LMFDB - Embedded newform 230.5.d.a.91.16

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			91.16
Character	$\chi$	$=$	230.91
Dual form			230.5.d.a.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843 q^{2} -5.93906 q^{3} +8.00000 q^{4} +11.1803i q^{5} +16.7982 q^{6} +85.3294i q^{7} -22.6274 q^{8} -45.7275 q^{9} +O(q^{10})$	\(q-2.82843 q^{2} -5.93906 q^{3} +8.00000 q^{4} +11.1803i q^{5} +16.7982 q^{6} +85.3294i q^{7} -22.6274 q^{8} -45.7275 q^{9} -31.6228i q^{10} +149.110i q^{11} -47.5125 q^{12} +94.2613 q^{13} -241.348i q^{14} -66.4007i q^{15} +64.0000 q^{16} -334.980i q^{17} +129.337 q^{18} +531.375i q^{19} +89.4427i q^{20} -506.777i q^{21} -421.746i q^{22} +(167.635 + 501.737i) q^{23} +134.386 q^{24} -125.000 q^{25} -266.611 q^{26} +752.643 q^{27} +682.635i q^{28} +1634.50 q^{29} +187.810i q^{30} -1720.16 q^{31} -181.019 q^{32} -885.571i q^{33} +947.467i q^{34} -954.012 q^{35} -365.820 q^{36} -102.130i q^{37} -1502.96i q^{38} -559.824 q^{39} -252.982i q^{40} -1858.79 q^{41} +1433.38i q^{42} -1442.95i q^{43} +1192.88i q^{44} -511.249i q^{45} +(-474.142 - 1419.13i) q^{46} -746.370 q^{47} -380.100 q^{48} -4880.11 q^{49} +353.553 q^{50} +1989.47i q^{51} +754.090 q^{52} +398.992i q^{53} -2128.80 q^{54} -1667.10 q^{55} -1930.78i q^{56} -3155.87i q^{57} -4623.07 q^{58} -1777.75 q^{59} -531.206i q^{60} +351.726i q^{61} +4865.34 q^{62} -3901.90i q^{63} +512.000 q^{64} +1053.87i q^{65} +2504.77i q^{66} -4943.05i q^{67} -2679.84i q^{68} +(-995.593 - 2979.85i) q^{69} +2698.35 q^{70} +115.111 q^{71} +1034.70 q^{72} -6257.45 q^{73} +288.868i q^{74} +742.383 q^{75} +4251.00i q^{76} -12723.4 q^{77} +1583.42 q^{78} +10009.4i q^{79} +715.542i q^{80} -766.062 q^{81} +5257.47 q^{82} +1700.98i q^{83} -4054.21i q^{84} +3745.19 q^{85} +4081.29i q^{86} -9707.42 q^{87} -3373.97i q^{88} +3518.07i q^{89} +1446.03i q^{90} +8043.26i q^{91} +(1341.08 + 4013.89i) q^{92} +10216.1 q^{93} +2111.05 q^{94} -5940.95 q^{95} +1075.09 q^{96} -10639.4i q^{97} +13803.0 q^{98} -6818.42i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−5.93906			−0.659896			−0.329948	−	0.943999i	$-0.607031\pi$
$3$	−5.93906			−0.659896			−0.329948	+	0.943999i	$0.607031\pi$
$4$	8.00000			0.500000
$5$			11.1803i			0.447214i
$5$			11.1803i			0.447214i
$6$	16.7982			0.466617
$7$			85.3294i			1.74142i	0.491800	+	0.870708i	$0.336339\pi$
$7$			85.3294i			1.74142i	−0.491800	+	0.870708i	$0.663661\pi$
$8$	−22.6274			−0.353553
$9$	−45.7275			−0.564537
$10$		−	31.6228i		−	0.316228i
$11$			149.110i			1.23231i	0.787625	+	0.616155i	$0.211311\pi$
$11$			149.110i			1.23231i	−0.787625	+	0.616155i	$0.788689\pi$
$12$	−47.5125			−0.329948
$13$	94.2613			0.557759			0.278880	−	0.960326i	$-0.410037\pi$
$13$	94.2613			0.557759			0.278880	+	0.960326i	$0.410037\pi$
$14$		−	241.348i		−	1.23137i
$15$		−	66.4007i		−	0.295114i
$16$	64.0000			0.250000
$17$		−	334.980i		−	1.15910i	−0.814936	−	0.579550i	$-0.803228\pi$
$17$		−	334.980i		−	1.15910i	0.814936	−	0.579550i	$-0.196772\pi$
$18$	129.337			0.399188
$19$			531.375i			1.47195i	0.677007	+	0.735977i	$0.263277\pi$
$19$			531.375i			1.47195i	−0.677007	+	0.735977i	$0.736723\pi$
$20$			89.4427i			0.223607i
$21$		−	506.777i		−	1.14915i
$22$		−	421.746i		−	0.871375i
$23$	167.635	+	501.737i	0.316890	+	0.948462i
$23$	167.635	+	501.737i	0.316890	+	0.948462i
$24$	134.386			0.233308
$25$	−125.000			−0.200000
$26$	−266.611			−0.394395
$27$	752.643			1.03243
$28$			682.635i			0.870708i
$29$	1634.50			1.94352			0.971762	−	0.235963i	$-0.0758245\pi$
$29$	1634.50			1.94352			0.971762	+	0.235963i	$0.0758245\pi$
$30$			187.810i			0.208677i
$31$	−1720.16			−1.78997			−0.894983	−	0.446101i	$-0.852812\pi$
$31$	−1720.16			−1.78997			−0.894983	+	0.446101i	$0.852812\pi$
$32$	−181.019			−0.176777
$33$		−	885.571i		−	0.813197i
$34$			947.467i			0.819608i
$35$	−954.012			−0.778785
$36$	−365.820			−0.282269
$37$		−	102.130i		−	0.0746021i	−0.999304	−	0.0373011i	$-0.988124\pi$
$37$		−	102.130i		−	0.0746021i	0.999304	−	0.0373011i	$-0.0118760\pi$
$38$		−	1502.96i		−	1.04083i
$39$	−559.824			−0.368063
$40$		−	252.982i		−	0.158114i
$41$	−1858.79			−1.10577			−0.552884	−	0.833258i	$-0.686473\pi$
$41$	−1858.79			−1.10577			−0.552884	+	0.833258i	$0.686473\pi$
$42$			1433.38i			0.812574i
$43$		−	1442.95i		−	0.780397i	−0.920731	−	0.390199i	$-0.872406\pi$
$43$		−	1442.95i		−	0.780397i	0.920731	−	0.390199i	$-0.127594\pi$
$44$			1192.88i			0.616155i
$45$		−	511.249i		−	0.252469i
$46$	−474.142	−	1419.13i	−0.224075	−	0.670664i
$47$	−746.370			−0.337877			−0.168938	−	0.985627i	$-0.554034\pi$
$47$	−746.370			−0.337877			−0.168938	+	0.985627i	$0.554034\pi$
$48$	−380.100			−0.164974
$49$	−4880.11			−2.03253
$50$	353.553			0.141421
$51$			1989.47i			0.764886i
$52$	754.090			0.278880
$53$			398.992i			0.142040i	0.997475	+	0.0710202i	$0.0226255\pi$
$53$			398.992i			0.142040i	−0.997475	+	0.0710202i	$0.977375\pi$
$54$	−2128.80			−0.730040
$55$	−1667.10			−0.551106
$56$		−	1930.78i		−	0.615684i
$57$		−	3155.87i		−	0.971336i
$58$	−4623.07			−1.37428
$59$	−1777.75			−0.510702			−0.255351	−	0.966848i	$-0.582191\pi$
$59$	−1777.75			−0.510702			−0.255351	+	0.966848i	$0.582191\pi$
$60$		−	531.206i		−	0.147557i
$61$			351.726i			0.0945245i	0.998883	+	0.0472622i	$0.0150496\pi$
$61$			351.726i			0.0945245i	−0.998883	+	0.0472622i	$0.984950\pi$
$62$	4865.34			1.26570
$63$		−	3901.90i		−	0.983095i
$64$	512.000			0.125000
$65$			1053.87i			0.249437i
$66$			2504.77i			0.575017i
$67$		−	4943.05i		−	1.10115i	−0.834787	−	0.550573i	$-0.814409\pi$
$67$		−	4943.05i		−	1.10115i	0.834787	−	0.550573i	$-0.185591\pi$
$68$		−	2679.84i		−	0.579550i
$69$	−995.593	−	2979.85i	−0.209114	−	0.625886i
$70$	2698.35			0.550684
$71$	115.111			0.0228349			0.0114175	−	0.999935i	$-0.496366\pi$
$71$	115.111			0.0228349			0.0114175	+	0.999935i	$0.496366\pi$
$72$	1034.70			0.199594
$73$	−6257.45			−1.17423			−0.587113	−	0.809505i	$-0.699735\pi$
$73$	−6257.45			−1.17423			−0.587113	+	0.809505i	$0.699735\pi$
$74$			288.868i			0.0527517i
$75$	742.383			0.131979
$76$			4251.00i			0.735977i
$77$	−12723.4			−2.14597
$78$	1583.42			0.260260
$79$			10009.4i			1.60381i	0.597452	+	0.801905i	$0.296180\pi$
$79$			10009.4i			1.60381i	−0.597452	+	0.801905i	$0.703820\pi$
$80$			715.542i			0.111803i
$81$	−766.062			−0.116760
$82$	5257.47			0.781895
