LMFDB - Embedded newform 230.5.f.b.47.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,5,Mod(47,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("230.47");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	230.f (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:	$23.7750915093$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.18
Character	$\chi$	$=$	230.47
Dual form			230.5.f.b.93.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 2.00000i) q^{2} +(7.50341 - 7.50341i) q^{3} +8.00000i q^{4} +(-23.5955 - 8.26153i) q^{5} +30.0136 q^{6} +(38.1189 + 38.1189i) q^{7} +(-16.0000 + 16.0000i) q^{8} -31.6022i q^{9} +O(q^{10})$	\(q+(2.00000 + 2.00000i) q^{2} +(7.50341 - 7.50341i) q^{3} +8.00000i q^{4} +(-23.5955 - 8.26153i) q^{5} +30.0136 q^{6} +(38.1189 + 38.1189i) q^{7} +(-16.0000 + 16.0000i) q^{8} -31.6022i q^{9} +(-30.6679 - 63.7140i) q^{10} +106.110 q^{11} +(60.0272 + 60.0272i) q^{12} +(121.249 - 121.249i) q^{13} +152.476i q^{14} +(-239.036 + 115.057i) q^{15} -64.0000 q^{16} +(157.436 + 157.436i) q^{17} +(63.2044 - 63.2044i) q^{18} -262.430i q^{19} +(66.0922 - 188.764i) q^{20} +572.043 q^{21} +(212.219 + 212.219i) q^{22} +(-77.9968 + 77.9968i) q^{23} +240.109i q^{24} +(488.494 + 389.870i) q^{25} +484.998 q^{26} +(370.652 + 370.652i) q^{27} +(-304.951 + 304.951i) q^{28} -50.2468i q^{29} +(-708.186 - 247.958i) q^{30} +1424.29 q^{31} +(-128.000 - 128.000i) q^{32} +(796.184 - 796.184i) q^{33} +629.744i q^{34} +(-584.513 - 1214.35i) q^{35} +252.818 q^{36} +(241.592 + 241.592i) q^{37} +(524.860 - 524.860i) q^{38} -1819.57i q^{39} +(509.712 - 245.343i) q^{40} -410.751 q^{41} +(1144.09 + 1144.09i) q^{42} +(2218.90 - 2218.90i) q^{43} +848.877i q^{44} +(-261.083 + 745.669i) q^{45} -311.987 q^{46} +(196.726 + 196.726i) q^{47} +(-480.218 + 480.218i) q^{48} +505.098i q^{49} +(197.249 + 1756.73i) q^{50} +2362.61 q^{51} +(969.995 + 969.995i) q^{52} +(-1751.50 + 1751.50i) q^{53} +1482.61i q^{54} +(-2503.71 - 876.628i) q^{55} -1219.80 q^{56} +(-1969.12 - 1969.12i) q^{57} +(100.494 - 100.494i) q^{58} -1229.67i q^{59} +(-920.455 - 1912.29i) q^{60} -2191.74 q^{61} +(2848.57 + 2848.57i) q^{62} +(1204.64 - 1204.64i) q^{63} -512.000i q^{64} +(-3862.64 + 1859.23i) q^{65} +3184.74 q^{66} +(-4393.93 - 4393.93i) q^{67} +(-1259.49 + 1259.49i) q^{68} +1170.48i q^{69} +(1259.68 - 3597.73i) q^{70} +8136.98 q^{71} +(505.635 + 505.635i) q^{72} +(-6782.82 + 6782.82i) q^{73} +966.370i q^{74} +(6590.72 - 740.020i) q^{75} +2099.44 q^{76} +(4044.78 + 4044.78i) q^{77} +(3639.13 - 3639.13i) q^{78} +3170.51i q^{79} +(1510.11 + 528.738i) q^{80} +8122.08 q^{81} +(-821.501 - 821.501i) q^{82} +(-1963.17 + 1963.17i) q^{83} +4576.34i q^{84} +(-2414.12 - 5015.44i) q^{85} +8875.60 q^{86} +(-377.022 - 377.022i) q^{87} +(-1697.75 + 1697.75i) q^{88} +12890.8i q^{89} +(-2013.50 + 969.173i) q^{90} +9243.78 q^{91} +(-623.974 - 623.974i) q^{92} +(10687.0 - 10687.0i) q^{93} +786.905i q^{94} +(-2168.07 + 6192.16i) q^{95} -1920.87 q^{96} +(-8553.52 - 8553.52i) q^{97} +(-1010.20 + 1010.20i) q^{98} -3353.30i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8}+O(q^{10}) $ 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8	$ 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8} - 136 q^{10} - 632 q^{11} + 500 q^{13} + 12 q^{15} - 2816 q^{16} + 120 q^{17} + 2648 q^{18} - 736 q^{20} - 856 q^{21} - 1264 q^{22} + 2052 q^{25} + 2000 q^{26} + 588 q^{27} + 640 q^{28} - 1704 q^{30} + 3220 q^{31} - 5632 q^{32} - 2884 q^{33} + 720 q^{35} + 10592 q^{36} + 1856 q^{37} - 1696 q^{38} - 1856 q^{40} - 5156 q^{41} - 1712 q^{42} + 960 q^{43} + 460 q^{45} - 1224 q^{47} + 4456 q^{50} + 3640 q^{51} + 4000 q^{52} + 13556 q^{53} + 12980 q^{55} + 2560 q^{56} - 3072 q^{57} - 3112 q^{58} - 6912 q^{60} - 4864 q^{61} + 6440 q^{62} - 13484 q^{63} - 4100 q^{65} - 11536 q^{66} - 1888 q^{67} - 960 q^{68} + 8824 q^{70} - 1060 q^{71} + 21184 q^{72} + 16616 q^{73} - 11044 q^{75} - 6784 q^{76} + 8892 q^{77} - 23152 q^{78} - 1536 q^{80} - 4044 q^{81} - 10312 q^{82} - 27024 q^{83} - 11068 q^{85} + 3840 q^{86} - 8392 q^{87} + 10112 q^{88} - 7184 q^{90} - 54024 q^{91} + 22528 q^{93} - 25968 q^{95} - 3252 q^{97} - 27984 q^{98}+O(q^{100}) $ 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8 - 136 * q^10 - 632 * q^11 + 500 * q^13 + 12 * q^15 - 2816 * q^16 + 120 * q^17 + 2648 * q^18 - 736 * q^20 - 856 * q^21 - 1264 * q^22 + 2052 * q^25 + 2000 * q^26 + 588 * q^27 + 640 * q^28 - 1704 * q^30 + 3220 * q^31 - 5632 * q^32 - 2884 * q^33 + 720 * q^35 + 10592 * q^36 + 1856 * q^37 - 1696 * q^38 - 1856 * q^40 - 5156 * q^41 - 1712 * q^42 + 960 * q^43 + 460 * q^45 - 1224 * q^47 + 4456 * q^50 + 3640 * q^51 + 4000 * q^52 + 13556 * q^53 + 12980 * q^55 + 2560 * q^56 - 3072 * q^57 - 3112 * q^58 - 6912 * q^60 - 4864 * q^61 + 6440 * q^62 - 13484 * q^63 - 4100 * q^65 - 11536 * q^66 - 1888 * q^67 - 960 * q^68 + 8824 * q^70 - 1060 * q^71 + 21184 * q^72 + 16616 * q^73 - 11044 * q^75 - 6784 * q^76 + 8892 * q^77 - 23152 * q^78 - 1536 * q^80 - 4044 * q^81 - 10312 * q^82 - 27024 * q^83 - 11068 * q^85 + 3840 * q^86 - 8392 * q^87 + 10112 * q^88 - 7184 * q^90 - 54024 * q^91 + 22528 * q^93 - 25968 * q^95 - 3252 * q^97 - 27984 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$3$	7.50341	−	7.50341i	0.833712	−	0.833712i	−0.154311	−	0.988022i	$-0.549316\pi$
$3$	7.50341	−	7.50341i	0.833712	−	0.833712i	0.988022	+	0.154311i	$0.0493157\pi$
$4$			8.00000i			0.500000i
$5$	−23.5955	−	8.26153i	−0.943820	−	0.330461i
$5$	−23.5955	−	8.26153i	−0.943820	−	0.330461i
$6$	30.0136			0.833712
$7$	38.1189	+	38.1189i	0.777936	+	0.777936i	0.979480	−	0.201543i	$-0.0645957\pi$
$7$	38.1189	+	38.1189i	0.777936	+	0.777936i	−0.201543	+	0.979480i	$0.564596\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$		−	31.6022i		−	0.390151i
$10$	−30.6679	−	63.7140i	−0.306679	−	0.637140i
$11$	106.110			0.876939			0.438470	−	0.898746i	$-0.355521\pi$
$11$	106.110			0.876939			0.438470	+	0.898746i	$0.355521\pi$
$12$	60.0272	+	60.0272i	0.416856	+	0.416856i
$13$	121.249	−	121.249i	0.717452	−	0.717452i	−0.250631	−	0.968083i	$-0.580638\pi$
$13$	121.249	−	121.249i	0.717452	−	0.717452i	0.968083	+	0.250631i	$0.0806380\pi$
$14$			152.476i			0.777936i
$15$	−239.036	+	115.057i	−1.06238	+	0.511364i
$16$	−64.0000			−0.250000
$17$	157.436	+	157.436i	0.544762	+	0.544762i	0.924921	−	0.380159i	$-0.124131\pi$
$17$	157.436	+	157.436i	0.544762	+	0.544762i	−0.380159	+	0.924921i	$0.624131\pi$
$18$	63.2044	−	63.2044i	0.195075	−	0.195075i
$19$		−	262.430i		−	0.726953i	−0.931603	−	0.363476i	$-0.881590\pi$
$19$		−	262.430i		−	0.726953i	0.931603	−	0.363476i	$-0.118410\pi$
$20$	66.0922	−	188.764i	0.165231	−	0.471910i
$21$	572.043			1.29715
$22$	212.219	+	212.219i	0.438470	+	0.438470i
$23$	−77.9968	+	77.9968i	−0.147442	+	0.147442i
$23$	−77.9968	+	77.9968i	−0.147442	+	0.147442i
$24$			240.109i			0.416856i
$25$	488.494	+	389.870i	0.781591	+	0.623792i
$26$	484.998			0.717452
$27$	370.652	+	370.652i	0.508439	+	0.508439i
$28$	−304.951	+	304.951i	−0.388968	+	0.388968i
$29$		−	50.2468i		−	0.0597465i	−0.999554	−	0.0298733i	$-0.990490\pi$
$29$		−	50.2468i		−	0.0597465i	0.999554	−	0.0298733i	$-0.00951037\pi$
$30$	−708.186	−	247.958i	−0.786873	−	0.275509i
$31$	1424.29			1.48209			0.741044	−	0.671456i	$-0.234331\pi$
$31$	1424.29			1.48209			0.741044	+	0.671456i	$0.234331\pi$
$32$	−128.000	−	128.000i	−0.125000	−	0.125000i
$33$	796.184	−	796.184i	0.731115	−	0.731115i
$34$			629.744i			0.544762i
$35$	−584.513	−	1214.35i	−0.477154	−	0.991309i
$36$	252.818			0.195075
$37$	241.592	+	241.592i	0.176474	+	0.176474i	0.789817	−	0.613343i	$-0.210176\pi$
$37$	241.592	+	241.592i	0.176474	+	0.176474i	−0.613343	+	0.789817i	$0.710176\pi$
$38$	524.860	−	524.860i	0.363476	−	0.363476i
$39$		−	1819.57i		−	1.19630i
$40$	509.712	−	245.343i	0.318570	−	0.153340i
$41$	−410.751			−0.244349			−0.122174	−	0.992509i	$-0.538987\pi$
$41$	−410.751			−0.244349			−0.122174	+	0.992509i	$0.538987\pi$
$42$	1144.09	+	1144.09i	0.648575	+	0.648575i
$43$	2218.90	−	2218.90i	1.20005	−	1.20005i	0.225904	−	0.974149i	$-0.427466\pi$
$43$	2218.90	−	2218.90i	1.20005	−	1.20005i	0.974149	−	0.225904i	$-0.0725337\pi$
$44$			848.877i			0.438470i
$45$	−261.083	+	745.669i	−0.128930	+	0.368232i
$46$	−311.987			−0.147442
$47$	196.726	+	196.726i	0.0890566	+	0.0890566i	0.750232	−	0.661175i	$-0.229942\pi$
$47$	196.726	+	196.726i	0.0890566	+	0.0890566i	−0.661175	+	0.750232i	$0.729942\pi$
$48$	−480.218	+	480.218i	−0.208428	+	0.208428i
$49$			505.098i			0.210370i
$50$	197.249	+	1756.73i	0.0788996	+	0.702691i
$51$	2362.61			0.908348
$52$	969.995	+	969.995i	0.358726	+	0.358726i
