LMFDB - Embedded newform 105.4.m.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(13,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("105.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.8
Character	$\chi$	$=$	105.13
Dual form			105.4.m.a.97.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.16465 + 2.16465i) q^{2} +(2.12132 - 2.12132i) q^{3} -1.37142i q^{4} +(-9.30469 + 6.19861i) q^{5} +9.18383i q^{6} +(16.4755 + 8.45914i) q^{7} +(-14.3486 - 14.3486i) q^{8} -9.00000i q^{9} +O(q^{10})$	\(q+(-2.16465 + 2.16465i) q^{2} +(2.12132 - 2.12132i) q^{3} -1.37142i q^{4} +(-9.30469 + 6.19861i) q^{5} +9.18383i q^{6} +(16.4755 + 8.45914i) q^{7} +(-14.3486 - 14.3486i) q^{8} -9.00000i q^{9} +(6.72356 - 33.5592i) q^{10} -21.5591 q^{11} +(-2.90922 - 2.90922i) q^{12} +(-48.3450 + 48.3450i) q^{13} +(-53.9748 + 17.3527i) q^{14} +(-6.58898 + 32.8875i) q^{15} +73.0906 q^{16} +(-30.9132 - 30.9132i) q^{17} +(19.4818 + 19.4818i) q^{18} -91.2683 q^{19} +(8.50090 + 12.7606i) q^{20} +(52.8944 - 17.0053i) q^{21} +(46.6680 - 46.6680i) q^{22} +(-143.277 - 143.277i) q^{23} -60.8758 q^{24} +(48.1544 - 115.352i) q^{25} -209.300i q^{26} +(-19.0919 - 19.0919i) q^{27} +(11.6010 - 22.5948i) q^{28} +284.854i q^{29} +(-56.9270 - 85.4527i) q^{30} +72.5971i q^{31} +(-43.4270 + 43.4270i) q^{32} +(-45.7338 + 45.7338i) q^{33} +133.833 q^{34} +(-205.735 + 23.4158i) q^{35} -12.3428 q^{36} +(160.934 - 160.934i) q^{37} +(197.564 - 197.564i) q^{38} +205.110i q^{39} +(222.450 + 44.5677i) q^{40} +404.234i q^{41} +(-77.6873 + 151.308i) q^{42} +(-73.2629 - 73.2629i) q^{43} +29.5666i q^{44} +(55.7875 + 83.7422i) q^{45} +620.287 q^{46} +(261.172 + 261.172i) q^{47} +(155.048 - 155.048i) q^{48} +(199.886 + 278.738i) q^{49} +(145.460 + 353.935i) q^{50} -131.154 q^{51} +(66.3012 + 66.3012i) q^{52} +(24.1316 + 24.1316i) q^{53} +82.6545 q^{54} +(200.601 - 133.637i) q^{55} +(-115.024 - 357.776i) q^{56} +(-193.609 + 193.609i) q^{57} +(-616.609 - 616.609i) q^{58} -157.812 q^{59} +(45.1025 + 9.03625i) q^{60} +557.621i q^{61} +(-157.147 - 157.147i) q^{62} +(76.1323 - 148.280i) q^{63} +396.716i q^{64} +(150.163 - 749.506i) q^{65} -197.996i q^{66} +(-206.634 + 206.634i) q^{67} +(-42.3950 + 42.3950i) q^{68} -607.871 q^{69} +(394.656 - 496.030i) q^{70} +690.798 q^{71} +(-129.137 + 129.137i) q^{72} +(159.388 - 159.388i) q^{73} +696.731i q^{74} +(-142.548 - 346.850i) q^{75} +125.167i q^{76} +(-355.198 - 182.372i) q^{77} +(-443.992 - 443.992i) q^{78} -998.194i q^{79} +(-680.085 + 453.060i) q^{80} -81.0000 q^{81} +(-875.025 - 875.025i) q^{82} +(66.4559 - 66.4559i) q^{83} +(-23.3214 - 72.5404i) q^{84} +(479.257 + 96.0188i) q^{85} +317.177 q^{86} +(604.267 + 604.267i) q^{87} +(309.343 + 309.343i) q^{88} +327.209 q^{89} +(-302.033 - 60.5121i) q^{90} +(-1205.47 + 387.552i) q^{91} +(-196.492 + 196.492i) q^{92} +(154.002 + 154.002i) q^{93} -1130.69 q^{94} +(849.223 - 565.737i) q^{95} +184.245i q^{96} +(-890.785 - 890.785i) q^{97} +(-1036.05 - 170.686i) q^{98} +194.032i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7} - 168 q^{8}+O(q^{10}) $ 48 * q + 4 * q^7 - 168 * q^8	$ 48 q + 4 q^{7} - 168 q^{8} + 112 q^{11} + 168 q^{15} - 544 q^{16} - 96 q^{21} - 192 q^{22} + 400 q^{23} + 520 q^{25} + 1052 q^{28} - 48 q^{30} - 1344 q^{32} + 392 q^{35} - 1728 q^{36} - 456 q^{37} + 1068 q^{42} + 192 q^{43} - 208 q^{46} + 3528 q^{50} + 672 q^{51} - 1728 q^{53} - 48 q^{56} + 696 q^{57} + 3016 q^{58} + 840 q^{60} - 36 q^{63} - 4720 q^{65} - 4784 q^{67} + 2220 q^{70} - 3088 q^{71} - 1512 q^{72} + 2352 q^{77} + 1416 q^{78} - 3888 q^{81} - 472 q^{85} + 10832 q^{86} + 2128 q^{88} - 5664 q^{91} + 10600 q^{92} - 1368 q^{93} - 6912 q^{95} - 3888 q^{98}+O(q^{100}) $ 48 * q + 4 * q^7 - 168 * q^8 + 112 * q^11 + 168 * q^15 - 544 * q^16 - 96 * q^21 - 192 * q^22 + 400 * q^23 + 520 * q^25 + 1052 * q^28 - 48 * q^30 - 1344 * q^32 + 392 * q^35 - 1728 * q^36 - 456 * q^37 + 1068 * q^42 + 192 * q^43 - 208 * q^46 + 3528 * q^50 + 672 * q^51 - 1728 * q^53 - 48 * q^56 + 696 * q^57 + 3016 * q^58 + 840 * q^60 - 36 * q^63 - 4720 * q^65 - 4784 * q^67 + 2220 * q^70 - 3088 * q^71 - 1512 * q^72 + 2352 * q^77 + 1416 * q^78 - 3888 * q^81 - 472 * q^85 + 10832 * q^86 + 2128 * q^88 - 5664 * q^91 + 10600 * q^92 - 1368 * q^93 - 6912 * q^95 - 3888 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−2.16465	+	2.16465i	−0.765319	+	0.765319i	−0.977279	−	0.211959i	$-0.932016\pi$
$2$	−2.16465	+	2.16465i	−0.765319	+	0.765319i	0.211959	+	0.977279i	$0.432016\pi$
$3$	2.12132	−	2.12132i	0.408248	−	0.408248i
$3$	2.12132	−	2.12132i	0.408248	−	0.408248i
$4$		−	1.37142i		−	0.171427i
$5$	−9.30469	+	6.19861i	−0.832236	+	0.554421i
$5$	−9.30469	+	6.19861i	−0.832236	+	0.554421i
$6$			9.18383i			0.624881i
$7$	16.4755	+	8.45914i	0.889595	+	0.456751i
$7$	16.4755	+	8.45914i	0.889595	+	0.456751i
$8$	−14.3486	−	14.3486i	−0.634123	−	0.634123i
$9$		−	9.00000i		−	0.333333i
$10$	6.72356	−	33.5592i	0.212618	−	1.06124i
$11$	−21.5591			−0.590939			−0.295469	−	0.955352i	$-0.595476\pi$
$11$	−21.5591			−0.590939			−0.295469	+	0.955352i	$0.595476\pi$
$12$	−2.90922	−	2.90922i	−0.0699849	−	0.0699849i
$13$	−48.3450	+	48.3450i	−1.03142	+	1.03142i	−0.0319314	+	0.999490i	$0.510166\pi$
$13$	−48.3450	+	48.3450i	−1.03142	+	1.03142i	−0.999490	+	0.0319314i	$0.989834\pi$
$14$	−53.9748	+	17.3527i	−1.03038	+	0.331264i
$15$	−6.58898	+	32.8875i	−0.113418	+	0.566100i
$16$	73.0906			1.14204
$17$	−30.9132	−	30.9132i	−0.441033	−	0.441033i	0.451326	−	0.892359i	$-0.350951\pi$
$17$	−30.9132	−	30.9132i	−0.441033	−	0.441033i	−0.892359	+	0.451326i	$0.850951\pi$
$18$	19.4818	+	19.4818i	0.255106	+	0.255106i
$19$	−91.2683			−1.10202			−0.551010	−	0.834499i	$-0.685757\pi$
$19$	−91.2683			−1.10202			−0.551010	+	0.834499i	$0.685757\pi$
$20$	8.50090	+	12.7606i	0.0950429	+	0.142668i
$21$	52.8944	−	17.0053i	0.549643	−	0.176708i
$22$	46.6680	−	46.6680i	0.452257	−	0.452257i
$23$	−143.277	−	143.277i	−1.29892	−	1.29892i	−0.929104	−	0.369819i	$-0.879420\pi$
$23$	−143.277	−	143.277i	−1.29892	−	1.29892i	−0.369819	−	0.929104i	$-0.620580\pi$
$24$	−60.8758			−0.517759
$25$	48.1544	−	115.352i	0.385235	−	0.922818i
$26$		−	209.300i		−	1.57873i
$27$	−19.0919	−	19.0919i	−0.136083	−	0.136083i
$28$	11.6010	−	22.5948i	0.0782996	−	0.152501i
$29$			284.854i			1.82400i	0.410187	+	0.912001i	$0.365463\pi$
$29$			284.854i			1.82400i	−0.410187	+	0.912001i	$0.634537\pi$
$30$	−56.9270	−	85.4527i	−0.346447	−	0.520048i
$31$			72.5971i			0.420607i	0.977636	+	0.210304i	$0.0674452\pi$
$31$			72.5971i			0.420607i	−0.977636	+	0.210304i	$0.932555\pi$
$32$	−43.4270	+	43.4270i	−0.239903	+	0.239903i
$33$	−45.7338	+	45.7338i	−0.241250	+	0.241250i
$34$	133.833			0.675062
$35$	−205.735	+	23.4158i	−0.993585	+	0.113085i
$36$	−12.3428			−0.0571425
$37$	160.934	−	160.934i	0.715064	−	0.715064i	−0.252526	−	0.967590i	$-0.581261\pi$
$37$	160.934	−	160.934i	0.715064	−	0.715064i	0.967590	+	0.252526i	$0.0812613\pi$
$38$	197.564	−	197.564i	0.843397	−	0.843397i
$39$			205.110i			0.842152i
$40$	222.450	+	44.5677i	0.879311	+	0.176169i
$41$			404.234i			1.53977i	0.638181	+	0.769887i	$0.279687\pi$
$41$			404.234i			1.53977i	−0.638181	+	0.769887i	$0.720313\pi$
$42$	−77.6873	+	151.308i	−0.285415	+	0.555891i
$43$	−73.2629	−	73.2629i	−0.259825	−	0.259825i	0.565158	−	0.824983i	$-0.308815\pi$
$43$	−73.2629	−	73.2629i	−0.259825	−	0.259825i	−0.824983	+	0.565158i	$0.808815\pi$
$44$			29.5666i			0.101303i
$45$	55.7875	+	83.7422i	0.184807	+	0.277412i
$46$	620.287			1.98818
$47$	261.172	+	261.172i	0.810551	+	0.810551i	0.984716	−	0.174166i	$-0.0557229\pi$
$47$	261.172	+	261.172i	0.810551	+	0.810551i	−0.174166	+	0.984716i	$0.555723\pi$
$48$	155.048	−	155.048i	0.466236	−	0.466236i
$49$	199.886	+	278.738i	0.582758	+	0.812646i
$50$	145.460	+	353.935i	0.411423	+	1.00108i
$51$	−131.154			−0.360102
$52$	66.3012	+	66.3012i	0.176814	+	0.176814i
$53$	24.1316	+	24.1316i	0.0625421	+	0.0625421i	0.737686	−	0.675144i	$-0.235918\pi$
$53$	24.1316	+	24.1316i	0.0625421	+	0.0625421i	−0.675144	+	0.737686i	$0.735918\pi$
$54$	82.6545			0.208294
$55$	200.601	−	133.637i	0.491801	−	0.327629i
$56$	−115.024	−	357.776i	−0.274476	−	0.853748i
$57$	−193.609	+	193.609i	−0.449898	+	0.449898i
$58$	−616.609	−	616.609i	−1.39594	−	1.39594i
$59$	−157.812			−0.348227			−0.174113	−	0.984726i	$-0.555706\pi$
$59$	−157.812			−0.348227			−0.174113	+	0.984726i	$0.555706\pi$
$60$	45.1025	+	9.03625i	0.0970451	+	0.0194429i
$61$			557.621i			1.17043i	0.810879	+	0.585214i	$0.198989\pi$
$61$			557.621i			1.17043i	−0.810879	+	0.585214i	$0.801011\pi$
