LMFDB - Embedded newform 230.5.f.b.47.9

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			47.9
Character	$\chi$	$=$	230.47
Dual form			230.5.f.b.93.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 2.00000i) q^{2} +(-4.05030 + 4.05030i) q^{3} +8.00000i q^{4} +(-24.3623 + 5.61047i) q^{5} -16.2012 q^{6} +(52.2645 + 52.2645i) q^{7} +(-16.0000 + 16.0000i) q^{8} +48.1901i q^{9} +O(q^{10})$	\(q+(2.00000 + 2.00000i) q^{2} +(-4.05030 + 4.05030i) q^{3} +8.00000i q^{4} +(-24.3623 + 5.61047i) q^{5} -16.2012 q^{6} +(52.2645 + 52.2645i) q^{7} +(-16.0000 + 16.0000i) q^{8} +48.1901i q^{9} +(-59.9456 - 37.5037i) q^{10} -41.6934 q^{11} +(-32.4024 - 32.4024i) q^{12} +(-35.5309 + 35.5309i) q^{13} +209.058i q^{14} +(75.9506 - 121.399i) q^{15} -64.0000 q^{16} +(59.1014 + 59.1014i) q^{17} +(-96.3803 + 96.3803i) q^{18} +32.4431i q^{19} +(-44.8838 - 194.899i) q^{20} -423.373 q^{21} +(-83.3868 - 83.3868i) q^{22} +(77.9968 - 77.9968i) q^{23} -129.610i q^{24} +(562.045 - 273.368i) q^{25} -142.124 q^{26} +(-523.259 - 523.259i) q^{27} +(-418.116 + 418.116i) q^{28} -163.050i q^{29} +(394.699 - 90.8963i) q^{30} -1708.49 q^{31} +(-128.000 - 128.000i) q^{32} +(168.871 - 168.871i) q^{33} +236.406i q^{34} +(-1566.51 - 980.055i) q^{35} -385.521 q^{36} +(-1297.57 - 1297.57i) q^{37} +(-64.8862 + 64.8862i) q^{38} -287.822i q^{39} +(300.030 - 479.565i) q^{40} +764.559 q^{41} +(-846.747 - 846.747i) q^{42} +(31.7858 - 31.7858i) q^{43} -333.547i q^{44} +(-270.369 - 1174.02i) q^{45} +311.987 q^{46} +(653.641 + 653.641i) q^{47} +(259.219 - 259.219i) q^{48} +3062.15i q^{49} +(1670.83 + 577.354i) q^{50} -478.757 q^{51} +(-284.247 - 284.247i) q^{52} +(3107.63 - 3107.63i) q^{53} -2093.04i q^{54} +(1015.75 - 233.920i) q^{55} -1672.46 q^{56} +(-131.404 - 131.404i) q^{57} +(326.100 - 326.100i) q^{58} +1210.26i q^{59} +(971.190 + 607.605i) q^{60} +9.70215 q^{61} +(-3416.98 - 3416.98i) q^{62} +(-2518.63 + 2518.63i) q^{63} -512.000i q^{64} +(666.270 - 1064.96i) q^{65} +675.483 q^{66} +(-216.280 - 216.280i) q^{67} +(-472.812 + 472.812i) q^{68} +631.821i q^{69} +(-1172.91 - 5093.13i) q^{70} +577.704 q^{71} +(-771.042 - 771.042i) q^{72} +(-6383.73 + 6383.73i) q^{73} -5190.27i q^{74} +(-1169.23 + 3383.67i) q^{75} -259.545 q^{76} +(-2179.08 - 2179.08i) q^{77} +(575.643 - 575.643i) q^{78} +6560.96i q^{79} +(1559.19 - 359.070i) q^{80} +335.309 q^{81} +(1529.12 + 1529.12i) q^{82} +(888.906 - 888.906i) q^{83} -3386.99i q^{84} +(-1771.44 - 1108.26i) q^{85} +127.143 q^{86} +(660.401 + 660.401i) q^{87} +(667.095 - 667.095i) q^{88} -4476.59i q^{89} +(1807.31 - 2888.79i) q^{90} -3714.01 q^{91} +(623.974 + 623.974i) q^{92} +(6919.90 - 6919.90i) q^{93} +2614.57i q^{94} +(-182.021 - 790.389i) q^{95} +1036.88 q^{96} +(9053.65 + 9053.65i) q^{97} +(-6124.30 + 6124.30i) q^{98} -2009.21i 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
$3$	−4.05030	+	4.05030i	−0.450033	+	0.450033i	−0.895365	−	0.445332i	$-0.853086\pi$
$3$	−4.05030	+	4.05030i	−0.450033	+	0.450033i	0.445332	+	0.895365i	$0.353086\pi$
$4$			8.00000i			0.500000i
$5$	−24.3623	+	5.61047i	−0.974493	+	0.224419i
$5$	−24.3623	+	5.61047i	−0.974493	+	0.224419i
$6$	−16.2012			−0.450033
$7$	52.2645	+	52.2645i	1.06662	+	1.06662i	0.997616	+	0.0690054i	$0.0219826\pi$
$7$	52.2645	+	52.2645i	1.06662	+	1.06662i	0.0690054	+	0.997616i	$0.478017\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$			48.1901i			0.594940i
$10$	−59.9456	−	37.5037i	−0.599456	−	0.375037i
$11$	−41.6934			−0.344574			−0.172287	−	0.985047i	$-0.555116\pi$
$11$	−41.6934			−0.344574			−0.172287	+	0.985047i	$0.555116\pi$
$12$	−32.4024	−	32.4024i	−0.225017	−	0.225017i
$13$	−35.5309	+	35.5309i	−0.210242	+	0.210242i	−0.804370	−	0.594128i	$-0.797497\pi$
$13$	−35.5309	+	35.5309i	−0.210242	+	0.210242i	0.594128	+	0.804370i	$0.297497\pi$
$14$			209.058i			1.06662i
$15$	75.9506	−	121.399i	0.337558	−	0.539550i
$16$	−64.0000			−0.250000
$17$	59.1014	+	59.1014i	0.204503	+	0.204503i	0.801926	−	0.597423i	$-0.203809\pi$
$17$	59.1014	+	59.1014i	0.204503	+	0.204503i	−0.597423	+	0.801926i	$0.703809\pi$
$18$	−96.3803	+	96.3803i	−0.297470	+	0.297470i
$19$			32.4431i			0.0898700i	0.998990	+	0.0449350i	$0.0143081\pi$
$19$			32.4431i			0.0898700i	−0.998990	+	0.0449350i	$0.985692\pi$
$20$	−44.8838	−	194.899i	−0.112209	−	0.487246i
$21$	−423.373			−0.960031
$22$	−83.3868	−	83.3868i	−0.172287	−	0.172287i
$23$	77.9968	−	77.9968i	0.147442	−	0.147442i
$23$	77.9968	−	77.9968i	0.147442	−	0.147442i
$24$		−	129.610i		−	0.225017i
$25$	562.045	−	273.368i	0.899272	−	0.437389i
$26$	−142.124			−0.210242
$27$	−523.259	−	523.259i	−0.717776	−	0.717776i
$28$	−418.116	+	418.116i	−0.533311	+	0.533311i
$29$		−	163.050i		−	0.193876i	−0.995290	−	0.0969380i	$-0.969095\pi$
$29$		−	163.050i		−	0.193876i	0.995290	−	0.0969380i	$-0.0309049\pi$
$30$	394.699	−	90.8963i	0.438554	−	0.100996i
$31$	−1708.49			−1.77783			−0.888913	−	0.458077i	$-0.848539\pi$
$31$	−1708.49			−1.77783			−0.888913	+	0.458077i	$0.848539\pi$
$32$	−128.000	−	128.000i	−0.125000	−	0.125000i
$33$	168.871	−	168.871i	0.155070	−	0.155070i
$34$			236.406i			0.204503i
$35$	−1566.51	−	980.055i	−1.27879	−	0.800045i
$36$	−385.521			−0.297470
$37$	−1297.57	−	1297.57i	−0.947822	−	0.947822i	0.0508829	−	0.998705i	$-0.483796\pi$
$37$	−1297.57	−	1297.57i	−0.947822	−	0.947822i	−0.998705	+	0.0508829i	$0.983796\pi$
$38$	−64.8862	+	64.8862i	−0.0449350	+	0.0449350i
$39$		−	287.822i		−	0.189232i
$40$	300.030	−	479.565i	0.187518	−	0.299728i
$41$	764.559			0.454824			0.227412	−	0.973799i	$-0.426974\pi$
$41$	764.559			0.454824			0.227412	+	0.973799i	$0.426974\pi$
$42$	−846.747	−	846.747i	−0.480015	−	0.480015i
$43$	31.7858	−	31.7858i	0.0171908	−	0.0171908i	−0.698459	−	0.715650i	$-0.746131\pi$
$43$	31.7858	−	31.7858i	0.0171908	−	0.0171908i	0.715650	+	0.698459i	$0.246131\pi$
$44$		−	333.547i		−	0.172287i
$45$	−270.369	−	1174.02i	−0.133516	−	0.579765i
$46$	311.987			0.147442
$47$	653.641	+	653.641i	0.295899	+	0.295899i	0.839405	−	0.543506i	$-0.182904\pi$
$47$	653.641	+	653.641i	0.295899	+	0.295899i	−0.543506	+	0.839405i	$0.682904\pi$
$48$	259.219	−	259.219i	0.112508	−	0.112508i
$49$			3062.15i			1.27536i
$50$	1670.83	+	577.354i	0.668331	+	0.230942i
$51$	−478.757			−0.184067
$52$	−284.247	−	284.247i	−0.105121	−	0.105121i
$53$	3107.63	−	3107.63i	1.10631	−	1.10631i	0.112682	−	0.993631i	$-0.464056\pi$
$53$	3107.63	−	3107.63i	1.10631	−	1.10631i	0.993631	−	0.112682i	$-0.0359442\pi$
$54$		−	2093.04i		−	0.717776i
$55$	1015.75	−	233.920i	0.335785	−	0.0773288i
$56$	−1672.46			−0.533311
$57$	−131.404	−	131.404i	−0.0404445	−	0.0404445i
$58$	326.100	−	326.100i	0.0969380	−	0.0969380i
$59$			1210.26i			0.347676i	0.984774	+	0.173838i	$0.0556169\pi$
$59$			1210.26i			0.347676i	−0.984774	+	0.173838i	$0.944383\pi$
$60$	971.190	+	607.605i	0.269775	+	0.168779i
$61$	9.70215			0.00260740			0.00130370	−	0.999999i	$-0.499585\pi$
$61$	9.70215			0.00260740			0.00130370	+	0.999999i	$0.499585\pi$
$62$	−3416.98	−	3416.98i	−0.888913	−	0.888913i
$63$	−2518.63	+	2518.63i	−0.634576	+	0.634576i
$64$		−	512.000i		−	0.125000i
$65$	666.270	−	1064.96i	0.157697	−	0.252062i
$66$	675.483			0.155070
$67$	−216.280	−	216.280i	−0.0481800	−	0.0481800i	0.682606	−	0.730786i	$-0.260846\pi$
$67$	−216.280	−	216.280i	−0.0481800	−	0.0481800i	−0.730786	+	0.682606i	$0.760846\pi$
$68$	−472.812	+	472.812i	−0.102252	+	0.102252i
$69$			631.821i			0.132708i
$70$	−1172.91	−	5093.13i	−0.239370	−	1.03942i
$71$	577.704			0.114601			0.0573005	−	0.998357i	$-0.481751\pi$
$71$	577.704			0.114601			0.0573005	+	0.998357i	$0.481751\pi$
$72$	−771.042	−	771.042i	−0.148735	−	0.148735i
$73$	−6383.73	+	6383.73i	−1.19792	+	1.19792i	−0.223134	+	0.974788i	$0.571629\pi$
$73$	−6383.73	+	6383.73i	−1.19792	+	1.19792i	−0.974788	+	0.223134i	$0.928371\pi$
$74$		−	5190.27i		−	0.947822i
$75$	−1169.23	+	3383.67i	−0.207863	+	0.601542i
$76$	−259.545			−0.0449350
$77$	−2179.08	−	2179.08i	−0.367530	−	0.367530i
$78$	575.643	−	575.643i	0.0946159	−	0.0946159i
$79$			6560.96i			1.05127i	0.850711	+	0.525634i	$0.176172\pi$
$79$			6560.96i			1.05127i	−0.850711	+	0.525634i	$0.823828\pi$
