LMFDB - Embedded newform 547.6.a.b.1.4

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			1.4
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)

$f(q)$	$=$	$q-10.7784 q^{2} +5.40058 q^{3} +84.1742 q^{4} -17.6434 q^{5} -58.2097 q^{6} +32.8655 q^{7} -562.355 q^{8} -213.834 q^{9} +O(q^{10})$	\(q-10.7784 q^{2} +5.40058 q^{3} +84.1742 q^{4} -17.6434 q^{5} -58.2097 q^{6} +32.8655 q^{7} -562.355 q^{8} -213.834 q^{9} +190.168 q^{10} +452.265 q^{11} +454.589 q^{12} -177.079 q^{13} -354.238 q^{14} -95.2845 q^{15} +3367.72 q^{16} -1701.42 q^{17} +2304.79 q^{18} -1148.26 q^{19} -1485.12 q^{20} +177.493 q^{21} -4874.70 q^{22} +276.254 q^{23} -3037.04 q^{24} -2813.71 q^{25} +1908.63 q^{26} -2467.17 q^{27} +2766.43 q^{28} +791.983 q^{29} +1027.02 q^{30} -3583.19 q^{31} -18303.3 q^{32} +2442.49 q^{33} +18338.6 q^{34} -579.859 q^{35} -17999.3 q^{36} +9012.87 q^{37} +12376.4 q^{38} -956.327 q^{39} +9921.85 q^{40} +7681.94 q^{41} -1913.09 q^{42} -8110.89 q^{43} +38069.1 q^{44} +3772.75 q^{45} -2977.58 q^{46} +11571.1 q^{47} +18187.6 q^{48} -15726.9 q^{49} +30327.3 q^{50} -9188.66 q^{51} -14905.4 q^{52} +34575.8 q^{53} +26592.1 q^{54} -7979.49 q^{55} -18482.1 q^{56} -6201.26 q^{57} -8536.31 q^{58} +44568.7 q^{59} -8020.50 q^{60} -22725.7 q^{61} +38621.1 q^{62} -7027.76 q^{63} +89513.7 q^{64} +3124.27 q^{65} -26326.2 q^{66} +35359.1 q^{67} -143216. q^{68} +1491.93 q^{69} +6249.96 q^{70} -59886.5 q^{71} +120250. q^{72} -77770.4 q^{73} -97144.4 q^{74} -15195.7 q^{75} -96653.7 q^{76} +14863.9 q^{77} +10307.7 q^{78} -89318.2 q^{79} -59418.0 q^{80} +38637.5 q^{81} -82799.1 q^{82} +85059.6 q^{83} +14940.3 q^{84} +30018.8 q^{85} +87422.5 q^{86} +4277.17 q^{87} -254334. q^{88} +43228.1 q^{89} -40664.3 q^{90} -5819.78 q^{91} +23253.4 q^{92} -19351.3 q^{93} -124718. q^{94} +20259.2 q^{95} -98848.5 q^{96} +78467.3 q^{97} +169511. q^{98} -96709.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−10.7784	−1.90537	−0.952686	−	0.303956i	$-0.901692\pi$
$2$	−10.7784	−1.90537	−0.952686	+	0.303956i	$0.901692\pi$
$3$	5.40058	0.346447	0.173224	−	0.984883i	$-0.444582\pi$
$3$	5.40058	0.346447	0.173224	+	0.984883i	$0.444582\pi$
$4$	84.1742	2.63044
$5$	−17.6434	−0.315614	−0.157807	−	0.987470i	$-0.550442\pi$
$5$	−17.6434	−0.315614	−0.157807	+	0.987470i	$0.550442\pi$
$6$	−58.2097	−0.660111
$7$	32.8655	0.253510	0.126755	−	0.991934i	$-0.459544\pi$
$7$	32.8655	0.253510	0.126755	+	0.991934i	$0.459544\pi$
$8$	−562.355	−3.10660
$9$	−213.834	−0.879974
$10$	190.168	0.601363
$11$	452.265	1.12697	0.563484	−	0.826127i	$-0.309461\pi$
$11$	452.265	1.12697	0.563484	+	0.826127i	$0.309461\pi$
$12$	454.589	0.911310
$13$	−177.079	−0.290608	−0.145304	−	0.989387i	$-0.546416\pi$
$13$	−177.079	−0.290608	−0.145304	+	0.989387i	$0.546416\pi$
$14$	−354.238	−0.483032
$15$	−95.2845	−0.109344
$16$	3367.72	3.28879
$17$	−1701.42	−1.42787	−0.713936	−	0.700211i	$-0.753089\pi$
$17$	−1701.42	−1.42787	−0.713936	+	0.700211i	$0.753089\pi$
$18$	2304.79	1.67668
$19$	−1148.26	−0.729719	−0.364860	−	0.931063i	$-0.618883\pi$
$19$	−1148.26	−0.729719	−0.364860	+	0.931063i	$0.618883\pi$
$20$	−1485.12	−0.830206
$21$	177.493	0.0878280
$22$	−4874.70	−2.14729
$23$	276.254	0.108890	0.0544450	−	0.998517i	$-0.482661\pi$
$23$	276.254	0.108890	0.0544450	+	0.998517i	$0.482661\pi$
$24$	−3037.04	−1.07627
$25$	−2813.71	−0.900387
$26$	1908.63	0.553717
$27$	−2467.17	−0.651312
$28$	2766.43	0.666845
$29$	791.983	0.174872	0.0874361	−	0.996170i	$-0.472133\pi$
$29$	791.983	0.174872	0.0874361	+	0.996170i	$0.472133\pi$
$30$	1027.02	0.208341
$31$	−3583.19	−0.669678	−0.334839	−	0.942275i	$-0.608682\pi$
$31$	−3583.19	−0.669678	−0.334839	+	0.942275i	$0.608682\pi$
$32$	−18303.3	−3.15977
$33$	2442.49	0.390435
$34$	18338.6	2.72063
$35$	−579.859	−0.0800115
$36$	−17999.3	−2.31472
$37$	9012.87	1.08233	0.541164	−	0.840917i	$-0.317984\pi$
$37$	9012.87	1.08233	0.541164	+	0.840917i	$0.317984\pi$
$38$	12376.4	1.39039
$39$	−956.327	−0.100680
$40$	9921.85	0.980488
$41$	7681.94	0.713693	0.356846	−	0.934163i	$-0.383852\pi$
$41$	7681.94	0.713693	0.356846	+	0.934163i	$0.383852\pi$
$42$	−1913.09	−0.167345
$43$	−8110.89	−0.668956	−0.334478	−	0.942404i	$-0.608560\pi$
$43$	−8110.89	−0.668956	−0.334478	+	0.942404i	$0.608560\pi$
$44$	38069.1	2.96442
$45$	3772.75	0.277733
$46$	−2977.58	−0.207476
$47$	11571.1	0.764065	0.382033	−	0.924149i	$-0.375224\pi$
$47$	11571.1	0.764065	0.382033	+	0.924149i	$0.375224\pi$
$48$	18187.6	1.13939
$49$	−15726.9	−0.935733
$50$	30327.3	1.71557
$51$	−9188.66	−0.494683
$52$	−14905.4	−0.764428
$53$	34575.8	1.69076	0.845380	−	0.534165i	$-0.179374\pi$
$53$	34575.8	1.69076	0.845380	+	0.534165i	$0.179374\pi$
$54$	26592.1	1.24099
$55$	−7979.49	−0.355687
$56$	−18482.1	−0.787556
$57$	−6201.26	−0.252809
$58$	−8536.31	−0.333197
$59$	44568.7	1.66686	0.833432	−	0.552622i	$-0.186373\pi$
$59$	44568.7	1.66686	0.833432	+	0.552622i	$0.186373\pi$
$60$	−8020.50	−0.287623
$61$	−22725.7	−0.781976	−0.390988	−	0.920396i	$-0.627867\pi$
$61$	−22725.7	−0.781976	−0.390988	+	0.920396i	$0.627867\pi$
$62$	38621.1	1.27599
$63$	−7027.76	−0.223083
$64$	89513.7	2.73174
$65$	3124.27	0.0917201
$66$	−26326.2	−0.743924
$67$	35359.1	0.962308	0.481154	−	0.876636i	$-0.340218\pi$
$67$	35359.1	0.962308	0.481154	+	0.876636i	$0.340218\pi$
$68$	−143216.	−3.75594
$69$	1491.93	0.0377247
$70$	6249.96	0.152452
$71$	−59886.5	−1.40988	−0.704941	−	0.709266i	$-0.749027\pi$
$71$	−59886.5	−1.40988	−0.704941	+	0.709266i	$0.749027\pi$
$72$	120250.	2.73373
$73$	−77770.4	−1.70808	−0.854038	−	0.520210i	$-0.825854\pi$
$73$	−77770.4	−1.70808	−0.854038	+	0.520210i	$0.825854\pi$
$74$	−97144.4	−2.06224
$75$	−15195.7	−0.311937
$76$	−96653.7	−1.91948
$77$	14863.9	0.285698
$78$	10307.7	0.191834
