LMFDB - Embedded newform 471.6.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,6,Mod(1,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, 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("471.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	471.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:	$75.5407791319$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	471.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.892048 q^{2} -9.00000 q^{3} -31.2043 q^{4} -60.6723 q^{5} -8.02843 q^{6} +242.261 q^{7} -56.3812 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+0.892048 q^{2} -9.00000 q^{3} -31.2043 q^{4} -60.6723 q^{5} -8.02843 q^{6} +242.261 q^{7} -56.3812 q^{8} +81.0000 q^{9} -54.1226 q^{10} -595.829 q^{11} +280.838 q^{12} -384.991 q^{13} +216.108 q^{14} +546.051 q^{15} +948.241 q^{16} -886.507 q^{17} +72.2559 q^{18} +1685.16 q^{19} +1893.23 q^{20} -2180.34 q^{21} -531.507 q^{22} +1777.56 q^{23} +507.431 q^{24} +556.127 q^{25} -343.431 q^{26} -729.000 q^{27} -7559.56 q^{28} +3365.99 q^{29} +487.103 q^{30} +9489.91 q^{31} +2650.07 q^{32} +5362.46 q^{33} -790.807 q^{34} -14698.5 q^{35} -2527.54 q^{36} +14763.8 q^{37} +1503.24 q^{38} +3464.92 q^{39} +3420.78 q^{40} -20355.0 q^{41} -1944.97 q^{42} +10917.4 q^{43} +18592.4 q^{44} -4914.46 q^{45} +1585.67 q^{46} -17681.3 q^{47} -8534.17 q^{48} +41883.2 q^{49} +496.092 q^{50} +7978.56 q^{51} +12013.4 q^{52} +33222.7 q^{53} -650.303 q^{54} +36150.3 q^{55} -13658.9 q^{56} -15166.5 q^{57} +3002.63 q^{58} -8473.54 q^{59} -17039.1 q^{60} -35733.9 q^{61} +8465.45 q^{62} +19623.1 q^{63} -27979.7 q^{64} +23358.3 q^{65} +4783.57 q^{66} -40515.7 q^{67} +27662.8 q^{68} -15998.0 q^{69} -13111.8 q^{70} -54063.8 q^{71} -4566.88 q^{72} -29765.8 q^{73} +13170.0 q^{74} -5005.15 q^{75} -52584.2 q^{76} -144346. q^{77} +3090.87 q^{78} -16.3869 q^{79} -57532.0 q^{80} +6561.00 q^{81} -18157.6 q^{82} +7751.38 q^{83} +68036.0 q^{84} +53786.4 q^{85} +9738.80 q^{86} -30293.9 q^{87} +33593.5 q^{88} -88823.4 q^{89} -4383.93 q^{90} -93268.2 q^{91} -55467.3 q^{92} -85409.2 q^{93} -15772.5 q^{94} -102243. q^{95} -23850.7 q^{96} -125881. q^{97} +37361.8 q^{98} -48262.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9}+O(q^{10}) $ 30 * q - 8 * q^2 - 270 * q^3 + 470 * q^4 - 136 * q^5 + 72 * q^6 + 68 * q^7 - 261 * q^8 + 2430 * q^9	\( 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9} - 383 q^{10} - 875 q^{11} - 4230 q^{12} + 101 q^{13} - 2279 q^{14} + 1224 q^{15} + 7454 q^{16} - 4042 q^{17} - 648 q^{18} + 846 q^{19} - 5089 q^{20} - 612 q^{21} - 700 q^{22} - 5902 q^{23} + 2349 q^{24} + 12880 q^{25} - 7567 q^{26} - 21870 q^{27} - 375 q^{28} - 10301 q^{29} + 3447 q^{30} - 4099 q^{31} - 1560 q^{32} + 7875 q^{33} - 3683 q^{34} - 20686 q^{35} + 38070 q^{36} + 8468 q^{37} - 11848 q^{38} - 909 q^{39} - 5132 q^{40} - 47958 q^{41} + 20511 q^{42} + 63916 q^{43} + 3101 q^{44} - 11016 q^{45} + 19654 q^{46} + 8589 q^{47} - 67086 q^{48} + 27834 q^{49} + 121727 q^{50} + 36378 q^{51} + 56510 q^{52} + 10134 q^{53} + 5832 q^{54} - 11473 q^{55} - 68192 q^{56} - 7614 q^{57} + 32006 q^{58} - 64236 q^{59} + 45801 q^{60} - 98194 q^{61} - 67276 q^{62} + 5508 q^{63} + 138849 q^{64} - 155917 q^{65} + 6300 q^{66} + 62323 q^{67} - 117531 q^{68} + 53118 q^{69} - 220939 q^{70} - 179713 q^{71} - 21141 q^{72} - 148343 q^{73} - 214732 q^{74} - 115920 q^{75} - 189758 q^{76} - 142357 q^{77} + 68103 q^{78} + 26916 q^{79} - 463727 q^{80} + 196830 q^{81} - 206514 q^{82} - 89285 q^{83} + 3375 q^{84} - 23932 q^{85} - 477235 q^{86} + 92709 q^{87} - 114708 q^{88} - 474411 q^{89} - 31023 q^{90} + 51305 q^{91} - 1030074 q^{92} + 36891 q^{93} - 485800 q^{94} - 169960 q^{95} + 14040 q^{96} - 169188 q^{97} - 629739 q^{98} - 70875 q^{99}+O(q^{100}) \) 30 * q - 8 * q^2 - 270 * q^3 + 470 * q^4 - 136 * q^5 + 72 * q^6 + 68 * q^7 - 261 * q^8 + 2430 * q^9 - 383 * q^10 - 875 * q^11 - 4230 * q^12 + 101 * q^13 - 2279 * q^14 + 1224 * q^15 + 7454 * q^16 - 4042 * q^17 - 648 * q^18 + 846 * q^19 - 5089 * q^20 - 612 * q^21 - 700 * q^22 - 5902 * q^23 + 2349 * q^24 + 12880 * q^25 - 7567 * q^26 - 21870 * q^27 - 375 * q^28 - 10301 * q^29 + 3447 * q^30 - 4099 * q^31 - 1560 * q^32 + 7875 * q^33 - 3683 * q^34 - 20686 * q^35 + 38070 * q^36 + 8468 * q^37 - 11848 * q^38 - 909 * q^39 - 5132 * q^40 - 47958 * q^41 + 20511 * q^42 + 63916 * q^43 + 3101 * q^44 - 11016 * q^45 + 19654 * q^46 + 8589 * q^47 - 67086 * q^48 + 27834 * q^49 + 121727 * q^50 + 36378 * q^51 + 56510 * q^52 + 10134 * q^53 + 5832 * q^54 - 11473 * q^55 - 68192 * q^56 - 7614 * q^57 + 32006 * q^58 - 64236 * q^59 + 45801 * q^60 - 98194 * q^61 - 67276 * q^62 + 5508 * q^63 + 138849 * q^64 - 155917 * q^65 + 6300 * q^66 + 62323 * q^67 - 117531 * q^68 + 53118 * q^69 - 220939 * q^70 - 179713 * q^71 - 21141 * q^72 - 148343 * q^73 - 214732 * q^74 - 115920 * q^75 - 189758 * q^76 - 142357 * q^77 + 68103 * q^78 + 26916 * q^79 - 463727 * q^80 + 196830 * q^81 - 206514 * q^82 - 89285 * q^83 + 3375 * q^84 - 23932 * q^85 - 477235 * q^86 + 92709 * q^87 - 114708 * q^88 - 474411 * q^89 - 31023 * q^90 + 51305 * q^91 - 1030074 * q^92 + 36891 * q^93 - 485800 * q^94 - 169960 * q^95 + 14040 * q^96 - 169188 * q^97 - 629739 * q^98 - 70875 * 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 $

$2$	0.892048	0.157693	0.0788466	−	0.996887i	$-0.474876\pi$
$2$	0.892048	0.157693	0.0788466	+	0.996887i	$0.474876\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−31.2043	−0.975133
$5$	−60.6723	−1.08534	−0.542670	−	0.839946i	$-0.682586\pi$
$5$	−60.6723	−1.08534	−0.542670	+	0.839946i	$0.682586\pi$
$6$	−8.02843	−0.0910442
$7$	242.261	1.86869	0.934346	−	0.356368i	$-0.115985\pi$
$7$	242.261	1.86869	0.934346	+	0.356368i	$0.115985\pi$
$8$	−56.3812	−0.311465
$9$	81.0000	0.333333
$10$	−54.1226	−0.171151
$11$	−595.829	−1.48470	−0.742352	−	0.670011i	$-0.766290\pi$
$11$	−595.829	−1.48470	−0.742352	+	0.670011i	$0.766290\pi$
$12$	280.838	0.562993
$13$	−384.991	−0.631819	−0.315909	−	0.948789i	$-0.602310\pi$
$13$	−384.991	−0.631819	−0.315909	+	0.948789i	$0.602310\pi$
$14$	216.108	0.294680
$15$	546.051	0.626621
$16$	948.241	0.926017
$17$	−886.507	−0.743978	−0.371989	−	0.928237i	$-0.621324\pi$
$17$	−886.507	−0.743978	−0.371989	+	0.928237i	$0.621324\pi$
$18$	72.2559	0.0525644
$19$	1685.16	1.07092	0.535461	−	0.844560i	$-0.320138\pi$
$19$	1685.16	1.07092	0.535461	+	0.844560i	$0.320138\pi$
$20$	1893.23	1.05835
$21$	−2180.34	−1.07889
$22$	−531.507	−0.234128
$23$	1777.56	0.700655	0.350327	−	0.936627i	$-0.386070\pi$
