LMFDB - Embedded newform 147.7.d.a.97.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,7,Mod(97,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("147.97");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	147.d (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$33.8179502921$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} - 787x^{5} + 38792x^{4} - 92833x^{3} + 1563109x^{2} + 3107772x + 38787984 $ x^8 - x^7 + 212x^6 - 787x^5 + 38792x^4 - 92833x^3 + 1563109x^2 + 3107772x + 38787984
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			97.7
Root			$5.73828 - 9.93899i$ of defining polynomial
Character	$\chi$	$=$	147.97
Dual form			147.7.d.a.97.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+12.4766 q^{2} -15.5885i q^{3} +91.6646 q^{4} -202.496i q^{5} -194.490i q^{6} +345.159 q^{8} -243.000 q^{9} +O(q^{10})$	\(q+12.4766 q^{2} -15.5885i q^{3} +91.6646 q^{4} -202.496i q^{5} -194.490i q^{6} +345.159 q^{8} -243.000 q^{9} -2526.46i q^{10} +875.768 q^{11} -1428.91i q^{12} -275.049i q^{13} -3156.61 q^{15} -1560.14 q^{16} +4386.83i q^{17} -3031.80 q^{18} -13507.5i q^{19} -18561.8i q^{20} +10926.6 q^{22} -12735.2 q^{23} -5380.49i q^{24} -25379.8 q^{25} -3431.66i q^{26} +3788.00i q^{27} +6262.53 q^{29} -39383.6 q^{30} +20426.3i q^{31} -41555.3 q^{32} -13651.9i q^{33} +54732.5i q^{34} -22274.5 q^{36} +15724.2 q^{37} -168527. i q^{38} -4287.58 q^{39} -69893.4i q^{40} -69941.8i q^{41} +113322. q^{43} +80276.9 q^{44} +49206.6i q^{45} -158892. q^{46} -46322.2i q^{47} +24320.1i q^{48} -316653. q^{50} +68383.9 q^{51} -25212.2i q^{52} +128026. q^{53} +47261.2i q^{54} -177340. i q^{55} -210561. q^{57} +78134.9 q^{58} -280442. i q^{59} -289349. q^{60} +97871.6i q^{61} +254850. i q^{62} -418619. q^{64} -55696.4 q^{65} -170329. i q^{66} +174558. q^{67} +402117. i q^{68} +198522. i q^{69} +345712. q^{71} -83873.6 q^{72} +120769. i q^{73} +196184. q^{74} +395632. i q^{75} -1.23816e6i q^{76} -53494.3 q^{78} +763865. q^{79} +315922. i q^{80} +59049.0 q^{81} -872633. i q^{82} +859402. i q^{83} +888317. q^{85} +1.41387e6 q^{86} -97623.2i q^{87} +302279. q^{88} -179877. i q^{89} +613930. i q^{90} -1.16737e6 q^{92} +318415. q^{93} -577942. i q^{94} -2.73522e6 q^{95} +647783. i q^{96} +340171. i q^{97} -212812. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 10 q^{2} + 346 q^{4} - 454 q^{8} - 1944 q^{9}+O(q^{10}) $ 8 * q + 10 * q^2 + 346 * q^4 - 454 * q^8 - 1944 * q^9	$ 8 q + 10 q^{2} + 346 q^{4} - 454 q^{8} - 1944 q^{9} + 2140 q^{11} - 756 q^{15} - 7822 q^{16} - 2430 q^{18} - 78 q^{22} + 30448 q^{23} - 44548 q^{25} + 32524 q^{29} - 4698 q^{30} - 140406 q^{32} - 84078 q^{36} + 91340 q^{37} - 186732 q^{39} - 445660 q^{43} + 377658 q^{44} - 1051608 q^{46} - 1218884 q^{50} - 129816 q^{51} + 26068 q^{53} - 442908 q^{57} + 319002 q^{58} - 859410 q^{60} - 1410446 q^{64} + 778008 q^{65} - 768188 q^{67} + 225688 q^{71} + 110322 q^{72} - 2371060 q^{74} - 342792 q^{78} + 1119184 q^{79} + 472392 q^{81} + 1953576 q^{85} + 4604804 q^{86} - 609774 q^{88} - 113064 q^{92} - 723600 q^{93} - 2320224 q^{95} - 520020 q^{99}+O(q^{100}) $ 8 * q + 10 * q^2 + 346 * q^4 - 454 * q^8 - 1944 * q^9 + 2140 * q^11 - 756 * q^15 - 7822 * q^16 - 2430 * q^18 - 78 * q^22 + 30448 * q^23 - 44548 * q^25 + 32524 * q^29 - 4698 * q^30 - 140406 * q^32 - 84078 * q^36 + 91340 * q^37 - 186732 * q^39 - 445660 * q^43 + 377658 * q^44 - 1051608 * q^46 - 1218884 * q^50 - 129816 * q^51 + 26068 * q^53 - 442908 * q^57 + 319002 * q^58 - 859410 * q^60 - 1410446 * q^64 + 778008 * q^65 - 768188 * q^67 + 225688 * q^71 + 110322 * q^72 - 2371060 * q^74 - 342792 * q^78 + 1119184 * q^79 + 472392 * q^81 + 1953576 * q^85 + 4604804 * q^86 - 609774 * q^88 - 113064 * q^92 - 723600 * q^93 - 2320224 * q^95 - 520020 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$-1$

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 $

$2$	12.4766	1.55957	0.779785	−	0.626047i	$-0.215328\pi$
$2$	12.4766	1.55957	0.779785	+	0.626047i	$0.215328\pi$
$3$	− 15.5885i	− 0.577350i
$3$	− 15.5885i	− 0.577350i
$4$	91.6646	1.43226
$5$	− 202.496i	− 1.61997i	−0.586450	−	0.809986i	$-0.699475\pi$
$5$	− 202.496i	− 1.61997i	0.586450	−	0.809986i	$-0.300525\pi$
$6$	− 194.490i	− 0.900418i
$7$	0	0
$7$	0	0
$8$	345.159	0.674138
$9$	−243.000	−0.333333
$10$	− 2526.46i	− 2.52646i
$11$	875.768	0.657978	0.328989	−	0.944334i	$-0.393292\pi$
$11$	875.768	0.657978	0.328989	+	0.944334i	$0.393292\pi$
$12$	− 1428.91i	− 0.826915i
$13$	− 275.049i	− 0.125193i	−0.998039	−	0.0625964i	$-0.980062\pi$
$13$	− 275.049i	− 0.125193i	0.998039	−	0.0625964i	$-0.0199381\pi$
$14$	0	0
$15$	−3156.61	−0.935291
$16$	−1560.14	−0.380893
$17$	4386.83i	0.892902i	0.894808	+	0.446451i	$0.147312\pi$
$17$	4386.83i	0.892902i	−0.894808	+	0.446451i	$0.852688\pi$
$18$	−3031.80	−0.519857
$19$	− 13507.5i	− 1.96931i	−0.174510	−	0.984655i	$-0.555834\pi$
$19$	− 13507.5i	− 1.96931i	0.174510	−	0.984655i	$-0.444166\pi$
$20$	− 18561.8i	− 2.32022i
$21$	0	0
$22$	10926.6	1.02616
$23$	−12735.2	−1.04670	−0.523351	−	0.852117i	$-0.675318\pi$
$23$	−12735.2	−1.04670	−0.523351	+	0.852117i	$0.675318\pi$
$24$	− 5380.49i	− 0.389214i
$25$	−25379.8	−1.62431
$26$	− 3431.66i	− 0.195247i
$27$	3788.00i	0.192450i
$28$	0	0
$29$	6262.53	0.256777	0.128388	−	0.991724i	$-0.459020\pi$
$29$	6262.53	0.256777	0.128388	+	0.991724i	$0.459020\pi$
$30$	−39383.6	−1.45865
$31$	20426.3i	0.685653i	0.939399	+	0.342827i	$0.111384\pi$
$31$	20426.3i	0.685653i	−0.939399	+	0.342827i	$0.888616\pi$
$32$	−41555.3	−1.26817
$33$	− 13651.9i	− 0.379884i
$34$	54732.5i	1.39254i
$35$	0	0
$36$	−22274.5	−0.477420
$37$	15724.2	0.310429	0.155215	−	0.987881i	$-0.450393\pi$
$37$	15724.2	0.310429	0.155215	+	0.987881i	$0.450393\pi$
$38$	− 168527.i	− 3.07128i
$39$	−4287.58	−0.0722801
$40$	− 69893.4i	− 1.09208i
$41$	− 69941.8i	− 1.01481i	−0.861707	−	0.507405i	$-0.830605\pi$
$41$	− 69941.8i	− 1.01481i	0.861707	−	0.507405i	$-0.169395\pi$
$42$	0	0
$43$	113322.	1.42530	0.712652	−	0.701517i	$-0.247494\pi$
$43$	113322.	1.42530	0.712652	+	0.701517i	$0.247494\pi$
$44$	80276.9	0.942395
$45$	49206.6i	0.539990i
$46$	−158892.	−1.63240
$47$	− 46322.2i	− 0.446165i	−0.974800	−	0.223083i	$-0.928388\pi$
