LMFDB - Embedded newform 230.5.f.a.47.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("230.47");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	230.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$23.7750915093$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 - 2.00000i) q^{2} +(6.67173 - 6.67173i) q^{3} +8.00000i q^{4} +(5.03883 - 24.4869i) q^{5} -26.6869 q^{6} +(-43.7544 - 43.7544i) q^{7} +(16.0000 - 16.0000i) q^{8} -8.02391i q^{9} +O(q^{10})$	\(q+(-2.00000 - 2.00000i) q^{2} +(6.67173 - 6.67173i) q^{3} +8.00000i q^{4} +(5.03883 - 24.4869i) q^{5} -26.6869 q^{6} +(-43.7544 - 43.7544i) q^{7} +(16.0000 - 16.0000i) q^{8} -8.02391i q^{9} +(-59.0515 + 38.8962i) q^{10} -158.200 q^{11} +(53.3738 + 53.3738i) q^{12} +(-13.0760 + 13.0760i) q^{13} +175.018i q^{14} +(-129.753 - 196.988i) q^{15} -64.0000 q^{16} +(108.442 + 108.442i) q^{17} +(-16.0478 + 16.0478i) q^{18} +274.639i q^{19} +(195.896 + 40.3106i) q^{20} -583.835 q^{21} +(316.400 + 316.400i) q^{22} +(-77.9968 + 77.9968i) q^{23} -213.495i q^{24} +(-574.220 - 246.771i) q^{25} +52.3040 q^{26} +(486.877 + 486.877i) q^{27} +(350.035 - 350.035i) q^{28} -869.872i q^{29} +(-134.471 + 653.481i) q^{30} +77.4553 q^{31} +(128.000 + 128.000i) q^{32} +(-1055.47 + 1055.47i) q^{33} -433.767i q^{34} +(-1291.88 + 850.941i) q^{35} +64.1913 q^{36} +(-1189.38 - 1189.38i) q^{37} +(549.279 - 549.279i) q^{38} +174.479i q^{39} +(-311.170 - 472.412i) q^{40} -428.375 q^{41} +(1167.67 + 1167.67i) q^{42} +(601.764 - 601.764i) q^{43} -1265.60i q^{44} +(-196.481 - 40.4311i) q^{45} +311.987 q^{46} +(1753.36 + 1753.36i) q^{47} +(-426.991 + 426.991i) q^{48} +1427.90i q^{49} +(654.899 + 1641.98i) q^{50} +1446.99 q^{51} +(-104.608 - 104.608i) q^{52} +(-52.8509 + 52.8509i) q^{53} -1947.51i q^{54} +(-797.142 + 3873.83i) q^{55} -1400.14 q^{56} +(1832.32 + 1832.32i) q^{57} +(-1739.74 + 1739.74i) q^{58} +3674.49i q^{59} +(1575.90 - 1038.02i) q^{60} -4018.52 q^{61} +(-154.911 - 154.911i) q^{62} +(-351.082 + 351.082i) q^{63} -512.000i q^{64} +(254.304 + 386.079i) q^{65} +4221.87 q^{66} +(4081.31 + 4081.31i) q^{67} +(-867.534 + 867.534i) q^{68} +1040.75i q^{69} +(4285.65 + 881.884i) q^{70} -9043.18 q^{71} +(-128.383 - 128.383i) q^{72} +(-4872.18 + 4872.18i) q^{73} +4757.50i q^{74} +(-5477.43 + 2184.65i) q^{75} -2197.11 q^{76} +(6921.94 + 6921.94i) q^{77} +(348.958 - 348.958i) q^{78} -10018.6i q^{79} +(-322.485 + 1567.16i) q^{80} +7146.55 q^{81} +(856.750 + 856.750i) q^{82} +(-2996.62 + 2996.62i) q^{83} -4670.68i q^{84} +(3201.82 - 2108.99i) q^{85} -2407.06 q^{86} +(-5803.55 - 5803.55i) q^{87} +(-2531.20 + 2531.20i) q^{88} +784.202i q^{89} +(312.100 + 473.824i) q^{90} +1144.27 q^{91} +(-623.974 - 623.974i) q^{92} +(516.761 - 516.761i) q^{93} -7013.45i q^{94} +(6725.07 + 1383.86i) q^{95} +1707.96 q^{96} +(-10750.8 - 10750.8i) q^{97} +(2855.79 - 2855.79i) q^{98} +1269.38i 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
$3$	6.67173	−	6.67173i	0.741303	−	0.741303i	−0.231526	−	0.972829i	$-0.574372\pi$
$3$	6.67173	−	6.67173i	0.741303	−	0.741303i	0.972829	+	0.231526i	$0.0743717\pi$
$4$			8.00000i			0.500000i
$5$	5.03883	−	24.4869i	0.201553	−	0.979478i
$5$	5.03883	−	24.4869i	0.201553	−	0.979478i
$6$	−26.6869			−0.741303
$7$	−43.7544	−	43.7544i	−0.892947	−	0.892947i	0.101852	−	0.994800i	$-0.467523\pi$
$7$	−43.7544	−	43.7544i	−0.892947	−	0.892947i	−0.994800	+	0.101852i	$0.967523\pi$
$8$	16.0000	−	16.0000i	0.250000	−	0.250000i
$9$		−	8.02391i		−	0.0990607i
$10$	−59.0515	+	38.8962i	−0.590515	+	0.388962i
$11$	−158.200			−1.30744			−0.653719	−	0.756738i	$-0.726792\pi$
$11$	−158.200			−1.30744			−0.653719	+	0.756738i	$0.726792\pi$
$12$	53.3738	+	53.3738i	0.370652	+	0.370652i
$13$	−13.0760	+	13.0760i	−0.0773728	+	0.0773728i	−0.744734	−	0.667361i	$-0.767424\pi$
$13$	−13.0760	+	13.0760i	−0.0773728	+	0.0773728i	0.667361	+	0.744734i	$0.267424\pi$
$14$			175.018i			0.892947i
$15$	−129.753	−	196.988i	−0.576678	−	0.875502i
$16$	−64.0000			−0.250000
$17$	108.442	+	108.442i	0.375231	+	0.375231i	0.869378	−	0.494147i	$-0.164520\pi$
$17$	108.442	+	108.442i	0.375231	+	0.375231i	−0.494147	+	0.869378i	$0.664520\pi$
$18$	−16.0478	+	16.0478i	−0.0495303	+	0.0495303i
$19$			274.639i			0.760774i	0.924827	+	0.380387i	$0.124209\pi$
$19$			274.639i			0.760774i	−0.924827	+	0.380387i	$0.875791\pi$
$20$	195.896	+	40.3106i	0.489739	+	0.100777i
$21$	−583.835			−1.32389
$22$	316.400	+	316.400i	0.653719	+	0.653719i
$23$	−77.9968	+	77.9968i	−0.147442	+	0.147442i
$23$	−77.9968	+	77.9968i	−0.147442	+	0.147442i
$24$		−	213.495i		−	0.370652i
$25$	−574.220	−	246.771i	−0.918753	−	0.394833i
$26$	52.3040			0.0773728
$27$	486.877	+	486.877i	0.667869	+	0.667869i
$28$	350.035	−	350.035i	0.446474	−	0.446474i
$29$		−	869.872i		−	1.03433i	−0.855886	−	0.517165i	$-0.826987\pi$
$29$		−	869.872i		−	1.03433i	0.855886	−	0.517165i	$-0.173013\pi$
$30$	−134.471	+	653.481i	−0.149412	+	0.726090i
$31$	77.4553			0.0805987			0.0402993	−	0.999188i	$-0.487169\pi$
$31$	77.4553			0.0805987			0.0402993	+	0.999188i	$0.487169\pi$
$32$	128.000	+	128.000i	0.125000	+	0.125000i
$33$	−1055.47	+	1055.47i	−0.969207	+	0.969207i
$34$		−	433.767i		−	0.375231i
$35$	−1291.88	+	850.941i	−1.05460	+	0.694646i
$36$	64.1913			0.0495303
$37$	−1189.38	−	1189.38i	−0.868792	−	0.868792i	0.123547	−	0.992339i	$-0.460573\pi$
$37$	−1189.38	−	1189.38i	−0.868792	−	0.868792i	−0.992339	+	0.123547i	$0.960573\pi$
$38$	549.279	−	549.279i	0.380387	−	0.380387i
$39$			174.479i			0.114713i
$40$	−311.170	−	472.412i	−0.194481	−	0.295258i
$41$	−428.375			−0.254833			−0.127417	−	0.991849i	$-0.540669\pi$
$41$	−428.375			−0.254833			−0.127417	+	0.991849i	$0.540669\pi$
$42$	1167.67	+	1167.67i	0.661945	+	0.661945i
$43$	601.764	−	601.764i	0.325454	−	0.325454i	−0.525401	−	0.850855i	$-0.676085\pi$
$43$	601.764	−	601.764i	0.325454	−	0.325454i	0.850855	+	0.525401i	$0.176085\pi$
$44$		−	1265.60i		−	0.653719i
$45$	−196.481	−	40.4311i	−0.0970277	−	0.0199660i
$46$	311.987			0.147442
$47$	1753.36	+	1753.36i	0.793736	+	0.793736i	0.982099	−	0.188363i	$-0.0603183\pi$
$47$	1753.36	+	1753.36i	0.793736	+	0.793736i	−0.188363	+	0.982099i	$0.560318\pi$
$48$	−426.991	+	426.991i	−0.185326	+	0.185326i
$49$			1427.90i			0.594709i
$50$	654.899	+	1641.98i	0.261960	+	0.656793i
$51$	1446.99			0.556320
$52$	−104.608	−	104.608i	−0.0386864	−	0.0386864i
$53$	−52.8509	+	52.8509i	−0.0188148	+	0.0188148i	−0.716452	−	0.697637i	$-0.754235\pi$
$53$	−52.8509	+	52.8509i	−0.0188148	+	0.0188148i	0.697637	+	0.716452i	$0.254235\pi$
$54$		−	1947.51i		−	0.667869i
$55$	−797.142	+	3873.83i	−0.263518	+	1.28061i
$56$	−1400.14			−0.446474
$57$	1832.32	+	1832.32i	0.563964	+	0.563964i
$58$	−1739.74	+	1739.74i	−0.517165	+	0.517165i
$59$			3674.49i			1.05558i	0.849374	+	0.527792i	$0.176980\pi$
$59$			3674.49i			1.05558i	−0.849374	+	0.527792i	$0.823020\pi$
$60$	1575.90	−	1038.02i	0.437751	−	0.288339i
$61$	−4018.52			−1.07996			−0.539978	−	0.841679i	$-0.681568\pi$
$61$	−4018.52			−1.07996			−0.539978	+	0.841679i	$0.681568\pi$
$62$	−154.911	−	154.911i	−0.0402993	−	0.0402993i
$63$	−351.082	+	351.082i	−0.0884559	+	0.0884559i
$64$		−	512.000i		−	0.125000i
$65$	254.304	+	386.079i	0.0601902	+	0.0913796i
$66$	4221.87			0.969207
$67$	4081.31	+	4081.31i	0.909179	+	0.909179i	0.996206	−	0.0870266i	$-0.0277365\pi$
$67$	4081.31	+	4081.31i	0.909179	+	0.909179i	−0.0870266	+	0.996206i	$0.527737\pi$
$68$	−867.534	+	867.534i	−0.187615	+	0.187615i
$69$			1040.75i			0.218598i
$70$	4285.65	+	881.884i	0.874622	+	0.179976i
$71$	−9043.18			−1.79393			−0.896963	−	0.442106i	$-0.854231\pi$
$71$	−9043.18			−1.79393			−0.896963	+	0.442106i	$0.854231\pi$
$72$	−128.383	−	128.383i	−0.0247652	−	0.0247652i
$73$	−4872.18	+	4872.18i	−0.914276	+	0.914276i	−0.996605	−	0.0823290i	$-0.973764\pi$
$73$	−4872.18	+	4872.18i	−0.914276	+	0.914276i	0.0823290	+	0.996605i	$0.473764\pi$
$74$			4757.50i			0.868792i
$75$	−5477.43	+	2184.65i	−0.973766	+	0.388383i
$76$	−2197.11			−0.380387
$77$	6921.94	+	6921.94i	1.16747	+	1.16747i
$78$	348.958	−	348.958i	0.0573567	−	0.0573567i
