LMFDB - Embedded newform 471.6.a.b.1.13

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			1.13
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)

$f(q)$	$=$	$q-1.89378 q^{2} -9.00000 q^{3} -28.4136 q^{4} +13.1753 q^{5} +17.0440 q^{6} -20.4742 q^{7} +114.410 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-1.89378 q^{2} -9.00000 q^{3} -28.4136 q^{4} +13.1753 q^{5} +17.0440 q^{6} -20.4742 q^{7} +114.410 q^{8} +81.0000 q^{9} -24.9510 q^{10} -194.815 q^{11} +255.723 q^{12} -1005.72 q^{13} +38.7735 q^{14} -118.577 q^{15} +692.569 q^{16} +332.259 q^{17} -153.396 q^{18} +3039.12 q^{19} -374.357 q^{20} +184.268 q^{21} +368.935 q^{22} -524.947 q^{23} -1029.69 q^{24} -2951.41 q^{25} +1904.61 q^{26} -729.000 q^{27} +581.746 q^{28} +3255.11 q^{29} +224.559 q^{30} -2284.78 q^{31} -4972.68 q^{32} +1753.33 q^{33} -629.224 q^{34} -269.753 q^{35} -2301.50 q^{36} +1437.11 q^{37} -5755.41 q^{38} +9051.50 q^{39} +1507.38 q^{40} +21244.1 q^{41} -348.962 q^{42} +5570.15 q^{43} +5535.39 q^{44} +1067.20 q^{45} +994.131 q^{46} +16347.3 q^{47} -6233.12 q^{48} -16387.8 q^{49} +5589.31 q^{50} -2990.33 q^{51} +28576.2 q^{52} +26345.8 q^{53} +1380.56 q^{54} -2566.74 q^{55} -2342.45 q^{56} -27352.1 q^{57} -6164.46 q^{58} +23539.1 q^{59} +3369.21 q^{60} +17136.2 q^{61} +4326.87 q^{62} -1658.41 q^{63} -12745.1 q^{64} -13250.7 q^{65} -3320.42 q^{66} -33808.9 q^{67} -9440.68 q^{68} +4724.52 q^{69} +510.852 q^{70} -48999.9 q^{71} +9267.19 q^{72} +18191.0 q^{73} -2721.56 q^{74} +26562.7 q^{75} -86352.4 q^{76} +3988.68 q^{77} -17141.5 q^{78} -67008.1 q^{79} +9124.79 q^{80} +6561.00 q^{81} -40231.6 q^{82} -3208.20 q^{83} -5235.72 q^{84} +4377.61 q^{85} -10548.6 q^{86} -29296.0 q^{87} -22288.7 q^{88} -84484.8 q^{89} -2021.03 q^{90} +20591.4 q^{91} +14915.6 q^{92} +20563.1 q^{93} -30958.0 q^{94} +40041.3 q^{95} +44754.2 q^{96} +140586. q^{97} +31034.8 q^{98} -15780.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.89378	−0.334775	−0.167388	−	0.985891i	$-0.553533\pi$
$2$	−1.89378	−0.334775	−0.167388	+	0.985891i	$0.553533\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−28.4136	−0.887925
$5$	13.1753	0.235686	0.117843	−	0.993032i	$-0.462402\pi$
$5$	13.1753	0.235686	0.117843	+	0.993032i	$0.462402\pi$
$6$	17.0440	0.193283
$7$	−20.4742	−0.157929	−0.0789645	−	0.996877i	$-0.525161\pi$
$7$	−20.4742	−0.157929	−0.0789645	+	0.996877i	$0.525161\pi$
$8$	114.410	0.632031
$9$	81.0000	0.333333
$10$	−24.9510	−0.0789020
$11$	−194.815	−0.485445	−0.242723	−	0.970096i	$-0.578040\pi$
$11$	−194.815	−0.485445	−0.242723	+	0.970096i	$0.578040\pi$
$12$	255.723	0.512644
$13$	−1005.72	−1.65052	−0.825258	−	0.564756i	$-0.808970\pi$
$13$	−1005.72	−1.65052	−0.825258	+	0.564756i	$0.808970\pi$
$14$	38.7735	0.0528707
$15$	−118.577	−0.136074
$16$	692.569	0.676337
$17$	332.259	0.278840	0.139420	−	0.990233i	$-0.455476\pi$
$17$	332.259	0.278840	0.139420	+	0.990233i	$0.455476\pi$
$18$	−153.396	−0.111592
$19$	3039.12	1.93136	0.965682	−	0.259728i	$-0.0836329\pi$
$19$	3039.12	1.93136	0.965682	+	0.259728i	$0.0836329\pi$
$20$	−374.357	−0.209272
$21$	184.268	0.0911804
$22$	368.935	0.162515
$23$	−524.947	−0.206917	−0.103458	−	0.994634i	$-0.532991\pi$
$23$	−524.947	−0.206917	−0.103458	+	0.994634i	$0.532991\pi$
$24$	−1029.69	−0.364903
$25$	−2951.41	−0.944452
$26$	1904.61	0.552552
$27$	−729.000	−0.192450
$28$	581.746	0.140229
$29$	3255.11	0.718739	0.359370	−	0.933195i	$-0.382992\pi$
$29$	3255.11	0.718739	0.359370	+	0.933195i	$0.382992\pi$
$30$	224.559	0.0455541
$31$	−2284.78	−0.427013	−0.213506	−	0.976942i	$-0.568488\pi$
$31$	−2284.78	−0.427013	−0.213506	+	0.976942i	$0.568488\pi$
$32$	−4972.68	−0.858452
$33$	1753.33	0.280272
$34$	−629.224	−0.0933487
$35$	−269.753	−0.0372217
$36$	−2301.50	−0.295975
$37$	1437.11	0.172578	0.0862891	−	0.996270i	$-0.472499\pi$
$37$	1437.11	0.172578	0.0862891	+	0.996270i	$0.472499\pi$
$38$	−5755.41	−0.646573
$39$	9051.50	0.952926
$40$	1507.38	0.148961
$41$	21244.1	1.97369	0.986845	−	0.161668i	$-0.0516874\pi$
$41$	21244.1	1.97369	0.986845	+	0.161668i	$0.0516874\pi$
$42$	−348.962	−0.0305249
$43$	5570.15	0.459405	0.229703	−	0.973261i	$-0.426225\pi$
$43$	5570.15	0.459405	0.229703	+	0.973261i	$0.426225\pi$
$44$	5535.39	0.431039
$45$	1067.20	0.0785622
$46$	994.131	0.0692706
$47$	16347.3	1.07944	0.539722	−	0.841843i	$-0.318529\pi$
$47$	16347.3	1.07944	0.539722	+	0.841843i	$0.318529\pi$
$48$	−6233.12	−0.390483
$49$	−16387.8	−0.975058
$50$	5589.31	0.316179
$51$	−2990.33	−0.160988
$52$	28576.2	1.46553
$53$	26345.8	1.28832	0.644158	−	0.764893i	$-0.277208\pi$
$53$	26345.8	1.28832	0.644158	+	0.764893i	$0.277208\pi$
$54$	1380.56	0.0644275
$55$	−2566.74	−0.114413
$56$	−2342.45	−0.0998160
$57$	−27352.1	−1.11507
$58$	−6164.46	−0.240616
$59$	23539.1	0.880359	0.440180	−	0.897910i	$-0.354915\pi$
$59$	23539.1	0.880359	0.440180	+	0.897910i	$0.354915\pi$
$60$	3369.21	0.120823
$61$	17136.2	0.589646	0.294823	−	0.955552i	$-0.404739\pi$
$61$	17136.2	0.589646	0.294823	+	0.955552i	$0.404739\pi$
$62$	4326.87	0.142953
$63$	−1658.41	−0.0526430
$64$	−12745.1	−0.388949
$65$	−13250.7	−0.389004
$66$	−3320.42	−0.0938281
$67$	−33808.9	−0.920119	−0.460059	−	0.887888i	$-0.652172\pi$
$67$	−33808.9	−0.920119	−0.460059	+	0.887888i	$0.652172\pi$
$68$	−9440.68	−0.247589
$69$	4724.52	0.119463
$70$	510.852	0.0124609
$71$	−48999.9	−1.15358	−0.576792	−	0.816891i	$-0.695696\pi$
$71$	−48999.9	−1.15358	−0.576792	+	0.816891i	$0.695696\pi$
$72$	9267.19	0.210677
$73$	18191.0	0.399529	0.199765	−	0.979844i	$-0.435982\pi$
$73$	18191.0	0.399529	0.199765	+	0.979844i	$0.435982\pi$
$74$	−2721.56	−0.0577749
$75$	26562.7	0.545280
$76$	−86352.4	−1.71491
$77$	3988.68	0.0766659
$78$	−17141.5	−0.319016
$79$	−67008.1	−1.20798	−0.603990	−	0.796992i	$-0.706423\pi$
