LMFDB - Embedded newform 354.8.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,8,Mod(1,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("354.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	354.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$110.584299021$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4 x^{8} - 260588 x^{7} - 2627755 x^{6} + 16696953355 x^{5} + 808091684078 x^{4} + \cdots + 15\!\cdots\!00 $ x^9 - 4x^8 - 260588x^7 - 2627755x^6 + 16696953355x^5 + 808091684078x^4 - 191825159847522x^3 - 12153827093891319x^2 + 237398587398357570x + 15300107670464479800
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{5}\cdot 5\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$37.3239$ of defining polynomial
Character	$\chi$	$=$	354.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -551.934 q^{5} +216.000 q^{6} -627.747 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -551.934 q^{5} +216.000 q^{6} -627.747 q^{7} -512.000 q^{8} +729.000 q^{9} +4415.47 q^{10} +1460.00 q^{11} -1728.00 q^{12} -4953.61 q^{13} +5021.98 q^{14} +14902.2 q^{15} +4096.00 q^{16} -15903.9 q^{17} -5832.00 q^{18} -45486.1 q^{19} -35323.8 q^{20} +16949.2 q^{21} -11680.0 q^{22} -49695.3 q^{23} +13824.0 q^{24} +226506. q^{25} +39628.9 q^{26} -19683.0 q^{27} -40175.8 q^{28} +189447. q^{29} -119218. q^{30} +141124. q^{31} -32768.0 q^{32} -39420.0 q^{33} +127231. q^{34} +346475. q^{35} +46656.0 q^{36} +154533. q^{37} +363889. q^{38} +133748. q^{39} +282590. q^{40} +81277.8 q^{41} -135593. q^{42} +258567. q^{43} +93440.1 q^{44} -402360. q^{45} +397562. q^{46} -239572. q^{47} -110592. q^{48} -429477. q^{49} -1.81205e6 q^{50} +429406. q^{51} -317031. q^{52} +1.09472e6 q^{53} +157464. q^{54} -805824. q^{55} +321407. q^{56} +1.22812e6 q^{57} -1.51557e6 q^{58} +205379. q^{59} +953742. q^{60} +1.21153e6 q^{61} -1.12899e6 q^{62} -457628. q^{63} +262144. q^{64} +2.73407e6 q^{65} +315360. q^{66} +4.51520e6 q^{67} -1.01785e6 q^{68} +1.34177e6 q^{69} -2.77180e6 q^{70} -4.35107e6 q^{71} -373248. q^{72} +5.35710e6 q^{73} -1.23627e6 q^{74} -6.11566e6 q^{75} -2.91111e6 q^{76} -916512. q^{77} -1.06998e6 q^{78} +1.66011e6 q^{79} -2.26072e6 q^{80} +531441. q^{81} -650222. q^{82} -3.04539e6 q^{83} +1.08475e6 q^{84} +8.77792e6 q^{85} -2.06854e6 q^{86} -5.11506e6 q^{87} -747521. q^{88} -1.24797e7 q^{89} +3.21888e6 q^{90} +3.10962e6 q^{91} -3.18050e6 q^{92} -3.81034e6 q^{93} +1.91657e6 q^{94} +2.51053e7 q^{95} +884736. q^{96} +1.50734e7 q^{97} +3.43581e6 q^{98} +1.06434e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9}+O(q^{10}) $ 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9	\( 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9} + 1840 q^{10} - 5472 q^{11} - 15552 q^{12} + 3144 q^{13} + 2720 q^{14} + 6210 q^{15} + 36864 q^{16} - 3662 q^{17} - 52488 q^{18} + 692 q^{19} - 14720 q^{20} + 9180 q^{21} + 43776 q^{22} - 92046 q^{23} + 124416 q^{24} + 74731 q^{25} - 25152 q^{26} - 177147 q^{27} - 21760 q^{28} - 41060 q^{29} - 49680 q^{30} - 324504 q^{31} - 294912 q^{32} + 147744 q^{33} + 29296 q^{34} - 415602 q^{35} + 419904 q^{36} + 338612 q^{37} - 5536 q^{38} - 84888 q^{39} + 117760 q^{40} - 104312 q^{41} - 73440 q^{42} + 1000602 q^{43} - 350208 q^{44} - 167670 q^{45} + 736368 q^{46} - 365148 q^{47} - 995328 q^{48} + 2307505 q^{49} - 597848 q^{50} + 98874 q^{51} + 201216 q^{52} + 2017498 q^{53} + 1417176 q^{54} + 1120520 q^{55} + 174080 q^{56} - 18684 q^{57} + 328480 q^{58} + 1848411 q^{59} + 397440 q^{60} + 5102340 q^{61} + 2596032 q^{62} - 247860 q^{63} + 2359296 q^{64} + 7512810 q^{65} - 1181952 q^{66} + 10920464 q^{67} - 234368 q^{68} + 2485242 q^{69} + 3324816 q^{70} + 3607024 q^{71} - 3359232 q^{72} + 12949418 q^{73} - 2708896 q^{74} - 2017737 q^{75} + 44288 q^{76} + 7127994 q^{77} + 679104 q^{78} + 7489472 q^{79} - 942080 q^{80} + 4782969 q^{81} + 834496 q^{82} + 2760502 q^{83} + 587520 q^{84} + 11815354 q^{85} - 8004816 q^{86} + 1108620 q^{87} + 2801664 q^{88} - 9948196 q^{89} + 1341360 q^{90} + 19400656 q^{91} - 5890944 q^{92} + 8761608 q^{93} + 2921184 q^{94} + 24045208 q^{95} + 7962624 q^{96} + 38157642 q^{97} - 18460040 q^{98} - 3989088 q^{99}+O(q^{100}) \) 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9 + 1840 * q^10 - 5472 * q^11 - 15552 * q^12 + 3144 * q^13 + 2720 * q^14 + 6210 * q^15 + 36864 * q^16 - 3662 * q^17 - 52488 * q^18 + 692 * q^19 - 14720 * q^20 + 9180 * q^21 + 43776 * q^22 - 92046 * q^23 + 124416 * q^24 + 74731 * q^25 - 25152 * q^26 - 177147 * q^27 - 21760 * q^28 - 41060 * q^29 - 49680 * q^30 - 324504 * q^31 - 294912 * q^32 + 147744 * q^33 + 29296 * q^34 - 415602 * q^35 + 419904 * q^36 + 338612 * q^37 - 5536 * q^38 - 84888 * q^39 + 117760 * q^40 - 104312 * q^41 - 73440 * q^42 + 1000602 * q^43 - 350208 * q^44 - 167670 * q^45 + 736368 * q^46 - 365148 * q^47 - 995328 * q^48 + 2307505 * q^49 - 597848 * q^50 + 98874 * q^51 + 201216 * q^52 + 2017498 * q^53 + 1417176 * q^54 + 1120520 * q^55 + 174080 * q^56 - 18684 * q^57 + 328480 * q^58 + 1848411 * q^59 + 397440 * q^60 + 5102340 * q^61 + 2596032 * q^62 - 247860 * q^63 + 2359296 * q^64 + 7512810 * q^65 - 1181952 * q^66 + 10920464 * q^67 - 234368 * q^68 + 2485242 * q^69 + 3324816 * q^70 + 3607024 * q^71 - 3359232 * q^72 + 12949418 * q^73 - 2708896 * q^74 - 2017737 * q^75 + 44288 * q^76 + 7127994 * q^77 + 679104 * q^78 + 7489472 * q^79 - 942080 * q^80 + 4782969 * q^81 + 834496 * q^82 + 2760502 * q^83 + 587520 * q^84 + 11815354 * q^85 - 8004816 * q^86 + 1108620 * q^87 + 2801664 * q^88 - 9948196 * q^89 + 1341360 * q^90 + 19400656 * q^91 - 5890944 * q^92 + 8761608 * q^93 + 2921184 * q^94 + 24045208 * q^95 + 7962624 * q^96 + 38157642 * q^97 - 18460040 * q^98 - 3989088 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−8.00000	−0.707107
$2$	−8.00000	−0.707107
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	64.0000	0.500000
$5$	−551.934	−1.97466	−0.987329	−	0.158685i	$-0.949274\pi$
$5$	−551.934	−1.97466	−0.987329	+	0.158685i	$0.949274\pi$
$6$	216.000	0.408248
$7$	−627.747	−0.691738	−0.345869	−	0.938283i	$-0.612416\pi$
$7$	−627.747	−0.691738	−0.345869	+	0.938283i	$0.612416\pi$
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	4415.47	1.39629
$11$	1460.00	0.330734	0.165367	−	0.986232i	$-0.447119\pi$
$11$	1460.00	0.330734	0.165367	+	0.986232i	$0.447119\pi$
$12$	−1728.00	−0.288675
$13$	−4953.61	−0.625346	−0.312673	−	0.949861i	$-0.601224\pi$
$13$	−4953.61	−0.625346	−0.312673	+	0.949861i	$0.601224\pi$
$14$	5021.98	0.489133
$15$	14902.2	1.14007
$16$	4096.00	0.250000
$17$	−15903.9	−0.785115	−0.392557	−	0.919727i	$-0.628410\pi$
$17$	−15903.9	−0.785115	−0.392557	+	0.919727i	$0.628410\pi$
$18$	−5832.00	−0.235702