$79$		−	10018.6i		−	1.60529i	−0.596457	−	0.802645i	$-0.703425\pi$
$79$		−	10018.6i		−	1.60529i	0.596457	−	0.802645i	$-0.296575\pi$
$80$	−322.485	+	1567.16i	−0.0503883	+	0.244869i
$81$	7146.55			1.08925
$82$	856.750	+	856.750i	0.127417	+	0.127417i
$83$	−2996.62	+	2996.62i	−0.434987	+	0.434987i	−0.890321	−	0.455334i	$-0.849520\pi$
$83$	−2996.62	+	2996.62i	−0.434987	+	0.434987i	0.455334	+	0.890321i	$0.349520\pi$
$84$		−	4670.68i		−	0.661945i
$85$	3201.82	−	2108.99i	0.443159	−	0.291901i
$86$	−2407.06			−0.325454
$87$	−5803.55	−	5803.55i	−0.766753	−	0.766753i
$88$	−2531.20	+	2531.20i	−0.326859	+	0.326859i
$89$			784.202i			0.0990029i	0.998774	+	0.0495015i	$0.0157633\pi$
$89$			784.202i			0.0990029i	−0.998774	+	0.0495015i	$0.984237\pi$
$90$	312.100	+	473.824i	0.0385309	+	0.0584968i
$91$	1144.27			0.138180
$92$	−623.974	−	623.974i	−0.0737210	−	0.0737210i
$93$	516.761	−	516.761i	0.0597480	−	0.0597480i
$94$		−	7013.45i		−	0.793736i
$95$	6725.07	+	1383.86i	0.745161	+	0.153336i
$96$	1707.96			0.185326
$97$	−10750.8	−	10750.8i	−1.14261	−	1.14261i	−0.987971	−	0.154638i	$-0.950579\pi$
$97$	−10750.8	−	10750.8i	−1.14261	−	1.14261i	−0.154638	−	0.987971i	$-0.549421\pi$
$98$	2855.79	−	2855.79i	0.297355	−	0.297355i
$99$			1269.38i			0.129516i
$100$	1974.17	−	4593.76i	0.197417	−	0.459376i
$101$	−10042.5			−0.984462			−0.492231	−	0.870465i	$-0.663818\pi$
$101$	−10042.5			−0.984462			−0.492231	+	0.870465i	$0.663818\pi$
$102$	−2893.97	−	2893.97i	−0.278160	−	0.278160i
$103$	8682.87	−	8682.87i	0.818443	−	0.818443i	−0.167439	−	0.985882i	$-0.553550\pi$
$103$	8682.87	−	8682.87i	0.818443	−	0.818443i	0.985882	+	0.167439i	$0.0535497\pi$
$104$			418.432i			0.0386864i
$105$	−2941.84	+	14296.3i	−0.266834	+	1.29672i
$106$	211.403			0.0188148
$107$	−103.562	−	103.562i	−0.00904553	−	0.00904553i	0.702570	−	0.711615i	$-0.252036\pi$
$107$	−103.562	−	103.562i	−0.00904553	−	0.00904553i	−0.711615	+	0.702570i	$0.752036\pi$
$108$	−3895.01	+	3895.01i	−0.333935	+	0.333935i
$109$		−	495.982i		−	0.0417458i	−0.999782	−	0.0208729i	$-0.993355\pi$
$109$		−	495.982i		−	0.0417458i	0.999782	−	0.0208729i	$-0.00664453\pi$
$110$	9341.95	−	6153.38i	0.772062	−	0.508544i
$111$	−15870.4			−1.28808
$112$	2800.28	+	2800.28i	0.223237	+	0.223237i
$113$	−203.290	+	203.290i	−0.0159206	+	0.0159206i	−0.715022	−	0.699102i	$-0.753583\pi$
$113$	−203.290	+	203.290i	−0.0159206	+	0.0159206i	0.699102	+	0.715022i	$0.253583\pi$
$114$		−	7329.27i		−	0.563964i
$115$	1516.89	+	2302.92i	0.114699	+	0.174133i
$116$	6958.98			0.517165
$117$	104.921	+	104.921i	0.00766460	+	0.00766460i
$118$	7348.98	−	7348.98i	0.527792	−	0.527792i
$119$		−	9489.61i		−	0.670123i
$120$	−5227.85	−	1075.77i	−0.363045	−	0.0747060i
$121$	10386.2			0.709392
$122$	8037.04	+	8037.04i	0.539978	+	0.539978i
$123$	−2858.00	+	2858.00i	−0.188909	+	0.188909i
$124$			619.642i			0.0402993i
$125$	−8936.06	+	12817.5i	−0.571908	+	0.820318i
$126$	1404.33			0.0884559
$127$	−6259.21	−	6259.21i	−0.388071	−	0.388071i	0.485928	−	0.873999i	$-0.338482\pi$
$127$	−6259.21	−	6259.21i	−0.388071	−	0.388071i	−0.873999	+	0.485928i	$0.838482\pi$
$128$	−1024.00	+	1024.00i	−0.0625000	+	0.0625000i
$129$		−	8029.62i		−	0.482520i
$130$	263.551	−	1280.77i	0.0155947	−	0.0757849i
$131$	−1816.29			−0.105838			−0.0529192	−	0.998599i	$-0.516853\pi$
$131$	−1816.29			−0.105838			−0.0529192	+	0.998599i	$0.516853\pi$
$132$	−8443.73	−	8443.73i	−0.484604	−	0.484604i
$133$	12016.7	−	12016.7i	0.679331	−	0.679331i
$134$		−	16325.2i		−	0.909179i
$135$	14375.4	−	9468.83i	0.788774	−	0.519552i
$136$	3470.13			0.187615
$137$	−18210.6	−	18210.6i	−0.970247	−	0.970247i	0.0293231	−	0.999570i	$-0.490665\pi$
$137$	−18210.6	−	18210.6i	−0.970247	−	0.970247i	−0.999570	+	0.0293231i	$0.990665\pi$
$138$	2081.49	−	2081.49i	0.109299	−	0.109299i
$139$		−	25924.6i		−	1.34178i	−0.741556	−	0.670891i	$-0.765912\pi$
$139$		−	25924.6i		−	1.34178i	0.741556	−	0.670891i	$-0.234088\pi$
$140$	−6807.53	−	10335.1i	−0.347323	−	0.527299i
$141$	23395.9			1.17680
$142$	18086.4	+	18086.4i	0.896963	+	0.896963i
$143$	2068.62	−	2068.62i	0.101160	−	0.101160i
$144$			513.531i			0.0247652i
$145$	−21300.5	−	4383.13i	−1.01310	−	0.208473i
$146$	19488.7			0.914276
$147$	9526.54	+	9526.54i	0.440860	+	0.440860i
$148$	9515.01	−	9515.01i	0.434396	−	0.434396i
$149$		−	36526.6i		−	1.64527i	−0.568572	−	0.822633i	$-0.692504\pi$
$149$		−	36526.6i		−	1.64527i	0.568572	−	0.822633i	$-0.307496\pi$
$150$	15324.2	+	6585.55i	0.681074	+	0.292691i
$151$	32487.3			1.42482			0.712410	−	0.701764i	$-0.247604\pi$
$151$	32487.3			1.42482			0.712410	+	0.701764i	$0.247604\pi$
$152$	4394.23	+	4394.23i	0.190193	+	0.190193i
$153$	870.127	−	870.127i	0.0371706	−	0.0371706i
$154$		−	27687.8i		−	1.16747i
$155$	390.284	−	1896.64i	0.0162449	−	0.0789446i
$156$	−1395.83			−0.0573567
$157$	−13070.7	−	13070.7i	−0.530273	−	0.530273i	0.390380	−	0.920654i	$-0.372344\pi$
$157$	−13070.7	−	13070.7i	−0.530273	−	0.530273i	−0.920654	+	0.390380i	$0.872344\pi$
$158$	−20037.2	+	20037.2i	−0.802645	+	0.802645i
$159$			705.213i			0.0278950i
$160$	3779.30	−	2489.36i	0.147629	−	0.0972406i
$161$	6825.41			0.263316
$162$	−14293.1	−	14293.1i	−0.544624	−	0.544624i
$163$	−2355.48	+	2355.48i	−0.0886551	+	0.0886551i	−0.750044	−	0.661388i	$-0.769968\pi$
$163$	−2355.48	+	2355.48i	−0.0886551	+	0.0886551i	0.661388	+	0.750044i	$0.269968\pi$
$164$		−	3427.00i		−	0.127417i
$165$	20526.8	+	31163.5i	0.753970	+	1.14466i
$166$	11986.5			0.434987
$167$	−10516.3	−	10516.3i	−0.377077	−	0.377077i	0.492970	−	0.870046i	$-0.335911\pi$
$167$	−10516.3	−	10516.3i	−0.377077	−	0.377077i	−0.870046	+	0.492970i	$0.835911\pi$
$168$	−9341.36	+	9341.36i	−0.330972	+	0.330972i
$169$			28219.0i			0.988027i
$170$	−10621.6	−	2185.68i	−0.367530	−	0.0756289i
$171$	2203.68			0.0753627
$172$	4814.11	+	4814.11i	0.162727	+	0.162727i
$173$	−26901.4	+	26901.4i	−0.898839	+	0.898839i	−0.995334	−	0.0964945i	$-0.969237\pi$
$173$	−26901.4	+	26901.4i	−0.898839	+	0.898839i	0.0964945	+	0.995334i	$0.469237\pi$
$174$			23214.2i			0.766753i
$175$	14327.4	+	35922.0i	0.467832	+	1.17296i
$176$	10124.8			0.326859
$177$	24515.2	+	24515.2i	0.782508	+	0.782508i
$178$	1568.40	−	1568.40i	0.0495015	−	0.0495015i
$179$		−	46211.9i		−	1.44227i	−0.692792	−	0.721137i	$-0.743620\pi$
$179$		−	46211.9i		−	1.44227i	0.692792	−	0.721137i	$-0.256380\pi$
$180$	323.449	−	1571.85i	0.00998299	−	0.0485139i
$181$	4262.59			0.130112			0.0650558	−	0.997882i	$-0.479277\pi$
$181$	4262.59			0.130112			0.0650558	+	0.997882i	$0.479277\pi$
$182$	−2288.53	−	2288.53i	−0.0690898	−	0.0690898i
$183$	−26810.5	+	26810.5i	−0.800575	+	0.800575i
$184$			2495.90i			0.0737210i
$185$	−35117.2	+	23131.1i	−1.02607	+	0.675855i
$186$	−2067.04			−0.0597480
$187$	−17155.5	−	17155.5i	−0.490591	−	0.490591i
$188$	−14026.9	+	14026.9i	−0.396868	+	0.396868i
$189$		−	42606.0i		−	1.19274i
$190$	−10682.4	−	16217.9i	−0.295912	−	0.449248i
$191$	−50432.8			−1.38244			−0.691220	−	0.722644i	$-0.742927\pi$
$191$	−50432.8			−1.38244			−0.691220	+	0.722644i	$0.742927\pi$
$192$	−3415.92	−	3415.92i	−0.0926629	−	0.0926629i
$193$	−7401.00	+	7401.00i	−0.198690	+	0.198690i	−0.799438	−	0.600748i	$-0.794869\pi$
$193$	−7401.00	+	7401.00i	−0.198690	+	0.198690i	0.600748	+	0.799438i	$0.294869\pi$
$194$			43003.2i			1.14261i
$195$	4272.46	+	879.170i	0.112359	+	0.0231208i
$196$	−11423.2			−0.297355
$197$	−34814.9	−	34814.9i	−0.897083	−	0.897083i	0.0980939	−	0.995177i	$-0.468725\pi$
$197$	−34814.9	−	34814.9i	−0.897083	−	0.897083i	−0.995177	+	0.0980939i	$0.968725\pi$
$198$	2538.76	−	2538.76i	0.0647578	−	0.0647578i
$199$		−	5398.39i		−	0.136320i	−0.997674	−	0.0681598i	$-0.978287\pi$
$199$		−	5398.39i		−	0.136320i	0.997674	−	0.0681598i	$-0.0217128\pi$
$200$	−13135.9	+	5239.19i	−0.328397	+	0.130980i
$201$	54458.7			1.34796
$202$	20085.0	+	20085.0i	0.492231	+	0.492231i
$203$	−38060.7	+	38060.7i	−0.923603	+	0.923603i
$204$			11575.9i			0.278160i
$205$	−2158.51	+	10489.6i	−0.0513625	+	0.249604i
$206$	−34731.5			−0.818443
$207$	625.840	+	625.840i	0.0146057	+	0.0146057i
$208$	836.864	−	836.864i	0.0193432	−	0.0193432i
$209$		−	43447.9i		−	0.994664i
