LMFDB - Embedded newform 65.5.g.a.34.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,5,Mod(34,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("65.34");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	65.g (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:	$6.71904760045$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			34.20
Character	$\chi$	$=$	65.34
Dual form			65.5.g.a.44.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.95432 - 2.95432i) q^{2} +14.1332i q^{3} -1.45602i q^{4} +(-24.9994 - 0.166336i) q^{5} +(41.7539 + 41.7539i) q^{6} +(-27.9563 - 27.9563i) q^{7} +(42.9676 + 42.9676i) q^{8} -118.747 q^{9} +O(q^{10})$	\(q+(2.95432 - 2.95432i) q^{2} +14.1332i q^{3} -1.45602i q^{4} +(-24.9994 - 0.166336i) q^{5} +(41.7539 + 41.7539i) q^{6} +(-27.9563 - 27.9563i) q^{7} +(42.9676 + 42.9676i) q^{8} -118.747 q^{9} +(-74.3478 + 73.3650i) q^{10} +(-119.488 + 119.488i) q^{11} +20.5781 q^{12} +(100.389 + 135.952i) q^{13} -165.184 q^{14} +(2.35086 - 353.321i) q^{15} +277.176 q^{16} +125.919 q^{17} +(-350.815 + 350.815i) q^{18} +(-95.7902 - 95.7902i) q^{19} +(-0.242188 + 36.3996i) q^{20} +(395.111 - 395.111i) q^{21} +706.011i q^{22} +676.620 q^{23} +(-607.268 + 607.268i) q^{24} +(624.945 + 8.31663i) q^{25} +(698.228 + 105.065i) q^{26} -533.478i q^{27} +(-40.7048 + 40.7048i) q^{28} -261.902 q^{29} +(-1036.88 - 1050.77i) q^{30} +(578.874 + 578.874i) q^{31} +(131.386 - 131.386i) q^{32} +(-1688.74 - 1688.74i) q^{33} +(372.004 - 372.004i) q^{34} +(694.242 + 703.542i) q^{35} +172.897i q^{36} +(-1055.74 - 1055.74i) q^{37} -565.990 q^{38} +(-1921.44 + 1418.82i) q^{39} +(-1067.02 - 1081.31i) q^{40} +(-43.1941 - 43.1941i) q^{41} -2334.57i q^{42} -71.2779 q^{43} +(173.976 + 173.976i) q^{44} +(2968.60 + 19.7519i) q^{45} +(1998.95 - 1998.95i) q^{46} +(1492.28 + 1492.28i) q^{47} +3917.38i q^{48} -837.889i q^{49} +(1870.86 - 1821.72i) q^{50} +1779.63i q^{51} +(197.949 - 146.168i) q^{52} +5441.28i q^{53} +(-1576.06 - 1576.06i) q^{54} +(3007.01 - 2967.26i) q^{55} -2402.43i q^{56} +(1353.82 - 1353.82i) q^{57} +(-773.741 + 773.741i) q^{58} +(4673.28 - 4673.28i) q^{59} +(-514.442 - 3.42289i) q^{60} -4913.70 q^{61} +3420.36 q^{62} +(3319.71 + 3319.71i) q^{63} +3658.51i q^{64} +(-2487.06 - 3415.43i) q^{65} -9978.17 q^{66} +(-5608.35 + 5608.35i) q^{67} -183.340i q^{68} +9562.78i q^{69} +(4129.50 + 27.4761i) q^{70} +(-308.024 - 308.024i) q^{71} +(-5102.25 - 5102.25i) q^{72} +(-1563.74 - 1563.74i) q^{73} -6237.98 q^{74} +(-117.540 + 8832.45i) q^{75} +(-139.472 + 139.472i) q^{76} +6680.88 q^{77} +(-1484.90 + 9868.18i) q^{78} +5424.58 q^{79} +(-6929.25 - 46.1045i) q^{80} -2078.73 q^{81} -255.219 q^{82} +(3066.23 - 3066.23i) q^{83} +(-575.289 - 575.289i) q^{84} +(-3147.90 - 20.9449i) q^{85} +(-210.578 + 210.578i) q^{86} -3701.50i q^{87} -10268.2 q^{88} +(5743.40 - 5743.40i) q^{89} +(8828.54 - 8711.83i) q^{90} +(994.215 - 6607.23i) q^{91} -985.169i q^{92} +(-8181.33 + 8181.33i) q^{93} +8817.35 q^{94} +(2378.77 + 2410.63i) q^{95} +(1856.90 + 1856.90i) q^{96} +(9009.14 - 9009.14i) q^{97} +(-2475.39 - 2475.39i) q^{98} +(14188.8 - 14188.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9}+O(q^{10}) $ 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9	$ 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9} + 8 q^{11} + 424 q^{14} - 508 q^{15} - 3128 q^{16} + 268 q^{19} + 2116 q^{20} - 668 q^{21} + 2032 q^{24} + 1100 q^{26} - 3704 q^{29} - 1660 q^{31} + 1252 q^{34} + 6692 q^{35} + 7408 q^{39} + 3644 q^{40} + 5960 q^{41} + 1444 q^{44} - 8674 q^{45} + 17620 q^{46} - 3928 q^{50} - 30588 q^{54} + 14784 q^{55} - 5548 q^{59} - 13976 q^{60} - 20008 q^{61} - 15614 q^{65} + 24752 q^{66} + 26908 q^{70} - 16360 q^{71} - 7304 q^{74} - 5760 q^{76} - 9536 q^{79} - 62348 q^{80} - 36516 q^{81} + 66564 q^{84} - 11604 q^{85} - 5264 q^{86} - 940 q^{89} + 37644 q^{91} + 55448 q^{94} - 61644 q^{96} + 16140 q^{99}+O(q^{100}) $ 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9 + 8 * q^11 + 424 * q^14 - 508 * q^15 - 3128 * q^16 + 268 * q^19 + 2116 * q^20 - 668 * q^21 + 2032 * q^24 + 1100 * q^26 - 3704 * q^29 - 1660 * q^31 + 1252 * q^34 + 6692 * q^35 + 7408 * q^39 + 3644 * q^40 + 5960 * q^41 + 1444 * q^44 - 8674 * q^45 + 17620 * q^46 - 3928 * q^50 - 30588 * q^54 + 14784 * q^55 - 5548 * q^59 - 13976 * q^60 - 20008 * q^61 - 15614 * q^65 + 24752 * q^66 + 26908 * q^70 - 16360 * q^71 - 7304 * q^74 - 5760 * q^76 - 9536 * q^79 - 62348 * q^80 - 36516 * q^81 + 66564 * q^84 - 11604 * q^85 - 5264 * q^86 - 940 * q^89 + 37644 * q^91 + 55448 * q^94 - 61644 * q^96 + 16140 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	2.95432	−	2.95432i	0.738580	−	0.738580i	−0.233723	−	0.972303i	$-0.575091\pi$
$2$	2.95432	−	2.95432i	0.738580	−	0.738580i	0.972303	+	0.233723i	$0.0750909\pi$
$3$			14.1332i			1.57035i	0.619273	+	0.785176i	$0.287428\pi$
$3$			14.1332i			1.57035i	−0.619273	+	0.785176i	$0.712572\pi$
$4$		−	1.45602i		−	0.0910010i
$5$	−24.9994	−	0.166336i	−0.999978	−	0.00665345i
$5$	−24.9994	−	0.166336i	−0.999978	−	0.00665345i
$6$	41.7539	+	41.7539i	1.15983	+	1.15983i
$7$	−27.9563	−	27.9563i	−0.570537	−	0.570537i	0.361742	−	0.932278i	$-0.382182\pi$
$7$	−27.9563	−	27.9563i	−0.570537	−	0.570537i	−0.932278	+	0.361742i	$0.882182\pi$
$8$	42.9676	+	42.9676i	0.671369	+	0.671369i
$9$	−118.747			−1.46601
$10$	−74.3478	+	73.3650i	−0.743478	+	0.733650i
$11$	−119.488	+	119.488i	−0.987503	+	0.987503i	−0.999923	−	0.0124197i	$-0.996047\pi$
$11$	−119.488	+	119.488i	−0.987503	+	0.987503i	0.0124197	+	0.999923i	$0.496047\pi$
$12$	20.5781			0.142904
$13$	100.389	+	135.952i	0.594018	+	0.804451i
$13$	100.389	+	135.952i	0.594018	+	0.804451i
$14$	−165.184			−0.842774
$15$	2.35086	−	353.321i	0.0104483	−	1.57032i
$16$	277.176			1.08272
$17$	125.919			0.435705			0.217852	−	0.975982i	$-0.430095\pi$
$17$	125.919			0.435705			0.217852	+	0.975982i	$0.430095\pi$
$18$	−350.815	+	350.815i	−1.08276	+	1.08276i
$19$	−95.7902	−	95.7902i	−0.265347	−	0.265347i	0.561875	−	0.827222i	$-0.310080\pi$
$19$	−95.7902	−	95.7902i	−0.265347	−	0.265347i	−0.827222	+	0.561875i	$0.810080\pi$
$20$	−0.242188	+	36.3996i	−0.000605471	+	0.0909990i
$21$	395.111	−	395.111i	0.895944	−	0.895944i
$22$			706.011i			1.45870i
$23$	676.620			1.27905			0.639527	−	0.768769i	$-0.279130\pi$
$23$	676.620			1.27905			0.639527	+	0.768769i	$0.279130\pi$
$24$	−607.268	+	607.268i	−1.05429	+	1.05429i
$25$	624.945	+	8.31663i	0.999911	+	0.0133066i
$26$	698.228	+	105.065i	1.03288	+	0.155422i
$27$		−	533.478i		−	0.731794i
$28$	−40.7048	+	40.7048i	−0.0519194	+	0.0519194i
$29$	−261.902			−0.311417			−0.155708	−	0.987803i	$-0.549766\pi$
$29$	−261.902			−0.311417			−0.155708	+	0.987803i	$0.549766\pi$
$30$	−1036.88	−	1050.77i	−1.15209	−	1.16752i
$31$	578.874	+	578.874i	0.602367	+	0.602367i	0.940940	−	0.338573i	$-0.109944\pi$
$31$	578.874	+	578.874i	0.602367	+	0.602367i	−0.338573	+	0.940940i	$0.609944\pi$
$32$	131.386	−	131.386i	0.128307	−	0.128307i
$33$	−1688.74	−	1688.74i	−1.55073	−	1.55073i
$34$	372.004	−	372.004i	0.321803	−	0.321803i
$35$	694.242	+	703.542i	0.566728	+	0.574320i
$36$			172.897i			0.133408i
$37$	−1055.74	−	1055.74i	−0.771175	−	0.771175i	0.207137	−	0.978312i	$-0.433586\pi$
$37$	−1055.74	−	1055.74i	−0.771175	−	0.771175i	−0.978312	+	0.207137i	$0.933586\pi$
$38$	−565.990			−0.391960
$39$	−1921.44	+	1418.82i	−1.26327	+	0.932818i
$40$	−1067.02	−	1081.31i	−0.666887	−	0.675821i
$41$	−43.1941	−	43.1941i	−0.0256955	−	0.0256955i	0.694142	−	0.719838i	$-0.255784\pi$
$41$	−43.1941	−	43.1941i	−0.0256955	−	0.0256955i	−0.719838	+	0.694142i	$0.755784\pi$
$42$		−	2334.57i		−	1.32345i
$43$	−71.2779			−0.0385494			−0.0192747	−	0.999814i	$-0.506136\pi$
$43$	−71.2779			−0.0385494			−0.0192747	+	0.999814i	$0.506136\pi$
$44$	173.976	+	173.976i	0.0898638	+	0.0898638i
$45$	2968.60	+	19.7519i	1.46597	+	0.00975400i
$46$	1998.95	−	1998.95i	0.944684	−	0.944684i
$47$	1492.28	+	1492.28i	0.675546	+	0.675546i	0.958989	−	0.283443i	$-0.0914767\pi$
$47$	1492.28	+	1492.28i	0.675546	+	0.675546i	−0.283443	+	0.958989i	$0.591477\pi$
$48$			3917.38i			1.70025i
$49$		−	837.889i		−	0.348975i
$50$	1870.86	−	1821.72i	0.748343	−	0.728687i
$51$			1779.63i			0.684210i
$52$	197.949	−	146.168i	0.0732059	−	0.0540563i
$53$			5441.28i			1.93709i	0.248841	+	0.968544i	$0.419950\pi$
$53$			5441.28i			1.93709i	−0.248841	+	0.968544i	$0.580050\pi$
$54$	−1576.06	−	1576.06i	−0.540488	−	0.540488i
$55$	3007.01	−	2967.26i	0.994052	−	0.980911i
$56$		−	2402.43i		−	0.766081i
$57$	1353.82	−	1353.82i	0.416688	−	0.416688i
$58$	−773.741	+	773.741i	−0.230006	+	0.230006i
