LMFDB - Embedded newform 230.5.d.a.91.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,5,Mod(91,230)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("230.91");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	230.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$23.7750915093$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.8
Character	$\chi$	$=$	230.91
Dual form			230.5.d.a.91.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843 q^{2} +7.86848 q^{3} +8.00000 q^{4} -11.1803i q^{5} -22.2554 q^{6} -5.16947i q^{7} -22.6274 q^{8} -19.0870 q^{9} +O(q^{10})$	\(q-2.82843 q^{2} +7.86848 q^{3} +8.00000 q^{4} -11.1803i q^{5} -22.2554 q^{6} -5.16947i q^{7} -22.6274 q^{8} -19.0870 q^{9} +31.6228i q^{10} +104.451i q^{11} +62.9478 q^{12} -97.0715 q^{13} +14.6215i q^{14} -87.9723i q^{15} +64.0000 q^{16} +308.523i q^{17} +53.9863 q^{18} +515.306i q^{19} -89.4427i q^{20} -40.6758i q^{21} -295.432i q^{22} +(520.500 + 94.4523i) q^{23} -178.043 q^{24} -125.000 q^{25} +274.560 q^{26} -787.533 q^{27} -41.3557i q^{28} +716.017 q^{29} +248.823i q^{30} +852.655 q^{31} -181.019 q^{32} +821.870i q^{33} -872.634i q^{34} -57.7964 q^{35} -152.696 q^{36} -952.354i q^{37} -1457.50i q^{38} -763.805 q^{39} +252.982i q^{40} -2842.83 q^{41} +115.049i q^{42} +2584.77i q^{43} +835.608i q^{44} +213.400i q^{45} +(-1472.20 - 267.151i) q^{46} +2647.65 q^{47} +503.583 q^{48} +2374.28 q^{49} +353.553 q^{50} +2427.60i q^{51} -776.572 q^{52} -996.361i q^{53} +2227.48 q^{54} +1167.80 q^{55} +116.972i q^{56} +4054.67i q^{57} -2025.20 q^{58} +1116.47 q^{59} -703.778i q^{60} +6509.03i q^{61} -2411.67 q^{62} +98.6698i q^{63} +512.000 q^{64} +1085.29i q^{65} -2324.60i q^{66} +7118.58i q^{67} +2468.18i q^{68} +(4095.54 + 743.196i) q^{69} +163.473 q^{70} -3464.76 q^{71} +431.890 q^{72} -2915.77 q^{73} +2693.66i q^{74} -983.560 q^{75} +4122.45i q^{76} +539.956 q^{77} +2160.37 q^{78} -19.8956i q^{79} -715.542i q^{80} -4650.63 q^{81} +8040.73 q^{82} +4922.50i q^{83} -325.407i q^{84} +3449.39 q^{85} -7310.84i q^{86} +5633.97 q^{87} -2363.46i q^{88} +7075.44i q^{89} -603.585i q^{90} +501.808i q^{91} +(4164.00 + 755.618i) q^{92} +6709.10 q^{93} -7488.67 q^{94} +5761.29 q^{95} -1424.35 q^{96} -5816.44i q^{97} -6715.47 q^{98} -1993.66i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9}+O(q^{10}) $ 32 * q + 256 * q^4 + 64 * q^6 + 832 * q^9	$ 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9} - 408 q^{13} + 2048 q^{16} + 1024 q^{18} + 1332 q^{23} + 512 q^{24} - 4000 q^{25} + 2208 q^{27} + 3732 q^{29} - 412 q^{31} + 300 q^{35} + 6656 q^{36} - 9208 q^{39} - 6156 q^{41} + 4480 q^{46} + 5184 q^{47} - 13820 q^{49} - 3264 q^{52} - 3328 q^{54} - 6000 q^{55} + 3200 q^{58} - 30468 q^{59} - 10752 q^{62} + 16384 q^{64} - 1168 q^{69} + 4800 q^{70} - 37644 q^{71} + 8192 q^{72} + 19984 q^{73} + 27528 q^{77} + 15744 q^{78} + 69056 q^{81} - 17408 q^{82} + 3300 q^{85} + 28936 q^{87} + 10656 q^{92} + 40648 q^{93} - 23808 q^{94} - 21600 q^{95} + 4096 q^{96} + 43008 q^{98}+O(q^{100}) $ 32 * q + 256 * q^4 + 64 * q^6 + 832 * q^9 - 408 * q^13 + 2048 * q^16 + 1024 * q^18 + 1332 * q^23 + 512 * q^24 - 4000 * q^25 + 2208 * q^27 + 3732 * q^29 - 412 * q^31 + 300 * q^35 + 6656 * q^36 - 9208 * q^39 - 6156 * q^41 + 4480 * q^46 + 5184 * q^47 - 13820 * q^49 - 3264 * q^52 - 3328 * q^54 - 6000 * q^55 + 3200 * q^58 - 30468 * q^59 - 10752 * q^62 + 16384 * q^64 - 1168 * q^69 + 4800 * q^70 - 37644 * q^71 + 8192 * q^72 + 19984 * q^73 + 27528 * q^77 + 15744 * q^78 + 69056 * q^81 - 17408 * q^82 + 3300 * q^85 + 28936 * q^87 + 10656 * q^92 + 40648 * q^93 - 23808 * q^94 - 21600 * q^95 + 4096 * q^96 + 43008 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.82843			−0.707107
$2$	−2.82843			−0.707107
$3$	7.86848			0.874275			0.437138	−	0.899395i	$-0.355992\pi$
$3$	7.86848			0.874275			0.437138	+	0.899395i	$0.355992\pi$
$4$	8.00000			0.500000
$5$		−	11.1803i		−	0.447214i
$5$		−	11.1803i		−	0.447214i
$6$	−22.2554			−0.618206
$7$		−	5.16947i		−	0.105499i	−0.998608	−	0.0527497i	$-0.983201\pi$
$7$		−	5.16947i		−	0.105499i	0.998608	−	0.0527497i	$-0.0167985\pi$
$8$	−22.6274			−0.353553
$9$	−19.0870			−0.235643
$10$			31.6228i			0.316228i
$11$			104.451i			0.863231i	0.902058	+	0.431616i	$0.142056\pi$
$11$			104.451i			0.863231i	−0.902058	+	0.431616i	$0.857944\pi$
$12$	62.9478			0.437138
$13$	−97.0715			−0.574387			−0.287194	−	0.957873i	$-0.592722\pi$
$13$	−97.0715			−0.574387			−0.287194	+	0.957873i	$0.592722\pi$
$14$			14.6215i			0.0745993i
$15$		−	87.9723i		−	0.390988i
$16$	64.0000			0.250000
$17$			308.523i			1.06755i	0.845626	+	0.533776i	$0.179228\pi$
$17$			308.523i			1.06755i	−0.845626	+	0.533776i	$0.820772\pi$
$18$	53.9863			0.166624
$19$			515.306i			1.42744i	0.700431	+	0.713720i	$0.252991\pi$
$19$			515.306i			1.42744i	−0.700431	+	0.713720i	$0.747009\pi$
$20$		−	89.4427i		−	0.223607i
$21$		−	40.6758i		−	0.0922355i
$22$		−	295.432i		−	0.610397i
$23$	520.500	+	94.4523i	0.983931	+	0.178549i
$23$	520.500	+	94.4523i	0.983931	+	0.178549i
$24$	−178.043			−0.309103
$25$	−125.000			−0.200000
$26$	274.560			0.406153
$27$	−787.533			−1.08029
$28$		−	41.3557i		−	0.0527497i
$29$	716.017			0.851388			0.425694	−	0.904867i	$-0.360030\pi$
$29$	716.017			0.851388			0.425694	+	0.904867i	$0.360030\pi$
$30$			248.823i			0.276470i
$31$	852.655			0.887258			0.443629	−	0.896211i	$-0.353691\pi$
$31$	852.655			0.887258			0.443629	+	0.896211i	$0.353691\pi$
$32$	−181.019			−0.176777
$33$			821.870i			0.754702i
$34$		−	872.634i		−	0.754874i
$35$	−57.7964			−0.0471807
$36$	−152.696			−0.117821
$37$		−	952.354i		−	0.695657i	−0.937558	−	0.347828i	$-0.886919\pi$
$37$		−	952.354i		−	0.695657i	0.937558	−	0.347828i	$-0.113081\pi$
$38$		−	1457.50i		−	1.00935i
$39$	−763.805			−0.502173
$40$			252.982i			0.158114i
$41$	−2842.83			−1.69115			−0.845577	−	0.533854i	$-0.820743\pi$
$41$	−2842.83			−1.69115			−0.845577	+	0.533854i	$0.820743\pi$
$42$			115.049i			0.0652203i
$43$			2584.77i			1.39793i	0.715156	+	0.698965i	$0.246356\pi$
$43$			2584.77i			1.39793i	−0.715156	+	0.698965i	$0.753644\pi$
$44$			835.608i			0.431616i
$45$			213.400i			0.105383i
$46$	−1472.20	−	267.151i	−0.695744	−	0.126253i
$47$	2647.65			1.19857			0.599286	−	0.800535i	$-0.295451\pi$
$47$	2647.65			1.19857			0.599286	+	0.800535i	$0.295451\pi$
$48$	503.583			0.218569
$49$	2374.28			0.988870
$50$	353.553			0.141421
$51$			2427.60i			0.933335i
$52$	−776.572			−0.287194
$53$		−	996.361i		−	0.354703i	−0.984148	−	0.177351i	$-0.943247\pi$
$53$		−	996.361i		−	0.354703i	0.984148	−	0.177351i	$-0.0567529\pi$
$54$	2227.48			0.763882
$55$	1167.80			0.386049
$56$			116.972i			0.0372996i
$57$			4054.67i			1.24798i
$58$	−2025.20			−0.602022
