LMFDB - Embedded newform 230.6.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,6,Mod(1,230)]

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, 0]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("230.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	230.a (trivial)

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:	yes
Analytic conductor:	$36.8882785570$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 774x^{3} - 197x^{2} + 66287x + 154128 $ x^5 - x^4 - 774x^3 - 197x^2 + 66287*x + 154128
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$10.8366$ of defining polynomial
Character	$\chi$	$=$	230.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +10.8366 q^{3} +16.0000 q^{4} +25.0000 q^{5} -43.3465 q^{6} +46.1561 q^{7} -64.0000 q^{8} -125.567 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +10.8366 q^{3} +16.0000 q^{4} +25.0000 q^{5} -43.3465 q^{6} +46.1561 q^{7} -64.0000 q^{8} -125.567 q^{9} -100.000 q^{10} +8.88634 q^{11} +173.386 q^{12} +229.106 q^{13} -184.624 q^{14} +270.916 q^{15} +256.000 q^{16} +561.534 q^{17} +502.269 q^{18} +1957.16 q^{19} +400.000 q^{20} +500.176 q^{21} -35.5454 q^{22} -529.000 q^{23} -693.545 q^{24} +625.000 q^{25} -916.423 q^{26} -3994.03 q^{27} +738.497 q^{28} +576.364 q^{29} -1083.66 q^{30} +7333.04 q^{31} -1024.00 q^{32} +96.2981 q^{33} -2246.14 q^{34} +1153.90 q^{35} -2009.08 q^{36} +2330.56 q^{37} -7828.64 q^{38} +2482.74 q^{39} -1600.00 q^{40} +89.3538 q^{41} -2000.71 q^{42} -1692.41 q^{43} +142.181 q^{44} -3139.18 q^{45} +2116.00 q^{46} -2617.45 q^{47} +2774.18 q^{48} -14676.6 q^{49} -2500.00 q^{50} +6085.14 q^{51} +3665.69 q^{52} +19388.3 q^{53} +15976.1 q^{54} +222.159 q^{55} -2953.99 q^{56} +21209.0 q^{57} -2305.45 q^{58} +37460.4 q^{59} +4334.65 q^{60} -17456.6 q^{61} -29332.2 q^{62} -5795.69 q^{63} +4096.00 q^{64} +5727.65 q^{65} -385.192 q^{66} +25612.4 q^{67} +8984.55 q^{68} -5732.58 q^{69} -4615.61 q^{70} -6079.31 q^{71} +8036.31 q^{72} +67969.4 q^{73} -9322.23 q^{74} +6772.90 q^{75} +31314.5 q^{76} +410.159 q^{77} -9930.95 q^{78} +70755.0 q^{79} +6400.00 q^{80} -12769.0 q^{81} -357.415 q^{82} +54086.0 q^{83} +8002.82 q^{84} +14038.4 q^{85} +6769.65 q^{86} +6245.84 q^{87} -568.726 q^{88} +67687.8 q^{89} +12556.7 q^{90} +10574.6 q^{91} -8464.00 q^{92} +79465.5 q^{93} +10469.8 q^{94} +48929.0 q^{95} -11096.7 q^{96} +103840. q^{97} +58706.5 q^{98} -1115.83 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 20 q^{2} + q^{3} + 80 q^{4} + 125 q^{5} - 4 q^{6} + 102 q^{7} - 320 q^{8} + 334 q^{9}+O(q^{10}) $ 5 * q - 20 * q^2 + q^3 + 80 * q^4 + 125 * q^5 - 4 * q^6 + 102 * q^7 - 320 * q^8 + 334 * q^9	\( 5 q - 20 q^{2} + q^{3} + 80 q^{4} + 125 q^{5} - 4 q^{6} + 102 q^{7} - 320 q^{8} + 334 q^{9} - 500 q^{10} + 251 q^{11} + 16 q^{12} + 1743 q^{13} - 408 q^{14} + 25 q^{15} + 1280 q^{16} + 1944 q^{17} - 1336 q^{18} - 845 q^{19} + 2000 q^{20} + 4682 q^{21} - 1004 q^{22} - 2645 q^{23} - 64 q^{24} + 3125 q^{25} - 6972 q^{26} + 2428 q^{27} + 1632 q^{28} - 4021 q^{29} - 100 q^{30} - 15752 q^{31} - 5120 q^{32} + 2931 q^{33} - 7776 q^{34} + 2550 q^{35} + 5344 q^{36} - 3455 q^{37} + 3380 q^{38} - 16708 q^{39} - 8000 q^{40} - 11898 q^{41} - 18728 q^{42} + 6968 q^{43} + 4016 q^{44} + 8350 q^{45} + 10580 q^{46} + 13412 q^{47} + 256 q^{48} + 91041 q^{49} - 12500 q^{50} - 2115 q^{51} + 27888 q^{52} + 53029 q^{53} - 9712 q^{54} + 6275 q^{55} - 6528 q^{56} - 21730 q^{57} + 16084 q^{58} - 31223 q^{59} + 400 q^{60} + 71477 q^{61} + 63008 q^{62} + 262199 q^{63} + 20480 q^{64} + 43575 q^{65} - 11724 q^{66} + 76003 q^{67} + 31104 q^{68} - 529 q^{69} - 10200 q^{70} + 54418 q^{71} - 21376 q^{72} + 69418 q^{73} + 13820 q^{74} + 625 q^{75} - 13520 q^{76} + 283598 q^{77} + 66832 q^{78} + 105024 q^{79} + 32000 q^{80} + 102913 q^{81} + 47592 q^{82} + 89399 q^{83} + 74912 q^{84} + 48600 q^{85} - 27872 q^{86} + 276726 q^{87} - 16064 q^{88} + 96240 q^{89} - 33400 q^{90} + 59261 q^{91} - 42320 q^{92} + 84434 q^{93} - 53648 q^{94} - 21125 q^{95} - 1024 q^{96} + 216087 q^{97} - 364164 q^{98} + 386925 q^{99}+O(q^{100}) \) 5 * q - 20 * q^2 + q^3 + 80 * q^4 + 125 * q^5 - 4 * q^6 + 102 * q^7 - 320 * q^8 + 334 * q^9 - 500 * q^10 + 251 * q^11 + 16 * q^12 + 1743 * q^13 - 408 * q^14 + 25 * q^15 + 1280 * q^16 + 1944 * q^17 - 1336 * q^18 - 845 * q^19 + 2000 * q^20 + 4682 * q^21 - 1004 * q^22 - 2645 * q^23 - 64 * q^24 + 3125 * q^25 - 6972 * q^26 + 2428 * q^27 + 1632 * q^28 - 4021 * q^29 - 100 * q^30 - 15752 * q^31 - 5120 * q^32 + 2931 * q^33 - 7776 * q^34 + 2550 * q^35 + 5344 * q^36 - 3455 * q^37 + 3380 * q^38 - 16708 * q^39 - 8000 * q^40 - 11898 * q^41 - 18728 * q^42 + 6968 * q^43 + 4016 * q^44 + 8350 * q^45 + 10580 * q^46 + 13412 * q^47 + 256 * q^48 + 91041 * q^49 - 12500 * q^50 - 2115 * q^51 + 27888 * q^52 + 53029 * q^53 - 9712 * q^54 + 6275 * q^55 - 6528 * q^56 - 21730 * q^57 + 16084 * q^58 - 31223 * q^59 + 400 * q^60 + 71477 * q^61 + 63008 * q^62 + 262199 * q^63 + 20480 * q^64 + 43575 * q^65 - 11724 * q^66 + 76003 * q^67 + 31104 * q^68 - 529 * q^69 - 10200 * q^70 + 54418 * q^71 - 21376 * q^72 + 69418 * q^73 + 13820 * q^74 + 625 * q^75 - 13520 * q^76 + 283598 * q^77 + 66832 * q^78 + 105024 * q^79 + 32000 * q^80 + 102913 * q^81 + 47592 * q^82 + 89399 * q^83 + 74912 * q^84 + 48600 * q^85 - 27872 * q^86 + 276726 * q^87 - 16064 * q^88 + 96240 * q^89 - 33400 * q^90 + 59261 * q^91 - 42320 * q^92 + 84434 * q^93 - 53648 * q^94 - 21125 * q^95 - 1024 * q^96 + 216087 * q^97 - 364164 * q^98 + 386925 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	10.8366	0.695171	0.347585	−	0.937648i	$-0.387002\pi$
$3$	10.8366	0.695171	0.347585	+	0.937648i	$0.387002\pi$
$4$	16.0000	0.500000
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−43.3465	−0.491560
$7$	46.1561	0.356028	0.178014	−	0.984028i	$-0.443033\pi$
$7$	46.1561	0.356028	0.178014	+	0.984028i	$0.443033\pi$
$8$	−64.0000	−0.353553
$9$	−125.567	−0.516738
$10$	−100.000	−0.316228
$11$	8.88634	0.0221432	0.0110716	−	0.999939i	$-0.496476\pi$
$11$	8.88634	0.0221432	0.0110716	+	0.999939i	$0.496476\pi$
$12$	173.386	0.347585
$13$	229.106	0.375991	0.187996	−	0.982170i	$-0.439801\pi$
$13$	229.106	0.375991	0.187996	+	0.982170i	$0.439801\pi$
$14$	−184.624	−0.251750
$15$	270.916	0.310890
$16$	256.000	0.250000
$17$	561.534	0.471253	0.235626	−	0.971844i	$-0.424286\pi$
$17$	561.534	0.471253	0.235626	+	0.971844i	$0.424286\pi$
$18$	502.269	0.365389
$19$	1957.16	1.24378	0.621888	−	0.783106i	$-0.286366\pi$
$19$	1957.16	1.24378	0.621888	+	0.783106i	$0.286366\pi$
$20$	400.000	0.223607