$47$	− 46322.2i	− 0.446165i	0.974800	−	0.223083i	$-0.0716120\pi$
$48$	24320.1i	0.219909i
$49$	0	0
$50$	−316653.	−2.53322
$51$	68383.9	0.515517
$52$	− 25212.2i	− 0.179309i
$53$	128026.	0.859947	0.429973	−	0.902842i	$-0.358523\pi$
$53$	128026.	0.859947	0.429973	+	0.902842i	$0.358523\pi$
$54$	47261.2i	0.300139i
$55$	− 177340.i	− 1.06591i
$56$	0	0
$57$	−210561.	−1.13698
$58$	78134.9	0.400462
$59$	− 280442.i	− 1.36548i	−0.730659	−	0.682742i	$-0.760787\pi$
$59$	− 280442.i	− 1.36548i	0.730659	−	0.682742i	$-0.239213\pi$
$60$	−289349.	−1.33958
$61$	97871.6i	0.431189i	0.976483	+	0.215594i	$0.0691689\pi$
$61$	97871.6i	0.431189i	−0.976483	+	0.215594i	$0.930831\pi$
$62$	254850.i	1.06932i
$63$	0	0
$64$	−418619.	−1.59690
$65$	−55696.4	−0.202809
$66$	− 170329.i	− 0.592455i
$67$	174558.	0.580383	0.290191	−	0.956969i	$-0.406281\pi$
$67$	174558.	0.580383	0.290191	+	0.956969i	$0.406281\pi$
$68$	402117.i	1.27887i
$69$	198522.i	0.604314i
$70$	0	0
$71$	345712.	0.965915	0.482957	−	0.875644i	$-0.339563\pi$
$71$	345712.	0.965915	0.482957	+	0.875644i	$0.339563\pi$
$72$	−83873.6	−0.224713
$73$	120769.i	0.310446i	0.987879	+	0.155223i	$0.0496096\pi$
$73$	120769.i	0.310446i	−0.987879	+	0.155223i	$0.950390\pi$
$74$	196184.	0.484136
$75$	395632.i	0.937794i
$76$	− 1.23816e6i	− 2.82056i
$77$	0	0
$78$	−53494.3	−0.112726
$79$	763865.	1.54930	0.774650	−	0.632390i	$-0.217926\pi$
$79$	763865.	1.54930	0.774650	+	0.632390i	$0.217926\pi$
$80$	315922.i	0.617036i
$81$	59049.0	0.111111
$82$	− 872633.i	− 1.58267i
$83$	859402.i	1.50301i	0.659727	+	0.751505i	$0.270672\pi$
$83$	859402.i	1.50301i	−0.659727	+	0.751505i	$0.729328\pi$
$84$	0	0
$85$	888317.	1.44648
$86$	1.41387e6	2.22286
$87$	− 97623.2i	− 0.148250i
$88$	302279.	0.443568
$89$	− 179877.i	− 0.255155i	−0.991829	−	0.127578i	$-0.959280\pi$
$89$	− 179877.i	− 0.255155i	0.991829	−	0.127578i	$-0.0407202\pi$
$90$	613930.i	0.842153i
$91$	0	0
$92$	−1.16737e6	−1.49915
$93$	318415.	0.395862
$94$	− 577942.i	− 0.695826i
$95$	−2.73522e6	−3.19023
$96$	647783.i	0.732177i
$97$	340171.i	0.372720i	0.982482	+	0.186360i	$0.0596690\pi$
$97$	340171.i	0.372720i	−0.982482	+	0.186360i	$0.940331\pi$
$98$	0	0
$99$	−212812.	−0.219326
$100$	−2.32643e6	−2.32643
$101$	− 1.04337e6i	− 1.01269i	−0.862332	−	0.506344i	$-0.830997\pi$
$101$	− 1.04337e6i	− 1.01269i	0.862332	−	0.506344i	$-0.169003\pi$
$102$	853196.	0.803985
$103$	− 780025.i	− 0.713834i	−0.934136	−	0.356917i	$-0.883828\pi$
$103$	− 780025.i	− 0.713834i	0.934136	−	0.356917i	$-0.116172\pi$
$104$	− 94935.5i	− 0.0843973i
$105$	0	0
$106$	1.59733e6	1.34115
$107$	−997688.	−0.814411	−0.407205	−	0.913337i	$-0.633497\pi$
$107$	−997688.	−0.814411	−0.407205	+	0.913337i	$0.633497\pi$
$108$	347225.i	0.275638i
$109$	1.45567e6	1.12405	0.562023	−	0.827122i	$-0.310023\pi$
$109$	1.45567e6	1.12405	0.562023	+	0.827122i	$0.310023\pi$
$110$	− 2.21259e6i	− 1.66235i
$111$	− 245116.i	− 0.179226i
$112$	0	0
$113$	177612.	0.123094	0.0615469	−	0.998104i	$-0.480397\pi$
$113$	177612.	0.123094	0.0615469	+	0.998104i	$0.480397\pi$
$114$	−2.62708e6	−1.77320
$115$	2.57884e6i	1.69563i
$116$	574053.	0.367771
$117$	66836.8i	0.0417309i
$118$	− 3.49895e6i	− 2.12957i
$119$	0	0
$120$	−1.08953e6	−0.630516
$121$	−1.00459e6	−0.567065
$122$	1.22110e6i	0.672469i
$123$	−1.09028e6	−0.585901
$124$	1.87237e6i	0.982033i
$125$	1.97531e6i	1.01136i
$126$	0	0
$127$	924373.	0.451269	0.225635	−	0.974212i	$-0.427554\pi$
$127$	924373.	0.451269	0.225635	+	0.974212i	$0.427554\pi$
$128$	−2.56338e6	−1.22232
$129$	− 1.76651e6i	− 0.822900i
$130$	−694899.	−0.316295
$131$	967205.i	0.430234i	0.976588	+	0.215117i	$0.0690133\pi$
$131$	967205.i	0.430234i	−0.976588	+	0.215117i	$0.930987\pi$
$132$	− 1.25139e6i	− 0.544092i
$133$	0	0
$134$	2.17788e6	0.905148
$135$	767055.	0.311764
$136$	1.51415e6i	0.601939i
$137$	4.70012e6	1.82788	0.913940	−	0.405850i	$-0.133025\pi$
$137$	4.70012e6	1.82788	0.913940	+	0.405850i	$0.133025\pi$
$138$	2.47688e6i	0.942469i
$139$	1.64306e6i	0.611798i	0.952064	+	0.305899i	$0.0989570\pi$
$139$	1.64306e6i	0.611798i	−0.952064	+	0.305899i	$0.901043\pi$
$140$	0	0
$141$	−722092.	−0.257594
$142$	4.31329e6	1.50641
$143$	− 240879.i	− 0.0823741i
$144$	379113.	0.126964
$145$	− 1.26814e6i	− 0.415971i
$146$	1.50678e6i	0.484162i
$147$	0	0
$148$	1.44135e6	0.444615
$149$	4.62738e6	1.39887	0.699433	−	0.714698i	$-0.253436\pi$
$149$	4.62738e6	1.39887	0.699433	+	0.714698i	$0.253436\pi$
$150$	4.93613e6i	1.46256i
$151$	−4.49220e6	−1.30475	−0.652377	−	0.757895i	$-0.726228\pi$
$151$	−4.49220e6	−1.30475	−0.652377	+	0.757895i	$0.726228\pi$
$152$	− 4.66223e6i	− 1.32759i
$153$	− 1.06600e6i	− 0.297634i
$154$	0	0
$155$	4.13625e6	1.11074
$156$	−393020.	−0.103524
$157$	4.82502e6i	1.24681i	0.781899	+	0.623405i	$0.214251\pi$
$157$	4.82502e6i	1.24681i	−0.781899	+	0.623405i	$0.785749\pi$
$158$	9.53041e6	2.41624
$159$	− 1.99573e6i	− 0.496491i
$160$	8.41480e6i	2.05440i
$161$	0	0
$162$	736728.	0.173286
$163$	−3.39526e6	−0.783989	−0.391994	−	0.919968i	$-0.628215\pi$
$163$	−3.39526e6	−0.783989	−0.391994	+	0.919968i	$0.628215\pi$
$164$	− 6.41118e6i	− 1.45347i
$165$	−2.76446e6	−0.615401
$166$	1.07224e7i	2.34405i
$167$	− 2.04579e6i	− 0.439249i	−0.975584	−	0.219625i	$-0.929517\pi$
$167$	− 2.04579e6i	− 0.439249i	0.975584	−	0.219625i	$-0.0704832\pi$
$168$	0	0
$169$	4.75116e6	0.984327
$170$	1.10831e7	2.25588
$171$	3.28232e6i	0.656437i
$172$	1.03876e7	2.04141
$173$	− 314954.i	− 0.0608287i	−0.999537	−	0.0304144i	$-0.990317\pi$
$173$	− 314954.i	− 0.0608287i	0.999537	−	0.0304144i	$-0.00968269\pi$
$174$	− 1.21800e6i	− 0.231207i
$175$	0	0
$176$	−1.36632e6	−0.250619
$177$	−4.37166e6	−0.788363
$178$	− 2.24424e6i	− 0.397933i
$179$	−4.02407e6	−0.701627	−0.350814	−	0.936445i	$-0.614095\pi$
$179$	−4.02407e6	−0.701627	−0.350814	+	0.936445i	$0.614095\pi$
$180$	4.51051e6i	0.773406i
$181$	1.53820e6i	0.259405i	0.991553	+	0.129703i	$0.0414022\pi$
$181$	1.53820e6i	0.259405i	−0.991553	+	0.129703i	$0.958598\pi$
$182$	0	0
$183$	1.52567e6	0.248947
$184$	−4.39567e6	−0.705622
$185$	− 3.18409e6i	− 0.502886i
$186$	3.97272e6	0.617375
$187$	3.84184e6i	0.587510i
$188$	− 4.24611e6i	− 0.639024i
$189$	0	0
$190$	−3.41262e7	−4.97538
$191$	4.27730e6	0.613861	0.306931	−	0.951732i	$-0.400698\pi$
