LMFDB - Embedded newform 200.6.f.d.149.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,6,Mod(149,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("200.149");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	200.f (of order $2$, degree $1$, not 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:	$32.0767639626$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.8
Character	$\chi$	$=$	200.149
Dual form			200.6.f.d.149.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.94424 + 2.74854i) q^{2} -23.5470 q^{3} +(16.8910 - 27.1789i) q^{4} +(116.422 - 64.7200i) q^{6} +39.5751i q^{7} +(-8.81071 + 180.805i) q^{8} +311.462 q^{9} +O(q^{10})$	\(q+(-4.94424 + 2.74854i) q^{2} -23.5470 q^{3} +(16.8910 - 27.1789i) q^{4} +(116.422 - 64.7200i) q^{6} +39.5751i q^{7} +(-8.81071 + 180.805i) q^{8} +311.462 q^{9} +236.639i q^{11} +(-397.733 + 639.982i) q^{12} -942.728 q^{13} +(-108.774 - 195.669i) q^{14} +(-453.388 - 918.159i) q^{16} -1103.34i q^{17} +(-1539.94 + 856.066i) q^{18} -2313.21i q^{19} -931.874i q^{21} +(-650.411 - 1170.00i) q^{22} +861.158i q^{23} +(207.466 - 4257.41i) q^{24} +(4661.07 - 2591.13i) q^{26} -1612.07 q^{27} +(1075.61 + 668.463i) q^{28} -1669.97i q^{29} -4184.75 q^{31} +(4765.26 + 3293.44i) q^{32} -5572.13i q^{33} +(3032.59 + 5455.19i) q^{34} +(5260.90 - 8465.19i) q^{36} -14588.1 q^{37} +(6357.97 + 11437.1i) q^{38} +22198.4 q^{39} -20018.4 q^{41} +(2561.30 + 4607.41i) q^{42} +5248.34 q^{43} +(6431.58 + 3997.06i) q^{44} +(-2366.93 - 4257.77i) q^{46} -21631.2i q^{47} +(10675.9 + 21619.9i) q^{48} +15240.8 q^{49} +25980.4i q^{51} +(-15923.6 + 25622.3i) q^{52} +14960.7 q^{53} +(7970.46 - 4430.84i) q^{54} +(-7155.36 - 348.684i) q^{56} +54469.3i q^{57} +(4589.97 + 8256.71i) q^{58} +42436.9i q^{59} +31181.5i q^{61} +(20690.4 - 11502.0i) q^{62} +12326.1i q^{63} +(-32612.7 - 3186.04i) q^{64} +(15315.2 + 27549.9i) q^{66} +27868.1 q^{67} +(-29987.7 - 18636.6i) q^{68} -20277.7i q^{69} +42393.2 q^{71} +(-2744.20 + 56313.8i) q^{72} -11778.7i q^{73} +(72127.1 - 40096.1i) q^{74} +(-62870.6 - 39072.5i) q^{76} -9364.98 q^{77} +(-109754. + 61013.4i) q^{78} +69871.7 q^{79} -37725.8 q^{81} +(98975.9 - 55021.5i) q^{82} +6454.09 q^{83} +(-25327.3 - 15740.3i) q^{84} +(-25949.1 + 14425.3i) q^{86} +39322.7i q^{87} +(-42785.4 - 2084.95i) q^{88} -25638.9 q^{89} -37308.5i q^{91} +(23405.3 + 14545.8i) q^{92} +98538.3 q^{93} +(59454.2 + 106950. i) q^{94} +(-112208. - 77550.7i) q^{96} +151510. i q^{97} +(-75354.2 + 41890.1i) q^{98} +73703.8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9}+O(q^{10}) $ 40 * q - 2 * q^4 + 66 * q^6 + 3240 * q^9	$ 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9} + 848 q^{14} - 110 q^{16} - 18918 q^{24} + 18344 q^{26} + 14320 q^{31} + 19182 q^{34} + 29656 q^{36} - 44904 q^{39} - 11608 q^{41} + 23186 q^{44} - 75224 q^{46} - 125304 q^{49} - 177894 q^{54} - 73816 q^{56} - 230354 q^{64} + 262878 q^{66} - 15448 q^{71} - 4224 q^{74} + 111902 q^{76} + 15560 q^{79} + 193968 q^{81} + 195112 q^{84} - 131972 q^{86} + 6320 q^{89} + 117080 q^{94} + 115582 q^{96}+O(q^{100}) $ 40 * q - 2 * q^4 + 66 * q^6 + 3240 * q^9 + 848 * q^14 - 110 * q^16 - 18918 * q^24 + 18344 * q^26 + 14320 * q^31 + 19182 * q^34 + 29656 * q^36 - 44904 * q^39 - 11608 * q^41 + 23186 * q^44 - 75224 * q^46 - 125304 * q^49 - 177894 * q^54 - 73816 * q^56 - 230354 * q^64 + 262878 * q^66 - 15448 * q^71 - 4224 * q^74 + 111902 * q^76 + 15560 * q^79 + 193968 * q^81 + 195112 * q^84 - 131972 * q^86 + 6320 * q^89 + 117080 * q^94 + 115582 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−4.94424	+	2.74854i	−0.874026	+	0.485879i
$2$	−4.94424	+	2.74854i	−0.874026	+	0.485879i
$3$	−23.5470			−1.51054			−0.755271	−	0.655413i	$-0.772495\pi$
$3$	−23.5470			−1.51054			−0.755271	+	0.655413i	$0.772495\pi$
$4$	16.8910	−	27.1789i	0.527844	−	0.849341i
$5$		0			0
$5$		0			0
$6$	116.422	−	64.7200i	1.32025	−	0.733940i
$7$			39.5751i			0.305265i	0.988283	+	0.152632i	$0.0487750\pi$
$7$			39.5751i			0.305265i	−0.988283	+	0.152632i	$0.951225\pi$
$8$	−8.81071	+	180.805i	−0.0486727	+	0.998815i
$9$	311.462			1.28174
$10$		0			0
$11$			236.639i			0.589663i	0.955549	+	0.294831i	$0.0952635\pi$
$11$			236.639i			0.589663i	−0.955549	+	0.294831i	$0.904737\pi$
$12$	−397.733	+	639.982i	−0.797330	+	1.28297i
$13$	−942.728			−1.54713			−0.773567	−	0.633714i	$-0.781530\pi$
$13$	−942.728			−1.54713			−0.773567	+	0.633714i	$0.781530\pi$
$14$	−108.774	−	195.669i	−0.148322	−	0.266809i
$15$		0			0
$16$	−453.388	−	918.159i	−0.442761	−	0.896639i
$17$		−	1103.34i		−	0.925952i	−0.886371	−	0.462976i	$-0.846782\pi$
$17$		−	1103.34i		−	0.925952i	0.886371	−	0.462976i	$-0.153218\pi$
$18$	−1539.94	+	856.066i	−1.12027	+	0.622768i
$19$		−	2313.21i		−	1.47005i	−0.678041	−	0.735024i	$-0.737171\pi$
$19$		−	2313.21i		−	1.47005i	0.678041	−	0.735024i	$-0.262829\pi$
$20$		0			0
$21$		−	931.874i		−	0.461115i
$22$	−650.411	−	1170.00i	−0.286505	−	0.515381i
$23$			861.158i			0.339440i	0.985492	+	0.169720i	$0.0542864\pi$
$23$			861.158i			0.339440i	−0.985492	+	0.169720i	$0.945714\pi$
$24$	207.466	−	4257.41i	0.0735222	−	1.50875i
$25$		0			0
$26$	4661.07	−	2591.13i	1.35224	−	0.751720i
$27$	−1612.07			−0.425573
$28$	1075.61	+	668.463i	0.259274	+	0.161132i
$29$		−	1669.97i		−	0.368733i	−0.982858	−	0.184367i	$-0.940977\pi$
$29$		−	1669.97i		−	0.368733i	0.982858	−	0.184367i	$-0.0590234\pi$
$30$		0			0
$31$	−4184.75			−0.782105			−0.391053	−	0.920368i	$-0.627889\pi$
$31$	−4184.75			−0.782105			−0.391053	+	0.920368i	$0.627889\pi$
$32$	4765.26	+	3293.44i	0.822643	+	0.568558i
$33$		−	5572.13i		−	0.890710i
$34$	3032.59	+	5455.19i	0.449900	+	0.809306i
$35$		0			0
$36$	5260.90	−	8465.19i	0.676556	−	1.08863i
$37$	−14588.1			−1.75184			−0.875920	−	0.482456i	$-0.839745\pi$
$37$	−14588.1			−1.75184			−0.875920	+	0.482456i	$0.839745\pi$
$38$	6357.97	+	11437.1i	0.714265	+	1.28486i
$39$	22198.4			2.33701
$40$		0			0
$41$	−20018.4			−1.85982			−0.929909	−	0.367791i	$-0.880114\pi$
$41$	−20018.4			−1.85982			−0.929909	+	0.367791i	$0.880114\pi$
$42$	2561.30	+	4607.41i	0.224046	+	0.403027i
$43$	5248.34			0.432864			0.216432	−	0.976298i	$-0.430558\pi$
$43$	5248.34			0.432864			0.216432	+	0.976298i	$0.430558\pi$
$44$	6431.58	+	3997.06i	0.500825	+	0.311250i
$45$		0			0
$46$	−2366.93	−	4257.77i	−0.164927	−	0.296680i
$47$		−	21631.2i		−	1.42835i	−0.699966	−	0.714176i	$-0.746802\pi$
$47$		−	21631.2i		−	1.42835i	0.699966	−	0.714176i	$-0.253198\pi$
$48$	10675.9	+	21619.9i	0.668810	+	1.35441i
$49$	15240.8			0.906813
$50$		0			0
$51$			25980.4i			1.39869i
$52$	−15923.6	+	25622.3i	−0.816646	+	1.31405i
$53$	14960.7			0.731581			0.365791	−	0.930697i	$-0.380799\pi$
$53$	14960.7			0.731581			0.365791	+	0.930697i	$0.380799\pi$
$54$	7970.46	−	4430.84i	0.371962	−	0.206777i
$55$		0			0
$56$	−7155.36	−	348.684i	−0.304903	−	0.0148581i
$57$			54469.3i			2.22057i
$58$	4589.97	+	8256.71i	0.179160	+	0.322283i
$59$			42436.9i			1.58713i	0.608483	+	0.793567i	$0.291778\pi$
$59$			42436.9i			1.58713i	−0.608483	+	0.793567i	$0.708222\pi$
$60$		0			0
$61$			31181.5i			1.07293i	0.843922	+	0.536467i	$0.180241\pi$
$61$			31181.5i			1.07293i	−0.843922	+	0.536467i	$0.819759\pi$
$62$	20690.4	−	11502.0i	0.683580	−	0.380008i
$63$			12326.1i			0.391269i
$64$	−32612.7	−	3186.04i	−0.995262	−	0.0972301i
$65$		0			0
$66$	15315.2	+	27549.9i	0.432777	+	0.778504i
$67$	27868.1			0.758439			0.379220	−	0.925307i	$-0.376192\pi$
$67$	27868.1			0.758439			0.379220	+	0.925307i	$0.376192\pi$
