LMFDB - Embedded newform 17.4.b.a.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,4,Mod(16,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("17.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	17.b (of order $2$, degree $1$, 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:	$1.00303247010$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.4669632.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 74x^{2} + 1072 $ x^4 + 74*x^2 + 1072
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			16.2
Root			$7.36435i$ of defining polynomial
Character	$\chi$	$=$	17.16
Dual form			17.4.b.a.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.37228 q^{2} +7.36435i q^{3} +3.37228 q^{4} +10.1060i q^{5} -24.8347i q^{6} -17.4703i q^{7} +15.6060 q^{8} -27.2337 q^{9} +O(q^{10})$	\(q-3.37228 q^{2} +7.36435i q^{3} +3.37228 q^{4} +10.1060i q^{5} -24.8347i q^{6} -17.4703i q^{7} +15.6060 q^{8} -27.2337 q^{9} -34.0802i q^{10} +51.5505i q^{11} +24.8347i q^{12} +75.2119 q^{13} +58.9148i q^{14} -74.4239 q^{15} -79.6060 q^{16} +(-12.2119 - 69.0208i) q^{17} +91.8397 q^{18} -28.0000 q^{19} +34.0802i q^{20} +128.658 q^{21} -173.843i q^{22} +19.1913i q^{23} +114.928i q^{24} +22.8695 q^{25} -253.636 q^{26} -1.72096i q^{27} -58.9148i q^{28} -70.7417i q^{29} +250.978 q^{30} -41.4445i q^{31} +143.606 q^{32} -379.636 q^{33} +(41.1821 + 232.757i) q^{34} +176.554 q^{35} -91.8397 q^{36} -135.460i q^{37} +94.4239 q^{38} +553.887i q^{39} +157.713i q^{40} -288.771i q^{41} -433.870 q^{42} +88.2934 q^{43} +173.843i q^{44} -275.223i q^{45} -64.7184i q^{46} +157.576 q^{47} -586.246i q^{48} +37.7881 q^{49} -77.1224 q^{50} +(508.293 - 89.9330i) q^{51} +253.636 q^{52} +120.250 q^{53} +5.80356i q^{54} -520.967 q^{55} -272.641i q^{56} -206.202i q^{57} +238.561i q^{58} -696.119 q^{59} -250.978 q^{60} +683.544i q^{61} +139.763i q^{62} +475.781i q^{63} +152.568 q^{64} +760.089i q^{65} +1280.24 q^{66} +123.826 q^{67} +(-41.1821 - 232.757i) q^{68} -141.331 q^{69} -595.391 q^{70} -225.393i q^{71} -425.008 q^{72} -919.423i q^{73} +456.810i q^{74} +168.419i q^{75} -94.4239 q^{76} +900.603 q^{77} -1867.86i q^{78} +354.830i q^{79} -804.495i q^{80} -722.636 q^{81} +973.815i q^{82} -955.272 q^{83} +433.870 q^{84} +(697.522 - 123.413i) q^{85} -297.750 q^{86} +520.967 q^{87} +804.495i q^{88} +617.636 q^{89} +928.128i q^{90} -1313.98i q^{91} +64.7184i q^{92} +305.212 q^{93} -531.391 q^{94} -282.967i q^{95} +1057.56i q^{96} +428.533i q^{97} -127.432 q^{98} -1403.91i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{4} - 18 q^{8} - 40 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^4 - 18 * q^8 - 40 * q^9	$ 4 q - 2 q^{2} + 2 q^{4} - 18 q^{8} - 40 q^{9} + 140 q^{13} + 24 q^{15} - 238 q^{16} + 112 q^{17} + 218 q^{18} - 112 q^{19} + 124 q^{21} - 460 q^{25} - 532 q^{26} + 912 q^{30} + 494 q^{32} - 1036 q^{33} + 406 q^{34} + 936 q^{35} - 218 q^{36} + 56 q^{38} - 1184 q^{42} - 520 q^{43} + 952 q^{47} + 312 q^{49} - 1354 q^{50} + 1160 q^{51} + 532 q^{52} - 576 q^{53} + 168 q^{55} - 1176 q^{59} - 912 q^{60} + 1426 q^{64} + 1904 q^{66} - 240 q^{67} - 406 q^{68} + 1204 q^{69} + 192 q^{70} - 1206 q^{72} - 56 q^{76} + 868 q^{77} - 2408 q^{81} - 2856 q^{83} + 1184 q^{84} + 768 q^{85} - 2248 q^{86} - 168 q^{87} + 1988 q^{89} + 1060 q^{93} + 448 q^{94} + 306 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^4 - 18 * q^8 - 40 * q^9 + 140 * q^13 + 24 * q^15 - 238 * q^16 + 112 * q^17 + 218 * q^18 - 112 * q^19 + 124 * q^21 - 460 * q^25 - 532 * q^26 + 912 * q^30 + 494 * q^32 - 1036 * q^33 + 406 * q^34 + 936 * q^35 - 218 * q^36 + 56 * q^38 - 1184 * q^42 - 520 * q^43 + 952 * q^47 + 312 * q^49 - 1354 * q^50 + 1160 * q^51 + 532 * q^52 - 576 * q^53 + 168 * q^55 - 1176 * q^59 - 912 * q^60 + 1426 * q^64 + 1904 * q^66 - 240 * q^67 - 406 * q^68 + 1204 * q^69 + 192 * q^70 - 1206 * q^72 - 56 * q^76 + 868 * q^77 - 2408 * q^81 - 2856 * q^83 + 1184 * q^84 + 768 * q^85 - 2248 * q^86 - 168 * q^87 + 1988 * q^89 + 1060 * q^93 + 448 * q^94 + 306 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	−3.37228			−1.19228			−0.596141	−	0.802880i	$-0.703300\pi$
$2$	−3.37228			−1.19228			−0.596141	+	0.802880i	$0.703300\pi$
$3$			7.36435i			1.41727i	0.705575	+	0.708635i	$0.250689\pi$
$3$			7.36435i			1.41727i	−0.705575	+	0.708635i	$0.749311\pi$
$4$	3.37228			0.421535
$5$			10.1060i			0.903905i	0.892042	+	0.451952i	$0.149272\pi$
$5$			10.1060i			0.903905i	−0.892042	+	0.451952i	$0.850728\pi$
$6$		−	24.8347i		−	1.68979i
$7$		−	17.4703i		−	0.943308i	−0.881784	−	0.471654i	$-0.843657\pi$
$7$		−	17.4703i		−	0.943308i	0.881784	−	0.471654i	$-0.156343\pi$
$8$	15.6060			0.689693
$9$	−27.2337			−1.00866
$10$		−	34.0802i		−	1.07771i
$11$			51.5505i			1.41300i	0.707711	+	0.706502i	$0.249728\pi$
$11$			51.5505i			1.41300i	−0.707711	+	0.706502i	$0.750272\pi$
$12$			24.8347i			0.597429i
$13$	75.2119			1.60462			0.802309	−	0.596909i	$-0.203605\pi$
$13$	75.2119			1.60462			0.802309	+	0.596909i	$0.203605\pi$
$14$			58.9148i			1.12469i
$15$	−74.4239			−1.28108
$16$	−79.6060			−1.24384
$17$	−12.2119	−	69.0208i	−0.174225	−	0.984706i
$17$	−12.2119	−	69.0208i	−0.174225	−	0.984706i
$18$	91.8397			1.20260
$19$	−28.0000			−0.338086			−0.169043	−	0.985609i	$-0.554068\pi$
$19$	−28.0000			−0.338086			−0.169043	+	0.985609i	$0.554068\pi$
$20$			34.0802i			0.381028i
$21$	128.658			1.33692
$22$		−	173.843i		−	1.68470i
$23$			19.1913i			0.173985i	0.996209	+	0.0869926i	$0.0277256\pi$
$23$			19.1913i			0.173985i	−0.996209	+	0.0869926i	$0.972274\pi$
$24$			114.928i			0.977481i
$25$	22.8695			0.182956
$26$	−253.636			−1.91316
$27$		−	1.72096i		−	0.0122666i
$28$		−	58.9148i		−	0.397638i
$29$		−	70.7417i		−	0.452980i	−0.974014	−	0.226490i	$-0.927275\pi$
$29$		−	70.7417i		−	0.452980i	0.974014	−	0.226490i	$-0.0727250\pi$
$30$	250.978			1.52740
$31$		−	41.4445i		−	0.240118i	−0.992767	−	0.120059i	$-0.961692\pi$
$31$		−	41.4445i		−	0.240118i	0.992767	−	0.120059i	$-0.0383083\pi$
$32$	143.606			0.793318
$33$	−379.636			−2.00261
$34$	41.1821	+	232.757i	0.207726	+	1.17405i
$35$	176.554			0.852661
$36$	−91.8397			−0.425184
$37$		−	135.460i		−	0.601879i	−0.953643	−	0.300939i	$-0.902700\pi$
$37$		−	135.460i		−	0.601879i	0.953643	−	0.300939i	$-0.0973002\pi$
$38$	94.4239			0.403094
$39$			553.887i			2.27418i
$40$			157.713i			0.623417i
$41$		−	288.771i		−	1.09996i	−0.835178	−	0.549980i	$-0.814635\pi$
$41$		−	288.771i		−	1.09996i	0.835178	−	0.549980i	$-0.185365\pi$
$42$	−433.870			−1.59399
$43$	88.2934			0.313131			0.156565	−	0.987668i	$-0.449958\pi$
$43$	88.2934			0.313131			0.156565	+	0.987668i	$0.449958\pi$
$44$			173.843i			0.595631i
$45$		−	275.223i		−	0.911728i
$46$		−	64.7184i		−	0.207439i
$47$	157.576			0.489039			0.244520	−	0.969644i	$-0.421370\pi$
$47$	157.576			0.489039			0.244520	+	0.969644i	$0.421370\pi$
$48$		−	586.246i		−	1.76286i
$49$	37.7881			0.110169
$50$	−77.1224			−0.218135