$191$	4.27730e6	0.613861	0.306931	+	0.951732i	$0.400698\pi$
$192$	6.52562e6i	0.921973i
$193$	−6.44624e6	−0.896674	−0.448337	−	0.893865i	$-0.647984\pi$
$193$	−6.44624e6	−0.896674	−0.448337	+	0.893865i	$0.647984\pi$
$194$	4.24417e6i	0.581283i
$195$	868220.i	0.117092i
$196$	0	0
$197$	−2.73215e6	−0.357359	−0.178680	−	0.983907i	$-0.557183\pi$
$197$	−2.73215e6	−0.357359	−0.178680	+	0.983907i	$0.557183\pi$
$198$	−2.65516e6	−0.342054
$199$	− 597246.i	− 0.0757869i	−0.999282	−	0.0378935i	$-0.987935\pi$
$199$	− 597246.i	− 0.0757869i	0.999282	−	0.0378935i	$-0.0120648\pi$
$200$	−8.76006e6	−1.09501
$201$	− 2.72109e6i	− 0.335084i
$202$	− 1.30177e7i	− 1.57936i
$203$	0	0
$204$	6.26838e6	0.738354
$205$	−1.41630e7	−1.64396
$206$	− 9.73203e6i	− 1.11327i
$207$	3.09466e6	0.348901
$208$	429114.i	0.0476851i
$209$	− 1.18294e7i	− 1.29576i
$210$	0	0
$211$	−3.67602e6	−0.391319	−0.195659	−	0.980672i	$-0.562685\pi$
$211$	−3.67602e6	−0.391319	−0.195659	+	0.980672i	$0.562685\pi$
$212$	1.17355e7	1.23167
$213$	− 5.38911e6i	− 0.557671i
$214$	−1.24477e7	−1.27013
$215$	− 2.29472e7i	− 2.30895i
$216$	1.30746e6i	0.129738i
$217$	0	0
$218$	1.81618e7	1.75303
$219$	1.88260e6	0.179236
$220$	− 1.62558e7i	− 1.52665i
$221$	1.20659e6	0.111785
$222$	− 3.05820e6i	− 0.279516i
$223$	1.43225e7i	1.29153i	0.763535	+	0.645766i	$0.223462\pi$
$223$	1.43225e7i	1.29153i	−0.763535	+	0.645766i	$0.776538\pi$
$224$	0	0
$225$	6.16729e6	0.541436
$226$	2.21598e6	0.191973
$227$	3.03111e6i	0.259134i	0.991571	+	0.129567i	$0.0413587\pi$
$227$	3.03111e6i	0.259134i	−0.991571	+	0.129567i	$0.958641\pi$
$228$	−1.93010e7	−1.62845
$229$	− 6.26071e6i	− 0.521336i	−0.965429	−	0.260668i	$-0.916057\pi$
$229$	− 6.26071e6i	− 0.521336i	0.965429	−	0.260668i	$-0.0839427\pi$
$230$	3.21750e7i	2.64445i
$231$	0	0
$232$	2.16157e6	0.173103
$233$	−1.18472e7	−0.936586	−0.468293	−	0.883573i	$-0.655131\pi$
$233$	−1.18472e7	−0.936586	−0.468293	+	0.883573i	$0.655131\pi$
$234$	833894.i	0.0650823i
$235$	−9.38008e6	−0.722775
$236$	− 2.57066e7i	− 1.95573i
$237$	− 1.19075e7i	− 0.894489i
$238$	0	0
$239$	4.29229e6	0.314410	0.157205	−	0.987566i	$-0.449752\pi$
$239$	4.29229e6	0.314410	0.157205	+	0.987566i	$0.449752\pi$
$240$	4.92474e6	0.356246
$241$	− 1.58617e7i	− 1.13318i	−0.824000	−	0.566589i	$-0.808263\pi$
$241$	− 1.58617e7i	− 1.13318i	0.824000	−	0.566589i	$-0.191737\pi$
$242$	−1.25338e7	−0.884378
$243$	− 920483.i	− 0.0641500i
$244$	8.97136e6i	0.617574i
$245$	0	0
$246$	−1.36030e7	−0.913754
$247$	−3.71522e6	−0.246544
$248$	7.05032e6i	0.462225i
$249$	1.33968e7	0.867764
$250$	2.46451e7i	1.57729i
$251$	− 7.11752e6i	− 0.450099i	−0.974347	−	0.225049i	$-0.927746\pi$
$251$	− 7.11752e6i	− 0.450099i	0.974347	−	0.225049i	$-0.0722543\pi$
$252$	0	0
$253$	−1.11531e7	−0.688707
$254$	1.15330e7	0.703786
$255$	− 1.38475e7i	− 0.835123i
$256$	−5.19059e6	−0.309383
$257$	− 7.21359e6i	− 0.424964i	−0.977165	−	0.212482i	$-0.931845\pi$
$257$	− 7.21359e6i	− 0.424964i	0.977165	−	0.212482i	$-0.0681547\pi$
$258$	− 2.20400e7i	− 1.28337i
$259$	0	0
$260$	−5.10538e6	−0.290475
$261$	−1.52180e6	−0.0855923
$262$	1.20674e7i	0.670980i
$263$	−1.65609e7	−0.910369	−0.455184	−	0.890397i	$-0.650427\pi$
$263$	−1.65609e7	−0.910369	−0.455184	+	0.890397i	$0.650427\pi$
$264$	− 4.71207e6i	− 0.256094i
$265$	− 2.59249e7i	− 1.39309i
$266$	0	0
$267$	−2.80400e6	−0.147314
$268$	1.60008e7	0.831259
$269$	− 5.46747e6i	− 0.280886i	−0.990089	−	0.140443i	$-0.955147\pi$
$269$	− 5.46747e6i	− 0.280886i	0.990089	−	0.140443i	$-0.0448526\pi$
$270$	9.57021e6	0.486217
$271$	− 1.86592e7i	− 0.937531i	−0.883323	−	0.468765i	$-0.844699\pi$
$271$	− 1.86592e7i	− 0.937531i	0.883323	−	0.468765i	$-0.155301\pi$
$272$	− 6.84405e6i	− 0.340100i
$273$	0	0
$274$	5.86414e7	2.85071
$275$	−2.22268e7	−1.06876
$276$	1.81975e7i	0.865534i
$277$	−7.63501e6	−0.359228	−0.179614	−	0.983737i	$-0.557485\pi$
$277$	−7.63501e6	−0.359228	−0.179614	+	0.983737i	$0.557485\pi$
$278$	2.04997e7i	0.954142i
$279$	− 4.96359e6i	− 0.228551i
$280$	0	0
$281$	−2.86272e7	−1.29021	−0.645103	−	0.764095i	$-0.723186\pi$
$281$	−2.86272e7	−1.29021	−0.645103	+	0.764095i	$0.723186\pi$
$282$	−9.00922e6	−0.401735
$283$	2.12910e7i	0.939370i	0.882834	+	0.469685i	$0.155632\pi$
$283$	2.12910e7i	0.939370i	−0.882834	+	0.469685i	$0.844368\pi$
$284$	3.16895e7	1.38344
$285$	4.26379e7i	1.84188i
$286$	− 3.00534e6i	− 0.128468i
$287$	0	0
$288$	1.00979e7	0.422723
$289$	4.89332e6	0.202726
$290$	− 1.58220e7i	− 0.648737i
$291$	5.30275e6	0.215190
$292$	1.10702e7i	0.444639i
$293$	− 1.72102e7i	− 0.684199i	−0.939664	−	0.342100i	$-0.888862\pi$
$293$	− 1.72102e7i	− 0.684199i	0.939664	−	0.342100i	$-0.111138\pi$
$294$	0	0
$295$	−5.67885e7	−2.21205
$296$	5.42734e6	0.209272
$297$	3.31741e6i	0.126628i
$298$	5.77338e7	2.18163
$299$	3.50280e6i	0.131040i
$300$	3.62654e7i	1.34316i
$301$	0	0
$302$	−5.60472e7	−2.03485
$303$	−1.62646e7	−0.584675
$304$	2.10736e7i	0.750097i
$305$	1.98187e7	0.698513
$306$	− 1.33000e7i	− 0.464181i
$307$	4.11253e7i	1.42133i	0.703533	+	0.710663i	$0.251605\pi$
$307$	4.11253e7i	1.42133i	−0.703533	+	0.710663i	$0.748395\pi$
$308$	0	0
$309$	−1.21594e7	−0.412132
$310$	5.16062e7	1.73228
$311$	− 1.14094e7i	− 0.379300i	−0.981852	−	0.189650i	$-0.939265\pi$
$311$	− 1.14094e7i	− 0.379300i	0.981852	−	0.189650i	$-0.0607353\pi$
$312$	−1.47990e6	−0.0487268
$313$	− 1.07410e6i	− 0.0350278i	−0.999847	−	0.0175139i	$-0.994425\pi$
$313$	− 1.07410e6i	− 0.0350278i	0.999847	−	0.0175139i	$-0.00557513\pi$
$314$	6.01997e7i	1.94449i
$315$	0	0
$316$	7.00194e7	2.21900
$317$	−1.97996e7	−0.621552	−0.310776	−	0.950483i	$-0.600589\pi$
$317$	−1.97996e7	−0.621552	−0.310776	+	0.950483i	$0.600589\pi$
$318$	− 2.48999e7i	− 0.774312i
$319$	5.48453e6	0.168954
$320$	8.47688e7i	2.58694i
$321$	1.55524e7i	0.470200i
$322$	0	0
$323$	5.92551e7	1.75840
$324$	5.41270e6	0.159140
$325$	6.98068e6i	0.203352i
$326$	−4.23611e7	−1.22269
$327$	− 2.26917e7i	− 0.648968i
$328$	− 2.41410e7i	− 0.684123i
$329$	0	0
$330$	−3.44909e7	−0.959761
$331$	−1.91322e7	−0.527571	−0.263785	−	0.964581i	$-0.584971\pi$
$331$	−1.91322e7	−0.527571	−0.263785	+	0.964581i	$0.584971\pi$
$332$	7.87767e7i	2.15270i
$333$	−3.82097e6	−0.103476
$334$	− 2.55244e7i	− 0.685040i
$335$	− 3.53473e7i	− 0.940204i