$19$	−45486.1	−1.52139	−0.760696	−	0.649108i	$-0.775142\pi$
$19$	−45486.1	−1.52139	−0.760696	+	0.649108i	$0.775142\pi$
$20$	−35323.8	−0.987329
$21$	16949.2	0.399375
$22$	−11680.0	−0.233864
$23$	−49695.3	−0.851662	−0.425831	−	0.904803i	$-0.640018\pi$
$23$	−49695.3	−0.851662	−0.425831	+	0.904803i	$0.640018\pi$
$24$	13824.0	0.204124
$25$	226506.	2.89928
$26$	39628.9	0.442186
$27$	−19683.0	−0.192450
$28$	−40175.8	−0.345869
$29$	189447.	1.44243	0.721214	−	0.692713i	$-0.243585\pi$
$29$	189447.	1.44243	0.721214	+	0.692713i	$0.243585\pi$
$30$	−119218.	−0.806151
$31$	141124.	0.850812	0.425406	−	0.905003i	$-0.360131\pi$
$31$	141124.	0.850812	0.425406	+	0.905003i	$0.360131\pi$
$32$	−32768.0	−0.176777
$33$	−39420.0	−0.190949
$34$	127231.	0.555160
$35$	346475.	1.36595
$36$	46656.0	0.166667
$37$	154533.	0.501552	0.250776	−	0.968045i	$-0.419314\pi$
$37$	154533.	0.501552	0.250776	+	0.968045i	$0.419314\pi$
$38$	363889.	1.07579
$39$	133748.	0.361044
$40$	282590.	0.698147
$41$	81277.8	0.184174	0.0920870	−	0.995751i	$-0.470646\pi$
$41$	81277.8	0.184174	0.0920870	+	0.995751i	$0.470646\pi$
$42$	−135593.	−0.282401
$43$	258567.	0.495946	0.247973	−	0.968767i	$-0.420236\pi$
$43$	258567.	0.495946	0.247973	+	0.968767i	$0.420236\pi$
$44$	93440.1	0.165367
$45$	−402360.	−0.658219
$46$	397562.	0.602216
$47$	−239572.	−0.336584	−0.168292	−	0.985737i	$-0.553825\pi$
$47$	−239572.	−0.336584	−0.168292	+	0.985737i	$0.553825\pi$
$48$	−110592.	−0.144338
$49$	−429477.	−0.521499
$50$	−1.81205e6	−2.05010
$51$	429406.	0.453286
$52$	−317031.	−0.312673
$53$	1.09472e6	1.01004	0.505019	−	0.863108i	$-0.331485\pi$
$53$	1.09472e6	1.01004	0.505019	+	0.863108i	$0.331485\pi$
$54$	157464.	0.136083
$55$	−805824.	−0.653087
$56$	321407.	0.244566
$57$	1.22812e6	0.878376
$58$	−1.51557e6	−1.01995
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	953742.	0.570035
$61$	1.21153e6	0.683409	0.341704	−	0.939807i	$-0.388996\pi$
$61$	1.21153e6	0.683409	0.341704	+	0.939807i	$0.388996\pi$
$62$	−1.12899e6	−0.601615
$63$	−457628.	−0.230579
$64$	262144.	0.125000
$65$	2.73407e6	1.23484
$66$	315360.	0.135022
$67$	4.51520e6	1.83407	0.917033	−	0.398810i	$-0.130577\pi$
$67$	4.51520e6	1.83407	0.917033	+	0.398810i	$0.130577\pi$
$68$	−1.01785e6	−0.392557
$69$	1.34177e6	0.491708
$70$	−2.77180e6	−0.965870
$71$	−4.35107e6	−1.44275	−0.721376	−	0.692543i	$-0.756490\pi$
$71$	−4.35107e6	−1.44275	−0.721376	+	0.692543i	$0.756490\pi$
$72$	−373248.	−0.117851
$73$	5.35710e6	1.61176	0.805879	−	0.592080i	$-0.201693\pi$
$73$	5.35710e6	1.61176	0.805879	+	0.592080i	$0.201693\pi$
$74$	−1.23627e6	−0.354651
$75$	−6.11566e6	−1.67390
$76$	−2.91111e6	−0.760696
$77$	−916512.	−0.228781
$78$	−1.06998e6	−0.255296
$79$	1.66011e6	0.378828	0.189414	−	0.981897i	$-0.439341\pi$
$79$	1.66011e6	0.378828	0.189414	+	0.981897i	$0.439341\pi$
$80$	−2.26072e6	−0.493665
$81$	531441.	0.111111
$82$	−650222.	−0.130231
$83$	−3.04539e6	−0.584614	−0.292307	−	0.956325i	$-0.594423\pi$
$83$	−3.04539e6	−0.584614	−0.292307	+	0.956325i	$0.594423\pi$
$84$	1.08475e6	0.199688
$85$	8.77792e6	1.55033
$86$	−2.06854e6	−0.350687
$87$	−5.11506e6	−0.832786
$88$	−747521.	−0.116932
$89$	−1.24797e7	−1.87646	−0.938228	−	0.346018i	$-0.887534\pi$
$89$	−1.24797e7	−1.87646	−0.938228	+	0.346018i	$0.887534\pi$
$90$	3.21888e6	0.465431
$91$	3.10962e6	0.432575
$92$	−3.18050e6	−0.425831
$93$	−3.81034e6	−0.491217
$94$	1.91657e6	0.238001
$95$	2.51053e7	3.00423
$96$	884736.	0.102062
$97$	1.50734e7	1.67691	0.838456	−	0.544969i	$-0.183459\pi$
$97$	1.50734e7	1.67691	0.838456	+	0.544969i	$0.183459\pi$
$98$	3.43581e6	0.368755
$99$	1.06434e6	0.110245
$100$	1.44964e7	1.44964
$101$	−6.12652e6	−0.591683	−0.295842	−	0.955237i	$-0.595600\pi$
$101$	−6.12652e6	−0.591683	−0.295842	+	0.955237i	$0.595600\pi$
$102$	−3.43525e6	−0.320522
$103$	1.06713e7	0.962252	0.481126	−	0.876651i	$-0.340228\pi$
$103$	1.06713e7	0.962252	0.481126	+	0.876651i	$0.340228\pi$
$104$	2.53625e6	0.221093
$105$	−9.35482e6	−0.788629
$106$	−8.75777e6	−0.714205
$107$	−804241.	−0.0634663	−0.0317331	−	0.999496i	$-0.510103\pi$
$107$	−804241.	−0.0634663	−0.0317331	+	0.999496i	$0.510103\pi$
$108$	−1.25971e6	−0.0962250
$109$	−1.93909e7	−1.43418	−0.717091	−	0.696979i	$-0.754527\pi$
$109$	−1.93909e7	−1.43418	−0.717091	+	0.696979i	$0.754527\pi$
$110$	6.44659e6	0.461802
$111$	−4.17240e6	−0.289571
$112$	−2.57125e6	−0.172934
$113$	2.23210e7	1.45525	0.727627	−	0.685973i	$-0.240623\pi$
$113$	2.23210e7	1.45525	0.727627	+	0.685973i	$0.240623\pi$
$114$	−9.82500e6	−0.621106
$115$	2.74285e7	1.68174
$116$	1.21246e7	0.721214
$117$	−3.61118e6	−0.208449
$118$	−1.64303e6	−0.0920575
$119$	9.98365e6	0.543094
$120$	−7.62993e6	−0.403075
$121$	−1.73556e7	−0.890615
$122$	−9.69226e6	−0.483243
$123$	−2.19450e6	−0.106333
$124$	9.03191e6	0.425406
$125$	−8.18964e7	−3.75042
$126$	3.66102e6	0.163044
$127$	−1.27789e7	−0.553580	−0.276790	−	0.960930i	$-0.589271\pi$
$127$	−1.27789e7	−0.553580	−0.276790	+	0.960930i	$0.589271\pi$
$128$	−2.09715e6	−0.0883883
$129$	−6.98132e6	−0.286334
$130$	−2.18725e7	−0.873167
$131$	−2.55823e7	−0.994237	−0.497119	−	0.867683i	$-0.665609\pi$
$131$	−2.55823e7	−0.994237	−0.497119	+	0.867683i	$0.665609\pi$
$132$	−2.52288e6	−0.0954747
$133$	2.85538e7	1.05240
$134$	−3.61216e7	−1.29688
$135$	1.08637e7	0.380023
$136$	8.14281e6	0.277580
$137$	3.24964e7	1.07972	0.539862	−	0.841754i	$-0.318476\pi$
$137$	3.24964e7	1.07972	0.539862	+	0.841754i	$0.318476\pi$
$138$	−1.07342e7	−0.347690
$139$	2.41690e7	0.763321	0.381660	−	0.924303i	$-0.375352\pi$
$139$	2.41690e7	0.763321	0.381660	+	0.924303i	$0.375352\pi$
$140$	2.21744e7	0.682973
$141$	6.46844e6	0.194327
$142$	3.48086e7	1.02018
$143$	−7.23228e6	−0.206823
$144$	2.98598e6	0.0833333
$145$	−1.04562e8	−2.84830
$146$	−4.28568e7	−1.13969
$147$	1.15959e7	0.301087
$148$	9.89014e6	0.250776
$149$	−3.11694e7	−0.771929	−0.385964	−	0.922514i	$-0.626131\pi$
$149$	−3.11694e7	−0.771929	−0.385964	+	0.922514i	$0.626131\pi$
$150$	4.89253e7	1.18362
$151$	2.95035e7	0.697354	0.348677	−	0.937243i	$-0.386631\pi$
$151$	2.95035e7	0.697354	0.348677	+	0.937243i	$0.386631\pi$
$152$	2.32889e7	0.537893
$153$	−1.15940e7	−0.261705
$154$	7.33209e6	0.161773
$155$	−7.78909e7	−1.68006
$156$	8.55984e6	0.180522
$157$	−7.52975e7	−1.55286	−0.776429	−	0.630204i	$-0.782971\pi$
$157$	−7.52975e7	−1.55286	−0.776429	+	0.630204i	$0.782971\pi$
$158$	−1.32809e7	−0.267872
$159$	−2.95575e7	−0.583146
$160$	1.80858e7	0.349074
$161$	3.11961e7	0.589127
$162$	−4.25153e6	−0.0785674
$163$	9.25954e7	1.67468	0.837342	−	0.546680i	$-0.184108\pi$
$163$	9.25954e7	1.67468	0.837342	+	0.546680i	$0.184108\pi$
$164$	5.20178e6	0.0920870
$165$	2.17573e7	0.377060
$166$	2.43631e7	0.413385
$167$	−5.16224e6	−0.0857691	−0.0428846	−	0.999080i	$-0.513655\pi$
