LMFDB - Embedded newform 147.7.d.a.97.4

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			97.4
Root			$-2.30325 - 3.98935i$ of defining polynomial
Character	$\chi$	$=$	147.97
Dual form			147.7.d.a.97.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.60650 q^{2} +15.5885i q^{3} -50.9932 q^{4} -83.0589i q^{5} -56.2198i q^{6} +414.723 q^{8} -243.000 q^{9} +O(q^{10})$	\(q-3.60650 q^{2} +15.5885i q^{3} -50.9932 q^{4} -83.0589i q^{5} -56.2198i q^{6} +414.723 q^{8} -243.000 q^{9} +299.552i q^{10} -442.608 q^{11} -794.905i q^{12} -696.494i q^{13} +1294.76 q^{15} +1767.86 q^{16} -6289.93i q^{17} +876.380 q^{18} +2687.64i q^{19} +4235.44i q^{20} +1596.27 q^{22} +15770.6 q^{23} +6464.89i q^{24} +8726.22 q^{25} +2511.91i q^{26} -3788.00i q^{27} -23274.5 q^{29} -4669.55 q^{30} +47547.1i q^{31} -32918.1 q^{32} -6899.58i q^{33} +22684.6i q^{34} +12391.3 q^{36} -10159.8 q^{37} -9692.96i q^{38} +10857.3 q^{39} -34446.4i q^{40} -38165.4i q^{41} -151197. q^{43} +22570.0 q^{44} +20183.3i q^{45} -56876.7 q^{46} +50279.2i q^{47} +27558.3i q^{48} -31471.1 q^{50} +98050.2 q^{51} +35516.4i q^{52} -199556. q^{53} +13661.4i q^{54} +36762.6i q^{55} -41896.1 q^{57} +83939.6 q^{58} +387225. i q^{59} -66023.9 q^{60} +11782.0i q^{61} -171479. i q^{62} +5575.73 q^{64} -57850.0 q^{65} +24883.3i q^{66} -384276. q^{67} +320743. i q^{68} +245840. i q^{69} +156126. q^{71} -100778. q^{72} +375539. i q^{73} +36641.3 q^{74} +136028. i q^{75} -137051. i q^{76} -39156.7 q^{78} +33183.6 q^{79} -146837. i q^{80} +59049.0 q^{81} +137644. i q^{82} +984986. i q^{83} -522434. q^{85} +545292. q^{86} -362814. i q^{87} -183560. q^{88} +262613. i q^{89} -72791.1i q^{90} -804193. q^{92} -741187. q^{93} -181332. i q^{94} +223232. q^{95} -513142. i q^{96} -575147. i q^{97} +107554. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.60650	−0.450813	−0.225406	−	0.974265i	$-0.572371\pi$
$2$	−3.60650	−0.450813	−0.225406	+	0.974265i	$0.572371\pi$
$3$	15.5885i	0.577350i
$3$	15.5885i	0.577350i
$4$	−50.9932	−0.796768
$5$	− 83.0589i	− 0.664471i	−0.943196	−	0.332236i	$-0.892197\pi$
$5$	− 83.0589i	− 0.664471i	0.943196	−	0.332236i	$-0.107803\pi$
$6$	− 56.2198i	− 0.260277i
$7$	0	0
$7$	0	0
$8$	414.723	0.810006
$9$	−243.000	−0.333333
$10$	299.552i	0.299552i
$11$	−442.608	−0.332538	−0.166269	−	0.986080i	$-0.553172\pi$
$11$	−442.608	−0.332538	−0.166269	+	0.986080i	$0.553172\pi$
$12$	− 794.905i	− 0.460014i
$13$	− 696.494i	− 0.317020i	−0.987357	−	0.158510i	$-0.949331\pi$
$13$	− 696.494i	− 0.317020i	0.987357	−	0.158510i	$-0.0506691\pi$
$14$	0	0
$15$	1294.76	0.383633
$16$	1767.86	0.431607
$17$	− 6289.93i	− 1.28026i	−0.768266	−	0.640131i	$-0.778880\pi$
$17$	− 6289.93i	− 1.28026i	0.768266	−	0.640131i	$-0.221120\pi$
$18$	876.380	0.150271
$19$	2687.64i	0.391841i	0.980620	+	0.195920i	$0.0627694\pi$
$19$	2687.64i	0.391841i	−0.980620	+	0.195920i	$0.937231\pi$
$20$	4235.44i	0.529430i
$21$	0	0
$22$	1596.27	0.149912
$23$	15770.6	1.29618	0.648090	−	0.761564i	$-0.275568\pi$
$23$	15770.6	1.29618	0.648090	+	0.761564i	$0.275568\pi$
$24$	6464.89i	0.467657i
$25$	8726.22	0.558478
$26$	2511.91i	0.142917i
$27$	− 3788.00i	− 0.192450i
$28$	0	0
$29$	−23274.5	−0.954304	−0.477152	−	0.878821i	$-0.658331\pi$
$29$	−23274.5	−0.954304	−0.477152	+	0.878821i	$0.658331\pi$
$30$	−4669.55	−0.172946
$31$	47547.1i	1.59602i	0.602642	+	0.798012i	$0.294115\pi$
$31$	47547.1i	1.59602i	−0.602642	+	0.798012i	$0.705885\pi$
$32$	−32918.1	−1.00458
$33$	− 6899.58i	− 0.191991i
$34$	22684.6i	0.577158i
$35$	0	0
$36$	12391.3	0.265589
$37$	−10159.8	−0.200576	−0.100288	−	0.994958i	$-0.531976\pi$
$37$	−10159.8	−0.200576	−0.100288	+	0.994958i	$0.531976\pi$
$38$	− 9692.96i	− 0.176647i
$39$	10857.3	0.183032
$40$	− 34446.4i	− 0.538226i
$41$	− 38165.4i	− 0.553756i	−0.960905	−	0.276878i	$-0.910700\pi$
$41$	− 38165.4i	− 0.553756i	0.960905	−	0.276878i	$-0.0892998\pi$
$42$	0	0
$43$	−151197.	−1.90168	−0.950841	−	0.309679i	$-0.899779\pi$
$43$	−151197.	−1.90168	−0.950841	+	0.309679i	$0.899779\pi$
$44$	22570.0	0.264956
$45$	20183.3i	0.221490i
$46$	−56876.7	−0.584334
$47$	50279.2i	0.484278i	0.970242	+	0.242139i	$0.0778491\pi$
$47$	50279.2i	0.484278i	−0.970242	+	0.242139i	$0.922151\pi$
$48$	27558.3i	0.249189i
$49$	0	0
$50$	−31471.1	−0.251769
$51$	98050.2	0.739159
$52$	35516.4i	0.252592i
$53$	−199556.	−1.34041	−0.670206	−	0.742175i	$-0.733794\pi$
$53$	−199556.	−1.34041	−0.670206	+	0.742175i	$0.733794\pi$
$54$	13661.4i	0.0867589i
$55$	36762.6i	0.220962i
$56$	0	0
$57$	−41896.1	−0.226229
$58$	83939.6	0.430212
$59$	387225.i	1.88542i	0.333619	+	0.942708i	$0.391730\pi$
$59$	387225.i	1.88542i	−0.333619	+	0.942708i	$0.608270\pi$
$60$	−66023.9	−0.305666
$61$	11782.0i	0.0519073i	0.999663	+	0.0259536i	$0.00826223\pi$
$61$	11782.0i	0.0519073i	−0.999663	+	0.0259536i	$0.991738\pi$
$62$	− 171479.i	− 0.719508i
$63$	0	0
$64$	5575.73	0.0212697
$65$	−57850.0	−0.210651
$66$	24883.3i	0.0865519i
$67$	−384276.	−1.27767	−0.638834	−	0.769344i	$-0.720583\pi$
$67$	−384276.	−1.27767	−0.638834	+	0.769344i	$0.720583\pi$
$68$	320743.i	1.02007i
$69$	245840.i	0.748350i
$70$	0	0
$71$	156126.	0.436213	0.218107	−	0.975925i	$-0.430012\pi$
$71$	156126.	0.436213	0.218107	+	0.975925i	$0.430012\pi$
$72$	−100778.	−0.270002
$73$	375539.i	0.965355i	0.875798	+	0.482677i	$0.160336\pi$
$73$	375539.i	0.965355i	−0.875798	+	0.482677i	$0.839664\pi$
$74$	36641.3	0.0904223
$75$	136028.i	0.322437i
$76$	− 137051.i	− 0.312206i
$77$	0	0
$78$	−39156.7	−0.0825130
$79$	33183.6	0.0673042	0.0336521	−	0.999434i	$-0.489286\pi$
$79$	33183.6	0.0673042	0.0336521	+	0.999434i	$0.489286\pi$
$80$	− 146837.i	− 0.286791i
$81$	59049.0	0.111111
$82$	137644.i	0.249640i
$83$	984986.i	1.72264i	0.508059	+	0.861322i	$0.330363\pi$
$83$	984986.i	1.72264i	−0.508059	+	0.861322i	$0.669637\pi$
$84$	0	0