$80$	1559.19	−	359.070i	0.243623	−	0.0561047i
$81$	335.309			0.0511063
$82$	1529.12	+	1529.12i	0.227412	+	0.227412i
$83$	888.906	−	888.906i	0.129033	−	0.129033i	−0.639641	−	0.768674i	$-0.720917\pi$
$83$	888.906	−	888.906i	0.129033	−	0.129033i	0.768674	+	0.639641i	$0.220917\pi$
$84$		−	3386.99i		−	0.480015i
$85$	−1771.44	−	1108.26i	−0.245181	−	0.153393i
$86$	127.143			0.0171908
$87$	660.401	+	660.401i	0.0872507	+	0.0872507i
$88$	667.095	−	667.095i	0.0861434	−	0.0861434i
$89$		−	4476.59i		−	0.565155i	−0.959245	−	0.282577i	$-0.908811\pi$
$89$		−	4476.59i		−	0.565155i	0.959245	−	0.282577i	$-0.0911894\pi$
$90$	1807.31	−	2888.79i	0.223125	−	0.356640i
$91$	−3714.01			−0.448497
$92$	623.974	+	623.974i	0.0737210	+	0.0737210i
$93$	6919.90	−	6919.90i	0.800081	−	0.800081i
$94$			2614.57i			0.295899i
$95$	−182.021	−	790.389i	−0.0201685	−	0.0875777i
$96$	1036.88			0.112508
$97$	9053.65	+	9053.65i	0.962233	+	0.962233i	0.999312	−	0.0370796i	$-0.0118055\pi$
$97$	9053.65	+	9053.65i	0.962233	+	0.962233i	−0.0370796	+	0.999312i	$0.511806\pi$
$98$	−6124.30	+	6124.30i	−0.637682	+	0.637682i
$99$		−	2009.21i		−	0.205001i
$100$	2186.95	+	4496.36i	0.218695	+	0.449636i
$101$	10597.7			1.03889			0.519445	−	0.854504i	$-0.326139\pi$
$101$	10597.7			1.03889			0.519445	+	0.854504i	$0.326139\pi$
$102$	−957.514	−	957.514i	−0.0920333	−	0.0920333i
$103$	−12084.2	+	12084.2i	−1.13905	+	1.13905i	−0.150435	+	0.988620i	$0.548067\pi$
$103$	−12084.2	+	12084.2i	−1.13905	+	1.13905i	−0.988620	+	0.150435i	$0.951933\pi$
$104$		−	1136.99i		−	0.105121i
$105$	10314.4	−	2375.32i	0.935543	−	0.215449i
$106$	12430.5			1.10631
$107$	−599.397	−	599.397i	−0.0523537	−	0.0523537i	0.680445	−	0.732799i	$-0.261786\pi$
$107$	−599.397	−	599.397i	−0.0523537	−	0.0523537i	−0.732799	+	0.680445i	$0.761786\pi$
$108$	4186.07	−	4186.07i	0.358888	−	0.358888i
$109$			7074.55i			0.595451i	0.954652	+	0.297726i	$0.0962280\pi$
$109$			7074.55i			0.595451i	−0.954652	+	0.297726i	$0.903772\pi$
$110$	2499.34	+	1563.66i	0.206557	+	0.129228i
$111$	10511.1			0.853103
$112$	−3344.93	−	3344.93i	−0.266655	−	0.266655i
$113$	−8651.73	+	8651.73i	−0.677558	+	0.677558i	−0.959447	−	0.281889i	$-0.909039\pi$
$113$	−8651.73	+	8651.73i	−0.677558	+	0.677558i	0.281889	+	0.959447i	$0.409039\pi$
$114$		−	525.617i		−	0.0404445i
$115$	−1462.58	+	2337.78i	−0.110592	+	0.176770i
$116$	1304.40			0.0969380
$117$	−1712.24	−	1712.24i	−0.125081	−	0.125081i
$118$	−2420.52	+	2420.52i	−0.173838	+	0.173838i
$119$			6177.81i			0.436255i
$120$	727.171	+	3157.59i	0.0504980	+	0.219277i
$121$	−12902.7			−0.881269
$122$	19.4043	+	19.4043i	0.00130370	+	0.00130370i
$123$	−3096.69	+	3096.69i	−0.204686	+	0.204686i
$124$		−	13667.9i		−	0.888913i
$125$	−12159.0	+	9813.22i	−0.778176	+	0.628046i
$126$	−10074.5			−0.634576
$127$	−3123.53	−	3123.53i	−0.193659	−	0.193659i	0.603616	−	0.797275i	$-0.293726\pi$
$127$	−3123.53	−	3123.53i	−0.193659	−	0.193659i	−0.797275	+	0.603616i	$0.793726\pi$
$128$	1024.00	−	1024.00i	0.0625000	−	0.0625000i
$129$			257.484i			0.0154729i
$130$	3462.46	−	797.380i	0.204879	−	0.0471823i
$131$	24757.3			1.44265			0.721325	−	0.692597i	$-0.243534\pi$
$131$	24757.3			1.44265			0.721325	+	0.692597i	$0.243534\pi$
$132$	1350.97	+	1350.97i	0.0775348	+	0.0775348i
$133$	−1695.62	+	1695.62i	−0.0958573	+	0.0958573i
$134$		−	865.121i		−	0.0481800i
$135$	15683.5	+	9812.07i	0.860550	+	0.538385i
$136$	−1891.25			−0.102252
$137$	−9154.10	−	9154.10i	−0.487724	−	0.487724i	0.419863	−	0.907587i	$-0.362078\pi$
$137$	−9154.10	−	9154.10i	−0.487724	−	0.487724i	−0.907587	+	0.419863i	$0.862078\pi$
$138$	−1263.64	+	1263.64i	−0.0663538	+	0.0663538i
$139$			8526.58i			0.441312i	0.975352	+	0.220656i	$0.0708197\pi$
$139$			8526.58i			0.441312i	−0.975352	+	0.220656i	$0.929180\pi$
$140$	7840.44	−	12532.1i	0.400023	−	0.639393i
$141$	−5294.89			−0.266329
$142$	1155.41	+	1155.41i	0.0573005	+	0.0573005i
$143$	1481.40	−	1481.40i	0.0724439	−	0.0724439i
$144$		−	3084.17i		−	0.148735i
$145$	914.786	+	3972.27i	0.0435094	+	0.188931i
$146$	−25534.9			−1.19792
$147$	−12402.6	−	12402.6i	−0.573956	−	0.573956i
$148$	10380.5	−	10380.5i	0.473911	−	0.473911i
$149$			31212.9i			1.40592i	0.711229	+	0.702961i	$0.248139\pi$
$149$			31212.9i			1.40592i	−0.711229	+	0.702961i	$0.751861\pi$
$150$	−9105.81	+	4428.89i	−0.404703	+	0.196840i
$151$	−3518.63			−0.154319			−0.0771596	−	0.997019i	$-0.524585\pi$
$151$	−3518.63			−0.154319			−0.0771596	+	0.997019i	$0.524585\pi$
$152$	−519.089	−	519.089i	−0.0224675	−	0.0224675i
$153$	−2848.11	+	2848.11i	−0.121667	+	0.121667i
$154$		−	8716.34i		−	0.367530i
$155$	41622.8	−	9585.43i	1.73248	−	0.398977i
$156$	2302.57			0.0946159
$157$	−24356.1	−	24356.1i	−0.988116	−	0.988116i	0.0118145	−	0.999930i	$-0.496239\pi$
$157$	−24356.1	−	24356.1i	−0.988116	−	0.988116i	−0.999930	+	0.0118145i	$0.996239\pi$
$158$	−13121.9	+	13121.9i	−0.525634	+	0.525634i
$159$			25173.7i			0.995756i
$160$	3836.52	+	2400.24i	0.149864	+	0.0937592i
$161$	8152.92			0.314530
$162$	670.617	+	670.617i	0.0255532	+	0.0255532i
$163$	22375.8	−	22375.8i	0.842176	−	0.842176i	−0.146966	−	0.989142i	$-0.546951\pi$
$163$	22375.8	−	22375.8i	0.842176	−	0.842176i	0.989142	+	0.146966i	$0.0469506\pi$
$164$			6116.47i			0.227412i
$165$	−3166.64	+	5061.53i	−0.116314	+	0.185915i
$166$	3555.62			0.129033
$167$	19417.5	+	19417.5i	0.696241	+	0.696241i	0.963598	−	0.267357i	$-0.0861502\pi$
$167$	19417.5	+	19417.5i	0.696241	+	0.696241i	−0.267357	+	0.963598i	$0.586150\pi$
$168$	6773.98	−	6773.98i	0.240008	−	0.240008i
$169$			26036.1i			0.911597i
$170$	−1326.35	−	5759.39i	−0.0458944	−	0.199287i
$171$	−1563.44			−0.0534673
$172$	254.286	+	254.286i	0.00859539	+	0.00859539i
$173$	−40122.1	+	40122.1i	−1.34057	+	1.34057i	−0.445088	+	0.895487i	$0.646827\pi$
$173$	−40122.1	+	40122.1i	−1.34057	+	1.34057i	−0.895487	+	0.445088i	$0.853173\pi$
$174$			2641.60i			0.0872507i
$175$	43662.4	+	15087.6i	1.42571	+	0.492655i
$176$	2668.38			0.0861434
$177$	−4901.92	−	4901.92i	−0.156466	−	0.156466i
$178$	8953.18	−	8953.18i	0.282577	−	0.282577i
$179$		−	2983.80i		−	0.0931243i	−0.998915	−	0.0465622i	$-0.985173\pi$
$179$		−	2983.80i		−	0.0931243i	0.998915	−	0.0465622i	$-0.0148266\pi$
$180$	9392.19	−	2162.95i	0.289882	−	0.0667579i
$181$	35046.8			1.06977			0.534886	−	0.844924i	$-0.320355\pi$
$181$	35046.8			1.06977			0.534886	+	0.844924i	$0.320355\pi$
$182$	−7428.01	−	7428.01i	−0.224249	−	0.224249i
$183$	−39.2966	+	39.2966i	−0.00117342	+	0.00117342i
$184$			2495.90i			0.0737210i
$185$	38891.7	+	24331.8i	1.13635	+	0.710936i
$186$	27679.6			0.800081
$187$	−2464.14	−	2464.14i	−0.0704664	−	0.0704664i
$188$	−5229.13	+	5229.13i	−0.147950	+	0.147950i
$189$		−	54695.7i		−	1.53119i
$190$	1216.74	−	1944.82i	0.0337046	−	0.0538731i
$191$	51508.1			1.41192			0.705958	−	0.708253i	$-0.250517\pi$
$191$	51508.1			1.41192			0.705958	+	0.708253i	$0.250517\pi$
$192$	2073.75	+	2073.75i	0.0562542	+	0.0562542i
$193$	7195.41	−	7195.41i	0.193170	−	0.193170i	−0.603894	−	0.797065i	$-0.706385\pi$
$193$	7195.41	−	7195.41i	0.193170	−	0.193170i	0.797065	+	0.603894i	$0.206385\pi$
$194$			36214.6i			0.962233i
$195$	1614.81	+	7012.00i	0.0424672	+	0.184405i
$196$	−24497.2			−0.637682
$197$	−32237.1	−	32237.1i	−0.830661	−	0.830661i	0.156946	−	0.987607i	$-0.449835\pi$
$197$	−32237.1	−	32237.1i	−0.830661	−	0.830661i	−0.987607	+	0.156946i	$0.949835\pi$
$198$	4018.42	−	4018.42i	0.102500	−	0.102500i
$199$		−	18805.9i		−	0.474884i	−0.971402	−	0.237442i	$-0.923691\pi$
$199$		−	18805.9i		−	0.474884i	0.971402	−	0.237442i	$-0.0763089\pi$
$200$	−4618.83	+	13366.6i	−0.115471	+	0.334165i
$201$	1752.00			0.0433652
$202$	21195.4	+	21195.4i	0.519445	+	0.519445i
$203$	8521.71	−	8521.71i	0.206792	−	0.206792i
$204$		−	3830.06i		−	0.0920333i
$205$	−18626.4	+	4289.53i	−0.443222	+	0.102071i
$206$	−48336.9			−1.13905
$207$	3758.68	+	3758.68i	0.0877191	+	0.0877191i
$208$	2273.98	−	2273.98i	0.0525605	−	0.0525605i
$209$		−	1352.66i		−	0.0309669i
$210$	25379.4	+	15878.1i	0.575496	+	0.360047i
$211$	−69381.4			−1.55840			−0.779198	−	0.626777i	$-0.784374\pi$
$211$	−69381.4			−1.55840			−0.779198	+	0.626777i	$0.784374\pi$
