LMFDB - Embedded newform 471.6.a.b.1.16

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			1.16
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)

$f(q)$	$=$	$q+0.614444 q^{2} -9.00000 q^{3} -31.6225 q^{4} -56.4863 q^{5} -5.52999 q^{6} -140.573 q^{7} -39.0924 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+0.614444 q^{2} -9.00000 q^{3} -31.6225 q^{4} -56.4863 q^{5} -5.52999 q^{6} -140.573 q^{7} -39.0924 q^{8} +81.0000 q^{9} -34.7077 q^{10} +344.435 q^{11} +284.602 q^{12} -542.921 q^{13} -86.3744 q^{14} +508.377 q^{15} +987.899 q^{16} +1201.70 q^{17} +49.7699 q^{18} -1138.01 q^{19} +1786.24 q^{20} +1265.16 q^{21} +211.636 q^{22} +3550.17 q^{23} +351.832 q^{24} +65.7056 q^{25} -333.595 q^{26} -729.000 q^{27} +4445.27 q^{28} +5307.12 q^{29} +312.369 q^{30} -4770.11 q^{31} +1857.97 q^{32} -3099.91 q^{33} +738.375 q^{34} +7940.47 q^{35} -2561.42 q^{36} +4227.38 q^{37} -699.242 q^{38} +4886.29 q^{39} +2208.19 q^{40} +5657.31 q^{41} +777.369 q^{42} +9591.77 q^{43} -10891.9 q^{44} -4575.39 q^{45} +2181.38 q^{46} -2287.87 q^{47} -8891.09 q^{48} +2953.84 q^{49} +40.3724 q^{50} -10815.3 q^{51} +17168.5 q^{52} -706.058 q^{53} -447.929 q^{54} -19455.9 q^{55} +5495.35 q^{56} +10242.1 q^{57} +3260.93 q^{58} +3971.04 q^{59} -16076.1 q^{60} -45299.0 q^{61} -2930.96 q^{62} -11386.4 q^{63} -30471.1 q^{64} +30667.6 q^{65} -1904.72 q^{66} -19240.6 q^{67} -38000.6 q^{68} -31951.5 q^{69} +4878.97 q^{70} +55394.1 q^{71} -3166.49 q^{72} +7686.00 q^{73} +2597.48 q^{74} -591.350 q^{75} +35986.6 q^{76} -48418.4 q^{77} +3002.35 q^{78} +26082.4 q^{79} -55802.8 q^{80} +6561.00 q^{81} +3476.10 q^{82} -58429.4 q^{83} -40007.5 q^{84} -67879.5 q^{85} +5893.61 q^{86} -47764.1 q^{87} -13464.8 q^{88} +16441.3 q^{89} -2811.32 q^{90} +76320.2 q^{91} -112265. q^{92} +42931.0 q^{93} -1405.77 q^{94} +64281.9 q^{95} -16721.7 q^{96} -89938.8 q^{97} +1814.97 q^{98} +27899.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.614444	0.108619	0.0543097	−	0.998524i	$-0.482704\pi$
$2$	0.614444	0.108619	0.0543097	+	0.998524i	$0.482704\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−31.6225	−0.988202
$5$	−56.4863	−1.01046	−0.505229	−	0.862985i	$-0.668592\pi$
$5$	−56.4863	−1.01046	−0.505229	+	0.862985i	$0.668592\pi$
$6$	−5.52999	−0.0627114
$7$	−140.573	−1.08432	−0.542160	−	0.840275i	$-0.682393\pi$
$7$	−140.573	−1.08432	−0.542160	+	0.840275i	$0.682393\pi$
$8$	−39.0924	−0.215957
$9$	81.0000	0.333333
$10$	−34.7077	−0.109755
$11$	344.435	0.858273	0.429137	−	0.903240i	$-0.358818\pi$
$11$	344.435	0.858273	0.429137	+	0.903240i	$0.358818\pi$
$12$	284.602	0.570539
$13$	−542.921	−0.891002	−0.445501	−	0.895281i	$-0.646974\pi$
$13$	−542.921	−0.891002	−0.445501	+	0.895281i	$0.646974\pi$
$14$	−86.3744	−0.117778
$15$	508.377	0.583388
$16$	987.899	0.964745
$17$	1201.70	1.00849	0.504246	−	0.863560i	$-0.331770\pi$
$17$	1201.70	1.00849	0.504246	+	0.863560i	$0.331770\pi$
$18$	49.7699	0.0362064
$19$	−1138.01	−0.723205	−0.361602	−	0.932332i	$-0.617770\pi$
$19$	−1138.01	−0.723205	−0.361602	+	0.932332i	$0.617770\pi$
$20$	1786.24	0.998537
$21$	1265.16	0.626033
$22$	211.636	0.0932250
$23$	3550.17	1.39936	0.699681	−	0.714456i	$-0.253326\pi$
$23$	3550.17	1.39936	0.699681	+	0.714456i	$0.253326\pi$
$24$	351.832	0.124683
$25$	65.7056	0.0210258
$26$	−333.595	−0.0967800
$27$	−729.000	−0.192450
$28$	4445.27	1.07153
$29$	5307.12	1.17183	0.585914	−	0.810373i	$-0.300736\pi$
$29$	5307.12	1.17183	0.585914	+	0.810373i	$0.300736\pi$
$30$	312.369	0.0633672
$31$	−4770.11	−0.891506	−0.445753	−	0.895156i	$-0.647064\pi$
$31$	−4770.11	−0.891506	−0.445753	+	0.895156i	$0.647064\pi$
$32$	1857.97	0.320747
$33$	−3099.91	−0.495524
$34$	738.375	0.109542
$35$	7940.47	1.09566
$36$	−2561.42	−0.329401
$37$	4227.38	0.507653	0.253826	−	0.967250i	$-0.418311\pi$
$37$	4227.38	0.507653	0.253826	+	0.967250i	$0.418311\pi$
$38$	−699.242	−0.0785540
$39$	4886.29	0.514420
$40$	2208.19	0.218216
$41$	5657.31	0.525594	0.262797	−	0.964851i	$-0.415355\pi$
$41$	5657.31	0.525594	0.262797	+	0.964851i	$0.415355\pi$
$42$	777.369	0.0679992
$43$	9591.77	0.791093	0.395547	−	0.918446i	$-0.370555\pi$
$43$	9591.77	0.791093	0.395547	+	0.918446i	$0.370555\pi$
$44$	−10891.9	−0.848147
$45$	−4575.39	−0.336819
$46$	2181.38	0.151998
$47$	−2287.87	−0.151073	−0.0755365	−	0.997143i	$-0.524067\pi$
$47$	−2287.87	−0.151073	−0.0755365	+	0.997143i	$0.524067\pi$
$48$	−8891.09	−0.556996
$49$	2953.84	0.175751
$50$	40.3724	0.00228381
$51$	−10815.3	−0.582254
$52$	17168.5	0.880490
$53$	−706.058	−0.0345263	−0.0172632	−	0.999851i	$-0.505495\pi$
$53$	−706.058	−0.0345263	−0.0172632	+	0.999851i	$0.505495\pi$
$54$	−447.929	−0.0209038
$55$	−19455.9	−0.867249
$56$	5495.35	0.234167
$57$	10242.1	0.417543
$58$	3260.93	0.127283
$59$	3971.04	0.148516	0.0742581	−	0.997239i	$-0.476341\pi$
$59$	3971.04	0.148516	0.0742581	+	0.997239i	$0.476341\pi$
$60$	−16076.1	−0.576505
$61$	−45299.0	−1.55871	−0.779353	−	0.626585i	$-0.784452\pi$
$61$	−45299.0	−1.55871	−0.779353	+	0.626585i	$0.784452\pi$
$62$	−2930.96	−0.0968348
$63$	−11386.4	−0.361440
$64$	−30471.1	−0.929905
$65$	30667.6	0.900320
$66$	−1904.72	−0.0538235
$67$	−19240.6	−0.523638	−0.261819	−	0.965117i	$-0.584322\pi$
$67$	−19240.6	−0.523638	−0.261819	+	0.965117i	$0.584322\pi$
$68$	−38000.6	−0.996595
$69$	−31951.5	−0.807921
$70$	4878.97	0.119010
$71$	55394.1	1.30412	0.652060	−	0.758167i	$-0.273905\pi$
$71$	55394.1	1.30412	0.652060	+	0.758167i	$0.273905\pi$
$72$	−3166.49	−0.0719857
$73$	7686.00	0.168808	0.0844040	−	0.996432i	$-0.473101\pi$
$73$	7686.00	0.168808	0.0844040	+	0.996432i	$0.473101\pi$
$74$	2597.48	0.0551409
$75$	−591.350	−0.0121392
$76$	35986.6	0.714672
$77$	−48418.4	−0.930643
$78$	3002.35	0.0558760
$79$	26082.4	0.470196	0.235098	−	0.971972i	$-0.424459\pi$
