LMFDB - Embedded newform 43.6.a.b.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,6,Mod(1,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, 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("43.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	43.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:	$6.89650425196$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} - 256 x^{8} + 266 x^{7} + 21986 x^{6} - 10450 x^{5} - 719484 x^{4} + 384582 x^{3} + \cdots - 22734604 $ x^10 - 2x^9 - 256x^8 + 266x^7 + 21986x^6 - 10450x^5 - 719484x^4 + 384582x^3 + 8437093x^2 - 5752252*x - 22734604
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-8.57770$ of defining polynomial
Character	$\chi$	$=$	43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.57770 q^{2} -7.84343 q^{3} +59.7324 q^{4} +28.1028 q^{5} -75.1221 q^{6} +195.604 q^{7} +265.613 q^{8} -181.481 q^{9} +O(q^{10})$	\(q+9.57770 q^{2} -7.84343 q^{3} +59.7324 q^{4} +28.1028 q^{5} -75.1221 q^{6} +195.604 q^{7} +265.613 q^{8} -181.481 q^{9} +269.160 q^{10} +72.8476 q^{11} -468.507 q^{12} +301.666 q^{13} +1873.44 q^{14} -220.422 q^{15} +632.525 q^{16} -1207.20 q^{17} -1738.17 q^{18} -2350.21 q^{19} +1678.65 q^{20} -1534.21 q^{21} +697.713 q^{22} +516.070 q^{23} -2083.32 q^{24} -2335.23 q^{25} +2889.27 q^{26} +3329.38 q^{27} +11683.9 q^{28} +1531.55 q^{29} -2111.14 q^{30} +1126.13 q^{31} -2441.48 q^{32} -571.375 q^{33} -11562.2 q^{34} +5497.02 q^{35} -10840.3 q^{36} -9339.18 q^{37} -22509.6 q^{38} -2366.10 q^{39} +7464.47 q^{40} +19704.2 q^{41} -14694.2 q^{42} +1849.00 q^{43} +4351.37 q^{44} -5100.11 q^{45} +4942.77 q^{46} -13797.6 q^{47} -4961.16 q^{48} +21453.9 q^{49} -22366.2 q^{50} +9468.56 q^{51} +18019.2 q^{52} -3351.03 q^{53} +31887.9 q^{54} +2047.22 q^{55} +51954.9 q^{56} +18433.7 q^{57} +14668.7 q^{58} +2511.18 q^{59} -13166.4 q^{60} +49249.3 q^{61} +10785.7 q^{62} -35498.3 q^{63} -43624.6 q^{64} +8477.66 q^{65} -5472.46 q^{66} +9116.54 q^{67} -72108.8 q^{68} -4047.76 q^{69} +52648.8 q^{70} +43397.3 q^{71} -48203.6 q^{72} +80067.4 q^{73} -89447.9 q^{74} +18316.2 q^{75} -140384. q^{76} +14249.3 q^{77} -22661.8 q^{78} -65991.7 q^{79} +17775.7 q^{80} +17986.0 q^{81} +188721. q^{82} -76880.9 q^{83} -91641.8 q^{84} -33925.6 q^{85} +17709.2 q^{86} -12012.6 q^{87} +19349.3 q^{88} -75722.6 q^{89} -48847.4 q^{90} +59007.1 q^{91} +30826.1 q^{92} -8832.73 q^{93} -132150. q^{94} -66047.5 q^{95} +19149.6 q^{96} -67921.7 q^{97} +205479. q^{98} -13220.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 8 q^{2} + 28 q^{3} + 202 q^{4} + 138 q^{5} + 75 q^{6} + 60 q^{7} + 294 q^{8} + 1356 q^{9}+O(q^{10}) $ 10 * q + 8 * q^2 + 28 * q^3 + 202 * q^4 + 138 * q^5 + 75 * q^6 + 60 * q^7 + 294 * q^8 + 1356 * q^9	\( 10 q + 8 q^{2} + 28 q^{3} + 202 q^{4} + 138 q^{5} + 75 q^{6} + 60 q^{7} + 294 q^{8} + 1356 q^{9} - 17 q^{10} + 745 q^{11} + 4627 q^{12} + 1917 q^{13} + 1936 q^{14} + 1688 q^{15} + 5354 q^{16} + 4017 q^{17} - 2725 q^{18} - 2404 q^{19} + 1311 q^{20} - 228 q^{21} - 5836 q^{22} + 1733 q^{23} - 10711 q^{24} + 7120 q^{25} - 1484 q^{26} - 2324 q^{27} - 15028 q^{28} + 6996 q^{29} - 48420 q^{30} - 4899 q^{31} - 7554 q^{32} - 15734 q^{33} - 27033 q^{34} + 7084 q^{35} + 4433 q^{36} + 1466 q^{37} + 13905 q^{38} - 26542 q^{39} - 93211 q^{40} + 10297 q^{41} - 37642 q^{42} + 18490 q^{43} - 36140 q^{44} + 73822 q^{45} + 17991 q^{46} + 48592 q^{47} + 83607 q^{48} + 29458 q^{49} + 983 q^{50} + 92972 q^{51} + 14232 q^{52} + 127165 q^{53} - 92002 q^{54} + 106672 q^{55} - 7780 q^{56} + 34060 q^{57} - 10305 q^{58} + 99372 q^{59} + 111372 q^{60} + 17408 q^{61} + 28265 q^{62} + 2244 q^{63} + 47202 q^{64} + 54484 q^{65} - 150292 q^{66} - 2021 q^{67} + 192151 q^{68} + 1654 q^{69} - 33194 q^{70} + 11286 q^{71} - 298365 q^{72} + 49892 q^{73} - 125431 q^{74} - 44662 q^{75} - 249803 q^{76} + 98144 q^{77} - 28494 q^{78} - 91524 q^{79} + 12251 q^{80} - 26450 q^{81} - 158909 q^{82} - 105203 q^{83} - 357682 q^{84} - 87212 q^{85} + 14792 q^{86} + 181200 q^{87} - 461824 q^{88} - 62682 q^{89} - 522670 q^{90} - 295304 q^{91} + 183783 q^{92} - 238430 q^{93} + 7259 q^{94} - 305340 q^{95} - 162399 q^{96} + 108383 q^{97} + 354656 q^{98} - 270499 q^{99}+O(q^{100}) \) 10 * q + 8 * q^2 + 28 * q^3 + 202 * q^4 + 138 * q^5 + 75 * q^6 + 60 * q^7 + 294 * q^8 + 1356 * q^9 - 17 * q^10 + 745 * q^11 + 4627 * q^12 + 1917 * q^13 + 1936 * q^14 + 1688 * q^15 + 5354 * q^16 + 4017 * q^17 - 2725 * q^18 - 2404 * q^19 + 1311 * q^20 - 228 * q^21 - 5836 * q^22 + 1733 * q^23 - 10711 * q^24 + 7120 * q^25 - 1484 * q^26 - 2324 * q^27 - 15028 * q^28 + 6996 * q^29 - 48420 * q^30 - 4899 * q^31 - 7554 * q^32 - 15734 * q^33 - 27033 * q^34 + 7084 * q^35 + 4433 * q^36 + 1466 * q^37 + 13905 * q^38 - 26542 * q^39 - 93211 * q^40 + 10297 * q^41 - 37642 * q^42 + 18490 * q^43 - 36140 * q^44 + 73822 * q^45 + 17991 * q^46 + 48592 * q^47 + 83607 * q^48 + 29458 * q^49 + 983 * q^50 + 92972 * q^51 + 14232 * q^52 + 127165 * q^53 - 92002 * q^54 + 106672 * q^55 - 7780 * q^56 + 34060 * q^57 - 10305 * q^58 + 99372 * q^59 + 111372 * q^60 + 17408 * q^61 + 28265 * q^62 + 2244 * q^63 + 47202 * q^64 + 54484 * q^65 - 150292 * q^66 - 2021 * q^67 + 192151 * q^68 + 1654 * q^69 - 33194 * q^70 + 11286 * q^71 - 298365 * q^72 + 49892 * q^73 - 125431 * q^74 - 44662 * q^75 - 249803 * q^76 + 98144 * q^77 - 28494 * q^78 - 91524 * q^79 + 12251 * q^80 - 26450 * q^81 - 158909 * q^82 - 105203 * q^83 - 357682 * q^84 - 87212 * q^85 + 14792 * q^86 + 181200 * q^87 - 461824 * q^88 - 62682 * q^89 - 522670 * q^90 - 295304 * q^91 + 183783 * q^92 - 238430 * q^93 + 7259 * q^94 - 305340 * q^95 - 162399 * q^96 + 108383 * q^97 + 354656 * q^98 - 270499 * 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 $

$2$	9.57770	1.69311	0.846557	−	0.532297i	$-0.178671\pi$
$2$	9.57770	1.69311	0.846557	+	0.532297i	$0.178671\pi$
$3$	−7.84343	−0.503156	−0.251578	−	0.967837i	$-0.580950\pi$
$3$	−7.84343	−0.503156	−0.251578	+	0.967837i	$0.580950\pi$
$4$	59.7324	1.86664
$5$	28.1028	0.502718	0.251359	−	0.967894i	$-0.419122\pi$
$5$	28.1028	0.502718	0.251359	+	0.967894i	$0.419122\pi$
$6$	−75.1221	−0.851901
$7$	195.604	1.50880	0.754401	−	0.656413i	$-0.227927\pi$
$7$	195.604	1.50880	0.754401	+	0.656413i	$0.227927\pi$
$8$	265.613	1.46732
$9$	−181.481	−0.746834
$10$	269.160	0.851160
$11$	72.8476	0.181524	0.0907619	−	0.995873i	$-0.471070\pi$
$11$	72.8476	0.181524	0.0907619	+	0.995873i	$0.471070\pi$
$12$	−468.507	−0.939211
$13$	301.666	0.495072	0.247536	−	0.968879i	$-0.420379\pi$
$13$	301.666	0.495072	0.247536	+	0.968879i	$0.420379\pi$
$14$	1873.44	2.55458
$15$	−220.422	−0.252946