$83$			1700.98i			0.246912i	0.992350	+	0.123456i	$0.0393978\pi$
$83$			1700.98i			0.246912i	−0.992350	+	0.123456i	$0.960602\pi$
$84$		−	4054.21i		−	0.574577i
$85$	3745.19			0.518366
$86$			4081.29i			0.551824i
$87$	−9707.42			−1.28252
$88$		−	3373.97i		−	0.435688i
$89$			3518.07i			0.444144i	0.975030	+	0.222072i	$0.0712820\pi$
$89$			3518.07i			0.444144i	−0.975030	+	0.222072i	$0.928718\pi$
$90$			1446.03i			0.178522i
$91$			8043.26i			0.971291i
$92$	1341.08	+	4013.89i	0.158445	+	0.474231i
$93$	10216.1			1.18119
$94$	2111.05			0.238915
$95$	−5940.95			−0.658277
$96$	1075.09			0.116654
$97$		−	10639.4i		−	1.13076i	−0.824829	−	0.565382i	$-0.808729\pi$
$97$		−	10639.4i		−	1.13076i	0.824829	−	0.565382i	$-0.191271\pi$
$98$	13803.0			1.43722
$99$		−	6818.42i		−	0.695686i
$100$	−1000.00			−0.100000
$101$	3332.79			0.326712			0.163356	−	0.986567i	$-0.447768\pi$
$101$	3332.79			0.326712			0.163356	+	0.986567i	$0.447768\pi$
$102$		−	5627.07i		−	0.540856i
$103$		−	5503.72i		−	0.518779i	−0.965773	−	0.259389i	$-0.916479\pi$
$103$		−	5503.72i		−	0.518779i	0.965773	−	0.259389i	$-0.0835213\pi$
$104$	−2132.89			−0.197198
$105$	5665.94			0.513917
$106$		−	1128.52i		−	0.100438i
$107$		−	10165.8i		−	0.887918i	−0.896047	−	0.443959i	$-0.853574\pi$
$107$		−	10165.8i		−	0.887918i	0.896047	−	0.443959i	$-0.146426\pi$
$108$	6021.14			0.516216
$109$		−	1522.66i		−	0.128159i	−0.997945	−	0.0640796i	$-0.979589\pi$
$109$		−	1522.66i		−	0.128159i	0.997945	−	0.0640796i	$-0.0204112\pi$
$110$	4715.26			0.389691
$111$			606.558i			0.0492296i
$112$			5461.08i			0.435354i
$113$			11315.6i			0.886175i	0.896478	+	0.443087i	$0.146117\pi$
$113$			11315.6i			0.886175i	−0.896478	+	0.443087i	$0.853883\pi$
$114$			8926.15i			0.686838i
$115$	−5609.59	+	1874.21i	−0.424165	+	0.141717i
$116$	13076.0			0.971762
$117$	−4310.34			−0.314876
$118$	5028.24			0.361120
$119$	28583.7			2.01848
$120$			1502.48i			0.104339i
$121$	−7592.68			−0.518590
$122$		−	994.830i		−	0.0668389i
$123$	11039.5			0.729691
$124$	−13761.3			−0.894983
$125$		−	1397.54i		−	0.0894427i
$126$			11036.3i			0.695153i
$127$	27956.1			1.73328			0.866641	−	0.498931i	$-0.166274\pi$
$127$	27956.1			1.73328			0.866641	+	0.498931i	$0.166274\pi$
$128$	−1448.15			−0.0883883
$129$			8569.79i			0.514981i
$130$		−	2980.80i		−	0.176379i
$131$	16037.2			0.934512			0.467256	−	0.884122i	$-0.345243\pi$
$131$	16037.2			0.934512			0.467256	+	0.884122i	$0.345243\pi$
$132$		−	7084.57i		−	0.406598i
$133$	−45341.9			−2.56328
$134$			13981.0i			0.778628i
$135$			8414.80i			0.461718i
$136$			7579.74i			0.409804i
$137$		−	23560.9i		−	1.25531i	−0.778492	−	0.627654i	$-0.784015\pi$
$137$		−	23560.9i		−	1.25531i	0.778492	−	0.627654i	$-0.215985\pi$
$138$	2815.96	+	8428.27i	0.147866	+	0.442569i
$139$	−11762.3			−0.608782			−0.304391	−	0.952547i	$-0.598453\pi$
$139$	−11762.3			−0.608782			−0.304391	+	0.952547i	$0.598453\pi$
$140$	−7632.09			−0.389393
$141$	4432.74			0.222964
$142$	−325.583			−0.0161467
$143$			14055.3i			0.687333i
$144$	−2926.56			−0.141134
$145$			18274.3i			0.869170i
$146$	17698.7			0.830303
$147$	28983.3			1.34126
$148$		−	817.042i		−	0.0373011i
$149$			9318.54i			0.419735i	0.977730	+	0.209867i	$0.0673033\pi$
$149$			9318.54i			0.419735i	−0.977730	+	0.209867i	$0.932697\pi$
$150$	−2099.78			−0.0933234
$151$	10160.5			0.445614			0.222807	−	0.974863i	$-0.428478\pi$
$151$	10160.5			0.445614			0.222807	+	0.974863i	$0.428478\pi$
$152$		−	12023.6i		−	0.520414i
$153$			15317.8i			0.654356i
$154$	35987.3			1.51743
$155$		−	19231.9i		−	0.800497i
$156$	−4478.59			−0.184031
$157$		−	5254.31i		−	0.213165i	−0.994304	−	0.106583i	$-0.966009\pi$
$157$		−	5254.31i		−	0.213165i	0.994304	−	0.106583i	$-0.0339909\pi$
$158$		−	28310.8i		−	1.13406i
$159$		−	2369.64i		−	0.0937319i
$160$		−	2023.86i		−	0.0790569i
$161$	−42812.9	+	14304.2i	−1.65167	+	0.551837i
$162$	2166.75			0.0825617
$163$	−33103.9			−1.24596			−0.622980	−	0.782238i	$-0.714078\pi$
$163$	−33103.9			−1.24596			−0.622980	+	0.782238i	$0.714078\pi$
$164$	−14870.4			−0.552884
$165$	9900.99			0.363673
$166$		−	4811.09i		−	0.174593i
$167$	29963.5			1.07438			0.537192	−	0.843460i	$-0.319485\pi$
$167$	29963.5			1.07438			0.537192	+	0.843460i	$0.319485\pi$
$168$			11467.0i			0.406287i
$169$	−19675.8			−0.688905
$170$	−10593.0			−0.366540
$171$		−	24298.5i		−	0.830973i
$172$		−	11543.6i		−	0.390199i
$173$	57509.9			1.92154			0.960772	−	0.277338i	$-0.0894522\pi$
$173$	57509.9			1.92154			0.960772	+	0.277338i	$0.0894522\pi$
$174$	27456.7			0.906881
$175$		−	10666.2i		−	0.348283i
$176$			9543.01i			0.308078i
$177$	10558.2			0.337010
$178$		−	9950.59i		−	0.314057i
$179$	−6031.23			−0.188235			−0.0941174	−	0.995561i	$-0.530003\pi$
$179$	−6031.23			−0.188235			−0.0941174	+	0.995561i	$0.530003\pi$
$180$		−	4090.00i		−	0.126234i
$181$		−	31436.4i		−	0.959568i	−0.877387	−	0.479784i	$-0.840715\pi$
$181$		−	31436.4i		−	0.959568i	0.877387	−	0.479784i	$-0.159285\pi$
$182$		−	22749.8i		−	0.686807i
$183$		−	2088.92i		−	0.0623763i
$184$	−3793.14	−	11353.0i	−0.112037	−	0.335332i
$185$	1141.85			0.0333631
$186$	−28895.5			−0.835228
$187$	49948.8			1.42837
$188$	−5970.96			−0.168938
$189$			64222.6i			1.79789i
$190$	16803.6			0.465472
$191$			17818.4i			0.488430i	0.969721	+	0.244215i	$0.0785303\pi$
$191$			17818.4i			0.488430i	−0.969721	+	0.244215i	$0.921470\pi$
$192$	−3040.80			−0.0824870
$193$	26259.3			0.704967			0.352484	−	0.935818i	$-0.385337\pi$
$193$	26259.3			0.704967			0.352484	+	0.935818i	$0.385337\pi$
$194$			30092.6i			0.799571i
$195$		−	6259.02i		−	0.164603i
$196$	−39040.9			−1.01627
$197$	−10911.3			−0.281154			−0.140577	−	0.990070i	$-0.544896\pi$
$197$	−10911.3			−0.281154			−0.140577	+	0.990070i	$0.544896\pi$
$198$			19285.4i			0.491924i
$199$		−	53585.3i		−	1.35313i	−0.736383	−	0.676565i	$-0.763468\pi$
$199$		−	53585.3i		−	1.35313i	0.736383	−	0.676565i	$-0.236532\pi$
$200$	2828.43			0.0707107
$201$			29357.1i			0.726642i
$202$	−9426.55			−0.231020
$203$			139471.i			3.38449i
$204$			15915.7i			0.382443i
$205$		−	20782.0i		−	0.494514i
$206$			15566.9i			0.366832i
$207$	−7665.52	−	22943.2i	−0.178896	−	0.535443i
$208$	6032.72			0.139440
$209$	−79233.1			−1.81390
$210$	−16025.7			−0.363394
$211$	−75559.1			−1.69716			−0.848578	−	0.529070i	$-0.822541\pi$
$211$	−75559.1			−1.69716			−0.848578	+	0.529070i	$0.822541\pi$