$68$	−29987.7	−	18636.6i	−0.786449	−	0.488758i
$69$		−	20277.7i		−	0.512738i
$70$		0			0
$71$	42393.2			0.998047			0.499023	−	0.866589i	$-0.333692\pi$
$71$	42393.2			0.998047			0.499023	+	0.866589i	$0.333692\pi$
$72$	−2744.20	+	56313.8i	−0.0623856	+	1.28022i
$73$		−	11778.7i		−	0.258696i	−0.991599	−	0.129348i	$-0.958711\pi$
$73$		−	11778.7i		−	0.258696i	0.991599	−	0.129348i	$-0.0412885\pi$
$74$	72127.1	−	40096.1i	1.53115	−	0.851182i
$75$		0			0
$76$	−62870.6	−	39072.5i	−1.24857	−	0.775956i
$77$	−9364.98			−0.180003
$78$	−109754.	+	61013.4i	−2.04261	+	1.13550i
$79$	69871.7			1.25960			0.629801	−	0.776756i	$-0.283136\pi$
$79$	69871.7			1.25960			0.629801	+	0.776756i	$0.283136\pi$
$80$		0			0
$81$	−37725.8			−0.638890
$82$	98975.9	−	55021.5i	1.62553	−	0.903645i
$83$	6454.09			0.102835			0.0514173	−	0.998677i	$-0.483626\pi$
$83$	6454.09			0.102835			0.0514173	+	0.998677i	$0.483626\pi$
$84$	−25327.3	−	15740.3i	−0.391644	−	0.243397i
$85$		0			0
$86$	−25949.1	+	14425.3i	−0.378334	+	0.210319i
$87$			39322.7i			0.556987i
$88$	−42785.4	−	2084.95i	−0.588964	−	0.0287005i
$89$	−25638.9			−0.343103			−0.171551	−	0.985175i	$-0.554878\pi$
$89$	−25638.9			−0.343103			−0.171551	+	0.985175i	$0.554878\pi$
$90$		0			0
$91$		−	37308.5i		−	0.472285i
$92$	23405.3	+	14545.8i	0.288301	+	0.179171i
$93$	98538.3			1.18140
$94$	59454.2	+	106950.i	0.694006	+	1.24842i
$95$		0			0
$96$	−112208.	−	77550.7i	−1.24264	−	0.858831i
$97$			151510.i			1.63498i	0.575941	+	0.817491i	$0.304636\pi$
$97$			151510.i			1.63498i	−0.575941	+	0.817491i	$0.695364\pi$
$98$	−75354.2	+	41890.1i	−0.792579	+	0.440601i
$99$			73703.8i			0.755792i
$100$		0			0
$101$		−	49375.7i		−	0.481626i	−0.970572	−	0.240813i	$-0.922586\pi$
$101$		−	49375.7i		−	0.481626i	0.970572	−	0.240813i	$-0.0774140\pi$
$102$	−71408.4	−	128453.i	−0.679593	−	1.22249i
$103$			66301.7i			0.615789i	0.951421	+	0.307894i	$0.0996244\pi$
$103$			66301.7i			0.615789i	−0.951421	+	0.307894i	$0.900376\pi$
$104$	8306.10	−	170450.i	0.0753033	−	1.54530i
$105$		0			0
$106$	−73969.4	+	41120.2i	−0.639421	+	0.355460i
$107$	152470.			1.28743			0.643715	−	0.765265i	$-0.277392\pi$
$107$	152470.			1.28743			0.643715	+	0.765265i	$0.277392\pi$
$108$	−27229.5	+	43814.3i	−0.224636	+	0.361457i
$109$			130835.i			1.05477i	0.849627	+	0.527384i	$0.176827\pi$
$109$			130835.i			1.05477i	−0.849627	+	0.527384i	$0.823173\pi$
$110$		0			0
$111$	343506.			2.64623
$112$	36336.2	−	17942.8i	0.273712	−	0.135159i
$113$		−	164703.i		−	1.21340i	−0.794931	−	0.606700i	$-0.792493\pi$
$113$		−	164703.i		−	1.21340i	0.794931	−	0.606700i	$-0.207507\pi$
$114$	−149711.	−	269309.i	−1.07893	−	1.94084i
$115$		0			0
$116$	−45387.9	−	28207.4i	−0.313181	−	0.194634i
$117$	−293624.			−1.98302
$118$	−116640.	−	209818.i	−0.771154	−	1.38720i
$119$	43664.9			0.282660
$120$		0			0
$121$	105053.			0.652298
$122$	−85703.8	−	154169.i	−0.521315	−	0.937772i
$123$	471374.			2.80933
$124$	−70684.6	+	113737.i	−0.412829	+	0.664274i
$125$		0			0
$126$	−33878.9	−	60943.3i	−0.190109	−	0.341979i
$127$		−	205568.i		−	1.13096i	−0.824763	−	0.565479i	$-0.808691\pi$
$127$		−	205568.i		−	1.13096i	0.824763	−	0.565479i	$-0.191309\pi$
$128$	170002.	−	73885.0i	0.917127	−	0.398595i
$129$	−123583.			−0.653859
$130$		0			0
$131$			132988.i			0.677071i	0.940954	+	0.338536i	$0.109932\pi$
$131$			132988.i			0.677071i	−0.940954	+	0.338536i	$0.890068\pi$
$132$	−151444.	−	94118.9i	−0.756517	−	0.470156i
$133$	91545.6			0.448754
$134$	−137787.	+	76596.8i	−0.662896	+	0.368509i
$135$		0			0
$136$	199490.	+	9721.23i	0.924854	+	0.0450686i
$137$		−	186663.i		−	0.849685i	−0.905267	−	0.424842i	$-0.860330\pi$
$137$		−	186663.i		−	0.849685i	0.905267	−	0.424842i	$-0.139670\pi$
$138$	55734.1	+	100258.i	0.249129	+	0.448147i
$139$			224455.i			0.985356i	0.870212	+	0.492678i	$0.163982\pi$
$139$			224455.i			0.985356i	−0.870212	+	0.492678i	$0.836018\pi$
$140$		0			0
$141$			509349.i			2.15759i
$142$	−209602.	+	116520.i	−0.872319	+	0.484929i
$143$		−	223086.i		−	0.912288i
$144$	−141213.	−	285971.i	−0.567503	−	1.14925i
$145$		0			0
$146$	32374.3	+	58236.7i	0.125695	+	0.226108i
$147$	−358876.			−1.36978
$148$	−246408.	+	396489.i	−0.924699	+	1.48791i
$149$		−	151619.i		−	0.559483i	−0.960075	−	0.279741i	$-0.909751\pi$
$149$		−	151619.i		−	0.559483i	0.960075	−	0.279741i	$-0.0902487\pi$
$150$		0			0
$151$	−209403.			−0.747378			−0.373689	−	0.927554i	$-0.621907\pi$
$151$	−209403.			−0.747378			−0.373689	+	0.927554i	$0.621907\pi$
$152$	418240.	+	20381.0i	1.46831	+	0.0715513i
$153$		−	343649.i		−	1.18682i
$154$	46302.7	−	25740.1i	0.157328	−	0.0874597i
$155$		0			0
$156$	374954.	−	603329.i	1.23358	−	1.98492i
$157$	−161536.			−0.523022			−0.261511	−	0.965201i	$-0.584221\pi$
$157$	−161536.			−0.523022			−0.261511	+	0.965201i	$0.584221\pi$
$158$	−345462.	+	192045.i	−1.10093	+	0.612014i
$159$	−352280.			−1.10508
$160$		0			0
$161$	−34080.4			−0.103619
$162$	186525.	−	103691.i	0.558406	−	0.310423i
$163$	54872.4			0.161765			0.0808826	−	0.996724i	$-0.474226\pi$
$163$	54872.4			0.161765			0.0808826	+	0.996724i	$0.474226\pi$
$164$	−338131.	+	544079.i	−0.981693	+	1.57962i
$165$		0			0
$166$	−31910.6	+	17739.3i	−0.0898802	+	0.0499652i
$167$			596243.i			1.65437i	0.561932	+	0.827183i	$0.310058\pi$
$167$			596243.i			1.65437i	−0.561932	+	0.827183i	$0.689942\pi$
$168$	168487.	+	8210.47i	0.460568	+	0.0224437i
$169$	517443.			1.39362
$170$		0			0
$171$		−	720477.i		−	1.88421i
$172$	88649.8	−	142644.i	0.228484	−	0.367649i
$173$	−318433.			−0.808915			−0.404458	−	0.914557i	$-0.632540\pi$
$173$	−318433.			−0.808915			−0.404458	+	0.914557i	$0.632540\pi$
$174$	−108080.	−	194421.i	−0.270628	−	0.486821i
$175$		0			0
$176$	217272.	−	107289.i	0.528715	−	0.261080i
$177$		−	999262.i		−	2.39743i
$178$	126765.	−	70469.6i	0.299881	−	0.166706i
$179$		−	17777.4i		−	0.0414702i	−0.999785	−	0.0207351i	$-0.993399\pi$
$179$		−	17777.4i		−	0.0414702i	0.999785	−	0.0207351i	$-0.00660067\pi$
$180$		0			0
$181$			716752.i			1.62619i	0.582128	+	0.813097i	$0.302220\pi$
$181$			716752.i			1.62619i	−0.582128	+	0.813097i	$0.697780\pi$
$182$	102544.	+	184462.i	0.229473	+	0.412790i
$183$		−	734232.i		−	1.62071i
$184$	−155701.	−	7587.41i	−0.339038	−	0.0165215i
$185$		0			0
$186$	−487197.	+	270837.i	−1.03258	+	0.574018i
$187$	261093.			0.545999
$188$	−587912.	−	365372.i	−1.21316	−	0.753947i
$189$		−	63797.7i		−	0.129912i
$190$		0			0
$191$	−67548.7			−0.133978			−0.0669890	−	0.997754i	$-0.521339\pi$
$191$	−67548.7			−0.133978			−0.0669890	+	0.997754i	$0.521339\pi$
$192$	767933.	+	75021.6i	1.50338	+	0.146870i
$193$		−	123441.i		−	0.238543i	−0.992862	−	0.119272i	$-0.961944\pi$
$193$		−	123441.i		−	0.238543i	0.992862	−	0.119272i	$-0.0380560\pi$
$194$	−416433.	−	749104.i	−0.794403	−	1.42902i
$195$		0			0
$196$	257433.	−	414229.i	0.478656	−	0.770194i
$197$	752341.			1.38118			0.690589	−	0.723248i	$-0.257352\pi$
$197$	752341.			1.38118			0.690589	+	0.723248i	$0.257352\pi$
$198$	−202578.	−	364409.i	−0.367223	−	0.660582i
$199$	−852251.			−1.52558			−0.762790	−	0.646646i	$-0.776171\pi$
$199$	−852251.			−1.52558			−0.762790	+	0.646646i	$0.776171\pi$
$200$		0			0
$201$	−656211.			−1.14565
$202$	135711.	+	244125.i	0.234012	+	0.420953i
$203$	66089.0			0.112561
$204$	706120.	+	438836.i	1.18796	+	0.738289i
$205$		0			0
$206$	−182233.	−	327812.i	−0.299199	−	0.538216i
$207$			268218.i			0.435073i
$208$	427421.	+	865574.i	0.685012	+	1.38722i
$209$	547395.			0.866833
$210$		0			0