$51$	508.293	−	89.9330i	1.39559	−	0.246924i
$52$	253.636			0.676403
$53$	120.250			0.311653			0.155826	−	0.987784i	$-0.450196\pi$
$53$	120.250			0.311653			0.155826	+	0.987784i	$0.450196\pi$
$54$			5.80356i			0.0146253i
$55$	−520.967			−1.27722
$56$		−	272.641i		−	0.650593i
$57$		−	206.202i		−	0.479160i
$58$			238.561i			0.540079i
$59$	−696.119			−1.53605			−0.768026	−	0.640419i	$-0.778761\pi$
$59$	−696.119			−1.53605			−0.768026	+	0.640419i	$0.778761\pi$
$60$	−250.978			−0.540019
$61$			683.544i			1.43473i	0.696695	+	0.717367i	$0.254653\pi$
$61$			683.544i			1.43473i	−0.696695	+	0.717367i	$0.745347\pi$
$62$			139.763i			0.286288i
$63$			475.781i			0.951473i
$64$	152.568			0.297984
$65$			760.089i			1.45042i
$66$	1280.24			2.38767
$67$	123.826			0.225787			0.112894	−	0.993607i	$-0.463988\pi$
$67$	123.826			0.225787			0.112894	+	0.993607i	$0.463988\pi$
$68$	−41.1821	−	232.757i	−0.0734421	−	0.415088i
$69$	−141.331			−0.246584
$70$	−595.391			−1.01661
$71$		−	225.393i		−	0.376750i	−0.982097	−	0.188375i	$-0.939678\pi$
$71$		−	225.393i		−	0.376750i	0.982097	−	0.188375i	$-0.0603220\pi$
$72$	−425.008			−0.695662
$73$		−	919.423i		−	1.47411i	−0.675831	−	0.737057i	$-0.736215\pi$
$73$		−	919.423i		−	1.47411i	0.675831	−	0.737057i	$-0.263785\pi$
$74$			456.810i			0.717609i
$75$			168.419i			0.259298i
$76$	−94.4239			−0.142515
$77$	900.603			1.33290
$78$		−	1867.86i		−	2.71146i
$79$			354.830i			0.505335i	0.967553	+	0.252668i	$0.0813079\pi$
$79$			354.830i			0.505335i	−0.967553	+	0.252668i	$0.918692\pi$
$80$		−	804.495i		−	1.12432i
$81$	−722.636			−0.991270
$82$			973.815i			1.31146i
$83$	−955.272			−1.26331			−0.631655	−	0.775250i	$-0.717624\pi$
$83$	−955.272			−1.26331			−0.631655	+	0.775250i	$0.717624\pi$
$84$	433.870			0.563560
$85$	697.522	−	123.413i	0.890080	−	0.157483i
$86$	−297.750			−0.373340
$87$	520.967			0.641995
$88$			804.495i			0.974539i
$89$	617.636			0.735610			0.367805	−	0.929903i	$-0.380109\pi$
$89$	617.636			0.735610			0.367805	+	0.929903i	$0.380109\pi$
$90$			928.128i			1.08704i
$91$		−	1313.98i		−	1.51365i
$92$			64.7184i			0.0733408i
$93$	305.212			0.340312
$94$	−531.391			−0.583072
$95$		−	282.967i		−	0.305598i
$96$			1057.56i			1.12435i
$97$			428.533i			0.448566i	0.974524	+	0.224283i	$0.0720041\pi$
$97$			428.533i			0.448566i	−0.974524	+	0.224283i	$0.927996\pi$
$98$	−127.432			−0.131353
$99$		−	1403.91i		−	1.42523i
$100$	77.1224			0.0771224
$101$	−686.722			−0.676549			−0.338274	−	0.941048i	$-0.609843\pi$
$101$	−686.722			−0.676549			−0.338274	+	0.941048i	$0.609843\pi$
$102$	−1714.11	+	303.279i	−1.66394	+	0.294403i
$103$	−168.000			−0.160714			−0.0803570	−	0.996766i	$-0.525606\pi$
$103$	−168.000			−0.160714			−0.0803570	+	0.996766i	$0.525606\pi$
$104$	1173.76			1.10669
$105$			1300.21i			1.20845i
$106$	−405.516			−0.371578
$107$		−	39.5037i		−	0.0356913i	−0.999841	−	0.0178457i	$-0.994319\pi$
$107$		−	39.5037i		−	0.0356913i	0.999841	−	0.0178457i	$-0.00568075\pi$
$108$		−	5.80356i		−	0.00517082i
$109$		−	701.394i		−	0.616343i	−0.951331	−	0.308171i	$-0.900283\pi$
$109$		−	701.394i		−	0.616343i	0.951331	−	0.308171i	$-0.0997170\pi$
$110$	1756.85			1.52281
$111$	997.576			0.853025
$112$			1390.74i			1.17333i
$113$		−	465.075i		−	0.387174i	−0.981083	−	0.193587i	$-0.937988\pi$
$113$		−	465.075i		−	0.387174i	0.981083	−	0.193587i	$-0.0620121\pi$
$114$			695.371i			0.571293i
$115$	−193.946			−0.157266
$116$		−	238.561i		−	0.190947i
$117$	−2048.30			−1.61851
$118$	2347.51			1.83141
$119$	−1205.81	+	213.346i	−0.928881	+	0.164348i
$120$	−1161.46			−0.883550
$121$	−1326.45			−0.996582
$122$		−	2305.10i		−	1.71061i
$123$	2126.61			1.55894
$124$		−	139.763i		−	0.101218i
$125$			1494.36i			1.06928i
$126$		−	1604.47i		−	1.13442i
$127$	2131.46			1.48926			0.744630	−	0.667477i	$-0.232626\pi$
$127$	2131.46			1.48926			0.744630	+	0.667477i	$0.232626\pi$
$128$	−1663.35			−1.14860
$129$			650.224i			0.443791i
$130$		−	2563.23i		−	1.72931i
$131$		−	242.264i		−	0.161578i	−0.996731	−	0.0807888i	$-0.974256\pi$
$131$		−	242.264i		−	0.161578i	0.996731	−	0.0807888i	$-0.0257439\pi$
$132$	−1280.24			−0.844170
$133$			489.169i			0.318920i
$134$	−417.576			−0.269202
$135$	17.3920			0.0110879
$136$	−190.579	−	1077.14i	−0.120162	−	0.679145i
$137$	947.505			0.590882			0.295441	−	0.955361i	$-0.404533\pi$
$137$	947.505			0.590882			0.295441	+	0.955361i	$0.404533\pi$
$138$	476.609			0.293997
$139$		−	2624.99i		−	1.60179i	−0.598805	−	0.800895i	$-0.704357\pi$
$139$		−	2624.99i		−	1.60179i	0.598805	−	0.800895i	$-0.295643\pi$
$140$	595.391			0.359427
$141$			1160.45i			0.693101i
$142$			760.089i			0.449192i
$143$			3877.21i			2.26733i
$144$	2167.96			1.25461
$145$	714.913			0.409451
$146$			3100.55i			1.75756i
$147$			278.285i			0.156140i
$148$		−	456.810i		−	0.253713i
$149$	−902.435			−0.496177			−0.248088	−	0.968737i	$-0.579802\pi$
$149$	−902.435			−0.496177			−0.248088	+	0.968737i	$0.579802\pi$
$150$		−	567.957i		−	0.309156i
$151$	−2790.61			−1.50395			−0.751975	−	0.659192i	$-0.770899\pi$
$151$	−2790.61			−1.50395			−0.751975	+	0.659192i	$0.770899\pi$
$152$	−436.967			−0.233176
$153$	332.576	+	1879.69i	0.175733	+	0.993229i
$154$	−3037.09			−1.58919
$155$	418.837			0.217044
$156$			1867.86i			0.958646i
$157$	−2241.75			−1.13956			−0.569780	−	0.821797i	$-0.692972\pi$
$157$	−2241.75			−1.13956			−0.569780	+	0.821797i	$0.692972\pi$
$158$		−	1196.59i		−	0.602502i
$159$			885.563i			0.441696i
$160$			1451.28i			0.717084i
$161$	335.278			0.164122
$162$	2436.93			1.18187
$163$		−	3437.35i		−	1.65174i	−0.563859	−	0.825871i	$-0.690684\pi$
$163$		−	3437.35i		−	1.65174i	0.563859	−	0.825871i	$-0.309316\pi$
$164$		−	973.815i		−	0.463672i
$165$		−	3836.59i		−	1.81017i
$166$	3221.44			1.50622
$167$		−	667.694i		−	0.309387i	−0.987962	−	0.154694i	$-0.950561\pi$
$167$		−	667.694i		−	0.309387i	0.987962	−	0.154694i	$-0.0494391\pi$
$168$	2007.83			0.922066
$169$	3459.84			1.57480
$170$	−2352.24	+	416.185i	−1.06123	+	0.187764i
$171$	762.543			0.341013
$172$	297.750			0.131996
$173$			2692.89i			1.18345i	0.806140	+	0.591725i	$0.201553\pi$
$173$			2692.89i			1.18345i	−0.806140	+	0.591725i	$0.798447\pi$
$174$	−1756.85			−0.765438
$175$		−	399.537i		−	0.172584i
$176$		−	4103.72i		−	1.75756i
$177$		−	5126.47i		−	2.17700i
$178$	−2082.84			−0.877054
$179$	−1077.28			−0.449832			−0.224916	−	0.974378i	$-0.572211\pi$
$179$	−1077.28			−0.449832			−0.224916	+	0.974378i	$0.572211\pi$
$180$		−	928.128i		−	0.384326i
$181$			1812.61i			0.744366i	0.928159	+	0.372183i	$0.121391\pi$
$181$			1812.61i			0.744366i	−0.928159	+	0.372183i	$0.878609\pi$
$182$			4431.10i			1.80470i
$183$	−5033.86			−2.03341
$184$			299.498i			0.119996i
$185$	1368.96			0.544041
$186$	−1029.26			−0.405748
$187$	3558.05	−	629.531i	1.39139	−	0.246181i
$188$	531.391			0.206147
$189$	−30.0657			−0.0115712
$190$			954.244i			0.364359i
