LMFDB - Embedded newform 230.5.f.a.47.2

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			47.2
Character	$\chi$	$=$	230.47
Dual form			230.5.f.a.93.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 - 2.00000i) q^{2} +(-10.5012 + 10.5012i) q^{3} +8.00000i q^{4} +(10.9451 + 22.4768i) q^{5} +42.0050 q^{6} +(-20.3725 - 20.3725i) q^{7} +(16.0000 - 16.0000i) q^{8} -139.552i q^{9} +O(q^{10})$	\(q+(-2.00000 - 2.00000i) q^{2} +(-10.5012 + 10.5012i) q^{3} +8.00000i q^{4} +(10.9451 + 22.4768i) q^{5} +42.0050 q^{6} +(-20.3725 - 20.3725i) q^{7} +(16.0000 - 16.0000i) q^{8} -139.552i q^{9} +(23.0634 - 66.8437i) q^{10} +3.75381 q^{11} +(-84.0100 - 84.0100i) q^{12} +(-110.920 + 110.920i) q^{13} +81.4900i q^{14} +(-350.971 - 121.097i) q^{15} -64.0000 q^{16} +(-262.668 - 262.668i) q^{17} +(-279.105 + 279.105i) q^{18} -305.041i q^{19} +(-179.814 + 87.5607i) q^{20} +427.873 q^{21} +(-7.50762 - 7.50762i) q^{22} +(-77.9968 + 77.9968i) q^{23} +336.040i q^{24} +(-385.410 + 492.020i) q^{25} +443.678 q^{26} +(614.872 + 614.872i) q^{27} +(162.980 - 162.980i) q^{28} -27.2586i q^{29} +(459.748 + 944.136i) q^{30} +843.542 q^{31} +(128.000 + 128.000i) q^{32} +(-39.4197 + 39.4197i) q^{33} +1050.67i q^{34} +(234.929 - 680.887i) q^{35} +1116.42 q^{36} +(323.683 + 323.683i) q^{37} +(-610.083 + 610.083i) q^{38} -2329.59i q^{39} +(534.750 + 184.507i) q^{40} +105.408 q^{41} +(-855.747 - 855.747i) q^{42} +(1725.87 - 1725.87i) q^{43} +30.0305i q^{44} +(3136.68 - 1527.41i) q^{45} +311.987 q^{46} +(-574.622 - 574.622i) q^{47} +(672.080 - 672.080i) q^{48} -1570.92i q^{49} +(1754.86 - 213.220i) q^{50} +5516.69 q^{51} +(-887.356 - 887.356i) q^{52} +(-790.765 + 790.765i) q^{53} -2459.49i q^{54} +(41.0858 + 84.3735i) q^{55} -651.920 q^{56} +(3203.31 + 3203.31i) q^{57} +(-54.5171 + 54.5171i) q^{58} +194.702i q^{59} +(968.776 - 2807.77i) q^{60} +2985.12 q^{61} +(-1687.08 - 1687.08i) q^{62} +(-2843.03 + 2843.03i) q^{63} -512.000i q^{64} +(-3707.14 - 1279.09i) q^{65} +157.679 q^{66} +(1253.37 + 1253.37i) q^{67} +(2101.35 - 2101.35i) q^{68} -1638.13i q^{69} +(-1831.63 + 891.916i) q^{70} +5433.53 q^{71} +(-2232.84 - 2232.84i) q^{72} +(-6108.29 + 6108.29i) q^{73} -1294.73i q^{74} +(-1119.54 - 9214.11i) q^{75} +2440.33 q^{76} +(-76.4745 - 76.4745i) q^{77} +(-4659.17 + 4659.17i) q^{78} -2583.99i q^{79} +(-700.486 - 1438.51i) q^{80} -1610.10 q^{81} +(-210.815 - 210.815i) q^{82} +(-580.635 + 580.635i) q^{83} +3422.99i q^{84} +(3029.01 - 8778.86i) q^{85} -6903.48 q^{86} +(286.249 + 286.249i) q^{87} +(60.0610 - 60.0610i) q^{88} +1893.55i q^{89} +(-9328.19 - 3218.54i) q^{90} +4519.42 q^{91} +(-623.974 - 623.974i) q^{92} +(-8858.25 + 8858.25i) q^{93} +2298.49i q^{94} +(6856.35 - 3338.71i) q^{95} -2688.32 q^{96} +(10500.7 + 10500.7i) q^{97} +(-3141.84 + 3141.84i) q^{98} -523.853i 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} - 184 q^{10} + 8 q^{11} + 20 q^{13} + 396 q^{15} - 2816 q^{16} + 1080 q^{17} - 2648 q^{18} + 544 q^{20} - 3096 q^{21} - 16 q^{22} - 1884 q^{25} - 80 q^{26} - 3828 q^{27} + 640 q^{28} - 2520 q^{30} - 1580 q^{31} + 5632 q^{32} + 3644 q^{33} + 8208 q^{35} + 10592 q^{36} + 3104 q^{37} - 4064 q^{38} - 704 q^{40} + 4124 q^{41} + 6192 q^{42} - 960 q^{43} - 11316 q^{45} + 2424 q^{47} + 7832 q^{50} + 14840 q^{51} + 160 q^{52} - 3116 q^{53} - 2572 q^{55} - 2560 q^{56} - 9408 q^{57} - 3928 q^{58} + 6912 q^{60} + 19136 q^{61} + 3160 q^{62} + 4564 q^{63} - 9220 q^{65} - 14576 q^{66} - 5152 q^{67} - 8640 q^{68} - 23672 q^{70} + 7900 q^{71} - 21184 q^{72} + 16424 q^{73} + 24156 q^{75} + 16256 q^{76} - 27012 q^{77} - 1808 q^{78} - 1536 q^{80} - 116684 q^{81} - 8248 q^{82} + 11184 q^{83} - 14620 q^{85} + 3840 q^{86} + 8312 q^{87} + 128 q^{88} + 14544 q^{90} + 10296 q^{91} - 7488 q^{93} + 19536 q^{95} + 41292 q^{97} + 51024 q^{98}+O(q^{100}) $ 44 * q - 88 * q^2 + 24 * q^5 - 80 * q^7 + 704 * q^8 - 184 * q^10 + 8 * q^11 + 20 * q^13 + 396 * q^15 - 2816 * q^16 + 1080 * q^17 - 2648 * q^18 + 544 * q^20 - 3096 * q^21 - 16 * q^22 - 1884 * q^25 - 80 * q^26 - 3828 * q^27 + 640 * q^28 - 2520 * q^30 - 1580 * q^31 + 5632 * q^32 + 3644 * q^33 + 8208 * q^35 + 10592 * q^36 + 3104 * q^37 - 4064 * q^38 - 704 * q^40 + 4124 * q^41 + 6192 * q^42 - 960 * q^43 - 11316 * q^45 + 2424 * q^47 + 7832 * q^50 + 14840 * q^51 + 160 * q^52 - 3116 * q^53 - 2572 * q^55 - 2560 * q^56 - 9408 * q^57 - 3928 * q^58 + 6912 * q^60 + 19136 * q^61 + 3160 * q^62 + 4564 * q^63 - 9220 * q^65 - 14576 * q^66 - 5152 * q^67 - 8640 * q^68 - 23672 * q^70 + 7900 * q^71 - 21184 * q^72 + 16424 * q^73 + 24156 * q^75 + 16256 * q^76 - 27012 * q^77 - 1808 * q^78 - 1536 * q^80 - 116684 * q^81 - 8248 * q^82 + 11184 * q^83 - 14620 * q^85 + 3840 * q^86 + 8312 * q^87 + 128 * q^88 + 14544 * q^90 + 10296 * q^91 - 7488 * q^93 + 19536 * q^95 + 41292 * q^97 + 51024 * 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
$3$	−10.5012	+	10.5012i	−1.16680	+	1.16680i	−0.183851	+	0.982954i	$0.558856\pi$
$3$	−10.5012	+	10.5012i	−1.16680	+	1.16680i	−0.982954	+	0.183851i	$0.941144\pi$
$4$			8.00000i			0.500000i
$5$	10.9451	+	22.4768i	0.437803	+	0.899071i
$5$	10.9451	+	22.4768i	0.437803	+	0.899071i
$6$	42.0050			1.16680
$7$	−20.3725	−	20.3725i	−0.415765	−	0.415765i	0.467976	−	0.883741i	$-0.344983\pi$
$7$	−20.3725	−	20.3725i	−0.415765	−	0.415765i	−0.883741	+	0.467976i	$0.844983\pi$
$8$	16.0000	−	16.0000i	0.250000	−	0.250000i
$9$		−	139.552i		−	1.72287i
$10$	23.0634	−	66.8437i	0.230634	−	0.668437i
$11$	3.75381			0.0310232			0.0155116	−	0.999880i	$-0.495062\pi$
$11$	3.75381			0.0310232			0.0155116	+	0.999880i	$0.495062\pi$
$12$	−84.0100	−	84.0100i	−0.583402	−	0.583402i
$13$	−110.920	+	110.920i	−0.656328	+	0.656328i	−0.954509	−	0.298181i	$-0.903620\pi$
$13$	−110.920	+	110.920i	−0.656328	+	0.656328i	0.298181	+	0.954509i	$0.403620\pi$
$14$			81.4900i			0.415765i
$15$	−350.971	−	121.097i	−1.55987	−	0.538209i
$16$	−64.0000			−0.250000
$17$	−262.668	−	262.668i	−0.908887	−	0.908887i	0.0872958	−	0.996182i	$-0.472177\pi$
$17$	−262.668	−	262.668i	−0.908887	−	0.908887i	−0.996182	+	0.0872958i	$0.972177\pi$
$18$	−279.105	+	279.105i	−0.861434	+	0.861434i
$19$		−	305.041i		−	0.844990i	−0.906365	−	0.422495i	$-0.861154\pi$
$19$		−	305.041i		−	0.844990i	0.906365	−	0.422495i	$-0.138846\pi$
$20$	−179.814	+	87.5607i	−0.449535	+	0.218902i
$21$	427.873			0.970234
$22$	−7.50762	−	7.50762i	−0.0155116	−	0.0155116i
$23$	−77.9968	+	77.9968i	−0.147442	+	0.147442i
$23$	−77.9968	+	77.9968i	−0.147442	+	0.147442i
$24$			336.040i			0.583402i
$25$	−385.410	+	492.020i	−0.616656	+	0.787233i
$26$	443.678			0.656328
$27$	614.872	+	614.872i	0.843445	+	0.843445i
$28$	162.980	−	162.980i	0.207883	−	0.207883i
$29$		−	27.2586i		−	0.0324121i	−0.999869	−	0.0162060i	$-0.994841\pi$
$29$		−	27.2586i		−	0.0324121i	0.999869	−	0.0162060i	$-0.00515877\pi$
$30$	459.748	+	944.136i	0.510831	+	1.04904i
$31$	843.542			0.877776			0.438888	−	0.898542i	$-0.355373\pi$
$31$	843.542			0.877776			0.438888	+	0.898542i	$0.355373\pi$
$32$	128.000	+	128.000i	0.125000	+	0.125000i
$33$	−39.4197	+	39.4197i	−0.0361981	+	0.0361981i
$34$			1050.67i			0.908887i
$35$	234.929	−	680.887i	0.191779	−	0.555826i
$36$	1116.42			0.861434
$37$	323.683	+	323.683i	0.236438	+	0.236438i	0.815373	−	0.578936i	$-0.196532\pi$
$37$	323.683	+	323.683i	0.236438	+	0.236438i	−0.578936	+	0.815373i	$0.696532\pi$
$38$	−610.083	+	610.083i	−0.422495	+	0.422495i
$39$		−	2329.59i		−	1.53161i
$40$	534.750	+	184.507i	0.334219	+	0.115317i
$41$	105.408			0.0627053			0.0313526	−	0.999508i	$-0.490019\pi$
$41$	105.408			0.0627053			0.0313526	+	0.999508i	$0.490019\pi$
$42$	−855.747	−	855.747i	−0.485117	−	0.485117i
$43$	1725.87	−	1725.87i	0.933408	−	0.933408i	−0.0645093	−	0.997917i	$-0.520548\pi$
$43$	1725.87	−	1725.87i	0.933408	−	0.933408i	0.997917	+	0.0645093i	$0.0205482\pi$
$44$			30.0305i			0.0155116i
$45$	3136.68	−	1527.41i	1.54898	−	0.754277i
$46$	311.987			0.147442
$47$	−574.622	−	574.622i	−0.260128	−	0.260128i	0.564978	−	0.825106i	$-0.308885\pi$
$47$	−574.622	−	574.622i	−0.260128	−	0.260128i	−0.825106	+	0.564978i	$0.808885\pi$
$48$	672.080	−	672.080i	0.291701	−	0.291701i
$49$		−	1570.92i		−	0.654278i
$50$	1754.86	−	213.220i	0.701944	−	0.0852882i
$51$	5516.69			2.12099
$52$	−887.356	−	887.356i	−0.328164	−	0.328164i
$53$	−790.765	+	790.765i	−0.281511	+	0.281511i	−0.833712	−	0.552200i	$-0.813788\pi$
$53$	−790.765	+	790.765i	−0.281511	+	0.281511i	0.552200	+	0.833712i	$0.313788\pi$
$54$		−	2459.49i		−	0.843445i
$55$	41.0858	+	84.3735i	0.0135821	+	0.0278921i
$56$	−651.920			−0.207883
$57$	3203.31	+	3203.31i	0.985939	+	0.985939i