$62$	−157.147	−	157.147i	−0.321899	−	0.321899i
$63$	76.1323	−	148.280i	0.152250	−	0.296532i
$64$			396.716i			0.774836i
$65$	150.163	−	749.506i	0.286545	−	1.43023i
$66$		−	197.996i		−	0.369266i
$67$	−206.634	+	206.634i	−0.376782	+	0.376782i	−0.869940	−	0.493158i	$-0.835842\pi$
$67$	−206.634	+	206.634i	−0.376782	+	0.376782i	0.493158	+	0.869940i	$0.335842\pi$
$68$	−42.3950	+	42.3950i	−0.0756051	+	0.0756051i
$69$	−607.871			−1.06057
$70$	394.656	−	496.030i	0.673864	−	0.846956i
$71$	690.798			1.15468			0.577342	−	0.816502i	$-0.304090\pi$
$71$	690.798			1.15468			0.577342	+	0.816502i	$0.304090\pi$
$72$	−129.137	+	129.137i	−0.211374	+	0.211374i
$73$	159.388	−	159.388i	0.255547	−	0.255547i	−0.567693	−	0.823240i	$-0.692164\pi$
$73$	159.388	−	159.388i	0.255547	−	0.255547i	0.823240	+	0.567693i	$0.192164\pi$
$74$			696.731i			1.09450i
$75$	−142.548	−	346.850i	−0.219467	−	0.534011i
$76$			125.167i			0.188916i
$77$	−355.198	−	182.372i	−0.525696	−	0.269912i
$78$	−443.992	−	443.992i	−0.644515	−	0.644515i
$79$		−	998.194i		−	1.42159i	−0.703399	−	0.710795i	$-0.748335\pi$
$79$		−	998.194i		−	1.42159i	0.703399	−	0.710795i	$-0.251665\pi$
$80$	−680.085	+	453.060i	−0.950447	+	0.633171i
$81$	−81.0000			−0.111111
$82$	−875.025	−	875.025i	−1.17842	−	1.17842i
$83$	66.4559	−	66.4559i	0.0878854	−	0.0878854i	−0.661797	−	0.749683i	$-0.730206\pi$
$83$	66.4559	−	66.4559i	0.0878854	−	0.0878854i	0.749683	+	0.661797i	$0.230206\pi$
$84$	−23.3214	−	72.5404i	−0.0302926	−	0.0942239i
$85$	479.257	+	96.0188i	0.611562	+	0.122526i
$86$	317.177			0.397699
$87$	604.267	+	604.267i	0.744646	+	0.744646i
$88$	309.343	+	309.343i	0.374728	+	0.374728i
$89$	327.209			0.389708			0.194854	−	0.980832i	$-0.437577\pi$
$89$	327.209			0.389708			0.194854	+	0.980832i	$0.437577\pi$
$90$	−302.033	−	60.5121i	−0.353745	−	0.0708726i
$91$	−1205.47	+	387.552i	−1.38865	+	0.446445i
$92$	−196.492	+	196.492i	−0.222671	+	0.222671i
$93$	154.002	+	154.002i	0.171712	+	0.171712i
$94$	−1130.69			−1.24066
$95$	849.223	−	565.737i	0.917141	−	0.610983i
$96$			184.245i			0.195880i
$97$	−890.785	−	890.785i	−0.932428	−	0.932428i	0.0654287	−	0.997857i	$-0.479158\pi$
$97$	−890.785	−	890.785i	−0.932428	−	0.932428i	−0.997857	+	0.0654287i	$0.979158\pi$
$98$	−1036.05	−	170.686i	−1.06793	−	0.175938i
$99$			194.032i			0.196980i
$100$	−158.196	−	66.0398i	−0.158196	−	0.0660398i
$101$		−	225.295i		−	0.221957i	−0.993823	−	0.110979i	$-0.964602\pi$
$101$		−	225.295i		−	0.221957i	0.993823	−	0.110979i	$-0.0353985\pi$
$102$	283.902	−	283.902i	0.275593	−	0.275593i
$103$	−431.419	+	431.419i	−0.412709	+	0.412709i	−0.882681	−	0.469972i	$-0.844264\pi$
$103$	−431.419	+	431.419i	−0.412709	+	0.412709i	0.469972	+	0.882681i	$0.344264\pi$
$104$	1387.36			1.30810
$105$	−386.757	+	486.101i	−0.359463	+	0.451796i
$106$	−104.473			−0.0957294
$107$	−811.915	+	811.915i	−0.733559	+	0.733559i	−0.971323	−	0.237764i	$-0.923585\pi$
$107$	−811.915	+	811.915i	−0.733559	+	0.733559i	0.237764	+	0.971323i	$0.423585\pi$
$108$	−26.1830	+	26.1830i	−0.0233283	+	0.0233283i
$109$			1443.13i			1.26813i	0.773279	+	0.634066i	$0.218615\pi$
$109$			1443.13i			1.26813i	−0.773279	+	0.634066i	$0.781385\pi$
$110$	−144.954	+	723.508i	−0.125644	+	0.627125i
$111$		−	682.785i		−	0.583847i
$112$	1204.21	+	618.283i	1.01595	+	0.521628i
$113$	247.193	+	247.193i	0.205788	+	0.205788i	0.802474	−	0.596687i	$-0.203516\pi$
$113$	247.193	+	247.193i	0.205788	+	0.205788i	−0.596687	+	0.802474i	$0.703516\pi$
$114$		−	838.193i		−	0.688631i
$115$	2221.26	+	445.028i	1.80116	+	0.360861i
$116$	390.654			0.312684
$117$	435.105	+	435.105i	0.343807	+	0.343807i
$118$	341.608	−	341.608i	0.266505	−	0.266505i
$119$	−247.812	−	770.811i	−0.190899	−	0.593783i
$120$	566.430	−	377.345i	0.430898	−	0.287056i
$121$	−866.203			−0.650791
$122$	−1207.06	−	1207.06i	−0.895751	−	0.895751i
$123$	857.509	+	857.509i	0.628610	+	0.628610i
$124$	99.5610			0.0721036
$125$	266.963	+	1371.81i	0.191023	+	0.981586i
$126$	156.174	+	485.773i	0.110421	+	0.343461i
$127$	−592.864	+	592.864i	−0.414238	+	0.414238i	−0.883212	−	0.468974i	$-0.844624\pi$
$127$	−592.864	+	592.864i	−0.414238	+	0.414238i	0.468974	+	0.883212i	$0.344624\pi$
$128$	−1206.17	−	1206.17i	−0.832899	−	0.832899i
$129$	−310.828			−0.212146
$130$	1297.37	+	1947.47i	0.875283	+	1.31388i
$131$		−	1348.37i		−	0.899296i	−0.893206	−	0.449648i	$-0.851549\pi$
$131$		−	1348.37i		−	0.899296i	0.893206	−	0.449648i	$-0.148451\pi$
$132$	62.7203	+	62.7203i	0.0413568	+	0.0413568i
$133$	−1503.69	−	772.051i	−0.980351	−	0.503348i
$134$		−	894.582i		−	0.576717i
$135$	295.987	+	59.3008i	0.188700	+	0.0378059i
$136$			887.121i			0.559338i
$137$	−278.458	+	278.458i	−0.173652	+	0.173652i	−0.788582	−	0.614930i	$-0.789184\pi$
$137$	−278.458	+	278.458i	−0.173652	+	0.173652i	0.614930	+	0.788582i	$0.289184\pi$
$138$	1315.83	−	1315.83i	0.811672	−	0.811672i
$139$	364.219			0.222250			0.111125	−	0.993806i	$-0.464555\pi$
$139$	364.219			0.222250			0.111125	+	0.993806i	$0.464555\pi$
$140$	32.1128	+	282.148i	0.0193859	+	0.170328i
$141$	1108.06			0.661812
$142$	−1495.34	+	1495.34i	−0.883703	+	0.883703i
$143$	1042.28	−	1042.28i	0.609507	−	0.609507i
$144$		−	657.815i		−	0.380680i
$145$	−1765.70	−	2650.48i	−1.01127	−	1.51800i
$146$			690.038i			0.391151i
$147$	1015.31	+	167.270i	0.569671	+	0.0938515i
$148$	−220.708	−	220.708i	−0.122582	−	0.122582i
$149$		−	210.257i		−	0.115604i	−0.998328	−	0.0578018i	$-0.981591\pi$
$149$		−	210.257i		−	0.115604i	0.998328	−	0.0578018i	$-0.0184091\pi$
$150$	1059.38	+	442.242i	0.576651	+	0.240726i
$151$	−41.7546			−0.0225029			−0.0112515	−	0.999937i	$-0.503582\pi$
$151$	−41.7546			−0.0225029			−0.0112515	+	0.999937i	$0.503582\pi$
$152$	1309.57	+	1309.57i	0.698816	+	0.698816i
$153$	−278.219	+	278.219i	−0.147011	+	0.147011i
$154$	1163.65	−	374.109i	0.608894	−	0.195757i
$155$	−450.001	−	675.493i	−0.233193	−	0.350044i
$156$	281.292			0.144368
$157$	−1122.47	−	1122.47i	−0.570589	−	0.570589i	0.361704	−	0.932293i	$-0.382195\pi$
$157$	−1122.47	−	1122.47i	−0.570589	−	0.570589i	−0.932293	+	0.361704i	$0.882195\pi$
$158$	2160.74	+	2160.74i	1.08797	+	1.08797i
$159$	102.382			0.0510654
$160$	134.888	−	673.262i	0.0666487	−	0.332663i
$161$	−1148.56	−	3572.55i	−0.562231	−	1.74880i
$162$	175.337	−	175.337i	0.0850355	−	0.0850355i
$163$	2531.73	+	2531.73i	1.21657	+	1.21657i	0.968826	+	0.247742i	$0.0796884\pi$
$163$	2531.73	+	2531.73i	1.21657	+	1.21657i	0.247742	+	0.968826i	$0.420312\pi$
$164$	554.374			0.263959
$165$	142.053	−	709.026i	0.0670230	−	0.334531i
$166$			287.708i			0.134521i
$167$	1141.66	+	1141.66i	0.529006	+	0.529006i	0.920276	−	0.391270i	$-0.127964\pi$
$167$	1141.66	+	1141.66i	0.529006	+	0.529006i	−0.391270	+	0.920276i	$0.627964\pi$
$168$	−1002.96	−	514.957i	−0.460596	−	0.236487i
$169$		−	2477.47i		−	1.12766i
$170$	−1245.27	+	829.577i	−0.561811	+	0.374268i
$171$			821.415i			0.367340i
$172$	−100.474	+	100.474i	−0.0445412	+	0.0445412i
$173$	−947.443	+	947.443i	−0.416374	+	0.416374i	−0.883952	−	0.467578i	$-0.845127\pi$
$173$	−947.443	+	947.443i	−0.416374	+	0.416374i	0.467578	+	0.883952i	$0.345127\pi$
$174$	−2616.05			−1.13978
$175$	1769.15	−	1493.15i	0.764201	−	0.644978i
$176$	−1575.77			−0.674876
$177$	−334.770	+	334.770i	−0.142163	+	0.142163i
$178$	−708.292	+	708.292i	−0.298251	+	0.298251i
$179$			1110.86i			0.463853i	0.972733	+	0.231926i	$0.0745028\pi$
$179$			1110.86i			0.463853i	−0.972733	+	0.231926i	$0.925497\pi$
$180$	114.846	−	76.5081i	0.0475560	−	0.0316810i
$181$			1000.87i			0.411015i	0.978656	+	0.205508i	$0.0658845\pi$
$181$			1000.87i			0.411015i	−0.978656	+	0.205508i	$0.934115\pi$
$182$	1770.50	−	3448.32i	0.721088	−	1.40443i
$183$	1182.89	+	1182.89i	0.477825	+	0.477825i
$184$			4111.62i			1.64735i
$185$	−499.873	+	2495.01i	−0.198656	+	0.991549i
$186$	−666.719			−0.262829
$187$	666.463	+	666.463i	0.260623	+	0.260623i
$188$	358.176	−	358.176i	0.138951	−	0.138951i
$189$	−153.048	−	476.050i	−0.0589026	−	0.183214i
$190$	−613.648	+	3062.89i	−0.234309	+	1.16950i
$191$	1741.53			0.659751			0.329875	−	0.944024i	$-0.392993\pi$
$191$	1741.53			0.659751			0.329875	+	0.944024i	$0.392993\pi$
$192$	841.562	+	841.562i	0.316325	+	0.316325i
$193$	−1474.31	−	1474.31i	−0.549863	−	0.549863i	0.376538	−	0.926401i	$-0.377114\pi$
$193$	−1474.31	−	1474.31i	−0.549863	−	0.549863i	−0.926401	+	0.376538i	$0.877114\pi$
$194$	3856.48			1.42721
$195$	−1271.40	−	1908.49i	−0.466907	−	0.700870i
$196$	382.266	−	274.127i	0.139310	−	0.0999006i
$197$	2850.56	−	2850.56i	1.03093	−	1.03093i	0.0314271	−	0.999506i	$-0.489995\pi$
$197$	2850.56	−	2850.56i	1.03093	−	1.03093i	0.999506	−	0.0314271i	$-0.0100052\pi$