$21$	500.176	0.247500
$22$	−35.5454	−0.0156576
$23$	−529.000	−0.208514
$23$	−529.000	−0.208514
$24$	−693.545	−0.245780
$25$	625.000	0.200000
$26$	−916.423	−0.265866
$27$	−3994.03	−1.05439
$28$	738.497	0.178014
$29$	576.364	0.127263	0.0636314	−	0.997973i	$-0.479732\pi$
$29$	576.364	0.127263	0.0636314	+	0.997973i	$0.479732\pi$
$30$	−1083.66	−0.219832
$31$	7333.04	1.37050	0.685251	−	0.728307i	$-0.259692\pi$
$31$	7333.04	1.37050	0.685251	+	0.728307i	$0.259692\pi$
$32$	−1024.00	−0.176777
$33$	96.2981	0.0153933
$34$	−2246.14	−0.333226
$35$	1153.90	0.159220
$36$	−2009.08	−0.258369
$37$	2330.56	0.279869	0.139935	−	0.990161i	$-0.455311\pi$
$37$	2330.56	0.279869	0.139935	+	0.990161i	$0.455311\pi$
$38$	−7828.64	−0.879482
$39$	2482.74	0.261378
$40$	−1600.00	−0.158114
$41$	89.3538	0.00830144	0.00415072	−	0.999991i	$-0.498679\pi$
$41$	89.3538	0.00830144	0.00415072	+	0.999991i	$0.498679\pi$
$42$	−2000.71	−0.175009
$43$	−1692.41	−0.139584	−0.0697919	−	0.997562i	$-0.522234\pi$
$43$	−1692.41	−0.139584	−0.0697919	+	0.997562i	$0.522234\pi$
$44$	142.181	0.0110716
$45$	−3139.18	−0.231092
$46$	2116.00	0.147442
$47$	−2617.45	−0.172836	−0.0864179	−	0.996259i	$-0.527542\pi$
$47$	−2617.45	−0.172836	−0.0864179	+	0.996259i	$0.527542\pi$
$48$	2774.18	0.173793
$49$	−14676.6	−0.873244
$50$	−2500.00	−0.141421
$51$	6085.14	0.327601
$52$	3665.69	0.187996
$53$	19388.3	0.948092	0.474046	−	0.880500i	$-0.342793\pi$
$53$	19388.3	0.948092	0.474046	+	0.880500i	$0.342793\pi$
$54$	15976.1	0.745567
$55$	222.159	0.00990276
$56$	−2953.99	−0.125875
$57$	21209.0	0.864636
$58$	−2305.45	−0.0899884
$59$	37460.4	1.40101	0.700507	−	0.713646i	$-0.252957\pi$
$59$	37460.4	1.40101	0.700507	+	0.713646i	$0.252957\pi$
$60$	4334.65	0.155445
$61$	−17456.6	−0.600670	−0.300335	−	0.953834i	$-0.597098\pi$
$61$	−17456.6	−0.600670	−0.300335	+	0.953834i	$0.597098\pi$
$62$	−29332.2	−0.969091
$63$	−5795.69	−0.183973
$64$	4096.00	0.125000
$65$	5727.65	0.168148
$66$	−385.192	−0.0108847
$67$	25612.4	0.697050	0.348525	−	0.937300i	$-0.386683\pi$
$67$	25612.4	0.697050	0.348525	+	0.937300i	$0.386683\pi$
$68$	8984.55	0.235626
$69$	−5732.58	−0.144953
$70$	−4615.61	−0.112586
$71$	−6079.31	−0.143123	−0.0715614	−	0.997436i	$-0.522798\pi$
$71$	−6079.31	−0.143123	−0.0715614	+	0.997436i	$0.522798\pi$
$72$	8036.31	0.182694
$73$	67969.4	1.49282	0.746408	−	0.665488i	$-0.231777\pi$
$73$	67969.4	1.49282	0.746408	+	0.665488i	$0.231777\pi$
$74$	−9322.23	−0.197898
$75$	6772.90	0.139034
$76$	31314.5	0.621888
$77$	410.159	0.00788361
$78$	−9930.95	−0.184822
$79$	70755.0	1.27553	0.637763	−	0.770233i	$-0.279860\pi$
$79$	70755.0	1.27553	0.637763	+	0.770233i	$0.279860\pi$
$80$	6400.00	0.111803
$81$	−12769.0	−0.216244
$82$	−357.415	−0.00587000
$83$	54086.0	0.861766	0.430883	−	0.902408i	$-0.358202\pi$
$83$	54086.0	0.861766	0.430883	+	0.902408i	$0.358202\pi$
$84$	8002.82	0.123750
$85$	14038.4	0.210751
$86$	6769.65	0.0987007
$87$	6245.84	0.0884694
$88$	−568.726	−0.00782882
$89$	67687.8	0.905807	0.452903	−	0.891560i	$-0.350388\pi$
$89$	67687.8	0.905807	0.452903	+	0.891560i	$0.350388\pi$
$90$	12556.7	0.163407
$91$	10574.6	0.133863
$92$	−8464.00	−0.104257
$93$	79465.5	0.952733
$94$	10469.8	0.122213
$95$	48929.0	0.556233
$96$	−11096.7	−0.122890
$97$	103840.	1.12056	0.560281	−	0.828303i	$-0.310693\pi$
$97$	103840.	1.12056	0.560281	+	0.828303i	$0.310693\pi$
$98$	58706.5	0.617477
$99$	−1115.83	−0.0114423
$100$	10000.0	0.100000
$101$	−90122.4	−0.879082	−0.439541	−	0.898223i	$-0.644859\pi$
$101$	−90122.4	−0.879082	−0.439541	+	0.898223i	$0.644859\pi$
$102$	−24340.6	−0.231649
$103$	−86411.2	−0.802559	−0.401280	−	0.915956i	$-0.631434\pi$
$103$	−86411.2	−0.802559	−0.401280	+	0.915956i	$0.631434\pi$
$104$	−14662.8	−0.132933
$105$	12504.4	0.110685
$106$	−77553.3	−0.670403
$107$	135629.	1.14523	0.572617	−	0.819823i	$-0.305928\pi$
$107$	135629.	1.14523	0.572617	+	0.819823i	$0.305928\pi$
$108$	−63904.5	−0.527196
$109$	180022.	1.45131	0.725654	−	0.688060i	$-0.241537\pi$
$109$	180022.	1.45131	0.725654	+	0.688060i	$0.241537\pi$
$110$	−888.634	−0.00700231
$111$	25255.4	0.194557
$112$	11816.0	0.0890069
$113$	−159472.	−1.17486	−0.587432	−	0.809274i	$-0.699861\pi$
$113$	−159472.	−1.17486	−0.587432	+	0.809274i	$0.699861\pi$
$114$	−84836.1	−0.611390
$115$	−13225.0	−0.0932505
$116$	9221.82	0.0636314
$117$	−28768.2	−0.194289
$118$	−149842.	−0.990666
$119$	25918.2	0.167779
$120$	−17338.6	−0.109916
$121$	−160972.	−0.999510
$122$	69826.5	0.424738
$123$	968.294	0.00577091
$124$	117329.	0.685251
$125$	15625.0	0.0894427
$126$	23182.8	0.130089
$127$	63419.2	0.348909	0.174454	−	0.984665i	$-0.444184\pi$
$127$	63419.2	0.348909	0.174454	+	0.984665i	$0.444184\pi$
$128$	−16384.0	−0.0883883
$129$	−18340.1	−0.0970346
$130$	−22910.6	−0.118899
$131$	−189912.	−0.966881	−0.483441	−	0.875377i	$-0.660613\pi$
$131$	−189912.	−0.966881	−0.483441	+	0.875377i	$0.660613\pi$
$132$	1540.77	0.00769667
$133$	90334.8	0.442819
$134$	−102450.	−0.492889
$135$	−99850.8	−0.471538
$136$	−35938.2	−0.166613
$137$	75422.5	0.343320	0.171660	−	0.985156i	$-0.445087\pi$
$137$	75422.5	0.343320	0.171660	+	0.985156i	$0.445087\pi$
$138$	22930.3	0.102497
$139$	47836.5	0.210002	0.105001	−	0.994472i	$-0.466515\pi$
$139$	47836.5	0.210002	0.105001	+	0.994472i	$0.466515\pi$
$140$	18462.4	0.0796102
$141$	−28364.4	−0.120150
$142$	24317.3	0.101203
$143$	2035.91	0.00832567
$144$	−32145.2	−0.129184
$145$	14409.1	0.0569137
$146$	−271878.	−1.05558
$147$	−159045.	−0.607054
$148$	37288.9	0.139935
$149$	−415547.	−1.53340	−0.766699	−	0.642007i	$-0.778102\pi$
$149$	−415547.	−1.53340	−0.766699	+	0.642007i	$0.778102\pi$
$150$	−27091.6	−0.0983120
$151$	−246.134	−0.000878474 0	−0.000439237	−	1.00000i	$-0.500140\pi$
$151$	−246.134	−0.000878474 0	−0.000439237		1.00000i	$0.500140\pi$
$152$	−125258.	−0.439741
$153$	−70510.3	−0.243514
$154$	−1640.63	−0.00557455
$155$	183326.	0.612907
$156$	39723.8	0.130689
$157$	49843.7	0.161384	0.0806922	−	0.996739i	$-0.474287\pi$
$157$	49843.7	0.161384	0.0806922	+	0.996739i	$0.474287\pi$
$158$	−283020.	−0.901933
$159$	210104.	0.659086
$160$	−25600.0	−0.0790569
$161$	−24416.6	−0.0742369
$162$	51076.0	0.152908
$163$	−428050.	−1.26190	−0.630951	−	0.775823i	$-0.717335\pi$
$163$	−428050.	−1.26190	−0.630951	+	0.775823i	$0.717335\pi$
$164$	1429.66	0.00415072
$165$	2407.45	0.00688411
$166$	−216344.	−0.609361
$167$	387299.	1.07462	0.537310	−	0.843385i	$-0.319440\pi$
$167$	387299.	1.07462	0.537310	+	0.843385i	$0.319440\pi$
$168$	−32011.3	−0.0875044
$169$	−318804.	−0.858631
$170$	−56153.4	−0.149023