$210$	34476.4	−	22709.0i	0.781777	−	0.514943i
$211$	64758.5			1.45456			0.727281	−	0.686340i	$-0.240784\pi$
$211$	64758.5			1.45456			0.727281	+	0.686340i	$0.240784\pi$
$212$	−422.807	−	422.807i	−0.00940742	−	0.00940742i
$213$	−60333.6	+	60333.6i	−1.32984	+	1.32984i
$214$			414.249i			0.00904553i
$215$	−11703.2	−	17767.6i	−0.253179	−	0.384371i
$216$	15580.1			0.333935
$217$	−3389.01	−	3389.01i	−0.0719703	−	0.0719703i
$218$	−991.964	+	991.964i	−0.0208729	+	0.0208729i
$219$			65011.7i			1.35551i
$220$	−30990.6	−	6377.13i	−0.640303	−	0.131759i
$221$	−2835.97			−0.0580653
$222$	31740.8	+	31740.8i	0.644038	+	0.644038i
$223$	1034.44	−	1034.44i	0.0208016	−	0.0208016i	−0.696629	−	0.717431i	$-0.745318\pi$
$223$	1034.44	−	1034.44i	0.0208016	−	0.0208016i	0.717431	+	0.696629i	$0.245318\pi$
$224$		−	11201.1i		−	0.223237i
$225$	−1980.07	+	4607.50i	−0.0391125	+	0.0910123i
$226$	813.161			0.0159206
$227$	33573.2	+	33573.2i	0.651540	+	0.651540i	0.953364	−	0.301824i	$-0.0975955\pi$
$227$	33573.2	+	33573.2i	0.651540	+	0.651540i	−0.301824	+	0.953364i	$0.597596\pi$
$228$	−14658.5	+	14658.5i	−0.281982	+	0.281982i
$229$			61152.9i			1.16613i	0.812426	+	0.583064i	$0.198146\pi$
$229$			61152.9i			1.16613i	−0.812426	+	0.583064i	$0.801854\pi$
$230$	1572.05	−	7639.61i	0.0297174	−	0.144416i
$231$	92362.6			1.73090
$232$	−13918.0	−	13918.0i	−0.258583	−	0.258583i
$233$	23157.0	−	23157.0i	0.426550	−	0.426550i	−0.460901	−	0.887451i	$-0.652474\pi$
$233$	23157.0	−	23157.0i	0.426550	−	0.426550i	0.887451	+	0.460901i	$0.152474\pi$
$234$		−	419.683i		−	0.00766460i
$235$	51769.4	−	34099.6i	0.937426	−	0.617467i
$236$	−29395.9			−0.527792
$237$	−66841.5	−	66841.5i	−1.19001	−	1.19001i
$238$	−18979.2	+	18979.2i	−0.335061	+	0.335061i
$239$			61047.7i			1.06874i	0.845249	+	0.534372i	$0.179452\pi$
$239$			61047.7i			1.06874i	−0.845249	+	0.534372i	$0.820548\pi$
$240$	8304.16	+	12607.2i	0.144169	+	0.218875i
$241$	31792.2			0.547377			0.273688	−	0.961818i	$-0.411756\pi$
$241$	31792.2			0.547377			0.273688	+	0.961818i	$0.411756\pi$
$242$	−20772.4	−	20772.4i	−0.354696	−	0.354696i
$243$	8242.86	−	8242.86i	0.139594	−	0.139594i
$244$		−	32148.2i		−	0.539978i
$245$	34964.8	+	7194.93i	0.582504	+	0.119865i
$246$	11432.0			0.188909
$247$	−3591.18	−	3591.18i	−0.0588632	−	0.0588632i
$248$	1239.28	−	1239.28i	0.0201497	−	0.0201497i
$249$			39985.3i			0.644914i
$250$	43507.1	−	7762.81i	0.696113	−	0.124205i
$251$	−67761.5			−1.07556			−0.537781	−	0.843085i	$-0.680737\pi$
$251$	−67761.5			−1.07556			−0.537781	+	0.843085i	$0.680737\pi$
$252$	−2808.65	−	2808.65i	−0.0442280	−	0.0442280i
$253$	12339.1	−	12339.1i	0.192771	−	0.192771i
$254$			25036.8i			0.388071i
$255$	7291.12	−	35432.3i	0.112128	−	0.544903i
$256$	4096.00			0.0625000
$257$	49055.6	+	49055.6i	0.742716	+	0.742716i	0.973100	−	0.230384i	$-0.0739983\pi$
$257$	49055.6	+	49055.6i	0.742716	+	0.742716i	−0.230384	+	0.973100i	$0.573998\pi$
$258$	−16059.2	+	16059.2i	−0.241260	+	0.241260i
$259$			104081.i			1.55157i
$260$	−3088.63	+	2034.43i	−0.0456898	+	0.0300951i
$261$	−6979.78			−0.102461
$262$	3632.59	+	3632.59i	0.0529192	+	0.0529192i
$263$	66558.4	−	66558.4i	0.962258	−	0.962258i	−0.0370555	−	0.999313i	$-0.511798\pi$
$263$	66558.4	−	66558.4i	0.962258	−	0.962258i	0.999313	+	0.0370555i	$0.0117978\pi$
$264$			33774.9i			0.484604i
$265$	1027.85	+	1560.46i	0.0146365	+	0.0222209i
$266$	−48066.7			−0.679331
$267$	5231.98	+	5231.98i	0.0733912	+	0.0733912i
$268$	−32650.5	+	32650.5i	−0.454590	+	0.454590i
$269$		−	118202.i		−	1.63351i	−0.576987	−	0.816753i	$-0.695772\pi$
$269$		−	118202.i		−	1.63351i	0.576987	−	0.816753i	$-0.304228\pi$
$270$	−47688.5	−	9813.15i	−0.654163	−	0.134611i
$271$	143037.			1.94765			0.973825	−	0.227301i	$-0.0729900\pi$
$271$	143037.			1.94765			0.973825	+	0.227301i	$0.0729900\pi$
$272$	−6940.27	−	6940.27i	−0.0938077	−	0.0938077i
$273$	7634.23	−	7634.23i	0.102433	−	0.102433i
$274$			72842.3i			0.970247i
$275$	90841.6	+	39039.1i	1.20121	+	0.516220i
$276$	−8325.97			−0.109299
$277$	−32302.8	−	32302.8i	−0.420999	−	0.420999i	0.464549	−	0.885548i	$-0.346217\pi$
$277$	−32302.8	−	32302.8i	−0.420999	−	0.420999i	−0.885548	+	0.464549i	$0.846217\pi$
$278$	−51849.2	+	51849.2i	−0.670891	+	0.670891i
$279$		−	621.495i		−	0.00798416i
$280$	−7055.07	+	34285.2i	−0.0899881	+	0.437311i
$281$	10534.1			0.133408			0.0667041	−	0.997773i	$-0.478752\pi$
$281$	10534.1			0.133408			0.0667041	+	0.997773i	$0.478752\pi$
$282$	−46791.8	−	46791.8i	−0.588399	−	0.588399i
$283$	19097.6	−	19097.6i	0.238455	−	0.238455i	−0.577755	−	0.816210i	$-0.696071\pi$
$283$	19097.6	−	19097.6i	0.238455	−	0.238455i	0.816210	+	0.577755i	$0.196071\pi$
$284$		−	72345.4i		−	0.896963i
$285$	54100.6	−	35635.1i	0.666059	−	0.438721i
$286$	−8274.49			−0.101160
$287$	18743.3	+	18743.3i	0.227553	+	0.227553i
$288$	1027.06	−	1027.06i	0.0123826	−	0.0123826i
$289$		−	60001.8i		−	0.718404i
$290$	33834.7	+	51367.3i	0.402316	+	0.610788i
$291$	−143453.			−1.69404
$292$	−38977.4	−	38977.4i	−0.457138	−	0.457138i
$293$	−41661.1	+	41661.1i	−0.485283	+	0.485283i	−0.906814	−	0.421531i	$-0.861493\pi$
$293$	−41661.1	+	41661.1i	−0.485283	+	0.485283i	0.421531	+	0.906814i	$0.361493\pi$
$294$		−	38106.2i		−	0.440860i
$295$	89977.0	+	18515.1i	1.03392	+	0.212756i
$296$	−38060.0			−0.434396
$297$	−77023.8	−	77023.8i	−0.873197	−	0.873197i
$298$	−73053.1	+	73053.1i	−0.822633	+	0.822633i
$299$		−	2039.77i		−	0.0228160i
$300$	−17477.2	−	43819.4i	−0.194192	−	0.486883i
$301$	−52659.7			−0.581226
$302$	−64974.6	−	64974.6i	−0.712410	−	0.712410i
$303$	−67000.8	+	67000.8i	−0.729785	+	0.729785i
$304$		−	17576.9i		−	0.190193i
$305$	−20248.6	+	98401.2i	−0.217669	+	1.05779i
$306$	−3480.51			−0.0371706
$307$	−16384.7	−	16384.7i	−0.173845	−	0.173845i	0.614822	−	0.788666i	$-0.289228\pi$
$307$	−16384.7	−	16384.7i	−0.173845	−	0.173845i	−0.788666	+	0.614822i	$0.789228\pi$
$308$	−55375.5	+	55375.5i	−0.583736	+	0.583736i
$309$		−	115859.i		−	1.21343i
$310$	−4573.85	+	3012.72i	−0.0475947	+	0.0313498i
$311$	1114.06			0.0115183			0.00575916	−	0.999983i	$-0.498167\pi$
$311$	1114.06			0.0115183			0.00575916	+	0.999983i	$0.498167\pi$
$312$	2791.66	+	2791.66i	0.0286783	+	0.0286783i
$313$	−41025.2	+	41025.2i	−0.418757	+	0.418757i	−0.884775	−	0.466018i	$-0.845688\pi$
$313$	−41025.2	+	41025.2i	−0.418757	+	0.418757i	0.466018	+	0.884775i	$0.345688\pi$
$314$			52282.8i			0.530273i
$315$	6827.88	+	10366.0i	0.0688121	+	0.104469i
$316$	80148.9			0.802645
$317$	−34370.9	−	34370.9i	−0.342036	−	0.342036i	0.515096	−	0.857132i	$-0.327756\pi$
$317$	−34370.9	−	34370.9i	−0.342036	−	0.342036i	−0.857132	+	0.515096i	$0.827756\pi$
$318$	1410.43	−	1410.43i	0.0139475	−	0.0139475i
$319$			137614.i			1.35232i
$320$	−12537.3	−	2579.88i	−0.122435	−	0.0251941i
$321$	−1381.88			−0.0134110
$322$	−13650.8	−	13650.8i	−0.131658	−	0.131658i
$323$	−29782.4	+	29782.4i	−0.285466	+	0.285466i
$324$			57172.4i			0.544624i
$325$	10735.3	−	4281.73i	0.101636	−	0.0405371i
$326$	9421.91			0.0886551
$327$	−3309.06	−	3309.06i	−0.0309463	−	0.0309463i
$328$	−6854.00	+	6854.00i	−0.0637084	+	0.0637084i
$329$		−	153435.i		−	1.41753i
$330$	21273.3	−	103381.i	0.195347	−	0.949317i
$331$	−201923.			−1.84302			−0.921510	−	0.388355i	$-0.873043\pi$
$331$	−201923.			−1.84302			−0.921510	+	0.388355i	$0.873043\pi$
$332$	−23973.0	−	23973.0i	−0.217493	−	0.217493i
$333$	−9543.45	+	9543.45i	−0.0860631	+	0.0860631i
$334$			42065.2i			0.377077i
$335$	120504.	−	79373.7i	1.07377	−	0.707273i
$336$	37365.4			0.330972
$337$	−35770.3	−	35770.3i	−0.314965	−	0.314965i	0.531864	−	0.846830i	$-0.321492\pi$
$337$	−35770.3	−	35770.3i	−0.314965	−	0.314965i	−0.846830	+	0.531864i	$0.821492\pi$
$338$	56438.1	−	56438.1i	0.494013	−	0.494013i
$339$			2712.59i			0.0236040i
$340$	16871.9	+	25614.6i	0.145951	+	0.221580i
$341$	−12253.4			−0.105378
$342$	−4407.36	−	4407.36i	−0.0376814	−	0.0376814i
$343$	−42577.5	+	42577.5i	−0.361903	+	0.361903i
$344$		−	19256.5i		−	0.162727i
$345$	25484.7	+	5244.14i	0.214112	+	0.0440592i
$346$	107605.			0.898839
$347$	83714.9	+	83714.9i	0.695255	+	0.695255i	0.963383	−	0.268129i	$-0.0864052\pi$