$79$	26082.4	0.470196	0.235098	+	0.971972i	$0.424459\pi$
$80$	−55802.8	−0.974834
$81$	6561.00	0.111111
$82$	3476.10	0.0570897
$83$	−58429.4	−0.930972	−0.465486	−	0.885055i	$-0.654120\pi$
$83$	−58429.4	−0.930972	−0.465486	+	0.885055i	$0.654120\pi$
$84$	−40007.5	−0.618647
$85$	−67879.5	−1.01904
$86$	5893.61	0.0859280
$87$	−47764.1	−0.676555
$88$	−13464.8	−0.185350
$89$	16441.3	0.220019	0.110010	−	0.993931i	$-0.464912\pi$
$89$	16441.3	0.220019	0.110010	+	0.993931i	$0.464912\pi$
$90$	−2811.32	−0.0365851
$91$	76320.2	0.966132
$92$	−112265.	−1.38285
$93$	42931.0	0.514711
$94$	−1405.77	−0.0164094
$95$	64281.9	0.730768
$96$	−16721.7	−0.185183
$97$	−89938.8	−0.970550	−0.485275	−	0.874362i	$-0.661280\pi$
$97$	−89938.8	−0.970550	−0.485275	+	0.874362i	$0.661280\pi$
$98$	1814.97	0.0190899
$99$	27899.2	0.286091
$100$	−2077.77	−0.0207777
$101$	33404.4	0.325837	0.162918	−	0.986640i	$-0.447909\pi$
$101$	33404.4	0.325837	0.162918	+	0.986640i	$0.447909\pi$
$102$	−6645.38	−0.0632440
$103$	−68265.5	−0.634027	−0.317014	−	0.948421i	$-0.602680\pi$
$103$	−68265.5	−0.634027	−0.317014	+	0.948421i	$0.602680\pi$
$104$	21224.1	0.192418
$105$	−71464.2	−0.632580
$106$	−433.833	−0.00375023
$107$	154111.	1.30129	0.650645	−	0.759382i	$-0.274498\pi$
$107$	154111.	1.30129	0.650645	+	0.759382i	$0.274498\pi$
$108$	23052.8	0.190180
$109$	155028.	1.24981	0.624903	−	0.780702i	$-0.285138\pi$
$109$	155028.	1.24981	0.624903	+	0.780702i	$0.285138\pi$
$110$	−11954.5	−0.0942000
$111$	−38046.4	−0.293093
$112$	−138872.	−1.04609
$113$	−29603.6	−0.218096	−0.109048	−	0.994036i	$-0.534780\pi$
$113$	−29603.6	−0.218096	−0.109048	+	0.994036i	$0.534780\pi$
$114$	6293.18	0.0453532
$115$	−200536.	−1.41400
$116$	−167824.	−1.15800
$117$	−43976.6	−0.297001
$118$	2439.98	0.0161317
$119$	−168927.	−1.09353
$120$	−19873.7	−0.125987
$121$	−42415.6	−0.263367
$122$	−27833.7	−0.169306
$123$	−50915.8	−0.303452
$124$	150843.	0.880988
$125$	172808.	0.989213
$126$	−6996.32	−0.0392594
$127$	−107755.	−0.592828	−0.296414	−	0.955059i	$-0.595791\pi$
$127$	−107755.	−0.592828	−0.296414	+	0.955059i	$0.595791\pi$
$128$	−78177.7	−0.421753
$129$	−86326.0	−0.456738
$130$	18843.5	0.0977922
$131$	−193485.	−0.985076	−0.492538	−	0.870291i	$-0.663931\pi$
$131$	−193485.	−0.985076	−0.492538	+	0.870291i	$0.663931\pi$
$132$	98026.9	0.489678
$133$	159974.	0.784186
$134$	−11822.2	−0.0568772
$135$	41178.5	0.194463
$136$	−46977.3	−0.217791
$137$	−38469.5	−0.175112	−0.0875559	−	0.996160i	$-0.527906\pi$
$137$	−38469.5	−0.175112	−0.0875559	+	0.996160i	$0.527906\pi$
$138$	−19632.4	−0.0877559
$139$	−140401.	−0.616359	−0.308179	−	0.951328i	$-0.599720\pi$
$139$	−140401.	−0.616359	−0.308179	+	0.951328i	$0.599720\pi$
$140$	−251097.	−1.08273
$141$	20590.8	0.0872220
$142$	34036.5	0.141653
$143$	−187001.	−0.764723
$144$	80019.8	0.321582
$145$	−299780.	−1.18408
$146$	4722.61	0.0183358
$147$	−26584.6	−0.101470
$148$	−133680.	−0.501663
$149$	67519.5	0.249151	0.124576	−	0.992210i	$-0.460243\pi$
$149$	67519.5	0.249151	0.124576	+	0.992210i	$0.460243\pi$
$150$	−363.351	−0.00131856
$151$	467866.	1.66985	0.834927	−	0.550360i	$-0.185510\pi$
$151$	467866.	1.66985	0.834927	+	0.550360i	$0.185510\pi$
$152$	44487.5	0.156181
$153$	97337.5	0.336164
$154$	−29750.3	−0.101086
$155$	269446.	0.900830
$156$	−154517.	−0.508351
$157$	−24649.0	−0.0798087
$157$	−24649.0	−0.0798087
$158$	16026.1	0.0510724
$159$	6354.52	0.0199338
$160$	−104950.	−0.324101
$161$	−499059.	−1.51736
$162$	4031.36	0.0120688
$163$	68283.4	0.201301	0.100650	−	0.994922i	$-0.467908\pi$
$163$	68283.4	0.201301	0.100650	+	0.994922i	$0.467908\pi$
$164$	−178898.	−0.519393
$165$	175103.	0.500707
$166$	−35901.6	−0.101122
$167$	480226.	1.33246	0.666230	−	0.745746i	$-0.267907\pi$
$167$	480226.	1.33246	0.666230	+	0.745746i	$0.267907\pi$
$168$	−49458.1	−0.135196
$169$	−76529.3	−0.206116
$170$	−41708.1	−0.110687
$171$	−92178.7	−0.241068
$172$	−303315.	−0.781760
$173$	232724.	0.591188	0.295594	−	0.955314i	$-0.404482\pi$
$173$	232724.	0.591188	0.295594	+	0.955314i	$0.404482\pi$
$174$	−29348.3	−0.0734869
$175$	−9236.45	−0.0227987
$176$	340267.	0.828014
$177$	−35739.3	−0.0857459
$178$	10102.3	0.0238984
$179$	−16060.7	−0.0374656	−0.0187328	−	0.999825i	$-0.505963\pi$
$179$	−16060.7	−0.0374656	−0.0187328	+	0.999825i	$0.505963\pi$
$180$	144685.	0.332846
$181$	302428.	0.686161	0.343080	−	0.939306i	$-0.388530\pi$
$181$	302428.	0.686161	0.343080	+	0.939306i	$0.388530\pi$
$182$	46894.5	0.104941
$183$	407691.	0.899919
$184$	−138785.	−0.302202
$185$	−238789.	−0.512962
$186$	26378.7	0.0559076
$187$	413907.	0.865562
$188$	72348.1	0.149291
$189$	102478.	0.208678
$190$	39497.6	0.0793756
$191$	−406930.	−0.807116	−0.403558	−	0.914954i	$-0.632227\pi$
$191$	−406930.	−0.807116	−0.403558	+	0.914954i	$0.632227\pi$
$192$	274240.	0.536881
$193$	−722066.	−1.39535	−0.697676	−	0.716414i	$-0.745782\pi$
$193$	−722066.	−1.39535	−0.697676	+	0.716414i	$0.745782\pi$
$194$	−55262.3	−0.105420
$195$	−276009.	−0.519800
$196$	−93407.8	−0.173677
$197$	678698.	1.24598	0.622990	−	0.782230i	$-0.285918\pi$
$197$	678698.	1.24598	0.622990	+	0.782230i	$0.285918\pi$
$198$	17142.5	0.0310750
$199$	−735695.	−1.31694	−0.658469	−	0.752608i	$-0.728796\pi$
$199$	−735695.	−1.31694	−0.658469	+	0.752608i	$0.728796\pi$
$200$	−2568.59	−0.00454067
$201$	173165.	0.302322
$202$	20525.1	0.0353922
$203$	−746039.	−1.27064
$204$	342006.	0.575384
$205$	−319561.	−0.531091
$206$	−41945.3	−0.0688676
$207$	287564.	0.466454
$208$	−536351.	−0.859589
$209$	−391970.	−0.620707
$210$	−43910.7	−0.0687104
$211$	−98424.3	−0.152194	−0.0760968	−	0.997100i	$-0.524246\pi$
$211$	−98424.3	−0.152194	−0.0760968	+	0.997100i	$0.524246\pi$
$212$	22327.3	0.0341190
$213$	−498547.	−0.752934
