LMFDB - Embedded newform 65.5.g.a.34.18

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			34.18
Character	$\chi$	$=$	65.34
Dual form			65.5.g.a.44.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.29180 - 2.29180i) q^{2} -1.09931i q^{3} +5.49535i q^{4} +(20.3578 + 14.5107i) q^{5} +(-2.51939 - 2.51939i) q^{6} +(-7.15078 - 7.15078i) q^{7} +(49.2629 + 49.2629i) q^{8} +79.7915 q^{9} +O(q^{10})$	\(q+(2.29180 - 2.29180i) q^{2} -1.09931i q^{3} +5.49535i q^{4} +(20.3578 + 14.5107i) q^{5} +(-2.51939 - 2.51939i) q^{6} +(-7.15078 - 7.15078i) q^{7} +(49.2629 + 49.2629i) q^{8} +79.7915 q^{9} +(79.9114 - 13.4005i) q^{10} +(-80.3092 + 80.3092i) q^{11} +6.04107 q^{12} +(103.977 - 133.229i) q^{13} -32.7762 q^{14} +(15.9517 - 22.3795i) q^{15} +137.876 q^{16} +378.127 q^{17} +(182.866 - 182.866i) q^{18} +(-327.356 - 327.356i) q^{19} +(-79.7411 + 111.873i) q^{20} +(-7.86090 + 7.86090i) q^{21} +368.104i q^{22} -658.035 q^{23} +(54.1551 - 54.1551i) q^{24} +(203.881 + 590.811i) q^{25} +(-67.0396 - 543.626i) q^{26} -176.759i q^{27} +(39.2960 - 39.2960i) q^{28} -324.909 q^{29} +(-14.7312 - 87.8472i) q^{30} +(902.122 + 902.122i) q^{31} +(-472.224 + 472.224i) q^{32} +(88.2844 + 88.2844i) q^{33} +(866.590 - 866.590i) q^{34} +(-41.8117 - 249.337i) q^{35} +438.482i q^{36} +(-1038.88 - 1038.88i) q^{37} -1500.46 q^{38} +(-146.459 - 114.302i) q^{39} +(288.048 + 1717.72i) q^{40} +(-746.822 - 746.822i) q^{41} +36.0311i q^{42} -2968.76 q^{43} +(-441.327 - 441.327i) q^{44} +(1624.38 + 1157.83i) q^{45} +(-1508.08 + 1508.08i) q^{46} +(1107.36 + 1107.36i) q^{47} -151.568i q^{48} -2298.73i q^{49} +(1821.27 + 886.763i) q^{50} -415.678i q^{51} +(732.138 + 571.388i) q^{52} -5376.66i q^{53} +(-405.096 - 405.096i) q^{54} +(-2800.26 + 469.580i) q^{55} -704.536i q^{56} +(-359.864 + 359.864i) q^{57} +(-744.624 + 744.624i) q^{58} +(201.833 - 201.833i) q^{59} +(122.983 + 87.6600i) q^{60} +1181.04 q^{61} +4134.96 q^{62} +(-570.571 - 570.571i) q^{63} +4370.49i q^{64} +(4049.97 - 1203.47i) q^{65} +404.660 q^{66} +(2112.90 - 2112.90i) q^{67} +2077.94i q^{68} +723.382i q^{69} +(-667.253 - 475.605i) q^{70} +(47.3270 + 47.3270i) q^{71} +(3930.76 + 3930.76i) q^{72} +(-3564.71 - 3564.71i) q^{73} -4761.82 q^{74} +(649.482 - 224.128i) q^{75} +(1798.93 - 1798.93i) q^{76} +1148.55 q^{77} +(-597.612 + 73.6971i) q^{78} +9655.76 q^{79} +(2806.85 + 2000.67i) q^{80} +6268.80 q^{81} -3423.13 q^{82} +(5501.76 - 5501.76i) q^{83} +(-43.1984 - 43.1984i) q^{84} +(7697.84 + 5486.87i) q^{85} +(-6803.79 + 6803.79i) q^{86} +357.174i q^{87} -7912.53 q^{88} +(-7002.82 + 7002.82i) q^{89} +(6376.25 - 1069.24i) q^{90} +(-1696.20 + 209.174i) q^{91} -3616.13i q^{92} +(991.709 - 991.709i) q^{93} +5075.70 q^{94} +(-1914.10 - 11414.4i) q^{95} +(519.120 + 519.120i) q^{96} +(-7025.25 + 7025.25i) q^{97} +(-5268.23 - 5268.23i) q^{98} +(-6407.99 + 6407.99i) 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 $

$2$	2.29180	−	2.29180i	0.572949	−	0.572949i	−0.360002	−	0.932951i	$-0.617224\pi$
$2$	2.29180	−	2.29180i	0.572949	−	0.572949i	0.932951	+	0.360002i	$0.117224\pi$
$3$		−	1.09931i		−	0.122145i	−0.998133	−	0.0610726i	$-0.980548\pi$
$3$		−	1.09931i		−	0.122145i	0.998133	−	0.0610726i	$-0.0194521\pi$
$4$			5.49535i			0.343459i
$5$	20.3578	+	14.5107i	0.814313	+	0.580426i
$5$	20.3578	+	14.5107i	0.814313	+	0.580426i
$6$	−2.51939	−	2.51939i	−0.0699830	−	0.0699830i
$7$	−7.15078	−	7.15078i	−0.145934	−	0.145934i	0.630365	−	0.776299i	$-0.282905\pi$
$7$	−7.15078	−	7.15078i	−0.145934	−	0.145934i	−0.776299	+	0.630365i	$0.782905\pi$
$8$	49.2629	+	49.2629i	0.769733	+	0.769733i
$9$	79.7915			0.985081
$10$	79.9114	−	13.4005i	0.799114	−	0.134005i
$11$	−80.3092	+	80.3092i	−0.663712	+	0.663712i	−0.956253	−	0.292541i	$-0.905499\pi$
$11$	−80.3092	+	80.3092i	−0.663712	+	0.663712i	0.292541	+	0.956253i	$0.405499\pi$
$12$	6.04107			0.0419519
$13$	103.977	−	133.229i	0.615246	−	0.788335i
$13$	103.977	−	133.229i	0.615246	−	0.788335i
$14$	−32.7762			−0.167226
$15$	15.9517	−	22.3795i	0.0708963	−	0.0994644i
$16$	137.876			0.538577
$17$	378.127			1.30840			0.654199	−	0.756323i	$-0.273006\pi$
$17$	378.127			1.30840			0.654199	+	0.756323i	$0.273006\pi$
$18$	182.866	−	182.866i	0.564401	−	0.564401i
$19$	−327.356	−	327.356i	−0.906802	−	0.906802i	0.0892105	−	0.996013i	$-0.471566\pi$
$19$	−327.356	−	327.356i	−0.906802	−	0.906802i	−0.996013	+	0.0892105i	$0.971566\pi$
$20$	−79.7411	+	111.873i	−0.199353	+	0.279683i
$21$	−7.86090	+	7.86090i	−0.0178252	+	0.0178252i
$22$			368.104i			0.760546i
$23$	−658.035			−1.24392			−0.621961	−	0.783048i	$-0.713664\pi$
$23$	−658.035			−1.24392			−0.621961	+	0.783048i	$0.713664\pi$
$24$	54.1551	−	54.1551i	0.0940193	−	0.0940193i
$25$	203.881	+	590.811i	0.326210	+	0.945297i
$26$	−67.0396	−	543.626i	−0.0991710	−	0.804180i
$27$		−	176.759i		−	0.242468i
$28$	39.2960	−	39.2960i	0.0501224	−	0.0501224i
$29$	−324.909			−0.386336			−0.193168	−	0.981166i	$-0.561876\pi$
$29$	−324.909			−0.386336			−0.193168	+	0.981166i	$0.561876\pi$
$30$	−14.7312	−	87.8472i	−0.0163680	−	0.0976080i
$31$	902.122	+	902.122i	0.938732	+	0.938732i	0.998229	−	0.0594963i	$-0.0189495\pi$
$31$	902.122	+	902.122i	0.938732	+	0.938732i	−0.0594963	+	0.998229i	$0.518949\pi$
$32$	−472.224	+	472.224i	−0.461157	+	0.461157i
$33$	88.2844	+	88.2844i	0.0810693	+	0.0810693i
$34$	866.590	−	866.590i	0.749645	−	0.749645i
$35$	−41.8117	−	249.337i	−0.0341320	−	0.203540i
$36$			438.482i			0.338335i
$37$	−1038.88	−	1038.88i	−0.758863	−	0.758863i	0.217253	−	0.976115i	$-0.430290\pi$
$37$	−1038.88	−	1038.88i	−0.758863	−	0.758863i	−0.976115	+	0.217253i	$0.930290\pi$
$38$	−1500.46			−1.03910
$39$	−146.459	−	114.302i	−0.0962913	−	0.0751494i
$40$	288.048	+	1717.72i	0.180030	+	1.07358i
$41$	−746.822	−	746.822i	−0.444273	−	0.444273i	0.449172	−	0.893445i	$-0.351719\pi$
$41$	−746.822	−	746.822i	−0.444273	−	0.444273i	−0.893445	+	0.449172i	$0.851719\pi$
$42$			36.0311i			0.0204258i
$43$	−2968.76			−1.60560			−0.802801	−	0.596247i	$-0.796658\pi$
$43$	−2968.76			−1.60560			−0.802801	+	0.596247i	$0.796658\pi$
$44$	−441.327	−	441.327i	−0.227958	−	0.227958i
$45$	1624.38	+	1157.83i	0.802164	+	0.571767i
$46$	−1508.08	+	1508.08i	−0.712704	+	0.712704i
$47$	1107.36	+	1107.36i	0.501296	+	0.501296i	0.911840	−	0.410545i	$-0.134661\pi$
$47$	1107.36	+	1107.36i	0.501296	+	0.501296i	−0.410545	+	0.911840i	$0.634661\pi$
$48$		−	151.568i		−	0.0657845i
$49$		−	2298.73i		−	0.957406i
$50$	1821.27	+	886.763i	0.728509	+	0.354705i
$51$		−	415.678i		−	0.159815i
$52$	732.138	+	571.388i	0.270761	+	0.211312i
$53$		−	5376.66i		−	1.91408i	−0.289951	−	0.957042i	$-0.593639\pi$
$53$		−	5376.66i		−	1.91408i	0.289951	−	0.957042i	$-0.406361\pi$
$54$	−405.096	−	405.096i	−0.138922	−	0.138922i
$55$	−2800.26	+	469.580i	−0.925705	+	0.155233i
$56$		−	704.536i		−	0.224661i
$57$	−359.864	+	359.864i	−0.110762	+	0.110762i
$58$	−744.624	+	744.624i	−0.221351	+	0.221351i
$59$	201.833	−	201.833i	0.0579812	−	0.0579812i	−0.677522	−	0.735503i	$-0.736946\pi$
$59$	201.833	−	201.833i	0.0579812	−	0.0579812i	0.735503	+	0.677522i	$0.236946\pi$
$60$	122.983	+	87.6600i	0.0341620	+	0.0243500i
$61$	1181.04			0.317399			0.158700	−	0.987327i	$-0.449270\pi$
$61$	1181.04			0.317399			0.158700	+	0.987327i	$0.449270\pi$
$62$	4134.96			1.07569
$63$	−570.571	−	570.571i	−0.143757	−	0.143757i
$64$			4370.49i			1.06701i
$65$	4049.97	−	1203.47i	0.958573	−	0.284846i
$66$	404.660			0.0928971
$67$	2112.90	−	2112.90i	0.470683	−	0.470683i	−0.431452	−	0.902136i	$-0.641999\pi$
$67$	2112.90	−	2112.90i	0.470683	−	0.470683i	0.902136	+	0.431452i	$0.141999\pi$
$68$			2077.94i			0.449381i
$69$			723.382i			0.151939i
$70$	−667.253	−	475.605i	−0.136174	−	0.0970622i
$71$	47.3270	+	47.3270i	0.00938841	+	0.00938841i	0.711785	−	0.702397i	$-0.247887\pi$
$71$	47.3270	+	47.3270i	0.00938841	+	0.00938841i	−0.702397	+	0.711785i	$0.747887\pi$
$72$	3930.76	+	3930.76i	0.758249	+	0.758249i
$73$	−3564.71	−	3564.71i	−0.668927	−	0.668927i	0.288541	−	0.957468i	$-0.406830\pi$
$73$	−3564.71	−	3564.71i	−0.668927	−	0.668927i	−0.957468	+	0.288541i	$0.906830\pi$
$74$	−4761.82			−0.869579
$75$	649.482	−	224.128i	0.115464	−	0.0398450i
$76$	1798.93	−	1798.93i	0.311450	−	0.311450i
$77$	1148.55			0.193717