$58$	−54.5171	+	54.5171i	−0.0162060	+	0.0162060i
$59$			194.702i			0.0559327i	0.999609	+	0.0279664i	$0.00890313\pi$
$59$			194.702i			0.0559327i	−0.999609	+	0.0279664i	$0.991097\pi$
$60$	968.776	−	2807.77i	0.269104	−	0.779936i
$61$	2985.12			0.802236			0.401118	−	0.916026i	$-0.368622\pi$
$61$	2985.12			0.802236			0.401118	+	0.916026i	$0.368622\pi$
$62$	−1687.08	−	1687.08i	−0.438888	−	0.438888i
$63$	−2843.03	+	2843.03i	−0.716309	+	0.716309i
$64$		−	512.000i		−	0.125000i
$65$	−3707.14	−	1279.09i	−0.877429	−	0.302743i
$66$	157.679			0.0361981
$67$	1253.37	+	1253.37i	0.279210	+	0.279210i	0.832794	−	0.553584i	$-0.186740\pi$
$67$	1253.37	+	1253.37i	0.279210	+	0.279210i	−0.553584	+	0.832794i	$0.686740\pi$
$68$	2101.35	−	2101.35i	0.454443	−	0.454443i
$69$		−	1638.13i		−	0.344072i
$70$	−1831.63	+	891.916i	−0.373803	+	0.182024i
$71$	5433.53			1.07787			0.538934	−	0.842348i	$-0.318827\pi$
$71$	5433.53			1.07787			0.538934	+	0.842348i	$0.318827\pi$
$72$	−2232.84	−	2232.84i	−0.430717	−	0.430717i
$73$	−6108.29	+	6108.29i	−1.14624	+	1.14624i	−0.158949	+	0.987287i	$0.550811\pi$
$73$	−6108.29	+	6108.29i	−1.14624	+	1.14624i	−0.987287	+	0.158949i	$0.949189\pi$
$74$		−	1294.73i		−	0.236438i
$75$	−1119.54	−	9214.11i	−0.199029	−	1.63806i
$76$	2440.33			0.422495
$77$	−76.4745	−	76.4745i	−0.0128984	−	0.0128984i
$78$	−4659.17	+	4659.17i	−0.765807	+	0.765807i
$79$		−	2583.99i		−	0.414035i	−0.978337	−	0.207018i	$-0.933624\pi$
$79$		−	2583.99i		−	0.414035i	0.978337	−	0.207018i	$-0.0663757\pi$
$80$	−700.486	−	1438.51i	−0.109451	−	0.224768i
$81$	−1610.10			−0.245405
$82$	−210.815	−	210.815i	−0.0313526	−	0.0313526i
$83$	−580.635	+	580.635i	−0.0842843	+	0.0842843i	−0.747992	−	0.663708i	$-0.768982\pi$
$83$	−580.635	+	580.635i	−0.0842843	+	0.0842843i	0.663708	+	0.747992i	$0.268982\pi$
$84$			3422.99i			0.485117i
$85$	3029.01	−	8778.86i	0.419240	−	1.21507i
$86$	−6903.48			−0.933408
$87$	286.249	+	286.249i	0.0378186	+	0.0378186i
$88$	60.0610	−	60.0610i	0.00775581	−	0.00775581i
$89$			1893.55i			0.239055i	0.992831	+	0.119527i	$0.0381379\pi$
$89$			1893.55i			0.239055i	−0.992831	+	0.119527i	$0.961862\pi$
$90$	−9328.19	−	3218.54i	−1.15163	−	0.397351i
$91$	4519.42			0.545757
$92$	−623.974	−	623.974i	−0.0737210	−	0.0737210i
$93$	−8858.25	+	8858.25i	−1.02419	+	1.02419i
$94$			2298.49i			0.260128i
$95$	6856.35	−	3338.71i	0.759706	−	0.369940i
$96$	−2688.32			−0.291701
$97$	10500.7	+	10500.7i	1.11602	+	1.11602i	0.992319	+	0.123704i	$0.0394772\pi$
$97$	10500.7	+	10500.7i	1.11602	+	1.11602i	0.123704	+	0.992319i	$0.460523\pi$
$98$	−3141.84	+	3141.84i	−0.327139	+	0.327139i
$99$		−	523.853i		−	0.0534489i
$100$	−3936.16	−	3083.28i	−0.393616	−	0.308328i
$101$	15856.4			1.55440			0.777200	−	0.629253i	$-0.216639\pi$
$101$	15856.4			1.55440			0.777200	+	0.629253i	$0.216639\pi$
$102$	−11033.4	−	11033.4i	−1.06049	−	1.06049i
$103$	9244.58	−	9244.58i	0.871390	−	0.871390i	−0.121234	−	0.992624i	$-0.538685\pi$
$103$	9244.58	−	9244.58i	0.871390	−	0.871390i	0.992624	+	0.121234i	$0.0386850\pi$
$104$			3549.42i			0.328164i
$105$	4683.11	+	9617.21i	0.424772	+	0.872309i
$106$	3163.06			0.281511
$107$	1269.84	+	1269.84i	0.110913	+	0.110913i	0.760385	−	0.649472i	$-0.225010\pi$
$107$	1269.84	+	1269.84i	0.110913	+	0.110913i	−0.649472	+	0.760385i	$0.725010\pi$
$108$	−4918.97	+	4918.97i	−0.421723	+	0.421723i
$109$			197.855i			0.0166530i	0.999965	+	0.00832651i	$0.00265044\pi$
$109$			197.855i			0.0166530i	−0.999965	+	0.00832651i	$0.997350\pi$
$110$	86.5755	−	250.919i	0.00715500	−	0.0207371i
$111$	−6798.16			−0.551754
$112$	1303.84	+	1303.84i	0.103941	+	0.103941i
$113$	−6804.69	+	6804.69i	−0.532907	+	0.532907i	−0.921436	−	0.388529i	$-0.872983\pi$
$113$	−6804.69	+	6804.69i	−0.532907	+	0.532907i	0.388529	+	0.921436i	$0.372983\pi$
$114$		−	12813.3i		−	0.985939i
$115$	−2606.80	−	899.434i	−0.197111	−	0.0680101i
$116$	218.069			0.0162060
$117$	15479.1	+	15479.1i	1.13077	+	1.13077i
$118$	389.403	−	389.403i	0.0279664	−	0.0279664i
$119$			10702.4i			0.755767i
$120$	−7553.09	+	3677.99i	−0.524520	+	0.255416i
$121$	−14626.9			−0.999038
$122$	−5970.24	−	5970.24i	−0.401118	−	0.401118i
$123$	−1106.91	+	1106.91i	−0.0731649	+	0.0731649i
$124$			6748.34i			0.438888i
$125$	−15277.4	−	3277.57i	−0.977752	−	0.209764i
$126$	11372.1			0.716309
$127$	−22305.2	−	22305.2i	−1.38293	−	1.38293i	−0.839377	−	0.543549i	$-0.817080\pi$
$127$	−22305.2	−	22305.2i	−1.38293	−	1.38293i	−0.543549	−	0.839377i	$-0.682920\pi$
$128$	−1024.00	+	1024.00i	−0.0625000	+	0.0625000i
$129$			36247.6i			2.17821i
$130$	4856.09	+	9972.45i	0.287343	+	0.590086i
$131$	23831.1			1.38868			0.694338	−	0.719649i	$-0.255697\pi$
$131$	23831.1			1.38868			0.694338	+	0.719649i	$0.255697\pi$
$132$	−315.357	−	315.357i	−0.0180990	−	0.0180990i
$133$	−6214.46	+	6214.46i	−0.351318	+	0.351318i
$134$		−	5013.49i		−	0.279210i
$135$	−7090.50	+	20550.2i	−0.389054	+	1.12758i
$136$	−8405.38			−0.454443
$137$	4123.12	+	4123.12i	0.219677	+	0.219677i	0.808362	−	0.588685i	$-0.200354\pi$
$137$	4123.12	+	4123.12i	0.219677	+	0.219677i	−0.588685	+	0.808362i	$0.700354\pi$
$138$	−3276.25	+	3276.25i	−0.172036	+	0.172036i
$139$		−	7348.52i		−	0.380338i	−0.981751	−	0.190169i	$-0.939096\pi$
$139$		−	7348.52i		−	0.380338i	0.981751	−	0.190169i	$-0.0609036\pi$
$140$	5447.10	+	1879.43i	0.277913	+	0.0958895i
$141$	12068.5			0.607037
$142$	−10867.1	−	10867.1i	−0.538934	−	0.538934i
$143$	−416.371	+	416.371i	−0.0203614	+	0.0203614i
$144$			8931.34i			0.430717i
$145$	612.684	−	298.347i	0.0291408	−	0.0141901i
$146$	24433.2			1.14624
$147$	16496.6	+	16496.6i	0.763415	+	0.763415i
$148$	−2589.47	+	2589.47i	−0.118219	+	0.118219i
$149$		−	34237.7i		−	1.54217i	−0.636732	−	0.771085i	$-0.719714\pi$
$149$		−	34237.7i		−	1.54217i	0.636732	−	0.771085i	$-0.280286\pi$
$150$	−16189.1	+	20667.3i	−0.719517	+	0.918547i
$151$	−13777.7			−0.604259			−0.302130	−	0.953267i	$-0.597698\pi$
$151$	−13777.7			−0.604259			−0.302130	+	0.953267i	$0.597698\pi$
$152$	−4880.66	−	4880.66i	−0.211248	−	0.211248i
$153$	−36655.9	+	36655.9i	−1.56589	+	1.56589i
$154$			305.898i			0.0128984i
$155$	9232.65	+	18960.1i	0.384293	+	0.789182i
$156$	18636.7			0.765807
$157$	−32758.5	−	32758.5i	−1.32900	−	1.32900i	−0.906244	−	0.422756i	$-0.861063\pi$
$157$	−32758.5	−	32758.5i	−1.32900	−	1.32900i	−0.422756	−	0.906244i	$-0.638937\pi$
$158$	−5167.99	+	5167.99i	−0.207018	+	0.207018i
$159$		−	16608.0i		−	0.656938i
$160$	−1476.06	+	4278.00i	−0.0576584	+	0.167109i
$161$	3177.98			0.122603
$162$	3220.20	+	3220.20i	0.122702	+	0.122702i
$163$	23200.1	−	23200.1i	0.873200	−	0.873200i	−0.119620	−	0.992820i	$-0.538168\pi$
$163$	23200.1	−	23200.1i	0.873200	−	0.873200i	0.992820	+	0.119620i	$0.0381675\pi$
$164$			843.261i			0.0313526i
$165$	−1317.48	−	454.575i	−0.0483922	−	0.0166970i
$166$	2322.54			0.0842843
$167$	15530.7	+	15530.7i	0.556877	+	0.556877i	0.928417	−	0.371540i	$-0.121170\pi$
$167$	15530.7	+	15530.7i	0.556877	+	0.556877i	−0.371540	+	0.928417i	$0.621170\pi$
$168$	6845.97	−	6845.97i	0.242559	−	0.242559i
$169$			3954.73i			0.138466i
$170$	−23615.7	+	11499.7i	−0.817153	+	0.397914i
$171$	−42569.2			−1.45581
$172$	13807.0	+	13807.0i	0.466704	+	0.466704i
$173$	18034.8	−	18034.8i	0.602585	−	0.602585i	−0.338413	−	0.940998i	$-0.609890\pi$
$173$	18034.8	−	18034.8i	0.602585	−	0.602585i	0.940998	+	0.338413i	$0.109890\pi$
$174$		−	1145.00i		−	0.0378186i
$175$	17875.5	−	2171.92i	0.583688	−	0.0709198i
$176$	−240.244			−0.00775581
$177$	−2044.61	−	2044.61i	−0.0652626	−	0.0652626i
$178$	3787.10	−	3787.10i	0.119527	−	0.119527i
$179$		−	61383.5i		−	1.91578i	−0.287135	−	0.957890i	$-0.592703\pi$
$179$		−	61383.5i		−	1.91578i	0.287135	−	0.957890i	$-0.407297\pi$
$180$	12219.3	+	25093.5i	0.377139	+	0.774490i
$181$	−56563.6			−1.72655			−0.863276	−	0.504732i	$-0.831591\pi$
$181$	−56563.6			−1.72655			−0.863276	+	0.504732i	$0.831591\pi$
$182$	−9038.83	−	9038.83i	−0.272879	−	0.272879i
$183$	−31347.5	+	31347.5i	−0.936053	+	0.936053i
$184$			2495.90i			0.0737210i
$185$	−3732.61	+	10818.1i	−0.109061	+	0.316088i
$186$	35433.0			1.02419
$187$	−986.007	−	986.007i	−0.0281966	−	0.0281966i
$188$	4596.98	−	4596.98i	0.130064	−	0.130064i
$189$		−	25053.0i		−	0.701351i
$190$	−20390.1	−	7035.28i	−0.564823	−	0.194883i
$191$	12138.3			0.332728			0.166364	−	0.986064i	$-0.446797\pi$
$191$	12138.3			0.332728			0.166364	+	0.986064i	$0.446797\pi$
$192$	5376.64	+	5376.64i	0.145851	+	0.145851i
$193$	−22853.6	+	22853.6i	−0.613536	+	0.613536i	−0.943866	−	0.330329i	$-0.892840\pi$
$193$	−22853.6	+	22853.6i	−0.613536	+	0.613536i	0.330329	+	0.943866i	$0.392840\pi$
$194$		−	42002.6i		−	1.11602i