$59$	1116.47			0.320732			0.160366	−	0.987058i	$-0.448733\pi$
$59$	1116.47			0.320732			0.160366	+	0.987058i	$0.448733\pi$
$60$		−	703.778i		−	0.195494i
$61$			6509.03i			1.74927i	0.484783	+	0.874634i	$0.338898\pi$
$61$			6509.03i			1.74927i	−0.484783	+	0.874634i	$0.661102\pi$
$62$	−2411.67			−0.627386
$63$			98.6698i			0.0248601i
$64$	512.000			0.125000
$65$			1085.29i			0.256874i
$66$		−	2324.60i		−	0.533655i
$67$			7118.58i			1.58578i	0.609362	+	0.792892i	$0.291426\pi$
$67$			7118.58i			1.58578i	−0.609362	+	0.792892i	$0.708574\pi$
$68$			2468.18i			0.533776i
$69$	4095.54	+	743.196i	0.860227	+	0.156101i
$70$	163.473			0.0333618
$71$	−3464.76			−0.687317			−0.343658	−	0.939095i	$-0.611666\pi$
$71$	−3464.76			−0.687317			−0.343658	+	0.939095i	$0.611666\pi$
$72$	431.890			0.0833122
$73$	−2915.77			−0.547151			−0.273575	−	0.961851i	$-0.588206\pi$
$73$	−2915.77			−0.547151			−0.273575	+	0.961851i	$0.588206\pi$
$74$			2693.66i			0.491904i
$75$	−983.560			−0.174855
$76$			4122.45i			0.713720i
$77$	539.956			0.0910703
$78$	2160.37			0.355090
$79$		−	19.8956i		−	0.00318788i	−0.999999	−	0.00159394i	$-0.999493\pi$
$79$		−	19.8956i		−	0.00318788i	0.999999	−	0.00159394i	$-0.000507367\pi$
$80$		−	715.542i		−	0.111803i
$81$	−4650.63			−0.708830
$82$	8040.73			1.19583
$83$			4922.50i			0.714545i	0.934000	+	0.357272i	$0.116293\pi$
$83$			4922.50i			0.714545i	−0.934000	+	0.357272i	$0.883707\pi$
$84$		−	325.407i		−	0.0461177i
$85$	3449.39			0.477424
$86$		−	7310.84i		−	0.988486i
$87$	5633.97			0.744347
$88$		−	2363.46i		−	0.305198i
$89$			7075.44i			0.893250i	0.894721	+	0.446625i	$0.147374\pi$
$89$			7075.44i			0.893250i	−0.894721	+	0.446625i	$0.852626\pi$
$90$		−	603.585i		−	0.0745167i
$91$			501.808i			0.0605975i
$92$	4164.00	+	755.618i	0.491966	+	0.0892744i
$93$	6709.10			0.775708
$94$	−7488.67			−0.847518
$95$	5761.29			0.638370
$96$	−1424.35			−0.154552
$97$		−	5816.44i		−	0.618178i	−0.951033	−	0.309089i	$-0.899976\pi$
$97$		−	5816.44i		−	0.618178i	0.951033	−	0.309089i	$-0.100024\pi$
$98$	−6715.47			−0.699237
$99$		−	1993.66i		−	0.203414i
$100$	−1000.00			−0.100000
$101$	−19724.7			−1.93361			−0.966804	−	0.255518i	$-0.917754\pi$
$101$	−19724.7			−1.93361			−0.966804	+	0.255518i	$0.917754\pi$
$102$		−	6866.30i		−	0.659967i
$103$			9376.08i			0.883785i	0.897068	+	0.441893i	$0.145693\pi$
$103$			9376.08i			0.883785i	−0.897068	+	0.441893i	$0.854307\pi$
$104$	2196.48			0.203077
$105$	−454.770			−0.0412489
$106$			2818.13i			0.250813i
$107$		−	9118.68i		−	0.796461i	−0.917285	−	0.398231i	$-0.869624\pi$
$107$		−	9118.68i		−	0.796461i	0.917285	−	0.398231i	$-0.130376\pi$
$108$	−6300.26			−0.540146
$109$		−	12782.3i		−	1.07586i	−0.842989	−	0.537931i	$-0.819206\pi$
$109$		−	12782.3i		−	1.07586i	0.842989	−	0.537931i	$-0.180794\pi$
$110$	−3303.03			−0.272978
$111$		−	7493.58i		−	0.608196i
$112$		−	330.846i		−	0.0263748i
$113$		−	19523.7i		−	1.52899i	−0.644628	−	0.764496i	$-0.722988\pi$
$113$		−	19523.7i		−	1.52899i	0.644628	−	0.764496i	$-0.277012\pi$
$114$		−	11468.3i		−	0.882452i
$115$	1056.01	−	5819.36i	0.0798494	−	0.440027i
$116$	5728.14			0.425694
$117$	1852.81			0.135350
$118$	−3157.85			−0.226792
$119$	1594.90			0.112626
$120$			1990.59i			0.138235i
$121$	3731.00			0.254832
$122$		−	18410.3i		−	1.23692i
$123$	−22368.7			−1.47853
$124$	6821.24			0.443629
$125$			1397.54i			0.0894427i
$126$		−	279.080i		−	0.0175788i
$127$	21301.7			1.32071			0.660354	−	0.750954i	$-0.270406\pi$
$127$	21301.7			1.32071			0.660354	+	0.750954i	$0.270406\pi$
$128$	−1448.15			−0.0883883
$129$			20338.2i			1.22218i
$130$		−	3069.67i		−	0.181637i
$131$	−21423.8			−1.24840			−0.624201	−	0.781264i	$-0.714575\pi$
$131$	−21423.8			−1.24840			−0.624201	+	0.781264i	$0.714575\pi$
$132$			6574.96i			0.377351i
$133$	2663.86			0.150594
$134$		−	20134.4i		−	1.12132i
$135$			8804.88i			0.483121i
$136$		−	6981.07i		−	0.377437i
$137$		−	29458.4i		−	1.56952i	−0.619797	−	0.784762i	$-0.712785\pi$
$137$		−	29458.4i		−	1.56952i	0.619797	−	0.784762i	$-0.287215\pi$
$138$	−11583.9	−	2102.07i	−0.608272	−	0.110380i
$139$	−16298.5			−0.843566			−0.421783	−	0.906697i	$-0.638596\pi$
$139$	−16298.5			−0.843566			−0.421783	+	0.906697i	$0.638596\pi$
$140$	−462.371			−0.0235904
$141$	20832.9			1.04788
$142$	9799.83			0.486006
$143$		−	10139.2i		−	0.495829i
$144$	−1221.57			−0.0589106
$145$		−	8005.32i		−	0.380752i
$146$	8247.04			0.386894
$147$	18681.9			0.864545
$148$		−	7618.83i		−	0.347828i
$149$		−	3398.59i		−	0.153083i	−0.997066	−	0.0765414i	$-0.975612\pi$
$149$		−	3398.59i		−	0.153083i	0.997066	−	0.0765414i	$-0.0243877\pi$
$150$	2781.93			0.123641
$151$	−32817.5			−1.43930			−0.719650	−	0.694337i	$-0.755698\pi$
$151$	−32817.5			−1.43930			−0.719650	+	0.694337i	$0.755698\pi$
$152$		−	11660.0i		−	0.504676i
$153$		−	5888.79i		−	0.251561i
$154$	−1527.23			−0.0643964
$155$		−	9532.97i		−	0.396794i
$156$	−6110.44			−0.251086
$157$			32345.4i			1.31224i	0.754657	+	0.656120i	$0.227803\pi$
$157$			32345.4i			1.31224i	−0.754657	+	0.656120i	$0.772197\pi$
$158$			56.2732i			0.00225417i
$159$		−	7839.84i		−	0.310108i
$160$			2023.86i			0.0790569i
$161$	488.268	−	2690.70i	0.0188368	−	0.103804i
$162$	13154.0			0.501219
$163$	18831.0			0.708759			0.354380	−	0.935102i	$-0.384692\pi$
$163$	18831.0			0.708759			0.354380	+	0.935102i	$0.384692\pi$
$164$	−22742.6			−0.845577
$165$	9188.79			0.337513
$166$		−	13922.9i		−	0.505259i
$167$	52564.4			1.88477			0.942386	−	0.334527i	$-0.108577\pi$
$167$	52564.4			1.88477			0.942386	+	0.334527i	$0.108577\pi$
$168$			920.389i			0.0326102i
$169$	−19138.1			−0.670079
$170$	−9756.34			−0.337590
$171$		−	9835.66i		−	0.336365i
$172$			20678.2i			0.698965i
$173$	−29068.0			−0.971232			−0.485616	−	0.874172i	$-0.661405\pi$
$173$	−29068.0			−0.971232			−0.485616	+	0.874172i	$0.661405\pi$
$174$	−15935.3			−0.526333
$175$			646.183i			0.0210999i
$176$			6684.86i			0.215808i
$177$	8784.91			0.280408
$178$		−	20012.4i		−	0.631623i
$179$	16655.8			0.519829			0.259914	−	0.965632i	$-0.416306\pi$
$179$	16655.8			0.519829			0.259914	+	0.965632i	$0.416306\pi$
$180$			1707.20i			0.0526913i
$181$			1316.67i			0.0401902i	0.999798	+	0.0200951i	$0.00639690\pi$
$181$			1316.67i			0.0401902i	−0.999798	+	0.0200951i	$0.993603\pi$
$182$		−	1419.33i		−	0.0428489i
$183$			51216.2i			1.52934i
$184$	−11777.6	−	2137.21i	−0.347872	−	0.0631265i
$185$	−10647.6			−0.311107
$186$	−18976.2			−0.548508
$187$	−32225.5			−0.921544
$188$	21181.2			0.599286
$189$			4071.12i			0.113970i
$190$	−16295.4			−0.451396
$191$			8316.14i			0.227958i	0.993483	+	0.113979i	$0.0363597\pi$
$191$			8316.14i			0.227958i	−0.993483	+	0.113979i	$0.963640\pi$
$192$	4028.66			0.109284