$78$	−597.612	+	73.6971i	−0.0982268	+	0.0121133i
$79$	9655.76			1.54715			0.773574	−	0.633705i	$-0.218467\pi$
$79$	9655.76			1.54715			0.773574	+	0.633705i	$0.218467\pi$
$80$	2806.85	+	2000.67i	0.438570	+	0.312604i
$81$	6268.80			0.955464
$82$	−3423.13			−0.509091
$83$	5501.76	−	5501.76i	0.798630	−	0.798630i	−0.184249	−	0.982880i	$-0.558985\pi$
$83$	5501.76	−	5501.76i	0.798630	−	0.798630i	0.982880	+	0.184249i	$0.0589853\pi$
$84$	−43.1984	−	43.1984i	−0.00612222	−	0.00612222i
$85$	7697.84	+	5486.87i	1.06544	+	0.759429i
$86$	−6803.79	+	6803.79i	−0.919928	+	0.919928i
$87$			357.174i			0.0471891i
$88$	−7912.53			−1.02176
$89$	−7002.82	+	7002.82i	−0.884082	+	0.884082i	−0.993947	−	0.109864i	$-0.964958\pi$
$89$	−7002.82	+	7002.82i	−0.884082	+	0.884082i	0.109864	+	0.993947i	$0.464958\pi$
$90$	6376.25	−	1069.24i	0.787192	−	0.132006i
$91$	−1696.20	+	209.174i	−0.204831	+	0.0252596i
$92$		−	3616.13i		−	0.427237i
$93$	991.709	−	991.709i	0.114662	−	0.114662i
$94$	5075.70			0.574434
$95$	−1914.10	−	11414.4i	−0.212089	−	1.26475i
$96$	519.120	+	519.120i	0.0563281	+	0.0563281i
$97$	−7025.25	+	7025.25i	−0.746652	+	0.746652i	−0.973849	−	0.227197i	$-0.927044\pi$
$97$	−7025.25	+	7025.25i	−0.746652	+	0.746652i	0.227197	+	0.973849i	$0.427044\pi$
$98$	−5268.23	−	5268.23i	−0.548545	−	0.548545i
$99$	−6407.99	+	6407.99i	−0.653810	+	0.653810i
$100$	−3246.71	+	1120.40i	−0.324671	+	0.112040i
$101$		−	9633.24i		−	0.944342i	−0.881507	−	0.472171i	$-0.843470\pi$
$101$		−	9633.24i		−	0.944342i	0.881507	−	0.472171i	$-0.156530\pi$
$102$	−952.648	−	952.648i	−0.0915655	−	0.0915655i
$103$	−16937.9			−1.59656			−0.798281	−	0.602286i	$-0.794257\pi$
$103$	−16937.9			−1.59656			−0.798281	+	0.602286i	$0.794257\pi$
$104$	11685.4	−	1441.04i	1.08038	−	0.133232i
$105$	−274.098	+	45.9639i	−0.0248615	+	0.00416906i
$106$	−12322.2	−	12322.2i	−1.09667	−	1.09667i
$107$			11406.2i			0.996265i	0.867101	+	0.498132i	$0.165981\pi$
$107$			11406.2i			0.996265i	−0.867101	+	0.498132i	$0.834019\pi$
$108$	971.353			0.0832779
$109$	−1699.18	−	1699.18i	−0.143017	−	0.143017i	0.631973	−	0.774990i	$-0.282245\pi$
$109$	−1699.18	−	1699.18i	−0.143017	−	0.143017i	−0.774990	+	0.631973i	$0.782245\pi$
$110$	−5341.44	+	7493.80i	−0.441441	+	0.619322i
$111$	−1142.05	+	1142.05i	−0.0926915	+	0.0926915i
$112$	−985.917	−	985.917i	−0.0785967	−	0.0785967i
$113$			2274.22i			0.178105i	0.996027	+	0.0890524i	$0.0283838\pi$
$113$			2274.22i			0.178105i	−0.996027	+	0.0890524i	$0.971616\pi$
$114$			1649.47i			0.126921i
$115$	−13396.2	−	9548.52i	−1.01294	−	0.722005i
$116$		−	1785.49i		−	0.132691i
$117$	8296.45	−	10630.5i	0.606067	−	0.776573i
$118$		−	925.118i		−	0.0664406i
$119$	−2703.90	−	2703.90i	−0.190940	−	0.190940i
$120$	1888.31	−	316.653i	0.131132	−	0.0219898i
$121$			1741.87i			0.118972i
$122$	2706.71	−	2706.71i	0.181853	−	0.181853i
$123$	−820.987	+	820.987i	−0.0542658	+	0.0542658i
$124$	−4957.47	+	4957.47i	−0.322416	+	0.322416i
$125$	−4422.48	+	14986.1i	−0.283039	+	0.959109i
$126$	−2615.27			−0.164731
$127$	−13365.0			−0.828634			−0.414317	−	0.910133i	$-0.635979\pi$
$127$	−13365.0			−0.828634			−0.414317	+	0.910133i	$0.635979\pi$
$128$	2460.69	+	2460.69i	0.150188	+	0.150188i
$129$			3263.58i			0.196117i
$130$	6523.59	−	12039.8i	0.386011	−	0.712416i
$131$	28375.0			1.65346			0.826729	−	0.562600i	$-0.190199\pi$
$131$	28375.0			1.65346			0.826729	+	0.562600i	$0.190199\pi$
$132$	−485.154	+	485.154i	−0.0278440	+	0.0278440i
$133$			4681.69i			0.264667i
$134$		−	9684.66i		−	0.539355i
$135$	2564.89	−	3598.43i	0.140735	−	0.197445i
$136$	18627.6	+	18627.6i	1.00712	+	1.00712i
$137$	7824.49	+	7824.49i	0.416884	+	0.416884i	0.884128	−	0.467244i	$-0.154753\pi$
$137$	7824.49	+	7824.49i	0.416884	+	0.416884i	−0.467244	+	0.884128i	$0.654753\pi$
$138$	1657.84	+	1657.84i	0.0870534	+	0.0870534i
$139$	−9023.30			−0.467020			−0.233510	−	0.972354i	$-0.575021\pi$
$139$	−9023.30			−0.467020			−0.233510	+	0.972354i	$0.575021\pi$
$140$	1370.19	−	229.770i	0.0699077	−	0.0117229i
$141$	1217.33	−	1217.33i	0.0612309	−	0.0612309i
$142$	216.927			0.0107582
$143$	2349.20	+	19049.8i	0.114881	+	0.931574i
$144$	11001.3			0.530541
$145$	−6614.43	−	4714.64i	−0.314598	−	0.224240i
$146$	−16339.2			−0.766522
$147$	−2527.01			−0.116943
$148$	5709.02	−	5709.02i	0.260638	−	0.260638i
$149$	6661.73	+	6661.73i	0.300065	+	0.300065i	0.841039	−	0.540974i	$-0.181944\pi$
$149$	6661.73	+	6661.73i	0.300065	+	0.300065i	−0.540974	+	0.841039i	$0.681944\pi$
$150$	974.825	−	2002.14i	0.0433255	−	0.0889839i
$151$	−11958.7	+	11958.7i	−0.524480	+	0.524480i	−0.918921	−	0.394441i	$-0.870938\pi$
$151$	−11958.7	+	11958.7i	−0.524480	+	0.524480i	0.394441	+	0.918921i	$0.370938\pi$
$152$		−	32253.0i		−	1.39599i
$153$	30171.3			1.28888
$154$	2632.23	−	2632.23i	0.110990	−	0.110990i
$155$	5274.84	+	31455.6i	0.219556	+	1.30929i
$156$	628.130	−	804.844i	0.0258107	−	0.0330722i
$157$			12185.8i			0.494373i	0.968968	+	0.247186i	$0.0795060\pi$
$157$			12185.8i			0.494373i	−0.968968	+	0.247186i	$0.920494\pi$
$158$	22129.0	−	22129.0i	0.886437	−	0.886437i
$159$	−5910.60			−0.233796
$160$	−16465.7	+	2761.17i	−0.643193	+	0.107858i
$161$	4705.46	+	4705.46i	0.181531	+	0.181531i
$162$	14366.8	−	14366.8i	0.547432	−	0.547432i
$163$	12033.8	+	12033.8i	0.452926	+	0.452926i	0.896325	−	0.443399i	$-0.146227\pi$
$163$	12033.8	+	12033.8i	0.452926	+	0.452926i	−0.443399	+	0.896325i	$0.646227\pi$
$164$	4104.05	−	4104.05i	0.152590	−	0.152590i
$165$	516.213	+	3078.34i	0.0189610	+	0.113070i
$166$		−	25217.8i		−	0.915149i
$167$	7341.17	+	7341.17i	0.263228	+	0.263228i	0.826364	−	0.563136i	$-0.190405\pi$
$167$	7341.17	+	7341.17i	0.263228	+	0.263228i	−0.563136	+	0.826364i	$0.690405\pi$
$168$	−774.502			−0.0274413
$169$	−6938.73	−	27705.3i	−0.242944	−	0.970040i
$170$	30216.7	−	5067.08i	1.04556	−	0.175332i
$171$	−26120.2	−	26120.2i	−0.893273	−	0.893273i
$172$		−	16314.4i		−	0.551459i
$173$	22248.3			0.743370			0.371685	−	0.928359i	$-0.378780\pi$
$173$	22248.3			0.743370			0.371685	+	0.928359i	$0.378780\pi$
$174$	818.570	+	818.570i	0.0270369	+	0.0270369i
$175$	2766.85	−	5682.67i	0.0903460	−	0.185556i
$176$	−11072.7	+	11072.7i	−0.357460	+	0.357460i
$177$	−221.876	−	221.876i	−0.00708213	−	0.00708213i
$178$			32098.0i			1.01307i
$179$		−	13136.4i		−	0.409986i	−0.978763	−	0.204993i	$-0.934283\pi$
$179$		−	13136.4i		−	0.409986i	0.978763	−	0.204993i	$-0.0657171\pi$
$180$	−6362.67	+	8926.54i	−0.196379	+	0.275510i
$181$			50636.4i			1.54563i	0.634631	+	0.772815i	$0.281152\pi$
$181$			50636.4i			1.54563i	−0.634631	+	0.772815i	$0.718848\pi$
$182$	−3407.96	+	4366.73i	−0.102885	+	0.131830i
$183$		−	1298.33i		−	0.0387688i
$184$	−32416.7	−	32416.7i	−0.957489	−	0.957489i
$185$	−6074.51	−	36224.3i	−0.177488	−	1.05842i
$186$		−	4545.59i		−	0.131391i
$187$	−30367.1	+	30367.1i	−0.868399	+	0.868399i
$188$	−6085.34	+	6085.34i	−0.172175	+	0.172175i
$189$	−1263.97	+	1263.97i	−0.0353844	+	0.0353844i
$190$	−30546.2	−	21772.7i	−0.846154	−	0.603123i
$191$	12466.4			0.341724			0.170862	−	0.985295i	$-0.445345\pi$
$191$	12466.4			0.341724			0.170862	+	0.985295i	$0.445345\pi$
$192$	4804.51			0.130331
$193$	14951.3	+	14951.3i	0.401387	+	0.401387i	0.878722	−	0.477335i	$-0.158397\pi$
$193$	14951.3	+	14951.3i	0.401387	+	0.401387i	−0.477335	+	0.878722i	$0.658397\pi$
$194$			32200.9i			0.855587i
$195$	−1322.99	−	4452.16i	−0.0347926	−	0.117085i
$196$	12632.3			0.328830
$197$	−8402.67	+	8402.67i	−0.216514	+	0.216514i	−0.807027	−	0.590514i	$-0.798925\pi$
$197$	−8402.67	+	8402.67i	−0.216514	+	0.216514i	0.590514	+	0.807027i	$0.298925\pi$
$198$			29371.6i			0.749199i
$199$		−	44195.0i		−	1.11601i	−0.829838	−	0.558004i	$-0.811567\pi$
$199$		−	44195.0i		−	1.11601i	0.829838	−	0.558004i	$-0.188433\pi$
$200$	−19061.3	+	39148.9i	−0.476532	+	0.978722i
$201$	−2322.72	−	2322.72i	−0.0574917	−	0.0574917i
$202$	−22077.4	−	22077.4i	−0.541060	−	0.541060i
$203$	2323.35	+	2323.35i	0.0563796	+	0.0563796i
$204$	2284.29			0.0548898
$205$	−4366.78	−	26040.6i	−0.103909	−	0.619644i
$206$	−38818.2	+	38818.2i	−0.914748	+	0.914748i
$207$	−52505.6			−1.22536
$208$	14335.8	−	18369.0i	0.331357	−	0.424579i
$209$	52579.3			1.20371
$210$	−522.836	+	733.515i	−0.0118557	+	0.0166330i
$211$	39531.6			0.887932			0.443966	−	0.896044i	$-0.353571\pi$