$171$	−245755.	−0.642706
$172$	−27078.6	−0.0697919
$173$	−168861.	−0.428959	−0.214479	−	0.976729i	$-0.568805\pi$
$173$	−168861.	−0.428959	−0.214479	+	0.976729i	$0.568805\pi$
$174$	−24983.4	−0.0625573
$175$	28847.5	0.0712055
$176$	2274.90	0.00553581
$177$	405945.	0.973944
$178$	−270751.	−0.640502
$179$	−507780.	−1.18452	−0.592260	−	0.805747i	$-0.701764\pi$
$179$	−507780.	−1.18452	−0.592260	+	0.805747i	$0.701764\pi$
$180$	−50226.9	−0.115546
$181$	22218.5	0.0504102	0.0252051	−	0.999682i	$-0.491976\pi$
$181$	22218.5	0.0504102	0.0252051	+	0.999682i	$0.491976\pi$
$182$	−42298.5	−0.0946556
$183$	−189171.	−0.417568
$184$	33856.0	0.0737210
$185$	58263.9	0.125161
$186$	−317862.	−0.673684
$187$	4989.99	0.0104351
$188$	−41879.2	−0.0864179
$189$	−184349.	−0.375392
$190$	−195716.	−0.393316
$191$	−543158.	−1.07732	−0.538658	−	0.842525i	$-0.681068\pi$
$191$	−543158.	−1.07732	−0.538658	+	0.842525i	$0.681068\pi$
$192$	44386.9	0.0868963
$193$	647088.	1.25046	0.625231	−	0.780440i	$-0.285005\pi$
$193$	647088.	1.25046	0.625231	+	0.780440i	$0.285005\pi$
$194$	−415360.	−0.792357
$195$	62068.4	0.116892
$196$	−234826.	−0.436622
$197$	−37986.4	−0.0697368	−0.0348684	−	0.999392i	$-0.511101\pi$
$197$	−37986.4	−0.0697368	−0.0348684	+	0.999392i	$0.511101\pi$
$198$	4463.34	0.00809089
$199$	552686.	0.989340	0.494670	−	0.869081i	$-0.335289\pi$
$199$	552686.	0.989340	0.494670	+	0.869081i	$0.335289\pi$
$200$	−40000.0	−0.0707107
$201$	277553.	0.484568
$202$	360489.	0.621605
$203$	26602.7	0.0453091
$204$	97362.3	0.163801
$205$	2233.84	0.00371252
$206$	345645.	0.567495
$207$	66425.1	0.107747
$208$	58651.1	0.0939978
$209$	17392.0	0.0275412
$210$	−50017.6	−0.0782663
$211$	−49704.3	−0.0768578	−0.0384289	−	0.999261i	$-0.512235\pi$
$211$	−49704.3	−0.0768578	−0.0384289	+	0.999261i	$0.512235\pi$
$212$	310213.	0.474046
$213$	−65879.3	−0.0994947
$214$	−542518.	−0.809803
$215$	−42310.3	−0.0624238
$216$	255618.	0.372784
$217$	338464.	0.487937
$218$	−720088.	−1.02623
$219$	736560.	1.03776
$220$	3554.54	0.00495138
$221$	128651.	0.177187
$222$	−101022.	−0.137573
$223$	49037.1	0.0660333	0.0330166	−	0.999455i	$-0.489489\pi$
$223$	49037.1	0.0660333	0.0330166	+	0.999455i	$0.489489\pi$
$224$	−47263.8	−0.0629374
$225$	−78479.6	−0.103348
$226$	637887.	0.830754
$227$	228515.	0.294340	0.147170	−	0.989111i	$-0.452984\pi$
$227$	228515.	0.294340	0.147170	+	0.989111i	$0.452984\pi$
$228$	339344.	0.432318
$229$	−202746.	−0.255484	−0.127742	−	0.991807i	$-0.540773\pi$
$229$	−202746.	−0.255484	−0.127742	+	0.991807i	$0.540773\pi$
$230$	52900.0	0.0659380
$231$	4444.74	0.00548045
$232$	−36887.3	−0.0449942
$233$	−327542.	−0.395255	−0.197628	−	0.980277i	$-0.563324\pi$
$233$	−327542.	−0.395255	−0.197628	+	0.980277i	$0.563324\pi$
$234$	115073.	0.137383
$235$	−65436.3	−0.0772946
$236$	599366.	0.700507
$237$	766746.	0.886708
$238$	−103673.	−0.118638
$239$	−544856.	−0.617002	−0.308501	−	0.951224i	$-0.599827\pi$
$239$	−544856.	−0.617002	−0.308501	+	0.951224i	$0.599827\pi$
$240$	69354.5	0.0777224
$241$	41076.8	0.0455569	0.0227784	−	0.999741i	$-0.492749\pi$
$241$	41076.8	0.0455569	0.0227784	+	0.999741i	$0.492749\pi$
$242$	643888.	0.706760
$243$	832176.	0.904065
$244$	−279306.	−0.300335
$245$	−366915.	−0.390527
$246$	−3873.18	−0.00408065
$247$	448396.	0.467649
$248$	−469315.	−0.484546
$249$	586110.	0.599074
$250$	−62500.0	−0.0632456
$251$	325565.	0.326177	0.163088	−	0.986611i	$-0.447854\pi$
$251$	325565.	0.326177	0.163088	+	0.986611i	$0.447854\pi$
$252$	−92731.1	−0.0919865
$253$	−4700.87	−0.00461719
$254$	−253677.	−0.246716
$255$	152129.	0.146508
$256$	65536.0	0.0625000
$257$	164107.	0.154986	0.0774932	−	0.996993i	$-0.475308\pi$
$257$	164107.	0.154986	0.0774932	+	0.996993i	$0.475308\pi$
$258$	73360.3	0.0686138
$259$	107569.	0.0996413
$260$	91642.3	0.0840742
$261$	−72372.4	−0.0657615
$262$	759646.	0.683688
$263$	414875.	0.369852	0.184926	−	0.982752i	$-0.440795\pi$
$263$	414875.	0.369852	0.184926	+	0.982752i	$0.440795\pi$
$264$	−6163.08	−0.00544236
$265$	484708.	0.424000
$266$	−361339.	−0.313120
$267$	733508.	0.629690
$268$	409799.	0.348525
$269$	−1.03395e6	−0.871199	−0.435600	−	0.900141i	$-0.643464\pi$
$269$	−1.03395e6	−0.871199	−0.435600	+	0.900141i	$0.643464\pi$
$270$	399403.	0.333428
$271$	−905248.	−0.748763	−0.374381	−	0.927275i	$-0.622145\pi$
$271$	−905248.	−0.748763	−0.374381	+	0.927275i	$0.622145\pi$
$272$	143753.	0.117813
$273$	114593.	0.0930578
$274$	−301690.	−0.242764
$275$	5553.96	0.00442865
$276$	−91721.3	−0.0724765
$277$	−736609.	−0.576817	−0.288408	−	0.957507i	$-0.593126\pi$
$277$	−736609.	−0.576817	−0.288408	+	0.957507i	$0.593126\pi$
$278$	−191346.	−0.148494
$279$	−920790.	−0.708190
$280$	−73849.7	−0.0562929
$281$	−1.52991e6	−1.15584	−0.577921	−	0.816093i	$-0.696136\pi$
$281$	−1.52991e6	−1.15584	−0.577921	+	0.816093i	$0.696136\pi$
$282$	113457.	0.0849592
$283$	136848.	0.101572	0.0507860	−	0.998710i	$-0.483827\pi$
$283$	136848.	0.101572	0.0507860	+	0.998710i	$0.483827\pi$
$284$	−97269.0	−0.0715614
$285$	530226.	0.386677
$286$	−8143.65	−0.00588713
$287$	4124.22	0.00295554
$288$	128581.	0.0913472
$289$	−1.10454e6	−0.777921
$290$	−57636.4	−0.0402440
$291$	1.12528e6	0.778981
$292$	1.08751e6	0.746408
$293$	−509931.	−0.347010	−0.173505	−	0.984833i	$-0.555509\pi$
$293$	−509931.	−0.347010	−0.173505	+	0.984833i	$0.555509\pi$
$294$	636181.	0.429252
$295$	936510.	0.626552
$296$	−149156.	−0.0989488
$297$	−35492.3	−0.0233477
$298$	1.66219e6	1.08428
$299$	−121197.	−0.0783996
$300$	108366.	0.0695171
$301$	−78115.1	−0.0496957
$302$	984.535	0.000621175 0
$303$	−976623.	−0.611112
$304$	501033.	0.310944
$305$	−436416.	−0.268628
$306$	282041.	0.172191
$307$	60837.0	0.0368402	0.0184201	−	0.999830i	$-0.494136\pi$
$307$	60837.0	0.0368402	0.0184201	+	0.999830i	$0.494136\pi$
$308$	6562.54	0.00394180
$309$	−936407.	−0.557916
$310$	−733304.	−0.433391
$311$	−2.46113e6	−1.44289	−0.721447	−	0.692470i	$-0.756522\pi$
$311$	−2.46113e6	−1.44289	−0.721447	+	0.692470i	$0.756522\pi$
$312$	−158895.	−0.0924111
$313$	1.07570e6	0.620628	0.310314	−	0.950634i	$-0.399566\pi$
$313$	1.07570e6	0.620628	0.310314	+	0.950634i	$0.399566\pi$
$314$	−199375.	−0.114116
$315$	−144892.	−0.0822752
$316$	1.13208e6	0.637763
$317$	183297.	0.102449	0.0512244	−	0.998687i	$-0.483688\pi$
$317$	183297.	0.102449	0.0512244	+	0.998687i	$0.483688\pi$
$318$	−840417.	−0.466044
$319$	5121.76	0.00281801
$320$	102400.	0.0559017
$321$	1.46977e6	0.796133
$322$	97666.2	0.0524934
$323$	1.09901e6	0.586133
$324$	−204304.	−0.108122
$325$	143191.	0.0751982
$326$	1.71220e6	0.892299
