LMFDB - Embedded newform 230.5.c.a.229.19

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			229.19
Character	$\chi$	$=$	230.229
Dual form			230.5.c.a.229.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843i q^{2} -1.19309i q^{3} -8.00000 q^{4} +(-1.65984 - 24.9448i) q^{5} -3.37456 q^{6} +28.6899 q^{7} +22.6274i q^{8} +79.5765 q^{9} +O(q^{10})$	\(q-2.82843i q^{2} -1.19309i q^{3} -8.00000 q^{4} +(-1.65984 - 24.9448i) q^{5} -3.37456 q^{6} +28.6899 q^{7} +22.6274i q^{8} +79.5765 q^{9} +(-70.5547 + 4.69474i) q^{10} -13.9487i q^{11} +9.54469i q^{12} -186.135i q^{13} -81.1473i q^{14} +(-29.7613 + 1.98033i) q^{15} +64.0000 q^{16} +309.261 q^{17} -225.076i q^{18} -55.0841i q^{19} +(13.2787 + 199.559i) q^{20} -34.2295i q^{21} -39.4528 q^{22} +(480.261 - 221.789i) q^{23} +26.9965 q^{24} +(-619.490 + 82.8089i) q^{25} -526.471 q^{26} -191.582i q^{27} -229.519 q^{28} -973.150 q^{29} +(5.60123 + 84.1778i) q^{30} -382.271 q^{31} -181.019i q^{32} -16.6420 q^{33} -874.723i q^{34} +(-47.6207 - 715.665i) q^{35} -636.612 q^{36} -1345.99 q^{37} -155.801 q^{38} -222.076 q^{39} +(564.437 - 37.5579i) q^{40} -103.473 q^{41} -96.8157 q^{42} +1376.78 q^{43} +111.589i q^{44} +(-132.084 - 1985.02i) q^{45} +(-627.315 - 1358.38i) q^{46} -1768.49i q^{47} -76.3575i q^{48} -1577.89 q^{49} +(234.219 + 1752.18i) q^{50} -368.976i q^{51} +1489.08i q^{52} +783.674 q^{53} -541.875 q^{54} +(-347.947 + 23.1526i) q^{55} +649.178i q^{56} -65.7201 q^{57} +2752.48i q^{58} -3562.36 q^{59} +(238.091 - 15.8427i) q^{60} -4456.11i q^{61} +1081.23i q^{62} +2283.04 q^{63} -512.000 q^{64} +(-4643.12 + 308.955i) q^{65} +47.0706i q^{66} +227.429 q^{67} -2474.09 q^{68} +(-264.614 - 572.993i) q^{69} +(-2024.21 + 134.692i) q^{70} -5193.33 q^{71} +1800.61i q^{72} -704.059i q^{73} +3807.03i q^{74} +(98.7982 + 739.105i) q^{75} +440.673i q^{76} -400.186i q^{77} +628.125i q^{78} +5466.30i q^{79} +(-106.230 - 1596.47i) q^{80} +6217.13 q^{81} +292.665i q^{82} -363.960 q^{83} +273.836i q^{84} +(-513.325 - 7714.48i) q^{85} -3894.12i q^{86} +1161.05i q^{87} +315.622 q^{88} +7685.89i q^{89} +(-5614.50 + 373.591i) q^{90} -5340.21i q^{91} +(-3842.09 + 1774.31i) q^{92} +456.083i q^{93} -5002.05 q^{94} +(-1374.06 + 91.4309i) q^{95} -215.972 q^{96} +3733.23 q^{97} +4462.95i q^{98} -1109.99i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$		−	1.19309i		−	0.132565i	−0.997801	−	0.0662826i	$-0.978886\pi$
$3$		−	1.19309i		−	0.132565i	0.997801	−	0.0662826i	$-0.0211139\pi$
$4$	−8.00000			−0.500000
$5$	−1.65984	−	24.9448i	−0.0663936	−	0.997794i
$5$	−1.65984	−	24.9448i	−0.0663936	−	0.997794i
$6$	−3.37456			−0.0937377
$7$	28.6899			0.585508			0.292754	−	0.956188i	$-0.405428\pi$
$7$	28.6899			0.585508			0.292754	+	0.956188i	$0.405428\pi$
$8$			22.6274i			0.353553i
$9$	79.5765			0.982426
$10$	−70.5547	+	4.69474i	−0.705547	+	0.0469474i
$11$		−	13.9487i		−	0.115278i	−0.998337	−	0.0576391i	$-0.981643\pi$
$11$		−	13.9487i		−	0.115278i	0.998337	−	0.0576391i	$-0.0183573\pi$
$12$			9.54469i			0.0662826i
$13$		−	186.135i		−	1.10139i	−0.834705	−	0.550697i	$-0.814362\pi$
$13$		−	186.135i		−	1.10139i	0.834705	−	0.550697i	$-0.185638\pi$
$14$		−	81.1473i		−	0.414017i
$15$	−29.7613	+	1.98033i	−0.132273	+	0.00880148i
$16$	64.0000			0.250000
$17$	309.261			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$17$	309.261			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$18$		−	225.076i		−	0.694680i
$19$		−	55.0841i		−	0.152588i	−0.997085	−	0.0762938i	$-0.975691\pi$
$19$		−	55.0841i		−	0.152588i	0.997085	−	0.0762938i	$-0.0243087\pi$
$20$	13.2787	+	199.559i	0.0331968	+	0.498897i
$21$		−	34.2295i		−	0.0776180i
$22$	−39.4528			−0.0815140
$23$	480.261	−	221.789i	0.907866	−	0.419261i
$23$	480.261	−	221.789i	0.907866	−	0.419261i
$24$	26.9965			0.0468689
$25$	−619.490	+	82.8089i	−0.991184	+	0.132494i
$26$	−526.471			−0.778803
$27$		−	191.582i		−	0.262801i
$28$	−229.519			−0.292754
$29$	−973.150			−1.15713			−0.578567	−	0.815635i	$-0.696388\pi$
$29$	−973.150			−1.15713			−0.578567	+	0.815635i	$0.696388\pi$
$30$	5.60123	+	84.1778i	0.00622359	+	0.0935309i
$31$	−382.271			−0.397785			−0.198892	−	0.980021i	$-0.563734\pi$
$31$	−382.271			−0.397785			−0.198892	+	0.980021i	$0.563734\pi$
$32$		−	181.019i		−	0.176777i
$33$	−16.6420			−0.0152819
$34$		−	874.723i		−	0.756681i
$35$	−47.6207	−	715.665i	−0.0388740	−	0.584216i
$36$	−636.612			−0.491213
$37$	−1345.99			−0.983191			−0.491596	−	0.870824i	$-0.663586\pi$
$37$	−1345.99			−0.983191			−0.491596	+	0.870824i	$0.663586\pi$
$38$	−155.801			−0.107896
$39$	−222.076			−0.146006
$40$	564.437	−	37.5579i	0.352773	−	0.0234737i
$41$	−103.473			−0.0615542			−0.0307771	−	0.999526i	$-0.509798\pi$
$41$	−103.473			−0.0615542			−0.0307771	+	0.999526i	$0.509798\pi$
$42$	−96.8157			−0.0548842
$43$	1376.78			0.744608			0.372304	−	0.928111i	$-0.378568\pi$
$43$	1376.78			0.744608			0.372304	+	0.928111i	$0.378568\pi$
$44$			111.589i			0.0576391i
$45$	−132.084	−	1985.02i	−0.0652269	−	0.980259i
$46$	−627.315	−	1358.38i	−0.296462	−	0.641958i
$47$		−	1768.49i		−	0.800584i	−0.916388	−	0.400292i	$-0.868909\pi$
$47$		−	1768.49i		−	0.800584i	0.916388	−	0.400292i	$-0.131091\pi$
$48$		−	76.3575i		−	0.0331413i
$49$	−1577.89			−0.657180
$50$	234.219	+	1752.18i	0.0936876	+	0.700873i
$51$		−	368.976i		−	0.141859i
$52$			1489.08i			0.550697i
$53$	783.674			0.278987			0.139493	−	0.990223i	$-0.455453\pi$
$53$	783.674			0.278987			0.139493	+	0.990223i	$0.455453\pi$
$54$	−541.875			−0.185828
$55$	−347.947	+	23.1526i	−0.115024	+	0.00765374i
$56$			649.178i			0.207008i
$57$	−65.7201			−0.0202278
$58$			2752.48i			0.818218i
$59$	−3562.36			−1.02337			−0.511687	−	0.859172i	$-0.670979\pi$
$59$	−3562.36			−1.02337			−0.511687	+	0.859172i	$0.670979\pi$
$60$	238.091	−	15.8427i	0.0661363	−	0.00440074i
$61$		−	4456.11i		−	1.19756i	−0.800915	−	0.598778i	$-0.795653\pi$
$61$		−	4456.11i		−	1.19756i	0.800915	−	0.598778i	$-0.204347\pi$
$62$			1081.23i			0.281276i
$63$	2283.04			0.575219
$64$	−512.000			−0.125000
$65$	−4643.12	+	308.955i	−1.09896	+	0.0731255i
$66$			47.0706i			0.0108059i
$67$	227.429			0.0506635			0.0253318	−	0.999679i	$-0.491936\pi$
$67$	227.429			0.0506635			0.0253318	+	0.999679i	$0.491936\pi$
$68$	−2474.09			−0.535054
$69$	−264.614	−	572.993i	−0.0555794	−	0.120351i
$70$	−2024.21	+	134.692i	−0.413103	+	0.0274881i
$71$	−5193.33			−1.03022			−0.515109	−	0.857125i	$-0.672249\pi$
$71$	−5193.33			−1.03022			−0.515109	+	0.857125i	$0.672249\pi$
$72$			1800.61i			0.347340i
$73$		−	704.059i		−	0.132118i	−0.997816	−	0.0660592i	$-0.978957\pi$
$73$		−	704.059i		−	0.132118i	0.997816	−	0.0660592i	$-0.0210426\pi$
$74$			3807.03i			0.695221i
$75$	98.7982	+	739.105i	0.0175641	+	0.131396i
$76$			440.673i			0.0762938i
$77$		−	400.186i		−	0.0674963i
$78$			628.125i			0.103242i
$79$			5466.30i			0.875870i	0.899007	+	0.437935i	$0.144290\pi$
$79$			5466.30i			0.875870i	−0.899007	+	0.437935i	$0.855710\pi$
