LMFDB - Embedded newform 230.5.d.a.91.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,5,Mod(91,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("230.91");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	230.d (of order $2$, degree $1$, 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:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.20
Character	$\chi$	$=$	230.91
Dual form			230.5.d.a.91.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.82843 q^{2} -2.20532 q^{3} +8.00000 q^{4} -11.1803i q^{5} -6.23758 q^{6} -53.7736i q^{7} +22.6274 q^{8} -76.1366 q^{9} +O(q^{10})$	\(q+2.82843 q^{2} -2.20532 q^{3} +8.00000 q^{4} -11.1803i q^{5} -6.23758 q^{6} -53.7736i q^{7} +22.6274 q^{8} -76.1366 q^{9} -31.6228i q^{10} +91.7745i q^{11} -17.6425 q^{12} -249.593 q^{13} -152.095i q^{14} +24.6562i q^{15} +64.0000 q^{16} +211.972i q^{17} -215.347 q^{18} -160.839i q^{19} -89.4427i q^{20} +118.588i q^{21} +259.578i q^{22} +(-18.3241 + 528.683i) q^{23} -49.9006 q^{24} -125.000 q^{25} -705.956 q^{26} +346.536 q^{27} -430.189i q^{28} -994.498 q^{29} +69.7383i q^{30} -547.649 q^{31} +181.019 q^{32} -202.392i q^{33} +599.547i q^{34} -601.207 q^{35} -609.093 q^{36} -1811.16i q^{37} -454.921i q^{38} +550.433 q^{39} -252.982i q^{40} -2491.55 q^{41} +335.417i q^{42} -941.560i q^{43} +734.196i q^{44} +851.233i q^{45} +(-51.8285 + 1495.34i) q^{46} -590.911 q^{47} -141.140 q^{48} -490.597 q^{49} -353.553 q^{50} -467.465i q^{51} -1996.75 q^{52} +487.435i q^{53} +980.152 q^{54} +1026.07 q^{55} -1216.76i q^{56} +354.701i q^{57} -2812.87 q^{58} -1918.19 q^{59} +197.250i q^{60} -418.982i q^{61} -1548.98 q^{62} +4094.14i q^{63} +512.000 q^{64} +2790.54i q^{65} -572.451i q^{66} -2909.93i q^{67} +1695.78i q^{68} +(40.4106 - 1165.91i) q^{69} -1700.47 q^{70} +1037.53 q^{71} -1722.77 q^{72} +665.030 q^{73} -5122.75i q^{74} +275.665 q^{75} -1286.71i q^{76} +4935.05 q^{77} +1556.86 q^{78} -6965.66i q^{79} -715.542i q^{80} +5402.84 q^{81} -7047.17 q^{82} +6456.07i q^{83} +948.703i q^{84} +2369.92 q^{85} -2663.13i q^{86} +2193.18 q^{87} +2076.62i q^{88} -4579.57i q^{89} +2407.65i q^{90} +13421.5i q^{91} +(-146.593 + 4229.46i) q^{92} +1207.74 q^{93} -1671.35 q^{94} -1798.23 q^{95} -399.205 q^{96} +2681.09i q^{97} -1387.62 q^{98} -6987.40i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9}+O(q^{10}) $ 32 * q + 256 * q^4 + 64 * q^6 + 832 * q^9	$ 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9} - 408 q^{13} + 2048 q^{16} + 1024 q^{18} + 1332 q^{23} + 512 q^{24} - 4000 q^{25} + 2208 q^{27} + 3732 q^{29} - 412 q^{31} + 300 q^{35} + 6656 q^{36} - 9208 q^{39} - 6156 q^{41} + 4480 q^{46} + 5184 q^{47} - 13820 q^{49} - 3264 q^{52} - 3328 q^{54} - 6000 q^{55} + 3200 q^{58} - 30468 q^{59} - 10752 q^{62} + 16384 q^{64} - 1168 q^{69} + 4800 q^{70} - 37644 q^{71} + 8192 q^{72} + 19984 q^{73} + 27528 q^{77} + 15744 q^{78} + 69056 q^{81} - 17408 q^{82} + 3300 q^{85} + 28936 q^{87} + 10656 q^{92} + 40648 q^{93} - 23808 q^{94} - 21600 q^{95} + 4096 q^{96} + 43008 q^{98}+O(q^{100}) $ 32 * q + 256 * q^4 + 64 * q^6 + 832 * q^9 - 408 * q^13 + 2048 * q^16 + 1024 * q^18 + 1332 * q^23 + 512 * q^24 - 4000 * q^25 + 2208 * q^27 + 3732 * q^29 - 412 * q^31 + 300 * q^35 + 6656 * q^36 - 9208 * q^39 - 6156 * q^41 + 4480 * q^46 + 5184 * q^47 - 13820 * q^49 - 3264 * q^52 - 3328 * q^54 - 6000 * q^55 + 3200 * q^58 - 30468 * q^59 - 10752 * q^62 + 16384 * q^64 - 1168 * q^69 + 4800 * q^70 - 37644 * q^71 + 8192 * q^72 + 19984 * q^73 + 27528 * q^77 + 15744 * q^78 + 69056 * q^81 - 17408 * q^82 + 3300 * q^85 + 28936 * q^87 + 10656 * q^92 + 40648 * q^93 - 23808 * q^94 - 21600 * q^95 + 4096 * q^96 + 43008 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$47$	$51$
$\chi(n)$	$1$	$-1$

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 $

$2$	2.82843			0.707107
$2$	2.82843			0.707107
$3$	−2.20532			−0.245035			−0.122518	−	0.992466i	$-0.539097\pi$
$3$	−2.20532			−0.245035			−0.122518	+	0.992466i	$0.539097\pi$
$4$	8.00000			0.500000
$5$		−	11.1803i		−	0.447214i
$5$		−	11.1803i		−	0.447214i
$6$	−6.23758			−0.173266
$7$		−	53.7736i		−	1.09742i	−0.836013	−	0.548710i	$-0.815119\pi$
$7$		−	53.7736i		−	1.09742i	0.836013	−	0.548710i	$-0.184881\pi$
$8$	22.6274			0.353553
$9$	−76.1366			−0.939958
$10$		−	31.6228i		−	0.316228i
$11$			91.7745i			0.758467i	0.925301	+	0.379234i	$0.123812\pi$
$11$			91.7745i			0.758467i	−0.925301	+	0.379234i	$0.876188\pi$
$12$	−17.6425			−0.122518
$13$	−249.593			−1.47688			−0.738442	−	0.674317i	$-0.764438\pi$
$13$	−249.593			−1.47688			−0.738442	+	0.674317i	$0.764438\pi$
$14$		−	152.095i		−	0.775993i
$15$			24.6562i			0.109583i
$16$	64.0000			0.250000
$17$			211.972i			0.733467i	0.930326	+	0.366733i	$0.119524\pi$
$17$			211.972i			0.733467i	−0.930326	+	0.366733i	$0.880476\pi$
$18$	−215.347			−0.664650
$19$		−	160.839i		−	0.445537i	−0.974871	−	0.222768i	$-0.928491\pi$
$19$		−	160.839i		−	0.445537i	0.974871	−	0.222768i	$-0.0715094\pi$
$20$		−	89.4427i		−	0.223607i
$21$			118.588i			0.268907i
$22$			259.578i			0.536317i
$23$	−18.3241	+	528.683i	−0.0346392	+	0.999400i
$23$	−18.3241	+	528.683i	−0.0346392	+	0.999400i
$24$	−49.9006			−0.0866331
$25$	−125.000			−0.200000
$26$	−705.956			−1.04431
$27$	346.536			0.475358
$28$		−	430.189i		−	0.548710i
$29$	−994.498			−1.18252			−0.591259	−	0.806481i	$-0.701369\pi$
$29$	−994.498			−1.18252			−0.591259	+	0.806481i	$0.701369\pi$
$30$			69.7383i			0.0774870i
$31$	−547.649			−0.569874			−0.284937	−	0.958546i	$-0.591973\pi$
$31$	−547.649			−0.569874			−0.284937	+	0.958546i	$0.591973\pi$
$32$	181.019			0.176777
$33$		−	202.392i		−	0.185851i
$34$			599.547i			0.518639i
$35$	−601.207			−0.490781
$36$	−609.093			−0.469979
$37$		−	1811.16i		−	1.32298i	−0.749952	−	0.661492i	$-0.769924\pi$
$37$		−	1811.16i		−	1.32298i	0.749952	−	0.661492i	$-0.230076\pi$
$38$		−	454.921i		−	0.315042i
$39$	550.433			0.361889
$40$		−	252.982i		−	0.158114i
$41$	−2491.55			−1.48218			−0.741092	−	0.671403i	$-0.765692\pi$
$41$	−2491.55			−1.48218			−0.741092	+	0.671403i	$0.765692\pi$
$42$			335.417i			0.190146i
$43$		−	941.560i		−	0.509227i	−0.967043	−	0.254613i	$-0.918052\pi$
$43$		−	941.560i		−	0.509227i	0.967043	−	0.254613i	$-0.0819482\pi$
$44$			734.196i			0.379234i
$45$			851.233i			0.420362i
$46$	−51.8285	+	1495.34i	−0.0244936	+	0.706682i
$47$	−590.911			−0.267502			−0.133751	−	0.991015i	$-0.542702\pi$
$47$	−590.911			−0.267502			−0.133751	+	0.991015i	$0.542702\pi$
$48$	−141.140			−0.0612588
$49$	−490.597			−0.204330
$50$	−353.553			−0.141421
$51$		−	467.465i		−	0.179725i
$52$	−1996.75			−0.738442
$53$			487.435i			0.173526i	0.996229	+	0.0867631i	$0.0276523\pi$
$53$			487.435i			0.173526i	−0.996229	+	0.0867631i	$0.972348\pi$
$54$	980.152			0.336129
