LMFDB - Embedded newform 43.6.a.b.1.8

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			1.8
Root			$-6.91219$ 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)

$f(q)$	$=$	$q+7.91219 q^{2} +12.8799 q^{3} +30.6028 q^{4} +79.5677 q^{5} +101.908 q^{6} -172.354 q^{7} -11.0549 q^{8} -77.1083 q^{9} +O(q^{10})$	\(q+7.91219 q^{2} +12.8799 q^{3} +30.6028 q^{4} +79.5677 q^{5} +101.908 q^{6} -172.354 q^{7} -11.0549 q^{8} -77.1083 q^{9} +629.555 q^{10} +452.247 q^{11} +394.161 q^{12} -22.7429 q^{13} -1363.70 q^{14} +1024.82 q^{15} -1066.76 q^{16} -521.824 q^{17} -610.096 q^{18} +1558.56 q^{19} +2434.99 q^{20} -2219.90 q^{21} +3578.27 q^{22} -3464.36 q^{23} -142.385 q^{24} +3206.01 q^{25} -179.946 q^{26} -4122.96 q^{27} -5274.51 q^{28} +4324.79 q^{29} +8108.60 q^{30} -3987.66 q^{31} -8086.64 q^{32} +5824.90 q^{33} -4128.77 q^{34} -13713.8 q^{35} -2359.73 q^{36} +10080.4 q^{37} +12331.6 q^{38} -292.926 q^{39} -879.609 q^{40} -16408.5 q^{41} -17564.3 q^{42} +1849.00 q^{43} +13840.0 q^{44} -6135.33 q^{45} -27410.7 q^{46} +24153.7 q^{47} -13739.7 q^{48} +12898.8 q^{49} +25366.6 q^{50} -6721.04 q^{51} -695.997 q^{52} +21214.2 q^{53} -32621.7 q^{54} +35984.2 q^{55} +1905.34 q^{56} +20074.0 q^{57} +34218.6 q^{58} -25849.7 q^{59} +31362.5 q^{60} +28577.7 q^{61} -31551.2 q^{62} +13289.9 q^{63} -29846.8 q^{64} -1809.60 q^{65} +46087.7 q^{66} +66762.2 q^{67} -15969.3 q^{68} -44620.6 q^{69} -108506. q^{70} -10031.8 q^{71} +852.421 q^{72} +32145.0 q^{73} +79758.3 q^{74} +41293.1 q^{75} +47696.2 q^{76} -77946.5 q^{77} -2317.69 q^{78} -21913.4 q^{79} -84879.4 q^{80} -34366.0 q^{81} -129827. q^{82} -66782.4 q^{83} -67935.1 q^{84} -41520.3 q^{85} +14629.6 q^{86} +55702.8 q^{87} -4999.53 q^{88} +48984.7 q^{89} -48543.9 q^{90} +3919.82 q^{91} -106019. q^{92} -51360.7 q^{93} +191108. q^{94} +124011. q^{95} -104155. q^{96} +93075.8 q^{97} +102058. q^{98} -34872.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	7.91219	1.39869	0.699346	−	0.714784i	$-0.253475\pi$
$2$	7.91219	1.39869	0.699346	+	0.714784i	$0.253475\pi$
$3$	12.8799	0.826246	0.413123	−	0.910675i	$-0.364438\pi$
$3$	12.8799	0.826246	0.413123	+	0.910675i	$0.364438\pi$
$4$	30.6028	0.956338
$5$	79.5677	1.42335	0.711675	−	0.702509i	$-0.247937\pi$
$5$	79.5677	1.42335	0.711675	+	0.702509i	$0.247937\pi$
$6$	101.908	1.15566
$7$	−172.354	−1.32946	−0.664730	−	0.747083i	$-0.731454\pi$
$7$	−172.354	−1.32946	−0.664730	+	0.747083i	$0.731454\pi$
$8$	−11.0549	−0.0610700
$9$	−77.1083	−0.317318
$10$	629.555	1.99083
$11$	452.247	1.12692	0.563461	−	0.826142i	$-0.309469\pi$
$11$	452.247	1.12692	0.563461	+	0.826142i	$0.309469\pi$
$12$	394.161	0.790170
$13$	−22.7429	−0.0373240	−0.0186620	−	0.999826i	$-0.505941\pi$
$13$	−22.7429	−0.0373240	−0.0186620	+	0.999826i	$0.505941\pi$
$14$	−1363.70	−1.85950
$15$	1024.82	1.17604
$16$	−1066.76	−1.04176
$17$	−521.824	−0.437927	−0.218964	−	0.975733i	$-0.570268\pi$
$17$	−521.824	−0.437927	−0.218964	+	0.975733i	$0.570268\pi$
$18$	−610.096	−0.443830
$19$	1558.56	0.990463	0.495232	−	0.868761i	$-0.335083\pi$
$19$	1558.56	0.990463	0.495232	+	0.868761i	$0.335083\pi$
$20$	2434.99	1.36120
$21$	−2219.90	−1.09846
$22$	3578.27	1.57622
$23$	−3464.36	−1.36554	−0.682769	−	0.730635i	$-0.739224\pi$
$23$	−3464.36	−1.36554	−0.682769	+	0.730635i	$0.739224\pi$
$24$	−142.385	−0.0504588
$25$	3206.01	1.02592
$26$	−179.946	−0.0522047
$27$	−4122.96	−1.08843
$28$	−5274.51	−1.27141
$29$	4324.79	0.954926	0.477463	−	0.878652i	$-0.341556\pi$
$29$	4324.79	0.954926	0.477463	+	0.878652i	$0.341556\pi$
$30$	8108.60	1.64491
$31$	−3987.66	−0.745271	−0.372635	−	0.927978i	$-0.621546\pi$
$31$	−3987.66	−0.745271	−0.372635	+	0.927978i	$0.621546\pi$
$32$	−8086.64	−1.39602
$33$	5824.90	0.931115
$34$	−4128.77	−0.612525
$35$	−13713.8	−1.89229
$36$	−2359.73	−0.303463
$37$	10080.4	1.21053	0.605264	−	0.796025i	$-0.293068\pi$
$37$	10080.4	1.21053	0.605264	+	0.796025i	$0.293068\pi$
$38$	12331.6	1.38535
$39$	−292.926	−0.0308388
$40$	−879.609	−0.0869240
$41$	−16408.5	−1.52444	−0.762219	−	0.647319i	$-0.775890\pi$
$41$	−16408.5	−1.52444	−0.762219	+	0.647319i	$0.775890\pi$
$42$	−17564.3	−1.53641
$43$	1849.00	0.152499
$43$	1849.00	0.152499
$44$	13840.0	1.07772
$45$	−6135.33	−0.451654
$46$	−27410.7	−1.90997
$47$	24153.7	1.59492	0.797459	−	0.603373i	$-0.206177\pi$
$47$	24153.7	1.59492	0.797459	+	0.603373i	$0.206177\pi$
$48$	−13739.7	−0.860746
$49$	12898.8	0.767465
$50$	25366.6	1.43495
$51$	−6721.04	−0.361835
$52$	−695.997	−0.0356943
$53$	21214.2	1.03738	0.518688	−	0.854963i	$-0.326420\pi$
$53$	21214.2	1.03738	0.518688	+	0.854963i	$0.326420\pi$
$54$	−32621.7	−1.52238
$55$	35984.2	1.60400
$56$	1905.34	0.0811902
$57$	20074.0	0.818366
$58$	34218.6	1.33565
$59$	−25849.7	−0.966775	−0.483387	−	0.875407i	$-0.660594\pi$
$59$	−25849.7	−0.966775	−0.483387	+	0.875407i	$0.660594\pi$
$60$	31362.5	1.12469
$61$	28577.7	0.983338	0.491669	−	0.870782i	$-0.336387\pi$
$61$	28577.7	0.983338	0.491669	+	0.870782i	$0.336387\pi$
$62$	−31551.2	−1.04240
$63$	13289.9	0.421862
$64$	−29846.8	−0.910852
$65$	−1809.60	−0.0531250
$66$	46087.7	1.30234
$67$	66762.2	1.81695	0.908477	−	0.417935i	$-0.137246\pi$
$67$	66762.2	1.81695	0.908477	+	0.417935i	$0.137246\pi$
$68$	−15969.3	−0.418806
$69$	−44620.6	−1.12827
$70$	−108506.	−2.64673
$71$	−10031.8	−0.236173	−0.118087	−	0.993003i	$-0.537676\pi$
$71$	−10031.8	−0.236173	−0.118087	+	0.993003i	$0.537676\pi$
$72$	852.421	0.0193786
$73$	32145.0	0.706003	0.353001	−	0.935623i	$-0.385161\pi$
$73$	32145.0	0.706003	0.353001	+	0.935623i	$0.385161\pi$
$74$	79758.3	1.69315
$75$	41293.1	0.847665
$76$	47696.2	0.947217
$77$	−77946.5	−1.49820
$78$	−2317.69	−0.0431339
$79$	−21913.4	−0.395040	−0.197520	−	0.980299i	$-0.563289\pi$
$79$	−21913.4	−0.395040	−0.197520	+	0.980299i	$0.563289\pi$
