LMFDB - Embedded newform 69.6.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,6,Mod(1,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("69.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	69.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:	$11.0664835671$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 113x^{3} - 257x^{2} + 1404x + 2197 $ x^5 - 113x^3 - 257x^2 + 1404*x + 2197
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.42196$ of defining polynomial
Character	$\chi$	$=$	69.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.32729 q^{2} +9.00000 q^{3} +54.9984 q^{4} +99.7124 q^{5} -83.9456 q^{6} +125.983 q^{7} -214.513 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-9.32729 q^{2} +9.00000 q^{3} +54.9984 q^{4} +99.7124 q^{5} -83.9456 q^{6} +125.983 q^{7} -214.513 q^{8} +81.0000 q^{9} -930.047 q^{10} +177.715 q^{11} +494.986 q^{12} -919.618 q^{13} -1175.08 q^{14} +897.412 q^{15} +240.875 q^{16} +1568.24 q^{17} -755.511 q^{18} +447.960 q^{19} +5484.02 q^{20} +1133.85 q^{21} -1657.60 q^{22} -529.000 q^{23} -1930.62 q^{24} +6817.57 q^{25} +8577.55 q^{26} +729.000 q^{27} +6928.86 q^{28} -1298.72 q^{29} -8370.42 q^{30} -6651.88 q^{31} +4617.70 q^{32} +1599.43 q^{33} -14627.4 q^{34} +12562.1 q^{35} +4454.87 q^{36} -8056.80 q^{37} -4178.25 q^{38} -8276.56 q^{39} -21389.6 q^{40} +17941.4 q^{41} -10575.7 q^{42} +10710.7 q^{43} +9774.04 q^{44} +8076.71 q^{45} +4934.14 q^{46} -17886.9 q^{47} +2167.87 q^{48} -935.293 q^{49} -63589.5 q^{50} +14114.1 q^{51} -50577.5 q^{52} -20343.9 q^{53} -6799.60 q^{54} +17720.4 q^{55} -27025.0 q^{56} +4031.64 q^{57} +12113.5 q^{58} +28488.5 q^{59} +49356.2 q^{60} +16222.3 q^{61} +62044.1 q^{62} +10204.6 q^{63} -50778.6 q^{64} -91697.4 q^{65} -14918.4 q^{66} +54128.0 q^{67} +86250.6 q^{68} -4761.00 q^{69} -117170. q^{70} +42505.6 q^{71} -17375.5 q^{72} +40936.2 q^{73} +75148.1 q^{74} +61358.1 q^{75} +24637.1 q^{76} +22389.1 q^{77} +77197.9 q^{78} -24760.6 q^{79} +24018.2 q^{80} +6561.00 q^{81} -167345. q^{82} -30825.2 q^{83} +62359.7 q^{84} +156373. q^{85} -99901.7 q^{86} -11688.4 q^{87} -38122.1 q^{88} -66531.6 q^{89} -75333.8 q^{90} -115856. q^{91} -29094.2 q^{92} -59866.9 q^{93} +166836. q^{94} +44667.2 q^{95} +41559.3 q^{96} -104506. q^{97} +8723.75 q^{98} +14394.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 8 q^{2} + 45 q^{3} + 118 q^{4} + 94 q^{5} + 72 q^{6} + 272 q^{7} + 258 q^{8} + 405 q^{9}+O(q^{10}) $ 5 * q + 8 * q^2 + 45 * q^3 + 118 * q^4 + 94 * q^5 + 72 * q^6 + 272 * q^7 + 258 * q^8 + 405 * q^9	\( 5 q + 8 q^{2} + 45 q^{3} + 118 q^{4} + 94 q^{5} + 72 q^{6} + 272 q^{7} + 258 q^{8} + 405 q^{9} - 172 q^{10} + 1100 q^{11} + 1062 q^{12} - 978 q^{13} - 344 q^{14} + 846 q^{15} + 1218 q^{16} + 2522 q^{17} + 648 q^{18} + 2060 q^{19} + 7720 q^{20} + 2448 q^{21} - 2572 q^{22} - 2645 q^{23} + 2322 q^{24} + 12035 q^{25} + 9280 q^{26} + 3645 q^{27} + 8072 q^{28} + 1526 q^{29} - 1548 q^{30} - 7392 q^{31} - 5086 q^{32} + 9900 q^{33} - 15608 q^{34} + 6056 q^{35} + 9558 q^{36} - 8210 q^{37} - 14276 q^{38} - 8802 q^{39} - 37472 q^{40} + 21250 q^{41} - 3096 q^{42} - 4548 q^{43} - 4260 q^{44} + 7614 q^{45} - 4232 q^{46} + 536 q^{47} + 10962 q^{48} - 27979 q^{49} - 81872 q^{50} + 22698 q^{51} - 76380 q^{52} - 11482 q^{53} + 5832 q^{54} - 77064 q^{55} - 28624 q^{56} + 18540 q^{57} - 79680 q^{58} + 74676 q^{59} + 69480 q^{60} - 44618 q^{61} + 64880 q^{62} + 22032 q^{63} - 137382 q^{64} - 24388 q^{65} - 23148 q^{66} - 1412 q^{67} + 80196 q^{68} - 23805 q^{69} - 222304 q^{70} + 37912 q^{71} + 20898 q^{72} + 46546 q^{73} + 111604 q^{74} + 108315 q^{75} - 79548 q^{76} + 157008 q^{77} + 83520 q^{78} + 50544 q^{79} + 69424 q^{80} + 32805 q^{81} - 233720 q^{82} + 89588 q^{83} + 72648 q^{84} + 147892 q^{85} + 77428 q^{86} + 13734 q^{87} + 54484 q^{88} + 280410 q^{89} - 13932 q^{90} - 27416 q^{91} - 62422 q^{92} - 66528 q^{93} + 113632 q^{94} + 203120 q^{95} - 45774 q^{96} + 90074 q^{97} + 32976 q^{98} + 89100 q^{99}+O(q^{100}) \) 5 * q + 8 * q^2 + 45 * q^3 + 118 * q^4 + 94 * q^5 + 72 * q^6 + 272 * q^7 + 258 * q^8 + 405 * q^9 - 172 * q^10 + 1100 * q^11 + 1062 * q^12 - 978 * q^13 - 344 * q^14 + 846 * q^15 + 1218 * q^16 + 2522 * q^17 + 648 * q^18 + 2060 * q^19 + 7720 * q^20 + 2448 * q^21 - 2572 * q^22 - 2645 * q^23 + 2322 * q^24 + 12035 * q^25 + 9280 * q^26 + 3645 * q^27 + 8072 * q^28 + 1526 * q^29 - 1548 * q^30 - 7392 * q^31 - 5086 * q^32 + 9900 * q^33 - 15608 * q^34 + 6056 * q^35 + 9558 * q^36 - 8210 * q^37 - 14276 * q^38 - 8802 * q^39 - 37472 * q^40 + 21250 * q^41 - 3096 * q^42 - 4548 * q^43 - 4260 * q^44 + 7614 * q^45 - 4232 * q^46 + 536 * q^47 + 10962 * q^48 - 27979 * q^49 - 81872 * q^50 + 22698 * q^51 - 76380 * q^52 - 11482 * q^53 + 5832 * q^54 - 77064 * q^55 - 28624 * q^56 + 18540 * q^57 - 79680 * q^58 + 74676 * q^59 + 69480 * q^60 - 44618 * q^61 + 64880 * q^62 + 22032 * q^63 - 137382 * q^64 - 24388 * q^65 - 23148 * q^66 - 1412 * q^67 + 80196 * q^68 - 23805 * q^69 - 222304 * q^70 + 37912 * q^71 + 20898 * q^72 + 46546 * q^73 + 111604 * q^74 + 108315 * q^75 - 79548 * q^76 + 157008 * q^77 + 83520 * q^78 + 50544 * q^79 + 69424 * q^80 + 32805 * q^81 - 233720 * q^82 + 89588 * q^83 + 72648 * q^84 + 147892 * q^85 + 77428 * q^86 + 13734 * q^87 + 54484 * q^88 + 280410 * q^89 - 13932 * q^90 - 27416 * q^91 - 62422 * q^92 - 66528 * q^93 + 113632 * q^94 + 203120 * q^95 - 45774 * q^96 + 90074 * q^97 + 32976 * q^98 + 89100 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−9.32729	−1.64885	−0.824424	−	0.565973i	$-0.808501\pi$
$2$	−9.32729	−1.64885	−0.824424	+	0.565973i	$0.808501\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	54.9984	1.71870
$5$	99.7124	1.78371	0.891855	−	0.452321i	$-0.149404\pi$
$5$	99.7124	1.78371	0.891855	+	0.452321i	$0.149404\pi$
$6$	−83.9456	−0.951963
$7$	125.983	0.971777	0.485889	−	0.874021i	$-0.338496\pi$
$7$	125.983	0.971777	0.485889	+	0.874021i	$0.338496\pi$
$8$	−214.513	−1.18503
$9$	81.0000	0.333333
$10$	−930.047	−2.94107
$11$	177.715	0.442835	0.221418	−	0.975179i	$-0.428932\pi$
$11$	177.715	0.442835	0.221418	+	0.975179i	$0.428932\pi$
$12$	494.986	0.992292
$13$	−919.618	−1.50921	−0.754604	−	0.656180i	$-0.772171\pi$
$13$	−919.618	−1.50921	−0.754604	+	0.656180i	$0.772171\pi$
$14$	−1175.08	−1.60231
$15$	897.412	1.02983
$16$	240.875	0.235229
$17$	1568.24	1.31610	0.658051	−	0.752973i	$-0.271381\pi$
$17$	1568.24	1.31610	0.658051	+	0.752973i	$0.271381\pi$
$18$	−755.511	−0.549616
$19$	447.960	0.284679	0.142339	−	0.989818i	$-0.454538\pi$
$19$	447.960	0.284679	0.142339	+	0.989818i	$0.454538\pi$