$336$	0	0
$337$	6.12984e7	1.60162	0.800810	−	0.598919i	$-0.204403\pi$
$337$	6.12984e7	1.60162	0.800810	+	0.598919i	$0.204403\pi$
$338$	5.92781e7	1.53513
$339$	− 2.76869e6i	− 0.0710682i
$340$	8.14272e7	2.07173
$341$	1.78887e7i	0.451145i
$342$	4.09521e7i	1.02376i
$343$	0	0
$344$	3.91140e7	0.960853
$345$	4.02001e7	0.978971
$346$	− 3.92954e6i	− 0.0948667i
$347$	7.75814e7	1.85682	0.928409	−	0.371560i	$-0.121177\pi$
$347$	7.75814e7	1.85682	0.928409	+	0.371560i	$0.121177\pi$
$348$	− 8.94859e6i	− 0.212333i
$349$	− 3.32443e7i	− 0.782061i	−0.920378	−	0.391031i	$-0.872119\pi$
$349$	− 3.32443e7i	− 0.782061i	0.920378	−	0.391031i	$-0.127881\pi$
$350$	0	0
$351$	1.04188e6	0.0240934
$352$	−3.63928e7	−0.834426
$353$	1.94432e7i	0.442022i	0.975271	+	0.221011i	$0.0709357\pi$
$353$	1.94432e7i	0.442022i	−0.975271	+	0.221011i	$0.929064\pi$
$354$	−5.45432e7	−1.22951
$355$	− 7.00054e7i	− 1.56475i
$356$	− 1.64883e7i	− 0.365448i
$357$	0	0
$358$	−5.02066e7	−1.09424
$359$	2.54474e7	0.549997	0.274999	−	0.961445i	$-0.411323\pi$
$359$	2.54474e7	0.549997	0.274999	+	0.961445i	$0.411323\pi$
$360$	1.69841e7i	0.364028i
$361$	−1.35407e8	−2.87819
$362$	1.91915e7i	0.404560i
$363$	1.56600e7i	0.327395i
$364$	0	0
$365$	2.44552e7	0.502914
$366$	1.90351e7	0.388250
$367$	8.11430e6i	0.164155i	0.996626	+	0.0820773i	$0.0261554\pi$
$367$	8.11430e6i	0.164155i	−0.996626	+	0.0820773i	$0.973845\pi$
$368$	1.98687e7	0.398681
$369$	1.69959e7i	0.338270i
$370$	− 3.97265e7i	− 0.784287i
$371$	0	0
$372$	2.91873e7	0.566977
$373$	−7.20647e7	−1.38866	−0.694330	−	0.719656i	$-0.744299\pi$
$373$	−7.20647e7	−1.38866	−0.694330	+	0.719656i	$0.744299\pi$
$374$	4.79330e7i	0.916263i
$375$	3.07921e7	0.583909
$376$	− 1.59885e7i	− 0.300777i
$377$	− 1.72250e6i	− 0.0321466i
$378$	0	0
$379$	4.53715e7	0.833423	0.416711	−	0.909039i	$-0.363183\pi$
$379$	4.53715e7	0.833423	0.416711	+	0.909039i	$0.363183\pi$
$380$	−2.50723e8	−4.56923
$381$	− 1.44095e7i	− 0.260541i
$382$	5.33661e7	0.957359
$383$	7.57325e7i	1.34799i	0.738737	+	0.673994i	$0.235422\pi$
$383$	7.57325e7i	1.34799i	−0.738737	+	0.673994i	$0.764578\pi$
$384$	3.99592e7i	0.705704i
$385$	0	0
$386$	−8.04269e7	−1.39843
$387$	−2.75372e7	−0.475102
$388$	3.11817e7i	0.533831i
$389$	8.82941e6	0.149997	0.0749986	−	0.997184i	$-0.476105\pi$
$389$	8.82941e6	0.149997	0.0749986	+	0.997184i	$0.476105\pi$
$390$	1.08324e7i	0.182613i
$391$	− 5.58672e7i	− 0.934602i
$392$	0	0
$393$	1.50772e7	0.248396
$394$	−3.40878e7	−0.557327
$395$	− 1.54680e8i	− 2.50982i
$396$	−1.95073e7	−0.314132
$397$	− 3.98533e7i	− 0.636932i	−0.947934	−	0.318466i	$-0.896832\pi$
$397$	− 3.98533e7i	− 0.636932i	0.947934	−	0.318466i	$-0.103168\pi$
$398$	− 7.45158e6i	− 0.118195i
$399$	0	0
$400$	3.95960e7	0.618687
$401$	−3.31133e6	−0.0513533	−0.0256767	−	0.999670i	$-0.508174\pi$
$401$	−3.31133e6	−0.0513533	−0.0256767	+	0.999670i	$0.508174\pi$
$402$	− 3.39498e7i	− 0.522587i
$403$	5.61823e6	0.0858389
$404$	− 9.56403e7i	− 1.45043i
$405$	− 1.19572e7i	− 0.179997i
$406$	0	0
$407$	1.37707e7	0.204255
$408$	2.36033e7	0.347530
$409$	1.03696e8i	1.51562i	0.652475	+	0.757811i	$0.273731\pi$
$409$	1.03696e8i	1.51562i	−0.652475	+	0.757811i	$0.726269\pi$
$410$	−1.76705e8	−2.56388
$411$	− 7.32677e7i	− 1.05533i
$412$	− 7.15007e7i	− 1.02239i
$413$	0	0
$414$	3.86107e7	0.544135
$415$	1.74026e8	2.43483
$416$	1.14297e7i	0.158765i
$417$	2.56127e7	0.353222
$418$	− 1.47591e8i	− 2.02083i
$419$	2.42723e7i	0.329965i	0.986296	+	0.164983i	$0.0527568\pi$
$419$	2.42723e7i	0.329965i	−0.986296	+	0.164983i	$0.947243\pi$
$420$	0	0
$421$	−8.03195e7	−1.07640	−0.538201	−	0.842816i	$-0.680896\pi$
$421$	−8.03195e7	−1.07640	−0.538201	+	0.842816i	$0.680896\pi$
$422$	−4.58641e7	−0.610289
$423$	1.12563e7i	0.148722i
$424$	4.41894e7	0.579723
$425$	− 1.11337e8i	− 1.45035i
$426$	− 6.72376e7i	− 0.869727i
$427$	0	0
$428$	−9.14527e7	−1.16645
$429$	−3.75493e6	−0.0475587
$430$	− 2.86303e8i	− 3.60097i
$431$	−5.86903e7	−0.733052	−0.366526	−	0.930408i	$-0.619453\pi$
$431$	−5.86903e7	−0.733052	−0.366526	+	0.930408i	$0.619453\pi$
$432$	− 5.90979e6i	− 0.0733029i
$433$	1.51707e8i	1.86871i	0.356344	+	0.934355i	$0.384023\pi$
$433$	1.51707e8i	1.86871i	−0.356344	+	0.934355i	$0.615977\pi$
$434$	0	0
$435$	−1.97684e7	−0.240161
$436$	1.33433e8	1.60992
$437$	1.72021e8i	2.06128i
$438$	2.34884e7	0.279531
$439$	1.21631e8i	1.43764i	0.695195	+	0.718821i	$0.255318\pi$
$439$	1.21631e8i	1.43764i	−0.695195	+	0.718821i	$0.744682\pi$
$440$	− 6.12105e7i	− 0.718568i
$441$	0	0
$442$	1.50541e7	0.174336
$443$	9.26620e7	1.06584	0.532918	−	0.846167i	$-0.321095\pi$
$443$	9.26620e7	1.06584	0.532918	+	0.846167i	$0.321095\pi$
$444$	− 2.24684e7i	− 0.256699i
$445$	−3.64244e7	−0.413344
$446$	1.78696e8i	2.01423i
$447$	− 7.21337e7i	− 0.807636i
$448$	0	0
$449$	−2.40772e7	−0.265991	−0.132996	−	0.991117i	$-0.542460\pi$
$449$	−2.40772e7	−0.265991	−0.132996	+	0.991117i	$0.542460\pi$
$450$	7.69466e7	0.844407
$451$	− 6.12528e7i	− 0.667723i
$452$	1.62807e7	0.176302
$453$	7.00265e7i	0.753300i
$454$	3.78178e7i	0.404137i
$455$	0	0
$456$	−7.26770e7	−0.766483
$457$	−6.50795e7	−0.681860	−0.340930	−	0.940089i	$-0.610742\pi$
$457$	−6.50795e7	−0.681860	−0.340930	+	0.940089i	$0.610742\pi$
$458$	− 7.81122e7i	− 0.813059i
$459$	−1.66173e7	−0.171839
$460$	2.36388e8i	2.42858i
$461$	1.22022e8i	1.24548i	0.782429	+	0.622740i	$0.213980\pi$
$461$	1.22022e8i	1.24548i	−0.782429	+	0.622740i	$0.786020\pi$
$462$	0	0
$463$	2.62985e7	0.264965	0.132482	−	0.991185i	$-0.457705\pi$
$463$	2.62985e7	0.264965	0.132482	+	0.991185i	$0.457705\pi$
$464$	−9.77042e6	−0.0978046
$465$	− 6.44778e7i	− 0.641285i
$466$	−1.47812e8	−1.46067
$467$	6.13737e7i	0.602604i	0.953529	+	0.301302i	$0.0974212\pi$
$467$	6.13737e7i	0.602604i	−0.953529	+	0.301302i	$0.902579\pi$
$468$	6.12657e6i	0.0597695i
$469$	0	0
$470$	−1.17031e8	−1.12722
$471$	7.52146e7	0.719846
$472$	− 9.67970e7i	− 0.920525i
$473$	9.92436e7	0.937819
$474$	− 1.48564e8i	− 1.39502i
$475$	3.42818e8i	3.19877i
$476$	0	0
$477$	−3.11104e7	−0.286649
$478$	5.35531e7	0.490344
$479$	1.93268e8i	1.75855i	0.476316	+	0.879274i	$0.341972\pi$
$479$	1.93268e8i	1.75855i	−0.476316	+	0.879274i	$0.658028\pi$
$480$	1.31174e8	1.18611
$481$	− 4.32491e6i	− 0.0388635i
