LMFDB - Embedded newform 230.5.c.a.229.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,5,Mod(229,230)]

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([1, 1]))

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

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

chi := DirichletCharacter("230.229");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	230.c (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:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.4
Character	$\chi$	$=$	230.229
Dual form			230.5.c.a.229.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.82843i q^{2} +15.3728i q^{3} -8.00000 q^{4} +(-24.9424 - 1.69556i) q^{5} -43.4808 q^{6} -85.1277 q^{7} -22.6274i q^{8} -155.323 q^{9} +O(q^{10})$	\(q+2.82843i q^{2} +15.3728i q^{3} -8.00000 q^{4} +(-24.9424 - 1.69556i) q^{5} -43.4808 q^{6} -85.1277 q^{7} -22.6274i q^{8} -155.323 q^{9} +(4.79578 - 70.5479i) q^{10} +59.9093i q^{11} -122.982i q^{12} +296.626i q^{13} -240.778i q^{14} +(26.0656 - 383.435i) q^{15} +64.0000 q^{16} +408.596 q^{17} -439.319i q^{18} +18.6778i q^{19} +(199.539 + 13.5645i) q^{20} -1308.65i q^{21} -169.449 q^{22} +(-146.668 + 508.261i) q^{23} +347.847 q^{24} +(619.250 + 84.5830i) q^{25} -838.986 q^{26} -1142.55i q^{27} +681.022 q^{28} -895.716 q^{29} +(1084.52 + 73.7246i) q^{30} +578.910 q^{31} +181.019i q^{32} -920.974 q^{33} +1155.68i q^{34} +(2123.29 + 144.340i) q^{35} +1242.58 q^{36} +622.745 q^{37} -52.8288 q^{38} -4559.98 q^{39} +(-38.3663 + 564.383i) q^{40} -1791.23 q^{41} +3701.43 q^{42} -572.052 q^{43} -479.275i q^{44} +(3874.13 + 263.360i) q^{45} +(-1437.58 - 414.840i) q^{46} -2218.30i q^{47} +983.859i q^{48} +4845.73 q^{49} +(-239.237 + 1751.50i) q^{50} +6281.26i q^{51} -2373.01i q^{52} -3715.77 q^{53} +3231.62 q^{54} +(101.580 - 1494.28i) q^{55} +1926.22i q^{56} -287.130 q^{57} -2533.47i q^{58} +2380.82 q^{59} +(-208.525 + 3067.48i) q^{60} +2027.08i q^{61} +1637.41i q^{62} +13222.3 q^{63} -512.000 q^{64} +(502.949 - 7398.58i) q^{65} -2604.91i q^{66} -946.554 q^{67} -3268.77 q^{68} +(-7813.40 - 2254.70i) q^{69} +(-408.254 + 6005.58i) q^{70} +3822.76 q^{71} +3514.56i q^{72} +86.9828i q^{73} +1761.39i q^{74} +(-1300.28 + 9519.61i) q^{75} -149.422i q^{76} -5099.95i q^{77} -12897.6i q^{78} -7860.70i q^{79} +(-1596.32 - 108.516i) q^{80} +4983.05 q^{81} -5066.38i q^{82} +8551.78 q^{83} +10469.2i q^{84} +(-10191.4 - 692.801i) q^{85} -1618.01i q^{86} -13769.7i q^{87} +1355.59 q^{88} +1082.78i q^{89} +(-744.895 + 10957.7i) q^{90} -25251.1i q^{91} +(1173.35 - 4066.09i) q^{92} +8899.47i q^{93} +6274.30 q^{94} +(31.6694 - 465.870i) q^{95} -2782.77 q^{96} -15153.5 q^{97} +13705.8i q^{98} -9305.29i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9}+O(q^{10}) $ 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9	$ 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9} + 3072 q^{16} + 512 q^{24} + 1488 q^{25} - 384 q^{26} - 2940 q^{29} + 4732 q^{31} + 2556 q^{35} + 12864 q^{36} + 2736 q^{39} + 828 q^{41} - 64 q^{46} + 32572 q^{49} - 3264 q^{50} + 10112 q^{54} + 12824 q^{55} + 7092 q^{59} - 24576 q^{64} + 14000 q^{69} - 6592 q^{70} - 12708 q^{71} + 24728 q^{75} - 13040 q^{81} - 15700 q^{85} - 9728 q^{94} - 46608 q^{95} - 4096 q^{96}+O(q^{100}) $ 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9 + 3072 * q^16 + 512 * q^24 + 1488 * q^25 - 384 * q^26 - 2940 * q^29 + 4732 * q^31 + 2556 * q^35 + 12864 * q^36 + 2736 * q^39 + 828 * q^41 - 64 * q^46 + 32572 * q^49 - 3264 * q^50 + 10112 * q^54 + 12824 * q^55 + 7092 * q^59 - 24576 * q^64 + 14000 * q^69 - 6592 * q^70 - 12708 * q^71 + 24728 * q^75 - 13040 * q^81 - 15700 * q^85 - 9728 * q^94 - 46608 * q^95 - 4096 * q^96

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 $

$2$			2.82843i			0.707107i
$2$			2.82843i			0.707107i
$3$			15.3728i			1.70809i	0.520200	+	0.854044i	$0.325857\pi$
$3$			15.3728i			1.70809i	−0.520200	+	0.854044i	$0.674143\pi$
$4$	−8.00000			−0.500000
$5$	−24.9424	−	1.69556i	−0.997697	−	0.0678226i
$5$	−24.9424	−	1.69556i	−0.997697	−	0.0678226i
$6$	−43.4808			−1.20780
$7$	−85.1277			−1.73730			−0.868650	−	0.495426i	$-0.835012\pi$
$7$	−85.1277			−1.73730			−0.868650	+	0.495426i	$0.835012\pi$
$8$		−	22.6274i		−	0.353553i
$9$	−155.323			−1.91757
$10$	4.79578	−	70.5479i	0.0479578	−	0.705479i
$11$			59.9093i			0.495119i	0.968873	+	0.247559i	$0.0796285\pi$
$11$			59.9093i			0.495119i	−0.968873	+	0.247559i	$0.920371\pi$
$12$		−	122.982i		−	0.854044i
$13$			296.626i			1.75519i	0.479407	+	0.877593i	$0.340852\pi$
$13$			296.626i			1.75519i	−0.479407	+	0.877593i	$0.659148\pi$
$14$		−	240.778i		−	1.22846i
$15$	26.0656	−	383.435i	0.115847	−	1.70416i
$16$	64.0000			0.250000
$17$	408.596			1.41383			0.706913	−	0.707300i	$-0.250087\pi$
$17$	408.596			1.41383			0.706913	+	0.707300i	$0.250087\pi$
$18$		−	439.319i		−	1.35592i
$19$			18.6778i			0.0517390i	0.999665	+	0.0258695i	$0.00823544\pi$
$19$			18.6778i			0.0517390i	−0.999665	+	0.0258695i	$0.991765\pi$
$20$	199.539	+	13.5645i	0.498849	+	0.0339113i
$21$		−	1308.65i		−	2.96746i
$22$	−169.449			−0.350102
$23$	−146.668	+	508.261i	−0.277256	+	0.960796i
$23$	−146.668	+	508.261i	−0.277256	+	0.960796i
$24$	347.847			0.603901
$25$	619.250	+	84.5830i	0.990800	+	0.135333i
$26$	−838.986			−1.24110
$27$		−	1142.55i		−	1.56729i
$28$	681.022			0.868650
$29$	−895.716			−1.06506			−0.532530	−	0.846411i	$-0.678759\pi$
$29$	−895.716			−1.06506			−0.532530	+	0.846411i	$0.678759\pi$
$30$	1084.52	+	73.7246i	1.20502	+	0.0819162i
$31$	578.910			0.602404			0.301202	−	0.953560i	$-0.402612\pi$
$31$	578.910			0.602404			0.301202	+	0.953560i	$0.402612\pi$
$32$			181.019i			0.176777i
$33$	−920.974			−0.845706
$34$			1155.68i			0.999726i
$35$	2123.29	+	144.340i	1.73330	+	0.117828i
$36$	1242.58			0.958783
$37$	622.745			0.454890			0.227445	−	0.973791i	$-0.426963\pi$
$37$	622.745			0.454890			0.227445	+	0.973791i	$0.426963\pi$
$38$	−52.8288			−0.0365850
$39$	−4559.98			−2.99801
$40$	−38.3663	+	564.383i	−0.0239789	+	0.352739i
$41$	−1791.23			−1.06558			−0.532788	−	0.846249i	$-0.678856\pi$
$41$	−1791.23			−1.06558			−0.532788	+	0.846249i	$0.678856\pi$
$42$	3701.43			2.09831
$43$	−572.052			−0.309384			−0.154692	−	0.987963i	$-0.549439\pi$
$43$	−572.052			−0.309384			−0.154692	+	0.987963i	$0.549439\pi$
$44$		−	479.275i		−	0.247559i
$45$	3874.13	+	263.360i	1.91315	+	0.130054i
$46$	−1437.58	−	414.840i	−0.679386	−	0.196049i
$47$		−	2218.30i		−	1.00421i	−0.864807	−	0.502105i	$-0.832559\pi$
$47$		−	2218.30i		−	1.00421i	0.864807	−	0.502105i	$-0.167441\pi$
$48$			983.859i			0.427022i
$49$	4845.73			2.01821
$50$	−239.237	+	1751.50i	−0.0956948	+	0.700602i
$51$			6281.26i			2.41494i
$52$		−	2373.01i		−	0.877593i
$53$	−3715.77			−1.32281			−0.661404	−	0.750030i	$-0.730039\pi$
$53$	−3715.77			−1.32281			−0.661404	+	0.750030i	$0.730039\pi$
$54$	3231.62			1.10824
$55$	101.580	−	1494.28i	0.0335802	−	0.493979i
$56$			1926.22i			0.614229i
$57$	−287.130			−0.0883748
$58$		−	2533.47i		−	0.753111i
$59$	2380.82			0.683946			0.341973	−	0.939710i	$-0.388905\pi$
$59$	2380.82			0.683946			0.341973	+	0.939710i	$0.388905\pi$
$60$	−208.525	+	3067.48i	−0.0579235	+	0.852078i
