LMFDB - Embedded newform 147.7.d.a.97.1

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			97.1
Root			$-7.08935 + 12.2791i$ of defining polynomial
Character	$\chi$	$=$	147.97
Dual form			147.7.d.a.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-13.1787 q^{2} -15.5885i q^{3} +109.678 q^{4} -79.5668i q^{5} +205.435i q^{6} -601.976 q^{8} -243.000 q^{9} +O(q^{10})$	\(q-13.1787 q^{2} -15.5885i q^{3} +109.678 q^{4} -79.5668i q^{5} +205.435i q^{6} -601.976 q^{8} -243.000 q^{9} +1048.59i q^{10} +822.239 q^{11} -1709.71i q^{12} -2429.15i q^{13} -1240.32 q^{15} +913.863 q^{16} -7795.51i q^{17} +3202.42 q^{18} +6682.23i q^{19} -8726.73i q^{20} -10836.0 q^{22} +18832.6 q^{23} +9383.87i q^{24} +9294.12 q^{25} +32013.0i q^{26} +3788.00i q^{27} +13888.2 q^{29} +16345.9 q^{30} +27864.2i q^{31} +26482.9 q^{32} -12817.4i q^{33} +102735. i q^{34} -26651.7 q^{36} +79675.3 q^{37} -88063.1i q^{38} -37866.6 q^{39} +47897.3i q^{40} -59196.1i q^{41} -91825.9 q^{43} +90181.5 q^{44} +19334.7i q^{45} -248189. q^{46} -5019.99i q^{47} -14245.7i q^{48} -122484. q^{50} -121520. q^{51} -266424. i q^{52} +186390. q^{53} -49920.8i q^{54} -65422.9i q^{55} +104166. q^{57} -183029. q^{58} -225203. i q^{59} -136036. q^{60} -144358. i q^{61} -367214. i q^{62} -407497. q^{64} -193279. q^{65} +168917. i q^{66} -235480. q^{67} -854996. i q^{68} -293571. i q^{69} +96269.3 q^{71} +146280. q^{72} -275551. i q^{73} -1.05002e6 q^{74} -144881. i q^{75} +732893. i q^{76} +499033. q^{78} -681334. q^{79} -72713.2i q^{80} +59049.0 q^{81} +780127. i q^{82} +128019. i q^{83} -620264. q^{85} +1.21015e6 q^{86} -216496. i q^{87} -494968. q^{88} -372686. i q^{89} -254807. i q^{90} +2.06552e6 q^{92} +434360. q^{93} +66156.9i q^{94} +531684. q^{95} -412828. i q^{96} -620049. i q^{97} -199804. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−13.1787	−1.64734	−0.823668	−	0.567072i	$-0.808076\pi$
$2$	−13.1787	−1.64734	−0.823668	+	0.567072i	$0.808076\pi$
$3$	− 15.5885i	− 0.577350i
$3$	− 15.5885i	− 0.577350i
$4$	109.678	1.71372
$5$	− 79.5668i	− 0.636535i	−0.948001	−	0.318267i	$-0.896899\pi$
$5$	− 79.5668i	− 0.636535i	0.948001	−	0.318267i	$-0.103101\pi$
$6$	205.435i	0.951090i
$7$	0	0
$7$	0	0
$8$	−601.976	−1.17573
$9$	−243.000	−0.333333
$10$	1048.59i	1.04859i
$11$	822.239	0.617760	0.308880	−	0.951101i	$-0.400046\pi$
$11$	822.239	0.617760	0.308880	+	0.951101i	$0.400046\pi$
$12$	− 1709.71i	− 0.989415i
$13$	− 2429.15i	− 1.10567i	−0.833292	−	0.552833i	$-0.813547\pi$
$13$	− 2429.15i	− 1.10567i	0.833292	−	0.552833i	$-0.186453\pi$
$14$	0	0
$15$	−1240.32	−0.367503
$16$	913.863	0.223111
$17$	− 7795.51i	− 1.58671i	−0.608759	−	0.793355i	$-0.708332\pi$
$17$	− 7795.51i	− 1.58671i	0.608759	−	0.793355i	$-0.291668\pi$
$18$	3202.42	0.549112
$19$	6682.23i	0.974228i	0.873338	+	0.487114i	$0.161950\pi$
$19$	6682.23i	0.974228i	−0.873338	+	0.487114i	$0.838050\pi$
$20$	− 8726.73i	− 1.09084i
$21$	0	0
$22$	−10836.0	−1.01766
$23$	18832.6	1.54784	0.773921	−	0.633282i	$-0.218293\pi$
$23$	18832.6	1.54784	0.773921	+	0.633282i	$0.218293\pi$
$24$	9383.87i	0.678810i
$25$	9294.12	0.594824
$26$	32013.0i	1.82140i
$27$	3788.00i	0.192450i
$28$	0	0
$29$	13888.2	0.569446	0.284723	−	0.958610i	$-0.408098\pi$
$29$	13888.2	0.569446	0.284723	+	0.958610i	$0.408098\pi$
$30$	16345.9	0.605402
$31$	27864.2i	0.935324i	0.883907	+	0.467662i	$0.154904\pi$
$31$	27864.2i	0.935324i	−0.883907	+	0.467662i	$0.845096\pi$
$32$	26482.9	0.808194
$33$	− 12817.4i	− 0.356664i
$34$	102735.i	2.61385i
$35$	0	0
$36$	−26651.7	−0.571239
$37$	79675.3	1.57296	0.786481	−	0.617614i	$-0.211901\pi$
$37$	79675.3	1.57296	0.786481	+	0.617614i	$0.211901\pi$
$38$	− 88063.1i	− 1.60488i
$39$	−37866.6	−0.638356
$40$	47897.3i	0.748395i
$41$	− 59196.1i	− 0.858898i	−0.903091	−	0.429449i	$-0.858708\pi$
$41$	− 59196.1i	− 0.858898i	0.903091	−	0.429449i	$-0.141292\pi$
$42$	0	0
$43$	−91825.9	−1.15494	−0.577471	−	0.816411i	$-0.695960\pi$
$43$	−91825.9	−1.15494	−0.577471	+	0.816411i	$0.695960\pi$
$44$	90181.5	1.05867
$45$	19334.7i	0.212178i
$46$	−248189.	−2.54982
$47$	− 5019.99i	− 0.0483514i	−0.999708	−	0.0241757i	$-0.992304\pi$
$47$	− 5019.99i	− 0.0483514i	0.999708	−	0.0241757i	$-0.00769611\pi$
$48$	− 14245.7i	− 0.128813i
$49$	0	0
$50$	−122484.	−0.979875
$51$	−121520.	−0.916088
$52$	− 266424.i	− 1.89480i
$53$	186390.	1.25197	0.625985	−	0.779835i	$-0.284697\pi$
$53$	186390.	1.25197	0.625985	+	0.779835i	$0.284697\pi$
$54$	− 49920.8i	− 0.317030i
$55$	− 65422.9i	− 0.393226i
$56$	0	0
$57$	104166.	0.562471
$58$	−183029.	−0.938069
$59$	− 225203.i	− 1.09652i	−0.836306	−	0.548262i	$-0.815290\pi$
$59$	− 225203.i	− 1.09652i	0.836306	−	0.548262i	$-0.184710\pi$
$60$	−136036.	−0.629797
$61$	− 144358.i	− 0.635992i	−0.948092	−	0.317996i	$-0.896990\pi$
$61$	− 144358.i	− 0.635992i	0.948092	−	0.317996i	$-0.103010\pi$
$62$	− 367214.i	− 1.54079i
$63$	0	0
$64$	−407497.	−1.55448
$65$	−193279.	−0.703794
$66$	168917.i	0.587546i
$67$	−235480.	−0.782942	−0.391471	−	0.920190i	$-0.628034\pi$
$67$	−235480.	−0.782942	−0.391471	+	0.920190i	$0.628034\pi$
$68$	− 854996.i	− 2.71917i
$69$	− 293571.i	− 0.893647i
$70$	0	0
$71$	96269.3	0.268975	0.134488	−	0.990915i	$-0.457061\pi$
$71$	96269.3	0.268975	0.134488	+	0.990915i	$0.457061\pi$
$72$	146280.	0.391911
$73$	− 275551.i	− 0.708325i	−0.935184	−	0.354163i	$-0.884766\pi$
$73$	− 275551.i	− 0.708325i	0.935184	−	0.354163i	$-0.115234\pi$
$74$	−1.05002e6	−2.59120
$75$	− 144881.i	− 0.343422i
$76$	732893.i	1.66955i
$77$	0	0
$78$	499033.	1.05159
$79$	−681334.	−1.38191	−0.690953	−	0.722900i	$-0.742809\pi$
$79$	−681334.	−1.38191	−0.690953	+	0.722900i	$0.742809\pi$
$80$	− 72713.2i	− 0.142018i
$81$	59049.0	0.111111
$82$	780127.i	1.41489i
$83$	128019.i	0.223893i	0.993714	+	0.111946i	$0.0357085\pi$