$85$	−522434.	−0.850697
$86$	545292.	0.857302
$87$	− 362814.i	− 0.550968i
$88$	−183560.	−0.269358
$89$	262613.i	0.372517i	0.982501	+	0.186259i	$0.0596362\pi$
$89$	262613.i	0.372517i	−0.982501	+	0.186259i	$0.940364\pi$
$90$	− 72791.1i	− 0.0998507i
$91$	0	0
$92$	−804193.	−1.03275
$93$	−741187.	−0.921465
$94$	− 181332.i	− 0.218319i
$95$	223232.	0.260367
$96$	− 513142.i	− 0.579994i
$97$	− 575147.i	− 0.630179i	−0.949062	−	0.315089i	$-0.897966\pi$
$97$	− 575147.i	− 0.630179i	0.949062	−	0.315089i	$-0.102034\pi$
$98$	0	0
$99$	107554.	0.110846
$100$	−444977.	−0.444977
$101$	732875.i	0.711321i	0.934615	+	0.355661i	$0.115744\pi$
$101$	732875.i	0.711321i	−0.934615	+	0.355661i	$0.884256\pi$
$102$	−353618.	−0.333222
$103$	− 1.04871e6i	− 0.959715i	−0.877346	−	0.479858i	$-0.840688\pi$
$103$	− 1.04871e6i	− 0.959715i	0.877346	−	0.479858i	$-0.159312\pi$
$104$	− 288852.i	− 0.256788i
$105$	0	0
$106$	719700.	0.604274
$107$	1.17482e6	0.959006	0.479503	−	0.877540i	$-0.340817\pi$
$107$	1.17482e6	0.959006	0.479503	+	0.877540i	$0.340817\pi$
$108$	193162.i	0.153338i
$109$	734090.	0.566852	0.283426	−	0.958994i	$-0.408529\pi$
$109$	734090.	0.566852	0.283426	+	0.958994i	$0.408529\pi$
$110$	− 132584.i	− 0.0996125i
$111$	− 158375.i	− 0.115803i
$112$	0	0
$113$	2.04925e6	1.42023	0.710116	−	0.704085i	$-0.248643\pi$
$113$	2.04925e6	1.42023	0.710116	+	0.704085i	$0.248643\pi$
$114$	151098.	0.101987
$115$	− 1.30989e6i	− 0.861274i
$116$	1.18684e6	0.760359
$117$	169248.i	0.105673i
$118$	− 1.39653e6i	− 0.849969i
$119$	0	0
$120$	536967.	0.310745
$121$	−1.57566e6	−0.889418
$122$	− 42491.7i	− 0.0234005i
$123$	594940.	0.319711
$124$	− 2.42458e6i	− 1.27166i
$125$	− 2.02259e6i	− 1.03556i
$126$	0	0
$127$	−1.64688e6	−0.803991	−0.401995	−	0.915642i	$-0.631683\pi$
$127$	−1.64688e6	−0.803991	−0.401995	+	0.915642i	$0.631683\pi$
$128$	2.08665e6	0.994991
$129$	− 2.35693e6i	− 1.09794i
$130$	208636.	0.0949641
$131$	2.06081e6i	0.916695i	0.888773	+	0.458348i	$0.151559\pi$
$131$	2.06081e6i	0.916695i	−0.888773	+	0.458348i	$0.848441\pi$
$132$	351831.i	0.152972i
$133$	0	0
$134$	1.38589e6	0.575989
$135$	−314627.	−0.127878
$136$	− 2.60858e6i	− 1.03702i
$137$	3.22920e6	1.25584	0.627919	−	0.778279i	$-0.283907\pi$
$137$	3.22920e6	1.25584	0.627919	+	0.778279i	$0.283907\pi$
$138$	− 886620.i	− 0.337365i
$139$	4.06719e6i	1.51443i	0.653163	+	0.757217i	$0.273442\pi$
$139$	4.06719e6i	1.51443i	−0.653163	+	0.757217i	$0.726558\pi$
$140$	0	0
$141$	−783776.	−0.279598
$142$	−563067.	−0.196650
$143$	308274.i	0.105421i
$144$	−429591.	−0.143869
$145$	1.93316e6i	0.634108i
$146$	− 1.35438e6i	− 0.435194i
$147$	0	0
$148$	518080.	0.159813
$149$	−2.79474e6	−0.844855	−0.422427	−	0.906397i	$-0.638822\pi$
$149$	−2.79474e6	−0.844855	−0.422427	+	0.906397i	$0.638822\pi$
$150$	− 490586.i	− 0.145359i
$151$	603099.	0.175169	0.0875846	−	0.996157i	$-0.472085\pi$
$151$	603099.	0.175169	0.0875846	+	0.996157i	$0.472085\pi$
$152$	1.11462e6i	0.317393i
$153$	1.52845e6i	0.426754i
$154$	0	0
$155$	3.94921e6	1.06051
$156$	−553646.	−0.145834
$157$	− 1.42909e6i	− 0.369285i	−0.982806	−	0.184642i	$-0.940887\pi$
$157$	− 1.42909e6i	− 0.369285i	0.982806	−	0.184642i	$-0.0591127\pi$
$158$	−119677.	−0.0303416
$159$	− 3.11078e6i	− 0.773887i
$160$	2.73414e6i	0.667514i
$161$	0	0
$162$	−212960.	−0.0500903
$163$	−5.57288e6	−1.28682	−0.643408	−	0.765523i	$-0.722480\pi$
$163$	−5.57288e6	−1.28682	−0.643408	+	0.765523i	$0.722480\pi$
$164$	1.94617e6i	0.441215i
$165$	−573072.	−0.127572
$166$	− 3.55235e6i	− 0.776590i
$167$	− 2.24388e6i	− 0.481781i	−0.970552	−	0.240890i	$-0.922561\pi$
$167$	− 2.24388e6i	− 0.481781i	0.970552	−	0.240890i	$-0.0774394\pi$
$168$	0	0
$169$	4.34171e6	0.899498
$170$	1.88416e6	0.383505
$171$	− 653096.i	− 0.130614i
$172$	7.71002e6	1.51520
$173$	6.88044e6i	1.32886i	0.747352	+	0.664428i	$0.231325\pi$
$173$	6.88044e6i	1.32886i	−0.747352	+	0.664428i	$0.768675\pi$
$174$	1.30849e6i	0.248383i
$175$	0	0
$176$	−782471.	−0.143526
$177$	−6.03624e6	−1.08855
$178$	− 947114.i	− 0.167935i
$179$	−7.89287e6	−1.37618	−0.688091	−	0.725625i	$-0.741551\pi$
$179$	−7.89287e6	−1.37618	−0.688091	+	0.725625i	$0.741551\pi$
$180$	− 1.02921e6i	− 0.176477i
$181$	− 2.63639e6i	− 0.444604i	−0.974978	−	0.222302i	$-0.928643\pi$
$181$	− 2.63639e6i	− 0.444604i	0.974978	−	0.222302i	$-0.0713571\pi$
$182$	0	0
$183$	−183663.	−0.0299687
$184$	6.54043e6	1.04991
$185$	843861.i	0.133277i
$186$	2.67309e6	0.415408
$187$	2.78397e6i	0.425736i
$188$	− 2.56390e6i	− 0.385858i
$189$	0	0
$190$	−805087.	−0.117377
$191$	1.23424e7	1.77133	0.885665	−	0.464325i	$-0.153703\pi$
$191$	1.23424e7	1.77133	0.885665	+	0.464325i	$0.153703\pi$
$192$	86917.0i	0.0122801i
$193$	−1.33923e7	−1.86287	−0.931435	−	0.363908i	$-0.881442\pi$
$193$	−1.33923e7	−1.86287	−0.931435	+	0.363908i	$0.881442\pi$
$194$	2.07427e6i	0.284092i
$195$	− 901793.i	− 0.121619i
$196$	0	0
$197$	−9.42468e6	−1.23273	−0.616365	−	0.787460i	$-0.711396\pi$
$197$	−9.42468e6	−1.23273	−0.616365	+	0.787460i	$0.711396\pi$
$198$	−387893.	−0.0499708
$199$	5.67696e6i	0.720372i	0.932881	+	0.360186i	$0.117287\pi$
$199$	5.67696e6i	0.720372i	−0.932881	+	0.360186i	$0.882713\pi$
$200$	3.61896e6	0.452370
$201$	− 5.99026e6i	− 0.737662i
$202$	− 2.64311e6i	− 0.320672i
$203$	0	0
$204$	−4.99989e6	−0.588939
$205$	−3.16998e6	−0.367955
$206$	3.78216e6i	0.432652i
$207$	−3.83226e6	−0.432060
$208$	− 1.23131e6i	− 0.136828i
$209$	− 1.18957e6i	− 0.130302i
$210$	0	0
$211$	1.05196e6	0.111983	0.0559914	−	0.998431i	$-0.482168\pi$
$211$	1.05196e6	0.111983	0.0559914	+	0.998431i	$0.482168\pi$
$212$	1.01760e7	1.06800
$213$	2.43376e6i	0.251848i
$214$	−4.23700e6	−0.432332
$215$	1.25583e7i	1.26361i
$216$	− 1.57097e6i	− 0.155886i
$217$	0	0
$218$	−2.64750e6	−0.255544
$219$	−5.85408e6	−0.557348
$220$	− 1.87464e6i	− 0.176055i
$221$	−4.38089e6	−0.405869