$55$	1026.07			0.339197
$56$		−	1216.76i		−	0.387997i
$57$			354.701i			0.109172i
$58$	−2812.87			−0.836167
$59$	−1918.19			−0.551046			−0.275523	−	0.961294i	$-0.588851\pi$
$59$	−1918.19			−0.551046			−0.275523	+	0.961294i	$0.588851\pi$
$60$			197.250i			0.0547916i
$61$		−	418.982i		−	0.112599i	−0.998414	−	0.0562997i	$-0.982070\pi$
$61$		−	418.982i		−	0.112599i	0.998414	−	0.0562997i	$-0.0179302\pi$
$62$	−1548.98			−0.402962
$63$			4094.14i			1.03153i
$64$	512.000			0.125000
$65$			2790.54i			0.660482i
$66$		−	572.451i		−	0.131417i
$67$		−	2909.93i		−	0.648235i	−0.946017	−	0.324117i	$-0.894933\pi$
$67$		−	2909.93i		−	0.648235i	0.946017	−	0.324117i	$-0.105067\pi$
$68$			1695.78i			0.366733i
$69$	40.4106	−	1165.91i	0.00848783	−	0.244888i
$70$	−1700.47			−0.347035
$71$	1037.53			0.205818			0.102909	−	0.994691i	$-0.467185\pi$
$71$	1037.53			0.205818			0.102909	+	0.994691i	$0.467185\pi$
$72$	−1722.77			−0.332325
$73$	665.030			0.124794			0.0623972	−	0.998051i	$-0.480125\pi$
$73$	665.030			0.124794			0.0623972	+	0.998051i	$0.480125\pi$
$74$		−	5122.75i		−	0.935491i
$75$	275.665			0.0490071
$76$		−	1286.71i		−	0.222768i
$77$	4935.05			0.832357
$78$	1556.86			0.255894
$79$		−	6965.66i		−	1.11611i	−0.829803	−	0.558056i	$-0.811547\pi$
$79$		−	6965.66i		−	1.11611i	0.829803	−	0.558056i	$-0.188453\pi$
$80$		−	715.542i		−	0.111803i
$81$	5402.84			0.823478
$82$	−7047.17			−1.04806
$83$			6456.07i			0.937156i	0.883422	+	0.468578i	$0.155234\pi$
$83$			6456.07i			0.937156i	−0.883422	+	0.468578i	$0.844766\pi$
$84$			948.703i			0.134453i
$85$	2369.92			0.328016
$86$		−	2663.13i		−	0.360078i
$87$	2193.18			0.289759
$88$			2076.62i			0.268159i
$89$		−	4579.57i		−	0.578156i	−0.957306	−	0.289078i	$-0.906651\pi$
$89$		−	4579.57i		−	0.578156i	0.957306	−	0.289078i	$-0.0933486\pi$
$90$			2407.65i			0.297241i
$91$			13421.5i			1.62076i
$92$	−146.593	+	4229.46i	−0.0173196	+	0.499700i
$93$	1207.74			0.139639
$94$	−1671.35			−0.189152
$95$	−1798.23			−0.199250
$96$	−399.205			−0.0433165
$97$			2681.09i			0.284950i	0.989798	+	0.142475i	$0.0455060\pi$
$97$			2681.09i			0.284950i	−0.989798	+	0.142475i	$0.954494\pi$
$98$	−1387.62			−0.144483
$99$		−	6987.40i		−	0.712927i
$100$	−1000.00			−0.100000
$101$	15327.8			1.50258			0.751290	−	0.659972i	$-0.229432\pi$
$101$	15327.8			1.50258			0.751290	+	0.659972i	$0.229432\pi$
$102$		−	1322.19i		−	0.127085i
$103$		−	3617.08i		−	0.340945i	−0.985362	−	0.170472i	$-0.945471\pi$
$103$		−	3617.08i		−	0.340945i	0.985362	−	0.170472i	$-0.0545294\pi$
$104$	−5647.65			−0.522157
$105$	1325.85			0.120259
$106$			1378.68i			0.122702i
$107$		−	2714.02i		−	0.237053i	−0.992951	−	0.118527i	$-0.962183\pi$
$107$		−	2714.02i		−	0.237053i	0.992951	−	0.118527i	$-0.0378171\pi$
$108$	2772.29			0.237679
$109$		−	6708.24i		−	0.564619i	−0.959323	−	0.282310i	$-0.908899\pi$
$109$		−	6708.24i		−	0.564619i	0.959323	−	0.282310i	$-0.0911006\pi$
$110$	2902.17			0.239848
$111$			3994.19i			0.324178i
$112$		−	3441.51i		−	0.274355i
$113$		−	7559.66i		−	0.592032i	−0.955183	−	0.296016i	$-0.904342\pi$
$113$		−	7559.66i		−	0.592032i	0.955183	−	0.296016i	$-0.0956582\pi$
$114$			1003.24i			0.0771964i
$115$	5910.85	+	204.870i	0.446945	+	0.0154911i
$116$	−7955.99			−0.591259
$117$	19003.2			1.38821
$118$	−5425.46			−0.389648
$119$	11398.5			0.804921
$120$			557.906i			0.0387435i
$121$	6218.43			0.424727
$122$		−	1185.06i		−	0.0796198i
$123$	5494.66			0.363187
$124$	−4381.19			−0.284937
$125$			1397.54i			0.0894427i
$126$			11580.0i			0.729401i
$127$	−17443.7			−1.08151			−0.540757	−	0.841179i	$-0.681862\pi$
$127$	−17443.7			−1.08151			−0.540757	+	0.841179i	$0.681862\pi$
$128$	1448.15			0.0883883
$129$			2076.44i			0.124779i
$130$			7892.83i			0.467032i
$131$	−17703.5			−1.03161			−0.515807	−	0.856705i	$-0.672508\pi$
$131$	−17703.5			−1.03161			−0.515807	+	0.856705i	$0.672508\pi$
$132$		−	1619.14i		−	0.0929256i
$133$	−8648.88			−0.488941
$134$		−	8230.52i		−	0.458371i
$135$		−	3874.39i		−	0.212587i
$136$			4796.38i			0.259320i
$137$			26053.5i			1.38811i	0.719921	+	0.694056i	$0.244178\pi$
$137$			26053.5i			1.38811i	−0.719921	+	0.694056i	$0.755822\pi$
$138$	114.298	−	3297.70i	0.00600180	−	0.173162i
$139$	835.955			0.0432667			0.0216333	−	0.999766i	$-0.493113\pi$
$139$	835.955			0.0432667			0.0216333	+	0.999766i	$0.493113\pi$
$140$	−4809.65			−0.245391
$141$	1303.15			0.0655473
$142$	2934.58			0.145536
$143$		−	22906.3i		−	1.12017i
$144$	−4872.74			−0.234989
$145$			11118.8i			0.528838i
$146$	1880.99			0.0882430
$147$	1081.92			0.0500682
$148$		−	14489.3i		−	0.661492i
$149$		−	17048.6i		−	0.767919i	−0.923350	−	0.383960i	$-0.874560\pi$
$149$		−	17048.6i		−	0.767919i	0.923350	−	0.383960i	$-0.125440\pi$
$150$	779.698			0.0346532
$151$	−8853.42			−0.388291			−0.194146	−	0.980973i	$-0.562193\pi$
$151$	−8853.42			−0.388291			−0.194146	+	0.980973i	$0.562193\pi$
$152$		−	3639.37i		−	0.157521i
$153$		−	16138.8i		−	0.689428i
$154$	13958.4			0.588565
$155$			6122.90i			0.254855i
$156$	4403.46			0.180944
$157$			22769.1i			0.923732i	0.886950	+	0.461866i	$0.152820\pi$
$157$			22769.1i			0.923732i	−0.886950	+	0.461866i	$0.847180\pi$
$158$		−	19701.9i		−	0.789211i
$159$		−	1074.95i		−	0.0425201i
$160$		−	2023.86i		−	0.0790569i
$161$	28429.1	+	985.355i	1.09676	+	0.0380138i
$162$	15281.5			0.582287
$163$	50189.0			1.88901			0.944503	−	0.328504i	$-0.106545\pi$
$163$	50189.0			1.88901			0.944503	+	0.328504i	$0.106545\pi$
$164$	−19932.4			−0.741092
$165$	−2262.81			−0.0831152
$166$			18260.5i			0.662670i
$167$	23264.9			0.834195			0.417098	−	0.908862i	$-0.363047\pi$
$167$	23264.9			0.834195			0.417098	+	0.908862i	$0.363047\pi$
$168$			2683.34i			0.0950728i
$169$	33735.8			1.18118
$170$	6703.14			0.231943
$171$			12245.7i			0.418786i
$172$		−	7532.48i		−	0.254613i
$173$	−732.375			−0.0244704			−0.0122352	−	0.999925i	$-0.503895\pi$
$173$	−732.375			−0.0244704			−0.0122352	+	0.999925i	$0.503895\pi$
$174$	6203.26			0.204890
$175$			6721.70i			0.219484i
$176$			5873.57i			0.189617i
$177$	4230.22			0.135026
$178$		−	12953.0i		−	0.408818i
$179$	14160.3			0.441943			0.220972	−	0.975280i	$-0.429077\pi$
$179$	14160.3			0.441943			0.220972	+	0.975280i	$0.429077\pi$
$180$			6809.86i			0.210181i
$181$			35636.7i			1.08778i	0.839157	+	0.543889i	$0.183049\pi$
$181$			35636.7i			1.08778i	−0.839157	+	0.543889i	$0.816951\pi$
$182$			37961.8i			1.14605i
$183$			923.989i			0.0275908i
$184$	−414.628	+	11962.7i	−0.0122468	+	0.353341i
$185$	−20249.4			−0.591656
$186$	3416.00			0.0987398
$187$	−19453.6			−0.556311
$188$	−4727.29			−0.133751
$189$		−	18634.5i		−	0.521667i
$190$	−5086.17			−0.140891
$191$		−	45275.9i		−	1.24108i	−0.784174	−	0.620541i	$-0.786913\pi$