$167$	−5.16224e6	−0.0857691	−0.0428846	+	0.999080i	$0.513655\pi$
$168$	−8.67798e6	−0.141200
$169$	−3.82102e7	−0.608942
$170$	−7.02233e7	−1.09625
$171$	−3.31594e7	−0.507131
$172$	1.65483e7	0.247973
$173$	−2.12255e7	−0.311671	−0.155835	−	0.987783i	$-0.549807\pi$
$173$	−2.12255e7	−0.311671	−0.155835	+	0.987783i	$0.549807\pi$
$174$	4.09205e7	0.588868
$175$	−1.42188e8	−2.00554
$176$	5.98017e6	0.0826835
$177$	−5.54523e6	−0.0751646
$178$	9.98374e7	1.32685
$179$	−3.78611e7	−0.493410	−0.246705	−	0.969091i	$-0.579348\pi$
$179$	−3.78611e7	−0.493410	−0.246705	+	0.969091i	$0.579348\pi$
$180$	−2.57510e7	−0.329110
$181$	−1.47920e7	−0.185417	−0.0927087	−	0.995693i	$-0.529553\pi$
$181$	−1.47920e7	−0.185417	−0.0927087	+	0.995693i	$0.529553\pi$
$182$	−2.48769e7	−0.305877
$183$	−3.27114e7	−0.394566
$184$	2.54440e7	0.301108
$185$	−8.52922e7	−0.990395
$186$	3.04827e7	0.347343
$187$	−2.32198e7	−0.259664
$188$	−1.53326e7	−0.168292
$189$	1.23559e7	0.133125
$190$	−2.00843e8	−2.12431
$191$	−1.56723e8	−1.62749	−0.813743	−	0.581225i	$-0.802574\pi$
$191$	−1.56723e8	−1.62749	−0.813743	+	0.581225i	$0.802574\pi$
$192$	−7.07789e6	−0.0721688
$193$	−5.65311e6	−0.0566026	−0.0283013	−	0.999599i	$-0.509010\pi$
$193$	−5.65311e6	−0.0566026	−0.0283013	+	0.999599i	$0.509010\pi$
$194$	−1.20587e8	−1.18576
$195$	−7.38198e7	−0.712938
$196$	−2.74865e7	−0.260749
$197$	1.47028e8	1.37015	0.685077	−	0.728471i	$-0.259769\pi$
$197$	1.47028e8	1.37015	0.685077	+	0.728471i	$0.259769\pi$
$198$	−8.51473e6	−0.0779548
$199$	5.61839e6	0.0505389	0.0252695	−	0.999681i	$-0.491956\pi$
$199$	5.61839e6	0.0505389	0.0252695	+	0.999681i	$0.491956\pi$
$200$	−1.15971e8	−1.02505
$201$	−1.21910e8	−1.05890
$202$	4.90122e7	0.418383
$203$	−1.18925e8	−0.997781
$204$	2.74820e7	0.226643
$205$	−4.48599e7	−0.363681
$206$	−8.53708e7	−0.680415
$207$	−3.62278e7	−0.283887
$208$	−2.02900e7	−0.156336
$209$	−6.64098e7	−0.503176
$210$	7.48386e7	0.557645
$211$	−1.85420e8	−1.35884	−0.679418	−	0.733751i	$-0.737768\pi$
$211$	−1.85420e8	−1.35884	−0.679418	+	0.733751i	$0.737768\pi$
$212$	7.00621e7	0.505019
$213$	1.17479e8	0.832974
$214$	6.43393e6	0.0448774
$215$	−1.42712e8	−0.979323
$216$	1.00777e7	0.0680414
$217$	−8.85899e7	−0.588539
$218$	1.55127e8	1.01412
$219$	−1.44642e8	−0.930549
$220$	−5.15728e7	−0.326543
$221$	7.87819e7	0.490968
$222$	3.33792e7	0.204758
$223$	−1.52833e7	−0.0922891	−0.0461446	−	0.998935i	$-0.514693\pi$
$223$	−1.52833e7	−0.0922891	−0.0461446	+	0.998935i	$0.514693\pi$
$224$	2.05700e7	0.122283
$225$	1.65123e8	0.966425
$226$	−1.78568e8	−1.02902
$227$	1.25648e8	0.712962	0.356481	−	0.934303i	$-0.383976\pi$
$227$	1.25648e8	0.712962	0.356481	+	0.934303i	$0.383976\pi$
$228$	7.86000e7	0.439188
$229$	7.36164e7	0.405089	0.202545	−	0.979273i	$-0.435079\pi$
$229$	7.36164e7	0.405089	0.202545	+	0.979273i	$0.435079\pi$
$230$	−2.19428e8	−1.18917
$231$	2.47458e7	0.132087
$232$	−9.69967e7	−0.509975
$233$	−1.18825e8	−0.615408	−0.307704	−	0.951482i	$-0.599561\pi$
$233$	−1.18825e8	−0.615408	−0.307704	+	0.951482i	$0.599561\pi$
$234$	2.88895e7	0.147395
$235$	1.32228e8	0.664638
$236$	1.31443e7	0.0650945
$237$	−4.48230e7	−0.218717
$238$	−7.98692e7	−0.384025
$239$	2.08905e8	0.989821	0.494910	−	0.868944i	$-0.335201\pi$
$239$	2.08905e8	0.989821	0.494910	+	0.868944i	$0.335201\pi$
$240$	6.10395e7	0.285017
$241$	3.09665e8	1.42506	0.712530	−	0.701642i	$-0.247549\pi$
$241$	3.09665e8	1.42506	0.712530	+	0.701642i	$0.247549\pi$
$242$	1.38845e8	0.629760
$243$	−1.43489e7	−0.0641500
$244$	7.75381e7	0.341704
$245$	2.37043e8	1.02978
$246$	1.75560e7	0.0751887
$247$	2.25321e8	0.951396
$248$	−7.22553e7	−0.300807
$249$	8.22255e7	0.337527
$250$	6.55172e8	2.65195
$251$	−3.72436e7	−0.148660	−0.0743299	−	0.997234i	$-0.523682\pi$
$251$	−3.72436e7	−0.148660	−0.0743299	+	0.997234i	$0.523682\pi$
$252$	−2.92882e7	−0.115290
$253$	−7.25552e7	−0.281674
$254$	1.02231e8	0.391440
$255$	−2.37004e8	−0.895086
$256$	1.67772e7	0.0625000
$257$	−3.05774e8	−1.12366	−0.561829	−	0.827253i	$-0.689902\pi$
$257$	−3.05774e8	−1.12366	−0.561829	+	0.827253i	$0.689902\pi$
$258$	5.58506e7	0.202469
$259$	−9.70079e7	−0.346943
$260$	1.74980e8	0.617422
$261$	1.38107e8	0.480809
$262$	2.04658e8	0.703032
$263$	6.81093e7	0.230867	0.115433	−	0.993315i	$-0.463174\pi$
$263$	6.81093e7	0.230867	0.115433	+	0.993315i	$0.463174\pi$
$264$	2.01831e7	0.0675108
$265$	−6.04213e8	−1.99448
$266$	−2.28430e8	−0.744162
$267$	3.36951e8	1.08337
$268$	2.88973e8	0.917033
$269$	2.12517e8	0.665674	0.332837	−	0.942984i	$-0.391994\pi$
$269$	2.12517e8	0.665674	0.332837	+	0.942984i	$0.391994\pi$
$270$	−8.69097e7	−0.268717
$271$	−2.41968e8	−0.738525	−0.369263	−	0.929325i	$-0.620390\pi$
$271$	−2.41968e8	−0.738525	−0.369263	+	0.929325i	$0.620390\pi$
$272$	−6.51425e7	−0.196279
$273$	−8.39596e7	−0.249748
$274$	−2.59971e8	−0.763480
$275$	3.30699e8	0.958889
$276$	8.58734e7	0.245854
$277$	−4.11359e8	−1.16290	−0.581449	−	0.813583i	$-0.697514\pi$
$277$	−4.11359e8	−1.16290	−0.581449	+	0.813583i	$0.697514\pi$
$278$	−1.93352e8	−0.539749
$279$	1.02879e8	0.283604
$280$	−1.77395e8	−0.482935
$281$	−2.53714e7	−0.0682138	−0.0341069	−	0.999418i	$-0.510859\pi$
$281$	−2.53714e7	−0.0682138	−0.0341069	+	0.999418i	$0.510859\pi$
$282$	−5.17475e7	−0.137410
$283$	3.57095e8	0.936551	0.468276	−	0.883582i	$-0.344875\pi$
$283$	3.57095e8	0.936551	0.468276	+	0.883582i	$0.344875\pi$
$284$	−2.78469e8	−0.721376
$285$	−6.77844e8	−1.73449
$286$	5.78583e7	0.146246
$287$	−5.10219e7	−0.127400
$288$	−2.38879e7	−0.0589256
$289$	−1.57404e8	−0.383595
$290$	8.36496e8	2.01405
$291$	−4.06982e8	−0.968166
$292$	3.42855e8	0.805879
$293$	5.66735e8	1.31626	0.658132	−	0.752902i	$-0.271347\pi$
$293$	5.66735e8	1.31626	0.658132	+	0.752902i	$0.271347\pi$
$294$	−9.27669e7	−0.212901
$295$	−1.13356e8	−0.257079
$296$	−7.91211e7	−0.177326
$297$	−2.87372e7	−0.0636498
$298$	2.49356e8	0.545836
$299$	2.46171e8	0.532584
$300$	−3.91402e8	−0.836949
$301$	−1.62315e8	−0.343064
$302$	−2.36028e8	−0.493104
$303$	1.65416e8	0.341609
$304$	−1.86311e8	−0.380348
$305$	−6.68686e8	−1.34950
$306$	9.27517e7	0.185053
$307$	−6.57171e8	−1.29627	−0.648133	−	0.761528i	$-0.724450\pi$
$307$	−6.57171e8	−1.29627	−0.648133	+	0.761528i	$0.724450\pi$
$308$	−5.86568e7	−0.114391
$309$	−2.88126e8	−0.555557
$310$	6.23127e8	1.18798
$311$	2.92415e8	0.551236	0.275618	−	0.961267i	$-0.411117\pi$
$311$	2.92415e8	0.551236	0.275618	+	0.961267i	$0.411117\pi$
$312$	−6.84787e7	−0.127648
$313$	1.45502e8	0.268203	0.134101	−	0.990968i	$-0.457185\pi$
$313$	1.45502e8	0.268203	0.134101	+	0.990968i	$0.457185\pi$
$314$	6.02380e8	1.09804
$315$	2.52580e8	0.455315
$316$	1.06247e8	0.189414
$317$	2.31052e8	0.407383	0.203692	−	0.979035i	$-0.434706\pi$