$198$	−420.012	−	420.012i	−0.150752	−	0.150752i
$199$	−1659.17			−0.591032			−0.295516	−	0.955338i	$-0.595492\pi$
$199$	−1659.17			−0.591032			−0.295516	+	0.955338i	$0.595492\pi$
$200$	−2346.09	+	964.193i	−0.829466	+	0.340894i
$201$			876.675i			0.307641i
$202$	487.684	+	487.684i	0.169868	+	0.169868i
$203$	−2409.62	+	4693.12i	−0.833114	+	1.62262i
$204$			179.867i			0.0617313i
$205$	−2505.69	−	3761.27i	−0.853682	−	1.28146i
$206$		−	1867.74i		−	0.631708i
$207$	−1289.49	+	1289.49i	−0.432974	+	0.432974i
$208$	−3533.56	+	3533.56i	−1.17792	+	1.17792i
$209$	1967.67			0.651226
$210$	−215.046	−	1889.43i	−0.0706648	−	0.620872i
$211$	−907.467			−0.296079			−0.148039	−	0.988981i	$-0.547296\pi$
$211$	−907.467			−0.296079			−0.148039	+	0.988981i	$0.547296\pi$
$212$	33.0945	−	33.0945i	0.0107214	−	0.0107214i
$213$	1465.40	−	1465.40i	0.471398	−	0.471398i
$214$		−	3515.02i		−	1.12281i
$215$	1135.82	+	227.560i	0.360289	+	0.0721835i
$216$			547.882i			0.172586i
$217$	−614.109	+	1196.07i	−0.192113	+	0.374170i
$218$	−3123.86	−	3123.86i	−0.970525	−	0.970525i
$219$		−	676.226i		−	0.208653i
$220$	−183.272	−	275.108i	−0.0561645	−	0.0843081i
$221$	2989.00			0.909782
$222$	1477.99	+	1477.99i	0.446830	+	0.446830i
$223$	3807.52	−	3807.52i	1.14336	−	1.14336i	0.155534	−	0.987830i	$-0.450290\pi$
$223$	3807.52	−	3807.52i	1.14336	−	1.14336i	0.987830	−	0.155534i	$-0.0497100\pi$
$224$	−1082.84	+	348.128i	−0.322992	+	0.103840i
$225$	−1038.17	−	433.390i	−0.307606	−	0.128412i
$226$	−1070.17			−0.314986
$227$	−3870.29	−	3870.29i	−1.13163	−	1.13163i	−0.989906	−	0.141724i	$-0.954735\pi$
$227$	−3870.29	−	3870.29i	−1.13163	−	1.13163i	−0.141724	−	0.989906i	$-0.545265\pi$
$228$	265.519	+	265.519i	0.0771248	+	0.0771248i
$229$	−5375.98			−1.55133			−0.775666	−	0.631144i	$-0.782586\pi$
$229$	−5375.98			−1.55133			−0.775666	+	0.631144i	$0.782586\pi$
$230$	−5771.58	+	3844.92i	−1.65464	+	1.10229i
$231$	−1140.36	+	366.620i	−0.324805	+	0.104424i
$232$	4087.25	−	4087.25i	1.15664	−	1.15664i
$233$	3141.46	+	3141.46i	0.883279	+	0.883279i	0.993866	−	0.110587i	$-0.0352732\pi$
$233$	3141.46	+	3141.46i	0.883279	+	0.883279i	−0.110587	+	0.993866i	$0.535273\pi$
$234$	−1883.70			−0.526245
$235$	−4049.03	−	811.220i	−1.12396	−	0.225184i
$236$			216.426i			0.0596956i
$237$	−2117.49	−	2117.49i	−0.580361	−	0.580361i
$238$	2204.96	+	1132.11i	0.600532	+	0.308335i
$239$			5547.74i			1.50148i	0.660598	+	0.750740i	$0.270303\pi$
$239$			5547.74i			1.50148i	−0.660598	+	0.750740i	$0.729697\pi$
$240$	−481.592	+	2403.76i	−0.129528	+	0.646509i
$241$			1103.25i			0.294881i	0.989071	+	0.147441i	$0.0471035\pi$
$241$			1103.25i			0.294881i	−0.989071	+	0.147441i	$0.952896\pi$
$242$	1875.03	−	1875.03i	0.498063	−	0.498063i
$243$	−171.827	+	171.827i	−0.0453609	+	0.0453609i
$244$	764.732			0.200643
$245$	−3587.66	−	1354.55i	−0.935540	−	0.353221i
$246$	−3712.41			−0.962174
$247$	4412.36	−	4412.36i	1.13665	−	1.13665i
$248$	1041.66	−	1041.66i	0.266716	−	0.266716i
$249$		−	281.949i		−	0.0717581i
$250$	−3547.36	−	2391.60i	−0.897420	−	0.605033i
$251$			2821.29i			0.709476i	0.934966	+	0.354738i	$0.115430\pi$
$251$			2821.29i			0.709476i	−0.934966	+	0.354738i	$0.884570\pi$
$252$	−203.354	−	104.409i	−0.0508336	−	0.0260999i
$253$	3088.92	+	3088.92i	0.767584	+	0.767584i
$254$		−	2566.69i		−	0.634048i
$255$	1220.34	−	812.971i	0.299690	−	0.199648i
$256$	2048.13			0.500032
$257$	−759.083	−	759.083i	−0.184242	−	0.184242i	0.608959	−	0.793202i	$-0.291587\pi$
$257$	−759.083	−	759.083i	−0.184242	−	0.184242i	−0.793202	+	0.608959i	$0.791587\pi$
$258$	672.834	−	672.834i	0.162360	−	0.162360i
$259$	4012.83	−	1290.11i	0.962723	−	0.309511i
$260$	−1027.89	−	205.936i	−0.245180	−	0.0491217i
$261$	2563.69			0.608001
$262$	2918.75	+	2918.75i	0.688249	+	0.688249i
$263$	−1726.16	−	1726.16i	−0.404712	−	0.404712i	0.475178	−	0.879890i	$-0.342384\pi$
$263$	−1726.16	−	1726.16i	−0.404712	−	0.404712i	−0.879890	+	0.475178i	$0.842384\pi$
$264$	1312.43			0.305964
$265$	−374.120	−	74.9545i	−0.0867245	−	0.0173752i
$266$	4926.19	−	1583.75i	1.13550	−	0.365060i
$267$	694.114	−	694.114i	0.159098	−	0.159098i
$268$	283.382	+	283.382i	0.0645907	+	0.0645907i
$269$	−2996.41			−0.679160			−0.339580	−	0.940577i	$-0.610285\pi$
$269$	−2996.41			−0.679160			−0.339580	+	0.940577i	$0.610285\pi$
$270$	−769.074	+	512.343i	−0.173349	+	0.115482i
$271$		−	1226.22i		−	0.274862i	−0.990511	−	0.137431i	$-0.956115\pi$
$271$		−	1226.22i		−	0.274862i	0.990511	−	0.137431i	$-0.0438845\pi$
$272$	−2259.47	−	2259.47i	−0.503677	−	0.503677i
$273$	−1735.06	+	3379.30i	−0.384654	+	0.749174i
$274$		−	1205.53i		−	0.265798i
$275$	−1038.17	+	2486.90i	−0.227650	+	0.545329i
$276$			833.646i			0.181810i
$277$	508.870	−	508.870i	0.110379	−	0.110379i	−0.649760	−	0.760139i	$-0.725131\pi$
$277$	508.870	−	508.870i	0.110379	−	0.110379i	0.760139	+	0.649760i	$0.225131\pi$
$278$	−788.408	+	788.408i	−0.170092	+	0.170092i
$279$	653.374			0.140202
$280$	3287.98	+	2616.01i	0.701765	+	0.558345i
$281$	−2910.49			−0.617883			−0.308941	−	0.951081i	$-0.599975\pi$
$281$	−2910.49			−0.617883			−0.308941	+	0.951081i	$0.599975\pi$
$282$	−2398.56	+	2398.56i	−0.506497	+	0.506497i
$283$	3673.95	−	3673.95i	0.771709	−	0.771709i	−0.206696	−	0.978405i	$-0.566271\pi$
$283$	3673.95	−	3673.95i	0.771709	−	0.771709i	0.978405	+	0.206696i	$0.0662711\pi$
$284$		−	947.373i		−	0.197945i
$285$	601.365	−	3001.58i	0.124989	−	0.623854i
$286$			4512.32i			0.932935i
$287$	−3419.47	+	6659.96i	−0.703292	+	1.36977i
$288$	390.843	+	390.843i	0.0799676	+	0.0799676i
$289$		−	3001.74i		−	0.610980i
$290$	9559.48	+	1915.23i	1.93570	+	0.387815i
$291$	−3779.28			−0.761325
$292$	−218.588	−	218.588i	−0.0438078	−	0.0438078i
$293$	−785.514	+	785.514i	−0.156622	+	0.156622i	−0.781068	−	0.624446i	$-0.785325\pi$
$293$	−785.514	+	785.514i	−0.156622	+	0.156622i	0.624446	+	0.781068i	$0.285325\pi$
$294$	−2559.88	+	1835.72i	−0.507807	+	0.364154i
$295$	1468.39	−	978.215i	0.289807	−	0.193064i
$296$	−4618.34			−0.906877
$297$	411.605	+	411.605i	0.0804166	+	0.0804166i
$298$	455.133	+	455.133i	0.0884736	+	0.0884736i
$299$	13853.4			2.67947
$300$	−475.677	+	195.493i	−0.0915440	+	0.0376227i
$301$	−587.304	−	1826.79i	−0.112464	−	0.349815i
$302$	90.3840	−	90.3840i	0.0172219	−	0.0172219i
$303$	−477.922	−	477.922i	−0.0906136	−	0.0906136i
$304$	−6670.85			−1.25855
$305$	−3456.48	−	5188.49i	−0.648910	−	0.974073i
$306$		−	1204.49i		−	0.225021i
$307$	4762.69	+	4762.69i	0.885410	+	0.885410i	0.994078	−	0.108668i	$-0.0346584\pi$
$307$	4762.69	+	4762.69i	0.885410	+	0.885410i	−0.108668	+	0.994078i	$0.534658\pi$
$308$	−250.108	+	487.126i	−0.0462702	+	0.0901187i
$309$			1830.36i			0.336975i
$310$	2436.30	+	488.111i	0.446363	+	0.0894285i
$311$		−	3510.27i		−	0.640030i	−0.947413	−	0.320015i	$-0.896312\pi$
$311$		−	3510.27i		−	0.640030i	0.947413	−	0.320015i	$-0.103688\pi$
$312$	2943.04	−	2943.04i	0.534028	−	0.534028i
$313$	−16.5066	+	16.5066i	−0.00298085	+	0.00298085i	−0.708596	−	0.705615i	$-0.750671\pi$
$313$	−16.5066	+	16.5066i	−0.00298085	+	0.00298085i	0.705615	+	0.708596i	$0.250671\pi$
$314$	4859.49			0.873366
$315$	210.742	+	1851.61i	0.0376951	+	0.331195i
$316$	−1368.94			−0.243699
$317$	1198.46	−	1198.46i	0.212342	−	0.212342i	−0.592920	−	0.805262i	$-0.702025\pi$
$317$	1198.46	−	1198.46i	0.212342	−	0.212342i	0.805262	+	0.592920i	$0.202025\pi$
$318$	−221.621	+	221.621i	−0.0390813	+	0.0390813i
$319$		−	6141.21i		−	1.07787i
$320$	−2459.09	−	3691.32i	−0.429585	−	0.644847i
$321$			3444.66i			0.598948i
$322$	10219.6	+	5247.10i	1.76868	+	0.908103i
$323$	2821.40	+	2821.40i	0.486027	+	0.486027i
$324$			111.085i			0.0190475i
$325$	3248.68	+	7904.72i	0.554475	+	1.34915i
$326$	−10960.6			−1.86213
$327$	3061.33	+	3061.33i	0.517712	+	0.517712i
$328$	5800.17	−	5800.17i	0.976405	−	0.976405i
$329$	2093.66	+	6512.24i	0.350842	+	1.09128i
$330$	1227.30	+	1842.29i	0.204729	+	0.307317i
$331$	8097.27			1.34461			0.672306	−	0.740274i	$-0.265304\pi$
$331$	8097.27			1.34461			0.672306	+	0.740274i	$0.265304\pi$
$332$	−91.1389	−	91.1389i	−0.0150660	−	0.0150660i
$333$	−1448.41	−	1448.41i	−0.238355	−	0.238355i
$334$	−4942.57			−0.809717
$335$	641.821	−	3203.51i	0.104676	−	0.522467i
$336$	3866.08	−	1242.93i	0.627715	−	0.201807i
$337$	−8390.39	+	8390.39i	−1.35624	+	1.35624i	−0.477742	+	0.878500i	$0.658545\pi$
$337$	−8390.39	+	8390.39i	−1.35624	+	1.35624i	−0.878500	+	0.477742i	$0.841455\pi$
$338$	5362.86	+	5362.86i	0.863020	+	0.863020i
$339$	1048.75			0.168025
$340$	131.682	−	657.262i	0.0210043	−	0.104838i
$341$		−	1565.13i		−	0.248553i
