LMFDB - Embedded newform 230.5.c.a.229.18

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			229.18
Character	$\chi$	$=$	230.229
Dual form			230.5.c.a.229.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.82843i q^{2} +15.7740i q^{3} -8.00000 q^{4} +(-12.1414 + 21.8538i) q^{5} -44.6155 q^{6} +29.1236 q^{7} -22.6274i q^{8} -167.818 q^{9} +O(q^{10})$	\(q+2.82843i q^{2} +15.7740i q^{3} -8.00000 q^{4} +(-12.1414 + 21.8538i) q^{5} -44.6155 q^{6} +29.1236 q^{7} -22.6274i q^{8} -167.818 q^{9} +(-61.8118 - 34.3409i) q^{10} -152.391i q^{11} -126.192i q^{12} -330.234i q^{13} +82.3741i q^{14} +(-344.720 - 191.517i) q^{15} +64.0000 q^{16} +194.828 q^{17} -474.660i q^{18} +526.110i q^{19} +(97.1308 - 174.830i) q^{20} +459.395i q^{21} +431.026 q^{22} +(-527.482 - 40.0500i) q^{23} +356.924 q^{24} +(-330.175 - 530.669i) q^{25} +934.042 q^{26} -1369.46i q^{27} -232.989 q^{28} -1278.64 q^{29} +(541.692 - 975.017i) q^{30} -437.462 q^{31} +181.019i q^{32} +2403.80 q^{33} +551.057i q^{34} +(-353.601 + 636.462i) q^{35} +1342.54 q^{36} -2250.61 q^{37} -1488.06 q^{38} +5209.09 q^{39} +(494.494 + 274.728i) q^{40} +713.512 q^{41} -1299.37 q^{42} +459.640 q^{43} +1219.13i q^{44} +(2037.53 - 3667.45i) q^{45} +(113.279 - 1491.94i) q^{46} +1663.50i q^{47} +1009.53i q^{48} -1552.81 q^{49} +(1500.96 - 933.876i) q^{50} +3073.21i q^{51} +2641.87i q^{52} +1465.30 q^{53} +3873.41 q^{54} +(3330.31 + 1850.23i) q^{55} -658.993i q^{56} -8298.83 q^{57} -3616.55i q^{58} -909.066 q^{59} +(2757.76 + 1532.14i) q^{60} -2701.86i q^{61} -1237.33i q^{62} -4887.46 q^{63} -512.000 q^{64} +(7216.86 + 4009.49i) q^{65} +6798.98i q^{66} +1995.64 q^{67} -1558.63 q^{68} +(631.747 - 8320.47i) q^{69} +(-1800.19 - 1000.13i) q^{70} -2473.67 q^{71} +3797.28i q^{72} -7865.35i q^{73} -6365.70i q^{74} +(8370.75 - 5208.16i) q^{75} -4208.88i q^{76} -4438.17i q^{77} +14733.5i q^{78} +7620.76i q^{79} +(-777.047 + 1398.64i) q^{80} +8008.52 q^{81} +2018.12i q^{82} +10525.0 q^{83} -3675.16i q^{84} +(-2365.48 + 4257.73i) q^{85} +1300.06i q^{86} -20169.2i q^{87} -3448.21 q^{88} +3144.69i q^{89} +(10373.1 + 5763.01i) q^{90} -9617.61i q^{91} +(4219.85 + 320.400i) q^{92} -6900.51i q^{93} -4705.09 q^{94} +(-11497.5 - 6387.68i) q^{95} -2855.39 q^{96} -15409.7 q^{97} -4392.02i q^{98} +25573.8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$			15.7740i			1.75266i	0.481710	+	0.876331i	$0.340016\pi$
$3$			15.7740i			1.75266i	−0.481710	+	0.876331i	$0.659984\pi$
$4$	−8.00000			−0.500000
$5$	−12.1414	+	21.8538i	−0.485654	+	0.874151i
$5$	−12.1414	+	21.8538i	−0.485654	+	0.874151i
$6$	−44.6155			−1.23932
$7$	29.1236			0.594360			0.297180	−	0.954821i	$-0.403954\pi$
$7$	29.1236			0.594360			0.297180	+	0.954821i	$0.403954\pi$
$8$		−	22.6274i		−	0.353553i
$9$	−167.818			−2.07182
$10$	−61.8118	−	34.3409i	−0.618118	−	0.343409i
$11$		−	152.391i		−	1.25943i	−0.776828	−	0.629713i	$-0.783172\pi$
$11$		−	152.391i		−	1.25943i	0.776828	−	0.629713i	$-0.216828\pi$
$12$		−	126.192i		−	0.876331i
$13$		−	330.234i		−	1.95405i	−0.213133	−	0.977023i	$-0.568367\pi$
$13$		−	330.234i		−	1.95405i	0.213133	−	0.977023i	$-0.431633\pi$
$14$			82.3741i			0.420276i
$15$	−344.720	−	191.517i	−1.53209	−	0.851187i
$16$	64.0000			0.250000
$17$	194.828			0.674146			0.337073	−	0.941478i	$-0.390563\pi$
$17$	194.828			0.674146			0.337073	+	0.941478i	$0.390563\pi$
$18$		−	474.660i		−	1.46500i
$19$			526.110i			1.45737i	0.684850	+	0.728684i	$0.259868\pi$
$19$			526.110i			1.45737i	−0.684850	+	0.728684i	$0.740132\pi$
$20$	97.1308	−	174.830i	0.242827	−	0.437076i
$21$			459.395i			1.04171i
$22$	431.026			0.890549
$23$	−527.482	−	40.0500i	−0.997130	−	0.0757089i
$23$	−527.482	−	40.0500i	−0.997130	−	0.0757089i
$24$	356.924			0.619659
$25$	−330.175	−	530.669i	−0.528280	−	0.849070i
$26$	934.042			1.38172
$27$		−	1369.46i		−	1.87854i
$28$	−232.989			−0.297180
$29$	−1278.64			−1.52038			−0.760191	−	0.649699i	$-0.774895\pi$
$29$	−1278.64			−1.52038			−0.760191	+	0.649699i	$0.774895\pi$
$30$	541.692	−	975.017i	0.601880	−	1.08335i
$31$	−437.462			−0.455215			−0.227608	−	0.973753i	$-0.573090\pi$
$31$	−437.462			−0.455215			−0.227608	+	0.973753i	$0.573090\pi$
$32$			181.019i			0.176777i
$33$	2403.80			2.20735
$34$			551.057i			0.476693i
$35$	−353.601	+	636.462i	−0.288654	+	0.519561i
$36$	1342.54			1.03591
$37$	−2250.61			−1.64398			−0.821992	−	0.569499i	$-0.807137\pi$
$37$	−2250.61			−1.64398			−0.821992	+	0.569499i	$0.807137\pi$
$38$	−1488.06			−1.03051
$39$	5209.09			3.42478
$40$	494.494	+	274.728i	0.309059	+	0.171705i
$41$	713.512			0.424457			0.212228	−	0.977220i	$-0.431928\pi$
$41$	713.512			0.424457			0.212228	+	0.977220i	$0.431928\pi$
$42$	−1299.37			−0.736602
$43$	459.640			0.248588			0.124294	−	0.992245i	$-0.460333\pi$
$43$	459.640			0.248588			0.124294	+	0.992245i	$0.460333\pi$
$44$			1219.13i			0.629713i
$45$	2037.53	−	3667.45i	1.00619	−	1.81109i
$46$	113.279	−	1491.94i	0.0535343	−	0.705077i
$47$			1663.50i			0.753055i	0.926405	+	0.376528i	$0.122882\pi$
$47$			1663.50i			0.753055i	−0.926405	+	0.376528i	$0.877118\pi$
$48$			1009.53i			0.438165i
$49$	−1552.81			−0.646736
$50$	1500.96	−	933.876i	0.600383	−	0.373550i
$51$			3073.21i			1.18155i
$52$			2641.87i			0.977023i
$53$	1465.30			0.521645			0.260823	−	0.965387i	$-0.416006\pi$
$53$	1465.30			0.521645			0.260823	+	0.965387i	$0.416006\pi$
$54$	3873.41			1.32833
$55$	3330.31	+	1850.23i	1.10093	+	0.611646i
$56$		−	658.993i		−	0.210138i
$57$	−8298.83			−2.55427
$58$		−	3616.55i		−	1.07507i
$59$	−909.066			−0.261151			−0.130575	−	0.991438i	$-0.541682\pi$
$59$	−909.066			−0.261151			−0.130575	+	0.991438i	$0.541682\pi$
$60$	2757.76	+	1532.14i	0.766045	+	0.425594i
$61$		−	2701.86i		−	0.726112i	−0.931767	−	0.363056i	$-0.881733\pi$
$61$		−	2701.86i		−	0.726112i	0.931767	−	0.363056i	$-0.118267\pi$
$62$		−	1237.33i		−	0.321886i
$63$	−4887.46			−1.23141
$64$	−512.000			−0.125000
$65$	7216.86	+	4009.49i	1.70813	+	0.948991i
$66$			6798.98i			1.56083i
$67$	1995.64			0.444563			0.222281	−	0.974983i	$-0.428650\pi$
$67$	1995.64			0.444563			0.222281	+	0.974983i	$0.428650\pi$
$68$	−1558.63			−0.337073
$69$	631.747	−	8320.47i	0.132692	−	1.74763i
$70$	−1800.19	−	1000.13i	−0.367385	−	0.204109i
$71$	−2473.67			−0.490711			−0.245356	−	0.969433i	$-0.578905\pi$
$71$	−2473.67			−0.490711			−0.245356	+	0.969433i	$0.578905\pi$
$72$			3797.28i			0.732500i
$73$		−	7865.35i		−	1.47595i	−0.674827	−	0.737976i	$-0.735782\pi$
$73$		−	7865.35i		−	1.47595i	0.674827	−	0.737976i	$-0.264218\pi$
$74$		−	6365.70i		−	1.16247i
$75$	8370.75	−	5208.16i	1.48813	−	0.925896i
$76$		−	4208.88i		−	0.728684i
$77$		−	4438.17i		−	0.748553i
$78$			14733.5i			2.42169i
$79$			7620.76i			1.22108i	0.791986	+	0.610540i	$0.209047\pi$
$79$			7620.76i			1.22108i	−0.791986	+	0.610540i	$0.790953\pi$
$80$	−777.047	+	1398.64i	−0.121414	+	0.218538i
$81$	8008.52			1.22062