$211$		−	226264.i		−	0.349871i	−0.984580	−	0.174936i	$-0.944028\pi$
$211$		−	226264.i		−	0.349871i	0.984580	−	0.174936i	$-0.0559718\pi$
$212$	252702.	−	406616.i	0.386161	−	0.621362i
$213$	−998234.			−1.50759
$214$	−753846.	+	419069.i	−1.12525	+	0.625535i
$215$		0			0
$216$	14203.5	−	291470.i	0.0207138	−	0.425069i
$217$		−	165612.i		−	0.238749i
$218$	−359605.	−	646878.i	−0.512489	−	0.921894i
$219$			277353.i			0.390772i
$220$		0			0
$221$			1.04015e6i			1.43257i
$222$	−1.69838e6	+	944142.i	−2.31287	+	1.28575i
$223$			1.40153e6i			1.88730i	0.330944	+	0.943651i	$0.392633\pi$
$223$			1.40153e6i			1.88730i	−0.330944	+	0.943651i	$0.607367\pi$
$224$	−130338.	+	188585.i	−0.173561	+	0.251124i
$225$		0			0
$226$	452692.	+	814329.i	0.589565	+	1.06054i
$227$	692106.			0.891472			0.445736	−	0.895164i	$-0.352942\pi$
$227$	692106.			0.891472			0.445736	+	0.895164i	$0.352942\pi$
$228$	1.48042e6	+	920041.i	1.88602	+	1.17211i
$229$			390771.i			0.492418i	0.969217	+	0.246209i	$0.0791850\pi$
$229$			390771.i			0.492418i	−0.969217	+	0.246209i	$0.920815\pi$
$230$		0			0
$231$	220517.			0.271902
$232$	301938.	+	14713.6i	0.368296	+	0.0179473i
$233$			612536.i			0.739166i	0.929198	+	0.369583i	$0.120499\pi$
$233$			612536.i			0.739166i	−0.929198	+	0.369583i	$0.879501\pi$
$234$	1.45175e6	−	807038.i	1.73321	−	0.963506i
$235$		0			0
$236$	1.15339e6	+	716802.i	1.34802	+	0.837759i
$237$	−1.64527e6			−1.90268
$238$	−215890.	+	120015.i	−0.247053	+	0.137339i
$239$	1.27434e6			1.44308			0.721542	−	0.692370i	$-0.243434\pi$
$239$	1.27434e6			1.44308			0.721542	+	0.692370i	$0.243434\pi$
$240$		0			0
$241$	436449.			0.484050			0.242025	−	0.970270i	$-0.422188\pi$
$241$	436449.			0.484050			0.242025	+	0.970270i	$0.422188\pi$
$242$	−519408.	+	288743.i	−0.570125	+	0.316938i
$243$	1.28006e6			1.39064
$244$	847480.	+	526687.i	0.911287	+	0.566341i
$245$		0			0
$246$	−2.33059e6	+	1.29559e6i	−2.45543	+	1.36499i
$247$			2.18073e6i			2.27436i
$248$	36870.6	−	756623.i	0.0380672	−	0.781178i
$249$	−151974.			−0.155336
$250$		0			0
$251$		−	1.86942e6i		−	1.87294i	−0.350753	−	0.936468i	$-0.614074\pi$
$251$		−	1.86942e6i		−	1.87294i	0.350753	−	0.936468i	$-0.385926\pi$
$252$	335011.	+	208201.i	0.332321	+	0.206529i
$253$	−203783.			−0.200155
$254$	565013.	+	1.01638e6i	0.549508	+	0.988487i
$255$		0			0
$256$	−637455.	+	832564.i	−0.607925	+	0.793995i
$257$			218963.i			0.206794i	0.994640	+	0.103397i	$0.0329713\pi$
$257$			218963.i			0.206794i	−0.994640	+	0.103397i	$0.967029\pi$
$258$	611023.	−	339673.i	0.571490	−	0.317696i
$259$		−	577325.i		−	0.534775i
$260$		0			0
$261$		−	520130.i		−	0.472619i
$262$	−365524.	−	657525.i	−0.328974	−	0.591778i
$263$			1.37614e6i			1.22680i	0.789773	+	0.613399i	$0.210198\pi$
$263$			1.37614e6i			1.22680i	−0.789773	+	0.613399i	$0.789802\pi$
$264$	1.00747e6	+	49094.4i	0.889654	+	0.0433533i
$265$		0			0
$266$	−452623.	+	251617.i	−0.392223	+	0.218040i
$267$	603719.			0.518271
$268$	470721.	−	757426.i	0.400338	−	0.644174i
$269$		−	1.42265e6i		−	1.19872i	−0.800480	−	0.599360i	$-0.795422\pi$
$269$		−	1.42265e6i		−	1.19872i	0.800480	−	0.599360i	$-0.204578\pi$
$270$		0			0
$271$	1.08639e6			0.898594			0.449297	−	0.893383i	$-0.351675\pi$
$271$	1.08639e6			0.898594			0.449297	+	0.893383i	$0.351675\pi$
$272$	−1.01304e6	+	500242.i	−0.830245	+	0.409976i
$273$			878504.i			0.713407i
$274$	513053.	+	922908.i	0.412844	+	0.742647i
$275$		0			0
$276$	−551126.	−	342511.i	−0.435490	−	0.270646i
$277$	257988.			0.202022			0.101011	−	0.994885i	$-0.467792\pi$
$277$	257988.			0.202022			0.101011	+	0.994885i	$0.467792\pi$
$278$	−616925.	−	1.10976e6i	−0.478763	−	0.861227i
$279$	−1.30339e6			−1.00245
$280$		0			0
$281$	−420828.			−0.317935			−0.158967	−	0.987284i	$-0.550817\pi$
$281$	−420828.			−0.317935			−0.158967	+	0.987284i	$0.550817\pi$
$282$	−1.39997e6	−	2.51835e6i	−1.04832	−	1.88579i
$283$	58134.7			0.0431489			0.0215744	−	0.999767i	$-0.493132\pi$
$283$	58134.7			0.0431489			0.0215744	+	0.999767i	$0.493132\pi$
$284$	716065.	−	1.15220e6i	0.526813	−	0.847682i
$285$		0			0
$286$	613161.	+	1.10299e6i	0.443261	+	0.797363i
$287$		−	792230.i		−	0.567736i
$288$	1.48420e6	+	1.02578e6i	1.05441	+	0.728741i
$289$	202491.			0.142614
$290$		0			0
$291$		−	3.56762e6i		−	2.46971i
$292$	−320133.	−	198954.i	−0.219722	−	0.136551i
$293$	−1.27146e6			−0.865235			−0.432618	−	0.901578i	$-0.642410\pi$
$293$	−1.27146e6			−0.865235			−0.432618	+	0.901578i	$0.642410\pi$
$294$	1.77437e6	−	986386.i	1.19722	−	0.665546i
$295$		0			0
$296$	128532.	−	2.63760e6i	0.0852669	−	1.74976i
$297$		−	381478.i		−	0.250945i
$298$	416730.	+	749638.i	0.271841	+	0.489003i
$299$		−	811838.i		−	0.525160i
$300$		0			0
$301$			207704.i			0.132138i
$302$	1.03534e6	−	575553.i	0.653228	−	0.363135i
$303$			1.16265e6i			0.727515i
$304$	−2.12390e6	+	1.04878e6i	−1.31810	+	0.650881i
$305$		0			0
$306$	944535.	+	1.69908e6i	0.576653	+	1.03732i
$307$	2.09626e6			1.26940			0.634700	−	0.772759i	$-0.281124\pi$
$307$	2.09626e6			1.26940			0.634700	+	0.772759i	$0.281124\pi$
$308$	−158184.	+	254530.i	−0.0950136	+	0.152884i
$309$		−	1.56121e6i		−	0.930175i
$310$		0			0
$311$	83803.9			0.0491318			0.0245659	−	0.999698i	$-0.492180\pi$
$311$	83803.9			0.0491318			0.0245659	+	0.999698i	$0.492180\pi$
$312$	−195584.	+	4.01358e6i	−0.113749	+	2.33424i
$313$			803753.i			0.463726i	0.972748	+	0.231863i	$0.0744822\pi$
$313$			803753.i			0.463726i	−0.972748	+	0.231863i	$0.925518\pi$
$314$	798672.	−	443988.i	0.457135	−	0.254125i
$315$		0			0
$316$	1.18020e6	−	1.89904e6i	0.664874	−	1.06983i
$317$	−297696.			−0.166389			−0.0831946	−	0.996533i	$-0.526512\pi$
$317$	−297696.			−0.166389			−0.0831946	+	0.996533i	$0.526512\pi$
$318$	1.74176e6	−	968257.i	0.965872	−	0.536937i
$319$	395178.			0.217428
$320$		0			0
$321$	−3.59020e6			−1.94472
$322$	168502.	−	93671.4i	0.0905658	−	0.0503463i
$323$	−2.55227e6			−1.36119
$324$	−637227.	+	1.02535e6i	−0.337234	+	0.542635i
$325$		0			0
$326$	−271302.	+	150819.i	−0.141387	+	0.0785982i
$327$		−	3.08077e6i		−	1.59327i
$328$	176376.	−	3.61943e6i	0.0905224	−	1.85761i
$329$	856055.			0.436025
$330$		0			0
$331$			1.78127e6i			0.893632i	0.894626	+	0.446816i	$0.147442\pi$
$331$			1.78127e6i			0.893632i	−0.894626	+	0.446816i	$0.852558\pi$
$332$	109016.	−	175415.i	0.0542807	−	0.0873417i
$333$	−4.54364e6			−2.24540
$334$	−1.63880e6	−	2.94797e6i	−0.803821	−	1.44596i
$335$		0			0
$336$	−855609.	+	422500.i	−0.413454	+	0.204164i
$337$			1.83390e6i			0.879632i	0.898088	+	0.439816i	$0.144956\pi$
$337$			1.83390e6i			0.879632i	−0.898088	+	0.439816i	$0.855044\pi$
$338$	−2.55836e6	+	1.42222e6i	−1.21806	+	0.677133i
$339$			3.87825e6i			1.83289i
$340$		0			0
$341$		−	990273.i		−	0.461178i
$342$	1.98026e6	+	3.56221e6i	0.915499	+	1.64685i
$343$			1.26829e6i			0.582083i
$344$	−46241.6	+	948926.i	−0.0210687	+	0.432351i
$345$		0			0
$346$	1.57441e6	−	875227.i	0.707013	−	0.393035i
$347$	909819.			0.405631			0.202816	−	0.979217i	$-0.434991\pi$
$347$	909819.			0.405631			0.202816	+	0.979217i	$0.434991\pi$
$348$	1.06875e6	+	664200.i	0.473072	+	0.294002i
$349$		−	4.18391e6i		−	1.83874i	−0.393399	−	0.919368i	$-0.628701\pi$
$349$		−	4.18391e6i		−	1.83874i	0.393399	−	0.919368i	$-0.371299\pi$
$350$		0			0
$351$	1.51974e6			0.658419
$352$	−779355.	+	1.12764e6i	−0.335258	+	0.485082i
$353$		−	4.32651e6i		−	1.84800i	−0.382398	−	0.923998i	$-0.624902\pi$
$353$		−	4.32651e6i		−	1.84800i	0.382398	−	0.923998i	$-0.375098\pi$
$354$	2.74652e6	+	4.94059e6i	1.16486	+	2.09542i
