LMFDB - Embedded newform 547.6.a.a.1.16

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:	$1$
Dimension:	$111$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-8.49621 q^{2} -28.8934 q^{3} +40.1856 q^{4} -77.1552 q^{5} +245.484 q^{6} +144.097 q^{7} -69.5467 q^{8} +591.826 q^{9} +O(q^{10})$	\(q-8.49621 q^{2} -28.8934 q^{3} +40.1856 q^{4} -77.1552 q^{5} +245.484 q^{6} +144.097 q^{7} -69.5467 q^{8} +591.826 q^{9} +655.527 q^{10} -555.691 q^{11} -1161.10 q^{12} +264.983 q^{13} -1224.28 q^{14} +2229.27 q^{15} -695.056 q^{16} +485.646 q^{17} -5028.28 q^{18} -1867.98 q^{19} -3100.53 q^{20} -4163.44 q^{21} +4721.27 q^{22} -4401.25 q^{23} +2009.44 q^{24} +2827.92 q^{25} -2251.35 q^{26} -10078.8 q^{27} +5790.62 q^{28} -1351.64 q^{29} -18940.4 q^{30} +8122.34 q^{31} +8130.84 q^{32} +16055.8 q^{33} -4126.15 q^{34} -11117.8 q^{35} +23782.9 q^{36} -3935.04 q^{37} +15870.8 q^{38} -7656.25 q^{39} +5365.89 q^{40} -11610.3 q^{41} +35373.5 q^{42} +11012.8 q^{43} -22330.8 q^{44} -45662.5 q^{45} +37393.9 q^{46} +9537.75 q^{47} +20082.5 q^{48} +3956.88 q^{49} -24026.6 q^{50} -14031.9 q^{51} +10648.5 q^{52} -5284.86 q^{53} +85631.3 q^{54} +42874.5 q^{55} -10021.5 q^{56} +53972.3 q^{57} +11483.9 q^{58} -11997.5 q^{59} +89584.7 q^{60} +1472.52 q^{61} -69009.1 q^{62} +85280.2 q^{63} -46839.5 q^{64} -20444.8 q^{65} -136413. q^{66} +2015.16 q^{67} +19516.0 q^{68} +127167. q^{69} +94459.3 q^{70} +41974.4 q^{71} -41159.6 q^{72} -23582.1 q^{73} +33432.9 q^{74} -81708.2 q^{75} -75066.0 q^{76} -80073.3 q^{77} +65049.1 q^{78} +2136.27 q^{79} +53627.2 q^{80} +147395. q^{81} +98643.6 q^{82} +80430.6 q^{83} -167310. q^{84} -37470.1 q^{85} -93567.5 q^{86} +39053.6 q^{87} +38646.5 q^{88} +112717. q^{89} +387958. q^{90} +38183.2 q^{91} -176867. q^{92} -234682. q^{93} -81034.7 q^{94} +144125. q^{95} -234927. q^{96} -141177. q^{97} -33618.5 q^{98} -328873. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 111 q - 28 q^{2} - 98 q^{3} + 1722 q^{4} - 801 q^{5} - 414 q^{6} - 587 q^{7} - 1344 q^{8} + 8241 q^{9}+O(q^{10}) $ 111 * q - 28 * q^2 - 98 * q^3 + 1722 * q^4 - 801 * q^5 - 414 * q^6 - 587 * q^7 - 1344 * q^8 + 8241 * q^9	\( 111 q - 28 q^{2} - 98 q^{3} + 1722 q^{4} - 801 q^{5} - 414 q^{6} - 587 q^{7} - 1344 q^{8} + 8241 q^{9} - 950 q^{10} - 1832 q^{11} - 4143 q^{12} - 4369 q^{13} - 4777 q^{14} - 3487 q^{15} + 26274 q^{16} - 13648 q^{17} - 10269 q^{18} - 5446 q^{19} - 26032 q^{20} - 8428 q^{21} - 8248 q^{22} - 24142 q^{23} - 18577 q^{24} + 58062 q^{25} - 17656 q^{26} - 33269 q^{27} - 23512 q^{28} - 33752 q^{29} - 12418 q^{30} - 13781 q^{31} - 44076 q^{32} - 39186 q^{33} - 7207 q^{34} - 30833 q^{35} + 120044 q^{36} - 61582 q^{37} - 91259 q^{38} - 20077 q^{39} - 66032 q^{40} - 54181 q^{41} - 69252 q^{42} - 38600 q^{43} - 95712 q^{44} - 190880 q^{45} - 9354 q^{46} - 83886 q^{47} - 173886 q^{48} + 194148 q^{49} - 70896 q^{50} - 60673 q^{51} - 145186 q^{52} - 286874 q^{53} - 116519 q^{54} - 74821 q^{55} - 240407 q^{56} - 95180 q^{57} - 66900 q^{58} - 135740 q^{59} - 144550 q^{60} - 227450 q^{61} - 308766 q^{62} - 249721 q^{63} + 347514 q^{64} - 290374 q^{65} - 178980 q^{66} - 91006 q^{67} - 521943 q^{68} - 414510 q^{69} - 165057 q^{70} - 236165 q^{71} - 527945 q^{72} - 184618 q^{73} - 206443 q^{74} - 243897 q^{75} - 221676 q^{76} - 751131 q^{77} - 306839 q^{78} - 107446 q^{79} - 856691 q^{80} + 382187 q^{81} - 244614 q^{82} - 499547 q^{83} - 330289 q^{84} - 287103 q^{85} - 272441 q^{86} - 391281 q^{87} - 588937 q^{88} - 740774 q^{89} - 687179 q^{90} - 237213 q^{91} - 1367678 q^{92} - 754880 q^{93} - 32851 q^{94} - 295814 q^{95} - 816078 q^{96} - 320770 q^{97} - 661922 q^{98} - 547439 q^{99}+O(q^{100}) \) 111 * q - 28 * q^2 - 98 * q^3 + 1722 * q^4 - 801 * q^5 - 414 * q^6 - 587 * q^7 - 1344 * q^8 + 8241 * q^9 - 950 * q^10 - 1832 * q^11 - 4143 * q^12 - 4369 * q^13 - 4777 * q^14 - 3487 * q^15 + 26274 * q^16 - 13648 * q^17 - 10269 * q^18 - 5446 * q^19 - 26032 * q^20 - 8428 * q^21 - 8248 * q^22 - 24142 * q^23 - 18577 * q^24 + 58062 * q^25 - 17656 * q^26 - 33269 * q^27 - 23512 * q^28 - 33752 * q^29 - 12418 * q^30 - 13781 * q^31 - 44076 * q^32 - 39186 * q^33 - 7207 * q^34 - 30833 * q^35 + 120044 * q^36 - 61582 * q^37 - 91259 * q^38 - 20077 * q^39 - 66032 * q^40 - 54181 * q^41 - 69252 * q^42 - 38600 * q^43 - 95712 * q^44 - 190880 * q^45 - 9354 * q^46 - 83886 * q^47 - 173886 * q^48 + 194148 * q^49 - 70896 * q^50 - 60673 * q^51 - 145186 * q^52 - 286874 * q^53 - 116519 * q^54 - 74821 * q^55 - 240407 * q^56 - 95180 * q^57 - 66900 * q^58 - 135740 * q^59 - 144550 * q^60 - 227450 * q^61 - 308766 * q^62 - 249721 * q^63 + 347514 * q^64 - 290374 * q^65 - 178980 * q^66 - 91006 * q^67 - 521943 * q^68 - 414510 * q^69 - 165057 * q^70 - 236165 * q^71 - 527945 * q^72 - 184618 * q^73 - 206443 * q^74 - 243897 * q^75 - 221676 * q^76 - 751131 * q^77 - 306839 * q^78 - 107446 * q^79 - 856691 * q^80 + 382187 * q^81 - 244614 * q^82 - 499547 * q^83 - 330289 * q^84 - 287103 * q^85 - 272441 * q^86 - 391281 * q^87 - 588937 * q^88 - 740774 * q^89 - 687179 * q^90 - 237213 * q^91 - 1367678 * q^92 - 754880 * q^93 - 32851 * q^94 - 295814 * q^95 - 816078 * q^96 - 320770 * q^97 - 661922 * q^98 - 547439 * 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 $

$2$	−8.49621	−1.50193	−0.750966	−	0.660341i	$-0.770412\pi$
$2$	−8.49621	−1.50193	−0.750966	+	0.660341i	$0.770412\pi$
$3$	−28.8934	−1.85351	−0.926755	−	0.375667i	$-0.877414\pi$
$3$	−28.8934	−1.85351	−0.926755	+	0.375667i	$0.877414\pi$
$4$	40.1856	1.25580
$5$	−77.1552	−1.38019	−0.690097	−	0.723717i	$-0.742432\pi$
$5$	−77.1552	−1.38019	−0.690097	+	0.723717i	$0.742432\pi$
$6$	245.484	2.78385
$7$	144.097	1.11150	0.555750	−	0.831350i	$-0.312431\pi$
$7$	144.097	1.11150	0.555750	+	0.831350i	$0.312431\pi$
$8$	−69.5467	−0.384195
$9$	591.826	2.43550
$10$	655.527	2.07296
$11$	−555.691	−1.38469	−0.692344	−	0.721568i	$-0.743422\pi$
$11$	−555.691	−1.38469	−0.692344	+	0.721568i	$0.743422\pi$
$12$	−1161.10	−2.32764
$13$	264.983	0.434870	0.217435	−	0.976075i	$-0.430231\pi$
$13$	264.983	0.434870	0.217435	+	0.976075i	$0.430231\pi$
$14$	−1224.28	−1.66940
$15$	2229.27	2.55820
$16$	−695.056	−0.678766
$17$	485.646	0.407565	0.203783	−	0.979016i	$-0.434676\pi$
$17$	485.646	0.407565	0.203783	+	0.979016i	$0.434676\pi$
$18$	−5028.28	−3.65795
$19$	−1867.98	−1.18710	−0.593552	−	0.804796i	$-0.702275\pi$
$19$	−1867.98	−1.18710	−0.593552	+	0.804796i	$0.702275\pi$
$20$	−3100.53	−1.73325
$21$	−4163.44	−2.06017
$22$	4721.27	2.07971