$82$			2018.12i			0.300136i
$83$	10525.0			1.52780			0.763898	−	0.645337i	$-0.223283\pi$
$83$	10525.0			1.52780			0.763898	+	0.645337i	$0.223283\pi$
$84$		−	3675.16i		−	0.520856i
$85$	−2365.48	+	4257.73i	−0.327402	+	0.589306i
$86$			1300.06i			0.175778i
$87$		−	20169.2i		−	2.66472i
$88$	−3448.21			−0.445275
$89$			3144.69i			0.397007i	0.980100	+	0.198504i	$0.0636081\pi$
$89$			3144.69i			0.397007i	−0.980100	+	0.198504i	$0.936392\pi$
$90$	10373.1	+	5763.01i	1.28063	+	0.711483i
$91$		−	9617.61i		−	1.16141i
$92$	4219.85	+	320.400i	0.498565	+	0.0378545i
$93$		−	6900.51i		−	0.797839i
$94$	−4705.09			−0.532491
$95$	−11497.5	−	6387.68i	−1.27396	−	0.707777i
$96$	−2855.39			−0.309830
$97$	−15409.7			−1.63776			−0.818879	−	0.573966i	$-0.805404\pi$
$97$	−15409.7			−1.63776			−0.818879	+	0.573966i	$0.805404\pi$
$98$		−	4392.02i		−	0.457311i
$99$			25573.8i			2.60931i
$100$	2641.40	+	4245.35i	0.264140	+	0.424535i
$101$	−11403.6			−1.11790			−0.558948	−	0.829203i	$-0.688795\pi$
$101$	−11403.6			−1.11790			−0.558948	+	0.829203i	$0.688795\pi$
$102$	−8692.35			−0.835482
$103$	−4667.41			−0.439948			−0.219974	−	0.975506i	$-0.570597\pi$
$103$	−4667.41			−0.439948			−0.219974	+	0.975506i	$0.570597\pi$
$104$	−7472.34			−0.690860
$105$	−10039.5	−	5577.68i	−0.910614	−	0.505912i
$106$			4144.50i			0.368859i
$107$	−13154.3			−1.14895			−0.574476	−	0.818522i	$-0.694794\pi$
$107$	−13154.3			−1.14895			−0.574476	+	0.818522i	$0.694794\pi$
$108$			10955.7i			0.939271i
$109$			6531.58i			0.549750i	0.961480	+	0.274875i	$0.0886365\pi$
$109$			6531.58i			0.549750i	−0.961480	+	0.274875i	$0.911363\pi$
$110$	−5233.24	+	9419.54i	−0.432499	+	0.778474i
$111$		−	35501.1i		−	2.88135i
$112$	1863.91			0.148590
$113$	1520.01			0.119039			0.0595197	−	0.998227i	$-0.481043\pi$
$113$	1520.01			0.119039			0.0595197	+	0.998227i	$0.481043\pi$
$114$		−	23472.6i		−	1.80614i
$115$	7279.59	−	11041.2i	0.550441	−	0.834874i
$116$	10229.1			0.760191
$117$			55419.1i			4.04844i
$118$		−	2571.23i		−	0.184662i
$119$	5674.11			0.400686
$120$	−4333.54	+	7800.13i	−0.300940	+	0.541676i
$121$	−8581.91			−0.586156
$122$	7642.02			0.513439
$123$			11254.9i			0.743929i
$124$	3499.70			0.227608
$125$	15605.9	−	772.530i	0.998777	−	0.0494419i
$126$		−	13823.8i		−	0.870737i
$127$		−	18022.3i		−	1.11739i	−0.829374	−	0.558693i	$-0.811303\pi$
$127$		−	18022.3i		−	1.11739i	0.829374	−	0.558693i	$-0.188697\pi$
$128$		−	1448.15i		−	0.0883883i
$129$			7250.33i			0.435691i
$130$	−11340.5	+	20412.4i	−0.671038	+	1.20783i
$131$	13818.3			0.805217			0.402609	−	0.915372i	$-0.368104\pi$
$131$	13818.3			0.805217			0.402609	+	0.915372i	$0.368104\pi$
$132$	−19230.4			−1.10367
$133$			15322.2i			0.866201i
$134$			5644.53i			0.314353i
$135$	29927.8	+	16627.1i	1.64213	+	0.912321i
$136$		−	4408.46i		−	0.238347i
$137$	18032.8			0.960774			0.480387	−	0.877057i	$-0.340496\pi$
$137$	18032.8			0.960774			0.480387	+	0.877057i	$0.340496\pi$
$138$	23533.8	+	1786.85i	1.23576	+	0.0938275i
$139$	−19065.8			−0.986791			−0.493396	−	0.869805i	$-0.664245\pi$
$139$	−19065.8			−0.986791			−0.493396	+	0.869805i	$0.664245\pi$
$140$	2828.80	−	5091.69i	0.144327	−	0.259780i
$141$	−26240.0			−1.31985
$142$		−	6996.61i		−	0.346985i
$143$	−50324.6			−2.46098
$144$	−10740.3			−0.517956
$145$	15524.4	−	27943.2i	0.738380	−	1.32904i
$146$	22246.6			1.04366
$147$		−	24494.0i		−	1.13351i
$148$	18004.9			0.821992
$149$			42775.2i			1.92673i	0.268202	+	0.963363i	$0.413570\pi$
$149$			42775.2i			1.92673i	−0.268202	+	0.963363i	$0.586430\pi$
$150$	14730.9	+	23676.0i	0.654707	+	1.05227i
$151$	−17131.7			−0.751359			−0.375679	−	0.926750i	$-0.622591\pi$
$151$	−17131.7			−0.751359			−0.375679	+	0.926750i	$0.622591\pi$
$152$	11904.5			0.515257
$153$	−32695.6			−1.39671
$154$	12553.0			0.529307
$155$	5311.38	−	9560.20i	0.221077	−	0.397927i
$156$	−41672.7			−1.71239
$157$	24313.4			0.986383			0.493192	−	0.869921i	$-0.335830\pi$
$157$	24313.4			0.986383			0.493192	+	0.869921i	$0.335830\pi$
$158$	−21554.8			−0.863434
$159$			23113.6i			0.914268i
$160$	−3955.96	−	2197.82i	−0.154530	−	0.0858523i
$161$	−15362.2	−	1166.40i	−0.592654	−	0.0449984i
$162$			22651.5i			0.863112i
$163$		−	31717.6i		−	1.19378i	−0.802322	−	0.596891i	$-0.796402\pi$
$163$		−	31717.6i		−	1.19378i	0.802322	−	0.596891i	$-0.203598\pi$
$164$	−5708.09			−0.212228
$165$	−29185.4	+	52532.2i	−1.07201	+	1.92956i
$166$			29769.1i			1.08031i
$167$			36304.6i			1.30175i	0.759184	+	0.650876i	$0.225598\pi$
$167$			36304.6i			1.30175i	−0.759184	+	0.650876i	$0.774402\pi$
$168$	10394.9			0.368301
$169$	−80493.4			−2.81830
$170$	−12042.7	−	6690.58i	−0.416702	−	0.231508i
$171$		−	88290.4i		−	3.01941i
$172$	−3677.12			−0.124294
$173$			25708.9i			0.858998i	0.903067	+	0.429499i	$0.141310\pi$
$173$			25708.9i			0.858998i	−0.903067	+	0.429499i	$0.858690\pi$
$174$	57047.2			1.88424
$175$	−9615.90	−	15455.0i	−0.313989	−	0.504654i
$176$		−	9753.00i		−	0.314857i
$177$		−	14339.6i		−	0.457709i
$178$	−8894.54			−0.280726
$179$	1995.19			0.0622700			0.0311350	−	0.999515i	$-0.490088\pi$
$179$	1995.19			0.0622700			0.0311350	+	0.999515i	$0.490088\pi$
$180$	−16300.3	+	29339.6i	−0.503095	+	0.905543i
$181$			734.002i			0.0224047i	0.999937	+	0.0112024i	$0.00356590\pi$
$181$			734.002i			0.0224047i	−0.999937	+	0.0112024i	$0.996434\pi$
$182$	27202.7			0.821239
$183$	42619.1			1.27263
$184$	−906.228	+	11935.5i	−0.0267671	+	0.352539i
$185$	27325.5	−	49184.4i	0.798408	−	1.43709i
$186$	19517.6			0.564157
$187$		−	29690.0i		−	0.849038i
$188$		−	13308.0i		−	0.376528i
$189$		−	39883.6i		−	1.11653i
$190$	18067.1	−	32519.8i	0.500474	−	0.900825i
$191$			34389.0i			0.942656i	0.881958	+	0.471328i	$0.156225\pi$
$191$			34389.0i			0.942656i	−0.881958	+	0.471328i	$0.843775\pi$
$192$		−	8076.26i		−	0.219083i
$193$		−	19465.2i		−	0.522571i	−0.965262	−	0.261285i	$-0.915854\pi$
$193$		−	19465.2i		−	0.522571i	0.965262	−	0.261285i	$-0.0841464\pi$
$194$		−	43585.1i		−	1.15807i
$195$	−63245.5	+	113838.i	−1.66326	+	2.99378i
$196$	12422.5			0.323368
$197$			15588.5i			0.401672i	0.979625	+	0.200836i	$0.0643659\pi$
$197$			15588.5i			0.401672i	−0.979625	+	0.200836i	$0.935634\pi$
$198$	−72333.7			−1.84506
$199$		−	37625.0i		−	0.950103i	−0.879958	−	0.475052i	$-0.842429\pi$
$199$		−	37625.0i		−	0.950103i	0.879958	−	0.475052i	$-0.157571\pi$
$200$	−12007.7	+	7471.01i	−0.300192	+	0.186775i
$201$			31479.1i			0.779168i
$202$		−	32254.4i		−	0.790471i
$203$	−37238.7			−0.903655
$204$		−	24585.7i		−	0.590775i
$205$	−8663.00	+	15592.9i	−0.206139	+	0.371039i
$206$		−	13201.4i		−	0.311090i
$207$	88520.7	+	6721.10i	2.06588	+	0.156855i
$208$		−	21135.0i		−	0.488512i
$209$	80174.2			1.83545
$210$	15776.1	−	28396.0i	0.357734	−	0.643901i
$211$	29305.8			0.658246			0.329123	−	0.944287i	$-0.393247\pi$
$211$	29305.8			0.658246			0.329123	+	0.944287i	$0.393247\pi$
$212$	−11722.4			−0.260823