$16$	632.525	0.617700
$17$	−1207.20	−1.01311	−0.506554	−	0.862208i	$-0.669081\pi$
$17$	−1207.20	−1.01311	−0.506554	+	0.862208i	$0.669081\pi$
$18$	−1738.17	−1.26448
$19$	−2350.21	−1.49356	−0.746780	−	0.665071i	$-0.768401\pi$
$19$	−2350.21	−1.49356	−0.746780	+	0.665071i	$0.768401\pi$
$20$	1678.65	0.938393
$21$	−1534.21	−0.759164
$22$	697.713	0.307341
$23$	516.070	0.203418	0.101709	−	0.994814i	$-0.467569\pi$
$23$	516.070	0.203418	0.101709	+	0.994814i	$0.467569\pi$
$24$	−2083.32	−0.738290
$25$	−2335.23	−0.747274
$26$	2889.27	0.838213
$27$	3329.38	0.878930
$28$	11683.9	2.81639
$29$	1531.55	0.338171	0.169085	−	0.985601i	$-0.445919\pi$
$29$	1531.55	0.338171	0.169085	+	0.985601i	$0.445919\pi$
$30$	−2111.14	−0.428266
$31$	1126.13	0.210467	0.105234	−	0.994448i	$-0.466441\pi$
$31$	1126.13	0.210467	0.105234	+	0.994448i	$0.466441\pi$
$32$	−2441.48	−0.421481
$33$	−571.375	−0.0913349
$34$	−11562.2	−1.71531
$35$	5497.02	0.758503
$36$	−10840.3	−1.39407
$37$	−9339.18	−1.12151	−0.560756	−	0.827981i	$-0.689490\pi$
$37$	−9339.18	−1.12151	−0.560756	+	0.827981i	$0.689490\pi$
$38$	−22509.6	−2.52877
$39$	−2366.10	−0.249098
$40$	7464.47	0.737647
$41$	19704.2	1.83062	0.915310	−	0.402750i	$-0.131946\pi$
$41$	19704.2	1.83062	0.915310	+	0.402750i	$0.131946\pi$
$42$	−14694.2	−1.28535
$43$	1849.00	0.152499
$43$	1849.00	0.152499
$44$	4351.37	0.338839
$45$	−5100.11	−0.375447
$46$	4942.77	0.344410
$47$	−13797.6	−0.911088	−0.455544	−	0.890213i	$-0.650555\pi$
$47$	−13797.6	−0.911088	−0.455544	+	0.890213i	$0.650555\pi$
$48$	−4961.16	−0.310800
$49$	21453.9	1.27649
$50$	−22366.2	−1.26522
$51$	9468.56	0.509752
$52$	18019.2	0.924120
$53$	−3351.03	−0.163866	−0.0819330	−	0.996638i	$-0.526109\pi$
$53$	−3351.03	−0.163866	−0.0819330	+	0.996638i	$0.526109\pi$
$54$	31887.9	1.48813
$55$	2047.22	0.0912554
$56$	51954.9	2.21389
$57$	18433.7	0.751494
$58$	14668.7	0.572562
$59$	2511.18	0.0939177	0.0469588	−	0.998897i	$-0.485047\pi$
$59$	2511.18	0.0939177	0.0469588	+	0.998897i	$0.485047\pi$
$60$	−13166.4	−0.472158
$61$	49249.3	1.69463	0.847316	−	0.531088i	$-0.178217\pi$
$61$	49249.3	1.69463	0.847316	+	0.531088i	$0.178217\pi$
$62$	10785.7	0.356345
$63$	−35498.3	−1.12682
$64$	−43624.6	−1.33132
$65$	8477.66	0.248882
$66$	−5472.46	−0.154640
$67$	9116.54	0.248109	0.124055	−	0.992275i	$-0.460410\pi$
$67$	9116.54	0.248109	0.124055	+	0.992275i	$0.460410\pi$
$68$	−72108.8	−1.89111
$69$	−4047.76	−0.102351
$70$	52648.8	1.28423
$71$	43397.3	1.02168	0.510842	−	0.859675i	$-0.329334\pi$
$71$	43397.3	1.02168	0.510842	+	0.859675i	$0.329334\pi$
$72$	−48203.6	−1.09584
$73$	80067.4	1.75852	0.879262	−	0.476338i	$-0.158036\pi$
$73$	80067.4	1.75852	0.879262	+	0.476338i	$0.158036\pi$
$74$	−89447.9	−1.89885
$75$	18316.2	0.375996
$76$	−140384.	−2.78794
$77$	14249.3	0.273884
$78$	−22661.8	−0.421752
$79$	−65991.7	−1.18966	−0.594828	−	0.803853i	$-0.702780\pi$
$79$	−65991.7	−1.18966	−0.594828	+	0.803853i	$0.702780\pi$
$80$	17775.7	0.310529
$81$	17986.0	0.304594
$82$	188721.	3.09945
$83$	−76880.9	−1.22496	−0.612482	−	0.790484i	$-0.709829\pi$
$83$	−76880.9	−1.22496	−0.612482	+	0.790484i	$0.709829\pi$
$84$	−91641.8	−1.41708
$85$	−33925.6	−0.509308
$86$	17709.2	0.258198
$87$	−12012.6	−0.170153
$88$	19349.3	0.266353
$89$	−75722.6	−1.01333	−0.506665	−	0.862143i	$-0.669122\pi$
$89$	−75722.6	−1.01333	−0.506665	+	0.862143i	$0.669122\pi$
$90$	−48847.4	−0.635675
$91$	59007.1	0.746965
$92$	30826.1	0.379708
$93$	−8832.73	−0.105898
$94$	−132150.	−1.54258
$95$	−66047.5	−0.750840
$96$	19149.6	0.212071
$97$	−67921.7	−0.732958	−0.366479	−	0.930426i	$-0.619437\pi$
$97$	−67921.7	−0.732958	−0.366479	+	0.930426i	$0.619437\pi$
$98$	205479.	2.16124
$99$	−13220.4	−0.135568
$100$	−139489.	−1.39489
$101$	130824.	1.27610	0.638051	−	0.769994i	$-0.279741\pi$
$101$	130824.	1.27610	0.638051	+	0.769994i	$0.279741\pi$
$102$	90687.1	0.863068
$103$	41945.9	0.389580	0.194790	−	0.980845i	$-0.437597\pi$
$103$	41945.9	0.389580	0.194790	+	0.980845i	$0.437597\pi$
$104$	80126.4	0.726428
$105$	−43115.5	−0.381645
$106$	−32095.2	−0.277444
$107$	−5277.45	−0.0445620	−0.0222810	−	0.999752i	$-0.507093\pi$
$107$	−5277.45	−0.0445620	−0.0222810	+	0.999752i	$0.507093\pi$
$108$	198872.	1.64064
$109$	−138680.	−1.11802	−0.559008	−	0.829163i	$-0.688818\pi$
$109$	−138680.	−1.11802	−0.559008	+	0.829163i	$0.688818\pi$
$110$	19607.7	0.154506
$111$	73251.2	0.564296
$112$	123724.	0.931988
$113$	251325.	1.85157	0.925783	−	0.378055i	$-0.123407\pi$
$113$	251325.	1.85157	0.925783	+	0.378055i	$0.123407\pi$
$114$	176553.	1.27237
$115$	14503.0	0.102262
$116$	91483.1	0.631242
$117$	−54746.5	−0.369736
$118$	24051.3	0.159013
$119$	−236132.	−1.52858
$120$	−58547.0	−0.371152
$121$	−155744.	−0.967049
$122$	471695.	2.86921
$123$	−154548.	−0.921088
$124$	67266.5	0.392866
$125$	−153448.	−0.878387
$126$	−339992.	−1.90784
$127$	−175695.	−0.966606	−0.483303	−	0.875453i	$-0.660563\pi$
$127$	−175695.	−0.966606	−0.483303	+	0.875453i	$0.660563\pi$
$128$	−339696.	−1.83259
$129$	−14502.5	−0.0767306
$130$	81196.5	0.421385
$131$	213758.	1.08829	0.544144	−	0.838992i	$-0.316854\pi$
$131$	213758.	1.08829	0.544144	+	0.838992i	$0.316854\pi$
$132$	−34129.6	−0.170489
$133$	−459711.	−2.25349
$134$	87315.5	0.420077
$135$	93565.0	0.441854
$136$	−320647.	−1.48655
$137$	126026.	0.573664	0.286832	−	0.957981i	$-0.407398\pi$
$137$	126026.	0.573664	0.286832	+	0.957981i	$0.407398\pi$
$138$	−38768.2	−0.173292
$139$	181105.	0.795049	0.397524	−	0.917592i	$-0.369869\pi$
$139$	181105.	0.795049	0.397524	+	0.917592i	$0.369869\pi$
$140$	328350.	1.41585
$141$	108221.	0.458419
$142$	415646.	1.72983
$143$	21975.7	0.0898673
$144$	−114791.	−0.461319
$145$	43040.8	0.170004
$146$	766862.	2.97738
$147$	−168272.	−0.642272
$148$	−557852.	−2.09346
$149$	187084.	0.690354	0.345177	−	0.938538i	$-0.387819\pi$
$149$	187084.	0.690354	0.345177	+	0.938538i	$0.387819\pi$
$150$	175427.	0.636604
$151$	−396158.	−1.41392	−0.706962	−	0.707252i	$-0.749935\pi$
$151$	−396158.	−1.41392	−0.706962	+	0.707252i	$0.749935\pi$
$152$	−624247.	−2.19153
$153$	219083.	0.756623
$154$	136475.	0.463717
$155$	31647.4	0.105806
$156$	−141333.	−0.464977
$157$	504286.	1.63278	0.816390	−	0.577501i	$-0.195972\pi$
$157$	504286.	1.63278	0.816390	+	0.577501i	$0.195972\pi$
$158$	−632049.	−2.01423
$159$	26283.6	0.0824502
$160$	−68612.4	−0.211886
$161$	100945.	0.306917
$162$	172265.	0.515713
$163$	−466039.	−1.37389	−0.686946	−	0.726708i	$-0.741049\pi$
$163$	−466039.	−1.37389	−0.686946	+	0.726708i	$0.741049\pi$
$164$	1.17698e6	3.41711
$165$	−16057.2	−0.0459157
$166$	−736343.	−2.07401
$167$	−142267.	−0.394742	−0.197371	−	0.980329i	$-0.563240\pi$
