LMFDB - Embedded newform 230.5.d.a.91.4

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			91.4
Character	$\chi$	$=$	230.91
Dual form			230.5.d.a.91.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843 q^{2} +15.6893 q^{3} +8.00000 q^{4} +11.1803i q^{5} -44.3761 q^{6} +65.6030i q^{7} -22.6274 q^{8} +165.154 q^{9} +O(q^{10})$	\(q-2.82843 q^{2} +15.6893 q^{3} +8.00000 q^{4} +11.1803i q^{5} -44.3761 q^{6} +65.6030i q^{7} -22.6274 q^{8} +165.154 q^{9} -31.6228i q^{10} +29.7000i q^{11} +125.514 q^{12} -101.638 q^{13} -185.553i q^{14} +175.412i q^{15} +64.0000 q^{16} +114.039i q^{17} -467.127 q^{18} +373.929i q^{19} +89.4427i q^{20} +1029.27i q^{21} -84.0043i q^{22} +(-528.956 - 6.85963i) q^{23} -355.008 q^{24} -125.000 q^{25} +287.476 q^{26} +1320.32 q^{27} +524.824i q^{28} -512.737 q^{29} -496.139i q^{30} +883.636 q^{31} -181.019 q^{32} +465.972i q^{33} -322.550i q^{34} -733.464 q^{35} +1321.23 q^{36} -811.483i q^{37} -1057.63i q^{38} -1594.63 q^{39} -252.982i q^{40} -397.583 q^{41} -2911.20i q^{42} -2001.98i q^{43} +237.600i q^{44} +1846.48i q^{45} +(1496.11 + 19.4020i) q^{46} +2911.99 q^{47} +1004.12 q^{48} -1902.76 q^{49} +353.553 q^{50} +1789.19i q^{51} -813.104 q^{52} +1560.86i q^{53} -3734.43 q^{54} -332.056 q^{55} -1484.43i q^{56} +5866.68i q^{57} +1450.24 q^{58} +521.741 q^{59} +1403.29i q^{60} +3790.94i q^{61} -2499.30 q^{62} +10834.6i q^{63} +512.000 q^{64} -1136.35i q^{65} -1317.97i q^{66} +6223.95i q^{67} +912.310i q^{68} +(-8298.94 - 107.623i) q^{69} +2074.55 q^{70} +5633.40 q^{71} -3737.01 q^{72} +7633.63 q^{73} +2295.22i q^{74} -1961.16 q^{75} +2991.43i q^{76} -1948.41 q^{77} +4510.30 q^{78} +8977.10i q^{79} +715.542i q^{80} +7337.43 q^{81} +1124.53 q^{82} -8227.93i q^{83} +8234.13i q^{84} -1274.99 q^{85} +5662.44i q^{86} -8044.48 q^{87} -672.034i q^{88} -11502.8i q^{89} -5222.64i q^{90} -6667.76i q^{91} +(-4231.64 - 54.8770i) q^{92} +13863.6 q^{93} -8236.36 q^{94} -4180.65 q^{95} -2840.07 q^{96} -7778.70i q^{97} +5381.81 q^{98} +4905.08i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	15.6893			1.74326			0.871628	−	0.490168i	$-0.163065\pi$
$3$	15.6893			1.74326			0.871628	+	0.490168i	$0.163065\pi$
$4$	8.00000			0.500000
$5$			11.1803i			0.447214i
$5$			11.1803i			0.447214i
$6$	−44.3761			−1.23267
$7$			65.6030i			1.33884i	0.742885	+	0.669419i	$0.233457\pi$
$7$			65.6030i			1.33884i	−0.742885	+	0.669419i	$0.766543\pi$
$8$	−22.6274			−0.353553
$9$	165.154			2.03894
$10$		−	31.6228i		−	0.316228i
$11$			29.7000i			0.245455i	0.992440	+	0.122727i	$0.0391641\pi$
$11$			29.7000i			0.245455i	−0.992440	+	0.122727i	$0.960836\pi$
$12$	125.514			0.871628
$13$	−101.638			−0.601409			−0.300704	−	0.953717i	$-0.597222\pi$
$13$	−101.638			−0.601409			−0.300704	+	0.953717i	$0.597222\pi$
$14$		−	185.553i		−	0.946701i
$15$			175.412i			0.779608i
$16$	64.0000			0.250000
$17$			114.039i			0.394598i	0.980343	+	0.197299i	$0.0632170\pi$
$17$			114.039i			0.394598i	−0.980343	+	0.197299i	$0.936783\pi$
$18$	−467.127			−1.44175
$19$			373.929i			1.03581i	0.855437	+	0.517907i	$0.173289\pi$
$19$			373.929i			1.03581i	−0.855437	+	0.517907i	$0.826711\pi$
$20$			89.4427i			0.223607i
$21$			1029.27i			2.33394i
$22$		−	84.0043i		−	0.173563i
$23$	−528.956	−	6.85963i	−0.999916	−	0.0129672i
$23$	−528.956	−	6.85963i	−0.999916	−	0.0129672i
$24$	−355.008			−0.616334
$25$	−125.000			−0.200000
$26$	287.476			0.425260
$27$	1320.32			1.81114
$28$			524.824i			0.669419i
$29$	−512.737			−0.609675			−0.304838	−	0.952404i	$-0.598602\pi$
$29$	−512.737			−0.609675			−0.304838	+	0.952404i	$0.598602\pi$
$30$		−	496.139i		−	0.551266i
$31$	883.636			0.919496			0.459748	−	0.888049i	$-0.347940\pi$
$31$	883.636			0.919496			0.459748	+	0.888049i	$0.347940\pi$
$32$	−181.019			−0.176777
$33$			465.972i			0.427890i
$34$		−	322.550i		−	0.279023i
$35$	−733.464			−0.598746
$36$	1321.23			1.01947
$37$		−	811.483i		−	0.592756i	−0.955071	−	0.296378i	$-0.904221\pi$
$37$		−	811.483i		−	0.592756i	0.955071	−	0.296378i	$-0.0957788\pi$
$38$		−	1057.63i		−	0.732431i
$39$	−1594.63			−1.04841
$40$		−	252.982i		−	0.158114i
$41$	−397.583			−0.236516			−0.118258	−	0.992983i	$-0.537731\pi$
$41$	−397.583			−0.236516			−0.118258	+	0.992983i	$0.537731\pi$
$42$		−	2911.20i		−	1.65034i
$43$		−	2001.98i		−	1.08273i	−0.840786	−	0.541367i	$-0.817907\pi$
$43$		−	2001.98i		−	1.08273i	0.840786	−	0.541367i	$-0.182093\pi$
$44$			237.600i			0.122727i
$45$			1846.48i			0.911842i
$46$	1496.11	+	19.4020i	0.707047	+	0.00916917i
$47$	2911.99			1.31824			0.659120	−	0.752038i	$-0.270929\pi$
$47$	2911.99			1.31824			0.659120	+	0.752038i	$0.270929\pi$
$48$	1004.12			0.435814
$49$	−1902.76			−0.792486
$50$	353.553			0.141421
$51$			1789.19i			0.687885i
$52$	−813.104			−0.300704
$53$			1560.86i			0.555663i	0.960630	+	0.277832i	$0.0896157\pi$
$53$			1560.86i			0.555663i	−0.960630	+	0.277832i	$0.910384\pi$
$54$	−3734.43			−1.28067
$55$	−332.056			−0.109771
$56$		−	1484.43i		−	0.473350i
$57$			5866.68i			1.80569i
$58$	1450.24			0.431105
$59$	521.741			0.149882			0.0749412	−	0.997188i	$-0.476123\pi$
$59$	521.741			0.149882			0.0749412	+	0.997188i	$0.476123\pi$
$60$			1403.29i			0.389804i
$61$			3790.94i			1.01880i	0.860531	+	0.509398i	$0.170132\pi$
$61$			3790.94i			1.01880i	−0.860531	+	0.509398i	$0.829868\pi$
$62$	−2499.30			−0.650182
$63$			10834.6i			2.72981i
$64$	512.000			0.125000
$65$		−	1136.35i		−	0.268958i
$66$		−	1317.97i		−	0.302564i
$67$			6223.95i			1.38649i	0.720702	+	0.693245i	$0.243820\pi$
$67$			6223.95i			1.38649i	−0.720702	+	0.693245i	$0.756180\pi$
$68$			912.310i			0.197299i
$69$	−8298.94	−	107.623i	−1.74311	−	0.0226051i
$70$	2074.55			0.423378
$71$	5633.40			1.11752			0.558758	−	0.829331i	$-0.311278\pi$
$71$	5633.40			1.11752			0.558758	+	0.829331i	$0.311278\pi$
$72$	−3737.01			−0.720875
$73$	7633.63			1.43247			0.716235	−	0.697859i	$-0.245864\pi$
$73$	7633.63			1.43247			0.716235	+	0.697859i	$0.245864\pi$
$74$			2295.22i			0.419142i
$75$	−1961.16			−0.348651
$76$			2991.43i			0.517907i
$77$	−1948.41			−0.328624
$78$	4510.30			0.741337
$79$			8977.10i			1.43841i	0.694799	+	0.719204i	$0.255493\pi$
$79$			8977.10i			1.43841i	−0.694799	+	0.719204i	$0.744507\pi$
$80$			715.542i			0.111803i
$81$	7337.43			1.11834
$82$	1124.53			0.167242
$83$		−	8227.93i		−	1.19436i	−0.802108	−	0.597179i	$-0.796288\pi$