$80$	−106.230	−	1596.47i	−0.0165984	−	0.249448i
$81$	6217.13			0.947588
$82$			292.665i			0.0435254i
$83$	−363.960			−0.0528321			−0.0264160	−	0.999651i	$-0.508409\pi$
$83$	−363.960			−0.0528321			−0.0264160	+	0.999651i	$0.508409\pi$
$84$			273.836i			0.0388090i
$85$	−513.325	−	7714.48i	−0.0710484	−	1.06775i
$86$		−	3894.12i		−	0.526518i
$87$			1161.05i			0.153396i
$88$	315.622			0.0407570
$89$			7685.89i			0.970319i	0.874426	+	0.485159i	$0.161238\pi$
$89$			7685.89i			0.970319i	−0.874426	+	0.485159i	$0.838762\pi$
$90$	−5614.50	+	373.591i	−0.693148	+	0.0461224i
$91$		−	5340.21i		−	0.644875i
$92$	−3842.09	+	1774.31i	−0.453933	+	0.209631i
$93$			456.083i			0.0527324i
$94$	−5002.05			−0.566099
$95$	−1374.06	+	91.4309i	−0.152251	+	0.0101308i
$96$	−215.972			−0.0234344
$97$	3733.23			0.396773			0.198386	−	0.980124i	$-0.436430\pi$
$97$	3733.23			0.396773			0.198386	+	0.980124i	$0.436430\pi$
$98$			4462.95i			0.464697i
$99$		−	1109.99i		−	0.113252i
$100$	4955.92	−	662.471i	0.495592	−	0.0662471i
$101$	778.596			0.0763255			0.0381627	−	0.999272i	$-0.487849\pi$
$101$	778.596			0.0763255			0.0381627	+	0.999272i	$0.487849\pi$
$102$	−1043.62			−0.100310
$103$	13426.8			1.26560			0.632802	−	0.774314i	$-0.281905\pi$
$103$	13426.8			1.26560			0.632802	+	0.774314i	$0.281905\pi$
$104$	4211.76			0.389401
$105$	−853.850	+	56.8155i	−0.0774467	+	0.00515334i
$106$		−	2216.56i		−	0.197273i
$107$	13917.7			1.21562			0.607811	−	0.794082i	$-0.292048\pi$
$107$	13917.7			1.21562			0.607811	+	0.794082i	$0.292048\pi$
$108$			1532.65i			0.131400i
$109$		−	8762.65i		−	0.737535i	−0.929522	−	0.368767i	$-0.879780\pi$
$109$		−	8762.65i		−	0.737535i	0.929522	−	0.368767i	$-0.120220\pi$
$110$	65.4853	+	984.143i	0.00541201	+	0.0813341i
$111$			1605.88i			0.130337i
$112$	1836.15			0.146377
$113$	−114.549			−0.00897090			−0.00448545	−	0.999990i	$-0.501428\pi$
$113$	−114.549			−0.00897090			−0.00448545	+	0.999990i	$0.501428\pi$
$114$			185.885i			0.0143032i
$115$	−6329.65	−	11611.9i	−0.478613	−	0.878026i
$116$	7785.20			0.578567
$117$		−	14812.0i		−	1.08204i
$118$			10075.9i			0.723635i
$119$	8872.68			0.626557
$120$	−44.8098	−	673.422i	−0.00311179	−	0.0467654i
$121$	14446.4			0.986711
$122$	−12603.8			−0.846800
$123$			123.452i			0.00815994i
$124$	3058.17			0.198892
$125$	3093.91	+	15315.6i	0.198010	+	0.980200i
$126$		−	6457.42i		−	0.406741i
$127$		−	16534.0i		−	1.02511i	−0.858655	−	0.512554i	$-0.828700\pi$
$127$		−	16534.0i		−	1.02511i	0.858655	−	0.512554i	$-0.171300\pi$
$128$			1448.15i			0.0883883i
$129$		−	1642.62i		−	0.0987091i
$130$	873.857	+	13132.7i	0.0517075	+	0.777084i
$131$	14981.6			0.873004			0.436502	−	0.899703i	$-0.356217\pi$
$131$	14981.6			0.873004			0.436502	+	0.899703i	$0.356217\pi$
$132$	133.136			0.00764094
$133$		−	1580.36i		−	0.0893413i
$134$		−	643.265i		−	0.0358245i
$135$	−4778.97	+	317.995i	−0.262221	+	0.0174483i
$136$			6997.79i			0.378341i
$137$	−10493.4			−0.559080			−0.279540	−	0.960134i	$-0.590182\pi$
$137$	−10493.4			−0.559080			−0.279540	+	0.960134i	$0.590182\pi$
$138$	−1620.67	+	748.440i	−0.0851012	+	0.0393006i
$139$	28379.4			1.46884			0.734418	−	0.678698i	$-0.237455\pi$
$139$	28379.4			1.46884			0.734418	+	0.678698i	$0.237455\pi$
$140$	380.965	+	5725.32i	0.0194370	+	0.292108i
$141$	−2109.96			−0.106130
$142$			14689.0i			0.728474i
$143$	−2596.34			−0.126967
$144$	5092.90			0.245607
$145$	1615.27	+	24275.1i	0.0768264	+	1.15458i
$146$	−1991.38			−0.0934218
$147$			1882.56i			0.0871192i
$148$	10767.9			0.491596
$149$			19296.8i			0.869187i	0.900627	+	0.434593i	$0.143108\pi$
$149$			19296.8i			0.869187i	−0.900627	+	0.434593i	$0.856892\pi$
$150$	2090.50	−	279.443i	0.0929113	−	0.0124197i
$151$	13446.6			0.589737			0.294868	−	0.955538i	$-0.404724\pi$
$151$	13446.6			0.589737			0.294868	+	0.955538i	$0.404724\pi$
$152$	1246.41			0.0539479
$153$	24610.0			1.05130
$154$	−1131.90			−0.0477271
$155$	634.509	+	9535.70i	0.0264104	+	0.396907i
$156$	1776.61			0.0730032
$157$	−20730.0			−0.841008			−0.420504	−	0.907291i	$-0.638147\pi$
$157$	−20730.0			−0.841008			−0.420504	+	0.907291i	$0.638147\pi$
$158$	15461.0			0.619333
$159$		−	934.990i		−	0.0369839i
$160$	−4515.50	+	300.463i	−0.176387	+	0.0117368i
$161$	13778.6	−	6363.11i	0.531563	−	0.245481i
$162$		−	17584.7i		−	0.670046i
$163$		−	17854.8i		−	0.672016i	−0.941859	−	0.336008i	$-0.890923\pi$
$163$		−	17854.8i		−	0.672016i	0.941859	−	0.336008i	$-0.109077\pi$
$164$	827.781			0.0307771
$165$	27.6230	+	415.131i	0.00101462	+	0.0152482i
$166$			1029.44i			0.0373579i
$167$			24275.0i			0.870414i	0.900330	+	0.435207i	$0.143325\pi$
$167$			24275.0i			0.870414i	−0.900330	+	0.435207i	$0.856675\pi$
$168$	774.526			0.0274421
$169$	−6085.41			−0.213067
$170$	−21819.8	+	1451.90i	−0.755011	+	0.0502388i
$171$		−	4383.41i		−	0.149906i
$172$	−11014.2			−0.372304
$173$		−	22882.7i		−	0.764565i	−0.924046	−	0.382282i	$-0.875138\pi$
$173$		−	22882.7i		−	0.764565i	0.924046	−	0.382282i	$-0.124862\pi$
$174$	3283.95			0.108467
$175$	−17773.1	+	2375.78i	−0.580346	+	0.0775765i
$176$		−	892.714i		−	0.0288196i
$177$			4250.21i			0.135664i
$178$	21739.0			0.686119
$179$	−29057.2			−0.906876			−0.453438	−	0.891288i	$-0.649803\pi$
$179$	−29057.2			−0.906876			−0.453438	+	0.891288i	$0.649803\pi$
$180$	1056.68	+	15880.2i	0.0326134	+	0.490129i
$181$		−	52452.9i		−	1.60108i	−0.599282	−	0.800538i	$-0.704547\pi$
$181$		−	52452.9i		−	1.60108i	0.599282	−	0.800538i	$-0.295453\pi$
$182$	−15104.4			−0.455995
$183$	−5316.52			−0.158754
$184$	5018.52	+	10867.1i	0.148231	+	0.320979i
$185$	2234.13	+	33575.5i	0.0652776	+	0.981022i
$186$	1290.00			0.0372874
$187$		−	4313.78i		−	0.123360i
$188$			14147.9i			0.400292i
$189$		−	5496.46i		−	0.153872i
$190$	258.606	+	3886.44i	0.00716359	+	0.107658i
$191$		−	17775.5i		−	0.487254i	−0.969869	−	0.243627i	$-0.921663\pi$
$191$		−	17775.5i		−	0.487254i	0.969869	−	0.243627i	$-0.0783372\pi$
$192$			610.860i			0.0165706i
$193$			56281.6i			1.51096i	0.655174	+	0.755478i	$0.272595\pi$
$193$			56281.6i			1.51096i	−0.655174	+	0.755478i	$0.727405\pi$
$194$		−	10559.2i		−	0.280561i
$195$	368.610	+	5539.64i	0.00969389	+	0.145684i
$196$	12623.1			0.328590
$197$			38045.2i			0.980319i	0.871633	+	0.490160i	$0.163062\pi$
$197$			38045.2i			0.980319i	−0.871633	+	0.490160i	$0.836938\pi$
$198$	−3139.52			−0.0800815
$199$			14457.7i			0.365084i	0.983198	+	0.182542i	$0.0584325\pi$
$199$			14457.7i			0.365084i	−0.983198	+	0.182542i	$0.941567\pi$
$200$	−1873.75	−	14017.5i	−0.0468438	−	0.350436i
$201$		−	271.342i		−	0.00671622i
$202$		−	2202.20i		−	0.0539703i
$203$	−27919.6			−0.677512
$204$			2951.80i			0.0709295i
$205$	171.748	+	2581.11i	0.00408681	+	0.0614184i
$206$		−	37976.7i		−	0.894917i
$207$	38217.5	−	17649.2i	0.891911	−	0.411893i
$208$		−	11912.7i		−	0.275348i
$209$	−768.350			−0.0175900
$210$	160.699	+	2415.05i	0.00364396	+	0.0547631i
$211$	−32830.9			−0.737424			−0.368712	−	0.929544i	$-0.620201\pi$
