LMFDB - Embedded newform 547.6.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,6,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("547.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	547.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:	$87.7299494377$
Analytic rank:	$0$
Dimension:	$117$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.64600 q^{2} +29.4222 q^{3} +61.0453 q^{4} +73.3026 q^{5} -283.807 q^{6} +119.769 q^{7} -280.171 q^{8} +622.666 q^{9} +O(q^{10})$	\(q-9.64600 q^{2} +29.4222 q^{3} +61.0453 q^{4} +73.3026 q^{5} -283.807 q^{6} +119.769 q^{7} -280.171 q^{8} +622.666 q^{9} -707.077 q^{10} -594.939 q^{11} +1796.09 q^{12} +1175.39 q^{13} -1155.29 q^{14} +2156.72 q^{15} +749.082 q^{16} +334.599 q^{17} -6006.23 q^{18} -2718.29 q^{19} +4474.78 q^{20} +3523.87 q^{21} +5738.78 q^{22} -560.026 q^{23} -8243.26 q^{24} +2248.28 q^{25} -11337.8 q^{26} +11170.6 q^{27} +7311.35 q^{28} -2350.32 q^{29} -20803.8 q^{30} -5647.72 q^{31} +1739.83 q^{32} -17504.4 q^{33} -3227.54 q^{34} +8779.40 q^{35} +38010.8 q^{36} +339.784 q^{37} +26220.7 q^{38} +34582.4 q^{39} -20537.3 q^{40} +14990.8 q^{41} -33991.3 q^{42} -1042.13 q^{43} -36318.2 q^{44} +45643.0 q^{45} +5402.01 q^{46} +14704.8 q^{47} +22039.6 q^{48} -2462.34 q^{49} -21686.9 q^{50} +9844.63 q^{51} +71751.8 q^{52} +32615.8 q^{53} -107752. q^{54} -43610.6 q^{55} -33555.9 q^{56} -79978.2 q^{57} +22671.1 q^{58} +39171.1 q^{59} +131658. q^{60} +38790.9 q^{61} +54477.9 q^{62} +74576.2 q^{63} -40753.1 q^{64} +86158.8 q^{65} +168848. q^{66} +32376.5 q^{67} +20425.7 q^{68} -16477.2 q^{69} -84686.1 q^{70} +76263.2 q^{71} -174453. q^{72} -75958.2 q^{73} -3277.56 q^{74} +66149.2 q^{75} -165939. q^{76} -71255.4 q^{77} -333582. q^{78} +28063.9 q^{79} +54909.7 q^{80} +177356. q^{81} -144601. q^{82} +26728.9 q^{83} +215116. q^{84} +24527.0 q^{85} +10052.4 q^{86} -69151.5 q^{87} +166685. q^{88} -62659.1 q^{89} -440273. q^{90} +140775. q^{91} -34187.0 q^{92} -166168. q^{93} -141842. q^{94} -199258. q^{95} +51189.7 q^{96} +44225.9 q^{97} +23751.7 q^{98} -370448. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9}+O(q^{10}) $ 117 * q + 24 * q^2 + 100 * q^3 + 1962 * q^4 + 749 * q^5 + 306 * q^6 + 393 * q^7 + 1152 * q^8 + 10671 * q^9	\( 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9} + 850 q^{10} + 1798 q^{11} + 5361 q^{12} + 4419 q^{13} + 3847 q^{14} + 1913 q^{15} + 34722 q^{16} + 15252 q^{17} + 2367 q^{18} + 1052 q^{19} + 23568 q^{20} + 9212 q^{21} + 9176 q^{22} + 18178 q^{23} + 15983 q^{24} + 84312 q^{25} + 21552 q^{26} + 30883 q^{27} + 23528 q^{28} + 43620 q^{29} + 23582 q^{30} + 13127 q^{31} + 49108 q^{32} + 39222 q^{33} + 32097 q^{34} + 52467 q^{35} + 217244 q^{36} + 56152 q^{37} + 76245 q^{38} + 28595 q^{39} + 20368 q^{40} + 46679 q^{41} + 78924 q^{42} + 39058 q^{43} + 78528 q^{44} + 185770 q^{45} + 41430 q^{46} + 150268 q^{47} + 180930 q^{48} + 323802 q^{49} + 91604 q^{50} + 43367 q^{51} + 136030 q^{52} + 297398 q^{53} + 116761 q^{54} + 94579 q^{55} + 173545 q^{56} + 164740 q^{57} + 87844 q^{58} + 135778 q^{59} + 114650 q^{60} + 166976 q^{61} + 229394 q^{62} + 147179 q^{63} + 630138 q^{64} + 216626 q^{65} + 82380 q^{66} + 133444 q^{67} + 634057 q^{68} + 232986 q^{69} + 30943 q^{70} + 126787 q^{71} + 78583 q^{72} + 241702 q^{73} + 242589 q^{74} + 374853 q^{75} + 90228 q^{76} + 766693 q^{77} + 82537 q^{78} + 117230 q^{79} + 730509 q^{80} + 1051409 q^{81} + 468130 q^{82} + 368467 q^{83} + 234191 q^{84} + 261997 q^{85} + 230487 q^{86} + 214239 q^{87} + 247415 q^{88} + 494902 q^{89} + 41821 q^{90} + 259647 q^{91} + 663682 q^{92} + 767344 q^{93} + 373605 q^{94} + 426186 q^{95} + 474162 q^{96} + 733038 q^{97} + 461746 q^{98} + 334651 q^{99}+O(q^{100}) \) 117 * q + 24 * q^2 + 100 * q^3 + 1962 * q^4 + 749 * q^5 + 306 * q^6 + 393 * q^7 + 1152 * q^8 + 10671 * q^9 + 850 * q^10 + 1798 * q^11 + 5361 * q^12 + 4419 * q^13 + 3847 * q^14 + 1913 * q^15 + 34722 * q^16 + 15252 * q^17 + 2367 * q^18 + 1052 * q^19 + 23568 * q^20 + 9212 * q^21 + 9176 * q^22 + 18178 * q^23 + 15983 * q^24 + 84312 * q^25 + 21552 * q^26 + 30883 * q^27 + 23528 * q^28 + 43620 * q^29 + 23582 * q^30 + 13127 * q^31 + 49108 * q^32 + 39222 * q^33 + 32097 * q^34 + 52467 * q^35 + 217244 * q^36 + 56152 * q^37 + 76245 * q^38 + 28595 * q^39 + 20368 * q^40 + 46679 * q^41 + 78924 * q^42 + 39058 * q^43 + 78528 * q^44 + 185770 * q^45 + 41430 * q^46 + 150268 * q^47 + 180930 * q^48 + 323802 * q^49 + 91604 * q^50 + 43367 * q^51 + 136030 * q^52 + 297398 * q^53 + 116761 * q^54 + 94579 * q^55 + 173545 * q^56 + 164740 * q^57 + 87844 * q^58 + 135778 * q^59 + 114650 * q^60 + 166976 * q^61 + 229394 * q^62 + 147179 * q^63 + 630138 * q^64 + 216626 * q^65 + 82380 * q^66 + 133444 * q^67 + 634057 * q^68 + 232986 * q^69 + 30943 * q^70 + 126787 * q^71 + 78583 * q^72 + 241702 * q^73 + 242589 * q^74 + 374853 * q^75 + 90228 * q^76 + 766693 * q^77 + 82537 * q^78 + 117230 * q^79 + 730509 * q^80 + 1051409 * q^81 + 468130 * q^82 + 368467 * q^83 + 234191 * q^84 + 261997 * q^85 + 230487 * q^86 + 214239 * q^87 + 247415 * q^88 + 494902 * q^89 + 41821 * q^90 + 259647 * q^91 + 663682 * q^92 + 767344 * q^93 + 373605 * q^94 + 426186 * q^95 + 474162 * q^96 + 733038 * q^97 + 461746 * q^98 + 334651 * 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 $

$2$	−9.64600	−1.70519	−0.852594	−	0.522574i	$-0.824972\pi$
$2$	−9.64600	−1.70519	−0.852594	+	0.522574i	$0.824972\pi$
$3$	29.4222	1.88743	0.943717	−	0.330753i	$-0.107303\pi$
$3$	29.4222	1.88743	0.943717	+	0.330753i	$0.107303\pi$
$4$	61.0453	1.90767
$5$	73.3026	1.31128	0.655639	−	0.755075i	$-0.272399\pi$
$5$	73.3026	1.31128	0.655639	+	0.755075i	$0.272399\pi$
$6$	−283.807	−3.21843
$7$	119.769	0.923847	0.461924	−	0.886920i	$-0.347159\pi$
$7$	119.769	0.923847	0.461924	+	0.886920i	$0.347159\pi$
$8$	−280.171	−1.54774
$9$	622.666	2.56241
$10$	−707.077	−2.23597
$11$	−594.939	−1.48249	−0.741243	−	0.671237i	$-0.765763\pi$
$11$	−594.939	−1.48249	−0.741243	+	0.671237i	$0.765763\pi$
$12$	1796.09	3.60060
$13$	1175.39	1.92895	0.964477	−	0.264167i	$-0.0850970\pi$
$13$	1175.39	1.92895	0.964477	+	0.264167i	$0.0850970\pi$
$14$	−1155.29	−1.57533
$15$	2156.72	2.47495
$16$	749.082	0.731526
$17$	334.599	0.280803	0.140402	−	0.990095i	$-0.455161\pi$
$17$	334.599	0.280803	0.140402	+	0.990095i	$0.455161\pi$
$18$	−6006.23	−4.36939
$19$	−2718.29	−1.72748	−0.863739	−	0.503940i	$-0.831883\pi$
$19$	−2718.29	−1.72748	−0.863739	+	0.503940i	$0.831883\pi$
$20$	4474.78	2.50148
$21$	3523.87	1.74370