$347$	83714.9	+	83714.9i	0.695255	+	0.695255i	−0.268129	+	0.963383i	$0.586405\pi$
$348$	46428.4	−	46428.4i	0.383376	−	0.383376i
$349$		−	58493.3i		−	0.480237i	−0.970744	−	0.240118i	$-0.922814\pi$
$349$		−	58493.3i		−	0.480237i	0.970744	−	0.240118i	$-0.0771863\pi$
$350$	43189.3	−	100499.i	0.352565	−	0.820398i
$351$	−12732.8			−0.103350
$352$	−20249.6	−	20249.6i	−0.163430	−	0.163430i
$353$	16153.5	−	16153.5i	0.129634	−	0.129634i	−0.639313	−	0.768947i	$-0.720781\pi$
$353$	16153.5	−	16153.5i	0.129634	−	0.129634i	0.768947	+	0.639313i	$0.220781\pi$
$354$		−	98060.7i		−	0.782508i
$355$	−45567.0	+	221440.i	−0.361571	+	1.75711i
$356$	−6273.62			−0.0495015
$357$	−63312.1	−	63312.1i	−0.496764	−	0.496764i
$358$	−92423.8	+	92423.8i	−0.721137	+	0.721137i
$359$		−	44740.4i		−	0.347145i	−0.984821	−	0.173573i	$-0.944469\pi$
$359$		−	44740.4i		−	0.347145i	0.984821	−	0.173573i	$-0.0555311\pi$
$360$	−3790.60	+	2496.80i	−0.0292484	+	0.0192654i
$361$	54894.3			0.421224
$362$	−8525.17	−	8525.17i	−0.0650558	−	0.0650558i
$363$	69293.9	−	69293.9i	0.525874	−	0.525874i
$364$			9154.12i			0.0690898i
$365$	94754.7	+	143855.i	0.711238	+	1.07979i
$366$	107242.			0.800575
$367$	146066.	+	146066.i	1.08447	+	1.08447i	0.996087	+	0.0883787i	$0.0281686\pi$
$367$	146066.	+	146066.i	1.08447	+	1.08447i	0.0883787	+	0.996087i	$0.471831\pi$
$368$	4991.79	−	4991.79i	0.0368605	−	0.0368605i
$369$			3437.24i			0.0252440i
$370$	116497.	+	23972.2i	0.850962	+	0.175108i
$371$	4624.92			0.0336013
$372$	4134.09	+	4134.09i	0.0298740	+	0.0298740i
$373$	162405.	−	162405.i	1.16730	−	1.16730i	0.184462	−	0.982840i	$-0.440946\pi$
$373$	162405.	−	162405.i	1.16730	−	1.16730i	0.982840	−	0.184462i	$-0.0590542\pi$
$374$			68621.9i			0.490591i
$375$	25895.7	+	145134.i	0.184147	+	1.03206i
$376$	56107.6			0.396868
$377$	11374.4	+	11374.4i	0.0800291	+	0.0800291i
$378$	−85212.0	+	85212.0i	−0.596372	+	0.596372i
$379$		−	235187.i		−	1.63733i	−0.574273	−	0.818664i	$-0.694715\pi$
$379$		−	235187.i		−	1.63733i	0.574273	−	0.818664i	$-0.305285\pi$
$380$	−11070.9	+	53800.6i	−0.0766681	+	0.372580i
$381$	−83519.4			−0.575357
$382$	100866.	+	100866.i	0.691220	+	0.691220i
$383$	53131.6	−	53131.6i	0.362206	−	0.362206i	−0.502419	−	0.864624i	$-0.667556\pi$
$383$	53131.6	−	53131.6i	0.362206	−	0.362206i	0.864624	+	0.502419i	$0.167556\pi$
$384$			13663.7i			0.0926629i
$385$	204376.	−	134619.i	1.37882	−	0.908205i
$386$	29604.0			0.198690
$387$	−4828.51	−	4828.51i	−0.0322397	−	0.0322397i
$388$	86006.5	−	86006.5i	0.571304	−	0.571304i
$389$		−	194320.i		−	1.28416i	−0.766639	−	0.642078i	$-0.778073\pi$
$389$		−	194320.i		−	1.28416i	0.766639	−	0.642078i	$-0.221927\pi$
$390$	−6786.58	−	10303.3i	−0.0446192	−	0.0677400i
$391$	−16916.2			−0.110650
$392$	22846.4	+	22846.4i	0.148677	+	0.148677i
$393$	−12117.8	+	12117.8i	−0.0784584	+	0.0784584i
$394$			139260.i			0.897083i
$395$	−245325.	−	50482.1i	−1.57235	−	0.323551i
$396$	−10155.1			−0.0647578
$397$	87534.4	+	87534.4i	0.555390	+	0.555390i	0.927991	−	0.372602i	$-0.121534\pi$
$397$	87534.4	+	87534.4i	0.555390	+	0.555390i	−0.372602	+	0.927991i	$0.621534\pi$
$398$	−10796.8	+	10796.8i	−0.0681598	+	0.0681598i
$399$		−	160344.i		−	1.00718i
$400$	36750.1	+	15793.3i	0.229688	+	0.0987084i
$401$	−154376.			−0.960043			−0.480022	−	0.877257i	$-0.659371\pi$
$401$	−154376.			−0.960043			−0.480022	+	0.877257i	$0.659371\pi$
$402$	−108917.	−	108917.i	−0.673978	−	0.673978i
$403$	−1012.81	+	1012.81i	−0.00623614	+	0.00623614i
$404$		−	80340.0i		−	0.492231i
$405$	36010.2	−	174997.i	0.219541	−	1.06689i
$406$	152243.			0.923603
$407$	188159.	+	188159.i	1.13589	+	1.13589i
$408$	23151.8	−	23151.8i	0.139080	−	0.139080i
$409$		−	119180.i		−	0.712454i	−0.934399	−	0.356227i	$-0.884063\pi$
$409$		−	119180.i		−	0.712454i	0.934399	−	0.356227i	$-0.115937\pi$
$410$	25296.2	−	16662.2i	0.150483	−	0.0991206i
$411$	−242992.			−1.43849
$412$	69462.9	+	69462.9i	0.409222	+	0.409222i
$413$	160775.	−	160775.i	0.942581	−	0.942581i
$414$		−	2503.36i		−	0.0146057i
$415$	58278.6	+	88477.6i	0.338387	+	0.513732i
$416$	−3347.46			−0.0193432
$417$	−172962.	−	172962.i	−0.994668	−	0.994668i
$418$	−86895.8	+	86895.8i	−0.497332	+	0.497332i
$419$			143591.i			0.817899i	0.912557	+	0.408950i	$0.134105\pi$
$419$			143591.i			0.817899i	−0.912557	+	0.408950i	$0.865895\pi$
$420$	−114371.	−	23534.7i	−0.648360	−	0.133417i
$421$	23762.3			0.134068			0.0670339	−	0.997751i	$-0.478646\pi$
$421$	23762.3			0.134068			0.0670339	+	0.997751i	$0.478646\pi$
$422$	−129517.	−	129517.i	−0.727281	−	0.727281i
$423$	14068.8	−	14068.8i	0.0786280	−	0.0786280i
$424$			1691.23i			0.00940742i
$425$	−35509.2	−	89029.7i	−0.196591	−	0.492898i
$426$	241335.			1.32984
$427$	175828.	+	175828.i	0.964344	+	0.964344i
$428$	828.498	−	828.498i	0.00452276	−	0.00452276i
$429$		−	27602.6i		−	0.149981i
$430$	−12128.7	+	58941.5i	−0.0655962	+	0.318775i
$431$	−88790.2			−0.477981			−0.238991	−	0.971022i	$-0.576816\pi$
$431$	−88790.2			−0.477981			−0.238991	+	0.971022i	$0.576816\pi$
$432$	−31160.1	−	31160.1i	−0.166967	−	0.166967i
$433$	185573.	−	185573.i	0.989779	−	0.989779i	−0.0101692	−	0.999948i	$-0.503237\pi$
$433$	185573.	−	185573.i	0.989779	−	0.989779i	0.999948	+	0.0101692i	$0.00323702\pi$
$434$			13556.0i			0.0719703i
$435$	−171354.	+	112868.i	−0.905558	+	0.596476i
$436$	3967.85			0.0208729
$437$	−21421.0	−	21421.0i	−0.112170	−	0.112170i
$438$	130023.	−	130023.i	0.677756	−	0.677756i
$439$		−	2465.67i		−	0.0127940i	−0.999980	−	0.00639700i	$-0.997964\pi$
$439$		−	2465.67i		−	0.0127940i	0.999980	−	0.00639700i	$-0.00203624\pi$
$440$	49227.0	+	74735.6i	0.254272	+	0.386031i
$441$	11457.3			0.0589123
$442$	5671.94	+	5671.94i	0.0290327	+	0.0290327i
$443$	−204663.	+	204663.i	−1.04287	+	1.04287i	−0.0438336	+	0.999039i	$0.513957\pi$
$443$	−204663.	+	204663.i	−1.04287	+	1.04287i	−0.999039	+	0.0438336i	$0.986043\pi$
$444$		−	126963.i		−	0.644038i
$445$	19202.7	+	3951.46i	0.0969712	+	0.0199543i
$446$	−4137.78			−0.0208016
$447$	−243695.	−	243695.i	−1.21964	−	1.21964i
$448$	−22402.3	+	22402.3i	−0.111618	+	0.111618i
$449$			369080.i			1.83075i	0.402607	+	0.915373i	$0.368104\pi$
$449$			369080.i			1.83075i	−0.402607	+	0.915373i	$0.631896\pi$
$450$	13175.1	−	5254.85i	0.0650624	−	0.0259499i
$451$	67768.9			0.333179
$452$	−1626.32	−	1626.32i	−0.00796030	−	0.00796030i
$453$	216746.	−	216746.i	1.05622	−	1.05622i
$454$		−	134293.i		−	0.651540i
$455$	5765.76	−	28019.6i	0.0278505	−	0.135344i
$456$	58634.2			0.281982
$457$	−153467.	−	153467.i	−0.734823	−	0.734823i	0.236748	−	0.971571i	$-0.423918\pi$
$457$	−153467.	−	153467.i	−0.734823	−	0.734823i	−0.971571	+	0.236748i	$0.923918\pi$
$458$	122306.	−	122306.i	0.583064	−	0.583064i
$459$			105595.i			0.501210i
$460$	−18423.3	+	12135.1i	−0.0870667	+	0.0573494i
$461$	−155181.			−0.730191			−0.365096	−	0.930970i	$-0.618964\pi$
$461$	−155181.			−0.730191			−0.365096	+	0.930970i	$0.618964\pi$
$462$	−184725.	−	184725.i	−0.865451	−	0.865451i
$463$	−42903.7	+	42903.7i	−0.200140	+	0.200140i	−0.800060	−	0.599920i	$-0.795199\pi$
$463$	−42903.7	+	42903.7i	−0.200140	+	0.200140i	0.599920	+	0.800060i	$0.295199\pi$
$464$			55671.8i			0.258583i
$465$	−10050.0	−	15257.8i	−0.0464795	−	0.0705643i
$466$	−92627.9			−0.426550
$467$	−43826.8	−	43826.8i	−0.200958	−	0.200958i	0.599452	−	0.800411i	$-0.295385\pi$
$467$	−43826.8	−	43826.8i	−0.200958	−	0.200958i	−0.800411	+	0.599452i	$0.795385\pi$
$468$	−839.366	+	839.366i	−0.00383230	+	0.00383230i
$469$		−	357150.i		−	1.62370i
$470$	−171738.	−	35339.6i	−0.777447	−	0.159980i
$471$	−174408.			−0.786187
$472$	58791.8	+	58791.8i	0.263896	+	0.263896i
$473$	−95199.0	+	95199.0i	−0.425511	+	0.425511i
$474$			267366.i			1.19001i
$475$	67773.0	−	157703.i	0.300379	−	0.698963i
$476$	75916.9			0.335061
$477$	424.071	+	424.071i	0.00186381	+	0.00186381i
$478$	122095.	−	122095.i	0.534372	−	0.534372i
$479$			74038.7i			0.322692i	0.986898	+	0.161346i	$0.0515834\pi$
$479$			74038.7i			0.322692i	−0.986898	+	0.161346i	$0.948417\pi$
$480$	8606.13	−	41822.8i	0.0373530	−	0.181522i
$481$	31104.6			0.134442