$83$	128019.i	0.223893i	−0.993714	+	0.111946i	$0.964291\pi$
$84$	0	0
$85$	−620264.	−1.01000
$86$	1.21015e6	1.90258
$87$	− 216496.i	− 0.328770i
$88$	−494968.	−0.726321
$89$	− 372686.i	− 0.528656i	−0.964433	−	0.264328i	$-0.914850\pi$
$89$	− 372686.i	− 0.528656i	0.964433	−	0.264328i	$-0.0851501\pi$
$90$	− 254807.i	− 0.349529i
$91$	0	0
$92$	2.06552e6	2.65257
$93$	434360.	0.540009
$94$	66156.9i	0.0796510i
$95$	531684.	0.620130
$96$	− 412828.i	− 0.466611i
$97$	− 620049.i	− 0.679377i	−0.940538	−	0.339688i	$-0.889678\pi$
$97$	− 620049.i	− 0.679377i	0.940538	−	0.339688i	$-0.110322\pi$
$98$	0	0
$99$	−199804.	−0.205920
$100$	1.01936e6	1.01936
$101$	668222.i	0.648570i	0.945959	+	0.324285i	$0.105124\pi$
$101$	668222.i	0.648570i	−0.945959	+	0.324285i	$0.894876\pi$
$102$	1.60147e6	1.50911
$103$	1.54938e6i	1.41790i	0.705257	+	0.708952i	$0.250832\pi$
$103$	1.54938e6i	1.41790i	−0.705257	+	0.708952i	$0.749168\pi$
$104$	1.46229e6i	1.29997i
$105$	0	0
$106$	−2.45637e6	−2.06242
$107$	−955895.	−0.780295	−0.390148	−	0.920752i	$-0.627576\pi$
$107$	−955895.	−0.780295	−0.390148	+	0.920752i	$0.627576\pi$
$108$	415460.i	0.329805i
$109$	1.57173e6	1.21366	0.606830	−	0.794831i	$-0.292441\pi$
$109$	1.57173e6	1.21366	0.606830	+	0.794831i	$0.292441\pi$
$110$	862189.i	0.647775i
$111$	− 1.24201e6i	− 0.908150i
$112$	0	0
$113$	−2.47576e6	−1.71582	−0.857912	−	0.513797i	$-0.828238\pi$
$113$	−2.47576e6	−1.71582	−0.857912	+	0.513797i	$0.828238\pi$
$114$	−1.37277e6	−0.926579
$115$	− 1.49845e6i	− 0.985255i
$116$	1.52323e6	0.975870
$117$	590283.i	0.368555i
$118$	2.96788e6i	1.80634i
$119$	0	0
$120$	746645.	0.432086
$121$	−1.09548e6	−0.618372
$122$	1.90245e6i	1.04769i
$123$	−922776.	−0.495885
$124$	3.05609e6i	1.60288i
$125$	− 1.98274e6i	− 1.01516i
$126$	0	0
$127$	292592.	0.142840	0.0714202	−	0.997446i	$-0.477247\pi$
$127$	292592.	0.142840	0.0714202	+	0.997446i	$0.477247\pi$
$128$	3.67538e6	1.75256
$129$	1.43142e6i	0.666806i
$130$	2.54717e6	1.15939
$131$	− 2.72884e6i	− 1.21385i	−0.794760	−	0.606924i	$-0.792403\pi$
$131$	− 2.72884e6i	− 1.21385i	0.794760	−	0.606924i	$-0.207597\pi$
$132$	− 1.40579e6i	− 0.611222i
$133$	0	0
$134$	3.10332e6	1.28977
$135$	301399.	0.122501
$136$	4.69271e6i	1.86555i
$137$	−907844.	−0.353061	−0.176530	−	0.984295i	$-0.556487\pi$
$137$	−907844.	−0.353061	−0.176530	+	0.984295i	$0.556487\pi$
$138$	3.86888e6i	1.47214i
$139$	4640.07i	0.00172775i	1.00000		0.000863874i	$0.000274980\pi$
$139$	4640.07i	0.00172775i	−1.00000		0.000863874i	$0.999725\pi$
$140$	0	0
$141$	−78253.8	−0.0279157
$142$	−1.26870e6	−0.443093
$143$	− 1.99734e6i	− 0.683036i
$144$	−222069.	−0.0743704
$145$	− 1.10504e6i	− 0.362472i
$146$	3.63140e6i	1.16685i
$147$	0	0
$148$	8.73862e6	2.69561
$149$	−1.64720e6	−0.497953	−0.248976	−	0.968510i	$-0.580094\pi$
$149$	−1.64720e6	−0.497953	−0.248976	+	0.968510i	$0.580094\pi$
$150$	1.90934e6i	0.565731i
$151$	−2.44589e6	−0.710405	−0.355203	−	0.934789i	$-0.615588\pi$
$151$	−2.44589e6	−0.710405	−0.355203	+	0.934789i	$0.615588\pi$
$152$	− 4.02254e6i	− 1.14543i
$153$	1.89431e6i	0.528904i
$154$	0	0
$155$	2.21707e6	0.595366
$156$	−4.15314e6	−1.09396
$157$	2.81542e6i	0.727518i	0.931493	+	0.363759i	$0.118507\pi$
$157$	2.81542e6i	0.727518i	−0.931493	+	0.363759i	$0.881493\pi$
$158$	8.97909e6	2.27646
$159$	− 2.90553e6i	− 0.722825i
$160$	− 2.10716e6i	− 0.514444i
$161$	0	0
$162$	−778189.	−0.183037
$163$	−1.56281e6	−0.360865	−0.180432	−	0.983587i	$-0.557750\pi$
$163$	−1.56281e6	−0.360865	−0.180432	+	0.983587i	$0.557750\pi$
$164$	− 6.49251e6i	− 1.47191i
$165$	−1.01984e6	−0.227029
$166$	− 1.68712e6i	− 0.368827i
$167$	− 1.15538e6i	− 0.248070i	−0.992278	−	0.124035i	$-0.960416\pi$
$167$	− 1.15538e6i	− 0.248070i	0.992278	−	0.124035i	$-0.0395835\pi$
$168$	0	0
$169$	−1.07394e6	−0.222495
$170$	8.17427e6	1.66380
$171$	− 1.62378e6i	− 0.324743i
$172$	−1.00713e7	−1.97924
$173$	− 5.76104e6i	− 1.11266i	−0.830962	−	0.556330i	$-0.812209\pi$
$173$	− 5.76104e6i	− 1.11266i	0.830962	−	0.556330i	$-0.187791\pi$
$174$	2.85313e6i	0.541594i
$175$	0	0
$176$	751414.	0.137829
$177$	−3.51057e6	−0.633079
$178$	4.91151e6i	0.870874i
$179$	−1.19560e6	−0.208462	−0.104231	−	0.994553i	$-0.533238\pi$
$179$	−1.19560e6	−0.208462	−0.104231	+	0.994553i	$0.533238\pi$
$180$	2.12059e6i	0.363614i
$181$	− 1.00030e7i	− 1.68692i	−0.537191	−	0.843461i	$-0.680514\pi$
$181$	− 1.00030e7i	− 1.68692i	0.537191	−	0.843461i	$-0.319486\pi$
$182$	0	0
$183$	−2.25032e6	−0.367190
$184$	−1.13368e7	−1.81985
$185$	− 6.33951e6i	− 1.00124i
$186$	−5.72430e6	−0.889577
$187$	− 6.40977e6i	− 0.980207i
$188$	− 550582.i	− 0.0828606i
$189$	0	0
$190$	−7.00690e6	−1.02156
$191$	−7.58271e6	−1.08824	−0.544120	−	0.839008i	$-0.683136\pi$
$191$	−7.58271e6	−1.08824	−0.544120	+	0.839008i	$0.683136\pi$
$192$	6.35226e6i	0.897479i
$193$	7.09613e6	0.987073	0.493537	−	0.869725i	$-0.335704\pi$
$193$	7.09613e6	0.987073	0.493537	+	0.869725i	$0.335704\pi$
$194$	8.17143e6i	1.11916i
$195$	3.01293e6i	0.406336i
$196$	0	0
$197$	2.00096e6	0.261722	0.130861	−	0.991401i	$-0.458226\pi$
$197$	2.00096e6	0.261722	0.130861	+	0.991401i	$0.458226\pi$
$198$	2.63316e6	0.339220
$199$	4.34608e6i	0.551491i	0.961231	+	0.275745i	$0.0889246\pi$
$199$	4.34608e6i	0.551491i	−0.961231	+	0.275745i	$0.911075\pi$
$200$	−5.59483e6	−0.699354
$201$	3.67077e6i	0.452032i
$202$	− 8.80630e6i	− 1.06841i
$203$	0	0
$204$	−1.33281e7	−1.56992
$205$	−4.71005e6	−0.546718
$206$	− 2.04188e7i	− 2.33577i
$207$	−4.57632e6	−0.515947
$208$	− 2.21991e6i	− 0.246686i
$209$	5.49439e6i	0.601839i
$210$	0	0
$211$	1.03642e7	1.10328	0.551641	−	0.834082i	$-0.314002\pi$
$211$	1.03642e7	1.10328	0.551641	+	0.834082i	$0.314002\pi$
$212$	2.04428e7	2.14552
$213$	− 1.50069e6i	− 0.155293i
$214$	1.25974e7	1.28541
$215$	7.30630e6i	0.735160i
$216$	− 2.28028e6i	− 0.226270i
$217$	0	0