$79$	−67008.1	−1.20798	−0.603990	+	0.796992i	$0.706423\pi$
$80$	9124.79	0.159404
$81$	6561.00	0.111111
$82$	−40231.6	−0.660743
$83$	−3208.20	−0.0511171	−0.0255585	−	0.999673i	$-0.508136\pi$
$83$	−3208.20	−0.0511171	−0.0255585	+	0.999673i	$0.508136\pi$
$84$	−5235.72	−0.0809614
$85$	4377.61	0.0657188
$86$	−10548.6	−0.153798
$87$	−29296.0	−0.414964
$88$	−22288.7	−0.306816
$89$	−84484.8	−1.13059	−0.565293	−	0.824890i	$-0.691237\pi$
$89$	−84484.8	−1.13059	−0.565293	+	0.824890i	$0.691237\pi$
$90$	−2021.03	−0.0263007
$91$	20591.4	0.260664
$92$	14915.6	0.183727
$93$	20563.1	0.246536
$94$	−30958.0	−0.361371
$95$	40041.3	0.455196
$96$	44754.2	0.495627
$97$	140586.	1.51709	0.758546	−	0.651619i	$-0.225910\pi$
$97$	140586.	1.51709	0.758546	+	0.651619i	$0.225910\pi$
$98$	31034.8	0.326426
$99$	−15780.0	−0.161815
$100$	83860.3	0.838603
$101$	−31427.1	−0.306549	−0.153275	−	0.988184i	$-0.548982\pi$
$101$	−31427.1	−0.306549	−0.153275	+	0.988184i	$0.548982\pi$
$102$	5663.02	0.0538949
$103$	72536.4	0.673695	0.336847	−	0.941559i	$-0.390639\pi$
$103$	72536.4	0.673695	0.336847	+	0.941559i	$0.390639\pi$
$104$	−115064.	−1.04318
$105$	2427.78	0.0214900
$106$	−49893.1	−0.431296
$107$	−182154.	−1.53808	−0.769041	−	0.639200i	$-0.779266\pi$
$107$	−182154.	−1.53808	−0.769041	+	0.639200i	$0.779266\pi$
$108$	20713.5	0.170881
$109$	−149366.	−1.20416	−0.602082	−	0.798434i	$-0.705662\pi$
$109$	−149366.	−1.20416	−0.602082	+	0.798434i	$0.705662\pi$
$110$	4860.82	0.0383026
$111$	−12934.0	−0.0996381
$112$	−14179.8	−0.106813
$113$	7988.33	0.0588518	0.0294259	−	0.999567i	$-0.490632\pi$
$113$	7988.33	0.0588518	0.0294259	+	0.999567i	$0.490632\pi$
$114$	51798.7	0.373299
$115$	−6916.32	−0.0487675
$116$	−92489.6	−0.638187
$117$	−81463.5	−0.550172
$118$	−44577.8	−0.294723
$119$	−6802.74	−0.0440369
$120$	−13566.4	−0.0860028
$121$	−123098.	−0.764343
$122$	−32452.2	−0.197399
$123$	−191197.	−1.13951
$124$	64919.0	0.379156
$125$	−80058.4	−0.458281
$126$	3140.66	0.0176236
$127$	−261795.	−1.44030	−0.720148	−	0.693821i	$-0.755926\pi$
$127$	−261795.	−1.44030	−0.720148	+	0.693821i	$0.755926\pi$
$128$	183262.	0.988662
$129$	−50131.4	−0.265238
$130$	25093.8	0.130229
$131$	−104945.	−0.534297	−0.267149	−	0.963655i	$-0.586081\pi$
$131$	−104945.	−0.534297	−0.267149	+	0.963655i	$0.586081\pi$
$132$	−49818.5	−0.248861
$133$	−62223.6	−0.305018
$134$	64026.4	0.308033
$135$	−9604.78	−0.0453579
$136$	38013.7	0.176235
$137$	115165.	0.524225	0.262113	−	0.965037i	$-0.415581\pi$
$137$	115165.	0.524225	0.262113	+	0.965037i	$0.415581\pi$
$138$	−8947.18	−0.0399934
$139$	−170947.	−0.750457	−0.375228	−	0.926932i	$-0.622436\pi$
$139$	−170947.	−0.750457	−0.375228	+	0.926932i	$0.622436\pi$
$140$	7664.67	0.0330501
$141$	−147125.	−0.623218
$142$	92794.8	0.386192
$143$	195930.	0.801235
$144$	56098.1	0.225446
$145$	42887.0	0.169397
$146$	−34449.6	−0.133753
$147$	147490.	0.562950
$148$	−40833.5	−0.153237
$149$	−291331.	−1.07503	−0.537515	−	0.843254i	$-0.680637\pi$
$149$	−291331.	−1.07503	−0.537515	+	0.843254i	$0.680637\pi$
$150$	−50303.8	−0.182546
$151$	−161094.	−0.574959	−0.287479	−	0.957787i	$-0.592817\pi$
$151$	−161094.	−0.574959	−0.287479	+	0.957787i	$0.592817\pi$
$152$	347705.	1.22068
$153$	26913.0	0.0929466
$154$	−7553.66	−0.0256658
$155$	−30102.7	−0.100641
$156$	−257186.	−0.846127
$157$	−24649.0	−0.0798087
$157$	−24649.0	−0.0798087
$158$	126898.	0.404402
$159$	−237112.	−0.743809
$160$	−65516.5	−0.202326
$161$	10747.9	0.0326782
$162$	−12425.1	−0.0371973
$163$	−451107.	−1.32988	−0.664938	−	0.746899i	$-0.731542\pi$
$163$	−451107.	−1.32988	−0.664938	+	0.746899i	$0.731542\pi$
$164$	−603622.	−1.75249
$165$	23100.6	0.0660563
$166$	6075.61	0.0171127
$167$	61323.1	0.170151	0.0850753	−	0.996375i	$-0.472887\pi$
$167$	61323.1	0.170151	0.0850753	+	0.996375i	$0.472887\pi$
$168$	21082.1	0.0576288
$169$	640184.	1.72420
$170$	−8290.20	−0.0220010
$171$	246169.	0.643788
$172$	−158268.	−0.407918
$173$	401201.	1.01917	0.509585	−	0.860420i	$-0.329799\pi$
$173$	401201.	1.01917	0.509585	+	0.860420i	$0.329799\pi$
$174$	55480.1	0.138920
$175$	60427.8	0.149156
$176$	−134923.	−0.328325
$177$	−211852.	−0.508276
$178$	159995.	0.378492
$179$	−240543.	−0.561127	−0.280563	−	0.959835i	$-0.590521\pi$
$179$	−240543.	−0.561127	−0.280563	+	0.959835i	$0.590521\pi$
$180$	−30322.9	−0.0697573
$181$	−27585.3	−0.0625865	−0.0312932	−	0.999510i	$-0.509963\pi$
$181$	−27585.3	−0.0625865	−0.0312932	+	0.999510i	$0.509963\pi$
$182$	−38995.4	−0.0872640
$183$	−154226.	−0.340432
$184$	−60059.0	−0.130778
$185$	18934.3	0.0406743
$186$	−38941.8	−0.0825342
$187$	−64729.0	−0.135361
$188$	−464485.	−0.958466
$189$	14925.7	0.0303935
$190$	−75829.1	−0.152388
$191$	35205.8	0.0698281	0.0349141	−	0.999390i	$-0.488884\pi$
$191$	35205.8	0.0698281	0.0349141	+	0.999390i	$0.488884\pi$
$192$	114706.	0.224560
$193$	982772.	1.89915	0.949576	−	0.313538i	$-0.101514\pi$
$193$	982772.	1.89915	0.949576	+	0.313538i	$0.101514\pi$
$194$	−266238.	−0.507885
$195$	119256.	0.224592
$196$	465637.	0.865779
$197$	−786773.	−1.44439	−0.722194	−	0.691691i	$-0.756866\pi$
$197$	−786773.	−1.44439	−0.722194	+	0.691691i	$0.756866\pi$
$198$	29883.8	0.0541717
$199$	266278.	0.476653	0.238326	−	0.971185i	$-0.423401\pi$
$199$	266278.	0.476653	0.238326	+	0.971185i	$0.423401\pi$
$200$	−337670.	−0.596923
$201$	304280.	0.531231
$202$	59515.8	0.102625
$203$	−66645.9	−0.113510
$204$	84966.2	0.142946
$205$	279897.	0.465172
$206$	−137368.	−0.225536
$207$	−42520.7	−0.0689722
$208$	−696532.	−1.11631
$209$	−592066.	−0.937571
$210$	−4597.67	−0.00719432
$211$	−226234.	−0.349825	−0.174913	−	0.984584i	$-0.555964\pi$
$211$	−226234.	−0.349825	−0.174913	+	0.984584i	$0.555964\pi$
$212$	−748580.	−1.14393
$213$	440999.	0.666022