$79$	−89318.2	−1.61017	−0.805086	−	0.593158i	$-0.797881\pi$
$79$	−89318.2	−1.61017	−0.805086	+	0.593158i	$0.797881\pi$
$80$	−59418.0	−1.03799
$81$	38637.5	0.654329
$82$	−82799.1	−1.35985
$83$	85059.6	1.35528	0.677639	−	0.735395i	$-0.263003\pi$
$83$	85059.6	1.35528	0.677639	+	0.735395i	$0.263003\pi$
$84$	14940.3	0.231027
$85$	30018.8	0.450657
$86$	87422.5	1.27461
$87$	4277.17	0.0605840
$88$	−254334.	−3.50104
$89$	43228.1	0.578484	0.289242	−	0.957256i	$-0.406597\pi$
$89$	43228.1	0.578484	0.289242	+	0.957256i	$0.406597\pi$
$90$	−40664.3	−0.529184
$91$	−5819.78	−0.0736721
$92$	23253.4	0.286429
$93$	−19351.3	−0.232008
$94$	−124718.	−1.45583
$95$	20259.2	0.230310
$96$	−98848.5	−1.09469
$97$	78467.3	0.846758	0.423379	−	0.905953i	$-0.360844\pi$
$97$	78467.3	0.846758	0.423379	+	0.905953i	$0.360844\pi$
$98$	169511.	1.78292
$99$	−96709.6	−0.991703
$100$	−236842.	−2.36842
$101$	−153677.	−1.49902	−0.749508	−	0.661995i	$-0.769710\pi$
$101$	−153677.	−1.49902	−0.749508	+	0.661995i	$0.769710\pi$
$102$	99039.2	0.942555
$103$	83809.4	0.778394	0.389197	−	0.921155i	$-0.372753\pi$
$103$	83809.4	0.778394	0.389197	+	0.921155i	$0.372753\pi$
$104$	99581.0	0.902803
$105$	−3131.58	−0.0277198
$106$	−372672.	−3.22153
$107$	−186092.	−1.57133	−0.785666	−	0.618650i	$-0.787680\pi$
$107$	−186092.	−1.57133	−0.785666	+	0.618650i	$0.787680\pi$
$108$	−207672.	−1.71324
$109$	17349.1	0.139866	0.0699328	−	0.997552i	$-0.477722\pi$
$109$	17349.1	0.139866	0.0699328	+	0.997552i	$0.477722\pi$
$110$	86006.2	0.677717
$111$	48674.7	0.374970
$112$	110682.	0.833742
$113$	−71161.0	−0.524259	−0.262129	−	0.965033i	$-0.584425\pi$
$113$	−71161.0	−0.524259	−0.262129	+	0.965033i	$0.584425\pi$
$114$	66839.8	0.481696
$115$	−4874.05	−0.0343673
$116$	66664.5	0.459991
$117$	37865.4	0.255728
$118$	−480380.	−3.17600
$119$	−55918.1	−0.361980
$120$	53583.7	0.339688
$121$	43492.9	0.270056
$122$	244947.	1.48995
$123$	41486.9	0.247257
$124$	−301612.	−1.76155
$125$	104779.	0.599790
$126$	75748.1	0.425055
$127$	334203.	1.83866	0.919330	−	0.393487i	$-0.128731\pi$
$127$	334203.	1.83866	0.919330	+	0.393487i	$0.128731\pi$
$128$	−379109.	−2.04522
$129$	−43803.5	−0.231758
$130$	−33674.6	−0.174761
$131$	−126483.	−0.643954	−0.321977	−	0.946748i	$-0.604347\pi$
$131$	−126483.	−0.643954	−0.321977	+	0.946748i	$0.604347\pi$
$132$	205595.	1.02702
$133$	−37738.1	−0.184991
$134$	−381115.	−1.83355
$135$	43529.2	0.205564
$136$	956802.	4.43583
$137$	85994.0	0.391441	0.195721	−	0.980660i	$-0.437295\pi$
$137$	85994.0	0.391441	0.195721	+	0.980660i	$0.437295\pi$
$138$	−16080.6	−0.0718796
$139$	252434.	1.10818	0.554091	−	0.832456i	$-0.313066\pi$
$139$	252434.	1.10818	0.554091	+	0.832456i	$0.313066\pi$
$140$	−48809.2	−0.210466
$141$	62490.7	0.264709
$142$	645481.	2.68635
$143$	−80086.5	−0.327506
$144$	−720132.	−2.89405
$145$	−13973.3	−0.0551922
$146$	838242.	3.25452
$147$	−84934.2	−0.324182
$148$	758651.	2.84700
$149$	−466456.	−1.72125	−0.860627	−	0.509236i	$-0.829928\pi$
$149$	−466456.	−1.72125	−0.860627	+	0.509236i	$0.829928\pi$
$150$	163785.	0.594356
$151$	390612.	1.39413	0.697066	−	0.717007i	$-0.254489\pi$
$151$	390612.	1.39413	0.697066	+	0.717007i	$0.254489\pi$
$152$	645729.	2.26695
$153$	363821.	1.25649
$154$	−160210.	−0.544361
$155$	63219.6	0.211360
$156$	−80498.1	−0.264834
$157$	−340813.	−1.10349	−0.551743	−	0.834014i	$-0.686037\pi$
$157$	−340813.	−1.10349	−0.551743	+	0.834014i	$0.686037\pi$
$158$	962709.	3.06798
$159$	186729.	0.585759
$160$	322933.	0.997268
$161$	9079.22	0.0276048
$162$	−416451.	−1.24674
$163$	−172637.	−0.508939	−0.254469	−	0.967081i	$-0.581901\pi$
$163$	−172637.	−0.508939	−0.254469	+	0.967081i	$0.581901\pi$
$164$	646621.	1.87733
$165$	−43093.9	−0.123227
$166$	−916807.	−2.58231
$167$	682939.	1.89492	0.947459	−	0.319877i	$-0.103642\pi$
$167$	682939.	1.89492	0.947459	+	0.319877i	$0.103642\pi$
$168$	−99814.1	−0.272847
$169$	−339936.	−0.915547
$170$	−323555.	−0.858670
$171$	245536.	0.642134
$172$	−682727.	−1.75965
$173$	−143881.	−0.365500	−0.182750	−	0.983159i	$-0.558500\pi$
$173$	−143881.	−0.365500	−0.182750	+	0.983159i	$0.558500\pi$
$174$	−46101.1	−0.115435
$175$	−92474.1	−0.228258
$176$	1.52310e6	3.70636
$177$	240697.	0.577480
$178$	−465931.	−1.10223
$179$	771094.	1.79877	0.899384	−	0.437160i	$-0.144016\pi$
$179$	771094.	1.79877	0.899384	+	0.437160i	$0.144016\pi$
$180$	317568.	0.730560
$181$	−441904.	−1.00261	−0.501305	−	0.865271i	$-0.667146\pi$
$181$	−441904.	−1.00261	−0.501305	+	0.865271i	$0.667146\pi$
$182$	62728.0	0.140373
$183$	−122732.	−0.270913
$184$	−155353.	−0.338278
$185$	−159018.	−0.341598
$186$	208576.	0.442062
$187$	−769493.	−1.60917
$188$	973989.	2.00983
$189$	−81084.8	−0.165114
$190$	−218362.	−0.438826
$191$	661998.	1.31303	0.656513	−	0.754315i	$-0.272031\pi$
$191$	661998.	1.31303	0.656513	+	0.754315i	$0.272031\pi$
$192$	483426.	0.946404
$193$	−28234.6	−0.0545617	−0.0272809	−	0.999628i	$-0.508685\pi$
$193$	−28234.6	−0.0545617	−0.0272809	+	0.999628i	$0.508685\pi$
$194$	−845752.	−1.61339
$195$	16872.8	0.0317762
$196$	−1.32380e6	−2.46139
$197$	−200799.	−0.368635	−0.184318	−	0.982867i	$-0.559008\pi$
$197$	−200799.	−0.368635	−0.184318	+	0.982867i	$0.559008\pi$
$198$	1.04238e6	1.88956
$199$	−18393.2	−0.0329249	−0.0164625	−	0.999864i	$-0.505240\pi$
$199$	−18393.2	−0.0329249	−0.0164625	+	0.999864i	$0.505240\pi$
$200$	1.58230e6	2.79715
$201$	190960.	0.333389
$202$	1.65640e6	2.85618
$203$	26028.9	0.0443319
$204$	−773448.	−1.30123
$205$	−135535.	−0.225252
$206$	−903332.	−1.48313
$207$	−59072.3	−0.0958205
$208$	−596351.	−0.955749
$209$	−519318.	−0.822370
$210$	33753.4	0.0528165
$211$	534710.	0.826822	0.413411	−	0.910545i	$-0.364337\pi$
$211$	534710.	0.826822	0.413411	+	0.910545i	$0.364337\pi$
