LMFDB - Embedded newform 147.7.d.b.97.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("147.97");

S:= CuspForms(chi, 7);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$33.8179502921$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} + 473x^{5} + 39800x^{4} + 36821x^{3} + 985651x^{2} - 601290x + 21068100 $ x^8 - x^7 + 212x^6 + 473x^5 + 39800x^4 + 36821x^3 + 985651x^2 - 601290x + 21068100
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			97.7
Root			$7.29767 - 12.6399i$ of defining polynomial
Character	$\chi$	$=$	147.97
Dual form			147.7.d.b.97.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+15.5953 q^{2} -15.5885i q^{3} +179.215 q^{4} -25.8331i q^{5} -243.107i q^{6} +1796.81 q^{8} -243.000 q^{9} +O(q^{10})$	\(q+15.5953 q^{2} -15.5885i q^{3} +179.215 q^{4} -25.8331i q^{5} -243.107i q^{6} +1796.81 q^{8} -243.000 q^{9} -402.876i q^{10} +623.935 q^{11} -2793.68i q^{12} -3257.26i q^{13} -402.698 q^{15} +16552.1 q^{16} +317.827i q^{17} -3789.67 q^{18} +6000.67i q^{19} -4629.67i q^{20} +9730.47 q^{22} -42.0166 q^{23} -28009.5i q^{24} +14957.7 q^{25} -50798.1i q^{26} +3788.00i q^{27} -24273.4 q^{29} -6280.21 q^{30} -20262.4i q^{31} +143140. q^{32} -9726.18i q^{33} +4956.62i q^{34} -43549.2 q^{36} -17377.1 q^{37} +93582.4i q^{38} -50775.7 q^{39} -46417.2i q^{40} +100535. i q^{41} -67873.7 q^{43} +111818. q^{44} +6277.44i q^{45} -655.263 q^{46} -65863.5i q^{47} -258022. i q^{48} +233270. q^{50} +4954.43 q^{51} -583749. i q^{52} +99222.0 q^{53} +59075.1i q^{54} -16118.2i q^{55} +93541.1 q^{57} -378552. q^{58} +100679. i q^{59} -72169.4 q^{60} +232201. i q^{61} -315999. i q^{62} +1.17299e6 q^{64} -84145.1 q^{65} -151683. i q^{66} +41088.0 q^{67} +56959.2i q^{68} +654.974i q^{69} -400361. q^{71} -436625. q^{72} +553224. i q^{73} -271002. q^{74} -233167. i q^{75} +1.07541e6i q^{76} -791864. q^{78} -10481.5 q^{79} -427593. i q^{80} +59049.0 q^{81} +1.56788e6i q^{82} +712797. i q^{83} +8210.45 q^{85} -1.05851e6 q^{86} +378385. i q^{87} +1.12109e6 q^{88} +190458. i q^{89} +97898.8i q^{90} -7529.99 q^{92} -315860. q^{93} -1.02716e6i q^{94} +155016. q^{95} -2.23134e6i q^{96} +1.07270e6i q^{97} -151616. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 10 q^{2} + 346 q^{4} + 3326 q^{8} - 1944 q^{9}+O(q^{10}) $ 8 * q + 10 * q^2 + 346 * q^4 + 3326 * q^8 - 1944 * q^9	$ 8 q + 10 q^{2} + 346 q^{4} + 3326 q^{8} - 1944 q^{9} + 628 q^{11} + 5292 q^{15} + 25442 q^{16} - 2430 q^{18} + 86106 q^{22} - 7856 q^{23} + 34076 q^{25} - 8300 q^{29} - 61398 q^{30} + 372414 q^{32} - 84078 q^{36} - 129412 q^{37} - 58212 q^{39} + 45740 q^{43} - 185058 q^{44} + 223008 q^{46} + 967216 q^{50} - 99576 q^{51} + 1081948 q^{53} + 328212 q^{57} - 1079598 q^{58} + 292734 q^{60} + 2378626 q^{64} + 828408 q^{65} + 2317804 q^{67} + 1442344 q^{71} - 808218 q^{72} + 865880 q^{74} - 222588 q^{78} - 1222904 q^{79} + 472392 q^{81} - 275112 q^{85} - 1632448 q^{86} + 732882 q^{88} + 678720 q^{92} - 1611144 q^{93} + 1183584 q^{95} - 152604 q^{99}+O(q^{100}) $ 8 * q + 10 * q^2 + 346 * q^4 + 3326 * q^8 - 1944 * q^9 + 628 * q^11 + 5292 * q^15 + 25442 * q^16 - 2430 * q^18 + 86106 * q^22 - 7856 * q^23 + 34076 * q^25 - 8300 * q^29 - 61398 * q^30 + 372414 * q^32 - 84078 * q^36 - 129412 * q^37 - 58212 * q^39 + 45740 * q^43 - 185058 * q^44 + 223008 * q^46 + 967216 * q^50 - 99576 * q^51 + 1081948 * q^53 + 328212 * q^57 - 1079598 * q^58 + 292734 * q^60 + 2378626 * q^64 + 828408 * q^65 + 2317804 * q^67 + 1442344 * q^71 - 808218 * q^72 + 865880 * q^74 - 222588 * q^78 - 1222904 * q^79 + 472392 * q^81 - 275112 * q^85 - 1632448 * q^86 + 732882 * q^88 + 678720 * q^92 - 1611144 * q^93 + 1183584 * q^95 - 152604 * 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 $

$2$	15.5953	1.94942	0.974709	−	0.223479i	$-0.0717415\pi$
$2$	15.5953	1.94942	0.974709	+	0.223479i	$0.0717415\pi$
$3$	− 15.5885i	− 0.577350i
$3$	− 15.5885i	− 0.577350i
$4$	179.215	2.80023
$5$	− 25.8331i	− 0.206665i	−0.994647	−	0.103332i	$-0.967049\pi$
$5$	− 25.8331i	− 0.206665i	0.994647	−	0.103332i	$-0.0329505\pi$
$6$	− 243.107i	− 1.12550i
$7$	0	0
$7$	0	0
$8$	1796.81	3.50940
$9$	−243.000	−0.333333
$10$	− 402.876i	− 0.402876i
$11$	623.935	0.468771	0.234386	−	0.972144i	$-0.424692\pi$
$11$	623.935	0.468771	0.234386	+	0.972144i	$0.424692\pi$
$12$	− 2793.68i	− 1.61671i
$13$	− 3257.26i	− 1.48259i	−0.671177	−	0.741297i	$-0.734211\pi$
$13$	− 3257.26i	− 1.48259i	0.671177	−	0.741297i	$-0.265789\pi$
$14$	0	0
$15$	−402.698	−0.119318
$16$	16552.1	4.04105
$17$	317.827i	0.0646910i	0.999477	+	0.0323455i	$0.0102977\pi$
$17$	317.827i	0.0646910i	−0.999477	+	0.0323455i	$0.989702\pi$
$18$	−3789.67	−0.649806
$19$	6000.67i	0.874860i	0.899252	+	0.437430i	$0.144111\pi$
$19$	6000.67i	0.874860i	−0.899252	+	0.437430i	$0.855889\pi$
$20$	− 4629.67i	− 0.578709i
$21$	0	0
$22$	9730.47	0.913831
$23$	−42.0166	−0.00345332	−0.00172666	−	0.999999i	$-0.500550\pi$
$23$	−42.0166	−0.00345332	−0.00172666	+	0.999999i	$0.500550\pi$
$24$	− 28009.5i	− 2.02615i
$25$	14957.7	0.957290
$26$	− 50798.1i	− 2.89020i
$27$	3788.00i	0.192450i
$28$	0	0
$29$	−24273.4	−0.995260	−0.497630	−	0.867389i	$-0.665796\pi$
$29$	−24273.4	−0.995260	−0.497630	+	0.867389i	$0.665796\pi$
$30$	−6280.21	−0.232601
$31$	− 20262.4i	− 0.680153i	−0.940398	−	0.340076i	$-0.889547\pi$
$31$	− 20262.4i	− 0.680153i	0.940398	−	0.340076i	$-0.110453\pi$
$32$	143140.	4.36830
$33$	− 9726.18i	− 0.270645i
$34$	4956.62i	0.126110i
$35$	0	0
$36$	−43549.2	−0.933409
$37$	−17377.1	−0.343062	−0.171531	−	0.985179i	$-0.554871\pi$
$37$	−17377.1	−0.343062	−0.171531	+	0.985179i	$0.554871\pi$
$38$	93582.4i	1.70547i
$39$	−50775.7	−0.855976
$40$	− 46417.2i	− 0.725269i
$41$	100535.i	1.45870i	0.684141	+	0.729350i	$0.260177\pi$
$41$	100535.i	1.45870i	−0.684141	+	0.729350i	$0.739823\pi$
$42$	0	0
$43$	−67873.7	−0.853682	−0.426841	−	0.904327i	$-0.640374\pi$
$43$	−67873.7	−0.853682	−0.426841	+	0.904327i	$0.640374\pi$
$44$	111818.	1.31267
$45$	6277.44i	0.0688883i
$46$	−655.263	−0.00673197
$47$	− 65863.5i	− 0.634383i	−0.948362	−	0.317191i	$-0.897260\pi$
$47$	− 65863.5i	− 0.634383i	0.948362	−	0.317191i	$-0.102740\pi$
$48$	− 258022.i	− 2.33310i
$49$	0	0