$61$			2027.08i			0.544768i	0.962189	+	0.272384i	$0.0878120\pi$
$61$			2027.08i			0.544768i	−0.962189	+	0.272384i	$0.912188\pi$
$62$			1637.41i			0.425964i
$63$	13222.3			3.33139
$64$	−512.000			−0.125000
$65$	502.949	−	7398.58i	0.119041	−	1.75114i
$66$		−	2604.91i		−	0.598005i
$67$	−946.554			−0.210861			−0.105430	−	0.994427i	$-0.533622\pi$
$67$	−946.554			−0.210861			−0.105430	+	0.994427i	$0.533622\pi$
$68$	−3268.77			−0.706913
$69$	−7813.40	−	2254.70i	−1.64113	−	0.473577i
$70$	−408.254	+	6005.58i	−0.0833171	+	1.22563i
$71$	3822.76			0.758334			0.379167	−	0.925328i	$-0.376211\pi$
$71$	3822.76			0.758334			0.379167	+	0.925328i	$0.376211\pi$
$72$			3514.56i			0.677962i
$73$			86.9828i			0.0163225i	0.999967	+	0.00816127i	$0.00259784\pi$
$73$			86.9828i			0.0163225i	−0.999967	+	0.00816127i	$0.997402\pi$
$74$			1761.39i			0.321656i
$75$	−1300.28	+	9519.61i	−0.231161	+	1.69237i
$76$		−	149.422i		−	0.0258695i
$77$		−	5099.95i		−	0.860170i
$78$		−	12897.6i		−	2.11992i
$79$		−	7860.70i		−	1.25953i	−0.776787	−	0.629763i	$-0.783152\pi$
$79$		−	7860.70i		−	1.25953i	0.776787	−	0.629763i	$-0.216848\pi$
$80$	−1596.32	−	108.516i	−0.249424	−	0.0169556i
$81$	4983.05			0.759495
$82$		−	5066.38i		−	0.753476i
$83$	8551.78			1.24137			0.620684	−	0.784061i	$-0.286855\pi$
$83$	8551.78			1.24137			0.620684	+	0.784061i	$0.286855\pi$
$84$			10469.2i			1.48373i
$85$	−10191.4	−	692.801i	−1.41057	−	0.0958894i
$86$		−	1618.01i		−	0.218768i
$87$		−	13769.7i		−	1.81922i
$88$	1355.59			0.175051
$89$			1082.78i			0.136697i	0.997661	+	0.0683486i	$0.0217730\pi$
$89$			1082.78i			0.136697i	−0.997661	+	0.0683486i	$0.978227\pi$
$90$	−744.895	+	10957.7i	−0.0919623	+	1.35280i
$91$		−	25251.1i		−	3.04929i
$92$	1173.35	−	4066.09i	0.138628	−	0.480398i
$93$			8899.47i			1.02896i
$94$	6274.30			0.710083
$95$	31.6694	−	465.870i	0.00350908	−	0.0516199i
$96$	−2782.77			−0.301950
$97$	−15153.5			−1.61054			−0.805269	−	0.592910i	$-0.797979\pi$
$97$	−15153.5			−1.61054			−0.805269	+	0.592910i	$0.797979\pi$
$98$			13705.8i			1.42709i
$99$		−	9305.29i		−	0.949423i
$100$	−4954.00	−	676.664i	−0.495400	−	0.0676664i
$101$	2533.48			0.248356			0.124178	−	0.992260i	$-0.460371\pi$
$101$	2533.48			0.248356			0.124178	+	0.992260i	$0.460371\pi$
$102$	−17766.1			−1.70762
$103$	4966.93			0.468181			0.234090	−	0.972215i	$-0.424789\pi$
$103$	4966.93			0.468181			0.234090	+	0.972215i	$0.424789\pi$
$104$	6711.89			0.620552
$105$	−2218.90	+	32641.0i	−0.201261	+	2.96063i
$106$		−	10509.8i		−	0.935366i
$107$	13687.9			1.19555			0.597775	−	0.801664i	$-0.296052\pi$
$107$	13687.9			1.19555			0.597775	+	0.801664i	$0.296052\pi$
$108$			9140.41i			0.783643i
$109$			18553.8i			1.56163i	0.624760	+	0.780817i	$0.285197\pi$
$109$			18553.8i			1.56163i	−0.624760	+	0.780817i	$0.714803\pi$
$110$	4226.48	+	287.312i	0.349296	+	0.0237448i
$111$			9573.33i			0.776993i
$112$	−5448.17			−0.434325
$113$	−16118.1			−1.26228			−0.631141	−	0.775668i	$-0.717413\pi$
$113$	−16118.1			−1.26228			−0.631141	+	0.775668i	$0.717413\pi$
$114$		−	812.126i		−	0.0624905i
$115$	4520.05	−	12428.6i	0.341781	−	0.939780i
$116$	7165.73			0.532530
$117$		−	46072.9i		−	3.36569i
$118$			6733.97i			0.483623i
$119$	−34782.8			−2.45624
$120$	−8676.14	−	589.797i	−0.602510	−	0.0409581i
$121$	11051.9			0.754858
$122$	−5733.45			−0.385209
$123$		−	27536.3i		−	1.82010i
$124$	−4631.28			−0.301202
$125$	−15302.2	−	3159.69i	−0.979340	−	0.202220i
$126$			37398.3i			2.35565i
$127$			29031.3i			1.79995i	0.435945	+	0.899973i	$0.356414\pi$
$127$			29031.3i			1.79995i	−0.435945	+	0.899973i	$0.643586\pi$
$128$		−	1448.15i		−	0.0883883i
$129$		−	8794.03i		−	0.528456i
$130$	20926.4	+	1422.56i	1.23825	+	0.0841749i
$131$	23819.8			1.38802			0.694009	−	0.719966i	$-0.255843\pi$
$131$	23819.8			1.38802			0.694009	+	0.719966i	$0.255843\pi$
$132$	7367.79			0.422853
$133$		−	1590.00i		−	0.0898863i
$134$		−	2677.26i		−	0.149101i
$135$	−1937.27	+	28498.0i	−0.106297	+	1.56368i
$136$		−	9245.47i		−	0.499863i
$137$	−8675.21			−0.462209			−0.231105	−	0.972929i	$-0.574234\pi$
$137$	−8675.21			−0.462209			−0.231105	+	0.972929i	$0.574234\pi$
$138$	6377.26	−	22099.6i	0.334870	−	1.16045i
$139$	−16925.2			−0.876001			−0.438000	−	0.898975i	$-0.644313\pi$
$139$	−16925.2			−0.876001			−0.438000	+	0.898975i	$0.644313\pi$
$140$	−16986.3	−	1154.72i	−0.866650	−	0.0589141i
$141$	34101.5			1.71528
$142$			10812.4i			0.536223i
$143$	−17770.7			−0.869025
$144$	−9940.67			−0.479392
$145$	22341.3	+	1518.74i	1.06261	+	0.0722352i
$146$	−246.024			−0.0115418
$147$			74492.4i			3.44729i
$148$	−4981.96			−0.227445
$149$			35583.9i			1.60281i	0.598125	+	0.801403i	$0.295913\pi$
$149$			35583.9i			1.60281i	−0.598125	+	0.801403i	$0.704087\pi$
$150$	−26925.5	−	3677.74i	−1.19669	−	0.163455i
$151$	−23587.6			−1.03450			−0.517249	−	0.855835i	$-0.673044\pi$
$151$	−23587.6			−1.03450			−0.517249	+	0.855835i	$0.673044\pi$
$152$	422.630			0.0182925
$153$	−63464.3			−2.71111
$154$	14424.8			0.608232
$155$	−14439.4	−	981.580i	−0.601017	−	0.0408566i
$156$	36479.8			1.49901
$157$	−23565.9			−0.956057			−0.478029	−	0.878344i	$-0.658648\pi$
$157$	−23565.9			−0.956057			−0.478029	+	0.878344i	$0.658648\pi$
$158$	22233.4			0.890619
$159$		−	57121.7i		−	2.25947i
$160$	306.930	−	4515.06i	0.0119895	−	0.176370i
$161$	12485.5	−	43267.1i	0.481676	−	1.66919i
$162$			14094.2i			0.537044i
$163$		−	24466.5i		−	0.920868i	−0.887694	−	0.460434i	$-0.847694\pi$
$163$		−	24466.5i		−	0.920868i	0.887694	−	0.460434i	$-0.152306\pi$
$164$	14329.9			0.532788
$165$	22971.3	+	1561.57i	0.843759	+	0.0573580i
$166$			24188.1i			0.877779i
$167$		−	18524.3i		−	0.664215i	−0.943242	−	0.332107i	$-0.892240\pi$
$167$		−	18524.3i		−	0.664215i	0.943242	−	0.332107i	$-0.107760\pi$
$168$	−29611.4			−1.04916
$169$	−59426.2			−2.08068
$170$	1959.54	−	28825.6i	0.0678040	−	0.997424i
$171$		−	2901.09i		−	0.0992130i
$172$	4576.41			0.154692
$173$		−	968.894i		−	0.0323731i	−0.999869	−	0.0161865i	$-0.994847\pi$
$173$		−	968.894i		−	0.0323731i	0.999869	−	0.0161865i	$-0.00515256\pi$
$174$	38946.5			1.28638
$175$	−52715.4	−	7200.36i	−1.72132	−	0.235114i
$176$			3834.20i			0.123780i
$177$			36599.8i			1.16824i
$178$	−3062.56			−0.0966596
$179$	27655.8			0.863137			0.431569	−	0.902080i	$-0.357960\pi$
$179$	27655.8			0.863137			0.431569	+	0.902080i	$0.357960\pi$
$180$	−30993.0	−	2106.88i	−0.956576	−	0.0650272i
$181$		−	33773.2i		−	1.03090i	−0.856921	−	0.515448i	$-0.827626\pi$
$181$		−	33773.2i		−	1.03090i	0.856921	−	0.515448i	$-0.172374\pi$
$182$	71421.0			2.15617
$183$	−31161.9			−0.930511
$184$	11500.6	+	3318.72i	0.339693	+	0.0980246i
$185$	−15532.8	−	1055.90i	−0.453843	−	0.0308519i
$186$	−25171.5			−0.727584
$187$			24478.7i			0.700012i
$188$			17746.4i			0.502105i
$189$			97262.8i			2.72285i
$190$	1317.68	+	89.5746i	0.0365008	+	0.00248129i
$191$		−	28899.8i		−	0.792188i	−0.918210	−	0.396094i	$-0.870365\pi$
$191$		−	28899.8i		−	0.792188i	0.918210	−	0.396094i	$-0.129635\pi$
$192$		−	7870.87i		−	0.213511i
$193$		−	58187.3i		−	1.56212i	−0.624458	−	0.781059i	$-0.714680\pi$
$193$		−	58187.3i		−	1.56212i	0.624458	−	0.781059i	$-0.285320\pi$
$194$		−	42860.7i		−	1.13882i
$195$	113737.	+	7731.74i	2.99111	+	0.203333i