$213$		−	39019.6i		−	0.860050i
$214$		−	37206.1i		−	0.812431i
$215$	−5580.65	+	10044.9i	−0.120728	+	0.217304i
$216$	−30987.3			−0.664165
$217$	−12740.5			−0.270562
$218$	−18474.1			−0.388732
$219$	124068.			2.58684
$220$	−26642.5	−	14801.8i	−0.550465	−	0.305823i
$221$		−	64338.9i		−	1.31731i
$222$	100412.			2.03742
$223$			39322.5i			0.790735i	0.918523	+	0.395367i	$0.129383\pi$
$223$			39322.5i			0.790735i	−0.918523	+	0.395367i	$0.870617\pi$
$224$			5271.94i			0.105069i
$225$	55409.2	+	89055.6i	1.09450	+	1.75912i
$226$			4299.25i			0.0841736i
$227$	12157.6			0.235937			0.117969	−	0.993017i	$-0.462362\pi$
$227$	12157.6			0.235937			0.117969	+	0.993017i	$0.462362\pi$
$228$	66390.6			1.27714
$229$		−	16942.0i		−	0.323068i	−0.986867	−	0.161534i	$-0.948356\pi$
$229$		−	16942.0i		−	0.323068i	0.986867	−	0.161534i	$-0.0516441\pi$
$230$	31229.2	+	20589.8i	0.590345	+	0.389221i
$231$	70007.5			1.31196
$232$			28932.4i			0.537537i
$233$		−	698.804i		−	0.0128719i	−0.999979	−	0.00643596i	$-0.997951\pi$
$233$		−	698.804i		−	0.0128719i	0.999979	−	0.00643596i	$-0.00204864\pi$
$234$	−156749.			−2.86268
$235$	−36353.7	−	20197.1i	−0.658284	−	0.365725i
$236$	7272.53			0.130575
$237$	−120209.			−2.14014
$238$			16048.8i			0.283328i
$239$	−43819.7			−0.767139			−0.383569	−	0.923512i	$-0.625305\pi$
$239$	−43819.7			−0.767139			−0.383569	+	0.923512i	$0.625305\pi$
$240$	−22062.1	−	12257.1i	−0.383023	−	0.212797i
$241$			73504.5i			1.26555i	0.774335	+	0.632775i	$0.218084\pi$
$241$			73504.5i			1.26555i	−0.774335	+	0.632775i	$0.781916\pi$
$242$		−	24273.3i		−	0.414475i
$243$			15400.0i			0.260801i
$244$			21614.9i			0.363056i
$245$	18853.3	−	33934.8i	0.314090	−	0.565345i
$246$	−31833.7			−0.526037
$247$	173739.			2.84776
$248$			9898.64i			0.160943i
$249$			166021.i			2.67771i
$250$	2185.04	+	44140.1i	0.0349607	+	0.706242i
$251$		−	111041.i		−	1.76253i	−0.472619	−	0.881267i	$-0.656691\pi$
$251$		−	111041.i		−	1.76253i	0.472619	−	0.881267i	$-0.343309\pi$
$252$	39099.7			0.615704
$253$	−6103.25	+	80383.3i	−0.0953498	+	1.25581i
$254$	50974.8			0.790112
$255$	−67161.3	−	37313.0i	−1.03285	−	0.573825i
$256$	4096.00			0.0625000
$257$		−	41762.6i		−	0.632297i	−0.948710	−	0.316148i	$-0.897610\pi$
$257$		−	41762.6i		−	0.632297i	0.948710	−	0.316148i	$-0.102390\pi$
$258$	−20507.0			−0.308080
$259$	−65546.1			−0.977119
$260$	−57734.9	−	32075.9i	−0.854066	−	0.474495i
$261$	214579.			3.14996
$262$			39084.2i			0.569375i
$263$	−75888.8			−1.09715			−0.548575	−	0.836101i	$-0.684830\pi$
$263$	−75888.8			−1.09715			−0.548575	+	0.836101i	$0.684830\pi$
$264$		−	54391.8i		−	0.780416i
$265$	−17790.7	+	32022.4i	−0.253339	+	0.455997i
$266$	−43337.8			−0.612497
$267$	−49604.2			−0.695819
$268$	−15965.1			−0.222281
$269$	113539.			1.56907			0.784535	−	0.620085i	$-0.212902\pi$
$269$	113539.			1.56907			0.784535	+	0.620085i	$0.212902\pi$
$270$	−47028.4	+	84648.6i	−0.645109	+	1.16116i
$271$	−45102.0			−0.614125			−0.307063	−	0.951689i	$-0.599346\pi$
$271$	−45102.0			−0.614125			−0.307063	+	0.951689i	$0.599346\pi$
$272$	12469.0			0.168537
$273$	151708.			2.03555
$274$			51004.4i			0.679370i
$275$	−80869.0	+	50315.6i	−1.06934	+	0.665330i
$276$	−5053.98	+	66563.8i	−0.0663461	+	0.873816i
$277$		−	2346.19i		−	0.0305776i	−0.999883	−	0.0152888i	$-0.995133\pi$
$277$		−	2346.19i		−	0.0305776i	0.999883	−	0.0152888i	$-0.00486676\pi$
$278$		−	53926.2i		−	0.697767i
$279$	73413.8			0.943125
$280$	14401.5	+	8001.07i	0.183692	+	0.102054i
$281$		−	89939.3i		−	1.13903i	−0.821979	−	0.569517i	$-0.807130\pi$
$281$		−	89939.3i		−	1.13903i	0.821979	−	0.569517i	$-0.192870\pi$
$282$		−	74217.8i		−	0.933276i
$283$	146762.			1.83249			0.916243	−	0.400623i	$-0.131206\pi$
$283$	146762.			1.83249			0.916243	+	0.400623i	$0.131206\pi$
$284$	19789.4			0.245356
$285$	100759.	−	181361.i	1.24049	−	2.23282i
$286$		−	142339.i		−	1.74017i
$287$	20780.1			0.252280
$288$		−	30378.2i		−	0.366250i
$289$	−45563.0			−0.545527
$290$	79035.2	+	43909.8i	0.939776	+	0.522114i
$291$		−	243071.i		−	2.87044i
$292$			62922.8i			0.737976i
$293$	33584.3			0.391202			0.195601	−	0.980684i	$-0.437334\pi$
$293$	33584.3			0.391202			0.195601	+	0.980684i	$0.437334\pi$
$294$	69279.5			0.801512
$295$	11037.3	−	19866.5i	0.126829	−	0.228285i
$296$			50925.6i			0.581236i
$297$	−208692.			−2.36589
$298$	−120987.			−1.36240
$299$	−13225.9	+	174192.i	−0.147939	+	1.94844i
$300$	−66966.0	+	41665.3i	−0.744066	+	0.462948i
$301$	13386.4			0.147751
$302$		−	48455.8i		−	0.531291i
$303$		−	179881.i		−	1.95929i
$304$			33671.0i			0.364342i
$305$	59045.9	+	32804.3i	0.634732	+	0.352639i
$306$		−	92477.1i		−	0.987624i
$307$			22110.9i			0.234601i	0.993096	+	0.117300i	$0.0374240\pi$
$307$			22110.9i			0.234601i	−0.993096	+	0.117300i	$0.962576\pi$
$308$			35505.4i			0.374277i
$309$		−	73623.5i		−	0.771080i
$310$	27040.3	+	15022.9i	0.281377	+	0.156325i
$311$	−53061.2			−0.548601			−0.274300	−	0.961644i	$-0.588446\pi$
$311$	−53061.2			−0.548601			−0.274300	+	0.961644i	$0.588446\pi$
$312$		−	117868.i		−	1.21084i
$313$	−126229.			−1.28846			−0.644231	−	0.764831i	$-0.722822\pi$
$313$	−126229.			−1.28846			−0.644231	+	0.764831i	$0.722822\pi$
$314$			68768.6i			0.697478i
$315$	59340.4	−	106809.i	0.598039	−	1.07644i
$316$		−	60966.1i		−	0.610540i
$317$			21200.1i			0.210969i	0.994421	+	0.105485i	$0.0336394\pi$
$317$			21200.1i			0.210969i	−0.994421	+	0.105485i	$0.966361\pi$
$318$	−65375.1			−0.646485
$319$			194853.i			1.91481i
$320$	6216.37	−	11189.1i	0.0607068	−	0.109269i
$321$		−	207496.i		−	2.01372i
$322$	3299.08	−	43450.8i	0.0318186	−	0.419070i
$323$			102501.i			0.982479i
$324$	−64068.1			−0.610312
$325$	−175245.	+	109035.i	−1.65912	+	1.03228i
$326$	89710.9			0.844132
$327$	−103029.			−0.963526
$328$		−	16144.9i		−	0.150068i
$329$			48447.2i			0.447586i
$330$	−148583.	−	82548.8i	−1.36440	−	0.758024i
$331$	−100592.			−0.918136			−0.459068	−	0.888401i	$-0.651817\pi$
$331$	−100592.			−0.918136			−0.459068	+	0.888401i	$0.651817\pi$
$332$	−84199.9			−0.763898
$333$	377693.			3.40604
$334$	−102685.			−0.920478
$335$	−24229.8	+	43612.3i	−0.215904	+	0.388615i
$336$			29401.3i			0.260428i
$337$	−30010.0			−0.264244			−0.132122	−	0.991233i	$-0.542179\pi$
$337$	−30010.0			−0.264244			−0.132122	+	0.991233i	$0.542179\pi$
$338$		−	227670.i		−	1.99284i
$339$			23976.6i			0.208636i
$340$	18923.8	−	34061.9i	0.163701	−	0.294653i
$341$			66665.1i			0.573310i
$342$	249723.			2.13504
$343$	−115149.			−0.978754
$344$		−	10400.5i		−	0.0878892i
$345$	174163.	+	114828.i	1.46325	+	0.964737i
$346$	−72715.9			−0.607403
$347$		−	123470.i		−	1.02542i	−0.858561	−	0.512711i	$-0.828641\pi$
$347$		−	123470.i		−	1.02542i	0.858561	−	0.512711i	$-0.171359\pi$
$348$			161354.i			1.33236i
$349$	30376.7			0.249396			0.124698	−	0.992195i	$-0.460204\pi$
$349$	30376.7			0.249396			0.124698	+	0.992195i	$0.460204\pi$