$212$			3191.93i			0.0710202i
$213$	−683.650			−0.0150687
$214$			28753.1i			0.627853i
$215$	16132.7			0.349004
$216$	−17030.4			−0.365020
$217$		−	146780.i		−	3.11708i
$218$			4306.73i			0.0906223i
$219$	37163.4			0.774866
$220$	−13336.8			−0.275553
$221$		−	31575.7i		−	0.646499i
$222$		−	1715.61i		−	0.0348106i
$223$	−85808.9			−1.72553			−0.862765	−	0.505605i	$-0.831269\pi$
$223$	−85808.9			−1.72553			−0.862765	+	0.505605i	$0.831269\pi$
$224$		−	15446.3i		−	0.307842i
$225$	5715.94			0.112907
$226$		−	32005.3i		−	0.626620i
$227$			46928.4i			0.910717i	0.890308	+	0.455359i	$0.150489\pi$
$227$			46928.4i			0.910717i	−0.890308	+	0.455359i	$0.849511\pi$
$228$		−	25247.0i		−	0.485668i
$229$		−	35820.6i		−	0.683064i	−0.939870	−	0.341532i	$-0.889054\pi$
$229$		−	35820.6i		−	0.683064i	0.939870	−	0.341532i	$-0.110946\pi$
$230$	15866.3	−	5301.07i	0.299930	−	0.100209i
$231$	75565.3			1.41611
$232$	−36984.6			−0.687140
$233$	45702.7			0.841841			0.420921	−	0.907097i	$-0.361707\pi$
$233$	45702.7			0.841841			0.420921	+	0.907097i	$0.361707\pi$
$234$	12191.5			0.222651
$235$		−	8344.67i		−	0.151103i
$236$	−14222.0			−0.255351
$237$		−	59446.3i		−	1.05835i
$238$	−80846.8			−1.42728
$239$	−31882.2			−0.558152			−0.279076	−	0.960269i	$-0.590028\pi$
$239$	−31882.2			−0.558152			−0.279076	+	0.960269i	$0.590028\pi$
$240$		−	4249.65i		−	0.0737786i
$241$			90751.7i			1.56250i	0.624217	+	0.781251i	$0.285418\pi$
$241$			90751.7i			1.56250i	−0.624217	+	0.781251i	$0.714582\pi$
$242$	21475.3			0.366698
$243$	−56414.4			−0.955382
$244$			2813.80i			0.0472622i
$245$		−	54561.3i		−	0.908976i
$246$	−31224.4			−0.515970
$247$			50088.1i			0.820995i
$248$	38922.7			0.632848
$249$		−	10102.2i		−	0.162936i
$250$			3952.85i			0.0632456i
$251$			62387.2i			0.990258i	0.868820	+	0.495129i	$0.164879\pi$
$251$			62387.2i			0.990258i	−0.868820	+	0.495129i	$0.835121\pi$
$252$		−	31215.2i		−	0.491547i
$253$	−74813.7	+	24995.9i	−1.16880	+	0.390507i
$254$	−79071.8			−1.22562
$255$	−22242.9			−0.342067
$256$	4096.00			0.0625000
$257$	−40003.8			−0.605669			−0.302835	−	0.953043i	$-0.597933\pi$
$257$	−40003.8			−0.605669			−0.302835	+	0.953043i	$0.597933\pi$
$258$		−	24239.0i		−	0.364146i
$259$	8714.72			0.129913
$260$			8430.99i			0.124719i
$261$	−74741.8			−1.09719
$262$	−45359.9			−0.660800
$263$		−	84759.9i		−	1.22540i	−0.790314	−	0.612702i	$-0.790083\pi$
$263$		−	84759.9i		−	1.22540i	0.790314	−	0.612702i	$-0.209917\pi$
$264$			20038.2i			0.287508i
$265$	−4460.86			−0.0635224
$266$	128246.			1.81252
$267$		−	20894.0i		−	0.293089i
$268$		−	39544.4i		−	0.550573i
$269$	5521.93			0.0763108			0.0381554	−	0.999272i	$-0.487852\pi$
$269$	5521.93			0.0763108			0.0381554	+	0.999272i	$0.487852\pi$
$270$		−	23800.7i		−	0.326484i
$271$	122326.			1.66564			0.832820	−	0.553544i	$-0.186725\pi$
$271$	122326.			1.66564			0.832820	+	0.553544i	$0.186725\pi$
$272$		−	21438.7i		−	0.289775i
$273$		−	47769.4i		−	0.640951i
$274$			66640.3i			0.887637i
$275$		−	18638.7i		−	0.246462i
$276$	−7964.74	−	23838.8i	−0.104557	−	0.312943i
$277$	−61558.0			−0.802278			−0.401139	−	0.916017i	$-0.631386\pi$
$277$	−61558.0			−0.802278			−0.401139	+	0.916017i	$0.631386\pi$
$278$	33268.8			0.430474
$279$	78658.5			1.01050
$280$	21586.8			0.275342
$281$		−	101701.i		−	1.28799i	−0.765031	−	0.643994i	$-0.777276\pi$
$281$		−	101701.i		−	1.28799i	0.765031	−	0.643994i	$-0.222724\pi$
$282$	−12537.7			−0.157659
$283$			110681.i			1.38198i	0.722866	+	0.690988i	$0.242824\pi$
$283$			110681.i			1.38198i	−0.722866	+	0.690988i	$0.757176\pi$
$284$	920.887			0.0114175
$285$	35283.7			0.434395
$286$		−	39754.3i		−	0.486018i
$287$		−	158610.i		−	1.92560i
$288$	8277.57			0.0997971
$289$	−28690.7			−0.343515
$290$		−	51687.5i		−	0.614596i
$291$			63187.8i			0.746186i
$292$	−50059.6			−0.587113
$293$			161940.i			1.88634i	0.332313	+	0.943169i	$0.392171\pi$
$293$			161940.i			1.88634i	−0.332313	+	0.943169i	$0.607829\pi$
$294$	−81977.1			−0.948414
$295$		−	19875.9i		−	0.228393i
$296$			2310.94i			0.0263758i
$297$			112226.i			1.27228i
$298$		−	26356.8i		−	0.296797i
$299$	15801.5	+	47294.3i	0.176748	+	0.529014i
$300$	5939.06			0.0659896
$301$	123126.			1.35900
$302$	−28738.1			−0.315097
$303$	−19793.6			−0.215596
$304$			34008.0i			0.367988i
$305$	−3932.41			−0.0422726
$306$		−	43325.3i		−	0.462699i
$307$	−93304.7			−0.989981			−0.494990	−	0.868898i	$-0.664828\pi$
$307$	−93304.7			−0.989981			−0.494990	+	0.868898i	$0.664828\pi$
$308$	−101787.			−1.07298
$309$			32687.0i			0.342340i
$310$			54396.1i			0.566037i
$311$	20547.6			0.212442			0.106221	−	0.994343i	$-0.466125\pi$
$311$	20547.6			0.212442			0.106221	+	0.994343i	$0.466125\pi$
$312$	12667.4			0.130130
$313$			86902.9i			0.887044i	0.896263	+	0.443522i	$0.146271\pi$
$313$			86902.9i			0.887044i	−0.896263	+	0.443522i	$0.853729\pi$
$314$			14861.4i			0.150731i
$315$	43624.6			0.439653
$316$			80075.0i			0.801905i
$317$	144586.			1.43882			0.719412	−	0.694584i	$-0.244412\pi$
$317$	144586.			1.43882			0.719412	+	0.694584i	$0.244412\pi$
$318$			6702.34i			0.0662785i
$319$			243720.i			2.39503i
$320$			5724.33i			0.0559017i
$321$			60375.1i			0.585933i
$322$	121093.	−	40458.3i	1.16791	−	0.390208i
$323$	178000.			1.70614
$324$	−6128.50			−0.0583800
$325$	−11782.7			−0.111552
$326$	93632.0			0.881027
$327$			9043.18i			0.0845718i
$328$	42059.7			0.390948
$329$		−	63687.3i		−	0.588384i
$330$	−28004.2			−0.257155
$331$	−87042.5			−0.794466			−0.397233	−	0.917718i	$-0.630030\pi$
$331$	−87042.5			−0.794466			−0.397233	+	0.917718i	$0.630030\pi$
$332$			13607.8i			0.123456i
$333$			4670.17i			0.0421157i
$334$	−84749.6			−0.759704
$335$	55264.9			0.492448
$336$		−	32433.7i		−	0.287288i
$337$		−	14596.7i		−	0.128527i	−0.997933	−	0.0642636i	$-0.979530\pi$
$337$		−	14596.7i		−	0.128527i	0.997933	−	0.0642636i	$-0.0204698\pi$
$338$	55651.6			0.487129
$339$		−	67203.9i		−	0.584783i
$340$	29961.5			0.259183
$341$		−	256492.i		−	2.20579i
$342$			68726.5i			0.587586i
$343$		−	211541.i		−	1.79807i
$344$			32650.3i			0.275912i
$345$	33315.7	−	11131.1i	0.279905	−	0.0935187i
$346$	−162663.			−1.35874
$347$	206196.			1.71246			0.856231	−	0.516594i	$-0.172800\pi$
$347$	206196.			1.71246			0.856231	+	0.516594i	$0.172800\pi$
$348$	−77659.4			−0.641262
