LMFDB - Embedded newform 547.6.a.b.1.19

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			1.19
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)

$f(q)$	$=$	$q-8.37802 q^{2} -14.0231 q^{3} +38.1912 q^{4} +95.5871 q^{5} +117.486 q^{6} +24.4634 q^{7} -51.8698 q^{8} -46.3528 q^{9} +O(q^{10})$	\(q-8.37802 q^{2} -14.0231 q^{3} +38.1912 q^{4} +95.5871 q^{5} +117.486 q^{6} +24.4634 q^{7} -51.8698 q^{8} -46.3528 q^{9} -800.830 q^{10} +529.305 q^{11} -535.558 q^{12} -1017.94 q^{13} -204.954 q^{14} -1340.43 q^{15} -787.552 q^{16} -1592.10 q^{17} +388.345 q^{18} +2054.08 q^{19} +3650.58 q^{20} -343.052 q^{21} -4434.53 q^{22} +1817.58 q^{23} +727.375 q^{24} +6011.89 q^{25} +8528.30 q^{26} +4057.62 q^{27} +934.285 q^{28} -4673.99 q^{29} +11230.1 q^{30} +2869.61 q^{31} +8257.95 q^{32} -7422.50 q^{33} +13338.6 q^{34} +2338.38 q^{35} -1770.27 q^{36} +272.304 q^{37} -17209.1 q^{38} +14274.6 q^{39} -4958.08 q^{40} -10793.2 q^{41} +2874.10 q^{42} +5779.65 q^{43} +20214.8 q^{44} -4430.73 q^{45} -15227.7 q^{46} +14708.0 q^{47} +11043.9 q^{48} -16208.5 q^{49} -50367.7 q^{50} +22326.1 q^{51} -38876.2 q^{52} +8994.93 q^{53} -33994.8 q^{54} +50594.8 q^{55} -1268.91 q^{56} -28804.6 q^{57} +39158.8 q^{58} +7700.81 q^{59} -51192.5 q^{60} +24406.9 q^{61} -24041.6 q^{62} -1133.95 q^{63} -43983.6 q^{64} -97301.6 q^{65} +62185.8 q^{66} +9072.70 q^{67} -60804.0 q^{68} -25488.1 q^{69} -19591.0 q^{70} -59109.1 q^{71} +2404.31 q^{72} +85946.1 q^{73} -2281.37 q^{74} -84305.3 q^{75} +78447.8 q^{76} +12948.6 q^{77} -119593. q^{78} -22549.0 q^{79} -75279.8 q^{80} -45636.7 q^{81} +90425.2 q^{82} +64478.0 q^{83} -13101.6 q^{84} -152184. q^{85} -48422.0 q^{86} +65543.9 q^{87} -27455.0 q^{88} -115912. q^{89} +37120.8 q^{90} -24902.2 q^{91} +69415.6 q^{92} -40240.7 q^{93} -123224. q^{94} +196344. q^{95} -115802. q^{96} +73682.0 q^{97} +135795. q^{98} -24534.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−8.37802	−1.48104	−0.740519	−	0.672035i	$-0.765420\pi$
$2$	−8.37802	−1.48104	−0.740519	+	0.672035i	$0.765420\pi$
$3$	−14.0231	−0.899582	−0.449791	−	0.893134i	$-0.648502\pi$
$3$	−14.0231	−0.899582	−0.449791	+	0.893134i	$0.648502\pi$
$4$	38.1912	1.19347
$5$	95.5871	1.70991	0.854957	−	0.518699i	$-0.173584\pi$
$5$	95.5871	1.70991	0.854957	+	0.518699i	$0.173584\pi$
$6$	117.486	1.33232
$7$	24.4634	0.188700	0.0943498	−	0.995539i	$-0.469923\pi$
$7$	24.4634	0.188700	0.0943498	+	0.995539i	$0.469923\pi$
$8$	−51.8698	−0.286543
$9$	−46.3528	−0.190752
$10$	−800.830	−2.53245
$11$	529.305	1.31894	0.659469	−	0.751731i	$-0.270781\pi$
$11$	529.305	1.31894	0.659469	+	0.751731i	$0.270781\pi$
$12$	−535.558	−1.07363
$13$	−1017.94	−1.67056	−0.835281	−	0.549823i	$-0.814695\pi$
$13$	−1017.94	−1.67056	−0.835281	+	0.549823i	$0.814695\pi$
$14$	−204.954	−0.279471
$15$	−1340.43	−1.53821
$16$	−787.552	−0.769093
$17$	−1592.10	−1.33612	−0.668062	−	0.744105i	$-0.732876\pi$
$17$	−1592.10	−1.33612	−0.668062	+	0.744105i	$0.732876\pi$
$18$	388.345	0.282512
$19$	2054.08	1.30537	0.652685	−	0.757629i	$-0.273642\pi$
$19$	2054.08	1.30537	0.652685	+	0.757629i	$0.273642\pi$
$20$	3650.58	2.04074
$21$	−343.052	−0.169751
$22$	−4434.53	−1.95340
$23$	1817.58	0.716431	0.358216	−	0.933639i	$-0.383385\pi$
$23$	1817.58	0.716431	0.358216	+	0.933639i	$0.383385\pi$
$24$	727.375	0.257769
$25$	6011.89	1.92380
$26$	8528.30	2.47417
$27$	4057.62	1.07118
$28$	934.285	0.225208
$29$	−4673.99	−1.03203	−0.516016	−	0.856579i	$-0.672585\pi$
$29$	−4673.99	−1.03203	−0.516016	+	0.856579i	$0.672585\pi$
$30$	11230.1	2.27814
$31$	2869.61	0.536313	0.268156	−	0.963375i	$-0.413586\pi$
$31$	2869.61	0.536313	0.268156	+	0.963375i	$0.413586\pi$
$32$	8257.95	1.42560
$33$	−7422.50	−1.18649
$34$	13338.6	1.97885
$35$	2338.38	0.322660
$36$	−1770.27	−0.227658
$37$	272.304	0.0327001	0.0163501	−	0.999866i	$-0.494795\pi$
$37$	272.304	0.0327001	0.0163501	+	0.999866i	$0.494795\pi$
$38$	−17209.1	−1.93330
$39$	14274.6	1.50281
$40$	−4958.08	−0.489963
$41$	−10793.2	−1.00274	−0.501371	−	0.865233i	$-0.667171\pi$
$41$	−10793.2	−1.00274	−0.501371	+	0.865233i	$0.667171\pi$
$42$	2874.10	0.251407
$43$	5779.65	0.476684	0.238342	−	0.971181i	$-0.423396\pi$
$43$	5779.65	0.476684	0.238342	+	0.971181i	$0.423396\pi$
$44$	20214.8	1.57412
$45$	−4430.73	−0.326170
$46$	−15227.7	−1.06106
$47$	14708.0	0.971203	0.485601	−	0.874180i	$-0.338601\pi$
$47$	14708.0	0.971203	0.485601	+	0.874180i	$0.338601\pi$
$48$	11043.9	0.691862
$49$	−16208.5	−0.964392
$50$	−50367.7	−2.84923
$51$	22326.1	1.20195
$52$	−38876.2	−1.99377
$53$	8994.93	0.439854	0.219927	−	0.975516i	$-0.429418\pi$
$53$	8994.93	0.439854	0.219927	+	0.975516i	$0.429418\pi$
$54$	−33994.8	−1.58646
$55$	50594.8	2.25527
$56$	−1268.91	−0.0540705
$57$	−28804.6	−1.17429
$58$	39158.8	1.52848
$59$	7700.81	0.288009	0.144005	−	0.989577i	$-0.454002\pi$
$59$	7700.81	0.288009	0.144005	+	0.989577i	$0.454002\pi$
$60$	−51192.5	−1.83581
$61$	24406.9	0.839823	0.419912	−	0.907565i	$-0.362061\pi$
$61$	24406.9	0.839823	0.419912	+	0.907565i	$0.362061\pi$
$62$	−24041.6	−0.794299
$63$	−1133.95	−0.0359949
$64$	−43983.6	−1.34227
$65$	−97301.6	−2.85652
$66$	62185.8	1.75724
$67$	9072.70	0.246916	0.123458	−	0.992350i	$-0.460602\pi$
$67$	9072.70	0.246916	0.123458	+	0.992350i	$0.460602\pi$
$68$	−60804.0	−1.59463
$69$	−25488.1	−0.644489
$70$	−19591.0	−0.477872
$71$	−59109.1	−1.39158	−0.695790	−	0.718245i	$-0.744946\pi$
$71$	−59109.1	−1.39158	−0.695790	+	0.718245i	$0.744946\pi$
$72$	2404.31	0.0546588
$73$	85946.1	1.88764	0.943819	−	0.330462i	$-0.107205\pi$
$73$	85946.1	1.88764	0.943819	+	0.330462i	$0.107205\pi$
$74$	−2281.37	−0.0484301
$75$	−84305.3	−1.73062
$76$	78447.8	1.55793
$77$	12948.6	0.248883
$78$	−119593.	−2.22572