$23$	−4401.25	−1.73483	−0.867414	−	0.497588i	$-0.834219\pi$
$23$	−4401.25	−1.73483	−0.867414	+	0.497588i	$0.834219\pi$
$24$	2009.44	0.712109
$25$	2827.92	0.904936
$26$	−2251.35	−0.653146
$27$	−10078.8	−2.66071
$28$	5790.62	1.39582
$29$	−1351.64	−0.298447	−0.149224	−	0.988803i	$-0.547677\pi$
$29$	−1351.64	−0.298447	−0.149224	+	0.988803i	$0.547677\pi$
$30$	−18940.4	−3.84225
$31$	8122.34	1.51802	0.759009	−	0.651081i	$-0.225684\pi$
$31$	8122.34	1.51802	0.759009	+	0.651081i	$0.225684\pi$
$32$	8130.84	1.40365
$33$	16055.8	2.56653
$34$	−4126.15	−0.612136
$35$	−11117.8	−1.53408
$36$	23782.9	3.05850
$37$	−3935.04	−0.472546	−0.236273	−	0.971687i	$-0.575926\pi$
$37$	−3935.04	−0.472546	−0.236273	+	0.971687i	$0.575926\pi$
$38$	15870.8	1.78295
$39$	−7656.25	−0.806036
$40$	5365.89	0.530264
$41$	−11610.3	−1.07866	−0.539329	−	0.842095i	$-0.681322\pi$
$41$	−11610.3	−1.07866	−0.539329	+	0.842095i	$0.681322\pi$
$42$	35373.5	3.09424
$43$	11012.8	0.908298	0.454149	−	0.890926i	$-0.349943\pi$
$43$	11012.8	0.908298	0.454149	+	0.890926i	$0.349943\pi$
$44$	−22330.8	−1.73889
$45$	−45662.5	−3.36146
$46$	37393.9	2.60559
$47$	9537.75	0.629798	0.314899	−	0.949125i	$-0.398029\pi$
$47$	9537.75	0.629798	0.314899	+	0.949125i	$0.398029\pi$
$48$	20082.5	1.25810
$49$	3956.88	0.235430
$50$	−24026.6	−1.35915
$51$	−14031.9	−0.755426
$52$	10648.5	0.546110
$53$	−5284.86	−0.258430	−0.129215	−	0.991617i	$-0.541246\pi$
$53$	−5284.86	−0.258430	−0.129215	+	0.991617i	$0.541246\pi$
$54$	85631.3	3.99621
$55$	42874.5	1.91114
$56$	−10021.5	−0.427033
$57$	53972.3	2.20031
$58$	11483.9	0.448248
$59$	−11997.5	−0.448705	−0.224352	−	0.974508i	$-0.572027\pi$
$59$	−11997.5	−0.448705	−0.224352	+	0.974508i	$0.572027\pi$
$60$	89584.7	3.21259
$61$	1472.52	0.0506683	0.0253341	−	0.999679i	$-0.491935\pi$
$61$	1472.52	0.0506683	0.0253341	+	0.999679i	$0.491935\pi$
$62$	−69009.1	−2.27996
$63$	85280.2	2.70705
$64$	−46839.5	−1.42943
$65$	−20444.8	−0.600206
$66$	−136413.	−3.85476
$67$	2015.16	0.0548433	0.0274216	−	0.999624i	$-0.491270\pi$
$67$	2015.16	0.0548433	0.0274216	+	0.999624i	$0.491270\pi$
$68$	19516.0	0.511821
$69$	127167.	3.21552
$70$	94459.3	2.30409
$71$	41974.4	0.988186	0.494093	−	0.869409i	$-0.335500\pi$
$71$	41974.4	0.988186	0.494093	+	0.869409i	$0.335500\pi$
$72$	−41159.6	−0.935707
$73$	−23582.1	−0.517935	−0.258968	−	0.965886i	$-0.583382\pi$
$73$	−23582.1	−0.517935	−0.258968	+	0.965886i	$0.583382\pi$
$74$	33432.9	0.709733
$75$	−81708.2	−1.67731
$76$	−75066.0	−1.49077
$77$	−80073.3	−1.53908
$78$	65049.1	1.21061
$79$	2136.27	0.0385112	0.0192556	−	0.999815i	$-0.493870\pi$
$79$	2136.27	0.0385112	0.0192556	+	0.999815i	$0.493870\pi$
$80$	53627.2	0.936828
$81$	147395.	2.49615
$82$	98643.6	1.62007
$83$	80430.6	1.28152	0.640761	−	0.767740i	$-0.278619\pi$
$83$	80430.6	1.28152	0.640761	+	0.767740i	$0.278619\pi$
$84$	−167310.	−2.58717
$85$	−37470.1	−0.562519
$86$	−93567.5	−1.36420
$87$	39053.6	0.553175
$88$	38646.5	0.531990
$89$	112717.	1.50840	0.754199	−	0.656646i	$-0.228025\pi$
$89$	112717.	1.50840	0.754199	+	0.656646i	$0.228025\pi$
$90$	387958.	5.04869
$91$	38183.2	0.483358
$92$	−176867.	−2.17860
$93$	−234682.	−2.81366
$94$	−81034.7	−0.945914
$95$	144125.	1.63843
$96$	−234927.	−2.60169
$97$	−141177.	−1.52347	−0.761735	−	0.647889i	$-0.775652\pi$
$97$	−141177.	−1.52347	−0.761735	+	0.647889i	$0.775652\pi$
$98$	−33618.5	−0.353600
$99$	−328873.	−3.37240
$100$	113642.	1.13642
$101$	−125092.	−1.22019	−0.610093	−	0.792329i	$-0.708868\pi$
$101$	−125092.	−1.22019	−0.610093	+	0.792329i	$0.708868\pi$
$102$	119218.	1.13460
$103$	148149.	1.37596	0.687982	−	0.725728i	$-0.258497\pi$
$103$	148149.	1.37596	0.687982	+	0.725728i	$0.258497\pi$
$104$	−18428.7	−0.167075
$105$	321231.	2.84344
$106$	44901.3	0.388145
$107$	−192420.	−1.62477	−0.812384	−	0.583123i	$-0.801831\pi$
$107$	−192420.	−1.62477	−0.812384	+	0.583123i	$0.801831\pi$
$108$	−405021.	−3.34132
$109$	120042.	0.967762	0.483881	−	0.875134i	$-0.339227\pi$
$109$	120042.	0.967762	0.483881	+	0.875134i	$0.339227\pi$
$110$	−364270.	−2.87040
$111$	113696.	0.875869
$112$	−100155.	−0.754447
$113$	−90093.5	−0.663739	−0.331869	−	0.943325i	$-0.607679\pi$
$113$	−90093.5	−0.663739	−0.331869	+	0.943325i	$0.607679\pi$
$114$	−458560.	−3.30471
$115$	339579.	2.39440
$116$	−54316.7	−0.374790
$117$	156824.	1.05913
$118$	101933.	0.673924
$119$	69980.0	0.453008
$120$	−155039.	−0.982849
$121$	147742.	0.917359
$122$	−12510.8	−0.0761003
$123$	335461.	1.99930
$124$	326401.	1.90633
$125$	22920.9	0.131207
$126$	−724559.	−4.06581
$127$	333796.	1.83642	0.918209	−	0.396096i	$-0.129635\pi$
$127$	333796.	1.83642	0.918209	+	0.396096i	$0.129635\pi$
$128$	137772.	0.743251
$129$	−318198.	−1.68354
$130$	173704.	0.901468
$131$	74976.5	0.381722	0.190861	−	0.981617i	$-0.438872\pi$
$131$	74976.5	0.381722	0.190861	+	0.981617i	$0.438872\pi$
$132$	645212.	3.22305
$133$	−269170.	−1.31946
$134$	−17121.3	−0.0823709
$135$	777629.	3.67230
$136$	−33775.1	−0.156585
$137$	419102.	1.90773	0.953867	−	0.300229i	$-0.0970632\pi$
$137$	419102.	1.90773	0.953867	+	0.300229i	$0.0970632\pi$
$138$	−1.08044e6	−4.82949
$139$	247538.	1.08669	0.543345	−	0.839509i	$-0.317158\pi$
$139$	247538.	1.08669	0.543345	+	0.839509i	$0.317158\pi$
$140$	−446776.	−1.92650
$141$	−275577.	−1.16734
$142$	−356623.	−1.48419
$143$	−147249.	−0.602160
$144$	−411352.	−1.65313
$145$	104286.	0.411915
$146$	200359.	0.777904
$147$	−114327.	−0.436372
$148$	−158132.	−0.593424
$149$	217208.	0.801512	0.400756	−	0.916185i	$-0.368748\pi$
$149$	217208.	0.801512	0.400756	+	0.916185i	$0.368748\pi$
$150$	694211.	2.51920
$151$	411244.	1.46777	0.733884	−	0.679275i	$-0.237706\pi$
$151$	411244.	1.46777	0.733884	+	0.679275i	$0.237706\pi$
$152$	129912.	0.456080
$153$	287418.	0.992625
$154$	680320.	2.31159
$155$	−626680.	−2.09516
$156$	−307671.	−1.01222
$157$	316846.	1.02589	0.512943	−	0.858423i	$-0.328555\pi$
$157$	316846.	1.02589	0.512943	+	0.858423i	$0.328555\pi$
$158$	−18150.2	−0.0578413
$159$	152697.	0.479003
$160$	−627336.	−1.93732
$161$	−634206.	−1.92826
$162$	−1.25230e6	−3.74905
$163$	−631709.	−1.86229	−0.931147	−	0.364645i	$-0.881190\pi$
$163$	−631709.	−1.86229	−0.931147	+	0.364645i	$0.881190\pi$
$164$	−466567.	−1.35458
$165$	−1.23879e6	−3.54231
$166$	−683356.	−1.92476
$167$	−406979.	−1.12923	−0.564613	−	0.825356i	$-0.690975\pi$
$167$	−406979.	−1.12923	−0.564613	+	0.825356i	$0.690975\pi$
$168$	289554.	0.791509
$169$	−301077.	−0.810888
$170$	318354.	0.844866
$171$	−1.10552e6	−2.89119
$172$	442558.	1.14064
$173$	−201425.	−0.511680	−0.255840	−	0.966719i	$-0.582352\pi$