$355$		0			0
$356$	−433067.	+	696837.i	−0.181105	+	0.291411i
$357$	−1.02818e6			−0.426970
$358$	48862.1	+	87895.9i	0.0201495	+	0.0362461i
$359$	965628.			0.395434			0.197717	−	0.980259i	$-0.436647\pi$
$359$	965628.			0.395434			0.197717	+	0.980259i	$0.436647\pi$
$360$		0			0
$361$	−2.87486e6			−1.16104
$362$	−1.97003e6	−	3.54379e6i	−0.790133	−	1.42134i
$363$	−2.47369e6			−0.985323
$364$	−1.01401e6	−	630179.i	−0.401132	−	0.249293i
$365$		0			0
$366$	2.01807e6	+	3.63022e6i	0.787468	+	1.41654i
$367$		−	1.95847e6i		−	0.759016i	−0.925188	−	0.379508i	$-0.876093\pi$
$367$		−	1.95847e6i		−	0.759016i	0.925188	−	0.379508i	$-0.123907\pi$
$368$	790680.	−	390438.i	0.304355	−	0.150291i
$369$	−6.23497e6			−2.38379
$370$		0			0
$371$			592071.i			0.223326i
$372$	1.66441e6	−	2.67817e6i	0.623596	−	1.00341i
$373$	4.07168e6			1.51531			0.757656	−	0.652654i	$-0.226345\pi$
$373$	4.07168e6			1.51531			0.757656	+	0.652654i	$0.226345\pi$
$374$	−1.29091e6	+	717627.i	−0.477218	+	0.265289i
$375$		0			0
$376$	3.91102e6	+	190586.i	1.42666	+	0.0695218i
$377$			1.57432e6i			0.570480i
$378$	175351.	+	315431.i	0.0631217	+	0.113547i
$379$		−	807643.i		−	0.288816i	−0.989518	−	0.144408i	$-0.953872\pi$
$379$		−	807643.i		−	0.288816i	0.989518	−	0.144408i	$-0.0461278\pi$
$380$		0			0
$381$			4.84051e6i			1.70836i
$382$	333977.	−	185661.i	0.117100	−	0.0650971i
$383$		−	502071.i		−	0.174891i	−0.996169	−	0.0874456i	$-0.972130\pi$
$383$		−	502071.i		−	0.174891i	0.996169	−	0.0874456i	$-0.0278704\pi$
$384$	−4.00304e6	+	1.73977e6i	−1.38536	+	0.602094i
$385$		0			0
$386$	339284.	+	610324.i	0.115903	+	0.208493i
$387$	1.63466e6			0.554817
$388$	4.11789e6	+	2.55916e6i	1.38866	+	0.863016i
$389$			2.82149e6i			0.945377i	0.881230	+	0.472688i	$0.156716\pi$
$389$			2.82149e6i			0.945377i	−0.881230	+	0.472688i	$0.843284\pi$
$390$		0			0
$391$	950153.			0.314305
$392$	−134282.	+	2.75561e6i	−0.0441371	+	0.905739i
$393$		−	3.13147e6i		−	1.02274i
$394$	−3.71976e6	+	2.06784e6i	−1.20719	+	0.671085i
$395$		0			0
$396$	2.00319e6	+	1.24493e6i	0.641925	+	0.398940i
$397$	−3.84651e6			−1.22487			−0.612436	−	0.790521i	$-0.709810\pi$
$397$	−3.84651e6			−1.22487			−0.612436	+	0.790521i	$0.709810\pi$
$398$	4.21373e6	−	2.34245e6i	1.33340	−	0.741247i
$399$	−2.15562e6			−0.677861
$400$		0			0
$401$	−952906.			−0.295930			−0.147965	−	0.988993i	$-0.547272\pi$
$401$	−952906.			−0.295930			−0.147965	+	0.988993i	$0.547272\pi$
$402$	3.24447e6	−	1.80363e6i	1.00133	−	0.556649i
$403$	3.94508e6			1.21002
$404$	−1.34198e6	−	834005.i	−0.409065	−	0.254223i
$405$		0			0
$406$	−326760.	+	181649.i	−0.0983815	+	0.0546911i
$407$		−	3.45211e6i		−	1.03300i
$408$	−4.69739e6	−	228906.i	−1.39703	−	0.0680780i
$409$	−2.12056e6			−0.626819			−0.313410	−	0.949618i	$-0.601471\pi$
$409$	−2.12056e6			−0.626819			−0.313410	+	0.949618i	$0.601471\pi$
$410$		0			0
$411$			4.39536e6i			1.28348i
$412$	1.80201e6	+	1.11990e6i	0.523015	+	0.325040i
$413$	−1.67944e6			−0.484496
$414$	−737208.	−	1.32613e6i	−0.211392	−	0.380265i
$415$		0			0
$416$	−4.49234e6	−	3.10482e6i	−1.27274	−	0.879636i
$417$		−	5.28525e6i		−	1.48842i
$418$	−2.70645e6	+	1.50454e6i	−0.757635	+	0.421176i
$419$		−	3.26837e6i		−	0.909486i	−0.890623	−	0.454743i	$-0.849731\pi$
$419$		−	3.26837e6i		−	0.909486i	0.890623	−	0.454743i	$-0.150269\pi$
$420$		0			0
$421$		−	4.53790e6i		−	1.24781i	−0.781499	−	0.623907i	$-0.785545\pi$
$421$		−	4.53790e6i		−	1.24781i	0.781499	−	0.623907i	$-0.214455\pi$
$422$	621895.	+	1.11870e6i	0.169995	+	0.305797i
$423$		−	6.73728e6i		−	1.83077i
$424$	−131814.	+	2.70497e6i	−0.0356081	+	0.730714i
$425$		0			0
$426$	4.93551e6	−	2.74369e6i	1.31767	−	0.732506i
$427$	−1.23401e6			−0.327529
$428$	2.57536e6	−	4.14396e6i	0.679562	−	1.09347i
$429$			5.25300e6i			1.37805i
$430$		0			0
$431$	−4.36156e6			−1.13096			−0.565482	−	0.824761i	$-0.691310\pi$
$431$	−4.36156e6			−1.13096			−0.565482	+	0.824761i	$0.691310\pi$
$432$	730892.	+	1.48014e6i	0.188427	+	0.381586i
$433$			3.61247e6i			0.925944i	0.886373	+	0.462972i	$0.153217\pi$
$433$			3.61247e6i			0.925944i	−0.886373	+	0.462972i	$0.846783\pi$
$434$	455191.	+	818824.i	0.116003	+	0.208673i
$435$		0			0
$436$	3.55595e6	+	2.20993e6i	0.895857	+	0.556753i
$437$	1.99204e6			0.498994
$438$	−762318.	−	1.37130e6i	−0.189868	−	0.341545i
$439$	2.32906e6			0.576791			0.288396	−	0.957511i	$-0.406878\pi$
$439$	2.32906e6			0.576791			0.288396	+	0.957511i	$0.406878\pi$
$440$		0			0
$441$	4.74693e6			1.16230
$442$	−2.85891e6	−	5.14276e6i	−0.696056	−	1.25211i
$443$	1.29652e6			0.313885			0.156943	−	0.987608i	$-0.449836\pi$
$443$	1.29652e6			0.313885			0.156943	+	0.987608i	$0.449836\pi$
$444$	5.80217e6	−	9.33613e6i	1.39680	−	2.24755i
$445$		0			0
$446$	−3.85218e6	−	6.92951e6i	−0.916999	−	1.64955i
$447$			3.57016e6i			0.845122i
$448$	126088.	−	1.29065e6i	0.0296809	−	0.303818i
$449$	6.61418e6			1.54832			0.774159	−	0.632991i	$-0.218173\pi$
$449$	6.61418e6			1.54832			0.774159	+	0.632991i	$0.218173\pi$
$450$		0			0
$451$		−	4.73713e6i		−	1.09666i
$452$	−4.47644e6	−	2.78199e6i	−1.03059	−	0.640486i
$453$	4.93081e6			1.12894
$454$	−3.42194e6	+	1.90228e6i	−0.779170	+	0.433147i
$455$		0			0
$456$	−9.84830e6	−	479913.i	−2.21794	−	0.108081i
$457$			943843.i			0.211402i	0.994398	+	0.105701i	$0.0337087\pi$
$457$			943843.i			0.211402i	−0.994398	+	0.105701i	$0.966291\pi$
$458$	−1.07405e6	−	1.93207e6i	−0.239255	−	0.430386i
$459$			1.77867e6i			0.394060i
$460$		0			0
$461$			3.55134e6i			0.778287i	0.921177	+	0.389144i	$0.127229\pi$
$461$			3.55134e6i			0.778287i	−0.921177	+	0.389144i	$0.872771\pi$
$462$	−1.09029e6	+	606102.i	−0.237650	+	0.132111i
$463$			1.65685e6i			0.359194i	0.983740	+	0.179597i	$0.0574794\pi$
$463$			1.65685e6i			0.359194i	−0.983740	+	0.179597i	$0.942521\pi$
$464$	−1.53329e6	+	757142.i	−0.330621	+	0.163261i
$465$		0			0
$466$	−1.68358e6	−	3.02852e6i	−0.359145	−	0.646050i
$467$	−1.75032e6			−0.371386			−0.185693	−	0.982608i	$-0.559453\pi$
$467$	−1.75032e6			−0.371386			−0.185693	+	0.982608i	$0.559453\pi$
$468$	−4.95960e6	+	7.98038e6i	−1.04672	+	1.68426i
$469$			1.10288e6i			0.231525i
$470$		0			0
$471$	3.80368e6			0.790046
$472$	−7.67279e6	−	373899.i	−1.58525	−	0.0772501i
$473$			1.24196e6i			0.255244i
$474$	8.13461e6	−	4.52210e6i	1.66299	−	0.924473i
$475$		0			0
$476$	737544.	−	1.18676e6i	0.149201	−	0.240075i
$477$	4.65969e6			0.937694
$478$	−6.30066e6	+	3.50259e6i	−1.26129	+	0.701164i
$479$	−5.04270e6			−1.00421			−0.502105	−	0.864807i	$-0.667441\pi$
$479$	−5.04270e6			−1.00421			−0.502105	+	0.864807i	$0.667441\pi$
$480$		0			0
$481$	1.37526e7			2.71033
$482$	−2.15791e6	+	1.19960e6i	−0.423073	+	0.235190i
$483$	802491.			0.156521
$484$	1.77445e6	−	2.85523e6i	0.344311	−	0.554024i
$485$		0			0
$486$	−6.32894e6	+	3.51831e6i	−1.21546	+	0.675683i
$487$			7.89934e6i			1.50927i	0.656142	+	0.754637i	$0.272187\pi$
$487$			7.89934e6i			1.50927i	−0.656142	+	0.754637i	$0.727813\pi$
$488$	−5.63777e6	−	274731.i	−1.07166	−	0.0522226i
$489$	−1.29208e6			−0.244353
$490$		0			0
$491$		−	393115.i		−	0.0735895i	−0.999323	−	0.0367947i	$-0.988285\pi$
$491$		−	393115.i		−	0.0735895i	0.999323	−	0.0367947i	$-0.0117148\pi$
$492$	7.96198e6	−	1.28114e7i	1.48289	−	2.38608i
$493$	−1.84254e6			−0.341429
$494$	−5.99384e6	−	1.07821e7i	−1.10506	−	1.98785i
$495$		0			0
$496$	1.89731e6	+	3.84226e6i	0.346286	+	0.701266i
$497$			1.67772e6i			0.304668i
$498$	751398.	−	417709.i	0.135768	−	0.0754745i
$499$		−	2.09991e6i		−	0.377529i	−0.982022	−	0.188764i	$-0.939552\pi$