$20$	5484.02	3.06566
$21$	1133.85	0.561056
$22$	−1657.60	−0.730168
$23$	−529.000	−0.208514
$23$	−529.000	−0.208514
$24$	−1930.62	−0.684176
$25$	6817.57	2.18162
$26$	8577.55	2.48846
$27$	729.000	0.192450
$28$	6928.86	1.67019
$29$	−1298.72	−0.286760	−0.143380	−	0.989668i	$-0.545797\pi$
$29$	−1298.72	−0.286760	−0.143380	+	0.989668i	$0.545797\pi$
$30$	−8370.42	−1.69803
$31$	−6651.88	−1.24320	−0.621599	−	0.783336i	$-0.713517\pi$
$31$	−6651.88	−1.24320	−0.621599	+	0.783336i	$0.713517\pi$
$32$	4617.70	0.797169
$33$	1599.43	0.255671
$34$	−14627.4	−2.17005
$35$	12562.1	1.73337
$36$	4454.87	0.572900
$37$	−8056.80	−0.967516	−0.483758	−	0.875202i	$-0.660728\pi$
$37$	−8056.80	−0.967516	−0.483758	+	0.875202i	$0.660728\pi$
$38$	−4178.25	−0.469392
$39$	−8276.56	−0.871342
$40$	−21389.6	−2.11374
$41$	17941.4	1.66685	0.833427	−	0.552630i	$-0.186376\pi$
$41$	17941.4	1.66685	0.833427	+	0.552630i	$0.186376\pi$
$42$	−10575.7	−0.925096
$43$	10710.7	0.883377	0.441688	−	0.897169i	$-0.354380\pi$
$43$	10710.7	0.883377	0.441688	+	0.897169i	$0.354380\pi$
$44$	9774.04	0.761101
$45$	8076.71	0.594570
$46$	4934.14	0.343809
$47$	−17886.9	−1.18111	−0.590555	−	0.806997i	$-0.701091\pi$
$47$	−17886.9	−1.18111	−0.590555	+	0.806997i	$0.701091\pi$
$48$	2167.87	0.135810
$49$	−935.293	−0.0556490
$50$	−63589.5	−3.59716
$51$	14114.1	0.759852
$52$	−50577.5	−2.59388
$53$	−20343.9	−0.994820	−0.497410	−	0.867516i	$-0.665716\pi$
$53$	−20343.9	−0.994820	−0.497410	+	0.867516i	$0.665716\pi$
$54$	−6799.60	−0.317321
$55$	17720.4	0.789890
$56$	−27025.0	−1.15158
$57$	4031.64	0.164359
$58$	12113.5	0.472824
$59$	28488.5	1.06547	0.532734	−	0.846283i	$-0.321165\pi$
$59$	28488.5	1.06547	0.532734	+	0.846283i	$0.321165\pi$
$60$	49356.2	1.76996
$61$	16222.3	0.558196	0.279098	−	0.960263i	$-0.409965\pi$
$61$	16222.3	0.558196	0.279098	+	0.960263i	$0.409965\pi$
$62$	62044.1	2.04984
$63$	10204.6	0.323926
$64$	−50778.6	−1.54964
$65$	−91697.4	−2.69199
$66$	−14918.4	−0.421563
$67$	54128.0	1.47311	0.736555	−	0.676378i	$-0.236451\pi$
$67$	54128.0	1.47311	0.736555	+	0.676378i	$0.236451\pi$
$68$	86250.6	2.26198
$69$	−4761.00	−0.120386
$70$	−117170.	−2.85806
$71$	42505.6	1.00069	0.500346	−	0.865826i	$-0.333206\pi$
$71$	42505.6	1.00069	0.500346	+	0.865826i	$0.333206\pi$
$72$	−17375.5	−0.395009
$73$	40936.2	0.899084	0.449542	−	0.893259i	$-0.351587\pi$
$73$	40936.2	0.899084	0.449542	+	0.893259i	$0.351587\pi$
$74$	75148.1	1.59529
$75$	61358.1	1.25956
$76$	24637.1	0.489277
$77$	22389.1	0.430337
$78$	77197.9	1.43671
$79$	−24760.6	−0.446369	−0.223185	−	0.974776i	$-0.571645\pi$
$79$	−24760.6	−0.446369	−0.223185	+	0.974776i	$0.571645\pi$
$80$	24018.2	0.419581
$81$	6561.00	0.111111
$82$	−167345.	−2.74839
$83$	−30825.2	−0.491147	−0.245573	−	0.969378i	$-0.578976\pi$
$83$	−30825.2	−0.491147	−0.245573	+	0.969378i	$0.578976\pi$
$84$	62359.7	0.964287
$85$	156373.	2.34755
$86$	−99901.7	−1.45655
$87$	−11688.4	−0.165561
$88$	−38122.1	−0.524772
$89$	−66531.6	−0.890334	−0.445167	−	0.895448i	$-0.646856\pi$
$89$	−66531.6	−0.890334	−0.445167	+	0.895448i	$0.646856\pi$
$90$	−75333.8	−0.980356
$91$	−115856.	−1.46661
$92$	−29094.2	−0.358374
$93$	−59866.9	−0.717761
$94$	166836.	1.94747
$95$	44667.2	0.507784
$96$	41559.3	0.460246
$97$	−104506.	−1.12774	−0.563872	−	0.825862i	$-0.690689\pi$
$97$	−104506.	−1.12774	−0.563872	+	0.825862i	$0.690689\pi$
$98$	8723.75	0.0917568
$99$	14394.9	0.147612
$100$	374956.	3.74956
$101$	−203117.	−1.98127	−0.990635	−	0.136540i	$-0.956402\pi$
$101$	−203117.	−1.98127	−0.990635	+	0.136540i	$0.956402\pi$
$102$	−131647.	−1.25288
$103$	−148132.	−1.37580	−0.687901	−	0.725805i	$-0.741468\pi$
$103$	−148132.	−1.37580	−0.687901	+	0.725805i	$0.741468\pi$
$104$	197270.	1.78845
$105$	113059.	1.00076
$106$	189754.	1.64031
$107$	−43750.9	−0.369426	−0.184713	−	0.982793i	$-0.559136\pi$
$107$	−43750.9	−0.369426	−0.184713	+	0.982793i	$0.559136\pi$
$108$	40093.8	0.330764
$109$	189052.	1.52410	0.762052	−	0.647516i	$-0.224192\pi$
$109$	189052.	1.52410	0.762052	+	0.647516i	$0.224192\pi$
$110$	−165283.	−1.30241
$111$	−72511.2	−0.558596
$112$	30346.1	0.228591
$113$	−82382.3	−0.606929	−0.303465	−	0.952843i	$-0.598143\pi$
$113$	−82382.3	−0.606929	−0.303465	+	0.952843i	$0.598143\pi$
$114$	−37604.3	−0.271003
$115$	−52747.9	−0.371929
$116$	−71427.2	−0.492855
$117$	−74489.1	−0.503069
$118$	−265721.	−1.75679
$119$	197571.	1.27896
$120$	−192506.	−1.22037
$121$	−129468.	−0.803897
$122$	−151310.	−0.920381
$123$	161473.	0.962358
$124$	−365843.	−2.13668
$125$	368195.	2.10767
$126$	−95181.5	−0.534104
$127$	−95322.4	−0.524428	−0.262214	−	0.965010i	$-0.584453\pi$
$127$	−95322.4	−0.524428	−0.262214	+	0.965010i	$0.584453\pi$
$128$	325861.	1.75795
$129$	96396.1	0.510018
$130$	855288.	4.43868
$131$	181975.	0.926474	0.463237	−	0.886234i	$-0.346688\pi$
$131$	181975.	0.926474	0.463237	+	0.886234i	$0.346688\pi$
$132$	87966.4	0.439422
$133$	56435.3	0.276644
$134$	−504868.	−2.42893
$135$	72690.4	0.343275
$136$	−336407.	−1.55962
$137$	175024.	0.796705	0.398352	−	0.917232i	$-0.369582\pi$
$137$	175024.	0.796705	0.398352	+	0.917232i	$0.369582\pi$
$138$	44407.2	0.198498
$139$	199672.	0.876556	0.438278	−	0.898839i	$-0.355588\pi$
$139$	199672.	0.876556	0.438278	+	0.898839i	$0.355588\pi$
$140$	690894.	2.97914
$141$	−160982.	−0.681914
$142$	−396462.	−1.64999
$143$	−163430.	−0.668331
$144$	19510.9	0.0784098
$145$	−129498.	−0.511497
$146$	−381824.	−1.48245
$147$	−8417.64	−0.0321290
$148$	−443111.	−1.66287
$149$	71174.8	0.262640	0.131320	−	0.991340i	$-0.458079\pi$
$149$	71174.8	0.262640	0.131320	+	0.991340i	$0.458079\pi$
$150$	−572305.	−2.07682
$151$	133491.	0.476440	0.238220	−	0.971211i	$-0.423436\pi$
$151$	133491.	0.476440	0.238220	+	0.971211i	$0.423436\pi$
$152$	−96093.1	−0.337352
$153$	127027.	0.438701
$154$	−208829.	−0.709561
$155$	−663276.	−2.21751
$156$	−455198.	−1.49757
$157$	−361773.	−1.17135	−0.585675	−	0.810546i	$-0.699171\pi$
$157$	−361773.	−1.17135	−0.585675	+	0.810546i	$0.699171\pi$
$158$	230950.	0.735995
$159$	−183095.	−0.574360
$160$	460442.	1.42192
$161$	−66645.0	−0.202630
$162$	−61196.4	−0.183205
$163$	−627275.	−1.84922	−0.924611	−	0.380912i	$-0.875610\pi$
$163$	−627275.	−1.84922	−0.924611	+	0.380912i	$0.875610\pi$
$164$	986750.	2.86482
$165$	159484.	0.456043
$166$	287516.	0.809826
$167$	9849.85	0.0273299	0.0136650	−	0.999907i	$-0.495650\pi$
$167$	9849.85	0.0273299	0.0136650	+	0.999907i	$0.495650\pi$
$168$	−243225.	−0.664866
$169$	474405.	1.27771
$170$	−1.45854e6	−3.87075
$171$	36284.7	0.0948929
$172$	589070.	1.51826