$53$	−1751.50	+	1751.50i	−0.623530	+	0.623530i	−0.946432	−	0.322902i	$-0.895341\pi$
$53$	−1751.50	+	1751.50i	−0.623530	+	0.623530i	0.322902	+	0.946432i	$0.395341\pi$
$54$			1482.61i			0.508439i
$55$	−2503.71	−	876.628i	−0.827673	−	0.289794i
$56$	−1219.80			−0.388968
$57$	−1969.12	−	1969.12i	−0.606069	−	0.606069i
$58$	100.494	−	100.494i	0.0298733	−	0.0298733i
$59$		−	1229.67i		−	0.353251i	−0.984278	−	0.176626i	$-0.943482\pi$
$59$		−	1229.67i		−	0.353251i	0.984278	−	0.176626i	$-0.0565182\pi$
$60$	−920.455	−	1912.29i	−0.255682	−	0.531191i
$61$	−2191.74			−0.589018			−0.294509	−	0.955649i	$-0.595156\pi$
$61$	−2191.74			−0.589018			−0.294509	+	0.955649i	$0.595156\pi$
$62$	2848.57	+	2848.57i	0.741044	+	0.741044i
$63$	1204.64	−	1204.64i	0.303512	−	0.303512i
$64$		−	512.000i		−	0.125000i
$65$	−3862.64	+	1859.23i	−0.914235	+	0.440055i
$66$	3184.74			0.731115
$67$	−4393.93	−	4393.93i	−0.978822	−	0.978822i	0.0209582	−	0.999780i	$-0.493328\pi$
$67$	−4393.93	−	4393.93i	−0.978822	−	0.978822i	−0.999780	+	0.0209582i	$0.993328\pi$
$68$	−1259.49	+	1259.49i	−0.272381	+	0.272381i
$69$			1170.48i			0.245848i
$70$	1259.68	−	3597.73i	0.257078	−	0.734232i
$71$	8136.98			1.61416			0.807080	−	0.590443i	$-0.201047\pi$
$71$	8136.98			1.61416			0.807080	+	0.590443i	$0.201047\pi$
$72$	505.635	+	505.635i	0.0975376	+	0.0975376i
$73$	−6782.82	+	6782.82i	−1.27281	+	1.27281i	−0.328206	+	0.944606i	$0.606444\pi$
$73$	−6782.82	+	6782.82i	−1.27281	+	1.27281i	−0.944606	+	0.328206i	$0.893556\pi$
$74$			966.370i			0.176474i
$75$	6590.72	−	740.020i	1.17168	−	0.131559i
$76$	2099.44			0.363476
$77$	4044.78	+	4044.78i	0.682203	+	0.682203i
$78$	3639.13	−	3639.13i	0.598148	−	0.598148i
$79$			3170.51i			0.508014i	0.967202	+	0.254007i	$0.0817486\pi$
$79$			3170.51i			0.508014i	−0.967202	+	0.254007i	$0.918251\pi$
$80$	1510.11	+	528.738i	0.235955	+	0.0826153i
$81$	8122.08			1.23793
$82$	−821.501	−	821.501i	−0.122174	−	0.122174i
$83$	−1963.17	+	1963.17i	−0.284972	+	0.284972i	−0.835088	−	0.550116i	$-0.814583\pi$
$83$	−1963.17	+	1963.17i	−0.284972	+	0.284972i	0.550116	+	0.835088i	$0.314583\pi$
$84$			4576.34i			0.648575i
$85$	−2414.12	−	5015.44i	−0.334134	−	0.694179i
$86$	8875.60			1.20005
$87$	−377.022	−	377.022i	−0.0498114	−	0.0498114i
$88$	−1697.75	+	1697.75i	−0.219235	+	0.219235i
$89$			12890.8i			1.62743i	0.581267	+	0.813713i	$0.302557\pi$
$89$			12890.8i			1.62743i	−0.581267	+	0.813713i	$0.697443\pi$
$90$	−2013.50	+	969.173i	−0.248581	+	0.119651i
$91$	9243.78			1.11626
$92$	−623.974	−	623.974i	−0.0737210	−	0.0737210i
$93$	10687.0	−	10687.0i	1.23563	−	1.23563i
$94$			786.905i			0.0890566i
$95$	−2168.07	+	6192.16i	−0.240230	+	0.686112i
$96$	−1920.87			−0.208428
$97$	−8553.52	−	8553.52i	−0.909078	−	0.909078i	0.0871197	−	0.996198i	$-0.472234\pi$
$97$	−8553.52	−	8553.52i	−0.909078	−	0.909078i	−0.996198	+	0.0871197i	$0.972234\pi$
$98$	−1010.20	+	1010.20i	−0.105185	+	0.105185i
$99$		−	3353.30i		−	0.342138i
$100$	−3118.96	+	3907.95i	−0.311896	+	0.390795i
$101$	−13454.3			−1.31892			−0.659458	−	0.751742i	$-0.729214\pi$
$101$	−13454.3			−1.31892			−0.659458	+	0.751742i	$0.729214\pi$
$102$	4725.23	+	4725.23i	0.454174	+	0.454174i
$103$	−10827.4	+	10827.4i	−1.02059	+	1.02059i	−0.0208073	+	0.999784i	$0.506624\pi$
$103$	−10827.4	+	10827.4i	−1.02059	+	1.02059i	−0.999784	+	0.0208073i	$0.993376\pi$
$104$			3879.98i			0.358726i
$105$	−13497.6	−	4725.95i	−1.22427	−	0.428658i
$106$	−7005.98			−0.623530
$107$	386.785	+	386.785i	0.0337833	+	0.0337833i	0.723797	−	0.690013i	$-0.242395\pi$
$107$	386.785	+	386.785i	0.0337833	+	0.0337833i	−0.690013	+	0.723797i	$0.742395\pi$
$108$	−2965.21	+	2965.21i	−0.254219	+	0.254219i
$109$		−	4007.38i		−	0.337293i	−0.985677	−	0.168647i	$-0.946060\pi$
$109$		−	4007.38i		−	0.337293i	0.985677	−	0.168647i	$-0.0539396\pi$
$110$	−3254.16	−	6760.68i	−0.268939	−	0.558733i
$111$	3625.53			0.294256
$112$	−2439.61	−	2439.61i	−0.194484	−	0.194484i
$113$	−3707.46	+	3707.46i	−0.290348	+	0.290348i	−0.837218	−	0.546870i	$-0.815819\pi$
$113$	−3707.46	+	3707.46i	−0.290348	+	0.290348i	0.546870	+	0.837218i	$0.315819\pi$
$114$		−	7876.47i		−	0.606069i
$115$	2484.75	−	1196.00i	0.187882	−	0.0904348i
$116$	401.975			0.0298733
$117$	−3831.75	−	3831.75i	−0.279914	−	0.279914i
$118$	2459.33	−	2459.33i	0.176626	−	0.176626i
$119$			12002.6i			0.847580i
$120$	1983.67	−	5665.49i	0.137755	−	0.393437i
$121$	−3381.74			−0.230977
$122$	−4383.47	−	4383.47i	−0.294509	−	0.294509i
$123$	−3082.03	+	3082.03i	−0.203717	+	0.203717i
$124$			11394.3i			0.741044i
$125$	−8305.34	−	13234.9i	−0.531542	−	0.847032i
$126$	4818.56			0.303512
$127$	−9008.66	−	9008.66i	−0.558538	−	0.558538i	0.370353	−	0.928891i	$-0.379237\pi$
$127$	−9008.66	−	9008.66i	−0.558538	−	0.558538i	−0.928891	+	0.370353i	$0.879237\pi$
$128$	1024.00	−	1024.00i	0.0625000	−	0.0625000i
$129$		−	33298.6i		−	2.00100i
$130$	−11443.8	−	4006.82i	−0.677145	−	0.237090i
$131$	−14035.4			−0.817866			−0.408933	−	0.912564i	$-0.634099\pi$
$131$	−14035.4			−0.817866			−0.408933	+	0.912564i	$0.634099\pi$
$132$	6369.47	+	6369.47i	0.365557	+	0.365557i
$133$	10003.5	−	10003.5i	0.565523	−	0.565523i
$134$		−	17575.7i		−	0.978822i
$135$	−5683.56	−	11807.9i	−0.311855	−	0.647894i
$136$	−5037.95			−0.272381
$137$	5013.28	+	5013.28i	0.267105	+	0.267105i	0.827932	−	0.560828i	$-0.189517\pi$
$137$	5013.28	+	5013.28i	0.267105	+	0.267105i	−0.560828	+	0.827932i	$0.689517\pi$
$138$	−2340.97	+	2340.97i	−0.122924	+	0.122924i
$139$		−	30844.0i		−	1.59640i	−0.602393	−	0.798200i	$-0.705786\pi$
$139$		−	30844.0i		−	1.59640i	0.602393	−	0.798200i	$-0.294214\pi$
$140$	9714.83	−	4676.11i	0.495655	−	0.238577i
$141$	2952.23			0.148495
$142$	16274.0	+	16274.0i	0.807080	+	0.807080i
$143$	12865.7	−	12865.7i	0.629162	−	0.629162i
$144$			2022.54i			0.0975376i
$145$	−415.116	+	1185.60i	−0.0197439	+	0.0563899i
$146$	−27131.3			−1.27281
$147$	3789.95	+	3789.95i	0.175388	+	0.175388i
$148$	−1932.74	+	1932.74i	−0.0882368	+	0.0882368i
$149$		−	5723.16i		−	0.257788i	−0.991658	−	0.128894i	$-0.958857\pi$
$149$		−	5723.16i		−	0.257788i	0.991658	−	0.128894i	$-0.0411428\pi$
$150$	14661.5	+	11701.4i	0.651621	+	0.520062i
$151$	−15703.6			−0.688726			−0.344363	−	0.938837i	$-0.611905\pi$
$151$	−15703.6			−0.688726			−0.344363	+	0.938837i	$0.611905\pi$
$152$	4198.88	+	4198.88i	0.181738	+	0.181738i
$153$	4975.33	−	4975.33i	0.212539	−	0.212539i
$154$			16179.1i			0.682203i
$155$	−33606.8	−	11766.8i	−1.39882	−	0.489773i
$156$	14556.5			0.598148
$157$	−14042.0	−	14042.0i	−0.569680	−	0.569680i	0.362359	−	0.932039i	$-0.381971\pi$
$157$	−14042.0	−	14042.0i	−0.569680	−	0.569680i	−0.932039	+	0.362359i	$0.881971\pi$
$158$	−6341.03	+	6341.03i	−0.254007	+	0.254007i
$159$			26284.4i			1.03969i
$160$	1962.75	+	4077.70i	0.0766698	+	0.159285i
$161$	−5946.30			−0.229401
$162$	16244.2	+	16244.2i	0.618967	+	0.618967i
$163$	28136.8	−	28136.8i	1.05901	−	1.05901i	0.0608605	−	0.998146i	$-0.480616\pi$
$163$	28136.8	−	28136.8i	1.05901	−	1.05901i	0.998146	−	0.0608605i	$-0.0193845\pi$
$164$		−	3286.00i		−	0.122174i
$165$	−25364.0	+	12208.6i	−0.931645	+	0.448435i
$166$	−7852.69			−0.284972
$167$	21117.0	+	21117.0i	0.757180	+	0.757180i	0.975808	−	0.218628i	$-0.0701581\pi$
$167$	21117.0	+	21117.0i	0.757180	+	0.757180i	−0.218628	+	0.975808i	$0.570158\pi$
$168$	−9152.69	+	9152.69i	−0.324287	+	0.324287i
$169$		−	841.835i		−	0.0294750i
$170$	5202.65	−	14859.1i	0.180023	−	0.514157i
$171$	−8293.36			−0.283621
$172$	17751.2	+	17751.2i	0.600027	+	0.600027i
$173$	−15813.3	+	15813.3i	−0.528360	+	0.528360i	−0.920083	−	0.391723i	$-0.871879\pi$
$173$	−15813.3	+	15813.3i	−0.528360	+	0.528360i	0.391723	+	0.920083i	$0.371879\pi$
$174$		−	1508.09i		−	0.0498114i
$175$	3759.46	+	33482.2i	0.122758	+	1.09330i
$176$	−6791.02			−0.219235
$177$	−9226.69	−	9226.69i	−0.294510	−	0.294510i
$178$	−25781.7	+	25781.7i	−0.813713	+	0.813713i
$179$		−	35485.2i		−	1.10749i	−0.832685	−	0.553747i	$-0.813197\pi$
$179$		−	35485.2i		−	1.10749i	0.832685	−	0.553747i	$-0.186803\pi$
$180$	−5965.35	−	2088.66i	−0.184116	−	0.0644648i
$181$	14056.8			0.429070			0.214535	−	0.976716i	$-0.431176\pi$
$181$	14056.8			0.429070			0.214535	+	0.976716i	$0.431176\pi$
$182$	18487.6	+	18487.6i	0.558132	+	0.558132i
$183$	−16445.5	+	16445.5i	−0.491072	+	0.491072i
$184$		−	2495.90i		−	0.0737210i
$185$	−3704.57	−	7696.41i	−0.108242	−	0.224877i
$186$	42748.0			1.23563
$187$	16705.5	+	16705.5i	0.477723	+	0.477723i
$188$	−1573.81	+	1573.81i	−0.0445283	+	0.0445283i
$189$			28257.7i			0.791066i
$190$	−16720.5	+	8048.18i	−0.463171	+	0.222941i
$191$	−31212.9			−0.855592			−0.427796	−	0.903875i	$-0.640710\pi$
