LMFDB - Embedded newform 983.6.a.a.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,6,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, 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("983.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	983.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:	$157.657294876$
Analytic rank:	$1$
Dimension:	$191$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.78124 q^{2} +27.6828 q^{3} +63.6727 q^{4} +21.4120 q^{5} -270.772 q^{6} +51.6520 q^{7} -309.799 q^{8} +523.335 q^{9} +O(q^{10})$	\(q-9.78124 q^{2} +27.6828 q^{3} +63.6727 q^{4} +21.4120 q^{5} -270.772 q^{6} +51.6520 q^{7} -309.799 q^{8} +523.335 q^{9} -209.436 q^{10} -270.376 q^{11} +1762.64 q^{12} +90.5053 q^{13} -505.221 q^{14} +592.744 q^{15} +992.690 q^{16} -374.150 q^{17} -5118.87 q^{18} +1146.98 q^{19} +1363.36 q^{20} +1429.87 q^{21} +2644.61 q^{22} -2259.44 q^{23} -8576.09 q^{24} -2666.52 q^{25} -885.254 q^{26} +7760.45 q^{27} +3288.82 q^{28} -4390.69 q^{29} -5797.77 q^{30} -7896.91 q^{31} +203.818 q^{32} -7484.76 q^{33} +3659.65 q^{34} +1105.97 q^{35} +33322.2 q^{36} -2348.90 q^{37} -11218.9 q^{38} +2505.44 q^{39} -6633.42 q^{40} +4049.03 q^{41} -13985.9 q^{42} -10048.1 q^{43} -17215.6 q^{44} +11205.7 q^{45} +22100.1 q^{46} +12445.9 q^{47} +27480.4 q^{48} -14139.1 q^{49} +26081.9 q^{50} -10357.5 q^{51} +5762.72 q^{52} -9160.77 q^{53} -75906.9 q^{54} -5789.30 q^{55} -16001.7 q^{56} +31751.6 q^{57} +42946.4 q^{58} +41780.9 q^{59} +37741.6 q^{60} -10875.7 q^{61} +77241.6 q^{62} +27031.3 q^{63} -33759.7 q^{64} +1937.90 q^{65} +73210.2 q^{66} -24213.1 q^{67} -23823.1 q^{68} -62547.4 q^{69} -10817.8 q^{70} -33238.1 q^{71} -162129. q^{72} -7020.09 q^{73} +22975.2 q^{74} -73816.8 q^{75} +73031.5 q^{76} -13965.5 q^{77} -24506.3 q^{78} -25511.9 q^{79} +21255.5 q^{80} +87660.3 q^{81} -39604.6 q^{82} -75662.7 q^{83} +91043.7 q^{84} -8011.30 q^{85} +98283.2 q^{86} -121546. q^{87} +83762.2 q^{88} -31639.6 q^{89} -109605. q^{90} +4674.78 q^{91} -143864. q^{92} -218608. q^{93} -121737. q^{94} +24559.2 q^{95} +5642.25 q^{96} -6821.02 q^{97} +138298. q^{98} -141497. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 191 q - 37 q^{2} - 74 q^{3} + 2821 q^{4} - 247 q^{5} - 335 q^{6} - 1569 q^{7} - 1761 q^{8} + 13251 q^{9}+O(q^{10}) $ 191 * q - 37 * q^2 - 74 * q^3 + 2821 * q^4 - 247 * q^5 - 335 * q^6 - 1569 * q^7 - 1761 * q^8 + 13251 * q^9	\( 191 q - 37 q^{2} - 74 q^{3} + 2821 q^{4} - 247 q^{5} - 335 q^{6} - 1569 q^{7} - 1761 q^{8} + 13251 q^{9} - 2867 q^{10} - 1878 q^{11} - 3400 q^{12} - 6854 q^{13} - 1601 q^{14} - 3461 q^{15} + 38457 q^{16} - 10730 q^{17} - 17249 q^{18} - 5817 q^{19} - 9988 q^{20} - 15999 q^{21} - 20287 q^{22} - 15625 q^{23} - 19747 q^{24} + 67082 q^{25} - 9868 q^{26} - 22892 q^{27} - 72720 q^{28} - 17960 q^{29} - 27464 q^{30} - 25604 q^{31} - 68869 q^{32} - 60654 q^{33} - 42876 q^{34} - 30018 q^{35} + 172922 q^{36} - 114862 q^{37} + 4404 q^{38} - 73500 q^{39} - 137154 q^{40} - 90896 q^{41} - 10652 q^{42} - 121447 q^{43} - 57962 q^{44} - 109019 q^{45} - 136262 q^{46} - 86994 q^{47} - 133347 q^{48} + 278242 q^{49} - 93911 q^{50} - 66966 q^{51} - 284241 q^{52} - 122112 q^{53} - 130806 q^{54} - 134904 q^{55} - 100292 q^{56} - 423426 q^{57} - 307669 q^{58} - 85704 q^{59} - 238277 q^{60} - 206736 q^{61} - 190602 q^{62} - 387623 q^{63} + 411903 q^{64} - 244408 q^{65} - 113963 q^{66} - 337002 q^{67} - 388031 q^{68} - 165342 q^{69} - 183925 q^{70} - 174806 q^{71} - 753621 q^{72} - 1009738 q^{73} - 204958 q^{74} - 282676 q^{75} - 326869 q^{76} - 332288 q^{77} - 591801 q^{78} - 488092 q^{79} - 259068 q^{80} + 385959 q^{81} - 523996 q^{82} - 315720 q^{83} - 750486 q^{84} - 1001755 q^{85} - 287709 q^{86} - 316995 q^{87} - 836923 q^{88} - 298065 q^{89} - 751039 q^{90} - 521459 q^{91} - 640932 q^{92} - 554391 q^{93} - 623481 q^{94} - 491883 q^{95} - 767843 q^{96} - 1468693 q^{97} - 714146 q^{98} - 842507 q^{99}+O(q^{100}) \) 191 * q - 37 * q^2 - 74 * q^3 + 2821 * q^4 - 247 * q^5 - 335 * q^6 - 1569 * q^7 - 1761 * q^8 + 13251 * q^9 - 2867 * q^10 - 1878 * q^11 - 3400 * q^12 - 6854 * q^13 - 1601 * q^14 - 3461 * q^15 + 38457 * q^16 - 10730 * q^17 - 17249 * q^18 - 5817 * q^19 - 9988 * q^20 - 15999 * q^21 - 20287 * q^22 - 15625 * q^23 - 19747 * q^24 + 67082 * q^25 - 9868 * q^26 - 22892 * q^27 - 72720 * q^28 - 17960 * q^29 - 27464 * q^30 - 25604 * q^31 - 68869 * q^32 - 60654 * q^33 - 42876 * q^34 - 30018 * q^35 + 172922 * q^36 - 114862 * q^37 + 4404 * q^38 - 73500 * q^39 - 137154 * q^40 - 90896 * q^41 - 10652 * q^42 - 121447 * q^43 - 57962 * q^44 - 109019 * q^45 - 136262 * q^46 - 86994 * q^47 - 133347 * q^48 + 278242 * q^49 - 93911 * q^50 - 66966 * q^51 - 284241 * q^52 - 122112 * q^53 - 130806 * q^54 - 134904 * q^55 - 100292 * q^56 - 423426 * q^57 - 307669 * q^58 - 85704 * q^59 - 238277 * q^60 - 206736 * q^61 - 190602 * q^62 - 387623 * q^63 + 411903 * q^64 - 244408 * q^65 - 113963 * q^66 - 337002 * q^67 - 388031 * q^68 - 165342 * q^69 - 183925 * q^70 - 174806 * q^71 - 753621 * q^72 - 1009738 * q^73 - 204958 * q^74 - 282676 * q^75 - 326869 * q^76 - 332288 * q^77 - 591801 * q^78 - 488092 * q^79 - 259068 * q^80 + 385959 * q^81 - 523996 * q^82 - 315720 * q^83 - 750486 * q^84 - 1001755 * q^85 - 287709 * q^86 - 316995 * q^87 - 836923 * q^88 - 298065 * q^89 - 751039 * q^90 - 521459 * q^91 - 640932 * q^92 - 554391 * q^93 - 623481 * q^94 - 491883 * q^95 - 767843 * q^96 - 1468693 * q^97 - 714146 * q^98 - 842507 * 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 $

$2$	−9.78124	−1.72910	−0.864548	−	0.502550i	$-0.832395\pi$
$2$	−9.78124	−1.72910	−0.864548	+	0.502550i	$0.832395\pi$
$3$	27.6828	1.77585	0.887925	−	0.459988i	$-0.152146\pi$
$3$	27.6828	1.77585	0.887925	+	0.459988i	$0.152146\pi$
$4$	63.6727	1.98977
$5$	21.4120	0.383030	0.191515	−	0.981490i	$-0.438660\pi$
$5$	21.4120	0.383030	0.191515	+	0.981490i	$0.438660\pi$
$6$	−270.772	−3.07062
$7$	51.6520	0.398421	0.199210	−	0.979957i	$-0.436162\pi$
$7$	51.6520	0.398421	0.199210	+	0.979957i	$0.436162\pi$
$8$	−309.799	−1.71141
$9$	523.335	2.15364
$10$	−209.436	−0.662296
$11$	−270.376	−0.673731	−0.336865	−	0.941553i	$-0.609367\pi$
$11$	−270.376	−0.673731	−0.336865	+	0.941553i	$0.609367\pi$
$12$	1762.64	3.53354
$13$	90.5053	0.148531	0.0742653	−	0.997239i	$-0.476339\pi$
$13$	90.5053	0.148531	0.0742653	+	0.997239i	$0.476339\pi$
$14$	−505.221	−0.688908
$15$	592.744	0.680204
$16$	992.690	0.969424
$17$	−374.150	−0.313995	−0.156998	−	0.987599i	$-0.550181\pi$
$17$	−374.150	−0.313995	−0.156998	+	0.987599i	$0.550181\pi$