$499$		−	2.09991e6i		−	0.377529i	0.982022	−	0.188764i	$-0.0604482\pi$
$500$		0			0
$501$		−	1.40397e7i		−	2.49899i
$502$	5.13819e6	+	9.24287e6i	0.910020	+	1.63700i
$503$			5.73021e6i			1.00984i	0.863168	+	0.504918i	$0.168477\pi$
$503$			5.73021e6i			1.00984i	−0.863168	+	0.504918i	$0.831523\pi$
$504$	−2.22862e6	−	108602.i	−0.390805	−	0.0190441i
$505$		0			0
$506$	1.00755e6	−	560107.i	0.174941	−	0.0972511i
$507$	−1.21842e7			−2.10513
$508$	−5.58712e6	−	3.47225e6i	−0.960569	−	0.596969i
$509$		−	3.82387e6i		−	0.654197i	−0.944990	−	0.327099i	$-0.893929\pi$
$509$		−	3.82387e6i		−	0.654197i	0.944990	−	0.327099i	$-0.106071\pi$
$510$		0			0
$511$	466143.			0.0789709
$512$	863392.	−	5.86847e6i	0.145557	−	0.989350i
$513$			3.72906e6i			0.625613i
$514$	−601831.	−	1.08261e6i	−0.100477	−	0.180744i
$515$		0			0
$516$	−2.08744e6	+	3.35885e6i	−0.345135	+	0.555349i
$517$	5.11877e6			0.842246
$518$	1.58680e6	+	2.85443e6i	0.259836	+	0.467407i
$519$	7.49815e6			1.22190
$520$		0			0
$521$	1.86739e6			0.301398			0.150699	−	0.988580i	$-0.451848\pi$
$521$	1.86739e6			0.301398			0.150699	+	0.988580i	$0.451848\pi$
$522$	1.42960e6	+	2.57165e6i	0.229635	+	0.413081i
$523$	16319.3			0.00260883			0.00130442	−	0.999999i	$-0.499585\pi$
$523$	16319.3			0.00260883			0.00130442	+	0.999999i	$0.499585\pi$
$524$	3.61447e6	+	2.24630e6i	0.575065	+	0.357388i
$525$		0			0
$526$	−3.78238e6	−	6.80396e6i	−0.596075	−	1.07225i
$527$			4.61721e6i			0.724191i
$528$	−5.11610e6	+	2.52634e6i	−0.798646	+	0.394372i
$529$	5.69475e6			0.884780
$530$		0			0
$531$			1.32175e7i			2.03429i
$532$	1.54630e6	−	2.48811e6i	0.236872	−	0.381145i
$533$	1.88719e7			2.87739
$534$	−2.98493e6	+	1.65935e6i	−0.452982	+	0.251817i
$535$		0			0
$536$	−245538.	+	5.03869e6i	−0.0369153	+	0.757540i
$537$			418606.i			0.0626425i
$538$	3.91022e6	+	7.03393e6i	0.582432	+	1.04771i
$539$			3.60656e6i			0.534714i
$540$		0			0
$541$			9.59912e6i			1.41006i	0.709177	+	0.705031i	$0.249067\pi$
$541$			9.59912e6i			1.41006i	−0.709177	+	0.705031i	$0.750933\pi$
$542$	−5.37138e6	+	2.98600e6i	−0.785395	+	0.436607i
$543$		−	1.68774e7i		−	2.45643i
$544$	3.63379e6	−	5.25771e6i	0.526457	−	0.761728i
$545$		0			0
$546$	−2.41461e6	−	4.34353e6i	−0.346629	−	0.623536i
$547$	−9.28164e6			−1.32635			−0.663173	−	0.748466i	$-0.730790\pi$
$547$	−9.28164e6			−1.32635			−0.663173	+	0.748466i	$0.730790\pi$
$548$	−5.07331e6	−	3.15293e6i	−0.721672	−	0.448501i
$549$			9.71185e6i			1.37522i
$550$		0			0
$551$	−3.86299e6			−0.542056
$552$	3.66630e6	+	178661.i	0.512131	+	0.0249564i
$553$			2.76518e6i			0.384512i
$554$	−1.27555e6	+	709090.i	−0.176573	+	0.0981583i
$555$		0			0
$556$	6.10045e6	+	3.79128e6i	0.836903	+	0.520114i
$557$	−2.03429e6			−0.277827			−0.138914	−	0.990305i	$-0.544361\pi$
$557$	−2.03429e6			−0.277827			−0.138914	+	0.990305i	$0.544361\pi$
$558$	6.44427e6	−	3.58242e6i	0.876169	−	0.487070i
$559$	−4.94776e6			−0.669698
$560$		0			0
$561$	−6.14797e6			−0.824754
$562$	2.08067e6	−	1.15666e6i	0.277884	−	0.154478i
$563$	1.09045e6			0.144989			0.0724946	−	0.997369i	$-0.476904\pi$
$563$	1.09045e6			0.144989			0.0724946	+	0.997369i	$0.476904\pi$
$564$	1.38436e7	+	8.60342e6i	1.83253	+	1.13887i
$565$		0			0
$566$	−287432.	+	159786.i	−0.0377132	+	0.0209651i
$567$		−	1.49300e6i		−	0.195030i
$568$	−373514.	+	7.66490e6i	−0.0485777	+	0.996864i
$569$	1.35027e7			1.74839			0.874197	−	0.485571i	$-0.161388\pi$
$569$	1.35027e7			1.74839			0.874197	+	0.485571i	$0.161388\pi$
$570$		0			0
$571$			763375.i			0.0979823i	0.998799	+	0.0489912i	$0.0156006\pi$
$571$			763375.i			0.0979823i	−0.998799	+	0.0489912i	$0.984399\pi$
$572$	−6.06323e6	−	3.76814e6i	−0.774844	−	0.481545i
$573$	1.59057e6			0.202379
$574$	2.17748e6	+	3.91698e6i	0.275851	+	0.496217i
$575$		0			0
$576$	−1.01576e7	−	992328.i	−1.27566	−	0.124623i
$577$			1.12137e7i			1.40220i	0.713063	+	0.701100i	$0.247307\pi$
$577$			1.12137e7i			1.40220i	−0.713063	+	0.701100i	$0.752693\pi$
$578$	−1.00116e6	+	556556.i	−0.124648	+	0.0692930i
$579$			2.90668e6i			0.360330i
$580$		0			0
$581$			255421.i			0.0313918i
$582$	9.80575e6	+	1.76392e7i	1.19998	+	2.15859i
$583$			3.54028e6i			0.431386i
$584$	2.12965e6	+	103779.i	0.258390	+	0.0125915i
$585$		0			0
$586$	6.28641e6	−	3.49467e6i	0.756238	−	0.420399i
$587$	9.81694e6			1.17593			0.587964	−	0.808887i	$-0.299930\pi$
$587$	9.81694e6			1.17593			0.587964	+	0.808887i	$0.299930\pi$
$588$	−6.06177e6	+	9.75385e6i	−0.723030	+	1.16341i
$589$			9.68022e6i			1.14973i
$590$		0			0
$591$	−1.77154e7			−2.08633
$592$	6.61407e6	+	1.33942e7i	0.775648	+	1.57077i
$593$			436559.i			0.0509808i	0.999675	+	0.0254904i	$0.00811472\pi$
$593$			436559.i			0.0509808i	−0.999675	+	0.0254904i	$0.991885\pi$
$594$	1.04851e6	+	1.88612e6i	0.121929	+	0.219332i
$595$		0			0
$596$	−4.12083e6	−	2.56099e6i	−0.475192	−	0.295320i
$597$	2.00680e7			2.30445
$598$	2.23137e6	+	4.01392e6i	0.255164	+	0.459003i
$599$	7.26208e6			0.826978			0.413489	−	0.910509i	$-0.364310\pi$
$599$	7.26208e6			0.826978			0.413489	+	0.910509i	$0.364310\pi$
$600$		0			0
$601$	1.18166e7			1.33446			0.667232	−	0.744850i	$-0.267479\pi$
$601$	1.18166e7			1.33446			0.667232	+	0.744850i	$0.267479\pi$
$602$	−570882.	−	1.02694e6i	−0.0642030	−	0.115492i
$603$	8.67986e6			0.972119
$604$	−3.53702e6	+	5.69134e6i	−0.394499	+	0.634779i
$605$		0			0
$606$	−3.19559e6	−	5.74842e6i	−0.353484	−	0.635868i
$607$			9.00834e6i			0.992369i	0.868217	+	0.496185i	$0.165266\pi$
$607$			9.00834e6i			0.992369i	−0.868217	+	0.496185i	$0.834734\pi$
$608$	7.61843e6	−	1.10231e7i	0.835808	−	1.20933i
$609$	−1.55620e6			−0.170028
$610$		0			0
$611$			2.03923e7i			2.20985i
$612$	−9.34001e6	−	5.80458e6i	−1.00802	−	0.626458i
$613$	811870.			0.0872641			0.0436320	−	0.999048i	$-0.486107\pi$
$613$	811870.			0.0872641			0.0436320	+	0.999048i	$0.486107\pi$
$614$	−1.03644e7	+	5.76165e6i	−1.10949	+	0.616774i
$615$		0			0
$616$	82512.1	−	1.69323e6i	0.00876125	−	0.179790i
$617$		−	1.51284e7i		−	1.59985i	−0.600101	−	0.799924i	$-0.704873\pi$
$617$		−	1.51284e7i		−	1.59985i	0.600101	−	0.799924i	$-0.295127\pi$
$618$	4.29105e6	+	7.71898e6i	0.451952	+	0.812997i
$619$		−	9.71390e6i		−	1.01898i	−0.860476	−	0.509491i	$-0.829834\pi$
$619$		−	9.71390e6i		−	1.01898i	0.860476	−	0.509491i	$-0.170166\pi$
$620$		0			0
$621$		−	1.38825e6i		−	0.144457i
$622$	−414346.	+	230339.i	−0.0429425	+	0.0238721i
$623$		−	1.01466e6i		−	0.104737i
$624$	−1.00645e7	−	2.03817e7i	−1.03474	−	2.09546i
$625$		0			0
$626$	−2.20915e6	−	3.97395e6i	−0.225315	−	0.405309i
$627$	−1.28895e7			−1.30939
$628$	−2.72850e6	+	4.39037e6i	−0.276074	+	0.444224i
$629$			1.60957e7i			1.62212i
$630$		0			0
$631$	−7.58729e6			−0.758601			−0.379300	−	0.925274i	$-0.623835\pi$
$631$	−7.58729e6			−0.758601			−0.379300	+	0.925274i	$0.623835\pi$
$632$	−615619.	+	1.26331e7i	−0.0613083	+	1.25811i
$633$			5.32783e6i			0.528495i
$634$	1.47188e6	−	818231.i	0.145429	−	0.0808449i
$635$		0			0
$636$	−5.95037e6	+	9.57459e6i	−0.583312	+	0.938594i
$637$	−1.43679e7			−1.40296
$638$	−1.95386e6	+	1.08616e6i	−0.190038	+	0.105644i
$639$	1.32039e7			1.27923
$640$		0			0
$641$	3.27092e6			0.314431			0.157215	−	0.987564i	$-0.449748\pi$
$641$	3.27092e6			0.314431			0.157215	+	0.987564i	$0.449748\pi$
$642$	1.77508e7	−	9.86783e6i	1.69973	−	0.944896i
$643$	−1.84464e7			−1.75948			−0.879741	−	0.475454i	$-0.842284\pi$
$643$	−1.84464e7			−1.75948			−0.879741	+	0.475454i	$0.842284\pi$
$644$	−575652.	+	926268.i	−0.0546947	+	0.0880080i