$167$	−142267.	−0.394742	−0.197371	+	0.980329i	$0.563240\pi$
$168$	−407505.	−1.11393
$169$	−280291.	−0.754904
$170$	−324930.	−0.862317
$171$	426518.	1.11544
$172$	110445.	0.284660
$173$	526184.	1.33666	0.668332	−	0.743863i	$-0.267009\pi$
$173$	526184.	1.33666	0.668332	+	0.743863i	$0.267009\pi$
$174$	−115053.	−0.288088
$175$	−456781.	−1.12749
$176$	46077.9	0.112127
$177$	−19696.2	−0.0472553
$178$	−725249.	−1.71568
$179$	692470.	1.61536	0.807678	−	0.589624i	$-0.200724\pi$
$179$	692470.	1.61536	0.807678	+	0.589624i	$0.200724\pi$
$180$	−304642.	−0.700824
$181$	286664.	0.650393	0.325197	−	0.945646i	$-0.394569\pi$
$181$	286664.	0.650393	0.325197	+	0.945646i	$0.394569\pi$
$182$	565152.	1.26470
$183$	−386284.	−0.852665
$184$	137075.	0.298479
$185$	−262457.	−0.563805
$186$	−84597.3	−0.179297
$187$	−87941.4	−0.183903
$188$	−824167.	−1.70067
$189$	651241.	1.32613
$190$	−632584.	−1.27126
$191$	−692472.	−1.37347	−0.686734	−	0.726909i	$-0.740956\pi$
$191$	−692472.	−1.37347	−0.686734	+	0.726909i	$0.740956\pi$
$192$	342166.	0.669860
$193$	855425.	1.65306	0.826530	−	0.562893i	$-0.190312\pi$
$193$	855425.	1.65306	0.826530	+	0.562893i	$0.190312\pi$
$194$	−650534.	−1.24098
$195$	−66493.9	−0.125226
$196$	1.28149e6	2.38274
$197$	−749649.	−1.37623	−0.688117	−	0.725600i	$-0.741562\pi$
$197$	−749649.	−1.37623	−0.688117	+	0.725600i	$0.741562\pi$
$198$	−126621.	−0.229532
$199$	990082.	1.77230	0.886152	−	0.463394i	$-0.153369\pi$
$199$	990082.	1.77230	0.886152	+	0.463394i	$0.153369\pi$
$200$	−620268.	−1.09649
$201$	−71504.9	−0.124838
$202$	1.25300e6	2.16059
$203$	299577.	0.510233
$204$	565580.	0.951522
$205$	553742.	0.920286
$206$	401746.	0.659604
$207$	−93656.7	−0.151919
$208$	190811.	0.305806
$209$	−171207.	−0.271117
$210$	−412947.	−0.646169
$211$	−274555.	−0.424545	−0.212272	−	0.977211i	$-0.568086\pi$
$211$	−274555.	−0.424545	−0.212272	+	0.977211i	$0.568086\pi$
$212$	−200165.	−0.305879
$213$	−340384.	−0.514067
$214$	−50545.8	−0.0754486
$215$	51962.1	0.0766638
$216$	884327.	1.28967
$217$	220276.	0.317554
$218$	−1.32824e6	−1.89293
$219$	−628003.	−0.884813
$220$	122286.	0.170341
$221$	−364170.	−0.501561
$222$	701578.	0.955418
$223$	−568751.	−0.765878	−0.382939	−	0.923774i	$-0.625088\pi$
$223$	−568751.	−0.765878	−0.382939	+	0.923774i	$0.625088\pi$
$224$	−477563.	−0.635932
$225$	423799.	0.558090
$226$	2.40712e6	3.13492
$227$	607473.	0.782461	0.391230	−	0.920293i	$-0.372050\pi$
$227$	607473.	0.782461	0.391230	+	0.920293i	$0.372050\pi$
$228$	1.10109e6	1.40277
$229$	104213.	0.131320	0.0656600	−	0.997842i	$-0.479085\pi$
$229$	104213.	0.131320	0.0656600	+	0.997842i	$0.479085\pi$
$230$	138906.	0.173141
$231$	−111763.	−0.137806
$232$	406799.	0.496204
$233$	1.28050e6	1.54521	0.772606	−	0.634885i	$-0.218953\pi$
$233$	1.28050e6	1.54521	0.772606	+	0.634885i	$0.218953\pi$
$234$	−524346.	−0.626006
$235$	−387752.	−0.458020
$236$	149999.	0.175310
$237$	517601.	0.598583
$238$	−2.26161e6	−2.58806
$239$	221000.	0.250264	0.125132	−	0.992140i	$-0.460065\pi$
$239$	221000.	0.250264	0.125132	+	0.992140i	$0.460065\pi$
$240$	−139423.	−0.156245
$241$	−480522.	−0.532931	−0.266465	−	0.963845i	$-0.585856\pi$
$241$	−480522.	−0.532931	−0.266465	+	0.963845i	$0.585856\pi$
$242$	−1.49167e6	−1.63733
$243$	−950112.	−1.03219
$244$	2.94178e6	3.16327
$245$	602915.	0.641713
$246$	−1.48022e6	−1.55951
$247$	−708979.	−0.739420
$248$	299115.	0.308822
$249$	603010.	0.616348
$250$	−1.46968e6	−1.48721
$251$	722732.	0.724091	0.362045	−	0.932161i	$-0.382079\pi$
$251$	722732.	0.724091	0.362045	+	0.932161i	$0.382079\pi$
$252$	−2.12040e6	−2.10337
$253$	37594.5	0.0369252
$254$	−1.68275e6	−1.63657
$255$	266093.	0.256261
$256$	−1.85752e6	−1.77147
$257$	−1.34492e6	−1.27018	−0.635089	−	0.772439i	$-0.719037\pi$
$257$	−1.34492e6	−1.27018	−0.635089	+	0.772439i	$0.719037\pi$
$258$	−138901.	−0.129914
$259$	−1.82678e6	−1.69214
$260$	506391.	0.464572
$261$	−277946.	−0.252557
$262$	2.04731e6	1.84260
$263$	−18066.1	−0.0161055	−0.00805275	−	0.999968i	$-0.502563\pi$
$263$	−18066.1	−0.0161055	−0.00805275	+	0.999968i	$0.502563\pi$
$264$	−151765.	−0.134017
$265$	−94173.4	−0.0823784
$266$	−4.40297e6	−3.81542
$267$	593925.	0.509863
$268$	544553.	0.463130
$269$	−549502.	−0.463008	−0.231504	−	0.972834i	$-0.574365\pi$
$269$	−549502.	−0.463008	−0.231504	+	0.972834i	$0.574365\pi$
$270$	896138.	0.748110
$271$	13732.4	0.0113586	0.00567929	−	0.999984i	$-0.498192\pi$
$271$	13732.4	0.0113586	0.00567929	+	0.999984i	$0.498192\pi$
$272$	−763582.	−0.625797
$273$	−462818.	−0.375840
$274$	1.20704e6	0.971278
$275$	−170116.	−0.135648
$276$	−241782.	−0.191052
$277$	−501657.	−0.392833	−0.196416	−	0.980521i	$-0.562930\pi$
$277$	−501657.	−0.392833	−0.196416	+	0.980521i	$0.562930\pi$
$278$	1.73457e6	1.34611
$279$	−204371.	−0.157184
$280$	1.46008e6	1.11296
$281$	605657.	0.457574	0.228787	−	0.973477i	$-0.426524\pi$
$281$	605657.	0.457574	0.228787	+	0.973477i	$0.426524\pi$
$282$	1.03651e6	0.776157
$283$	−1.85484e6	−1.37671	−0.688353	−	0.725376i	$-0.741666\pi$
$283$	−1.85484e6	−1.37671	−0.688353	+	0.725376i	$0.741666\pi$
$284$	2.59223e6	1.90711
$285$	518039.	0.377790
$286$	210476.	0.152156
$287$	3.85421e6	2.76204
$288$	443081.	0.314776
$289$	37467.4	0.0263882
$290$	412232.	0.287837
$291$	532739.	0.368792
$292$	4.78262e6	3.28253
$293$	950968.	0.647138	0.323569	−	0.946205i	$-0.395117\pi$
$293$	950968.	0.647138	0.323569	+	0.946205i	$0.395117\pi$
$294$	−1.61166e6	−1.08744
$295$	70571.1	0.0472141
$296$	−2.48061e6	−1.64562
$297$	242538.	0.159547
$298$	1.79184e6	1.16885
$299$	155681.	0.100706
$300$	1.09407e6	0.701848
$301$	361672.	0.230090
$302$	−3.79428e6	−2.39393
$303$	−1.02611e6	−0.642079
$304$	−1.48657e6	−0.922572
$305$	1.38404e6	0.851923
$306$	2.09831e6	1.28105
$307$	−736219.	−0.445822	−0.222911	−	0.974839i	$-0.571556\pi$
$307$	−736219.	−0.445822	−0.222911	+	0.974839i	$0.571556\pi$
$308$	851144.	0.511242
$309$	−329000.	−0.196020
$310$	303110.	0.179141
$311$	−1.02220e6	−0.599286	−0.299643	−	0.954051i	$-0.596867\pi$
$311$	−1.02220e6	−0.599286	−0.299643	+	0.954051i	$0.596867\pi$
$312$	−628466.	−0.365507
$313$	−60474.7	−0.0348909	−0.0174455	−	0.999848i	$-0.505553\pi$
$313$	−60474.7	−0.0348909	−0.0174455	+	0.999848i	$0.505553\pi$
$314$	4.82990e6	2.76448
$315$	−997602.	−0.566475
$316$	−3.94184e6	−2.22066
$317$	842265.	0.470761	0.235381	−	0.971903i	$-0.424366\pi$
$317$	842265.	0.470761	0.235381	+	0.971903i	$0.424366\pi$
$318$	251736.	0.139598
$319$	111570.	0.0613860
$320$	−1.22597e6	−0.669277
$321$	41393.3	0.0224216
$322$	966825.	0.519646
$323$	2.83717e6	1.51314
$324$	1.07435e6	0.568568
