i	$-0.955693\pi$
$419$		−	116.269i		−	0.277492i	0.990328	−	0.138746i	$-0.0443072\pi$
$420$	−369.939	−	11.0568i	−0.880806	−	0.0263258i
$421$	534.449			1.26948			0.634738	−	0.772728i	$-0.281108\pi$
$421$	534.449			1.26948			0.634738	+	0.772728i	$0.281108\pi$
$422$	65.0438	+	242.747i	0.154132	+	0.575229i
$423$	103.119	−	384.846i	0.243780	−	0.909801i
$424$	−27.8706	+	16.0911i	−0.0657325	+	0.0379507i
$425$	245.818	+	5.40756i	0.578394	+	0.0127237i
$426$	−301.636			−0.708065
$427$	−427.660	−	579.680i	−1.00155	−	1.35756i
$428$	84.8395	+	84.8395i	0.198223	+	0.198223i
$429$	−246.658	−	142.408i	−0.574960	−	0.331953i
$430$	−37.8974	+	88.7200i	−0.0881335	+	0.206326i
$431$	238.737	+	413.504i	0.553913	+	0.959406i	0.997987	+	0.0634155i	$0.0201994\pi$
$431$	238.737	+	413.504i	0.553913	+	0.959406i	−0.444074	+	0.895990i	$0.646467\pi$
$432$	54.4878	+	203.351i	0.126129	+	0.470720i
$433$	−542.271	−	542.271i	−1.25236	−	1.25236i	−0.954660	−	0.297699i	$-0.903781\pi$
$433$	−542.271	−	542.271i	−1.25236	−	1.25236i	−0.297699	−	0.954660i	$-0.596219\pi$
$434$	−57.8402	−	147.453i	−0.133272	−	0.339754i
$435$	1304.94	+	186.420i	2.99986	+	0.428551i
$436$	−37.2733	+	64.5592i	−0.0854892	+	0.148072i
$437$	−319.588	−	85.6333i	−0.731322	−	0.195957i
$438$	171.799	−	641.161i	0.392234	−	1.46384i
$439$	−232.568	−	134.273i	−0.529768	−	0.305862i	0.211154	−	0.977453i	$-0.432278\pi$
$439$	−232.568	−	134.273i	−0.529768	−	0.305862i	−0.740922	+	0.671591i	$0.765611\pi$
$440$	6.95445	−	48.6812i	0.0158056	−	0.110639i
$441$	206.341	+	905.557i	0.467892	+	2.05342i
$442$	152.364	−	152.364i	0.344716	−	0.344716i
$443$	−85.1751	+	22.8226i	−0.192269	+	0.0515183i	−0.353668	−	0.935371i	$-0.615066\pi$
$443$	−85.1751	+	22.8226i	−0.192269	+	0.0515183i	0.161400	+	0.986889i	$0.448399\pi$
$444$	324.363	−	187.271i	0.730548	−	0.421782i
$445$	380.384	+	162.484i	0.854795	+	0.365132i
$446$	249.113	−	431.476i	0.558549	−	0.967435i
$447$	781.711	−	781.711i	1.74879	−	1.74879i
$448$	−51.3234	−	22.4033i	−0.114561	−	0.0500074i
$449$		−	100.410i		−	0.223630i	−0.993729	−	0.111815i	$-0.964334\pi$
$449$		−	100.410i		−	0.223630i	0.993729	−	0.111815i	$-0.0356664\pi$
$450$	−14.7384	+	669.979i	−0.0327519	+	1.48884i
$451$	10.5109	+	18.2054i	0.0233057	+	0.0403666i
$452$	324.119	+	86.8473i	0.717076	+	0.192140i
$453$	−827.806	+	221.810i	−1.82739	+	0.489647i
$454$		−	58.6377i		−	0.129158i
$455$	−477.464	+	256.959i	−1.04937	+	0.564746i
$456$	−275.636			−0.604464
$457$	−180.050	−	671.954i	−0.393982	−	1.47036i	−0.823508	−	0.567305i	$-0.807986\pi$
$457$	−180.050	−	671.954i	−0.393982	−	1.47036i	0.429526	−	0.903055i	$-0.358681\pi$
$458$	−115.331	+	430.420i	−0.251814	+	0.939781i
$459$	−448.282	+	258.816i	−0.976649	+	0.563869i
$460$	−110.836	+	141.202i	−0.240949	+	0.306961i
$461$	−191.636			−0.415695			−0.207848	−	0.978161i	$-0.566646\pi$
$461$	−191.636			−0.415695			−0.207848	+	0.978161i	$0.566646\pi$
$462$	−180.859	+	20.3446i	−0.391470	+	0.0440359i
$463$	268.079	+	268.079i	0.579005	+	0.579005i	0.934629	−	0.355624i	$-0.115732\pi$
$463$	268.079	+	268.079i	0.579005	+	0.579005i	−0.355624	+	0.934629i	$0.615732\pi$
$464$	172.732	+	99.7267i	0.372267	+	0.214928i
$465$	−392.535	+	157.559i	−0.844161	+	0.338836i
$466$	81.3623	+	140.924i	0.174597	+	0.302411i
$467$	49.9577	+	186.445i	0.106976	+	0.399239i	0.998562	−	0.0536121i	$-0.0170734\pi$
$467$	49.9577	+	186.445i	0.106976	+	0.399239i	−0.891586	+	0.452851i	$0.850407\pi$
$468$	415.271	+	415.271i	0.887332	+	0.887332i
$469$	−140.661	+	176.318i	−0.299917	+	0.375944i
$470$	118.907	−	89.1801i	0.252993	−	0.189745i
$471$	−364.170	+	630.761i	−0.773185	+	1.33920i
$472$	−206.208	−	55.2532i	−0.436881	−	0.117062i
$473$	−12.2789	+	45.8255i	−0.0259596	+	0.0968826i
$474$	655.343	+	378.362i	1.38258	+	0.798233i
$475$	−442.360	−	129.022i	−0.931285	−	0.271625i
$476$	20.5466	−	136.149i	0.0431651	−	0.286028i
$477$	152.499	−	152.499i	0.319704	−	0.319704i
$478$	−599.309	+	160.584i	−1.25378	+	0.335951i
$479$	642.196	−	370.772i	1.34070	−	0.774055i	0.353792	−	0.935324i	$-0.384892\pi$
$479$	642.196	−	370.772i	1.34070	−	0.774055i	0.986910	+	0.161269i	$0.0515588\pi$
$480$	−58.7441	+	137.523i	−0.122384	+	0.286507i
$481$	274.360	−	475.206i	0.570396	−	0.987954i
$482$	156.182	−	156.182i	0.324029	−	0.324029i
$483$	608.881	+	265.784i	1.26062	+	0.550278i
$484$			217.818i			0.450037i
$485$	199.843	−	254.593i	0.412047	−	0.524935i
$486$	−67.6356	−	117.148i	−0.139168	−	0.241046i
$487$	761.430	+	204.025i	1.56351	+	0.418942i	0.933773	−	0.357865i	$-0.116495\pi$
$487$	761.430	+	204.025i	1.56351	+	0.418942i	0.629739	+	0.776807i	$0.283162\pi$
$488$	−281.152	+	75.3345i	−0.576132	+	0.154374i
$489$			502.677i			1.02797i
$490$	−148.038	+	313.265i	−0.302119	+	0.639315i
$491$	−232.000			−0.472505			−0.236253	−	0.971692i	$-0.575919\pi$
$491$	−232.000			−0.472505			−0.236253	+	0.971692i	$0.575919\pi$
$492$	−16.5458	−	61.7497i	−0.0336296	−	0.125508i
$493$	−126.927	+	473.700i	−0.257459	+	0.960851i
$494$	−349.716	+	201.909i	−0.707928	+	0.408722i
$495$	39.4185	+	327.178i	0.0796334	+	0.660967i
$496$	−64.0000			−0.129032
$497$	−112.970	+	258.802i	−0.227304	+	0.520728i
$498$	−382.271	−	382.271i	−0.767613	−	0.767613i
$499$	570.335	+	329.283i	1.14296	+	0.659886i	0.947161	−	0.320759i	$-0.103938\pi$