$222$	571181.i	0.0522053i
$223$	9.96615e6i	0.898696i	0.893357	+	0.449348i	$0.148344\pi$
$223$	9.96615e6i	0.898696i	−0.893357	+	0.449348i	$0.851656\pi$
$224$	0	0
$225$	−2.12047e6	−0.186159
$226$	−7.39061e6	−0.640258
$227$	1.84709e7i	1.57910i	0.613684	+	0.789552i	$0.289687\pi$
$227$	1.84709e7i	1.57910i	−0.613684	+	0.789552i	$0.710313\pi$
$228$	2.13641e6	0.180252
$229$	− 1.36157e7i	− 1.13379i	−0.823790	−	0.566896i	$-0.808144\pi$
$229$	− 1.36157e7i	− 1.13379i	0.823790	−	0.566896i	$-0.191856\pi$
$230$	4.72412e6i	0.388273i
$231$	0	0
$232$	−9.65248e6	−0.772992
$233$	10206.0	0.000806843 0	0.000403422	−	1.00000i	$-0.499872\pi$
$233$	10206.0	0.000806843 0	0.000403422		1.00000i	$0.499872\pi$
$234$	− 610393.i	− 0.0476389i
$235$	4.17614e6	0.321789
$236$	− 1.97458e7i	− 1.50224i
$237$	517281.i	0.0388581i
$238$	0	0
$239$	2.49567e6	0.182807	0.0914037	−	0.995814i	$-0.470865\pi$
$239$	2.49567e6	0.182807	0.0914037	+	0.995814i	$0.470865\pi$
$240$	2.28896e6	0.165579
$241$	− 5.47041e6i	− 0.390813i	−0.980722	−	0.195407i	$-0.937397\pi$
$241$	− 5.47041e6i	− 0.390813i	0.980722	−	0.195407i	$-0.0626026\pi$
$242$	5.68261e6	0.400961
$243$	920483.i	0.0641500i
$244$	− 600800.i	− 0.0413581i
$245$	0	0
$246$	−2.14565e6	−0.144130
$247$	1.87192e6	0.124222
$248$	1.97189e7i	1.29279i
$249$	−1.53544e7	−0.994569
$250$	7.29446e6i	0.466845i
$251$	− 2.18424e6i	− 0.138127i	−0.997612	−	0.0690637i	$-0.977999\pi$
$251$	− 2.18424e6i	− 0.138127i	0.997612	−	0.0690637i	$-0.0220012\pi$
$252$	0	0
$253$	−6.98020e6	−0.431029
$254$	5.93948e6	0.362449
$255$	− 8.14395e6i	− 0.491150i
$256$	−7.88234e6	−0.469824
$257$	3.14815e7i	1.85463i	0.374287	+	0.927313i	$0.377887\pi$
$257$	3.14815e7i	1.85463i	−0.374287	+	0.927313i	$0.622113\pi$
$258$	8.50027e6i	0.494964i
$259$	0	0
$260$	2.94996e6	0.167840
$261$	5.65571e6	0.318101
$262$	− 7.43233e6i	− 0.413258i
$263$	6.57763e6	0.361578	0.180789	−	0.983522i	$-0.442135\pi$
$263$	6.57763e6	0.361578	0.180789	+	0.983522i	$0.442135\pi$
$264$	− 2.86141e6i	− 0.155514i
$265$	1.65749e7i	0.890665i
$266$	0	0
$267$	−4.09373e6	−0.215073
$268$	1.95954e7	1.01801
$269$	219878.i	0.0112960i	0.999984	+	0.00564801i	$0.00179783\pi$
$269$	219878.i	0.0112960i	−0.999984	+	0.00564801i	$0.998202\pi$
$270$	1.13470e6	0.0576488
$271$	2.78378e7i	1.39871i	0.714776	+	0.699354i	$0.246529\pi$
$271$	2.78378e7i	1.39871i	−0.714776	+	0.699354i	$0.753471\pi$
$272$	− 1.11197e7i	− 0.552570i
$273$	0	0
$274$	−1.16461e7	−0.566147
$275$	−3.86229e6	−0.185715
$276$	− 1.25361e7i	− 0.596261i
$277$	−5.75450e6	−0.270750	−0.135375	−	0.990794i	$-0.543224\pi$
$277$	−5.75450e6	−0.270750	−0.135375	+	0.990794i	$0.543224\pi$
$278$	− 1.46683e7i	− 0.682726i
$279$	− 1.15540e7i	− 0.532008i
$280$	0	0
$281$	1.75833e7	0.792467	0.396233	−	0.918150i	$-0.370317\pi$
$281$	1.75833e7	0.792467	0.396233	+	0.918150i	$0.370317\pi$
$282$	2.82669e6	0.126046
$283$	1.47184e7i	0.649386i	0.945820	+	0.324693i	$0.105261\pi$
$283$	1.47184e7i	0.649386i	−0.945820	+	0.324693i	$0.894739\pi$
$284$	−7.96134e6	−0.347561
$285$	3.47985e6i	0.150323i
$286$	− 1.11179e6i	− 0.0475253i
$287$	0	0
$288$	7.99909e6	0.334860
$289$	−1.54256e7	−0.639070
$290$	− 6.97193e6i	− 0.285864i
$291$	8.96565e6	0.363834
$292$	− 1.91499e7i	− 0.769164i
$293$	3.49743e6i	0.139042i	0.997580	+	0.0695210i	$0.0221471\pi$
$293$	3.49743e6i	0.139042i	−0.997580	+	0.0695210i	$0.977853\pi$
$294$	0	0
$295$	3.21625e7	1.25280
$296$	−4.21350e6	−0.162468
$297$	1.67660e6i	0.0639970i
$298$	1.00792e7	0.380871
$299$	− 1.09841e7i	− 0.410915i
$300$	− 6.93651e6i	− 0.256908i
$301$	0	0
$302$	−2.17508e6	−0.0789685
$303$	−1.14244e7	−0.410681
$304$	4.75138e6i	0.169121i
$305$	978597.	0.0344909
$306$	− 5.51236e6i	− 0.192386i
$307$	− 3.99694e7i	− 1.38138i	−0.723152	−	0.690689i	$-0.757308\pi$
$307$	− 3.99694e7i	− 1.38138i	0.723152	−	0.690689i	$-0.242692\pi$
$308$	0	0
$309$	1.63477e7	0.554092
$310$	−1.42428e7	−0.478092
$311$	− 3.33495e7i	− 1.10868i	−0.832289	−	0.554342i	$-0.812970\pi$
$311$	− 3.33495e7i	− 1.10868i	0.832289	−	0.554342i	$-0.187030\pi$
$312$	4.50276e6	0.148257
$313$	− 1.87899e7i	− 0.612761i	−0.951909	−	0.306381i	$-0.900882\pi$
$313$	− 1.87899e7i	− 0.612761i	0.951909	−	0.306381i	$-0.0991180\pi$
$314$	5.15402e6i	0.166478i
$315$	0	0
$316$	−1.69214e6	−0.0536259
$317$	−2.03972e7	−0.640313	−0.320156	−	0.947365i	$-0.603735\pi$
$317$	−2.03972e7	−0.640313	−0.320156	+	0.947365i	$0.603735\pi$
$318$	1.12190e7i	0.348878i
$319$	1.03015e7	0.317343
$320$	− 463114.i	− 0.0141331i
$321$	1.83137e7i	0.553682i
$322$	0	0
$323$	1.69050e7	0.501659
$324$	−3.01109e6	−0.0885298
$325$	− 6.07776e6i	− 0.177049i
$326$	2.00986e7	0.580113
$327$	1.14433e7i	0.327272i
$328$	− 1.58281e7i	− 0.448545i
$329$	0	0
$330$	2.06678e6	0.0575113
$331$	−2.13549e7	−0.588862	−0.294431	−	0.955673i	$-0.595130\pi$
$331$	−2.13549e7	−0.588862	−0.294431	+	0.955673i	$0.595130\pi$
$332$	− 5.02275e7i	− 1.37255i
$333$	2.46883e6	0.0668588
$334$	8.09254e6i	0.217193i
$335$	3.19175e7i	0.848974i
$336$	0	0
$337$	−1.98824e7	−0.519493	−0.259746	−	0.965677i	$-0.583639\pi$
$337$	−1.98824e7	−0.519493	−0.259746	+	0.965677i	$0.583639\pi$
$338$	−1.56584e7	−0.405505
$339$	3.19446e7i	0.819971i
$340$	2.66406e7	0.677808
$341$	− 2.10448e7i	− 0.530739i
$342$	2.35539e6i	0.0588823i
$343$	0	0
$344$	−6.27049e7	−1.54037
$345$	2.04192e7	0.497257
$346$	− 2.48143e7i	− 0.599065i
$347$	−3.32395e7	−0.795548	−0.397774	−	0.917483i	$-0.630217\pi$
$347$	−3.32395e7	−0.795548	−0.397774	+	0.917483i	$0.630217\pi$
$348$	1.85010e7i	0.438994i
$349$	2.57850e7i	0.606584i	0.952898	+	0.303292i	$0.0980858\pi$
$349$	2.57850e7i	0.606584i	−0.952898	+	0.303292i	$0.901914\pi$
$350$	0	0
$351$	−2.63832e6	−0.0610106
$352$	1.45698e7	0.334061
$353$	− 5.56607e7i	− 1.26539i	−0.774401	−	0.632695i	$-0.781949\pi$
$353$	− 5.56607e7i	− 1.26539i	0.774401	−	0.632695i	$-0.218051\pi$