$59$	4673.28	−	4673.28i	1.34251	−	1.34251i	0.448955	−	0.893554i	$-0.351796\pi$
$59$	4673.28	−	4673.28i	1.34251	−	1.34251i	0.893554	−	0.448955i	$-0.148204\pi$
$60$	−514.442	−	3.42289i	−0.142901	−	0.000950803i
$61$	−4913.70			−1.32053			−0.660266	−	0.751032i	$-0.729557\pi$
$61$	−4913.70			−1.32053			−0.660266	+	0.751032i	$0.729557\pi$
$62$	3420.36			0.889792
$63$	3319.71	+	3319.71i	0.836411	+	0.836411i
$64$			3658.51i			0.893190i
$65$	−2487.06	−	3415.43i	−0.588653	−	0.808386i
$66$	−9978.17			−2.29067
$67$	−5608.35	+	5608.35i	−1.24935	+	1.24935i	−0.293349	+	0.956005i	$0.594770\pi$
$67$	−5608.35	+	5608.35i	−1.24935	+	1.24935i	−0.956005	+	0.293349i	$0.905230\pi$
$68$		−	183.340i		−	0.0396496i
$69$			9562.78i			2.00857i
$70$	4129.50	+	27.4761i	0.842756	+	0.00560736i
$71$	−308.024	−	308.024i	−0.0611038	−	0.0611038i	0.675895	−	0.736998i	$-0.263757\pi$
$71$	−308.024	−	308.024i	−0.0611038	−	0.0611038i	−0.736998	+	0.675895i	$0.763757\pi$
$72$	−5102.25	−	5102.25i	−0.984230	−	0.984230i
$73$	−1563.74	−	1563.74i	−0.293440	−	0.293440i	0.544997	−	0.838438i	$-0.316531\pi$
$73$	−1563.74	−	1563.74i	−0.293440	−	0.293440i	−0.838438	+	0.544997i	$0.816531\pi$
$74$	−6237.98			−1.13915
$75$	−117.540	+	8832.45i	−0.0208961	+	1.57021i
$76$	−139.472	+	139.472i	−0.0241468	+	0.0241468i
$77$	6680.88			1.12681
$78$	−1484.90	+	9868.18i	−0.244067	+	1.62199i
$79$	5424.58			0.869185			0.434593	−	0.900627i	$-0.356892\pi$
$79$	5424.58			0.869185			0.434593	+	0.900627i	$0.356892\pi$
$80$	−6929.25	−	46.1045i	−1.08270	−	0.00720383i
$81$	−2078.73			−0.316832
$82$	−255.219			−0.0379564
$83$	3066.23	−	3066.23i	0.445091	−	0.445091i	−0.448628	−	0.893719i	$-0.648087\pi$
$83$	3066.23	−	3066.23i	0.445091	−	0.445091i	0.893719	+	0.448628i	$0.148087\pi$
$84$	−575.289	−	575.289i	−0.0815318	−	0.0815318i
$85$	−3147.90	−	20.9449i	−0.435695	−	0.00289894i
$86$	−210.578	+	210.578i	−0.0284718	+	0.0284718i
$87$		−	3701.50i		−	0.489034i
$88$	−10268.2			−1.32596
$89$	5743.40	−	5743.40i	0.725085	−	0.725085i	−0.244551	−	0.969636i	$-0.578641\pi$
$89$	5743.40	−	5743.40i	0.725085	−	0.725085i	0.969636	+	0.244551i	$0.0786406\pi$
$90$	8828.54	−	8711.83i	1.08994	−	1.07553i
$91$	994.215	−	6607.23i	0.120060	−	0.797879i
$92$		−	985.169i		−	0.116395i
$93$	−8181.33	+	8181.33i	−0.945928	+	0.945928i
$94$	8817.35			0.997890
$95$	2378.77	+	2410.63i	0.263575	+	0.267106i
$96$	1856.90	+	1856.90i	0.201487	+	0.201487i
$97$	9009.14	−	9009.14i	0.957502	−	0.957502i	−0.0416307	−	0.999133i	$-0.513255\pi$
$97$	9009.14	−	9009.14i	0.957502	−	0.957502i	0.999133	+	0.0416307i	$0.0132553\pi$
$98$	−2475.39	−	2475.39i	−0.257746	−	0.257746i
$99$	14188.8	−	14188.8i	1.44769	−	1.44769i
$100$	12.1092	−	909.930i	0.00121092	−	0.0909930i
$101$			16175.9i			1.58572i	0.609405	+	0.792859i	$0.291408\pi$
$101$			16175.9i			1.58572i	−0.609405	+	0.792859i	$0.708592\pi$
$102$	5257.60	+	5257.60i	0.505344	+	0.505344i
$103$	7221.94			0.680737			0.340369	−	0.940292i	$-0.389448\pi$
$103$	7221.94			0.680737			0.340369	+	0.940292i	$0.389448\pi$
$104$	−1528.06	+	10155.0i	−0.141278	+	0.938889i
$105$	−9943.28	+	9811.84i	−0.901885	+	0.889963i
$106$	16075.3	+	16075.3i	1.43070	+	1.43070i
$107$			8593.86i			0.750621i	0.926899	+	0.375311i	$0.122464\pi$
$107$			8593.86i			0.750621i	−0.926899	+	0.375311i	$0.877536\pi$
$108$	−776.752			−0.0665940
$109$	−15463.5	−	15463.5i	−1.30153	−	1.30153i	−0.927359	−	0.374174i	$-0.877926\pi$
$109$	−15463.5	−	15463.5i	−1.30153	−	1.30153i	−0.374174	−	0.927359i	$-0.622074\pi$
$110$	117.435	−	17649.9i	0.00970539	−	1.45867i
$111$	14920.9	−	14920.9i	1.21102	−	1.21102i
$112$	−7748.83	−	7748.83i	−0.617732	−	0.617732i
$113$			2556.86i			0.200240i	0.994975	+	0.100120i	$0.0319226\pi$
$113$			2556.86i			0.200240i	−0.994975	+	0.100120i	$0.968077\pi$
$114$		−	7999.23i		−	0.615515i
$115$	−16915.1	−	112.546i	−1.27903	−	0.00851013i
$116$			381.333i			0.0283393i
$117$	−11920.9	−	16143.9i	−0.870835	−	1.17933i
$118$		−	27612.7i		−	1.98310i
$119$	−3520.22	−	3520.22i	−0.248586	−	0.248586i
$120$	15282.4	−	15080.4i	1.06128	−	1.04725i
$121$		−	13913.7i		−	0.950325i
$122$	−14516.6	+	14516.6i	−0.975319	+	0.975319i
$123$	610.470	−	610.470i	0.0403510	−	0.0403510i
$124$	842.851	−	842.851i	0.0548160	−	0.0548160i
$125$	−15621.9	−	311.862i	−0.999801	−	0.0199592i
$126$	19615.0			1.23551
$127$	10842.0			0.672205			0.336102	−	0.941825i	$-0.390891\pi$
$127$	10842.0			0.672205			0.336102	+	0.941825i	$0.390891\pi$
$128$	12910.6	+	12910.6i	0.787999	+	0.787999i
$129$		−	1007.38i		−	0.0605362i
$130$	−17437.8	−	2742.71i	−1.03183	−	0.162290i
$131$	−15516.4			−0.904165			−0.452082	−	0.891976i	$-0.649319\pi$
$131$	−15516.4			−0.904165			−0.452082	+	0.891976i	$0.649319\pi$
$132$	−2458.84	+	2458.84i	−0.141118	+	0.141118i
$133$			5355.88i			0.302780i
$134$			33137.7i			1.84550i
$135$	−88.7367	+	13336.7i	−0.00486896	+	0.731778i
$136$	5410.42	+	5410.42i	0.292519	+	0.292519i
$137$	5470.30	+	5470.30i	0.291454	+	0.291454i	0.837654	−	0.546201i	$-0.183926\pi$
$137$	5470.30	+	5470.30i	0.291454	+	0.291454i	−0.546201	+	0.837654i	$0.683926\pi$
$138$	28251.5	+	28251.5i	1.48349	+	1.48349i
$139$	19155.3			0.991424			0.495712	−	0.868487i	$-0.334907\pi$
$139$	19155.3			0.991424			0.495712	+	0.868487i	$0.334907\pi$
$140$	1024.37	−	1010.83i	0.0522637	−	0.0515729i
$141$	−21090.7	+	21090.7i	−1.06085	+	1.06085i
$142$	−1820.01			−0.0902601
$143$	−28239.9	−	4249.37i	−1.38099	−	0.207803i
$144$	−32913.7			−1.58727
$145$	6547.40	+	43.5638i	0.311410	+	0.00207200i
$146$	−9239.60			−0.433458
$147$	11842.0			0.548014
$148$	−1537.17	+	1537.17i	−0.0701777	+	0.0701777i
$149$	22559.7	+	22559.7i	1.01616	+	1.01616i	0.999867	+	0.0162892i	$0.00518524\pi$
$149$	22559.7	+	22559.7i	1.01616	+	1.01616i	0.0162892	+	0.999867i	$0.494815\pi$
$150$	25746.6	+	26441.1i	1.14429	+	1.17516i
$151$	14307.3	−	14307.3i	0.627486	−	0.627486i	−0.319949	−	0.947435i	$-0.603666\pi$
$151$	14307.3	−	14307.3i	0.627486	−	0.627486i	0.947435	+	0.319949i	$0.103666\pi$
$152$		−	8231.74i		−	0.356291i
$153$	−14952.4			−0.638746
$154$	19737.5	−	19737.5i	0.832242	−	0.832242i
$155$	−14375.3	−	14567.8i	−0.598345	−	0.606361i
$156$	2065.82	+	2797.64i	0.0848874	+	0.114959i
$157$		−	1583.85i		−	0.0642561i	−0.999484	−	0.0321281i	$-0.989772\pi$
$157$		−	1583.85i		−	0.0642561i	0.999484	−	0.0321281i	$-0.0102284\pi$
$158$	16026.0	−	16026.0i	0.641963	−	0.641963i
$159$	−76902.6			−3.04191
$160$	−3306.43	+	3262.73i	−0.129158	+	0.127450i
$161$	−18915.8	−	18915.8i	−0.729748	−	0.729748i
$162$	−6141.25	+	6141.25i	−0.234006	+	0.234006i
$163$	−20438.9	−	20438.9i	−0.769275	−	0.769275i	0.208704	−	0.977979i	$-0.433076\pi$
$163$	−20438.9	−	20438.9i	−0.769275	−	0.769275i	−0.977979	+	0.208704i	$0.933076\pi$
$164$	−62.8914	+	62.8914i	−0.00233832	+	0.00233832i
$165$	41936.7	+	42498.5i	1.54038	+	1.56101i
$166$		−	18117.2i		−	0.657470i
$167$	−1867.53	−	1867.53i	−0.0669629	−	0.0669629i	0.672832	−	0.739795i	$-0.265078\pi$
$167$	−1867.53	−	1867.53i	−0.0669629	−	0.0669629i	−0.739795	+	0.672832i	$0.765078\pi$
$168$	33954.0			1.20302
$169$	−8405.05	+	27296.3i	−0.294284	+	0.955718i
$170$	−9361.78	+	9238.02i	−0.323937	+	0.319655i
$171$	11374.7	+	11374.7i	0.389000	+	0.389000i
$172$			103.782i			0.00350804i
$173$	3599.35			0.120263			0.0601314	−	0.998190i	$-0.480848\pi$
$173$	3599.35			0.120263			0.0601314	+	0.998190i	$0.480848\pi$
$174$	−10935.4	−	10935.4i	−0.361191	−	0.361191i
$175$	−17238.6	−	17703.6i	−0.562895	−	0.578078i
$176$	−33119.2	+	33119.2i	−1.06919	+	1.06919i
$177$	66048.2	+	66048.2i	2.10821	+	2.10821i
$178$		−	33935.7i		−	1.07107i
$179$		−	4205.92i		−	0.131267i	−0.997844	−	0.0656334i	$-0.979093\pi$
$179$		−	4205.92i		−	0.131267i	0.997844	−	0.0656334i	$-0.0209068\pi$
$180$	28.7590	−	4322.33i	0.000887624	−	0.133405i
$181$		−	44052.0i		−	1.34465i	−0.740258	−	0.672323i	$-0.765297\pi$
$181$		−	44052.0i		−	1.34465i	0.740258	−	0.672323i	$-0.234703\pi$
$182$	−16582.7	−	22457.1i	−0.500624	−	0.677971i
$183$		−	69446.2i		−	2.07370i
$184$	29072.7	+	29072.7i	0.858717	+	0.858717i
$185$	26217.3	+	26568.5i	0.766027	+	0.776289i
$186$			48340.5i			1.39729i
$187$	−15045.8	+	15045.8i	−0.430260	+	0.430260i
$188$	2172.79	−	2172.79i	0.0614754	−	0.0614754i
$189$	−14914.1	+	14914.1i	−0.417515	+	0.417515i
$190$	14149.4	+	94.1447i	0.391951	+	0.00260789i
$191$	−1830.18			−0.0501681			−0.0250841	−	0.999685i	$-0.507985\pi$
$191$	−1830.18			−0.0501681			−0.0250841	+	0.999685i	$0.507985\pi$
$192$	−51706.3			−1.40262
$193$	15266.8	+	15266.8i	0.409859	+	0.409859i	0.881689	−	0.471830i	$-0.156407\pi$
$193$	15266.8	+	15266.8i	0.409859	+	0.409859i	−0.471830	+	0.881689i	$0.656407\pi$
$194$		−	53231.8i		−	1.41438i