$327$	1.95083e6	1.00891
$328$	−5718.64	−0.00293500
$329$	−120811.	−0.0615343
$330$	−9629.81	−0.00486780
$331$	−620020.	−0.311054	−0.155527	−	0.987832i	$-0.549708\pi$
$331$	−620020.	−0.311054	−0.155527	+	0.987832i	$0.549708\pi$
$332$	865375.	0.430883
$333$	−292642.	−0.144619
$334$	−1.54920e6	−0.759871
$335$	640311.	0.311730
$336$	128045.	0.0618750
$337$	3.89502e6	1.86825	0.934125	−	0.356947i	$-0.116182\pi$
$337$	3.89502e6	1.86825	0.934125	+	0.356947i	$0.116182\pi$
$338$	1.27521e6	0.607144
$339$	−1.72814e6	−0.816731
$340$	224614.	0.105375
$341$	65163.9	0.0303474
$342$	983021.	0.454462
$343$	−1.45316e6	−0.666927
$344$	108314.	0.0493503
$345$	−143315.	−0.0648250
$346$	675446.	0.303319
$347$	−2.39495e6	−1.06776	−0.533879	−	0.845561i	$-0.679266\pi$
$347$	−2.39495e6	−1.06776	−0.533879	+	0.845561i	$0.679266\pi$
$348$	99933.5	0.0442347
$349$	3.14342e6	1.38146	0.690731	−	0.723112i	$-0.257289\pi$
$349$	3.14342e6	1.38146	0.690731	+	0.723112i	$0.257289\pi$
$350$	−115390.	−0.0503499
$351$	−915055.	−0.396442
$352$	−9099.61	−0.00391441
$353$	−2.35756e6	−1.00699	−0.503497	−	0.863997i	$-0.667953\pi$
$353$	−2.35756e6	−1.00699	−0.503497	+	0.863997i	$0.667953\pi$
$354$	−1.62378e6	−0.688682
$355$	−151983.	−0.0640064
$356$	1.08300e6	0.452903
$357$	280866.	0.116635
$358$	2.03112e6	0.837583
$359$	−3.97376e6	−1.62729	−0.813647	−	0.581360i	$-0.802521\pi$
$359$	−3.97376e6	−1.62729	−0.813647	+	0.581360i	$0.802521\pi$
$360$	200908.	0.0817034
$361$	1.35437e6	0.546978
$362$	−88874.0	−0.0356454
$363$	−1.74440e6	−0.694830
$364$	169194.	0.0669316
$365$	1.69924e6	0.667608
$366$	756685.	0.295265
$367$	1.44453e6	0.559837	0.279919	−	0.960024i	$-0.409692\pi$
$367$	1.44453e6	0.559837	0.279919	+	0.960024i	$0.409692\pi$
$368$	−135424.	−0.0521286
$369$	−11219.9	−0.00428967
$370$	−233056.	−0.0885025
$371$	894889.	0.337547
$372$	1.27145e6	0.476366
$373$	−1.45357e6	−0.540957	−0.270478	−	0.962726i	$-0.587182\pi$
$373$	−1.45357e6	−0.540957	−0.270478	+	0.962726i	$0.587182\pi$
$374$	−19959.9	−0.00737871
$375$	169322.	0.0621779
$376$	167517.	0.0611067
$377$	132048.	0.0478497
$378$	737395.	0.265443
$379$	−5.11661e6	−1.82972	−0.914860	−	0.403771i	$-0.867699\pi$
$379$	−5.11661e6	−1.82972	−0.914860	+	0.403771i	$0.867699\pi$
$380$	782864.	0.278117
$381$	687251.	0.242551
$382$	2.17263e6	0.761777
$383$	−1.70140e6	−0.592664	−0.296332	−	0.955085i	$-0.595763\pi$
$383$	−1.70140e6	−0.592664	−0.296332	+	0.955085i	$0.595763\pi$
$384$	−177547.	−0.0614450
$385$	10254.0	0.00352566
$386$	−2.58835e6	−0.884210
$387$	212512.	0.0721283
$388$	1.66144e6	0.560281
$389$	−2.48418e6	−0.832357	−0.416179	−	0.909283i	$-0.636631\pi$
$389$	−2.48418e6	−0.832357	−0.416179	+	0.909283i	$0.636631\pi$
$390$	−248274.	−0.0826550
$391$	−297052.	−0.0982630
$392$	939304.	0.308739
$393$	−2.05800e6	−0.672147
$394$	151945.	0.0493114
$395$	1.76887e6	0.570433
$396$	−17853.3	−0.00572113
$397$	2.81139e6	0.895251	0.447626	−	0.894221i	$-0.352270\pi$
$397$	2.81139e6	0.895251	0.447626	+	0.894221i	$0.352270\pi$
$398$	−2.21074e6	−0.699569
$399$	978925.	0.307834
$400$	160000.	0.0500000
$401$	584078.	0.181389	0.0906943	−	0.995879i	$-0.471091\pi$
$401$	584078.	0.181389	0.0906943	+	0.995879i	$0.471091\pi$
$402$	−1.11021e6	−0.342642
$403$	1.68004e6	0.515297
$404$	−1.44196e6	−0.439541
$405$	−319225.	−0.0967073
$406$	−106411.	−0.0320384
$407$	20710.1	0.00619722
$408$	−389449.	−0.115824
$409$	1.06930e6	0.316076	0.158038	−	0.987433i	$-0.449483\pi$
$409$	1.06930e6	0.316076	0.158038	+	0.987433i	$0.449483\pi$
$410$	−8935.38	−0.00262514
$411$	817326.	0.238666
$412$	−1.38258e6	−0.401280
$413$	1.72902e6	0.498800
$414$	−265700.	−0.0761888
$415$	1.35215e6	0.385393
$416$	−234604.	−0.0664665
$417$	518387.	0.145987
$418$	−69567.9	−0.0194746
$419$	−1.73494e6	−0.482780	−0.241390	−	0.970428i	$-0.577603\pi$
$419$	−1.73494e6	−0.482780	−0.241390	+	0.970428i	$0.577603\pi$
$420$	200071.	0.0553427
$421$	−4.58077e6	−1.25960	−0.629801	−	0.776757i	$-0.716864\pi$
$421$	−4.58077e6	−1.25960	−0.629801	+	0.776757i	$0.716864\pi$
$422$	198817.	0.0543467
$423$	328666.	0.0893108
$424$	−1.24085e6	−0.335201
$425$	350959.	0.0942506
$426$	263517.	0.0703534
$427$	−805729.	−0.213855
$428$	2.17007e6	0.572617
$429$	22062.4	0.00578776
$430$	169241.	0.0441403
$431$	−2.49767e6	−0.647652	−0.323826	−	0.946117i	$-0.604969\pi$
$431$	−2.49767e6	−0.647652	−0.323826	+	0.946117i	$0.604969\pi$
$432$	−1.02247e6	−0.263598
$433$	3.20773e6	0.822202	0.411101	−	0.911590i	$-0.365144\pi$
$433$	3.20773e6	0.822202	0.411101	+	0.911590i	$0.365144\pi$
$434$	−1.35386e6	−0.345023
$435$	156146.	0.0395647
$436$	2.88035e6	0.725654
$437$	−1.03534e6	−0.259345
$438$	−2.94624e6	−0.733809
$439$	540078.	0.133750	0.0668752	−	0.997761i	$-0.478697\pi$
$439$	540078.	0.133750	0.0668752	+	0.997761i	$0.478697\pi$
$440$	−14218.1	−0.00350115
$441$	1.84290e6	0.451238
$442$	−514603.	−0.125290
$443$	−5.25495e6	−1.27221	−0.636106	−	0.771601i	$-0.719456\pi$
$443$	−5.25495e6	−1.27221	−0.636106	+	0.771601i	$0.719456\pi$
$444$	404086.	0.0972785
$445$	1.69220e6	0.405089
$446$	−196149.	−0.0466926
$447$	−4.50314e6	−1.06597
$448$	189055.	0.0445034
$449$	4.84754e6	1.13476	0.567382	−	0.823455i	$-0.307956\pi$
$449$	4.84754e6	1.13476	0.567382	+	0.823455i	$0.307956\pi$
$450$	313918.	0.0730778
$451$	794.028	0.000183821 0
$452$	−2.55155e6	−0.587432
$453$	−2667.26	−0.000610689 0
$454$	−914059.	−0.208130
$455$	264366.	0.0598655
$456$	−1.35738e6	−0.305695
$457$	3.76038e6	0.842250	0.421125	−	0.907003i	$-0.361635\pi$
$457$	3.76038e6	0.842250	0.421125	+	0.907003i	$0.361635\pi$
$458$	810986.	0.180655
$459$	−2.24278e6	−0.496885
$460$	−211600.	−0.0466252
$461$	759278.	0.166398	0.0831991	−	0.996533i	$-0.473486\pi$
$461$	759278.	0.166398	0.0831991	+	0.996533i	$0.473486\pi$
$462$	−17779.0	−0.00387526
$463$	−5.74798e6	−1.24613	−0.623064	−	0.782171i	$-0.714112\pi$
$463$	−5.74798e6	−1.24613	−0.623064	+	0.782171i	$0.714112\pi$
$464$	147549.	0.0318157
$465$	1.98664e6	0.426075
$466$	1.31017e6	0.279488
$467$	−4.81148e6	−1.02091	−0.510454	−	0.859905i	$-0.670523\pi$
$467$	−4.81148e6	−1.02091	−0.510454	+	0.859905i	$0.670523\pi$
$468$	−460291.	−0.0971445
$469$	1.18217e6	0.248169
$470$	261745.	0.0546555
$471$	540138.	0.112190
$472$	−2.39747e6	−0.495333
$473$	−15039.4	−0.00309084
$474$	−3.06698e6	−0.626997
$475$	1.22322e6	0.248755
$476$	414691.	0.0838895
$477$	−2.43454e6	−0.489915
$478$	2.17942e6	0.436287
$479$	2.53290e6	0.504405	0.252202	−	0.967675i	$-0.418845\pi$
$479$	2.53290e6	0.504405	0.252202	+	0.967675i	$0.418845\pi$
$480$	−277418.	−0.0549581
$481$	533944.	0.105228