$196$	−38765.8			−1.00911
$197$		−	2583.13i		−	0.0665601i	−0.999446	−	0.0332801i	$-0.989405\pi$
$197$		−	2583.13i		−	0.0665601i	0.999446	−	0.0332801i	$-0.0105953\pi$
$198$	26319.3			0.671343
$199$			21019.3i			0.530776i	0.964142	+	0.265388i	$0.0855000\pi$
$199$			21019.3i			0.530776i	−0.964142	+	0.265388i	$0.914500\pi$
$200$	1913.90	−	14012.0i	0.0478474	−	0.350301i
$201$		−	14551.2i		−	0.360169i
$202$			7165.75i			0.175614i
$203$	76250.3			1.85033
$204$		−	50250.1i		−	1.20747i
$205$	44677.7	+	3037.15i	1.06312	+	0.0722702i
$206$			14048.6i			0.331054i
$207$	22780.9	−	78944.6i	0.531656	−	1.84239i
$208$			18984.1i			0.438796i
$209$	−1118.97			−0.0256170
$210$	−92322.6	−	6276.01i	−2.09348	−	0.142313i
$211$	19219.9			0.431704			0.215852	−	0.976426i	$-0.430747\pi$
$211$	19219.9			0.431704			0.215852	+	0.976426i	$0.430747\pi$
$212$	29726.1			0.661404
$213$			58766.6i			1.29530i
$214$			38715.1i			0.845381i
$215$	14268.4	+	969.951i	0.308672	+	0.0209832i
$216$	−25853.0			−0.554119
$217$	−49281.3			−1.04656
$218$	−52478.0			−1.10424
$219$	−1337.17			−0.0278803
$220$	−812.642	+	11954.3i	−0.0167901	+	0.246989i
$221$			121200.i			2.48153i
$222$	−27077.5			−0.549417
$223$		−	4046.84i		−	0.0813779i	−0.999172	−	0.0406890i	$-0.987045\pi$
$223$		−	4046.84i		−	0.0813779i	0.999172	−	0.0406890i	$-0.0129553\pi$
$224$		−	15409.8i		−	0.307114i
$225$	−96183.7	−	13137.7i	−1.89993	−	0.259510i
$226$		−	45588.8i		−	0.892568i
$227$	35503.5			0.689001			0.344500	−	0.938786i	$-0.388048\pi$
$227$	35503.5			0.689001			0.344500	+	0.938786i	$0.388048\pi$
$228$	2297.04			0.0441874
$229$		−	94797.2i		−	1.80769i	−0.427857	−	0.903846i	$-0.640731\pi$
$229$		−	94797.2i		−	1.80769i	0.427857	−	0.903846i	$-0.359269\pi$
$230$	35153.4	+	12784.6i	0.664525	+	0.241676i
$231$	78400.4			1.46925
$232$			20267.7i			0.376556i
$233$			57867.9i			1.06592i	0.846139	+	0.532962i	$0.178921\pi$
$233$			57867.9i			1.06592i	−0.846139	+	0.532962i	$0.821079\pi$
$234$	130314.			2.37990
$235$	−3761.27	+	55329.8i	−0.0681081	+	1.00190i
$236$	−19046.5			−0.341973
$237$	120841.			2.15138
$238$		−	98380.7i		−	1.73683i
$239$	13497.0			0.236287			0.118144	−	0.992997i	$-0.462306\pi$
$239$	13497.0			0.236287			0.118144	+	0.992997i	$0.462306\pi$
$240$	1668.20	−	24539.8i	0.0289618	−	0.426039i
$241$		−	21034.1i		−	0.362152i	−0.983469	−	0.181076i	$-0.942042\pi$
$241$		−	21034.1i		−	0.362152i	0.983469	−	0.181076i	$-0.0579579\pi$
$242$			31259.4i			0.533765i
$243$		−	15943.2i		−	0.270000i
$244$		−	16216.6i		−	0.272384i
$245$	−120864.	−	8216.25i	−2.01357	−	0.136880i
$246$	77884.4			1.28700
$247$	−5540.33			−0.0908116
$248$		−	13099.2i		−	0.212982i
$249$			131465.i			2.12037i
$250$	8936.94	−	43281.1i	0.142991	−	0.692498i
$251$			100255.i			1.59132i	0.605745	+	0.795659i	$0.292875\pi$
$251$			100255.i			1.59132i	−0.605745	+	0.795659i	$0.707125\pi$
$252$	−105778.			−1.66569
$253$	−30449.6	−	8786.80i	−0.475708	−	0.137274i
$254$	−82113.0			−1.27275
$255$	10650.3	−	156670.i	0.163788	−	2.40938i
$256$	4096.00			0.0625000
$257$			61042.8i			0.924204i	0.886827	+	0.462102i	$0.152905\pi$
$257$			61042.8i			0.924204i	−0.886827	+	0.462102i	$0.847095\pi$
$258$	24873.3			0.373675
$259$	−53012.9			−0.790282
$260$	−4023.59	+	59188.7i	−0.0595206	+	0.875572i
$261$	139125.			2.04232
$262$			67372.5i			0.981477i
$263$	−1354.50			−0.0195824			−0.00979121	−	0.999952i	$-0.503117\pi$
$263$	−1354.50			−0.0195824			−0.00979121	+	0.999952i	$0.503117\pi$
$264$			20839.3i			0.299002i
$265$	92680.3	+	6300.32i	1.31976	+	0.0897162i
$266$	4497.19			0.0635592
$267$	−16645.3			−0.233491
$268$	7572.43			0.105430
$269$	−9416.22			−0.130128			−0.0650642	−	0.997881i	$-0.520725\pi$
$269$	−9416.22			−0.130128			−0.0650642	+	0.997881i	$0.520725\pi$
$270$	−80604.5	−	5479.42i	−1.10569	−	0.0751636i
$271$	13816.5			0.188131			0.0940653	−	0.995566i	$-0.470014\pi$
$271$	13816.5			0.188131			0.0940653	+	0.995566i	$0.470014\pi$
$272$	26150.1			0.353457
$273$	388181.			5.20845
$274$		−	24537.2i		−	0.326831i
$275$	−5067.31	+	37098.9i	−0.0670058	+	0.490564i
$276$	62507.2	+	18037.6i	0.820563	+	0.236789i
$277$			31564.8i			0.411380i	0.978617	+	0.205690i	$0.0659438\pi$
$277$			31564.8i			0.411380i	−0.978617	+	0.205690i	$0.934056\pi$
$278$		−	47871.7i		−	0.619426i
$279$	−89918.0			−1.15515
$280$	3266.03	−	48044.6i	0.0416586	−	0.612814i
$281$		−	111285.i		−	1.40936i	−0.709524	−	0.704681i	$-0.751090\pi$
$281$		−	111285.i		−	1.40936i	0.709524	−	0.704681i	$-0.248910\pi$
$282$			96453.5i			1.21289i
$283$	−71794.8			−0.896438			−0.448219	−	0.893924i	$-0.647942\pi$
$283$	−71794.8			−0.896438			−0.448219	+	0.893924i	$0.647942\pi$
$284$	−30582.1			−0.379167
$285$	7161.72	+	486.847i	0.0881714	+	0.00599381i
$286$		−	50263.1i		−	0.614494i
$287$	152484.			1.85123
$288$		−	28116.4i		−	0.338981i
$289$	83429.6			0.998905
$290$	−4295.66	+	63190.8i	−0.0510780	+	0.751377i
$291$		−	232952.i		−	2.75094i
$292$		−	695.862i		−	0.00816127i
$293$	123823.			1.44234			0.721168	−	0.692760i	$-0.243606\pi$
$293$	123823.			1.44234			0.721168	+	0.692760i	$0.243606\pi$
$294$	−210696.			−2.43760
$295$	−59383.4	−	4036.83i	−0.682371	−	0.0463870i
$296$		−	14091.1i		−	0.160828i
$297$	68449.5			0.775992
$298$	−100646.			−1.13336
$299$	−150764.	−	43505.7i	−1.68638	−	0.486635i
$300$	10402.2	−	76156.9i	0.115580	−	0.846187i
$301$	48697.5			0.537494
$302$		−	66715.8i		−	0.731501i
$303$			38946.6i			0.424213i
$304$			1195.38i			0.0129348i
$305$	3437.05	−	50560.3i	0.0369476	−	0.543513i
$306$		−	179504.i		−	1.91704i
$307$		−	35002.3i		−	0.371381i	−0.982608	−	0.185690i	$-0.940548\pi$
$307$		−	35002.3i		−	0.371381i	0.982608	−	0.185690i	$-0.0594522\pi$
$308$			40799.6i			0.430085i
$309$			76355.6i			0.799694i
$310$	2776.33	−	40840.9i	0.0288900	−	0.424983i
$311$	−89863.6			−0.929102			−0.464551	−	0.885546i	$-0.653784\pi$
$311$	−89863.6			−0.929102			−0.464551	+	0.885546i	$0.653784\pi$
$312$			103181.i			1.05996i
$313$	−41947.4			−0.428171			−0.214085	−	0.976815i	$-0.568677\pi$
$313$	−41947.4			−0.428171			−0.214085	+	0.976815i	$0.568677\pi$
$314$		−	66654.3i		−	0.676034i
$315$	−329796.	−	22419.2i	−3.32372	−	0.225944i
$316$			62885.6i			0.629763i
$317$		−	141111.i		−	1.40424i	−0.712056	−	0.702122i	$-0.752236\pi$
$317$		−	141111.i		−	1.40424i	0.712056	−	0.702122i	$-0.247764\pi$
$318$	161565.			1.59769
$319$		−	53661.8i		−	0.527331i
$320$	12770.5	+	868.129i	0.124712	+	0.00847782i
$321$			210421.i			2.04211i
$322$	122378.	+	35314.4i	1.18030	+	0.340597i
$323$			7631.67i			0.0731500i
$324$	−39864.4			−0.379748
$325$	−25089.6	+	183686.i	−0.237534	+	1.73904i
$326$	69201.8			0.651152
$327$	−285223.			−2.66741
$328$			40531.0i			0.376738i
$329$			188839.i			1.74461i
$330$	−4416.79	+	64972.8i	−0.0405582	+	0.596628i
$331$	138905.			1.26784			0.633918	−	0.773400i	$-0.281446\pi$
$331$	138905.			1.26784			0.633918	+	0.773400i	$0.281446\pi$
$332$	−68414.2			−0.620684
$333$	−96726.6			−0.872283
$334$	52394.6			0.469671
$335$	23609.4	+	1604.94i	0.210375	+	0.0143011i
$336$		−	83753.7i		−	0.741866i
$337$	−203580.			−1.79257			−0.896284	−	0.443480i	$-0.853744\pi$
$337$	−203580.			−1.79257			−0.896284	+	0.443480i	$0.853744\pi$
$338$		−	168083.i		−	1.47126i
$339$		−	247780.i		−	2.15609i