$350$	43713.4	−	27197.9i	0.356844	−	0.222023i
$351$	−452241.			−3.67076
$352$	27585.7			0.222637
$353$			157208.i			1.26161i	0.775941	+	0.630805i	$0.217275\pi$
$353$			157208.i			1.26161i	−0.775941	+	0.630805i	$0.782725\pi$
$354$	40558.4			0.323649
$355$	30033.8	−	54059.1i	0.238316	−	0.428956i
$356$		−	25157.5i		−	0.198504i
$357$			89503.1i			0.702266i
$358$			5643.26i			0.0440315i
$359$		−	68755.7i		−	0.533482i	−0.963768	−	0.266741i	$-0.914053\pi$
$359$		−	68755.7i		−	0.533482i	0.963768	−	0.266741i	$-0.0859469\pi$
$360$	−82984.9	−	46104.1i	−0.640315	−	0.355742i
$361$	−146470.			−1.12392
$362$	−2076.07			−0.0158425
$363$		−	135371.i		−	1.02733i
$364$			76940.9i			0.580704i
$365$	171888.	+	95496.0i	1.29020	+	0.716802i
$366$			120545.i			0.899885i
$367$	−178094.			−1.32226			−0.661131	−	0.750270i	$-0.729923\pi$
$367$	−178094.			−1.32226			−0.661131	+	0.750270i	$0.729923\pi$
$368$	−33758.8	−	2563.20i	−0.249282	−	0.0189272i
$369$	−119740.			−0.879399
$370$	139115.	+	77288.2i	1.01618	+	0.564560i
$371$	42674.9			0.310045
$372$			55204.0i			0.398919i
$373$	−107326.			−0.771411			−0.385705	−	0.922622i	$-0.626042\pi$
$373$	−107326.			−0.771411			−0.385705	+	0.922622i	$0.626042\pi$
$374$	83976.0			0.600360
$375$	12185.8	+	246167.i	0.0866549	+	1.75052i
$376$	37640.7			0.266245
$377$			422251.i			2.97090i
$378$	112808.			0.789506
$379$		−	55291.9i		−	0.384931i	−0.981304	−	0.192466i	$-0.938352\pi$
$379$		−	55291.9i		−	0.384931i	0.981304	−	0.192466i	$-0.0616484\pi$
$380$	91979.8	+	51101.5i	0.636980	+	0.353888i
$381$	284283.			1.95840
$382$	−97266.9			−0.666558
$383$	241157.			1.64400			0.822001	−	0.569486i	$-0.192858\pi$
$383$	241157.			1.64400			0.822001	+	0.569486i	$0.192858\pi$
$384$	22843.1			0.154915
$385$	96990.8	+	53885.4i	0.654348	+	0.363538i
$386$	55056.0			0.369513
$387$	−77135.6			−0.515031
$388$	123277.			0.818879
$389$		−	66619.2i		−	0.440251i	−0.975472	−	0.220125i	$-0.929353\pi$
$389$		−	66619.2i		−	0.440251i	0.975472	−	0.220125i	$-0.0706466\pi$
$390$	−321984.	−	178885.i	−2.11692	−	1.17610i
$391$	−102768.	−	7802.87i	−0.672211	−	0.0510389i
$392$			35136.2i			0.228656i
$393$			217970.i			1.41127i
$394$	−44091.0			−0.284025
$395$	−166542.	−	92526.3i	−1.06741	−	0.593022i
$396$		−	204591.i		−	1.30465i
$397$			112055.i			0.710965i	0.934683	+	0.355483i	$0.115683\pi$
$397$			112055.i			0.710965i	−0.934683	+	0.355483i	$0.884317\pi$
$398$	106420.			0.671825
$399$	−241692.			−1.51816
$400$	−21131.2	−	33962.8i	−0.132070	−	0.212268i
$401$		−	24949.3i		−	0.155156i	−0.996986	−	0.0775782i	$-0.975281\pi$
$401$		−	24949.3i		−	0.155156i	0.996986	−	0.0775782i	$-0.0247188\pi$
$402$	−89036.5			−0.550955
$403$			144465.i			0.889512i
$404$	91229.2			0.558948
$405$	−97234.3	+	175016.i	−0.592802	+	1.06701i
$406$		−	105327.i		−	0.638981i
$407$			342973.i			2.07048i
$408$	69538.8			0.417741
$409$	−55306.2			−0.330619			−0.165309	−	0.986242i	$-0.552862\pi$
$409$	−55306.2			−0.330619			−0.165309	+	0.986242i	$0.552862\pi$
$410$	−44103.4	−	24502.7i	−0.262364	−	0.145762i
$411$			284448.i			1.68391i
$412$	37339.3			0.219974
$413$	−26475.3			−0.155218
$414$	−19010.1	+	250374.i	−0.110914	+	1.46079i
$415$	−127788.	+	230011.i	−0.741980	+	1.33552i
$416$	59778.7			0.345430
$417$		−	300743.i		−	1.72951i
$418$			226767.i			1.29786i
$419$		−	94596.2i		−	0.538822i	−0.963025	−	0.269411i	$-0.913171\pi$
$419$		−	94596.2i		−	0.538822i	0.963025	−	0.269411i	$-0.0868291\pi$
$420$	80316.1	+	44621.4i	0.455307	+	0.252956i
$421$			60097.0i			0.339069i	0.985524	+	0.169535i	$0.0542265\pi$
$421$			60097.0i			0.339069i	−0.985524	+	0.169535i	$0.945774\pi$
$422$			82889.2i			0.465450i
$423$		−	279164.i		−	1.56020i
$424$		−	33156.0i		−	0.184429i
$425$	−64327.4	−	103389.i	−0.356138	−	0.572397i
$426$	110364.			0.608147
$427$		−	78688.1i		−	0.431572i
$428$	105235.			0.574476
$429$		−	793817.i		−	4.31326i
$430$	−28411.2	−	15784.5i	−0.153657	−	0.0853675i
$431$			6845.04i			0.0368487i	0.999830	+	0.0184243i	$0.00586498\pi$
$431$			6845.04i			0.0368487i	−0.999830	+	0.0184243i	$0.994135\pi$
$432$		−	87645.2i		−	0.469635i
$433$	3852.76			0.0205492			0.0102746	−	0.999947i	$-0.496729\pi$
$433$	3852.76			0.0205492			0.0102746	+	0.999947i	$0.496729\pi$
$434$		−	36035.5i		−	0.191316i
$435$	440774.	+	244882.i	2.32936	+	1.29413i
$436$		−	52252.7i		−	0.274875i
$437$	21070.7	−	277513.i	0.110336	−	1.45318i
$438$			350916.i			1.82917i
$439$	−199222.			−1.03373			−0.516867	−	0.856066i	$-0.672902\pi$
$439$	−199222.			−1.03373			−0.516867	+	0.856066i	$0.672902\pi$
$440$	41865.9	−	75356.3i	0.216249	−	0.389237i
$441$	260589.			1.33992
$442$	181978.			0.931481
$443$			9495.80i			0.0483865i	0.999707	+	0.0241932i	$0.00770170\pi$
$443$			9495.80i			0.0483865i	−0.999707	+	0.0241932i	$0.992298\pi$
$444$			284009.i			1.44067i
$445$	−68723.4	−	38180.8i	−0.347044	−	0.192808i
$446$	−111221.			−0.559134
$447$	−674734.			−3.37690
$448$	−14911.3			−0.0742950
$449$	141119.			0.699989			0.349995	−	0.936752i	$-0.386183\pi$
$449$	141119.			0.699989			0.349995	+	0.936752i	$0.386183\pi$
$450$	−251887.	+	156721.i	−1.24389	+	0.773930i
$451$		−	108732.i		−	0.534572i
$452$	−12160.1			−0.0595197
$453$		−	270235.i		−	1.31688i
$454$			34386.9i			0.166833i
$455$	210181.	+	116771.i	1.01525	+	0.564042i
$456$			187781.i			0.903071i
$457$	−127359.			−0.609815			−0.304907	−	0.952382i	$-0.598626\pi$
$457$	−127359.			−0.609815			−0.304907	+	0.952382i	$0.598626\pi$
$458$	47919.2			0.228444
$459$		−	266809.i		−	1.26641i
$460$	−58236.7	+	88329.6i	−0.275221	+	0.417437i
$461$	60662.6			0.285443			0.142721	−	0.989763i	$-0.454415\pi$
$461$	60662.6			0.285443			0.142721	+	0.989763i	$0.454415\pi$
$462$			198011.i			0.927696i
$463$			96909.4i			0.452068i	0.974119	+	0.226034i	$0.0725761\pi$
$463$			96909.4i			0.452068i	−0.974119	+	0.226034i	$0.927424\pi$
$464$	−81833.1			−0.380096
$465$	150802.	+	83781.5i	0.697431	+	0.387474i
$466$	1976.52			0.00910182
$467$	−136861.			−0.627545			−0.313773	−	0.949498i	$-0.601593\pi$
$467$	−136861.			−0.627545			−0.313773	+	0.949498i	$0.601593\pi$
$468$		−	443352.i		−	2.02422i
$469$	58120.3			0.264230
$470$	57126.1	−	102824.i	0.258606	−	0.465477i
$471$			383518.i			1.72880i
$472$			20569.8i			0.0923308i
$473$		−	70044.8i		−	0.313079i
$474$		−	340004.i		−	1.51331i
$475$	279190.	−	173708.i	1.23741	−	0.769898i
$476$	−45392.9			−0.200343
$477$	−245903.			−1.08076
$478$		−	123941.i		−	0.542449i
$479$		−	239398.i		−	1.04340i	−0.853130	−	0.521699i	$-0.825298\pi$
$479$		−	239398.i		−	1.04340i	0.853130	−	0.521699i	$-0.174702\pi$
$480$	34668.3	−	62401.1i	0.150470	−	0.270838i
$481$			743229.i			3.21242i
$482$	−207902.			−0.894880
$483$	18398.8	−	242322.i	0.0788669	−	1.03872i
$484$	68655.2			0.293078
$485$	187094.	−	336759.i	0.795384	−	1.43165i
$486$	−43557.8			−0.184414
$487$			454517.i			1.91643i	0.286054	+	0.958214i	$0.407656\pi$