$18$	−5118.87	−3.72386
$19$	1146.98	0.728908	0.364454	−	0.931221i	$-0.381256\pi$
$19$	1146.98	0.728908	0.364454	+	0.931221i	$0.381256\pi$
$20$	1363.36	0.762143
$21$	1429.87	0.707535
$22$	2644.61	1.16495
$23$	−2259.44	−0.890595	−0.445298	−	0.895383i	$-0.646902\pi$
$23$	−2259.44	−0.890595	−0.445298	+	0.895383i	$0.646902\pi$
$24$	−8576.09	−3.03921
$25$	−2666.52	−0.853288
$26$	−885.254	−0.256824
$27$	7760.45	2.04870
$28$	3288.82	0.792767
$29$	−4390.69	−0.969477	−0.484739	−	0.874659i	$-0.661085\pi$
$29$	−4390.69	−0.969477	−0.484739	+	0.874659i	$0.661085\pi$
$30$	−5797.77	−1.17614
$31$	−7896.91	−1.47589	−0.737943	−	0.674863i	$-0.764203\pi$
$31$	−7896.91	−1.47589	−0.737943	+	0.674863i	$0.764203\pi$
$32$	203.818	0.0351859
$33$	−7484.76	−1.19645
$34$	3659.65	0.542928
$35$	1105.97	0.152607
$36$	33322.2	4.28526
$37$	−2348.90	−0.282072	−0.141036	−	0.990004i	$-0.545043\pi$
$37$	−2348.90	−0.282072	−0.141036	+	0.990004i	$0.545043\pi$
$38$	−11218.9	−1.26035
$39$	2505.44	0.263768
$40$	−6633.42	−0.655522
$41$	4049.03	0.376176	0.188088	−	0.982152i	$-0.439771\pi$
$41$	4049.03	0.376176	0.188088	+	0.982152i	$0.439771\pi$
$42$	−13985.9	−1.22340
$43$	−10048.1	−0.828732	−0.414366	−	0.910110i	$-0.635997\pi$
$43$	−10048.1	−0.828732	−0.414366	+	0.910110i	$0.635997\pi$
$44$	−17215.6	−1.34057
$45$	11205.7	0.824910
$46$	22100.1	1.53992
$47$	12445.9	0.821832	0.410916	−	0.911673i	$-0.365209\pi$
$47$	12445.9	0.821832	0.410916	+	0.911673i	$0.365209\pi$
$48$	27480.4	1.72155
$49$	−14139.1	−0.841261
$50$	26081.9	1.47542
$51$	−10357.5	−0.557608
$52$	5762.72	0.295542
$53$	−9160.77	−0.447963	−0.223981	−	0.974593i	$-0.571906\pi$
$53$	−9160.77	−0.447963	−0.223981	+	0.974593i	$0.571906\pi$
$54$	−75906.9	−3.54239
$55$	−5789.30	−0.258059
$56$	−16001.7	−0.681862
$57$	31751.6	1.29443
$58$	42946.4	1.67632
$59$	41780.9	1.56260	0.781301	−	0.624155i	$-0.214556\pi$
$59$	41780.9	1.56260	0.781301	+	0.624155i	$0.214556\pi$
$60$	37741.6	1.35345
$61$	−10875.7	−0.374226	−0.187113	−	0.982338i	$-0.559913\pi$
$61$	−10875.7	−0.374226	−0.187113	+	0.982338i	$0.559913\pi$
$62$	77241.6	2.55195
$63$	27031.3	0.858056
$64$	−33759.7	−1.03026
$65$	1937.90	0.0568916
$66$	73210.2	2.06877
$67$	−24213.1	−0.658966	−0.329483	−	0.944162i	$-0.606874\pi$
$67$	−24213.1	−0.658966	−0.329483	+	0.944162i	$0.606874\pi$
$68$	−23823.1	−0.624779
$69$	−62547.4	−1.58156
$70$	−10817.8	−0.263872
$71$	−33238.1	−0.782510	−0.391255	−	0.920282i	$-0.627959\pi$
$71$	−33238.1	−0.782510	−0.391255	+	0.920282i	$0.627959\pi$
$72$	−162129.	−3.68577
$73$	−7020.09	−0.154183	−0.0770913	−	0.997024i	$-0.524563\pi$
$73$	−7020.09	−0.154183	−0.0770913	+	0.997024i	$0.524563\pi$
$74$	22975.2	0.487730
$75$	−73816.8	−1.51531
$76$	73031.5	1.45036
$77$	−13965.5	−0.268428
$78$	−24506.3	−0.456080
$79$	−25511.9	−0.459912	−0.229956	−	0.973201i	$-0.573858\pi$
$79$	−25511.9	−0.459912	−0.229956	+	0.973201i	$0.573858\pi$
$80$	21255.5	0.371318
$81$	87660.3	1.48454
$82$	−39604.6	−0.650445
$83$	−75662.7	−1.20555	−0.602777	−	0.797910i	$-0.705939\pi$
$83$	−75662.7	−1.20555	−0.602777	+	0.797910i	$0.705939\pi$
$84$	91043.7	1.40783
$85$	−8011.30	−0.120270
$86$	98283.2	1.43296
$87$	−121546.	−1.72165
$88$	83762.2	1.15303
$89$	−31639.6	−0.423404	−0.211702	−	0.977334i	$-0.567901\pi$
$89$	−31639.6	−0.423404	−0.211702	+	0.977334i	$0.567901\pi$
$90$	−109605.	−1.42635
$91$	4674.78	0.0591776
$92$	−143864.	−1.77208
$93$	−218608.	−2.62095
$94$	−121737.	−1.42103
$95$	24559.2	0.279194
$96$	5642.25	0.0624848
$97$	−6821.02	−0.0736071	−0.0368036	−	0.999323i	$-0.511718\pi$
$97$	−6821.02	−0.0736071	−0.0368036	+	0.999323i	$0.511718\pi$
$98$	138298.	1.45462
$99$	−141497.	−1.45098
$100$	−169785.	−1.69785
$101$	19281.5	0.188078	0.0940390	−	0.995569i	$-0.470022\pi$
$101$	19281.5	0.188078	0.0940390	+	0.995569i	$0.470022\pi$
$102$	101309.	0.964158
$103$	−17033.5	−0.158201	−0.0791007	−	0.996867i	$-0.525205\pi$
$103$	−17033.5	−0.158201	−0.0791007	+	0.996867i	$0.525205\pi$
$104$	−28038.4	−0.254197
$105$	30616.4	0.271007
$106$	89603.7	0.774571
$107$	−169275.	−1.42934	−0.714668	−	0.699463i	$-0.753422\pi$
$107$	−169275.	−1.42934	−0.714668	+	0.699463i	$0.753422\pi$
$108$	494129.	4.07644
$109$	−165582.	−1.33489	−0.667446	−	0.744658i	$-0.732613\pi$
$109$	−165582.	−1.33489	−0.667446	+	0.744658i	$0.732613\pi$
$110$	56626.6	0.446209
$111$	−65024.1	−0.500918
$112$	51274.4	0.386238
$113$	−66783.4	−0.492008	−0.246004	−	0.969269i	$-0.579118\pi$
$113$	−66783.4	−0.492008	−0.246004	+	0.969269i	$0.579118\pi$
$114$	−310571.	−2.23820
$115$	−48379.1	−0.341125
$116$	−279567.	−1.92904
$117$	47364.6	0.319882
$118$	−408670.	−2.70189
$119$	−19325.6	−0.125102
$120$	−183631.	−1.16411
$121$	−87947.8	−0.546087
$122$	106378.	0.647072
$123$	112088.	0.668033
$124$	−502818.	−2.93668
$125$	−124008.	−0.709865
$126$	−264400.	−1.48366
$127$	71408.9	0.392864	0.196432	−	0.980517i	$-0.437064\pi$
$127$	71408.9	0.392864	0.196432	+	0.980517i	$0.437064\pi$
$128$	323689.	1.74624
$129$	−278160.	−1.47170
$130$	−18955.1	−0.0983711
$131$	234190.	1.19231	0.596156	−	0.802868i	$-0.296694\pi$
$131$	234190.	1.19231	0.596156	+	0.802868i	$0.296694\pi$
$132$	−476575.	−2.38065
$133$	59243.9	0.290412
$134$	236834.	1.13942
$135$	166167.	0.784713
$136$	115911.	0.537375
$137$	232334.	1.05757	0.528787	−	0.848755i	$-0.322647\pi$
$137$	232334.	1.05757	0.528787	+	0.848755i	$0.322647\pi$
$138$	611791.	2.73467
$139$	−296845.	−1.30314	−0.651572	−	0.758587i	$-0.725890\pi$
$139$	−296845.	−1.30314	−0.651572	+	0.758587i	$0.725890\pi$
$140$	70420.4	0.303653
$141$	344538.	1.45945
$142$	325110.	1.35303
$143$	−24470.5	−0.100070
$144$	519510.	2.08779
$145$	−94013.6	−0.371339
$146$	68665.2	0.266597
$147$	−391409.	−1.49395
$148$	−149561.	−0.561260
$149$	370189.	1.36602	0.683011	−	0.730408i	$-0.260670\pi$
$149$	370189.	1.36602	0.683011	+	0.730408i	$0.260670\pi$
$150$	722020.	2.62012
$151$	−346052.	−1.23509	−0.617545	−	0.786536i	$-0.711873\pi$
$151$	−346052.	−1.23509	−0.617545	+	0.786536i	$0.711873\pi$
$152$	−355334.	−1.24746
$153$	−195806.	−0.676233
$154$	136600.	0.464138
$155$	−169089.	−0.565309
$156$	159528.	0.524838
$157$	348975.	1.12991	0.564957	−	0.825120i	$-0.308893\pi$
$157$	348975.	1.12991	0.564957	+	0.825120i	$0.308893\pi$
$158$	249538.	0.795233
$159$	−253595.	−0.795515
$160$	4364.16	0.0134772
$161$	−116704.	−0.354831
$162$	−857427.	−2.56690
$163$	216932.	0.639519	0.319760	−	0.947499i	$-0.396398\pi$
$163$	216932.	0.639519	0.319760	+	0.947499i	$0.396398\pi$
$164$	257813.	0.748505
$165$	−160264.	−0.458274
$166$	740075.	2.08452
$167$	143759.	0.398882	0.199441	−	0.979910i	$-0.436087\pi$