$214$	344959.	0.514912
$215$	73388.3	0.108276
$216$	−83404.8	−0.121634
$217$	46779.1	0.0674377
$218$	282866.	0.403125
$219$	−163719.	−0.230668
$220$	72930.3	0.101590
$221$	−334160.	−0.460229
$222$	24494.1	0.0333564
$223$	614136.	0.826995	0.413497	−	0.910505i	$-0.364307\pi$
$223$	614136.	0.826995	0.413497	+	0.910505i	$0.364307\pi$
$224$	101812.	0.135574
$225$	−239064.	−0.314817
$226$	−15128.1	−0.0197021
$227$	234165.	0.301617	0.150809	−	0.988563i	$-0.451812\pi$
$227$	234165.	0.301617	0.150809	+	0.988563i	$0.451812\pi$
$228$	777172.	0.990102
$229$	−680622.	−0.857664	−0.428832	−	0.903384i	$-0.641075\pi$
$229$	−680622.	−0.857664	−0.428832	+	0.903384i	$0.641075\pi$
$230$	13097.9	0.0163261
$231$	−35898.1	−0.0442631
$232$	372417.	0.454265
$233$	−1.09501e6	−1.32139	−0.660693	−	0.750656i	$-0.729738\pi$
$233$	−1.09501e6	−1.32139	−0.660693	+	0.750656i	$0.729738\pi$
$234$	154274.	0.184184
$235$	215380.	0.254411
$236$	−668831.	−0.781694
$237$	603073.	0.697427
$238$	12882.9	0.0147425
$239$	158044.	0.178972	0.0894858	−	0.995988i	$-0.471478\pi$
$239$	158044.	0.178972	0.0894858	+	0.995988i	$0.471478\pi$
$240$	−82123.1	−0.0920317
$241$	460065.	0.510242	0.255121	−	0.966909i	$-0.417885\pi$
$241$	460065.	0.510242	0.255121	+	0.966909i	$0.417885\pi$
$242$	233120.	0.255883
$243$	−59049.0	−0.0641500
$244$	−486903.	−0.523561
$245$	−215914.	−0.229808
$246$	362084.	0.381480
$247$	−3.05651e6	−3.18775
$248$	−261402.	−0.269885
$249$	28873.8	0.0295125
$250$	151613.	0.153421
$251$	−566029.	−0.567093	−0.283546	−	0.958958i	$-0.591511\pi$
$251$	−566029.	−0.567093	−0.283546	+	0.958958i	$0.591511\pi$
$252$	47121.4	0.0467431
$253$	102267.	0.100447
$254$	495780.	0.482175
$255$	−39398.5	−0.0379427
$256$	60784.8	0.0579689
$257$	−925531.	−0.874094	−0.437047	−	0.899439i	$-0.643976\pi$
$257$	−925531.	−0.874094	−0.437047	+	0.899439i	$0.643976\pi$
$258$	94937.6	0.0887951
$259$	−29423.7	−0.0272551
$260$	376499.	0.345407
$261$	263664.	0.239580
$262$	198742.	0.178870
$263$	2.06549e6	1.84134	0.920671	−	0.390340i	$-0.127642\pi$
$263$	2.06549e6	1.84134	0.920671	+	0.390340i	$0.127642\pi$
$264$	200598.	0.177140
$265$	347114.	0.303639
$266$	117838.	0.102113
$267$	760363.	0.652744
$268$	960633.	0.816997
$269$	−1.97341e6	−1.66279	−0.831393	−	0.555685i	$-0.812456\pi$
$269$	−1.97341e6	−1.66279	−0.831393	+	0.555685i	$0.812456\pi$
$270$	18189.3	0.0151847
$271$	1.59177e6	1.31661	0.658303	−	0.752753i	$-0.271274\pi$
$271$	1.59177e6	1.31661	0.658303	+	0.752753i	$0.271274\pi$
$272$	230112.	0.188590
$273$	−185322.	−0.150495
$274$	−218096.	−0.175498
$275$	574979.	0.458480
$276$	−134241.	−0.106075
$277$	1.25322e6	0.981361	0.490680	−	0.871340i	$-0.336748\pi$
$277$	1.25322e6	0.981361	0.490680	+	0.871340i	$0.336748\pi$
$278$	323736.	0.251234
$279$	−185068.	−0.142338
$280$	−30862.4	−0.0235253
$281$	−1.24950e6	−0.943996	−0.471998	−	0.881600i	$-0.656467\pi$
$281$	−1.24950e6	−0.943996	−0.471998	+	0.881600i	$0.656467\pi$
$282$	278622.	0.208638
$283$	459135.	0.340780	0.170390	−	0.985377i	$-0.445497\pi$
$283$	459135.	0.340780	0.170390	+	0.985377i	$0.445497\pi$
$284$	1.39226e6	1.02430
$285$	−360371.	−0.262808
$286$	−371046.	−0.268234
$287$	−434956.	−0.311703
$288$	−402787.	−0.286151
$289$	−1.30946e6	−0.922248
$290$	−81218.4	−0.0567100
$291$	−1.26527e6	−0.875894
$292$	−516871.	−0.354752
$293$	−1.07510e6	−0.731611	−0.365806	−	0.930691i	$-0.619207\pi$
$293$	−1.07510e6	−0.731611	−0.365806	+	0.930691i	$0.619207\pi$
$294$	−279313.	−0.188462
$295$	310134.	0.207489
$296$	164420.	0.109075
$297$	142020.	0.0934240
$298$	551715.	0.359894
$299$	527950.	0.341519
$300$	−754743.	−0.484168
$301$	−114044.	−0.0725534
$302$	305076.	0.192482
$303$	282843.	0.176986
$304$	2.10480e6	1.30625
$305$	225775.	0.138972
$306$	−50967.2	−0.0311162
$307$	2.05471e6	1.24424	0.622122	−	0.782920i	$-0.286271\pi$
$307$	2.05471e6	1.24424	0.622122	+	0.782920i	$0.286271\pi$
$308$	−113333.	−0.0680736
$309$	−652828.	−0.388958
$310$	57007.7	0.0336922
$311$	1.21819e6	0.714189	0.357095	−	0.934068i	$-0.383767\pi$
$311$	1.21819e6	0.714189	0.357095	+	0.934068i	$0.383767\pi$
$312$	1.03558e6	0.602278
$313$	−2.93385e6	−1.69269	−0.846345	−	0.532636i	$-0.821202\pi$
$313$	−2.93385e6	−1.69269	−0.846345	+	0.532636i	$0.821202\pi$
$314$	46679.7	0.0267180
$315$	−21850.0	−0.0124072
$316$	1.90394e6	1.07260
$317$	−1.51672e6	−0.847727	−0.423864	−	0.905726i	$-0.639326\pi$
$317$	−1.51672e6	−0.847727	−0.423864	+	0.905726i	$0.639326\pi$
$318$	449038.	0.249009
$319$	−634144.	−0.348908
$320$	−167920.	−0.0916699
$321$	1.63939e6	0.888012
$322$	−20354.0	−0.0109398
$323$	1.00978e6	0.538541
$324$	−186422.	−0.0986584
$325$	2.96830e6	1.55883
$326$	854296.	0.445209
$327$	1.34430e6	0.695225
$328$	2.43054e6	1.24743
$329$	−334697.	−0.170476
$330$	−43747.4	−0.0221140
$331$	1.51894e6	0.762026	0.381013	−	0.924570i	$-0.375575\pi$
$331$	1.51894e6	0.762026	0.381013	+	0.924570i	$0.375575\pi$
$332$	91156.5	0.0453881
$333$	116406.	0.0575261
$334$	−116132.	−0.0569622
$335$	−445441.	−0.216860
$336$	127618.	0.0616687
$337$	−829411.	−0.397828	−0.198914	−	0.980017i	$-0.563741\pi$
$337$	−829411.	−0.397828	−0.198914	+	0.980017i	$0.563741\pi$
$338$	−1.21236e6	−0.577220
$339$	−71895.0	−0.0339781
$340$	−124384.	−0.0583534
$341$	445110.	0.207291
$342$	−466188.	−0.215524
$343$	679637.	0.311919
$344$	637280.	0.290358
$345$	62246.8	0.0281559
$346$	−759784.	−0.341193
$347$	2.39950e6	1.06978	0.534892	−	0.844920i	$-0.320352\pi$
$347$	2.39950e6	1.06978	0.534892	+	0.844920i	$0.320352\pi$
$348$	832406.	0.368457
$349$	747194.	0.328375	0.164187	−	0.986429i	$-0.447500\pi$
$349$	747194.	0.328375	0.164187	+	0.986429i	$0.447500\pi$
$350$	−114437.	−0.0499339
$351$	733172.	0.317642
$352$	968752.	0.416731