$212$	2.91039e6	4.44745
$213$	−323422.	−0.488450
$214$	2.00578e6	2.99397
$215$	143104.	0.211132
$216$	1.38742e6	2.02337
$217$	−117764.	−0.169770
$218$	−186996.	−0.266496
$219$	−420006.	−0.591759
$220$	−671667.	−0.935615
$221$	301285.	0.414951
$222$	−524636.	−0.714457
$223$	500716.	0.674263	0.337131	−	0.941458i	$-0.390543\pi$
$223$	500716.	0.674263	0.337131	+	0.941458i	$0.390543\pi$
$224$	−601548.	−0.801033
$225$	601666.	0.792318
$226$	767002.	0.998908
$227$	737096.	0.949423	0.474711	−	0.880142i	$-0.342552\pi$
$227$	737096.	0.949423	0.474711	+	0.880142i	$0.342552\pi$
$228$	−521986.	−0.665001
$229$	−331153.	−0.417292	−0.208646	−	0.977991i	$-0.566906\pi$
$229$	−331153.	−0.417292	−0.208646	+	0.977991i	$0.566906\pi$
$230$	52534.5	0.0654825
$231$	80273.9	0.0989793
$232$	−445375.	−0.543258
$233$	386256.	0.466107	0.233053	−	0.972464i	$-0.425128\pi$
$233$	386256.	0.466107	0.233053	+	0.972464i	$0.425128\pi$
$234$	−408129.	−0.487256
$235$	−204154.	−0.241150
$236$	3.75153e6	4.38459
$237$	−482370.	−0.557840
$238$	602708.	0.689707
$239$	1.16212e6	1.31600	0.658001	−	0.753017i	$-0.271402\pi$
$239$	1.16212e6	1.31600	0.658001	+	0.753017i	$0.271402\pi$
$240$	−320892.	−0.359609
$241$	918004.	1.01813	0.509064	−	0.860729i	$-0.329992\pi$
$241$	918004.	1.01813	0.509064	+	0.860729i	$0.329992\pi$
$242$	−468784.	−0.514558
$243$	808186.	0.878003
$244$	−1.91292e6	−2.05694
$245$	277475.	0.295331
$246$	−447163.	−0.471116
$247$	203332.	0.212062
$248$	2.01503e6	2.08042
$249$	459371.	0.469532
$250$	−1.12935e6	−1.14282
$251$	815247.	0.816779	0.408390	−	0.912808i	$-0.366090\pi$
$251$	815247.	0.816779	0.408390	+	0.912808i	$0.366090\pi$
$252$	−591556.	−0.586806
$253$	124940.	0.122716
$254$	−3.60218e6	−3.50333
$255$	162119.	0.156129
$256$	1.22176e6	1.16516
$257$	−22498.0	−0.0212477	−0.0106239	−	0.999944i	$-0.503382\pi$
$257$	−22498.0	−0.0212477	−0.0106239	+	0.999944i	$0.503382\pi$
$258$	472132.	0.441585
$259$	296213.	0.274381
$260$	262983.	0.241265
$261$	−169353.	−0.153883
$262$	1.36329e6	1.22697
$263$	1.59145e6	1.41875	0.709373	−	0.704833i	$-0.248978\pi$
$263$	1.59145e6	1.41875	0.709373	+	0.704833i	$0.248978\pi$
$264$	−1.37355e6	−1.21293
$265$	−610033.	−0.533628
$266$	406757.	0.352477
$267$	233457.	0.200414
$268$	2.97632e6	2.53130
$269$	−707751.	−0.596348	−0.298174	−	0.954512i	$-0.596378\pi$
$269$	−707751.	−0.596348	−0.298174	+	0.954512i	$0.596378\pi$
$270$	−469176.	−0.391675
$271$	−886264.	−0.733060	−0.366530	−	0.930406i	$-0.619454\pi$
$271$	−886264.	−0.733060	−0.366530	+	0.930406i	$0.619454\pi$
$272$	−5.72991e6	−4.69597
$273$	−31430.2	−0.0255235
$274$	−926879.	−0.745842
$275$	−1.27254e6	−1.01471
$276$	125582.	0.0992327
$277$	674013.	0.527799	0.263900	−	0.964550i	$-0.414991\pi$
$277$	674013.	0.527799	0.263900	+	0.964550i	$0.414991\pi$
$278$	−2.72084e6	−2.11150
$279$	766207.	0.589299
$280$	326087.	0.248564
$281$	1.89112e6	1.42874	0.714369	−	0.699769i	$-0.246714\pi$
$281$	1.89112e6	1.42874	0.714369	+	0.699769i	$0.246714\pi$
$282$	−673551.	−0.504368
$283$	780421.	0.579246	0.289623	−	0.957141i	$-0.406470\pi$
$283$	780421.	0.579246	0.289623	+	0.957141i	$0.406470\pi$
$284$	−5.04089e6	−3.70861
$285$	109411.	0.0797903
$286$	863205.	0.624021
$287$	252471.	0.180928
$288$	3.91387e6	2.78051
$289$	1.47498e6	1.03882
$290$	150610.	0.105162
$291$	423769.	0.293357
$292$	−6.54626e6	−4.49300
$293$	166501.	0.113304	0.0566522	−	0.998394i	$-0.481957\pi$
$293$	166501.	0.113304	0.0566522	+	0.998394i	$0.481957\pi$
$294$	915455.	0.617688
$295$	−786343.	−0.526086
$296$	−5.06843e6	−3.36236
$297$	−1.11581e6	−0.734008
$298$	5.02765e6	3.27963
$299$	−48918.6	−0.0316443
$300$	−1.27908e6	−0.820532
$301$	−266569.	−0.169587
$302$	−4.21018e6	−2.65634
$303$	−829947.	−0.519330
$304$	−3.86701e6	−2.39989
$305$	400959.	0.246803
$306$	−3.92141e6	−2.39408
$307$	−1.24957e6	−0.756687	−0.378343	−	0.925665i	$-0.623506\pi$
$307$	−1.24957e6	−0.756687	−0.378343	+	0.925665i	$0.623506\pi$
$308$	1.25116e6	0.751512
$309$	452619.	0.269673
$310$	−681407.	−0.402719
$311$	−3.12763e6	−1.83364	−0.916820	−	0.399301i	$-0.869253\pi$
$311$	−3.12763e6	−1.83364	−0.916820	+	0.399301i	$0.869253\pi$
$312$	537795.	0.312774
$313$	−141408.	−0.0815853	−0.0407927	−	0.999168i	$-0.512988\pi$
$313$	−141408.	−0.0815853	−0.0407927	+	0.999168i	$0.512988\pi$
$314$	3.67342e6	2.10255
$315$	123994.	0.0704081
$316$	−7.51829e6	−4.23547
$317$	−1.93357e6	−1.08071	−0.540357	−	0.841436i	$-0.681711\pi$
$317$	−1.93357e6	−1.08071	−0.540357	+	0.841436i	$0.681711\pi$
$318$	−2.01264e6	−1.11609
$319$	358186.	0.197075
$320$	−1.57932e6	−0.862177
$321$	−1.00500e6	−0.544384
$322$	−97859.6	−0.0525973
$323$	1.95367e6	1.04195
$324$	3.25228e6	1.72117
$325$	498248.	0.261660
$326$	1.86076e6	0.969718
$327$	93695.3	0.0484561
$328$	−4.31998e6	−2.21716
$329$	380291.	0.193698
$330$	464484.	0.234793
$331$	2.26827e6	1.13795	0.568977	−	0.822353i	$-0.307339\pi$
$331$	2.26827e6	1.13795	0.568977	+	0.822353i	$0.307339\pi$
$332$	7.15982e6	3.56498
$333$	−1.92726e6	−0.952421
$334$	−7.36099e6	−3.61052
$335$	−623854.	−0.303718
$336$	597747.	0.288848
$337$	2.37517e6	1.13925	0.569626	−	0.821904i	$-0.307088\pi$
$337$	2.37517e6	1.13925	0.569626	+	0.821904i	$0.307088\pi$
$338$	3.66397e6	1.74446
$339$	−384310.	−0.181628
$340$	2.52681e6	1.18543
$341$	−1.62055e6	−0.754705
$342$	−2.64649e6	−1.22350
$343$	−1.06924e6	−0.490728
$344$	4.56120e6	2.07818
$345$	−26322.7	−0.0119065
$346$	1.55081e6	0.696414
$347$	3.31616e6	1.47847	0.739235	−	0.673448i	$-0.235187\pi$
$347$	3.31616e6	1.47847	0.739235	+	0.673448i	$0.235187\pi$
$348$	360027.	0.159363
$349$	3.74748e6	1.64693	0.823467	−	0.567365i	$-0.192037\pi$
$349$	3.74748e6	1.64693	0.823467	+	0.567365i	$0.192037\pi$
$350$	996724.	0.434916