$499$	570.335	+	329.283i	1.14296	+	0.659886i	0.195795	+	0.980645i	$0.437271\pi$
$500$	−158.650	+	193.210i	−0.317300	+	0.386420i
$501$	−500.930	−	867.636i	−0.999859	−	1.73181i
$502$	−67.9807	−	253.707i	−0.135420	−	0.505393i
$503$	230.055	+	230.055i	0.457367	+	0.457367i	0.897790	−	0.440424i	$-0.145172\pi$
$503$	230.055	+	230.055i	0.457367	+	0.457367i	−0.440424	+	0.897790i	$0.645172\pi$
$504$	371.077	+	56.0000i	0.736264	+	0.111111i
$505$	−430.497	−	573.996i	−0.852469	−	1.13663i
$506$	−44.1366	+	76.4469i	−0.0872266	+	0.151081i
$507$	362.600	+	97.1583i	0.715187	+	0.191634i
$508$	−18.2679	+	68.1768i	−0.0359605	+	0.134206i
$509$	−105.300	−	60.7950i	−0.206876	−	0.119440i	0.392983	−	0.919546i	$-0.371443\pi$
$509$	−105.300	−	60.7950i	−0.206876	−	0.119440i	−0.599859	+	0.800106i	$0.704777\pi$
$510$	−364.000	−	52.0000i	−0.713725	−	0.101961i
$511$	−485.770	−	387.534i	−0.950627	−	0.758383i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	937.026	−	251.075i	1.82656	−	0.489425i
$514$	292.164	−	168.681i	0.568413	−	0.328173i
$515$	−260.772	+	104.670i	−0.506353	+	0.203244i
$516$	72.1366	−	124.944i	0.139800	−	0.242140i
$517$	51.6832	−	51.6832i	0.0999676	−	0.0999676i
$518$	−39.1955	−	348.440i	−0.0756670	−	0.672664i
$519$		−	1.36232i		−	0.00262489i
$520$	26.2064	+	217.516i	0.0503969	+	0.418300i
$521$	244.135	+	422.853i	0.468588	+	0.811619i	0.999355	−	0.0358988i	$-0.0114294\pi$
$521$	244.135	+	422.853i	0.468588	+	0.811619i	−0.530767	+	0.847518i	$0.678096\pi$
$522$	−1291.08	−	345.943i	−2.47332	−	0.662725i
$523$	−631.039	+	169.086i	−1.20657	+	0.323301i	−0.805417	−	0.592708i	$-0.798059\pi$
$523$	−631.039	+	169.086i	−1.20657	+	0.323301i	−0.401158	+	0.916009i	$0.631392\pi$
$524$			140.182i			0.267523i
$525$	839.645	+	388.719i	1.59932	+	0.740416i
$526$	464.523			0.883123
$527$	−40.7281	−	151.999i	−0.0772829	−	0.288424i
$528$	−19.0333	+	71.0333i	−0.0360480	+	0.134533i
$529$	−179.070	+	103.386i	−0.338507	+	0.195437i
$530$	79.8778	−	9.62370i	0.150713	−	0.0181579i
$531$	1430.63			2.69422
$532$	−103.233	+	236.494i	−0.194046	+	0.444538i
$533$	−66.2257	−	66.2257i	−0.124251	−	0.124251i
$534$	−535.694	−	309.283i	−1.00317	−	0.579182i
$535$	−111.733	−	278.366i	−0.208846	−	0.520310i
$536$	45.5683	+	78.9267i	0.0850155	+	0.147251i
$537$	−59.7122	−	222.849i	−0.111196	−	0.414988i
$538$	−286.180	−	286.180i	−0.531933	−	0.531933i
$539$	−50.2809	+	162.796i	−0.0932855	+	0.302034i
$540$	74.4317	−	521.022i	0.137836	−	0.964855i
$541$	−221.793	+	384.157i	−0.409968	+	0.710086i	−0.994886	−	0.101007i	$-0.967794\pi$
$541$	−221.793	+	384.157i	−0.409968	+	0.710086i	0.584917	+	0.811093i	$0.301127\pi$
$542$	559.416	+	149.895i	1.03213	+	0.276559i
$543$	5.03740	−	18.7998i	0.00927697	−	0.0346221i
$544$	−48.1819	−	27.8178i	−0.0885696	−	0.0511357i
$545$	149.093	−	111.820i	0.273565	−	0.205174i
$546$	754.859	−	296.102i	1.38253	−	0.542311i
$547$	−686.507	+	686.507i	−1.25504	+	1.25504i	−0.301608	+	0.953432i	$0.597523\pi$
$547$	−686.507	+	686.507i	−1.25504	+	1.25504i	−0.953432	+	0.301608i	$0.902477\pi$
$548$	−18.5021	+	4.95764i	−0.0337630	+	0.00904678i
$549$	1689.25	−	975.291i	3.07696	−	1.77649i
$550$	−63.7959	+	105.090i	−0.115993	+	0.191073i
$551$	459.533	−	795.934i	0.833997	−	1.44453i
$552$	189.818	−	189.818i	0.343873	−	0.343873i
$553$	570.076	−	420.575i	1.03088	−	0.760533i
$554$		−	23.0021i		−	0.0415200i
$555$	−929.633	+	112.002i	−1.67502	+	0.201806i
$556$	−53.0217	−	91.8363i	−0.0953628	−	0.165173i
$557$	−44.0239	−	11.7962i	−0.0790376	−	0.0211780i	0.219084	−	0.975706i	$-0.429693\pi$
$557$	−44.0239	−	11.7962i	−0.0790376	−	0.0211780i	−0.298121	+	0.954528i	$0.596360\pi$
$558$	414.276	−	111.005i	0.742430	−	0.198934i
$559$		−	211.366i		−	0.378115i
$560$	95.9933	+	101.908i	0.171417	+	0.181979i
$561$	−180.816			−0.322310
$562$	−110.738	−	413.281i	−0.197043	−	0.735375i
$563$	−185.429	+	692.031i	−0.329359	+	1.22919i	0.580497	+	0.814262i	$0.302858\pi$
$563$	−185.429	+	692.031i	−0.329359	+	1.22919i	−0.909857	+	0.414923i	$0.863809\pi$
$564$	−192.494	+	111.137i	−0.341302	+	0.197051i
$565$	−659.872	−	517.966i	−1.16792	−	0.916754i
$566$	−224.087			−0.395913
$567$	−749.044	+	84.2589i	−1.32107	+	0.148605i
$568$	80.6812	+	80.6812i	0.142044	+	0.142044i
$569$	−724.073	−	418.043i	−1.27254	−	0.734699i	−0.297071	−	0.954855i	$-0.596010\pi$
$569$	−724.073	−	418.043i	−1.27254	−	0.734699i	−0.975464	+	0.220157i	$0.929343\pi$
$570$	633.697	+	270.688i	1.11175	+	0.474892i
$571$	−517.327	−	896.036i	−0.906001	−	1.56924i	−0.819568	−	0.572982i	$-0.805786\pi$
$571$	−517.327	−	896.036i	−0.906001	−	1.56924i	−0.0864332	−	0.996258i	$-0.527547\pi$
$572$	27.8846	+	104.067i	0.0487493	+	0.181935i
$573$	67.0435	+	67.0435i	0.117004	+	0.117004i
$574$	−59.1778	−	8.93064i	−0.103097	−	0.0155586i
$575$	393.485	−	215.782i	0.684322	−	0.375273i
$576$	75.8178	−	131.320i	0.131628	−	0.227987i
$577$	−115.431	−	30.9295i	−0.200053	−	0.0536040i	0.157401	−	0.987535i	$-0.449688\pi$
$577$	−115.431	−	30.9295i	−0.200053	−	0.0536040i	−0.357454	+	0.933931i	$0.616355\pi$
$578$	−70.3762	+	262.647i	−0.121758	+	0.454407i
$579$	−973.666	−	562.146i	−1.68163	−	0.970892i
$580$	−299.180	−	398.907i	−0.515828	−	0.687770i
$581$	−471.157	+	184.817i	−0.810942	+	0.318101i
$582$	−342.249	+	342.249i	−0.588058	+	0.588058i