$23$	1777.56	0.700655	0.350327	+	0.936627i	$0.386070\pi$
$24$	507.431	0.179824
$25$	556.127	0.177961
$26$	−343.431	−0.0996335
$27$	−729.000	−0.192450
$28$	−7559.56	−1.82222
$29$	3365.99	0.743222	0.371611	−	0.928389i	$-0.378806\pi$
$29$	3365.99	0.743222	0.371611	+	0.928389i	$0.378806\pi$
$30$	487.103	0.0988138
$31$	9489.91	1.77361	0.886804	−	0.462145i	$-0.152920\pi$
$31$	9489.91	1.77361	0.886804	+	0.462145i	$0.152920\pi$
$32$	2650.07	0.457492
$33$	5362.46	0.857194
$34$	−790.807	−0.117320
$35$	−14698.5	−2.02816
$36$	−2527.54	−0.325044
$37$	14763.8	1.77294	0.886471	−	0.462783i	$-0.153149\pi$
$37$	14763.8	1.77294	0.886471	+	0.462783i	$0.153149\pi$
$38$	1503.24	0.168877
$39$	3464.92	0.364781
$40$	3420.78	0.338045
$41$	−20355.0	−1.89109	−0.945543	−	0.325496i	$-0.894469\pi$
$41$	−20355.0	−1.89109	−0.945543	+	0.325496i	$0.894469\pi$
$42$	−1944.97	−0.170134
$43$	10917.4	0.900423	0.450211	−	0.892922i	$-0.351349\pi$
$43$	10917.4	0.900423	0.450211	+	0.892922i	$0.351349\pi$
$44$	18592.4	1.44778
$45$	−4914.46	−0.361780
$46$	1585.67	0.110488
$47$	−17681.3	−1.16753	−0.583766	−	0.811922i	$-0.698421\pi$
$47$	−17681.3	−1.16753	−0.583766	+	0.811922i	$0.698421\pi$
$48$	−8534.17	−0.534636
$49$	41883.2	2.49201
$50$	496.092	0.0280632
$51$	7978.56	0.429536
$52$	12013.4	0.616107
$53$	33222.7	1.62460	0.812298	−	0.583243i	$-0.198216\pi$
$53$	33222.7	1.62460	0.812298	+	0.583243i	$0.198216\pi$
$54$	−650.303	−0.0303481
$55$	36150.3	1.61141
$56$	−13658.9	−0.582032
$57$	−15166.5	−0.618297
$58$	3002.63	0.117201
$59$	−8473.54	−0.316909	−0.158455	−	0.987366i	$-0.550651\pi$
$59$	−8473.54	−0.316909	−0.158455	+	0.987366i	$0.550651\pi$
$60$	−17039.1	−0.611038
$61$	−35733.9	−1.22958	−0.614789	−	0.788691i	$-0.710759\pi$
$61$	−35733.9	−1.22958	−0.614789	+	0.788691i	$0.710759\pi$
$62$	8465.45	0.279686
$63$	19623.1	0.622897
$64$	−27979.7	−0.853874
$65$	23358.3	0.685738
$66$	4783.57	0.135174
$67$	−40515.7	−1.10265	−0.551323	−	0.834292i	$-0.685877\pi$
$67$	−40515.7	−1.10265	−0.551323	+	0.834292i	$0.685877\pi$
$68$	27662.8	0.725477
$69$	−15998.0	−0.404523
$70$	−13111.8	−0.319828
$71$	−54063.8	−1.27280	−0.636401	−	0.771358i	$-0.719578\pi$
$71$	−54063.8	−1.27280	−0.636401	+	0.771358i	$0.719578\pi$
$72$	−4566.88	−0.103822
$73$	−29765.8	−0.653749	−0.326875	−	0.945068i	$-0.605995\pi$
$73$	−29765.8	−0.653749	−0.326875	+	0.945068i	$0.605995\pi$
$74$	13170.0	0.279581
$75$	−5005.15	−0.102746
$76$	−52584.2	−1.04429
$77$	−144346.	−2.77445
$78$	3090.87	0.0575234
$79$	−16.3869	−0.000295413 0	−0.000147707	−	1.00000i	$-0.500047\pi$
$79$	−16.3869	−0.000295413 0	−0.000147707		1.00000i	$0.500047\pi$
$80$	−57532.0	−1.00504
$81$	6561.00	0.111111
$82$	−18157.6	−0.298212
$83$	7751.38	0.123505	0.0617524	−	0.998091i	$-0.480331\pi$
$83$	7751.38	0.123505	0.0617524	+	0.998091i	$0.480331\pi$
$84$	68036.0	1.05206
$85$	53786.4	0.807468
$86$	9738.80	0.141991
$87$	−30293.9	−0.429099
$88$	33593.5	0.462433
$89$	−88823.4	−1.18865	−0.594323	−	0.804227i	$-0.702580\pi$
$89$	−88823.4	−1.18865	−0.594323	+	0.804227i	$0.702580\pi$
$90$	−4383.93	−0.0570502
$91$	−93268.2	−1.18067
$92$	−55467.3	−0.683231
$93$	−85409.2	−1.02399
$94$	−15772.5	−0.184112
$95$	−102243.	−1.16231
$96$	−23850.7	−0.264133
$97$	−125881.	−1.35841	−0.679204	−	0.733950i	$-0.737675\pi$
$97$	−125881.	−1.35841	−0.679204	+	0.733950i	$0.737675\pi$
$98$	37361.8	0.392973
$99$	−48262.1	−0.494901
$100$	−17353.5	−0.173535
$101$	7861.90	0.0766874	0.0383437	−	0.999265i	$-0.487792\pi$
$101$	7861.90	0.0766874	0.0383437	+	0.999265i	$0.487792\pi$
$102$	7117.26	0.0677349
$103$	−154935.	−1.43898	−0.719491	−	0.694502i	$-0.755625\pi$
$103$	−154935.	−1.43898	−0.719491	+	0.694502i	$0.755625\pi$
$104$	21706.3	0.196789
$105$	132287.	1.17096
$106$	29636.2	0.256188
$107$	52795.4	0.445797	0.222898	−	0.974842i	$-0.428448\pi$
$107$	52795.4	0.445797	0.222898	+	0.974842i	$0.428448\pi$
$108$	22747.9	0.187664
$109$	92036.9	0.741986	0.370993	−	0.928636i	$-0.379017\pi$
$109$	92036.9	0.741986	0.370993	+	0.928636i	$0.379017\pi$
$110$	32247.8	0.254108
$111$	−132874.	−1.02361
$112$	229721.	1.73044
$113$	45718.6	0.336819	0.168409	−	0.985717i	$-0.446137\pi$
$113$	45718.6	0.336819	0.168409	+	0.985717i	$0.446137\pi$
$114$	−13529.2	−0.0975012
$115$	−107848.	−0.760448
$116$	−105033.	−0.724740
$117$	−31184.3	−0.210606
$118$	−7558.80	−0.0499744
$119$	−214766.	−1.39026
$120$	−30787.0	−0.195170
$121$	193961.	1.20434
$122$	−31876.4	−0.193896
$123$	183195.	1.09182
$124$	−296126.	−1.72950
$125$	155859.	0.892191
$126$	17504.7	0.0982267
$127$	79670.1	0.438315	0.219157	−	0.975689i	$-0.429669\pi$
$127$	79670.1	0.438315	0.219157	+	0.975689i	$0.429669\pi$
$128$	−109762.	−0.592142
$129$	−98256.2	−0.519859
$130$	20836.7	0.108136
$131$	279571.	1.42336	0.711680	−	0.702504i	$-0.247935\pi$
$131$	279571.	1.42336	0.711680	+	0.702504i	$0.247935\pi$
$132$	−167331.	−0.835878
$133$	408248.	2.00122
$134$	−36141.9	−0.173880
$135$	44230.1	0.208874
$136$	49982.3	0.231723
$137$	142210.	0.647332	0.323666	−	0.946171i	$-0.395085\pi$
$137$	142210.	0.647332	0.323666	+	0.946171i	$0.395085\pi$
$138$	−14271.0	−0.0637906
$139$	−344849.	−1.51388	−0.756941	−	0.653484i	$-0.773307\pi$
$139$	−344849.	−1.51388	−0.756941	+	0.653484i	$0.773307\pi$
$140$	458656.	1.97773
$141$	159131.	0.674075
$142$	−48227.5	−0.200712
$143$	229389.	0.938063
$144$	76807.5	0.308672
$145$	−204223.	−0.806647
$146$	−26552.6	−0.103092
$147$	−376949.	−1.43876
$148$	−460694.	−1.72885
$149$	209379.	0.772624	0.386312	−	0.922368i	$-0.373749\pi$
$149$	209379.	0.772624	0.386312	+	0.922368i	$0.373749\pi$
$150$	−4464.83	−0.0162023
$151$	−200026.	−0.713910	−0.356955	−	0.934122i	$-0.616185\pi$
$151$	−200026.	−0.713910	−0.356955	+	0.934122i	$0.616185\pi$
$152$	−95011.5	−0.333555
$153$	−71807.1	−0.247993
$154$	−128763.	−0.437512
$155$	−575775.	−1.92497
$156$	−108120.	−0.355710
$157$	−24649.0	−0.0798087
$157$	−24649.0	−0.0798087
$158$	−14.6179	−4.65847e−5 0
$159$	−299004.	−0.937961
$160$	−160786.	−0.496534
$161$	430632.	1.30931
$162$	5852.72	0.0175215
$163$	139004.	0.409787	0.204893	−	0.978784i	$-0.434315\pi$
$163$	139004.	0.409787	0.204893	+	0.978784i	$0.434315\pi$
$164$	635162.	1.84406
$165$	−325353.	−0.930346
$166$	6914.60	0.0194759
$167$	−131363.	−0.364487	−0.182243	−	0.983253i	$-0.558336\pi$
$167$	−131363.	−0.364487	−0.182243	+	0.983253i	$0.558336\pi$
$168$	122930.	0.336036
$169$	−223075.	−0.600805
$170$	47980.0	0.127332
$171$	136498.	0.356974
$172$	−340668.	−0.878032
$173$	−342959.	−0.871218	−0.435609	−	0.900136i	$-0.643467\pi$