$482$	− 1.97899e8i	− 1.76727i
$483$	0	0
$484$	−9.20854e7	−0.812184
$485$	6.88835e7	0.603795
$486$	− 1.14845e7i	− 0.100046i
$487$	1.48373e6	0.0128460	0.00642302	−	0.999979i	$-0.497955\pi$
$487$	1.48373e6	0.0128460	0.00642302	+	0.999979i	$0.497955\pi$
$488$	3.37813e7i	0.290681i
$489$	5.29268e7i	0.452636i
$490$	0	0
$491$	1.33332e8	1.12639	0.563195	−	0.826324i	$-0.309572\pi$
$491$	1.33332e8	1.12639	0.563195	+	0.826324i	$0.309572\pi$
$492$	−9.99405e7	−0.839162
$493$	2.74727e7i	0.229277i
$494$	−4.63532e7	−0.384502
$495$	4.30936e7i	0.355302i
$496$	− 3.18678e7i	− 0.261161i
$497$	0	0
$498$	1.67145e8	1.35334
$499$	1.50984e8	1.21515	0.607573	−	0.794264i	$-0.292143\pi$
$499$	1.50984e8	1.21515	0.607573	+	0.794264i	$0.292143\pi$
$500$	1.81066e8i	1.44853i
$501$	−3.18907e7	−0.253601
$502$	− 8.88022e7i	− 0.701960i
$503$	− 9.92575e7i	− 0.779937i	−0.920828	−	0.389968i	$-0.872486\pi$
$503$	− 9.92575e7i	− 0.779937i	0.920828	−	0.389968i	$-0.127514\pi$
$504$	0	0
$505$	−2.11279e8	−1.64052
$506$	−1.39152e8	−1.07409
$507$	− 7.40632e7i	− 0.568301i
$508$	8.47322e7	0.646335
$509$	1.23621e8i	0.937426i	0.883350	+	0.468713i	$0.155282\pi$
$509$	1.23621e8i	0.937426i	−0.883350	+	0.468713i	$0.844718\pi$
$510$	− 1.72769e8i	− 1.30243i
$511$	0	0
$512$	9.92957e7	0.739811
$513$	5.11664e7	0.378994
$514$	− 9.00008e7i	− 0.662761i
$515$	−1.57952e8	−1.15639
$516$	− 1.61926e8i	− 1.17861i
$517$	− 4.05675e7i	− 0.293567i
$518$	0	0
$519$	−4.90965e6	−0.0351195
$520$	−1.92241e7	−0.136721
$521$	− 1.63659e8i	− 1.15725i	−0.815594	−	0.578625i	$-0.803589\pi$
$521$	− 1.63659e8i	− 1.15725i	0.815594	−	0.578625i	$-0.196411\pi$
$522$	−1.89868e7	−0.133487
$523$	2.55632e8i	1.78694i	0.449122	+	0.893471i	$0.351737\pi$
$523$	2.55632e8i	1.78694i	−0.449122	+	0.893471i	$0.648263\pi$
$524$	8.86584e7i	0.616206i
$525$	0	0
$526$	−2.06623e8	−1.41978
$527$	−8.96066e7	−0.612221
$528$	2.12988e7i	0.144695i
$529$	1.41500e7	0.0955847
$530$	− 3.23453e8i	− 2.17262i
$531$	6.81474e7i	0.455161i
$532$	0	0
$533$	−1.92374e7	−0.127047
$534$	−3.49843e7	−0.229746
$535$	2.02028e8i	1.31932i
$536$	6.02501e7	0.391258
$537$	6.27291e7i	0.405085i
$538$	− 6.82152e7i	− 0.438061i
$539$	0	0
$540$	7.03118e7	0.446526
$541$	−2.42070e8	−1.52880	−0.764398	−	0.644744i	$-0.776964\pi$
$541$	−2.42070e8	−1.52880	−0.764398	+	0.644744i	$0.776964\pi$
$542$	− 2.32803e8i	− 1.46214i
$543$	2.39782e7	0.149768
$544$	− 1.82296e8i	− 1.13235i
$545$	− 2.94768e8i	− 1.82092i
$546$	0	0
$547$	−3.05715e7	−0.186790	−0.0933952	−	0.995629i	$-0.529772\pi$
$547$	−3.05715e7	−0.186790	−0.0933952	+	0.995629i	$0.529772\pi$
$548$	4.30835e8	2.61800
$549$	− 2.37828e7i	− 0.143730i
$550$	−2.77314e8	−1.66680
$551$	− 8.45912e7i	− 0.505674i
$552$	6.85218e7i	0.407391i
$553$	0	0
$554$	−9.52587e7	−0.560242
$555$	−4.96350e7	−0.290342
$556$	1.50610e8i	0.876253i
$557$	2.33083e8	1.34879	0.674396	−	0.738369i	$-0.264404\pi$
$557$	2.33083e8	1.34879	0.674396	+	0.738369i	$0.264404\pi$
$558$	− 6.19285e7i	− 0.356442i
$559$	− 3.11690e7i	− 0.178438i
$560$	0	0
$561$	5.98884e7	0.339199
$562$	−3.57168e8	−2.01217
$563$	− 2.25479e8i	− 1.26352i	−0.775165	−	0.631758i	$-0.782333\pi$
$563$	− 2.25479e8i	− 1.26352i	0.775165	−	0.631758i	$-0.217667\pi$
$564$	−6.61902e7	−0.368941
$565$	− 3.59657e7i	− 0.199408i
$566$	2.65638e8i	1.46501i
$567$	0	0
$568$	1.19325e8	0.651160
$569$	2.14779e8	1.16589	0.582943	−	0.812513i	$-0.301901\pi$
$569$	2.14779e8	1.16589	0.582943	+	0.812513i	$0.301901\pi$
$570$	5.31974e8i	2.87254i
$571$	3.42723e8	1.84092	0.920460	−	0.390836i	$-0.127814\pi$
$571$	3.42723e8	1.84092	0.920460	+	0.390836i	$0.127814\pi$
$572$	− 2.20801e7i	− 0.117981i
$573$	− 6.66766e7i	− 0.354413i
$574$	0	0
$575$	3.23217e8	1.70017
$576$	1.01724e8	0.532301
$577$	− 2.80183e8i	− 1.45853i	−0.684233	−	0.729263i	$-0.739863\pi$
$577$	− 2.80183e8i	− 1.45853i	0.684233	−	0.729263i	$-0.260137\pi$
$578$	6.10518e7	0.316166
$579$	1.00487e8i	0.517695i
$580$	− 1.16244e8i	− 0.595779i
$581$	0	0
$582$	6.61600e7	0.335604
$583$	1.12121e8	0.565826
$584$	4.16844e7i	0.209283i
$585$	1.35342e7	0.0676029
$586$	− 2.14724e8i	− 1.06706i
$587$	− 2.73172e8i	− 1.35059i	−0.737549	−	0.675293i	$-0.764017\pi$
$587$	− 2.73172e8i	− 1.35059i	0.737549	−	0.675293i	$-0.235983\pi$
$588$	0	0
$589$	2.75908e8	1.35026
$590$	−7.08525e8	−3.44984
$591$	4.25899e7i	0.206322i
$592$	−2.45319e7	−0.118240
$593$	− 3.66864e8i	− 1.75930i	−0.475619	−	0.879651i	$-0.657776\pi$
$593$	− 3.66864e8i	− 1.75930i	0.475619	−	0.879651i	$-0.342224\pi$
$594$	4.13898e7i	0.197485i
$595$	0	0
$596$	4.24167e8	2.00354
$597$	−9.31015e6	−0.0437556
$598$	4.37030e7i	0.204365i
$599$	−1.69051e8	−0.786568	−0.393284	−	0.919417i	$-0.628661\pi$
$599$	−1.69051e8	−0.786568	−0.393284	+	0.919417i	$0.628661\pi$
$600$	1.36556e8i	0.632203i
$601$	1.61411e8i	0.743551i	0.928323	+	0.371775i	$0.121251\pi$
$601$	1.61411e8i	0.743551i	−0.928323	+	0.371775i	$0.878749\pi$
$602$	0	0
$603$	−4.24175e7	−0.193461
$604$	−4.11776e8	−1.86875
$605$	2.03426e8i	0.918629i
$606$	−2.02926e8	−0.911842
$607$	1.93913e8i	0.867042i	0.901143	+	0.433521i	$0.142729\pi$
$607$	1.93913e8i	0.867042i	−0.901143	+	0.433521i	$0.857271\pi$
$608$	5.61309e8i	2.49742i
$609$	0	0
$610$	2.47269e8	1.08938
$611$	−1.27409e7	−0.0558567
$612$	− 9.77144e7i	− 0.426289i
$613$	−1.04355e8	−0.453034	−0.226517	−	0.974007i	$-0.572734\pi$
$613$	−1.04355e8	−0.453034	−0.226517	+	0.974007i	$0.572734\pi$
$614$	5.13102e8i	2.21666i
$615$	2.20779e8i	0.949143i
$616$	0	0
$617$	−3.99769e8	−1.70198	−0.850989	−	0.525183i	$-0.823997\pi$
$617$	−3.99769e8	−1.70198	−0.850989	+	0.525183i	$0.823997\pi$
$618$	−1.51707e8	−0.642749
$619$	2.44515e8i	1.03094i	0.856907	+	0.515471i	$0.172383\pi$
$619$	2.44515e8i	1.03094i	−0.856907	+	0.515471i	$0.827617\pi$
$620$	3.79148e8	1.59087
$621$	− 4.82410e7i	− 0.201438i
$622$	− 1.42350e8i	− 0.591544i
$623$	0	0
$624$	6.68922e6	0.0275310
$625$	3.43439e6	0.0140673
$626$	− 1.34011e7i	− 0.0546283i
$627$	−1.84403e8	−0.748109
$628$	4.42283e8i	1.78575i
$629$	6.89792e7i	0.277183i
$630$	0	0
$631$	−2.46592e8	−0.981500	−0.490750	−	0.871301i	$-0.663277\pi$
$631$	−2.46592e8	−0.981500	−0.490750	+	0.871301i	$0.663277\pi$
$632$	2.63655e8	1.04444
$633$	5.73035e7i	0.225928i
$634$	−2.47030e8	−0.969355
$635$	− 1.87182e8i	− 0.731044i