$191$	−31212.9			−0.855592			−0.427796	+	0.903875i	$0.640710\pi$
$192$	−3841.74	−	3841.74i	−0.104214	−	0.104214i
$193$	20899.2	−	20899.2i	0.561067	−	0.561067i	−0.368544	−	0.929610i	$-0.620144\pi$
$193$	20899.2	−	20899.2i	0.561067	−	0.561067i	0.929610	+	0.368544i	$0.120144\pi$
$194$		−	34214.1i		−	0.909078i
$195$	−15032.4	+	42933.6i	−0.395330	+	1.12909i
$196$	−4040.78			−0.105185
$197$	11886.8	+	11886.8i	0.306291	+	0.306291i	0.843469	−	0.537178i	$-0.180510\pi$
$197$	11886.8	+	11886.8i	0.306291	+	0.306291i	−0.537178	+	0.843469i	$0.680510\pi$
$198$	6706.60	−	6706.60i	0.171069	−	0.171069i
$199$			39902.6i			1.00762i	0.863816	+	0.503808i	$0.168068\pi$
$199$			39902.6i			1.00762i	−0.863816	+	0.503808i	$0.831932\pi$
$200$	−14053.8	+	1577.99i	−0.351346	+	0.0394498i
$201$	−65938.9			−1.63211
$202$	−26908.5	−	26908.5i	−0.659458	−	0.659458i
$203$	1915.35	−	1915.35i	0.0464790	−	0.0464790i
$204$			18900.9i			0.454174i
$205$	9691.86	+	3393.43i	0.230621	+	0.0807478i
$206$	−43309.8			−1.02059
$207$	2464.87	+	2464.87i	0.0575246	+	0.0575246i
$208$	−7759.96	+	7759.96i	−0.179363	+	0.179363i
$209$		−	27846.4i		−	0.637493i
$210$	−17543.4	−	36447.2i	−0.397809	−	0.826466i
$211$	28835.2			0.647676			0.323838	−	0.946113i	$-0.395027\pi$
$211$	28835.2			0.647676			0.323838	+	0.946113i	$0.395027\pi$
$212$	−14012.0	−	14012.0i	−0.311765	−	0.311765i
$213$	61055.0	−	61055.0i	1.34574	−	1.34574i
$214$			1547.14i			0.0337833i
$215$	−70687.5	+	34024.5i	−1.52921	+	0.736063i
$216$	−11860.9			−0.254219
$217$	54292.2	+	54292.2i	1.15297	+	1.15297i
$218$	8014.76	−	8014.76i	0.168647	−	0.168647i
$219$			101788.i			2.12232i
$220$	7013.03	−	20029.7i	0.144897	−	0.413836i
$221$	38178.1			0.781681
$222$	7251.06	+	7251.06i	0.147128	+	0.147128i
$223$	68544.5	−	68544.5i	1.37836	−	1.37836i	0.530968	−	0.847392i	$-0.321829\pi$
$223$	68544.5	−	68544.5i	1.37836	−	1.37836i	0.847392	−	0.530968i	$-0.178171\pi$
$224$		−	9758.43i		−	0.194484i
$225$	12320.7	−	15437.5i	0.243373	−	0.304938i
$226$	−14829.8			−0.290348
$227$	37631.1	+	37631.1i	0.730290	+	0.730290i	0.970677	−	0.240387i	$-0.0772744\pi$
$227$	37631.1	+	37631.1i	0.730290	+	0.730290i	−0.240387	+	0.970677i	$0.577274\pi$
$228$	15752.9	−	15752.9i	0.303035	−	0.303035i
$229$			63549.3i			1.21182i	0.795532	+	0.605912i	$0.207192\pi$
$229$			63549.3i			1.21182i	−0.795532	+	0.605912i	$0.792808\pi$
$230$	7361.49	+	2577.49i	0.139159	+	0.0487239i
$231$	60699.3			1.13752
$232$	803.949	+	803.949i	0.0149366	+	0.0149366i
$233$	69287.2	−	69287.2i	1.27627	−	1.27627i	0.333524	−	0.942742i	$-0.391762\pi$
$233$	69287.2	−	69287.2i	1.27627	−	1.27627i	0.942742	−	0.333524i	$-0.108238\pi$
$234$		−	15327.0i		−	0.279914i
$235$	−3016.59	−	6267.11i	−0.0546236	−	0.113483i
$236$	9837.34			0.176626
$237$	23789.6	+	23789.6i	0.423537	+	0.423537i
$238$	−24005.1	+	24005.1i	−0.423790	+	0.423790i
$239$			2849.22i			0.0498805i	0.999689	+	0.0249402i	$0.00793955\pi$
$239$			2849.22i			0.0498805i	−0.999689	+	0.0249402i	$0.992060\pi$
$240$	15298.3	−	7363.64i	0.265596	−	0.127841i
$241$	−25671.8			−0.441999			−0.221000	−	0.975274i	$-0.570932\pi$
$241$	−25671.8			−0.441999			−0.221000	+	0.975274i	$0.570932\pi$
$242$	−6763.48	−	6763.48i	−0.115489	−	0.115489i
$243$	30920.5	−	30920.5i	0.523641	−	0.523641i
$244$		−	17533.9i		−	0.294509i
$245$	4172.88	−	11918.0i	0.0695191	−	0.198551i
$246$	−12328.1			−0.203717
$247$	−31819.5	−	31819.5i	−0.521554	−	0.521554i
$248$	−22788.6	+	22788.6i	−0.370522	+	0.370522i
$249$			29460.9i			0.475169i
$250$	9859.08	−	43080.4i	0.157745	−	0.689287i
$251$	−22997.3			−0.365030			−0.182515	−	0.983203i	$-0.558424\pi$
$251$	−22997.3			−0.365030			−0.182515	+	0.983203i	$0.558424\pi$
$252$	9637.12	+	9637.12i	0.151756	+	0.151756i
$253$	−8276.21	+	8276.21i	−0.129298	+	0.129298i
$254$		−	36034.6i		−	0.558538i
$255$	−55747.0	−	19518.8i	−0.857317	−	0.300174i
$256$	4096.00			0.0625000
$257$	21331.8	+	21331.8i	0.322970	+	0.322970i	0.849905	−	0.526935i	$-0.176659\pi$
$257$	21331.8	+	21331.8i	0.322970	+	0.322970i	−0.526935	+	0.849905i	$0.676659\pi$
$258$	66597.2	−	66597.2i	1.00050	−	1.00050i
$259$			18418.5i			0.274570i
$260$	−14873.9	−	30901.2i	−0.220028	−	0.457118i
$261$	−1587.91			−0.0233101
$262$	−28070.8	−	28070.8i	−0.408933	−	0.408933i
$263$	18294.4	−	18294.4i	0.264489	−	0.264489i	−0.562386	−	0.826875i	$-0.690117\pi$
$263$	18294.4	−	18294.4i	0.264489	−	0.264489i	0.826875	+	0.562386i	$0.190117\pi$
$264$			25477.9i			0.365557i
$265$	55797.4	−	26857.4i	0.794552	−	0.382447i
$266$	40014.1			0.565523
$267$	96725.2	+	96725.2i	1.35680	+	1.35680i
$268$	35151.5	−	35151.5i	0.489411	−	0.489411i
$269$		−	35425.0i		−	0.489560i	−0.969579	−	0.244780i	$-0.921284\pi$
$269$		−	35425.0i		−	0.489560i	0.969579	−	0.244780i	$-0.0787157\pi$
$270$	12248.6	−	34982.8i	0.168019	−	0.479874i
$271$	−85074.1			−1.15840			−0.579200	−	0.815185i	$-0.696635\pi$
$271$	−85074.1			−1.15840			−0.579200	+	0.815185i	$0.696635\pi$
$272$	−10075.9	−	10075.9i	−0.136190	−	0.136190i
$273$	69359.9	−	69359.9i	0.930642	−	0.930642i
$274$			20053.1i			0.267105i
$275$	51834.0	+	41368.9i	0.685408	+	0.547027i
$276$	−9363.87			−0.122924
$277$	63796.8	+	63796.8i	0.831456	+	0.831456i	0.987716	−	0.156260i	$-0.0499437\pi$
$277$	63796.8	+	63796.8i	0.831456	+	0.831456i	−0.156260	+	0.987716i	$0.549944\pi$
$278$	61688.1	−	61688.1i	0.798200	−	0.798200i
$279$		−	45010.6i		−	0.578238i
$280$	28781.9	+	10077.4i	0.367116	+	0.128539i
$281$	−118978.			−1.50680			−0.753400	−	0.657563i	$-0.771587\pi$
$281$	−118978.			−1.50680			−0.753400	+	0.657563i	$0.771587\pi$
$282$	5904.46	+	5904.46i	0.0742476	+	0.0742476i
$283$	34835.0	−	34835.0i	0.434954	−	0.434954i	−0.455356	−	0.890310i	$-0.650488\pi$
$283$	34835.0	−	34835.0i	0.434954	−	0.434954i	0.890310	+	0.455356i	$0.150488\pi$
$284$			65095.8i			0.807080i
$285$	30194.4	+	62730.2i	0.371738	+	0.772302i
$286$	51462.9			0.629162
$287$	−15657.4	−	15657.4i	−0.190088	−	0.190088i
$288$	−4045.08	+	4045.08i	−0.0487688	+	0.0487688i
$289$		−	33948.8i		−	0.406470i
$290$	−3201.43	+	1540.97i	−0.0380669	+	0.0183230i
$291$	−128361.			−1.51582
$292$	−54262.5	−	54262.5i	−0.636406	−	0.636406i
$293$	−44489.7	+	44489.7i	−0.518232	+	0.518232i	−0.917036	−	0.398804i	$-0.869425\pi$
$293$	−44489.7	+	44489.7i	−0.518232	+	0.518232i	0.398804	+	0.917036i	$0.369425\pi$
$294$			15159.8i			0.175388i
$295$	−10158.9	+	29014.6i	−0.116736	+	0.333405i
$296$	−7730.96			−0.0882368
$297$	39329.7	+	39329.7i	0.445870	+	0.445870i
$298$	11446.3	−	11446.3i	0.128894	−	0.128894i
$299$			18914.1i			0.211565i
$300$	5920.16	+	52725.8i	0.0657795	+	0.585842i
$301$	169164.			1.86713
$302$	−31407.3	−	31407.3i	−0.344363	−	0.344363i
$303$	−100953.	+	100953.i	−1.09960	+	1.09960i
$304$			16795.5i			0.181738i
$305$	51715.1	+	18107.1i	0.555927	+	0.194648i
$306$	19901.3			0.212539
$307$	−28491.1	−	28491.1i	−0.302296	−	0.302296i	0.539615	−	0.841912i	$-0.318570\pi$
$307$	−28491.1	−	28491.1i	−0.302296	−	0.302296i	−0.841912	+	0.539615i	$0.818570\pi$
$308$	−32358.3	+	32358.3i	−0.341101	+	0.341101i
$309$			162485.i			1.70176i
$310$	−43679.9	−	90747.1i	−0.454526	−	0.944299i
$311$	−129794.			−1.34194			−0.670970	−	0.741485i	$-0.734122\pi$
$311$	−129794.			−1.34194			−0.670970	+	0.741485i	$0.734122\pi$
$312$	29113.1	+	29113.1i	0.299074	+	0.299074i
$313$	54715.1	−	54715.1i	0.558494	−	0.558494i	−0.370384	−	0.928879i	$-0.620774\pi$
$313$	54715.1	−	54715.1i	0.558494	−	0.558494i	0.928879	+	0.370384i	$0.120774\pi$
$314$		−	56168.1i		−	0.569680i
$315$	−38376.2	+	18471.9i	−0.386760	+	0.186162i
$316$	−25364.1			−0.254007
$317$	−96246.7	−	96246.7i	−0.957784	−	0.957784i	0.0413604	−	0.999144i	$-0.486831\pi$
$317$	−96246.7	−	96246.7i	−0.957784	−	0.957784i	−0.999144	+	0.0413604i	$0.986831\pi$
$318$	−52568.7	+	52568.7i	−0.519844	+	0.519844i
$319$		−	5331.67i		−	0.0523941i
$320$	−4229.90	+	12080.9i	−0.0413077	+	0.117977i
$321$	5804.41			0.0563311
$322$	−11892.6	−	11892.6i	−0.114700	−	0.114700i
$323$	41315.9	−	41315.9i	0.396016	−	0.396016i
$324$			64976.6i			0.618967i
$325$	106501.	−	11958.2i	1.00829	−	0.113213i
$326$	112547.			1.05901
$327$	−30069.0	−	30069.0i	−0.281205	−	0.281205i
$328$	6572.01	−	6572.01i	0.0610872	−	0.0610872i
$329$			14998.0i			0.138561i
$330$	−75145.4	−	26310.8i	−0.690040	−	0.241605i
$331$	2479.20			0.0226285			0.0113142	−	0.999936i	$-0.496398\pi$
$331$	2479.20			0.0226285			0.0113142	+	0.999936i	$0.496398\pi$
$332$	−15705.4	−	15705.4i	−0.142486	−	0.142486i
$333$	7634.85	−	7634.85i	0.0688513	−	0.0688513i
$334$			84468.0i			0.757180i
$335$	67376.4	+	139978.i	0.600369	+	1.24729i
$336$	−36610.7			−0.324287
$337$	−19340.8	−	19340.8i	−0.170300	−	0.170300i	0.616811	−	0.787111i	$-0.288424\pi$