$214$	94692.6	0.141345
$215$	−541804.	−0.799367
$216$	28498.4	0.0415610
$217$	670550.	0.966678
$218$	95255.7	0.135753
$219$	−69174.0	−0.0974614
$220$	615242.	0.857017
$221$	−652427.	−0.898569
$222$	−23377.4	−0.0318356
$223$	−1.26864e6	−1.70834	−0.854171	−	0.519992i	$-0.825935\pi$
$223$	−1.26864e6	−1.70834	−0.854171	+	0.519992i	$0.825935\pi$
$224$	−261180.	−0.347793
$225$	5322.15	0.00700860
$226$	−18189.8	−0.0236895
$227$	−263274.	−0.339112	−0.169556	−	0.985521i	$-0.554233\pi$
$227$	−263274.	−0.339112	−0.169556	+	0.985521i	$0.554233\pi$
$228$	−323880.	−0.412616
$229$	−950204.	−1.19737	−0.598685	−	0.800985i	$-0.704310\pi$
$229$	−950204.	−1.19737	−0.598685	+	0.800985i	$0.704310\pi$
$230$	−123218.	−0.153587
$231$	435765.	0.537307
$232$	−207468.	−0.253065
$233$	1.31533e6	1.58725	0.793626	−	0.608406i	$-0.208191\pi$
$233$	1.31533e6	1.58725	0.793626	+	0.608406i	$0.208191\pi$
$234$	−27021.2	−0.0322600
$235$	129233.	0.152653
$236$	−125574.	−0.146764
$237$	−234741.	−0.271468
$238$	−103796.	−0.118778
$239$	−1.53549e6	−1.73881	−0.869403	−	0.494104i	$-0.835496\pi$
$239$	−1.53549e6	−1.73881	−0.869403	+	0.494104i	$0.835496\pi$
$240$	502225.	0.562821
$241$	876339.	0.971918	0.485959	−	0.873982i	$-0.338470\pi$
$241$	876339.	0.971918	0.485959	+	0.873982i	$0.338470\pi$
$242$	−26062.0	−0.0286068
$243$	−59049.0	−0.0641500
$244$	1.43247e6	1.54032
$245$	−166852.	−0.177589
$246$	−31284.9	−0.0329607
$247$	617849.	0.644377
$248$	186475.	0.192527
$249$	525865.	0.537497
$250$	106181.	0.107448
$251$	295424.	0.295979	0.147990	−	0.988989i	$-0.452720\pi$
$251$	295424.	0.295979	0.147990	+	0.988989i	$0.452720\pi$
$252$	360067.	0.357176
$253$	1.22280e6	1.20103
$254$	−66209.5	−0.0643926
$255$	610915.	0.588343
$256$	927041.	0.884095
$257$	−867807.	−0.819578	−0.409789	−	0.912180i	$-0.634398\pi$
$257$	−867807.	−0.819578	−0.409789	+	0.912180i	$0.634398\pi$
$258$	−53042.4	−0.0496106
$259$	−594256.	−0.550458
$260$	−969786.	−0.889698
$261$	429877.	0.390609
$262$	−118886.	−0.106998
$263$	162256.	0.144648	0.0723239	−	0.997381i	$-0.476958\pi$
$263$	162256.	0.144648	0.0723239	+	0.997381i	$0.476958\pi$
$264$	121183.	0.107012
$265$	39882.6	0.0348874
$266$	98294.7	0.0851777
$267$	−147972.	−0.127028
$268$	608434.	0.517460
$269$	59710.7	0.0503119	0.0251560	−	0.999684i	$-0.491992\pi$
$269$	59710.7	0.0503119	0.0251560	+	0.999684i	$0.491992\pi$
$270$	25301.9	0.0211224
$271$	1.18076e6	0.976647	0.488324	−	0.872663i	$-0.337609\pi$
$271$	1.18076e6	0.976647	0.488324	+	0.872663i	$0.337609\pi$
$272$	1.18716e6	0.972938
$273$	−686882.	−0.557796
$274$	−23637.3	−0.0190205
$275$	22631.3	0.0180459
$276$	1.01039e6	0.798389
$277$	−638733.	−0.500172	−0.250086	−	0.968224i	$-0.580459\pi$
$277$	−638733.	−0.500172	−0.250086	+	0.968224i	$0.580459\pi$
$278$	−86268.6	−0.0669485
$279$	−386379.	−0.297169
$280$	−310412.	−0.236616
$281$	1.22272e6	0.923762	0.461881	−	0.886942i	$-0.347175\pi$
$281$	1.22272e6	0.923762	0.461881	+	0.886942i	$0.347175\pi$
$282$	12651.9	0.00947400
$283$	917909.	0.681292	0.340646	−	0.940192i	$-0.389354\pi$
$283$	917909.	0.681292	0.340646	+	0.940192i	$0.389354\pi$
$284$	−1.75170e6	−1.28873
$285$	−578537.	−0.421909
$286$	−114902.	−0.0830637
$287$	−795267.	−0.569912
$288$	150495.	0.106916
$289$	24219.7	0.0170579
$290$	−184198.	−0.128614
$291$	809449.	0.560347
$292$	−243050.	−0.166816
$293$	−2.27112e6	−1.54550	−0.772752	−	0.634708i	$-0.781120\pi$
$293$	−2.27112e6	−1.54550	−0.772752	+	0.634708i	$0.781120\pi$
$294$	−16334.7	−0.0110216
$295$	−224309.	−0.150069
$296$	−165258.	−0.109631
$297$	−251093.	−0.165175
$298$	41486.9	0.0270627
$299$	−1.92746e6	−1.24683
$300$	18700.0	0.0119960
$301$	−1.34835e6	−0.857799
$302$	287477.	0.181379
$303$	−300640.	−0.188122
$304$	−1.12424e6	−0.697708
$305$	2.55877e6	1.57501
$306$	59808.4	0.0365139
$307$	963006.	0.583154	0.291577	−	0.956547i	$-0.405820\pi$
$307$	963006.	0.583154	0.291577	+	0.956547i	$0.405820\pi$
$308$	1.53111e6	0.919663
$309$	614389.	0.366056
$310$	165559.	0.0978475
$311$	441991.	0.259127	0.129563	−	0.991571i	$-0.458642\pi$
$311$	441991.	0.259127	0.129563	+	0.991571i	$0.458642\pi$
$312$	−191017.	−0.111093
$313$	873569.	0.504007	0.252003	−	0.967726i	$-0.418911\pi$
$313$	873569.	0.504007	0.252003	+	0.967726i	$0.418911\pi$
$314$	−15145.4	−0.00866877
$315$	643178.	0.365220
$316$	−824789.	−0.464649
$317$	618512.	0.345700	0.172850	−	0.984948i	$-0.444702\pi$
$317$	618512.	0.345700	0.172850	+	0.984948i	$0.444702\pi$
$318$	3904.50	0.00216520
$319$	1.82796e6	1.00575
$320$	1.72120e6	0.939631
$321$	−1.38700e6	−0.751301
$322$	−306644.	−0.164814
$323$	−1.36754e6	−0.729347
$324$	−207475.	−0.109800
$325$	−35673.0	−0.0187340
$326$	41956.3	0.0218652
$327$	−1.39525e6	−0.721576
$328$	−221158.	−0.113506
$329$	321613.	0.163812
$330$	107591.	0.0543864
$331$	1.49070e6	0.747860	0.373930	−	0.927457i	$-0.378010\pi$
$331$	1.49070e6	0.747860	0.373930	+	0.927457i	$0.378010\pi$
$332$	1.84768e6	0.919988
$333$	342418.	0.169218
$334$	295072.	0.144731
$335$	1.08683e6	0.529114
$336$	1.24985e6	0.603962
$337$	3.78851e6	1.81716	0.908581	−	0.417708i	$-0.137167\pi$
$337$	3.78851e6	1.81716	0.908581	+	0.417708i	$0.137167\pi$
$338$	−47022.9	−0.0223881
$339$	266432.	0.125918
$340$	2.14652e6	1.00702
$341$	−1.64299e6	−0.765156
$342$	−56638.6	−0.0261847
$343$	1.94738e6	0.893750
$344$	−374966.	−0.170842
$345$	1.80483e6	0.816371
$346$	142996.	0.0642144
$347$	1.94084e6	0.865297	0.432649	−	0.901563i	$-0.357579\pi$
$347$	1.94084e6	0.865297	0.432649	+	0.901563i	$0.357579\pi$
$348$	1.51042e6	0.668573
$349$	249412.	0.109611	0.0548055	−	0.998497i	$-0.482546\pi$
$349$	249412.	0.109611	0.0548055	+	0.998497i	$0.482546\pi$
$350$	−5675.28	−0.00247638
$351$	395790.	0.171473
$352$	639948.	0.275289