$83$		−	8227.93i		−	1.19436i	0.802108	−	0.597179i	$-0.203712\pi$
$84$			8234.13i			1.16697i
$85$	−1274.99			−0.176470
$86$			5662.44i			0.765609i
$87$	−8044.48			−1.06282
$88$		−	672.034i		−	0.0867813i
$89$		−	11502.8i		−	1.45219i	−0.687594	−	0.726095i	$-0.741333\pi$
$89$		−	11502.8i		−	1.45219i	0.687594	−	0.726095i	$-0.258667\pi$
$90$		−	5222.64i		−	0.644770i
$91$		−	6667.76i		−	0.805188i
$92$	−4231.64	−	54.8770i	−0.499958	−	0.00648358i
$93$	13863.6			1.60292
$94$	−8236.36			−0.932137
$95$	−4180.65			−0.463230
$96$	−2840.07			−0.308167
$97$		−	7778.70i		−	0.826729i	−0.910566	−	0.413365i	$-0.864353\pi$
$97$		−	7778.70i		−	0.826729i	0.910566	−	0.413365i	$-0.135647\pi$
$98$	5381.81			0.560372
$99$			4905.08i			0.500468i
$100$	−1000.00			−0.100000
$101$	1804.84			0.176928			0.0884639	−	0.996079i	$-0.471804\pi$
$101$	1804.84			0.176928			0.0884639	+	0.996079i	$0.471804\pi$
$102$		−	5060.59i		−	0.486408i
$103$			5528.89i			0.521151i	0.965453	+	0.260576i	$0.0839123\pi$
$103$			5528.89i			0.521151i	−0.965453	+	0.260576i	$0.916088\pi$
$104$	2299.81			0.212630
$105$	−11507.5			−1.04377
$106$		−	4414.77i		−	0.392913i
$107$			16683.8i			1.45722i	0.684927	+	0.728612i	$0.259834\pi$
$107$			16683.8i			1.45722i	−0.684927	+	0.728612i	$0.740166\pi$
$108$	10562.6			0.905570
$109$			10818.1i			0.910535i	0.890355	+	0.455268i	$0.150456\pi$
$109$			10818.1i			0.910535i	−0.890355	+	0.455268i	$0.849544\pi$
$110$	939.197			0.0776196
$111$		−	12731.6i		−	1.03333i
$112$			4198.59i			0.334709i
$113$		−	23095.9i		−	1.80875i	−0.426743	−	0.904373i	$-0.640339\pi$
$113$		−	23095.9i		−	1.80875i	0.426743	−	0.904373i	$-0.359661\pi$
$114$		−	16593.5i		−	1.27681i
$115$	76.6930	−	5913.90i	0.00579909	−	0.447176i
$116$	−4101.89			−0.304838
$117$	−16786.0			−1.22624
$118$	−1475.71			−0.105983
$119$	−7481.29			−0.528302
$120$		−	3969.11i		−	0.275633i
$121$	13758.9			0.939752
$122$		−	10722.4i		−	0.720398i
$123$	−6237.80			−0.412308
$124$	7069.08			0.459748
$125$		−	1397.54i		−	0.0894427i
$126$		−	30644.9i		−	1.93027i
$127$	−7472.66			−0.463306			−0.231653	−	0.972798i	$-0.574413\pi$
$127$	−7472.66			−0.463306			−0.231653	+	0.972798i	$0.574413\pi$
$128$	−1448.15			−0.0883883
$129$		−	31409.6i		−	1.88748i
$130$			3214.08i			0.190182i
$131$	31759.0			1.85065			0.925324	−	0.379178i	$-0.123793\pi$
$131$	31759.0			1.85065			0.925324	+	0.379178i	$0.123793\pi$
$132$			3727.78i			0.213945i
$133$	−24530.9			−1.38679
$134$		−	17604.0i		−	0.980396i
$135$			14761.6i			0.809967i
$136$		−	2580.40i		−	0.139511i
$137$		−	14686.5i		−	0.782489i	−0.920287	−	0.391245i	$-0.872045\pi$
$137$		−	14686.5i		−	0.782489i	0.920287	−	0.391245i	$-0.127955\pi$
$138$	23473.0	+	304.403i	1.23256	+	0.0159842i
$139$	15907.5			0.823326			0.411663	−	0.911336i	$-0.364948\pi$
$139$	15907.5			0.823326			0.411663	+	0.911336i	$0.364948\pi$
$140$	−5867.71			−0.299373
$141$	45687.2			2.29803
$142$	−15933.7			−0.790203
$143$		−	3018.65i		−	0.147619i
$144$	10569.9			0.509735
$145$		−	5732.57i		−	0.272655i
$146$	−21591.2			−1.01291
$147$	−29852.9			−1.38151
$148$		−	6491.86i		−	0.296378i
$149$		−	14125.4i		−	0.636249i	−0.948049	−	0.318124i	$-0.896947\pi$
$149$		−	14125.4i		−	0.636249i	0.948049	−	0.318124i	$-0.103053\pi$
$150$	5547.01			0.246534
$151$	13272.9			0.582118			0.291059	−	0.956705i	$-0.405992\pi$
$151$	13272.9			0.582118			0.291059	+	0.956705i	$0.405992\pi$
$152$		−	8461.04i		−	0.366215i
$153$			18834.0i			0.804562i
$154$	5510.94			0.232372
$155$			9879.35i			0.411211i
$156$	−12757.0			−0.524205
$157$		−	35604.8i		−	1.44447i	−0.691647	−	0.722236i	$-0.743115\pi$
$157$		−	35604.8i		−	1.44447i	0.691647	−	0.722236i	$-0.256885\pi$
$158$		−	25391.1i		−	1.01711i
$159$			24488.8i			0.968663i
$160$		−	2023.86i		−	0.0790569i
$161$	450.012	−	34701.1i	0.0173609	−	1.33872i
$162$	−20753.4			−0.790786
$163$	−25988.5			−0.978151			−0.489075	−	0.872241i	$-0.662666\pi$
$163$	−25988.5			−0.978151			−0.489075	+	0.872241i	$0.662666\pi$
$164$	−3180.66			−0.118258
$165$	−5209.73			−0.191358
$166$			23272.1i			0.844539i
$167$	−25795.2			−0.924925			−0.462463	−	0.886639i	$-0.653034\pi$
$167$	−25795.2			−0.924925			−0.462463	+	0.886639i	$0.653034\pi$
$168$		−	23289.6i		−	0.825171i
$169$	−18230.7			−0.638308
$170$	3606.22			0.124783
$171$			61755.9i			2.11196i
$172$		−	16015.8i		−	0.541367i
$173$	−17411.8			−0.581770			−0.290885	−	0.956758i	$-0.593950\pi$
$173$	−17411.8			−0.581770			−0.290885	+	0.956758i	$0.593950\pi$
$174$	22753.2			0.751527
$175$		−	8200.38i		−	0.267767i
$176$			1900.80i			0.0613637i
$177$	8185.75			0.261284
$178$			32534.8i			1.02685i
$179$	52955.9			1.65275			0.826376	−	0.563118i	$-0.190398\pi$
$179$	52955.9			1.65275			0.826376	+	0.563118i	$0.190398\pi$
$180$			14771.8i			0.455921i
$181$			29310.0i			0.894663i	0.894368	+	0.447331i	$0.147626\pi$
$181$			29310.0i			0.894663i	−0.894368	+	0.447331i	$0.852374\pi$
$182$			18859.3i			0.569354i
$183$			59477.2i			1.77602i
$184$	11968.9	+	155.216i	0.353524	+	0.00458458i
$185$	9072.65			0.265088
$186$	−39212.3			−1.13343
$187$	−3386.95			−0.0968559
$188$	23295.9			0.659120
$189$			86617.1i			2.42482i
$190$	11824.7			0.327553
$191$		−	21562.8i		−	0.591069i	−0.955332	−	0.295534i	$-0.904502\pi$
$191$		−	21562.8i		−	0.591069i	0.955332	−	0.295534i	$-0.0954977\pi$
$192$	8032.92			0.217907
$193$	21580.4			0.579354			0.289677	−	0.957124i	$-0.406452\pi$
$193$	21580.4			0.579354			0.289677	+	0.957124i	$0.406452\pi$
$194$			22001.5i			0.584586i
$195$		−	17828.5i		−	0.468863i
$196$	−15222.1			−0.396243
$197$	9080.87			0.233989			0.116994	−	0.993133i	$-0.462674\pi$
$197$	9080.87			0.233989			0.116994	+	0.993133i	$0.462674\pi$
$198$		−	13873.7i		−	0.353884i
$199$		−	67605.3i		−	1.70716i	−0.520960	−	0.853581i	$-0.674426\pi$
$199$		−	67605.3i		−	1.70716i	0.520960	−	0.853581i	$-0.325574\pi$
$200$	2828.43			0.0707107
$201$			97649.5i			2.41701i
$202$	−5104.86			−0.125107
$203$		−	33637.1i		−	0.816256i
$204$			14313.5i			0.343943i
$205$		−	4445.11i		−	0.105773i
$206$		−	15638.1i		−	0.368510i
$207$	−87359.3	−	1132.90i	−2.03877	−	0.0264393i
$208$	−6504.84			−0.150352
$209$	−11105.7			−0.254245
$210$	32548.2			0.738055
$211$	−36926.4			−0.829415			−0.414708	−	0.909955i	$-0.636116\pi$
$211$	−36926.4			−0.829415			−0.414708	+	0.909955i	$0.636116\pi$