$337$	−19340.8	−	19340.8i	−0.170300	−	0.170300i	−0.787111	+	0.616811i	$0.788424\pi$
$338$	1683.67	−	1683.67i	0.0147375	−	0.0147375i
$339$			55637.1i			0.484133i
$340$	40123.6	−	19312.9i	0.347090	−	0.167067i
$341$	151131.			1.29970
$342$	−16586.7	−	16586.7i	−0.141811	−	0.141811i
$343$	72269.7	−	72269.7i	0.614282	−	0.614282i
$344$			71004.8i			0.600027i
$345$	9669.98	−	27618.1i	0.0812433	−	0.232036i
$346$	−63253.1			−0.528360
$347$	−72375.3	−	72375.3i	−0.601079	−	0.601079i	0.339520	−	0.940599i	$-0.389735\pi$
$347$	−72375.3	−	72375.3i	−0.601079	−	0.601079i	−0.940599	+	0.339520i	$0.889735\pi$
$348$	3016.18	−	3016.18i	0.0249057	−	0.0249057i
$349$		−	86632.1i		−	0.711259i	−0.934627	−	0.355630i	$-0.884266\pi$
$349$		−	86632.1i		−	0.711259i	0.934627	−	0.355630i	$-0.115734\pi$
$350$	−59445.6	+	74483.4i	−0.485270	+	0.608028i
$351$	89882.6			0.729561
$352$	−13582.0	−	13582.0i	−0.109617	−	0.109617i
$353$	−3824.47	+	3824.47i	−0.0306918	+	0.0306918i	−0.722286	−	0.691594i	$-0.756909\pi$
$353$	−3824.47	+	3824.47i	−0.0306918	+	0.0306918i	0.691594	+	0.722286i	$0.256909\pi$
$354$		−	36906.8i		−	0.294510i
$355$	−191996.	−	67223.9i	−1.52348	−	0.533417i
$356$	−103127.			−0.813713
$357$	90060.2	+	90060.2i	0.706637	+	0.706637i
$358$	70970.4	−	70970.4i	0.553747	−	0.553747i
$359$			229287.i			1.77906i	0.456873	+	0.889532i	$0.348969\pi$
$359$			229287.i			1.77906i	−0.456873	+	0.889532i	$0.651031\pi$
$360$	−7753.39	−	16108.0i	−0.0598255	−	0.124290i
$361$	61451.5			0.471540
$362$	28113.5	+	28113.5i	0.214535	+	0.214535i
$363$	−25374.6	+	25374.6i	−0.192569	+	0.192569i
$364$			73950.3i			0.558132i
$365$	216080.	−	104007.i	1.62192	−	0.780690i
$366$	−65782.0			−0.491072
$367$	−86929.4	−	86929.4i	−0.645408	−	0.645408i	0.306472	−	0.951880i	$-0.400852\pi$
$367$	−86929.4	−	86929.4i	−0.645408	−	0.645408i	−0.951880	+	0.306472i	$0.900852\pi$
$368$	4991.79	−	4991.79i	0.0368605	−	0.0368605i
$369$			12980.6i			0.0953329i
$370$	7983.69	−	22802.0i	0.0583177	−	0.166559i
$371$	−133530.			−0.970133
$372$	85496.1	+	85496.1i	0.617817	+	0.617817i
$373$	−127875.	+	127875.i	−0.919114	+	0.919114i	−0.996965	−	0.0778510i	$-0.975194\pi$
$373$	−127875.	+	127875.i	−0.919114	+	0.919114i	0.0778510	+	0.996965i	$0.475194\pi$
$374$			66822.0i			0.477723i
$375$	−161625.	−	36988.3i	−1.14933	−	0.263028i
$376$	−6295.24			−0.0445283
$377$	−6092.40	−	6092.40i	−0.0428653	−	0.0428653i
$378$	−56515.3	+	56515.3i	−0.395533	+	0.395533i
$379$		−	165876.i		−	1.15479i	−0.816464	−	0.577397i	$-0.804069\pi$
$379$		−	165876.i		−	1.15479i	0.816464	−	0.577397i	$-0.195931\pi$
$380$	−49537.3	−	17344.6i	−0.343056	−	0.120115i
$381$	−135191.			−0.931320
$382$	−62425.7	−	62425.7i	−0.427796	−	0.427796i
$383$	−168259.	+	168259.i	−1.14704	+	1.14704i	−0.159913	+	0.987131i	$0.551121\pi$
$383$	−168259.	+	168259.i	−1.14704	+	1.14704i	−0.987131	+	0.159913i	$0.948879\pi$
$384$		−	15367.0i		−	0.104214i
$385$	−62022.5	−	128855.i	−0.418435	−	0.869318i
$386$	83596.7			0.561067
$387$	−70122.1	−	70122.1i	−0.468202	−	0.468202i
$388$	68428.1	−	68428.1i	0.454539	−	0.454539i
$389$		−	7064.40i		−	0.0466848i	−0.999728	−	0.0233424i	$-0.992569\pi$
$389$		−	7064.40i		−	0.0466848i	0.999728	−	0.0233424i	$-0.00743080\pi$
$390$	−115932.	+	55802.3i	−0.762209	+	0.366879i
$391$	−24559.0			−0.160641
$392$	−8081.57	−	8081.57i	−0.0525925	−	0.0525925i
$393$	−105313.	+	105313.i	−0.681864	+	0.681864i
$394$			47547.4i			0.306291i
$395$	26193.3	−	74809.8i	0.167879	−	0.479473i
$396$	26826.4			0.171069
$397$	184004.	+	184004.i	1.16747	+	1.16747i	0.982800	+	0.184672i	$0.0591223\pi$
$397$	184004.	+	184004.i	1.16747	+	1.16747i	0.184672	+	0.982800i	$0.440878\pi$
$398$	−79805.2	+	79805.2i	−0.503808	+	0.503808i
$399$		−	150121.i		−	0.942966i
$400$	−31263.6	−	24951.7i	−0.195398	−	0.155948i
$401$	−70939.1			−0.441161			−0.220580	−	0.975369i	$-0.570795\pi$
$401$	−70939.1			−0.441161			−0.220580	+	0.975369i	$0.570795\pi$
$402$	−131878.	−	131878.i	−0.816055	−	0.816055i
$403$	172694.	−	172694.i	1.06333	−	1.06333i
$404$		−	107634.i		−	0.659458i
$405$	−191644.	−	67100.8i	−1.16839	−	0.409089i
$406$	7661.41			0.0464790
$407$	25635.3	+	25635.3i	0.154757	+	0.154757i
$408$	−37801.8	+	37801.8i	−0.227087	+	0.227087i
$409$		−	206177.i		−	1.23252i	−0.787543	−	0.616260i	$-0.788647\pi$
$409$		−	206177.i		−	1.23252i	0.787543	−	0.616260i	$-0.211353\pi$
$410$	12596.9	+	26170.6i	0.0749367	+	0.155685i
$411$	75233.4			0.445376
$412$	−86619.6	−	86619.6i	−0.510295	−	0.510295i
$413$	46873.5	−	46873.5i	0.274807	−	0.274807i
$414$			9859.48i			0.0575246i
$415$	62540.8	−	30103.2i	0.363134	−	0.174790i
$416$	−31039.8			−0.179363
$417$	−231435.	−	231435.i	−1.33094	−	1.33094i
$418$	55692.7	−	55692.7i	0.318747	−	0.318747i
$419$			138544.i			0.789148i	0.918864	+	0.394574i	$0.129108\pi$
$419$			138544.i			0.789148i	−0.918864	+	0.394574i	$0.870892\pi$
$420$	37807.6	−	107981.i	0.214329	−	0.612137i
$421$	−222302.			−1.25424			−0.627118	−	0.778924i	$-0.715766\pi$
$421$	−222302.			−1.25424			−0.627118	+	0.778924i	$0.715766\pi$
$422$	57670.3	+	57670.3i	0.323838	+	0.323838i
$423$	6216.98	−	6216.98i	0.0347455	−	0.0347455i
$424$		−	56047.9i		−	0.311765i
$425$	15527.1	+	138286.i	0.0859629	+	0.765598i
$426$	244220.			1.34574
$427$	−83546.6	−	83546.6i	−0.458219	−	0.458219i
$428$	−3094.28	+	3094.28i	−0.0168917	+	0.0168917i
$429$		−	193074.i		−	1.04908i
$430$	−209424.	−	73326.0i	−1.13263	−	0.396571i
$431$	−242345.			−1.30461			−0.652303	−	0.757958i	$-0.726197\pi$
$431$	−242345.			−1.30461			−0.652303	+	0.757958i	$0.726197\pi$
$432$	−23721.7	−	23721.7i	−0.127110	−	0.127110i
$433$	−61651.3	+	61651.3i	−0.328826	+	0.328826i	−0.852140	−	0.523314i	$-0.824696\pi$
$433$	−61651.3	+	61651.3i	−0.328826	+	0.328826i	0.523314	+	0.852140i	$0.324696\pi$
$434$			217169.i			1.15297i
$435$	5781.25	+	12010.8i	0.0305522	+	0.0634737i
$436$	32059.0			0.168647
$437$	20468.7	+	20468.7i	0.107183	+	0.107183i
$438$	−203577.	+	203577.i	−1.06116	+	1.06116i
$439$			261480.i			1.35678i	0.734701	+	0.678391i	$0.237322\pi$
$439$			261480.i			1.35678i	−0.734701	+	0.678391i	$0.762678\pi$
$440$	54085.4	−	26033.3i	0.279367	−	0.134470i
$441$	15962.2			0.0820759
$442$	76356.1	+	76356.1i	0.390840	+	0.390840i
$443$	71729.0	−	71729.0i	0.365500	−	0.365500i	−0.500333	−	0.865833i	$-0.666789\pi$
$443$	71729.0	−	71729.0i	0.365500	−	0.365500i	0.865833	+	0.500333i	$0.166789\pi$
$444$			29004.3i			0.147128i
$445$	106498.	−	304166.i	0.537801	−	1.53600i
$446$	274178.			1.37836
$447$	−42943.2	−	42943.2i	−0.214921	−	0.214921i
$448$	19516.9	−	19516.9i	0.0972420	−	0.0972420i
$449$			11804.0i			0.0585511i	0.999571	+	0.0292755i	$0.00932002\pi$
$449$			11804.0i			0.0585511i	−0.999571	+	0.0292755i	$0.990680\pi$
$450$	55516.5	−	6233.50i	0.274155	−	0.0307827i
$451$	−43584.6			−0.214279
$452$	−29659.6	−	29659.6i	−0.145174	−	0.145174i
$453$	−117831.	+	117831.i	−0.574199	+	0.574199i
$454$			150524.i			0.730290i
$455$	−218112.	−	76367.8i	−1.05355	−	0.368882i
$456$	63011.8			0.303035
$457$	55988.7	+	55988.7i	0.268082	+	0.268082i	0.828327	−	0.560245i	$-0.189293\pi$
$457$	55988.7	+	55988.7i	0.268082	+	0.268082i	−0.560245	+	0.828327i	$0.689293\pi$
$458$	−127099.	+	127099.i	−0.605912	+	0.605912i
$459$			116708.i			0.553956i
$460$	9568.00	+	19878.0i	0.0452174	+	0.0939412i
$461$	67413.4			0.317208			0.158604	−	0.987342i	$-0.449301\pi$
$461$	67413.4			0.317208			0.158604	+	0.987342i	$0.449301\pi$
$462$	121399.	+	121399.i	0.568761	+	0.568761i
$463$	−8133.95	+	8133.95i	−0.0379437	+	0.0379437i	−0.725824	−	0.687880i	$-0.758541\pi$
$463$	−8133.95	+	8133.95i	−0.0379437	+	0.0379437i	0.687880	+	0.725824i	$0.258541\pi$
$464$			3215.80i			0.0149366i
$465$	−340456.	+	163874.i	−1.57455	+	0.757887i
$466$	277149.			1.27627
$467$	−51529.7	−	51529.7i	−0.236278	−	0.236278i	0.579029	−	0.815307i	$-0.303432\pi$
$467$	−51529.7	−	51529.7i	−0.236278	−	0.236278i	−0.815307	+	0.579029i	$0.803432\pi$
$468$	30654.0	−	30654.0i	0.139957	−	0.139957i
$469$		−	334984.i		−	1.52292i
$470$	6501.04	−	18567.4i	0.0294298	−	0.0840534i
$471$	−210726.			−0.949897
$472$	19674.7	+	19674.7i	0.0883128	+	0.0883128i
$473$	235447.	−	235447.i	1.05237	−	1.05237i
$474$			95158.6i			0.423537i
$475$	102313.	−	128196.i	0.453467	−	0.568180i
$476$	−96020.6			−0.423790
$477$	55351.1	+	55351.1i	0.243271	+	0.243271i
$478$	−5698.45	+	5698.45i	−0.0249402	+	0.0249402i
$479$			269666.i			1.17532i	0.809109	+	0.587658i	$0.199950\pi$
$479$			269666.i			1.17532i	−0.809109	+	0.587658i	$0.800050\pi$
$480$	45323.9	+	15869.3i	0.196718	+	0.0688774i
$481$	58585.9			0.253223
$482$	−51343.5	−	51343.5i	−0.221000	−	0.221000i