$583$	38.2162	−	10.2400i	0.0655509	−	0.0175643i
$584$	−217.449	+	125.545i	−0.372345	+	0.214973i
$585$	−546.907	−	1362.54i	−0.934884	−	2.32913i
$586$	−100.182	+	173.521i	−0.170959	+	0.296110i
$587$	−808.313	+	808.313i	−1.37702	+	1.37702i	−0.527416	+	0.849607i	$0.676839\pi$
$587$	−808.313	+	808.313i	−1.37702	+	1.37702i	−0.849607	+	0.527416i	$0.823161\pi$
$588$	275.830	−	438.626i	0.469098	−	0.745962i
$589$			294.907i			0.500691i
$590$	419.818	+	329.535i	0.711556	+	0.558535i
$591$	−153.624	−	266.084i	−0.259939	−	0.450227i
$592$	−136.851	−	36.6692i	−0.231168	−	0.0619413i
$593$	86.3085	−	23.1263i	0.145546	−	0.0389988i	−0.185311	−	0.982680i	$-0.559329\pi$
$593$	86.3085	−	23.1263i	0.145546	−	0.0389988i	0.330856	+	0.943681i	$0.392662\pi$
$594$		−	258.816i		−	0.435717i
$595$	−180.943	+	292.835i	−0.304106	+	0.492160i
$596$	−418.182			−0.701648
$597$	412.642	+	1540.00i	0.691192	+	2.57956i
$598$	101.788	−	379.880i	0.170215	−	0.635250i
$599$	337.198	−	194.681i	0.562934	−	0.325010i	−0.191388	−	0.981514i	$-0.561299\pi$
$599$	337.198	−	194.681i	0.562934	−	0.325010i	0.754322	+	0.656504i	$0.227966\pi$
$600$	270.110	−	258.482i	0.450183	−	0.430803i
$601$	478.638			0.796402			0.398201	−	0.917298i	$-0.369635\pi$
$601$	478.638			0.796402			0.398201	+	0.917298i	$0.369635\pi$
$602$	−80.1847	−	108.688i	−0.133197	−	0.180544i
$603$	−431.861	−	431.861i	−0.716188	−	0.716188i
$604$	280.750	+	162.091i	0.464818	+	0.268363i
$605$	213.908	−	500.771i	0.353567	−	0.827721i
$606$	536.487	+	929.223i	0.885292	+	1.53337i
$607$	165.729	+	618.509i	0.273030	+	1.01896i	0.957150	+	0.289592i	$0.0935195\pi$
$607$	165.729	+	618.509i	0.273030	+	1.01896i	−0.684121	+	0.729369i	$0.739814\pi$
$608$	73.7267	+	73.7267i	0.121261	+	0.121261i
$609$	−1150.89	+	1442.63i	−1.88980	+	2.36885i
$610$	720.362	+	102.909i	1.18092	+	0.168703i
$611$	−162.820	+	282.012i	−0.266481	+	0.461559i
$612$	360.133	+	96.4973i	0.588453	+	0.157675i
$613$	−295.398	+	1102.44i	−0.481889	+	1.79843i	0.111792	+	0.993732i	$0.464341\pi$
$613$	−295.398	+	1102.44i	−0.481889	+	1.79843i	−0.593681	+	0.804701i	$0.702326\pi$
$614$	420.199	+	242.602i	0.684363	+	0.395117i
$615$	−22.6020	+	158.214i	−0.0367512	+	0.257258i
$616$	53.8178	+	42.9343i	0.0873666	+	0.0696985i
$617$	15.0890	−	15.0890i	0.0244555	−	0.0244555i	−0.694773	−	0.719229i	$-0.744495\pi$
$617$	15.0890	−	15.0890i	0.0244555	−	0.0244555i	0.719229	+	0.694773i	$0.244495\pi$
$618$	405.893	−	108.759i	0.656785	−	0.175985i
$619$	−124.687	+	71.9881i	−0.201433	+	0.116297i	−0.597324	−	0.802000i	$-0.703769\pi$
$619$	−124.687	+	71.9881i	−0.201433	+	0.116297i	0.395891	+	0.918298i	$0.370436\pi$
$620$	147.138	+	62.8513i	0.237320	+	0.101373i
$621$	−472.383	+	818.191i	−0.760681	+	1.31754i
$622$	−7.47723	+	7.47723i	−0.0120213	+	0.0120213i
$623$	−465.995	+	343.789i	−0.747985	+	0.551828i
$624$		−	327.636i		−	0.525057i
$625$	554.485	−	288.395i	0.887175	−	0.461433i
$626$	−423.089	−	732.812i	−0.675861	−	1.17063i
$627$	327.316	+	87.7040i	0.522035	+	0.139879i
$628$	266.123	−	71.3075i	0.423763	−	0.113547i
$629$		−	348.356i		−	0.553825i
$630$	−798.126	−	493.163i	−1.26687	−	0.782798i
$631$	395.200			0.626307			0.313154	−	0.949703i	$-0.398615\pi$
$631$	395.200			0.626307			0.313154	+	0.949703i	$0.398615\pi$
$632$	−74.0864	−	276.494i	−0.117225	−	0.437491i
$633$	−243.173	+	907.536i	−0.384160	+	1.43371i
$634$	−498.831	+	288.000i	−0.786799	+	0.454259i
$635$	108.952	−	138.801i	0.171578	−	0.218584i
$636$	−120.317			−0.189177
$637$	28.6601	−	758.564i	0.0449923	−	1.19084i
$638$	−173.386	−	173.386i	−0.271765	−	0.271765i
$639$	−662.192	−	382.317i	−1.03629	−	0.598305i
$640$	52.4974	−	21.0718i	0.0820272	−	0.0329247i
$641$	50.3416	+	87.1942i	0.0785361	+	0.136028i	0.902619	−	0.430441i	$-0.141642\pi$
$641$	50.3416	+	87.1942i	0.0785361	+	0.136028i	−0.824082	+	0.566470i	$0.808309\pi$
$642$	116.097	+	433.279i	0.180836	+	0.674889i
$643$	301.770	+	301.770i	0.469316	+	0.469316i	0.901693	−	0.432377i	$-0.142325\pi$
$643$	301.770	+	301.770i	0.469316	+	0.469316i	−0.432377	+	0.901693i	$0.642325\pi$
$644$	−91.7712	−	233.954i	−0.142502	−	0.363283i
$645$	−288.547	+	216.410i	−0.447359	+	0.335519i
$646$	−128.182	+	222.018i	−0.198424	+	0.343681i
$647$	517.894	+	138.769i	0.800454	+	0.214481i	0.635784	−	0.771867i	$-0.280677\pi$
$647$	517.894	+	138.769i	0.800454	+	0.214481i	0.164671	+	0.986349i	$0.447344\pi$
$648$	−78.8281	+	294.190i	−0.121648	+	0.453998i
$649$	227.290	+	131.226i	0.350215	+	0.202197i
$650$	153.362	−	525.814i	0.235942	−	0.808944i
$651$	88.3644	−	585.536i	0.135736	−	0.899441i
$652$	134.455	−	134.455i	0.206220	−	0.206220i
$653$	938.581	−	251.492i	1.43734	−	0.385133i	0.545737	−	0.837957i	$-0.316250\pi$
$653$	938.581	−	251.492i	1.43734	−	0.385133i	0.891600	+	0.452823i	$0.149583\pi$
$654$	−241.362	+	139.350i	−0.369055	+	0.213074i
$655$	137.666	−	322.284i	0.210177	−	0.492037i
$656$	−12.0911	+	20.9424i	−0.0184316	+	0.0319244i
$657$	1189.81	−	1189.81i	1.81098	−	1.81098i
$658$	23.2607	+	206.783i	0.0353506	+	0.314260i
$659$		−	735.842i		−	1.11660i	−0.829638	−	0.558302i	$-0.811453\pi$
$659$		−	735.842i		−	1.11660i	0.829638	−	0.558302i	$-0.188547\pi$
$660$	113.517	−	144.617i	0.171995	−	0.219116i
$661$	−23.0901	−	39.9932i	−0.0349320	−	0.0605040i	0.848031	−	0.529947i	$-0.177788\pi$