$211$	−32830.9			−0.737424			−0.368712	+	0.929544i	$0.620201\pi$
$212$	−6269.39			−0.139493
$213$			6196.09i			0.136571i
$214$		−	39365.1i		−	0.859574i
$215$	−2285.24	−	34343.6i	−0.0494373	−	0.742965i
$216$	4335.00			0.0929141
$217$	−10967.3			−0.232906
$218$	−24784.5			−0.521516
$219$	−840.003			−0.0175143
$220$	2783.58	−	185.220i	0.0575119	−	0.00382687i
$221$		−	57564.5i		−	1.17861i
$222$	4542.12			0.0921621
$223$		−	45121.3i		−	0.907344i	−0.891169	−	0.453672i	$-0.850114\pi$
$223$		−	45121.3i		−	0.907344i	0.891169	−	0.453672i	$-0.149886\pi$
$224$		−	5193.43i		−	0.103504i
$225$	−49296.9	+	6589.65i	−0.973765	+	0.130166i
$226$			323.995i			0.00634338i
$227$	41995.5			0.814987			0.407493	−	0.913208i	$-0.366403\pi$
$227$	41995.5			0.814987			0.407493	+	0.913208i	$0.366403\pi$
$228$	525.761			0.0101139
$229$			86160.1i			1.64299i	0.570215	+	0.821496i	$0.306860\pi$
$229$			86160.1i			1.64299i	−0.570215	+	0.821496i	$0.693140\pi$
$230$	−32843.4	+	17903.0i	−0.620858	+	0.338430i
$231$	−477.456			−0.00894766
$232$		−	22019.9i		−	0.409109i
$233$			96011.6i			1.76853i	0.466987	+	0.884264i	$0.345340\pi$
$233$			96011.6i			1.76853i	−0.466987	+	0.884264i	$0.654660\pi$
$234$	−41894.7			−0.765116
$235$	−44114.7	+	2935.41i	−0.798818	+	0.0531537i
$236$	28498.9			0.511687
$237$	6521.77			0.116110
$238$		−	25095.7i		−	0.443043i
$239$	−63284.1			−1.10790			−0.553948	−	0.832551i	$-0.686879\pi$
$239$	−63284.1			−1.10790			−0.553948	+	0.832551i	$0.686879\pi$
$240$	−1904.73	+	126.741i	−0.0330682	+	0.00220037i
$241$		−	10485.2i		−	0.180528i	−0.995918	−	0.0902638i	$-0.971229\pi$
$241$		−	10485.2i		−	0.180528i	0.995918	−	0.0902638i	$-0.0287710\pi$
$242$		−	40860.7i		−	0.697710i
$243$		−	22935.7i		−	0.388418i
$244$			35648.8i			0.598778i
$245$	2619.05	+	39360.2i	0.0436326	+	0.655730i
$246$	349.174			0.00576995
$247$	−10253.1			−0.168059
$248$		−	8649.81i		−	0.140638i
$249$			434.236i			0.00700369i
$250$	43319.1	−	8750.90i	0.693106	−	0.140014i
$251$		−	96830.8i		−	1.53697i	−0.639866	−	0.768487i	$-0.721010\pi$
$251$		−	96830.8i		−	1.53697i	0.639866	−	0.768487i	$-0.278990\pi$
$252$	−18264.3			−0.287609
$253$	−3093.66	−	6699.00i	−0.0483317	−	0.104657i
$254$	−46765.1			−0.724860
$255$	−9204.03	+	612.441i	−0.141546	+	0.00941854i
$256$	4096.00			0.0625000
$257$			99727.4i			1.50990i	0.655782	+	0.754950i	$0.272339\pi$
$257$			99727.4i			1.50990i	−0.655782	+	0.754950i	$0.727661\pi$
$258$	−4646.03			−0.0697979
$259$	−38616.3			−0.575666
$260$	37144.9	−	2471.64i	0.549481	−	0.0365627i
$261$	−77439.9			−1.13680
$262$		−	42374.4i		−	0.617307i
$263$	−16646.4			−0.240662			−0.120331	−	0.992734i	$-0.538396\pi$
$263$	−16646.4			−0.240662			−0.120331	+	0.992734i	$0.538396\pi$
$264$		−	376.565i		−	0.00540296i
$265$	−1300.77	−	19548.6i	−0.0185229	−	0.278371i
$266$	−4469.93			−0.0631738
$267$	9169.93			0.128630
$268$	−1819.43			−0.0253318
$269$	5401.90			0.0746521			0.0373261	−	0.999303i	$-0.488116\pi$
$269$	5401.90			0.0746521			0.0373261	+	0.999303i	$0.488116\pi$
$270$	899.426	+	13517.0i	0.0123378	+	0.185418i
$271$	79510.9			1.08265			0.541325	−	0.840814i	$-0.317923\pi$
$271$	79510.9			1.08265			0.541325	+	0.840814i	$0.317923\pi$
$272$	19792.7			0.267527
$273$	−6371.33			−0.0854879
$274$			29679.7i			0.395329i
$275$	1155.07	+	8641.06i	0.0152737	+	0.114262i
$276$	2116.91	+	4583.94i	0.0277897	+	0.0601757i
$277$		−	15846.1i		−	0.206520i	−0.994654	−	0.103260i	$-0.967073\pi$
$277$		−	15846.1i		−	0.206520i	0.994654	−	0.103260i	$-0.0329274\pi$
$278$		−	80269.0i		−	1.03862i
$279$	−30419.8			−0.390794
$280$	16193.6	−	1077.53i	0.206552	−	0.0137440i
$281$		−	107842.i		−	1.36576i	−0.730531	−	0.682879i	$-0.760727\pi$
$281$		−	107842.i		−	1.36576i	0.730531	−	0.682879i	$-0.239273\pi$
$282$			5967.87i			0.0750449i
$283$	51447.1			0.642374			0.321187	−	0.947016i	$-0.395918\pi$
$283$	51447.1			0.642374			0.321187	+	0.947016i	$0.395918\pi$
$284$	41546.7			0.515109
$285$	109.085	+	1639.38i	0.00134300	+	0.0201832i
$286$			7343.56i			0.0897790i
$287$	−2968.62			−0.0360405
$288$		−	14404.9i		−	0.173670i
$289$	12121.6			0.145133
$290$	68660.3	−	4568.69i	0.816412	−	0.0543245i
$291$		−	4454.07i		−	0.0525982i
$292$			5632.47i			0.0660592i
$293$	−130339.			−1.51824			−0.759121	−	0.650950i	$-0.774371\pi$
$293$	−130339.			−1.51824			−0.759121	+	0.650950i	$0.774371\pi$
$294$	5324.68			0.0616026
$295$	5912.96	+	88862.6i	0.0679455	+	1.02112i
$296$		−	30456.2i		−	0.347611i
$297$	−2672.31			−0.0302952
$298$	54579.6			0.614608
$299$	−41282.8	−	89393.6i	−0.461772	−	0.999917i
$300$	−790.385	−	5912.84i	−0.00878206	−	0.0656982i
$301$	39499.7			0.435974
$302$		−	38032.7i		−	0.417007i
$303$		−	928.932i		−	0.0101181i
$304$		−	3525.38i		−	0.0381469i
$305$	−111157.	+	7396.43i	−1.19491	+	0.0795101i
$306$		−	69607.5i		−	0.743384i
$307$		−	29809.2i		−	0.316281i	−0.987417	−	0.158141i	$-0.949450\pi$
$307$		−	29809.2i		−	0.316281i	0.987417	−	0.158141i	$-0.0505499\pi$
$308$			3201.49i			0.0337482i
$309$		−	16019.3i		−	0.167775i
$310$	26971.0	−	1794.66i	0.280656	−	0.0186750i
$311$	−47276.4			−0.488792			−0.244396	−	0.969676i	$-0.578590\pi$
$311$	−47276.4			−0.488792			−0.244396	+	0.969676i	$0.578590\pi$
$312$		−	5025.00i		−	0.0516210i
$313$	56302.6			0.574698			0.287349	−	0.957826i	$-0.407226\pi$
$313$	56302.6			0.574698			0.287349	+	0.957826i	$0.407226\pi$
$314$			58633.3i			0.594682i
$315$	−3789.49	−	56950.1i	−0.0381909	−	0.573949i
$316$		−	43730.4i		−	0.437935i
$317$		−	22207.7i		−	0.220996i	−0.993876	−	0.110498i	$-0.964755\pi$
$317$		−	22207.7i		−	0.220996i	0.993876	−	0.110498i	$-0.0352446\pi$
$318$	−2644.55			−0.0261516
$319$			13574.1i			0.133392i
$320$	849.838	+	12771.8i	0.00829920	+	0.124724i
$321$		−	16605.0i		−	0.161149i
$322$	−17997.6	−	38971.9i	−0.173581	−	0.375872i
$323$		−	17035.4i		−	0.163285i
$324$	−49737.0			−0.473794
$325$	15413.7	+	115309.i	0.145928	+	1.09168i
$326$	−50501.0			−0.475187
$327$	−10454.6			−0.0977714
$328$		−	2341.32i		−	0.0217627i
$329$		−	50737.8i		−	0.468749i
$330$	1174.17	−	78.1296i	0.0107821	−	0.000717444i
$331$	210755.			1.92364			0.961818	−	0.273690i	$-0.0882442\pi$
$331$	210755.			1.92364			0.961818	+	0.273690i	$0.0882442\pi$
$332$	2911.68			0.0264160
$333$	−107109.			−0.965913
$334$	68660.0			0.615476
$335$	−377.495	−	5673.17i	−0.00336373	−	0.0505517i
$336$		−	2190.69i		−	0.0194045i
$337$	45019.0			0.396402			0.198201	−	0.980161i	$-0.436490\pi$
$337$	45019.0			0.396402			0.198201	+	0.980161i	$0.436490\pi$
$338$			17212.1i			0.150661i
$339$			136.667i			0.00118923i
$340$	4106.60	+	61715.8i	0.0355242	+	0.533874i
$341$			5332.17i			0.0458559i
$342$	−12398.1			−0.106000
$343$	−114154.			−0.970292
$344$			31153.0i			0.263259i
$345$	−13854.0	+	7551.82i	−0.116396	+	0.0634474i
$346$	−64721.9			−0.540629
$347$			71870.9i			0.596890i	0.954427	+	0.298445i	$0.0964679\pi$
$347$			71870.9i			0.596890i	−0.954427	+	0.298445i	$0.903532\pi$
$348$		−	9288.42i		−	0.0766979i
$349$	129213.			1.06086			0.530428	−	0.847730i	$-0.322031\pi$