$342$	−1778.07	−	1778.07i	−0.281132	−	0.281132i
$343$	935.345	+	6283.21i	0.147242	+	0.989101i
$344$			2102.43i			0.329522i
$345$	5656.05	−	3767.96i	0.882642	−	0.588000i
$346$		−	4101.77i		−	0.637319i
$347$	−3445.00	+	3445.00i	−0.532960	+	0.532960i	−0.921452	−	0.388492i	$-0.872996\pi$
$347$	−3445.00	+	3445.00i	−0.532960	+	0.532960i	0.388492	+	0.921452i	$0.372996\pi$
$348$	828.703	−	828.703i	0.127653	−	0.127653i
$349$	5230.77			0.802282			0.401141	−	0.916016i	$-0.368614\pi$
$349$	5230.77			0.802282			0.401141	+	0.916016i	$0.368614\pi$
$350$	−597.454	+	7061.73i	−0.0912437	+	1.07847i
$351$	1845.99			0.280717
$352$	936.249	−	936.249i	0.141768	−	0.141768i
$353$	−7791.69	+	7791.69i	−1.17482	+	1.17482i	−0.193769	+	0.981047i	$0.562071\pi$
$353$	−7791.69	+	7791.69i	−1.17482	+	1.17482i	−0.981047	+	0.193769i	$0.937929\pi$
$354$		−	1449.32i		−	0.217600i
$355$	−6427.66	+	4281.99i	−0.960971	+	0.640181i
$356$		−	448.740i		−	0.0668067i
$357$	−2160.83	−	1109.45i	−0.320345	−	0.164477i
$358$	−2404.62	−	2404.62i	−0.354995	−	0.354995i
$359$		−	8002.32i		−	1.17645i	−0.808697	−	0.588226i	$-0.799827\pi$
$359$		−	8002.32i		−	1.17645i	0.808697	−	0.588226i	$-0.200173\pi$
$360$	401.109	−	2002.05i	0.0587231	−	0.293104i
$361$	1470.90			0.214448
$362$	−2166.52	−	2166.52i	−0.314558	−	0.314558i
$363$	−1837.49	+	1837.49i	−0.265684	+	0.265684i
$364$	531.496	+	1653.20i	0.0765328	+	0.238053i
$365$	−495.071	+	2471.04i	−0.0709950	+	0.354357i
$366$	−5121.10			−0.731378
$367$	−4321.66	−	4321.66i	−0.614683	−	0.614683i	0.329479	−	0.944163i	$-0.393127\pi$
$367$	−4321.66	−	4321.66i	−0.614683	−	0.614683i	−0.944163	+	0.329479i	$0.893127\pi$
$368$	−10472.2	−	10472.2i	−1.48342	−	1.48342i
$369$	3638.10			0.513258
$370$	−4318.77	−	6482.86i	−0.606816	−	0.910887i
$371$	193.448	+	601.714i	0.0270710	+	0.0842033i
$372$	211.201	−	211.201i	0.0294362	−	0.0294362i
$373$	−3068.89	−	3068.89i	−0.426008	−	0.426008i	0.461258	−	0.887266i	$-0.347398\pi$
$373$	−3068.89	−	3068.89i	−0.426008	−	0.426008i	−0.887266	+	0.461258i	$0.847398\pi$
$374$	−2885.32			−0.398920
$375$	3476.36	+	2343.73i	0.478715	+	0.322746i
$376$		−	7494.89i		−	1.02798i
$377$	−13771.3	−	13771.3i	−1.88132	−	1.88132i
$378$	1361.78	+	699.186i	0.185297	+	0.0951382i
$379$		−	4485.09i		−	0.607872i	−0.952692	−	0.303936i	$-0.901699\pi$
$379$		−	4485.09i		−	0.607872i	0.952692	−	0.303936i	$-0.0983009\pi$
$380$	−775.862	−	1164.64i	−0.104739	−	0.157223i
$381$			2515.31i			0.338224i
$382$	−3769.80	+	3769.80i	−0.504920	+	0.504920i
$383$	−2030.11	+	2030.11i	−0.270846	+	0.270846i	−0.829441	−	0.558595i	$-0.811341\pi$
$383$	−2030.11	+	2030.11i	−0.270846	+	0.270846i	0.558595	+	0.829441i	$0.311341\pi$
$384$	−5117.33			−0.680060
$385$	4435.46	−	504.824i	0.587148	−	0.0668265i
$386$	6382.75			0.841641
$387$	−659.366	+	659.366i	−0.0866084	+	0.0866084i
$388$	−1221.64	+	1221.64i	−0.159844	+	0.159844i
$389$		−	9181.56i		−	1.19672i	−0.801228	−	0.598360i	$-0.795819\pi$
$389$		−	9181.56i		−	1.19672i	0.801228	−	0.598360i	$-0.204181\pi$
$390$	6883.34	+	1379.07i	0.893722	+	0.179056i
$391$			8858.28i			1.14574i
$392$	1131.41	−	6867.56i	0.145777	−	0.884857i
$393$	−2860.33	−	2860.33i	−0.367136	−	0.367136i
$394$			12340.9i			1.57799i
$395$	6187.42	+	9287.88i	0.788159	+	1.18310i
$396$	266.100			0.0337677
$397$	−1980.83	−	1980.83i	−0.250415	−	0.250415i	0.570726	−	0.821141i	$-0.306662\pi$
$397$	−1980.83	−	1980.83i	−0.250415	−	0.250415i	−0.821141	+	0.570726i	$0.806662\pi$
$398$	3591.52	−	3591.52i	0.452328	−	0.452328i
$399$	−4827.58	+	1552.05i	−0.605718	+	0.194736i
$400$	3519.63	−	8431.16i	0.439954	−	1.05390i
$401$	7351.41			0.915491			0.457745	−	0.889083i	$-0.348657\pi$
$401$	7351.41			0.915491			0.457745	+	0.889083i	$0.348657\pi$
$402$	−1897.69	−	1897.69i	−0.235444	−	0.235444i
$403$	−3509.70	−	3509.70i	−0.433823	−	0.433823i
$404$	−308.973			−0.0380495
$405$	753.680	−	502.088i	0.0924707	−	0.0616023i
$406$	−4942.98	−	15374.9i	−0.604226	−	1.87942i
$407$	−3469.60	+	3469.60i	−0.422559	+	0.422559i
$408$	1881.87	+	1881.87i	0.228349	+	0.228349i
$409$	−13654.6			−1.65080			−0.825402	−	0.564546i	$-0.809051\pi$
$409$	−13654.6			−1.65080			−0.825402	+	0.564546i	$0.809051\pi$
$410$	13565.8	+	2717.89i	1.63406	+	0.327383i
$411$			1181.40i			0.141786i
$412$	591.657	+	591.657i	0.0707496	+	0.0707496i
$413$	−2600.04	−	1334.95i	−0.309781	−	0.159053i
$414$		−	5582.59i		−	0.662727i
$415$	−206.417	+	1030.29i	−0.0244159	+	0.121867i
$416$		−	4198.95i		−	0.494881i
$417$	772.626	−	772.626i	0.0907330	−	0.0907330i
$418$	−4259.31	+	4259.31i	−0.498396	+	0.498396i
$419$	−8801.44			−1.02620			−0.513101	−	0.858328i	$-0.671503\pi$
$419$	−8801.44			−1.02620			−0.513101	+	0.858328i	$0.671503\pi$
$420$	666.648	+	530.405i	0.0774503	+	0.0616217i
$421$	−6602.18			−0.764301			−0.382150	−	0.924100i	$-0.624816\pi$
$421$	−6602.18			−0.764301			−0.382150	+	0.924100i	$0.624816\pi$
$422$	1964.35	−	1964.35i	0.226595	−	0.226595i
$423$	2350.55	−	2350.55i	0.270184	−	0.270184i
$424$		−	692.508i		−	0.0793187i
$425$	−5054.52	+	2077.30i	−0.576895	+	0.237092i
$426$			6344.17i			0.721540i
$427$	−4717.00	+	9187.11i	−0.534594	+	1.04121i
$428$	1113.48	+	1113.48i	0.125752	+	0.125752i
$429$		−	4422.00i		−	0.497660i
$430$	−2951.23	+	1966.06i	−0.330979	+	0.220492i
$431$	6237.46			0.697095			0.348547	−	0.937291i	$-0.386675\pi$
$431$	6237.46			0.697095			0.348547	+	0.937291i	$0.386675\pi$
$432$	−1395.44	−	1395.44i	−0.155412	−	0.155412i
$433$	4296.22	−	4296.22i	0.476821	−	0.476821i	−0.427293	−	0.904113i	$-0.640533\pi$
$433$	4296.22	−	4296.22i	0.476821	−	0.476821i	0.904113	+	0.427293i	$0.140533\pi$
$434$	−1259.75	−	3918.41i	−0.139332	−	0.433387i
$435$	−9368.13	−	1876.90i	−1.03257	−	0.206874i
$436$	1979.13			0.217392
$437$	13076.6	+	13076.6i	1.43144	+	1.43144i
$438$	1463.79	+	1463.79i	0.159687	+	0.159687i
$439$	−3338.10			−0.362914			−0.181457	−	0.983399i	$-0.558081\pi$
$439$	−3338.10			−0.362914			−0.181457	+	0.983399i	$0.558081\pi$
$440$	−4795.83	−	960.841i	−0.519619	−	0.104105i
$441$	2508.64	−	1798.97i	0.270882	−	0.194253i
$442$	−6470.13	+	6470.13i	−0.696274	+	0.696274i
$443$	−3504.18	−	3504.18i	−0.375820	−	0.375820i	0.493771	−	0.869592i	$-0.335618\pi$
$443$	−3504.18	−	3504.18i	−0.375820	−	0.375820i	−0.869592	+	0.493771i	$0.835618\pi$
$444$	−936.384			−0.100087
$445$	−3044.57	+	2028.24i	−0.324330	+	0.216062i
$446$			16483.9i			1.75008i
$447$	−446.023	−	446.023i	−0.0471950	−	0.0471950i
$448$	−3355.88	+	6536.10i	−0.353907	+	0.689290i
$449$		−	3414.83i		−	0.358922i	−0.983765	−	0.179461i	$-0.942565\pi$
$449$		−	3414.83i		−	0.358922i	0.983765	−	0.179461i	$-0.0574354\pi$
$450$	3185.41	−	1309.14i	0.333693	−	0.137141i
$451$		−	8714.93i		−	0.909912i
$452$	339.006	−	339.006i	0.0352776	−	0.0352776i
$453$	−88.5748	+	88.5748i	−0.00918677	+	0.00918677i
$454$	16755.6			1.73212
$455$	8814.19	−	11078.3i	0.908167	−	1.14144i
$456$	5556.03			0.570581
$457$	−10063.9	+	10063.9i	−1.03013	+	1.03013i	−0.0305984	+	0.999532i	$0.509741\pi$
$457$	−10063.9	+	10063.9i	−1.03013	+	1.03013i	−0.999532	+	0.0305984i	$0.990259\pi$
$458$	11637.1	−	11637.1i	1.18726	−	1.18726i
$459$			1180.38i			0.120034i
$460$	610.319	−	3046.28i	0.0618615	−	0.308768i
$461$			8392.20i			0.847861i	0.905695	+	0.423931i	$0.139350\pi$
$461$			8392.20i			0.847861i	−0.905695	+	0.423931i	$0.860650\pi$
$462$	1674.87	−	3262.08i	0.168663	−	0.328497i
$463$	4334.55	+	4334.55i	0.435083	+	0.435083i	0.890353	−	0.455270i	$-0.150457\pi$
$463$	4334.55	+	4334.55i	0.435083	+	0.435083i	−0.455270	+	0.890353i	$0.650457\pi$
$464$			20820.1i			2.08308i
$465$	−2387.53	−	478.340i	−0.238106	−	0.0477043i
$466$	−13600.3			−1.35198
$467$	2870.03	+	2870.03i	0.284387	+	0.284387i	0.834856	−	0.550468i	$-0.185551\pi$
$467$	2870.03	+	2870.03i	0.284387	+	0.284387i	−0.550468	+	0.834856i	$0.685551\pi$
$468$	596.711	−	596.711i	0.0589380	−	0.0589380i
$469$	−5152.36	+	1656.46i	−0.507279	+	0.163088i
$470$	10520.7	−	7008.73i	1.03252	−	0.687848i
$471$	−4762.22			−0.465884
$472$	2264.37	+	2264.37i	0.220818	+	0.220818i
$473$	1579.48	+	1579.48i	0.153541	+	0.153541i
$474$	9167.24			0.888324
$475$	−4394.97	+	10528.0i	−0.424537	+	1.01696i
$476$	−1057.10	+	339.855i	−0.101791	+	0.0327252i
$477$	217.184	−	217.184i	0.0208474	−	0.0208474i
$478$	−12008.9	−	12008.9i	−1.14911	−	1.14911i
$479$	−798.144			−0.0761338			−0.0380669	−	0.999275i	$-0.512120\pi$
$479$	−798.144			−0.0761338			−0.0380669	+	0.999275i	$0.512120\pi$
$480$	−1142.06	−	1714.34i	−0.108600	−	0.163018i
$481$			15560.7i			1.47506i
$482$	−2388.14	−	2388.14i	−0.225678	−	0.225678i
$483$	−10015.0	−	5142.07i	−0.943474	−	0.484414i