$173$	−201425.	−0.511680	−0.255840	+	0.966719i	$0.582352\pi$
$174$	−331807.	−0.830831
$175$	407495.	1.00584
$176$	386236.	0.939878
$177$	346648.	0.831679
$178$	−957671.	−2.26551
$179$	−445319.	−1.03882	−0.519408	−	0.854526i	$-0.673848\pi$
$179$	−445319.	−1.03882	−0.519408	+	0.854526i	$0.673848\pi$
$180$	−1.83497e6	−4.22132
$181$	120762.	0.273990	0.136995	−	0.990572i	$-0.456256\pi$
$181$	120762.	0.273990	0.136995	+	0.990572i	$0.456256\pi$
$182$	−324413.	−0.725971
$183$	−42546.0	−0.0939141
$184$	306093.	0.666512
$185$	303609.	0.652206
$186$	1.99390e6	4.22593
$187$	−269869.	−0.564351
$188$	383280.	0.790900
$189$	−1.45232e6	−2.95738
$190$	−1.22451e6	−2.46082
$191$	−29931.6	−0.0593673	−0.0296836	−	0.999559i	$-0.509450\pi$
$191$	−29931.6	−0.0593673	−0.0296836	+	0.999559i	$0.509450\pi$
$192$	1.35335e6	2.64946
$193$	−466759.	−0.901984	−0.450992	−	0.892528i	$-0.648930\pi$
$193$	−466759.	−0.901984	−0.450992	+	0.892528i	$0.648930\pi$
$194$	1.19947e6	2.28815
$195$	590720.	1.11249
$196$	159009.	0.295653
$197$	262318.	0.481574	0.240787	−	0.970578i	$-0.422595\pi$
$197$	262318.	0.481574	0.240787	+	0.970578i	$0.422595\pi$
$198$	2.79417e6	5.06512
$199$	797048.	1.42676	0.713381	−	0.700776i	$-0.247163\pi$
$199$	797048.	1.42676	0.713381	+	0.700776i	$0.247163\pi$
$200$	−196673.	−0.347672
$201$	−58224.8	−0.101653
$202$	1.06281e6	1.83264
$203$	−194768.	−0.331724
$204$	−563882.	−0.948665
$205$	895796.	1.48876
$206$	−1.25871e6	−2.06660
$207$	−2.60477e6	−4.22517
$208$	−184178.	−0.295175
$209$	1.03802e6	1.64377
$210$	−2.72925e6	−4.27066
$211$	1.08585e6	1.67905	0.839527	−	0.543319i	$-0.182832\pi$
$211$	1.08585e6	1.67905	0.839527	+	0.543319i	$0.182832\pi$
$212$	−212375.	−0.324537
$213$	−1.21278e6	−1.83161
$214$	1.63484e6	2.44029
$215$	−849698.	−1.25363
$216$	700945.	1.02223
$217$	1.17040e6	1.68727
$218$	−1.01991e6	−1.45351
$219$	681367.	0.959998
$220$	1.72294e6	2.40001
$221$	128688.	0.177238
$222$	−965989.	−1.31550
$223$	−1.06008e6	−1.42750	−0.713749	−	0.700401i	$-0.753004\pi$
$223$	−1.06008e6	−1.42750	−0.713749	+	0.700401i	$0.753004\pi$
$224$	1.17163e6	1.56016
$225$	1.67364e6	2.20397
$226$	765453.	0.996891
$227$	−527020.	−0.678832	−0.339416	−	0.940636i	$-0.610229\pi$
$227$	−527020.	−0.678832	−0.339416	+	0.940636i	$0.610229\pi$
$228$	2.16891e6	2.76315
$229$	−834768.	−1.05191	−0.525953	−	0.850514i	$-0.676291\pi$
$229$	−834768.	−1.05191	−0.525953	+	0.850514i	$0.676291\pi$
$230$	−2.88514e6	−3.59622
$231$	2.31359e6	2.85270
$232$	94002.5	0.114662
$233$	316118.	0.381469	0.190735	−	0.981642i	$-0.438913\pi$
$233$	316118.	0.381469	0.190735	+	0.981642i	$0.438913\pi$
$234$	−1.33241e6	−1.59074
$235$	−735887.	−0.869243
$236$	−482127.	−0.563484
$237$	−61723.9	−0.0713810
$238$	−594565.	−0.680388
$239$	30893.7	0.0349844	0.0174922	−	0.999847i	$-0.494432\pi$
$239$	30893.7	0.0349844	0.0174922	+	0.999847i	$0.494432\pi$
$240$	−1.54947e6	−1.73642
$241$	632879.	0.701904	0.350952	−	0.936393i	$-0.385858\pi$
$241$	632879.	0.701904	0.350952	+	0.936393i	$0.385858\pi$
$242$	−1.25524e6	−1.37781
$243$	−1.80961e6	−1.96594
$244$	59174.0	0.0636292
$245$	−305294.	−0.324939
$246$	−2.85015e6	−3.00282
$247$	−494984.	−0.516236
$248$	−564882.	−0.583215
$249$	−2.32391e6	−2.37531
$250$	−194741.	−0.197064
$251$	1.93764e6	1.94128	0.970642	−	0.240530i	$-0.0773212\pi$
$251$	1.93764e6	1.94128	0.970642	+	0.240530i	$0.0773212\pi$
$252$	3.42704e6	3.39952
$253$	2.44573e6	2.40219
$254$	−2.83600e6	−2.75818
$255$	1.08264e6	1.04263
$256$	328327.	0.313117
$257$	−522131.	−0.493113	−0.246557	−	0.969128i	$-0.579299\pi$
$257$	−522131.	−0.493113	−0.246557	+	0.969128i	$0.579299\pi$
$258$	2.70348e6	2.52856
$259$	−567026.	−0.525235
$260$	−821588.	−0.753738
$261$	−799939.	−0.726868
$262$	−637016.	−0.573320
$263$	−931638.	−0.830535	−0.415268	−	0.909699i	$-0.636312\pi$
$263$	−931638.	−0.830535	−0.415268	+	0.909699i	$0.636312\pi$
$264$	−1.11663e6	−0.986049
$265$	407754.	0.356684
$266$	2.28693e6	1.98175
$267$	−3.25678e6	−2.79583
$268$	80980.6	0.0688722
$269$	496206.	0.418101	0.209050	−	0.977905i	$-0.432963\pi$
$269$	496206.	0.418101	0.209050	+	0.977905i	$0.432963\pi$
$270$	−6.60690e6	−5.51554
$271$	949067.	0.785008	0.392504	−	0.919750i	$-0.371609\pi$
$271$	949067.	0.785008	0.392504	+	0.919750i	$0.371609\pi$
$272$	−337551.	−0.276641
$273$	−1.10324e6	−0.895909
$274$	−3.56078e6	−2.86529
$275$	−1.57145e6	−1.25305
$276$	5.11028e6	4.03805
$277$	1.56888e6	1.22854	0.614271	−	0.789095i	$-0.289450\pi$
$277$	1.56888e6	1.22854	0.614271	+	0.789095i	$0.289450\pi$
$278$	−2.10314e6	−1.63213
$279$	4.80701e6	3.69713
$280$	773208.	0.589388
$281$	1.84765e6	1.39590	0.697948	−	0.716148i	$-0.254097\pi$
$281$	1.84765e6	1.39590	0.697948	+	0.716148i	$0.254097\pi$
$282$	2.34136e6	1.75326
$283$	540381.	0.401083	0.200541	−	0.979685i	$-0.435730\pi$
$283$	540381.	0.401083	0.200541	+	0.979685i	$0.435730\pi$
$284$	1.68677e6	1.24096
$285$	−4.16424e6	−3.03685
$286$	1.25106e6	0.904403
$287$	−1.67301e6	−1.19893
$288$	4.81204e6	3.41860
$289$	−1.18401e6	−0.833891
$290$	−886040.	−0.618669
$291$	4.07907e6	2.82377
$292$	−947662.	−0.650424
$293$	999741.	0.680328	0.340164	−	0.940366i	$-0.389517\pi$
$293$	999741.	0.680328	0.340164	+	0.940366i	$0.389517\pi$
$294$	971350.	0.655402
$295$	925670.	0.619300
$296$	273669.	0.181550
$297$	5.60068e6	3.68425
$298$	−1.84544e6	−1.20382
$299$	−1.16626e6	−0.754425
$300$	−3.28350e6	−2.10636
$301$	1.58692e6	1.00957
$302$	−3.49402e6	−2.20449
$303$	3.61433e6	2.26163
$304$	1.29835e6	0.805765
$305$	−113612.	−0.0699320
$306$	−2.44196e6	−1.49086
$307$	803299.	0.486442	0.243221	−	0.969971i	$-0.421796\pi$
$307$	803299.	0.486442	0.243221	+	0.969971i	$0.421796\pi$
$308$	−3.21779e6	−1.93278
$309$	−4.28053e6	−2.55036
$310$	5.32441e6	3.14679
$311$	1.20432e6	0.706061	0.353030	−	0.935612i	$-0.385151\pi$
$311$	1.20432e6	0.706061	0.353030	+	0.935612i	$0.385151\pi$
$312$	532467.	0.309675
$313$	−4758.42	−0.00274538	−0.00137269	−	0.999999i	$-0.500437\pi$
$313$	−4758.42	−0.00274538	−0.00137269	+	0.999999i	$0.500437\pi$
$314$	−2.69199e6	−1.54081
$315$	−6.57981e6	−3.73626
$316$	85847.2	0.0483624
$317$	384213.	0.214746	0.107373	−	0.994219i	$-0.465756\pi$
$317$	384213.	0.214746	0.107373	+	0.994219i	$0.465756\pi$
$318$	−1.29735e6	−0.719431
$319$	751097.	0.413256
$320$	3.61391e6	1.97289
$321$	5.55967e6	3.01152
$322$	5.38835e6	2.89611
$323$	−907177.	−0.483822
$324$	5.92318e6	3.13467
$325$	749352.	0.393530
$326$	5.36713e6	2.79704
$327$	−3.46843e6	−1.79376
$328$	807459.	0.414415
$329$	1.37436e6	0.700020
$330$	1.05250e7	5.32031