$325$	−704460.	−0.369954
$326$	−4.46358e6	−2.32616
$327$	1.08773e6	0.562536
$328$	5.23368e6	2.68610
$329$	−2.69887e6	−1.37465
$330$	−153792.	−0.0777406
$331$	−3.50942e6	−1.76062	−0.880308	−	0.474402i	$-0.842664\pi$
$331$	−3.50942e6	−1.76062	−0.880308	+	0.474402i	$0.842664\pi$
$332$	−4.59228e6	−2.28657
$333$	1.69488e6	0.837584
$334$	−1.36259e6	−0.668344
$335$	256200.	0.124729
$336$	−970423.	−0.468935
$337$	−1.49987e6	−0.719414	−0.359707	−	0.933065i	$-0.617123\pi$
$337$	−1.49987e6	−0.719414	−0.359707	+	0.933065i	$0.617123\pi$
$338$	−2.68454e6	−1.27814
$339$	−1.97125e6	−0.931627
$340$	−2.02646e6	−0.950694
$341$	82036.0	0.0382048
$342$	4.08506e6	1.88857
$343$	908952.	0.417163
$344$	491118.	0.223764
$345$	−113753.	−0.0514537
$346$	5.03963e6	2.26313
$347$	2.16958e6	0.967280	0.483640	−	0.875267i	$-0.339314\pi$
$347$	2.16958e6	0.967280	0.483640	+	0.875267i	$0.339314\pi$
$348$	−717541.	−0.317613
$349$	393576.	0.172968	0.0864838	−	0.996253i	$-0.472437\pi$
$349$	393576.	0.172968	0.0864838	+	0.996253i	$0.472437\pi$
$350$	−4.37491e6	−1.90897
$351$	1.00436e6	0.435133
$352$	−177856.	−0.0765089
$353$	272744.	0.116498	0.0582491	−	0.998302i	$-0.481448\pi$
$353$	272744.	0.116498	0.0582491	+	0.998302i	$0.481448\pi$
$354$	−188645.	−0.0800086
$355$	1.21959e6	0.513619
$356$	−4.52309e6	−1.89152
$357$	1.85209e6	0.769115
$358$	6.63227e6	2.73498
$359$	−3.96827e6	−1.62504	−0.812521	−	0.582932i	$-0.801906\pi$
$359$	−3.96827e6	−1.62504	−0.812521	+	0.582932i	$0.801906\pi$
$360$	−1.35466e6	−0.550900
$361$	3.04739e6	1.23072
$362$	2.74558e6	1.10119
$363$	1.22157e6	0.486577
$364$	3.52464e6	1.39431
$365$	2.25012e6	0.884042
$366$	−3.69971e6	−1.44366
$367$	−4.90395e6	−1.90056	−0.950278	−	0.311404i	$-0.899201\pi$
$367$	−4.90395e6	−1.90056	−0.950278	+	0.311404i	$0.899201\pi$
$368$	326427.	0.125651
$369$	−3.57592e6	−1.36717
$370$	−2.51374e6	−0.954587
$371$	−655475.	−0.247242
$372$	−527600.	−0.197673
$373$	2.52633e6	0.940196	0.470098	−	0.882614i	$-0.344219\pi$
$373$	2.52633e6	0.940196	0.470098	+	0.882614i	$0.344219\pi$
$374$	−842277.	−0.311369
$375$	1.20356e6	0.441966
$376$	−3.66483e6	−1.33686
$377$	462016.	0.167419
$378$	6.23739e6	2.24529
$379$	−607631.	−0.217291	−0.108646	−	0.994081i	$-0.534651\pi$
$379$	−607631.	−0.217291	−0.108646	+	0.994081i	$0.534651\pi$
$380$	−3.94518e6	−1.40155
$381$	1.37805e6	0.486354
$382$	−6.63229e6	−2.32544
$383$	−3.94370e6	−1.37375	−0.686874	−	0.726777i	$-0.741018\pi$
$383$	−3.94370e6	−1.37375	−0.686874	+	0.726777i	$0.741018\pi$
$384$	2.66438e6	0.922079
$385$	400445.	0.137686
$386$	8.19301e6	2.79882
$387$	−335558.	−0.113891
$388$	−4.05713e6	−1.36817
$389$	−2.42464e6	−0.812405	−0.406203	−	0.913783i	$-0.633147\pi$
$389$	−2.42464e6	−0.812405	−0.406203	+	0.913783i	$0.633147\pi$
$390$	−636859.	−0.212023
$391$	−622998.	−0.206084
$392$	5.69843e6	1.87301
$393$	−1.67660e6	−0.547579
$394$	−7.17991e6	−2.33012
$395$	−1.85455e6	−0.598062
$396$	−789689.	−0.253057
$397$	−2.94322e6	−0.937232	−0.468616	−	0.883402i	$-0.655247\pi$
$397$	−2.94322e6	−0.937232	−0.468616	+	0.883402i	$0.655247\pi$
$398$	9.48271e6	3.00072
$399$	3.60571e6	1.13386
$400$	−1.47709e6	−0.461591
$401$	−5.82714e6	−1.80965	−0.904824	−	0.425785i	$-0.859998\pi$
$401$	−5.82714e6	−1.80965	−0.904824	+	0.425785i	$0.859998\pi$
$402$	−684853.	−0.211365
$403$	339715.	0.104196
$404$	7.81446e6	2.38202
$405$	505457.	0.153125
$406$	2.86926e6	0.863883
$407$	−680337.	−0.203581
$408$	2.51497e6	0.747968
$409$	1.22650e6	0.362542	0.181271	−	0.983433i	$-0.441979\pi$
$409$	1.22650e6	0.362542	0.181271	+	0.983433i	$0.441979\pi$
$410$	5.30358e6	1.55815
$411$	−988473.	−0.288642
$412$	2.50553e6	0.727205
$413$	491196.	0.141703
$414$	−897016.	−0.257217
$415$	−2.16057e6	−0.615812
$416$	−736511.	−0.208663
$417$	−1.42049e6	−0.400034
$418$	−1.63977e6	−0.459032
$419$	1.13490e6	0.315809	0.157904	−	0.987454i	$-0.449526\pi$
$419$	1.13490e6	0.315809	0.157904	+	0.987454i	$0.449526\pi$
$420$	−2.57539e6	−0.712394
$421$	−5.21555e6	−1.43415	−0.717075	−	0.696996i	$-0.754520\pi$
$421$	−5.21555e6	−1.43415	−0.717075	+	0.696996i	$0.754520\pi$
$422$	−2.62961e6	−0.718803
$423$	2.50400e6	0.680431
$424$	−890078.	−0.240444
$425$	2.81909e6	0.757070
$426$	−3.26009e6	−0.870374
$427$	9.63336e6	2.55687
$428$	−315235.	−0.0831811
$429$	−172365.	−0.0452173
$430$	497677.	0.129801
$431$	4.94938e6	1.28339	0.641693	−	0.766961i	$-0.278232\pi$
$431$	4.94938e6	1.28339	0.641693	+	0.766961i	$0.278232\pi$
$432$	2.10592e6	0.542915
$433$	−2.02994e6	−0.520311	−0.260156	−	0.965567i	$-0.583774\pi$
$433$	−2.02994e6	−0.520311	−0.260156	+	0.965567i	$0.583774\pi$
$434$	2.10973e6	0.537655
$435$	−337588.	−0.0855388
$436$	−8.28369e6	−2.08693
$437$	−1.21287e6	−0.303817
$438$	−6.01482e6	−1.49809
$439$	−4.05767e6	−1.00488	−0.502442	−	0.864611i	$-0.667565\pi$
$439$	−4.05767e6	−1.00488	−0.502442	+	0.864611i	$0.667565\pi$
$440$	543769.	0.133901
$441$	−3.89347e6	−0.953323
$442$	−3.48792e6	−0.849201
$443$	3.73717e6	0.904761	0.452380	−	0.891825i	$-0.350575\pi$
$443$	3.73717e6	0.904761	0.452380	+	0.891825i	$0.350575\pi$
$444$	4.37547e6	1.05334
$445$	−2.12802e6	−0.509419
$446$	−5.44733e6	−1.29672
$447$	−1.46738e6	−0.347356
$448$	−8.53313e6	−2.00869
$449$	−2.08643e6	−0.488414	−0.244207	−	0.969723i	$-0.578528\pi$
$449$	−2.08643e6	−0.488414	−0.244207	+	0.969723i	$0.578528\pi$
$450$	4.05903e6	0.944910
$451$	1.43540e6	0.332301
$452$	1.50122e7	3.45620
$453$	3.10724e6	0.711424
$454$	5.81820e6	1.32480
$455$	1.65826e6	0.375513
$456$	4.89623e6	1.10268
$457$	383012.	0.0857871	0.0428936	−	0.999080i	$-0.486342\pi$
$457$	383012.	0.0857871	0.0428936	+	0.999080i	$0.486342\pi$
$458$	998117.	0.222340
$459$	−4.01922e6	−0.890452
$460$	866300.	0.190886
$461$	−767599.	−0.168222	−0.0841109	−	0.996456i	$-0.526805\pi$
$461$	−767599.	−0.168222	−0.0841109	+	0.996456i	$0.526805\pi$
$462$	−1.07044e6	−0.233322
$463$	2.87956e6	0.624272	0.312136	−	0.950037i	$-0.398955\pi$
$463$	2.87956e6	0.624272	0.312136	+	0.950037i	$0.398955\pi$
$464$	968743.	0.208888
$465$	−248224.	−0.0532368
$466$	1.22642e7	2.61622
$467$	4.73971e6	1.00568	0.502840	−	0.864379i	$-0.332288\pi$
$467$	4.73971e6	1.00568	0.502840	+	0.864379i	$0.332288\pi$
$468$	−3.27014e6	−0.690164
$469$	1.78323e6	0.374348
$470$	−3.71378e6	−0.775481
$471$	−3.95533e6	−0.821543
$472$	667001.	0.137807
$473$	134695.	0.0276821
$474$	4.95743e6	1.01347
$475$	5.48829e6	1.11610
$476$	−1.41048e7	−2.85331
$477$	608147.	0.122381
$478$	2.11668e6	0.423726
$479$	5.41230e6	1.07781	0.538906	−	0.842366i	$-0.318838\pi$
$479$	5.41230e6	1.07781	0.538906	+	0.842366i	$0.318838\pi$
$480$	538156.	0.106612
$481$	−2.81731e6	−0.555229
$482$	−4.60230e6	−0.902313