$211$	39531.6			0.887932			0.443966	+	0.896044i	$0.353571\pi$
$212$	29546.6			0.657409
$213$	52.0268	−	52.0268i	0.00114675	−	0.00114675i
$214$	26140.8	+	26140.8i	0.570809	+	0.570809i
$215$	−60437.5	−	43078.7i	−1.30746	−	0.931934i
$216$	8707.68	−	8707.68i	0.186636	−	0.186636i
$217$		−	12901.7i		−	0.273986i
$218$	−7788.35			−0.163882
$219$	−3918.71	+	3918.71i	−0.0817062	+	0.0817062i
$220$	−2580.51	−	15388.4i	−0.0533162	−	0.317942i
$221$	39316.4	−	50377.3i	0.804987	−	1.03146i
$222$			5234.70i			0.106215i
$223$	−35838.2	+	35838.2i	−0.720671	+	0.720671i	−0.968742	−	0.248071i	$-0.920203\pi$
$223$	−35838.2	+	35838.2i	−0.720671	+	0.720671i	0.248071	+	0.968742i	$0.420203\pi$
$224$	6753.54			0.134597
$225$	16268.0	+	47141.7i	0.321343	+	0.931194i
$226$	5212.05	+	5212.05i	0.102045	+	0.102045i
$227$	−19169.7	+	19169.7i	−0.372018	+	0.372018i	−0.868212	−	0.496194i	$-0.834731\pi$
$227$	−19169.7	+	19169.7i	−0.372018	+	0.372018i	0.496194	+	0.868212i	$0.334731\pi$
$228$	−1977.58	−	1977.58i	−0.0380421	−	0.0380421i
$229$	−60689.1	+	60689.1i	−1.15728	+	1.15728i	−0.172225	+	0.985058i	$0.555096\pi$
$229$	−60689.1	+	60689.1i	−1.15728	+	1.15728i	−0.985058	+	0.172225i	$0.944904\pi$
$230$	−52584.5	+	8817.98i	−0.994036	+	0.166692i
$231$		−	1262.60i		−	0.0236616i
$232$	−16005.9	−	16005.9i	−0.297376	−	0.297376i
$233$	56089.6			1.03317			0.516584	−	0.856237i	$-0.327203\pi$
$233$	56089.6			1.03317			0.516584	+	0.856237i	$0.327203\pi$
$234$	−5349.19	−	43376.7i	−0.0976914	−	0.792182i
$235$	6474.92	+	38612.0i	0.117246	+	0.699177i
$236$	1109.14	+	1109.14i	0.0199142	+	0.0199142i
$237$		−	10614.6i		−	0.188977i
$238$	−12393.6			−0.218798
$239$	−3412.27	−	3412.27i	−0.0597376	−	0.0597376i	0.676607	−	0.736344i	$-0.263450\pi$
$239$	−3412.27	−	3412.27i	−0.0597376	−	0.0597376i	−0.736344	+	0.676607i	$0.763450\pi$
$240$	2199.35	−	3085.59i	0.0381831	−	0.0535692i
$241$	−3152.50	+	3152.50i	−0.0542776	+	0.0542776i	−0.733725	−	0.679447i	$-0.762220\pi$
$241$	−3152.50	+	3152.50i	−0.0542776	+	0.0542776i	0.679447	+	0.733725i	$0.262220\pi$
$242$	3992.02	+	3992.02i	0.0681650	+	0.0681650i
$243$		−	21208.8i		−	0.359173i
$244$			6490.24i			0.109014i
$245$	33356.1	−	46797.2i	0.555704	−	0.779628i
$246$			3763.07i			0.0621830i
$247$	−77650.5	+	9575.81i	−1.27277	+	0.156957i
$248$			88882.3i			1.44515i
$249$	−6048.13	−	6048.13i	−0.0975489	−	0.0975489i
$250$	24209.6	+	44480.4i	0.387354	+	0.711687i
$251$		−	85216.5i		−	1.35262i	−0.736616	−	0.676311i	$-0.763578\pi$
$251$		−	85216.5i		−	1.35262i	0.736616	−	0.676311i	$-0.236422\pi$
$252$	3135.49	−	3135.49i	0.0493746	−	0.0493746i
$253$	52846.2	−	52846.2i	0.825606	−	0.825606i
$254$	−30629.9	+	30629.9i	−0.474765	+	0.474765i
$255$	6031.76	−	8462.29i	0.0927606	−	0.130139i
$256$	−58649.1			−0.894914
$257$	3884.88			0.0588181			0.0294091	−	0.999567i	$-0.490637\pi$
$257$	3884.88			0.0588181			0.0294091	+	0.999567i	$0.490637\pi$
$258$	7479.45	+	7479.45i	0.112365	+	0.112365i
$259$			14857.6i			0.221488i
$260$	6613.51	+	22256.0i	0.0978330	+	0.329231i
$261$	−25924.9			−0.380572
$262$	65029.7	−	65029.7i	0.947347	−	0.947347i
$263$		−	84154.9i		−	1.21666i	−0.793686	−	0.608328i	$-0.791840\pi$
$263$		−	84154.9i		−	1.21666i	0.793686	−	0.608328i	$-0.208160\pi$
$264$			8698.30i			0.124803i
$265$	78018.9	−	109457.i	1.11098	−	1.55866i
$266$	10729.5	+	10729.5i	0.151641	+	0.151641i
$267$	7698.24	+	7698.24i	0.107986	+	0.107986i
$268$	11611.1	+	11611.1i	0.161661	+	0.161661i
$269$	535.078			0.00739457			0.00369728	−	0.999993i	$-0.498823\pi$
$269$	535.078			0.00739457			0.00369728	+	0.999993i	$0.498823\pi$
$270$	−2368.66	−	14125.1i	−0.0324919	−	0.193760i
$271$	−38486.2	+	38486.2i	−0.524042	+	0.524042i	−0.918790	−	0.394748i	$-0.870832\pi$
$271$	−38486.2	+	38486.2i	−0.524042	+	0.524042i	0.394748	+	0.918790i	$0.370832\pi$
$272$	52134.5			0.704672
$273$	229.947	+	1864.65i	0.00308533	+	0.0250191i
$274$	35864.3			0.477706
$275$	−63821.1	−	31074.0i	−0.843915	−	0.410896i
$276$	−3975.24			−0.0521849
$277$	142370.			1.85550			0.927748	−	0.373207i	$-0.121742\pi$
$277$	142370.			1.85550			0.927748	+	0.373207i	$0.121742\pi$
$278$	−20679.6	+	20679.6i	−0.267579	+	0.267579i
$279$	71981.7	+	71981.7i	0.924727	+	0.924727i
$280$	10223.3	−	14342.8i	0.130399	−	0.182944i
$281$	−44390.2	+	44390.2i	−0.562179	+	0.562179i	−0.929926	−	0.367747i	$-0.880129\pi$
$281$	−44390.2	+	44390.2i	−0.562179	+	0.562179i	0.367747	+	0.929926i	$0.380129\pi$
$282$		−	5579.75i		−	0.0701643i
$283$	28274.1			0.353034			0.176517	−	0.984298i	$-0.443517\pi$
$283$	28274.1			0.353034			0.176517	+	0.984298i	$0.443517\pi$
$284$	−260.078	+	260.078i	−0.00322453	+	0.00322453i
$285$	−12547.9	+	2104.18i	−0.154483	+	0.0259056i
$286$	49042.0	+	38274.3i	0.599565	+	0.467923i
$287$			10680.7i			0.129669i
$288$	−37679.5	+	37679.5i	−0.454276	+	0.454276i
$289$	59459.0			0.711904
$290$	−25963.9	+	4353.93i	−0.308727	+	0.0517709i
$291$	7722.90	+	7722.90i	0.0912000	+	0.0912000i
$292$	19589.3	−	19589.3i	0.229749	−	0.229749i
$293$	−52408.5	−	52408.5i	−0.610473	−	0.610473i	0.332596	−	0.943069i	$-0.392075\pi$
$293$	−52408.5	−	52408.5i	−0.610473	−	0.610473i	−0.943069	+	0.332596i	$0.892075\pi$
$294$	−5791.40	+	5791.40i	−0.0670021	+	0.0670021i
$295$	7037.60	−	1180.15i	0.0808687	−	0.0135610i
$296$		−	102357.i		−	1.16824i
$297$	14195.4	+	14195.4i	0.160929	+	0.160929i
$298$	30534.7			0.343843
$299$	−68420.2	+	87669.1i	−0.765319	+	0.980627i
$300$	1231.66	+	3569.13i	0.0136851	+	0.0396570i
$301$	21228.9	+	21228.9i	0.234312	+	0.234312i
$302$			54813.7i			0.601001i
$303$	−10589.9			−0.115347
$304$	−45134.4	−	45134.4i	−0.488382	−	0.488382i
$305$	24043.4	+	17137.7i	0.258462	+	0.184227i
$306$	69146.5	−	69146.5i	0.738461	−	0.738461i
$307$	4814.93	+	4814.93i	0.0510873	+	0.0510873i	0.732189	−	0.681102i	$-0.238499\pi$
$307$	4814.93	+	4814.93i	0.0510873	+	0.0510873i	−0.681102	+	0.732189i	$0.738499\pi$
$308$			6311.66i			0.0665338i
$309$			18620.0i			0.195012i
$310$	84178.7	+	60001.0i	0.875949	+	0.624360i
$311$		−	38167.0i		−	0.394609i	−0.980342	−	0.197305i	$-0.936781\pi$
$311$		−	38167.0i		−	0.394609i	0.980342	−	0.197305i	$-0.0632188\pi$
$312$	−1584.14	−	12845.9i	−0.0162737	−	0.131964i
$313$			10314.7i			0.105285i	0.998613	+	0.0526427i	$0.0167644\pi$
$313$			10314.7i			0.105285i	−0.998613	+	0.0526427i	$0.983236\pi$
$314$	27927.4	+	27927.4i	0.283250	+	0.283250i
$315$	−3336.22	−	19895.0i	−0.0336228	−	0.200503i
$316$			53061.7i			0.531383i
$317$	−87689.0	+	87689.0i	−0.872623	+	0.872623i	−0.992758	−	0.120134i	$-0.961667\pi$
$317$	−87689.0	+	87689.0i	−0.872623	+	0.872623i	0.120134	+	0.992758i	$0.461667\pi$
$318$	−13545.9	+	13545.9i	−0.133953	+	0.133953i
$319$	26093.1	−	26093.1i	0.256416	−	0.256416i
$320$	−63418.7	+	88973.7i	−0.619324	+	0.868884i
$321$	12539.0			0.121689
$322$	21567.9			0.208016
$323$	−123782.	−	123782.i	−1.18646	−	1.18646i
$324$			34449.2i			0.328163i
$325$	99911.8	+	34267.7i	0.945910	+	0.324428i
$326$	55158.0			0.519007
$327$	−1867.92	+	1867.92i	−0.0174688	+	0.0174688i
$328$		−	73581.3i		−	0.683943i
$329$		−	15837.0i		−	0.146312i
$330$	8237.99	+	5871.88i	0.0756473	+	0.0539199i
$331$	46064.0	+	46064.0i	0.420442	+	0.420442i	0.885356	−	0.464914i	$-0.153915\pi$
$331$	46064.0	+	46064.0i	0.420442	+	0.420442i	−0.464914	+	0.885356i	$0.653915\pi$
$332$	30234.1	+	30234.1i	0.274297	+	0.274297i
$333$	−82894.1	−	82894.1i	−0.747541	−	0.747541i
$334$	33648.9			0.301632
$335$	73673.5	−	12354.4i	0.656481	−	0.110086i
$336$	−1083.83	+	1083.83i	−0.00960022	+	0.00960022i
$337$	−99764.7			−0.878450			−0.439225	−	0.898377i	$-0.644747\pi$
$337$	−99764.7			−0.878450			−0.439225	+	0.898377i	$0.644747\pi$
$338$	−79397.1	−	47592.8i	−0.694978	−	0.416589i
$339$	2500.07			0.0217546
$340$	−30152.3	+	42302.3i	−0.260833	+	0.365937i
$341$	−144897.			−1.24610
$342$	−119724.			−1.02360
$343$	−33606.7	+	33606.7i	−0.285653	+	0.285653i
$344$	−146250.	−	146250.i	−1.23589	−	1.23589i
$345$	−10496.8	+	14726.5i	−0.0881895	+	0.123726i
$346$	50988.6	−	50988.6i	0.425913	−	0.425913i
$347$		−	77520.9i		−	0.643813i	−0.946771	−	0.321906i	$-0.895676\pi$
$347$		−	77520.9i		−	0.643813i	0.946771	−	0.321906i	$-0.104324\pi$
$348$	−1962.80			−0.0162075
$349$	−5913.25	+	5913.25i	−0.0485484	+	0.0485484i	−0.730964	−	0.682416i	$-0.760929\pi$
