LMFDB - Embedded newform 35.5.g.a.8.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(8,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("35.8");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.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:	$3.61794870793$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.12
Character	$\chi$	$=$	35.8
Dual form			35.5.g.a.22.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.12784 - 5.12784i) q^{2} +(10.3372 + 10.3372i) q^{3} -36.5894i q^{4} +(-22.2980 + 11.3048i) q^{5} +106.015 q^{6} +(13.0958 - 13.0958i) q^{7} +(-105.579 - 105.579i) q^{8} +132.716i q^{9} +O(q^{10})$	\(q+(5.12784 - 5.12784i) q^{2} +(10.3372 + 10.3372i) q^{3} -36.5894i q^{4} +(-22.2980 + 11.3048i) q^{5} +106.015 q^{6} +(13.0958 - 13.0958i) q^{7} +(-105.579 - 105.579i) q^{8} +132.716i q^{9} +(-56.3718 + 172.310i) q^{10} -135.891 q^{11} +(378.233 - 378.233i) q^{12} +(-35.4752 - 35.4752i) q^{13} -134.306i q^{14} +(-347.360 - 113.640i) q^{15} -497.356 q^{16} +(146.269 - 146.269i) q^{17} +(680.549 + 680.549i) q^{18} +408.482i q^{19} +(413.634 + 815.873i) q^{20} +270.749 q^{21} +(-696.826 + 696.826i) q^{22} +(212.278 + 212.278i) q^{23} -2182.79i q^{24} +(369.405 - 504.148i) q^{25} -363.822 q^{26} +(-534.605 + 534.605i) q^{27} +(-479.168 - 479.168i) q^{28} -195.559i q^{29} +(-2363.93 + 1198.48i) q^{30} +965.178 q^{31} +(-861.090 + 861.090i) q^{32} +(-1404.73 - 1404.73i) q^{33} -1500.08i q^{34} +(-143.966 + 440.055i) q^{35} +4856.02 q^{36} +(925.201 - 925.201i) q^{37} +(2094.63 + 2094.63i) q^{38} -733.431i q^{39} +(3547.76 + 1160.66i) q^{40} -2299.21 q^{41} +(1388.35 - 1388.35i) q^{42} +(-1190.20 - 1190.20i) q^{43} +4972.17i q^{44} +(-1500.33 - 2959.32i) q^{45} +2177.05 q^{46} +(-1550.35 + 1550.35i) q^{47} +(-5141.28 - 5141.28i) q^{48} -343.000i q^{49} +(-690.938 - 4479.44i) q^{50} +3024.03 q^{51} +(-1298.02 + 1298.02i) q^{52} +(645.219 + 645.219i) q^{53} +5482.73i q^{54} +(3030.10 - 1536.21i) q^{55} -2765.29 q^{56} +(-4222.57 + 4222.57i) q^{57} +(-1002.79 - 1002.79i) q^{58} -2295.44i q^{59} +(-4158.03 + 12709.7i) q^{60} +3198.88 q^{61} +(4949.28 - 4949.28i) q^{62} +(1738.03 + 1738.03i) q^{63} +873.373i q^{64} +(1192.07 + 389.989i) q^{65} -14406.5 q^{66} +(-6113.48 + 6113.48i) q^{67} +(-5351.89 - 5351.89i) q^{68} +4388.73i q^{69} +(1518.30 + 2994.77i) q^{70} +740.397 q^{71} +(14012.1 - 14012.1i) q^{72} +(1763.21 + 1763.21i) q^{73} -9488.56i q^{74} +(9030.11 - 1392.86i) q^{75} +14946.1 q^{76} +(-1779.60 + 1779.60i) q^{77} +(-3760.91 - 3760.91i) q^{78} -8409.12i q^{79} +(11090.1 - 5622.48i) q^{80} -302.630 q^{81} +(-11790.0 + 11790.0i) q^{82} +(5894.49 + 5894.49i) q^{83} -9906.53i q^{84} +(-1607.97 + 4915.04i) q^{85} -12206.3 q^{86} +(2021.54 - 2021.54i) q^{87} +(14347.2 + 14347.2i) q^{88} +4763.09i q^{89} +(-22868.3 - 7481.47i) q^{90} -929.153 q^{91} +(7767.12 - 7767.12i) q^{92} +(9977.27 + 9977.27i) q^{93} +15899.8i q^{94} +(-4617.78 - 9108.34i) q^{95} -17802.6 q^{96} +(687.835 - 687.835i) q^{97} +(-1758.85 - 1758.85i) q^{98} -18034.9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6}+O(q^{10}) $ 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97}+O(q^{100}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6 - 112 * q^10 + 156 * q^11 - 80 * q^12 - 560 * q^13 + 896 * q^15 - 1480 * q^16 + 1320 * q^17 + 340 * q^18 + 180 * q^20 + 196 * q^21 - 2020 * q^22 + 1920 * q^23 - 676 * q^25 + 2208 * q^26 - 340 * q^27 - 5356 * q^30 - 2112 * q^31 - 1200 * q^32 - 6140 * q^33 + 3904 * q^36 + 3980 * q^37 + 9120 * q^38 + 14716 * q^40 + 6384 * q^41 + 4900 * q^42 - 12220 * q^43 - 10528 * q^45 - 8080 * q^46 - 11820 * q^47 - 4040 * q^48 + 10728 * q^50 - 5900 * q^51 + 3600 * q^52 + 24240 * q^53 + 4636 * q^55 - 10584 * q^56 + 6460 * q^57 + 6100 * q^58 - 30088 * q^60 + 440 * q^61 - 16680 * q^62 + 7840 * q^63 - 14652 * q^65 + 4832 * q^66 - 5940 * q^67 - 47040 * q^68 - 6272 * q^70 + 8928 * q^71 + 46720 * q^72 - 2500 * q^73 + 60708 * q^75 + 47816 * q^76 + 5880 * q^77 - 17940 * q^78 + 16140 * q^80 - 11360 * q^81 - 32120 * q^82 + 15120 * q^83 + 18816 * q^85 - 41208 * q^86 - 25460 * q^87 + 52920 * q^88 - 55680 * q^90 - 11172 * q^91 + 19800 * q^92 + 1460 * q^93 - 35508 * q^95 + 20568 * q^96 - 33840 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	5.12784	−	5.12784i	1.28196	−	1.28196i	0.342408	−	0.939551i	$-0.388758\pi$
$2$	5.12784	−	5.12784i	1.28196	−	1.28196i	0.939551	−	0.342408i	$-0.111242\pi$
$3$	10.3372	+	10.3372i	1.14858	+	1.14858i	0.986832	+	0.161749i	$0.0517134\pi$
$3$	10.3372	+	10.3372i	1.14858	+	1.14858i	0.161749	+	0.986832i	$0.448287\pi$
$4$		−	36.5894i		−	2.28684i
$5$	−22.2980	+	11.3048i	−0.891922	+	0.452190i
$5$	−22.2980	+	11.3048i	−0.891922	+	0.452190i
$6$	106.015			2.94487
$7$	13.0958	−	13.0958i	0.267261	−	0.267261i
$7$	13.0958	−	13.0958i	0.267261	−	0.267261i
$8$	−105.579	−	105.579i	−1.64968	−	1.64968i
$9$			132.716i			1.63848i
$10$	−56.3718	+	172.310i	−0.563718	+	1.72310i
$11$	−135.891			−1.12306			−0.561532	−	0.827455i	$-0.689788\pi$
$11$	−135.891			−1.12306			−0.561532	+	0.827455i	$0.689788\pi$
$12$	378.233	−	378.233i	2.62662	−	2.62662i
$13$	−35.4752	−	35.4752i	−0.209913	−	0.209913i	0.594318	−	0.804230i	$-0.297422\pi$
$13$	−35.4752	−	35.4752i	−0.209913	−	0.209913i	−0.804230	+	0.594318i	$0.797422\pi$
$14$		−	134.306i		−	0.685236i
$15$	−347.360	−	113.640i	−1.54382	−	0.505067i
$16$	−497.356			−1.94280
$17$	146.269	−	146.269i	0.506120	−	0.506120i	−0.407213	−	0.913333i	$-0.633499\pi$
$17$	146.269	−	146.269i	0.506120	−	0.506120i	0.913333	+	0.407213i	$0.133499\pi$
$18$	680.549	+	680.549i	2.10046	+	2.10046i
$19$			408.482i			1.13153i	0.824567	+	0.565764i	$0.191419\pi$
$19$			408.482i			1.13153i	−0.824567	+	0.565764i	$0.808581\pi$
$20$	413.634	+	815.873i	1.03409	+	2.03968i
$21$	270.749			0.613942
$22$	−696.826	+	696.826i	−1.43972	+	1.43972i
$23$	212.278	+	212.278i	0.401281	+	0.401281i	0.878684	−	0.477403i	$-0.158422\pi$
$23$	212.278	+	212.278i	0.401281	+	0.401281i	−0.477403	+	0.878684i	$0.658422\pi$
$24$		−	2182.79i		−	3.78957i
$25$	369.405	−	504.148i	0.591048	−	0.806636i
$26$	−363.822			−0.538199
$27$	−534.605	+	534.605i	−0.733340	+	0.733340i
$28$	−479.168	−	479.168i	−0.611184	−	0.611184i
$29$		−	195.559i		−	0.232531i	−0.993218	−	0.116266i	$-0.962908\pi$
$29$		−	195.559i		−	0.232531i	0.993218	−	0.116266i	$-0.0370924\pi$
$30$	−2363.93	+	1198.48i	−2.62659	+	1.33164i
$31$	965.178			1.00435			0.502174	−	0.864767i	$-0.332534\pi$
$31$	965.178			1.00435			0.502174	+	0.864767i	$0.332534\pi$
$32$	−861.090	+	861.090i	−0.840908	+	0.840908i
$33$	−1404.73	−	1404.73i	−1.28993	−	1.28993i
$34$		−	1500.08i		−	1.29765i
$35$	−143.966	+	440.055i	−0.117523	+	0.359229i
$36$	4856.02			3.74693
$37$	925.201	−	925.201i	0.675822	−	0.675822i	−0.283230	−	0.959052i	$-0.591406\pi$
$37$	925.201	−	925.201i	0.675822	−	0.675822i	0.959052	+	0.283230i	$0.0914059\pi$
$38$	2094.63	+	2094.63i	1.45057	+	1.45057i
$39$		−	733.431i		−	0.482203i
$40$	3547.76	+	1160.66i	2.21735	+	0.725414i
$41$	−2299.21			−1.36776			−0.683881	−	0.729594i	$-0.739709\pi$
$41$	−2299.21			−1.36776			−0.683881	+	0.729594i	$0.739709\pi$
$42$	1388.35	−	1388.35i	0.787049	−	0.787049i
$43$	−1190.20	−	1190.20i	−0.643701	−	0.643701i	0.307763	−	0.951463i	$-0.400420\pi$
$43$	−1190.20	−	1190.20i	−0.643701	−	0.643701i	−0.951463	+	0.307763i	$0.900420\pi$
$44$			4972.17i			2.56827i
$45$	−1500.33	−	2959.32i	−0.740902	−	1.46139i
$46$	2177.05			1.02885
$47$	−1550.35	+	1550.35i	−0.701832	+	0.701832i	−0.964804	−	0.262972i	$-0.915297\pi$
$47$	−1550.35	+	1550.35i	−0.701832	+	0.701832i	0.262972	+	0.964804i	$0.415297\pi$
$48$	−5141.28	−	5141.28i	−2.23146	−	2.23146i
$49$		−	343.000i		−	0.142857i
$50$	−690.938	−	4479.44i	−0.276375	−	1.79177i
$51$	3024.03			1.16264
$52$	−1298.02	+	1298.02i	−0.480036	+	0.480036i
$53$	645.219	+	645.219i	0.229697	+	0.229697i	0.812566	−	0.582869i	$-0.198070\pi$
$53$	645.219	+	645.219i	0.229697	+	0.229697i	−0.582869	+	0.812566i	$0.698070\pi$
$54$			5482.73i			1.88022i
$55$	3030.10	−	1536.21i	1.00169	−	0.507839i
$56$	−2765.29			−0.881789
$57$	−4222.57	+	4222.57i	−1.29965	+	1.29965i
$58$	−1002.79	−	1002.79i	−0.298096	−	0.298096i
$59$		−	2295.44i		−	0.659419i	−0.944082	−	0.329710i	$-0.893049\pi$
$59$		−	2295.44i		−	0.659419i	0.944082	−	0.329710i	$-0.106951\pi$
$60$	−4158.03	+	12709.7i	−1.15501	+	3.53047i
$61$	3198.88			0.859682			0.429841	−	0.902905i	$-0.358570\pi$