$195$	52361.6	−	25497.5i	1.37703	−	0.670546i
$196$	12567.4			0.327139
$197$	−36633.2	−	36633.2i	−0.943935	−	0.943935i	0.0545747	−	0.998510i	$-0.482620\pi$
$197$	−36633.2	−	36633.2i	−0.943935	−	0.943935i	−0.998510	+	0.0545747i	$0.982620\pi$
$198$	−1047.71	+	1047.71i	−0.0267245	+	0.0267245i
$199$		−	56337.4i		−	1.42263i	−0.702875	−	0.711313i	$-0.748101\pi$
$199$		−	56337.4i		−	1.42263i	0.702875	−	0.711313i	$-0.251899\pi$
$200$	1705.76	+	14038.9i	0.0426441	+	0.350972i
$201$	−26324.0			−0.651567
$202$	−31712.9	−	31712.9i	−0.777200	−	0.777200i
$203$	−555.325	+	555.325i	−0.0134758	+	0.0134758i
$204$			44133.5i			1.06049i
$205$	1153.70	+	2369.22i	0.0274526	+	0.0563765i
$206$	−36978.3			−0.871390
$207$	10884.6	+	10884.6i	0.254023	+	0.254023i
$208$	7098.85	−	7098.85i	0.164082	−	0.164082i
$209$		−	1145.07i		−	0.0262143i
$210$	9868.20	−	28600.6i	0.223769	−	0.648541i
$211$	−58513.6			−1.31429			−0.657146	−	0.753763i	$-0.728237\pi$
$211$	−58513.6			−1.31429			−0.657146	+	0.753763i	$0.728237\pi$
$212$	−6326.12	−	6326.12i	−0.140756	−	0.140756i
$213$	−57058.9	+	57058.9i	−1.25766	+	1.25766i
$214$		−	5079.36i		−	0.110913i
$215$	57681.8	+	19902.2i	1.24785	+	0.430550i
$216$	19675.9			0.421723
$217$	−17185.1	−	17185.1i	−0.364949	−	0.364949i
$218$	395.709	−	395.709i	0.00832651	−	0.00832651i
$219$		−	128289.i		−	2.67487i
$220$	−674.988	+	328.686i	−0.0139460	+	0.00679104i
$221$	58270.1			1.19306
$222$	13596.3	+	13596.3i	0.275877	+	0.275877i
$223$	23604.0	−	23604.0i	0.474652	−	0.474652i	−0.428765	−	0.903416i	$-0.641051\pi$
$223$	23604.0	−	23604.0i	0.474652	−	0.474652i	0.903416	+	0.428765i	$0.141051\pi$
$224$		−	5215.36i		−	0.103941i
$225$	68662.6	+	53784.9i	1.35630	+	1.06242i
$226$	27218.8			0.532907
$227$	68669.6	+	68669.6i	1.33264	+	1.33264i	0.903001	+	0.429639i	$0.141359\pi$
$227$	68669.6	+	68669.6i	1.33264	+	1.33264i	0.429639	+	0.903001i	$0.358641\pi$
$228$	−25626.5	+	25626.5i	−0.492969	+	0.492969i
$229$		−	69470.8i		−	1.32474i	−0.749176	−	0.662371i	$-0.769550\pi$
$229$		−	69470.8i		−	1.32474i	0.749176	−	0.662371i	$-0.230450\pi$
$230$	3414.73	+	7012.46i	0.0645506	+	0.132561i
$231$	1606.16			0.0300998
$232$	−436.137	−	436.137i	−0.00810302	−	0.00810302i
$233$	−11882.1	+	11882.1i	−0.218867	+	0.218867i	−0.808021	−	0.589154i	$-0.799461\pi$
$233$	−11882.1	+	11882.1i	−0.218867	+	0.218867i	0.589154	+	0.808021i	$0.299461\pi$
$234$		−	61916.3i		−	1.13077i
$235$	6626.36	−	19204.9i	0.119988	−	0.347758i
$236$	−1557.61			−0.0279664
$237$	27135.1	+	27135.1i	0.483098	+	0.483098i
$238$	21404.8	−	21404.8i	0.377884	−	0.377884i
$239$			49225.1i			0.861769i	0.902407	+	0.430885i	$0.141798\pi$
$239$			49225.1i			0.861769i	−0.902407	+	0.430885i	$0.858202\pi$
$240$	22462.1	+	7750.21i	0.389968	+	0.134552i
$241$	4850.95			0.0835205			0.0417602	−	0.999128i	$-0.486703\pi$
$241$	4850.95			0.0835205			0.0417602	+	0.999128i	$0.486703\pi$
$242$	29253.8	+	29253.8i	0.499519	+	0.499519i
$243$	−32896.5	+	32896.5i	−0.557106	+	0.557106i
$244$			23881.0i			0.401118i
$245$	35309.2	−	17193.9i	0.588242	−	0.286445i
$246$	4427.64			0.0731649
$247$	33835.0	+	33835.0i	0.554591	+	0.554591i
$248$	13496.7	−	13496.7i	0.219444	−	0.219444i
$249$		−	12194.8i		−	0.196687i
$250$	23999.6	+	37109.9i	0.383994	+	0.593758i
$251$	55845.9			0.886429			0.443215	−	0.896416i	$-0.353838\pi$
$251$	55845.9			0.886429			0.443215	+	0.896416i	$0.353838\pi$
$252$	−22744.2	−	22744.2i	−0.358154	−	0.358154i
$253$	−292.785	+	292.785i	−0.00457413	+	0.00457413i
$254$			89220.9i			1.38293i
$255$	60380.6	+	123997.i	0.928575	+	1.90692i
$256$	4096.00			0.0625000
$257$	−14431.7	−	14431.7i	−0.218500	−	0.218500i	0.589366	−	0.807866i	$-0.299378\pi$
$257$	−14431.7	−	14431.7i	−0.218500	−	0.218500i	−0.807866	+	0.589366i	$0.799378\pi$
$258$	72495.2	−	72495.2i	1.08910	−	1.08910i
$259$		−	13188.5i		−	0.196605i
$260$	10232.7	−	29657.1i	0.151371	−	0.438714i
$261$	−3803.99			−0.0558417
$262$	−47662.1	−	47662.1i	−0.694338	−	0.694338i
$263$	77015.5	−	77015.5i	1.11344	−	1.11344i	0.120757	−	0.992682i	$-0.461468\pi$
$263$	77015.5	−	77015.5i	1.11344	−	1.11344i	0.992682	−	0.120757i	$-0.0385321\pi$
$264$			1261.43i			0.0180990i
$265$	−26428.8	−	9118.85i	−0.376345	−	0.129852i
$266$	24857.8			0.351318
$267$	−19884.7	−	19884.7i	−0.278930	−	0.278930i
$268$	−10027.0	+	10027.0i	−0.139605	+	0.139605i
$269$			8631.81i			0.119288i	0.998220	+	0.0596441i	$0.0189966\pi$
$269$			8631.81i			0.119288i	−0.998220	+	0.0596441i	$0.981003\pi$
$270$	55281.3	−	26919.3i	0.758317	−	0.369263i
$271$	117399.			1.59855			0.799274	−	0.600967i	$-0.205218\pi$
$271$	117399.			1.59855			0.799274	+	0.600967i	$0.205218\pi$
$272$	16810.8	+	16810.8i	0.227222	+	0.227222i
$273$	−47459.5	+	47459.5i	−0.636792	+	0.636792i
$274$		−	16492.5i		−	0.219677i
$275$	−1446.76	+	1846.95i	−0.0191307	+	0.0244225i
$276$	13105.0			0.172036
$277$	−26832.3	−	26832.3i	−0.349703	−	0.349703i	0.510296	−	0.859999i	$-0.329536\pi$
$277$	−26832.3	−	26832.3i	−0.349703	−	0.349703i	−0.859999	+	0.510296i	$0.829536\pi$
$278$	−14697.0	+	14697.0i	−0.190169	+	0.190169i
$279$		−	117718.i		−	1.51229i
$280$	−7135.32	−	14653.1i	−0.0910118	−	0.186901i
$281$	25523.8			0.323245			0.161623	−	0.986853i	$-0.448327\pi$
$281$	25523.8			0.323245			0.161623	+	0.986853i	$0.448327\pi$
$282$	−24137.0	−	24137.0i	−0.303518	−	0.303518i
$283$	77927.3	−	77927.3i	0.973009	−	0.973009i	−0.0266364	−	0.999645i	$-0.508480\pi$
$283$	77927.3	−	77927.3i	0.973009	−	0.973009i	0.999645	+	0.0266364i	$0.00847964\pi$
$284$			43468.3i			0.538934i
$285$	−36939.6	+	107061.i	−0.454781	+	1.31808i
$286$	1665.48			0.0203614
$287$	−2147.42	−	2147.42i	−0.0260707	−	0.0260707i
$288$	17862.7	−	17862.7i	0.215358	−	0.215358i
$289$			54468.2i			0.652150i
$290$	−1822.06	−	628.674i	−0.0216654	−	0.00747532i
$291$	−220540.			−2.60436
$292$	−48866.3	−	48866.3i	−0.573118	−	0.573118i
$293$	110810.	−	110810.i	1.29076	−	1.29076i	0.356443	−	0.934317i	$-0.383990\pi$
$293$	110810.	−	110810.i	1.29076	−	1.29076i	0.934317	−	0.356443i	$-0.116010\pi$
$294$		−	65986.5i		−	0.763415i
$295$	−4376.27	+	2131.03i	−0.0502875	+	0.0244875i
$296$	10357.9			0.118219
$297$	2308.11	+	2308.11i	0.0261664	+	0.0261664i
$298$	−68475.4	+	68475.4i	−0.771085	+	0.771085i
$299$		−	17302.7i		−	0.193541i
$300$	73712.9	−	8956.32i	0.819032	−	0.0995147i
$301$	−70320.6			−0.776158
$302$	27555.4	+	27555.4i	0.302130	+	0.302130i
$303$	−166512.	+	166512.i	−1.81368	+	1.81368i
$304$			19522.7i			0.211248i
$305$	32672.4	+	67095.9i	0.351222	+	0.721267i
$306$	146624.			1.56589
$307$	−101368.	−	101368.i	−1.07554	−	1.07554i	−0.996904	−	0.0786319i	$-0.974945\pi$
$307$	−101368.	−	101368.i	−1.07554	−	1.07554i	−0.0786319	−	0.996904i	$-0.525055\pi$
$308$	611.796	−	611.796i	0.00644919	−	0.00644919i
$309$			194159.i			2.03349i
$310$	19454.9	−	56385.5i	0.202445	−	0.586738i
$311$	−152560.			−1.57732			−0.788660	−	0.614830i	$-0.789225\pi$
$311$	−152560.			−1.57732			−0.788660	+	0.614830i	$0.789225\pi$
$312$	−37273.4	−	37273.4i	−0.382904	−	0.382904i
$313$	34302.0	−	34302.0i	0.350131	−	0.350131i	−0.510027	−	0.860158i	$-0.670365\pi$
$313$	34302.0	−	34302.0i	0.350131	−	0.350131i	0.860158	+	0.510027i	$0.170365\pi$
$314$			131034.i			1.32900i
$315$	−95019.3	−	32784.9i	−0.957615	−	0.330410i
$316$	20671.9			0.207018
$317$	106672.	+	106672.i	1.06153	+	1.06153i	0.997979	+	0.0635515i	$0.0202427\pi$
$317$	106672.	+	106672.i	1.06153	+	1.06153i	0.0635515	+	0.997979i	$0.479757\pi$
$318$	−33216.1	+	33216.1i	−0.328469	+	0.328469i
$319$		−	102.324i		−	0.00100553i
$320$	11508.1	−	5603.88i	0.112384	−	0.0547254i
$321$	−26669.8			−0.258827
$322$	−6355.96	−	6355.96i	−0.0613013	−	0.0613013i
$323$	−80124.7	+	80124.7i	−0.768000	+	0.768000i
$324$		−	12880.8i		−	0.122702i
$325$	−11825.2	−	97324.2i	−0.111954	−	0.921412i
$326$	−92800.2			−0.873200
$327$	−2077.72	−	2077.72i	−0.0194308	−	0.0194308i
$328$	1686.52	−	1686.52i	0.0156763	−	0.0156763i
$329$			23413.0i			0.216304i
$330$	1725.81	+	3544.11i	0.0158476	+	0.0325446i
$331$	−73808.8			−0.673678			−0.336839	−	0.941562i	$-0.609358\pi$
$331$	−73808.8			−0.673678			−0.336839	+	0.941562i	$0.609358\pi$
$332$	−4645.08	−	4645.08i	−0.0421422	−	0.0421422i
$333$	45170.7	−	45170.7i	0.407351	−	0.407351i
$334$		−	62122.9i		−	0.556877i
$335$	−14453.5	+	41890.1i	−0.128790	+	0.373269i
$336$	−27383.9			−0.242559
$337$	−1156.44	−	1156.44i	−0.0101827	−	0.0101827i	0.701997	−	0.712180i	$-0.252292\pi$
$337$	−1156.44	−	1156.44i	−0.0101827	−	0.0101827i	−0.712180	+	0.701997i	$0.752292\pi$
$338$	7909.45	−	7909.45i	0.0692330	−	0.0692330i
$339$		−	142916.i		−	1.24360i
$340$	70230.9	+	24232.0i	0.607534	+	0.209620i