$79$	−22549.0	−0.406499	−0.203250	−	0.979127i	$-0.565150\pi$
$79$	−22549.0	−0.406499	−0.203250	+	0.979127i	$0.565150\pi$
$80$	−75279.8	−1.31508
$81$	−45636.7	−0.772861
$82$	90425.2	1.48510
$83$	64478.0	1.02735	0.513673	−	0.857986i	$-0.328285\pi$
$83$	64478.0	1.02735	0.513673	+	0.857986i	$0.328285\pi$
$84$	−13101.6	−0.202593
$85$	−152184.	−2.28466
$86$	−48422.0	−0.705987
$87$	65543.9	0.928397
$88$	−27455.0	−0.377932
$89$	−115912.	−1.55114	−0.775572	−	0.631259i	$-0.782538\pi$
$89$	−115912.	−1.55114	−0.775572	+	0.631259i	$0.782538\pi$
$90$	37120.8	0.483071
$91$	−24902.2	−0.315234
$92$	69415.6	0.855042
$93$	−40240.7	−0.482457
$94$	−123224.	−1.43839
$95$	196344.	2.23207
$96$	−115802.	−1.28244
$97$	73682.0	0.795119	0.397559	−	0.917576i	$-0.369857\pi$
$97$	73682.0	0.795119	0.397559	+	0.917576i	$0.369857\pi$
$98$	135795.	1.42830
$99$	−24534.8	−0.251591
$100$	229601.	2.29601
$101$	−107789.	−1.05141	−0.525703	−	0.850668i	$-0.676198\pi$
$101$	−107789.	−1.05141	−0.525703	+	0.850668i	$0.676198\pi$
$102$	−187049.	−1.78014
$103$	−146495.	−1.36059	−0.680297	−	0.732937i	$-0.738149\pi$
$103$	−146495.	−1.36059	−0.680297	+	0.732937i	$0.738149\pi$
$104$	52800.2	0.478688
$105$	−32791.3	−0.290259
$106$	−75359.7	−0.651440
$107$	−20995.5	−0.177283	−0.0886413	−	0.996064i	$-0.528252\pi$
$107$	−20995.5	−0.177283	−0.0886413	+	0.996064i	$0.528252\pi$
$108$	154965.	1.27842
$109$	−67194.7	−0.541713	−0.270856	−	0.962620i	$-0.587307\pi$
$109$	−67194.7	−0.541713	−0.270856	+	0.962620i	$0.587307\pi$
$110$	−423884.	−3.34014
$111$	−3818.54	−0.0294164
$112$	−19266.2	−0.145128
$113$	153163.	1.12839	0.564193	−	0.825643i	$-0.309187\pi$
$113$	153163.	1.12839	0.564193	+	0.825643i	$0.309187\pi$
$114$	241325.	1.73916
$115$	173737.	1.22504
$116$	−178505.	−1.23170
$117$	47184.3	0.318664
$118$	−64517.6	−0.426553
$119$	−38948.0	−0.252126
$120$	69527.6	0.440762
$121$	119113.	0.739600
$122$	−204481.	−1.24381
$123$	151353.	0.902048
$124$	109594.	0.640075
$125$	275949.	1.57963
$126$	9500.23	0.0533099
$127$	214880.	1.18219	0.591094	−	0.806603i	$-0.298696\pi$
$127$	214880.	1.18219	0.591094	+	0.806603i	$0.298696\pi$
$128$	104241.	0.562360
$129$	−81048.6	−0.428816
$130$	815195.	4.23061
$131$	3267.55	0.0166358	0.00831791	−	0.999965i	$-0.497352\pi$
$131$	3267.55	0.0166358	0.00831791	+	0.999965i	$0.497352\pi$
$132$	−283474.	−1.41605
$133$	50249.8	0.246323
$134$	−76011.2	−0.365692
$135$	387856.	1.83162
$136$	82581.7	0.382857
$137$	383621.	1.74623	0.873114	−	0.487515i	$-0.162097\pi$
$137$	383621.	1.74623	0.873114	+	0.487515i	$0.162097\pi$
$138$	213540.	0.954512
$139$	224755.	0.986669	0.493334	−	0.869840i	$-0.335778\pi$
$139$	224755.	0.986669	0.493334	+	0.869840i	$0.335778\pi$
$140$	89305.5	0.385087
$141$	−206252.	−0.873677
$142$	495217.	2.06098
$143$	−538800.	−2.20337
$144$	36505.3	0.146706
$145$	−446773.	−1.76469
$146$	−720058.	−2.79566
$147$	227294.	0.867550
$148$	10399.6	0.0390267
$149$	298377.	1.10103	0.550516	−	0.834825i	$-0.314431\pi$
$149$	298377.	1.10103	0.550516	+	0.834825i	$0.314431\pi$
$150$	706311.	2.56311
$151$	−216993.	−0.774469	−0.387234	−	0.921981i	$-0.626570\pi$
$151$	−216993.	−0.774469	−0.387234	+	0.921981i	$0.626570\pi$
$152$	−106545.	−0.374045
$153$	73798.2	0.254869
$154$	−108484.	−0.368606
$155$	274297.	0.917048
$156$	545165.	1.79356
$157$	413639.	1.33928	0.669641	−	0.742685i	$-0.266448\pi$
$157$	413639.	1.33928	0.669641	+	0.742685i	$0.266448\pi$
$158$	188916.	0.602041
$159$	−126137.	−0.395684
$160$	789354.	2.43765
$161$	44464.2	0.135190
$162$	382345.	1.14464
$163$	−329207.	−0.970509	−0.485254	−	0.874373i	$-0.661273\pi$
$163$	−329207.	−0.970509	−0.485254	+	0.874373i	$0.661273\pi$
$164$	−412203.	−1.19675
$165$	−709495.	−2.02880
$166$	−540198.	−1.52154
$167$	−292049.	−0.810336	−0.405168	−	0.914242i	$-0.632787\pi$
$167$	−292049.	−0.810336	−0.405168	+	0.914242i	$0.632787\pi$
$168$	17794.0	0.0486409
$169$	664903.	1.79078
$170$	1.27500e6	3.38367
$171$	−95212.6	−0.249003
$172$	220732.	0.568910
$173$	−184788.	−0.469416	−0.234708	−	0.972066i	$-0.575413\pi$
$173$	−184788.	−0.469416	−0.234708	+	0.972066i	$0.575413\pi$
$174$	−549128.	−1.37499
$175$	147071.	0.363021
$176$	−416855.	−1.01439
$177$	−107989.	−0.259088
$178$	971110.	2.29730
$179$	−89139.0	−0.207939	−0.103969	−	0.994581i	$-0.533154\pi$
$179$	−89139.0	−0.207939	−0.103969	+	0.994581i	$0.533154\pi$
$180$	−169215.	−0.389276
$181$	−334572.	−0.759090	−0.379545	−	0.925173i	$-0.623920\pi$
$181$	−334572.	−0.759090	−0.379545	+	0.925173i	$0.623920\pi$
$182$	208631.	0.466874
$183$	−342260.	−0.755490
$184$	−94277.6	−0.205288
$185$	26028.7	0.0559144
$186$	337138.	0.714537
$187$	−842705.	−1.76227
$188$	561717.	1.15911
$189$	99263.1	0.202131
$190$	−1.64497e6	−3.30578
$191$	941142.	1.86669	0.933344	−	0.358982i	$-0.116876\pi$
$191$	941142.	1.86669	0.933344	+	0.358982i	$0.116876\pi$
$192$	616787.	1.20749
$193$	48333.1	0.0934010	0.0467005	−	0.998909i	$-0.485129\pi$
$193$	48333.1	0.0934010	0.0467005	+	0.998909i	$0.485129\pi$
$194$	−617309.	−1.17760
$195$	1.36447e6	2.56967
$196$	−619023.	−1.15098
$197$	−719559.	−1.32099	−0.660497	−	0.750828i	$-0.729655\pi$
$197$	−719559.	−1.32099	−0.660497	+	0.750828i	$0.729655\pi$
$198$	205553.	0.372616
$199$	−633742.	−1.13443	−0.567217	−	0.823568i	$-0.691980\pi$
$199$	−633742.	−1.13443	−0.567217	+	0.823568i	$0.691980\pi$
$200$	−311835.	−0.551252
$201$	−127227.	−0.222121
$202$	903057.	1.55717
$203$	−114342.	−0.194744
$204$	852661.	1.43450
$205$	−1.03169e6	−1.71460
$206$	1.22733e6	2.01509
$207$	−84250.1	−0.136661
$208$	801678.	1.28482
$209$	1.08724e6	1.72170
$210$	274726.	0.429885
$211$	1.06303e6	1.64376	0.821879	−	0.569661i	$-0.192926\pi$
$211$	1.06303e6	1.64376	0.821879	+	0.569661i	$0.192926\pi$
$212$	343527.	0.524954