$61$	3198.88			0.859682			0.429841	+	0.902905i	$0.358570\pi$
$62$	4949.28	−	4949.28i	1.28753	−	1.28753i
$63$	1738.03	+	1738.03i	0.437901	+	0.437901i
$64$			873.373i			0.213226i
$65$	1192.07	+	389.989i	0.282146	+	0.0923052i
$66$	−14406.5			−3.30728
$67$	−6113.48	+	6113.48i	−1.36188	+	1.36188i	−0.490360	+	0.871520i	$0.663135\pi$
$67$	−6113.48	+	6113.48i	−1.36188	+	1.36188i	−0.871520	+	0.490360i	$0.836865\pi$
$68$	−5351.89	−	5351.89i	−1.15742	−	1.15742i
$69$			4388.73i			0.921808i
$70$	1518.30	+	2994.77i	0.309857	+	0.611177i
$71$	740.397			0.146875			0.0734375	−	0.997300i	$-0.476603\pi$
$71$	740.397			0.146875			0.0734375	+	0.997300i	$0.476603\pi$
$72$	14012.1	−	14012.1i	2.70295	−	2.70295i
$73$	1763.21	+	1763.21i	0.330870	+	0.330870i	0.852917	−	0.522047i	$-0.174831\pi$
$73$	1763.21	+	1763.21i	0.330870	+	0.330870i	−0.522047	+	0.852917i	$0.674831\pi$
$74$		−	9488.56i		−	1.73275i
$75$	9030.11	−	1392.86i	1.60535	−	0.247620i
$76$	14946.1			2.58762
$77$	−1779.60	+	1779.60i	−0.300152	+	0.300152i
$78$	−3760.91	−	3760.91i	−0.618165	−	0.618165i
$79$		−	8409.12i		−	1.34740i	−0.739005	−	0.673700i	$-0.764704\pi$
$79$		−	8409.12i		−	1.34740i	0.739005	−	0.673700i	$-0.235296\pi$
$80$	11090.1	−	5622.48i	1.73282	−	0.878513i
$81$	−302.630			−0.0461256
$82$	−11790.0	+	11790.0i	−1.75342	+	1.75342i
$83$	5894.49	+	5894.49i	0.855637	+	0.855637i	0.990821	−	0.135183i	$-0.0431623\pi$
$83$	5894.49	+	5894.49i	0.855637	+	0.855637i	−0.135183	+	0.990821i	$0.543162\pi$
$84$		−	9906.53i		−	1.40399i
$85$	−1607.97	+	4915.04i	−0.222557	+	0.680282i
$86$	−12206.3			−1.65040
$87$	2021.54	−	2021.54i	0.267081	−	0.267081i
$88$	14347.2	+	14347.2i	1.85269	+	1.85269i
$89$			4763.09i			0.601324i	0.953731	+	0.300662i	$0.0972076\pi$
$89$			4763.09i			0.601324i	−0.953731	+	0.300662i	$0.902792\pi$
$90$	−22868.3	−	7481.47i	−2.82325	−	0.923638i
$91$	−929.153			−0.112203
$92$	7767.12	−	7767.12i	0.917666	−	0.917666i
$93$	9977.27	+	9977.27i	1.15357	+	1.15357i
$94$			15899.8i			1.79944i
$95$	−4617.78	−	9108.34i	−0.511666	−	1.00923i
$96$	−17802.6			−1.93170
$97$	687.835	−	687.835i	0.0731039	−	0.0731039i	−0.669609	−	0.742713i	$-0.733539\pi$
$97$	687.835	−	687.835i	0.0731039	−	0.0731039i	0.742713	+	0.669609i	$0.233539\pi$
$98$	−1758.85	−	1758.85i	−0.183137	−	0.183137i
$99$		−	18034.9i		−	1.84011i
$100$	−18446.5	−	13516.3i	−1.84465	−	1.35163i
$101$	−10449.3			−1.02434			−0.512172	−	0.858883i	$-0.671159\pi$
$101$	−10449.3			−1.02434			−0.512172	+	0.858883i	$0.671159\pi$
$102$	15506.7	−	15506.7i	1.49046	−	1.49046i
$103$	8531.35	+	8531.35i	0.804161	+	0.804161i	0.983743	−	0.179582i	$-0.0574744\pi$
$103$	8531.35	+	8531.35i	0.804161	+	0.804161i	−0.179582	+	0.983743i	$0.557474\pi$
$104$			7490.90i			0.692576i
$105$	−6037.16	+	3060.74i	−0.547588	+	0.277619i
$106$	6617.16			0.588925
$107$	−7239.61	+	7239.61i	−0.632336	+	0.632336i	−0.948653	−	0.316318i	$-0.897553\pi$
$107$	−7239.61	+	7239.61i	−0.632336	+	0.632336i	0.316318	+	0.948653i	$0.397553\pi$
$108$	19560.9	+	19560.9i	1.67703	+	1.67703i
$109$			12097.6i			1.01823i	0.860699	+	0.509115i	$0.170027\pi$
$109$			12097.6i			1.01823i	−0.860699	+	0.509115i	$0.829973\pi$
$110$	7660.41	−	23415.3i	0.633091	−	1.93515i
$111$	19128.0			1.55247
$112$	−6513.27	+	6513.27i	−0.519234	+	0.519234i
$113$	−11639.0	−	11639.0i	−0.911507	−	0.911507i	0.0848839	−	0.996391i	$-0.472948\pi$
$113$	−11639.0	−	11639.0i	−0.911507	−	0.911507i	−0.996391	+	0.0848839i	$0.972948\pi$
$114$			43305.3i			3.33220i
$115$	−7133.12	−	2333.63i	−0.539367	−	0.176456i
$116$	−7155.39			−0.531762
$117$	4708.15	−	4708.15i	0.343937	−	0.343937i
$118$	−11770.6	−	11770.6i	−0.845349	−	0.845349i
$119$		−	3831.01i		−	0.270533i
$120$	24675.9	+	48672.0i	1.71361	+	3.38000i
$121$	3825.30			0.261273
$122$	16403.3	−	16403.3i	1.10208	−	1.10208i
$123$	−23767.4	−	23767.4i	−1.57098	−	1.57098i
$124$		−	35315.3i		−	2.29678i
$125$	−2537.75	+	15417.5i	−0.162416	+	0.986722i
$126$	17824.7			1.12274
$127$	12421.7	−	12421.7i	0.770148	−	0.770148i	−0.207985	−	0.978132i	$-0.566690\pi$
$127$	12421.7	−	12421.7i	0.770148	−	0.770148i	0.978132	+	0.207985i	$0.0666904\pi$
$128$	−9298.93	−	9298.93i	−0.567562	−	0.567562i
$129$		−	24606.8i		−	1.47868i
$130$	8112.53	−	4112.92i	0.480031	−	0.243368i
$131$	−12976.3			−0.756151			−0.378076	−	0.925775i	$-0.623414\pi$
$131$	−12976.3			−0.756151			−0.378076	+	0.925775i	$0.623414\pi$
$132$	−51398.4	+	51398.4i	−2.94986	+	2.94986i
$133$	5349.39	+	5349.39i	0.302414	+	0.302414i
$134$			62697.9i			3.49175i
$135$	5877.07	−	17964.2i	0.322473	−	0.985691i
$136$	−30885.9			−1.66987
$137$	−13425.8	+	13425.8i	−0.715316	+	0.715316i	−0.967642	−	0.252326i	$-0.918804\pi$
$137$	−13425.8	+	13425.8i	−0.715316	+	0.715316i	0.252326	+	0.967642i	$0.418804\pi$
$138$	22504.7	+	22504.7i	1.18172	+	1.18172i
$139$		−	21541.5i		−	1.11493i	−0.830201	−	0.557464i	$-0.811775\pi$
$139$		−	21541.5i		−	1.11493i	0.830201	−	0.557464i	$-0.188225\pi$
$140$	16101.4	+	5267.63i	0.821499	+	0.268757i
$141$	−32052.6			−1.61222
$142$	3796.64	−	3796.64i	0.188288	−	0.188288i
$143$	4820.76	+	4820.76i	0.235745	+	0.235745i
$144$		−	66007.3i		−	3.18322i
$145$	2210.74	+	4360.58i	0.105148	+	0.207400i
$146$	18082.9			0.848325
$147$	3545.67	−	3545.67i	0.164083	−	0.164083i
$148$	−33852.6	−	33852.6i	−1.54550	−	1.54550i
$149$			23088.6i			1.03998i	0.854173	+	0.519989i	$0.174064\pi$
$149$			23088.6i			1.03998i	−0.854173	+	0.519989i	$0.825936\pi$
$150$	39162.6	−	53447.3i	1.74056	−	2.37544i
$151$	37589.4			1.64858			0.824292	−	0.566165i	$-0.191574\pi$
$151$	37589.4			1.64858			0.824292	+	0.566165i	$0.191574\pi$
$152$	43127.2	−	43127.2i	1.86665	−	1.86665i
$153$	19412.3	+	19412.3i	0.829265	+	0.829265i
$154$			18251.0i			0.769564i
$155$	−21521.6	+	10911.1i	−0.895799	+	0.454156i
$156$	−26835.8			−1.10272
$157$	−9237.11	+	9237.11i	−0.374746	+	0.374746i	−0.869202	−	0.494457i	$-0.835367\pi$
$157$	−9237.11	+	9237.11i	−0.374746	+	0.374746i	0.494457	+	0.869202i	$0.335367\pi$
$158$	−43120.6	−	43120.6i	−1.72731	−	1.72731i
$159$			13339.6i			0.527651i
$160$	9466.21	−	28935.0i	0.369774	−	1.13027i
$161$	5559.89			0.214494
$162$	−1551.84	+	1551.84i	−0.0591311	+	0.0591311i
$163$	15066.0	+	15066.0i	0.567052	+	0.567052i	0.931302	−	0.364249i	$-0.118674\pi$
$163$	15066.0	+	15066.0i	0.567052	+	0.567052i	−0.364249	+	0.931302i	$0.618674\pi$
$164$			84126.7i			3.12785i
$165$	47203.0	+	15442.6i	1.73381	+	0.567223i
$166$	60451.9			2.19378
$167$	10051.7	−	10051.7i	0.360416	−	0.360416i	−0.503550	−	0.863966i	$-0.667973\pi$
$167$	10051.7	−	10051.7i	0.360416	−	0.360416i	0.863966	+	0.503550i	$0.167973\pi$
$168$	−28585.4	−	28585.4i	−1.01281	−	1.01281i
$169$		−	26044.0i		−	0.911873i
$170$	16958.1	+	33449.0i	0.586785	+	1.15740i
$171$	−54212.2			−1.85398
$172$	−43548.8	+	43548.8i	−1.47204	+	1.47204i
$173$	−21678.9	−	21678.9i	−0.724345	−	0.724345i	0.245142	−	0.969487i	$-0.421165\pi$
$173$	−21678.9	−	21678.9i	−0.724345	−	0.724345i	−0.969487	+	0.245142i	$0.921165\pi$
$174$		−	20732.2i		−	0.684774i
$175$	−1764.56	−	11439.9i	−0.0576183	−	0.373547i
$176$	67586.0			2.18188
$177$	23728.5	−	23728.5i	0.757396	−	0.757396i
$178$	24424.3	+	24424.3i	0.770873	+	0.770873i
$179$		−	18170.8i		−	0.567111i	−0.958956	−	0.283556i	$-0.908486\pi$
$179$		−	18170.8i		−	0.567111i	0.958956	−	0.283556i	$-0.0915141\pi$
$180$	−108280.	+	54896.1i	−3.34197	+	1.69432i
$181$	−43196.5			−1.31853			−0.659267	−	0.751909i	$-0.729133\pi$
$181$	−43196.5			−1.31853			−0.659267	+	0.751909i	$0.729133\pi$
$182$	−4764.55	+	4764.55i	−0.143840	+	0.143840i
$183$	33067.5	+	33067.5i	0.987415	+	0.987415i
$184$		−	44824.2i		−	1.32397i
$185$	−10171.0	+	31089.3i	−0.297180	+	0.908381i
$186$	102324.			2.95767
$187$	−19876.6	+	19876.6i	−0.568406	+	0.568406i
$188$	56726.3	+	56726.3i	1.60498	+	1.60498i
$189$			14002.2i			0.391987i
$190$	−70385.3	−	23026.8i	−1.94973	−	0.637863i
$191$	22892.9			0.627529			0.313764	−	0.949501i	$-0.398410\pi$
$191$	22892.9			0.627529			0.313764	+	0.949501i	$0.398410\pi$
$192$	−9028.25	+	9028.25i	−0.244907	+	0.244907i
$193$	−37038.1	−	37038.1i	−0.994338	−	0.994338i	0.00564628	−	0.999984i	$-0.498203\pi$
$193$	−37038.1	−	37038.1i	−0.994338	−	0.994338i	−0.999984	+	0.00564628i	$0.998203\pi$
$194$		−	7054.21i		−	0.187433i
$195$	8291.26	+	16354.1i	0.218047	+	0.430087i
$196$	−12550.2			−0.326691
$197$	−2584.45	+	2584.45i	−0.0665940	+	0.0665940i	−0.739619	−	0.673025i	$-0.764994\pi$