$331$	−871928.	−0.437432	−0.218716	−	0.975789i	$-0.570187\pi$
$331$	−871928.	−0.437432	−0.218716	+	0.975789i	$0.570187\pi$
$332$	3.23215e6	1.60934
$333$	−2.32886e6	−1.15089
$334$	3.45778e6	1.69602
$335$	−155480.	−0.0756944
$336$	2.89382e6	1.39838
$337$	−446562.	−0.214194	−0.107097	−	0.994249i	$-0.534156\pi$
$337$	−446562.	−0.214194	−0.107097	+	0.994249i	$0.534156\pi$
$338$	2.55801e6	1.21790
$339$	2.60310e6	1.23025
$340$	−1.50576e6	−0.706412
$341$	−4.51351e6	−2.10198
$342$	9.39274e6	4.34237
$343$	−1.85166e6	−0.849819
$344$	−765908.	−0.348964
$345$	−9.81158e6	−4.43804
$346$	1.71135e6	0.768508
$347$	2.12680e6	0.948208	0.474104	−	0.880469i	$-0.342772\pi$
$347$	2.12680e6	0.948208	0.474104	+	0.880469i	$0.342772\pi$
$348$	1.56939e6	0.694677
$349$	−3.38749e6	−1.48872	−0.744362	−	0.667777i	$-0.767246\pi$
$349$	−3.38749e6	−1.48872	−0.744362	+	0.667777i	$0.767246\pi$
$350$	−3.46216e6	−1.51070
$351$	−2.67070e6	−1.15706
$352$	−4.51823e6	−1.94362
$353$	−1.60157e6	−0.684085	−0.342042	−	0.939685i	$-0.611119\pi$
$353$	−1.60157e6	−0.684085	−0.342042	+	0.939685i	$0.611119\pi$
$354$	−2.94520e6	−1.24913
$355$	−3.23854e6	−1.36389
$356$	4.52962e6	1.89425
$357$	−2.02196e6	−0.839656
$358$	3.78353e6	1.56023
$359$	3.68608e6	1.50949	0.754743	−	0.656021i	$-0.227762\pi$
$359$	3.68608e6	1.50949	0.754743	+	0.656021i	$0.227762\pi$
$360$	3.17568e6	1.29146
$361$	1.01326e6	0.409216
$362$	−1.02602e6	−0.411514
$363$	−4.26875e6	−1.70033
$364$	1.53442e6	0.607001
$365$	1.81948e6	0.714852
$366$	361480.	0.141053
$367$	1.86132e6	0.721367	0.360683	−	0.932688i	$-0.382544\pi$
$367$	1.86132e6	0.721367	0.360683	+	0.932688i	$0.382544\pi$
$368$	3.05911e6	1.17754
$369$	−6.87128e6	−2.62707
$370$	−2.57952e6	−0.979569
$371$	−761531.	−0.287245
$372$	−9.43082e6	−3.53340
$373$	−3.95379e6	−1.47144	−0.735718	−	0.677288i	$-0.763155\pi$
$373$	−3.95379e6	−1.47144	−0.735718	+	0.677288i	$0.763155\pi$
$374$	2.29286e6	0.847616
$375$	−662261.	−0.243193
$376$	−663319.	−0.241965
$377$	−358163.	−0.129786
$378$	1.23392e7	4.44178
$379$	912028.	0.326145	0.163072	−	0.986614i	$-0.447860\pi$
$379$	912028.	0.326145	0.163072	+	0.986614i	$0.447860\pi$
$380$	5.79173e6	2.05755
$381$	−9.64448e6	−3.40382
$382$	254306.	0.0891656
$383$	3.83279e6	1.33511	0.667556	−	0.744559i	$-0.267340\pi$
$383$	3.83279e6	1.33511	0.667556	+	0.744559i	$0.267340\pi$
$384$	−3.98069e6	−1.37762
$385$	6.17807e6	2.12423
$386$	3.96568e6	1.35472
$387$	6.51769e6	2.21216
$388$	−5.67327e6	−1.91317
$389$	5.50371e6	1.84409	0.922044	−	0.387086i	$-0.126518\pi$
$389$	5.50371e6	1.84409	0.922044	+	0.387086i	$0.126518\pi$
$390$	−5.01888e6	−1.67088
$391$	−2.13745e6	−0.707056
$392$	−275188.	−0.0904511
$393$	−2.16632e6	−0.707525
$394$	−2.22871e6	−0.723291
$395$	−164824.	−0.0531530
$396$	−1.32159e7	−4.23507
$397$	−1.17833e6	−0.375226	−0.187613	−	0.982243i	$-0.560075\pi$
$397$	−1.17833e6	−0.375226	−0.187613	+	0.982243i	$0.560075\pi$
$398$	−6.77189e6	−2.14290
$399$	7.77723e6	2.44564
$400$	−1.96557e6	−0.614239
$401$	−2.26114e6	−0.702208	−0.351104	−	0.936336i	$-0.614194\pi$
$401$	−2.26114e6	−0.702208	−0.351104	+	0.936336i	$0.614194\pi$
$402$	494691.	0.152675
$403$	2.15228e6	0.660141
$404$	−5.02690e6	−1.53231
$405$	−1.13723e7	−3.44518
$406$	1.65479e6	0.498227
$407$	2.18666e6	0.654329
$408$	975875.	0.290231
$409$	−4.49207e6	−1.32782	−0.663908	−	0.747814i	$-0.731103\pi$
$409$	−4.49207e6	−1.32782	−0.663908	+	0.747814i	$0.731103\pi$
$410$	−7.61087e6	−2.23601
$411$	−1.21093e7	−3.53600
$412$	5.95348e6	1.72794
$413$	−1.72880e6	−0.498735
$414$	2.21307e7	6.34592
$415$	−6.20564e6	−1.76875
$416$	2.15453e6	0.610408
$417$	−7.15222e6	−2.01419
$418$	−8.81925e6	−2.46883
$419$	1.68934e6	0.470092	0.235046	−	0.971984i	$-0.424476\pi$
$419$	1.68934e6	0.470092	0.235046	+	0.971984i	$0.424476\pi$
$420$	1.29089e7	3.57079
$421$	2.59975e6	0.714868	0.357434	−	0.933938i	$-0.383652\pi$
$421$	2.59975e6	0.714868	0.357434	+	0.933938i	$0.383652\pi$
$422$	−9.22563e6	−2.52182
$423$	5.64469e6	1.53387
$424$	367545.	0.0992877
$425$	1.37337e6	0.368821
$426$	1.03040e7	2.75096
$427$	212185.	0.0563177
$428$	−7.73253e6	−2.04038
$429$	4.25451e6	1.11611
$430$	7.21922e6	1.88286
$431$	1.40825e6	0.365164	0.182582	−	0.983191i	$-0.441555\pi$
$431$	1.40825e6	0.365164	0.182582	+	0.983191i	$0.441555\pi$
$432$	7.00530e6	1.80600
$433$	−865118.	−0.221746	−0.110873	−	0.993835i	$-0.535365\pi$
$433$	−865118.	−0.221746	−0.110873	+	0.993835i	$0.535365\pi$
$434$	−9.94399e6	−2.53417
$435$	−3.01318e6	−0.763489
$436$	4.82398e6	1.21532
$437$	8.22145e6	2.05942
$438$	−5.78903e6	−1.44185
$439$	−743689.	−0.184175	−0.0920874	−	0.995751i	$-0.529354\pi$
$439$	−743689.	−0.184175	−0.0920874	+	0.995751i	$0.529354\pi$
$440$	−2.98178e6	−0.734250
$441$	2.34178e6	0.573390
$442$	−1.09336e6	−0.266200
$443$	2.90699e6	0.703776	0.351888	−	0.936042i	$-0.385540\pi$
$443$	2.90699e6	0.703776	0.351888	+	0.936042i	$0.385540\pi$
$444$	4.56896e6	1.09992
$445$	−8.69673e6	−2.08188
$446$	9.00665e6	2.14401
$447$	−6.27586e6	−1.48561
$448$	−6.74943e6	−1.58881
$449$	−4.19513e6	−0.982042	−0.491021	−	0.871148i	$-0.663376\pi$
$449$	−4.19513e6	−0.982042	−0.491021	+	0.871148i	$0.663376\pi$
$450$	−1.42196e7	−3.31021
$451$	6.45175e6	1.49361
$452$	−3.62046e6	−0.833524
$453$	−1.18822e7	−2.72052
$454$	4.47767e6	1.01956
$455$	−2.94603e6	−0.667128
$456$	−3.75360e6	−0.845348
$457$	7.08719e6	1.58739	0.793695	−	0.608316i	$-0.208154\pi$
$457$	7.08719e6	1.58739	0.793695	+	0.608316i	$0.208154\pi$
$458$	7.09237e6	1.57989
$459$	−4.89471e6	−1.08441
$460$	1.36462e7	3.00689
$461$	−2.47309e6	−0.541985	−0.270992	−	0.962582i	$-0.587352\pi$
$461$	−2.47309e6	−0.541985	−0.270992	+	0.962582i	$0.587352\pi$
$462$	−1.96567e7	−4.28456
$463$	−5.10211e6	−1.10611	−0.553054	−	0.833145i	$-0.686538\pi$
$463$	−5.10211e6	−1.10611	−0.553054	+	0.833145i	$0.686538\pi$
$464$	939469.	0.202576
$465$	1.81069e7	3.88340
$466$	−2.68581e6	−0.572941
$467$	495452.	0.105126	0.0525629	−	0.998618i	$-0.483261\pi$
$467$	495452.	0.105126	0.0525629	+	0.998618i	$0.483261\pi$
$468$	6.30207e6	1.33005
$469$	290379.	0.0609582
$470$	6.25225e6	1.30554
$471$	−9.15474e6	−1.90149
$472$	834387.	0.172390
$473$	−6.11974e6	−1.25771
$474$	524419.	0.107209
$475$	−5.28251e6	−1.07425
$476$	2.81219e6	0.568888
$477$	−3.12772e6	−0.629407
$478$	−262479.	−0.0525443
$479$	−3.28586e6	−0.654350	−0.327175	−	0.944964i	$-0.606097\pi$
$479$	−3.28586e6	−0.654350	−0.327175	+	0.944964i	$0.606097\pi$
$480$	1.81259e7	3.59083
$481$	−1.04272e6	−0.205496
$482$	−5.37707e6	−1.05421
$483$	1.83243e7	3.57405
$484$	5.93709e6	1.15202