$349$	129213.			1.06086			0.530428	+	0.847730i	$0.322031\pi$
$350$	6719.72	+	50269.9i	0.0548548	+	0.410367i
$351$	−35660.1			−0.289447
$352$	−2524.98			−0.0203785
$353$			1173.49i			0.00941740i	0.999989	+	0.00470870i	$0.00149883\pi$
$353$			1173.49i			0.00941740i	−0.999989	+	0.00470870i	$0.998501\pi$
$354$	12021.4			0.0959287
$355$	8620.10	+	129547.i	0.0683999	+	1.02795i
$356$		−	61487.2i		−	0.485159i
$357$		−	10585.9i		−	0.0830596i
$358$			82186.2i			0.641258i
$359$			195019.i			1.51317i	0.653893	+	0.756587i	$0.273135\pi$
$359$			195019.i			1.51317i	−0.653893	+	0.756587i	$0.726865\pi$
$360$	44916.0	−	2988.73i	0.346574	−	0.0230612i
$361$	127287.			0.976717
$362$	−148359.			−1.13213
$363$		−	17235.8i		−	0.130803i
$364$			42721.7i			0.322437i
$365$	−17562.6	+	1168.63i	−0.131827	+	0.00877182i
$366$			15037.4i			0.112256i
$367$	244091.			1.81225			0.906127	−	0.423005i	$-0.139025\pi$
$367$	244091.			1.81225			0.906127	+	0.423005i	$0.139025\pi$
$368$	30736.7	−	14194.5i	0.226966	−	0.104815i
$369$	−8233.99			−0.0604725
$370$	94965.8	−	6319.07i	0.693687	−	0.0461583i
$371$	22483.5			0.163349
$372$		−	3648.66i		−	0.0263662i
$373$	−159180.			−1.14411			−0.572057	−	0.820214i	$-0.693854\pi$
$373$	−159180.			−1.14411			−0.572057	+	0.820214i	$0.693854\pi$
$374$	−12201.2			−0.0872288
$375$	18272.9	−	3691.30i	0.129940	−	0.0262492i
$376$	40016.4			0.283049
$377$			181138.i			1.27446i
$378$	−15546.3			−0.108804
$379$			154471.i			1.07539i	0.843138	+	0.537697i	$0.180705\pi$
$379$			154471.i			1.07539i	−0.843138	+	0.537697i	$0.819295\pi$
$380$	10992.5	−	731.447i	0.0761255	−	0.00506542i
$381$	−19726.4			−0.135893
$382$	−50276.7			−0.344540
$383$	58535.9			0.399048			0.199524	−	0.979893i	$-0.436060\pi$
$383$	58535.9			0.399048			0.199524	+	0.979893i	$0.436060\pi$
$384$	1727.77			0.0117172
$385$	−9982.57	+	664.245i	−0.0673474	+	0.00448133i
$386$	159188.			1.06841
$387$	109559.			0.731523
$388$	−29865.9			−0.198386
$389$			164288.i			1.08569i	0.839831	+	0.542847i	$0.182654\pi$
$389$			164288.i			1.08569i	−0.839831	+	0.542847i	$0.817346\pi$
$390$	15668.5	−	1042.59i	0.103014	−	0.00685462i
$391$	148526.	−	68590.8i	0.971515	−	0.448655i
$392$		−	35703.6i		−	0.232348i
$393$		−	17874.4i		−	0.115730i
$394$	107608.			0.693190
$395$	136356.	−	9073.19i	0.873937	−	0.0581522i
$396$			8879.89i			0.0566262i
$397$			249567.i			1.58346i	0.610874	+	0.791728i	$0.290818\pi$
$397$			249567.i			1.58346i	−0.610874	+	0.791728i	$0.709182\pi$
$398$	40892.5			0.258153
$399$	−1885.50			−0.0118435
$400$	−39647.4	+	5299.77i	−0.247796	+	0.0331236i
$401$			209546.i			1.30314i	0.758590	+	0.651569i	$0.225889\pi$
$401$			209546.i			1.30314i	−0.758590	+	0.651569i	$0.774111\pi$
$402$	−767.471			−0.00474908
$403$			71154.2i			0.438118i
$404$	−6228.77			−0.0381627
$405$	−10319.4	−	155085.i	−0.0629138	−	0.945497i
$406$			78968.5i			0.479073i
$407$			18774.7i			0.113341i
$408$	8348.96			0.0501548
$409$	31205.4			0.186545			0.0932725	−	0.995641i	$-0.470267\pi$
$409$	31205.4			0.186545			0.0932725	+	0.995641i	$0.470267\pi$
$410$	7300.47	−	485.777i	0.0434293	−	0.00288981i
$411$			12519.5i			0.0741145i
$412$	−107414.			−0.632802
$413$	−102204.			−0.599194
$414$	−49919.5	−	108095.i	−0.291253	−	0.630676i
$415$	604.116	+	9078.93i	0.00350771	+	0.0527155i
$416$	−33694.1			−0.194701
$417$		−	33859.0i		−	0.194716i
$418$			2173.22i			0.0124380i
$419$		−	177765.i		−	1.01256i	−0.862371	−	0.506278i	$-0.831021\pi$
$419$		−	177765.i		−	1.01256i	0.862371	−	0.506278i	$-0.168979\pi$
$420$	6830.80	−	454.524i	0.0387233	−	0.00257667i
$421$		−	71925.6i		−	0.405807i	−0.979199	−	0.202903i	$-0.934962\pi$
$421$		−	71925.6i		−	0.405807i	0.979199	−	0.202903i	$-0.0650378\pi$
$422$			92859.7i			0.521438i
$423$		−	140730.i		−	0.786515i
$424$			17732.5i			0.0986367i
$425$	−191584.	+	25609.6i	−1.06067	+	0.141783i
$426$	17525.2			0.0965703
$427$		−	127845.i		−	0.701179i
$428$	−111341.			−0.607811
$429$			3097.66i			0.0168313i
$430$	−97138.3	+	6463.63i	−0.525356	+	0.0349574i
$431$		−	239858.i		−	1.29122i	−0.763668	−	0.645609i	$-0.776604\pi$
$431$		−	239858.i		−	1.29122i	0.763668	−	0.645609i	$-0.223396\pi$
$432$		−	12261.2i		−	0.0657002i
$433$	64245.2			0.342661			0.171331	−	0.985214i	$-0.445193\pi$
$433$	64245.2			0.342661			0.171331	+	0.985214i	$0.445193\pi$
$434$			31020.3i			0.164690i
$435$	28962.3	−	1927.16i	0.153057	−	0.0101845i
$436$			70101.2i			0.368767i
$437$	−12217.1	−	26454.8i	−0.0639741	−	0.138529i
$438$			2375.89i			0.0123845i
$439$	259393.			1.34595			0.672975	−	0.739665i	$-0.265016\pi$
$439$	259393.			1.34595			0.672975	+	0.739665i	$0.265016\pi$
$440$	−523.883	−	7873.15i	−0.00270601	−	0.0406671i
$441$	−125563.			−0.645631
$442$	−162817.			−0.833403
$443$		−	242470.i		−	1.23552i	−0.786365	−	0.617762i	$-0.788039\pi$
$443$		−	242470.i		−	1.23552i	0.786365	−	0.617762i	$-0.211961\pi$
$444$		−	12847.0i		−	0.0651684i
$445$	191723.	−	12757.4i	0.968178	−	0.0644230i
$446$	−127622.			−0.641589
$447$	23022.8			0.115224
$448$	−14689.2			−0.0731885
$449$	−87673.3			−0.434885			−0.217443	−	0.976073i	$-0.569771\pi$
$449$	−87673.3			−0.434885			−0.217443	+	0.976073i	$0.569771\pi$
$450$	18638.3	+	139433.i	0.0920412	+	0.688556i
$451$			1443.30i			0.00709586i
$452$	916.395			0.00448545
$453$		−	16042.9i		−	0.0781786i
$454$		−	118781.i		−	0.576283i
$455$	−133211.	+	8863.89i	−0.643452	+	0.0428156i
$456$		−	1487.08i		−	0.00715161i
$457$	272494.			1.30474			0.652372	−	0.757899i	$-0.273774\pi$
$457$	272494.			1.30474			0.652372	+	0.757899i	$0.273774\pi$
$458$	243698.			1.16177
$459$		−	59248.8i		−	0.281225i
$460$	50637.2	+	92895.2i	0.239306	+	0.439013i
$461$	98251.5			0.462314			0.231157	−	0.972916i	$-0.425749\pi$
$461$	98251.5			0.462314			0.231157	+	0.972916i	$0.425749\pi$
$462$			1350.45i			0.00632695i
$463$		−	196181.i		−	0.915157i	−0.889169	−	0.457578i	$-0.848717\pi$
$463$		−	196181.i		−	0.915157i	0.889169	−	0.457578i	$-0.151283\pi$
$464$	−62281.6			−0.289284
$465$	11376.9	−	757.024i	0.0526161	−	0.00350110i
$466$	271562.			1.25054
$467$	225224.			1.03271			0.516357	−	0.856373i	$-0.327288\pi$
$467$	225224.			1.03271			0.516357	+	0.856373i	$0.327288\pi$
$468$			118496.i			0.541019i
$469$	6524.90			0.0296639
$470$	8302.60	+	124775.i	0.0375853	+	0.564850i
$471$			24732.7i			0.111488i
$472$		−	80607.1i		−	0.361817i
$473$		−	19204.3i		−	0.0858371i
$474$		−	18446.3i		−	0.0821020i
$475$	4561.46	+	34124.1i	0.0202170	+	0.151242i
$476$	−70981.4			−0.313279
$477$	62362.1			0.274084
$478$			178995.i			0.783401i
$479$		−	16780.0i		−	0.0731343i	−0.999331	−	0.0365671i	$-0.988358\pi$
$479$		−	16780.0i		−	0.0731343i	0.999331	−	0.0365671i	$-0.0116423\pi$
$480$	358.479	+	5387.38i	0.00155590	+	0.0233827i
$481$			250536.i			1.08288i
$482$	−29656.7			−0.127652
$483$	−7591.74	−	16439.1i	−0.0325422	−	0.0704667i
$484$	−115571.			−0.493355
$485$	−6196.58	−	93124.9i	−0.0263432	−	0.395897i
$486$	−64871.9			−0.274653