$483$	−44617.5	+	44617.5i	−0.191254	+	0.191254i
$484$		−	27053.9i		−	0.115489i
$485$	131159.	+	272490.i	0.557591	+	1.15842i
$486$	123682.			0.523641
$487$	301677.	+	301677.i	1.27199	+	1.27199i	0.945041	+	0.326951i	$0.106021\pi$
$487$	301677.	+	301677.i	1.27199	+	1.27199i	0.326951	+	0.945041i	$0.393979\pi$
$488$	35067.8	−	35067.8i	0.147255	−	0.147255i
$489$		−	422243.i		−	1.76581i
$490$	32181.8	−	15490.3i	0.134035	−	0.0645160i
$491$	−215813.			−0.895190			−0.447595	−	0.894236i	$-0.647719\pi$
$491$	−215813.			−0.895190			−0.447595	+	0.894236i	$0.647719\pi$
$492$	−24656.2	−	24656.2i	−0.101858	−	0.101858i
$493$	7910.66	−	7910.66i	0.0325476	−	0.0325476i
$494$		−	127278.i		−	0.521554i
$495$	−27703.4	+	79122.7i	−0.113063	+	0.322917i
$496$	−91154.4			−0.370522
$497$	310172.	+	310172.i	1.25571	+	1.25571i
$498$	−58921.9	+	58921.9i	−0.237584	+	0.237584i
$499$			248396.i			0.997572i	0.866725	+	0.498786i	$0.166221\pi$
$499$			248396.i			0.997572i	−0.866725	+	0.498786i	$0.833779\pi$
$500$	105879.	−	66442.7i	0.423516	−	0.265771i
$501$	316899.			1.26254
$502$	−45994.6	−	45994.6i	−0.182515	−	0.182515i
$503$	224750.	−	224750.i	0.888307	−	0.888307i	−0.106054	−	0.994360i	$-0.533822\pi$
$503$	224750.	−	224750.i	0.888307	−	0.888307i	0.994360	+	0.106054i	$0.0338216\pi$
$504$			38548.5i			0.151756i
$505$	317460.	+	111153.i	1.24482	+	0.435851i
$506$	−33104.9			−0.129298
$507$	−6316.63	−	6316.63i	−0.0245736	−	0.0245736i
$508$	72069.3	−	72069.3i	0.279269	−	0.279269i
$509$		−	257133.i		−	0.992483i	−0.868185	−	0.496241i	$-0.834713\pi$
$509$		−	257133.i		−	0.992483i	0.868185	−	0.496241i	$-0.165287\pi$
$510$	−72456.4	−	150532.i	−0.278571	−	0.578745i
$511$	−517107.			−1.98033
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	97270.1	−	97270.1i	0.369611	−	0.369611i
$514$			85327.4i			0.322970i
$515$	344930.	−	166028.i	1.30052	−	0.625988i
$516$	266389.			1.00050
$517$	20874.5	+	20874.5i	0.0780973	+	0.0780973i
$518$	−36836.9	+	36836.9i	−0.137285	+	0.137285i
$519$			237307.i			0.880999i
$520$	32054.6	−	91550.0i	0.118545	−	0.338573i
$521$	221324.			0.815368			0.407684	−	0.913123i	$-0.366336\pi$
$521$	221324.			0.815368			0.407684	+	0.913123i	$0.366336\pi$
$522$	−3175.82	−	3175.82i	−0.0116551	−	0.0116551i
$523$	163470.	−	163470.i	0.597633	−	0.597633i	−0.342049	−	0.939682i	$-0.611121\pi$
$523$	163470.	−	163470.i	0.597633	−	0.597633i	0.939682	+	0.342049i	$0.111121\pi$
$524$		−	112283.i		−	0.408933i
$525$	279440.	+	223022.i	1.01384	+	0.809151i
$526$	73177.6			0.264489
$527$	224234.	+	224234.i	0.807385	+	0.807385i
$528$	−50955.8	+	50955.8i	−0.182779	+	0.182779i
$529$		−	12167.0i		−	0.0434783i
$530$	165310.	+	57880.1i	0.588500	+	0.206052i
$531$	−38860.2			−0.137821
$532$	80028.3	+	80028.3i	0.282761	+	0.282761i
$533$	−49803.3	+	49803.3i	−0.175309	+	0.175309i
$534$			386901.i			1.35680i
$535$	−5930.95	−	12321.8i	−0.0207213	−	0.0430494i
$536$	140606.			0.489411
$537$	−266260.	−	266260.i	−0.923331	−	0.923331i
$538$	70850.1	−	70850.1i	0.244780	−	0.244780i
$539$			53595.8i			0.184482i
$540$	94462.9	−	45468.5i	0.323947	−	0.155928i
$541$	320821.			1.09615			0.548073	−	0.836431i	$-0.315362\pi$
$541$	320821.			1.09615			0.548073	+	0.836431i	$0.315362\pi$
$542$	−170148.	−	170148.i	−0.579200	−	0.579200i
$543$	105474.	−	105474.i	0.357721	−	0.357721i
$544$		−	40303.6i		−	0.136190i
$545$	−33107.1	+	94556.1i	−0.111462	+	0.318344i
$546$	277439.			0.930642
$547$	51446.7	+	51446.7i	0.171942	+	0.171942i	0.787832	−	0.615890i	$-0.211203\pi$
$547$	51446.7	+	51446.7i	0.171942	+	0.171942i	−0.615890	+	0.787832i	$0.711203\pi$
$548$	−40106.3	+	40106.3i	−0.133552	+	0.133552i
$549$			69263.7i			0.229806i
$550$	20930.0	+	186406.i	0.0691902	+	0.616218i
$551$	−13186.3			−0.0434329
$552$	−18727.7	−	18727.7i	−0.0614620	−	0.0614620i
$553$	−120856.	+	120856.i	−0.395202	+	0.395202i
$554$			255187.i			0.831456i
$555$	−85546.2	−	29952.4i	−0.277725	−	0.0972403i
$556$	246752.			0.798200
$557$	107401.	+	107401.i	0.346178	+	0.346178i	0.858684	−	0.512506i	$-0.171283\pi$
$557$	107401.	+	107401.i	0.346178	+	0.346178i	−0.512506	+	0.858684i	$0.671283\pi$
$558$	90021.2	−	90021.2i	0.289119	−	0.289119i
$559$		−	538080.i		−	1.72196i
$560$	37408.9	+	77718.6i	0.119288	+	0.247827i
$561$	250696.			0.796566
$562$	−237957.	−	237957.i	−0.753400	−	0.753400i
$563$	−249996.	+	249996.i	−0.788709	+	0.788709i	−0.981283	−	0.192574i	$-0.938317\pi$
$563$	−249996.	+	249996.i	−0.788709	+	0.788709i	0.192574	+	0.981283i	$0.438317\pi$
$564$			23617.9i			0.0742476i
$565$	118109.	−	56850.0i	0.369985	−	0.178087i
$566$	139340.			0.434954
$567$	309605.	+	309605.i	0.963033	+	0.963033i
$568$	−130192.	+	130192.i	−0.403540	+	0.403540i
$569$		−	492345.i		−	1.52071i	−0.649510	−	0.760353i	$-0.725026\pi$
$569$		−	492345.i		−	1.52071i	0.649510	−	0.760353i	$-0.274974\pi$
$570$	−65071.7	+	185849.i	−0.200282	+	0.572020i
$571$	−471247.			−1.44536			−0.722681	−	0.691182i	$-0.757090\pi$
$571$	−471247.			−1.44536			−0.722681	+	0.691182i	$0.757090\pi$
$572$	102926.	+	102926.i	0.314581	+	0.314581i
$573$	−234203.	+	234203.i	−0.713317	+	0.713317i
$574$		−	62629.4i		−	0.190088i
$575$	−68509.6	+	7692.39i	−0.207212	+	0.0232662i
$576$	−16180.3			−0.0487688
$577$	−364896.	−	364896.i	−1.09602	−	1.09602i	−0.994872	−	0.101145i	$-0.967749\pi$
$577$	−364896.	−	364896.i	−1.09602	−	1.09602i	−0.101145	−	0.994872i	$-0.532251\pi$
$578$	67897.5	−	67897.5i	0.203235	−	0.203235i
$579$		−	313630.i		−	0.935536i
$580$	−9484.79	−	3320.93i	−0.0281950	−	0.00987196i
$581$	−149668.			−0.443380
$582$	−256722.	−	256722.i	−0.757909	−	0.757909i
$583$	−185851.	+	185851.i	−0.546798	+	0.546798i
$584$		−	217050.i		−	0.636406i
$585$	58755.9	+	122068.i	0.171688	+	0.356689i
$586$	−177959.			−0.518232
$587$	−359894.	−	359894.i	−1.04448	−	1.04448i	−0.998964	−	0.0455132i	$-0.985508\pi$
$587$	−359894.	−	359894.i	−1.04448	−	1.04448i	−0.0455132	−	0.998964i	$-0.514492\pi$
$588$	−30319.6	+	30319.6i	−0.0876939	+	0.0876939i
$589$		−	373776.i		−	1.07741i
$590$	−78347.1	+	37711.3i	−0.225071	+	0.108335i
$591$	178384.			0.510717
$592$	−15461.9	−	15461.9i	−0.0441184	−	0.0441184i
$593$	−173478.	+	173478.i	−0.493328	+	0.493328i	−0.909353	−	0.416025i	$-0.863423\pi$
$593$	−173478.	+	173478.i	−0.493328	+	0.493328i	0.416025	+	0.909353i	$0.363423\pi$
$594$			157319.i			0.445870i
$595$	99159.6	−	283207.i	0.280092	−	0.799962i
$596$	45785.3			0.128894
$597$	299405.	+	299405.i	0.840061	+	0.840061i
$598$	−37828.3	+	37828.3i	−0.105783	+	0.105783i
$599$			492349.i			1.37221i	0.727505	+	0.686103i	$0.240680\pi$
$599$			492349.i			1.37221i	−0.727505	+	0.686103i	$0.759320\pi$
$600$	−93611.2	+	117292.i	−0.260031	+	0.325811i
$601$	−303871.			−0.841279			−0.420639	−	0.907228i	$-0.638194\pi$
$601$	−303871.			−0.841279			−0.420639	+	0.907228i	$0.638194\pi$
$602$	338328.	+	338328.i	0.933565	+	0.933565i
$603$	−138858.	+	138858.i	−0.381888	+	0.381888i
$604$		−	125629.i		−	0.344363i
$605$	79793.8	+	27938.3i	0.218001	+	0.0763291i
$606$	−403811.			−1.09960
$607$	25175.2	+	25175.2i	0.0683274	+	0.0683274i	0.740445	−	0.672117i	$-0.234615\pi$
$607$	25175.2	+	25175.2i	0.0683274	+	0.0683274i	−0.672117	+	0.740445i	$0.734615\pi$
$608$	−33591.0	+	33591.0i	−0.0908691	+	0.0908691i
$609$		−	28743.3i		−	0.0775002i
$610$	67216.0	+	139644.i	0.180640	+	0.375287i
$611$	47705.9			0.127788
$612$	39802.6	+	39802.6i	0.106270	+	0.106270i
$613$	476029.	−	476029.i	1.26681	−	1.26681i	0.319089	−	0.947725i	$-0.396623\pi$
$613$	476029.	−	476029.i	1.26681	−	1.26681i	0.947725	−	0.319089i	$-0.103377\pi$
$614$		−	113964.i		−	0.302296i
$615$	98184.2	−	47259.7i	0.259592	−	0.124951i
$616$	−129433.			−0.341101
$617$	−260323.	−	260323.i	−0.683821	−	0.683821i	0.277038	−	0.960859i	$-0.410647\pi$
$617$	−260323.	−	260323.i	−0.683821	−	0.683821i	−0.960859	+	0.277038i	$0.910647\pi$
$618$	−324971.	+	324971.i	−0.850879	+	0.850879i
$619$		−	578270.i		−	1.50921i	−0.656180	−	0.754605i	$-0.727829\pi$
$619$		−	578270.i		−	1.50921i	0.656180	−	0.754605i	$-0.272171\pi$
$620$	94134.4	−	268854.i	0.244886	−	0.699412i
$621$	−57819.3			−0.149930
$622$	−259588.	−	259588.i	−0.670970	−	0.670970i
$623$	−491384.	+	491384.i	−1.26603	+	1.26603i
$624$			116452.i			0.299074i
$625$	86628.2	+	380898.i	0.221768	+	0.975099i
$626$	218860.			0.558494
$627$	−208942.	−	208942.i	−0.531486	−	0.531486i
$628$	112336.	−	112336.i	0.284840	−	0.284840i
$629$			76070.7i			0.192272i
$630$	−113696.	−	39808.7i	−0.286461	−	0.100299i
$631$	478317.			1.20132			0.600658	−	0.799506i	$-0.294905\pi$
$631$	478317.			1.20132			0.600658	+	0.799506i	$0.294905\pi$
$632$	−50728.2	−	50728.2i	−0.127003	−	0.127003i
$633$	216362.	−	216362.i	0.539975	−	0.539975i