$173$	−342959.	−0.871218	−0.435609	+	0.900136i	$0.643467\pi$
$174$	−27023.6	−0.0676660
$175$	134728.	0.332554
$176$	−564989.	−1.37486
$177$	76261.9	0.182968
$178$	−79234.7	−0.187441
$179$	518100.	1.20859	0.604297	−	0.796759i	$-0.293454\pi$
$179$	518100.	1.20859	0.604297	+	0.796759i	$0.293454\pi$
$180$	153352.	0.352783
$181$	557281.	1.26438	0.632190	−	0.774813i	$-0.282156\pi$
$181$	557281.	1.26438	0.632190	+	0.774813i	$0.282156\pi$
$182$	−83199.7	−0.186184
$183$	321605.	0.709898
$184$	−100221.	−0.218229
$185$	−895756.	−1.92424
$186$	−76189.1	−0.161477
$187$	528206.	1.10459
$188$	551731.	1.13850
$189$	−176608.	−0.359630
$190$	−91205.3	−0.183289
$191$	−849286.	−1.68450	−0.842249	−	0.539089i	$-0.818769\pi$
$191$	−849286.	−1.68450	−0.842249	+	0.539089i	$0.818769\pi$
$192$	251818.	0.492984
$193$	−11796.0	−0.0227952	−0.0113976	−	0.999935i	$-0.503628\pi$
$193$	−11796.0	−0.0227952	−0.0113976	+	0.999935i	$0.503628\pi$
$194$	−112292.	−0.214212
$195$	−210225.	−0.395911
$196$	−1.30693e6	−2.43004
$197$	−499452.	−0.916913	−0.458457	−	0.888717i	$-0.651598\pi$
$197$	−499452.	−0.916913	−0.458457	+	0.888717i	$0.651598\pi$
$198$	−43052.1	−0.0780425
$199$	−311311.	−0.557265	−0.278633	−	0.960398i	$-0.589881\pi$
$199$	−311311.	−0.557265	−0.278633	+	0.960398i	$0.589881\pi$
$200$	−31355.1	−0.0554286
$201$	364641.	0.636613
$202$	7013.19	0.0120931
$203$	815447.	1.38885
$204$	−248965.	−0.418854
$205$	1.23498e6	2.05247
$206$	−138209.	−0.226918
$207$	143982.	0.233552
$208$	−365065.	−0.585075
$209$	−1.00407e6	−1.59000
$210$	118006.	0.184653
$211$	−786525.	−1.21620	−0.608102	−	0.793859i	$-0.708069\pi$
$211$	−786525.	−1.21620	−0.608102	+	0.793859i	$0.708069\pi$
$212$	−1.03669e6	−1.58420
$213$	486574.	0.734853
$214$	47096.0	0.0702991
$215$	−662381.	−0.977264
$216$	41101.9	0.0599415
$217$	2.29903e6	3.31433
$218$	82101.3	0.117006
$219$	267893.	0.377442
$220$	−1.12804e6	−1.57134
$221$	341298.	0.470059
$222$	−118530.	−0.161416
$223$	−859677.	−1.15764	−0.578820	−	0.815456i	$-0.696487\pi$
$223$	−859677.	−1.15764	−0.578820	+	0.815456i	$0.696487\pi$
$224$	642009.	0.854911
$225$	45046.3	0.0593203
$226$	40783.1	0.0531141
$227$	66949.7	0.0862351	0.0431176	−	0.999070i	$-0.486271\pi$
$227$	66949.7	0.0862351	0.0431176	+	0.999070i	$0.486271\pi$
$228$	473258.	0.602922
$229$	−623307.	−0.785441	−0.392720	−	0.919658i	$-0.628466\pi$
$229$	−623307.	−0.785441	−0.392720	+	0.919658i	$0.628466\pi$
$230$	−96206.0	−0.119917
$231$	1.29911e6	1.60183
$232$	−189779.	−0.231488
$233$	315441.	0.380652	0.190326	−	0.981721i	$-0.439046\pi$
$233$	315441.	0.380652	0.190326	+	0.981721i	$0.439046\pi$
$234$	−27817.9	−0.0332112
$235$	1.07276e6	1.26717
$236$	264411.	0.309029
$237$	147.482	0.000170557 0
$238$	−191581.	−0.219235
$239$	450309.	0.509936	0.254968	−	0.966949i	$-0.417935\pi$
$239$	450309.	0.509936	0.254968	+	0.966949i	$0.417935\pi$
$240$	517788.	0.580261
$241$	68141.1	0.0755730	0.0377865	−	0.999286i	$-0.487969\pi$
$241$	68141.1	0.0755730	0.0377865	+	0.999286i	$0.487969\pi$
$242$	173022.	0.189917
$243$	−59049.0	−0.0641500
$244$	1.11505e6	1.19900
$245$	−2.54115e6	−2.70467
$246$	163419.	0.172173
$247$	−648773.	−0.676628
$248$	−535053.	−0.552417
$249$	−69762.5	−0.0713056
$250$	139034.	0.140693
$251$	113386.	0.113599	0.0567996	−	0.998386i	$-0.481910\pi$
$251$	113386.	0.113599	0.0567996	+	0.998386i	$0.481910\pi$
$252$	−612324.	−0.607407
$253$	−1.05912e6	−1.04026
$254$	71069.6	0.0691193
$255$	−484078.	−0.466192
$256$	797439.	0.760497
$257$	959038.	0.905739	0.452870	−	0.891577i	$-0.350400\pi$
$257$	959038.	0.905739	0.452870	+	0.891577i	$0.350400\pi$
$258$	−87649.2	−0.0819783
$259$	3.57669e6	3.31308
$260$	−728878.	−0.668685
$261$	272645.	0.247741
$262$	249391.	0.224454
$263$	−392273.	−0.349703	−0.174851	−	0.984595i	$-0.555945\pi$
$263$	−392273.	−0.349703	−0.174851	+	0.984595i	$0.555945\pi$
$264$	−302342.	−0.266986
$265$	−2.01570e6	−1.76324
$266$	364177.	0.315579
$267$	799410.	0.686265
$268$	1.26426e6	1.07523
$269$	−1.36677e6	−1.15164	−0.575818	−	0.817578i	$-0.695316\pi$
$269$	−1.36677e6	−1.15164	−0.575818	+	0.817578i	$0.695316\pi$
$270$	39455.4	0.0329379
$271$	−1.29172e6	−1.06842	−0.534212	−	0.845350i	$-0.679392\pi$
$271$	−1.29172e6	−1.06842	−0.534212	+	0.845350i	$0.679392\pi$
$272$	−840623.	−0.688936
$273$	839414.	0.681663
$274$	126858.	0.102080
$275$	−331357.	−0.264219
$276$	499206.	0.394464
$277$	−67254.2	−0.0526647	−0.0263324	−	0.999653i	$-0.508383\pi$
$277$	−67254.2	−0.0526647	−0.0263324	+	0.999653i	$0.508383\pi$
$278$	−307622.	−0.238729
$279$	768683.	0.591203
$280$	828719.	0.631702
$281$	2.19459e6	1.65801	0.829006	−	0.559240i	$-0.188907\pi$
$281$	2.19459e6	1.65801	0.829006	+	0.559240i	$0.188907\pi$
$282$	141953.	0.106297
$283$	−438334.	−0.325342	−0.162671	−	0.986680i	$-0.552011\pi$
$283$	−438334.	−0.325342	−0.162671	+	0.986680i	$0.552011\pi$
$284$	1.68702e6	1.24115
$285$	920184.	0.671062
$286$	204626.	0.147926
$287$	−4.93121e6	−3.53386
$288$	214656.	0.152497
$289$	−633962.	−0.446497
$290$	−182176.	−0.127203
$291$	1.13293e6	0.784277
$292$	928821.	0.637492
$293$	−742876.	−0.505530	−0.252765	−	0.967528i	$-0.581340\pi$
$293$	−742876.	−0.505530	−0.252765	+	0.967528i	$0.581340\pi$
$294$	−336256.	−0.226883
$295$	514109.	0.343954
$296$	−832402.	−0.552210
$297$	434359.	0.285731
$298$	186776.	0.121838
$299$	−684344.	−0.442687
$300$	156182.	0.100191
$301$	2.64485e6	1.68261
$302$	−178433.	−0.112579
$303$	−70757.1	−0.0442755
$304$	1.59794e6	0.991692
$305$	2.16806e6	1.33451
$306$	−64055.3	−0.0391067
$307$	823855.	0.498890	0.249445	−	0.968389i	$-0.419752\pi$
$307$	823855.	0.498890	0.249445	+	0.968389i	$0.419752\pi$
$308$	4.50420e6	2.70546
$309$	1.39441e6	0.830797
$310$	−513618.	−0.303554
$311$	1.61532e6	0.947019	0.473510	−	0.880789i	$-0.342987\pi$
$311$	1.61532e6	0.947019	0.473510	+	0.880789i	$0.342987\pi$
$312$	−195356.	−0.113616
$313$	−512288.	−0.295565	−0.147783	−	0.989020i	$-0.547214\pi$
$313$	−512288.	−0.295565	−0.147783	+	0.989020i	$0.547214\pi$
$314$	−21988.1	−0.0125853
$315$	−1.19058e6	−0.676055
$316$	511.342	0.000288067 0
$317$	−3.08005e6	−1.72151	−0.860755	−	0.509019i	$-0.830008\pi$
$317$	−3.08005e6	−1.72151	−0.860755	+	0.509019i	$0.830008\pi$
$318$	−266726.	−0.147910
$319$	−2.00556e6	−1.10346
$320$	1.69759e6	0.926742
$321$	−475159.	−0.257381
$322$	384144.	0.206469
$323$	−1.49391e6	−0.796742
$324$	−204731.	−0.108348
$325$	−214104.	−0.112439
$326$	123998.	0.0646206
$327$	−828332.	−0.428386
$328$	1.14764e6	0.589007
$329$	−4.28347e6	−2.18176
$330$	−290230.	−0.146709
$331$	−2.63018e6	−1.31952	−0.659760	−	0.751476i	$-0.729342\pi$