$213$	828892.	1.25184
$214$	175900.	0.262562
$215$	552460.	0.815089
$216$	−210468.	−0.306939
$217$	70200.2	0.101202
$218$	562959.	0.802297
$219$	−1.20523e6	−1.69809
$220$	1.93227e6	2.69161
$221$	1.62065e6	2.23208
$222$	31991.8	0.0435669
$223$	773253.	1.04126	0.520631	−	0.853782i	$-0.325697\pi$
$223$	773253.	1.04126	0.520631	+	0.853782i	$0.325697\pi$
$224$	202017.	0.269010
$225$	−278668.	−0.366970
$226$	−1.28320e6	−1.67118
$227$	68137.4	0.0877649	0.0438824	−	0.999037i	$-0.486027\pi$
$227$	68137.4	0.0877649	0.0438824	+	0.999037i	$0.486027\pi$
$228$	−1.10008e6	−1.40148
$229$	−1.50536e6	−1.89693	−0.948464	−	0.316885i	$-0.897363\pi$
$229$	−1.50536e6	−1.89693	−0.948464	+	0.316885i	$0.897363\pi$
$230$	−1.45557e6	−1.81432
$231$	−181579.	−0.223891
$232$	242439.	0.295721
$233$	−1.27884e6	−1.54322	−0.771610	−	0.636096i	$-0.780548\pi$
$233$	−1.27884e6	−1.54322	−0.771610	+	0.636096i	$0.780548\pi$
$234$	−395311.	−0.471953
$235$	1.40590e6	1.66067
$236$	294103.	0.343732
$237$	316207.	0.365679
$238$	326307.	0.373409
$239$	1.28173e6	1.45145	0.725725	−	0.687985i	$-0.241504\pi$
$239$	1.28173e6	1.45145	0.725725	+	0.687985i	$0.241504\pi$
$240$	1.05566e6	1.18302
$241$	907699.	1.00670	0.503349	−	0.864083i	$-0.332101\pi$
$241$	907699.	1.00670	0.503349	+	0.864083i	$0.332101\pi$
$242$	−997933.	−1.09538
$243$	−346035.	−0.375928
$244$	932128.	1.00231
$245$	−1.54933e6	−1.64903
$246$	−1.26804e6	−1.33597
$247$	−2.09093e6	−2.18070
$248$	−148846.	−0.153677
$249$	−904181.	−0.924181
$250$	−2.31191e6	−2.33949
$251$	−610225.	−0.611372	−0.305686	−	0.952132i	$-0.598886\pi$
$251$	−610225.	−0.611372	−0.305686	+	0.952132i	$0.598886\pi$
$252$	−43306.8	−0.0429590
$253$	962056.	0.944929
$254$	−1.80027e6	−1.75087
$255$	2.13409e6	2.05524
$256$	534142.	0.509398
$257$	388950.	0.367333	0.183667	−	0.982989i	$-0.441203\pi$
$257$	388950.	0.367333	0.183667	+	0.982989i	$0.441203\pi$
$258$	679027.	0.635093
$259$	6661.47	0.00617050
$260$	−3.71606e6	−3.40918
$261$	216653.	0.196863
$262$	−27375.6	−0.0246383
$263$	737943.	0.657860	0.328930	−	0.944354i	$-0.393312\pi$
$263$	737943.	0.657860	0.328930	+	0.944354i	$0.393312\pi$
$264$	385004.	0.339981
$265$	859799.	0.752112
$266$	−420993.	−0.364814
$267$	1.62544e6	1.39538
$268$	346497.	0.294688
$269$	1.34467e6	1.13301	0.566505	−	0.824059i	$-0.308295\pi$
$269$	1.34467e6	1.13301	0.566505	+	0.824059i	$0.308295\pi$
$270$	−3.24947e6	−2.71271
$271$	104826.	0.0867050	0.0433525	−	0.999060i	$-0.486196\pi$
$271$	104826.	0.0867050	0.0433525	+	0.999060i	$0.486196\pi$
$272$	1.25386e6	1.02760
$273$	349205.	0.283579
$274$	−3.21398e6	−2.58623
$275$	3.18213e6	2.53738
$276$	−973422.	−0.769181
$277$	−263679.	−0.206479	−0.103240	−	0.994657i	$-0.532921\pi$
$277$	−263679.	−0.206479	−0.103240	+	0.994657i	$0.532921\pi$
$278$	−1.88300e6	−1.46129
$279$	−133014.	−0.102303
$280$	−121291.	−0.0924559
$281$	−970893.	−0.733509	−0.366755	−	0.930318i	$-0.619531\pi$
$281$	−970893.	−0.733509	−0.366755	+	0.930318i	$0.619531\pi$
$282$	1.72798e6	1.29395
$283$	1.95601e6	1.45179	0.725897	−	0.687804i	$-0.241425\pi$
$283$	1.95601e6	1.45179	0.725897	+	0.687804i	$0.241425\pi$
$284$	−2.25745e6	−1.66082
$285$	−2.75335e6	−2.00793
$286$	4.51407e6	3.26327
$287$	−264037.	−0.189217
$288$	−382780.	−0.271937
$289$	1.11491e6	0.785230
$290$	3.74308e6	2.61357
$291$	−1.03325e6	−0.715274
$292$	3.28238e6	2.25285
$293$	1.99228e6	1.35575	0.677877	−	0.735175i	$-0.262900\pi$
$293$	1.99228e6	1.35575	0.677877	+	0.735175i	$0.262900\pi$
$294$	−1.90427e6	−1.28487
$295$	736098.	0.492471
$296$	−14124.3	−0.00936998
$297$	2.14772e6	1.41282
$298$	−2.49981e6	−1.63067
$299$	−1.85018e6	−1.19684
$300$	−3.21972e6	−2.06545
$301$	141390.	0.0899501
$302$	1.81797e6	1.14702
$303$	1.51153e6	0.945825
$304$	−1.61770e6	−1.00395
$305$	2.33298e6	1.43602
$306$	−618283.	−0.377471
$307$	−1.53603e6	−0.930149	−0.465074	−	0.885272i	$-0.653972\pi$
$307$	−1.53603e6	−0.930149	−0.465074	+	0.885272i	$0.653972\pi$
$308$	494522.	0.297036
$309$	2.05431e6	1.22397
$310$	−2.29807e6	−1.35818
$311$	2.30584e6	1.35185	0.675924	−	0.736971i	$-0.263745\pi$
$311$	2.30584e6	1.35185	0.675924	+	0.736971i	$0.263745\pi$
$312$	−740422.	−0.430619
$313$	−170545.	−0.0983964	−0.0491982	−	0.998789i	$-0.515667\pi$
$313$	−170545.	−0.0983964	−0.0491982	+	0.998789i	$0.515667\pi$
$314$	−3.46547e6	−1.98353
$315$	−108391.	−0.0615482
$316$	−861173.	−0.485147
$317$	2.73170e6	1.52681	0.763405	−	0.645920i	$-0.223526\pi$
$317$	2.73170e6	1.52681	0.763405	+	0.645920i	$0.223526\pi$
$318$	1.05678e6	0.586024
$319$	−2.47397e6	−1.36119
$320$	−4.20427e6	−2.29517
$321$	294421.	0.159480
$322$	−372522.	−0.200222
$323$	−3.27030e6	−1.74414
$324$	−1.74292e6	−0.922390
$325$	−6.11973e6	−3.21383
$326$	2.75810e6	1.43736
$327$	942278.	0.487315
$328$	559839.	0.287328
$329$	359808.	0.183266
$330$	5.94416e6	3.00473
$331$	1.47214e6	0.738549	0.369274	−	0.929320i	$-0.379606\pi$
$331$	1.47214e6	0.738549	0.369274	+	0.929320i	$0.379606\pi$
$332$	2.46249e6	1.22611
$333$	−12622.1	−0.00623763
$334$	2.44679e6	1.20014
$335$	867233.	0.422205
$336$	270171.	0.130554
$337$	−3.14257e6	−1.50734	−0.753669	−	0.657254i	$-0.771718\pi$
$337$	−3.14257e6	−1.50734	−0.753669	+	0.657254i	$0.771718\pi$
$338$	−5.57057e6	−2.65221
$339$	−2.14782e6	−1.01508
$340$	−5.81208e6	−2.72668
$341$	1.51890e6	0.707363
$342$	797693.	0.368782
$343$	−807671.	−0.370680
$344$	−299789.	−0.136590
$345$	−2.43634e6	−1.10202
$346$	1.54815e6	0.695223
$347$	82962.7	0.0369878	0.0184939	−	0.999829i	$-0.494113\pi$
$347$	82962.7	0.0369878	0.0184939	+	0.999829i	$0.494113\pi$
$348$	2.50320e6	1.10802
$349$	−2.40951e6	−1.05893	−0.529463	−	0.848333i	$-0.677607\pi$
$349$	−2.40951e6	−1.05893	−0.529463	+	0.848333i	$0.677607\pi$
$350$	−1.23216e6	−0.537648