$341$	3166.50			0.0272314
$342$	85138.5	+	85138.5i	0.727903	+	0.727903i
$343$	−80918.0	+	80918.0i	−0.687792	+	0.687792i
$344$		−	55227.9i		−	0.466704i
$345$	36819.8	−	17929.4i	0.309345	−	0.150636i
$346$	−72139.1			−0.602585
$347$	−107109.	−	107109.i	−0.889547	−	0.889547i	0.104932	−	0.994479i	$-0.466537\pi$
$347$	−107109.	−	107109.i	−0.889547	−	0.889547i	−0.994479	+	0.104932i	$0.966537\pi$
$348$	−2289.99	+	2289.99i	−0.0189093	+	0.0189093i
$349$			173268.i			1.42255i	0.702912	+	0.711276i	$0.251883\pi$
$349$			173268.i			1.42255i	−0.702912	+	0.711276i	$0.748117\pi$
$350$	−40094.8	−	31407.1i	−0.327304	−	0.256384i
$351$	−136403.			−1.10715
$352$	480.488	+	480.488i	0.00387790	+	0.00387790i
$353$	83614.3	−	83614.3i	0.671013	−	0.671013i	−0.286936	−	0.957950i	$-0.592637\pi$
$353$	83614.3	−	83614.3i	0.671013	−	0.671013i	0.957950	+	0.286936i	$0.0926368\pi$
$354$			8178.44i			0.0652626i
$355$	59470.5	+	122128.i	0.471895	+	0.969080i
$356$	−15148.4			−0.119527
$357$	−112389.	−	112389.i	−0.881833	−	0.881833i
$358$	−122767.	+	122767.i	−0.957890	+	0.957890i
$359$		−	101438.i		−	0.787068i	−0.919310	−	0.393534i	$-0.871252\pi$
$359$		−	101438.i		−	0.787068i	0.919310	−	0.393534i	$-0.128748\pi$
$360$	25748.4	−	74625.5i	0.198676	−	0.575814i
$361$	37270.7			0.285992
$362$	113127.	+	113127.i	0.863276	+	0.863276i
$363$	153601.	−	153601.i	1.16568	−	1.16568i
$364$			36155.3i			0.272879i
$365$	−204150.	−	70438.9i	−1.53237	−	0.528721i
$366$	125390.			0.936053
$367$	−151165.	−	151165.i	−1.12233	−	1.12233i	−0.991390	−	0.130939i	$-0.958201\pi$
$367$	−151165.	−	151165.i	−1.12233	−	1.12233i	−0.130939	−	0.991390i	$-0.541799\pi$
$368$	4991.79	−	4991.79i	0.0368605	−	0.0368605i
$369$		−	14709.9i		−	0.108033i
$370$	29101.4	−	14171.0i	0.212574	−	0.103513i
$371$	32219.8			0.234085
$372$	−70866.0	−	70866.0i	−0.512096	−	0.512096i
$373$	55517.7	−	55517.7i	0.399037	−	0.399037i	−0.478856	−	0.877893i	$-0.658948\pi$
$373$	55517.7	−	55517.7i	0.399037	−	0.399037i	0.877893	+	0.478856i	$0.158948\pi$
$374$			3944.03i			0.0281966i
$375$	194850.	−	126013.i	1.38560	−	0.896092i
$376$	−18387.9			−0.130064
$377$	3023.51	+	3023.51i	0.0212730	+	0.0212730i
$378$	−50105.9	+	50105.9i	−0.350675	+	0.350675i
$379$			65456.4i			0.455695i	0.973697	+	0.227847i	$0.0731687\pi$
$379$			65456.4i			0.455695i	−0.973697	+	0.227847i	$0.926831\pi$
$380$	26709.6	+	54850.8i	0.184970	+	0.379853i
$381$	468465.			3.22721
$382$	−24276.5	−	24276.5i	−0.166364	−	0.166364i
$383$	−68464.8	+	68464.8i	−0.466734	+	0.466734i	−0.900855	−	0.434120i	$-0.857059\pi$
$383$	−68464.8	+	68464.8i	−0.466734	+	0.466734i	0.434120	+	0.900855i	$0.357059\pi$
$384$		−	21506.5i		−	0.145851i
$385$	881.880	−	2555.92i	0.00594960	−	0.0172435i
$386$	91414.5			0.613536
$387$	−240849.	−	240849.i	−1.60814	−	1.60814i
$388$	−84005.3	+	84005.3i	−0.558011	+	0.558011i
$389$			191083.i			1.26277i	0.775471	+	0.631383i	$0.217512\pi$
$389$			191083.i			1.26277i	−0.775471	+	0.631383i	$0.782488\pi$
$390$	−155718.	−	53728.1i	−1.02379	−	0.353242i
$391$	40974.6			0.268016
$392$	−25134.7	−	25134.7i	−0.163570	−	0.163570i
$393$	−250256.	+	250256.i	−1.62031	+	1.62031i
$394$			146533.i			0.943935i
$395$	58079.8	−	28282.0i	0.372247	−	0.181266i
$396$	4190.82			0.0267245
$397$	130961.	+	130961.i	0.830921	+	0.830921i	0.987643	−	0.156721i	$-0.0500925\pi$
$397$	130961.	+	130961.i	0.830921	+	0.830921i	−0.156721	+	0.987643i	$0.550092\pi$
$398$	−112675.	+	112675.i	−0.711313	+	0.711313i
$399$		−	130519.i		−	0.819839i
$400$	24666.2	−	31489.3i	0.154164	−	0.196808i
$401$	−181339.			−1.12772			−0.563860	−	0.825870i	$-0.690684\pi$
$401$	−181339.			−1.12772			−0.563860	+	0.825870i	$0.690684\pi$
$402$	52647.9	+	52647.9i	0.325784	+	0.325784i
$403$	−93565.3	+	93565.3i	−0.576109	+	0.576109i
$404$			126852.i			0.777200i
$405$	−17622.7	−	36189.9i	−0.107439	−	0.220636i
$406$	2221.30			0.0134758
$407$	1215.05	+	1215.05i	0.00733506	+	0.00733506i
$408$	88267.0	−	88267.0i	0.530247	−	0.530247i
$409$		−	235166.i		−	1.40581i	−0.711282	−	0.702907i	$-0.751885\pi$
$409$		−	235166.i		−	1.40581i	0.711282	−	0.702907i	$-0.248115\pi$
$410$	2431.05	−	7045.84i	0.0144619	−	0.0419145i
$411$	−86595.7			−0.512640
$412$	73956.7	+	73956.7i	0.435695	+	0.435695i
$413$	3966.56	−	3966.56i	0.0232549	−	0.0232549i
$414$		−	43538.5i		−	0.254023i
$415$	−19405.9	−	6695.69i	−0.112678	−	0.0388776i
$416$	−28395.4			−0.164082
$417$	77168.6	+	77168.6i	0.443781	+	0.443781i
$418$	−2290.14	+	2290.14i	−0.0131072	+	0.0131072i
$419$			243262.i			1.38562i	0.721118	+	0.692812i	$0.243628\pi$
$419$			243262.i			1.38562i	−0.721118	+	0.692812i	$0.756372\pi$
$420$	−76937.7	+	37464.9i	−0.436155	+	0.212386i
$421$	181903.			1.02630			0.513151	−	0.858298i	$-0.328478\pi$
$421$	181903.			1.02630			0.513151	+	0.858298i	$0.328478\pi$
$422$	117027.	+	117027.i	0.657146	+	0.657146i
$423$	−80189.8	+	80189.8i	−0.448166	+	0.448166i
$424$			25304.5i			0.140756i
$425$	230473.	−	28003.1i	1.27598	−	0.155035i
$426$	228235.			1.25766
$427$	−60814.4	−	60814.4i	−0.333542	−	0.333542i
$428$	−10158.7	+	10158.7i	−0.0554564	+	0.0554564i
$429$		−	8744.82i		−	0.0475156i
$430$	−75559.2	−	155168.i	−0.408649	−	0.839200i
$431$	60651.9			0.326505			0.163252	−	0.986584i	$-0.447801\pi$
$431$	60651.9			0.326505			0.163252	+	0.986584i	$0.447801\pi$
$432$	−39351.8	−	39351.8i	−0.210861	−	0.210861i
$433$	176437.	−	176437.i	0.941054	−	0.941054i	−0.0573031	−	0.998357i	$-0.518250\pi$
$433$	176437.	−	176437.i	0.941054	−	0.941054i	0.998357	+	0.0573031i	$0.0182501\pi$
$434$			68740.3i			0.364949i
$435$	−3300.93	+	9566.97i	−0.0174445	+	0.0505587i
$436$	−1582.84			−0.00832651
$437$	23792.3	+	23792.3i	0.124587	+	0.124587i
$438$	−256579.	+	256579.i	−1.33743	+	1.33743i
$439$			107828.i			0.559505i	0.960072	+	0.279752i	$0.0902523\pi$
$439$			107828.i			0.559505i	−0.960072	+	0.279752i	$0.909748\pi$
$440$	2007.35	+	692.604i	0.0103685	+	0.00357750i
$441$	−219226.			−1.12723
$442$	−116540.	−	116540.i	−0.596528	−	0.596528i
$443$	5091.30	−	5091.30i	0.0259431	−	0.0259431i	−0.694016	−	0.719959i	$-0.744160\pi$
$443$	5091.30	−	5091.30i	0.0259431	−	0.0259431i	0.719959	+	0.694016i	$0.244160\pi$
$444$		−	54385.2i		−	0.275877i
$445$	−42560.9	+	20725.1i	−0.214927	+	0.104659i
$446$	−94415.8			−0.474652
$447$	359539.	+	359539.i	1.79941	+	1.79941i
$448$	−10430.7	+	10430.7i	−0.0519707	+	0.0519707i
$449$			235260.i			1.16696i	0.812129	+	0.583478i	$0.198309\pi$
$449$			235260.i			1.16696i	−0.812129	+	0.583478i	$0.801691\pi$
$450$	−29755.4	−	244895.i	−0.146940	−	1.20936i
$451$	395.680			0.00194532
$452$	−54437.6	−	54437.6i	−0.266454	−	0.266454i
$453$	144683.	−	144683.i	0.705053	−	0.705053i
$454$		−	274678.i		−	1.33264i
$455$	49465.4	+	101582.i	0.238935	+	0.490675i
$456$	102506.			0.492969
$457$	−141909.	−	141909.i	−0.679482	−	0.679482i	0.280401	−	0.959883i	$-0.409533\pi$
$457$	−141909.	−	141909.i	−0.679482	−	0.679482i	−0.959883	+	0.280401i	$0.909533\pi$
$458$	−138942.	+	138942.i	−0.662371	+	0.662371i
$459$		−	323015.i		−	1.53319i
$460$	7195.47	−	20854.4i	0.0340051	−	0.0985557i
$461$	−114938.			−0.540830			−0.270415	−	0.962744i	$-0.587161\pi$
$461$	−114938.			−0.540830			−0.270415	+	0.962744i	$0.587161\pi$
$462$	−3212.31	−	3212.31i	−0.0150499	−	0.0150499i
$463$	−190826.	+	190826.i	−0.890173	+	0.890173i	−0.994539	−	0.104366i	$-0.966719\pi$
$463$	−190826.	+	190826.i	−0.890173	+	0.890173i	0.104366	+	0.994539i	$0.466719\pi$
$464$			1744.55i			0.00810302i
$465$	−296059.	−	102150.i	−1.36922	−	0.472427i
$466$	47528.3			0.218867
$467$	−47627.5	−	47627.5i	−0.218386	−	0.218386i	0.589432	−	0.807818i	$-0.299352\pi$
$467$	−47627.5	−	47627.5i	−0.218386	−	0.218386i	−0.807818	+	0.589432i	$0.799352\pi$
$468$	−123833.	+	123833.i	−0.565383	+	0.565383i
$469$		−	51068.7i		−	0.232172i
$470$	−51662.6	+	25157.2i	−0.233873	+	0.113885i
$471$	688010.			3.10137
$472$	3115.23	+	3115.23i	0.0139832	+	0.0139832i
$473$	6478.59	−	6478.59i	0.0289573	−	0.0289573i
$474$		−	108541.i		−	0.483098i
$475$	150087.	+	117566.i	0.665204	+	0.521068i
$476$	−85619.4			−0.377884
$477$	110353.	+	110353.i	0.485007	+	0.485007i
$478$	98450.3	−	98450.3i	0.430885	−	0.430885i
$479$		−	28181.9i		−	0.122829i	−0.998112	−	0.0614144i	$-0.980439\pi$
$479$		−	28181.9i		−	0.122829i	0.998112	−	0.0614144i	$-0.0195611\pi$
$480$	−29423.9	−	60424.7i	−0.127708	−	0.262260i
$481$	−71805.6			−0.310362
$482$	−9701.91	−	9701.91i	−0.0417602	−	0.0417602i
$483$	−33372.8	+	33372.8i	−0.143053	+	0.143053i
$484$		−	117015.i		−	0.499519i
$485$	−121090.	+	350951.i	−0.514785	+	1.49198i
$486$	131586.			0.557106
$487$	−146464.	−	146464.i	−0.617551	−	0.617551i	0.327351	−	0.944903i	$-0.393844\pi$