$485$	1.08925e7	2.10268
$486$	1.53748e7	2.95270
$487$	−1.07506e6	−0.205404	−0.102702	−	0.994712i	$-0.532749\pi$
$487$	−1.07506e6	−0.205404	−0.102702	+	0.994712i	$0.532749\pi$
$488$	−102409.	−0.0194665
$489$	1.82522e7	3.45178
$490$	2.59384e6	0.488037
$491$	−7.57941e6	−1.41883	−0.709417	−	0.704789i	$-0.751042\pi$
$491$	−7.57941e6	−1.41883	−0.709417	+	0.704789i	$0.751042\pi$
$492$	1.34807e7	2.51073
$493$	−656420.	−0.121637
$494$	4.20549e6	0.775352
$495$	2.53742e7	4.65457
$496$	−5.64548e6	−1.03038
$497$	6.04837e6	1.09837
$498$	1.97444e7	3.56756
$499$	342904.	0.0616483	0.0308242	−	0.999525i	$-0.490187\pi$
$499$	342904.	0.0616483	0.0308242	+	0.999525i	$0.490187\pi$
$500$	921090.	0.164770
$501$	1.17590e7	2.09303
$502$	−1.64626e7	−2.91568
$503$	−7.62717e6	−1.34414	−0.672068	−	0.740489i	$-0.734594\pi$
$503$	−7.62717e6	−1.34414	−0.672068	+	0.740489i	$0.734594\pi$
$504$	−5.93096e6	−1.04004
$505$	9.65150e6	1.68409
$506$	−2.07795e7	−3.60793
$507$	8.69912e6	1.50299
$508$	1.34138e7	2.30618
$509$	−9.27026e6	−1.58598	−0.792990	−	0.609235i	$-0.791477\pi$
$509$	−9.27026e6	−1.58598	−0.792990	+	0.609235i	$0.791477\pi$
$510$	−9.19831e6	−1.56597
$511$	−3.39811e6	−0.575685
$512$	−7.19823e6	−1.21353
$513$	1.88269e7	3.15854
$514$	4.43614e6	0.740623
$515$	−1.14305e7	−1.89910
$516$	−1.27870e7	−2.11419
$517$	−5.30004e6	−0.872073
$518$	4.81757e6	0.788867
$519$	5.81984e6	0.948403
$520$	1.42187e6	0.230596
$521$	−1.20858e7	−1.95065	−0.975326	−	0.220772i	$-0.929142\pi$
$521$	−1.20858e7	−1.95065	−0.975326	+	0.220772i	$0.929142\pi$
$522$	6.79645e6	1.09171
$523$	−1.02801e7	−1.64339	−0.821696	−	0.569926i	$-0.806972\pi$
$523$	−1.02801e7	−1.64339	−0.821696	+	0.569926i	$0.806972\pi$
$524$	3.01298e6	0.479366
$525$	−1.17739e7	−1.86433
$526$	7.91540e6	1.24741
$527$	3.94458e6	0.618691
$528$	−1.11597e7	−1.74207
$529$	1.29346e7	2.00963
$530$	−3.46437e6	−0.535715
$531$	−7.10044e6	−1.09282
$532$	−1.08168e7	−1.65698
$533$	−3.07654e6	−0.469077
$534$	2.76703e7	4.19915
$535$	1.48462e7	2.24249
$536$	−140148.	−0.0210705
$537$	1.28668e7	1.92546
$538$	−4.21587e6	−0.627959
$539$	−2.19880e6	−0.325997
$540$	3.12495e7	4.61167
$541$	1.67758e6	0.246428	0.123214	−	0.992380i	$-0.460680\pi$
$541$	1.67758e6	0.246428	0.123214	+	0.992380i	$0.460680\pi$
$542$	−8.06348e6	−1.17903
$543$	−3.48923e6	−0.507843
$544$	3.94871e6	0.572081
$545$	−9.26189e6	−1.33570
$546$	9.37337e6	1.34559
$547$	−299209.	−0.0427569
$547$	−299209.	−0.0427569
$548$	1.68419e7	2.39573
$549$	871474.	0.123402
$550$	1.33514e7	1.88200
$551$	2.52485e6	0.354288
$552$	−8.84404e6	−1.23539
$553$	307829.	0.0428052
$554$	−1.33295e7	−1.84519
$555$	−8.77227e6	−1.20887
$556$	9.94749e6	1.36467
$557$	5.24141e6	0.715830	0.357915	−	0.933754i	$-0.383488\pi$
$557$	5.24141e6	0.715830	0.357915	+	0.933754i	$0.383488\pi$
$558$	−4.08414e7	−5.55284
$559$	2.91822e6	0.394992
$560$	7.72750e6	1.04128
$561$	7.79742e6	1.04603
$562$	−1.56980e7	−2.09654
$563$	−6.81669e6	−0.906363	−0.453182	−	0.891418i	$-0.649711\pi$
$563$	−6.81669e6	−0.906363	−0.453182	+	0.891418i	$0.649711\pi$
$564$	−1.10743e7	−1.46594
$565$	6.95118e6	0.916089
$566$	−4.59119e6	−0.602399
$567$	2.12392e7	2.77447
$568$	−2.91918e6	−0.379656
$569$	−7.94667e6	−1.02897	−0.514487	−	0.857498i	$-0.672018\pi$
$569$	−7.94667e6	−1.02897	−0.514487	+	0.857498i	$0.672018\pi$
$570$	3.53803e7	4.56115
$571$	−3.74406e6	−0.480565	−0.240283	−	0.970703i	$-0.577240\pi$
$571$	−3.74406e6	−0.480565	−0.240283	+	0.970703i	$0.577240\pi$
$572$	−5.91728e6	−0.756192
$573$	864826.	0.110038
$574$	1.42142e7	1.80071
$575$	−1.24464e7	−1.56991
$576$	−2.77209e7	−3.48137
$577$	−1.29740e7	−1.62231	−0.811153	−	0.584834i	$-0.801160\pi$
$577$	−1.29740e7	−1.62231	−0.811153	+	0.584834i	$0.801160\pi$
$578$	1.00596e7	1.25245
$579$	1.34862e7	1.67184
$580$	4.19081e6	0.517283
$581$	1.15898e7	1.42441
$582$	−3.46566e7	−4.24110
$583$	2.93675e6	0.357845
$584$	1.64006e6	0.198988
$585$	−1.20998e7	−1.46180
$586$	−8.49401e6	−1.02181
$587$	−1.26037e7	−1.50974	−0.754871	−	0.655873i	$-0.772301\pi$
$587$	−1.26037e7	−1.50974	−0.754871	+	0.655873i	$0.772301\pi$
$588$	−4.59432e6	−0.547996
$589$	−1.51724e7	−1.80204
$590$	−7.86469e6	−0.930147
$591$	−7.57925e6	−0.892602
$592$	2.73507e6	0.320748
$593$	1.02251e7	1.19407	0.597035	−	0.802215i	$-0.296345\pi$
$593$	1.02251e7	1.19407	0.597035	+	0.802215i	$0.296345\pi$
$594$	−4.75845e7	−5.53350
$595$	−5.39932e6	−0.625240
$596$	8.72863e6	1.00654
$597$	−2.30294e7	−2.64452
$598$	9.90876e6	1.13310
$599$	−7.71994e6	−0.879117	−0.439559	−	0.898214i	$-0.644865\pi$
$599$	−7.71994e6	−0.879117	−0.439559	+	0.898214i	$0.644865\pi$
$600$	5.68254e6	0.644413
$601$	−656938.	−0.0741888	−0.0370944	−	0.999312i	$-0.511810\pi$
$601$	−656938.	−0.0741888	−0.0370944	+	0.999312i	$0.511810\pi$
$602$	−1.34828e7	−1.51631
$603$	1.19263e6	0.133571
$604$	1.65261e7	1.84322
$605$	−1.13990e7	−1.26613
$606$	−3.07081e7	−3.39681
$607$	1.63504e7	1.80118	0.900589	−	0.434673i	$-0.143136\pi$
$607$	1.63504e7	1.80118	0.900589	+	0.434673i	$0.143136\pi$
$608$	−1.51883e7	−1.66628
$609$	5.62749e6	0.614853
$610$	965275.	0.105033
$611$	2.52734e6	0.273880
$612$	1.15501e7	1.24654
$613$	−3.07482e6	−0.330498	−0.165249	−	0.986252i	$-0.552843\pi$
$613$	−3.07482e6	−0.330498	−0.165249	+	0.986252i	$0.552843\pi$
$614$	−6.82500e6	−0.730603
$615$	−2.58825e7	−2.75943
$616$	5.56884e6	0.591307
$617$	−1.69033e7	−1.78755	−0.893774	−	0.448518i	$-0.851952\pi$
$617$	−1.69033e7	−1.78755	−0.893774	+	0.448518i	$0.851952\pi$
$618$	3.63683e7	3.83047
$619$	−4.75907e6	−0.499224	−0.249612	−	0.968346i	$-0.580303\pi$
$619$	−4.75907e6	−0.499224	−0.249612	+	0.968346i	$0.580303\pi$
$620$	−2.51835e7	−2.63110
$621$	4.43591e7	4.61587
$622$	−1.02322e7	−1.06046
$623$	1.62422e7	1.67658
$624$	5.32152e6	0.547110
$625$	−1.06057e7	−1.08603
$626$	40428.6	0.00412337
$627$	−2.99919e7	−3.04674
$628$	1.27326e7	1.28831
$629$	−1.91103e6	−0.192594
$630$	5.59035e7	5.61161
$631$	2.80238e6	0.280190	0.140095	−	0.990138i	$-0.455259\pi$
$631$	2.80238e6	0.280190	0.140095	+	0.990138i	$0.455259\pi$
$632$	−148570.	−0.0147958
$633$	−3.13739e7	−3.11214
$634$	−3.26436e6	−0.322533
$635$	−2.57541e7	−2.53461
$636$	6.13624e6	0.601533
$637$	1.04851e6	0.102382
$638$	−6.38148e6	−0.620683
$639$	2.48415e7	2.40672
$640$	−1.06298e7	−1.02583
$641$	1.58974e7	1.52820	0.764099	−	0.645099i	$-0.223184\pi$
$641$	1.58974e7	1.52820	0.764099	+	0.645099i	$0.223184\pi$
$642$	−4.72361e7	−4.52310
$643$	−1.37605e7	−1.31253	−0.656263	−	0.754532i	$-0.727864\pi$
$643$	−1.37605e7	−1.31253	−0.656263	+	0.754532i	$0.727864\pi$