$195$	48270.9	−	35150.0i	1.26945	−	0.924392i
$196$	−1219.98			−0.0317571
$197$	−17720.7	+	17720.7i	−0.456613	+	0.456613i	−0.897542	−	0.440929i	$-0.854649\pi$
$197$	−17720.7	+	17720.7i	−0.456613	+	0.456613i	0.440929	+	0.897542i	$0.354649\pi$
$198$		−	83836.3i		−	2.13846i
$199$			3056.82i			0.0771905i	0.999255	+	0.0385952i	$0.0122883\pi$
$199$			3056.82i			0.0771905i	−0.999255	+	0.0385952i	$0.987712\pi$
$200$	26495.0	+	27209.7i	0.662375	+	0.680243i
$201$	−79263.8	−	79263.8i	−1.96193	−	1.96193i
$202$	47788.8	+	47788.8i	1.17118	+	1.17118i
$203$	7321.80	+	7321.80i	0.177675	+	0.177675i
$204$	2591.17			0.0622638
$205$	1072.64	+	1087.01i	0.0255240	+	0.0258659i
$206$	21335.9	−	21335.9i	0.502779	−	0.502779i
$207$	−80346.2			−1.87510
$208$	27825.5	+	37682.8i	0.643156	+	0.870996i
$209$	22891.5			0.524061
$210$	−388.324	+	58363.0i	−0.00880553	+	1.32342i
$211$	56735.3			1.27435			0.637175	−	0.770719i	$-0.280103\pi$
$211$	56735.3			1.27435			0.637175	+	0.770719i	$0.280103\pi$
$212$	7922.60			0.176277
$213$	4353.36	−	4353.36i	0.0959545	−	0.0959545i
$214$	25389.0	+	25389.0i	0.554394	+	0.554394i
$215$	1781.91	+	11.8561i	0.0385486	+	0.000256487i
$216$	22922.3	−	22922.3i	0.491303	−	0.491303i
$217$		−	32366.4i		−	0.687345i
$218$	−91368.3			−1.92257
$219$	22100.7	−	22100.7i	0.460805	−	0.460805i
$220$	−4320.37	−	4378.25i	−0.0892639	−	0.0904597i
$221$	12640.9	+	17118.9i	0.258817	+	0.350503i
$222$		−	88162.5i		−	1.78887i
$223$	17094.2	−	17094.2i	0.343747	−	0.343747i	−0.514027	−	0.857774i	$-0.671847\pi$
$223$	17094.2	−	17094.2i	0.343747	−	0.343747i	0.857774	+	0.514027i	$0.171847\pi$
$224$	−7346.14			−0.146408
$225$	−74210.0	−	987.571i	−1.46588	−	0.0195076i
$226$	7553.78	+	7553.78i	0.147893	+	0.147893i
$227$	50519.8	−	50519.8i	0.980416	−	0.980416i	−0.0193961	−	0.999812i	$-0.506174\pi$
$227$	50519.8	−	50519.8i	0.980416	−	0.980416i	0.999812	+	0.0193961i	$0.00617435\pi$
$228$	−1971.18	−	1971.18i	−0.0379190	−	0.0379190i
$229$	677.316	−	677.316i	0.0129158	−	0.0129158i	−0.700619	−	0.713535i	$-0.747093\pi$
$229$	677.316	−	677.316i	0.0129158	−	0.0129158i	0.713535	+	0.700619i	$0.247093\pi$
$230$	−50305.2	+	49640.2i	−0.950948	+	0.938377i
$231$			94422.0i			1.76949i
$232$	−11253.3	−	11253.3i	−0.209075	−	0.209075i
$233$	97142.5			1.78936			0.894679	−	0.446709i	$-0.147404\pi$
$233$	97142.5			1.78936			0.894679	+	0.446709i	$0.147404\pi$
$234$	−82912.2	−	12476.1i	−1.51421	−	0.227849i
$235$	−37058.0	−	37554.4i	−0.671036	−	0.680026i
$236$	−6804.37	−	6804.37i	−0.122170	−	0.122170i
$237$			76666.6i			1.36493i
$238$	−20799.7			−0.367201
$239$	15238.5	+	15238.5i	0.266775	+	0.266775i	0.827799	−	0.561024i	$-0.189593\pi$
$239$	15238.5	+	15238.5i	0.266775	+	0.266775i	−0.561024	+	0.827799i	$0.689593\pi$
$240$	651.603	−	97932.3i	0.0113125	−	1.70021i
$241$	811.899	−	811.899i	0.0139787	−	0.0139787i	−0.700083	−	0.714062i	$-0.746854\pi$
$241$	811.899	−	811.899i	0.0139787	−	0.0139787i	0.714062	+	0.700083i	$0.246854\pi$
$242$	−41105.5	−	41105.5i	−0.701891	−	0.701891i
$243$		−	72590.8i		−	1.22933i
$244$			7154.43i			0.120170i
$245$	−139.371	+	20946.8i	−0.00232189	+	0.348967i
$246$		−	3607.05i		−	0.0596049i
$247$	3406.60	−	22639.2i	0.0558377	−	0.371079i
$248$			49745.7i			0.808820i
$249$	43335.5	+	43335.5i	0.698949	+	0.698949i
$250$	−47073.4	+	45230.7i	−0.753174	+	0.723691i
$251$		−	2512.83i		−	0.0398856i	−0.999801	−	0.0199428i	$-0.993652\pi$
$251$		−	2512.83i		−	0.0398856i	0.999801	−	0.0199428i	$-0.00634841\pi$
$252$	4833.56	−	4833.56i	0.0761142	−	0.0761142i
$253$	−80847.8	+	80847.8i	−1.26307	+	1.26307i
$254$	32030.7	−	32030.7i	0.496477	−	0.496477i
$255$	296.017	−	44489.8i	0.00455236	−	0.684195i
$256$	17747.9			0.270811
$257$	51617.0			0.781495			0.390747	−	0.920498i	$-0.372217\pi$
$257$	51617.0			0.781495			0.390747	+	0.920498i	$0.372217\pi$
$258$	−2976.13	−	2976.13i	−0.0447108	−	0.0447108i
$259$			59029.1i			0.879968i
$260$	−4972.92	+	3621.20i	−0.0735639	+	0.0535680i
$261$	31099.9			0.456539
$262$	−45840.3	+	45840.3i	−0.667798	+	0.667798i
$263$			67114.7i			0.970300i	0.874431	+	0.485150i	$0.161235\pi$
$263$			67114.7i			0.970300i	−0.874431	+	0.485150i	$0.838765\pi$
$264$		−	145122.i		−	2.08222i
$265$	905.083	−	136029.i	0.0128883	−	1.93705i
$266$	15823.0	+	15823.0i	0.223627	+	0.223627i
$267$	81172.4	+	81172.4i	1.13864	+	1.13864i
$268$	8165.85	+	8165.85i	0.113693	+	0.113693i
$269$	40295.2			0.556863			0.278431	−	0.960456i	$-0.410185\pi$
$269$	40295.2			0.556863			0.278431	+	0.960456i	$0.410185\pi$
$270$	39138.6	+	39662.9i	0.536880	+	0.544073i
$271$	52437.1	−	52437.1i	0.714003	−	0.714003i	−0.253367	−	0.967370i	$-0.581538\pi$
$271$	52437.1	−	52437.1i	0.714003	−	0.714003i	0.967370	+	0.253367i	$0.0815381\pi$
$272$	34901.7			0.471746
$273$	93381.2	+	14051.4i	1.25295	+	0.188536i
$274$	32322.0			0.430524
$275$	−75667.1	+	73679.6i	−1.00056	+	0.974275i
$276$	13923.6			0.182782
$277$	−39225.4			−0.511220			−0.255610	−	0.966780i	$-0.582276\pi$
$277$	−39225.4			−0.511220			−0.255610	+	0.966780i	$0.582276\pi$
$278$	56590.9	−	56590.9i	0.732246	−	0.732246i
$279$	−68739.3	−	68739.3i	−0.883073	−	0.883073i
$280$	−399.611	+	60059.4i	−0.00509708	+	0.766064i
$281$	−65168.9	+	65168.9i	−0.825330	+	0.825330i	−0.986867	−	0.161537i	$-0.948355\pi$
$281$	−65168.9	+	65168.9i	−0.825330	+	0.825330i	0.161537	+	0.986867i	$0.448355\pi$
$282$			124617.i			1.56704i
$283$	56307.6			0.703062			0.351531	−	0.936176i	$-0.385661\pi$
$283$	56307.6			0.703062			0.351531	+	0.936176i	$0.385661\pi$
$284$	−448.489	+	448.489i	−0.00556051	+	0.00556051i
$285$	−34069.9	+	33619.5i	−0.419451	+	0.413906i
$286$	−95983.8	+	70875.8i	−1.17345	+	0.866495i
$287$			2415.10i			0.0293205i
$288$	−15601.6	+	15601.6i	−0.188099	+	0.188099i
$289$	−67665.5			−0.810161
$290$	19471.8	−	19214.4i	0.231532	−	0.228471i
$291$	127328.	+	127328.i	1.50362	+	1.50362i
$292$	−2276.84	+	2276.84i	−0.0267034	+	0.0267034i
$293$	−95953.5	−	95953.5i	−1.11770	−	1.11770i	−0.992078	−	0.125623i	$-0.959907\pi$
$293$	−95953.5	−	95953.5i	−1.11770	−	1.11770i	−0.125623	−	0.992078i	$-0.540093\pi$
$294$	34985.2	−	34985.2i	0.404752	−	0.404752i
$295$	−117607.	+	116052.i	−1.35141	+	1.33355i
$296$		−	90725.1i		−	1.03549i
$297$	63744.1	+	63744.1i	0.722649	+	0.722649i
$298$	133297.			1.50103
$299$	67925.2	+	91988.0i	0.759782	+	1.02894i
$300$	12860.2	+	171.141i	0.142891	+	0.00190156i
$301$	1992.67	+	1992.67i	0.0219939	+	0.0219939i
$302$		−	84536.7i		−	0.926897i
$303$	−228617.			−2.49014
$304$	−26550.8	−	26550.8i	−0.287296	−	0.287296i
$305$	122840.	+	817.327i	1.32050	+	0.00878610i
$306$	−44174.2	+	44174.2i	−0.471765	+	0.471765i
$307$	−42019.3	−	42019.3i	−0.445833	−	0.445833i	0.448134	−	0.893967i	$-0.352089\pi$
$307$	−42019.3	−	42019.3i	−0.445833	−	0.445833i	−0.893967	+	0.448134i	$0.852089\pi$
$308$		−	9727.47i		−	0.102541i
$309$			102069.i			1.06900i
$310$	−85507.1	−	568.930i	−0.889772	−	0.00592019i
$311$		−	83843.5i		−	0.866860i	−0.901187	−	0.433430i	$-0.857303\pi$
$311$		−	83843.5i		−	0.866860i	0.901187	−	0.433430i	$-0.142697\pi$
$312$	−143523.	−	21596.4i	−1.47439	−	0.221856i
$313$		−	109679.i		−	1.11953i	−0.828652	−	0.559764i	$-0.810892\pi$
$313$		−	109679.i		−	1.11953i	0.828652	−	0.559764i	$-0.189108\pi$
$314$	−4679.20	−	4679.20i	−0.0474583	−	0.0474583i
$315$	−82438.8	−	83543.2i	−0.830827	−	0.841957i
$316$		−	7898.28i		−	0.0790967i
$317$	3015.42	−	3015.42i	0.0300075	−	0.0300075i	−0.691944	−	0.721951i	$-0.743245\pi$
$317$	3015.42	−	3015.42i	0.0300075	−	0.0300075i	0.721951	+	0.691944i	$0.243245\pi$
$318$	−227195.	+	227195.i	−2.24670	+	2.24670i
$319$	31294.1	−	31294.1i	0.307525	−	0.307525i
$320$	608.543	−	91460.7i	0.00594280	−	0.893170i
$321$	−121458.			−1.17874
$322$	−111767.			−1.07795
$323$	−12061.8	−	12061.8i	−0.115613	−	0.115613i
$324$			3026.67i			0.0288320i
$325$	61607.0	+	85797.6i	0.583261	+	0.812285i
$326$	−120766.			−1.13634
$327$	218548.	−	218548.i	2.04386	−	2.04386i
$328$		−	3711.90i		−	0.0345023i
$329$		−	83437.3i		−	0.770848i
$330$	249449.	+	1659.73i	2.29062	+	0.0152409i
$331$	55649.0	+	55649.0i	0.507927	+	0.507927i	0.913890	−	0.405963i	$-0.133064\pi$
$331$	55649.0	+	55649.0i	0.507927	+	0.507927i	−0.405963	+	0.913890i	$0.633064\pi$
$332$	−4464.48	−	4464.48i	−0.0405037	−	0.0405037i
$333$	125365.	+	125365.i	1.13055	+	1.13055i
$334$	−11034.6			−0.0989150
$335$	141139.	−	139273.i	1.25764	−	1.24101i
$336$	109515.	−	109515.i	0.970056	−	0.970056i
$337$	25081.6			0.220849			0.110425	−	0.993885i	$-0.464779\pi$
$337$	25081.6			0.220849			0.110425	+	0.993885i	$0.464779\pi$
$338$	55810.7	+	105473.i	0.488522	+	0.923227i
$339$	−36136.5			−0.314447
$340$	−30.4961	+	4583.39i	−0.000263807	+	0.0396487i