$487$		−	333008.i		−	1.40409i	−0.712130	−	0.702047i	$-0.752270\pi$
$487$		−	333008.i		−	1.40409i	0.712130	−	0.702047i	$-0.247730\pi$
$488$	100830.			0.423400
$489$	−21302.3			−0.0890859
$490$	111327.	−	7407.78i	0.463671	−	0.0308529i
$491$	−226203.			−0.938288			−0.469144	−	0.883122i	$-0.655437\pi$
$491$	−226203.			−0.938288			−0.469144	+	0.883122i	$0.655437\pi$
$492$		−	987.614i		−	0.00407997i
$493$	−300958.			−1.23826
$494$			29000.2i			0.118836i
$495$	−27688.4	+	1842.40i	−0.113002	+	0.00751924i
$496$	−24465.4			−0.0994462
$497$	−148996.			−0.603201
$498$	1228.20			0.00495236
$499$	−161175.			−0.647285			−0.323643	−	0.946179i	$-0.604908\pi$
$499$	−161175.			−0.647285			−0.323643	+	0.946179i	$0.604908\pi$
$500$	−24751.3	−	122525.i	−0.0990051	−	0.490100i
$501$	28962.1			0.115387
$502$	−273879.			−1.08680
$503$	369427.			1.46013			0.730067	−	0.683375i	$-0.239489\pi$
$503$	369427.			1.46013			0.730067	+	0.683375i	$0.239489\pi$
$504$			51659.4i			0.203371i
$505$	−1292.35	−	19422.0i	−0.00506753	−	0.0761571i
$506$	−18947.6	+	8750.20i	−0.0740038	+	0.0341757i
$507$			7260.41i			0.0282453i
$508$			132272.i			0.512554i
$509$	−184112.			−0.710635			−0.355318	−	0.934746i	$-0.615627\pi$
$509$	−184112.			−0.710635			−0.355318	+	0.934746i	$0.615627\pi$
$510$	1732.24	+	26032.9i	0.00665991	+	0.100088i
$511$		−	20199.4i		−	0.0773564i
$512$		−	11585.2i		−	0.0441942i
$513$	−10553.1			−0.0401001
$514$	282072.			1.06766
$515$	−22286.3	−	334929.i	−0.0840280	−	1.26281i
$516$			13140.9i			0.0493546i
$517$	−24668.1			−0.0922899
$518$			109223.i			0.407058i
$519$	−27301.0			−0.101355
$520$	−6990.86	−	105062.i	−0.0258538	−	0.388542i
$521$			231924.i			0.854416i	0.904153	+	0.427208i	$0.140503\pi$
$521$			231924.i			0.854416i	−0.904153	+	0.427208i	$0.859497\pi$
$522$			219033.i			0.803839i
$523$	53021.8			0.193843			0.0969217	−	0.995292i	$-0.469100\pi$
$523$	53021.8			0.193843			0.0969217	+	0.995292i	$0.469100\pi$
$524$	−119853.			−0.436502
$525$	2834.51	+	21204.8i	0.0102839	+	0.0769337i
$526$			47083.0i			0.170174i
$527$	−118222.			−0.425673
$528$	−1065.09			−0.00382047
$529$	181460.	−	213033.i	0.648440	−	0.761266i
$530$	−55291.8	+	3679.14i	−0.196838	+	0.0130977i
$531$	−283481.			−1.00539
$532$			12642.9i			0.0446706i
$533$			19259.9i			0.0677954i
$534$		−	25936.5i		−	0.0909554i
$535$	−23101.1	−	347174.i	−0.0807095	−	1.21294i
$536$			5146.12i			0.0179123i
$537$			34667.8i			0.120220i
$538$		−	15278.9i		−	0.0527870i
$539$			22009.5i			0.0757586i
$540$	38231.8	−	2543.96i	0.131110	−	0.00872414i
$541$	−437046.			−1.49325			−0.746624	−	0.665246i	$-0.768327\pi$
$541$	−437046.			−1.49325			−0.746624	+	0.665246i	$0.768327\pi$
$542$		−	224891.i		−	0.765549i
$543$	−62580.8			−0.212247
$544$		−	55982.3i		−	0.189170i
$545$	−218583.	+	14544.6i	−0.735907	+	0.0489676i
$546$			18020.8i			0.0604491i
$547$		−	449791.i		−	1.50327i	−0.659581	−	0.751634i	$-0.729266\pi$
$547$		−	449791.i		−	1.50327i	0.659581	−	0.751634i	$-0.270734\pi$
$548$	83947.0			0.279540
$549$		−	354601.i		−	1.17651i
$550$	24440.6	−	3267.04i	0.0807954	−	0.0108001i
$551$			53605.1i			0.176564i
$552$	12965.3	−	5987.52i	0.0425506	−	0.0196503i
$553$			156828.i			0.512829i
$554$	−44819.5			−0.146032
$555$	40058.4	−	2665.51i	0.130049	−	0.00865354i
$556$	−227035.			−0.734418
$557$	370241.			1.19337			0.596684	−	0.802476i	$-0.296485\pi$
$557$	370241.			1.19337			0.596684	+	0.802476i	$0.296485\pi$
$558$			86040.3i			0.276333i
$559$		−	256268.i		−	0.820107i
$560$	−3047.72	−	45802.5i	−0.00971850	−	0.146054i
$561$	−5146.72			−0.0163533
$562$	−305022.			−0.965737
$563$	−5971.73			−0.0188401			−0.00942005	−	0.999956i	$-0.502999\pi$
$563$	−5971.73			−0.0188401			−0.00942005	+	0.999956i	$0.502999\pi$
$564$	16879.7			0.0530648
$565$	190.134	+	2857.42i	0.000595610	+	0.00895110i
$566$		−	145514.i		−	0.454227i
$567$	178369.			0.554821
$568$		−	117512.i		−	0.364237i
$569$		−	342314.i		−	1.05730i	−0.848839	−	0.528652i	$-0.822698\pi$
$569$		−	342314.i		−	1.05730i	0.848839	−	0.528652i	$-0.177302\pi$
$570$	4636.86	−	308.539i	0.0142717	−	0.000949642i
$571$			402571.i			1.23473i	0.786678	+	0.617363i	$0.211799\pi$
$571$			402571.i			1.23473i	−0.786678	+	0.617363i	$0.788201\pi$
$572$	20770.7			0.0634833
$573$	−21207.7			−0.0645928
$574$			8396.52i			0.0254845i
$575$	−279151.	+	177166.i	−0.844312	+	0.535852i
$576$	−40743.2			−0.122803
$577$			300558.i			0.902770i	0.892329	+	0.451385i	$0.149070\pi$
$577$			300558.i			0.902770i	−0.892329	+	0.451385i	$0.850930\pi$
$578$		−	34285.1i		−	0.102624i
$579$	67148.8			0.200300
$580$	−12922.2	−	194201.i	−0.0384132	−	0.577291i
$581$	−10442.0			−0.0309336
$582$	−12598.0			−0.0371926
$583$		−	10931.2i		−	0.0321611i
$584$	15931.0			0.0467109
$585$	−369483.	+	24585.6i	−1.07965	+	0.0718404i
$586$			368656.i			1.07356i
$587$			228630.i			0.663523i	0.943363	+	0.331762i	$0.107643\pi$
$587$			228630.i			0.663523i	−0.943363	+	0.331762i	$0.892357\pi$
$588$		−	15060.5i		−	0.0435596i
$589$			21057.1i			0.0606971i
$590$	251341.	−	16724.4i	0.722038	−	0.0480447i
$591$	45391.2			0.129956
$592$	−86143.3			−0.245798
$593$			335054.i			0.952807i	0.879227	+	0.476404i	$0.158060\pi$
$593$			335054.i			0.952807i	−0.879227	+	0.476404i	$0.841940\pi$
$594$			7558.43i			0.0214219i
$595$	−14727.2	−	221328.i	−0.0415994	−	0.625175i
$596$		−	154375.i		−	0.434593i
$597$	17249.3			0.0483974
$598$	−252843.	+	116765.i	−0.707048	+	0.326522i
$599$	368031.			1.02572			0.512862	−	0.858471i	$-0.328585\pi$
$599$	368031.			1.02572			0.512862	+	0.858471i	$0.328585\pi$
$600$	−16724.0	+	2235.55i	−0.0464556	+	0.00620985i
$601$	−105250.			−0.291390			−0.145695	−	0.989330i	$-0.546542\pi$
$601$	−105250.			−0.291390			−0.145695	+	0.989330i	$0.546542\pi$
$602$		−	111722.i		−	0.308280i
$603$	18098.0			0.0497732
$604$	−107573.			−0.294868
$605$	−23978.8	−	360364.i	−0.0655113	−	0.984534i
$606$	−2627.42			−0.00715457
$607$			537037.i			1.45756i	0.684748	+	0.728780i	$0.259912\pi$
$607$			537037.i			1.45756i	−0.684748	+	0.728780i	$0.740088\pi$
$608$	−9971.29			−0.0269739
$609$			33310.5i			0.0898144i
$610$	20920.2	+	314399.i	0.0562221	+	0.844931i
$611$	−329179.			−0.881758
$612$	−196880.			−0.525652
$613$	686826.			1.82779			0.913894	−	0.405954i	$-0.133061\pi$
$613$	686826.			1.82779			0.913894	+	0.405954i	$0.133061\pi$
$614$	−84313.1			−0.223645
$615$	3079.48	−	204.910i	0.00814193	−	0.000541768i
$616$	9055.17			0.0238636
$617$	236076.			0.620128			0.310064	−	0.950716i	$-0.399650\pi$
$617$	236076.			0.620128			0.310064	+	0.950716i	$0.399650\pi$
$618$	−45309.5			−0.118635
$619$		−	284526.i		−	0.742576i	−0.928518	−	0.371288i	$-0.878916\pi$
$619$		−	284526.i		−	0.742576i	0.928518	−	0.371288i	$-0.121084\pi$
$620$	−5076.08	−	76285.6i	−0.0132052	−	0.198454i
$621$	−42490.7	−	92009.2i	−0.110182	−	0.238588i
$622$			133718.i			0.345628i
$623$			220507.i			0.568129i
$624$	−14212.8			−0.0365016
$625$	376910.	−	102599.i	0.964891	−	0.262652i
$626$		−	159248.i		−	0.406373i