$167$	143759.	0.398882	0.199441	+	0.979910i	$0.436087\pi$
$168$	−442972.	−1.21088
$169$	−363102.	−0.977939
$170$	78360.5	0.207958
$171$	600256.	1.56981
$172$	−639792.	−1.64899
$173$	403402.	1.02476	0.512381	−	0.858758i	$-0.328764\pi$
$173$	403402.	1.02476	0.512381	+	0.858758i	$0.328764\pi$
$174$	1.18887e6	2.97689
$175$	−137731.	−0.339968
$176$	−268400.	−0.653131
$177$	1.15661e6	2.77495
$178$	309474.	0.732107
$179$	287248.	0.670076	0.335038	−	0.942205i	$-0.391251\pi$
$179$	287248.	0.670076	0.335038	+	0.942205i	$0.391251\pi$
$180$	713496.	1.64138
$181$	466618.	1.05868	0.529341	−	0.848409i	$-0.322439\pi$
$181$	466618.	1.05868	0.529341	+	0.848409i	$0.322439\pi$
$182$	−45725.1	−0.102324
$183$	−301070.	−0.664569
$184$	699970.	1.52418
$185$	−50294.8	−0.108042
$186$	2.13826e6	4.53188
$187$	101161.	0.211548
$188$	792467.	1.63526
$189$	400843.	0.816243
$190$	−240220.	−0.482753
$191$	300714.	0.596445	0.298222	−	0.954496i	$-0.403606\pi$
$191$	300714.	0.596445	0.298222	+	0.954496i	$0.403606\pi$
$192$	−934561.	−1.82959
$193$	125166.	0.241877	0.120938	−	0.992660i	$-0.461410\pi$
$193$	125166.	0.241877	0.120938	+	0.992660i	$0.461410\pi$
$194$	66718.0	0.127274
$195$	53646.5	0.101031
$196$	−900274.	−1.67392
$197$	−392216.	−0.720044	−0.360022	−	0.932944i	$-0.617231\pi$
$197$	−392216.	−0.720044	−0.360022	+	0.932944i	$0.617231\pi$
$198$	1.38402e6	2.50888
$199$	−10710.3	−0.0191720	−0.00958601	−	0.999954i	$-0.503051\pi$
$199$	−10710.3	−0.0191720	−0.00958601	+	0.999954i	$0.503051\pi$
$200$	826086.	1.46033
$201$	−670285.	−1.17022
$202$	−188597.	−0.325205
$203$	−226788.	−0.386260
$204$	−659490.	−1.10951
$205$	86698.0	0.144087
$206$	166609.	0.273545
$207$	−1.18244e6	−1.91802
$208$	89843.7	0.143989
$209$	−310117.	−0.491088
$210$	−299467.	−0.468598
$211$	292775.	0.452718	0.226359	−	0.974044i	$-0.427318\pi$
$211$	292775.	0.452718	0.226359	+	0.974044i	$0.427318\pi$
$212$	−583291.	−0.891345
$213$	−920121.	−1.38962
$214$	1.65572e6	2.47146
$215$	−215151.	−0.317429
$216$	−2.40418e6	−3.50617
$217$	−407891.	−0.588024
$218$	1.61960e6	2.30816
$219$	−194336.	−0.273805
$220$	−368621.	−0.513479
$221$	−33862.5	−0.0466379
$222$	636017.	0.866136
$223$	−404334.	−0.544475	−0.272238	−	0.962230i	$-0.587764\pi$
$223$	−404334.	−0.544475	−0.272238	+	0.962230i	$0.587764\pi$
$224$	10527.6	0.0140188
$225$	−1.39549e6	−1.83768
$226$	653225.	0.850730
$227$	−410245.	−0.528419	−0.264209	−	0.964465i	$-0.585111\pi$
$227$	−410245.	−0.528419	−0.264209	+	0.964465i	$0.585111\pi$
$228$	2.02171e6	2.57563
$229$	438710.	0.552826	0.276413	−	0.961039i	$-0.410854\pi$
$229$	438710.	0.552826	0.276413	+	0.961039i	$0.410854\pi$
$230$	473208.	0.589837
$231$	−386602.	−0.476688
$232$	1.36023e6	1.65918
$233$	449238.	0.542109	0.271055	−	0.962564i	$-0.412628\pi$
$233$	449238.	0.542109	0.271055	+	0.962564i	$0.412628\pi$
$234$	−463285.	−0.553106
$235$	266493.	0.314786
$236$	2.66031e6	3.10922
$237$	−706240.	−0.816735
$238$	189028.	0.216314
$239$	−299972.	−0.339693	−0.169847	−	0.985471i	$-0.554327\pi$
$239$	−299972.	−0.339693	−0.169847	+	0.985471i	$0.554327\pi$
$240$	588411.	0.659406
$241$	1.19396e6	1.32418	0.662088	−	0.749426i	$-0.269670\pi$
$241$	1.19396e6	1.32418	0.662088	+	0.749426i	$0.269670\pi$
$242$	860239.	0.944236
$243$	540890.	0.587615
$244$	−692487.	−0.744624
$245$	−302746.	−0.322228
$246$	−1.09636e6	−1.15509
$247$	103808.	0.108265
$248$	2.44645e6	2.52585
$249$	−2.09455e6	−2.14088
$250$	1.21296e6	1.22742
$251$	−850338.	−0.851937	−0.425968	−	0.904738i	$-0.640066\pi$
$251$	−850338.	−0.851937	−0.425968	+	0.904738i	$0.640066\pi$
$252$	1.72116e6	1.70734
$253$	610897.	0.600022
$254$	−698467.	−0.679300
$255$	−221775.	−0.213581
$256$	−2.08578e6	−1.98915
$257$	119963.	0.113296	0.0566479	−	0.998394i	$-0.481959\pi$
$257$	119963.	0.113296	0.0566479	+	0.998394i	$0.481959\pi$
$258$	2.72075e6	2.54472
$259$	−121325.	−0.112383
$260$	123392.	0.113201
$261$	−2.29780e6	−2.08791
$262$	−2.29067e6	−2.06162
$263$	646348.	0.576205	0.288102	−	0.957600i	$-0.406976\pi$
$263$	646348.	0.576205	0.288102	+	0.957600i	$0.406976\pi$
$264$	2.31877e6	2.04761
$265$	−196151.	−0.171583
$266$	−579479.	−0.502150
$267$	−875870.	−0.751903
$268$	−1.54171e6	−1.31119
$269$	994408.	0.837884	0.418942	−	0.908013i	$-0.362401\pi$
$269$	994408.	0.837884	0.418942	+	0.908013i	$0.362401\pi$
$270$	−1.62532e6	−1.35684
$271$	1.82035e6	1.50568	0.752839	−	0.658205i	$-0.228684\pi$
$271$	1.82035e6	1.50568	0.752839	+	0.658205i	$0.228684\pi$
$272$	−371415.	−0.304394
$273$	129411.	0.105091
$274$	−2.27251e6	−1.82865
$275$	720964.	0.574887
$276$	−3.98256e6	−3.14695
$277$	302360.	0.236769	0.118384	−	0.992968i	$-0.462228\pi$
$277$	302360.	0.236769	0.118384	+	0.992968i	$0.462228\pi$
$278$	2.90351e6	2.25326
$279$	−4.13273e6	−3.17853
$280$	−342629.	−0.261174
$281$	−2.53667e6	−1.91645	−0.958227	−	0.286008i	$-0.907672\pi$
$281$	−2.53667e6	−1.91645	−0.958227	+	0.286008i	$0.907672\pi$
$282$	−3.37001e6	−2.52353
$283$	−391477.	−0.290563	−0.145281	−	0.989390i	$-0.546409\pi$
$283$	−391477.	−0.290563	−0.145281	+	0.989390i	$0.546409\pi$
$284$	−2.11636e6	−1.55702
$285$	679867.	0.495806
$286$	239352.	0.173030
$287$	209140.	0.149876
$288$	106665.	0.0757778
$289$	−1.27987e6	−0.901407
$290$	919570.	0.642081
$291$	−188825.	−0.130715
$292$	−446988.	−0.306789
$293$	402262.	0.273741	0.136871	−	0.990589i	$-0.456296\pi$
$293$	402262.	0.273741	0.136871	+	0.990589i	$0.456296\pi$
$294$	3.82846e6	2.58319
$295$	894615.	0.598523
$296$	727687.	0.482742
$297$	−2.09824e6	−1.38027
$298$	−3.62091e6	−2.36198
$299$	−204491.	−0.132281
$300$	−4.70012e6	−3.01513
$301$	−519006.	−0.330184
$302$	3.38482e6	2.13559
$303$	533766.	0.333998
$304$	1.13860e6	0.706621
$305$	−232871.	−0.143340
$306$	1.91522e6	1.16927
$307$	−363667.	−0.220220	−0.110110	−	0.993919i	$-0.535120\pi$
$307$	−363667.	−0.220220	−0.110110	+	0.993919i	$0.535120\pi$
$308$	−889219.	−0.534111
$309$	−471534.	−0.280942
$310$	1.65390e6	0.977473
$311$	1.48427e6	0.870183	0.435092	−	0.900386i	$-0.356716\pi$
$311$	1.48427e6	0.870183	0.435092	+	0.900386i	$0.356716\pi$
$312$	−776181.	−0.451416
$313$	916372.	0.528702	0.264351	−	0.964426i	$-0.414842\pi$
$313$	916372.	0.528702	0.264351	+	0.964426i	$0.414842\pi$
$314$	−3.41341e6	−1.95373
$315$	578795.	0.328661
$316$	−1.62441e6	−0.915121
$317$	−415607.	−0.232292	−0.116146	−	0.993232i	$-0.537054\pi$
$317$	−415607.	−0.232292	−0.116146	+	0.993232i	$0.537054\pi$
$318$	2.48048e6	1.37552
$319$	1.18714e6	0.653167
$320$	−722863.	−0.394622
$321$	−4.68601e6	−2.53829
$322$	1.14151e6	0.613538
$323$	−429143.	−0.228874
$324$	5.58157e6	2.95389
$325$	−241335.	−0.126739
$326$	−2.12186e6	−1.10579