$645$		0			0
$646$	1.26190e7	−	7.01502e6i	1.18972	−	0.661375i
$647$		−	1.70674e7i		−	1.60290i	−0.598064	−	0.801448i	$-0.704063\pi$
$647$		−	1.70674e7i		−	1.60290i	0.598064	−	0.801448i	$-0.295937\pi$
$648$	332391.	−	6.82100e6i	0.0310965	−	0.638132i
$649$	−1.00422e7			−0.935874
$650$		0			0
$651$			3.89966e6i			0.360640i
$652$	926850.	−	1.49137e6i	0.0853868	−	0.137394i
$653$	−9.92803e6			−0.911130			−0.455565	−	0.890203i	$-0.650563\pi$
$653$	−9.92803e6			−0.911130			−0.455565	+	0.890203i	$0.650563\pi$
$654$	8.46762e6	+	1.52320e7i	0.774136	+	1.39256i
$655$		0			0
$656$	9.07611e6	+	1.83801e7i	0.823455	+	1.66759i
$657$		−	3.66862e6i		−	0.331580i
$658$	−4.23254e6	+	2.35290e6i	−0.381098	+	0.211855i
$659$		−	4.71879e6i		−	0.423270i	−0.977349	−	0.211635i	$-0.932121\pi$
$659$		−	4.71879e6i		−	0.423270i	0.977349	−	0.211635i	$-0.0678788\pi$
$660$		0			0
$661$		−	2.12098e7i		−	1.88814i	−0.329751	−	0.944068i	$-0.606965\pi$
$661$		−	2.12098e7i		−	1.88814i	0.329751	−	0.944068i	$-0.393035\pi$
$662$	−4.89589e6	−	8.80700e6i	−0.434197	−	0.781058i
$663$		−	2.44925e7i		−	2.16396i
$664$	−56865.1	+	1.16693e6i	−0.00500525	+	0.102713i
$665$		0			0
$666$	2.24648e7	−	1.24884e7i	1.96254	−	1.09099i
$667$	1.43810e6			0.125163
$668$	1.62052e7	+	1.00711e7i	1.40512	+	0.873248i
$669$		−	3.30019e7i		−	2.85085i
$670$		0			0
$671$	−7.37875e6			−0.632669
$672$	3.06907e6	−	4.44062e6i	0.262171	−	0.379333i
$673$		−	1.85764e7i		−	1.58097i	−0.612479	−	0.790487i	$-0.709828\pi$
$673$		−	1.85764e7i		−	1.58097i	0.612479	−	0.790487i	$-0.290172\pi$
$674$	−5.04056e6	−	9.06724e6i	−0.427394	−	0.768822i
$675$		0			0
$676$	8.74014e6	−	1.40635e7i	0.735617	−	1.18366i
$677$	1.06647e7			0.894289			0.447145	−	0.894462i	$-0.352441\pi$
$677$	1.06647e7			0.894289			0.447145	+	0.894462i	$0.352441\pi$
$678$	−1.06596e7	−	1.91750e7i	−0.890563	−	1.60200i
$679$	−5.99603e6			−0.499102
$680$		0			0
$681$	−1.62970e7			−1.34661
$682$	2.72181e6	+	4.89614e6i	0.224077	+	0.403082i
$683$	−1.53081e7			−1.25565			−0.627825	−	0.778354i	$-0.716055\pi$
$683$	−1.53081e7			−1.25565			−0.627825	+	0.778354i	$0.716055\pi$
$684$	−1.95818e7	−	1.21696e7i	−1.60034	−	0.994571i
$685$		0			0
$686$	−3.48596e6	−	6.27075e6i	−0.282822	−	0.508756i
$687$		−	9.20149e6i		−	0.743818i
$688$	−2.37953e6	−	4.81881e6i	−0.191655	−	0.388123i
$689$	−1.41039e7			−1.13185
$690$		0			0
$691$			18748.9i			0.00149376i	1.00000		0.000746879i	$0.000237739\pi$
$691$			18748.9i			0.00149376i	−1.00000		0.000746879i	$0.999762\pi$
$692$	−5.37866e6	+	8.65467e6i	−0.426981	+	0.687045i
$693$	−2.91683e6			−0.230716
$694$	−4.49836e6	+	2.50068e6i	−0.354532	+	0.197088i
$695$		0			0
$696$	−7.10973e6	−	346461.i	−0.556327	−	0.0271101i
$697$			2.20872e7i			1.72210i
$698$	1.14997e7	+	2.06863e7i	0.893402	+	1.60710i
$699$		−	1.44234e7i		−	1.11654i
$700$		0			0
$701$			9.58215e6i			0.736492i	0.929728	+	0.368246i	$0.120042\pi$
$701$			9.58215e6i			0.736492i	−0.929728	+	0.368246i	$0.879958\pi$
$702$	−7.51397e6	+	4.17708e6i	−0.575476	+	0.319912i
$703$			3.37454e7i			2.57529i
$704$	753939.	−	7.71743e6i	0.0573330	−	0.586869i
$705$		0			0
$706$	1.18916e7	+	2.13913e7i	0.897901	+	1.61520i
$707$	1.95405e6			0.147023
$708$	−2.71589e7	−	1.68785e7i	−2.03624	−	1.26547i
$709$			3.86069e6i			0.288436i	0.989546	+	0.144218i	$0.0460667\pi$
$709$			3.86069e6i			0.288436i	−0.989546	+	0.144218i	$0.953933\pi$
$710$		0			0
$711$	2.17624e7			1.61448
$712$	225897.	−	4.63563e6i	0.0166998	−	0.342696i
$713$		−	3.60373e6i		−	0.265478i
$714$	5.08355e6	−	2.82599e6i	0.373183	−	0.207456i
$715$		0			0
$716$	−483172.	−	300279.i	−0.0352224	−	0.0218898i
$717$	−3.00070e7			−2.17984
$718$	−4.77429e6	+	2.65407e6i	−0.345619	+	0.192133i
$719$	−4.99905e6			−0.360633			−0.180317	−	0.983609i	$-0.557712\pi$
$719$	−4.99905e6			−0.360633			−0.180317	+	0.983609i	$0.557712\pi$
$720$		0			0
$721$	−2.62390e6			−0.187979
$722$	1.42140e7	−	7.90167e6i	1.01478	−	0.564126i
$723$	−1.02771e7			−0.731178
$724$	1.94806e7	+	1.21067e7i	1.38119	+	0.858377i
$725$		0			0
$726$	1.22305e7	−	6.79904e6i	0.861198	−	0.478747i
$727$		−	2.02268e7i		−	1.41935i	−0.704528	−	0.709676i	$-0.748841\pi$
$727$		−	2.02268e7i		−	1.41935i	0.704528	−	0.709676i	$-0.251159\pi$
$728$	6.74556e6	+	328714.i	0.471726	+	0.0229874i
$729$	−2.09743e7			−1.46173
$730$		0			0
$731$		−	5.79072e6i		−	0.400811i
$732$	−1.99556e7	−	1.24019e7i	−1.37654	−	0.855482i
$733$	1.44588e7			0.993969			0.496985	−	0.867759i	$-0.334441\pi$
$733$	1.44588e7			0.993969			0.496985	+	0.867759i	$0.334441\pi$
$734$	5.38293e6	+	9.68312e6i	0.368790	+	0.663400i
$735$		0			0
$736$	−2.83617e6	+	4.10364e6i	−0.192991	+	0.279238i
$737$			6.59467e6i			0.447223i
$738$	3.08272e7	−	1.71371e7i	2.08350	−	1.15823i
$739$		−	4.05126e6i		−	0.272885i	−0.990648	−	0.136442i	$-0.956433\pi$
$739$		−	4.05126e6i		−	0.272885i	0.990648	−	0.136442i	$-0.0435668\pi$
$740$		0			0
$741$		−	5.13497e7i		−	3.43552i
$742$	−1.62733e6	−	2.92734e6i	−0.108509	−	0.195193i
$743$		−	2.27919e6i		−	0.151464i	−0.997128	−	0.0757320i	$-0.975871\pi$
$743$		−	2.27919e6i		−	0.151464i	0.997128	−	0.0757320i	$-0.0241293\pi$
$744$	−868192.	+	1.78162e7i	−0.0575021	+	1.18000i
$745$		0			0
$746$	−2.01314e7	+	1.11912e7i	−1.32442	+	0.736258i
$747$	2.01020e6			0.131807
$748$	4.41013e6	−	7.09624e6i	0.288202	−	0.463740i
$749$			6.03399e6i			0.393007i
$750$		0			0
$751$	2.24272e7			1.45103			0.725514	−	0.688208i	$-0.241602\pi$
$751$	2.24272e7			1.45103			0.725514	+	0.688208i	$0.241602\pi$
$752$	−1.98608e7	+	9.80731e6i	−1.28072	+	0.632419i
$753$			4.40193e7i			2.82915i
$754$	−4.32710e6	−	7.78383e6i	−0.277184	−	0.498615i
$755$		0			0
$756$	−1.73395e6	−	1.07761e6i	−0.110340	−	0.0685735i
$757$	1.34464e7			0.852840			0.426420	−	0.904525i	$-0.359775\pi$
$757$	1.34464e7			0.852840			0.426420	+	0.904525i	$0.359775\pi$
$758$	2.21984e6	+	3.99318e6i	0.140330	+	0.252433i
$759$	4.79848e6			0.302343
$760$		0			0
$761$	6.89332e6			0.431486			0.215743	−	0.976450i	$-0.430783\pi$
$761$	6.89332e6			0.431486			0.215743	+	0.976450i	$0.430783\pi$
$762$	−1.33044e7	−	2.39327e7i	−0.830055	−	1.49315i
$763$	−5.17779e6			−0.321983
$764$	−1.14097e6	+	1.83590e6i	−0.0707195	+	0.113793i
$765$		0			0
$766$	1.37996e6	+	2.48236e6i	0.0849759	+	0.152860i
$767$		−	4.00064e7i		−	2.45551i
$768$	1.50102e7	−	1.96044e7i	0.918295	−	1.19936i
$769$	350223.			0.0213564			0.0106782	−	0.999943i	$-0.496601\pi$
$769$	350223.			0.0213564			0.0106782	+	0.999943i	$0.496601\pi$
$770$		0			0
$771$		−	5.15593e6i		−	0.312371i
$772$	−3.35500e6	−	2.08505e6i	−0.202605	−	0.125914i
$773$	1.76767e7			1.06403			0.532014	−	0.846736i	$-0.321435\pi$
$773$	1.76767e7			1.06403			0.532014	+	0.846736i	$0.321435\pi$
$774$	−8.08214e6	+	4.49293e6i	−0.484924	+	0.269574i
$775$		0			0
$776$	−2.73938e7	−	1.33491e6i	−1.63304	−	0.0795791i
$777$			1.35943e7i			0.807800i
$778$	−7.75500e6	−	1.39501e7i	−0.459338	−	0.826284i
$779$			4.63069e7i			2.73402i
$780$		0			0
$781$			1.00319e7i			0.588511i
$782$	−4.69778e6	+	2.61154e6i	−0.274711	+	0.152714i
$783$			2.69210e6i			0.156923i
$784$	−6.91000e6	−	1.39935e7i	−0.401502	−	0.813085i
$785$		0			0
$786$	8.60699e6	+	1.54827e7i	0.496930	+	0.893905i
$787$	2.19370e7			1.26252			0.631262	−	0.775569i	$-0.282537\pi$
$787$	2.19370e7			1.26252			0.631262	+	0.775569i	$0.282537\pi$
$788$	1.27078e7	−	2.04478e7i	0.729046	−	1.17309i
$789$		−	3.24040e7i		−	1.85313i
$790$		0			0
$791$	6.51811e6			0.370408
$792$	−1.33260e7	−	649383.i	−0.754896	−	0.0367865i
$793$		−	2.93957e7i		−	1.65997i