$483$	−791758.	−0.154427
$484$	−9.30298e6	−1.80513
$485$	−1.90879e6	−0.368471
$486$	−9.09989e6	−1.74761
$487$	5.16701e6	0.987227	0.493614	−	0.869681i	$-0.335676\pi$
$487$	5.16701e6	0.987227	0.493614	+	0.869681i	$0.335676\pi$
$488$	1.30813e7	2.48657
$489$	3.65534e6	0.691283
$490$	5.77454e6	1.08649
$491$	1.68112e6	0.314698	0.157349	−	0.987543i	$-0.449705\pi$
$491$	1.68112e6	0.314698	0.157349	+	0.987543i	$0.449705\pi$
$492$	−9.23154e6	−1.71934
$493$	−1.84888e6	−0.342603
$494$	−6.79039e6	−1.25192
$495$	−371531.	−0.0681526
$496$	712306.	0.130006
$497$	8.48868e6	1.54152
$498$	5.77545e6	1.04355
$499$	3.57956e6	0.643545	0.321772	−	0.946817i	$-0.395721\pi$
$499$	3.57956e6	0.643545	0.321772	+	0.946817i	$0.395721\pi$
$500$	−9.16581e6	−1.63963
$501$	1.11586e6	0.198617
$502$	6.92211e6	1.22597
$503$	−1.07972e6	−0.190279	−0.0951397	−	0.995464i	$-0.530330\pi$
$503$	−1.07972e6	−0.190279	−0.0951397	+	0.995464i	$0.530330\pi$
$504$	−9.42881e6	−1.65341
$505$	3.67653e6	0.641520
$506$	360069.	0.0625186
$507$	2.19844e6	0.379835
$508$	−1.04947e7	−1.80430
$509$	1.11760e6	0.191202	0.0956012	−	0.995420i	$-0.469523\pi$
$509$	1.11760e6	0.191202	0.0956012	+	0.995420i	$0.469523\pi$
$510$	2.54856e6	0.433880
$511$	1.56615e7	2.65327
$512$	−6.92051e6	−1.16671
$513$	−7.82475e6	−1.31274
$514$	−1.28813e7	−2.15056
$515$	1.17880e6	0.195849
$516$	−866270.	−0.143228
$517$	−1.00513e6	−0.165384
$518$	−1.74964e7	−2.86499
$519$	−4.12709e6	−0.672551
$520$	2.25178e6	0.365188
$521$	−6.50399e6	−1.04975	−0.524874	−	0.851180i	$-0.675888\pi$
$521$	−6.50399e6	−1.04975	−0.524874	+	0.851180i	$0.675888\pi$
$522$	−2.66209e6	−0.427608
$523$	437675.	0.0699677	0.0349838	−	0.999388i	$-0.488862\pi$
$523$	437675.	0.0699677	0.0349838	+	0.999388i	$0.488862\pi$
$524$	1.27683e7	2.03144
$525$	3.58273e6	0.567304
$526$	−173031.	−0.0272685
$527$	−1.35946e6	−0.213226
$528$	−361409.	−0.0564176
$529$	−6.17001e6	−0.958621
$530$	−901965.	−0.139476
$531$	−455730.	−0.0701409
$532$	−2.74596e7	−4.20645
$533$	5.94407e6	0.906288
$534$	5.68844e6	0.863256
$535$	−148311.	−0.0224021
$536$	2.42147e6	0.364055
$537$	−5.43134e6	−0.812777
$538$	−5.26297e6	−0.783926
$539$	1.56287e6	0.231713
$540$	5.58886e6	0.824782
$541$	6.56956e6	0.965035	0.482518	−	0.875886i	$-0.339722\pi$
$541$	6.56956e6	0.965035	0.482518	+	0.875886i	$0.339722\pi$
$542$	131525.	0.0192314
$543$	−2.24843e6	−0.327249
$544$	2.94735e6	0.427006
$545$	−3.89730e6	−0.562047
$546$	−4.43273e6	−0.636341
$547$	−2.84947e6	−0.407189	−0.203595	−	0.979055i	$-0.565262\pi$
$547$	−2.84947e6	−0.407189	−0.203595	+	0.979055i	$0.565262\pi$
$548$	7.52781e6	1.07082
$549$	−8.93780e6	−1.26561
$550$	−1.62932e6	−0.229668
$551$	−3.59946e6	−0.505078
$552$	−1.07514e6	−0.150181
$553$	−1.29082e7	−1.79496
$554$	−4.80472e6	−0.665111
$555$	2.05856e6	0.283682
$556$	1.08178e7	1.48407
$557$	1.14478e7	1.56344	0.781722	−	0.623627i	$-0.214342\pi$
$557$	1.14478e7	1.56344	0.781722	+	0.623627i	$0.214342\pi$
$558$	−1.95740e6	−0.266131
$559$	557781.	0.0754977
$560$	3.47700e6	0.468527
$561$	689763.	0.0925321
$562$	5.80080e6	0.774725
$563$	3.98082e6	0.529300	0.264650	−	0.964345i	$-0.414744\pi$
$563$	3.98082e6	0.529300	0.264650	+	0.964345i	$0.414744\pi$
$564$	6.46429e6	0.855703
$565$	7.06293e6	0.930816
$566$	−1.77652e7	−2.33092
$567$	3.51813e6	0.459573
$568$	1.15269e7	1.49914
$569$	8.49999e6	1.10062	0.550311	−	0.834960i	$-0.314509\pi$
$569$	8.49999e6	1.10062	0.550311	+	0.834960i	$0.314509\pi$
$570$	4.96162e6	0.639642
$571$	5.24847e6	0.673663	0.336831	−	0.941565i	$-0.390645\pi$
$571$	5.24847e6	0.673663	0.336831	+	0.941565i	$0.390645\pi$
$572$	1.31266e6	0.167750
$573$	5.43135e6	0.691069
$574$	3.69145e7	4.67646
$575$	−1.20514e6	−0.152009
$576$	7.91701e6	0.994272
$577$	1.94309e6	0.242970	0.121485	−	0.992593i	$-0.461234\pi$
$577$	1.94309e6	0.242970	0.121485	+	0.992593i	$0.461234\pi$
$578$	358852.	0.0446782
$579$	−6.70946e6	−0.831747
$580$	2.57093e6	0.317337
$581$	−1.50382e7	−1.84823
$582$	5.10242e6	0.624408
$583$	−244115.	−0.0297456
$584$	2.12669e7	2.58031
$585$	−1.53853e6	−0.185873
$586$	9.10809e6	1.09568
$587$	924441.	0.110735	0.0553674	−	0.998466i	$-0.482367\pi$
$587$	924441.	0.110735	0.0553674	+	0.998466i	$0.482367\pi$
$588$	−1.00513e7	−1.19889
$589$	−2.64665e6	−0.314346
$590$	675909.	0.0799389
$591$	5.87982e6	0.692461
$592$	−5.90726e6	−0.692759
$593$	−1.09140e7	−1.27453	−0.637263	−	0.770646i	$-0.719934\pi$
$593$	−1.09140e7	−1.27453	−0.637263	+	0.770646i	$0.719934\pi$
$594$	2.32296e6	0.270131
$595$	−6.63598e6	−0.768445
$596$	1.11750e7	1.28864
$597$	−7.76564e6	−0.891746
$598$	1.49106e6	0.170508
$599$	−6.47200e6	−0.737006	−0.368503	−	0.929626i	$-0.620130\pi$
$599$	−6.47200e6	−0.737006	−0.368503	+	0.929626i	$0.620130\pi$
$600$	4.86503e6	0.551705
$601$	−9.66608e6	−1.09160	−0.545801	−	0.837915i	$-0.683775\pi$
$601$	−9.66608e6	−1.09160	−0.545801	+	0.837915i	$0.683775\pi$
$602$	3.46398e6	0.389569
$603$	−1.65447e6	−0.185296
$604$	−2.36635e7	−2.63928
$605$	−4.37685e6	−0.486153
$606$	−9.82780e6	−1.08711
$607$	1.50825e7	1.66151	0.830753	−	0.556641i	$-0.187910\pi$
$607$	1.50825e7	1.66151	0.830753	+	0.556641i	$0.187910\pi$
$608$	5.73799e6	0.629507
$609$	−2.34971e6	−0.256727
$610$	1.32560e7	1.44240
$611$	−4.16228e6	−0.451054
$612$	1.30863e7	1.41234
$613$	−2.07592e6	−0.223131	−0.111565	−	0.993757i	$-0.535586\pi$
$613$	−2.07592e6	−0.223131	−0.111565	+	0.993757i	$0.535586\pi$
$614$	−7.05129e6	−0.754827
$615$	−4.34324e6	−0.463048
$616$	3.78479e6	0.401875
$617$	1.05100e7	1.11145	0.555727	−	0.831365i	$-0.312440\pi$
$617$	1.05100e7	1.11145	0.555727	+	0.831365i	$0.312440\pi$
$618$	−3.15106e6	−0.331884
$619$	−6.33902e6	−0.664960	−0.332480	−	0.943110i	$-0.607885\pi$
$619$	−6.33902e6	−0.664960	−0.332480	+	0.943110i	$0.607885\pi$
$620$	1.89038e6	0.197501
$621$	1.71820e6	0.178790
$622$	−9.79030e6	−1.01466
$623$	−1.48116e7	−1.52891
$624$	−1.49661e6	−0.153868
$625$	2.98529e6	0.305694
$626$	−579208.	−0.0590744
$627$	1.34285e6	0.136414
$628$	3.01222e7	3.04781
$629$	1.12742e7	1.13621
$630$	−9.55474e6	−0.959108
$631$	−1.15541e7	−1.15521	−0.577606	−	0.816316i	$-0.696013\pi$
$631$	−1.15541e7	−1.15521	−0.577606	+	0.816316i	$0.696013\pi$
$632$	−1.75283e7	−1.74560
$633$	2.15345e6	0.213612
$634$	8.06697e6	0.797053
$635$	−4.93751e6	−0.485930
$636$	1.56998e6	0.153905
$637$	6.47191e6	0.631952
$638$	1.06858e6	0.103934
$639$	−7.87577e6	−0.763028
$640$	−9.54640e6	−0.921276
$641$	−3.92627e6	−0.377429	−0.188714	−	0.982032i	$-0.560432\pi$
$641$	−3.92627e6	−0.377429	−0.188714	+	0.982032i	$0.560432\pi$
$642$	396453.	0.0379624
$643$	−1.87570e7	−1.78911	−0.894553	−	0.446961i	$-0.852506\pi$