$331$	−2.63018e6	−1.31952	−0.659760	+	0.751476i	$0.729342\pi$
$332$	−241876.	−0.120434
$333$	1.19587e6	0.590981
$334$	−117182.	−0.0574771
$335$	2.45818e6	1.19675
$336$	−2.06749e6	−0.999070
$337$	−3.76965e6	−1.80812	−0.904059	−	0.427408i	$-0.859427\pi$
$337$	−3.76965e6	−1.80812	−0.904059	+	0.427408i	$0.859427\pi$
$338$	−198993.	−0.0947429
$339$	−411467.	−0.194462
$340$	−1.67837e6	−0.787389
$341$	−5.65436e6	−2.63328
$342$	121763.	0.0562924
$343$	6.07497e6	2.78810
$344$	−615534.	−0.280450
$345$	970636.	0.439045
$346$	−305936.	−0.137385
$347$	−4.04101e6	−1.80163	−0.900815	−	0.434203i	$-0.857030\pi$
$347$	−4.04101e6	−1.80163	−0.900815	+	0.434203i	$0.857030\pi$
$348$	945300.	0.418429
$349$	935027.	0.410923	0.205461	−	0.978665i	$-0.434130\pi$
$349$	935027.	0.410923	0.205461	+	0.978665i	$0.434130\pi$
$350$	120184.	0.0524415
$351$	280659.	0.121594
$352$	−1.57899e6	−0.679239
$353$	411616.	0.175815	0.0879075	−	0.996129i	$-0.471982\pi$
$353$	411616.	0.175815	0.0879075	+	0.996129i	$0.471982\pi$
$354$	68029.2	0.0288528
$355$	3.28018e6	1.38142
$356$	2.77167e6	1.15909
$357$	1.93289e6	0.802670
$358$	462169.	0.190587
$359$	−2.61487e6	−1.07081	−0.535407	−	0.844594i	$-0.679842\pi$
$359$	−2.61487e6	−1.07081	−0.535407	+	0.844594i	$0.679842\pi$
$360$	277083.	0.112682
$361$	363672.	0.146873
$362$	497121.	0.199384
$363$	−1.74565e6	−0.695328
$364$	2.91036e6	1.15131
$365$	1.80596e6	0.709539
$366$	286887.	0.111946
$367$	1.77506e6	0.687937	0.343968	−	0.938981i	$-0.388229\pi$
$367$	1.77506e6	0.687937	0.343968	+	0.938981i	$0.388229\pi$
$368$	1.68555e6	0.648818
$369$	−1.64875e6	−0.630362
$370$	−799057.	−0.303440
$371$	8.04855e6	3.03587
$372$	2.66513e6	0.998530
$373$	−2.44279e6	−0.909103	−0.454552	−	0.890720i	$-0.650201\pi$
$373$	−2.44279e6	−0.909103	−0.454552	+	0.890720i	$0.650201\pi$
$374$	471185.	0.174186
$375$	−1.40273e6	−0.515107
$376$	996891.	0.363645
$377$	−1.29588e6	−0.469581
$378$	−157543.	−0.0567112
$379$	341034.	0.121955	0.0609776	−	0.998139i	$-0.480578\pi$
$379$	341034.	0.121955	0.0609776	+	0.998139i	$0.480578\pi$
$380$	3.19041e6	1.13341
$381$	−717031.	−0.253061
$382$	−757603.	−0.265634
$383$	324360.	0.112988	0.0564938	−	0.998403i	$-0.482008\pi$
$383$	324360.	0.112988	0.0564938	+	0.998403i	$0.482008\pi$
$384$	987855.	0.341873
$385$	8.75779e6	3.01122
$386$	−10522.6	−0.00359465
$387$	884306.	0.300141
$388$	3.92802e6	1.32463
$389$	1.31569e6	0.440839	0.220419	−	0.975405i	$-0.429257\pi$
$389$	1.31569e6	0.440839	0.220419	+	0.975405i	$0.429257\pi$
$390$	−187530.	−0.0624324
$391$	−1.57582e6	−0.521271
$392$	−2.36142e6	−0.776173
$393$	−2.51614e6	−0.821777
$394$	−445535.	−0.144591
$395$	994.233	0.000320623 0
$396$	1.50598e6	0.482594
$397$	4.51341e6	1.43724	0.718619	−	0.695404i	$-0.244774\pi$
$397$	4.51341e6	1.43724	0.718619	+	0.695404i	$0.244774\pi$
$398$	−277704.	−0.0878769
$399$	−3.67423e6	−1.15541
$400$	527343.	0.164795
$401$	−811325.	−0.251961	−0.125981	−	0.992033i	$-0.540208\pi$
$401$	−811325.	−0.251961	−0.125981	+	0.992033i	$0.540208\pi$
$402$	325277.	0.100390
$403$	−3.65353e6	−1.12060
$404$	−245325.	−0.0747804
$405$	−398071.	−0.120593
$406$	727418.	0.219013
$407$	−8.79671e6	−2.63229
$408$	−449841.	−0.133785
$409$	2.71952e6	0.803866	0.401933	−	0.915669i	$-0.368338\pi$
$409$	2.71952e6	0.803866	0.401933	+	0.915669i	$0.368338\pi$
$410$	1.10166e6	0.323661
$411$	−1.27989e6	−0.373737
$412$	4.83462e6	1.40320
$413$	−2.05280e6	−0.592206
$414$	128439.	0.0368295
$415$	−470294.	−0.134045
$416$	−1.02026e6	−0.289052
$417$	3.10364e6	0.874040
$418$	−895676.	−0.250732
$419$	332120.	0.0924188	0.0462094	−	0.998932i	$-0.485286\pi$
$419$	332120.	0.0924188	0.0462094	+	0.998932i	$0.485286\pi$
$420$	−4.12790e6	−1.14184
$421$	6.81642e6	1.87435	0.937176	−	0.348858i	$-0.113430\pi$
$421$	6.81642e6	1.87435	0.937176	+	0.348858i	$0.113430\pi$
$422$	−701617.	−0.191787
$423$	−1.43218e6	−0.389177
$424$	−1.87314e6	−0.506005
$425$	−493011.	−0.132399
$426$	434048.	0.115881
$427$	−8.65692e6	−2.29770
$428$	−1.64744e6	−0.434711
$429$	−2.06450e6	−0.541591
$430$	−590876.	−0.154108
$431$	7.60805e6	1.97279	0.986394	−	0.164400i	$-0.0525689\pi$
$431$	7.60805e6	1.97279	0.986394	+	0.164400i	$0.0525689\pi$
$432$	−691268.	−0.178212
$433$	6.14571e6	1.57526	0.787630	−	0.616148i	$-0.211308\pi$
$433$	6.14571e6	1.57526	0.787630	+	0.616148i	$0.211308\pi$
$434$	2.05084e6	0.522647
$435$	1.83800e6	0.465718
$436$	−2.87194e6	−0.723535
$437$	2.99547e6	0.750346
$438$	238973.	0.0595201
$439$	−4.11855e6	−1.01996	−0.509980	−	0.860186i	$-0.670347\pi$
$439$	−4.11855e6	−1.01996	−0.509980	+	0.860186i	$0.670347\pi$
$440$	−2.03820e6	−0.501897
$441$	3.39254e6	0.830669
$442$	304454.	0.0741251
$443$	1.35595e6	0.328271	0.164136	−	0.986438i	$-0.447517\pi$
$443$	1.35595e6	0.328271	0.164136	+	0.986438i	$0.447517\pi$
$444$	4.14625e6	0.998155
$445$	5.38912e6	1.29008
$446$	−766873.	−0.182552
$447$	−1.88441e6	−0.446074
$448$	−6.77838e6	−1.59563
$449$	5.71149e6	1.33701	0.668504	−	0.743709i	$-0.266935\pi$
$449$	5.71149e6	1.33701	0.668504	+	0.743709i	$0.266935\pi$
$450$	40183.5	0.00935440
$451$	1.21281e7	2.80770
$452$	−1.42661e6	−0.328443
$453$	1.80023e6	0.412176
$454$	59722.4	0.0135987
$455$	5.65880e6	1.28143
$456$	855103.	0.192578
$457$	−1.01841e6	−0.228104	−0.114052	−	0.993475i	$-0.536383\pi$
$457$	−1.01841e6	−0.228104	−0.114052	+	0.993475i	$0.536383\pi$
$458$	−556020.	−0.123859
$459$	646264.	0.143179
$460$	3.36533e6	0.741538
$461$	−124938.	−0.0273805	−0.0136903	−	0.999906i	$-0.504358\pi$
$461$	−124938.	−0.0273805	−0.0136903	+	0.999906i	$0.504358\pi$
$462$	1.15887e6	0.252598
$463$	−5.45051e6	−1.18164	−0.590820	−	0.806804i	$-0.701195\pi$
$463$	−5.45051e6	−1.18164	−0.590820	+	0.806804i	$0.701195\pi$
$464$	3.19177e6	0.688236
$465$	5.18197e6	1.11138
$466$	281388.	0.0600262
$467$	−5.69930e6	−1.20929	−0.604643	−	0.796497i	$-0.706684\pi$
$467$	−5.69930e6	−1.20929	−0.604643	+	0.796497i	$0.706684\pi$
$468$	973083.	0.205369
$469$	−9.81535e6	−2.06051
$470$	956956.	0.199824
$471$	221841.	0.0460776
$472$	477748.	0.0987062
$473$	−6.50487e6	−1.33686
$474$	131.561	2.68957e−5 0
$475$	937165.	0.190582
$476$	6.70160e6	1.35569
$477$	2.69104e6	0.541532
$478$	401697.	0.0804135
$479$	−2.92027e6	−0.581547	−0.290774	−	0.956792i	$-0.593913\pi$
$479$	−2.92027e6	−0.581547	−0.290774	+	0.956792i	$0.593913\pi$
$480$	1.44708e6	0.286674
$481$	−5.68395e6	−1.12018
$482$	60785.1	0.0119173
$483$	−3.87569e6	−0.755929
$484$	−6.05240e6	−1.17439
$485$	7.63748e6	1.47433
$486$	−52674.5	−0.0101160