$22$	5738.78	2.52792
$23$	−560.026	−0.220744	−0.110372	−	0.993890i	$-0.535204\pi$
$23$	−560.026	−0.220744	−0.110372	+	0.993890i	$0.535204\pi$
$24$	−8243.26	−2.92126
$25$	2248.28	0.719448
$26$	−11337.8	−3.28923
$27$	11170.6	2.94895
$28$	7311.35	1.76239
$29$	−2350.32	−0.518957	−0.259478	−	0.965749i	$-0.583551\pi$
$29$	−2350.32	−0.518957	−0.259478	+	0.965749i	$0.583551\pi$
$30$	−20803.8	−4.22026
$31$	−5647.72	−1.05553	−0.527763	−	0.849392i	$-0.676969\pi$
$31$	−5647.72	−1.05553	−0.527763	+	0.849392i	$0.676969\pi$
$32$	1739.83	0.300354
$33$	−17504.4	−2.79810
$34$	−3227.54	−0.478822
$35$	8779.40	1.21142
$36$	38010.8	4.88822
$37$	339.784	0.0408036	0.0204018	−	0.999792i	$-0.493505\pi$
$37$	339.784	0.0408036	0.0204018	+	0.999792i	$0.493505\pi$
$38$	26220.7	2.94567
$39$	34582.4	3.64077
$40$	−20537.3	−2.02952
$41$	14990.8	1.39272	0.696361	−	0.717692i	$-0.254801\pi$
$41$	14990.8	1.39272	0.696361	+	0.717692i	$0.254801\pi$
$42$	−33991.3	−2.97334
$43$	−1042.13	−0.0859513	−0.0429757	−	0.999076i	$-0.513684\pi$
$43$	−1042.13	−0.0859513	−0.0429757	+	0.999076i	$0.513684\pi$
$44$	−36318.2	−2.82809
$45$	45643.0	3.36003
$46$	5402.01	0.376410
$47$	14704.8	0.970987	0.485493	−	0.874240i	$-0.338640\pi$
$47$	14704.8	0.970987	0.485493	+	0.874240i	$0.338640\pi$
$48$	22039.6	1.38071
$49$	−2462.34	−0.146507
$50$	−21686.9	−1.22679
$51$	9844.63	0.529998
$52$	71751.8	3.67980
$53$	32615.8	1.59492	0.797460	−	0.603372i	$-0.206177\pi$
$53$	32615.8	1.59492	0.797460	+	0.603372i	$0.206177\pi$
$54$	−107752.	−5.02851
$55$	−43610.6	−1.94395
$56$	−33555.9	−1.42988
$57$	−79978.2	−3.26050
$58$	22671.1	0.884919
$59$	39171.1	1.46499	0.732496	−	0.680771i	$-0.238355\pi$
$59$	39171.1	1.46499	0.732496	+	0.680771i	$0.238355\pi$
$60$	131658.	4.72138
$61$	38790.9	1.33477	0.667384	−	0.744714i	$-0.267414\pi$
$61$	38790.9	1.33477	0.667384	+	0.744714i	$0.267414\pi$
$62$	54477.9	1.79987
$63$	74576.2	2.36728
$64$	−40753.1	−1.24369
$65$	86158.8	2.52939
$66$	168848.	4.77128
$67$	32376.5	0.881135	0.440568	−	0.897719i	$-0.354777\pi$
$67$	32376.5	0.881135	0.440568	+	0.897719i	$0.354777\pi$
$68$	20425.7	0.535679
$69$	−16477.2	−0.416640
$70$	−84686.1	−2.06570
$71$	76263.2	1.79543	0.897717	−	0.440573i	$-0.145225\pi$
$71$	76263.2	1.79543	0.897717	+	0.440573i	$0.145225\pi$
$72$	−174453.	−3.96595
$73$	−75958.2	−1.66828	−0.834138	−	0.551556i	$-0.814034\pi$
$73$	−75958.2	−1.66828	−0.834138	+	0.551556i	$0.814034\pi$
$74$	−3277.56	−0.0695779
$75$	66149.2	1.35791
$76$	−165939.	−3.29545
$77$	−71255.4	−1.36959
$78$	−333582.	−6.20821
$79$	28063.9	0.505918	0.252959	−	0.967477i	$-0.418596\pi$
$79$	28063.9	0.505918	0.252959	+	0.967477i	$0.418596\pi$
$80$	54909.7	0.959233
$81$	177356.	3.00354
$82$	−144601.	−2.37485
$83$	26728.9	0.425879	0.212939	−	0.977065i	$-0.431696\pi$
$83$	26728.9	0.425879	0.212939	+	0.977065i	$0.431696\pi$
$84$	215116.	3.32640
$85$	24527.0	0.368211
$86$	10052.4	0.146563
$87$	−69151.5	−0.979497
$88$	166685.	2.29451
$89$	−62659.1	−0.838512	−0.419256	−	0.907868i	$-0.637709\pi$
$89$	−62659.1	−0.838512	−0.419256	+	0.907868i	$0.637709\pi$
$90$	−440273.	−5.72948
$91$	140775.	1.78206
$92$	−34187.0	−0.421106
$93$	−166168.	−1.99224
$94$	−141842.	−1.65572
$95$	−199258.	−2.26520
$96$	51189.7	0.566898
$97$	44225.9	0.477251	0.238626	−	0.971112i	$-0.423303\pi$
$97$	44225.9	0.477251	0.238626	+	0.971112i	$0.423303\pi$
$98$	23751.7	0.249821
$99$	−370448.	−3.79874
$100$	137247.	1.37247
$101$	−82005.6	−0.799908	−0.399954	−	0.916535i	$-0.630974\pi$
$101$	−82005.6	−0.799908	−0.399954	+	0.916535i	$0.630974\pi$
$102$	−94961.4	−0.903746
$103$	−97036.3	−0.901242	−0.450621	−	0.892715i	$-0.648797\pi$
$103$	−97036.3	−0.901242	−0.450621	+	0.892715i	$0.648797\pi$
$104$	−329309.	−2.98552
$105$	258309.	2.28648
$106$	−314612.	−2.71964
$107$	−120502.	−1.01750	−0.508750	−	0.860914i	$-0.669892\pi$
$107$	−120502.	−1.01750	−0.508750	+	0.860914i	$0.669892\pi$
$108$	681913.	5.62561
$109$	31219.0	0.251682	0.125841	−	0.992050i	$-0.459837\pi$
$109$	31219.0	0.251682	0.125841	+	0.992050i	$0.459837\pi$
$110$	420668.	3.31480
$111$	9997.20	0.0770142
$112$	89717.0	0.675818
$113$	24551.2	0.180874	0.0904371	−	0.995902i	$-0.471174\pi$
$113$	24551.2	0.180874	0.0904371	+	0.995902i	$0.471174\pi$
$114$	771470.	5.55977
$115$	−41051.4	−0.289456
$116$	−143476.	−0.989997
$117$	731872.	4.94277
$118$	−377844.	−2.49809
$119$	40074.6	0.259419
$120$	−604252.	−3.83059
$121$	192901.	1.19777
$122$	−374178.	−2.27603
$123$	441061.	2.62867
$124$	−344767.	−2.01359
$125$	−64266.2	−0.367881
$126$	−719362.	−4.03665
$127$	−116450.	−0.640664	−0.320332	−	0.947305i	$-0.603795\pi$
$127$	−116450.	−0.640664	−0.320332	+	0.947305i	$0.603795\pi$
$128$	337430.	1.82036
$129$	−30661.9	−0.162227
$130$	−831088.	−4.31309
$131$	233866.	1.19066	0.595331	−	0.803481i	$-0.297021\pi$
$131$	233866.	1.19066	0.595331	+	0.803481i	$0.297021\pi$
$132$	−1.06856e6	−5.33783
$133$	−325568.	−1.59593
$134$	−312304.	−1.50250
$135$	818834.	3.86689
$136$	−93745.0	−0.434611
$137$	−114049.	−0.519147	−0.259574	−	0.965723i	$-0.583582\pi$
$137$	−114049.	−0.519147	−0.259574	+	0.965723i	$0.583582\pi$
$138$	158939.	0.710449
$139$	−13823.6	−0.0606853	−0.0303426	−	0.999540i	$-0.509660\pi$
$139$	−13823.6	−0.0606853	−0.0303426	+	0.999540i	$0.509660\pi$
$140$	535941.	2.31099
$141$	432646.	1.83267
$142$	−735635.	−3.06155
$143$	−699282.	−2.85965
$144$	466428.	1.87447
$145$	−172284.	−0.680496
$146$	732693.	2.84472
$147$	−72447.3	−0.276522
$148$	20742.2	0.0778398
$149$	−110693.	−0.408465	−0.204232	−	0.978922i	$-0.565470\pi$
$149$	−110693.	−0.408465	−0.204232	+	0.978922i	$0.565470\pi$
$150$	−638075.	−2.31549
$151$	259461.	0.926040	0.463020	−	0.886348i	$-0.346766\pi$
$151$	259461.	0.926040	0.463020	+	0.886348i	$0.346766\pi$
$152$	761588.	2.67369
$153$	208343.	0.719533
$154$	687329.	2.33541
$155$	−413993.	−1.38409
$156$	2.11110e6	6.94539
$157$	515195.	1.66810	0.834051	−	0.551687i	$-0.186016\pi$
$157$	515195.	1.66810	0.834051	+	0.551687i	$0.186016\pi$
$158$	−270704.	−0.862686
$159$	959629.	3.01031
$160$	127534.	0.393847
$161$	−67073.9	−0.203934
$162$	−1.71077e6	−5.12159
$163$	−125762.	−0.370751	−0.185375	−	0.982668i	$-0.559350\pi$
$163$	−125762.	−0.370751	−0.185375	+	0.982668i	$0.559350\pi$
$164$	915117.	2.65685
$165$	−1.28312e6	−3.66908
$166$	−257827.	−0.726204
$167$	−611303.	−1.69615	−0.848077	−	0.529874i	$-0.822239\pi$
$167$	−611303.	−1.69615	−0.848077	+	0.529874i	$0.822239\pi$
$168$	−987288.	−2.69880
$169$	1.01024e6	2.72086
$170$	−236587.	−0.627869
$171$	−1.69259e6	−4.42651