$191$		−	45275.9i		−	1.24108i	0.784174	−	0.620541i	$-0.213087\pi$
$192$	−1129.12			−0.0306294
$193$	−82.3045			−0.00220958			−0.00110479	−	0.999999i	$-0.500352\pi$
$193$	−82.3045			−0.00220958			−0.00110479	+	0.999999i	$0.500352\pi$
$194$			7583.28i			0.201490i
$195$		−	6154.02i		−	0.161841i
$196$	−3924.78			−0.102165
$197$	−13705.4			−0.353150			−0.176575	−	0.984287i	$-0.556502\pi$
$197$	−13705.4			−0.353150			−0.176575	+	0.984287i	$0.556502\pi$
$198$		−	19763.3i		−	0.504116i
$199$		−	64694.3i		−	1.63365i	−0.576884	−	0.816826i	$-0.695732\pi$
$199$		−	64694.3i		−	1.63365i	0.576884	−	0.816826i	$-0.304268\pi$
$200$	−2828.43			−0.0707107
$201$			6417.31i			0.158840i
$202$	43353.6			1.06248
$203$			53477.7i			1.29772i
$204$		−	3739.72i		−	0.0898626i
$205$			27856.4i			0.662853i
$206$		−	10230.7i		−	0.241084i
$207$	1395.14	−	40252.1i	0.0325594	−	0.939394i
$208$	−15974.0			−0.369221
$209$	14760.9			0.337925
$210$	3750.08			0.0850357
$211$	−67379.0			−1.51342			−0.756710	−	0.653751i	$-0.773194\pi$
$211$	−67379.0			−1.51342			−0.756710	+	0.653751i	$0.773194\pi$
$212$			3899.48i			0.0867631i
$213$	−2288.08			−0.0504328
$214$		−	7676.42i		−	0.167622i
$215$	−10527.0			−0.227733
$216$	7841.22			0.168064
$217$			29449.0i			0.625391i
$218$		−	18973.8i		−	0.399246i
$219$	−1466.60			−0.0305791
$220$	8208.56			0.169598
$221$		−	52906.8i		−	1.08325i
$222$			11297.3i			0.229228i
$223$	−53396.1			−1.07374			−0.536871	−	0.843664i	$-0.680394\pi$
$223$	−53396.1			−1.07374			−0.536871	+	0.843664i	$0.680394\pi$
$224$		−	9734.06i		−	0.193998i
$225$	9517.07			0.187992
$226$		−	21381.9i		−	0.418630i
$227$			85437.6i			1.65805i	0.559212	+	0.829025i	$0.311104\pi$
$227$			85437.6i			1.65805i	−0.559212	+	0.829025i	$0.688896\pi$
$228$			2837.60i			0.0545861i
$229$		−	76890.3i		−	1.46622i	−0.680108	−	0.733112i	$-0.738067\pi$
$229$		−	76890.3i		−	1.46622i	0.680108	−	0.733112i	$-0.261933\pi$
$230$	16718.4	+	579.460i	0.316038	+	0.0109539i
$231$	−10883.3			−0.203957
$232$	−22502.9			−0.418084
$233$	14784.9			0.272337			0.136169	−	0.990686i	$-0.456521\pi$
$233$	14784.9			0.272337			0.136169	+	0.990686i	$0.456521\pi$
$234$	53749.1			0.981611
$235$			6606.59i			0.119630i
$236$	−15345.5			−0.275523
$237$			15361.5i			0.273487i
$238$	32239.8			0.569165
$239$	−107649.			−1.88457			−0.942287	−	0.334805i	$-0.891330\pi$
$239$	−107649.			−1.88457			−0.942287	+	0.334805i	$0.891330\pi$
$240$			1578.00i			0.0273958i
$241$		−	14530.9i		−	0.250183i	−0.992145	−	0.125092i	$-0.960078\pi$
$241$		−	14530.9i		−	0.250183i	0.992145	−	0.125092i	$-0.0399225\pi$
$242$	17588.4			0.300328
$243$	−39984.4			−0.677139
$244$		−	3351.86i		−	0.0562997i
$245$			5485.04i			0.0913793i
$246$	15541.3			0.256812
$247$			40144.3i			0.658006i
$248$	−12391.9			−0.201481
$249$		−	14237.7i		−	0.229636i
$250$			3952.85i			0.0632456i
$251$			68030.4i			1.07983i	0.841719	+	0.539915i	$0.181544\pi$
$251$			68030.4i			1.07983i	−0.841719	+	0.539915i	$0.818456\pi$
$252$			32753.1i			0.515764i
$253$	−48519.6	−	1681.69i	−0.758012	−	0.0262727i
$254$	−49338.3			−0.764746
$255$	−5226.42			−0.0803756
$256$	4096.00			0.0625000
$257$	−103551.			−1.56779			−0.783897	−	0.620892i	$-0.786771\pi$
$257$	−103551.			−1.56779			−0.783897	+	0.620892i	$0.786771\pi$
$258$			5873.06i			0.0882317i
$259$	−97392.8			−1.45187
$260$			22324.3i			0.330241i
$261$	75717.7			1.11152
$262$	−50073.1			−0.729461
$263$			26699.8i			0.386008i	0.981198	+	0.193004i	$0.0618231\pi$
$263$			26699.8i			0.386008i	−0.981198	+	0.193004i	$0.938177\pi$
$264$		−	4579.61i		−	0.0657083i
$265$	5449.69			0.0776033
$266$	−24462.7			−0.345733
$267$			10099.4i			0.141669i
$268$		−	23279.4i		−	0.324117i
$269$	−105219.			−1.45408			−0.727040	−	0.686595i	$-0.759104\pi$
$269$	−105219.			−1.45408			−0.727040	+	0.686595i	$0.759104\pi$
$270$		−	10958.4i		−	0.150321i
$271$	−70042.7			−0.953727			−0.476863	−	0.878977i	$-0.658226\pi$
$271$	−70042.7			−0.953727			−0.476863	+	0.878977i	$0.658226\pi$
$272$			13566.2i			0.183367i
$273$		−	29598.7i		−	0.397144i
$274$			73690.4i			0.981543i
$275$		−	11471.8i		−	0.151693i
$276$	323.284	−	9327.30i	0.00424391	−	0.122444i
$277$	1334.85			0.0173970			0.00869849	−	0.999962i	$-0.497231\pi$
$277$	1334.85			0.0173970			0.00869849	+	0.999962i	$0.497231\pi$
$278$	2364.44			0.0305941
$279$	41696.1			0.535657
$280$	−13603.8			−0.173517
$281$		−	39557.7i		−	0.500977i	−0.968120	−	0.250489i	$-0.919409\pi$
$281$		−	39557.7i		−	0.500977i	0.968120	−	0.250489i	$-0.0805913\pi$
$282$	3685.85			0.0463490
$283$			34909.6i			0.435885i	0.975962	+	0.217942i	$0.0699345\pi$
$283$			34909.6i			0.435885i	−0.975962	+	0.217942i	$0.930066\pi$
$284$	8300.25			0.102909
$285$	3965.67			0.0488233
$286$		−	64788.8i		−	0.792078i
$287$			133980.i			1.62658i
$288$	−13782.2			−0.166163
$289$	38588.9			0.462026
$290$			31448.8i			0.373945i
$291$		−	5912.66i		−	0.0698228i
$292$	5320.24			0.0623972
$293$		−	93350.3i		−	1.08738i	−0.839287	−	0.543689i	$-0.817027\pi$
$293$		−	93350.3i		−	1.08738i	0.839287	−	0.543689i	$-0.182973\pi$
$294$	3060.14			0.0354035
$295$			21446.0i			0.246435i
$296$		−	40982.0i		−	0.467745i
$297$			31803.2i			0.360544i
$298$		−	48220.6i		−	0.543001i
$299$	4573.58	−	131956.i	0.0511581	−	1.47600i
$300$	2205.32			0.0245035
$301$	−50631.1			−0.558836
$302$	−25041.3			−0.274563
$303$	−33802.7			−0.368185
$304$		−	10293.7i		−	0.111384i
$305$	−4684.36			−0.0503560
$306$		−	45647.5i		−	0.487499i
$307$	−151577.			−1.60826			−0.804132	−	0.594451i	$-0.797369\pi$
$307$	−151577.			−1.60826			−0.804132	+	0.594451i	$0.797369\pi$
$308$	39480.4			0.416179
$309$			7976.82i			0.0835435i
$310$			17318.2i			0.180210i
$311$	49003.5			0.506648			0.253324	−	0.967382i	$-0.418476\pi$
$311$	49003.5			0.506648			0.253324	+	0.967382i	$0.418476\pi$
$312$	12454.9			0.127947
$313$		−	116147.i		−	1.18555i	−0.805369	−	0.592774i	$-0.798033\pi$
$313$		−	116147.i		−	1.18555i	0.805369	−	0.592774i	$-0.201967\pi$
$314$			64400.7i			0.653177i
$315$	45773.8			0.461313
$316$		−	55725.3i		−	0.558056i
$317$	90689.1			0.902478			0.451239	−	0.892403i	$-0.350982\pi$
$317$	90689.1			0.902478			0.451239	+	0.892403i	$0.350982\pi$
$318$		−	3040.42i		−	0.0300662i
$319$		−	91269.6i		−	0.896902i
$320$		−	5724.33i		−	0.0559017i
$321$			5985.29i			0.0580864i
$322$	80409.8	+	2787.00i	0.775527	+	0.0268798i
$323$	34093.3			0.326786
$324$	43222.7			0.411739
$325$	31199.2			0.295377
$326$	141956.			1.33573
$327$			14793.8i			0.138352i
$328$	−56377.4			−0.524031
$329$			31775.4i			0.293562i
$330$	−6400.20			−0.0587713
$331$	6321.31			0.0576968			0.0288484	−	0.999584i	$-0.490816\pi$
$331$	6321.31			0.0576968			0.0288484	+	0.999584i	$0.490816\pi$
$332$			51648.6i			0.468578i
$333$			137896.i			1.24355i
$334$	65803.0			0.589865
$335$	−32534.0			−0.289899