$340$	81531.0	+	5542.41i	0.705286	+	0.0479447i
$341$			34682.1i			0.298261i
$342$	8205.52			0.0701542
$343$	−208114.			−1.76894
$344$			12944.0i			0.109384i
$345$	191062.	+	69485.8i	1.60523	+	0.583792i
$346$	2740.44			0.0228912
$347$			166855.i			1.38574i	0.721063	+	0.692869i	$0.243654\pi$
$347$			166855.i			1.38574i	−0.721063	+	0.692869i	$0.756346\pi$
$348$			110157.i			0.909609i
$349$	−172799.			−1.41870			−0.709351	−	0.704855i	$-0.751012\pi$
$349$	−172799.			−1.41870			−0.709351	+	0.704855i	$0.751012\pi$
$350$	20365.7	−	149102.i	0.166251	−	1.21716i
$351$	338911.			2.75088
$352$	−10844.8			−0.0875254
$353$			82460.3i			0.661752i	0.943674	+	0.330876i	$0.107344\pi$
$353$			82460.3i			0.661752i	−0.943674	+	0.330876i	$0.892656\pi$
$354$	−103520.			−0.826071
$355$	−95349.0	−	6481.74i	−0.756588	−	0.0514322i
$356$		−	8662.23i		−	0.0683486i
$357$		−	534710.i		−	4.19548i
$358$			78222.4i			0.610330i
$359$			61113.3i			0.474184i	0.971487	+	0.237092i	$0.0761942\pi$
$359$			61113.3i			0.474184i	−0.971487	+	0.237092i	$0.923806\pi$
$360$	5959.16	−	87661.6i	0.0459812	−	0.676401i
$361$	129972.			0.997323
$362$	95524.9			0.728953
$363$			169898.i			1.28936i
$364$			202009.i			1.52464i
$365$	147.485	−	2169.56i	0.00110704	−	0.0162849i
$366$		−	88139.1i		−	0.657971i
$367$	−213157.			−1.58259			−0.791295	−	0.611435i	$-0.790593\pi$
$367$	−213157.			−1.58259			−0.791295	+	0.611435i	$0.790593\pi$
$368$	−9386.76	+	32528.7i	−0.0693139	+	0.240199i
$369$	278220.			2.04331
$370$	2986.55	−	43933.3i	0.0218156	−	0.320916i
$371$	316315.			2.29811
$372$		−	71195.8i		−	0.514480i
$373$	−84380.0			−0.606488			−0.303244	−	0.952913i	$-0.598070\pi$
$373$	−84380.0			−0.606488			−0.303244	+	0.952913i	$0.598070\pi$
$374$	−69236.2			−0.494983
$375$	48573.2	−	235237.i	0.345409	−	1.67280i
$376$	−50194.4			−0.355042
$377$		−	265693.i		−	1.86938i
$378$	−275101.			−1.92534
$379$		−	36046.7i		−	0.250950i	−0.992097	−	0.125475i	$-0.959955\pi$
$379$		−	36046.7i		−	0.250950i	0.992097	−	0.125475i	$-0.0400455\pi$
$380$	−253.355	+	3726.96i	−0.00175454	+	0.0258099i
$381$	−446293.			−3.07447
$382$	81741.0			0.560161
$383$	−174233.			−1.18777			−0.593887	−	0.804548i	$-0.702407\pi$
$383$	−174233.			−1.18777			−0.593887	+	0.804548i	$0.702407\pi$
$384$	22262.2			0.150975
$385$	−8647.29	+	127205.i	−0.0583390	+	0.858189i
$386$	164579.			1.10458
$387$	88852.7			0.593265
$388$	121228.			0.805269
$389$			123456.i			0.815858i	0.913014	+	0.407929i	$0.133749\pi$
$389$			123456.i			0.815858i	−0.913014	+	0.407929i	$0.866251\pi$
$390$	−21868.7	+	321697.i	−0.143778	+	2.11503i
$391$	−59928.0	+	207673.i	−0.391991	+	1.35840i
$392$		−	109646.i		−	0.713546i
$393$			366177.i			2.37086i
$394$	7306.20			0.0470651
$395$	−13328.3	+	196065.i	−0.0854243	+	1.25663i
$396$			74442.3i			0.474711i
$397$			254777.i			1.61651i	0.588832	+	0.808256i	$0.299588\pi$
$397$			254777.i			1.61651i	−0.588832	+	0.808256i	$0.700412\pi$
$398$	−59451.4			−0.375315
$399$	24442.7			0.153534
$400$	39632.0	+	5413.31i	0.247700	+	0.0338332i
$401$			173663.i			1.07999i	0.841669	+	0.539994i	$0.181574\pi$
$401$			173663.i			1.07999i	−0.841669	+	0.539994i	$0.818426\pi$
$402$	41157.0			0.254678
$403$			171720.i			1.05733i
$404$	−20267.8			−0.124178
$405$	−124289.	−	8449.08i	−0.757746	−	0.0515109i
$406$			215668.i			1.30838i
$407$			37308.3i			0.225225i
$408$	142129.			0.853811
$409$	159703.			0.954697			0.477348	−	0.878714i	$-0.341598\pi$
$409$	159703.			0.954697			0.477348	+	0.878714i	$0.341598\pi$
$410$	−8590.37	+	126368.i	−0.0511027	+	0.751741i
$411$		−	133362.i		−	0.789494i
$412$	−39735.4			−0.234090
$413$	−202673.			−1.18822
$414$	223289.	+	64434.2i	1.30277	+	0.375938i
$415$	−213302.	−	14500.1i	−1.23851	−	0.0841927i
$416$	−53695.1			−0.310276
$417$		−	260188.i		−	1.49629i
$418$		−	3164.94i		−	0.0181139i
$419$			247890.i			1.41199i	0.708217	+	0.705994i	$0.249500\pi$
$419$			247890.i			1.41199i	−0.708217	+	0.705994i	$0.750500\pi$
$420$	17751.2	−	261128.i	0.100631	−	1.48032i
$421$			220824.i			1.24590i	0.782263	+	0.622948i	$0.214065\pi$
$421$			220824.i			1.24590i	−0.782263	+	0.622948i	$0.785935\pi$
$422$			54362.1i			0.305261i
$423$			344553.i			1.92564i
$424$			84078.2i			0.467683i
$425$	253023.	+	34560.3i	1.40082	+	0.191337i
$426$	−166217.			−0.915917
$427$		−	172561.i		−	0.946425i
$428$	−109503.			−0.597775
$429$		−	273185.i		−	1.48437i
$430$	−2743.43	+	40357.0i	−0.0148374	+	0.218264i
$431$		−	198258.i		−	1.06728i	−0.845713	−	0.533639i	$-0.820824\pi$
$431$		−	198258.i		−	1.06728i	0.845713	−	0.533639i	$-0.179176\pi$
$432$		−	73123.2i		−	0.391821i
$433$	149984.			0.799961			0.399980	−	0.916524i	$-0.369017\pi$
$433$	149984.			0.799961			0.399980	+	0.916524i	$0.369017\pi$
$434$		−	139389.i		−	0.740028i
$435$	−23347.3	+	343449.i	−0.123384	+	1.81503i
$436$		−	148430.i		−	0.780817i
$437$	−9493.20	−	2739.44i	−0.0497107	−	0.0143449i
$438$		−	3782.08i		−	0.0197144i
$439$	−25852.6			−0.134145			−0.0670727	−	0.997748i	$-0.521366\pi$
$439$	−25852.6			−0.134145			−0.0670727	+	0.997748i	$0.521366\pi$
$440$	−33811.8	−	2298.50i	−0.174648	−	0.0118724i
$441$	−752653.			−3.87006
$442$	−342806.			−1.75471
$443$		−	357610.i		−	1.82223i	−0.412157	−	0.911113i	$-0.635224\pi$
$443$		−	357610.i		−	1.82223i	0.412157	−	0.911113i	$-0.364776\pi$
$444$		−	76586.7i		−	0.388497i
$445$	1835.92	−	27007.1i	0.00927116	−	0.136383i
$446$	11446.2			0.0575429
$447$	−547024.			−2.73774
$448$	43585.4			0.217163
$449$	368971.			1.83021			0.915103	−	0.403221i	$-0.132109\pi$
$449$	368971.			1.83021			0.915103	+	0.403221i	$0.132109\pi$
$450$	37159.0	−	272049.i	0.183501	−	1.34345i
$451$		−	107312.i		−	0.527587i
$452$	128945.			0.631141
$453$		−	362608.i		−	1.76702i
$454$			100419.i			0.487197i
$455$	−42814.9	+	629825.i	−0.206810	+	3.04226i
$456$			6497.01i			0.0312452i
$457$	−113843.			−0.545095			−0.272548	−	0.962142i	$-0.587866\pi$
$457$	−113843.			−0.545095			−0.272548	+	0.962142i	$0.587866\pi$
$458$	268127.			1.27823
$459$		−	466842.i		−	2.21587i
$460$	−36160.4	+	99428.7i	−0.170890	+	0.469890i
$461$	−75347.8			−0.354543			−0.177271	−	0.984162i	$-0.556727\pi$
$461$	−75347.8			−0.354543			−0.177271	+	0.984162i	$0.556727\pi$
$462$			221750.i			1.03891i
$463$		−	267332.i		−	1.24707i	−0.781797	−	0.623533i	$-0.785697\pi$
$463$		−	267332.i		−	1.24707i	0.781797	−	0.623533i	$-0.214303\pi$
$464$	−57325.8			−0.266265
$465$	15089.6	−	221974.i	0.0697867	−	1.02659i
$466$	−163675.			−0.753722
$467$	424990.			1.94870			0.974349	−	0.225041i	$-0.0722516\pi$
$467$	424990.			1.94870			0.974349	+	0.225041i	$0.0722516\pi$
$468$			368583.i			1.68284i
$469$	80578.0			0.366329
$470$	−156496.	−	10638.5i	−0.708448	−	0.0481597i
$471$		−	362273.i		−	1.63303i
$472$		−	53871.7i		−	0.241811i
$473$		−	34271.2i		−	0.153182i
$474$			341790.i			1.52126i
$475$	−1579.82	+	11566.2i	−0.00700199	+	0.0512630i
$476$	278263.			1.22812
$477$	577144.			2.53657
$478$			38175.2i			0.167080i
$479$		−	268412.i		−	1.16985i	−0.811086	−	0.584926i	$-0.801123\pi$
$479$		−	268412.i		−	1.16985i	0.811086	−	0.584926i	$-0.198877\pi$
$480$	69409.1	+	4718.37i	0.301255	+	0.0204791i
$481$			184723.i			0.798417i
$482$	59493.5			0.256080