$351$	436882.	0.189277
$352$	−8.27795e6	−3.56095
$353$	1.99274e6	0.851167	0.425583	−	0.904919i	$-0.360069\pi$
$353$	1.99274e6	0.851167	0.425583	+	0.904919i	$0.360069\pi$
$354$	−2.59433e6	−1.10032
$355$	1.05660e6	0.444979
$356$	3.63869e6	1.52167
$357$	−301990.	−0.125407
$358$	−8.31117e6	−3.42732
$359$	−4.02240e6	−1.64721	−0.823605	−	0.567164i	$-0.808040\pi$
$359$	−4.02240e6	−1.64721	−0.823605	+	0.567164i	$0.808040\pi$
$360$	−2.12163e6	−0.862805
$361$	−1.15760e6	−0.467510
$362$	4.76303e6	1.91034
$363$	234887.	0.0935603
$364$	−489876.	−0.193790
$365$	1.37213e6	0.539094
$366$	1.32286e6	0.516191
$367$	3.61705e6	1.40181	0.700906	−	0.713254i	$-0.252779\pi$
$367$	3.61705e6	1.40181	0.700906	+	0.713254i	$0.252779\pi$
$368$	930345.	0.358117
$369$	−1.64266e6	−0.628031
$370$	1.71396e6	0.650872
$371$	1.13635e6	0.428625
$372$	−1.62888e6	−0.610284
$373$	−3.28416e6	−1.22223	−0.611114	−	0.791543i	$-0.709278\pi$
$373$	−3.28416e6	−1.22223	−0.611114	+	0.791543i	$0.709278\pi$
$374$	8.29392e6	3.06606
$375$	565867.	0.207796
$376$	−6.50707e6	−2.37365
$377$	−140243.	−0.0508193
$378$	873965.	0.314604
$379$	962339.	0.344136	0.172068	−	0.985085i	$-0.444955\pi$
$379$	962339.	0.344136	0.172068	+	0.985085i	$0.444955\pi$
$380$	1.70530e6	0.605817
$381$	1.80489e6	0.636999
$382$	−7.13529e6	−2.50180
$383$	−291058.	−0.101387	−0.0506935	−	0.998714i	$-0.516143\pi$
$383$	−291058.	−0.101387	−0.0506935	+	0.998714i	$0.516143\pi$
$384$	−2.04741e6	−0.708560
$385$	−262250.	−0.0901704
$386$	304324.	0.103960
$387$	1.73438e6	0.588664
$388$	6.60492e6	2.22735
$389$	2.72609e6	0.913411	0.456706	−	0.889618i	$-0.349029\pi$
$389$	2.72609e6	0.913411	0.456706	+	0.889618i	$0.349029\pi$
$390$	−181863.	−0.0605455
$391$	−470024.	−0.155481
$392$	8.84408e6	2.90695
$393$	−683083.	−0.223096
$394$	2.16430e6	0.702388
$395$	1.57588e6	0.508194
$396$	−8.14045e6	−2.60862
$397$	−744620.	−0.237115	−0.118557	−	0.992947i	$-0.537827\pi$
$397$	−744620.	−0.237115	−0.118557	+	0.992947i	$0.537827\pi$
$398$	198250.	0.0627342
$399$	−203808.	−0.0640898
$400$	−9.47579e6	−2.96118
$401$	−2.42259e6	−0.752347	−0.376174	−	0.926549i	$-0.622760\pi$
$401$	−2.42259e6	−0.752347	−0.376174	+	0.926549i	$0.622760\pi$
$402$	−2.05824e6	−0.635230
$403$	634507.	0.194614
$404$	−1.29357e7	−3.94308
$405$	−681696.	−0.206516
$406$	−280551.	−0.0844688
$407$	4.07621e6	1.21975
$408$	5.16729e6	1.53678
$409$	−1.78139e6	−0.526564	−0.263282	−	0.964719i	$-0.584805\pi$
$409$	−1.78139e6	−0.526564	−0.263282	+	0.964719i	$0.584805\pi$
$410$	1.46086e6	0.429188
$411$	464418.	0.135614
$412$	7.05458e6	2.04752
$413$	1.46477e6	0.422567
$414$	636706.	0.182574
$415$	−1.50074e6	−0.427745
$416$	3.24113e6	0.918253
$417$	1.36329e6	0.383926
$418$	5.59742e6	1.56692
$419$	6.77227e6	1.88451	0.942257	−	0.334892i	$-0.108700\pi$
$419$	6.77227e6	1.88451	0.942257	+	0.334892i	$0.108700\pi$
$420$	−263598.	−0.0729153
$421$	−857549.	−0.235805	−0.117903	−	0.993025i	$-0.537617\pi$
$421$	−857549.	−0.235805	−0.117903	+	0.993025i	$0.537617\pi$
$422$	−5.76332e6	−1.57540
$423$	−2.47429e6	−0.672358
$424$	−1.94438e7	−5.25252
$425$	4.78731e6	1.28564
$426$	3.48597e6	0.930679
$427$	−746893.	−0.198239
$428$	−1.56641e7	−4.13330
$429$	−432514.	−0.113464
$430$	−1.54243e6	−0.402285
$431$	406400.	0.105381	0.0526903	−	0.998611i	$-0.483220\pi$
$431$	406400.	0.105381	0.0526903	+	0.998611i	$0.483220\pi$
$432$	−8.30873e6	−2.14203
$433$	4.70396e6	1.20571	0.602857	−	0.797850i	$-0.294029\pi$
$433$	4.70396e6	1.20571	0.602857	+	0.797850i	$0.294029\pi$
$434$	1.26930e6	0.323475
$435$	−75463.7	−0.0191212
$436$	1.46035e6	0.367909
$437$	−317211.	−0.0794592
$438$	4.52699e6	1.12752
$439$	5.98671e6	1.48261	0.741305	−	0.671168i	$-0.234207\pi$
$439$	5.98671e6	1.48261	0.741305	+	0.671168i	$0.234207\pi$
$440$	4.48731e6	1.10498
$441$	3.36293e6	0.823420
$442$	−3.24738e6	−0.790637
$443$	−353492.	−0.0855795	−0.0427898	−	0.999084i	$-0.513625\pi$
$443$	−353492.	−0.0855795	−0.0427898	+	0.999084i	$0.513625\pi$
$444$	4.09716e6	0.986336
$445$	−762691.	−0.182578
$446$	−5.39692e6	−1.28472
$447$	−2.51913e6	−0.596324
$448$	2.94192e6	0.692524
$449$	3.29115e6	0.770427	0.385213	−	0.922828i	$-0.374128\pi$
$449$	3.29115e6	0.770427	0.385213	+	0.922828i	$0.374128\pi$
$450$	−6.48501e6	−1.50966
$451$	3.47427e6	0.804309
$452$	−5.98992e6	−1.37903
$453$	2.10953e6	0.482993
$454$	−7.94473e6	−1.80900
$455$	102681.	0.0232520
$456$	3.48731e6	0.785378
$457$	5.52103e6	1.23660	0.618300	−	0.785942i	$-0.287822\pi$
$457$	5.52103e6	1.23660	0.618300	+	0.785942i	$0.287822\pi$
$458$	3.56930e6	0.795096
$459$	4.19769e6	0.929991
$460$	−410269.	−0.0904012
$461$	1.66004e6	0.363803	0.181901	−	0.983317i	$-0.441775\pi$
$461$	1.66004e6	0.363803	0.181901	+	0.983317i	$0.441775\pi$
$462$	−865225.	−0.188592
$463$	−1.06034e6	−0.229876	−0.114938	−	0.993373i	$-0.536667\pi$
$463$	−1.06034e6	−0.229876	−0.114938	+	0.993373i	$0.536667\pi$
$464$	2.66718e6	0.575118
$465$	341423.	0.0732251
$466$	−4.16323e6	−0.888107
$467$	2.51542e6	0.533725	0.266863	−	0.963735i	$-0.414013\pi$
$467$	2.51542e6	0.533725	0.266863	+	0.963735i	$0.414013\pi$
$468$	3.18729e6	0.672677
$469$	1.16210e6	0.243955
$470$	2.20045e6	0.459481
$471$	−1.84059e6	−0.382300
$472$	−2.50634e7	−5.17828
$473$	−3.66827e6	−0.753891
$474$	5.19919e6	1.06289
$475$	3.23087e6	0.657030
$476$	−4.70686e6	−0.952169
$477$	−7.39346e6	−1.48783
$478$	−1.25258e7	−2.50747
$479$	−1.02486e6	−0.204092	−0.102046	−	0.994780i	$-0.532539\pi$
$479$	−1.02486e6	−0.204092	−0.102046	+	0.994780i	$0.532539\pi$
$480$	1.74402e6	0.345501
$481$	−1.59599e6	−0.314533
$482$	−9.89463e6	−1.93991
$483$	49033.1	0.00956360
$484$	3.66098e6	0.710368
$485$	−1.38443e6	−0.267249
$486$	−8.71097e6	−1.67292
$487$	5.20945e6	0.995335	0.497667	−	0.867368i	$-0.334190\pi$