$212$	24861.1	+	24861.1i	0.553157	+	0.553157i
$213$	−2339.87	+	2339.87i	−0.0515743	+	0.0515743i
$214$		−	2397.59i		−	0.0523537i
$215$	−596.042	+	952.708i	−0.0128944	+	0.0206102i
$216$	16744.3			0.358888
$217$	−89293.3	−	89293.3i	−1.89627	−	1.89627i
$218$	−14149.1	+	14149.1i	−0.297726	+	0.297726i
$219$		−	51712.0i		−	1.07821i
$220$	1871.36	+	8125.99i	0.0386644	+	0.167892i
$221$	−4199.85			−0.0859903
$222$	21022.2	+	21022.2i	0.426551	+	0.426551i
$223$	−14432.3	+	14432.3i	−0.290218	+	0.290218i	−0.837166	−	0.546948i	$-0.815789\pi$
$223$	−14432.3	+	14432.3i	−0.290218	+	0.290218i	0.546948	+	0.837166i	$0.315789\pi$
$224$		−	13379.7i		−	0.266655i
$225$	13173.6	+	27085.0i	0.260220	+	0.535013i
$226$	−34606.9			−0.677558
$227$	20961.3	+	20961.3i	0.406786	+	0.406786i	0.880616	−	0.473830i	$-0.157129\pi$
$227$	20961.3	+	20961.3i	0.406786	+	0.406786i	−0.473830	+	0.880616i	$0.657129\pi$
$228$	1051.23	−	1051.23i	0.0202223	−	0.0202223i
$229$		−	32183.6i		−	0.613711i	−0.951756	−	0.306856i	$-0.900723\pi$
$229$		−	32183.6i		−	0.613711i	0.951756	−	0.306856i	$-0.0992768\pi$
$230$	−7600.73	+	1750.39i	−0.143681	+	0.0330887i
$231$	17651.9			0.330801
$232$	2608.80	+	2608.80i	0.0484690	+	0.0484690i
$233$	−20903.3	+	20903.3i	−0.385038	+	0.385038i	−0.872913	−	0.487875i	$-0.837772\pi$
$233$	−20903.3	+	20903.3i	−0.385038	+	0.385038i	0.487875	+	0.872913i	$0.337772\pi$
$234$		−	6848.96i		−	0.125081i
$235$	−19591.5	−	12257.0i	−0.354757	−	0.221946i
$236$	−9682.08			−0.173838
$237$	−26573.9	−	26573.9i	−0.473106	−	0.473106i
$238$	−12355.6	+	12355.6i	−0.218128	+	0.218128i
$239$		−	60822.6i		−	1.06480i	−0.846492	−	0.532402i	$-0.821290\pi$
$239$		−	60822.6i		−	1.06480i	0.846492	−	0.532402i	$-0.178710\pi$
$240$	−4860.84	+	7769.52i	−0.0843896	+	0.134888i
$241$	−10567.6			−0.181947			−0.0909733	−	0.995853i	$-0.528998\pi$
$241$	−10567.6			−0.181947			−0.0909733	+	0.995853i	$0.528998\pi$
$242$	−25805.3	−	25805.3i	−0.440634	−	0.440634i
$243$	41025.9	−	41025.9i	0.694777	−	0.694777i
$244$			77.6172i			0.00130370i
$245$	−17180.1	−	74601.0i	−0.286216	−	1.24283i
$246$	−12386.8			−0.204686
$247$	−1152.73	−	1152.73i	−0.0188945	−	0.0188945i
$248$	27335.8	−	27335.8i	0.444456	−	0.444456i
$249$			7200.67i			0.116138i
$250$	−43944.4	−	4691.56i	−0.703111	−	0.0750650i
$251$	−30694.8			−0.487212			−0.243606	−	0.969874i	$-0.578330\pi$
$251$	−30694.8			−0.487212			−0.243606	+	0.969874i	$0.578330\pi$
$252$	−20149.1	−	20149.1i	−0.317288	−	0.317288i
$253$	−3251.95	+	3251.95i	−0.0508046	+	0.0508046i
$254$		−	12494.1i		−	0.193659i
$255$	11663.6	−	2686.05i	0.179372	−	0.0413080i
$256$	4096.00			0.0625000
$257$	−75192.3	−	75192.3i	−1.13843	−	1.13843i	−0.988731	−	0.149700i	$-0.952169\pi$
$257$	−75192.3	−	75192.3i	−1.13843	−	1.13843i	−0.149700	−	0.988731i	$-0.547831\pi$
$258$	−514.967	+	514.967i	−0.00773643	+	0.00773643i
$259$		−	135633.i		−	2.02193i
$260$	8519.68	+	5330.16i	0.126031	+	0.0788485i
$261$	7857.39			0.115345
$262$	49514.6	+	49514.6i	0.721325	+	0.721325i
$263$	−82563.3	+	82563.3i	−1.19365	+	1.19365i	−0.217611	+	0.976036i	$0.569826\pi$
$263$	−82563.3	+	82563.3i	−1.19365	+	1.19365i	−0.976036	+	0.217611i	$0.930174\pi$
$264$			5403.87i			0.0775348i
$265$	−58273.9	+	93144.5i	−0.829817	+	1.32637i
$266$	−6782.48			−0.0958573
$267$	18131.5	+	18131.5i	0.254338	+	0.254338i
$268$	1730.24	−	1730.24i	0.0240900	−	0.0240900i
$269$			6834.51i			0.0944502i	0.998884	+	0.0472251i	$0.0150378\pi$
$269$			6834.51i			0.0944502i	−0.998884	+	0.0472251i	$0.984962\pi$
$270$	11742.9	+	50991.2i	0.161082	+	0.699468i
$271$	133426.			1.81678			0.908388	−	0.418128i	$-0.137314\pi$
$271$	133426.			1.81678			0.908388	+	0.418128i	$0.137314\pi$
$272$	−3782.49	−	3782.49i	−0.0511258	−	0.0511258i
$273$	15042.8	−	15042.8i	0.201839	−	0.201839i
$274$		−	36616.4i		−	0.487724i
$275$	−23433.6	+	11397.7i	−0.309866	+	0.150713i
$276$	−5054.57			−0.0663538
$277$	−34667.8	−	34667.8i	−0.451821	−	0.451821i	0.444138	−	0.895959i	$-0.353510\pi$
$277$	−34667.8	−	34667.8i	−0.451821	−	0.451821i	−0.895959	+	0.444138i	$0.853510\pi$
$278$	−17053.2	+	17053.2i	−0.220656	+	0.220656i
$279$		−	82332.4i		−	1.05770i
$280$	40745.1	−	9383.30i	0.519708	−	0.119685i
$281$	5137.88			0.0650686			0.0325343	−	0.999471i	$-0.489642\pi$
$281$	5137.88			0.0650686			0.0325343	+	0.999471i	$0.489642\pi$
$282$	−10589.8	−	10589.8i	−0.133164	−	0.133164i
$283$	−96600.7	+	96600.7i	−1.20617	+	1.20617i	−0.233908	+	0.972259i	$0.575151\pi$
$283$	−96600.7	+	96600.7i	−1.20617	+	1.20617i	−0.972259	+	0.233908i	$0.924849\pi$
$284$			4621.63i			0.0573005i
$285$	3938.55	+	2464.07i	0.0484894	+	0.0303364i
$286$	5925.62			0.0724439
$287$	39959.3	+	39959.3i	0.485125	+	0.485125i
$288$	6168.34	−	6168.34i	0.0743675	−	0.0743675i
$289$		−	76535.0i		−	0.916357i
$290$	−6114.97	+	9774.11i	−0.0727107	+	0.116220i
$291$	−73340.0			−0.866074
$292$	−51069.8	−	51069.8i	−0.598961	−	0.598961i
$293$	−7055.18	+	7055.18i	−0.0821813	+	0.0821813i	−0.747003	−	0.664821i	$-0.768508\pi$
$293$	−7055.18	+	7055.18i	−0.0821813	+	0.0821813i	0.664821	+	0.747003i	$0.268508\pi$
$294$		−	49610.5i		−	0.573956i
$295$	−6790.13	−	29484.7i	−0.0780250	−	0.338808i
$296$	41522.2			0.473911
$297$	21816.4	+	21816.4i	0.247327	+	0.247327i
$298$	−62425.7	+	62425.7i	−0.702961	+	0.702961i
$299$			5542.59i			0.0619970i
$300$	−27069.4	−	9353.83i	−0.300771	−	0.103931i
$301$	3322.53			0.0366721
$302$	−7037.26	−	7037.26i	−0.0771596	−	0.0771596i
$303$	−42923.9	+	42923.9i	−0.467535	+	0.467535i
$304$		−	2076.36i		−	0.0224675i
$305$	−236.367	+	54.4336i	−0.00254090	+	0.000585150i
$306$	−11392.4			−0.121667
$307$	60268.2	+	60268.2i	0.639458	+	0.639458i	0.950422	−	0.310964i	$-0.100652\pi$
$307$	60268.2	+	60268.2i	0.639458	+	0.639458i	−0.310964	+	0.950422i	$0.600652\pi$
$308$	17432.7	−	17432.7i	0.183765	−	0.183765i
$309$		−	97889.5i		−	1.02523i
$310$	102416.	+	64074.7i	1.06573	+	0.666750i
$311$	47016.6			0.486106			0.243053	−	0.970013i	$-0.421851\pi$
$311$	47016.6			0.486106			0.243053	+	0.970013i	$0.421851\pi$
$312$	4605.15	+	4605.15i	0.0473080	+	0.0473080i
$313$	−95074.1	+	95074.1i	−0.970451	+	0.970451i	−0.999576	−	0.0291253i	$-0.990728\pi$
$313$	−95074.1	+	95074.1i	−0.970451	+	0.970451i	0.0291253	+	0.999576i	$0.490728\pi$
$314$		−	97424.3i		−	0.988116i
$315$	47229.0	−	75490.4i	0.475979	−	0.760800i
$316$	−52487.7			−0.525634
$317$	24704.9	+	24704.9i	0.245847	+	0.245847i	0.819264	−	0.573417i	$-0.194382\pi$
$317$	24704.9	+	24704.9i	0.245847	+	0.245847i	−0.573417	+	0.819264i	$0.694382\pi$
$318$	−50347.4	+	50347.4i	−0.497878	+	0.497878i
$319$			6798.10i			0.0668046i
$320$	2872.56	+	12473.5i	0.0280524	+	0.121812i
$321$	4855.47			0.0471218
$322$	16305.8	+	16305.8i	0.157265	+	0.157265i
$323$	−1917.43	+	1917.43i	−0.0183787	+	0.0183787i
$324$			2682.47i			0.0255532i
$325$	−10257.0	+	29683.0i	−0.0971073	+	0.281022i
$326$	89503.1			0.842176
$327$	−28654.1	−	28654.1i	−0.267973	−	0.267973i
$328$	−12232.9	+	12232.9i	−0.113706	+	0.113706i
$329$			68324.4i			0.631225i
$330$	−16456.3	+	3789.78i	−0.151114	+	0.0348005i
$331$	−75086.3			−0.685338			−0.342669	−	0.939456i	$-0.611331\pi$
$331$	−75086.3			−0.685338			−0.342669	+	0.939456i	$0.611331\pi$
$332$	7111.25	+	7111.25i	0.0645163	+	0.0645163i
$333$	62530.0	−	62530.0i	0.563897	−	0.563897i
$334$			77669.9i			0.696241i
$335$	6482.52	+	4055.65i	0.0577636	+	0.0361386i
$336$	27095.9			0.240008
$337$	38612.4	+	38612.4i	0.339991	+	0.339991i	0.856364	−	0.516373i	$-0.172718\pi$
$337$	38612.4	+	38612.4i	0.339991	+	0.339991i	−0.516373	+	0.856364i	$0.672718\pi$
$338$	−52072.2	+	52072.2i	−0.455798	+	0.455798i
$339$		−	70084.2i		−	0.609847i
$340$	8866.09	−	14171.5i	0.0766963	−	0.122591i
$341$	71232.8			0.612592
$342$	−3126.87	−	3126.87i	−0.0267336	−	0.0267336i
$343$	−34554.5	+	34554.5i	−0.293709	+	0.293709i
$344$			1017.14i			0.00859539i
$345$	−3544.81	−	15392.6i	−0.0297821	−	0.129323i
$346$	−160488.			−1.34057
$347$	5630.22	+	5630.22i	0.0467592	+	0.0467592i	0.730100	−	0.683341i	$-0.239474\pi$
$347$	5630.22	+	5630.22i	0.0467592	+	0.0467592i	−0.683341	+	0.730100i	$0.739474\pi$
$348$	−5283.20	+	5283.20i	−0.0436254	+	0.0436254i