$483$	665137.	+	191938.i	2.85113	+	0.822746i
$484$	−88415.0			−0.377429
$485$	377966.	+	25693.8i	1.60683	+	0.109231i
$486$	45094.3			0.190919
$487$			15502.5i			0.0653650i	0.999466	+	0.0326825i	$0.0104050\pi$
$487$			15502.5i			0.0653650i	−0.999466	+	0.0326825i	$0.989595\pi$
$488$	45867.6			0.192604
$489$	376119.			1.57292
$490$	23239.1	−	341856.i	0.0967891	−	1.42381i
$491$	−6454.72			−0.0267741			−0.0133870	−	0.999910i	$-0.504261\pi$
$491$	−6454.72			−0.0267741			−0.0133870	+	0.999910i	$0.504261\pi$
$492$			220290.i			0.910050i
$493$	−365986.			−1.50581
$494$		−	15670.4i		−	0.0642135i
$495$	−15777.7	+	232097.i	−0.0643923	+	0.947237i
$496$	37050.3			0.150601
$497$	−325423.			−1.31745
$498$	−371838.			−1.49932
$499$	−240589.			−0.966217			−0.483108	−	0.875561i	$-0.660492\pi$
$499$	−240589.			−0.966217			−0.483108	+	0.875561i	$0.660492\pi$
$500$	122418.	+	25277.5i	0.489670	+	0.101110i
$501$	284770.			1.13454
$502$	−283563.			−1.12523
$503$	−41105.9			−0.162468			−0.0812340	−	0.996695i	$-0.525886\pi$
$503$	−41105.9			−0.162468			−0.0812340	+	0.996695i	$0.525886\pi$
$504$		−	299186.i		−	1.17782i
$505$	−63191.0	−	4295.67i	−0.247784	−	0.0168441i
$506$	24852.8	−	86124.5i	0.0970676	−	0.336376i
$507$		−	913547.i		−	3.55398i
$508$		−	232251.i		−	0.899973i
$509$	−65093.6			−0.251248			−0.125624	−	0.992078i	$-0.540093\pi$
$509$	−65093.6			−0.251248			−0.125624	+	0.992078i	$0.540093\pi$
$510$	443130.	+	30123.6i	1.70369	+	0.115815i
$511$		−	7404.65i		−	0.0283571i
$512$			11585.2i			0.0441942i
$513$	21340.3			0.0810898
$514$	−172655.			−0.653511
$515$	−123887.	−	8421.75i	−0.467103	−	0.0317532i
$516$			70352.3i			0.264228i
$517$	132897.			0.497203
$518$		−	149943.i		−	0.558813i
$519$	14894.6			0.0552961
$520$	−167411.	−	11380.4i	−0.619123	−	0.0420874i
$521$		−	393594.i		−	1.45002i	−0.688740	−	0.725009i	$-0.741836\pi$
$521$		−	393594.i		−	1.45002i	0.688740	−	0.725009i	$-0.258164\pi$
$522$			393505.i			1.44414i
$523$	−51557.8			−0.188491			−0.0942455	−	0.995549i	$-0.530044\pi$
$523$	−51557.8			−0.188491			−0.0942455	+	0.995549i	$0.530044\pi$
$524$	−190558.			−0.694009
$525$	110690.	−	810383.i	0.401595	−	2.94016i
$526$		−	3831.09i		−	0.0138469i
$527$	236540.			0.851695
$528$	−58942.4			−0.211427
$529$	−236818.	−	149092.i	−0.846259	−	0.532772i
$530$	−17820.0	+	262139.i	−0.0634390	+	0.933212i
$531$	−369795.			−1.31151
$532$			12720.0i			0.0449431i
$533$		−	531327.i		−	1.87029i
$534$		−	47080.1i		−	0.165103i
$535$	−341408.	−	23208.6i	−1.19280	−	0.0810853i
$536$			21418.1i			0.0745505i
$537$			425147.i			1.47431i
$538$		−	26633.1i		−	0.0920147i
$539$			290305.i			0.999255i
$540$	15498.2	−	227984.i	0.0531487	−	0.781838i
$541$	−276365.			−0.944252			−0.472126	−	0.881531i	$-0.656513\pi$
$541$	−276365.			−0.944252			−0.472126	+	0.881531i	$0.656513\pi$
$542$			39079.0i			0.133028i
$543$	519188.			1.76086
$544$			73963.8i			0.249932i
$545$	31459.1	−	462776.i	0.105914	−	1.55804i
$546$			1.09794e6i			3.68293i
$547$		−	367638.i		−	1.22870i	−0.789034	−	0.614349i	$-0.789419\pi$
$547$		−	367638.i		−	1.22870i	0.789034	−	0.614349i	$-0.210581\pi$
$548$	69401.6			0.231105
$549$		−	314852.i		−	1.04463i
$550$	−104931.	−	14332.5i	−0.346881	−	0.0473803i
$551$		−	16730.0i		−	0.0551052i
$552$	−51018.0	+	176797.i	−0.167435	+	0.580225i
$553$			669164.i			2.18817i
$554$	−89278.7			−0.290890
$555$	16232.2	−	238782.i	0.0526977	−	0.775204i
$556$	135402.			0.438000
$557$	120723.			0.389115			0.194558	−	0.980891i	$-0.437673\pi$
$557$	120723.			0.389115			0.194558	+	0.980891i	$0.437673\pi$
$558$		−	254327.i		−	0.816814i
$559$		−	169686.i		−	0.543027i
$560$	135891.	+	9237.73i	0.433325	+	0.0294571i
$561$	−376306.			−1.19568
$562$	314760.			0.996569
$563$	232673.			0.734057			0.367028	−	0.930210i	$-0.380375\pi$
$563$	232673.			0.734057			0.367028	+	0.930210i	$0.380375\pi$
$564$	−272812.			−0.857639
$565$	402024.	+	27329.3i	1.25938	+	0.0856113i
$566$		−	203066.i		−	0.633878i
$567$	−424195.			−1.31947
$568$		−	86499.3i		−	0.268112i
$569$			141949.i			0.438437i	0.975676	+	0.219219i	$0.0703508\pi$
$569$			141949.i			0.438437i	−0.975676	+	0.219219i	$0.929649\pi$
$570$	−1377.01	+	20256.4i	−0.00423826	+	0.0623466i
$571$		−	432828.i		−	1.32752i	−0.747944	−	0.663762i	$-0.768959\pi$
$571$		−	432828.i		−	1.32752i	0.747944	−	0.663762i	$-0.231041\pi$
$572$	142166.			0.434513
$573$	444271.			1.35313
$574$			431289.i			1.30902i
$575$	−133815.	+	302335.i	−0.404732	+	0.914435i
$576$	79525.3			0.239696
$577$			219932.i			0.660599i	0.943876	+	0.330299i	$0.107150\pi$
$577$			219932.i			0.660599i	−0.943876	+	0.330299i	$0.892850\pi$
$578$			235974.i			0.706333i
$579$	894502.			2.66824
$580$	−178731.	−	12150.0i	−0.531304	−	0.0361176i
$581$	−727993.			−2.15663
$582$	658889.			1.94521
$583$		−	222609.i		−	0.654947i
$584$	1968.20			0.00577089
$585$	−78119.5	+	1.14917e6i	−0.228270	+	3.35794i
$586$			350225.i			1.01989i
$587$			158206.i			0.459142i	0.973292	+	0.229571i	$0.0737323\pi$
$587$			158206.i			0.459142i	−0.973292	+	0.229571i	$0.926268\pi$
$588$		−	595939.i		−	1.72364i
$589$			10812.8i			0.0311678i
$590$	11417.9	−	167961.i	0.0328006	−	0.482509i
$591$	39710.0			0.113691
$592$	39855.7			0.113723
$593$		−	255037.i		−	0.725259i	−0.931933	−	0.362630i	$-0.881879\pi$
$593$		−	255037.i		−	0.725259i	0.931933	−	0.362630i	$-0.118121\pi$
$594$			193604.i			0.548709i
$595$	867569.	+	58976.6i	2.45059	+	0.166589i
$596$		−	284671.i		−	0.801403i
$597$	−323125.			−0.906612
$598$	123053.	−	426424.i	0.344103	−	1.19245i
$599$	−211136.			−0.588450			−0.294225	−	0.955736i	$-0.595062\pi$
$599$	−211136.			−0.588450			−0.294225	+	0.955736i	$0.595062\pi$
$600$	215404.	+	29421.9i	0.598345	+	0.0817276i
$601$	−90985.5			−0.251897			−0.125949	−	0.992037i	$-0.540197\pi$
$601$	−90985.5			−0.251897			−0.125949	+	0.992037i	$0.540197\pi$
$602$			137737.i			0.380065i
$603$	147022.			0.404340
$604$	188701.			0.517249
$605$	−275661.	−	18739.2i	−0.753119	−	0.0511964i
$606$	−110158.			−0.299964
$607$			450698.i			1.22323i	0.791155	+	0.611615i	$0.209480\pi$
$607$			450698.i			1.22323i	−0.791155	+	0.611615i	$0.790520\pi$
$608$	−3381.04			−0.00914625
$609$			1.17218e6i			3.16053i
$610$	143006.	+	9721.43i	0.384322	+	0.0261259i
$611$	658006.			1.76257
$612$	507714.			1.35555
$613$	380265.			1.01197			0.505983	−	0.862543i	$-0.331130\pi$
$613$	380265.			1.01197			0.505983	+	0.862543i	$0.331130\pi$
$614$	99001.4			0.262606
$615$	−46689.6	+	686822.i	−0.123444	+	1.81591i
$616$	−115399.			−0.304116
$617$	238336.			0.626064			0.313032	−	0.949743i	$-0.398655\pi$
$617$	238336.			0.626064			0.313032	+	0.949743i	$0.398655\pi$
$618$	−215966.			−0.565469
$619$		−	318726.i		−	0.831833i	−0.909403	−	0.415916i	$-0.863461\pi$
$619$		−	318726.i		−	0.831833i	0.909403	−	0.415916i	$-0.136539\pi$
$620$	115515.	+	7852.64i	0.300509	+	0.0204283i
$621$	580714.	+	167576.i	1.50584	+	0.434539i
$622$		−	254173.i		−	0.656974i
$623$		−	92174.5i		−	0.237484i
$624$	−291839.			−0.749503
$625$	376316.	+	104756.i	0.963370	+	0.268176i
$626$		−	118645.i		−	0.302762i
$627$		−	17201.8i		−	0.0437560i
$628$	188527.			0.478029
$629$	254451.			0.643136
$630$	63411.2	−	932804.i	0.159766	−	2.35022i