$317$	2.31052e8	0.407383	0.203692	+	0.979035i	$0.434706\pi$
$318$	2.36460e8	0.412346
$319$	2.76592e8	0.477060
$320$	−1.44686e8	−0.246832
$321$	2.17145e7	0.0366423
$322$	−2.49568e8	−0.416576
$323$	7.23408e8	1.19447
$324$	3.40122e7	0.0555556
$325$	−1.12202e9	−1.81305
$326$	−7.40763e8	−1.18418
$327$	5.23553e8	0.828025
$328$	−4.16142e7	−0.0651153
$329$	1.50390e8	0.232828
$330$	−1.74058e8	−0.266622
$331$	2.17918e8	0.330289	0.165145	−	0.986269i	$-0.447191\pi$
$331$	2.17918e8	0.330289	0.165145	+	0.986269i	$0.447191\pi$
$332$	−1.94905e8	−0.292307
$333$	1.12655e8	0.167184
$334$	4.12980e7	0.0606479
$335$	−2.49209e9	−3.62166
$336$	6.94238e7	0.0998438
$337$	−6.82562e8	−0.971488	−0.485744	−	0.874101i	$-0.661451\pi$
$337$	−6.82562e8	−0.971488	−0.485744	+	0.874101i	$0.661451\pi$
$338$	3.05682e8	0.430587
$339$	−6.02666e8	−0.840191
$340$	5.61787e8	0.775167
$341$	2.06041e8	0.281393
$342$	2.65275e8	0.358596
$343$	7.86579e8	1.05248
$344$	−1.32387e8	−0.175343
$345$	−7.40569e8	−0.970954
$346$	1.69804e8	0.220385
$347$	6.55917e8	0.842744	0.421372	−	0.906888i	$-0.361549\pi$
$347$	6.55917e8	0.842744	0.421372	+	0.906888i	$0.361549\pi$
$348$	−3.27364e8	−0.416393
$349$	2.21140e8	0.278470	0.139235	−	0.990259i	$-0.455536\pi$
$349$	2.21140e8	0.278470	0.139235	+	0.990259i	$0.455536\pi$
$350$	1.13751e9	1.41813
$351$	9.75020e7	0.120348
$352$	−4.78413e7	−0.0584661
$353$	−9.42536e8	−1.14048	−0.570239	−	0.821479i	$-0.693149\pi$
$353$	−9.42536e8	−1.14048	−0.570239	+	0.821479i	$0.693149\pi$
$354$	4.43619e7	0.0531494
$355$	2.40150e9	2.84894
$356$	−7.98699e8	−0.938228
$357$	−2.69558e8	−0.313555
$358$	3.02889e8	0.348894
$359$	−4.29136e8	−0.489513	−0.244757	−	0.969585i	$-0.578708\pi$
$359$	−4.29136e8	−0.489513	−0.244757	+	0.969585i	$0.578708\pi$
$360$	2.06008e8	0.232716
$361$	1.17511e9	1.31463
$362$	1.18336e8	0.131110
$363$	4.68600e8	0.514197
$364$	1.99015e8	0.216288
$365$	−2.95677e9	−3.18267
$366$	2.61691e8	0.279001
$367$	−1.63993e8	−0.173178	−0.0865891	−	0.996244i	$-0.527597\pi$
$367$	−1.63993e8	−0.173178	−0.0865891	+	0.996244i	$0.527597\pi$
$368$	−2.03552e8	−0.212916
$369$	5.92515e7	0.0613913
$370$	6.82338e8	0.700315
$371$	−6.87208e8	−0.698682
$372$	−2.43862e8	−0.245608
$373$	9.36147e8	0.934035	0.467017	−	0.884248i	$-0.345329\pi$
$373$	9.36147e8	0.934035	0.467017	+	0.884248i	$0.345329\pi$
$374$	1.85758e8	0.183610
$375$	2.21120e9	2.16531
$376$	1.22661e8	0.119000
$377$	−9.38445e8	−0.902016
$378$	−9.88476e7	−0.0941336
$379$	1.62263e9	1.53102	0.765511	−	0.643422i	$-0.222486\pi$
$379$	1.62263e9	1.53102	0.765511	+	0.643422i	$0.222486\pi$
$380$	1.60674e9	1.50212
$381$	3.45031e8	0.319610
$382$	1.25379e9	1.15081
$383$	−1.44733e9	−1.31635	−0.658174	−	0.752866i	$-0.728671\pi$
$383$	−1.44733e9	−1.31635	−0.658174	+	0.752866i	$0.728671\pi$
$384$	5.66231e7	0.0510310
$385$	5.05854e8	0.451765
$386$	4.52249e7	0.0400241
$387$	1.88496e8	0.165315
$388$	9.64698e8	0.838456
$389$	6.62552e8	0.570685	0.285342	−	0.958426i	$-0.407893\pi$
$389$	6.62552e8	0.570685	0.285342	+	0.958426i	$0.407893\pi$
$390$	5.90558e8	0.504123
$391$	7.90350e8	0.668653
$392$	2.19892e8	0.184378
$393$	6.90722e8	0.574023
$394$	−1.17623e9	−0.968845
$395$	−9.16271e8	−0.748056
$396$	6.81178e7	0.0551223
$397$	1.37227e9	1.10071	0.550355	−	0.834931i	$-0.314492\pi$
$397$	1.37227e9	1.10071	0.550355	+	0.834931i	$0.314492\pi$
$398$	−4.49471e7	−0.0357364
$399$	−7.70952e8	−0.607606
$400$	9.27768e8	0.724819
$401$	2.40079e9	1.85930	0.929648	−	0.368448i	$-0.120111\pi$
$401$	2.40079e9	1.85930	0.929648	+	0.368448i	$0.120111\pi$
$402$	9.75283e8	0.748755
$403$	−6.99071e8	−0.532052
$404$	−3.92098e8	−0.295842
$405$	−2.93320e8	−0.219406
$406$	9.51396e8	0.705538
$407$	2.25619e8	0.165880
$408$	−2.19856e8	−0.160261
$409$	1.25468e9	0.906780	0.453390	−	0.891312i	$-0.350215\pi$
$409$	1.25468e9	0.906780	0.453390	+	0.891312i	$0.350215\pi$
$410$	3.58880e8	0.257161
$411$	−8.77402e8	−0.623379
$412$	6.82966e8	0.481126
$413$	−1.28926e8	−0.0900566
$414$	2.89823e8	0.200739
$415$	1.68085e9	1.15441
$416$	1.62320e8	0.110547
$417$	−6.52563e8	−0.440703
$418$	5.31278e8	0.355799
$419$	−2.64159e9	−1.75435	−0.877175	−	0.480170i	$-0.840575\pi$
$419$	−2.64159e9	−1.75435	−0.877175	+	0.480170i	$0.840575\pi$
$420$	−5.98709e8	−0.394315
$421$	1.36887e9	0.894075	0.447037	−	0.894515i	$-0.352479\pi$
$421$	1.36887e9	0.894075	0.447037	+	0.894515i	$0.352479\pi$
$422$	1.48336e9	0.960842
$423$	−1.74648e8	−0.112195
$424$	−5.60497e8	−0.357102
$425$	−3.60233e9	−2.27626
$426$	−9.39831e8	−0.589001
$427$	−7.60536e8	−0.472740
$428$	−5.14714e7	−0.0317331
$429$	1.95272e8	0.119409
$430$	1.14170e9	0.692486
$431$	−7.90347e6	−0.00475496	−0.00237748	−	0.999997i	$-0.500757\pi$
$431$	−7.90347e6	−0.00475496	−0.00237748	+	0.999997i	$0.500757\pi$
$432$	−8.06216e7	−0.0481125
$433$	−5.56334e8	−0.329327	−0.164664	−	0.986350i	$-0.552654\pi$
$433$	−5.56334e8	−0.329327	−0.164664	+	0.986350i	$0.552654\pi$
$434$	7.08719e8	0.416160
$435$	2.82317e9	1.64447
$436$	−1.24102e9	−0.717091
$437$	2.26044e9	1.29571
$438$	1.15713e9	0.657998
$439$	−1.58861e9	−0.896174	−0.448087	−	0.893990i	$-0.647895\pi$
$439$	−1.58861e9	−0.896174	−0.448087	+	0.893990i	$0.647895\pi$
$440$	4.12582e8	0.230901
$441$	−3.13088e8	−0.173833
$442$	−6.30255e8	−0.347167
$443$	3.02089e9	1.65090	0.825451	−	0.564474i	$-0.190921\pi$
$443$	3.02089e9	1.65090	0.825451	+	0.564474i	$0.190921\pi$
$444$	−2.67034e8	−0.144786
$445$	6.88796e9	3.70536
$446$	1.22267e8	0.0652583
$447$	8.41575e8	0.445673
$448$	−1.64560e8	−0.0864672
$449$	−5.11697e8	−0.266779	−0.133389	−	0.991064i	$-0.542586\pi$
$449$	−5.11697e8	−0.266779	−0.133389	+	0.991064i	$0.542586\pi$
$450$	−1.32098e9	−0.683366
$451$	1.18666e8	0.0609126
$452$	1.42854e9	0.727627
$453$	−7.96593e8	−0.402618
$454$	−1.00519e9	−0.504140
$455$	−1.71630e9	−0.854189
$456$	−6.28800e8	−0.310553
$457$	−2.26219e9	−1.10872	−0.554359	−	0.832277i	$-0.687037\pi$
$457$	−2.26219e9	−1.10872	−0.554359	+	0.832277i	$0.687037\pi$
$458$	−5.88931e8	−0.286441
$459$	3.13037e8	0.151095
$460$	1.75542e9	0.840871
$461$	2.37263e9	1.12792	0.563959	−	0.825803i	$-0.309278\pi$
$461$	2.37263e9	1.12792	0.563959	+	0.825803i	$0.309278\pi$
$462$	−1.97967e8	−0.0933996
$463$	1.41490e9	0.662509	0.331254	−	0.943541i	$-0.392528\pi$
$463$	1.41490e9	0.662509	0.331254	+	0.943541i	$0.392528\pi$
$464$	7.75973e8	0.360607
$465$	2.10305e9	0.969985
$466$	9.50602e8	0.435159
$467$	1.92301e9	0.873719	0.436859	−	0.899530i	$-0.356091\pi$
$467$	1.92301e9	0.873719	0.436859	+	0.899530i	$0.356091\pi$
$468$	−2.31116e8	−0.104224
$469$	−2.83440e9	−1.26869
$470$	−1.05782e9	−0.469970
$471$	2.03303e9	0.896543
$472$	−1.05154e8	−0.0460287
$473$	3.77509e8	0.164026
$474$	3.58584e8	0.154656
$475$	−1.03029e10	−4.41094
$476$	6.38953e8	0.271547
$477$	7.98052e8	0.336679