$193$	11700.2			0.314107			0.157054	−	0.987590i	$-0.449800\pi$
$193$	11700.2			0.314107			0.157054	+	0.987590i	$0.449800\pi$
$194$			16451.4i			0.437118i
$195$			8539.60i			0.224578i
$196$	18994.2			0.494435
$197$	35889.5			0.924772			0.462386	−	0.886679i	$-0.346994\pi$
$197$	35889.5			0.924772			0.462386	+	0.886679i	$0.346994\pi$
$198$			5638.92i			0.143835i
$199$			28667.4i			0.723905i	0.932197	+	0.361953i	$0.117890\pi$
$199$			28667.4i			0.723905i	−0.932197	+	0.361953i	$0.882110\pi$
$200$	2828.43			0.0707107
$201$			56012.4i			1.38641i
$202$	55790.0			1.36727
$203$		−	3701.43i		−	0.0898208i
$204$			19420.8i			0.466667i
$205$			31783.8i			0.756307i
$206$		−	26519.6i		−	0.624931i
$207$	−9934.80	−	1802.81i	−0.231856	−	0.0420737i
$208$	−6212.57			−0.143597
$209$	−53824.2			−1.23221
$210$	1286.28			0.0291674
$211$	18654.7			0.419008			0.209504	−	0.977808i	$-0.432815\pi$
$211$	18654.7			0.419008			0.209504	+	0.977808i	$0.432815\pi$
$212$		−	7970.88i		−	0.177351i
$213$	−27262.4			−0.600904
$214$			25791.5i			0.563183i
$215$	28898.6			0.625173
$216$	17819.8			0.381941
$217$		−	4407.77i		−	0.0936051i
$218$			36153.9i			0.760749i
$219$	−22942.7			−0.478361
$220$	9342.38			0.193024
$221$		−	29948.7i		−	0.613189i
$222$			21195.0i			0.430059i
$223$	−2861.05			−0.0575327			−0.0287664	−	0.999586i	$-0.509158\pi$
$223$	−2861.05			−0.0575327			−0.0287664	+	0.999586i	$0.509158\pi$
$224$			935.773i			0.0186498i
$225$	2385.88			0.0471285
$226$			55221.4i			1.08116i
$227$		−	11919.8i		−	0.231321i	−0.993289	−	0.115661i	$-0.963101\pi$
$227$		−	11919.8i		−	0.231321i	0.993289	−	0.115661i	$-0.0368985\pi$
$228$			32437.4i			0.623988i
$229$		−	66973.3i		−	1.27712i	−0.769573	−	0.638559i	$-0.779531\pi$
$229$		−	66973.3i		−	1.27712i	0.769573	−	0.638559i	$-0.220469\pi$
$230$	−2986.84	+	16459.6i	−0.0564621	+	0.311146i
$231$	4248.63			0.0796205
$232$	−16201.6			−0.301011
$233$	50977.9			0.939010			0.469505	−	0.882930i	$-0.344432\pi$
$233$	50977.9			0.939010			0.469505	+	0.882930i	$0.344432\pi$
$234$	−5240.53			−0.0957070
$235$		−	29601.6i		−	0.536018i
$236$	8931.75			0.160366
$237$		−	156.548i		−	0.00278709i
$238$	−4511.05			−0.0796386
$239$	−76598.6			−1.34099			−0.670495	−	0.741914i	$-0.733918\pi$
$239$	−76598.6			−1.34099			−0.670495	+	0.741914i	$0.733918\pi$
$240$		−	5630.23i		−	0.0977470i
$241$			108285.i			1.86437i	0.361979	+	0.932186i	$0.382101\pi$
$241$			108285.i			1.86437i	−0.361979	+	0.932186i	$0.617899\pi$
$242$	−10552.9			−0.180194
$243$	27196.7			0.460579
$244$			52072.2i			0.874634i
$245$		−	26545.2i		−	0.442236i
$246$	63268.3			1.04548
$247$		−	50021.5i		−	0.819903i
$248$	−19293.4			−0.313693
$249$			38732.6i			0.624709i
$250$		−	3952.85i		−	0.0632456i
$251$		−	73017.5i		−	1.15899i	−0.814976	−	0.579495i	$-0.803250\pi$
$251$		−	73017.5i		−	1.15899i	0.814976	−	0.579495i	$-0.196750\pi$
$252$			789.359i			0.0124301i
$253$	−9865.63	+	54366.7i	−0.154129	+	0.849360i
$254$	−60250.3			−0.933882
$255$	27141.4			0.417400
$256$	4096.00			0.0625000
$257$	64865.9			0.982087			0.491044	−	0.871135i	$-0.336616\pi$
$257$	64865.9			0.982087			0.491044	+	0.871135i	$0.336616\pi$
$258$		−	57525.2i		−	0.864209i
$259$	−4923.16			−0.0733913
$260$			8682.34i			0.128437i
$261$	−13666.7			−0.200623
$262$	60595.7			0.882753
$263$		−	111213.i		−	1.60785i	−0.594733	−	0.803924i	$-0.702742\pi$
$263$		−	111213.i		−	1.60785i	0.594733	−	0.803924i	$-0.297258\pi$
$264$		−	18596.8i		−	0.266827i
$265$	−11139.7			−0.158628
$266$	−7534.52			−0.106486
$267$			55672.9i			0.780947i
$268$			56948.7i			0.792892i
$269$	14040.7			0.194037			0.0970185	−	0.995283i	$-0.469069\pi$
$269$	14040.7			0.194037			0.0970185	+	0.995283i	$0.469069\pi$
$270$		−	24904.0i		−	0.341618i
$271$	−95290.1			−1.29750			−0.648752	−	0.761000i	$-0.724709\pi$
$271$	−95290.1			−1.29750			−0.648752	+	0.761000i	$0.724709\pi$
$272$			19745.5i			0.266888i
$273$			3948.46i			0.0529789i
$274$			83320.9i			1.10982i
$275$		−	13056.4i		−	0.172646i
$276$	32764.3	+	5945.57i	0.430113	+	0.0780504i
$277$	65310.4			0.851183			0.425591	−	0.904915i	$-0.360066\pi$
$277$	65310.4			0.851183			0.425591	+	0.904915i	$0.360066\pi$
$278$	46099.2			0.596491
$279$	−16274.7			−0.209076
$280$	1307.78			0.0166809
$281$		−	92547.7i		−	1.17207i	−0.810286	−	0.586034i	$-0.800688\pi$
$281$		−	92547.7i		−	1.17207i	0.810286	−	0.586034i	$-0.199312\pi$
$282$	−58924.5			−0.740964
$283$		−	119520.i		−	1.49234i	−0.665758	−	0.746168i	$-0.731892\pi$
$283$		−	119520.i		−	1.49234i	0.665758	−	0.746168i	$-0.268108\pi$
$284$	−27718.1			−0.343658
$285$	45332.6			0.558112
$286$			28678.0i			0.350604i
$287$			14695.9i			0.178415i
$288$	3455.12			0.0416561
$289$	−11665.2			−0.139668
$290$			22642.5i			0.269232i
$291$		−	45766.5i		−	0.540458i
$292$	−23326.1			−0.273575
$293$			71013.8i			0.827194i	0.910460	+	0.413597i	$0.135728\pi$
$293$			71013.8i			0.827194i	−0.910460	+	0.413597i	$0.864272\pi$
$294$	−52840.5			−0.611325
$295$		−	12482.5i		−	0.143436i
$296$			21549.3i			0.245952i
$297$		−	82258.6i		−	0.932541i
$298$			9612.66i			0.108246i
$299$	−50525.6	−	9168.62i	−0.565158	−	0.102556i
$300$	−7868.48			−0.0874275
$301$	13361.9			0.147481
$302$	92821.8			1.01774
$303$	−155204.			−1.69051
$304$			32979.6i			0.356860i
$305$	72773.2			0.782297
$306$			16656.0i			0.177880i
$307$	115857.			1.22926			0.614632	−	0.788814i	$-0.289304\pi$
$307$	115857.			1.22926			0.614632	+	0.788814i	$0.289304\pi$
$308$	4319.65			0.0455351
$309$			73775.5i			0.772672i
$310$			26963.3i			0.280576i
$311$	−16494.1			−0.170533			−0.0852665	−	0.996358i	$-0.527174\pi$
$311$	−16494.1			−0.170533			−0.0852665	+	0.996358i	$0.527174\pi$
$312$	17282.9			0.177545
$313$			159842.i			1.63156i	0.578363	+	0.815779i	$0.303692\pi$
$313$			159842.i			1.63156i	−0.578363	+	0.815779i	$0.696308\pi$
$314$		−	91486.6i		−	0.927893i
$315$	1103.16			0.0111178
$316$		−	159.165i		−	0.00159394i
$317$	−74855.5			−0.744912			−0.372456	−	0.928050i	$-0.621484\pi$
$317$	−74855.5			−0.744912			−0.372456	+	0.928050i	$0.621484\pi$
$318$			22174.4i			0.219280i
$319$			74788.7i			0.734944i
$320$		−	5724.33i		−	0.0559017i
$321$		−	71750.2i		−	0.696326i
$322$	−1381.03	+	7610.46i	−0.0133196	+	0.0734005i
$323$	−158983.			−1.52387
$324$	−37205.1			−0.354415
$325$	12133.9			0.114877
$326$	−53262.2			−0.501168
$327$		−	100577.i		−	0.940600i
$328$	64325.9			0.597913
$329$		−	13686.9i		−	0.126449i
$330$	−25989.8			−0.238658
$331$	105469.			0.962648			0.481324	−	0.876543i	$-0.340156\pi$
$331$	105469.			0.962648			0.481324	+	0.876543i	$0.340156\pi$
$332$			39380.0i			0.357272i
$333$			18177.6i			0.163926i
$334$	−148675.			−1.33274
$335$	79588.2			0.709184
$336$		−	2603.25i		−	0.0230589i