$341$	−138337.			−1.18968
$342$	67209.3			0.574615
$343$	−90547.4	+	90547.4i	−0.769640	+	0.769640i
$344$	−3062.64	−	3062.64i	−0.0258809	−	0.0258809i
$345$	1590.64	−	239064.i	0.0133639	−	2.00852i
$346$	10633.6	−	10633.6i	0.0888237	−	0.0888237i
$347$		−	153831.i		−	1.27757i	−0.769385	−	0.638785i	$-0.779437\pi$
$347$		−	153831.i		−	1.27757i	0.769385	−	0.638785i	$-0.220563\pi$
$348$	−5389.44			−0.0445026
$349$	−131579.	+	131579.i	−1.08028	+	1.08028i	−0.0837961	+	0.996483i	$0.526704\pi$
$349$	−131579.	+	131579.i	−1.08028	+	1.08028i	−0.996483	+	0.0837961i	$0.973296\pi$
$350$	−103231.	−	1373.77i	−0.842700	−	0.0112145i
$351$	72527.5	−	53555.4i	0.588693	−	0.434699i
$352$			31398.1i			0.253407i
$353$	−127997.	+	127997.i	−1.02719	+	1.02719i	−0.0275724	+	0.999620i	$0.508778\pi$
$353$	−127997.	+	127997.i	−1.02719	+	1.02719i	−0.999620	+	0.0275724i	$0.991222\pi$
$354$	390255.			3.11417
$355$	7649.20	+	7751.67i	0.0606959	+	0.0615090i
$356$	−8362.48	−	8362.48i	−0.0659835	−	0.0659835i
$357$	49751.9	−	49751.9i	0.390367	−	0.390367i
$358$	−12425.6	−	12425.6i	−0.0969510	−	0.0969510i
$359$	120810.	−	120810.i	0.937380	−	0.937380i	−0.0607717	−	0.998152i	$-0.519356\pi$
$359$	120810.	−	120810.i	0.937380	−	0.937380i	0.998152	+	0.0607717i	$0.0193562\pi$
$360$	126705.	+	128402.i	0.977660	+	0.990757i
$361$		−	111969.i		−	0.859182i
$362$	−130144.	−	130144.i	−0.993129	−	0.993129i
$363$	196645.			1.49234
$364$	−9620.24	−	1447.59i	−0.0726078	−	0.0109256i
$365$	38832.6	+	39352.8i	0.291481	+	0.295386i
$366$	−205166.	−	205166.i	−1.53159	−	1.53159i
$367$			165347.i			1.22762i	0.789455	+	0.613809i	$0.210363\pi$
$367$			165347.i			1.22762i	−0.789455	+	0.613809i	$0.789637\pi$
$368$	187543.			1.38486
$369$	5129.15	+	5129.15i	0.0376698	+	0.0376698i
$370$	155946.	+	1037.60i	1.13912	+	0.00757928i
$371$	152118.	−	152118.i	1.10518	−	1.10518i
$372$	11912.2	+	11912.2i	0.0860804	+	0.0860804i
$373$			80113.0i			0.575818i	0.957658	+	0.287909i	$0.0929601\pi$
$373$			80113.0i			0.575818i	−0.957658	+	0.287909i	$0.907040\pi$
$374$			88900.0i			0.635563i
$375$	4407.60	−	220787.i	0.0313429	−	1.57004i
$376$			128239.i			0.907081i
$377$	−26292.1	−	35606.1i	−0.184987	−	0.250520i
$378$			88121.9i			0.616737i
$379$	−140511.	−	140511.i	−0.978207	−	0.978207i	0.0215603	−	0.999768i	$-0.493137\pi$
$379$	−140511.	−	140511.i	−0.978207	−	0.978207i	−0.999768	+	0.0215603i	$0.993137\pi$
$380$	3509.92	−	3463.53i	0.0243070	−	0.0239856i
$381$			153232.i			1.05560i
$382$	−5406.95	+	5406.95i	−0.0370532	+	0.0370532i
$383$	−22317.4	+	22317.4i	−0.152141	+	0.152141i	−0.779074	−	0.626933i	$-0.784310\pi$
$383$	−22317.4	+	22317.4i	−0.152141	+	0.152141i	0.626933	+	0.779074i	$0.284310\pi$
$384$	−182467.	+	182467.i	−1.23744	+	1.23744i
$385$	−167018.	−	1111.27i	−1.12679	−	0.00749720i
$386$	90206.2			0.605427
$387$	8464.00			0.0565137
$388$	−13117.5	−	13117.5i	−0.0871337	−	0.0871337i
$389$			65211.2i			0.430946i	0.976510	+	0.215473i	$0.0691294\pi$
$389$			65211.2i			0.430946i	−0.976510	+	0.215473i	$0.930871\pi$
$390$	38763.2	−	246452.i	0.254853	−	1.62033i
$391$	85199.1			0.557290
$392$	36002.1	−	36002.1i	0.234291	−	0.234291i
$393$		−	219295.i		−	1.41986i
$394$			104705.i			0.674491i
$395$	−135612.	−	902.306i	−0.869166	−	0.00578308i
$396$	−20659.1	−	20659.1i	−0.131741	−	0.131741i
$397$	80244.0	+	80244.0i	0.509133	+	0.509133i	0.914260	−	0.405127i	$-0.132773\pi$
$397$	80244.0	+	80244.0i	0.509133	+	0.509133i	−0.405127	+	0.914260i	$0.632773\pi$
$398$	9030.83	+	9030.83i	0.0570114	+	0.0570114i
$399$	−75695.6			−0.475472
$400$	173220.	+	2305.17i	1.08262	+	0.0144073i
$401$	−194563.	+	194563.i	−1.20996	+	1.20996i	−0.238926	+	0.971038i	$0.576795\pi$
$401$	−194563.	+	194563.i	−1.20996	+	1.20996i	−0.971038	+	0.238926i	$0.923205\pi$
$402$	−468341.			−2.89808
$403$	−20586.6	+	136812.i	−0.126758	+	0.842392i
$404$	23552.4			0.144302
$405$	51967.2	+	345.769i	0.316825	+	0.00210803i
$406$	43261.9			0.262454
$407$	252296.			1.52308
$408$	−76466.4	+	76466.4i	−0.459357	+	0.459357i
$409$	−141917.	−	141917.i	−0.848374	−	0.848374i	0.141556	−	0.989930i	$-0.454789\pi$
$409$	−141917.	−	141917.i	−0.848374	−	0.848374i	−0.989930	+	0.141556i	$0.954789\pi$
$410$	6380.32	+	42.4521i	0.0379555	+	0.000252541i
$411$	−77312.7	+	77312.7i	−0.457685	+	0.457685i
$412$		−	10515.3i		−	0.0619478i
$413$	−261295.			−1.53190
$414$	−237368.	+	237368.i	−1.38491	+	1.38491i
$415$	−77164.0	+	76144.0i	−0.448042	+	0.442119i
$416$	31052.0	+	4672.51i	0.179433	+	0.0270000i
$417$			270725.i			1.55688i
$418$	67628.9	−	67628.9i	0.387061	−	0.387061i
$419$	110475.			0.629267			0.314634	−	0.949213i	$-0.398118\pi$
$419$	110475.			0.629267			0.314634	+	0.949213i	$0.398118\pi$
$420$	14286.2	+	14477.6i	0.0809875	+	0.0820725i
$421$	−99477.0	−	99477.0i	−0.561253	−	0.561253i	0.368411	−	0.929663i	$-0.379902\pi$
$421$	−99477.0	−	99477.0i	−0.561253	−	0.561253i	−0.929663	+	0.368411i	$0.879902\pi$
$422$	167614.	−	167614.i	0.941209	−	0.941209i
$423$	−177203.	−	177203.i	−0.990355	−	0.990355i
$424$	−233799.	+	233799.i	−1.30050	+	1.30050i
$425$	78692.2	+	1047.22i	0.435666	+	0.00579776i
$426$		−	25722.4i		−	0.141740i
$427$	137369.	+	137369.i	0.753413	+	0.753413i
$428$	12512.8			0.0683073
$429$	60057.1	−	399120.i	0.326324	−	2.16865i
$430$	5299.35	−	5229.30i	0.0286607	−	0.0282818i
$431$	230154.	+	230154.i	1.23898	+	1.23898i	0.960418	+	0.278564i	$0.0898583\pi$
$431$	230154.	+	230154.i	1.23898	+	1.23898i	0.278564	+	0.960418i	$0.410142\pi$
$432$		−	147867.i		−	0.792328i
$433$	−112475.			−0.599902			−0.299951	−	0.953955i	$-0.596970\pi$
$433$	−112475.			−0.599902			−0.299951	+	0.953955i	$0.596970\pi$
$434$	−95620.7	−	95620.7i	−0.507659	−	0.507659i
$435$	−615.694	+	92535.5i	−0.00325377	+	0.489023i
$436$	−22515.1	+	22515.1i	−0.118441	+	0.118441i
$437$	−64813.5	−	64813.5i	−0.339393	−	0.339393i
$438$		−	130585.i		−	0.680682i
$439$			180764.i			0.937955i	0.883210	+	0.468978i	$0.155377\pi$
$439$			180764.i			0.937955i	−0.883210	+	0.468978i	$0.844623\pi$
$440$	256700.	+	1707.98i	1.32593	+	0.00882219i
$441$			99496.5i			0.511600i
$442$	87920.0	+	13229.7i	0.450032	+	0.0677180i
$443$			213619.i			1.08851i	0.838919	+	0.544256i	$0.183188\pi$
$443$			213619.i			1.08851i	−0.838919	+	0.544256i	$0.816812\pi$
$444$	−21725.1	−	21725.1i	−0.110204	−	0.110204i
$445$	−144537.	+	142626.i	−0.729893	+	0.720245i
$446$		−	101004.i		−	0.507770i
$447$	−318840.	+	318840.i	−1.59572	+	1.59572i
$448$	102278.	−	102278.i	0.509598	−	0.509598i
$449$	−127032.	+	127032.i	−0.630116	+	0.630116i	−0.948097	−	0.317981i	$-0.896995\pi$
$449$	−127032.	+	127032.i	−0.630116	+	0.630116i	0.317981	+	0.948097i	$0.396995\pi$
$450$	−222158.	+	216322.i	−1.09708	+	1.06826i
$451$	10322.4			0.0507488
$452$	3722.83			0.0182220
$453$	202208.	+	202208.i	0.985373	+	0.985373i
$454$		−	298504.i		−	1.44823i
$455$	−25953.9	+	165012.i	−0.125366	+	0.797062i
$456$	116341.			0.559502
$457$	5512.01	−	5512.01i	0.0263923	−	0.0263923i	−0.693787	−	0.720180i	$-0.744059\pi$
$457$	5512.01	−	5512.01i	0.0263923	−	0.0263923i	0.720180	+	0.693787i	$0.244059\pi$
$458$		−	4002.02i		−	0.0190787i
$459$		−	67174.8i		−	0.318846i
$460$	−163.869	+	24628.7i	−0.000774430	+	0.116393i
$461$	175156.	+	175156.i	0.824183	+	0.824183i	0.986705	−	0.162522i	$-0.0519629\pi$
$461$	175156.	+	175156.i	0.824183	+	0.824183i	−0.162522	+	0.986705i	$0.551963\pi$
$462$	278953.	+	278953.i	1.30691	+	1.30691i
$463$	68826.7	+	68826.7i	0.321066	+	0.321066i	0.849176	−	0.528110i	$-0.177099\pi$
$463$	68826.7	+	68826.7i	0.321066	+	0.321066i	−0.528110	+	0.849176i	$0.677099\pi$
$464$	−72592.9			−0.337177
$465$	205890.	−	203168.i	0.952201	−	0.939613i
$466$	286990.	−	286990.i	1.32158	−	1.32158i
$467$	−132077.			−0.605612			−0.302806	−	0.953052i	$-0.597923\pi$
$467$	−132077.			−0.605612			−0.302806	+	0.953052i	$0.597923\pi$
$468$	−23505.7	+	17357.0i	−0.107320	+	0.0792469i
$469$	313578.			1.42561
$470$	−220429.	−	1466.65i	−0.997867	−	0.00663941i
$471$	22384.8			0.100905
$472$	401599.			1.80264
$473$	8516.85	−	8516.85i	0.0380677	−	0.0380677i
$474$	226498.	+	226498.i	1.00811	+	1.00811i
$475$	−59066.9	−	60660.2i	−0.261792	−	0.268854i
$476$	−5125.50	+	5125.50i	−0.0226216	+	0.0226216i
$477$		−	646133.i		−	2.83978i
$478$	90038.6			0.394070
$479$	−76889.9	+	76889.9i	−0.335118	+	0.335118i	−0.854526	−	0.519408i	$-0.826152\pi$
$479$	−76889.9	+	76889.9i	−0.335118	+	0.335118i	0.519408	+	0.854526i	$0.326152\pi$
$480$	−46112.7	−	46730.4i	−0.200142	−	0.202823i
$481$	37545.4	−	249515.i	0.162281	−	1.07847i
$482$		−	4797.22i		−	0.0206488i
$483$	267340.	−	267340.i	1.14596	−	1.14596i
$484$	−20258.6			−0.0864805
$485$	−226722.	+	223725.i	−0.963852	+	0.951110i