$354$	2.17697e7	0.490730
$355$	− 1.29676e7i	− 0.289851i
$356$	− 1.33915e7i	− 0.296810i
$357$	0	0
$358$	2.84656e7	0.620400
$359$	−1.61743e7	−0.349576	−0.174788	−	0.984606i	$-0.555924\pi$
$359$	−1.61743e7	−0.349576	−0.174788	+	0.984606i	$0.555924\pi$
$360$	8.37048e6i	0.179409i
$361$	3.98225e7	0.846461
$362$	9.50813e6i	0.200433i
$363$	− 2.45621e7i	− 0.513506i
$364$	0	0
$365$	3.11919e7	0.641451
$366$	662380.	0.0135103
$367$	1.12274e7i	0.227133i	0.993530	+	0.113566i	$0.0362274\pi$
$367$	1.12274e7i	0.227133i	−0.993530	+	0.113566i	$0.963773\pi$
$368$	2.78803e7	0.559441
$369$	9.27419e6i	0.184585i
$370$	− 3.04339e6i	− 0.0600830i
$371$	0	0
$372$	3.77954e7	0.734194
$373$	3.99976e7	0.770739	0.385369	−	0.922762i	$-0.374074\pi$
$373$	3.99976e7	0.770739	0.385369	+	0.922762i	$0.374074\pi$
$374$	− 1.00404e7i	− 0.191927i
$375$	3.15290e7	0.597883
$376$	2.08519e7i	0.392268i
$377$	1.62106e7i	0.302534i
$378$	0	0
$379$	2.92098e7	0.536551	0.268276	−	0.963342i	$-0.413546\pi$
$379$	2.92098e7	0.536551	0.268276	+	0.963342i	$0.413546\pi$
$380$	−1.13833e7	−0.207452
$381$	− 2.56723e7i	− 0.464184i
$382$	−4.45129e7	−0.798538
$383$	− 4.58625e7i	− 0.816321i	−0.912910	−	0.408161i	$-0.866170\pi$
$383$	− 4.58625e7i	− 0.816321i	0.912910	−	0.408161i	$-0.133830\pi$
$384$	3.25276e7i	0.574458i
$385$	0	0
$386$	4.82993e7	0.839805
$387$	3.67409e7	0.633894
$388$	2.93286e7i	0.502106i
$389$	1.54486e7	0.262446	0.131223	−	0.991353i	$-0.458110\pi$
$389$	1.54486e7	0.262446	0.131223	+	0.991353i	$0.458110\pi$
$390$	3.25232e6i	0.0548276i
$391$	− 9.91960e7i	− 1.65945i
$392$	0	0
$393$	−3.21249e7	−0.529254
$394$	3.39901e7	0.555730
$395$	− 2.75619e6i	− 0.0447217i
$396$	−5.48451e6	−0.0883186
$397$	− 2.94145e7i	− 0.470100i	−0.971983	−	0.235050i	$-0.924475\pi$
$397$	− 2.94145e7i	− 0.470100i	0.971983	−	0.235050i	$-0.0755253\pi$
$398$	− 2.04740e7i	− 0.324753i
$399$	0	0
$400$	1.54268e7	0.241043
$401$	−1.14011e8	−1.76813	−0.884064	−	0.467366i	$-0.845203\pi$
$401$	−1.14011e8	−1.76813	−0.884064	+	0.467366i	$0.845203\pi$
$402$	2.16039e7i	0.332548i
$403$	3.31163e7	0.505972
$404$	− 3.73716e7i	− 0.566758i
$405$	− 4.90455e6i	− 0.0738302i
$406$	0	0
$407$	4.49681e6	0.0666992
$408$	4.06637e7	0.598723
$409$	3.45589e7i	0.505114i	0.967582	+	0.252557i	$0.0812715\pi$
$409$	3.45589e7i	0.505114i	−0.967582	+	0.252557i	$0.918728\pi$
$410$	1.14325e7	0.165879
$411$	5.03383e7i	0.725058i
$412$	5.34769e7i	0.764671i
$413$	0	0
$414$	1.38210e7	0.194778
$415$	8.18118e7	1.14465
$416$	2.29272e7i	0.318472i
$417$	−6.34013e7	−0.874359
$418$	4.29018e6i	0.0587418i
$419$	3.73902e7i	0.508294i	0.967166	+	0.254147i	$0.0817948\pi$
$419$	3.73902e7i	0.508294i	−0.967166	+	0.254147i	$0.918205\pi$
$420$	0	0
$421$	−5.93910e7	−0.795929	−0.397965	−	0.917401i	$-0.630283\pi$
$421$	−5.93910e7	−0.795929	−0.397965	+	0.917401i	$0.630283\pi$
$422$	−3.79389e6	−0.0504832
$423$	− 1.22179e7i	− 0.161426i
$424$	−8.27606e7	−1.08574
$425$	− 5.48872e7i	− 0.714998i
$426$	− 8.77734e6i	− 0.113536i
$427$	0	0
$428$	−5.99080e7	−0.764105
$429$	−4.80551e6	−0.0608651
$430$	− 4.52914e7i	− 0.569653i
$431$	−5.95395e7	−0.743658	−0.371829	−	0.928301i	$-0.621269\pi$
$431$	−5.95395e7	−0.743658	−0.371829	+	0.928301i	$0.621269\pi$
$432$	− 6.69666e6i	− 0.0830629i
$433$	6.40730e7i	0.789244i	0.918843	+	0.394622i	$0.129124\pi$
$433$	6.40730e7i	0.789244i	−0.918843	+	0.394622i	$0.870876\pi$
$434$	0	0
$435$	−3.01349e7	−0.366102
$436$	−3.74336e7	−0.451650
$437$	4.23857e7i	0.507896i
$438$	2.11127e7	0.251259
$439$	1.52164e8i	1.79853i	0.437405	+	0.899265i	$0.355898\pi$
$439$	1.52164e8i	1.79853i	−0.437405	+	0.899265i	$0.644102\pi$
$440$	1.52463e7i	0.178980i
$441$	0	0
$442$	1.57997e7	0.182971
$443$	3.45839e7	0.397799	0.198899	−	0.980020i	$-0.436263\pi$
$443$	3.45839e7	0.397799	0.198899	+	0.980020i	$0.436263\pi$
$444$	8.07606e6i	0.0922679i
$445$	2.18124e7	0.247527
$446$	− 3.59429e7i	− 0.405143i
$447$	− 4.35656e7i	− 0.487777i
$448$	0	0
$449$	−1.33795e8	−1.47809	−0.739047	−	0.673654i	$-0.764724\pi$
$449$	−1.33795e8	−1.47809	−0.739047	+	0.673654i	$0.764724\pi$
$450$	7.64748e6	0.0839229
$451$	1.68923e7i	0.184145i
$452$	−1.04498e8	−1.13160
$453$	9.40138e6i	0.101134i
$454$	− 6.66153e7i	− 0.711880i
$455$	0	0
$456$	−1.73753e7	−0.183247
$457$	1.52528e7	0.159809	0.0799043	−	0.996803i	$-0.474539\pi$
$457$	1.52528e7	0.159809	0.0799043	+	0.996803i	$0.474539\pi$
$458$	4.91050e7i	0.511127i
$459$	−2.38262e7	−0.246386
$460$	6.67954e7i	0.686236i
$461$	3.05013e7i	0.311326i	0.987810	+	0.155663i	$0.0497514\pi$
$461$	3.05013e7i	0.311326i	−0.987810	+	0.155663i	$0.950249\pi$
$462$	0	0
$463$	−1.61661e8	−1.62878	−0.814388	−	0.580320i	$-0.802927\pi$
$463$	−1.61661e8	−1.62878	−0.814388	+	0.580320i	$0.802927\pi$
$464$	−4.11462e7	−0.411885
$465$	6.15622e7i	0.612287i
$466$	−36808.1	−0.000363735 0
$467$	− 6.59141e7i	− 0.647184i	−0.946197	−	0.323592i	$-0.895110\pi$
$467$	− 6.59141e7i	− 0.647184i	0.946197	−	0.323592i	$-0.104890\pi$
$468$	− 8.63049e6i	− 0.0841972i
$469$	0	0
$470$	−1.50612e7	−0.145067
$471$	2.22773e7	0.213207
$472$	1.60591e8i	1.52720i
$473$	6.69211e7	0.632382
$474$	− 1.86558e6i	− 0.0175177i
$475$	2.34529e7i	0.218834i
$476$	0	0
$477$	4.84922e7	0.446804
$478$	−9.00064e6	−0.0824119
$479$	− 9.19759e7i	− 0.836889i	−0.908242	−	0.418444i	$-0.862576\pi$
$479$	− 9.19759e7i	− 0.836889i	0.908242	−	0.418444i	$-0.137424\pi$
$480$	−4.26210e7	−0.385390
$481$	7.07623e6i	0.0635868i
$482$	1.97291e7i	0.176183i
$483$	0	0
$484$	8.03478e7	0.708660
$485$	−4.77711e7	−0.418736
$486$	− 3.31972e6i	− 0.0289196i
$487$	−1.90753e8	−1.65152	−0.825759	−	0.564023i	$-0.809253\pi$
$487$	−1.90753e8	−1.65152	−0.825759	+	0.564023i	$0.809253\pi$
$488$	4.88625e6i	0.0420452i
$489$	− 8.68725e7i	− 0.742944i
$490$	0	0
$491$	8.85504e7	0.748077	0.374038	−	0.927413i	$-0.377973\pi$