$349$	−5913.25	+	5913.25i	−0.0485484	+	0.0485484i	0.682416	+	0.730964i	$0.260929\pi$
$350$	−6682.46	−	19364.6i	−0.0545507	−	0.158078i
$351$	−23549.4	−	18378.8i	−0.191146	−	0.149178i
$352$		−	75847.9i		−	0.612151i
$353$	−60622.2	+	60622.2i	−0.486499	+	0.486499i	−0.907200	−	0.420700i	$-0.861784\pi$
$353$	−60622.2	+	60622.2i	−0.486499	+	0.486499i	0.420700	+	0.907200i	$0.361784\pi$
$354$	−1016.99			−0.00811540
$355$	276.728	+	1650.22i	0.00219582	+	0.0130944i
$356$	−38482.9	−	38482.9i	−0.303646	−	0.303646i
$357$	−2972.42	+	2972.42i	−0.0233224	+	0.0233224i
$358$	−30105.8	−	30105.8i	−0.234901	−	0.234901i
$359$	105255.	−	105255.i	0.816682	−	0.816682i	−0.168943	−	0.985626i	$-0.554036\pi$
$359$	105255.	−	105255.i	0.816682	−	0.816682i	0.985626	+	0.168943i	$0.0540355\pi$
$360$	22983.8	+	137060.i	0.177344	+	1.05756i
$361$			84002.4i			0.644581i
$362$	116048.	+	116048.i	0.885567	+	0.885567i
$363$	1914.85			0.0145319
$364$	−1149.49	−	9321.22i	−0.00867563	−	0.0703509i
$365$	−20843.4	−	124296.i	−0.156453	−	0.932978i
$366$	−2975.50	−	2975.50i	−0.0222125	−	0.0222125i
$367$			86356.1i			0.641151i	0.947223	+	0.320576i	$0.103876\pi$
$367$			86356.1i			0.641151i	−0.947223	+	0.320576i	$0.896124\pi$
$368$	−90727.0			−0.669947
$369$	−59590.1	−	59590.1i	−0.437644	−	0.437644i
$370$	−96940.2	−	69097.1i	−0.708109	−	0.504727i
$371$	−38447.3	+	38447.3i	−0.279330	+	0.279330i
$372$	5449.78	+	5449.78i	0.0393816	+	0.0393816i
$373$		−	7869.47i		−	0.0565624i	−0.999600	−	0.0282812i	$-0.990997\pi$
$373$		−	7869.47i		−	0.0565624i	0.999600	−	0.0282812i	$-0.00900339\pi$
$374$			139190.i			0.995097i
$375$	16474.3	+	4861.66i	0.117151	+	0.0345718i
$376$			109104.i			0.771728i
$377$	−33782.9	+	43287.1i	−0.237692	+	0.304562i
$378$			5793.50i			0.0405469i
$379$	−48947.9	−	48947.9i	−0.340766	−	0.340766i	0.515889	−	0.856655i	$-0.327462\pi$
$379$	−48947.9	−	48947.9i	−0.340766	−	0.340766i	−0.856655	+	0.515889i	$0.827462\pi$
$380$	62726.1	−	10518.6i	0.434391	−	0.0728438i
$381$			14692.3i			0.101214i
$382$	28570.5	−	28570.5i	0.195790	−	0.195790i
$383$	−89959.9	+	89959.9i	−0.613270	+	0.613270i	−0.943797	−	0.330527i	$-0.892774\pi$
$383$	−89959.9	+	89959.9i	−0.613270	+	0.613270i	0.330527	+	0.943797i	$0.392774\pi$
$384$	2705.05	−	2705.05i	0.0183448	−	0.0183448i
$385$	23381.9	+	16666.2i	0.157746	+	0.112438i
$386$	68530.5			0.459948
$387$	−236882.			−1.58165
$388$	−38606.2	−	38606.2i	−0.256444	−	0.256444i
$389$		−	230603.i		−	1.52393i	−0.647618	−	0.761965i	$-0.724235\pi$
$389$		−	230603.i		−	1.52393i	0.647618	−	0.761965i	$-0.275765\pi$
$390$	−13235.5	−	7171.43i	−0.0870182	−	0.0471494i
$391$	−248821.			−1.62755
$392$	113242.	−	113242.i	0.736948	−	0.736948i
$393$		−	31192.8i		−	0.201962i
$394$			38514.4i			0.248102i
$395$	196570.	+	140111.i	1.25986	+	0.898006i
$396$	−35214.1	−	35214.1i	−0.224557	−	0.224557i
$397$	190193.	+	190193.i	1.20674	+	1.20674i	0.972077	+	0.234664i	$0.0753989\pi$
$397$	190193.	+	190193.i	1.20674	+	1.20674i	0.234664	+	0.972077i	$0.424601\pi$
$398$	−101286.	−	101286.i	−0.639416	−	0.639416i
$399$	5146.62			0.0323278
$400$	28110.3	+	81458.4i	0.175689	+	0.509115i
$401$	130603.	−	130603.i	0.812206	−	0.812206i	−0.172759	−	0.984964i	$-0.555268\pi$
$401$	130603.	−	130603.i	0.812206	−	0.812206i	0.984964	+	0.172759i	$0.0552681\pi$
$402$	−10646.4			−0.0658796
$403$	213988.	−	26388.9i	1.31759	−	0.162484i
$404$	52938.0			0.324343
$405$	127619.	+	90964.5i	0.778047	+	0.554577i
$406$	10649.3			0.0646053
$407$	166864.			1.00733
$408$	20477.5	−	20477.5i	0.123015	−	0.123015i
$409$	18615.3	+	18615.3i	0.111282	+	0.111282i	0.760555	−	0.649273i	$-0.224927\pi$
$409$	18615.3	+	18615.3i	0.111282	+	0.111282i	−0.649273	+	0.760555i	$0.724927\pi$
$410$	−69687.4	−	49671.8i	−0.414559	−	0.295490i
$411$	8601.52	−	8601.52i	0.0509204	−	0.0509204i
$412$		−	93079.7i		−	0.548354i
$413$	−2886.52			−0.0169229
$414$	−120332.	+	120332.i	−0.702071	+	0.702071i
$415$	191838.	−	32169.7i	1.11388	−	0.186789i
$416$	13813.5	+	112014.i	0.0798210	+	0.647271i
$417$			9919.38i			0.0570443i
$418$	120501.	−	120501.i	0.689665	−	0.689665i
$419$	−28942.0			−0.164854			−0.0824271	−	0.996597i	$-0.526267\pi$
$419$	−28942.0			−0.164854			−0.0824271	+	0.996597i	$0.526267\pi$
$420$	−252.587	−	1506.26i	−0.00143190	−	0.00853890i
$421$	164840.	+	164840.i	0.930033	+	0.930033i	0.997707	−	0.0676742i	$-0.0215578\pi$
$421$	164840.	+	164840.i	0.930033	+	0.930033i	−0.0676742	+	0.997707i	$0.521558\pi$
$422$	90598.4	−	90598.4i	0.508740	−	0.508740i
$423$	88358.1	+	88358.1i	0.493817	+	0.493817i
$424$	264870.	−	264870.i	1.47333	−	1.47333i
$425$	77093.0	+	223401.i	0.426813	+	1.23682i
$426$		−	238.470i		−	0.00131406i
$427$	−8445.37	−	8445.37i	−0.0463194	−	0.0463194i
$428$	−62681.2			−0.342176
$429$	20941.5	−	2582.50i	0.113787	−	0.0140322i
$430$	−237238.	+	39782.8i	−1.28306	+	0.215158i
$431$	55454.5	+	55454.5i	0.298526	+	0.298526i	0.840436	−	0.541910i	$-0.182299\pi$
$431$	55454.5	+	55454.5i	0.298526	+	0.298526i	−0.541910	+	0.840436i	$0.682299\pi$
$432$		−	24370.8i		−	0.130588i
$433$	−182899.			−0.975517			−0.487759	−	0.872979i	$-0.662185\pi$
$433$	−182899.			−0.975517			−0.487759	+	0.872979i	$0.662185\pi$
$434$	−29568.1	−	29568.1i	−0.156980	−	0.156980i
$435$	−5182.83	+	7271.29i	−0.0273898	+	0.0384267i
$436$	9337.58	−	9337.58i	0.0491204	−	0.0491204i
$437$	215411.	+	215411.i	1.12799	+	1.12799i
$438$			17961.8i			0.0936270i
$439$			153939.i			0.798766i	0.916784	+	0.399383i	$0.130776\pi$
$439$			153939.i			0.798766i	−0.916784	+	0.399383i	$0.869224\pi$
$440$	−161082.	−	114816.i	−0.832034	−	0.593058i
$441$		−	183419.i		−	0.943122i
$442$	−25349.5	−	205560.i	−0.129755	−	1.05219i
$443$		−	204083.i		−	1.03992i	−0.854191	−	0.519959i	$-0.825947\pi$
$443$		−	204083.i		−	1.03992i	0.854191	−	0.519959i	$-0.174053\pi$
$444$	−6275.97	−	6275.97i	−0.0318357	−	0.0318357i
$445$	−244178.	+	40946.5i	−1.23306	+	0.206775i
$446$			164268.i			0.825815i
$447$	7323.29	−	7323.29i	0.0366515	−	0.0366515i
$448$	31252.4	−	31252.4i	0.155714	−	0.155714i
$449$	−126288.	+	126288.i	−0.626423	+	0.626423i	−0.947166	−	0.320743i	$-0.896067\pi$
$449$	−126288.	+	126288.i	−0.626423	+	0.626423i	0.320743	+	0.947166i	$0.396067\pi$
$450$	145322.	+	70756.2i	0.717640	+	0.349413i
$451$	119953.			0.589738
$452$	−12497.6			−0.0611717
$453$	13146.2	+	13146.2i	0.0640627	+	0.0640627i
$454$			87866.2i			0.426295i
$455$	−37566.2	−	20354.7i	−0.181457	−	0.0983199i
$456$	−35455.9			−0.170514
$457$	−69518.2	+	69518.2i	−0.332864	+	0.332864i	−0.853673	−	0.520809i	$-0.825630\pi$
$457$	−69518.2	+	69518.2i	−0.332864	+	0.332864i	0.520809	+	0.853673i	$0.325630\pi$
$458$			278174.i			1.32613i
$459$		−	66837.4i		−	0.317245i
$460$	52472.4	−	73616.5i	0.247979	−	0.347904i
$461$	−157674.	−	157674.i	−0.741921	−	0.741921i	0.231026	−	0.972948i	$-0.425792\pi$
$461$	−157674.	−	157674.i	−0.741921	−	0.741921i	−0.972948	+	0.231026i	$0.925792\pi$
$462$	−2893.63	−	2893.63i	−0.0135569	−	0.0135569i
$463$	259833.	+	259833.i	1.21209	+	1.21209i	0.970340	+	0.241745i	$0.0777199\pi$
$463$	259833.	+	259833.i	1.21209	+	1.21209i	0.241745	+	0.970340i	$0.422280\pi$
$464$	−44797.0			−0.208071
$465$	34579.4	−	5798.67i	0.159923	−	0.0268178i
$466$	128546.	−	128546.i	0.591952	−	0.591952i
$467$	−157706.			−0.723126			−0.361563	−	0.932348i	$-0.617757\pi$
$467$	−157706.			−0.723126			−0.361563	+	0.932348i	$0.617757\pi$
$468$	58418.4	+	45591.9i	0.266721	+	0.208159i
$469$	−30217.7			−0.137378
$470$	103330.	+	73651.7i	0.467769	+	0.333417i
$471$	13395.9			0.0603853
$472$	19885.7			0.0892602
$473$	238419.	−	238419.i	1.06566	−	1.06566i
$474$	−24326.6	−	24326.6i	−0.108274	−	0.108274i
$475$	126664.	−	260147.i	0.561390	−	1.15301i
$476$	14858.9	−	14858.9i	0.0655801	−	0.0655801i
$477$		−	429012.i		−	1.88553i
$478$	−15640.5			−0.0684532
$479$	97819.8	−	97819.8i	0.426340	−	0.426340i	−0.461040	−	0.887379i	$-0.652523\pi$
$479$	97819.8	−	97819.8i	0.426340	−	0.426340i	0.887379	+	0.461040i	$0.152523\pi$
$480$	3035.37	+	18100.9i	0.0131744	+	0.0785630i
$481$	−246429.	+	30389.4i	−1.06513	+	0.131351i
$482$			14449.8i			0.0621966i
$483$	5172.74	−	5172.74i	0.0221731	−	0.0221731i
$484$	−9572.19			−0.0408621
$485$	−244960.	+	41077.7i	−1.04138	+	0.174632i