$478$	−1.67124e9	−0.699909
$479$	2.72972e9	1.13487	0.567433	−	0.823420i	$-0.307937\pi$
$479$	2.72972e9	1.13487	0.567433	+	0.823420i	$0.307937\pi$
$480$	−4.88316e8	−0.201538
$481$	−7.65499e8	−0.313644
$482$	−2.47732e9	−1.00767
$483$	−8.42293e8	−0.340133
$484$	−1.11076e9	−0.445307
$485$	−8.31952e9	−3.31133
$486$	1.14791e8	0.0453609
$487$	1.13299e9	0.444503	0.222251	−	0.974989i	$-0.428659\pi$
$487$	1.13299e9	0.444503	0.222251	+	0.974989i	$0.428659\pi$
$488$	−6.20305e8	−0.241622
$489$	−2.50008e9	−0.966879
$490$	−1.89634e9	−0.728166
$491$	−3.16364e9	−1.20615	−0.603076	−	0.797684i	$-0.706058\pi$
$491$	−3.16364e9	−1.20615	−0.603076	+	0.797684i	$0.706058\pi$
$492$	−1.40448e8	−0.0531664
$493$	−3.01295e9	−1.13247
$494$	−1.80256e9	−0.672739
$495$	−5.87446e8	−0.217696
$496$	5.78042e8	0.212703
$497$	2.73137e9	0.998007
$498$	−6.57804e8	−0.238668
$499$	3.49852e9	1.26047	0.630235	−	0.776404i	$-0.282958\pi$
$499$	3.49852e9	1.26047	0.630235	+	0.776404i	$0.282958\pi$
$500$	−5.24137e9	−1.87521
$501$	1.39381e8	0.0495188
$502$	2.97949e8	0.105118
$503$	−2.32644e9	−0.815088	−0.407544	−	0.913186i	$-0.633615\pi$
$503$	−2.32644e9	−0.815088	−0.407544	+	0.913186i	$0.633615\pi$
$504$	2.34305e8	0.0815221
$505$	3.38144e9	1.16837
$506$	5.80441e8	0.199173
$507$	1.03168e9	0.351573
$508$	−8.17850e8	−0.276790
$509$	8.17673e8	0.274832	0.137416	−	0.990513i	$-0.456120\pi$
$509$	8.17673e8	0.274832	0.137416	+	0.990513i	$0.456120\pi$
$510$	1.89603e9	0.632921
$511$	−3.36291e9	−1.11491
$512$	−1.34218e8	−0.0441942
$513$	8.95303e8	0.292792
$514$	2.44619e9	0.794547
$515$	−5.88988e9	−1.90012
$516$	−4.46804e8	−0.143167
$517$	−3.49775e8	−0.111320
$518$	7.76063e8	0.245326
$519$	5.73088e8	0.179943
$520$	−1.39984e9	−0.436583
$521$	−5.89955e9	−1.82762	−0.913812	−	0.406138i	$-0.866875\pi$
$521$	−5.89955e9	−1.82762	−0.913812	+	0.406138i	$0.866875\pi$
$522$	−1.10485e9	−0.339983
$523$	−9.34456e8	−0.285629	−0.142815	−	0.989749i	$-0.545615\pi$
$523$	−9.34456e8	−0.285629	−0.142815	+	0.989749i	$0.545615\pi$
$524$	−1.63727e9	−0.497119
$525$	3.83909e9	1.15790
$526$	−5.44874e8	−0.163247
$527$	−2.24442e9	−0.667985
$528$	−1.61465e8	−0.0477374
$529$	−9.35207e8	−0.274671
$530$	4.83371e9	1.41031
$531$	1.49721e8	0.0433963
$532$	1.82744e9	0.526202
$533$	−4.02619e8	−0.115172
$534$	−2.69561e9	−0.766060
$535$	4.43888e8	0.125324
$536$	−2.31178e9	−0.648441
$537$	1.02225e9	0.284870
$538$	−1.70014e9	−0.470702
$539$	−6.27037e8	−0.172477
$540$	6.95278e8	0.190012
$541$	−3.88061e9	−1.05368	−0.526841	−	0.849964i	$-0.676624\pi$
$541$	−3.88061e9	−1.05368	−0.526841	+	0.849964i	$0.676624\pi$
$542$	1.93574e9	0.522216
$543$	3.99383e8	0.107051
$544$	5.21140e8	0.138790
$545$	1.07025e10	2.83202
$546$	6.71677e8	0.176598
$547$	4.30658e9	1.12506	0.562532	−	0.826776i	$-0.309827\pi$
$547$	4.30658e9	1.12506	0.562532	+	0.826776i	$0.309827\pi$
$548$	2.07977e9	0.539862
$549$	8.83207e8	0.227803
$550$	−2.64559e9	−0.678037
$551$	−8.61719e9	−2.19450
$552$	−6.86987e8	−0.173845
$553$	−1.04213e9	−0.262050
$554$	3.29087e9	0.822293
$555$	2.30289e9	0.571805
$556$	1.54682e9	0.381660
$557$	7.76816e9	1.90469	0.952346	−	0.305019i	$-0.0986628\pi$
$557$	7.76816e9	1.90469	0.952346	+	0.305019i	$0.0986628\pi$
$558$	−8.23033e8	−0.200538
$559$	−1.28084e9	−0.310138
$560$	1.41916e9	0.341487
$561$	6.26934e8	0.149917
$562$	2.02971e8	0.0482344
$563$	1.96781e9	0.464733	0.232367	−	0.972628i	$-0.425353\pi$
$563$	1.96781e9	0.464733	0.232367	+	0.972628i	$0.425353\pi$
$564$	4.13980e8	0.0971633
$565$	−1.23197e10	−2.87363
$566$	−2.85676e9	−0.662242
$567$	−3.33611e8	−0.0768598
$568$	2.22775e9	0.510090
$569$	−3.45453e9	−0.786133	−0.393067	−	0.919510i	$-0.628586\pi$
$569$	−3.45453e9	−0.786133	−0.393067	+	0.919510i	$0.628586\pi$
$570$	5.42275e9	1.22647
$571$	2.58214e9	0.580435	0.290217	−	0.956961i	$-0.406272\pi$
$571$	2.58214e9	0.580435	0.290217	+	0.956961i	$0.406272\pi$
$572$	−4.62866e8	−0.103412
$573$	4.23153e9	0.939629
$574$	4.08175e8	0.0900855
$575$	−1.12563e10	−2.46920
$576$	1.91103e8	0.0416667
$577$	−1.10521e9	−0.239514	−0.119757	−	0.992803i	$-0.538212\pi$
$577$	−1.10521e9	−0.239514	−0.119757	+	0.992803i	$0.538212\pi$
$578$	1.25923e9	0.271242
$579$	1.52634e8	0.0326796
$580$	−6.69197e9	−1.42415
$581$	1.91173e9	0.404400
$582$	3.25586e9	0.684597
$583$	1.59829e9	0.334054
$584$	−2.74284e9	−0.569843
$585$	1.99313e9	0.411615
$586$	−4.53388e9	−0.930740
$587$	3.24181e9	0.661538	0.330769	−	0.943712i	$-0.392692\pi$
$587$	3.24181e9	0.661538	0.330769	+	0.943712i	$0.392692\pi$
$588$	7.42136e8	0.150544
$589$	−6.41916e9	−1.29442
$590$	9.06845e8	0.181782
$591$	−3.96977e9	−0.791059
$592$	6.32969e8	0.125388
$593$	−4.96985e8	−0.0978705	−0.0489353	−	0.998802i	$-0.515583\pi$
$593$	−4.96985e8	−0.0978705	−0.0489353	+	0.998802i	$0.515583\pi$
$594$	2.29898e8	0.0450072
$595$	−5.51031e9	−1.07242
$596$	−1.99484e9	−0.385964
$597$	−1.51696e8	−0.0291786
$598$	−1.96937e9	−0.376594
$599$	−8.38881e9	−1.59480	−0.797401	−	0.603450i	$-0.793792\pi$
$599$	−8.38881e9	−1.59480	−0.797401	+	0.603450i	$0.793792\pi$
$600$	3.13122e9	0.591812
$601$	9.21864e9	1.73223	0.866116	−	0.499843i	$-0.166609\pi$
$601$	9.21864e9	1.73223	0.866116	+	0.499843i	$0.166609\pi$
$602$	1.29852e9	0.242583
$603$	3.29158e9	0.611356
$604$	1.88822e9	0.348677
$605$	9.57912e9	1.75866
$606$	−1.32333e9	−0.241554
$607$	−6.21355e9	−1.12766	−0.563832	−	0.825890i	$-0.690673\pi$
$607$	−6.21355e9	−1.12766	−0.563832	+	0.825890i	$0.690673\pi$
$608$	1.49049e9	0.268947
$609$	3.21096e9	0.576069
$610$	5.34949e9	0.954240
$611$	1.18675e9	0.210481
$612$	−7.42014e8	−0.130852
$613$	7.22402e9	1.26668	0.633341	−	0.773873i	$-0.281683\pi$
$613$	7.22402e9	1.26668	0.633341	+	0.773873i	$0.281683\pi$
$614$	5.25737e9	0.916598
$615$	1.21122e9	0.209971
$616$	4.69254e8	0.0808864
$617$	−1.07814e8	−0.0184789	−0.00923945	−	0.999957i	$-0.502941\pi$
$617$	−1.07814e8	−0.0184789	−0.00923945	+	0.999957i	$0.502941\pi$
$618$	2.30501e9	0.392838
$619$	−7.92290e9	−1.34266	−0.671331	−	0.741157i	$-0.734277\pi$
$619$	−7.92290e9	−1.34266	−0.671331	+	0.741157i	$0.734277\pi$
$620$	−4.98502e9	−0.840032
$621$	9.78152e8	0.163903
$622$	−2.33932e9	−0.389783
$623$	7.83408e9	1.29802
$624$	5.47830e8	0.0902609
$625$	2.75056e10	4.50652
$626$	−1.16401e9	−0.189648
$627$	1.79306e9	0.290509
$628$	−4.81904e9	−0.776429
$629$	−2.45769e9	−0.393776
$630$	−2.02064e9	−0.321957
$631$	7.94246e9	1.25850	0.629248	−	0.777204i	$-0.283363\pi$
$631$	7.94246e9	1.25850	0.629248	+	0.777204i	$0.283363\pi$
$632$	−8.49977e8	−0.133936
$633$	5.00633e9	0.784524
$634$	−1.84842e9	−0.288063
$635$	7.05311e9	1.09313
$636$	−1.89168e9	−0.291573
$637$	2.12746e9	0.326117
$638$	−2.21274e9	−0.337332
$639$	−3.17193e9	−0.480918
$640$	1.15749e9	0.174537
$641$	−2.54582e9	−0.381790	−0.190895	−	0.981610i	$-0.561139\pi$