$353$	−3.79350e6	−1.62033	−0.810165	−	0.586201i	$-0.800623\pi$
$353$	−3.79350e6	−1.62033	−0.810165	+	0.586201i	$0.800623\pi$
$354$	−21959.8	−0.00931366
$355$	−3.12901e6	−1.31776
$356$	−519914.	−0.217424
$357$	1.52034e6	0.631350
$358$	−9868.42	−0.00406949
$359$	−874422.	−0.358084	−0.179042	−	0.983841i	$-0.557300\pi$
$359$	−874422.	−0.358084	−0.179042	+	0.983841i	$0.557300\pi$
$360$	178863.	0.0727386
$361$	−1.18104e6	−0.476975
$362$	185825.	0.0745303
$363$	381740.	0.152055
$364$	−2.41343e6	−0.954733
$365$	−434154.	−0.170573
$366$	250503.	0.0977486
$367$	2.16264e6	0.838144	0.419072	−	0.907953i	$-0.362355\pi$
$367$	2.16264e6	0.838144	0.419072	+	0.907953i	$0.362355\pi$
$368$	3.50721e6	1.35003
$369$	458242.	0.175198
$370$	−146722.	−0.0557176
$371$	99252.9	0.0374376
$372$	−1.35758e6	−0.508639
$373$	318374.	0.118486	0.0592428	−	0.998244i	$-0.481131\pi$
$373$	318374.	0.118486	0.0592428	+	0.998244i	$0.481131\pi$
$374$	254322.	0.0940168
$375$	−1.55527e6	−0.571122
$376$	89438.4	0.0326253
$377$	−2.88135e6	−1.04410
$378$	62966.9	0.0226664
$379$	−1.96985e6	−0.704427	−0.352213	−	0.935920i	$-0.614571\pi$
$379$	−1.96985e6	−0.704427	−0.352213	+	0.935920i	$0.614571\pi$
$380$	−2.03275e6	−0.722147
$381$	969797.	0.342270
$382$	−250035.	−0.0876684
$383$	−939792.	−0.327367	−0.163684	−	0.986513i	$-0.552338\pi$
$383$	−939792.	−0.327367	−0.163684	+	0.986513i	$0.552338\pi$
$384$	703599.	0.243499
$385$	2.73497e6	0.940376
$386$	−443669.	−0.151562
$387$	776934.	0.263698
$388$	2.84409e6	0.959099
$389$	−3.98669e6	−1.33579	−0.667895	−	0.744255i	$-0.732805\pi$
$389$	−3.98669e6	−1.33579	−0.667895	+	0.744255i	$0.732805\pi$
$390$	−169592.	−0.0564603
$391$	4.26623e6	1.41125
$392$	−115473.	−0.0379547
$393$	1.74137e6	0.568734
$394$	417022.	0.135337
$395$	−1.47330e6	−0.475114
$396$	−882242.	−0.282716
$397$	48363.5	0.0154007	0.00770036	−	0.999970i	$-0.497549\pi$
$397$	48363.5	0.0154007	0.00770036	+	0.999970i	$0.497549\pi$
$398$	−452043.	−0.143045
$399$	−1.43976e6	−0.452750
$400$	64910.5	0.0202845
$401$	−1.10869e6	−0.344310	−0.172155	−	0.985070i	$-0.555073\pi$
$401$	−1.10869e6	−0.344310	−0.172155	+	0.985070i	$0.555073\pi$
$402$	106400.	0.0328380
$403$	2.58980e6	0.794334
$404$	−1.05633e6	−0.321993
$405$	−370607.	−0.112273
$406$	−458399.	−0.138016
$407$	1.45606e6	0.435705
$408$	422795.	0.125742
$409$	−871295.	−0.257547	−0.128774	−	0.991674i	$-0.541104\pi$
$409$	−871295.	−0.257547	−0.128774	+	0.991674i	$0.541104\pi$
$410$	−196352.	−0.0576867
$411$	346226.	0.101101
$412$	2.15872e6	0.626547
$413$	−558222.	−0.161039
$414$	176692.	0.0506659
$415$	3.30046e6	0.940708
$416$	−1.00873e6	−0.285786
$417$	1.26361e6	0.355855
$418$	−240843.	−0.0674208
$419$	−1.03894e6	−0.289105	−0.144552	−	0.989497i	$-0.546174\pi$
$419$	−1.03894e6	−0.289105	−0.144552	+	0.989497i	$0.546174\pi$
$420$	2.25987e6	0.625117
$421$	−4.23746e6	−1.16520	−0.582600	−	0.812759i	$-0.697964\pi$
$421$	−4.23746e6	−1.16520	−0.582600	+	0.812759i	$0.697964\pi$
$422$	−60476.2	−0.0165312
$423$	−185317.	−0.0503577
$424$	27601.5	0.00745621
$425$	78958.2	0.0212044
$426$	−306329.	−0.0817832
$427$	6.36783e6	1.69014
$428$	−4.87337e6	−1.28594
$429$	1.68301e6	0.441513
$430$	−332908.	−0.0868267
$431$	137045.	0.0355362	0.0177681	−	0.999842i	$-0.494344\pi$
$431$	137045.	0.0355362	0.0177681	+	0.999842i	$0.494344\pi$
$432$	−720178.	−0.185665
$433$	−3.25653e6	−0.834709	−0.417355	−	0.908744i	$-0.637043\pi$
$433$	−3.25653e6	−0.834709	−0.417355	+	0.908744i	$0.637043\pi$
$434$	412015.	0.105000
$435$	2.69802e6	0.683631
$436$	−4.90235e6	−1.23506
$437$	−4.04012e6	−1.01202
$438$	−42503.5	−0.0105862
$439$	−2.44288e6	−0.604980	−0.302490	−	0.953153i	$-0.597818\pi$
$439$	−2.44288e6	−0.604980	−0.302490	+	0.953153i	$0.597818\pi$
$440$	760577.	0.187289
$441$	239261.	0.0585836
$442$	−400880.	−0.0976020
$443$	5.34971e6	1.29515	0.647576	−	0.762001i	$-0.275783\pi$
$443$	5.34971e6	1.29515	0.647576	+	0.762001i	$0.275783\pi$
$444$	1.20312e6	0.289635
$445$	−928709.	−0.222321
$446$	−779506.	−0.185559
$447$	−607675.	−0.143848
$448$	4.28343e6	1.00832
$449$	−2.70070e6	−0.632208	−0.316104	−	0.948725i	$-0.602375\pi$
$449$	−2.70070e6	−0.632208	−0.316104	+	0.948725i	$0.602375\pi$
$450$	3270.16	0.000761269 0
$451$	1.94858e6	0.451103
$452$	936139.	0.215523
$453$	−4.21079e6	−0.964091
$454$	−161767.	−0.0368341
$455$	−4.31105e6	−0.976236
$456$	−400387.	−0.0901713
$457$	6.52433e6	1.46132	0.730660	−	0.682742i	$-0.239213\pi$
$457$	6.52433e6	1.46132	0.730660	+	0.682742i	$0.239213\pi$
$458$	−583847.	−0.130057
$459$	−876037.	−0.194085
$460$	6.34145e6	1.39731
$461$	7.60277e6	1.66617	0.833085	−	0.553144i	$-0.186572\pi$
$461$	7.60277e6	1.66617	0.833085	+	0.553144i	$0.186572\pi$
$462$	267753.	0.0583619
$463$	1.02732e6	0.222718	0.111359	−	0.993780i	$-0.464480\pi$
$463$	1.02732e6	0.222718	0.111359	+	0.993780i	$0.464480\pi$
$464$	5.24289e6	1.13051
$465$	−2.42501e6	−0.520094
$466$	808198.	0.172406
$467$	−4.17375e6	−0.885593	−0.442797	−	0.896622i	$-0.646014\pi$
$467$	−4.17375e6	−0.885593	−0.442797	+	0.896622i	$0.646014\pi$
$468$	1.39065e6	0.293497
$469$	2.70471e6	0.567791
$470$	79406.6	0.0165811
$471$	221841.	0.0460776
$472$	−155237.	−0.0320731
$473$	3.30374e6	0.678974
$474$	−144235.	−0.0294867
$475$	−74773.5	−0.0152060
$476$	5.34187e6	1.08063
$477$	−57190.7	−0.0115088
$478$	−943469.	−0.188868
$479$	1.99136e6	0.396562	0.198281	−	0.980145i	$-0.436464\pi$
$479$	1.99136e6	0.396562	0.198281	+	0.980145i	$0.436464\pi$
$480$	944547.	0.187120
$481$	−2.29513e6	−0.452319
$482$	538461.	0.105569
$483$	4.49153e6	0.876046
$484$	1.34128e6	0.260260
$485$	5.08031e6	0.980700
$486$	−36282.3	−0.00696793
$487$	−4.01402e6	−0.766932	−0.383466	−	0.923555i	$-0.625270\pi$
$487$	−4.01402e6	−0.766932	−0.383466	+	0.923555i	$0.625270\pi$