$661$	−23.0901	−	39.9932i	−0.0349320	−	0.0605040i	−0.882963	+	0.469443i	$0.844455\pi$
$662$	323.247	+	86.6139i	0.488289	+	0.130837i
$663$	778.131	−	208.500i	1.17365	−	0.314479i
$664$			204.499i			0.307980i
$665$	469.585	−	442.329i	0.706143	−	0.665157i
$666$	949.449			1.42560
$667$	231.664	+	864.583i	0.347323	+	1.29623i
$668$	−98.0861	+	366.062i	−0.146835	+	0.547997i
$669$	1613.12	−	931.336i	2.41124	−	1.39213i
$670$	−27.2533	−	226.206i	−0.0406766	−	0.337621i
$671$	357.837			0.533290
$672$	−124.293	−	168.475i	−0.184960	−	0.250707i
$673$	−122.772	−	122.772i	−0.182425	−	0.182425i	0.609986	−	0.792412i	$-0.291175\pi$
$673$	−122.772	−	122.772i	−0.182425	−	0.182425i	−0.792412	+	0.609986i	$0.791175\pi$
$674$	−547.798	−	316.271i	−0.812756	−	0.469245i
$675$	−682.791	+	1124.75i	−1.01154	+	1.66630i
$676$	−71.0000	−	122.976i	−0.105030	−	0.181917i
$677$	−89.4436	−	333.808i	−0.132118	−	0.493069i	0.867876	−	0.496782i	$-0.165485\pi$
$677$	−89.4436	−	333.808i	−0.132118	−	0.493069i	−0.999993	+	0.00371227i	$0.998818\pi$
$678$	887.065	+	887.065i	1.30836	+	1.30836i
$679$	165.467	+	421.830i	0.243693	+	0.621251i
$680$	83.4534	+	111.271i	0.122726	+	0.163634i
$681$	109.612	−	189.853i	0.160957	−	0.278786i
$682$	75.9997	+	20.3640i	0.111436	+	0.0298593i
$683$	183.607	−	685.231i	0.268824	−	1.00327i	−0.691043	−	0.722813i	$-0.742849\pi$
$683$	183.607	−	685.231i	0.268824	−	1.00327i	0.959868	−	0.280453i	$-0.0904846\pi$
$684$	−605.113	−	349.362i	−0.884669	−	0.510764i
$685$	47.4058	+	6.77226i	0.0692055	+	0.00988650i
$686$	−273.034	−	400.937i	−0.398008	−	0.584457i
$687$	−1178.00	+	1178.00i	−1.71470	+	1.71470i
$688$	−52.7150	+	14.1249i	−0.0766206	+	0.0205304i
$689$	−152.654	+	88.1346i	−0.221558	+	0.127917i
$690$	−622.809	+	249.988i	−0.902622	+	0.362301i
$691$	−572.329	+	991.302i	−0.828261	+	1.43459i	0.0711395	+	0.997466i	$0.477336\pi$
$691$	−572.329	+	991.302i	−0.828261	+	1.43459i	−0.899401	+	0.437125i	$0.855997\pi$
$692$	−0.364391	+	0.364391i	−0.000526576	+	0.000526576i
$693$	−422.834	−	184.572i	−0.610150	−	0.266338i
$694$		−	200.657i		−	0.289132i
$695$	31.7110	+	263.205i	0.0456274	+	0.378713i
$696$	372.840	+	645.777i	0.535689	+	0.927841i
$697$	−57.4325	−	15.3890i	−0.0823995	−	0.0220789i
$698$	−408.252	+	109.391i	−0.584888	+	0.156720i
$699$			608.364i			0.870335i
$700$	−120.613	−	328.561i	−0.172305	−	0.469373i
$701$	496.362			0.708077			0.354039	−	0.935231i	$-0.384808\pi$
$701$	496.362			0.708077			0.354039	+	0.935231i	$0.384808\pi$
$702$	298.442	+	1113.80i	0.425131	+	1.58661i
$703$	−168.969	+	630.600i	−0.240354	+	0.897013i
$704$	24.0909	−	13.9089i	0.0342201	−	0.0197570i
$705$	551.694	−	66.4682i	0.782544	−	0.0942811i
$706$	48.7246			0.0690151
$707$	998.197	−	112.286i	1.41188	−	0.158820i
$708$	−564.360	−	564.360i	−0.797119	−	0.797119i
$709$	282.281	+	162.975i	0.398140	+	0.229866i	0.685681	−	0.727902i	$-0.259504\pi$
$709$	282.281	+	162.975i	0.398140	+	0.229866i	−0.287541	+	0.957768i	$0.592838\pi$
$710$	−106.256	−	264.722i	−0.149656	−	0.372848i
$711$	959.132	+	1661.27i	1.34899	+	2.33652i
$712$	60.5602	+	226.014i	0.0850564	+	0.317435i
$713$	−203.089	−	203.089i	−0.284837	−	0.284837i
$714$	321.029	−	402.408i	0.449621	−	0.563596i
$715$	38.0911	−	266.638i	0.0532743	−	0.372920i
$716$	−43.6356	+	75.5791i	−0.0609436	+	0.105557i
$717$	−2240.58	−	600.363i	−3.12494	−	0.837326i
$718$	180.116	−	672.203i	0.250858	−	0.936216i
$719$	−543.130	−	313.576i	−0.755396	−	0.436128i	0.0722443	−	0.997387i	$-0.476984\pi$
$719$	−543.130	−	313.576i	−0.755396	−	0.436128i	−0.827640	+	0.561259i	$0.810317\pi$
$720$	−303.271	+	227.453i	−0.421210	+	0.315908i
$721$	58.7029	−	388.988i	0.0814187	−	0.539511i
$722$	−21.2733	+	21.2733i	−0.0294644	+	0.0294644i
$723$	797.629	−	213.724i	1.10322	−	0.295607i
$724$	−6.37595	+	3.68116i	−0.00880656	+	0.00508447i
$725$	296.080	+	1210.91i	0.408386	+	1.67022i
$726$	−407.168	+	705.236i	−0.560838	+	0.971399i
$727$	−9.62370	+	9.62370i	−0.0132376	+	0.0132376i	−0.713695	−	0.700457i	$-0.752980\pi$
$727$	−9.62370	+	9.62370i	−0.0132376	+	0.0132376i	0.700457	+	0.713695i	$0.252980\pi$
$728$	−281.110	−	122.708i	−0.386140	−	0.168555i
$729$			463.404i			0.635670i
$730$	623.216	−	75.0852i	0.853720	−	0.102856i
$731$	−67.0932	−	116.209i	−0.0917827	−	0.158972i
$732$	−1051.12	−	281.647i	−1.43596	−	0.384763i
$733$	−211.301	+	56.6180i	−0.288269	+	0.0772415i	−0.400056	−	0.916491i	$-0.631009\pi$
$733$	−211.301	+	56.6180i	−0.288269	+	0.0772415i	0.111787	+	0.993732i	$0.464343\pi$
$734$		−	102.978i		−	0.140297i
$735$	−1064.90	+	737.539i	−1.44884	+	1.00345i
$736$	−101.545			−0.137968
$737$	−28.9986	−	108.224i	−0.0393468	−	0.146844i
$738$	41.9429	−	156.533i	0.0568332	−	0.212104i
$739$	−467.750	+	270.055i	−0.632949	+	0.365434i	−0.781893	−	0.623412i	$-0.785746\pi$
$739$	−467.750	+	270.055i	−0.632949	+	0.365434i	0.148944	+	0.988846i	$0.452413\pi$
$740$	278.616	+	218.699i	0.376508	+	0.295539i
$741$	−1509.72			−2.03741
$742$	−45.0617	+	103.231i	−0.0607301	+	0.139126i
$743$	142.376	+	142.376i	0.191624	+	0.191624i	0.796397	−	0.604774i	$-0.206736\pi$
$743$	142.376	+	142.376i	0.191624	+	0.191624i	−0.604774	+	0.796397i	$0.706736\pi$
$744$	−207.215	−	119.636i	−0.278515	−	0.160801i
$745$	961.417	+	410.676i	1.29049	+	0.551243i