$487$	−3.42572e6	−0.654529	−0.327265	−	0.944933i	$-0.606127\pi$
$487$	−3.42572e6	−0.654529	−0.327265	+	0.944933i	$0.606127\pi$
$488$	2.01472e6	0.382971
$489$	−1.25104e6	−0.236591
$490$	−2.26682e6	−0.426509
$491$	−1.44484e6	−0.270467	−0.135234	−	0.990814i	$-0.543179\pi$
$491$	−1.44484e6	−0.270467	−0.135234	+	0.990814i	$0.543179\pi$
$492$	−5.71646e6	−1.06467
$493$	−2.98398e6	−0.552940
$494$	−578736.	−0.106700
$495$	2.92817e6	0.537135
$496$	8.99873e6	1.64239
$497$	−1.30975e7	−2.37847
$498$	−62231.4	−0.0112444
$499$	−202894.	−0.0364768	−0.0182384	−	0.999834i	$-0.505806\pi$
$499$	−202894.	−0.0364768	−0.0182384	+	0.999834i	$0.505806\pi$
$500$	−4.86348e6	−0.870005
$501$	1.18227e6	0.210437
$502$	101146.	0.0179138
$503$	−4.20200e6	−0.740518	−0.370259	−	0.928929i	$-0.620731\pi$
$503$	−4.20200e6	−0.740518	−0.370259	+	0.928929i	$0.620731\pi$
$504$	−1.10637e6	−0.194011
$505$	−477000.	−0.0832319
$506$	−944785.	−0.164043
$507$	2.00767e6	0.346875
$508$	−2.48605e6	−0.427415
$509$	−1.72717e6	−0.295489	−0.147744	−	0.989026i	$-0.547201\pi$
$509$	−1.72717e6	−0.295489	−0.147744	+	0.989026i	$0.547201\pi$
$510$	−431820.	−0.0735153
$511$	−7.21109e6	−1.22166
$512$	4.22373e6	0.712067
$513$	−1.22848e6	−0.206099
$514$	855508.	0.142829
$515$	9.40024e6	1.56178
$516$	3.06601e6	0.506932
$517$	1.05350e7	1.73344
$518$	3.19058e6	0.522451
$519$	3.08663e6	0.502998
$520$	−1.31697e6	−0.213583
$521$	9.16708e6	1.47957	0.739787	−	0.672841i	$-0.234926\pi$
$521$	9.16708e6	1.47957	0.739787	+	0.672841i	$0.234926\pi$
$522$	243213.	0.0390670
$523$	−4.19122e6	−0.670017	−0.335009	−	0.942215i	$-0.608739\pi$
$523$	−4.19122e6	−0.670017	−0.335009	+	0.942215i	$0.608739\pi$
$524$	−8.72382e6	−1.38796
$525$	−1.21255e6	−0.192000
$526$	−349926.	−0.0551458
$527$	−8.41287e6	−1.31953
$528$	5.08490e6	0.793776
$529$	−3.27663e6	−0.509083
$530$	−1.79810e6	−0.278051
$531$	−686357.	−0.105636
$532$	−1.27391e7	−1.95146
$533$	7.83650e6	1.19482
$534$	713112.	0.108219
$535$	−3.20322e6	−0.483841
$536$	2.28432e6	0.343436
$537$	−4.66290e6	−0.697782
$538$	−1.21923e6	−0.181605
$539$	−2.49552e7	−3.69989
$540$	−1.38017e6	−0.203679
$541$	6.99181e6	1.02706	0.513531	−	0.858071i	$-0.328337\pi$
$541$	6.99181e6	1.02706	0.513531	+	0.858071i	$0.328337\pi$
$542$	−1.15227e6	−0.168483
$543$	−5.01553e6	−0.729990
$544$	−2.34931e6	−0.340364
$545$	−5.58409e6	−0.805306
$546$	748797.	0.107494
$547$	9.91317e6	1.41659	0.708295	−	0.705917i	$-0.249465\pi$
$547$	9.91317e6	1.41659	0.708295	+	0.705917i	$0.249465\pi$
$548$	−4.43754e6	−0.631235
$549$	−2.89445e6	−0.409860
$550$	−295586.	−0.0416655
$551$	5.67225e6	0.795932
$552$	901987.	0.125995
$553$	−3969.91	−0.000552036 0
$554$	−59993.9	−0.00830487
$555$	8.06180e6	1.11096
$556$	1.07608e7	1.47624
$557$	−3.56129e6	−0.486372	−0.243186	−	0.969980i	$-0.578193\pi$
$557$	−3.56129e6	−0.486372	−0.243186	+	0.969980i	$0.578193\pi$
$558$	685702.	0.0932287
$559$	−4.20309e6	−0.568904
$560$	−1.39377e7	−1.87811
$561$	−4.75386e6	−0.637733
$562$	1.95768e6	0.261457
$563$	−1.26474e7	−1.68162	−0.840812	−	0.541327i	$-0.817922\pi$
$563$	−1.26474e7	−1.68162	−0.840812	+	0.541327i	$0.817922\pi$
$564$	−4.96558e6	−0.657313
$565$	−2.77385e6	−0.365563
$566$	−391015.	−0.0513041
$567$	1.58947e6	0.207632
$568$	3.04818e6	0.396433
$569$	4.20830e6	0.544912	0.272456	−	0.962168i	$-0.412164\pi$
$569$	4.20830e6	0.544912	0.272456	+	0.962168i	$0.412164\pi$
$570$	820848.	0.105822
$571$	−8.40258e6	−1.07851	−0.539253	−	0.842144i	$-0.681293\pi$
$571$	−8.40258e6	−1.07851	−0.539253	+	0.842144i	$0.681293\pi$
$572$	−7.15791e6	−0.914736
$573$	7.64357e6	0.972545
$574$	−4.39888e6	−0.557265
$575$	988548.	0.124689
$576$	−2.26636e6	−0.284625
$577$	−1.67435e6	−0.209367	−0.104683	−	0.994506i	$-0.533383\pi$
$577$	−1.67435e6	−0.209367	−0.104683	+	0.994506i	$0.533383\pi$
$578$	−565524.	−0.0704096
$579$	106164.	0.0131608
$580$	6.37261e6	0.786588
$581$	1.87785e6	0.230792
$582$	1.01062e6	0.123675
$583$	−1.97950e7	−2.41204
$584$	1.67823e6	0.203620
$585$	1.89202e6	0.228579
$586$	−662681.	−0.0797187
$587$	8.95288e6	1.07243	0.536213	−	0.844083i	$-0.319854\pi$
$587$	8.95288e6	1.07243	0.536213	+	0.844083i	$0.319854\pi$
$588$	1.17624e7	1.40298
$589$	1.59920e7	1.89940
$590$	458610.	0.0542392
$591$	4.49507e6	0.529380
$592$	1.39997e7	1.64178
$593$	−1.46185e6	−0.170713	−0.0853564	−	0.996350i	$-0.527203\pi$
$593$	−1.46185e6	−0.170713	−0.0853564	+	0.996350i	$0.527203\pi$
$594$	387469.	0.0450579
$595$	1.30303e7	1.50891
$596$	−6.53352e6	−0.753411
$597$	2.80180e6	0.321737
$598$	−610467.	−0.0698087
$599$	1.36254e7	1.55161	0.775807	−	0.630971i	$-0.217343\pi$
$599$	1.36254e7	1.55161	0.775807	+	0.630971i	$0.217343\pi$
$600$	282196.	0.0320017
$601$	9.34616e6	1.05547	0.527736	−	0.849408i	$-0.323041\pi$
$601$	9.34616e6	1.05547	0.527736	+	0.849408i	$0.323041\pi$
$602$	2.35933e6	0.265337
$603$	−3.28177e6	−0.367549
$604$	6.24166e6	0.696157
$605$	−1.17680e7	−1.30712
$606$	−63118.7	−0.00698195
$607$	−5.89215e6	−0.649085	−0.324543	−	0.945871i	$-0.605210\pi$
$607$	−5.89215e6	−0.649085	−0.324543	+	0.945871i	$0.605210\pi$
$608$	4.46581e6	0.489938
$609$	−7.33903e6	−0.801854
$610$	1.93401e6	0.210443
$611$	6.80713e6	0.737669
$612$	2.24069e6	0.241826
$613$	1.58136e7	1.69973	0.849866	−	0.526999i	$-0.176683\pi$
$613$	1.58136e7	1.69973	0.849866	+	0.526999i	$0.176683\pi$
$614$	734918.	0.0786716
$615$	−1.11149e7	−1.18499
$616$	8.13839e6	0.864145
$617$	−1.29264e7	−1.36698	−0.683492	−	0.729958i	$-0.739540\pi$
$617$	−1.29264e7	−1.36698	−0.683492	+	0.729958i	$0.739540\pi$
$618$	1.24388e6	0.131011
$619$	1.23898e7	1.29969	0.649843	−	0.760069i	$-0.274835\pi$
$619$	1.23898e7	1.29969	0.649843	+	0.760069i	$0.274835\pi$
$620$	1.79666e7	1.87710
$621$	−1.29584e6	−0.134841
$622$	1.44095e6	0.149338
$623$	−2.15184e7	−2.22121
$624$	3.28558e6	0.337793
$625$	−1.11942e7	−1.14629
$626$	−456985.	−0.0466086
$627$	9.03661e6	0.917987
$628$	769154.	0.0778241
$629$	−1.30882e7	−1.31903
$630$	−1.06205e6	−0.106609
$631$	−4.55343e6	−0.455266	−0.227633	−	0.973747i	$-0.573099\pi$
$631$	−4.55343e6	−0.455266	−0.227633	+	0.973747i	$0.573099\pi$
$632$	923.915	9.20109e−5 0
$633$	7.07872e6	0.702175
$634$	−2.74755e6	−0.271471
$635$	−4.83377e6	−0.475720
$636$	9.33021e6	0.914637
$637$	−1.61247e7	−1.57450
$638$	−1.78905e6	−0.174009
$639$	−4.37917e6	−0.424267
$640$	6.65949e6	0.642675
$641$	−1.62024e7	−1.55752	−0.778761	−	0.627320i	$-0.784152\pi$
$641$	−1.62024e7	−1.55752	−0.778761	+	0.627320i	$0.784152\pi$
$642$	−423864.	−0.0405872
$643$	−2.69183e6	−0.256756	−0.128378	−	0.991725i	$-0.540977\pi$
$643$	−2.69183e6	−0.256756	−0.128378	+	0.991725i	$0.540977\pi$