$487$			454517.i			1.91643i	−0.286054	+	0.958214i	$0.592344\pi$
$488$	−61136.2			−0.256719
$489$	500312.			2.09230
$490$	95982.2	+	53325.1i	0.399759	+	0.222095i
$491$	427447.			1.77304			0.886522	−	0.462686i	$-0.153114\pi$
$491$	427447.			1.77304			0.886522	+	0.462686i	$0.153114\pi$
$492$		−	90039.2i		−	0.371964i
$493$	−249116.			−1.02496
$494$			491409.i			2.01367i
$495$	−558885.	−	310501.i	−2.28093	−	1.26722i
$496$	−27997.6			−0.113804
$497$	−72042.4			−0.291659
$498$	−469577.			−1.89343
$499$	38222.3			0.153503			0.0767513	−	0.997050i	$-0.475545\pi$
$499$	38222.3			0.153503			0.0767513	+	0.997050i	$0.475545\pi$
$500$	−124847.	+	6180.24i	−0.499389	+	0.0247209i
$501$	−572667.			−2.28153
$502$	314072.			1.24630
$503$	21659.9			0.0856092			0.0428046	−	0.999083i	$-0.486371\pi$
$503$	21659.9			0.0856092			0.0428046	+	0.999083i	$0.486371\pi$
$504$			110591.i			0.435369i
$505$	138456.	−	249213.i	0.542911	−	0.977209i
$506$	−227358.	−	17262.6i	−0.887993	−	0.0674225i
$507$		−	1.26970e6i		−	4.93952i
$508$			144179.i			0.558693i
$509$	−406758.			−1.57000			−0.785001	−	0.619495i	$-0.787337\pi$
$509$	−406758.			−1.57000			−0.785001	+	0.619495i	$0.787337\pi$
$510$	105537.	−	189961.i	0.405755	−	0.730337i
$511$		−	229068.i		−	0.877247i
$512$			11585.2i			0.0441942i
$513$	720484.			2.73772
$514$	118122.			0.447101
$515$	56668.7	−	102001.i	0.213663	−	0.384581i
$516$		−	58002.7i		−	0.217845i
$517$	253502.			0.948418
$518$		−	185392.i		−	0.690927i
$519$	−405532.			−1.50553
$520$	90724.3	−	163299.i	0.335519	−	0.603916i
$521$			166903.i			0.614879i	0.951568	+	0.307439i	$0.0994721\pi$
$521$			166903.i			0.614879i	−0.951568	+	0.307439i	$0.900528\pi$
$522$			606920.i			2.22736i
$523$	−161826.			−0.591622			−0.295811	−	0.955246i	$-0.595590\pi$
$523$	−161826.			−0.591622			−0.295811	+	0.955246i	$0.595590\pi$
$524$	−110547.			−0.402609
$525$	243787.	−	151681.i	0.884487	−	0.550316i
$526$		−	214646.i		−	0.775802i
$527$	−85230.0			−0.306882
$528$	153843.			0.551837
$529$	276633.	+	42251.3i	0.988536	+	0.150983i
$530$	−90572.9	−	50319.8i	−0.322438	−	0.179138i
$531$	152557.			0.541058
$532$		−	122578.i		−	0.433101i
$533$		−	235626.i		−	0.829408i
$534$		−	140302.i		−	0.492018i
$535$	159712.	−	287472.i	0.557993	−	1.00436i
$536$		−	45156.2i		−	0.157177i
$537$			31472.1i			0.109138i
$538$			321138.i			1.10950i
$539$			236634.i			0.814517i
$540$	−239422.	−	133016.i	−0.821064	−	0.456161i
$541$	−406550.			−1.38906			−0.694528	−	0.719466i	$-0.744387\pi$
$541$	−406550.			−1.38906			−0.694528	+	0.719466i	$0.744387\pi$
$542$		−	127568.i		−	0.434252i
$543$	−11578.1			−0.0392679
$544$			35267.7i			0.119173i
$545$	−142740.	−	79302.3i	−0.480565	−	0.266989i
$546$			429094.i			1.43935i
$547$		−	320484.i		−	1.07110i	−0.844502	−	0.535552i	$-0.820103\pi$
$547$		−	320484.i		−	1.07110i	0.844502	−	0.535552i	$-0.179897\pi$
$548$	−144262.			−0.480387
$549$			453420.i			1.50438i
$550$	−142314.	−	228732.i	−0.470459	−	0.756139i
$551$		−	672706.i		−	2.21576i
$552$	−188271.	−	14294.8i	−0.617881	−	0.0469137i
$553$			221944.i			0.725761i
$554$	6636.02			0.0216216
$555$	775833.	+	431031.i	2.51873	+	1.39934i
$556$	152526.			0.493396
$557$	3608.33			0.0116304			0.00581522	−	0.999983i	$-0.498149\pi$
$557$	3608.33			0.0116304			0.00581522	+	0.999983i	$0.498149\pi$
$558$			207646.i			0.666890i
$559$		−	151789.i		−	0.485753i
$560$	−22630.4	+	40733.5i	−0.0721634	+	0.129890i
$561$	468329.			1.48808
$562$	254387.			0.805419
$563$	−58590.4			−0.184846			−0.0924229	−	0.995720i	$-0.529461\pi$
$563$	−58590.4			−0.184846			−0.0924229	+	0.995720i	$0.529461\pi$
$564$	209920.			0.659926
$565$	−18455.0	+	33218.0i	−0.0578120	+	0.104058i
$566$			415106.i			1.29576i
$567$	233237.			0.725491
$568$			55972.9i			0.173493i
$569$			547172.i			1.69005i	0.534727	+	0.845025i	$0.320415\pi$
$569$			547172.i			1.69005i	−0.534727	+	0.845025i	$0.679585\pi$
$570$	512966.	+	284990.i	1.57884	+	0.877161i
$571$		−	35911.1i		−	0.110143i	−0.998482	−	0.0550715i	$-0.982461\pi$
$571$		−	35911.1i		−	0.110143i	0.998482	−	0.0550715i	$-0.0175387\pi$
$572$	402596.			1.23049
$573$	−542451.			−1.65216
$574$			58774.9i			0.178389i
$575$	152908.	+	293142.i	0.462482	+	0.886629i
$576$	85922.6			0.258978
$577$		−	40714.7i		−	0.122292i	−0.998129	−	0.0611462i	$-0.980524\pi$
$577$		−	40714.7i		−	0.122292i	0.998129	−	0.0611462i	$-0.0194756\pi$
$578$		−	128872.i		−	0.385746i
$579$	307044.			0.915890
$580$	−124196.	+	223545.i	−0.369190	+	0.664522i
$581$	306526.			0.908061
$582$	687510.			2.02970
$583$		−	223298.i		−	0.656974i
$584$	−177972.			−0.521828
$585$	−1.21112e6	−	672862.i	−3.53895	−	1.96614i
$586$			94990.7i			0.276622i
$587$		−	463833.i		−	1.34613i	−0.739585	−	0.673063i	$-0.764978\pi$
$587$		−	463833.i		−	1.34613i	0.739585	−	0.673063i	$-0.235022\pi$
$588$			195952.i			0.566755i
$589$		−	230153.i		−	0.663416i
$590$	56191.0	+	31218.2i	0.161422	+	0.0896817i
$591$	−245892.			−0.703996
$592$	−144039.			−0.410996
$593$			404063.i			1.14905i	0.818486	+	0.574527i	$0.194814\pi$
$593$			404063.i			1.14905i	−0.818486	+	0.574527i	$0.805186\pi$
$594$		−	590271.i		−	1.67293i
$595$	−68891.4	+	124001.i	−0.194595	+	0.350260i
$596$		−	342202.i		−	0.963363i
$597$	593496.			1.66521
$598$	−492690.	−	37408.4i	−1.37775	−	0.104608i
$599$	638220.			1.77876			0.889379	−	0.457170i	$-0.151137\pi$
$599$	638220.			1.77876			0.889379	+	0.457170i	$0.151137\pi$
$600$	−117847.	−	189408.i	−0.327354	−	0.526134i
$601$	70665.8			0.195641			0.0978206	−	0.995204i	$-0.468813\pi$
$601$	70665.8			0.195641			0.0978206	+	0.995204i	$0.468813\pi$
$602$			37862.4i			0.104476i
$603$	−334904.			−0.921054
$604$	137054.			0.375679
$605$	104196.	−	187547.i	0.284669	−	0.512389i
$606$	508779.			1.38543
$607$		−	14809.2i		−	0.0401932i	−0.999798	−	0.0200966i	$-0.993603\pi$
$607$		−	14809.2i		−	0.0401932i	0.999798	−	0.0200966i	$-0.00639738\pi$
$608$	−95236.0			−0.257629
$609$		−	587402.i		−	1.58380i
$610$	−92784.5	+	167007.i	−0.249354	+	0.448823i
$611$	549344.			1.47151
$612$	261565.			0.698355
$613$	−591217.			−1.57335			−0.786677	−	0.617365i	$-0.788200\pi$
$613$	−591217.			−1.57335			−0.786677	+	0.617365i	$0.788200\pi$
$614$	−62539.0			−0.165888
$615$	−245962.	−	136650.i	−0.650306	−	0.361292i
$616$	−100424.			−0.264653
$617$	283392.			0.744418			0.372209	−	0.928149i	$-0.378600\pi$
$617$	283392.			0.744418			0.372209	+	0.928149i	$0.378600\pi$
$618$	208239.			0.545236
$619$		−	116449.i		−	0.303916i	−0.988387	−	0.151958i	$-0.951442\pi$
$619$		−	116449.i		−	0.303916i	0.988387	−	0.151958i	$-0.0485578\pi$
$620$	−42491.1	+	76481.6i	−0.110539	+	0.198964i
$621$	−54846.8	+	722363.i	−0.142222	+	1.87315i
$622$		−	150080.i		−	0.387919i
$623$			91584.9i			0.235965i
$624$	333382.			0.856196
$625$	−172594.	+	350427.i	−0.441841	+	0.897094i
$626$		−	357030.i		−	0.911080i
$627$			1.26466e6i			3.21692i
$628$	−194507.			−0.493192