$172$	−63617.4	−0.163966
$173$	126303.	0.320848	0.160424	−	0.987048i	$-0.448714\pi$
$173$	126303.	0.320848	0.160424	+	0.987048i	$0.448714\pi$
$174$	667035.	1.67023
$175$	269274.	0.664660
$176$	−445658.	−1.08448
$177$	1.15250e6	2.76508
$178$	604410.	1.42982
$179$	223795.	0.522057	0.261029	−	0.965331i	$-0.415938\pi$
$179$	223795.	0.522057	0.261029	+	0.965331i	$0.415938\pi$
$180$	2.78629e6	6.40982
$181$	−450678.	−1.02251	−0.511257	−	0.859428i	$-0.670820\pi$
$181$	−450678.	−1.02251	−0.511257	+	0.859428i	$0.670820\pi$
$182$	−1.35792e6	−3.03875
$183$	1.14131e6	2.51929
$184$	156903.	0.341655
$185$	24907.1	0.0535049
$186$	1.60286e6	3.39714
$187$	−199066.	−0.416287
$188$	897657.	1.85232
$189$	1.33789e6	2.72438
$190$	1.92204e6	3.86260
$191$	380935.	0.755557	0.377778	−	0.925896i	$-0.376688\pi$
$191$	380935.	0.755557	0.377778	+	0.925896i	$0.376688\pi$
$192$	−1.19905e6	−2.34737
$193$	−356833.	−0.689560	−0.344780	−	0.938684i	$-0.612046\pi$
$193$	−356833.	−0.689560	−0.344780	+	0.938684i	$0.612046\pi$
$194$	−426603.	−0.813803
$195$	2.53498e6	4.77407
$196$	−150314.	−0.279486
$197$	−945688.	−1.73613	−0.868066	−	0.496450i	$-0.834637\pi$
$197$	−945688.	−1.73613	−0.868066	+	0.496450i	$0.834637\pi$
$198$	3.57334e6	6.47756
$199$	−233276.	−0.417577	−0.208789	−	0.977961i	$-0.566952\pi$
$199$	−233276.	−0.417577	−0.208789	+	0.977961i	$0.566952\pi$
$200$	−629902.	−1.11352
$201$	952587.	1.66309
$202$	791026.	1.36399
$203$	−281495.	−0.479437
$204$	600969.	1.01106
$205$	1.09886e6	1.82624
$206$	936012.	1.53679
$207$	−348709.	−0.565636
$208$	880460.	1.41108
$209$	1.61722e6	2.56096
$210$	−2.49165e6	−3.89887
$211$	−1.14081e6	−1.76404	−0.882021	−	0.471211i	$-0.843817\pi$
$211$	−1.14081e6	−1.76404	−0.882021	+	0.471211i	$0.843817\pi$
$212$	1.99104e6	3.04257
$213$	2.24383e6	3.38876
$214$	1.16236e6	1.73503
$215$	−76391.2	−0.112706
$216$	−3.12968e6	−4.56421
$217$	−676423.	−0.975144
$218$	−301138.	−0.429166
$219$	−2.23486e6	−3.14876
$220$	−2.66222e6	−3.70841
$221$	393283.	0.541657
$222$	−96433.0	−0.131324
$223$	−661050.	−0.890168	−0.445084	−	0.895489i	$-0.646826\pi$
$223$	−661050.	−0.890168	−0.445084	+	0.895489i	$0.646826\pi$
$224$	208379.	0.277481
$225$	1.39992e6	1.84352
$226$	−236821.	−0.308425
$227$	85832.6	0.110557	0.0552787	−	0.998471i	$-0.482395\pi$
$227$	85832.6	0.110557	0.0552787	+	0.998471i	$0.482395\pi$
$228$	−4.88230e6	−6.21995
$229$	−985544.	−1.24190	−0.620951	−	0.783850i	$-0.713253\pi$
$229$	−985544.	−1.24190	−0.620951	+	0.783850i	$0.713253\pi$
$230$	395982.	0.493578
$231$	−2.09649e6	−2.58501
$232$	658491.	0.803212
$233$	1.37736e6	1.66210	0.831049	−	0.556200i	$-0.187741\pi$
$233$	1.37736e6	1.66210	0.831049	+	0.556200i	$0.187741\pi$
$234$	−7.05964e6	−8.42836
$235$	1.07790e6	1.27323
$236$	2.39121e6	2.79472
$237$	825701.	0.954887
$238$	−386560.	−0.442359
$239$	380903.	0.431339	0.215670	−	0.976466i	$-0.430807\pi$
$239$	380903.	0.431339	0.215670	+	0.976466i	$0.430807\pi$
$240$	1.61556e6	1.81049
$241$	−212775.	−0.235981	−0.117991	−	0.993015i	$-0.537645\pi$
$241$	−212775.	−0.235981	−0.117991	+	0.993015i	$0.537645\pi$
$242$	−1.86073e6	−2.04241
$243$	2.50374e6	2.72003
$244$	2.36801e6	2.54629
$245$	−180496.	−0.192111
$246$	−4.25448e6	−4.48238
$247$	−3.19504e6	−3.33223
$248$	1.58233e6	1.63368
$249$	786423.	0.803819
$250$	619912.	0.627307
$251$	−366590.	−0.367279	−0.183640	−	0.982994i	$-0.558788\pi$
$251$	−366590.	−0.367279	−0.183640	+	0.982994i	$0.558788\pi$
$252$	4.55253e6	4.51597
$253$	333181.	0.327250
$254$	1.12328e6	1.09245
$255$	721638.	0.694974
$256$	−1.95075e6	−1.86038
$257$	1.17415e6	1.10889	0.554447	−	0.832219i	$-0.312930\pi$
$257$	1.17415e6	1.10889	0.554447	+	0.832219i	$0.312930\pi$
$258$	295764.	0.276628
$259$	40695.7	0.0376963
$260$	5.25959e6	4.82524
$261$	−1.46346e6	−1.32978
$262$	−2.25587e6	−2.03030
$263$	−937574.	−0.835827	−0.417913	−	0.908487i	$-0.637238\pi$
$263$	−937574.	−0.835827	−0.417913	+	0.908487i	$0.637238\pi$
$264$	4.90423e6	4.33073
$265$	2.39083e6	2.09138
$266$	3.14043e6	2.72135
$267$	−1.84357e6	−1.58264
$268$	1.97643e6	1.68091
$269$	171534.	0.144534	0.0722670	−	0.997385i	$-0.476977\pi$
$269$	171534.	0.144534	0.0722670	+	0.997385i	$0.476977\pi$
$270$	−7.89848e6	−6.59377
$271$	−1.98600e6	−1.64269	−0.821347	−	0.570429i	$-0.806777\pi$
$271$	−1.98600e6	−1.64269	−0.821347	+	0.570429i	$0.806777\pi$
$272$	250642.	0.205415
$273$	4.14191e6	3.36352
$274$	1.10012e6	0.885244
$275$	−1.33759e6	−1.06657
$276$	−1.00586e6	−0.794810
$277$	−1.30421e6	−1.02128	−0.510642	−	0.859793i	$-0.670592\pi$
$277$	−1.30421e6	−1.02128	−0.510642	+	0.859793i	$0.670592\pi$
$278$	133342.	0.103480
$279$	−3.51664e6	−2.70469
$280$	−2.45974e6	−1.87497
$281$	−250109.	−0.188957	−0.0944786	−	0.995527i	$-0.530118\pi$
$281$	−250109.	−0.188957	−0.0944786	+	0.995527i	$0.530118\pi$
$282$	−4.17331e6	−3.12506
$283$	589994.	0.437907	0.218953	−	0.975735i	$-0.429736\pi$
$283$	589994.	0.437907	0.218953	+	0.975735i	$0.429736\pi$
$284$	4.65551e6	3.42509
$285$	−5.86261e6	−4.27542
$286$	6.74528e6	4.87624
$287$	1.79543e6	1.28666
$288$	1.08334e6	0.769629
$289$	−1.30790e6	−0.921150
$290$	1.66185e6	1.16037
$291$	1.30122e6	0.900780
$292$	−4.63690e6	−3.18251
$293$	141354.	0.0961920	0.0480960	−	0.998843i	$-0.484685\pi$
$293$	141354.	0.0961920	0.0480960	+	0.998843i	$0.484685\pi$
$294$	698827.	0.471521
$295$	2.87134e6	1.92101
$296$	−95197.8	−0.0631535
$297$	−6.64582e6	−4.37177
$298$	1.06775e6	0.696509
$299$	−658247.	−0.425805
$300$	4.03810e6	2.59044
$301$	−124816.	−0.0794059
$302$	−2.50276e6	−1.57907
$303$	−2.41279e6	−1.50977
$304$	−2.03623e6	−1.26369
$305$	2.84348e6	1.75025
$306$	−2.00968e6	−1.22694
$307$	718408.	0.435036	0.217518	−	0.976056i	$-0.430204\pi$
$307$	718408.	0.435036	0.217518	+	0.976056i	$0.430204\pi$
$308$	−4.34981e6	−2.61272
$309$	−2.85502e6	−1.70103
$310$	3.99337e6	2.36013
$311$	−261310.	−0.153199	−0.0765994	−	0.997062i	$-0.524406\pi$
$311$	−261310.	−0.153199	−0.0765994	+	0.997062i	$0.524406\pi$
$312$	−9.68900e6	−5.63498
$313$	−450891.	−0.260142	−0.130071	−	0.991505i	$-0.541521\pi$
$313$	−450891.	−0.260142	−0.130071	+	0.991505i	$0.541521\pi$
$314$	−4.96957e6	−2.84443
$315$	5.46663e6	3.10415
$316$	1.71317e6	0.965123
$317$	−1.79519e6	−1.00337	−0.501685	−	0.865050i	$-0.667286\pi$
$317$	−1.79519e6	−1.00337	−0.501685	+	0.865050i	$0.667286\pi$
$318$	−9.25659e6	−5.13314
$319$	1.39829e6	0.769346
$320$	−2.98731e6	−1.63082
$321$	−3.54543e6	−1.92047
$322$	646995.	0.347745
$323$	−909538.	−0.485081
$324$	1.08267e7	5.72974
$325$	2.64259e6	1.38778
$326$	1.21310e6	0.632200