$218$	−2.07133e7	−1.99931
$219$	−4.29541e6	−0.408952
$220$	− 7.17545e6i	− 0.673878i
$221$	−1.89364e7	−1.75437
$222$	1.63681e7i	1.49603i
$223$	4.84791e6i	0.437159i	0.975819	+	0.218580i	$0.0701424\pi$
$223$	4.84791e6i	0.437159i	−0.975819	+	0.218580i	$0.929858\pi$
$224$	0	0
$225$	−2.25847e6	−0.198275
$226$	3.26272e7	2.82654
$227$	1.51079e7i	1.29160i	0.763508	+	0.645798i	$0.223475\pi$
$227$	1.51079e7i	1.29160i	−0.763508	+	0.645798i	$0.776525\pi$
$228$	1.14247e7	0.963916
$229$	− 4.25371e6i	− 0.354210i	−0.984192	−	0.177105i	$-0.943327\pi$
$229$	− 4.25371e6i	− 0.354210i	0.984192	−	0.177105i	$-0.0566733\pi$
$230$	1.97476e7i	1.62305i
$231$	0	0
$232$	−8.36037e6	−0.669517
$233$	1.25817e7	0.994656	0.497328	−	0.867563i	$-0.334315\pi$
$233$	1.25817e7	0.994656	0.497328	+	0.867563i	$0.334315\pi$
$234$	− 7.77915e6i	− 0.607134i
$235$	−399424.	−0.0307773
$236$	− 2.46998e7i	− 1.87913i
$237$	1.06209e7i	0.797844i
$238$	0	0
$239$	7.54342e6	0.552554	0.276277	−	0.961078i	$-0.410899\pi$
$239$	7.54342e6	0.552554	0.276277	+	0.961078i	$0.410899\pi$
$240$	−1.13349e6	−0.0819941
$241$	− 1.95783e7i	− 1.39870i	−0.714781	−	0.699348i	$-0.753474\pi$
$241$	− 1.95783e7i	− 1.39870i	0.714781	−	0.699348i	$-0.246526\pi$
$242$	1.44371e7	1.01867
$243$	− 920483.i	− 0.0641500i
$244$	− 1.58329e7i	− 1.08991i
$245$	0	0
$246$	1.21610e7	0.816890
$247$	1.62321e7	1.07717
$248$	− 1.67736e7i	− 1.09969i
$249$	1.99562e6	0.129265
$250$	2.61299e7i	1.67231i
$251$	1.39590e7i	0.882743i	0.897324	+	0.441372i	$0.145508\pi$
$251$	1.39590e7i	0.882743i	−0.897324	+	0.441372i	$0.854492\pi$
$252$	0	0
$253$	1.54849e7	0.956195
$254$	−3.85598e6	−0.235306
$255$	9.66896e6i	0.583122i
$256$	−2.23568e7	−1.33257
$257$	− 655465.i	− 0.0386145i	−0.999814	−	0.0193072i	$-0.993854\pi$
$257$	− 655465.i	− 0.0386145i	0.999814	−	0.0193072i	$-0.00614606\pi$
$258$	− 1.88643e7i	− 1.09845i
$259$	0	0
$260$	−2.11985e7	−1.20610
$261$	−3.37484e6	−0.189815
$262$	3.59625e7i	1.99962i
$263$	−1.49400e7	−0.821263	−0.410632	−	0.911801i	$-0.634692\pi$
$263$	−1.49400e7	−0.821263	−0.410632	+	0.911801i	$0.634692\pi$
$264$	7.71578e6i	0.419342i
$265$	− 1.48304e7i	− 0.796922i
$266$	0	0
$267$	−5.80960e6	−0.305220
$268$	−2.58270e7	−1.34174
$269$	3.14099e7i	1.61365i	0.590791	+	0.806825i	$0.298816\pi$
$269$	3.14099e7i	1.61365i	−0.590791	+	0.806825i	$0.701184\pi$
$270$	−3.97204e6	−0.201801
$271$	− 1.49534e6i	− 0.0751333i	−0.999294	−	0.0375666i	$-0.988039\pi$
$271$	− 1.49534e6i	− 0.0751333i	0.999294	−	0.0375666i	$-0.0119606\pi$
$272$	− 7.12403e6i	− 0.354013i
$273$	0	0
$274$	1.19642e7	0.581610
$275$	7.64199e6	0.367458
$276$	− 3.21983e7i	− 1.53146i
$277$	−1.98349e6	−0.0933237	−0.0466618	−	0.998911i	$-0.514858\pi$
$277$	−1.98349e6	−0.0933237	−0.0466618	+	0.998911i	$0.514858\pi$
$278$	− 61150.1i	− 0.00284618i
$279$	− 6.77101e6i	− 0.311775i
$280$	0	0
$281$	−3.50353e6	−0.157902	−0.0789508	−	0.996879i	$-0.525157\pi$
$281$	−3.50353e6	−0.157902	−0.0789508	+	0.996879i	$0.525157\pi$
$282$	1.03128e6	0.0459865
$283$	− 3.26452e7i	− 1.44032i	−0.693807	−	0.720161i	$-0.744068\pi$
$283$	− 3.26452e7i	− 1.44032i	0.693807	−	0.720161i	$-0.255932\pi$
$284$	1.05586e7	0.460948
$285$	− 8.28813e6i	− 0.358032i
$286$	2.63223e7i	1.12519i
$287$	0	0
$288$	−6.43535e6	−0.269398
$289$	−3.66324e7	−1.51765
$290$	1.45630e7i	0.597113i
$291$	−9.66561e6	−0.392238
$292$	− 3.02218e7i	− 1.21387i
$293$	− 2.57653e7i	− 1.02431i	−0.858892	−	0.512156i	$-0.828847\pi$
$293$	− 2.57653e7i	− 1.02431i	0.858892	−	0.512156i	$-0.171153\pi$
$294$	0	0
$295$	−1.79187e7	−0.697976
$296$	−4.79626e7	−1.84938
$297$	3.11464e6i	0.118888i
$298$	2.17080e7	0.820295
$299$	− 4.57471e7i	− 1.71140i
$300$	− 1.58902e7i	− 0.588528i
$301$	0	0
$302$	3.22336e7	1.17028
$303$	1.04166e7	0.374452
$304$	6.10664e6i	0.217361i
$305$	−1.14861e7	−0.404831
$306$	− 2.49645e7i	− 0.871282i
$307$	1.89894e7i	0.656289i	0.944628	+	0.328145i	$0.106423\pi$
$307$	1.89894e7i	0.656289i	−0.944628	+	0.328145i	$0.893577\pi$
$308$	0	0
$309$	2.41525e7	0.818627
$310$	−2.92181e7	−0.980768
$311$	− 3.23738e7i	− 1.07625i	−0.842866	−	0.538124i	$-0.819133\pi$
$311$	− 3.23738e7i	− 1.07625i	0.842866	−	0.538124i	$-0.180867\pi$
$312$	2.27948e7	0.750537
$313$	3.24930e7i	1.05964i	0.848112	+	0.529818i	$0.177740\pi$
$313$	3.24930e7i	1.05964i	−0.848112	+	0.529818i	$0.822260\pi$
$314$	− 3.71035e7i	− 1.19847i
$315$	0	0
$316$	−7.47273e7	−2.36820
$317$	−1.63428e7	−0.513038	−0.256519	−	0.966539i	$-0.582576\pi$
$317$	−1.63428e7	−0.513038	−0.256519	+	0.966539i	$0.582576\pi$
$318$	3.82910e7i	1.19074i
$319$	1.14194e7	0.351781
$320$	3.24233e7i	0.989480i
$321$	1.49009e7i	0.450504i
$322$	0	0
$323$	5.20914e7	1.54582
$324$	6.47637e6	0.190413
$325$	− 2.25768e7i	− 0.657676i
$326$	2.05958e7	0.594466
$327$	− 2.45008e7i	− 0.700707i
$328$	3.56346e7i	1.00984i
$329$	0	0
$330$	1.34402e7	0.373993
$331$	5.17570e7	1.42720	0.713601	−	0.700553i	$-0.247063\pi$
$331$	5.17570e7	1.42720	0.713601	+	0.700553i	$0.247063\pi$
$332$	1.40409e7i	0.383689i
$333$	−1.93611e7	−0.524321
$334$	1.52264e7i	0.408655i
$335$	1.87364e7i	0.498370i
$336$	0	0
$337$	6.13986e7	1.60424	0.802119	−	0.597164i	$-0.203706\pi$
$337$	6.13986e7	1.60424	0.802119	+	0.597164i	$0.203706\pi$
$338$	1.41532e7	0.366525
$339$	3.85932e7i	0.990631i
$340$	−6.80293e7	−1.73085
$341$	2.29111e7i	0.577806i
$342$	2.13993e7i	0.534961i
$343$	0	0
$344$	5.52770e7	1.35790
$345$	−2.33585e7	−0.568837
$346$	7.59229e7i	1.83292i
$347$	3.55667e7	0.851246	0.425623	−	0.904901i	$-0.360055\pi$
$347$	3.55667e7	0.851246	0.425623	+	0.904901i	$0.360055\pi$
$348$	− 2.37448e7i	− 0.563419i
$349$	5.17156e7i	1.21659i	0.793710	+	0.608297i	$0.208147\pi$
$349$	5.17156e7i	1.21659i	−0.793710	+	0.608297i	$0.791853\pi$
$350$	0	0
$351$	9.20159e6	0.212785
$352$	2.17753e7	0.499270
$353$	772562.i	0.0175634i	0.999961	+	0.00878171i	$0.00279534\pi$