$50$	233270.	1.86616
$51$	4954.43	0.0373493
$52$	− 583749.i	− 4.15160i
$53$	99222.0	0.666470	0.333235	−	0.942844i	$-0.391860\pi$
$53$	99222.0	0.666470	0.333235	+	0.942844i	$0.391860\pi$
$54$	59075.1i	0.375166i
$55$	− 16118.2i	− 0.0968785i
$56$	0	0
$57$	93541.1	0.505101
$58$	−378552.	−1.94018
$59$	100679.i	0.490212i	0.969496	+	0.245106i	$0.0788227\pi$
$59$	100679.i	0.490212i	−0.969496	+	0.245106i	$0.921177\pi$
$60$	−72169.4	−0.334118
$61$	232201.i	1.02300i	0.859284	+	0.511499i	$0.170910\pi$
$61$	232201.i	1.02300i	−0.859284	+	0.511499i	$0.829090\pi$
$62$	− 315999.i	− 1.32590i
$63$	0	0
$64$	1.17299e6	4.47458
$65$	−84145.1	−0.306400
$66$	− 151683.i	− 0.527601i
$67$	41088.0	0.136613	0.0683063	−	0.997664i	$-0.478240\pi$
$67$	41088.0	0.136613	0.0683063	+	0.997664i	$0.478240\pi$
$68$	56959.2i	0.181149i
$69$	654.974i	0.00199378i
$70$	0	0
$71$	−400361.	−1.11861	−0.559303	−	0.828963i	$-0.688931\pi$
$71$	−400361.	−1.11861	−0.559303	+	0.828963i	$0.688931\pi$
$72$	−436625.	−1.16980
$73$	553224.i	1.42211i	0.703137	+	0.711054i	$0.251782\pi$
$73$	553224.i	1.42211i	−0.703137	+	0.711054i	$0.748218\pi$
$74$	−271002.	−0.668772
$75$	− 233167.i	− 0.552691i
$76$	1.07541e6i	2.44981i
$77$	0	0
$78$	−791864.	−1.66866
$79$	−10481.5	−0.0212591	−0.0106295	−	0.999944i	$-0.503384\pi$
$79$	−10481.5	−0.0212591	−0.0106295	+	0.999944i	$0.503384\pi$
$80$	− 427593.i	− 0.835143i
$81$	59049.0	0.111111
$82$	1.56788e6i	2.84362i
$83$	712797.i	1.24661i	0.781978	+	0.623306i	$0.214211\pi$
$83$	712797.i	1.24661i	−0.781978	+	0.623306i	$0.785789\pi$
$84$	0	0
$85$	8210.45	0.0133693
$86$	−1.05851e6	−1.66418
$87$	378385.i	0.574613i
$88$	1.12109e6	1.64510
$89$	190458.i	0.270166i	0.990834	+	0.135083i	$0.0431300\pi$
$89$	190458.i	0.270166i	−0.990834	+	0.135083i	$0.956870\pi$
$90$	97898.8i	0.134292i
$91$	0	0
$92$	−7529.99	−0.00967009
$93$	−315860.	−0.392686
$94$	− 1.02716e6i	− 1.23668i
$95$	155016.	0.180803
$96$	− 2.23134e6i	− 2.52204i
$97$	1.07270e6i	1.17533i	0.809103	+	0.587667i	$0.199954\pi$
$97$	1.07270e6i	1.17533i	−0.809103	+	0.587667i	$0.800046\pi$
$98$	0	0
$99$	−151616.	−0.156257
$100$	2.68063e6	2.68063
$101$	− 532553.i	− 0.516891i	−0.966026	−	0.258445i	$-0.916790\pi$
$101$	− 532553.i	− 0.516891i	0.966026	−	0.258445i	$-0.0832102\pi$
$102$	77266.0	0.0728095
$103$	− 1.04460e6i	− 0.955961i	−0.878370	−	0.477980i	$-0.841369\pi$
$103$	− 1.04460e6i	− 0.955961i	0.878370	−	0.477980i	$-0.158631\pi$
$104$	− 5.85268e6i	− 5.20301i
$105$	0	0
$106$	1.54740e6	1.29923
$107$	358843.	0.292923	0.146461	−	0.989216i	$-0.453212\pi$
$107$	358843.	0.292923	0.146461	+	0.989216i	$0.453212\pi$
$108$	678864.i	0.538904i
$109$	752374.	0.580971	0.290485	−	0.956879i	$-0.406183\pi$
$109$	752374.	0.580971	0.290485	+	0.956879i	$0.406183\pi$
$110$	− 251368.i	− 0.188857i
$111$	270883.i	0.198067i
$112$	0	0
$113$	−2.37249e6	−1.64425	−0.822126	−	0.569306i	$-0.807212\pi$
$113$	−2.37249e6	−1.64425	−0.822126	+	0.569306i	$0.807212\pi$
$114$	1.45881e6	0.984652
$115$	1085.42i	0 0.000713680i
$116$	−4.35015e6	−2.78695
$117$	791514.i	0.494198i
$118$	1.57013e6i	0.955627i
$119$	0	0
$120$	−723572.	−0.418734
$121$	−1.38227e6	−0.780253
$122$	3.62126e6i	1.99425i
$123$	1.56719e6	0.842181
$124$	− 3.63132e6i	− 1.90458i
$125$	− 790045.i	− 0.404503i
$126$	0	0
$127$	−1.06403e6	−0.519447	−0.259724	−	0.965683i	$-0.583631\pi$
$127$	−1.06403e6	−0.519447	−0.259724	+	0.965683i	$0.583631\pi$
$128$	9.13212e6	4.35454
$129$	1.05805e6i	0.492874i
$130$	−1.31227e6	−0.597302
$131$	652468.i	0.290232i	0.989415	+	0.145116i	$0.0463556\pi$
$131$	652468.i	0.290232i	−0.989415	+	0.145116i	$0.953644\pi$
$132$	− 1.74307e6i	− 0.757869i
$133$	0	0
$134$	640782.	0.266315
$135$	97855.6	0.0397727
$136$	571074.i	0.227026i
$137$	4.59750e6	1.78797	0.893985	−	0.448097i	$-0.147898\pi$
$137$	4.59750e6	1.78797	0.893985	+	0.448097i	$0.147898\pi$
$138$	10214.5i	0.00388670i
$139$	1.96781e6i	0.732720i	0.930473	+	0.366360i	$0.119396\pi$
$139$	1.96781e6i	0.732720i	−0.930473	+	0.366360i	$0.880604\pi$
$140$	0	0
$141$	−1.02671e6	−0.366261
$142$	−6.24377e6	−2.18063
$143$	− 2.03232e6i	− 0.694998i
$144$	−4.02217e6	−1.34702
$145$	627057.i	0.205685i
$146$	8.62772e6i	2.77228i
$147$	0	0
$148$	−3.11424e6	−0.960653
$149$	−3.11125e6	−0.940537	−0.470268	−	0.882524i	$-0.655843\pi$
$149$	−3.11125e6	−0.940537	−0.470268	+	0.882524i	$0.655843\pi$
$150$	− 3.63631e6i	− 1.07743i
$151$	−1.73921e6	−0.505152	−0.252576	−	0.967577i	$-0.581278\pi$
$151$	−1.73921e6	−0.505152	−0.252576	+	0.967577i	$0.581278\pi$
$152$	1.07821e7i	3.07023i
$153$	− 77231.9i	− 0.0215637i
$154$	0	0
$155$	−523441.	−0.140564
$156$	−9.09974e6	−2.39693
$157$	− 848996.i	− 0.219385i	−0.993966	−	0.109692i	$-0.965013\pi$
$157$	− 848996.i	− 0.219385i	0.993966	−	0.109692i	$-0.0349866\pi$
$158$	−163463.	−0.0414428
$159$	− 1.54672e6i	− 0.384787i
$160$	− 3.69776e6i	− 0.902773i
$161$	0	0
$162$	920889.	0.216602
$163$	1.34322e6	0.310158	0.155079	−	0.987902i	$-0.450437\pi$
$163$	1.34322e6	0.310158	0.155079	+	0.987902i	$0.450437\pi$
$164$	1.80174e7i	4.08469i
$165$	−251257.	−0.0559328
$166$	1.11163e7i	2.43017i
$167$	6.60321e6i	1.41777i	0.705324	+	0.708885i	$0.250801\pi$
$167$	6.60321e6i	1.41777i	−0.705324	+	0.708885i	$0.749199\pi$
$168$	0	0
$169$	−5.78293e6	−1.19809
$170$	128045.	0.0260624
$171$	− 1.45816e6i	− 0.291620i
$172$	−1.21640e7	−2.39050
$173$	− 9.42017e6i	− 1.81937i	−0.415302	−	0.909684i	$-0.636324\pi$
$173$	− 9.42017e6i	− 1.81937i	0.415302	−	0.909684i	$-0.363676\pi$
$174$	5.90104e6i	1.12016i
$175$	0	0
$176$	1.03275e7	1.89433
$177$	1.56943e6	0.283024
$178$	2.97026e6i	0.526665i
$179$	−3.00765e6	−0.524406	−0.262203	−	0.965013i	$-0.584449\pi$
$179$	−3.00765e6	−0.524406	−0.262203	+	0.965013i	$0.584449\pi$
$180$	1.12501e6i	0.192903i
$181$	− 8.77281e6i	− 1.47946i	−0.672904	−	0.739730i	$-0.734953\pi$
$181$	− 8.77281e6i	− 1.47946i	0.672904	−	0.739730i	$-0.265047\pi$
$182$	0	0
$183$	3.61966e6	0.590628
$184$	−75495.9	−0.0121191
$185$	448905.i	0.0708989i
$186$	−4.92594e6	−0.765510
$187$	198303.i	0.0303253i
$188$	− 1.18037e7i	− 1.77642i
$189$	0	0
$190$	2.41752e6	0.352460
$191$	1.44143e6	0.206868	0.103434	−	0.994636i	$-0.467017\pi$
$191$	1.44143e6	0.206868	0.103434	+	0.994636i	$0.467017\pi$