$349$	−515.138			−0.00422934			−0.00211467	−	0.999998i	$-0.500673\pi$
$349$	−515.138			−0.00422934			−0.00211467	+	0.999998i	$0.500673\pi$
$350$			30168.5i			0.246274i
$351$	70945.1			0.575848
$352$		−	26991.7i		−	0.217844i
$353$	110582.			0.887430			0.443715	−	0.896168i	$-0.353660\pi$
$353$	110582.			0.887430			0.443715	+	0.896168i	$0.353660\pi$
$354$	−29863.0			−0.238302
$355$			1286.98i			0.0102121i
$356$			28144.5i			0.222072i
$357$	−169760.			−1.33198
$358$	17058.9			0.133102
$359$		−	130425.i		−	1.01198i	−0.862540	−	0.505988i	$-0.831128\pi$
$359$		−	130425.i		−	1.01198i	0.862540	−	0.505988i	$-0.168872\pi$
$360$			11568.3i			0.0892612i
$361$	−152038.			−1.16665
$362$			88915.6i			0.678517i
$363$	45093.4			0.342215
$364$			64346.1i			0.485646i
$365$		−	69960.4i		−	0.525129i
$366$			5908.36i			0.0441067i
$367$			68617.3i			0.509450i	0.967014	+	0.254725i	$0.0819849\pi$
$367$			68617.3i			0.509450i	−0.967014	+	0.254725i	$0.918015\pi$
$368$	10728.6	+	32111.1i	0.0792224	+	0.237116i
$369$	84998.1			0.624247
$370$	−3229.64			−0.0235913
$371$	−34045.7			−0.247352
$372$	81728.9			0.590595
$373$			26807.9i			0.192684i	0.995348	+	0.0963420i	$0.0307143\pi$
$373$			26807.9i			0.192684i	−0.995348	+	0.0963420i	$0.969286\pi$
$374$	−141276.			−1.01001
$375$			8300.09i			0.0590229i
$376$	16888.4			0.119457
$377$	154070.			1.08402
$378$		−	181649.i		−	1.27130i
$379$			51916.4i			0.361432i	0.983535	+	0.180716i	$0.0578414\pi$
$379$			51916.4i			0.361432i	−0.983535	+	0.180716i	$0.942159\pi$
$380$	−47527.6			−0.329139
$381$	−166033.			−1.14379
$382$		−	50398.1i		−	0.345372i
$383$			106530.i			0.726230i	0.931744	+	0.363115i	$0.118287\pi$
$383$			106530.i			0.726230i	−0.931744	+	0.363115i	$0.881713\pi$
$384$	8600.68			0.0583271
$385$		−	142252.i		−	0.959705i
$386$	−74272.6			−0.498487
$387$			65982.7i			0.440563i
$388$		−	85114.9i		−	0.565382i
$389$			184564.i			1.21969i	0.792522	+	0.609843i	$0.208767\pi$
$389$			184564.i			1.21969i	−0.792522	+	0.609843i	$0.791233\pi$
$390$			17703.2i			0.116392i
$391$	168072.	−	56154.3i	1.09936	−	0.367307i
$392$	110424.			0.718609
$393$	−95245.7			−0.616680
$394$	30861.9			0.198806
$395$	−111908.			−0.717245
$396$		−	54547.3i		−	0.347843i
$397$	−76881.4			−0.487798			−0.243899	−	0.969801i	$-0.578427\pi$
$397$	−76881.4			−0.487798			−0.243899	+	0.969801i	$0.578427\pi$
$398$			151562.i			0.956808i
$399$	269289.			1.69150
$400$	−8000.00			−0.0500000
$401$		−	65738.1i		−	0.408816i	−0.978886	−	0.204408i	$-0.934473\pi$
$401$		−	65738.1i		−	0.408816i	0.978886	−	0.204408i	$-0.0655270\pi$
$402$		−	83034.3i		−	0.513813i
$403$	−162144.			−0.998370
$404$	26662.3			0.163356
$405$		−	8564.83i		−	0.0522166i
$406$		−	394484.i		−	2.39319i
$407$	15228.6			0.0919330
$408$		−	45016.5i		−	0.270428i
$409$	−207846.			−1.24250			−0.621248	−	0.783614i	$-0.713374\pi$
$409$	−207846.			−1.24250			−0.621248	+	0.783614i	$0.713374\pi$
$410$			58780.2i			0.349674i
$411$			139930.i			0.828373i
$412$		−	44029.8i		−	0.259389i
$413$		−	151695.i		−	0.889344i
$414$	21681.4	+	64893.1i	0.126499	+	0.378615i
$415$	−19017.5			−0.110422
$416$	−17063.1			−0.0985988
$417$	69856.9			0.401733
$418$	224105.			1.28262
$419$			215727.i			1.22878i	0.789001	+	0.614392i	$0.210599\pi$
$419$			215727.i			1.22878i	−0.789001	+	0.614392i	$0.789401\pi$
$420$	45327.5			0.256959
$421$			257211.i			1.45119i	0.688122	+	0.725595i	$0.258436\pi$
$421$			257211.i			1.45119i	−0.688122	+	0.725595i	$0.741564\pi$
$422$	213713.			1.20007
$423$	34129.7			0.190744
$424$		−	9028.15i		−	0.0502189i
$425$			41872.5i			0.231820i
$426$	1933.66			0.0106552
$427$	−30012.5			−0.164606
$428$		−	81326.2i		−	0.443959i
$429$		−	83475.1i		−	0.453568i
$430$	−45630.2			−0.246783
$431$			305693.i			1.64562i	0.568314	+	0.822812i	$0.307596\pi$
$431$			305693.i			1.64562i	−0.568314	+	0.822812i	$0.692404\pi$
$432$	48169.1			0.258108
$433$			291970.i			1.55726i	0.627482	+	0.778631i	$0.284086\pi$
$433$			291970.i			1.55726i	−0.627482	+	0.778631i	$0.715914\pi$
$434$			415156.i			2.20411i
$435$		−	108532.i		−	0.573562i
$436$		−	12181.3i		−	0.0640796i
$437$	−266610.	+	89076.9i	−1.39609	+	0.466447i
$438$	−105114.			−0.547913
$439$	274558.			1.42464			0.712320	−	0.701855i	$-0.247645\pi$
$439$	274558.			1.42464			0.712320	+	0.701855i	$0.247645\pi$
$440$	37722.1			0.194845
$441$	223155.			1.14744
$442$			89309.5i			0.457144i
$443$	−254265.			−1.29562			−0.647811	−	0.761801i	$-0.724315\pi$
$443$	−254265.			−1.29562			−0.647811	+	0.761801i	$0.724315\pi$
$444$			4852.47i			0.0246148i
$445$	−39333.2			−0.198627
$446$	242704.			1.22013
$447$		−	55343.4i		−	0.276981i
$448$			43688.7i			0.217677i
$449$	−142386.			−0.706274			−0.353137	−	0.935572i	$-0.614885\pi$
$449$	−142386.			−0.706274			−0.353137	+	0.935572i	$0.614885\pi$
$450$	−16167.1			−0.0798377
$451$		−	277164.i		−	1.36265i
$452$			90524.5i			0.443087i
$453$	−60343.6			−0.294059
$454$		−	132733.i		−	0.643974i
$455$	−89926.4			−0.434375
$456$			71409.2i			0.343419i
$457$		−	28652.7i		−	0.137194i	−0.997644	−	0.0685968i	$-0.978148\pi$
$457$		−	28652.7i		−	0.137194i	0.997644	−	0.0685968i	$-0.0218522\pi$
$458$			101316.i			0.482999i
$459$		−	252120.i		−	1.19669i
$460$	−44876.7	+	14993.7i	−0.212083	+	0.0708587i
$461$	−272575.			−1.28258			−0.641290	−	0.767298i	$-0.721601\pi$
$461$	−272575.			−1.28258			−0.641290	+	0.767298i	$0.721601\pi$
$462$	−213731.			−1.00134
$463$	148219.			0.691420			0.345710	−	0.938341i	$-0.387638\pi$
$463$	148219.			0.691420			0.345710	+	0.938341i	$0.387638\pi$
$464$	104608.			0.485881
$465$			114220.i			0.528245i
$466$	−129267.			−0.595272
$467$		−	118935.i		−	0.545350i	−0.962106	−	0.272675i	$-0.912092\pi$
$467$		−	118935.i		−	0.545350i	0.962106	−	0.272675i	$-0.0879083\pi$
$468$	−34482.7			−0.157438
$469$	421787.			1.91755
$470$			23602.3i			0.106846i
$471$			31205.7i			0.140667i
$472$	40225.9			0.180560
$473$	215158.			0.961692
$474$			168140.i			0.748364i
$475$		−	66421.9i		−	0.294391i
$476$	228669.			1.00924
$477$		−	18244.9i		−	0.0801872i
$478$	90176.5			0.394673
$479$		−	253474.i		−	1.10475i	−0.833597	−	0.552373i	$-0.813722\pi$
$479$		−	253474.i		−	1.10475i	0.833597	−	0.552373i	$-0.186278\pi$
$480$			12019.8i			0.0521693i
$481$		−	9626.93i		−	0.0416100i
$482$		−	256685.i		−	1.10486i
$483$	254268.	−	84953.3i	1.08993	−	0.364155i
$484$	−60741.4			−0.259295