$197$	−2584.45	+	2584.45i	−0.0665940	+	0.0665940i	0.673025	+	0.739619i	$0.264994\pi$
$198$	−92480.3	−	92480.3i	−2.35895	−	2.35895i
$199$			21774.1i			0.549837i	0.961468	+	0.274919i	$0.0886509\pi$
$199$			21774.1i			0.549837i	−0.961468	+	0.274919i	$0.911349\pi$
$200$	−92229.0	+	14226.0i	−2.30573	+	0.355650i
$201$	−126393.			−3.12846
$202$	−53582.5	+	53582.5i	−1.31317	+	1.31317i
$203$	−2561.00	−	2561.00i	−0.0621466	−	0.0621466i
$204$		−	110647.i		−	2.65877i
$205$	51267.8	−	25992.0i	1.21994	−	0.618488i
$206$	87494.7			2.06180
$207$	−28172.8	+	28172.8i	−0.657489	+	0.657489i
$208$	17643.8	+	17643.8i	0.407817	+	0.407817i
$209$		−	55508.9i		−	1.27078i
$210$	−15262.6	+	46652.6i	−0.346090	+	1.05788i
$211$	75363.5			1.69276			0.846382	−	0.532576i	$-0.178776\pi$
$211$	75363.5			1.69276			0.846382	+	0.532576i	$0.178776\pi$
$212$	23608.2	−	23608.2i	0.525280	−	0.525280i
$213$	7653.65	+	7653.65i	0.168698	+	0.168698i
$214$			74247.1i			1.62126i
$215$	39994.1	+	13084.2i	0.865205	+	0.283055i
$216$	112886.			2.41955
$217$	12639.8	−	12639.8i	0.268423	−	0.268423i
$218$	62034.4	+	62034.4i	1.30533	+	1.30533i
$219$			36453.4i			0.760063i
$220$	−56209.1	−	110870.i	−1.16135	−	2.29069i
$221$	−10377.8			−0.212482
$222$	98085.4	−	98085.4i	1.99021	−	1.99021i
$223$	−272.650	−	272.650i	−0.00548271	−	0.00548271i	0.704360	−	0.709843i	$-0.251234\pi$
$223$	−272.650	−	272.650i	−0.00548271	−	0.00548271i	−0.709843	+	0.704360i	$0.751234\pi$
$224$			22553.3i			0.449484i
$225$	66908.7	+	49026.2i	1.32165	+	0.968418i
$226$	−119366.			−2.33703
$227$	−14283.0	+	14283.0i	−0.277184	+	0.277184i	−0.831984	−	0.554800i	$-0.812795\pi$
$227$	−14283.0	+	14283.0i	−0.277184	+	0.277184i	0.554800	+	0.831984i	$0.312795\pi$
$228$	154501.	+	154501.i	2.97209	+	2.97209i
$229$		−	34740.0i		−	0.662458i	−0.943550	−	0.331229i	$-0.892537\pi$
$229$		−	34740.0i		−	0.662458i	0.943550	−	0.331229i	$-0.107463\pi$
$230$	−48544.0	+	24611.0i	−0.917655	+	0.465237i
$231$	−36792.2			−0.689497
$232$	−20647.0	+	20647.0i	−0.383601	+	0.383601i
$233$	−12274.1	−	12274.1i	−0.226088	−	0.226088i	0.584968	−	0.811056i	$-0.301107\pi$
$233$	−12274.1	−	12274.1i	−0.226088	−	0.226088i	−0.811056	+	0.584968i	$0.801107\pi$
$234$		−	48285.2i		−	0.881825i
$235$	17043.4	−	52096.0i	0.308618	−	0.943340i
$236$	−83988.8			−1.50799
$237$	86927.0	−	86927.0i	1.54760	−	1.54760i
$238$	−19644.8	−	19644.8i	−0.346812	−	0.346812i
$239$		−	94956.1i		−	1.66237i	−0.555997	−	0.831184i	$-0.687664\pi$
$239$		−	94956.1i		−	1.66237i	0.555997	−	0.831184i	$-0.312336\pi$
$240$	172761.	+	56519.5i	2.99933	+	0.981242i
$241$	44563.2			0.767260			0.383630	−	0.923487i	$-0.374674\pi$
$241$	44563.2			0.767260			0.383630	+	0.923487i	$0.374674\pi$
$242$	19615.5	−	19615.5i	0.334942	−	0.334942i
$243$	40174.6	+	40174.6i	0.680361	+	0.680361i
$244$		−	117045.i		−	1.96596i
$245$	3877.53	+	7648.23i	0.0645986	+	0.127417i
$246$	−243751.			−4.02788
$247$	14491.0	−	14491.0i	0.237522	−	0.237522i
$248$	−101903.	−	101903.i	−1.65685	−	1.65685i
$249$			121865.i			1.96554i
$250$	66045.5	+	92071.8i	1.05673	+	1.47315i
$251$	−29296.1			−0.465010			−0.232505	−	0.972595i	$-0.574692\pi$
$251$	−29296.1			−0.465010			−0.232505	+	0.972595i	$0.574692\pi$
$252$	63593.5	−	63593.5i	1.00141	−	1.00141i
$253$	−28846.6	−	28846.6i	−0.450665	−	0.450665i
$254$		−	127393.i		−	1.97460i
$255$	−67429.9	+	34185.9i	−1.03698	+	0.525734i
$256$	−109341.			−1.66841
$257$	−26697.7	+	26697.7i	−0.404210	+	0.404210i	−0.879714	−	0.475504i	$-0.842266\pi$
$257$	−26697.7	+	26697.7i	−0.404210	+	0.404210i	0.475504	+	0.879714i	$0.342266\pi$
$258$	−126180.	−	126180.i	−1.89561	−	1.89561i
$259$		−	24232.5i		−	0.361242i
$260$	14269.5	−	43617.0i	0.211087	−	0.645223i
$261$	25953.9			0.380997
$262$	−66540.4	+	66540.4i	−0.969355	+	0.969355i
$263$	−69822.4	−	69822.4i	−1.00945	−	1.00945i	−0.999955	−	0.00949086i	$-0.996979\pi$
$263$	−69822.4	−	69822.4i	−1.00945	−	1.00945i	−0.00949086	−	0.999955i	$-0.503021\pi$
$264$			296621.i			4.25593i
$265$	−21681.2	−	7093.08i	−0.308739	−	0.101005i
$266$	54861.6			0.775364
$267$	−49237.1	+	49237.1i	−0.690669	+	0.690669i
$268$	223689.	+	223689.i	3.11440	+	3.11440i
$269$			73355.9i			1.01375i	0.862020	+	0.506875i	$0.169199\pi$
$269$			73355.9i			1.01375i	−0.862020	+	0.506875i	$0.830801\pi$
$270$	−61981.0	−	122254.i	−0.850219	−	1.67701i
$271$	125134.			1.70388			0.851939	−	0.523642i	$-0.175427\pi$
$271$	125134.			1.70388			0.851939	+	0.523642i	$0.175427\pi$
$272$	−72747.6	+	72747.6i	−0.983288	+	0.983288i
$273$	−9604.87	−	9604.87i	−0.128874	−	0.128874i
$274$			137690.i			1.83401i
$275$	−50198.8	+	68509.0i	−0.663785	+	0.905904i
$276$	160581.			2.10803
$277$	44216.3	−	44216.3i	0.576266	−	0.576266i	−0.357607	−	0.933872i	$-0.616407\pi$
$277$	44216.3	−	44216.3i	0.576266	−	0.576266i	0.933872	+	0.357607i	$0.116407\pi$
$278$	−110461.	−	110461.i	−1.42929	−	1.42929i
$279$			128095.i			1.64560i
$280$	61660.5	−	31260.9i	0.786486	−	0.398736i
$281$	148338.			1.87862			0.939312	−	0.343065i	$-0.111465\pi$
$281$	148338.			1.87862			0.939312	+	0.343065i	$0.111465\pi$
$282$	−164360.	+	164360.i	−2.06680	+	2.06680i
$283$	−31339.4	−	31339.4i	−0.391307	−	0.391307i	0.483846	−	0.875153i	$-0.339239\pi$
$283$	−31339.4	−	31339.4i	−0.391307	−	0.391307i	−0.875153	+	0.483846i	$0.839239\pi$
$284$		−	27090.7i		−	0.335880i
$285$	46419.9	−	141890.i	0.571498	−	1.74688i
$286$	49440.1			0.604432
$287$	−30110.0	+	30110.0i	−0.365550	+	0.365550i
$288$	−114281.	−	114281.i	−1.37781	−	1.37781i
$289$			40731.9i			0.487685i
$290$	33696.7	+	11024.0i	0.400674	+	0.131082i
$291$	14220.6			0.167932
$292$	64514.8	−	64514.8i	0.756648	−	0.756648i
$293$	65192.3	+	65192.3i	0.759383	+	0.759383i	0.976210	−	0.216827i	$-0.0695708\pi$
$293$	65192.3	+	65192.3i	0.759383	+	0.759383i	−0.216827	+	0.976210i	$0.569571\pi$
$294$		−	36363.2i		−	0.420695i
$295$	25949.4	+	51183.8i	0.298183	+	0.588150i
$296$	−195364.			−2.22978
$297$	72647.9	−	72647.9i	0.823588	−	0.823588i
$298$	118394.	+	118394.i	1.33321	+	1.33321i
$299$		−	15061.2i		−	0.168468i
$300$	−50964.1	−	330407.i	−0.566268	−	3.67119i
$301$	−31173.3			−0.344072
$302$	192752.	−	192752.i	2.11342	−	2.11342i
$303$	−108017.	−	108017.i	−1.17654	−	1.17654i
$304$		−	203161.i		−	2.19833i
$305$	−71328.7	+	36162.5i	−0.766769	+	0.388740i
$306$	199086.			2.12617
$307$	−67430.3	+	67430.3i	−0.715448	+	0.715448i	−0.967670	−	0.252221i	$-0.918839\pi$
$307$	−67430.3	+	67430.3i	−0.715448	+	0.715448i	0.252221	+	0.967670i	$0.418839\pi$
$308$	65114.5	+	65114.5i	0.686398	+	0.686398i
$309$			176381.i			1.84729i
$310$	−54408.8	+	166310.i	−0.566169	+	1.73059i
$311$	8860.75			0.0916114			0.0458057	−	0.998950i	$-0.485414\pi$
$311$	8860.75			0.0916114			0.0458057	+	0.998950i	$0.485414\pi$
$312$	−77435.1	+	77435.1i	−0.795479	+	0.795479i
$313$	−104602.	−	104602.i	−1.06771	−	1.06771i	−0.997535	−	0.0701733i	$-0.977645\pi$
$313$	−104602.	−	104602.i	−1.06771	−	1.06771i	−0.0701733	−	0.997535i	$-0.522355\pi$
$314$			94732.7i			0.960817i
$315$	−58402.6	−	19106.6i	−0.588588	−	0.192559i
$316$	−307685.			−3.08129
$317$	40820.0	−	40820.0i	0.406213	−	0.406213i	−0.474203	−	0.880416i	$-0.657264\pi$
$317$	40820.0	−	40820.0i	0.406213	−	0.406213i	0.880416	+	0.474203i	$0.157264\pi$
$318$	68403.0	+	68403.0i	0.676427	+	0.676427i
$319$			26574.6i			0.261148i
$320$	−9873.26	−	19474.5i	−0.0964186	−	0.190181i
$321$	−149675.			−1.45258
$322$	28510.2	−	28510.2i	0.274972	−	0.274972i
$323$	59748.1	+	59748.1i	0.572689	+	0.572689i
$324$			11073.1i			0.105482i
$325$	−30989.5	+	4780.02i	−0.293392	+	0.0452546i
$326$	154512.			1.45388
$327$	−125055.	+	125055.i	−1.16952	+	1.16952i
$328$	242749.	+	242749.i	2.25636	+	2.25636i
$329$			40606.1i			0.375145i
$330$	321237.	−	162862.i	2.94983	−	1.49552i
$331$	−14561.0			−0.132903			−0.0664514	−	0.997790i	$-0.521168\pi$
$331$	−14561.0			−0.132903			−0.0664514	+	0.997790i	$0.521168\pi$
$332$	215676.	−	215676.i	1.95671	−	1.95671i
$333$	122789.	+	122789.i	1.10732	+	1.10732i
$334$		−	103087.i		−	0.924079i
$335$	67207.2	−	205430.i	0.598862	−	1.83052i
$336$	−134658.			−1.19276
$337$	−52044.1	+	52044.1i	−0.458259	+	0.458259i	−0.898084	−	0.439824i	$-0.855041\pi$
$337$	−52044.1	+	52044.1i	−0.458259	+	0.458259i	0.439824	+	0.898084i	$0.355041\pi$
$338$	−133549.	−	133549.i	−1.16898	−	1.16898i
$339$		−	240631.i		−	2.09388i
$340$	179838.	+	58834.9i	1.55570	+	0.508952i
$341$	−131159.			−1.12795