$173$	−250617.	−0.636641	−0.318320	−	0.947983i	$-0.603119\pi$
$173$	−250617.	−0.636641	−0.318320	+	0.947983i	$0.603119\pi$
$174$	109021.	0.272985
$175$	858898.	2.12005
$176$	42807.1	0.104168
$177$	256397.	0.615148
$178$	620560.	1.46802
$179$	742331.	1.73167	0.865835	−	0.500330i	$-0.166788\pi$
$179$	742331.	1.73167	0.865835	+	0.500330i	$0.166788\pi$
$180$	444206.	1.02189
$181$	−292957.	−0.664673	−0.332336	−	0.943161i	$-0.607837\pi$
$181$	−292957.	−0.664673	−0.332336	+	0.943161i	$0.607837\pi$
$182$	1.08062e6	2.41822
$183$	146000.	0.322275
$184$	113477.	0.247095
$185$	−803363.	−1.72577
$186$	558397.	1.18348
$187$	278699.	0.582817
$188$	−983751.	−2.02997
$189$	91841.6	0.187019
$190$	−416624.	−0.837259
$191$	57674.2	0.114393	0.0571963	−	0.998363i	$-0.481784\pi$
$191$	57674.2	0.114393	0.0571963	+	0.998363i	$0.481784\pi$
$192$	−457008.	−0.894685
$193$	−178690.	−0.345308	−0.172654	−	0.984983i	$-0.555234\pi$
$193$	−178690.	−0.345308	−0.172654	+	0.984983i	$0.555234\pi$
$194$	974754.	1.85948
$195$	−825276.	−1.55422
$196$	−51439.6	−0.0956439
$197$	−525992.	−0.965636	−0.482818	−	0.875721i	$-0.660387\pi$
$197$	−525992.	−0.965636	−0.482818	+	0.875721i	$0.660387\pi$
$198$	−134266.	−0.243389
$199$	−184283.	−0.329877	−0.164939	−	0.986304i	$-0.552743\pi$
$199$	−184283.	−0.329877	−0.164939	+	0.986304i	$0.552743\pi$
$200$	−1.46246e6	−2.58528
$201$	487152.	0.850500
$202$	1.89453e6	3.26681
$203$	−163616.	−0.278667
$204$	776255.	1.30596
$205$	1.78898e6	2.97318
$206$	1.38167e6	2.26849
$207$	−42849.0	−0.0695048
$208$	−221513.	−0.355010
$209$	79609.1	0.126066
$210$	−1.05453e6	−1.65010
$211$	−313460.	−0.484703	−0.242352	−	0.970188i	$-0.577919\pi$
$211$	−313460.	−0.484703	−0.242352	+	0.970188i	$0.577919\pi$
$212$	−1.11888e6	−1.70980
$213$	382550.	0.577749
$214$	408077.	0.609127
$215$	1.06799e6	1.57569
$216$	−156380.	−0.228059
$217$	−838024.	−1.20811
$218$	−1.76334e6	−2.51302
$219$	368426.	0.519086
$220$	974593.	1.35758
$221$	−1.44218e6	−1.98627
$222$	676333.	0.921039
$223$	−1.00274e6	−1.35028	−0.675141	−	0.737689i	$-0.735917\pi$
$223$	−1.00274e6	−1.35028	−0.675141	+	0.737689i	$0.735917\pi$
$224$	581751.	0.774671
$225$	552223.	0.727208
$226$	768404.	1.00073
$227$	−1.02818e6	−1.32435	−0.662176	−	0.749348i	$-0.730367\pi$
$227$	−1.02818e6	−1.32435	−0.662176	+	0.749348i	$0.730367\pi$
$228$	221734.	0.282484
$229$	−83843.9	−0.105653	−0.0528266	−	0.998604i	$-0.516823\pi$
$229$	−83843.9	−0.105653	−0.0528266	+	0.998604i	$0.516823\pi$
$230$	491995.	0.613255
$231$	201502.	0.248455
$232$	278591.	0.339819
$233$	−241626.	−0.291577	−0.145789	−	0.989316i	$-0.546572\pi$
$233$	−241626.	−0.291577	−0.145789	+	0.989316i	$0.546572\pi$
$234$	694781.	0.829485
$235$	−1.78355e6	−2.10676
$236$	1.56682e6	1.83122
$237$	−222846.	−0.257711
$238$	−1.84281e6	−2.10881
$239$	1.32779e6	1.50361	0.751806	−	0.659384i	$-0.229183\pi$
$239$	1.32779e6	1.50361	0.751806	+	0.659384i	$0.229183\pi$
$240$	216164.	0.242245
$241$	−1.21493e6	−1.34744	−0.673721	−	0.738986i	$-0.735305\pi$
$241$	−1.21493e6	−1.34744	−0.673721	+	0.738986i	$0.735305\pi$
$242$	1.20759e6	1.32550
$243$	59049.0	0.0641500
$244$	892199.	0.959372
$245$	−93260.3	−0.0992617
$246$	−1.50610e6	−1.58678
$247$	−411952.	−0.429639
$248$	1.42691e6	1.47322
$249$	−277427.	−0.283564
$250$	−3.43427e6	−3.47523
$251$	1.21766e6	1.21995	0.609977	−	0.792419i	$-0.291179\pi$
$251$	1.21766e6	1.21995	0.609977	+	0.792419i	$0.291179\pi$
$252$	561238.	0.556731
$253$	−94011.2	−0.0923376
$254$	889100.	0.864702
$255$	1.40736e6	1.35536
$256$	−1.41448e6	−1.34896
$257$	1.21439e6	1.14690	0.573450	−	0.819241i	$-0.305605\pi$
$257$	1.21439e6	1.14690	0.573450	+	0.819241i	$0.305605\pi$
$258$	−899115.	−0.840942
$259$	−1.01502e6	−0.940210
$260$	−5.04321e6	−4.62672
$261$	−105196.	−0.0955867
$262$	−1.69733e6	−1.52761
$263$	93687.8	0.0835206	0.0417603	−	0.999128i	$-0.486703\pi$
$263$	93687.8	0.0835206	0.0417603	+	0.999128i	$0.486703\pi$
$264$	−343099.	−0.302977
$265$	−2.02854e6	−1.77447
$266$	−526388.	−0.456144
$267$	−598784.	−0.514034
$268$	2.97695e6	2.53183
$269$	−323647.	−0.272703	−0.136352	−	0.990660i	$-0.543538\pi$
$269$	−323647.	−0.272703	−0.136352	+	0.990660i	$0.543538\pi$
$270$	−678004.	−0.566009
$271$	1.76235e6	1.45771	0.728853	−	0.684670i	$-0.240054\pi$
$271$	1.76235e6	1.45771	0.728853	+	0.684670i	$0.240054\pi$
$272$	377749.	0.309586
$273$	−1.04271e6	−0.846750
$274$	−1.63250e6	−1.31364
$275$	1.21158e6	0.966100
$276$	−261847.	−0.206907
$277$	−1.83478e6	−1.43676	−0.718381	−	0.695650i	$-0.755117\pi$
$277$	−1.83478e6	−1.43676	−0.718381	+	0.695650i	$0.755117\pi$
$278$	−1.86240e6	−1.44531
$279$	−538803.	−0.414399
$280$	−2.69472e6	−2.05409
$281$	−1.71252e6	−1.29381	−0.646903	−	0.762572i	$-0.723936\pi$
$281$	−1.71252e6	−1.29381	−0.646903	+	0.762572i	$0.723936\pi$
$282$	1.50153e6	1.12437
$283$	1.53094e6	1.13629	0.568147	−	0.822927i	$-0.307660\pi$
$283$	1.53094e6	1.13629	0.568147	+	0.822927i	$0.307660\pi$
$284$	2.33774e6	1.71989
$285$	402004.	0.293169
$286$	1.52436e6	1.10198
$287$	2.26031e6	1.61981
$288$	374034.	0.265723
$289$	1.03951e6	0.732125
$290$	1.20787e6	0.843381
$291$	−940550.	−0.651103
$292$	2.25142e6	1.54526
$293$	−2.02997e6	−1.38140	−0.690701	−	0.723141i	$-0.742698\pi$
$293$	−2.02997e6	−1.38140	−0.690701	+	0.723141i	$0.742698\pi$
$294$	78513.8	0.0529758
$295$	2.84066e6	1.90049
$296$	1.72829e6	1.14653
$297$	129554.	0.0852237
$298$	−663868.	−0.433053
$299$	486478.	0.314692
$300$	3.37460e6	2.16481
$301$	1.34936e6	0.858445
$302$	−1.24511e6	−0.785578
$303$	−1.82806e6	−1.14389
$304$	107902.	0.0669648
$305$	1.61756e6	0.995661
$306$	−1.18482e6	−0.723351
$307$	396907.	0.240349	0.120175	−	0.992753i	$-0.461655\pi$
$307$	396907.	0.240349	0.120175	+	0.992753i	$0.461655\pi$
$308$	1.23136e6	0.739621
$309$	−1.33319e6	−0.794319
$310$	6.18657e6	3.65633
$311$	1.27993e6	0.750385	0.375192	−	0.926947i	$-0.377577\pi$
$311$	1.27993e6	0.750385	0.375192	+	0.926947i	$0.377577\pi$
$312$	1.77543e6	1.03256
$313$	−2.41300e6	−1.39218	−0.696091	−	0.717953i	$-0.745079\pi$
$313$	−2.41300e6	−1.39218	−0.696091	+	0.717953i	$0.745079\pi$
$314$	3.37436e6	1.93138
$315$	1.01753e6	0.577790
$316$	−1.36180e6	−0.767175
$317$	1.03063e6	0.576043	0.288022	−	0.957624i	$-0.407002\pi$
$317$	1.03063e6	0.576043	0.288022	+	0.957624i	$0.407002\pi$
$318$	1.70778e6	0.947032
$319$	−230801.	−0.126988
$320$	−5.06326e6	−2.76411
$321$	−393758.	−0.213288
$322$	621617.	0.334105
$323$	702507.	0.374666
$324$	360844.	0.190967
$325$	−6.26956e6	−3.29252
$326$	5.85078e6	3.04909
$327$	1.70147e6	0.879942
$328$	−3.84867e6	−1.97527
$329$	−2.25345e6	−1.14778