$337$			170609.i			1.50225i	0.660160	+	0.751125i	$0.270489\pi$
$337$			170609.i			1.50225i	−0.660160	+	0.751125i	$0.729511\pi$
$338$	54130.8			0.473818
$339$		−	153622.i		−	1.33676i
$340$	27595.1			0.238712
$341$			89060.6i			0.765909i
$342$			27819.5i			0.237846i
$343$		−	24685.6i		−	0.209824i
$344$		−	58486.7i		−	0.494243i
$345$	8309.18	−	45789.5i	0.0698104	−	0.384705i
$346$	82216.8			0.686765
$347$	41344.4			0.343366			0.171683	−	0.985152i	$-0.445079\pi$
$347$	41344.4			0.343366			0.171683	+	0.985152i	$0.445079\pi$
$348$	45071.7			0.372174
$349$	−33326.0			−0.273610			−0.136805	−	0.990598i	$-0.543683\pi$
$349$	−33326.0			−0.273610			−0.136805	+	0.990598i	$0.543683\pi$
$350$		−	1827.68i		−	0.0149199i
$351$	76447.0			0.620506
$352$		−	18907.6i		−	0.152599i
$353$	−2256.24			−0.0181065			−0.00905326	−	0.999959i	$-0.502882\pi$
$353$	−2256.24			−0.0181065			−0.00905326	+	0.999959i	$0.502882\pi$
$354$	−24847.5			−0.198279
$355$			38737.2i			0.307377i
$356$			56603.5i			0.446625i
$357$	12549.4			0.0984662
$358$	−47109.8			−0.367574
$359$		−	170319.i		−	1.32152i	−0.750595	−	0.660762i	$-0.770233\pi$
$359$		−	170319.i		−	1.32152i	0.750595	−	0.660762i	$-0.229767\pi$
$360$		−	4828.68i		−	0.0372584i
$361$	−135219.			−1.03758
$362$		−	3724.11i		−	0.0284188i
$363$	29357.3			0.222793
$364$			4014.46i			0.0302987i
$365$			32599.3i			0.244693i
$366$		−	144861.i		−	1.08141i
$367$		−	137119.i		−	1.01804i	−0.860755	−	0.509020i	$-0.830008\pi$
$367$		−	137119.i		−	1.01804i	0.860755	−	0.509020i	$-0.169992\pi$
$368$	33312.0	+	6044.95i	0.245983	+	0.0446372i
$369$	54261.2			0.398508
$370$	30116.1			0.219986
$371$	−5150.65			−0.0374209
$372$	53672.8			0.387854
$373$		−	170005.i		−	1.22192i	−0.791660	−	0.610962i	$-0.790783\pi$
$373$		−	170005.i		−	1.22192i	0.791660	−	0.610962i	$-0.209217\pi$
$374$	91147.4			0.651630
$375$			10996.5i			0.0781976i
$376$	−59909.4			−0.423759
$377$	−69504.8			−0.489026
$378$		−	11514.9i		−	0.0805890i
$379$			166470.i			1.15893i	0.814997	+	0.579466i	$0.196739\pi$
$379$			166470.i			1.15893i	−0.814997	+	0.579466i	$0.803261\pi$
$380$	46090.3			0.319185
$381$	167612.			1.15466
$382$		−	23521.6i		−	0.161191i
$383$		−	72581.5i		−	0.494799i	−0.968914	−	0.247399i	$-0.920424\pi$
$383$		−	72581.5i		−	0.494799i	0.968914	−	0.247399i	$-0.0795760\pi$
$384$	−11394.8			−0.0772758
$385$		−	6036.89i		−	0.0407279i
$386$	−33093.1			−0.222107
$387$		−	49335.7i		−	0.329412i
$388$		−	46531.5i		−	0.309089i
$389$			205687.i			1.35928i	0.733547	+	0.679639i	$0.237863\pi$
$389$			205687.i			1.35928i	−0.733547	+	0.679639i	$0.762137\pi$
$390$		−	24153.6i		−	0.158801i
$391$	−29140.7	+	160586.i	−0.190610	+	1.05040i
$392$	−53723.7			−0.349618
$393$	−168573.			−1.09145
$394$	−101511.			−0.653912
$395$	−222.439			−0.00142566
$396$		−	15949.3i		−	0.101707i
$397$	−79765.8			−0.506099			−0.253050	−	0.967453i	$-0.581434\pi$
$397$	−79765.8			−0.506099			−0.253050	+	0.967453i	$0.581434\pi$
$398$		−	81083.6i		−	0.511878i
$399$	20960.5			0.131661
$400$	−8000.00			−0.0500000
$401$			151556.i			0.942504i	0.881999	+	0.471252i	$0.156198\pi$
$401$			151556.i			0.942504i	−0.881999	+	0.471252i	$0.843802\pi$
$402$		−	158427.i		−	0.980341i
$403$	−82768.5			−0.509630
$404$	−157798.			−0.966804
$405$			51995.7i			0.316998i
$406$			10469.2i			0.0635129i
$407$	99474.3			0.600513
$408$		−	54930.4i		−	0.329984i
$409$	79437.4			0.474874			0.237437	−	0.971403i	$-0.423693\pi$
$409$	79437.4			0.474874			0.237437	+	0.971403i	$0.423693\pi$
$410$		−	89898.1i		−	0.534790i
$411$		−	231793.i		−	1.37220i
$412$			75008.6i			0.441893i
$413$		−	5771.55i		−	0.0338370i
$414$	28099.9	+	5099.13i	0.163947	+	0.0297506i
$415$	55035.2			0.319554
$416$	17571.8			0.101538
$417$	−128245.			−0.737509
$418$	152238.			0.871304
$419$		−	253785.i		−	1.44556i	−0.691076	−	0.722782i	$-0.742863\pi$
$419$		−	253785.i		−	1.44556i	0.691076	−	0.722782i	$-0.257137\pi$
$420$	−3638.16			−0.0206245
$421$			3381.69i			0.0190796i	0.999954	+	0.00953981i	$0.00303666\pi$
$421$			3381.69i			0.0190796i	−0.999954	+	0.00953981i	$0.996963\pi$
$422$	−52763.4			−0.296284
$423$	−50535.7			−0.282434
$424$			22545.1i			0.125406i
$425$		−	38565.3i		−	0.213510i
$426$	77109.8			0.424903
$427$	33648.2			0.184547
$428$		−	72949.5i		−	0.398231i
$429$		−	79780.1i		−	0.433491i
$430$	−81737.7			−0.442064
$431$		−	94146.6i		−	0.506816i	−0.967360	−	0.253408i	$-0.918449\pi$
$431$		−	94146.6i		−	0.506816i	0.967360	−	0.253408i	$-0.0815515\pi$
$432$	−50402.1			−0.270073
$433$			282780.i			1.50825i	0.656733	+	0.754123i	$0.271938\pi$
$433$			282780.i			1.50825i	−0.656733	+	0.754123i	$0.728062\pi$
$434$			12467.1i			0.0661888i
$435$		−	62989.7i		−	0.332882i
$436$		−	102259.i		−	0.537931i
$437$	−48671.8	+	268216.i	−0.254868	+	1.40450i
$438$	64891.6			0.338252
$439$	290983.			1.50986			0.754932	−	0.655803i	$-0.227670\pi$
$439$	290983.			1.50986			0.754932	+	0.655803i	$0.227670\pi$
$440$	−26424.2			−0.136489
$441$	−45317.9			−0.233020
$442$			84707.8i			0.433590i
$443$	−207160.			−1.05560			−0.527800	−	0.849369i	$-0.676983\pi$
$443$	−207160.			−1.05560			−0.527800	+	0.849369i	$0.676983\pi$
$444$		−	59948.6i		−	0.304098i
$445$	79105.8			0.399474
$446$	8092.26			0.0406818
$447$		−	26741.7i		−	0.133836i
$448$		−	2646.77i		−	0.0131874i
$449$	207678.			1.03014			0.515072	−	0.857147i	$-0.327765\pi$
$449$	207678.			1.03014			0.515072	+	0.857147i	$0.327765\pi$
$450$	−6748.29			−0.0333249
$451$		−	296936.i		−	1.45986i
$452$		−	156190.i		−	0.764496i
$453$	−258224.			−1.25834
$454$			33714.2i			0.163569i
$455$	5610.38			0.0271000
$456$		−	91746.7i		−	0.441226i
$457$			12780.6i			0.0611952i	0.999532	+	0.0305976i	$0.00974105\pi$
$457$			12780.6i			0.0611952i	−0.999532	+	0.0305976i	$0.990259\pi$
$458$			189429.i			0.903058i
$459$		−	242972.i		−	1.15327i
$460$	8448.07	−	46554.9i	0.0399247	−	0.220014i
$461$	60661.7			0.285439			0.142719	−	0.989763i	$-0.454415\pi$
$461$	60661.7			0.285439			0.142719	+	0.989763i	$0.454415\pi$
$462$	−12016.9			−0.0563002
$463$	−101227.			−0.472211			−0.236105	−	0.971727i	$-0.575871\pi$
$463$	−101227.			−0.472211			−0.236105	+	0.971727i	$0.575871\pi$
$464$	45825.1			0.212847
$465$		−	75010.0i		−	0.346907i
$466$	−144187.			−0.663980
$467$		−	329731.i		−	1.51191i	−0.654625	−	0.755954i	$-0.727173\pi$
$467$		−	329731.i		−	1.51191i	0.654625	−	0.755954i	$-0.272827\pi$
$468$	14822.5			0.0676750
$469$	36799.3			0.167299
$470$			83725.9i			0.379022i
$471$			254509.i			1.14726i
$472$	−25262.8			−0.113396
$473$	−269982.			−1.20674
$474$			442.784i			0.00197077i
$475$		−	64413.2i		−	0.285488i
$476$	12759.2			0.0563130
$477$			19017.6i			0.0835831i
$478$	216654.			0.948223
$479$			208762.i			0.909873i	0.890524	+	0.454937i	$0.150338\pi$