$631$			687055.i			1.72557i	0.505570	+	0.862786i	$0.331282\pi$
$631$			687055.i			1.72557i	−0.505570	+	0.862786i	$0.668718\pi$
$632$	−177867.			−0.445310
$633$			295464.i			0.737389i
$634$	399123.			0.992951
$635$	49224.5	−	724112.i	0.122077	−	1.79580i
$636$			456974.i			1.12974i
$637$			1.43737e6i			3.54234i
$638$	151778.			0.372879
$639$	−593763.			−1.45416
$640$	−2455.44	+	36120.5i	−0.00599473	+	0.0881848i
$641$			595449.i			1.44920i	0.689169	+	0.724601i	$0.257976\pi$
$641$			595449.i			1.44920i	−0.689169	+	0.724601i	$0.742024\pi$
$642$	−595159.			−1.44399
$643$	−475909.			−1.15107			−0.575535	−	0.817777i	$-0.695206\pi$
$643$	−475909.			−1.15107			−0.575535	+	0.817777i	$0.695206\pi$
$644$	−99884.3	+	346137.i	−0.240838	+	0.834596i
$645$	−14910.9	+	219345.i	−0.0358412	+	0.527239i
$646$	−21585.6			−0.0517249
$647$		−	498511.i		−	1.19088i	−0.803402	−	0.595438i	$-0.796979\pi$
$647$		−	498511.i		−	1.19088i	0.803402	−	0.595438i	$-0.203021\pi$
$648$		−	112753.i		−	0.268522i
$649$			142633.i			0.338634i
$650$	−519542.	−	70964.0i	−1.22969	−	0.167962i
$651$		−	757592.i		−	1.78761i
$652$			195732.i			0.460434i
$653$		−	329827.i		−	0.773499i	−0.922185	−	0.386749i	$-0.873598\pi$
$653$		−	329827.i		−	0.773499i	0.922185	−	0.386749i	$-0.126402\pi$
$654$		−	806734.i		−	1.88614i
$655$	−594123.	−	40388.0i	−1.38482	−	0.0941390i
$656$	−114639.			−0.266394
$657$		−	13510.4i		−	0.0312995i
$658$	−534117.			−1.23363
$659$			386839.i			0.890758i	0.895342	+	0.445379i	$0.146931\pi$
$659$			386839.i			0.890758i	−0.895342	+	0.445379i	$0.853069\pi$
$660$	−183771.	−	12492.6i	−0.421880	−	0.0286790i
$661$		−	438787.i		−	1.00427i	−0.864789	−	0.502136i	$-0.832548\pi$
$661$		−	438787.i		−	1.00427i	0.864789	−	0.502136i	$-0.167452\pi$
$662$			392884.i			0.896495i
$663$	−1.86319e6			−4.23867
$664$		−	193505.i		−	0.438890i
$665$	−2695.94	+	39658.4i	−0.00609632	+	0.0896793i
$666$		−	273584.i		−	0.616797i
$667$	131373.	−	455258.i	0.295294	−	1.02331i
$668$			148194.i			0.332107i
$669$	62211.3			0.139001
$670$	−4539.47	+	66777.4i	−0.0101124	+	0.148758i
$671$	−121441.			−0.269725
$672$	236891.			0.524578
$673$		−	167506.i		−	0.369829i	−0.982755	−	0.184914i	$-0.940799\pi$
$673$		−	167506.i		−	0.369829i	0.982755	−	0.184914i	$-0.0592008\pi$
$674$		−	575812.i		−	1.26754i
$675$	96640.4	−	707525.i	0.212105	−	1.55287i
$676$	475410.			1.04034
$677$	−171345.			−0.373847			−0.186924	−	0.982374i	$-0.559852\pi$
$677$	−171345.			−0.373847			−0.186924	+	0.982374i	$0.559852\pi$
$678$	700828.			1.52459
$679$	1.28999e6			2.79799
$680$	−15676.3	+	230605.i	−0.0339020	+	0.498712i
$681$			545789.i			1.17687i
$682$	−98095.9			−0.210903
$683$		−	327272.i		−	0.701565i	−0.936457	−	0.350782i	$-0.885916\pi$
$683$		−	327272.i		−	0.701565i	0.936457	−	0.350782i	$-0.114084\pi$
$684$			23208.7i			0.0496065i
$685$	216381.	+	14709.4i	0.461145	+	0.0313482i
$686$		−	588636.i		−	1.25083i
$687$	1.45730e6			3.08770
$688$	−36611.3			−0.0773461
$689$		−	1.10219e6i		−	2.32177i
$690$	−196536.	+	540405.i	−0.412803	+	1.13507i
$691$	−709067.			−1.48502			−0.742508	−	0.669838i	$-0.766364\pi$
$691$	−709067.			−1.48502			−0.742508	+	0.669838i	$0.766364\pi$
$692$			7751.15i			0.0161865i
$693$			792139.i			1.64943i
$694$	−471938.			−0.979865
$695$	422156.	+	28697.8i	0.873983	+	0.0594126i
$696$	−311572.			−0.643191
$697$	−731891.			−1.50654
$698$		−	488751.i		−	1.00317i
$699$	−889592.			−1.82069
$700$	421723.	+	57602.9i	0.860659	+	0.117557i
$701$			112002.i			0.227923i	0.993485	+	0.113962i	$0.0363541\pi$
$701$			112002.i			0.227923i	−0.993485	+	0.113962i	$0.963646\pi$
$702$			958584.i			1.94516i
$703$			11631.5i			0.0235356i
$704$		−	30673.6i		−	0.0618898i
$705$	−850573.	−	57821.2i	−1.71133	−	0.116335i
$706$	−233233.			−0.467929
$707$	−215669.			−0.431468
$708$		−	292798.i		−	0.584120i
$709$			172878.i			0.343913i	0.985105	+	0.171956i	$0.0550088\pi$
$709$			172878.i			0.343913i	−0.985105	+	0.171956i	$0.944991\pi$
$710$	18333.1	−	269688.i	0.0363681	−	0.534989i
$711$			1.22095e6i			2.41522i
$712$	24500.5			0.0483298
$713$	−84907.7	+	294238.i	−0.167020	+	0.578788i
$714$	1.51239e6			2.96665
$715$	443244.	+	30131.4i	0.867024	+	0.0589395i
$716$	−221246.			−0.431569
$717$			207486.i			0.403600i
$718$	−172854.			−0.335298
$719$	−687706.			−1.33029			−0.665143	−	0.746716i	$-0.731629\pi$
$719$	−687706.			−1.33029			−0.665143	+	0.746716i	$0.731629\pi$
$720$	247944.	+	16855.0i	0.478288	+	0.0325136i
$721$	−422824.			−0.813371
$722$			367617.i			0.705214i
$723$	323353.			0.618587
$724$			270185.i			0.515448i
$725$	−554672.	−	75762.4i	−1.05526	−	0.144138i
$726$	−480545.			−0.911718
$727$	558799.			1.05727			0.528636	−	0.848849i	$-0.322704\pi$
$727$	558799.			1.05727			0.528636	+	0.848849i	$0.322704\pi$
$728$	−571368.			−1.07809
$729$	648719.			1.22068
$730$	6136.45	+	417.150i	0.0115152	+	0.000782793i
$731$	−233738.			−0.437416
$732$	249295.			0.465256
$733$	−309640.			−0.576300			−0.288150	−	0.957585i	$-0.593040\pi$
$733$	−309640.			−0.576300			−0.288150	+	0.957585i	$0.593040\pi$
$734$		−	602900.i		−	1.11906i
$735$	126307.	−	1.85802e6i	0.233804	−	3.43935i
$736$	−92005.1	−	26549.8i	−0.169846	−	0.0490123i
$737$		−	56707.4i		−	0.104401i
$738$			786924.i			1.44484i
$739$	−69290.8			−0.126878			−0.0634390	−	0.997986i	$-0.520207\pi$
$739$	−69290.8			−0.126878			−0.0634390	+	0.997986i	$0.520207\pi$
$740$	124262.	+	8447.24i	0.226922	+	0.0154259i
$741$		−	85170.3i		−	0.155114i
$742$			894673.i			1.62501i
$743$	280737.			0.508537			0.254268	−	0.967134i	$-0.418165\pi$
$743$	280737.			0.508537			0.254268	+	0.967134i	$0.418165\pi$
$744$	201372.			0.363792
$745$	60334.8	−	887549.i	0.108706	−	1.59912i
$746$		−	238663.i		−	0.428852i
$747$	−1.32829e6			−2.38040
$748$		−	195830.i		−	0.350006i
$749$	−1.16522e6			−2.07703
$750$	665352.	+	137386.i	1.18285	+	0.244241i
$751$		−	490618.i		−	0.869888i	−0.900457	−	0.434944i	$-0.856768\pi$
$751$		−	490618.i		−	0.869888i	0.900457	−	0.434944i	$-0.143232\pi$
$752$		−	141971.i		−	0.251052i
$753$	−1.54119e6			−2.71811
$754$	751493.			1.32185
$755$	588332.	+	39994.3i	1.03212	+	0.0701624i
$756$		−	778102.i		−	1.36142i
$757$	227659.			0.397276			0.198638	−	0.980073i	$-0.436348\pi$
$757$	227659.			0.397276			0.198638	+	0.980073i	$0.436348\pi$
$758$	101955.			0.177448
$759$	135078.	−	468095.i	0.234477	−	0.812551i
$760$	−10541.4	−	716.597i	−0.0182504	−	0.00124065i
$761$	−636432.			−1.09896			−0.549481	−	0.835506i	$-0.685174\pi$
$761$	−636432.			−1.09896			−0.549481	+	0.835506i	$0.685174\pi$
$762$		−	1.26231e6i		−	2.17398i
$763$		−	1.57944e6i		−	2.71303i
$764$			231198.i			0.396094i
$765$	1.58295e6	+	107608.i	2.70486	+	0.183874i
$766$		−	492806.i		−	0.839883i
$767$			706213.i			1.20045i
$768$			62967.0i			0.106756i
$769$		−	259730.i		−	0.439207i	−0.975589	−	0.219604i	$-0.929524\pi$
$769$		−	259730.i		−	0.439207i	0.975589	−	0.219604i	$-0.0704764\pi$
$770$	−359790.	−	24458.2i	−0.606831	−	0.0412519i
$771$	−938398.			−1.57862
$772$			465499.i			0.781059i
$773$	−716448.			−1.19902			−0.599509	−	0.800368i	$-0.704637\pi$
$773$	−716448.			−1.19902			−0.599509	+	0.800368i	$0.704637\pi$
$774$			251313.i			0.419502i
$775$	358490.	+	48966.0i	0.596862	+	0.0815251i
$776$			342886.i			0.569411i