$484$			1187.93i			0.111563i
$485$	13810.1	+	2766.85i	1.29296	+	0.259043i
$486$		−	743.890i		−	0.0694312i
$487$	7852.11	−	7852.11i	0.730622	−	0.730622i	−0.240121	−	0.970743i	$-0.577187\pi$
$487$	7852.11	−	7852.11i	0.730622	−	0.730622i	0.970743	+	0.240121i	$0.0771871\pi$
$488$	8001.06	−	8001.06i	0.742195	−	0.742195i
$489$	10741.2			0.993323
$490$	10698.2	−	4833.90i	0.986313	−	0.445660i
$491$	10482.7			0.963501			0.481751	−	0.876308i	$-0.340001\pi$
$491$	10482.7			0.963501			0.481751	+	0.876308i	$0.340001\pi$
$492$	1176.00	−	1176.00i	0.107761	−	0.107761i
$493$	8805.76	−	8805.76i	0.804445	−	0.804445i
$494$			19102.4i			1.73980i
$495$	−1202.73	−	1805.41i	−0.109210	−	0.163934i
$496$			5306.16i			0.480350i
$497$	11381.3	+	5843.56i	1.02720	+	0.527403i
$498$	610.320	+	610.320i	0.0549179	+	0.0549179i
$499$			11543.1i			1.03556i	0.855515	+	0.517778i	$0.173241\pi$
$499$			11543.1i			1.03556i	−0.855515	+	0.517778i	$0.826759\pi$
$500$	1881.32	−	366.118i	0.168271	−	0.0327466i
$501$	4843.64			0.431932
$502$	−6107.11	−	6107.11i	−0.542976	−	0.542976i
$503$	3220.79	−	3220.79i	0.285503	−	0.285503i	−0.549796	−	0.835299i	$-0.685295\pi$
$503$	3220.79	−	3220.79i	0.285503	−	0.285503i	0.835299	+	0.549796i	$0.185295\pi$
$504$	−3219.99	+	1035.21i	−0.284583	+	0.0914921i
$505$	1396.51	+	2096.30i	0.123058	+	0.184721i
$506$	−13372.9			−1.17489
$507$	−5255.51	−	5255.51i	−0.460365	−	0.460365i
$508$	813.065	+	813.065i	0.0710117	+	0.0710117i
$509$	2975.34			0.259095			0.129548	−	0.991573i	$-0.458647\pi$
$509$	2975.34			0.259095			0.129548	+	0.991573i	$0.458647\pi$
$510$	−881.820	+	4401.42i	−0.0765640	+	0.382153i
$511$	3974.29	−	1277.72i	0.344055	−	0.110612i
$512$	5215.85	−	5215.85i	0.450215	−	0.450215i
$513$	1742.48	+	1742.48i	0.149966	+	0.149966i
$514$	3286.30			0.282009
$515$	1340.02	−	6688.42i	0.114657	−	0.572286i
$516$			426.276i			0.0363677i
$517$	−5630.65	−	5630.65i	−0.478986	−	0.478986i
$518$	−5893.75	+	11479.0i	−0.499916	+	0.973666i
$519$			4019.66i			0.339968i
$520$	−12909.0	+	8599.71i	−1.08864	+	0.725235i
$521$		−	1537.34i		−	0.129275i	−0.997909	−	0.0646374i	$-0.979411\pi$
$521$		−	1537.34i		−	0.129275i	0.997909	−	0.0646374i	$-0.0205891\pi$
$522$	−5549.48	+	5549.48i	−0.465315	+	0.465315i
$523$	50.7677	−	50.7677i	0.00424459	−	0.00424459i	−0.704981	−	0.709226i	$-0.749045\pi$
$523$	50.7677	−	50.7677i	0.00424459	−	0.00424459i	0.709226	+	0.704981i	$0.249045\pi$
$524$	−1849.18			−0.154164
$525$	585.495	−	6920.37i	0.0486726	−	0.575295i
$526$	7473.05			0.619468
$527$	2244.21	−	2244.21i	0.185502	−	0.185502i
$528$	−3342.71	+	3342.71i	−0.275517	+	0.275517i
$529$			28889.4i			2.37440i
$530$	972.088	−	647.587i	0.0796695	−	0.0530743i
$531$			1420.31i			0.116076i
$532$	−1058.81	+	2062.19i	−0.0862877	+	0.168059i
$533$	−19542.7	−	19542.7i	−1.58816	−	1.58816i
$534$			3005.03i			0.243521i
$535$	2521.87	−	12587.4i	0.203794	−	1.01719i
$536$	5929.81			0.477852
$537$	2356.49	+	2356.49i	0.189367	+	0.189367i
$538$	6486.17	−	6486.17i	0.519774	−	0.519774i
$539$	−4309.37	−	6009.34i	−0.344374	−	0.480224i
$540$	81.3262	−	405.922i	0.00648097	−	0.0323484i
$541$	18943.2			1.50542			0.752711	−	0.658351i	$-0.228746\pi$
$541$	18943.2			1.50542			0.752711	+	0.658351i	$0.228746\pi$
$542$	2654.34	+	2654.34i	0.210357	+	0.210357i
$543$	2123.16	+	2123.16i	0.167796	+	0.167796i
$544$	2684.94			0.211610
$545$	−8945.37	−	13427.8i	−0.703078	−	1.05539i
$546$	−3559.21	−	11070.8i	−0.278975	−	0.867740i
$547$	2674.74	−	2674.74i	0.209074	−	0.209074i	−0.594800	−	0.803874i	$-0.702769\pi$
$547$	2674.74	−	2674.74i	0.209074	−	0.209074i	0.803874	+	0.594800i	$0.202769\pi$
$548$	381.883	+	381.883i	0.0297686	+	0.0297686i
$549$	5018.59			0.390143
$550$	−3135.99	−	7630.53i	−0.243126	−	0.591576i
$551$		−	25998.1i		−	2.01009i
$552$	8722.07	+	8722.07i	0.672529	+	0.672529i
$553$	8443.86	−	16445.8i	0.649312	−	1.26464i
$554$			2203.05i			0.168951i
$555$	4232.32	+	6353.10i	0.323697	+	0.485899i
$556$		−	499.497i		−	0.0380997i
$557$	−8226.33	+	8226.33i	−0.625782	+	0.625782i	−0.947004	−	0.321222i	$-0.895906\pi$
$557$	−8226.33	+	8226.33i	−0.625782	+	0.625782i	0.321222	+	0.947004i	$0.395906\pi$
$558$	−1414.33	+	1414.33i	−0.107300	+	0.107300i
$559$	7083.78			0.535979
$560$	−15037.3	+	1711.47i	−1.13471	+	0.129148i
$561$	2827.56			0.212798
$562$	6300.19	−	6300.19i	0.472878	−	0.472878i
$563$	−16530.4	+	16530.4i	−1.23743	+	1.23743i	−0.276378	+	0.961049i	$0.589134\pi$
$563$	−16530.4	+	16530.4i	−1.23743	+	1.23743i	−0.961049	+	0.276378i	$0.910866\pi$
$564$		−	1519.61i		−	0.113453i
$565$	−3832.31	−	767.801i	−0.285357	−	0.0571710i
$566$			15905.6i			1.18121i
$567$	−1334.52	−	685.190i	−0.0988439	−	0.0507501i
$568$	−9911.95	−	9911.95i	−0.732212	−	0.732212i
$569$		−	13158.9i		−	0.969509i	−0.874650	−	0.484754i	$-0.838909\pi$
$569$		−	13158.9i		−	0.969509i	0.874650	−	0.484754i	$-0.161091\pi$
$570$	5195.63	+	7799.12i	0.381791	+	0.573104i
$571$	7527.15			0.551666			0.275833	−	0.961206i	$-0.411046\pi$
$571$	7527.15			0.551666			0.275833	+	0.961206i	$0.411046\pi$
$572$	−1429.40	−	1429.40i	−0.104486	−	0.104486i
$573$	3694.34	−	3694.34i	0.269342	−	0.269342i
$574$	−7014.53	−	21818.4i	−0.510071	−	1.58656i
$575$	−23426.7	+	9627.89i	−1.69906	+	0.698279i
$576$	3570.44			0.258279
$577$	−6999.70	−	6999.70i	−0.505028	−	0.505028i	0.407968	−	0.912996i	$-0.366238\pi$
$577$	−6999.70	−	6999.70i	−0.505028	−	0.505028i	−0.912996	+	0.407968i	$0.866238\pi$
$578$	6497.73	+	6497.73i	0.467595	+	0.467595i
$579$	−6254.99			−0.448961
$580$	−3634.92	+	2421.51i	−0.260227	+	0.173358i
$581$	1657.06	−	532.736i	0.118324	−	0.0380407i
$582$	8180.82	−	8180.82i	0.582656	−	0.582656i
$583$	−520.257	−	520.257i	−0.0369585	−	0.0369585i
$584$	−4573.98			−0.324097
$585$	−6745.56	−	1351.47i	−0.476743	−	0.0955150i
$586$		−	3400.73i		−	0.239732i
$587$	−208.143	−	208.143i	−0.0146354	−	0.0146354i	0.699751	−	0.714387i	$-0.253294\pi$
$587$	−208.143	−	208.143i	−0.0146354	−	0.0146354i	−0.714387	+	0.699751i	$0.753294\pi$
$588$	229.397	−	1392.42i	0.0160887	−	0.0976572i
$589$		−	6625.81i		−	0.463517i
$590$	−1061.06	+	5296.05i	−0.0740391	+	0.369551i
$591$		−	12093.9i		−	0.841753i
$592$	11762.7	−	11762.7i	0.816632	−	0.816632i
$593$	17536.1	−	17536.1i	1.21437	−	1.21437i	0.244798	−	0.969574i	$-0.421278\pi$
$593$	17536.1	−	17536.1i	1.21437	−	1.21437i	0.969574	−	0.244798i	$-0.0787216\pi$
$594$	−1781.96			−0.123089
$595$	7083.78	+	5636.06i	0.488078	+	0.388330i
$596$	−288.351			−0.0198176
$597$	−3519.63	+	3519.63i	−0.241288	+	0.241288i
$598$	−29987.8	+	29987.8i	−2.05065	+	2.05065i
$599$			4938.10i			0.336837i	0.985716	+	0.168419i	$0.0538660\pi$
$599$			4938.10i			0.336837i	−0.985716	+	0.168419i	$0.946134\pi$
$600$	−2931.44	+	7022.16i	−0.199459	+	0.477798i
$601$			23949.9i			1.62552i	0.582598	+	0.812760i	$0.302036\pi$
$601$			23949.9i			1.62552i	−0.582598	+	0.812760i	$0.697964\pi$
$602$	5225.66	+	2683.04i	0.353791	+	0.181649i
$603$	1859.71	+	1859.71i	0.125594	+	0.125594i
$604$			57.2630i			0.00385761i
$605$	8059.75	−	5369.26i	0.541612	−	0.360812i
$606$	2069.07			0.138697
$607$	−2020.06	−	2020.06i	−0.135077	−	0.135077i	0.636336	−	0.771412i	$-0.280449\pi$
$607$	−2020.06	−	2020.06i	−0.135077	−	0.135077i	−0.771412	+	0.636336i	$0.780449\pi$
$608$	3963.51	−	3963.51i	0.264378	−	0.264378i
$609$	4844.04	+	15067.2i	0.322316	+	1.00255i
$610$	18713.3	+	3749.20i	1.24210	+	0.248854i
$611$	−25252.7			−1.67204
$612$	381.555	+	381.555i	0.0252017	+	0.0252017i
$613$	17769.2	+	17769.2i	1.17078	+	1.17078i	0.982023	+	0.188760i	$0.0604469\pi$
$613$	17769.2	+	17769.2i	1.17078	+	1.17078i	0.188760	+	0.982023i	$0.439553\pi$
$614$	−20619.1			−1.35524
$615$	−13294.2	−	2663.49i	−0.871666	−	0.174638i
$616$	2479.81	+	7713.35i	0.162199	+	0.504513i
$617$	285.908	−	285.908i	0.0186552	−	0.0186552i	−0.697718	−	0.716373i	$-0.745801\pi$
$617$	285.908	−	285.908i	0.0186552	−	0.0186552i	0.716373	+	0.697718i	$0.245801\pi$
$618$	−3962.08	−	3962.08i	−0.257894	−	0.257894i
$619$	10757.7			0.698527			0.349263	−	0.937025i	$-0.386432\pi$
$619$	10757.7			0.698527			0.349263	+	0.937025i	$0.386432\pi$
$620$	−926.384	+	617.140i	−0.0600072	+	0.0399757i
$621$			5470.84i			0.353522i
$622$	7598.51	+	7598.51i	0.489827	+	0.489827i
$623$	5390.93	+	2767.90i	0.346683	+	0.178000i
$624$			14991.6i			0.961771i
$625$	−10987.3	−	11109.4i	−0.703188	−	0.711004i
$626$		−	71.4619i		−	0.00456260i
$627$	4174.05	−	4174.05i	0.265862	−	0.265862i
$628$	−1539.37	+	1539.37i	−0.0978146	+	0.0978146i
$629$	−9949.97			−0.630734
$630$	−4464.27	−	3551.91i	−0.282319	−	0.224621i
$631$	−1230.57			−0.0776357			−0.0388178	−	0.999246i	$-0.512359\pi$