$212$			12486.9i			0.277832i
$213$	88384.1			1.94812
$214$		−	47188.8i		−	1.03041i
$215$	22382.8			0.484214
$216$	−29875.5			−0.640335
$217$			57969.2i			1.23106i
$218$		−	30598.1i		−	0.643846i
$219$	119766.			2.49716
$220$	−2656.45			−0.0548853
$221$		−	11590.7i		−	0.237315i
$222$			36010.4i			0.730671i
$223$	−35463.9			−0.713144			−0.356572	−	0.934268i	$-0.616055\pi$
$223$	−35463.9			−0.713144			−0.356572	+	0.934268i	$0.616055\pi$
$224$		−	11875.4i		−	0.236675i
$225$	−20644.3			−0.407788
$226$			65325.0i			1.27898i
$227$		−	78401.1i		−	1.52149i	−0.649048	−	0.760747i	$-0.724833\pi$
$227$		−	78401.1i		−	1.52149i	0.649048	−	0.760747i	$-0.275167\pi$
$228$			46933.5i			0.902844i
$229$			97058.3i			1.85081i	0.378981	+	0.925405i	$0.376275\pi$
$229$			97058.3i			1.85081i	−0.378981	+	0.925405i	$0.623725\pi$
$230$	−216.920	+	16727.0i	−0.00410058	+	0.316201i
$231$	−30569.2			−0.572875
$232$	11601.9			0.215553
$233$	−95297.6			−1.75538			−0.877688	−	0.479233i	$-0.840915\pi$
$233$	−95297.6			−1.75538			−0.877688	+	0.479233i	$0.840915\pi$
$234$	47477.9			0.867080
$235$			32557.1i			0.589535i
$236$	4173.93			0.0749412
$237$			140844.i			2.50751i
$238$	21160.3			0.373566
$239$	33367.1			0.584148			0.292074	−	0.956396i	$-0.405655\pi$
$239$	33367.1			0.584148			0.292074	+	0.956396i	$0.405655\pi$
$240$			11226.4i			0.194902i
$241$		−	112375.i		−	1.93479i	−0.253268	−	0.967396i	$-0.581505\pi$
$241$		−	112375.i		−	1.93479i	0.253268	−	0.967396i	$-0.418495\pi$
$242$	−38916.1			−0.664505
$243$	8173.15			0.138413
$244$			30327.5i			0.509398i
$245$		−	21273.5i		−	0.354410i
$246$	17643.2			0.291546
$247$		−	38005.4i		−	0.622947i
$248$	−19994.4			−0.325091
$249$		−	129091.i		−	2.08207i
$250$			3952.85i			0.0632456i
$251$		−	83681.6i		−	1.32826i	−0.747618	−	0.664130i	$-0.768802\pi$
$251$		−	83681.6i		−	1.32826i	0.747618	−	0.664130i	$-0.231198\pi$
$252$			86677.0i			1.36491i
$253$	203.731	−	15710.0i	0.00318285	−	0.245434i
$254$	21135.9			0.327607
$255$	−20003.7			−0.307632
$256$	4096.00			0.0625000
$257$	34980.5			0.529614			0.264807	−	0.964301i	$-0.414692\pi$
$257$	34980.5			0.529614			0.264807	+	0.964301i	$0.414692\pi$
$258$			88839.8i			1.33465i
$259$	53235.7			0.793604
$260$		−	9090.78i		−	0.134479i
$261$	−84680.6			−1.24309
$262$	−89827.9			−1.30861
$263$		−	7700.32i		−	0.111326i	−0.998450	−	0.0556631i	$-0.982273\pi$
$263$		−	7700.32i		−	0.111326i	0.998450	−	0.0556631i	$-0.0177273\pi$
$264$		−	10543.8i		−	0.151282i
$265$	−17450.9			−0.248500
$266$	69383.8			0.980606
$267$		−	180471.i		−	2.53154i
$268$			49791.6i			0.693245i
$269$	−89439.8			−1.23602			−0.618011	−	0.786169i	$-0.712061\pi$
$269$	−89439.8			−1.23602			−0.618011	+	0.786169i	$0.712061\pi$
$270$		−	41752.2i		−	0.572733i
$271$	−44120.2			−0.600757			−0.300378	−	0.953820i	$-0.597113\pi$
$271$	−44120.2			−0.600757			−0.300378	+	0.953820i	$0.597113\pi$
$272$			7298.48i			0.0986495i
$273$		−	104613.i		−	1.40365i
$274$			41539.8i			0.553304i
$275$		−	3712.50i		−	0.0490909i
$276$	−66391.6	−	860.982i	−0.871555	−	0.0113025i
$277$	38040.5			0.495777			0.247888	−	0.968789i	$-0.420263\pi$
$277$	38040.5			0.495777			0.247888	+	0.968789i	$0.420263\pi$
$278$	−44993.2			−0.582179
$279$	145936.			1.87480
$280$	16596.4			0.211689
$281$		−	32647.1i		−	0.413459i	−0.978398	−	0.206729i	$-0.933718\pi$
$281$		−	32647.1i		−	0.413459i	0.978398	−	0.206729i	$-0.0662820\pi$
$282$	−129223.			−1.62495
$283$			46075.2i			0.575300i	0.957736	+	0.287650i	$0.0928740\pi$
$283$			46075.2i			0.575300i	−0.957736	+	0.287650i	$0.907126\pi$
$284$	45067.2			0.558758
$285$	−65591.5			−0.807528
$286$			8538.03i			0.104382i
$287$		−	26082.7i		−	0.316656i
$288$	−29896.1			−0.360437
$289$	70516.2			0.844293
$290$			16214.2i			0.192796i
$291$		−	122042.i		−	1.44120i
$292$	61069.0			0.716235
$293$		−	62058.8i		−	0.722883i	−0.932395	−	0.361441i	$-0.882285\pi$
$293$		−	62058.8i		−	0.722883i	0.932395	−	0.361441i	$-0.117715\pi$
$294$	84436.9			0.976872
$295$			5833.24i			0.0670295i
$296$			18361.8i			0.209571i
$297$			39213.6i			0.444553i
$298$			39952.6i			0.449896i
$299$	53762.0	+	697.199i	0.601358	+	0.00779856i
$300$	−15689.3			−0.174326
$301$	131336.			1.44961
$302$	−37541.4			−0.411620
$303$	28316.7			0.308431
$304$			23931.4i			0.258953i
$305$	−42384.0			−0.455620
$306$		−	53270.6i		−	0.568911i
$307$	8065.71			0.0855788			0.0427894	−	0.999084i	$-0.486376\pi$
$307$	8065.71			0.0855788			0.0427894	+	0.999084i	$0.486376\pi$
$308$	−15587.3			−0.164312
$309$			86744.5i			0.908500i
$310$		−	27943.0i		−	0.290770i
$311$	73383.7			0.758715			0.379357	−	0.925250i	$-0.376145\pi$
$311$	73383.7			0.758715			0.379357	+	0.925250i	$0.376145\pi$
$312$	36082.4			0.370669
$313$			186857.i			1.90730i	0.300913	+	0.953652i	$0.402709\pi$
$313$			186857.i			1.90730i	−0.300913	+	0.953652i	$0.597291\pi$
$314$			100706.i			1.02140i
$315$	−121135.			−1.22081
$316$			71816.8i			0.719204i
$317$	−92513.9			−0.920637			−0.460319	−	0.887754i	$-0.652265\pi$
$317$	−92513.9			−0.920637			−0.460319	+	0.887754i	$0.652265\pi$
$318$		−	69264.7i		−	0.684948i
$319$		−	15228.3i		−	0.149648i
$320$			5724.33i			0.0559017i
$321$			261756.i			2.54031i
$322$	−1272.83	+	98149.5i	−0.0122760	+	0.946621i
$323$	−42642.4			−0.408730
$324$	58699.5			0.559170
$325$	12704.8			0.120282
$326$	73506.6			0.691657
$327$			169728.i			1.58730i
$328$	8996.28			0.0836210
$329$			191036.i			1.76491i
$330$	14735.3			0.135311
$331$	177870.			1.62348			0.811738	−	0.584021i	$-0.198522\pi$
$331$	177870.			1.62348			0.811738	+	0.584021i	$0.198522\pi$
$332$		−	65823.5i		−	0.597179i
$333$		−	134020.i		−	1.20859i
$334$	72960.0			0.654021
$335$	−69585.9			−0.620057
$336$			65873.0i			0.583484i
$337$			70660.9i			0.622185i	0.950380	+	0.311092i	$0.100695\pi$
$337$			70660.9i			0.622185i	−0.950380	+	0.311092i	$0.899305\pi$
$338$	51564.2			0.451352
$339$		−	362358.i		−	3.15311i
$340$	−10199.9			−0.0882348
$341$			26244.0i			0.225694i
$342$		−	174672.i		−	1.49338i
$343$			32686.2i			0.277828i
$344$			45299.6i			0.382805i
$345$	1203.26	−	92785.0i	0.0101093	−	0.779542i
$346$	49248.0			0.411374
$347$	−179683.			−1.49227			−0.746136	−	0.665793i	$-0.768093\pi$
$347$	−179683.			−1.49227			−0.746136	+	0.665793i	$0.768093\pi$
$348$	−64355.9			−0.531410
$349$	−110788.			−0.909578			−0.454789	−	0.890599i	$-0.650285\pi$