$342$	−277992.	+	277992.i	−2.37673	+	2.37673i
$343$	−4491.86	−	4491.86i	−0.0381802	−	0.0381802i
$344$			251321.i			2.12379i
$345$	−49613.5	−	97860.0i	−0.416832	−	0.822180i
$346$	−222332.			−1.85716
$347$	17334.3	−	17334.3i	0.143962	−	0.143962i	−0.631453	−	0.775414i	$-0.717541\pi$
$347$	17334.3	−	17334.3i	0.143962	−	0.143962i	0.775414	+	0.631453i	$0.217541\pi$
$348$	−73966.8	−	73966.8i	−0.610771	−	0.610771i
$349$		−	125838.i		−	1.03314i	−0.856244	−	0.516572i	$-0.827208\pi$
$349$		−	125838.i		−	1.03314i	0.856244	−	0.516572i	$-0.172792\pi$
$350$	−67710.2	−	49613.4i	−0.552736	−	0.405008i
$351$	37930.5			0.307875
$352$	117014.	−	117014.i	0.944394	−	0.944394i
$353$	58739.2	+	58739.2i	0.471388	+	0.471388i	0.902364	−	0.430976i	$-0.141830\pi$
$353$	58739.2	+	58739.2i	0.471388	+	0.471388i	−0.430976	+	0.902364i	$0.641830\pi$
$354$		−	243351.i		−	1.94190i
$355$	−16509.4	+	8370.01i	−0.131001	+	0.0664155i
$356$	174279.			1.37513
$357$	39602.0	−	39602.0i	0.310729	−	0.310729i
$358$	−93177.0	−	93177.0i	−0.727014	−	0.727014i
$359$		−	131534.i		−	1.02059i	−0.860000	−	0.510294i	$-0.829537\pi$
$359$		−	131534.i		−	1.02059i	0.860000	−	0.510294i	$-0.170463\pi$
$360$	−154039.	+	470846.i	−1.18857	+	3.63307i
$361$	−36536.2			−0.280355
$362$	−221505.	+	221505.i	−1.69031	+	1.69031i
$363$	39543.0	+	39543.0i	0.300094	+	0.300094i
$364$			33997.2i			0.256590i
$365$	−59248.7	−	19383.5i	−0.444727	−	0.145494i
$366$	339130.			2.53165
$367$	13662.1	−	13662.1i	0.101434	−	0.101434i	−0.654568	−	0.756003i	$-0.727150\pi$
$367$	13662.1	−	13662.1i	0.101434	−	0.101434i	0.756003	+	0.654568i	$0.227150\pi$
$368$	−105577.	−	105577.i	−0.779607	−	0.779607i
$369$		−	305143.i		−	2.24104i
$370$	107266.	+	211576.i	0.783534	+	1.54548i
$371$	16899.3			0.122778
$372$	365062.	−	365062.i	2.63804	−	2.63804i
$373$	155910.	+	155910.i	1.12061	+	1.12061i	0.991649	+	0.128964i	$0.0411652\pi$
$373$	155910.	+	155910.i	1.12061	+	1.12061i	0.128964	+	0.991649i	$0.458835\pi$
$374$			203848.i			1.45735i
$375$	−185608.	+	133141.i	−1.31988	+	0.946783i
$376$	327369.			2.31559
$377$	−6937.49	+	6937.49i	−0.0488112	+	0.0488112i
$378$	71800.8	+	71800.8i	0.502511	+	0.502511i
$379$		−	74194.8i		−	0.516530i	−0.966074	−	0.258265i	$-0.916849\pi$
$379$		−	74194.8i		−	0.516530i	0.966074	−	0.258265i	$-0.0831507\pi$
$380$	−333269.	+	168962.i	−2.30796	+	1.17010i
$381$	256812.			1.76915
$382$	117391.	−	117391.i	0.804467	−	0.804467i
$383$	153589.	+	153589.i	1.04704	+	1.04704i	0.998838	+	0.0482041i	$0.0153498\pi$
$383$	153589.	+	153589.i	1.04704	+	1.04704i	0.0482041	+	0.998838i	$0.484650\pi$
$384$		−	192250.i		−	1.30378i
$385$	19563.6	−	59799.5i	0.131986	−	0.403437i
$386$	−379851.			−2.54940
$387$	157959.	−	157959.i	1.05469	−	1.05469i
$388$	−25167.5	−	25167.5i	−0.167177	−	0.167177i
$389$		−	5566.71i		−	0.0367874i	−0.999831	−	0.0183937i	$-0.994145\pi$
$389$		−	5566.71i		−	0.0367874i	0.999831	−	0.0183937i	$-0.00585523\pi$
$390$	126377.	+	41344.8i	0.830883	+	0.271827i
$391$	62099.2			0.406193
$392$	−36213.7	+	36213.7i	−0.235668	+	0.235668i
$393$	−134139.	−	134139.i	−0.868501	−	0.868501i
$394$			26505.2i			0.170742i
$395$	95063.0	+	187507.i	0.609281	+	1.20177i
$396$	−659888.			−4.20804
$397$	−88916.2	+	88916.2i	−0.564157	+	0.564157i	−0.930486	−	0.366329i	$-0.880615\pi$
$397$	−88916.2	+	88916.2i	−0.564157	+	0.564157i	0.366329	+	0.930486i	$0.380615\pi$
$398$	111654.	+	111654.i	0.704869	+	0.704869i
$399$			110596.i			0.694693i
$400$	−183726.	+	250741.i	−1.14829	+	1.56713i
$401$	140901.			0.876242			0.438121	−	0.898916i	$-0.355644\pi$
$401$	140901.			0.876242			0.438121	+	0.898916i	$0.355644\pi$
$402$	−648122.	+	648122.i	−4.01056	+	4.01056i
$403$	−34239.9	−	34239.9i	−0.210825	−	0.210825i
$404$			382335.i			2.34251i
$405$	6748.05	−	3421.16i	0.0411404	−	0.0208575i
$406$	−26264.8			−0.159339
$407$	−125726.	+	125726.i	−0.758992	+	0.758992i
$408$	−319274.	−	319274.i	−1.91798	−	1.91798i
$409$			36303.3i			0.217020i	0.994095	+	0.108510i	$0.0346079\pi$
$409$			36303.3i			0.217020i	−0.994095	+	0.108510i	$0.965392\pi$
$410$	129610.	−	396176.i	0.771032	−	2.35679i
$411$	−277570.			−1.64320
$412$	312157.	−	312157.i	1.83899	−	1.83899i
$413$	−30060.6	−	30060.6i	−0.176237	−	0.176237i
$414$			288931.i			1.68575i
$415$	−198071.	−	64799.8i	−1.15007	−	0.376251i
$416$	61094.8			0.353035
$417$	222679.	−	222679.i	1.28058	−	1.28058i
$418$	−284641.	−	284641.i	−1.62909	−	1.62909i
$419$			135974.i			0.774510i	0.921973	+	0.387255i	$0.126577\pi$
$419$			135974.i			0.774510i	−0.921973	+	0.387255i	$0.873423\pi$
$420$	111991.	+	220896.i	0.634869	+	1.25225i
$421$	−48464.2			−0.273437			−0.136718	−	0.990610i	$-0.543656\pi$
$421$	−48464.2			−0.273437			−0.136718	+	0.990610i	$0.543656\pi$
$422$	386452.	−	386452.i	2.17005	−	2.17005i
$423$	−205757.	−	205757.i	−1.14993	−	1.14993i
$424$		−	136243.i		−	0.757851i
$425$	−19708.6	−	127773.i	−0.109113	−	0.707396i
$426$	78493.4			0.432528
$427$	41891.9	−	41891.9i	0.229760	−	0.229760i
$428$	264893.	+	264893.i	1.44605	+	1.44605i
$429$			99666.5i			0.541545i
$430$	272177.	−	137990.i	1.47202	−	0.746293i
$431$	103330.			0.556251			0.278126	−	0.960545i	$-0.410287\pi$
$431$	103330.			0.556251			0.278126	+	0.960545i	$0.410287\pi$
$432$	265889.	−	265889.i	1.42473	−	1.42473i
$433$	−166967.	−	166967.i	−0.890541	−	0.890541i	0.104033	−	0.994574i	$-0.466825\pi$
$433$	−166967.	−	166967.i	−0.890541	−	0.890541i	−0.994574	+	0.104033i	$0.966825\pi$
$434$		−	129629.i		−	0.688215i
$435$	−22223.3	+	67929.2i	−0.117444	+	0.358987i
$436$	442644.			2.32853
$437$	−86711.5	+	86711.5i	−0.454061	+	0.454061i
$438$	186927.	+	186927.i	0.974370	+	0.974370i
$439$			153188.i			0.794870i	0.917630	+	0.397435i	$0.130100\pi$
$439$			153188.i			0.794870i	−0.917630	+	0.397435i	$0.869900\pi$
$440$	−482108.	−	157723.i	−2.49022	−	0.814687i
$441$	45521.8			0.234068
$442$	−53215.9	+	53215.9i	−0.272393	+	0.272393i
$443$	193497.	+	193497.i	0.985977	+	0.985977i	0.999903	−	0.0139263i	$-0.00443303\pi$
$443$	193497.	+	193497.i	0.985977	+	0.985977i	−0.0139263	+	0.999903i	$0.504433\pi$
$444$		−	699883.i		−	3.55026i
$445$	−53845.5	−	106208.i	−0.271913	−	0.536334i
$446$	−2796.21			−0.0140572
$447$	−238672.	+	238672.i	−1.19450	+	1.19450i
$448$	11437.5	+	11437.5i	0.0569870	+	0.0569870i
$449$		−	197644.i		−	0.980371i	−0.871618	−	0.490185i	$-0.836929\pi$
$449$		−	197644.i		−	0.980371i	0.871618	−	0.490185i	$-0.163071\pi$
$450$	594495.	−	91698.8i	2.93578	−	0.452834i
$451$	312441.			1.53608
$452$	−425866.	+	425866.i	−2.08447	+	2.08447i
$453$	388570.	+	388570.i	1.89353	+	1.89353i
$454$			146482.i			0.710677i
$455$	20718.3	−	10503.8i	0.100076	−	0.0507371i
$456$	891631.			4.28801
$457$	−112416.	+	112416.i	−0.538264	+	0.538264i	−0.923019	−	0.384755i	$-0.874286\pi$
$457$	−112416.	+	112416.i	−0.538264	+	0.538264i	0.384755	+	0.923019i	$0.374286\pi$
$458$	−178141.	−	178141.i	−0.849244	−	0.849244i
$459$			156392.i			0.742317i
$460$	−85386.2	+	260997.i	−0.403526	+	1.23344i
$461$	99283.0			0.467168			0.233584	−	0.972337i	$-0.424955\pi$
$461$	99283.0			0.467168			0.233584	+	0.972337i	$0.424955\pi$
$462$	−188665.	+	188665.i	−0.883907	+	0.883907i
$463$	−102537.	−	102537.i	−0.478319	−	0.478319i	0.426275	−	0.904594i	$-0.359826\pi$
$463$	−102537.	−	102537.i	−0.478319	−	0.478319i	−0.904594	+	0.426275i	$0.859826\pi$
$464$			97262.2i			0.451761i
$465$	−335264.	−	109683.i	−1.55053	−	0.507263i
$466$	−125879.			−0.579671
$467$	265905.	−	265905.i	1.21925	−	1.21925i	0.251353	−	0.967895i	$-0.419124\pi$
$467$	265905.	−	265905.i	1.21925	−	1.21925i	0.967895	−	0.251353i	$-0.0808755\pi$
$468$	−172268.	−	172268.i	−0.786528	−	0.786528i
$469$			160122.i			0.727956i
$470$	−179744.	−	354535.i	−0.813689	−	1.60496i
$471$	−190972.			−0.860851
$472$	−242351.	+	242351.i	−1.08783	+	1.08783i
$473$	161738.	+	161738.i	0.722917	+	0.722917i
$474$		−	891495.i		−	3.96791i
$475$	205935.	+	150895.i	0.912731	+	0.668788i
$476$	−140175.			−0.618665
$477$	−85631.2	+	85631.2i	−0.376353	+	0.376353i
$478$	−486920.	−	486920.i	−2.13109	−	2.13109i
$479$			246167.i			1.07290i	0.843932	+	0.536449i	$0.180235\pi$
$479$			246167.i			1.07290i	−0.843932	+	0.536449i	$0.819765\pi$
$480$	396962.	−	201254.i	1.72293	−	0.873497i
$481$	−65643.4			−0.283727
$482$	228513.	−	228513.i	0.983596	−	0.983596i
$483$	57473.9	+	57473.9i	0.246363	+	0.246363i
$484$		−	139966.i		−	0.597490i
$485$	−7561.57	+	23113.2i	−0.0321461	+	0.0982598i