$487$	−146464.	−	146464.i	−0.617551	−	0.617551i	−0.944903	+	0.327351i	$0.893844\pi$
$488$	47761.9	−	47761.9i	0.200559	−	0.200559i
$489$			487259.i			2.03771i
$490$	−105006.	−	36230.7i	−0.437344	−	0.150899i
$491$	−1633.48			−0.00677566			−0.00338783	−	0.999994i	$-0.501078\pi$
$491$	−1633.48			−0.00677566			−0.00338783	+	0.999994i	$0.501078\pi$
$492$	−8855.29	−	8855.29i	−0.0365824	−	0.0365824i
$493$	−7159.96	+	7159.96i	−0.0294589	+	0.0294589i
$494$		−	135340.i		−	0.554591i
$495$	11774.5	−	5733.61i	0.0480544	−	0.0234001i
$496$	−53986.7			−0.219444
$497$	−110695.	−	110695.i	−0.448140	−	0.448140i
$498$	−24389.5	+	24389.5i	−0.0983434	+	0.0983434i
$499$		−	89801.6i		−	0.360648i	−0.983607	−	0.180324i	$-0.942285\pi$
$499$		−	89801.6i		−	0.360648i	0.983607	−	0.180324i	$-0.0577146\pi$
$500$	26220.5	−	122219.i	0.104882	−	0.488876i
$501$	−326184.			−1.29953
$502$	−111692.	−	111692.i	−0.443215	−	0.443215i
$503$	−28061.2	+	28061.2i	−0.110910	+	0.110910i	−0.760384	−	0.649474i	$-0.774989\pi$
$503$	−28061.2	+	28061.2i	−0.110910	+	0.110910i	0.649474	+	0.760384i	$0.274989\pi$
$504$			90977.0i			0.358154i
$505$	173550.	+	356402.i	0.680522	+	1.39752i
$506$	1171.14			0.00457413
$507$	−41529.5	−	41529.5i	−0.161563	−	0.161563i
$508$	178442.	−	178442.i	0.691463	−	0.691463i
$509$			157366.i			0.607399i	0.952768	+	0.303700i	$0.0982219\pi$
$509$			157366.i			0.607399i	−0.952768	+	0.303700i	$0.901778\pi$
$510$	127233.	−	368756.i	0.489171	−	1.41775i
$511$	248882.			0.953131
$512$	−8192.00	−	8192.00i	−0.0312500	−	0.0312500i
$513$	187561.	−	187561.i	0.712703	−	0.712703i
$514$			57726.8i			0.218500i
$515$	308971.	+	106606.i	1.16494	+	0.401944i
$516$	−289981.			−1.08910
$517$	−2157.02	−	2157.02i	−0.00807000	−	0.00807000i
$518$	−26377.0	+	26377.0i	−0.0983027	+	0.0983027i
$519$			378775.i			1.40620i
$520$	−79779.6	+	38848.8i	−0.295043	+	0.143671i
$521$	196151.			0.722630			0.361315	−	0.932444i	$-0.382328\pi$
$521$	196151.			0.722630			0.361315	+	0.932444i	$0.382328\pi$
$522$	7607.99	+	7607.99i	0.0279209	+	0.0279209i
$523$	195683.	−	195683.i	0.715401	−	0.715401i	−0.252259	−	0.967660i	$-0.581173\pi$
$523$	195683.	−	195683.i	0.715401	−	0.715401i	0.967660	+	0.252259i	$0.0811734\pi$
$524$			190649.i			0.694338i
$525$	−164907.	+	210522.i	−0.598301	+	0.763800i
$526$	−308062.			−1.11344
$527$	−221572.	−	221572.i	−0.797799	−	0.797799i
$528$	2522.86	−	2522.86i	0.00904951	−	0.00904951i
$529$		−	12167.0i		−	0.0434783i
$530$	34620.0	+	71095.4i	0.123247	+	0.253099i
$531$	27171.1			0.0963646
$532$	−49715.7	−	49715.7i	−0.175659	−	0.175659i
$533$	−11691.8	+	11691.8i	−0.0411553	+	0.0411553i
$534$			79538.6i			0.278930i
$535$	−14643.4	+	42440.4i	−0.0511604	+	0.148276i
$536$	40108.0			0.139605
$537$	644603.	+	644603.i	2.23534	+	2.23534i
$538$	17263.6	−	17263.6i	0.0596441	−	0.0596441i
$539$		−	5896.94i		−	0.0202978i
$540$	−164401.	−	56724.0i	−0.563790	−	0.194527i
$541$	−484273.			−1.65461			−0.827305	−	0.561753i	$-0.810127\pi$
$541$	−484273.			−1.65461			−0.827305	+	0.561753i	$0.810127\pi$
$542$	−234798.	−	234798.i	−0.799274	−	0.799274i
$543$	593988.	−	593988.i	2.01455	−	2.01455i
$544$		−	67243.1i		−	0.227222i
$545$	−4447.13	+	2165.53i	−0.0149722	+	0.00729075i
$546$	189838.			0.636792
$547$	−289849.	−	289849.i	−0.968718	−	0.968718i	0.0308075	−	0.999525i	$-0.490192\pi$
$547$	−289849.	−	289849.i	−0.968718	−	0.968718i	−0.999525	+	0.0308075i	$0.990192\pi$
$548$	−32984.9	+	32984.9i	−0.109839	+	0.109839i
$549$		−	416580.i		−	1.38215i
$550$	6587.42	−	800.389i	0.0217766	−	0.00264592i
$551$	−8314.99			−0.0273879
$552$	−26210.0	−	26210.0i	−0.0860180	−	0.0860180i
$553$	−52642.4	+	52642.4i	−0.172142	+	0.172142i
$554$			107329.i			0.349703i
$555$	−74406.4	−	152801.i	−0.241560	−	0.496065i
$556$	58788.1			0.190169
$557$	−52671.1	−	52671.1i	−0.169770	−	0.169770i	0.617108	−	0.786878i	$-0.288304\pi$
$557$	−52671.1	−	52671.1i	−0.169770	−	0.169770i	−0.786878	+	0.617108i	$0.788304\pi$
$558$	−235437.	+	235437.i	−0.756146	+	0.756146i
$559$			382866.i			1.22524i
$560$	−15035.5	+	43576.8i	−0.0479447	+	0.138957i
$561$	20708.6			0.0657999
$562$	−51047.6	−	51047.6i	−0.161623	−	0.161623i
$563$	354437.	−	354437.i	1.11821	−	1.11821i	0.126202	−	0.992005i	$-0.459721\pi$
$563$	354437.	−	354437.i	1.11821	−	1.11821i	0.992005	−	0.126202i	$-0.0402788\pi$
$564$			96548.0i			0.303518i
$565$	−227425.	−	78469.6i	−0.712430	−	0.245813i
$566$	−311709.			−0.973009
$567$	32801.8	+	32801.8i	0.102031	+	0.102031i
$568$	86936.6	−	86936.6i	0.269467	−	0.269467i
$569$		−	304244.i		−	0.939719i	−0.882741	−	0.469860i	$-0.844305\pi$
$569$		−	304244.i		−	0.939719i	0.882741	−	0.469860i	$-0.155695\pi$
$570$	288001.	−	140242.i	0.886429	−	0.431647i
$571$	212244.			0.650973			0.325487	−	0.945547i	$-0.394472\pi$
$571$	212244.			0.650973			0.325487	+	0.945547i	$0.394472\pi$
$572$	−3330.97	−	3330.97i	−0.0101807	−	0.0101807i
$573$	−127467.	+	127467.i	−0.388229	+	0.388229i
$574$			8589.67i			0.0260707i
$575$	−8315.26	−	68436.8i	−0.0251501	−	0.206992i
$576$	−71450.8			−0.215358
$577$	−134420.	−	134420.i	−0.403751	−	0.403751i	0.475802	−	0.879552i	$-0.342158\pi$
$577$	−134420.	−	134420.i	−0.403751	−	0.403751i	−0.879552	+	0.475802i	$0.842158\pi$
$578$	108936.	−	108936.i	0.326075	−	0.326075i
$579$		−	479983.i		−	1.43175i
$580$	2386.78	+	4901.48i	0.00709506	+	0.0145704i
$581$	23658.0			0.0700850
$582$	441080.	+	441080.i	1.30218	+	1.30218i
$583$	−2968.38	+	2968.38i	−0.00873339	+	0.00873339i
$584$			195465.i			0.573118i
$585$	−178500.	+	517339.i	−0.521586	+	1.51169i
$586$	−443242.			−1.29076
$587$	−84049.1	−	84049.1i	−0.243925	−	0.243925i	0.574547	−	0.818472i	$-0.305178\pi$
$587$	−84049.1	−	84049.1i	−0.243925	−	0.243925i	−0.818472	+	0.574547i	$0.805178\pi$
$588$	−131973.	+	131973.i	−0.381707	+	0.381707i
$589$		−	257315.i		−	0.741712i
$590$	13014.6	+	4490.48i	0.0373875	+	0.0129000i
$591$	769388.			2.20278
$592$	−20715.7	−	20715.7i	−0.0591094	−	0.0591094i
$593$	432198.	−	432198.i	1.22906	−	1.22906i	0.264740	−	0.964320i	$-0.414714\pi$
$593$	432198.	−	432198.i	1.22906	−	1.22906i	0.964320	−	0.264740i	$-0.0852862\pi$
$594$		−	9232.45i		−	0.0261664i
$595$	−240556.	+	117139.i	−0.679488	+	0.330878i
$596$	273902.			0.771085
$597$	591613.	+	591613.i	1.65993	+	1.65993i
$598$	−34605.5	+	34605.5i	−0.0967703	+	0.0967703i
$599$		−	228551.i		−	0.636985i	−0.947925	−	0.318492i	$-0.896824\pi$
$599$		−	228551.i		−	0.636985i	0.947925	−	0.318492i	$-0.103176\pi$
$600$	−165338.	−	129513.i	−0.459273	−	0.359759i
$601$	290112.			0.803188			0.401594	−	0.915818i	$-0.368456\pi$
$601$	290112.			0.803188			0.401594	+	0.915818i	$0.368456\pi$
$602$	140641.	+	140641.i	0.388079	+	0.388079i
$603$	174911.	−	174911.i	0.481042	−	0.481042i
$604$		−	110222.i		−	0.302130i
$605$	−160093.	−	328766.i	−0.437382	−	0.898205i
$606$	666050.			1.81368
$607$	278484.	+	278484.i	0.755827	+	0.755827i	0.975560	−	0.219733i	$-0.0705187\pi$
$607$	278484.	+	278484.i	0.755827	+	0.755827i	−0.219733	+	0.975560i	$0.570519\pi$
$608$	39045.3	−	39045.3i	0.105624	−	0.105624i
$609$		−	11663.2i		−	0.0314473i
$610$	68846.9	−	199537.i	0.185023	−	0.536244i
$611$	127474.			0.341458
$612$	−293248.	−	293248.i	−0.782946	−	0.782946i
$613$	434985.	−	434985.i	1.15759	−	1.15759i	0.172594	−	0.984993i	$-0.444785\pi$
$613$	434985.	−	434985.i	1.15759	−	1.15759i	0.984993	−	0.172594i	$-0.0552149\pi$
$614$			405473.i			1.07554i
$615$	−36995.0	−	12764.5i	−0.0978122	−	0.0337485i
$616$	−2447.19			−0.00644919
$617$	82496.1	+	82496.1i	0.216702	+	0.216702i	0.807107	−	0.590405i	$-0.201032\pi$
$617$	82496.1	+	82496.1i	0.216702	+	0.216702i	−0.590405	+	0.807107i	$0.701032\pi$
$618$	388318.	−	388318.i	1.01674	−	1.01674i
$619$		−	75195.0i		−	0.196249i	−0.995174	−	0.0981246i	$-0.968716\pi$
$619$		−	75195.0i		−	0.196249i	0.995174	−	0.0981246i	$-0.0312844\pi$
$620$	−151681.	+	73861.2i	−0.394591	+	0.192147i
$621$	−95916.0			−0.248718
$622$	305120.	+	305120.i	0.788660	+	0.788660i
$623$	38576.4	−	38576.4i	0.0993907	−	0.0993907i
$624$			149093.i			0.382904i
$625$	−93543.1	−	379259.i	−0.239470	−	0.970904i
$626$	−137208.			−0.350131
$627$	12024.6	+	12024.6i	0.0305870	+	0.0305870i
$628$	262068.	−	262068.i	0.664500	−	0.664500i
$629$		−	170043.i		−	0.429790i
$630$	124469.	+	255608.i	0.313603	+	0.644012i
$631$	−766605.			−1.92536			−0.962682	−	0.270635i	$-0.912766\pi$
$631$	−766605.			−1.92536			−0.962682	+	0.270635i	$0.912766\pi$
$632$	−41343.9	−	41343.9i	−0.103509	−	0.103509i
$633$	614466.	−	614466.i	1.53352	−	1.53352i
$634$		−	426688.i		−	1.06153i
$635$	257217.	−	745482.i	0.637899	−	1.84880i
$636$	132864.			0.328469