$349$	−110788.			−0.909578			−0.454789	+	0.890599i	$0.650285\pi$
$350$			23194.2i			0.189340i
$351$	−134195.			−1.08924
$352$		−	5376.28i		−	0.0433907i
$353$	129330.			1.03789			0.518943	−	0.854809i	$-0.326326\pi$
$353$	129330.			1.03789			0.518943	+	0.854809i	$0.326326\pi$
$354$	−23152.8			−0.184755
$355$			62983.3i			0.499768i
$356$		−	92022.4i		−	0.726095i
$357$	−117376.			−0.920966
$358$	−149782.			−1.16867
$359$		−	6476.55i		−	0.0502522i	−0.999684	−	0.0251261i	$-0.992001\pi$
$359$		−	6476.55i		−	0.0502522i	0.999684	−	0.0251261i	$-0.00799873\pi$
$360$		−	41781.1i		−	0.322385i
$361$	−9501.73			−0.0729102
$362$		−	82901.3i		−	0.632622i
$363$	215868.			1.63823
$364$		−	53342.1i		−	0.402594i
$365$			85346.6i			0.640620i
$366$		−	168227.i		−	1.25584i
$367$			236864.i			1.75860i	0.476267	+	0.879300i	$0.341989\pi$
$367$			236864.i			1.75860i	−0.476267	+	0.879300i	$0.658011\pi$
$368$	−33853.2	−	439.016i	−0.249979	−	0.00324179i
$369$	−65662.5			−0.482242
$370$	−25661.3			−0.187446
$371$	−102397.			−0.743942
$372$	110909.			0.801458
$373$			19565.6i			0.140629i	0.997525	+	0.0703145i	$0.0224003\pi$
$373$			19565.6i			0.140629i	−0.997525	+	0.0703145i	$0.977600\pi$
$374$	9579.75			0.0684874
$375$		−	21926.5i		−	0.155922i
$376$	−65890.9			−0.466068
$377$	52113.6			0.366664
$378$		−	244990.i		−	1.71461i
$379$		−	154713.i		−	1.07708i	−0.842601	−	0.538539i	$-0.818977\pi$
$379$		−	154713.i		−	1.07708i	0.842601	−	0.538539i	$-0.181023\pi$
$380$	−33445.2			−0.231615
$381$	−117241.			−0.807661
$382$			60988.8i			0.417949i
$383$		−	157655.i		−	1.07476i	−0.843342	−	0.537378i	$-0.819415\pi$
$383$		−	157655.i		−	1.07476i	0.843342	−	0.537378i	$-0.180585\pi$
$384$	−22720.5			−0.154084
$385$		−	21783.9i		−	0.146965i
$386$	−61038.5			−0.409665
$387$		−	330635.i		−	2.20763i
$388$		−	62229.6i		−	0.413365i
$389$		−	62828.5i		−	0.415200i	−0.978214	−	0.207600i	$-0.933435\pi$
$389$		−	62828.5i		−	0.415200i	0.978214	−	0.207600i	$-0.0665652\pi$
$390$			50426.6i			0.331536i
$391$	782.264	−	60321.4i	0.00511681	−	0.394565i
$392$	43054.5			0.280186
$393$	498276.			3.22615
$394$	−25684.6			−0.165455
$395$	−100367.			−0.643275
$396$			39240.7i			0.250234i
$397$	61812.0			0.392186			0.196093	−	0.980585i	$-0.437175\pi$
$397$	61812.0			0.392186			0.196093	+	0.980585i	$0.437175\pi$
$398$			191217.i			1.20715i
$399$	−384872.			−2.41752
$400$	−8000.00			−0.0500000
$401$			68287.1i			0.424668i	0.977197	+	0.212334i	$0.0681065\pi$
$401$			68287.1i			0.424668i	−0.977197	+	0.212334i	$0.931893\pi$
$402$		−	276194.i		−	1.70908i
$403$	−89811.0			−0.552993
$404$	14438.7			0.0884639
$405$			82035.0i			0.500137i
$406$			95140.0i			0.577180i
$407$	24101.0			0.145495
$408$		−	40484.7i		−	0.243204i
$409$	156352.			0.934668			0.467334	−	0.884081i	$-0.345215\pi$
$409$	156352.			0.934668			0.467334	+	0.884081i	$0.345215\pi$
$410$			12572.7i			0.0747929i
$411$		−	230422.i		−	1.36408i
$412$			44231.2i			0.260576i
$413$			34227.8i			0.200668i
$414$	247089.	+	3204.32i	1.44163	+	0.0186954i
$415$	91991.1			0.534133
$416$	18398.5			0.106315
$417$	249577.			1.43527
$418$	31411.6			0.179779
$419$			134388.i			0.765477i	0.923857	+	0.382738i	$0.125019\pi$
$419$			134388.i			0.765477i	−0.923857	+	0.382738i	$0.874981\pi$
$420$	−92060.3			−0.521884
$421$			230724.i			1.30175i	0.759183	+	0.650877i	$0.225599\pi$
$421$			230724.i			1.30175i	−0.759183	+	0.650877i	$0.774401\pi$
$422$	104444.			0.586485
$423$	480928.			2.68782
$424$		−	35318.2i		−	0.196457i
$425$		−	14254.8i		−	0.0789196i
$426$	−249988.			−1.37753
$427$	−248697.			−1.36400
$428$			133470.i			0.728612i
$429$		−	47360.5i		−	0.257337i
$430$	−63308.1			−0.342391
$431$			51580.0i			0.277669i	0.990316	+	0.138834i	$0.0443356\pi$
$431$			51580.0i			0.277669i	−0.990316	+	0.138834i	$0.955664\pi$
$432$	84500.6			0.452785
$433$			193923.i			1.03431i	0.855890	+	0.517157i	$0.173010\pi$
$433$			193923.i			1.03431i	−0.855890	+	0.517157i	$0.826990\pi$
$434$		−	163962.i		−	0.870488i
$435$		−	89940.0i		−	0.475307i
$436$			86544.6i			0.455268i
$437$	2565.01	−	197792.i	0.0134316	−	1.03573i
$438$	−338750.			−1.76576
$439$	−252444.			−1.30990			−0.654948	−	0.755674i	$-0.727309\pi$
$439$	−252444.			−1.30990			−0.654948	+	0.755674i	$0.727309\pi$
$440$	7513.57			0.0388098
$441$	−314249.			−1.61583
$442$			32783.4i			0.167807i
$443$	241986.			1.23306			0.616528	−	0.787333i	$-0.288539\pi$
$443$	241986.			1.23306			0.616528	+	0.787333i	$0.288539\pi$
$444$		−	101853.i		−	0.516663i
$445$	128605.			0.649439
$446$	100307.			0.504269
$447$		−	221617.i		−	1.10914i
$448$			33588.8i			0.167355i
$449$	−300698.			−1.49155			−0.745776	−	0.666197i	$-0.767921\pi$
$449$	−300698.			−1.49155			−0.745776	+	0.666197i	$0.767921\pi$
$450$	58390.8			0.288350
$451$		−	11808.2i		−	0.0580539i
$452$		−	184767.i		−	0.904373i
$453$	208242.			1.01478
$454$			221752.i			1.07586i
$455$	74547.9			0.360091
$456$		−	132748.i		−	0.638407i
$457$		−	76245.8i		−	0.365076i	−0.983199	−	0.182538i	$-0.941569\pi$
$457$		−	76245.8i		−	0.365076i	0.983199	−	0.182538i	$-0.0584313\pi$
$458$		−	274522.i		−	1.30872i
$459$			150568.i			0.714672i
$460$	613.544	−	47311.2i	0.00289955	−	0.223588i
$461$	245704.			1.15614			0.578070	−	0.815987i	$-0.303806\pi$
$461$	245704.			1.15614			0.578070	+	0.815987i	$0.303806\pi$
$462$	86462.8			0.405084
$463$	119233.			0.556205			0.278102	−	0.960551i	$-0.410295\pi$
$463$	119233.			0.556205			0.278102	+	0.960551i	$0.410295\pi$
$464$	−32815.1			−0.152419
$465$			155000.i			0.716846i
$466$	269542.			1.24124
$467$		−	107162.i		−	0.491368i	−0.969350	−	0.245684i	$-0.920988\pi$
$467$		−	107162.i		−	0.491368i	0.969350	−	0.245684i	$-0.0790125\pi$
$468$	−134288.			−0.613118
$469$	−408310.			−1.85628
$470$		−	92085.3i		−	0.416864i
$471$		−	558614.i		−	2.51808i
$472$	−11805.6			−0.0529915
$473$	59458.7			0.265762
$474$		−	398368.i		−	1.77308i
$475$		−	46741.1i		−	0.207163i
$476$	−59850.3			−0.264151
$477$			257782.i			1.13296i
$478$	−94376.4			−0.413055
$479$			175156.i			0.763405i	0.924285	+	0.381703i	$0.124662\pi$
$479$			175156.i			0.763405i	−0.924285	+	0.381703i	$0.875338\pi$
$480$		−	31752.9i		−	0.137816i
$481$			82477.5i			0.356488i
$482$			317844.i			1.36810i
$483$	7060.38	−	544436.i	0.0302645	−	2.33374i
$484$	110071.			0.469876
$485$	86968.5			0.369725