$486$	−48606.3	−	48606.3i	−0.205788	−	0.205788i
$487$	−189834.	+	189834.i	−0.800415	+	0.800415i	−0.983160	−	0.182745i	$-0.941502\pi$
$487$	−189834.	+	189834.i	−0.800415	+	0.800415i	0.182745	+	0.983160i	$0.441502\pi$
$488$	58181.6	+	58181.6i	0.244313	+	0.244313i
$489$	13228.8	−	13228.8i	0.0553227	−	0.0553227i
$490$	−30804.1	−	183695.i	−0.128297	−	0.765077i
$491$			98605.8i			0.409015i	0.978865	+	0.204508i	$0.0655593\pi$
$491$			98605.8i			0.409015i	−0.978865	+	0.204508i	$0.934441\pi$
$492$	−4511.61	−	4511.61i	−0.0186381	−	0.0186381i
$493$	−122857.			−0.505481
$494$	−156013.	+	199905.i	−0.639304	+	0.819161i
$495$	−223437.	+	37468.5i	−0.911894	+	0.152917i
$496$	124381.	+	124381.i	0.505579	+	0.505579i
$497$		−	676.849i		−	0.00274018i
$498$	−27722.1			−0.111781
$499$	−268778.	−	268778.i	−1.07943	−	1.07943i	−0.996561	−	0.0828653i	$-0.973593\pi$
$499$	−268778.	−	268778.i	−1.07943	−	1.07943i	−0.0828653	−	0.996561i	$-0.526407\pi$
$500$	−82353.7	−	24303.0i	−0.329415	−	0.0972122i
$501$	8070.20	−	8070.20i	0.0321520	−	0.0321520i
$502$	−195299.	−	195299.i	−0.774983	−	0.774983i
$503$			415881.i			1.64374i	0.569676	+	0.821869i	$0.307069\pi$
$503$			415881.i			1.64374i	−0.569676	+	0.821869i	$0.692931\pi$
$504$		−	56216.0i		−	0.221309i
$505$	139785.	−	196112.i	0.548121	−	0.768990i
$506$		−	242226.i		−	0.946060i
$507$	−30456.7	+	7627.79i	−0.118486	+	0.0296745i
$508$		−	73445.5i		−	0.284602i
$509$	351664.	+	351664.i	1.35735	+	1.35735i	0.877168	+	0.480183i	$0.159430\pi$
$509$	351664.	+	351664.i	1.35735	+	1.35735i	0.480183	+	0.877168i	$0.340570\pi$
$510$	−5570.28	−	33217.4i	−0.0214159	−	0.127710i
$511$			50980.9i			0.195239i
$512$	−173783.	+	173783.i	−0.662928	+	0.662928i
$513$	−57863.1	+	57863.1i	−0.219871	+	0.219871i
$514$	8903.35	−	8903.35i	0.0336998	−	0.0336998i
$515$	−344819.	−	245780.i	−1.30010	−	0.926686i
$516$	−17934.5			−0.0673581
$517$	−177863.			−0.665432
$518$	34050.7	+	34050.7i	0.126901	+	0.126901i
$519$		−	24457.7i		−	0.0907991i
$520$	258800.	+	140227.i	0.957101	+	0.518590i
$521$	−173706.			−0.639941			−0.319971	−	0.947427i	$-0.603673\pi$
$521$	−173706.			−0.639941			−0.319971	+	0.947427i	$0.603673\pi$
$522$	−59414.7	+	59414.7i	−0.218048	+	0.218048i
$523$			3878.28i			0.0141787i	0.999975	+	0.00708934i	$0.00225663\pi$
$523$			3878.28i			0.0141787i	−0.999975	+	0.00708934i	$0.997743\pi$
$524$			155931.i			0.567896i
$525$	−6246.99	−	3041.61i	−0.0226648	−	0.0110353i
$526$	−192866.	−	192866.i	−0.697082	−	0.697082i
$527$	341116.	+	341116.i	1.22824	+	1.22824i
$528$	12172.3	+	12172.3i	0.0436620	+	0.0436620i
$529$	153169.			0.547343
$530$	−72049.8	−	429656.i	−0.256496	−	1.52957i
$531$	16104.5	−	16104.5i	0.0571162	−	0.0571162i
$532$	−25727.5			−0.0909023
$533$	−177150.	+	21846.0i	−0.623573	+	0.0768986i
$534$	35285.6			0.123741
$535$	−165512.	+	232206.i	−0.578259	+	0.811271i
$536$	208175.			0.724602
$537$	−14440.9			−0.0500778
$538$	1226.29	−	1226.29i	0.00423671	−	0.00423671i
$539$	184609.	+	184609.i	0.635442	+	0.635442i
$540$	19774.6	+	14095.0i	0.0678142	+	0.0483367i
$541$	−33703.7	+	33703.7i	−0.115155	+	0.115155i	−0.762336	−	0.647181i	$-0.775948\pi$
$541$	−33703.7	+	33703.7i	−0.115155	+	0.115155i	0.647181	+	0.762336i	$0.275948\pi$
$542$			176405.i			0.600499i
$543$	55664.9			0.188791
$544$	−178561.	+	178561.i	−0.603376	+	0.603376i
$545$	−9935.37	−	59247.8i	−0.0334496	−	0.199471i
$546$	4800.38	+	3746.40i	0.0161024	+	0.0125669i
$547$		−	461325.i		−	1.54182i	−0.636946	−	0.770908i	$-0.719803\pi$
$547$		−	461325.i		−	1.54182i	0.636946	−	0.770908i	$-0.280197\pi$
$548$	−42998.3	+	42998.3i	−0.143183	+	0.143183i
$549$	94237.2			0.312664
$550$	−217480.	+	75049.6i	−0.718942	+	0.248098i
$551$	106361.	+	106361.i	0.350330	+	0.350330i
$552$	−35635.9	+	35635.9i	−0.116953	+	0.116953i
$553$	−69046.2	−	69046.2i	−0.225782	−	0.225782i
$554$	326284.	−	326284.i	1.06310	−	1.06310i
$555$	−39821.6	+	6677.75i	−0.129280	+	0.0216792i
$556$		−	49586.2i		−	0.160402i
$557$	−148643.	−	148643.i	−0.479107	−	0.479107i	0.425739	−	0.904846i	$-0.360014\pi$
$557$	−148643.	−	148643.i	−0.479107	−	0.479107i	−0.904846	+	0.425739i	$0.860014\pi$
$558$	329934.			1.05964
$559$	−308682.	+	395524.i	−0.987841	+	1.26575i
$560$	−5764.81	−	34377.4i	−0.0183827	−	0.109622i
$561$	33382.7	+	33382.7i	0.106071	+	0.106071i
$562$			203467.i			0.644200i
$563$	372874.			1.17637			0.588186	−	0.808725i	$-0.299842\pi$
$563$	372874.			1.17637			0.588186	+	0.808725i	$0.299842\pi$
$564$	6689.66	+	6689.66i	0.0210303	+	0.0210303i
$565$	−33000.4	+	46298.1i	−0.103377	+	0.145033i
$566$	64798.5	−	64798.5i	0.202270	−	0.202270i
$567$	−44826.8	−	44826.8i	−0.139435	−	0.139435i
$568$			4662.93i			0.0144531i
$569$			613694.i			1.89552i	0.318989	+	0.947758i	$0.396657\pi$
$569$			613694.i			1.89552i	−0.318989	+	0.947758i	$0.603343\pi$
$570$	−23934.9	+	33579.6i	−0.0736686	+	0.103354i
$571$		−	295982.i		−	0.907805i	−0.891051	−	0.453903i	$-0.850031\pi$
$571$		−	295982.i		−	0.907805i	0.891051	−	0.453903i	$-0.149969\pi$
$572$	−104685.	+	12909.7i	−0.319958	+	0.0394570i
$573$		−	13704.4i		−	0.0417399i
$574$	24478.0	+	24478.0i	0.0742938	+	0.0742938i
$575$	−134161.	−	388774.i	−0.405780	−	1.17588i
$576$			348728.i			1.05110i
$577$	−306997.	+	306997.i	−0.922111	+	0.922111i	−0.997178	−	0.0750676i	$-0.976083\pi$
$577$	−306997.	+	306997.i	−0.922111	+	0.922111i	0.0750676	+	0.997178i	$0.476083\pi$
$578$	136268.	−	136268.i	0.407885	−	0.407885i
$579$	16436.0	−	16436.0i	0.0490275	−	0.0490275i
$580$	25908.6	−	36348.6i	0.0770172	−	0.108052i
$581$	−78683.8			−0.233095
$582$	35398.6			0.104506
$583$	431795.	+	431795.i	1.27040	+	1.27040i
$584$		−	351216.i		−	1.02979i
$585$	323153.	−	96027.0i	0.944272	−	0.280596i
$586$	−240219.			−0.699540
$587$	414611.	−	414611.i	1.20327	−	1.20327i	0.230108	−	0.973165i	$-0.426092\pi$
$587$	414611.	−	414611.i	1.20327	−	1.20327i	0.973165	−	0.230108i	$-0.0739080\pi$
$588$		−	13886.8i		−	0.0401650i
$589$		−	590629.i		−	1.70249i
$590$	13424.1	−	18833.4i	0.0385639	−	0.0541034i
$591$	9237.12	+	9237.12i	0.0264461	+	0.0264461i
$592$	−143237.	−	143237.i	−0.408706	−	0.408706i
$593$	−73896.8	−	73896.8i	−0.210144	−	0.210144i	0.594185	−	0.804328i	$-0.297475\pi$
$593$	−73896.8	−	73896.8i	−0.210144	−	0.210144i	−0.804328	+	0.594185i	$0.797475\pi$
$594$	65065.9			0.184408
$595$	−15810.1	−	94280.9i	−0.0446582	−	0.266311i
$596$	−36608.5	+	36608.5i	−0.103060	+	0.103060i
$597$	−48583.9			−0.136315
$598$	44114.4	+	357725.i	0.123361	+	1.00034i
$599$	−345614.			−0.963246			−0.481623	−	0.876379i	$-0.659953\pi$
$599$	−345614.			−0.963246			−0.481623	+	0.876379i	$0.659953\pi$
$600$	43036.6	+	20954.2i	0.119546	+	0.0582061i
$601$	317296.			0.878447			0.439224	−	0.898378i	$-0.355254\pi$
$601$	317296.			0.878447			0.439224	+	0.898378i	$0.355254\pi$
$602$	97304.7			0.268498
$603$	168591.	−	168591.i	0.463661	−	0.463661i
$604$	−65717.1	−	65717.1i	−0.180138	−	0.180138i
$605$	−25275.7	+	35460.7i	−0.0690546	+	0.0968806i
$606$	−24269.8	+	24269.8i	−0.0660879	+	0.0660879i
$607$		−	314157.i		−	0.852647i	−0.904571	−	0.426324i	$-0.859808\pi$
$607$		−	314157.i		−	0.852647i	0.904571	−	0.426324i	$-0.140192\pi$
$608$	309171.			0.836356
$609$	2554.07	−	2554.07i	0.00688650	−	0.00688650i
$610$	94378.8	−	15826.5i	0.253638	−	0.0425330i
$611$	262672.	−	32392.6i	0.703609	−	0.0867686i
$612$			165802.i			0.442677i
$613$	−275656.	+	275656.i	−0.733578	+	0.733578i	−0.971327	−	0.237749i	$-0.923590\pi$
$613$	−275656.	+	275656.i	−0.733578	+	0.733578i	0.237749	+	0.971327i	$0.423590\pi$
$614$	22069.7			0.0585409
$615$	−28626.6	+	4800.44i	−0.0756866	+	0.0126920i
$616$	56580.7	+	56580.7i	0.149110	+	0.149110i
$617$	261496.	−	261496.i	0.686901	−	0.686901i	−0.274645	−	0.961546i	$-0.588560\pi$
$617$	261496.	−	261496.i	0.686901	−	0.686901i	0.961546	+	0.274645i	$0.0885602\pi$
$618$	42673.2	+	42673.2i	0.111732	+	0.111732i
$619$	−51179.9	+	51179.9i	−0.133573	+	0.133573i	−0.770732	−	0.637159i	$-0.780109\pi$
$619$	−51179.9	+	51179.9i	−0.133573	+	0.133573i	0.637159	+	0.770732i	$0.280109\pi$
$620$	−172860.	+	28987.1i	−0.449687	+	0.0754087i
$621$			116314.i			0.301611i
$622$	−87470.9	−	87470.9i	−0.226091	−	0.226091i
$623$	100151.			0.258036
$624$	−20193.1	−	15759.5i	−0.0518603	−	0.0404737i