$336$			7589.62i			0.0672267i
$337$			138356.i			1.21826i	0.793071	+	0.609129i	$0.208481\pi$
$337$			138356.i			1.21826i	−0.793071	+	0.609129i	$0.791519\pi$
$338$	95419.3			0.835224
$339$			16671.4i			0.145069i
$340$	18959.3			0.164008
$341$		−	50260.2i		−	0.432231i
$342$			34636.1i			0.296126i
$343$		−	102729.i		−	0.873184i
$344$		−	21305.1i		−	0.180039i
$345$	−13035.3	−	451.804i	−0.109517	−	0.00379587i
$346$	−2071.47			−0.0173032
$347$	−1906.44			−0.0158330			−0.00791652	−	0.999969i	$-0.502520\pi$
$347$	−1906.44			−0.0158330			−0.00791652	+	0.999969i	$0.502520\pi$
$348$	17545.5			0.144879
$349$	86630.0			0.711242			0.355621	−	0.934630i	$-0.384269\pi$
$349$	86630.0			0.711242			0.355621	+	0.934630i	$0.384269\pi$
$350$			19011.8i			0.155199i
$351$	−86493.1			−0.702049
$352$			16613.0i			0.134079i
$353$	−9788.99			−0.0785576			−0.0392788	−	0.999228i	$-0.512506\pi$
$353$	−9788.99			−0.0785576			−0.0392788	+	0.999228i	$0.512506\pi$
$354$	11964.9			0.0954776
$355$		−	11599.9i		−	0.0920448i
$356$		−	36636.6i		−	0.289078i
$357$	−25137.3			−0.197234
$358$	40051.4			0.312501
$359$		−	149482.i		−	1.15985i	−0.814670	−	0.579924i	$-0.803082\pi$
$359$		−	149482.i		−	1.15985i	0.814670	−	0.579924i	$-0.196918\pi$
$360$			19261.2i			0.148620i
$361$	104452.			0.801497
$362$			100796.i			0.769175i
$363$	−13713.6			−0.104073
$364$			107372.i			0.810381i
$365$		−	7435.26i		−	0.0558098i
$366$			2613.43i			0.0195096i
$367$			87565.7i			0.650132i	0.945691	+	0.325066i	$0.105387\pi$
$367$			87565.7i			0.650132i	−0.945691	+	0.325066i	$0.894613\pi$
$368$	−1172.75	+	33835.7i	−0.00865980	+	0.249850i
$369$	189698.			1.39319
$370$	−57274.1			−0.418364
$371$	26211.1			0.190431
$372$	9661.92			0.0698196
$373$			201618.i			1.44915i	0.689198	+	0.724573i	$0.257963\pi$
$373$			201618.i			1.44915i	−0.689198	+	0.724573i	$0.742037\pi$
$374$	−55023.2			−0.393371
$375$		−	3082.03i		−	0.0219166i
$376$	−13370.8			−0.0945761
$377$	248220.			1.74644
$378$		−	52706.3i		−	0.368875i
$379$		−	21342.4i		−	0.148582i	−0.997237	−	0.0742909i	$-0.976331\pi$
$379$		−	21342.4i		−	0.148582i	0.997237	−	0.0742909i	$-0.0236693\pi$
$380$	−14385.9			−0.0996251
$381$	38469.0			0.265009
$382$		−	128060.i		−	0.877578i
$383$			94960.5i			0.647360i	0.946167	+	0.323680i	$0.104920\pi$
$383$			94960.5i			0.647360i	−0.946167	+	0.323680i	$0.895080\pi$
$384$	−3193.64			−0.0216583
$385$		−	55175.5i		−	0.372241i
$386$	−232.792			−0.00156241
$387$			71687.2i			0.478652i
$388$			21448.7i			0.142475i
$389$		−	57142.1i		−	0.377622i	−0.982013	−	0.188811i	$-0.939537\pi$
$389$		−	57142.1i		−	0.377622i	0.982013	−	0.188811i	$-0.0604634\pi$
$390$		−	17406.2i		−	0.114439i
$391$	−112066.	−	3884.20i	−0.733027	−	0.0254067i
$392$	−11100.9			−0.0722417
$393$	39041.9			0.252782
$394$	−38764.7			−0.249715
$395$	−77878.4			−0.499141
$396$		−	55899.2i		−	0.356464i
$397$	250995.			1.59252			0.796260	−	0.604955i	$-0.206809\pi$
$397$	250995.			1.59252			0.796260	+	0.604955i	$0.206809\pi$
$398$		−	182983.i		−	1.15517i
$399$	19073.5			0.119808
$400$	−8000.00			−0.0500000
$401$		−	47059.9i		−	0.292659i	−0.989236	−	0.146330i	$-0.953254\pi$
$401$		−	47059.9i		−	0.292659i	0.989236	−	0.146330i	$-0.0467460\pi$
$402$			18150.9i			0.112317i
$403$	136689.			0.841637
$404$	122623.			0.751290
$405$		−	60405.6i		−	0.368271i
$406$			151258.i			0.917626i
$407$	166219.			1.00344
$408$		−	10577.5i		−	0.0635425i
$409$	−129458.			−0.773894			−0.386947	−	0.922102i	$-0.626470\pi$
$409$	−129458.			−0.773894			−0.386947	+	0.922102i	$0.626470\pi$
$410$			78789.8i			0.468708i
$411$		−	57456.2i		−	0.340136i
$412$		−	28936.7i		−	0.170472i
$413$			103148.i			0.604729i
$414$	3946.04	−	113850.i	0.0230230	−	0.664252i
$415$	72181.0			0.419109
$416$	−45181.2			−0.261079
$417$	−1843.55			−0.0106019
$418$	41750.1			0.238949
$419$		−	310214.i		−	1.76699i	−0.468445	−	0.883493i	$-0.655186\pi$
$419$		−	310214.i		−	1.76699i	0.468445	−	0.883493i	$-0.344814\pi$
$420$	10606.8			0.0601293
$421$		−	214498.i		−	1.21021i	−0.796148	−	0.605103i	$-0.793132\pi$
$421$		−	214498.i		−	1.21021i	0.796148	−	0.605103i	$-0.206868\pi$
$422$	−190576.			−1.07015
$423$	44989.9			0.251440
$424$			11029.4i			0.0613508i
$425$		−	26496.5i		−	0.146693i
$426$	−6471.68			−0.0356614
$427$	−22530.2			−0.123569
$428$		−	21712.2i		−	0.118527i
$429$			50515.7i			0.274481i
$430$	−29774.8			−0.161032
$431$			199689.i			1.07498i	0.843270	+	0.537490i	$0.180628\pi$
$431$			199689.i			1.07498i	−0.843270	+	0.537490i	$0.819372\pi$
$432$	22178.3			0.118840
$433$			335596.i			1.78995i	0.446114	+	0.894976i	$0.352808\pi$
$433$			335596.i			1.78995i	−0.446114	+	0.894976i	$0.647192\pi$
$434$			83294.4i			0.442218i
$435$		−	24520.5i		−	0.129584i
$436$		−	53666.0i		−	0.282310i
$437$	85032.7	+	2947.23i	0.445269	+	0.0154330i
$438$	−4148.18			−0.0216227
$439$	−35483.5			−0.184118			−0.0920592	−	0.995754i	$-0.529345\pi$
$439$	−35483.5			−0.184118			−0.0920592	+	0.995754i	$0.529345\pi$
$440$	23217.3			0.119924
$441$	37352.4			0.192062
$442$		−	149643.i		−	0.765970i
$443$	171962.			0.876246			0.438123	−	0.898915i	$-0.355643\pi$
$443$	171962.			0.876246			0.438123	+	0.898915i	$0.355643\pi$
$444$			31953.5i			0.162089i
$445$	−51201.2			−0.258559
$446$	−151027.			−0.759250
$447$			37597.5i			0.188167i
$448$		−	27532.1i		−	0.137177i
$449$	224578.			1.11397			0.556986	−	0.830522i	$-0.311958\pi$
$449$	224578.			1.11397			0.556986	+	0.830522i	$0.311958\pi$
$450$	26918.3			0.132930
$451$		−	228661.i		−	1.12419i
$452$		−	60477.3i		−	0.296016i
$453$	19524.6			0.0951450
$454$			241654.i			1.17242i
$455$	150057.			0.724826
$456$			8025.96i			0.0385982i
$457$		−	17876.2i		−	0.0855938i	−0.999084	−	0.0427969i	$-0.986373\pi$
$457$		−	17876.2i		−	0.0855938i	0.999084	−	0.0427969i	$-0.0136268\pi$
$458$		−	217479.i		−	1.03678i
$459$			73455.9i			0.348659i
$460$	47286.8	+	1638.96i	0.223473	+	0.00774556i
$461$	128471.			0.604511			0.302256	−	0.953227i	$-0.402260\pi$
$461$	128471.			0.604511			0.302256	+	0.953227i	$0.402260\pi$
$462$	−30782.7			−0.144219
$463$	−323685.			−1.50994			−0.754971	−	0.655758i	$-0.772349\pi$
$463$	−323685.			−1.50994			−0.754971	+	0.655758i	$0.772349\pi$
$464$	−63647.9			−0.295630
$465$		−	13502.9i		−	0.0624486i
$466$	41818.1			0.192572
$467$			55458.9i			0.254295i	0.991884	+	0.127148i	$0.0405822\pi$
$467$			55458.9i			0.254295i	−0.991884	+	0.127148i	$0.959418\pi$
$468$	152025.			0.694104
$469$	−156477.			−0.711386
$470$			18686.2i			0.0845914i
$471$		−	50213.0i		−	0.226347i
$472$	−43403.7			−0.194824
$473$	86411.3			0.386232
$474$			43448.8i			0.193384i
$475$			20104.8i			0.0891074i
$476$	91187.9			0.402461
$477$		−	37111.7i		−	0.163107i
$478$	−304477.			−1.33260