$353$	−3.97380e6	−1.69734	−0.848671	−	0.528921i	$-0.822597\pi$
$353$	−3.97380e6	−1.69734	−0.848671	+	0.528921i	$0.822597\pi$
$354$	401200.	0.170158
$355$	−645587.	−0.271884
$356$	2.40052e6	1.00388
$357$	61224.7	0.0254247
$358$	455535.	0.187851
$359$	−3.26776e6	−1.33818	−0.669090	−	0.743182i	$-0.733316\pi$
$359$	−3.26776e6	−1.33818	−0.669090	+	0.743182i	$0.733316\pi$
$360$	122098.	0.0496537
$361$	6.76016e6	2.73017
$362$	52240.3	0.0209524
$363$	1.10788e6	0.441294
$364$	−585075.	−0.231451
$365$	239671.	0.0941637
$366$	292070.	0.113968
$367$	3.07881e6	1.19321	0.596606	−	0.802535i	$-0.296516\pi$
$367$	3.07881e6	1.19321	0.596606	+	0.802535i	$0.296516\pi$
$368$	−363562.	−0.139945
$369$	1.72077e6	0.657897
$370$	−35857.4	−0.0136168
$371$	−539410.	−0.203462
$372$	−584271.	−0.218906
$373$	330917.	0.123153	0.0615767	−	0.998102i	$-0.480387\pi$
$373$	330917.	0.123153	0.0615767	+	0.998102i	$0.480387\pi$
$374$	122582.	0.0453157
$375$	720526.	0.264589
$376$	1.87029e6	0.682242
$377$	−3.27374e6	−1.18629
$378$	−28265.9	−0.0101750
$379$	−1.76494e6	−0.631148	−0.315574	−	0.948901i	$-0.602197\pi$
$379$	−1.76494e6	−0.631148	−0.315574	+	0.948901i	$0.602197\pi$
$380$	−1.13772e6	−0.404180
$381$	2.35615e6	0.831555
$382$	−66671.8	−0.0233767
$383$	2.33279e6	0.812602	0.406301	−	0.913739i	$-0.366818\pi$
$383$	2.33279e6	0.812602	0.406301	+	0.913739i	$0.366818\pi$
$384$	−1.64936e6	−0.570804
$385$	52551.9	0.0180691
$386$	−1.86115e6	−0.635789
$387$	451182.	0.153135
$388$	−3.99455e6	−1.34707
$389$	4.54868e6	1.52409	0.762047	−	0.647522i	$-0.224195\pi$
$389$	4.54868e6	1.52409	0.762047	+	0.647522i	$0.224195\pi$
$390$	−225844.	−0.0751878
$391$	−174418.	−0.0576966
$392$	−1.87493e6	−0.616267
$393$	944504.	0.308477
$394$	1.48997e6	0.483545
$395$	−882850.	−0.284704
$396$	448367.	0.143680
$397$	628207.	0.200044	0.100022	−	0.994985i	$-0.468109\pi$
$397$	628207.	0.200044	0.100022	+	0.994985i	$0.468109\pi$
$398$	−504270.	−0.159572
$399$	560012.	0.176102
$400$	−2.04406e6	−0.638768
$401$	−2.79041e6	−0.866576	−0.433288	−	0.901255i	$-0.642647\pi$
$401$	−2.79041e6	−0.866576	−0.433288	+	0.901255i	$0.642647\pi$
$402$	−576238.	−0.177843
$403$	2.29786e6	0.704791
$404$	892956.	0.272193
$405$	86443.0	0.0261874
$406$	126212.	0.0380003
$407$	−279970.	−0.0837772
$408$	−342123.	−0.101750
$409$	−1.77436e6	−0.524487	−0.262243	−	0.965002i	$-0.584462\pi$
$409$	−1.77436e6	−0.524487	−0.262243	+	0.965002i	$0.584462\pi$
$410$	−530062.	−0.155728
$411$	−1.03648e6	−0.302662
$412$	−2.06102e6	−0.598191
$413$	−481945.	−0.139034
$414$	80524.6	0.0230902
$415$	−42268.9	−0.0120476
$416$	5.00114e6	1.41689
$417$	1.53853e6	0.433276
$418$	1.12124e6	0.313876
$419$	−1.39496e6	−0.388173	−0.194086	−	0.980984i	$-0.562174\pi$
$419$	−1.39496e6	−0.388173	−0.194086	+	0.980984i	$0.562174\pi$
$420$	−68982.0	−0.0190815
$421$	−4.30364e6	−1.18340	−0.591699	−	0.806159i	$-0.701542\pi$
$421$	−4.30364e6	−1.18340	−0.591699	+	0.806159i	$0.701542\pi$
$422$	428436.	0.117113
$423$	1.32413e6	0.359815
$424$	3.01422e6	0.814255
$425$	−980634.	−0.263351
$426$	−835153.	−0.222968
$427$	−350851.	−0.0931222
$428$	5.17565e6	1.36570
$429$	−1.76337e6	−0.462593
$430$	−138981.	−0.0362480
$431$	−4.82164e6	−1.25026	−0.625132	−	0.780519i	$-0.714955\pi$
$431$	−4.82164e6	−1.25026	−0.625132	+	0.780519i	$0.714955\pi$
$432$	−504883.	−0.130161
$433$	−2.07416e6	−0.531646	−0.265823	−	0.964022i	$-0.585644\pi$
$433$	−2.07416e6	−0.531646	−0.265823	+	0.964022i	$0.585644\pi$
$434$	−88589.2	−0.0225765
$435$	−385983.	−0.0978015
$436$	4.24403e6	1.06921
$437$	−1.59538e6	−0.399631
$438$	310046.	0.0772221
$439$	4.33190e6	1.07279	0.536397	−	0.843966i	$-0.319785\pi$
$439$	4.33190e6	1.07279	0.536397	+	0.843966i	$0.319785\pi$
$440$	−293660.	−0.0723125
$441$	−1.32741e6	−0.325019
$442$	632825.	0.154073
$443$	−6.36375e6	−1.54065	−0.770324	−	0.637653i	$-0.779906\pi$
$443$	−6.36375e6	−1.54065	−0.770324	+	0.637653i	$0.779906\pi$
$444$	367502.	0.0884712
$445$	−1.11311e6	−0.266464
$446$	−1.16304e6	−0.276857
$447$	2.62198e6	0.620669
$448$	260945.	0.0614263
$449$	−3.09278e6	−0.723990	−0.361995	−	0.932180i	$-0.617904\pi$
$449$	−3.09278e6	−0.723990	−0.361995	+	0.932180i	$0.617904\pi$
$450$	452734.	0.105393
$451$	−4.13867e6	−0.958118
$452$	−226977.	−0.0522560
$453$	1.44985e6	0.331953
$454$	−443455.	−0.100974
$455$	271297.	0.0614351
$456$	−3.12935e6	−0.704761
$457$	−2.89914e6	−0.649350	−0.324675	−	0.945826i	$-0.605255\pi$
$457$	−2.89914e6	−0.649350	−0.324675	+	0.945826i	$0.605255\pi$
$458$	1.28894e6	0.287125
$459$	−242217.	−0.0536627
$460$	196518.	0.0433019
$461$	−2.14973e6	−0.471121	−0.235560	−	0.971860i	$-0.575693\pi$
$461$	−2.14973e6	−0.471121	−0.235560	+	0.971860i	$0.575693\pi$
$462$	67982.9	0.0148182
$463$	−4.02390e6	−0.872359	−0.436179	−	0.899860i	$-0.643669\pi$
$463$	−4.02390e6	−0.872359	−0.436179	+	0.899860i	$0.643669\pi$
$464$	2.25439e6	0.486110
$465$	270924.	0.0581052
$466$	2.07371e6	0.442368
$467$	8.64610e6	1.83454	0.917272	−	0.398262i	$-0.130386\pi$
$467$	8.64610e6	1.83454	0.917272	+	0.398262i	$0.130386\pi$
$468$	2.31467e6	0.488512
$469$	692210.	0.145313
$470$	−407881.	−0.0851704
$471$	221841.	0.0460776
$472$	2.69310e6	0.556414
$473$	−1.08515e6	−0.223016
$474$	−1.14208e6	−0.233481
$475$	−8.96970e6	−1.82408
$476$	193291.	0.0391015
$477$	2.13401e6	0.429438
$478$	−299301.	−0.0599153
$479$	1.04155e6	0.207415	0.103708	−	0.994608i	$-0.466929\pi$
$479$	1.04155e6	0.207415	0.103708	+	0.994608i	$0.466929\pi$
$480$	589648.	0.116813
$481$	−1.44533e6	−0.284843
$482$	−871259.	−0.170816
$483$	−96730.8	−0.0188667
$484$	3.49767e6	0.678680
$485$	1.85226e6	0.357558
$486$	111826.	0.0214758
$487$	3.04977e6	0.582699	0.291350	−	0.956617i	$-0.405896\pi$
$487$	3.04977e6	0.582699	0.291350	+	0.956617i	$0.405896\pi$
$488$	1.96055e6	0.372674