$330$	−1.48755e6	−0.751946
$331$	231656.	0.116218	0.0581089	−	0.998310i	$-0.481493\pi$
$331$	231656.	0.116218	0.0581089	+	0.998310i	$0.481493\pi$
$332$	−1.69534e6	−0.844134
$333$	−652601.	−0.322505
$334$	−91872.4	−0.0450629
$335$	5.39723e6	2.62760
$336$	273115.	0.131977
$337$	−351073.	−0.168393	−0.0841963	−	0.996449i	$-0.526832\pi$
$337$	−351073.	−0.168393	−0.0841963	+	0.996449i	$0.526832\pi$
$338$	−4.42491e6	−2.10675
$339$	−741441.	−0.350411
$340$	8.60026e6	4.03473
$341$	−1.18214e6	−0.550532
$342$	−338438.	−0.156464
$343$	−2.23523e6	−1.02586
$344$	−2.29758e6	−1.04683
$345$	−474731.	−0.214734
$346$	2.33757e6	1.04972
$347$	−550941.	−0.245630	−0.122815	−	0.992430i	$-0.539192\pi$
$347$	−550941.	−0.245630	−0.122815	+	0.992430i	$0.539192\pi$
$348$	−642845.	−0.284550
$349$	−1.30593e6	−0.573928	−0.286964	−	0.957941i	$-0.592646\pi$
$349$	−1.30593e6	−0.573928	−0.286964	+	0.957941i	$0.592646\pi$
$350$	−8.01119e6	−3.49564
$351$	−670402.	−0.290447
$352$	820634.	0.353015
$353$	2.13442e6	0.911682	0.455841	−	0.890061i	$-0.349339\pi$
$353$	2.13442e6	0.911682	0.455841	+	0.890061i	$0.349339\pi$
$354$	−2.39149e6	−1.01429
$355$	4.23834e6	1.78494
$356$	−3.65913e6	−1.53022
$357$	1.77814e6	0.738407
$358$	−6.92394e6	−2.85526
$359$	1.06632e6	0.436670	0.218335	−	0.975874i	$-0.429937\pi$
$359$	1.06632e6	0.436670	0.218335	+	0.975874i	$0.429937\pi$
$360$	−1.73256e6	−0.704582
$361$	−2.27543e6	−0.918958
$362$	2.73250e6	1.09594
$363$	−1.16522e6	−0.464130
$364$	−6.37191e6	−2.52067
$365$	4.08185e6	1.60371
$366$	−1.36179e6	−0.531382
$367$	1.34294e6	0.520464	0.260232	−	0.965546i	$-0.416201\pi$
$367$	1.34294e6	0.520464	0.260232	+	0.965546i	$0.416201\pi$
$368$	−127423.	−0.0490487
$369$	1.45326e6	0.555618
$370$	7.49320e6	2.84553
$371$	−2.56299e6	−0.966744
$372$	−3.29259e6	−1.23362
$373$	3.22658e6	1.20080	0.600400	−	0.799700i	$-0.295008\pi$
$373$	3.22658e6	1.20080	0.600400	+	0.799700i	$0.295008\pi$
$374$	−2.59951e6	−0.960976
$375$	3.31376e6	1.21687
$376$	3.83697e6	1.39965
$377$	1.19432e6	0.432781
$378$	−856633.	−0.308365
$379$	−2.41939e6	−0.865184	−0.432592	−	0.901590i	$-0.642401\pi$
$379$	−2.41939e6	−0.865184	−0.432592	+	0.901590i	$0.642401\pi$
$380$	2.45662e6	0.872729
$381$	−857902.	−0.302779
$382$	−537944.	−0.188616
$383$	1.03280e6	0.359764	0.179882	−	0.983688i	$-0.442428\pi$
$383$	1.03280e6	0.359764	0.179882	+	0.983688i	$0.442428\pi$
$384$	2.93275e6	1.01495
$385$	2.23247e6	0.767597
$386$	1.66669e6	0.569360
$387$	867565.	0.294459
$388$	−5.74764e6	−1.93825
$389$	2.56135e6	0.858212	0.429106	−	0.903254i	$-0.358829\pi$
$389$	2.56135e6	0.858212	0.429106	+	0.903254i	$0.358829\pi$
$390$	7.69759e6	2.56267
$391$	−829598.	−0.274426
$392$	200632.	0.0659456
$393$	1.63777e6	0.534900
$394$	4.90608e6	1.59219
$395$	−2.46894e6	−0.796193
$396$	791697.	0.253700
$397$	−2.07970e6	−0.662255	−0.331128	−	0.943586i	$-0.607429\pi$
$397$	−2.07970e6	−0.662255	−0.331128	+	0.943586i	$0.607429\pi$
$398$	1.71886e6	0.543917
$399$	507918.	0.159721
$400$	1.64218e6	0.513182
$401$	−1.97329e6	−0.612817	−0.306408	−	0.951900i	$-0.599127\pi$
$401$	−1.97329e6	−0.612817	−0.306408	+	0.951900i	$0.599127\pi$
$402$	−4.54381e6	−1.40235
$403$	6.11719e6	1.87624
$404$	−1.11711e7	−3.40521
$405$	654213.	0.198190
$406$	1.52609e6	0.459480
$407$	−1.43181e6	−0.428450
$408$	−3.02766e6	−0.900445
$409$	1.68806e6	0.498975	0.249488	−	0.968378i	$-0.419738\pi$
$409$	1.68806e6	0.498975	0.249488	+	0.968378i	$0.419738\pi$
$410$	−1.66864e7	−4.90233
$411$	1.57522e6	0.459978
$412$	−8.14702e6	−2.36459
$413$	3.58907e6	1.03540
$414$	399665.	0.114603
$415$	−3.07366e6	−0.876064
$416$	−4.24652e6	−1.20309
$417$	1.79705e6	0.506080
$418$	−742538.	−0.207863
$419$	1.72868e6	0.481039	0.240520	−	0.970644i	$-0.422682\pi$
$419$	1.72868e6	0.481039	0.240520	+	0.970644i	$0.422682\pi$
$420$	6.21804e6	1.72001
$421$	932870.	0.256517	0.128258	−	0.991741i	$-0.459061\pi$
$421$	932870.	0.256517	0.128258	+	0.991741i	$0.459061\pi$
$422$	2.92373e6	0.799202
$423$	−1.44884e6	−0.393703
$424$	4.36403e6	1.17889
$425$	1.06916e7	2.87124
$426$	−3.56816e6	−0.952621
$427$	2.04373e6	0.542443
$428$	−2.40623e6	−0.634932
$429$	−1.47087e6	−0.385861
$430$	−9.96144e6	−2.59807
$431$	−7.62939e6	−1.97832	−0.989161	−	0.146838i	$-0.953091\pi$
$431$	−7.62939e6	−1.97832	−0.989161	+	0.146838i	$0.953091\pi$
$432$	175598.	0.0452699
$433$	4.68013e6	1.19960	0.599802	−	0.800148i	$-0.295246\pi$
$433$	4.68013e6	1.19960	0.599802	+	0.800148i	$0.295246\pi$
$434$	7.81650e6	1.99199
$435$	−1.16548e6	−0.295313
$436$	1.03976e7	2.61948
$437$	−236971.	−0.0593596
$438$	−3.43641e6	−0.855895
$439$	1.21981e6	0.302087	0.151043	−	0.988527i	$-0.451737\pi$
$439$	1.21981e6	0.302087	0.151043	+	0.988527i	$0.451737\pi$
$440$	−3.80125e6	−0.936041
$441$	−75758.7	−0.0185497
$442$	1.34516e7	3.27506
$443$	−1.82127e6	−0.440926	−0.220463	−	0.975395i	$-0.570757\pi$
$443$	−1.82127e6	−0.440926	−0.220463	+	0.975395i	$0.570757\pi$
$444$	−3.98800e6	−0.960058
$445$	−6.63403e6	−1.58810
$446$	9.35281e6	2.22641
$447$	640573.	0.151635
$448$	−6.39724e6	−1.50591
$449$	−3.31712e6	−0.776506	−0.388253	−	0.921553i	$-0.626921\pi$
$449$	−3.31712e6	−0.776506	−0.388253	+	0.921553i	$0.626921\pi$
$450$	−5.15075e6	−1.19905
$451$	3.18846e6	0.738142
$452$	−4.53090e6	−1.04313
$453$	1.20142e6	0.275073
$454$	9.59012e6	2.18366
$455$	−1.15523e7	−2.61602
$456$	−864838.	−0.194770
$457$	−2.14897e6	−0.481326	−0.240663	−	0.970609i	$-0.577365\pi$
$457$	−2.14897e6	−0.481326	−0.240663	+	0.970609i	$0.577365\pi$
$458$	782036.	0.174206
$459$	1.14325e6	0.253284
$460$	−2.90105e6	−0.639235
$461$	−6.83686e6	−1.49832	−0.749160	−	0.662389i	$-0.769543\pi$
$461$	−6.83686e6	−1.49832	−0.749160	+	0.662389i	$0.769543\pi$
$462$	−1.87946e6	−0.409665
$463$	3.26293e6	0.707385	0.353692	−	0.935362i	$-0.384926\pi$
$463$	3.26293e6	0.707385	0.353692	+	0.935362i	$0.384926\pi$
$464$	−312828.	−0.0674544
$465$	−5.96948e6	−1.28028
$466$	2.25372e6	0.480767
$467$	−4.30238e6	−0.912886	−0.456443	−	0.889753i	$-0.650877\pi$
$467$	−4.30238e6	−0.912886	−0.456443	+	0.889753i	$0.650877\pi$
$468$	−4.09678e6	−0.864625
$469$	6.81920e6	1.43153
$470$	1.66357e7	3.47373
$471$	−3.25595e6	−0.676279
$472$	−6.11116e6	−1.26261
$473$	1.90345e6	0.391191
$474$	2.07855e6	0.424927
$475$	3.05400e6	0.621061
$476$	1.08661e7	2.19815
$477$	−1.64786e6	−0.331607
$478$	−1.23847e7	−2.47923
$479$	3.15612e6	0.628514	0.314257	−	0.949338i	$-0.398245\pi$
$479$	3.15612e6	0.628514	0.314257	+	0.949338i	$0.398245\pi$
$480$	4.14398e6	0.820946
$481$	7.40918e6	1.46018
$482$	1.13320e7	2.22173
$483$	−599805.	−0.116988
$484$	−7.12055e6	−1.38166