$479$			30012.2i			0.130806i	0.997859	+	0.0654028i	$0.0208332\pi$
$479$			30012.2i			0.130806i	−0.997859	+	0.0654028i	$0.979167\pi$
$480$			4463.25i			0.0193717i
$481$			452055.i			1.95389i
$482$		−	41099.5i		−	0.176906i
$483$	−62695.3	−	2173.02i	−0.268745	−	0.00931471i
$484$	49747.5			0.212364
$485$	29975.5			0.127433
$486$	−113093.			−0.478810
$487$	−467896.			−1.97284			−0.986419	−	0.164251i	$-0.947479\pi$
$487$	−467896.			−1.97284			−0.986419	+	0.164251i	$0.947479\pi$
$488$		−	9480.48i		−	0.0398099i
$489$	−110683.			−0.462873
$490$			15514.0i			0.0646149i
$491$	25141.7			0.104287			0.0521437	−	0.998640i	$-0.483395\pi$
$491$	25141.7			0.104287			0.0521437	+	0.998640i	$0.483395\pi$
$492$	43957.3			0.181594
$493$		−	210806.i		−	0.867338i
$494$			113545.i			0.465280i
$495$	−78121.5			−0.318831
$496$	−35049.5			−0.142468
$497$		−	55791.7i		−	0.225869i
$498$		−	40270.3i		−	0.162377i
$499$	−197698.			−0.793963			−0.396981	−	0.917827i	$-0.629942\pi$
$499$	−197698.			−0.793963			−0.396981	+	0.917827i	$0.629942\pi$
$500$			11180.3i			0.0447214i
$501$	−51306.4			−0.204407
$502$			192419.i			0.763555i
$503$			180995.i			0.715369i	0.933842	+	0.357685i	$0.116434\pi$
$503$			180995.i			0.715369i	−0.933842	+	0.357685i	$0.883566\pi$
$504$			92639.7i			0.364700i
$505$		−	171370.i		−	0.671974i
$506$	−137234.	−	4756.54i	−0.535996	−	0.0185776i
$507$	−74398.2			−0.289432
$508$	−139550.			−0.540757
$509$	439084.			1.69477			0.847387	−	0.530976i	$-0.178175\pi$
$509$	439084.			1.69477			0.847387	+	0.530976i	$0.178175\pi$
$510$	−14782.6			−0.0568341
$511$		−	35761.0i		−	0.136952i
$512$	11585.2			0.0441942
$513$		−	55736.4i		−	0.211790i
$514$	−292887.			−1.10860
$515$	−40440.2			−0.152475
$516$			16611.5i			0.0623893i
$517$		−	54230.6i		−	0.202891i
$518$	−275468.			−1.02663
$519$	1615.12			0.00599611
$520$			63142.7i			0.233516i
$521$			431021.i			1.58790i	0.607985	+	0.793949i	$0.291978\pi$
$521$			431021.i			1.58790i	−0.607985	+	0.793949i	$0.708022\pi$
$522$	214162.			0.785962
$523$		−	527847.i		−	1.92976i	−0.262682	−	0.964882i	$-0.584607\pi$
$523$		−	527847.i		−	1.92976i	0.262682	−	0.964882i	$-0.415393\pi$
$524$	−141628.			−0.515807
$525$		−	14823.5i		−	0.0537813i
$526$			75518.4i			0.272949i
$527$		−	116086.i		−	0.417984i
$528$		−	12953.1i		−	0.0464628i
$529$	−279169.	−	19375.3i	−0.997600	−	0.0692368i
$530$	15414.1			0.0548738
$531$	146044.			0.517960
$532$	−69191.0			−0.244470
$533$	621875.			2.18901
$534$			28565.4i			0.100175i
$535$	−30343.7			−0.106013
$536$		−	65844.1i		−	0.229186i
$537$	−31228.0			−0.108292
$538$	−297603.			−1.02819
$539$		−	45024.3i		−	0.154978i
$540$		−	30995.1i		−	0.106293i
$541$	18504.5			0.0632242			0.0316121	−	0.999500i	$-0.489936\pi$
$541$	18504.5			0.0632242			0.0316121	+	0.999500i	$0.489936\pi$
$542$	−198111.			−0.674387
$543$		−	78590.2i		−	0.266544i
$544$			38371.0i			0.129660i
$545$	−75000.4			−0.252506
$546$		−	83717.8i		−	0.280823i
$547$	−34603.3			−0.115649			−0.0578246	−	0.998327i	$-0.518416\pi$
$547$	−34603.3			−0.115649			−0.0578246	+	0.998327i	$0.518416\pi$
$548$			208428.i			0.694056i
$549$			31899.9i			0.105839i
$550$		−	32447.2i		−	0.107263i
$551$			159954.i			0.526856i
$552$	914.387	−	26381.6i	0.00300090	−	0.0865811i
$553$	−374568.			−1.22484
$554$	3775.53			0.0123015
$555$	44656.4			0.144977
$556$	6687.64			0.0216333
$557$		−	544404.i		−	1.75473i	−0.479821	−	0.877366i	$-0.659298\pi$
$557$		−	544404.i		−	1.75473i	0.479821	−	0.877366i	$-0.340702\pi$
$558$	117934.			0.378767
$559$			235007.i			0.752069i
$560$	−38477.2			−0.122695
$561$	42901.4			0.136316
$562$		−	111886.i		−	0.354244i
$563$			381928.i			1.20494i	0.798142	+	0.602469i	$0.205816\pi$
$563$			381928.i			1.20494i	−0.798142	+	0.602469i	$0.794184\pi$
$564$	10425.2			0.0327737
$565$	−84519.5			−0.264765
$566$			98739.1i			0.308217i
$567$		−	290530.i		−	0.903701i
$568$	23476.6			0.0727678
$569$		−	478472.i		−	1.47785i	−0.673785	−	0.738927i	$-0.735333\pi$
$569$		−	478472.i		−	1.47785i	0.673785	−	0.738927i	$-0.264667\pi$
$570$	11216.6			0.0345233
$571$			555916.i			1.70505i	0.522686	+	0.852525i	$0.324930\pi$
$571$			555916.i			1.70505i	−0.522686	+	0.852525i	$0.675070\pi$
$572$		−	183250.i		−	0.560084i
$573$			99847.8i			0.304109i
$574$			378952.i			1.15016i
$575$	2290.52	−	66085.3i	0.00692784	−	0.199880i
$576$	−38981.9			−0.117495
$577$	−402137.			−1.20788			−0.603938	−	0.797031i	$-0.706403\pi$
$577$	−402137.			−1.20788			−0.603938	+	0.797031i	$0.706403\pi$
$578$	109146.			0.326702
$579$	181.508			0.000541424
$580$			88950.6i			0.264419i
$581$	347166.			1.02845
$582$		−	16723.5i		−	0.0493722i
$583$	−44734.2			−0.131614
$584$	15047.9			0.0441215
$585$		−	212462.i		−	0.620825i
$586$		−	264034.i		−	0.768892i
$587$	−279973.			−0.812530			−0.406265	−	0.913755i	$-0.633169\pi$
$587$	−279973.			−0.812530			−0.406265	+	0.913755i	$0.633169\pi$
$588$	8655.38			0.0250341
$589$			88083.2i			0.253900i
$590$			60658.5i			0.174256i
$591$	30224.7			0.0865341
$592$		−	115915.i		−	0.330746i
$593$	−298419.			−0.848626			−0.424313	−	0.905516i	$-0.639484\pi$
$593$	−298419.			−0.848626			−0.424313	+	0.905516i	$0.639484\pi$
$594$			89953.0i			0.254943i
$595$		−	127439.i		−	0.359972i
$596$		−	136389.i		−	0.383960i
$597$			142671.i			0.400302i
$598$	12936.0	−	373227.i	0.0361742	−	1.04369i
$599$	129729.			0.361562			0.180781	−	0.983523i	$-0.442137\pi$
$599$	129729.			0.361562			0.180781	+	0.983523i	$0.442137\pi$
$600$	6237.58			0.0173266
$601$	−527005.			−1.45904			−0.729518	−	0.683961i	$-0.760256\pi$
$601$	−527005.			−1.45904			−0.729518	+	0.683961i	$0.760256\pi$
$602$	−143206.			−0.395156
$603$			221552.i			0.609313i
$604$	−70827.4			−0.194146
$605$		−	69524.2i		−	0.189944i
$606$	−95608.5			−0.260346
$607$	−135735.			−0.368396			−0.184198	−	0.982889i	$-0.558969\pi$
$607$	−135735.			−0.368396			−0.184198	+	0.982889i	$0.558969\pi$
$608$		−	29114.9i		−	0.0787605i
$609$		−	117935.i		−	0.317987i
$610$	−13249.4			−0.0356070
$611$	147487.			0.395069
$612$		−	129111.i		−	0.344714i
$613$			615665.i			1.63841i	0.573499	+	0.819206i	$0.305586\pi$
$613$			615665.i			1.63841i	−0.573499	+	0.819206i	$0.694414\pi$
$614$	−428725.			−1.13721
$615$		−	61432.2i		−	0.162422i
$616$	111667.			0.294283
$617$		−	472812.i		−	1.24199i	−0.783814	−	0.620995i	$-0.786729\pi$
$617$		−	472812.i		−	1.24199i	0.783814	−	0.620995i	$-0.213271\pi$
$618$			22561.9i			0.0590742i
$619$			52658.8i			0.137432i	0.997636	+	0.0687162i	$0.0218903\pi$
$619$			52658.8i			0.137432i	−0.997636	+	0.0687162i	$0.978110\pi$
$620$			48983.2i			0.127428i
$621$	−6349.98	+	183208.i	−0.0164660	+	0.475073i
$622$	138603.			0.358254
$623$	−246260.			−0.634479
$624$	35227.7			0.0904721
$625$	15625.0			0.0400000
$626$		−	328513.i		−	0.838309i
$627$	−32552.5			−0.0828036