$487$	5.20945e6	0.995335	0.497667	+	0.867368i	$0.334190\pi$
$488$	1.27799e7	2.42929
$489$	−932342.	−0.176321
$490$	−2.99074e6	−0.562715
$491$	−3.29007e6	−0.615887	−0.307943	−	0.951405i	$-0.599641\pi$
$491$	−3.29007e6	−0.615887	−0.307943	+	0.951405i	$0.599641\pi$
$492$	3.49213e6	0.650395
$493$	−1.34750e6	−0.249695
$494$	−2.19160e6	−0.404058
$495$	1.70628e6	0.312996
$496$	−1.20672e7	−2.20243
$497$	−1.96820e6	−0.357420
$498$	−4.95129e6	−0.894634
$499$	1.04686e6	0.188207	0.0941036	−	0.995562i	$-0.470002\pi$
$499$	1.04686e6	0.188207	0.0941036	+	0.995562i	$0.470002\pi$
$500$	8.81968e6	1.57771
$501$	3.68826e6	0.656489
$502$	−8.78707e6	−1.55627
$503$	3.98013e6	0.701419	0.350710	−	0.936484i	$-0.385940\pi$
$503$	3.98013e6	0.701419	0.350710	+	0.936484i	$0.385940\pi$
$504$	3.95210e6	0.693029
$505$	2.71139e6	0.473111
$506$	−1.34665e6	−0.233819
$507$	−1.83585e6	−0.317189
$508$	2.81313e7	4.83649
$509$	6.92206e6	1.18424	0.592122	−	0.805848i	$-0.298290\pi$
$509$	6.92206e6	1.18424	0.592122	+	0.805848i	$0.298290\pi$
$510$	−1.74739e6	−0.297484
$511$	−2.55597e6	−0.433015
$512$	−1.03712e6	−0.174845
$513$	2.83295e6	0.475275
$514$	242493.	0.0404848
$515$	−1.47868e6	−0.245672
$516$	−3.68712e6	−0.609626
$517$	5.23321e6	0.861077
$518$	−3.19270e6	−0.522798
$519$	−777040.	−0.126627
$520$	−1.75695e6	−0.284938
$521$	7.40570e6	1.19529	0.597643	−	0.801762i	$-0.296104\pi$
$521$	7.40570e6	1.19529	0.597643	+	0.801762i	$0.296104\pi$
$522$	1.82535e6	0.293204
$523$	1.54203e6	0.246513	0.123256	−	0.992375i	$-0.460666\pi$
$523$	1.54203e6	0.246513	0.123256	+	0.992375i	$0.460666\pi$
$524$	−1.06466e7	−1.69388
$525$	−499414.	−0.0790792
$526$	−1.71534e7	−2.70324
$527$	6.09652e6	0.956214
$528$	8.22564e6	1.28406
$529$	−6.36003e6	−0.988143
$530$	6.57519e6	1.01676
$531$	−9.53029e6	−1.46680
$532$	−3.17658e6	−0.486609
$533$	−1.36031e6	−0.207405
$534$	−2.51630e6	−0.381864
$535$	3.28329e6	0.495935
$536$	−1.98844e7	−2.98951
$537$	4.16436e6	0.623178
$538$	7.62843e6	1.13626
$539$	−7.11271e6	−1.05454
$540$	3.66403e6	0.540723
$541$	−4.38624e6	−0.644316	−0.322158	−	0.946686i	$-0.604408\pi$
$541$	−4.38624e6	−0.644316	−0.322158	+	0.946686i	$0.604408\pi$
$542$	9.55251e6	1.39675
$543$	−2.38654e6	−0.347351
$544$	3.11416e7	4.51174
$545$	−306097.	−0.0441436
$546$	338768.	0.0486318
$547$	299209.	0.0427569
$547$	299209.	0.0427569
$548$	7.23848e6	1.02966
$549$	4.85953e6	0.688118
$550$	1.37160e7	1.93340
$551$	−909401.	−0.127608
$552$	−838994.	−0.117196
$553$	−2.93549e6	−0.408195
$554$	−7.26479e6	−1.00565
$555$	−858787.	−0.118346
$556$	2.12484e7	2.91501
$557$	936460.	0.127894	0.0639472	−	0.997953i	$-0.479631\pi$
$557$	936460.	0.127894	0.0639472	+	0.997953i	$0.479631\pi$
$558$	−8.25850e6	−1.12283
$559$	1.43626e6	0.194404
$560$	−1.95280e6	−0.263141
$561$	−4.15571e6	−0.557491
$562$	−2.03833e7	−2.72228
$563$	−3.26265e6	−0.433811	−0.216905	−	0.976193i	$-0.569596\pi$
$563$	−3.26265e6	−0.433811	−0.216905	+	0.976193i	$0.569596\pi$
$564$	5.26011e6	0.696301
$565$	1.25552e6	0.165464
$566$	−8.41170e6	−1.10368
$567$	1.26984e6	0.165879
$568$	3.36774e7	4.37994
$569$	−1.37968e6	−0.178647	−0.0893236	−	0.996003i	$-0.528471\pi$
$569$	−1.37968e6	−0.178647	−0.0893236	+	0.996003i	$0.528471\pi$
$570$	−1.17928e6	−0.152030
$571$	−4.75394e6	−0.610187	−0.305094	−	0.952322i	$-0.598688\pi$
$571$	−4.75394e6	−0.610187	−0.305094	+	0.952322i	$0.598688\pi$
$572$	−6.74122e6	−0.861486
$573$	3.57517e6	0.454894
$574$	−2.72124e6	−0.344736
$575$	−777298.	−0.0980433
$576$	−1.91410e7	−2.40386
$577$	−8.77583e6	−1.09736	−0.548680	−	0.836033i	$-0.684869\pi$
$577$	−8.77583e6	−1.09736	−0.548680	+	0.836033i	$0.684869\pi$
$578$	−1.58979e7	−1.97934
$579$	−152483.	−0.0189028
$580$	−1.17619e6	−0.145180
$581$	2.79553e6	0.343577
$582$	−4.56755e6	−0.558954
$583$	1.56374e7	1.90543
$584$	4.37346e7	5.30631
$585$	−668073.	−0.0807113
$586$	−1.79461e6	−0.215887
$587$	5.46612e6	0.654762	0.327381	−	0.944892i	$-0.393834\pi$
$587$	5.46612e6	0.654762	0.327381	+	0.944892i	$0.393834\pi$
$588$	−7.14926e6	−0.852743
$589$	4.11443e6	0.488677
$590$	8.47553e6	1.00239
$591$	−1.08443e6	−0.127713
$592$	3.03528e7	3.55955
$593$	6.31044e6	0.736924	0.368462	−	0.929643i	$-0.379884\pi$
$593$	6.31044e6	0.736924	0.368462	+	0.929643i	$0.379884\pi$
$594$	1.20267e7	1.39856
$595$	986585.	0.114246
$596$	−3.92635e7	−4.52766
$597$	−99334.0	−0.0114067
$598$	527265.	0.0602942
$599$	323677.	0.0368591	0.0184295	−	0.999830i	$-0.494133\pi$
$599$	323677.	0.0368591	0.0184295	+	0.999830i	$0.494133\pi$
$600$	8.54536e6	0.969064
$601$	−6.39046e6	−0.721682	−0.360841	−	0.932627i	$-0.617510\pi$
$601$	−6.39046e6	−0.721682	−0.360841	+	0.932627i	$0.617510\pi$
$602$	2.87319e6	0.323127
$603$	−7.56096e6	−0.846806
$604$	3.28795e7	3.66718
$605$	−767361.	−0.0852337
$606$	8.94551e6	0.989518
$607$	−1.05409e7	−1.16120	−0.580600	−	0.814189i	$-0.697182\pi$
$607$	−1.05409e7	−1.16120	−0.580600	+	0.814189i	$0.697182\pi$
$608$	2.10169e7	2.30574
$609$	140571.	0.0153587
$610$	−4.32170e6	−0.470251
$611$	−2.04900e6	−0.222044
$612$	3.06243e7	3.30513
$613$	−1.27549e7	−1.37096	−0.685482	−	0.728090i	$-0.740408\pi$
$613$	−1.27549e7	−1.37096	−0.685482	+	0.728090i	$0.740408\pi$
$614$	1.34684e7	1.44177
$615$	−731970.	−0.0780379
$616$	−8.35881e6	−0.887550
$617$	2.96578e6	0.313636	0.156818	−	0.987627i	$-0.449876\pi$
$617$	2.96578e6	0.313636	0.156818	+	0.987627i	$0.449876\pi$
$618$	−4.87852e6	−0.513827
$619$	9.88278e6	1.03670	0.518349	−	0.855169i	$-0.326547\pi$
$619$	9.88278e6	1.03670	0.518349	+	0.855169i	$0.326547\pi$
$620$	5.32146e6	0.555970
$621$	−681564.	−0.0709214
$622$	3.37109e7	3.49377
$623$	1.42072e6	0.146652
$624$	−3.22064e6	−0.331117
$625$	6.94419e6	0.711085
$626$	1.52415e6	0.155450
$627$	−2.80462e6	−0.284908