$327$	918531.	0.475034
$328$	−4.19998e6	−2.15557
$329$	1.76118e6	0.897043
$330$	1.23770e7	6.25647
$331$	−2.57576e6	−1.29221	−0.646107	−	0.763246i	$-0.723604\pi$
$331$	−2.57576e6	−1.29221	−0.646107	+	0.763246i	$0.723604\pi$
$332$	1.63168e6	0.812435
$333$	211572.	0.104556
$334$	5.89663e6	2.89226
$335$	2.37328e6	1.15541
$336$	2.63967e6	1.27556
$337$	739135.	0.354527	0.177263	−	0.984163i	$-0.443276\pi$
$337$	739135.	0.354527	0.177263	+	0.984163i	$0.443276\pi$
$338$	−9.74475e6	−4.63958
$339$	722351.	0.341388
$340$	1.49726e6	0.702424
$341$	3.36005e6	1.56480
$342$	1.63267e7	7.54803
$343$	−2.30787e6	−1.05920
$344$	291976.	0.133031
$345$	−1.20782e6	−0.546330
$346$	−1.21832e6	−0.547106
$347$	−1.09207e6	−0.486886	−0.243443	−	0.969915i	$-0.578277\pi$
$347$	−1.09207e6	−0.486886	−0.243443	+	0.969915i	$0.578277\pi$
$348$	−4.22137e6	−1.86855
$349$	−4.30814e6	−1.89333	−0.946664	−	0.322221i	$-0.895571\pi$
$349$	−4.30814e6	−1.89333	−0.946664	+	0.322221i	$0.895571\pi$
$350$	−2.59742e6	−1.13337
$351$	1.31298e7	5.68838
$352$	−1.03510e6	−0.445270
$353$	2.41838e6	1.03297	0.516484	−	0.856297i	$-0.327240\pi$
$353$	2.41838e6	1.03297	0.516484	+	0.856297i	$0.327240\pi$
$354$	−1.11170e7	−4.71498
$355$	5.59030e6	2.35431
$356$	−3.82505e6	−1.59960
$357$	1.17908e6	0.489637
$358$	−2.15873e6	−0.890206
$359$	−151874.	−0.0621937	−0.0310968	−	0.999516i	$-0.509900\pi$
$359$	−151874.	−0.0621937	−0.0310968	+	0.999516i	$0.509900\pi$
$360$	−1.27879e7	−5.20046
$361$	4.91302e6	1.98418
$362$	4.34724e6	1.74358
$363$	5.67558e6	2.26070
$364$	8.59366e6	3.39957
$365$	−5.56794e6	−2.18757
$366$	−1.10091e7	−4.29586
$367$	110661.	0.0428874	0.0214437	−	0.999770i	$-0.493174\pi$
$367$	110661.	0.0428874	0.0214437	+	0.999770i	$0.493174\pi$
$368$	−419506.	−0.161480
$369$	9.33424e6	3.56872
$370$	−240254.	−0.0912359
$371$	3.90637e6	1.47346
$372$	−1.01438e7	−3.80052
$373$	3.46686e6	1.29022	0.645110	−	0.764090i	$-0.276811\pi$
$373$	3.46686e6	1.29022	0.645110	+	0.764090i	$0.276811\pi$
$374$	1.92019e6	0.709848
$375$	−1.89085e6	−0.694352
$376$	−4.11985e6	−1.50284
$377$	−2.76253e6	−1.00104
$378$	−1.29053e7	−4.64557
$379$	−99423.8	−0.0355543	−0.0177772	−	0.999842i	$-0.505659\pi$
$379$	−99423.8	−0.0355543	−0.0177772	+	0.999842i	$0.505659\pi$
$380$	−1.21638e7	−4.32125
$381$	−3.42622e6	−1.20921
$382$	−3.67450e6	−1.28837
$383$	−296999.	−0.103457	−0.0517283	−	0.998661i	$-0.516473\pi$
$383$	−296999.	−0.103457	−0.0517283	+	0.998661i	$0.516473\pi$
$384$	9.92792e6	3.43582
$385$	−5.22321e6	−1.79591
$386$	3.44201e6	1.17583
$387$	−648901.	−0.220243
$388$	2.69978e6	0.910436
$389$	2.79456e6	0.936354	0.468177	−	0.883635i	$-0.344911\pi$
$389$	2.79456e6	0.936354	0.468177	+	0.883635i	$0.344911\pi$
$390$	−2.44524e7	−8.14068
$391$	−187384.	−0.0619856
$392$	689876.	0.226754
$393$	6.88085e6	2.24730
$394$	9.12211e6	2.96043
$395$	2.05716e6	0.663399
$396$	−2.26141e7	−7.24673
$397$	754050.	0.240118	0.120059	−	0.992767i	$-0.461692\pi$
$397$	754050.	0.240118	0.120059	+	0.992767i	$0.461692\pi$
$398$	2.25018e6	0.712048
$399$	−9.57892e6	−3.01220
$400$	1.68414e6	0.526295
$401$	235564.	0.0731558	0.0365779	−	0.999331i	$-0.488354\pi$
$401$	235564.	0.0731558	0.0365779	+	0.999331i	$0.488354\pi$
$402$	−9.18866e6	−2.83587
$403$	−6.63825e6	−2.03606
$404$	−5.00606e6	−1.52596
$405$	1.30006e7	3.93847
$406$	2.71531e6	0.817530
$407$	−202151.	−0.0604908
$408$	−2.75818e6	−0.820300
$409$	−1.48028e6	−0.437559	−0.218779	−	0.975774i	$-0.570207\pi$
$409$	−1.48028e6	−0.437559	−0.218779	+	0.975774i	$0.570207\pi$
$410$	−1.05996e7	−3.11409
$411$	−3.35558e6	−0.979857
$412$	−5.92361e6	−1.71927
$413$	4.69149e6	1.35343
$414$	3.36365e6	0.964517
$415$	1.95930e6	0.558445
$416$	2.04498e6	0.579368
$417$	−406720.	−0.114539
$418$	−1.55997e7	−4.36692
$419$	−1.65430e6	−0.460342	−0.230171	−	0.973150i	$-0.573929\pi$
$419$	−1.65430e6	−0.460342	−0.230171	+	0.973150i	$0.573929\pi$
$420$	1.57686e7	4.36183
$421$	1.17799e6	0.323919	0.161959	−	0.986797i	$-0.448219\pi$
$421$	1.17799e6	0.323919	0.161959	+	0.986797i	$0.448219\pi$
$422$	1.10043e7	3.00802
$423$	9.15615e6	2.48807
$424$	−9.13802e6	−2.46852
$425$	752270.	0.202023
$426$	−2.16440e7	−5.77848
$427$	4.64596e6	1.23312
$428$	−7.35608e6	−1.94105
$429$	−2.05744e7	−5.39740
$430$	736869.	0.192185
$431$	−3.51790e6	−0.912201	−0.456100	−	0.889928i	$-0.650754\pi$
$431$	−3.51790e6	−0.912201	−0.456100	+	0.889928i	$0.650754\pi$
$432$	8.36770e6	2.15723
$433$	3.10905e6	0.796908	0.398454	−	0.917188i	$-0.369547\pi$
$433$	3.10905e6	0.796908	0.398454	+	0.917188i	$0.369547\pi$
$434$	6.52478e6	1.66280
$435$	−5.06898e6	−1.28439
$436$	1.90577e6	0.480126
$437$	1.52232e6	0.381330
$438$	2.15574e7	5.36923
$439$	5.28250e6	1.30821	0.654106	−	0.756403i	$-0.273045\pi$
$439$	5.28250e6	1.30821	0.654106	+	0.756403i	$0.273045\pi$
$440$	1.22184e7	3.00873
$441$	−1.53321e6	−0.375410
$442$	−3.79360e6	−0.923626
$443$	−1.86197e6	−0.450780	−0.225390	−	0.974269i	$-0.572366\pi$
$443$	−1.86197e6	−0.450780	−0.225390	+	0.974269i	$0.572366\pi$
$444$	610282.	0.146917
$445$	−4.59308e6	−1.09952
$446$	6.37649e6	1.51790
$447$	−3.25683e6	−0.770951
$448$	−4.88096e6	−1.14897
$449$	743082.	0.173949	0.0869743	−	0.996211i	$-0.472280\pi$
$449$	743082.	0.173949	0.0869743	+	0.996211i	$0.472280\pi$
$450$	−1.35037e7	−3.14355
$451$	−8.91859e6	−2.06469
$452$	1.49874e6	0.345048
$453$	7.63391e6	1.74784
$454$	−827941.	−0.188521
$455$	1.03192e7	2.33677
$456$	2.24076e7	5.04642
$457$	3.54440e6	0.793876	0.396938	−	0.917846i	$-0.370073\pi$
$457$	3.54440e6	0.793876	0.396938	+	0.917846i	$0.370073\pi$
$458$	9.50656e6	2.11768
$459$	3.73767e6	0.828074
$460$	−2.50600e6	−0.552186
$461$	−2.00819e6	−0.440101	−0.220051	−	0.975488i	$-0.570622\pi$
$461$	−2.00819e6	−0.440101	−0.220051	+	0.975488i	$0.570622\pi$
$462$	2.02227e7	4.40793
$463$	556563.	0.120660	0.0603298	−	0.998178i	$-0.480785\pi$
$463$	556563.	0.120660	0.0603298	+	0.998178i	$0.480785\pi$
$464$	−1.76058e6	−0.379630
$465$	−1.21806e7	−2.61237
$466$	−1.32860e7	−2.83419
$467$	3.15029e6	0.668434	0.334217	−	0.942496i	$-0.391528\pi$
$467$	3.15029e6	0.668434	0.334217	+	0.942496i	$0.391528\pi$
$468$	4.46774e7	9.42916
$469$	3.87771e6	0.814034
$470$	−1.03974e7	−2.17110
$471$	1.51582e7	3.14843
$472$	−1.09746e7	−2.26743
$473$	620006.	0.127422
$474$	−7.96472e6	−1.62826
$475$	−6.11147e6	−1.24283
$476$	2.44637e6	0.494886
$477$	2.03088e7	4.08684
$478$	−3.67419e6	−0.735515
$479$	−4.21863e6	−0.840103	−0.420051	−	0.907500i	$-0.637988\pi$
$479$	−4.21863e6	−0.840103	−0.420051	+	0.907500i	$0.637988\pi$
$480$	3.75234e6	0.743360