$644$	−2.54859e7	−2.42151
$645$	2.45506e7	2.32361
$646$	7.70757e6	0.726668
$647$	2.63314e6	0.247294	0.123647	−	0.992326i	$-0.460541\pi$
$647$	2.63314e6	0.247294	0.123647	+	0.992326i	$0.460541\pi$
$648$	−1.02509e7	−0.959010
$649$	6.66691e6	0.621316
$650$	−6.36666e6	−0.591055
$651$	−3.38168e7	−3.12738
$652$	−2.53856e7	−2.33867
$653$	−1.29271e7	−1.18636	−0.593181	−	0.805069i	$-0.702128\pi$
$653$	−1.29271e7	−1.18636	−0.593181	+	0.805069i	$0.702128\pi$
$654$	2.94685e7	2.69410
$655$	−5.78482e6	−0.526850
$656$	8.06981e6	0.732156
$657$	−1.39565e7	−1.26143
$658$	−1.16768e7	−1.05138
$659$	1.54851e7	1.38899	0.694497	−	0.719496i	$-0.255627\pi$
$659$	1.54851e7	1.38899	0.694497	+	0.719496i	$0.255627\pi$
$660$	−4.97814e7	−4.44844
$661$	1.38761e7	1.23527	0.617636	−	0.786464i	$-0.288090\pi$
$661$	1.38761e7	1.23527	0.617636	+	0.786464i	$0.288090\pi$
$662$	7.40809e6	0.656993
$663$	−3.71823e6	−0.328513
$664$	−5.59369e6	−0.492355
$665$	2.07679e7	1.82112
$666$	1.97865e7	1.72855
$667$	5.94892e6	0.517754
$668$	−1.63547e7	−1.41808
$669$	3.06292e7	2.64588
$670$	1.32099e6	0.113688
$671$	−818265.	−0.0701597
$672$	−3.38522e7	−2.89177
$673$	−3.67643e6	−0.312887	−0.156444	−	0.987687i	$-0.550003\pi$
$673$	−3.67643e6	−0.312887	−0.156444	+	0.987687i	$0.550003\pi$
$674$	3.79409e6	0.321705
$675$	−2.85020e7	−2.40777
$676$	−1.20990e7	−1.01831
$677$	5.19537e6	0.435657	0.217828	−	0.975987i	$-0.430103\pi$
$677$	5.19537e6	0.435657	0.217828	+	0.975987i	$0.430103\pi$
$678$	−2.21165e7	−1.84775
$679$	−2.03431e7	−1.69334
$680$	2.60592e6	0.216117
$681$	1.52274e7	1.25822
$682$	3.83477e7	3.15703
$683$	−1.16688e7	−0.957139	−0.478569	−	0.878050i	$-0.658844\pi$
$683$	−1.16688e7	−0.957139	−0.478569	+	0.878050i	$0.658844\pi$
$684$	−4.44260e7	−3.63076
$685$	−3.23359e7	−2.63304
$686$	1.57321e7	1.27637
$687$	2.41193e7	1.94972
$688$	−7.65454e6	−0.616522
$689$	−1.40040e6	−0.112384
$690$	8.33613e7	6.66564
$691$	−5.61111e6	−0.447047	−0.223524	−	0.974698i	$-0.571756\pi$
$691$	−5.61111e6	−0.447047	−0.223524	+	0.974698i	$0.571756\pi$
$692$	−8.09439e6	−0.642568
$693$	−4.73895e7	−3.74842
$694$	−1.80698e7	−1.42414
$695$	−1.90989e7	−1.49984
$696$	−2.71605e6	−0.212527
$697$	−5.63850e6	−0.439624
$698$	2.87808e7	2.23596
$699$	−9.13372e6	−0.707057
$700$	1.63754e7	1.26313
$701$	2.18890e7	1.68240	0.841202	−	0.540722i	$-0.181849\pi$
$701$	2.18890e7	1.68240	0.841202	+	0.540722i	$0.181849\pi$
$702$	2.26908e7	1.73783
$703$	7.35058e6	0.560962
$704$	2.60283e7	1.97931
$705$	2.12622e7	1.61115
$706$	1.36073e7	1.02745
$707$	−1.80254e7	−1.35624
$708$	1.39303e7	1.04442
$709$	−8.03116e6	−0.600016	−0.300008	−	0.953937i	$-0.596989\pi$
$709$	−8.03116e6	−0.600016	−0.300008	+	0.953937i	$0.596989\pi$
$710$	2.75153e7	2.04847
$711$	1.26430e6	0.0937941
$712$	−7.83913e6	−0.579519
$713$	−3.57484e7	−2.63350
$714$	1.71790e7	1.26111
$715$	1.13610e7	0.831097
$716$	−1.78954e7	−1.30455
$717$	−892622.	−0.0648440
$718$	−3.13177e7	−2.26714
$719$	−1.94850e7	−1.40565	−0.702827	−	0.711360i	$-0.748079\pi$
$719$	−1.94850e7	−1.40565	−0.702827	+	0.711360i	$0.748079\pi$
$720$	3.17380e7	2.28164
$721$	2.13479e7	1.52938
$722$	−8.60886e6	−0.614614
$723$	−1.82860e7	−1.30099
$724$	4.85290e6	0.344077
$725$	−3.82235e6	−0.270076
$726$	3.62682e7	2.55379
$727$	3.81990e6	0.268050	0.134025	−	0.990978i	$-0.457210\pi$
$727$	3.81990e6	0.268050	0.134025	+	0.990978i	$0.457210\pi$
$728$	−2.65552e6	−0.185704
$729$	1.64686e7	1.14773
$730$	−1.54587e7	−1.07366
$731$	5.34834e6	0.370191
$732$	−1.70974e6	−0.117937
$733$	5.28725e6	0.363471	0.181735	−	0.983347i	$-0.441829\pi$
$733$	5.28725e6	0.363471	0.181735	+	0.983347i	$0.441829\pi$
$734$	−1.58142e7	−1.08344
$735$	8.82096e6	0.602278
$736$	−3.57858e7	−2.43510
$737$	−1.11981e6	−0.0759408
$738$	5.83799e7	3.94568
$739$	2.33173e7	1.57061	0.785303	−	0.619112i	$-0.212507\pi$
$739$	2.33173e7	1.57061	0.785303	+	0.619112i	$0.212507\pi$
$740$	1.22007e7	0.819040
$741$	1.43017e7	0.956849
$742$	6.47013e6	0.431423
$743$	4.42062e6	0.293773	0.146886	−	0.989153i	$-0.453075\pi$
$743$	4.42062e6	0.293773	0.146886	+	0.989153i	$0.453075\pi$
$744$	1.63213e7	1.08099
$745$	−1.67587e7	−1.10624
$746$	3.35922e7	2.21000
$747$	4.76009e7	3.12115
$748$	−1.08449e7	−0.708712
$749$	−2.77271e7	−1.80593
$750$	5.62671e6	0.365260
$751$	1.59941e7	1.03481	0.517406	−	0.855740i	$-0.326898\pi$
$751$	1.59941e7	1.03481	0.517406	+	0.855740i	$0.326898\pi$
$752$	−6.62927e6	−0.427485
$753$	−5.59849e7	−3.59819
$754$	3.04303e6	0.194930
$755$	−3.17296e7	−2.02580
$756$	−5.83622e7	−3.71388
$757$	1.53372e7	0.972761	0.486381	−	0.873747i	$-0.338317\pi$
$757$	1.53372e7	0.972761	0.486381	+	0.873747i	$0.338317\pi$
$758$	−7.74878e6	−0.489847
$759$	−7.06655e7	−4.45249
$760$	−1.00234e7	−0.629478
$761$	−4.06637e6	−0.254534	−0.127267	−	0.991869i	$-0.540620\pi$
$761$	−4.06637e6	−0.254534	−0.127267	+	0.991869i	$0.540620\pi$
$762$	8.19416e7	5.11231
$763$	1.72977e7	1.07567
$764$	−1.20282e6	−0.0745534
$765$	−2.21758e7	−1.37001
$766$	−3.25642e7	−2.00525
$767$	−3.17914e6	−0.195128
$768$	−9.48646e6	−0.580365
$769$	−2.25196e7	−1.37324	−0.686618	−	0.727018i	$-0.740905\pi$
$769$	−2.25196e7	−1.37324	−0.686618	+	0.727018i	$0.740905\pi$
$770$	−5.24902e7	−3.19045
$771$	1.50861e7	0.913990
$772$	−1.87570e7	−1.13271
$773$	8.00792e6	0.482026	0.241013	−	0.970522i	$-0.422520\pi$
$773$	8.00792e6	0.482026	0.241013	+	0.970522i	$0.422520\pi$
$774$	−5.53757e7	−3.32251
$775$	2.29694e7	1.37371
$776$	9.81838e6	0.585310
$777$	1.63833e7	0.973528
$778$	−4.67607e7	−2.76969
$779$	2.16878e7	1.28048
$780$	2.37384e7	1.39706
$781$	−2.33248e7	−1.36833
$782$	1.81602e7	1.06195
$783$	1.36229e7	0.794082
$784$	−2.75025e6	−0.159802
$785$	−2.44463e7	−1.41592
$786$	1.84055e7	1.06265
$787$	9.54969e6	0.549607	0.274803	−	0.961500i	$-0.411387\pi$
$787$	9.54969e6	0.549607	0.274803	+	0.961500i	$0.411387\pi$
$788$	1.05414e7	0.604761
$789$	2.69182e7	1.53940
$790$	1.40038e6	0.0798322
$791$	−1.29822e7	−0.737745
$792$	2.28720e7	1.29566
$793$	390192.	0.0220341
$794$	1.00114e7	0.563563
$795$	−1.17814e7	−0.661118
$796$	3.20299e7	1.79173
$797$	7.52797e6	0.419790	0.209895	−	0.977724i	$-0.432688\pi$
$797$	7.52797e6	0.419790	0.209895	+	0.977724i	$0.432688\pi$
$798$	−6.60770e7	−3.67319
$799$	4.63196e6	0.256684
$800$	2.29934e7	1.27022
$801$	6.67091e7	3.67370
$802$	1.92111e7	1.05467
$803$	1.31044e7	0.717179
$804$	−2.33980e6	−0.127655
$805$	4.89323e7	2.66137
$806$	−1.82862e7	−0.991487
$807$	−1.43371e7	−0.774954
$808$	8.69975e6	0.468790
$809$	2.51683e7	1.35202	0.676009	−	0.736893i	$-0.263708\pi$