$191$	3893.40			1.47496			0.737478	−	0.675371i	$-0.236016\pi$
$191$	3893.40			1.47496			0.737478	+	0.675371i	$0.236016\pi$
$192$			1123.56i			0.422324i
$193$			4030.74i			1.50331i	0.659556	+	0.751656i	$0.270744\pi$
$193$			4030.74i			1.50331i	−0.659556	+	0.751656i	$0.729256\pi$
$194$		−	1445.13i		−	0.534817i
$195$	−5597.56			−2.05564
$196$	127.432			0.0464402
$197$		−	3964.48i		−	1.43380i	−0.697178	−	0.716898i	$-0.745561\pi$
$197$		−	3964.48i		−	1.43380i	0.697178	−	0.716898i	$-0.254439\pi$
$198$			4734.38i			1.69928i
$199$			1881.25i			0.670143i	0.942193	+	0.335071i	$0.108760\pi$
$199$			1881.25i			0.670143i	−0.942193	+	0.335071i	$0.891240\pi$
$200$	356.901			0.126183
$201$			911.898i			0.320002i
$202$	2315.82			0.806637
$203$	−1235.88			−0.427300
$204$	1714.11	−	303.279i	0.588292	−	0.104087i
$205$	2918.30			0.994260
$206$	566.543			0.191616
$207$		−	522.649i		−	0.175491i
$208$	−5987.32			−1.99589
$209$		−	1443.41i		−	0.477718i
$210$		−	4384.67i		−	1.44081i
$211$			3983.68i			1.29975i	0.760041	+	0.649876i	$0.225179\pi$
$211$			3983.68i			1.29975i	−0.760041	+	0.649876i	$0.774821\pi$
$212$	405.516			0.131373
$213$	1659.87			0.533956
$214$			133.218i			0.0425541i
$215$			892.290i			0.283040i
$216$		−	26.8573i		−	0.00846021i
$217$	−724.049			−0.226505
$218$			2365.30i			0.734854i
$219$	6770.95			2.08922
$220$	−1756.85			−0.538394
$221$	−918.484	−	5191.19i	−0.279565	−	1.58008i
$222$	−3364.11			−1.01705
$223$	−4221.07			−1.26755			−0.633776	−	0.773517i	$-0.718496\pi$
$223$	−4221.07			−1.26755			−0.633776	+	0.773517i	$0.718496\pi$
$224$		−	2508.84i		−	0.748344i
$225$	−622.821			−0.184540
$226$			1568.37i			0.461620i
$227$		−	2920.00i		−	0.853778i	−0.904304	−	0.426889i	$-0.859610\pi$
$227$		−	2920.00i		−	0.853778i	0.904304	−	0.426889i	$-0.140390\pi$
$228$		−	695.371i		−	0.201983i
$229$	−2340.55			−0.675405			−0.337703	−	0.941253i	$-0.609650\pi$
$229$	−2340.55			−0.675405			−0.337703	+	0.941253i	$0.609650\pi$
$230$	654.042			0.187505
$231$			6632.36i			1.88908i
$232$		−	1103.99i		−	0.312417i
$233$		−	1160.45i		−	0.326280i	−0.986603	−	0.163140i	$-0.947838\pi$
$233$		−	1160.45i		−	0.326280i	0.986603	−	0.163140i	$-0.0521623\pi$
$234$	6907.44			1.92972
$235$			1592.46i			0.442045i
$236$	−2347.51			−0.647500
$237$	−2613.09			−0.716197
$238$	4066.35	−	719.464i	1.10749	−	0.195949i
$239$	803.816			0.217550			0.108775	−	0.994066i	$-0.465307\pi$
$239$	803.816			0.217550			0.108775	+	0.994066i	$0.465307\pi$
$240$	5924.58			1.59346
$241$			1464.03i			0.391312i	0.980673	+	0.195656i	$0.0626837\pi$
$241$			1464.03i			0.391312i	−0.980673	+	0.195656i	$0.937316\pi$
$242$	4473.16			1.18821
$243$		−	5368.21i		−	1.41716i
$244$			2305.10i			0.604791i
$245$			381.885i			0.0995825i
$246$	−7171.52			−1.85870
$247$	−2105.93			−0.542500
$248$		−	646.782i		−	0.165608i
$249$		−	7034.96i		−	1.79045i
$250$		−	5039.42i		−	1.27488i
$251$	2262.67			0.568999			0.284500	−	0.958676i	$-0.408173\pi$
$251$	2262.67			0.568999			0.284500	+	0.958676i	$0.408173\pi$
$252$			1604.47i			0.401079i
$253$	−989.319			−0.245842
$254$	−7187.87			−1.77562
$255$	908.860	+	5136.79i	0.223196	+	1.26148i
$256$	4388.74			1.07147
$257$	−3588.91			−0.871089			−0.435545	−	0.900167i	$-0.643444\pi$
$257$	−3588.91			−0.871089			−0.435545	+	0.900167i	$0.643444\pi$
$258$		−	2192.74i		−	0.529123i
$259$	−2366.53			−0.567757
$260$			2563.23i			0.611404i
$261$			1926.56i			0.456900i
$262$			816.981i			0.192646i
$263$	2793.93			0.655062			0.327531	−	0.944840i	$-0.393783\pi$
$263$	2793.93			0.655062			0.327531	+	0.944840i	$0.393783\pi$
$264$	−5924.58			−1.38119
$265$			1215.24i			0.281704i
$266$		−	1649.61i		−	0.380242i
$267$			4548.49i			1.04256i
$268$	417.576			0.0951773
$269$		−	1611.57i		−	0.365276i	−0.983180	−	0.182638i	$-0.941536\pi$
$269$		−	1611.57i		−	0.365276i	0.983180	−	0.182638i	$-0.0584636\pi$
$270$	−58.6506			−0.0132199
$271$	6536.70			1.46523			0.732613	−	0.680645i	$-0.238300\pi$
$271$	6536.70			1.46523			0.732613	+	0.680645i	$0.238300\pi$
$272$	972.143	+	5494.47i	0.216709	+	1.22482i
$273$	9676.58			2.14525
$274$	−3195.25			−0.704498
$275$			1178.93i			0.258518i
$276$	−476.609			−0.103944
$277$			6038.55i			1.30982i	0.755705	+	0.654912i	$0.227294\pi$
$277$			6038.55i			1.30982i	−0.755705	+	0.654912i	$0.772706\pi$
$278$			8852.21i			1.90978i
$279$			1128.69i			0.242196i
$280$	2755.30			0.588074
$281$	−5514.52			−1.17071			−0.585354	−	0.810778i	$-0.699044\pi$
$281$	−5514.52			−1.17071			−0.585354	+	0.810778i	$0.699044\pi$
$282$		−	3913.35i		−	0.826371i
$283$			2113.17i			0.443868i	0.975062	+	0.221934i	$0.0712370\pi$
$283$			2113.17i			0.443868i	−0.975062	+	0.221934i	$0.928763\pi$
$284$		−	760.089i		−	0.158813i
$285$	2083.87			0.433115
$286$		−	13075.0i		−	2.70330i
$287$	−5044.91			−1.03760
$288$	−3910.92			−0.800185
$289$	−4614.74	+	1685.76i	−0.939291	+	0.343121i
$290$	−2410.89			−0.488180
$291$	−3155.87			−0.635740
$292$		−	3100.55i		−	0.621391i
$293$	8127.91			1.62061			0.810303	−	0.586011i	$-0.199303\pi$
$293$	8127.91			1.62061			0.810303	+	0.586011i	$0.199303\pi$
$294$		−	938.454i		−	0.186162i
$295$		−	7034.96i		−	1.38844i
$296$		−	2113.99i		−	0.415111i
$297$	88.7163			0.0173328
$298$	3043.26			0.591583
$299$			1443.41i			0.279180i
$300$			567.957i			0.109303i
$301$		−	1542.51i		−	0.295379i
$302$	9410.72			1.79313
$303$		−	5057.27i		−	0.958852i
$304$	2228.97			0.420526
$305$	−6907.87			−1.29686
$306$	−1121.54	−	6338.85i	−0.209523	−	1.18421i
$307$	−3518.19			−0.654050			−0.327025	−	0.945016i	$-0.606046\pi$
$307$	−3518.19			−0.654050			−0.327025	+	0.945016i	$0.606046\pi$
$308$	3037.09			0.561864
$309$		−	1237.21i		−	0.227775i
$310$	−1412.43			−0.258777
$311$			2346.41i			0.427822i	0.976853	+	0.213911i	$0.0686202\pi$
$311$			2346.41i			0.427822i	−0.976853	+	0.213911i	$0.931380\pi$
$312$			8643.95i			1.56848i
$313$		−	7459.81i		−	1.34714i	−0.739126	−	0.673568i	$-0.764761\pi$
$313$		−	7459.81i		−	1.34714i	0.739126	−	0.673568i	$-0.235239\pi$
$314$	7559.81			1.35868
$315$	−4808.23			−0.860041
$316$			1196.59i			0.213017i
$317$		−	588.489i		−	0.104268i	−0.998640	−	0.0521338i	$-0.983398\pi$
$317$		−	588.489i		−	0.104268i	0.998640	−	0.0521338i	$-0.0166022\pi$
$318$		−	2986.37i		−	0.526626i
$319$	3646.77			0.640062
$320$			1541.85i			0.269350i
$321$	290.920			0.0505842
$322$	−1130.65			−0.195679
$323$	341.934	+	1932.58i	0.0589032	+	0.332916i
$324$	−2436.93			−0.417855
$325$	1720.06			0.293575
$326$			11591.7i			1.96934i
$327$	5165.31			0.873524
$328$		−	4506.54i		−	0.758635i
$329$		−	2752.90i		−	0.461315i
$330$			12938.0i			2.15823i
$331$	−1450.49			−0.240865			−0.120432	−	0.992722i	$-0.538428\pi$
$331$	−1450.49			−0.240865			−0.120432	+	0.992722i	$0.538428\pi$
$332$	−3221.44			−0.532529
$333$			3689.08i			0.607088i
$334$			2251.65i			0.368877i
$335$			1251.38i			0.204090i
$336$	−10241.9			−1.66292
$337$			11211.7i			1.81228i	0.422978	+	0.906140i	$0.360985\pi$