$486$	412018.			1.74439
$487$	−47449.1	+	47449.1i	−0.200065	+	0.200065i	−0.800028	−	0.599963i	$-0.795182\pi$
$487$	−47449.1	+	47449.1i	−0.200065	+	0.200065i	0.599963	+	0.800028i	$0.295182\pi$
$488$	−337735.	−	337735.i	−1.41820	−	1.41820i
$489$			311482.i			1.30261i
$490$	59102.2	+	19335.5i	0.246157	+	0.0805311i
$491$	138021.			0.572508			0.286254	−	0.958154i	$-0.407590\pi$
$491$	138021.			0.572508			0.286254	+	0.958154i	$0.407590\pi$
$492$	−869637.	+	869637.i	−3.59259	+	3.59259i
$493$	−28604.1	−	28604.1i	−0.117689	−	0.117689i
$494$		−	148615.i		−	0.608987i
$495$	203881.	+	402144.i	0.832081	+	1.64124i
$496$	−480037.			−1.95124
$497$	9696.09	−	9696.09i	0.0392540	−	0.0392540i
$498$	624905.	+	624905.i	2.51974	+	2.51974i
$499$			450282.i			1.80835i	0.427158	+	0.904177i	$0.359515\pi$
$499$			450282.i			1.80835i	−0.427158	+	0.904177i	$0.640485\pi$
$500$	564119.	+	92854.7i	2.25648	+	0.371419i
$501$	207812.			0.827935
$502$	−150226.	+	150226.i	−0.596124	+	0.596124i
$503$	−269041.	−	269041.i	−1.06337	−	1.06337i	−0.997852	−	0.0655153i	$-0.979131\pi$
$503$	−269041.	−	269041.i	−1.06337	−	1.06337i	−0.0655153	−	0.997852i	$-0.520869\pi$
$504$		−	367000.i		−	1.44479i
$505$	233000.	−	118127.i	0.913635	−	0.463198i
$506$	−295841.			−1.15547
$507$	269223.	−	269223.i	1.04736	−	1.04736i
$508$	−454503.	−	454503.i	−1.76120	−	1.76120i
$509$		−	91831.8i		−	0.354452i	−0.984170	−	0.177226i	$-0.943288\pi$
$509$		−	91831.8i		−	0.354452i	0.984170	−	0.177226i	$-0.0567123\pi$
$510$	−170470.	+	521069.i	−0.655401	+	2.00334i
$511$	46181.3			0.176858
$512$	−411899.	+	411899.i	−1.57127	+	1.57127i
$513$	−218376.	−	218376.i	−0.829795	−	0.829795i
$514$			273803.i			1.03636i
$515$	−286677.	−	93787.6i	−1.08088	−	0.353615i
$516$	−900348.			−3.38151
$517$	210678.	−	210678.i	0.788202	−	0.788202i
$518$	−124260.	−	124260.i	−0.463098	−	0.463098i
$519$		−	448200.i		−	1.66394i
$520$	−84682.7	−	167032.i	−0.313176	−	0.617723i
$521$	−317145.			−1.16838			−0.584189	−	0.811618i	$-0.698587\pi$
$521$	−317145.			−1.16838			−0.584189	+	0.811618i	$0.698587\pi$
$522$	133087.	−	133087.i	0.488422	−	0.488422i
$523$	201425.	+	201425.i	0.736394	+	0.736394i	0.971878	−	0.235484i	$-0.0756676\pi$
$523$	201425.	+	201425.i	0.736394	+	0.736394i	−0.235484	+	0.971878i	$0.575668\pi$
$524$			474796.i			1.72920i
$525$	100016.	−	136497.i	0.362869	−	0.495228i
$526$	−716075.			−2.58814
$527$	141175.	−	141175.i	0.508321	−	0.508321i
$528$	698652.	+	698652.i	2.50607	+	2.50607i
$529$		−	189717.i		−	0.677947i
$530$	−147550.	+	74805.3i	−0.525275	+	0.266306i
$531$	304642.			1.08044
$532$	195731.	−	195731.i	0.691571	−	0.691571i
$533$	81564.9	+	81564.9i	0.287110	+	0.287110i
$534$			504960.i			1.77082i
$535$	79587.1	−	243271.i	0.278058	−	0.849930i
$536$	1.29091e6			4.49332
$537$	187836.	−	187836.i	0.651373	−	0.651373i
$538$	376157.	+	376157.i	1.29959	+	1.29959i
$539$			46610.5i			0.160438i
$540$	−657301.	−	215039.i	−2.25412	−	0.737443i
$541$	−288032.			−0.984115			−0.492058	−	0.870563i	$-0.663755\pi$
$541$	−288032.			−0.984115			−0.492058	+	0.870563i	$0.663755\pi$
$542$	641669.	−	641669.i	2.18430	−	2.18430i
$543$	−446532.	−	446532.i	−1.51444	−	1.51444i
$544$			251901.i			0.851202i
$545$	−136760.	−	269752.i	−0.460433	−	0.908181i
$546$	−98504.4			−0.330423
$547$	84502.3	−	84502.3i	0.282419	−	0.282419i	−0.551654	−	0.834073i	$-0.686003\pi$
$547$	84502.3	−	84502.3i	0.282419	−	0.282419i	0.834073	+	0.551654i	$0.186003\pi$
$548$	491241.	+	491241.i	1.63581	+	1.63581i
$549$			424544.i			1.40857i
$550$	93892.0	+	608714.i	0.310387	+	2.01228i
$551$	79882.2			0.263116
$552$	463358.	−	463358.i	1.52068	−	1.52068i
$553$	−110124.	−	110124.i	−0.360108	−	0.360108i
$554$		−	453468.i		−	1.47750i
$555$	−426517.	+	216237.i	−1.38468	+	0.702013i
$556$	−788192.			−2.54966
$557$	−83519.3	+	83519.3i	−0.269201	+	0.269201i	−0.828778	−	0.559577i	$-0.810964\pi$
$557$	−83519.3	+	83519.3i	−0.269201	+	0.269201i	0.559577	+	0.828778i	$0.310964\pi$
$558$	656851.	+	656851.i	2.10959	+	2.10959i
$559$			84445.4i			0.270242i
$560$	71602.2	−	218864.i	0.228323	−	0.697908i
$561$	−410937.			−1.30572
$562$	760653.	−	760653.i	2.40832	−	2.40832i
$563$	−377217.	−	377217.i	−1.19008	−	1.19008i	−0.977046	−	0.213030i	$-0.931667\pi$
$563$	−377217.	−	377217.i	−1.19008	−	1.19008i	−0.213030	−	0.977046i	$-0.568333\pi$
$564$			1.17279e6i			3.68689i
$565$	391104.	+	127951.i	1.22517	+	0.400818i
$566$	−321406.			−1.00328
$567$	−3963.18	+	3963.18i	−0.0123276	+	0.0123276i
$568$	−78170.6	−	78170.6i	−0.242296	−	0.242296i
$569$		−	4157.76i		−	0.0128421i	−0.999979	−	0.00642103i	$-0.997956\pi$
$569$		−	4157.76i		−	0.0128421i	0.999979	−	0.00642103i	$-0.00204389\pi$
$570$	−489555.	−	965623.i	−1.50679	−	2.97206i
$571$	281259.			0.862650			0.431325	−	0.902197i	$-0.358046\pi$
$571$	281259.			0.862650			0.431325	+	0.902197i	$0.358046\pi$
$572$	176389.	−	176389.i	0.539112	−	0.539112i
$573$	236649.	+	236649.i	0.720768	+	0.720768i
$574$			308798.i			0.937240i
$575$	185436.	−	28602.8i	0.560864	−	0.0865114i
$576$	−115911.			−0.349365
$577$	−363376.	+	363376.i	−1.09145	+	1.09145i	−0.0960790	+	0.995374i	$0.530630\pi$
$577$	−363376.	+	363376.i	−1.09145	+	1.09145i	−0.995374	+	0.0960790i	$0.969370\pi$
$578$	208867.	+	208867.i	0.625192	+	0.625192i
$579$		−	765742.i		−	2.28415i
$580$	159551.	−	80889.9i	0.474290	−	0.240457i
$581$	154386.			0.457357
$582$	72921.0	−	72921.0i	0.215281	−	0.215281i
$583$	−87679.3	−	87679.3i	−0.257965	−	0.257965i
$584$		−	372317.i		−	1.09166i
$585$	−51758.0	+	158207.i	−0.151240	+	0.462289i
$586$	668591.			1.94700
$587$	−90438.2	+	90438.2i	−0.262467	+	0.262467i	−0.826056	−	0.563588i	$-0.809420\pi$
$587$	−90438.2	+	90438.2i	−0.262467	+	0.262467i	0.563588	+	0.826056i	$0.309420\pi$
$588$	−129734.	−	129734.i	−0.375231	−	0.375231i
$589$			394258.i			1.13645i
$590$	395526.	+	129398.i	1.13624	+	0.371726i
$591$	−53432.0			−0.152977
$592$	−460154.	+	460154.i	−1.31298	+	1.31298i
$593$	54345.8	+	54345.8i	0.154546	+	0.154546i	0.780145	−	0.625599i	$-0.215145\pi$
$593$	54345.8	+	54345.8i	0.154546	+	0.154546i	−0.625599	+	0.780145i	$0.715145\pi$
$594$		−	745053.i		−	2.11161i
$595$	43308.7	+	85424.1i	0.122332	+	0.241294i
$596$	844798.			2.37826
$597$	−225084.	+	225084.i	−0.631532	+	0.631532i
$598$	−77231.4	−	77231.4i	−0.215969	−	0.215969i
$599$			49282.3i			0.137353i	0.997639	+	0.0686764i	$0.0218776\pi$
$599$			49282.3i			0.137353i	−0.997639	+	0.0686764i	$0.978122\pi$
$600$	−1.10045e6	−	806335.i	−3.05681	−	2.23982i
$601$	−520219.			−1.44025			−0.720123	−	0.693846i	$-0.755915\pi$
$601$	−520219.			−1.44025			−0.720123	+	0.693846i	$0.755915\pi$
$602$	−159852.	+	159852.i	−0.441087	+	0.441087i
$603$	−811360.	−	811360.i	−2.23141	−	2.23141i
$604$		−	1.37537e6i		−	3.77005i
$605$	−85296.8	+	43244.1i	−0.233035	+	0.118145i
$606$	−1.10779e6			−3.01656
$607$	151266.	−	151266.i	0.410547	−	0.410547i	−0.471382	−	0.881929i	$-0.656245\pi$
$607$	151266.	−	151266.i	0.410547	−	0.410547i	0.881929	+	0.471382i	$0.156245\pi$
$608$	−351740.	−	351740.i	−0.951511	−	0.951511i
$609$		−	52947.3i		−	0.142761i
$610$	−180326.	+	551198.i	−0.484618	+	1.48132i
$611$	109998.			0.294647
$612$	710284.	−	710284.i	1.89640	−	1.89640i
$613$	55744.1	+	55744.1i	0.148347	+	0.148347i	0.777379	−	0.629032i	$-0.216549\pi$
$613$	55744.1	+	55744.1i	0.148347	+	0.148347i	−0.629032	+	0.777379i	$0.716549\pi$
$614$			691543.i			1.83435i
$615$	798652.	+	261282.i	2.11158	+	0.690812i
$616$	375777.			0.990306
$617$	−298648.	+	298648.i	−0.784493	+	0.784493i	−0.980585	−	0.196093i	$-0.937175\pi$
$617$	−298648.	+	298648.i	−0.784493	+	0.784493i	0.196093	+	0.980585i	$0.437175\pi$
$618$	904453.	+	904453.i	2.36815	+	2.36815i
$619$		−	345096.i		−	0.900656i	−0.892863	−	0.450328i	$-0.851307\pi$
$619$		−	345096.i		−	0.900656i	0.892863	−	0.450328i	$-0.148693\pi$
$620$	399231.	+	787462.i	1.03858	+	2.04855i
$621$	−226969.			−0.588551
$622$	45436.5	−	45436.5i	0.117442	−	0.117442i
$623$	62376.5	+	62376.5i	0.160711	+	0.160711i
$624$			364776.i			0.936822i
$625$	−117705.	−	372469.i	−0.301324	−	0.953522i
$626$	−1.07277e6			−2.73752
$627$	573808.	−	573808.i	1.45959	−	1.45959i
$628$	337980.	+	337980.i	0.856983	+	0.856983i
$629$		−	270656.i		−	0.684095i
$630$	−397455.	+	201503.i	−1.00140	+	0.507693i
$631$	−184294.			−0.462864			−0.231432	−	0.972851i	$-0.574341\pi$
$631$	−184294.			−0.462864			−0.231432	+	0.972851i	$0.574341\pi$