$489$	4.05997e6	0.767804
$490$	408892.	0.0769341
$491$	−3.46702e6	−0.649012	−0.324506	−	0.945884i	$-0.605198\pi$
$491$	−3.46702e6	−0.649012	−0.324506	+	0.945884i	$0.605198\pi$
$492$	5.43260e6	1.01180
$493$	1.08154e6	0.200413
$494$	5.78835e6	1.06718
$495$	−207906.	−0.0381376
$496$	−1.58237e6	−0.288805
$497$	1.00323e6	0.182184
$498$	−54680.5	−0.00988004
$499$	251685.	0.0452487	0.0226244	−	0.999744i	$-0.492798\pi$
$499$	251685.	0.0452487	0.0226244	+	0.999744i	$0.492798\pi$
$500$	2.27475e6	0.406919
$501$	−551908.	−0.0982364
$502$	1.07193e6	0.189849
$503$	6.46260e6	1.13890	0.569452	−	0.822025i	$-0.307156\pi$
$503$	6.46260e6	1.13890	0.569452	+	0.822025i	$0.307156\pi$
$504$	−189738.	−0.0332720
$505$	−414060.	−0.0722495
$506$	−193671.	−0.0336271
$507$	−5.76166e6	−0.995469
$508$	7.43854e6	1.27888
$509$	5.63316e6	0.963735	0.481867	−	0.876244i	$-0.339959\pi$
$509$	5.63316e6	0.963735	0.481867	+	0.876244i	$0.339959\pi$
$510$	74611.8	0.0127023
$511$	−372446.	−0.0630973
$512$	−5.97950e6	−1.00807
$513$	−2.21552e6	−0.371691
$514$	1.75275e6	0.292625
$515$	955688.	0.158781
$516$	1.42441e6	0.235511
$517$	−3.18469e6	−0.524011
$518$	55721.9	0.00912434
$519$	−3.61081e6	−0.588418
$520$	−1.51601e6	−0.245863
$521$	−1.08511e7	−1.75138	−0.875689	−	0.482876i	$-0.839592\pi$
$521$	−1.08511e7	−1.75138	−0.875689	+	0.482876i	$0.839592\pi$
$522$	−499321.	−0.0802054
$523$	−8.68430e6	−1.38829	−0.694146	−	0.719834i	$-0.744218\pi$
$523$	−8.68430e6	−1.38829	−0.694146	+	0.719834i	$0.744218\pi$
$524$	2.98186e6	0.474416
$525$	−543850.	−0.0861155
$526$	−3.91158e6	−0.616436
$527$	−759140.	−0.119068
$528$	1.21430e6	0.189558
$529$	−6.16077e6	−0.957185
$530$	−657355.	−0.101651
$531$	1.90667e6	0.293453
$532$	1.76800e6	0.270834
$533$	−2.13657e7	−3.25761
$534$	−1.43996e6	−0.218523
$535$	−2.39993e6	−0.362505
$536$	−3.86807e6	−0.581543
$537$	2.16489e6	0.323967
$538$	3.73719e6	0.556660
$539$	3.19259e6	0.473337
$540$	272906.	0.0402744
$541$	6.71663e6	0.986639	0.493320	−	0.869848i	$-0.335783\pi$
$541$	6.71663e6	0.986639	0.493320	+	0.869848i	$0.335783\pi$
$542$	−3.01445e6	−0.440767
$543$	248267.	0.0361343
$544$	−1.65222e6	−0.239370
$545$	−1.96794e6	−0.283805
$546$	350959.	0.0503819
$547$	−8.10854e6	−1.15871	−0.579355	−	0.815075i	$-0.696695\pi$
$547$	−8.10854e6	−1.15871	−0.579355	+	0.815075i	$0.696695\pi$
$548$	−3.27225e6	−0.465473
$549$	1.38804e6	0.196549
$550$	−1.08888e6	−0.153488
$551$	9.89269e6	1.38815
$552$	540531.	0.0755046
$553$	1.37194e6	0.190775
$554$	−2.37332e6	−0.328535
$555$	−170409.	−0.0234833
$556$	4.85724e6	0.666350
$557$	−3.31587e6	−0.452856	−0.226428	−	0.974028i	$-0.572705\pi$
$557$	−3.31587e6	−0.452856	−0.226428	+	0.974028i	$0.572705\pi$
$558$	350476.	0.0476511
$559$	−5.60203e6	−0.758256
$560$	−186823.	−0.0251744
$561$	582561.	0.0781509
$562$	2.36627e6	0.316026
$563$	−5.11918e6	−0.680658	−0.340329	−	0.940306i	$-0.610539\pi$
$563$	−5.11918e6	−0.680658	−0.340329	+	0.940306i	$0.610539\pi$
$564$	4.18036e6	0.553371
$565$	105248.	0.0138706
$566$	−869499.	−0.114085
$567$	−134331.	−0.0175477
$568$	−5.60607e6	−0.729101
$569$	9.97142e6	1.29115	0.645574	−	0.763697i	$-0.276618\pi$
$569$	9.97142e6	1.29115	0.645574	+	0.763697i	$0.276618\pi$
$570$	682462.	0.0879815
$571$	2.26524e6	0.290753	0.145377	−	0.989376i	$-0.453561\pi$
$571$	2.26524e6	0.290753	0.145377	+	0.989376i	$0.453561\pi$
$572$	−5.56707e6	−0.711437
$573$	−316852.	−0.0403153
$574$	823710.	0.104350
$575$	1.54933e6	0.195423
$576$	−1.03235e6	−0.129650
$577$	6.85594e6	0.857290	0.428645	−	0.903473i	$-0.358991\pi$
$577$	6.85594e6	0.857290	0.428645	+	0.903473i	$0.358991\pi$
$578$	2.47982e6	0.308746
$579$	−8.84495e6	−1.09648
$580$	−1.21858e6	−0.150412
$581$	65685.3	0.00807287
$582$	2.39614e6	0.293228
$583$	−5.13256e6	−0.625406
$584$	2.08123e6	0.252515
$585$	−1.07330e6	−0.129668
$586$	2.03600e6	0.244925
$587$	−553806.	−0.0663380	−0.0331690	−	0.999450i	$-0.510560\pi$
$587$	−553806.	−0.0663380	−0.0331690	+	0.999450i	$0.510560\pi$
$588$	−4.19073e6	−0.499858
$589$	−6.94374e6	−0.824717
$590$	−587325.	−0.0694621
$591$	7.08095e6	0.833917
$592$	995299.	0.116721
$593$	−1.46226e7	−1.70760	−0.853802	−	0.520598i	$-0.825709\pi$
$593$	−1.46226e7	−1.70760	−0.853802	+	0.520598i	$0.825709\pi$
$594$	−268954.	−0.0312760
$595$	−89628.0	−0.0103789
$596$	8.27777e6	0.954547
$597$	−2.39650e6	−0.275196
$598$	−999820.	−0.114332
$599$	6.70289e6	0.763300	0.381650	−	0.924307i	$-0.375356\pi$
$599$	6.70289e6	0.763300	0.381650	+	0.924307i	$0.375356\pi$
$600$	3.03903e6	0.344634
$601$	−1.35572e7	−1.53103	−0.765517	−	0.643416i	$-0.777517\pi$
$601$	−1.35572e7	−1.53103	−0.765517	+	0.643416i	$0.777517\pi$
$602$	215975.	0.0242891
$603$	−2.73852e6	−0.306706
$604$	4.57726e6	0.510521
$605$	−1.62185e6	−0.180145
$606$	−535642.	−0.0592506
$607$	8.42319e6	0.927908	0.463954	−	0.885859i	$-0.346430\pi$
$607$	8.42319e6	0.927908	0.463954	+	0.885859i	$0.346430\pi$
$608$	−1.51126e7	−1.65798
$609$	599813.	0.0655349
$610$	−427567.	−0.0465242
$611$	−1.64408e7	−1.78164
$612$	−764695.	−0.0825296
$613$	847934.	0.0911404	0.0455702	−	0.998961i	$-0.485490\pi$
$613$	847934.	0.0911404	0.0455702	+	0.998961i	$0.485490\pi$
$614$	−3.89117e6	−0.416542
$615$	−2.51907e6	−0.268567
$616$	456344.	0.0484552
$617$	3.67886e6	0.389045	0.194523	−	0.980898i	$-0.437684\pi$
$617$	3.67886e6	0.389045	0.194523	+	0.980898i	$0.437684\pi$
$618$	1.23631e6	0.130213
$619$	3.26873e6	0.342888	0.171444	−	0.985194i	$-0.445157\pi$
$619$	3.26873e6	0.342888	0.171444	+	0.985194i	$0.445157\pi$
$620$	855325.	0.0893619
$621$	382686.	0.0398211
$622$	−2.30697e6	−0.239093
$623$	1.72976e6	0.178552
$624$	6.26879e6	0.644499
$625$	8.16837e6	0.836441
$626$	5.55606e6	0.566671
$627$	5.32859e6	0.541307
$628$	700367.	0.0708642
$629$	477493.	0.0481217