$631$	−1230.57			−0.0776357			−0.0388178	+	0.999246i	$0.512359\pi$
$632$	−14322.6	+	14322.6i	−0.901462	+	0.901462i
$633$	−1925.03	+	1925.03i	−0.120874	+	0.120874i
$634$			5188.50i			0.325018i
$635$	1841.48	−	9191.35i	0.115082	−	0.574406i
$636$		−	140.408i		−	0.00875401i
$637$	−23139.0	−	3812.08i	−1.43925	−	0.237112i
$638$	13293.6	+	13293.6i	0.824918	+	0.824918i
$639$		−	6217.18i		−	0.384895i
$640$	18699.6	+	3746.44i	1.15495	+	0.231393i
$641$	21955.2			1.35285			0.676427	−	0.736510i	$-0.263528\pi$
$641$	21955.2			1.35285			0.676427	+	0.736510i	$0.263528\pi$
$642$	−7456.49	−	7456.49i	−0.458387	−	0.458387i
$643$	−3432.43	+	3432.43i	−0.210516	+	0.210516i	−0.804487	−	0.593971i	$-0.797559\pi$
$643$	−3432.43	+	3432.43i	−0.210516	+	0.210516i	0.593971	+	0.804487i	$0.297559\pi$
$644$	−4899.47	+	1575.16i	−0.299792	+	0.0963818i
$645$	2892.16	−	1926.70i	0.176556	−	0.117618i
$646$	−12214.7			−0.743932
$647$	639.729	+	639.729i	0.0388722	+	0.0388722i	0.726276	−	0.687403i	$-0.241250\pi$
$647$	639.729	+	639.729i	0.0388722	+	0.0388722i	−0.687403	+	0.726276i	$0.741250\pi$
$648$	1162.23	+	1162.23i	0.0704581	+	0.0704581i
$649$	3402.29			0.205781
$650$	−24143.2	−	10078.7i	−1.45688	−	0.608184i
$651$	1234.54	+	3839.98i	0.0743246	+	0.231184i
$652$	3472.07	−	3472.07i	0.208553	−	0.208553i
$653$	−4083.19	−	4083.19i	−0.244697	−	0.244697i	0.574093	−	0.818790i	$-0.305355\pi$
$653$	−4083.19	−	4083.19i	−0.244697	−	0.244697i	−0.818790	+	0.574093i	$0.805355\pi$
$654$	−13253.4			−0.792431
$655$	8358.04	+	12546.2i	0.498589	+	0.748427i
$656$			29545.7i			1.75848i
$657$	−1434.49	−	1434.49i	−0.0851824	−	0.0851824i
$658$	−18628.8	−	9564.69i	−1.10368	−	0.566672i
$659$			786.609i			0.0464976i	0.999730	+	0.0232488i	$0.00740099\pi$
$659$			786.609i			0.0464976i	−0.999730	+	0.0232488i	$0.992599\pi$
$660$	−972.371	−	194.814i	−0.0573477	−	0.0114896i
$661$		−	18176.9i		−	1.06959i	−0.844982	−	0.534794i	$-0.820389\pi$
$661$		−	18176.9i		−	1.06959i	0.844982	−	0.534794i	$-0.179611\pi$
$662$	−17527.8	+	17527.8i	−1.02906	+	1.02906i
$663$	6340.62	−	6340.62i	0.371417	−	0.371417i
$664$	−1907.09			−0.111460
$665$	18777.0	−	2137.12i	1.09495	−	0.124622i
$666$	6270.58			0.364835
$667$	40812.9	−	40812.9i	2.36924	−	2.36924i
$668$	1565.69	−	1565.69i	0.0906861	−	0.0906861i
$669$		−	16153.9i		−	0.933554i
$670$	5545.16	+	8323.80i	0.319744	+	0.479965i
$671$		−	12021.8i		−	0.691651i
$672$	−1558.56	+	3035.54i	−0.0894682	+	0.174254i
$673$	13196.2	+	13196.2i	0.755833	+	0.755833i	0.975561	−	0.219728i	$-0.0705170\pi$
$673$	13196.2	+	13196.2i	0.755833	+	0.755833i	−0.219728	+	0.975561i	$0.570517\pi$
$674$		−	36324.5i		−	2.07592i
$675$	−3121.65	+	1282.93i	−0.178004	+	0.0731558i
$676$	−3397.65			−0.193312
$677$	17823.9	+	17823.9i	1.01186	+	1.01186i	0.999929	+	0.0119324i	$0.00379828\pi$
$677$	17823.9	+	17823.9i	1.01186	+	1.01186i	0.0119324	+	0.999929i	$0.496202\pi$
$678$	−2270.18	+	2270.18i	−0.128593	+	0.128593i
$679$	−7140.88	−	22211.4i	−0.403596	−	1.25537i
$680$	−5498.92	−	8254.38i	−0.310109	−	0.465501i
$681$	−16420.2			−0.923972
$682$	3387.96	+	3387.96i	0.190222	+	0.190222i
$683$	−2199.72	−	2199.72i	−0.123236	−	0.123236i	0.642799	−	0.766035i	$-0.277773\pi$
$683$	−2199.72	−	2199.72i	−0.123236	−	0.123236i	−0.766035	+	0.642799i	$0.777773\pi$
$684$	1126.50			0.0629721
$685$	864.911	−	4317.02i	0.0482431	−	0.240795i
$686$	−15625.6	−	11576.3i	−0.869665	−	0.644291i
$687$	−11404.2	+	11404.2i	−0.633328	+	0.633328i
$688$	−5354.83	−	5354.83i	−0.296731	−	0.296731i
$689$	−2333.28			−0.129015
$690$	−4087.06	+	20399.7i	−0.225495	+	1.12551i
$691$			9477.75i			0.521781i	0.965368	+	0.260891i	$0.0840162\pi$
$691$			9477.75i			0.521781i	−0.965368	+	0.260891i	$0.915984\pi$
$692$	1299.34	+	1299.34i	0.0713780	+	0.0713780i
$693$	−1641.35	+	3196.78i	−0.0899705	+	0.175232i
$694$		−	14914.4i		−	0.815769i
$695$	−3388.95	+	2257.66i	−0.184964	+	0.123220i
$696$		−	17340.7i		−	0.944394i
$697$	12496.2	−	12496.2i	0.679091	−	0.679091i
$698$	−11322.8	+	11322.8i	−0.614002	+	0.614002i
$699$	13328.1			0.721194
$700$	−2047.73	−	2426.25i	−0.110567	−	0.131005i
$701$	−23915.2			−1.28854			−0.644270	−	0.764798i	$-0.722839\pi$
$701$	−23915.2			−1.28854			−0.644270	+	0.764798i	$0.722839\pi$
$702$	−3995.93	+	3995.93i	−0.214838	+	0.214838i
$703$	−14688.2	+	14688.2i	−0.788015	+	0.788015i
$704$		−	8552.85i		−	0.457880i
$705$	−10310.1	+	6868.43i	−0.550784	+	0.366922i
$706$		−	33732.6i		−	1.79822i
$707$	1905.80	−	3711.85i	0.101379	−	0.197452i
$708$	459.110	+	459.110i	0.0243706	+	0.0243706i
$709$			22930.3i			1.21462i	0.794466	+	0.607309i	$0.207751\pi$
$709$			22930.3i			1.21462i	−0.794466	+	0.607309i	$0.792249\pi$
$710$	4644.62	−	23182.6i	0.245506	−	1.22539i
$711$	−8983.74			−0.473863
$712$	−4694.97	−	4694.97i	−0.247123	−	0.247123i
$713$	10401.5	−	10401.5i	0.546336	−	0.546336i
$714$	7079.00	−	2275.87i	0.371043	−	0.119289i
$715$	−3237.39	+	16158.7i	−0.169331	+	0.845177i
$716$	1523.46			0.0795170
$717$	11768.5	+	11768.5i	0.612976	+	0.612976i
$718$	17322.2	+	17322.2i	0.900361	+	0.900361i
$719$	−36265.7			−1.88106			−0.940530	−	0.339711i	$-0.889671\pi$
$719$	−36265.7			−1.88106			−0.940530	+	0.339711i	$0.889671\pi$
$720$	4077.54	+	6120.76i	0.211057	+	0.316816i
$721$	−10757.3	+	3458.42i	−0.555649	+	0.178639i
$722$	−3183.98	+	3183.98i	−0.164121	+	0.164121i
$723$	2340.34	+	2340.34i	0.120385	+	0.120385i
$724$	1372.61			0.0704593
$725$	32858.6	+	13717.0i	1.68322	+	0.702670i
$726$		−	7955.07i		−	0.406667i
$727$	−24124.3	−	24124.3i	−1.23070	−	1.23070i	−0.963694	−	0.267009i	$-0.913965\pi$
$727$	−24124.3	−	24124.3i	−1.23070	−	1.23070i	−0.267009	−	0.963694i	$-0.586035\pi$
$728$	22857.5	+	11735.9i	1.16367	+	0.597473i
$729$			729.000i			0.0370370i
$730$	−4277.28	−	6420.59i	−0.216862	−	0.325530i
$731$			4529.59i			0.229183i
$732$	1622.24	−	1622.24i	0.0819123	−	0.0819123i
$733$	5601.91	−	5601.91i	0.282280	−	0.282280i	−0.551738	−	0.834018i	$-0.686035\pi$
$733$	5601.91	−	5601.91i	0.282280	−	0.282280i	0.834018	+	0.551738i	$0.186035\pi$
$734$	18709.8			0.940858
$735$	−10484.0	+	4737.15i	−0.526134	+	0.237731i
$736$	12444.1			0.623230
$737$	4454.86	−	4454.86i	0.222655	−	0.222655i
$738$	−7875.22	+	7875.22i	−0.392806	+	0.392806i
$739$		−	28013.0i		−	1.39442i	−0.716867	−	0.697209i	$-0.754425\pi$
$739$		−	28013.0i		−	1.39442i	0.716867	−	0.697209i	$-0.245575\pi$
$740$	3421.70	+	685.535i	0.169979	+	0.0340551i
$741$		−	18720.1i		−	0.928068i
$742$	−1721.25	−	883.751i	−0.0851603	−	0.0437244i
$743$	16633.1	+	16633.1i	0.821277	+	0.821277i	0.986291	−	0.165014i	$-0.0527669\pi$
$743$	16633.1	+	16633.1i	0.821277	+	0.821277i	−0.165014	+	0.986291i	$0.552767\pi$
$744$		−	4419.40i		−	0.217773i
$745$	1303.30	+	1956.38i	0.0640930	+	0.0962095i
$746$	13286.1			0.652064
$747$	−598.103	−	598.103i	−0.0292951	−	0.0292951i
$748$	914.000	−	914.000i	0.0446780	−	0.0446780i
$749$	−20244.8	+	6508.62i	−0.987623	+	0.317517i
$750$	−12598.4	+	2451.74i	−0.613374	+	0.119367i
$751$	−5945.30			−0.288878			−0.144439	−	0.989514i	$-0.546138\pi$
$751$	−5945.30			−0.288878			−0.144439	+	0.989514i	$0.546138\pi$
$752$	19089.2	+	19089.2i	0.925681	+	0.925681i
$753$	5984.87	+	5984.87i	0.289642	+	0.289642i
$754$	59619.9			2.87961
$755$	388.513	−	258.820i	0.0187277	−	0.0124761i
$756$	−652.864	+	209.893i	−0.0314080	+	0.0100975i
$757$	−14588.8	+	14588.8i	−0.700449	+	0.700449i	−0.964507	−	0.264058i	$-0.914939\pi$
$757$	−14588.8	+	14588.8i	−0.700449	+	0.700449i	0.264058	+	0.964507i	$0.414939\pi$
$758$	9708.64	+	9708.64i	0.465216	+	0.465216i
$759$	13105.2			0.626730
$760$	−20302.6	−	4067.62i	−0.969018	−	0.194142i
$761$		−	11552.9i		−	0.550318i	−0.961399	−	0.275159i	$-0.911270\pi$
$761$		−	11552.9i		−	0.550318i	0.961399	−	0.275159i	$-0.0887304\pi$
$762$	−5444.76	−	5444.76i	−0.258849	−	0.258849i
$763$	−12207.6	+	23776.2i	−0.579220	+	1.12812i
$764$		−	2388.36i		−	0.113099i
$765$	864.169	−	4313.31i	0.0408420	−	0.203854i
$766$		−	8788.97i		−	0.414567i
$767$	7629.41	−	7629.41i	0.359168	−	0.359168i
$768$	4344.74	−	4344.74i	0.204137	−	0.204137i
$769$	39641.9			1.85894			0.929470	−	0.368898i	$-0.120265\pi$
$769$	39641.9			1.85894			0.929470	+	0.368898i	$0.120265\pi$
$770$	−8508.45	+	10694.0i	−0.398212	+	0.500499i
$771$	−3220.52			−0.150433
$772$	−2021.90	+	2021.90i	−0.0942615	+	0.0942615i
$773$	−9389.49	+	9389.49i	−0.436891	+	0.436891i	−0.890964	−	0.454073i	$-0.849970\pi$
$773$	−9389.49	+	9389.49i	−0.436891	+	0.436891i	0.454073	+	0.890964i	$0.349970\pi$
$774$		−	2854.59i		−	0.132566i
$775$	8374.24	+	3495.87i	0.388144	+	0.162033i
$776$			25563.0i			1.18255i