$628$	−2.86876e7	−2.90265
$629$	−1.53347e7	−1.54543
$630$	−1.33645e6	−0.134154
$631$	−5.66716e6	−0.566621	−0.283310	−	0.959028i	$-0.591433\pi$
$631$	−5.66716e6	−0.566621	−0.283310	+	0.959028i	$0.591433\pi$
$632$	5.02285e7	5.00216
$633$	2.88774e6	0.286450
$634$	2.08408e7	2.05916
$635$	−5.89648e6	−0.580308
$636$	1.57178e7	1.54081
$637$	2.78489e6	0.271931
$638$	−3.86068e6	−0.375502
$639$	1.28057e7	1.24066
$640$	6.68877e6	0.645500
$641$	−1.38579e7	−1.33215	−0.666074	−	0.745886i	$-0.732026\pi$
$641$	−1.38579e7	−1.33215	−0.666074	+	0.745886i	$0.732026\pi$
$642$	1.08324e7	1.03725
$643$	−1.58461e7	−1.51146	−0.755728	−	0.654886i	$-0.772717\pi$
$643$	−1.58461e7	−1.51146	−0.755728	+	0.654886i	$0.772717\pi$
$644$	764236.	0.0726128
$645$	772842.	0.0731462
$646$	−2.10575e7	−1.98529
$647$	157554.	0.0147969	0.00739844	−	0.999973i	$-0.497645\pi$
$647$	157554.	0.0147969	0.00739844	+	0.999973i	$0.497645\pi$
$648$	−2.17280e7	−2.03274
$649$	2.01569e7	1.87850
$650$	−5.37032e6	−0.498559
$651$	−635991.	−0.0588165
$652$	−1.45316e7	−1.33873
$653$	−2.15573e6	−0.197839	−0.0989193	−	0.995095i	$-0.531539\pi$
$653$	−2.15573e6	−0.197839	−0.0989193	+	0.995095i	$0.531539\pi$
$654$	−1.00989e6	−0.0923269
$655$	2.23159e6	0.203241
$656$	2.58706e7	2.34718
$657$	1.66299e7	1.50306
$658$	−4.09893e6	−0.369068
$659$	−1.25019e7	−1.12140	−0.560701	−	0.828018i	$-0.689468\pi$
$659$	−1.25019e7	−1.12140	−0.560701	+	0.828018i	$0.689468\pi$
$660$	−3.62739e6	−0.324142
$661$	−347746.	−0.0309570	−0.0154785	−	0.999880i	$-0.504927\pi$
$661$	−347746.	−0.0309570	−0.0154785	+	0.999880i	$0.504927\pi$
$662$	−2.44484e7	−2.16823
$663$	1.62711e6	0.143759
$664$	−4.78337e7	−4.21031
$665$	665829.	0.0583859
$666$	2.07728e7	1.81472
$667$	218788.	0.0190418
$668$	5.74858e7	4.98448
$669$	2.70416e6	0.233597
$670$	6.72416e6	0.578696
$671$	−1.02781e7	−0.881261
$672$	−3.24871e6	−0.277516
$673$	−2.00811e6	−0.170903	−0.0854515	−	0.996342i	$-0.527233\pi$
$673$	−2.00811e6	−0.170903	−0.0854515	+	0.996342i	$0.527233\pi$
$674$	−2.56006e7	−2.17070
$675$	6.94190e6	0.586433
$676$	−2.86139e7	−2.40829
$677$	−1.51622e7	−1.27143	−0.635713	−	0.771925i	$-0.719294\pi$
$677$	−1.51622e7	−1.27143	−0.635713	+	0.771925i	$0.719294\pi$
$678$	4.14226e6	0.346069
$679$	2.57887e6	0.214662
$680$	−1.68812e7	−1.40001
$681$	3.98075e6	0.328925
$682$	1.74670e7	1.43799
$683$	−1.01152e7	−0.829706	−0.414853	−	0.909889i	$-0.636167\pi$
$683$	−1.01152e7	−0.829706	−0.414853	+	0.909889i	$0.636167\pi$
$684$	2.06678e7	1.68910
$685$	−1.51723e6	−0.123545
$686$	1.15247e7	0.935020
$687$	−1.78842e6	−0.144570
$688$	−2.73152e7	−2.20005
$689$	−6.12262e6	−0.491348
$690$	283717.	0.0226862
$691$	−478605.	−0.0381313	−0.0190657	−	0.999818i	$-0.506069\pi$
$691$	−478605.	−0.0381313	−0.0190657	+	0.999818i	$0.506069\pi$
$692$	−1.21111e7	−0.961428
$693$	−3.17841e6	−0.251407
$694$	−3.57430e7	−2.81703
$695$	−4.45379e6	−0.349758
$696$	−2.40529e6	−0.188210
$697$	−1.30702e7	−1.01906
$698$	−4.03919e7	−3.13802
$699$	2.08601e6	0.161481
$700$	−7.78393e6	−0.600419
$701$	−1.62373e7	−1.24801	−0.624006	−	0.781420i	$-0.714496\pi$
$701$	−1.62373e7	−1.24801	−0.624006	+	0.781420i	$0.714496\pi$
$702$	−4.70890e6	−0.360642
$703$	−1.03491e7	−0.789795
$704$	4.04839e7	3.07858
$705$	−1.10255e6	−0.0835458
$706$	−2.14786e7	−1.62179
$707$	−5.05069e6	−0.380016
$708$	2.02605e7	1.51903
$709$	1.33287e7	0.995802	0.497901	−	0.867234i	$-0.334104\pi$
$709$	1.33287e7	0.995802	0.497901	+	0.867234i	$0.334104\pi$
$710$	−1.13885e7	−0.847851
$711$	1.90992e7	1.41691
$712$	−2.43096e7	−1.79712
$713$	−989870.	−0.0729213
$714$	3.25498e6	0.238947
$715$	1.41300e6	0.103366
$716$	6.49063e7	4.73156
$717$	6.27613e6	0.455926
$718$	4.33551e7	3.13855
$719$	1.08751e7	0.784534	0.392267	−	0.919851i	$-0.371691\pi$
$719$	1.08751e7	0.784534	0.392267	+	0.919851i	$0.371691\pi$
$720$	1.27056e7	0.913404
$721$	2.75444e6	0.197331
$722$	1.24771e7	0.890781
$723$	4.95776e6	0.352728
$724$	−3.71969e7	−2.63731
$725$	−2.22841e6	−0.157453
$726$	−2.53171e6	−0.178267
$727$	1.58219e7	1.11025	0.555127	−	0.831766i	$-0.312670\pi$
$727$	1.58219e7	1.11025	0.555127	+	0.831766i	$0.312670\pi$
$728$	3.27278e6	0.228870
$729$	−5.02423e6	−0.350147
$730$	−1.47894e7	−1.02717
$731$	1.38000e7	0.955183
$732$	−1.03309e7	−0.712622
$733$	1.09677e7	0.753975	0.376987	−	0.926218i	$-0.376960\pi$
$733$	1.09677e7	0.753975	0.376987	+	0.926218i	$0.376960\pi$
$734$	−3.89861e7	−2.67097
$735$	1.49853e6	0.102317
$736$	−5.05636e6	−0.344067
$737$	1.59917e7	1.08449
$738$	1.77052e7	1.19663
$739$	−1.41022e7	−0.949898	−0.474949	−	0.880013i	$-0.657534\pi$
$739$	−1.41022e7	−0.949898	−0.474949	+	0.880013i	$0.657534\pi$
$740$	−1.33852e7	−0.898555
$741$	1.09811e6	0.0734684
$742$	−1.22481e7	−0.816690
$743$	1.49292e7	0.992117	0.496059	−	0.868289i	$-0.334780\pi$
$743$	1.49292e7	0.992117	0.496059	+	0.868289i	$0.334780\pi$
$744$	1.08823e7	0.720757
$745$	8.22986e6	0.543253
$746$	3.53980e7	2.32880
$747$	−1.81886e7	−1.19261
$748$	−6.47715e7	−4.23282
$749$	−6.11601e6	−0.398349
$750$	−6.09915e6	−0.395928
$751$	−1.24606e7	−0.806192	−0.403096	−	0.915158i	$-0.632066\pi$
$751$	−1.24606e7	−0.806192	−0.403096	+	0.915158i	$0.632066\pi$
$752$	3.89683e7	2.51285
$753$	4.40281e6	0.282971
$754$	1.51160e6	0.0968296
$755$	−6.89173e6	−0.440008
$756$	−6.82525e6	−0.434324
$757$	7.33588e6	0.465278	0.232639	−	0.972563i	$-0.425264\pi$
$757$	7.33588e6	0.465278	0.232639	+	0.972563i	$0.425264\pi$
$758$	−1.03725e7	−0.655707
$759$	674748.	0.0425145
$760$	−1.13928e7	−0.715481
$761$	1.12243e6	0.0702585	0.0351293	−	0.999383i	$-0.488816\pi$
$761$	1.12243e6	0.0702585	0.0351293	+	0.999383i	$0.488816\pi$
$762$	−1.94539e7	−1.21372
$763$	570188.	0.0354574
$764$	5.57231e7	3.45384
$765$	−6.41904e6	−0.396567
$766$	3.13714e6	0.193180