$80$	−84879.4	−1.48278
$81$	−34366.0	−0.581991
$82$	−129827.	−2.13222
$83$	−66782.4	−1.06406	−0.532031	−	0.846725i	$-0.678571\pi$
$83$	−66782.4	−1.06406	−0.532031	+	0.846725i	$0.678571\pi$
$84$	−67935.1	−1.05050
$85$	−41520.3	−0.623323
$86$	14629.6	0.213298
$87$	55702.8	0.789004
$88$	−4999.53	−0.0688212
$89$	48984.7	0.655520	0.327760	−	0.944761i	$-0.393706\pi$
$89$	48984.7	0.655520	0.327760	+	0.944761i	$0.393706\pi$
$90$	−48543.9	−0.631725
$91$	3919.82	0.0496207
$92$	−106019.	−1.30591
$93$	−51360.7	−0.615777
$94$	191108.	2.23080
$95$	124011.	1.40978
$96$	−104155.	−1.15346
$97$	93075.8	1.00440	0.502201	−	0.864751i	$-0.332524\pi$
$97$	93075.8	1.00440	0.502201	+	0.864751i	$0.332524\pi$
$98$	102058.	1.07345
$99$	−34872.0	−0.357593
$100$	98112.9	0.981129
$101$	47004.9	0.458500	0.229250	−	0.973368i	$-0.426373\pi$
$101$	47004.9	0.458500	0.229250	+	0.973368i	$0.426373\pi$
$102$	−53178.2	−0.506096
$103$	−51489.8	−0.478220	−0.239110	−	0.970992i	$-0.576856\pi$
$103$	−51489.8	−0.478220	−0.239110	+	0.970992i	$0.576856\pi$
$104$	251.420	0.00227938
$105$	−176632.	−1.56349
$106$	167851.	1.45097
$107$	74331.3	0.627642	0.313821	−	0.949482i	$-0.398391\pi$
$107$	74331.3	0.627642	0.313821	+	0.949482i	$0.398391\pi$
$108$	−126174.	−1.04091
$109$	−204775.	−1.65086	−0.825430	−	0.564505i	$-0.809067\pi$
$109$	−204775.	−1.65086	−0.825430	+	0.564505i	$0.809067\pi$
$110$	284714.	2.24351
$111$	129835.	1.00019
$112$	183860.	1.38497
$113$	125866.	0.927281	0.463640	−	0.886023i	$-0.346543\pi$
$113$	125866.	0.927281	0.463640	+	0.886023i	$0.346543\pi$
$114$	158830.	1.14464
$115$	−275651.	−1.94364
$116$	132351.	0.913232
$117$	1753.67	0.0118436
$118$	−204528.	−1.35222
$119$	89938.3	0.582207
$120$	−11329.3	−0.0718206
$121$	43476.5	0.269955
$122$	226112.	1.37539
$123$	−211340.	−1.25956
$124$	−122034.	−0.712731
$125$	6445.88	0.0368984
$126$	105152.	0.590054
$127$	−318214.	−1.75069	−0.875347	−	0.483495i	$-0.839367\pi$
$127$	−318214.	−1.75069	−0.875347	+	0.483495i	$0.839367\pi$
$128$	22618.8	0.122024
$129$	23814.9	0.126001
$130$	−14317.9	−0.0743055
$131$	−261871.	−1.33324	−0.666620	−	0.745398i	$-0.732260\pi$
$131$	−261871.	−1.33324	−0.666620	+	0.745398i	$0.732260\pi$
$132$	178258.	0.890460
$133$	−268623.	−1.31678
$134$	528236.	2.54136
$135$	−328054.	−1.54921
$136$	5768.69	0.0267442
$137$	−20837.0	−0.0948492	−0.0474246	−	0.998875i	$-0.515101\pi$
$137$	−20837.0	−0.0948492	−0.0474246	+	0.998875i	$0.515101\pi$
$138$	−353047.	−1.57810
$139$	−182520.	−0.801260	−0.400630	−	0.916240i	$-0.631209\pi$
$139$	−182520.	−0.801260	−0.400630	+	0.916240i	$0.631209\pi$
$140$	−419680.	−1.80967
$141$	311097.	1.31779
$142$	−79373.1	−0.330334
$143$	−10285.4	−0.0420612
$144$	82255.9	0.330568
$145$	344113.	1.35919
$146$	254337.	0.987480
$147$	166135.	0.634115
$148$	308489.	1.15767
$149$	478460.	1.76555	0.882775	−	0.469796i	$-0.155673\pi$
$149$	478460.	1.76555	0.882775	+	0.469796i	$0.155673\pi$
$150$	326719.	1.18562
$151$	244853.	0.873901	0.436951	−	0.899485i	$-0.356058\pi$
$151$	244853.	0.873901	0.436951	+	0.899485i	$0.356058\pi$
$152$	−17229.6	−0.0604876
$153$	40237.0	0.138962
$154$	−616727.	−2.09552
$155$	−317289.	−1.06078
$156$	−8964.37	−0.0294923
$157$	12990.1	0.0420594	0.0210297	−	0.999779i	$-0.493306\pi$
$157$	12990.1	0.0420594	0.0210297	+	0.999779i	$0.493306\pi$
$158$	−173383.	−0.552539
$159$	273236.	0.857128
$160$	−643435.	−1.98703
$161$	597095.	1.81543
$162$	−271910.	−0.814026
$163$	43866.4	0.129319	0.0646596	−	0.997907i	$-0.479404\pi$
$163$	43866.4	0.129319	0.0646596	+	0.997907i	$0.479404\pi$
$164$	−502147.	−1.45788
$165$	463473.	1.32530
$166$	−528395.	−1.48829
$167$	454884.	1.26215	0.631073	−	0.775724i	$-0.282615\pi$
$167$	454884.	1.26215	0.631073	+	0.775724i	$0.282615\pi$
$168$	24540.6	0.0670830
$169$	−370776.	−0.998607
$170$	−328517.	−0.871837
$171$	−120178.	−0.314292
$172$	56584.6	0.145840
$173$	−649198.	−1.64916	−0.824579	−	0.565747i	$-0.808588\pi$
$173$	−649198.	−1.64916	−0.824579	+	0.565747i	$0.808588\pi$
$174$	440731.	1.10357
$175$	−552568.	−1.36392
$176$	−482438.	−1.17398
$177$	−332941.	−0.798793
$178$	387577.	0.916870
$179$	−570828.	−1.33160	−0.665798	−	0.746132i	$-0.731909\pi$
$179$	−570828.	−1.33160	−0.665798	+	0.746132i	$0.731909\pi$
$180$	−187758.	−0.431934
$181$	−90744.3	−0.205884	−0.102942	−	0.994687i	$-0.532826\pi$
$181$	−90744.3	−0.205884	−0.102942	+	0.994687i	$0.532826\pi$
$182$	31014.4	0.0694041
$183$	368078.	0.812479
$184$	38298.0	0.0833934
$185$	802076.	1.72300
$186$	−406376.	−0.861282
$187$	−235994.	−0.493510
$188$	739170.	1.52528
$189$	710607.	1.44702
$190$	981196.	1.97184
$191$	−546924.	−1.08478	−0.542392	−	0.840126i	$-0.682481\pi$
$191$	−546924.	−1.08478	−0.542392	+	0.840126i	$0.682481\pi$
$192$	−384424.	−0.752588
$193$	25064.4	0.0484356	0.0242178	−	0.999707i	$-0.492290\pi$
$193$	25064.4	0.0484356	0.0242178	+	0.999707i	$0.492290\pi$
$194$	736434.	1.40485
$195$	−23307.5	−0.0438943
$196$	394739.	0.733956
$197$	579350.	1.06359	0.531797	−	0.846872i	$-0.321517\pi$
$197$	579350.	1.06359	0.531797	+	0.846872i	$0.321517\pi$
$198$	−275914.	−0.500162
$199$	411324.	0.736295	0.368147	−	0.929767i	$-0.379992\pi$
$199$	411324.	0.736295	0.368147	+	0.929767i	$0.379992\pi$
$200$	−35442.0	−0.0626532
$201$	859891.	1.50125
$202$	371912.	0.641301
$203$	−745393.	−1.26954
$204$	−205683.	−0.346037
$205$	−1.30559e6	−2.16981
$206$	−407397.	−0.668883
$207$	267131.	0.433310
$208$	24261.2	0.0388825
$209$	704852.	1.11618
$210$	−1.39755e6	−2.18685
$211$	−385582.	−0.596225	−0.298113	−	0.954531i	$-0.596357\pi$
$211$	−385582.	−0.596225	−0.298113	+	0.954531i	$0.596357\pi$
$212$	649213.	0.992083
$213$	−129208.	−0.195137
$214$	588123.	0.877878
$215$	147121.	0.217059
$216$	45578.7	0.0664703
$217$	687288.	0.990808