$327$	−4.58376e6	−2.37057
$328$	−1.25438e6	−0.643793
$329$	642858.	0.327435
$330$	1.56758e6	0.792400
$331$	2.11805e6	1.06259	0.531295	−	0.847187i	$-0.321705\pi$
$331$	2.11805e6	1.06259	0.531295	+	0.847187i	$0.321705\pi$
$332$	−4.81765e6	−2.39878
$333$	−1.22926e6	−0.607483
$334$	−1.40614e6	−0.689705
$335$	−518451.	−0.252404
$336$	1.41942e6	0.685902
$337$	157635.	0.0756097	0.0378048	−	0.999285i	$-0.487963\pi$
$337$	157635.	0.0756097	0.0378048	+	0.999285i	$0.487963\pi$
$338$	3.55159e6	1.69095
$339$	−1.84875e6	−0.873733
$340$	−510102.	−0.239309
$341$	2.13514e6	0.994351
$342$	−5.87126e6	−2.71435
$343$	−1.59843e6	−0.733596
$344$	3.11290e6	1.41830
$345$	−1.33927e6	−0.605786
$346$	−3.94577e6	−1.77191
$347$	−3.95735e6	−1.76433	−0.882166	−	0.470938i	$-0.843916\pi$
$347$	−3.95735e6	−1.76433	−0.882166	+	0.470938i	$0.843916\pi$
$348$	−7.73919e6	−3.42569
$349$	−288148.	−0.126634	−0.0633171	−	0.997993i	$-0.520168\pi$
$349$	−288148.	−0.126634	−0.0633171	+	0.997993i	$0.520168\pi$
$350$	1.34718e6	0.587837
$351$	702362.	0.304294
$352$	−55107.6	−0.0237058
$353$	−1.88912e6	−0.806905	−0.403452	−	0.915001i	$-0.632190\pi$
$353$	−1.88912e6	−0.806905	−0.403452	+	0.915001i	$0.632190\pi$
$354$	−1.13131e7	−4.79815
$355$	−711694.	−0.299725
$356$	−2.01458e6	−0.842479
$357$	−534985.	−0.222163
$358$	−2.80964e6	−1.15863
$359$	−2.13867e6	−0.875807	−0.437903	−	0.899022i	$-0.644279\pi$
$359$	−2.13867e6	−0.875807	−0.437903	+	0.899022i	$0.644279\pi$
$360$	−3.47150e6	−1.41176
$361$	−1.16053e6	−0.468693
$362$	−4.56411e6	−1.83056
$363$	−2.43464e6	−0.969768
$364$	297656.	0.117750
$365$	−150314.	−0.0590566
$366$	2.94484e6	1.14910
$367$	1.18735e6	0.460166	0.230083	−	0.973171i	$-0.426100\pi$
$367$	1.18735e6	0.460166	0.230083	+	0.973171i	$0.426100\pi$
$368$	−2.24292e6	−0.863364
$369$	2.11900e6	0.810149
$370$	491945.	0.186815
$371$	−473172.	−0.178478
$372$	−1.39194e7	−5.21510
$373$	−3.20895e6	−1.19424	−0.597120	−	0.802152i	$-0.703688\pi$
$373$	−3.20895e6	−1.19424	−0.597120	+	0.802152i	$0.703688\pi$
$374$	−989481.	−0.365787
$375$	−3.43289e6	−1.26061
$376$	−3.85574e6	−1.40649
$377$	−397381.	−0.143997
$378$	−3.92074e6	−1.41136
$379$	2.63438e6	0.942065	0.471033	−	0.882116i	$-0.343881\pi$
$379$	2.63438e6	0.942065	0.471033	+	0.882116i	$0.343881\pi$
$380$	1.56375e6	0.555532
$381$	1.97679e6	0.697668
$382$	−2.94136e6	−1.03131
$383$	4.93062e6	1.71753	0.858766	−	0.512369i	$-0.171232\pi$
$383$	4.93062e6	1.71753	0.858766	+	0.512369i	$0.171232\pi$
$384$	8.96062e6	3.10106
$385$	−299029.	−0.102816
$386$	−1.22428e6	−0.418228
$387$	−5.25854e6	−1.78479
$388$	−434313.	−0.146461
$389$	2.45795e6	0.823569	0.411784	−	0.911281i	$-0.364906\pi$
$389$	2.45795e6	0.823569	0.411784	+	0.911281i	$0.364906\pi$
$390$	−524729.	−0.174692
$391$	845367.	0.279643
$392$	4.38027e6	1.43974
$393$	6.48303e6	2.11737
$394$	3.83636e6	1.24503
$395$	−546262.	−0.176160
$396$	−9.00952e6	−2.88711
$397$	−83297.7	−0.0265251	−0.0132625	−	0.999912i	$-0.504222\pi$
$397$	−83297.7	−0.0265251	−0.0132625	+	0.999912i	$0.504222\pi$
$398$	104760.	0.0331503
$399$	1.64004e6	0.515728
$400$	−2.64703e6	−0.827198
$401$	2.52517e6	0.784205	0.392103	−	0.919921i	$-0.371748\pi$
$401$	2.52517e6	0.784205	0.392103	+	0.919921i	$0.371748\pi$
$402$	6.55622e6	2.02343
$403$	−714712.	−0.219214
$404$	1.22771e6	0.374233
$405$	1.87699e6	0.568622
$406$	2.21827e6	0.667880
$407$	635087.	0.190041
$408$	3.20874e6	0.954298
$409$	−3.60815e6	−1.06654	−0.533268	−	0.845946i	$-0.679036\pi$
$409$	−3.60815e6	−1.06654	−0.533268	+	0.845946i	$0.679036\pi$
$410$	−848014.	−0.249140
$411$	6.43164e6	1.87809
$412$	−1.08457e6	−0.314785
$413$	2.15807e6	0.622573
$414$	1.15658e7	3.31645
$415$	−1.62009e6	−0.461763
$416$	18446.6	0.00522617
$417$	−8.21748e6	−2.31419
$418$	3.03333e6	0.849138
$419$	2.08949e6	0.581441	0.290721	−	0.956808i	$-0.406105\pi$
$419$	2.08949e6	0.581441	0.290721	+	0.956808i	$0.406105\pi$
$420$	1.94943e6	0.539243
$421$	−708251.	−0.194752	−0.0973760	−	0.995248i	$-0.531045\pi$
$421$	−708251.	−0.194752	−0.0973760	+	0.995248i	$0.531045\pi$
$422$	−2.86370e6	−0.782793
$423$	6.51340e6	1.76993
$424$	2.83799e6	0.766649
$425$	997679.	0.267928
$426$	8.99993e6	2.40279
$427$	−561753.	−0.149099
$428$	−1.07782e7	−2.84406
$429$	−677410.	−0.177709
$430$	2.10444e6	0.548865
$431$	−680338.	−0.176413	−0.0882067	−	0.996102i	$-0.528114\pi$
$431$	−680338.	−0.176413	−0.0882067	+	0.996102i	$0.528114\pi$
$432$	7.70373e6	1.98606
$433$	6.45129e6	1.65359	0.826793	−	0.562506i	$-0.190163\pi$
$433$	6.45129e6	1.65359	0.826793	+	0.562506i	$0.190163\pi$
$434$	3.98968e6	1.01675
$435$	−2.60256e6	−0.659442
$436$	−1.05430e7	−2.65613
$437$	−2.59153e6	−0.649162
$438$	1.90084e6	0.473436
$439$	2.29731e6	0.568930	0.284465	−	0.958686i	$-0.408184\pi$
$439$	2.29731e6	0.568930	0.284465	+	0.958686i	$0.408184\pi$
$440$	1.79352e6	0.441646
$441$	−7.39948e6	−1.81178
$442$	331218.	0.0806413
$443$	1.35335e6	0.327643	0.163822	−	0.986490i	$-0.447618\pi$
$443$	1.35335e6	0.327643	0.163822	+	0.986490i	$0.447618\pi$
$444$	−4.14026e6	−0.996714
$445$	−677467.	−0.162177
$446$	3.95489e6	0.941450
$447$	1.02478e7	2.42585
$448$	−1.74375e6	−0.410478
$449$	3.86683e6	0.905190	0.452595	−	0.891716i	$-0.350498\pi$
$449$	3.86683e6	0.905190	0.452595	+	0.891716i	$0.350498\pi$
$450$	1.36496e7	3.17752
$451$	−1.09476e6	−0.253442
$452$	−4.25228e6	−0.978985
$453$	−9.57966e6	−2.19333
$454$	4.01270e6	0.913687
$455$	100096.	0.0226668
$456$	−9.83662e6	−2.21531
$457$	−4.36749e6	−0.978231	−0.489115	−	0.872219i	$-0.662680\pi$
$457$	−4.36749e6	−0.978231	−0.489115	+	0.872219i	$0.662680\pi$
$458$	−4.29113e6	−0.955889
$459$	−2.90357e6	−0.643281
$460$	−3.08043e6	−0.678761
$461$	−5.70770e6	−1.25086	−0.625431	−	0.780280i	$-0.715077\pi$
$461$	−5.70770e6	−1.25086	−0.625431	+	0.780280i	$0.715077\pi$
$462$	3.78145e6	0.824240
$463$	−4.08285e6	−0.885139	−0.442569	−	0.896734i	$-0.645933\pi$
$463$	−4.08285e6	−0.885139	−0.442569	+	0.896734i	$0.645933\pi$
$464$	−4.35859e6	−0.939834
$465$	−4.68085e6	−1.00390
$466$	−4.39411e6	−0.937359
$467$	7.33970e6	1.55735	0.778674	−	0.627428i	$-0.215892\pi$
$467$	7.33970e6	1.55735	0.778674	+	0.627428i	$0.215892\pi$
$468$	3.01583e6	0.636492
$469$	−1.25065e6	−0.262546
$470$	−2.60663e6	−0.544296
$471$	9.66060e6	2.00656
$472$	−1.29437e7	−2.67426
$473$	2.71677e6	0.558342
$474$	6.90791e6	1.41221
$475$	−3.05846e6	−0.621969
$476$	−1.23051e6	−0.248925
$477$	−4.79415e6	−0.964752
$478$	2.93410e6	0.587362
$479$	−5.81440e6	−1.15789	−0.578943	−	0.815368i	$-0.696535\pi$
$479$	−5.81440e6	−1.15789	−0.578943	+	0.815368i	$0.696535\pi$
$480$	120812.	0.0239336
$481$	−212588.	−0.0418964