$482$	−63584.4	−	63584.4i	−0.273688	−	0.273688i
$483$	45537.3	−	45537.3i	0.195197	−	0.195197i
$484$			83089.6i			0.354696i
$485$	−317426.	+	209083.i	−1.34946	+	0.888864i
$486$	−32971.4			−0.139594
$487$	295139.	+	295139.i	1.24443	+	1.24443i	0.958146	+	0.286279i	$0.0924184\pi$
$487$	295139.	+	295139.i	1.24443	+	1.24443i	0.286279	+	0.958146i	$0.407582\pi$
$488$	−64296.3	+	64296.3i	−0.269989	+	0.269989i
$489$			31430.2i			0.131441i
$490$	−55539.8	−	84319.5i	−0.231319	−	0.351185i
$491$	−293038.			−1.21552			−0.607758	−	0.794122i	$-0.707931\pi$
$491$	−293038.			−1.21552			−0.607758	+	0.794122i	$0.707931\pi$
$492$	−22864.0	−	22864.0i	−0.0944544	−	0.0944544i
$493$	94330.4	−	94330.4i	0.388113	−	0.388113i
$494$			14364.7i			0.0588632i
$495$	31083.3	+	6396.20i	0.126858	+	0.0261043i
$496$	−4957.14			−0.0201497
$497$	395679.	+	395679.i	1.60188	+	1.60188i
$498$	79970.6	−	79970.6i	0.322457	−	0.322457i
$499$			145192.i			0.583099i	0.956556	+	0.291549i	$0.0941708\pi$
$499$			145192.i			0.583099i	−0.956556	+	0.291549i	$0.905829\pi$
$500$	−102540.	−	71488.5i	−0.410159	−	0.285954i
$501$	−140324.			−0.559056
$502$	135523.	+	135523.i	0.537781	+	0.537781i
$503$	−188560.	+	188560.i	−0.745269	+	0.745269i	−0.973587	−	0.228318i	$-0.926678\pi$
$503$	−188560.	+	188560.i	−0.745269	+	0.745269i	0.228318	+	0.973587i	$0.426678\pi$
$504$			11234.6i			0.0442280i
$505$	−50602.4	+	245910.i	−0.198421	+	0.964258i
$506$	−49356.3			−0.192771
$507$	188270.	+	188270.i	0.732427	+	0.732427i
$508$	50073.6	−	50073.6i	0.194036	−	0.194036i
$509$			293633.i			1.13336i	0.823937	+	0.566681i	$0.191773\pi$
$509$			293633.i			1.13336i	−0.823937	+	0.566681i	$0.808227\pi$
$510$	−85446.8	+	56282.3i	−0.328515	+	0.216387i
$511$	426359.			1.63280
$512$	−8192.00	−	8192.00i	−0.0312500	−	0.0312500i
$513$	−133715.	+	133715.i	−0.508097	+	0.508097i
$514$		−	196222.i		−	0.742716i
$515$	−168865.	−	256368.i	−0.636687	−	0.966607i
$516$	64236.9			0.241260
$517$	−277382.	−	277382.i	−1.03776	−	1.03776i
$518$	208162.	−	208162.i	0.775785	−	0.775785i
$519$			358957.i			1.33262i
$520$	10246.1	+	2108.41i	0.0378925	+	0.00779736i
$521$	−142881.			−0.526378			−0.263189	−	0.964744i	$-0.584774\pi$
$521$	−142881.			−0.526378			−0.263189	+	0.964744i	$0.584774\pi$
$522$	13959.6	+	13959.6i	0.0512307	+	0.0512307i
$523$	98343.6	−	98343.6i	0.359536	−	0.359536i	−0.504106	−	0.863642i	$-0.668178\pi$
$523$	98343.6	−	98343.6i	0.359536	−	0.359536i	0.863642	+	0.504106i	$0.168178\pi$
$524$		−	14530.3i		−	0.0529192i
$525$	335250.	+	144073.i	1.21633	+	0.522716i
$526$	−266234.			−0.962258
$527$	8399.39	+	8399.39i	0.0302431	+	0.0302431i
$528$	67549.9	−	67549.9i	0.242302	−	0.242302i
$529$		−	12167.0i		−	0.0434783i
$530$	1065.23	−	5176.62i	0.00379219	−	0.0184287i
$531$	29483.8			0.104567
$532$	96133.4	+	96133.4i	0.339665	+	0.339665i
$533$	5601.43	−	5601.43i	0.0197172	−	0.0197172i
$534$		−	20927.9i		−	0.0733912i
$535$	−3057.76	+	2014.09i	−0.0106830	+	0.00703674i
$536$	130602.			0.454590
$537$	−308313.	−	308313.i	−1.06916	−	1.06916i
$538$	−236404.	+	236404.i	−0.816753	+	0.816753i
$539$		−	225893.i		−	0.777545i
$540$	75750.7	+	115003.i	0.259776	+	0.394387i
$541$	−340898.			−1.16474			−0.582371	−	0.812923i	$-0.697875\pi$
$541$	−340898.			−1.16474			−0.582371	+	0.812923i	$0.697875\pi$
$542$	−286075.	−	286075.i	−0.973825	−	0.973825i
$543$	28438.8	−	28438.8i	0.0964521	−	0.0964521i
$544$			27761.1i			0.0938077i
$545$	−12145.1	−	2499.17i	−0.0408891	−	0.00841399i
$546$	−30536.9			−0.102433
$547$	99026.8	+	99026.8i	0.330962	+	0.330962i	0.852952	−	0.521990i	$-0.174810\pi$
$547$	99026.8	+	99026.8i	0.330962	+	0.330962i	−0.521990	+	0.852952i	$0.674810\pi$
$548$	145685.	−	145685.i	0.485123	−	0.485123i
$549$			32244.3i			0.106981i
$550$	−103605.	−	259761.i	−0.342496	−	0.858716i
$551$	238901.			0.786891
$552$	16651.9	+	16651.9i	0.0546496	+	0.0546496i
$553$	−438359.	+	438359.i	−1.43344	+	1.43344i
$554$			129211.i			0.420999i
$555$	−79968.1	+	388617.i	−0.259616	+	1.26164i
$556$	207397.			0.670891
$557$	225503.	+	225503.i	0.726846	+	0.726846i	0.969990	−	0.243144i	$-0.0781787\pi$
$557$	225503.	+	225503.i	0.726846	+	0.726846i	−0.243144	+	0.969990i	$0.578179\pi$
$558$	−1242.99	+	1242.99i	−0.00399208	+	0.00399208i
$559$			15737.3i			0.0503626i
$560$	82680.5	−	54460.2i	0.263649	−	0.173661i
$561$	−228913.			−0.727353
$562$	−21068.1	−	21068.1i	−0.0667041	−	0.0667041i
$563$	371085.	−	371085.i	1.17073	−	1.17073i	0.188694	−	0.982036i	$-0.439575\pi$
$563$	371085.	−	371085.i	1.17073	−	1.17073i	0.982036	−	0.188694i	$-0.0604255\pi$
$564$			187167.i			0.588399i
$565$	3953.61	+	6002.30i	0.0123850	+	0.0188027i
$566$	−76390.5			−0.238455
$567$	−312693.	−	312693.i	−0.972641	−	0.972641i
$568$	−144691.	+	144691.i	−0.448481	+	0.448481i
$569$		−	298348.i		−	0.921506i	−0.887528	−	0.460753i	$-0.847579\pi$
$569$		−	298348.i		−	0.921506i	0.887528	−	0.460753i	$-0.152421\pi$
$570$	−179471.	−	36930.9i	−0.552390	−	0.113669i
$571$	−206669.			−0.633873			−0.316937	−	0.948447i	$-0.602654\pi$
$571$	−206669.			−0.633873			−0.316937	+	0.948447i	$0.602654\pi$
$572$	16549.0	+	16549.0i	0.0505800	+	0.0505800i
$573$	−336474.	+	336474.i	−1.02481	+	1.02481i
$574$		−	74973.2i		−	0.227553i
$575$	64034.7	−	25540.0i	0.193678	−	0.0772477i
$576$	−4108.24			−0.0123826
$577$	137589.	+	137589.i	0.413268	+	0.413268i	0.882875	−	0.469607i	$-0.155604\pi$
$577$	137589.	+	137589.i	0.413268	+	0.413268i	−0.469607	+	0.882875i	$0.655604\pi$
$578$	−120004.	+	120004.i	−0.359202	+	0.359202i
$579$			98754.9i			0.294579i
$580$	35065.1	−	170404.i	0.104236	−	0.506552i
$581$	262231.			0.776840
$582$	286906.	+	286906.i	0.847020	+	0.847020i
$583$	8361.00	−	8361.00i	0.0245992	−	0.0245992i
$584$			155910.i			0.457138i
$585$	3097.86	−	2040.51i	0.00905213	−	0.00596248i
$586$	166644.			0.485283
$587$	326365.	+	326365.i	0.947169	+	0.947169i	0.998673	−	0.0515036i	$-0.0164014\pi$
$587$	326365.	+	326365.i	0.947169	+	0.947169i	−0.0515036	+	0.998673i	$0.516401\pi$
$588$	−76212.3	+	76212.3i	−0.220430	+	0.220430i
$589$			21272.3i			0.0613173i
$590$	−142924.	−	216984.i	−0.410582	−	0.623339i
$591$	−464551.			−1.33002
$592$	76120.1	+	76120.1i	0.217198	+	0.217198i
$593$	−462341.	+	462341.i	−1.31478	+	1.31478i	−0.396931	+	0.917849i	$0.629925\pi$
$593$	−462341.	+	462341.i	−1.31478	+	1.31478i	−0.917849	+	0.396931i	$0.870075\pi$
$594$			308095.i			0.873197i
$595$	−232371.	−	47816.5i	−0.656370	−	0.135065i
$596$	292213.			0.822633
$597$	−36016.6	−	36016.6i	−0.101054	−	0.101054i
$598$	−4079.54	+	4079.54i	−0.0114080	+	0.0114080i
$599$			53529.9i			0.149191i	0.997214	+	0.0745955i	$0.0237666\pi$
$599$			53529.9i			0.149191i	−0.997214	+	0.0745955i	$0.976233\pi$
$600$	−52684.4	+	122593.i	−0.146346	+	0.340537i
$601$	422645.			1.17011			0.585055	−	0.810993i	$-0.301073\pi$
$601$	422645.			1.17011			0.585055	+	0.810993i	$0.301073\pi$
$602$	105319.	+	105319.i	0.290613	+	0.290613i
$603$	32748.1	−	32748.1i	0.0900639	−	0.0900639i
$604$			259898.i			0.712410i
$605$	52334.3	−	254326.i	0.142980	−	0.694833i
$606$	268003.			0.729785
$607$	346563.	+	346563.i	0.940600	+	0.940600i	0.998332	−	0.0577321i	$-0.0183869\pi$
$607$	346563.	+	346563.i	0.940600	+	0.940600i	−0.0577321	+	0.998332i	$0.518387\pi$
$608$	−35153.8	+	35153.8i	−0.0950967	+	0.0950967i
$609$			507862.i			1.36934i
$610$	237300.	−	156305.i	0.637731	−	0.420062i
$611$	−45853.9			−0.122827
$612$	6961.02	+	6961.02i	0.0185853	+	0.0185853i
$613$	−195128.	+	195128.i	−0.519278	+	0.519278i	−0.917353	−	0.398075i	$-0.869678\pi$
$613$	−195128.	+	195128.i	−0.519278	+	0.519278i	0.398075	+	0.917353i	$0.369678\pi$
$614$			65538.7i			0.173845i
$615$	55582.7	+	84384.7i	0.146957	+	0.223107i
$616$	221502.			0.583736
$617$	70571.1	+	70571.1i	0.185377	+	0.185377i	0.793694	−	0.608317i	$-0.208155\pi$
$617$	70571.1	+	70571.1i	0.185377	+	0.185377i	−0.608317	+	0.793694i	$0.708155\pi$
$618$	−231719.	+	231719.i	−0.606715	+	0.606715i
$619$		−	313398.i		−	0.817928i	−0.912551	−	0.408964i	$-0.865890\pi$
$619$		−	313398.i		−	0.817928i	0.912551	−	0.408964i	$-0.134110\pi$
$620$	15173.1	+	3122.27i	0.0394723	+	0.00812245i