$643$	−1.87570e7	−1.78911	−0.894553	+	0.446961i	$0.852506\pi$
$644$	6.02971e6	0.572904
$645$	−407561.	−0.0385739
$646$	2.71736e7	2.56192
$647$	−9.03463e6	−0.848496	−0.424248	−	0.905546i	$-0.639462\pi$
$647$	−9.03463e6	−0.848496	−0.424248	+	0.905546i	$0.639462\pi$
$648$	4.77731e6	0.446937
$649$	182933.	0.0170483
$650$	−6.74711e6	−0.626375
$651$	−1.72772e6	−0.159779
$652$	−2.78376e7	−2.56456
$653$	1.74423e7	1.60074	0.800371	−	0.599505i	$-0.204636\pi$
$653$	1.74423e7	1.60074	0.800371	+	0.599505i	$0.204636\pi$
$654$	1.04179e7	0.952439
$655$	6.00720e6	0.547103
$656$	1.24634e7	1.13077
$657$	−1.45307e7	−1.31333
$658$	−2.58490e7	−2.32744
$659$	1.74636e7	1.56646	0.783230	−	0.621732i	$-0.213571\pi$
$659$	1.74636e7	1.56646	0.783230	+	0.621732i	$0.213571\pi$
$660$	−959138.	−0.0857080
$661$	5.12626e6	0.456348	0.228174	−	0.973620i	$-0.426724\pi$
$661$	5.12626e6	0.456348	0.228174	+	0.973620i	$0.426724\pi$
$662$	−3.36121e7	−2.98093
$663$	2.85634e6	0.252364
$664$	−2.04206e7	−1.79741
$665$	−1.29192e7	−1.13287
$666$	1.62331e7	1.41813
$667$	790386.	0.0687899
$668$	−8.49796e6	−0.736841
$669$	4.46096e6	0.385356
$670$	2.45381e6	0.211181
$671$	3.58770e6	0.307616
$672$	3.74573e6	0.319973
$673$	4.98529e6	0.424280	0.212140	−	0.977239i	$-0.431957\pi$
$673$	4.98529e6	0.424280	0.212140	+	0.977239i	$0.431957\pi$
$674$	−1.43653e7	−1.21805
$675$	−7.77489e6	−0.656802
$676$	−1.67424e7	−1.40913
$677$	8.15170e6	0.683560	0.341780	−	0.939780i	$-0.388970\pi$
$677$	8.15170e6	0.683560	0.341780	+	0.939780i	$0.388970\pi$
$678$	−1.88800e7	−1.57735
$679$	−1.32857e7	−1.10589
$680$	−9.01108e6	−0.747317
$681$	−4.76467e6	−0.393700
$682$	785716.	0.0646852
$683$	−3.28051e6	−0.269085	−0.134543	−	0.990908i	$-0.542957\pi$
$683$	−3.28051e6	−0.269085	−0.134543	+	0.990908i	$0.542957\pi$
$684$	2.54769e7	2.08213
$685$	3.54167e6	0.288391
$686$	8.70567e6	0.706305
$687$	−817384.	−0.0660745
$688$	1.16954e6	0.0941984
$689$	−1.01089e6	−0.0811254
$690$	−1.08950e6	−0.0871170
$691$	1.54825e7	1.23352	0.616758	−	0.787153i	$-0.288446\pi$
$691$	1.54825e7	1.23352	0.616758	+	0.787153i	$0.288446\pi$
$692$	3.14302e7	2.49507
$693$	−2.58597e6	−0.204546
$694$	2.07796e7	1.63772
$695$	5.08956e6	0.399685
$696$	−3.19070e6	−0.249668
$697$	−2.37868e7	−1.85462
$698$	3.76955e6	0.292854
$699$	−1.00435e7	−0.777483
$700$	−2.72846e7	−2.10462
$701$	−4.91809e6	−0.378008	−0.189004	−	0.981976i	$-0.560526\pi$
$701$	−4.91809e6	−0.378008	−0.189004	+	0.981976i	$0.560526\pi$
$702$	9.61948e6	0.736731
$703$	2.19490e7	1.67505
$704$	−3.17795e6	−0.241666
$705$	3.04131e6	0.230456
$706$	2.61227e6	0.197245
$707$	2.55898e7	1.92539
$708$	−1.17650e6	−0.0882085
$709$	−8.69925e6	−0.649930	−0.324965	−	0.945726i	$-0.605352\pi$
$709$	−8.69925e6	−0.649930	−0.324965	+	0.945726i	$0.605352\pi$
$710$	1.16808e7	0.869616
$711$	1.19762e7	0.888476
$712$	−2.01129e7	−1.48688
$713$	581162.	0.0428128
$714$	1.77388e7	1.30220
$715$	617578.	0.0451779
$716$	4.13629e7	3.01529
$717$	−1.73340e6	−0.125922
$718$	−3.80069e7	−2.75138
$719$	−8.92512e6	−0.643861	−0.321930	−	0.946763i	$-0.604332\pi$
$719$	−8.92512e6	−0.643861	−0.321930	+	0.946763i	$0.604332\pi$
$720$	−3.22595e6	−0.231914
$721$	8.20479e6	0.587799
$722$	2.91870e7	2.08376
$723$	3.76894e6	0.268147
$724$	1.71231e7	1.21405
$725$	−3.57652e6	−0.252706
$726$	1.16998e7	0.823830
$727$	1.33205e7	0.934729	0.467365	−	0.884065i	$-0.345204\pi$
$727$	1.33205e7	0.934729	0.467365	+	0.884065i	$0.345204\pi$
$728$	1.56730e7	1.09604
$729$	3.08154e6	0.214758
$730$	2.15510e7	1.49678
$731$	−2.23211e6	−0.154498
$732$	−2.30737e7	−1.59162
$733$	1.41244e7	0.970981	0.485490	−	0.874242i	$-0.338641\pi$
$733$	1.41244e7	0.970981	0.485490	+	0.874242i	$0.338641\pi$
$734$	−4.69685e7	−3.21786
$735$	−4.72892e6	−0.322882
$736$	−1.25997e6	−0.0857368
$737$	664118.	0.0450377
$738$	−3.42491e7	−2.31477
$739$	−1.65506e7	−1.11482	−0.557408	−	0.830239i	$-0.688204\pi$
$739$	−1.65506e7	−1.11482	−0.557408	+	0.830239i	$0.688204\pi$
$740$	−1.56772e7	−1.05242
$741$	5.56083e6	0.372044
$742$	−6.27795e6	−0.418608
$743$	1.32085e7	0.877771	0.438885	−	0.898543i	$-0.355373\pi$
$743$	1.32085e7	0.877771	0.438885	+	0.898543i	$0.355373\pi$
$744$	−2.34609e6	−0.155386
$745$	5.25759e6	0.347054
$746$	2.41965e7	1.59186
$747$	1.39524e7	0.914845
$748$	−5.25296e6	−0.343281
$749$	−1.03229e6	−0.0672353
$750$	1.15273e7	0.748299
$751$	1.62740e6	0.105291	0.0526457	−	0.998613i	$-0.483235\pi$
$751$	1.62740e6	0.105291	0.0526457	+	0.998613i	$0.483235\pi$
$752$	−8.72735e6	−0.562779
$753$	−5.66870e6	−0.364331
$754$	4.42506e6	0.283459
$755$	−1.11331e7	−0.710805
$756$	3.89002e7	2.47541
$757$	−1.41817e7	−0.899472	−0.449736	−	0.893162i	$-0.648482\pi$
$757$	−1.41817e7	−0.899472	−0.449736	+	0.893162i	$0.648482\pi$
$758$	−5.81971e6	−0.367899
$759$	−294870.	−0.0185791
$760$	−1.75431e7	−1.10172
$761$	−631434.	−0.0395245	−0.0197622	−	0.999805i	$-0.506291\pi$
$761$	−631434.	−0.0395245	−0.0197622	+	0.999805i	$0.506291\pi$
$762$	1.31985e7	0.823453
$763$	−2.71264e7	−1.68686
$764$	−4.13630e7	−2.56377
$765$	6.15684e6	0.380368
$766$	−3.77716e7	−2.32591
$767$	757537.	0.0464960
$768$	1.45693e7	0.891326
$769$	2920.58	0.000178096 0	8.90480e−5	−	1.00000i	$-0.499972\pi$
$769$	2920.58	0.000178096 0	8.90480e−5		1.00000i	$0.499972\pi$
$770$	3.83534e6	0.233119
$771$	1.05488e7	0.639098
$772$	5.10966e7	3.08566
$773$	−8.64224e6	−0.520209	−0.260104	−	0.965580i	$-0.583757\pi$
$773$	−8.64224e6	−0.520209	−0.260104	+	0.965580i	$0.583757\pi$
$774$	−3.21387e6	−0.192831
$775$	−2.62978e6	−0.157277
$776$	−1.80409e7	−1.07548
$777$	1.43282e7	0.851412
$778$	−2.32225e7	−1.37550
$779$	−4.63089e7	−2.73414
$780$	−3.97184e6	−0.233752
$781$	3.16139e6	0.185460
$782$	−5.96689e6	−0.348924
$783$	5.09911e6	0.297228
$784$	1.35701e7	0.788485
$785$	1.41718e7	0.820828
$786$	−1.60579e7	−0.927115
$787$	6.88838e6	0.396443	0.198221	−	0.980157i	$-0.436484\pi$
$787$	6.88838e6	0.396443	0.198221	+	0.980157i	$0.436484\pi$
$788$	−4.47783e7	−2.56893
$789$	141700.	0.00810358
$790$	−1.77623e7	−1.01259
$791$	4.91601e7	2.79365
$792$	−3.51152e6	−0.198922
$793$	1.48568e7	0.838965
$794$	−2.81893e7	−1.58684
$795$	738642.	0.0414492
$796$	5.91400e7	3.30825
$797$	2.93617e7	1.63733	0.818664	−	0.574273i	$-0.194715\pi$
$797$	2.93617e7	1.63733	0.818664	+	0.574273i	$0.194715\pi$
$798$	3.45344e7	1.91975
$799$	1.66565e7	0.923030
$800$	5.70142e6	0.314962
$801$	1.37422e7	0.756788
$802$	−5.58106e7	−3.06394
$803$	5.83272e6	0.319214
$804$	−4.27116e6	−0.233027
$805$	2.83685e6	0.154293
$806$	3.25369e6	0.176416
$807$	4.30998e6	0.232965
$808$	3.47487e7	1.87245
$809$	−2.84195e6	−0.152667	−0.0763334	−	0.997082i	$-0.524321\pi$