$641$	−2.54582e9	−0.381790	−0.190895	+	0.981610i	$0.561139\pi$
$642$	−1.73716e8	−0.0259100
$643$	−6.20451e9	−0.920384	−0.460192	−	0.887819i	$-0.652219\pi$
$643$	−6.20451e9	−0.920384	−0.460192	+	0.887819i	$0.652219\pi$
$644$	1.99655e9	0.294564
$645$	3.85323e9	0.565413
$646$	−5.78726e9	−0.844616
$647$	−1.28588e10	−1.86653	−0.933263	−	0.359194i	$-0.883052\pi$
$647$	−1.28588e10	−1.86653	−0.933263	+	0.359194i	$0.883052\pi$
$648$	−2.72098e8	−0.0392837
$649$	2.99854e8	0.0430579
$650$	8.97618e9	1.28202
$651$	2.39193e9	0.339793
$652$	5.92611e9	0.837342
$653$	3.54700e8	0.0498500	0.0249250	−	0.999689i	$-0.492065\pi$
$653$	3.54700e8	0.0498500	0.0249250	+	0.999689i	$0.492065\pi$
$654$	−4.18843e9	−0.585502
$655$	1.41197e10	1.96328
$656$	3.32914e8	0.0460435
$657$	3.90533e9	0.537253
$658$	−1.20312e9	−0.164634
$659$	−5.50754e9	−0.749651	−0.374825	−	0.927095i	$-0.622297\pi$
$659$	−5.50754e9	−0.749651	−0.374825	+	0.927095i	$0.622297\pi$
$660$	1.39246e9	0.188530
$661$	−6.16955e9	−0.830899	−0.415449	−	0.909616i	$-0.636376\pi$
$661$	−6.16955e9	−0.830899	−0.415449	+	0.909616i	$0.636376\pi$
$662$	−1.74334e9	−0.233550
$663$	−2.12711e9	−0.283461
$664$	1.55924e9	0.206692
$665$	−1.57598e10	−2.07814
$666$	−9.01239e8	−0.118217
$667$	−9.41460e9	−1.22846
$668$	−3.30384e8	−0.0428846
$669$	4.12650e8	0.0532832
$670$	1.99367e10	2.56090
$671$	1.76884e9	0.226027
$672$	−5.55390e8	−0.0706002
$673$	−5.21698e9	−0.659730	−0.329865	−	0.944028i	$-0.607003\pi$
$673$	−5.21698e9	−0.659730	−0.329865	+	0.944028i	$0.607003\pi$
$674$	5.46050e9	0.686946
$675$	−4.45832e9	−0.557966
$676$	−2.44546e9	−0.304471
$677$	−2.62554e9	−0.325206	−0.162603	−	0.986692i	$-0.551989\pi$
$677$	−2.62554e9	−0.325206	−0.162603	+	0.986692i	$0.551989\pi$
$678$	4.82133e9	0.594105
$679$	−9.46229e9	−1.15998
$680$	−4.49429e9	−0.548126
$681$	−3.39251e9	−0.411629
$682$	−1.64832e9	−0.198975
$683$	−9.02856e9	−1.08429	−0.542146	−	0.840284i	$-0.682388\pi$
$683$	−9.02856e9	−1.08429	−0.542146	+	0.840284i	$0.682388\pi$
$684$	−2.12220e9	−0.253565
$685$	−1.79358e10	−2.13209
$686$	−6.29264e9	−0.744215
$687$	−1.98764e9	−0.233878
$688$	1.05909e9	0.123986
$689$	−5.42282e9	−0.631623
$690$	5.92455e9	0.686568
$691$	2.34849e9	0.270779	0.135389	−	0.990792i	$-0.456771\pi$
$691$	2.34849e9	0.270779	0.135389	+	0.990792i	$0.456771\pi$
$692$	−1.35843e9	−0.155835
$693$	−6.68137e8	−0.0762604
$694$	−5.24733e9	−0.595910
$695$	−1.33397e10	−1.50730
$696$	2.61891e9	0.294434
$697$	−1.29264e9	−0.144598
$698$	−1.76912e9	−0.196908
$699$	3.20828e9	0.355306
$700$	−9.10006e9	−1.00277
$701$	6.20812e9	0.680686	0.340343	−	0.940301i	$-0.389457\pi$
$701$	6.20812e9	0.680686	0.340343	+	0.940301i	$0.389457\pi$
$702$	−7.80016e8	−0.0850988
$703$	−7.02912e9	−0.763058
$704$	3.82731e8	0.0413418
$705$	−3.57015e9	−0.383729
$706$	7.54029e9	0.806439
$707$	3.84591e9	0.409290
$708$	−3.54895e8	−0.0375823
$709$	−1.46978e10	−1.54878	−0.774390	−	0.632709i	$-0.781943\pi$
$709$	−1.46978e10	−1.54878	−0.774390	+	0.632709i	$0.781943\pi$
$710$	−1.92120e10	−2.01451
$711$	1.21022e9	0.126276
$712$	6.38960e9	0.663427
$713$	−7.01317e9	−0.724605
$714$	2.15647e9	0.221717
$715$	3.99174e9	0.408405
$716$	−2.42311e9	−0.246705
$717$	−5.64044e9	−0.571473
$718$	3.43309e9	0.346138
$719$	5.58919e9	0.560787	0.280393	−	0.959885i	$-0.409535\pi$
$719$	5.58919e9	0.560787	0.280393	+	0.959885i	$0.409535\pi$
$720$	−1.64807e9	−0.164555
$721$	−6.69891e9	−0.665626
$722$	−9.40092e9	−0.929587
$723$	−8.36097e9	−0.822759
$724$	−9.46685e8	−0.0927087
$725$	4.29108e10	4.18199
$726$	−3.74880e9	−0.363592
$727$	−1.01516e10	−0.979860	−0.489930	−	0.871762i	$-0.662978\pi$
$727$	−1.01516e10	−0.979860	−0.489930	+	0.871762i	$0.662978\pi$
$728$	−1.59212e9	−0.152939
$729$	3.87420e8	0.0370370
$730$	2.36541e10	2.25049
$731$	−4.11224e9	−0.389374
$732$	−2.09353e9	−0.197283
$733$	−1.13797e10	−1.06725	−0.533624	−	0.845722i	$-0.679170\pi$
$733$	−1.13797e10	−1.06725	−0.533624	+	0.845722i	$0.679170\pi$
$734$	1.31194e9	0.122455
$735$	−6.40015e9	−0.594545
$736$	1.62841e9	0.150554
$737$	6.59220e9	0.606588
$738$	−4.74012e8	−0.0434102
$739$	1.40436e10	1.28003	0.640017	−	0.768361i	$-0.278927\pi$
$739$	1.40436e10	1.28003	0.640017	+	0.768361i	$0.278927\pi$
$740$	−5.45870e9	−0.495197
$741$	−6.08366e9	−0.549289
$742$	5.49766e9	0.494043
$743$	3.61475e9	0.323309	0.161655	−	0.986847i	$-0.448317\pi$
$743$	3.61475e9	0.323309	0.161655	+	0.986847i	$0.448317\pi$
$744$	1.95089e9	0.173671
$745$	1.72035e10	1.52430
$746$	−7.48917e9	−0.660462
$747$	−2.22009e9	−0.194871
$748$	−1.48606e9	−0.129832
$749$	5.04860e8	0.0439020
$750$	−1.76896e10	−1.53110
$751$	−8.65111e9	−0.745302	−0.372651	−	0.927972i	$-0.621551\pi$
$751$	−8.65111e9	−0.745302	−0.372651	+	0.927972i	$0.621551\pi$
$752$	−9.81286e8	−0.0841459
$753$	1.00558e9	0.0858288
$754$	7.50756e9	0.637822
$755$	−1.62840e10	−1.37704
$756$	7.90781e8	0.0665625
$757$	−1.11408e10	−0.933425	−0.466712	−	0.884409i	$-0.654562\pi$
$757$	−1.11408e10	−0.933425	−0.466712	+	0.884409i	$0.654562\pi$
$758$	−1.29810e10	−1.08260
$759$	1.95899e9	0.162624
$760$	−1.28539e10	−1.06216
$761$	1.51523e10	1.24633	0.623164	−	0.782091i	$-0.285847\pi$
$761$	1.51523e10	1.24633	0.623164	+	0.782091i	$0.285847\pi$
$762$	−2.76024e9	−0.225998
$763$	1.21726e10	0.992078
$764$	−1.00303e10	−0.813743
$765$	6.39910e9	0.516778
$766$	1.15786e10	0.930798
$767$	−1.01737e9	−0.0814131
$768$	−4.52985e8	−0.0360844
$769$	1.20075e10	0.952164	0.476082	−	0.879401i	$-0.342057\pi$
$769$	1.20075e10	0.952164	0.476082	+	0.879401i	$0.342057\pi$
$770$	−4.04683e9	−0.319446
$771$	8.25589e9	0.648745
$772$	−3.61799e8	−0.0283013
$773$	1.01927e9	0.0793708	0.0396854	−	0.999212i	$-0.487364\pi$
$773$	1.01927e9	0.0793708	0.0396854	+	0.999212i	$0.487364\pi$
$774$	−1.50797e9	−0.116896
$775$	3.19653e10	2.46674
$776$	−7.71758e9	−0.592878
$777$	2.61921e9	0.200308
$778$	−5.30042e9	−0.403535
$779$	−3.69701e9	−0.280201
$780$	−4.72447e9	−0.356469
$781$	−6.35257e9	−0.477167
$782$	−6.32280e9	−0.472809
$783$	−3.72888e9	−0.277595
$784$	−1.75914e9	−0.130375
$785$	4.15592e10	3.06637
$786$	−5.52578e9	−0.405896
$787$	−1.91480e9	−0.140027	−0.0700134	−	0.997546i	$-0.522304\pi$
$787$	−1.91480e9	−0.140027	−0.0700134	+	0.997546i	$0.522304\pi$
$788$	9.40981e9	0.685077
$789$	−1.83895e9	−0.133291
$790$	7.33017e9	0.528956
$791$	−1.40119e10	−1.00665
$792$	−5.44943e8	−0.0389774
$793$	−6.00146e9	−0.427367
$794$	−1.09782e10	−0.778320
$795$	1.63138e10	1.15151
$796$	3.59577e8	0.0252695
$797$	8.92290e9	0.624312	0.312156	−	0.950031i	$-0.398949\pi$
$797$	8.92290e9	0.624312	0.312156	+	0.950031i	$0.398949\pi$
$798$	6.16762e9	0.429642
$799$	3.81013e9	0.264257
$800$	−7.42215e9	−0.512524
$801$	−9.09769e9	−0.625485
$802$	−1.92063e10	−1.31472