$630$	41379.0	0.00415364
$631$	97194.1	0.00971777	0.00485889	−	0.999988i	$-0.498453\pi$
$631$	97194.1	0.00971777	0.00485889	+	0.999988i	$0.498453\pi$
$632$	−7.66638e6	−0.763480
$633$	2.03610e6	0.201972
$634$	2.87232e6	0.283798
$635$	−3.44922e6	−0.339458
$636$	6.73722e6	0.660447
$637$	1.64816e7	1.60935
$638$	1.20093e6	0.116806
$639$	−3.96899e6	−0.384528
$640$	2.41453e6	0.233014
$641$	284306.	0.0273301	0.0136651	−	0.999907i	$-0.495650\pi$
$641$	284306.	0.0273301	0.0136651	+	0.999907i	$0.495650\pi$
$642$	−3.10463e6	−0.297284
$643$	33344.6	0.00318052	0.00159026	−	0.999999i	$-0.499494\pi$
$643$	33344.6	0.00318052	0.00159026	+	0.999999i	$0.499494\pi$
$644$	−305386.	−0.0290158
$645$	−660495.	−0.0625130
$646$	−1.91229e6	−0.180290
$647$	−1.42088e7	−1.33443	−0.667216	−	0.744865i	$-0.732514\pi$
$647$	−1.42088e7	−1.33443	−0.667216	+	0.744865i	$0.732514\pi$
$648$	750643.	0.0702257
$649$	−4.58577e6	−0.427366
$650$	−5.62129e6	−0.521859
$651$	−421012.	−0.0389352
$652$	1.28176e7	1.18083
$653$	−1.52382e7	−1.39846	−0.699232	−	0.714895i	$-0.746475\pi$
$653$	−1.52382e7	−1.39846	−0.699232	+	0.714895i	$0.746475\pi$
$654$	−2.54579e6	−0.232744
$655$	−1.38268e6	−0.125927
$656$	1.47130e7	1.33488
$657$	1.47347e6	0.133176
$658$	633841.	0.0570710
$659$	9.17395e6	0.822892	0.411446	−	0.911434i	$-0.365024\pi$
$659$	9.17395e6	0.822892	0.411446	+	0.911434i	$0.365024\pi$
$660$	−656373.	−0.0586531
$661$	−1.63580e7	−1.45622	−0.728111	−	0.685459i	$-0.759602\pi$
$661$	−1.63580e7	−1.45622	−0.728111	+	0.685459i	$0.759602\pi$
$662$	−2.87653e6	−0.255108
$663$	3.00744e6	0.265714
$664$	−367049.	−0.0323076
$665$	−819813.	−0.0718887
$666$	−220447.	−0.0192583
$667$	−1.70876e6	−0.148719
$668$	−1.74241e6	−0.151081
$669$	−5.52723e6	−0.477466
$670$	843566.	0.0725992
$671$	−3.33839e6	−0.286241
$672$	−916306.	−0.0782740
$673$	1.16880e6	0.0994727	0.0497364	−	0.998762i	$-0.484162\pi$
$673$	1.16880e6	0.0994727	0.0497364	+	0.998762i	$0.484162\pi$
$674$	1.57072e6	0.133183
$675$	2.15158e6	0.181760
$676$	−1.81899e7	−1.53096
$677$	−1.75703e6	−0.147336	−0.0736678	−	0.997283i	$-0.523470\pi$
$677$	−1.75703e6	−0.147336	−0.0736678	+	0.997283i	$0.523470\pi$
$678$	136153.	0.0113750
$679$	−2.87838e6	−0.239593
$680$	500841.	0.0415363
$681$	−2.10748e6	−0.174139
$682$	−842938.	−0.0693960
$683$	−1.07518e7	−0.881918	−0.440959	−	0.897527i	$-0.645362\pi$
$683$	−1.07518e7	−0.881918	−0.440959	+	0.897527i	$0.645362\pi$
$684$	−6.99455e6	−0.571636
$685$	1.51733e6	0.123553
$686$	−1.28708e6	−0.104423
$687$	6.12560e6	0.495172
$688$	3.85772e6	0.310713
$689$	−2.64966e7	−2.12638
$690$	−117882.	−0.00942591
$691$	−4.83477e6	−0.385195	−0.192597	−	0.981278i	$-0.561691\pi$
$691$	−4.83477e6	−0.385195	−0.192597	+	0.981278i	$0.561691\pi$
$692$	−1.13996e7	−0.904947
$693$	323083.	0.0255553
$694$	−4.54411e6	−0.358137
$695$	−2.25228e6	−0.176873
$696$	−3.35175e6	−0.262270
$697$	7.05855e6	0.550343
$698$	−1.41502e6	−0.109932
$699$	9.85513e6	0.762903
$700$	−1.71697e6	−0.132440
$701$	1.92337e7	1.47832	0.739159	−	0.673531i	$-0.235223\pi$
$701$	1.92337e7	1.47832	0.739159	+	0.673531i	$0.235223\pi$
$702$	−1.38846e6	−0.106339
$703$	4.36755e6	0.333311
$704$	2.48293e6	0.188813
$705$	−1.93842e6	−0.146884
$706$	7.52549e6	0.568228
$707$	643444.	0.0484130
$708$	6.01948e6	0.451311
$709$	1.64927e6	0.123218	0.0616092	−	0.998100i	$-0.480377\pi$
$709$	1.64927e6	0.123218	0.0616092	+	0.998100i	$0.480377\pi$
$710$	1.22260e6	0.0910201
$711$	−5.42765e6	−0.402660
$712$	−9.66589e6	−0.714565
$713$	1.19939e6	0.0883561
$714$	−115946.	−0.00851157
$715$	2.58143e6	0.188840
$716$	6.83471e6	0.498239
$717$	−1.42240e6	−0.103329
$718$	6.18841e6	0.447989
$719$	−793857.	−0.0572691	−0.0286345	−	0.999590i	$-0.509116\pi$
$719$	−793857.	−0.0572691	−0.0286345	+	0.999590i	$0.509116\pi$
$720$	739108.	0.0531345
$721$	−1.48513e6	−0.106396
$722$	−1.28022e7	−0.913992
$723$	−4.14058e6	−0.294588
$724$	783797.	0.0555721
$725$	−9.60719e6	−0.678815
$726$	−2.09808e6	−0.147734
$727$	9.98333e6	0.700550	0.350275	−	0.936647i	$-0.386088\pi$
$727$	9.98333e6	0.700550	0.350275	+	0.936647i	$0.386088\pi$
$728$	2.35585e6	0.164748
$729$	531441.	0.0370370
$730$	−453883.	−0.0315237
$731$	1.85073e6	0.128100
$732$	4.38212e6	0.302278
$733$	−1.22764e7	−0.843936	−0.421968	−	0.906611i	$-0.638661\pi$
$733$	−1.22764e7	−0.843936	−0.421968	+	0.906611i	$0.638661\pi$
$734$	−5.83057e6	−0.399458
$735$	1.94322e6	0.132680
$736$	2.61039e6	0.177628
$737$	6.58647e6	0.446667
$738$	−3.25876e6	−0.220248
$739$	4.53873e6	0.305719	0.152860	−	0.988248i	$-0.451152\pi$
$739$	4.53873e6	0.305719	0.152860	+	0.988248i	$0.451152\pi$
$740$	−537993.	−0.0361158
$741$	2.75086e7	1.84045
$742$	1.02152e6	0.0681142
$743$	−4.59161e6	−0.305136	−0.152568	−	0.988293i	$-0.548754\pi$
$743$	−4.59161e6	−0.305136	−0.152568	+	0.988293i	$0.548754\pi$
$744$	2.35262e6	0.155818
$745$	−3.83837e6	−0.253370
$746$	−626682.	−0.0412288
$747$	−259864.	−0.0170390
$748$	1.83918e6	0.120191
$749$	3.72946e6	0.242908
$750$	−1.36451e6	−0.0885778
$751$	−1.35516e7	−0.876782	−0.438391	−	0.898784i	$-0.644451\pi$
$751$	−1.35516e7	−0.876782	−0.438391	+	0.898784i	$0.644451\pi$
$752$	1.13216e7	0.730069
$753$	5.09426e6	0.327411
$754$	6.19973e6	0.397141
$755$	−2.12246e6	−0.135510
$756$	−424093.	−0.0269871
$757$	1.95628e7	1.24077	0.620385	−	0.784297i	$-0.286976\pi$
$757$	1.95628e7	1.24077	0.620385	+	0.784297i	$0.286976\pi$
$758$	3.34240e6	0.211293
$759$	−920406.	−0.0579929
$760$	4.58111e6	0.287698
$761$	−4.80480e6	−0.300755	−0.150378	−	0.988629i	$-0.548049\pi$
$761$	−4.80480e6	−0.300755	−0.150378	+	0.988629i	$0.548049\pi$
$762$	−4.46202e6	−0.278384
$763$	3.05815e6	0.190173
$764$	−1.00032e6	−0.0620022
$765$	354586.	0.0219063
$766$	−4.41777e6	−0.272039
$767$	−2.36738e7	−1.45305
$768$	−547063.	−0.0334684