$485$	−1.04205e7	−2.01157
$486$	−550767.	−0.105774
$487$	−1.04981e6	−0.200581	−0.100290	−	0.994958i	$-0.531977\pi$
$487$	−1.04981e6	−0.200581	−0.100290	+	0.994958i	$0.531977\pi$
$488$	−3.47988e6	−0.661478
$489$	−5.64548e6	−1.06765
$490$	869867.	0.163667
$491$	1.67278e6	0.313138	0.156569	−	0.987667i	$-0.449957\pi$
$491$	1.67278e6	0.313138	0.156569	+	0.987667i	$0.449957\pi$
$492$	8.88075e6	1.65401
$493$	−2.03669e6	−0.377406
$494$	3.84240e6	0.708410
$495$	1.43535e6	0.263297
$496$	−1.60227e6	−0.292437
$497$	5.35498e6	0.972449
$498$	2.58765e6	0.467554
$499$	−3.07979e6	−0.553695	−0.276847	−	0.960914i	$-0.589290\pi$
$499$	−3.07979e6	−0.553695	−0.276847	+	0.960914i	$0.589290\pi$
$500$	2.02502e7	3.62246
$501$	88648.7	0.0157789
$502$	−1.13575e7	−2.01152
$503$	4.06934e6	0.717140	0.358570	−	0.933503i	$-0.383264\pi$
$503$	4.06934e6	0.717140	0.358570	+	0.933503i	$0.383264\pi$
$504$	−2.18902e6	−0.383861
$505$	−2.02533e7	−3.53401
$506$	876870.	0.152251
$507$	4.26964e6	0.737686
$508$	−5.24258e6	−0.901334
$509$	5.65269e6	0.967077	0.483538	−	0.875323i	$-0.339351\pi$
$509$	5.65269e6	0.967077	0.483538	+	0.875323i	$0.339351\pi$
$510$	−1.31268e7	−2.23478
$511$	5.15726e6	0.873709
$512$	2.76575e6	0.466271
$513$	326563.	0.0547864
$514$	−1.13270e7	−1.89106
$515$	−1.47706e7	−2.45403
$516$	5.30163e6	0.876568
$517$	−3.17877e6	−0.523038
$518$	9.46738e6	1.55026
$519$	−2.25555e6	−0.367565
$520$	1.96703e7	3.19008
$521$	−729056.	−0.117670	−0.0588351	−	0.998268i	$-0.518739\pi$
$521$	−729056.	−0.117670	−0.0588351	+	0.998268i	$0.518739\pi$
$522$	981193.	0.157608
$523$	5.74086e6	0.917747	0.458873	−	0.888502i	$-0.348253\pi$
$523$	5.74086e6	0.917747	0.458873	+	0.888502i	$0.348253\pi$
$524$	1.00083e7	1.59233
$525$	7.73008e6	1.22401
$526$	−873853.	−0.137713
$527$	−1.04317e7	−1.63618
$528$	385264.	0.0601414
$529$	279841.	0.0434783
$530$	1.89208e7	2.92583
$531$	2.30757e6	0.355156
$532$	3.10385e6	0.475468
$533$	−1.64993e7	−2.51563
$534$	5.58504e6	0.847565
$535$	−4.36250e6	−0.658948
$536$	−1.16111e7	−1.74567
$537$	6.68098e6	0.999780
$538$	3.01875e6	0.449647
$539$	−166216.	−0.0246434
$540$	3.99785e6	0.589987
$541$	1.12666e7	1.65500	0.827500	−	0.561466i	$-0.189762\pi$
$541$	1.12666e7	1.65500	0.827500	+	0.561466i	$0.189762\pi$
$542$	−1.64380e7	−2.40354
$543$	−2.63661e6	−0.383749
$544$	7.24165e6	1.04916
$545$	1.88508e7	2.71856
$546$	9.72562e6	1.39616
$547$	1.92802e6	0.275513	0.137757	−	0.990466i	$-0.456011\pi$
$547$	1.92802e6	0.275513	0.137757	+	0.990466i	$0.456011\pi$
$548$	9.62606e6	1.36930
$549$	1.31400e6	0.186065
$550$	−1.13008e7	−1.59295
$551$	−581772.	−0.0816345
$552$	1.02130e6	0.142660
$553$	−3.11942e6	−0.433771
$554$	1.71135e7	2.36900
$555$	−7.23027e6	−0.996373
$556$	1.09816e7	1.50654
$557$	−1.27385e7	−1.73973	−0.869865	−	0.493290i	$-0.835794\pi$
$557$	−1.27385e7	−1.73973	−0.869865	+	0.493290i	$0.835794\pi$
$558$	5.02557e6	0.683282
$559$	−9.84974e6	−1.33320
$560$	3.02589e6	0.407739
$561$	2.50829e6	0.336489
$562$	1.59732e7	2.13329
$563$	1.30970e7	1.74140	0.870702	−	0.491810i	$-0.163665\pi$
$563$	1.30970e7	1.74140	0.870702	+	0.491810i	$0.163665\pi$
$564$	−8.85376e6	−1.17201
$565$	−8.21454e6	−1.08259
$566$	−1.42795e7	−1.87358
$567$	826574.	0.107975
$568$	−9.11799e6	−1.18585
$569$	1.32454e7	1.71509	0.857543	−	0.514413i	$-0.171990\pi$
$569$	1.32454e7	1.71509	0.857543	+	0.514413i	$0.171990\pi$
$570$	−3.74961e6	−0.483392
$571$	−4.22643e6	−0.542480	−0.271240	−	0.962512i	$-0.587434\pi$
$571$	−4.22643e6	−0.542480	−0.271240	+	0.962512i	$0.587434\pi$
$572$	−8.98838e6	−1.14866
$573$	519068.	0.0660446
$574$	−2.10826e7	−2.67082
$575$	−3.60650e6	−0.454900
$576$	−4.11307e6	−0.516547
$577$	−224943.	−0.0281276	−0.0140638	−	0.999901i	$-0.504477\pi$
$577$	−224943.	−0.0281276	−0.0140638	+	0.999901i	$0.504477\pi$
$578$	−9.69584e6	−1.20716
$579$	−1.60821e6	−0.199364
$580$	−7.12219e6	−0.879110
$581$	−3.88346e6	−0.477285
$582$	8.77279e6	1.07357
$583$	−3.61542e6	−0.440542
$584$	−8.78134e6	−1.06544
$585$	−7.42749e6	−0.897330
$586$	1.89341e7	2.27772
$587$	4.80198e6	0.575209	0.287604	−	0.957749i	$-0.407141\pi$
$587$	4.80198e6	0.575209	0.287604	+	0.957749i	$0.407141\pi$
$588$	−462956.	−0.0552201
$589$	−2.97978e6	−0.353912
$590$	−2.64957e7	−3.13361
$591$	−4.73392e6	−0.557510
$592$	−1.94068e6	−0.227588
$593$	−9.07891e6	−1.06022	−0.530111	−	0.847928i	$-0.677850\pi$
$593$	−9.07891e6	−1.06022	−0.530111	+	0.847928i	$0.677850\pi$
$594$	−1.20839e6	−0.140521
$595$	1.97003e7	2.28129
$596$	3.91450e6	0.451399
$597$	−1.65855e6	−0.190455
$598$	−4.53752e6	−0.518879
$599$	−487665.	−0.0555334	−0.0277667	−	0.999614i	$-0.508840\pi$
$599$	−487665.	−0.0555334	−0.0277667	+	0.999614i	$0.508840\pi$
$600$	−1.31621e7	−1.49261
$601$	−9.72337e6	−1.09807	−0.549036	−	0.835799i	$-0.685005\pi$
$601$	−9.72337e6	−1.09807	−0.549036	+	0.835799i	$0.685005\pi$
$602$	−1.25859e7	−1.41545
$603$	4.38437e6	0.491036
$604$	7.34177e6	0.818858
$605$	−1.29096e7	−1.43392
$606$	1.70508e7	1.88609
$607$	−3.30773e6	−0.364384	−0.182192	−	0.983263i	$-0.558319\pi$
$607$	−3.30773e6	−0.364384	−0.182192	+	0.983263i	$0.558319\pi$
$608$	2.06854e6	0.226937
$609$	−1.47254e6	−0.160888
$610$	−1.50875e7	−1.64169
$611$	1.64491e7	1.78254
$612$	6.98630e6	0.753995
$613$	−234065.	−0.0251585	−0.0125793	−	0.999921i	$-0.504004\pi$
$613$	−234065.	−0.0251585	−0.0125793	+	0.999921i	$0.504004\pi$
$614$	−3.70207e6	−0.396300
$615$	1.61009e7	1.71657
$616$	−4.80274e6	−0.509961
$617$	−9.19095e6	−0.971958	−0.485979	−	0.873970i	$-0.661537\pi$
$617$	−9.19095e6	−0.971958	−0.485979	+	0.873970i	$0.661537\pi$
$618$	1.24350e7	1.30971
$619$	7.15853e6	0.750926	0.375463	−	0.926837i	$-0.377484\pi$
$619$	7.15853e6	0.750926	0.375463	+	0.926837i	$0.377484\pi$
$620$	−3.64791e7	−3.81123
$621$	−385641.	−0.0401286
$622$	−1.19382e7	−1.23727
$623$	−8.38185e6	−0.865206
$624$	−1.99362e6	−0.204965
$625$	1.54088e7	1.57786
$626$	2.25067e7	2.29550
$627$	716482.	0.0727841
$628$	−1.98969e7	−2.01320
$629$	−1.26350e7	−1.27335
$630$	−9.49078e6	−0.952687
$631$	1.00474e7	1.00457	0.502283	−	0.864703i	$-0.332493\pi$
$631$	1.00474e7	1.00457	0.502283	+	0.864703i	$0.332493\pi$
$632$	5.31147e6	0.528960
$633$	−2.82114e6	−0.279844
$634$	−9.61300e6	−0.949808
$635$	−9.50483e6	−0.935427
$636$	−1.00699e7	−0.987152
$637$	860112.	0.0839859
$638$	2.15275e6	0.209383
$639$	3.44295e6	0.333564
$640$	3.24924e7	3.13568
$641$	4.21517e6	0.405201	0.202600	−	0.979262i	$-0.435061\pi$
$641$	4.21517e6	0.405201	0.202600	+	0.979262i	$0.435061\pi$
$642$	3.67269e6	0.351680
$643$	9.48561e6	0.904770	0.452385	−	0.891823i	$-0.350573\pi$