$777$		−	814956.i		−	1.34987i
$778$	−349188.			−0.576899
$779$		−	33456.3i		−	0.0551319i
$780$	−909896.	−	61853.9i	−1.49555	−	0.101667i
$781$			229019.i			0.375465i
$782$	−587389.	−	169502.i	−0.960533	−	0.277180i
$783$			1.02340e6i			1.66925i
$784$	310127.			0.504553
$785$	587790.	+	39957.4i	0.953856	+	0.0648423i
$786$	−1.03570e6			−1.67645
$787$	611866.			0.987886			0.493943	−	0.869494i	$-0.335555\pi$
$787$	611866.			0.987886			0.493943	+	0.869494i	$0.335555\pi$
$788$			20665.1i			0.0332801i
$789$		−	20822.4i		−	0.0334485i
$790$	−554556.	−	37698.2i	−0.888568	−	0.0604041i
$791$	1.37210e6			2.19296
$792$	−210555.			−0.335672
$793$	−601286.			−0.956168
$794$	−720617.			−1.14305
$795$	−96853.6	+	1.42475e6i	−0.153243	+	2.25427i
$796$		−	168154.i		−	0.265388i
$797$	−528932.			−0.832689			−0.416345	−	0.909207i	$-0.636689\pi$
$797$	−528932.			−0.832689			−0.416345	+	0.909207i	$0.636689\pi$
$798$			69134.4i			0.108565i
$799$		−	906388.i		−	1.41978i
$800$	−15311.2	+	112096.i	−0.0239237	+	0.175150i
$801$		−	168180.i		−	0.262126i
$802$	−491194.			−0.763667
$803$	−5211.08			−0.00808159
$804$			116409.i			0.180084i
$805$	−384782.	+	1.05802e6i	−0.593776	+	1.63268i
$806$	−485698.			−0.747646
$807$		−	144754.i		−	0.222271i
$808$		−	57326.0i		−	0.0878070i
$809$	7379.39			0.0112752			0.00563759	−	0.999984i	$-0.498205\pi$
$809$	7379.39			0.0112752			0.00563759	+	0.999984i	$0.498205\pi$
$810$	23897.6	−	351543.i	0.0364237	−	0.535807i
$811$	1.13411e6			1.72431			0.862155	−	0.506645i	$-0.169115\pi$
$811$	1.13411e6			1.72431			0.862155	+	0.506645i	$0.169115\pi$
$812$	−610002.			−0.925165
$813$			212398.i			0.321344i
$814$	−105524.			−0.159258
$815$	−41484.6	+	610255.i	−0.0624556	+	0.918747i
$816$			402001.i			0.603735i
$817$		−	10684.7i		−	0.0160072i
$818$			451707.i			0.675072i
$819$			3.92208e6i			5.84721i
$820$	−357422.	−	24297.2i	−0.531562	−	0.0361351i
$821$	−67148.7			−0.0996211			−0.0498105	−	0.998759i	$-0.515862\pi$
$821$	−67148.7			−0.0996211			−0.0498105	+	0.998759i	$0.515862\pi$
$822$	377205.			0.558257
$823$		−	740408.i		−	1.09313i	−0.837417	−	0.546565i	$-0.815935\pi$
$823$		−	740408.i		−	1.09313i	0.837417	−	0.546565i	$-0.184065\pi$
$824$		−	112389.i		−	0.165527i
$825$	−570313.	−	77898.8i	−0.837926	−	0.114452i
$826$		−	573247.i		−	0.840198i
$827$	51035.7			0.0746213			0.0373106	−	0.999304i	$-0.488121\pi$
$827$	51035.7			0.0746213			0.0373106	+	0.999304i	$0.488121\pi$
$828$	−182247.	+	631557.i	−0.265828	+	0.921195i
$829$	−836430.			−1.21708			−0.608542	−	0.793521i	$-0.708245\pi$
$829$	−836430.			−1.21708			−0.608542	+	0.793521i	$0.708245\pi$
$830$	41012.5	−	603310.i	0.0595333	−	0.875758i
$831$	−485239.			−0.702673
$832$		−	151873.i		−	0.219398i
$833$	1.97995e6			2.85340
$834$	735922.			1.05803
$835$	−31409.1	+	462041.i	−0.0450488	+	0.662685i
$836$	8951.79			0.0128085
$837$		−	661434.i		−	0.944139i
$838$	−701139.			−0.998427
$839$			869643.i			1.23543i	0.786403	+	0.617713i	$0.211941\pi$
$839$			869643.i			1.23543i	−0.786403	+	0.617713i	$0.788059\pi$
$840$	738580.	+	50208.1i	1.04674	+	0.0711565i
$841$	95025.9			0.134354
$842$	−624584.			−0.880981
$843$	1.71076e6			2.40731
$844$	−153759.			−0.215852
$845$	1.48223e6	+	100761.i	2.07589	+	0.141117i
$846$	−974542.			−1.36163
$847$	−940821.			−1.31141
$848$	−237809.			−0.330702
$849$		−	1.10369e6i		−	1.53120i
$850$	−97751.2	+	715657.i	−0.135296	+	0.990529i
$851$	−91336.9	+	316517.i	−0.126121	+	0.437057i
$852$		−	470133.i		−	0.647651i
$853$		−	811351.i		−	1.11509i	−0.830146	−	0.557546i	$-0.811743\pi$
$853$		−	811351.i		−	1.11509i	0.830146	−	0.557546i	$-0.188257\pi$
$854$	488075.			0.669224
$855$	−4918.98	+	72360.2i	−0.00672889	+	0.0989846i
$856$		−	309721.i		−	0.422691i
$857$		−	709698.i		−	0.966300i	−0.875538	−	0.483150i	$-0.839493\pi$
$857$		−	709698.i		−	0.966300i	0.875538	−	0.483150i	$-0.160507\pi$
$858$	772685.			1.04961
$859$	−304991.			−0.413334			−0.206667	−	0.978411i	$-0.566262\pi$
$859$	−304991.			−0.413334			−0.206667	+	0.978411i	$0.566262\pi$
$860$	−114147.	−	7759.60i	−0.154336	−	0.0104916i
$861$			2.34410e6i			3.16206i
$862$	560760.			0.754679
$863$			981435.i			1.31777i	0.752243	+	0.658885i	$0.228972\pi$
$863$			981435.i			1.31777i	−0.752243	+	0.658885i	$0.771028\pi$
$864$	206824.			0.277059
$865$	−1642.82	+	24166.6i	−0.00219563	+	0.0322985i
$866$			424218.i			0.565658i
$867$			1.28255e6i			1.70622i
$868$	394251.			0.523279
$869$	470929.			0.623615
$870$	−971420.	−	66036.3i	−1.28342	−	0.0872457i
$871$		−	280773.i		−	0.370100i
$872$	419824.			0.552121
$873$	2.35369e6			3.08831
$874$	7748.30	−	26850.8i	0.0101434	−	0.0351507i
$875$	1.30264e6	+	268977.i	1.70141	+	0.351317i
$876$	10697.3			0.0139402
$877$		−	161647.i		−	0.210168i	−0.994463	−	0.105084i	$-0.966489\pi$
$877$		−	161647.i		−	0.210168i	0.994463	−	0.105084i	$-0.0335112\pi$
$878$		−	73122.2i		−	0.0948551i
$879$			1.90351e6i			2.46364i
$880$	6501.13	−	95634.2i	0.00839506	−	0.123495i
$881$			407411.i			0.524906i	0.964945	+	0.262453i	$0.0845314\pi$
$881$			407411.i			0.524906i	−0.964945	+	0.262453i	$0.915469\pi$
$882$		−	2.12882e6i		−	2.73654i
$883$			579215.i			0.742880i	0.928457	+	0.371440i	$0.121136\pi$
$883$			579215.i			0.742880i	−0.928457	+	0.371440i	$0.878864\pi$
$884$		−	969603.i		−	1.24076i
$885$	62057.3	−	912888.i	0.0792331	−	1.16555i
$886$	1.01147e6			1.28851
$887$		−	207700.i		−	0.263991i	−0.991250	−	0.131996i	$-0.957862\pi$
$887$		−	207700.i		−	0.263991i	0.991250	−	0.131996i	$-0.0421385\pi$
$888$	216620.			0.274709
$889$		−	2.47137e6i		−	3.12705i
$890$	76387.7	+	5192.77i	0.0964370	+	0.00655570i
$891$			298531.i			0.376040i
$892$			32374.7i			0.0406890i
$893$	41432.9			0.0519568
$894$		−	1.54722e6i		−	1.93587i
$895$	−689802.	−	46892.2i	−0.861150	−	0.0585402i
$896$			123278.i			0.153557i
$897$	668804.	−	2.31766e6i	0.831216	−	2.88048i
$898$			1.04361e6i			1.29415i
$899$	−518539.			−0.641597
$900$	769470.	+	105101.i	0.949963	+	0.129755i
$901$	−1.51825e6			−1.87022
$902$	303523.			0.373060
$903$			748616.i			0.918087i
$904$			364711.i			0.446284i
$905$	−57264.6	+	842385.i	−0.0699180	+	1.02852i
$906$	1.02561e6			1.24947
$907$	1.34756e6			1.63807			0.819036	−	0.573743i	$-0.194509\pi$
$907$	1.34756e6			1.63807			0.819036	+	0.573743i	$0.194509\pi$
$908$	−284028.			−0.344500
$909$	−393507.			−0.476238
$910$	−1.78141e6	−	121099.i	−2.15121	−	0.146237i
$911$			994531.i			1.19834i	0.800620	+	0.599172i	$0.204503\pi$
$911$			994531.i			1.19834i	−0.800620	+	0.599172i	$0.795497\pi$
$912$	−18376.3			−0.0220937
$913$			512331.i			0.614624i
$914$		−	321995.i		−	0.385440i
$915$	777253.	+	52837.0i	0.928369	+	0.0631097i
$916$			758378.i			0.903846i
$917$	−2.02772e6			−2.41140
$918$	1.32043e6			1.56686
$919$			108374.i			0.128320i	0.997940	+	0.0641598i	$0.0204367\pi$
$919$			108374.i			0.128320i	−0.997940	+	0.0641598i	$0.979563\pi$
$920$	−281227.	−	102277.i	−0.332262	−	0.120838i
$921$	538083.			0.634351
$922$		−	213116.i		−	0.250700i
$923$			1.13393e6i			1.33102i
$924$	−627204.			−0.734623
$925$	385635.	+	52673.7i	0.450706	+	0.0615616i
$926$	756130.			0.881809
$927$	−771478.			−0.897768
$928$		−	162142.i		−	0.188278i
$929$	922150.			1.06849			0.534244	−	0.845330i	$-0.320596\pi$