$482$	−164307.	−0.0322136
$483$	−264593.	−0.0516073
$484$	−2.57555e6	−0.499755
$485$	2.59600e6	0.501130
$486$	−3.32871e6	−0.639270
$487$	7.92170e6	1.51355	0.756774	−	0.653677i	$-0.226774\pi$
$487$	7.92170e6	1.51355	0.756774	+	0.653677i	$0.226774\pi$
$488$	1.11722e6	0.212369
$489$	−4.63862e6	−0.877237
$490$	1.46766e6	0.276144
$491$	−6.16346e6	−1.15378	−0.576888	−	0.816824i	$-0.695733\pi$
$491$	−6.16346e6	−1.15378	−0.576888	+	0.816824i	$0.695733\pi$
$492$	15492.7	0.00288546
$493$	323648.	0.0599730
$494$	−1.79359e6	−0.330678
$495$	−27895.8	−0.00511713
$496$	1.87726e6	0.342626
$497$	−280597.	−0.0509557
$498$	−2.34444e6	−0.423609
$499$	−3.52751e6	−0.634186	−0.317093	−	0.948394i	$-0.602707\pi$
$499$	−3.52751e6	−0.634186	−0.317093	+	0.948394i	$0.602707\pi$
$500$	250000.	0.0447214
$501$	4.19702e6	0.747044
$502$	−1.30226e6	−0.230642
$503$	−9.79646e6	−1.72643	−0.863216	−	0.504835i	$-0.831553\pi$
$503$	−9.79646e6	−1.72643	−0.863216	+	0.504835i	$0.831553\pi$
$504$	370924.	0.0650443
$505$	−2.25306e6	−0.393137
$506$	18803.5	0.00326484
$507$	−3.45476e6	−0.596895
$508$	1.01471e6	0.174454
$509$	5.69781e6	0.974795	0.487398	−	0.873180i	$-0.337946\pi$
$509$	5.69781e6	0.974795	0.487398	+	0.873180i	$0.337946\pi$
$510$	−608514.	−0.103597
$511$	3.13720e6	0.531484
$512$	−262144.	−0.0441942
$513$	−7.81695e6	−1.31143
$514$	−656427.	−0.109592
$515$	−2.16028e6	−0.358915
$516$	−293441.	−0.0485173
$517$	−23259.6	−0.00382715
$518$	−430277.	−0.0704570
$519$	−1.82989e6	−0.298199
$520$	−366569.	−0.0594494
$521$	−226080.	−0.0364895	−0.0182447	−	0.999834i	$-0.505808\pi$
$521$	−226080.	−0.0364895	−0.0182447	+	0.999834i	$0.505808\pi$
$522$	289490.	0.0465004
$523$	−8.28092e6	−1.32381	−0.661903	−	0.749589i	$-0.730251\pi$
$523$	−8.28092e6	−1.32381	−0.661903	+	0.749589i	$0.730251\pi$
$524$	−3.03858e6	−0.483441
$525$	312610.	0.0495000
$526$	−1.65950e6	−0.261525
$527$	4.11775e6	0.645853
$528$	24652.3	0.00384833
$529$	279841.	0.0434783
$530$	−1.93883e6	−0.299813
$531$	−4.70380e6	−0.723957
$532$	1.44536e6	0.221409
$533$	20471.5	0.00312127
$534$	−2.93403e6	−0.445258
$535$	3.39074e6	0.512165
$536$	−1.63920e6	−0.246444
$537$	−5.50262e6	−0.823444
$538$	4.13579e6	0.616031
$539$	−130421.	−0.0193365
$540$	−1.59761e6	−0.235769
$541$	1.32891e7	1.95210	0.976049	−	0.217551i	$-0.0698069\pi$
$541$	1.32891e7	1.95210	0.976049	+	0.217551i	$0.0698069\pi$
$542$	3.62099e6	0.529455
$543$	240774.	0.0350437
$544$	−575011.	−0.0833065
$545$	4.50055e6	0.649044
$546$	−458373.	−0.0658018
$547$	−8.07986e6	−1.15461	−0.577306	−	0.816528i	$-0.695896\pi$
$547$	−8.07986e6	−1.15461	−0.577306	+	0.816528i	$0.695896\pi$
$548$	1.20676e6	0.171660
$549$	2.19198e6	0.310389
$550$	−22215.9	−0.00313153
$551$	1.12804e6	0.158286
$552$	366885.	0.0512487
$553$	3.26577e6	0.454123
$554$	2.94644e6	0.407871
$555$	631385.	0.0870085
$556$	765384.	0.105001
$557$	49436.4	0.00675163	0.00337582	−	0.999994i	$-0.498925\pi$
$557$	49436.4	0.00675163	0.00337582	+	0.999994i	$0.498925\pi$
$558$	3.68316e6	0.500766
$559$	−387742.	−0.0524823
$560$	295399.	0.0398051
$561$	54074.7	0.00725415
$562$	6.11962e6	0.817304
$563$	−1.23559e6	−0.164286	−0.0821432	−	0.996621i	$-0.526176\pi$
$563$	−1.23559e6	−0.164286	−0.0821432	+	0.996621i	$0.526176\pi$
$564$	−453830.	−0.0600752
$565$	−3.98679e6	−0.525415
$566$	−547394.	−0.0718222
$567$	−589367.	−0.0769889
$568$	389076.	0.0506015
$569$	8.02461e6	1.03907	0.519533	−	0.854450i	$-0.326106\pi$
$569$	8.02461e6	1.03907	0.519533	+	0.854450i	$0.326106\pi$
$570$	−2.12090e6	−0.273422
$571$	−8.09912e6	−1.03956	−0.519778	−	0.854302i	$-0.673985\pi$
$571$	−8.09912e6	−1.03956	−0.519778	+	0.854302i	$0.673985\pi$
$572$	32574.6	0.00416283
$573$	−5.88601e6	−0.748918
$574$	−16496.9	−0.00208988
$575$	−330625.	−0.0417029
$576$	−514324.	−0.0645922
$577$	2.77223e6	0.346648	0.173324	−	0.984865i	$-0.444549\pi$
$577$	2.77223e6	0.346648	0.173324	+	0.984865i	$0.444549\pi$
$578$	4.41815e6	0.550073
$579$	7.01226e6	0.869284
$580$	230545.	0.0284568
$581$	2.49639e6	0.306812
$582$	−4.50111e6	−0.550823
$583$	172291.	0.0209938
$584$	−4.35004e6	−0.527790
$585$	−719205.	−0.0868886
$586$	2.03972e6	0.245373
$587$	1.19837e7	1.43548	0.717739	−	0.696312i	$-0.245177\pi$
$587$	1.19837e7	1.43548	0.717739	+	0.696312i	$0.245177\pi$
$588$	−2.54472e6	−0.303527
$589$	1.43519e7	1.70460
$590$	−3.74604e6	−0.443039
$591$	−411644.	−0.0484790
$592$	596623.	0.0699674
$593$	2.37354e6	0.277179	0.138590	−	0.990350i	$-0.455743\pi$
$593$	2.37354e6	0.277179	0.138590	+	0.990350i	$0.455743\pi$
$594$	141969.	0.0165093
$595$	647955.	0.0750331
$596$	−6.64876e6	−0.766699
$597$	5.98926e6	0.687760
$598$	484788.	0.0554369
$599$	7.06059e6	0.804033	0.402017	−	0.915632i	$-0.368309\pi$
$599$	7.06059e6	0.804033	0.402017	+	0.915632i	$0.368309\pi$
$600$	−433465.	−0.0491560
$601$	3.04137e6	0.343466	0.171733	−	0.985144i	$-0.445063\pi$
$601$	3.04137e6	0.343466	0.171733	+	0.985144i	$0.445063\pi$
$602$	312460.	0.0351402
$603$	−3.21608e6	−0.360192
$604$	−3938.14	−0.000439237 0
$605$	−4.02430e6	−0.446994
$606$	3.90649e6	0.432121
$607$	1.15515e6	0.127252	0.0636262	−	0.997974i	$-0.479733\pi$
$607$	1.15515e6	0.127252	0.0636262	+	0.997974i	$0.479733\pi$
$608$	−2.00413e6	−0.219871
$609$	288284.	0.0314975
$610$	1.74566e6	0.189949
$611$	−599673.	−0.0649848
$612$	−1.12817e6	−0.121757
$613$	3.83998e6	0.412742	0.206371	−	0.978474i	$-0.433835\pi$
$613$	3.83998e6	0.412742	0.206371	+	0.978474i	$0.433835\pi$
$614$	−243348.	−0.0260499
$615$	24207.4	0.00258083
$616$	−26250.1	−0.00278728
$617$	2.47164e6	0.261380	0.130690	−	0.991423i	$-0.458281\pi$
$617$	2.47164e6	0.261380	0.130690	+	0.991423i	$0.458281\pi$
$618$	3.74563e6	0.394506
$619$	1.47166e7	1.54376	0.771879	−	0.635769i	$-0.219317\pi$
$619$	1.47166e7	1.54376	0.771879	+	0.635769i	$0.219317\pi$
$620$	2.93322e6	0.306454
$621$	2.11284e6	0.219856
$622$	9.84453e6	1.02028
$623$	3.12420e6	0.322492
$624$	635581.	0.0653445
$625$	390625.	0.0400000
$626$	−4.30281e6	−0.438850
$627$	188471.	0.0191459
$628$	797500.	0.0806922
$629$	1.30869e6	0.131889
$630$	579569.	0.0581774
$631$	−6.71247e6	−0.671134	−0.335567	−	0.942016i	$-0.608928\pi$
$631$	−6.71247e6	−0.671134	−0.335567	+	0.942016i	$0.608928\pi$
$632$	−4.52832e6	−0.450967
$633$	−538628.	−0.0534293
$634$	−733188.	−0.0724423
$635$	1.58548e6	0.156037
$636$	3.36167e6	0.329543
$637$	−3.36250e6	−0.328332
$638$	−20487.1	−0.00199264
$639$	763363.	0.0739570
$640$	−409600.	−0.0395285
$641$	1.45715e7	1.40075	0.700373	−	0.713777i	$-0.253017\pi$
$641$	1.45715e7	1.40075	0.700373	+	0.713777i	$0.253017\pi$
$642$	−5.87907e6	−0.562951