$629$	−438483.			−1.10829
$630$	302103.	+	167840.i	0.761156	+	0.422877i
$631$			406865.i			1.02186i	0.859622	+	0.510930i	$0.170699\pi$
$631$			406865.i			1.02186i	−0.859622	+	0.510930i	$0.829301\pi$
$632$	172438.			0.431717
$633$			462268.i			1.15368i
$634$	−59962.9			−0.149178
$635$	393856.	+	218815.i	0.976765	+	0.542663i
$636$		−	184909.i		−	0.457134i
$637$			512792.i			1.26375i
$638$	−551128.			−1.35398
$639$	415126.			1.01667
$640$	31647.6	+	17582.6i	0.0772648	+	0.0429262i
$641$			125919.i			0.306462i	0.988190	+	0.153231i	$0.0489678\pi$
$641$			125919.i			0.306462i	−0.988190	+	0.153231i	$0.951032\pi$
$642$	586887.			1.42392
$643$	355760.			0.860468			0.430234	−	0.902717i	$-0.358431\pi$
$643$	355760.			0.860468			0.430234	+	0.902717i	$0.358431\pi$
$644$	122898.	+	9331.22i	0.296327	+	0.0224992i
$645$	−158447.	−	88028.9i	−0.380860	−	0.211595i
$646$	−289917.			−0.694717
$647$		−	555323.i		−	1.32659i	−0.748357	−	0.663296i	$-0.769157\pi$
$647$		−	555323.i		−	1.32659i	0.748357	−	0.663296i	$-0.230843\pi$
$648$		−	181212.i		−	0.431556i
$649$			138533.i			0.328900i
$650$	−308397.	−	495667.i	−0.729935	−	1.17318i
$651$		−	200968.i		−	0.474203i
$652$			253741.i			0.596891i
$653$			252357.i			0.591819i	0.955216	+	0.295910i	$0.0956227\pi$
$653$			252357.i			0.591819i	−0.955216	+	0.295910i	$0.904377\pi$
$654$		−	291410.i		−	0.681316i
$655$	−167773.	+	301983.i	−0.391057	+	0.703882i
$656$	45664.7			0.106114
$657$			1.31994e6i			3.05791i
$658$	−137029.			−0.316491
$659$			608460.i			1.40107i	0.713616	+	0.700537i	$0.247056\pi$
$659$			608460.i			1.40107i	−0.713616	+	0.700537i	$0.752944\pi$
$660$	233483.	−	420257.i	0.536004	−	0.964778i
$661$			297914.i			0.681848i	0.940091	+	0.340924i	$0.110740\pi$
$661$			297914.i			0.681848i	−0.940091	+	0.340924i	$0.889260\pi$
$662$		−	284517.i		−	0.649220i
$663$	1.01488e6			2.30880
$664$		−	238153.i		−	0.540157i
$665$	−334849.	−	186033.i	−0.757191	−	0.420674i
$666$			1.06828e6i			2.40844i
$667$	674460.	+	51209.6i	1.51602	+	0.115107i
$668$		−	290437.i		−	0.650876i
$669$	−620271.			−1.38589
$670$	−123354.	−	68532.2i	−0.274792	−	0.152667i
$671$	−411739.			−0.914485
$672$	−83159.4			−0.184150
$673$		−	502358.i		−	1.10913i	−0.832140	−	0.554566i	$-0.812884\pi$
$673$		−	502358.i		−	1.10913i	0.832140	−	0.554566i	$-0.187116\pi$
$674$		−	84881.0i		−	0.186849i
$675$	−726728.	+	452160.i	−1.59501	+	0.992396i
$676$	643947.			1.40915
$677$	−494379.			−1.07866			−0.539328	−	0.842096i	$-0.681322\pi$
$677$	−494379.			−1.07866			−0.539328	+	0.842096i	$0.681322\pi$
$678$	−67816.2			−0.147528
$679$	−448786.			−0.973418
$680$	96341.5	+	53524.7i	0.208351	+	0.115754i
$681$			191774.i			0.413518i
$682$	−188557.			−0.405392
$683$		−	593863.i		−	1.27305i	−0.771257	−	0.636524i	$-0.780372\pi$
$683$		−	593863.i		−	1.27305i	0.771257	−	0.636524i	$-0.219628\pi$
$684$			706324.i			1.50970i
$685$	−218942.	+	394084.i	−0.466604	+	0.839862i
$686$		−	325692.i		−	0.692084i
$687$	267242.			0.566229
$688$	29416.9			0.0621471
$689$		−	483892.i		−	1.01932i
$690$	−324782.	+	492609.i	−0.682172	+	1.03467i
$691$	−368387.			−0.771522			−0.385761	−	0.922599i	$-0.626061\pi$
$691$	−368387.			−0.771522			−0.385761	+	0.922599i	$0.626061\pi$
$692$		−	205672.i		−	0.429499i
$693$			744803.i			1.55087i
$694$	349226.			0.725083
$695$	231485.	−	416660.i	0.479239	−	0.862605i
$696$	−456378.			−0.942120
$697$	139012.			0.286146
$698$			85918.2i			0.176350i
$699$	11022.9			0.0225601
$700$	76927.2	+	123640.i	0.156994	+	0.252327i
$701$		−	99227.4i		−	0.201928i	−0.994890	−	0.100964i	$-0.967807\pi$
$701$		−	99227.4i		−	0.201928i	0.994890	−	0.100964i	$-0.0321926\pi$
$702$		−	1.27913e6i		−	2.59562i
$703$		−	1.18407e6i		−	2.39589i
$704$			78024.0i			0.157428i
$705$	318589.	−	573442.i	0.640991	−	1.15375i
$706$	−444651.			−0.892093
$707$	−332116.			−0.664432
$708$			114717.i			0.228855i
$709$		−	406648.i		−	0.808958i	−0.914547	−	0.404479i	$-0.867453\pi$
$709$		−	406648.i		−	0.808958i	0.914547	−	0.404479i	$-0.132547\pi$
$710$	152902.	+	84948.3i	0.303317	+	0.168515i
$711$		−	1.27890e6i		−	2.52986i
$712$	71156.3			0.140363
$713$	230753.	+	17520.4i	0.453909	+	0.0344639i
$714$	−253153.			−0.496577
$715$	611008.	−	1.09978e6i	1.19518	−	2.15127i
$716$	−15961.5			−0.0311350
$717$		−	691210.i		−	1.34453i
$718$	194471.			0.377229
$719$	−82950.3			−0.160458			−0.0802288	−	0.996776i	$-0.525565\pi$
$719$	−82950.3			−0.160458			−0.0802288	+	0.996776i	$0.525565\pi$
$720$	130402.	−	234717.i	0.251547	−	0.452771i
$721$	−135932.			−0.261488
$722$		−	414281.i		−	0.794731i
$723$	−1.15946e6			−2.21808
$724$		−	5872.01i		−	0.0112024i
$725$	422176.	+	678536.i	0.803188	+	1.29091i
$726$	382886.			0.726434
$727$	−220573.			−0.417334			−0.208667	−	0.977987i	$-0.566913\pi$
$727$	−220573.			−0.417334			−0.208667	+	0.977987i	$0.566913\pi$
$728$	−217622.			−0.410620
$729$	405771.			0.763530
$730$	−270103.	+	486171.i	−0.506856	+	0.912313i
$731$	89550.8			0.167585
$732$	−340953.			−0.636314
$733$	167066.			0.310942			0.155471	−	0.987840i	$-0.450311\pi$
$733$	167066.			0.310942			0.155471	+	0.987840i	$0.450311\pi$
$734$		−	503726.i		−	0.934980i
$735$	535286.	+	297390.i	0.990858	+	0.550494i
$736$	7249.83	−	95484.4i	0.0133836	−	0.176269i
$737$		−	304117.i		−	0.559894i
$738$		−	338675.i		−	0.621829i
$739$	354542.			0.649201			0.324600	−	0.945851i	$-0.394770\pi$
$739$	354542.			0.649201			0.324600	+	0.945851i	$0.394770\pi$
$740$	−218604.	+	393475.i	−0.399204	+	0.718545i
$741$			2.74055e6i			4.99117i
$742$			120703.i			0.219235i
$743$	−713227.			−1.29196			−0.645981	−	0.763353i	$-0.723552\pi$
$743$	−713227.			−1.29196			−0.645981	+	0.763353i	$0.723552\pi$
$744$	−156141.			−0.282079
$745$	−934800.	−	519349.i	−1.68425	−	0.935722i
$746$		−	303563.i		−	0.545470i
$747$	−1.76628e6			−3.16532
$748$			237520.i			0.424519i
$749$	−383102.			−0.682891
$750$	−696264.	+	34466.8i	−1.23780	+	0.0612743i
$751$		−	139576.i		−	0.247475i	−0.992315	−	0.123737i	$-0.960512\pi$
$751$		−	139576.i		−	0.247475i	0.992315	−	0.123737i	$-0.0394881\pi$
$752$			106464.i			0.188264i
$753$	1.75156e6			3.08913
$754$	−1.19431e6			−2.10074
$755$	208002.	−	374393.i	0.364900	−	0.656801i
$756$			319069.i			0.558265i
$757$	716258.			1.24991			0.624953	−	0.780662i	$-0.285118\pi$
$757$	716258.			1.24991			0.624953	+	0.780662i	$0.285118\pi$
$758$	156389.			0.272187
$759$	−1.26796e6	−	96272.3i	−2.20101	−	0.167116i
$760$	−144537.	+	260158.i	−0.250237	+	0.450413i
$761$	−833237.			−1.43880			−0.719398	−	0.694598i	$-0.755582\pi$
$761$	−833237.			−1.43880			−0.719398	+	0.694598i	$0.755582\pi$
$762$			804075.i			1.38480i
$763$			190224.i			0.326750i
$764$		−	275112.i		−	0.471328i
$765$	396969.	−	714522.i	0.678319	−	1.22094i
$766$			682095.i			1.16248i
$767$			300205.i			0.510301i
$768$			64610.1i			0.109541i
$769$		−	237891.i		−	0.402277i	−0.979563	−	0.201138i	$-0.935536\pi$