$769$	−8.60529e6	−0.524746	−0.262373	−	0.964966i	$-0.584505\pi$
$769$	−8.60529e6	−0.524746	−0.262373	+	0.964966i	$0.584505\pi$
$770$	−99521.5	−0.00604909
$771$	8.32978e6	0.504659
$772$	−2.79241e7	−1.68630
$773$	−2.17117e6	−0.130691	−0.0653454	−	0.997863i	$-0.520815\pi$
$773$	−2.17117e6	−0.130691	−0.0653454	+	0.997863i	$0.520815\pi$
$774$	−854438.	−0.0512659
$775$	6.74334e6	0.403293
$776$	1.60844e7	0.958849
$777$	264813.	0.0157357
$778$	−8.61418e6	−0.510229
$779$	6.45634e7	3.81191
$780$	−3.38849e6	−0.199421
$781$	9.54590e6	0.560002
$782$	330309.	0.0193154
$783$	−2.37298e6	−0.138321
$784$	−1.13497e7	−0.659468
$785$	−324757.	−0.0188098
$786$	−1.78868e6	−0.103270
$787$	2.14078e7	1.23207	0.616034	−	0.787719i	$-0.288738\pi$
$787$	2.14078e7	1.23207	0.616034	+	0.787719i	$0.288738\pi$
$788$	2.23551e7	1.28251
$789$	−1.85894e7	−1.06310
$790$	1.67192e6	0.0953120
$791$	−163555.	−0.00929441
$792$	−1.80539e6	−0.102272
$793$	−1.72343e7	−0.973219
$794$	−1.18968e6	−0.0669699
$795$	−3.12402e6	−0.175306
$796$	−7.56591e6	−0.423232
$797$	8.89466e6	0.496002	0.248001	−	0.968760i	$-0.420226\pi$
$797$	8.89466e6	0.496002	0.248001	+	0.968760i	$0.420226\pi$
$798$	−1.06054e6	−0.0589548
$799$	5.43153e6	0.300992
$800$	1.46764e7	0.810766
$801$	−6.84327e6	−0.376862
$802$	5.28441e6	0.290108
$803$	−3.54387e6	−0.193950
$804$	−8.64569e6	−0.471693
$805$	141606.	0.00770180
$806$	−4.35163e6	−0.235947
$807$	1.77607e7	0.960010
$808$	−3.59556e6	−0.193749
$809$	−1.77835e7	−0.955315	−0.477658	−	0.878546i	$-0.658514\pi$
$809$	−1.77835e7	−0.955315	−0.477658	+	0.878546i	$0.658514\pi$
$810$	−163704.	−0.00876689
$811$	−1.10472e7	−0.589795	−0.294897	−	0.955529i	$-0.595285\pi$
$811$	−1.10472e7	−0.589795	−0.294897	+	0.955529i	$0.595285\pi$
$812$	1.89365e6	0.100788
$813$	−1.43259e7	−0.760143
$814$	530201.	0.0280465
$815$	−5.94346e6	−0.313434
$816$	−2.07101e6	−0.108882
$817$	1.69284e7	0.887279
$818$	3.36025e6	0.175585
$819$	1.66790e6	0.0868881
$820$	−7.95289e6	−0.413038
$821$	1.93741e7	1.00315	0.501573	−	0.865115i	$-0.332755\pi$
$821$	1.93741e7	1.00315	0.501573	+	0.865115i	$0.332755\pi$
$822$	1.96287e6	0.101324
$823$	2.22378e7	1.14444	0.572219	−	0.820101i	$-0.306083\pi$
$823$	2.22378e7	1.14444	0.572219	+	0.820101i	$0.306083\pi$
$824$	8.29888e6	0.425796
$825$	−5.17481e6	−0.264703
$826$	912695.	0.0465453
$827$	1.13244e7	0.575772	0.287886	−	0.957665i	$-0.407048\pi$
$827$	1.13244e7	0.575772	0.287886	+	0.957665i	$0.407048\pi$
$828$	1.20817e6	0.0612422
$829$	−7.42428e6	−0.375205	−0.187602	−	0.982245i	$-0.560072\pi$
$829$	−7.42428e6	−0.375205	−0.187602	+	0.982245i	$0.560072\pi$
$830$	80047.8	0.00403324
$831$	−1.12790e7	−0.566589
$832$	1.28180e7	0.641966
$833$	−5.44500e6	−0.271885
$834$	−2.91362e6	−0.145050
$835$	807949.	0.0401022
$836$	1.68227e7	0.832493
$837$	1.66561e6	0.0821787
$838$	2.64173e6	0.129951
$839$	−3.56558e7	−1.74874	−0.874370	−	0.485261i	$-0.838725\pi$
$839$	−3.56558e7	−1.74874	−0.874370	+	0.485261i	$0.838725\pi$
$840$	277762.	0.0135823
$841$	−9.91538e6	−0.483414
$842$	8.15013e6	0.396172
$843$	1.12455e7	0.545016
$844$	6.42812e6	0.310619
$845$	8.43460e6	0.406371
$846$	−2.50760e6	−0.120457
$847$	2.52034e6	0.120712
$848$	1.82463e7	0.871336
$849$	−4.13222e6	−0.196750
$850$	1.85710e6	0.0881633
$851$	−754406.	−0.0357093
$852$	−1.25304e7	−0.591378
$853$	−2.03029e7	−0.955401	−0.477701	−	0.878523i	$-0.658530\pi$
$853$	−2.03029e7	−0.955401	−0.477701	+	0.878523i	$0.658530\pi$
$854$	664433.	0.0311750
$855$	3.24334e6	0.151732
$856$	−2.08402e7	−0.972115
$857$	5.43042e6	0.252570	0.126285	−	0.991994i	$-0.459695\pi$
$857$	5.43042e6	0.252570	0.126285	+	0.991994i	$0.459695\pi$
$858$	3.33942e6	0.154865
$859$	−3.46363e7	−1.60158	−0.800789	−	0.598946i	$-0.795586\pi$
$859$	−3.46363e7	−1.60158	−0.800789	+	0.598946i	$0.795586\pi$
$860$	−2.08523e6	−0.0961407
$861$	3.91461e6	0.179962
$862$	9.13110e6	0.418557
$863$	9.44281e6	0.431593	0.215796	−	0.976438i	$-0.430765\pi$
$863$	9.44281e6	0.431593	0.215796	+	0.976438i	$0.430765\pi$
$864$	3.62509e6	0.165209
$865$	5.28593e6	0.240205
$866$	3.92799e6	0.177982
$867$	1.17851e7	0.532460
$868$	−1.32916e6	−0.0598797
$869$	1.30542e7	0.586408
$870$	730966.	0.0327415
$871$	3.40023e7	1.51867
$872$	−1.70889e7	−0.761069
$873$	1.13874e7	0.505698
$874$	3.02128e6	0.133787
$875$	1.63913e6	0.0723759
$876$	4.65184e6	0.204816
$877$	2.30727e7	1.01298	0.506488	−	0.862247i	$-0.330943\pi$
$877$	2.30727e7	1.01298	0.506488	+	0.862247i	$0.330943\pi$
$878$	−8.20364e6	−0.359145
$879$	9.67591e6	0.422396
$880$	−1.77764e6	−0.0773817
$881$	−759246.	−0.0329566	−0.0164783	−	0.999864i	$-0.505245\pi$
$881$	−759246.	−0.0329566	−0.0164783	+	0.999864i	$0.505245\pi$
$882$	2.51382e6	0.108809
$883$	−4.83031e6	−0.208484	−0.104242	−	0.994552i	$-0.533242\pi$
$883$	−4.83031e6	−0.208484	−0.104242	+	0.994552i	$0.533242\pi$
$884$	9.49471e6	0.408649
$885$	−2.79121e6	−0.119794
$886$	1.20515e7	0.515771
$887$	−1.50463e7	−0.642126	−0.321063	−	0.947058i	$-0.604040\pi$
$887$	−1.50463e7	−0.642126	−0.321063	+	0.947058i	$0.604040\pi$
$888$	−1.47978e6	−0.0629743
$889$	5.36004e6	0.227465
$890$	2.10798e6	0.0892055
$891$	−1.27818e6	−0.0539383
$892$	−1.74498e7	−0.734310
$893$	4.96813e7	2.08480
$894$	−4.96544e6	−0.207785
$895$	−3.16923e6	−0.132250
$896$	−3.75215e6	−0.156138
$897$	−4.75155e6	−0.197176
$898$	5.85703e6	0.242374
$899$	−7.43723e6	−0.306911
$900$	6.79268e6	0.279534
$901$	8.75364e6	0.359234
$902$	7.83771e6	0.320754
$903$	1.02640e6	0.0418887
$904$	913943.	0.0371962
$905$	−363443.	−0.0147508
$906$	−2.74568e6	−0.111130
$907$	3.98484e7	1.60839	0.804197	−	0.594363i	$-0.202596\pi$
$907$	3.98484e7	1.60839	0.804197	+	0.594363i	$0.202596\pi$
$908$	−6.65346e6	−0.267814
$909$	−2.54559e6	−0.102183
$910$	−513775.	−0.0205669