$746$	−243.271	−	421.358i	−0.326101	−	0.564823i
$747$	−354.694	−	1323.74i	−0.474824	−	1.77207i
$748$	48.3644	+	48.3644i	0.0646583	+	0.0646583i
$749$	415.233	+	62.6636i	0.554383	+	0.0836630i
$750$	−874.835	+	328.998i	−1.16645	+	0.438664i
$751$	602.043	−	1042.77i	0.801656	−	1.38851i	−0.116870	−	0.993147i	$-0.537286\pi$
$751$	602.043	−	1042.77i	0.801656	−	1.38851i	0.918526	−	0.395361i	$-0.129381\pi$
$752$	81.2149	+	21.7615i	0.107999	+	0.0289381i
$753$	254.153	−	948.514i	0.337521	−	1.25965i
$754$	946.091	+	546.226i	1.25476	+	0.724437i
$755$	−486.273	−	648.364i	−0.644071	−	0.858761i
$756$	575.998	+	459.515i	0.761902	+	0.607824i
$757$	−297.410	+	297.410i	−0.392880	+	0.392880i	−0.875713	−	0.482833i	$-0.839608\pi$
$757$	−297.410	+	297.410i	−0.392880	+	0.392880i	0.482833	+	0.875713i	$0.339608\pi$
$758$	45.8552	−	12.2869i	0.0604950	−	0.0162096i
$759$	−285.805	+	165.010i	−0.376555	+	0.217404i
$760$	−97.0971	−	241.904i	−0.127759	−	0.318295i
$761$	368.271	−	637.864i	0.483931	−	0.838192i	−0.515899	−	0.856649i	$-0.672542\pi$
$761$	368.271	−	637.864i	0.483931	−	0.838192i	0.999830	+	0.0184569i	$0.00587536\pi$
$762$	−186.590	+	186.590i	−0.244869	+	0.244869i
$763$	29.1658	+	259.278i	0.0382251	+	0.339814i
$764$		−	35.8654i		−	0.0469443i
$765$	−733.194	−	575.520i	−0.958424	−	0.752314i
$766$	−508.693	−	881.082i	−0.664090	−	1.15024i
$767$	−1129.45	−	302.634i	−1.47255	−	0.394569i
$768$	−81.7126	+	21.8948i	−0.106397	+	0.0285089i
$769$		−	1006.45i		−	1.30877i	−0.756160	−	0.654387i	$-0.772927\pi$
$769$		−	1006.45i		−	1.30877i	0.756160	−	0.654387i	$-0.227073\pi$
$770$	−81.5655	−	151.559i	−0.105929	−	0.196830i
$771$	1261.27			1.63588
$772$	110.073	+	410.797i	0.142581	+	0.532121i
$773$	208.117	−	776.703i	0.269233	−	1.00479i	−0.690376	−	0.723451i	$-0.742555\pi$
$773$	208.117	−	776.703i	0.269233	−	1.00479i	0.959608	−	0.281339i	$-0.0907786\pi$
$774$	316.729	−	182.863i	0.409210	−	0.236258i
$775$	−276.554	−	288.995i	−0.356844	−	0.372897i
$776$	183.089			0.235939
$777$	524.437	−	1201.42i	0.674951	−	1.54624i
$778$	531.089	+	531.089i	0.682634	+	0.682634i
$779$	96.5009	+	55.7148i	0.123878	+	0.0715209i
$780$	−321.755	+	753.247i	−0.412506	+	0.965701i
$781$	−70.1366	−	121.480i	−0.0898036	−	0.155544i
$782$	−64.6205	−	241.167i	−0.0826350	−	0.308398i
$783$	−1855.71	−	1855.71i	−2.37000	−	2.37000i
$784$	−191.102	+	43.5445i	−0.243752	+	0.0555415i
$785$	−681.855	−	97.4079i	−0.868605	−	0.124086i
$786$	−262.043	+	453.873i	−0.333389	+	0.577446i
$787$	643.687	+	172.475i	0.817900	+	0.219156i	0.643428	−	0.765507i	$-0.277512\pi$
$787$	643.687	+	172.475i	0.817900	+	0.219156i	0.174472	+	0.984662i	$0.444178\pi$
$788$	−30.0808	+	112.263i	−0.0381736	+	0.142466i
$789$	1504.00	+	868.335i	1.90621	+	1.10055i
$790$	−101.204	+	708.428i	−0.128106	+	0.896744i
$791$	1093.33	−	428.869i	1.38221	−	0.542186i
$792$	−131.818	+	131.818i	−0.166437	+	0.166437i
$793$	−1539.93	+	412.624i	−1.94191	+	0.520333i
$794$	329.326	−	190.137i	0.414769	−	0.239467i
$795$	276.613	+	118.157i	0.347941	+	0.148625i
$796$	301.545	−	522.290i	0.378825	−	0.656144i
$797$	202.408	−	202.408i	0.253962	−	0.253962i	−0.568631	−	0.822593i	$-0.692527\pi$
$797$	202.408	−	202.408i	0.253962	−	0.253962i	0.822593	+	0.568631i	$0.192527\pi$
$798$	−776.320	+	572.732i	−0.972832	+	0.717709i
$799$			206.733i			0.258740i
$800$	−141.387	−	3.11027i	−0.176734	−	0.00388784i
$801$	−784.020	−	1357.96i	−0.978801	−	1.69533i
$802$	754.784	+	202.244i	0.941127	+	0.252174i
$803$	298.167	−	79.8936i	0.371316	−	0.0994939i
$804$			340.725i			0.423787i
$805$	−18.7697	+	627.994i	−0.0233164	+	0.780117i
$806$	−350.542			−0.434916
$807$	−391.617	−	1461.53i	−0.485275	−	1.81107i
$808$	105.049	−	392.046i	0.130011	−	0.485206i
$809$	138.014	−	79.6822i	0.170598	−	0.0984947i	−0.412270	−	0.911062i	$-0.635264\pi$
$809$	138.014	−	79.6822i	0.170598	−	0.0984947i	0.582868	+	0.812567i	$0.301931\pi$
$810$	470.139	−	598.942i	0.580418	−	0.739434i
$811$	741.545			0.914358			0.457179	−	0.889375i	$-0.348860\pi$
$811$	741.545			0.914358			0.457179	+	0.889375i	$0.348860\pi$
$812$	693.712	−	78.0346i	0.854325	−	0.0961018i
$813$	1531.04	+	1531.04i	1.88320	+	1.88320i
$814$	150.843	+	87.0890i	0.185310	+	0.106989i
$815$	−441.160	+	177.076i	−0.541301	+	0.217271i
$816$	−104.000	−	180.133i	−0.127451	−	0.220752i
$817$	65.0866	+	242.906i	0.0796654	+	0.297315i
$818$	125.317	+	125.317i	0.153199	+	0.153199i
$819$	2032.47	+	306.725i	2.48165	+	0.374511i
$820$	48.3644	−	36.2733i	0.0589810	−	0.0442357i
$821$	−788.950	+	1366.50i	−0.960963	+	1.66444i	−0.240871	+	0.970557i	$0.577433\pi$
$821$	−788.950	+	1366.50i	−0.960963	+	1.66444i	−0.720092	+	0.693879i	$0.755900\pi$
$822$	−69.1724	−	18.5347i	−0.0841513	−	0.0225483i
$823$	−157.478	+	587.715i	−0.191346	+	0.714114i	0.801836	+	0.597544i	$0.203857\pi$
$823$	−157.478	+	587.715i	−0.191346	+	0.714114i	−0.993182	+	0.116570i	$0.962810\pi$
$824$	−137.659	−	79.4772i	−0.167061	−	0.0964529i
$825$	−403.000	+	221.000i	−0.488485	+	0.267879i
$826$	−695.586	+	272.851i	−0.842114	+	0.330328i
$827$	1014.44	−	1014.44i	1.22665	−	1.22665i	0.261426	−	0.965223i	$-0.415807\pi$
$827$	1014.44	−	1014.44i	1.22665	−	1.22665i	0.965223	−	0.261426i	$-0.0841929\pi$
$828$	657.304	−	176.124i	0.793846	−	0.212710i