$218$	−1.62022e6	−2.30904
$219$	414024.	0.583332
$220$	1.10122e6	1.53397
$221$	11867.8	0.0163452
$222$	1.02728e6	1.39896
$223$	−1.03807e6	−1.39786	−0.698930	−	0.715190i	$-0.746340\pi$
$223$	−1.03807e6	−1.39786	−0.698930	+	0.715190i	$0.746340\pi$
$224$	1.39376e6	1.85596
$225$	−247210.	−0.325544
$226$	995874.	1.29698
$227$	1.14006e6	1.46846	0.734229	−	0.678902i	$-0.237544\pi$
$227$	1.14006e6	1.46846	0.734229	+	0.678902i	$0.237544\pi$
$228$	614322.	0.782634
$229$	548999.	0.691804	0.345902	−	0.938271i	$-0.387573\pi$
$229$	548999.	0.691804	0.345902	+	0.938271i	$0.387573\pi$
$230$	−2.18100e6	−2.71855
$231$	−1.00394e6	−1.23788
$232$	−47809.9	−0.0583174
$233$	−1.11203e6	−1.34191	−0.670957	−	0.741496i	$-0.734117\pi$
$233$	−1.11203e6	−1.34191	−0.670957	+	0.741496i	$0.734117\pi$
$234$	13875.4	0.0165655
$235$	1.92185e6	2.27013
$236$	−791073.	−0.924563
$237$	−282242.	−0.326400
$238$	711609.	0.814328
$239$	−1.28067e6	−1.45025	−0.725123	−	0.688620i	$-0.758217\pi$
$239$	−1.28067e6	−1.45025	−0.725123	+	0.688620i	$0.758217\pi$
$240$	−1.09324e6	−1.22514
$241$	725022.	0.804097	0.402049	−	0.915618i	$-0.368298\pi$
$241$	725022.	0.804097	0.402049	+	0.915618i	$0.368298\pi$
$242$	343995.	0.377584
$243$	559249.	0.607561
$244$	874558.	0.940403
$245$	1.02633e6	1.09237
$246$	−1.67216e6	−1.76174
$247$	−35446.1	−0.0369680
$248$	44083.0	0.0455137
$249$	−860150.	−0.879176
$250$	51001.1	0.0516095
$251$	−1.43637e6	−1.43907	−0.719533	−	0.694458i	$-0.755644\pi$
$251$	−1.43637e6	−1.43907	−0.719533	+	0.694458i	$0.755644\pi$
$252$	406708.	0.403442
$253$	−1.56675e6	−1.53886
$254$	−2.51777e6	−2.44868
$255$	−534777.	−0.515018
$256$	1.13406e6	1.08153
$257$	607070.	0.573331	0.286666	−	0.958031i	$-0.407453\pi$
$257$	607070.	0.573331	0.286666	+	0.958031i	$0.407453\pi$
$258$	188428.	0.176237
$259$	−1.73740e6	−1.60935
$260$	−55378.9	−0.0508055
$261$	−333477.	−0.303015
$262$	−2.07197e6	−1.86479
$263$	169221.	0.150856	0.0754282	−	0.997151i	$-0.475968\pi$
$263$	169221.	0.150856	0.0754282	+	0.997151i	$0.475968\pi$
$264$	−64393.4	−0.0568632
$265$	1.68796e6	1.47655
$266$	−2.12540e6	−1.84177
$267$	630918.	0.541620
$268$	2.04311e6	1.73762
$269$	1.41683e6	1.19382	0.596908	−	0.802310i	$-0.296396\pi$
$269$	1.41683e6	1.19382	0.596908	+	0.802310i	$0.296396\pi$
$270$	−2.59563e6	−2.16687
$271$	947582.	0.783779	0.391889	−	0.920012i	$-0.371822\pi$
$271$	947582.	0.783779	0.391889	+	0.920012i	$0.371822\pi$
$272$	556660.	0.456213
$273$	50486.9	0.0409989
$274$	−164866.	−0.132665
$275$	1.44991e6	1.15614
$276$	−1.36552e6	−1.07901
$277$	37913.3	0.0296888	0.0148444	−	0.999890i	$-0.495275\pi$
$277$	37913.3	0.0296888	0.0148444	+	0.999890i	$0.495275\pi$
$278$	−1.44413e6	−1.12072
$279$	307482.	0.236488
$280$	151604.	0.115562
$281$	−2.05268e6	−1.55080	−0.775400	−	0.631471i	$-0.782452\pi$
$281$	−2.05268e6	−1.55080	−0.775400	+	0.631471i	$0.782452\pi$
$282$	2.46146e6	1.84319
$283$	−2.35101e6	−1.74497	−0.872487	−	0.488636i	$-0.837494\pi$
$283$	−2.35101e6	−1.74497	−0.872487	+	0.488636i	$0.837494\pi$
$284$	−307000.	−0.225861
$285$	1.59724e6	1.16482
$286$	−81380.2	−0.0588307
$287$	2.82807e6	2.02668
$288$	623547.	0.442984
$289$	−1.14756e6	−0.808220
$290$	2.72269e6	1.90109
$291$	1.19881e6	0.829882
$292$	983727.	0.675177
$293$	1.11432e6	0.758300	0.379150	−	0.925335i	$-0.376216\pi$
$293$	1.11432e6	0.758300	0.379150	+	0.925335i	$0.376216\pi$
$294$	1.31449e6	0.886931
$295$	−2.05680e6	−1.37606
$296$	−111438.	−0.0739269
$297$	−1.86460e6	−1.22657
$298$	3.78567e6	2.46946
$299$	78789.7	0.0509673
$300$	1.26368e6	0.810654
$301$	−318682.	−0.202741
$302$	1.93732e6	1.22232
$303$	605418.	0.378834
$304$	−1.66260e6	−1.03182
$305$	2.27386e6	1.39963
$306$	318363.	0.194365
$307$	−1.15903e6	−0.701854	−0.350927	−	0.936403i	$-0.614134\pi$
$307$	−1.15903e6	−0.701854	−0.350927	+	0.936403i	$0.614134\pi$
$308$	−2.38538e6	−1.43278
$309$	−663183.	−0.395127
$310$	−2.51045e6	−1.48371
$311$	−1.18671e6	−0.695736	−0.347868	−	0.937543i	$-0.613094\pi$
$311$	−1.18671e6	−0.695736	−0.347868	+	0.937543i	$0.613094\pi$
$312$	3238.26	0.00188332
$313$	571287.	0.329605	0.164802	−	0.986327i	$-0.447301\pi$
$313$	571287.	0.329605	0.164802	+	0.986327i	$0.447301\pi$
$314$	102780.	0.0588282
$315$	1.05745e6	0.600457
$316$	−670610.	−0.377792
$317$	−796360.	−0.445104	−0.222552	−	0.974921i	$-0.571439\pi$
$317$	−796360.	−0.445104	−0.222552	+	0.974921i	$0.571439\pi$
$318$	2.16190e6	1.19886
$319$	1.95587e6	1.07613
$320$	−2.37484e6	−1.29646
$321$	957379.	0.518587
$322$	4.72433e6	2.53922
$323$	−813292.	−0.433751
$324$	−1.05170e6	−0.556580
$325$	−72914.0	−0.0382915
$326$	347080.	0.180878
$327$	−2.63748e6	−1.36402
$328$	181394.	0.0930975
$329$	−4.16297e6	−2.12038
$330$	3.66709e6	1.85369
$331$	−390295.	−0.195805	−0.0979023	−	0.995196i	$-0.531213\pi$
$331$	−390295.	−0.195805	−0.0979023	+	0.995196i	$0.531213\pi$
$332$	−2.04373e6	−1.01760
$333$	−777285.	−0.384122
$334$	3.59913e6	1.76535
$335$	5.31212e6	2.58616
$336$	2.36809e6	1.14433
$337$	765533.	0.367189	0.183594	−	0.983002i	$-0.441227\pi$
$337$	765533.	0.367189	0.183594	+	0.983002i	$0.441227\pi$
$338$	−2.93365e6	−1.39674
$339$	1.62114e6	0.766162
$340$	−1.27064e6	−0.596108
$341$	−1.80341e6	−0.839863
$342$	−950868.	−0.439597
$343$	673595.	0.309146
$344$	−20440.4	−0.00931309
$345$	−3.55036e6	−1.60592
$346$	−5.13658e6	−2.30666
$347$	−1.47170e6	−0.656140	−0.328070	−	0.944653i	$-0.606398\pi$
$347$	−1.47170e6	−0.656140	−0.328070	+	0.944653i	$0.606398\pi$
$348$	1.70466e6	0.754554
$349$	3.61738e6	1.58975	0.794877	−	0.606770i	$-0.207535\pi$
$349$	3.61738e6	1.58975	0.794877	+	0.606770i	$0.207535\pi$
$350$	−4.37202e6	−1.90771
$351$	93768.2	0.0406245
$352$	−3.65716e6	−1.57321
$353$	500946.	0.213971	0.106985	−	0.994261i	$-0.465880\pi$