$481$	399377.	0.0787084
$482$	2.05242e6	0.402392
$483$	−1.97346e6	−0.384911
$484$	1.17757e7	2.28494
$485$	3.24187e6	0.625809
$486$	−2.41511e7	−4.63816
$487$	5.60048e6	1.07005	0.535023	−	0.844837i	$-0.320303\pi$
$487$	5.60048e6	1.07005	0.535023	+	0.844837i	$0.320303\pi$
$488$	−1.08681e7	−2.06588
$489$	−3.70021e6	−0.699768
$490$	1.74106e6	0.327585
$491$	−8.60437e6	−1.61070	−0.805351	−	0.592798i	$-0.798023\pi$
$491$	−8.60437e6	−1.61070	−0.805351	+	0.592798i	$0.798023\pi$
$492$	2.69247e7	5.01463
$493$	−786413.	−0.145725
$494$	3.08194e7	5.68207
$495$	−2.71548e7	−4.98120
$496$	−4.23061e6	−0.772144
$497$	9.13399e6	1.65871
$498$	−7.58584e6	−1.37066
$499$	2.62688e6	0.472268	0.236134	−	0.971721i	$-0.424120\pi$
$499$	2.62688e6	0.472268	0.236134	+	0.971721i	$0.424120\pi$
$500$	−3.92315e6	−0.701795
$501$	−1.79859e7	−3.20138
$502$	3.53613e6	0.626281
$503$	−1.01112e7	−1.78189	−0.890946	−	0.454109i	$-0.849958\pi$
$503$	−1.01112e7	−1.78189	−0.890946	+	0.454109i	$0.849958\pi$
$504$	−2.08941e7	−3.66393
$505$	−6.01123e6	−1.04890
$506$	−3.21387e6	−0.558022
$507$	2.97234e7	5.13545
$508$	−7.10873e6	−1.22217
$509$	−2.79663e6	−0.478454	−0.239227	−	0.970964i	$-0.576894\pi$
$509$	−2.79663e6	−0.478454	−0.239227	+	0.970964i	$0.576894\pi$
$510$	−6.96092e6	−1.18506
$511$	−9.09746e6	−1.54123
$512$	8.01916e6	1.35193
$513$	−3.03650e7	−5.09424
$514$	−1.13258e7	−1.89087
$515$	−7.11302e6	−1.18178
$516$	−1.87176e6	−0.309476
$517$	−8.74844e6	−1.43947
$518$	−392551.	−0.0642793
$519$	3.71612e6	0.605579
$520$	−2.41392e7	−3.91485
$521$	1.12139e7	1.80994	0.904970	−	0.425476i	$-0.139893\pi$
$521$	1.12139e7	1.80994	0.904970	+	0.425476i	$0.139893\pi$
$522$	1.41165e7	2.26753
$523$	−7.76487e6	−1.24131	−0.620654	−	0.784084i	$-0.713133\pi$
$523$	−7.76487e6	−1.24131	−0.620654	+	0.784084i	$0.713133\pi$
$524$	1.42764e7	2.27139
$525$	7.92264e6	1.25450
$526$	9.04384e6	1.42524
$527$	−1.88972e6	−0.296395
$528$	−1.31122e7	−2.04688
$529$	−6.12271e6	−0.951272
$530$	−2.30619e7	−3.56620
$531$	2.43905e7	3.75391
$532$	−1.98744e7	−3.04449
$533$	1.76199e7	2.68650
$534$	1.77831e7	2.69869
$535$	−8.83311e6	−1.33423
$536$	−9.07096e6	−1.36377
$537$	6.58454e6	0.985349
$538$	−1.65462e6	−0.246458
$539$	1.46494e6	0.217194
$540$	4.99860e7	7.37673
$541$	−3.86032e6	−0.567062	−0.283531	−	0.958963i	$-0.591506\pi$
$541$	−3.86032e6	−0.567062	−0.283531	+	0.958963i	$0.591506\pi$
$542$	1.91570e7	2.80110
$543$	−1.32599e7	−1.92993
$544$	582147.	0.0843403
$545$	2.28843e6	0.330025
$546$	−3.99529e7	−5.73543
$547$	299209.	0.0427569
$547$	299209.	0.0427569
$548$	−6.96217e6	−0.990360
$549$	2.41538e7	3.42022
$550$	1.29024e7	1.81871
$551$	6.38885e6	0.896486
$552$	4.61644e6	0.644851
$553$	3.36119e6	0.467391
$554$	1.25804e7	1.74148
$555$	732821.	0.100987
$556$	−843865.	−0.115767
$557$	−6.54600e6	−0.894000	−0.447000	−	0.894534i	$-0.647508\pi$
$557$	−6.54600e6	−0.894000	−0.447000	+	0.894534i	$0.647508\pi$
$558$	3.39215e7	4.61201
$559$	−1.22491e6	−0.165796
$560$	6.57649e6	0.886185
$561$	−5.85696e6	−0.785715
$562$	2.41255e6	0.322207
$563$	−7.35006e6	−0.977283	−0.488641	−	0.872485i	$-0.662507\pi$
$563$	−7.35006e6	−0.977283	−0.488641	+	0.872485i	$0.662507\pi$
$564$	2.64110e7	3.49613
$565$	1.79967e6	0.237176
$566$	−5.69108e6	−0.746713
$567$	2.12418e7	2.77481
$568$	−2.13668e7	−2.77887
$569$	6.79818e6	0.880262	0.440131	−	0.897934i	$-0.354932\pi$
$569$	6.79818e6	0.880262	0.440131	+	0.897934i	$0.354932\pi$
$570$	5.65508e7	7.29040
$571$	−1.37389e6	−0.176344	−0.0881721	−	0.996105i	$-0.528103\pi$
$571$	−1.37389e6	−0.176344	−0.0881721	+	0.996105i	$0.528103\pi$
$572$	−4.26879e7	−5.45525
$573$	1.12079e7	1.42606
$574$	−1.73187e7	−2.19400
$575$	−1.25909e6	−0.158814
$576$	−2.53755e7	−3.18683
$577$	−1.42731e7	−1.78476	−0.892379	−	0.451286i	$-0.850965\pi$
$577$	−1.42731e7	−1.78476	−0.892379	+	0.451286i	$0.850965\pi$
$578$	1.26160e7	1.57073
$579$	−1.04988e7	−1.30150
$580$	−1.05172e7	−1.29816
$581$	3.20130e6	0.393447
$582$	−1.25516e7	−1.53600
$583$	−1.94044e7	−2.36445
$584$	2.12813e7	2.58206
$585$	5.36481e7	6.48134
$586$	−1.36350e6	−0.164026
$587$	−1.91512e6	−0.229404	−0.114702	−	0.993400i	$-0.536591\pi$
$587$	−1.91512e6	−0.229404	−0.114702	+	0.993400i	$0.536591\pi$
$588$	−4.42257e6	−0.527511
$589$	1.53522e7	1.82340
$590$	−2.76970e7	−3.27568
$591$	−2.78242e7	−3.27683
$592$	254526.	0.0298489
$593$	−6.87251e6	−0.802562	−0.401281	−	0.915955i	$-0.631435\pi$
$593$	−6.87251e6	−0.802562	−0.401281	+	0.915955i	$0.631435\pi$
$594$	6.41056e7	7.45470
$595$	2.93758e6	0.340171
$596$	−6.75730e6	−0.779215
$597$	−6.86348e6	−0.788150
$598$	6.34945e6	0.726077
$599$	5.29148e6	0.602574	0.301287	−	0.953534i	$-0.402584\pi$
$599$	5.29148e6	0.602574	0.301287	+	0.953534i	$0.402584\pi$
$600$	−1.85331e7	−2.10170
$601$	−4.34201e6	−0.490349	−0.245174	−	0.969479i	$-0.578845\pi$
$601$	−4.34201e6	−0.490349	−0.245174	+	0.969479i	$0.578845\pi$
$602$	1.20397e6	0.135402
$603$	2.01597e7	2.25783
$604$	1.58389e7	1.76658
$605$	1.41402e7	1.57060
$606$	2.32737e7	2.57445
$607$	−1.43737e6	−0.158342	−0.0791709	−	0.996861i	$-0.525227\pi$
$607$	−1.43737e6	−0.158342	−0.0791709	+	0.996861i	$0.525227\pi$
$608$	−4.72938e6	−0.518854
$609$	−8.28221e6	−0.904906
$610$	−2.74282e7	−2.98451
$611$	1.72838e7	1.87299
$612$	1.27184e7	1.37263
$613$	1.08692e7	1.16828	0.584141	−	0.811652i	$-0.301431\pi$
$613$	1.08692e7	1.16828	0.584141	+	0.811652i	$0.301431\pi$
$614$	−6.92977e6	−0.741819
$615$	3.23310e7	3.44692
$616$	1.99637e7	2.11977
$617$	−2.41927e6	−0.255841	−0.127921	−	0.991784i	$-0.540830\pi$
$617$	−2.41927e6	−0.255841	−0.127921	+	0.991784i	$0.540830\pi$
$618$	2.75395e7	2.90058
$619$	1.18596e7	1.24406	0.622030	−	0.782993i	$-0.286308\pi$
$619$	1.18596e7	1.24406	0.622030	+	0.782993i	$0.286308\pi$
$620$	−2.52723e7	−2.64038
$621$	−6.25583e6	−0.650962
$622$	2.52060e6	0.261233
$623$	−7.50464e6	−0.774657
$624$	2.59051e7	2.66332
$625$	−1.17367e7	−1.20184
$626$	4.34929e6	0.443591
$627$	4.75821e7	4.83365
$628$	3.14503e7	3.18218
$629$	113691.	0.0114578
$630$	−5.27311e7	−5.29317
$631$	−1.51509e7	−1.51484	−0.757419	−	0.652929i	$-0.773540\pi$
$631$	−1.51509e7	−1.51484	−0.757419	+	0.652929i	$0.773540\pi$
$632$	−7.86270e6	−0.783031
$633$	−3.35653e7	−3.32951
$634$	1.73164e7	1.71093
$635$	−8.53610e6	−0.840088
$636$	5.85809e7	5.74266
$637$	−2.89419e6	−0.282604
$638$	−1.34879e7	−1.31188
$639$	4.74865e7	4.60064
$640$	2.47345e7	2.38700
$641$	1.16300e6	0.111798	0.0558991	−	0.998436i	$-0.482197\pi$
$641$	1.16300e6	0.111798	0.0558991	+	0.998436i	$0.482197\pi$
$642$	3.41992e7	3.27476