$482$	−1.16784e7	−2.28963
$483$	−3.23070e6	−0.630127
$484$	−5.59988e6	−1.08659
$485$	−146052.	−0.0281937
$486$	−5.29057e6	−1.01604
$487$	412526.	0.0788187	0.0394094	−	0.999223i	$-0.487452\pi$
$487$	412526.	0.0788187	0.0394094	+	0.999223i	$0.487452\pi$
$488$	3.36929e6	0.640455
$489$	6.00526e6	1.13569
$490$	2.96124e6	0.557164
$491$	4.58582e6	0.858446	0.429223	−	0.903199i	$-0.358787\pi$
$491$	4.58582e6	0.858446	0.429223	+	0.903199i	$0.358787\pi$
$492$	7.13697e6	1.32923
$493$	1.64277e6	0.304411
$494$	−1.01537e6	−0.187201
$495$	−3.02974e6	−0.555767
$496$	−7.83918e6	−1.43076
$497$	−1.71681e6	−0.311768
$498$	2.04873e7	3.70179
$499$	−1.24644e6	−0.224089	−0.112045	−	0.993703i	$-0.535740\pi$
$499$	−1.24644e6	−0.224089	−0.112045	+	0.993703i	$0.535740\pi$
$500$	−7.89595e6	−1.41247
$501$	3.97965e6	0.708354
$502$	8.31736e6	1.47308
$503$	6.22284e6	1.09665	0.548326	−	0.836265i	$-0.315265\pi$
$503$	6.22284e6	1.09665	0.548326	+	0.836265i	$0.315265\pi$
$504$	−8.37426e6	−1.46849
$505$	412857.	0.0720396
$506$	−5.97533e6	−1.03749
$507$	−1.00517e7	−1.73667
$508$	4.54680e6	0.781711
$509$	−5.36630e6	−0.918080	−0.459040	−	0.888416i	$-0.651807\pi$
$509$	−5.36630e6	−0.918080	−0.459040	+	0.888416i	$0.651807\pi$
$510$	2.16923e6	0.369302
$511$	−362602.	−0.0614296
$512$	1.00434e7	1.69319
$513$	8.90111e6	1.49331
$514$	−1.17339e6	−0.195899
$515$	−364721.	−0.0605959
$516$	−1.77112e7	−2.92836
$517$	−3.36509e6	−0.553694
$518$	1.18671e6	0.194322
$519$	1.11673e7	1.81982
$520$	−600360.	−0.0973651
$521$	−968498.	−0.156316	−0.0781581	−	0.996941i	$-0.524904\pi$
$521$	−968498.	−0.156316	−0.0781581	+	0.996941i	$0.524904\pi$
$522$	2.24754e7	3.61019
$523$	−8.23472e6	−1.31642	−0.658211	−	0.752834i	$-0.728686\pi$
$523$	−8.23472e6	−1.31642	−0.658211	+	0.752834i	$0.728686\pi$
$524$	1.49115e7	2.37243
$525$	−3.81278e6	−0.603731
$526$	−6.32209e6	−0.996313
$527$	2.95463e6	0.463421
$528$	−7.43004e6	−1.15986
$529$	−1.33130e6	−0.206840
$530$	1.91860e6	0.296684
$531$	2.18654e7	3.36529
$532$	3.77222e6	0.577854
$533$	366459.	0.0558737
$534$	8.56710e6	1.30011
$535$	−3.62453e6	−0.547479
$536$	7.50118e6	1.12776
$537$	7.95181e6	1.18995
$538$	−9.72655e6	−1.44878
$539$	3.82287e6	0.566784
$540$	1.05803e7	1.56140
$541$	−9.99186e6	−1.46775	−0.733877	−	0.679282i	$-0.762291\pi$
$541$	−9.99186e6	−1.46775	−0.733877	+	0.679282i	$0.762291\pi$
$542$	−1.78053e7	−2.60346
$543$	1.29173e7	1.88006
$544$	−76258.5	−0.0110482
$545$	−3.54544e6	−0.511304
$546$	−1.26580e6	−0.181712
$547$	−5.07803e6	−0.725649	−0.362825	−	0.931857i	$-0.618188\pi$
$547$	−5.07803e6	−0.725649	−0.362825	+	0.931857i	$0.618188\pi$
$548$	1.47933e7	2.10433
$549$	−5.69165e6	−0.805949
$550$	−7.05193e6	−0.994034
$551$	−5.03604e6	−0.706660
$552$	1.93771e7	2.70671
$553$	−1.31774e6	−0.183239
$554$	−2.95745e6	−0.409396
$555$	−1.39230e6	−0.191867
$556$	−1.89009e7	−2.59296
$557$	−1.24075e7	−1.69452	−0.847259	−	0.531180i	$-0.821749\pi$
$557$	−1.24075e7	−1.69452	−0.847259	+	0.531180i	$0.821749\pi$
$558$	4.04233e7	5.49599
$559$	−909409.	−0.123092
$560$	1.09789e6	0.147941
$561$	2.80042e6	0.375678
$562$	2.48118e7	3.31373
$563$	2.69988e6	0.358982	0.179491	−	0.983760i	$-0.442555\pi$
$563$	2.69988e6	0.358982	0.179491	+	0.983760i	$0.442555\pi$
$564$	2.19377e7	2.90398
$565$	−1.42997e6	−0.188454
$566$	3.82913e6	0.502411
$567$	4.52783e6	0.591470
$568$	1.02971e7	1.33920
$569$	4.19229e6	0.542838	0.271419	−	0.962461i	$-0.412507\pi$
$569$	4.19229e6	0.542838	0.271419	+	0.962461i	$0.412507\pi$
$570$	−6.64995e6	−0.857297
$571$	−2.33643e6	−0.299891	−0.149945	−	0.988694i	$-0.547910\pi$
$571$	−2.33643e6	−0.299891	−0.149945	+	0.988694i	$0.547910\pi$
$572$	−1.55810e6	−0.199116
$573$	8.32459e6	1.05920
$574$	−2.04565e6	−0.259151
$575$	6.02484e6	0.759934
$576$	−1.76676e7	−2.21882
$577$	2.44888e6	0.306216	0.153108	−	0.988209i	$-0.451072\pi$
$577$	2.44888e6	0.306216	0.153108	+	0.988209i	$0.451072\pi$
$578$	1.25187e7	1.55862
$579$	3.46495e6	0.429537
$580$	−5.98610e6	−0.738880
$581$	−3.90813e6	−0.480317
$582$	1.84694e6	0.226019
$583$	2.47685e6	0.301807
$584$	2.17482e6	0.263870
$585$	1.01417e6	0.122524
$586$	−3.93463e6	−0.473325
$587$	1.34796e6	0.161466	0.0807328	−	0.996736i	$-0.474274\pi$
$587$	1.34796e6	0.161466	0.0807328	+	0.996736i	$0.474274\pi$
$588$	−2.49221e7	−2.97263
$589$	−9.05762e6	−1.07579
$590$	−8.75045e6	−1.03490
$591$	−1.08576e7	−1.27869
$592$	−2.33173e6	−0.273448
$593$	2735.74	0.000319476 0	0.000159738	−	1.00000i	$-0.499949\pi$
$593$	2735.74	0.000319476 0	0.000159738		1.00000i	$0.499949\pi$
$594$	2.05234e7	2.38662
$595$	−413800.	−0.0479179
$596$	2.35709e7	2.71807
$597$	−296490.	−0.0340466
$598$	2.00018e6	0.228726
$599$	−3.26790e6	−0.372136	−0.186068	−	0.982537i	$-0.559574\pi$
$599$	−3.26790e6	−0.372136	−0.186068	+	0.982537i	$0.559574\pi$
$600$	2.28683e7	2.59332
$601$	−7.04498e6	−0.795598	−0.397799	−	0.917473i	$-0.630226\pi$
$601$	−7.04498e6	−0.795598	−0.397799	+	0.917473i	$0.630226\pi$
$602$	5.07652e6	0.570920
$603$	−1.26716e7	−1.41918
$604$	−2.20341e7	−2.45755
$605$	−1.88314e6	−0.209168
$606$	−5.22090e6	−0.577515
$607$	−1.91003e6	−0.210411	−0.105205	−	0.994451i	$-0.533550\pi$
$607$	−1.91003e6	−0.210411	−0.105205	+	0.994451i	$0.533550\pi$
$608$	233776.	0.0256473
$609$	−6.27811e6	−0.685939
$610$	2.27777e6	0.247848
$611$	1.12642e6	0.122067
$612$	−1.24675e7	−1.34555
$613$	9.22224e6	0.991254	0.495627	−	0.868535i	$-0.334938\pi$
$613$	9.22224e6	0.991254	0.495627	+	0.868535i	$0.334938\pi$
$614$	3.55711e6	0.380782
$615$	2.40004e6	0.255877
$616$	4.32648e6	0.459392
$617$	2.34588e6	0.248081	0.124040	−	0.992277i	$-0.460415\pi$
$617$	2.34588e6	0.248081	0.124040	+	0.992277i	$0.460415\pi$
$618$	4.61219e6	0.485776
$619$	−7.42694e6	−0.779082	−0.389541	−	0.921009i	$-0.627366\pi$
$619$	−7.42694e6	−0.779082	−0.389541	+	0.921009i	$0.627366\pi$
$620$	−1.07664e7	−1.12484
$621$	−1.75342e7	−1.82456
$622$	−1.45180e7	−1.50463
$623$	−1.63425e6	−0.168693
$624$	2.48712e6	0.255703
$625$	5.67762e6	0.581388
$626$	−8.96326e6	−0.914177
$627$	−8.58489e6	−0.872099
$628$	2.22202e7	2.24827
$629$	878841.	0.0885694
$630$	−5.66134e6	−0.568287
$631$	−1.72186e7	−1.72157	−0.860786	−	0.508967i	$-0.830028\pi$
$631$	−1.72186e7	−1.72157	−0.860786	+	0.508967i	$0.830028\pi$
$632$	7.90356e6	0.787100
$633$	8.10482e6	0.803959
$634$	4.06516e6	0.401656
$635$	1.52901e6	0.150479
$636$	−1.61471e7	−1.58289
$637$	−1.27966e6	−0.124953
$638$	−1.16117e7	−1.12939
$639$	−1.73946e7	−1.68525
$640$	6.93085e6	0.668862
$641$	1.84161e6	0.177032	0.0885162	−	0.996075i	$-0.471788\pi$
$641$	1.84161e6	0.177032	0.0885162	+	0.996075i	$0.471788\pi$
$642$	4.58350e7	4.38894