$192$	− 1.82850e7i	− 2.58340i
$193$	1.70219e6	0.236775	0.118387	−	0.992967i	$-0.462228\pi$
$193$	1.70219e6	0.236775	0.118387	+	0.992967i	$0.462228\pi$
$194$	1.67291e7i	2.29122i
$195$	1.31169e6i	0.176900i
$196$	0	0
$197$	6.42619e6	0.840534	0.420267	−	0.907401i	$-0.361936\pi$
$197$	6.42619e6	0.840534	0.420267	+	0.907401i	$0.361936\pi$
$198$	−2.36451e6	−0.304610
$199$	− 6.66384e6i	− 0.845601i	−0.906223	−	0.422801i	$-0.861047\pi$
$199$	− 6.66384e6i	− 0.845601i	0.906223	−	0.422801i	$-0.138953\pi$
$200$	2.68761e7	3.35951
$201$	− 640499.i	− 0.0788734i
$202$	− 8.30534e6i	− 1.00764i
$203$	0	0
$204$	887906.	0.104587
$205$	2.59713e6	0.301462
$206$	− 1.62910e7i	− 1.86357i
$207$	10210.0	0.00115111
$208$	− 5.39146e7i	− 5.99124i
$209$	3.74402e6i	0.410109i
$210$	0	0
$211$	1.06742e6	0.113629	0.0568144	−	0.998385i	$-0.481906\pi$
$211$	1.06742e6	0.113629	0.0568144	+	0.998385i	$0.481906\pi$
$212$	1.77820e7	1.86627
$213$	6.24102e6i	0.645827i
$214$	5.59628e6	0.571029
$215$	1.75339e6i	0.176426i
$216$	6.80631e6i	0.675384i
$217$	0	0
$218$	1.17335e7	1.13255
$219$	8.62392e6	0.821055
$220$	− 2.88861e6i	− 0.271282i
$221$	1.03524e6	0.0959105
$222$	4.22451e6i	0.386115i
$223$	− 1.67396e7i	− 1.50949i	−0.656016	−	0.754747i	$-0.727760\pi$
$223$	− 1.67396e7i	− 1.50949i	0.656016	−	0.754747i	$-0.272240\pi$
$224$	0	0
$225$	−3.63471e6	−0.319097
$226$	−3.69997e7	−3.20533
$227$	1.89616e7i	1.62105i	0.585701	+	0.810527i	$0.300819\pi$
$227$	1.89616e7i	1.62105i	−0.585701	+	0.810527i	$0.699181\pi$
$228$	1.67639e7	1.41440
$229$	4.25745e6i	0.354522i	0.984164	+	0.177261i	$0.0567236\pi$
$229$	4.25745e6i	0.354522i	−0.984164	+	0.177261i	$0.943276\pi$
$230$	16927.5i	0.00139126i
$231$	0	0
$232$	−4.36147e7	−3.49276
$233$	1.21795e7	0.962857	0.481429	−	0.876485i	$-0.340118\pi$
$233$	1.21795e7	0.962857	0.481429	+	0.876485i	$0.340118\pi$
$234$	1.23439e7i	0.963398i
$235$	−1.70146e6	−0.131105
$236$	1.80432e7i	1.37270i
$237$	163391.i	0.0122739i
$238$	0	0
$239$	−1.03799e7	−0.760328	−0.380164	−	0.924919i	$-0.624132\pi$
$239$	−1.03799e7	−0.760328	−0.380164	+	0.924919i	$0.624132\pi$
$240$	−6.66552e6	−0.482170
$241$	− 1.12120e7i	− 0.800997i	−0.916297	−	0.400498i	$-0.868837\pi$
$241$	− 1.12120e7i	− 0.800997i	0.916297	−	0.400498i	$-0.131163\pi$
$242$	−2.15569e7	−1.52104
$243$	− 920483.i	− 0.0641500i
$244$	4.16139e7i	2.86463i
$245$	0	0
$246$	2.44408e7	1.64176
$247$	1.95457e7	1.29706
$248$	− 3.64078e7i	− 2.38693i
$249$	1.11114e7	0.719732
$250$	− 1.23210e7i	− 0.788545i
$251$	− 2.63644e7i	− 1.66724i	−0.552341	−	0.833618i	$-0.686265\pi$
$251$	− 2.63644e7i	− 1.66724i	0.552341	−	0.833618i	$-0.313735\pi$
$252$	0	0
$253$	−26215.6	−0.00161882
$254$	−1.65939e7	−1.01262
$255$	− 127988.i	− 0.00771879i
$256$	6.73475e7	4.01422
$257$	− 2.57305e7i	− 1.51583i	−0.652356	−	0.757913i	$-0.726219\pi$
$257$	− 2.57305e7i	− 1.51583i	0.652356	−	0.757913i	$-0.273781\pi$
$258$	1.65006e7i	0.960816i
$259$	0	0
$260$	−1.50800e7	−0.857990
$261$	5.89843e6	0.331753
$262$	1.01755e7i	0.565784i
$263$	1.69184e7	0.930018	0.465009	−	0.885306i	$-0.346051\pi$
$263$	1.69184e7	0.930018	0.465009	+	0.885306i	$0.346051\pi$
$264$	− 1.74761e7i	− 0.949802i
$265$	− 2.56321e6i	− 0.137736i
$266$	0	0
$267$	2.96895e6	0.155980
$268$	7.36358e6	0.382547
$269$	− 2.63942e7i	− 1.35597i	−0.735074	−	0.677987i	$-0.762853\pi$
$269$	− 2.63942e7i	− 1.35597i	0.735074	−	0.677987i	$-0.237147\pi$
$270$	1.52609e6	0.0775335
$271$	− 6.36742e6i	− 0.319931i	−0.987123	−	0.159965i	$-0.948862\pi$
$271$	− 6.36742e6i	− 0.319931i	0.987123	−	0.159965i	$-0.0511382\pi$
$272$	5.26071e6i	0.261419i
$273$	0	0
$274$	7.16996e7	3.48550
$275$	9.33260e6	0.448750
$276$	117381.i	0.00558303i
$277$	−3.45112e7	−1.62376	−0.811878	−	0.583827i	$-0.801555\pi$
$277$	−3.45112e7	−1.62376	−0.811878	+	0.583827i	$0.801555\pi$
$278$	3.06886e7i	1.42838i
$279$	4.92377e6i	0.226718i
$280$	0	0
$281$	4.02256e7	1.81294	0.906470	−	0.422270i	$-0.138767\pi$
$281$	4.02256e7	1.81294	0.906470	+	0.422270i	$0.138767\pi$
$282$	−1.60119e7	−0.713996
$283$	− 2.92541e6i	− 0.129070i	−0.997915	−	0.0645352i	$-0.979444\pi$
$283$	− 2.92541e6i	− 0.129070i	0.997915	−	0.0645352i	$-0.0205565\pi$
$284$	−7.17506e7	−3.13235
$285$	− 2.41646e6i	− 0.104387i
$286$	− 3.16947e7i	− 1.35484i
$287$	0	0
$288$	−3.47831e7	−1.45610
$289$	2.40366e7	0.995815
$290$	9.77916e6i	0.400966i
$291$	1.67217e7	0.678580
$292$	9.91459e7i	3.98223i
$293$	1.16741e7i	0.464109i	0.972703	+	0.232054i	$0.0745448\pi$
$293$	1.16741e7i	0.464109i	−0.972703	+	0.232054i	$0.925455\pi$
$294$	0	0
$295$	2.60086e6	0.101309
$296$	−3.12234e7	−1.20394
$297$	2.36346e6i	0.0902151i
$298$	−4.85210e7	−1.83350
$299$	136859.i	0.00511988i
$300$	− 4.17869e7i	− 1.54766i
$301$	0	0
$302$	−2.71236e7	−0.984753
$303$	−8.30168e6	−0.298427
$304$	9.93239e7i	3.53535i
$305$	5.99848e6	0.211418
$306$	− 1.20446e6i	− 0.0420366i
$307$	− 3.20193e7i	− 1.10661i	−0.832977	−	0.553307i	$-0.813366\pi$
$307$	− 3.20193e7i	− 1.10661i	0.832977	−	0.553307i	$-0.186634\pi$
$308$	0	0
$309$	−1.62838e7	−0.551924
$310$	−8.16324e6	−0.274017
$311$	2.42586e6i	0.0806464i	0.999187	+	0.0403232i	$0.0128388\pi$
$311$	2.42586e6i	0.0806464i	−0.999187	+	0.0403232i	$0.987161\pi$
$312$	−9.12343e7	−3.00396
$313$	− 2.80719e7i	− 0.915458i	−0.889092	−	0.457729i	$-0.848663\pi$
$313$	− 2.80719e7i	− 0.915458i	0.889092	−	0.457729i	$-0.151337\pi$
$314$	− 1.32404e7i	− 0.427673i
$315$	0	0
$316$	−1.87845e6	−0.0595302
$317$	7.68215e6	0.241160	0.120580	−	0.992704i	$-0.461525\pi$
$317$	7.68215e6	0.241160	0.120580	+	0.992704i	$0.461525\pi$
$318$	− 2.41216e7i	− 0.750110i
$319$	−1.51450e7	−0.466549
$320$	− 3.03018e7i	− 0.924739i
$321$	− 5.59381e6i	− 0.169119i
$322$	0	0
$323$	−1.90717e6	−0.0565955
$324$	1.05824e7	0.311136
$325$	− 4.87210e7i	− 1.41927i
$326$	2.09479e7	0.604628
$327$	− 1.17284e7i	− 0.335424i
$328$	1.80642e8i	5.11916i
$329$	0	0
$330$	−3.91844e6	−0.109036
$331$	−5.12805e7	−1.41406	−0.707031	−	0.707183i	$-0.749966\pi$
$331$	−5.12805e7	−1.41406	−0.707031	+	0.707183i	$0.749966\pi$
$332$	1.27744e8i	3.49080i
$333$	4.22264e6	0.114354
$334$	1.02979e8i	2.76382i
$335$	− 1.06143e6i	− 0.0282330i
$336$	0	0
$337$	1.62829e7	0.425443	0.212721	−	0.977113i	$-0.431767\pi$