$491$	8.85504e7	0.748077	0.374038	+	0.927413i	$0.377973\pi$
$492$	−3.03379e7	−0.254736
$493$	1.46395e8i	1.22176i
$494$	−6.75109e6	−0.0560006
$495$	− 8.93330e6i	− 0.0736540i
$496$	8.40569e7i	0.688856i
$497$	0	0
$498$	5.53757e7	0.448364
$499$	−5.23508e7	−0.421330	−0.210665	−	0.977558i	$-0.567563\pi$
$499$	−5.23508e7	−0.421330	−0.210665	+	0.977558i	$0.567563\pi$
$500$	1.03138e8i	0.825104i
$501$	3.49786e7	0.278156
$502$	7.87748e6i	0.0622696i
$503$	1.34114e8i	1.05383i	0.849919	+	0.526914i	$0.176651\pi$
$503$	1.34114e8i	1.05383i	−0.849919	+	0.526914i	$0.823349\pi$
$504$	0	0
$505$	6.08718e7	0.472653
$506$	2.51741e7	0.194313
$507$	6.76805e7i	0.519325i
$508$	8.39797e7	0.640594
$509$	1.87318e8i	1.42045i	0.703976	+	0.710224i	$0.251406\pi$
$509$	1.87318e8i	1.42045i	−0.703976	+	0.710224i	$0.748594\pi$
$510$	2.93711e7i	0.221417i
$511$	0	0
$512$	−1.05118e8	−0.783188
$513$	1.01808e7	0.0754098
$514$	− 1.13538e8i	− 0.836088i
$515$	−8.71045e7	−0.637703
$516$	1.20187e8i	0.874801i
$517$	− 2.22540e7i	− 0.161041i
$518$	0	0
$519$	−1.07255e8	−0.767216
$520$	−2.39917e7	−0.170628
$521$	− 4.49210e7i	− 0.317641i	−0.987307	−	0.158820i	$-0.949231\pi$
$521$	− 4.49210e7i	− 0.317641i	0.987307	−	0.158820i	$-0.0507691\pi$
$522$	−2.03973e7	−0.143404
$523$	− 1.65990e8i	− 1.16032i	−0.814503	−	0.580160i	$-0.802990\pi$
$523$	− 1.65990e8i	− 1.16032i	0.814503	−	0.580160i	$-0.197010\pi$
$524$	− 1.05087e8i	− 0.730394i
$525$	0	0
$526$	−2.37222e7	−0.163004
$527$	2.99068e8	2.04333
$528$	− 1.21975e7i	− 0.0828647i
$529$	1.00676e8	0.680081
$530$	− 5.97775e7i	− 0.401523i
$531$	− 9.40956e7i	− 0.628472i
$532$	0	0
$533$	−2.65820e7	−0.175552
$534$	1.47640e7	0.0969575
$535$	− 9.75796e7i	− 0.637232i
$536$	−1.59368e8	−1.03492
$537$	− 1.23038e8i	− 0.794539i
$538$	− 792991.i	− 0.00509238i
$539$	0	0
$540$	1.60438e7	0.101889
$541$	1.26303e8	0.797666	0.398833	−	0.917024i	$-0.369415\pi$
$541$	1.26303e8	0.797666	0.398833	+	0.917024i	$0.369415\pi$
$542$	− 1.00397e8i	− 0.630555i
$543$	4.10972e7	0.256692
$544$	2.07052e8i	1.28612i
$545$	− 6.09727e7i	− 0.376657i
$546$	0	0
$547$	2.31931e8	1.41709	0.708545	−	0.705666i	$-0.249352\pi$
$547$	2.31931e8	1.41709	0.708545	+	0.705666i	$0.249352\pi$
$548$	−1.64667e8	−1.00061
$549$	− 2.86302e6i	− 0.0173024i
$550$	1.39294e7	0.0837227
$551$	− 6.25535e7i	− 0.373935i
$552$	1.01955e8i	0.606167i
$553$	0	0
$554$	2.07536e7	0.122057
$555$	−1.31545e7	−0.0769476
$556$	− 2.07399e8i	− 1.20665i
$557$	2.41077e8	1.39505	0.697525	−	0.716560i	$-0.254285\pi$
$557$	2.41077e8	1.39505	0.697525	+	0.716560i	$0.254285\pi$
$558$	4.16693e7i	0.239836i
$559$	1.05308e8i	0.602872i
$560$	0	0
$561$	−4.33978e7	−0.245799
$562$	−6.34141e7	−0.357254
$563$	− 1.17176e8i	− 0.656617i	−0.944571	−	0.328308i	$-0.893521\pi$
$563$	− 1.17176e8i	− 0.656617i	0.944571	−	0.328308i	$-0.106479\pi$
$564$	3.99672e7	0.222775
$565$	− 1.70208e8i	− 0.943703i
$566$	− 5.30821e7i	− 0.292751i
$567$	0	0
$568$	6.47488e7	0.353335
$569$	−1.20860e8	−0.656066	−0.328033	−	0.944666i	$-0.606386\pi$
$569$	−1.20860e8	−0.656066	−0.328033	+	0.944666i	$0.606386\pi$
$570$	− 1.25501e7i	− 0.0677675i
$571$	1.07812e8	0.579109	0.289555	−	0.957161i	$-0.406493\pi$
$571$	1.07812e8	0.579109	0.289555	+	0.957161i	$0.406493\pi$
$572$	− 1.57199e7i	− 0.0839964i
$573$	1.92399e8i	1.02268i
$574$	0	0
$575$	1.37618e8	0.723887
$576$	−1.35490e6	−0.00708990
$577$	− 7.84554e7i	− 0.408409i	−0.978928	−	0.204205i	$-0.934539\pi$
$577$	− 7.84554e7i	− 0.408409i	0.978928	−	0.204205i	$-0.0654608\pi$
$578$	5.56324e7	0.288101
$579$	− 2.08765e8i	− 1.07553i
$580$	− 9.85778e7i	− 0.505237i
$581$	0	0
$582$	−3.23346e7	−0.164021
$583$	8.83253e7	0.445738
$584$	1.55745e8i	0.781943i
$585$	1.40576e7	0.0702170
$586$	− 1.26135e7i	− 0.0626819i
$587$	− 1.98030e8i	− 0.979075i	−0.871982	−	0.489538i	$-0.837166\pi$
$587$	− 1.98030e8i	− 0.979075i	0.871982	−	0.489538i	$-0.162834\pi$
$588$	0	0
$589$	−1.27789e8	−0.625387
$590$	−1.15994e8	−0.564780
$591$	− 1.46916e8i	− 0.711717i
$592$	−1.79611e7	−0.0865702
$593$	3.77084e6i	0.0180831i	0.999959	+	0.00904157i	$0.00287806\pi$
$593$	3.77084e6i	0.0180831i	−0.999959	+	0.00904157i	$0.997122\pi$
$594$	− 6.04665e6i	− 0.0288506i
$595$	0	0
$596$	1.42512e8	0.673153
$597$	−8.84950e7	−0.415907
$598$	3.96143e7i	0.185246i
$599$	2.67305e8	1.24373	0.621867	−	0.783123i	$-0.286375\pi$
$599$	2.67305e8	1.24373	0.621867	+	0.783123i	$0.286375\pi$
$600$	5.64140e7i	0.261176i
$601$	− 9.26866e7i	− 0.426966i	−0.976947	−	0.213483i	$-0.931519\pi$
$601$	− 9.26866e7i	− 0.426966i	0.976947	−	0.213483i	$-0.0684809\pi$
$602$	0	0
$603$	9.33790e7	0.425890
$604$	−3.07539e7	−0.139569
$605$	1.30873e8i	0.590993i
$606$	4.12021e7	0.185140
$607$	− 1.60412e8i	− 0.717251i	−0.933482	−	0.358625i	$-0.883246\pi$
$607$	− 1.60412e8i	− 0.717251i	0.933482	−	0.358625i	$-0.116754\pi$
$608$	− 8.84718e7i	− 0.393635i
$609$	0	0
$610$	−3.52931e6	−0.0155489
$611$	3.50192e7	0.153526
$612$	− 7.79406e7i	− 0.340024i
$613$	7.21961e7	0.313424	0.156712	−	0.987644i	$-0.449911\pi$
$613$	7.21961e7	0.313424	0.156712	+	0.987644i	$0.449911\pi$
$614$	1.44150e8i	0.622742i
$615$	− 4.94151e7i	− 0.212439i
$616$	0	0
$617$	3.16720e6	0.0134841	0.00674203	−	0.999977i	$-0.497854\pi$
$617$	3.16720e6	0.0134841	0.00674203	+	0.999977i	$0.497854\pi$
$618$	−5.89581e7	−0.249792
$619$	1.38699e8i	0.584791i	0.956297	+	0.292396i	$0.0944524\pi$
$619$	1.38699e8i	0.584791i	−0.956297	+	0.292396i	$0.905548\pi$
$620$	−2.01383e8	−0.844982
$621$	− 5.97390e7i	− 0.249450i
$622$	1.20275e8i	0.499809i
$623$	0	0
$624$	1.91942e7	0.0789979
$625$	−3.16467e7	−0.129625
$626$	6.77658e7i	0.276240i
$627$	1.85436e7	0.0752299
$628$	7.28739e7i	0.294234i
$629$	6.39043e7i	0.256790i
$630$	0	0
$631$	−1.98716e8	−0.790944	−0.395472	−	0.918478i	$-0.629419\pi$
$631$	−1.98716e8	−0.790944	−0.395472	+	0.918478i	$0.629419\pi$
$632$	1.37620e7	0.0545168