$634$		−	384987.i		−	0.957784i
$635$	138138.	+	286989.i	0.342584	+	0.711734i
$636$	−210275.			−0.519844
$637$	61242.8	+	61242.8i	0.150930	+	0.150930i
$638$	10663.3	−	10663.3i	0.0261970	−	0.0261970i
$639$		−	257146.i		−	0.629765i
$640$	−32621.6	+	15702.0i	−0.0796426	+	0.0383349i
$641$	−356708.			−0.868155			−0.434077	−	0.900876i	$-0.642926\pi$
$641$	−356708.			−0.868155			−0.434077	+	0.900876i	$0.642926\pi$
$642$	11608.8	+	11608.8i	0.0281656	+	0.0281656i
$643$	−248633.	+	248633.i	−0.601363	+	0.601363i	−0.940674	−	0.339311i	$-0.889806\pi$
$643$	−248633.	+	248633.i	−0.601363	+	0.601363i	0.339311	+	0.940674i	$0.389806\pi$
$644$		−	47570.4i		−	0.114700i
$645$	−275097.	+	785697.i	−0.661252	+	1.88858i
$646$	165264.			0.396016
$647$	417496.	+	417496.i	0.997341	+	0.997341i	0.999996	−	0.00265518i	$-0.000845170\pi$
$647$	417496.	+	417496.i	0.997341	+	0.997341i	−0.00265518	+	0.999996i	$0.500845\pi$
$648$	−129953.	+	129953.i	−0.309483	+	0.309483i
$649$		−	130480.i		−	0.309780i
$650$	236919.	+	189086.i	0.560754	+	0.447541i
$651$	814753.			1.92249
$652$	225094.	+	225094.i	0.529503	+	0.529503i
$653$	−555165.	+	555165.i	−1.30196	+	1.30196i	−0.374883	+	0.927072i	$0.622317\pi$
$653$	−555165.	+	555165.i	−1.30196	+	1.30196i	−0.927072	+	0.374883i	$0.877683\pi$
$654$		−	120276.i		−	0.281205i
$655$	331172.	+	115954.i	0.771918	+	0.270273i
$656$	26288.0			0.0610872
$657$	214352.	+	214352.i	0.496588	+	0.496588i
$658$	−29995.9	+	29995.9i	−0.0692804	+	0.0692804i
$659$			455881.i			1.04974i	0.851183	+	0.524868i	$0.175885\pi$
$659$			455881.i			1.04974i	−0.851183	+	0.524868i	$0.824115\pi$
$660$	−97669.2	−	202912.i	−0.224218	−	0.465823i
$661$	−448737.			−1.02704			−0.513522	−	0.858076i	$-0.671660\pi$
$661$	−448737.			−1.02704			−0.513522	+	0.858076i	$0.671660\pi$
$662$	4958.40	+	4958.40i	0.0113142	+	0.0113142i
$663$	286465.	−	286465.i	0.651696	−	0.651696i
$664$		−	62821.5i		−	0.142486i
$665$	−318683.	+	153394.i	−0.720635	+	0.346868i
$666$	30539.4			0.0688513
$667$	3919.09	+	3919.09i	0.00880915	+	0.00880915i
$668$	−168936.	+	168936.i	−0.378590	+	0.378590i
$669$		−	1.02863e6i		−	2.29831i
$670$	−145202.	+	414708.i	−0.323463	+	0.923831i
$671$	−232565.			−0.516533
$672$	−73221.5	−	73221.5i	−0.162144	−	0.162144i
$673$	483002.	−	483002.i	1.06640	−	1.06640i	0.0687629	−	0.997633i	$-0.478095\pi$
$673$	483002.	−	483002.i	1.06640	−	1.06640i	0.997633	−	0.0687629i	$-0.0219052\pi$
$674$		−	77363.1i		−	0.170300i
$675$	36555.3	+	325567.i	0.0802312	+	0.714551i
$676$	6734.68			0.0147375
$677$	−391784.	−	391784.i	−0.854809	−	0.854809i	0.135912	−	0.990721i	$-0.456603\pi$
$677$	−391784.	−	391784.i	−0.854809	−	0.854809i	−0.990721	+	0.135912i	$0.956603\pi$
$678$	−111274.	+	111274.i	−0.242067	+	0.242067i
$679$		−	652101.i		−	1.41441i
$680$	118873.	+	41621.2i	0.257078	+	0.0900113i
$681$	564723.			1.21770
$682$	302261.	+	302261.i	0.649851	+	0.649851i
$683$	440518.	−	440518.i	0.944327	−	0.944327i	−0.0542033	−	0.998530i	$-0.517262\pi$
$683$	440518.	−	440518.i	0.944327	−	0.944327i	0.998530	+	0.0542033i	$0.0172619\pi$
$684$		−	66346.9i		−	0.141811i
$685$	−76873.5	−	159708.i	−0.163831	−	0.340366i
$686$	289079.			0.614282
$687$	476836.	+	476836.i	1.01031	+	1.01031i
$688$	−142010.	+	142010.i	−0.300013	+	0.300013i
$689$			424736.i			0.894706i
$690$	74576.2	−	35896.3i	0.156640	−	0.0753965i
$691$	−566803.			−1.18707			−0.593534	−	0.804809i	$-0.702268\pi$
$691$	−566803.			−1.18707			−0.593534	+	0.804809i	$0.702268\pi$
$692$	−126506.	−	126506.i	−0.264180	−	0.264180i
$693$	127824.	−	127824.i	0.266162	−	0.266162i
$694$		−	289501.i		−	0.601079i
$695$	−254819.	+	727780.i	−0.527548	+	1.50671i
$696$	12064.7			0.0249057
$697$	−64667.0	−	64667.0i	−0.133112	−	0.133112i
$698$	173264.	−	173264.i	0.355630	−	0.355630i
$699$		−	1.03978e6i		−	2.12807i
$700$	−267858.	+	30075.6i	−0.546649	+	0.0613789i
$701$	635318.			1.29287			0.646435	−	0.762969i	$-0.276259\pi$
$701$	635318.			1.29287			0.646435	+	0.762969i	$0.276259\pi$
$702$	179765.	+	179765.i	0.364780	+	0.364780i
$703$	63401.1	−	63401.1i	0.128288	−	0.128288i
$704$		−	54328.1i		−	0.109617i
$705$	−69659.4	−	24390.0i	−0.140153	−	0.0490719i
$706$	−15297.9			−0.0306918
$707$	−512861.	−	512861.i	−1.02603	−	1.02603i
$708$	73813.5	−	73813.5i	0.147255	−	0.147255i
$709$		−	166136.i		−	0.330499i	−0.986252	−	0.165249i	$-0.947157\pi$
$709$		−	166136.i		−	0.330499i	0.986252	−	0.165249i	$-0.0528429\pi$
$710$	−249544.	−	518440.i	−0.495029	−	1.02845i
$711$	100195.			0.198202
$712$	−206253.	−	206253.i	−0.406857	−	0.406857i
$713$	−111090.	+	111090.i	−0.218522	+	0.218522i
$714$			360241.i			0.706637i
$715$	−409864.	+	197283.i	−0.801729	+	0.385902i
$716$	283882.			0.553747
$717$	21378.9	+	21378.9i	0.0415859	+	0.0415859i
$718$	−458575.	+	458575.i	−0.889532	+	0.889532i
$719$			453157.i			0.876578i	0.898834	+	0.438289i	$0.144415\pi$
$719$			453157.i			0.876578i	−0.898834	+	0.438289i	$0.855585\pi$
$720$	16709.3	−	47722.8i	0.0322324	−	0.0920579i
$721$	−825460.			−1.58791
$722$	122903.	+	122903.i	0.235770	+	0.235770i
$723$	−192626.	+	192626.i	−0.368500	+	0.368500i
$724$			112454.i			0.214535i
$725$	19589.7	−	24545.3i	0.0372694	−	0.0466973i
$726$	−101498.			−0.192569
$727$	411690.	+	411690.i	0.778936	+	0.778936i	0.979650	−	0.200714i	$-0.0643261\pi$
$727$	411690.	+	411690.i	0.778936	+	0.778936i	−0.200714	+	0.979650i	$0.564326\pi$
$728$	−147901.	+	147901.i	−0.279066	+	0.279066i
$729$			193871.i			0.364802i
$730$	640176.	+	224146.i	1.20131	+	0.420615i
$731$	698670.			1.30749
$732$	−131564.	−	131564.i	−0.245536	−	0.245536i
$733$	−169722.	+	169722.i	−0.315887	+	0.315887i	−0.847185	−	0.531298i	$-0.821704\pi$
$733$	−169722.	+	169722.i	−0.315887	+	0.315887i	0.531298	+	0.847185i	$0.321704\pi$
$734$		−	347717.i		−	0.645408i
$735$	−58115.0	−	120737.i	−0.107576	−	0.223493i
$736$	19967.2			0.0368605
$737$	−466239.	−	466239.i	−0.858368	−	0.858368i
$738$	−25961.2	+	25961.2i	−0.0476664	+	0.0476664i
$739$		−	15371.8i		−	0.0281472i	−0.999901	−	0.0140736i	$-0.995520\pi$
$739$		−	15371.8i		−	0.0281472i	0.999901	−	0.0140736i	$-0.00447991\pi$
$740$	61571.3	−	29636.5i	0.112438	−	0.0541208i
$741$	−477509.			−0.869651
$742$	−267060.	−	267060.i	−0.485067	−	0.485067i
$743$	540663.	−	540663.i	0.979375	−	0.979375i	−0.0204167	−	0.999792i	$-0.506499\pi$
$743$	540663.	−	540663.i	0.979375	−	0.979375i	0.999792	+	0.0204167i	$0.00649929\pi$
$744$			341984.i			0.617817i
$745$	−47282.1	+	135041.i	−0.0851891	+	0.243306i
$746$	−511502.			−0.919114
$747$	62040.5	+	62040.5i	0.111182	+	0.111182i
$748$	−133644.	+	133644.i	−0.238861	+	0.238861i
$749$			29487.6i			0.0525626i
$750$	−249273.	−	397227.i	−0.443153	−	0.706181i
$751$	−475768.			−0.843558			−0.421779	−	0.906699i	$-0.638594\pi$
$751$	−475768.			−0.843558			−0.421779	+	0.906699i	$0.638594\pi$
$752$	−12590.5	−	12590.5i	−0.0222642	−	0.0222642i
$753$	−172558.	+	172558.i	−0.304330	+	0.304330i
$754$		−	24369.6i		−	0.0428653i
$755$	370535.	+	129736.i	0.650033	+	0.227597i
$756$	−226061.			−0.395533
$757$	−431637.	−	431637.i	−0.753229	−	0.753229i	0.221851	−	0.975081i	$-0.428790\pi$
$757$	−431637.	−	431637.i	−0.753229	−	0.753229i	−0.975081	+	0.221851i	$0.928790\pi$
$758$	331751.	−	331751.i	0.577397	−	0.577397i
$759$			124200.i			0.215594i
$760$	−64385.4	−	133764.i	−0.111471	−	0.231585i
$761$	−170707.			−0.294769			−0.147384	−	0.989079i	$-0.547085\pi$
$761$	−170707.			−0.294769			−0.147384	+	0.989079i	$0.547085\pi$
$762$	−270383.	−	270383.i	−0.465660	−	0.465660i
$763$	152757.	−	152757.i	0.262392	−	0.262392i
$764$		−	249703.i		−	0.427796i
$765$	−158499.	+	76291.4i	−0.270834	+	0.130363i
$766$	−673035.			−1.14704
$767$	−149096.	−	149096.i	−0.253441	−	0.253441i
$768$	30733.9	−	30733.9i	0.0521070	−	0.0521070i
$769$			763088.i			1.29039i	0.764017	+	0.645196i	$0.223224\pi$
$769$			763088.i			1.29039i	−0.764017	+	0.645196i	$0.776776\pi$
$770$	133664.	−	381754.i	0.225442	−	0.643877i
$771$	320123.			0.538528
$772$	167193.	+	167193.i	0.280533	+	0.280533i
$773$	−583340.	+	583340.i	−0.976254	+	0.976254i	−0.999725	−	0.0234705i	$-0.992528\pi$
$773$	−583340.	+	583340.i	−0.976254	+	0.976254i	0.0234705	+	0.999725i	$0.492528\pi$
$774$		−	280488.i		−	0.468202i
$775$	695756.	+	555287.i	1.15839	+	0.924515i
$776$	273713.			0.454539
$777$	138201.	+	138201.i	0.228913	+	0.228913i
$778$	14128.8	−	14128.8i	0.0233424	−	0.0233424i
$779$			107793.i			0.177630i
$780$	−343469.	−	120259.i	−0.564544	−	0.197665i
$781$	863412.			1.41552
$782$	−49118.0	−	49118.0i	−0.0803207	−	0.0803207i
$783$	18624.1	−	18624.1i	0.0303774	−	0.0303774i
$784$		−	32326.3i		−	0.0525925i
$785$	215320.	+	447337.i	0.349418	+	0.725932i