$486$	−214456.	−	214456.i	−0.907960	−	0.907960i
$487$	−87159.6	+	87159.6i	−0.367500	+	0.367500i	−0.866565	−	0.499065i	$-0.833677\pi$
$487$	−87159.6	+	87159.6i	−0.367500	+	0.367500i	0.499065	+	0.866565i	$0.333677\pi$
$488$	−211130.	−	211130.i	−0.886564	−	0.886564i
$489$	288866.	−	288866.i	1.20803	−	1.20803i
$490$	61471.7	+	62295.2i	0.256026	+	0.259455i
$491$		−	145138.i		−	0.602030i	−0.953619	−	0.301015i	$-0.902675\pi$
$491$		−	145138.i		−	0.602030i	0.953619	−	0.301015i	$-0.0973255\pi$
$492$	−888.854	−	888.854i	−0.00367198	−	0.00367198i
$493$	−32978.3			−0.135686
$494$	−56819.2	−	76947.6i	−0.232831	−	0.315312i
$495$	−357071.	+	352351.i	−1.45729	+	1.43802i
$496$	160450.	+	160450.i	0.652194	+	0.652194i
$497$			17222.4i			0.0697240i
$498$	256054.			1.03246
$499$	−196741.	−	196741.i	−0.790122	−	0.790122i	0.191392	−	0.981514i	$-0.438700\pi$
$499$	−196741.	−	196741.i	−0.790122	−	0.790122i	−0.981514	+	0.191392i	$0.938700\pi$
$500$	−454.077	+	22745.7i	−0.00181631	+	0.0909829i
$501$	26394.1	−	26394.1i	0.105155	−	0.105155i
$502$	−7423.71	−	7423.71i	−0.0294587	−	0.0294587i
$503$		−	341498.i		−	1.34975i	−0.737933	−	0.674873i	$-0.764198\pi$
$503$		−	341498.i		−	1.34975i	0.737933	−	0.674873i	$-0.235802\pi$
$504$			285280.i			1.12308i
$505$	2690.64	−	404389.i	0.0105505	−	1.58568i
$506$			477701.i			1.86576i
$507$	−385783.	−	118790.i	−1.50081	−	0.462130i
$508$		−	15786.1i		−	0.0611713i
$509$	−145299.	−	145299.i	−0.560825	−	0.560825i	0.368717	−	0.929542i	$-0.379797\pi$
$509$	−145299.	−	145299.i	−0.560825	−	0.560825i	−0.929542	+	0.368717i	$0.879797\pi$
$510$	−130563.	−	132312.i	−0.501970	−	0.508695i
$511$			87433.0i			0.334837i
$512$	−154136.	+	154136.i	−0.587984	+	0.587984i
$513$	−51101.9	+	51101.9i	−0.194179	+	0.194179i
$514$	152493.	−	152493.i	0.577197	−	0.577197i
$515$	−180545.	−	1201.27i	−0.680722	−	0.00452925i
$516$	−1466.77			−0.00550886
$517$	−356619.			−1.33421
$518$	174391.	+	174391.i	0.649927	+	0.649927i
$519$			50870.2i			0.188855i
$520$	39889.9	−	253616.i	0.147522	−	0.937928i
$521$	73730.0			0.271625			0.135812	−	0.990735i	$-0.456636\pi$
$521$	73730.0			0.271625			0.135812	+	0.990735i	$0.456636\pi$
$522$	91879.1	−	91879.1i	0.337191	−	0.337191i
$523$			139617.i			0.510428i	0.966885	+	0.255214i	$0.0821459\pi$
$523$			139617.i			0.510428i	−0.966885	+	0.255214i	$0.917854\pi$
$524$			22592.1i			0.0822799i
$525$	250209.	−	243637.i	0.907787	−	0.883943i
$526$	198278.	+	198278.i	0.716644	+	0.716644i
$527$	72891.1	+	72891.1i	0.262454	+	0.262454i
$528$	−468079.	−	468079.i	−1.67900	−	1.67900i
$529$	177973.			0.635979
$530$	−399199.	−	404547.i	−1.42114	−	1.44018i
$531$	−554935.	+	554935.i	−1.96813	+	1.96813i
$532$	7798.25			0.0275533
$533$	1536.12	−	10208.6i	0.00540718	−	0.0359344i
$534$	479619.			1.68195
$535$	1429.47	−	214842.i	0.00499422	−	0.750604i
$536$	−481955.			−1.67755
$537$	59443.0			0.206135
$538$	119045.	−	119045.i	0.411288	−	0.411288i
$539$	100118.	+	100118.i	0.344614	+	0.344614i
$540$	19418.4	+	129.202i	0.0665925	+	0.000443080i
$541$	119290.	−	119290.i	0.407576	−	0.407576i	−0.473317	−	0.880892i	$-0.656943\pi$
$541$	119290.	−	119290.i	0.407576	−	0.407576i	0.880892	+	0.473317i	$0.156943\pi$
$542$		−	309832.i		−	1.05470i
$543$	622594.			2.11157
$544$	16544.0	−	16544.0i	0.0559039	−	0.0559039i
$545$	384007.	+	389151.i	1.29284	+	1.31016i
$546$	317390.	−	234365.i	1.06465	−	0.786155i
$547$			128267.i			0.428687i	0.976758	+	0.214344i	$0.0687612\pi$
$547$			128267.i			0.428687i	−0.976758	+	0.214344i	$0.931239\pi$
$548$	7964.85	−	7964.85i	0.0265226	−	0.0265226i
$549$	583485.			1.93591
$550$	−5871.63	+	441218.i	−0.0194104	+	1.45857i
$551$	25087.6	+	25087.6i	0.0826335	+	0.0826335i
$552$	−410890.	+	410890.i	−1.34849	+	1.34849i
$553$	−151651.	−	151651.i	−0.495902	−	0.495902i
$554$	−115884.	+	115884.i	−0.377577	+	0.377577i
$555$	−375497.	+	370533.i	−1.21905	+	1.20293i
$556$		−	27890.4i		−	0.0902206i
$557$	72755.4	+	72755.4i	0.234506	+	0.234506i	0.814571	−	0.580064i	$-0.196973\pi$
$557$	72755.4	+	72755.4i	0.234506	+	0.234506i	−0.580064	+	0.814571i	$0.696973\pi$
$558$	−406156.			−1.30444
$559$	−7155.53	−	9690.40i	−0.0228991	−	0.0310112i
$560$	192427.	+	195005.i	0.613608	+	0.621828i
$561$	−212644.	−	212644.i	−0.675660	−	0.675660i
$562$			385059.i			1.21914i
$563$	218865.			0.690492			0.345246	−	0.938512i	$-0.387795\pi$
$563$	218865.			0.690492			0.345246	+	0.938512i	$0.387795\pi$
$564$	30708.4	+	30708.4i	0.0965380	+	0.0965380i
$565$	425.299	−	63920.1i	0.00133229	−	0.200235i
$566$	166351.	−	166351.i	0.519268	−	0.519268i
$567$	58113.7	+	58113.7i	0.180764	+	0.180764i
$568$		−	26470.1i		−	0.0820464i
$569$		−	346520.i		−	1.07030i	−0.844759	−	0.535148i	$-0.820256\pi$
$569$		−	346520.i		−	1.07030i	0.844759	−	0.535148i	$-0.179744\pi$
$570$	−1330.56	+	199976.i	−0.00409530	+	0.615501i
$571$		−	329098.i		−	1.00937i	−0.863302	−	0.504687i	$-0.831608\pi$
$571$		−	329098.i		−	1.00937i	0.863302	−	0.504687i	$-0.168392\pi$
$572$	−6187.15	+	41117.8i	−0.0189103	+	0.125672i
$573$		−	25866.3i		−	0.0787816i
$574$	7134.97	+	7134.97i	0.0216555	+	0.0216555i
$575$	422850.	+	5627.20i	1.27894	+	0.0170199i
$576$		−	434435.i		−	1.30942i
$577$	−68750.8	+	68750.8i	−0.206503	+	0.206503i	−0.802779	−	0.596276i	$-0.796646\pi$
$577$	−68750.8	+	68750.8i	−0.206503	+	0.206503i	0.596276	+	0.802779i	$0.296646\pi$
$578$	−199906.	+	199906.i	−0.598369	+	0.598369i
$579$	−215769.	+	215769.i	−0.643623	+	0.643623i
$580$	63.4295	−	9533.12i	0.000188554	−	0.0283386i
$581$	−171441.			−0.507881
$582$	752334.			2.22108
$583$	−650167.	−	650167.i	−1.91288	−	1.91288i
$584$		−	134381.i		−	0.394013i
$585$	295329.	+	405570.i	0.862969	+	1.18510i
$586$	−566955.			−1.65102
$587$	258864.	−	258864.i	0.751269	−	0.751269i	−0.223447	−	0.974716i	$-0.571731\pi$
$587$	258864.	−	258864.i	0.751269	−	0.751269i	0.974716	+	0.223447i	$0.0717310\pi$
$588$		−	17242.2i		−	0.0498698i
$589$		−	110901.i		−	0.319672i
$590$	−4593.00	+	690302.i	−0.0131945	+	1.98306i
$591$	−250450.	−	250450.i	−0.717044	−	0.717044i
$592$	−292626.	−	292626.i	−0.834967	−	0.834967i
$593$	−8856.45	−	8856.45i	−0.0251855	−	0.0251855i	0.694402	−	0.719587i	$-0.255669\pi$
$593$	−8856.45	−	8856.45i	−0.0251855	−	0.0251855i	−0.719587	+	0.694402i	$0.755669\pi$
$594$	376641.			1.06747
$595$	87418.1	+	88589.1i	0.246926	+	0.250234i
$596$	32847.3	−	32847.3i	0.0924713	−	0.0924713i
$597$	−43202.6			−0.121216
$598$	472435.	+	71089.1i	1.32111	+	0.198793i
$599$	−191225.			−0.532955			−0.266478	−	0.963841i	$-0.585860\pi$
$599$	−191225.			−0.532955			−0.266478	+	0.963841i	$0.585860\pi$
$600$	−384559.	+	374459.i	−1.06822	+	1.04016i
$601$	−58721.2			−0.162572			−0.0812861	−	0.996691i	$-0.525903\pi$
$601$	−58721.2			−0.162572			−0.0812861	+	0.996691i	$0.525903\pi$
$602$	11774.0			0.0324885
$603$	665972.	−	665972.i	1.83156	−	1.83156i
$604$	−20831.7	−	20831.7i	−0.0571018	−	0.0571018i
$605$	−2314.36	+	347835.i	−0.00632294	+	0.950304i
$606$	−675407.	+	675407.i	−1.83916	+	1.83916i
$607$			436131.i			1.18369i	0.806050	+	0.591847i	$0.201601\pi$
$607$			436131.i			1.18369i	−0.806050	+	0.591847i	$0.798399\pi$
$608$	−25171.0			−0.0680916
$609$	−103480.	+	103480.i	−0.279012	+	0.279012i
$610$	365323.	−	360494.i	0.981787	−	0.968808i
$611$	−53070.3	+	352688.i	−0.142157	+	0.944731i
$612$			21770.9i			0.0581265i
$613$	153456.	−	153456.i	0.408379	−	0.408379i	−0.472794	−	0.881173i	$-0.656754\pi$
$613$	153456.	−	153456.i	0.408379	−	0.408379i	0.881173	+	0.472794i	$0.156754\pi$
$614$	−248277.			−0.658566
$615$	−15363.0	+	15159.9i	−0.0406186	+	0.0400816i
$616$	287061.	+	287061.i	0.756507	+	0.756507i
$617$	384111.	−	384111.i	1.00899	−	1.00899i	0.00902908	−	0.999959i	$-0.497126\pi$
$617$	384111.	−	384111.i	1.00899	−	1.00899i	0.999959	−	0.00902908i	$-0.00287408\pi$
$618$	301544.	+	301544.i	0.789540	+	0.789540i
$619$	78470.1	−	78470.1i	0.204797	−	0.204797i	−0.597255	−	0.802052i	$-0.703742\pi$
$619$	78470.1	−	78470.1i	0.204797	−	0.204797i	0.802052	+	0.597255i	$0.203742\pi$
$620$	−21211.0	+	20930.6i	−0.0551795	+	0.0544501i
$621$		−	360962.i		−	0.936004i
$622$	−247701.	−	247701.i	−0.640245	−	0.640245i
$623$	−321129.			−0.827376
$624$	−532577.	+	393262.i	−1.36777	+	1.00998i
$625$	390487.	+	10394.9i	0.999646	+	0.0266109i
$626$	−324027.	−	324027.i	−0.826861	−	0.826861i
$627$			323530.i			0.822961i
$628$	−2306.11			−0.00584737
$629$	−132937.	−	132937.i	−0.336005	−	0.336005i
$630$	−490364.	−	3262.69i	−1.23549	−	0.00822043i
$631$	−328999.	+	328999.i	−0.826297	+	0.826297i	−0.987002	−	0.160705i	$-0.948623\pi$
$631$	−328999.	+	328999.i	−0.826297	+	0.826297i	0.160705	+	0.987002i	$0.448623\pi$