$621$	−75949.6			−0.196944
$622$	−2228.13	−	2228.13i	−0.00575916	−	0.00575916i
$623$	34312.3	−	34312.3i	0.0884044	−	0.0884044i
$624$		−	11166.7i		−	0.0286783i
$625$	268833.	+	283402.i	0.688213	+	0.725509i
$626$	164101.			0.418757
$627$	−289873.	−	289873.i	−0.737347	−	0.737347i
$628$	104566.	−	104566.i	0.265137	−	0.265137i
$629$		−	257956.i		−	0.651995i
$630$	7076.16	−	34387.7i	0.0178286	−	0.0866406i
$631$	527376.			1.32453			0.662265	−	0.749270i	$-0.269595\pi$
$631$	527376.			1.32453			0.662265	+	0.749270i	$0.269595\pi$
$632$	−160298.	−	160298.i	−0.401322	−	0.401322i
$633$	432051.	−	432051.i	1.07827	−	1.07827i
$634$			137484.i			0.342036i
$635$	−184808.	+	121730.i	−0.458324	+	0.301890i
$636$	−5641.71			−0.0139475
$637$	−18671.2	−	18671.2i	−0.0460143	−	0.0460143i
$638$	275227.	−	275227.i	0.676161	−	0.676161i
$639$			72561.7i			0.177707i
$640$	19914.9	+	30234.4i	0.0486203	+	0.0738144i
$641$	−542087.			−1.31933			−0.659664	−	0.751560i	$-0.729301\pi$
$641$	−542087.			−1.31933			−0.659664	+	0.751560i	$0.729301\pi$
$642$	2763.76	+	2763.76i	0.00670548	+	0.00670548i
$643$	414249.	−	414249.i	1.00193	−	1.00193i	0.00193642	−	0.999998i	$-0.499384\pi$
$643$	414249.	−	414249.i	1.00193	−	1.00193i	0.999998	−	0.00193642i	$-0.000616383\pi$
$644$			54603.3i			0.131658i
$645$	−196621.	−	40459.8i	−0.472618	−	0.0972534i
$646$	119129.			0.285466
$647$	−293873.	−	293873.i	−0.702023	−	0.702023i	0.262822	−	0.964844i	$-0.415347\pi$
$647$	−293873.	−	293873.i	−0.702023	−	0.702023i	−0.964844	+	0.262822i	$0.915347\pi$
$648$	114345.	−	114345.i	0.272312	−	0.272312i
$649$		−	581304.i		−	1.38011i
$650$	−30034.0	−	12907.1i	−0.0710865	−	0.0305494i
$651$	−45221.1			−0.106704
$652$	−18843.8	−	18843.8i	−0.0443276	−	0.0443276i
$653$	−173309.	+	173309.i	−0.406437	+	0.406437i	−0.880494	−	0.474057i	$-0.842789\pi$
$653$	−173309.	+	173309.i	−0.406437	+	0.406437i	0.474057	+	0.880494i	$0.342789\pi$
$654$			13236.2i			0.0309463i
$655$	−9151.99	+	44475.5i	−0.0213321	+	0.103666i
$656$	27416.0			0.0637084
$657$	39093.9	+	39093.9i	0.0905688	+	0.0905688i
$658$	−306869.	+	306869.i	−0.708764	+	0.708764i
$659$		−	427747.i		−	0.984954i	−0.870326	−	0.492477i	$-0.836092\pi$
$659$		−	427747.i		−	0.984954i	0.870326	−	0.492477i	$-0.163908\pi$
$660$	−249308.	+	164215.i	−0.572332	+	0.376985i
$661$	−393371.			−0.900326			−0.450163	−	0.892947i	$-0.648634\pi$
$661$	−393371.			−0.900326			−0.450163	+	0.892947i	$0.648634\pi$
$662$	403846.	+	403846.i	0.921510	+	0.921510i
$663$	−18920.8	+	18920.8i	−0.0430440	+	0.0430440i
$664$			95891.9i			0.217493i
$665$	−233702.	−	354802.i	−0.528468	−	0.802310i
$666$	38173.8			0.0860631
$667$	67847.2	+	67847.2i	0.152504	+	0.152504i
$668$	84130.3	−	84130.3i	0.188538	−	0.188538i
$669$		−	13803.1i		−	0.0308406i
$670$	−399755.	−	82260.0i	−0.890521	−	0.183248i
$671$	635729.			1.41198
$672$	−74730.9	−	74730.9i	−0.165486	−	0.165486i
$673$	452116.	−	452116.i	0.998205	−	0.998205i	−0.00179336	−	0.999998i	$-0.500571\pi$
$673$	452116.	−	452116.i	0.998205	−	0.998205i	0.999998	+	0.00179336i	$0.000570844\pi$
$674$			143081.i			0.314965i
$675$	−159428.	−	399721.i	−0.349910	−	0.877304i
$676$	−225752.			−0.494013
$677$	48310.6	+	48310.6i	0.105406	+	0.105406i	0.757843	−	0.652437i	$-0.226253\pi$
$677$	48310.6	+	48310.6i	0.105406	+	0.105406i	−0.652437	+	0.757843i	$0.726253\pi$
$678$	5425.19	−	5425.19i	0.0118020	−	0.0118020i
$679$			940790.i			2.04058i
$680$	17485.4	−	84973.0i	0.0378145	−	0.183765i
$681$	447982.			0.965977
$682$	24506.8	+	24506.8i	0.0526888	+	0.0526888i
$683$	467682.	−	467682.i	1.00256	−	1.00256i	0.00256009	−	0.999997i	$-0.499185\pi$
$683$	467682.	−	467682.i	1.00256	−	1.00256i	0.999997	−	0.00256009i	$-0.000814904\pi$
$684$			17629.5i			0.0376814i
$685$	−537681.	+	354161.i	−1.14589	+	0.754779i
$686$	170310.			0.361903
$687$	407996.	+	407996.i	0.864455	+	0.864455i
$688$	−38512.9	+	38512.9i	−0.0813635	+	0.0813635i
$689$		−	1382.16i		−	0.00291151i
$690$	−40481.1	−	61457.7i	−0.0850265	−	0.129086i
$691$	−637361.			−1.33484			−0.667420	−	0.744681i	$-0.732601\pi$
$691$	−637361.			−1.33484			−0.667420	+	0.744681i	$0.732601\pi$
$692$	−215211.	−	215211.i	−0.449420	−	0.449420i
$693$	55541.1	−	55541.1i	0.115651	−	0.115651i
$694$		−	334860.i		−	0.695255i
$695$	−634814.	−	130629.i	−1.31425	−	0.270440i
$696$	−185714.			−0.383376
$697$	−46453.7	−	46453.7i	−0.0956214	−	0.0956214i
$698$	−116987.	+	116987.i	−0.240118	+	0.240118i
$699$		−	308994.i		−	0.632406i
$700$	−287376.	+	114619.i	−0.586482	+	0.233916i
$701$	876116.			1.78289			0.891447	−	0.453125i	$-0.149691\pi$
$701$	876116.			1.78289			0.891447	+	0.453125i	$0.149691\pi$
$702$	25465.6	+	25465.6i	0.0516749	+	0.0516749i
$703$	326649.	−	326649.i	0.660954	−	0.660954i
$704$			80998.3i			0.163430i
$705$	117888.	−	572894.i	0.237187	−	1.15265i
$706$	−64614.1			−0.129634
$707$	439403.	+	439403.i	0.879072	+	0.879072i
$708$	−196121.	+	196121.i	−0.391254	+	0.391254i
$709$		−	98598.9i		−	0.196146i	−0.995179	−	0.0980730i	$-0.968732\pi$
$709$		−	98598.9i		−	0.196146i	0.995179	−	0.0980730i	$-0.0312679\pi$
$710$	534014.	−	351746.i	1.05934	−	0.697769i
$711$	−80388.5			−0.159021
$712$	12547.2	+	12547.2i	0.0247507	+	0.0247507i
$713$	−6041.27	+	6041.27i	−0.0118836	+	0.0118836i
$714$			253248.i			0.496764i
$715$	−40230.8	−	61077.6i	−0.0786949	−	0.119473i
$716$	369695.			0.721137
$717$	407294.	+	407294.i	0.792263	+	0.792263i
$718$	−89480.8	+	89480.8i	−0.173573	+	0.173573i
$719$		−	67219.4i		−	0.130028i	−0.997884	−	0.0650140i	$-0.979291\pi$
$719$		−	67219.4i		−	0.130028i	0.997884	−	0.0650140i	$-0.0207092\pi$
$720$	12574.8	+	2587.59i	0.0242569	+	0.00499150i
$721$	−759827.			−1.46165
$722$	−109789.	−	109789.i	−0.210612	−	0.210612i
$723$	212109.	−	212109.i	0.405772	−	0.405772i
$724$			34100.7i			0.0650558i
$725$	−214659.	+	499498.i	−0.408388	+	0.950294i
$726$	−277176.			−0.525874
$727$	617299.	+	617299.i	1.16796	+	1.16796i	0.982688	+	0.185269i	$0.0593157\pi$
$727$	617299.	+	617299.i	1.16796	+	1.16796i	0.185269	+	0.982688i	$0.440684\pi$
$728$	18308.2	−	18308.2i	0.0345449	−	0.0345449i
$729$			468883.i			0.882285i
$730$	98200.2	−	477219.i	0.184275	−	0.895513i
$731$	130513.			0.244241
$732$	−214484.	−	214484.i	−0.400288	−	0.400288i
$733$	−109052.	+	109052.i	−0.202967	+	0.202967i	−0.801270	−	0.598303i	$-0.795842\pi$
$733$	−109052.	+	109052.i	−0.202967	+	0.202967i	0.598303	+	0.801270i	$0.295842\pi$
$734$		−	584262.i		−	1.08447i
$735$	281278.	−	185273.i	0.520669	−	0.342956i
$736$	−19967.2			−0.0368605
$737$	−645662.	−	645662.i	−1.18869	−	1.18869i
$738$	6874.49	−	6874.49i	0.0126220	−	0.0126220i
$739$			560742.i			1.02677i	0.858158	+	0.513386i	$0.171609\pi$
$739$			560742.i			1.02677i	−0.858158	+	0.513386i	$0.828391\pi$
$740$	−185049.	−	280938.i	−0.337927	−	0.513035i
$741$	−47918.8			−0.0872709
$742$	−9249.84	−	9249.84i	−0.0168007	−	0.0168007i
$743$	313283.	−	313283.i	0.567491	−	0.567491i	−0.363934	−	0.931425i	$-0.618567\pi$
$743$	313283.	−	313283.i	0.567491	−	0.567491i	0.931425	+	0.363934i	$0.118567\pi$
$744$		−	16536.3i		−	0.0298740i
$745$	−894424.	−	184051.i	−1.61150	−	0.331608i
$746$	−649622.			−1.16730
$747$	24044.6	+	24044.6i	0.0430901	+	0.0430901i
$748$	137244.	−	137244.i	0.245295	−	0.245295i
$749$			9062.61i			0.0161544i
$750$	238476.	−	342059.i	0.423957	−	0.608104i
$751$	−477113.			−0.845943			−0.422971	−	0.906143i	$-0.639013\pi$
$751$	−477113.			−0.845943			−0.422971	+	0.906143i	$0.639013\pi$
$752$	−112215.	−	112215.i	−0.198434	−	0.198434i
$753$	−452086.	+	452086.i	−0.797317	+	0.797317i
$754$		−	45497.8i		−	0.0800291i
$755$	163698.	−	795515.i	0.287177	−	1.39558i
$756$	340848.			0.596372
$757$	211415.	+	211415.i	0.368930	+	0.368930i	0.867087	−	0.498157i	$-0.165990\pi$
$757$	211415.	+	211415.i	0.368930	+	0.368930i	−0.498157	+	0.867087i	$0.665990\pi$
$758$	−470375.	+	470375.i	−0.818664	+	0.818664i
$759$		−	164646.i		−	0.285804i
$760$	129743.	−	85459.4i	0.224624	−	0.147956i
$761$	−600219.			−1.03643			−0.518216	−	0.855250i	$-0.673404\pi$
$761$	−600219.			−1.03643			−0.518216	+	0.855250i	$0.673404\pi$
$762$	167039.	+	167039.i	0.287679	+	0.287679i