$485$	118952.			0.505693
$486$	159564.			0.675557
$487$	−263626.			−1.11155			−0.555776	−	0.831332i	$-0.687579\pi$
$487$	−263626.			−1.11155			−0.555776	+	0.831332i	$0.687579\pi$
$488$		−	7958.64i		−	0.0334194i
$489$	196606.			0.822204
$490$			154323.i			0.642743i
$491$	163005.			0.676142			0.338071	−	0.941121i	$-0.390226\pi$
$491$	163005.			0.676142			0.338071	+	0.941121i	$0.390226\pi$
$492$	88316.0			0.364846
$493$		−	547526.i		−	2.25274i
$494$		−	141671.i		−	0.580531i
$495$	76232.2			0.311120
$496$	−110090.			−0.447491
$497$			9822.34i			0.0397651i
$498$			28573.3i			0.115213i
$499$	−494365.			−1.98539			−0.992697	−	0.120634i	$-0.961507\pi$
$499$	−494365.			−1.98539			−0.992697	+	0.120634i	$0.961507\pi$
$500$		−	11180.3i		−	0.0447214i
$501$	−177955.			−0.708982
$502$		−	176458.i		−	0.700218i
$503$			119236.i			0.471274i	0.971841	+	0.235637i	$0.0757176\pi$
$503$			119236.i			0.471274i	−0.971841	+	0.235637i	$0.924282\pi$
$504$			88290.0i			0.347577i
$505$			37261.7i			0.146110i
$506$	211605.	−	70699.2i	0.826467	−	0.276130i
$507$	116856.			0.454605
$508$	223649.			0.866641
$509$	−443038.			−1.71004			−0.855018	−	0.518598i	$-0.826454\pi$
$509$	−443038.			−1.71004			−0.855018	+	0.518598i	$0.826454\pi$
$510$	62912.5			0.241878
$511$		−	533944.i		−	2.04482i
$512$	−11585.2			−0.0441942
$513$			399936.i			1.51969i
$514$	113148.			0.428273
$515$	61533.5			0.232005
$516$			68558.4i			0.257490i
$517$		−	111291.i		−	0.416369i
$518$	−24648.9			−0.0918626
$519$	−341555.			−1.26802
$520$		−	23846.4i		−	0.0881895i
$521$		−	44127.0i		−	0.162566i	−0.996691	−	0.0812829i	$-0.974098\pi$
$521$		−	44127.0i		−	0.162566i	0.996691	−	0.0812829i	$-0.0259017\pi$
$522$	211402.			0.775832
$523$			46128.2i			0.168641i	0.996439	+	0.0843204i	$0.0268719\pi$
$523$			46128.2i			0.168641i	−0.996439	+	0.0843204i	$0.973128\pi$
$524$	128297.			0.467256
$525$			63347.1i			0.229831i
$526$			239737.i			0.866491i
$527$			576218.i			2.07475i
$528$		−	56676.6i		−	0.203299i
$529$	−223638.	+	168217.i	−0.799162	+	0.601116i
$530$	12617.2			0.0449171
$531$	81292.2			0.288310
$532$	−362735.			−1.28164
$533$	−175212.			−0.616752
$534$			59097.2i			0.207245i
$535$	113657.			0.397089
$536$			111848.i			0.389314i
$537$	35819.8			0.124215
$538$	−15618.4			−0.0539599
$539$		−	727671.i		−	2.50471i
$540$			67318.4i			0.230859i
$541$	−43640.4			−0.149106			−0.0745529	−	0.997217i	$-0.523753\pi$
$541$	−43640.4			−0.149106			−0.0745529	+	0.997217i	$0.523753\pi$
$542$	−345991.			−1.17778
$543$			186703.i			0.633215i
$544$			60637.9i			0.204902i
$545$	17023.9			0.0573146
$546$			135112.i			0.453221i
$547$	271102.			0.906064			0.453032	−	0.891494i	$-0.350342\pi$
$547$	271102.			0.906064			0.453032	+	0.891494i	$0.350342\pi$
$548$		−	188487.i		−	0.627654i
$549$		−	16083.5i		−	0.0533626i
$550$			52718.2i			0.174275i
$551$			868535.i			2.86078i
$552$	22527.7	+	67426.2i	0.0739330	+	0.221284i
$553$	−854094.			−2.79290
$554$	174112.			0.567296
$555$	−6781.53			−0.0220162
$556$	−94098.3			−0.304391
$557$		−	177219.i		−	0.571217i	−0.958346	−	0.285608i	$-0.907804\pi$
$557$		−	177219.i		−	0.571217i	0.958346	−	0.285608i	$-0.0921957\pi$
$558$	−222480.			−0.714533
$559$		−	136015.i		−	0.435274i
$560$	−61056.8			−0.194696
$561$	−296649.			−0.942577
$562$			287653.i			0.910745i
$563$			52495.8i			0.165618i	0.996565	+	0.0828091i	$0.0263892\pi$
$563$			52495.8i			0.165618i	−0.996565	+	0.0828091i	$0.973611\pi$
$564$	35461.9			0.111482
$565$	−126512.			−0.396309
$566$		−	313053.i		−	0.977204i
$567$		−	65367.6i		−	0.203328i
$568$	−2604.66			−0.00807336
$569$			15765.3i			0.0486942i	0.999704	+	0.0243471i	$0.00775069\pi$
$569$			15765.3i			0.0486942i	−0.999704	+	0.0243471i	$0.992249\pi$
$570$	−99797.4			−0.307163
$571$		−	458343.i		−	1.40578i	−0.711296	−	0.702892i	$-0.751892\pi$
$571$		−	458343.i		−	1.40578i	0.711296	−	0.702892i	$-0.248108\pi$
$572$			112442.i			0.343666i
$573$		−	105825.i		−	0.322313i
$574$			448616.i			1.36161i
$575$	−20954.3	−	62717.1i	−0.0633779	−	0.189692i
$576$	−23412.5			−0.0705672
$577$	−103757.			−0.311650			−0.155825	−	0.987785i	$-0.549804\pi$
$577$	−103757.			−0.311650			−0.155825	+	0.987785i	$0.549804\pi$
$578$	81149.5			0.242902
$579$	−155956.			−0.465205
$580$			146194.i			0.434585i
$581$	−145143.			−0.429976
$582$		−	178722.i		−	0.527633i
$583$	−59493.5			−0.175038
$584$	141590.			0.415151
$585$		−	48191.0i		−	0.140817i
$586$		−	458036.i		−	1.33384i
$587$	−195271.			−0.566709			−0.283355	−	0.959015i	$-0.591447\pi$
$587$	−195271.			−0.566709			−0.283355	+	0.959015i	$0.591447\pi$
$588$	231866.			0.670630
$589$		−	914048.i		−	2.63475i
$590$			56217.5i			0.161498i
$591$	64803.0			0.185533
$592$		−	6536.34i		−	0.0186505i
$593$	−231646.			−0.658741			−0.329371	−	0.944201i	$-0.606837\pi$
$593$	−231646.			−0.658741			−0.329371	+	0.944201i	$0.606837\pi$
$594$		−	317424.i		−	0.899636i
$595$			319575.i			0.902691i
$596$			74548.3i			0.209867i
$597$			318247.i			0.892925i
$598$	−44693.3	−	133769.i	−0.124980	−	0.374069i
$599$	236370.			0.658779			0.329389	−	0.944194i	$-0.393157\pi$
$599$	236370.			0.658779			0.329389	+	0.944194i	$0.393157\pi$
$600$	−16798.2			−0.0466617
$601$	−249508.			−0.690773			−0.345386	−	0.938461i	$-0.612252\pi$
$601$	−249508.			−0.690773			−0.345386	+	0.938461i	$0.612252\pi$
$602$	−348254.			−0.960956
$603$			226033.i			0.621638i
$604$	81283.6			0.222807
$605$		−	84888.7i		−	0.231920i
$606$	55984.8			0.152449
$607$	−217474.			−0.590242			−0.295121	−	0.955460i	$-0.595360\pi$
$607$	−217474.			−0.590242			−0.295121	+	0.955460i	$0.595360\pi$
$608$		−	96189.2i		−	0.260207i
$609$		−	828328.i		−	2.23341i
$610$	11122.5			0.0298913
$611$	−70353.8			−0.188454
$612$			122543.i			0.327178i
$613$			143646.i			0.382271i	0.981564	+	0.191136i	$0.0612170\pi$
$613$			143646.i			0.382271i	−0.981564	+	0.191136i	$0.938783\pi$
$614$	263906.			0.700022
$615$			123425.i			0.326328i
$616$	287898.			0.758714
$617$			42091.4i			0.110566i	0.998471	+	0.0552832i	$0.0176062\pi$
$617$			42091.4i			0.110566i	−0.998471	+	0.0552832i	$0.982394\pi$
$618$		−	92452.7i		−	0.242071i
$619$		−	510269.i		−	1.33174i	−0.746070	−	0.665868i	$-0.768061\pi$
$619$		−	510269.i		−	1.33174i	0.746070	−	0.665868i	$-0.231939\pi$
$620$		−	153855.i		−	0.400248i
$621$	126169.	+	377628.i	0.327167	+	0.979223i