$643$	−1.08000e7	−1.03014	−0.515068	−	0.857149i	$-0.672233\pi$
$643$	−1.08000e7	−1.03014	−0.515068	+	0.857149i	$0.672233\pi$
$644$	−7.43088e6	−0.706034
$645$	−5.95597e6	−0.563707
$646$	4.19755e6	0.395745
$647$	1.08221e6	0.101637	0.0508184	−	0.998708i	$-0.483817\pi$
$647$	1.08221e6	0.101637	0.0508184	+	0.998708i	$0.483817\pi$
$648$	−2.71571e7	−2.54065
$649$	−1.12966e7	−1.05277
$650$	2.36055e6	0.219144
$651$	−1.12916e7	−1.04424
$652$	1.38126e7	1.27250
$653$	1.81063e6	0.166167	0.0830837	−	0.996543i	$-0.473523\pi$
$653$	1.81063e6	0.166167	0.0830837	+	0.996543i	$0.473523\pi$
$654$	4.48349e7	4.09894
$655$	5.01448e6	0.456692
$656$	4.01943e6	0.364674
$657$	−3.67386e6	−0.332054
$658$	−6.28795e6	−0.566166
$659$	−1.87810e7	−1.68464	−0.842318	−	0.538981i	$-0.818809\pi$
$659$	−1.87810e7	−1.68464	−0.842318	+	0.538981i	$0.818809\pi$
$660$	−1.02044e7	−0.911862
$661$	−1.53483e7	−1.36634	−0.683168	−	0.730262i	$-0.739398\pi$
$661$	−1.53483e7	−1.36634	−0.683168	+	0.730262i	$0.739398\pi$
$662$	−2.07172e7	−1.83732
$663$	−937408.	−0.0828218
$664$	2.34402e7	2.06320
$665$	1.26853e6	0.111237
$666$	1.20237e7	1.05040
$667$	9.92048e6	0.863412
$668$	9.15354e6	0.793684
$669$	−1.11931e7	−0.966906
$670$	5.07110e6	0.436430
$671$	2.94054e6	0.252128
$672$	291433.	0.0248952
$673$	4.57180e6	0.389089	0.194545	−	0.980894i	$-0.437677\pi$
$673$	4.57180e6	0.389089	0.194545	+	0.980894i	$0.437677\pi$
$674$	−1.54186e6	−0.130736
$675$	−2.06934e7	−1.74813
$676$	−2.31197e7	−1.94588
$677$	−7.21335e6	−0.604874	−0.302437	−	0.953169i	$-0.597800\pi$
$677$	−7.21335e6	−0.604874	−0.302437	+	0.953169i	$0.597800\pi$
$678$	1.80831e7	1.51077
$679$	−352319.	−0.0293266
$680$	2.48189e6	0.205831
$681$	−1.13567e7	−0.938393
$682$	−2.08843e7	−1.71933
$683$	−2.92603e6	−0.240009	−0.120004	−	0.992773i	$-0.538291\pi$
$683$	−2.92603e6	−0.240009	−0.120004	+	0.992773i	$0.538291\pi$
$684$	3.82200e7	3.12356
$685$	4.97474e6	0.405083
$686$	1.56346e7	1.26846
$687$	1.21447e7	0.981736
$688$	−9.97467e6	−0.803392
$689$	−829098.	−0.0665362
$690$	1.30997e7	1.04746
$691$	−2.85096e6	−0.227141	−0.113571	−	0.993530i	$-0.536229\pi$
$691$	−2.85096e6	−0.227141	−0.113571	+	0.993530i	$0.536229\pi$
$692$	2.56857e7	2.03904
$693$	−7.30862e6	−0.578099
$694$	3.87078e7	3.05070
$695$	−6.35605e6	−0.499143
$696$	3.76549e7	2.94645
$697$	−1.51494e6	−0.118118
$698$	2.81844e6	0.218963
$699$	1.24362e7	0.962705
$700$	−8.76973e6	−0.676458
$701$	2.17991e7	1.67550	0.837749	−	0.546055i	$-0.183871\pi$
$701$	2.17991e7	1.67550	0.837749	+	0.546055i	$0.183871\pi$
$702$	−6.86998e6	−0.526154
$703$	−2.69415e6	−0.205605
$704$	9.12781e6	0.694120
$705$	7.37726e6	0.559014
$706$	1.84779e7	1.39522
$707$	995929.	0.0749342
$708$	7.36447e7	5.52151
$709$	−7.08427e6	−0.529273	−0.264637	−	0.964348i	$-0.585252\pi$
$709$	−7.08427e6	−0.529273	−0.264637	+	0.964348i	$0.585252\pi$
$710$	6.96125e6	0.518253
$711$	−1.33513e7	−0.990487
$712$	9.80190e6	0.724620
$713$	1.78426e7	1.31442
$714$	5.23282e6	0.384141
$715$	−523962.	−0.0383297
$716$	1.82898e7	1.33330
$717$	−8.30407e6	−0.603244
$718$	2.09189e7	1.51435
$719$	−1.86457e7	−1.34510	−0.672551	−	0.740051i	$-0.734801\pi$
$719$	−1.86457e7	−1.34510	−0.672551	+	0.740051i	$0.734801\pi$
$720$	1.11238e7	0.799687
$721$	−879813.	−0.0630307
$722$	1.13514e7	0.810415
$723$	3.30520e7	2.35154
$724$	2.97109e7	2.10654
$725$	1.17079e7	0.827243
$726$	2.38138e7	1.67682
$727$	2.10993e7	1.48058	0.740289	−	0.672289i	$-0.234689\pi$
$727$	2.10993e7	1.48058	0.740289	+	0.672289i	$0.234689\pi$
$728$	−1.44824e6	−0.101277
$729$	−6.32814e6	−0.441019
$730$	1.47026e6	0.102115
$731$	3.75950e6	0.260218
$732$	−1.91700e7	−1.32234
$733$	−5.73193e6	−0.394041	−0.197020	−	0.980399i	$-0.563127\pi$
$733$	−5.73193e6	−0.394041	−0.197020	+	0.980399i	$0.563127\pi$
$734$	−1.16138e7	−0.795671
$735$	−8.38085e6	−0.572229
$736$	−460514.	−0.0313364
$737$	6.54663e6	0.443966
$738$	−2.07265e7	−1.40083
$739$	−5.94992e6	−0.400775	−0.200387	−	0.979717i	$-0.564220\pi$
$739$	−5.94992e6	−0.400775	−0.200387	+	0.979717i	$0.564220\pi$
$740$	−3.20240e6	−0.214979
$741$	2.87369e6	0.192263
$742$	4.62821e6	0.308605
$743$	−8.10286e6	−0.538476	−0.269238	−	0.963074i	$-0.586772\pi$
$743$	−8.10286e6	−0.538476	−0.269238	+	0.963074i	$0.586772\pi$
$744$	6.77246e7	4.48553
$745$	7.92649e6	0.523227
$746$	3.13876e7	2.06495
$747$	−3.95970e7	−2.59633
$748$	6.44120e6	0.420933
$749$	−8.74341e6	−0.569477
$750$	3.35780e7	2.17972
$751$	−9.43454e6	−0.610409	−0.305205	−	0.952287i	$-0.598725\pi$
$751$	−9.43454e6	−0.610409	−0.305205	+	0.952287i	$0.598725\pi$
$752$	1.23550e7	0.796704
$753$	−2.35397e7	−1.51291
$754$	3.88688e6	0.248985
$755$	−7.40967e6	−0.473076
$756$	2.55228e7	1.62414
$757$	−1.42056e7	−0.900991	−0.450495	−	0.892779i	$-0.648753\pi$
$757$	−1.42056e7	−0.900991	−0.450495	+	0.892779i	$0.648753\pi$
$758$	−2.57676e7	−1.62892
$759$	1.69113e7	1.06555
$760$	−7.60842e6	−0.477816
$761$	1.25292e7	0.784261	0.392130	−	0.919910i	$-0.371738\pi$
$761$	1.25292e7	0.784261	0.392130	+	0.919910i	$0.371738\pi$
$762$	−1.93355e7	−1.20634
$763$	−8.55263e6	−0.531849
$764$	1.91473e7	1.18679
$765$	−4.19260e6	−0.259018
$766$	−4.82276e7	−2.96978
$767$	3.78140e6	0.232094
$768$	−5.77400e7	−3.53243
$769$	−1.76135e7	−1.07407	−0.537033	−	0.843561i	$-0.680455\pi$
$769$	−1.76135e7	−1.07407	−0.537033	+	0.843561i	$0.680455\pi$
$770$	2.92487e6	0.177779
$771$	3.32090e6	0.201196
$772$	7.96968e6	0.481280
$773$	−1.30817e7	−0.787438	−0.393719	−	0.919231i	$-0.628812\pi$
$773$	−1.30817e7	−0.787438	−0.393719	+	0.919231i	$0.628812\pi$
$774$	5.14351e7	3.08608
$775$	2.10573e7	1.25936
$776$	2.11314e6	0.125972
$777$	−3.35862e6	−0.199576
$778$	−2.40419e7	−1.42403
$779$	4.64417e6	0.274198
$780$	3.41582e6	0.201029
$781$	8.98677e6	0.527201
$782$	−8.26874e6	−0.483529
$783$	−3.40737e7	−1.98617
$784$	−1.40357e7	−0.815538
$785$	7.47227e6	0.432791
$786$	−6.34121e7	−3.66113
$787$	−6.24654e6	−0.359503	−0.179752	−	0.983712i	$-0.557529\pi$
$787$	−6.24654e6	−0.359503	−0.179752	+	0.983712i	$0.557529\pi$
$788$	−2.49734e7	−1.43272
$789$	1.78927e7	1.02325
$790$	5.34312e6	0.304598
$791$	−3.44950e6	−0.196026
$792$	4.38357e7	2.48322
$793$	−984311.	−0.0555840
$794$	814755.	0.0458644
$795$	−5.42999e6	−0.304706
$796$	−681952.	−0.0381480
$797$	2.86190e7	1.59591	0.797955	−	0.602718i	$-0.205915\pi$
$797$	2.86190e7	1.59591	0.797955	+	0.602718i	$0.205915\pi$
$798$	−1.60416e7	−0.891744
$799$	−4.65664e6	−0.258051
$800$	−543486.	−0.0300237
$801$	−1.65581e7	−0.911862
$802$	−2.46993e7	−1.35597
$803$	1.89806e6	0.103878
$804$	−4.26789e7	−2.32848
$805$	−2.49888e6	−0.135911
$806$	6.99078e6	0.379042
$807$	2.75280e7	1.48796