$479$			208762.i			0.909873i	−0.890524	+	0.454937i	$0.849662\pi$
$480$			15924.7i			0.0691175i
$481$			92446.4i			0.399576i
$482$		−	306275.i		−	1.31831i
$483$	3841.93	−	21171.8i	0.0164685	−	0.0907533i
$484$	29848.0			0.127416
$485$	−65029.7			−0.276458
$486$	−76924.0			−0.325679
$487$	−4785.77			−0.0201787			−0.0100894	−	0.999949i	$-0.503212\pi$
$487$	−4785.77			−0.0201787			−0.0100894	+	0.999949i	$0.503212\pi$
$488$		−	147283.i		−	0.618460i
$489$	148172.			0.619651
$490$			75081.2i			0.312708i
$491$	−336281.			−1.39489			−0.697444	−	0.716639i	$-0.745679\pi$
$491$	−336281.			−1.39489			−0.697444	+	0.716639i	$0.745679\pi$
$492$	−178950.			−0.739267
$493$			220908.i			0.908901i
$494$			141482.i			0.579759i
$495$	−22289.8			−0.0909695
$496$	54569.9			0.221815
$497$			17911.0i			0.0725115i
$498$		−	109552.i		−	0.441736i
$499$	259268.			1.04123			0.520617	−	0.853790i	$-0.325702\pi$
$499$	259268.			1.04123			0.520617	+	0.853790i	$0.325702\pi$
$500$			11180.3i			0.0447214i
$501$	413602.			1.64781
$502$			206525.i			0.819529i
$503$			169716.i			0.670789i	0.942078	+	0.335394i	$0.108870\pi$
$503$			169716.i			0.670789i	−0.942078	+	0.335394i	$0.891130\pi$
$504$		−	2232.64i		−	0.00878938i
$505$			220529.i			0.864736i
$506$	27904.2	−	153772.i	0.108986	−	0.600588i
$507$	−150588.			−0.585834
$508$	170414.			0.660354
$509$	434757.			1.67807			0.839037	−	0.544075i	$-0.183119\pi$
$509$	434757.			1.67807			0.839037	+	0.544075i	$0.183119\pi$
$510$	−76767.6			−0.295146
$511$			15073.0i			0.0577240i
$512$	−11585.2			−0.0441942
$513$		−	405820.i		−	1.54205i
$514$	−183468.			−0.694441
$515$	104828.			0.395241
$516$			162706.i			0.611088i
$517$			276549.i			1.03464i
$518$	13924.8			0.0518955
$519$	−228721.			−0.849125
$520$		−	24557.4i		−	0.0908186i
$521$		−	60242.5i		−	0.221936i	−0.993824	−	0.110968i	$-0.964605\pi$
$521$		−	60242.5i		−	0.221936i	0.993824	−	0.110968i	$-0.0353951\pi$
$522$	38655.1			0.141862
$523$			313999.i			1.14795i	0.818871	+	0.573977i	$0.194600\pi$
$523$			313999.i			1.14795i	−0.818871	+	0.573977i	$0.805400\pi$
$524$	−171391.			−0.624201
$525$			5084.48i			0.0184471i
$526$			314558.i			1.13692i
$527$			263063.i			0.947195i
$528$			52599.7i			0.188675i
$529$	261999.	+	98324.7i	0.936241	+	0.351359i
$530$	31507.7			0.112167
$531$	−21310.1			−0.0755781
$532$	21310.8			0.0752969
$533$	275957.			0.971377
$534$		−	157467.i		−	0.552213i
$535$	−101950.			−0.356188
$536$		−	161075.i		−	0.560659i
$537$	131056.			0.454473
$538$	−39713.1			−0.137205
$539$			247995.i			0.853623i
$540$			70439.1i			0.241561i
$541$	16399.7			0.0560326			0.0280163	−	0.999607i	$-0.491081\pi$
$541$	16399.7			0.0560326			0.0280163	+	0.999607i	$0.491081\pi$
$542$	269521.			0.917474
$543$			10360.2i			0.0351373i
$544$		−	55848.6i		−	0.188718i
$545$	−142911.			−0.481140
$546$		−	11167.9i		−	0.0374617i
$547$	86925.5			0.290518			0.145259	−	0.989394i	$-0.453599\pi$
$547$	86925.5			0.290518			0.145259	+	0.989394i	$0.453599\pi$
$548$		−	235667.i		−	0.784762i
$549$		−	124238.i		−	0.412202i
$550$			36929.0i			0.122079i
$551$			368968.i			1.21530i
$552$	−92671.5	−	16816.6i	−0.304136	−	0.0551900i
$553$	−102.849			−0.000336319
$554$	−184726.			−0.601877
$555$	−83780.8			−0.271993
$556$	−130388.			−0.421783
$557$			113858.i			0.366988i	0.983021	+	0.183494i	$0.0587408\pi$
$557$			113858.i			0.366988i	−0.983021	+	0.183494i	$0.941259\pi$
$558$	46031.7			0.147839
$559$		−	250908.i		−	0.802953i
$560$	−3698.97			−0.0117952
$561$	−253566.			−0.805684
$562$			261765.i			0.828778i
$563$			326849.i			1.03117i	0.856838	+	0.515585i	$0.172425\pi$
$563$			326849.i			1.03117i	−0.856838	+	0.515585i	$0.827575\pi$
$564$	166664.			0.523941
$565$	−218282.			−0.683786
$566$			338053.i			1.05524i
$567$			24041.3i			0.0747811i
$568$	78398.7			0.243003
$569$			100028.i			0.308957i	0.987996	+	0.154479i	$0.0493698\pi$
$569$			100028.i			0.308957i	−0.987996	+	0.154479i	$0.950630\pi$
$570$	−128220.			−0.394644
$571$			301054.i			0.923363i	0.887046	+	0.461682i	$0.152754\pi$
$571$			301054.i			0.923363i	−0.887046	+	0.461682i	$0.847246\pi$
$572$		−	81113.7i		−	0.247914i
$573$			65435.3i			0.199298i
$574$		−	41566.3i		−	0.126159i
$575$	−65062.4	−	11806.5i	−0.196786	−	0.0357097i
$576$	−9772.57			−0.0294553
$577$	−472831.			−1.42022			−0.710108	−	0.704092i	$-0.751354\pi$
$577$	−472831.			−1.42022			−0.710108	+	0.704092i	$0.751354\pi$
$578$	32994.3			0.0987604
$579$	92062.7			0.274616
$580$		−	64042.5i		−	0.190376i
$581$	25446.7			0.0753840
$582$			129447.i			0.382161i
$583$	104071.			0.306191
$584$	65976.3			0.193447
$585$		−	20715.0i		−	0.0605304i
$586$		−	200857.i		−	0.584915i
$587$	420421.			1.22014			0.610068	−	0.792349i	$-0.291142\pi$
$587$	420421.			1.22014			0.610068	+	0.792349i	$0.291142\pi$
$588$	149456.			0.432272
$589$			439378.i			1.26651i
$590$			35305.8i			0.101424i
$591$	282395.			0.808505
$592$		−	60950.7i		−	0.173914i
$593$	138281.			0.393235			0.196618	−	0.980480i	$-0.437004\pi$
$593$	138281.			0.393235			0.196618	+	0.980480i	$0.437004\pi$
$594$			232662.i			0.659406i
$595$		−	17831.5i		−	0.0503679i
$596$		−	27188.7i		−	0.0765414i
$597$			225569.i			0.632892i
$598$	142908.	+	25932.8i	0.399627	+	0.0725181i
$599$	−65778.5			−0.183329			−0.0916644	−	0.995790i	$-0.529219\pi$
$599$	−65778.5			−0.183329			−0.0916644	+	0.995790i	$0.529219\pi$
$600$	22255.4			0.0618206
$601$	67205.0			0.186060			0.0930300	−	0.995663i	$-0.470345\pi$
$601$	67205.0			0.186060			0.0930300	+	0.995663i	$0.470345\pi$
$602$	−37793.1			−0.104285
$603$		−	135873.i		−	0.373678i
$604$	−262540.			−0.719650
$605$		−	41713.8i		−	0.113964i
$606$	438982.			1.19537
$607$	−14054.7			−0.0381457			−0.0190729	−	0.999818i	$-0.506071\pi$
$607$	−14054.7			−0.0381457			−0.0190729	+	0.999818i	$0.506071\pi$
$608$		−	93280.3i		−	0.252338i
$609$		−	29124.6i		−	0.0785281i
$610$	−205834.			−0.553167
$611$	−257011.			−0.688445
$612$		−	47110.3i		−	0.125780i
$613$			238490.i			0.634672i	0.948313	+	0.317336i	$0.102788\pi$
$613$			238490.i			0.634672i	−0.948313	+	0.317336i	$0.897212\pi$
$614$	−327693.			−0.869221
$615$			250090.i			0.661220i
$616$	−12217.8			−0.0321982
$617$			3017.70i			0.00792696i	0.999992	+	0.00396348i	$0.00126162\pi$
$617$			3017.70i			0.00792696i	−0.999992	+	0.00396348i	$0.998738\pi$
$618$		−	208669.i		−	0.546361i
$619$		−	370487.i		−	0.966923i	−0.875366	−	0.483461i	$-0.839379\pi$
$619$		−	370487.i		−	0.966923i	0.875366	−	0.483461i	$-0.160621\pi$
$620$		−	76263.8i		−	0.198397i
$621$	−409910.	−	74384.3i	−1.06293	−	0.192885i
$622$	46652.4			0.120585
$623$	36576.2			0.0942373
$624$	−48883.5			−0.125543
$625$	15625.0			0.0400000
$626$		−	452102.i		−	1.15369i
$627$	−423514.			−1.07729