$637$	174246.	+	174246.i	0.429421	+	0.429421i
$638$	−204.647	+	204.647i	−0.000502764	+	0.000502764i
$639$		−	758262.i		−	1.85702i
$640$	−34224.0	−	11808.4i	−0.0835546	−	0.0288292i
$641$	−375004.			−0.912682			−0.456341	−	0.889805i	$-0.650840\pi$
$641$	−375004.			−0.912682			−0.456341	+	0.889805i	$0.650840\pi$
$642$	53339.6	+	53339.6i	0.129414	+	0.129414i
$643$	216270.	−	216270.i	0.523087	−	0.523087i	−0.395415	−	0.918502i	$-0.629399\pi$
$643$	216270.	−	216270.i	0.523087	−	0.523087i	0.918502	+	0.395415i	$0.129399\pi$
$644$			25423.8i			0.0613013i
$645$	−814729.	+	396733.i	−1.95836	+	0.953628i
$646$	320499.			0.768000
$647$	99291.6	+	99291.6i	0.237194	+	0.237194i	0.815687	−	0.578493i	$-0.196359\pi$
$647$	99291.6	+	99291.6i	0.237194	+	0.237194i	−0.578493	+	0.815687i	$0.696359\pi$
$648$	−25761.6	+	25761.6i	−0.0613512	+	0.0613512i
$649$			730.874i			0.00173521i
$650$	−170998.	+	218299.i	−0.404729	+	0.516683i
$651$	360929.			0.851648
$652$	185600.	+	185600.i	0.436600	+	0.436600i
$653$	−101165.	+	101165.i	−0.237249	+	0.237249i	−0.815710	−	0.578461i	$-0.803653\pi$
$653$	−101165.	+	101165.i	−0.237249	+	0.237249i	0.578461	+	0.815710i	$0.303653\pi$
$654$			8310.87i			0.0194308i
$655$	260833.	+	535645.i	0.607967	+	1.24852i
$656$	−6746.09			−0.0156763
$657$	852426.	+	852426.i	1.97481	+	1.97481i
$658$	46826.0	−	46826.0i	0.108152	−	0.108152i
$659$			471887.i			1.08659i	0.839541	+	0.543297i	$0.182824\pi$
$659$			471887.i			1.08659i	−0.839541	+	0.543297i	$0.817176\pi$
$660$	3636.60	−	10539.8i	0.00834849	−	0.0241961i
$661$	−564539.			−1.29208			−0.646042	−	0.763302i	$-0.723577\pi$
$661$	−564539.			−1.29208			−0.646042	+	0.763302i	$0.723577\pi$
$662$	147618.	+	147618.i	0.336839	+	0.336839i
$663$	−611908.	+	611908.i	−1.39206	+	1.39206i
$664$			18580.3i			0.0421422i
$665$	−207699.	−	71663.2i	−0.469668	−	0.162051i
$666$	−180683.			−0.407351
$667$	2126.08	+	2126.08i	0.00477890	+	0.00477890i
$668$	−124246.	+	124246.i	−0.278438	+	0.278438i
$669$			495742.i			1.10765i
$670$	112687.	−	54873.1i	0.251030	−	0.122239i
$671$	11205.6			0.0248880
$672$	54767.8	+	54767.8i	0.121279	+	0.121279i
$673$	134901.	−	134901.i	0.297842	−	0.297842i	−0.542326	−	0.840168i	$-0.682456\pi$
$673$	134901.	−	134901.i	0.297842	−	0.297842i	0.840168	+	0.542326i	$0.182456\pi$
$674$			4625.77i			0.0101827i
$675$	−539507.	+	65551.6i	−1.18410	+	0.143872i
$676$	−31637.8			−0.0692330
$677$	289692.	+	289692.i	0.632062	+	0.632062i	0.948585	−	0.316523i	$-0.102515\pi$
$677$	289692.	+	289692.i	0.632062	+	0.632062i	−0.316523	+	0.948585i	$0.602515\pi$
$678$	−285831.	+	285831.i	−0.621799	+	0.621799i
$679$		−	427850.i		−	0.928008i
$680$	−91997.7	−	188926.i	−0.198957	−	0.408577i
$681$	−1.44223e6			−3.10986
$682$	−6333.00	−	6333.00i	−0.0136157	−	0.0136157i
$683$	−407808.	+	407808.i	−0.874207	+	0.874207i	−0.992928	−	0.118721i	$-0.962121\pi$
$683$	−407808.	+	407808.i	−0.874207	+	0.874207i	0.118721	+	0.992928i	$0.462121\pi$
$684$		−	340554.i		−	0.727903i
$685$	−47546.5	+	137802.i	−0.101330	+	0.293681i
$686$	323672.			0.687792
$687$	729530.	+	729530.i	1.54572	+	1.54572i
$688$	−110456.	+	110456.i	−0.233352	+	0.233352i
$689$		−	175423.i		−	0.369528i
$690$	−109498.	−	37780.7i	−0.229990	−	0.0793546i
$691$	−631192.			−1.32192			−0.660961	−	0.750421i	$-0.729851\pi$
$691$	−631192.			−1.32192			−0.660961	+	0.750421i	$0.729851\pi$
$692$	144278.	+	144278.i	0.301292	+	0.301292i
$693$	−10672.2	+	10672.2i	−0.0222222	+	0.0222222i
$694$			428438.i			0.889547i
$695$	165171.	−	80430.1i	0.341951	−	0.166513i
$696$	9159.96			0.0189093
$697$	−27687.2	−	27687.2i	−0.0569920	−	0.0569920i
$698$	346537.	−	346537.i	0.711276	−	0.711276i
$699$		−	249553.i		−	0.510751i
$700$	17375.3	+	143004.i	0.0354599	+	0.291844i
$701$	−639951.			−1.30230			−0.651149	−	0.758950i	$-0.725713\pi$
$701$	−639951.			−1.30230			−0.651149	+	0.758950i	$0.725713\pi$
$702$	272805.	+	272805.i	0.553577	+	0.553577i
$703$	98736.8	−	98736.8i	0.199788	−	0.199788i
$704$		−	1921.95i		−	0.00387790i
$705$	132091.	+	271261.i	0.265763	+	0.545769i
$706$	−334457.			−0.671013
$707$	−323036.	−	323036.i	−0.646266	−	0.646266i
$708$	16356.9	−	16356.9i	0.0326313	−	0.0326313i
$709$		−	227546.i		−	0.452664i	−0.974050	−	0.226332i	$-0.927327\pi$
$709$		−	227546.i		−	0.452664i	0.974050	−	0.226332i	$-0.0726734\pi$
$710$	125316.	−	363198.i	0.248593	−	0.720487i
$711$	−360602.			−0.713328
$712$	30296.8	+	30296.8i	0.0597637	+	0.0597637i
$713$	−65793.6	+	65793.6i	−0.129421	+	0.129421i
$714$			449555.i			0.881833i
$715$	−13915.9	−	4801.46i	−0.0272207	−	0.00939206i
$716$	491068.			0.957890
$717$	−516925.	−	516925.i	−1.00552	−	1.00552i
$718$	−202876.	+	202876.i	−0.393534	+	0.393534i
$719$		−	385498.i		−	0.745700i	−0.927892	−	0.372850i	$-0.878381\pi$
$719$		−	385498.i		−	0.745700i	0.927892	−	0.372850i	$-0.121619\pi$
$720$	−200748.	+	97754.4i	−0.387245	+	0.188569i
$721$	−376671.			−0.724588
$722$	−74541.4	−	74541.4i	−0.142996	−	0.142996i
$723$	−50941.0	+	50941.0i	−0.0974521	+	0.0974521i
$724$		−	452509.i		−	0.863276i
$725$	13411.8	+	10505.7i	0.0255159	+	0.0199871i
$726$	−614403.			−1.16568
$727$	195246.	+	195246.i	0.369413	+	0.369413i	0.867263	−	0.497850i	$-0.165877\pi$
$727$	195246.	+	195246.i	0.369413	+	0.369413i	−0.497850	+	0.867263i	$0.665877\pi$
$728$	72310.7	−	72310.7i	0.136439	−	0.136439i
$729$		−	821327.i		−	1.54547i
$730$	267423.	+	549179.i	0.501826	+	1.03055i
$731$	−906663.			−1.69672
$732$	−250780.	−	250780.i	−0.468027	−	0.468027i
$733$	62623.7	−	62623.7i	0.116555	−	0.116555i	−0.646424	−	0.762979i	$-0.723736\pi$
$733$	62623.7	−	62623.7i	0.116555	−	0.116555i	0.762979	+	0.646424i	$0.223736\pi$
$734$			604662.i			1.12233i
$735$	−190234.	+	551348.i	−0.352138	+	1.02059i
$736$	−19967.2			−0.0368605
$737$	4704.93	+	4704.93i	0.00866200	+	0.00866200i
$738$	−29419.7	+	29419.7i	−0.0540165	+	0.0540165i
$739$			172001.i			0.314950i	0.987523	+	0.157475i	$0.0503353\pi$
$739$			172001.i			0.314950i	−0.987523	+	0.157475i	$0.949665\pi$
$740$	−86544.8	−	29860.9i	−0.158044	−	0.0545305i
$741$	−710620.			−1.29420
$742$	−64439.5	−	64439.5i	−0.117043	−	0.117043i
$743$	−66463.0	+	66463.0i	−0.120393	+	0.120393i	−0.764736	−	0.644343i	$-0.777131\pi$
$743$	−66463.0	+	66463.0i	−0.120393	+	0.120393i	0.644343	+	0.764736i	$0.277131\pi$
$744$			283464.i			0.512096i
$745$	769553.	−	374735.i	1.38652	−	0.675167i
$746$	−222071.			−0.399037
$747$	81028.9	+	81028.9i	0.145211	+	0.145211i
$748$	7888.06	−	7888.06i	0.0140983	−	0.0140983i
$749$		−	51739.7i		−	0.0922274i
$750$	−641726.	−	137674.i	−1.14085	−	0.244754i
$751$	−694043.			−1.23057			−0.615285	−	0.788305i	$-0.710959\pi$
$751$	−694043.			−1.23057			−0.615285	+	0.788305i	$0.710959\pi$
$752$	36775.8	+	36775.8i	0.0650319	+	0.0650319i
$753$	−586452.	+	586452.i	−1.03429	+	1.03429i
$754$		−	12094.0i		−	0.0212730i
$755$	−150798.	−	309678.i	−0.264547	−	0.543272i
$756$	200424.			0.350675
$757$	−359421.	−	359421.i	−0.627208	−	0.627208i	0.320157	−	0.947365i	$-0.396264\pi$
$757$	−359421.	−	359421.i	−0.627208	−	0.627208i	−0.947365	+	0.320157i	$0.896264\pi$
$758$	130913.	−	130913.i	0.227847	−	0.227847i
$759$		−	6149.22i		−	0.0106742i
$760$	56282.2	−	163121.i	0.0974416	−	0.282411i
$761$	−606183.			−1.04673			−0.523364	−	0.852109i	$-0.675323\pi$
$761$	−606183.			−1.04673			−0.523364	+	0.852109i	$0.675323\pi$
$762$	−936930.	−	936930.i	−1.61361	−	1.61361i
$763$	4030.79	−	4030.79i	0.00692375	−	0.00692375i
$764$			97106.1i			0.166364i
$765$	−1.22511e6	−	422705.i	−2.09340	−	0.722294i
$766$	273859.			0.466734
$767$	−21596.2	−	21596.2i	−0.0367102	−	0.0367102i
$768$	−43013.1	+	43013.1i	−0.0729253	+	0.0729253i
$769$			994938.i			1.68245i	0.540682	+	0.841227i	$0.318166\pi$
$769$			994938.i			1.68245i	−0.540682	+	0.841227i	$0.681834\pi$
$770$	−6875.60	+	3348.08i	−0.0115966	+	0.00564696i
$771$	303101.			0.509893
$772$	−182829.	−	182829.i	−0.306768	−	0.306768i
$773$	247020.	−	247020.i	0.413402	−	0.413402i	−0.469520	−	0.882922i	$-0.655573\pi$
$773$	247020.	−	247020.i	0.413402	−	0.413402i	0.882922	+	0.469520i	$0.155573\pi$
$774$			963397.i			1.60814i
$775$	−325110.	+	415040.i	−0.541286	+	0.691014i
$776$	336021.			0.558011
$777$	138495.	+	138495.i	0.229400	+	0.229400i
$778$	382166.	−	382166.i	0.631383	−	0.631383i
$779$		−	32153.7i		−	0.0529854i
$780$	203980.	+	418892.i	0.335273	+	0.688515i
$781$	20396.5			0.0334390
$782$	−81949.1	−	81949.1i	−0.134008	−	0.134008i
$783$	16760.5	−	16760.5i	0.0273378	−	0.0273378i
$784$			100539.i			0.163570i
$785$	377761.	−	1.09485e6i	0.613024	−	1.77671i
$786$	1.00102e6			1.62031
$787$	−297771.	−	297771.i	−0.480766	−	0.480766i	0.424611	−	0.905376i	$-0.360411\pi$