$769$		−	237891.i		−	0.402277i	0.979563	−	0.201138i	$-0.0644641\pi$
$770$	−152411.	+	274331.i	−0.257060	+	0.462694i
$771$	658761.			1.10820
$772$			155722.i			0.261285i
$773$	−908634.			−1.52065			−0.760327	−	0.649541i	$-0.774961\pi$
$773$	−908634.			−1.52065			−0.760327	+	0.649541i	$0.774961\pi$
$774$		−	218172.i		−	0.364182i
$775$	144439.	+	232147.i	0.240481	+	0.386510i
$776$			348681.i			0.579035i
$777$		−	1.03392e6i		−	1.71256i
$778$	188427.			0.311304
$779$			375385.i			0.618589i
$780$	505964.	−	910707.i	0.831630	−	1.49689i
$781$			376965.i			0.618015i
$782$	22069.9	−	290673.i	0.0360899	−	0.475325i
$783$			1.75104e6i			2.85610i
$784$	−99380.0			−0.161684
$785$	−295197.	+	531339.i	−0.479041	+	0.862248i
$786$	−616512.			−0.997921
$787$	854343.			1.37938			0.689688	−	0.724106i	$-0.257748\pi$
$787$	854343.			1.37938			0.689688	+	0.724106i	$0.257748\pi$
$788$		−	124708.i		−	0.200836i
$789$		−	1.19707e6i		−	1.92293i
$790$	261704.	−	471053.i	0.419330	−	0.754771i
$791$	44268.4			0.0707523
$792$	578670.			0.922530
$793$	−892247.			−1.41886
$794$	−316938.			−0.502728
$795$	−505119.	−	280630.i	−0.799208	−	0.444018i
$796$			301000.i			0.475052i
$797$	449588.			0.707779			0.353890	−	0.935287i	$-0.384859\pi$
$797$	449588.			0.707779			0.353890	+	0.935287i	$0.384859\pi$
$798$		−	683609.i		−	1.07350i
$799$			324097.i			0.507669i
$800$	96061.3	−	59768.1i	0.150096	−	0.0933876i
$801$		−	527735.i		−	0.822528i
$802$	70567.3			0.109712
$803$	−1.19861e6			−1.85885
$804$		−	251833.i		−	0.389584i
$805$	212008.	−	321560.i	0.327160	−	0.496216i
$806$	−408608.			−0.628980
$807$			1.79097e6i			2.75005i
$808$			258035.i			0.395236i
$809$	−123741.			−0.189068			−0.0945338	−	0.995522i	$-0.530136\pi$
$809$	−123741.			−0.189068			−0.0945338	+	0.995522i	$0.530136\pi$
$810$	−495021.	−	275020.i	−0.754490	−	0.419174i
$811$	−500818.			−0.761445			−0.380723	−	0.924689i	$-0.624325\pi$
$811$	−500818.			−0.761445			−0.380723	+	0.924689i	$0.624325\pi$
$812$	297910.			0.451827
$813$		−	711436.i		−	1.07635i
$814$	−970073.			−1.46405
$815$	693149.	+	385095.i	1.04355	+	0.579765i
$816$			196686.i			0.295387i
$817$			241821.i			0.362284i
$818$		−	156430.i		−	0.233783i
$819$			1.61400e6i			2.40623i
$820$	69304.0	−	124743.i	0.103070	−	0.185520i
$821$	−666059.			−0.988157			−0.494079	−	0.869417i	$-0.664495\pi$
$821$	−666059.			−0.988157			−0.494079	+	0.869417i	$0.664495\pi$
$822$	−804541.			−1.19071
$823$			719526.i			1.06230i	0.847278	+	0.531149i	$0.178240\pi$
$823$			719526.i			1.06230i	−0.847278	+	0.531149i	$0.821760\pi$
$824$			105611.i			0.155545i
$825$	−793675.	−	1.27562e6i	−1.16610	−	1.87419i
$826$		−	74883.5i		−	0.109756i
$827$	436353.			0.638009			0.319005	−	0.947753i	$-0.396651\pi$
$827$	436353.			0.638009			0.319005	+	0.947753i	$0.396651\pi$
$828$	−708166.	−	53768.8i	−1.03294	−	0.0784277i
$829$	685568.			0.997566			0.498783	−	0.866727i	$-0.333780\pi$
$829$	685568.			0.997566			0.498783	+	0.866727i	$0.333780\pi$
$830$	−650568.	−	361438.i	−0.944358	−	0.524659i
$831$	37008.7			0.0535922
$832$			169080.i			0.244256i
$833$	−302532.			−0.435995
$834$	850629.			1.22295
$835$	−793392.	−	440787.i	−1.13793	−	0.632202i
$836$	−641393.			−0.917724
$837$			599085.i			0.855141i
$838$	267558.			0.381005
$839$		−	379533.i		−	0.539169i	−0.962977	−	0.269585i	$-0.913114\pi$
$839$		−	379533.i		−	0.539169i	0.962977	−	0.269585i	$-0.0868864\pi$
$840$	−126208.	+	227168.i	−0.178867	+	0.321951i
$841$	927644.			1.31156
$842$	−169980.			−0.239758
$843$	1.41870e6			1.99634
$844$	−234446.			−0.329123
$845$	977299.	−	1.75908e6i	1.36872	−	2.46362i
$846$	789596.			1.10323
$847$	−249936.			−0.348388
$848$	93779.3			0.130411
$849$			2.31502e6i			3.21173i
$850$	292429.	−	181945.i	0.404746	−	0.251828i
$851$	1.18716e6	+	90137.2i	1.63927	+	0.124464i
$852$			312157.i			0.430025i
$853$			739840.i			1.01681i	0.861118	+	0.508405i	$0.169765\pi$
$853$			739840.i			1.01681i	−0.861118	+	0.508405i	$0.830235\pi$
$854$	222564.			0.305168
$855$	1.92948e6	+	1.07197e6i	2.63942	+	1.46639i
$856$			297649.i			0.406216i
$857$			423424.i			0.576519i	0.957552	+	0.288259i	$0.0930766\pi$
$857$			423424.i			0.576519i	−0.957552	+	0.288259i	$0.906923\pi$
$858$	2.24525e6			3.04994
$859$	705499.			0.956115			0.478058	−	0.878328i	$-0.341341\pi$
$859$	705499.			0.956115			0.478058	+	0.878328i	$0.341341\pi$
$860$	44645.2	−	80358.9i	0.0603640	−	0.108652i
$861$			327784.i			0.442162i
$862$	−19360.7			−0.0260559
$863$		−	402240.i		−	0.540086i	−0.962848	−	0.270043i	$-0.912962\pi$
$863$		−	402240.i		−	0.540086i	0.962848	−	0.270043i	$-0.0870380\pi$
$864$	247898.			0.332082
$865$	−561838.	−	312141.i	−0.750894	−	0.417176i
$866$			10897.2i			0.0145305i
$867$		−	718708.i		−	0.956124i
$868$	101924.			0.135281
$869$	1.16133e6			1.53786
$870$	−692631.	+	1.24670e6i	−0.915089	+	1.64711i
$871$		−	659028.i		−	0.868696i
$872$	147793.			0.194366
$873$	2.58601e6			3.39314
$874$	784926.	+	59596.9i	1.02756	+	0.0780191i
$875$	454500.	−	22498.9i	0.593633	−	0.0293863i
$876$	−992541.			−1.29342
$877$		−	1.15506e6i		−	1.50178i	−0.660427	−	0.750890i	$-0.729625\pi$
$877$		−	1.15506e6i		−	1.50178i	0.660427	−	0.750890i	$-0.270375\pi$
$878$		−	563486.i		−	0.730961i
$879$			529757.i			0.685645i
$880$	213140.	+	118415.i	0.275232	+	0.152911i
$881$			1.28080e6i			1.65018i	0.565005	+	0.825088i	$0.308874\pi$
$881$			1.28080e6i			1.65018i	−0.565005	+	0.825088i	$0.691126\pi$
$882$			737058.i			0.947468i
$883$			1.06642e6i			1.36775i	0.729599	+	0.683875i	$0.239707\pi$
$883$			1.06642e6i			1.36775i	−0.729599	+	0.683875i	$0.760293\pi$
$884$			514711.i			0.658656i
$885$	313374.	+	174102.i	0.400107	+	0.222288i
$886$	−26858.2			−0.0342144
$887$			75671.6i			0.0961802i	0.998843	+	0.0480901i	$0.0153135\pi$
$887$			75671.6i			0.0961802i	−0.998843	+	0.0480901i	$0.984687\pi$
$888$	−803298.			−1.01871
$889$		−	524876.i		−	0.664130i
$890$	107992.	−	194379.i	0.136336	−	0.245397i
$891$		−	1.22042e6i		−	1.53729i
$892$		−	314580.i		−	0.395367i
$893$	−875183.			−1.09748
$894$		−	1.90844e6i		−	2.38783i
$895$	−24224.3	+	43602.5i	−0.0302417	+	0.0544334i
$896$		−	42175.5i		−	0.0525345i
$897$	−2.74770e6	−	208624.i	−3.41495	−	0.259287i
$898$			399144.i			0.494967i
$899$	559357.			0.692102
$900$	−443273.	−	712445.i	−0.547251	−	0.879561i
$901$	285482.			0.351665
$902$	307542.			0.377999
$903$			211156.i			0.258957i
$904$		−	34394.0i		−	0.0420868i
$905$	−16040.7	−	8911.77i	−0.0195851	−	0.0108810i
$906$	764340.			0.931173
$907$	−976664.			−1.18722			−0.593609	−	0.804753i	$-0.702298\pi$
$907$	−976664.			−1.18722			−0.593609	+	0.804753i	$0.702298\pi$
$908$	−97260.9			−0.117969
$909$	1.91373e6			2.31608
$910$	−330278.	+	594482.i	−0.398838	+	0.717887i
$911$			928581.i			1.11888i	0.828871	+	0.559439i	$0.188983\pi$
$911$			928581.i			1.11888i	−0.828871	+	0.559439i	$0.811017\pi$
$912$	−531125.			−0.638568
$913$		−	1.60391e6i		−	1.92415i