$636$	− 1.82938e8i	− 0.711103i
$637$	0	0
$638$	6.84281e7	0.263495
$639$	−8.40079e7	−0.321972
$640$	5.19076e8i	1.98012i
$641$	3.60845e8	1.37008	0.685040	−	0.728505i	$-0.259785\pi$
$641$	3.60845e8	1.37008	0.685040	+	0.728505i	$0.259785\pi$
$642$	1.94041e8i	0.733311i
$643$	− 9.49305e7i	− 0.357086i	−0.983932	−	0.178543i	$-0.942862\pi$
$643$	− 9.49305e7i	− 0.357086i	0.983932	−	0.178543i	$-0.0571384\pi$
$644$	0	0
$645$	−3.57712e8	−1.33307
$646$	7.39300e8	2.74235
$647$	1.49128e8i	0.550614i	0.961356	+	0.275307i	$0.0887796\pi$
$647$	1.49128e8i	0.550614i	−0.961356	+	0.275307i	$0.911220\pi$
$648$	2.03813e7	0.0749043
$649$	− 2.45602e8i	− 0.898458i
$650$	8.70949e7i	0.317141i
$651$	0	0
$652$	−3.11225e8	−1.12288
$653$	−5.09334e6	−0.0182921	−0.00914604	−	0.999958i	$-0.502911\pi$
$653$	−5.09334e6	−0.0182921	−0.00914604	+	0.999958i	$0.502911\pi$
$654$	− 2.83114e8i	− 1.01211i
$655$	1.95856e8	0.696967
$656$	1.09119e8i	0.386534i
$657$	− 2.93468e7i	− 0.103482i
$658$	0	0
$659$	5.76822e6	0.0201551	0.0100776	−	0.999949i	$-0.496792\pi$
$659$	5.76822e6	0.0201551	0.0100776	+	0.999949i	$0.496792\pi$
$660$	−2.53403e8	−0.881413
$661$	− 1.49220e7i	− 0.0516682i	−0.999666	−	0.0258341i	$-0.991776\pi$
$661$	− 1.49220e7i	− 0.0516682i	0.999666	−	0.0258341i	$-0.00822417\pi$
$662$	−2.38704e8	−0.822784
$663$	− 1.88089e7i	− 0.0645390i
$664$	2.96630e8i	1.01324i
$665$	0	0
$666$	−4.76726e7	−0.161379
$667$	−7.97548e7	−0.268769
$668$	− 1.87526e8i	− 0.629119i
$669$	2.23266e8	0.745666
$670$	− 4.41013e8i	− 1.46631i
$671$	8.57129e7i	0.283713i
$672$	0	0
$673$	2.64968e8	0.869257	0.434629	−	0.900610i	$-0.356880\pi$
$673$	2.64968e8	0.869257	0.434629	+	0.900610i	$0.356880\pi$
$674$	7.64793e8	2.49784
$675$	− 9.61386e7i	− 0.312598i
$676$	4.35513e8	1.40981
$677$	3.05842e8i	0.985670i	0.870123	+	0.492835i	$0.164039\pi$
$677$	3.05842e8i	0.985670i	−0.870123	+	0.492835i	$0.835961\pi$
$678$	− 3.45438e7i	− 0.110836i
$679$	0	0
$680$	3.06610e8	0.975125
$681$	4.72503e7	0.149611
$682$	2.23190e8i	0.703592i
$683$	1.49691e8	0.469822	0.234911	−	0.972017i	$-0.424520\pi$
$683$	1.49691e8	0.469822	0.234911	+	0.972017i	$0.424520\pi$
$684$	3.00873e8i	0.940188i
$685$	− 9.51758e8i	− 2.96111i
$686$	0	0
$687$	−9.75949e7	−0.300993
$688$	−1.76797e8	−0.542889
$689$	− 3.52135e7i	− 0.107659i
$690$	5.01559e8	1.52677
$691$	2.55157e8i	0.773345i	0.922217	+	0.386672i	$0.126376\pi$
$691$	2.55157e8i	0.773345i	−0.922217	+	0.386672i	$0.873624\pi$
$692$	− 2.88701e7i	− 0.0871225i
$693$	0	0
$694$	9.67949e8	2.89584
$695$	3.32713e8	0.991095
$696$	− 3.36955e7i	− 0.0999412i
$697$	3.06822e8	0.906127
$698$	− 4.14774e8i	− 1.21968i
$699$	1.84679e8i	0.540738i
$700$	0	0
$701$	−2.47105e8	−0.717343	−0.358672	−	0.933464i	$-0.616770\pi$
$701$	−2.47105e8	−0.717343	−0.358672	+	0.933464i	$0.616770\pi$
$702$	1.29991e7	0.0375753
$703$	− 2.12394e8i	− 0.611331i
$704$	−3.66613e8	−1.05073
$705$	1.46221e8i	0.417294i
$706$	2.42584e8i	0.689364i
$707$	0	0
$708$	−4.00726e8	−1.12914
$709$	−1.04207e8	−0.292388	−0.146194	−	0.989256i	$-0.546702\pi$
$709$	−1.04207e8	−0.292388	−0.146194	+	0.989256i	$0.546702\pi$
$710$	− 8.73426e8i	− 2.44034i
$711$	−1.85619e8	−0.516433
$712$	− 6.20860e7i	− 0.172010i
$713$	− 2.60133e8i	− 0.717675i
$714$	0	0
$715$	−4.87771e7	−0.133444
$716$	−3.68865e8	−1.00491
$717$	− 6.69102e7i	− 0.181524i
$718$	3.17496e8	0.857759
$719$	− 4.74727e8i	− 1.27720i	−0.769541	−	0.638598i	$-0.779515\pi$
$719$	− 4.74727e8i	− 1.27720i	0.769541	−	0.638598i	$-0.220485\pi$
$720$	− 7.67691e7i	− 0.205679i
$721$	0	0
$722$	−1.68941e9	−4.48873
$723$	−2.47259e8	−0.654241
$724$	1.40999e8i	0.371535i
$725$	−1.58942e8	−0.417085
$726$	1.95383e8i	0.510596i
$727$	− 1.04048e8i	− 0.270790i	−0.990792	−	0.135395i	$-0.956770\pi$
$727$	− 1.04048e8i	− 0.270790i	0.990792	−	0.135395i	$-0.0432303\pi$
$728$	0	0
$729$	−1.43489e7	−0.0370370
$730$	3.05117e8	0.784329
$731$	4.97123e8i	1.27266i
$732$	1.39850e8	0.356556
$733$	6.68982e8i	1.69864i	0.527875	+	0.849322i	$0.322989\pi$
$733$	6.68982e8i	1.69864i	−0.527875	+	0.849322i	$0.677011\pi$
$734$	1.01239e8i	0.256010i
$735$	0	0
$736$	5.29216e8	1.32739
$737$	1.52872e8	0.381879
$738$	2.12050e8i	0.527556i
$739$	−3.08296e8	−0.763896	−0.381948	−	0.924184i	$-0.624747\pi$
$739$	−3.08296e8	−0.763896	−0.381948	+	0.924184i	$0.624747\pi$
$740$	− 2.91868e8i	− 0.720264i
$741$	5.79145e7i	0.142342i
$742$	0	0
$743$	1.83763e8	0.448014	0.224007	−	0.974588i	$-0.428086\pi$
$743$	1.83763e8	0.448014	0.224007	+	0.974588i	$0.428086\pi$
$744$	1.09904e8	0.266866
$745$	− 9.37028e8i	− 2.26612i
$746$	−8.99120e8	−2.16571
$747$	− 2.08835e8i	− 0.501004i
$748$	3.52161e8i	0.841466i
$749$	0	0
$750$	3.84179e8	0.910647
$751$	2.45331e8	0.579206	0.289603	−	0.957147i	$-0.406477\pi$
$751$	2.45331e8	0.579206	0.289603	+	0.957147i	$0.406477\pi$
$752$	7.22690e7i	0.169941i
$753$	−1.10951e8	−0.259865
$754$	− 2.14909e7i	− 0.0501349i
$755$	9.09655e8i	2.11366i
$756$	0	0
$757$	−8.44770e8	−1.94738	−0.973690	−	0.227876i	$-0.926822\pi$
$757$	−8.44770e8	−1.94738	−0.973690	+	0.227876i	$0.926822\pi$
$758$	5.66080e8	1.29978
$759$	1.73860e8i	0.397625i
$760$	−9.44086e8	−2.15065
$761$	5.67694e8i	1.28813i	0.764970	+	0.644066i	$0.222754\pi$
$761$	5.67694e8i	1.28813i	−0.764970	+	0.644066i	$0.777246\pi$
$762$	− 1.79782e8i	− 0.406331i
$763$	0	0
$764$	3.92077e8	0.879208
$765$	−2.15861e8	−0.482159
$766$	9.44881e8i	2.10228i
$767$	−7.71351e7	−0.170949
$768$	8.09132e7i	0.178622i
$769$	2.83103e6i	0.00622536i	0.999995	+	0.00311268i	$0.000990799\pi$
$769$	2.83103e6i	0.00622536i	−0.999995	+	0.00311268i	$0.999009\pi$
$770$	0	0
$771$	−1.12449e8	−0.245353
$772$	−5.90892e8	−1.28427
$773$	− 4.43306e8i	− 0.959766i	−0.877333	−	0.479883i	$-0.840679\pi$
$773$	− 4.43306e8i	− 0.959766i	0.877333	−	0.479883i	$-0.159321\pi$
$774$	−3.43569e8	−0.740954
$775$	− 5.18415e8i	− 1.11371i
$776$	1.17413e8i	0.251265i
$777$	0	0
$778$	1.10161e8	0.233931
$779$	−9.44739e8	−1.99848
$780$	7.95850e7i	0.167706i
$781$	3.02763e8	0.635551
$782$	− 6.97031e8i	− 1.45758i
$783$	2.37224e7i	0.0494168i
$784$	0	0
$785$	9.77049e8	2.01980
$786$	1.88112e8	0.387390
$787$	− 7.23808e7i	− 0.148491i	−0.997240	−	0.0742454i	$-0.976345\pi$
$787$	− 7.23808e7i	− 0.148491i	0.997240	−	0.0742454i	$-0.0236548\pi$
$788$	−2.50441e8	−0.511831