$632$	233081.	+	233081.i	0.583544	+	0.583544i
$633$			801850.i			2.00118i
$634$		−	17817.0i		−	0.0443259i
$635$	−271044.	−	1803.42i	−0.672190	−	0.00447248i
$636$			111971.i			0.276817i
$637$	113913.	−	84115.0i	0.280734	−	0.207298i
$638$		−	184905.i		−	0.454264i
$639$	36576.8	+	36576.8i	0.0895786	+	0.0895786i
$640$	−320610.	−	324905.i	−0.782739	−	0.793225i
$641$		−	272732.i		−	0.663774i	−0.943319	−	0.331887i	$-0.892315\pi$
$641$		−	272732.i		−	0.663774i	0.943319	−	0.331887i	$-0.107685\pi$
$642$	−358827.	+	358827.i	−0.870593	+	0.870593i
$643$	394547.	−	394547.i	0.954282	−	0.954282i	−0.0447179	−	0.999000i	$-0.514239\pi$
$643$	394547.	−	394547.i	0.954282	−	0.954282i	0.999000	+	0.0447179i	$0.0142389\pi$
$644$	−27541.7	+	27541.7i	−0.0664078	+	0.0664078i
$645$	−167.564	+	25184.0i	−0.000402775	+	0.0605349i
$646$	−71268.7			−0.170779
$647$	−469845.			−1.12240			−0.561198	−	0.827681i	$-0.689659\pi$
$647$	−469845.			−1.12240			−0.561198	+	0.827681i	$0.689659\pi$
$648$	−89318.2	−	89318.2i	−0.212711	−	0.212711i
$649$			1.11680e6i			2.65146i
$650$	435480.	+	71466.7i	1.03072	+	0.169152i
$651$	457440.			1.07937
$652$	−29759.3	+	29759.3i	−0.0700048	+	0.0700048i
$653$			312828.i			0.733633i	0.930293	+	0.366817i	$0.119552\pi$
$653$			312828.i			0.733633i	−0.930293	+	0.366817i	$0.880448\pi$
$654$		−	1.29132e6i		−	3.01911i
$655$	387901.	+	2580.94i	0.904145	+	0.00601582i
$656$	−11972.4	−	11972.4i	−0.0278210	−	0.0278210i
$657$	185689.	+	185689.i	0.430185	+	0.430185i
$658$	−246501.	−	246501.i	−0.569333	−	0.569333i
$659$	42829.3			0.0986212			0.0493106	−	0.998783i	$-0.484298\pi$
$659$	42829.3			0.0986212			0.0493106	+	0.998783i	$0.484298\pi$
$660$	61878.6	−	61060.6i	0.142054	−	0.140176i
$661$	223114.	−	223114.i	0.510650	−	0.510650i	−0.404076	−	0.914726i	$-0.632407\pi$
$661$	223114.	−	223114.i	0.510650	−	0.510650i	0.914726	+	0.404076i	$0.132407\pi$
$662$	328810.			0.750290
$663$	−241945.	+	178656.i	−0.550414	+	0.406433i
$664$	263497.			0.597640
$665$	890.877	−	133894.i	0.00201453	−	0.302774i
$666$	740739.			1.67000
$667$	−177208.			−0.398319
$668$	−2719.15	+	2719.15i	−0.00609369	+	0.00609369i
$669$	241595.	+	241595.i	0.539804	+	0.539804i
$670$	5512.01	−	828425.i	0.0122789	−	1.84546i
$671$	587128.	−	587128.i	1.30403	−	1.30403i
$672$		−	103824.i		−	0.229911i
$673$	−230452.			−0.508805			−0.254402	−	0.967098i	$-0.581879\pi$
$673$	−230452.			−0.508805			−0.254402	+	0.967098i	$0.581879\pi$
$674$	74099.1	−	74099.1i	0.163115	−	0.163115i
$675$	4436.74	−	333394.i	0.00973770	−	0.731729i
$676$	39743.8	+	12237.9i	0.0869713	+	0.0267802i
$677$		−	220832.i		−	0.481820i	−0.970547	−	0.240910i	$-0.922554\pi$
$677$		−	220832.i		−	0.481820i	0.970547	−	0.240910i	$-0.0774459\pi$
$678$	−106759.	+	106759.i	−0.232244	+	0.232244i
$679$	−503725.			−1.09258
$680$	−134358.	−	136158.i	−0.290566	−	0.294458i
$681$	714006.	+	714006.i	1.53960	+	1.53960i
$682$	−408692.	+	408692.i	−0.878672	+	0.878672i
$683$	368709.	+	368709.i	0.790392	+	0.790392i	0.981558	−	0.191166i	$-0.0612269\pi$
$683$	368709.	+	368709.i	0.790392	+	0.790392i	−0.191166	+	0.981558i	$0.561227\pi$
$684$	16561.8	−	16561.8i	0.0353994	−	0.0353994i
$685$	−135845.	−	137664.i	−0.289508	−	0.293387i
$686$			535012.i			1.13688i
$687$	9572.63	+	9572.63i	0.0202823	+	0.0202823i
$688$	−19756.5			−0.0417382
$689$	−739755.	+	546245.i	−1.55829	+	1.15067i
$690$	−701573.	−	710971.i	−1.47358	−	1.49332i
$691$	333650.	+	333650.i	0.698772	+	0.698772i	0.964146	−	0.265374i	$-0.0854954\pi$
$691$	333650.	+	333650.i	0.698772	+	0.698772i	−0.265374	+	0.964146i	$0.585495\pi$
$692$		−	5240.71i		−	0.0109440i
$693$	−793331.			−1.65192
$694$	−454466.	−	454466.i	−0.943588	−	0.943588i
$695$	−478872.	−	3186.22i	−0.991402	−	0.00659639i
$696$	159045.	−	159045.i	0.328322	−	0.328322i
$697$	−5438.95	−	5438.95i	−0.0111957	−	0.0111957i
$698$			777453.i			1.59575i
$699$			1.37293e6i			2.80992i
$700$	−25776.8	+	25099.7i	−0.0526057	+	0.0512240i
$701$		−	404499.i		−	0.823155i	−0.911375	−	0.411577i	$-0.864978\pi$
$701$		−	404499.i		−	0.823155i	0.911375	−	0.411577i	$-0.135022\pi$
$702$	56049.9	−	372489.i	0.113737	−	0.755857i
$703$			202259.i			0.409258i
$704$	−437147.	−	437147.i	−0.882028	−	0.882028i
$705$	530763.	−	523747.i	1.06788	−	1.05376i
$706$			756291.i			1.51733i
$707$	452219.	−	452219.i	0.904711	−	0.904711i
$708$	96167.3	−	96167.3i	0.191850	−	0.191850i
$709$	−141126.	+	141126.i	−0.280747	+	0.280747i	−0.833407	−	0.552660i	$-0.813613\pi$
$709$	−141126.	+	141126.i	−0.280747	+	0.280747i	0.552660	+	0.833407i	$0.313613\pi$
$710$	45499.1	+	302.733i	0.0902581	+	0.000600542i
$711$	−644151.			−1.27423
$712$	493560.			0.973599
$713$	391678.	+	391678.i	0.770459	+	0.770459i
$714$		−	293966.i		−	0.576635i
$715$	705276.	+	110929.i	1.37958	+	0.216987i
$716$	−6123.89			−0.0119454
$717$	−215368.	+	215368.i	−0.418931	+	0.418931i
$718$		−	713826.i		−	1.38466i
$719$		−	61925.9i		−	0.119788i	−0.998205	−	0.0598941i	$-0.980924\pi$
$719$		−	61925.9i		−	0.119788i	0.998205	−	0.0598941i	$-0.0190763\pi$
$720$	822825.	+	5474.75i	1.58724	+	0.0105609i
$721$	−201899.	−	201899.i	−0.388386	−	0.388386i
$722$	−330794.	−	330794.i	−0.634575	−	0.634575i
$723$	11474.7	+	11474.7i	0.0219516	+	0.0219516i
$724$	−64140.4			−0.122364
$725$	−163674.	−	2178.14i	−0.311389	−	0.00414390i
$726$	580952.	−	580952.i	1.10222	−	1.10222i
$727$	−851651.			−1.61136			−0.805680	−	0.592351i	$-0.798200\pi$
$727$	−851651.			−1.61136			−0.805680	+	0.592351i	$0.798200\pi$
$728$	326616.	−	241178.i	0.616275	−	0.455066i
$729$	857561.			1.61365
$730$	230985.	+	1536.88i	0.433449	+	0.00288400i
$731$	−8975.22			−0.0167962
$732$	−101115.			−0.188709
$733$	−177456.	+	177456.i	−0.330280	+	0.330280i	−0.852693	−	0.522413i	$-0.825032\pi$
$733$	−177456.	+	177456.i	−0.330280	+	0.330280i	0.522413	+	0.852693i	$0.325032\pi$
$734$	488487.	+	488487.i	0.906694	+	0.906694i
$735$	−296044.	−	1969.76i	−0.548002	−	0.00364619i
$736$	88898.4	−	88898.4i	0.164111	−	0.164111i
$737$		−	1.34026e6i		−	2.46748i
$738$	30306.3			0.0556443
$739$	491073.	−	491073.i	0.899202	−	0.899202i	−0.0961635	−	0.995366i	$-0.530657\pi$
$739$	491073.	−	491073.i	0.899202	−	0.899202i	0.995366	+	0.0961635i	$0.0306572\pi$
$740$	38684.2	−	38172.8i	0.0706431	−	0.0697093i
$741$	319963.	+	48146.1i	0.582725	+	0.0876849i
$742$		−	898812.i		−	1.63253i
$743$	−442300.	+	442300.i	−0.801198	+	0.801198i	−0.983283	−	0.182085i	$-0.941715\pi$
$743$	−442300.	+	442300.i	−0.801198	+	0.801198i	0.182085	+	0.983283i	$0.441715\pi$
$744$	−703064.			−1.27013
$745$	−560227.	−	567732.i	−1.00937	−	1.02289i
$746$	236680.	+	236680.i	0.425288	+	0.425288i
$747$	−364104.	+	364104.i	−0.652506	+	0.652506i
$748$	21906.9	+	21906.9i	0.0391541	+	0.0391541i
$749$	240253.	−	240253.i	0.428257	−	0.428257i
$750$	−639253.	−	665296.i	−1.13645	−	1.18275i
$751$		−	966451.i		−	1.71356i	−0.515680	−	0.856782i	$-0.672460\pi$
$751$		−	966451.i		−	1.71356i	0.515680	−	0.856782i	$-0.327540\pi$
$752$	413625.	+	413625.i	0.731427	+	0.731427i
$753$	35514.3			0.0626344
$754$	−182867.	−	27516.7i	−0.321657	−	0.0484009i
$755$	−360054.	+	355295.i	−0.631647	+	0.623297i
$756$	21715.1	+	21715.1i	0.0379943	+	0.0379943i
$757$		−	712516.i		−	1.24338i	−0.783264	−	0.621689i	$-0.786447\pi$
$757$		−	712516.i		−	1.24338i	0.783264	−	0.621689i	$-0.213553\pi$
$758$	−830227.			−1.44497
$759$	−1.14264e6	−	1.14264e6i	−1.98346	−	1.98346i
$760$	−1369.24	+	205789.i	−0.00237056	+	0.356283i
$761$	319639.	−	319639.i	0.551939	−	0.551939i	−0.375061	−	0.927000i	$-0.622378\pi$
$761$	319639.	−	319639.i	0.551939	−	0.551939i	0.927000	+	0.375061i	$0.122378\pi$
$762$	452696.	+	452696.i	0.779644	+	0.779644i
$763$			864605.i			1.48514i
$764$			2664.78i			0.00456535i
$765$	373802.	+	2487.13i	0.638732	+	0.00424987i
$766$			131866.i			0.224737i
$767$	1.10449e6	+	166197.i	1.87746	+	0.282508i
$768$			250834.i			0.425268i
$769$	439382.	+	439382.i	0.743001	+	0.743001i	0.973154	−	0.230153i	$-0.0739227\pi$
$769$	439382.	+	439382.i	0.743001	+	0.743001i	−0.230153	+	0.973154i	$0.573923\pi$
$770$	−496709.	+	490143.i	−0.837761	+	0.826687i
$771$			729511.i			1.22722i
$772$	22228.8	−	22228.8i	0.0372976	−	0.0372976i
$773$	788641.	−	788641.i	1.31984	−	1.31984i	0.405935	−	0.913902i	$-0.366946\pi$
$773$	788641.	−	788641.i	1.31984	−	1.31984i	0.913902	−	0.405935i	$-0.133054\pi$
$774$	25005.4	−	25005.4i	0.0417399	−	0.0417399i
$775$	356950.	+	366579.i	0.594298	+	0.610329i
$776$	774202.			1.28567
$777$	−834269.			−1.38186
$778$	192655.	+	192655.i	0.318288	+	0.318288i
$779$			8275.15i			0.0136364i
$780$	−51179.0	−	70283.2i	−0.0841207	−	0.115521i
$781$	73610.4			0.120680
$782$	251705.	−	251705.i	0.411603	−	0.411603i