$337$			11211.7i			1.81228i	−0.422978	+	0.906140i	$0.639015\pi$
$338$	−11667.5			−1.87760
$339$	3424.98			0.548730
$340$	2352.24	−	416.185i	0.375200	−	0.0663847i
$341$	2136.48			0.339288
$342$	−2571.51			−0.406583
$343$		−	6652.49i		−	1.04723i
$344$	1377.90			0.215964
$345$		−	1428.29i		−	0.222888i
$346$		−	9081.19i		−	1.41100i
$347$		−	7072.22i		−	1.09411i	−0.837096	−	0.547056i	$-0.815749\pi$
$347$		−	7072.22i		−	1.09411i	0.837096	−	0.547056i	$-0.184251\pi$
$348$	1756.85			0.270623
$349$	5303.95			0.813506			0.406753	−	0.913538i	$-0.366661\pi$
$349$	5303.95			0.813506			0.406753	+	0.913538i	$0.366661\pi$
$350$			1347.35i			0.205769i
$351$		−	129.437i		−	0.0196833i
$352$			7402.95i			1.12096i
$353$	−6324.04			−0.953526			−0.476763	−	0.879032i	$-0.658190\pi$
$353$	−6324.04			−0.953526			−0.476763	+	0.879032i	$0.658190\pi$
$354$			17287.9i			2.59560i
$355$	2277.81			0.340546
$356$	2082.84			0.310085
$357$	−1571.16	−	8880.05i	−0.232926	−	1.31648i
$358$	3632.90			0.536326
$359$	6046.36			0.888898			0.444449	−	0.895804i	$-0.353399\pi$
$359$	6046.36			0.888898			0.444449	+	0.895804i	$0.353399\pi$
$360$		−	4295.12i		−	0.628813i
$361$	−6075.00			−0.885698
$362$		−	6112.63i		−	0.887494i
$363$		−	9768.45i		−	1.41243i
$364$		−	4431.10i		−	0.638057i
$365$	9291.65			1.33246
$366$	16975.6			2.42439
$367$		−	5225.15i		−	0.743190i	−0.928395	−	0.371595i	$-0.878811\pi$
$367$		−	5225.15i		−	0.743190i	0.928395	−	0.371595i	$-0.121189\pi$
$368$		−	1527.74i		−	0.216410i
$369$			7864.29i			1.10948i
$370$	−4616.50			−0.648650
$371$		−	2100.80i		−	0.293985i
$372$	1029.26			0.143453
$373$	1475.62			0.204839			0.102420	−	0.994741i	$-0.467342\pi$
$373$	1475.62			0.204839			0.102420	+	0.994741i	$0.467342\pi$
$374$	−11998.8	+	2122.96i	−1.65893	+	0.293517i
$375$	−11005.0			−1.51546
$376$	2459.13			0.337287
$377$		−	5320.62i		−	0.726860i
$378$	101.390			0.0137961
$379$			4206.41i			0.570102i	0.958512	+	0.285051i	$0.0920106\pi$
$379$			4206.41i			0.570102i	−0.958512	+	0.285051i	$0.907989\pi$
$380$		−	954.244i		−	0.128820i
$381$			15696.8i			2.11069i
$382$	−13129.6			−1.75856
$383$	−9207.28			−1.22838			−0.614191	−	0.789157i	$-0.710518\pi$
$383$	−9207.28			−1.22838			−0.614191	+	0.789157i	$0.710518\pi$
$384$		−	12249.5i		−	1.62788i
$385$			9101.46i			1.20481i
$386$		−	13592.8i		−	1.79237i
$387$	−2404.55			−0.315841
$388$			1445.13i			0.189087i
$389$	9926.14			1.29377			0.646884	−	0.762589i	$-0.276072\pi$
$389$	9926.14			1.29377			0.646884	+	0.762589i	$0.276072\pi$
$390$	18876.6			2.45090
$391$	1324.60	−	234.363i	0.171324	−	0.0303126i
$392$	589.719			0.0759830
$393$	1784.12			0.228999
$394$			13369.4i			1.70949i
$395$	−3585.90			−0.456775
$396$		−	4734.38i		−	0.600786i
$397$			7428.89i			0.939157i	0.882891	+	0.469578i	$0.155594\pi$
$397$			7428.89i			0.939157i	−0.882891	+	0.469578i	$0.844406\pi$
$398$		−	6344.11i		−	0.798999i
$399$	−3602.41			−0.451995
$400$	−1820.55			−0.227569
$401$		−	1753.55i		−	0.218374i	−0.994021	−	0.109187i	$-0.965175\pi$
$401$		−	1753.55i		−	0.218374i	0.994021	−	0.109187i	$-0.0348248\pi$
$402$		−	3075.18i		−	0.381532i
$403$		−	3117.12i		−	0.385297i
$404$	−2315.82			−0.285189
$405$		−	7302.93i		−	0.896014i
$406$	4167.74			0.509461
$407$	6983.03			0.850457
$408$	7932.41	−	1403.49i	0.962532	−	0.170302i
$409$	−12643.3			−1.52853			−0.764267	−	0.644900i	$-0.776899\pi$
$409$	−12643.3			−1.52853			−0.764267	+	0.644900i	$0.776899\pi$
$410$	−9841.34			−1.18544
$411$			6977.76i			0.837440i
$412$	−566.543			−0.0677466
$413$			12161.4i			1.44897i
$414$			1762.52i			0.209235i
$415$		−	9653.94i		−	1.14191i
$416$	10800.9			1.27297
$417$	19331.4			2.27017
$418$			4867.60i			0.569574i
$419$			14833.8i			1.72954i	0.502166	+	0.864772i	$0.332537\pi$
$419$			14833.8i			1.72954i	−0.502166	+	0.864772i	$0.667463\pi$
$420$			4384.67i			0.509405i
$421$	−9029.55			−1.04530			−0.522652	−	0.852546i	$-0.675057\pi$
$421$	−9029.55			−1.04530			−0.522652	+	0.852546i	$0.675057\pi$
$422$		−	13434.1i		−	1.54967i
$423$	−4291.38			−0.493272
$424$	1876.62			0.214945
$425$	−279.281	−	1578.47i	−0.0318756	−	0.180158i
$426$	−5597.56			−0.636626
$427$	11941.7			1.35340
$428$		−	133.218i		−	0.0150451i
$429$	−28553.1			−3.21342
$430$		−	3009.05i		−	0.337464i
$431$			10493.5i			1.17274i	0.810043	+	0.586371i	$0.199444\pi$
$431$			10493.5i			1.17274i	−0.810043	+	0.586371i	$0.800556\pi$
$432$			136.999i			0.0152578i
$433$	3681.66			0.408613			0.204306	−	0.978907i	$-0.434506\pi$
$433$	3681.66			0.408613			0.204306	+	0.978907i	$0.434506\pi$
$434$	2441.70			0.270058
$435$			5264.87i			0.580302i
$436$		−	2365.30i		−	0.259810i
$437$		−	537.356i		−	0.0588220i
$438$	−22833.6			−2.49094
$439$		−	6126.72i		−	0.666088i	−0.942911	−	0.333044i	$-0.891924\pi$
$439$		−	6126.72i		−	0.666088i	0.942911	−	0.333044i	$-0.108076\pi$
$440$	−8130.20			−0.880891
$441$	−1029.11			−0.111123
$442$	3097.38	+	17506.1i	0.333320	+	1.88390i
$443$	1815.61			0.194722			0.0973612	−	0.995249i	$-0.468960\pi$
$443$	1815.61			0.194722			0.0973612	+	0.995249i	$0.468960\pi$
$444$	3364.11			0.359580
$445$			6241.80i			0.664921i
$446$	14234.7			1.51128
$447$		−	6645.85i		−	0.703217i
$448$		−	2665.41i		−	0.281091i
$449$			1580.41i			0.166112i	0.996545	+	0.0830560i	$0.0264680\pi$
$449$			1580.41i			0.166112i	−0.996545	+	0.0830560i	$0.973532\pi$
$450$	2100.33			0.220023
$451$	14886.3			1.55425
$452$		−	1568.37i		−	0.163207i
$453$		−	20551.0i		−	2.13150i
$454$			9847.08i			1.01794i
$455$	13279.0			1.36820
$456$		−	3217.98i		−	0.330473i
$457$	3095.29			0.316830			0.158415	−	0.987373i	$-0.449362\pi$
$457$	3095.29			0.316830			0.158415	+	0.987373i	$0.449362\pi$
$458$	7892.99			0.805273
$459$	−118.782	+	21.0163i	−0.0120790	+	0.00213716i
$460$	−654.042			−0.0662931
$461$	−12123.9			−1.22487			−0.612437	−	0.790519i	$-0.709811\pi$
$461$	−12123.9			−1.22487			−0.612437	+	0.790519i	$0.709811\pi$
$462$		−	22366.2i		−	2.25231i
$463$	9125.21			0.915949			0.457975	−	0.888965i	$-0.348575\pi$
$463$	9125.21			0.915949			0.457975	+	0.888965i	$0.348575\pi$
$464$			5631.47i			0.563436i
$465$			3084.46i			0.307610i
$466$			3913.35i			0.389018i
$467$	−6146.76			−0.609075			−0.304538	−	0.952500i	$-0.598502\pi$
$467$	−6146.76			−0.609075			−0.304538	+	0.952500i	$0.598502\pi$
$468$	−6907.44			−0.682257
$469$		−	2163.28i		−	0.212987i
$470$		−	5370.22i		−	0.527042i
$471$		−	16509.0i		−	1.61507i
$472$	−10863.6			−1.05940
$473$			4551.57i			0.442455i
$474$	8812.08			0.853908
$475$	−640.346			−0.0618549
$476$	−4066.35	+	719.464i	−0.391556	+	0.0692785i
$477$	−3274.85			−0.314350
$478$	−2710.69			−0.259381
$479$		−	11690.5i		−	1.11514i	−0.830129	−	0.557572i	$-0.811733\pi$
$479$		−	11690.5i		−	1.11514i	0.830129	−	0.557572i	$-0.188267\pi$
$480$	−10687.7			−1.01630
$481$		−	10188.2i		−	0.965785i
$482$		−	4937.11i		−	0.466554i
$483$			2469.10i			0.232605i
$484$	−4473.16			−0.420094