$929$	922150.			1.06849			0.534244	+	0.845330i	$0.320596\pi$
$930$	627839.	+	42679.9i	0.725909	+	0.0493467i
$931$			90507.5i			0.104420i
$932$		−	462943.i		−	0.532962i
$933$		−	1.38146e6i		−	1.58699i
$934$			1.20205e6i			1.37794i
$935$	41505.2	−	610559.i	0.0474766	−	0.698400i
$936$	−1.04251e6			−1.18995
$937$	−441378.			−0.502726			−0.251363	−	0.967893i	$-0.580879\pi$
$937$	−441378.			−0.502726			−0.251363	+	0.967893i	$0.580879\pi$
$938$			227909.i			0.259033i
$939$		−	644849.i		−	0.731353i
$940$	30090.2	−	442638.i	0.0340541	−	0.500949i
$941$		−	1.05416e6i		−	1.19049i	−0.803544	−	0.595246i	$-0.797055\pi$
$941$		−	1.05416e6i		−	1.19049i	0.803544	−	0.595246i	$-0.202945\pi$
$942$	1.02466e6			1.15473
$943$	262717.	−	910415.i	0.295437	−	1.02380i
$944$	152372.			0.170987
$945$	164915.	−	2.42597e6i	0.184670	−	2.71658i
$946$	96933.7			0.108316
$947$			238906.i			0.266395i	0.991090	+	0.133198i	$0.0425245\pi$
$947$			238906.i			0.266395i	−0.991090	+	0.133198i	$0.957476\pi$
$948$	−966728.			−1.07569
$949$	−25801.4			−0.0286491
$950$	−32714.2	−	4468.42i	−0.0362484	−	0.00495116i
$951$	2.16927e6			2.39857
$952$			787046.i			0.868413i
$953$	−368077.			−0.405278			−0.202639	−	0.979253i	$-0.564952\pi$
$953$	−368077.			−0.405278			−0.202639	+	0.979253i	$0.564952\pi$
$954$			1.63241e6i			1.79363i
$955$	−49001.5	+	720832.i	−0.0537282	+	0.790364i
$956$	−107976.			−0.118144
$957$	824931.			0.900728
$958$	759184.			0.827211
$959$	738501.			0.802996
$960$	−13345.6	+	196319.i	−0.0144809	+	0.213019i
$961$	−588384.			−0.637109
$962$	−522475.			−0.564566
$963$	−2.12604e6			−2.29255
$964$			168273.i			0.181076i
$965$	−98660.4	+	1.45133e6i	−0.105947	+	1.55852i
$966$	−542881.	+	1.88129e6i	−0.581769	+	2.01605i
$967$		−	127405.i		−	0.136250i	−0.997677	−	0.0681248i	$-0.978298\pi$
$967$		−	127405.i		−	0.136250i	0.997677	−	0.0681248i	$-0.0217016\pi$
$968$		−	250075.i		−	0.266882i
$969$	−117320.			−0.124947
$970$	−72673.1	+	1.06905e6i	−0.0772379	+	1.13620i
$971$		−	738230.i		−	0.782984i	−0.920181	−	0.391492i	$-0.871959\pi$
$971$		−	738230.i		−	0.782984i	0.920181	−	0.391492i	$-0.128041\pi$
$972$			127546.i			0.135000i
$973$	1.44080e6			1.52188
$974$	−43847.8			−0.0462200
$975$	−2.82377e6	−	385697.i	−2.97043	−	0.405730i
$976$			129733.i			0.136192i
$977$	414141.			0.433869			0.216935	−	0.976186i	$-0.430394\pi$
$977$	414141.			0.433869			0.216935	+	0.976186i	$0.430394\pi$
$978$			1.06383e6i			1.11222i
$979$	−64868.6			−0.0676814
$980$	966915.	+	65730.0i	1.00678	+	0.0684402i
$981$		−	2.88183e6i		−	2.99454i
$982$		−	18256.7i		−	0.0189321i
$983$	−150903.			−0.156167			−0.0780836	−	0.996947i	$-0.524880\pi$
$983$	−150903.			−0.156167			−0.0780836	+	0.996947i	$0.524880\pi$
$984$	−623075.			−0.643502
$985$	−4379.87	+	64429.6i	−0.00451428	+	0.0664069i
$986$		−	1.03516e6i		−	1.06477i
$987$	−2.90298e6			−2.97996
$988$	44322.6			0.0454058
$989$	83901.8	−	290752.i	0.0857785	−	0.297255i
$990$	−656469.	−	44626.2i	−0.669797	−	0.0455322i
$991$	−1.43219e6			−1.45832			−0.729159	−	0.684344i	$-0.760089\pi$
$991$	−1.43219e6			−1.45832			−0.729159	+	0.684344i	$0.760089\pi$
$992$			104794.i			0.106491i
$993$			2.13536e6i			2.16558i
$994$		−	920436.i		−	0.931581i
$995$	35639.5	−	524272.i	0.0359986	−	0.529554i
$996$		−	1.05172e6i		−	1.06018i
$997$		−	466609.i		−	0.469421i	−0.972065	−	0.234711i	$-0.924586\pi$
$997$		−	466609.i		−	0.469421i	0.972065	−	0.234711i	$-0.0754142\pi$
$998$		−	680488.i		−	0.683219i
$999$		−	711518.i		−	0.712943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.c.a.229.4	yes	48
5.4	even	2	inner	230.5.c.a.229.45	yes	48
23.22	odd	2	inner	230.5.c.a.229.46	yes	48
115.114	odd	2	inner	230.5.c.a.229.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.c.a.229.3	✓	48	115.114	odd	2	inner
230.5.c.a.229.4	yes	48	1.1	even	1	trivial
230.5.c.a.229.45	yes	48	5.4	even	2	inner
230.5.c.a.229.46	yes	48	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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.82843i q^{2} +15.3728i q^{3} -8.00000 q^{4} +(-24.9424 - 1.69556i) q^{5} -43.4808 q^{6} -85.1277 q^{7} -22.6274i q^{8} -155.323 q^{9} +O(q^{10})\)	\(q+2.82843i q^{2} +15.3728i q^{3} -8.00000 q^{4} +(-24.9424 - 1.69556i) q^{5} -43.4808 q^{6} -85.1277 q^{7} -22.6274i q^{8} -155.323 q^{9} +(4.79578 - 70.5479i) q^{10} +59.9093i q^{11} -122.982i q^{12} +296.626i q^{13} -240.778i q^{14} +(26.0656 - 383.435i) q^{15} +64.0000 q^{16} +408.596 q^{17} -439.319i q^{18} +18.6778i q^{19} +(199.539 + 13.5645i) q^{20} -1308.65i q^{21} -169.449 q^{22} +(-146.668 + 508.261i) q^{23} +347.847 q^{24} +(619.250 + 84.5830i) q^{25} -838.986 q^{26} -1142.55i q^{27} +681.022 q^{28} -895.716 q^{29} +(1084.52 + 73.7246i) q^{30} +578.910 q^{31} +181.019i q^{32} -920.974 q^{33} +1155.68i q^{34} +(2123.29 + 144.340i) q^{35} +1242.58 q^{36} +622.745 q^{37} -52.8288 q^{38} -4559.98 q^{39} +(-38.3663 + 564.383i) q^{40} -1791.23 q^{41} +3701.43 q^{42} -572.052 q^{43} -479.275i q^{44} +(3874.13 + 263.360i) q^{45} +(-1437.58 - 414.840i) q^{46} -2218.30i q^{47} +983.859i q^{48} +4845.73 q^{49} +(-239.237 + 1751.50i) q^{50} +6281.26i q^{51} -2373.01i q^{52} -3715.77 q^{53} +3231.62 q^{54} +(101.580 - 1494.28i) q^{55} +1926.22i q^{56} -287.130 q^{57} -2533.47i q^{58} +2380.82 q^{59} +(-208.525 + 3067.48i) q^{60} +2027.08i q^{61} +1637.41i q^{62} +13222.3 q^{63} -512.000 q^{64} +(502.949 - 7398.58i) q^{65} -2604.91i q^{66} -946.554 q^{67} -3268.77 q^{68} +(-7813.40 - 2254.70i) q^{69} +(-408.254 + 6005.58i) q^{70} +3822.76 q^{71} +3514.56i q^{72} +86.9828i q^{73} +1761.39i q^{74} +(-1300.28 + 9519.61i) q^{75} -149.422i q^{76} -5099.95i q^{77} -12897.6i q^{78} -7860.70i q^{79} +(-1596.32 - 108.516i) q^{80} +4983.05 q^{81} -5066.38i q^{82} +8551.78 q^{83} +10469.2i q^{84} +(-10191.4 - 692.801i) q^{85} -1618.01i q^{86} -13769.7i q^{87} +1355.59 q^{88} +1082.78i q^{89} +(-744.895 + 10957.7i) q^{90} -25251.1i q^{91} +(1173.35 - 4066.09i) q^{92} +8899.47i q^{93} +6274.30 q^{94} +(31.6694 - 465.870i) q^{95} -2782.77 q^{96} -15153.5 q^{97} +13705.8i q^{98} -9305.29i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9}+O(q^{10}) \) 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9	\( 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9} + 3072 q^{16} + 512 q^{24} + 1488 q^{25} - 384 q^{26} - 2940 q^{29} + 4732 q^{31} + 2556 q^{35} + 12864 q^{36} + 2736 q^{39} + 828 q^{41} - 64 q^{46} + 32572 q^{49} - 3264 q^{50} + 10112 q^{54} + 12824 q^{55} + 7092 q^{59} - 24576 q^{64} + 14000 q^{69} - 6592 q^{70} - 12708 q^{71} + 24728 q^{75} - 13040 q^{81} - 15700 q^{85} - 9728 q^{94} - 46608 q^{95} - 4096 q^{96}+O(q^{100}) \) 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9 + 3072 * q^16 + 512 * q^24 + 1488 * q^25 - 384 * q^26 - 2940 * q^29 + 4732 * q^31 + 2556 * q^35 + 12864 * q^36 + 2736 * q^39 + 828 * q^41 - 64 * q^46 + 32572 * q^49 - 3264 * q^50 + 10112 * q^54 + 12824 * q^55 + 7092 * q^59 - 24576 * q^64 + 14000 * q^69 - 6592 * q^70 - 12708 * q^71 + 24728 * q^75 - 13040 * q^81 - 15700 * q^85 - 9728 * q^94 - 46608 * q^95 - 4096 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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