$353$	772562.i	0.0175634i	−0.999961	+	0.00878171i	$0.997205\pi$
$354$	4.62647e7	1.04289
$355$	− 7.65984e6i	− 0.171212i
$356$	− 4.08754e7i	− 0.905967i
$357$	0	0
$358$	1.57565e7	0.343407
$359$	−4.16680e7	−0.900574	−0.450287	−	0.892884i	$-0.648678\pi$
$359$	−4.16680e7	−0.900574	−0.450287	+	0.892884i	$0.648678\pi$
$360$	− 1.16390e7i	− 0.249465i
$361$	2.39367e6	0.0508795
$362$	1.31827e8i	2.77893i
$363$	1.70769e7i	0.357017i
$364$	0	0
$365$	−2.19247e7	−0.450874
$366$	2.96563e7	0.604886
$367$	− 6.60182e6i	− 0.133557i	−0.997768	−	0.0667783i	$-0.978728\pi$
$367$	− 6.60182e6i	− 0.133557i	0.997768	−	0.0667783i	$-0.0212720\pi$
$368$	1.72104e7	0.345341
$369$	1.43847e7i	0.286299i
$370$	8.35464e7i	1.64939i
$371$	0	0
$372$	4.76398e7	0.925424
$373$	−4.95162e6	−0.0954159	−0.0477080	−	0.998861i	$-0.515192\pi$
$373$	−4.95162e6	−0.0954159	−0.0477080	+	0.998861i	$0.515192\pi$
$374$	8.44724e7i	1.61473i
$375$	−3.09078e7	−0.586103
$376$	3.02191e6i	0.0568483i
$377$	− 3.37365e7i	− 0.629616i
$378$	0	0
$379$	−1.05876e8	−1.94482	−0.972409	−	0.233282i	$-0.925053\pi$
$379$	−1.05876e8	−1.94482	−0.972409	+	0.233282i	$0.925053\pi$
$380$	5.83140e7	1.06273
$381$	− 4.56106e6i	− 0.0824690i
$382$	9.99302e7	1.79270
$383$	− 4.92008e7i	− 0.875742i	−0.899038	−	0.437871i	$-0.855733\pi$
$383$	− 4.92008e7i	− 0.875742i	0.899038	−	0.437871i	$-0.144267\pi$
$384$	− 5.72935e7i	− 1.01184i
$385$	0	0
$386$	−9.35177e7	−1.62604
$387$	2.23137e7	0.384980
$388$	− 6.80057e7i	− 1.16426i
$389$	6.66198e7	1.13176	0.565880	−	0.824487i	$-0.308536\pi$
$389$	6.66198e7	1.13176	0.565880	+	0.824487i	$0.308536\pi$
$390$	− 3.97065e7i	− 0.669372i
$391$	− 1.46810e8i	− 2.45598i
$392$	0	0
$393$	−4.25384e7	−0.700815
$394$	−2.63701e7	−0.431144
$395$	5.42116e7i	0.879631i
$396$	−2.19141e7	−0.352889
$397$	4.80402e7i	0.767774i	0.923380	+	0.383887i	$0.125415\pi$
$397$	4.80402e7i	0.767774i	−0.923380	+	0.383887i	$0.874585\pi$
$398$	− 5.72756e7i	− 0.908491i
$399$	0	0
$400$	8.49355e6	0.132712
$401$	1.39431e7	0.216236	0.108118	−	0.994138i	$-0.465518\pi$
$401$	1.39431e7	0.216236	0.108118	+	0.994138i	$0.465518\pi$
$402$	− 4.83760e7i	− 0.744649i
$403$	6.76863e7	1.03415
$404$	7.32893e7i	1.11147i
$405$	− 4.69834e6i	− 0.0707261i
$406$	0	0
$407$	6.55121e7	0.971713
$408$	7.31521e7	1.07708
$409$	− 2.23838e7i	− 0.327163i	−0.986530	−	0.163581i	$-0.947695\pi$
$409$	− 2.23838e7i	− 0.327163i	0.986530	−	0.163581i	$-0.0523046\pi$
$410$	6.20723e7	0.900629
$411$	1.41519e7i	0.203840i
$412$	1.69933e8i	2.42989i
$413$	0	0
$414$	6.03099e7	0.849939
$415$	1.01861e7	0.142516
$416$	− 6.43309e7i	− 0.893592i
$417$	72331.6	0.000997516 0
$418$	− 7.24089e7i	− 0.991432i
$419$	5.41233e7i	0.735770i	0.929871	+	0.367885i	$0.119918\pi$
$419$	5.41233e7i	0.735770i	−0.929871	+	0.367885i	$0.880082\pi$
$420$	0	0
$421$	−1.30034e8	−1.74265	−0.871323	−	0.490709i	$-0.836738\pi$
$421$	−1.30034e8	−1.74265	−0.871323	+	0.490709i	$0.836738\pi$
$422$	−1.36586e8	−1.81748
$423$	1.21986e6i	0.0161171i
$424$	−1.12202e8	−1.47198
$425$	− 7.24524e7i	− 0.943813i
$426$	1.97771e7i	0.255820i
$427$	0	0
$428$	−1.04841e8	−1.33721
$429$	−3.11354e7	−0.394351
$430$	− 9.62874e7i	− 1.21106i
$431$	−1.19942e8	−1.49809	−0.749047	−	0.662517i	$-0.769488\pi$
$431$	−1.19942e8	−1.49809	−0.749047	+	0.662517i	$0.769488\pi$
$432$	3.46171e6i	0.0429378i
$433$	− 1.11549e8i	− 1.37404i	−0.726636	−	0.687022i	$-0.758917\pi$
$433$	− 1.11549e8i	− 1.37404i	0.726636	−	0.687022i	$-0.241083\pi$
$434$	0	0
$435$	−1.72259e7	−0.209273
$436$	1.72384e8	2.07987
$437$	1.25844e8i	1.50795i
$438$	5.66079e7	0.673681
$439$	1.23257e8i	1.45686i	0.685121	+	0.728429i	$0.259749\pi$
$439$	1.23257e8i	1.45686i	−0.685121	+	0.728429i	$0.740251\pi$
$440$	3.93830e7i	0.462329i
$441$	0	0
$442$	2.49557e8	2.89004
$443$	−7.11416e7	−0.818300	−0.409150	−	0.912467i	$-0.634175\pi$
$443$	−7.11416e7	−0.818300	−0.409150	+	0.912467i	$0.634175\pi$
$444$	− 1.36222e8i	− 1.55631i
$445$	−2.96534e7	−0.336508
$446$	− 6.38891e7i	− 0.720149i
$447$	2.56773e7i	0.287493i
$448$	0	0
$449$	−1.07566e8	−1.18833	−0.594165	−	0.804343i	$-0.702517\pi$
$449$	−1.07566e8	−1.18833	−0.594165	+	0.804343i	$0.702517\pi$
$450$	2.97637e7	0.326625
$451$	− 4.86734e7i	− 0.530593i
$452$	−2.71536e8	−2.94044
$453$	3.81277e7i	0.410153i
$454$	− 1.99103e8i	− 2.12769i
$455$	0	0
$456$	−6.27052e7	−0.661316
$457$	1.28676e7	0.134819	0.0674093	−	0.997725i	$-0.478527\pi$
$457$	1.28676e7	0.134819	0.0674093	+	0.997725i	$0.478527\pi$
$458$	5.60583e7i	0.583504i
$459$	2.95294e7	0.305363
$460$	− 1.64347e8i	− 1.68845i
$461$	7.08717e6i	0.0723386i	0.999346	+	0.0361693i	$0.0115156\pi$
$461$	7.08717e6i	0.0723386i	−0.999346	+	0.0361693i	$0.988484\pi$
$462$	0	0
$463$	1.44698e8	1.45788	0.728938	−	0.684580i	$-0.240014\pi$
$463$	1.44698e8	1.45788	0.728938	+	0.684580i	$0.240014\pi$
$464$	1.26919e7	0.127050
$465$	− 3.45607e7i	− 0.343735i
$466$	−1.65811e8	−1.63853
$467$	8.48427e7i	0.833036i	0.909127	+	0.416518i	$0.136750\pi$
$467$	8.48427e7i	0.833036i	−0.909127	+	0.416518i	$0.863250\pi$
$468$	6.47410e7i	0.631599i
$469$	0	0
$470$	5.26389e6	0.0507006
$471$	4.38880e7	0.420033
$472$	1.35567e8i	1.28922i
$473$	−7.55028e7	−0.713477
$474$	− 1.39970e8i	− 1.31432i
$475$	6.21054e7i	0.579494i
$476$	0	0
$477$	−4.52927e7	−0.417323
$478$	−9.94124e7	−0.910242
$479$	− 1.59637e8i	− 1.45254i	−0.687411	−	0.726268i	$-0.741253\pi$
$479$	− 1.59637e8i	− 1.45254i	0.687411	−	0.726268i	$-0.258747\pi$
$480$	−3.28474e7	−0.297014
$481$	− 1.93543e8i	− 1.73917i
$482$	2.58016e8i	2.30412i
$483$	0	0
$484$	−1.20150e8	−1.05972
$485$	−4.93353e7	−0.432447
$486$	1.21308e7i	0.105677i
$487$	1.38003e8	1.19482	0.597411	−	0.801935i	$-0.296196\pi$
$487$	1.38003e8	1.19482	0.597411	+	0.801935i	$0.296196\pi$
$488$	8.69001e7i	0.747758i
$489$	2.43619e7i	0.208345i
$490$	0	0