$829$	344.517	−	198.907i	0.415581	−	0.239936i	−0.277604	−	0.960696i	$-0.589540\pi$
$829$	344.517	−	198.907i	0.415581	−	0.239936i	0.693185	+	0.720760i	$0.256207\pi$
$830$	200.828	−	470.151i	0.241962	−	0.566447i
$831$	42.9979	−	74.4746i	0.0517424	−	0.0896204i
$832$	−87.6356	+	87.6356i	−0.105331	+	0.105331i
$833$	−225.030	−	426.154i	−0.270145	−	0.511589i
$834$		−	396.455i		−	0.475366i
$835$	584.995	−	745.266i	0.700593	−	0.892534i
$836$	−64.0911	−	111.009i	−0.0766640	−	0.132786i
$837$	813.404	+	217.951i	0.971809	+	0.260396i
$838$	−158.827	+	42.5575i	−0.189531	+	0.0507846i
$839$			1475.70i			1.75888i	0.476011	+	0.879439i	$0.342082\pi$
$839$			1475.70i			1.75888i	−0.476011	+	0.879439i	$0.657918\pi$
$840$	120.303	+	509.393i	0.143218	+	0.606420i
$841$	−1645.35			−1.95643
$842$	−195.622	−	730.071i	−0.232330	−	0.867068i
$843$	414.007	−	1545.10i	0.491112	−	1.83285i
$844$	307.790	−	177.703i	0.364681	−	0.210548i
$845$	42.4634	+	352.451i	0.0502526	+	0.417102i
$846$	−563.453			−0.666021
$847$	452.594	+	613.477i	0.534350	+	0.724295i
$848$	32.1822	+	32.1822i	0.0379507	+	0.0379507i
$849$	−725.534	−	418.887i	−0.854575	−	0.493389i
$850$	−82.5886	−	337.772i	−0.0971630	−	0.397379i
$851$	−317.905	−	550.627i	−0.373566	−	0.647035i
$852$	110.406	+	412.042i	0.129585	+	0.483617i
$853$	307.404	+	307.404i	0.360380	+	0.360380i	0.863953	−	0.503573i	$-0.167982\pi$
$853$	307.404	+	307.404i	0.360380	+	0.360380i	−0.503573	+	0.863953i	$0.667982\pi$
$854$	−635.323	+	796.372i	−0.743938	+	0.932520i
$855$	1048.09	+	1397.45i	1.22583	+	1.63444i
$856$	84.8395	−	146.946i	0.0991116	−	0.171666i
$857$	−1162.11	−	311.386i	−1.35602	−	0.363344i	−0.493666	−	0.869651i	$-0.664344\pi$
$857$	−1162.11	−	311.386i	−1.35602	−	0.363344i	−0.862353	+	0.506307i	$0.831010\pi$
$858$	−104.250	+	389.066i	−0.121503	+	0.453456i
$859$	−795.008	−	458.998i	−0.925504	−	0.534340i	−0.0401170	−	0.999195i	$-0.512773\pi$
$859$	−795.008	−	458.998i	−0.925504	−	0.534340i	−0.885387	+	0.464855i	$0.846106\pi$
$860$	135.065	+	19.2950i	0.157053	+	0.0224361i
$861$	−174.908	−	139.536i	−0.203145	−	0.162063i
$862$	477.473	−	477.473i	0.553913	−	0.553913i
$863$	−1226.45	+	328.625i	−1.42114	+	0.380794i	−0.885889	−	0.463897i	$-0.846451\pi$
$863$	−1226.45	+	328.625i	−1.42114	+	0.380794i	−0.535254	+	0.844691i	$0.679784\pi$
$864$	257.839	−	148.863i	0.298425	−	0.172296i
$865$	1.19560	−	0.479898i	0.00138219	−	0.000554795i
$866$	−542.271	+	939.241i	−0.626179	+	1.08457i
$867$	−718.828	+	718.828i	−0.829098	+	0.829098i
$868$	−180.254	+	132.983i	−0.207666	+	0.153206i
$869$			351.909i			0.404958i
$870$	−222.986	−	1850.81i	−0.256306	−	2.12737i
$871$	249.588	+	432.299i	0.286553	+	0.496325i
$872$	101.833	+	27.2859i	0.116780	+	0.0312912i
$873$	−1185.15	+	317.559i	−1.35756	+	0.363756i
$874$			467.909i			0.535365i
$875$	−45.3695	+	873.823i	−0.0518509	+	0.998655i
$876$	−938.725			−1.07160
$877$	104.335	+	389.382i	0.118968	+	0.443993i	0.999553	−	0.0298940i	$-0.00951699\pi$
$877$	104.335	+	389.382i	0.118968	+	0.443993i	−0.880585	+	0.473888i	$0.842850\pi$
$878$	−98.2949	+	366.841i	−0.111953	+	0.417815i
$879$	−648.727	+	374.542i	−0.738028	+	0.426101i
$880$	−69.0452	+	8.31858i	−0.0784605	+	0.00945294i
$881$	338.402			0.384111			0.192055	−	0.981384i	$-0.438485\pi$
$881$	338.402			0.384111			0.192055	+	0.981384i	$0.438485\pi$
$882$	1161.49	−	613.323i	1.31688	−	0.695378i
$883$	−455.410	−	455.410i	−0.515753	−	0.515753i	0.400530	−	0.916283i	$-0.368826\pi$
$883$	−455.410	−	455.410i	−0.515753	−	0.515753i	−0.916283	+	0.400530i	$0.868826\pi$
$884$	−263.903	−	152.364i	−0.298533	−	0.172358i
$885$	743.255	+	1851.72i	0.839836	+	2.09233i
$886$	62.3525	+	107.998i	0.0703753	+	0.121894i
$887$	104.463	+	389.861i	0.117771	+	0.439528i	0.999479	−	0.0322675i	$-0.0102729\pi$
$887$	104.463	+	389.861i	0.117771	+	0.439528i	−0.881708	+	0.471795i	$0.843606\pi$
$888$	−374.542	−	374.542i	−0.421782	−	0.421782i
$889$	90.2107	+	229.976i	0.101474	+	0.258691i
$890$	82.7267	−	579.087i	0.0929514	−	0.650659i
$891$	187.216	−	324.267i	0.210119	−	0.363936i
$892$	−680.589	−	182.363i	−0.762992	−	0.204443i
$893$	100.275	−	374.232i	0.112290	−	0.419072i
$894$	−1353.96	−	781.711i	−1.51450	−	0.874397i
$895$	174.542	−	130.907i	0.195019	−	0.146265i
$896$	−11.8178	+	78.3093i	−0.0131895	+	0.0873987i
$897$	1039.67	−	1039.67i	1.15906	−	1.15906i
$898$	−137.163	+	36.7526i	−0.152742	+	0.0409272i
$899$	690.927	−	398.907i	0.768550	−	0.443723i
$900$	920.603	−	225.096i	1.02289	−	0.250107i
$901$	−55.9524	+	96.9124i	−0.0621003	+	0.107561i
$902$	21.0217	−	21.0217i	0.0233057	−	0.0233057i
$903$	−56.4458	−	501.792i	−0.0625092	−	0.555694i
$904$		−	474.542i		−	0.524936i
$905$	18.2736	−	2.20161i	0.0201919	−	0.00243272i
$906$	605.996	+	1049.62i	0.668870	+	1.15852i
$907$	589.236	+	157.885i	0.649653	+	0.174074i	0.568572	−	0.822633i	$-0.307496\pi$
$907$	589.236	+	157.885i	0.649653	+	0.174074i	0.0810812	+	0.996707i	$0.474163\pi$
$908$	−80.1006	+	21.4629i	−0.0882165	+	0.0236375i
$909$			2719.94i			2.99224i
$910$	525.777	+	558.174i	0.577777	+	0.613378i
$911$	−716.063			−0.786019			−0.393009	−	0.919534i	$-0.628566\pi$
$911$	−716.063			−0.786019			−0.393009	+	0.919534i	$0.628566\pi$
$912$	100.890	+	376.525i	0.110625	+	0.412857i
$913$	65.0692	−	242.841i	0.0712696	−	0.265982i