$633$	1.63984e7i	0.0646533i
$634$	7.35624e7	0.288661
$635$	1.36788e8i	0.534229i
$636$	1.58628e8i	0.616608i
$637$	0	0
$638$	−3.71523e7	−0.143062
$639$	−3.79385e7	−0.145404
$640$	− 1.73315e8i	− 0.661143i
$641$	1.44347e8	0.548068	0.274034	−	0.961720i	$-0.411642\pi$
$641$	1.44347e8	0.548068	0.274034	+	0.961720i	$0.411642\pi$
$642$	− 6.60483e7i	− 0.249607i
$643$	− 2.68271e8i	− 1.00911i	−0.863378	−	0.504557i	$-0.831656\pi$
$643$	− 2.68271e8i	− 1.00911i	0.863378	−	0.504557i	$-0.168344\pi$
$644$	0	0
$645$	−1.95764e8	−0.729548
$646$	−6.09680e7	−0.226154
$647$	− 3.91410e8i	− 1.44517i	−0.691282	−	0.722585i	$-0.742954\pi$
$647$	− 3.91410e8i	− 1.44517i	0.691282	−	0.722585i	$-0.257046\pi$
$648$	2.44890e7	0.0900006
$649$	− 1.71389e8i	− 0.626973i
$650$	2.19194e7i	0.0798158i
$651$	0	0
$652$	2.84179e8	1.02529
$653$	4.61183e8	1.65628	0.828139	−	0.560522i	$-0.189400\pi$
$653$	4.61183e8	1.65628	0.828139	+	0.560522i	$0.189400\pi$
$654$	− 4.12704e7i	− 0.147538i
$655$	1.71169e8	0.609118
$656$	− 6.74712e7i	− 0.239005i
$657$	− 9.12561e7i	− 0.321785i
$658$	0	0
$659$	2.90612e8	1.01545	0.507724	−	0.861520i	$-0.330487\pi$
$659$	2.90612e8	1.01545	0.507724	+	0.861520i	$0.330487\pi$
$660$	2.92227e7	0.101646
$661$	− 2.80781e8i	− 0.972218i	−0.873898	−	0.486109i	$-0.838416\pi$
$661$	− 2.80781e8i	− 0.972218i	0.873898	−	0.486109i	$-0.161584\pi$
$662$	7.70164e7	0.265466
$663$	− 6.82914e7i	− 0.234329i
$664$	4.08496e8i	1.39535i
$665$	0	0
$666$	−8.90383e6	−0.0301408
$667$	−3.67054e8	−1.23695
$668$	1.14422e8i	0.383867i
$669$	−1.55357e8	−0.518862
$670$	− 1.15111e8i	− 0.382728i
$671$	− 5.21480e6i	− 0.0172611i
$672$	0	0
$673$	−2.35293e8	−0.771904	−0.385952	−	0.922519i	$-0.626127\pi$
$673$	−2.35293e8	−0.771904	−0.385952	+	0.922519i	$0.626127\pi$
$674$	7.17060e7	0.234194
$675$	− 3.30549e7i	− 0.107479i
$676$	−2.21397e8	−0.716691
$677$	6.18148e8i	1.99217i	0.0884002	+	0.996085i	$0.471825\pi$
$677$	6.18148e8i	1.99217i	−0.0884002	+	0.996085i	$0.528175\pi$
$678$	− 1.15208e8i	− 0.369653i
$679$	0	0
$680$	−2.16665e8	−0.689069
$681$	−2.87933e8	−0.911696
$682$	7.58979e7i	0.239264i
$683$	1.30744e7	0.0410356	0.0205178	−	0.999789i	$-0.493469\pi$
$683$	1.30744e7	0.0410356	0.0205178	+	0.999789i	$0.493469\pi$
$684$	3.33034e7i	0.104069i
$685$	− 2.68214e8i	− 0.834468i
$686$	0	0
$687$	2.12248e8	0.654595
$688$	−2.67296e8	−0.820780
$689$	1.38990e8i	0.424938i
$690$	−7.36417e7	−0.224170
$691$	− 2.74064e8i	− 0.830648i	−0.909674	−	0.415324i	$-0.863668\pi$
$691$	− 2.74064e8i	− 0.830648i	0.909674	−	0.415324i	$-0.136332\pi$
$692$	− 3.50855e8i	− 1.05879i
$693$	0	0
$694$	1.19878e8	0.358643
$695$	3.37817e8	1.00630
$696$	− 1.50467e8i	− 0.446287i
$697$	−2.40058e8	−0.708952
$698$	− 9.29937e7i	− 0.273456i
$699$	159096.i	0 0.000465831i
$700$	0	0
$701$	4.35624e8	1.26461	0.632307	−	0.774718i	$-0.282108\pi$
$701$	4.35624e8	1.26461	0.632307	+	0.774718i	$0.282108\pi$
$702$	9.51508e6	0.0275043
$703$	− 2.73058e7i	− 0.0785940i
$704$	−2.46786e6	−0.00707299
$705$	6.50996e7i	0.185785i
$706$	2.00740e8i	0.570454i
$707$	0	0
$708$	3.07807e8	0.867318
$709$	−3.61813e8	−1.01518	−0.507592	−	0.861597i	$-0.669464\pi$
$709$	−3.61813e8	−1.01518	−0.507592	+	0.861597i	$0.669464\pi$
$710$	4.67677e7i	0.130669i
$711$	−8.06362e6	−0.0224347
$712$	1.08912e8i	0.301741i
$713$	7.49848e8i	2.06873i
$714$	0	0
$715$	2.56049e7	0.0700495
$716$	4.02482e8	1.09650
$717$	3.89037e7i	0.105544i
$718$	5.83325e7	0.157593
$719$	2.45377e8i	0.660157i	0.943953	+	0.330079i	$0.107075\pi$
$719$	2.45377e8i	0.660157i	−0.943953	+	0.330079i	$0.892925\pi$
$720$	3.56814e7i	0.0955969i
$721$	0	0
$722$	−1.43620e8	−0.381595
$723$	8.52753e7	0.225636
$724$	1.34438e8i	0.354246i
$725$	−2.03099e8	−0.532958
$726$	8.85832e7i	0.231495i
$727$	− 2.59949e8i	− 0.676526i	−0.941052	−	0.338263i	$-0.890161\pi$
$727$	− 2.59949e8i	− 0.676526i	0.941052	−	0.338263i	$-0.109839\pi$
$728$	0	0
$729$	−1.43489e7	−0.0370370
$730$	−1.12494e8	−0.289174
$731$	9.51018e8i	2.43465i
$732$	9.36554e6	0.0238781
$733$	1.25030e8i	0.317471i	0.987321	+	0.158735i	$0.0507417\pi$
$733$	1.25030e8i	0.317471i	−0.987321	+	0.158735i	$0.949258\pi$
$734$	− 4.04915e7i	− 0.102394i
$735$	0	0
$736$	−5.19138e8	−1.30212
$737$	1.70084e8	0.424874
$738$	− 3.34474e7i	− 0.0832133i
$739$	−5.64721e8	−1.39927	−0.699634	−	0.714502i	$-0.746654\pi$
$739$	−5.64721e8	−1.39927	−0.699634	+	0.714502i	$0.746654\pi$
$740$	− 4.30311e7i	− 0.106191i
$741$	2.91804e7i	0.0717194i
$742$	0	0
$743$	2.68677e8	0.655035	0.327518	−	0.944845i	$-0.393788\pi$
$743$	2.68677e8	0.655035	0.327518	+	0.944845i	$0.393788\pi$
$744$	−3.07387e8	−0.746392
$745$	2.32128e8i	0.561382i
$746$	−1.44251e8	−0.347459
$747$	− 2.39351e8i	− 0.574215i
$748$	− 1.41964e8i	− 0.339213i
$749$	0	0
$750$	−1.13709e8	−0.269533
$751$	3.90960e8	0.923023	0.461512	−	0.887134i	$-0.347307\pi$
$751$	3.90960e8	0.923023	0.461512	+	0.887134i	$0.347307\pi$
$752$	8.88868e7i	0.209018i
$753$	3.40490e7	0.0797479
$754$	− 5.84634e7i	− 0.136386i
$755$	− 5.00927e7i	− 0.116395i
$756$	0	0
$757$	−5.67872e8	−1.30907	−0.654535	−	0.756031i	$-0.727136\pi$
$757$	−5.67872e8	−1.30907	−0.654535	+	0.756031i	$0.727136\pi$
$758$	−1.05345e8	−0.241884
$759$	− 1.08811e8i	− 0.248855i
$760$	9.25795e7	0.210899
$761$	1.92045e8i	0.435762i	0.975975	+	0.217881i	$0.0699144\pi$
$761$	1.92045e8i	0.435762i	−0.975975	+	0.217881i	$0.930086\pi$
$762$	9.25873e7i	0.209260i
$763$	0	0
$764$	−6.29378e8	−1.41134
$765$	1.26952e8	0.283566
$766$	1.65403e8i	0.368008i
$767$	2.69700e8	0.597715
$768$	− 1.22874e8i	− 0.271253i
$769$	7.75766e8i	1.70589i	0.521999	+	0.852946i	$0.325187\pi$
$769$	7.75766e8i	1.70589i	−0.521999	+	0.852946i	$0.674813\pi$
$770$	0	0
$771$	−4.90748e8	−1.07077
$772$	6.82914e8	1.48428
$773$	2.70408e7i	0.0585438i	0.999571	+	0.0292719i	$0.00931887\pi$
$773$	2.70408e7i	0.0585438i	−0.999571	+	0.0292719i	$0.990681\pi$