$353$	500946.	0.213971	0.106985	+	0.994261i	$0.465880\pi$
$354$	−2.63430e6	−1.11727
$355$	−798203.	−0.336157
$356$	1.49907e6	0.626898
$357$	1.15840e6	0.481046
$358$	−4.51650e6	−1.86249
$359$	−3.84739e6	−1.57554	−0.787770	−	0.615969i	$-0.788765\pi$
$359$	−3.84739e6	−1.57554	−0.787770	+	0.615969i	$0.788765\pi$
$360$	67825.1	0.0275825
$361$	−47002.6	−0.0189825
$362$	−717987.	−0.287968
$363$	559973.	0.223049
$364$	119958.	0.0474542
$365$	2.55770e6	1.00489
$366$	2.91230e6	1.13641
$367$	2.28572e6	0.885844	0.442922	−	0.896560i	$-0.353942\pi$
$367$	2.28572e6	0.885844	0.442922	+	0.896560i	$0.353942\pi$
$368$	3.69563e6	1.42256
$369$	1.26523e6	0.483732
$370$	6.34618e6	2.40995
$371$	−3.65634e6	−1.37915
$372$	−1.57178e6	−0.588891
$373$	−753658.	−0.280480	−0.140240	−	0.990118i	$-0.544787\pi$
$373$	−753658.	−0.280480	−0.140240	+	0.990118i	$0.544787\pi$
$374$	−1.86723e6	−0.690268
$375$	83022.3	0.0304871
$376$	−267015.	−0.0974017
$377$	−98358.3	−0.0356416
$378$	5.62246e6	2.02394
$379$	−3.54911e6	−1.26917	−0.634587	−	0.772851i	$-0.718830\pi$
$379$	−3.54911e6	−1.26917	−0.634587	+	0.772851i	$0.718830\pi$
$380$	3.79507e6	1.34822
$381$	−4.09857e6	−1.44650
$382$	−4.32737e6	−1.51728
$383$	2.29101e6	0.798049	0.399025	−	0.916940i	$-0.369349\pi$
$383$	2.29101e6	0.798049	0.399025	+	0.916940i	$0.369349\pi$
$384$	291327.	0.100821
$385$	−6.20202e6	−2.13246
$386$	198314.	0.0677464
$387$	−142573.	−0.0483906
$388$	2.84838e6	0.960547
$389$	3.75998e6	1.25983	0.629914	−	0.776665i	$-0.283090\pi$
$389$	3.75998e6	1.25983	0.629914	+	0.776665i	$0.283090\pi$
$390$	−184413.	−0.0613946
$391$	1.80779e6	0.598006
$392$	−142594.	−0.0468691
$393$	−3.37287e6	−1.10158
$394$	4.58393e6	1.48764
$395$	−1.74359e6	−0.562280
$396$	−1.06718e6	−0.341980
$397$	5.66320e6	1.80337	0.901686	−	0.432392i	$-0.142330\pi$
$397$	5.66320e6	1.80337	0.901686	+	0.432392i	$0.142330\pi$
$398$	3.25448e6	1.02985
$399$	−3.45983e6	−1.08799
$400$	−3.42004e6	−1.06876
$401$	3.53734e6	1.09854	0.549270	−	0.835645i	$-0.314906\pi$
$401$	3.53734e6	1.09854	0.549270	+	0.835645i	$0.314906\pi$
$402$	6.80362e6	2.09979
$403$	90691.1	0.0278165
$404$	1.43848e6	0.438481
$405$	−2.73442e6	−0.828377
$406$	−5.89769e6	−1.77569
$407$	4.55885e6	1.36417
$408$	74300.1	0.0220973
$409$	−2.11034e6	−0.623798	−0.311899	−	0.950115i	$-0.600965\pi$
$409$	−2.11034e6	−0.623798	−0.311899	+	0.950115i	$0.600965\pi$
$410$	−1.03301e7	−3.03489
$411$	−268378.	−0.0783688
$412$	−1.57573e6	−0.457340
$413$	4.45529e6	1.28529
$414$	2.11359e6	0.606066
$415$	−5.31372e6	−1.51453
$416$	183914.	0.0521052
$417$	−2.35084e6	−0.662038
$418$	5.57693e6	1.56119
$419$	896357.	0.249428	0.124714	−	0.992193i	$-0.460199\pi$
$419$	896357.	0.249428	0.124714	+	0.992193i	$0.460199\pi$
$420$	−5.40544e6	−1.49523
$421$	4.09292e6	1.12545	0.562727	−	0.826643i	$-0.309752\pi$
$421$	4.09292e6	1.12545	0.562727	+	0.826643i	$0.309752\pi$
$422$	−3.05080e6	−0.833935
$423$	−1.86245e6	−0.506096
$424$	−234520.	−0.0633526
$425$	−1.67297e6	−0.449280
$426$	−1.02232e6	−0.272937
$427$	−4.92547e6	−1.30731
$428$	2.27475e6	0.600238
$429$	−132475.	−0.0347529
$430$	1.16405e6	0.303598
$431$	−1.18319e6	−0.306804	−0.153402	−	0.988164i	$-0.549023\pi$
$431$	−1.18319e6	−0.306804	−0.153402	+	0.988164i	$0.549023\pi$
$432$	4.39820e6	1.13388
$433$	1.63492e6	0.419061	0.209530	−	0.977802i	$-0.432806\pi$
$433$	1.63492e6	0.419061	0.209530	+	0.977802i	$0.432806\pi$
$434$	5.43796e6	1.38583
$435$	4.43214e6	1.12303
$436$	−6.26668e6	−1.57878
$437$	−5.39940e6	−1.35251
$438$	3.27584e6	0.815901
$439$	−2.23900e6	−0.554488	−0.277244	−	0.960800i	$-0.589421\pi$
$439$	−2.23900e6	−0.554488	−0.277244	+	0.960800i	$0.589421\pi$
$440$	−397801.	−0.0979566
$441$	−994603.	−0.243531
$442$	93900.4	0.0228619
$443$	4.42567e6	1.07144	0.535722	−	0.844394i	$-0.320039\pi$
$443$	4.42567e6	1.07144	0.535722	+	0.844394i	$0.320039\pi$
$444$	3.97331e6	0.956522
$445$	3.89760e6	0.933034
$446$	−8.21339e6	−1.95517
$447$	6.16252e6	1.45878
$448$	5.14421e6	1.21094
$449$	824623.	0.193037	0.0965183	−	0.995331i	$-0.469229\pi$
$449$	824623.	0.193037	0.0965183	+	0.995331i	$0.469229\pi$
$450$	−1.95597e6	−0.455336
$451$	−7.42071e6	−1.71792
$452$	3.85184e6	0.886794
$453$	3.15368e6	0.722057
$454$	9.02034e6	2.05392
$455$	311891.	0.0706276
$456$	−221916.	−0.0499776
$457$	4.78062e6	1.07076	0.535382	−	0.844610i	$-0.320168\pi$
$457$	4.78062e6	1.07076	0.535382	+	0.844610i	$0.320168\pi$
$458$	4.34379e6	0.967621
$459$	2.15146e6	0.476652
$460$	−8.43570e6	−1.85877
$461$	177573.	0.0389157	0.0194578	−	0.999811i	$-0.493806\pi$
$461$	177573.	0.0389157	0.0194578	+	0.999811i	$0.493806\pi$
$462$	−7.94339e6	−1.73141
$463$	8.24149e6	1.78671	0.893353	−	0.449355i	$-0.148346\pi$
$463$	8.24149e6	1.78671	0.893353	+	0.449355i	$0.148346\pi$
$464$	−4.61350e6	−0.994800
$465$	−4.08665e6	−0.876466
$466$	−8.79856e6	−1.87692
$467$	2.93483e6	0.622718	0.311359	−	0.950292i	$-0.399216\pi$
$467$	2.93483e6	0.622718	0.311359	+	0.950292i	$0.399216\pi$
$468$	53667.1	0.0113265
$469$	−1.15067e7	−2.41557
$470$	1.52061e7	3.17521
$471$	167311.	0.0347514
$472$	285765.	0.0590410
$473$	836205.	0.171854
$474$	−2.23315e6	−0.456533
$475$	4.99675e6	1.01614
$476$	2.75236e6	0.556786
$477$	−1.63579e6	−0.329178
$478$	−1.01329e7	−2.02845
$479$	7.53163e6	1.49986	0.749929	−	0.661518i	$-0.230088\pi$
$479$	7.53163e6	1.49986	0.749929	+	0.661518i	$0.230088\pi$
$480$	−8.28738e6	−1.64178
$481$	−229258.	−0.0451817
$482$	5.73651e6	1.12468
$483$	7.69053e6	1.49999
$484$	1.33050e6	0.258168
$485$	7.40582e6	1.42961
$486$	4.42489e6	0.849790
$487$	−2.30284e6	−0.439988	−0.219994	−	0.975501i	$-0.570604\pi$
$487$	−2.30284e6	−0.439988	−0.219994	+	0.975501i	$0.570604\pi$
$488$	−315922.	−0.0600525
$489$	564995.	0.106849
$490$	8.12049e6	1.52789
$491$	4.43974e6	0.831100	0.415550	−	0.909570i	$-0.363589\pi$