$643$	9.48561e6	0.904770	0.452385	+	0.891823i	$0.350573\pi$
$644$	−3.66537e6	−0.348259
$645$	9.61189e6	0.909724
$646$	−6.55249e6	−0.617768
$647$	2.54033e6	0.238578	0.119289	−	0.992860i	$-0.461939\pi$
$647$	2.54033e6	0.238578	0.119289	+	0.992860i	$0.461939\pi$
$648$	−1.40742e6	−0.131670
$649$	5.06284e6	0.471827
$650$	5.84781e7	5.42887
$651$	−7.54222e6	−0.697504
$652$	−3.44991e7	−3.17826
$653$	9.06671e6	0.832083	0.416042	−	0.909346i	$-0.363417\pi$
$653$	9.06671e6	0.832083	0.416042	+	0.909346i	$0.363417\pi$
$654$	−1.58701e7	−1.45089
$655$	1.81452e7	1.65256
$656$	4.32164e6	0.392093
$657$	3.31583e6	0.299695
$658$	2.10185e7	1.89251
$659$	−1.63938e7	−1.47050	−0.735251	−	0.677795i	$-0.762936\pi$
$659$	−1.63938e7	−1.47050	−0.735251	+	0.677795i	$0.762936\pi$
$660$	8.77134e6	0.783802
$661$	−1.06203e7	−0.945435	−0.472717	−	0.881214i	$-0.656727\pi$
$661$	−1.06203e7	−0.945435	−0.472717	+	0.881214i	$0.656727\pi$
$662$	−2.16072e6	−0.191626
$663$	−1.29796e7	−1.14677
$664$	6.61241e6	0.582022
$665$	5.62730e6	0.493453
$666$	6.08700e6	0.531762
$667$	687020.	0.0597936
$668$	541726.	0.0469719
$669$	−9.02462e6	−0.779586
$670$	−5.03416e7	−4.33251
$671$	2.88294e6	0.247189
$672$	5.23576e6	0.447257
$673$	−1.19056e7	−1.01324	−0.506620	−	0.862169i	$-0.669105\pi$
$673$	−1.19056e7	−1.01324	−0.506620	+	0.862169i	$0.669105\pi$
$674$	3.27456e6	0.277654
$675$	4.97001e6	0.419854
$676$	2.60915e7	2.19600
$677$	2.17878e7	1.82701	0.913507	−	0.406822i	$-0.133363\pi$
$677$	2.17878e7	1.82701	0.913507	+	0.406822i	$0.133363\pi$
$678$	6.91564e6	0.577774
$679$	−1.31659e7	−1.09592
$680$	−3.35440e7	−2.78190
$681$	−9.25360e6	−0.764615
$682$	1.10262e7	0.907744
$683$	8.27503e6	0.678762	0.339381	−	0.940649i	$-0.389782\pi$
$683$	8.27503e6	0.678762	0.339381	+	0.940649i	$0.389782\pi$
$684$	1.99560e6	0.163092
$685$	1.74521e7	1.42109
$686$	2.08486e7	1.69148
$687$	−754595.	−0.0609989
$688$	2.57993e6	0.207796
$689$	1.87086e7	1.50139
$690$	4.42795e6	0.354063
$691$	8.37140e6	0.666965	0.333483	−	0.942756i	$-0.391776\pi$
$691$	8.37140e6	0.666965	0.333483	+	0.942756i	$0.391776\pi$
$692$	−1.37835e7	−1.09419
$693$	1.81351e6	0.143446
$694$	5.13879e6	0.405007
$695$	1.99098e7	1.56352
$696$	2.50732e6	0.196194
$697$	2.81364e7	2.19375
$698$	1.21808e7	0.946320
$699$	−2.17463e6	−0.168342
$700$	4.72380e7	3.64373
$701$	3.01421e6	0.231675	0.115837	−	0.993268i	$-0.463045\pi$
$701$	3.01421e6	0.231675	0.115837	+	0.993268i	$0.463045\pi$
$702$	6.25303e6	0.478903
$703$	−3.60912e6	−0.275431
$704$	−9.02412e6	−0.686236
$705$	−1.60519e7	−1.21634
$706$	−1.99084e7	−1.50323
$707$	−2.55893e7	−1.92535
$708$	1.41014e7	1.05725
$709$	−5.74628e6	−0.429310	−0.214655	−	0.976690i	$-0.568863\pi$
$709$	−5.74628e6	−0.429310	−0.214655	+	0.976690i	$0.568863\pi$
$710$	−3.95322e7	−2.94310
$711$	−2.00561e6	−0.148790
$712$	1.42719e7	1.05507
$713$	3.51885e6	0.259225
$714$	−1.65852e7	−1.21752
$715$	−1.62960e7	−1.19211
$716$	4.08270e7	2.97622
$717$	1.19501e7	0.868111
$718$	−9.94592e6	−0.720002
$719$	−1.64352e7	−1.18564	−0.592821	−	0.805334i	$-0.701986\pi$
$719$	−1.64352e7	−1.18564	−0.592821	+	0.805334i	$0.701986\pi$
$720$	1.94548e6	0.139860
$721$	−1.86621e7	−1.33697
$722$	2.12236e7	1.51522
$723$	−1.09344e7	−0.777945
$724$	−1.61122e7	−1.14237
$725$	−8.85408e6	−0.625603
$726$	1.08683e7	0.765280
$727$	−4.65331e6	−0.326532	−0.163266	−	0.986582i	$-0.552203\pi$
$727$	−4.65331e6	−0.326532	−0.163266	+	0.986582i	$0.552203\pi$
$728$	2.48526e7	1.73798
$729$	531441.	0.0370370
$730$	−3.80726e7	−2.64427
$731$	1.67969e7	1.16261
$732$	8.02979e6	0.553894
$733$	1.76748e7	1.21505	0.607527	−	0.794299i	$-0.292162\pi$
$733$	1.76748e7	1.21505	0.607527	+	0.794299i	$0.292162\pi$
$734$	−1.25260e7	−0.858166
$735$	−839343.	−0.0573088
$736$	−2.44276e6	−0.166221
$737$	9.61936e6	0.652345
$738$	−1.35549e7	−0.916129
$739$	2.32944e7	1.56907	0.784533	−	0.620087i	$-0.212903\pi$
$739$	2.32944e7	1.56907	0.784533	+	0.620087i	$0.212903\pi$
$740$	−4.41837e7	−2.96608
$741$	−3.70757e6	−0.248052
$742$	2.39057e7	1.59401
$743$	1.77107e7	1.17696	0.588482	−	0.808511i	$-0.299726\pi$
$743$	1.77107e7	1.17696	0.588482	+	0.808511i	$0.299726\pi$
$744$	1.28422e7	0.850566
$745$	7.09701e6	0.468473
$746$	−3.00953e7	−1.97994
$747$	−2.49685e6	−0.163716
$748$	1.53280e7	1.00169
$749$	−5.51186e6	−0.358999
$750$	−3.09084e7	−2.00643
$751$	−9.59704e6	−0.620922	−0.310461	−	0.950586i	$-0.600483\pi$
$751$	−9.59704e6	−0.620922	−0.310461	+	0.950586i	$0.600483\pi$
$752$	−4.30851e6	−0.277832
$753$	1.09590e7	0.704340
$754$	−1.11398e7	−0.713590
$755$	1.33107e7	0.849832
$756$	5.05114e6	0.321429
$757$	1.81520e7	1.15129	0.575645	−	0.817700i	$-0.304751\pi$
$757$	1.81520e7	1.15129	0.575645	+	0.817700i	$0.304751\pi$
$758$	2.25664e7	1.42656
$759$	−846101.	−0.0533111
$760$	−9.58167e6	−0.601738
$761$	2.18570e7	1.36813	0.684067	−	0.729419i	$-0.260210\pi$
$761$	2.18570e7	1.36813	0.684067	+	0.729419i	$0.260210\pi$
$762$	8.00190e6	0.499236
$763$	2.38173e7	1.48109
$764$	3.17199e6	0.196607
$765$	1.26662e7	0.782515
$766$	−9.63319e6	−0.593196
$767$	−2.61986e7	−1.60801
$768$	−1.27303e7	−0.778820
$769$	−3.01818e6	−0.184047	−0.0920237	−	0.995757i	$-0.529334\pi$
$769$	−3.01818e6	−0.184047	−0.0920237	+	0.995757i	$0.529334\pi$
$770$	−2.08229e7	−1.26565
$771$	1.09295e7	0.662163
$772$	−9.82765e6	−0.593480
$773$	7.09462e6	0.427052	0.213526	−	0.976937i	$-0.431505\pi$
$773$	7.09462e6	0.427052	0.213526	+	0.976937i	$0.431505\pi$
$774$	−8.09204e6	−0.485518
$775$	−4.53497e7	−2.71219
$776$	2.24178e7	1.33641
$777$	−9.13517e6	−0.542830
$778$	−2.38904e7	−1.41506
$779$	8.03704e6	0.474518
$780$	−4.53889e7	−2.67124
$781$	7.55388e6	0.443142
$782$	7.73790e6	0.452487
$783$	−946763.	−0.0551870
$784$	−225289.	−0.0130903
$785$	−3.60732e7	−2.08935
$786$	−1.52760e7	−0.881969
$787$	2.85125e7	1.64096	0.820482	−	0.571672i	$-0.193705\pi$
$787$	2.85125e7	1.64096	0.820482	+	0.571672i	$0.193705\pi$
$788$	−2.89287e7	−1.65964
$789$	843190.	0.0482206
$790$	2.30286e7	1.31280
$791$	−1.03788e7	−0.589800
$792$	−3.08789e6	−0.174924
$793$	−1.49183e7	−0.842435
$794$	1.93980e7	1.09196
$795$	−1.82569e7	−1.02449
$796$	−1.01353e7	−0.566960
$797$	7.59475e6	0.423514	0.211757	−	0.977322i	$-0.432081\pi$
$797$	7.59475e6	0.423514	0.211757	+	0.977322i	$0.432081\pi$
$798$	−4.73750e6	−0.263355
$799$	−2.80509e7	−1.55446
$800$	3.14815e7	1.73912
$801$	−5.38906e6	−0.296778
$802$	1.84055e7	1.01044
$803$	7.27497e6	0.398146
$804$	2.67926e7	1.46175
$805$	−6.64533e6	−0.361432
$806$	−5.70568e7	−3.09364
$807$	−2.91282e6	−0.157445
$808$	4.35713e7	2.34786
$809$	135394.	0.00727324	0.00363662	−	0.999993i	$-0.498842\pi$