$627$			916.708i			0.00233182i
$628$	165840.			0.420504
$629$	−416262.			−1.05212
$630$	−161079.	+	10718.3i	−0.405844	+	0.0270050i
$631$			244401.i			0.613825i	0.951738	+	0.306912i	$0.0992958\pi$
$631$			244401.i			0.613825i	−0.951738	+	0.306912i	$0.900704\pi$
$632$	−123688.			−0.309667
$633$			39170.0i			0.0977567i
$634$	−62812.8			−0.156268
$635$	−412437.	+	27443.7i	−1.02285	+	0.0680606i
$636$			7479.92i			0.0184920i
$637$			293701.i			0.723814i
$638$	38393.5			0.0943227
$639$	−413267.			−1.01211
$640$	36124.0	−	2403.71i	0.0881933	−	0.00586842i
$641$		−	105817.i		−	0.257537i	−0.991675	−	0.128769i	$-0.958898\pi$
$641$		−	105817.i		−	0.257537i	0.991675	−	0.128769i	$-0.0411025\pi$
$642$	−46965.9			−0.113950
$643$	226174.			0.547043			0.273522	−	0.961866i	$-0.411812\pi$
$643$	226174.			0.547043			0.273522	+	0.961866i	$0.411812\pi$
$644$	−110229.	+	50904.9i	−0.265781	+	0.122740i
$645$	−40974.8	+	2726.48i	−0.0984913	+	0.00655366i
$646$	−48183.4			−0.115460
$647$		−	800374.i		−	1.91198i	−0.293391	−	0.955992i	$-0.594784\pi$
$647$		−	800374.i		−	1.91198i	0.293391	−	0.955992i	$-0.405216\pi$
$648$			140678.i			0.335023i
$649$			49690.2i			0.117973i
$650$	326143.	−	43596.5i	0.771937	−	0.103187i
$651$			13085.0i			0.0308753i
$652$			142838.i			0.336008i
$653$		−	448992.i		−	1.05296i	−0.850188	−	0.526480i	$-0.823512\pi$
$653$		−	448992.i		−	1.05296i	0.850188	−	0.526480i	$-0.176488\pi$
$654$			29570.1i			0.0691348i
$655$	−24867.1	−	373714.i	−0.0579619	−	0.871078i
$656$	−6622.25			−0.0153885
$657$		−	56026.6i		−	0.129797i
$658$	−143508.			−0.331455
$659$			767179.i			1.76655i	0.468856	+	0.883275i	$0.344666\pi$
$659$			767179.i			1.76655i	−0.468856	+	0.883275i	$0.655334\pi$
$660$	−220.984	−	3321.05i	−0.000507309	−	0.00762408i
$661$			533243.i			1.22046i	0.792226	+	0.610228i	$0.208922\pi$
$661$			533243.i			1.22046i	−0.792226	+	0.610228i	$0.791078\pi$
$662$		−	596107.i		−	1.36022i
$663$	−68679.4			−0.156243
$664$		−	8235.48i		−	0.0186790i
$665$	−39421.8	+	2623.14i	−0.0891442	+	0.00593169i
$666$			302950.i			0.683004i
$667$	−467366.	+	215834.i	−1.05052	+	0.485142i
$668$		−	194200.i		−	0.435207i
$669$	−53833.6			−0.120282
$670$	−16046.1	+	1067.72i	−0.0357455	+	0.00237852i
$671$	−62156.7			−0.138052
$672$	−6196.20			−0.0137210
$673$		−	16190.4i		−	0.0357461i	−0.999840	−	0.0178730i	$-0.994311\pi$
$673$		−	16190.4i		−	0.0357461i	0.999840	−	0.0178730i	$-0.00568947\pi$
$674$		−	127333.i		−	0.280299i
$675$	15864.7	+	118683.i	0.0348196	+	0.260484i
$676$	48683.3			0.106533
$677$	−256385.			−0.559391			−0.279695	−	0.960089i	$-0.590233\pi$
$677$	−256385.			−0.559391			−0.279695	+	0.960089i	$0.590233\pi$
$678$	386.553			0.000840911
$679$	107106.			0.232314
$680$	174559.	−	11615.2i	0.377506	−	0.0251194i
$681$		−	50104.2i		−	0.108039i
$682$	15081.7			0.0324250
$683$			369391.i			0.791853i	0.918282	+	0.395927i	$0.129577\pi$
$683$			369391.i			0.791853i	−0.918282	+	0.395927i	$0.870423\pi$
$684$			35067.2i			0.0749531i
$685$	17417.3	+	261755.i	0.0371193	+	0.557846i
$686$			322876.i			0.686100i
$687$	102796.			0.217803
$688$	88114.0			0.186152
$689$		−	145869.i		−	0.307274i
$690$	21359.8	+	39185.0i	0.0448641	+	0.0823042i
$691$	67450.6			0.141263			0.0706317	−	0.997502i	$-0.477499\pi$
$691$	67450.6			0.141263			0.0706317	+	0.997502i	$0.477499\pi$
$692$			183061.i			0.382282i
$693$		−	31845.4i		−	0.0663102i
$694$	203282.			0.422065
$695$	−47105.2	−	707919.i	−0.0975213	−	1.46559i
$696$	−26271.6			−0.0542336
$697$	−32000.1			−0.0658697
$698$		−	365471.i		−	0.750139i
$699$	114550.			0.234445
$700$	142185.	−	19006.2i	0.290173	−	0.0387882i
$701$		−	71251.3i		−	0.144996i	−0.997369	−	0.0724981i	$-0.976903\pi$
$701$		−	71251.3i		−	0.144996i	0.997369	−	0.0724981i	$-0.0230971\pi$
$702$			100862.i			0.204670i
$703$			74142.6i			0.150023i
$704$			7141.72i			0.0144098i
$705$	3502.20	+	52632.7i	0.00704633	+	0.105895i
$706$	3319.14			0.00665911
$707$	22337.8			0.0446892
$708$		−	34001.7i		−	0.0678319i
$709$			972451.i			1.93453i	0.253771	+	0.967264i	$0.418329\pi$
$709$			972451.i			1.93453i	−0.253771	+	0.967264i	$0.581671\pi$
$710$	366414.	−	24381.3i	0.726867	−	0.0483661i
$711$			434989.i			0.860477i
$712$	−173912.			−0.343059
$713$	−183590.	+	84783.7i	−0.361135	+	0.166776i
$714$	−29941.4			−0.0587320
$715$	4309.51	+	64765.3i	0.00842978	+	0.126686i
$716$	232458.			0.453438
$717$			75503.4i			0.146868i
$718$	551598.			1.06998
$719$	147536.			0.285391			0.142695	−	0.989767i	$-0.454423\pi$
$719$	147536.			0.285391			0.142695	+	0.989767i	$0.454423\pi$
$720$	−8453.40	−	127042.i	−0.0163067	−	0.245065i
$721$	385213.			0.741021
$722$		−	360021.i		−	0.690643i
$723$	−12509.8			−0.0239317
$724$			419623.i			0.800538i
$725$	602857.	−	80585.5i	1.14693	−	0.153314i
$726$	−48750.3			−0.0924920
$727$	−851079.			−1.61028			−0.805140	−	0.593085i	$-0.797910\pi$
$727$	−851079.			−1.61028			−0.805140	+	0.593085i	$0.797910\pi$
$728$	120835.			0.227998
$729$	476223.			0.896098
$730$	3305.37	+	49674.6i	0.00620261	+	0.0932157i
$731$	425785.			0.796812
$732$	42532.1			0.0793771
$733$	290622.			0.540904			0.270452	−	0.962733i	$-0.412827\pi$
$733$	290622.			0.540904			0.270452	+	0.962733i	$0.412827\pi$
$734$		−	690393.i		−	1.28146i
$735$	46960.1	−	3124.75i	0.0869270	−	0.00578416i
$736$	−40148.1	−	86936.5i	−0.0741156	−	0.160489i
$737$		−	3172.32i		−	0.00584040i
$738$			23289.2i			0.0427605i
$739$	304261.			0.557131			0.278566	−	0.960417i	$-0.410141\pi$
$739$	304261.			0.557131			0.278566	+	0.960417i	$0.410141\pi$
$740$	−17873.0	−	268604.i	−0.0326388	−	0.490511i
$741$			12232.8i			0.0222788i
$742$		−	63593.0i		−	0.115505i
$743$	540087.			0.978331			0.489165	−	0.872191i	$-0.337301\pi$
$743$	540087.			0.978331			0.489165	+	0.872191i	$0.337301\pi$
$744$	−10320.0			−0.0186437
$745$	481356.	−	32029.6i	0.867269	−	0.0577085i
$746$			450228.i			0.809011i
$747$	−28962.7			−0.0519036
$748$			34510.3i			0.0616801i
$749$	399296.			0.711756
$750$	−10440.6	−	51683.5i	−0.0185610	−	0.0918817i
$751$			763288.i			1.35335i	0.736284	+	0.676673i	$0.236579\pi$
$751$			763288.i			1.35335i	−0.736284	+	0.676673i	$0.763421\pi$
$752$		−	113183.i		−	0.200146i
$753$	−115528.			−0.203749
$754$	512335.			0.901180
$755$	−22319.2	−	335423.i	−0.0391548	−	0.588436i
$756$			43971.7i			0.0769359i
$757$	830084.			1.44854			0.724269	−	0.689517i	$-0.242177\pi$
$757$	830084.			1.44854			0.724269	+	0.689517i	$0.242177\pi$
$758$	436909.			0.760418
$759$	−7992.48	+	3691.01i	−0.0138739	+	0.00640710i
$760$	−2068.84	−	31091.5i	−0.00358180	−	0.0538288i
$761$	−252896.			−0.436689			−0.218344	−	0.975872i	$-0.570066\pi$
$761$	−252896.			−0.436689			−0.218344	+	0.975872i	$0.570066\pi$
$762$			55794.8i			0.0960912i
$763$		−	251400.i		−	0.431833i
$764$			142204.i			0.243627i
$765$	−40848.6	−	613891.i	−0.0697998	−	1.04898i
$766$		−	165565.i		−	0.282169i
$767$			663082.i			1.12714i
$768$		−	4886.88i		−	0.00828532i
$769$		−	281760.i		−	0.476460i	−0.971209	−	0.238230i	$-0.923433\pi$