$632$	−887829.	+	887829.i	−2.22277	+	2.22277i
$633$	779050.	+	779050.i	1.94428	+	1.94428i
$634$		−	418636.i		−	1.04150i
$635$	−136555.	+	417404.i	−0.338658	+	1.03516i
$636$	488087.			1.20665
$637$	−12168.0	+	12168.0i	−0.0299875	+	0.0299875i
$638$	136270.	+	136270.i	0.334781	+	0.334781i
$639$			98262.9i			0.240651i
$640$	312470.	+	102226.i	0.762866	+	0.249575i
$641$	−538716.			−1.31112			−0.655562	−	0.755142i	$-0.727568\pi$
$641$	−538716.			−1.31112			−0.655562	+	0.755142i	$0.727568\pi$
$642$	−767509.	+	767509.i	−1.86214	+	1.86214i
$643$	−95071.3	−	95071.3i	−0.229947	−	0.229947i	0.582724	−	0.812670i	$-0.301987\pi$
$643$	−95071.3	−	95071.3i	−0.229947	−	0.229947i	−0.812670	+	0.582724i	$0.801987\pi$
$644$		−	203433.i		−	0.490513i
$645$	278174.	+	548683.i	0.668646	+	1.31887i
$646$	612757.			1.46833
$647$	90118.2	−	90118.2i	0.215280	−	0.215280i	−0.591226	−	0.806506i	$-0.701356\pi$
$647$	90118.2	−	90118.2i	0.215280	−	0.215280i	0.806506	+	0.591226i	$0.201356\pi$
$648$	31951.4	+	31951.4i	0.0760922	+	0.0760922i
$649$			311929.i			0.740570i
$650$	−134398.	+	183420.i	−0.318102	+	0.434131i
$651$	261321.			0.616611
$652$	551257.	−	551257.i	1.29676	−	1.29676i
$653$	−242315.	−	242315.i	−0.568268	−	0.568268i	0.363375	−	0.931643i	$-0.381624\pi$
$653$	−242315.	−	242315.i	−0.568268	−	0.568268i	−0.931643	+	0.363375i	$0.881624\pi$
$654$			1.28253e6i			2.99855i
$655$	289346.	−	146694.i	0.674428	−	0.341924i
$656$	1.14352e6			2.65728
$657$	−234007.	+	234007.i	−0.542123	+	0.542123i
$658$	208221.	+	208221.i	0.480921	+	0.480921i
$659$		−	682462.i		−	1.57148i	−0.618559	−	0.785738i	$-0.712283\pi$
$659$		−	682462.i		−	1.57148i	0.618559	−	0.785738i	$-0.287717\pi$
$660$	565037.	−	1.72713e6i	1.29715	−	3.96494i
$661$	125400.			0.287008			0.143504	−	0.989650i	$-0.454163\pi$
$661$	125400.			0.287008			0.143504	+	0.989650i	$0.454163\pi$
$662$	−74666.2	+	74666.2i	−0.170376	+	0.170376i
$663$	−107278.	−	107278.i	−0.244053	−	0.244053i
$664$		−	1.24467e6i		−	2.82305i
$665$	−179755.	−	58807.4i	−0.406478	−	0.132981i
$666$	1.25929e6			2.83907
$667$	41512.8	−	41512.8i	0.0933104	−	0.0933104i
$668$	−367784.	−	367784.i	−0.824215	−	0.824215i
$669$		−	5636.88i		−	0.0125947i
$670$	−708784.	−	1.39804e6i	−1.57893	−	3.11437i
$671$	−434698.			−0.965479
$672$	−233139.	+	233139.i	−0.516269	+	0.516269i
$673$	103115.	+	103115.i	0.227662	+	0.227662i	0.811715	−	0.584053i	$-0.198534\pi$
$673$	103115.	+	103115.i	0.227662	+	0.227662i	−0.584053	+	0.811715i	$0.698534\pi$
$674$			533747.i			1.17494i
$675$	72034.0	+	467006.i	0.158099	+	1.02498i
$676$	−952936.			−2.08531
$677$	−620376.	+	620376.i	−1.35356	+	1.35356i	−0.471917	+	0.881643i	$0.656438\pi$
$677$	−620376.	+	620376.i	−1.35356	+	1.35356i	−0.881643	+	0.471917i	$0.843562\pi$
$678$	−1.23391e6	−	1.23391e6i	−2.68427	−	2.68427i
$679$		−	18015.5i		−	0.0390757i
$680$	688695.	−	349157.i	1.48939	−	0.755098i
$681$	−295294.			−0.636736
$682$	−672561.	+	672561.i	−1.44598	+	1.44598i
$683$	484076.	+	484076.i	1.03770	+	1.03770i	0.999261	+	0.0384396i	$0.0122387\pi$
$683$	484076.	+	484076.i	1.03770	+	1.03770i	0.0384396	+	0.999261i	$0.487761\pi$
$684$			1.98359e6i			4.23976i
$685$	147593.	−	451143.i	0.314547	−	0.961465i
$686$	−46067.1			−0.0978909
$687$	359115.	−	359115.i	0.760886	−	0.760886i
$688$	591954.	+	591954.i	1.25058	+	1.25058i
$689$		−	45778.6i		−	0.0964326i
$690$	−756220.	−	247400.i	−1.58836	−	0.519639i
$691$	−813004.			−1.70269			−0.851347	−	0.524603i	$-0.824214\pi$
$691$	−813004.			−1.70269			−0.851347	+	0.524603i	$0.824214\pi$
$692$	−793219.	+	793219.i	−1.65646	+	1.65646i
$693$	−236182.	−	236182.i	−0.491791	−	0.491791i
$694$		−	177775.i		−	0.369106i
$695$	243521.	+	480334.i	0.504159	+	0.994428i
$696$	−426864.			−0.881194
$697$	−336302.	+	336302.i	−0.692252	+	0.692252i
$698$	−645277.	−	645277.i	−1.32445	−	1.32445i
$699$		−	253760.i		−	0.519360i
$700$	−418578.	+	64564.3i	−0.854242	+	0.131764i
$701$	409417.			0.833163			0.416581	−	0.909098i	$-0.363228\pi$
$701$	409417.			0.833163			0.416581	+	0.909098i	$0.363228\pi$
$702$	194501.	−	194501.i	0.394683	−	0.394683i
$703$	377927.	+	377927.i	0.764712	+	0.764712i
$704$		−	118683.i		−	0.239466i
$705$	714709.	−	362346.i	1.43797	−	0.729030i
$706$	602410.			1.20860
$707$	−136842.	+	136842.i	−0.273768	+	0.273768i
$708$	−868211.	−	868211.i	−1.73204	−	1.73204i
$709$			147502.i			0.293430i	0.989179	+	0.146715i	$0.0468701\pi$
$709$			147502.i			0.293430i	−0.989179	+	0.146715i	$0.953130\pi$
$710$	−41737.5	+	127578.i	−0.0827961	+	0.253080i
$711$	1.11603e6			2.20768
$712$	502883.	−	502883.i	0.991990	−	0.991990i
$713$	204886.	+	204886.i	0.403026	+	0.403026i
$714$		−	406146.i		−	0.796683i
$715$	−161991.	−	52996.0i	−0.316868	−	0.103665i
$716$	−664860.			−1.29689
$717$	981583.	−	981583.i	1.90936	−	1.90936i
$718$	−674487.	−	674487.i	−1.30835	−	1.30835i
$719$		−	60901.4i		−	0.117807i	−0.998264	−	0.0589033i	$-0.981240\pi$
$719$		−	60901.4i		−	0.117807i	0.998264	−	0.0589033i	$-0.0187604\pi$
$720$	746196.	+	1.47183e6i	1.43942	+	2.83918i
$721$	223450.			0.429842
$722$	−187352.	+	187352.i	−0.359404	+	0.359404i
$723$	460660.	+	460660.i	0.881260	+	0.881260i
$724$			1.58054e6i			3.01528i
$725$	−98590.5	−	72240.4i	−0.187568	−	0.137437i
$726$	405541.			0.769416
$727$	−401016.	+	401016.i	−0.758739	+	0.758739i	−0.976093	−	0.217354i	$-0.930257\pi$
$727$	−401016.	+	401016.i	−0.758739	+	0.758739i	0.217354	+	0.976093i	$0.430257\pi$
$728$	98099.3	+	98099.3i	0.185099	+	0.185099i
$729$			855102.i			1.60903i
$730$	−403213.	+	204423.i	−0.756639	+	0.383604i
$731$	−348179.			−0.651580
$732$	1.20992e6	−	1.20992e6i	2.25806	−	2.25806i
$733$	−171074.	−	171074.i	−0.318403	−	0.318403i	0.529751	−	0.848153i	$-0.322285\pi$
$733$	−171074.	−	171074.i	−0.318403	−	0.318403i	−0.848153	+	0.529751i	$0.822285\pi$
$734$		−	140114.i		−	0.260070i
$735$	−38978.6	+	119144.i	−0.0721524	+	0.220546i
$736$	−365581.			−0.674881
$737$	830766.	−	830766.i	1.52948	−	1.52948i
$738$	−1.56472e6	−	1.56472e6i	−2.87293	−	2.87293i
$739$			698841.i			1.27965i	0.768522	+	0.639823i	$0.220992\pi$
$739$			698841.i			1.27965i	−0.768522	+	0.639823i	$0.779008\pi$
$740$	1.13754e6	+	372151.i	2.07732	+	0.679604i
$741$	299593.			0.545626
$742$	86657.0	−	86657.0i	0.157397	−	0.157397i
$743$	−163993.	−	163993.i	−0.297062	−	0.297062i	0.542800	−	0.839862i	$-0.317364\pi$
$743$	−163993.	−	163993.i	−0.297062	−	0.297062i	−0.839862	+	0.542800i	$0.817364\pi$
$744$		−	2.10678e6i		−	3.80605i
$745$	−261011.	−	514830.i	−0.470268	−	0.927580i
$746$	1.59896e6			2.87316
$747$	−782295.	+	782295.i	−1.40194	+	1.40194i
$748$	727273.	+	727273.i	1.29985	+	1.29985i
$749$			189617.i			0.337998i
$750$	−269040.	+	1.63449e6i	−0.478293	+	2.90577i
$751$	648908.			1.15054			0.575272	−	0.817962i	$-0.304896\pi$
$751$	648908.			1.15054			0.575272	+	0.817962i	$0.304896\pi$
$752$	771073.	−	771073.i	1.36352	−	1.36352i
$753$	−302840.	−	302840.i	−0.534101	−	0.534101i
$754$			71148.7i			0.125148i
$755$	−838169.	+	424938.i	−1.47041	+	0.745473i
$756$	512331.			0.896411
$757$	−427480.	+	427480.i	−0.745975	+	0.745975i	−0.973721	−	0.227746i	$-0.926865\pi$
$757$	−427480.	+	427480.i	−0.745975	+	0.745975i	0.227746	+	0.973721i	$0.426865\pi$
$758$	−380459.	−	380459.i	−0.662170	−	0.662170i
$759$		−	596387.i		−	1.03525i
$760$	−474109.	+	1.44919e6i	−0.820827	+	2.50899i
$761$	277901.			0.479867			0.239934	−	0.970789i	$-0.422874\pi$
$761$	277901.			0.479867			0.239934	+	0.970789i	$0.422874\pi$
$762$	1.31689e6	−	1.31689e6i	2.26798	−	2.26798i
$763$	158428.	+	158428.i	0.272133	+	0.272133i
$764$		−	837638.i		−	1.43506i
$765$	−652307.	−	213405.i	−1.11463	−	0.364654i
$766$	1.57516e6			2.68453
$767$	−81431.2	+	81431.2i	−0.138420	+	0.138420i
$768$	−1.13028e6	−	1.13028e6i	−1.91630	−	1.91630i
$769$			347634.i			0.587855i	0.955828	+	0.293927i	$0.0949624\pi$
$769$			347634.i			0.587855i	−0.955828	+	0.293927i	$0.905038\pi$
$770$	−206323.	−	406961.i	−0.347989	−	0.686391i
$771$	−551960.			−0.928536
$772$	−1.35520e6	+	1.35520e6i	−2.27389	+	2.27389i
$773$	264187.	+	264187.i	0.442132	+	0.442132i	0.892728	−	0.450596i	$-0.148788\pi$
$773$	264187.	+	264187.i	0.442132	+	0.442132i	−0.450596	+	0.892728i	$0.648788\pi$
$774$		−	1.61998e6i		−	2.70413i
$775$	356542.	−	486592.i	0.593618	−	0.810143i
$776$	−145242.			−0.241196
$777$	250497.	−	250497.i	0.414916	−	0.414916i
$778$	−28545.2	−	28545.2i	−0.0471600	−	0.0471600i
$779$		−	939184.i		−	1.54766i