$622$	−58117.4			−0.150219
$623$	−300195.			−0.773440
$624$	−35828.7			−0.0920157
$625$	15625.0			0.0400000
$626$		−	245798.i		−	0.627235i
$627$	470571.			1.19699
$628$		−	42034.5i		−	0.106583i
$629$	−34211.6			−0.0864714
$630$	−123389.			−0.310882
$631$			548628.i			1.37791i	0.724806	+	0.688953i	$0.241929\pi$
$631$			548628.i			1.37791i	−0.724806	+	0.688953i	$0.758071\pi$
$632$		−	226486.i		−	0.567032i
$633$	448750.			1.11995
$634$	−408951.			−1.01740
$635$			312559.i			0.775148i
$636$		−	18957.1i		−	0.0468660i
$637$	−460005.			−1.13366
$638$		−	689345.i		−	1.69354i
$639$	−5263.74			−0.0128912
$640$		−	16190.9i		−	0.0395285i
$641$			319072.i			0.776555i	0.921543	+	0.388277i	$0.126930\pi$
$641$			319072.i			0.776555i	−0.921543	+	0.388277i	$0.873070\pi$
$642$		−	170767.i		−	0.414317i
$643$		−	671481.i		−	1.62410i	−0.583590	−	0.812049i	$-0.698352\pi$
$643$		−	671481.i		−	1.62410i	0.583590	−	0.812049i	$-0.301648\pi$
$644$	−342503.	+	114433.i	−0.825834	+	0.275918i
$645$	−95813.2			−0.230306
$646$	−503460.			−1.20642
$647$	−661570.			−1.58040			−0.790200	−	0.612849i	$-0.790023\pi$
$647$	−661570.			−1.58040			−0.790200	+	0.612849i	$0.790023\pi$
$648$	17334.0			0.0412809
$649$		−	265080.i		−	0.629343i
$650$	33326.4			0.0788791
$651$			871735.i			2.05695i
$652$	−264831.			−0.622980
$653$	−319234.			−0.748658			−0.374329	−	0.927296i	$-0.622127\pi$
$653$	−319234.			−0.748658			−0.374329	+	0.927296i	$0.622127\pi$
$654$		−	25578.0i		−	0.0598013i
$655$			179301.i			0.417926i
$656$	−118963.			−0.276442
$657$	286138.			0.662894
$658$			180135.i			0.416051i
$659$			52524.7i			0.120946i	0.998170	+	0.0604732i	$0.0192610\pi$
$659$			52524.7i			0.120946i	−0.998170	+	0.0604732i	$0.980739\pi$
$660$	79207.9			0.181836
$661$			338560.i			0.774877i	0.921896	+	0.387439i	$0.126640\pi$
$661$			338560.i			0.774877i	−0.921896	+	0.387439i	$0.873360\pi$
$662$	246193.			0.561773
$663$			187530.i			0.426622i
$664$		−	38488.7i		−	0.0872965i
$665$		−	506938.i		−	1.14634i
$666$		−	13209.2i		−	0.0297803i
$667$	273999.	+	820090.i	0.615883	+	1.84336i
$668$	239708.			0.537192
$669$	509624.			1.13867
$670$	−156313.			−0.348213
$671$	−52445.7			−0.116484
$672$			91736.4i			0.203144i
$673$	92825.5			0.204945			0.102472	−	0.994736i	$-0.467325\pi$
$673$	92825.5			0.204945			0.102472	+	0.994736i	$0.467325\pi$
$674$			41285.7i			0.0908825i
$675$	−94080.3			−0.206486
$676$	−157406.			−0.344452
$677$		−	633324.i		−	1.38181i	−0.722945	−	0.690906i	$-0.757212\pi$
$677$		−	633324.i		−	1.38181i	0.722945	−	0.690906i	$-0.242788\pi$
$678$			190081.i			0.413504i
$679$	907850.			1.96913
$680$	−84744.0			−0.183270
$681$		−	278710.i		−	0.600979i
$682$			725469.i			1.55973i
$683$	730326.			1.56558			0.782790	−	0.622286i	$-0.213796\pi$
$683$	730326.			1.56558			0.782790	+	0.622286i	$0.213796\pi$
$684$		−	194388.i		−	0.415486i
$685$	263419.			0.561391
$686$			598328.i			1.27143i
$687$			212741.i			0.450751i
$688$		−	92349.1i		−	0.195099i
$689$			37609.5i			0.0792244i
$690$	−94231.0	+	31483.4i	−0.197923	+	0.0661277i
$691$	34127.6			0.0714743			0.0357371	−	0.999361i	$-0.488622\pi$
$691$	34127.6			0.0714743			0.0357371	+	0.999361i	$0.488622\pi$
$692$	460079.			0.960772
$693$	581811.			1.21148
$694$	−583210.			−1.21089
$695$		−	131506.i		−	0.272256i
$696$	219654.			0.453440
$697$			622659.i			1.28170i
$698$	1457.03			0.00299060
$699$	−271431.			−0.555527
$700$		−	85329.4i		−	0.174142i
$701$		−	864909.i		−	1.76009i	−0.474891	−	0.880044i	$-0.657513\pi$
$701$		−	864909.i		−	1.76009i	0.474891	−	0.880044i	$-0.342487\pi$
$702$	−200663.			−0.407186
$703$	54269.5			0.109811
$704$			76344.1i			0.154039i
$705$			49559.5i			0.0997123i
$706$	−312772.			−0.627508
$707$			284385.i			0.568941i
$708$	84465.4			0.168505
$709$			626107.i			1.24553i	0.782407	+	0.622767i	$0.213992\pi$
$709$			626107.i			1.24553i	−0.782407	+	0.622767i	$0.786008\pi$
$710$		−	3640.12i		−	0.00722104i
$711$		−	457704.i		−	0.905411i
$712$		−	79604.8i		−	0.157029i
$713$	−288358.	−	863066.i	−0.567222	−	1.69771i
$714$	480154.			0.941856
$715$	−157143.			−0.307385
$716$	−48249.8			−0.0941174
$717$	189350.			0.368322
$718$			368896.i			0.715575i
$719$	844872.			1.63431			0.817153	−	0.576421i	$-0.195551\pi$
$719$	844872.			1.63431			0.817153	+	0.576421i	$0.195551\pi$
$720$		−	32720.0i		−	0.0631172i
$721$	469629.			0.903410
$722$	430030.			0.824943
$723$		−	538980.i		−	1.03109i
$724$		−	251491.i		−	0.479784i
$725$	−204313.			−0.388705
$726$	−127543.			−0.241983
$727$		−	56780.1i		−	0.107430i	−0.998556	−	0.0537152i	$-0.982894\pi$
$727$		−	56780.1i		−	0.107430i	0.998556	−	0.0537152i	$-0.0171063\pi$
$728$		−	181998.i		−	0.343403i
$729$	397100.			0.747213
$730$			197878.i			0.371323i
$731$	−483361.			−0.904559
$732$		−	16711.4i		−	0.0311882i
$733$			780811.i			1.45324i	0.687039	+	0.726621i	$0.258910\pi$
$733$			780811.i			1.45324i	−0.687039	+	0.726621i	$0.741090\pi$
$734$		−	194079.i		−	0.360235i
$735$			324043.i			0.599829i
$736$	−30345.1	−	90824.0i	−0.0560187	−	0.167666i
$737$	737056.			1.35695
$738$	−240411.			−0.441409
$739$	591467.			1.08303			0.541516	−	0.840690i	$-0.317850\pi$
$739$	591467.			1.08303			0.541516	+	0.840690i	$0.317850\pi$
$740$	9134.81			0.0166815
$741$		−	297476.i		−	0.541771i
$742$	96295.9			0.174904
$743$			836416.i			1.51511i	0.652770	+	0.757556i	$0.273607\pi$
$743$			836416.i			1.51511i	−0.652770	+	0.757556i	$0.726393\pi$
$744$	−231164.			−0.417614
$745$	−104184.			−0.187711
$746$		−	75824.3i		−	0.136248i
$747$		−	77781.4i		−	0.139391i
$748$	399590.			0.714186
$749$	867439.			1.54623
$750$		−	23476.2i		−	0.0417355i
$751$			505020.i			0.895423i	0.894178	+	0.447712i	$0.147761\pi$
$751$			505020.i			0.895423i	−0.894178	+	0.447712i	$0.852239\pi$
$752$	−47767.7			−0.0844692
$753$		−	370522.i		−	0.653467i
$754$	−435777.			−0.766517
$755$			113597.i			0.199285i
$756$			513781.i			0.898947i
$757$			747008.i			1.30357i	0.758405	+	0.651783i	$0.225979\pi$
$757$			747008.i			1.30357i	−0.758405	+	0.651783i	$0.774021\pi$
$758$		−	146842.i		−	0.255571i
$759$	444324.	−	148452.i	0.771287	−	0.257694i
$760$	134428.			0.232736
$761$	117471.			0.202844			0.101422	−	0.994843i	$-0.467661\pi$
$761$	117471.			0.202844			0.101422	+	0.994843i	$0.467661\pi$
$762$	469613.			0.808779
$763$	129928.			0.223179
$764$			142547.i			0.244215i