$337$	1.62829e7	0.425443	0.212721	+	0.977113i	$0.431767\pi$
$338$	−9.01868e7	−2.33557
$339$	3.69834e7i	0.949309i
$340$	1.47143e6	0.0374372
$341$	− 1.26424e7i	− 0.318836i
$342$	− 2.27405e7i	− 0.568489i
$343$	0	0
$344$	−1.21956e8	−2.99591
$345$	16920.0	0.000412043 0
$346$	− 1.46911e8i	− 3.54671i
$347$	7.58000e7	1.81418	0.907091	−	0.420936i	$-0.138298\pi$
$347$	7.58000e7	1.81418	0.907091	+	0.420936i	$0.138298\pi$
$348$	6.78121e7i	1.60905i
$349$	− 2.89740e7i	− 0.681605i	−0.940135	−	0.340802i	$-0.889301\pi$
$349$	− 2.89740e7i	− 0.681605i	0.940135	−	0.340802i	$-0.110699\pi$
$350$	0	0
$351$	1.23385e7	0.285325
$352$	8.93102e7	2.04773
$353$	5.89377e7i	1.33989i	0.742411	+	0.669945i	$0.233682\pi$
$353$	5.89377e7i	1.33989i	−0.742411	+	0.669945i	$0.766318\pi$
$354$	2.44758e7	0.551732
$355$	1.03426e7i	0.231176i
$356$	3.41329e7i	0.756525i
$357$	0	0
$358$	−4.69053e7	−1.02229
$359$	7.75157e7	1.67535	0.837677	−	0.546167i	$-0.183913\pi$
$359$	7.75157e7	1.67535	0.837677	+	0.546167i	$0.183913\pi$
$360$	1.12794e7i	0.241756i
$361$	1.10379e7	0.234620
$362$	− 1.36815e8i	− 2.88408i
$363$	2.15474e7i	0.450479i
$364$	0	0
$365$	1.42915e7	0.293900
$366$	5.64498e7	1.15138
$367$	− 4.14007e7i	− 0.837548i	−0.908091	−	0.418774i	$-0.862460\pi$
$367$	− 4.14007e7i	− 0.837548i	0.908091	−	0.418774i	$-0.137540\pi$
$368$	−695464.	−0.0139551
$369$	− 2.44300e7i	− 0.486233i
$370$	7.00083e6i	0.138212i
$371$	0	0
$372$	−5.66067e7	−1.09961
$373$	−4.79377e7	−0.923741	−0.461871	−	0.886947i	$-0.652822\pi$
$373$	−4.79377e7	−0.923741	−0.461871	+	0.886947i	$0.652822\pi$
$374$	3.09260e6i	0.0591166i
$375$	−1.23156e7	−0.233540
$376$	− 1.18344e8i	− 2.22630i
$377$	7.90647e7i	1.47557i
$378$	0	0
$379$	−1.73029e7	−0.317835	−0.158917	−	0.987292i	$-0.550800\pi$
$379$	−1.73029e7	−0.317835	−0.158917	+	0.987292i	$0.550800\pi$
$380$	2.77811e7	0.506289
$381$	1.65865e7i	0.299903i
$382$	2.24796e7	0.403272
$383$	6.47023e7i	1.15166i	0.817570	+	0.575829i	$0.195321\pi$
$383$	6.47023e7i	1.15166i	−0.817570	+	0.575829i	$0.804679\pi$
$384$	− 1.42356e8i	− 2.51409i
$385$	0	0
$386$	2.65462e7	0.461573
$387$	1.64933e7	0.284561
$388$	1.92243e8i	3.29121i
$389$	−7.94278e7	−1.34935	−0.674673	−	0.738117i	$-0.735715\pi$
$389$	−7.94278e7	−1.34935	−0.674673	+	0.738117i	$0.735715\pi$
$390$	2.04563e7i	0.344852i
$391$	− 13354.0i	0 0.000223399i
$392$	0	0
$393$	1.01710e7	0.167566
$394$	1.00219e8	1.63855
$395$	270771.i	0.00439350i
$396$	−2.71718e7	−0.437556
$397$	2.53070e7i	0.404454i	0.979339	+	0.202227i	$0.0648178\pi$
$397$	2.53070e7i	0.404454i	−0.979339	+	0.202227i	$0.935182\pi$
$398$	− 1.03925e8i	− 1.64843i
$399$	0	0
$400$	2.47581e8	3.86846
$401$	1.13184e7	0.175530	0.0877651	−	0.996141i	$-0.472027\pi$
$401$	1.13184e7	0.175530	0.0877651	+	0.996141i	$0.472027\pi$
$402$	− 9.98880e6i	− 0.153757i
$403$	−6.60000e7	−1.00839
$404$	− 9.54413e7i	− 1.44741i
$405$	− 1.52542e6i	− 0.0229628i
$406$	0	0
$407$	−1.08422e7	−0.160818
$408$	8.90217e6	0.131074
$409$	− 3.84473e7i	− 0.561948i	−0.959715	−	0.280974i	$-0.909342\pi$
$409$	− 3.84473e7i	− 0.561948i	0.959715	−	0.280974i	$-0.0906575\pi$
$410$	4.05032e7	0.587675
$411$	− 7.16680e7i	− 1.03228i
$412$	− 1.87208e8i	− 2.67691i
$413$	0	0
$414$	159229.	0.00224399
$415$	1.84138e7	0.257631
$416$	− 4.66245e8i	− 6.47641i
$417$	3.06751e7	0.423036
$418$	5.83893e7i	0.799474i
$419$	5.55673e7i	0.755401i	0.925928	+	0.377701i	$0.123285\pi$
$419$	5.55673e7i	0.755401i	−0.925928	+	0.377701i	$0.876715\pi$
$420$	0	0
$421$	−9.27660e7	−1.24320	−0.621602	−	0.783333i	$-0.713518\pi$
$421$	−9.27660e7	−1.24320	−0.621602	+	0.783333i	$0.713518\pi$
$422$	1.66468e7	0.221510
$423$	1.60048e7i	0.211461i
$424$	1.78283e8	2.33891
$425$	4.75394e6i	0.0619280i
$426$	9.73308e7i	1.25899i
$427$	0	0
$428$	6.43099e7	0.820251
$429$	−3.16807e7	−0.401257
$430$	2.73447e7i	0.343928i
$431$	1.31740e8	1.64545	0.822726	−	0.568438i	$-0.192452\pi$
$431$	1.31740e8	1.64545	0.822726	+	0.568438i	$0.192452\pi$
$432$	6.26994e7i	0.777700i
$433$	− 9.64602e7i	− 1.18819i	−0.804396	−	0.594093i	$-0.797511\pi$
$433$	− 9.64602e7i	− 1.18819i	0.804396	−	0.594093i	$-0.202489\pi$
$434$	0	0
$435$	9.77485e6	0.118752
$436$	1.34836e8	1.62685
$437$	− 252127.i	− 0.00302117i
$438$	1.34493e8	1.60058
$439$	9.72209e7i	1.14912i	0.818462	+	0.574561i	$0.194827\pi$
$439$	9.72209e7i	1.14912i	−0.818462	+	0.574561i	$0.805173\pi$
$440$	− 2.89613e7i	− 0.339985i
$441$	0	0
$442$	1.61450e7	0.186970
$443$	−1.66397e8	−1.91397	−0.956983	−	0.290144i	$-0.906297\pi$
$443$	−1.66397e8	−1.91397	−0.956983	+	0.290144i	$0.906297\pi$
$444$	4.85461e7i	0.554633i
$445$	4.92013e6	0.0558337
$446$	− 2.61060e8i	− 2.94263i
$447$	4.84995e7i	0.543019i
$448$	0	0
$449$	−1.03969e8	−1.14859	−0.574294	−	0.818649i	$-0.694723\pi$
$449$	−1.03969e8	−1.14859	−0.574294	+	0.818649i	$0.694723\pi$
$450$	−5.66845e7	−0.622052
$451$	6.27273e7i	0.683797i
$452$	−4.25184e8	−4.60428
$453$	2.71117e7i	0.291650i
$454$	2.95713e8i	3.16011i
$455$	0	0
$456$	1.68076e8	1.77260
$457$	−7.08988e7	−0.742832	−0.371416	−	0.928467i	$-0.621128\pi$
$457$	−7.08988e7	−0.742832	−0.371416	+	0.928467i	$0.621128\pi$
$458$	6.63964e7i	0.691111i
$459$	−1.20393e6	−0.0124498
$460$	194523.i	0.00199847i
$461$	2.94715e7i	0.300815i	0.988624	+	0.150408i	$0.0480586\pi$
$461$	2.94715e7i	0.300815i	−0.988624	+	0.150408i	$0.951941\pi$
$462$	0	0
$463$	−7.67219e7	−0.772994	−0.386497	−	0.922291i	$-0.626315\pi$
$463$	−7.67219e7	−0.772994	−0.386497	+	0.922291i	$0.626315\pi$
$464$	−4.01777e8	−4.02189
$465$	8.15964e6i	0.0811544i
$466$	1.89943e8	1.87701
$467$	1.95758e8i	1.92207i	0.276426	+	0.961035i	$0.410850\pi$
$467$	1.95758e8i	1.92207i	−0.276426	+	0.961035i	$0.589150\pi$
$468$	1.41851e8i	1.38387i
$469$	0	0
$470$	−2.65348e7	−0.255578
$471$	−1.32345e7	−0.126662
$472$	1.80901e8i	1.72035i
$473$	−4.23488e7	−0.400182
$474$	2.54814e6i	0.0239270i
$475$	8.97559e7i	0.837495i
$476$	0	0
$477$	−2.41110e7	−0.222157
$478$	−1.61879e8	−1.48220
$479$	− 3.21276e7i	− 0.292329i	−0.989260	−	0.146164i	$-0.953307\pi$
$479$	− 3.21276e7i	− 0.292329i	0.989260	−	0.146164i	$-0.0466929\pi$
$480$	−5.76424e7	−0.521216
$481$	5.66018e7i	0.508622i
$482$	− 1.74854e8i	− 1.56148i
$483$	0	0
$484$	−2.47722e8	−2.18489
$485$	2.77111e7	0.242900