$349$			101423.i			0.832698i	0.909205	+	0.416349i	$0.136691\pi$
$349$			101423.i			0.832698i	−0.909205	+	0.416349i	$0.863309\pi$
$350$	57149.8	+	117500.i	0.466529	+	0.959183i
$351$	37183.7			0.301813
$352$	5336.76	+	5336.76i	0.0430717	+	0.0430717i
$353$	28823.4	−	28823.4i	0.231311	−	0.231311i	−0.581929	−	0.813240i	$-0.697702\pi$
$353$	28823.4	−	28823.4i	0.231311	−	0.231311i	0.813240	+	0.581929i	$0.197702\pi$
$354$		−	19607.7i		−	0.156466i
$355$	−14074.2	+	3241.19i	−0.111678	+	0.0257186i
$356$	35812.7			0.282577
$357$	−25022.0	−	25022.0i	−0.196329	−	0.196329i
$358$	5967.59	−	5967.59i	0.0465622	−	0.0465622i
$359$			101027.i			0.783875i	0.919992	+	0.391938i	$0.128195\pi$
$359$			101027.i			0.783875i	−0.919992	+	0.391938i	$0.871805\pi$
$360$	23110.3	+	14458.5i	0.178320	+	0.111562i
$361$	129268.			0.991923
$362$	70093.6	+	70093.6i	0.534886	+	0.534886i
$363$	52259.6	−	52259.6i	0.396600	−	0.396600i
$364$		−	29712.1i		−	0.224249i
$365$	119707.	−	191338.i	0.898530	−	1.43620i
$366$	−157.186			−0.00117342
$367$	67918.9	+	67918.9i	0.504265	+	0.504265i	0.912760	−	0.408496i	$-0.133946\pi$
$367$	67918.9	+	67918.9i	0.504265	+	0.504265i	−0.408496	+	0.912760i	$0.633946\pi$
$368$	−4991.79	+	4991.79i	−0.0368605	+	0.0368605i
$369$			36844.2i			0.270593i
$370$	29119.9	+	126447.i	0.212709	+	0.923645i
$371$	324838.			2.36004
$372$	55359.2	+	55359.2i	0.400040	+	0.400040i
$373$	−120903.	+	120903.i	−0.868998	+	0.868998i	−0.992362	−	0.123364i	$-0.960632\pi$
$373$	−120903.	+	120903.i	−0.868998	+	0.868998i	0.123364	+	0.992362i	$0.460632\pi$
$374$		−	9856.56i		−	0.0704664i
$375$	9501.12	−	88994.1i	0.0675635	−	0.632847i
$376$	−20916.5			−0.147950
$377$	5793.31	+	5793.31i	0.0407609	+	0.0407609i
$378$	109391.	−	109391.i	0.765596	−	0.765596i
$379$		−	13205.7i		−	0.0919355i	−0.998943	−	0.0459678i	$-0.985363\pi$
$379$		−	13205.7i		−	0.0919355i	0.998943	−	0.0459678i	$-0.0146372\pi$
$380$	6323.11	−	1456.17i	0.0437889	−	0.0100843i
$381$	25302.4			0.174306
$382$	103016.	+	103016.i	0.705958	+	0.705958i
$383$	1195.94	−	1195.94i	0.00815293	−	0.00815293i	−0.703019	−	0.711171i	$-0.748165\pi$
$383$	1195.94	−	1195.94i	0.00815293	−	0.00815293i	0.711171	+	0.703019i	$0.248165\pi$
$384$			8295.01i			0.0562542i
$385$	65313.2	+	40861.9i	0.440636	+	0.275675i
$386$	28781.6			0.193170
$387$	1531.76	+	1531.76i	0.0102275	+	0.0102275i
$388$	−72429.2	+	72429.2i	−0.481116	+	0.481116i
$389$		−	72363.0i		−	0.478209i	−0.970994	−	0.239104i	$-0.923146\pi$
$389$		−	72363.0i		−	0.478209i	0.970994	−	0.239104i	$-0.0768538\pi$
$390$	−10794.4	+	17253.6i	−0.0709689	+	0.113436i
$391$	9219.45			0.0603047
$392$	−48994.4	−	48994.4i	−0.318841	−	0.318841i
$393$	−100275.	+	100275.i	−0.649240	+	0.649240i
$394$		−	128948.i		−	0.830661i
$395$	−36810.1	−	159840.i	−0.235924	−	1.02445i
$396$	16073.7			0.102500
$397$	−114721.	−	114721.i	−0.727885	−	0.727885i	0.242313	−	0.970198i	$-0.422094\pi$
$397$	−114721.	−	114721.i	−0.727885	−	0.727885i	−0.970198	+	0.242313i	$0.922094\pi$
$398$	37611.7	−	37611.7i	0.237442	−	0.237442i
$399$		−	13735.5i		−	0.0862780i
$400$	−35970.9	+	17495.6i	−0.224818	+	0.109347i
$401$	124870.			0.776549			0.388275	−	0.921544i	$-0.373071\pi$
$401$	124870.			0.776549			0.388275	+	0.921544i	$0.373071\pi$
$402$	3504.00	+	3504.00i	0.0216826	+	0.0216826i
$403$	60704.2	−	60704.2i	0.373774	−	0.373774i
$404$			84781.8i			0.519445i
$405$	−8168.89	+	1881.24i	−0.0498027	+	0.0114692i
$406$	34086.8			0.206792
$407$	54100.0	+	54100.0i	0.326594	+	0.326594i
$408$	7660.11	−	7660.11i	0.0460166	−	0.0460166i
$409$			145516.i			0.869887i	0.900458	+	0.434944i	$0.143232\pi$
$409$			145516.i			0.869887i	−0.900458	+	0.434944i	$0.856768\pi$
$410$	−45831.9	−	28673.8i	−0.272647	−	0.170576i
$411$	74153.7			0.438984
$412$	−96673.9	−	96673.9i	−0.569527	−	0.569527i
$413$	−63253.6	+	63253.6i	−0.370839	+	0.370839i
$414$			15034.7i			0.0877191i
$415$	−16668.6	+	26643.0i	−0.0967840	+	0.154699i
$416$	9095.91			0.0525605
$417$	−34535.2	−	34535.2i	−0.198605	−	0.198605i
$418$	2705.33	−	2705.33i	0.0154834	−	0.0154834i
$419$			285124.i			1.62408i	0.583605	+	0.812038i	$0.301642\pi$
$419$			285124.i			1.62408i	−0.583605	+	0.812038i	$0.698358\pi$
$420$	19002.6	+	82514.9i	0.107724	+	0.467771i
$421$	153954.			0.868616			0.434308	−	0.900764i	$-0.356993\pi$
$421$	153954.			0.868616			0.434308	+	0.900764i	$0.356993\pi$
$422$	−138763.	−	138763.i	−0.779198	−	0.779198i
$423$	−31499.1	+	31499.1i	−0.176042	+	0.176042i
$424$			99444.3i			0.553157i
$425$	49374.1	+	17061.2i	0.273352	+	0.0944566i
$426$	−9359.49			−0.0515743
$427$	507.077	+	507.077i	0.00278111	+	0.00278111i
$428$	4795.18	−	4795.18i	0.0261768	−	0.0261768i
$429$			12000.3i			0.0652043i
$430$	−3097.50	+	713.332i	−0.0167523	+	0.00385794i
$431$	−21642.1			−0.116505			−0.0582524	−	0.998302i	$-0.518553\pi$
$431$	−21642.1			−0.116505			−0.0582524	+	0.998302i	$0.518553\pi$
$432$	33488.6	+	33488.6i	0.179444	+	0.179444i
$433$	−248068.	+	248068.i	−1.32311	+	1.32311i	−0.411863	+	0.911246i	$0.635122\pi$
$433$	−248068.	+	248068.i	−1.32311	+	1.32311i	−0.911246	+	0.411863i	$0.864878\pi$
$434$		−	357173.i		−	1.89627i
$435$	−19794.0	−	12383.7i	−0.104606	−	0.0654445i
$436$	−56596.4			−0.297726
$437$	2530.46	+	2530.46i	0.0132506	+	0.0132506i
$438$	103424.	−	103424.i	0.539105	−	0.539105i
$439$			215298.i			1.11715i	0.829454	+	0.558575i	$0.188652\pi$
$439$			215298.i			1.11715i	−0.829454	+	0.558575i	$0.811348\pi$
$440$	−12509.3	+	19994.7i	−0.0646139	+	0.103278i
$441$	−147565.			−0.758765
$442$	−8399.71	−	8399.71i	−0.0429952	−	0.0429952i
$443$	258262.	−	258262.i	1.31599	−	1.31599i	0.399075	−	0.916918i	$-0.369331\pi$
$443$	258262.	−	258262.i	1.31599	−	1.31599i	0.916918	−	0.399075i	$-0.130669\pi$
$444$			84088.6i			0.426551i
$445$	25115.8	+	109060.i	0.126831	+	0.550739i
$446$	−57729.0			−0.290218
$447$	−126421.	−	126421.i	−0.632712	−	0.632712i
$448$	26759.4	−	26759.4i	0.133328	−	0.133328i
$449$			82092.6i			0.407203i	0.979054	+	0.203602i	$0.0652647\pi$
$449$			82092.6i			0.407203i	−0.979054	+	0.203602i	$0.934735\pi$
$450$	−27822.8	+	80517.4i	−0.137396	+	0.397617i
$451$	−31877.1			−0.156720
$452$	−69213.9	−	69213.9i	−0.338779	−	0.338779i
$453$	14251.5	−	14251.5i	0.0694488	−	0.0694488i
$454$			83845.0i			0.406786i
$455$	90481.8	−	20837.3i	0.437057	−	0.100651i
$456$	4204.94			0.0202223
$457$	9496.26	+	9496.26i	0.0454695	+	0.0454695i	0.729476	−	0.684006i	$-0.239764\pi$
$457$	9496.26	+	9496.26i	0.0454695	+	0.0454695i	−0.684006	+	0.729476i	$0.739764\pi$
$458$	64367.2	−	64367.2i	0.306856	−	0.306856i
$459$		−	61850.7i		−	0.293575i
$460$	−18702.3	−	11700.7i	−0.0883849	−	0.0552962i
$461$	−141341.			−0.665069			−0.332535	−	0.943091i	$-0.607904\pi$
$461$	−141341.			−0.665069			−0.332535	+	0.943091i	$0.607904\pi$
$462$	35303.8	+	35303.8i	0.165401	+	0.165401i
$463$	246224.	−	246224.i	1.14860	−	1.14860i	0.161771	−	0.986828i	$-0.448280\pi$
$463$	246224.	−	246224.i	1.14860	−	1.14860i	0.986828	−	0.161771i	$-0.0517205\pi$
$464$			10435.2i			0.0484690i
$465$	−129761.	+	207409.i	−0.600120	+	0.959226i
$466$	−83613.3			−0.385038
$467$	213108.	+	213108.i	0.977163	+	0.977163i	0.999745	−	0.0225825i	$-0.00718884\pi$
$467$	213108.	+	213108.i	0.977163	+	0.977163i	−0.0225825	+	0.999745i	$0.507189\pi$
$468$	13697.9	−	13697.9i	0.0625407	−	0.0625407i
$469$		−	22607.5i		−	0.102780i
$470$	−14668.9	−	63696.9i	−0.0664053	−	0.288352i
$471$	197299.			0.889370
$472$	−19364.2	−	19364.2i	−0.0869190	−	0.0869190i
$473$	−1325.26	+	1325.26i	−0.00592349	+	0.00592349i
$474$		−	106295.i		−	0.473106i
$475$	8868.91	+	18234.5i	0.0393082	+	0.0808176i
$476$	−49422.5			−0.218128
$477$	149757.	+	149757.i	0.658190	+	0.658190i
$478$	121645.	−	121645.i	0.532402	−	0.532402i
$479$			99960.8i			0.435671i	0.975985	+	0.217836i	$0.0698997\pi$
$479$			99960.8i			0.435671i	−0.975985	+	0.217836i	$0.930100\pi$
$480$	−25260.7	+	5817.37i	−0.109639	+	0.0252490i
$481$	92207.5			0.398544
$482$	−21135.3	−	21135.3i	−0.0909733	−	0.0909733i
$483$	−33021.8	+	33021.8i	−0.141549	+	0.141549i
$484$		−	103221.i		−	0.440634i
$485$	−271363.	−	169773.i	−1.15363	−	0.721746i
$486$	164103.			0.694777