$783$			139719.i			0.227893i
$784$		−	232243.i		−	0.377842i
$785$	−263.452	+	39595.3i	−0.000427525	+	0.0642547i
$786$	−647869.	−	647869.i	−1.04868	−	1.04868i
$787$	163774.	+	163774.i	0.264421	+	0.264421i	0.826847	−	0.562426i	$-0.190132\pi$
$787$	163774.	+	163774.i	0.264421	+	0.264421i	−0.562426	+	0.826847i	$0.690132\pi$
$788$	25801.6	+	25801.6i	0.0415523	+	0.0415523i
$789$	−948543.			−1.52371
$790$	−403306.	+	397974.i	−0.646220	+	0.637677i
$791$	71480.4	−	71480.4i	0.114244	−	0.114244i
$792$	1.21931e6			1.94386
$793$	−493282.	−	668029.i	−0.784421	−	1.06230i
$794$	474133.			0.752071
$795$	1.92252e6	+	12791.7i	3.04184	+	0.0202392i
$796$	4450.78			0.00702441
$797$	−653474.			−1.02875			−0.514377	−	0.857564i	$-0.671977\pi$
$797$	−653474.			−1.02875			−0.514377	+	0.857564i	$0.671977\pi$
$798$	−223629.	+	223629.i	−0.351174	+	0.351174i
$799$	187906.	+	187906.i	0.294339	+	0.294339i
$800$	83201.8	−	81016.4i	0.130003	−	0.126588i
$801$	−682009.	+	682009.i	−1.06298	+	1.06298i
$802$			1.14961e6i			1.78731i
$803$	373697.			0.579547
$804$	−115409.	+	115409.i	−0.178537	+	0.178537i
$805$	469738.	+	476031.i	0.724876	+	0.734587i
$806$	343367.	+	465006.i	0.528553	+	0.715794i
$807$			569498.i			0.874471i
$808$	−695040.	+	695040.i	−1.06460	+	1.06460i
$809$	−130304.			−0.199095			−0.0995475	−	0.995033i	$-0.531740\pi$
$809$	−130304.			−0.199095			−0.0995475	+	0.995033i	$0.531740\pi$
$810$	154549.	−	152506.i	0.235558	−	0.232444i
$811$	19279.0	+	19279.0i	0.0293119	+	0.0293119i	0.721611	−	0.692299i	$-0.243402\pi$
$811$	19279.0	+	19279.0i	0.0293119	+	0.0293119i	−0.692299	+	0.721611i	$0.743402\pi$
$812$	10660.7	−	10660.7i	0.0161686	−	0.0161686i
$813$	741102.	+	741102.i	1.12124	+	1.12124i
$814$	745363.	−	745363.i	1.12491	−	1.12491i
$815$	507561.	+	514360.i	0.764140	+	0.774377i
$816$			493271.i			0.740808i
$817$	6827.72	+	6827.72i	0.0102290	+	0.0102290i
$818$	−838536.			−1.25318
$819$	−118060.	+	784586.i	−0.176008	+	1.16970i
$820$	1582.71	−	1561.79i	0.00235382	−	0.00232271i
$821$	−558984.	−	558984.i	−0.829302	−	0.829302i	0.158118	−	0.987420i	$-0.449457\pi$
$821$	−558984.	−	558984.i	−0.829302	−	0.829302i	−0.987420	+	0.158118i	$0.949457\pi$
$822$			456813.i			0.676075i
$823$	224877.			0.332005			0.166002	−	0.986125i	$-0.446914\pi$
$823$	224877.			0.332005			0.166002	+	0.986125i	$0.446914\pi$
$824$	310309.	+	310309.i	0.457026	+	0.457026i
$825$	−1.04133e6	−	1.06942e6i	−1.52996	−	1.57123i
$826$	−771949.	+	771949.i	−1.13143	+	1.13143i
$827$	−235326.	−	235326.i	−0.344079	−	0.344079i	0.513819	−	0.857898i	$-0.328230\pi$
$827$	−235326.	−	235326.i	−0.344079	−	0.344079i	−0.857898	+	0.513819i	$0.828230\pi$
$828$			116985.i			0.170636i
$829$		−	1.01079e6i		−	1.47080i	−0.677636	−	0.735398i	$-0.736995\pi$
$829$		−	1.01079e6i		−	1.47080i	0.677636	−	0.735398i	$-0.263005\pi$
$830$	−3013.56	+	452921.i	−0.00437445	+	0.657455i
$831$		−	554379.i		−	0.802795i
$832$	−497382.	+	367274.i	−0.718528	+	0.530571i
$833$		−	105506.i		−	0.152050i
$834$	799809.	+	799809.i	1.14988	+	1.14988i
$835$	46376.6	+	46997.8i	0.0665159	+	0.0674070i
$836$		−	33330.4i		−	0.0476901i
$837$	308817.	−	308817.i	0.440808	−	0.440808i
$838$	326378.	−	326378.i	0.464764	−	0.464764i
$839$	−112737.	+	112737.i	−0.160156	+	0.160156i	−0.782636	−	0.622480i	$-0.786125\pi$
$839$	−112737.	+	112737.i	−0.160156	+	0.160156i	0.622480	+	0.782636i	$0.286125\pi$
$840$	−848830.	−	5647.78i	−1.20299	−	0.00800422i
$841$	−638689.			−0.903020
$842$	−587774.			−0.829060
$843$	−921043.	−	921043.i	−1.29606	−	1.29606i
$844$		−	82607.6i		−	0.115967i
$845$	214662.	−	680993.i	0.300637	−	0.953739i
$846$	−1.04703e6			−1.46291
$847$	−388976.	+	388976.i	−0.542195	+	0.542195i
$848$			1.50819e6i			2.09732i
$849$			795804.i			1.10406i
$850$	235576.	−	229388.i	0.326057	−	0.317492i
$851$	−714334.	−	714334.i	−0.986375	−	0.986375i
$852$	−6338.57	−	6338.57i	−0.00873196	−	0.00873196i
$853$	655957.	+	655957.i	0.901524	+	0.901524i	0.995568	−	0.0940441i	$-0.0299795\pi$
$853$	655957.	+	655957.i	0.901524	+	0.901524i	−0.0940441	+	0.995568i	$0.529979\pi$
$854$	811664.			1.11291
$855$	−282470.	−	286254.i	−0.386403	−	0.391580i
$856$	−369257.	+	369257.i	−0.503943	+	0.503943i
$857$	−565354.			−0.769766			−0.384883	−	0.922965i	$-0.625758\pi$
$857$	−565354.			−0.769766			−0.384883	+	0.922965i	$0.625758\pi$
$858$	−1.00170e6	−	1.35656e6i	−1.36070	−	1.84274i
$859$	303649.			0.411515			0.205758	−	0.978603i	$-0.434034\pi$
$859$	303649.			0.411515			0.205758	+	0.978603i	$0.434034\pi$
$860$	17.2627	−	2594.49i	2.33406e−5	−	0.00350796i
$861$	−34133.0			−0.0460435
$862$	1.35990e6			1.83017
$863$	−345731.	+	345731.i	−0.464213	+	0.464213i	−0.900033	−	0.435821i	$-0.856458\pi$
$863$	−345731.	+	345731.i	−0.464213	+	0.464213i	0.435821	+	0.900033i	$0.356458\pi$
$864$	−70091.6	−	70091.6i	−0.0938941	−	0.0938941i
$865$	−89981.7	−	598.702i	−0.120260	−	0.000800163i
$866$	−332287.	+	332287.i	−0.443076	+	0.443076i
$867$		−	956328.i		−	1.27224i
$868$	−47126.0			−0.0625491
$869$	−648172.	+	648172.i	−0.858323	+	0.858323i
$870$	271560.	+	275198.i	0.358780	+	0.363586i
$871$	−1.32549e6	−	199451.i	−1.74718	−	0.262905i
$872$		−	1.32886e6i		−	1.74762i
$873$	−1.06980e6	+	1.06980e6i	−1.40370	+	1.40370i
$874$	−382960.			−0.501337
$875$	428012.	+	445449.i	0.559036	+	0.581811i
$876$	−32178.9	−	32178.9i	−0.0419337	−	0.0419337i
$877$	439813.	−	439813.i	0.571833	−	0.571833i	−0.360808	−	0.932640i	$-0.617499\pi$
$877$	439813.	−	439813.i	0.571833	−	0.571833i	0.932640	+	0.360808i	$0.117499\pi$
$878$	534034.	+	534034.i	0.692755	+	0.692755i
$879$	1.35613e6	−	1.35613e6i	1.75518	−	1.75518i
$880$	833471.	−	822453.i	1.07628	−	1.06205i
$881$		−	70186.3i		−	0.0904275i	−0.998977	−	0.0452137i	$-0.985603\pi$
$881$		−	70186.3i		−	0.0904275i	0.998977	−	0.0452137i	$-0.0143969\pi$
$882$	293944.	+	293944.i	0.377857	+	0.377857i
$883$	686593.			0.880599			0.440300	−	0.897851i	$-0.354872\pi$
$883$	686593.			0.880599			0.440300	+	0.897851i	$0.354872\pi$
$884$	24925.5	−	18405.3i	0.0318962	−	0.0235526i
$885$	−1.64018e6	−	1.66215e6i	−2.09414	−	2.12219i
$886$	631100.	+	631100.i	0.803953	+	0.803953i
$887$		−	192839.i		−	0.245102i	−0.992462	−	0.122551i	$-0.960893\pi$
$887$		−	192839.i		−	0.245102i	0.992462	−	0.122551i	$-0.0391075\pi$
$888$	1.28223e6			1.62608
$889$	−303102.	−	303102.i	−0.383518	−	0.383518i
$890$	−5644.74	+	848373.i	−0.00712629	+	1.07104i
$891$	248384.	−	248384.i	0.312873	−	0.312873i
$892$	−24889.5	−	24889.5i	−0.0312814	−	0.0312814i
$893$		−	285892.i		−	0.358508i
$894$			1.88391e6i			2.35714i
$895$	−699.597	+	105146.i	−0.000873377	+	0.131264i
$896$		−	721864.i		−	0.899165i
$897$	−1.30008e6	+	959999.i	−1.61579	+	1.19312i
$898$			750587.i			0.930782i
$899$	−151608.	−	151608.i	−0.187587	−	0.187587i
$900$	−1437.92	+	108051.i	−0.00177521	+	0.133396i
$901$			685159.i			0.843999i
$902$	30495.5	−	30495.5i	0.0374820	−	0.0374820i
$903$	−28162.7	+	28162.7i	−0.0345381	+	0.0345381i
$904$	−109862.	+	109862.i	−0.134435	+	0.134435i
$905$	−7327.44	+	1.10127e6i	−0.00894654	+	1.34462i
$906$	1.19477e6			1.45555
$907$	152925.			0.185894			0.0929469	−	0.995671i	$-0.470371\pi$
$907$	152925.			0.185894			0.0929469	+	0.995671i	$0.470371\pi$
$908$	−73557.7	−	73557.7i	−0.0892188	−	0.0892188i
$909$		−	1.92083e6i		−	2.32467i
$910$	410822.	+	564174.i	0.496102	+	0.681287i
$911$	−1.31077e6			−1.57939			−0.789696	−	0.613498i	$-0.789762\pi$
$911$	−1.31077e6			−1.57939			−0.789696	+	0.613498i	$0.789762\pi$
$912$	375246.	−	375246.i	0.451156	−	0.451156i
$913$			732754.i			0.879057i
$914$		−	32568.5i		−	0.0389857i
$915$	−11551.4	+	1.73612e6i	−0.0137973	+	2.07366i
$916$	−986.184	−	986.184i	−0.00117535	−	0.00117535i
$917$	433780.	+	433780.i	0.515859	+	0.515859i
$918$	−198456.	−	198456.i	−0.235493	−	0.235493i
$919$	1.08149e6			1.28054			0.640268	−	0.768152i	$-0.278823\pi$
$919$	1.08149e6			1.28054			0.640268	+	0.768152i	$0.278823\pi$
$920$	−721966.	−	731637.i	−0.852984	−	0.864411i
$921$	593866.	−	593866.i	0.700114	−	0.700114i
$922$	1.03493e6			1.21745
$923$	10954.3	−	72798.9i	0.0128583	−	0.0854519i
$924$	137480.			0.161026
$925$	−650998.	−	668559.i	−0.760845	−	0.781369i
$926$	406672.			0.474266
$927$	−857580.			−0.997965
$928$	−34410.2	+	34410.2i	−0.0399569	+	0.0399569i
$929$	599649.	+	599649.i	0.694809	+	0.694809i	0.963286	−	0.268477i	$-0.0865204\pi$
$929$	599649.	+	599649.i	0.694809	+	0.694809i	−0.268477	+	0.963286i	$0.586520\pi$
$930$	8040.79	−	1.20849e6i	0.00929678	−	1.39726i
$931$	−80261.6	+	80261.6i	−0.0925994	+	0.0925994i
$932$		−	141441.i		−	0.162833i
$933$	1.18497e6			1.36127
$934$	−390199.	+	390199.i	−0.447293	+	0.447293i