$643$	3.97709e6	0.379348	0.189674	−	0.981847i	$-0.439257\pi$
$643$	3.97709e6	0.379348	0.189674	+	0.981847i	$0.439257\pi$
$644$	−390665.	−0.0371184
$645$	−458502.	−0.0433952
$646$	−4.39605e6	−0.414459
$647$	1.12008e7	1.05194	0.525968	−	0.850504i	$-0.323703\pi$
$647$	1.12008e7	1.05194	0.525968	+	0.850504i	$0.323703\pi$
$648$	817216.	0.0764538
$649$	332886.	0.0310230
$650$	−572765.	−0.0531732
$651$	3.66781e6	0.339199
$652$	−6.84880e6	−0.630951
$653$	−5.84459e6	−0.536378	−0.268189	−	0.963366i	$-0.586425\pi$
$653$	−5.84459e6	−0.536378	−0.268189	+	0.963366i	$0.586425\pi$
$654$	−7.80333e6	−0.713404
$655$	−4.74779e6	−0.432402
$656$	22874.6	0.00207536
$657$	−8.53474e6	−0.771395
$658$	483245.	0.0435113
$659$	−8.73888e6	−0.783867	−0.391933	−	0.919994i	$-0.628194\pi$
$659$	−8.73888e6	−0.783867	−0.391933	+	0.919994i	$0.628194\pi$
$660$	38519.2	0.00344205
$661$	−326006.	−0.0290217	−0.0145108	−	0.999895i	$-0.504619\pi$
$661$	−326006.	−0.0290217	−0.0145108	+	0.999895i	$0.504619\pi$
$662$	2.48008e6	0.219948
$663$	1.39414e6	0.123175
$664$	−3.46150e6	−0.304680
$665$	2.25837e6	0.198034
$666$	1.17057e6	0.102261
$667$	−304896.	−0.0265361
$668$	6.19678e6	0.537310
$669$	531398.	0.0459044
$670$	−2.56124e6	−0.220426
$671$	−155126.	−0.0133008
$672$	−512181.	−0.0437522
$673$	1.23201e7	1.04852	0.524260	−	0.851558i	$-0.324342\pi$
$673$	1.23201e7	1.04852	0.524260	+	0.851558i	$0.324342\pi$
$674$	−1.55801e7	−1.32105
$675$	−2.49627e6	−0.210878
$676$	−5.10086e6	−0.429315
$677$	1.46730e7	1.23040	0.615202	−	0.788369i	$-0.289074\pi$
$677$	1.46730e7	1.23040	0.615202	+	0.788369i	$0.289074\pi$
$678$	6.91255e6	0.577516
$679$	4.79285e6	0.398951
$680$	−898455.	−0.0745116
$681$	2.47633e6	0.204617
$682$	−260656.	−0.0214588
$683$	−4.14801e6	−0.340242	−0.170121	−	0.985423i	$-0.554416\pi$
$683$	−4.14801e6	−0.340242	−0.170121	+	0.985423i	$0.554416\pi$
$684$	−3.93208e6	−0.321353
$685$	1.88556e6	0.153538
$686$	5.81264e6	0.471588
$687$	−2.19709e6	−0.177605
$688$	−433258.	−0.0348960
$689$	4.44198e6	0.356474
$690$	573258.	0.0458382
$691$	1.42489e7	1.13524	0.567618	−	0.823292i	$-0.307865\pi$
$691$	1.42489e7	1.13524	0.567618	+	0.823292i	$0.307865\pi$
$692$	−2.70178e6	−0.214479
$693$	−51502.5	−0.00407376
$694$	9.57980e6	0.755019
$695$	1.19591e6	0.0939156
$696$	−399734.	−0.0312786
$697$	50175.2	0.00391208
$698$	−1.25737e7	−0.976842
$699$	−3.54946e6	−0.274770
$700$	461561.	0.0356028
$701$	−1.37111e7	−1.05385	−0.526924	−	0.849913i	$-0.676655\pi$
$701$	−1.37111e7	−1.05385	−0.526924	+	0.849913i	$0.676655\pi$
$702$	3.66022e6	0.280327
$703$	4.56127e6	0.348095
$704$	36398.5	0.00276791
$705$	−709109.	−0.0537329
$706$	9.43025e6	0.712052
$707$	−4.15969e6	−0.312977
$708$	6.49512e6	0.486972
$709$	1.45280e7	1.08540	0.542701	−	0.839926i	$-0.317402\pi$
$709$	1.45280e7	1.08540	0.542701	+	0.839926i	$0.317402\pi$
$710$	607931.	0.0452594
$711$	−8.88451e6	−0.659113
$712$	−4.33202e6	−0.320251
$713$	−3.87918e6	−0.285769
$714$	−1.12346e6	−0.0824734
$715$	50897.8	0.00372335
$716$	−8.12447e6	−0.592260
$717$	−5.90440e6	−0.428922
$718$	1.58951e7	1.15067
$719$	−1.31122e6	−0.0945918	−0.0472959	−	0.998881i	$-0.515060\pi$
$719$	−1.31122e6	−0.0945918	−0.0472959	+	0.998881i	$0.515060\pi$
$720$	−803631.	−0.0577730
$721$	−3.98840e6	−0.285733
$722$	−5.41749e6	−0.386772
$723$	445134.	0.0316698
$724$	355496.	0.0252051
$725$	360227.	0.0254526
$726$	6.97758e6	0.491319
$727$	1.77409e7	1.24491	0.622456	−	0.782655i	$-0.286135\pi$
$727$	1.77409e7	1.24491	0.622456	+	0.782655i	$0.286135\pi$
$728$	−676776.	−0.0473278
$729$	1.21209e7	0.844723
$730$	−6.79694e6	−0.472070
$731$	−950348.	−0.0657793
$732$	−3.02674e6	−0.208784
$733$	1.04193e7	0.716272	0.358136	−	0.933669i	$-0.383412\pi$
$733$	1.04193e7	0.716272	0.358136	+	0.933669i	$0.383412\pi$
$734$	−5.77813e6	−0.395865
$735$	−3.97613e6	−0.271483
$736$	541696.	0.0368605
$737$	227601.	0.0154349
$738$	44879.7	0.00303325
$739$	1.11987e7	0.754318	0.377159	−	0.926148i	$-0.376901\pi$
$739$	1.11987e7	0.754318	0.377159	+	0.926148i	$0.376901\pi$
$740$	932223.	0.0625807
$741$	4.85911e6	0.325096
$742$	−3.57956e6	−0.238682
$743$	−1.18961e7	−0.790557	−0.395279	−	0.918561i	$-0.629352\pi$
$743$	−1.18961e7	−0.790557	−0.395279	+	0.918561i	$0.629352\pi$
$744$	−5.08579e6	−0.336842
$745$	−1.03887e7	−0.685756
$746$	5.81426e6	0.382514
$747$	−6.79143e6	−0.445307
$748$	79839.8	0.00521753
$749$	6.26012e6	0.407735
$750$	−677290.	−0.0439664
$751$	−1.35790e7	−0.878552	−0.439276	−	0.898352i	$-0.644765\pi$
$751$	−1.35790e7	−0.878552	−0.439276	+	0.898352i	$0.644765\pi$
$752$	−670067.	−0.0432090
$753$	3.52803e6	0.226748
$754$	−528193.	−0.0338349
$755$	−6153.35	−0.000392866 0
$756$	−2.94958e6	−0.187696
$757$	−5.81377e6	−0.368738	−0.184369	−	0.982857i	$-0.559024\pi$
$757$	−5.81377e6	−0.368738	−0.184369	+	0.982857i	$0.559024\pi$
$758$	2.04665e7	1.29381
$759$	−50941.7	−0.00320973
$760$	−3.13145e6	−0.196658
$761$	−1.50951e7	−0.944874	−0.472437	−	0.881365i	$-0.656626\pi$
$761$	−1.50951e7	−0.944874	−0.472437	+	0.881365i	$0.656626\pi$
$762$	−2.74900e6	−0.171509
$763$	8.30911e6	0.516705
$764$	−8.69053e6	−0.538658
$765$	−1.76276e6	−0.108903
$766$	6.80559e6	0.419077
$767$	8.58240e6	0.526769
$768$	710190.	0.0434482
$769$	−8.65959e6	−0.528058	−0.264029	−	0.964515i	$-0.585051\pi$
$769$	−8.65959e6	−0.528058	−0.264029	+	0.964515i	$0.585051\pi$
$770$	−41015.9	−0.00249302
$771$	1.77836e6	0.107742
$772$	1.03534e7	0.625231
$773$	2.22807e7	1.34116	0.670579	−	0.741838i	$-0.266046\pi$
$773$	2.22807e7	1.34116	0.670579	+	0.741838i	$0.266046\pi$
$774$	−850047.	−0.0510024
$775$	4.58315e6	0.274100
$776$	−6.64577e6	−0.396178
$777$	1.16569e6	0.0692677
$778$	9.93673e6	0.588565
$779$	174880.	0.0103251
$780$	993095.	0.0584459
$781$	−54022.9	−0.00316920
$782$	1.18821e6	0.0694824
$783$	−2.30201e6	−0.134185
$784$	−3.75721e6	−0.218311
$785$	1.24609e6	0.0721733
$786$	8.23201e6	0.475280
$787$	−3.09584e6	−0.178173	−0.0890865	−	0.996024i	$-0.528395\pi$
$787$	−3.09584e6	−0.178173	−0.0890865	+	0.996024i	$0.528395\pi$
$788$	−607782.	−0.0348684
$789$	4.49585e6	0.257110
$790$	−7.07550e6	−0.403357
$791$	−7.36058e6	−0.418284
$792$	71413.4	0.00404545
$793$	−3.99942e6	−0.225847
$794$	−1.12456e7	−0.633038
$795$	5.25261e6	0.294752
$796$	8.84297e6	0.494670
$797$	−1.55315e7	−0.866100	−0.433050	−	0.901370i	$-0.642563\pi$
$797$	−1.55315e7	−0.866100	−0.433050	+	0.901370i	$0.642563\pi$
$798$	−3.91570e6	−0.217672
$799$	−1.46979e6	−0.0814494
$800$	−640000.	−0.0353553
$801$	−8.49938e6	−0.468065
$802$	−2.33631e6	−0.128261
$803$	604000.	0.0330558
$804$	4.44084e6	0.242284