$491$	4.43974e6	0.831100	0.415550	+	0.909570i	$0.363589\pi$
$492$	−6.46760e6	−1.20457
$493$	−2.25678e6	−0.418188
$494$	−280456.	−0.0517068
$495$	−2.77468e6	−0.508980
$496$	4.25387e6	0.776390
$497$	1.72901e6	0.313983
$498$	−6.80567e6	−1.22970
$499$	7.95785e6	1.43069	0.715343	−	0.698774i	$-0.246271\pi$
$499$	7.95785e6	1.43069	0.715343	+	0.698774i	$0.246271\pi$
$500$	197262.	0.0352873
$501$	5.85886e6	1.04284
$502$	−1.13648e7	−2.01281
$503$	−4.75804e6	−0.838510	−0.419255	−	0.907868i	$-0.637709\pi$
$503$	−4.75804e6	−0.838510	−0.419255	+	0.907868i	$0.637709\pi$
$504$	−146918.	−0.0257631
$505$	3.74007e6	0.652606
$506$	−1.23964e7	−2.15238
$507$	−4.77555e6	−0.825095
$508$	−9.73825e6	−1.67425
$509$	−5.42576e6	−0.928252	−0.464126	−	0.885769i	$-0.653632\pi$
$509$	−5.42576e6	−0.928252	−0.464126	+	0.885769i	$0.653632\pi$
$510$	−4.23126e6	−0.720352
$511$	−5.54031e6	−0.938603
$512$	8.24912e6	1.39070
$513$	−6.42587e6	−1.07805
$514$	4.80325e6	0.801914
$515$	−4.09692e6	−0.680675
$516$	728804.	0.120500
$517$	1.09234e7	1.79735
$518$	−1.37466e7	−2.25098
$519$	−8.36161e6	−1.36261
$520$	20004.9	0.00324435
$521$	−8.88444e6	−1.43396	−0.716978	−	0.697096i	$-0.754475\pi$
$521$	−8.88444e6	−1.43396	−0.716978	+	0.697096i	$0.754475\pi$
$522$	−2.63853e6	−0.423825
$523$	−5.03938e6	−0.805606	−0.402803	−	0.915287i	$-0.631964\pi$
$523$	−5.03938e6	−0.805606	−0.402803	+	0.915287i	$0.631964\pi$
$524$	−8.01397e6	−1.27503
$525$	−7.11702e6	−1.12694
$526$	1.33891e6	0.211002
$527$	2.08086e6	0.326374
$528$	−6.21375e6	−0.969995
$529$	5.56545e6	0.864692
$530$	1.33555e7	2.06524
$531$	1.99323e6	0.306775
$532$	−8.22061e6	−1.25929
$533$	373178.	0.0568981
$534$	4.99195e6	0.757560
$535$	5.91436e6	0.893354
$536$	−738047.	−0.110961
$537$	−7.35221e6	−1.10023
$538$	1.12102e7	1.66978
$539$	5.83344e6	0.864874
$540$	−1.00394e7	−1.48157
$541$	3.49430e6	0.513295	0.256648	−	0.966505i	$-0.417382\pi$
$541$	3.49430e6	0.513295	0.256648	+	0.966505i	$0.417382\pi$
$542$	7.49745e6	1.09626
$543$	−1.16878e6	−0.170111
$544$	4.21980e6	0.611357
$545$	−1.62934e7	−2.34975
$546$	399462.	0.0573448
$547$	−2.50382e6	−0.357796	−0.178898	−	0.983868i	$-0.557253\pi$
$547$	−2.50382e6	−0.357796	−0.178898	+	0.983868i	$0.557253\pi$
$548$	−637671.	−0.0907079
$549$	−2.20358e6	−0.312031
$550$	1.14720e7	1.61708
$551$	6.74042e6	0.945819
$552$	493274.	0.0689034
$553$	3.77685e6	0.525190
$554$	299977.	0.0415254
$555$	1.03307e7	1.42362
$556$	−5.58563e6	−0.766276
$557$	−1.53305e6	−0.209371	−0.104686	−	0.994505i	$-0.533384\pi$
$557$	−1.53305e6	−0.209371	−0.104686	+	0.994505i	$0.533384\pi$
$558$	2.43286e6	0.330774
$559$	−42051.7	−0.00569185
$560$	1.46293e7	1.97130
$561$	−3.03957e6	−0.407761
$562$	−1.62412e7	−2.16909
$563$	8.52078e6	1.13294	0.566472	−	0.824081i	$-0.308308\pi$
$563$	8.52078e6	1.13294	0.566472	+	0.824081i	$0.308308\pi$
$564$	9.52043e6	1.26026
$565$	1.00148e7	1.31984
$566$	−1.86017e7	−2.44068
$567$	5.92311e6	0.773734
$568$	110900.	0.0144231
$569$	−429293.	−0.0555870	−0.0277935	−	0.999614i	$-0.508848\pi$
$569$	−429293.	−0.0555870	−0.0277935	+	0.999614i	$0.508848\pi$
$570$	1.26377e7	1.62922
$571$	−6.30376e6	−0.809114	−0.404557	−	0.914513i	$-0.632574\pi$
$571$	−6.30376e6	−0.809114	−0.404557	+	0.914513i	$0.632574\pi$
$572$	−314763.	−0.0402247
$573$	−7.04432e6	−0.896298
$574$	2.23762e7	2.83470
$575$	−1.11068e7	−1.40094
$576$	2.30144e6	0.289030
$577$	−8.10411e6	−1.01337	−0.506683	−	0.862133i	$-0.669128\pi$
$577$	−8.10411e6	−1.01337	−0.506683	+	0.862133i	$0.669128\pi$
$578$	−9.07969e6	−1.13045
$579$	322827.	0.0400197
$580$	1.05308e7	1.29985
$581$	1.15102e7	1.41463
$582$	9.48519e6	1.16075
$583$	9.59405e6	1.16904
$584$	−355358.	−0.0431156
$585$	139535.	0.0168575
$586$	8.81672e6	1.06063
$587$	5.93951e6	0.711468	0.355734	−	0.934587i	$-0.384231\pi$
$587$	5.93951e6	0.711468	0.355734	+	0.934587i	$0.384231\pi$
$588$	5.08420e6	0.606428
$589$	−6.21499e6	−0.738163
$590$	−1.62738e7	−1.92468
$591$	7.46197e6	0.878789
$592$	−1.07534e7	−1.26107
$593$	−1.03054e6	−0.120345	−0.0601727	−	0.998188i	$-0.519165\pi$
$593$	−1.03054e6	−0.120345	−0.0601727	+	0.998188i	$0.519165\pi$
$594$	−1.47531e7	−1.71560
$595$	7.15618e6	0.828684
$596$	1.46422e7	1.68846
$597$	5.29781e6	0.608360
$598$	623399.	0.0712875
$599$	8.75551e6	0.997044	0.498522	−	0.866877i	$-0.333876\pi$
$599$	8.75551e6	0.997044	0.498522	+	0.866877i	$0.333876\pi$
$600$	−456489.	−0.0517669
$601$	−6.36534e6	−0.718845	−0.359423	−	0.933175i	$-0.617026\pi$
$601$	−6.36534e6	−0.718845	−0.359423	+	0.933175i	$0.617026\pi$
$602$	−2.52147e6	−0.283572
$603$	−5.14792e6	−0.576552
$604$	7.49318e6	0.835745
$605$	3.45932e6	0.384240
$606$	4.79019e6	0.529872
$607$	1.44657e7	1.59356	0.796779	−	0.604270i	$-0.206535\pi$
$607$	1.44657e7	1.59356	0.796779	+	0.604270i	$0.206535\pi$
$608$	−1.26035e7	−1.38271
$609$	−9.60058e6	−1.04895
$610$	1.79912e7	1.95766
$611$	−549325.	−0.0595287
$612$	1.23136e6	0.132895
$613$	−1.78097e7	−1.91428	−0.957142	−	0.289619i	$-0.906471\pi$
$613$	−1.78097e7	−1.91428	−0.957142	+	0.289619i	$0.906471\pi$
$614$	−9.17043e6	−0.981678
$615$	−1.68158e7	−1.79279
$616$	861687.	0.0914951
$617$	4.11393e6	0.435054	0.217527	−	0.976054i	$-0.430201\pi$
$617$	4.11393e6	0.435054	0.217527	+	0.976054i	$0.430201\pi$
$618$	−5.24723e6	−0.552661
$619$	−3.56813e6	−0.374295	−0.187148	−	0.982332i	$-0.559924\pi$
$619$	−3.56813e6	−0.374295	−0.187148	+	0.982332i	$0.559924\pi$
$620$	−9.70993e6	−1.01446
$621$	1.42834e7	1.48629
$622$	−9.38950e6	−0.973120
$623$	−8.44270e6	−0.871488
$624$	312482.	0.0321265
$625$	−9.50590e6	−0.973404
$626$	4.52013e6	0.461015
$627$	9.07843e6	0.922235
$628$	397534.	0.0402230
$629$	−5.26021e6	−0.530123
$630$	8.36672e6	0.839854
$631$	8.10764e6	0.810627	0.405314	−	0.914178i	$-0.367162\pi$
$631$	8.10764e6	0.810627	0.405314	+	0.914178i	$0.367162\pi$