$351$	−4.13040e6	−1.78947
$352$	4.37098e6	1.88028
$353$	−2.81142e6	−1.20085	−0.600424	−	0.799682i	$-0.705002\pi$
$353$	−2.81142e6	−1.20085	−0.600424	+	0.799682i	$0.705002\pi$
$354$	904736.	0.383719
$355$	−5.65006e6	−2.37948
$356$	−4.42680e6	−1.85125
$357$	546172.	0.226808
$358$	746808.	0.307965
$359$	−1.57610e6	−0.645427	−0.322713	−	0.946497i	$-0.604595\pi$
$359$	−1.57610e6	−0.645427	−0.322713	+	0.946497i	$0.604595\pi$
$360$	229821.	0.0934617
$361$	1.74315e6	0.703992
$362$	2.80305e6	1.12424
$363$	−1.67034e6	−0.665330
$364$	−951043.	−0.376224
$365$	8.21533e6	3.22770
$366$	2.86746e6	1.11891
$367$	3.13791e6	1.21612	0.608058	−	0.793892i	$-0.291949\pi$
$367$	3.13791e6	1.21612	0.608058	+	0.793892i	$0.291949\pi$
$368$	−1.43144e6	−0.551003
$369$	500294.	0.191275
$370$	−218069.	−0.0828113
$371$	220046.	0.0830002
$372$	−1.53684e6	−0.575800
$373$	−485782.	−0.180788	−0.0903940	−	0.995906i	$-0.528813\pi$
$373$	−485782.	−0.180788	−0.0903940	+	0.995906i	$0.528813\pi$
$374$	7.06020e6	2.60998
$375$	−3.86966e6	−1.42100
$376$	−762903.	−0.278291
$377$	4.75783e6	1.72407
$378$	−831628.	−0.299364
$379$	−11227.9	−0.00401513	−0.00200756	−	0.999998i	$-0.500639\pi$
$379$	−11227.9	−0.00401513	−0.00200756	+	0.999998i	$0.500639\pi$
$380$	7.49860e6	2.66392
$381$	−3.01328e6	−1.06347
$382$	−7.88491e6	−2.76464
$383$	4.39606e6	1.53132	0.765661	−	0.643245i	$-0.222412\pi$
$383$	4.39606e6	1.53132	0.765661	+	0.643245i	$0.222412\pi$
$384$	−1.46178e6	−0.505889
$385$	1.23772e6	0.425569
$386$	−404936.	−0.138330
$387$	−267903.	−0.0909287
$388$	2.81400e6	0.948954
$389$	4.01478e6	1.34520	0.672602	−	0.740005i	$-0.265177\pi$
$389$	4.01478e6	1.34520	0.672602	+	0.740005i	$0.265177\pi$
$390$	−1.14316e7	−3.80578
$391$	−2.89377e6	−0.957242
$392$	840734.	0.276340
$393$	−45821.2	−0.0149653
$394$	6.02848e6	1.95644
$395$	−2.15539e6	−0.695079
$396$	−937014.	−0.300267
$397$	3.75835e6	1.19680	0.598399	−	0.801199i	$-0.295804\pi$
$397$	3.75835e6	1.19680	0.598399	+	0.801199i	$0.295804\pi$
$398$	5.30950e6	1.68014
$399$	−704657.	−0.221588
$400$	−4.73467e6	−1.47959
$401$	3.56547e6	1.10728	0.553638	−	0.832758i	$-0.313239\pi$
$401$	3.56547e6	1.10728	0.553638	+	0.832758i	$0.313239\pi$
$402$	1.06591e6	0.328970
$403$	−2.92108e6	−0.895943
$404$	−4.11658e6	−1.25483
$405$	−4.36228e6	−1.32153
$406$	957956.	0.288423
$407$	144132.	0.0431295
$408$	−1.15805e6	−0.344411
$409$	199049.	0.0588370	0.0294185	−	0.999567i	$-0.490634\pi$
$409$	199049.	0.0588370	0.0294185	+	0.999567i	$0.490634\pi$
$410$	8.64348e6	2.53939
$411$	−5.37956e6	−1.57088
$412$	−5.59480e6	−1.62383
$413$	188388.	0.0543473
$414$	705849.	0.202400
$415$	6.16326e6	1.75667
$416$	−8.40608e6	−2.38155
$417$	−3.15175e6	−0.887589
$418$	−9.10889e6	−2.54991
$419$	−937364.	−0.260839	−0.130420	−	0.991459i	$-0.541632\pi$
$419$	−937364.	−0.260839	−0.130420	+	0.991459i	$0.541632\pi$
$420$	−1.25234e6	−0.346417
$421$	2.81489e6	0.774028	0.387014	−	0.922074i	$-0.373506\pi$
$421$	2.81489e6	0.774028	0.387014	+	0.922074i	$0.373506\pi$
$422$	−8.90606e6	−2.43447
$423$	−681759.	−0.185259
$424$	−466565.	−0.126037
$425$	−9.57150e6	−2.57044
$426$	−6.94447e6	−1.85402
$427$	597075.	0.158474
$428$	−801842.	−0.211582
$429$	7.55564e6	1.98211
$430$	−4.62852e6	−1.20718
$431$	836325.	0.216861	0.108431	−	0.994104i	$-0.465417\pi$
$431$	836325.	0.216861	0.108431	+	0.994104i	$0.465417\pi$
$432$	−3.19559e6	−0.823837
$433$	3.55965e6	0.912406	0.456203	−	0.889876i	$-0.349209\pi$
$433$	3.55965e6	0.912406	0.456203	+	0.889876i	$0.349209\pi$
$434$	−588139.	−0.149884
$435$	6.26514e6	1.58748
$436$	−2.56625e6	−0.646520
$437$	3.73346e6	0.935208
$438$	1.00974e7	2.51493
$439$	1.64605e6	0.407644	0.203822	−	0.979008i	$-0.434664\pi$
$439$	1.64605e6	0.407644	0.203822	+	0.979008i	$0.434664\pi$
$440$	−2.62434e6	−0.646232
$441$	751312.	0.183960
$442$	−1.35779e7	−3.30580
$443$	5.60090e6	1.35596	0.677982	−	0.735078i	$-0.262855\pi$
$443$	5.60090e6	1.35596	0.677982	+	0.735078i	$0.262855\pi$
$444$	−145835.	−0.0351078
$445$	−1.10797e7	−2.65232
$446$	−6.47833e6	−1.54215
$447$	−4.18417e6	−0.990468
$448$	−1.07599e6	−0.253287
$449$	−794000.	−0.185868	−0.0929340	−	0.995672i	$-0.529625\pi$
$449$	−794000.	−0.185868	−0.0929340	+	0.995672i	$0.529625\pi$
$450$	2.33469e6	0.543497
$451$	−5.71288e6	−1.32255
$452$	5.84947e6	1.34670
$453$	3.04292e6	0.696698
$454$	−570856.	−0.129983
$455$	−2.38033e6	−0.539024
$456$	1.49409e6	0.336484
$457$	−7.67991e6	−1.72015	−0.860074	−	0.510169i	$-0.829583\pi$
$457$	−7.67991e6	−1.72015	−0.860074	+	0.510169i	$0.829583\pi$
$458$	1.26119e7	2.80942
$459$	−6.46013e6	−1.43123
$460$	6.63524e6	1.46205
$461$	−525852.	−0.115242	−0.0576210	−	0.998339i	$-0.518352\pi$
$461$	−525852.	−0.115242	−0.0576210	+	0.998339i	$0.518352\pi$
$462$	1.52127e6	0.331591
$463$	4.10383e6	0.889687	0.444844	−	0.895608i	$-0.353259\pi$
$463$	4.10383e6	0.889687	0.444844	+	0.895608i	$0.353259\pi$
$464$	3.68101e6	0.793729
$465$	−3.84650e6	−0.824960
$466$	1.07142e7	2.28557
$467$	7.30106e6	1.54915	0.774575	−	0.632482i	$-0.217964\pi$
$467$	7.30106e6	1.54915	0.774575	+	0.632482i	$0.217964\pi$
$468$	1.80202e6	0.380317
$469$	221949.	0.0465930
$470$	−1.17786e7	−2.45952
$471$	−5.80049e6	−1.20479
$472$	−399440.	−0.0825270
$473$	3.05920e6	0.628717
$474$	−2.64919e6	−0.541585
$475$	1.23489e7	2.51128
$476$	−1.48747e6	−0.300906
$477$	−416941.	−0.0839032
$478$	−1.07384e7	−2.14965
$479$	1.92291e6	0.382930	0.191465	−	0.981499i	$-0.438676\pi$
$479$	1.92291e6	0.382930	0.191465	+	0.981499i	$0.438676\pi$
$480$	−1.10692e7	−2.19287
$481$	−277188.	−0.0546276
$482$	−7.60472e6	−1.49096
$483$	−623525.	−0.121615
$484$	4.54908e6	0.882693
$485$	7.04305e6	1.35958
$486$	2.89909e6	0.556763
$487$	2.13024e6	0.407010	0.203505	−	0.979074i	$-0.434767\pi$