$487$	−49887.0	−	49887.0i	−0.210344	−	0.210344i	0.594070	−	0.804414i	$-0.297520\pi$
$487$	−49887.0	−	49887.0i	−0.210344	−	0.210344i	−0.804414	+	0.594070i	$0.797520\pi$
$488$	−155.234	+	155.234i	−0.000651851	+	0.000651851i
$489$			181257.i			0.758015i
$490$	114842.	−	183562.i	0.478309	−	0.764524i
$491$	315603.			1.30911			0.654557	−	0.756012i	$-0.272855\pi$
$491$	315603.			1.30911			0.654557	+	0.756012i	$0.272855\pi$
$492$	−24773.5	−	24773.5i	−0.102343	−	0.102343i
$493$	9636.48	−	9636.48i	0.0396483	−	0.0396483i
$494$		−	4610.93i		−	0.0188945i
$495$	11272.6	+	48949.1i	0.0460060	+	0.199772i
$496$	109343.			0.444456
$497$	30193.4	+	30193.4i	0.122236	+	0.122236i
$498$	−14401.3	+	14401.3i	−0.0580690	+	0.0580690i
$499$			286915.i			1.15226i	0.817357	+	0.576132i	$0.195439\pi$
$499$			286915.i			1.15226i	−0.817357	+	0.576132i	$0.804561\pi$
$500$	−78505.8	−	97272.0i	−0.314023	−	0.389088i
$501$	−157293.			−0.626663
$502$	−61389.7	−	61389.7i	−0.243606	−	0.243606i
$503$	−188069.	+	188069.i	−0.743329	+	0.743329i	−0.973217	−	0.229888i	$-0.926164\pi$
$503$	−188069.	+	188069.i	−0.743329	+	0.743329i	0.229888	+	0.973217i	$0.426164\pi$
$504$		−	80596.2i		−	0.317288i
$505$	−258185.	+	59458.2i	−1.01239	+	0.233147i
$506$	−13007.8			−0.0508046
$507$	−105454.	−	105454.i	−0.410249	−	0.410249i
$508$	24988.2	−	24988.2i	0.0968295	−	0.0968295i
$509$			62166.3i			0.239949i	0.992777	+	0.119975i	$0.0382813\pi$
$509$			62166.3i			0.239949i	−0.992777	+	0.119975i	$0.961719\pi$
$510$	28699.4	+	17955.2i	0.110340	+	0.0690318i
$511$	−667284.			−2.55546
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	16976.1	−	16976.1i	0.0645066	−	0.0645066i
$514$		−	300769.i		−	1.13843i
$515$	226602.	−	362198.i	0.854375	−	1.36563i
$516$	−2059.87			−0.00773643
$517$	−27252.5	−	27252.5i	−0.101959	−	0.101959i
$518$	271267.	−	271267.i	1.01097	−	1.01097i
$519$		−	325013.i		−	1.20661i
$520$	6379.04	+	27699.7i	0.0235911	+	0.102440i
$521$	−520643.			−1.91807			−0.959036	−	0.283284i	$-0.908576\pi$
$521$	−520643.			−1.91807			−0.959036	+	0.283284i	$0.908576\pi$
$522$	15714.8	+	15714.8i	0.0576723	+	0.0576723i
$523$	−315459.	+	315459.i	−1.15329	+	1.15329i	−0.167404	+	0.985888i	$0.553538\pi$
$523$	−315459.	+	315459.i	−1.15329	+	1.15329i	−0.985888	+	0.167404i	$0.946462\pi$
$524$			198058.i			0.721325i
$525$	−237955.	+	115737.i	−0.863329	+	0.419907i
$526$	−330253.			−1.19365
$527$	−100974.	−	100974.i	−0.363571	−	0.363571i
$528$	−10807.7	+	10807.7i	−0.0387674	+	0.0387674i
$529$		−	12167.0i		−	0.0434783i
$530$	−302837.	+	69741.2i	−1.07809	+	0.248278i
$531$	−58322.6			−0.206846
$532$	−13565.0	−	13565.0i	−0.0479287	−	0.0479287i
$533$	−27165.5	+	27165.5i	−0.0956231	+	0.0956231i
$534$			72526.1i			0.254338i
$535$	17965.6	+	11239.8i	0.0627674	+	0.0392691i
$536$	6920.97			0.0240900
$537$	12085.3	+	12085.3i	0.0419090	+	0.0419090i
$538$	−13669.0	+	13669.0i	−0.0472251	+	0.0472251i
$539$		−	127671.i		−	0.439457i
$540$	−78496.6	+	125468.i	−0.269193	+	0.430275i
$541$	178273.			0.609102			0.304551	−	0.952496i	$-0.401494\pi$
$541$	178273.			0.609102			0.304551	+	0.952496i	$0.401494\pi$
$542$	266852.	+	266852.i	0.908388	+	0.908388i
$543$	−141950.	+	141950.i	−0.481433	+	0.481433i
$544$		−	15130.0i		−	0.0511258i
$545$	−39691.6	−	172353.i	−0.133630	−	0.580263i
$546$	60171.4			0.201839
$547$	107047.	+	107047.i	0.357767	+	0.357767i	0.862989	−	0.505222i	$-0.168589\pi$
$547$	107047.	+	107047.i	0.357767	+	0.357767i	−0.505222	+	0.862989i	$0.668589\pi$
$548$	73232.8	−	73232.8i	0.243862	−	0.243862i
$549$			467.548i			0.00155125i
$550$	−69662.5	−	24071.9i	−0.230289	−	0.0795764i
$551$	5289.84			0.0174237
$552$	−10109.1	−	10109.1i	−0.0331769	−	0.0331769i
$553$	−342905.	+	342905.i	−1.12131	+	1.12131i
$554$		−	138671.i		−	0.451821i
$555$	−256074.	+	58972.1i	−0.831342	+	0.191452i
$556$	−68212.6			−0.220656
$557$	−214679.	−	214679.i	−0.691958	−	0.691958i	0.270704	−	0.962663i	$-0.412743\pi$
$557$	−214679.	−	214679.i	−0.691958	−	0.691958i	−0.962663	+	0.270704i	$0.912743\pi$
$558$	164665.	−	164665.i	0.528850	−	0.528850i
$559$			2258.75i			0.00722845i
$560$	100257.	+	62723.5i	0.319696	+	0.200011i
$561$	19961.0			0.0634245
$562$	10275.8	+	10275.8i	0.0325343	+	0.0325343i
$563$	238529.	−	238529.i	0.752531	−	0.752531i	−0.222420	−	0.974951i	$-0.571396\pi$
$563$	238529.	−	238529.i	0.752531	−	0.752531i	0.974951	+	0.222420i	$0.0713955\pi$
$564$		−	42359.1i		−	0.133164i
$565$	162236.	−	259317.i	0.508218	−	0.812332i
$566$	−386403.			−1.20617
$567$	17524.7	+	17524.7i	0.0545111	+	0.0545111i
$568$	−9243.26	+	9243.26i	−0.0286502	+	0.0286502i
$569$		−	391528.i		−	1.20931i	−0.796487	−	0.604656i	$-0.793311\pi$
$569$		−	391528.i		−	1.20931i	0.796487	−	0.604656i	$-0.206689\pi$
$570$	2948.96	+	12805.2i	0.00907651	+	0.0394129i
$571$	217193.			0.666153			0.333076	−	0.942900i	$-0.391913\pi$
$571$	217193.			0.666153			0.333076	+	0.942900i	$0.391913\pi$
$572$	11851.2	+	11851.2i	0.0362219	+	0.0362219i
$573$	−208623.	+	208623.i	−0.635409	+	0.635409i
$574$			159837.i			0.485125i
$575$	22515.9	−	65159.6i	0.0681010	−	0.197080i
$576$	24673.4			0.0743675
$577$	−417869.	−	417869.i	−1.25513	−	1.25513i	−0.953391	−	0.301739i	$-0.902433\pi$
$577$	−417869.	−	417869.i	−1.25513	−	1.25513i	−0.301739	−	0.953391i	$-0.597567\pi$
$578$	153070.	−	153070.i	0.458178	−	0.458178i
$579$			58287.1i			0.173866i
$580$	−31778.2	+	7318.29i	−0.0944654	+	0.0217547i
$581$	92916.4			0.275258
$582$	−146680.	−	146680.i	−0.433037	−	0.433037i
$583$	−129568.	+	129568.i	−0.381206	+	0.381206i
$584$		−	204279.i		−	0.598961i
$585$	51320.6	+	32107.6i	0.149962	+	0.0938203i
$586$	−28220.7			−0.0821813
$587$	257567.	+	257567.i	0.747505	+	0.747505i	0.974010	−	0.226505i	$-0.0727299\pi$
$587$	257567.	+	257567.i	0.747505	+	0.747505i	−0.226505	+	0.974010i	$0.572730\pi$
$588$	99220.9	−	99220.9i	0.286978	−	0.286978i
$589$		−	55428.7i		−	0.159773i
$590$	45389.2	−	72549.7i	0.130391	−	0.208416i
$591$	261140.			0.747650
$592$	83044.4	+	83044.4i	0.236955	+	0.236955i
$593$	352147.	−	352147.i	1.00142	−	1.00142i	0.00141799	−	0.999999i	$-0.499549\pi$
$593$	352147.	−	352147.i	1.00142	−	1.00142i	0.999999	−	0.00141799i	$-0.000451362\pi$
$594$			87265.8i			0.247327i
$595$	−34660.4	−	150506.i	−0.0979039	−	0.425128i
$596$	−249703.			−0.702961
$597$	76169.4	+	76169.4i	0.213713	+	0.213713i
$598$	−11085.2	+	11085.2i	−0.0309985	+	0.0309985i
$599$			718.625i			0.00200285i	0.999999	+	0.00100143i	$0.000318764\pi$
$599$			718.625i			0.00200285i	−0.999999	+	0.00100143i	$0.999681\pi$
$600$	−35431.1	−	72846.5i	−0.0984198	−	0.202351i
$601$	289213.			0.800699			0.400349	−	0.916363i	$-0.368889\pi$
$601$	289213.			0.800699			0.400349	+	0.916363i	$0.368889\pi$
$602$	6645.06	+	6645.06i	0.0183361	+	0.0183361i
$603$	10422.6	−	10422.6i	0.0286642	−	0.0286642i
$604$		−	28149.0i		−	0.0771596i
$605$	314339.	−	72390.0i	0.858790	−	0.197773i
$606$	−171696.			−0.467535
$607$	55903.6	+	55903.6i	0.151727	+	0.151727i	0.778889	−	0.627162i	$-0.215784\pi$
$607$	55903.6	+	55903.6i	0.151727	+	0.151727i	−0.627162	+	0.778889i	$0.715784\pi$
$608$	4152.71	−	4152.71i	0.0112338	−	0.0112338i
$609$			69031.0i			0.186127i
$610$	−581.601	−	363.866i	−0.00156302	−	0.000977873i
$611$	−46448.9			−0.124421
$612$	−22784.9	−	22784.9i	−0.0608336	−	0.0608336i
$613$	−41008.0	+	41008.0i	−0.109131	+	0.109131i	−0.759564	−	0.650433i	$-0.774588\pi$
$613$	−41008.0	+	41008.0i	−0.109131	+	0.109131i	0.650433	+	0.759564i	$0.274588\pi$
$614$			241073.i			0.639458i
$615$	58068.7	−	92816.5i	0.153530	−	0.245400i
$616$	69730.7			0.183765
$617$	436441.	+	436441.i	1.14645	+	1.14645i	0.987246	+	0.159204i	$0.0508928\pi$
$617$	436441.	+	436441.i	1.14645	+	1.14645i	0.159204	+	0.987246i	$0.449107\pi$
$618$	195779.	−	195779.i	0.512613	−	0.512613i
$619$			686825.i			1.79252i	0.443527	+	0.896261i	$0.353727\pi$
$619$			686825.i			1.79252i	−0.443527	+	0.896261i	$0.646273\pi$
$620$	76683.5	+	332982.i	0.199489	+	0.866239i
$621$	−81625.0			−0.211661
$622$	94033.2	+	94033.2i	0.243053	+	0.243053i
$623$	233967.	−	233967.i	0.602806	−	0.602806i
$624$			18420.6i			0.0473080i
$625$	241165.	−	307291.i	0.617382	−	0.786664i