$632$	242249.	0.0241251
$633$	−4.96625e6	−0.492629
$634$	−6.30095e6	−0.622562
$635$	−2.53196e7	−2.49185
$636$	8.36180e6	0.819704
$637$	−293356.	−0.0286448
$638$	1.54752e7	1.50517
$639$	773531.	0.0749421
$640$	1.79972e6	0.173682
$641$	1.15748e7	1.11267	0.556335	−	0.830958i	$-0.312207\pi$
$641$	1.15748e7	1.11267	0.556335	+	0.830958i	$0.312207\pi$
$642$	7.57497e6	0.725343
$643$	−865667.	−0.0825702	−0.0412851	−	0.999147i	$-0.513145\pi$
$643$	−865667.	−0.0825702	−0.0412851	+	0.999147i	$0.513145\pi$
$644$	1.82728e7	1.73616
$645$	1.89490e6	0.179344
$646$	−6.43493e6	−0.606684
$647$	−3.32273e6	−0.312057	−0.156029	−	0.987753i	$-0.549869\pi$
$647$	−3.32273e6	−0.312057	−0.156029	+	0.987753i	$0.549869\pi$
$648$	379911.	0.0355422
$649$	−1.16904e7	−1.08948
$650$	−576910.	−0.0535580
$651$	8.85220e6	0.818651
$652$	1.34244e6	0.123673
$653$	−1.42689e7	−1.30951	−0.654754	−	0.755842i	$-0.727228\pi$
$653$	−1.42689e7	−1.30951	−0.654754	+	0.755842i	$0.727228\pi$
$654$	−2.08682e7	−1.90784
$655$	−2.08364e7	−1.89767
$656$	1.75039e7	1.58809
$657$	−2.47865e6	−0.224027
$658$	−3.29382e7	−2.96576
$659$	−1.73298e6	−0.155446	−0.0777230	−	0.996975i	$-0.524765\pi$
$659$	−1.73298e6	−0.155446	−0.0777230	+	0.996975i	$0.524765\pi$
$660$	1.41836e7	1.26744
$661$	456270.	0.0406180	0.0203090	−	0.999794i	$-0.493535\pi$
$661$	456270.	0.0406180	0.0203090	+	0.999794i	$0.493535\pi$
$662$	−3.08809e6	−0.273870
$663$	152856.	0.0135051
$664$	738269.	0.0649822
$665$	−2.13737e7	−1.87424
$666$	−6.15003e6	−0.537269
$667$	−1.49826e7	−1.30399
$668$	1.39207e7	1.20704
$669$	−1.33702e7	−1.15498
$670$	4.20305e7	3.61724
$671$	1.29242e7	1.10815
$672$	1.79515e7	1.53348
$673$	−1.34881e7	−1.14793	−0.573963	−	0.818881i	$-0.694595\pi$
$673$	−1.34881e7	−1.14793	−0.573963	+	0.818881i	$0.694595\pi$
$674$	6.05705e6	0.513584
$675$	−1.32183e7	−1.11664
$676$	−1.13468e7	−0.955005
$677$	1.96810e7	1.65035	0.825174	−	0.564879i	$-0.191077\pi$
$677$	1.96810e7	1.65035	0.825174	+	0.564879i	$0.191077\pi$
$678$	1.28268e7	1.07162
$679$	−1.60420e7	−1.33531
$680$	459001.	0.0380664
$681$	1.46838e7	1.21331
$682$	−1.42689e7	−1.17471
$683$	6.25887e6	0.513386	0.256693	−	0.966493i	$-0.417367\pi$
$683$	6.25887e6	0.513386	0.256693	+	0.966493i	$0.417367\pi$
$684$	−3.67777e6	−0.300569
$685$	−1.65795e6	−0.135004
$686$	5.32962e6	0.432400
$687$	7.07106e6	0.571600
$688$	−1.97244e6	−0.158866
$689$	−482472.	−0.0387190
$690$	−2.80911e7	−2.24619
$691$	3.10391e6	0.247295	0.123647	−	0.992326i	$-0.460541\pi$
$691$	3.10391e6	0.247295	0.123647	+	0.992326i	$0.460541\pi$
$692$	−1.98673e7	−1.57715
$693$	6.01032e6	0.475406
$694$	−1.16444e7	−0.917738
$695$	−1.45227e7	−1.14047
$696$	−615786.	−0.0481845
$697$	8.56236e6	0.667593
$698$	2.86214e7	2.22358
$699$	−1.43228e7	−1.10875
$700$	−1.69101e7	−1.30437
$701$	5.25605e6	0.403984	0.201992	−	0.979387i	$-0.435258\pi$
$701$	5.25605e6	0.403984	0.201992	+	0.979387i	$0.435258\pi$
$702$	741912.	0.0568211
$703$	1.57109e7	1.19898
$704$	−1.34981e7	−1.02646
$705$	2.47532e7	1.87568
$706$	3.96358e6	0.299279
$707$	−8.10147e6	−0.609558
$708$	−1.01889e7	−0.763916
$709$	8.29295e6	0.619574	0.309787	−	0.950806i	$-0.399742\pi$
$709$	8.29295e6	0.619574	0.309787	+	0.950806i	$0.399742\pi$
$710$	−6.31554e6	−0.470180
$711$	1.68970e6	0.125353
$712$	−541519.	−0.0400326
$713$	1.38147e7	1.01770
$714$	9.16545e6	0.672835
$715$	−818387.	−0.0598678
$716$	−1.74689e7	−1.27346
$717$	−1.64949e7	−1.19826
$718$	−3.04413e7	−2.20370
$719$	3.71146e6	0.267746	0.133873	−	0.990999i	$-0.457259\pi$
$719$	3.71146e6	0.267746	0.133873	+	0.990999i	$0.457259\pi$
$720$	6.54491e6	0.470514
$721$	8.87445e6	0.635775
$722$	−371894.	−0.0265507
$723$	9.33821e6	0.664382
$724$	−2.77703e6	−0.196895
$725$	1.38653e7	0.979681
$726$	4.43061e6	0.311977
$727$	−3.10084e6	−0.217592	−0.108796	−	0.994064i	$-0.534700\pi$
$727$	−3.10084e6	−0.217592	−0.108796	+	0.994064i	$0.534700\pi$
$728$	−43333.1	−0.00303034
$729$	1.55540e7	1.08399
$730$	2.02370e7	1.40553
$731$	−964853.	−0.0667833
$732$	1.12642e7	0.777004
$733$	−1.69858e7	−1.16769	−0.583844	−	0.811866i	$-0.698452\pi$
$733$	−1.69858e7	−1.16769	−0.583844	+	0.811866i	$0.698452\pi$
$734$	1.80850e7	1.23902
$735$	1.32190e7	0.902567
$736$	2.80150e7	1.90632
$737$	3.01930e7	2.04757
$738$	1.00108e7	0.676591
$739$	1.13197e7	0.762473	0.381236	−	0.924478i	$-0.375498\pi$
$739$	1.13197e7	0.762473	0.381236	+	0.924478i	$0.375498\pi$
$740$	2.45458e7	1.64777
$741$	−456542.	−0.0305447
$742$	−2.89297e7	−1.92901
$743$	−9.42589e6	−0.626398	−0.313199	−	0.949688i	$-0.601401\pi$
$743$	−9.42589e6	−0.626398	−0.313199	+	0.949688i	$0.601401\pi$
$744$	567785.	0.0376055
$745$	3.80699e7	2.51299
$746$	−5.96309e6	−0.392305
$747$	5.14947e6	0.337646
$748$	−7.22206e6	−0.471962
$749$	−1.28113e7	−0.834425
$750$	656888.	0.0426421
$751$	−3.73658e6	−0.241754	−0.120877	−	0.992667i	$-0.538571\pi$
$751$	−3.73658e6	−0.241754	−0.120877	+	0.992667i	$0.538571\pi$
$752$	−2.57661e7	−1.66152
$753$	−1.85002e7	−1.18902
$754$	−778230.	−0.0498516
$755$	1.94824e7	1.24387
$756$	2.17466e7	1.38384
$757$	1.39033e7	0.881815	0.440908	−	0.897552i	$-0.354657\pi$
$757$	1.39033e7	0.881815	0.440908	+	0.897552i	$0.354657\pi$
$758$	−2.80812e7	−1.77518
$759$	−2.01795e7	−1.27147
$760$	−1.37092e6	−0.0860950
$761$	−2.95291e7	−1.84837	−0.924185	−	0.381946i	$-0.875254\pi$
$761$	−2.95291e7	−1.84837	−0.924185	+	0.381946i	$0.875254\pi$
$762$	−3.24286e7	−2.02321
$763$	3.52937e7	2.19475
$764$	−1.67374e7	−1.03742
$765$	3.20156e6	0.197792
$766$	1.81269e7	1.11622
$767$	587897.	0.0360839
$768$	1.46066e7	0.893606
$769$	−9.04293e6	−0.551434	−0.275717	−	0.961239i	$-0.588915\pi$
$769$	−9.04293e6	−0.551434	−0.275717	+	0.961239i	$0.588915\pi$
$770$	−4.90716e7	−2.98265
$771$	7.81899e6	0.473713
$772$	767041.	0.0463207