$628$			258763.i			0.656120i
$629$	293823.			0.742650
$630$	−3120.21			−0.00786146
$631$			77170.7i			0.193818i	0.995293	+	0.0969089i	$0.0308955\pi$
$631$			77170.7i			0.193818i	−0.995293	+	0.0969089i	$0.969104\pi$
$632$			450.185i			0.00112709i
$633$	146784.			0.366329
$634$	211723.			0.526733
$635$		−	238160.i		−	0.590639i
$636$		−	62718.7i		−	0.155054i
$637$	−230474.			−0.567994
$638$		−	211534.i		−	0.519684i
$639$	66132.1			0.161961
$640$			16190.9i			0.0395285i
$641$		−	388749.i		−	0.946134i	−0.881026	−	0.473067i	$-0.843147\pi$
$641$		−	388749.i		−	0.946134i	0.881026	−	0.473067i	$-0.156853\pi$
$642$			202940.i			0.492377i
$643$		−	472721.i		−	1.14336i	−0.820477	−	0.571680i	$-0.806292\pi$
$643$		−	472721.i		−	1.14336i	0.820477	−	0.571680i	$-0.193708\pi$
$644$	3906.14	−	21525.6i	0.00941838	−	0.0519020i
$645$	227388.			0.546574
$646$	449673.			1.07754
$647$	−165300.			−0.394880			−0.197440	−	0.980315i	$-0.563263\pi$
$647$	−165300.			−0.394880			−0.197440	+	0.980315i	$0.563263\pi$
$648$	105232.			0.250609
$649$			116616.i			0.276866i
$650$	−34319.9			−0.0812306
$651$		−	34682.5i		−	0.0818367i
$652$	150648.			0.354380
$653$	−98688.5			−0.231441			−0.115720	−	0.993282i	$-0.536918\pi$
$653$	−98688.5			−0.231441			−0.115720	+	0.993282i	$0.536918\pi$
$654$			284476.i			0.665104i
$655$			239526.i			0.558302i
$656$	−181941.			−0.422788
$657$	55653.4			0.128932
$658$			38712.4i			0.0894126i
$659$			333035.i			0.766865i	0.923569	+	0.383432i	$0.125258\pi$
$659$			333035.i			0.766865i	−0.923569	+	0.383432i	$0.874742\pi$
$660$	73510.3			0.168756
$661$			290753.i			0.665458i	0.943022	+	0.332729i	$0.107969\pi$
$661$			290753.i			0.665458i	−0.943022	+	0.332729i	$0.892031\pi$
$662$	−298310.			−0.680695
$663$		−	235651.i		−	0.536096i
$664$		−	111383.i		−	0.252630i
$665$		−	29782.8i		−	0.0673476i
$666$		−	51414.1i		−	0.115913i
$667$	372687.	+	67629.5i	0.837707	+	0.152014i
$668$	420515.			0.942386
$669$	−22512.1			−0.0502995
$670$	−225109.			−0.501469
$671$	−679874.			−1.51002
$672$			7363.11i			0.0163051i
$673$	334427.			0.738366			0.369183	−	0.929357i	$-0.379638\pi$
$673$	334427.			0.738366			0.369183	+	0.929357i	$0.379638\pi$
$674$		−	482555.i		−	1.06225i
$675$	98441.6			0.216058
$676$	−153105.			−0.335040
$677$		−	132209.i		−	0.288459i	−0.989544	−	0.144229i	$-0.953930\pi$
$677$		−	132209.i		−	0.288459i	0.989544	−	0.144229i	$-0.0460703\pi$
$678$			434508.i			0.945232i
$679$	−30067.9			−0.0652173
$680$	−78050.7			−0.168795
$681$		−	93790.3i		−	0.202238i
$682$		−	251902.i		−	0.541579i
$683$	241122.			0.516888			0.258444	−	0.966026i	$-0.416790\pi$
$683$	241122.			0.516888			0.258444	+	0.966026i	$0.416790\pi$
$684$		−	78685.3i		−	0.168183i
$685$	−329355.			−0.701913
$686$			69821.5i			0.148368i
$687$		−	526978.i		−	1.11655i
$688$			165425.i			0.349483i
$689$			96718.2i			0.203737i
$690$	−23501.9	+	129512.i	−0.0493634	+	0.272028i
$691$	98057.4			0.205364			0.102682	−	0.994714i	$-0.467258\pi$
$691$	98057.4			0.205364			0.102682	+	0.994714i	$0.467258\pi$
$692$	−232544.			−0.485616
$693$	−10306.2			−0.0214600
$694$	−116940.			−0.242797
$695$			182223.i			0.377254i
$696$	−127482.			−0.263167
$697$		−	877077.i		−	1.80539i
$698$	94260.2			0.193472
$699$	401119.			0.820953
$700$			5169.47i			0.0105499i
$701$			663503.i			1.35023i	0.737714	+	0.675114i	$0.235906\pi$
$701$			663503.i			1.35023i	−0.737714	+	0.675114i	$0.764094\pi$
$702$	−216225.			−0.438764
$703$	490754.			0.993008
$704$			53478.9i			0.107904i
$705$		−	232919.i		−	0.468627i
$706$	6381.60			0.0128032
$707$			101966.i			0.203994i
$708$	70279.3			0.140204
$709$		−	579495.i		−	1.15281i	−0.817164	−	0.576405i	$-0.804455\pi$
$709$		−	579495.i		−	1.15281i	0.817164	−	0.576405i	$-0.195545\pi$
$710$		−	109565.i		−	0.217349i
$711$			379.747i			0.000751200i
$712$		−	160099.i		−	0.315812i
$713$	443807.	+	80535.2i	0.873001	+	0.158419i
$714$	−35495.1			−0.0696261
$715$	−113360.			−0.221741
$716$	133247.			0.259914
$717$	−602715.			−1.17239
$718$			481736.i			0.934459i
$719$	789630.			1.52745			0.763723	−	0.645544i	$-0.223369\pi$
$719$	789630.			1.52745			0.763723	+	0.645544i	$0.223369\pi$
$720$			13657.6i			0.0263456i
$721$	48469.3			0.0932387
$722$	382457.			0.733682
$723$			852035.i			1.62998i
$724$			10533.4i			0.0200951i
$725$	−89502.2			−0.170278
$726$	−83034.9			−0.157539
$727$			716102.i			1.35490i	0.735571	+	0.677448i	$0.236914\pi$
$727$			716102.i			1.35490i	−0.735571	+	0.677448i	$0.763086\pi$
$728$		−	11354.6i		−	0.0214244i
$729$	590698.			1.11150
$730$		−	92204.7i		−	0.173024i
$731$	−797461.			−1.49236
$732$			409729.i			0.764671i
$733$		−	659557.i		−	1.22756i	−0.789475	−	0.613782i	$-0.789647\pi$
$733$		−	659557.i		−	1.22756i	0.789475	−	0.613782i	$-0.210353\pi$
$734$			387831.i			0.719863i
$735$		−	208870.i		−	0.386636i
$736$	−94220.5	−	17097.7i	−0.173936	−	0.0315633i
$737$	−743543.			−1.36890
$738$	−153474.			−0.281787
$739$	−684772.			−1.25388			−0.626941	−	0.779066i	$-0.715693\pi$
$739$	−684772.			−1.25388			−0.626941	+	0.779066i	$0.715693\pi$
$740$	−85181.2			−0.155554
$741$		−	393593.i		−	0.716821i
$742$	14568.2			0.0264606
$743$		−	570296.i		−	1.03305i	−0.856271	−	0.516527i	$-0.827225\pi$
$743$		−	570296.i		−	1.03305i	0.856271	−	0.516527i	$-0.172775\pi$
$744$	−151810.			−0.274254
$745$	−37997.4			−0.0684607
$746$			480847.i			0.864031i
$747$		−	93956.0i		−	0.168377i
$748$	−257804.			−0.460772
$749$	−47138.7			−0.0840261
$750$		−	31102.9i		−	0.0552940i
$751$		−	1.01011e6i		−	1.79098i	−0.445081	−	0.895490i	$-0.646825\pi$
$751$		−	1.01011e6i		−	1.79098i	0.445081	−	0.895490i	$-0.353175\pi$
$752$	169449.			0.299643
$753$		−	574536.i		−	1.01328i
$754$	196589.			0.345794
$755$			366911.i			0.643674i
$756$			32569.0i			0.0569850i
$757$			284919.i			0.497199i	0.968606	+	0.248599i	$0.0799703\pi$
$757$			284919.i			0.497199i	−0.968606	+	0.248599i	$0.920030\pi$
$758$		−	470848.i		−	0.819488i
$759$	−77627.5	+	427783.i	−0.134751	+	0.742574i
$760$	−130363.			−0.225698
$761$	336503.			0.581058			0.290529	−	0.956866i	$-0.406169\pi$
$761$	336503.			0.581058			0.290529	+	0.956866i	$0.406169\pi$
$762$	−474078.			−0.816470
$763$	−66077.8			−0.113503
$764$			66529.1i			0.113979i
$765$	−65838.6			−0.112501
$766$			205292.i			0.349876i
$767$	−108377.			−0.184225
$768$	32229.3			0.0546422
$769$		−	604741.i		−	1.02263i	−0.859394	−	0.511313i	$-0.829159\pi$
$769$		−	604741.i		−	1.02263i	0.859394	−	0.511313i	$-0.170841\pi$
$770$			17074.9i			0.0287990i
$771$	510396.			0.858615
$772$	93601.5			0.157054
$773$		−	254194.i		−	0.425409i	−0.977117	−	0.212704i	$-0.931773\pi$
$773$		−	254194.i		−	0.425409i	0.977117	−	0.212704i	$-0.0682272\pi$
$774$			139542.i			0.232929i
$775$	−106582.			−0.177452