$644$	−1.34375e7	−1.27675
$645$	5.96143e6	0.564224
$646$	−1.33264e6	−0.125641
$647$	−2.41173e6	−0.226500	−0.113250	−	0.993567i	$-0.536126\pi$
$647$	−2.41173e6	−0.226500	−0.113250	+	0.993567i	$0.536126\pi$
$648$	−369917.	−0.0346072
$649$	5.04878e6	0.470516
$650$	−190991.	−0.0177309
$651$	−2.06913e7	−1.91353
$652$	−4.33751e6	−0.399597
$653$	−805191.	−0.0738951	−0.0369476	−	0.999317i	$-0.511763\pi$
$653$	−805191.	−0.0738951	−0.0369476	+	0.999317i	$0.511763\pi$
$654$	−738912.	−0.0675535
$655$	−1.69622e7	−1.54483
$656$	−1.93015e7	−1.75118
$657$	−2.41103e6	−0.217916
$658$	−3.82106e6	−0.344048
$659$	1.18027e7	1.05869	0.529346	−	0.848406i	$-0.322438\pi$
$659$	1.18027e7	1.05869	0.529346	+	0.848406i	$0.322438\pi$
$660$	1.01524e7	0.907211
$661$	−2.07249e7	−1.84497	−0.922483	−	0.386037i	$-0.873844\pi$
$661$	−2.07249e7	−1.84497	−0.922483	+	0.386037i	$0.873844\pi$
$662$	−2.34625e6	−0.208080
$663$	−3.07168e6	−0.271389
$664$	−437032.	−0.0384674
$665$	−2.47694e7	−2.17200
$666$	1.06677e6	0.0931937
$667$	5.98325e6	0.520742
$668$	4.09908e6	0.355423
$669$	7.73710e6	0.668363
$670$	2.19281e6	0.188719
$671$	2.12913e7	1.82556
$672$	−5.77808e6	−0.493583
$673$	−1.53931e7	−1.31005	−0.655026	−	0.755607i	$-0.727342\pi$
$673$	−1.53931e7	−1.31005	−0.655026	+	0.755607i	$0.727342\pi$
$674$	−3.36271e6	−0.285128
$675$	−405417.	−0.0342486
$676$	6.96088e6	0.585865
$677$	−2.38438e6	−0.199942	−0.0999710	−	0.994990i	$-0.531875\pi$
$677$	−2.38438e6	−0.199942	−0.0999710	+	0.994990i	$0.531875\pi$
$678$	−367048.	−0.0306654
$679$	−3.04959e7	−2.53844
$680$	−3.03254e6	−0.251498
$681$	−602548.	−0.0497879
$682$	−5.04396e6	−0.415251
$683$	−1.51827e7	−1.24537	−0.622685	−	0.782472i	$-0.713958\pi$
$683$	−1.51827e7	−1.24537	−0.622685	+	0.782472i	$0.713958\pi$
$684$	−4.25932e6	−0.348097
$685$	−8.62818e6	−0.702575
$686$	5.41916e6	0.439665
$687$	5.60977e6	0.453474
$688$	1.03523e7	0.833807
$689$	−1.27905e7	−1.02645
$690$	865854.	0.0692344
$691$	8.80597e6	0.701588	0.350794	−	0.936453i	$-0.385912\pi$
$691$	8.80597e6	0.701588	0.350794	+	0.936453i	$0.385912\pi$
$692$	1.07018e7	0.849554
$693$	−1.16920e7	−0.924817
$694$	−3.60477e6	−0.284105
$695$	2.09228e7	1.64307
$696$	1.70801e6	0.133649
$697$	1.80449e7	1.40693
$698$	834088.	0.0647998
$699$	−2.83896e6	−0.219769
$700$	−4.20408e6	−0.324284
$701$	−8.97588e6	−0.689893	−0.344947	−	0.938622i	$-0.612103\pi$
$701$	−8.97588e6	−0.689893	−0.344947	+	0.938622i	$0.612103\pi$
$702$	250361.	0.0191745
$703$	2.48794e7	1.89868
$704$	1.66711e7	1.26775
$705$	−9.65487e6	−0.731600
$706$	367181.	0.0277248
$707$	1.90463e6	0.143305
$708$	−2.37969e6	−0.178418
$709$	−8.79934e6	−0.657407	−0.328704	−	0.944433i	$-0.606612\pi$
$709$	−8.79934e6	−0.657407	−0.328704	+	0.944433i	$0.606612\pi$
$710$	2.92607e6	0.217841
$711$	−1327.34	−9.84711e−5 0
$712$	5.00797e6	0.370221
$713$	1.68689e7	1.24269
$714$	1.72423e6	0.126576
$715$	−1.39175e7	−1.01812
$716$	−1.61669e7	−1.17854
$717$	−4.05278e6	−0.294412
$718$	−2.33259e6	−0.168860
$719$	−7.35845e6	−0.530841	−0.265420	−	0.964133i	$-0.585511\pi$
$719$	−7.35845e6	−0.530841	−0.265420	+	0.964133i	$0.585511\pi$
$720$	−4.66009e6	−0.335014
$721$	−3.75345e7	−2.68901
$722$	324413.	0.0231609
$723$	−613270.	−0.0436321
$724$	−1.73895e7	−1.23294
$725$	1.87192e6	0.132264
$726$	−1.55720e6	−0.109649
$727$	−1.11954e7	−0.785604	−0.392802	−	0.919623i	$-0.628494\pi$
$727$	−1.11954e7	−0.785604	−0.392802	+	0.919623i	$0.628494\pi$
$728$	5.25857e6	0.367739
$729$	531441.	0.0370370
$730$	1.61100e6	0.111890
$731$	−9.67832e6	−0.669894
$732$	−1.00355e7	−0.692244
$733$	−4.91751e6	−0.338053	−0.169027	−	0.985611i	$-0.554062\pi$
$733$	−4.91751e6	−0.338053	−0.169027	+	0.985611i	$0.554062\pi$
$734$	1.58344e6	0.108483
$735$	2.28703e7	1.56154
$736$	4.71066e6	0.320544
$737$	2.41404e7	1.63710
$738$	−1.47077e6	−0.0994038
$739$	2.20477e7	1.48509	0.742544	−	0.669798i	$-0.233619\pi$
$739$	2.20477e7	1.48509	0.742544	+	0.669798i	$0.233619\pi$
$740$	2.79514e7	1.87639
$741$	5.83895e6	0.390652
$742$	7.17969e6	0.478736
$743$	−7.37303e6	−0.489975	−0.244988	−	0.969526i	$-0.578784\pi$
$743$	−7.37303e6	−0.489975	−0.244988	+	0.969526i	$0.578784\pi$
$744$	4.81547e6	0.318938
$745$	−1.27035e7	−0.838559
$746$	−2.17908e6	−0.143359
$747$	627862.	0.0411683
$748$	−1.64823e7	−1.07712
$749$	1.27902e7	0.833056
$750$	−1.25131e6	−0.0812289
$751$	1.91626e7	1.23981	0.619904	−	0.784677i	$-0.287171\pi$
$751$	1.91626e7	1.23981	0.619904	+	0.784677i	$0.287171\pi$
$752$	−1.67661e7	−1.08115
$753$	−1.02047e6	−0.0655865
$754$	−1.15599e6	−0.0740498
$755$	1.21360e7	0.774835
$756$	5.51092e6	0.350687
$757$	−1.39163e7	−0.882638	−0.441319	−	0.897350i	$-0.645489\pi$
$757$	−1.39163e7	−0.882638	−0.441319	+	0.897350i	$0.645489\pi$
$758$	304219.	0.0192315
$759$	9.53207e6	0.600597
$760$	5.76456e6	0.362020
$761$	−3.26931e6	−0.204642	−0.102321	−	0.994751i	$-0.532627\pi$
$761$	−3.26931e6	−0.204642	−0.102321	+	0.994751i	$0.532627\pi$
$762$	−639626.	−0.0399060
$763$	2.22969e7	1.38654
$764$	2.65013e7	1.64261
$765$	4.35670e6	0.269156
$766$	289345.	0.0178174
$767$	3.26224e6	0.200229
$768$	−7.17695e6	−0.439073
$769$	4.12163e6	0.251335	0.125668	−	0.992072i	$-0.459893\pi$
$769$	4.12163e6	0.251335	0.125668	+	0.992072i	$0.459893\pi$
$770$	7.81236e6	0.474849
$771$	−8.63134e6	−0.522929
$772$	368087.	0.0222283
$773$	4.00249e6	0.240925	0.120462	−	0.992718i	$-0.461562\pi$
$773$	4.00249e6	0.240925	0.120462	+	0.992718i	$0.461562\pi$
$774$	788843.	0.0473302
$775$	5.27760e6	0.315633
$776$	7.09731e6	0.423097
$777$	−3.21902e7	−1.91281
$778$	1.17366e6	0.0695173
$779$	−3.43015e7	−2.02521
$780$	6.55991e6	0.386066
$781$	3.22128e7	1.88973
$782$	−1.40570e6	−0.0822010
$783$	−2.45381e6	−0.143033
$784$	3.97153e7	2.30764
$785$	1.49551e6	0.0866195
$786$	−2.24452e6	−0.129589
$787$	2.58157e6	0.148575	0.0742876	−	0.997237i	$-0.476332\pi$
$787$	2.58157e6	0.148575	0.0742876	+	0.997237i	$0.476332\pi$
$788$	1.55850e7	0.894112
$789$	3.53046e6	0.201901
$790$	886.903	5.05602e−5 0
$791$	1.10758e7	0.629411
$792$	2.72108e6	0.154144
$793$	1.37573e7	0.776871
$794$	4.02618e6	0.226643
$795$	1.81413e7	1.01801
$796$	9.71423e6	0.543407
$797$	−2.27906e7	−1.27089	−0.635447	−	0.772145i	$-0.719184\pi$
$797$	−2.27906e7	−1.27089	−0.635447	+	0.772145i	$0.719184\pi$
$798$	−3.27759e6	−0.182200
$799$	1.56746e7	0.868618
$800$	1.47378e6	0.0814156
$801$	−7.19469e6	−0.396215
$802$	−723741.	−0.0397326
$803$	1.77353e7	0.970623
$804$	−1.13784e7	−0.620782
$805$	−2.61274e7	−1.42104
$806$	−3.25912e6	−0.176711
$807$	1.23009e7	0.664897