$914$	−852.004	+	491.905i	−0.932171	+	0.538189i
$915$	2139.97	+	1679.77i	2.33877	+	1.83581i
$916$	630.178			0.687967
$917$	291.279	+	394.819i	0.317643	+	0.430555i
$918$	517.631	+	517.631i	0.563869	+	0.563869i
$919$	−222.629	−	128.535i	−0.242251	−	0.139864i	0.373960	−	0.927445i	$-0.378000\pi$
$919$	−222.629	−	128.535i	−0.242251	−	0.139864i	−0.616211	+	0.787581i	$0.711333\pi$
$920$	233.455	+	99.7219i	0.253755	+	0.108393i
$921$	906.995	+	1570.96i	0.984793	+	1.70571i
$922$	70.1435	+	261.779i	0.0760776	+	0.283925i
$923$	441.909	+	441.909i	0.478775	+	0.478775i
$924$	93.9904	+	239.612i	0.101721	+	0.259320i
$925$	−425.774	−	776.412i	−0.460297	−	0.839364i
$926$	268.079	−	464.327i	0.289502	−	0.501433i
$927$	1028.92	+	275.699i	1.10995	+	0.297410i
$928$	73.0050	−	272.458i	0.0786692	−	0.293597i
$929$	−1104.77	−	637.841i	−1.18921	−	0.686588i	−0.231080	−	0.972935i	$-0.574226\pi$
$929$	−1104.77	−	637.841i	−1.18921	−	0.686588i	−0.958126	+	0.286346i	$0.907559\pi$
$930$	358.907	+	478.542i	0.385921	+	0.514562i
$931$	200.650	+	880.581i	0.215521	+	0.945845i
$932$	162.725	−	162.725i	0.174597	−	0.174597i
$933$	−38.1865	+	10.2320i	−0.0409287	+	0.0109668i
$934$	236.403	−	136.487i	0.253108	−	0.146132i
$935$	−63.6953	−	158.688i	−0.0681233	−	0.169720i
$936$	415.271	−	719.271i	0.443666	−	0.768452i
$937$	−589.180	+	589.180i	−0.628794	+	0.628794i	−0.947765	−	0.318970i	$-0.896663\pi$
$937$	−589.180	+	589.180i	−0.628794	+	0.628794i	0.318970	+	0.947765i	$0.396663\pi$
$938$	292.340	+	127.610i	0.311663	+	0.136045i
$939$		−	3163.53i		−	3.36904i
$940$	−165.345	−	129.788i	−0.175899	−	0.138072i
$941$	−98.6377	−	170.845i	−0.104822	−	0.181557i	0.808843	−	0.588024i	$-0.200094\pi$
$941$	−98.6377	−	170.845i	−0.104822	−	0.181557i	−0.913666	+	0.406467i	$0.866761\pi$
$942$	994.932	+	266.591i	1.05619	+	0.283005i
$943$	−104.824	+	28.0875i	−0.111160	+	0.0297853i
$944$			301.909i			0.319819i
$945$	−872.974	−	1622.10i	−0.923783	−	1.71651i
$946$	67.0932			0.0709230
$947$	−400.951	−	1496.37i	−0.423390	−	1.58011i	−0.767413	−	0.641153i	$-0.778456\pi$
$947$	−400.951	−	1496.37i	−0.423390	−	1.58011i	0.344023	−	0.938961i	$-0.388210\pi$
$948$	276.980	−	1033.71i	0.292173	−	1.09041i
$949$	−1191.02	+	687.636i	−1.25503	+	0.724590i
$950$	−14.3319	+	651.501i	−0.0150862	+	0.685790i
$951$	−2153.44			−2.26440
$952$	−193.504	+	21.7670i	−0.203261	+	0.0228645i
$953$	1139.41	+	1139.41i	1.19560	+	1.19560i	0.975471	+	0.220128i	$0.0706475\pi$
$953$	1139.41	+	1139.41i	1.19560	+	1.19560i	0.220128	+	0.975471i	$0.429353\pi$
$954$	−264.136	−	152.499i	−0.276872	−	0.159852i
$955$	−35.2217	+	82.4560i	−0.0368813	+	0.0863413i
$956$	438.725	+	759.893i	0.458917	+	0.794868i
$957$	−237.266	−	885.490i	−0.247927	−	0.925277i
$958$	−741.545	−	741.545i	−0.774055	−	0.774055i
$959$	−41.8095	+	52.4079i	−0.0435970	+	0.0546485i
$960$	209.362	+	29.9089i	0.218086	+	0.0311551i
$961$	352.500	−	610.548i	0.366805	−	0.635326i
$962$	−749.566	−	200.846i	−0.779175	−	0.208779i
$963$	−294.300	+	1098.34i	−0.305608	+	1.14054i
$964$	−270.515	−	156.182i	−0.280618	−	0.162015i
$965$	150.362	−	1052.54i	0.155816	−	1.09071i
$966$	140.202	−	929.031i	0.145136	−	0.961729i
$967$	−184.424	+	184.424i	−0.190718	+	0.190718i	−0.796006	−	0.605289i	$-0.793058\pi$
$967$	−184.424	+	184.424i	−0.190718	+	0.190718i	0.605289	+	0.796006i	$0.293058\pi$
$968$	297.545	−	79.7268i	0.307381	−	0.0823624i
$969$	−830.040	+	479.224i	−0.856594	+	0.494555i
$970$	−420.929	−	179.803i	−0.433947	−	0.185364i
$971$	−745.089	+	1290.53i	−0.767342	+	1.32908i	0.171658	+	0.985157i	$0.445088\pi$
$971$	−745.089	+	1290.53i	−0.767342	+	1.32908i	−0.938999	+	0.343919i	$0.888246\pi$
$972$	−135.271	+	135.271i	−0.139168	+	0.139168i
$973$	−340.157	−	148.483i	−0.349596	−	0.152603i
$974$		−	1114.81i		−	1.14457i
$975$	1479.45	−	1415.76i	1.51739	−	1.45207i
$976$	205.818	+	356.487i	0.210879	+	0.365253i
$977$	1016.44	+	272.355i	1.04037	+	0.278767i	0.738268	−	0.674507i	$-0.235644\pi$
$977$	1016.44	+	272.355i	1.04037	+	0.278767i	0.302105	+	0.953275i	$0.402311\pi$
$978$	686.670	−	183.993i	0.702116	−	0.188131i
$979$		−	287.659i		−	0.293830i
$980$	482.113	+	87.5611i	0.491952	+	0.0893481i
$981$	−706.495			−0.720178
$982$	84.9179	+	316.918i	0.0864744	+	0.322727i
$983$	185.170	−	691.062i	0.188372	−	0.703014i	−0.805512	−	0.592580i	$-0.798109\pi$
$983$	185.170	−	691.062i	0.188372	−	0.703014i	0.993884	−	0.110434i	$-0.0352240\pi$
$984$	−78.2955	+	45.2039i	−0.0795686	+	0.0459390i
$985$	179.405	−	228.556i	0.182137	−	0.232037i
$986$	693.545			0.703392
$987$	−311.228	+	712.989i	−0.315328	+	0.722380i
$988$	403.818	+	403.818i	0.408722	+	0.408722i
$989$	−212.101	−	122.457i	−0.214460	−	0.123819i
$990$	432.506	−	173.602i	0.436875	−	0.175356i
$991$	−646.768	−	1120.24i	−0.652642	−	1.13041i	−0.982479	−	0.186371i	$-0.940327\pi$
$991$	−646.768	−	1120.24i	−0.652642	−	1.13041i	0.329838	−	0.944038i	$-0.393006\pi$
$992$	23.4256	+	87.4256i	0.0236145	+	0.0881307i
$993$	884.681	+	884.681i	0.890918	+	0.890918i
$994$	394.880	+	59.5921i	0.397264	+	0.0599518i
$995$	−1206.18	+	904.634i	−1.21224	+	0.909179i
$996$	−382.271	+	662.113i	−0.383806	+	0.664772i
$997$	−175.157	−	46.9331i	−0.175684	−	0.0470743i	0.169905	−	0.985460i	$-0.445654\pi$
$997$	−175.157	−	46.9331i	−0.175684	−	0.0470743i	−0.345588	+	0.938386i	$0.612321\pi$