$485$	−4330.74			−0.405461
$486$			18103.1i			1.68966i
$487$		−	17916.7i		−	1.66711i	−0.552434	−	0.833557i	$-0.686301\pi$
$487$		−	17916.7i		−	1.66711i	0.552434	−	0.833557i	$-0.313699\pi$
$488$			10667.4i			0.989526i
$489$	25313.9			2.34097
$490$		−	1287.82i		−	0.118730i
$491$	−13472.0			−1.23825			−0.619127	−	0.785291i	$-0.712513\pi$
$491$	−13472.0			−1.23825			−0.619127	+	0.785291i	$0.712513\pi$
$492$	7171.52			0.657149
$493$	−4882.65	+	863.894i	−0.446052	+	0.0789205i
$494$	7101.80			0.646812
$495$	14187.9			1.28828
$496$			3299.23i			0.298669i
$497$	−3937.69			−0.355391
$498$			23723.9i			2.13472i
$499$			11286.5i			1.01253i	0.862378	+	0.506265i	$0.168974\pi$
$499$			11286.5i			1.01253i	−0.862378	+	0.506265i	$0.831026\pi$
$500$			5039.42i			0.450739i
$501$	4917.13			0.438486
$502$	−7630.38			−0.678407
$503$			9088.02i			0.805596i	0.915289	+	0.402798i	$0.131962\pi$
$503$			9088.02i			0.805596i	−0.915289	+	0.402798i	$0.868038\pi$
$504$			7425.03i			0.656224i
$505$		−	6939.99i		−	0.611536i
$506$	3336.26			0.293113
$507$			25479.4i			2.23192i
$508$	7187.87			0.627776
$509$	−9575.09			−0.833808			−0.416904	−	0.908951i	$-0.636885\pi$
$509$	−9575.09			−0.833808			−0.416904	+	0.908951i	$0.636885\pi$
$510$	−3064.93	−	17322.7i	−0.266113	−	1.50404i
$511$	−16062.6			−1.39054
$512$	−1493.27			−0.128894
$513$			48.1869i			0.00414718i
$514$	12102.8			1.03858
$515$		−	1697.80i		−	0.145270i
$516$			2192.74i			0.187073i
$517$			8123.12i			0.691015i
$518$	7980.61			0.676926
$519$	−19831.4			−1.67727
$520$			11861.9i			1.00035i
$521$			6270.47i			0.527283i	0.964621	+	0.263641i	$0.0849236\pi$
$521$			6270.47i			0.527283i	−0.964621	+	0.263641i	$0.915076\pi$
$522$		−	6496.90i		−	0.544754i
$523$	−16254.6			−1.35901			−0.679507	−	0.733669i	$-0.737806\pi$
$523$	−16254.6			−1.35901			−0.679507	+	0.733669i	$0.737806\pi$
$524$		−	816.981i		−	0.0681107i
$525$	2942.33			0.244598
$526$	−9421.93			−0.781019
$527$	−2860.53	+	506.118i	−0.236445	+	0.0418346i
$528$	30221.3			2.49093
$529$	11798.7			0.969729
$530$		−	4098.13i		−	0.335871i
$531$	18957.9			1.54935
$532$			1649.61i			0.134436i
$533$		−	21719.0i		−	1.76502i
$534$		−	15338.8i		−	1.24302i
$535$	399.223			0.0322616
$536$	1932.42			0.155724
$537$		−	7933.49i		−	0.637533i
$538$			5434.67i			0.435512i
$539$			1947.99i			0.155670i
$540$	58.6506			0.00467393
$541$		−	17293.9i		−	1.37435i	−0.726492	−	0.687175i	$-0.758850\pi$
$541$		−	17293.9i		−	1.37435i	0.726492	−	0.687175i	$-0.241150\pi$
$542$	−22043.6			−1.74696
$543$	−13348.7			−1.05497
$544$	−1753.71	−	9911.80i	−0.138216	−	0.781185i
$545$	7088.26			0.557115
$546$	−32632.2			−2.55774
$547$			13944.7i			1.09000i	0.838435	+	0.545001i	$0.183471\pi$
$547$			13944.7i			1.09000i	−0.838435	+	0.545001i	$0.816529\pi$
$548$	3195.25			0.249078
$549$		−	18615.4i		−	1.44715i
$550$		−	3975.70i		−	0.308226i
$551$			1980.77i			0.153146i
$552$	−2205.61			−0.170067
$553$	6198.99			0.476687
$554$		−	20363.7i		−	1.56168i
$555$			10081.5i			0.771053i
$556$		−	8852.21i		−	0.675211i
$557$	24065.0			1.83064			0.915320	−	0.402728i	$-0.131938\pi$
$557$	24065.0			1.83064			0.915320	+	0.402728i	$0.131938\pi$
$558$		−	3806.25i		−	0.288766i
$559$	6640.72			0.502455
$560$	−14054.8			−1.06058
$561$	4636.09	+	26202.8i	0.348905	+	1.97198i
$562$	18596.5			1.39581
$563$	9264.88			0.693549			0.346775	−	0.937948i	$-0.387277\pi$
$563$	9264.88			0.693549			0.346775	+	0.937948i	$0.387277\pi$
$564$			3913.35i			0.292166i
$565$	4700.03			0.349968
$566$		−	7126.19i		−	0.529216i
$567$			12624.7i			0.935073i
$568$		−	3517.48i		−	0.259842i
$569$	17133.7			1.26236			0.631181	−	0.775636i	$-0.282571\pi$
$569$	17133.7			1.26236			0.631181	+	0.775636i	$0.282571\pi$
$570$	−7027.39			−0.516395
$571$		−	24854.6i		−	1.82160i	−0.412850	−	0.910799i	$-0.635467\pi$
$571$		−	24854.6i		−	1.82160i	0.412850	−	0.910799i	$-0.364533\pi$
$572$			13075.0i			0.955761i
$573$			28672.4i			2.09041i
$574$	17012.9			1.23711
$575$			438.895i			0.0318316i
$576$	−4154.99			−0.300564
$577$	−23249.5			−1.67745			−0.838724	−	0.544556i	$-0.816698\pi$
$577$	−23249.5			−1.67745			−0.838724	+	0.544556i	$0.816698\pi$
$578$	15562.2	−	5684.84i	1.11990	−	0.409097i
$579$	−29683.8			−2.13060
$580$	2410.89			0.172598
$581$			16688.9i			1.19169i
$582$	10642.5			0.757981
$583$			6198.94i			0.440367i
$584$		−	14348.5i		−	1.01669i
$585$		−	20700.0i		−	1.46298i
$586$	−27409.6			−1.93222
$587$	−17715.0			−1.24562			−0.622808	−	0.782374i	$-0.714008\pi$
$587$	−17715.0			−1.24562			−0.622808	+	0.782374i	$0.714008\pi$
$588$			938.454i			0.0658183i
$589$			1160.45i			0.0811806i
$590$			23723.9i			1.65542i
$591$	29195.9			2.03208
$592$			10783.4i			0.748643i
$593$	−11766.2			−0.814803			−0.407401	−	0.913249i	$-0.633565\pi$
$593$	−11766.2			−0.814803			−0.407401	+	0.913249i	$0.633565\pi$
$594$	−299.176			−0.0206656
$595$	−2156.07	−	12185.9i	−0.148555	−	0.839620i
$596$	−3043.26			−0.209156
$597$	−13854.2			−0.949773
$598$		−	4867.60i		−	0.332861i
$599$	−12629.6			−0.861485			−0.430743	−	0.902475i	$-0.641748\pi$
$599$	−12629.6			−0.861485			−0.430743	+	0.902475i	$0.641748\pi$
$600$			2628.34i			0.178836i
$601$		−	1545.31i		−	0.104883i	−0.998624	−	0.0524415i	$-0.983300\pi$
$601$		−	1545.31i		−	0.104883i	0.998624	−	0.0524415i	$-0.0167003\pi$
$602$			5201.79i			0.352175i
$603$	−3372.24			−0.227742
$604$	−9410.72			−0.633968
$605$		−	13405.1i		−	0.900815i
$606$			17054.5i			1.14322i
$607$			662.896i			0.0443264i	0.999754	+	0.0221632i	$0.00705534\pi$
$607$			662.896i			0.0443264i	−0.999754	+	0.0221632i	$0.992945\pi$
$608$	−4020.97			−0.268210
$609$		−	9101.46i		−	0.605599i
$610$	23295.3			1.54623
$611$	11851.6			0.784721
$612$	1121.54	+	6338.85i	0.0740777	+	0.418681i
$613$	24447.0			1.61077			0.805387	−	0.592749i	$-0.201957\pi$
$613$	24447.0			1.61077			0.805387	+	0.592749i	$0.201957\pi$
$614$	11864.3			0.779812
$615$			21491.4i			1.40913i
$616$	14054.8			0.919291
$617$		−	4580.14i		−	0.298849i	−0.988773	−	0.149424i	$-0.952258\pi$
$617$		−	4580.14i		−	0.298849i	0.988773	−	0.149424i	$-0.0477420\pi$
$618$			4172.22i			0.271572i
$619$			13759.3i			0.893428i	0.894677	+	0.446714i	$0.147406\pi$
$619$			13759.3i			0.893428i	−0.894677	+	0.446714i	$0.852594\pi$
$620$	1412.43			0.0914915
$621$	33.0274			0.00213421
$622$		−	7912.75i		−	0.510084i
$623$		−	10790.3i		−	0.693907i
$624$		−	44092.7i		−	2.82872i
$625$	−12243.3			−0.783571
$626$			25156.6i			1.60616i
$627$	10629.8			0.677055
$628$	−7559.81			−0.480365
$629$	−9349.56	+	1654.23i	−0.592673	+	0.104862i
$630$	16214.7			1.02541
$631$	−433.667			−0.0273598			−0.0136799	−	0.999906i	$-0.504355\pi$
$631$	−433.667			−0.0273598			−0.0136799	+	0.999906i	$0.504355\pi$
$632$			5537.46i			0.348526i
$633$	−29337.2			−1.84210
$634$			1984.55i			0.124316i
$635$			21540.4i			1.34615i
$636$			2986.37i			0.186190i
$637$	2842.11			0.176780
$638$	−12297.9			−0.763135