$805$	−610414.	−0.0331997
$806$	−6.72017e6	−0.364370
$807$	−1.12045e7	−0.605632
$808$	5.76783e6	0.310802
$809$	1.34979e7	0.725097	0.362549	−	0.931965i	$-0.381907\pi$
$809$	1.34979e7	0.725097	0.362549	+	0.931965i	$0.381907\pi$
$810$	1.27690e6	0.0683824
$811$	−2.88614e6	−0.154087	−0.0770434	−	0.997028i	$-0.524548\pi$
$811$	−2.88614e6	−0.154087	−0.0770434	+	0.997028i	$0.524548\pi$
$812$	425643.	0.0226545
$813$	−9.80984e6	−0.520518
$814$	−82840.5	−0.00438209
$815$	−1.07012e7	−0.564339
$816$	1.55780e6	0.0819003
$817$	−3.31232e6	−0.173611
$818$	−4.27721e6	−0.223500
$819$	−1.32783e6	−0.0691722
$820$	35741.5	0.00185626
$821$	−1.86299e7	−0.964614	−0.482307	−	0.876002i	$-0.660201\pi$
$821$	−1.86299e7	−0.964614	−0.482307	+	0.876002i	$0.660201\pi$
$822$	−3.26931e6	−0.168763
$823$	1.26283e7	0.649899	0.324949	−	0.945731i	$-0.394653\pi$
$823$	1.26283e7	0.649899	0.324949	+	0.945731i	$0.394653\pi$
$824$	5.53032e6	0.283748
$825$	60186.3	0.00307867
$826$	−6.91610e6	−0.352705
$827$	−1.71877e7	−0.873882	−0.436941	−	0.899490i	$-0.643938\pi$
$827$	−1.71877e7	−0.873882	−0.436941	+	0.899490i	$0.643938\pi$
$828$	1.06280e6	0.0538736
$829$	5.98252e6	0.302342	0.151171	−	0.988508i	$-0.451696\pi$
$829$	5.98252e6	0.302342	0.151171	+	0.988508i	$0.451696\pi$
$830$	−5.40860e6	−0.272514
$831$	−7.98237e6	−0.400986
$832$	938417.	0.0469989
$833$	−8.24142e6	−0.411519
$834$	−2.07355e6	−0.103228
$835$	9.68247e6	0.480585
$836$	278272.	0.0137706
$837$	−2.92884e7	−1.44505
$838$	6.93975e6	0.341377
$839$	1.51819e7	0.744597	0.372299	−	0.928113i	$-0.378570\pi$
$839$	1.51819e7	0.744597	0.372299	+	0.928113i	$0.378570\pi$
$840$	−800282.	−0.0391332
$841$	−2.01790e7	−0.983804
$842$	1.83231e7	0.890673
$843$	−1.65790e7	−0.803508
$844$	−795269.	−0.0384289
$845$	−7.97009e6	−0.383991
$846$	−1.31466e6	−0.0631523
$847$	−7.42984e6	−0.355853
$848$	4.96341e6	0.237023
$849$	1.48298e6	0.0706098
$850$	−1.40384e6	−0.0666452
$851$	−1.23286e6	−0.0583568
$852$	−1.05407e6	−0.0497474
$853$	1.77368e7	0.834648	0.417324	−	0.908758i	$-0.362968\pi$
$853$	1.77368e7	0.834648	0.417324	+	0.908758i	$0.362968\pi$
$854$	3.22292e6	0.151218
$855$	−6.14388e6	−0.287427
$856$	−8.68028e6	−0.404902
$857$	−1.92352e7	−0.894633	−0.447316	−	0.894376i	$-0.647620\pi$
$857$	−1.92352e7	−0.894633	−0.447316	+	0.894376i	$0.647620\pi$
$858$	−88249.8	−0.00409256
$859$	−3.42966e7	−1.58587	−0.792935	−	0.609306i	$-0.791448\pi$
$859$	−3.42966e7	−1.58587	−0.792935	+	0.609306i	$0.791448\pi$
$860$	−676965.	−0.0312119
$861$	44692.7	0.00205460
$862$	9.99067e6	0.457959
$863$	1.92707e7	0.880784	0.440392	−	0.897806i	$-0.354839\pi$
$863$	1.92707e7	0.880784	0.440392	+	0.897806i	$0.354839\pi$
$864$	4.08989e6	0.186392
$865$	−4.22154e6	−0.191836
$866$	−1.28309e7	−0.581385
$867$	−1.19695e7	−0.540788
$868$	5.41543e6	0.243968
$869$	628753.	0.0282443
$870$	−624584.	−0.0279765
$871$	5.86796e6	0.262085
$872$	−1.15214e7	−0.513115
$873$	−1.30389e7	−0.579037
$874$	4.14135e6	0.183385
$875$	721188.	0.0318441
$876$	1.17850e7	0.518881
$877$	−3.64202e7	−1.59898	−0.799490	−	0.600680i	$-0.794897\pi$
$877$	−3.64202e7	−1.59898	−0.799490	+	0.600680i	$0.794897\pi$
$878$	−2.16031e6	−0.0945759
$879$	−5.52593e6	−0.241231
$880$	56872.6	0.00247569
$881$	−3.02637e7	−1.31366	−0.656828	−	0.754040i	$-0.728102\pi$
$881$	−3.02637e7	−1.31366	−0.656828	+	0.754040i	$0.728102\pi$
$882$	−7.37161e6	−0.319074
$883$	−3.95818e7	−1.70842	−0.854208	−	0.519932i	$-0.825957\pi$
$883$	−3.95818e7	−1.70842	−0.854208	+	0.519932i	$0.825957\pi$
$884$	2.05841e6	0.0885935
$885$	1.01486e7	0.435561
$886$	2.10198e7	0.899590
$887$	−1.51763e7	−0.647673	−0.323837	−	0.946113i	$-0.604973\pi$
$887$	−1.51763e7	−0.647673	−0.323837	+	0.946113i	$0.604973\pi$
$888$	−1.61635e6	−0.0687863
$889$	2.92718e6	0.124221
$890$	−6.76878e6	−0.286441
$891$	−113470.	−0.00478835
$892$	784594.	0.0330166
$893$	−5.12277e6	−0.214969
$894$	1.80125e7	0.753757
$895$	−1.26945e7	−0.529734
$896$	−756221.	−0.0314687
$897$	−1.31337e6	−0.0545011
$898$	−1.93902e7	−0.802399
$899$	4.22650e6	0.174414
$900$	−1.25567e6	−0.0516738
$901$	1.08872e7	0.446791
$902$	−3176.11	−0.000129981 0
$903$	−846505.	−0.0345470
$904$	1.02062e7	0.415377
$905$	555463.	0.0225441
$906$	10669.1	0.000431823 0
$907$	−3.82649e7	−1.54448	−0.772240	−	0.635331i	$-0.780864\pi$
$907$	−3.82649e7	−1.54448	−0.772240	+	0.635331i	$0.780864\pi$
$908$	3.65624e6	0.147170
$909$	1.13164e7	0.454255
$910$	−1.05746e6	−0.0423313
$911$	1.77305e7	0.707822	0.353911	−	0.935279i	$-0.384852\pi$
$911$	1.77305e7	0.707822	0.353911	+	0.935279i	$0.384852\pi$
$912$	5.42951e6	0.216159
$913$	480626.	0.0190823
$914$	−1.50415e7	−0.595560
$915$	−4.72928e6	−0.186742
$916$	−3.24394e6	−0.127742
$917$	−8.76557e6	−0.344236
$918$	8.97114e6	0.351351
$919$	1.45775e7	0.569371	0.284686	−	0.958621i	$-0.408111\pi$
$919$	1.45775e7	0.569371	0.284686	+	0.958621i	$0.408111\pi$
$920$	846400.	0.0329690
$921$	659268.	0.0256102
$922$	−3.03711e6	−0.117661
$923$	−1.39281e6	−0.0538129
$924$	71115.8	0.00274023
$925$	1.45660e6	0.0559739
$926$	2.29919e7	0.881146
$927$	1.08504e7	0.414713
$928$	−590196.	−0.0224971
$929$	1.28138e7	0.487123	0.243561	−	0.969885i	$-0.421684\pi$
$929$	1.28138e7	0.487123	0.243561	+	0.969885i	$0.421684\pi$
$930$	−7.94655e6	−0.301281
$931$	−2.87245e7	−1.08612
$932$	−5.24068e6	−0.197628
$933$	−2.66704e7	−1.00306
$934$	1.92459e7	0.721891
$935$	124750.	0.00466670
$936$	1.84116e6	0.0686915
$937$	1.33046e7	0.495055	0.247528	−	0.968881i	$-0.420382\pi$
$937$	1.33046e7	0.495055	0.247528	+	0.968881i	$0.420382\pi$
$938$	−4.72868e6	−0.175482
$939$	1.16570e7	0.431442
$940$	−1.04698e6	−0.0386473
$941$	9.32459e6	0.343286	0.171643	−	0.985159i	$-0.445093\pi$
$941$	9.32459e6	0.343286	0.171643	+	0.985159i	$0.445093\pi$
$942$	−2.16055e6	−0.0793301
$943$	−47268.1	−0.00173097
$944$	9.58986e6	0.350253
$945$	−4.60872e6	−0.167881
$946$	60157.4	0.00218555
$947$	2.89898e7	1.05044	0.525220	−	0.850967i	$-0.323983\pi$
$947$	2.89898e7	1.05044	0.525220	+	0.850967i	$0.323983\pi$
$948$	1.22679e7	0.443354
$949$	1.55722e7	0.561286
$950$	−4.89290e6	−0.175896
$951$	1.98632e6	0.0712194
$952$	−1.65877e6	−0.0593188
$953$	−2.60957e7	−0.930757	−0.465379	−	0.885112i	$-0.654082\pi$
$953$	−2.60957e7	−0.930757	−0.465379	+	0.885112i	$0.654082\pi$
$954$	9.73816e6	0.346422
$955$	−1.35789e7	−0.481790
$956$	−8.71769e6	−0.308501
$957$	55502.7	0.00195900
$958$	−1.01316e7	−0.356668
$959$	3.48121e6	0.122232
$960$	1.10967e6	0.0388612
$961$	2.51443e7	0.878277
$962$	−2.13578e6	−0.0744078
$963$	−1.70306e7	−0.591786
$964$	657228.	0.0227784
$965$	1.61772e7	0.559223