$626$	−380296.			−0.970451
$627$	5478.69	+	5478.69i	0.0139361	+	0.0139361i
$628$	194849.	−	194849.i	0.494058	−	0.494058i
$629$		−	153376.i		−	0.387665i
$630$	245439.	−	56522.8i	0.618390	−	0.142411i
$631$	187275.			0.470350			0.235175	−	0.971953i	$-0.424434\pi$
$631$	187275.			0.470350			0.235175	+	0.971953i	$0.424434\pi$
$632$	−104975.	−	104975.i	−0.262817	−	0.262817i
$633$	281015.	−	281015.i	0.701330	−	0.701330i
$634$			98819.7i			0.245847i
$635$	93620.8	+	58571.9i	0.232180	+	0.145259i
$636$	−201390.			−0.497878
$637$	−108801.	−	108801.i	−0.268135	−	0.268135i
$638$	−13596.2	+	13596.2i	−0.0334023	+	0.0334023i
$639$			27839.6i			0.0681807i
$640$	−19201.9	+	30692.1i	−0.0468796	+	0.0749320i
$641$	−413028.			−1.00523			−0.502613	−	0.864512i	$-0.667628\pi$
$641$	−413028.			−1.00523			−0.502613	+	0.864512i	$0.667628\pi$
$642$	9710.95	+	9710.95i	0.0235609	+	0.0235609i
$643$	417516.	−	417516.i	1.00984	−	1.00984i	0.00988450	−	0.999951i	$-0.496854\pi$
$643$	417516.	−	417516.i	1.00984	−	1.00984i	0.999951	−	0.00988450i	$-0.00314638\pi$
$644$			65223.4i			0.157265i
$645$	−1444.60	−	6272.90i	−0.00347240	−	0.0150782i
$646$	−7669.73			−0.0183787
$647$	−181380.	−	181380.i	−0.433291	−	0.433291i	0.456455	−	0.889746i	$-0.349119\pi$
$647$	−181380.	−	181380.i	−0.433291	−	0.433291i	−0.889746	+	0.456455i	$0.849119\pi$
$648$	−5364.94	+	5364.94i	−0.0127766	+	0.0127766i
$649$		−	50459.9i		−	0.119800i
$650$	−79879.9	+	38852.1i	−0.189065	+	0.0919575i
$651$	723329.			1.70677
$652$	179006.	+	179006.i	0.421088	+	0.421088i
$653$	130965.	−	130965.i	0.307134	−	0.307134i	−0.536663	−	0.843797i	$-0.680315\pi$
$653$	130965.	−	130965.i	0.307134	−	0.307134i	0.843797	+	0.536663i	$0.180315\pi$
$654$		−	114616.i		−	0.267973i
$655$	−603145.	+	138900.i	−1.40585	+	0.323758i
$656$	−48931.8			−0.113706
$657$	−307633.	−	307633.i	−0.712692	−	0.712692i
$658$	−136649.	+	136649.i	−0.315612	+	0.315612i
$659$			138434.i			0.318767i	0.987217	+	0.159383i	$0.0509506\pi$
$659$			138434.i			0.318767i	−0.987217	+	0.159383i	$0.949049\pi$
$660$	−40492.2	−	25333.1i	−0.0929574	−	0.0581569i
$661$	−122226.			−0.279745			−0.139872	−	0.990170i	$-0.544669\pi$
$661$	−122226.			−0.279745			−0.139872	+	0.990170i	$0.544669\pi$
$662$	−150173.	−	150173.i	−0.342669	−	0.342669i
$663$	17010.7	−	17010.7i	0.0386985	−	0.0386985i
$664$			28445.0i			0.0645163i
$665$	31796.0	−	50822.5i	0.0719001	−	0.114924i
$666$	250120.			0.563897
$667$	−12717.4	−	12717.4i	−0.0285855	−	0.0285855i
$668$	−155340.	+	155340.i	−0.348120	+	0.348120i
$669$		−	116910.i		−	0.261216i
$670$	4853.73	+	21076.4i	0.0108125	+	0.0469511i
$671$	−404.516			−0.000898442
$672$	54191.8	+	54191.8i	0.120004	+	0.120004i
$673$	290921.	−	290921.i	0.642311	−	0.642311i	−0.308812	−	0.951123i	$-0.599931\pi$
$673$	290921.	−	290921.i	0.642311	−	0.642311i	0.951123	+	0.308812i	$0.0999314\pi$
$674$			154450.i			0.339991i
$675$	−437137.	−	151053.i	−0.959424	−	0.331529i
$676$	−208289.			−0.455798
$677$	−570645.	−	570645.i	−1.24506	−	1.24506i	−0.957877	−	0.287179i	$-0.907283\pi$
$677$	−570645.	−	570645.i	−1.24506	−	1.24506i	−0.287179	−	0.957877i	$-0.592717\pi$
$678$	140168.	−	140168.i	0.304924	−	0.304924i
$679$			946368.i			2.05268i
$680$	46075.1	−	10610.8i	0.0996435	−	0.0229472i
$681$	−169799.			−0.366134
$682$	142466.	+	142466.i	0.306296	+	0.306296i
$683$	306806.	−	306806.i	0.657692	−	0.657692i	−0.297142	−	0.954833i	$-0.596033\pi$
$683$	306806.	−	306806.i	0.657692	−	0.657692i	0.954833	+	0.297142i	$0.0960334\pi$
$684$		−	12507.5i		−	0.0267336i
$685$	274374.	+	171656.i	0.584738	+	0.365829i
$686$	−138218.			−0.293709
$687$	130353.	+	130353.i	0.276190	+	0.276190i
$688$	−2034.29	+	2034.29i	−0.00429770	+	0.00429770i
$689$			220834.i			0.465187i
$690$	23695.6	−	37874.9i	0.0497703	−	0.0795523i
$691$	−333370.			−0.698185			−0.349093	−	0.937088i	$-0.613510\pi$
$691$	−333370.			−0.698185			−0.349093	+	0.937088i	$0.613510\pi$
$692$	−320976.	−	320976.i	−0.670287	−	0.670287i
$693$	105010.	−	105010.i	0.218658	−	0.218658i
$694$			22520.9i			0.0467592i
$695$	−47838.1	−	207727.i	−0.0990386	−	0.430055i
$696$	−21132.8			−0.0436254
$697$	45186.5	+	45186.5i	0.0930129	+	0.0930129i
$698$	−202847.	+	202847.i	−0.416349	+	0.416349i
$699$		−	169329.i		−	0.346560i
$700$	−120700.	+	349299.i	−0.246327	+	0.712856i
$701$	−386266.			−0.786051			−0.393025	−	0.919528i	$-0.628572\pi$
$701$	−386266.			−0.786051			−0.393025	+	0.919528i	$0.628572\pi$
$702$	74367.4	+	74367.4i	0.150907	+	0.150907i
$703$	42097.1	−	42097.1i	0.0851808	−	0.0851808i
$704$			21347.0i			0.0430717i
$705$	128996.	−	29706.8i	0.259536	−	0.0597692i
$706$	115293.			0.231311
$707$	553884.	+	553884.i	1.10810	+	1.10810i
$708$	39215.3	−	39215.3i	0.0782329	−	0.0782329i
$709$			214696.i			0.427102i	0.976932	+	0.213551i	$0.0685030\pi$
$709$			214696.i			0.427102i	−0.976932	+	0.213551i	$0.931497\pi$
$710$	−34630.8	−	21666.0i	−0.0686982	−	0.0429796i
$711$	−316174.			−0.625442
$712$	71625.5	+	71625.5i	0.141289	+	0.141289i
$713$	−133257.	+	133257.i	−0.262126	+	0.262126i
$714$		−	100088.i		−	0.196329i
$715$	−27779.1	+	44401.8i	−0.0543383	+	0.0868538i
$716$	23870.4			0.0465622
$717$	246350.	+	246350.i	0.479197	+	0.479197i
$718$	−202053.	+	202053.i	−0.391938	+	0.391938i
$719$		−	415586.i		−	0.803903i	−0.915661	−	0.401951i	$-0.868332\pi$
$719$		−	415586.i		−	0.803903i	0.915661	−	0.401951i	$-0.131668\pi$
$720$	17303.6	+	75137.5i	0.0333789	+	0.144941i
$721$	−1.26315e6			−2.42988
$722$	258537.	+	258537.i	0.495962	+	0.495962i
$723$	42802.1	−	42802.1i	0.0818821	−	0.0818821i
$724$			280374.i			0.534886i
$725$	−44572.6	−	91641.4i	−0.0847993	−	0.174347i
$726$	209039.			0.396600
$727$	406172.	+	406172.i	0.768495	+	0.768495i	0.977841	−	0.209347i	$-0.0671337\pi$
$727$	406172.	+	406172.i	0.768495	+	0.768495i	−0.209347	+	0.977841i	$0.567134\pi$
$728$	59424.1	−	59424.1i	0.112124	−	0.112124i
$729$			359494.i			0.676452i
$730$	622090.	−	143263.i	1.16737	−	0.268836i
$731$	3757.17			0.00703114
$732$	−314.373	−	314.373i	−0.000586709	−	0.000586709i
$733$	−146805.	+	146805.i	−0.273232	+	0.273232i	−0.830400	−	0.557168i	$-0.811888\pi$
$733$	−146805.	+	146805.i	−0.273232	+	0.273232i	0.557168	+	0.830400i	$0.311888\pi$
$734$			271676.i			0.504265i
$735$	371741.	+	232572.i	0.688123	+	0.430510i
$736$	−19967.2			−0.0368605
$737$	9017.46	+	9017.46i	0.0166016	+	0.0166016i
$738$	−73688.4	+	73688.4i	−0.135296	+	0.135296i
$739$			978173.i			1.79113i	0.444932	+	0.895564i	$0.353228\pi$
$739$			978173.i			1.79113i	−0.444932	+	0.895564i	$0.646772\pi$
$740$	−194654.	+	311134.i	−0.355468	+	0.568177i
$741$	9337.82			0.0170063
$742$	649675.	+	649675.i	1.18002	+	1.18002i
$743$	517321.	−	517321.i	0.937093	−	0.937093i	−0.0610423	−	0.998135i	$-0.519442\pi$
$743$	517321.	−	517321.i	0.937093	−	0.937093i	0.998135	+	0.0610423i	$0.0194424\pi$
$744$			221437.i			0.400040i
$745$	−175119.	−	760418.i	−0.315515	−	1.37006i
$746$	−483611.			−0.868998
$747$	42836.5	+	42836.5i	0.0767667	+	0.0767667i
$748$	19713.1	−	19713.1i	0.0352332	−	0.0352332i
$749$		−	62654.3i		−	0.111683i
$750$	196990.	−	158986.i	0.350205	−	0.282642i
$751$	380001.			0.673759			0.336880	−	0.941548i	$-0.390628\pi$
$751$	380001.			0.673759			0.336880	+	0.941548i	$0.390628\pi$
$752$	−41833.0	−	41833.0i	−0.0739748	−	0.0739748i
$753$	124323.	−	124323.i	0.219262	−	0.219262i
$754$			23173.2i			0.0407609i
$755$	85722.0	−	19741.2i	0.150383	−	0.0346321i
$756$	437565.			0.765596
$757$	−271163.	−	271163.i	−0.473193	−	0.473193i	0.429753	−	0.902946i	$-0.358601\pi$
$757$	−271163.	−	271163.i	−0.473193	−	0.473193i	−0.902946	+	0.429753i	$0.858601\pi$
$758$	26411.4	−	26411.4i	0.0459678	−	0.0459678i
$759$		−	26342.8i		−	0.0457275i
$760$	15558.6	+	9733.89i	0.0269366	+	0.0168523i
$761$	−66995.1			−0.115684			−0.0578421	−	0.998326i	$-0.518422\pi$
$761$	−66995.1			−0.115684			−0.0578421	+	0.998326i	$0.518422\pi$
$762$	50604.9	+	50604.9i	0.0871530	+	0.0871530i
$763$	−369748.	+	369748.i	−0.635121	+	0.635121i
$764$			412065.i			0.705958i
$765$	53407.3	−	85365.7i	0.0912594	−	0.145868i
$766$	4783.78			0.00815293
$767$	−43001.6	−	43001.6i	−0.0730961	−	0.0730961i