$776$			131611.i			0.218559i
$777$	−38737.8			−0.0641642
$778$		−	581771.i		−	0.961154i
$779$		−	1.46493e6i		−	2.41402i
$780$			68316.8i			0.112289i
$781$		−	361898.i		−	0.593313i
$782$	82422.3	−	454206.i	0.134782	−	0.742744i
$783$	−563887.			−0.919747
$784$	151954.			0.247217
$785$	361632.			0.586851
$786$	476796.			0.771769
$787$		−	556850.i		−	0.899060i	−0.893265	−	0.449530i	$-0.851591\pi$
$787$		−	556850.i		−	0.899060i	0.893265	−	0.449530i	$-0.148409\pi$
$788$	287116.			0.462386
$789$		−	875079.i		−	1.40570i
$790$	629.153			0.00100810
$791$	−100927.			−0.161308
$792$			45111.4i			0.0719177i
$793$		−	631841.i		−	1.00476i
$794$	225612.			0.357866
$795$	−87652.1			−0.138685
$796$			229339.i			0.361953i
$797$		−	225594.i		−	0.355150i	−0.984107	−	0.177575i	$-0.943175\pi$
$797$		−	225594.i		−	0.355150i	0.984107	−	0.177575i	$-0.0568252\pi$
$798$	−59285.2			−0.0930981
$799$			816859.i			1.27954i
$800$	22627.4			0.0353553
$801$		−	135049.i		−	0.210488i
$802$		−	428664.i		−	0.666451i
$803$		−	304555.i		−	0.472318i
$804$			448099.i			0.693206i
$805$	−30083.0	−	5459.00i	−0.0464226	−	0.00842406i
$806$	234105.			0.360363
$807$	110479.			0.169642
$808$	446320.			0.683634
$809$	1.03100e6			1.57529			0.787644	−	0.616130i	$-0.211301\pi$
$809$	1.03100e6			1.57529			0.787644	+	0.616130i	$0.211301\pi$
$810$		−	147066.i		−	0.224152i
$811$	−586932.			−0.892372			−0.446186	−	0.894940i	$-0.647218\pi$
$811$	−586932.			−0.892372			−0.446186	+	0.894940i	$0.647218\pi$
$812$		−	29611.4i		−	0.0449104i
$813$	−749788.			−1.13438
$814$	−281356.			−0.424627
$815$		−	210537.i		−	0.316967i
$816$			155367.i			0.233334i
$817$	−1.33195e6			−1.99546
$818$	−224683.			−0.335787
$819$		−	9578.02i		−	0.0142793i
$820$			254270.i			0.378153i
$821$	−193606.			−0.287232			−0.143616	−	0.989634i	$-0.545873\pi$
$821$	−193606.			−0.287232			−0.143616	+	0.989634i	$0.545873\pi$
$822$			655609.i			0.970289i
$823$	−175978.			−0.259811			−0.129906	−	0.991526i	$-0.541467\pi$
$823$	−175978.			−0.259811			−0.129906	+	0.991526i	$0.541467\pi$
$824$		−	212156.i		−	0.312465i
$825$		−	102734.i		−	0.150940i
$826$			16324.4i			0.0239264i
$827$			301957.i			0.441504i	0.975330	+	0.220752i	$0.0708511\pi$
$827$			301957.i			0.441504i	−0.975330	+	0.220752i	$0.929149\pi$
$828$	−79478.4	−	14422.5i	−0.115928	−	0.0210368i
$829$	366386.			0.533126			0.266563	−	0.963818i	$-0.414112\pi$
$829$	366386.			0.533126			0.266563	+	0.963818i	$0.414112\pi$
$830$	−155663.			−0.225959
$831$	513894.			0.744168
$832$	−49700.6			−0.0717984
$833$			732518.i			1.05567i
$834$	362731.			0.521497
$835$		−	587688.i		−	0.842896i
$836$	−430593.			−0.616105
$837$	−671494.			−0.958498
$838$			717811.i			1.02217i
$839$		−	140039.i		−	0.198941i	−0.995041	−	0.0994704i	$-0.968285\pi$
$839$		−	140039.i		−	0.198941i	0.995041	−	0.0994704i	$-0.0317149\pi$
$840$	10290.3			0.0145837
$841$	−194600.			−0.275139
$842$		−	9564.87i		−	0.0134913i
$843$		−	728210.i		−	1.02471i
$844$	149237.			0.209504
$845$			213971.i			0.299669i
$846$	142937.			0.199711
$847$		−	19287.3i		−	0.0268846i
$848$		−	63767.1i		−	0.0886757i
$849$		−	940438.i		−	1.30471i
$850$			109079.i			0.150975i
$851$	89952.0	−	495700.i	0.124209	−	0.684478i
$852$	−218099.			−0.300452
$853$	1.01374e6			1.39325			0.696626	−	0.717435i	$-0.254684\pi$
$853$	1.01374e6			1.39325			0.696626	+	0.717435i	$0.254684\pi$
$854$	−95171.5			−0.130494
$855$	−109966.			−0.150427
$856$			206332.i			0.281592i
$857$	−312959.			−0.426114			−0.213057	−	0.977040i	$-0.568342\pi$
$857$	−312959.			−0.426114			−0.213057	+	0.977040i	$0.568342\pi$
$858$			225652.i			0.306524i
$859$	−91874.5			−0.124511			−0.0622556	−	0.998060i	$-0.519829\pi$
$859$	−91874.5			−0.124511			−0.0622556	+	0.998060i	$0.519829\pi$
$860$	231189.			0.312587
$861$			115634.i			0.155984i
$862$			266287.i			0.358373i
$863$	236896.			0.318080			0.159040	−	0.987272i	$-0.449160\pi$
$863$	236896.			0.318080			0.159040	+	0.987272i	$0.449160\pi$
$864$	142559.			0.190970
$865$			324990.i			0.434348i
$866$		−	799821.i		−	1.06649i
$867$	−91787.7			−0.122109
$868$		−	35262.2i		−	0.0468026i
$869$	2078.11			0.00275188
$870$			178162.i			0.235383i
$871$		−	691011.i		−	0.910854i
$872$			289231.i			0.380375i
$873$			111019.i			0.145669i
$874$	137665.	−	758630.i	0.180219	−	0.993133i
$875$	7224.55			0.00943615
$876$	−183541.			−0.239180
$877$	−314557.			−0.408978			−0.204489	−	0.978869i	$-0.565553\pi$
$877$	−314557.			−0.408978			−0.204489	+	0.978869i	$0.565553\pi$
$878$	−823023.			−1.06764
$879$			558771.i			0.723196i
$880$	74739.0			0.0965122
$881$		−	757937.i		−	0.976520i	−0.872698	−	0.488260i	$-0.837632\pi$
$881$		−	757937.i		−	0.976520i	0.872698	−	0.488260i	$-0.162368\pi$
$882$	128178.			0.164770
$883$	409077.			0.524667			0.262334	−	0.964977i	$-0.415508\pi$
$883$	409077.			0.524667			0.262334	+	0.964977i	$0.415508\pi$
$884$		−	239590.i		−	0.306594i
$885$		−	98218.3i		−	0.125402i
$886$	585938.			0.746421
$887$	1.10006e6			1.39820			0.699099	−	0.715025i	$-0.253585\pi$
$887$	1.10006e6			1.39820			0.699099	+	0.715025i	$0.253585\pi$
$888$			169560.i			0.215030i
$889$		−	110118.i		−	0.139334i
$890$	−223745.			−0.282471
$891$		−	485763.i		−	0.611884i
$892$	−22888.4			−0.0287664
$893$			1.36435e6i			1.71089i
$894$			75637.0i			0.0946367i
$895$		−	186218.i		−	0.232474i
$896$			7486.19i			0.00932491i
$897$	−397560.	−	72143.1i	−0.494103	−	0.0896623i
$898$	−587403.			−0.728422
$899$	610516.			0.755401
$900$	19087.0			0.0235643
$901$	307400.			0.378664
$902$			839862.i			1.03227i
$903$	105138.			0.128939
$904$			441771.i			0.540580i
$905$	14720.8			0.0179736
$906$	730367.			0.889784
$907$			949722.i			1.15447i	0.816579	+	0.577234i	$0.195868\pi$
$907$			949722.i			1.15447i	−0.816579	+	0.577234i	$0.804132\pi$
$908$		−	95358.0i		−	0.115661i
$909$	376487.			0.455640
$910$	−15868.6			−0.0191626
$911$			1.57943e6i			1.90311i	0.307480	+	0.951555i	$0.400514\pi$
$911$			1.57943e6i			1.90311i	−0.307480	+	0.951555i	$0.599486\pi$
$912$			259499.i			0.311994i
$913$	−514160.			−0.616817
$914$		−	36148.9i		−	0.0432716i
$915$	572614.			0.683943
$916$		−	535786.i		−	0.638559i
$917$			110750.i			0.131705i
$918$			687228.i			0.815484i
$919$			624627.i			0.739588i	0.929114	+	0.369794i	$0.120572\pi$
$919$			624627.i			0.739588i	−0.929114	+	0.369794i	$0.879428\pi$
$920$	−23894.7	+	131677.i	−0.0282310	+	0.155573i
$921$	911618.			1.07472
$922$	−171577.			−0.201836
$923$	336330.			0.394786
$924$	33989.0			0.0398103
$925$			119044.i			0.139131i
$926$	286314.			0.333903
$927$		−	178962.i		−	0.208257i
$928$	−129613.			−0.150506
$929$	−932125.			−1.08005			−0.540024	−	0.841650i	$-0.681585\pi$
$929$	−932125.			−1.08005			−0.540024	+	0.841650i	$0.681585\pi$