$487$	2.13024e6	0.407010	0.203505	+	0.979074i	$0.434767\pi$
$488$	−1.26598e6	−0.240645
$489$	4.61649e6	0.873052
$490$	1.29803e7	2.44227
$491$	−175681.	−0.0328867	−0.0164434	−	0.999865i	$-0.505234\pi$
$491$	−175681.	−0.0328867	−0.0164434	+	0.999865i	$0.505234\pi$
$492$	5.78037e6	1.07657
$493$	7.44145e6	1.37892
$494$	1.75178e7	3.22970
$495$	−2.34521e6	−0.430199
$496$	−2.25996e6	−0.412474
$497$	−1.44601e6	−0.262591
$498$	7.57525e6	1.36875
$499$	265601.	0.0477506	0.0238753	−	0.999715i	$-0.492400\pi$
$499$	265601.	0.0477506	0.0238753	+	0.999715i	$0.492400\pi$
$500$	1.05388e7	1.88524
$501$	4.09543e6	0.728963
$502$	5.11247e6	0.905465
$503$	4.20896e6	0.741746	0.370873	−	0.928684i	$-0.379059\pi$
$503$	4.20896e6	0.741746	0.370873	+	0.928684i	$0.379059\pi$
$504$	58817.6	0.0103141
$505$	−1.03032e7	−1.79781
$506$	−8.06012e6	−1.39948
$507$	−9.32400e6	−1.61095
$508$	8.20652e6	1.41091
$509$	7.81356e6	1.33676	0.668381	−	0.743819i	$-0.266988\pi$
$509$	7.81356e6	1.33676	0.668381	+	0.743819i	$0.266988\pi$
$510$	−1.78794e7	−3.04388
$511$	2.10253e6	0.356197
$512$	−7.81077e6	−1.31680
$513$	8.33469e6	1.39829
$514$	−3.25863e6	−0.544035
$515$	−1.40030e7	−2.32650
$516$	−3.09534e6	−0.511781
$517$	7.78504e6	1.28096
$518$	−55809.9	−0.00913875
$519$	2.59130e6	0.422278
$520$	5.04702e6	0.818514
$521$	3.08688e6	0.498224	0.249112	−	0.968475i	$-0.419861\pi$
$521$	3.08688e6	0.498224	0.249112	+	0.968475i	$0.419861\pi$
$522$	−1.81512e6	−0.291561
$523$	3.22868e6	0.516144	0.258072	−	0.966126i	$-0.416913\pi$
$523$	3.22868e6	0.516144	0.258072	+	0.966126i	$0.416913\pi$
$524$	124792.	0.0198544
$525$	−2.06239e6	−0.326567
$526$	−6.18250e6	−0.974316
$527$	−4.56869e6	−0.716581
$528$	5.84560e6	0.912524
$529$	−3.13274e6	−0.486726
$530$	−7.20341e6	−1.11391
$531$	−356955.	−0.0549385
$532$	1.91910e6	0.293980
$533$	1.09868e7	1.67514
$534$	−1.36180e7	−2.06661
$535$	−2.00689e6	−0.303138
$536$	−470599.	−0.0707520
$537$	1.25000e6	0.187058
$538$	−1.12656e7	−1.67803
$539$	−8.57927e6	−1.27197
$540$	1.48127e7	2.18600
$541$	1.21291e7	1.78171	0.890853	−	0.454292i	$-0.150108\pi$
$541$	1.21291e7	1.78171	0.890853	+	0.454292i	$0.150108\pi$
$542$	−878231.	−0.128413
$543$	4.69174e6	0.682864
$544$	−1.31475e7	−1.90478
$545$	−6.42295e6	−0.926282
$546$	−2.92565e6	−0.419992
$547$	299209.	0.0427569
$547$	299209.	0.0427569
$548$	1.46509e7	2.08408
$549$	−1.13133e6	−0.160198
$550$	−2.66599e7	−3.75796
$551$	−9.60077e6	−1.34718
$552$	1.32206e6	0.184674
$553$	−551625.	−0.0767063
$554$	2.20911e6	0.305804
$555$	−365003.	−0.0502996
$556$	8.58364e6	1.17756
$557$	9.29368e6	1.26926	0.634629	−	0.772817i	$-0.281153\pi$
$557$	9.29368e6	1.26926	0.634629	+	0.772817i	$0.281153\pi$
$558$	1.11440e6	0.151515
$559$	−5.88332e6	−0.796330
$560$	−1.84160e6	−0.248156
$561$	1.18173e7	1.58530
$562$	8.13416e6	1.08636
$563$	−1.09221e7	−1.45222	−0.726112	−	0.687577i	$-0.758674\pi$
$563$	−1.09221e7	−1.45222	−0.726112	+	0.687577i	$0.758674\pi$
$564$	−7.87701e6	−1.04271
$565$	1.46404e7	1.92944
$566$	−1.63875e7	−2.15016
$567$	−1.11643e6	−0.145839
$568$	3.06598e6	0.398747
$569$	−2.95762e6	−0.382967	−0.191484	−	0.981496i	$-0.561330\pi$
$569$	−2.95762e6	−0.382967	−0.191484	+	0.981496i	$0.561330\pi$
$570$	2.30676e7	2.97382
$571$	1.63873e6	0.210337	0.105169	−	0.994454i	$-0.466462\pi$
$571$	1.63873e6	0.210337	0.105169	+	0.994454i	$0.466462\pi$
$572$	−2.05774e7	−2.62966
$573$	−1.31977e7	−1.67924
$574$	2.21211e6	0.280237
$575$	1.09271e7	1.37827
$576$	2.03877e6	0.256042
$577$	1.22382e7	1.53030	0.765151	−	0.643851i	$-0.222664\pi$
$577$	1.22382e7	1.53030	0.765151	+	0.643851i	$0.222664\pi$
$578$	−9.34077e6	−1.16295
$579$	−677780.	−0.0840218
$580$	−1.70628e7	−2.10611
$581$	1.57735e6	0.193860
$582$	8.65658e6	1.05935
$583$	4.76107e6	0.580140
$584$	−4.45800e6	−0.540889
$585$	4.51021e6	0.544888
$586$	−1.66913e7	−2.00792
$587$	−3.51105e6	−0.420573	−0.210287	−	0.977640i	$-0.567440\pi$
$587$	−3.51105e6	−0.420573	−0.210287	+	0.977640i	$0.567440\pi$
$588$	8.68062e6	1.03540
$589$	5.89441e6	0.700087
$590$	−6.16704e6	−0.729369
$591$	1.00904e7	1.18834
$592$	−214453.	−0.0251494
$593$	899644.	0.105059	0.0525296	−	0.998619i	$-0.483272\pi$
$593$	899644.	0.105059	0.0525296	+	0.998619i	$0.483272\pi$
$594$	−1.79936e7	−2.09244
$595$	−3.72293e6	−0.431114
$596$	1.13954e7	1.31405
$597$	8.88702e6	1.02052
$598$	1.55009e7	1.77257
$599$	7.32735e6	0.834411	0.417205	−	0.908812i	$-0.363010\pi$
$599$	7.32735e6	0.834411	0.417205	+	0.908812i	$0.363010\pi$
$600$	4.37290e6	0.495897
$601$	1.52299e7	1.71993	0.859966	−	0.510352i	$-0.170485\pi$
$601$	1.52299e7	1.71993	0.859966	+	0.510352i	$0.170485\pi$
$602$	−1.18457e6	−0.133220
$603$	−420545.	−0.0470999
$604$	−8.28723e6	−0.924308
$605$	1.13857e7	1.26465
$606$	−1.26636e7	−1.40080
$607$	1.08041e7	1.19020	0.595098	−	0.803653i	$-0.297113\pi$
$607$	1.08041e7	1.19020	0.595098	+	0.803653i	$0.297113\pi$
$608$	1.69625e7	1.86094
$609$	1.60342e6	0.175188
$610$	−1.95458e7	−2.12681
$611$	−1.49719e7	−1.62245
$612$	2.81844e6	0.304180
$613$	1.14638e7	1.23219	0.616093	−	0.787673i	$-0.288714\pi$
$613$	1.14638e7	1.23219	0.616093	+	0.787673i	$0.288714\pi$
$614$	1.28688e7	1.37759
$615$	1.44674e7	1.54242
$616$	−671641.	−0.0713157
$617$	4.34306e6	0.459286	0.229643	−	0.973275i	$-0.426244\pi$
$617$	4.34306e6	0.459286	0.229643	+	0.973275i	$0.426244\pi$
$618$	−1.72110e7	−1.81274
$619$	−1.89872e6	−0.199175	−0.0995875	−	0.995029i	$-0.531752\pi$
$619$	−1.89872e6	−0.199175	−0.0995875	+	0.995029i	$0.531752\pi$
$620$	1.04757e7	1.09447
$621$	7.37506e6	0.767426
$622$	−1.93184e7	−2.00214
$623$	−2.83559e6	−0.292700
$624$	−1.12420e7	−1.15580
$625$	7.59002e6	0.777218
$626$	1.42883e6	0.145729
$627$	−1.52464e7	−1.54881
$628$	1.57974e7	1.59840
$629$	−433534.	−0.0436914