$914$		−	360226.i		−	0.431204i
$915$	−517453.	+	931388.i	−0.618058	+	1.11247i
$916$			135536.i			0.161534i
$917$	402440.			0.478589
$918$	754649.			0.895488
$919$			625827.i			0.741008i	0.928831	+	0.370504i	$0.120815\pi$
$919$			625827.i			0.741008i	−0.928831	+	0.370504i	$0.879185\pi$
$920$	−249834.	−	164718.i	−0.295172	−	0.194610i
$921$	−348776.			−0.411176
$922$			171580.i			0.201839i
$923$			816891.i			0.958872i
$924$	−560060.			−0.655980
$925$	743097.	+	1.19433e6i	0.868484	+	1.39586i
$926$	−274101.			−0.319660
$927$	783273.			0.911494
$928$		−	231459.i		−	0.268768i
$929$	330895.			0.383406			0.191703	−	0.981453i	$-0.438599\pi$
$929$	330895.			0.383406			0.191703	+	0.981453i	$0.438599\pi$
$930$	−236970.	+	426533.i	−0.273985	+	0.493158i
$931$		−	816950.i		−	0.942532i
$932$			5590.43i			0.00643596i
$933$		−	836985.i		−	0.961512i
$934$		−	387101.i		−	0.443742i
$935$	648839.	+	360477.i	0.742187	+	0.412339i
$936$	1.25399e6			1.43134
$937$	276220.			0.314613			0.157306	−	0.987550i	$-0.449719\pi$
$937$	276220.			0.314613			0.157306	+	0.987550i	$0.449719\pi$
$938$			164389.i			0.186839i
$939$		−	1.99113e6i		−	2.25824i
$940$	290830.	+	161577.i	0.329142	+	0.182862i
$941$		−	1119.88i		−	0.00126471i	−1.00000		0.000632355i	$-0.999799\pi$
$941$		−	1119.88i		−	0.00126471i	1.00000		0.000632355i	$-0.000201285\pi$
$942$	−1.08475e6			−1.22244
$943$	−376364.	−	28576.1i	−0.423238	−	0.0321351i
$944$	−58180.3			−0.0652877
$945$	871607.	+	484241.i	0.976016	+	0.542248i
$946$	198117.			0.221380
$947$		−	515940.i		−	0.575306i	−0.957735	−	0.287653i	$-0.907125\pi$
$947$		−	515940.i		−	0.575306i	0.957735	−	0.287653i	$-0.0928750\pi$
$948$	961676.			1.07007
$949$	−2.59740e6			−2.88408
$950$	491321.	+	789669.i	0.544400	+	0.874979i
$951$	−334409.			−0.369758
$952$		−	128390.i		−	0.141664i
$953$	1.20850e6			1.33064			0.665318	−	0.746560i	$-0.268296\pi$
$953$	1.20850e6			1.33064			0.665318	+	0.746560i	$0.268296\pi$
$954$		−	695520.i		−	0.764210i
$955$	−751530.	−	417529.i	−0.824024	−	0.457805i
$956$	350558.			0.383569
$957$	−3.07360e6			−3.35602
$958$	677120.			0.737794
$959$	525180.			0.571046
$960$	176497.	+	98056.8i	0.191511	+	0.106398i
$961$	−732148.			−0.792779
$962$	−2.10217e6			−2.27153
$963$	2.20753e6			2.38042
$964$		−	588036.i		−	0.632775i
$965$	425389.	+	236334.i	0.456806	+	0.253789i
$966$	685392.	+	52039.6i	0.734488	+	0.0557673i
$967$			49195.7i			0.0526108i	0.999654	+	0.0263054i	$0.00837423\pi$
$967$			49195.7i			0.0526108i	−0.999654	+	0.0263054i	$0.991626\pi$
$968$			194186.i			0.207237i
$969$	−1.61685e6			−1.72195
$970$	952499.	+	529182.i	1.01233	+	0.562422i
$971$			303618.i			0.322024i	0.986952	+	0.161012i	$0.0514758\pi$
$971$			303618.i			0.322024i	−0.986952	+	0.161012i	$0.948524\pi$
$972$		−	123200.i		−	0.130400i
$973$	−555265.			−0.586509
$974$	−1.28557e6			−1.35512
$975$	−1.71991e6	−	2.76430e6i	−1.80924	−	2.90788i
$976$		−	172919.i		−	0.181528i
$977$	−604332.			−0.633121			−0.316560	−	0.948572i	$-0.602528\pi$
$977$	−604332.			−0.633121			−0.316560	+	0.948572i	$0.602528\pi$
$978$			1.41510e6i			1.47948i
$979$	479222.			0.500001
$980$	−150826.	+	271479.i	−0.157045	+	0.282672i
$981$		−	1.09611e6i		−	1.13898i
$982$			1.20900e6i			1.25373i
$983$	−1.01144e6			−1.04673			−0.523365	−	0.852109i	$-0.675324\pi$
$983$	−1.01144e6			−1.04673			−0.523365	+	0.852109i	$0.675324\pi$
$984$	254669.			0.263019
$985$	−340668.	−	189266.i	−0.351122	−	0.195074i
$986$		−	704605.i		−	0.724756i
$987$	−764203.			−0.784467
$988$	−1.38991e6			−1.42388
$989$	−242452.	−	18408.6i	−0.247875	−	0.0188203i
$990$	878229.	−	1.58076e6i	0.896061	−	1.61286i
$991$	−122441.			−0.124675			−0.0623374	−	0.998055i	$-0.519855\pi$
$991$	−122441.			−0.124675			−0.0623374	+	0.998055i	$0.519855\pi$
$992$		−	79189.1i		−	0.0804715i
$993$		−	1.58673e6i		−	1.60918i
$994$		−	203767.i		−	0.206234i
$995$	822249.	+	456819.i	0.830534	+	0.461422i
$996$		−	1.32816e6i		−	1.33885i
$997$		−	1.66838e6i		−	1.67844i	−0.543793	−	0.839219i	$-0.683012\pi$
$997$		−	1.66838e6i		−	1.67844i	0.543793	−	0.839219i	$-0.316988\pi$
$998$			108109.i			0.108543i
$999$			3.08212e6i			3.08829i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.c.a.229.18	yes	48
5.4	even	2	inner	230.5.c.a.229.31	yes	48
23.22	odd	2	inner	230.5.c.a.229.32	yes	48
115.114	odd	2	inner	230.5.c.a.229.17	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.c.a.229.17	✓	48	115.114	odd	2	inner
230.5.c.a.229.18	yes	48	1.1	even	1	trivial
230.5.c.a.229.31	yes	48	5.4	even	2	inner
230.5.c.a.229.32	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)

\(f(q)\)	\(=\)	\(q+2.82843i q^{2} +15.7740i q^{3} -8.00000 q^{4} +(-12.1414 + 21.8538i) q^{5} -44.6155 q^{6} +29.1236 q^{7} -22.6274i q^{8} -167.818 q^{9} +O(q^{10})\)	\(q+2.82843i q^{2} +15.7740i q^{3} -8.00000 q^{4} +(-12.1414 + 21.8538i) q^{5} -44.6155 q^{6} +29.1236 q^{7} -22.6274i q^{8} -167.818 q^{9} +(-61.8118 - 34.3409i) q^{10} -152.391i q^{11} -126.192i q^{12} -330.234i q^{13} +82.3741i q^{14} +(-344.720 - 191.517i) q^{15} +64.0000 q^{16} +194.828 q^{17} -474.660i q^{18} +526.110i q^{19} +(97.1308 - 174.830i) q^{20} +459.395i q^{21} +431.026 q^{22} +(-527.482 - 40.0500i) q^{23} +356.924 q^{24} +(-330.175 - 530.669i) q^{25} +934.042 q^{26} -1369.46i q^{27} -232.989 q^{28} -1278.64 q^{29} +(541.692 - 975.017i) q^{30} -437.462 q^{31} +181.019i q^{32} +2403.80 q^{33} +551.057i q^{34} +(-353.601 + 636.462i) q^{35} +1342.54 q^{36} -2250.61 q^{37} -1488.06 q^{38} +5209.09 q^{39} +(494.494 + 274.728i) q^{40} +713.512 q^{41} -1299.37 q^{42} +459.640 q^{43} +1219.13i q^{44} +(2037.53 - 3667.45i) q^{45} +(113.279 - 1491.94i) q^{46} +1663.50i q^{47} +1009.53i q^{48} -1552.81 q^{49} +(1500.96 - 933.876i) q^{50} +3073.21i q^{51} +2641.87i q^{52} +1465.30 q^{53} +3873.41 q^{54} +(3330.31 + 1850.23i) q^{55} -658.993i q^{56} -8298.83 q^{57} -3616.55i q^{58} -909.066 q^{59} +(2757.76 + 1532.14i) q^{60} -2701.86i q^{61} -1237.33i q^{62} -4887.46 q^{63} -512.000 q^{64} +(7216.86 + 4009.49i) q^{65} +6798.98i q^{66} +1995.64 q^{67} -1558.63 q^{68} +(631.747 - 8320.47i) q^{69} +(-1800.19 - 1000.13i) q^{70} -2473.67 q^{71} +3797.28i q^{72} -7865.35i q^{73} -6365.70i q^{74} +(8370.75 - 5208.16i) q^{75} -4208.88i q^{76} -4438.17i q^{77} +14733.5i q^{78} +7620.76i q^{79} +(-777.047 + 1398.64i) q^{80} +8008.52 q^{81} +2018.12i q^{82} +10525.0 q^{83} -3675.16i q^{84} +(-2365.48 + 4257.73i) q^{85} +1300.06i q^{86} -20169.2i q^{87} -3448.21 q^{88} +3144.69i q^{89} +(10373.1 + 5763.01i) q^{90} -9617.61i q^{91} +(4219.85 + 320.400i) q^{92} -6900.51i q^{93} -4705.09 q^{94} +(-11497.5 - 6387.68i) q^{95} -2855.39 q^{96} -15409.7 q^{97} -4392.02i q^{98} +25573.8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9}+O(q^{10}) \) 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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