$769$		−	281760.i		−	0.476460i	0.971209	−	0.238230i	$-0.0765672\pi$
$770$	1878.77	+	28235.0i	0.00316878	+	0.0476218i
$771$	118983.			0.200160
$772$		−	450253.i		−	0.755478i
$773$	−980588.			−1.64107			−0.820536	−	0.571595i	$-0.806325\pi$
$773$	−980588.			−1.64107			−0.820536	+	0.571595i	$0.806325\pi$
$774$		−	309881.i		−	0.517265i
$775$	236813.	−	31655.5i	0.394278	−	0.0527042i
$776$			84473.5i			0.140280i
$777$			46072.5i			0.0763133i
$778$	464678.			0.767702
$779$			5699.70i			0.00939241i
$780$	−2948.88	−	44317.1i	−0.00484695	−	0.0728421i
$781$			72440.0i			0.118762i
$782$	−194004.	−	420095.i	−0.317247	−	0.686965i
$783$			186438.i			0.304096i
$784$	−100985.			−0.164295
$785$	34408.5	+	517106.i	0.0558375	+	0.839152i
$786$	−50556.3			−0.0818334
$787$	−231074.			−0.373079			−0.186539	−	0.982447i	$-0.559727\pi$
$787$	−231074.			−0.373079			−0.186539	+	0.982447i	$0.559727\pi$
$788$		−	304362.i		−	0.490160i
$789$			19860.6i			0.0319034i
$790$	−25662.9	−	385673.i	−0.0411198	−	0.617967i
$791$	−3286.41			−0.00525253
$792$	25116.1			0.0400408
$793$	−829439.			−1.31898
$794$	705882.			1.11967
$795$	−23323.2	+	1551.94i	−0.0369023	+	0.00245550i
$796$		−	115661.i		−	0.182542i
$797$	784301.			1.23471			0.617356	−	0.786684i	$-0.288204\pi$
$797$	784301.			1.23471			0.617356	+	0.786684i	$0.288204\pi$
$798$			5333.01i			0.00837465i
$799$		−	546926.i		−	0.856712i
$800$	14990.0	+	112140.i	0.0234219	+	0.175218i
$801$			611617.i			0.953267i
$802$	592685.			0.921457
$803$	−9820.68			−0.0152304
$804$			2170.73i			0.00335811i
$805$	−181597.	−	333144.i	−0.280232	−	0.514091i
$806$	201255.			0.309796
$807$		−	6444.93i		−	0.00989627i
$808$			17617.6i			0.0269851i
$809$	−148359.			−0.226683			−0.113341	−	0.993556i	$-0.536155\pi$
$809$	−148359.			−0.226683			−0.113341	+	0.993556i	$0.536155\pi$
$810$	−438647.	+	29187.8i	−0.668568	+	0.0444868i
$811$	−335601.			−0.510249			−0.255124	−	0.966908i	$-0.582116\pi$
$811$	−335601.			−0.510249			−0.255124	+	0.966908i	$0.582116\pi$
$812$	223357.			0.338756
$813$		−	94863.3i		−	0.143522i
$814$	53103.0			0.0801439
$815$	−445385.	+	29636.1i	−0.670533	+	0.0446176i
$816$		−	23614.4i		−	0.0354648i
$817$		−	75838.8i		−	0.113618i
$818$		−	88262.3i		−	0.131907i
$819$		−	424955.i		−	0.633542i
$820$	−1373.98	−	20648.9i	−0.00204340	−	0.0307092i
$821$	314215.			0.466166			0.233083	−	0.972457i	$-0.425119\pi$
$821$	314215.			0.466166			0.233083	+	0.972457i	$0.425119\pi$
$822$	35410.5			0.0524069
$823$			233994.i			0.345466i	0.984969	+	0.172733i	$0.0552598\pi$
$823$			233994.i			0.345466i	−0.984969	+	0.172733i	$0.944740\pi$
$824$			303813.i			0.447458i
$825$	10309.5	−	1378.10i	0.0151471	−	0.00202476i
$826$			289076.i			0.423694i
$827$	831739.			1.21612			0.608059	−	0.793892i	$-0.291948\pi$
$827$	831739.			1.21612			0.608059	+	0.793892i	$0.291948\pi$
$828$	−305740.	+	141194.i	−0.445956	+	0.205947i
$829$	−348711.			−0.507407			−0.253703	−	0.967282i	$-0.581649\pi$
$829$	−348711.			−0.507407			−0.253703	+	0.967282i	$0.581649\pi$
$830$	25679.1	−	1708.70i	0.0372755	−	0.00248033i
$831$	−18905.7			−0.0273774
$832$			95301.4i			0.137674i
$833$	−487980.			−0.703254
$834$	−95767.8			−0.137685
$835$	605535.	−	40292.6i	0.868493	−	0.0577899i
$836$	6146.80			0.00879502
$837$			73236.2i			0.104538i
$838$	−502796.			−0.715985
$839$			311692.i			0.442795i	0.975184	+	0.221397i	$0.0710618\pi$
$839$			311692.i			0.442795i	−0.975184	+	0.221397i	$0.928938\pi$
$840$	−1285.59	−	19320.4i	−0.00182198	−	0.0273815i
$841$	239741.			0.338961
$842$	−203436.			−0.286949
$843$	−128664.			−0.181052
$844$	262647.			0.368712
$845$	10100.8	+	151799.i	0.0141463	+	0.212597i
$846$	−398046.			−0.556150
$847$	414467.			0.577727
$848$	50155.1			0.0697467
$849$		−	61380.8i		−	0.0851564i
$850$	72434.9	+	541882.i	0.100256	+	0.750010i
$851$	−646426.	+	298526.i	−0.892605	+	0.412214i
$852$		−	49568.7i		−	0.0682855i
$853$		−	423835.i		−	0.582504i	−0.956646	−	0.291252i	$-0.905928\pi$
$853$		−	423835.i		−	0.582504i	0.956646	−	0.291252i	$-0.0940718\pi$
$854$	−361601.			−0.495808
$855$	−109343.	+	7275.75i	−0.149575	+	0.00995281i
$856$			314921.i			0.429787i
$857$			934570.i			1.27248i	0.771492	+	0.636239i	$0.219511\pi$
$857$			934570.i			1.27248i	−0.771492	+	0.636239i	$0.780489\pi$
$858$	8761.50			0.0119016
$859$	192595.			0.261012			0.130506	−	0.991448i	$-0.458340\pi$
$859$	192595.			0.261012			0.130506	+	0.991448i	$0.458340\pi$
$860$	18281.9	+	274749.i	0.0247186	+	0.371483i
$861$			3541.82i			0.00477771i
$862$	−678420.			−0.913029
$863$			544496.i			0.731094i	0.930793	+	0.365547i	$0.119118\pi$
$863$			544496.i			0.731094i	−0.930793	+	0.365547i	$0.880882\pi$
$864$	−34680.0			−0.0464570
$865$	−570804.	+	37981.6i	−0.762878	+	0.0507622i
$866$		−	181713.i		−	0.242298i
$867$		−	14462.1i		−	0.0192395i
$868$	87738.6			0.116453
$869$	76247.6			0.100969
$870$	−5450.84	−	81917.6i	−0.00720153	−	0.108228i
$871$		−	42332.5i		−	0.0558004i
$872$	198276.			0.260758
$873$	297078.			0.389800
$874$	−74825.4	+	34555.1i	−0.0979548	+	0.0452365i
$875$	88763.9	+	439404.i	0.115937	+	0.573915i
$876$	6720.02			0.00875715
$877$		−	897403.i		−	1.16678i	−0.812193	−	0.583389i	$-0.801726\pi$
$877$		−	897403.i		−	1.16678i	0.812193	−	0.583389i	$-0.198274\pi$
$878$		−	733674.i		−	0.951731i
$879$			155506.i			0.201266i
$880$	−22268.6	+	1481.76i	−0.0287560	+	0.00191343i
$881$		−	115115.i		−	0.148313i	−0.997247	−	0.0741564i	$-0.976374\pi$
$881$		−	115115.i		−	0.148313i	0.997247	−	0.0741564i	$-0.0236264\pi$
$882$			355146.i			0.456530i
$883$		−	287663.i		−	0.368945i	−0.982838	−	0.184473i	$-0.940942\pi$
$883$		−	287663.i		−	0.368945i	0.982838	−	0.184473i	$-0.0590577\pi$
$884$			460516.i			0.589305i
$885$	106021.	−	7054.67i	0.135364	−	0.00900721i
$886$	−685810.			−0.873648
$887$			774395.i			0.984273i	0.870518	+	0.492136i	$0.163784\pi$
$887$			774395.i			0.984273i	−0.870518	+	0.492136i	$0.836216\pi$
$888$	−36336.9			−0.0460810
$889$		−	474357.i		−	0.600209i
$890$	−36083.3	−	542276.i	−0.0455539	−	0.684605i
$891$		−	86720.6i		−	0.109236i
$892$			360970.i			0.453672i
$893$	−97415.8			−0.122159
$894$		−	65118.2i		−	0.0814756i
$895$	48230.3	+	724827.i	0.0602108	+	0.904875i
$896$			41547.4i			0.0517521i
$897$	−106654.	+	49254.0i	−0.132554	+	0.0612148i
$898$			247977.i			0.307510i
$899$	372007.			0.460291
$900$	394375.	−	52717.2i	0.486883	−	0.0650829i
$901$	242360.			0.298546
$902$	4082.28			0.00501753
$903$		−	47126.6i		−	0.0577950i
$904$		−	2591.96i		−	0.00317169i
$905$	−1.30843e6	+	87063.4i	−1.59754	+	0.106301i
$906$	−45376.3			−0.0552806
$907$	−1.50869e6			−1.83395			−0.916973	−	0.398949i	$-0.869375\pi$
$907$	−1.50869e6			−1.83395			−0.916973	+	0.398949i	$0.869375\pi$
$908$	−335964.			−0.407493
$909$	61958.0			0.0749842
$910$	25070.9	+	376776.i	0.0302752	+	0.454989i
$911$			566238.i			0.682279i	0.940013	+	0.341140i	$0.110813\pi$
$911$			566238.i			0.682279i	−0.940013	+	0.341140i	$0.889187\pi$