$643$	−7.12756e6	−0.679850	−0.339925	−	0.940453i	$-0.610402\pi$
$643$	−7.12756e6	−0.679850	−0.339925	+	0.940453i	$0.610402\pi$
$644$	−4.09455e6	−0.389037
$645$	−2.24760e6	−0.212725
$646$	8.77341e6	0.827155
$647$	−4.61219e6	−0.433158	−0.216579	−	0.976265i	$-0.569490\pi$
$647$	−4.61219e6	−0.433158	−0.216579	+	0.976265i	$0.569490\pi$
$648$	−4.96900e7	−4.64870
$649$	−2.33044e7	−2.17183
$650$	−2.54904e7	−2.36643
$651$	−1.99018e7	−1.84052
$652$	−7.67721e6	−0.707269
$653$	−2.27317e6	−0.208616	−0.104308	−	0.994545i	$-0.533263\pi$
$653$	−2.27317e6	−0.208616	−0.104308	+	0.994545i	$0.533263\pi$
$654$	−8.86015e6	−0.810022
$655$	1.71430e7	1.56129
$656$	1.12293e7	1.01881
$657$	−4.72966e7	−4.27481
$658$	−1.69883e7	−1.52963
$659$	1.70506e6	0.152942	0.0764710	−	0.997072i	$-0.475635\pi$
$659$	1.70506e6	0.152942	0.0764710	+	0.997072i	$0.475635\pi$
$660$	−7.83284e7	−6.99938
$661$	−4.33652e6	−0.386045	−0.193022	−	0.981194i	$-0.561829\pi$
$661$	−4.33652e6	−0.386045	−0.193022	+	0.981194i	$0.561829\pi$
$662$	2.48457e7	2.20347
$663$	1.15712e7	1.02234
$664$	−7.48868e6	−0.659151
$665$	−2.38650e7	−2.09270
$666$	−2.04082e6	−0.178287
$667$	1.31624e6	0.114557
$668$	−3.73172e7	−3.23570
$669$	−1.94495e7	−1.68013
$670$	−2.28927e7	−1.97020
$671$	−2.30782e7	−1.97878
$672$	6.13096e6	0.523727
$673$	−1.03264e7	−0.878844	−0.439422	−	0.898281i	$-0.644817\pi$
$673$	−1.03264e7	−0.878844	−0.439422	+	0.898281i	$0.644817\pi$
$674$	−7.12970e6	−0.604535
$675$	2.51146e7	2.12161
$676$	6.16703e7	5.19050
$677$	1.13590e6	0.0952504	0.0476252	−	0.998865i	$-0.484835\pi$
$677$	1.13590e6	0.0952504	0.0476252	+	0.998865i	$0.484835\pi$
$678$	−6.96779e6	−0.582132
$679$	5.29690e6	0.440907
$680$	−6.87176e6	−0.569896
$681$	2.52538e6	0.208670
$682$	−3.24110e7	−2.66828
$683$	−3.63553e6	−0.298205	−0.149103	−	0.988822i	$-0.547639\pi$
$683$	−3.63553e6	−0.298205	−0.149103	+	0.988822i	$0.547639\pi$
$684$	−1.03325e8	−8.44430
$685$	−8.36010e6	−0.680746
$686$	2.22617e7	1.80613
$687$	−2.89969e7	−2.34401
$688$	−780644.	−0.0628756
$689$	3.83362e7	3.07653
$690$	1.16507e7	0.931596
$691$	−1.58052e7	−1.25923	−0.629615	−	0.776908i	$-0.716787\pi$
$691$	−1.58052e7	−1.25923	−0.629615	+	0.776908i	$0.716787\pi$
$692$	7.71022e6	0.612071
$693$	−4.43683e7	−3.50945
$694$	1.05341e7	0.830232
$695$	−1.01330e6	−0.0795752
$696$	1.93743e7	1.51601
$697$	5.01590e6	0.391081
$698$	4.15563e7	3.22848
$699$	4.05248e7	3.13710
$700$	1.64379e7	1.26795
$701$	−4.49623e6	−0.345584	−0.172792	−	0.984958i	$-0.555279\pi$
$701$	−4.49623e6	−0.345584	−0.172792	+	0.984958i	$0.555279\pi$
$702$	−1.26650e8	−9.69976
$703$	−923634.	−0.0704874
$704$	2.42456e7	1.84375
$705$	3.17141e7	2.40314
$706$	−2.33277e7	−1.76141
$707$	−9.82175e6	−0.738993
$708$	7.03547e7	5.27485
$709$	1.84236e7	1.37645	0.688224	−	0.725499i	$-0.258391\pi$
$709$	1.84236e7	1.37645	0.688224	+	0.725499i	$0.258391\pi$
$710$	−5.39240e7	−4.01454
$711$	1.74744e7	1.29637
$712$	1.75553e7	1.29780
$713$	3.16287e6	0.233001
$714$	−1.13734e7	−0.834923
$715$	−5.12592e7	−3.74979
$716$	1.36616e7	0.995911
$717$	1.12070e7	0.814125
$718$	1.46497e6	0.106052
$719$	−9.10097e6	−0.656547	−0.328273	−	0.944583i	$-0.606467\pi$
$719$	−9.10097e6	−0.656547	−0.328273	+	0.944583i	$0.606467\pi$
$720$	3.41904e7	2.45795
$721$	−1.16220e7	−0.832610
$722$	−4.73910e7	−3.38340
$723$	−6.26029e6	−0.445399
$724$	−2.75118e7	−1.95062
$725$	−5.28416e6	−0.373362
$726$	−5.47466e7	−3.85493
$727$	−1.54428e7	−1.08365	−0.541827	−	0.840490i	$-0.682267\pi$
$727$	−1.54428e7	−1.08365	−0.541827	+	0.840490i	$0.682267\pi$
$728$	−3.94411e7	−2.75817
$729$	3.05681e7	2.13034
$730$	5.37083e7	3.73022
$731$	−348697.	−0.0241354
$732$	6.96720e7	4.80596
$733$	−2.20731e7	−1.51741	−0.758707	−	0.651432i	$-0.774168\pi$
$733$	−2.20731e7	−1.51741	−0.758707	+	0.651432i	$0.774168\pi$
$734$	−1.06744e6	−0.0731312
$735$	−5.31058e6	−0.362596
$736$	−974353.	−0.0663012
$737$	−1.92620e7	−1.30627
$738$	−9.00381e7	−6.08535
$739$	−5.89109e6	−0.396812	−0.198406	−	0.980120i	$-0.563576\pi$
$739$	−5.89109e6	−0.396812	−0.198406	+	0.980120i	$0.563576\pi$
$740$	1.52046e6	0.102070
$741$	−9.40052e7	−6.28936
$742$	−3.76809e7	−2.51253
$743$	234905.	0.0156106	0.00780532	−	0.999970i	$-0.497515\pi$
$743$	234905.	0.0156106	0.00780532	+	0.999970i	$0.497515\pi$
$744$	4.65556e7	3.08347
$745$	−8.11409e6	−0.535611
$746$	−3.34413e7	−2.20007
$747$	1.66432e7	1.09128
$748$	−1.21520e7	−0.794137
$749$	−1.44324e7	−0.940015
$750$	1.82392e7	1.18400
$751$	1.81220e7	1.17248	0.586241	−	0.810137i	$-0.300607\pi$
$751$	1.81220e7	1.17248	0.586241	+	0.810137i	$0.300607\pi$
$752$	1.10151e7	0.710302
$753$	−1.07859e7	−0.693216
$754$	2.66473e7	1.70697
$755$	1.90192e7	1.21429
$756$	8.16722e7	5.19720
$757$	1.78488e7	1.13206	0.566030	−	0.824384i	$-0.308479\pi$
$757$	1.78488e7	1.13206	0.566030	+	0.824384i	$0.308479\pi$
$758$	959042.	0.0606268
$759$	9.80293e6	0.617663
$760$	5.58264e7	3.50595
$761$	1.96274e7	1.22858	0.614288	−	0.789082i	$-0.289443\pi$
$761$	1.96274e7	1.22858	0.614288	+	0.789082i	$0.289443\pi$
$762$	3.30493e7	2.06193
$763$	3.73907e6	0.232516
$764$	2.32543e7	1.44135
$765$	1.52721e7	0.943508
$766$	2.86485e6	0.176413
$767$	4.60411e7	2.82590
$768$	−5.73953e7	−3.51134
$769$	1.29894e7	0.792087	0.396043	−	0.918232i	$-0.370383\pi$
$769$	1.29894e7	0.792087	0.396043	+	0.918232i	$0.370383\pi$
$770$	5.03830e7	3.06237
$771$	3.45460e7	2.09296
$772$	−2.17830e7	−1.31545
$773$	3.03825e7	1.82884	0.914418	−	0.404771i	$-0.132649\pi$
$773$	3.03825e7	1.82884	0.914418	+	0.404771i	$0.132649\pi$
$774$	6.25930e6	0.375555
$775$	−1.26976e7	−0.759396
$776$	−1.23908e7	−0.738662
$777$	1.19736e6	0.0711494
$778$	−2.69564e7	−1.59666
$779$	−4.07493e7	−2.40590
$780$	1.54749e8	9.10733
$781$	−4.53720e7	−2.66171
$782$	1.80751e6	0.105697
$783$	−2.62544e7	−1.53038
$784$	−1.84449e6	−0.107173
$785$	3.77652e7	2.18734
$786$	−6.63726e7	−3.83206
$787$	1.48098e7	0.852338	0.426169	−	0.904644i	$-0.359863\pi$
$787$	1.48098e7	0.852338	0.426169	+	0.904644i	$0.359863\pi$
$788$	−5.77299e7	−3.31196
$789$	−2.75855e7	−1.57757
$790$	−1.98433e7	−1.13122
$791$	2.94048e6	0.167100
$792$	1.03789e8	5.87947
$793$	4.55943e7	2.57471
$794$	−7.27357e6	−0.409446
$795$	7.03434e7	3.94735
$796$	−1.42404e7	−0.796598
$797$	−1.88994e7	−1.05391	−0.526954	−	0.849894i	$-0.676666\pi$
$797$	−1.88994e7	−1.05391	−0.526954	+	0.849894i	$0.676666\pi$
$798$	9.23983e7	5.13638
$799$	4.92020e6	0.272656
$800$	3.91163e6	0.216089
$801$	−3.90157e7	−2.14861
$802$	−2.27225e6	−0.124744
$803$	4.51905e7	2.47319
$804$	5.81510e7	3.17261
$805$	−4.91669e6	−0.267414