$808$	−443263.	−0.0238855
$809$	4.16041e6	0.223494	0.111747	−	0.993737i	$-0.464355\pi$
$809$	4.16041e6	0.223494	0.111747	+	0.993737i	$0.464355\pi$
$810$	−355098.	−0.0190167
$811$	−2.09364e7	−1.11776	−0.558882	−	0.829247i	$-0.688769\pi$
$811$	−2.09364e7	−1.11776	−0.558882	+	0.829247i	$0.688769\pi$
$812$	−2.54454e7	−1.35431
$813$	1.16254e7	0.616855
$814$	−7.84709e6	−0.415095
$815$	−8.43369e6	−0.444758
$816$	7.56560e6	0.397757
$817$	1.83975e7	0.964282
$818$	2.42594e6	0.126764
$819$	−7.55472e6	−0.393558
$820$	−3.85368e7	−2.00143
$821$	−1.31577e7	−0.681273	−0.340636	−	0.940195i	$-0.610643\pi$
$821$	−1.31577e7	−0.681273	−0.340636	+	0.940195i	$0.610643\pi$
$822$	−1.14172e6	−0.0589359
$823$	1.14628e7	0.589915	0.294958	−	0.955510i	$-0.404694\pi$
$823$	1.14628e7	0.589915	0.294958	+	0.955510i	$0.404694\pi$
$824$	8.73540e6	0.448193
$825$	2.98221e6	0.152547
$826$	−1.83120e6	−0.0933868
$827$	1.49476e6	0.0759991	0.0379995	−	0.999278i	$-0.487901\pi$
$827$	1.49476e6	0.0759991	0.0379995	+	0.999278i	$0.487901\pi$
$828$	−4.49285e6	−0.227744
$829$	−5.86484e6	−0.296394	−0.148197	−	0.988958i	$-0.547347\pi$
$829$	−5.86484e6	−0.296394	−0.148197	+	0.988958i	$0.547347\pi$
$830$	−419525.	−0.0211379
$831$	605288.	0.0304060
$832$	1.07720e7	0.539493
$833$	−3.71297e7	−1.85400
$834$	2.76859e6	0.137830
$835$	7.97009e6	0.395592
$836$	3.13312e7	1.55046
$837$	−6.91814e6	−0.341331
$838$	296267.	0.0145738
$839$	4.67730e6	0.229398	0.114699	−	0.993400i	$-0.463410\pi$
$839$	4.67730e6	0.229398	0.114699	+	0.993400i	$0.463410\pi$
$840$	−7.45847e6	−0.364713
$841$	−9.18123e6	−0.447622
$842$	6.08057e6	0.295572
$843$	−1.97513e7	−0.957253
$844$	2.45429e7	1.18596
$845$	1.35345e7	0.652077
$846$	−1.27758e6	−0.0613706
$847$	4.69890e7	2.25055
$848$	3.15031e7	1.50440
$849$	3.94501e6	0.187836
$850$	−439789.	−0.0208784
$851$	2.62436e7	1.24222
$852$	−1.51832e7	−0.716579
$853$	−1.40469e7	−0.661011	−0.330505	−	0.943804i	$-0.607219\pi$
$853$	−1.40469e7	−0.661011	−0.330505	+	0.943804i	$0.607219\pi$
$854$	−7.72239e6	−0.362332
$855$	−8.28165e6	−0.387438
$856$	−2.97667e6	−0.138850
$857$	−1.05306e7	−0.489779	−0.244890	−	0.969551i	$-0.578752\pi$
$857$	−1.05306e7	−0.489779	−0.244890	+	0.969551i	$0.578752\pi$
$858$	−1.84163e6	−0.0854052
$859$	−4.25060e7	−1.96547	−0.982737	−	0.185007i	$-0.940769\pi$
$859$	−4.25060e7	−1.96547	−0.982737	+	0.185007i	$0.940769\pi$
$860$	2.06691e7	0.952962
$861$	4.43809e7	2.04027
$862$	6.78674e6	0.311095
$863$	1.53651e7	0.702276	0.351138	−	0.936324i	$-0.385795\pi$
$863$	1.53651e7	0.702276	0.351138	+	0.936324i	$0.385795\pi$
$864$	−1.93190e6	−0.0880443
$865$	2.08081e7	0.945567
$866$	5.48226e6	0.248408
$867$	5.70566e6	0.257785
$868$	−7.17395e7	−3.23191
$869$	9763.80	0.000438601 0
$870$	1.63959e6	0.0734406
$871$	1.55982e7	0.696673
$872$	−5.18915e6	−0.231103
$873$	−1.01963e7	−0.452803
$874$	2.67210e6	0.118324
$875$	3.77586e7	1.66723
$876$	−8.35939e6	−0.368056
$877$	−4.49693e6	−0.197432	−0.0987160	−	0.995116i	$-0.531474\pi$
$877$	−4.49693e6	−0.197432	−0.0987160	+	0.995116i	$0.531474\pi$
$878$	−3.67394e6	−0.160841
$879$	6.68588e6	0.291868
$880$	3.42792e7	1.49219
$881$	3.32819e6	0.144467	0.0722336	−	0.997388i	$-0.476987\pi$
$881$	3.32819e6	0.144467	0.0722336	+	0.997388i	$0.476987\pi$
$882$	3.02630e6	0.130991
$883$	4.11892e6	0.177779	0.0888897	−	0.996041i	$-0.471668\pi$
$883$	4.11892e6	0.177779	0.0888897	+	0.996041i	$0.471668\pi$
$884$	−1.06499e7	−0.458370
$885$	−4.62698e6	−0.198582
$886$	1.20957e6	0.0517662
$887$	8.02010e6	0.342271	0.171136	−	0.985247i	$-0.445256\pi$
$887$	8.02010e6	0.342271	0.171136	+	0.985247i	$0.445256\pi$
$888$	7.49162e6	0.318818
$889$	1.93009e7	0.819075
$890$	4.80735e6	0.203437
$891$	−3.90923e6	−0.164967
$892$	2.68256e7	1.12885
$893$	−2.97958e7	−1.25034
$894$	−1.68099e6	−0.0703429
$895$	−3.14343e7	−1.31173
$896$	−2.65909e7	−1.10653
$897$	6.15910e6	0.255585
$898$	5.09492e6	0.210837
$899$	3.19430e7	1.31818
$900$	−1.40564e6	−0.0578451
$901$	−2.94522e7	−1.20866
$902$	1.08188e7	0.442756
$903$	−2.38036e7	−0.971457
$904$	−2.57767e6	−0.104907
$905$	−3.38115e7	−1.37228
$906$	1.60589e6	0.0649974
$907$	1.84172e7	0.743372	0.371686	−	0.928358i	$-0.378780\pi$
$907$	1.84172e7	0.743372	0.371686	+	0.928358i	$0.378780\pi$
$908$	−2.08912e6	−0.0840907
$909$	636814.	0.0255625
$910$	5.04791e6	0.202073
$911$	−9.98071e6	−0.398442	−0.199221	−	0.979955i	$-0.563841\pi$
$911$	−9.98071e6	−0.398442	−0.199221	+	0.979955i	$0.563841\pi$
$912$	−1.43815e7	−0.572553
$913$	−4.61850e6	−0.183368
$914$	−908470.	−0.0359704
$915$	−1.95125e7	−0.770479
$916$	1.94498e7	0.765909
$917$	6.77291e7	2.65982
$918$	576498.	0.0225783
$919$	−3.56935e7	−1.39412	−0.697060	−	0.717012i	$-0.745509\pi$
$919$	−3.56935e7	−1.39412	−0.697060	+	0.717012i	$0.745509\pi$
$920$	6.08063e6	0.236853
$921$	−7.41470e6	−0.288034
$922$	−111451.	−0.00431773
$923$	2.08141e7	0.804180
$924$	−4.05378e7	−1.56200
$925$	8.21057e6	0.315514
$926$	−4.86212e6	−0.186336
$927$	−1.25497e7	−0.479661
$928$	8.92013e6	0.340018
$929$	−1.87728e7	−0.713657	−0.356829	−	0.934170i	$-0.616142\pi$
$929$	−1.87728e7	−0.713657	−0.356829	+	0.934170i	$0.616142\pi$
$930$	4.62257e6	0.175257
$931$	7.05799e7	2.66874
$932$	−9.84309e6	−0.371186
$933$	−1.45379e7	−0.546762
$934$	−5.08404e6	−0.190696
$935$	−3.20475e7	−1.19885
$936$	1.75821e6	0.0655965
$937$	2.29871e6	0.0855333	0.0427667	−	0.999085i	$-0.486383\pi$
$937$	2.29871e6	0.0855333	0.0427667	+	0.999085i	$0.486383\pi$
$938$	−8.75576e6	−0.324928
$939$	4.61059e6	0.170645
$940$	−3.34748e7	−1.23566
$941$	−1.86441e7	−0.686386	−0.343193	−	0.939265i	$-0.611508\pi$
$941$	−1.86441e7	−0.686386	−0.343193	+	0.939265i	$0.611508\pi$
$942$	197893.	0.00726612
$943$	−3.61822e7	−1.32500
$944$	−8.03496e6	−0.293463
$945$	1.07152e7	0.390320
$946$	−5.80266e6	−0.210814
$947$	4.04280e7	1.46490	0.732448	−	0.680823i	$-0.238378\pi$
$947$	4.04280e7	1.46490	0.732448	+	0.680823i	$0.238378\pi$
$948$	−4602.08	−0.000166316 0
$949$	1.14596e7	0.413051
$950$	835996.	0.0300535
$951$	2.77205e7	0.993915
$952$	1.21087e7	0.433019
$953$	−4.61107e7	−1.64463	−0.822317	−	0.569030i	$-0.807319\pi$
$953$	−4.61107e7	−1.64463	−0.822317	+	0.569030i	$0.807319\pi$
$954$	2.40054e6	0.0853959
$955$	5.15281e7	1.82825
$956$	−1.40516e7	−0.497256
$957$	1.80500e7	0.637085
$958$	−2.60502e6	−0.0917060
$959$	3.44518e7	1.20966
$960$	−1.52783e7	−0.535055
$961$	6.14292e7	2.14569
$962$	−5.07035e6	−0.176645
$963$	4.27643e6	0.148599
$964$	−2.12629e6	−0.0736937
$965$	715693.	0.0247405
$966$	−3.45730e6	−0.119205
$967$	−4.38914e7	−1.50943	−0.754716	−	0.656051i	$-0.772225\pi$