$803$	7.82138e9	0.533063
$804$	−7.80227e9	−0.529450
$805$	−1.72182e10	−1.16332
$806$	5.59257e9	0.376217
$807$	−5.73797e9	−0.384327
$808$	3.13678e9	0.209192
$809$	1.42740e10	0.947822	0.473911	−	0.880573i	$-0.342842\pi$
$809$	1.42740e10	0.947822	0.473911	+	0.880573i	$0.342842\pi$
$810$	2.34656e9	0.155144
$811$	2.60562e10	1.71529	0.857645	−	0.514243i	$-0.171927\pi$
$811$	2.60562e10	1.71529	0.857645	+	0.514243i	$0.171927\pi$
$812$	−7.61117e9	−0.498891
$813$	6.53313e9	0.426388
$814$	−1.80495e9	−0.117295
$815$	−5.11065e10	−3.30693
$816$	1.75885e9	0.113322
$817$	−1.17612e10	−0.754528
$818$	−1.00374e10	−0.641190
$819$	2.26691e9	0.144192
$820$	−2.87104e9	−0.181840
$821$	−1.09943e10	−0.693370	−0.346685	−	0.937982i	$-0.612693\pi$
$821$	−1.09943e10	−0.693370	−0.346685	+	0.937982i	$0.612693\pi$
$822$	7.01921e9	0.440795
$823$	5.54587e9	0.346793	0.173397	−	0.984852i	$-0.444526\pi$
$823$	5.54587e9	0.346793	0.173397	+	0.984852i	$0.444526\pi$
$824$	−5.46373e9	−0.340208
$825$	−8.92887e9	−0.553615
$826$	1.03141e9	0.0636796
$827$	3.01617e10	1.85433	0.927163	−	0.374659i	$-0.122240\pi$
$827$	3.01617e10	1.85433	0.927163	+	0.374659i	$0.122240\pi$
$828$	−2.31858e9	−0.141944
$829$	2.55576e10	1.55804	0.779021	−	0.626998i	$-0.215716\pi$
$829$	2.55576e10	1.55804	0.779021	+	0.626998i	$0.215716\pi$
$830$	−1.34468e10	−0.816294
$831$	1.11067e10	0.671399
$832$	−1.29856e9	−0.0781682
$833$	6.83037e9	0.409436
$834$	5.22051e9	0.311624
$835$	2.84922e9	0.169365
$836$	−4.25023e9	−0.251588
$837$	−2.77773e9	−0.163739
$838$	2.11327e10	1.24051
$839$	−9.86192e9	−0.576494	−0.288247	−	0.957556i	$-0.593072\pi$
$839$	−9.86192e9	−0.576494	−0.288247	+	0.957556i	$0.593072\pi$
$840$	4.78967e9	0.278823
$841$	1.86401e10	1.08060
$842$	−1.09509e10	−0.632206
$843$	6.85027e8	0.0393832
$844$	−1.18669e10	−0.679418
$845$	2.10895e10	1.20245
$846$	1.39718e9	0.0793335
$847$	1.08949e10	0.616072
$848$	4.48398e9	0.252510
$849$	−9.64157e9	−0.540718
$850$	2.88187e10	1.60956
$851$	−7.67958e9	−0.427153
$852$	7.51865e9	0.416487
$853$	2.28981e10	1.26322	0.631609	−	0.775287i	$-0.282395\pi$
$853$	2.28981e10	1.26322	0.631609	+	0.775287i	$0.282395\pi$
$854$	6.08429e9	0.334278
$855$	1.83018e10	1.00141
$856$	4.11771e8	0.0224387
$857$	2.63005e10	1.42735	0.713676	−	0.700476i	$-0.247029\pi$
$857$	2.63005e10	1.42735	0.713676	+	0.700476i	$0.247029\pi$
$858$	−1.56217e9	−0.0844352
$859$	4.83085e9	0.260044	0.130022	−	0.991511i	$-0.458495\pi$
$859$	4.83085e9	0.260044	0.130022	+	0.991511i	$0.458495\pi$
$860$	−9.13357e9	−0.489662
$861$	1.37759e9	0.0735545
$862$	6.32277e7	0.00336227
$863$	−6.20527e9	−0.328642	−0.164321	−	0.986407i	$-0.552543\pi$
$863$	−6.20527e9	−0.328642	−0.164321	+	0.986407i	$0.552543\pi$
$864$	6.44973e8	0.0340207
$865$	1.17151e10	0.615443
$866$	4.45067e9	0.232870
$867$	4.24990e9	0.221468
$868$	−5.66975e9	−0.294269
$869$	2.42376e9	0.125291
$870$	−2.25854e10	−1.16281
$871$	−2.23666e10	−1.14693
$872$	9.92812e9	0.507060
$873$	1.09885e10	0.558971
$874$	−1.80836e10	−0.916207
$875$	5.14103e10	2.59431
$876$	−9.25707e9	−0.465275
$877$	−3.25511e10	−1.62955	−0.814774	−	0.579779i	$-0.803139\pi$
$877$	−3.25511e10	−1.62955	−0.814774	+	0.579779i	$0.803139\pi$
$878$	1.27089e10	0.633691
$879$	−1.53018e10	−0.759946
$880$	−3.30066e9	−0.163272
$881$	−1.95232e10	−0.961911	−0.480955	−	0.876745i	$-0.659710\pi$
$881$	−1.95232e10	−0.961911	−0.480955	+	0.876745i	$0.659710\pi$
$882$	2.50471e9	0.122918
$883$	−1.81615e10	−0.887748	−0.443874	−	0.896089i	$-0.646396\pi$
$883$	−1.81615e10	−0.887748	−0.443874	+	0.896089i	$0.646396\pi$
$884$	5.04204e9	0.245484
$885$	3.06060e9	0.148424
$886$	−2.41671e10	−1.16736
$887$	−3.23070e9	−0.155440	−0.0777202	−	0.996975i	$-0.524764\pi$
$887$	−3.23070e9	−0.155440	−0.0777202	+	0.996975i	$0.524764\pi$
$888$	2.13627e9	0.102379
$889$	8.02192e9	0.382933
$890$	−5.51037e10	−2.62008
$891$	7.75905e8	0.0367482
$892$	−9.78132e8	−0.0461446
$893$	1.08972e10	0.512076
$894$	−6.73260e9	−0.315139
$895$	2.08968e10	0.974317
$896$	1.31648e9	0.0611416
$897$	−6.64662e9	−0.307487
$898$	4.09358e9	0.188641
$899$	2.67354e10	1.22723
$900$	1.05679e10	0.483213
$901$	−1.74104e10	−0.792996
$902$	−9.49325e8	−0.0430717
$903$	4.38250e9	0.198068
$904$	−1.14283e10	−0.514510
$905$	8.16418e9	0.366136
$906$	6.37275e9	0.284694
$907$	−3.33143e10	−1.48253	−0.741267	−	0.671210i	$-0.765775\pi$
$907$	−3.33143e10	−1.48253	−0.741267	+	0.671210i	$0.765775\pi$
$908$	8.04149e9	0.356481
$909$	−4.46624e9	−0.197228
$910$	1.37304e10	0.604003
$911$	−2.08952e10	−0.915654	−0.457827	−	0.889041i	$-0.651372\pi$
$911$	−2.08952e10	−0.915654	−0.457827	+	0.889041i	$0.651372\pi$
$912$	5.03040e9	0.219594
$913$	−4.44627e9	−0.193352
$914$	1.80975e10	0.783983
$915$	1.80545e10	0.779134
$916$	4.71145e9	0.202545
$917$	1.60592e10	0.687751
$918$	−2.50430e9	−0.106841
$919$	−2.08548e10	−0.886342	−0.443171	−	0.896437i	$-0.646147\pi$
$919$	−2.08548e10	−0.886342	−0.443171	+	0.896437i	$0.646147\pi$
$920$	−1.40434e10	−0.594586
$921$	1.77436e10	0.748399
$922$	−1.89811e10	−0.797558
$923$	2.15535e10	0.902220
$924$	1.58373e9	0.0660435
$925$	3.50027e10	1.45414
$926$	−1.13192e10	−0.468464
$927$	7.77941e9	0.320751
$928$	−6.20779e9	−0.254987
$929$	1.14029e10	0.466618	0.233309	−	0.972403i	$-0.425045\pi$
$929$	1.14029e10	0.466618	0.233309	+	0.972403i	$0.425045\pi$
$930$	−1.68244e10	−0.685883
$931$	1.95352e10	0.793404
$932$	−7.60482e9	−0.307704
$933$	−7.89520e9	−0.318257
$934$	−1.53840e10	−0.617812
$935$	1.28158e10	0.512748
$936$	1.84893e9	0.0736977
$937$	2.14172e10	0.850498	0.425249	−	0.905076i	$-0.360186\pi$
$937$	2.14172e10	0.850498	0.425249	+	0.905076i	$0.360186\pi$
$938$	2.26752e10	0.897102
$939$	−3.92855e9	−0.154847
$940$	8.46257e9	0.332319
$941$	−1.48402e10	−0.580599	−0.290300	−	0.956936i	$-0.593755\pi$
$941$	−1.48402e10	−0.580599	−0.290300	+	0.956936i	$0.593755\pi$
$942$	−1.62643e10	−0.633952
$943$	−4.03912e9	−0.156854
$944$	8.41232e8	0.0325472
$945$	−6.81966e9	−0.262876
$946$	−3.02007e9	−0.115984
$947$	−3.22552e10	−1.23417	−0.617084	−	0.786897i	$-0.711686\pi$
$947$	−3.22552e10	−1.23417	−0.617084	+	0.786897i	$0.711686\pi$
$948$	−2.86867e9	−0.109358
$949$	−2.65370e10	−1.00791
$950$	8.24230e10	3.11900
$951$	−6.23842e9	−0.235203
$952$	−5.11163e9	−0.192013
$953$	−4.37518e10	−1.63746	−0.818731	−	0.574177i	$-0.805322\pi$
$953$	−4.37518e10	−1.63746	−0.818731	+	0.574177i	$0.805322\pi$
$954$	−6.38441e9	−0.238068
$955$	8.65010e10	3.21373
$956$	1.33699e10	0.494910
$957$	−7.46799e9	−0.275431
$958$	−2.18378e10	−0.802471
$959$	−2.03995e10	−0.746886
$960$	3.90653e9	0.142509
$961$	−7.59676e9	−0.276119
$962$	6.12399e9	0.221780
$963$	−5.86292e8	−0.0211554
$964$	1.98186e10	0.712530
$965$	3.12014e9	0.111771
$966$	6.73835e9	0.240510