$966$	1.05837e6	0.0364919
$967$	−3.75886e7	−1.29268	−0.646338	−	0.763051i	$-0.723700\pi$
$967$	−3.75886e7	−1.29268	−0.646338	+	0.763051i	$0.723700\pi$
$968$	1.03022e7	0.353380
$969$	1.19096e7	0.407462
$970$	−1.03840e7	−0.354353
$971$	−2.83881e7	−0.966248	−0.483124	−	0.875552i	$-0.660498\pi$
$971$	−2.83881e7	−0.966248	−0.483124	+	0.875552i	$0.660498\pi$
$972$	1.33148e7	0.452032
$973$	2.20795e6	0.0747664
$974$	−3.16868e7	−1.07024
$975$	1.55171e6	0.0522756
$976$	−4.46890e6	−0.150167
$977$	−1.11673e7	−0.374293	−0.187146	−	0.982332i	$-0.559924\pi$
$977$	−1.11673e7	−0.374293	−0.187146	+	0.982332i	$0.559924\pi$
$978$	1.85545e7	0.620300
$979$	601497.	0.0200575
$980$	−5.87065e6	−0.195263
$981$	−2.26049e7	−0.749945
$982$	2.46539e7	0.815842
$983$	4.82265e7	1.59185	0.795924	−	0.605397i	$-0.206986\pi$
$983$	4.82265e7	1.59185	0.795924	+	0.605397i	$0.206986\pi$
$984$	−61970.8	−0.00204033
$985$	−949659.	−0.0311872
$986$	−1.29459e6	−0.0424073
$987$	−1.30919e6	−0.0427769
$988$	7.17434e6	0.233824
$989$	895286.	0.0291052
$990$	111583.	0.00361836
$991$	2.90191e6	0.0938643	0.0469322	−	0.998898i	$-0.485056\pi$
$991$	2.90191e6	0.0938643	0.0469322	+	0.998898i	$0.485056\pi$
$992$	−7.50903e6	−0.242273
$993$	−6.71893e6	−0.216236
$994$	1.12239e6	0.0360311
$995$	1.38171e7	0.442446
$996$	9.37776e6	0.299537
$997$	−3.01833e7	−0.961675	−0.480837	−	0.876810i	$-0.659667\pi$
$997$	−3.01833e7	−0.961675	−0.480837	+	0.876810i	$0.659667\pi$
$998$	1.41100e7	0.448437
$999$	−9.30832e6	−0.295092

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.a.f.1.4	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.a.f.1.4	✓	5	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +10.8366 q^{3} +16.0000 q^{4} +25.0000 q^{5} -43.3465 q^{6} +46.1561 q^{7} -64.0000 q^{8} -125.567 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +10.8366 q^{3} +16.0000 q^{4} +25.0000 q^{5} -43.3465 q^{6} +46.1561 q^{7} -64.0000 q^{8} -125.567 q^{9} -100.000 q^{10} +8.88634 q^{11} +173.386 q^{12} +229.106 q^{13} -184.624 q^{14} +270.916 q^{15} +256.000 q^{16} +561.534 q^{17} +502.269 q^{18} +1957.16 q^{19} +400.000 q^{20} +500.176 q^{21} -35.5454 q^{22} -529.000 q^{23} -693.545 q^{24} +625.000 q^{25} -916.423 q^{26} -3994.03 q^{27} +738.497 q^{28} +576.364 q^{29} -1083.66 q^{30} +7333.04 q^{31} -1024.00 q^{32} +96.2981 q^{33} -2246.14 q^{34} +1153.90 q^{35} -2009.08 q^{36} +2330.56 q^{37} -7828.64 q^{38} +2482.74 q^{39} -1600.00 q^{40} +89.3538 q^{41} -2000.71 q^{42} -1692.41 q^{43} +142.181 q^{44} -3139.18 q^{45} +2116.00 q^{46} -2617.45 q^{47} +2774.18 q^{48} -14676.6 q^{49} -2500.00 q^{50} +6085.14 q^{51} +3665.69 q^{52} +19388.3 q^{53} +15976.1 q^{54} +222.159 q^{55} -2953.99 q^{56} +21209.0 q^{57} -2305.45 q^{58} +37460.4 q^{59} +4334.65 q^{60} -17456.6 q^{61} -29332.2 q^{62} -5795.69 q^{63} +4096.00 q^{64} +5727.65 q^{65} -385.192 q^{66} +25612.4 q^{67} +8984.55 q^{68} -5732.58 q^{69} -4615.61 q^{70} -6079.31 q^{71} +8036.31 q^{72} +67969.4 q^{73} -9322.23 q^{74} +6772.90 q^{75} +31314.5 q^{76} +410.159 q^{77} -9930.95 q^{78} +70755.0 q^{79} +6400.00 q^{80} -12769.0 q^{81} -357.415 q^{82} +54086.0 q^{83} +8002.82 q^{84} +14038.4 q^{85} +6769.65 q^{86} +6245.84 q^{87} -568.726 q^{88} +67687.8 q^{89} +12556.7 q^{90} +10574.6 q^{91} -8464.00 q^{92} +79465.5 q^{93} +10469.8 q^{94} +48929.0 q^{95} -11096.7 q^{96} +103840. q^{97} +58706.5 q^{98} -1115.83 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 20 q^{2} + q^{3} + 80 q^{4} + 125 q^{5} - 4 q^{6} + 102 q^{7} - 320 q^{8} + 334 q^{9}+O(q^{10}) \) 5 * q - 20 * q^2 + q^3 + 80 * q^4 + 125 * q^5 - 4 * q^6 + 102 * q^7 - 320 * q^8 + 334 * q^9	\( 5 q - 20 q^{2} + q^{3} + 80 q^{4} + 125 q^{5} - 4 q^{6} + 102 q^{7} - 320 q^{8} + 334 q^{9} - 500 q^{10} + 251 q^{11} + 16 q^{12} + 1743 q^{13} - 408 q^{14} + 25 q^{15} + 1280 q^{16} + 1944 q^{17} - 1336 q^{18} - 845 q^{19} + 2000 q^{20} + 4682 q^{21} - 1004 q^{22} - 2645 q^{23} - 64 q^{24} + 3125 q^{25} - 6972 q^{26} + 2428 q^{27} + 1632 q^{28} - 4021 q^{29} - 100 q^{30} - 15752 q^{31} - 5120 q^{32} + 2931 q^{33} - 7776 q^{34} + 2550 q^{35} + 5344 q^{36} - 3455 q^{37} + 3380 q^{38} - 16708 q^{39} - 8000 q^{40} - 11898 q^{41} - 18728 q^{42} + 6968 q^{43} + 4016 q^{44} + 8350 q^{45} + 10580 q^{46} + 13412 q^{47} + 256 q^{48} + 91041 q^{49} - 12500 q^{50} - 2115 q^{51} + 27888 q^{52} + 53029 q^{53} - 9712 q^{54} + 6275 q^{55} - 6528 q^{56} - 21730 q^{57} + 16084 q^{58} - 31223 q^{59} + 400 q^{60} + 71477 q^{61} + 63008 q^{62} + 262199 q^{63} + 20480 q^{64} + 43575 q^{65} - 11724 q^{66} + 76003 q^{67} + 31104 q^{68} - 529 q^{69} - 10200 q^{70} + 54418 q^{71} - 21376 q^{72} + 69418 q^{73} + 13820 q^{74} + 625 q^{75} - 13520 q^{76} + 283598 q^{77} + 66832 q^{78} + 105024 q^{79} + 32000 q^{80} + 102913 q^{81} + 47592 q^{82} + 89399 q^{83} + 74912 q^{84} + 48600 q^{85} - 27872 q^{86} + 276726 q^{87} - 16064 q^{88} + 96240 q^{89} - 33400 q^{90} + 59261 q^{91} - 42320 q^{92} + 84434 q^{93} - 53648 q^{94} - 21125 q^{95} - 1024 q^{96} + 216087 q^{97} - 364164 q^{98} + 386925 q^{99}+O(q^{100}) \) 5 * q - 20 * q^2 + q^3 + 80 * q^4 + 125 * q^5 - 4 * q^6 + 102 * q^7 - 320 * q^8 + 334 * q^9 - 500 * q^10 + 251 * q^11 + 16 * q^12 + 1743 * q^13 - 408 * q^14 + 25 * q^15 + 1280 * q^16 + 1944 * q^17 - 1336 * q^18 - 845 * q^19 + 2000 * q^20 + 4682 * q^21 - 1004 * q^22 - 2645 * q^23 - 64 * q^24 + 3125 * q^25 - 6972 * q^26 + 2428 * q^27 + 1632 * q^28 - 4021 * q^29 - 100 * q^30 - 15752 * q^31 - 5120 * q^32 + 2931 * q^33 - 7776 * q^34 + 2550 * q^35 + 5344 * q^36 - 3455 * q^37 + 3380 * q^38 - 16708 * q^39 - 8000 * q^40 - 11898 * q^41 - 18728 * q^42 + 6968 * q^43 + 4016 * q^44 + 8350 * q^45 + 10580 * q^46 + 13412 * q^47 + 256 * q^48 + 91041 * q^49 - 12500 * q^50 - 2115 * q^51 + 27888 * q^52 + 53029 * q^53 - 9712 * q^54 + 6275 * q^55 - 6528 * q^56 - 21730 * q^57 + 16084 * q^58 - 31223 * q^59 + 400 * q^60 + 71477 * q^61 + 63008 * q^62 + 262199 * q^63 + 20480 * q^64 + 43575 * q^65 - 11724 * q^66 + 76003 * q^67 + 31104 * q^68 - 529 * q^69 - 10200 * q^70 + 54418 * q^71 - 21376 * q^72 + 69418 * q^73 + 13820 * q^74 + 625 * q^75 - 13520 * q^76 + 283598 * q^77 + 66832 * q^78 + 105024 * q^79 + 32000 * q^80 + 102913 * q^81 + 47592 * q^82 + 89399 * q^83 + 74912 * q^84 + 48600 * q^85 - 27872 * q^86 + 276726 * q^87 - 16064 * q^88 + 96240 * q^89 - 33400 * q^90 + 59261 * q^91 - 42320 * q^92 + 84434 * q^93 - 53648 * q^94 - 21125 * q^95 - 1024 * q^96 + 216087 * q^97 - 364164 * q^98 + 386925 * q^99

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