$628$			182153.i			0.461866i
$629$	383916.			0.970365
$630$	129468.			0.326198
$631$			300259.i			0.754115i	0.926190	+	0.377057i	$0.123064\pi$
$631$			300259.i			0.754115i	−0.926190	+	0.377057i	$0.876936\pi$
$632$		−	157615.i		−	0.394605i
$633$	148592.			0.370841
$634$	256508.			0.638149
$635$			195027.i			0.483668i
$636$		−	8599.60i		−	0.0212600i
$637$	122450.			0.301772
$638$		−	258149.i		−	0.634205i
$639$	−78994.0			−0.193461
$640$		−	16190.9i		−	0.0395285i
$641$			749425.i			1.82395i	0.410250	+	0.911973i	$0.365441\pi$
$641$			749425.i			1.82395i	−0.410250	+	0.911973i	$0.634559\pi$
$642$			16928.9i			0.0410733i
$643$		−	41396.1i		−	0.100124i	−0.998746	−	0.0500619i	$-0.984058\pi$
$643$		−	41396.1i		−	0.100124i	0.998746	−	0.0500619i	$-0.0159419\pi$
$644$	227433.	+	7882.84i	0.548381	+	0.0190069i
$645$	23215.3			0.0558027
$646$	96430.4			0.231073
$647$	687574.			1.64252			0.821260	−	0.570554i	$-0.193271\pi$
$647$	687574.			1.64252			0.821260	+	0.570554i	$0.193271\pi$
$648$	122252.			0.291144
$649$		−	176041.i		−	0.417950i
$650$	88244.6			0.208863
$651$		−	64944.5i		−	0.153243i
$652$	401512.			0.944503
$653$	407656.			0.956020			0.478010	−	0.878354i	$-0.341358\pi$
$653$	407656.			0.956020			0.478010	+	0.878354i	$0.341358\pi$
$654$			41843.2i			0.0978294i
$655$			197931.i			0.461352i
$656$	−159459.			−0.370546
$657$	−50633.1			−0.117302
$658$			89874.4i			0.207579i
$659$			603896.i			1.39057i	0.718736	+	0.695283i	$0.244721\pi$
$659$			603896.i			1.39057i	−0.718736	+	0.695283i	$0.755279\pi$
$660$	−18102.5			−0.0415576
$661$		−	681327.i		−	1.55938i	−0.626164	−	0.779691i	$-0.715376\pi$
$661$		−	681327.i		−	1.55938i	0.626164	−	0.779691i	$-0.284624\pi$
$662$	17879.4			0.0407978
$663$			116676.i			0.265433i
$664$			146084.i			0.331335i
$665$			96697.4i			0.218661i
$666$			390028.i			0.879322i
$667$	18223.3	−	525774.i	0.0409615	−	1.18181i
$668$	186119.			0.417098
$669$	117755.			0.263105
$670$	−92020.0			−0.204990
$671$	38451.9			0.0854029
$672$			21466.7i			0.0475364i
$673$	503317.			1.11125			0.555624	−	0.831433i	$-0.312479\pi$
$673$	503317.			1.11125			0.555624	+	0.831433i	$0.312479\pi$
$674$			391331.i			0.861438i
$675$	−43317.0			−0.0950716
$676$	269887.			0.590592
$677$			251613.i			0.548980i	0.961590	+	0.274490i	$0.0885090\pi$
$677$			251613.i			0.548980i	−0.961590	+	0.274490i	$0.911491\pi$
$678$			47154.0i			0.102579i
$679$	144172.			0.312710
$680$	53625.1			0.115971
$681$		−	188417.i		−	0.406281i
$682$		−	142157.i		−	0.305633i
$683$	−15240.1			−0.0326698			−0.0163349	−	0.999867i	$-0.505200\pi$
$683$	−15240.1			−0.0326698			−0.0163349	+	0.999867i	$0.505200\pi$
$684$			97965.7i			0.209393i
$685$	291287.			0.620783
$686$		−	290562.i		−	0.617434i
$687$			169567.i			0.359277i
$688$		−	60259.9i		−	0.127307i
$689$		−	121661.i		−	0.256278i
$690$	−36869.4	−	1277.89i	−0.0774405	−	0.00268409i
$691$	−821061.			−1.71957			−0.859784	−	0.510657i	$-0.829402\pi$
$691$	−821061.			−1.71957			−0.859784	+	0.510657i	$0.829402\pi$
$692$	−5859.00			−0.0122352
$693$	−375737.			−0.782380
$694$	−5392.23			−0.0111957
$695$		−	9346.26i		−	0.0193494i
$696$	49626.1			0.102445
$697$		−	528139.i		−	1.08713i
$698$	245027.			0.502924
$699$	−32605.4			−0.0667322
$700$			53773.6i			0.109742i
$701$		−	962308.i		−	1.95829i	−0.203151	−	0.979147i	$-0.565118\pi$
$701$		−	962308.i		−	1.95829i	0.203151	−	0.979147i	$-0.434882\pi$
$702$	−244639.			−0.496423
$703$	−291306.			−0.589438
$704$			46988.6i			0.0948084i
$705$		−	14569.6i		−	0.0293137i
$706$	−27687.4			−0.0555486
$707$		−	824231.i		−	1.64896i
$708$	33841.8			0.0675128
$709$			513023.i			1.02057i	0.860004	+	0.510287i	$0.170461\pi$
$709$			513023.i			1.02057i	−0.860004	+	0.510287i	$0.829539\pi$
$710$		−	32809.6i		−	0.0650855i
$711$			530341.i			1.04910i
$712$		−	103624.i		−	0.204409i
$713$	10035.2	−	289532.i	0.0197400	−	0.569532i
$714$	−71099.0			−0.139466
$715$	−256100.			−0.500954
$716$	113282.			0.220972
$717$	237400.			0.461787
$718$		−	422800.i		−	0.820137i
$719$	−837955.			−1.62092			−0.810462	−	0.585791i	$-0.800784\pi$
$719$	−837955.			−1.62092			−0.810462	+	0.585791i	$0.800784\pi$
$720$			54478.9i			0.105090i
$721$	−194504.			−0.374160
$722$	295435.			0.566744
$723$			32045.2i			0.0613037i
$724$			285093.i			0.543889i
$725$	124312.			0.236504
$726$	−38788.0			−0.0735909
$727$		−	898329.i		−	1.69968i	−0.527042	−	0.849839i	$-0.676699\pi$
$727$		−	898329.i		−	1.69968i	0.527042	−	0.849839i	$-0.323301\pi$
$728$			303694.i			0.573026i
$729$	−349452.			−0.657555
$730$		−	21030.1i		−	0.0394635i
$731$	199584.			0.373501
$732$			7391.91i			0.0137954i
$733$			354478.i			0.659752i	0.944024	+	0.329876i	$0.107007\pi$
$733$			354478.i			0.659752i	−0.944024	+	0.329876i	$0.892993\pi$
$734$			247673.i			0.459713i
$735$		−	12096.3i		−	0.0223912i
$736$	−3317.02	+	95701.8i	−0.00612341	+	0.176671i
$737$	267057.			0.491665
$738$	536547.			0.985134
$739$	560214.			1.02581			0.512903	−	0.858447i	$-0.328570\pi$
$739$	560214.			1.02581			0.512903	+	0.858447i	$0.328570\pi$
$740$	−161995.			−0.295828
$741$		−	88530.9i		−	0.161235i
$742$	74136.3			0.134655
$743$			879311.i			1.59281i	0.604761	+	0.796407i	$0.293269\pi$
$743$			879311.i			1.59281i	−0.604761	+	0.796407i	$0.706731\pi$
$744$	27328.0			0.0493699
$745$	−190609.			−0.343424
$746$			570263.i			1.02470i
$747$		−	491543.i		−	0.880887i
$748$	−155629.			−0.278155
$749$	−145943.			−0.260147
$750$		−	8717.28i		−	0.0154974i
$751$		−	235107.i		−	0.416855i	−0.978038	−	0.208428i	$-0.933165\pi$
$751$		−	235107.i		−	0.416855i	0.978038	−	0.208428i	$-0.0668346\pi$
$752$	−37818.3			−0.0668754
$753$		−	150029.i		−	0.264597i
$754$	702072.			1.23492
$755$			98984.3i			0.173649i
$756$		−	149076.i		−	0.260834i
$757$		−	35232.2i		−	0.0614819i	−0.999527	−	0.0307410i	$-0.990213\pi$
$757$		−	35232.2i		−	0.0614819i	0.999527	−	0.0307410i	$-0.00978669\pi$
$758$		−	60365.5i		−	0.105063i
$759$	107001.	+	3708.66i	0.185740	+	0.00643774i
$760$	−40689.4			−0.0704456
$761$	7990.67			0.0137979			0.00689896	−	0.999976i	$-0.497804\pi$
$761$	7990.67			0.0137979			0.00689896	+	0.999976i	$0.497804\pi$
$762$	108807.			0.187390
$763$	−360726.			−0.619625
$764$		−	362207.i		−	0.620541i
$765$	−180437.			−0.308321
$766$			268589.i			0.457752i
$767$	478768.			0.813831
$768$	−9032.98			−0.0153147
$769$			466909.i			0.789550i	0.918778	+	0.394775i	$0.129177\pi$
$769$			466909.i			0.789550i	−0.918778	+	0.394775i	$0.870823\pi$
$770$		−	156060.i		−	0.263214i
$771$	228363.			0.384165
$772$	−658.436			−0.00110479
$773$			1.04090e6i			1.74201i	0.491273	+	0.871005i	$0.336532\pi$
$773$			1.04090e6i			1.74201i	−0.491273	+	0.871005i	$0.663468\pi$
$774$			202762.i			0.338458i
$775$	68456.1			0.113975
$776$			60666.2i			0.100745i