$486$	− 1.43552e7i	− 0.125055i
$487$	−1.73246e8	−1.49995	−0.749973	−	0.661468i	$-0.769934\pi$
$487$	−1.73246e8	−1.49995	−0.749973	+	0.661468i	$0.769934\pi$
$488$	4.17222e8i	3.59011i
$489$	− 2.09387e7i	− 0.179070i
$490$	0	0
$491$	2.27726e7	0.192383	0.0961917	−	0.995363i	$-0.469334\pi$
$491$	2.27726e7	0.192383	0.0961917	+	0.995363i	$0.469334\pi$
$492$	2.80863e8	2.35830
$493$	− 7.71473e6i	− 0.0643843i
$494$	3.04822e8	2.52852
$495$	3.91671e6i	0.0322928i
$496$	− 3.35387e8i	− 2.74853i
$497$	0	0
$498$	1.73286e8	1.40306
$499$	−1.43117e8	−1.15183	−0.575917	−	0.817508i	$-0.695355\pi$
$499$	−1.43117e8	−1.15183	−0.575917	+	0.817508i	$0.695355\pi$
$500$	− 1.41588e8i	− 1.13270i
$501$	1.02934e8	0.818550
$502$	− 4.11162e8i	− 3.25014i
$503$	1.94323e8i	1.52693i	0.645848	+	0.763466i	$0.276504\pi$
$503$	1.94323e8i	1.52693i	−0.645848	+	0.763466i	$0.723496\pi$
$504$	0	0
$505$	−1.37575e7	−0.106823
$506$	−408841.	−0.00315575
$507$	9.01470e7i	0.691715i
$508$	−1.90689e8	−1.45457
$509$	1.68499e7i	0.127775i	0.997957	+	0.0638873i	$0.0203498\pi$
$509$	1.68499e7i	0.127775i	−0.997957	+	0.0638873i	$0.979650\pi$
$510$	− 1.99602e6i	− 0.0150472i
$511$	0	0
$512$	4.65851e8	3.47086
$513$	−2.27305e7	−0.168367
$514$	− 4.01276e8i	− 2.95498i
$515$	−2.69854e7	−0.197563
$516$	1.89617e8i	1.38016i
$517$	− 4.10946e7i	− 0.297381i
$518$	0	0
$519$	−1.46846e8	−1.05041
$520$	−1.51193e8	−1.07528
$521$	5.78764e7i	0.409250i	0.978840	+	0.204625i	$0.0655974\pi$
$521$	5.78764e7i	0.409250i	−0.978840	+	0.204625i	$0.934403\pi$
$522$	9.19881e7	0.646726
$523$	− 2.54491e8i	− 1.77897i	−0.456968	−	0.889483i	$-0.651064\pi$
$523$	− 2.54491e8i	− 1.77897i	0.456968	−	0.889483i	$-0.348936\pi$
$524$	1.16932e8i	0.812716i
$525$	0	0
$526$	2.63848e8	1.81299
$527$	6.43994e6	0.0439997
$528$	− 1.60989e8i	− 1.09369i
$529$	−1.48034e8	−0.999988
$530$	− 3.99742e7i	− 0.268505i
$531$	− 2.44650e7i	− 0.163404i
$532$	0	0
$533$	3.27469e8	2.16266
$534$	4.63018e7	0.304070
$535$	− 9.27003e6i	− 0.0605368i
$536$	7.38274e7	0.479428
$537$	4.68846e7i	0.302766i
$538$	− 4.11626e8i	− 2.64336i
$539$	0	0
$540$	1.75372e7	0.111373
$541$	−6.20974e7	−0.392177	−0.196088	−	0.980586i	$-0.562824\pi$
$541$	−6.20974e7	−0.392177	−0.196088	+	0.980586i	$0.562824\pi$
$542$	− 9.93021e7i	− 0.623678i
$543$	−1.36755e8	−0.854166
$544$	4.54938e7i	0.282589i
$545$	− 1.94362e7i	− 0.120066i
$546$	0	0
$547$	7.72887e6	0.0472230	0.0236115	−	0.999721i	$-0.492484\pi$
$547$	7.72887e6	0.0472230	0.0236115	+	0.999721i	$0.492484\pi$
$548$	8.23940e8	5.00672
$549$	− 5.64249e7i	− 0.340999i
$550$	1.45545e8	0.874801
$551$	− 1.45656e8i	− 0.870713i
$552$	1.17686e6i	0.00699695i
$553$	0	0
$554$	−5.38214e8	−3.16538
$555$	6.99774e6	0.0409335
$556$	3.52660e8i	2.05178i
$557$	2.53366e7	0.146617	0.0733083	−	0.997309i	$-0.476644\pi$
$557$	2.53366e7	0.146617	0.0733083	+	0.997309i	$0.476644\pi$
$558$	7.67879e7i	0.441967i
$559$	2.21082e8i	1.26566i
$560$	0	0
$561$	3.09124e6	0.0175083
$562$	6.27332e8	3.53418
$563$	7.61590e7i	0.426772i	0.976968	+	0.213386i	$0.0684492\pi$
$563$	7.61590e7i	0.426772i	−0.976968	+	0.213386i	$0.931551\pi$
$564$	−1.84002e8	−1.02561
$565$	6.12887e7i	0.339809i
$566$	− 4.56227e7i	− 0.251612i
$567$	0	0
$568$	−7.19374e8	−3.92563
$569$	−5.32966e7	−0.289310	−0.144655	−	0.989482i	$-0.546207\pi$
$569$	−5.32966e7	−0.289310	−0.144655	+	0.989482i	$0.546207\pi$
$570$	− 3.76855e7i	− 0.203493i
$571$	4.11381e7	0.220971	0.110486	−	0.993878i	$-0.464759\pi$
$571$	4.11381e7	0.220971	0.110486	+	0.993878i	$0.464759\pi$
$572$	− 3.64221e8i	− 1.94615i
$573$	− 2.24697e7i	− 0.119435i
$574$	0	0
$575$	−628469.	−0.00330583
$576$	−2.85035e8	−1.49153
$577$	− 8.77412e7i	− 0.456747i	−0.973574	−	0.228374i	$-0.926659\pi$
$577$	− 8.77412e7i	− 0.456747i	0.973574	−	0.228374i	$-0.0733408\pi$
$578$	3.74858e8	1.94126
$579$	− 2.65345e7i	− 0.136702i
$580$	1.12378e8i	0.575965i
$581$	0	0
$582$	2.60780e8	1.32284
$583$	6.19081e7	0.312422
$584$	9.94040e8i	4.99074i
$585$	2.04473e7	0.102133
$586$	1.82061e8i	0.904742i
$587$	− 4.55880e7i	− 0.225391i	−0.993630	−	0.112695i	$-0.964052\pi$
$587$	− 4.55880e7i	− 0.225391i	0.993630	−	0.112695i	$-0.0359485\pi$
$588$	0	0
$589$	1.21588e8	0.595039
$590$	4.05612e7	0.197495
$591$	− 1.00174e8i	− 0.485282i
$592$	−2.87629e8	−1.38633
$593$	1.45331e8i	0.696937i	0.937321	+	0.348468i	$0.113298\pi$
$593$	1.45331e8i	0.696937i	−0.937321	+	0.348468i	$0.886702\pi$
$594$	3.68590e7i	0.175867i
$595$	0	0
$596$	−5.57581e8	−2.63372
$597$	−1.03879e8	−0.488208
$598$	2.13436e6i	0.00998078i
$599$	5.63084e7	0.261995	0.130998	−	0.991383i	$-0.458182\pi$
$599$	5.63084e7	0.261995	0.130998	+	0.991383i	$0.458182\pi$
$600$	− 4.18956e8i	− 1.93961i
$601$	− 2.39440e8i	− 1.10299i	−0.834177	−	0.551497i	$-0.814057\pi$
$601$	− 2.39440e8i	− 1.10299i	0.834177	−	0.551497i	$-0.185943\pi$
$602$	0	0
$603$	−9.98439e6	−0.0455376
$604$	−3.11693e8	−1.41454
$605$	3.57082e7i	0.161251i
$606$	−1.29468e8	−0.581759
$607$	2.94325e8i	1.31602i	0.753011	+	0.658008i	$0.228601\pi$
$607$	2.94325e8i	1.31602i	−0.753011	+	0.658008i	$0.771399\pi$
$608$	8.58938e8i	3.82165i
$609$	0	0
$610$	9.35483e7	0.412141
$611$	−2.14535e8	−0.940533
$612$	− 1.38411e7i	− 0.0603832i
$613$	2.20783e8	0.958482	0.479241	−	0.877683i	$-0.340912\pi$
$613$	2.20783e8	0.958482	0.479241	+	0.877683i	$0.340912\pi$
$614$	− 4.99351e8i	− 2.15725i
$615$	− 4.04853e7i	− 0.174049i
$616$	0	0
$617$	3.86786e8	1.64670	0.823352	−	0.567531i	$-0.192101\pi$
$617$	3.86786e8	1.64670	0.823352	+	0.567531i	$0.192101\pi$
$618$	−2.53951e8	−1.07593
$619$	1.30592e8i	0.550610i	0.961357	+	0.275305i	$0.0887789\pi$
$619$	1.30592e8i	0.550610i	−0.961357	+	0.275305i	$0.911221\pi$
$620$	−9.38083e7	−0.393610
$621$	− 159159.i	0 0.000664592i
$622$	3.78321e7i	0.157213i
$623$	0	0
$624$	−8.40446e8	−3.45904
$625$	2.13304e8	0.873693
$626$	− 4.37790e8i	− 1.78461i
$627$	5.83636e7	0.236777
$628$	− 1.52152e8i	− 0.614328i
$629$	− 5.52292e6i	− 0.0221930i
$630$	0	0
$631$	−1.10414e8	−0.439475	−0.219738	−	0.975559i	$-0.570520\pi$
$631$	−1.10414e8	−0.439475	−0.219738	+	0.975559i	$0.570520\pi$
$632$	−1.88333e7	−0.0746064
$633$	− 1.66394e7i	− 0.0656036i
$634$	1.19806e8	0.470121
$635$	2.74871e7i	0.107351i
$636$	− 2.77195e8i	− 1.07749i
$637$	0	0