$491$	−3.91824e7	−0.331014	−0.165507	−	0.986209i	$-0.552926\pi$
$491$	−3.91824e7	−0.331014	−0.165507	+	0.986209i	$0.552926\pi$
$492$	−1.01208e8	−0.849807
$493$	− 1.08266e8i	− 0.903546i
$494$	−2.13918e8	−1.77446
$495$	1.58978e7i	0.131075i
$496$	2.54641e7i	0.208681i
$497$	0	0
$498$	−2.62997e7	−0.212942
$499$	2.28963e7	0.184274	0.0921370	−	0.995746i	$-0.470630\pi$
$499$	2.28963e7	0.184274	0.0921370	+	0.995746i	$0.470630\pi$
$500$	− 2.17462e8i	− 1.73970i
$501$	−1.80105e7	−0.143223
$502$	− 1.83962e8i	− 1.45418i
$503$	− 1.38751e8i	− 1.09027i	−0.838349	−	0.545133i	$-0.816479\pi$
$503$	− 1.38751e8i	− 1.09027i	0.838349	−	0.545133i	$-0.183521\pi$
$504$	0	0
$505$	5.31683e7	0.412837
$506$	−2.04071e8	−1.57518
$507$	1.67411e7i	0.128458i
$508$	3.20909e7	0.244788
$509$	− 5.86112e7i	− 0.444455i	−0.974995	−	0.222227i	$-0.928667\pi$
$509$	− 5.86112e7i	− 0.444455i	0.974995	−	0.222227i	$-0.0713327\pi$
$510$	− 1.27424e8i	− 0.960598i
$511$	0	0
$512$	5.94097e7	0.442636
$513$	−2.53123e7	−0.187490
$514$	8.63817e6i	0.0636110i
$515$	1.23279e8	0.902545
$516$	1.56996e8i	1.14272i
$517$	− 4.12763e6i	− 0.0298696i
$518$	0	0
$519$	−8.98057e7	−0.642394
$520$	1.16350e8	0.827474
$521$	2.17181e8i	1.53571i	0.640626	+	0.767853i	$0.278675\pi$
$521$	2.17181e8i	1.53571i	−0.640626	+	0.767853i	$0.721325\pi$
$522$	4.44759e7	0.312690
$523$	1.90443e7i	0.133125i	0.997782	+	0.0665627i	$0.0212032\pi$
$523$	1.90443e7i	0.133125i	−0.997782	+	0.0665627i	$0.978797\pi$
$524$	− 2.99294e8i	− 2.08019i
$525$	0	0
$526$	1.96889e8	1.35290
$527$	2.17216e8	1.48409
$528$	− 1.17134e7i	− 0.0795757i
$529$	2.06631e8	1.39582
$530$	1.95446e8i	1.31280i
$531$	5.47244e7i	0.365508i
$532$	0	0
$533$	−1.43796e8	−0.949654
$534$	7.65629e7	0.502799
$535$	7.60576e7i	0.496685i
$536$	1.41753e8	0.920532
$537$	1.86376e7i	0.120356i
$538$	− 4.13941e8i	− 2.65822i
$539$	0	0
$540$	3.30568e7	0.209932
$541$	−1.01072e8	−0.638321	−0.319161	−	0.947701i	$-0.603401\pi$
$541$	−1.01072e8	−0.638321	−0.319161	+	0.947701i	$0.603401\pi$
$542$	1.97066e7i	0.123770i
$543$	−1.55931e8	−0.973945
$544$	− 2.06448e8i	− 1.28237i
$545$	− 1.25057e8i	− 0.772537i
$546$	0	0
$547$	−2.29198e7	−0.140039	−0.0700196	−	0.997546i	$-0.522306\pi$
$547$	−2.29198e7	−0.140039	−0.0700196	+	0.997546i	$0.522306\pi$
$548$	−9.95704e7	−0.605046
$549$	3.50790e7i	0.211997i
$550$	−1.00711e8	−0.605328
$551$	9.28043e7i	0.554770i
$552$	1.76723e8i	1.05069i
$553$	0	0
$554$	2.61399e7	0.153735
$555$	−9.88231e7	−0.578069
$556$	508914.i	0.00296087i
$557$	1.38331e8	0.800487	0.400243	−	0.916409i	$-0.368926\pi$
$557$	1.38331e8	0.800487	0.400243	+	0.916409i	$0.368926\pi$
$558$	8.92330e7i	0.513598i
$559$	2.23059e8i	1.27698i
$560$	0	0
$561$	−9.99184e7	−0.565923
$562$	4.61719e7	0.260117
$563$	− 2.25278e8i	− 1.26239i	−0.775624	−	0.631195i	$-0.782565\pi$
$563$	− 2.25278e8i	− 1.26239i	0.775624	−	0.631195i	$-0.217435\pi$
$564$	−8.58272e6	−0.0478396
$565$	1.96988e8i	1.09218i
$566$	4.30221e8i	2.37270i
$567$	0	0
$568$	−5.79518e7	−0.316244
$569$	2.20552e8	1.19722	0.598609	−	0.801041i	$-0.295720\pi$
$569$	2.20552e8	1.19722	0.598609	+	0.801041i	$0.295720\pi$
$570$	1.09227e8i	0.589800i
$571$	−6.73189e7	−0.361600	−0.180800	−	0.983520i	$-0.557869\pi$
$571$	−6.73189e7	−0.361600	−0.180800	+	0.983520i	$0.557869\pi$
$572$	− 2.19064e8i	− 1.17053i
$573$	1.18203e8i	0.628295i
$574$	0	0
$575$	1.75032e8	0.920693
$576$	9.90219e7	0.518160
$577$	1.07347e7i	0.0558806i	0.999610	+	0.0279403i	$0.00889484\pi$
$577$	1.07347e7i	0.0558806i	−0.999610	+	0.0279403i	$0.991105\pi$
$578$	4.82767e8	2.50008
$579$	− 1.10618e8i	− 0.569887i
$580$	− 1.21199e8i	− 0.621175i
$581$	0	0
$582$	1.27380e8	0.646149
$583$	1.53257e8	0.773417
$584$	1.65875e8i	0.832802i
$585$	4.69669e7	0.234598
$586$	3.39553e8i	1.68739i
$587$	2.34143e8i	1.15762i	0.815461	+	0.578812i	$0.196484\pi$
$587$	2.34143e8i	1.15762i	−0.815461	+	0.578812i	$0.803516\pi$
$588$	0	0
$589$	−1.86195e8	−0.911219
$590$	2.36145e8	1.14980
$591$	− 3.11919e7i	− 0.151105i
$592$	7.28123e7	0.350945
$593$	1.67811e8i	0.804741i	0.915477	+	0.402370i	$0.131814\pi$
$593$	1.67811e8i	0.804741i	−0.915477	+	0.402370i	$0.868186\pi$
$594$	− 4.10468e7i	− 0.195849i
$595$	0	0
$596$	−1.80662e8	−0.853350
$597$	6.77486e7	0.318403
$598$	6.02887e8i	2.81924i
$599$	5.44275e7	0.253243	0.126622	−	0.991951i	$-0.459587\pi$
$599$	5.44275e7	0.253243	0.126622	+	0.991951i	$0.459587\pi$
$600$	8.72148e7i	0.403772i
$601$	1.02729e7i	0.0473226i	0.999720	+	0.0236613i	$0.00753233\pi$
$601$	1.02729e7i	0.0473226i	−0.999720	+	0.0236613i	$0.992468\pi$
$602$	0	0
$603$	5.72217e7	0.260981
$604$	−2.68260e8	−1.21743
$605$	8.71642e7i	0.393615i
$606$	−1.37277e8	−0.616849
$607$	3.69610e8i	1.65264i	0.563202	+	0.826319i	$0.309569\pi$
$607$	3.69610e8i	1.65264i	−0.563202	+	0.826319i	$0.690431\pi$
$608$	1.76965e8i	0.787366i
$609$	0	0
$610$	1.51372e8	0.666893
$611$	−1.21943e7	−0.0534604
$612$	2.07764e8i	0.906392i
$613$	4.66824e7	0.202662	0.101331	−	0.994853i	$-0.467690\pi$
$613$	4.66824e7	0.202662	0.101331	+	0.994853i	$0.467690\pi$
$614$	− 2.50255e8i	− 1.08113i
$615$	7.34224e7i	0.315648i
$616$	0	0
$617$	4.39158e8	1.86967	0.934836	−	0.355080i	$-0.115546\pi$
$617$	4.39158e8	1.86967	0.934836	+	0.355080i	$0.115546\pi$
$618$	−3.18298e8	−1.34855
$619$	2.13333e8i	0.899468i	0.893163	+	0.449734i	$0.148481\pi$
$619$	2.13333e8i	0.899468i	−0.893163	+	0.449734i	$0.851519\pi$
$620$	2.43164e8	1.02029
$621$	7.13378e7i	0.297882i
$622$	4.26644e8i	1.77294i
$623$	0	0
$624$	−3.46049e7	−0.142424
$625$	−1.25394e7	−0.0513612
$626$	− 4.28215e8i	− 1.74558i
$627$	8.56491e7	0.347472
$628$	3.08789e8i	1.24676i
$629$	− 6.21109e8i	− 2.49584i
$630$	0	0
$631$	2.58817e8	1.03016	0.515080	−	0.857142i	$-0.327762\pi$
$631$	2.58817e8	1.03016	0.515080	+	0.857142i	$0.327762\pi$
$632$	4.10146e8	1.62475
$633$	− 1.61561e8i	− 0.636980i