$488$	1.77085e6	0.336614
$489$	−614550.	−0.116221
$490$	−102521.	−0.0192896
$491$	−7.56267e6	−1.41570	−0.707851	−	0.706362i	$-0.750335\pi$
$491$	−7.56267e6	−1.41570	−0.707851	+	0.706362i	$0.750335\pi$
$492$	1.61008e6	0.299872
$493$	6.37755e6	1.18178
$494$	379633.	0.0699918
$495$	−1.57593e6	−0.289083
$496$	−4.71239e6	−0.860076
$497$	−7.78693e6	−1.41408
$498$	323114.	0.0583825
$499$	5.49280e6	0.987512	0.493756	−	0.869600i	$-0.335624\pi$
$499$	5.49280e6	0.987512	0.493756	+	0.869600i	$0.335624\pi$
$500$	−5.46462e6	−0.977542
$501$	−4.32203e6	−0.769296
$502$	181521.	0.0321490
$503$	1.40108e6	0.246913	0.123457	−	0.992350i	$-0.460602\pi$
$503$	1.40108e6	0.246913	0.123457	+	0.992350i	$0.460602\pi$
$504$	445123.	0.0780556
$505$	−1.88689e6	−0.329244
$506$	751344.	0.130455
$507$	688763.	0.119001
$508$	3.40748e6	0.585834
$509$	4.24891e6	0.726914	0.363457	−	0.931611i	$-0.381596\pi$
$509$	4.24891e6	0.726914	0.363457	+	0.931611i	$0.381596\pi$
$510$	375373.	0.0639054
$511$	−1.08045e6	−0.183042
$512$	3.07130e6	0.517783
$513$	829608.	0.139181
$514$	−533219.	−0.0890220
$515$	3.85607e6	0.640658
$516$	2.72984e6	0.451349
$517$	−788023.	−0.129662
$518$	−365137.	−0.0597904
$519$	−2.09451e6	−0.341323
$520$	−1.19887e6	−0.194431
$521$	−5.74220e6	−0.926796	−0.463398	−	0.886150i	$-0.653370\pi$
$521$	−5.74220e6	−0.926796	−0.463398	+	0.886150i	$0.653370\pi$
$522$	264135.	0.0424277
$523$	−8.93255e6	−1.42798	−0.713988	−	0.700158i	$-0.753113\pi$
$523$	−8.93255e6	−1.42798	−0.713988	+	0.700158i	$0.753113\pi$
$524$	6.11848e6	0.973454
$525$	83128.1	0.0131628
$526$	99697.3	0.0157115
$527$	−5.73223e6	−0.899077
$528$	−3.06240e6	−0.478054
$529$	6.16738e6	0.958211
$530$	24505.6	0.00378945
$531$	321654.	0.0495054
$532$	−5.05876e6	−0.774934
$533$	−3.07148e6	−0.468305
$534$	−90920.3	−0.0137977
$535$	−8.70517e6	−1.31490
$536$	752160.	0.113083
$537$	144547.	0.0216308
$538$	36688.8	0.00546485
$539$	1.01741e6	0.150842
$540$	−1.30217e6	−0.192168
$541$	−1.21222e7	−1.78069	−0.890347	−	0.455283i	$-0.849538\pi$
$541$	−1.21222e7	−1.78069	−0.890347	+	0.455283i	$0.849538\pi$
$542$	725509.	0.106083
$543$	−2.72185e6	−0.396155
$544$	2.23271e6	0.323471
$545$	−8.75694e6	−1.26288
$546$	−422050.	−0.0605875
$547$	−4.58544e6	−0.655259	−0.327630	−	0.944806i	$-0.606250\pi$
$547$	−4.58544e6	−0.655259	−0.327630	+	0.944806i	$0.606250\pi$
$548$	1.21650e6	0.173046
$549$	−3.66922e6	−0.519569
$550$	13905.7	0.00196013
$551$	−6.03954e6	−0.847472
$552$	1.24906e6	0.174476
$553$	−3.66648e6	−0.509844
$554$	−392465.	−0.0543284
$555$	2.14910e6	0.296159
$556$	4.43983e6	0.609087
$557$	72367.7	0.00988341	0.00494171	−	0.999988i	$-0.498427\pi$
$557$	72367.7	0.00988341	0.00494171	+	0.999988i	$0.498427\pi$
$558$	−237408.	−0.0322783
$559$	−5.20758e6	−0.704866
$560$	7.84438e6	1.05703
$561$	−3.72516e6	−0.499733
$562$	751291.	0.100338
$563$	−2.90372e6	−0.386086	−0.193043	−	0.981190i	$-0.561836\pi$
$563$	−2.90372e6	−0.386086	−0.193043	+	0.981190i	$0.561836\pi$
$564$	−651133.	−0.0861930
$565$	1.67220e6	0.220377
$566$	564003.	0.0740015
$567$	−922301.	−0.120480
$568$	−2.16549e6	−0.281634
$569$	−1.44699e7	−1.87363	−0.936816	−	0.349824i	$-0.886241\pi$
$569$	−1.44699e7	−1.87363	−0.936816	+	0.349824i	$0.886241\pi$
$570$	−355478.	−0.0458275
$571$	305861.	0.0392585	0.0196293	−	0.999807i	$-0.493751\pi$
$571$	305861.	0.0392585	0.0196293	+	0.999807i	$0.493751\pi$
$572$	5.91344e6	0.755701
$573$	3.66237e6	0.465989
$574$	−488647.	−0.0619035
$575$	233266.	0.0294227
$576$	−2.46816e6	−0.309968
$577$	−1.30522e7	−1.63209	−0.816045	−	0.577988i	$-0.803838\pi$
$577$	−1.30522e7	−1.63209	−0.816045	+	0.577988i	$0.803838\pi$
$578$	14881.6	0.00185281
$579$	6.49860e6	0.805607
$580$	9.47977e6	1.17011
$581$	8.21362e6	1.00947
$582$	497361.	0.0608645
$583$	−243191.	−0.0296330
$584$	−300464.	−0.0364553
$585$	2.48408e6	0.300107
$586$	−1.39547e6	−0.167872
$587$	−5.83915e6	−0.699447	−0.349723	−	0.936853i	$-0.613724\pi$
$587$	−5.83915e6	−0.699447	−0.349723	+	0.936853i	$0.613724\pi$
$588$	840671.	0.100273
$589$	5.42843e6	0.644742
$590$	−137825.	−0.0163004
$591$	−6.10828e6	−0.719367
$592$	4.17622e6	0.489755
$593$	4.87510e6	0.569307	0.284654	−	0.958630i	$-0.408121\pi$
$593$	4.87510e6	0.569307	0.284654	+	0.958630i	$0.408121\pi$
$594$	−154283.	−0.0179412
$595$	9.54204e6	1.10497
$596$	−2.13513e6	−0.246212
$597$	6.62126e6	0.760334
$598$	−1.18432e6	−0.135430
$599$	−1.44821e7	−1.64916	−0.824582	−	0.565743i	$-0.808590\pi$
$599$	−1.44821e7	−1.64916	−0.824582	+	0.565743i	$0.808590\pi$
$600$	23117.3	0.00262156
$601$	−1.46459e7	−1.65398	−0.826988	−	0.562219i	$-0.809948\pi$
$601$	−1.46459e7	−1.65398	−0.826988	+	0.562219i	$0.809948\pi$
$602$	−828483.	−0.0931735
$603$	−1.55849e6	−0.174546
$604$	−1.47951e7	−1.65015
$605$	2.39590e6	0.266122
$606$	−184726.	−0.0204337
$607$	−5.72602e6	−0.630785	−0.315392	−	0.948961i	$-0.602136\pi$
$607$	−5.72602e6	−0.630785	−0.315392	+	0.948961i	$0.602136\pi$
$608$	−2.11438e6	−0.231966
$609$	6.71435e6	0.733602
$610$	1.57222e6	0.171076
$611$	1.24213e6	0.134606
$612$	−3.07805e6	−0.332198
$613$	−9.47872e6	−1.01882	−0.509411	−	0.860523i	$-0.670137\pi$
$613$	−9.47872e6	−1.01882	−0.509411	+	0.860523i	$0.670137\pi$
$614$	591713.	0.0633417
$615$	2.87605e6	0.306625
$616$	1.89279e6	0.200979
$617$	−1.80423e7	−1.90800	−0.954000	−	0.299806i	$-0.903078\pi$
$617$	−1.80423e7	−1.90800	−0.954000	+	0.299806i	$0.903078\pi$
$618$	377508.	0.0397607
$619$	5.10552e6	0.535566	0.267783	−	0.963479i	$-0.413709\pi$
$619$	5.10552e6	0.535566	0.267783	+	0.963479i	$0.413709\pi$
$620$	−8.52055e6	−0.890201
$621$	−2.58808e6	−0.269307
$622$	271579.	0.0281462
$623$	−2.31121e6	−0.238572
$624$	4.82716e6	0.496284
$625$	−9.96664e6	−1.02058
$626$	536759.	0.0547449
$627$	3.52773e6	0.358366