$786$	−421253.			−0.681864
$787$	228926.	+	228926.i	0.369612	+	0.369612i	0.867336	−	0.497724i	$-0.165831\pi$
$787$	228926.	+	228926.i	0.369612	+	0.369612i	−0.497724	+	0.867336i	$0.665831\pi$
$788$	−95094.8	+	95094.8i	−0.153145	+	0.153145i
$789$		−	274541.i		−	0.441015i
$790$	202006.	−	97233.0i	0.323676	−	0.155797i
$791$	−282648.			−0.451745
$792$	53652.8	+	53652.8i	0.0855346	+	0.0855346i
$793$	−265747.	+	265747.i	−0.422592	+	0.422592i
$794$			736017.i			1.16747i
$795$	217149.	−	620192.i	0.343577	−	0.981278i
$796$	−319221.			−0.503808
$797$	−371964.	−	371964.i	−0.585577	−	0.585577i	0.350853	−	0.936431i	$-0.385892\pi$
$797$	−371964.	−	371964.i	−0.585577	−	0.585577i	−0.936431	+	0.350853i	$0.885892\pi$
$798$	300242.	−	300242.i	0.471483	−	0.471483i
$799$			61943.6i			0.0970293i
$800$	−12623.9	−	112431.i	−0.0197249	−	0.175673i
$801$	407379.			0.634941
$802$	−141878.	−	141878.i	−0.220580	−	0.220580i
$803$	−719722.	+	719722.i	−1.11618	+	1.11618i
$804$		−	527511.i		−	0.816055i
$805$	140306.	+	49125.5i	0.216513	+	0.0758081i
$806$	690776.			1.06333
$807$	−265808.	−	265808.i	−0.408152	−	0.408152i
$808$	215268.	−	215268.i	0.329729	−	0.329729i
$809$			169626.i			0.259176i	0.991568	+	0.129588i	$0.0413655\pi$
$809$			169626.i			0.259176i	−0.991568	+	0.129588i	$0.958635\pi$
$810$	−249087.	−	517490.i	−0.379648	−	0.788737i
$811$	−325773.			−0.495306			−0.247653	−	0.968849i	$-0.579659\pi$
$811$	−325773.			−0.495306			−0.247653	+	0.968849i	$0.579659\pi$
$812$	15322.8	+	15322.8i	0.0232395	+	0.0232395i
$813$	−638346.	+	638346.i	−0.965772	+	0.965772i
$814$			102541.i			0.154757i
$815$	−896353.	+	431448.i	−1.34947	+	0.649551i
$816$	−151207.			−0.227087
$817$	−582306.	−	582306.i	−0.872382	−	0.872382i
$818$	412354.	−	412354.i	0.616260	−	0.616260i
$819$		−	292124.i		−	0.435511i
$820$	−27147.4	+	77534.9i	−0.0403739	+	0.115311i
$821$	−111073.			−0.164787			−0.0823934	−	0.996600i	$-0.526256\pi$
$821$	−111073.			−0.164787			−0.0823934	+	0.996600i	$0.526256\pi$
$822$	150467.	+	150467.i	0.222688	+	0.222688i
$823$	740664.	−	740664.i	1.09351	−	1.09351i	0.0983558	−	0.995151i	$-0.468642\pi$
$823$	740664.	−	740664.i	1.09351	−	1.09351i	0.995151	−	0.0983558i	$-0.0313583\pi$
$824$		−	346478.i		−	0.510295i
$825$	699339.	−	78523.2i	1.02750	−	0.115369i
$826$	187494.			0.274807
$827$	−137778.	−	137778.i	−0.201451	−	0.201451i	0.599171	−	0.800621i	$-0.295497\pi$
$827$	−137778.	−	137778.i	−0.201451	−	0.201451i	−0.800621	+	0.599171i	$0.795497\pi$
$828$	−19719.0	+	19719.0i	−0.0287623	+	0.0287623i
$829$			873122.i			1.27047i	0.772317	+	0.635237i	$0.219098\pi$
$829$			873122.i			1.27047i	−0.772317	+	0.635237i	$0.780902\pi$
$830$	185288.	+	64875.2i	0.268962	+	0.0941722i
$831$	957387.			1.38639
$832$	−62079.7	−	62079.7i	−0.0896815	−	0.0896815i
$833$	−79520.6	+	79520.6i	−0.114601	+	0.114601i
$834$		−	925741.i		−	1.33094i
$835$	−323807.	−	672725.i	−0.464423	−	0.964860i
$836$	222771.			0.318747
$837$	527915.	+	527915.i	0.753551	+	0.753551i
$838$	−277087.	+	277087.i	−0.394574	+	0.394574i
$839$			151170.i			0.214755i	0.994218	+	0.107377i	$0.0342453\pi$
$839$			151170.i			0.214755i	−0.994218	+	0.107377i	$0.965755\pi$
$840$	291577.	−	140347.i	0.413233	−	0.198904i
$841$	704756.			0.996430
$842$	−444604.	−	444604.i	−0.627118	−	0.627118i
$843$	−892743.	+	892743.i	−1.25624	+	1.25624i
$844$			230681.i			0.323838i
$845$	−6954.84	+	19863.5i	−0.00974034	+	0.0278191i
$846$	24867.9			0.0347455
$847$	−128908.	−	128908.i	−0.179686	−	0.179686i
$848$	112096.	−	112096.i	0.155882	−	0.155882i
$849$		−	522763.i		−	0.725253i
$850$	−245518.	+	307626.i	−0.339818	+	0.425781i
$851$	−37686.9			−0.0520392
$852$	488440.	+	488440.i	0.672872	+	0.672872i
$853$	570694.	−	570694.i	0.784341	−	0.784341i	−0.196219	−	0.980560i	$-0.562866\pi$
$853$	570694.	−	570694.i	0.784341	−	0.784341i	0.980560	+	0.196219i	$0.0628664\pi$
$854$		−	334186.i		−	0.458219i
$855$	195686.	+	68515.9i	0.267687	+	0.0937258i
$856$	−12377.1			−0.0168917
$857$	−568492.	−	568492.i	−0.774039	−	0.774039i	0.204771	−	0.978810i	$-0.434355\pi$
$857$	−568492.	−	568492.i	−0.774039	−	0.774039i	−0.978810	+	0.204771i	$0.934355\pi$
$858$	386147.	−	386147.i	0.524540	−	0.524540i
$859$			582040.i			0.788799i	0.918939	+	0.394399i	$0.129047\pi$
$859$			582040.i			0.788799i	−0.918939	+	0.394399i	$0.870953\pi$
$860$	−272196.	−	565500.i	−0.368032	−	0.764603i
$861$	−234967.			−0.316957
$862$	−484690.	−	484690.i	−0.652303	−	0.652303i
$863$	−140875.	+	140875.i	−0.189153	+	0.189153i	−0.795330	−	0.606177i	$-0.792702\pi$
$863$	−140875.	+	140875.i	−0.189153	+	0.189153i	0.606177	+	0.795330i	$0.292702\pi$
$864$		−	94886.9i		−	0.127110i
$865$	503764.	−	242480.i	0.673278	−	0.324074i
$866$	−246605.			−0.328826
$867$	−254731.	−	254731.i	−0.338879	−	0.338879i
$868$	−434338.	+	434338.i	−0.576485	+	0.576485i
$869$			336422.i			0.445497i
$870$	−12459.1	+	35584.1i	−0.0164607	+	0.0470130i
$871$	−1.06552e6			−1.40452
$872$	64118.1	+	64118.1i	0.0843233	+	0.0843233i
$873$	−270310.	+	270310.i	−0.354677	+	0.354677i
$874$			81874.8i			0.107183i
$875$	187908.	−	821089.i	0.245431	−	1.07244i
$876$	−814308.			−1.06116
$877$	−177798.	−	177798.i	−0.231168	−	0.231168i	0.582012	−	0.813180i	$-0.302266\pi$
$877$	−177798.	−	177798.i	−0.231168	−	0.231168i	−0.813180	+	0.582012i	$0.802266\pi$
$878$	−522960.	+	522960.i	−0.678391	+	0.678391i
$879$			667648.i			0.864112i
$880$	160237.	+	56104.2i	0.206918	+	0.0724486i
$881$	1.30004e6			1.67496			0.837480	−	0.546468i	$-0.184028\pi$
$881$	1.30004e6			1.67496			0.837480	+	0.546468i	$0.184028\pi$
$882$	31924.4	+	31924.4i	0.0410380	+	0.0410380i
$883$	−644541.	+	644541.i	−0.826664	+	0.826664i	−0.987054	−	0.160390i	$-0.948725\pi$
$883$	−644541.	+	644541.i	−0.826664	+	0.826664i	0.160390	+	0.987054i	$0.448725\pi$
$884$			305425.i			0.390840i
$885$	141482.	+	293935.i	0.180640	+	0.375288i
$886$	286916.			0.365500
$887$	−606798.	−	606798.i	−0.771254	−	0.771254i	0.207072	−	0.978326i	$-0.433607\pi$
$887$	−606798.	−	606798.i	−0.771254	−	0.771254i	−0.978326	+	0.207072i	$0.933607\pi$
$888$	−58008.5	+	58008.5i	−0.0735641	+	0.0735641i
$889$		−	686800.i		−	0.869014i
$890$	821328.	−	395335.i	1.03690	−	0.499098i
$891$	861831.			1.08559
$892$	548356.	+	548356.i	0.689180	+	0.689180i
$893$	51626.8	−	51626.8i	0.0647400	−	0.0647400i
$894$		−	171773.i		−	0.214921i
$895$	−293162.	+	837291.i	−0.365984	+	1.04527i
$896$	78067.5			0.0972420
$897$	141920.	+	141920.i	0.176384	+	0.176384i
$898$	−23607.9	+	23607.9i	−0.0292755	+	0.0292755i
$899$		−	71565.9i		−	0.0885497i
$900$	123500.	+	98565.9i	0.152469	+	0.121686i
$901$	−551497.			−0.679350
$902$	−87169.2	−	87169.2i	−0.107140	−	0.107140i
$903$	1.26931e6	−	1.26931e6i	1.55665	−	1.55665i
$904$		−	118639.i		−	0.145174i
$905$	−331676.	−	116130.i	−0.404965	−	0.141791i
$906$	−471323.			−0.574199
$907$	1.06968e6	+	1.06968e6i	1.30029	+	1.30029i	0.928194	+	0.372096i	$0.121361\pi$
$907$	1.06968e6	+	1.06968e6i	1.30029	+	1.30029i	0.372096	+	0.928194i	$0.378639\pi$
$908$	−301049.	+	301049.i	−0.365145	+	0.365145i
$909$			425184.i			0.514576i
$910$	−283488.	−	588959.i	−0.342335	−	0.711217i
$911$	76680.2			0.0923946			0.0461973	−	0.998932i	$-0.485290\pi$
$911$	76680.2			0.0923946			0.0461973	+	0.998932i	$0.485290\pi$
$912$	126024.	+	126024.i	0.151517	+	0.151517i
$913$	−208311.	+	208311.i	−0.249903	+	0.249903i
$914$			223955.i			0.268082i
$915$	523904.	−	252175.i	0.625763	−	0.301203i
$916$	−508394.			−0.605912
$917$	−535014.	−	535014.i	−0.636248	−	0.636248i
$918$	−233416.	+	233416.i	−0.276978	+	0.276978i
$919$			522345.i			0.618482i	0.950984	+	0.309241i	$0.100075\pi$
$919$			522345.i			0.618482i	−0.950984	+	0.309241i	$0.899925\pi$
$920$	−20619.9	+	58891.9i	−0.0243619	+	0.0695793i
$921$	−427561.			−0.504056
$922$	134827.	+	134827.i	0.158604	+	0.158604i
$923$	986604.	−	986604.i	1.15808	−	1.15808i
$924$			485594.i			0.568761i
$925$	23826.9	+	212206.i	0.0278474	+	0.248013i
$926$	−32535.8			−0.0379437
$927$	342171.	+	342171.i	0.398184	+	0.398184i
$928$	−6431.59	+	6431.59i	−0.00746832	+	0.00746832i
$929$			518912.i			0.601260i	0.953741	+	0.300630i	$0.0971969\pi$
$929$			518912.i			0.601260i	−0.953741	+	0.300630i	$0.902803\pi$
$930$	−1.00866e6	−	353164.i	−1.16622	−	0.408329i
$931$	132553.			0.152929
$932$	554297.	+	554297.i	0.638133	+	0.638133i
$933$	−973895.	+	973895.i	−1.11879	+	1.11879i
$934$		−	206119.i		−	0.236278i
$935$	−256161.	−	532187.i	−0.293015	−	0.608753i
$936$	122616.			0.139957
$937$	895452.	+	895452.i	1.01991	+	1.01991i	0.999798	+	0.0201153i	$0.00640332\pi$
$937$	895452.	+	895452.i	1.01991	+	1.01991i	0.0201153	+	0.999798i	$0.493597\pi$
$938$	669967.	−	669967.i	0.761461	−	0.761461i