$768$	−16590.0	+	16590.0i	−0.0281271	+	0.0281271i
$769$			1.11199e6i			1.88040i	0.340624	+	0.940200i	$0.389362\pi$
$769$			1.11199e6i			1.88040i	−0.340624	+	0.940200i	$0.610638\pi$
$770$	48902.7	+	212350.i	0.0824806	+	0.358155i
$771$	609102.			1.02466
$772$	57563.3	+	57563.3i	0.0965852	+	0.0965852i
$773$	588988.	−	588988.i	0.985705	−	0.985705i	−0.0141938	−	0.999899i	$-0.504518\pi$
$773$	588988.	−	588988.i	0.985705	−	0.985705i	0.999899	+	0.0141938i	$0.00451818\pi$
$774$			6127.04i			0.0102275i
$775$	−960249.	+	467047.i	−1.59875	+	0.777601i
$776$	−289717.			−0.481116
$777$	549356.	+	549356.i	0.909938	+	0.909938i
$778$	144726.	−	144726.i	0.239104	−	0.239104i
$779$			24804.6i			0.0408750i
$780$	−56096.0	+	12918.5i	−0.0922025	+	0.0212336i
$781$	−24086.4			−0.0394885
$782$	18438.9	+	18438.9i	0.0301524	+	0.0301524i
$783$	−85317.2	+	85317.2i	−0.139160	+	0.139160i
$784$		−	195977.i		−	0.318841i
$785$	730019.	+	456721.i	1.18466	+	0.741160i
$786$	−401098.			−0.649240
$787$	−388926.	−	388926.i	−0.627940	−	0.627940i	0.319610	−	0.947549i	$-0.396448\pi$
$787$	−388926.	−	388926.i	−0.627940	−	0.627940i	−0.947549	+	0.319610i	$0.896448\pi$
$788$	257897.	−	257897.i	0.415330	−	0.415330i
$789$		−	668813.i		−	1.07436i
$790$	246060.	−	393301.i	0.394264	−	0.630189i
$791$	−904356.			−1.44540
$792$	32147.4	+	32147.4i	0.0512502	+	0.0512502i
$793$	−344.726	+	344.726i	−0.000548186	+	0.000548186i
$794$		−	458885.i		−	0.727885i
$795$	−141236.	−	613290.i	−0.223466	−	0.970357i
$796$	150447.			0.237442
$797$	560650.	+	560650.i	0.882624	+	0.882624i	0.993801	−	0.111177i	$-0.0354621\pi$
$797$	560650.	+	560650.i	0.882624	+	0.882624i	−0.111177	+	0.993801i	$0.535462\pi$
$798$	27471.1	−	27471.1i	0.0431390	−	0.0431390i
$799$			77262.3i			0.121025i
$800$	−106933.	−	36950.7i	−0.167083	−	0.0577354i
$801$	215728.			0.336233
$802$	249740.	+	249740.i	0.388275	+	0.388275i
$803$	266159.	−	266159.i	0.412772	−	0.412772i
$804$			14016.0i			0.0216826i
$805$	−198624.	+	45741.7i	−0.306507	+	0.0705864i
$806$	242817.			0.373774
$807$	−27681.8	−	27681.8i	−0.0425057	−	0.0425057i
$808$	−169564.	+	169564.i	−0.259723	+	0.259723i
$809$			1.22537e6i			1.87228i	0.351633	+	0.936138i	$0.385626\pi$
$809$			1.22537e6i			1.87228i	−0.351633	+	0.936138i	$0.614374\pi$
$810$	−20100.3	−	12575.3i	−0.0306360	−	0.0191668i
$811$	609150.			0.926152			0.463076	−	0.886318i	$-0.346746\pi$
$811$	609150.			0.926152			0.463076	+	0.886318i	$0.346746\pi$
$812$	68173.7	+	68173.7i	0.103396	+	0.103396i
$813$	−540415.	+	540415.i	−0.817610	+	0.817610i
$814$			216400.i			0.326594i
$815$	−419587.	+	670664.i	−0.631694	+	1.00969i
$816$	30640.5			0.0460166
$817$	1031.23	+	1031.23i	0.00154494	+	0.00154494i
$818$	−291031.	+	291031.i	−0.434944	+	0.434944i
$819$		−	178979.i		−	0.266829i
$820$	−34316.3	−	149011.i	−0.0510355	−	0.221611i
$821$	485521.			0.720313			0.360157	−	0.932892i	$-0.382723\pi$
$821$	485521.			0.720313			0.360157	+	0.932892i	$0.382723\pi$
$822$	148307.	+	148307.i	0.219492	+	0.219492i
$823$	152693.	−	152693.i	0.225434	−	0.225434i	−0.585348	−	0.810782i	$-0.699042\pi$
$823$	152693.	−	152693.i	0.225434	−	0.225434i	0.810782	+	0.585348i	$0.199042\pi$
$824$		−	386695.i		−	0.569527i
$825$	48749.1	−	141077.i	0.0716241	−	0.207276i
$826$	−253014.			−0.370839
$827$	−730682.	−	730682.i	−1.06836	−	1.06836i	−0.997485	−	0.0708736i	$-0.977421\pi$
$827$	−730682.	−	730682.i	−1.06836	−	1.06836i	−0.0708736	−	0.997485i	$-0.522579\pi$
$828$	−30069.4	+	30069.4i	−0.0438596	+	0.0438596i
$829$			232547.i			0.338377i	0.985584	+	0.169189i	$0.0541147\pi$
$829$			232547.i			0.338377i	−0.985584	+	0.169189i	$0.945885\pi$
$830$	−86623.2	+	19948.7i	−0.125741	+	0.0289574i
$831$	280830.			0.406669
$832$	18191.8	+	18191.8i	0.0262803	+	0.0262803i
$833$	−180977.	+	180977.i	−0.260816	+	0.260816i
$834$		−	138141.i		−	0.198605i
$835$	−581996.	−	364113.i	−0.834731	−	0.522232i
$836$	10821.3			0.0154834
$837$	893983.	+	893983.i	1.27608	+	1.27608i
$838$	−570249.	+	570249.i	−0.812038	+	0.812038i
$839$		−	1.30767e6i		−	1.85769i	−0.370469	−	0.928845i	$-0.620803\pi$
$839$		−	1.30767e6i		−	1.85769i	0.370469	−	0.928845i	$-0.379197\pi$
$840$	−127025.	+	203035.i	−0.180023	+	0.287748i
$841$	680696.			0.962412
$842$	307909.	+	307909.i	0.434308	+	0.434308i
$843$	−20810.0	+	20810.0i	−0.0292830	+	0.0292830i
$844$		−	555051.i		−	0.779198i
$845$	−146075.	−	634300.i	−0.204579	−	0.888344i
$846$	−125996.			−0.176042
$847$	−674351.	−	674351.i	−0.939981	−	0.939981i
$848$	−198889.	+	198889.i	−0.276578	+	0.276578i
$849$		−	782524.i		−	1.08563i
$850$	64625.8	+	132871.i	0.0894475	+	0.183904i
$851$	−202412.			−0.279497
$852$	−18719.0	−	18719.0i	−0.0257871	−	0.0257871i
$853$	724503.	−	724503.i	0.995731	−	0.995731i	−0.00425997	−	0.999991i	$-0.501356\pi$
$853$	724503.	−	724503.i	0.995731	−	0.995731i	0.999991	+	0.00425997i	$0.00135600\pi$
$854$			2028.31i			0.00278111i
$855$	38088.9	−	8771.62i	0.0521035	−	0.0119991i
$856$	19180.7			0.0261768
$857$	−189969.	−	189969.i	−0.258655	−	0.258655i	0.565852	−	0.824507i	$-0.308547\pi$
$857$	−189969.	−	189969.i	−0.258655	−	0.258655i	−0.824507	+	0.565852i	$0.808547\pi$
$858$	−24000.5	+	24000.5i	−0.0326022	+	0.0326022i
$859$		−	368893.i		−	0.499936i	−0.968254	−	0.249968i	$-0.919580\pi$
$859$		−	368893.i		−	0.499936i	0.968254	−	0.249968i	$-0.0804200\pi$
$860$	−7621.66	−	4768.33i	−0.0103051	−	0.00644718i
$861$	−323694.			−0.436645
$862$	−43284.1	−	43284.1i	−0.0582524	−	0.0582524i
$863$	−188070.	+	188070.i	−0.252522	+	0.252522i	−0.822004	−	0.569482i	$-0.807144\pi$
$863$	−188070.	+	188070.i	−0.252522	+	0.252522i	0.569482	+	0.822004i	$0.307144\pi$
$864$			133954.i			0.179444i
$865$	752363.	−	1.20257e6i	1.00553	−	1.60723i
$866$	−992273.			−1.32311
$867$	309990.	+	309990.i	0.412391	+	0.412391i
$868$	714347.	−	714347.i	0.948134	−	0.948134i
$869$		−	273549.i		−	0.362239i
$870$	−14820.6	−	64355.6i	−0.0195807	−	0.0850252i
$871$	15369.3			0.0202589
$872$	−113193.	−	113193.i	−0.148863	−	0.148863i
$873$	−436297.	+	436297.i	−0.572471	+	0.572471i
$874$			10121.8i			0.0132506i
$875$	−1.14837e6	−	122601.i	−1.49991	−	0.160132i
$876$	413696.			0.539105
$877$	−821253.	−	821253.i	−1.06777	−	1.06777i	−0.997530	−	0.0702398i	$-0.977624\pi$
$877$	−821253.	−	821253.i	−1.06777	−	1.06777i	−0.0702398	−	0.997530i	$-0.522376\pi$
$878$	−430597.	+	430597.i	−0.558575	+	0.558575i
$879$		−	57151.2i		−	0.0739687i
$880$	−65007.9	+	14970.9i	−0.0839461	+	0.0193322i
$881$	1.17238e6			1.51049			0.755243	−	0.655444i	$-0.227519\pi$
$881$	1.17238e6			1.51049			0.755243	+	0.655444i	$0.227519\pi$
$882$	−295131.	−	295131.i	−0.379382	−	0.379382i
$883$	813758.	−	813758.i	1.04370	−	1.04370i	0.0446954	−	0.999001i	$-0.485768\pi$
$883$	813758.	−	813758.i	1.04370	−	1.04370i	0.999001	−	0.0446954i	$-0.0142317\pi$
$884$		−	33598.8i		−	0.0429952i
$885$	146924.	+	91920.0i	0.187589	+	0.117361i
$886$	1.03305e6			1.31599
$887$	847139.	+	847139.i	1.07673	+	1.07673i	0.996800	+	0.0799305i	$0.0254698\pi$
$887$	847139.	+	847139.i	1.07673	+	1.07673i	0.0799305	+	0.996800i	$0.474530\pi$
$888$	−168177.	+	168177.i	−0.213276	+	0.213276i
$889$		−	326499.i		−	0.413122i
$890$	−167889.	+	268352.i	−0.211954	+	0.338785i
$891$	−13980.2			−0.0176099
$892$	−115458.	−	115458.i	−0.145109	−	0.145109i
$893$	−21206.1	+	21206.1i	−0.0265925	+	0.0265925i
$894$		−	505686.i		−	0.632712i
$895$	16740.5	+	72692.2i	0.0208988	+	0.0907490i
$896$	107038.			0.133328
$897$	−22449.2	−	22449.2i	−0.0279007	−	0.0279007i
$898$	−164185.	+	164185.i	−0.203602	+	0.203602i
$899$			278569.i			0.344678i
$900$	−216680.	+	105389.i	−0.267507	+	0.130110i
$901$	367331.			0.452489
$902$	−63754.1	−	63754.1i	−0.0783602	−	0.0783602i
$903$	−13457.2	+	13457.2i	−0.0165037	+	0.0165037i
$904$		−	276855.i		−	0.338779i
$905$	−853821.	+	196629.i	−1.04248	+	0.240077i
$906$	57006.0			0.0694488
$907$	−779229.	−	779229.i	−0.947220	−	0.947220i	0.0514556	−	0.998675i	$-0.483614\pi$
$907$	−779229.	−	779229.i	−0.947220	−	0.947220i	−0.998675	+	0.0514556i	$0.983614\pi$
$908$	−167690.	+	167690.i	−0.203393	+	0.203393i
$909$			510706.i			0.618077i
$910$	222638.	+	139289.i	0.268854	+	0.168203i