$486$	−23117.2			−0.0978728
$487$	110922.			0.467692			0.233846	−	0.972274i	$-0.424869\pi$
$487$	110922.			0.467692			0.233846	+	0.972274i	$0.424869\pi$
$488$		−	85779.2i		−	0.360199i
$489$	−407741.			−1.70517
$490$			60170.5i			0.250606i
$491$	365561.			1.51634			0.758170	−	0.652057i	$-0.226094\pi$
$491$	365561.			1.51634			0.758170	+	0.652057i	$0.226094\pi$
$492$	−49902.4			−0.206154
$493$		−	58471.9i		−	0.240576i
$494$			107495.i			0.440490i
$495$	−54840.5			−0.223816
$496$	56552.7			0.229874
$497$			369568.i			1.49617i
$498$			365123.i			1.47225i
$499$	−409609.			−1.64501			−0.822504	−	0.568759i	$-0.807424\pi$
$499$	−409609.			−1.64501			−0.822504	+	0.568759i	$0.807424\pi$
$500$		−	11180.3i		−	0.0447214i
$501$	−404709.			−1.61238
$502$			236687.i			0.939221i
$503$		−	42715.8i		−	0.168831i	−0.996431	−	0.0844156i	$-0.973098\pi$
$503$		−	42715.8i		−	0.168831i	0.996431	−	0.0844156i	$-0.0269023\pi$
$504$		−	245159.i		−	0.965134i
$505$			20178.7i			0.0791245i
$506$	−576.238	+	44434.5i	−0.00225061	+	0.173548i
$507$	−286027.			−1.11273
$508$	−59781.3			−0.231653
$509$	45041.2			0.173850			0.0869250	−	0.996215i	$-0.472296\pi$
$509$	45041.2			0.173850			0.0869250	+	0.996215i	$0.472296\pi$
$510$	56579.1			0.217528
$511$			500789.i			1.91784i
$512$	−11585.2			−0.0441942
$513$			493706.i			1.87600i
$514$	−98939.8			−0.374494
$515$	−61814.9			−0.233066
$516$		−	251277.i		−	0.943742i
$517$			86486.2i			0.323568i
$518$	−150573.			−0.561163
$519$	−273179.			−1.01417
$520$			25712.6i			0.0950910i
$521$			398414.i			1.46777i	0.679272	+	0.733887i	$0.262296\pi$
$521$			398414.i			1.46777i	−0.679272	+	0.733887i	$0.737704\pi$
$522$	239513.			0.878999
$523$			42473.4i			0.155279i	0.996981	+	0.0776397i	$0.0247384\pi$
$523$			42473.4i			0.155279i	−0.996981	+	0.0776397i	$0.975262\pi$
$524$	254072.			0.925324
$525$		−	128658.i		−	0.466787i
$526$			21779.8i			0.0787195i
$527$			100769.i			0.362831i
$528$			29822.2i			0.106973i
$529$	279747.	+	7256.88i	0.999664	+	0.0259321i
$530$	49358.6			0.175716
$531$	86167.7			0.305602
$532$	−196247.			−0.693393
$533$	40409.6			0.142243
$534$			510449.i			1.79007i
$535$	−186530.			−0.651690
$536$		−	140832.i		−	0.490198i
$537$	830840.			2.88117
$538$	252974.			0.874000
$539$		−	56511.9i		−	0.194519i
$540$			118093.i			0.404983i
$541$	519454.			1.77481			0.887407	−	0.460986i	$-0.152504\pi$
$541$	519454.			1.77481			0.887407	+	0.460986i	$0.152504\pi$
$542$	124791.			0.424799
$543$			459854.i			1.55963i
$544$		−	20643.2i		−	0.0697557i
$545$	−120950.			−0.407204
$546$			295889.i			0.992530i
$547$	−149179.			−0.498579			−0.249289	−	0.968429i	$-0.580197\pi$
$547$	−149179.			−0.498579			−0.249289	+	0.968429i	$0.580197\pi$
$548$		−	117492.i		−	0.391245i
$549$			626090.i			2.07727i
$550$			10500.5i			0.0347125i
$551$		−	191727.i		−	0.631510i
$552$	187784.	+	2435.23i	0.616282	+	0.00799210i
$553$	−588925.			−1.92579
$554$	−107595.			−0.350567
$555$	142344.			0.462117
$556$	127260.			0.411663
$557$			365560.i			1.17828i	0.808032	+	0.589139i	$0.200533\pi$
$557$			365560.i			1.17828i	−0.808032	+	0.589139i	$0.799467\pi$
$558$	−412770.			−1.32568
$559$			203477.i			0.651166i
$560$	−46941.7			−0.149687
$561$	−53138.9			−0.168845
$562$			92340.0i			0.292359i
$563$		−	161005.i		−	0.507953i	−0.967210	−	0.253976i	$-0.918261\pi$
$563$		−	161005.i		−	0.507953i	0.967210	−	0.253976i	$-0.0817385\pi$
$564$	365497.			1.14902
$565$	258220.			0.808896
$566$		−	130320.i		−	0.406799i
$567$			481358.i			1.49728i
$568$	−127469.			−0.395102
$569$		−	237016.i		−	0.732071i	−0.930601	−	0.366035i	$-0.880715\pi$
$569$		−	237016.i		−	0.732071i	0.930601	−	0.366035i	$-0.119285\pi$
$570$	185521.			0.571009
$571$		−	456756.i		−	1.40091i	−0.713694	−	0.700457i	$-0.752979\pi$
$571$		−	456756.i		−	1.40091i	0.713694	−	0.700457i	$-0.247021\pi$
$572$		−	24149.2i		−	0.0738093i
$573$		−	338305.i		−	1.03038i
$574$			73772.9i			0.223910i
$575$	66119.4	+	857.453i	0.199983	+	0.00259343i
$576$	84559.0			0.254868
$577$	−190050.			−0.570844			−0.285422	−	0.958402i	$-0.592134\pi$
$577$	−190050.			−0.570844			−0.285422	+	0.958402i	$0.592134\pi$
$578$	−199450.			−0.597005
$579$	338581.			1.00996
$580$		−	45860.6i		−	0.136327i
$581$	539777.			1.59905
$582$			345188.i			1.01908i
$583$	−46357.5			−0.136390
$584$	−172729.			−0.506454
$585$		−	187673.i		−	0.548390i
$586$			175529.i			0.511155i
$587$	159473.			0.462819			0.231410	−	0.972856i	$-0.425666\pi$
$587$	159473.			0.462819			0.231410	+	0.972856i	$0.425666\pi$
$588$	−238824.			−0.690753
$589$			330417.i			0.952427i
$590$		−	16498.9i		−	0.0473970i
$591$	142473.			0.407903
$592$		−	51934.9i		−	0.148189i
$593$	−680478.			−1.93511			−0.967553	−	0.252667i	$-0.918692\pi$
$593$	−680478.			−1.93511			−0.967553	+	0.252667i	$0.918692\pi$
$594$		−	110913.i		−	0.314346i
$595$		−	83643.4i		−	0.236264i
$596$		−	113003.i		−	0.318124i
$597$		−	1.06068e6i		−	2.97602i
$598$	−152062.	−	1971.98i	−0.425224	−	0.00551442i
$599$	285158.			0.794752			0.397376	−	0.917656i	$-0.369921\pi$
$599$	285158.			0.794752			0.397376	+	0.917656i	$0.369921\pi$
$600$	44376.1			0.123267
$601$	−516773.			−1.43071			−0.715354	−	0.698763i	$-0.753734\pi$
$601$	−516773.			−1.43071			−0.715354	+	0.698763i	$0.753734\pi$
$602$	−371474.			−1.02503
$603$			1.02791e6i			2.82697i
$604$	106183.			0.291059
$605$			153829.i			0.420270i
$606$	−80091.7			−0.218093
$607$	−53588.9			−0.145445			−0.0727223	−	0.997352i	$-0.523169\pi$
$607$	−53588.9			−0.145445			−0.0727223	+	0.997352i	$0.523169\pi$
$608$		−	67688.3i		−	0.183108i
$609$		−	527742.i		−	1.42294i
$610$	119880.			0.322172
$611$	−295969.			−0.792801
$612$			150672.i			0.402281i
$613$			390391.i			1.03891i	0.854497	+	0.519456i	$0.173865\pi$
$613$			390391.i			1.03891i	−0.854497	+	0.519456i	$0.826135\pi$
$614$	−22813.3			−0.0605133
$615$		−	69740.7i		−	0.184390i
$616$	44087.5			0.116186
$617$		−	566402.i		−	1.48783i	−0.668271	−	0.743917i	$-0.732966\pi$
$617$		−	566402.i		−	1.48783i	0.668271	−	0.743917i	$-0.267034\pi$
$618$		−	245350.i		−	0.642407i
$619$			99953.7i			0.260866i	0.991457	+	0.130433i	$0.0416368\pi$
$619$			99953.7i			0.260866i	−0.991457	+	0.130433i	$0.958363\pi$
$620$			79034.8i			0.205606i
$621$	−698391.	−	9056.91i	−1.81099	−	0.0234854i
$622$	−207560.			−0.536492
$623$	754619.			1.94425