$939$		−	821099.i		−	0.931246i
$940$	50136.9	−	24132.7i	0.0567416	−	0.0273118i
$941$	−919228.			−1.03811			−0.519056	−	0.854740i	$-0.673716\pi$
$941$	−919228.			−1.03811			−0.519056	+	0.854740i	$0.673716\pi$
$942$	−421452.	−	421452.i	−0.474949	−	0.474949i
$943$	32037.2	−	32037.2i	0.0360273	−	0.0360273i
$944$			78698.7i			0.0883128i
$945$	233452.	−	666753.i	0.261417	−	0.746623i
$946$	941787.			1.05237
$947$	354441.	+	354441.i	0.395225	+	0.395225i	0.876545	−	0.481320i	$-0.159842\pi$
$947$	354441.	+	354441.i	0.395225	+	0.395225i	−0.481320	+	0.876545i	$0.659842\pi$
$948$	−190317.	+	190317.i	−0.211768	+	0.211768i
$949$			1.64483e6i			1.82636i
$950$	461018.	−	51764.0i	0.510823	−	0.0573563i
$951$	−1.44436e6			−1.59703
$952$	−192041.	−	192041.i	−0.211895	−	0.211895i
$953$	−356072.	+	356072.i	−0.392059	+	0.392059i	−0.875421	−	0.483362i	$-0.839416\pi$
$953$	−356072.	+	356072.i	−0.392059	+	0.392059i	0.483362	+	0.875421i	$0.339416\pi$
$954$			221404.i			0.243271i
$955$	736483.	+	257866.i	0.807525	+	0.282740i
$956$	−22793.8			−0.0249402
$957$	−40005.7	−	40005.7i	−0.0436816	−	0.0436816i
$958$	−539332.	+	539332.i	−0.587658	+	0.587658i
$959$			382202.i			0.415581i
$960$	58909.1	+	122387.i	0.0639205	+	0.132798i
$961$	1.10507e6			1.19659
$962$	117172.	+	117172.i	0.126611	+	0.126611i
$963$	12223.3	−	12223.3i	0.0131806	−	0.0131806i
$964$		−	205374.i		−	0.221000i
$965$	−665785.	+	320467.i	−0.714956	+	0.344135i
$966$	−178470.			−0.191254
$967$	−1.28918e6	−	1.28918e6i	−1.37867	−	1.37867i	−0.846862	−	0.531813i	$-0.821511\pi$
$967$	−1.28918e6	−	1.28918e6i	−1.37867	−	1.37867i	−0.531813	−	0.846862i	$-0.678489\pi$
$968$	54107.8	−	54107.8i	0.0577443	−	0.0577443i
$969$		−	620021.i		−	0.660326i
$970$	−282661.	+	807298.i	−0.300415	+	0.858006i
$971$	341126.			0.361806			0.180903	−	0.983501i	$-0.442098\pi$
$971$	341126.			0.361806			0.180903	+	0.983501i	$0.442098\pi$
$972$	247364.	+	247364.i	0.261820	+	0.261820i
$973$	1.17574e6	−	1.17574e6i	1.24190	−	1.24190i
$974$			1.20671e6i			1.27199i
$975$	709394.	−	888848.i	0.746240	−	0.935014i
$976$	140271.			0.147255
$977$	140319.	+	140319.i	0.147004	+	0.147004i	0.776778	−	0.629775i	$-0.216853\pi$
$977$	140319.	+	140319.i	0.147004	+	0.147004i	−0.629775	+	0.776778i	$0.716853\pi$
$978$	844486.	−	844486.i	0.882906	−	0.882906i
$979$			1.36784e6i			1.42715i
$980$	95344.3	+	33383.1i	0.0992756	+	0.0347595i
$981$	−126642.			−0.131595
$982$	−431627.	−	431627.i	−0.447595	−	0.447595i
$983$	−44003.1	+	44003.1i	−0.0455383	+	0.0455383i	−0.729509	−	0.683971i	$-0.760251\pi$
$983$	−44003.1	+	44003.1i	−0.0455383	+	0.0455383i	0.683971	+	0.729509i	$0.260251\pi$
$984$		−	98624.9i		−	0.101858i
$985$	−182272.	−	378680.i	−0.187866	−	0.390301i
$986$	31642.7			0.0325476
$987$	112536.	+	112536.i	0.115520	+	0.115520i
$988$	254556.	−	254556.i	0.260777	−	0.260777i
$989$			346134.i			0.353877i
$990$	−213652.	+	102839.i	−0.217990	+	0.104927i
$991$	38362.4			0.0390623			0.0195312	−	0.999809i	$-0.493783\pi$
$991$	38362.4			0.0390623			0.0195312	+	0.999809i	$0.493783\pi$
$992$	−182309.	−	182309.i	−0.185261	−	0.185261i
$993$	18602.5	−	18602.5i	0.0188656	−	0.0188656i
$994$			1.24069e6i			1.25571i
$995$	329657.	−	941521.i	0.332978	−	0.951007i
$996$	−235688.			−0.237584
$997$	1.21832e6	+	1.21832e6i	1.22566	+	1.22566i	0.965588	+	0.260076i	$0.0837477\pi$
$997$	1.21832e6	+	1.21832e6i	1.22566	+	1.22566i	0.260076	+	0.965588i	$0.416252\pi$
$998$	−496793.	+	496793.i	−0.498786	+	0.498786i
$999$			179093.i			0.179452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.f.b.47.18	✓	44
5.3	odd	4	inner	230.5.f.b.93.18	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.f.b.47.18	✓	44	1.1	even	1	trivial
230.5.f.b.93.18	yes	44	5.3	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 2.00000i) q^{2} +(7.50341 - 7.50341i) q^{3} +8.00000i q^{4} +(-23.5955 - 8.26153i) q^{5} +30.0136 q^{6} +(38.1189 + 38.1189i) q^{7} +(-16.0000 + 16.0000i) q^{8} -31.6022i q^{9} +O(q^{10})\)	\(q+(2.00000 + 2.00000i) q^{2} +(7.50341 - 7.50341i) q^{3} +8.00000i q^{4} +(-23.5955 - 8.26153i) q^{5} +30.0136 q^{6} +(38.1189 + 38.1189i) q^{7} +(-16.0000 + 16.0000i) q^{8} -31.6022i q^{9} +(-30.6679 - 63.7140i) q^{10} +106.110 q^{11} +(60.0272 + 60.0272i) q^{12} +(121.249 - 121.249i) q^{13} +152.476i q^{14} +(-239.036 + 115.057i) q^{15} -64.0000 q^{16} +(157.436 + 157.436i) q^{17} +(63.2044 - 63.2044i) q^{18} -262.430i q^{19} +(66.0922 - 188.764i) q^{20} +572.043 q^{21} +(212.219 + 212.219i) q^{22} +(-77.9968 + 77.9968i) q^{23} +240.109i q^{24} +(488.494 + 389.870i) q^{25} +484.998 q^{26} +(370.652 + 370.652i) q^{27} +(-304.951 + 304.951i) q^{28} -50.2468i q^{29} +(-708.186 - 247.958i) q^{30} +1424.29 q^{31} +(-128.000 - 128.000i) q^{32} +(796.184 - 796.184i) q^{33} +629.744i q^{34} +(-584.513 - 1214.35i) q^{35} +252.818 q^{36} +(241.592 + 241.592i) q^{37} +(524.860 - 524.860i) q^{38} -1819.57i q^{39} +(509.712 - 245.343i) q^{40} -410.751 q^{41} +(1144.09 + 1144.09i) q^{42} +(2218.90 - 2218.90i) q^{43} +848.877i q^{44} +(-261.083 + 745.669i) q^{45} -311.987 q^{46} +(196.726 + 196.726i) q^{47} +(-480.218 + 480.218i) q^{48} +505.098i q^{49} +(197.249 + 1756.73i) q^{50} +2362.61 q^{51} +(969.995 + 969.995i) q^{52} +(-1751.50 + 1751.50i) q^{53} +1482.61i q^{54} +(-2503.71 - 876.628i) q^{55} -1219.80 q^{56} +(-1969.12 - 1969.12i) q^{57} +(100.494 - 100.494i) q^{58} -1229.67i q^{59} +(-920.455 - 1912.29i) q^{60} -2191.74 q^{61} +(2848.57 + 2848.57i) q^{62} +(1204.64 - 1204.64i) q^{63} -512.000i q^{64} +(-3862.64 + 1859.23i) q^{65} +3184.74 q^{66} +(-4393.93 - 4393.93i) q^{67} +(-1259.49 + 1259.49i) q^{68} +1170.48i q^{69} +(1259.68 - 3597.73i) q^{70} +8136.98 q^{71} +(505.635 + 505.635i) q^{72} +(-6782.82 + 6782.82i) q^{73} +966.370i q^{74} +(6590.72 - 740.020i) q^{75} +2099.44 q^{76} +(4044.78 + 4044.78i) q^{77} +(3639.13 - 3639.13i) q^{78} +3170.51i q^{79} +(1510.11 + 528.738i) q^{80} +8122.08 q^{81} +(-821.501 - 821.501i) q^{82} +(-1963.17 + 1963.17i) q^{83} +4576.34i q^{84} +(-2414.12 - 5015.44i) q^{85} +8875.60 q^{86} +(-377.022 - 377.022i) q^{87} +(-1697.75 + 1697.75i) q^{88} +12890.8i q^{89} +(-2013.50 + 969.173i) q^{90} +9243.78 q^{91} +(-623.974 - 623.974i) q^{92} +(10687.0 - 10687.0i) q^{93} +786.905i q^{94} +(-2168.07 + 6192.16i) q^{95} -1920.87 q^{96} +(-8553.52 - 8553.52i) q^{97} +(-1010.20 + 1010.20i) q^{98} -3353.30i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8}+O(q^{10}) \) 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8	\( 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8} - 136 q^{10} - 632 q^{11} + 500 q^{13} + 12 q^{15} - 2816 q^{16} + 120 q^{17} + 2648 q^{18} - 736 q^{20} - 856 q^{21} - 1264 q^{22} + 2052 q^{25} + 2000 q^{26} + 588 q^{27} + 640 q^{28} - 1704 q^{30} + 3220 q^{31} - 5632 q^{32} - 2884 q^{33} + 720 q^{35} + 10592 q^{36} + 1856 q^{37} - 1696 q^{38} - 1856 q^{40} - 5156 q^{41} - 1712 q^{42} + 960 q^{43} + 460 q^{45} - 1224 q^{47} + 4456 q^{50} + 3640 q^{51} + 4000 q^{52} + 13556 q^{53} + 12980 q^{55} + 2560 q^{56} - 3072 q^{57} - 3112 q^{58} - 6912 q^{60} - 4864 q^{61} + 6440 q^{62} - 13484 q^{63} - 4100 q^{65} - 11536 q^{66} - 1888 q^{67} - 960 q^{68} + 8824 q^{70} - 1060 q^{71} + 21184 q^{72} + 16616 q^{73} - 11044 q^{75} - 6784 q^{76} + 8892 q^{77} - 23152 q^{78} - 1536 q^{80} - 4044 q^{81} - 10312 q^{82} - 27024 q^{83} - 11068 q^{85} + 3840 q^{86} - 8392 q^{87} + 10112 q^{88} - 7184 q^{90} - 54024 q^{91} + 22528 q^{93} - 25968 q^{95} - 3252 q^{97} - 27984 q^{98}+O(q^{100}) \) 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8 - 136 * q^10 - 632 * q^11 + 500 * q^13 + 12 * q^15 - 2816 * q^16 + 120 * q^17 + 2648 * q^18 - 736 * q^20 - 856 * q^21 - 1264 * q^22 + 2052 * q^25 + 2000 * q^26 + 588 * q^27 + 640 * q^28 - 1704 * q^30 + 3220 * q^31 - 5632 * q^32 - 2884 * q^33 + 720 * q^35 + 10592 * q^36 + 1856 * q^37 - 1696 * q^38 - 1856 * q^40 - 5156 * q^41 - 1712 * q^42 + 960 * q^43 + 460 * q^45 - 1224 * q^47 + 4456 * q^50 + 3640 * q^51 + 4000 * q^52 + 13556 * q^53 + 12980 * q^55 + 2560 * q^56 - 3072 * q^57 - 3112 * q^58 - 6912 * q^60 - 4864 * q^61 + 6440 * q^62 - 13484 * q^63 - 4100 * q^65 - 11536 * q^66 - 1888 * q^67 - 960 * q^68 + 8824 * q^70 - 1060 * q^71 + 21184 * q^72 + 16616 * q^73 - 11044 * q^75 - 6784 * q^76 + 8892 * q^77 - 23152 * q^78 - 1536 * q^80 - 4044 * q^81 - 10312 * q^82 - 27024 * q^83 - 11068 * q^85 + 3840 * q^86 - 8392 * q^87 + 10112 * q^88 - 7184 * q^90 - 54024 * q^91 + 22528 * q^93 - 25968 * q^95 - 3252 * q^97 - 27984 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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