$638$	−2.36192e8	−0.909499
$639$	9.72878e7	0.372869
$640$	− 2.35911e8i	− 0.899929i
$641$	−5.12786e7	−0.194698	−0.0973491	−	0.995250i	$-0.531036\pi$
$641$	−5.12786e7	−0.194698	−0.0973491	+	0.995250i	$0.531036\pi$
$642$	− 8.72374e7i	− 0.329684i
$643$	− 2.95342e8i	− 1.11094i	−0.831535	−	0.555472i	$-0.812537\pi$
$643$	− 2.95342e8i	− 1.11094i	0.831535	−	0.555472i	$-0.187463\pi$
$644$	0	0
$645$	2.73326e7	0.101860
$646$	−2.97430e7	−0.110328
$647$	− 2.93490e8i	− 1.08363i	−0.840499	−	0.541814i	$-0.817738\pi$
$647$	− 2.93490e8i	− 1.08363i	0.840499	−	0.541814i	$-0.182262\pi$
$648$	1.06100e8	0.389933
$649$	6.28173e7i	0.229797i
$650$	− 7.59820e8i	− 2.76675i
$651$	0	0
$652$	2.40724e8	0.868515
$653$	3.17061e8	1.13868	0.569342	−	0.822101i	$-0.307198\pi$
$653$	3.17061e8	1.13868	0.569342	+	0.822101i	$0.307198\pi$
$654$	− 1.82908e8i	− 0.653881i
$655$	1.68553e7	0.0599808
$656$	1.66407e9i	5.89468i
$657$	− 1.34434e8i	− 0.474036i
$658$	0	0
$659$	1.86604e8	0.652026	0.326013	−	0.945365i	$-0.394295\pi$
$659$	1.86604e8	0.652026	0.326013	+	0.945365i	$0.394295\pi$
$660$	−4.50290e7	−0.156625
$661$	2.95944e8i	1.02472i	0.858771	+	0.512359i	$0.171228\pi$
$661$	2.95944e8i	1.02472i	−0.858771	+	0.512359i	$0.828772\pi$
$662$	−7.99737e8	−2.75660
$663$	− 1.61379e7i	− 0.0553739i
$664$	1.28076e9i	4.37486i
$665$	0	0
$666$	6.58536e7	0.222924
$667$	1.01988e6	0.00343695
$668$	1.18339e9i	3.97008i
$669$	−2.60945e8	−0.871507
$670$	− 1.65534e7i	− 0.0550380i
$671$	1.44878e8i	0.479552i
$672$	0	0
$673$	1.17111e8	0.384197	0.192098	−	0.981376i	$-0.438471\pi$
$673$	1.17111e8	0.384197	0.192098	+	0.981376i	$0.438471\pi$
$674$	2.53937e8	0.829365
$675$	5.66595e7i	0.184230i
$676$	−1.03639e9	−3.35491
$677$	9.38325e7i	0.302404i	0.988503	+	0.151202i	$0.0483144\pi$
$677$	9.38325e7i	0.302404i	−0.988503	+	0.151202i	$0.951686\pi$
$678$	5.76769e8i	1.85060i
$679$	0	0
$680$	1.47526e7	0.0469183
$681$	2.95582e8	0.935916
$682$	− 1.97163e8i	− 0.621545i
$683$	−2.95934e8	−0.928824	−0.464412	−	0.885619i	$-0.653734\pi$
$683$	−2.95934e8	−0.928824	−0.464412	+	0.885619i	$0.653734\pi$
$684$	− 2.61324e8i	− 0.816603i
$685$	− 1.18768e8i	− 0.369510i
$686$	0	0
$687$	6.63671e7	0.204683
$688$	−1.12346e9	−3.44977
$689$	− 3.23192e8i	− 0.988104i
$690$	263873.	0.000803245 0
$691$	1.07379e7i	0.0325450i	0.999868	+	0.0162725i	$0.00517992\pi$
$691$	1.07379e7i	0.0325450i	−0.999868	+	0.0162725i	$0.994820\pi$
$692$	− 1.68823e9i	− 5.09464i
$693$	0	0
$694$	1.18213e9	3.53660
$695$	5.08346e7	0.151427
$696$	6.79886e8i	2.01655i
$697$	−3.19527e7	−0.0943647
$698$	− 4.51860e8i	− 1.32873i
$699$	− 1.89860e8i	− 0.555906i
$700$	0	0
$701$	1.38696e8	0.402634	0.201317	−	0.979526i	$-0.435478\pi$
$701$	1.38696e8	0.402634	0.201317	+	0.979526i	$0.435478\pi$
$702$	1.92423e8	0.556218
$703$	− 1.04274e8i	− 0.300132i
$704$	7.31866e8	2.09756
$705$	2.65231e7i	0.0756933i
$706$	9.19153e8i	2.61200i
$707$	0	0
$708$	2.81265e8	0.792532
$709$	3.37569e8	0.947160	0.473580	−	0.880751i	$-0.342962\pi$
$709$	3.37569e8	0.947160	0.473580	+	0.880751i	$0.342962\pi$
$710$	1.61296e8i	0.450659i
$711$	2.54701e6	0.00708635
$712$	3.42218e8i	0.948118i
$713$	851358.i	0.00234879i
$714$	0	0
$715$	−5.25011e7	−0.143632
$716$	−5.39015e8	−1.46846
$717$	1.61807e8i	0.438975i
$718$	1.20888e9	3.26596
$719$	1.12999e8i	0.304009i	0.988380	+	0.152004i	$0.0485728\pi$
$719$	1.12999e8i	0.304009i	−0.988380	+	0.152004i	$0.951427\pi$
$720$	1.03905e8i	0.278381i
$721$	0	0
$722$	1.72140e8	0.457372
$723$	−1.74777e8	−0.462456
$724$	− 1.57222e9i	− 4.14282i
$725$	−3.63073e8	−0.952752
$726$	3.36039e8i	0.878173i
$727$	4.17662e8i	1.08698i	0.839415	+	0.543490i	$0.182898\pi$
$727$	4.17662e8i	1.08698i	−0.839415	+	0.543490i	$0.817102\pi$
$728$	0	0
$729$	−1.43489e7	−0.0370370
$730$	2.22881e8	0.572933
$731$	− 2.15721e7i	− 0.0552255i
$732$	6.48696e8	1.65389
$733$	− 7.32668e8i	− 1.86035i	−0.367113	−	0.930177i	$-0.619654\pi$
$733$	− 7.32668e8i	− 1.86035i	0.367113	−	0.930177i	$-0.380346\pi$
$734$	− 6.45658e8i	− 1.63273i
$735$	0	0
$736$	−6.01427e6	−0.0150851
$737$	2.56363e7	0.0640401
$738$	− 3.80994e8i	− 0.947872i
$739$	5.86928e8	1.45429	0.727146	−	0.686483i	$-0.240846\pi$
$739$	5.86928e8	1.45429	0.727146	+	0.686483i	$0.240846\pi$
$740$	8.04504e7i	0.198533i
$741$	− 3.04688e8i	− 0.748860i
$742$	0	0
$743$	−3.73015e8	−0.909411	−0.454705	−	0.890642i	$-0.650255\pi$
$743$	−3.73015e8	−0.909411	−0.454705	+	0.890642i	$0.650255\pi$
$744$	−5.67541e8	−1.37809
$745$	8.03731e7i	0.194376i
$746$	−7.47604e8	−1.80076
$747$	− 1.73210e8i	− 0.415538i
$748$	3.55388e7i	0.0849177i
$749$	0	0
$750$	−1.92066e8	−0.455267
$751$	−5.47818e8	−1.29335	−0.646675	−	0.762765i	$-0.723841\pi$
$751$	−5.47818e8	−1.29335	−0.646675	+	0.762765i	$0.723841\pi$
$752$	− 1.09018e9i	− 2.56357i
$753$	−4.10981e8	−0.962580
$754$	1.23304e9i	2.87649i
$755$	4.49293e7i	0.104397i
$756$	0	0
$757$	4.01667e8	0.925931	0.462966	−	0.886376i	$-0.346785\pi$
$757$	4.01667e8	0.925931	0.462966	+	0.886376i	$0.346785\pi$
$758$	−2.69845e8	−0.619592
$759$	408661.i	0 0.000934626i
$760$	2.78534e8	0.634509
$761$	1.09613e8i	0.248717i	0.992237	+	0.124359i	$0.0396874\pi$
$761$	1.09613e8i	0.248717i	−0.992237	+	0.124359i	$0.960313\pi$
$762$	2.58673e8i	0.584636i
$763$	0	0
$764$	2.58325e8	0.579278
$765$	−1.99514e6	−0.00445645
$766$	1.00905e9i	2.24506i
$767$	3.27938e8	0.726785
$768$	− 1.04984e9i	− 2.31761i
$769$	− 2.51373e8i	− 0.552763i	−0.961048	−	0.276381i	$-0.910865\pi$
$769$	− 2.51373e8i	− 0.552763i	0.961048	−	0.276381i	$-0.0891353\pi$
$770$	0	0
$771$	−4.01099e8	−0.875162
$772$	3.05057e8	0.663023
$773$	− 5.78306e8i	− 1.25204i	−0.779806	−	0.626022i	$-0.784682\pi$
$773$	− 5.78306e8i	− 1.25204i	0.779806	−	0.626022i	$-0.215318\pi$
$774$	2.57219e8	0.554728
$775$	− 3.03078e8i	− 0.651103i
$776$	1.92743e9i	4.12471i
$777$	0	0
$778$	−1.23870e9	−2.63044
$779$	−6.03277e8	−1.27616
$780$	2.35074e8i	0.495361i
$781$	−2.49799e8	−0.524370
$782$	− 208260.i	0 0.000435497i
$783$	− 9.19475e7i	− 0.191538i
$784$	0	0
$785$	−2.19322e7	−0.0453391
$786$	1.58620e8	0.326655
$787$	5.81321e8i	1.19259i	0.802765	+	0.596296i	$0.203361\pi$
$787$	5.81321e8i	1.19259i	−0.802765	+	0.596296i	$0.796639\pi$
$788$	1.15167e9	2.35369
$789$	− 2.63731e8i	− 0.536946i