$780$	598386.	−	303372.i	0.983541	−	0.498640i
$781$	−100613.			−0.164950
$782$	318435.	−	318435.i	0.520723	−	0.520723i
$783$	104547.	+	104547.i	0.170525	+	0.170525i
$784$			170593.i			0.277542i
$785$	101546.	−	310393.i	0.164787	−	0.503700i
$786$	−1.37569e6			−2.22677
$787$	228223.	−	228223.i	0.368477	−	0.368477i	−0.498445	−	0.866921i	$-0.666095\pi$
$787$	228223.	−	228223.i	0.368477	−	0.368477i	0.866921	+	0.498445i	$0.166095\pi$
$788$	94563.4	+	94563.4i	0.152290	+	0.152290i
$789$		−	1.44354e6i		−	2.31886i
$790$	1.44897e6	+	474037.i	2.32170	+	0.759553i
$791$	−304845.			−0.487221
$792$	−1.90412e6	+	1.90412e6i	−3.03559	+	3.03559i
$793$	−113481.	−	113481.i	−0.180458	−	0.180458i
$794$			911896.i			1.44645i
$795$	−150800.	−	297446.i	−0.238599	−	0.470624i
$796$	796702.			1.25739
$797$	703348.	−	703348.i	1.10727	−	1.10727i	0.113763	−	0.993508i	$-0.463710\pi$
$797$	703348.	−	703348.i	1.10727	−	1.10727i	0.993508	−	0.113763i	$-0.0362903\pi$
$798$	567117.	+	567117.i	0.890568	+	0.890568i
$799$			453535.i			0.710423i
$800$	116025.	+	752208.i	0.181290	+	1.17532i
$801$	−632140.			−0.985255
$802$	722515.	−	722515.i	1.12331	−	1.12331i
$803$	−239604.	−	239604.i	−0.371589	−	0.371589i
$804$			4.62464e6i			7.15428i
$805$	−123975.	+	62853.2i	−0.191312	+	0.0969920i
$806$	−351154.			−0.540539
$807$	−758297.	+	758297.i	−1.16437	+	1.16437i
$808$	1.10323e6	+	1.10323e6i	1.68984	+	1.68984i
$809$			117237.i			0.179129i	0.995981	+	0.0895646i	$0.0285476\pi$
$809$			117237.i			0.179129i	−0.995981	+	0.0895646i	$0.971452\pi$
$810$	17059.8	−	52146.1i	0.0260018	−	0.0794788i
$811$	−364516.			−0.554210			−0.277105	−	0.960840i	$-0.589375\pi$
$811$	−364516.			−0.554210			−0.277105	+	0.960840i	$0.589375\pi$
$812$	−93705.5	+	93705.5i	−0.142119	+	0.142119i
$813$	1.29354e6	+	1.29354e6i	1.95704	+	1.95704i
$814$			1.28941e6i			1.94599i
$815$	−506260.	−	165625.i	−0.762182	−	0.249351i
$816$	−1.50402e6			−2.25877
$817$	486176.	−	486176.i	0.728365	−	0.728365i
$818$	186157.	+	186157.i	0.278211	+	0.278211i
$819$		−	123314.i		−	0.183842i
$820$	−951032.	−	1.87586e6i	−1.41438	−	2.78980i
$821$	−437621.			−0.649249			−0.324625	−	0.945843i	$-0.605238\pi$
$821$	−437621.			−0.649249			−0.324625	+	0.945843i	$0.605238\pi$
$822$	−1.42334e6	+	1.42334e6i	−2.10651	+	2.10651i
$823$	−456640.	−	456640.i	−0.674178	−	0.674178i	0.284498	−	0.958676i	$-0.408173\pi$
$823$	−456640.	−	456640.i	−0.674178	−	0.674178i	−0.958676	+	0.284498i	$0.908173\pi$
$824$		−	1.80147e6i		−	2.65321i
$825$	−1.22711e6	+	189277.i	−1.80292	+	0.278093i
$826$	−308292.			−0.451858
$827$	−459888.	+	459888.i	−0.672421	+	0.672421i	−0.958274	−	0.285853i	$-0.907723\pi$
$827$	−459888.	+	459888.i	−0.672421	+	0.672421i	0.285853	+	0.958274i	$0.407723\pi$
$828$	1.03082e6	+	1.03082e6i	1.50357	+	1.50357i
$829$		−	746352.i		−	1.08601i	−0.839729	−	0.543006i	$-0.817286\pi$
$829$		−	746352.i		−	1.08601i	0.839729	−	0.543006i	$-0.182714\pi$
$830$	−1.34796e6	+	683394.i	−1.95668	+	0.992008i
$831$	914148.			1.32378
$832$	30983.1	−	30983.1i	0.0447588	−	0.0447588i
$833$	−50170.2	−	50170.2i	−0.0723029	−	0.0723029i
$834$		−	2.28373e6i		−	3.28331i
$835$	−110501.	+	337764.i	−0.158486	+	0.484440i
$836$	−2.03104e6			−2.90607
$837$	−515989.	+	515989.i	−0.736529	+	0.736529i
$838$	697251.	+	697251.i	0.992891	+	0.992891i
$839$		−	1.11049e6i		−	1.57758i	−0.614662	−	0.788791i	$-0.710708\pi$
$839$		−	1.11049e6i		−	1.57758i	0.614662	−	0.788791i	$-0.289292\pi$
$840$	960550.	+	314248.i	1.36132	+	0.445363i
$841$	669038.			0.945929
$842$	−248517.	+	248517.i	−0.350535	+	0.350535i
$843$	1.53340e6	+	1.53340e6i	2.15775	+	2.15775i
$844$		−	2.75751e6i		−	3.87108i
$845$	294421.	+	580730.i	0.412340	+	0.813320i
$846$	−2.11017e6			−2.94834
$847$	50095.4	−	50095.4i	0.0698283	−	0.0698283i
$848$	−320903.	−	320903.i	−0.446254	−	0.446254i
$849$		−	647924.i		−	0.898894i
$850$	−756264.	−	554139.i	−1.04673	−	0.766974i
$851$	392799.			0.542389
$852$	280043.	−	280043.i	0.385785	−	0.385785i
$853$	−444139.	−	444139.i	−0.610408	−	0.610408i	0.332644	−	0.943052i	$-0.392059\pi$
$853$	−444139.	−	444139.i	−0.610408	−	0.610408i	−0.943052	+	0.332644i	$0.892059\pi$
$854$		−	429629.i		−	0.589085i
$855$	1.20883e6	−	612856.i	1.65361	−	0.838352i
$856$	1.52871e6			2.08630
$857$	609160.	−	609160.i	0.829411	−	0.829411i	−0.158024	−	0.987435i	$-0.550512\pi$
$857$	609160.	−	609160.i	0.829411	−	0.829411i	0.987435	+	0.158024i	$0.0505125\pi$
$858$	511074.	+	511074.i	0.694239	+	0.694239i
$859$			291558.i			0.395129i	0.980290	+	0.197564i	$0.0633032\pi$
$859$			291558.i			0.395129i	−0.980290	+	0.197564i	$0.936697\pi$
$860$	478745.	−	1.46336e6i	0.647302	−	1.97859i
$861$	−622507.			−0.839727
$862$	529858.	−	529858.i	0.713091	−	0.713091i
$863$	−161287.	−	161287.i	−0.216559	−	0.216559i	0.590488	−	0.807047i	$-0.298935\pi$
$863$	−161287.	−	161287.i	−0.216559	−	0.216559i	−0.807047	+	0.590488i	$0.798935\pi$
$864$		−	920686.i		−	1.23334i
$865$	728472.	+	238322.i	0.973600	+	0.318517i
$866$	−1.71236e6			−2.28327
$867$	−421055.	+	421055.i	−0.560145	+	0.560145i
$868$	−462482.	−	462482.i	−0.613841	−	0.613841i
$869$			1.14272e6i			1.51322i
$870$	234373.	+	462288.i	0.309648	+	0.610764i
$871$	433754.			0.571752
$872$	1.27725e6	−	1.27725e6i	1.67975	−	1.67975i
$873$	91287.0	+	91287.0i	0.119779	+	0.119779i
$874$			889285.i			1.16417i
$875$	168671.	+	235139.i	0.220305	+	0.307120i
$876$	1.33381e6			1.73814
$877$	−500503.	+	500503.i	−0.650740	+	0.650740i	−0.953171	−	0.302431i	$-0.902202\pi$
$877$	−500503.	+	500503.i	−0.650740	+	0.650740i	0.302431	+	0.953171i	$0.402202\pi$
$878$	785524.	+	785524.i	1.01899	+	1.01899i
$879$			1.34781e6i			1.74443i
$880$	−1.50704e6	+	764043.i	−1.94607	+	0.986626i
$881$	1.05961e6			1.36519			0.682595	−	0.730797i	$-0.260851\pi$
$881$	1.05961e6			1.36519			0.682595	+	0.730797i	$0.260851\pi$
$882$	233428.	−	233428.i	0.300065	−	0.300065i
$883$	864065.	+	864065.i	1.10822	+	1.10822i	0.993385	+	0.114833i	$0.0366332\pi$
$883$	864065.	+	864065.i	1.10822	+	1.10822i	0.114833	+	0.993385i	$0.463367\pi$
$884$			379719.i			0.485912i
$885$	−260854.	+	797343.i	−0.333051	+	1.01802i
$886$	1.98444e6			2.52796
$887$	−224843.	+	224843.i	−0.285780	+	0.285780i	−0.835409	−	0.549629i	$-0.814769\pi$
$887$	−224843.	+	224843.i	−0.285780	+	0.285780i	0.549629	+	0.835409i	$0.314769\pi$
$888$	−2.01952e6	−	2.01952e6i	−2.56108	−	2.56108i
$889$		−	325344.i		−	0.411661i
$890$	−820726.	−	268504.i	−1.03614	−	0.338977i
$891$	41124.6			0.0518020
$892$	−9976.10	+	9976.10i	−0.0125381	+	0.0125381i
$893$	−633288.	−	633288.i	−0.794142	−	0.794142i
$894$			2.44774e6i			3.06260i
$895$	205417.	+	405174.i	0.256442	+	0.505819i
$896$	−243554.			−0.303374
$897$	155691.	−	155691.i	0.193499	−	0.193499i
$898$	−1.01348e6	−	1.01348e6i	−1.25680	−	1.25680i
$899$		−	188749.i		−	0.233542i
$900$	1.79384e6	−	2.44815e6i	2.21462	−	3.02241i
$901$	188751.			0.232509
$902$	1.60215e6	−	1.60215e6i	1.96920	−	1.96920i
$903$	−322246.	−	322246.i	−0.395195	−	0.395195i
$904$			2.45768e6i			3.00738i
$905$	963197.	−	488326.i	1.17603	−	0.596228i
$906$	3.98504e6			4.85486
$907$	−763805.	+	763805.i	−0.928470	+	0.928470i	−0.997607	−	0.0691372i	$-0.977975\pi$
$907$	−763805.	+	763805.i	−0.928470	+	0.928470i	0.0691372	+	0.997607i	$0.477975\pi$
$908$	522607.	+	522607.i	0.633875	+	0.633875i
$909$		−	1.38680e6i		−	1.67836i
$910$	52378.0	−	160102.i	0.0632508	−	0.193337i
$911$	−36782.5			−0.0443205			−0.0221602	−	0.999754i	$-0.507054\pi$
$911$	−36782.5			−0.0443205			−0.0221602	+	0.999754i	$0.507054\pi$
$912$	2.10012e6	−	2.10012e6i	2.52496	−	2.52496i
$913$	−801006.	−	801006.i	−0.960936	−	0.960936i
$914$			1.15290e6i			1.38007i
$915$	−1.11116e6	−	363521.i	−1.32720	−	0.434197i
$916$	−1.27112e6			−1.51493
$917$	−169935.	+	169935.i	−0.202090	+	0.202090i
$918$	801953.	+	801953.i	0.951620	+	0.951620i
$919$			1.21169e6i			1.43470i	0.696713	+	0.717350i	$0.254645\pi$
$919$			1.21169e6i			1.43470i	−0.696713	+	0.717350i	$0.745355\pi$
$920$	506727.	+	999493.i	0.598685	+	1.18088i
$921$	−1.39408e6			−1.64350
$922$	509107.	−	509107.i	0.598890	−	0.598890i
$923$	−26265.8	−	26265.8i	−0.0308309	−	0.0308309i
$924$			1.34621e6i			1.57677i
$925$	−124664.	−	808212.i	−0.145699	−	0.944586i
$926$	−1.05158e6			−1.22637
$927$	−1.13225e6	+	1.13225e6i	−1.31760	+	1.31760i
$928$	168394.	+	168394.i	0.195538	+	0.195538i
$929$		−	526211.i		−	0.609718i	−0.952398	−	0.304859i	$-0.901391\pi$