$628$	779462.	0.0788671
$629$	5.08003e6	0.511964
$630$	395197.	0.0396700
$631$	−9.73882e6	−0.973717	−0.486858	−	0.873481i	$-0.661857\pi$
$631$	−9.73882e6	−0.973717	−0.486858	+	0.873481i	$0.661857\pi$
$632$	−1.01962e6	−0.101542
$633$	885819.	0.0878690
$634$	380041.	0.0375497
$635$	6.08670e6	0.599028
$636$	−200946.	−0.0196986
$637$	−1.60371e6	−0.156594
$638$	1.12318e6	0.109244
$639$	4.48692e6	0.434707
$640$	4.41597e6	0.426164
$641$	−6.96903e6	−0.669927	−0.334963	−	0.942231i	$-0.608724\pi$
$641$	−6.96903e6	−0.669927	−0.334963	+	0.942231i	$0.608724\pi$
$642$	−852233.	−0.0816058
$643$	−8.53787e6	−0.814370	−0.407185	−	0.913346i	$-0.633490\pi$
$643$	−8.53787e6	−0.814370	−0.407185	+	0.913346i	$0.633490\pi$
$644$	1.57815e7	1.49945
$645$	4.87624e6	0.461515
$646$	−840277.	−0.0792212
$647$	9.86040e6	0.926048	0.463024	−	0.886346i	$-0.346764\pi$
$647$	9.86040e6	0.926048	0.463024	+	0.886346i	$0.346764\pi$
$648$	−256485.	−0.0239952
$649$	1.36776e6	0.127468
$650$	−21919.0	−0.00203488
$651$	−6.03495e6	−0.558112
$652$	−2.15929e6	−0.198926
$653$	−9.68284e6	−0.888628	−0.444314	−	0.895871i	$-0.646552\pi$
$653$	−9.68284e6	−0.888628	−0.444314	+	0.895871i	$0.646552\pi$
$654$	−857302.	−0.0783771
$655$	1.09293e7	0.995378
$656$	5.58885e6	0.507064
$657$	622566.	0.0562694
$658$	197613.	0.0177931
$659$	−9.25872e6	−0.830496	−0.415248	−	0.909708i	$-0.636305\pi$
$659$	−9.25872e6	−0.830496	−0.415248	+	0.909708i	$0.636305\pi$
$660$	−5.53718e6	−0.494799
$661$	5.66019e6	0.503880	0.251940	−	0.967743i	$-0.418931\pi$
$661$	5.66019e6	0.503880	0.251940	+	0.967743i	$0.418931\pi$
$662$	915951.	0.0812321
$663$	5.87185e6	0.518789
$664$	2.28415e6	0.201050
$665$	−9.03632e6	−0.792387
$666$	210396.	0.0183803
$667$	1.88412e7	1.63981
$668$	−1.51859e7	−1.31674
$669$	1.14177e7	0.986312
$670$	667795.	0.0574720
$671$	−1.56026e7	−1.33780
$672$	2.35062e6	0.200798
$673$	−1.30413e7	−1.10990	−0.554949	−	0.831884i	$-0.687262\pi$
$673$	−1.30413e7	−1.10990	−0.554949	+	0.831884i	$0.687262\pi$
$674$	2.32783e6	0.197379
$675$	−47899.4	−0.00404642
$676$	2.42004e6	0.203684
$677$	7.00449e6	0.587361	0.293680	−	0.955904i	$-0.405120\pi$
$677$	7.00449e6	0.587361	0.293680	+	0.955904i	$0.405120\pi$
$678$	163708.	0.0136771
$679$	1.26430e7	1.05239
$680$	2.65357e6	0.220069
$681$	2.36946e6	0.195786
$682$	−1.00953e6	−0.0831107
$683$	−1.79286e7	−1.47060	−0.735299	−	0.677743i	$-0.762958\pi$
$683$	−1.79286e7	−1.47060	−0.735299	+	0.677743i	$0.762958\pi$
$684$	2.91492e6	0.238224
$685$	2.17300e6	0.176943
$686$	1.19656e6	0.0970785
$687$	8.55184e6	0.691302
$688$	9.47570e6	0.763203
$689$	383334.	0.0307630
$690$	1.10896e6	0.0886737
$691$	−1.01169e7	−0.806035	−0.403018	−	0.915192i	$-0.632039\pi$
$691$	−1.01169e7	−0.806035	−0.403018	+	0.915192i	$0.632039\pi$
$692$	−7.35930e6	−0.584213
$693$	−3.92189e6	−0.310214
$694$	1.19253e6	0.0939880
$695$	7.93074e6	0.622805
$696$	1.86721e6	0.146107
$697$	6.79838e6	0.530058
$698$	153250.	0.0119059
$699$	−1.18380e7	−0.916400
$700$	292079.	0.0225297
$701$	−4.39775e6	−0.338015	−0.169007	−	0.985615i	$-0.554056\pi$
$701$	−4.39775e6	−0.338015	−0.169007	+	0.985615i	$0.554056\pi$
$702$	243191.	0.0186253
$703$	−4.81079e6	−0.367137
$704$	−1.04953e7	−0.798113
$705$	−1.16310e6	−0.0881342
$706$	−2.33089e6	−0.175999
$707$	−4.69576e6	−0.353311
$708$	1.13017e6	0.0847343
$709$	1.79270e7	1.33934	0.669671	−	0.742658i	$-0.266435\pi$
$709$	1.79270e7	1.33934	0.669671	+	0.742658i	$0.266435\pi$
$710$	−1.92260e6	−0.143134
$711$	2.11267e6	0.156732
$712$	−642730.	−0.0475148
$713$	−1.69347e7	−1.24754
$714$	934163.	0.0685768
$715$	1.05630e7	0.772721
$716$	507880.	0.0370236
$717$	1.38194e7	1.00390
$718$	−537283.	−0.0388948
$719$	−2.48736e6	−0.179439	−0.0897196	−	0.995967i	$-0.528597\pi$
$719$	−2.48736e6	−0.179439	−0.0897196	+	0.995967i	$0.528597\pi$
$720$	−4.52002e6	−0.324945
$721$	9.59630e6	0.687489
$722$	−725680.	−0.0518087
$723$	−7.88705e6	−0.561137
$724$	−9.56353e6	−0.678065
$725$	348707.	0.0246386
$726$	234558.	0.0165161
$727$	1.11908e7	0.785279	0.392640	−	0.919692i	$-0.371562\pi$
$727$	1.11908e7	0.785279	0.392640	+	0.919692i	$0.371562\pi$
$728$	−2.98354e6	−0.208643
$729$	531441.	0.0370370
$730$	−266763.	−0.0185276
$731$	1.15264e7	0.797812
$732$	−1.28922e7	−0.889302
$733$	8.00809e6	0.550515	0.275257	−	0.961371i	$-0.411237\pi$
$733$	8.00809e6	0.550515	0.275257	+	0.961371i	$0.411237\pi$
$734$	1.32882e6	0.0910387
$735$	1.50167e6	0.102531
$736$	6.59610e6	0.448841
$737$	−6.62712e6	−0.449424
$738$	281564.	0.0190299
$739$	6.18443e6	0.416571	0.208285	−	0.978068i	$-0.433212\pi$
$739$	6.18443e6	0.416571	0.208285	+	0.978068i	$0.433212\pi$
$740$	7.55110e6	0.506910
$741$	−5.56064e6	−0.372031
$742$	60985.3	0.00406645
$743$	1.64958e7	1.09623	0.548113	−	0.836404i	$-0.315346\pi$
$743$	1.64958e7	1.09623	0.548113	+	0.836404i	$0.315346\pi$
$744$	−1.67828e6	−0.111156
$745$	−3.81393e6	−0.251757
$746$	195623.	0.0128698
$747$	−4.73278e6	−0.310324
$748$	−1.30887e7	−0.855350
$749$	−2.16639e7	−1.41102
$750$	−955629.	−0.0620349
$751$	−1.77128e7	−1.14601	−0.573003	−	0.819553i	$-0.694222\pi$
$751$	−1.77128e7	−1.14601	−0.573003	+	0.819553i	$0.694222\pi$
$752$	−2.26018e6	−0.145747
$753$	−2.65881e6	−0.170884
$754$	−1.77043e6	−0.113410
$755$	−2.64280e7	−1.68732
$756$	−3.24060e6	−0.206216
$757$	−5.07500e6	−0.321882	−0.160941	−	0.986964i	$-0.551453\pi$
$757$	−5.07500e6	−0.321882	−0.160941	+	0.986964i	$0.551453\pi$
$758$	−1.21036e6	−0.0765144
$759$	−1.10052e7	−0.693417
$760$	−2.51294e6	−0.157815
$761$	7.70337e6	0.482191	0.241095	−	0.970501i	$-0.422493\pi$
$761$	7.70337e6	0.482191	0.241095	+	0.970501i	$0.422493\pi$
$762$	595886.	0.0371771
$763$	−2.17927e7	−1.35519
$764$	1.28681e7	0.797593
$765$	−5.49824e6	−0.339680
$766$	−577449.	−0.0355584
$767$	−2.15596e6	−0.132328