$790$	4.22276e6i	0.00856476i
$791$	0	0
$792$	−2.72426e8	−0.548368
$793$	7.56340e8	1.51669
$794$	3.94671e8i	0.788449i
$795$	−3.99565e7	−0.0795218
$796$	− 1.19426e9i	− 2.36788i
$797$	− 2.88172e8i	− 0.569215i	−0.958644	−	0.284607i	$-0.908137\pi$
$797$	− 2.88172e8i	− 0.569215i	0.958644	−	0.284607i	$-0.0918632\pi$
$798$	0	0
$799$	2.09332e7	0.0410388
$800$	2.14104e9	4.18173
$801$	− 4.62814e7i	− 0.0900552i
$802$	1.76514e8	0.342182
$803$	3.45176e8i	0.666644i
$804$	− 1.14787e8i	− 0.220863i
$805$	0	0
$806$	−1.02929e9	−1.96577
$807$	−4.11445e8	−0.782872
$808$	− 9.56897e8i	− 1.81397i
$809$	5.37358e7	0.101489	0.0507444	−	0.998712i	$-0.483841\pi$
$809$	5.37358e7	0.101489	0.0507444	+	0.998712i	$0.483841\pi$
$810$	− 2.37894e7i	− 0.0447640i
$811$	1.37731e8i	0.258208i	0.991631	+	0.129104i	$0.0412101\pi$
$811$	1.37731e8i	0.258208i	−0.991631	+	0.129104i	$0.958790\pi$
$812$	0	0
$813$	−9.92583e7	−0.184712
$814$	−1.69088e8	−0.313501
$815$	− 3.46995e7i	− 0.0640988i
$816$	8.20064e7	0.150931
$817$	− 4.07287e8i	− 0.746852i
$818$	− 5.99599e8i	− 1.09547i
$819$	0	0
$820$	4.65444e8	0.844162
$821$	4.54400e8	0.821125	0.410563	−	0.911832i	$-0.365332\pi$
$821$	4.54400e8	0.821125	0.410563	+	0.911832i	$0.365332\pi$
$822$	− 1.11769e9i	− 2.01235i
$823$	2.38303e8	0.427493	0.213747	−	0.976889i	$-0.431433\pi$
$823$	2.38303e8	0.427493	0.213747	+	0.976889i	$0.431433\pi$
$824$	− 1.87696e9i	− 3.35485i
$825$	− 1.45481e8i	− 0.259086i
$826$	0	0
$827$	1.39387e8	0.246437	0.123218	−	0.992380i	$-0.460678\pi$
$827$	1.39387e8	0.246437	0.123218	+	0.992380i	$0.460678\pi$
$828$	1.82979e6	0.00322336
$829$	7.90914e8i	1.38824i	0.719858	+	0.694121i	$0.244207\pi$
$829$	7.90914e8i	1.38824i	−0.719858	+	0.694121i	$0.755793\pi$
$830$	2.87169e8	0.502230
$831$	5.37977e8i	0.937476i
$832$	− 3.82072e9i	− 6.63399i
$833$	0	0
$834$	4.78388e8	0.824674
$835$	1.70581e8	0.293003
$836$	6.70984e8i	1.14840i
$837$	7.67540e7	0.130895
$838$	8.66592e8i	1.47259i
$839$	8.67968e8i	1.46966i	0.678250	+	0.734832i	$0.262739\pi$
$839$	8.67968e8i	1.46966i	−0.678250	+	0.734832i	$0.737261\pi$
$840$	0	0
$841$	−5.62593e6	−0.00945816
$842$	−1.44672e9	−2.42352
$843$	− 6.27055e8i	− 1.04670i
$844$	1.91297e8	0.318186
$845$	1.49391e8i	0.247602i
$846$	2.49601e8i	0.412226i
$847$	0	0
$848$	1.64234e9	2.69324
$849$	−4.56026e7	−0.0745189
$850$	7.41393e7i	0.120724i
$851$	730128.	0.00118470
$852$	1.11848e9i	1.80846i
$853$	7.06613e8i	1.13850i	0.822163	+	0.569252i	$0.192767\pi$
$853$	7.06613e8i	1.13850i	−0.822163	+	0.569252i	$0.807233\pi$
$854$	0	0
$855$	−3.76688e7	−0.0602676
$856$	6.44773e8	1.02798
$857$	− 5.56894e8i	− 0.884770i	−0.896825	−	0.442385i	$-0.854132\pi$
$857$	− 5.56894e8i	− 0.884770i	0.896825	−	0.442385i	$-0.145868\pi$
$858$	−4.94071e8	−0.782218
$859$	− 2.93583e8i	− 0.463181i	−0.972813	−	0.231591i	$-0.925607\pi$
$859$	− 2.93583e8i	− 0.463181i	0.972813	−	0.231591i	$-0.0743930\pi$
$860$	3.14233e8i	0.494033i
$861$	0	0
$862$	2.05453e9	3.20767
$863$	9.03505e8	1.40572	0.702859	−	0.711330i	$-0.251907\pi$
$863$	9.03505e8	1.40572	0.702859	+	0.711330i	$0.251907\pi$
$864$	5.42215e8i	0.840679i
$865$	−2.43352e8	−0.375999
$866$	− 1.50433e9i	− 2.31627i
$867$	− 3.74693e8i	− 0.574934i
$868$	0	0
$869$	−6.53980e6	−0.00996564
$870$	1.52442e8	0.231498
$871$	− 1.33834e8i	− 0.202541i
$872$	1.35187e9	2.03886
$873$	− 2.60665e8i	− 0.391778i
$874$	− 3.93201e6i	− 0.00588953i
$875$	0	0
$876$	1.54553e9	2.29914
$877$	1.79725e8	0.266446	0.133223	−	0.991086i	$-0.457467\pi$
$877$	1.79725e8	0.266446	0.133223	+	0.991086i	$0.457467\pi$
$878$	1.51619e9i	2.24012i
$879$	1.81981e8	0.267953
$880$	− 2.66790e8i	− 0.391491i
$881$	− 1.07737e9i	− 1.57556i	−0.615954	−	0.787782i	$-0.711229\pi$
$881$	− 1.07737e9i	− 1.57556i	0.615954	−	0.787782i	$-0.288771\pi$
$882$	0	0
$883$	−1.25270e9	−1.81955	−0.909775	−	0.415102i	$-0.863746\pi$
$883$	−1.25270e9	−1.81955	−0.909775	+	0.415102i	$0.863746\pi$
$884$	1.85531e8	0.268571
$885$	− 4.05433e7i	− 0.0584911i
$886$	−2.59502e9	−3.73112
$887$	− 3.80594e8i	− 0.545369i	−0.962103	−	0.272685i	$-0.912088\pi$
$887$	− 3.80594e8i	− 0.545369i	0.962103	−	0.272685i	$-0.0879116\pi$
$888$	4.86725e8i	0.695096i
$889$	0	0
$890$	7.67311e7	0.108843
$891$	3.68427e7	0.0520857
$892$	− 2.99999e9i	− 4.22693i
$893$	3.95225e8	0.554996
$894$	7.56367e8i	1.05857i
$895$	7.76969e7i	0.108376i
$896$	0	0
$897$	2.13342e6	0.00295596
$898$	−1.62143e9	−2.23908
$899$	4.91838e8i	0.676929i
$900$	−6.51393e8	−0.893543
$901$	3.15354e7i	0.0431146i
$902$	9.78254e8i	1.33301i
$903$	0	0
$904$	−4.26291e9	−5.77033
$905$	−2.26629e8	−0.305752
$906$	4.22816e8i	0.568547i
$907$	6.65062e8	0.891334	0.445667	−	0.895199i	$-0.352967\pi$
$907$	6.65062e8	0.891334	0.445667	+	0.895199i	$0.352967\pi$
$908$	3.39820e9i	4.53932i
$909$	1.29410e8i	0.172297i
$910$	0	0
$911$	−9.53125e8	−1.26065	−0.630325	−	0.776331i	$-0.717078\pi$
$911$	−9.53125e8	−1.26065	−0.630325	+	0.776331i	$0.717078\pi$
$912$	1.54831e9	2.04114
$913$	4.44739e8i	0.584376i
$914$	−1.10569e9	−1.44809
$915$	− 9.35070e7i	− 0.122062i
$916$	7.62997e8i	0.992742i
$917$	0	0
$918$	−1.87756e7	−0.0242698
$919$	−1.24972e9	−1.61015	−0.805076	−	0.593172i	$-0.797875\pi$
$919$	−1.24972e9	−1.61015	−0.805076	+	0.593172i	$0.797875\pi$
$920$	1.95029e6i	0.00250459i
$921$	−4.99131e8	−0.638904
$922$	4.59619e8i	0.586415i
$923$	1.30408e9i	1.65844i
$924$	0	0
$925$	−2.59921e8	−0.328410
$926$	−1.19650e9	−1.50689
$927$	2.53839e8i	0.318654i
$928$	−3.47450e9	−4.34759
$929$	1.04296e9i	1.30083i	0.759580	+	0.650414i	$0.225404\pi$
$929$	1.04296e9i	1.30083i	−0.759580	+	0.650414i	$0.774596\pi$
$930$	1.27252e8i	0.158204i
$931$	0	0
$932$	2.18274e9	2.69622
$933$	3.78154e7	0.0465612
$934$	3.05292e9i	3.74692i
$935$	5.12278e6	0.00626717
$936$	1.42220e9i	1.73434i
$937$	4.82808e8i	0.586889i	0.955976	+	0.293444i	$0.0948015\pi$
$937$	4.82808e8i	0.586889i	−0.955976	+	0.293444i	$0.905198\pi$
$938$	0	0
$939$	−4.37597e8	−0.528540
$940$	−3.04926e8	−0.367123
$941$	− 5.66343e8i	− 0.679690i	−0.940482	−	0.339845i	$-0.889625\pi$
$941$	− 5.66343e8i	− 0.679690i	0.940482	−	0.339845i	$-0.110375\pi$
$942$	−2.06397e8	−0.246917
$943$	− 4.22414e6i	− 0.00503736i
$944$	1.66646e9i	1.98097i
$945$	0	0
$946$	−6.60443e8	−0.780121