$777$	214782.			0.355759
$778$		−	161622.i		−	0.267019i
$779$			400738.i			0.660368i
$780$		−	49232.2i		−	0.0809207i
$781$			95218.9i			0.156107i
$782$	−316970.	−	10986.2i	−0.518328	−	0.0179653i
$783$	−344630.			−0.562120
$784$	−31398.2			−0.0510826
$785$	254566.			0.413106
$786$	110427.			0.178744
$787$		−	406017.i		−	0.655533i	−0.944759	−	0.327767i	$-0.893704\pi$
$787$		−	406017.i		−	0.655533i	0.944759	−	0.327767i	$-0.106296\pi$
$788$	−109643.			−0.176575
$789$		−	58881.5i		−	0.0945856i
$790$	−220273.			−0.352946
$791$	−406510.			−0.649708
$792$		−	158107.i		−	0.252058i
$793$			104575.i			0.166296i
$794$	709922.			1.12608
$795$	−12018.3			−0.0190156
$796$		−	517554.i		−	0.816826i
$797$			887600.i			1.39734i	0.715446	+	0.698668i	$0.246224\pi$
$797$			887600.i			1.39734i	−0.715446	+	0.698668i	$0.753776\pi$
$798$	53948.1			0.0847169
$799$		−	125257.i		−	0.196204i
$800$	−22627.4			−0.0353553
$801$			348673.i			0.543442i
$802$		−	133105.i		−	0.206941i
$803$			61032.8i			0.0946525i
$804$			51338.5i			0.0794202i
$805$	11016.6	−	317848.i	0.0170003	−	0.490487i
$806$	386616.			0.595127
$807$	232041.			0.356301
$808$	346829.			0.531242
$809$	614723.			0.939253			0.469627	−	0.882865i	$-0.344389\pi$
$809$	614723.			0.939253			0.469627	+	0.882865i	$0.344389\pi$
$810$		−	170853.i		−	0.260407i
$811$	576450.			0.876436			0.438218	−	0.898869i	$-0.355610\pi$
$811$	576450.			0.876436			0.438218	+	0.898869i	$0.355610\pi$
$812$			427822.i			0.648860i
$813$	154466.			0.233697
$814$	470138.			0.709539
$815$		−	561130.i		−	0.844789i
$816$		−	29917.8i		−	0.0449313i
$817$	−151439.			−0.226879
$818$	−366162.			−0.547226
$819$		−	1.02187e6i		−	1.52345i
$820$			222851.i			0.331426i
$821$	−561113.			−0.832462			−0.416231	−	0.909259i	$-0.636649\pi$
$821$	−561113.			−0.832462			−0.416231	+	0.909259i	$0.636649\pi$
$822$		−	162511.i		−	0.240513i
$823$	583548.			0.861543			0.430771	−	0.902461i	$-0.358242\pi$
$823$	583548.			0.861543			0.430771	+	0.902461i	$0.358242\pi$
$824$		−	81845.3i		−	0.120542i
$825$			25299.0i			0.0371703i
$826$			291747.i			0.427608i
$827$			907425.i			1.32678i	0.748272	+	0.663392i	$0.230884\pi$
$827$			907425.i			1.32678i	−0.748272	+	0.663392i	$0.769116\pi$
$828$	11161.1	−	322017.i	0.0162797	−	0.469697i
$829$	−668133.			−0.972196			−0.486098	−	0.873904i	$-0.661580\pi$
$829$	−668133.			−0.972196			−0.486098	+	0.873904i	$0.661580\pi$
$830$	204159.			0.296355
$831$	−2943.77			−0.00426287
$832$	−127792.			−0.184610
$833$		−	103993.i		−	0.149870i
$834$	−5214.34			−0.00749665
$835$		−	260109.i		−	0.373063i
$836$	118087.			0.168963
$837$	−189780.			−0.270894
$838$		−	877417.i		−	1.24945i
$839$		−	449748.i		−	0.638918i	−0.947600	−	0.319459i	$-0.896499\pi$
$839$		−	449748.i		−	0.638918i	0.947600	−	0.319459i	$-0.103501\pi$
$840$	30000.6			0.0425179
$841$	281746.			0.398351
$842$		−	606692.i		−	0.855744i
$843$			87237.2i			0.122757i
$844$	−539032.			−0.756710
$845$		−	377178.i		−	0.528242i
$846$	127251.			0.177795
$847$		−	334387.i		−	0.466104i
$848$			31195.9i			0.0433816i
$849$		−	76986.7i		−	0.106807i
$850$		−	74943.4i		−	0.103728i
$851$	957531.	+	33188.0i	1.32219	+	0.0458271i
$852$	−18304.7			−0.0252164
$853$	−52396.1			−0.0720114			−0.0360057	−	0.999352i	$-0.511463\pi$
$853$	−52396.1			−0.0720114			−0.0360057	+	0.999352i	$0.511463\pi$
$854$	−63724.9			−0.0873763
$855$	136911.			0.187287
$856$		−	61411.4i		−	0.0838110i
$857$	−1.17745e6			−1.60318			−0.801590	−	0.597874i	$-0.796012\pi$
$857$	−1.17745e6			−1.60318			−0.801590	+	0.597874i	$0.796012\pi$
$858$			142880.i			0.194087i
$859$	−701999.			−0.951372			−0.475686	−	0.879615i	$-0.657800\pi$
$859$	−701999.			−0.951372			−0.475686	+	0.879615i	$0.657800\pi$
$860$	−84215.7			−0.113867
$861$		−	295468.i		−	0.398569i
$862$			564807.i			0.760126i
$863$	−833727.			−1.11944			−0.559722	−	0.828680i	$-0.689092\pi$
$863$	−833727.			−1.11944			−0.559722	+	0.828680i	$0.689092\pi$
$864$	62729.7			0.0840322
$865$			8188.20i			0.0109435i
$866$			949210.i			1.26569i
$867$	−85100.8			−0.113213
$868$			235592.i			0.312695i
$869$	639270.			0.846535
$870$		−	69354.6i		−	0.0916298i
$871$			726298.i			0.957367i
$872$		−	151790.i		−	0.199623i
$873$		−	204129.i		−	0.267841i
$874$	240509.	+	8336.03i	0.314853	+	0.0109128i
$875$	75150.9			0.0981562
$876$	−11732.8			−0.0152895
$877$	−1.15389e6			−1.50025			−0.750125	−	0.661296i	$-0.770007\pi$
$877$	−1.15389e6			−1.50025			−0.750125	+	0.661296i	$0.770007\pi$
$878$	−100362.			−0.130191
$879$			205867.i			0.266446i
$880$	65668.5			0.0847992
$881$		−	179111.i		−	0.230766i	−0.993321	−	0.115383i	$-0.963191\pi$
$881$		−	179111.i		−	0.230766i	0.993321	−	0.115383i	$-0.0368095\pi$
$882$	105649.			0.135808
$883$	1.53577e6			1.96972			0.984862	−	0.173343i	$-0.0554569\pi$
$883$	1.53577e6			1.96972			0.984862	+	0.173343i	$0.0554569\pi$
$884$		−	423254.i		−	0.541623i
$885$		−	47295.3i		−	0.0603853i
$886$	486383.			0.619600
$887$	31493.6			0.0400290			0.0200145	−	0.999800i	$-0.493629\pi$
$887$	31493.6			0.0400290			0.0200145	+	0.999800i	$0.493629\pi$
$888$			90378.3i			0.114614i
$889$			938012.i			1.18687i
$890$	−144819.			−0.182829
$891$			495843.i			0.624581i
$892$	−427169.			−0.536871
$893$			95041.4i			0.119182i
$894$			106342.i			0.133054i
$895$		−	158317.i		−	0.197643i
$896$		−	77872.5i		−	0.0969991i
$897$	−10086.2	+	291004.i	−0.0125355	+	0.361671i
$898$	635202.			0.787697
$899$	544636.			0.673886
$900$	76136.6			0.0939958
$901$	−103323.			−0.127276
$902$		−	646751.i		−	0.794921i
$903$	111658.			0.136934
$904$		−	171056.i		−	0.209315i
$905$	398430.			0.486469
$906$	55223.9			0.0672777
$907$			130990.i			0.159229i	0.996826	+	0.0796146i	$0.0253690\pi$
$907$			130990.i			0.159229i	−0.996826	+	0.0796146i	$0.974631\pi$
$908$			683501.i			0.829025i
$909$	−1.16701e6			−1.41236
$910$	424426.			0.512530
$911$		−	1.22582e6i		−	1.47703i	−0.674236	−	0.738516i	$-0.735527\pi$
$911$		−	1.22582e6i		−	1.47703i	0.674236	−	0.738516i	$-0.264473\pi$
$912$			22700.8i			0.0272931i
$913$	−592503.			−0.710802
$914$		−	50561.5i		−	0.0605240i
$915$	10330.5			0.0123390
$916$		−	615122.i		−	0.733112i
$917$			951982.i			1.13211i
$918$			207765.i			0.246539i
$919$			1.42207e6i			1.68380i	0.539634	+	0.841900i	$0.318563\pi$
$919$			1.42207e6i			1.68380i	−0.539634	+	0.841900i	$0.681437\pi$
$920$	133747.	+	4635.68i	0.158019	+	0.00547694i
$921$	334276.			0.394081
$922$	363372.			0.427454
$923$	−258961.			−0.303970
$924$	−87066.7			−0.101978
$925$			226396.i			0.264597i
$926$	−915519.			−1.06769
$927$			275392.i			0.320474i
$928$	−180023.			−0.209042
$929$	−1.54673e6			−1.79218			−0.896091	−	0.443871i	$-0.853605\pi$
$929$	−1.54673e6			−1.79218			−0.896091	+	0.443871i	$0.853605\pi$
$930$		−	38192.1i		−	0.0441578i