$774$	−1.32506e8	−0.285767
$775$	4.14907e8i	0.891344i
$776$	− 2.38527e8i	− 0.510448i
$777$	0	0
$778$	−5.57154e7	−0.118314
$779$	1.02575e8	0.216984
$780$	4.59853e7i	0.0969025i
$781$	−6.91025e7	−0.145058
$782$	3.57750e8i	0.748100i
$783$	8.81638e7i	0.183656i
$784$	0	0
$785$	−1.18699e8	−0.245379
$786$	1.15859e8	0.238594
$787$	− 4.25592e8i	− 0.873111i	−0.899677	−	0.436555i	$-0.856198\pi$
$787$	− 4.25592e8i	− 0.873111i	0.899677	−	0.436555i	$-0.143802\pi$
$788$	4.80594e8	0.982200
$789$	1.02535e8i	0.208757i
$790$	9.94022e6i	0.0201611i
$791$	0	0
$792$	4.46050e7	0.0897859
$793$	8.20607e6	0.0164557
$794$	1.06083e8i	0.211927i
$795$	−2.58378e8	−0.514226
$796$	− 2.89486e8i	− 0.573969i
$797$	− 7.51386e7i	− 0.148419i	−0.997243	−	0.0742093i	$-0.976357\pi$
$797$	− 7.51386e7i	− 0.148419i	0.997243	−	0.0742093i	$-0.0236433\pi$
$798$	0	0
$799$	3.16253e8	0.620003
$800$	−2.87250e8	−0.561035
$801$	− 6.38150e7i	− 0.124172i
$802$	4.11181e8	0.797094
$803$	− 1.66217e8i	− 0.321017i
$804$	3.05462e8i	0.587746i
$805$	0	0
$806$	−1.19434e8	−0.228099
$807$	−3.42756e6	−0.00652176
$808$	3.03940e8i	0.576174i
$809$	−7.82317e8	−1.47753	−0.738766	−	0.673962i	$-0.764591\pi$
$809$	−7.82317e8	−1.47753	−0.738766	+	0.673962i	$0.764591\pi$
$810$	1.76882e7i	0.0332836i
$811$	− 8.00635e8i	− 1.50097i	−0.660888	−	0.750485i	$-0.729820\pi$
$811$	− 8.00635e8i	− 1.50097i	0.660888	−	0.750485i	$-0.270180\pi$
$812$	0	0
$813$	−4.33948e8	−0.807544
$814$	−1.62177e7	−0.0300689
$815$	4.62877e8i	0.855053i
$816$	1.73339e8	0.319027
$817$	− 4.06363e8i	− 0.745157i
$818$	− 1.24637e8i	− 0.227712i
$819$	0	0
$820$	1.61647e8	0.293175
$821$	−2.75662e8	−0.498135	−0.249067	−	0.968486i	$-0.580124\pi$
$821$	−2.75662e8	−0.498135	−0.249067	+	0.968486i	$0.580124\pi$
$822$	− 1.81545e8i	− 0.326865i
$823$	−7.57904e8	−1.35961	−0.679806	−	0.733392i	$-0.737936\pi$
$823$	−7.57904e8	−1.35961	−0.679806	+	0.733392i	$0.737936\pi$
$824$	− 4.34923e8i	− 0.777375i
$825$	− 6.02072e7i	− 0.107223i
$826$	0	0
$827$	3.06595e8	0.542061	0.271030	−	0.962571i	$-0.412636\pi$
$827$	3.06595e8	0.542061	0.271030	+	0.962571i	$0.412636\pi$
$828$	1.95419e8	0.344251
$829$	1.23659e8i	0.217052i	0.994094	+	0.108526i	$0.0346130\pi$
$829$	1.23659e8i	0.217052i	−0.994094	+	0.108526i	$0.965387\pi$
$830$	−2.95054e8	−0.516022
$831$	− 8.97038e7i	− 0.156318i
$832$	− 3.88346e6i	− 0.00674293i
$833$	0	0
$834$	2.28657e8	0.394172
$835$	−1.86374e8	−0.320129
$836$	6.06599e7i	0.103820i
$837$	1.80108e8	0.307155
$838$	− 1.34848e8i	− 0.229145i
$839$	− 2.04720e8i	− 0.346637i	−0.984866	−	0.173318i	$-0.944551\pi$
$839$	− 2.04720e8i	− 0.346637i	0.984866	−	0.173318i	$-0.0554489\pi$
$840$	0	0
$841$	−5.31198e7	−0.0893035
$842$	2.14194e8	0.358815
$843$	2.74096e8i	0.457531i
$844$	−5.36427e7	−0.0892243
$845$	− 3.60617e8i	− 0.597691i
$846$	4.40637e7i	0.0727729i
$847$	0	0
$848$	−3.52789e8	−0.578532
$849$	−2.29438e8	−0.374923
$850$	1.97951e8i	0.322330i
$851$	−1.60226e8	−0.259983
$852$	− 1.24105e8i	− 0.200664i
$853$	1.81851e8i	0.293001i	0.989211	+	0.146500i	$0.0468010\pi$
$853$	1.81851e8i	0.293001i	−0.989211	+	0.146500i	$0.953199\pi$
$854$	0	0
$855$	−5.42454e7	−0.0867890
$856$	4.87226e8	0.776800
$857$	− 6.14504e8i	− 0.976298i	−0.872760	−	0.488149i	$-0.837672\pi$
$857$	− 6.14504e8i	− 0.976298i	0.872760	−	0.488149i	$-0.162328\pi$
$858$	1.73311e7	0.0274387
$859$	2.18853e8i	0.345281i	0.984985	+	0.172640i	$0.0552299\pi$
$859$	2.18853e8i	0.345281i	−0.984985	+	0.172640i	$0.944770\pi$
$860$	− 6.40386e8i	− 1.00681i
$861$	0	0
$862$	2.14729e8	0.335250
$863$	−6.59431e8	−1.02598	−0.512988	−	0.858396i	$-0.671461\pi$
$863$	−6.59431e8	−1.02598	−0.512988	+	0.858396i	$0.671461\pi$
$864$	1.24693e8i	0.193331i
$865$	5.71482e8	0.882987
$866$	− 2.31079e8i	− 0.355801i
$867$	− 2.40461e8i	− 0.368967i
$868$	0	0
$869$	−1.46873e7	−0.0223812
$870$	1.08682e8	0.165044
$871$	2.67646e8i	0.405047i
$872$	3.04444e8	0.459153
$873$	1.39761e8i	0.210060i
$874$	− 1.52864e8i	− 0.228966i
$875$	0	0
$876$	2.98518e8	0.444077
$877$	1.62366e8	0.240711	0.120355	−	0.992731i	$-0.461597\pi$
$877$	1.62366e8	0.240711	0.120355	+	0.992731i	$0.461597\pi$
$878$	− 5.48778e8i	− 0.810800i
$879$	−5.45196e7	−0.0802760
$880$	6.49912e7i	0.0953688i
$881$	8.48365e8i	1.24067i	0.784338	+	0.620333i	$0.213003\pi$
$881$	8.48365e8i	1.24067i	−0.784338	+	0.620333i	$0.786997\pi$
$882$	0	0
$883$	3.14592e8	0.456947	0.228473	−	0.973550i	$-0.426627\pi$
$883$	3.14592e8	0.456947	0.228473	+	0.973550i	$0.426627\pi$
$884$	2.23396e8	0.323384
$885$	5.01363e8i	0.723307i
$886$	−1.24727e8	−0.179333
$887$	8.37224e8i	1.19970i	0.800114	+	0.599848i	$0.204772\pi$
$887$	8.37224e8i	1.19970i	−0.800114	+	0.599848i	$0.795228\pi$
$888$	− 6.56819e7i	− 0.0938009i
$889$	0	0
$890$	−7.86663e7	−0.111588
$891$	−2.61356e7	−0.0369487
$892$	− 5.08205e8i	− 0.716052i
$893$	−1.35132e8	−0.189760
$894$	1.57119e8i	0.219896i
$895$	6.55573e8i	0.914433i
$896$	0	0
$897$	1.71226e8	0.237242
$898$	4.82533e8	0.666344
$899$	− 1.10664e9i	− 1.52309i
$900$	1.08129e8	0.148326
$901$	1.25520e9i	1.71608i
$902$	− 6.09222e7i	− 0.0830148i
$903$	0	0
$904$	8.49870e8	1.15040
$905$	−2.18975e8	−0.295427
$906$	− 3.39061e7i	− 0.0455925i
$907$	6.88047e8	0.922139	0.461070	−	0.887364i	$-0.347466\pi$
$907$	6.88047e8	0.922139	0.461070	+	0.887364i	$0.347466\pi$
$908$	− 9.41890e8i	− 1.25818i
$909$	− 1.78089e8i	− 0.237107i
$910$	0	0
$911$	2.31613e8	0.306343	0.153171	−	0.988200i	$-0.451051\pi$
$911$	2.31613e8	0.306343	0.153171	+	0.988200i	$0.451051\pi$
$912$	−7.40666e7	−0.0976423
$913$	− 4.35963e8i	− 0.572845i
$914$	−5.50091e7	−0.0720437
$915$	1.52548e7i	0.0199133i
$916$	6.94307e8i	0.903369i
$917$	0	0
$918$	8.59292e7	0.111074
$919$	−1.12516e9	−1.44967	−0.724835	−	0.688922i	$-0.758084\pi$
$919$	−1.12516e9	−1.44967	−0.724835	+	0.688922i	$0.758084\pi$
$920$	− 5.43241e8i	− 0.697637i