$806$	6.40325e7	3.47187
$807$	5.04691e6	0.272798
$808$	2.29756e7	1.23805
$809$	−7.95291e6	−0.427223	−0.213612	−	0.976919i	$-0.568523\pi$
$809$	−7.95291e6	−0.427223	−0.213612	+	0.976919i	$0.568523\pi$
$810$	−1.25404e8	−6.71583
$811$	2.78296e7	1.48578	0.742889	−	0.669414i	$-0.233455\pi$
$811$	2.78296e7	1.48578	0.742889	+	0.669414i	$0.233455\pi$
$812$	−1.71840e7	−0.914606
$813$	−5.84325e7	−3.10048
$814$	1.94995e6	0.103148
$815$	−9.21872e6	−0.486157
$816$	7.37444e6	0.387707
$817$	2.83283e6	0.148479
$818$	1.42788e7	0.746120
$819$	8.76557e7	4.56636
$820$	6.70805e7	3.48387
$821$	−2.65805e7	−1.37627	−0.688137	−	0.725580i	$-0.741571\pi$
$821$	−2.65805e7	−1.37627	−0.688137	+	0.725580i	$0.741571\pi$
$822$	3.23679e7	1.67084
$823$	−2.73094e7	−1.40544	−0.702719	−	0.711467i	$-0.748031\pi$
$823$	−2.73094e7	−1.40544	−0.702719	+	0.711467i	$0.748031\pi$
$824$	2.71868e7	1.39489
$825$	−3.93547e7	−2.01308
$826$	−4.52541e7	−2.30785
$827$	−1.41034e7	−0.717066	−0.358533	−	0.933517i	$-0.616723\pi$
$827$	−1.41034e7	−0.717066	−0.358533	+	0.933517i	$0.616723\pi$
$828$	−2.12871e7	−1.07905
$829$	7.46289e6	0.377156	0.188578	−	0.982058i	$-0.439612\pi$
$829$	7.46289e6	0.377156	0.188578	+	0.982058i	$0.439612\pi$
$830$	−1.88994e7	−0.952254
$831$	−3.83726e7	−1.92761
$832$	−4.79006e7	−2.39901
$833$	−823895.	−0.0411395
$834$	3.92322e6	0.195311
$835$	−4.48101e7	−2.22413
$836$	9.87237e7	4.88546
$837$	−6.30884e7	−3.11269
$838$	1.59574e7	0.784969
$839$	−1.87276e7	−0.918495	−0.459247	−	0.888308i	$-0.651881\pi$
$839$	−1.87276e7	−0.918495	−0.459247	+	0.888308i	$0.651881\pi$
$840$	−7.23708e7	−3.53888
$841$	−1.49872e7	−0.730684
$842$	−1.13629e7	−0.552342
$843$	−7.35875e6	−0.356644
$844$	−6.96414e7	−3.36520
$845$	7.40531e7	3.56781
$846$	−8.83202e7	−4.24262
$847$	2.31036e7	1.10655
$848$	2.44319e7	1.16672
$849$	1.73589e7	0.826520
$850$	−7.25640e6	−0.344488
$851$	−190288.	−0.00900716
$852$	1.36975e8	6.46463
$853$	8.91693e6	0.419607	0.209803	−	0.977744i	$-0.432718\pi$
$853$	8.91693e6	0.419607	0.209803	+	0.977744i	$0.432718\pi$
$854$	−4.48149e7	−2.10270
$855$	−1.24071e8	−5.80438
$856$	3.37612e7	1.57483
$857$	2.45452e7	1.14160	0.570801	−	0.821088i	$-0.306633\pi$
$857$	2.45452e7	1.14160	0.570801	+	0.821088i	$0.306633\pi$
$858$	1.98461e8	9.20358
$859$	8.72160e6	0.403286	0.201643	−	0.979459i	$-0.435372\pi$
$859$	8.72160e6	0.403286	0.201643	+	0.979459i	$0.435372\pi$
$860$	−4.66332e6	−0.215005
$861$	5.28256e7	2.42849
$862$	3.39337e7	1.55547
$863$	−1.37521e7	−0.628552	−0.314276	−	0.949332i	$-0.601762\pi$
$863$	−1.37521e7	−0.628552	−0.314276	+	0.949332i	$0.601762\pi$
$864$	1.94350e7	0.885727
$865$	9.25836e6	0.420720
$866$	−2.99899e7	−1.35888
$867$	−3.84813e7	−1.73861
$868$	−4.12925e7	−1.86025
$869$	−1.66963e7	−0.750017
$870$	4.88954e7	2.19013
$871$	3.80548e7	1.69967
$872$	−8.74667e6	−0.389539
$873$	2.75379e7	1.22291
$874$	−1.46843e7	−0.650240
$875$	−7.69712e6	−0.339866
$876$	−1.36428e8	−6.00679
$877$	−3.27045e7	−1.43585	−0.717925	−	0.696121i	$-0.754908\pi$
$877$	−3.27045e7	−1.43585	−0.717925	+	0.696121i	$0.754908\pi$
$878$	−5.09550e7	−2.23075
$879$	4.15895e6	0.181556
$880$	−3.26679e7	−1.42205
$881$	−9.73641e6	−0.422629	−0.211314	−	0.977418i	$-0.567774\pi$
$881$	−9.73641e6	−0.422629	−0.211314	+	0.977418i	$0.567774\pi$
$882$	1.47894e7	0.640144
$883$	2.66331e7	1.14953	0.574764	−	0.818319i	$-0.305094\pi$
$883$	2.66331e7	1.14953	0.574764	+	0.818319i	$0.305094\pi$
$884$	2.40081e7	1.03330
$885$	8.44812e7	3.62578
$886$	1.79606e7	0.768664
$887$	1.31096e7	0.559475	0.279738	−	0.960077i	$-0.409753\pi$
$887$	1.31096e7	0.559475	0.279738	+	0.960077i	$0.409753\pi$
$888$	−2.80093e6	−0.119198
$889$	−1.39471e7	−0.591876
$890$	4.43049e7	1.87489
$891$	−1.05516e8	−4.45270
$892$	−4.03540e7	−1.69814
$893$	−3.99719e7	−1.67736
$894$	3.14154e7	1.31462
$895$	1.64048e7	0.684562
$896$	4.04137e7	1.68174
$897$	−1.93671e7	−0.803679
$898$	−7.16777e6	−0.296615
$899$	1.32739e7	0.547772
$900$	8.54588e7	3.51682
$901$	1.09132e7	0.447859
$902$	8.60288e7	3.52069
$903$	−3.67235e6	−0.149873
$904$	−6.87855e6	−0.279947
$905$	−3.30359e7	−1.34080
$906$	−7.36367e7	−2.98040
$907$	−1.45039e7	−0.585417	−0.292709	−	0.956202i	$-0.594557\pi$
$907$	−1.45039e7	−0.585417	−0.292709	+	0.956202i	$0.594557\pi$
$908$	5.23968e6	0.210907
$909$	−5.10621e7	−2.04969
$910$	−9.95388e7	−3.98464
$911$	3.31765e7	1.32445	0.662223	−	0.749307i	$-0.269613\pi$
$911$	3.31765e7	1.32445	0.662223	+	0.749307i	$0.269613\pi$
$912$	−5.99102e7	−2.38514
$913$	−1.59021e7	−0.631360
$914$	−3.41893e7	−1.35371
$915$	8.36614e7	3.30348
$916$	−6.01628e7	−2.36913
$917$	2.80099e7	1.09999
$918$	−3.60536e7	−1.41202
$919$	4.16701e7	1.62755	0.813777	−	0.581178i	$-0.197408\pi$
$919$	4.16701e7	1.62755	0.813777	+	0.581178i	$0.197408\pi$
$920$	1.15014e7	0.448004
$921$	2.11372e7	0.821103
$922$	1.93710e7	0.750456
$923$	8.96387e7	3.46331
$924$	−1.27981e8	−4.93134
$925$	763929.	0.0293561
$926$	−5.36861e6	−0.205747
$927$	−6.04212e7	−2.30935
$928$	−4.08916e6	−0.155871
$929$	2.09875e7	0.797851	0.398926	−	0.916983i	$-0.369383\pi$
$929$	2.09875e7	0.797851	0.398926	+	0.916983i	$0.369383\pi$
$930$	1.17494e8	4.45459
$931$	6.69335e6	0.253087
$932$	8.40812e7	3.17073
$933$	−7.68832e6	−0.289153
$934$	−3.03877e7	−1.13981
$935$	−1.45921e7	−0.545868
$936$	−2.05050e8	−7.65014
$937$	−3.12809e7	−1.16394	−0.581970	−	0.813210i	$-0.697718\pi$
$937$	−3.12809e7	−1.16394	−0.581970	+	0.813210i	$0.697718\pi$
$938$	−3.74044e7	−1.38808
$939$	−1.32662e7	−0.491001
$940$	6.58006e7	2.42890
$941$	4.28608e7	1.57793	0.788963	−	0.614441i	$-0.210618\pi$
$941$	4.28608e7	1.57793	0.788963	+	0.614441i	$0.210618\pi$
$942$	−1.46216e8	−5.36867
$943$	−8.39522e6	−0.307435
$944$	2.93423e7	1.07168
$945$	9.80711e7	3.57241
$946$	−5.98058e6	−0.217278
$947$	2.36755e7	0.857874	0.428937	−	0.903334i	$-0.358888\pi$
$947$	2.36755e7	0.857874	0.428937	+	0.903334i	$0.358888\pi$
$948$	5.04052e7	1.82161
$949$	−8.92802e7	−3.21803
$950$	5.89513e7	2.11926
$951$	−5.28183e7	−1.89380
$952$	−1.12278e7	−0.401514
$953$	−3.05243e6	−0.108871	−0.0544356	−	0.998517i	$-0.517336\pi$
$953$	−3.05243e6	−0.108871	−0.0544356	+	0.998517i	$0.517336\pi$
$954$	−1.95898e8	−6.96883
$955$	2.79235e7	0.990745
$956$	2.32523e7	0.822852
$957$	4.11409e7	1.45209
$958$	4.06929e7	1.43253
$959$	−1.36596e7	−0.479613
$960$	−8.78932e7	−3.07806
$961$	3.26758e6	0.114135
$962$	−3.85240e6	−0.134213
$963$	−7.50324e7	−2.60725
$964$	−1.29889e7	−0.450173
$965$	−2.61568e7	−0.904204
$966$	1.90360e7	0.656346
$967$	−5.12653e7	−1.76302	−0.881510	−	0.472166i	$-0.843472\pi$