$789$	2.58159e8i	0.525602i
$790$	− 1.92987e9i	− 3.91424i
$791$	0	0
$792$	−7.34539e7	−0.147856
$793$	2.69195e7	0.0539817
$794$	− 4.97233e8i	− 0.993340i
$795$	−4.04129e8	−0.804300
$796$	− 5.47463e7i	− 0.108547i
$797$	− 8.26919e8i	− 1.63338i	−0.577075	−	0.816691i	$-0.695806\pi$
$797$	− 8.26919e8i	− 1.63338i	0.577075	−	0.816691i	$-0.304194\pi$
$798$	0	0
$799$	2.03207e8	0.398382
$800$	1.05467e9	2.05989
$801$	4.37100e7i	0.0850518i
$802$	−4.13139e7	−0.0800891
$803$	1.05765e8i	0.204267i
$804$	− 2.49427e8i	− 0.479927i
$805$	0	0
$806$	7.00961e7	0.133872
$807$	−8.52294e7	−0.162169
$808$	− 3.60129e8i	− 0.682691i
$809$	−2.78807e8	−0.526573	−0.263287	−	0.964718i	$-0.584806\pi$
$809$	−2.78807e8	−0.526573	−0.263287	+	0.964718i	$0.584806\pi$
$810$	− 1.49185e8i	− 0.280718i
$811$	8.06633e8i	1.51222i	0.654447	+	0.756108i	$0.272901\pi$
$811$	8.06633e8i	1.51222i	−0.654447	+	0.756108i	$0.727099\pi$
$812$	0	0
$813$	−2.90868e8	−0.541284
$814$	1.71811e8	0.318551
$815$	6.87528e8i	1.27004i
$816$	−1.06688e8	−0.196357
$817$	− 1.53069e9i	− 2.80687i
$818$	1.29377e9i	2.36372i
$819$	0	0
$820$	−1.29824e9	−2.35458
$821$	−1.05901e9	−1.91368	−0.956840	−	0.290615i	$-0.906140\pi$
$821$	−1.05901e9	−1.91368	−0.956840	+	0.290615i	$0.906140\pi$
$822$	− 9.14128e8i	− 1.64586i
$823$	−1.08313e9	−1.94303	−0.971517	−	0.236968i	$-0.923846\pi$
$823$	−1.08313e9	−1.94303	−0.971517	+	0.236968i	$0.923846\pi$
$824$	− 2.69233e8i	− 0.481223i
$825$	3.46482e8i	0.617048i
$826$	0	0
$827$	−1.33362e8	−0.235785	−0.117892	−	0.993026i	$-0.537614\pi$
$827$	−1.33362e8	−0.235785	−0.117892	+	0.993026i	$0.537614\pi$
$828$	2.83671e8	0.499716
$829$	− 2.49474e8i	− 0.437887i	−0.975738	−	0.218944i	$-0.929739\pi$
$829$	− 2.49474e8i	− 0.437887i	0.975738	−	0.218944i	$-0.0702611\pi$
$830$	2.17124e9	3.79729
$831$	1.19018e8i	0.207401i
$832$	1.15140e8i	0.199921i
$833$	0	0
$834$	3.19558e8	0.550874
$835$	−4.14264e8	−0.711571
$836$	− 1.08434e9i	− 1.85587i
$837$	−7.73747e7	−0.131954
$838$	3.02834e8i	0.514604i
$839$	4.92485e8i	0.833887i	0.908932	+	0.416943i	$0.136899\pi$
$839$	4.92485e8i	0.833887i	−0.908932	+	0.416943i	$0.863101\pi$
$840$	0	0
$841$	−5.55604e8	−0.934066
$842$	−1.00211e9	−1.67873
$843$	4.46253e8i	0.744901i
$844$	−3.36961e8	−0.560470
$845$	− 9.62092e8i	− 1.59458i
$846$	1.40440e8i	0.231942i
$847$	0	0
$848$	−1.99739e8	−0.327548
$849$	3.31894e8	0.542345
$850$	− 1.38910e9i	− 2.26192i
$851$	−2.00251e8	−0.324927
$852$	− 4.93990e8i	− 0.798730i
$853$	− 6.41660e8i	− 1.03385i	−0.856031	−	0.516925i	$-0.827077\pi$
$853$	− 6.41660e8i	− 1.03385i	0.856031	−	0.516925i	$-0.172923\pi$
$854$	0	0
$855$	6.64659e8	1.06341
$856$	−3.44361e8	−0.549026
$857$	− 7.18526e8i	− 1.14156i	−0.821102	−	0.570782i	$-0.806640\pi$
$857$	− 7.18526e8i	− 1.14156i	0.821102	−	0.570782i	$-0.193360\pi$
$858$	−4.68486e7	−0.0741711
$859$	7.81708e8i	1.23329i	0.787241	+	0.616645i	$0.211509\pi$
$859$	7.81708e8i	1.23329i	−0.787241	+	0.616645i	$0.788491\pi$
$860$	− 2.10345e9i	− 3.30702i
$861$	0	0
$862$	−7.32253e8	−1.14325
$863$	1.08258e9	1.68433	0.842166	−	0.539218i	$-0.181280\pi$
$863$	1.08258e9	1.68433	0.842166	+	0.539218i	$0.181280\pi$
$864$	− 1.57411e8i	− 0.244059i
$865$	−6.37770e7	−0.0985408
$866$	1.89278e9i	2.91438i
$867$	− 7.62793e7i	− 0.117044i
$868$	0	0
$869$	6.68969e8	1.01940
$870$	−2.46641e8	−0.374548
$871$	− 4.80118e7i	− 0.0726598i
$872$	5.02438e8	0.757762
$873$	− 8.26616e7i	− 0.124240i
$874$	2.14623e9i	3.21471i
$875$	0	0
$876$	1.72568e8	0.256712
$877$	−2.43162e8	−0.360493	−0.180247	−	0.983621i	$-0.557690\pi$
$877$	−2.43162e8	−0.360493	−0.180247	+	0.983621i	$0.557690\pi$
$878$	1.51754e9i	2.24211i
$879$	−2.68280e8	−0.395023
$880$	2.76675e8i	0.405996i
$881$	− 1.21869e9i	− 1.78224i	−0.453767	−	0.891120i	$-0.649920\pi$
$881$	− 1.21869e9i	− 1.78224i	0.453767	−	0.891120i	$-0.350080\pi$
$882$	0	0
$883$	5.63745e8	0.818842	0.409421	−	0.912346i	$-0.365731\pi$
$883$	5.63745e8	0.818842	0.409421	+	0.912346i	$0.365731\pi$
$884$	1.10602e8	0.160105
$885$	8.85245e8i	1.27713i
$886$	1.15610e9	1.66225
$887$	− 2.69114e8i	− 0.385625i	−0.981236	−	0.192812i	$-0.938239\pi$
$887$	− 2.69114e8i	− 0.385625i	0.981236	−	0.192812i	$-0.0617609\pi$
$888$	− 8.46038e7i	− 0.120823i
$889$	0	0
$890$	−4.54451e8	−0.644639
$891$	5.17133e7	0.0731086
$892$	1.31287e9i	1.84981i
$893$	−6.25697e8	−0.878638
$894$	− 8.99980e8i	− 1.25956i
$895$	8.14860e8i	1.13662i
$896$	0	0
$897$	5.46033e7	0.0756557
$898$	−3.00401e8	−0.414832
$899$	1.27920e8i	0.176060i
$900$	5.65322e8	0.775476
$901$	5.61629e8i	0.767848i
$902$	− 7.64224e8i	− 1.04136i
$903$	0	0
$904$	6.13042e7	0.0829823
$905$	3.11481e8	0.420229
$906$	8.73690e8i	1.17482i
$907$	7.86454e8	1.05403	0.527013	−	0.849857i	$-0.323312\pi$
$907$	7.86454e8	1.05403	0.527013	+	0.849857i	$0.323312\pi$
$908$	2.77845e8i	0.371147i
$909$	2.53540e8i	0.337562i
$910$	0	0
$911$	1.05328e9	1.39312	0.696559	−	0.717500i	$-0.254713\pi$
$911$	1.05328e9	1.39312	0.696559	+	0.717500i	$0.254713\pi$
$912$	3.28504e8	0.433069
$913$	7.52637e8i	0.988948i
$914$	−8.11968e8	−1.06341
$915$	− 3.08942e8i	− 0.403287i
$916$	− 5.73886e8i	− 0.746688i
$917$	0	0
$918$	−2.07327e8	−0.267995
$919$	1.16313e9	1.49858	0.749290	−	0.662242i	$-0.230395\pi$
$919$	1.16313e9	1.49858	0.749290	+	0.662242i	$0.230395\pi$
$920$	8.90108e8i	1.14309i
$921$	6.41079e8	0.820603
$922$	1.52242e9i	1.94241i
$923$	− 9.50875e7i	− 0.120926i
$924$	0	0
$925$	−3.99076e8	−0.504232
$926$	3.28115e8	0.413231
$927$	1.89546e8i	0.237945i
$928$	−2.60242e8	−0.325636
$929$	− 1.17626e9i	− 1.46709i	−0.679641	−	0.733545i	$-0.737864\pi$
$929$	− 1.17626e9i	− 1.46709i	0.679641	−	0.733545i	$-0.262136\pi$
$930$	− 8.04461e8i	− 1.00013i
$931$	0	0
$932$	−1.08597e9	−1.34143
$933$	−1.77855e8	−0.218989
$934$	7.65733e8i	0.939803i
$935$	7.77960e8	0.951749
$936$	2.30693e7i	0.0281324i
$937$	4.63976e8i	0.563997i	0.959415	+	0.281999i	$0.0909974\pi$
$937$	4.63976e8i	0.563997i	−0.959415	+	0.281999i	$0.909003\pi$
$938$	0	0
$939$	−1.67436e7	−0.0202233
$940$	−8.59821e8	−1.03520
$941$	1.16826e9i	1.40207i	0.713126	+	0.701036i	$0.247279\pi$
$941$	1.16826e9i	1.40207i	−0.713126	+	0.701036i	$0.752721\pi$
$942$	9.38420e8	1.12265
$943$	8.90724e8i	1.06220i
$944$	4.37528e8i	0.520103i
$945$	0	0
$946$	1.23822e9	1.46259