$947$	−2.18515e7	−0.0257295	−0.0128648	−	0.999917i	$-0.504095\pi$
$947$	−2.18515e7	−0.0257295	−0.0128648	+	0.999917i	$0.504095\pi$
$948$	2.92821e7i	0.0343698i
$949$	1.80200e9	2.10841
$950$	1.39977e9i	1.63263i
$951$	− 1.19753e8i	− 0.139234i
$952$	0	0
$953$	1.05425e9	1.21805	0.609023	−	0.793152i	$-0.291562\pi$
$953$	1.05425e9	1.21805	0.609023	+	0.793152i	$0.291562\pi$
$954$	−3.76018e8	−0.433076
$955$	− 3.72366e7i	− 0.0427523i
$956$	−1.86024e9	−2.12909
$957$	2.36087e8i	0.269362i
$958$	− 5.01041e8i	− 0.569871i
$959$	0	0
$960$	−4.72359e8	−0.533898
$961$	4.76938e8	0.537392
$962$	8.82725e8i	0.991517i
$963$	−8.71989e7	−0.0976410
$964$	− 2.00935e9i	− 2.24297i
$965$	− 4.39728e7i	− 0.0489330i
$966$	0	0
$967$	−7.18604e8	−0.794713	−0.397356	−	0.917664i	$-0.630072\pi$
$967$	−7.18604e8	−0.794713	−0.397356	+	0.917664i	$0.630072\pi$
$968$	−2.48367e9	−2.73822
$969$	2.97299e7i	0.0326755i
$970$	4.32163e8	0.473514
$971$	− 6.32949e8i	− 0.691371i	−0.938350	−	0.345686i	$-0.887646\pi$
$971$	− 6.32949e8i	− 0.691371i	0.938350	−	0.345686i	$-0.112354\pi$
$972$	− 1.64964e8i	− 0.179635i
$973$	0	0
$974$	−2.70183e9	−2.92402
$975$	−7.59485e8	−0.819417
$976$	3.84343e9i	4.13399i
$977$	1.31932e9	1.41470	0.707351	−	0.706862i	$-0.249890\pi$
$977$	1.31932e9	1.41470	0.707351	+	0.706862i	$0.249890\pi$
$978$	− 3.26546e8i	− 0.349082i
$979$	1.18834e8i	0.126646i
$980$	0	0
$981$	−1.82827e8	−0.193657
$982$	3.55146e8	0.375036
$983$	− 7.43820e7i	− 0.0783082i	−0.999233	−	0.0391541i	$-0.987534\pi$
$983$	− 7.43820e7i	− 0.0783082i	0.999233	−	0.0391541i	$-0.0124663\pi$
$984$	2.81594e9	2.95555
$985$	− 1.66008e8i	− 0.173709i
$986$	− 1.20314e8i	− 0.125512i
$987$	0	0
$988$	3.50288e9	3.63207
$989$	2.85182e6	0.00294804
$990$	6.10825e7i	0.0629522i
$991$	1.59763e9	1.64155	0.820777	−	0.571249i	$-0.193541\pi$
$991$	1.59763e9	1.64155	0.820777	+	0.571249i	$0.193541\pi$
$992$	− 2.90037e9i	− 2.97111i
$993$	7.99384e8i	0.816409i
$994$	0	0
$995$	−1.72148e8	−0.174756
$996$	1.99133e9	2.01541
$997$	− 1.30659e9i	− 1.31842i	−0.751957	−	0.659212i	$-0.770890\pi$
$997$	− 1.30659e9i	− 1.31842i	0.751957	−	0.659212i	$-0.229110\pi$
$998$	−2.23196e9	−2.24541
$999$	− 6.58245e7i	− 0.0660224i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.7.d.b.97.7		8
3.2	odd	2		441.7.d.c.244.2		8
7.2	even	3		147.7.f.d.31.1		8
7.3	odd	6		147.7.f.d.19.1		8
7.4	even	3		21.7.f.a.19.1	yes	8
7.5	odd	6		21.7.f.a.10.1	✓	8
7.6	odd	2	inner	147.7.d.b.97.8		8
21.5	even	6		63.7.m.d.10.4		8
21.11	odd	6		63.7.m.d.19.4		8
21.20	even	2		441.7.d.c.244.1		8
28.11	odd	6		336.7.bh.d.145.3		8
28.19	even	6		336.7.bh.d.241.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.a.10.1	✓	8	7.5	odd	6
21.7.f.a.19.1	yes	8	7.4	even	3
63.7.m.d.10.4		8	21.5	even	6
63.7.m.d.19.4		8	21.11	odd	6
147.7.d.b.97.7		8	1.1	even	1	trivial
147.7.d.b.97.8		8	7.6	odd	2	inner
147.7.f.d.19.1		8	7.3	odd	6
147.7.f.d.31.1		8	7.2	even	3
336.7.bh.d.145.3		8	28.11	odd	6
336.7.bh.d.241.3		8	28.19	even	6
441.7.d.c.244.1		8	21.20	even	2
441.7.d.c.244.2		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+15.5953 q^{2} -15.5885i q^{3} +179.215 q^{4} -25.8331i q^{5} -243.107i q^{6} +1796.81 q^{8} -243.000 q^{9} +O(q^{10})\)	\(q+15.5953 q^{2} -15.5885i q^{3} +179.215 q^{4} -25.8331i q^{5} -243.107i q^{6} +1796.81 q^{8} -243.000 q^{9} -402.876i q^{10} +623.935 q^{11} -2793.68i q^{12} -3257.26i q^{13} -402.698 q^{15} +16552.1 q^{16} +317.827i q^{17} -3789.67 q^{18} +6000.67i q^{19} -4629.67i q^{20} +9730.47 q^{22} -42.0166 q^{23} -28009.5i q^{24} +14957.7 q^{25} -50798.1i q^{26} +3788.00i q^{27} -24273.4 q^{29} -6280.21 q^{30} -20262.4i q^{31} +143140. q^{32} -9726.18i q^{33} +4956.62i q^{34} -43549.2 q^{36} -17377.1 q^{37} +93582.4i q^{38} -50775.7 q^{39} -46417.2i q^{40} +100535. i q^{41} -67873.7 q^{43} +111818. q^{44} +6277.44i q^{45} -655.263 q^{46} -65863.5i q^{47} -258022. i q^{48} +233270. q^{50} +4954.43 q^{51} -583749. i q^{52} +99222.0 q^{53} +59075.1i q^{54} -16118.2i q^{55} +93541.1 q^{57} -378552. q^{58} +100679. i q^{59} -72169.4 q^{60} +232201. i q^{61} -315999. i q^{62} +1.17299e6 q^{64} -84145.1 q^{65} -151683. i q^{66} +41088.0 q^{67} +56959.2i q^{68} +654.974i q^{69} -400361. q^{71} -436625. q^{72} +553224. i q^{73} -271002. q^{74} -233167. i q^{75} +1.07541e6i q^{76} -791864. q^{78} -10481.5 q^{79} -427593. i q^{80} +59049.0 q^{81} +1.56788e6i q^{82} +712797. i q^{83} +8210.45 q^{85} -1.05851e6 q^{86} +378385. i q^{87} +1.12109e6 q^{88} +190458. i q^{89} +97898.8i q^{90} -7529.99 q^{92} -315860. q^{93} -1.02716e6i q^{94} +155016. q^{95} -2.23134e6i q^{96} +1.07270e6i q^{97} -151616. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{2} + 346 q^{4} + 3326 q^{8} - 1944 q^{9}+O(q^{10}) \) 8 * q + 10 * q^2 + 346 * q^4 + 3326 * q^8 - 1944 * q^9	\( 8 q + 10 q^{2} + 346 q^{4} + 3326 q^{8} - 1944 q^{9} + 628 q^{11} + 5292 q^{15} + 25442 q^{16} - 2430 q^{18} + 86106 q^{22} - 7856 q^{23} + 34076 q^{25} - 8300 q^{29} - 61398 q^{30} + 372414 q^{32} - 84078 q^{36} - 129412 q^{37} - 58212 q^{39} + 45740 q^{43} - 185058 q^{44} + 223008 q^{46} + 967216 q^{50} - 99576 q^{51} + 1081948 q^{53} + 328212 q^{57} - 1079598 q^{58} + 292734 q^{60} + 2378626 q^{64} + 828408 q^{65} + 2317804 q^{67} + 1442344 q^{71} - 808218 q^{72} + 865880 q^{74} - 222588 q^{78} - 1222904 q^{79} + 472392 q^{81} - 275112 q^{85} - 1632448 q^{86} + 732882 q^{88} + 678720 q^{92} - 1611144 q^{93} + 1183584 q^{95} - 152604 q^{99}+O(q^{100}) \) 8 * q + 10 * q^2 + 346 * q^4 + 3326 * q^8 - 1944 * q^9 + 628 * q^11 + 5292 * q^15 + 25442 * q^16 - 2430 * q^18 + 86106 * q^22 - 7856 * q^23 + 34076 * q^25 - 8300 * q^29 - 61398 * q^30 + 372414 * q^32 - 84078 * q^36 - 129412 * q^37 - 58212 * q^39 + 45740 * q^43 - 185058 * q^44 + 223008 * q^46 + 967216 * q^50 - 99576 * q^51 + 1081948 * q^53 + 328212 * q^57 - 1079598 * q^58 + 292734 * q^60 + 2378626 * q^64 + 828408 * q^65 + 2317804 * q^67 + 1442344 * q^71 - 808218 * q^72 + 865880 * q^74 - 222588 * q^78 - 1222904 * q^79 + 472392 * q^81 - 275112 * q^85 - 1632448 * q^86 + 732882 * q^88 + 678720 * q^92 - 1611144 * q^93 + 1183584 * q^95 - 152604 * q^99

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