$763$	−21701.4	+	21701.4i	−0.0372768	+	0.0372768i
$764$		−	403463.i		−	0.691220i
$765$	−16922.3	−	25691.2i	−0.0289159	−	0.0438996i
$766$	−212526.			−0.362206
$767$	−48047.6	−	48047.6i	−0.0816735	−	0.0816735i
$768$	27327.4	−	27327.4i	0.0463314	−	0.0463314i
$769$		−	916843.i		−	1.55039i	−0.631719	−	0.775197i	$-0.717650\pi$
$769$		−	916843.i		−	1.55039i	0.631719	−	0.775197i	$-0.282350\pi$
$770$	−677989.	−	139514.i	−1.14351	−	0.235308i
$771$	654572.			1.10115
$772$	−59208.0	−	59208.0i	−0.0993450	−	0.0993450i
$773$	−83364.3	+	83364.3i	−0.139515	+	0.139515i	−0.773415	−	0.633900i	$-0.781453\pi$
$773$	−83364.3	+	83364.3i	−0.139515	+	0.139515i	0.633900	+	0.773415i	$0.281453\pi$
$774$			19314.0i			0.0322397i
$775$	−44476.4	−	19113.7i	−0.0740502	−	0.0318230i
$776$	−344026.			−0.571304
$777$	694400.	+	694400.i	1.15018	+	1.15018i
$778$	−388639.	+	388639.i	−0.642078	+	0.642078i
$779$		−	117649.i		−	0.193871i
$780$	−7033.36	+	34179.7i	−0.0115604	+	0.0561796i
$781$	1.43063e6			2.34544
$782$	33832.4	+	33832.4i	0.0553248	+	0.0553248i
$783$	423520.	−	423520.i	0.690798	−	0.690798i
$784$		−	91385.4i		−	0.148677i
$785$	−385923.	+	254201.i	−0.626269	+	0.412513i
$786$	48471.3			0.0784584
$787$	−818877.	−	818877.i	−1.32212	−	1.32212i	−0.912061	−	0.410055i	$-0.865510\pi$
$787$	−818877.	−	818877.i	−1.32212	−	1.32212i	−0.410055	−	0.912061i	$-0.634490\pi$
$788$	278519.	−	278519.i	0.448542	−	0.448542i
$789$		−	888119.i		−	1.42665i
$790$	389686.	+	591615.i	0.624397	+	0.947948i
$791$	17789.7			0.0284325
$792$	20310.1	+	20310.1i	0.0323789	+	0.0323789i
$793$	52546.2	−	52546.2i	0.0835593	−	0.0835593i
$794$		−	350138.i		−	0.555390i
$795$	17268.5	+	3553.45i	0.0273225	+	0.00562232i
$796$	43187.1			0.0681598
$797$	532985.	+	532985.i	0.839070	+	0.839070i	0.988736	−	0.149667i	$-0.0478201\pi$
$797$	532985.	+	532985.i	0.839070	+	0.839070i	−0.149667	+	0.988736i	$0.547820\pi$
$798$	−320688.	+	320688.i	−0.503590	+	0.503590i
$799$			380275.i			0.595668i
$800$	−41913.5	−	105087.i	−0.0654899	−	0.164198i
$801$	6292.37			0.00980730
$802$	308752.	+	308752.i	0.480022	+	0.480022i
$803$	770778.	−	770778.i	1.19536	−	1.19536i
$804$			435670.i			0.673978i
$805$	34392.0	−	167133.i	0.0530721	−	0.257912i
$806$	4051.22			0.00623614
$807$	−788613.	−	788613.i	−1.21092	−	1.21092i
$808$	−160680.	+	160680.i	−0.246115	+	0.246115i
$809$		−	633443.i		−	0.967855i	−0.875108	−	0.483927i	$-0.839210\pi$
$809$		−	633443.i		−	0.967855i	0.875108	−	0.483927i	$-0.160790\pi$
$810$	−422015.	+	277974.i	−0.643217	+	0.423676i
$811$	−304882.			−0.463543			−0.231772	−	0.972770i	$-0.574452\pi$
$811$	−304882.			−0.463543			−0.231772	+	0.972770i	$0.574452\pi$
$812$	−304486.	−	304486.i	−0.461801	−	0.461801i
$813$	954306.	−	954306.i	1.44380	−	1.44380i
$814$		−	752637.i		−	1.13589i
$815$	45809.6	+	69547.3i	0.0689670	+	0.104704i
$816$	−92607.2			−0.139080
$817$	165268.	+	165268.i	0.247597	+	0.247597i
$818$	−238360.	+	238360.i	−0.356227	+	0.356227i
$819$		−	9181.49i		−	0.0136882i
$820$	−83916.8	−	17268.1i	−0.124802	−	0.0256812i
$821$	620516.			0.920591			0.460296	−	0.887766i	$-0.347743\pi$
$821$	620516.			0.920591			0.460296	+	0.887766i	$0.347743\pi$
$822$	485984.	+	485984.i	0.719247	+	0.719247i
$823$	276659.	−	276659.i	0.408456	−	0.408456i	−0.472744	−	0.881200i	$-0.656736\pi$
$823$	276659.	−	276659.i	0.408456	−	0.408456i	0.881200	+	0.472744i	$0.156736\pi$
$824$		−	277852.i		−	0.409222i
$825$	866529.	−	345612.i	1.27314	−	0.507786i
$826$	−643100.			−0.942581
$827$	−322574.	−	322574.i	−0.471648	−	0.471648i	0.430799	−	0.902448i	$-0.358232\pi$
$827$	−322574.	−	322574.i	−0.471648	−	0.471648i	−0.902448	+	0.430799i	$0.858232\pi$
$828$	−5006.72	+	5006.72i	−0.00730285	+	0.00730285i
$829$		−	795792.i		−	1.15795i	−0.815344	−	0.578976i	$-0.803452\pi$
$829$		−	795792.i		−	1.15795i	0.815344	−	0.578976i	$-0.196548\pi$
$830$	60397.8	−	293512.i	0.0876729	−	0.426060i
$831$	−431031.			−0.624175
$832$	6694.91	+	6694.91i	0.00967160	+	0.00967160i
$833$	−154844.	+	154844.i	−0.223153	+	0.223153i
$834$			691847.i			0.994668i
$835$	−310501.	+	204522.i	−0.445339	+	0.293337i
$836$	347583.			0.497332
$837$	37711.2	+	37711.2i	0.0538294	+	0.0538294i
$838$	287182.	−	287182.i	0.408950	−	0.408950i
$839$			1.32174e6i			1.87769i	0.344347	+	0.938843i	$0.388100\pi$
$839$			1.32174e6i			1.87769i	−0.344347	+	0.938843i	$0.611900\pi$
$840$	181672.	+	275811.i	0.257471	+	0.390888i
$841$	−49396.5			−0.0698400
$842$	−47524.6	−	47524.6i	−0.0670339	−	0.0670339i
$843$	70280.3	−	70280.3i	0.0988960	−	0.0988960i
$844$			518068.i			0.727281i
$845$	690998.	+	142191.i	0.967750	+	0.199140i
$846$	−56275.3			−0.0786280
$847$	−454442.	−	454442.i	−0.633449	−	0.633449i
$848$	3382.46	−	3382.46i	0.00470371	−	0.00470371i
$849$		−	254828.i		−	0.353535i
$850$	−107041.	+	249078.i	−0.148154	+	0.344744i
$851$	185535.			0.256193
$852$	−482669.	−	482669.i	−0.664921	−	0.664921i
$853$	716382.	−	716382.i	0.984569	−	0.984569i	−0.0153133	−	0.999883i	$-0.504875\pi$
$853$	716382.	−	716382.i	0.984569	−	0.984569i	0.999883	+	0.0153133i	$0.00487457\pi$
$854$		−	703312.i		−	0.964344i
$855$	11104.0	−	53961.4i	0.0151896	−	0.0738161i
$856$	−3313.99			−0.00452276
$857$	334093.	+	334093.i	0.454890	+	0.454890i	0.896974	−	0.442084i	$-0.145761\pi$
$857$	334093.	+	334093.i	0.454890	+	0.454890i	−0.442084	+	0.896974i	$0.645761\pi$
$858$	−55205.1	+	55205.1i	−0.0749903	+	0.0749903i
$859$			915744.i			1.24105i	0.784189	+	0.620523i	$0.213080\pi$
$859$			915744.i			1.24105i	−0.784189	+	0.620523i	$0.786920\pi$
$860$	142140.	−	93625.4i	0.192186	−	0.126589i
$861$	250100.			0.337371
$862$	177580.	+	177580.i	0.238991	+	0.238991i
$863$	527924.	−	527924.i	0.708842	−	0.708842i	−0.257450	−	0.966292i	$-0.582882\pi$
$863$	527924.	−	527924.i	0.708842	−	0.708842i	0.966292	+	0.257450i	$0.0828821\pi$
$864$			124640.i			0.166967i
$865$	523181.	+	794283.i	0.699229	+	1.06156i
$866$	−742291.			−0.989779
$867$	−400316.	−	400316.i	−0.532555	−	0.532555i
$868$	27112.1	−	27112.1i	0.0359852	−	0.0359852i
$869$			1.58494e6i			2.09882i
$870$	568445.	+	116972.i	0.751017	+	0.154541i
$871$	−106734.			−0.140691
$872$	−7935.71	−	7935.71i	−0.0104365	−	0.0104365i
$873$	−86263.6	+	86263.6i	−0.113188	+	0.113188i
$874$			85683.9i			0.112170i
$875$	951813.	−	169829.i	1.24318	−	0.221817i
$876$	−520094.			−0.677756
$877$	225325.	+	225325.i	0.292961	+	0.292961i	0.838249	−	0.545288i	$-0.183580\pi$
$877$	225325.	+	225325.i	0.292961	+	0.292961i	−0.545288	+	0.838249i	$0.683580\pi$
$878$	−4931.34	+	4931.34i	−0.00639700	+	0.00639700i
$879$			555903.i			0.719484i
$880$	51017.1	−	247925.i	0.0658795	−	0.320151i
$881$	−348418.			−0.448899			−0.224450	−	0.974486i	$-0.572058\pi$
$881$	−348418.			−0.448899			−0.224450	+	0.974486i	$0.572058\pi$
$882$	−22914.6	−	22914.6i	−0.0294562	−	0.0294562i
$883$	756286.	−	756286.i	0.969984	−	0.969984i	−0.0295786	−	0.999562i	$-0.509417\pi$
$883$	756286.	−	756286.i	0.969984	−	0.969984i	0.999562	+	0.0295786i	$0.00941654\pi$
$884$		−	22687.7i		−	0.0290327i
$885$	723830.	−	476774.i	0.924166	−	0.608732i
$886$	818651.			1.04287
$887$	−517548.	−	517548.i	−0.657814	−	0.657814i	0.297048	−	0.954862i	$-0.403998\pi$
$887$	−517548.	−	517548.i	−0.657814	−	0.657814i	−0.954862	+	0.297048i	$0.903998\pi$
$888$	−253926.	+	253926.i	−0.322019	+	0.322019i
$889$			547736.i			0.693055i
$890$	−30502.5	−	46308.3i	−0.0385084	−	0.0584628i
$891$	−1.13058e6			−1.42412
$892$	8275.55	+	8275.55i	0.0104008	+	0.0104008i
$893$	−481542.	+	481542.i	−0.603853	+	0.603853i
$894$			974781.i			1.21964i
$895$	−1.13159e6	−	232854.i	−1.41268	−	0.290695i
$896$	89609.0			0.111618
$897$	−13608.8	−	13608.8i	−0.0169136	−	0.0169136i
$898$	738160.	−	738160.i	0.915373	−	0.915373i
$899$		−	67376.2i		−	0.0833657i
$900$	−36860.0	−	15840.5i	−0.0455061	−	0.0195562i
$901$	−11462.5			−0.0141198
$902$	−135538.	−	135538.i	−0.166589	−	0.166589i
$903$	−351331.	+	351331.i	−0.430865	+	0.430865i
$904$			6505.29i			0.00796030i
$905$	21478.4	−	104378.i	0.0262244	−	0.127441i
$906$	−866986.			−1.05622
$907$	−777289.	−	777289.i	−0.944861	−	0.944861i	0.0536967	−	0.998557i	$-0.482900\pi$