$808$	−5.97340e6	−0.321879
$809$	2.09954e7	1.12785	0.563926	−	0.825825i	$-0.309290\pi$
$809$	2.09954e7	1.12785	0.563926	+	0.825825i	$0.309290\pi$
$810$	−1.83593e7	−0.983202
$811$	5.19633e6	0.277425	0.138712	−	0.990333i	$-0.455704\pi$
$811$	5.19633e6	0.277425	0.138712	+	0.990333i	$0.455704\pi$
$812$	−1.44402e7	−0.768569
$813$	5.03923e7	2.67386
$814$	−6.21194e6	−0.328599
$815$	4.64494e6	0.244955
$816$	−1.02818e7	−0.540559
$817$	−1.15250e7	−0.604069
$818$	3.52921e7	1.84414
$819$	2.44648e6	0.127447
$820$	5.52030e6	0.286700
$821$	2.72052e7	1.40862	0.704310	−	0.709892i	$-0.251256\pi$
$821$	2.72052e7	1.40862	0.704310	+	0.709892i	$0.251256\pi$
$822$	−6.29094e7	−3.24740
$823$	3.12917e7	1.61039	0.805193	−	0.593013i	$-0.202062\pi$
$823$	3.12917e7	1.61039	0.805193	+	0.593013i	$0.202062\pi$
$824$	5.27695e6	0.270748
$825$	1.99583e7	1.02091
$826$	−2.11086e7	−1.07649
$827$	3.30372e7	1.67973	0.839864	−	0.542797i	$-0.182635\pi$
$827$	3.30372e7	1.67973	0.839864	+	0.542797i	$0.182635\pi$
$828$	−7.52893e7	−3.81643
$829$	1.48688e7	0.751433	0.375717	−	0.926735i	$-0.377397\pi$
$829$	1.48688e7	0.751433	0.375717	+	0.926735i	$0.377397\pi$
$830$	1.58465e7	0.798433
$831$	8.37015e6	0.420466
$832$	−3.05543e6	−0.153026
$833$	5.29013e6	0.264152
$834$	8.03772e7	4.00145
$835$	3.07817e6	0.152784
$836$	−1.97460e7	−0.977154
$837$	−6.12836e7	−3.02364
$838$	−2.04378e7	−1.00537
$839$	1.51419e7	0.742633	0.371317	−	0.928506i	$-0.378906\pi$
$839$	1.51419e7	0.742633	0.371317	+	0.928506i	$0.378906\pi$
$840$	−9.48492e6	−0.463805
$841$	−1.23300e6	−0.0601136
$842$	6.92758e6	0.336745
$843$	−7.02221e7	−3.40334
$844$	1.86418e7	0.900806
$845$	−7.77475e6	−0.374580
$846$	−6.37092e7	−3.06038
$847$	−4.54268e6	−0.217572
$848$	−9.09380e6	−0.434266
$849$	−1.08372e7	−0.515996
$850$	−9.75854e6	−0.463274
$851$	5.30719e6	0.251212
$852$	−5.85866e7	−2.76503
$853$	−3.45638e7	−1.62648	−0.813240	−	0.581928i	$-0.802299\pi$
$853$	−3.45638e7	−1.62648	−0.813240	+	0.581928i	$0.802299\pi$
$854$	5.49464e6	0.257807
$855$	1.28527e7	0.601284
$856$	5.24413e7	2.44618
$857$	−3.24538e7	−1.50943	−0.754716	−	0.656051i	$-0.772225\pi$
$857$	−3.24538e7	−1.50943	−0.754716	+	0.656051i	$0.772225\pi$
$858$	6.62591e6	0.307275
$859$	2.23709e7	1.03443	0.517213	−	0.855857i	$-0.326969\pi$
$859$	2.23709e7	1.03443	0.517213	+	0.855857i	$0.326969\pi$
$860$	−1.36992e7	−0.631612
$861$	5.78958e6	0.266158
$862$	6.65455e6	0.305036
$863$	−2.05867e6	−0.0940933	−0.0470467	−	0.998893i	$-0.514981\pi$
$863$	−2.05867e6	−0.0940933	−0.0470467	+	0.998893i	$0.514981\pi$
$864$	1.58172e6	0.0720852
$865$	8.63766e6	0.392515
$866$	−6.31017e7	−2.85921
$867$	−3.54303e7	−1.60076
$868$	−2.59715e7	−1.17003
$869$	6.89781e6	0.309857
$870$	2.54562e7	1.14024
$871$	−2.19141e6	−0.0978765
$872$	5.12970e7	2.28455
$873$	−3.56968e6	−0.158523
$874$	2.53484e7	1.12246
$875$	−6.40527e6	−0.282825
$876$	−1.23739e7	−0.544810
$877$	1.69402e7	0.743735	0.371868	−	0.928286i	$-0.378718\pi$
$877$	1.69402e7	0.743735	0.371868	+	0.928286i	$0.378718\pi$
$878$	−2.24706e7	−0.983734
$879$	1.11357e7	0.486124
$880$	−5.74698e6	−0.250169
$881$	9.01236e6	0.391200	0.195600	−	0.980684i	$-0.437335\pi$
$881$	9.01236e6	0.391200	0.195600	+	0.980684i	$0.437335\pi$
$882$	7.23761e7	3.13273
$883$	−2.11802e7	−0.914172	−0.457086	−	0.889423i	$-0.651107\pi$
$883$	−2.11802e7	−0.914172	−0.457086	+	0.889423i	$0.651107\pi$
$884$	−2.15612e6	−0.0927988
$885$	2.47654e7	1.06289
$886$	−1.32375e7	−0.566526
$887$	9.17582e6	0.391594	0.195797	−	0.980644i	$-0.437271\pi$
$887$	9.17582e6	0.391594	0.195797	+	0.980644i	$0.437271\pi$
$888$	2.01444e7	0.857278
$889$	3.68841e6	0.156525
$890$	6.62647e6	0.280419
$891$	−2.37013e7	−1.00018
$892$	−2.57451e7	−1.08338
$893$	1.42753e7	0.599040
$894$	−1.00237e8	−4.19453
$895$	6.15056e6	0.256659
$896$	1.67192e7	0.695738
$897$	−5.66087e6	−0.234910
$898$	−3.78224e7	−1.56516
$899$	3.46729e7	1.43084
$900$	−8.88545e7	−3.65656
$901$	3.42750e6	0.140658
$902$	1.07081e7	0.438225
$903$	−1.43675e7	−0.586357
$904$	2.06894e7	0.842029
$905$	9.99124e6	0.405507
$906$	9.37010e7	3.79249
$907$	2.26890e7	0.915792	0.457896	−	0.889006i	$-0.348603\pi$
$907$	2.26890e7	0.915792	0.457896	+	0.889006i	$0.348603\pi$
$908$	−2.61214e7	−1.05143
$909$	1.00907e7	0.405053
$910$	−979068.	−0.0391931
$911$	2.75195e6	0.109861	0.0549307	−	0.998490i	$-0.482506\pi$
$911$	2.75195e6	0.109861	0.0549307	+	0.998490i	$0.482506\pi$
$912$	3.15195e7	1.25485
$913$	2.04574e7	0.812219
$914$	4.27195e7	1.69146
$915$	−6.44652e6	−0.254550
$916$	2.79338e7	1.10000
$917$	1.20964e7	0.475042
$918$	2.84005e7	1.11229
$919$	−1.11537e7	−0.435641	−0.217820	−	0.975989i	$-0.569895\pi$
$919$	−1.11537e7	−0.435641	−0.217820	+	0.975989i	$0.569895\pi$
$920$	1.49878e7	0.583805
$921$	−1.00673e7	−0.391079
$922$	5.58285e7	2.16286
$923$	−3.00822e6	−0.116227
$924$	−2.46160e7	−0.948502
$925$	6.26341e6	0.240689
$926$	3.99354e7	1.53049
$927$	−8.91422e6	−0.340709
$928$	−894903.	−0.0341119
$929$	−1.42612e7	−0.542149	−0.271074	−	0.962558i	$-0.587379\pi$
$929$	−1.42612e7	−0.542149	−0.271074	+	0.962558i	$0.587379\pi$
$930$	4.57845e7	1.73585
$931$	−1.62173e7	−0.613202
$932$	2.86042e7	1.07867
$933$	4.10886e7	1.54532
$934$	−7.17914e7	−2.69281
$935$	2.16606e6	0.0810293
$936$	−1.46735e7	−0.547450
$937$	−3.84068e7	−1.42909	−0.714544	−	0.699591i	$-0.753366\pi$
$937$	−3.84068e7	−1.42909	−0.714544	+	0.699591i	$0.753366\pi$
$938$	1.22329e7	0.453966
$939$	2.53677e7	0.938896
$940$	1.69683e7	0.626354
$941$	−2.00548e7	−0.738321	−0.369160	−	0.929366i	$-0.620355\pi$
$941$	−2.00548e7	−0.738321	−0.369160	+	0.929366i	$0.620355\pi$
$942$	−9.44927e7	−3.46953
$943$	−9.14852e6	−0.335021
$944$	4.14755e7	1.51482
$945$	8.58286e6	0.312646
$946$	−2.65734e7	−0.965427
$947$	−8.41217e6	−0.304813	−0.152406	−	0.988318i	$-0.548702\pi$
$947$	−8.41217e6	−0.304813	−0.152406	+	0.988318i	$0.548702\pi$
$948$	−4.49682e7	−1.62512
$949$	−635356.	−0.0229008
$950$	2.99155e7	1.07544
$951$	−1.15052e7	−0.412516
$952$	5.98704e6	0.214101
$953$	−4.64382e7	−1.65632	−0.828158	−	0.560495i	$-0.810611\pi$
$953$	−4.64382e7	−1.65632	−0.828158	+	0.560495i	$0.810611\pi$
$954$	4.68928e7	1.66815
$955$	6.43890e6	0.228456
$956$	−1.91001e7	−0.675912
$957$	3.28632e7	1.15993
$958$	5.68721e7	2.00210
$959$	1.20005e7	0.421359
$960$	−2.00108e7	−0.700789
$961$	3.37321e7	1.17824
$962$	2.07938e6	0.0724428
$963$	−8.85878e7	−3.07828
$964$	7.60225e7	2.63481
$965$	2.68006e6	0.0926460
$966$	3.16002e7	1.08955
$967$	3.56006e7	1.22431	0.612155	−	0.790738i	$-0.290303\pi$
$967$	3.56006e7	1.22431	0.612155	+	0.790738i	$0.290303\pi$
$968$	2.72461e7	0.934580
$969$	−1.18799e7	−0.406445