$768$	−8.34337e6	−0.510432
$769$	−1.94770e7	−1.18770	−0.593849	−	0.804576i	$-0.702392\pi$
$769$	−1.94770e7	−1.18770	−0.593849	+	0.804576i	$0.702392\pi$
$770$	1.68049e6	0.102143
$771$	7.81026e6	0.473184
$772$	2.28335e7	1.37889
$773$	1.96554e7	1.18313	0.591564	−	0.806258i	$-0.298511\pi$
$773$	1.96554e7	1.18313	0.591564	+	0.806258i	$0.298511\pi$
$774$	477382.	0.0286427
$775$	−313423.	−0.0187446
$776$	3.51593e6	0.209597
$777$	5.34831e6	0.317807
$778$	−2.44960e6	−0.145093
$779$	−6.43807e6	−0.380112
$780$	8.72808e6	0.513667
$781$	1.90797e7	1.11929
$782$	2.62136e6	0.153289
$783$	−3.86889e6	−0.225518
$784$	2.91810e6	0.169555
$785$	1.39233e6	0.0806433
$786$	1.06997e6	0.0617755
$787$	−1.70676e6	−0.0982281	−0.0491140	−	0.998793i	$-0.515640\pi$
$787$	−1.70676e6	−0.0982281	−0.0491140	+	0.998793i	$0.515640\pi$
$788$	−2.14621e7	−1.23128
$789$	−1.46031e6	−0.0835125
$790$	−905258.	−0.0516065
$791$	4.16148e6	0.236486
$792$	−1.09065e6	−0.0617834
$793$	2.45938e7	1.38881
$794$	29716.6	0.00167282
$795$	−358944.	−0.0201423
$796$	2.32645e7	1.30140
$797$	6.14860e6	0.342871	0.171435	−	0.985195i	$-0.445160\pi$
$797$	6.14860e6	0.342871	0.171435	+	0.985195i	$0.445160\pi$
$798$	−884653.	−0.0491774
$799$	−2.74933e6	−0.152356
$800$	122079.	0.00674396
$801$	1.33175e6	0.0733398
$802$	−681229.	−0.0373987
$803$	2.64733e6	0.144883
$804$	−5.47591e6	−0.298755
$805$	2.81900e7	1.53322
$806$	1.59128e6	0.0862800
$807$	−537396.	−0.0290476
$808$	−1.30586e6	−0.0703668
$809$	2.45160e7	1.31698	0.658488	−	0.752592i	$-0.271196\pi$
$809$	2.45160e7	1.31698	0.658488	+	0.752592i	$0.271196\pi$
$810$	−227717.	−0.0121950
$811$	1.22682e7	0.654982	0.327491	−	0.944854i	$-0.393797\pi$
$811$	1.22682e7	0.654982	0.327491	+	0.944854i	$0.393797\pi$
$812$	2.35916e7	1.25565
$813$	−1.06268e7	−0.563868
$814$	894665.	0.0473259
$815$	−3.85708e6	−0.203406
$816$	−1.06844e7	−0.561726
$817$	−1.09155e7	−0.572123
$818$	−535362.	−0.0279746
$819$	6.18194e6	0.322044
$820$	1.01053e7	0.524825
$821$	−1.21032e7	−0.626674	−0.313337	−	0.949642i	$-0.601447\pi$
$821$	−1.21032e7	−0.626674	−0.313337	+	0.949642i	$0.601447\pi$
$822$	212736.	0.0109815
$823$	1.52695e7	0.785823	0.392911	−	0.919576i	$-0.371468\pi$
$823$	1.52695e7	0.785823	0.392911	+	0.919576i	$0.371468\pi$
$824$	2.66866e6	0.136923
$825$	−203682.	−0.0104188
$826$	−342996.	−0.0174920
$827$	7.12088e6	0.362051	0.181026	−	0.983478i	$-0.442058\pi$
$827$	7.12088e6	0.362051	0.181026	+	0.983478i	$0.442058\pi$
$828$	−9.09348e6	−0.460950
$829$	−3.88862e7	−1.96521	−0.982605	−	0.185709i	$-0.940542\pi$
$829$	−3.88862e7	−1.96521	−0.982605	+	0.185709i	$0.940542\pi$
$830$	2.02795e6	0.102179
$831$	5.74859e6	0.288775
$832$	1.65434e7	0.828547
$833$	3.54963e6	0.177243
$834$	776417.	0.0386527
$835$	−2.71262e7	−1.34639
$836$	1.23950e7	0.613384
$837$	3.47741e6	0.171570
$838$	−638370.	−0.0314023
$839$	1.23151e7	0.603992	0.301996	−	0.953309i	$-0.402347\pi$
$839$	1.23151e7	0.603992	0.301996	+	0.953309i	$0.402347\pi$
$840$	2.79371e6	0.136610
$841$	7.65435e6	0.373180
$842$	−2.60368e6	−0.126563
$843$	−1.10045e7	−0.533334
$844$	3.11242e6	0.150398
$845$	4.32286e6	0.208271
$846$	−113867.	−0.00546981
$847$	5.96249e6	0.285574
$848$	−697514.	−0.0333091
$849$	−8.26118e6	−0.393344
$850$	48515.4	0.00230320
$851$	1.50079e7	0.710389
$852$	1.57653e7	0.744051
$853$	1.66080e7	0.781527	0.390763	−	0.920491i	$-0.372211\pi$
$853$	1.66080e7	0.781527	0.390763	+	0.920491i	$0.372211\pi$
$854$	3.91267e6	0.183581
$855$	5.20683e6	0.243589
$856$	−6.02457e6	−0.281023
$857$	3.85279e7	1.79194	0.895969	−	0.444116i	$-0.146482\pi$
$857$	3.85279e7	1.79194	0.895969	+	0.444116i	$0.146482\pi$
$858$	1.03411e6	0.0479568
$859$	−2.42173e7	−1.11981	−0.559904	−	0.828558i	$-0.689162\pi$
$859$	−2.42173e7	−1.11981	−0.559904	+	0.828558i	$0.689162\pi$
$860$	1.71332e7	0.789936
$861$	7.15740e6	0.329039
$862$	84206.6	0.00385992
$863$	−2.38422e7	−1.08973	−0.544866	−	0.838523i	$-0.683420\pi$
$863$	−2.38422e7	−1.08973	−0.544866	+	0.838523i	$0.683420\pi$
$864$	−1.35446e6	−0.0617278
$865$	−1.31457e7	−0.597371
$866$	−2.00095e6	−0.0906655
$867$	−217977.	−0.00984836
$868$	−2.12044e7	−0.955273
$869$	8.98368e6	0.403557
$870$	1.65778e6	0.0742555
$871$	1.04461e7	0.466562
$872$	−6.06040e6	−0.269905
$873$	−7.28504e6	−0.323517
$874$	−2.48243e6	−0.109925
$875$	−2.42922e7	−1.07262
$876$	2.18745e6	0.0963115
$877$	−3.02587e7	−1.32847	−0.664234	−	0.747524i	$-0.731242\pi$
$877$	−3.02587e7	−1.32847	−0.664234	+	0.747524i	$0.731242\pi$
$878$	−1.50101e6	−0.0657125
$879$	2.04400e7	0.892297
$880$	−1.92204e7	−0.836674
$881$	1.03568e7	0.449557	0.224778	−	0.974410i	$-0.427834\pi$
$881$	1.03568e7	0.449557	0.224778	+	0.974410i	$0.427834\pi$
$882$	147013.	0.00636331
$883$	3.13258e7	1.35207	0.676036	−	0.736868i	$-0.263696\pi$
$883$	3.13258e7	1.35207	0.676036	+	0.736868i	$0.263696\pi$
$884$	2.06314e7	0.887968
$885$	2.01878e6	0.0866427
$886$	3.28709e6	0.140678
$887$	−2.57569e7	−1.09922	−0.549611	−	0.835421i	$-0.685224\pi$
$887$	−2.57569e7	−1.09922	−0.549611	+	0.835421i	$0.685224\pi$
$888$	1.48733e6	0.0632956
$889$	1.51475e7	0.642816
$890$	−570639.	−0.0241483
$891$	2.25984e6	0.0953637
$892$	4.01174e7	1.68819
$893$	2.60362e6	0.109257
$894$	−373382.	−0.0156246
$895$	907212.	0.0378574
$896$	1.09897e7	0.457315
$897$	1.73472e7	0.719860
$898$	−1.65943e6	−0.0686700
$899$	−2.53155e7	−1.04469
$900$	−168300.	−0.00692591
$901$	−848468.	−0.0348196
$902$	1.19729e6	0.0489985
$903$	1.21351e7	0.495250
$904$	1.15728e6	0.0470995
$905$	−1.70831e7	−0.693337
$906$	−2.58729e6	−0.104719
$907$	−2.94599e7	−1.18909	−0.594543	−	0.804064i	$-0.702667\pi$
$907$	−2.94599e7	−1.18909	−0.594543	+	0.804064i	$0.702667\pi$
$908$	8.32536e6	0.335111
$909$	2.70576e6	0.108612
$910$	−2.64890e6	−0.106038