$767$	−7.89216e6	−0.484404
$768$	6.59820e6	0.403667
$769$	2.31882e6	0.141400	0.0707002	−	0.997498i	$-0.477477\pi$
$769$	2.31882e6	0.141400	0.0707002	+	0.997498i	$0.477477\pi$
$770$	2.82664e6	0.171808
$771$	−121502.	−0.00736121
$772$	−2.37662e6	−0.143522
$773$	−1.53230e7	−0.922346	−0.461173	−	0.887310i	$-0.652571\pi$
$773$	−1.53230e7	−0.922346	−0.461173	+	0.887310i	$0.652571\pi$
$774$	−1.86939e7	−1.12162
$775$	1.00821e7	0.602969
$776$	−4.41264e7	−2.63054
$777$	1.59972e6	0.0950587
$778$	−2.93829e7	−1.74039
$779$	−8.82085e6	−0.520795
$780$	1.42026e6	0.0835855
$781$	−2.70846e7	−1.58889
$782$	5.06611e6	0.296249
$783$	−1.95395e6	−0.113896
$784$	−5.29636e7	−3.07743
$785$	6.01309e6	0.348276
$786$	7.36255e6	0.425081
$787$	8.25317e6	0.474989	0.237495	−	0.971389i	$-0.423674\pi$
$787$	8.25317e6	0.474989	0.237495	+	0.971389i	$0.423674\pi$
$788$	−1.69021e7	−0.969674
$789$	8.59478e6	0.491521
$790$	−1.69854e7	−0.968298
$791$	−2.33874e6	−0.132905
$792$	5.43851e7	3.08082
$793$	4.02424e6	0.227248
$794$	8.02583e6	0.451792
$795$	−3.29453e6	−0.184874
$796$	−1.54823e6	−0.0866071
$797$	2.83973e7	1.58355	0.791774	−	0.610814i	$-0.209158\pi$
$797$	2.83973e7	1.58355	0.791774	+	0.610814i	$0.209158\pi$
$798$	2.19673e6	0.122115
$799$	−1.96873e7	−1.09099
$800$	5.15002e7	2.84501
$801$	−9.24363e6	−0.509051
$802$	2.61116e7	1.43350
$803$	−3.51729e7	−1.92495
$804$	1.60739e7	0.876961
$805$	−160188.	−0.00871246
$806$	−6.83897e6	−0.370812
$807$	−3.82226e6	−0.206603
$808$	8.64212e7	4.65685
$809$	1.44750e7	0.777585	0.388792	−	0.921325i	$-0.372892\pi$
$809$	1.44750e7	0.777585	0.388792	+	0.921325i	$0.372892\pi$
$810$	7.34760e6	0.393489
$811$	−8.35813e6	−0.446228	−0.223114	−	0.974792i	$-0.571622\pi$
$811$	−8.35813e6	−0.446228	−0.223114	+	0.974792i	$0.571622\pi$
$812$	2.19096e6	0.116613
$813$	−4.78634e6	−0.253967
$814$	−4.39351e7	−2.32408
$815$	3.04591e6	0.160628
$816$	−3.09448e7	−1.62691
$817$	9.31340e6	0.488150
$818$	1.92006e7	1.00330
$819$	1.24447e6	0.0648296
$820$	−1.14086e7	−0.592512
$821$	3.33489e6	0.172673	0.0863364	−	0.996266i	$-0.472484\pi$
$821$	3.33489e6	0.172673	0.0863364	+	0.996266i	$0.472484\pi$
$822$	−5.00568e6	−0.258395
$823$	2.00585e7	1.03228	0.516141	−	0.856504i	$-0.327368\pi$
$823$	2.00585e7	1.03228	0.516141	+	0.856504i	$0.327368\pi$
$824$	−4.71306e7	−2.41816
$825$	−6.87247e6	−0.351543
$826$	−1.57879e7	−0.805148
$827$	2.20910e7	1.12319	0.561593	−	0.827413i	$-0.310189\pi$
$827$	2.20910e7	1.12319	0.561593	+	0.827413i	$0.310189\pi$
$828$	−4.97237e6	−0.252050
$829$	−2.91870e7	−1.47504	−0.737518	−	0.675328i	$-0.764002\pi$
$829$	−2.91870e7	−1.47504	−0.737518	+	0.675328i	$0.764002\pi$
$830$	1.61756e7	0.815014
$831$	3.64006e6	0.182855
$832$	−1.58510e7	−0.793866
$833$	2.67580e7	1.33611
$834$	−1.46941e7	−0.731523
$835$	−1.20493e7	−0.598064
$836$	−4.37131e7	−2.16320
$837$	8.84033e6	0.436169
$838$	−7.29943e7	−3.59070
$839$	−2.29989e7	−1.12798	−0.563992	−	0.825780i	$-0.690735\pi$
$839$	−2.29989e7	−1.12798	−0.563992	+	0.825780i	$0.690735\pi$
$840$	1.76106e6	0.0861143
$841$	−1.98839e7	−0.969420
$842$	9.24302e6	0.449297
$843$	1.02131e7	0.494983
$844$	4.50088e7	2.17491
$845$	5.99763e6	0.288960
$846$	2.66690e7	1.28109
$847$	1.42942e6	0.0684621
$848$	1.16441e8	5.56055
$849$	4.21473e6	0.200678
$850$	−5.15996e7	−2.44962
$851$	2.48984e6	0.117855
$852$	−2.72238e7	−1.28484
$853$	1.72872e6	0.0813489	0.0406745	−	0.999172i	$-0.487049\pi$
$853$	1.72872e6	0.0813489	0.0406745	+	0.999172i	$0.487049\pi$
$854$	8.05032e6	0.377719
$855$	−4.33209e6	−0.202667
$856$	1.04650e8	4.88151
$857$	−2.23785e7	−1.04083	−0.520415	−	0.853914i	$-0.674223\pi$
$857$	−2.23785e7	−1.04083	−0.520415	+	0.853914i	$0.674223\pi$
$858$	4.66181e6	0.216190
$859$	1.46271e7	0.676355	0.338177	−	0.941082i	$-0.390190\pi$
$859$	1.46271e7	0.676355	0.338177	+	0.941082i	$0.390190\pi$
$860$	1.20456e7	0.555371
$861$	1.36349e6	0.0626822
$862$	−4.38035e6	−0.200789
$863$	−2.32267e7	−1.06160	−0.530798	−	0.847498i	$-0.678108\pi$
$863$	−2.32267e7	−1.06160	−0.530798	+	0.847498i	$0.678108\pi$
$864$	4.51573e7	2.05799
$865$	2.53855e6	0.115357
$866$	−5.07012e7	−2.29733
$867$	7.96572e6	0.359896
$868$	−9.91265e6	−0.446571
$869$	−4.03955e7	−1.81461
$870$	813379.	0.0364330
$871$	−6.26134e6	−0.279654
$872$	−9.75636e6	−0.434507
$873$	−1.67789e7	−0.745125
$874$	3.41903e6	0.151399
$875$	3.44362e6	0.152053
$876$	−3.53536e7	−1.55659
$877$	3.02805e6	0.132942	0.0664712	−	0.997788i	$-0.478826\pi$
$877$	3.02805e6	0.132942	0.0664712	+	0.997788i	$0.478826\pi$
$878$	−6.45272e7	−2.82492
$879$	899201.	0.0392540
$880$	−2.68727e7	−1.16978
$881$	2.51976e7	1.09375	0.546876	−	0.837213i	$-0.315817\pi$
$881$	2.51976e7	1.09375	0.546876	+	0.837213i	$0.315817\pi$
$882$	−3.62471e7	−1.56892
$883$	−3.67429e7	−1.58588	−0.792942	−	0.609297i	$-0.791452\pi$
$883$	−3.67429e7	−1.58588	−0.792942	+	0.609297i	$0.791452\pi$
$884$	2.53604e7	1.09151
$885$	−4.24671e6	−0.182261
$886$	3.81008e6	0.163061
$887$	−5.99882e6	−0.256010	−0.128005	−	0.991774i	$-0.540857\pi$
$887$	−5.99882e6	−0.256010	−0.128005	+	0.991774i	$0.540857\pi$
$888$	−2.73725e7	−1.16488
$889$	1.09838e7	0.466119
$890$	8.22060e6	0.347879
$891$	1.74744e7	0.737407
$892$	4.21474e7	1.77361
$893$	−1.32866e7	−0.557553
$894$	2.71522e7	1.13622
$895$	−1.36047e7	−0.567717
$896$	−1.24596e7	−0.518484
$897$	−264189.	−0.0109631
$898$	−3.54733e7	−1.46795
$899$	−2.83783e6	−0.117108
$900$	5.06448e7	2.08415
$901$	−5.88279e7	−2.41419
$902$	−3.74472e7	−1.53251
$903$	−1.43963e6	−0.0587530
$904$	4.00177e7	1.62866
$905$	7.79669e6	0.316438
$906$	−2.27374e7	−0.920282
$907$	2.91987e7	1.17854	0.589271	−	0.807935i	$-0.299415\pi$
$907$	2.91987e7	1.17854	0.589271	+	0.807935i	$0.299415\pi$
$908$	6.20445e7	2.49740
$909$	3.28614e7	1.31910