$794$	1.90181e7	−	1.05723e7i	1.07057	−	0.595139i
$795$		0			0
$796$	−1.43954e7	+	2.31633e7i	−0.805268	+	1.29574i
$797$	2.39587e7			1.33603			0.668016	−	0.744147i	$-0.267144\pi$
$797$	2.39587e7			1.33603			0.668016	+	0.744147i	$0.267144\pi$
$798$	1.06579e7	−	5.92483e6i	0.592469	−	0.329358i
$799$	−2.38666e7			−1.32259
$800$		0			0
$801$	−7.98553e6			−0.439767
$802$	4.71140e6	−	2.61911e6i	0.258651	−	0.143786i
$803$	2.78730e6			0.152544
$804$	−1.10841e7	+	1.78351e7i	−0.604727	+	0.973051i
$805$		0			0
$806$	−1.95054e7	+	1.08432e7i	−1.05759	+	0.587924i
$807$			3.34992e7i			1.81072i
$808$	8.92736e6	+	435035.i	0.481055	+	0.0234420i
$809$	−1.61175e7			−0.865816			−0.432908	−	0.901438i	$-0.642513\pi$
$809$	−1.61175e7			−0.865816			−0.432908	+	0.901438i	$0.642513\pi$
$810$		0			0
$811$		−	2.80711e6i		−	0.149868i	−0.997189	−	0.0749338i	$-0.976125\pi$
$811$		−	2.80711e6i		−	0.149868i	0.997189	−	0.0749338i	$-0.0238745\pi$
$812$	1.11631e6	−	1.79623e6i	0.0594148	−	0.0956029i
$813$	−2.55813e7			−1.35736
$814$	9.48827e6	+	1.70680e7i	0.501910	+	0.902865i
$815$		0			0
$816$	2.38542e7	−	1.17792e7i	1.25412	−	0.619285i
$817$		−	1.21405e7i		−	0.636331i
$818$	1.04846e7	−	5.82846e6i	0.547857	−	0.304558i
$819$		−	1.16202e7i		−	0.605345i
$820$		0			0
$821$			5.03447e6i			0.260673i	0.991470	+	0.130336i	$0.0416058\pi$
$821$			5.03447e6i			0.260673i	−0.991470	+	0.130336i	$0.958394\pi$
$822$	−1.20809e7	−	2.17317e7i	−0.623617	−	1.12180i
$823$			1.84102e6i			0.0947458i	0.998877	+	0.0473729i	$0.0150849\pi$
$823$			1.84102e6i			0.0947458i	−0.998877	+	0.0473729i	$0.984915\pi$
$824$	−1.19877e7	−	584165.i	−0.615059	−	0.0299721i
$825$		0			0
$826$	8.30357e6	−	4.61602e6i	0.423462	−	0.235406i
$827$	5.00894e6			0.254673			0.127336	−	0.991860i	$-0.459357\pi$
$827$	5.00894e6			0.254673			0.127336	+	0.991860i	$0.459357\pi$
$828$	7.28987e6	+	4.53047e6i	0.369525	+	0.229650i
$829$			4.22051e6i			0.213294i	0.994297	+	0.106647i	$0.0340115\pi$
$829$			4.22051e6i			0.213294i	−0.994297	+	0.106647i	$0.965989\pi$
$830$		0			0
$831$	−6.07484e6			−0.305163
$832$	3.07449e7	+	3.00357e6i	1.53980	+	0.150428i
$833$		−	1.68158e7i		−	0.839665i
$834$	1.45268e7	+	2.61316e7i	0.723192	+	1.30092i
$835$		0			0
$836$	9.24606e6	−	1.48776e7i	0.457553	−	0.736237i
$837$	6.74610e6			0.332843
$838$	8.98326e6	+	1.61596e7i	0.441900	+	0.794915i
$839$	−1.53769e7			−0.754160			−0.377080	−	0.926181i	$-0.623072\pi$
$839$	−1.53769e7			−0.754160			−0.377080	+	0.926181i	$0.623072\pi$
$840$		0			0
$841$	1.77224e7			0.864036
$842$	1.24726e7	+	2.24365e7i	0.606286	+	1.09062i
$843$	9.90923e6			0.480254
$844$	−6.14960e6	−	3.82182e6i	−0.297160	−	0.184677i
$845$		0			0
$846$	1.85177e7	+	3.33107e7i	0.889532	+	1.60014i
$847$			4.15749e6i			0.199123i
$848$	−6.78300e6	−	1.37363e7i	−0.323916	−	0.655965i
$849$	−1.36890e6			−0.0651782
$850$		0			0
$851$		−	1.25627e7i		−	0.594645i
$852$	−1.68612e7	+	2.71309e7i	−0.795773	+	1.28046i
$853$	−1.53932e7			−0.724361			−0.362181	−	0.932108i	$-0.617968\pi$
$853$	−1.53932e7			−0.724361			−0.362181	+	0.932108i	$0.617968\pi$
$854$	6.10124e6	−	3.39173e6i	0.286269	−	0.159139i
$855$		0			0
$856$	−1.34336e6	+	2.75672e7i	−0.0626627	+	1.28590i
$857$		−	1.26331e7i		−	0.587566i	−0.955872	−	0.293783i	$-0.905086\pi$
$857$		−	1.26331e7i		−	0.587566i	0.955872	−	0.293783i	$-0.0949143\pi$
$858$	−1.44381e7	−	2.59721e7i	−0.669564	−	1.20445i
$859$		−	2.76353e7i		−	1.27786i	−0.769266	−	0.638928i	$-0.779378\pi$
$859$		−	2.76353e7i		−	1.27786i	0.769266	−	0.638928i	$-0.220622\pi$
$860$		0			0
$861$			1.86547e7i			0.857589i
$862$	2.15646e7	−	1.19879e7i	0.988492	−	0.549511i
$863$			3.43800e7i			1.57137i	0.618626	+	0.785685i	$0.287689\pi$
$863$			3.43800e7i			1.57137i	−0.618626	+	0.785685i	$0.712311\pi$
$864$	−7.68193e6	−	5.30925e6i	−0.350095	−	0.241963i
$865$		0			0
$866$	−9.92904e6	−	1.78609e7i	−0.449897	−	0.809300i
$867$	−4.76806e6			−0.215424
$868$	−4.50115e6	−	2.79735e6i	−0.202779	−	0.126022i
$869$			1.65343e7i			0.742741i
$870$		0			0
$871$	−2.62721e7			−1.17341
$872$	−2.36555e7	−	1.15275e6i	−1.05352	−	0.0513384i
$873$			4.71897e7i			2.09562i
$874$	−9.84913e6	+	5.47522e6i	−0.436133	+	0.242450i
$875$		0			0
$876$	7.53817e6	+	4.68478e6i	0.331899	+	0.206266i
$877$	−1.99177e7			−0.874459			−0.437229	−	0.899350i	$-0.644040\pi$
$877$	−1.99177e7			−0.874459			−0.437229	+	0.899350i	$0.644040\pi$
$878$	−1.15154e7	+	6.40151e6i	−0.504131	+	0.280250i
$879$	2.99391e7			1.30697
$880$		0			0
$881$	−819934.			−0.0355909			−0.0177955	−	0.999842i	$-0.505665\pi$
$881$	−819934.			−0.0355909			−0.0177955	+	0.999842i	$0.505665\pi$
$882$	−2.34700e7	+	1.30471e7i	−1.01588	+	0.564734i
$883$	437377.			0.0188779			0.00943897	−	0.999955i	$-0.496995\pi$
$883$	437377.			0.0188779			0.00943897	+	0.999955i	$0.496995\pi$
$884$	2.82702e7	+	1.75692e7i	1.21674	+	0.756174i
$885$		0			0
$886$	−6.41032e6	+	3.56355e6i	−0.274344	+	0.152510i
$887$			2.96543e7i			1.26555i	0.774337	+	0.632774i	$0.218084\pi$
$887$			2.96543e7i			1.26555i	−0.774337	+	0.632774i	$0.781916\pi$
$888$	−3.02653e6	+	6.21076e7i	−0.128799	+	2.64309i
$889$	8.13537e6			0.345241
$890$		0			0
$891$		−	8.92737e6i		−	0.376729i
$892$	3.80922e7	+	2.36733e7i	1.60296	+	0.996200i
$893$	−5.00375e7			−2.09975
$894$	−9.81275e6	−	1.76517e7i	−0.410627	−	0.738659i
$895$		0			0
$896$	2.92401e6	+	6.72785e6i	0.121677	+	0.279966i
$897$			1.91164e7i			0.793275i
$898$	−3.27021e7	+	1.81794e7i	−1.35327	+	0.752295i
$899$			6.98839e6i			0.288388i
$900$		0			0
$901$		−	1.65068e7i		−	0.677409i
$902$	1.30202e7	+	2.34215e7i	0.532846	+	0.958514i
$903$		−	4.89080e6i		−	0.199600i
$904$	2.97790e7	+	1.45115e6i	1.21196	+	0.0590595i
$905$		0			0
$906$	−2.43791e7	+	1.35525e7i	−0.986727	+	0.548530i
$907$	1.21751e6			0.0491421			0.0245711	−	0.999698i	$-0.492178\pi$
$907$	1.21751e6			0.0491421			0.0245711	+	0.999698i	$0.492178\pi$
$908$	1.16904e7	−	1.88107e7i	0.470558	−	0.757164i
$909$		−	1.53786e7i		−	0.617317i
$910$		0			0
$911$	−1.22742e7			−0.490001			−0.245000	−	0.969523i	$-0.578788\pi$
$911$	−1.22742e7			−0.490001			−0.245000	+	0.969523i	$0.578788\pi$
$912$	5.00114e7	−	2.46957e7i	1.99105	−	0.983183i
$913$			1.52729e6i			0.0606378i
$914$	−2.59419e6	−	4.66659e6i	−0.102716	−	0.184771i
$915$		0			0
$916$	1.06207e7	+	6.60052e6i	0.418231	+	0.259920i
$917$	−5.26301e6			−0.206686
$918$	−4.88874e6	−	8.79415e6i	−0.191465	−	0.344419i
$919$	−6.26903e6			−0.244856			−0.122428	−	0.992477i	$-0.539068\pi$
$919$	−6.26903e6			−0.244856			−0.122428	+	0.992477i	$0.539068\pi$
$920$		0			0
$921$	−4.93606e7			−1.91748
$922$	−9.76102e6	−	1.75587e7i	−0.378153	−	0.680244i
$923$	−3.99653e7			−1.54411
$924$	3.72476e6	−	5.99342e6i	0.143522	−	0.230938i
$925$		0			0
$926$	−4.55391e6	−	8.19184e6i	−0.174525	−	0.313945i
$927$			2.06505e7i			0.789278i
$928$	5.49993e6	−	7.95782e6i	0.209646	−	0.303336i
$929$	3.64800e7			1.38681			0.693403	−	0.720550i	$-0.256110\pi$
$929$	3.64800e7			1.38681			0.693403	+	0.720550i	$0.256110\pi$
$930$		0			0
$931$		−	3.52553e7i		−	1.33306i
$932$	1.66481e7	+	1.03463e7i	0.627804	+	0.390164i
$933$	−1.97333e6			−0.0742157
$934$	8.65401e6	−	4.81084e6i	0.324601	−	0.180449i
$935$		0			0
$936$	2.58703e6	−	5.30886e7i	0.0965189	−	1.98067i
$937$		−	2.63533e7i		−	0.980585i	−0.871558	−	0.490293i	$-0.836890\pi$
$937$		−	2.63533e7i		−	0.980585i	0.871558	−	0.490293i	$-0.163110\pi$
$938$	−3.03132e6	−	5.45292e6i	−0.112493	−	0.202359i
$939$		−	1.89260e7i		−	0.700478i
$940$		0			0
$941$			4.53926e7i			1.67113i	0.549388	+	0.835567i	$0.314861\pi$