$777$	5775.77	−	11249.2i	0.266673	−	0.519388i
$778$	19874.9	+	19874.9i	0.915872	+	0.915872i
$779$		−	36893.7i		−	1.69686i
$780$	−2617.34	+	1743.62i	−0.120148	+	0.0800406i
$781$	−14893.0			−0.682348
$782$	−19175.1	−	19175.1i	−0.876854	−	0.876854i
$783$	5438.40	−	5438.40i	0.248215	−	0.248215i
$784$	14609.8	+	20373.1i	0.665533	+	0.928074i
$785$	17401.9	+	3486.46i	0.791212	+	0.158519i
$786$	12383.2			0.561953
$787$	24302.8	+	24302.8i	1.10076	+	1.10076i	0.994319	+	0.106444i	$0.0339464\pi$
$787$	24302.8	+	24302.8i	1.10076	+	1.10076i	0.106444	+	0.994319i	$0.466054\pi$
$788$	−3909.31	−	3909.31i	−0.176730	−	0.176730i
$789$	−7323.46			−0.330446
$790$	−33498.6	−	6711.42i	−1.50864	−	0.302255i
$791$	1981.60	+	6163.68i	0.0890739	+	0.277061i
$792$	2784.08	−	2784.08i	0.124909	−	0.124909i
$793$	−26958.2	−	26958.2i	−1.20720	−	1.20720i
$794$	8575.60			0.383295
$795$	−952.630	+	634.625i	−0.0424985	+	0.0283117i
$796$			2275.41i			0.101319i
$797$	26649.0	+	26649.0i	1.18438	+	1.18438i	0.978597	+	0.205788i	$0.0659756\pi$
$797$	26649.0	+	26649.0i	1.18438	+	1.18438i	0.205788	+	0.978597i	$0.434024\pi$
$798$	7090.39	−	13809.7i	0.314533	−	0.612602i
$799$		−	16147.4i		−	0.714959i
$800$	2918.21	+	7100.61i	0.128968	+	0.313806i
$801$		−	2944.88i		−	0.129903i
$802$	−15913.2	+	15913.2i	−0.700643	+	0.700643i
$803$	−3436.27	+	3436.27i	−0.151013	+	0.151013i
$804$	1202.29			0.0527381
$805$	32831.9	+	26122.0i	1.43748	+	1.14370i
$806$	15194.6			0.664026
$807$	−6356.34	+	6356.34i	−0.277266	+	0.277266i
$808$	−3232.65	+	3232.65i	−0.140748	+	0.140748i
$809$			26314.3i			1.14359i	0.820397	+	0.571794i	$0.193752\pi$
$809$			26314.3i			1.14359i	−0.820397	+	0.571794i	$0.806248\pi$
$810$	−544.609	+	2718.30i	−0.0236242	+	0.117915i
$811$			40631.0i			1.75925i	0.475672	+	0.879623i	$0.342205\pi$
$811$			40631.0i			1.75925i	−0.475672	+	0.879623i	$0.657795\pi$
$812$	6436.23	+	3304.60i	0.278162	+	0.142819i
$813$	−2601.21	−	2601.21i	−0.112212	−	0.112212i
$814$		−	15020.9i		−	0.646785i
$815$	−39250.2	−	7863.75i	−1.68696	−	0.337982i
$816$	−9586.10			−0.411251
$817$	6686.58	+	6686.58i	0.286333	+	0.286333i
$818$	29557.5	−	29557.5i	1.26339	−	1.26339i
$819$	3487.97	+	10849.2i	0.148815	+	0.462883i
$820$	−5158.27	+	3436.35i	−0.219677	+	0.146345i
$821$	−1466.86			−0.0623552			−0.0311776	−	0.999514i	$-0.509926\pi$
$821$	−1466.86			−0.0623552			−0.0311776	+	0.999514i	$0.509926\pi$
$822$	−2557.31	−	2557.31i	−0.108512	−	0.108512i
$823$	−5156.55	−	5156.55i	−0.218403	−	0.218403i	0.589422	−	0.807825i	$-0.299356\pi$
$823$	−5156.55	−	5156.55i	−0.218403	−	0.218403i	−0.807825	+	0.589422i	$0.799356\pi$
$824$	12380.5			0.523416
$825$	3073.22	+	7477.79i	0.129692	+	0.315568i
$826$	8517.87	−	2738.46i	0.358807	−	0.115355i
$827$	−5969.89	+	5969.89i	−0.251020	+	0.251020i	−0.821389	−	0.570369i	$-0.806800\pi$
$827$	−5969.89	+	5969.89i	−0.251020	+	0.251020i	0.570369	+	0.821389i	$0.306800\pi$
$828$	1768.43	+	1768.43i	0.0742237	+	0.0742237i
$829$	26543.7			1.11206			0.556031	−	0.831161i	$-0.312323\pi$
$829$	26543.7			1.11206			0.556031	+	0.831161i	$0.312323\pi$
$830$	−1783.39	−	2677.03i	−0.0745811	−	0.111953i
$831$		−	2158.95i		−	0.0901242i
$832$	−19179.2	−	19179.2i	−0.799182	−	0.799182i
$833$	2437.56	−	14795.8i	0.101388	−	0.615419i
$834$			3344.93i			0.138879i
$835$	−17699.4	−	3546.07i	−0.733550	−	0.146966i
$836$		−	2698.49i		−	0.111638i
$837$	1386.01	−	1386.01i	0.0572374	−	0.0572374i
$838$	19052.0	−	19052.0i	0.785372	−	0.785372i
$839$	30048.2			1.23645			0.618223	−	0.786003i	$-0.287853\pi$
$839$	30048.2			1.23645			0.618223	+	0.786003i	$0.287853\pi$
$840$	12524.2	−	1425.45i	0.514438	−	0.0585509i
$841$	−56752.9			−2.32699
$842$	14291.4	−	14291.4i	0.584934	−	0.584934i
$843$	−6174.08	+	6174.08i	−0.252250	+	0.252250i
$844$			1244.52i			0.0507560i
$845$	15356.9	+	23052.1i	0.625198	+	0.938480i
$846$			10176.2i			0.413553i
$847$	−14271.2	−	7327.34i	−0.578941	−	0.297249i
$848$	1763.79	+	1763.79i	0.0714256	+	0.0714256i
$849$		−	15587.3i		−	0.630098i
$850$	6444.63	−	15437.9i	0.260058	−	0.622960i
$851$	−46116.1			−1.85763
$852$	−2009.68	−	2009.68i	−0.0808105	−	0.0808105i
$853$	−28867.9	+	28867.9i	−1.15876	+	1.15876i	−0.174012	+	0.984744i	$0.555673\pi$
$853$	−28867.9	+	28867.9i	−1.15876	+	1.15876i	−0.984744	+	0.174012i	$0.944327\pi$
$854$	−9676.22	−	30097.5i	−0.387721	−	1.20599i
$855$	−5091.63	−	7643.00i	−0.203661	−	0.305714i
$856$	23299.6			0.930332
$857$	2894.79	+	2894.79i	0.115384	+	0.115384i	0.762441	−	0.647057i	$-0.224001\pi$
$857$	2894.79	+	2894.79i	0.115384	+	0.115384i	−0.647057	+	0.762441i	$0.724001\pi$
$858$	9572.09	+	9572.09i	0.380869	+	0.380869i
$859$	−44730.7			−1.77671			−0.888354	−	0.459159i	$-0.848151\pi$
$859$	−44730.7			−1.77671			−0.888354	+	0.459159i	$0.848151\pi$
$860$	312.080	−	1557.68i	0.0123742	−	0.0617633i
$861$	6874.12	+	21381.7i	0.272090	+	0.846326i
$862$	−13501.9	+	13501.9i	−0.533500	+	0.533500i
$863$	32327.5	+	32327.5i	1.27514	+	1.27514i	0.943357	+	0.331779i	$0.107649\pi$
$863$	32327.5	+	32327.5i	1.27514	+	1.27514i	0.331779	+	0.943357i	$0.392351\pi$
$864$	1658.21			0.0652932
$865$	2942.83	−	14688.5i	0.115675	−	0.577369i
$866$			18599.6i			0.729840i
$867$	−6367.66	−	6367.66i	−0.249431	−	0.249431i
$868$	1640.32	+	842.200i	0.0641429	+	0.0329333i
$869$			21520.2i			0.840072i
$870$	24341.5	−	16215.9i	0.948570	−	0.631920i
$871$		−	19979.4i		−	0.777242i
$872$	20706.8	−	20706.8i	0.804151	−	0.804151i
$873$	−8017.07	+	8017.07i	−0.310809	+	0.310809i
$874$	−56612.6			−2.19102
$875$	−7205.96	+	24859.5i	−0.278407	+	0.960463i
$876$	−927.389			−0.0357689
$877$	−8076.52	+	8076.52i	−0.310975	+	0.310975i	−0.845287	−	0.534312i	$-0.820571\pi$
$877$	−8076.52	+	8076.52i	−0.310975	+	0.310975i	0.534312	+	0.845287i	$0.320571\pi$
$878$	7225.83	−	7225.83i	0.277745	−	0.277745i
$879$			3332.65i			0.127881i
$880$	14662.0	−	9767.59i	0.561656	−	0.374165i
$881$			10929.4i			0.417959i	0.977920	+	0.208980i	$0.0670142\pi$
$881$			10929.4i			0.417959i	−0.977920	+	0.208980i	$0.932986\pi$
$882$	−1536.18	+	9324.47i	−0.0586460	+	0.355976i
$883$	17004.0	+	17004.0i	0.648053	+	0.648053i	0.952522	−	0.304469i	$-0.0984790\pi$
$883$	17004.0	+	17004.0i	0.648053	+	0.648053i	−0.304469	+	0.952522i	$0.598479\pi$
$884$		−	4099.17i		−	0.155961i
$885$	1039.82	−	5190.04i	0.0394951	−	0.197131i
$886$	15170.6			0.575245
$887$	−5813.25	−	5813.25i	−0.220056	−	0.220056i	0.588466	−	0.808522i	$-0.299732\pi$
$887$	−5813.25	−	5813.25i	−0.220056	−	0.220056i	−0.808522	+	0.588466i	$0.799732\pi$
$888$	−9796.98	+	9796.98i	−0.370231	+	0.370231i
$889$	−14782.9	+	4752.63i	−0.557707	+	0.179300i
$890$	2200.01	−	10980.9i	0.0828589	−	0.413572i
$891$	1746.29			0.0656599
$892$	−5221.70	−	5221.70i	−0.196004	−	0.196004i
$893$	−23836.7	−	23836.7i	−0.893243	−	0.893243i
$894$	1930.97			0.0722384
$895$	−6885.79	−	10336.2i	−0.257170	−	0.386035i
$896$	−9669.10	−	30075.4i	−0.360516	−	1.12137i
$897$	29387.5	−	29387.5i	1.09389	−	1.09389i
$898$	7391.92	+	7391.92i	0.274690	+	0.274690i
$899$	−20679.6			−0.767188
$900$	−594.359	+	1423.77i	−0.0220133	+	0.0527321i
$901$		−	1491.97i		−	0.0551663i
$902$	18864.8	+	18864.8i	0.696373	+	0.696373i
$903$	−5121.06	−	2629.34i	−0.188724	−	0.0968980i
$904$		−	7093.74i		−	0.260989i
$905$	−6203.98	−	9312.74i	−0.227875	−	0.342062i
$906$		−	383.467i		−	0.0140616i
$907$	7996.28	−	7996.28i	0.292737	−	0.292737i	−0.545424	−	0.838160i	$-0.683631\pi$
$907$	7996.28	−	7996.28i	0.292737	−	0.292737i	0.838160	+	0.545424i	$0.183631\pi$
$908$	−5307.79	+	5307.79i	−0.193992	+	0.193992i
$909$	−2027.65			−0.0739857
$910$	4900.91	+	43060.2i	0.178532	+	1.56861i
$911$	23650.7			0.860136			0.430068	−	0.902796i	$-0.358490\pi$
$911$	23650.7			0.860136			0.430068	+	0.902796i	$0.358490\pi$
$912$	−14151.0	+	14151.0i	−0.513801	+	0.513801i
$913$	−1432.73	+	1432.73i	−0.0519349	+	0.0519349i
$914$		−	43569.7i		−	1.57676i
$915$	−18338.8	−	3674.15i	−0.662580	−	0.132747i
$916$			7372.72i			0.265941i
$917$	11406.1	−	22215.1i	0.410754	−	0.800009i
$918$	−2555.12	−	2555.12i	−0.0918643	−	0.0918643i
$919$			50947.2i			1.82872i	0.404904	+	0.914359i	$0.367305\pi$
$919$			50947.2i			1.82872i	−0.404904	+	0.914359i	$0.632695\pi$
$920$	−25486.4	−	38257.4i	−0.913327	−	1.37099i
$921$	20206.4			0.722935
$922$	−18166.2	−	18166.2i	−0.648884	−	0.648884i
$923$	−33396.6	+	33396.6i	−1.19097	+	1.19097i
$924$	502.790	+	1563.91i	0.0179011	+	0.0556805i
$925$	−10814.4	−	26313.8i	−0.384407	−	0.935342i
$926$	−18765.6			−0.665955
$927$	3882.77	+	3882.77i	0.137570	+	0.137570i
$928$	−12370.4	−	12370.4i	−0.437583	−	0.437583i
$929$	−32525.3			−1.14867			−0.574337	−	0.818619i	$-0.694740\pi$