$787$	−297771.	−	297771.i	−0.480766	−	0.480766i	−0.905376	+	0.424611i	$0.860411\pi$
$788$	293065.	−	293065.i	0.471968	−	0.471968i
$789$			1.61752e6i			2.59833i
$790$	−172724.	−	59595.6i	−0.276756	−	0.0954904i
$791$	277257.			0.443129
$792$	−8381.64	−	8381.64i	−0.0133622	−	0.0133622i
$793$	−331108.	+	331108.i	−0.526530	+	0.526530i
$794$		−	523843.i		−	0.830921i
$795$	373295.	−	181776.i	0.590633	−	0.287610i
$796$	450699.			0.711313
$797$	684308.	+	684308.i	1.07730	+	1.07730i	0.996751	+	0.0805451i	$0.0256661\pi$
$797$	684308.	+	684308.i	1.07730	+	1.07730i	0.0805451	+	0.996751i	$0.474334\pi$
$798$	−261038.	+	261038.i	−0.409919	+	0.409919i
$799$			301870.i			0.472853i
$800$	−112311.	+	13646.1i	−0.175486	+	0.0213220i
$801$	264250.			0.411860
$802$	362677.	+	362677.i	0.563860	+	0.563860i
$803$	−22929.4	+	22929.4i	−0.0355599	+	0.0355599i
$804$		−	210592.i		−	0.325784i
$805$	34783.3	+	71430.7i	0.0536758	+	0.110228i
$806$	374261.			0.576109
$807$	−90644.7	−	90644.7i	−0.139186	−	0.139186i
$808$	253703.	−	253703.i	0.388600	−	0.388600i
$809$			500981.i			0.765464i	0.923859	+	0.382732i	$0.125017\pi$
$809$			500981.i			0.765464i	−0.923859	+	0.382732i	$0.874983\pi$
$810$	−37134.3	+	107625.i	−0.0565986	+	0.164038i
$811$	686753.			1.04414			0.522070	−	0.852903i	$-0.325160\pi$
$811$	686753.			1.04414			0.522070	+	0.852903i	$0.325160\pi$
$812$	−4442.60	−	4442.60i	−0.00673791	−	0.00673791i
$813$	−1.23283e6	+	1.23283e6i	−1.86519	+	1.86519i
$814$		−	4860.18i		−	0.00733506i
$815$	775389.	+	267536.i	1.16736	+	0.402779i
$816$	−353068.			−0.530247
$817$	−526462.	−	526462.i	−0.788720	−	0.788720i
$818$	−470332.	+	470332.i	−0.702907	+	0.702907i
$819$		−	630695.i		−	0.940268i
$820$	−18953.8	+	9229.56i	−0.0281882	+	0.0137263i
$821$	991491.			1.47096			0.735482	−	0.677544i	$-0.236956\pi$
$821$	991491.			1.47096			0.735482	+	0.677544i	$0.236956\pi$
$822$	173191.	+	173191.i	0.256320	+	0.256320i
$823$	631020.	−	631020.i	0.931630	−	0.931630i	−0.0661783	−	0.997808i	$-0.521081\pi$
$823$	631020.	−	631020.i	0.931630	−	0.931630i	0.997808	+	0.0661783i	$0.0210806\pi$
$824$		−	295827.i		−	0.435695i
$825$	−4202.54	−	34588.0i	−0.00617453	−	0.0508180i
$826$	−15866.3			−0.0232549
$827$	101466.	+	101466.i	0.148358	+	0.148358i	0.777384	−	0.629026i	$-0.216546\pi$
$827$	101466.	+	101466.i	0.148358	+	0.148358i	−0.629026	+	0.777384i	$0.716546\pi$
$828$	−87077.0	+	87077.0i	−0.127011	+	0.127011i
$829$		−	1.02106e6i		−	1.48574i	−0.669436	−	0.742870i	$-0.733464\pi$
$829$		−	1.02106e6i		−	1.48574i	0.669436	−	0.742870i	$-0.266536\pi$
$830$	25420.4	+	52203.2i	0.0369000	+	0.0757776i
$831$	563546.			0.816069
$832$	56790.8	+	56790.8i	0.0820411	+	0.0820411i
$833$	−412631.	+	412631.i	−0.594665	+	0.594665i
$834$		−	308674.i		−	0.443781i
$835$	−179095.	+	519066.i	−0.256869	+	0.744474i
$836$	9160.54			0.0131072
$837$	518670.	+	518670.i	0.740356	+	0.740356i
$838$	486523.	−	486523.i	0.692812	−	0.692812i
$839$			81001.2i			0.115071i	0.998343	+	0.0575357i	$0.0183243\pi$
$839$			81001.2i			0.115071i	−0.998343	+	0.0575357i	$0.981676\pi$
$840$	228805.	+	78945.6i	0.324270	+	0.111884i
$841$	706538.			0.998949
$842$	−363806.	−	363806.i	−0.513151	−	0.513151i
$843$	−268031.	+	268031.i	−0.377164	+	0.377164i
$844$		−	468109.i		−	0.657146i
$845$	−88889.5	+	43284.8i	−0.124491	+	0.0606209i
$846$	320759.			0.448166
$847$	297987.	+	297987.i	0.415365	+	0.415365i
$848$	50609.0	−	50609.0i	0.0703778	−	0.0703778i
$849$			1.63667e6i			2.27062i
$850$	−516953.	−	404940.i	−0.715505	−	0.560471i
$851$	−50492.5			−0.0697217
$852$	−456471.	−	456471.i	−0.628831	−	0.628831i
$853$	−136609.	+	136609.i	−0.187750	+	0.187750i	−0.794723	−	0.606973i	$-0.792384\pi$
$853$	−136609.	+	136609.i	−0.187750	+	0.187750i	0.606973	+	0.794723i	$0.292384\pi$
$854$			243258.i			0.333542i
$855$	−465924.	−	956819.i	−0.637357	−	1.30887i
$856$	40634.9			0.0554564
$857$	422001.	+	422001.i	0.574582	+	0.574582i	0.933406	−	0.358823i	$-0.116822\pi$
$857$	422001.	+	422001.i	0.574582	+	0.574582i	−0.358823	+	0.933406i	$0.616822\pi$
$858$	−17489.6	+	17489.6i	−0.0237578	+	0.0237578i
$859$			971802.i			1.31702i	0.752573	+	0.658509i	$0.228812\pi$
$859$			971802.i			1.31702i	−0.752573	+	0.658509i	$0.771188\pi$
$860$	−159218.	+	461454.i	−0.215275	+	0.623924i
$861$	45101.1			0.0608388
$862$	−121304.	−	121304.i	−0.163252	−	0.163252i
$863$	−19147.5	+	19147.5i	−0.0257092	+	0.0257092i	−0.719845	−	0.694135i	$-0.755787\pi$
$863$	−19147.5	+	19147.5i	−0.0257092	+	0.0257092i	0.694135	+	0.719845i	$0.255787\pi$
$864$			157407.i			0.210861i
$865$	602755.	+	207971.i	0.805580	+	0.277953i
$866$	−705749.			−0.941054
$867$	−571984.	−	571984.i	−0.760932	−	0.760932i
$868$	137481.	−	137481.i	0.182474	−	0.182474i
$869$		−	9699.82i		−	0.0128447i
$870$	25735.8	−	12532.1i	0.0340016	−	0.0165571i
$871$	−278047.			−0.366507
$872$	3165.67	+	3165.67i	0.00416325	+	0.00416325i
$873$	1.46539e6	−	1.46539e6i	1.92276	−	1.92276i
$874$		−	95169.0i		−	0.124587i
$875$	244466.	+	378011.i	0.319303	+	0.493728i
$876$	1.02631e6			1.33743
$877$	−837450.	−	837450.i	−1.08883	−	1.08883i	−0.995649	−	0.0931801i	$-0.970297\pi$
$877$	−837450.	−	837450.i	−1.08883	−	1.08883i	−0.0931801	−	0.995649i	$-0.529703\pi$
$878$	215657.	−	215657.i	0.279752	−	0.279752i
$879$			2.32729e6i			3.01213i
$880$	−2629.49	−	5399.91i	−0.00339552	−	0.00697302i
$881$	−691156.			−0.890481			−0.445240	−	0.895411i	$-0.646882\pi$
$881$	−691156.			−0.890481			−0.445240	+	0.895411i	$0.646882\pi$
$882$	438451.	+	438451.i	0.563617	+	0.563617i
$883$	−709401.	+	709401.i	−0.909852	+	0.909852i	−0.996260	−	0.0864083i	$-0.972461\pi$
$883$	−709401.	+	709401.i	−0.909852	+	0.909852i	0.0864083	+	0.996260i	$0.472461\pi$
$884$			466161.i			0.596528i
$885$	23577.8	−	68334.7i	0.0301035	−	0.0872478i
$886$	−20365.2			−0.0259431
$887$	163598.	+	163598.i	0.207937	+	0.207937i	0.803390	−	0.595453i	$-0.203027\pi$
$887$	163598.	+	163598.i	0.207937	+	0.207937i	−0.595453	+	0.803390i	$0.703027\pi$
$888$	−108770.	+	108770.i	−0.137938	+	0.137938i
$889$			908827.i			1.14995i
$890$	126572.	+	43671.7i	0.159793	+	0.0551341i
$891$	−6044.02			−0.00761325
$892$	188832.	+	188832.i	0.237326	+	0.237326i
$893$	−175284.	+	175284.i	−0.219805	+	0.219805i
$894$		−	1.43815e6i		−	1.79941i
$895$	1.37970e6	−	671848.i	1.72242	−	0.838735i
$896$	41722.9			0.0519707
$897$	181700.	+	181700.i	0.225824	+	0.225824i
$898$	470519.	−	470519.i	0.583478	−	0.583478i
$899$		−	22993.8i		−	0.0284505i
$900$	−430279.	+	549300.i	−0.531208	+	0.678149i
$901$	415418.			0.511724
$902$	−791.360	−	791.360i	−0.000972660	−	0.000972660i
$903$	738454.	−	738454.i	0.905624	−	0.905624i
$904$			217750.i			0.266454i
$905$	−619093.	−	1.27137e6i	−0.755891	−	1.55229i
$906$	−578733.			−0.705053
$907$	9477.87	+	9477.87i	0.0115212	+	0.0115212i	0.712844	−	0.701323i	$-0.247407\pi$
$907$	9477.87	+	9477.87i	0.0115212	+	0.0115212i	−0.701323	+	0.712844i	$0.747407\pi$
$908$	−549357.	+	549357.i	−0.666320	+	0.666320i
$909$		−	2.21280e6i		−	2.67803i
$910$	104233.	−	302095.i	0.125870	−	0.364805i
$911$	773530.			0.932053			0.466026	−	0.884771i	$-0.345685\pi$
$911$	773530.			0.932053			0.466026	+	0.884771i	$0.345685\pi$
$912$	−205012.	−	205012.i	−0.246485	−	0.246485i
$913$	−2179.59	+	2179.59i	−0.00261477	+	0.00261477i
$914$			567637.i			0.679482i
$915$	−1.04769e6	−	361489.i	−1.25139	−	0.431771i
$916$	555767.			0.662371
$917$	−485499.	−	485499.i	−0.577364	−	0.577364i
$918$	−646029.	+	646029.i	−0.766596	+	0.766596i
$919$		−	314712.i		−	0.372634i	−0.982490	−	0.186317i	$-0.940345\pi$
$919$		−	314712.i		−	0.372634i	0.982490	−	0.186317i	$-0.0596552\pi$
$920$	−56099.7	+	27317.8i	−0.0662804	+	0.0322753i
$921$	2.12898e6			2.50988
$922$	229876.	+	229876.i	0.270415	+	0.270415i
$923$	−602685.	+	602685.i	−0.707436	+	0.707436i
$924$			12849.2i			0.0150499i
$925$	−284010.	+	34508.0i	−0.331932	+	0.0403307i
$926$	763302.			0.890173
$927$	−1.29010e6	−	1.29010e6i	−1.50129	−	1.50129i
$928$	3489.10	−	3489.10i	0.00405151	−	0.00405151i
$929$		−	190826.i		−	0.221109i	−0.993870	−	0.110555i	$-0.964737\pi$
$929$		−	190826.i		−	0.221109i	0.993870	−	0.110555i	$-0.0352627\pi$
$930$	387817.	+	796419.i	0.448395	+	0.920822i
$931$	−479196.			−0.552859
$932$	−95056.7	−	95056.7i	−0.109434	−	0.109434i
$933$	1.60207e6	−	1.60207e6i	1.84042	−	1.84042i
$934$			190510.i			0.218386i
$935$	11370.3	−	32954.2i	0.0130062	−	0.0376953i
$936$	495330.			0.565383
$937$	−236484.	−	236484.i	−0.269354	−	0.269354i	0.559486	−	0.828840i	$-0.310999\pi$
$937$	−236484.	−	236484.i	−0.269354	−	0.269354i	−0.828840	+	0.559486i	$0.810999\pi$
$938$	−102137.	+	102137.i	−0.116086	+	0.116086i