$639$			6138.29i			0.380011i
$640$		−	16809.8i		−	1.03822i
$641$		−	18800.5i		−	1.15846i	−0.815163	−	0.579232i	$-0.803353\pi$
$641$		−	18800.5i		−	1.15846i	0.815163	−	0.579232i	$-0.196647\pi$
$642$	−981.062			−0.0603107
$643$			6265.70i			0.384285i	0.981367	+	0.192142i	$0.0615435\pi$
$643$			6265.70i			0.384285i	−0.981367	+	0.192142i	$0.938456\pi$
$644$	1130.65			0.0691830
$645$	−6571.14			−0.401145
$646$	−1153.10	−	6517.21i	−0.0702292	−	0.396929i
$647$	14193.6			0.862457			0.431228	−	0.902243i	$-0.358080\pi$
$647$	14193.6			0.862457			0.431228	+	0.902243i	$0.358080\pi$
$648$	−11277.4			−0.683672
$649$		−	35885.3i		−	2.17045i
$650$	−5800.53			−0.350024
$651$		−	5332.15i		−	0.321019i
$652$		−	11591.7i		−	0.696268i
$653$			24330.3i			1.45807i	0.684478	+	0.729033i	$0.260030\pi$
$653$			24330.3i			1.45807i	−0.684478	+	0.729033i	$0.739970\pi$
$654$	−17418.9			−1.04149
$655$	2448.31			0.146051
$656$			22987.9i			1.36818i
$657$			25039.3i			1.48687i
$658$			9283.57i			0.550017i
$659$	12012.0			0.710049			0.355024	−	0.934857i	$-0.384473\pi$
$659$	12012.0			0.710049			0.355024	+	0.934857i	$0.384473\pi$
$660$		−	12938.0i		−	0.763050i
$661$	4879.91			0.287151			0.143575	−	0.989639i	$-0.454140\pi$
$661$	4879.91			0.287151			0.143575	+	0.989639i	$0.454140\pi$
$662$	4891.46			0.287178
$663$	38229.7	−	6764.04i	2.23940	−	0.396219i
$664$	−14907.9			−0.871296
$665$	−4943.52			−0.288273
$666$		−	12440.6i		−	0.723820i
$667$	1357.62			0.0788117
$668$		−	2251.65i		−	0.130418i
$669$		−	31085.5i		−	1.79646i
$670$		−	4220.01i		−	0.243333i
$671$	−35237.0			−2.02729
$672$	18476.0			1.06061
$673$			31418.0i			1.79952i	0.436386	+	0.899760i	$0.356258\pi$
$673$			31418.0i			1.79952i	−0.436386	+	0.899760i	$0.643742\pi$
$674$		−	37808.9i		−	2.16075i
$675$		−	39.3575i		−	0.00224425i
$676$	11667.5			0.663834
$677$		−	14349.3i		−	0.814607i	−0.913293	−	0.407303i	$-0.866469\pi$
$677$		−	14349.3i		−	0.814607i	0.913293	−	0.407303i	$-0.133531\pi$
$678$	−11550.0			−0.654240
$679$	7486.61			0.423136
$680$	10885.5	−	1925.99i	0.613882	−	0.108615i
$681$	21503.9			1.21003
$682$	−7204.82			−0.404526
$683$		−	18620.4i		−	1.04317i	−0.853198	−	0.521587i	$-0.825340\pi$
$683$		−	18620.4i		−	1.04317i	0.853198	−	0.521587i	$-0.174660\pi$
$684$	2571.51			0.143749
$685$			9575.45i			0.534101i
$686$			22434.1i			1.24860i
$687$		−	17236.6i		−	0.957232i
$688$	−7028.68			−0.389485
$689$	9044.23			0.500084
$690$			4816.59i			0.265746i
$691$		−	8151.06i		−	0.448743i	−0.974504	−	0.224371i	$-0.927967\pi$
$691$		−	8151.06i		−	0.448743i	0.974504	−	0.224371i	$-0.0720328\pi$
$692$			9081.19i			0.498865i
$693$	−24526.7			−1.34444
$694$			23849.5i			1.30449i
$695$	26528.1			1.44787
$696$	8130.20			0.442779
$697$	−19931.2	+	3526.45i	−1.08314	+	0.191641i
$698$	−17886.4			−0.969929
$699$	8545.93			0.462428
$700$		−	1347.35i		−	0.0727502i
$701$	−286.484			−0.0154356			−0.00771779	−	0.999970i	$-0.502457\pi$
$701$	−286.484			−0.0154356			−0.00771779	+	0.999970i	$0.502457\pi$
$702$			436.497i			0.0234680i
$703$			3792.88i			0.203487i
$704$			7864.95i			0.421053i
$705$	−11727.4			−0.626497
$706$	21326.4			1.13687
$707$			11997.3i			0.638194i
$708$		−	17287.9i		−	0.917682i
$709$			15431.9i			0.817431i	0.912662	+	0.408716i	$0.134023\pi$
$709$			15431.9i			0.817431i	−0.912662	+	0.408716i	$0.865977\pi$
$710$	−7681.43			−0.406027
$711$		−	9663.33i		−	0.509709i
$712$	9638.81			0.507345
$713$	795.373			0.0417769
$714$	5298.39	+	29946.0i	0.277713	+	1.56961i
$715$	−39182.9			−2.04945
$716$	−3632.90			−0.189620
$717$			5919.58i			0.308328i
$718$	−20390.0			−1.05982
$719$			15386.1i			0.798058i	0.916938	+	0.399029i	$0.130653\pi$
$719$			15386.1i			0.798058i	−0.916938	+	0.399029i	$0.869347\pi$
$720$			21909.4i			1.13405i
$721$			2935.01i			0.151603i
$722$	20486.6			1.05600
$723$	−10781.6			−0.554595
$724$			6112.63i			0.313777i
$725$		−	1617.83i		−	0.0828754i
$726$			32942.0i			1.68401i
$727$	−16335.2			−0.833340			−0.416670	−	0.909058i	$-0.636803\pi$
$727$	−16335.2			−0.833340			−0.416670	+	0.909058i	$0.636803\pi$
$728$		−	20505.9i		−	1.04395i
$729$	20022.2			1.01723
$730$	−31334.1			−1.58867
$731$	−1078.23	−	6094.08i	−0.0545553	−	0.308341i
$732$	−16975.6			−0.857152
$733$	30443.3			1.53404			0.767018	−	0.641625i	$-0.221739\pi$
$733$	30443.3			1.53404			0.767018	+	0.641625i	$0.221739\pi$
$734$			17620.7i			0.886092i
$735$	−2812.33			−0.141135
$736$			2755.98i			0.138026i
$737$			6383.29i			0.319039i
$738$		−	26520.6i		−	1.32281i
$739$	13605.8			0.677264			0.338632	−	0.940919i	$-0.390036\pi$
$739$	13605.8			0.677264			0.338632	+	0.940919i	$0.390036\pi$
$740$	4616.50			0.229332
$741$		−	15508.8i		−	0.768869i
$742$			7084.50i			0.350512i
$743$		−	25753.0i		−	1.27158i	−0.771862	−	0.635790i	$-0.780674\pi$
$743$		−	25753.0i		−	1.27158i	0.771862	−	0.635790i	$-0.219326\pi$
$744$	4763.13			0.234711
$745$		−	9119.97i		−	0.448497i
$746$	−4976.22			−0.244226
$747$	26015.6			1.27424
$748$	11998.8	−	2122.96i	0.586521	−	0.103774i
$749$	−690.143			−0.0336679
$750$	37112.0			1.80685
$751$		−	14832.7i		−	0.720708i	−0.932816	−	0.360354i	$-0.882656\pi$
$751$		−	14832.7i		−	0.720708i	0.932816	−	0.360354i	$-0.117344\pi$
$752$	−12544.0			−0.608288
$753$			16663.1i			0.806425i
$754$			17942.6i			0.866621i
$755$		−	28201.8i		−	1.35943i
$756$	−101.390			−0.00487767
$757$	22646.1			1.08730			0.543649	−	0.839312i	$-0.317042\pi$
$757$	22646.1			1.08730			0.543649	+	0.839312i	$0.317042\pi$
$758$		−	14185.2i		−	0.679722i
$759$		−	7285.70i		−	0.348424i
$760$		−	4415.97i		−	0.210769i
$761$	−6033.28			−0.287393			−0.143697	−	0.989622i	$-0.545899\pi$
$761$	−6033.28			−0.287393			−0.143697	+	0.989622i	$0.545899\pi$
$762$		−	52934.0i		−	2.51653i
$763$	−12253.6			−0.581401
$764$	13129.6			0.621746
$765$	−18996.1	+	3361.00i	−0.897784	+	0.158846i
$766$	31049.6			1.46458
$767$	−52356.5			−2.46478
$768$			32320.2i			1.51856i
$769$	4780.05			0.224152			0.112076	−	0.993700i	$-0.464250\pi$
$769$	4780.05			0.224152			0.112076	+	0.993700i	$0.464250\pi$
$770$		−	30692.7i		−	1.43648i
$771$		−	26430.0i		−	1.23457i
$772$			13592.8i			0.633699i
$773$	−7420.72			−0.345284			−0.172642	−	0.984985i	$-0.555230\pi$
$773$	−7420.72			−0.345284			−0.172642	+	0.984985i	$0.555230\pi$
$774$	8108.83			0.376571
$775$		−	947.815i		−	0.0439310i
$776$			6687.67i			0.309373i
$777$		−	17428.0i		−	0.804665i
$778$	−33473.7			−1.54253
$779$			8085.58i			0.371882i
$780$	−18876.6			−0.866525
$781$	11619.1			0.532349
$782$	−4466.91	+	790.337i	−0.204267	+	0.0361412i
$783$	−121.744			−0.00555653
$784$	−3008.16			−0.137033
$785$		−	22655.0i		−	1.03005i
$786$	−6016.54			−0.273032
$787$			23193.3i			1.05051i	0.850945	+	0.525255i	$0.176030\pi$
$787$			23193.3i			1.05051i	−0.850945	+	0.525255i	$0.823970\pi$
$788$		−	13369.4i		−	0.604395i
$789$			20575.5i			0.928400i
$790$	12092.7			0.544604
$791$	−8125.01			−0.365224
$792$		−	21909.4i		−	0.982974i