$929$	−32525.3			−1.14867			−0.574337	+	0.818619i	$0.694740\pi$
$930$	6203.61	−	4132.73i	0.218736	−	0.145718i
$931$	−18243.2	−	25439.9i	−0.642211	−	0.895552i
$932$	4308.26	−	4308.26i	0.151418	−	0.151418i
$933$	−7446.41	−	7446.41i	−0.261291	−	0.261291i
$934$	−12425.2			−0.435294
$935$	−10332.4	−	2070.08i	−0.361395	−	0.0724053i
$936$		−	12486.2i		−	0.436032i
$937$	−3624.36	−	3624.36i	−0.126364	−	0.126364i	0.641097	−	0.767460i	$-0.278480\pi$
$937$	−3624.36	−	3624.36i	−0.126364	−	0.126364i	−0.767460	+	0.641097i	$0.778480\pi$
$938$	7567.39	−	14738.7i	0.263416	−	0.513044i
$939$			70.0314i			0.00243385i
$940$	−1112.52	+	5552.92i	−0.0386026	+	0.192677i
$941$		−	24247.4i		−	0.840003i	−0.907524	−	0.420001i	$-0.862030\pi$
$941$		−	24247.4i		−	0.840003i	0.907524	−	0.420001i	$-0.137970\pi$
$942$	10308.5	−	10308.5i	0.356550	−	0.356550i
$943$	57917.2	−	57917.2i	2.00005	−	2.00005i
$944$	−11534.6			−0.397689
$945$	4374.91	+	3480.81i	0.150599	+	0.119821i
$946$	−6838.06			−0.235015
$947$	−4001.35	+	4001.35i	−0.137303	+	0.137303i	−0.772418	−	0.635115i	$-0.780953\pi$
$947$	−4001.35	+	4001.35i	−0.137303	+	0.137303i	0.635115	+	0.772418i	$0.280953\pi$
$948$	−2903.96	+	2903.96i	−0.0994898	+	0.0994898i
$949$			15411.2i			0.527154i
$950$	−13275.9	−	32303.0i	−0.453396	−	1.10321i
$951$		−	5084.64i		−	0.173376i
$952$	−7504.28	+	14615.8i	−0.255478	+	0.497584i
$953$	−31705.0	−	31705.0i	−1.07768	−	1.07768i	−0.996717	−	0.0809598i	$-0.974201\pi$
$953$	−31705.0	−	31705.0i	−1.07768	−	1.07768i	−0.0809598	−	0.996717i	$-0.525799\pi$
$954$			940.257i			0.0319098i
$955$	−16204.4	+	10795.0i	−0.549069	+	0.365780i
$956$	7608.28			0.257395
$957$	−13027.5	−	13027.5i	−0.440040	−	0.440040i
$958$	1727.70	−	1727.70i	0.0582667	−	0.0582667i
$959$	−6943.26	+	2232.23i	−0.233795	+	0.0751641i
$960$	−13047.0	−	2613.95i	−0.438635	−	0.0878801i
$961$	24520.7			0.823090
$962$	−33683.4	−	33683.4i	−1.12890	−	1.12890i
$963$	7307.23	+	7307.23i	0.244520	+	0.244520i
$964$	1513.01			0.0505507
$965$	22856.7	+	4579.33i	0.762471	+	0.152760i
$966$	32809.7	−	10548.2i	1.09279	−	0.351327i
$967$	38123.6	−	38123.6i	1.26781	−	1.26781i	0.320593	−	0.947217i	$-0.396118\pi$
$967$	38123.6	−	38123.6i	1.26781	−	1.26781i	0.947217	−	0.320593i	$-0.103882\pi$
$968$	12428.8	+	12428.8i	0.412682	+	0.412682i
$969$	11970.2			0.396839
$970$	−35883.3	+	23904.8i	−1.18778	+	0.791276i
$971$			18384.5i			0.607609i	0.952734	+	0.303804i	$0.0982569\pi$
$971$			18384.5i			0.607609i	−0.952734	+	0.303804i	$0.901743\pi$
$972$	235.647	+	235.647i	0.00777610	+	0.00777610i
$973$	6000.71	+	3080.98i	0.197712	+	0.101513i
$974$			33994.1i			1.11832i
$975$	23659.9	+	9876.96i	0.777153	+	0.324427i
$976$			40756.9i			1.33668i
$977$	−34196.2	+	34196.2i	−1.11979	+	1.11979i	−0.128017	+	0.991772i	$0.540861\pi$
$977$	−34196.2	+	34196.2i	−1.11979	+	1.11979i	−0.991772	+	0.128017i	$0.959139\pi$
$978$	−23251.0	+	23251.0i	−0.760210	+	0.760210i
$979$	−7054.34			−0.230294
$980$	−1857.66	+	4920.19i	−0.0605517	+	0.160377i
$981$	12988.1			0.422710
$982$	−22691.4	+	22691.4i	−0.737386	+	0.737386i
$983$	−21228.3	+	21228.3i	−0.688787	+	0.688787i	−0.961964	−	0.273177i	$-0.911926\pi$
$983$	−21228.3	+	21228.3i	−0.688787	+	0.688787i	0.273177	+	0.961964i	$0.411926\pi$
$984$		−	24608.0i		−	0.797231i
$985$	−8854.04	+	44193.1i	−0.286409	+	1.42955i
$986$			38122.8i			1.23132i
$987$	18255.9	+	9373.23i	0.588744	+	0.302283i
$988$	−6051.20	−	6051.20i	−0.194852	−	0.194852i
$989$			20993.7i			0.674986i
$990$	6511.57	+	1304.59i	0.209042	+	0.0418813i
$991$	19082.1			0.611668			0.305834	−	0.952085i	$-0.401065\pi$
$991$	19082.1			0.611668			0.305834	+	0.952085i	$0.401065\pi$
$992$	−3152.67	−	3152.67i	−0.100905	−	0.100905i
$993$	17176.9	−	17176.9i	0.548935	−	0.548935i
$994$	−37285.7	+	11987.2i	−1.18977	+	0.382506i
$995$	15438.0	−	10284.5i	0.491878	−	0.327680i
$996$	−386.670			−0.0123013
$997$	1906.28	+	1906.28i	0.0605540	+	0.0605540i	0.736735	−	0.676181i	$-0.236366\pi$
$997$	1906.28	+	1906.28i	0.0605540	+	0.0605540i	−0.676181	+	0.736735i	$0.736366\pi$
$998$	−24986.9	−	24986.9i	−0.792531	−	0.792531i
$999$	−6145.06			−0.194616

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.m.a.13.8	yes	48
5.2	odd	4	inner	105.4.m.a.97.7	yes	48
7.6	odd	2	inner	105.4.m.a.13.7	✓	48
35.27	even	4	inner	105.4.m.a.97.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.m.a.13.7	✓	48	7.6	odd	2	inner
105.4.m.a.13.8	yes	48	1.1	even	1	trivial
105.4.m.a.97.7	yes	48	5.2	odd	4	inner
105.4.m.a.97.8	yes	48	35.27	even	4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.16465 + 2.16465i) q^{2} +(2.12132 - 2.12132i) q^{3} -1.37142i q^{4} +(-9.30469 + 6.19861i) q^{5} +9.18383i q^{6} +(16.4755 + 8.45914i) q^{7} +(-14.3486 - 14.3486i) q^{8} -9.00000i q^{9} +O(q^{10})\)	\(q+(-2.16465 + 2.16465i) q^{2} +(2.12132 - 2.12132i) q^{3} -1.37142i q^{4} +(-9.30469 + 6.19861i) q^{5} +9.18383i q^{6} +(16.4755 + 8.45914i) q^{7} +(-14.3486 - 14.3486i) q^{8} -9.00000i q^{9} +(6.72356 - 33.5592i) q^{10} -21.5591 q^{11} +(-2.90922 - 2.90922i) q^{12} +(-48.3450 + 48.3450i) q^{13} +(-53.9748 + 17.3527i) q^{14} +(-6.58898 + 32.8875i) q^{15} +73.0906 q^{16} +(-30.9132 - 30.9132i) q^{17} +(19.4818 + 19.4818i) q^{18} -91.2683 q^{19} +(8.50090 + 12.7606i) q^{20} +(52.8944 - 17.0053i) q^{21} +(46.6680 - 46.6680i) q^{22} +(-143.277 - 143.277i) q^{23} -60.8758 q^{24} +(48.1544 - 115.352i) q^{25} -209.300i q^{26} +(-19.0919 - 19.0919i) q^{27} +(11.6010 - 22.5948i) q^{28} +284.854i q^{29} +(-56.9270 - 85.4527i) q^{30} +72.5971i q^{31} +(-43.4270 + 43.4270i) q^{32} +(-45.7338 + 45.7338i) q^{33} +133.833 q^{34} +(-205.735 + 23.4158i) q^{35} -12.3428 q^{36} +(160.934 - 160.934i) q^{37} +(197.564 - 197.564i) q^{38} +205.110i q^{39} +(222.450 + 44.5677i) q^{40} +404.234i q^{41} +(-77.6873 + 151.308i) q^{42} +(-73.2629 - 73.2629i) q^{43} +29.5666i q^{44} +(55.7875 + 83.7422i) q^{45} +620.287 q^{46} +(261.172 + 261.172i) q^{47} +(155.048 - 155.048i) q^{48} +(199.886 + 278.738i) q^{49} +(145.460 + 353.935i) q^{50} -131.154 q^{51} +(66.3012 + 66.3012i) q^{52} +(24.1316 + 24.1316i) q^{53} +82.6545 q^{54} +(200.601 - 133.637i) q^{55} +(-115.024 - 357.776i) q^{56} +(-193.609 + 193.609i) q^{57} +(-616.609 - 616.609i) q^{58} -157.812 q^{59} +(45.1025 + 9.03625i) q^{60} +557.621i q^{61} +(-157.147 - 157.147i) q^{62} +(76.1323 - 148.280i) q^{63} +396.716i q^{64} +(150.163 - 749.506i) q^{65} -197.996i q^{66} +(-206.634 + 206.634i) q^{67} +(-42.3950 + 42.3950i) q^{68} -607.871 q^{69} +(394.656 - 496.030i) q^{70} +690.798 q^{71} +(-129.137 + 129.137i) q^{72} +(159.388 - 159.388i) q^{73} +696.731i q^{74} +(-142.548 - 346.850i) q^{75} +125.167i q^{76} +(-355.198 - 182.372i) q^{77} +(-443.992 - 443.992i) q^{78} -998.194i q^{79} +(-680.085 + 453.060i) q^{80} -81.0000 q^{81} +(-875.025 - 875.025i) q^{82} +(66.4559 - 66.4559i) q^{83} +(-23.3214 - 72.5404i) q^{84} +(479.257 + 96.0188i) q^{85} +317.177 q^{86} +(604.267 + 604.267i) q^{87} +(309.343 + 309.343i) q^{88} +327.209 q^{89} +(-302.033 - 60.5121i) q^{90} +(-1205.47 + 387.552i) q^{91} +(-196.492 + 196.492i) q^{92} +(154.002 + 154.002i) q^{93} -1130.69 q^{94} +(849.223 - 565.737i) q^{95} +184.245i q^{96} +(-890.785 - 890.785i) q^{97} +(-1036.05 - 170.686i) q^{98} +194.032i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 168 q^{8}+O(q^{10}) \) 48 * q + 4 * q^7 - 168 * q^8	\( 48 q + 4 q^{7} - 168 q^{8} + 112 q^{11} + 168 q^{15} - 544 q^{16} - 96 q^{21} - 192 q^{22} + 400 q^{23} + 520 q^{25} + 1052 q^{28} - 48 q^{30} - 1344 q^{32} + 392 q^{35} - 1728 q^{36} - 456 q^{37} + 1068 q^{42} + 192 q^{43} - 208 q^{46} + 3528 q^{50} + 672 q^{51} - 1728 q^{53} - 48 q^{56} + 696 q^{57} + 3016 q^{58} + 840 q^{60} - 36 q^{63} - 4720 q^{65} - 4784 q^{67} + 2220 q^{70} - 3088 q^{71} - 1512 q^{72} + 2352 q^{77} + 1416 q^{78} - 3888 q^{81} - 472 q^{85} + 10832 q^{86} + 2128 q^{88} - 5664 q^{91} + 10600 q^{92} - 1368 q^{93} - 6912 q^{95} - 3888 q^{98}+O(q^{100}) \) 48 * q + 4 * q^7 - 168 * q^8 + 112 * q^11 + 168 * q^15 - 544 * q^16 - 96 * q^21 - 192 * q^22 + 400 * q^23 + 520 * q^25 + 1052 * q^28 - 48 * q^30 - 1344 * q^32 + 392 * q^35 - 1728 * q^36 - 456 * q^37 + 1068 * q^42 + 192 * q^43 - 208 * q^46 + 3528 * q^50 + 672 * q^51 - 1728 * q^53 - 48 * q^56 + 696 * q^57 + 3016 * q^58 + 840 * q^60 - 36 * q^63 - 4720 * q^65 - 4784 * q^67 + 2220 * q^70 - 3088 * q^71 - 1512 * q^72 + 2352 * q^77 + 1416 * q^78 - 3888 * q^81 - 472 * q^85 + 10832 * q^86 + 2128 * q^88 - 5664 * q^91 + 10600 * q^92 - 1368 * q^93 - 6912 * q^95 - 3888 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more