$967$	−5.11460e9	−0.181894	−0.0909472	−	0.995856i	$-0.528989\pi$
$967$	−5.11460e9	−0.181894	−0.0909472	+	0.995856i	$0.528989\pi$
$968$	8.88605e9	0.314880
$969$	−1.95320e10	−0.689626
$970$	6.65562e10	2.34146
$971$	4.93923e10	1.73138	0.865688	−	0.500583i	$-0.166881\pi$
$971$	4.93923e10	1.73138	0.865688	+	0.500583i	$0.166881\pi$
$972$	−9.18330e8	−0.0320750
$973$	−1.51720e10	−0.528018
$974$	−9.06391e9	−0.314311
$975$	3.02946e10	1.04677
$976$	4.96244e9	0.170852
$977$	5.31627e10	1.82380	0.911898	−	0.410417i	$-0.134617\pi$
$977$	5.31627e10	1.82380	0.911898	+	0.410417i	$0.134617\pi$
$978$	2.00006e10	0.683687
$979$	−1.82204e10	−0.620608
$980$	1.51707e10	0.514891
$981$	−1.41359e10	−0.478061
$982$	2.53091e10	0.852878
$983$	−4.34780e10	−1.45993	−0.729966	−	0.683484i	$-0.760464\pi$
$983$	−4.34780e10	−1.45993	−0.729966	+	0.683484i	$0.760464\pi$
$984$	1.12358e9	0.0375944
$985$	−8.11499e10	−2.70559
$986$	2.41036e10	0.800778
$987$	−4.06054e9	−0.134423
$988$	1.44205e10	0.475698
$989$	−1.28496e10	−0.422378
$990$	4.69957e9	0.153934
$991$	−6.07775e10	−1.98374	−0.991871	−	0.127251i	$-0.959385\pi$
$991$	−6.07775e10	−1.98374	−0.991871	+	0.127251i	$0.959385\pi$
$992$	−4.62434e9	−0.150404
$993$	−5.88378e9	−0.190693
$994$	−2.18510e10	−0.705697
$995$	−3.10098e9	−0.0997971
$996$	5.26243e9	0.168764
$997$	−3.97258e10	−1.26952	−0.634760	−	0.772709i	$-0.718901\pi$
$997$	−3.97258e10	−1.26952	−0.634760	+	0.772709i	$0.718901\pi$
$998$	−2.79882e10	−0.891287
$999$	−3.04168e9	−0.0965238

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.8.a.e.1.1	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.8.a.e.1.1	✓	9	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	354.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -551.934 q^{5} +216.000 q^{6} -627.747 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -551.934 q^{5} +216.000 q^{6} -627.747 q^{7} -512.000 q^{8} +729.000 q^{9} +4415.47 q^{10} +1460.00 q^{11} -1728.00 q^{12} -4953.61 q^{13} +5021.98 q^{14} +14902.2 q^{15} +4096.00 q^{16} -15903.9 q^{17} -5832.00 q^{18} -45486.1 q^{19} -35323.8 q^{20} +16949.2 q^{21} -11680.0 q^{22} -49695.3 q^{23} +13824.0 q^{24} +226506. q^{25} +39628.9 q^{26} -19683.0 q^{27} -40175.8 q^{28} +189447. q^{29} -119218. q^{30} +141124. q^{31} -32768.0 q^{32} -39420.0 q^{33} +127231. q^{34} +346475. q^{35} +46656.0 q^{36} +154533. q^{37} +363889. q^{38} +133748. q^{39} +282590. q^{40} +81277.8 q^{41} -135593. q^{42} +258567. q^{43} +93440.1 q^{44} -402360. q^{45} +397562. q^{46} -239572. q^{47} -110592. q^{48} -429477. q^{49} -1.81205e6 q^{50} +429406. q^{51} -317031. q^{52} +1.09472e6 q^{53} +157464. q^{54} -805824. q^{55} +321407. q^{56} +1.22812e6 q^{57} -1.51557e6 q^{58} +205379. q^{59} +953742. q^{60} +1.21153e6 q^{61} -1.12899e6 q^{62} -457628. q^{63} +262144. q^{64} +2.73407e6 q^{65} +315360. q^{66} +4.51520e6 q^{67} -1.01785e6 q^{68} +1.34177e6 q^{69} -2.77180e6 q^{70} -4.35107e6 q^{71} -373248. q^{72} +5.35710e6 q^{73} -1.23627e6 q^{74} -6.11566e6 q^{75} -2.91111e6 q^{76} -916512. q^{77} -1.06998e6 q^{78} +1.66011e6 q^{79} -2.26072e6 q^{80} +531441. q^{81} -650222. q^{82} -3.04539e6 q^{83} +1.08475e6 q^{84} +8.77792e6 q^{85} -2.06854e6 q^{86} -5.11506e6 q^{87} -747521. q^{88} -1.24797e7 q^{89} +3.21888e6 q^{90} +3.10962e6 q^{91} -3.18050e6 q^{92} -3.81034e6 q^{93} +1.91657e6 q^{94} +2.51053e7 q^{95} +884736. q^{96} +1.50734e7 q^{97} +3.43581e6 q^{98} +1.06434e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9}+O(q^{10}) \) 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9	\( 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9} + 1840 q^{10} - 5472 q^{11} - 15552 q^{12} + 3144 q^{13} + 2720 q^{14} + 6210 q^{15} + 36864 q^{16} - 3662 q^{17} - 52488 q^{18} + 692 q^{19} - 14720 q^{20} + 9180 q^{21} + 43776 q^{22} - 92046 q^{23} + 124416 q^{24} + 74731 q^{25} - 25152 q^{26} - 177147 q^{27} - 21760 q^{28} - 41060 q^{29} - 49680 q^{30} - 324504 q^{31} - 294912 q^{32} + 147744 q^{33} + 29296 q^{34} - 415602 q^{35} + 419904 q^{36} + 338612 q^{37} - 5536 q^{38} - 84888 q^{39} + 117760 q^{40} - 104312 q^{41} - 73440 q^{42} + 1000602 q^{43} - 350208 q^{44} - 167670 q^{45} + 736368 q^{46} - 365148 q^{47} - 995328 q^{48} + 2307505 q^{49} - 597848 q^{50} + 98874 q^{51} + 201216 q^{52} + 2017498 q^{53} + 1417176 q^{54} + 1120520 q^{55} + 174080 q^{56} - 18684 q^{57} + 328480 q^{58} + 1848411 q^{59} + 397440 q^{60} + 5102340 q^{61} + 2596032 q^{62} - 247860 q^{63} + 2359296 q^{64} + 7512810 q^{65} - 1181952 q^{66} + 10920464 q^{67} - 234368 q^{68} + 2485242 q^{69} + 3324816 q^{70} + 3607024 q^{71} - 3359232 q^{72} + 12949418 q^{73} - 2708896 q^{74} - 2017737 q^{75} + 44288 q^{76} + 7127994 q^{77} + 679104 q^{78} + 7489472 q^{79} - 942080 q^{80} + 4782969 q^{81} + 834496 q^{82} + 2760502 q^{83} + 587520 q^{84} + 11815354 q^{85} - 8004816 q^{86} + 1108620 q^{87} + 2801664 q^{88} - 9948196 q^{89} + 1341360 q^{90} + 19400656 q^{91} - 5890944 q^{92} + 8761608 q^{93} + 2921184 q^{94} + 24045208 q^{95} + 7962624 q^{96} + 38157642 q^{97} - 18460040 q^{98} - 3989088 q^{99}+O(q^{100}) \) 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9 + 1840 * q^10 - 5472 * q^11 - 15552 * q^12 + 3144 * q^13 + 2720 * q^14 + 6210 * q^15 + 36864 * q^16 - 3662 * q^17 - 52488 * q^18 + 692 * q^19 - 14720 * q^20 + 9180 * q^21 + 43776 * q^22 - 92046 * q^23 + 124416 * q^24 + 74731 * q^25 - 25152 * q^26 - 177147 * q^27 - 21760 * q^28 - 41060 * q^29 - 49680 * q^30 - 324504 * q^31 - 294912 * q^32 + 147744 * q^33 + 29296 * q^34 - 415602 * q^35 + 419904 * q^36 + 338612 * q^37 - 5536 * q^38 - 84888 * q^39 + 117760 * q^40 - 104312 * q^41 - 73440 * q^42 + 1000602 * q^43 - 350208 * q^44 - 167670 * q^45 + 736368 * q^46 - 365148 * q^47 - 995328 * q^48 + 2307505 * q^49 - 597848 * q^50 + 98874 * q^51 + 201216 * q^52 + 2017498 * q^53 + 1417176 * q^54 + 1120520 * q^55 + 174080 * q^56 - 18684 * q^57 + 328480 * q^58 + 1848411 * q^59 + 397440 * q^60 + 5102340 * q^61 + 2596032 * q^62 - 247860 * q^63 + 2359296 * q^64 + 7512810 * q^65 - 1181952 * q^66 + 10920464 * q^67 - 234368 * q^68 + 2485242 * q^69 + 3324816 * q^70 + 3607024 * q^71 - 3359232 * q^72 + 12949418 * q^73 - 2708896 * q^74 - 2017737 * q^75 + 44288 * q^76 + 7127994 * q^77 + 679104 * q^78 + 7489472 * q^79 - 942080 * q^80 + 4782969 * q^81 + 834496 * q^82 + 2760502 * q^83 + 587520 * q^84 + 11815354 * q^85 - 8004816 * q^86 + 1108620 * q^87 + 2801664 * q^88 - 9948196 * q^89 + 1341360 * q^90 + 19400656 * q^91 - 5890944 * q^92 + 8761608 * q^93 + 2921184 * q^94 + 24045208 * q^95 + 7962624 * q^96 + 38157642 * q^97 - 18460040 * q^98 - 3989088 * q^99

Introduction

L-functions

Modular forms

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