$929$		−	526211.i		−	0.609718i	0.952398	−	0.304859i	$-0.0986093\pi$
$930$	−2.28162e6	+	1.15674e6i	−2.63801	+	1.33743i
$931$	140109.			0.161647
$932$	−449102.	+	449102.i	−0.517026	+	0.517026i
$933$	91595.5	+	91595.5i	0.105223	+	0.105223i
$934$		−	2.72703e6i		−	3.12605i
$935$	218509.	−	667908.i	0.249946	−	0.764001i
$936$	−994166.			−1.13477
$937$	−762510.	+	762510.i	−0.868493	+	0.868493i	−0.992306	−	0.123813i	$-0.960488\pi$
$937$	−762510.	+	762510.i	−0.868493	+	0.868493i	0.123813	+	0.992306i	$0.460488\pi$
$938$	821079.	+	821079.i	0.933209	+	0.933209i
$939$		−	2.16260e6i		−	2.45270i
$940$	−1.90616e6	−	623608.i	−2.15727	−	0.705759i
$941$	−98666.8			−0.111427			−0.0557137	−	0.998447i	$-0.517743\pi$
$941$	−98666.8			−0.111427			−0.0557137	+	0.998447i	$0.517743\pi$
$942$	−979274.	+	979274.i	−1.10358	+	1.10358i
$943$	−488071.	−	488071.i	−0.548857	−	0.548857i
$944$			1.14165e6i			1.28112i
$945$	−158291.	−	312221.i	−0.177253	−	0.349621i
$946$	1.65873e6			1.85350
$947$	835870.	−	835870.i	0.932049	−	0.932049i	−0.0657847	−	0.997834i	$-0.520955\pi$
$947$	835870.	−	835870.i	0.932049	−	0.932049i	0.997834	+	0.0657847i	$0.0209551\pi$
$948$	−3.18061e6	−	3.18061e6i	−3.53911	−	3.53911i
$949$		−	125100.i		−	0.138908i
$950$	1.82977e6	−	282235.i	2.02744	−	0.312726i
$951$	843930.			0.933137
$952$	−404475.	+	404475.i	−0.446291	+	0.446291i
$953$	992061.	+	992061.i	1.09233	+	1.09233i	0.995280	+	0.0970474i	$0.0309398\pi$
$953$	992061.	+	992061.i	1.09233	+	1.09233i	0.0970474	+	0.995280i	$0.469060\pi$
$954$			878206.i			0.964938i
$955$	−510466.	+	258798.i	−0.559707	+	0.283762i
$956$	−3.47439e6			−3.80157
$957$	−274708.	+	274708.i	−0.299949	+	0.299949i
$958$	1.26230e6	+	1.26230e6i	1.37541	+	1.37541i
$959$			351642.i			0.382353i
$960$	99250.2	−	303375.i	0.107693	−	0.329182i
$961$	8048.05			0.00871453
$962$	−336609.	+	336609.i	−0.363727	+	0.363727i
$963$	−960816.	−	960816.i	−1.03607	−	1.03607i
$964$		−	1.63054e6i		−	1.75460i
$965$	1.24458e6	+	407170.i	1.33650	+	0.437242i
$966$	589433.			0.631656
$967$	102132.	−	102132.i	0.109221	−	0.109221i	−0.650384	−	0.759605i	$-0.725392\pi$
$967$	102132.	−	102132.i	0.109221	−	0.109221i	0.759605	+	0.650384i	$0.225392\pi$
$968$	−403873.	−	403873.i	−0.431017	−	0.431017i
$969$			1.23526e6i			1.31556i
$970$	79746.1	+	157295.i	0.0847551	+	0.167175i
$971$	−476996.			−0.505913			−0.252957	−	0.967478i	$-0.581403\pi$
$971$	−476996.			−0.505913			−0.252957	+	0.967478i	$0.581403\pi$
$972$	1.46997e6	−	1.46997e6i	1.55588	−	1.55588i
$973$	−282103.	−	282103.i	−0.297977	−	0.297977i
$974$			486623.i			0.512949i
$975$	−369758.	−	270933.i	−0.388963	−	0.285005i
$976$	−1.59098e6			−1.67019
$977$	−434620.	+	434620.i	−0.455324	+	0.455324i	−0.897117	−	0.441793i	$-0.854343\pi$
$977$	−434620.	+	434620.i	−0.455324	+	0.455324i	0.441793	+	0.897117i	$0.354343\pi$
$978$	1.59723e6	+	1.59723e6i	1.66989	+	1.66989i
$979$		−	647260.i		−	0.675326i
$980$	279844.	−	141877.i	0.291383	−	0.147727i
$981$	−1.60555e6			−1.66834
$982$	707748.	−	707748.i	0.733932	−	0.733932i
$983$	−149156.	−	149156.i	−0.154359	−	0.154359i	0.625702	−	0.780062i	$-0.284812\pi$
$983$	−149156.	−	149156.i	−0.154359	−	0.154359i	−0.780062	+	0.625702i	$0.784812\pi$
$984$			5.01869e6i			5.18323i
$985$	28411.6	−	86844.6i	0.0292835	−	0.0895097i
$986$	−293355.			−0.301744
$987$	−419754.	+	419754.i	−0.430884	+	0.430884i
$988$	−530217.	−	530217.i	−0.543175	−	0.543175i
$989$		−	505307.i		−	0.516610i
$990$	3.10760e6	+	1.01666e6i	3.17069	+	1.03730i
$991$	116777.			0.118908			0.0594541	−	0.998231i	$-0.481064\pi$
$991$	116777.			0.118908			0.0594541	+	0.998231i	$0.481064\pi$
$992$	−831106.	+	831106.i	−0.844565	+	0.844565i
$993$	−150520.	−	150520.i	−0.152650	−	0.152650i
$994$		−	99440.0i		−	0.100644i
$995$	−246151.	−	485520.i	−0.248631	−	0.490412i
$996$	4.45898e6			4.49487
$997$	363823.	−	363823.i	0.366016	−	0.366016i	−0.500006	−	0.866022i	$-0.666669\pi$
$997$	363823.	−	363823.i	0.366016	−	0.366016i	0.866022	+	0.500006i	$0.166669\pi$
$998$	2.30897e6	+	2.30897e6i	2.31824	+	2.31824i
$999$			989234.i			0.991215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.5.g.a.8.12	✓	24
5.2	odd	4	inner	35.5.g.a.22.12	yes	24
5.3	odd	4		175.5.g.c.57.1		24
5.4	even	2		175.5.g.c.43.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.g.a.8.12	✓	24	1.1	even	1	trivial
35.5.g.a.22.12	yes	24	5.2	odd	4	inner
175.5.g.c.43.1		24	5.4	even	2
175.5.g.c.57.1		24	5.3	odd	4

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.12784 - 5.12784i) q^{2} +(10.3372 + 10.3372i) q^{3} -36.5894i q^{4} +(-22.2980 + 11.3048i) q^{5} +106.015 q^{6} +(13.0958 - 13.0958i) q^{7} +(-105.579 - 105.579i) q^{8} +132.716i q^{9} +O(q^{10})\)	\(q+(5.12784 - 5.12784i) q^{2} +(10.3372 + 10.3372i) q^{3} -36.5894i q^{4} +(-22.2980 + 11.3048i) q^{5} +106.015 q^{6} +(13.0958 - 13.0958i) q^{7} +(-105.579 - 105.579i) q^{8} +132.716i q^{9} +(-56.3718 + 172.310i) q^{10} -135.891 q^{11} +(378.233 - 378.233i) q^{12} +(-35.4752 - 35.4752i) q^{13} -134.306i q^{14} +(-347.360 - 113.640i) q^{15} -497.356 q^{16} +(146.269 - 146.269i) q^{17} +(680.549 + 680.549i) q^{18} +408.482i q^{19} +(413.634 + 815.873i) q^{20} +270.749 q^{21} +(-696.826 + 696.826i) q^{22} +(212.278 + 212.278i) q^{23} -2182.79i q^{24} +(369.405 - 504.148i) q^{25} -363.822 q^{26} +(-534.605 + 534.605i) q^{27} +(-479.168 - 479.168i) q^{28} -195.559i q^{29} +(-2363.93 + 1198.48i) q^{30} +965.178 q^{31} +(-861.090 + 861.090i) q^{32} +(-1404.73 - 1404.73i) q^{33} -1500.08i q^{34} +(-143.966 + 440.055i) q^{35} +4856.02 q^{36} +(925.201 - 925.201i) q^{37} +(2094.63 + 2094.63i) q^{38} -733.431i q^{39} +(3547.76 + 1160.66i) q^{40} -2299.21 q^{41} +(1388.35 - 1388.35i) q^{42} +(-1190.20 - 1190.20i) q^{43} +4972.17i q^{44} +(-1500.33 - 2959.32i) q^{45} +2177.05 q^{46} +(-1550.35 + 1550.35i) q^{47} +(-5141.28 - 5141.28i) q^{48} -343.000i q^{49} +(-690.938 - 4479.44i) q^{50} +3024.03 q^{51} +(-1298.02 + 1298.02i) q^{52} +(645.219 + 645.219i) q^{53} +5482.73i q^{54} +(3030.10 - 1536.21i) q^{55} -2765.29 q^{56} +(-4222.57 + 4222.57i) q^{57} +(-1002.79 - 1002.79i) q^{58} -2295.44i q^{59} +(-4158.03 + 12709.7i) q^{60} +3198.88 q^{61} +(4949.28 - 4949.28i) q^{62} +(1738.03 + 1738.03i) q^{63} +873.373i q^{64} +(1192.07 + 389.989i) q^{65} -14406.5 q^{66} +(-6113.48 + 6113.48i) q^{67} +(-5351.89 - 5351.89i) q^{68} +4388.73i q^{69} +(1518.30 + 2994.77i) q^{70} +740.397 q^{71} +(14012.1 - 14012.1i) q^{72} +(1763.21 + 1763.21i) q^{73} -9488.56i q^{74} +(9030.11 - 1392.86i) q^{75} +14946.1 q^{76} +(-1779.60 + 1779.60i) q^{77} +(-3760.91 - 3760.91i) q^{78} -8409.12i q^{79} +(11090.1 - 5622.48i) q^{80} -302.630 q^{81} +(-11790.0 + 11790.0i) q^{82} +(5894.49 + 5894.49i) q^{83} -9906.53i q^{84} +(-1607.97 + 4915.04i) q^{85} -12206.3 q^{86} +(2021.54 - 2021.54i) q^{87} +(14347.2 + 14347.2i) q^{88} +4763.09i q^{89} +(-22868.3 - 7481.47i) q^{90} -929.153 q^{91} +(7767.12 - 7767.12i) q^{92} +(9977.27 + 9977.27i) q^{93} +15899.8i q^{94} +(-4617.78 - 9108.34i) q^{95} -17802.6 q^{96} +(687.835 - 687.835i) q^{97} +(-1758.85 - 1758.85i) q^{98} -18034.9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6}+O(q^{10}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97}+O(q^{100}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6 - 112 * q^10 + 156 * q^11 - 80 * q^12 - 560 * q^13 + 896 * q^15 - 1480 * q^16 + 1320 * q^17 + 340 * q^18 + 180 * q^20 + 196 * q^21 - 2020 * q^22 + 1920 * q^23 - 676 * q^25 + 2208 * q^26 - 340 * q^27 - 5356 * q^30 - 2112 * q^31 - 1200 * q^32 - 6140 * q^33 + 3904 * q^36 + 3980 * q^37 + 9120 * q^38 + 14716 * q^40 + 6384 * q^41 + 4900 * q^42 - 12220 * q^43 - 10528 * q^45 - 8080 * q^46 - 11820 * q^47 - 4040 * q^48 + 10728 * q^50 - 5900 * q^51 + 3600 * q^52 + 24240 * q^53 + 4636 * q^55 - 10584 * q^56 + 6460 * q^57 + 6100 * q^58 - 30088 * q^60 + 440 * q^61 - 16680 * q^62 + 7840 * q^63 - 14652 * q^65 + 4832 * q^66 - 5940 * q^67 - 47040 * q^68 - 6272 * q^70 + 8928 * q^71 + 46720 * q^72 - 2500 * q^73 + 60708 * q^75 + 47816 * q^76 + 5880 * q^77 - 17940 * q^78 + 16140 * q^80 - 11360 * q^81 - 32120 * q^82 + 15120 * q^83 + 18816 * q^85 - 41208 * q^86 - 25460 * q^87 + 52920 * q^88 - 55680 * q^90 - 11172 * q^91 + 19800 * q^92 + 1460 * q^93 - 35508 * q^95 + 20568 * q^96 - 33840 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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