$809$	−2.84195e6	−0.152667	−0.0763334	+	0.997082i	$0.524321\pi$
$810$	4.84112e6	0.259259
$811$	1.67390e6	0.0893670	0.0446835	−	0.999001i	$-0.485772\pi$
$811$	1.67390e6	0.0893670	0.0446835	+	0.999001i	$0.485772\pi$
$812$	1.78945e7	0.952420
$813$	−107709.	−0.00571515
$814$	−6.51607e6	−0.344687
$815$	−1.30970e7	−0.690681
$816$	5.98910e6	0.314874
$817$	−4.34554e6	−0.227766
$818$	1.17470e7	0.613825
$819$	−1.07086e7	−0.557859
$820$	3.30763e7	1.71784
$821$	3.75970e7	1.94668	0.973340	−	0.229365i	$-0.0736650\pi$
$821$	3.75970e7	1.94668	0.973340	+	0.229365i	$0.0736650\pi$
$822$	−9.46730e6	−0.488705
$823$	1.67263e7	0.860797	0.430398	−	0.902639i	$-0.358373\pi$
$823$	1.67263e7	0.860797	0.430398	+	0.902639i	$0.358373\pi$
$824$	1.11414e7	0.571638
$825$	1.33429e6	0.0682522
$826$	4.70453e6	0.239920
$827$	−2.69145e7	−1.36843	−0.684216	−	0.729279i	$-0.739856\pi$
$827$	−2.69145e7	−1.36843	−0.684216	+	0.729279i	$0.739856\pi$
$828$	−5.59434e6	−0.283578
$829$	−7.34223e6	−0.371058	−0.185529	−	0.982639i	$-0.559400\pi$
$829$	−7.34223e6	−0.371058	−0.185529	+	0.982639i	$0.559400\pi$
$830$	−2.06933e7	−1.04264
$831$	3.93471e6	0.197656
$832$	−1.31600e7	−0.659097
$833$	−2.58991e7	−1.29322
$834$	−1.36050e7	−0.677303
$835$	−3.99811e6	−0.198444
$836$	−1.02266e7	−0.506077
$837$	3.74932e6	0.184986
$838$	1.08698e7	0.534701
$839$	−1.44619e7	−0.709284	−0.354642	−	0.935002i	$-0.615397\pi$
$839$	−1.44619e7	−0.709284	−0.354642	+	0.935002i	$0.615397\pi$
$840$	−1.14520e7	−0.559995
$841$	−1.81655e7	−0.885641
$842$	−4.99530e7	−2.42818
$843$	−4.75043e6	−0.230231
$844$	−1.63998e7	−0.792471
$845$	−7.87695e6	−0.379504
$846$	2.39826e7	1.15205
$847$	−3.04642e7	−1.45909
$848$	−2.11961e6	−0.101220
$849$	1.45483e7	0.692699
$850$	2.70004e7	1.28181
$851$	−4.81967e6	−0.228136
$852$	−2.03319e7	−0.959577
$853$	−3.00835e6	−0.141565	−0.0707825	−	0.997492i	$-0.522550\pi$
$853$	−3.00835e6	−0.141565	−0.0707825	+	0.997492i	$0.522550\pi$
$854$	9.22655e7	4.32907
$855$	1.19863e7	0.560753
$856$	−1.40176e6	−0.0653866
$857$	5.35883e6	0.249240	0.124620	−	0.992205i	$-0.460229\pi$
$857$	5.35883e6	0.249240	0.124620	+	0.992205i	$0.460229\pi$
$858$	−1.65086e6	−0.0765581
$859$	2.59898e7	1.20176	0.600882	−	0.799338i	$-0.294816\pi$
$859$	2.59898e7	1.20176	0.600882	+	0.799338i	$0.294816\pi$
$860$	3.10382e6	0.143104
$861$	−3.02302e7	−1.38974
$862$	4.74037e7	2.17292
$863$	−4.32743e7	−1.97789	−0.988947	−	0.148266i	$-0.952631\pi$
$863$	−4.32743e7	−1.97789	−0.988947	+	0.148266i	$0.952631\pi$
$864$	−8.12862e6	−0.370452
$865$	1.47872e7	0.671965
$866$	−1.94421e7	−0.880947
$867$	−293873.	−0.0132774
$868$	1.31576e7	0.592758
$869$	−4.80734e6	−0.215951
$870$	−3.23331e6	−0.144827
$871$	2.75015e6	0.122832
$872$	−3.68352e7	−1.64048
$873$	1.23265e7	0.547398
$874$	−1.16165e7	−0.514397
$875$	−3.00150e7	−1.32531
$876$	−3.75121e7	−1.65162
$877$	1.03640e7	0.455017	0.227508	−	0.973776i	$-0.426942\pi$
$877$	1.03640e7	0.455017	0.227508	+	0.973776i	$0.426942\pi$
$878$	−3.88632e7	−1.70138
$879$	−7.45885e6	−0.325611
$880$	1.29492e6	0.0563684
$881$	−2.43175e7	−1.05555	−0.527776	−	0.849384i	$-0.676974\pi$
$881$	−2.43175e7	−1.05555	−0.527776	+	0.849384i	$0.676974\pi$
$882$	−3.72905e7	−1.61409
$883$	1.78896e7	0.772147	0.386073	−	0.922468i	$-0.373831\pi$
$883$	1.78896e7	0.772147	0.386073	+	0.922468i	$0.373831\pi$
$884$	−2.17528e7	−0.936233
$885$	−553520.	−0.0237561
$886$	3.57935e7	1.53186
$887$	−2.17492e7	−0.928185	−0.464092	−	0.885787i	$-0.653619\pi$
$887$	−2.17492e7	−0.928185	−0.464092	+	0.885787i	$0.653619\pi$
$888$	1.94565e7	0.828002
$889$	−3.43666e7	−1.45842
$890$	−2.03815e7	−0.862505
$891$	1.31024e6	0.0552912
$892$	−3.39729e7	−1.42962
$893$	3.24274e7	1.36076
$894$	−1.40542e7	−0.588114
$895$	1.94603e7	0.812069
$896$	−6.64458e7	−2.76502
$897$	−1.22107e6	−0.0506711
$898$	−1.99832e7	−0.826941
$899$	1.72472e6	0.0711738
$900$	2.53146e7	1.04175
$901$	4.04536e6	0.166014
$902$	1.37478e7	0.562624
$903$	−2.83675e6	−0.115771
$904$	6.67551e7	2.71684
$905$	8.05605e6	0.326965
$906$	2.97602e7	1.20452
$907$	2.98499e7	1.20483	0.602414	−	0.798184i	$-0.294206\pi$
$907$	2.98499e7	1.20483	0.602414	+	0.798184i	$0.294206\pi$
$908$	3.62859e7	1.46057
$909$	−2.37421e7	−0.953036
$910$	1.58824e7	0.635787
$911$	−1.09193e7	−0.435912	−0.217956	−	0.975959i	$-0.569939\pi$
$911$	−1.09193e7	−0.435912	−0.217956	+	0.975959i	$0.569939\pi$
$912$	1.16598e7	0.464198
$913$	−5.60060e6	−0.222360
$914$	3.66838e6	0.145247
$915$	−1.08557e7	−0.428650
$916$	6.22487e6	0.245127
$917$	4.18119e7	1.64201
$918$	−3.84949e7	−1.50764
$919$	9.16828e6	0.358096	0.179048	−	0.983840i	$-0.442698\pi$
$919$	9.16828e6	0.358096	0.179048	+	0.983840i	$0.442698\pi$
$920$	3.85219e6	0.150051
$921$	5.77448e6	0.224318
$922$	−7.35184e6	−0.284819
$923$	1.30915e7	0.505807
$924$	−6.67589e6	−0.257235
$925$	2.18091e7	0.838078
$926$	2.75796e7	1.05697
$927$	−7.61237e6	−0.290952
$928$	−3.73924e6	−0.142532
$929$	−1.38913e6	−0.0528083	−0.0264041	−	0.999651i	$-0.508406\pi$
$929$	−1.38913e6	−0.0528083	−0.0264041	+	0.999651i	$0.508406\pi$
$930$	−2.37742e6	−0.0901361
$931$	−5.04212e7	−1.90651
$932$	7.64871e7	2.88435
$933$	8.01753e6	0.301534
$934$	4.53956e7	1.70273
$935$	−2.47140e6	−0.0924515
$936$	−1.45414e7	−0.542521
$937$	−2.52918e7	−0.941090	−0.470545	−	0.882376i	$-0.655943\pi$
$937$	−2.52918e7	−0.941090	−0.470545	+	0.882376i	$0.655943\pi$
$938$	1.70793e7	0.633814
$939$	474329.	0.0175556
$940$	−2.31614e7	−0.854958
$941$	2.69608e7	0.992563	0.496282	−	0.868162i	$-0.334698\pi$
$941$	2.69608e7	0.992563	0.496282	+	0.868162i	$0.334698\pi$
$942$	−3.78830e7	−1.39097
$943$	1.01687e7	0.372381
$944$	1.58838e6	0.0580129
$945$	1.83017e7	0.666671
$946$	1.29007e6	0.0468690
$947$	−3.19275e6	−0.115689	−0.0578443	−	0.998326i	$-0.518423\pi$
$947$	−3.19275e6	−0.115689	−0.0578443	+	0.998326i	$0.518423\pi$
$948$	3.09176e7	1.11734
$949$	2.41536e7	0.870596
$950$	5.25652e7	1.88969
$951$	−6.60625e6	−0.236866
$952$	−6.27198e7	−2.24291
$953$	−3.59618e7	−1.28265	−0.641327	−	0.767268i	$-0.721616\pi$
$953$	−3.59618e7	−1.28265	−0.641327	+	0.767268i	$0.721616\pi$
$954$	5.82466e6	0.207205
$955$	−1.94604e7	−0.690468
$956$	1.32009e7	0.467152
$957$	−875089.	−0.0308868
$958$	5.18374e7	1.82486
$959$	2.46511e7	0.865545
$960$	9.61583e6	0.336751
$961$	−2.73610e7	−0.955704
$962$	−2.69834e7	−0.940067
$963$	957755.	0.0332804
$964$	−2.87027e7	−0.994789
$965$	2.40398e7	0.831023
$966$	−7.58322e6	−0.261463
$967$	−1.05454e7	−0.362659	−0.181330	−	0.983422i	$-0.558040\pi$
$967$	−1.05454e7	−0.362659	−0.181330	+	0.983422i	$0.558040\pi$
$968$	−4.13677e7	−1.41897
$969$	−2.22531e7	−0.761345
$970$	−1.82818e7	−0.623864