$625$	−307490.	+	240911.i	−0.787174	+	0.616731i
$626$	23639.2	+	23639.2i	0.0603232	+	0.0603232i
$627$		−	57800.8i		−	0.147028i
$628$	−66965.2			−0.169797
$629$	−392830.	−	392830.i	−0.992894	−	0.992894i
$630$	−53241.1	−	37949.2i	−0.134142	−	0.0956141i
$631$	−52670.3	+	52670.3i	−0.132284	+	0.132284i	−0.770149	−	0.637865i	$-0.779818\pi$
$631$	−52670.3	+	52670.3i	−0.132284	+	0.132284i	0.637865	+	0.770149i	$0.279818\pi$
$632$	475671.	+	475671.i	1.19089	+	1.19089i
$633$		−	43457.4i		−	0.108457i
$634$			401931.i			0.999937i
$635$	−272083.	−	193935.i	−0.674767	−	0.480961i
$636$		−	32480.8i		−	0.0802994i
$637$	−306257.	−	239014.i	−0.754757	−	0.589041i
$638$		−	119600.i		−	0.293826i
$639$	3776.29	+	3776.29i	0.00924834	+	0.00924834i
$640$	14388.0	+	85800.4i	0.0351270	+	0.209474i
$641$		−	74016.5i		−	0.180141i	−0.995935	−	0.0900704i	$-0.971291\pi$
$641$		−	74016.5i		−	0.180141i	0.995935	−	0.0900704i	$-0.0287092\pi$
$642$	28736.7	−	28736.7i	0.0697216	−	0.0697216i
$643$	309642.	−	309642.i	0.748923	−	0.748923i	−0.225354	−	0.974277i	$-0.572354\pi$
$643$	309642.	−	309642.i	0.748923	−	0.748923i	0.974277	+	0.225354i	$0.0723538\pi$
$644$	−25858.1	+	25858.1i	−0.0623484	+	0.0623484i
$645$	−47356.7	+	66439.3i	−0.113831	+	0.159700i
$646$	−567366.			−1.35956
$647$	601528.			1.43697			0.718485	−	0.695543i	$-0.244836\pi$
$647$	601528.			1.43697			0.718485	+	0.695543i	$0.244836\pi$
$648$	308820.	+	308820.i	0.735453	+	0.735453i
$649$			32418.0i			0.0769657i
$650$	307512.	−	150443.i	0.727839	−	0.356078i
$651$	−14183.0			−0.0334661
$652$	−66129.9	+	66129.9i	−0.155562	+	0.155562i
$653$			26326.8i			0.0617408i	0.999523	+	0.0308704i	$0.00982791\pi$
$653$			26326.8i			0.0617408i	−0.999523	+	0.0308704i	$0.990172\pi$
$654$			8561.78i			0.0200174i
$655$	577653.	+	411740.i	1.34643	+	0.959711i
$656$	−102969.	−	102969.i	−0.239275	−	0.239275i
$657$	−284434.	−	284434.i	−0.658947	−	0.658947i
$658$	−36295.2	−	36295.2i	−0.0838295	−	0.0838295i
$659$	841602.			1.93792			0.968961	−	0.247216i	$-0.0795156\pi$
$659$	841602.			1.93792			0.968961	+	0.247216i	$0.0795156\pi$
$660$	−16916.6	+	2836.77i	−0.0388351	+	0.00651232i
$661$	391000.	−	391000.i	0.894898	−	0.894898i	−0.100081	−	0.994979i	$-0.531910\pi$
$661$	391000.	−	391000.i	0.894898	−	0.894898i	0.994979	+	0.100081i	$0.0319101\pi$
$662$	211139.			0.481783
$663$	−55380.1	−	43220.7i	−0.125987	−	0.0983253i
$664$	542066.			1.22946
$665$	−67934.5	+	95309.1i	−0.153620	+	0.215522i
$666$	−379953.			−0.856605
$667$	213801.			0.480572
$668$	−40342.3	+	40342.3i	−0.0904081	+	0.0904081i
$669$	39397.2	+	39397.2i	0.0880265	+	0.0880265i
$670$	140531.	−	197159.i	0.313056	−	0.439204i
$671$	−94848.5	+	94848.5i	−0.210662	+	0.210662i
$672$		−	7424.21i		−	0.0164404i
$673$	−455368.			−1.00539			−0.502693	−	0.864465i	$-0.667657\pi$
$673$	−455368.			−1.00539			−0.502693	+	0.864465i	$0.667657\pi$
$674$	−228640.	+	228640.i	−0.503307	+	0.503307i
$675$	104431.	−	36037.9i	0.229204	−	0.0790956i
$676$	152250.	−	38130.7i	0.333169	−	0.0834414i
$677$			412628.i			0.900288i	0.892956	+	0.450144i	$0.148627\pi$
$677$			412628.i			0.900288i	−0.892956	+	0.450144i	$0.851373\pi$
$678$	5729.64	−	5729.64i	0.0124643	−	0.0124643i
$679$	100472.			0.217924
$680$	108919.	+	649518.i	0.235551	+	1.40467i
$681$	21073.4	+	21073.4i	0.0454403	+	0.0454403i
$682$	−332075.	+	332075.i	−0.713949	+	0.713949i
$683$	−555312.	−	555312.i	−1.19041	−	1.19041i	−0.976953	−	0.213455i	$-0.931528\pi$
$683$	−555312.	−	555312.i	−1.19041	−	1.19041i	−0.213455	−	0.976953i	$-0.568472\pi$
$684$	143540.	−	143540.i	0.306803	−	0.306803i
$685$	45751.0	+	272828.i	0.0975033	+	0.581444i
$686$			154040.i			0.327329i
$687$	66715.9	+	66715.9i	0.141357	+	0.141357i
$688$	−409319.			−0.864740
$689$	−716325.	−	559047.i	−1.50894	−	1.17763i
$690$	9693.67	+	57806.5i	0.0203606	+	0.121417i
$691$	70722.9	+	70722.9i	0.148117	+	0.148117i	0.777276	−	0.629159i	$-0.216601\pi$
$691$	70722.9	+	70722.9i	0.148117	+	0.148117i	−0.629159	+	0.777276i	$0.716601\pi$
$692$			122262.i			0.255317i
$693$	91644.2			0.190826
$694$	−177662.	−	177662.i	−0.368872	−	0.368872i
$695$	−183695.	−	130934.i	−0.380301	−	0.271071i
$696$	−17595.5	+	17595.5i	−0.0363230	+	0.0363230i
$697$	−282394.	−	282394.i	−0.581285	−	0.581285i
$698$			27103.9i			0.0556316i
$699$		−	61659.7i		−	0.126196i
$700$	31228.2	+	15204.8i	0.0637311	+	0.0310302i
$701$			838440.i			1.70622i	0.521728	+	0.853112i	$0.325288\pi$
$701$			838440.i			1.70622i	−0.521728	+	0.853112i	$0.674712\pi$
$702$	−96090.9	+	11849.9i	−0.194988	+	0.0240458i
$703$			680169.i			1.37628i
$704$	−350991.	−	350991.i	−0.708191	−	0.708191i
$705$	42446.5	−	7117.92i	0.0854011	−	0.0143211i
$706$			277867.i			0.557478i
$707$	−68885.1	+	68885.1i	−0.137812	+	0.137812i
$708$	1219.29	−	1219.29i	0.00243242	−	0.00243242i
$709$	−2835.58	+	2835.58i	−0.00564091	+	0.00564091i	−0.709922	−	0.704281i	$-0.751270\pi$
$709$	−2835.58	+	2835.58i	−0.00564091	+	0.00564091i	0.704281	+	0.709922i	$0.251270\pi$
$710$	4416.17	+	3147.76i	0.00876050	+	0.00624432i
$711$	770448.			1.52407
$712$	−689959.			−1.36102
$713$	−593628.	−	593628.i	−1.16771	−	1.16771i
$714$			13624.3i			0.0267251i
$715$	−228600.	+	421900.i	−0.447161	+	0.825273i
$716$	72188.8			0.140813
$717$	−3751.13	+	3751.13i	−0.00729666	+	0.00729666i
$718$		−	482445.i		−	0.935834i
$719$		−	732382.i		−	1.41671i	−0.705858	−	0.708353i	$-0.749438\pi$
$719$		−	732382.i		−	1.41671i	0.705858	−	0.708353i	$-0.250562\pi$
$720$	223963.	+	159636.i	0.432026	+	0.307940i
$721$	121119.	+	121119.i	0.232993	+	0.232993i
$722$	192516.	+	192516.i	0.369312	+	0.369312i
$723$	3465.56	+	3465.56i	0.00662975	+	0.00662975i
$724$	−278265.			−0.530861
$725$	−66242.8	−	191959.i	−0.126027	−	0.365202i
$726$	4388.45	−	4388.45i	0.00832603	−	0.00832603i
$727$	47895.8			0.0906210			0.0453105	−	0.998973i	$-0.485572\pi$
$727$	47895.8			0.0906210			0.0453105	+	0.998973i	$0.485572\pi$
$728$	−93864.4	−	73255.3i	−0.177108	−	0.138222i
$729$	484458.			0.911593
$730$	−332630.	−	237092.i	−0.624188	−	0.444909i
$731$	−1.12257e6			−2.10077
$732$	7134.76			0.0133155
$733$	−159358.	+	159358.i	−0.296596	+	0.296596i	−0.839679	−	0.543083i	$-0.817257\pi$
$733$	−159358.	+	159358.i	−0.296596	+	0.296596i	0.543083	+	0.839679i	$0.317257\pi$
$734$	197910.	+	197910.i	0.367347	+	0.367347i
$735$	−51444.5	−	36668.6i	−0.0952278	−	0.0678766i
$736$	310740.	−	310740.i	0.573643	−	0.573643i
$737$			339370.i			0.624797i
$738$	−273137.			−0.501496
$739$	−219062.	+	219062.i	−0.401123	+	0.401123i	−0.878629	−	0.477506i	$-0.841541\pi$
$739$	−219062.	+	219062.i	−0.401123	+	0.401123i	0.477506	+	0.878629i	$0.341541\pi$
$740$	199065.	−	33381.5i	0.363523	−	0.0609597i
$741$	10526.7	+	85361.7i	0.0191716	+	0.155463i
$742$			176227.i			0.320084i
$743$	197852.	−	197852.i	0.358395	−	0.358395i	−0.504826	−	0.863221i	$-0.668443\pi$
$743$	197852.	−	197852.i	0.358395	−	0.358395i	0.863221	+	0.504826i	$0.168443\pi$
$744$	97709.0			0.176518
$745$	38952.2	+	232285.i	0.0701810	+	0.418512i
$746$	−18035.2	−	18035.2i	−0.0324074	−	0.0324074i
$747$	438994.	−	438994.i	0.786715	−	0.786715i
$748$	−166878.	−	166878.i	−0.298260	−	0.298260i
$749$	81563.5	−	81563.5i	0.145389	−	0.145389i
$750$	48897.6	−	26613.8i	0.0869291	−	0.0473134i
$751$		−	966280.i		−	1.71326i	−0.515932	−	0.856630i	$-0.672554\pi$
$751$		−	966280.i		−	1.71326i	0.515932	−	0.856630i	$-0.327446\pi$
$752$	152678.	+	152678.i	0.269986	+	0.269986i
$753$	−93679.1			−0.165216
$754$	21781.7	+	176629.i	0.0383133	+	0.310684i
$755$	−416981.	+	69924.2i	−0.731513	+	0.122669i
$756$	−6945.93	−	6945.93i	−0.0121531	−	0.0121531i
$757$		−	542749.i		−	0.947124i	−0.880760	−	0.473562i	$-0.842968\pi$
$757$		−	542749.i		−	0.947124i	0.880760	−	0.473562i	$-0.157032\pi$
$758$	−224357.			−0.390483
$759$	−58094.2	−	58094.2i	−0.100844	−	0.100844i
$760$	468012.	−	656601.i	0.810271	−	1.13677i
$761$	718135.	−	718135.i	1.24004	−	1.24004i	0.280060	−	0.959982i	$-0.409646\pi$
$761$	718135.	−	718135.i	1.24004	−	1.24004i	0.959982	−	0.280060i	$-0.0903545\pi$
$762$	33671.7	+	33671.7i	0.0579902	+	0.0579902i
$763$			24300.9i			0.0417420i
$764$			68507.3i			0.117368i
$765$	614222.	+	437806.i	1.04955	+	0.748098i
$766$			412340.i			0.702745i
$767$	−5904.01	−	47875.8i	−0.0100359	−	0.0813814i
$768$			64473.4i			0.109310i