$624$	−102056.			−0.262102
$625$	15625.0			0.0400000
$626$		−	528510.i		−	1.34867i
$627$	−174241.			−0.443215
$628$		−	284838.i		−	0.722236i
$629$	92540.5			0.233900
$630$	342621.			0.863242
$631$			412207.i			1.03528i	0.855599	+	0.517638i	$0.173189\pi$
$631$			412207.i			1.03528i	−0.855599	+	0.517638i	$0.826811\pi$
$632$		−	203129.i		−	0.508554i
$633$	−579349.			−1.44588
$634$	261669.			0.650989
$635$		−	83546.9i		−	0.207197i
$636$			195910.i			0.484331i
$637$	193393.			0.476608
$638$			43072.1i			0.105817i
$639$	930380.			2.27855
$640$		−	16190.9i		−	0.0395285i
$641$			309655.i			0.753637i	0.926287	+	0.376819i	$0.122982\pi$
$641$			309655.i			0.753637i	−0.926287	+	0.376819i	$0.877018\pi$
$642$		−	740359.i		−	1.79627i
$643$		−	446887.i		−	1.08087i	−0.841384	−	0.540437i	$-0.818259\pi$
$643$		−	446887.i		−	1.08087i	0.841384	−	0.540437i	$-0.181741\pi$
$644$	3600.10	−	277609.i	0.00868046	−	0.669362i
$645$	351170.			0.844108
$646$	120611.			0.289016
$647$	−753119.			−1.79910			−0.899550	−	0.436818i	$-0.856105\pi$
$647$	−753119.			−1.79910			−0.899550	+	0.436818i	$0.856105\pi$
$648$	−166027.			−0.395393
$649$			15495.7i			0.0367893i
$650$	−35934.5			−0.0850520
$651$			909496.i			2.14604i
$652$	−207908.			−0.489075
$653$	−554875.			−1.30127			−0.650637	−	0.759388i	$-0.725498\pi$
$653$	−554875.			−1.30127			−0.650637	+	0.759388i	$0.725498\pi$
$654$		−	480063.i		−	1.12239i
$655$			355076.i			0.827635i
$656$	−25445.3			−0.0591290
$657$	1.26073e6			2.92072
$658$		−	540330.i		−	1.24798i
$659$			272498.i			0.627470i	0.949511	+	0.313735i	$0.101580\pi$
$659$			272498.i			0.627470i	−0.949511	+	0.313735i	$0.898420\pi$
$660$	−41677.8			−0.0956792
$661$		−	679981.i		−	1.55630i	−0.628077	−	0.778151i	$-0.716158\pi$
$661$		−	679981.i		−	1.55630i	0.628077	−	0.778151i	$-0.283842\pi$
$662$	−503092.			−1.14797
$663$		−	181850.i		−	0.413700i
$664$			186177.i			0.422269i
$665$		−	274263.i		−	0.620190i
$666$			379065.i			0.854605i
$667$	271215.	+	3517.18i	0.609624	+	0.00790575i
$668$	−206362.			−0.462463
$669$	−556405.			−1.24319
$670$	196819.			0.438447
$671$	−112591.			−0.250068
$672$		−	186317.i		−	0.412586i
$673$	380330.			0.839711			0.419856	−	0.907591i	$-0.362081\pi$
$673$	380330.			0.839711			0.419856	+	0.907591i	$0.362081\pi$
$674$		−	199859.i		−	0.439951i
$675$	−165040.			−0.362228
$676$	−145846.			−0.319154
$677$			503348.i			1.09822i	0.835749	+	0.549112i	$0.185034\pi$
$677$			503348.i			1.09822i	−0.835749	+	0.549112i	$0.814966\pi$
$678$			1.02490e6i			2.22958i
$679$	510306.			1.10686
$680$	28849.8			0.0623914
$681$		−	1.23006e6i		−	2.65235i
$682$		−	74229.2i		−	0.159590i
$683$	336134.			0.720562			0.360281	−	0.932844i	$-0.382681\pi$
$683$	336134.			0.720562			0.360281	+	0.932844i	$0.382681\pi$
$684$			494047.i			1.05598i
$685$	164201.			0.349940
$686$		−	92450.5i		−	0.196454i
$687$			1.52278e6i			3.22643i
$688$		−	128126.i		−	0.270684i
$689$		−	158643.i		−	0.334181i
$690$	−3403.33	+	262436.i	−0.00714835	+	0.551220i
$691$	451586.			0.945766			0.472883	−	0.881125i	$-0.343213\pi$
$691$	451586.			0.945766			0.472883	+	0.881125i	$0.343213\pi$
$692$	−139294.			−0.290885
$693$	−321788.			−0.670045
$694$	508220.			1.05520
$695$			177851.i			0.368203i
$696$	182026.			0.375763
$697$		−	45339.9i		−	0.0933286i
$698$	313354.			0.643169
$699$	−1.49515e6			−3.06007
$700$		−	65603.0i		−	0.133884i
$701$			261852.i			0.532868i	0.963853	+	0.266434i	$0.0858454\pi$
$701$			261852.i			0.532868i	−0.963853	+	0.266434i	$0.914155\pi$
$702$	379561.			0.770206
$703$	303437.			0.613985
$704$			15206.4i			0.0306818i
$705$			510798.i			1.02771i
$706$	−365800.			−0.733896
$707$			118403.i			0.236878i
$708$	65486.0			0.130642
$709$		−	614433.i		−	1.22231i	−0.791510	−	0.611156i	$-0.790705\pi$
$709$		−	614433.i		−	1.22231i	0.791510	−	0.611156i	$-0.209295\pi$
$710$		−	178144.i		−	0.353390i
$711$			1.48261e6i			2.93283i
$712$			260279.i			0.513427i
$713$	−467404.	−	6061.41i	−0.919419	−	0.0119232i
$714$	331990.			0.651221
$715$	33749.5			0.0660170
$716$	423647.			0.826376
$717$	523507.			1.01832
$718$			18318.5i			0.0355337i
$719$	−427677.			−0.827290			−0.413645	−	0.910438i	$-0.635744\pi$
$719$	−427677.			−0.827290			−0.413645	+	0.910438i	$0.635744\pi$
$720$			118175.i			0.227961i
$721$	−362712.			−0.697737
$722$	26875.0			0.0515553
$723$		−	1.76308e6i		−	3.37284i
$724$			234480.i			0.447331i
$725$	64092.1			0.121935
$726$	−610566.			−1.15840
$727$		−	987802.i		−	1.86897i	−0.356009	−	0.934483i	$-0.615863\pi$
$727$		−	987802.i		−	1.86897i	0.356009	−	0.934483i	$-0.384137\pi$
$728$			150874.i			0.284677i
$729$	−466101.			−0.877051
$730$		−	241397.i		−	0.452987i
$731$	228303.			0.427245
$732$			475818.i			0.888012i
$733$			866621.i			1.61295i	0.591267	+	0.806476i	$0.298628\pi$
$733$			866621.i			1.61295i	−0.591267	+	0.806476i	$0.701372\pi$
$734$		−	669953.i		−	1.24352i
$735$		−	333766.i		−	0.617828i
$736$	95751.2	+	1241.73i	0.176762	+	0.00229229i
$737$	−184851.			−0.340320
$738$	185722.			0.340997
$739$	368481.			0.674724			0.337362	−	0.941375i	$-0.390465\pi$
$739$	368481.			0.674724			0.337362	+	0.941375i	$0.390465\pi$
$740$	72581.2			0.132544
$741$		−	596278.i		−	1.08596i
$742$	289622.			0.526047
$743$			548337.i			0.993276i	0.867958	+	0.496638i	$0.165432\pi$
$743$			548337.i			0.993276i	−0.867958	+	0.496638i	$0.834568\pi$
$744$	−313698.			−0.566717
$745$	157926.			0.284539
$746$		−	55339.8i		−	0.0994397i
$747$		−	1.35888e6i		−	2.43523i
$748$	−27095.6			−0.0484279
$749$	−1.09450e6			−1.95099
$750$			62017.4i			0.110253i
$751$		−	552918.i		−	0.980350i	−0.871624	−	0.490175i	$-0.836933\pi$
$751$		−	552918.i		−	0.980350i	0.871624	−	0.490175i	$-0.163067\pi$
$752$	186368.			0.329560
$753$		−	1.31291e6i		−	2.31550i
$754$	−147399.			−0.259270
$755$			148395.i			0.260331i
$756$			692937.i			1.21241i
$757$		−	233309.i		−	0.407137i	−0.979061	−	0.203569i	$-0.934746\pi$
$757$		−	233309.i		−	0.407137i	0.979061	−	0.203569i	$-0.0652540\pi$
$758$			437593.i			0.761609i
$759$	3196.40	−	246479.i	0.00554852	−	0.427854i
$760$	94597.3			0.163777
$761$	230402.			0.397848			0.198924	−	0.980015i	$-0.436255\pi$
$761$	230402.			0.397848			0.198924	+	0.980015i	$0.436255\pi$
$762$	331607.			0.571103
$763$	−709698.			−1.21906
$764$		−	172502.i		−	0.295534i
$765$	−210570.			−0.359811