$809$	135394.	0.00727324	0.00363662	+	0.999993i	$0.498842\pi$
$810$	−6.10204e6	−0.326785
$811$	−2.84394e7	−1.51834	−0.759168	−	0.650895i	$-0.774394\pi$
$811$	−2.84394e7	−1.51834	−0.759168	+	0.650895i	$0.774394\pi$
$812$	−8.99862e6	−0.478945
$813$	1.58612e7	0.841607
$814$	1.33549e7	0.706449
$815$	−6.25471e7	−3.29848
$816$	3.39974e6	0.178740
$817$	4.79795e6	0.251479
$818$	−1.57450e7	−0.822735
$819$	−9.38435e6	−0.488871
$820$	9.83913e7	5.11001
$821$	−9.25492e6	−0.479198	−0.239599	−	0.970872i	$-0.577016\pi$
$821$	−9.25492e6	−0.479198	−0.239599	+	0.970872i	$0.577016\pi$
$822$	−1.46925e7	−0.758433
$823$	8.81289e6	0.453543	0.226772	−	0.973948i	$-0.427183\pi$
$823$	8.81289e6	0.453543	0.226772	+	0.973948i	$0.427183\pi$
$824$	3.17762e7	1.63036
$825$	1.09043e7	0.557778
$826$	−3.34763e7	−1.70721
$827$	2.40557e7	1.22308	0.611539	−	0.791214i	$-0.290551\pi$
$827$	2.40557e7	1.22308	0.611539	+	0.791214i	$0.290551\pi$
$828$	−2.35663e6	−0.119458
$829$	3.34899e7	1.69249	0.846247	−	0.532791i	$-0.178857\pi$
$829$	3.34899e7	1.69249	0.846247	+	0.532791i	$0.178857\pi$
$830$	2.86689e7	1.44450
$831$	−1.65130e7	−0.829515
$832$	4.66969e7	2.33873
$833$	−1.46676e6	−0.0732398
$834$	−1.67616e7	−0.834449
$835$	982153.	0.0487487
$836$	4.37838e6	0.216669
$837$	−4.84922e6	−0.239254
$838$	−1.61239e7	−0.793160
$839$	6.66922e6	0.327092	0.163546	−	0.986536i	$-0.447707\pi$
$839$	6.66922e6	0.327092	0.163546	+	0.986536i	$0.447707\pi$
$840$	−2.42525e7	−1.18593
$841$	−1.88245e7	−0.917769
$842$	−8.70115e6	−0.422957
$843$	−1.54127e7	−0.746979
$844$	−1.72398e7	−0.833060
$845$	4.73040e7	2.27906
$846$	1.35137e7	0.649157
$847$	−1.63108e7	−0.781209
$848$	−4.90034e6	−0.234011
$849$	1.37784e7	0.656040
$850$	−9.97235e7	−4.73424
$851$	4.26205e6	0.201741
$852$	2.10397e7	0.992978
$853$	2.91274e6	0.137066	0.0685330	−	0.997649i	$-0.478168\pi$
$853$	2.91274e6	0.137066	0.0685330	+	0.997649i	$0.478168\pi$
$854$	−1.90625e7	−0.894405
$855$	3.61804e6	0.169261
$856$	9.38512e6	0.437779
$857$	1.52102e7	0.707429	0.353715	−	0.935353i	$-0.384918\pi$
$857$	1.52102e7	0.707429	0.353715	+	0.935353i	$0.384918\pi$
$858$	1.37192e7	0.636226
$859$	1.06621e7	0.493016	0.246508	−	0.969141i	$-0.420717\pi$
$859$	1.06621e7	0.493016	0.246508	+	0.969141i	$0.420717\pi$
$860$	5.87376e7	2.70814
$861$	2.03428e7	0.935198
$862$	7.11616e7	3.26195
$863$	−3.79585e7	−1.73493	−0.867465	−	0.497498i	$-0.834252\pi$
$863$	−3.79585e7	−1.73493	−0.867465	+	0.497498i	$0.834252\pi$
$864$	3.36630e6	0.153415
$865$	−2.49896e7	−1.13558
$866$	−4.36529e7	−1.97796
$867$	9.35562e6	0.422693
$868$	−4.60900e7	−2.07638
$869$	−4.40034e6	−0.197668
$870$	1.08708e7	0.486926
$871$	−4.97771e7	−2.22323
$872$	−4.05540e7	−1.80610
$873$	−8.46495e6	−0.375914
$874$	2.21029e6	0.0978750
$875$	4.63863e7	2.04819
$876$	2.02628e7	0.892154
$877$	2.72329e7	1.19562	0.597812	−	0.801636i	$-0.296037\pi$
$877$	2.72329e7	1.19562	0.597812	+	0.801636i	$0.296037\pi$
$878$	−1.13775e7	−0.498095
$879$	−1.82697e7	−0.797553
$880$	4.26840e6	0.185805
$881$	8.49018e6	0.368534	0.184267	−	0.982876i	$-0.441009\pi$
$881$	8.49018e6	0.368534	0.184267	+	0.982876i	$0.441009\pi$
$882$	706624.	0.0305856
$883$	−2.58940e7	−1.11763	−0.558815	−	0.829292i	$-0.688744\pi$
$883$	−2.58940e7	−1.11763	−0.558815	+	0.829292i	$0.688744\pi$
$884$	−7.93176e7	−3.41381
$885$	2.55660e7	1.09725
$886$	1.69875e7	0.727020
$887$	−1.57892e7	−0.673832	−0.336916	−	0.941535i	$-0.609384\pi$
$887$	−1.57892e7	−0.673832	−0.336916	+	0.941535i	$0.609384\pi$
$888$	1.55546e7	0.661951
$889$	−1.20090e7	−0.509627
$890$	6.18775e7	2.61853
$891$	1.16599e6	0.0492039
$892$	−5.51489e7	−2.32073
$893$	−8.01261e6	−0.336237
$894$	−5.97481e6	−0.250023
$895$	7.40196e7	3.08880
$896$	4.10529e7	1.70834
$897$	4.37830e6	0.181687
$898$	3.09397e7	1.28034
$899$	8.63890e6	0.356500
$900$	3.03714e7	1.24985
$901$	−3.19041e7	−1.30929
$902$	−2.97397e7	−1.21708
$903$	1.21443e7	0.495624
$904$	1.76721e7	0.719227
$905$	−2.92115e7	−1.18558
$906$	−1.12060e7	−0.453554
$907$	−1.12308e7	−0.453305	−0.226653	−	0.973976i	$-0.572778\pi$
$907$	−1.12308e7	−0.453305	−0.226653	+	0.973976i	$0.572778\pi$
$908$	−5.65481e7	−2.27616
$909$	−1.64525e7	−0.660423
$910$	1.07752e8	4.31341
$911$	2.61794e7	1.04511	0.522557	−	0.852604i	$-0.324978\pi$
$911$	2.61794e7	1.04511	0.522557	+	0.852604i	$0.324978\pi$
$912$	971120.	0.0386621
$913$	−5.47811e6	−0.217497
$914$	2.00441e7	0.793634
$915$	1.45581e7	0.574845
$916$	−4.61128e6	−0.181586
$917$	2.29257e7	0.900326
$918$	−1.06634e7	−0.417627
$919$	4.07119e7	1.59013	0.795065	−	0.606524i	$-0.207437\pi$
$919$	4.07119e7	1.59013	0.795065	+	0.606524i	$0.207437\pi$
$920$	1.13151e7	0.440746
$921$	3.57217e6	0.138766
$922$	6.37694e7	2.47050
$923$	−3.90889e7	−1.51025
$924$	1.10823e7	0.427020
$925$	−5.49278e7	−2.11075
$926$	−3.04343e7	−1.16637
$927$	−1.19987e7	−0.458600
$928$	−5.99707e6	−0.228596
$929$	8.89152e6	0.338015	0.169008	−	0.985615i	$-0.445944\pi$
$929$	8.89152e6	0.338015	0.169008	+	0.985615i	$0.445944\pi$
$930$	5.56791e7	2.11098
$931$	−418973.	−0.0158421
$932$	−1.32890e7	−0.501134
$933$	1.15193e7	0.433235
$934$	4.01296e7	1.50521
$935$	2.77898e7	1.03958
$936$	1.59789e7	0.596151
$937$	4.07318e6	0.151560	0.0757799	−	0.997125i	$-0.475855\pi$
$937$	4.07318e6	0.151560	0.0757799	+	0.997125i	$0.475855\pi$
$938$	−6.36047e7	−2.36038
$939$	−2.17170e7	−0.803777
$940$	−9.80922e7	−3.62089
$941$	−1.08008e7	−0.397634	−0.198817	−	0.980037i	$-0.563710\pi$
$941$	−1.08008e7	−0.397634	−0.198817	+	0.980037i	$0.563710\pi$
$942$	3.03692e7	1.11508
$943$	−9.49102e6	−0.347563
$944$	6.86218e6	0.250629
$945$	9.15775e6	0.333587
$946$	−1.77540e7	−0.645014
$947$	6.93307e6	0.251218	0.125609	−	0.992080i	$-0.459912\pi$
$947$	6.93307e6	0.251218	0.125609	+	0.992080i	$0.459912\pi$
$948$	−1.22562e7	−0.442929
$949$	−3.76457e7	−1.35690
$950$	−2.84855e7	−1.02404
$951$	9.27568e6	0.332579
$952$	−4.23816e7	−1.51560
$953$	3.81395e7	1.36033	0.680163	−	0.733060i	$-0.261909\pi$
$953$	3.81395e7	1.36033	0.680163	+	0.733060i	$0.261909\pi$
$954$	1.53700e7	0.546769
$955$	5.75084e6	0.204043
$956$	7.30265e7	2.58426
$957$	−2.07721e6	−0.0733163
$958$	−2.94381e7	−1.03632
$959$	2.20501e7	0.774219
$960$	−4.55693e7	−1.59586
$961$	1.56184e7	0.545542
$962$	−6.91076e7	−2.40762
$963$	−3.54382e6	−0.123142
$964$	−6.68194e7	−2.31585
$965$	−1.78176e7	−0.615929
$966$	5.59456e6	0.192896
$967$	1.52545e6	0.0524603	0.0262302	−	0.999656i	$-0.491650\pi$
$967$	1.52545e6	0.0524603	0.0262302	+	0.999656i	$0.491650\pi$
$968$	2.77726e7	0.952639
$969$	6.32257e6	0.216314
$970$	9.71951e7	3.31677
$971$	−4.37167e7	−1.48799	−0.743993	−	0.668187i	$-0.767071\pi$