$765$	−171258.			−0.292637
$766$		−	301312.i		−	0.513522i
$767$	−167573.			−0.284848
$768$	−24326.4			−0.0412435
$769$		−	406211.i		−	0.686909i	−0.939169	−	0.343455i	$-0.888403\pi$
$769$		−	406211.i		−	0.686909i	0.939169	−	0.343455i	$-0.111597\pi$
$770$			402350.i			0.678614i
$771$	237585.			0.399679
$772$	210075.			0.352484
$773$			733921.i			1.22826i	0.789205	+	0.614130i	$0.210493\pi$
$773$			733921.i			1.22826i	−0.789205	+	0.614130i	$0.789507\pi$
$774$		−	186627.i		−	0.311525i
$775$	215020.			0.357993
$776$			240741.i			0.399785i
$777$	−51757.2			−0.0857293
$778$		−	522026.i		−	0.862448i
$779$		−	987717.i		−	1.62764i
$780$		−	50072.2i		−	0.0823014i
$781$			17164.1i			0.0281397i
$782$	−475379.	+	158828.i	−0.777367	+	0.259725i
$783$	1.23020e6			2.00656
$784$	−312327.			−0.508133
$785$	58745.0			0.0953305
$786$	269395.			0.436059
$787$		−	236491.i		−	0.381826i	−0.981607	−	0.190913i	$-0.938855\pi$
$787$		−	236491.i		−	0.381826i	0.981607	−	0.190913i	$-0.0611449\pi$
$788$	−87290.5			−0.140577
$789$			503395.i			0.808639i
$790$	316524.			0.507169
$791$	−965551.			−1.54320
$792$			154283.i			0.245962i
$793$			33154.1i			0.0527219i
$794$	217454.			0.344926
$795$	26493.3			0.0419182
$796$		−	428683.i		−	0.676565i
$797$			369740.i			0.582077i	0.956711	+	0.291038i	$0.0940007\pi$
$797$			369740.i			0.582077i	−0.956711	+	0.291038i	$0.905999\pi$
$798$	−761663.			−1.19607
$799$			250019.i			0.391633i
$800$	22627.4			0.0353553
$801$		−	160873.i		−	0.250736i
$802$			185935.i			0.289077i
$803$		−	933045.i		−	1.44701i
$804$			234856.i			0.363321i
$805$	−159925.	−	478663.i	−0.246789	−	0.738648i
$806$	458613.			0.705954
$807$	−32795.1			−0.0503572
$808$	−75412.4			−0.115510
$809$	668853.			1.02196			0.510980	−	0.859593i	$-0.329283\pi$
$809$	668853.			1.02196			0.510980	+	0.859593i	$0.329283\pi$
$810$			24225.0i			0.0369227i
$811$	−575469.			−0.874944			−0.437472	−	0.899232i	$-0.644126\pi$
$811$	−575469.			−0.874944			−0.437472	+	0.899232i	$0.644126\pi$
$812$			1.11577e6i			1.69224i
$813$	−726503.			−1.09915
$814$	−43073.0			−0.0650064
$815$		−	370113.i		−	0.557210i
$816$			127326.i			0.191221i
$817$	766750.			1.14871
$818$	587877.			0.878577
$819$		−	367799.i		−	0.548330i
$820$		−	166256.i		−	0.247257i
$821$	936472.			1.38934			0.694670	−	0.719328i	$-0.255550\pi$
$821$	936472.			1.38934			0.694670	+	0.719328i	$0.255550\pi$
$822$		−	395781.i		−	0.585748i
$823$	827750.			1.22208			0.611040	−	0.791600i	$-0.290751\pi$
$823$	827750.			1.22208			0.611040	+	0.791600i	$0.290751\pi$
$824$			124535.i			0.183416i
$825$			110696.i			0.162639i
$826$			429057.i			0.628861i
$827$			476873.i			0.697256i	0.937261	+	0.348628i	$0.113352\pi$
$827$			476873.i			0.697256i	−0.937261	+	0.348628i	$0.886648\pi$
$828$	−61324.2	−	183545.i	−0.0894481	−	0.267721i
$829$	−1.12943e6			−1.64342			−0.821711	−	0.569904i	$-0.806980\pi$
$829$	−1.12943e6			−1.64342			−0.821711	+	0.569904i	$0.806980\pi$
$830$	53789.6			0.0780804
$831$	365597.			0.529420
$832$	48261.8			0.0697199
$833$			1.63474e6i			2.35591i
$834$	−197585.			−0.284068
$835$			335002.i			0.480479i
$836$	−633865.			−0.906952
$837$	−1.29466e6			−1.84802
$838$		−	610167.i		−	0.868881i
$839$			312339.i			0.443713i	0.975079	+	0.221856i	$0.0712116\pi$
$839$			312339.i			0.443713i	−0.975079	+	0.221856i	$0.928788\pi$
$840$	−128205.			−0.181697
$841$	1.96432e6			2.77729
$842$		−	727501.i		−	1.02615i
$843$			604007.i			0.849938i
$844$	−604473.			−0.848578
$845$		−	219982.i		−	0.308088i
$846$	−96533.2			−0.134876
$847$		−	647879.i		−	0.903081i
$848$			25535.5i			0.0355101i
$849$		−	657342.i		−	0.911960i
$850$		−	118433.i		−	0.163922i
$851$	51242.5	−	17120.6i	0.0707573	−	0.0236406i
$852$	−5469.20			−0.00753433
$853$	2283.67			0.00313860			0.00156930	−	0.999999i	$-0.499500\pi$
$853$	2283.67			0.00313860			0.00156930	+	0.999999i	$0.499500\pi$
$854$	84888.3			0.116394
$855$	271665.			0.371622
$856$			230025.i			0.313926i
$857$	−987597.			−1.34468			−0.672338	−	0.740244i	$-0.734710\pi$
$857$	−987597.			−1.34468			−0.672338	+	0.740244i	$0.734710\pi$
$858$			236103.i			0.320721i
$859$	−49378.7			−0.0669196			−0.0334598	−	0.999440i	$-0.510653\pi$
$859$	−49378.7			−0.0669196			−0.0334598	+	0.999440i	$0.510653\pi$
$860$	129062.			0.174502
$861$			941994.i			1.27070i
$862$		−	864630.i		−	1.16363i
$863$	−503130.			−0.675551			−0.337776	−	0.941227i	$-0.609675\pi$
$863$	−503130.			−0.675551			−0.337776	+	0.941227i	$0.609675\pi$
$864$	−136243.			−0.182510
$865$			642980.i			0.859341i
$866$		−	825815.i		−	1.10115i
$867$	170396.			0.226684
$868$		−	1.17424e6i		−	1.55854i
$869$	−1.49249e6			−1.97639
$870$			306976.i			0.405570i
$871$		−	465938.i		−	0.614174i
$872$			34453.9i			0.0453112i
$873$			486512.i			0.638359i
$874$	754088.	−	251947.i	0.987186	−	0.329828i
$875$	119251.			0.155757
$876$	297307.			0.387433
$877$	1.11909e6			1.45500			0.727502	−	0.686106i	$-0.240681\pi$
$877$	1.11909e6			1.45500			0.727502	+	0.686106i	$0.240681\pi$
$878$	−776567.			−1.00737
$879$		−	961773.i		−	1.24479i
$880$	−106694.			−0.137777
$881$		−	122132.i		−	0.157355i	−0.996900	−	0.0786773i	$-0.974930\pi$
$881$		−	122132.i		−	0.157355i	0.996900	−	0.0786773i	$-0.0250697\pi$
$882$	−631179.			−0.811363
$883$	100033.			0.128299			0.0641494	−	0.997940i	$-0.479567\pi$
$883$	100033.			0.128299			0.0641494	+	0.997940i	$0.479567\pi$
$884$		−	252605.i		−	0.323250i
$885$			118044.i			0.150715i
$886$	719169.			0.916143
$887$	−1.12318e6			−1.42759			−0.713793	−	0.700357i	$-0.753024\pi$
$887$	−1.12318e6			−1.42759			−0.713793	+	0.700357i	$0.753024\pi$
$888$		−	13724.8i		−	0.0174053i
$889$			2.38548e6i			3.01837i
$890$	111251.			0.140451
$891$		−	114227.i		−	0.143885i
$892$	−686471.			−0.862765
$893$		−	396602.i		−	0.497339i
$894$			156535.i			0.195855i
$895$		−	67431.2i		−	0.0841811i
$896$		−	123570.i		−	0.153921i
$897$	−93845.9	−	280884.i	−0.116635	−	0.349094i
$898$	402727.			0.499411
$899$	−2.81160e6			−3.47884
$900$	45727.5			0.0564537
$901$	133654.			0.164639
$902$			783939.i			0.963538i
$903$	−731256.			−0.896796
$904$		−	256042.i		−	0.313310i
$905$	351470.			0.429132
$906$	170677.			0.207931
$907$		−	954122.i		−	1.15982i	−0.814682	−	0.579908i	$-0.803088\pi$
$907$		−	954122.i		−	1.15982i	0.814682	−	0.579908i	$-0.196912\pi$
$908$			375427.i			0.455359i