$766$			445915.i			0.759967i
$767$	−53028.7			−0.0901406
$768$	64263.4			0.108953
$769$		−	289555.i		−	0.489642i	−0.969568	−	0.244821i	$-0.921271\pi$
$769$		−	289555.i		−	0.489642i	0.969568	−	0.244821i	$-0.0787292\pi$
$770$			61614.1i			0.103920i
$771$	548820.			0.923253
$772$	172643.			0.289677
$773$			164720.i			0.275668i	0.990455	+	0.137834i	$0.0440140\pi$
$773$			164720.i			0.275668i	−0.990455	+	0.137834i	$0.955986\pi$
$774$			935177.i			1.56103i
$775$	−110454.			−0.183899
$776$			176012.i			0.292293i
$777$	835232.			1.38345
$778$			177706.i			0.293591i
$779$		−	148668.i		−	0.244986i
$780$		−	142628.i		−	0.234431i
$781$			167312.i			0.274300i
$782$	−2212.58	+	170615.i	−0.00361813	+	0.278999i
$783$	−676977.			−1.10421
$784$	−121776.			−0.198121
$785$	398073.			0.645987
$786$	−1.40934e6			−2.28123
$787$		−	499158.i		−	0.805914i	−0.915219	−	0.402957i	$-0.867982\pi$
$787$		−	499158.i		−	0.805914i	0.915219	−	0.402957i	$-0.132018\pi$
$788$	72647.0			0.116994
$789$		−	120813.i		−	0.194070i
$790$	283881.			0.454864
$791$	1.51516e6			2.42162
$792$		−	110989.i		−	0.176942i
$793$		−	385304.i		−	0.612713i
$794$	−174831.			−0.277317
$795$	−273793.			−0.433199
$796$		−	540843.i		−	0.853581i
$797$		−	323402.i		−	0.509127i	−0.967056	−	0.254564i	$-0.918068\pi$
$797$		−	323402.i		−	0.509127i	0.967056	−	0.254564i	$-0.0819318\pi$
$798$	1.08858e6			1.70945
$799$			332080.i			0.520175i
$800$	22627.4			0.0353553
$801$		−	1.89974e6i		−	2.96093i
$802$		−	193145.i		−	0.300286i
$803$			226719.i			0.351606i
$804$			781196.i			1.20850i
$805$	387970.	+	5031.29i	0.598696	+	0.00776404i
$806$	254024.			0.391025
$807$	−1.40325e6			−2.15470
$808$	−40838.9			−0.0625534
$809$	296837.			0.453545			0.226773	−	0.973948i	$-0.427183\pi$
$809$	296837.			0.453545			0.226773	+	0.973948i	$0.427183\pi$
$810$		−	232030.i		−	0.353650i
$811$	1085.29			0.00165008			0.000825040	−	1.00000i	$-0.499737\pi$
$811$	1085.29			0.00165008			0.000825040		1.00000i	$0.499737\pi$
$812$		−	269097.i		−	0.408128i
$813$	−692215.			−1.04727
$814$	−68168.0			−0.102880
$815$		−	290560.i		−	0.437442i
$816$			114508.i			0.171971i
$817$	748597.			1.12151
$818$	−442231.			−0.660910
$819$		−	1.10121e6i		−	1.64173i
$820$		−	35560.9i		−	0.0528865i
$821$	762677.			1.13150			0.565749	−	0.824577i	$-0.308587\pi$
$821$	762677.			1.13150			0.565749	+	0.824577i	$0.308587\pi$
$822$			651731.i			0.964550i
$823$	−491480.			−0.725614			−0.362807	−	0.931864i	$-0.618182\pi$
$823$	−491480.			−0.725614			−0.362807	+	0.931864i	$0.618182\pi$
$824$		−	125105.i		−	0.184255i
$825$		−	58246.6i		−	0.0855780i
$826$		−	96810.8i		−	0.141894i
$827$		−	221221.i		−	0.323456i	−0.986835	−	0.161728i	$-0.948293\pi$
$827$		−	221221.i		−	0.323456i	0.986835	−	0.161728i	$-0.0517068\pi$
$828$	−698874.	−	9063.17i	−1.01938	−	0.0132196i
$829$	211209.			0.307329			0.153665	−	0.988123i	$-0.450892\pi$
$829$	211209.			0.307329			0.153665	+	0.988123i	$0.450892\pi$
$830$	−260190.			−0.377689
$831$	596828.			0.864266
$832$	−52038.7			−0.0751761
$833$		−	216988.i		−	0.312713i
$834$	−705911.			−1.01489
$835$		−	288400.i		−	0.413639i
$836$	−88845.5			−0.127123
$837$	1.16668e6			1.66534
$838$		−	380106.i		−	0.541274i
$839$		−	794484.i		−	1.12866i	−0.825551	−	0.564328i	$-0.809135\pi$
$839$		−	794484.i		−	1.12866i	0.825551	−	0.564328i	$-0.190865\pi$
$840$	260386.			0.369028
$841$	−444382.			−0.628296
$842$		−	652586.i		−	0.920479i
$843$		−	512210.i		−	0.720764i
$844$	−295411.			−0.414708
$845$		−	203825.i		−	0.285460i
$846$	−1.36027e6			−1.90057
$847$			902626.i			1.25818i
$848$			99894.9i			0.138916i
$849$			722888.i			1.00290i
$850$			40318.8i			0.0558046i
$851$	−5566.47	+	429238.i	−0.00768636	+	0.592706i
$852$	707073.			0.974058
$853$	84614.8			0.116292			0.0581458	−	0.998308i	$-0.481481\pi$
$853$	84614.8			0.116292			0.0581458	+	0.998308i	$0.481481\pi$
$854$	703422.			0.964496
$855$	−690452.			−0.944499
$856$		−	377510.i		−	0.515206i
$857$	34615.5			0.0471312			0.0235656	−	0.999722i	$-0.492498\pi$
$857$	34615.5			0.0471312			0.0235656	+	0.999722i	$0.492498\pi$
$858$			133956.i			0.181965i
$859$	−1.17805e6			−1.59653			−0.798263	−	0.602308i	$-0.794248\pi$
$859$	−1.17805e6			−1.59653			−0.798263	+	0.602308i	$0.794248\pi$
$860$	179062.			0.242107
$861$		−	409219.i		−	0.552013i
$862$		−	145890.i		−	0.196341i
$863$	−1.04737e6			−1.40630			−0.703149	−	0.711043i	$-0.748223\pi$
$863$	−1.04737e6			−1.40630			−0.703149	+	0.711043i	$0.748223\pi$
$864$	−239004.			−0.320167
$865$		−	194670.i		−	0.260176i
$866$		−	548496.i		−	0.731371i
$867$	1.10635e6			1.47182
$868$			463753.i			0.615528i
$869$	−266620.			−0.353064
$870$			254389.i			0.336093i
$871$		−	632591.i		−	0.833847i
$872$		−	244785.i		−	0.321923i
$873$		−	1.28468e6i		−	1.68565i
$874$	−7254.95	+	559439.i	−0.00949755	+	0.732369i
$875$	91683.0			0.119749
$876$	958131.			1.24858
$877$	−42738.7			−0.0555677			−0.0277839	−	0.999614i	$-0.508845\pi$
$877$	−42738.7			−0.0555677			−0.0277839	+	0.999614i	$0.508845\pi$
$878$	714020.			0.926236
$879$		−	973659.i		−	1.26017i
$880$	−21251.6			−0.0274427
$881$			416341.i			0.536411i	0.963362	+	0.268205i	$0.0864306\pi$
$881$			416341.i			0.536411i	−0.963362	+	0.268205i	$0.913569\pi$
$882$	888829.			1.14257
$883$	−428837.			−0.550010			−0.275005	−	0.961443i	$-0.588680\pi$
$883$	−428837.			−0.550010			−0.275005	+	0.961443i	$0.588680\pi$
$884$		−	92725.4i		−	0.118657i
$885$			91519.5i			0.116850i
$886$	−684440.			−0.871902
$887$	1.42438e6			1.81041			0.905207	−	0.424972i	$-0.139716\pi$
$887$	1.42438e6			1.81041			0.905207	+	0.424972i	$0.139716\pi$
$888$			288083.i			0.365336i
$889$		−	490229.i		−	0.620292i
$890$	−363751.			−0.459223
$891$			217922.i			0.274502i
$892$	−283712.			−0.356572
$893$			1.08888e6i			1.36545i
$894$			626828.i			0.784284i
$895$			592064.i			0.739134i
$896$		−	95003.3i		−	0.118338i
$897$	843488.	+	10938.6i	1.04832	+	0.0135949i
$898$	850503.			1.05469
$899$	−453072.			−0.560594
$900$	−165154.			−0.203894
$901$	−177998.			−0.219263
$902$			33398.7i			0.0410503i
$903$	2.06057e6			2.52703
$904$			522600.i			0.639488i
$905$	−327696.			−0.400105
$906$	−588998.			−0.717559
$907$		−	283145.i		−	0.344186i	−0.985081	−	0.172093i	$-0.944947\pi$
$907$		−	283145.i		−	0.344186i	0.985081	−	0.172093i	$-0.0550530\pi$
$908$		−	627209.i		−	0.760747i