$967$	−4.38914e7	−1.50943	−0.754716	+	0.656051i	$0.772225\pi$
$968$	−1.09357e7	−0.375111
$969$	1.34452e7	0.459999
$970$	6.81299e6	0.232492
$971$	4.29849e7	1.46308	0.731539	−	0.681800i	$-0.238802\pi$
$971$	4.29849e7	1.46308	0.731539	+	0.681800i	$0.238802\pi$
$972$	1.84258e6	0.0625548
$973$	−8.35433e7	−2.82898
$974$	−3.05590e6	−0.103215
$975$	1.92694e6	0.0649167
$976$	−3.38844e7	−1.13861
$977$	−5.79789e7	−1.94327	−0.971636	−	0.236482i	$-0.924006\pi$
$977$	−5.79789e7	−1.94327	−0.971636	+	0.236482i	$0.924006\pi$
$978$	−1.11598e6	−0.0373087
$979$	5.29235e7	1.76479
$980$	7.92946e7	2.63742
$981$	7.45499e6	0.247329
$982$	−1.28886e6	−0.0426509
$983$	−3.33459e7	−1.10067	−0.550337	−	0.834943i	$-0.685501\pi$
$983$	−3.33459e7	−1.10067	−0.550337	+	0.834943i	$0.685501\pi$
$984$	−1.03288e7	−0.340064
$985$	3.03029e7	0.995162
$986$	−2.66185e6	−0.0871949
$987$	3.85513e7	1.25964
$988$	2.02445e7	0.659803
$989$	1.94062e7	0.630885
$990$	2.61207e6	0.0847026
$991$	−2.09997e7	−0.679250	−0.339625	−	0.940561i	$-0.610300\pi$
$991$	−2.09997e7	−0.679250	−0.339625	+	0.940561i	$0.610300\pi$
$992$	2.51490e7	0.811411
$993$	2.36717e7	0.761826
$994$	−1.16836e7	−0.375069
$995$	1.88880e7	0.604821
$996$	2.17689e6	0.0695324
$997$	4.11583e7	1.31135	0.655676	−	0.755043i	$-0.272384\pi$
$997$	4.11583e7	1.31135	0.655676	+	0.755043i	$0.272384\pi$
$998$	−180991.	−0.00575215
$999$	−1.07628e7	−0.341203

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.6.a.b.1.17	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.6.a.b.1.17	✓	30	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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	471.a (trivial)

\(f(q)\)	\(=\)	\(q+0.892048 q^{2} -9.00000 q^{3} -31.2043 q^{4} -60.6723 q^{5} -8.02843 q^{6} +242.261 q^{7} -56.3812 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+0.892048 q^{2} -9.00000 q^{3} -31.2043 q^{4} -60.6723 q^{5} -8.02843 q^{6} +242.261 q^{7} -56.3812 q^{8} +81.0000 q^{9} -54.1226 q^{10} -595.829 q^{11} +280.838 q^{12} -384.991 q^{13} +216.108 q^{14} +546.051 q^{15} +948.241 q^{16} -886.507 q^{17} +72.2559 q^{18} +1685.16 q^{19} +1893.23 q^{20} -2180.34 q^{21} -531.507 q^{22} +1777.56 q^{23} +507.431 q^{24} +556.127 q^{25} -343.431 q^{26} -729.000 q^{27} -7559.56 q^{28} +3365.99 q^{29} +487.103 q^{30} +9489.91 q^{31} +2650.07 q^{32} +5362.46 q^{33} -790.807 q^{34} -14698.5 q^{35} -2527.54 q^{36} +14763.8 q^{37} +1503.24 q^{38} +3464.92 q^{39} +3420.78 q^{40} -20355.0 q^{41} -1944.97 q^{42} +10917.4 q^{43} +18592.4 q^{44} -4914.46 q^{45} +1585.67 q^{46} -17681.3 q^{47} -8534.17 q^{48} +41883.2 q^{49} +496.092 q^{50} +7978.56 q^{51} +12013.4 q^{52} +33222.7 q^{53} -650.303 q^{54} +36150.3 q^{55} -13658.9 q^{56} -15166.5 q^{57} +3002.63 q^{58} -8473.54 q^{59} -17039.1 q^{60} -35733.9 q^{61} +8465.45 q^{62} +19623.1 q^{63} -27979.7 q^{64} +23358.3 q^{65} +4783.57 q^{66} -40515.7 q^{67} +27662.8 q^{68} -15998.0 q^{69} -13111.8 q^{70} -54063.8 q^{71} -4566.88 q^{72} -29765.8 q^{73} +13170.0 q^{74} -5005.15 q^{75} -52584.2 q^{76} -144346. q^{77} +3090.87 q^{78} -16.3869 q^{79} -57532.0 q^{80} +6561.00 q^{81} -18157.6 q^{82} +7751.38 q^{83} +68036.0 q^{84} +53786.4 q^{85} +9738.80 q^{86} -30293.9 q^{87} +33593.5 q^{88} -88823.4 q^{89} -4383.93 q^{90} -93268.2 q^{91} -55467.3 q^{92} -85409.2 q^{93} -15772.5 q^{94} -102243. q^{95} -23850.7 q^{96} -125881. q^{97} +37361.8 q^{98} -48262.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9}+O(q^{10}) \) 30 * q - 8 * q^2 - 270 * q^3 + 470 * q^4 - 136 * q^5 + 72 * q^6 + 68 * q^7 - 261 * q^8 + 2430 * q^9	\( 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9} - 383 q^{10} - 875 q^{11} - 4230 q^{12} + 101 q^{13} - 2279 q^{14} + 1224 q^{15} + 7454 q^{16} - 4042 q^{17} - 648 q^{18} + 846 q^{19} - 5089 q^{20} - 612 q^{21} - 700 q^{22} - 5902 q^{23} + 2349 q^{24} + 12880 q^{25} - 7567 q^{26} - 21870 q^{27} - 375 q^{28} - 10301 q^{29} + 3447 q^{30} - 4099 q^{31} - 1560 q^{32} + 7875 q^{33} - 3683 q^{34} - 20686 q^{35} + 38070 q^{36} + 8468 q^{37} - 11848 q^{38} - 909 q^{39} - 5132 q^{40} - 47958 q^{41} + 20511 q^{42} + 63916 q^{43} + 3101 q^{44} - 11016 q^{45} + 19654 q^{46} + 8589 q^{47} - 67086 q^{48} + 27834 q^{49} + 121727 q^{50} + 36378 q^{51} + 56510 q^{52} + 10134 q^{53} + 5832 q^{54} - 11473 q^{55} - 68192 q^{56} - 7614 q^{57} + 32006 q^{58} - 64236 q^{59} + 45801 q^{60} - 98194 q^{61} - 67276 q^{62} + 5508 q^{63} + 138849 q^{64} - 155917 q^{65} + 6300 q^{66} + 62323 q^{67} - 117531 q^{68} + 53118 q^{69} - 220939 q^{70} - 179713 q^{71} - 21141 q^{72} - 148343 q^{73} - 214732 q^{74} - 115920 q^{75} - 189758 q^{76} - 142357 q^{77} + 68103 q^{78} + 26916 q^{79} - 463727 q^{80} + 196830 q^{81} - 206514 q^{82} - 89285 q^{83} + 3375 q^{84} - 23932 q^{85} - 477235 q^{86} + 92709 q^{87} - 114708 q^{88} - 474411 q^{89} - 31023 q^{90} + 51305 q^{91} - 1030074 q^{92} + 36891 q^{93} - 485800 q^{94} - 169960 q^{95} + 14040 q^{96} - 169188 q^{97} - 629739 q^{98} - 70875 q^{99}+O(q^{100}) \) 30 * q - 8 * q^2 - 270 * q^3 + 470 * q^4 - 136 * q^5 + 72 * q^6 + 68 * q^7 - 261 * q^8 + 2430 * q^9 - 383 * q^10 - 875 * q^11 - 4230 * q^12 + 101 * q^13 - 2279 * q^14 + 1224 * q^15 + 7454 * q^16 - 4042 * q^17 - 648 * q^18 + 846 * q^19 - 5089 * q^20 - 612 * q^21 - 700 * q^22 - 5902 * q^23 + 2349 * q^24 + 12880 * q^25 - 7567 * q^26 - 21870 * q^27 - 375 * q^28 - 10301 * q^29 + 3447 * q^30 - 4099 * q^31 - 1560 * q^32 + 7875 * q^33 - 3683 * q^34 - 20686 * q^35 + 38070 * q^36 + 8468 * q^37 - 11848 * q^38 - 909 * q^39 - 5132 * q^40 - 47958 * q^41 + 20511 * q^42 + 63916 * q^43 + 3101 * q^44 - 11016 * q^45 + 19654 * q^46 + 8589 * q^47 - 67086 * q^48 + 27834 * q^49 + 121727 * q^50 + 36378 * q^51 + 56510 * q^52 + 10134 * q^53 + 5832 * q^54 - 11473 * q^55 - 68192 * q^56 - 7614 * q^57 + 32006 * q^58 - 64236 * q^59 + 45801 * q^60 - 98194 * q^61 - 67276 * q^62 + 5508 * q^63 + 138849 * q^64 - 155917 * q^65 + 6300 * q^66 + 62323 * q^67 - 117531 * q^68 + 53118 * q^69 - 220939 * q^70 - 179713 * q^71 - 21141 * q^72 - 148343 * q^73 - 214732 * q^74 - 115920 * q^75 - 189758 * q^76 - 142357 * q^77 + 68103 * q^78 + 26916 * q^79 - 463727 * q^80 + 196830 * q^81 - 206514 * q^82 - 89285 * q^83 + 3375 * q^84 - 23932 * q^85 - 477235 * q^86 + 92709 * q^87 - 114708 * q^88 - 474411 * q^89 - 31023 * q^90 + 51305 * q^91 - 1030074 * q^92 + 36891 * q^93 - 485800 * q^94 - 169960 * q^95 + 14040 * q^96 - 169188 * q^97 - 629739 * q^98 - 70875 * q^99

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