$769$	−553880.	−	553880.i	−0.936618	−	0.936618i	0.0614893	−	0.998108i	$-0.480415\pi$
$769$	−553880.	−	553880.i	−0.936618	−	0.936618i	−0.998108	+	0.0614893i	$0.980415\pi$
$770$	91781.9	−	15391.1i	0.154802	−	0.0259590i
$771$		−	4270.67i		−	0.00718435i
$772$	−82162.4	+	82162.4i	−0.137860	+	0.137860i
$773$	−599453.	+	599453.i	−1.00322	+	1.00322i	−0.00322500	+	0.999995i	$0.501027\pi$
$773$	−599453.	+	599453.i	−1.00322	+	1.00322i	−0.999995	+	0.00322500i	$0.998973\pi$
$774$	−542885.	+	542885.i	−0.906203	+	0.906203i
$775$	−349057.	+	716909.i	−0.581157	+	1.19360i
$776$	−692169.			−1.14945
$777$	16333.1			0.0270537
$778$	−528494.	−	528494.i	−0.873134	−	0.873134i
$779$			488953.i			0.805735i
$780$	24466.2	−	7270.27i	0.0402140	−	0.0119498i
$781$	−7601.58			−0.0124624
$782$	−570246.	+	570246.i	−0.932500	+	0.932500i
$783$			57430.6i			0.0936741i
$784$		−	316939.i		−	0.515637i
$785$	−176824.	+	248076.i	−0.286947	+	0.402574i
$786$	−71487.6	−	71487.6i	−0.115714	−	0.115714i
$787$	−32541.3	−	32541.3i	−0.0525394	−	0.0525394i	0.680349	−	0.732888i	$-0.261828\pi$
$787$	−32541.3	−	32541.3i	−0.0525394	−	0.0525394i	−0.732888	+	0.680349i	$0.761828\pi$
$788$	−46175.6	−	46175.6i	−0.0743636	−	0.0743636i
$789$	−92512.1			−0.148609
$790$	771605.	−	129392.i	1.23635	−	0.207325i
$791$	16262.4	−	16262.4i	0.0259916	−	0.0259916i
$792$	−631353.			−1.00652
$793$	122801.	−	157349.i	0.195279	−	0.250217i
$794$	871767.			1.38280
$795$	−120327.	−	85766.7i	−0.190383	−	0.135701i
$796$	242867.			0.383303
$797$	693157.			1.09123			0.545613	−	0.838037i	$-0.316297\pi$
$797$	693157.			1.09123			0.545613	+	0.838037i	$0.316297\pi$
$798$	11795.0	−	11795.0i	0.0185222	−	0.0185222i
$799$	418724.	+	418724.i	0.655894	+	0.655894i
$800$	−375273.	−	182718.i	−0.586364	−	0.285496i
$801$	−558765.	+	558765.i	−0.870892	+	0.870892i
$802$		−	598633.i		−	0.930704i
$803$	572558.			0.887950
$804$	12764.2	−	12764.2i	0.0197461	−	0.0197461i
$805$	27513.5	+	164072.i	0.0424575	+	0.253188i
$806$	429939.	−	550894.i	0.661815	−	0.848005i
$807$		−	588.215i		−	0.000903211i
$808$	474561.	−	474561.i	0.726892	−	0.726892i
$809$	388831.			0.594106			0.297053	−	0.954861i	$-0.403996\pi$
$809$	388831.			0.594106			0.297053	+	0.954861i	$0.403996\pi$
$810$	500949.	−	84004.9i	0.763525	−	0.128037i
$811$	251143.	+	251143.i	0.381838	+	0.381838i	0.871764	−	0.489926i	$-0.162976\pi$
$811$	251143.	+	251143.i	0.381838	+	0.381838i	−0.489926	+	0.871764i	$0.662976\pi$
$812$	−12767.6	+	12767.6i	−0.0193641	+	0.0193641i
$813$	42308.1	+	42308.1i	0.0640092	+	0.0640092i
$814$	382417.	−	382417.i	0.577150	−	0.577150i
$815$	70363.4	+	419600.i	0.105933	+	0.631714i
$816$		−	57311.8i		−	0.0860723i
$817$	971840.	+	971840.i	1.45596	+	1.45596i
$818$	85325.0			0.127518
$819$	−135343.	+	16690.3i	−0.201775	+	0.0248827i
$820$	143102.	−	23997.0i	0.212823	−	0.0356886i
$821$	240527.	+	240527.i	0.356844	+	0.356844i	0.862648	−	0.505805i	$-0.168804\pi$
$821$	240527.	+	240527.i	0.356844	+	0.356844i	−0.505805	+	0.862648i	$0.668804\pi$
$822$		−	39425.8i		−	0.0583495i
$823$	−214335.			−0.316441			−0.158220	−	0.987404i	$-0.550576\pi$
$823$	−214335.			−0.316441			−0.158220	+	0.987404i	$0.550576\pi$
$824$	−834412.	−	834412.i	−1.22893	−	1.22893i
$825$	−34159.8	+	70158.9i	−0.0501889	+	0.103080i
$826$	−6615.32	+	6615.32i	−0.00969595	+	0.00969595i
$827$	−26731.5	−	26731.5i	−0.0390851	−	0.0390851i	0.687294	−	0.726379i	$-0.258798\pi$
$827$	−26731.5	−	26731.5i	−0.0390851	−	0.0390851i	−0.726379	+	0.687294i	$0.758798\pi$
$828$		−	288537.i		−	0.420862i
$829$			1.30798e6i			1.90323i	0.307286	+	0.951617i	$0.400579\pi$
$829$			1.30798e6i			1.90323i	−0.307286	+	0.951617i	$0.599421\pi$
$830$	365928.	−	513380.i	0.531177	−	0.745217i
$831$		−	156509.i		−	0.226640i
$832$	582275.	+	454429.i	0.841165	+	0.656477i
$833$		−	869213.i		−	1.25267i
$834$	22733.2	+	22733.2i	0.0326835	+	0.0326835i
$835$	42924.9	+	255975.i	0.0615654	+	0.367134i
$836$			288942.i			0.413426i
$837$	159458.	−	159458.i	0.227613	−	0.227613i
$838$	−66329.1	+	66329.1i	−0.0944530	+	0.0944530i
$839$	−446608.	+	446608.i	−0.634457	+	0.634457i	−0.949183	−	0.314725i	$-0.898088\pi$
$839$	−446608.	+	446608.i	−0.634457	+	0.634457i	0.314725	+	0.949183i	$0.398088\pi$
$840$	−15767.2	−	11238.5i	−0.0223458	−	0.0159276i
$841$	−601715.			−0.850745
$842$	755559.			1.06572
$843$	48798.5	+	48798.5i	0.0686675	+	0.0686675i
$844$			217240.i			0.304968i
$845$	260765.	−	664705.i	0.365205	−	0.930927i
$846$	404998.			0.565863
$847$	12455.7	−	12455.7i	0.0173621	−	0.0173621i
$848$		−	741310.i		−	1.03088i
$849$		−	31082.0i		−	0.0431214i
$850$	688672.	+	335309.i	0.953179	+	0.464096i
$851$	683621.	+	683621.i	0.943966	+	0.943966i
$852$	285.906	+	285.906i	0.000393861	+	0.000393861i
$853$	−608014.	−	608014.i	−0.835633	−	0.835633i	0.152647	−	0.988281i	$-0.451220\pi$
$853$	−608014.	−	608014.i	−0.835633	−	0.835633i	−0.988281	+	0.152647i	$0.951220\pi$
$854$	−38710.1			−0.0530773
$855$	−152729.	−	910772.i	−0.208924	−	1.24588i
$856$	−561905.	+	561905.i	−0.766858	+	0.766858i
$857$	638709.			0.869644			0.434822	−	0.900516i	$-0.356811\pi$
$857$	638709.			0.869644			0.434822	+	0.900516i	$0.356811\pi$
$858$	42075.1	−	53912.3i	0.0571546	−	0.0732340i
$859$	1.07644e6			1.45883			0.729416	−	0.684070i	$-0.239792\pi$
$859$	1.07644e6			1.45883			0.729416	+	0.684070i	$0.239792\pi$
$860$	236732.	−	332125.i	0.320081	−	0.449060i
$861$	11741.4			0.0158385
$862$	254181.			0.342080
$863$	−717541.	+	717541.i	−0.963441	+	0.963441i	−0.999355	−	0.0359138i	$-0.988566\pi$
$863$	−717541.	+	717541.i	−0.963441	+	0.963441i	0.0359138	+	0.999355i	$0.488566\pi$
$864$	83470.0	+	83470.0i	0.111816	+	0.111816i
$865$	452927.	+	322838.i	0.605336	+	0.431472i
$866$	−419166.	+	419166.i	−0.558921	+	0.558921i
$867$		−	65363.7i		−	0.0869557i
$868$	70899.5			0.0941031
$869$	−775446.	+	775446.i	−1.02686	+	1.02686i
$870$	4786.31	+	28542.3i	0.00632356	+	0.0377095i
$871$	−61806.5	−	501190.i	−0.0814700	−	0.660642i
$872$		−	167413.i		−	0.220169i
$873$	−560555.	+	560555.i	−0.735512	+	0.735512i
$874$	987358.			1.29256
$875$	138786.	−	75537.9i	0.181272	−	0.0986617i
$876$	−21534.7	−	21534.7i	−0.0280627	−	0.0280627i
$877$	402795.	−	402795.i	0.523703	−	0.523703i	−0.394984	−	0.918688i	$-0.629250\pi$
$877$	402795.	−	402795.i	0.523703	−	0.523703i	0.918688	+	0.394984i	$0.129250\pi$
$878$	352797.	+	352797.i	0.457652	+	0.457652i
$879$	−57613.0	+	57613.0i	−0.0745664	+	0.0745664i
$880$	−386087.	+	64743.6i	−0.498563	+	0.0836049i
$881$		−	280794.i		−	0.361773i	−0.983504	−	0.180887i	$-0.942103\pi$
$881$		−	280794.i		−	0.361773i	0.983504	−	0.180887i	$-0.0578967\pi$
$882$	−420360.	−	420360.i	−0.540361	−	0.540361i
$883$	781982.			1.00294			0.501470	−	0.865175i	$-0.332793\pi$
$883$	781982.			1.00294			0.501470	+	0.865175i	$0.332793\pi$
$884$	276841.	+	216057.i	0.354263	+	0.276480i
$885$	−1297.34	−	7736.48i	−0.00165641	−	0.00987772i
$886$	−467717.	−	467717.i	−0.595820	−	0.595820i
$887$			921183.i			1.17084i	0.810729	+	0.585422i	$0.199071\pi$
$887$			921183.i			1.17084i	−0.810729	+	0.585422i	$0.800929\pi$
$888$	−112522.			−0.142695
$889$	95570.4	+	95570.4i	0.120926	+	0.120926i
$890$	−465764.	+	653446.i	−0.588011	+	0.824954i
$891$	−503442.	+	503442.i	−0.634153	+	0.634153i
$892$	−196944.	−	196944.i	−0.247521	−	0.247521i
$893$		−	725003.i		−	0.909152i
$894$		−	33567.0i		−	0.0419988i
$895$	190617.	−	267427.i	0.237967	−	0.333857i
$896$		−	35191.6i		−	0.0438352i
$897$	96375.2	+	75214.8i	0.119779	+	0.0934800i
$898$			578850.i			0.717817i
$899$	−293107.	−	293107.i	−0.362666	−	0.362666i
$900$	−259060.	+	89398.3i	−0.319827	+	0.110368i
$901$		−	2.03306e6i		−	2.50438i
$902$	274909.	−	274909.i	0.337890	−	0.337890i
$903$	23337.1	−	23337.1i	0.0286201	−	0.0286201i
$904$	−112035.	+	112035.i	−0.137093	+	0.137093i
$905$	−734768.	+	1.03085e6i	−0.897125	+	1.25863i
$906$	60257.0			0.0734093
$907$	−739555.			−0.898993			−0.449496	−	0.893282i	$-0.648397\pi$
$907$	−739555.			−0.898993			−0.449496	+	0.893282i	$0.648397\pi$
$908$	−105344.	−	105344.i	−0.127773	−	0.127773i
$909$		−	768651.i		−	0.930253i
$910$	−132743.	+	39445.3i	−0.160298	+	0.0476335i
$911$	−76316.9			−0.0919568			−0.0459784	−	0.998942i	$-0.514641\pi$
$911$	−76316.9			−0.0919568			−0.0459784	+	0.998942i	$0.514641\pi$