$911$	4.73174e7	1.88897	0.944484	−	0.328557i	$-0.106562\pi$
$911$	4.73174e7	1.88897	0.944484	+	0.328557i	$0.106562\pi$
$912$	1.01181e7	0.402822
$913$	−2.01251e7	−0.799028
$914$	4.00883e6	0.158728
$915$	−2.30290e7	−0.909331
$916$	3.00478e7	1.18324
$917$	2.71989e7	1.06814
$918$	−538276.	−0.0210813
$919$	1.40506e7	0.548789	0.274394	−	0.961617i	$-0.411523\pi$
$919$	1.40506e7	0.548789	0.274394	+	0.961617i	$0.411523\pi$
$920$	7.83944e6	0.305362
$921$	−8.66705e6	−0.336684
$922$	4.67147e6	0.180978
$923$	−3.00746e7	−1.16197
$924$	−1.37800e7	−0.530968
$925$	277762.	0.0106738
$926$	631232.	0.0241914
$927$	−5.52950e6	−0.211342
$928$	9.86044e6	0.375860
$929$	1.56511e7	0.594984	0.297492	−	0.954724i	$-0.403850\pi$
$929$	1.56511e7	0.594984	0.297492	+	0.954724i	$0.403850\pi$
$930$	−1.49004e6	−0.0564923
$931$	−3.36150e6	−0.127104
$932$	−4.15940e7	−1.56852
$933$	−3.97792e6	−0.149607
$934$	−2.56453e6	−0.0961925
$935$	−2.33801e7	−0.874615
$936$	1.71915e6	0.0641394
$937$	−4.40124e7	−1.63767	−0.818835	−	0.574029i	$-0.805380\pi$
$937$	−4.40124e7	−1.63767	−0.818835	+	0.574029i	$0.805380\pi$
$938$	1.66189e6	0.0616731
$939$	−7.86212e6	−0.290988
$940$	−4.08668e6	−0.150852
$941$	5.03967e7	1.85536	0.927680	−	0.373377i	$-0.121800\pi$
$941$	5.03967e7	1.85536	0.927680	+	0.373377i	$0.121800\pi$
$942$	136309.	0.00500491
$943$	2.00844e7	0.735496
$944$	3.92298e6	0.143280
$945$	−5.78860e6	−0.210860
$946$	2.02996e6	0.0737497
$947$	4.88209e7	1.76901	0.884507	−	0.466527i	$-0.154495\pi$
$947$	4.88209e7	1.76901	0.884507	+	0.466527i	$0.154495\pi$
$948$	7.42310e6	0.268265
$949$	−4.17289e6	−0.150408
$950$	−45944.1	−0.00165166
$951$	−5.56661e6	−0.199590
$952$	6.60375e6	0.236155
$953$	−2.90983e6	−0.103785	−0.0518926	−	0.998653i	$-0.516525\pi$
$953$	−2.90983e6	−0.103785	−0.0518926	+	0.998653i	$0.516525\pi$
$954$	−35140.5	−0.00125008
$955$	2.29860e7	0.815557
$956$	4.85558e7	1.71829
$957$	−1.64516e7	−0.580669
$958$	1.22358e6	0.0430743
$959$	5.40778e6	0.189877
$960$	−1.54908e7	−0.542496
$961$	−5.87519e6	−0.205217
$962$	−1.41023e6	−0.0491306
$963$	1.24830e7	0.433764
$964$	−2.77120e7	−0.960451
$965$	4.07869e7	1.40994
$966$	2.75979e6	0.0951555
$967$	4.31477e7	1.48386	0.741928	−	0.670480i	$-0.233912\pi$
$967$	4.31477e7	1.48386	0.741928	+	0.670480i	$0.233912\pi$
$968$	1.65813e6	0.0568760
$969$	1.23079e7	0.421089
$970$	3.12157e6	0.106523
$971$	−3.68680e6	−0.125488	−0.0627439	−	0.998030i	$-0.519985\pi$
$971$	−3.68680e6	−0.125488	−0.0627439	+	0.998030i	$0.519985\pi$
$972$	1.86727e6	0.0633932
$973$	1.97366e7	0.668330
$974$	−2.46639e6	−0.0833036
$975$	321057.	0.0108161
$976$	−4.47508e7	−1.50375
$977$	9.86495e6	0.330642	0.165321	−	0.986240i	$-0.447134\pi$
$977$	9.86495e6	0.330642	0.165321	+	0.986240i	$0.447134\pi$
$978$	−377606.	−0.0126239
$979$	5.66296e6	0.188837
$980$	5.27627e6	0.175494
$981$	1.25572e7	0.416602
$982$	−4.64684e6	−0.153773
$983$	3.98220e7	1.31444	0.657218	−	0.753700i	$-0.271733\pi$
$983$	3.98220e7	1.31444	0.657218	+	0.753700i	$0.271733\pi$
$984$	1.99042e6	0.0655326
$985$	−3.83372e7	−1.25901
$986$	3.91865e6	0.128364
$987$	−2.89452e6	−0.0945766
$988$	−1.95379e7	−0.636775
$989$	3.40524e7	1.10703
$990$	−968317.	−0.0314000
$991$	−1.89214e6	−0.0612026	−0.0306013	−	0.999532i	$-0.509742\pi$
$991$	−1.89214e6	−0.0612026	−0.0306013	+	0.999532i	$0.509742\pi$
$992$	−8.86270e6	−0.285948
$993$	−1.34163e7	−0.431777
$994$	−4.78463e6	−0.153597
$995$	4.15567e7	1.33071
$996$	−1.66291e7	−0.531155
$997$	−1.15061e7	−0.366598	−0.183299	−	0.983057i	$-0.558678\pi$
$997$	−1.15061e7	−0.366598	−0.183299	+	0.983057i	$0.558678\pi$
$998$	3.37502e6	0.107263
$999$	−3.08176e6	−0.0976978

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.6.a.b.1.16	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.6.a.b.1.16	✓	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)

\(f(q)\)	\(=\)	\(q+0.614444 q^{2} -9.00000 q^{3} -31.6225 q^{4} -56.4863 q^{5} -5.52999 q^{6} -140.573 q^{7} -39.0924 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+0.614444 q^{2} -9.00000 q^{3} -31.6225 q^{4} -56.4863 q^{5} -5.52999 q^{6} -140.573 q^{7} -39.0924 q^{8} +81.0000 q^{9} -34.7077 q^{10} +344.435 q^{11} +284.602 q^{12} -542.921 q^{13} -86.3744 q^{14} +508.377 q^{15} +987.899 q^{16} +1201.70 q^{17} +49.7699 q^{18} -1138.01 q^{19} +1786.24 q^{20} +1265.16 q^{21} +211.636 q^{22} +3550.17 q^{23} +351.832 q^{24} +65.7056 q^{25} -333.595 q^{26} -729.000 q^{27} +4445.27 q^{28} +5307.12 q^{29} +312.369 q^{30} -4770.11 q^{31} +1857.97 q^{32} -3099.91 q^{33} +738.375 q^{34} +7940.47 q^{35} -2561.42 q^{36} +4227.38 q^{37} -699.242 q^{38} +4886.29 q^{39} +2208.19 q^{40} +5657.31 q^{41} +777.369 q^{42} +9591.77 q^{43} -10891.9 q^{44} -4575.39 q^{45} +2181.38 q^{46} -2287.87 q^{47} -8891.09 q^{48} +2953.84 q^{49} +40.3724 q^{50} -10815.3 q^{51} +17168.5 q^{52} -706.058 q^{53} -447.929 q^{54} -19455.9 q^{55} +5495.35 q^{56} +10242.1 q^{57} +3260.93 q^{58} +3971.04 q^{59} -16076.1 q^{60} -45299.0 q^{61} -2930.96 q^{62} -11386.4 q^{63} -30471.1 q^{64} +30667.6 q^{65} -1904.72 q^{66} -19240.6 q^{67} -38000.6 q^{68} -31951.5 q^{69} +4878.97 q^{70} +55394.1 q^{71} -3166.49 q^{72} +7686.00 q^{73} +2597.48 q^{74} -591.350 q^{75} +35986.6 q^{76} -48418.4 q^{77} +3002.35 q^{78} +26082.4 q^{79} -55802.8 q^{80} +6561.00 q^{81} +3476.10 q^{82} -58429.4 q^{83} -40007.5 q^{84} -67879.5 q^{85} +5893.61 q^{86} -47764.1 q^{87} -13464.8 q^{88} +16441.3 q^{89} -2811.32 q^{90} +76320.2 q^{91} -112265. q^{92} +42931.0 q^{93} -1405.77 q^{94} +64281.9 q^{95} -16721.7 q^{96} -89938.8 q^{97} +1814.97 q^{98} +27899.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9}+O(q^{10}) \) 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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