$930$			212160.i			0.245300i
$931$			1.22348e6i			1.41155i
$932$	407823.			0.469505
$933$	−129784.			−0.149093
$934$			932619.i			1.06908i
$935$			360292.i			0.412127i
$936$	−41924.2			−0.0478535
$937$		−	1.22146e6i		−	1.39124i	−0.718412	−	0.695618i	$-0.755131\pi$
$937$		−	1.22146e6i		−	1.39124i	0.718412	−	0.695618i	$-0.244869\pi$
$938$	−104084.			−0.118298
$939$			1.25771e6i			1.42643i
$940$		−	236813.i		−	0.268009i
$941$			556951.i			0.628981i	0.949261	+	0.314491i	$0.101834\pi$
$941$			556951.i			0.628981i	−0.949261	+	0.314491i	$0.898166\pi$
$942$		−	719860.i		−	0.811234i
$943$	−1.47969e6	−	268512.i	−1.66398	−	0.301953i
$944$	71454.0			0.0801831
$945$	45516.6			0.0509690
$946$	763624.			0.853292
$947$	−622255.			−0.693854			−0.346927	−	0.937892i	$-0.612775\pi$
$947$	−622255.			−0.693854			−0.346927	+	0.937892i	$0.612775\pi$
$948$		−	1252.38i		−	0.00139354i
$949$	283038.			0.314277
$950$			182188.i			0.201870i
$951$	−588999.			−0.651259
$952$	−36088.4			−0.0398193
$953$			1.00255e6i			1.10388i	0.833884	+	0.551940i	$0.186112\pi$
$953$			1.00255e6i			1.10388i	−0.833884	+	0.551940i	$0.813888\pi$
$954$		−	53789.8i		−	0.0591022i
$955$	92977.2			0.101946
$956$	−612789.			−0.670495
$957$			588473.i			0.642544i
$958$		−	590469.i		−	0.643377i
$959$	−152284.			−0.165584
$960$		−	45041.8i		−	0.0488735i
$961$	−196500.			−0.212773
$962$		−	261478.i		−	0.282543i
$963$			174049.i			0.187680i
$964$			866277.i			0.932186i
$965$		−	130812.i		−	0.140473i
$966$	−10866.6	+	59882.8i	−0.0116450	+	0.0641723i
$967$	796251.			0.851524			0.425762	−	0.904835i	$-0.360006\pi$
$967$	796251.			0.851524			0.425762	+	0.904835i	$0.360006\pi$
$968$	−84422.8			−0.0900968
$969$	−1.25096e6			−1.33228
$970$	183932.			0.195485
$971$			1.48349e6i			1.57343i	0.617318	+	0.786714i	$0.288219\pi$
$971$			1.48349e6i			1.57343i	−0.617318	+	0.786714i	$0.711781\pi$
$972$	217574.			0.230290
$973$			84254.7i			0.0889956i
$974$	13536.2			0.0142685
$975$	95475.6			0.100435
$976$			416578.i			0.437317i
$977$			1.39345e6i			1.45983i	0.683536	+	0.729917i	$0.260441\pi$
$977$			1.39345e6i			1.45983i	−0.683536	+	0.729917i	$0.739559\pi$
$978$	−419092.			−0.438159
$979$	−739036.			−0.771081
$980$		−	212362.i		−	0.221118i
$981$			243977.i			0.253519i
$982$	951146.			0.986335
$983$			1.13498e6i			1.17457i	0.809380	+	0.587286i	$0.199804\pi$
$983$			1.13498e6i			1.17457i	−0.809380	+	0.587286i	$0.800196\pi$
$984$	506147.			0.522741
$985$		−	401256.i		−	0.413570i
$986$		−	624821.i		−	0.642690i
$987$		−	107695.i		−	0.110551i
$988$		−	400172.i		−	0.409952i
$989$	−244138.	+	1.34537e6i	−0.249599	+	1.37547i
$990$	63045.1			0.0643251
$991$	1.00653e6			1.02490			0.512450	−	0.858717i	$-0.328738\pi$
$991$	1.00653e6			1.02490			0.512450	+	0.858717i	$0.328738\pi$
$992$	−154347.			−0.156847
$993$	829878.			0.841619
$994$		−	50659.9i		−	0.0512733i
$995$	320511.			0.323740
$996$			309861.i			0.312354i
$997$	1.27691e6			1.28460			0.642302	−	0.766452i	$-0.277979\pi$
$997$	1.27691e6			1.28460			0.642302	+	0.766452i	$0.277979\pi$
$998$	−733322.			−0.736264
$999$			750010.i			0.751512i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.d.a.91.8	✓	32
23.22	odd	2	inner	230.5.d.a.91.9	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.d.a.91.8	✓	32	1.1	even	1	trivial
230.5.d.a.91.9	yes	32	23.22	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	230.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.82843 q^{2} +7.86848 q^{3} +8.00000 q^{4} -11.1803i q^{5} -22.2554 q^{6} -5.16947i q^{7} -22.6274 q^{8} -19.0870 q^{9} +O(q^{10})\)	\(q-2.82843 q^{2} +7.86848 q^{3} +8.00000 q^{4} -11.1803i q^{5} -22.2554 q^{6} -5.16947i q^{7} -22.6274 q^{8} -19.0870 q^{9} +31.6228i q^{10} +104.451i q^{11} +62.9478 q^{12} -97.0715 q^{13} +14.6215i q^{14} -87.9723i q^{15} +64.0000 q^{16} +308.523i q^{17} +53.9863 q^{18} +515.306i q^{19} -89.4427i q^{20} -40.6758i q^{21} -295.432i q^{22} +(520.500 + 94.4523i) q^{23} -178.043 q^{24} -125.000 q^{25} +274.560 q^{26} -787.533 q^{27} -41.3557i q^{28} +716.017 q^{29} +248.823i q^{30} +852.655 q^{31} -181.019 q^{32} +821.870i q^{33} -872.634i q^{34} -57.7964 q^{35} -152.696 q^{36} -952.354i q^{37} -1457.50i q^{38} -763.805 q^{39} +252.982i q^{40} -2842.83 q^{41} +115.049i q^{42} +2584.77i q^{43} +835.608i q^{44} +213.400i q^{45} +(-1472.20 - 267.151i) q^{46} +2647.65 q^{47} +503.583 q^{48} +2374.28 q^{49} +353.553 q^{50} +2427.60i q^{51} -776.572 q^{52} -996.361i q^{53} +2227.48 q^{54} +1167.80 q^{55} +116.972i q^{56} +4054.67i q^{57} -2025.20 q^{58} +1116.47 q^{59} -703.778i q^{60} +6509.03i q^{61} -2411.67 q^{62} +98.6698i q^{63} +512.000 q^{64} +1085.29i q^{65} -2324.60i q^{66} +7118.58i q^{67} +2468.18i q^{68} +(4095.54 + 743.196i) q^{69} +163.473 q^{70} -3464.76 q^{71} +431.890 q^{72} -2915.77 q^{73} +2693.66i q^{74} -983.560 q^{75} +4122.45i q^{76} +539.956 q^{77} +2160.37 q^{78} -19.8956i q^{79} -715.542i q^{80} -4650.63 q^{81} +8040.73 q^{82} +4922.50i q^{83} -325.407i q^{84} +3449.39 q^{85} -7310.84i q^{86} +5633.97 q^{87} -2363.46i q^{88} +7075.44i q^{89} -603.585i q^{90} +501.808i q^{91} +(4164.00 + 755.618i) q^{92} +6709.10 q^{93} -7488.67 q^{94} +5761.29 q^{95} -1424.35 q^{96} -5816.44i q^{97} -6715.47 q^{98} -1993.66i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9}+O(q^{10}) \) 32 * q + 256 * q^4 + 64 * q^6 + 832 * q^9	\( 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9} - 408 q^{13} + 2048 q^{16} + 1024 q^{18} + 1332 q^{23} + 512 q^{24} - 4000 q^{25} + 2208 q^{27} + 3732 q^{29} - 412 q^{31} + 300 q^{35} + 6656 q^{36} - 9208 q^{39} - 6156 q^{41} + 4480 q^{46} + 5184 q^{47} - 13820 q^{49} - 3264 q^{52} - 3328 q^{54} - 6000 q^{55} + 3200 q^{58} - 30468 q^{59} - 10752 q^{62} + 16384 q^{64} - 1168 q^{69} + 4800 q^{70} - 37644 q^{71} + 8192 q^{72} + 19984 q^{73} + 27528 q^{77} + 15744 q^{78} + 69056 q^{81} - 17408 q^{82} + 3300 q^{85} + 28936 q^{87} + 10656 q^{92} + 40648 q^{93} - 23808 q^{94} - 21600 q^{95} + 4096 q^{96} + 43008 q^{98}+O(q^{100}) \) 32 * q + 256 * q^4 + 64 * q^6 + 832 * q^9 - 408 * q^13 + 2048 * q^16 + 1024 * q^18 + 1332 * q^23 + 512 * q^24 - 4000 * q^25 + 2208 * q^27 + 3732 * q^29 - 412 * q^31 + 300 * q^35 + 6656 * q^36 - 9208 * q^39 - 6156 * q^41 + 4480 * q^46 + 5184 * q^47 - 13820 * q^49 - 3264 * q^52 - 3328 * q^54 - 6000 * q^55 + 3200 * q^58 - 30468 * q^59 - 10752 * q^62 + 16384 * q^64 - 1168 * q^69 + 4800 * q^70 - 37644 * q^71 + 8192 * q^72 + 19984 * q^73 + 27528 * q^77 + 15744 * q^78 + 69056 * q^81 - 17408 * q^82 + 3300 * q^85 + 28936 * q^87 + 10656 * q^92 + 40648 * q^93 - 23808 * q^94 - 21600 * q^95 + 4096 * q^96 + 43008 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more