$931$			78907.1i			0.0910367i
$932$	118279.			0.136169
$933$	−108068.			−0.124147
$934$			156862.i			0.179814i
$935$			217498.i			0.248790i
$936$	429993.			0.490806
$937$			549221.i			0.625559i	0.949826	+	0.312779i	$0.101260\pi$
$937$			549221.i			0.625559i	−0.949826	+	0.312779i	$0.898740\pi$
$938$	−442584.			−0.503026
$939$			256141.i			0.290501i
$940$			52852.7i			0.0598152i
$941$		−	1.21778e6i		−	1.37528i	−0.726053	−	0.687638i	$-0.758647\pi$
$941$		−	1.21778e6i		−	1.37528i	0.726053	−	0.687638i	$-0.241353\pi$
$942$		−	142024.i		−	0.160051i
$943$	45655.5	−	1.31724e6i	0.0513417	−	1.48129i
$944$	−122764.			−0.137761
$945$	−208340.			−0.233297
$946$	244408.			0.273107
$947$	325393.			0.362835			0.181417	−	0.983406i	$-0.441932\pi$
$947$	325393.			0.362835			0.181417	+	0.983406i	$0.441932\pi$
$948$			122892.i			0.136743i
$949$	−165987.			−0.184307
$950$			56865.1i			0.0630084i
$951$	−199998.			−0.221139
$952$	257918.			0.284583
$953$		−	990803.i		−	1.09094i	−0.838130	−	0.545471i	$-0.816351\pi$
$953$		−	990803.i		−	1.09094i	0.838130	−	0.545471i	$-0.183649\pi$
$954$		−	104968.i		−	0.115334i
$955$	−506200.			−0.555029
$956$	−861190.			−0.942287
$957$			201279.i			0.219773i
$958$			84887.3i			0.0924936i
$959$	1.40099e6			1.52334
$960$			12624.0i			0.0136979i
$961$	−623602.			−0.675244
$962$			1.27860e6i			1.38161i
$963$			206636.i			0.222820i
$964$		−	116247.i		−	0.125092i
$965$			920.192i			0.000988152i
$966$	−177329.	−	6146.23i	−0.190032	−	0.00658650i
$967$	757105.			0.809661			0.404830	−	0.914392i	$-0.367331\pi$
$967$	757105.			0.809661			0.404830	+	0.914392i	$0.367331\pi$
$968$	140707.			0.150164
$969$	−75186.6			−0.0800742
$970$	84783.6			0.0901090
$971$		−	530305.i		−	0.562454i	−0.959641	−	0.281227i	$-0.909259\pi$
$971$		−	530305.i		−	0.562454i	0.959641	−	0.281227i	$-0.0907414\pi$
$972$	−319875.			−0.338570
$973$		−	44952.3i		−	0.0474817i
$974$	−1.32341e6			−1.39501
$975$	−68804.1			−0.0723777
$976$		−	26814.9i		−	0.0281498i
$977$		−	1.56519e6i		−	1.63975i	−0.572540	−	0.819877i	$-0.694042\pi$
$977$		−	1.56519e6i		−	1.63975i	0.572540	−	0.819877i	$-0.305958\pi$
$978$	−313058.			−0.327301
$979$	420288.			0.438512
$980$			43880.3i			0.0456897i
$981$			510743.i			0.530718i
$982$	71111.5			0.0737423
$983$		−	551640.i		−	0.570885i	−0.958396	−	0.285443i	$-0.907859\pi$
$983$		−	551640.i		−	0.570885i	0.958396	−	0.285443i	$-0.0921406\pi$
$984$	124330.			0.128406
$985$			153231.i			0.157933i
$986$		−	596249.i		−	0.613301i
$987$		−	70074.8i		−	0.0719329i
$988$			321154.i			0.329003i
$989$	497786.	+	17253.3i	0.508921	+	0.0176392i
$990$	−220961.			−0.225447
$991$	635422.			0.647016			0.323508	−	0.946225i	$-0.395138\pi$
$991$	635422.			0.647016			0.323508	+	0.946225i	$0.395138\pi$
$992$	−99135.0			−0.100740
$993$	−13940.5			−0.0141377
$994$		−	157803.i		−	0.159714i
$995$	−723304.			−0.730591
$996$		−	113901.i		−	0.114818i
$997$	467682.			0.470501			0.235251	−	0.971935i	$-0.424409\pi$
$997$	467682.			0.470501			0.235251	+	0.971935i	$0.424409\pi$
$998$	−559173.			−0.561417
$999$		−	627634.i		−	0.628891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.d.a.91.20	✓	32
23.22	odd	2	inner	230.5.d.a.91.29	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.d.a.91.20	✓	32	1.1	even	1	trivial
230.5.d.a.91.29	yes	32	23.22	odd	2	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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.82843 q^{2} -2.20532 q^{3} +8.00000 q^{4} -11.1803i q^{5} -6.23758 q^{6} -53.7736i q^{7} +22.6274 q^{8} -76.1366 q^{9} +O(q^{10})\)	\(q+2.82843 q^{2} -2.20532 q^{3} +8.00000 q^{4} -11.1803i q^{5} -6.23758 q^{6} -53.7736i q^{7} +22.6274 q^{8} -76.1366 q^{9} -31.6228i q^{10} +91.7745i q^{11} -17.6425 q^{12} -249.593 q^{13} -152.095i q^{14} +24.6562i q^{15} +64.0000 q^{16} +211.972i q^{17} -215.347 q^{18} -160.839i q^{19} -89.4427i q^{20} +118.588i q^{21} +259.578i q^{22} +(-18.3241 + 528.683i) q^{23} -49.9006 q^{24} -125.000 q^{25} -705.956 q^{26} +346.536 q^{27} -430.189i q^{28} -994.498 q^{29} +69.7383i q^{30} -547.649 q^{31} +181.019 q^{32} -202.392i q^{33} +599.547i q^{34} -601.207 q^{35} -609.093 q^{36} -1811.16i q^{37} -454.921i q^{38} +550.433 q^{39} -252.982i q^{40} -2491.55 q^{41} +335.417i q^{42} -941.560i q^{43} +734.196i q^{44} +851.233i q^{45} +(-51.8285 + 1495.34i) q^{46} -590.911 q^{47} -141.140 q^{48} -490.597 q^{49} -353.553 q^{50} -467.465i q^{51} -1996.75 q^{52} +487.435i q^{53} +980.152 q^{54} +1026.07 q^{55} -1216.76i q^{56} +354.701i q^{57} -2812.87 q^{58} -1918.19 q^{59} +197.250i q^{60} -418.982i q^{61} -1548.98 q^{62} +4094.14i q^{63} +512.000 q^{64} +2790.54i q^{65} -572.451i q^{66} -2909.93i q^{67} +1695.78i q^{68} +(40.4106 - 1165.91i) q^{69} -1700.47 q^{70} +1037.53 q^{71} -1722.77 q^{72} +665.030 q^{73} -5122.75i q^{74} +275.665 q^{75} -1286.71i q^{76} +4935.05 q^{77} +1556.86 q^{78} -6965.66i q^{79} -715.542i q^{80} +5402.84 q^{81} -7047.17 q^{82} +6456.07i q^{83} +948.703i q^{84} +2369.92 q^{85} -2663.13i q^{86} +2193.18 q^{87} +2076.62i q^{88} -4579.57i q^{89} +2407.65i q^{90} +13421.5i q^{91} +(-146.593 + 4229.46i) q^{92} +1207.74 q^{93} -1671.35 q^{94} -1798.23 q^{95} -399.205 q^{96} +2681.09i q^{97} -1387.62 q^{98} -6987.40i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9}+O(q^{10}) \) 32 * q + 256 * q^4 + 64 * q^6 + 832 * q^9	\( 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9} - 408 q^{13} + 2048 q^{16} + 1024 q^{18} + 1332 q^{23} + 512 q^{24} - 4000 q^{25} + 2208 q^{27} + 3732 q^{29} - 412 q^{31} + 300 q^{35} + 6656 q^{36} - 9208 q^{39} - 6156 q^{41} + 4480 q^{46} + 5184 q^{47} - 13820 q^{49} - 3264 q^{52} - 3328 q^{54} - 6000 q^{55} + 3200 q^{58} - 30468 q^{59} - 10752 q^{62} + 16384 q^{64} - 1168 q^{69} + 4800 q^{70} - 37644 q^{71} + 8192 q^{72} + 19984 q^{73} + 27528 q^{77} + 15744 q^{78} + 69056 q^{81} - 17408 q^{82} + 3300 q^{85} + 28936 q^{87} + 10656 q^{92} + 40648 q^{93} - 23808 q^{94} - 21600 q^{95} + 4096 q^{96} + 43008 q^{98}+O(q^{100}) \) 32 * q + 256 * q^4 + 64 * q^6 + 832 * q^9 - 408 * q^13 + 2048 * q^16 + 1024 * q^18 + 1332 * q^23 + 512 * q^24 - 4000 * q^25 + 2208 * q^27 + 3732 * q^29 - 412 * q^31 + 300 * q^35 + 6656 * q^36 - 9208 * q^39 - 6156 * q^41 + 4480 * q^46 + 5184 * q^47 - 13820 * q^49 - 3264 * q^52 - 3328 * q^54 - 6000 * q^55 + 3200 * q^58 - 30468 * q^59 - 10752 * q^62 + 16384 * q^64 - 1168 * q^69 + 4800 * q^70 - 37644 * q^71 + 8192 * q^72 + 19984 * q^73 + 27528 * q^77 + 15744 * q^78 + 69056 * q^81 - 17408 * q^82 + 3300 * q^85 + 28936 * q^87 + 10656 * q^92 + 40648 * q^93 - 23808 * q^94 - 21600 * q^95 + 4096 * q^96 + 43008 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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