$634$	2.15377e8	0.845146
$635$	− 2.32806e7i	− 0.0909229i
$636$	− 3.18672e8i	− 1.23872i
$637$	0	0
$638$	−1.50493e8	−0.579502
$639$	−2.33934e7	−0.0896585
$640$	− 2.92438e8i	− 1.11556i
$641$	1.32871e8	0.504495	0.252247	−	0.967663i	$-0.418830\pi$
$641$	1.32871e8	0.504495	0.252247	+	0.967663i	$0.418830\pi$
$642$	− 1.96375e8i	− 0.742131i
$643$	1.84168e8i	0.692757i	0.938095	+	0.346378i	$0.112589\pi$
$643$	1.84168e8i	0.692757i	−0.938095	+	0.346378i	$0.887411\pi$
$644$	0	0
$645$	1.13894e8	0.424445
$646$	−6.86497e8	−2.54648
$647$	3.32772e8i	1.22866i	0.789047	+	0.614332i	$0.210575\pi$
$647$	3.32772e8i	1.22866i	−0.789047	+	0.614332i	$0.789425\pi$
$648$	−3.55461e7	−0.130637
$649$	− 1.85171e8i	− 0.677389i
$650$	2.97532e8i	1.08341i
$651$	0	0
$652$	−1.71406e8	−0.618420
$653$	2.56582e8	0.921481	0.460741	−	0.887535i	$-0.347584\pi$
$653$	2.56582e8	0.921481	0.460741	+	0.887535i	$0.347584\pi$
$654$	3.22888e8i	1.15430i
$655$	−2.17125e8	−0.772656
$656$	− 5.40972e7i	− 0.191630i
$657$	6.69588e7i	0.236108i
$658$	0	0
$659$	1.84717e8	0.645431	0.322715	−	0.946496i	$-0.395404\pi$
$659$	1.84717e8	0.645431	0.322715	+	0.946496i	$0.395404\pi$
$660$	−1.11854e8	−0.389064
$661$	− 2.01472e8i	− 0.697606i	−0.937196	−	0.348803i	$-0.886588\pi$
$661$	− 2.01472e8i	− 0.697606i	0.937196	−	0.348803i	$-0.113412\pi$
$662$	−6.82090e8	−2.35108
$663$	2.95190e8i	1.01289i
$664$	− 7.70644e7i	− 0.263239i
$665$	0	0
$666$	2.55154e8	0.863733
$667$	2.61551e8	0.881412
$668$	− 1.26719e8i	− 0.425122i
$669$	7.55714e7	0.252394
$670$	− 2.46921e8i	− 0.820983i
$671$	− 1.18697e8i	− 0.392891i
$672$	0	0
$673$	−4.93893e8	−1.62027	−0.810135	−	0.586243i	$-0.800606\pi$
$673$	−4.93893e8	−1.62027	−0.810135	+	0.586243i	$0.800606\pi$
$674$	−8.09153e8	−2.64272
$675$	3.52061e7i	0.114474i
$676$	−1.17788e8	−0.381294
$677$	− 3.13515e8i	− 1.01040i	−0.863003	−	0.505199i	$-0.831419\pi$
$677$	− 3.13515e8i	− 1.01040i	0.863003	−	0.505199i	$-0.168581\pi$
$678$	− 5.08608e8i	− 1.63190i
$679$	0	0
$680$	3.73384e8	1.18749
$681$	2.35509e8	0.745704
$682$	− 3.01938e8i	− 0.951841i
$683$	−1.48500e8	−0.466086	−0.233043	−	0.972466i	$-0.574868\pi$
$683$	−1.48500e8	−0.466086	−0.233043	+	0.972466i	$0.574868\pi$
$684$	− 1.78093e8i	− 0.556517i
$685$	7.22343e7i	0.224735i
$686$	0	0
$687$	−6.63087e7	−0.204503
$688$	−8.39163e7	−0.257680
$689$	− 4.52767e8i	− 1.38426i
$690$	3.07835e8	0.937067
$691$	− 3.87820e8i	− 1.17543i	−0.809069	−	0.587714i	$-0.800028\pi$
$691$	− 3.87820e8i	− 1.17543i	0.809069	−	0.587714i	$-0.199972\pi$
$692$	− 6.31859e8i	− 1.90678i
$693$	0	0
$694$	−4.68722e8	−1.40229
$695$	369196.	0.00109977
$696$	1.30325e8i	0.386546i
$697$	−4.61464e8	−1.36282
$698$	− 6.81544e8i	− 2.00414i
$699$	− 1.96130e8i	− 0.574265i
$700$	0	0
$701$	4.86782e7	0.141312	0.0706562	−	0.997501i	$-0.477491\pi$
$701$	4.86782e7	0.141312	0.0706562	+	0.997501i	$0.477491\pi$
$702$	−1.21265e8	−0.350529
$703$	5.32408e8i	1.53242i
$704$	−3.35060e8	−0.960296
$705$	6.22641e6i	0.0177693i
$706$	− 1.01814e7i	− 0.0289329i
$707$	0	0
$708$	−3.85032e8	−1.08492
$709$	−3.17955e8	−0.892127	−0.446064	−	0.895001i	$-0.647175\pi$
$709$	−3.17955e8	−0.892127	−0.446064	+	0.895001i	$0.647175\pi$
$710$	1.00947e8i	0.282044i
$711$	1.65564e8	0.460635
$712$	2.24348e8i	0.621558i
$713$	5.24756e8i	1.44773i
$714$	0	0
$715$	−1.58922e8	−0.434776
$716$	−1.31131e8	−0.357245
$717$	− 1.17590e8i	− 0.319017i
$718$	5.49130e8	1.48355
$719$	− 1.73824e8i	− 0.467652i	−0.972279	−	0.233826i	$-0.924875\pi$
$719$	− 1.73824e8i	− 0.467652i	0.972279	−	0.233826i	$-0.0751245\pi$
$720$	1.76693e7i	0.0473393i
$721$	0	0
$722$	−3.15455e7	−0.0838157
$723$	−3.05195e8	−0.807538
$724$	− 1.09711e9i	− 2.89091i
$725$	1.29079e8	0.338720
$726$	− 2.25051e8i	− 0.588128i
$727$	4.58803e8i	1.19405i	0.802222	+	0.597026i	$0.203651\pi$
$727$	4.58803e8i	1.19405i	−0.802222	+	0.597026i	$0.796349\pi$
$728$	0	0
$729$	−1.43489e7	−0.0370370
$730$	2.88939e8	0.742741
$731$	7.15830e8i	1.83256i
$732$	−2.46811e8	−0.629261
$733$	6.41720e8i	1.62942i	0.579867	+	0.814711i	$0.303105\pi$
$733$	6.41720e8i	1.62942i	−0.579867	+	0.814711i	$0.696895\pi$
$734$	8.70033e7i	0.220013i
$735$	0	0
$736$	4.98742e8	1.25096
$737$	−1.93621e8	−0.483671
$738$	− 1.89571e8i	− 0.471631i
$739$	−3.40002e8	−0.842458	−0.421229	−	0.906954i	$-0.638401\pi$
$739$	−3.40002e8	−0.842458	−0.421229	+	0.906954i	$0.638401\pi$
$740$	− 6.95304e8i	− 1.71585i
$741$	− 2.53034e8i	− 0.621904i
$742$	0	0
$743$	6.08554e8	1.48365	0.741827	−	0.670591i	$-0.233960\pi$
$743$	6.08554e8	1.48365	0.741827	+	0.670591i	$0.233960\pi$
$744$	−2.61474e8	−0.634907
$745$	1.31063e8i	0.316964i
$746$	6.52559e7	0.157182
$747$	− 3.11086e7i	− 0.0746310i
$748$	− 7.03011e8i	− 1.67980i
$749$	0	0
$750$	4.07324e8	0.965509
$751$	1.61226e8	0.380642	0.190321	−	0.981722i	$-0.439047\pi$
$751$	1.61226e8	0.380642	0.190321	+	0.981722i	$0.439047\pi$
$752$	− 4.58758e6i	− 0.0107877i
$753$	2.17600e8	0.509652
$754$	4.44603e8i	1.03719i
$755$	1.94612e8i	0.452198i
$756$	0	0
$757$	1.60953e8	0.371031	0.185516	−	0.982641i	$-0.440604\pi$
$757$	1.60953e8	0.371031	0.185516	+	0.982641i	$0.440604\pi$
$758$	1.39530e9	3.20377
$759$	− 2.41386e8i	− 0.552060i
$760$	−3.20061e8	−0.729108
$761$	− 4.33712e8i	− 0.984118i	−0.870562	−	0.492059i	$-0.836244\pi$
$761$	− 4.33712e8i	− 0.984118i	0.870562	−	0.492059i	$-0.163756\pi$
$762$	6.01088e7i	0.135854i
$763$	0	0
$764$	−8.31656e8	−1.86493
$765$	1.50724e8	0.336665
$766$	6.48402e8i	1.44264i
$767$	−5.47051e8	−1.21239
$768$	3.48509e8i	0.769360i
$769$	3.73405e8i	0.821110i	0.911836	+	0.410555i	$0.134665\pi$
$769$	3.73405e8i	0.821110i	−0.911836	+	0.410555i	$0.865335\pi$
$770$	0	0
$771$	−1.02177e7	−0.0222941
$772$	7.78288e8	1.69156
$773$	− 6.84604e8i	− 1.48218i	−0.671405	−	0.741090i	$-0.734309\pi$
$773$	− 6.84604e8i	− 1.48218i	0.671405	−	0.741090i	$-0.265691\pi$