$947$	5.69109e8	0.670109	0.335055	−	0.942199i	$-0.391245\pi$
$947$	5.69109e8	0.670109	0.335055	+	0.942199i	$0.391245\pi$
$948$	− 1.09149e9i	− 1.28114i
$949$	3.32173e7	0.0388656
$950$	4.27719e9i	4.98870i
$951$	3.08645e8i	0.358853i
$952$	0	0
$953$	5.61708e8	0.648981	0.324491	−	0.945889i	$-0.394807\pi$
$953$	5.61708e8	0.648981	0.324491	+	0.945889i	$0.394807\pi$
$954$	−3.88151e8	−0.447049
$955$	− 8.66139e8i	− 0.994437i
$956$	3.93451e8	0.450316
$957$	− 8.54954e7i	− 0.0975454i
$958$	2.41132e9i	2.74258i
$959$	0	0
$960$	1.32141e9	1.49357
$961$	4.70270e8	0.529879
$962$	− 5.39600e7i	− 0.0606103i
$963$	2.42438e8	0.271470
$964$	− 1.45396e9i	− 1.62301i
$965$	1.30534e9i	1.45259i
$966$	0	0
$967$	6.95843e8	0.769541	0.384771	−	0.923012i	$-0.374281\pi$
$967$	6.95843e8	0.769541	0.384771	+	0.923012i	$0.374281\pi$
$968$	−3.46743e8	−0.382280
$969$	− 9.23695e8i	− 1.01521i
$970$	8.59429e8	0.941661
$971$	− 8.84195e8i	− 0.965807i	−0.875674	−	0.482903i	$-0.839582\pi$
$971$	− 8.84195e8i	− 0.965807i	0.875674	−	0.482903i	$-0.160418\pi$
$972$	− 8.43757e7i	− 0.0918795i
$973$	0	0
$974$	1.85119e7	0.0200343
$975$	1.08818e8	0.117405
$976$	− 1.52693e8i	− 0.164237i
$977$	−3.59873e8	−0.385892	−0.192946	−	0.981209i	$-0.561804\pi$
$977$	−3.59873e8	−0.385892	−0.192946	+	0.981209i	$0.561804\pi$
$978$	6.60345e8i	0.705918i
$979$	− 1.57530e8i	− 0.167887i
$980$	0	0
$981$	−3.53728e8	−0.374682
$982$	1.66352e9	1.75668
$983$	5.49868e7i	0.0578893i	0.999581	+	0.0289446i	$0.00921465\pi$
$983$	5.49868e7i	0.0578893i	−0.999581	+	0.0289446i	$0.990785\pi$
$984$	−3.76321e8	−0.394979
$985$	5.53250e8i	0.578912i
$986$	3.42764e8i	0.357573i
$987$	0	0
$988$	−3.40554e8	−0.353114
$989$	−1.44318e9	−1.49187
$990$	5.37660e8i	0.554118i
$991$	3.07113e8	0.315556	0.157778	−	0.987475i	$-0.449567\pi$
$991$	3.07113e8	0.315556	0.157778	+	0.987475i	$0.449567\pi$
$992$	− 8.48821e8i	− 0.869524i
$993$	2.98241e8i	0.304593i
$994$	0	0
$995$	−1.20940e8	−0.122773
$996$	1.22801e9	1.24286
$997$	− 1.19903e9i	− 1.20989i	−0.796268	−	0.604945i	$-0.793195\pi$
$997$	− 1.19903e9i	− 1.20989i	0.796268	−	0.604945i	$-0.206805\pi$
$998$	1.88376e9	1.89511
$999$	5.95631e7i	0.0597421i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.7.d.a.97.7		8
3.2	odd	2		441.7.d.d.244.2		8
7.2	even	3		21.7.f.b.10.1	✓	8
7.3	odd	6		21.7.f.b.19.1	yes	8
7.4	even	3		147.7.f.a.19.1		8
7.5	odd	6		147.7.f.a.31.1		8
7.6	odd	2	inner	147.7.d.a.97.8		8
21.2	odd	6		63.7.m.c.10.4		8
21.17	even	6		63.7.m.c.19.4		8
21.20	even	2		441.7.d.d.244.1		8
28.3	even	6		336.7.bh.b.145.1		8
28.23	odd	6		336.7.bh.b.241.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.b.10.1	✓	8	7.2	even	3
21.7.f.b.19.1	yes	8	7.3	odd	6
63.7.m.c.10.4		8	21.2	odd	6
63.7.m.c.19.4		8	21.17	even	6
147.7.d.a.97.7		8	1.1	even	1	trivial
147.7.d.a.97.8		8	7.6	odd	2	inner
147.7.f.a.19.1		8	7.4	even	3
147.7.f.a.31.1		8	7.5	odd	6
336.7.bh.b.145.1		8	28.3	even	6
336.7.bh.b.241.1		8	28.23	odd	6
441.7.d.d.244.1		8	21.20	even	2
441.7.d.d.244.2		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	147.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+12.4766 q^{2} -15.5885i q^{3} +91.6646 q^{4} -202.496i q^{5} -194.490i q^{6} +345.159 q^{8} -243.000 q^{9} +O(q^{10})\)	\(q+12.4766 q^{2} -15.5885i q^{3} +91.6646 q^{4} -202.496i q^{5} -194.490i q^{6} +345.159 q^{8} -243.000 q^{9} -2526.46i q^{10} +875.768 q^{11} -1428.91i q^{12} -275.049i q^{13} -3156.61 q^{15} -1560.14 q^{16} +4386.83i q^{17} -3031.80 q^{18} -13507.5i q^{19} -18561.8i q^{20} +10926.6 q^{22} -12735.2 q^{23} -5380.49i q^{24} -25379.8 q^{25} -3431.66i q^{26} +3788.00i q^{27} +6262.53 q^{29} -39383.6 q^{30} +20426.3i q^{31} -41555.3 q^{32} -13651.9i q^{33} +54732.5i q^{34} -22274.5 q^{36} +15724.2 q^{37} -168527. i q^{38} -4287.58 q^{39} -69893.4i q^{40} -69941.8i q^{41} +113322. q^{43} +80276.9 q^{44} +49206.6i q^{45} -158892. q^{46} -46322.2i q^{47} +24320.1i q^{48} -316653. q^{50} +68383.9 q^{51} -25212.2i q^{52} +128026. q^{53} +47261.2i q^{54} -177340. i q^{55} -210561. q^{57} +78134.9 q^{58} -280442. i q^{59} -289349. q^{60} +97871.6i q^{61} +254850. i q^{62} -418619. q^{64} -55696.4 q^{65} -170329. i q^{66} +174558. q^{67} +402117. i q^{68} +198522. i q^{69} +345712. q^{71} -83873.6 q^{72} +120769. i q^{73} +196184. q^{74} +395632. i q^{75} -1.23816e6i q^{76} -53494.3 q^{78} +763865. q^{79} +315922. i q^{80} +59049.0 q^{81} -872633. i q^{82} +859402. i q^{83} +888317. q^{85} +1.41387e6 q^{86} -97623.2i q^{87} +302279. q^{88} -179877. i q^{89} +613930. i q^{90} -1.16737e6 q^{92} +318415. q^{93} -577942. i q^{94} -2.73522e6 q^{95} +647783. i q^{96} +340171. i q^{97} -212812. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{2} + 346 q^{4} - 454 q^{8} - 1944 q^{9}+O(q^{10}) \) 8 * q + 10 * q^2 + 346 * q^4 - 454 * q^8 - 1944 * q^9	\( 8 q + 10 q^{2} + 346 q^{4} - 454 q^{8} - 1944 q^{9} + 2140 q^{11} - 756 q^{15} - 7822 q^{16} - 2430 q^{18} - 78 q^{22} + 30448 q^{23} - 44548 q^{25} + 32524 q^{29} - 4698 q^{30} - 140406 q^{32} - 84078 q^{36} + 91340 q^{37} - 186732 q^{39} - 445660 q^{43} + 377658 q^{44} - 1051608 q^{46} - 1218884 q^{50} - 129816 q^{51} + 26068 q^{53} - 442908 q^{57} + 319002 q^{58} - 859410 q^{60} - 1410446 q^{64} + 778008 q^{65} - 768188 q^{67} + 225688 q^{71} + 110322 q^{72} - 2371060 q^{74} - 342792 q^{78} + 1119184 q^{79} + 472392 q^{81} + 1953576 q^{85} + 4604804 q^{86} - 609774 q^{88} - 113064 q^{92} - 723600 q^{93} - 2320224 q^{95} - 520020 q^{99}+O(q^{100}) \) 8 * q + 10 * q^2 + 346 * q^4 - 454 * q^8 - 1944 * q^9 + 2140 * q^11 - 756 * q^15 - 7822 * q^16 - 2430 * q^18 - 78 * q^22 + 30448 * q^23 - 44548 * q^25 + 32524 * q^29 - 4698 * q^30 - 140406 * q^32 - 84078 * q^36 + 91340 * q^37 - 186732 * q^39 - 445660 * q^43 + 377658 * q^44 - 1051608 * q^46 - 1218884 * q^50 - 129816 * q^51 + 26068 * q^53 - 442908 * q^57 + 319002 * q^58 - 859410 * q^60 - 1410446 * q^64 + 778008 * q^65 - 768188 * q^67 + 225688 * q^71 + 110322 * q^72 - 2371060 * q^74 - 342792 * q^78 + 1119184 * q^79 + 472392 * q^81 + 1953576 * q^85 + 4604804 * q^86 - 609774 * q^88 - 113064 * q^92 - 723600 * q^93 - 2320224 * q^95 - 520020 * q^99

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