$793$			51410.7i			2.30220i
$794$		−	25052.3i		−	1.11974i
$795$	−8949.46			−0.399251
$796$			6344.11i			0.282489i
$797$	21722.8			0.965448			0.482724	−	0.875773i	$-0.339647\pi$
$797$	21722.8			0.965448			0.482724	+	0.875773i	$0.339647\pi$
$798$	12148.3			0.538906
$799$	−1924.31	−	10876.0i	−0.0852030	−	0.481560i
$800$	3284.20			0.145142
$801$	−16820.5			−0.741977
$802$			5913.47i			0.260364i
$803$	47396.7			2.08293
$804$			3075.18i			0.134892i
$805$			3388.30i			0.148350i
$806$			10511.8i			0.459383i
$807$	11868.2			0.517695
$808$	−10717.0			−0.466611
$809$			30924.4i			1.34394i	0.740581	+	0.671968i	$0.234551\pi$
$809$			30924.4i			1.34394i	−0.740581	+	0.671968i	$0.765449\pi$
$810$			24627.5i			1.06830i
$811$			8651.88i			0.374610i	0.982302	+	0.187305i	$0.0599753\pi$
$811$			8651.88i			0.374610i	−0.982302	+	0.187305i	$0.940025\pi$
$812$	−4167.74			−0.180122
$813$			48138.6i			2.07662i
$814$	−23548.8			−1.01398
$815$	34737.7			1.49302
$816$	−40463.2	+	7159.21i	−1.73590	+	0.307135i
$817$	−2472.21			−0.105865
$818$	42636.7			1.82244
$819$			35784.4i			1.52675i
$820$	9841.34			0.419115
$821$		−	12053.1i		−	0.512372i	−0.966628	−	0.256186i	$-0.917534\pi$
$821$		−	12053.1i		−	0.512372i	0.966628	−	0.256186i	$-0.0824659\pi$
$822$		−	23531.0i		−	0.998464i
$823$			18023.7i			0.763387i	0.924289	+	0.381694i	$0.124659\pi$
$823$			18023.7i			0.763387i	−0.924289	+	0.381694i	$0.875341\pi$
$824$	−2621.80			−0.110843
$825$	−8682.08			−0.366389
$826$		−	41011.7i		−	1.72758i
$827$		−	38583.0i		−	1.62232i	−0.584822	−	0.811162i	$-0.698836\pi$
$827$		−	38583.0i		−	1.62232i	0.584822	−	0.811162i	$-0.301164\pi$
$828$		−	1762.52i		−	0.0739756i
$829$	6804.98			0.285099			0.142549	−	0.989788i	$-0.454470\pi$
$829$	6804.98			0.285099			0.142549	+	0.989788i	$0.454470\pi$
$830$			32555.8i			1.36148i
$831$	−44470.0			−1.85637
$832$	11474.9			0.478151
$833$	−461.465	−	2608.16i	−0.0191943	−	0.108484i
$834$	−65190.8			−2.70668
$835$	6747.69			0.279657
$836$		−	4867.60i		−	0.201375i
$837$	−71.3243			−0.00294544
$838$		−	50023.7i		−	2.06210i
$839$			20445.0i			0.841288i	0.907226	+	0.420644i	$0.138196\pi$
$839$			20445.0i			0.841288i	−0.907226	+	0.420644i	$0.861804\pi$
$840$			20291.0i			0.833460i
$841$	19384.6			0.794809
$842$	30450.2			1.24630
$843$		−	40610.9i		−	1.65921i
$844$			13434.1i			0.547891i
$845$			34965.0i			1.42347i
$846$	14471.7			0.588119
$847$			23173.5i			0.940084i
$848$	−9572.61			−0.387647
$849$	−15562.1			−0.629081
$850$	941.814	+	5323.05i	0.0380047	+	0.214799i
$851$	2599.65			0.104718
$852$	5597.56			0.225081
$853$		−	14161.3i		−	0.568434i	−0.958760	−	0.284217i	$-0.908266\pi$
$853$		−	14161.3i		−	0.568434i	0.958760	−	0.284217i	$-0.0917336\pi$
$854$	−40270.9			−1.61363
$855$			7706.23i			0.308243i
$856$		−	616.494i		−	0.0246161i
$857$		−	20903.8i		−	0.833210i	−0.909088	−	0.416605i	$-0.863220\pi$
$857$		−	20903.8i		−	0.833210i	0.909088	−	0.416605i	$-0.136780\pi$
$858$	96289.2			3.83131
$859$	−29833.9			−1.18501			−0.592503	−	0.805568i	$-0.701860\pi$
$859$	−29833.9			−1.18501			−0.592503	+	0.805568i	$0.701860\pi$
$860$			3009.05i			0.119311i
$861$		−	37152.5i		−	1.47056i
$862$		−	35386.9i		−	1.39824i
$863$	−26659.9			−1.05158			−0.525789	−	0.850615i	$-0.676230\pi$
$863$	−26659.9			−1.05158			−0.525789	+	0.850615i	$0.676230\pi$
$864$		−	247.140i		−	0.00973134i
$865$	−27214.3			−1.06973
$866$	−12415.6			−0.487181
$867$	−12414.5	−	33984.6i	−0.486296	−	1.33123i
$868$	−2441.70			−0.0954799
$869$	−18291.6			−0.714041
$870$		−	17754.6i		−	0.691883i
$871$	9313.19			0.362303
$872$		−	10945.9i		−	0.425087i
$873$		−	11670.5i		−	0.452449i
$874$			1812.11i			0.0701324i
$875$	26107.0			1.00866
$876$	22833.6			0.880679
$877$			33636.8i			1.29514i	0.762008	+	0.647568i	$0.224214\pi$
$877$			33636.8i			1.29514i	−0.762008	+	0.647568i	$0.775786\pi$
$878$			20661.0i			0.794164i
$879$			59856.8i			2.29684i
$880$	41472.1			1.58866
$881$			38848.5i			1.48563i	0.669498	+	0.742814i	$0.266509\pi$
$881$			38848.5i			1.48563i	−0.669498	+	0.742814i	$0.733491\pi$
$882$	3470.44			0.132490
$883$	7339.75			0.279731			0.139865	−	0.990171i	$-0.455333\pi$
$883$	7339.75			0.279731			0.139865	+	0.990171i	$0.455333\pi$
$884$	−3097.38	−	17506.1i	−0.117847	−	0.666058i
$885$	51807.9			1.96780
$886$	−6122.73			−0.232164
$887$			22442.1i			0.849530i	0.905304	+	0.424765i	$0.139643\pi$
$887$			22442.1i			0.849530i	−0.905304	+	0.424765i	$0.860357\pi$
$888$	15568.1			0.588325
$889$		−	37237.2i		−	1.40483i
$890$		−	21049.1i		−	0.792773i
$891$		−	37252.2i		−	1.40067i
$892$	−14234.7			−0.534318
$893$	−4412.13			−0.165337
$894$			22411.7i			0.838432i
$895$		−	10887.0i		−	0.406605i
$896$			29059.3i			1.08348i
$897$	−10629.8			−0.395673
$898$		−	5329.59i		−	0.198052i
$899$	−2931.86			−0.108769
$900$	−2100.33			−0.0777899
$901$	−1468.48	−	8299.74i	−0.0542978	−	0.306886i
$902$	−50200.6			−1.85310
$903$	11359.6			0.418631
$904$		−	7257.95i		−	0.267031i
$905$	−18318.2			−0.672836
$906$			69303.8i			2.54135i
$907$		−	26670.6i		−	0.976388i	−0.872735	−	0.488194i	$-0.837656\pi$
$907$		−	26670.6i		−	0.976388i	0.872735	−	0.488194i	$-0.162344\pi$
$908$		−	9847.08i		−	0.359897i
$909$	18702.0			0.682404
$910$	−44780.5			−1.63127
$911$			713.989i			0.0259665i	0.999916	+	0.0129833i	$0.00413282\pi$
$911$			713.989i			0.0259665i	−0.999916	+	0.0129833i	$0.995867\pi$
$912$			16414.9i			0.596000i
$913$		−	49244.7i		−	1.78506i
$914$	−10438.2			−0.377751
$915$		−	50872.0i		−	1.83801i
$916$	−7892.99			−0.284707
$917$	−4232.42			−0.152418
$918$	400.566	−	70.8727i	0.0144016	−	0.00254809i
$919$	17196.7			0.617267			0.308633	−	0.951181i	$-0.400128\pi$
$919$	17196.7			0.617267			0.308633	+	0.951181i	$0.400128\pi$
$920$	−3026.72			−0.108465
$921$		−	25909.2i		−	0.926966i
$922$	40885.3			1.46040
$923$		−	16952.3i		−	0.604540i
$924$			22366.2i			0.796313i
$925$		−	3097.91i		−	0.110117i
$926$	−30772.8			−1.09207
$927$	4575.26			0.162105
$928$		−	10158.9i		−	0.359357i
$929$			47505.9i			1.67774i	0.544335	+	0.838868i	$0.316782\pi$
$929$			47505.9i			1.67774i	−0.544335	+	0.838868i	$0.683218\pi$
$930$		−	10401.7i		−	0.366757i
$931$	−1058.07			−0.0372467
$932$		−	3913.35i		−	0.137539i
$933$	−17279.8			−0.606339
$934$	20728.6			0.726189
$935$	6362.02	+	35957.6i	0.222524	+	1.25769i
$936$	−31965.7			−1.11627
$937$	−35704.6			−1.24484			−0.622422	−	0.782681i	$-0.713851\pi$
$937$	−35704.6			−1.24484			−0.622422	+	0.782681i	$0.713851\pi$
$938$			7295.19i			0.253941i
$939$	54936.7			1.90925
$940$			5370.22i			0.186337i
$941$			2418.89i			0.0837977i	0.999122	+	0.0418989i	$0.0133407\pi$
$941$			2418.89i			0.0837977i	−0.999122	+	0.0418989i	$0.986659\pi$
$942$			55673.1i			1.92561i
$943$	5541.88			0.191377
$944$	55415.3			1.91061
$945$		−	303.843i		−	0.0104593i
$946$		−	15349.2i		−	0.527531i
$947$		−	1807.08i		−	0.0620087i	−0.999519	−	0.0310044i	$-0.990129\pi$