$630$	908099.	0.0911552
$631$	−4.54532e6	−0.454455	−0.227228	−	0.973842i	$-0.572966\pi$
$631$	−4.54532e6	−0.454455	−0.227228	+	0.973842i	$0.572966\pi$
$632$	1.16961e6	0.116479
$633$	−1.49069e7	−1.47870
$634$	−2.28862e7	−2.26126
$635$	2.05397e7	2.02144
$636$	−4.81731e6	−0.472239
$637$	1.64993e7	1.61108
$638$	2.07270e7	2.01597
$639$	2.73987e6	0.265447
$640$	9.96410e6	0.961586
$641$	1.91824e7	1.84399	0.921995	−	0.387202i	$-0.126558\pi$
$641$	1.91824e7	1.84399	0.921995	+	0.387202i	$0.126558\pi$
$642$	−2.46667e6	−0.236196
$643$	1.77836e7	1.69626	0.848131	−	0.529787i	$-0.177728\pi$
$643$	1.77836e7	1.69626	0.848131	+	0.529787i	$0.177728\pi$
$644$	1.69814e6	0.161346
$645$	−7.74720e6	−0.733239
$646$	2.73986e7	2.58314
$647$	−3.50308e6	−0.328995	−0.164498	−	0.986377i	$-0.552600\pi$
$647$	−3.50308e6	−0.328995	−0.164498	+	0.986377i	$0.552600\pi$
$648$	2.36716e6	0.221458
$649$	4.07608e6	0.379867
$650$	5.12712e7	4.75981
$651$	−984424.	−0.0910395
$652$	−1.25728e7	−1.15828
$653$	−7.20892e6	−0.661587	−0.330794	−	0.943703i	$-0.607316\pi$
$653$	−7.20892e6	−0.661587	−0.330794	+	0.943703i	$0.607316\pi$
$654$	−7.89442e6	−0.721732
$655$	312336.	0.0284458
$656$	8.50017e6	0.771202
$657$	−3.98384e6	−0.360072
$658$	−3.01448e6	−0.271423
$659$	−2.71256e6	−0.243313	−0.121657	−	0.992572i	$-0.538821\pi$
$659$	−2.71256e6	−0.243313	−0.121657	+	0.992572i	$0.538821\pi$
$660$	−2.70964e7	−2.42132
$661$	−7.69277e6	−0.684824	−0.342412	−	0.939550i	$-0.611244\pi$
$661$	−7.69277e6	−0.684824	−0.342412	+	0.939550i	$0.611244\pi$
$662$	−1.23336e7	−1.09382
$663$	−2.27266e7	−2.00794
$664$	−3.34446e6	−0.294378
$665$	4.80323e6	0.421191
$666$	105748.	0.00923817
$667$	−8.49537e6	−0.739380
$668$	−1.11537e7	−0.967115
$669$	−1.08434e7	−0.936700
$670$	−7.26569e6	−0.625302
$671$	1.29187e7	1.10768
$672$	−2.83291e6	−0.241997
$673$	−2.62370e6	−0.223293	−0.111647	−	0.993748i	$-0.535613\pi$
$673$	−2.62370e6	−0.223293	−0.111647	+	0.993748i	$0.535613\pi$
$674$	2.63285e7	2.23243
$675$	2.43940e7	2.06074
$676$	2.53934e7	2.13725
$677$	−1.42963e7	−1.19882	−0.599408	−	0.800443i	$-0.704597\pi$
$677$	−1.42963e7	−1.19882	−0.599408	+	0.800443i	$0.704597\pi$
$678$	1.79945e7	1.50337
$679$	1.80251e6	0.150039
$680$	7.89374e6	0.654652
$681$	−955497.	−0.0789517
$682$	−1.27254e7	−1.04763
$683$	−1.58492e7	−1.30004	−0.650019	−	0.759918i	$-0.725239\pi$
$683$	−1.58492e7	−1.30004	−0.650019	+	0.759918i	$0.725239\pi$
$684$	−3.63628e6	−0.297178
$685$	3.66692e7	2.98590
$686$	6.76668e6	0.548991
$687$	2.11098e7	1.70644
$688$	−4.55178e6	−0.366615
$689$	−9.15628e6	−0.734803
$690$	2.04117e7	1.63213
$691$	−1.08042e7	−0.860790	−0.430395	−	0.902641i	$-0.641626\pi$
$691$	−1.08042e7	−0.860790	−0.430395	+	0.902641i	$0.641626\pi$
$692$	−7.05726e6	−0.560236
$693$	−600204.	−0.0474751
$694$	−695063.	−0.0547804
$695$	2.14836e7	1.68712
$696$	−3.39975e6	−0.266026
$697$	1.71837e7	1.33979
$698$	2.01869e7	1.56831
$699$	1.79333e7	1.38825
$700$	5.61681e6	0.433256
$701$	−1.85345e7	−1.42458	−0.712288	−	0.701887i	$-0.752341\pi$
$701$	−1.85345e7	−1.42458	−0.712288	+	0.701887i	$0.752341\pi$
$702$	3.46046e7	2.65028
$703$	559334.	0.0426858
$704$	−2.32808e7	−1.77038
$705$	−1.97150e7	−1.49391
$706$	2.35541e7	1.77850
$707$	−2.63688e6	−0.198400
$708$	−4.12424e6	−0.309215
$709$	−1.83722e7	−1.37260	−0.686302	−	0.727317i	$-0.740767\pi$
$709$	−1.83722e7	−1.37260	−0.686302	+	0.727317i	$0.740767\pi$
$710$	4.73363e7	3.52410
$711$	1.04521e6	0.0775408
$712$	6.01231e6	0.444469
$713$	5.21574e6	0.384231
$714$	−4.57584e6	−0.335912
$715$	−5.15023e7	−3.76757
$716$	−3.40432e6	−0.248169
$717$	−1.79738e7	−1.30570
$718$	1.32046e7	0.955902
$719$	−9.87807e6	−0.712607	−0.356303	−	0.934370i	$-0.615963\pi$
$719$	−9.87807e6	−0.712607	−0.356303	+	0.934370i	$0.615963\pi$
$720$	3.48943e6	0.250855
$721$	−3.58375e6	−0.256744
$722$	−1.46042e7	−1.04264
$723$	−1.27287e7	−0.905607
$724$	−1.27777e7	−0.905955
$725$	−2.80995e7	−1.98543
$726$	1.39941e7	0.985380
$727$	1.72164e7	1.20811	0.604054	−	0.796943i	$-0.293551\pi$
$727$	1.72164e7	1.20811	0.604054	+	0.796943i	$0.293551\pi$
$728$	1.29167e6	0.0903282
$729$	1.59422e7	1.11104
$730$	−6.88282e7	−4.78034
$731$	−9.20176e6	−0.636909
$732$	−1.30713e7	−0.901657
$733$	−2.88355e7	−1.98229	−0.991147	−	0.132771i	$-0.957612\pi$
$733$	−2.88355e7	−1.98229	−0.991147	+	0.132771i	$0.957612\pi$
$734$	−2.62895e7	−1.80111
$735$	2.17264e7	1.48344
$736$	1.50095e7	1.02134
$737$	4.80223e6	0.325667
$738$	−4.19147e6	−0.283286
$739$	1.46977e7	0.990006	0.495003	−	0.868891i	$-0.335167\pi$
$739$	1.46977e7	0.990006	0.495003	+	0.868891i	$0.335167\pi$
$740$	994067.	0.0667324
$741$	2.93213e7	1.96172
$742$	−1.84355e6	−0.122927
$743$	5.22368e6	0.347140	0.173570	−	0.984822i	$-0.444470\pi$
$743$	5.22368e6	0.347140	0.173570	+	0.984822i	$0.444470\pi$
$744$	2.08728e6	0.138245
$745$	2.85210e7	1.88267
$746$	4.06989e6	0.267754
$747$	−2.98874e6	−0.195969
$748$	−3.21839e7	−2.10322
$749$	−513620.	−0.0334532
$750$	3.24201e7	2.10456
$751$	−3.42686e6	−0.221716	−0.110858	−	0.993836i	$-0.535360\pi$
$751$	−3.42686e6	−0.221716	−0.110858	+	0.993836i	$0.535360\pi$
$752$	−1.15833e7	−0.746946
$753$	8.55724e6	0.549979
$754$	−3.98612e7	−2.55342
$755$	−2.07417e7	−1.32427
$756$	3.79097e6	0.241238
$757$	−2.07888e6	−0.131853	−0.0659265	−	0.997824i	$-0.521000\pi$
$757$	−2.07888e6	−0.131853	−0.0659265	+	0.997824i	$0.521000\pi$
$758$	94067.3	0.00594656
$759$	−1.34910e7	−0.850041
$760$	−1.01843e7	−0.639584
$761$	−1.19851e7	−0.750206	−0.375103	−	0.926983i	$-0.622393\pi$
$761$	−1.19851e7	−0.750206	−0.375103	+	0.926983i	$0.622393\pi$
$762$	2.52453e7	1.57505
$763$	−1.64381e6	−0.102221
$764$	3.59433e7	2.22785
$765$	7.05415e6	0.435804
$766$	−3.68302e7	−2.26795
$767$	−7.83895e6	−0.481138