$774$	−2.94065e8	−0.634192
$775$	2.58973e8i	0.556353i
$776$	3.73254e8i	0.798766i
$777$	0	0
$778$	−8.77962e8	−1.86439
$779$	3.95562e8	0.836763
$780$	3.30452e8i	0.696345i
$781$	7.91563e7	0.166162
$782$	1.93476e9i	4.04582i
$783$	5.26085e7i	0.109590i
$784$	0	0
$785$	2.24014e8	0.463091
$786$	5.60601e8	1.15448
$787$	− 7.24568e8i	− 1.48647i	−0.669033	−	0.743233i	$-0.733291\pi$
$787$	− 7.24568e8i	− 1.48647i	0.669033	−	0.743233i	$-0.266709\pi$
$788$	2.19462e8	0.448518
$789$	2.32891e8i	0.474156i
$790$	− 7.14438e8i	− 1.44905i
$791$	0	0
$792$	1.20277e8	0.242107
$793$	−3.50667e8	−0.703195
$794$	− 6.33107e8i	− 1.26478i
$795$	−2.31183e8	−0.460103
$796$	4.76669e8i	0.945099i
$797$	− 5.85510e7i	− 0.115654i	−0.998327	−	0.0578268i	$-0.981583\pi$
$797$	− 5.85510e7i	− 0.115654i	0.998327	−	0.0578268i	$-0.0184171\pi$
$798$	0	0
$799$	−3.91334e7	−0.0767197
$800$	2.46135e8	0.480733
$801$	9.05627e7i	0.176219i
$802$	−1.83752e8	−0.356213
$803$	− 2.26568e8i	− 0.437575i
$804$	4.02603e8i	0.774655i
$805$	0	0
$806$	−8.92017e8	−1.70360
$807$	4.89631e8	0.931641
$808$	− 4.02254e8i	− 0.762546i
$809$	5.11525e8	0.966098	0.483049	−	0.875593i	$-0.339529\pi$
$809$	5.11525e8	0.966098	0.483049	+	0.875593i	$0.339529\pi$
$810$	6.19180e7i	0.116510i
$811$	7.81509e8i	1.46511i	0.680706	+	0.732557i	$0.261673\pi$
$811$	7.81509e8i	1.46511i	−0.680706	+	0.732557i	$0.738327\pi$
$812$	0	0
$813$	−2.33101e7	−0.0433782
$814$	−8.63364e8	−1.60074
$815$	1.24348e8i	0.229703i
$816$	−1.11053e8	−0.204389
$817$	− 6.13602e8i	− 1.12518i
$818$	2.94989e8i	0.538947i
$819$	0	0
$820$	−5.16588e8	−0.936921
$821$	−5.51630e8	−0.996824	−0.498412	−	0.866940i	$-0.666083\pi$
$821$	−5.51630e8	−0.996824	−0.498412	+	0.866940i	$0.666083\pi$
$822$	− 1.86503e8i	− 0.335793i
$823$	−3.57291e8	−0.640948	−0.320474	−	0.947257i	$-0.603842\pi$
$823$	−3.57291e8	−0.640948	−0.320474	+	0.947257i	$0.603842\pi$
$824$	− 9.32690e8i	− 1.66708i
$825$	− 1.19127e8i	− 0.212152i
$826$	0	0
$827$	−4.42420e8	−0.782201	−0.391101	−	0.920348i	$-0.627906\pi$
$827$	−4.42420e8	−0.782201	−0.391101	+	0.920348i	$0.627906\pi$
$828$	−5.01922e8	−0.884188
$829$	1.18475e8i	0.207952i	0.994580	+	0.103976i	$0.0331566\pi$
$829$	1.18475e8i	0.207952i	−0.994580	+	0.103976i	$0.966843\pi$
$830$	−1.34239e8	−0.234771
$831$	3.09196e7i	0.0538804i
$832$	9.89871e8i	1.71873i
$833$	0	0
$834$	−953236.	−0.00164324
$835$	−9.19297e7	−0.157905
$836$	6.02613e8i	1.03138i
$837$	−1.05550e8	−0.180003
$838$	− 7.13274e8i	− 1.21206i
$839$	− 1.02452e9i	− 1.73474i	−0.497660	−	0.867372i	$-0.665807\pi$
$839$	− 1.02452e9i	− 1.73474i	0.497660	−	0.867372i	$-0.334193\pi$
$840$	0	0
$841$	−4.01941e8	−0.675731
$842$	1.71367e9	2.87073
$843$	5.46146e7i	0.0911645i
$844$	1.13672e9	1.89071
$845$	8.54502e7i	0.141626i
$846$	− 1.60761e7i	− 0.0265503i
$847$	0	0
$848$	1.70335e8	0.279328
$849$	−5.08888e8	−0.831570
$850$	9.54828e8i	1.55478i
$851$	1.50049e9	2.43470
$852$	− 1.64593e8i	− 0.266129i
$853$	− 1.03709e9i	− 1.67097i	−0.549517	−	0.835483i	$-0.685188\pi$
$853$	− 1.03709e9i	− 1.67097i	0.549517	−	0.835483i	$-0.314812\pi$
$854$	0	0
$855$	−1.29199e8	−0.206710
$856$	5.75426e8	0.917419
$857$	− 5.49762e8i	− 0.873438i	−0.899598	−	0.436719i	$-0.856140\pi$
$857$	− 5.49762e8i	− 0.873438i	0.899598	−	0.436719i	$-0.143860\pi$
$858$	4.10324e8	0.649629
$859$	1.42478e8i	0.224786i	0.993664	+	0.112393i	$0.0358516\pi$
$859$	1.42478e8i	0.224786i	−0.993664	+	0.112393i	$0.964148\pi$
$860$	8.01340e8i	1.25986i
$861$	0	0
$862$	1.58068e9	2.46787
$863$	−4.00833e8	−0.623637	−0.311818	−	0.950142i	$-0.600938\pi$
$863$	−4.00833e8	−0.623637	−0.311818	+	0.950142i	$0.600938\pi$
$864$	1.00317e8i	0.155537i
$865$	−4.58387e8	−0.708246
$866$	1.47007e9i	2.26351i
$867$	5.71043e8i	0.876216i
$868$	0	0
$869$	−5.60219e8	−0.853687
$870$	2.27015e8	0.344744
$871$	5.72016e8i	0.865672i
$872$	−9.46141e8	−1.42694
$873$	1.50672e8i	0.226459i
$874$	− 1.65846e9i	− 2.48410i
$875$	0	0
$876$	−4.71112e8	−0.700828
$877$	−3.60538e8	−0.534505	−0.267252	−	0.963627i	$-0.586116\pi$
$877$	−3.60538e8	−0.534505	−0.267252	+	0.963627i	$0.586116\pi$
$878$	− 1.62436e9i	− 2.39994i
$879$	−4.01642e8	−0.591387
$880$	− 5.97876e7i	− 0.0877331i
$881$	− 1.27541e9i	− 1.86519i	−0.360924	−	0.932595i	$-0.617539\pi$
$881$	− 1.27541e9i	− 1.86519i	0.360924	−	0.932595i	$-0.382461\pi$
$882$	0	0
$883$	−2.92638e8	−0.425058	−0.212529	−	0.977155i	$-0.568170\pi$
$883$	−2.92638e8	−0.425058	−0.212529	+	0.977155i	$0.568170\pi$
$884$	−2.07691e9	−3.00650
$885$	2.79325e8i	0.402977i
$886$	9.37554e8	1.34802
$887$	− 8.25244e8i	− 1.18253i	−0.806478	−	0.591264i	$-0.798629\pi$
$887$	− 8.25244e8i	− 1.18253i	0.806478	−	0.591264i	$-0.201371\pi$
$888$	7.47662e8i	1.06774i
$889$	0	0
$890$	3.90794e8	0.554342
$891$	4.85524e7	0.0686400
$892$	5.31709e8i	0.749168i
$893$	3.35447e7	0.0471053
$894$	− 3.38394e8i	− 0.473598i
$895$	9.51302e7i	0.132693i
$896$	0	0
$897$	−7.13127e8	−0.988075
$898$	1.41758e9	1.95758
$899$	3.86984e8i	0.532616i
$900$	−2.47704e8	−0.339787
$901$	− 1.45300e9i	− 1.98651i
$902$	6.41451e8i	0.874065i
$903$	0	0
$904$	1.49035e9	2.01735
$905$	−7.95908e8	−1.07378
$906$	− 5.02473e8i	− 0.675660i
$907$	−9.60696e8	−1.28755	−0.643775	−	0.765215i	$-0.722633\pi$
$907$	−9.60696e8	−1.28755	−0.643775	+	0.765215i	$0.722633\pi$
$908$	1.65700e9i	2.21343i
$909$	− 1.62378e8i	− 0.216190i
$910$	0	0
$911$	1.01677e9	1.34483	0.672413	−	0.740176i	$-0.265258\pi$
$911$	1.01677e9	1.34483	0.672413	+	0.740176i	$0.265258\pi$
$912$	9.51932e7	0.125494
$913$	1.05262e8i	0.138312i
$914$	−1.69578e8	−0.222092
$915$	1.79051e8i	0.233729i
$916$	− 4.66538e8i	− 0.607017i
$917$	0	0
$918$	−3.89158e8	−0.503035
$919$	−4.86186e8	−0.626406	−0.313203	−	0.949686i	$-0.601402\pi$
$919$	−4.86186e8	−0.626406	−0.313203	+	0.949686i	$0.601402\pi$
$920$	9.02030e8i	1.15840i