$947$		−	1807.08i		−	0.0620087i	0.999519	−	0.0310044i	$-0.00987058\pi$
$948$	−8812.08			−0.301902
$949$		−	69151.6i		−	2.36539i
$950$	2159.43			0.0737485
$951$	4333.84			0.147775
$952$	−18817.9	+	3329.48i	−0.640643	+	0.113350i
$953$	26920.2			0.915039			0.457520	−	0.889200i	$-0.348738\pi$
$953$	26920.2			0.915039			0.457520	+	0.889200i	$0.348738\pi$
$954$	11043.7			0.374794
$955$			39346.6i			1.33322i
$956$	2710.69			0.0917051
$957$			26856.1i			0.907141i
$958$			39423.7i			1.32956i
$959$		−	16553.2i		−	0.557384i
$960$	−11354.7			−0.381741
$961$	28073.4			0.942343
$962$			34357.5i			1.15149i
$963$			1075.83i			0.0360002i
$964$			4937.11i			0.164952i
$965$	−40734.5			−1.35885
$966$		−	8326.51i		−	0.277330i
$967$	−14880.3			−0.494848			−0.247424	−	0.968907i	$-0.579584\pi$
$967$	−14880.3			−0.494848			−0.247424	+	0.968907i	$0.579584\pi$
$968$	−20700.5			−0.687336
$969$	−14232.2	+	2518.12i	−0.471831	+	0.0834817i
$970$	14604.5			0.483424
$971$	28715.6			0.949049			0.474525	−	0.880242i	$-0.342620\pi$
$971$	28715.6			0.949049			0.474525	+	0.880242i	$0.342620\pi$
$972$		−	18103.1i		−	0.597385i
$973$	−45859.4			−1.51098
$974$			60420.2i			1.98767i
$975$			12667.1i			0.416075i
$976$		−	54414.2i		−	1.78459i
$977$	−12795.5			−0.419002			−0.209501	−	0.977808i	$-0.567184\pi$
$977$	−12795.5			−0.419002			−0.209501	+	0.977808i	$0.567184\pi$
$978$	−85365.4			−2.79109
$979$			31839.4i			1.03942i
$980$			1287.82i			0.0419775i
$981$			19101.5i			0.621677i
$982$	45431.4			1.47635
$983$		−	17706.4i		−	0.574514i	−0.957853	−	0.287257i	$-0.907257\pi$
$983$		−	17706.4i		−	0.574514i	0.957853	−	0.287257i	$-0.0927434\pi$
$984$	33187.8			1.07519
$985$	40064.9			1.29601
$986$	16465.7	−	2913.29i	0.531819	−	0.0940955i
$987$	20273.4			0.653808
$988$	−7101.80			−0.228683
$989$			1694.46i			0.0544801i
$990$	−47845.4			−1.53599
$991$			10462.4i			0.335366i	0.985841	+	0.167683i	$0.0536286\pi$
$991$			10462.4i			0.335366i	−0.985841	+	0.167683i	$0.946371\pi$
$992$		−	5951.68i		−	0.190490i
$993$		−	10681.9i		−	0.341370i
$994$	13279.0			0.423727
$995$	−19011.9			−0.605745
$996$		−	23723.9i		−	0.754738i
$997$		−	57331.5i		−	1.82117i	−0.413323	−	0.910585i	$-0.635632\pi$
$997$		−	57331.5i		−	1.82117i	0.413323	−	0.910585i	$-0.364368\pi$
$998$		−	38061.2i		−	1.20722i
$999$	−233.122			−0.00738302

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.4.b.a.16.2	yes	4
3.2	odd	2		153.4.d.b.118.3		4
4.3	odd	2		272.4.b.d.33.1		4
5.2	odd	4		425.4.c.c.424.2		8
5.3	odd	4		425.4.c.c.424.7		8
5.4	even	2		425.4.d.c.101.3		4
17.4	even	4		289.4.a.e.1.4		4
17.13	even	4		289.4.a.e.1.3		4
17.16	even	2	inner	17.4.b.a.16.1	✓	4
51.50	odd	2		153.4.d.b.118.4		4
68.67	odd	2		272.4.b.d.33.4		4
85.33	odd	4		425.4.c.c.424.8		8
85.67	odd	4		425.4.c.c.424.1		8
85.84	even	2		425.4.d.c.101.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.b.a.16.1	✓	4	17.16	even	2	inner
17.4.b.a.16.2	yes	4	1.1	even	1	trivial
153.4.d.b.118.3		4	3.2	odd	2
153.4.d.b.118.4		4	51.50	odd	2
272.4.b.d.33.1		4	4.3	odd	2
272.4.b.d.33.4		4	68.67	odd	2
289.4.a.e.1.3		4	17.13	even	4
289.4.a.e.1.4		4	17.4	even	4
425.4.c.c.424.1		8	85.67	odd	4
425.4.c.c.424.2		8	5.2	odd	4
425.4.c.c.424.7		8	5.3	odd	4
425.4.c.c.424.8		8	85.33	odd	4
425.4.d.c.101.3		4	5.4	even	2
425.4.d.c.101.4		4	85.84	even	2

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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	17.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.37228 q^{2} +7.36435i q^{3} +3.37228 q^{4} +10.1060i q^{5} -24.8347i q^{6} -17.4703i q^{7} +15.6060 q^{8} -27.2337 q^{9} +O(q^{10})\)	\(q-3.37228 q^{2} +7.36435i q^{3} +3.37228 q^{4} +10.1060i q^{5} -24.8347i q^{6} -17.4703i q^{7} +15.6060 q^{8} -27.2337 q^{9} -34.0802i q^{10} +51.5505i q^{11} +24.8347i q^{12} +75.2119 q^{13} +58.9148i q^{14} -74.4239 q^{15} -79.6060 q^{16} +(-12.2119 - 69.0208i) q^{17} +91.8397 q^{18} -28.0000 q^{19} +34.0802i q^{20} +128.658 q^{21} -173.843i q^{22} +19.1913i q^{23} +114.928i q^{24} +22.8695 q^{25} -253.636 q^{26} -1.72096i q^{27} -58.9148i q^{28} -70.7417i q^{29} +250.978 q^{30} -41.4445i q^{31} +143.606 q^{32} -379.636 q^{33} +(41.1821 + 232.757i) q^{34} +176.554 q^{35} -91.8397 q^{36} -135.460i q^{37} +94.4239 q^{38} +553.887i q^{39} +157.713i q^{40} -288.771i q^{41} -433.870 q^{42} +88.2934 q^{43} +173.843i q^{44} -275.223i q^{45} -64.7184i q^{46} +157.576 q^{47} -586.246i q^{48} +37.7881 q^{49} -77.1224 q^{50} +(508.293 - 89.9330i) q^{51} +253.636 q^{52} +120.250 q^{53} +5.80356i q^{54} -520.967 q^{55} -272.641i q^{56} -206.202i q^{57} +238.561i q^{58} -696.119 q^{59} -250.978 q^{60} +683.544i q^{61} +139.763i q^{62} +475.781i q^{63} +152.568 q^{64} +760.089i q^{65} +1280.24 q^{66} +123.826 q^{67} +(-41.1821 - 232.757i) q^{68} -141.331 q^{69} -595.391 q^{70} -225.393i q^{71} -425.008 q^{72} -919.423i q^{73} +456.810i q^{74} +168.419i q^{75} -94.4239 q^{76} +900.603 q^{77} -1867.86i q^{78} +354.830i q^{79} -804.495i q^{80} -722.636 q^{81} +973.815i q^{82} -955.272 q^{83} +433.870 q^{84} +(697.522 - 123.413i) q^{85} -297.750 q^{86} +520.967 q^{87} +804.495i q^{88} +617.636 q^{89} +928.128i q^{90} -1313.98i q^{91} +64.7184i q^{92} +305.212 q^{93} -531.391 q^{94} -282.967i q^{95} +1057.56i q^{96} +428.533i q^{97} -127.432 q^{98} -1403.91i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{4} - 18 q^{8} - 40 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^4 - 18 * q^8 - 40 * q^9	\( 4 q - 2 q^{2} + 2 q^{4} - 18 q^{8} - 40 q^{9} + 140 q^{13} + 24 q^{15} - 238 q^{16} + 112 q^{17} + 218 q^{18} - 112 q^{19} + 124 q^{21} - 460 q^{25} - 532 q^{26} + 912 q^{30} + 494 q^{32} - 1036 q^{33} + 406 q^{34} + 936 q^{35} - 218 q^{36} + 56 q^{38} - 1184 q^{42} - 520 q^{43} + 952 q^{47} + 312 q^{49} - 1354 q^{50} + 1160 q^{51} + 532 q^{52} - 576 q^{53} + 168 q^{55} - 1176 q^{59} - 912 q^{60} + 1426 q^{64} + 1904 q^{66} - 240 q^{67} - 406 q^{68} + 1204 q^{69} + 192 q^{70} - 1206 q^{72} - 56 q^{76} + 868 q^{77} - 2408 q^{81} - 2856 q^{83} + 1184 q^{84} + 768 q^{85} - 2248 q^{86} - 168 q^{87} + 1988 q^{89} + 1060 q^{93} + 448 q^{94} + 306 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^4 - 18 * q^8 - 40 * q^9 + 140 * q^13 + 24 * q^15 - 238 * q^16 + 112 * q^17 + 218 * q^18 - 112 * q^19 + 124 * q^21 - 460 * q^25 - 532 * q^26 + 912 * q^30 + 494 * q^32 - 1036 * q^33 + 406 * q^34 + 936 * q^35 - 218 * q^36 + 56 * q^38 - 1184 * q^42 - 520 * q^43 + 952 * q^47 + 312 * q^49 - 1354 * q^50 + 1160 * q^51 + 532 * q^52 - 576 * q^53 + 168 * q^55 - 1176 * q^59 - 912 * q^60 + 1426 * q^64 + 1904 * q^66 - 240 * q^67 - 406 * q^68 + 1204 * q^69 + 192 * q^70 - 1206 * q^72 - 56 * q^76 + 868 * q^77 - 2408 * q^81 - 2856 * q^83 + 1184 * q^84 + 768 * q^85 - 2248 * q^86 - 168 * q^87 + 1988 * q^89 + 1060 * q^93 + 448 * q^94 + 306 * q^98

Introduction

L-functions

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