$768$	−7.49033e6	−0.458245
$769$	8.23538e6	0.502190	0.251095	−	0.967963i	$-0.419209\pi$
$769$	8.23538e6	0.502190	0.251095	+	0.967963i	$0.419209\pi$
$770$	−1.03696e7	−0.630284
$771$	−5.45428e6	−0.330446
$772$	1.84590e6	0.111472
$773$	6.93234e6	0.417283	0.208642	−	0.977992i	$-0.433096\pi$
$773$	6.93234e6	0.417283	0.208642	+	0.977992i	$0.433096\pi$
$774$	2.24450e6	0.134669
$775$	1.72517e7	1.03176
$776$	−3.82187e6	−0.227836
$777$	−93414.4	−0.00555087
$778$	−3.36359e7	−1.99230
$779$	−2.21700e7	−1.30895
$780$	5.21107e7	3.06684
$781$	−3.12868e7	−1.83541
$782$	2.42440e7	1.41771
$783$	−1.89653e7	−1.10549
$784$	1.27651e7	0.741708
$785$	3.95385e7	2.29006
$786$	383890.	0.0221641
$787$	−1.59957e7	−0.920590	−0.460295	−	0.887766i	$-0.652256\pi$
$787$	−1.59957e7	−0.920590	−0.460295	+	0.887766i	$0.652256\pi$
$788$	−2.74808e7	−1.57657
$789$	−1.03482e7	−0.591799
$790$	1.80579e7	1.02944
$791$	3.74688e6	0.212926
$792$	1.27262e6	0.0720915
$793$	−2.48447e7	−1.40298
$794$	−3.14875e7	−1.77250
$795$	−1.20570e7	−0.676586
$796$	−2.42033e7	−1.35392
$797$	−2.18183e7	−1.21668	−0.608339	−	0.793678i	$-0.708164\pi$
$797$	−2.18183e7	−1.21668	−0.608339	+	0.793678i	$0.708164\pi$
$798$	5.90363e6	0.328180
$799$	−2.34166e7	−1.29765
$800$	4.96459e7	2.74257
$801$	5.37284e6	0.295885
$802$	−2.98715e7	−1.63992
$803$	4.54917e7	2.48968
$804$	−4.85896e6	−0.265096
$805$	4.25020e6	0.231164
$806$	2.44728e7	1.32693
$807$	−1.88564e7	−1.01923
$808$	5.59098e6	0.301273
$809$	−2.12931e7	−1.14385	−0.571923	−	0.820307i	$-0.693802\pi$
$809$	−2.12931e7	−1.14385	−0.571923	+	0.820307i	$0.693802\pi$
$810$	3.65472e7	1.95723
$811$	−1.19001e7	−0.635327	−0.317664	−	0.948203i	$-0.602898\pi$
$811$	−1.19001e7	−0.635327	−0.317664	+	0.948203i	$0.602898\pi$
$812$	−4.36684e6	−0.232422
$813$	−1.46998e6	−0.0779982
$814$	−1.20754e6	−0.0638764
$815$	−3.14679e7	−1.65949
$816$	−1.75830e7	−0.924415
$817$	1.18719e7	0.622249
$818$	−1.66763e6	−0.0871399
$819$	1.15429e6	0.0601318
$820$	−3.94013e7	−2.04633
$821$	5.16561e6	0.267463	0.133731	−	0.991018i	$-0.457304\pi$
$821$	5.16561e6	0.267463	0.133731	+	0.991018i	$0.457304\pi$
$822$	4.50700e7	2.32653
$823$	−2.78511e7	−1.43332	−0.716659	−	0.697424i	$-0.754330\pi$
$823$	−2.78511e7	−1.43332	−0.716659	+	0.697424i	$0.754330\pi$
$824$	7.59864e6	0.389868
$825$	−4.46232e7	−2.28258
$826$	−1.57832e6	−0.0804904
$827$	−5.60485e6	−0.284971	−0.142485	−	0.989797i	$-0.545509\pi$
$827$	−5.60485e6	−0.284971	−0.142485	+	0.989797i	$0.545509\pi$
$828$	−3.21761e6	−0.163101
$829$	−1.25664e6	−0.0635076	−0.0317538	−	0.999496i	$-0.510109\pi$
$829$	−1.25664e6	−0.0635076	−0.0317538	+	0.999496i	$0.510109\pi$
$830$	−5.16359e7	−2.60170
$831$	3.69760e6	0.185745
$832$	4.47726e7	2.24235
$833$	2.58056e7	1.28855
$834$	2.64054e7	1.31455
$835$	−2.79161e7	−1.38560
$836$	4.15229e7	2.05481
$837$	1.16438e7	0.574487
$838$	7.85325e6	0.386313
$839$	2.86281e7	1.40407	0.702033	−	0.712145i	$-0.252276\pi$
$839$	2.86281e7	1.40407	0.702033	+	0.712145i	$0.252276\pi$
$840$	1.70088e6	0.0831717
$841$	1.33507e6	0.0650899
$842$	−2.35832e7	−1.14637
$843$	1.36149e7	0.659852
$844$	4.05982e7	1.96178
$845$	6.35562e7	3.06208
$846$	5.71179e6	0.274376
$847$	2.91391e6	0.139562
$848$	−7.08397e6	−0.338289
$849$	−2.74293e7	−1.30601
$850$	8.01902e7	3.80692
$851$	494934.	0.0234274
$852$	3.16564e7	1.49404
$853$	−2.12996e7	−1.00230	−0.501150	−	0.865360i	$-0.667090\pi$
$853$	−2.12996e7	−1.00230	−0.501150	+	0.865360i	$0.667090\pi$
$854$	−5.00230e6	−0.234707
$855$	−9.10109e6	−0.425773
$856$	1.08903e6	0.0507990
$857$	−1.73684e7	−0.807808	−0.403904	−	0.914801i	$-0.632347\pi$
$857$	−1.73684e7	−0.807808	−0.403904	+	0.914801i	$0.632347\pi$
$858$	−6.33013e7	−2.93558
$859$	−1.25508e7	−0.580348	−0.290174	−	0.956974i	$-0.593713\pi$
$859$	−1.25508e7	−0.580348	−0.290174	+	0.956974i	$0.593713\pi$
$860$	2.10991e7	0.972787
$861$	3.70261e6	0.170216
$862$	−7.00675e6	−0.321180
$863$	2.03247e7	0.928961	0.464481	−	0.885583i	$-0.346241\pi$
$863$	2.03247e7	0.928961	0.464481	+	0.885583i	$0.346241\pi$
$864$	3.35077e7	1.52707
$865$	−1.76633e7	−0.802661
$866$	−2.98228e7	−1.35131
$867$	−1.56345e7	−0.706378
$868$	2.68103e6	0.120782
$869$	−1.19353e7	−0.536148
$870$	−5.24895e7	−2.35112
$871$	−9.23544e6	−0.412489
$872$	3.48538e6	0.155224
$873$	−3.41537e6	−0.151671
$874$	−3.12790e7	−1.38508
$875$	6.75065e6	0.298075
$876$	−4.60291e7	−2.02662
$877$	1.51571e7	0.665453	0.332726	−	0.943023i	$-0.392031\pi$
$877$	1.51571e7	0.665453	0.332726	+	0.943023i	$0.392031\pi$
$878$	−1.37906e7	−0.603736
$879$	−2.79379e7	−1.21961
$880$	−3.98460e7	−1.73451
$881$	3.23884e7	1.40588	0.702942	−	0.711248i	$-0.251870\pi$
$881$	3.23884e7	1.40588	0.702942	+	0.711248i	$0.251870\pi$
$882$	−6.29451e6	−0.272452
$883$	−3.35780e7	−1.44928	−0.724641	−	0.689127i	$-0.757994\pi$
$883$	−3.35780e7	−1.44928	−0.724641	+	0.689127i	$0.757994\pi$
$884$	6.18947e7	2.66393
$885$	−1.03224e7	−0.443018
$886$	−4.69244e7	−2.00824
$887$	2.57063e7	1.09706	0.548530	−	0.836131i	$-0.315188\pi$
$887$	2.57063e7	1.09706	0.548530	+	0.836131i	$0.315188\pi$
$888$	198067.	0.00842907
$889$	5.25669e6	0.223078
$890$	9.28256e7	3.92819
$891$	−2.41557e7	−1.01936
$892$	2.95315e7	1.24272
$893$	3.02115e7	1.26778
$894$	3.50551e7	1.46692
$895$	−8.52053e6	−0.355557
$896$	2.55009e6	0.106117
$897$	2.59453e7	1.07666
$898$	6.65215e6	0.275278
$899$	−1.34125e7	−0.553492
$900$	−1.06427e7	−0.437970
$901$	−1.43208e7	−0.587699
$902$	4.78626e7	1.95875
$903$	−1.98272e6	−0.0809175
$904$	−7.94453e6	−0.323331
$905$	−3.19808e7	−1.29798
$906$	−2.54936e7	−1.03184
$907$	−1.64110e6	−0.0662394	−0.0331197	−	0.999451i	$-0.510544\pi$
$907$	−1.64110e6	−0.0662394	−0.0331197	+	0.999451i	$0.510544\pi$
$908$	2.60225e6	0.104745
$909$	4.99632e6	0.200558
$910$	1.99424e7	0.798315