$773$	−661253.	−0.0398033	−0.0199016	−	0.999802i	$-0.506335\pi$
$773$	−661253.	−0.0398033	−0.0199016	+	0.999802i	$0.506335\pi$
$774$	−1.12807e6	−0.0676834
$775$	−1.27845e7	−0.764591
$776$	−1.02894e6	−0.0613388
$777$	−2.23775e7	−1.32972
$778$	2.97497e7	1.76211
$779$	−2.55736e7	−1.50990
$780$	−713274.	−0.0419778
$781$	−4.53683e6	−0.266149
$782$	1.43036e7	0.836426
$783$	−1.78309e7	−1.03937
$784$	−1.37599e7	−0.799511
$785$	1.03359e6	0.0598653
$786$	−2.66868e7	−1.54078
$787$	−6.46523e6	−0.372089	−0.186045	−	0.982541i	$-0.559567\pi$
$787$	−6.46523e6	−0.372089	−0.186045	+	0.982541i	$0.559567\pi$
$788$	1.77297e7	1.01715
$789$	2.17954e6	0.124644
$790$	−1.37957e7	−0.786456
$791$	−2.16934e7	−1.23278
$792$	385505.	0.0218382
$793$	−649940.	−0.0367021
$794$	4.48083e7	2.52236
$795$	2.17408e7	1.21999
$796$	1.25877e7	0.704146
$797$	2.62978e7	1.46647	0.733234	−	0.679976i	$-0.238010\pi$
$797$	2.62978e7	1.46647	0.733234	+	0.679976i	$0.238010\pi$
$798$	−2.73749e7	−1.52176
$799$	−1.26040e7	−0.698458
$800$	−2.59259e7	−1.43222
$801$	−3.77713e6	−0.208008
$802$	2.79881e7	1.53652
$803$	1.45375e7	0.795610
$804$	2.63151e7	1.43570
$805$	4.75095e7	2.58399
$806$	717565.	0.0389066
$807$	1.82486e7	0.986385
$808$	−519632.	−0.0280006
$809$	−9.92533e6	−0.533180	−0.266590	−	0.963810i	$-0.585897\pi$
$809$	−9.92533e6	−0.533180	−0.266590	+	0.963810i	$0.585897\pi$
$810$	−2.16353e7	−1.15864
$811$	1.86128e7	0.993712	0.496856	−	0.867833i	$-0.334488\pi$
$811$	1.86128e7	0.993712	0.496856	+	0.867833i	$0.334488\pi$
$812$	−2.28111e7	−1.21411
$813$	1.22048e7	0.647594
$814$	3.60705e7	1.90805
$815$	3.49035e6	0.184066
$816$	7.16972e6	0.376944
$817$	2.88177e6	0.151044
$818$	−1.66974e7	−0.872501
$819$	−302251.	−0.0157456
$820$	−3.99546e7	−2.07507
$821$	1.08487e7	0.561718	0.280859	−	0.959749i	$-0.409381\pi$
$821$	1.08487e7	0.561718	0.280859	+	0.959749i	$0.409381\pi$
$822$	−2.12346e6	−0.109614
$823$	−1.29473e7	−0.666316	−0.333158	−	0.942871i	$-0.608114\pi$
$823$	−1.29473e7	−0.666316	−0.333158	+	0.942871i	$0.608114\pi$
$824$	569212.	0.0292049
$825$	1.86747e7	0.955253
$826$	3.52511e7	1.79772
$827$	2.79589e7	1.42153	0.710767	−	0.703428i	$-0.248348\pi$
$827$	2.79589e7	1.42153	0.710767	+	0.703428i	$0.248348\pi$
$828$	8.17496e6	0.414390
$829$	−1.95464e7	−0.987825	−0.493913	−	0.869512i	$-0.664434\pi$
$829$	−1.95464e7	−0.987825	−0.493913	+	0.869512i	$0.664434\pi$
$830$	−4.20432e7	−2.11836
$831$	488319.	0.0245302
$832$	678803.	0.0339966
$833$	−6.73090e6	−0.336094
$834$	−1.86003e7	−0.925987
$835$	3.61940e7	1.79647
$836$	2.15705e7	1.06744
$837$	1.64410e7	0.811174
$838$	7.09215e6	0.348873
$839$	1.66180e7	0.815031	0.407516	−	0.913198i	$-0.366395\pi$
$839$	1.66180e7	0.815031	0.407516	+	0.913198i	$0.366395\pi$
$840$	1.95264e6	0.0954826
$841$	−1.80736e6	−0.0881161
$842$	3.23840e7	1.57416
$843$	−2.64383e7	−1.28134
$844$	−1.17999e7	−0.570193
$845$	−2.95018e7	−1.42137
$846$	−1.47360e7	−0.707873
$847$	−7.49334e6	−0.358894
$848$	−2.26304e7	−1.08069
$849$	−3.02808e7	−1.44178
$850$	−1.32369e7	−0.628404
$851$	−3.49222e7	−1.65302
$852$	−3.95412e6	−0.186617
$853$	−1.69144e7	−0.795947	−0.397974	−	0.917397i	$-0.630286\pi$
$853$	−1.69144e7	−0.795947	−0.397974	+	0.917397i	$0.630286\pi$
$854$	−3.89713e7	−1.82852
$855$	−9.56225e6	−0.447347
$856$	−821721.	−0.0383301
$857$	767365.	0.0356903	0.0178451	−	0.999841i	$-0.494319\pi$
$857$	767365.	0.0356903	0.0178451	+	0.999841i	$0.494319\pi$
$858$	−1.04817e6	−0.0486086
$859$	1.25709e7	0.581278	0.290639	−	0.956833i	$-0.406132\pi$
$859$	1.25709e7	0.581278	0.290639	+	0.956833i	$0.406132\pi$
$860$	4.50230e6	0.207581
$861$	3.64252e7	1.67454
$862$	−9.36163e6	−0.429124
$863$	4.15225e6	0.189783	0.0948913	−	0.995488i	$-0.469750\pi$
$863$	4.15225e6	0.189783	0.0948913	+	0.995488i	$0.469750\pi$
$864$	3.33409e7	1.51947
$865$	−5.16552e7	−2.34733
$866$	1.29358e7	0.586137
$867$	−1.47804e7	−0.667788
$868$	2.10329e7	0.947547
$869$	−9.91025e6	−0.445180
$870$	3.50680e7	1.57077
$871$	−1.51837e6	−0.0678159
$872$	2.26375e6	0.100818
$873$	−7.17691e6	−0.318715
$874$	−4.27211e7	−1.89175
$875$	−1.11097e6	−0.0490549
$876$	1.26703e7	0.557862
$877$	−2.05982e6	−0.0904337	−0.0452168	−	0.998977i	$-0.514398\pi$
$877$	−2.05982e6	−0.0904337	−0.0452168	+	0.998977i	$0.514398\pi$
$878$	−1.77154e7	−0.775558
$879$	1.43523e7	0.626542
$880$	−3.83865e7	−1.67098
$881$	3.31902e6	0.144069	0.0720345	−	0.997402i	$-0.477051\pi$
$881$	3.31902e6	0.144069	0.0720345	+	0.997402i	$0.477051\pi$
$882$	−7.86949e6	−0.340624
$883$	3.88804e6	0.167814	0.0839071	−	0.996474i	$-0.473260\pi$
$883$	3.88804e6	0.167814	0.0839071	+	0.996474i	$0.473260\pi$
$884$	363188.	0.0156315
$885$	−2.64914e7	−1.13696
$886$	3.50168e7	1.49862
$887$	−4.11225e6	−0.175497	−0.0877486	−	0.996143i	$-0.527967\pi$
$887$	−4.11225e6	−0.175497	−0.0877486	+	0.996143i	$0.527967\pi$
$888$	−1.43531e6	−0.0610818
$889$	5.48454e7	2.32748
$890$	3.08386e7	1.30503
$891$	−1.55419e7	−0.655859
$892$	−3.17678e7	−1.33683
$893$	3.76448e7	1.57971
$894$	4.87590e7	2.04038
$895$	−4.54195e7	−1.89533
$896$	−3.89843e6	−0.162226
$897$	1.01480e6	0.0421115
$898$	6.52458e6	0.269999
$899$	−1.72458e7	−0.711679
$900$	−7.56532e6	−0.311330
$901$	−1.10701e7	−0.454295
$902$	−5.87141e7	−2.40285
$903$	−4.10459e6	−0.167514
$904$	−1.39143e6	−0.0566291
$905$	−7.22031e6	−0.293045
$906$	2.49525e7	1.00994
$907$	−4.04945e7	−1.63447	−0.817236	−	0.576303i	$-0.804495\pi$
$907$	−4.04945e7	−1.63447	−0.817236	+	0.576303i	$0.804495\pi$
$908$	3.48889e7	1.40434
$909$	−3.62447e6	−0.145490
$910$	2.46774e6	0.0987863
$911$	−3.27575e7	−1.30772	−0.653860	−	0.756615i	$-0.726852\pi$
$911$	−3.27575e7	−1.30772	−0.653860	+	0.756615i	$0.726852\pi$
$912$	−2.14141e7	−0.852538
$913$	−3.02021e7	−1.19911
$914$	3.78252e7	1.49767
$915$	2.92871e7	1.15644