$967$	−5.12653e7	−1.76302	−0.881510	+	0.472166i	$0.843472\pi$
$968$	−5.40454e7	−1.85383
$969$	−2.67606e7	−0.915560
$970$	−3.12711e7	−1.06712
$971$	6.99696e6	0.238156	0.119078	−	0.992885i	$-0.462006\pi$
$971$	6.99696e6	0.238156	0.119078	+	0.992885i	$0.462006\pi$
$972$	1.52842e8	5.18891
$973$	−1.65564e6	−0.0560639
$974$	−5.40222e7	−1.82463
$975$	7.77508e7	2.61935
$976$	2.90576e7	0.976417
$977$	1.88024e7	0.630198	0.315099	−	0.949059i	$-0.397962\pi$
$977$	1.88024e7	0.630198	0.315099	+	0.949059i	$0.397962\pi$
$978$	3.56922e7	1.19324
$979$	3.72784e7	1.24308
$980$	−1.10184e7	−0.366483
$981$	1.94390e7	0.644913
$982$	8.29978e7	2.74655
$983$	7.02631e6	0.231923	0.115961	−	0.993254i	$-0.463005\pi$
$983$	7.02631e6	0.231923	0.115961	+	0.993254i	$0.463005\pi$
$984$	−1.23573e8	−4.06851
$985$	−6.93215e7	−2.27655
$986$	7.58574e6	0.248488
$987$	5.18177e7	1.69311
$988$	−1.95042e8	−6.35678
$989$	583622.	0.0189732
$990$	2.61935e8	8.49388
$991$	1.07272e7	0.346980	0.173490	−	0.984836i	$-0.444496\pi$
$991$	1.07272e7	0.346980	0.173490	+	0.984836i	$0.444496\pi$
$992$	−9.82610e6	−0.317031
$993$	−7.57844e7	−2.43897
$994$	−8.81065e7	−2.82841
$995$	−1.70997e7	−0.547559
$996$	4.80075e7	1.53342
$997$	1.40216e7	0.446744	0.223372	−	0.974733i	$-0.428293\pi$
$997$	1.40216e7	0.446744	0.223372	+	0.974733i	$0.428293\pi$
$998$	−2.53389e7	−0.805305
$999$	3.79559e6	0.120328

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.6.a.b.1.10	✓	117

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.6.a.b.1.10	✓	117	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-9.64600 q^{2} +29.4222 q^{3} +61.0453 q^{4} +73.3026 q^{5} -283.807 q^{6} +119.769 q^{7} -280.171 q^{8} +622.666 q^{9} +O(q^{10})\)	\(q-9.64600 q^{2} +29.4222 q^{3} +61.0453 q^{4} +73.3026 q^{5} -283.807 q^{6} +119.769 q^{7} -280.171 q^{8} +622.666 q^{9} -707.077 q^{10} -594.939 q^{11} +1796.09 q^{12} +1175.39 q^{13} -1155.29 q^{14} +2156.72 q^{15} +749.082 q^{16} +334.599 q^{17} -6006.23 q^{18} -2718.29 q^{19} +4474.78 q^{20} +3523.87 q^{21} +5738.78 q^{22} -560.026 q^{23} -8243.26 q^{24} +2248.28 q^{25} -11337.8 q^{26} +11170.6 q^{27} +7311.35 q^{28} -2350.32 q^{29} -20803.8 q^{30} -5647.72 q^{31} +1739.83 q^{32} -17504.4 q^{33} -3227.54 q^{34} +8779.40 q^{35} +38010.8 q^{36} +339.784 q^{37} +26220.7 q^{38} +34582.4 q^{39} -20537.3 q^{40} +14990.8 q^{41} -33991.3 q^{42} -1042.13 q^{43} -36318.2 q^{44} +45643.0 q^{45} +5402.01 q^{46} +14704.8 q^{47} +22039.6 q^{48} -2462.34 q^{49} -21686.9 q^{50} +9844.63 q^{51} +71751.8 q^{52} +32615.8 q^{53} -107752. q^{54} -43610.6 q^{55} -33555.9 q^{56} -79978.2 q^{57} +22671.1 q^{58} +39171.1 q^{59} +131658. q^{60} +38790.9 q^{61} +54477.9 q^{62} +74576.2 q^{63} -40753.1 q^{64} +86158.8 q^{65} +168848. q^{66} +32376.5 q^{67} +20425.7 q^{68} -16477.2 q^{69} -84686.1 q^{70} +76263.2 q^{71} -174453. q^{72} -75958.2 q^{73} -3277.56 q^{74} +66149.2 q^{75} -165939. q^{76} -71255.4 q^{77} -333582. q^{78} +28063.9 q^{79} +54909.7 q^{80} +177356. q^{81} -144601. q^{82} +26728.9 q^{83} +215116. q^{84} +24527.0 q^{85} +10052.4 q^{86} -69151.5 q^{87} +166685. q^{88} -62659.1 q^{89} -440273. q^{90} +140775. q^{91} -34187.0 q^{92} -166168. q^{93} -141842. q^{94} -199258. q^{95} +51189.7 q^{96} +44225.9 q^{97} +23751.7 q^{98} -370448. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9}+O(q^{10}) \) 117 * q + 24 * q^2 + 100 * q^3 + 1962 * q^4 + 749 * q^5 + 306 * q^6 + 393 * q^7 + 1152 * q^8 + 10671 * q^9	\( 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9} + 850 q^{10} + 1798 q^{11} + 5361 q^{12} + 4419 q^{13} + 3847 q^{14} + 1913 q^{15} + 34722 q^{16} + 15252 q^{17} + 2367 q^{18} + 1052 q^{19} + 23568 q^{20} + 9212 q^{21} + 9176 q^{22} + 18178 q^{23} + 15983 q^{24} + 84312 q^{25} + 21552 q^{26} + 30883 q^{27} + 23528 q^{28} + 43620 q^{29} + 23582 q^{30} + 13127 q^{31} + 49108 q^{32} + 39222 q^{33} + 32097 q^{34} + 52467 q^{35} + 217244 q^{36} + 56152 q^{37} + 76245 q^{38} + 28595 q^{39} + 20368 q^{40} + 46679 q^{41} + 78924 q^{42} + 39058 q^{43} + 78528 q^{44} + 185770 q^{45} + 41430 q^{46} + 150268 q^{47} + 180930 q^{48} + 323802 q^{49} + 91604 q^{50} + 43367 q^{51} + 136030 q^{52} + 297398 q^{53} + 116761 q^{54} + 94579 q^{55} + 173545 q^{56} + 164740 q^{57} + 87844 q^{58} + 135778 q^{59} + 114650 q^{60} + 166976 q^{61} + 229394 q^{62} + 147179 q^{63} + 630138 q^{64} + 216626 q^{65} + 82380 q^{66} + 133444 q^{67} + 634057 q^{68} + 232986 q^{69} + 30943 q^{70} + 126787 q^{71} + 78583 q^{72} + 241702 q^{73} + 242589 q^{74} + 374853 q^{75} + 90228 q^{76} + 766693 q^{77} + 82537 q^{78} + 117230 q^{79} + 730509 q^{80} + 1051409 q^{81} + 468130 q^{82} + 368467 q^{83} + 234191 q^{84} + 261997 q^{85} + 230487 q^{86} + 214239 q^{87} + 247415 q^{88} + 494902 q^{89} + 41821 q^{90} + 259647 q^{91} + 663682 q^{92} + 767344 q^{93} + 373605 q^{94} + 426186 q^{95} + 474162 q^{96} + 733038 q^{97} + 461746 q^{98} + 334651 q^{99}+O(q^{100}) \) 117 * q + 24 * q^2 + 100 * q^3 + 1962 * q^4 + 749 * q^5 + 306 * q^6 + 393 * q^7 + 1152 * q^8 + 10671 * q^9 + 850 * q^10 + 1798 * q^11 + 5361 * q^12 + 4419 * q^13 + 3847 * q^14 + 1913 * q^15 + 34722 * q^16 + 15252 * q^17 + 2367 * q^18 + 1052 * q^19 + 23568 * q^20 + 9212 * q^21 + 9176 * q^22 + 18178 * q^23 + 15983 * q^24 + 84312 * q^25 + 21552 * q^26 + 30883 * q^27 + 23528 * q^28 + 43620 * q^29 + 23582 * q^30 + 13127 * q^31 + 49108 * q^32 + 39222 * q^33 + 32097 * q^34 + 52467 * q^35 + 217244 * q^36 + 56152 * q^37 + 76245 * q^38 + 28595 * q^39 + 20368 * q^40 + 46679 * q^41 + 78924 * q^42 + 39058 * q^43 + 78528 * q^44 + 185770 * q^45 + 41430 * q^46 + 150268 * q^47 + 180930 * q^48 + 323802 * q^49 + 91604 * q^50 + 43367 * q^51 + 136030 * q^52 + 297398 * q^53 + 116761 * q^54 + 94579 * q^55 + 173545 * q^56 + 164740 * q^57 + 87844 * q^58 + 135778 * q^59 + 114650 * q^60 + 166976 * q^61 + 229394 * q^62 + 147179 * q^63 + 630138 * q^64 + 216626 * q^65 + 82380 * q^66 + 133444 * q^67 + 634057 * q^68 + 232986 * q^69 + 30943 * q^70 + 126787 * q^71 + 78583 * q^72 + 241702 * q^73 + 242589 * q^74 + 374853 * q^75 + 90228 * q^76 + 766693 * q^77 + 82537 * q^78 + 117230 * q^79 + 730509 * q^80 + 1051409 * q^81 + 468130 * q^82 + 368467 * q^83 + 234191 * q^84 + 261997 * q^85 + 230487 * q^86 + 214239 * q^87 + 247415 * q^88 + 494902 * q^89 + 41821 * q^90 + 259647 * q^91 + 663682 * q^92 + 767344 * q^93 + 373605 * q^94 + 426186 * q^95 + 474162 * q^96 + 733038 * q^97 + 461746 * q^98 + 334651 * q^99

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