$921$	2.96015e8	0.378909
$922$	− 9.33997e7i	− 0.119166i
$923$	− 2.33852e8i	− 0.297397i
$924$	0	0
$925$	7.40511e8	0.935635
$926$	−1.90693e9	−2.40161
$927$	− 3.76500e8i	− 0.472635i
$928$	3.67800e8	0.460223
$929$	9.01075e8i	1.12386i	0.827183	+	0.561932i	$0.189942\pi$
$929$	9.01075e8i	1.12386i	−0.827183	+	0.561932i	$0.810058\pi$
$930$	4.55465e8i	0.566247i
$931$	0	0
$932$	1.37994e9	1.70456
$933$	−5.04657e8	−0.621372
$934$	− 1.11812e9i	− 1.37229i
$935$	−5.10005e8	−0.623936
$936$	− 3.55336e8i	− 0.433323i
$937$	− 6.19442e8i	− 0.752977i	−0.926421	−	0.376489i	$-0.877131\pi$
$937$	− 6.19442e8i	− 0.752977i	0.926421	−	0.376489i	$-0.122869\pi$
$938$	0	0
$939$	5.06515e8	0.611781
$940$	−4.38080e7	−0.0527437
$941$	4.95727e8i	0.594941i	0.954731	+	0.297470i	$0.0961429\pi$
$941$	4.95727e8i	0.594941i	−0.954731	+	0.297470i	$0.903857\pi$
$942$	−5.78387e8	−0.691936
$943$	− 1.11482e9i	− 1.32944i
$944$	− 2.05805e8i	− 0.244647i
$945$	0	0
$946$	9.95029e8	1.17534
$947$	1.16940e9	1.37693	0.688467	−	0.725267i	$-0.258284\pi$
$947$	1.16940e9	1.37693	0.688467	+	0.725267i	$0.258284\pi$
$948$	1.16488e9i	1.36728i
$949$	−6.69353e8	−0.783171
$950$	− 8.18469e8i	− 0.954622i
$951$	2.54760e8i	0.296203i
$952$	0	0
$953$	−2.23017e8	−0.257667	−0.128834	−	0.991666i	$-0.541123\pi$
$953$	−2.23017e8	−0.257667	−0.128834	+	0.991666i	$0.541123\pi$
$954$	5.96898e8	0.687472
$955$	6.03332e8i	0.692702i
$956$	8.27347e8	0.946921
$957$	− 1.78011e8i	− 0.203101i
$958$	2.10381e9i	2.39282i
$959$	0	0
$960$	5.05429e8	0.571277
$961$	1.11088e8	0.125169
$962$	2.55064e9i	2.86500i
$963$	2.32283e8	0.260098
$964$	− 2.14731e9i	− 2.39697i
$965$	− 5.64616e8i	− 0.628306i
$966$	0	0
$967$	4.77842e8	0.528451	0.264226	−	0.964461i	$-0.414884\pi$
$967$	4.77842e8	0.528451	0.264226	+	0.964461i	$0.414884\pi$
$968$	6.59455e8	0.727041
$969$	− 8.12025e8i	− 0.892479i
$970$	6.50175e8	0.712386
$971$	1.00070e9i	1.09306i	0.837438	+	0.546532i	$0.184052\pi$
$971$	1.00070e9i	1.09306i	−0.837438	+	0.546532i	$0.815948\pi$
$972$	− 1.00957e8i	− 0.109935i
$973$	0	0
$974$	−1.81871e9	−1.96827
$975$	−3.51937e8	−0.379709
$976$	− 1.31924e8i	− 0.141897i
$977$	−5.31334e8	−0.569749	−0.284875	−	0.958565i	$-0.591952\pi$
$977$	−5.31334e8	−0.569749	−0.284875	+	0.958565i	$0.591952\pi$
$978$	− 3.21057e8i	− 0.343215i
$979$	− 3.06437e8i	− 0.326583i
$980$	0	0
$981$	−3.81929e8	−0.404554
$982$	5.16373e8	0.545291
$983$	− 6.97122e8i	− 0.733919i	−0.930237	−	0.366959i	$-0.880399\pi$
$983$	− 6.97122e8i	− 0.733919i	0.930237	−	0.366959i	$-0.119601\pi$
$984$	5.55489e8	0.583029
$985$	− 1.59210e8i	− 0.166595i
$986$	1.42680e9i	1.48844i
$987$	0	0
$988$	1.78031e9	1.84597
$989$	−1.72932e9	−1.78767
$990$	− 2.09512e8i	− 0.215925i
$991$	7.35179e8	0.755391	0.377696	−	0.925930i	$-0.376717\pi$
$991$	7.35179e8	0.755391	0.377696	+	0.925930i	$0.376717\pi$
$992$	7.37926e8i	0.755923i
$993$	− 8.06812e8i	− 0.823995i
$994$	0	0
$995$	3.45803e8	0.351043
$996$	2.18876e8	0.221523
$997$	5.60573e8i	0.565648i	0.959172	+	0.282824i	$0.0912713\pi$
$997$	5.60573e8i	0.565648i	−0.959172	+	0.282824i	$0.908729\pi$
$998$	−3.01744e8	−0.303561
$999$	3.01809e8i	0.302717i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.7.d.a.97.1		8
3.2	odd	2		441.7.d.d.244.8		8
7.2	even	3		21.7.f.b.10.4	✓	8
7.3	odd	6		21.7.f.b.19.4	yes	8
7.4	even	3		147.7.f.a.19.4		8
7.5	odd	6		147.7.f.a.31.4		8
7.6	odd	2	inner	147.7.d.a.97.2		8
21.2	odd	6		63.7.m.c.10.1		8
21.17	even	6		63.7.m.c.19.1		8
21.20	even	2		441.7.d.d.244.7		8
28.3	even	6		336.7.bh.b.145.2		8
28.23	odd	6		336.7.bh.b.241.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.b.10.4	✓	8	7.2	even	3
21.7.f.b.19.4	yes	8	7.3	odd	6
63.7.m.c.10.1		8	21.2	odd	6
63.7.m.c.19.1		8	21.17	even	6
147.7.d.a.97.1		8	1.1	even	1	trivial
147.7.d.a.97.2		8	7.6	odd	2	inner
147.7.f.a.19.4		8	7.4	even	3
147.7.f.a.31.4		8	7.5	odd	6
336.7.bh.b.145.2		8	28.3	even	6
336.7.bh.b.241.2		8	28.23	odd	6
441.7.d.d.244.7		8	21.20	even	2
441.7.d.d.244.8		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)

\(f(q)\)	\(=\)	\(q-13.1787 q^{2} -15.5885i q^{3} +109.678 q^{4} -79.5668i q^{5} +205.435i q^{6} -601.976 q^{8} -243.000 q^{9} +O(q^{10})\)	\(q-13.1787 q^{2} -15.5885i q^{3} +109.678 q^{4} -79.5668i q^{5} +205.435i q^{6} -601.976 q^{8} -243.000 q^{9} +1048.59i q^{10} +822.239 q^{11} -1709.71i q^{12} -2429.15i q^{13} -1240.32 q^{15} +913.863 q^{16} -7795.51i q^{17} +3202.42 q^{18} +6682.23i q^{19} -8726.73i q^{20} -10836.0 q^{22} +18832.6 q^{23} +9383.87i q^{24} +9294.12 q^{25} +32013.0i q^{26} +3788.00i q^{27} +13888.2 q^{29} +16345.9 q^{30} +27864.2i q^{31} +26482.9 q^{32} -12817.4i q^{33} +102735. i q^{34} -26651.7 q^{36} +79675.3 q^{37} -88063.1i q^{38} -37866.6 q^{39} +47897.3i q^{40} -59196.1i q^{41} -91825.9 q^{43} +90181.5 q^{44} +19334.7i q^{45} -248189. q^{46} -5019.99i q^{47} -14245.7i q^{48} -122484. q^{50} -121520. q^{51} -266424. i q^{52} +186390. q^{53} -49920.8i q^{54} -65422.9i q^{55} +104166. q^{57} -183029. q^{58} -225203. i q^{59} -136036. q^{60} -144358. i q^{61} -367214. i q^{62} -407497. q^{64} -193279. q^{65} +168917. i q^{66} -235480. q^{67} -854996. i q^{68} -293571. i q^{69} +96269.3 q^{71} +146280. q^{72} -275551. i q^{73} -1.05002e6 q^{74} -144881. i q^{75} +732893. i q^{76} +499033. q^{78} -681334. q^{79} -72713.2i q^{80} +59049.0 q^{81} +780127. i q^{82} +128019. i q^{83} -620264. q^{85} +1.21015e6 q^{86} -216496. i q^{87} -494968. q^{88} -372686. i q^{89} -254807. i q^{90} +2.06552e6 q^{92} +434360. q^{93} +66156.9i q^{94} +531684. q^{95} -412828. i q^{96} -620049. i q^{97} -199804. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{2} + 346 q^{4} - 454 q^{8} - 1944 q^{9}+O(q^{10}) \) 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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