$912$	−4206.09			−0.00505695
$913$			5076.76i			0.00609039i
$914$		−	770731.i		−	0.922593i
$915$	8824.57	+	132620.i	0.0105403	+	0.158404i
$916$		−	689281.i		−	0.821496i
$917$	429821.			0.511151
$918$	−167581.			−0.198856
$919$		−	1.28804e6i		−	1.52509i	−0.646933	−	0.762547i	$-0.723949\pi$
$919$		−	1.28804e6i		−	1.52509i	0.646933	−	0.762547i	$-0.276051\pi$
$920$	262747.	−	143224.i	0.310429	−	0.169215i
$921$	−35564.9			−0.0419278
$922$		−	277897.i		−	0.326905i
$923$			966663.i			1.13468i
$924$	3819.65			0.00447383
$925$	833826.	−	111460.i	0.974523	−	0.130267i
$926$	−554884.			−0.647114
$927$	1.06846e6			1.24336
$928$			176159.i			0.204554i
$929$	−1.22273e6			−1.41677			−0.708385	−	0.705826i	$-0.750576\pi$
$929$	−1.22273e6			−1.41677			−0.708385	+	0.705826i	$0.750576\pi$
$930$	−2141.19	−	32178.8i	−0.00247565	−	0.0372052i
$931$			86916.7i			0.100278i
$932$		−	768093.i		−	0.884264i
$933$			56404.8i			0.0647967i
$934$		−	637028.i		−	0.730239i
$935$	−107607.	+	7160.19i	−0.123088	+	0.00819033i
$936$	335158.			0.382558
$937$	−1.13706e6			−1.29511			−0.647553	−	0.762020i	$-0.724208\pi$
$937$	−1.13706e6			−1.29511			−0.647553	+	0.762020i	$0.724208\pi$
$938$		−	18455.2i		−	0.0209755i
$939$		−	67173.8i		−	0.0761849i
$940$	352918.	−	23483.3i	0.399409	−	0.0265768i
$941$			534582.i			0.603719i	0.953352	+	0.301859i	$0.0976073\pi$
$941$			534582.i			0.603719i	−0.953352	+	0.301859i	$0.902393\pi$
$942$	69954.6			0.0788341
$943$	−49693.8	+	22949.1i	−0.0558829	+	0.0258073i
$944$	−227991.			−0.255843
$945$	−137108.	+	9123.24i	−0.153532	+	0.0102161i
$946$	−54317.8			−0.0606960
$947$			1.17560e6i			1.31087i	0.755252	+	0.655435i	$0.227515\pi$
$947$			1.17560e6i			1.31087i	−0.755252	+	0.655435i	$0.772485\pi$
$948$	−52174.2			−0.0580549
$949$	−131050.			−0.145514
$950$	96517.4	−	12901.8i	0.106945	−	0.0142956i
$951$	−26495.7			−0.0292964
$952$			200766.i			0.221521i
$953$	−1.65634e6			−1.82374			−0.911872	−	0.410474i	$-0.865363\pi$
$953$	−1.65634e6			−1.82374			−0.911872	+	0.410474i	$0.865363\pi$
$954$		−	176387.i		−	0.193807i
$955$	−443407.	+	29504.5i	−0.486179	+	0.0323505i
$956$	506273.			0.553948
$957$	16195.1			0.0176832
$958$	−47461.0			−0.0517138
$959$	−301054.			−0.327346
$960$	15237.8	−	1013.93i	0.0165341	−	0.00110018i
$961$	−777390.			−0.841767
$962$	708623.			0.765712
$963$	1.10752e6			1.19426
$964$			83881.8i			0.0902638i
$965$	1.40394e6	−	93418.5i	1.50762	−	0.100318i
$966$	−46496.8	+	21472.7i	−0.0498275	+	0.0230108i
$967$		−	922781.i		−	0.986838i	−0.869792	−	0.493419i	$-0.835747\pi$
$967$		−	922781.i		−	0.986838i	0.869792	−	0.493419i	$-0.164253\pi$
$968$			326886.i			0.348855i
$969$	−20324.7			−0.0216459
$970$	−263397.	+	17526.6i	−0.279942	+	0.0186274i
$971$		−	1.74361e6i		−	1.84931i	−0.380801	−	0.924657i	$-0.624352\pi$
$971$		−	1.74361e6i		−	1.84931i	0.380801	−	0.924657i	$-0.375648\pi$
$972$			183485.i			0.194209i
$973$	814201.			0.860015
$974$	−941888.			−0.992845
$975$	137574.	−	18389.8i	0.144719	−	0.0193450i
$976$		−	285191.i		−	0.299389i
$977$	−1.31285e6			−1.37539			−0.687697	−	0.725998i	$-0.741378\pi$
$977$	−1.31285e6			−1.37539			−0.687697	+	0.725998i	$0.741378\pi$
$978$			60252.0i			0.0629932i
$979$	107208.			0.111857
$980$	−20952.4	−	314882.i	−0.0218163	−	0.327865i
$981$		−	697301.i		−	0.724574i
$982$			639800.i			0.663470i
$983$	−938277.			−0.971010			−0.485505	−	0.874234i	$-0.661364\pi$
$983$	−938277.			−0.971010			−0.485505	+	0.874234i	$0.661364\pi$
$984$	−2793.39			−0.00288497
$985$	949032.	−	63149.0i	0.978156	−	0.0650870i
$986$			851237.i			0.875582i
$987$	−60534.6			−0.0621397
$988$	82024.9			0.0840295
$989$	661214.	−	305355.i	0.676004	−	0.312185i
$990$	5211.10	+	78314.7i	0.00531690	+	0.0799048i
$991$	115855.			0.117969			0.0589847	−	0.998259i	$-0.481214\pi$
$991$	115855.			0.117969			0.0589847	+	0.998259i	$0.481214\pi$
$992$			69198.5i			0.0703191i
$993$		−	251449.i		−	0.255007i
$994$			421425.i			0.426528i
$995$	360645.	−	23997.5i	0.364278	−	0.0242392i
$996$		−	3473.89i		−	0.00350185i
$997$		−	1.44887e6i		−	1.45761i	−0.684723	−	0.728803i	$-0.740077\pi$
$997$		−	1.44887e6i		−	1.45761i	0.684723	−	0.728803i	$-0.259923\pi$
$998$			455871.i			0.457700i
$999$			257867.i			0.258383i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.c.a.229.19	✓	48
5.4	even	2	inner	230.5.c.a.229.30	yes	48
23.22	odd	2	inner	230.5.c.a.229.29	yes	48
115.114	odd	2	inner	230.5.c.a.229.20	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.c.a.229.19	✓	48	1.1	even	1	trivial
230.5.c.a.229.20	yes	48	115.114	odd	2	inner
230.5.c.a.229.29	yes	48	23.22	odd	2	inner
230.5.c.a.229.30	yes	48	5.4	even	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)

\(f(q)\)	\(=\)	\(q-2.82843i q^{2} -1.19309i q^{3} -8.00000 q^{4} +(-1.65984 - 24.9448i) q^{5} -3.37456 q^{6} +28.6899 q^{7} +22.6274i q^{8} +79.5765 q^{9} +O(q^{10})\)	\(q-2.82843i q^{2} -1.19309i q^{3} -8.00000 q^{4} +(-1.65984 - 24.9448i) q^{5} -3.37456 q^{6} +28.6899 q^{7} +22.6274i q^{8} +79.5765 q^{9} +(-70.5547 + 4.69474i) q^{10} -13.9487i q^{11} +9.54469i q^{12} -186.135i q^{13} -81.1473i q^{14} +(-29.7613 + 1.98033i) q^{15} +64.0000 q^{16} +309.261 q^{17} -225.076i q^{18} -55.0841i q^{19} +(13.2787 + 199.559i) q^{20} -34.2295i q^{21} -39.4528 q^{22} +(480.261 - 221.789i) q^{23} +26.9965 q^{24} +(-619.490 + 82.8089i) q^{25} -526.471 q^{26} -191.582i q^{27} -229.519 q^{28} -973.150 q^{29} +(5.60123 + 84.1778i) q^{30} -382.271 q^{31} -181.019i q^{32} -16.6420 q^{33} -874.723i q^{34} +(-47.6207 - 715.665i) q^{35} -636.612 q^{36} -1345.99 q^{37} -155.801 q^{38} -222.076 q^{39} +(564.437 - 37.5579i) q^{40} -103.473 q^{41} -96.8157 q^{42} +1376.78 q^{43} +111.589i q^{44} +(-132.084 - 1985.02i) q^{45} +(-627.315 - 1358.38i) q^{46} -1768.49i q^{47} -76.3575i q^{48} -1577.89 q^{49} +(234.219 + 1752.18i) q^{50} -368.976i q^{51} +1489.08i q^{52} +783.674 q^{53} -541.875 q^{54} +(-347.947 + 23.1526i) q^{55} +649.178i q^{56} -65.7201 q^{57} +2752.48i q^{58} -3562.36 q^{59} +(238.091 - 15.8427i) q^{60} -4456.11i q^{61} +1081.23i q^{62} +2283.04 q^{63} -512.000 q^{64} +(-4643.12 + 308.955i) q^{65} +47.0706i q^{66} +227.429 q^{67} -2474.09 q^{68} +(-264.614 - 572.993i) q^{69} +(-2024.21 + 134.692i) q^{70} -5193.33 q^{71} +1800.61i q^{72} -704.059i q^{73} +3807.03i q^{74} +(98.7982 + 739.105i) q^{75} +440.673i q^{76} -400.186i q^{77} +628.125i q^{78} +5466.30i q^{79} +(-106.230 - 1596.47i) q^{80} +6217.13 q^{81} +292.665i q^{82} -363.960 q^{83} +273.836i q^{84} +(-513.325 - 7714.48i) q^{85} -3894.12i q^{86} +1161.05i q^{87} +315.622 q^{88} +7685.89i q^{89} +(-5614.50 + 373.591i) q^{90} -5340.21i q^{91} +(-3842.09 + 1774.31i) q^{92} +456.083i q^{93} -5002.05 q^{94} +(-1374.06 + 91.4309i) q^{95} -215.972 q^{96} +3733.23 q^{97} +4462.95i q^{98} -1109.99i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9}+O(q^{10}) \) 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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