$911$	815758.			0.982935			0.491467	−	0.870896i	$-0.336461\pi$
$911$	815758.			0.982935			0.491467	+	0.870896i	$0.336461\pi$
$912$	8409.87	+	8409.87i	0.0101111	+	0.0101111i
$913$	−37061.5	+	37061.5i	−0.0444613	+	0.0444613i
$914$			37985.0i			0.0454695i
$915$	736.884	−	1177.83i	0.000880150	−	0.00140682i
$916$	257469.			0.306856
$917$	1.29393e6	+	1.29393e6i	1.53876	+	1.53876i
$918$	123701.	−	123701.i	0.146788	−	0.146788i
$919$		−	426975.i		−	0.505558i	−0.967524	−	0.252779i	$-0.918655\pi$
$919$		−	426975.i		−	0.505558i	0.967524	−	0.252779i	$-0.0813446\pi$
$920$	−14003.2	−	60805.9i	−0.0165444	−	0.0718406i
$921$	−488209.			−0.575554
$922$	−282682.	−	282682.i	−0.332535	−	0.332535i
$923$	−20526.3	+	20526.3i	−0.0240939	+	0.0240939i
$924$			141215.i			0.165401i
$925$	−1.08401e6	−	374578.i	−1.26692	−	0.437783i
$926$	984896.			1.14860
$927$	−582341.	−	582341.i	−0.677669	−	0.677669i
$928$	−20870.4	+	20870.4i	−0.0242345	+	0.0242345i
$929$			694233.i			0.804404i	0.915551	+	0.402202i	$0.131755\pi$
$929$			694233.i			0.804404i	−0.915551	+	0.402202i	$0.868245\pi$
$930$	−674339.	+	155296.i	−0.779673	+	0.179553i
$931$	−99345.5			−0.114617
$932$	−167227.	−	167227.i	−0.192519	−	0.192519i
$933$	−190431.	+	190431.i	−0.218764	+	0.218764i
$934$			852434.i			0.977163i
$935$	73857.2	+	46207.2i	0.0844830	+	0.0528550i
$936$	54791.7			0.0625407
$937$	139879.	+	139879.i	0.159321	+	0.159321i	0.782266	−	0.622945i	$-0.214064\pi$
$937$	139879.	+	139879.i	0.159321	+	0.159321i	−0.622945	+	0.782266i	$0.714064\pi$
$938$	45215.1	−	45215.1i	0.0513899	−	0.0513899i
$939$		−	770157.i		−	0.873470i
$940$	98055.9	−	156732.i	0.110973	−	0.177378i
$941$	−1.29173e6			−1.45879			−0.729396	−	0.684091i	$-0.760199\pi$
$941$	−1.29173e6			−1.45879			−0.729396	+	0.684091i	$0.760199\pi$
$942$	394597.	+	394597.i	0.444685	+	0.444685i
$943$	59633.1	−	59633.1i	0.0670601	−	0.0670601i
$944$		−	77456.6i		−	0.0869190i
$945$	306868.	+	1.33251e6i	0.343628	+	1.49213i
$946$	−5301.03			−0.00592349
$947$	935951.	+	935951.i	1.04365	+	1.04365i	0.999003	+	0.0446425i	$0.0142149\pi$
$947$	935951.	+	935951.i	1.04365	+	1.04365i	0.0446425	+	0.999003i	$0.485785\pi$
$948$	212591.	−	212591.i	0.236553	−	0.236553i
$949$		−	453639.i		−	0.503707i
$950$	−18731.2	+	54206.8i	−0.0207547	+	0.0600629i
$951$	−200125.			−0.221279
$952$	−98845.0	−	98845.0i	−0.109064	−	0.109064i
$953$	858953.	−	858953.i	0.945766	−	0.945766i	−0.0528371	−	0.998603i	$-0.516826\pi$
$953$	858953.	−	858953.i	0.945766	−	0.945766i	0.998603	+	0.0528371i	$0.0168264\pi$
$954$			599029.i			0.658190i
$955$	−1.25486e6	+	288985.i	−1.37590	+	0.316861i
$956$	486581.			0.532402
$957$	−27534.4	−	27534.4i	−0.0300643	−	0.0300643i
$958$	−199922.	+	199922.i	−0.217836	+	0.217836i
$959$		−	956868.i		−	1.04043i
$960$	−62156.2	−	38886.7i	−0.0674438	−	0.0421948i
$961$	1.99542e6			2.16066
$962$	184415.	+	184415.i	0.199272	+	0.199272i
$963$	28885.0	−	28885.0i	0.0311473	−	0.0311473i
$964$		−	84541.2i		−	0.0909733i
$965$	−134927.	+	215666.i	−0.144892	+	0.231594i
$966$	−132087.			−0.141549
$967$	−1.00637e6	−	1.00637e6i	−1.07623	−	1.07623i	−0.996844	−	0.0793884i	$-0.974703\pi$
$967$	−1.00637e6	−	1.00637e6i	−1.07623	−	1.07623i	−0.0793884	−	0.996844i	$-0.525297\pi$
$968$	206443.	−	206443.i	0.220317	−	0.220317i
$969$		−	15532.4i		−	0.0165421i
$970$	−203181.	−	882271.i	−0.215943	−	0.937689i
$971$	−629478.			−0.667640			−0.333820	−	0.942637i	$-0.608338\pi$
$971$	−629478.			−0.667640			−0.333820	+	0.942637i	$0.608338\pi$
$972$	328207.	+	328207.i	0.347388	+	0.347388i
$973$	−445637.	+	445637.i	−0.470712	+	0.470712i
$974$		−	199548.i		−	0.210344i
$975$	−78681.3	−	161769.i	−0.0827679	−	0.170171i
$976$	−620.937			−0.000651851
$977$	2990.89	+	2990.89i	0.00313337	+	0.00313337i	0.708672	−	0.705538i	$-0.249295\pi$
$977$	2990.89	+	2990.89i	0.00313337	+	0.00313337i	−0.705538	+	0.708672i	$0.749295\pi$
$978$	−362514.	+	362514.i	−0.379007	+	0.379007i
$979$			186644.i			0.194737i
$980$	596808.	−	137441.i	0.621416	−	0.143108i
$981$	−340924.			−0.354258
$982$	631206.	+	631206.i	0.654557	+	0.654557i
$983$	−468294.	+	468294.i	−0.484631	+	0.484631i	−0.906607	−	0.421976i	$-0.861337\pi$
$983$	−468294.	+	468294.i	−0.484631	+	0.484631i	0.421976	+	0.906607i	$0.361337\pi$
$984$		−	99094.1i		−	0.102343i
$985$	966236.	+	604505.i	0.995889	+	0.623057i
$986$	38545.9			0.0396483
$987$	−276734.	−	276734.i	−0.284072	−	0.284072i
$988$	9221.86	−	9221.86i	0.00944723	−	0.00944723i
$989$		−	4958.37i		−	0.00506929i
$990$	−75352.9	+	120443.i	−0.0768828	+	0.122889i
$991$	−4697.01			−0.00478271			−0.00239136	−	0.999997i	$-0.500761\pi$
$991$	−4697.01			−0.00478271			−0.00239136	+	0.999997i	$0.500761\pi$
$992$	218687.	+	218687.i	0.222228	+	0.222228i
$993$	304122.	−	304122.i	0.308425	−	0.308425i
$994$			120773.i			0.122236i
$995$	105510.	+	458155.i	0.106573	+	0.462771i
$996$	−57605.4			−0.0580690
$997$	−603976.	−	603976.i	−0.607617	−	0.607617i	0.334706	−	0.942323i	$-0.391363\pi$
$997$	−603976.	−	603976.i	−0.607617	−	0.607617i	−0.942323	+	0.334706i	$0.891363\pi$
$998$	−573830.	+	573830.i	−0.576132	+	0.576132i
$999$			1.35793e6i			1.36065i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.f.b.47.9	✓	44
5.3	odd	4	inner	230.5.f.b.93.9	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.f.b.47.9	✓	44	1.1	even	1	trivial
230.5.f.b.93.9	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)

\(f(q)\)	\(=\)	\(q+(2.00000 + 2.00000i) q^{2} +(-4.05030 + 4.05030i) q^{3} +8.00000i q^{4} +(-24.3623 + 5.61047i) q^{5} -16.2012 q^{6} +(52.2645 + 52.2645i) q^{7} +(-16.0000 + 16.0000i) q^{8} +48.1901i q^{9} +O(q^{10})\)	\(q+(2.00000 + 2.00000i) q^{2} +(-4.05030 + 4.05030i) q^{3} +8.00000i q^{4} +(-24.3623 + 5.61047i) q^{5} -16.2012 q^{6} +(52.2645 + 52.2645i) q^{7} +(-16.0000 + 16.0000i) q^{8} +48.1901i q^{9} +(-59.9456 - 37.5037i) q^{10} -41.6934 q^{11} +(-32.4024 - 32.4024i) q^{12} +(-35.5309 + 35.5309i) q^{13} +209.058i q^{14} +(75.9506 - 121.399i) q^{15} -64.0000 q^{16} +(59.1014 + 59.1014i) q^{17} +(-96.3803 + 96.3803i) q^{18} +32.4431i q^{19} +(-44.8838 - 194.899i) q^{20} -423.373 q^{21} +(-83.3868 - 83.3868i) q^{22} +(77.9968 - 77.9968i) q^{23} -129.610i q^{24} +(562.045 - 273.368i) q^{25} -142.124 q^{26} +(-523.259 - 523.259i) q^{27} +(-418.116 + 418.116i) q^{28} -163.050i q^{29} +(394.699 - 90.8963i) q^{30} -1708.49 q^{31} +(-128.000 - 128.000i) q^{32} +(168.871 - 168.871i) q^{33} +236.406i q^{34} +(-1566.51 - 980.055i) q^{35} -385.521 q^{36} +(-1297.57 - 1297.57i) q^{37} +(-64.8862 + 64.8862i) q^{38} -287.822i q^{39} +(300.030 - 479.565i) q^{40} +764.559 q^{41} +(-846.747 - 846.747i) q^{42} +(31.7858 - 31.7858i) q^{43} -333.547i q^{44} +(-270.369 - 1174.02i) q^{45} +311.987 q^{46} +(653.641 + 653.641i) q^{47} +(259.219 - 259.219i) q^{48} +3062.15i q^{49} +(1670.83 + 577.354i) q^{50} -478.757 q^{51} +(-284.247 - 284.247i) q^{52} +(3107.63 - 3107.63i) q^{53} -2093.04i q^{54} +(1015.75 - 233.920i) q^{55} -1672.46 q^{56} +(-131.404 - 131.404i) q^{57} +(326.100 - 326.100i) q^{58} +1210.26i q^{59} +(971.190 + 607.605i) q^{60} +9.70215 q^{61} +(-3416.98 - 3416.98i) q^{62} +(-2518.63 + 2518.63i) q^{63} -512.000i q^{64} +(666.270 - 1064.96i) q^{65} +675.483 q^{66} +(-216.280 - 216.280i) q^{67} +(-472.812 + 472.812i) q^{68} +631.821i q^{69} +(-1172.91 - 5093.13i) q^{70} +577.704 q^{71} +(-771.042 - 771.042i) q^{72} +(-6383.73 + 6383.73i) q^{73} -5190.27i q^{74} +(-1169.23 + 3383.67i) q^{75} -259.545 q^{76} +(-2179.08 - 2179.08i) q^{77} +(575.643 - 575.643i) q^{78} +6560.96i q^{79} +(1559.19 - 359.070i) q^{80} +335.309 q^{81} +(1529.12 + 1529.12i) q^{82} +(888.906 - 888.906i) q^{83} -3386.99i q^{84} +(-1771.44 - 1108.26i) q^{85} +127.143 q^{86} +(660.401 + 660.401i) q^{87} +(667.095 - 667.095i) q^{88} -4476.59i q^{89} +(1807.31 - 2888.79i) q^{90} -3714.01 q^{91} +(623.974 + 623.974i) q^{92} +(6919.90 - 6919.90i) q^{93} +2614.57i q^{94} +(-182.021 - 790.389i) q^{95} +1036.88 q^{96} +(9053.65 + 9053.65i) q^{97} +(-6124.30 + 6124.30i) q^{98} -2009.21i 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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