$911$	−4.77088e7	−1.90460	−0.952298	−	0.305171i	$-0.901286\pi$
$911$	−4.77088e7	−1.90460	−0.952298	+	0.305171i	$0.901286\pi$
$912$	−1.89432e7	−0.754165
$913$	625004.	0.0248145
$914$	5.49032e6	0.217386
$915$	−2.03197e6	−0.0802352
$916$	1.93389e7	0.761542
$917$	2.14866e6	0.0843811
$918$	458704.	0.0179650
$919$	−1.78587e7	−0.697526	−0.348763	−	0.937211i	$-0.613398\pi$
$919$	−1.78587e7	−0.697526	−0.348763	+	0.937211i	$0.613398\pi$
$920$	−791294.	−0.0308225
$921$	−1.84924e7	−0.718365
$922$	4.07111e6	0.157720
$923$	4.92803e7	1.90401
$924$	1.01999e6	0.0393023
$925$	−4.24151e6	−0.162992
$926$	7.62037e6	0.292044
$927$	5.87545e6	0.224565
$928$	−1.61867e7	−0.617003
$929$	−2.74827e7	−1.04477	−0.522385	−	0.852710i	$-0.674958\pi$
$929$	−2.74827e7	−1.04477	−0.522385	+	0.852710i	$0.674958\pi$
$930$	−513069.	−0.0194522
$931$	−4.98045e7	−1.88319
$932$	3.11133e7	1.17329
$933$	−1.09637e7	−0.412337
$934$	−1.63738e7	−0.614160
$935$	−852822.	−0.0319028
$936$	−9.32022e6	−0.347726
$937$	3.73061e7	1.38813	0.694066	−	0.719911i	$-0.255818\pi$
$937$	3.73061e7	1.38813	0.694066	+	0.719911i	$0.255818\pi$
$938$	−1.31089e6	−0.0486474
$939$	2.64047e7	0.977275
$940$	−6.11972e6	−0.225898
$941$	4.57103e7	1.68283	0.841414	−	0.540391i	$-0.181724\pi$
$941$	4.57103e7	1.68283	0.841414	+	0.540391i	$0.181724\pi$
$942$	−420117.	−0.0154256
$943$	−1.11520e7	−0.408390
$944$	1.63025e7	0.595420
$945$	196650.	0.00716333
$946$	2.05503e6	0.0746603
$947$	−3.99656e7	−1.44814	−0.724071	−	0.689726i	$-0.757731\pi$
$947$	−3.99656e7	−1.44814	−0.724071	+	0.689726i	$0.757731\pi$
$948$	−1.71355e7	−0.619263
$949$	−1.82951e7	−0.659429
$950$	1.69866e7	0.610657
$951$	1.36504e7	0.489436
$952$	−778300.	−0.0278327
$953$	−9.21440e6	−0.328651	−0.164325	−	0.986406i	$-0.552545\pi$
$953$	−9.21440e6	−0.328651	−0.164325	+	0.986406i	$0.552545\pi$
$954$	−4.04134e6	−0.143765
$955$	463846.	0.0164575
$956$	−4.49061e6	−0.158914
$957$	5.70730e6	0.201442
$958$	−1.97246e6	−0.0694374
$959$	−2.35791e6	−0.0827904
$960$	1.51128e6	0.0529257
$961$	−2.34089e7	−0.817660
$962$	2.73714e6	0.0953584
$963$	−1.47545e7	−0.512694
$964$	−1.30721e7	−0.453057
$965$	1.29483e7	0.447604
$966$	183186.	0.00631612
$967$	584138.	0.0200886	0.0100443	−	0.999950i	$-0.496803\pi$
$967$	584138.	0.0200886	0.0100443	+	0.999950i	$0.496803\pi$
$968$	−1.40836e7	−0.483088
$969$	−9.08798e6	−0.310927
$970$	−3.50776e6	−0.119702
$971$	2.17465e7	0.740186	0.370093	−	0.928995i	$-0.379326\pi$
$971$	2.17465e7	0.740186	0.370093	+	0.928995i	$0.379326\pi$
$972$	1.67780e6	0.0569604
$973$	3.50001e6	0.118519
$974$	−5.77557e6	−0.195073
$975$	−2.67147e7	−0.899992
$976$	1.18680e7	0.398799
$977$	−1.79749e7	−0.602462	−0.301231	−	0.953551i	$-0.597398\pi$
$977$	−1.79749e7	−0.602462	−0.301231	+	0.953551i	$0.597398\pi$
$978$	−7.68866e6	−0.257042
$979$	1.64589e7	0.548837
$980$	6.13489e6	0.204052
$981$	−1.20987e7	−0.401388
$982$	6.56576e6	0.217273
$983$	2.76817e7	0.913711	0.456856	−	0.889541i	$-0.348976\pi$
$983$	2.76817e7	0.913711	0.456856	+	0.889541i	$0.348976\pi$
$984$	−2.18748e7	−0.720206
$985$	−1.03659e7	−0.340423
$986$	−2.04820e6	−0.0670933
$987$	3.01228e6	0.0984242
$988$	8.68466e7	2.83048
$989$	−2.92403e6	−0.0950586
$990$	393727.	0.0127675
$991$	3.98101e7	1.28768	0.643842	−	0.765159i	$-0.277339\pi$
$991$	3.98101e7	1.28768	0.643842	+	0.765159i	$0.277339\pi$
$992$	1.13615e7	0.366570
$993$	−1.36704e7	−0.439956
$994$	−1.89990e6	−0.0609909
$995$	3.50828e6	0.112341
$996$	−820408.	−0.0262049
$997$	−1.45958e6	−0.0465039	−0.0232519	−	0.999730i	$-0.507402\pi$
$997$	−1.45958e6	−0.0465039	−0.0232519	+	0.999730i	$0.507402\pi$
$998$	−476635.	−0.0151482
$999$	−1.04765e6	−0.0332127

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.6.a.b.1.13	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.6.a.b.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-1.89378 q^{2} -9.00000 q^{3} -28.4136 q^{4} +13.1753 q^{5} +17.0440 q^{6} -20.4742 q^{7} +114.410 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-1.89378 q^{2} -9.00000 q^{3} -28.4136 q^{4} +13.1753 q^{5} +17.0440 q^{6} -20.4742 q^{7} +114.410 q^{8} +81.0000 q^{9} -24.9510 q^{10} -194.815 q^{11} +255.723 q^{12} -1005.72 q^{13} +38.7735 q^{14} -118.577 q^{15} +692.569 q^{16} +332.259 q^{17} -153.396 q^{18} +3039.12 q^{19} -374.357 q^{20} +184.268 q^{21} +368.935 q^{22} -524.947 q^{23} -1029.69 q^{24} -2951.41 q^{25} +1904.61 q^{26} -729.000 q^{27} +581.746 q^{28} +3255.11 q^{29} +224.559 q^{30} -2284.78 q^{31} -4972.68 q^{32} +1753.33 q^{33} -629.224 q^{34} -269.753 q^{35} -2301.50 q^{36} +1437.11 q^{37} -5755.41 q^{38} +9051.50 q^{39} +1507.38 q^{40} +21244.1 q^{41} -348.962 q^{42} +5570.15 q^{43} +5535.39 q^{44} +1067.20 q^{45} +994.131 q^{46} +16347.3 q^{47} -6233.12 q^{48} -16387.8 q^{49} +5589.31 q^{50} -2990.33 q^{51} +28576.2 q^{52} +26345.8 q^{53} +1380.56 q^{54} -2566.74 q^{55} -2342.45 q^{56} -27352.1 q^{57} -6164.46 q^{58} +23539.1 q^{59} +3369.21 q^{60} +17136.2 q^{61} +4326.87 q^{62} -1658.41 q^{63} -12745.1 q^{64} -13250.7 q^{65} -3320.42 q^{66} -33808.9 q^{67} -9440.68 q^{68} +4724.52 q^{69} +510.852 q^{70} -48999.9 q^{71} +9267.19 q^{72} +18191.0 q^{73} -2721.56 q^{74} +26562.7 q^{75} -86352.4 q^{76} +3988.68 q^{77} -17141.5 q^{78} -67008.1 q^{79} +9124.79 q^{80} +6561.00 q^{81} -40231.6 q^{82} -3208.20 q^{83} -5235.72 q^{84} +4377.61 q^{85} -10548.6 q^{86} -29296.0 q^{87} -22288.7 q^{88} -84484.8 q^{89} -2021.03 q^{90} +20591.4 q^{91} +14915.6 q^{92} +20563.1 q^{93} -30958.0 q^{94} +40041.3 q^{95} +44754.2 q^{96} +140586. q^{97} +31034.8 q^{98} -15780.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9}+O(q^{10}) \) 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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