$911$	−3.98143e7	−1.58943	−0.794717	−	0.606980i	$-0.792381\pi$
$911$	−3.98143e7	−1.58943	−0.794717	+	0.606980i	$0.792381\pi$
$912$	2.26851e7	0.903137
$913$	3.41286e7	1.35501
$914$	6.43424e7	2.54760
$915$	−3.27156e7	−1.29182
$916$	−5.74914e7	−2.26393
$917$	79935.3	0.00313917
$918$	5.41230e7	2.11971
$919$	3.66707e7	1.43229	0.716145	−	0.697952i	$-0.245905\pi$
$919$	3.66707e7	1.43229	0.716145	+	0.697952i	$0.245905\pi$
$920$	−9.01172e6	−0.351025
$921$	2.15398e7	0.836745
$922$	4.40559e6	0.170678
$923$	6.01693e7	2.32472
$924$	−6.93473e6	−0.267208
$925$	1.63706e6	0.0629086
$926$	−3.43820e7	−1.31766
$927$	6.79044e6	0.259537
$928$	−3.85976e7	−1.47126
$929$	4.60800e7	1.75176	0.875878	−	0.482533i	$-0.160283\pi$
$929$	4.60800e7	1.75176	0.875878	+	0.482533i	$0.160283\pi$
$930$	3.22260e7	1.22180
$931$	−3.32937e7	−1.25889
$932$	−4.88406e7	−1.84179
$933$	−3.23350e7	−1.21610
$934$	−6.11684e7	−2.29435
$935$	−8.05517e7	−3.01332
$936$	−2.44744e6	−0.0913108
$937$	4.47844e6	0.166639	0.0833197	−	0.996523i	$-0.473448\pi$
$937$	4.47844e6	0.166639	0.0833197	+	0.996523i	$0.473448\pi$
$938$	−1.85949e6	−0.0690060
$939$	2.39157e6	0.0885156
$940$	5.36929e7	1.98197
$941$	2.77879e7	1.02301	0.511507	−	0.859279i	$-0.329087\pi$
$941$	2.77879e7	1.02301	0.511507	+	0.859279i	$0.329087\pi$
$942$	4.85966e7	1.78435
$943$	−1.96175e7	−0.718395
$944$	−6.06479e6	−0.221506
$945$	9.48827e6	0.345627
$946$	−2.56300e7	−0.931154
$947$	7.01756e6	0.254279	0.127140	−	0.991885i	$-0.459420\pi$
$947$	7.01756e6	0.254279	0.127140	+	0.991885i	$0.459420\pi$
$948$	1.20763e7	0.436429
$949$	−8.74877e7	−3.15342
$950$	−1.03459e8	−3.71930
$951$	−3.83069e7	−1.37349
$952$	2.02023e6	0.0722450
$953$	3.82962e7	1.36591	0.682957	−	0.730459i	$-0.260694\pi$
$953$	3.82962e7	1.36591	0.682957	+	0.730459i	$0.260694\pi$
$954$	3.49314e6	0.124264
$955$	8.99611e7	3.19188
$956$	4.89508e7	1.73227
$957$	3.46927e7	1.22450
$958$	−1.61101e7	−0.567134
$959$	9.38466e6	0.329513
$960$	5.89568e7	2.06470
$961$	−2.03945e7	−0.712369
$962$	2.32229e6	0.0809055
$963$	973200.	0.0338171
$964$	3.46661e7	1.20147
$965$	4.62002e6	0.159708
$966$	5.22391e6	0.180116
$967$	3.32734e7	1.14428	0.572138	−	0.820158i	$-0.306114\pi$
$967$	3.32734e7	1.14428	0.572138	+	0.820158i	$0.306114\pi$
$968$	−6.17838e6	−0.211927
$969$	4.58597e7	1.56899
$970$	−5.90068e7	−2.01360
$971$	−3.28557e6	−0.111831	−0.0559156	−	0.998435i	$-0.517808\pi$
$971$	−3.28557e6	−0.111831	−0.0559156	+	0.998435i	$0.517808\pi$
$972$	−1.32155e7	−0.448660
$973$	5.49825e6	0.186184
$974$	−1.78472e7	−0.602798
$975$	8.58175e7	2.89111
$976$	−1.92217e7	−0.645902
$977$	−1.75022e7	−0.586620	−0.293310	−	0.956017i	$-0.594757\pi$
$977$	−1.75022e7	−0.586620	−0.293310	+	0.956017i	$0.594757\pi$
$978$	−3.86771e7	−1.29302
$979$	−6.13527e7	−2.04586
$980$	−5.91706e7	−1.96807
$981$	3.11467e6	0.103333
$982$	1.47186e6	0.0487065
$983$	6.12725e6	0.202247	0.101123	−	0.994874i	$-0.467756\pi$
$983$	6.12725e6	0.202247	0.101123	+	0.994874i	$0.467756\pi$
$984$	−7.85067e6	−0.258475
$985$	−6.87806e7	−2.25879
$986$	−6.23446e7	−2.04224
$987$	−5.04562e6	−0.164862
$988$	−7.98550e7	−2.60261
$989$	1.05050e7	0.341511
$990$	1.96482e7	0.637141
$991$	5.14427e7	1.66395	0.831974	−	0.554814i	$-0.187211\pi$
$991$	5.14427e7	1.66395	0.831974	+	0.554814i	$0.187211\pi$
$992$	2.36971e7	0.764567
$993$	−2.06440e7	−0.664385
$994$	1.21147e7	0.388907
$995$	−6.05775e7	−1.93979
$996$	−3.45317e7	−1.10299
$997$	−1.20029e7	−0.382428	−0.191214	−	0.981548i	$-0.561242\pi$
$997$	−1.20029e7	−0.382428	−0.191214	+	0.981548i	$0.561242\pi$
$998$	−2.22521e6	−0.0707205
$999$	1.10491e6	0.0350277

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.6.a.b.1.19	✓	117

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.6.a.b.1.19	✓	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)

\(f(q)\)	\(=\)	\(q-8.37802 q^{2} -14.0231 q^{3} +38.1912 q^{4} +95.5871 q^{5} +117.486 q^{6} +24.4634 q^{7} -51.8698 q^{8} -46.3528 q^{9} +O(q^{10})\)	\(q-8.37802 q^{2} -14.0231 q^{3} +38.1912 q^{4} +95.5871 q^{5} +117.486 q^{6} +24.4634 q^{7} -51.8698 q^{8} -46.3528 q^{9} -800.830 q^{10} +529.305 q^{11} -535.558 q^{12} -1017.94 q^{13} -204.954 q^{14} -1340.43 q^{15} -787.552 q^{16} -1592.10 q^{17} +388.345 q^{18} +2054.08 q^{19} +3650.58 q^{20} -343.052 q^{21} -4434.53 q^{22} +1817.58 q^{23} +727.375 q^{24} +6011.89 q^{25} +8528.30 q^{26} +4057.62 q^{27} +934.285 q^{28} -4673.99 q^{29} +11230.1 q^{30} +2869.61 q^{31} +8257.95 q^{32} -7422.50 q^{33} +13338.6 q^{34} +2338.38 q^{35} -1770.27 q^{36} +272.304 q^{37} -17209.1 q^{38} +14274.6 q^{39} -4958.08 q^{40} -10793.2 q^{41} +2874.10 q^{42} +5779.65 q^{43} +20214.8 q^{44} -4430.73 q^{45} -15227.7 q^{46} +14708.0 q^{47} +11043.9 q^{48} -16208.5 q^{49} -50367.7 q^{50} +22326.1 q^{51} -38876.2 q^{52} +8994.93 q^{53} -33994.8 q^{54} +50594.8 q^{55} -1268.91 q^{56} -28804.6 q^{57} +39158.8 q^{58} +7700.81 q^{59} -51192.5 q^{60} +24406.9 q^{61} -24041.6 q^{62} -1133.95 q^{63} -43983.6 q^{64} -97301.6 q^{65} +62185.8 q^{66} +9072.70 q^{67} -60804.0 q^{68} -25488.1 q^{69} -19591.0 q^{70} -59109.1 q^{71} +2404.31 q^{72} +85946.1 q^{73} -2281.37 q^{74} -84305.3 q^{75} +78447.8 q^{76} +12948.6 q^{77} -119593. q^{78} -22549.0 q^{79} -75279.8 q^{80} -45636.7 q^{81} +90425.2 q^{82} +64478.0 q^{83} -13101.6 q^{84} -152184. q^{85} -48422.0 q^{86} +65543.9 q^{87} -27455.0 q^{88} -115912. q^{89} +37120.8 q^{90} -24902.2 q^{91} +69415.6 q^{92} -40240.7 q^{93} -123224. q^{94} +196344. q^{95} -115802. q^{96} +73682.0 q^{97} +135795. q^{98} -24534.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9}+O(q^{10}) \) 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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