$921$	6.23061e8	0.797538
$922$	− 1.10003e8i	− 0.140350i
$923$	− 1.08740e8i	− 0.138289i
$924$	0	0
$925$	−8.86565e7	−0.112017
$926$	5.83029e8	0.734273
$927$	2.54836e8i	0.319905i
$928$	7.66152e8	0.958675
$929$	6.85223e8i	0.854644i	0.904100	+	0.427322i	$0.140543\pi$
$929$	6.85223e8i	0.854644i	−0.904100	+	0.427322i	$0.859457\pi$
$930$	− 2.22024e8i	− 0.276027i
$931$	0	0
$932$	−520438.	−0.000642867 0
$933$	5.19867e8	0.640099
$934$	2.37719e8i	0.291759i
$935$	2.31234e8	0.282889
$936$	7.01910e7i	0.0855961i
$937$	− 7.87984e8i	− 0.957852i	−0.877855	−	0.478926i	$-0.841026\pi$
$937$	− 7.87984e8i	− 0.957852i	0.877855	−	0.478926i	$-0.158974\pi$
$938$	0	0
$939$	2.92905e8	0.353778
$940$	−2.12954e8	−0.256391
$941$	2.07328e8i	0.248822i	0.992231	+	0.124411i	$0.0397041\pi$
$941$	2.07328e8i	0.248822i	−0.992231	+	0.124411i	$0.960296\pi$
$942$	−8.03433e7	−0.0961162
$943$	− 6.01892e8i	− 0.717767i
$944$	6.84561e8i	0.813759i
$945$	0	0
$946$	−2.41351e8	−0.285086
$947$	−3.54059e8	−0.416894	−0.208447	−	0.978034i	$-0.566841\pi$
$947$	−3.54059e8	−0.416894	−0.208447	+	0.978034i	$0.566841\pi$
$948$	− 2.63778e7i	− 0.0309609i
$949$	2.61561e8	0.306037
$950$	− 8.45829e7i	− 0.0986533i
$951$	− 3.17960e8i	− 0.369685i
$952$	0	0
$953$	−4.28652e8	−0.495252	−0.247626	−	0.968856i	$-0.579650\pi$
$953$	−4.28652e8	−0.495252	−0.247626	+	0.968856i	$0.579650\pi$
$954$	−1.74887e8	−0.201425
$955$	− 1.02515e9i	− 1.17700i
$956$	−1.27262e8	−0.145655
$957$	1.60584e8i	0.183218i
$958$	3.31711e8i	0.377280i
$959$	0	0
$960$	7.21923e6	0.00815975
$961$	−1.37323e9	−1.54729
$962$	− 2.55204e7i	− 0.0286657i
$963$	−2.85482e8	−0.319669
$964$	2.78954e8i	0.311387i
$965$	1.11235e9i	1.23782i
$966$	0	0
$967$	1.16972e9	1.29361	0.646805	−	0.762655i	$-0.276105\pi$
$967$	1.16972e9	1.29361	0.646805	+	0.762655i	$0.276105\pi$
$968$	−6.53462e8	−0.720434
$969$	2.63523e8i	0.289633i
$970$	1.72286e8	0.188771
$971$	− 7.03804e8i	− 0.768766i	−0.923174	−	0.384383i	$-0.874414\pi$
$971$	− 7.03804e8i	− 0.768766i	0.923174	−	0.384383i	$-0.125586\pi$
$972$	− 4.69383e7i	− 0.0511127i
$973$	0	0
$974$	6.87949e8	0.744525
$975$	9.47428e7	0.102219
$976$	2.08289e7i	0.0224036i
$977$	4.42412e8	0.474399	0.237199	−	0.971461i	$-0.423771\pi$
$977$	4.42412e8	0.474399	0.237199	+	0.971461i	$0.423771\pi$
$978$	3.13306e8i	0.334928i
$979$	− 1.16235e8i	− 0.123876i
$980$	0	0
$981$	−1.78384e8	−0.188951
$982$	−3.19357e8	−0.337242
$983$	− 1.16835e9i	− 1.23002i	−0.788519	−	0.615011i	$-0.789152\pi$
$983$	− 1.16835e9i	− 1.23002i	0.788519	−	0.615011i	$-0.210848\pi$
$984$	2.46735e8	0.258968
$985$	7.82804e8i	0.819114i
$986$	− 5.27974e8i	− 0.550784i
$987$	0	0
$988$	−9.54552e7	−0.0989758
$989$	−2.38447e9	−2.46492
$990$	3.22180e7i	0.0332042i
$991$	−1.00364e9	−1.03123	−0.515615	−	0.856821i	$-0.672436\pi$
$991$	−1.00364e9	−1.03123	−0.515615	+	0.856821i	$0.672436\pi$
$992$	− 1.56516e9i	− 1.60333i
$993$	− 3.32890e8i	− 0.339979i
$994$	0	0
$995$	4.71522e8	0.478666
$996$	7.82970e8	0.792441
$997$	1.84885e9i	1.86559i	0.360409	+	0.932794i	$0.382637\pi$
$997$	1.84885e9i	1.86559i	−0.360409	+	0.932794i	$0.617363\pi$
$998$	1.88803e8	0.189941
$999$	3.84852e7i	0.0386009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.7.d.a.97.4		8
3.2	odd	2		441.7.d.d.244.6		8
7.2	even	3		147.7.f.a.31.3		8
7.3	odd	6		147.7.f.a.19.3		8
7.4	even	3		21.7.f.b.19.3	yes	8
7.5	odd	6		21.7.f.b.10.3	✓	8
7.6	odd	2	inner	147.7.d.a.97.3		8
21.5	even	6		63.7.m.c.10.2		8
21.11	odd	6		63.7.m.c.19.2		8
21.20	even	2		441.7.d.d.244.5		8
28.11	odd	6		336.7.bh.b.145.3		8
28.19	even	6		336.7.bh.b.241.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.b.10.3	✓	8	7.5	odd	6
21.7.f.b.19.3	yes	8	7.4	even	3
63.7.m.c.10.2		8	21.5	even	6
63.7.m.c.19.2		8	21.11	odd	6
147.7.d.a.97.3		8	7.6	odd	2	inner
147.7.d.a.97.4		8	1.1	even	1	trivial
147.7.f.a.19.3		8	7.3	odd	6
147.7.f.a.31.3		8	7.2	even	3
336.7.bh.b.145.3		8	28.11	odd	6
336.7.bh.b.241.3		8	28.19	even	6
441.7.d.d.244.5		8	21.20	even	2
441.7.d.d.244.6		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)

\(f(q)\)	\(=\)	\(q-3.60650 q^{2} +15.5885i q^{3} -50.9932 q^{4} -83.0589i q^{5} -56.2198i q^{6} +414.723 q^{8} -243.000 q^{9} +O(q^{10})\)	\(q-3.60650 q^{2} +15.5885i q^{3} -50.9932 q^{4} -83.0589i q^{5} -56.2198i q^{6} +414.723 q^{8} -243.000 q^{9} +299.552i q^{10} -442.608 q^{11} -794.905i q^{12} -696.494i q^{13} +1294.76 q^{15} +1767.86 q^{16} -6289.93i q^{17} +876.380 q^{18} +2687.64i q^{19} +4235.44i q^{20} +1596.27 q^{22} +15770.6 q^{23} +6464.89i q^{24} +8726.22 q^{25} +2511.91i q^{26} -3788.00i q^{27} -23274.5 q^{29} -4669.55 q^{30} +47547.1i q^{31} -32918.1 q^{32} -6899.58i q^{33} +22684.6i q^{34} +12391.3 q^{36} -10159.8 q^{37} -9692.96i q^{38} +10857.3 q^{39} -34446.4i q^{40} -38165.4i q^{41} -151197. q^{43} +22570.0 q^{44} +20183.3i q^{45} -56876.7 q^{46} +50279.2i q^{47} +27558.3i q^{48} -31471.1 q^{50} +98050.2 q^{51} +35516.4i q^{52} -199556. q^{53} +13661.4i q^{54} +36762.6i q^{55} -41896.1 q^{57} +83939.6 q^{58} +387225. i q^{59} -66023.9 q^{60} +11782.0i q^{61} -171479. i q^{62} +5575.73 q^{64} -57850.0 q^{65} +24883.3i q^{66} -384276. q^{67} +320743. i q^{68} +245840. i q^{69} +156126. q^{71} -100778. q^{72} +375539. i q^{73} +36641.3 q^{74} +136028. i q^{75} -137051. i q^{76} -39156.7 q^{78} +33183.6 q^{79} -146837. i q^{80} +59049.0 q^{81} +137644. i q^{82} +984986. i q^{83} -522434. q^{85} +545292. q^{86} -362814. i q^{87} -183560. q^{88} +262613. i q^{89} -72791.1i q^{90} -804193. q^{92} -741187. q^{93} -181332. i q^{94} +223232. q^{95} -513142. i q^{96} -575147. i q^{97} +107554. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{2} + 346 q^{4} - 454 q^{8} - 1944 q^{9}+O(q^{10}) \) 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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