$971$	−4.37167e7	−1.48799	−0.743993	+	0.668187i	$0.767071\pi$
$972$	3.24760e6	0.110255
$973$	2.51553e7	0.851817
$974$	9.79190e6	0.330727
$975$	−5.64261e7	−1.90094
$976$	3.90754e6	0.131304
$977$	1.59223e6	0.0533666	0.0266833	−	0.999644i	$-0.491505\pi$
$977$	1.59223e6	0.0533666	0.0266833	+	0.999644i	$0.491505\pi$
$978$	5.26570e7	1.76039
$979$	−1.18237e7	−0.394271
$980$	−5.12917e6	−0.170601
$981$	1.53132e7	0.508035
$982$	−1.56025e7	−0.516316
$983$	1.98366e7	0.654762	0.327381	−	0.944892i	$-0.393834\pi$
$983$	1.98366e7	0.654762	0.327381	+	0.944892i	$0.393834\pi$
$984$	−3.46380e7	−1.14042
$985$	−5.24479e7	−1.72241
$986$	1.89968e7	0.622285
$987$	−2.02810e7	−0.662669
$988$	−2.26567e7	−0.738421
$989$	−5.66595e6	−0.184197
$990$	−1.33879e7	−0.434136
$991$	5.77793e7	1.86891	0.934454	−	0.356083i	$-0.115888\pi$
$991$	5.77793e7	1.86891	0.934454	+	0.356083i	$0.115888\pi$
$992$	−3.07164e7	−0.991040
$993$	2.08490e6	0.0670984
$994$	−4.99475e7	−1.60342
$995$	−1.83753e7	−0.588405
$996$	−1.52581e7	−0.487361
$997$	−2.48258e7	−0.790980	−0.395490	−	0.918470i	$-0.629425\pi$
$997$	−2.48258e7	−0.790980	−0.395490	+	0.918470i	$0.629425\pi$
$998$	2.87261e7	0.912958
$999$	−5.87341e6	−0.186199

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.6.a.e.1.1	✓	5
3.2	odd	2		207.6.a.f.1.5		5
4.3	odd	2		1104.6.a.r.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.6.a.e.1.1	✓	5	1.1	even	1	trivial
207.6.a.f.1.5		5	3.2	odd	2
1104.6.a.r.1.5		5	4.3	odd	2

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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	69.a (trivial)

\(f(q)\)	\(=\)	\(q-9.32729 q^{2} +9.00000 q^{3} +54.9984 q^{4} +99.7124 q^{5} -83.9456 q^{6} +125.983 q^{7} -214.513 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-9.32729 q^{2} +9.00000 q^{3} +54.9984 q^{4} +99.7124 q^{5} -83.9456 q^{6} +125.983 q^{7} -214.513 q^{8} +81.0000 q^{9} -930.047 q^{10} +177.715 q^{11} +494.986 q^{12} -919.618 q^{13} -1175.08 q^{14} +897.412 q^{15} +240.875 q^{16} +1568.24 q^{17} -755.511 q^{18} +447.960 q^{19} +5484.02 q^{20} +1133.85 q^{21} -1657.60 q^{22} -529.000 q^{23} -1930.62 q^{24} +6817.57 q^{25} +8577.55 q^{26} +729.000 q^{27} +6928.86 q^{28} -1298.72 q^{29} -8370.42 q^{30} -6651.88 q^{31} +4617.70 q^{32} +1599.43 q^{33} -14627.4 q^{34} +12562.1 q^{35} +4454.87 q^{36} -8056.80 q^{37} -4178.25 q^{38} -8276.56 q^{39} -21389.6 q^{40} +17941.4 q^{41} -10575.7 q^{42} +10710.7 q^{43} +9774.04 q^{44} +8076.71 q^{45} +4934.14 q^{46} -17886.9 q^{47} +2167.87 q^{48} -935.293 q^{49} -63589.5 q^{50} +14114.1 q^{51} -50577.5 q^{52} -20343.9 q^{53} -6799.60 q^{54} +17720.4 q^{55} -27025.0 q^{56} +4031.64 q^{57} +12113.5 q^{58} +28488.5 q^{59} +49356.2 q^{60} +16222.3 q^{61} +62044.1 q^{62} +10204.6 q^{63} -50778.6 q^{64} -91697.4 q^{65} -14918.4 q^{66} +54128.0 q^{67} +86250.6 q^{68} -4761.00 q^{69} -117170. q^{70} +42505.6 q^{71} -17375.5 q^{72} +40936.2 q^{73} +75148.1 q^{74} +61358.1 q^{75} +24637.1 q^{76} +22389.1 q^{77} +77197.9 q^{78} -24760.6 q^{79} +24018.2 q^{80} +6561.00 q^{81} -167345. q^{82} -30825.2 q^{83} +62359.7 q^{84} +156373. q^{85} -99901.7 q^{86} -11688.4 q^{87} -38122.1 q^{88} -66531.6 q^{89} -75333.8 q^{90} -115856. q^{91} -29094.2 q^{92} -59866.9 q^{93} +166836. q^{94} +44667.2 q^{95} +41559.3 q^{96} -104506. q^{97} +8723.75 q^{98} +14394.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 8 q^{2} + 45 q^{3} + 118 q^{4} + 94 q^{5} + 72 q^{6} + 272 q^{7} + 258 q^{8} + 405 q^{9}+O(q^{10}) \) 5 * q + 8 * q^2 + 45 * q^3 + 118 * q^4 + 94 * q^5 + 72 * q^6 + 272 * q^7 + 258 * q^8 + 405 * q^9	\( 5 q + 8 q^{2} + 45 q^{3} + 118 q^{4} + 94 q^{5} + 72 q^{6} + 272 q^{7} + 258 q^{8} + 405 q^{9} - 172 q^{10} + 1100 q^{11} + 1062 q^{12} - 978 q^{13} - 344 q^{14} + 846 q^{15} + 1218 q^{16} + 2522 q^{17} + 648 q^{18} + 2060 q^{19} + 7720 q^{20} + 2448 q^{21} - 2572 q^{22} - 2645 q^{23} + 2322 q^{24} + 12035 q^{25} + 9280 q^{26} + 3645 q^{27} + 8072 q^{28} + 1526 q^{29} - 1548 q^{30} - 7392 q^{31} - 5086 q^{32} + 9900 q^{33} - 15608 q^{34} + 6056 q^{35} + 9558 q^{36} - 8210 q^{37} - 14276 q^{38} - 8802 q^{39} - 37472 q^{40} + 21250 q^{41} - 3096 q^{42} - 4548 q^{43} - 4260 q^{44} + 7614 q^{45} - 4232 q^{46} + 536 q^{47} + 10962 q^{48} - 27979 q^{49} - 81872 q^{50} + 22698 q^{51} - 76380 q^{52} - 11482 q^{53} + 5832 q^{54} - 77064 q^{55} - 28624 q^{56} + 18540 q^{57} - 79680 q^{58} + 74676 q^{59} + 69480 q^{60} - 44618 q^{61} + 64880 q^{62} + 22032 q^{63} - 137382 q^{64} - 24388 q^{65} - 23148 q^{66} - 1412 q^{67} + 80196 q^{68} - 23805 q^{69} - 222304 q^{70} + 37912 q^{71} + 20898 q^{72} + 46546 q^{73} + 111604 q^{74} + 108315 q^{75} - 79548 q^{76} + 157008 q^{77} + 83520 q^{78} + 50544 q^{79} + 69424 q^{80} + 32805 q^{81} - 233720 q^{82} + 89588 q^{83} + 72648 q^{84} + 147892 q^{85} + 77428 q^{86} + 13734 q^{87} + 54484 q^{88} + 280410 q^{89} - 13932 q^{90} - 27416 q^{91} - 62422 q^{92} - 66528 q^{93} + 113632 q^{94} + 203120 q^{95} - 45774 q^{96} + 90074 q^{97} + 32976 q^{98} + 89100 q^{99}+O(q^{100}) \) 5 * q + 8 * q^2 + 45 * q^3 + 118 * q^4 + 94 * q^5 + 72 * q^6 + 272 * q^7 + 258 * q^8 + 405 * q^9 - 172 * q^10 + 1100 * q^11 + 1062 * q^12 - 978 * q^13 - 344 * q^14 + 846 * q^15 + 1218 * q^16 + 2522 * q^17 + 648 * q^18 + 2060 * q^19 + 7720 * q^20 + 2448 * q^21 - 2572 * q^22 - 2645 * q^23 + 2322 * q^24 + 12035 * q^25 + 9280 * q^26 + 3645 * q^27 + 8072 * q^28 + 1526 * q^29 - 1548 * q^30 - 7392 * q^31 - 5086 * q^32 + 9900 * q^33 - 15608 * q^34 + 6056 * q^35 + 9558 * q^36 - 8210 * q^37 - 14276 * q^38 - 8802 * q^39 - 37472 * q^40 + 21250 * q^41 - 3096 * q^42 - 4548 * q^43 - 4260 * q^44 + 7614 * q^45 - 4232 * q^46 + 536 * q^47 + 10962 * q^48 - 27979 * q^49 - 81872 * q^50 + 22698 * q^51 - 76380 * q^52 - 11482 * q^53 + 5832 * q^54 - 77064 * q^55 - 28624 * q^56 + 18540 * q^57 - 79680 * q^58 + 74676 * q^59 + 69480 * q^60 - 44618 * q^61 + 64880 * q^62 + 22032 * q^63 - 137382 * q^64 - 24388 * q^65 - 23148 * q^66 - 1412 * q^67 + 80196 * q^68 - 23805 * q^69 - 222304 * q^70 + 37912 * q^71 + 20898 * q^72 + 46546 * q^73 + 111604 * q^74 + 108315 * q^75 - 79548 * q^76 + 157008 * q^77 + 83520 * q^78 + 50544 * q^79 + 69424 * q^80 + 32805 * q^81 - 233720 * q^82 + 89588 * q^83 + 72648 * q^84 + 147892 * q^85 + 77428 * q^86 + 13734 * q^87 + 54484 * q^88 + 280410 * q^89 - 13932 * q^90 - 27416 * q^91 - 62422 * q^92 - 66528 * q^93 + 113632 * q^94 + 203120 * q^95 - 45774 * q^96 + 90074 * q^97 + 32976 * q^98 + 89100 * q^99

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