$935$	378638.	−	373633.i	0.433113	−	0.427388i
$936$	181452.	−	1.20587e6i	0.207115	−	1.37642i
$937$		−	89175.4i		−	0.101570i	−0.998710	−	0.0507851i	$-0.983828\pi$
$937$		−	89175.4i		−	0.101570i	0.998710	−	0.0507851i	$-0.0161723\pi$
$938$	926409.	−	926409.i	1.05292	−	1.05292i
$939$	1.55011e6			1.75805
$940$	−54679.9	+	53957.0i	−0.0618830	+	0.0610650i
$941$	424214.	+	424214.i	0.479078	+	0.479078i	0.904837	−	0.425759i	$-0.139993\pi$
$941$	424214.	+	424214.i	0.479078	+	0.479078i	−0.425759	+	0.904837i	$0.639993\pi$
$942$	66131.9	−	66131.9i	0.0745262	−	0.0745262i
$943$	−29226.0	−	29226.0i	−0.0328659	−	0.0328659i
$944$	1.29532e6	−	1.29532e6i	1.45356	−	1.45356i
$945$	375324.	−	370363.i	0.420284	−	0.414728i
$946$		−	50323.0i		−	0.0562321i
$947$	−486024.	−	486024.i	−0.541948	−	0.541948i	0.382151	−	0.924100i	$-0.375183\pi$
$947$	−486024.	−	486024.i	−0.541948	−	0.541948i	−0.924100	+	0.382151i	$0.875183\pi$
$948$	111628.			0.124210
$949$	55611.7	−	369577.i	0.0617495	−	0.410367i
$950$	−353712.	−	4707.13i	−0.391925	−	0.00521565i
$951$	42617.5	+	42617.5i	0.0471223	+	0.0471223i
$952$		−	302511.i		−	0.333785i
$953$	45019.1			0.0495691			0.0247845	−	0.999693i	$-0.492110\pi$
$953$	45019.1			0.0495691			0.0247845	+	0.999693i	$0.492110\pi$
$954$	−1.90888e6	−	1.90888e6i	−2.09741	−	2.09741i
$955$	45753.6	+	304.426i	0.0501670	+	0.000333791i
$956$	22187.5	−	22187.5i	0.0242768	−	0.0242768i
$957$	442284.	+	442284.i	0.482923	+	0.482923i
$958$			454315.i			0.495023i
$959$		−	305859.i		−	0.332570i
$960$	1.29263e6	+	8600.64i	1.40259	+	0.00933229i
$961$		−	253330.i		−	0.274309i
$962$	−626225.	−	848068.i	−0.676676	−	0.916390i
$963$		−	1.02049e6i		−	1.10042i
$964$	−1182.14	−	1182.14i	−0.00127208	−	0.00127208i
$965$	−379123.	−	384202.i	−0.407123	−	0.412577i
$966$		−	1.57962e6i		−	1.69277i
$967$	−447122.	+	447122.i	−0.478160	+	0.478160i	−0.904543	−	0.426383i	$-0.859788\pi$
$967$	−447122.	+	447122.i	−0.478160	+	0.478160i	0.426383	+	0.904543i	$0.359788\pi$
$968$	597838.	−	597838.i	0.638018	−	0.638018i
$969$	170471.	−	170471.i	0.181553	−	0.181553i
$970$	−8854.38	+	1.33076e6i	−0.00941054	+	1.41435i
$971$	1.78725e6			1.89560			0.947802	−	0.318859i	$-0.103300\pi$
$971$	1.78725e6			1.89560			0.947802	+	0.318859i	$0.103300\pi$
$972$	−105693.			−0.111870
$973$	−535511.	−	535511.i	−0.565644	−	0.565644i
$974$			514995.i			0.542856i
$975$	−1.21259e6	+	870702.i	−1.27557	+	0.915926i
$976$	−1.36196e6			−1.42977
$977$	−909342.	+	909342.i	−0.952660	+	0.952660i	−0.998929	−	0.0462690i	$-0.985267\pi$
$977$	−909342.	+	909342.i	−0.952660	+	0.952660i	0.0462690	+	0.998929i	$0.485267\pi$
$978$		−	1.70681e6i		−	1.78446i
$979$			1.37253e6i			1.43205i
$980$	30498.8	+	202.927i	0.0317564	+	0.000211294i
$981$	1.83624e6	+	1.83624e6i	1.90805	+	1.90805i
$982$	−428784.	−	428784.i	−0.444648	−	0.444648i
$983$	−1.09863e6	−	1.09863e6i	−1.13696	−	1.13696i	−0.988993	−	0.147963i	$-0.952728\pi$
$983$	−1.09863e6	−	1.09863e6i	−1.13696	−	1.13696i	−0.147963	−	0.988993i	$-0.547272\pi$
$984$	52460.8			0.0541808
$985$	445955.	−	440060.i	0.459641	−	0.453565i
$986$	−97428.5	+	97428.5i	−0.100215	+	0.100215i
$987$	1.17923e6			1.21050
$988$	−32963.0	−	4960.07i	−0.0337686	−	0.00508129i
$989$	−48228.0			−0.0493068
$990$	−13945.0	+	2.09586e6i	−0.0142282	+	2.13842i
$991$	−560441.			−0.570667			−0.285333	−	0.958428i	$-0.592104\pi$
$991$	−560441.			−0.570667			−0.285333	+	0.958428i	$0.592104\pi$
$992$	152112.			0.154575
$993$	−786497.	+	786497.i	−0.797624	+	0.797624i
$994$	50880.6	+	50880.6i	0.0514967	+	0.0514967i
$995$	508.460	−	76418.8i	0.000513583	−	0.0771888i
$996$	63097.2	−	63097.2i	0.0636051	−	0.0636051i
$997$			851439.i			0.856571i	0.903643	+	0.428286i	$0.140882\pi$
$997$			851439.i			0.856571i	−0.903643	+	0.428286i	$0.859118\pi$
$998$	−1.16247e6			−1.16714
$999$	−563213.	+	563213.i	−0.564341	+	0.564341i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.5.g.a.34.20	yes	52
5.4	even	2	inner	65.5.g.a.34.7	✓	52
13.5	odd	4	inner	65.5.g.a.44.7	yes	52
65.44	odd	4	inner	65.5.g.a.44.20	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.5.g.a.34.7	✓	52	5.4	even	2	inner
65.5.g.a.34.20	yes	52	1.1	even	1	trivial
65.5.g.a.44.7	yes	52	13.5	odd	4	inner
65.5.g.a.44.20	yes	52	65.44	odd	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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	65.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.95432 - 2.95432i) q^{2} +14.1332i q^{3} -1.45602i q^{4} +(-24.9994 - 0.166336i) q^{5} +(41.7539 + 41.7539i) q^{6} +(-27.9563 - 27.9563i) q^{7} +(42.9676 + 42.9676i) q^{8} -118.747 q^{9} +O(q^{10})\)	\(q+(2.95432 - 2.95432i) q^{2} +14.1332i q^{3} -1.45602i q^{4} +(-24.9994 - 0.166336i) q^{5} +(41.7539 + 41.7539i) q^{6} +(-27.9563 - 27.9563i) q^{7} +(42.9676 + 42.9676i) q^{8} -118.747 q^{9} +(-74.3478 + 73.3650i) q^{10} +(-119.488 + 119.488i) q^{11} +20.5781 q^{12} +(100.389 + 135.952i) q^{13} -165.184 q^{14} +(2.35086 - 353.321i) q^{15} +277.176 q^{16} +125.919 q^{17} +(-350.815 + 350.815i) q^{18} +(-95.7902 - 95.7902i) q^{19} +(-0.242188 + 36.3996i) q^{20} +(395.111 - 395.111i) q^{21} +706.011i q^{22} +676.620 q^{23} +(-607.268 + 607.268i) q^{24} +(624.945 + 8.31663i) q^{25} +(698.228 + 105.065i) q^{26} -533.478i q^{27} +(-40.7048 + 40.7048i) q^{28} -261.902 q^{29} +(-1036.88 - 1050.77i) q^{30} +(578.874 + 578.874i) q^{31} +(131.386 - 131.386i) q^{32} +(-1688.74 - 1688.74i) q^{33} +(372.004 - 372.004i) q^{34} +(694.242 + 703.542i) q^{35} +172.897i q^{36} +(-1055.74 - 1055.74i) q^{37} -565.990 q^{38} +(-1921.44 + 1418.82i) q^{39} +(-1067.02 - 1081.31i) q^{40} +(-43.1941 - 43.1941i) q^{41} -2334.57i q^{42} -71.2779 q^{43} +(173.976 + 173.976i) q^{44} +(2968.60 + 19.7519i) q^{45} +(1998.95 - 1998.95i) q^{46} +(1492.28 + 1492.28i) q^{47} +3917.38i q^{48} -837.889i q^{49} +(1870.86 - 1821.72i) q^{50} +1779.63i q^{51} +(197.949 - 146.168i) q^{52} +5441.28i q^{53} +(-1576.06 - 1576.06i) q^{54} +(3007.01 - 2967.26i) q^{55} -2402.43i q^{56} +(1353.82 - 1353.82i) q^{57} +(-773.741 + 773.741i) q^{58} +(4673.28 - 4673.28i) q^{59} +(-514.442 - 3.42289i) q^{60} -4913.70 q^{61} +3420.36 q^{62} +(3319.71 + 3319.71i) q^{63} +3658.51i q^{64} +(-2487.06 - 3415.43i) q^{65} -9978.17 q^{66} +(-5608.35 + 5608.35i) q^{67} -183.340i q^{68} +9562.78i q^{69} +(4129.50 + 27.4761i) q^{70} +(-308.024 - 308.024i) q^{71} +(-5102.25 - 5102.25i) q^{72} +(-1563.74 - 1563.74i) q^{73} -6237.98 q^{74} +(-117.540 + 8832.45i) q^{75} +(-139.472 + 139.472i) q^{76} +6680.88 q^{77} +(-1484.90 + 9868.18i) q^{78} +5424.58 q^{79} +(-6929.25 - 46.1045i) q^{80} -2078.73 q^{81} -255.219 q^{82} +(3066.23 - 3066.23i) q^{83} +(-575.289 - 575.289i) q^{84} +(-3147.90 - 20.9449i) q^{85} +(-210.578 + 210.578i) q^{86} -3701.50i q^{87} -10268.2 q^{88} +(5743.40 - 5743.40i) q^{89} +(8828.54 - 8711.83i) q^{90} +(994.215 - 6607.23i) q^{91} -985.169i q^{92} +(-8181.33 + 8181.33i) q^{93} +8817.35 q^{94} +(2378.77 + 2410.63i) q^{95} +(1856.90 + 1856.90i) q^{96} +(9009.14 - 9009.14i) q^{97} +(-2475.39 - 2475.39i) q^{98} +(14188.8 - 14188.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9}+O(q^{10}) \) 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9	\( 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9} + 8 q^{11} + 424 q^{14} - 508 q^{15} - 3128 q^{16} + 268 q^{19} + 2116 q^{20} - 668 q^{21} + 2032 q^{24} + 1100 q^{26} - 3704 q^{29} - 1660 q^{31} + 1252 q^{34} + 6692 q^{35} + 7408 q^{39} + 3644 q^{40} + 5960 q^{41} + 1444 q^{44} - 8674 q^{45} + 17620 q^{46} - 3928 q^{50} - 30588 q^{54} + 14784 q^{55} - 5548 q^{59} - 13976 q^{60} - 20008 q^{61} - 15614 q^{65} + 24752 q^{66} + 26908 q^{70} - 16360 q^{71} - 7304 q^{74} - 5760 q^{76} - 9536 q^{79} - 62348 q^{80} - 36516 q^{81} + 66564 q^{84} - 11604 q^{85} - 5264 q^{86} - 940 q^{89} + 37644 q^{91} + 55448 q^{94} - 61644 q^{96} + 16140 q^{99}+O(q^{100}) \) 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9 + 8 * q^11 + 424 * q^14 - 508 * q^15 - 3128 * q^16 + 268 * q^19 + 2116 * q^20 - 668 * q^21 + 2032 * q^24 + 1100 * q^26 - 3704 * q^29 - 1660 * q^31 + 1252 * q^34 + 6692 * q^35 + 7408 * q^39 + 3644 * q^40 + 5960 * q^41 + 1444 * q^44 - 8674 * q^45 + 17620 * q^46 - 3928 * q^50 - 30588 * q^54 + 14784 * q^55 - 5548 * q^59 - 13976 * q^60 - 20008 * q^61 - 15614 * q^65 + 24752 * q^66 + 26908 * q^70 - 16360 * q^71 - 7304 * q^74 - 5760 * q^76 - 9536 * q^79 - 62348 * q^80 - 36516 * q^81 + 66564 * q^84 - 11604 * q^85 - 5264 * q^86 - 940 * q^89 + 37644 * q^91 + 55448 * q^94 - 61644 * q^96 + 16140 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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