$809$	2.51683e7	1.35202	0.676009	+	0.736893i	$0.263708\pi$
$810$	9.66217e7	5.17442
$811$	2.56581e7	1.36985	0.684924	−	0.728615i	$-0.259835\pi$
$811$	2.56581e7	1.36985	0.684924	+	0.728615i	$0.259835\pi$
$812$	−7.82686e6	−0.416579
$813$	−2.74217e7	−1.45502
$814$	−1.85784e7	−0.982758
$815$	4.87396e7	2.57033
$816$	9.75298e6	0.512757
$817$	−2.05718e7	−1.07824
$818$	3.81656e7	1.99429
$819$	2.25978e7	1.17722
$820$	3.59981e7	1.86958
$821$	−2.17846e7	−1.12796	−0.563978	−	0.825790i	$-0.690730\pi$
$821$	−2.17846e7	−1.12796	−0.563978	+	0.825790i	$0.690730\pi$
$822$	1.02883e8	5.31084
$823$	2.46699e7	1.26960	0.634802	−	0.772675i	$-0.281082\pi$
$823$	2.46699e7	1.26960	0.634802	+	0.772675i	$0.281082\pi$
$824$	−1.03033e7	−0.528638
$825$	4.54045e7	2.32255
$826$	1.46883e7	0.749066
$827$	−2.12572e7	−1.08079	−0.540396	−	0.841411i	$-0.681726\pi$
$827$	−2.12572e7	−1.08079	−0.540396	+	0.841411i	$0.681726\pi$
$828$	−1.04674e8	−5.30597
$829$	9.09873e6	0.459827	0.229913	−	0.973211i	$-0.426156\pi$
$829$	9.09873e6	0.459827	0.229913	+	0.973211i	$0.426156\pi$
$830$	5.27244e7	2.65654
$831$	−4.53302e7	−2.27712
$832$	−1.24117e7	−0.621616
$833$	1.92164e6	0.0959532
$834$	6.07668e7	3.02518
$835$	3.14006e7	1.55855
$836$	4.17135e7	2.06424
$837$	−8.18631e7	−4.03900
$838$	−1.43530e7	−0.706046
$839$	9.64376e6	0.472979	0.236489	−	0.971634i	$-0.424003\pi$
$839$	9.64376e6	0.472979	0.236489	+	0.971634i	$0.424003\pi$
$840$	−2.23406e7	−1.09244
$841$	−1.86842e7	−0.910929
$842$	−2.20880e7	−1.07368
$843$	−5.33847e7	−2.58731
$844$	4.36356e7	2.10856
$845$	2.32297e7	1.11918
$846$	−4.79585e7	−2.30377
$847$	2.12891e7	1.01964
$848$	3.67327e6	0.175414
$849$	−1.56134e7	−0.743411
$850$	−1.16684e7	−0.553943
$851$	1.73191e7	0.819787
$852$	−4.87364e7	−2.30014
$853$	−780158.	−0.0367122	−0.0183561	−	0.999832i	$-0.505843\pi$
$853$	−780158.	−0.0367122	−0.0183561	+	0.999832i	$0.505843\pi$
$854$	−1.80277e6	−0.0845854
$855$	8.52967e7	3.99040
$856$	1.33822e7	0.624228
$857$	2.83144e6	0.131691	0.0658453	−	0.997830i	$-0.479026\pi$
$857$	2.83144e6	0.131691	0.0658453	+	0.997830i	$0.479026\pi$
$858$	−3.61472e7	−1.67632
$859$	2.37609e7	1.09870	0.549350	−	0.835592i	$-0.314875\pi$
$859$	2.37609e7	1.09870	0.549350	+	0.835592i	$0.314875\pi$
$860$	−3.41457e7	−1.57431
$861$	4.83388e7	2.22223
$862$	−1.19648e7	−0.548451
$863$	2.50810e7	1.14635	0.573176	−	0.819432i	$-0.305711\pi$
$863$	2.50810e7	1.14635	0.573176	+	0.819432i	$0.305711\pi$
$864$	−8.19487e7	−3.73472
$865$	1.55410e7	0.706217
$866$	7.35022e6	0.333047
$867$	3.42099e7	1.54562
$868$	4.70333e7	2.11888
$869$	−1.18710e6	−0.0533260
$870$	2.56007e7	1.14671
$871$	533984.	0.0238497
$872$	−8.34856e6	−0.371809
$873$	−8.35521e7	−3.71041
$874$	−6.98512e7	−3.09311
$875$	3.30283e6	0.145836
$876$	2.73811e7	1.20557
$877$	3.19667e7	1.40346	0.701729	−	0.712444i	$-0.252412\pi$
$877$	3.19667e7	1.40346	0.701729	+	0.712444i	$0.252412\pi$
$878$	6.31854e6	0.276618
$879$	−2.88859e7	−1.26099
$880$	−2.98001e7	−1.29721
$881$	1.49942e7	0.650854	0.325427	−	0.945567i	$-0.394492\pi$
$881$	1.49942e7	0.650854	0.325427	+	0.945567i	$0.394492\pi$
$882$	−1.98963e7	−0.861193
$883$	−4.08162e7	−1.76170	−0.880848	−	0.473399i	$-0.843027\pi$
$883$	−4.08162e7	−1.76170	−0.880848	+	0.473399i	$0.843027\pi$
$884$	5.17140e6	0.222576
$885$	−2.67457e7	−1.14788
$886$	−2.46984e7	−1.05702
$887$	−1.33743e7	−0.570770	−0.285385	−	0.958413i	$-0.592121\pi$
$887$	−1.33743e7	−0.570770	−0.285385	+	0.958413i	$0.592121\pi$
$888$	−7.90722e6	−0.336505
$889$	4.80989e7	2.04118
$890$	7.38893e7	3.12685
$891$	−8.19063e7	−3.45639
$892$	−4.25999e7	−1.79265
$893$	−1.78163e7	−0.747635
$894$	5.33211e7	2.23129
$895$	3.43587e7	1.43377
$896$	1.98525e7	0.826123
$897$	3.36971e7	1.39833
$898$	3.56428e7	1.47496
$899$	−1.09785e7	−0.453048
$900$	6.72563e7	2.76775
$901$	−2.56657e6	−0.105327
$902$	−5.48154e7	−2.24329
$903$	−4.58513e7	−1.87125
$904$	6.26571e6	0.255005
$905$	−9.31743e6	−0.378159
$906$	1.00954e8	4.08604
$907$	2.04498e7	0.825413	0.412707	−	0.910864i	$-0.364583\pi$
$907$	2.04498e7	0.825413	0.412707	+	0.910864i	$0.364583\pi$
$908$	−2.11786e7	−0.852478
$909$	−7.40328e7	−2.97176
$910$	2.50301e7	1.00198
$911$	−1.00490e7	−0.401170	−0.200585	−	0.979676i	$-0.564284\pi$
$911$	−1.00490e7	−0.401170	−0.200585	+	0.979676i	$0.564284\pi$
$912$	−3.75137e7	−1.49349
$913$	−4.46946e7	−1.77451
$914$	−6.02143e7	−2.38415
$915$	3.28264e6	0.129620
$916$	−3.35457e7	−1.32098
$917$	1.08039e7	0.424283
$918$	4.15865e7	1.62872
$919$	5.35960e6	0.209336	0.104668	−	0.994507i	$-0.466622\pi$
$919$	5.35960e6	0.209336	0.104668	+	0.994507i	$0.466622\pi$
$920$	−2.36166e7	−0.919916
$921$	−2.32100e7	−0.901625
$922$	2.10119e7	0.814024
$923$	1.11225e7	0.429733
$924$	9.29729e7	3.58242
$925$	−1.11280e7	−0.427624
$926$	4.33486e7	1.66130
$927$	8.76787e7	3.35116
$928$	−1.09900e7	−0.418917
$929$	−3.62740e7	−1.37898	−0.689488	−	0.724297i	$-0.742164\pi$
$929$	−3.62740e7	−1.37898	−0.689488	+	0.724297i	$0.742164\pi$
$930$	−1.53840e8	−5.83260
$931$	−7.39137e6	−0.279480
$932$	1.27034e7	0.479049
$933$	−3.47969e7	−1.30869
$934$	−4.20946e6	−0.157892
$935$	2.08218e7	0.778913
$936$	−1.09066e7	−0.406911
$937$	−3.13096e7	−1.16501	−0.582504	−	0.812828i	$-0.697927\pi$
$937$	−3.13096e7	−1.16501	−0.582504	+	0.812828i	$0.697927\pi$
$938$	−2.46712e6	−0.0915552
$939$	137487.	0.00508859
$940$	−2.95721e7	−1.09160
$941$	6.69262e6	0.246389	0.123195	−	0.992383i	$-0.460686\pi$
$941$	6.69262e6	0.246389	0.123195	+	0.992383i	$0.460686\pi$
$942$	7.77806e7	2.85591
$943$	5.10999e7	1.87129
$944$	8.33894e6	0.304565
$945$	1.12054e8	4.08175
$946$	5.19946e7	1.88899
$947$	9.90774e6	0.359004	0.179502	−	0.983758i	$-0.442551\pi$
$947$	9.90774e6	0.359004	0.179502	+	0.983758i	$0.442551\pi$
$948$	−2.48041e6	−0.0896403
$949$	−6.24886e6	−0.225235
$950$	4.48814e7	1.61346
$951$	−1.11012e7	−0.398033
$952$	−4.86688e6	−0.174044
$953$	2.71489e6	0.0968323	0.0484162	−	0.998827i	$-0.484583\pi$
$953$	2.71489e6	0.0968323	0.0484162	+	0.998827i	$0.484583\pi$
$954$	2.65737e7	0.945327
$955$	2.30938e6	0.0819384
$956$	1.24148e6	0.0439335
$957$	−2.17017e7	−0.765974
$958$	2.79173e7	0.982789
$959$	6.03912e7	2.12044
$960$	−1.04418e8	−3.65677
$961$	3.73432e7	1.30438
$962$	8.85916e6	0.308642
$963$	−1.13879e8	−3.95712
$964$	2.54326e7	0.881452
$965$	3.60129e7	1.24491
$966$	−1.55687e8	−5.36798
$967$	−1.02833e7	−0.353645	−0.176822	−	0.984243i	$-0.556582\pi$
$967$	−1.02833e7	−0.353645	−0.176822	+	0.984243i	$0.556582\pi$
$968$	−1.02749e7	−0.352445
$969$	2.62114e7	0.896769
$970$	−9.25451e7	−3.15809
$971$	−4.62551e6	−0.157439	−0.0787193	−	0.996897i	$-0.525083\pi$