$998$	241.052	−	899.618i	0.241535	−	0.901421i
$999$	1614.43	+	932.091i	1.61605	+	0.933024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.3.l.a.23.2	✓	8
5.2	odd	4	inner	70.3.l.a.37.1	yes	8
5.3	odd	4		350.3.p.c.107.2		8
5.4	even	2		350.3.p.c.93.1		8
7.2	even	3		490.3.f.l.393.2		4
7.4	even	3	inner	70.3.l.a.53.1	yes	8
7.5	odd	6		490.3.f.e.393.1		4
35.2	odd	12		490.3.f.l.197.2		4
35.4	even	6		350.3.p.c.193.2		8
35.12	even	12		490.3.f.e.197.1		4
35.18	odd	12		350.3.p.c.207.1		8
35.32	odd	12	inner	70.3.l.a.67.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.a.23.2	✓	8	1.1	even	1	trivial
70.3.l.a.37.1	yes	8	5.2	odd	4	inner
70.3.l.a.53.1	yes	8	7.4	even	3	inner
70.3.l.a.67.2	yes	8	35.32	odd	12	inner
350.3.p.c.93.1		8	5.4	even	2
350.3.p.c.107.2		8	5.3	odd	4
350.3.p.c.193.2		8	35.4	even	6
350.3.p.c.207.1		8	35.18	odd	12
490.3.f.e.197.1		4	35.12	even	12
490.3.f.e.393.1		4	7.5	odd	6
490.3.f.l.197.2		4	35.2	odd	12
490.3.f.l.393.2		4	7.2	even	3

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:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	70.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} +(1.36843 - 5.10704i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(4.96410 - 0.598076i) q^{5} -7.47723 q^{6} +(-2.80041 + 6.41543i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-16.4150 - 9.47723i) q^{9} +(-2.63397 - 6.56218i) q^{10} +(-1.73861 - 3.01137i) q^{11} +(2.73685 + 10.2141i) q^{12} +(10.9545 + 10.9545i) q^{13} +(9.78866 + 1.47723i) q^{14} +(3.73861 - 26.1703i) q^{15} +(2.00000 - 3.46410i) q^{16} +(9.49996 + 2.54551i) q^{17} +(-6.93781 + 25.8923i) q^{18} +(-15.9623 - 9.21584i) q^{19} +(-8.00000 + 6.00000i) q^{20} +(28.9317 + 23.0809i) q^{21} +(-3.47723 + 3.47723i) q^{22} +(17.3390 - 4.64598i) q^{23} +(12.9509 - 7.47723i) q^{24} +(24.2846 - 5.93782i) q^{25} +(10.9545 - 18.9737i) q^{26} +(-37.2158 + 37.2158i) q^{27} +(-1.56497 - 13.9123i) q^{28} +49.8634i q^{29} +(-37.1177 + 4.47195i) q^{30} +(-8.00000 - 13.8564i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-17.7583 + 4.75833i) q^{33} -13.9089i q^{34} +(-10.0646 + 33.5217i) q^{35} +37.9089 q^{36} +(-9.16731 - 34.2129i) q^{37} +(-6.74646 + 25.1781i) q^{38} +(70.9352 - 40.9545i) q^{39} +(11.1244 + 8.73205i) q^{40} -6.04555 q^{41} +(20.9393 - 47.9696i) q^{42} +(-9.64752 - 9.64752i) q^{43} +(6.02273 + 3.47723i) q^{44} +(-87.1540 - 37.2285i) q^{45} +(-12.6931 - 21.9850i) q^{46} +(5.44036 + 20.3037i) q^{47} +(-14.9545 - 14.9545i) q^{48} +(-33.3154 - 35.9317i) q^{49} +(-17.0000 - 31.0000i) q^{50} +(26.0000 - 45.0333i) q^{51} +(-29.9281 - 8.01921i) q^{52} +(-2.94488 + 10.9904i) q^{53} +(64.4597 + 37.2158i) q^{54} +(-10.4317 - 13.9089i) q^{55} +(-18.4317 + 7.23003i) q^{56} +(-68.9089 + 68.9089i) q^{57} +(68.1146 - 18.2513i) q^{58} +(-65.3652 + 37.7386i) q^{59} +(19.6948 + 49.0669i) q^{60} +(-51.4545 + 89.1217i) q^{61} +(-16.0000 + 16.0000i) q^{62} +(106.769 - 78.7693i) q^{63} +8.00000i q^{64} +(60.9306 + 47.8274i) q^{65} +(13.0000 + 22.5167i) q^{66} +(31.1237 + 8.33958i) q^{67} +(-18.9999 + 5.09101i) q^{68} -94.9089i q^{69} +(49.4754 + 1.47874i) q^{70} +40.3406 q^{71} +(-13.8756 - 51.7845i) q^{72} +(-22.9762 + 85.7485i) q^{73} +(-43.3802 + 25.0455i) q^{74} +(2.90703 - 132.148i) q^{75} +36.8634 q^{76} +(24.1880 - 2.72088i) q^{77} +(-81.9089 - 81.9089i) q^{78} +(-87.6452 - 50.6020i) q^{79} +(7.85641 - 18.3923i) q^{80} +(53.8406 + 93.2546i) q^{81} +(2.21282 + 8.25837i) q^{82} +(51.1247 + 51.1247i) q^{83} +(-73.1920 - 11.0455i) q^{84} +(48.6812 + 6.95445i) q^{85} +(-9.64752 + 16.7100i) q^{86} +(254.654 + 68.2344i) q^{87} +(2.54551 - 9.49996i) q^{88} +(71.6434 + 41.3634i) q^{89} +(-18.9545 + 132.681i) q^{90} +(-100.954 + 39.6005i) q^{91} +(-25.3861 + 25.3861i) q^{92} +(-81.7126 + 21.8948i) q^{93} +(25.7441 - 14.8634i) q^{94} +(-84.7503 - 36.2017i) q^{95} +(-14.9545 + 25.9019i) q^{96} +(45.7723 - 45.7723i) q^{97} +(-36.8893 + 58.6616i) q^{98} +65.9089i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{3} + 12 q^{5} - 16 q^{6} - 4 q^{7} + 16 q^{8} - 28 q^{10} + 8 q^{11} - 8 q^{12} + 8 q^{15} + 16 q^{16} - 16 q^{17} + 32 q^{18} - 64 q^{20} + 100 q^{21} + 16 q^{22} - 4 q^{23} + 28 q^{25}+ \cdots - 132 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^3 + 12 * q^5 - 16 * q^6 - 4 * q^7 + 16 * q^8 - 28 * q^10 + 8 * q^11 - 8 * q^12 + 8 * q^15 + 16 * q^16 - 16 * q^17 + 32 * q^18 - 64 * q^20 + 100 * q^21 + 16 * q^22 - 4 * q^23 + 28 * q^25 - 232 * q^27 - 40 * q^28 - 24 * q^30 - 64 * q^31 - 16 * q^32 - 52 * q^33 + 112 * q^35 + 128 * q^36 + 144 * q^37 + 8 * q^38 - 8 * q^40 - 136 * q^41 + 188 * q^42 + 120 * q^43 - 128 * q^45 + 8 * q^46 + 72 * q^47 - 32 * q^48 - 136 * q^50 + 208 * q^51 + 76 * q^53 + 48 * q^55 - 16 * q^56 - 376 * q^57 + 68 * q^58 + 56 * q^60 - 324 * q^61 - 128 * q^62 + 112 * q^63 + 104 * q^66 + 124 * q^67 + 32 * q^68 + 160 * q^70 + 16 * q^71 + 64 * q^72 + 32 * q^73 + 124 * q^75 + 32 * q^76 + 20 * q^77 - 480 * q^78 - 48 * q^80 + 124 * q^81 - 68 * q^82 + 168 * q^83 - 224 * q^85 + 120 * q^86 + 428 * q^87 + 16 * q^88 - 64 * q^90 - 720 * q^91 + 16 * q^92 - 64 * q^93 - 32 * q^95 - 32 * q^96 - 72 * q^97 - 132 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more