$909$	−152400.			−0.184441
$910$	254350.			0.307149
$911$		−	579124.i		−	0.697806i	−0.937159	−	0.348903i	$-0.886554\pi$
$911$		−	579124.i		−	0.697806i	0.937159	−	0.348903i	$-0.113446\pi$
$912$		−	201976.i		−	0.242834i
$913$	−253632.			−0.304272
$914$			81042.2i			0.0970105i
$915$	23354.8			0.0278955
$916$		−	286564.i		−	0.341532i
$917$			1.36844e6i			1.62737i
$918$			713104.i			0.846189i
$919$			693043.i			0.820595i	0.911952	+	0.410298i	$0.134575\pi$
$919$			693043.i			0.820595i	−0.911952	+	0.410298i	$0.865425\pi$
$920$	126930.	−	42408.6i	0.149965	−	0.0501047i
$921$	554142.			0.653284
$922$	770959.			0.906922
$923$	10850.5			0.0127364
$924$	604522.			0.708057
$925$			12766.3i			0.0149204i
$926$	−419227.			−0.488908
$927$			251672.i			0.292870i
$928$	−295877.			−0.343570
$929$	935251.			1.08367			0.541835	−	0.840485i	$-0.317730\pi$
$929$	935251.			1.08367			0.541835	+	0.840485i	$0.317730\pi$
$930$		−	323062.i		−	0.373525i
$931$		−	2.59317e6i		−	2.99179i
$932$	365622.			0.420921
$933$	−122034.			−0.140190
$934$			336398.i			0.385620i
$935$			558444.i			0.638788i
$936$	97531.8			0.111325
$937$			514336.i			0.585825i	0.956139	+	0.292912i	$0.0946244\pi$
$937$			514336.i			0.585825i	−0.956139	+	0.292912i	$0.905376\pi$
$938$	−1.19299e6			−1.35592
$939$		−	516121.i		−	0.585357i
$940$		−	66757.4i		−	0.0755516i
$941$		−	651835.i		−	0.736137i	−0.929799	−	0.368069i	$-0.880019\pi$
$941$		−	651835.i		−	0.736137i	0.929799	−	0.368069i	$-0.119981\pi$
$942$		−	88263.0i		−	0.0994666i
$943$	−311598.	−	932625.i	−0.350406	−	1.04878i
$944$	−113776.			−0.127675
$945$	−718030.			−0.804043
$946$	−608560.			−0.680019
$947$	−514702.			−0.573927			−0.286963	−	0.957942i	$-0.592646\pi$
$947$	−514702.			−0.573927			−0.286963	+	0.957942i	$0.592646\pi$
$948$		−	475570.i		−	0.529174i
$949$	−589835.			−0.654935
$950$			187869.i			0.208166i
$951$	−858705.			−0.949473
$952$	−646774.			−0.713640
$953$		−	1.30417e6i		−	1.43598i	−0.696055	−	0.717989i	$-0.745063\pi$
$953$		−	1.30417e6i		−	1.43598i	0.696055	−	0.717989i	$-0.254937\pi$
$954$			51604.4i			0.0567009i
$955$	−199216.			−0.218433
$956$	−255058.			−0.279076
$957$		−	1.44747e6i		−	1.58047i
$958$			716933.i			0.781174i
$959$	2.01044e6			2.18602
$960$		−	33997.2i		−	0.0368893i
$961$	2.03542e6			2.20398
$962$			27229.1i			0.0294227i
$963$			464856.i			0.501263i
$964$			726014.i			0.781251i
$965$			293588.i			0.315271i
$966$	−719180.	+	240284.i	−0.770696	+	0.257496i
$967$	−553354.			−0.591766			−0.295883	−	0.955224i	$-0.595614\pi$
$967$	−553354.			−0.591766			−0.295883	+	0.955224i	$0.595614\pi$
$968$	171803.			0.183349
$969$	−1.05715e6			−1.12588
$970$	−336446.			−0.357579
$971$		−	32994.2i		−	0.0349944i	−0.999847	−	0.0174972i	$-0.994430\pi$
$971$		−	32994.2i		−	0.0349944i	0.999847	−	0.0174972i	$-0.00556982\pi$
$972$	−451315.			−0.477691
$973$		−	1.00367e6i		−	1.06014i
$974$	745646.			0.785986
$975$	69978.0			0.0736126
$976$			22510.4i			0.0236311i
$977$		−	968151.i		−	1.01427i	−0.861866	−	0.507135i	$-0.830704\pi$
$977$		−	968151.i		−	1.01427i	0.861866	−	0.507135i	$-0.169296\pi$
$978$	−556086.			−0.581386
$979$	−524577.			−0.547324
$980$		−	436490.i		−	0.454488i
$981$			69627.5i			0.0723507i
$982$	−461048.			−0.478105
$983$		−	1.71293e6i		−	1.77269i	−0.463023	−	0.886346i	$-0.653235\pi$
$983$		−	1.71293e6i		−	1.77269i	0.463023	−	0.886346i	$-0.346765\pi$
$984$	−249795.			−0.257985
$985$		−	121992.i		−	0.125736i
$986$			1.54864e6i			1.59293i
$987$			378243.i			0.388272i
$988$			400705.i			0.410498i
$989$	723983.	−	241889.i	0.740177	−	0.247300i
$990$	−215617.			−0.219995
$991$	−1.64449e6			−1.67450			−0.837250	−	0.546820i	$-0.815838\pi$
$991$	−1.64449e6			−1.67450			−0.837250	+	0.546820i	$0.815838\pi$
$992$	311382.			0.316424
$993$	516951.			0.524265
$994$		−	27781.8i		−	0.0281182i
$995$	599102.			0.605138
$996$		−	80817.6i		−	0.0814680i
$997$	−707.962			−0.000712229			−0.000356114	−	1.00000i	$-0.500113\pi$
$997$	−707.962			−0.000712229			−0.000356114		1.00000i	$0.500113\pi$
$998$	1.39828e6			1.40389
$999$		−	76867.6i		−	0.0770216i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.d.a.91.16	yes	32
23.22	odd	2	inner	230.5.d.a.91.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.d.a.91.1	✓	32	23.22	odd	2	inner
230.5.d.a.91.16	yes	32	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-2.82843 q^{2} -5.93906 q^{3} +8.00000 q^{4} +11.1803i q^{5} +16.7982 q^{6} +85.3294i q^{7} -22.6274 q^{8} -45.7275 q^{9} +O(q^{10})\)	\(q-2.82843 q^{2} -5.93906 q^{3} +8.00000 q^{4} +11.1803i q^{5} +16.7982 q^{6} +85.3294i q^{7} -22.6274 q^{8} -45.7275 q^{9} -31.6228i q^{10} +149.110i q^{11} -47.5125 q^{12} +94.2613 q^{13} -241.348i q^{14} -66.4007i q^{15} +64.0000 q^{16} -334.980i q^{17} +129.337 q^{18} +531.375i q^{19} +89.4427i q^{20} -506.777i q^{21} -421.746i q^{22} +(167.635 + 501.737i) q^{23} +134.386 q^{24} -125.000 q^{25} -266.611 q^{26} +752.643 q^{27} +682.635i q^{28} +1634.50 q^{29} +187.810i q^{30} -1720.16 q^{31} -181.019 q^{32} -885.571i q^{33} +947.467i q^{34} -954.012 q^{35} -365.820 q^{36} -102.130i q^{37} -1502.96i q^{38} -559.824 q^{39} -252.982i q^{40} -1858.79 q^{41} +1433.38i q^{42} -1442.95i q^{43} +1192.88i q^{44} -511.249i q^{45} +(-474.142 - 1419.13i) q^{46} -746.370 q^{47} -380.100 q^{48} -4880.11 q^{49} +353.553 q^{50} +1989.47i q^{51} +754.090 q^{52} +398.992i q^{53} -2128.80 q^{54} -1667.10 q^{55} -1930.78i q^{56} -3155.87i q^{57} -4623.07 q^{58} -1777.75 q^{59} -531.206i q^{60} +351.726i q^{61} +4865.34 q^{62} -3901.90i q^{63} +512.000 q^{64} +1053.87i q^{65} +2504.77i q^{66} -4943.05i q^{67} -2679.84i q^{68} +(-995.593 - 2979.85i) q^{69} +2698.35 q^{70} +115.111 q^{71} +1034.70 q^{72} -6257.45 q^{73} +288.868i q^{74} +742.383 q^{75} +4251.00i q^{76} -12723.4 q^{77} +1583.42 q^{78} +10009.4i q^{79} +715.542i q^{80} -766.062 q^{81} +5257.47 q^{82} +1700.98i q^{83} -4054.21i q^{84} +3745.19 q^{85} +4081.29i q^{86} -9707.42 q^{87} -3373.97i q^{88} +3518.07i q^{89} +1446.03i q^{90} +8043.26i q^{91} +(1341.08 + 4013.89i) q^{92} +10216.1 q^{93} +2111.05 q^{94} -5940.95 q^{95} +1075.09 q^{96} -10639.4i q^{97} +13803.0 q^{98} -6818.42i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9}+O(q^{10}) \) 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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