$971$	−4.62551e6	−0.157439	−0.0787193	+	0.996897i	$0.525083\pi$
$972$	−7.27203e7	−2.46882
$973$	3.56695e7	1.20785
$974$	9.13391e6	0.308503
$975$	−2.16513e7	−0.729411
$976$	−1.02348e6	−0.0343919
$977$	4.30298e7	1.44222	0.721112	−	0.692819i	$-0.243631\pi$
$977$	4.30298e7	1.44222	0.721112	+	0.692819i	$0.243631\pi$
$978$	−1.55075e8	−5.18434
$979$	−6.26361e7	−2.08866
$980$	−1.22684e7	−0.408059
$981$	7.10442e7	2.35698
$982$	6.43963e7	2.13099
$983$	−4.44842e7	−1.46832	−0.734162	−	0.678974i	$-0.762425\pi$
$983$	−4.44842e7	−1.46832	−0.734162	+	0.678974i	$0.762425\pi$
$984$	−2.33302e7	−0.768123
$985$	−2.02392e7	−0.664665
$986$	5.57709e6	0.182690
$987$	−3.97098e7	−1.29749
$988$	−1.98912e7	−0.648290
$989$	−4.84703e7	−1.57574
$990$	−2.15585e8	−6.99085
$991$	784672.	0.0253807	0.0126904	−	0.999919i	$-0.495960\pi$
$991$	784672.	0.0253807	0.0126904	+	0.999919i	$0.495960\pi$
$992$	6.60414e7	2.13077
$993$	2.51929e7	0.810785
$994$	−5.13883e7	−1.64967
$995$	−6.14964e7	−1.96921
$996$	−9.33878e7	−2.98292
$997$	3.02220e7	0.962908	0.481454	−	0.876471i	$-0.340109\pi$
$997$	3.02220e7	0.962908	0.481454	+	0.876471i	$0.340109\pi$
$998$	−2.91338e6	−0.0925916
$999$	3.96603e7	1.25731

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.6.a.a.1.16	✓	111

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.6.a.a.1.16	✓	111	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)

\(f(q)\)	\(=\)	\(q-8.49621 q^{2} -28.8934 q^{3} +40.1856 q^{4} -77.1552 q^{5} +245.484 q^{6} +144.097 q^{7} -69.5467 q^{8} +591.826 q^{9} +O(q^{10})\)	\(q-8.49621 q^{2} -28.8934 q^{3} +40.1856 q^{4} -77.1552 q^{5} +245.484 q^{6} +144.097 q^{7} -69.5467 q^{8} +591.826 q^{9} +655.527 q^{10} -555.691 q^{11} -1161.10 q^{12} +264.983 q^{13} -1224.28 q^{14} +2229.27 q^{15} -695.056 q^{16} +485.646 q^{17} -5028.28 q^{18} -1867.98 q^{19} -3100.53 q^{20} -4163.44 q^{21} +4721.27 q^{22} -4401.25 q^{23} +2009.44 q^{24} +2827.92 q^{25} -2251.35 q^{26} -10078.8 q^{27} +5790.62 q^{28} -1351.64 q^{29} -18940.4 q^{30} +8122.34 q^{31} +8130.84 q^{32} +16055.8 q^{33} -4126.15 q^{34} -11117.8 q^{35} +23782.9 q^{36} -3935.04 q^{37} +15870.8 q^{38} -7656.25 q^{39} +5365.89 q^{40} -11610.3 q^{41} +35373.5 q^{42} +11012.8 q^{43} -22330.8 q^{44} -45662.5 q^{45} +37393.9 q^{46} +9537.75 q^{47} +20082.5 q^{48} +3956.88 q^{49} -24026.6 q^{50} -14031.9 q^{51} +10648.5 q^{52} -5284.86 q^{53} +85631.3 q^{54} +42874.5 q^{55} -10021.5 q^{56} +53972.3 q^{57} +11483.9 q^{58} -11997.5 q^{59} +89584.7 q^{60} +1472.52 q^{61} -69009.1 q^{62} +85280.2 q^{63} -46839.5 q^{64} -20444.8 q^{65} -136413. q^{66} +2015.16 q^{67} +19516.0 q^{68} +127167. q^{69} +94459.3 q^{70} +41974.4 q^{71} -41159.6 q^{72} -23582.1 q^{73} +33432.9 q^{74} -81708.2 q^{75} -75066.0 q^{76} -80073.3 q^{77} +65049.1 q^{78} +2136.27 q^{79} +53627.2 q^{80} +147395. q^{81} +98643.6 q^{82} +80430.6 q^{83} -167310. q^{84} -37470.1 q^{85} -93567.5 q^{86} +39053.6 q^{87} +38646.5 q^{88} +112717. q^{89} +387958. q^{90} +38183.2 q^{91} -176867. q^{92} -234682. q^{93} -81034.7 q^{94} +144125. q^{95} -234927. q^{96} -141177. q^{97} -33618.5 q^{98} -328873. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 111 q - 28 q^{2} - 98 q^{3} + 1722 q^{4} - 801 q^{5} - 414 q^{6} - 587 q^{7} - 1344 q^{8} + 8241 q^{9}+O(q^{10}) \) 111 * q - 28 * q^2 - 98 * q^3 + 1722 * q^4 - 801 * q^5 - 414 * q^6 - 587 * q^7 - 1344 * q^8 + 8241 * q^9	\( 111 q - 28 q^{2} - 98 q^{3} + 1722 q^{4} - 801 q^{5} - 414 q^{6} - 587 q^{7} - 1344 q^{8} + 8241 q^{9} - 950 q^{10} - 1832 q^{11} - 4143 q^{12} - 4369 q^{13} - 4777 q^{14} - 3487 q^{15} + 26274 q^{16} - 13648 q^{17} - 10269 q^{18} - 5446 q^{19} - 26032 q^{20} - 8428 q^{21} - 8248 q^{22} - 24142 q^{23} - 18577 q^{24} + 58062 q^{25} - 17656 q^{26} - 33269 q^{27} - 23512 q^{28} - 33752 q^{29} - 12418 q^{30} - 13781 q^{31} - 44076 q^{32} - 39186 q^{33} - 7207 q^{34} - 30833 q^{35} + 120044 q^{36} - 61582 q^{37} - 91259 q^{38} - 20077 q^{39} - 66032 q^{40} - 54181 q^{41} - 69252 q^{42} - 38600 q^{43} - 95712 q^{44} - 190880 q^{45} - 9354 q^{46} - 83886 q^{47} - 173886 q^{48} + 194148 q^{49} - 70896 q^{50} - 60673 q^{51} - 145186 q^{52} - 286874 q^{53} - 116519 q^{54} - 74821 q^{55} - 240407 q^{56} - 95180 q^{57} - 66900 q^{58} - 135740 q^{59} - 144550 q^{60} - 227450 q^{61} - 308766 q^{62} - 249721 q^{63} + 347514 q^{64} - 290374 q^{65} - 178980 q^{66} - 91006 q^{67} - 521943 q^{68} - 414510 q^{69} - 165057 q^{70} - 236165 q^{71} - 527945 q^{72} - 184618 q^{73} - 206443 q^{74} - 243897 q^{75} - 221676 q^{76} - 751131 q^{77} - 306839 q^{78} - 107446 q^{79} - 856691 q^{80} + 382187 q^{81} - 244614 q^{82} - 499547 q^{83} - 330289 q^{84} - 287103 q^{85} - 272441 q^{86} - 391281 q^{87} - 588937 q^{88} - 740774 q^{89} - 687179 q^{90} - 237213 q^{91} - 1367678 q^{92} - 754880 q^{93} - 32851 q^{94} - 295814 q^{95} - 816078 q^{96} - 320770 q^{97} - 661922 q^{98} - 547439 q^{99}+O(q^{100}) \) 111 * q - 28 * q^2 - 98 * q^3 + 1722 * q^4 - 801 * q^5 - 414 * q^6 - 587 * q^7 - 1344 * q^8 + 8241 * q^9 - 950 * q^10 - 1832 * q^11 - 4143 * q^12 - 4369 * q^13 - 4777 * q^14 - 3487 * q^15 + 26274 * q^16 - 13648 * q^17 - 10269 * q^18 - 5446 * q^19 - 26032 * q^20 - 8428 * q^21 - 8248 * q^22 - 24142 * q^23 - 18577 * q^24 + 58062 * q^25 - 17656 * q^26 - 33269 * q^27 - 23512 * q^28 - 33752 * q^29 - 12418 * q^30 - 13781 * q^31 - 44076 * q^32 - 39186 * q^33 - 7207 * q^34 - 30833 * q^35 + 120044 * q^36 - 61582 * q^37 - 91259 * q^38 - 20077 * q^39 - 66032 * q^40 - 54181 * q^41 - 69252 * q^42 - 38600 * q^43 - 95712 * q^44 - 190880 * q^45 - 9354 * q^46 - 83886 * q^47 - 173886 * q^48 + 194148 * q^49 - 70896 * q^50 - 60673 * q^51 - 145186 * q^52 - 286874 * q^53 - 116519 * q^54 - 74821 * q^55 - 240407 * q^56 - 95180 * q^57 - 66900 * q^58 - 135740 * q^59 - 144550 * q^60 - 227450 * q^61 - 308766 * q^62 - 249721 * q^63 + 347514 * q^64 - 290374 * q^65 - 178980 * q^66 - 91006 * q^67 - 521943 * q^68 - 414510 * q^69 - 165057 * q^70 - 236165 * q^71 - 527945 * q^72 - 184618 * q^73 - 206443 * q^74 - 243897 * q^75 - 221676 * q^76 - 751131 * q^77 - 306839 * q^78 - 107446 * q^79 - 856691 * q^80 + 382187 * q^81 - 244614 * q^82 - 499547 * q^83 - 330289 * q^84 - 287103 * q^85 - 272441 * q^86 - 391281 * q^87 - 588937 * q^88 - 740774 * q^89 - 687179 * q^90 - 237213 * q^91 - 1367678 * q^92 - 754880 * q^93 - 32851 * q^94 - 295814 * q^95 - 816078 * q^96 - 320770 * q^97 - 661922 * q^98 - 547439 * q^99

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