$909$	298077.			0.360746
$910$	−210853.			−0.254623
$911$			168290.i			0.202779i	0.994847	+	0.101389i	$0.0323288\pi$
$911$			168290.i			0.202779i	−0.994847	+	0.101389i	$0.967671\pi$
$912$			375468.i			0.451422i
$913$	244370.			0.293161
$914$			215656.i			0.258148i
$915$	−664976.			−0.794262
$916$			776466.i			0.925405i
$917$			2.08348e6i			2.47772i
$918$		−	425870.i		−	0.505350i
$919$			22565.6i			0.0267188i	0.999911	+	0.0133594i	$0.00425255\pi$
$919$			22565.6i			0.0267188i	−0.999911	+	0.0133594i	$0.995747\pi$
$920$	−1735.36	+	133816.i	−0.00205029	+	0.158101i
$921$	126545.			0.149186
$922$	−694956.			−0.817514
$923$	−572568.			−0.672084
$924$	−244554.			−0.286438
$925$			101435.i			0.118551i
$926$	−337242.			−0.393296
$927$			913120.i			1.06260i
$928$	92815.3			0.107776
$929$	−1.48132e6			−1.71639			−0.858197	−	0.513320i	$-0.828415\pi$
$929$	−1.48132e6			−1.71639			−0.858197	+	0.513320i	$0.828415\pi$
$930$		−	438406.i		−	0.506887i
$931$		−	711496.i		−	0.820867i
$932$	−762381.			−0.877688
$933$	1.15134e6			1.32263
$934$			303100.i			0.347449i
$935$		−	37867.3i		−	0.0433153i
$936$	379823.			0.433540
$937$			120147.i			0.136847i	0.997656	+	0.0684233i	$0.0217968\pi$
$937$			120147.i			0.136847i	−0.997656	+	0.0684233i	$0.978203\pi$
$938$	1.15488e6			1.31259
$939$			2.93165e6i			3.32492i
$940$			260457.i			0.294768i
$941$			775117.i			0.875363i	0.899130	+	0.437681i	$0.144200\pi$
$941$			775117.i			0.875363i	−0.899130	+	0.437681i	$0.855800\pi$
$942$			1.58000e6i			1.78055i
$943$	210304.	+	2727.27i	0.236496	+	0.00306694i
$944$	33391.4			0.0374706
$945$	−968409.			−1.08441
$946$	−168175.			−0.187922
$947$	−1.29596e6			−1.44508			−0.722542	−	0.691327i	$-0.757027\pi$
$947$	−1.29596e6			−1.44508			−0.722542	+	0.691327i	$0.757027\pi$
$948$			1.12676e6i			1.25376i
$949$	−775867.			−0.861500
$950$			132204.i			0.146486i
$951$	−1.45148e6			−1.60491
$952$	169282.			0.186783
$953$			1.60332e6i			1.76536i	0.469972	+	0.882681i	$0.344264\pi$
$953$			1.60332e6i			1.76536i	−0.469972	+	0.882681i	$0.655736\pi$
$954$		−	729118.i		−	0.801127i
$955$	241079.			0.264334
$956$	266937.			0.292074
$957$		−	238921.i		−	0.260874i
$958$		−	495417.i		−	0.539809i
$959$	963482.			1.04763
$960$			89810.8i			0.0974510i
$961$	−142709.			−0.154527
$962$		−	233282.i		−	0.252075i
$963$			2.75539e6i			2.97119i
$964$		−	898997.i		−	0.967396i
$965$			241276.i			0.259095i
$966$	−19969.8	+	1.53990e6i	−0.0214003	+	1.65020i
$967$	−1.25618e6			−1.34338			−0.671688	−	0.740834i	$-0.734430\pi$
$967$	−1.25618e6			−1.34338			−0.671688	+	0.740834i	$0.734430\pi$
$968$	−311329.			−0.332253
$969$	−669029.			−0.712521
$970$	−245984.			−0.261435
$971$		−	1.21944e6i		−	1.29336i	−0.762760	−	0.646682i	$-0.776156\pi$
$971$		−	1.21944e6i		−	1.29336i	0.762760	−	0.646682i	$-0.223844\pi$
$972$	65385.2			0.0692065
$973$			1.04358e6i			1.10230i
$974$	−313735.			−0.330708
$975$	199329.			0.209682
$976$			242620.i			0.254699i
$977$			233545.i			0.244671i	0.992489	+	0.122335i	$0.0390384\pi$
$977$			233545.i			0.244671i	−0.992489	+	0.122335i	$0.960962\pi$
$978$	1.15327e6			1.20574
$979$	341633.			0.356447
$980$		−	170188.i		−	0.177205i
$981$			1.78665e6i			1.85653i
$982$	−1.03396e6			−1.07221
$983$		−	1.28395e6i		−	1.32875i	−0.747401	−	0.664373i	$-0.768699\pi$
$983$		−	1.28395e6i		−	1.32875i	0.747401	−	0.664373i	$-0.231301\pi$
$984$	141145.			0.145773
$985$			101527.i			0.104643i
$986$			165383.i			0.170113i
$987$			2.99722e6i			3.07669i
$988$		−	304043.i		−	0.311474i
$989$	−13732.8	+	1.05896e6i	−0.0140400	+	1.08264i
$990$	155112.			0.158262
$991$	1.03206e6			1.05089			0.525446	−	0.850827i	$-0.323898\pi$
$991$	1.03206e6			1.05089			0.525446	+	0.850827i	$0.323898\pi$
$992$	−159955.			−0.162545
$993$	2.79065e6			2.83014
$994$		−	1.04530e6i		−	1.05795i
$995$	755851.			0.763466
$996$		−	1.03272e6i		−	1.04104i
$997$	146873.			0.147758			0.0738789	−	0.997267i	$-0.476462\pi$
$997$	146873.			0.147758			0.0738789	+	0.997267i	$0.476462\pi$
$998$	1.15855e6			1.16320
$999$		−	1.07142e6i		−	1.07356i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.d.a.91.4	✓	32
23.22	odd	2	inner	230.5.d.a.91.13	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.d.a.91.4	✓	32	1.1	even	1	trivial
230.5.d.a.91.13	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)

\(f(q)\)	\(=\)	\(q-2.82843 q^{2} +15.6893 q^{3} +8.00000 q^{4} +11.1803i q^{5} -44.3761 q^{6} +65.6030i q^{7} -22.6274 q^{8} +165.154 q^{9} +O(q^{10})\)	\(q-2.82843 q^{2} +15.6893 q^{3} +8.00000 q^{4} +11.1803i q^{5} -44.3761 q^{6} +65.6030i q^{7} -22.6274 q^{8} +165.154 q^{9} -31.6228i q^{10} +29.7000i q^{11} +125.514 q^{12} -101.638 q^{13} -185.553i q^{14} +175.412i q^{15} +64.0000 q^{16} +114.039i q^{17} -467.127 q^{18} +373.929i q^{19} +89.4427i q^{20} +1029.27i q^{21} -84.0043i q^{22} +(-528.956 - 6.85963i) q^{23} -355.008 q^{24} -125.000 q^{25} +287.476 q^{26} +1320.32 q^{27} +524.824i q^{28} -512.737 q^{29} -496.139i q^{30} +883.636 q^{31} -181.019 q^{32} +465.972i q^{33} -322.550i q^{34} -733.464 q^{35} +1321.23 q^{36} -811.483i q^{37} -1057.63i q^{38} -1594.63 q^{39} -252.982i q^{40} -397.583 q^{41} -2911.20i q^{42} -2001.98i q^{43} +237.600i q^{44} +1846.48i q^{45} +(1496.11 + 19.4020i) q^{46} +2911.99 q^{47} +1004.12 q^{48} -1902.76 q^{49} +353.553 q^{50} +1789.19i q^{51} -813.104 q^{52} +1560.86i q^{53} -3734.43 q^{54} -332.056 q^{55} -1484.43i q^{56} +5866.68i q^{57} +1450.24 q^{58} +521.741 q^{59} +1403.29i q^{60} +3790.94i q^{61} -2499.30 q^{62} +10834.6i q^{63} +512.000 q^{64} -1136.35i q^{65} -1317.97i q^{66} +6223.95i q^{67} +912.310i q^{68} +(-8298.94 - 107.623i) q^{69} +2074.55 q^{70} +5633.40 q^{71} -3737.01 q^{72} +7633.63 q^{73} +2295.22i q^{74} -1961.16 q^{75} +2991.43i q^{76} -1948.41 q^{77} +4510.30 q^{78} +8977.10i q^{79} +715.542i q^{80} +7337.43 q^{81} +1124.53 q^{82} -8227.93i q^{83} +8234.13i q^{84} -1274.99 q^{85} +5662.44i q^{86} -8044.48 q^{87} -672.034i q^{88} -11502.8i q^{89} -5222.64i q^{90} -6667.76i q^{91} +(-4231.64 - 54.8770i) q^{92} +13863.6 q^{93} -8236.36 q^{94} -4180.65 q^{95} -2840.07 q^{96} -7778.70i q^{97} +5381.81 q^{98} +4905.08i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9}+O(q^{10}) \) 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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