$941$			4.53926e7i			1.67113i	−0.549388	+	0.835567i	$0.685139\pi$
$942$	−1.88063e7	+	1.04546e7i	−0.690521	+	0.383866i
$943$		−	1.72390e7i		−	0.631297i
$944$	3.89638e7	−	1.92404e7i	1.42309	−	0.702722i
$945$		0			0
$946$	−3.41358e6	−	6.14055e6i	−0.124017	−	0.223090i
$947$	4.83840e7			1.75318			0.876590	−	0.481237i	$-0.159813\pi$
$947$	4.83840e7			1.75318			0.876590	+	0.481237i	$0.159813\pi$
$948$	−2.77903e7	+	4.47167e7i	−1.00432	+	1.61603i
$949$			1.11041e7i			0.400238i
$950$		0			0
$951$	7.00985e6			0.251338
$952$	−384718.	+	7.89482e6i	−0.0137578	+	0.282325i
$953$		−	1.20828e7i		−	0.430957i	−0.976509	−	0.215479i	$-0.930869\pi$
$953$		−	1.20828e7i		−	0.430957i	0.976509	−	0.215479i	$-0.0691312\pi$
$954$	−2.30386e7	+	1.28074e7i	−0.819569	+	0.455605i
$955$		0			0
$956$	2.15249e7	−	3.46353e7i	0.761724	−	1.22567i
$957$	−9.30526e6			−0.328435
$958$	2.49323e7	−	1.38601e7i	0.877706	−	0.487924i
$959$	7.38721e6			0.259379
$960$		0			0
$961$	−1.11170e7			−0.388312
$962$	−6.79962e7	+	3.77997e7i	−2.36890	+	1.31689i
$963$	4.74884e7			1.65014
$964$	7.37206e6	−	1.18622e7i	0.255503	−	0.411124i
$965$		0			0
$966$	−3.96771e6	+	2.20568e6i	−0.136803	+	0.0760502i
$967$			1.03344e7i			0.355403i	0.984084	+	0.177702i	$0.0568662\pi$
$967$			1.03344e7i			0.355403i	−0.984084	+	0.177702i	$0.943134\pi$
$968$	−925593.	+	1.89941e7i	−0.0317491	+	0.651525i
$969$	6.00983e7			2.05614
$970$		0			0
$971$			2.55375e7i			0.869221i	0.900619	+	0.434610i	$0.143114\pi$
$971$			2.55375e7i			0.869221i	−0.900619	+	0.434610i	$0.856886\pi$
$972$	2.16215e7	−	3.47907e7i	0.734042	−	1.18113i
$973$	−8.88283e6			−0.300794
$974$	−2.17117e7	−	3.90562e7i	−0.733324	−	1.31915i
$975$		0			0
$976$	2.86296e7	−	1.41373e7i	0.962034	−	0.475054i
$977$		−	3.91421e7i		−	1.31192i	−0.754796	−	0.655960i	$-0.772264\pi$
$977$		−	3.91421e7i		−	1.31192i	0.754796	−	0.655960i	$-0.227736\pi$
$978$	6.38836e6	−	3.55134e6i	0.213571	−	0.118726i
$979$		−	6.06715e6i		−	0.202315i
$980$		0			0
$981$			4.07500e7i			1.35193i
$982$	1.08049e6	+	1.94365e6i	0.0357555	+	0.0643191i
$983$		−	1.53449e7i		−	0.506501i	−0.967401	−	0.253250i	$-0.918500\pi$
$983$		−	1.53449e7i		−	0.506501i	0.967401	−	0.253250i	$-0.0814996\pi$
$984$	−4.15314e6	+	8.52267e7i	−0.136738	+	2.80600i
$985$		0			0
$986$	9.10998e6	−	5.06432e6i	0.298418	−	0.165893i
$987$	−2.01575e7			−0.658635
$988$	5.92699e7	+	3.68347e7i	1.93171	+	1.20051i
$989$			4.51965e6i			0.146931i
$990$		0			0
$991$	−1.46946e7			−0.475306			−0.237653	−	0.971350i	$-0.576378\pi$
$991$	−1.46946e7			−0.475306			−0.237653	+	0.971350i	$0.576378\pi$
$992$	−1.99414e7	−	1.37822e7i	−0.643393	−	0.444672i
$993$		−	4.19435e7i		−	1.34987i
$994$	−4.61128e6	−	8.29503e6i	−0.148032	−	0.266288i
$995$		0			0
$996$	−2.56700e6	+	4.13050e6i	−0.0819932	+	0.131933i
$997$	−3.18523e7			−1.01485			−0.507426	−	0.861695i	$-0.669403\pi$
$997$	−3.18523e7			−1.01485			−0.507426	+	0.861695i	$0.669403\pi$
$998$	5.77170e6	+	1.03825e7i	0.183433	+	0.329970i
$999$	2.35170e7			0.745536

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.f.d.149.8		40
4.3	odd	2		800.6.f.d.49.36		40
5.2	odd	4		200.6.d.c.101.7	✓	20
5.3	odd	4		200.6.d.d.101.14	yes	20
5.4	even	2	inner	200.6.f.d.149.33		40
8.3	odd	2		800.6.f.d.49.6		40
8.5	even	2	inner	200.6.f.d.149.34		40
20.3	even	4		800.6.d.b.401.18		20
20.7	even	4		800.6.d.d.401.3		20
20.19	odd	2		800.6.f.d.49.5		40
40.3	even	4		800.6.d.b.401.3		20
40.13	odd	4		200.6.d.d.101.13	yes	20
40.19	odd	2		800.6.f.d.49.35		40
40.27	even	4		800.6.d.d.401.18		20
40.29	even	2	inner	200.6.f.d.149.7		40
40.37	odd	4		200.6.d.c.101.8	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.6.d.c.101.7	✓	20	5.2	odd	4
200.6.d.c.101.8	yes	20	40.37	odd	4
200.6.d.d.101.13	yes	20	40.13	odd	4
200.6.d.d.101.14	yes	20	5.3	odd	4
200.6.f.d.149.7		40	40.29	even	2	inner
200.6.f.d.149.8		40	1.1	even	1	trivial
200.6.f.d.149.33		40	5.4	even	2	inner
200.6.f.d.149.34		40	8.5	even	2	inner
800.6.d.b.401.3		20	40.3	even	4
800.6.d.b.401.18		20	20.3	even	4
800.6.d.d.401.3		20	20.7	even	4
800.6.d.d.401.18		20	40.27	even	4
800.6.f.d.49.5		40	20.19	odd	2
800.6.f.d.49.6		40	8.3	odd	2
800.6.f.d.49.35		40	40.19	odd	2
800.6.f.d.49.36		40	4.3	odd	2

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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	200.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.94424 + 2.74854i) q^{2} -23.5470 q^{3} +(16.8910 - 27.1789i) q^{4} +(116.422 - 64.7200i) q^{6} +39.5751i q^{7} +(-8.81071 + 180.805i) q^{8} +311.462 q^{9} +O(q^{10})\)	\(q+(-4.94424 + 2.74854i) q^{2} -23.5470 q^{3} +(16.8910 - 27.1789i) q^{4} +(116.422 - 64.7200i) q^{6} +39.5751i q^{7} +(-8.81071 + 180.805i) q^{8} +311.462 q^{9} +236.639i q^{11} +(-397.733 + 639.982i) q^{12} -942.728 q^{13} +(-108.774 - 195.669i) q^{14} +(-453.388 - 918.159i) q^{16} -1103.34i q^{17} +(-1539.94 + 856.066i) q^{18} -2313.21i q^{19} -931.874i q^{21} +(-650.411 - 1170.00i) q^{22} +861.158i q^{23} +(207.466 - 4257.41i) q^{24} +(4661.07 - 2591.13i) q^{26} -1612.07 q^{27} +(1075.61 + 668.463i) q^{28} -1669.97i q^{29} -4184.75 q^{31} +(4765.26 + 3293.44i) q^{32} -5572.13i q^{33} +(3032.59 + 5455.19i) q^{34} +(5260.90 - 8465.19i) q^{36} -14588.1 q^{37} +(6357.97 + 11437.1i) q^{38} +22198.4 q^{39} -20018.4 q^{41} +(2561.30 + 4607.41i) q^{42} +5248.34 q^{43} +(6431.58 + 3997.06i) q^{44} +(-2366.93 - 4257.77i) q^{46} -21631.2i q^{47} +(10675.9 + 21619.9i) q^{48} +15240.8 q^{49} +25980.4i q^{51} +(-15923.6 + 25622.3i) q^{52} +14960.7 q^{53} +(7970.46 - 4430.84i) q^{54} +(-7155.36 - 348.684i) q^{56} +54469.3i q^{57} +(4589.97 + 8256.71i) q^{58} +42436.9i q^{59} +31181.5i q^{61} +(20690.4 - 11502.0i) q^{62} +12326.1i q^{63} +(-32612.7 - 3186.04i) q^{64} +(15315.2 + 27549.9i) q^{66} +27868.1 q^{67} +(-29987.7 - 18636.6i) q^{68} -20277.7i q^{69} +42393.2 q^{71} +(-2744.20 + 56313.8i) q^{72} -11778.7i q^{73} +(72127.1 - 40096.1i) q^{74} +(-62870.6 - 39072.5i) q^{76} -9364.98 q^{77} +(-109754. + 61013.4i) q^{78} +69871.7 q^{79} -37725.8 q^{81} +(98975.9 - 55021.5i) q^{82} +6454.09 q^{83} +(-25327.3 - 15740.3i) q^{84} +(-25949.1 + 14425.3i) q^{86} +39322.7i q^{87} +(-42785.4 - 2084.95i) q^{88} -25638.9 q^{89} -37308.5i q^{91} +(23405.3 + 14545.8i) q^{92} +98538.3 q^{93} +(59454.2 + 106950. i) q^{94} +(-112208. - 77550.7i) q^{96} +151510. i q^{97} +(-75354.2 + 41890.1i) q^{98} +73703.8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9}+O(q^{10}) \) 40 * q - 2 * q^4 + 66 * q^6 + 3240 * q^9	\( 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9} + 848 q^{14} - 110 q^{16} - 18918 q^{24} + 18344 q^{26} + 14320 q^{31} + 19182 q^{34} + 29656 q^{36} - 44904 q^{39} - 11608 q^{41} + 23186 q^{44} - 75224 q^{46} - 125304 q^{49} - 177894 q^{54} - 73816 q^{56} - 230354 q^{64} + 262878 q^{66} - 15448 q^{71} - 4224 q^{74} + 111902 q^{76} + 15560 q^{79} + 193968 q^{81} + 195112 q^{84} - 131972 q^{86} + 6320 q^{89} + 117080 q^{94} + 115582 q^{96}+O(q^{100}) \) 40 * q - 2 * q^4 + 66 * q^6 + 3240 * q^9 + 848 * q^14 - 110 * q^16 - 18918 * q^24 + 18344 * q^26 + 14320 * q^31 + 19182 * q^34 + 29656 * q^36 - 44904 * q^39 - 11608 * q^41 + 23186 * q^44 - 75224 * q^46 - 125304 * q^49 - 177894 * q^54 - 73816 * q^56 - 230354 * q^64 + 262878 * q^66 - 15448 * q^71 - 4224 * q^74 + 111902 * q^76 + 15560 * q^79 + 193968 * q^81 + 195112 * q^84 - 131972 * q^86 + 6320 * q^89 + 117080 * q^94 + 115582 * q^96

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