$907$	−777289.	−	777289.i	−0.944861	−	0.944861i	−0.998557	+	0.0536967i	$0.982900\pi$
$908$	−268585.	+	268585.i	−0.325770	+	0.325770i
$909$			80580.1i			0.0975214i
$910$	−67570.6	+	44507.6i	−0.0815972	+	0.0537467i
$911$	378849.			0.456488			0.228244	−	0.973604i	$-0.426702\pi$
$911$	378849.			0.456488			0.228244	+	0.973604i	$0.426702\pi$
$912$	−117268.	−	117268.i	−0.140991	−	0.140991i
$913$	474065.	−	474065.i	0.568717	−	0.568717i
$914$			613868.i			0.734823i
$915$	521413.	+	791600.i	0.622787	+	0.945504i
$916$	−489224.			−0.583064
$917$	79470.9	+	79470.9i	0.0945081	+	0.0945081i
$918$	211191.	−	211191.i	0.250605	−	0.250605i
$919$		−	350933.i		−	0.415521i	−0.978180	−	0.207760i	$-0.933383\pi$
$919$		−	350933.i		−	0.415521i	0.978180	−	0.207760i	$-0.0666175\pi$
$920$	61116.9	+	12576.4i	0.0722080	+	0.0148587i
$921$	−218628.			−0.257743
$922$	310362.	+	310362.i	0.365096	+	0.365096i
$923$	118249.	−	118249.i	0.138801	−	0.138801i
$924$			738901.i			0.865451i
$925$	389461.	+	976468.i	0.455177	+	1.14123i
$926$	171615.			0.200140
$927$	−69670.6	−	69670.6i	−0.0810756	−	0.0810756i
$928$	111344.	−	111344.i	0.129291	−	0.129291i
$929$			889726.i			1.03092i	0.856914	+	0.515460i	$0.172379\pi$
$929$			889726.i			1.03092i	−0.856914	+	0.515460i	$0.827621\pi$
$930$	−10415.5	+	50615.6i	−0.0120424	+	0.0585219i
$931$	−392157.			−0.452439
$932$	185256.	+	185256.i	0.213275	+	0.213275i
$933$	7432.73	−	7432.73i	0.00853856	−	0.00853856i
$934$			175307.i			0.200958i
$935$	−506528.	+	333641.i	−0.579403	+	0.381643i
$936$	3357.46			0.00383230
$937$	535527.	+	535527.i	0.609961	+	0.609961i	0.942936	−	0.332975i	$-0.108052\pi$
$937$	535527.	+	535527.i	0.609961	+	0.609961i	−0.332975	+	0.942936i	$0.608052\pi$
$938$	−714301.	+	714301.i	−0.811849	+	0.811849i
$939$			547419.i			0.620852i
$940$	272797.	+	414155.i	0.308733	+	0.468713i
$941$	960812.			1.08507			0.542537	−	0.840032i	$-0.317464\pi$
$941$	960812.			1.08507			0.542537	+	0.840032i	$0.317464\pi$
$942$	348817.	+	348817.i	0.393093	+	0.393093i
$943$	33411.9	−	33411.9i	0.0375731	−	0.0375731i
$944$		−	235167.i		−	0.263896i
$945$	−1.04329e6	−	214684.i	−1.16827	−	0.240401i
$946$	380796.			0.425511
$947$	1.07393e6	+	1.07393e6i	1.19750	+	1.19750i	0.974912	+	0.222591i	$0.0714513\pi$
$947$	1.07393e6	+	1.07393e6i	1.19750	+	1.19750i	0.222591	+	0.974912i	$0.428549\pi$
$948$	534732.	−	534732.i	0.595003	−	0.595003i
$949$		−	127417.i		−	0.141480i
$950$	−450953.	+	179861.i	−0.499671	+	0.199292i
$951$	−458626.			−0.507105
$952$	−151834.	−	151834.i	−0.167531	−	0.167531i
$953$	102950.	−	102950.i	0.113355	−	0.113355i	−0.648154	−	0.761509i	$-0.724459\pi$
$953$	102950.	−	102950.i	0.113355	−	0.113355i	0.761509	+	0.648154i	$0.224459\pi$
$954$		−	1696.28i		−	0.00186381i
$955$	−254122.	+	1.23495e6i	−0.278635	+	1.35407i
$956$	−488382.			−0.534372
$957$	918121.	+	918121.i	1.00248	+	1.00248i
$958$	148077.	−	148077.i	0.161346	−	0.161346i
$959$			1.59359e6i			1.73276i
$960$	−100858.	+	66433.3i	−0.109438	+	0.0720847i
$961$	−917522.			−0.993504
$962$	−62209.1	−	62209.1i	−0.0672209	−	0.0672209i
$963$	−830.975	+	830.975i	−0.000896056	+	0.000896056i
$964$			254338.i			0.273688i
$965$	143936.	+	218520.i	0.154566	+	0.234659i
$966$	−182149.			−0.195197
$967$	−895382.	−	895382.i	−0.957537	−	0.957537i	0.0415977	−	0.999134i	$-0.486755\pi$
$967$	−895382.	−	895382.i	−0.957537	−	0.957537i	−0.999134	+	0.0415977i	$0.986755\pi$
$968$	166179.	−	166179.i	0.177348	−	0.177348i
$969$			397400.i			0.423233i
$970$	1.05302e6	+	216686.i	1.11916	+	0.230296i
$971$	−1.46580e6			−1.55466			−0.777330	−	0.629093i	$-0.783427\pi$
$971$	−1.46580e6			−1.55466			−0.777330	+	0.629093i	$0.783427\pi$
$972$	65942.9	+	65942.9i	0.0697968	+	0.0697968i
$973$	−1.13431e6	+	1.13431e6i	−1.19814	+	1.19814i
$974$		−	1.18056e6i		−	1.24443i
$975$	43056.3	−	100189.i	0.0452927	−	0.105393i
$976$	257185.			0.269989
$977$	845660.	+	845660.i	0.885945	+	0.885945i	0.994131	−	0.108186i	$-0.0345042\pi$
$977$	845660.	+	845660.i	0.885945	+	0.885945i	−0.108186	+	0.994131i	$0.534504\pi$
$978$	62860.4	−	62860.4i	0.0657203	−	0.0657203i
$979$		−	124061.i		−	0.129440i
$980$	−57559.4	+	279719.i	−0.0599327	+	0.291252i
$981$	−3979.72			−0.00413537
$982$	586076.	+	586076.i	0.607758	+	0.607758i
$983$	−1.29715e6	+	1.29715e6i	−1.34240	+	1.34240i	−0.448739	+	0.893663i	$0.648127\pi$
$983$	−1.29715e6	+	1.29715e6i	−1.34240	+	1.34240i	−0.893663	+	0.448739i	$0.851873\pi$
$984$			91456.1i			0.0944544i
$985$	−1.02794e6	+	677084.i	−1.05948	+	0.697863i
$986$	−377322.			−0.388113
$987$	−1.02367e6	−	1.02367e6i	−1.05082	−	1.05082i
$988$	28729.5	−	28729.5i	0.0294316	−	0.0294316i
$989$			93871.4i			0.0959711i
$990$	−49374.2	−	74959.0i	−0.0503767	−	0.0764809i
$991$	394874.			0.402079			0.201040	−	0.979583i	$-0.435568\pi$
$991$	394874.			0.402079			0.201040	+	0.979583i	$0.435568\pi$
$992$	9914.28	+	9914.28i	0.0100748	+	0.0100748i
$993$	−1.34718e6	+	1.34718e6i	−1.36624	+	1.36624i
$994$		−	1.58272e6i		−	1.60188i
$995$	−132190.	−	27201.6i	−0.133522	−	0.0274756i
$996$	−319882.			−0.322457
$997$	−1.11500e6	−	1.11500e6i	−1.12172	−	1.12172i	−0.991483	−	0.130239i	$-0.958426\pi$
$997$	−1.11500e6	−	1.11500e6i	−1.12172	−	1.12172i	−0.130239	−	0.991483i	$-0.541574\pi$
$998$	290384.	−	290384.i	0.291549	−	0.291549i
$999$		−	1.15816e6i		−	1.16048i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 2.00000i) q^{2} +(6.67173 - 6.67173i) q^{3} +8.00000i q^{4} +(5.03883 - 24.4869i) q^{5} -26.6869 q^{6} +(-43.7544 - 43.7544i) q^{7} +(16.0000 - 16.0000i) q^{8} -8.02391i q^{9} +O(q^{10})\)	\(q+(-2.00000 - 2.00000i) q^{2} +(6.67173 - 6.67173i) q^{3} +8.00000i q^{4} +(5.03883 - 24.4869i) q^{5} -26.6869 q^{6} +(-43.7544 - 43.7544i) q^{7} +(16.0000 - 16.0000i) q^{8} -8.02391i q^{9} +(-59.0515 + 38.8962i) q^{10} -158.200 q^{11} +(53.3738 + 53.3738i) q^{12} +(-13.0760 + 13.0760i) q^{13} +175.018i q^{14} +(-129.753 - 196.988i) q^{15} -64.0000 q^{16} +(108.442 + 108.442i) q^{17} +(-16.0478 + 16.0478i) q^{18} +274.639i q^{19} +(195.896 + 40.3106i) q^{20} -583.835 q^{21} +(316.400 + 316.400i) q^{22} +(-77.9968 + 77.9968i) q^{23} -213.495i q^{24} +(-574.220 - 246.771i) q^{25} +52.3040 q^{26} +(486.877 + 486.877i) q^{27} +(350.035 - 350.035i) q^{28} -869.872i q^{29} +(-134.471 + 653.481i) q^{30} +77.4553 q^{31} +(128.000 + 128.000i) q^{32} +(-1055.47 + 1055.47i) q^{33} -433.767i q^{34} +(-1291.88 + 850.941i) q^{35} +64.1913 q^{36} +(-1189.38 - 1189.38i) q^{37} +(549.279 - 549.279i) q^{38} +174.479i q^{39} +(-311.170 - 472.412i) q^{40} -428.375 q^{41} +(1167.67 + 1167.67i) q^{42} +(601.764 - 601.764i) q^{43} -1265.60i q^{44} +(-196.481 - 40.4311i) q^{45} +311.987 q^{46} +(1753.36 + 1753.36i) q^{47} +(-426.991 + 426.991i) q^{48} +1427.90i q^{49} +(654.899 + 1641.98i) q^{50} +1446.99 q^{51} +(-104.608 - 104.608i) q^{52} +(-52.8509 + 52.8509i) q^{53} -1947.51i q^{54} +(-797.142 + 3873.83i) q^{55} -1400.14 q^{56} +(1832.32 + 1832.32i) q^{57} +(-1739.74 + 1739.74i) q^{58} +3674.49i q^{59} +(1575.90 - 1038.02i) q^{60} -4018.52 q^{61} +(-154.911 - 154.911i) q^{62} +(-351.082 + 351.082i) q^{63} -512.000i q^{64} +(254.304 + 386.079i) q^{65} +4221.87 q^{66} +(4081.31 + 4081.31i) q^{67} +(-867.534 + 867.534i) q^{68} +1040.75i q^{69} +(4285.65 + 881.884i) q^{70} -9043.18 q^{71} +(-128.383 - 128.383i) q^{72} +(-4872.18 + 4872.18i) q^{73} +4757.50i q^{74} +(-5477.43 + 2184.65i) q^{75} -2197.11 q^{76} +(6921.94 + 6921.94i) q^{77} +(348.958 - 348.958i) q^{78} -10018.6i q^{79} +(-322.485 + 1567.16i) q^{80} +7146.55 q^{81} +(856.750 + 856.750i) q^{82} +(-2996.62 + 2996.62i) q^{83} -4670.68i q^{84} +(3201.82 - 2108.99i) q^{85} -2407.06 q^{86} +(-5803.55 - 5803.55i) q^{87} +(-2531.20 + 2531.20i) q^{88} +784.202i q^{89} +(312.100 + 473.824i) q^{90} +1144.27 q^{91} +(-623.974 - 623.974i) q^{92} +(516.761 - 516.761i) q^{93} -7013.45i q^{94} +(6725.07 + 1383.86i) q^{95} +1707.96 q^{96} +(-10750.8 - 10750.8i) q^{97} +(2855.79 - 2855.79i) q^{98} +1269.38i 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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