$916$	1.68009e7	0.661599
$917$	4.51343e7	1.77249
$918$	1.70228e7	0.666690
$919$	−8.68701e6	−0.339298	−0.169649	−	0.985505i	$-0.554263\pi$
$919$	−8.68701e6	−0.339298	−0.169649	+	0.985505i	$0.554263\pi$
$920$	3.04728e6	0.118698
$921$	−1.49281e7	−0.579904
$922$	1.40499e6	0.0544310
$923$	228151.	0.00881492
$924$	−3.07235e7	−1.18383
$925$	3.23180e7	1.24191
$926$	6.52083e7	2.49905
$927$	3.97029e6	0.151748
$928$	−3.49730e7	−1.33310
$929$	−6.29057e6	−0.239139	−0.119570	−	0.992826i	$-0.538151\pi$
$929$	−6.29057e6	−0.239139	−0.119570	+	0.992826i	$0.538151\pi$
$930$	−3.23344e7	−1.22590
$931$	2.01035e7	0.760146
$932$	−3.40311e7	−1.28332
$933$	−1.52847e7	−0.574849
$934$	2.32210e7	0.870990
$935$	−1.87775e7	−0.702437
$936$	−19386.5	−0.000723287 0
$937$	−6.97275e6	−0.259451	−0.129725	−	0.991550i	$-0.541410\pi$
$937$	−6.97275e6	−0.259451	−0.129725	+	0.991550i	$0.541410\pi$
$938$	−9.10434e7	−3.37863
$939$	7.35812e6	0.272335
$940$	5.88140e7	2.17101
$941$	1.67294e7	0.615894	0.307947	−	0.951404i	$-0.400358\pi$
$941$	1.67294e7	0.615894	0.307947	+	0.951404i	$0.400358\pi$
$942$	1.32380e6	0.0486065
$943$	5.68450e7	2.08168
$944$	2.75754e7	1.00714
$945$	5.65414e7	2.05962
$946$	6.61622e6	0.240371
$947$	−4.20327e7	−1.52304	−0.761522	−	0.648140i	$-0.775547\pi$
$947$	−4.20327e7	−1.52304	−0.761522	+	0.648140i	$0.775547\pi$
$948$	−8.63739e6	−0.312149
$949$	−731071.	−0.0263508
$950$	3.95352e7	1.42127
$951$	−1.02570e7	−0.367765
$952$	−994255.	−0.0355554
$953$	4.38940e7	1.56557	0.782787	−	0.622290i	$-0.213798\pi$
$953$	4.38940e7	1.56557	0.782787	+	0.622290i	$0.213798\pi$
$954$	−1.29427e7	−0.460419
$955$	−4.35174e7	−1.54403
$956$	−3.91920e7	−1.38692
$957$	2.51914e7	0.889146
$958$	5.95917e7	2.09784
$959$	3.59133e6	0.126098
$960$	−3.05877e7	−1.07120
$961$	−1.27277e7	−0.444571
$962$	−1.81394e6	−0.0631952
$963$	−5.73156e6	−0.199162
$964$	2.21877e7	0.768989
$965$	1.99432e6	0.0689407
$966$	6.08489e7	2.09802
$967$	1.42055e6	0.0488530	0.0244265	−	0.999702i	$-0.492224\pi$
$967$	1.42055e6	0.0488530	0.0244265	+	0.999702i	$0.492224\pi$
$968$	−480626.	−0.0164862
$969$	−1.04751e7	−0.358385
$970$	5.85963e7	1.99959
$971$	−4.66877e7	−1.58911	−0.794556	−	0.607191i	$-0.792296\pi$
$971$	−4.66877e7	−1.58911	−0.794556	+	0.607191i	$0.792296\pi$
$972$	1.71146e7	0.581033
$973$	3.14580e7	1.06524
$974$	−1.82205e7	−0.615407
$975$	−939125.	−0.0316382
$976$	−3.04855e7	−1.02440
$977$	5.11806e6	0.171541	0.0857707	−	0.996315i	$-0.472665\pi$
$977$	5.11806e6	0.171541	0.0857707	+	0.996315i	$0.472665\pi$
$978$	4.47035e6	0.149449
$979$	2.21532e7	0.738720
$980$	3.14085e7	1.04468
$981$	1.57898e7	0.523848
$982$	3.51280e7	1.16245
$983$	−1.29865e6	−0.0428654	−0.0214327	−	0.999770i	$-0.506823\pi$
$983$	−1.29865e6	−0.0428654	−0.0214327	+	0.999770i	$0.506823\pi$
$984$	2.33633e6	0.0769214
$985$	4.60975e7	1.51387
$986$	−1.78561e7	−0.584916
$987$	−5.36187e7	−1.75196
$988$	−1.08475e6	−0.0353539
$989$	−6.40560e6	−0.208242
$990$	−2.19538e7	−0.711906
$991$	2.92905e7	0.947422	0.473711	−	0.880680i	$-0.342914\pi$
$991$	2.92905e7	0.947422	0.473711	+	0.880680i	$0.342914\pi$
$992$	3.22468e7	1.04042
$993$	−5.02696e6	−0.161783
$994$	1.36803e7	0.439165
$995$	3.27281e7	1.04800
$996$	−2.63230e7	−0.840789
$997$	−2.66478e7	−0.849031	−0.424515	−	0.905421i	$-0.639555\pi$
$997$	−2.66478e7	−0.849031	−0.424515	+	0.905421i	$0.639555\pi$
$998$	6.29640e7	2.00109
$999$	−4.15612e7	−1.31757

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.a.b.1.8	✓	10
3.2	odd	2		387.6.a.e.1.3		10
4.3	odd	2		688.6.a.h.1.5		10
5.4	even	2		1075.6.a.b.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.a.b.1.8	✓	10	1.1	even	1	trivial
387.6.a.e.1.3		10	3.2	odd	2
688.6.a.h.1.5		10	4.3	odd	2
1075.6.a.b.1.3		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)

\(f(q)\)	\(=\)	\(q+7.91219 q^{2} +12.8799 q^{3} +30.6028 q^{4} +79.5677 q^{5} +101.908 q^{6} -172.354 q^{7} -11.0549 q^{8} -77.1083 q^{9} +O(q^{10})\)	\(q+7.91219 q^{2} +12.8799 q^{3} +30.6028 q^{4} +79.5677 q^{5} +101.908 q^{6} -172.354 q^{7} -11.0549 q^{8} -77.1083 q^{9} +629.555 q^{10} +452.247 q^{11} +394.161 q^{12} -22.7429 q^{13} -1363.70 q^{14} +1024.82 q^{15} -1066.76 q^{16} -521.824 q^{17} -610.096 q^{18} +1558.56 q^{19} +2434.99 q^{20} -2219.90 q^{21} +3578.27 q^{22} -3464.36 q^{23} -142.385 q^{24} +3206.01 q^{25} -179.946 q^{26} -4122.96 q^{27} -5274.51 q^{28} +4324.79 q^{29} +8108.60 q^{30} -3987.66 q^{31} -8086.64 q^{32} +5824.90 q^{33} -4128.77 q^{34} -13713.8 q^{35} -2359.73 q^{36} +10080.4 q^{37} +12331.6 q^{38} -292.926 q^{39} -879.609 q^{40} -16408.5 q^{41} -17564.3 q^{42} +1849.00 q^{43} +13840.0 q^{44} -6135.33 q^{45} -27410.7 q^{46} +24153.7 q^{47} -13739.7 q^{48} +12898.8 q^{49} +25366.6 q^{50} -6721.04 q^{51} -695.997 q^{52} +21214.2 q^{53} -32621.7 q^{54} +35984.2 q^{55} +1905.34 q^{56} +20074.0 q^{57} +34218.6 q^{58} -25849.7 q^{59} +31362.5 q^{60} +28577.7 q^{61} -31551.2 q^{62} +13289.9 q^{63} -29846.8 q^{64} -1809.60 q^{65} +46087.7 q^{66} +66762.2 q^{67} -15969.3 q^{68} -44620.6 q^{69} -108506. q^{70} -10031.8 q^{71} +852.421 q^{72} +32145.0 q^{73} +79758.3 q^{74} +41293.1 q^{75} +47696.2 q^{76} -77946.5 q^{77} -2317.69 q^{78} -21913.4 q^{79} -84879.4 q^{80} -34366.0 q^{81} -129827. q^{82} -66782.4 q^{83} -67935.1 q^{84} -41520.3 q^{85} +14629.6 q^{86} +55702.8 q^{87} -4999.53 q^{88} +48984.7 q^{89} -48543.9 q^{90} +3919.82 q^{91} -106019. q^{92} -51360.7 q^{93} +191108. q^{94} +124011. q^{95} -104155. q^{96} +93075.8 q^{97} +102058. q^{98} -34872.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 8 q^{2} + 28 q^{3} + 202 q^{4} + 138 q^{5} + 75 q^{6} + 60 q^{7} + 294 q^{8} + 1356 q^{9}+O(q^{10}) \) 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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