$939$			720426.i			0.817069i
$940$	153640.	+	53010.9i	0.173879	+	0.0599942i
$941$	567752.			0.641180			0.320590	−	0.947218i	$-0.396119\pi$
$941$	567752.			0.641180			0.320590	+	0.947218i	$0.396119\pi$
$942$	−1.37602e6	−	1.37602e6i	−1.55068	−	1.55068i
$943$	−8221.46	+	8221.46i	−0.00924539	+	0.00924539i
$944$		−	12460.9i		−	0.0139832i
$945$	563109.	−	274207.i	0.630564	−	0.307054i
$946$	−25914.4			−0.0289573
$947$	−255364.	−	255364.i	−0.284748	−	0.284748i	0.550251	−	0.834999i	$-0.314532\pi$
$947$	−255364.	−	255364.i	−0.284748	−	0.284748i	−0.834999	+	0.550251i	$0.814532\pi$
$948$	−217081.	+	217081.i	−0.241549	+	0.241549i
$949$		−	1.35506e6i		−	1.50461i
$950$	−65041.1	−	535305.i	−0.0720677	−	0.593136i
$951$	−2.24038e6			−2.47720
$952$	171239.	+	171239.i	0.188942	+	0.188942i
$953$	1.05009e6	−	1.05009e6i	1.15622	−	1.15622i	0.170940	−	0.985281i	$-0.445319\pi$
$953$	1.05009e6	−	1.05009e6i	1.15622	−	1.15622i	0.985281	−	0.170940i	$-0.0546806\pi$
$954$		−	441412.i		−	0.485007i
$955$	132854.	+	272829.i	0.145670	+	0.299146i
$956$	−393801.			−0.430885
$957$	1074.52	+	1074.52i	0.00117325	+	0.00117325i
$958$	−56363.9	+	56363.9i	−0.0614144	+	0.0614144i
$959$		−	167997.i		−	0.182668i
$960$	−62001.7	+	179697.i	−0.0672761	+	0.194984i
$961$	−211957.			−0.229510
$962$	143611.	+	143611.i	0.155181	+	0.155181i
$963$	177209.	−	177209.i	0.191088	−	0.191088i
$964$			38807.6i			0.0417602i
$965$	−763810.	−	263541.i	−0.820221	−	0.283004i
$966$	133491.			0.143053
$967$	453011.	+	453011.i	0.484458	+	0.484458i	0.906552	−	0.422094i	$-0.138705\pi$
$967$	453011.	+	453011.i	0.484458	+	0.484458i	−0.422094	+	0.906552i	$0.638705\pi$
$968$	−234031.	+	234031.i	−0.249759	+	0.249759i
$969$		−	1.68282e6i		−	1.79221i
$970$	944083.	−	459722.i	1.00338	−	0.488599i
$971$	−84341.3			−0.0894544			−0.0447272	−	0.998999i	$-0.514242\pi$
$971$	−84341.3			−0.0894544			−0.0447272	+	0.998999i	$0.514242\pi$
$972$	−263172.	−	263172.i	−0.278553	−	0.278553i
$973$	−149708.	+	149708.i	−0.158132	+	0.158132i
$974$			585856.i			0.617551i
$975$	1.14620e6	+	897846.i	1.20574	+	0.944480i
$976$	−191048.			−0.200559
$977$	−743684.	−	743684.i	−0.779111	−	0.779111i	0.200569	−	0.979680i	$-0.435721\pi$
$977$	−743684.	−	743684.i	−0.779111	−	0.779111i	−0.979680	+	0.200569i	$0.935721\pi$
$978$	974518.	−	974518.i	1.01885	−	1.01885i
$979$			7108.04i			0.00741625i
$980$	137551.	+	282474.i	0.143223	+	0.294121i
$981$	27611.0			0.0286909
$982$	3266.96	+	3266.96i	0.00338783	+	0.00338783i
$983$	−1.18676e6	+	1.18676e6i	−1.22816	+	1.22816i	−0.263507	+	0.964658i	$0.584879\pi$
$983$	−1.18676e6	+	1.18676e6i	−1.22816	+	1.22816i	−0.964658	+	0.263507i	$0.915121\pi$
$984$			35421.2i			0.0365824i
$985$	422442.	−	1.22435e6i	0.435406	−	1.26192i
$986$	28639.8			0.0294589
$987$	−245866.	−	245866.i	−0.252385	−	0.252385i
$988$	−270680.	+	270680.i	−0.277296	+	0.277296i
$989$			269225.i			0.275247i
$990$	−35016.3	−	12081.8i	−0.0357272	−	0.0123271i
$991$	−682716.			−0.695173			−0.347587	−	0.937648i	$-0.612999\pi$
$991$	−682716.			−0.695173			−0.347587	+	0.937648i	$0.612999\pi$
$992$	107973.	+	107973.i	0.109722	+	0.109722i
$993$	775084.	−	775084.i	0.786050	−	0.786050i
$994$			442779.i			0.448140i
$995$	1.26628e6	−	616618.i	1.27904	−	0.622831i
$996$	97558.2			0.0983434
$997$	713536.	+	713536.i	0.717836	+	0.717836i	0.968162	−	0.250325i	$-0.0805376\pi$
$997$	713536.	+	713536.i	0.717836	+	0.717836i	−0.250325	+	0.968162i	$0.580538\pi$
$998$	−179603.	+	179603.i	−0.180324	+	0.180324i
$999$			398047.i			0.398845i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.f.a.47.2	✓	44
5.3	odd	4	inner	230.5.f.a.93.2	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.f.a.47.2	✓	44	1.1	even	1	trivial
230.5.f.a.93.2	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)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 2.00000i) q^{2} +(-10.5012 + 10.5012i) q^{3} +8.00000i q^{4} +(10.9451 + 22.4768i) q^{5} +42.0050 q^{6} +(-20.3725 - 20.3725i) q^{7} +(16.0000 - 16.0000i) q^{8} -139.552i q^{9} +O(q^{10})\)	\(q+(-2.00000 - 2.00000i) q^{2} +(-10.5012 + 10.5012i) q^{3} +8.00000i q^{4} +(10.9451 + 22.4768i) q^{5} +42.0050 q^{6} +(-20.3725 - 20.3725i) q^{7} +(16.0000 - 16.0000i) q^{8} -139.552i q^{9} +(23.0634 - 66.8437i) q^{10} +3.75381 q^{11} +(-84.0100 - 84.0100i) q^{12} +(-110.920 + 110.920i) q^{13} +81.4900i q^{14} +(-350.971 - 121.097i) q^{15} -64.0000 q^{16} +(-262.668 - 262.668i) q^{17} +(-279.105 + 279.105i) q^{18} -305.041i q^{19} +(-179.814 + 87.5607i) q^{20} +427.873 q^{21} +(-7.50762 - 7.50762i) q^{22} +(-77.9968 + 77.9968i) q^{23} +336.040i q^{24} +(-385.410 + 492.020i) q^{25} +443.678 q^{26} +(614.872 + 614.872i) q^{27} +(162.980 - 162.980i) q^{28} -27.2586i q^{29} +(459.748 + 944.136i) q^{30} +843.542 q^{31} +(128.000 + 128.000i) q^{32} +(-39.4197 + 39.4197i) q^{33} +1050.67i q^{34} +(234.929 - 680.887i) q^{35} +1116.42 q^{36} +(323.683 + 323.683i) q^{37} +(-610.083 + 610.083i) q^{38} -2329.59i q^{39} +(534.750 + 184.507i) q^{40} +105.408 q^{41} +(-855.747 - 855.747i) q^{42} +(1725.87 - 1725.87i) q^{43} +30.0305i q^{44} +(3136.68 - 1527.41i) q^{45} +311.987 q^{46} +(-574.622 - 574.622i) q^{47} +(672.080 - 672.080i) q^{48} -1570.92i q^{49} +(1754.86 - 213.220i) q^{50} +5516.69 q^{51} +(-887.356 - 887.356i) q^{52} +(-790.765 + 790.765i) q^{53} -2459.49i q^{54} +(41.0858 + 84.3735i) q^{55} -651.920 q^{56} +(3203.31 + 3203.31i) q^{57} +(-54.5171 + 54.5171i) q^{58} +194.702i q^{59} +(968.776 - 2807.77i) q^{60} +2985.12 q^{61} +(-1687.08 - 1687.08i) q^{62} +(-2843.03 + 2843.03i) q^{63} -512.000i q^{64} +(-3707.14 - 1279.09i) q^{65} +157.679 q^{66} +(1253.37 + 1253.37i) q^{67} +(2101.35 - 2101.35i) q^{68} -1638.13i q^{69} +(-1831.63 + 891.916i) q^{70} +5433.53 q^{71} +(-2232.84 - 2232.84i) q^{72} +(-6108.29 + 6108.29i) q^{73} -1294.73i q^{74} +(-1119.54 - 9214.11i) q^{75} +2440.33 q^{76} +(-76.4745 - 76.4745i) q^{77} +(-4659.17 + 4659.17i) q^{78} -2583.99i q^{79} +(-700.486 - 1438.51i) q^{80} -1610.10 q^{81} +(-210.815 - 210.815i) q^{82} +(-580.635 + 580.635i) q^{83} +3422.99i q^{84} +(3029.01 - 8778.86i) q^{85} -6903.48 q^{86} +(286.249 + 286.249i) q^{87} +(60.0610 - 60.0610i) q^{88} +1893.55i q^{89} +(-9328.19 - 3218.54i) q^{90} +4519.42 q^{91} +(-623.974 - 623.974i) q^{92} +(-8858.25 + 8858.25i) q^{93} +2298.49i q^{94} +(6856.35 - 3338.71i) q^{95} -2688.32 q^{96} +(10500.7 + 10500.7i) q^{97} +(-3141.84 + 3141.84i) q^{98} -523.853i 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	\( 44 q - 88 q^{2} + 24 q^{5} - 80 q^{7} + 704 q^{8} - 184 q^{10} + 8 q^{11} + 20 q^{13} + 396 q^{15} - 2816 q^{16} + 1080 q^{17} - 2648 q^{18} + 544 q^{20} - 3096 q^{21} - 16 q^{22} - 1884 q^{25} - 80 q^{26} - 3828 q^{27} + 640 q^{28} - 2520 q^{30} - 1580 q^{31} + 5632 q^{32} + 3644 q^{33} + 8208 q^{35} + 10592 q^{36} + 3104 q^{37} - 4064 q^{38} - 704 q^{40} + 4124 q^{41} + 6192 q^{42} - 960 q^{43} - 11316 q^{45} + 2424 q^{47} + 7832 q^{50} + 14840 q^{51} + 160 q^{52} - 3116 q^{53} - 2572 q^{55} - 2560 q^{56} - 9408 q^{57} - 3928 q^{58} + 6912 q^{60} + 19136 q^{61} + 3160 q^{62} + 4564 q^{63} - 9220 q^{65} - 14576 q^{66} - 5152 q^{67} - 8640 q^{68} - 23672 q^{70} + 7900 q^{71} - 21184 q^{72} + 16424 q^{73} + 24156 q^{75} + 16256 q^{76} - 27012 q^{77} - 1808 q^{78} - 1536 q^{80} - 116684 q^{81} - 8248 q^{82} + 11184 q^{83} - 14620 q^{85} + 3840 q^{86} + 8312 q^{87} + 128 q^{88} + 14544 q^{90} + 10296 q^{91} - 7488 q^{93} + 19536 q^{95} + 41292 q^{97} + 51024 q^{98}+O(q^{100}) \) 44 * q - 88 * q^2 + 24 * q^5 - 80 * q^7 + 704 * q^8 - 184 * q^10 + 8 * q^11 + 20 * q^13 + 396 * q^15 - 2816 * q^16 + 1080 * q^17 - 2648 * q^18 + 544 * q^20 - 3096 * q^21 - 16 * q^22 - 1884 * q^25 - 80 * q^26 - 3828 * q^27 + 640 * q^28 - 2520 * q^30 - 1580 * q^31 + 5632 * q^32 + 3644 * q^33 + 8208 * q^35 + 10592 * q^36 + 3104 * q^37 - 4064 * q^38 - 704 * q^40 + 4124 * q^41 + 6192 * q^42 - 960 * q^43 - 11316 * q^45 + 2424 * q^47 + 7832 * q^50 + 14840 * q^51 + 160 * q^52 - 3116 * q^53 - 2572 * q^55 - 2560 * q^56 - 9408 * q^57 - 3928 * q^58 + 6912 * q^60 + 19136 * q^61 + 3160 * q^62 + 4564 * q^63 - 9220 * q^65 - 14576 * q^66 - 5152 * q^67 - 8640 * q^68 - 23672 * q^70 + 7900 * q^71 - 21184 * q^72 + 16424 * q^73 + 24156 * q^75 + 16256 * q^76 - 27012 * q^77 - 1808 * q^78 - 1536 * q^80 - 116684 * q^81 - 8248 * q^82 + 11184 * q^83 - 14620 * q^85 + 3840 * q^86 + 8312 * q^87 + 128 * q^88 + 14544 * q^90 + 10296 * q^91 - 7488 * q^93 + 19536 * q^95 + 41292 * q^97 + 51024 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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