$912$	−49616.5	+	49616.5i	−0.0596536	+	0.0596536i
$913$			883684.i			1.06012i
$914$			318643.i			0.381428i
$915$	18839.6	−	26431.1i	0.0225024	−	0.0315699i
$916$	−333508.	−	333508.i	−0.397479	−	0.397479i
$917$	−202903.	−	202903.i	−0.241296	−	0.241296i
$918$	−153178.	−	153178.i	−0.181765	−	0.181765i
$919$	−554885.			−0.657010			−0.328505	−	0.944502i	$-0.606545\pi$
$919$	−554885.			−0.657010			−0.328505	+	0.944502i	$0.606545\pi$
$920$	−189546.	−	1.13032e6i	−0.223943	−	1.33545i
$921$	5293.09	−	5293.09i	0.00624007	−	0.00624007i
$922$	−722712.			−0.850166
$923$	11226.2	−	1384.41i	0.0131774	−	0.00162503i
$924$	6938.45			0.00812678
$925$	401974.	−	825592.i	0.469802	−	0.964900i
$926$	1.19097e6			1.38893
$927$	−1.35150e6			−1.57274
$928$	153430.	−	153430.i	0.178161	−	0.178161i
$929$	673721.	+	673721.i	0.780637	+	0.780637i	0.979938	−	0.199302i	$-0.0638673\pi$
$929$	673721.	+	673721.i	0.780637	+	0.780637i	−0.199302	+	0.979938i	$0.563867\pi$
$930$	65959.5	−	92538.2i	0.0762625	−	0.106993i
$931$	−752503.	+	752503.i	−0.868178	+	0.868178i
$932$			308232.i			0.354851i
$933$	−41957.2			−0.0481996
$934$	−361430.	+	361430.i	−0.414314	+	0.414314i
$935$	−1.05885e6	+	177561.i	−1.21119	+	0.203107i
$936$	932398.	−	114983.i	1.06426	−	0.131244i
$937$			124606.i			0.141926i	0.997479	+	0.0709629i	$0.0226072\pi$
$937$			124606.i			0.141926i	−0.997479	+	0.0709629i	$0.977393\pi$
$938$	−69252.8	+	69252.8i	−0.0787104	+	0.0787104i
$939$	11339.0			0.0128601
$940$	−212187.	+	35581.9i	−0.240139	+	0.0402693i
$941$	255592.	+	255592.i	0.288647	+	0.288647i	0.836545	−	0.547898i	$-0.184572\pi$
$941$	255592.	+	255592.i	0.288647	+	0.288647i	−0.547898	+	0.836545i	$0.684572\pi$
$942$	30700.7	−	30700.7i	0.0345977	−	0.0345977i
$943$	491435.	+	491435.i	0.552641	+	0.552641i
$944$	27827.8	−	27827.8i	0.0312273	−	0.0312273i
$945$	−44072.6	+	7390.60i	−0.0493520	+	0.00827592i
$946$		−	1.09281e6i		−	1.22114i
$947$	−1.06098e6	−	1.06098e6i	−1.18306	−	1.18306i	−0.978948	−	0.204112i	$-0.934569\pi$
$947$	−1.06098e6	−	1.06098e6i	−1.18306	−	1.18306i	−0.204112	−	0.978948i	$-0.565431\pi$
$948$	58331.1			0.0649058
$949$	−845568.	+	104275.i	−0.938893	+	0.115784i
$950$	−305917.	−	886491.i	−0.338966	−	0.982261i
$951$	96397.2	+	96397.2i	0.106587	+	0.106587i
$952$		−	266404.i		−	0.293946i
$953$	−632149.			−0.696039			−0.348019	−	0.937487i	$-0.613146\pi$
$953$	−632149.			−0.696039			−0.348019	+	0.937487i	$0.613146\pi$
$954$	−983207.	−	983207.i	−1.08031	−	1.08031i
$955$	253789.	+	180896.i	0.278270	+	0.198346i
$956$	18751.6	−	18751.6i	0.0205174	−	0.0205174i
$957$	−28684.4	−	28684.4i	−0.0313200	−	0.0313200i
$958$		−	448366.i		−	0.488542i
$959$		−	111902.i		−	0.121675i
$960$	97809.4	+	69716.7i	0.106130	+	0.0756474i
$961$			704126.i			0.762436i
$962$	−495117.	+	634410.i	−0.535005	+	0.685520i
$963$			910121.i			0.981401i
$964$	−17324.1	−	17324.1i	−0.0186421	−	0.0186421i
$965$	87422.3	+	521328.i	0.0938788	+	0.559830i
$966$		−	23709.7i		−	0.0254081i
$967$	732467.	−	732467.i	0.783312	−	0.783312i	−0.197076	−	0.980388i	$-0.563145\pi$
$967$	732467.	−	732467.i	0.783312	−	0.783312i	0.980388	+	0.197076i	$0.0631446\pi$
$968$	−85809.8	+	85809.8i	−0.0915769	+	0.0915769i
$969$	−136074.	+	136074.i	−0.144920	+	0.144920i
$970$	−467256.	+	655539.i	−0.496605	+	0.696715i
$971$	296674.			0.314659			0.157330	−	0.987546i	$-0.449711\pi$
$971$	296674.			0.314659			0.157330	+	0.987546i	$0.449711\pi$
$972$	116550.			0.123361
$973$	64523.6	+	64523.6i	0.0681542	+	0.0681542i
$974$			870120.i			0.917194i
$975$	37670.7	−	109834.i	0.0396273	−	0.115538i
$976$	162837.			0.170944
$977$	1.21596e6	−	1.21596e6i	1.27388	−	1.27388i	0.329852	−	0.944033i	$-0.393001\pi$
$977$	1.21596e6	−	1.21596e6i	1.27388	−	1.27388i	0.944033	−	0.329852i	$-0.106999\pi$
$978$		−	60635.5i		−	0.0633942i
$979$		−	1.12478e6i		−	1.17355i
$980$	257167.	+	183304.i	0.267770	+	0.190862i
$981$	−135580.	−	135580.i	−0.140883	−	0.140883i
$982$	225984.	+	225984.i	0.234345	+	0.234345i
$983$	767938.	+	767938.i	0.794729	+	0.794729i	0.982259	−	0.187530i	$-0.0600481\pi$
$983$	767938.	+	767938.i	0.794729	+	0.794729i	−0.187530	+	0.982259i	$0.560048\pi$
$984$	−80888.4			−0.0835403
$985$	−292988.	+	49131.7i	−0.301980	+	0.0506395i
$986$	−281562.	+	281562.i	−0.289615	+	0.289615i
$987$	−17409.7			−0.0178714
$988$	−52622.4	−	426716.i	−0.0539084	−	0.437145i
$989$	1.95355e6			1.99724
$990$	−426202.	+	597942.i	−0.434855	+	0.610083i
$991$	−486551.			−0.495428			−0.247714	−	0.968833i	$-0.579679\pi$
$991$	−486551.			−0.495428			−0.247714	+	0.968833i	$0.579679\pi$
$992$	−852008.			−0.865805
$993$	50638.5	−	50638.5i	0.0513549	−	0.0513549i
$994$	−1551.20	−	1551.20i	−0.00156998	−	0.00156998i
$995$	641299.	−	899714.i	0.647761	−	0.908779i
$996$	33236.6	−	33236.6i	0.0335041	−	0.0335041i
$997$			1.44589e6i			1.45460i	0.686319	+	0.727301i	$0.259226\pi$
$997$			1.44589e6i			1.45460i	−0.686319	+	0.727301i	$0.740774\pi$
$998$	−1.23197e6			−1.23691
$999$	−183632.	+	183632.i	−0.184000	+	0.184000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.5.g.a.34.18	yes	52
5.4	even	2	inner	65.5.g.a.34.9	✓	52
13.5	odd	4	inner	65.5.g.a.44.9	yes	52
65.44	odd	4	inner	65.5.g.a.44.18	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.5.g.a.34.9	✓	52	5.4	even	2	inner
65.5.g.a.34.18	yes	52	1.1	even	1	trivial
65.5.g.a.44.9	yes	52	13.5	odd	4	inner
65.5.g.a.44.18	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)

\(f(q)\)	\(=\)	\(q+(2.29180 - 2.29180i) q^{2} -1.09931i q^{3} +5.49535i q^{4} +(20.3578 + 14.5107i) q^{5} +(-2.51939 - 2.51939i) q^{6} +(-7.15078 - 7.15078i) q^{7} +(49.2629 + 49.2629i) q^{8} +79.7915 q^{9} +O(q^{10})\)	\(q+(2.29180 - 2.29180i) q^{2} -1.09931i q^{3} +5.49535i q^{4} +(20.3578 + 14.5107i) q^{5} +(-2.51939 - 2.51939i) q^{6} +(-7.15078 - 7.15078i) q^{7} +(49.2629 + 49.2629i) q^{8} +79.7915 q^{9} +(79.9114 - 13.4005i) q^{10} +(-80.3092 + 80.3092i) q^{11} +6.04107 q^{12} +(103.977 - 133.229i) q^{13} -32.7762 q^{14} +(15.9517 - 22.3795i) q^{15} +137.876 q^{16} +378.127 q^{17} +(182.866 - 182.866i) q^{18} +(-327.356 - 327.356i) q^{19} +(-79.7411 + 111.873i) q^{20} +(-7.86090 + 7.86090i) q^{21} +368.104i q^{22} -658.035 q^{23} +(54.1551 - 54.1551i) q^{24} +(203.881 + 590.811i) q^{25} +(-67.0396 - 543.626i) q^{26} -176.759i q^{27} +(39.2960 - 39.2960i) q^{28} -324.909 q^{29} +(-14.7312 - 87.8472i) q^{30} +(902.122 + 902.122i) q^{31} +(-472.224 + 472.224i) q^{32} +(88.2844 + 88.2844i) q^{33} +(866.590 - 866.590i) q^{34} +(-41.8117 - 249.337i) q^{35} +438.482i q^{36} +(-1038.88 - 1038.88i) q^{37} -1500.46 q^{38} +(-146.459 - 114.302i) q^{39} +(288.048 + 1717.72i) q^{40} +(-746.822 - 746.822i) q^{41} +36.0311i q^{42} -2968.76 q^{43} +(-441.327 - 441.327i) q^{44} +(1624.38 + 1157.83i) q^{45} +(-1508.08 + 1508.08i) q^{46} +(1107.36 + 1107.36i) q^{47} -151.568i q^{48} -2298.73i q^{49} +(1821.27 + 886.763i) q^{50} -415.678i q^{51} +(732.138 + 571.388i) q^{52} -5376.66i q^{53} +(-405.096 - 405.096i) q^{54} +(-2800.26 + 469.580i) q^{55} -704.536i q^{56} +(-359.864 + 359.864i) q^{57} +(-744.624 + 744.624i) q^{58} +(201.833 - 201.833i) q^{59} +(122.983 + 87.6600i) q^{60} +1181.04 q^{61} +4134.96 q^{62} +(-570.571 - 570.571i) q^{63} +4370.49i q^{64} +(4049.97 - 1203.47i) q^{65} +404.660 q^{66} +(2112.90 - 2112.90i) q^{67} +2077.94i q^{68} +723.382i q^{69} +(-667.253 - 475.605i) q^{70} +(47.3270 + 47.3270i) q^{71} +(3930.76 + 3930.76i) q^{72} +(-3564.71 - 3564.71i) q^{73} -4761.82 q^{74} +(649.482 - 224.128i) q^{75} +(1798.93 - 1798.93i) q^{76} +1148.55 q^{77} +(-597.612 + 73.6971i) q^{78} +9655.76 q^{79} +(2806.85 + 2000.67i) q^{80} +6268.80 q^{81} -3423.13 q^{82} +(5501.76 - 5501.76i) q^{83} +(-43.1984 - 43.1984i) q^{84} +(7697.84 + 5486.87i) q^{85} +(-6803.79 + 6803.79i) q^{86} +357.174i q^{87} -7912.53 q^{88} +(-7002.82 + 7002.82i) q^{89} +(6376.25 - 1069.24i) q^{90} +(-1696.20 + 209.174i) q^{91} -3616.13i q^{92} +(991.709 - 991.709i) q^{93} +5075.70 q^{94} +(-1914.10 - 11414.4i) q^{95} +(519.120 + 519.120i) q^{96} +(-7025.25 + 7025.25i) q^{97} +(-5268.23 - 5268.23i) q^{98} +(-6407.99 + 6407.99i) 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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