$970$	1.42857e6	0.0487497
$971$	−2.10949e7	−0.718008	−0.359004	−	0.933336i	$-0.616884\pi$
$971$	−2.10949e7	−0.718008	−0.359004	+	0.933336i	$0.616884\pi$
$972$	3.44399e7	1.16922
$973$	−1.53326e7	−0.519199
$974$	−4.03502e6	−0.136285
$975$	−6.68081e6	−0.225070
$976$	−1.07962e7	−0.362783
$977$	1.84560e7	0.618588	0.309294	−	0.950966i	$-0.399907\pi$
$977$	1.84560e7	0.618588	0.309294	+	0.950966i	$0.399907\pi$
$978$	−5.87389e7	−1.96372
$979$	8.55458e6	0.285261
$980$	−1.92767e7	−0.641161
$981$	−8.66548e7	−2.87488
$982$	−4.48550e7	−1.48434
$983$	−966289.	−0.0318950
$983$	−966289.	−0.0318950
$984$	−3.47248e7	−1.14328
$985$	−8.39813e6	−0.275799
$986$	−1.60684e7	−0.526356
$987$	1.77961e7	0.581475
$988$	6.60974e6	0.215423
$989$	2.27031e7	0.738064
$990$	2.96347e7	0.960975
$991$	9.23706e6	0.298779	0.149389	−	0.988778i	$-0.452269\pi$
$991$	9.23706e6	0.298779	0.149389	+	0.988778i	$0.452269\pi$
$992$	−1.60953e6	−0.0519303
$993$	5.86334e7	1.88700
$994$	1.67925e7	0.539077
$995$	−229329.	−0.00734346
$996$	−1.33366e8	−4.25987
$997$	3.08179e7	0.981896	0.490948	−	0.871189i	$-0.336651\pi$
$997$	3.08179e7	0.981896	0.490948	+	0.871189i	$0.336651\pi$
$998$	1.21918e7	0.387472
$999$	−1.82285e7	−0.577881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.6.a.a.1.16	✓	191

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.6.a.a.1.16	✓	191	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:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-9.78124 q^{2} +27.6828 q^{3} +63.6727 q^{4} +21.4120 q^{5} -270.772 q^{6} +51.6520 q^{7} -309.799 q^{8} +523.335 q^{9} +O(q^{10})\)	\(q-9.78124 q^{2} +27.6828 q^{3} +63.6727 q^{4} +21.4120 q^{5} -270.772 q^{6} +51.6520 q^{7} -309.799 q^{8} +523.335 q^{9} -209.436 q^{10} -270.376 q^{11} +1762.64 q^{12} +90.5053 q^{13} -505.221 q^{14} +592.744 q^{15} +992.690 q^{16} -374.150 q^{17} -5118.87 q^{18} +1146.98 q^{19} +1363.36 q^{20} +1429.87 q^{21} +2644.61 q^{22} -2259.44 q^{23} -8576.09 q^{24} -2666.52 q^{25} -885.254 q^{26} +7760.45 q^{27} +3288.82 q^{28} -4390.69 q^{29} -5797.77 q^{30} -7896.91 q^{31} +203.818 q^{32} -7484.76 q^{33} +3659.65 q^{34} +1105.97 q^{35} +33322.2 q^{36} -2348.90 q^{37} -11218.9 q^{38} +2505.44 q^{39} -6633.42 q^{40} +4049.03 q^{41} -13985.9 q^{42} -10048.1 q^{43} -17215.6 q^{44} +11205.7 q^{45} +22100.1 q^{46} +12445.9 q^{47} +27480.4 q^{48} -14139.1 q^{49} +26081.9 q^{50} -10357.5 q^{51} +5762.72 q^{52} -9160.77 q^{53} -75906.9 q^{54} -5789.30 q^{55} -16001.7 q^{56} +31751.6 q^{57} +42946.4 q^{58} +41780.9 q^{59} +37741.6 q^{60} -10875.7 q^{61} +77241.6 q^{62} +27031.3 q^{63} -33759.7 q^{64} +1937.90 q^{65} +73210.2 q^{66} -24213.1 q^{67} -23823.1 q^{68} -62547.4 q^{69} -10817.8 q^{70} -33238.1 q^{71} -162129. q^{72} -7020.09 q^{73} +22975.2 q^{74} -73816.8 q^{75} +73031.5 q^{76} -13965.5 q^{77} -24506.3 q^{78} -25511.9 q^{79} +21255.5 q^{80} +87660.3 q^{81} -39604.6 q^{82} -75662.7 q^{83} +91043.7 q^{84} -8011.30 q^{85} +98283.2 q^{86} -121546. q^{87} +83762.2 q^{88} -31639.6 q^{89} -109605. q^{90} +4674.78 q^{91} -143864. q^{92} -218608. q^{93} -121737. q^{94} +24559.2 q^{95} +5642.25 q^{96} -6821.02 q^{97} +138298. q^{98} -141497. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 191 q - 37 q^{2} - 74 q^{3} + 2821 q^{4} - 247 q^{5} - 335 q^{6} - 1569 q^{7} - 1761 q^{8} + 13251 q^{9}+O(q^{10}) \) 191 * q - 37 * q^2 - 74 * q^3 + 2821 * q^4 - 247 * q^5 - 335 * q^6 - 1569 * q^7 - 1761 * q^8 + 13251 * q^9	\( 191 q - 37 q^{2} - 74 q^{3} + 2821 q^{4} - 247 q^{5} - 335 q^{6} - 1569 q^{7} - 1761 q^{8} + 13251 q^{9} - 2867 q^{10} - 1878 q^{11} - 3400 q^{12} - 6854 q^{13} - 1601 q^{14} - 3461 q^{15} + 38457 q^{16} - 10730 q^{17} - 17249 q^{18} - 5817 q^{19} - 9988 q^{20} - 15999 q^{21} - 20287 q^{22} - 15625 q^{23} - 19747 q^{24} + 67082 q^{25} - 9868 q^{26} - 22892 q^{27} - 72720 q^{28} - 17960 q^{29} - 27464 q^{30} - 25604 q^{31} - 68869 q^{32} - 60654 q^{33} - 42876 q^{34} - 30018 q^{35} + 172922 q^{36} - 114862 q^{37} + 4404 q^{38} - 73500 q^{39} - 137154 q^{40} - 90896 q^{41} - 10652 q^{42} - 121447 q^{43} - 57962 q^{44} - 109019 q^{45} - 136262 q^{46} - 86994 q^{47} - 133347 q^{48} + 278242 q^{49} - 93911 q^{50} - 66966 q^{51} - 284241 q^{52} - 122112 q^{53} - 130806 q^{54} - 134904 q^{55} - 100292 q^{56} - 423426 q^{57} - 307669 q^{58} - 85704 q^{59} - 238277 q^{60} - 206736 q^{61} - 190602 q^{62} - 387623 q^{63} + 411903 q^{64} - 244408 q^{65} - 113963 q^{66} - 337002 q^{67} - 388031 q^{68} - 165342 q^{69} - 183925 q^{70} - 174806 q^{71} - 753621 q^{72} - 1009738 q^{73} - 204958 q^{74} - 282676 q^{75} - 326869 q^{76} - 332288 q^{77} - 591801 q^{78} - 488092 q^{79} - 259068 q^{80} + 385959 q^{81} - 523996 q^{82} - 315720 q^{83} - 750486 q^{84} - 1001755 q^{85} - 287709 q^{86} - 316995 q^{87} - 836923 q^{88} - 298065 q^{89} - 751039 q^{90} - 521459 q^{91} - 640932 q^{92} - 554391 q^{93} - 623481 q^{94} - 491883 q^{95} - 767843 q^{96} - 1468693 q^{97} - 714146 q^{98} - 842507 q^{99}+O(q^{100}) \) 191 * q - 37 * q^2 - 74 * q^3 + 2821 * q^4 - 247 * q^5 - 335 * q^6 - 1569 * q^7 - 1761 * q^8 + 13251 * q^9 - 2867 * q^10 - 1878 * q^11 - 3400 * q^12 - 6854 * q^13 - 1601 * q^14 - 3461 * q^15 + 38457 * q^16 - 10730 * q^17 - 17249 * q^18 - 5817 * q^19 - 9988 * q^20 - 15999 * q^21 - 20287 * q^22 - 15625 * q^23 - 19747 * q^24 + 67082 * q^25 - 9868 * q^26 - 22892 * q^27 - 72720 * q^28 - 17960 * q^29 - 27464 * q^30 - 25604 * q^31 - 68869 * q^32 - 60654 * q^33 - 42876 * q^34 - 30018 * q^35 + 172922 * q^36 - 114862 * q^37 + 4404 * q^38 - 73500 * q^39 - 137154 * q^40 - 90896 * q^41 - 10652 * q^42 - 121447 * q^43 - 57962 * q^44 - 109019 * q^45 - 136262 * q^46 - 86994 * q^47 - 133347 * q^48 + 278242 * q^49 - 93911 * q^50 - 66966 * q^51 - 284241 * q^52 - 122112 * q^53 - 130806 * q^54 - 134904 * q^55 - 100292 * q^56 - 423426 * q^57 - 307669 * q^58 - 85704 * q^59 - 238277 * q^60 - 206736 * q^61 - 190602 * q^62 - 387623 * q^63 + 411903 * q^64 - 244408 * q^65 - 113963 * q^66 - 337002 * q^67 - 388031 * q^68 - 165342 * q^69 - 183925 * q^70 - 174806 * q^71 - 753621 * q^72 - 1009738 * q^73 - 204958 * q^74 - 282676 * q^75 - 326869 * q^76 - 332288 * q^77 - 591801 * q^78 - 488092 * q^79 - 259068 * q^80 + 385959 * q^81 - 523996 * q^82 - 315720 * q^83 - 750486 * q^84 - 1001755 * q^85 - 287709 * q^86 - 316995 * q^87 - 836923 * q^88 - 298065 * q^89 - 751039 * q^90 - 521459 * q^91 - 640932 * q^92 - 554391 * q^93 - 623481 * q^94 - 491883 * q^95 - 767843 * q^96 - 1468693 * q^97 - 714146 * q^98 - 842507 * q^99

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