$910$	−1.10673e6	−0.0443037
$911$	−9.61939e6	−0.384018	−0.192009	−	0.981393i	$-0.561500\pi$
$911$	−9.61939e6	−0.384018	−0.192009	+	0.981393i	$0.561500\pi$
$912$	−2.08841e7	−0.831436
$913$	3.84695e7	1.52735
$914$	−5.95079e7	−2.35618
$915$	2.16541e6	0.0855042
$916$	−2.78745e7	−1.09766
$917$	−4.15694e6	−0.163249
$918$	−4.52444e7	−1.77198
$919$	1.51250e7	0.590754	0.295377	−	0.955381i	$-0.404555\pi$
$919$	1.51250e7	0.590754	0.295377	+	0.955381i	$0.404555\pi$
$920$	2.74095e6	0.106765
$921$	−6.74843e6	−0.262152
$922$	−1.78926e7	−0.693180
$923$	1.06046e7	0.409723
$924$	6.75699e6	0.260360
$925$	−2.53596e7	−0.974514
$926$	1.14288e7	0.438000
$927$	−1.79213e7	−0.684967
$928$	−1.44959e7	−0.552555
$929$	−4.59941e7	−1.74849	−0.874243	−	0.485488i	$-0.838642\pi$
$929$	−4.59941e7	−1.74849	−0.874243	+	0.485488i	$0.838642\pi$
$930$	−3.68000e6	−0.139521
$931$	1.80585e7	0.682822
$932$	3.25128e7	1.22607
$933$	−1.68910e7	−0.635260
$934$	−2.71122e7	−1.01695
$935$	1.35765e7	0.507876
$936$	−2.12938e7	−0.794444
$937$	−4.82541e6	−0.179550	−0.0897749	−	0.995962i	$-0.528615\pi$
$937$	−4.82541e6	−0.179550	−0.0897749	+	0.995962i	$0.528615\pi$
$938$	−1.25255e7	−0.464825
$939$	−763684.	−0.0282650
$940$	−1.71845e7	−0.634332
$941$	3.64706e7	1.34267	0.671335	−	0.741154i	$-0.265721\pi$
$941$	3.64706e7	1.34267	0.671335	+	0.741154i	$0.265721\pi$
$942$	1.98386e7	0.728423
$943$	2.12216e6	0.0777140
$944$	1.50095e8	5.48196
$945$	1.43061e6	0.0521125
$946$	3.95382e7	1.43644
$947$	2.69801e7	0.977618	0.488809	−	0.872391i	$-0.337431\pi$
$947$	2.69801e7	0.977618	0.488809	+	0.872391i	$0.337431\pi$
$948$	−4.06031e7	−1.46737
$949$	1.37715e7	0.496381
$950$	−3.48236e7	−1.25189
$951$	−1.04424e7	−0.374411
$952$	3.14458e7	1.12453
$953$	−7.18858e6	−0.256396	−0.128198	−	0.991749i	$-0.540919\pi$
$953$	−7.18858e6	−0.256396	−0.128198	+	0.991749i	$0.540919\pi$
$954$	7.96898e7	2.83486
$955$	−1.16799e7	−0.414410
$956$	9.78206e7	3.46167
$957$	1.93441e6	0.0682762
$958$	1.10464e7	0.388871
$959$	2.82624e6	0.0992345
$960$	−8.52927e6	−0.298699
$961$	−1.57899e7	−0.551532
$962$	1.72022e7	0.599303
$963$	3.97927e7	1.38273
$964$	7.72723e7	2.67813
$965$	498154.	0.0172205
$966$	−528499.	−0.0182222
$967$	−9.30841e6	−0.320117	−0.160059	−	0.987108i	$-0.551168\pi$
$967$	−9.30841e6	−0.320117	−0.160059	+	0.987108i	$0.551168\pi$
$968$	−2.44584e7	−0.838958
$969$	1.05510e7	0.360979
$970$	1.49219e7	0.509209
$971$	4.59109e7	1.56267	0.781335	−	0.624112i	$-0.214539\pi$
$971$	4.59109e7	1.56267	0.781335	+	0.624112i	$0.214539\pi$
$972$	6.80284e7	2.30954
$973$	8.29638e6	0.280935
$974$	−5.61496e7	−1.89648
$975$	2.69083e6	0.0906514
$976$	−7.65339e7	−2.57175
$977$	1.93808e7	0.649585	0.324793	−	0.945785i	$-0.394706\pi$
$977$	1.93808e7	0.649585	0.324793	+	0.945785i	$0.394706\pi$
$978$	1.00492e7	0.335956
$979$	1.95506e7	0.651933
$980$	2.33562e7	0.776851
$981$	−3.70982e6	−0.123078
$982$	3.54617e7	1.17349
$983$	1.36663e7	0.451093	0.225546	−	0.974232i	$-0.427583\pi$
$983$	1.36663e7	0.451093	0.225546	+	0.974232i	$0.427583\pi$
$984$	−2.33304e7	−0.768129
$985$	3.54278e6	0.116347
$986$	1.45239e7	0.475762
$987$	2.05379e6	0.0671063
$988$	1.71153e7	0.557818
$989$	−2.24066e6	−0.0728426
$990$	−1.83910e7	−0.596373
$991$	3.84249e7	1.24288	0.621440	−	0.783462i	$-0.286548\pi$
$991$	3.84249e7	1.24288	0.621440	+	0.783462i	$0.286548\pi$
$992$	6.55843e7	2.11602
$993$	1.22500e7	0.394241
$994$	2.12141e7	0.681017
$995$	324518.	0.0103916
$996$	3.86672e7	1.23508
$997$	3.87458e7	1.23449	0.617244	−	0.786772i	$-0.288249\pi$
$997$	3.87458e7	1.23449	0.617244	+	0.786772i	$0.288249\pi$
$998$	−1.12835e7	−0.358605
$999$	−2.22363e7	−0.704933

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.6.a.b.1.4	✓	117

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.6.a.b.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-10.7784 q^{2} +5.40058 q^{3} +84.1742 q^{4} -17.6434 q^{5} -58.2097 q^{6} +32.8655 q^{7} -562.355 q^{8} -213.834 q^{9} +O(q^{10})\)	\(q-10.7784 q^{2} +5.40058 q^{3} +84.1742 q^{4} -17.6434 q^{5} -58.2097 q^{6} +32.8655 q^{7} -562.355 q^{8} -213.834 q^{9} +190.168 q^{10} +452.265 q^{11} +454.589 q^{12} -177.079 q^{13} -354.238 q^{14} -95.2845 q^{15} +3367.72 q^{16} -1701.42 q^{17} +2304.79 q^{18} -1148.26 q^{19} -1485.12 q^{20} +177.493 q^{21} -4874.70 q^{22} +276.254 q^{23} -3037.04 q^{24} -2813.71 q^{25} +1908.63 q^{26} -2467.17 q^{27} +2766.43 q^{28} +791.983 q^{29} +1027.02 q^{30} -3583.19 q^{31} -18303.3 q^{32} +2442.49 q^{33} +18338.6 q^{34} -579.859 q^{35} -17999.3 q^{36} +9012.87 q^{37} +12376.4 q^{38} -956.327 q^{39} +9921.85 q^{40} +7681.94 q^{41} -1913.09 q^{42} -8110.89 q^{43} +38069.1 q^{44} +3772.75 q^{45} -2977.58 q^{46} +11571.1 q^{47} +18187.6 q^{48} -15726.9 q^{49} +30327.3 q^{50} -9188.66 q^{51} -14905.4 q^{52} +34575.8 q^{53} +26592.1 q^{54} -7979.49 q^{55} -18482.1 q^{56} -6201.26 q^{57} -8536.31 q^{58} +44568.7 q^{59} -8020.50 q^{60} -22725.7 q^{61} +38621.1 q^{62} -7027.76 q^{63} +89513.7 q^{64} +3124.27 q^{65} -26326.2 q^{66} +35359.1 q^{67} -143216. q^{68} +1491.93 q^{69} +6249.96 q^{70} -59886.5 q^{71} +120250. q^{72} -77770.4 q^{73} -97144.4 q^{74} -15195.7 q^{75} -96653.7 q^{76} +14863.9 q^{77} +10307.7 q^{78} -89318.2 q^{79} -59418.0 q^{80} +38637.5 q^{81} -82799.1 q^{82} +85059.6 q^{83} +14940.3 q^{84} +30018.8 q^{85} +87422.5 q^{86} +4277.17 q^{87} -254334. q^{88} +43228.1 q^{89} -40664.3 q^{90} -5819.78 q^{91} +23253.4 q^{92} -19351.3 q^{93} -124718. q^{94} +20259.2 q^{95} -98848.5 q^{96} +78467.3 q^{97} +169511. q^{98} -96709.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9}+O(q^{10}) \) 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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