$971$	−1.47340e7	−0.501500	−0.250750	−	0.968052i	$-0.580677\pi$
$971$	−1.47340e7	−0.501500	−0.250750	+	0.968052i	$0.580677\pi$
$972$	−5.67525e7	−1.92672
$973$	3.54249e7	1.19957
$974$	4.94881e7	1.67149
$975$	5.52539e6	0.186145
$976$	3.11514e7	1.04677
$977$	4.83492e7	1.62051	0.810257	−	0.586075i	$-0.199327\pi$
$977$	4.83492e7	1.62051	0.810257	+	0.586075i	$0.199327\pi$
$978$	3.50098e7	1.17042
$979$	−5.51621e6	−0.183943
$980$	3.60136e7	1.19785
$981$	2.51677e7	0.834971
$982$	1.61012e7	0.532820
$983$	−1.25654e7	−0.414754	−0.207377	−	0.978261i	$-0.566493\pi$
$983$	−1.25654e7	−0.414754	−0.207377	+	0.978261i	$0.566493\pi$
$984$	−4.10500e7	−1.35153
$985$	−2.10672e7	−0.691858
$986$	−1.77080e7	−0.580067
$987$	2.11684e7	0.691665
$988$	−4.23490e7	−1.38023
$989$	954214.	0.0310209
$990$	−3.55842e6	−0.115390
$991$	−4.25363e7	−1.37586	−0.687932	−	0.725776i	$-0.741481\pi$
$991$	−4.25363e7	−1.37586	−0.687932	+	0.725776i	$0.741481\pi$
$992$	−2.74942e6	−0.0887080
$993$	2.75259e7	0.885865
$994$	8.13021e7	2.60997
$995$	2.78241e7	0.890970
$996$	3.60193e7	1.15050
$997$	−3.70772e7	−1.18132	−0.590662	−	0.806919i	$-0.701133\pi$
$997$	−3.70772e7	−1.18132	−0.590662	+	0.806919i	$0.701133\pi$
$998$	3.42840e7	1.08960
$999$	−3.10937e7	−0.985732

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.a.b.1.9	✓	10
3.2	odd	2		387.6.a.e.1.2		10
4.3	odd	2		688.6.a.h.1.7		10
5.4	even	2		1075.6.a.b.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.a.b.1.9	✓	10	1.1	even	1	trivial
387.6.a.e.1.2		10	3.2	odd	2
688.6.a.h.1.7		10	4.3	odd	2
1075.6.a.b.1.2		10	5.4	even	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.a (trivial)

\(f(q)\)	\(=\)	\(q+9.57770 q^{2} -7.84343 q^{3} +59.7324 q^{4} +28.1028 q^{5} -75.1221 q^{6} +195.604 q^{7} +265.613 q^{8} -181.481 q^{9} +O(q^{10})\)	\(q+9.57770 q^{2} -7.84343 q^{3} +59.7324 q^{4} +28.1028 q^{5} -75.1221 q^{6} +195.604 q^{7} +265.613 q^{8} -181.481 q^{9} +269.160 q^{10} +72.8476 q^{11} -468.507 q^{12} +301.666 q^{13} +1873.44 q^{14} -220.422 q^{15} +632.525 q^{16} -1207.20 q^{17} -1738.17 q^{18} -2350.21 q^{19} +1678.65 q^{20} -1534.21 q^{21} +697.713 q^{22} +516.070 q^{23} -2083.32 q^{24} -2335.23 q^{25} +2889.27 q^{26} +3329.38 q^{27} +11683.9 q^{28} +1531.55 q^{29} -2111.14 q^{30} +1126.13 q^{31} -2441.48 q^{32} -571.375 q^{33} -11562.2 q^{34} +5497.02 q^{35} -10840.3 q^{36} -9339.18 q^{37} -22509.6 q^{38} -2366.10 q^{39} +7464.47 q^{40} +19704.2 q^{41} -14694.2 q^{42} +1849.00 q^{43} +4351.37 q^{44} -5100.11 q^{45} +4942.77 q^{46} -13797.6 q^{47} -4961.16 q^{48} +21453.9 q^{49} -22366.2 q^{50} +9468.56 q^{51} +18019.2 q^{52} -3351.03 q^{53} +31887.9 q^{54} +2047.22 q^{55} +51954.9 q^{56} +18433.7 q^{57} +14668.7 q^{58} +2511.18 q^{59} -13166.4 q^{60} +49249.3 q^{61} +10785.7 q^{62} -35498.3 q^{63} -43624.6 q^{64} +8477.66 q^{65} -5472.46 q^{66} +9116.54 q^{67} -72108.8 q^{68} -4047.76 q^{69} +52648.8 q^{70} +43397.3 q^{71} -48203.6 q^{72} +80067.4 q^{73} -89447.9 q^{74} +18316.2 q^{75} -140384. q^{76} +14249.3 q^{77} -22661.8 q^{78} -65991.7 q^{79} +17775.7 q^{80} +17986.0 q^{81} +188721. q^{82} -76880.9 q^{83} -91641.8 q^{84} -33925.6 q^{85} +17709.2 q^{86} -12012.6 q^{87} +19349.3 q^{88} -75722.6 q^{89} -48847.4 q^{90} +59007.1 q^{91} +30826.1 q^{92} -8832.73 q^{93} -132150. q^{94} -66047.5 q^{95} +19149.6 q^{96} -67921.7 q^{97} +205479. q^{98} -13220.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 8 q^{2} + 28 q^{3} + 202 q^{4} + 138 q^{5} + 75 q^{6} + 60 q^{7} + 294 q^{8} + 1356 q^{9}+O(q^{10}) \) 10 * q + 8 * q^2 + 28 * q^3 + 202 * q^4 + 138 * q^5 + 75 * q^6 + 60 * q^7 + 294 * q^8 + 1356 * q^9	\( 10 q + 8 q^{2} + 28 q^{3} + 202 q^{4} + 138 q^{5} + 75 q^{6} + 60 q^{7} + 294 q^{8} + 1356 q^{9} - 17 q^{10} + 745 q^{11} + 4627 q^{12} + 1917 q^{13} + 1936 q^{14} + 1688 q^{15} + 5354 q^{16} + 4017 q^{17} - 2725 q^{18} - 2404 q^{19} + 1311 q^{20} - 228 q^{21} - 5836 q^{22} + 1733 q^{23} - 10711 q^{24} + 7120 q^{25} - 1484 q^{26} - 2324 q^{27} - 15028 q^{28} + 6996 q^{29} - 48420 q^{30} - 4899 q^{31} - 7554 q^{32} - 15734 q^{33} - 27033 q^{34} + 7084 q^{35} + 4433 q^{36} + 1466 q^{37} + 13905 q^{38} - 26542 q^{39} - 93211 q^{40} + 10297 q^{41} - 37642 q^{42} + 18490 q^{43} - 36140 q^{44} + 73822 q^{45} + 17991 q^{46} + 48592 q^{47} + 83607 q^{48} + 29458 q^{49} + 983 q^{50} + 92972 q^{51} + 14232 q^{52} + 127165 q^{53} - 92002 q^{54} + 106672 q^{55} - 7780 q^{56} + 34060 q^{57} - 10305 q^{58} + 99372 q^{59} + 111372 q^{60} + 17408 q^{61} + 28265 q^{62} + 2244 q^{63} + 47202 q^{64} + 54484 q^{65} - 150292 q^{66} - 2021 q^{67} + 192151 q^{68} + 1654 q^{69} - 33194 q^{70} + 11286 q^{71} - 298365 q^{72} + 49892 q^{73} - 125431 q^{74} - 44662 q^{75} - 249803 q^{76} + 98144 q^{77} - 28494 q^{78} - 91524 q^{79} + 12251 q^{80} - 26450 q^{81} - 158909 q^{82} - 105203 q^{83} - 357682 q^{84} - 87212 q^{85} + 14792 q^{86} + 181200 q^{87} - 461824 q^{88} - 62682 q^{89} - 522670 q^{90} - 295304 q^{91} + 183783 q^{92} - 238430 q^{93} + 7259 q^{94} - 305340 q^{95} - 162399 q^{96} + 108383 q^{97} + 354656 q^{98} - 270499 q^{99}+O(q^{100}) \) 10 * q + 8 * q^2 + 28 * q^3 + 202 * q^4 + 138 * q^5 + 75 * q^6 + 60 * q^7 + 294 * q^8 + 1356 * q^9 - 17 * q^10 + 745 * q^11 + 4627 * q^12 + 1917 * q^13 + 1936 * q^14 + 1688 * q^15 + 5354 * q^16 + 4017 * q^17 - 2725 * q^18 - 2404 * q^19 + 1311 * q^20 - 228 * q^21 - 5836 * q^22 + 1733 * q^23 - 10711 * q^24 + 7120 * q^25 - 1484 * q^26 - 2324 * q^27 - 15028 * q^28 + 6996 * q^29 - 48420 * q^30 - 4899 * q^31 - 7554 * q^32 - 15734 * q^33 - 27033 * q^34 + 7084 * q^35 + 4433 * q^36 + 1466 * q^37 + 13905 * q^38 - 26542 * q^39 - 93211 * q^40 + 10297 * q^41 - 37642 * q^42 + 18490 * q^43 - 36140 * q^44 + 73822 * q^45 + 17991 * q^46 + 48592 * q^47 + 83607 * q^48 + 29458 * q^49 + 983 * q^50 + 92972 * q^51 + 14232 * q^52 + 127165 * q^53 - 92002 * q^54 + 106672 * q^55 - 7780 * q^56 + 34060 * q^57 - 10305 * q^58 + 99372 * q^59 + 111372 * q^60 + 17408 * q^61 + 28265 * q^62 + 2244 * q^63 + 47202 * q^64 + 54484 * q^65 - 150292 * q^66 - 2021 * q^67 + 192151 * q^68 + 1654 * q^69 - 33194 * q^70 + 11286 * q^71 - 298365 * q^72 + 49892 * q^73 - 125431 * q^74 - 44662 * q^75 - 249803 * q^76 + 98144 * q^77 - 28494 * q^78 - 91524 * q^79 + 12251 * q^80 - 26450 * q^81 - 158909 * q^82 - 105203 * q^83 - 357682 * q^84 - 87212 * q^85 + 14792 * q^86 + 181200 * q^87 - 461824 * q^88 - 62682 * q^89 - 522670 * q^90 - 295304 * q^91 + 183783 * q^92 - 238430 * q^93 + 7259 * q^94 - 305340 * q^95 - 162399 * q^96 + 108383 * q^97 + 354656 * q^98 - 270499 * q^99

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