LMFDB - Embedded newform 177.8.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,8,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, 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("177.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	177.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:	$55.2921495107$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 1669 x^{15} + 2385 x^{14} + 1108684 x^{13} - 848131 x^{12} - 377920980 x^{11} + \cdots + 24\!\cdots\!16 $ x^17 - 2x^16 - 1669x^15 + 2385x^14 + 1108684x^13 - 848131x^12 - 377920980x^11 + 12724944x^10 + 71331230512x^9 + 50741131904x^8 - 7480805165760x^7 - 10751966150272x^6 + 413177144536320x^5 + 886760582981376x^4 - 10454479722123264x^3 - 29180140031461376x^2 + 79787300207378432x + 248723246810300416
Coefficient ring:	$\Z[a_1, \ldots, a_{31}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$7.49302$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+7.49302 q^{2} -27.0000 q^{3} -71.8546 q^{4} +400.807 q^{5} -202.312 q^{6} -272.200 q^{7} -1497.52 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+7.49302 q^{2} -27.0000 q^{3} -71.8546 q^{4} +400.807 q^{5} -202.312 q^{6} -272.200 q^{7} -1497.52 q^{8} +729.000 q^{9} +3003.25 q^{10} +1287.50 q^{11} +1940.08 q^{12} +9535.11 q^{13} -2039.60 q^{14} -10821.8 q^{15} -2023.52 q^{16} -35497.8 q^{17} +5462.41 q^{18} -14418.3 q^{19} -28799.8 q^{20} +7349.41 q^{21} +9647.27 q^{22} +51239.1 q^{23} +40432.9 q^{24} +82520.9 q^{25} +71446.8 q^{26} -19683.0 q^{27} +19558.9 q^{28} -79916.8 q^{29} -81087.8 q^{30} +228626. q^{31} +176520. q^{32} -34762.5 q^{33} -265986. q^{34} -109100. q^{35} -52382.0 q^{36} -139882. q^{37} -108037. q^{38} -257448. q^{39} -600214. q^{40} +497679. q^{41} +55069.3 q^{42} +299840. q^{43} -92512.8 q^{44} +292188. q^{45} +383936. q^{46} +280623. q^{47} +54635.0 q^{48} -749450. q^{49} +618331. q^{50} +958441. q^{51} -685142. q^{52} +1.78864e6 q^{53} -147485. q^{54} +516038. q^{55} +407624. q^{56} +389294. q^{57} -598818. q^{58} -205379. q^{59} +777595. q^{60} +3.36147e6 q^{61} +1.71310e6 q^{62} -198434. q^{63} +1.58168e6 q^{64} +3.82174e6 q^{65} -260476. q^{66} -585455. q^{67} +2.55068e6 q^{68} -1.38346e6 q^{69} -817487. q^{70} +2.83547e6 q^{71} -1.09169e6 q^{72} -758408. q^{73} -1.04814e6 q^{74} -2.22806e6 q^{75} +1.03602e6 q^{76} -350458. q^{77} -1.92906e6 q^{78} +3.27559e6 q^{79} -811040. q^{80} +531441. q^{81} +3.72912e6 q^{82} +9.92122e6 q^{83} -528089. q^{84} -1.42278e7 q^{85} +2.24671e6 q^{86} +2.15775e6 q^{87} -1.92805e6 q^{88} -634907. q^{89} +2.18937e6 q^{90} -2.59546e6 q^{91} -3.68177e6 q^{92} -6.17290e6 q^{93} +2.10271e6 q^{94} -5.77895e6 q^{95} -4.76603e6 q^{96} +8.12879e6 q^{97} -5.61564e6 q^{98} +938588. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 2 q^{2} - 459 q^{3} + 1166 q^{4} - 318 q^{5} - 54 q^{6} + 3145 q^{7} + 2355 q^{8} + 12393 q^{9}+O(q^{10}) $ 17 * q + 2 * q^2 - 459 * q^3 + 1166 * q^4 - 318 * q^5 - 54 * q^6 + 3145 * q^7 + 2355 * q^8 + 12393 * q^9	\( 17 q + 2 q^{2} - 459 q^{3} + 1166 q^{4} - 318 q^{5} - 54 q^{6} + 3145 q^{7} + 2355 q^{8} + 12393 q^{9} + 6521 q^{10} - 1764 q^{11} - 31482 q^{12} + 18192 q^{13} - 7827 q^{14} + 8586 q^{15} + 139226 q^{16} - 15507 q^{17} + 1458 q^{18} + 52083 q^{19} + 721 q^{20} - 84915 q^{21} - 234434 q^{22} + 63823 q^{23} - 63585 q^{24} + 202153 q^{25} - 367956 q^{26} - 334611 q^{27} + 182306 q^{28} - 502955 q^{29} - 176067 q^{30} + 347531 q^{31} - 243908 q^{32} + 47628 q^{33} - 330872 q^{34} + 92641 q^{35} + 850014 q^{36} + 447615 q^{37} + 775669 q^{38} - 491184 q^{39} + 2203270 q^{40} + 940335 q^{41} + 211329 q^{42} + 478562 q^{43} - 596924 q^{44} - 231822 q^{45} - 3078663 q^{46} + 703121 q^{47} - 3759102 q^{48} + 1895082 q^{49} - 876967 q^{50} + 418689 q^{51} + 6278296 q^{52} - 1005974 q^{53} - 39366 q^{54} + 5212846 q^{55} + 3425294 q^{56} - 1406241 q^{57} + 6710166 q^{58} - 3491443 q^{59} - 19467 q^{60} + 11510749 q^{61} + 5996234 q^{62} + 2292705 q^{63} + 29496941 q^{64} + 11094180 q^{65} + 6329718 q^{66} + 14007144 q^{67} + 19688159 q^{68} - 1723221 q^{69} + 30909708 q^{70} + 5229074 q^{71} + 1716795 q^{72} + 5452211 q^{73} + 12819662 q^{74} - 5458131 q^{75} + 41929340 q^{76} + 9930777 q^{77} + 9934812 q^{78} + 15275654 q^{79} + 36576105 q^{80} + 9034497 q^{81} + 32025935 q^{82} + 7826609 q^{83} - 4922262 q^{84} + 11836945 q^{85} + 51649136 q^{86} + 13579785 q^{87} + 30223741 q^{88} - 6436185 q^{89} + 4753809 q^{90} + 11633535 q^{91} + 43357972 q^{92} - 9383337 q^{93} - 4494252 q^{94} + 23741055 q^{95} + 6585516 q^{96} + 26377540 q^{97} + 26517816 q^{98} - 1285956 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 - 459 * q^3 + 1166 * q^4 - 318 * q^5 - 54 * q^6 + 3145 * q^7 + 2355 * q^8 + 12393 * q^9 + 6521 * q^10 - 1764 * q^11 - 31482 * q^12 + 18192 * q^13 - 7827 * q^14 + 8586 * q^15 + 139226 * q^16 - 15507 * q^17 + 1458 * q^18 + 52083 * q^19 + 721 * q^20 - 84915 * q^21 - 234434 * q^22 + 63823 * q^23 - 63585 * q^24 + 202153 * q^25 - 367956 * q^26 - 334611 * q^27 + 182306 * q^28 - 502955 * q^29 - 176067 * q^30 + 347531 * q^31 - 243908 * q^32 + 47628 * q^33 - 330872 * q^34 + 92641 * q^35 + 850014 * q^36 + 447615 * q^37 + 775669 * q^38 - 491184 * q^39 + 2203270 * q^40 + 940335 * q^41 + 211329 * q^42 + 478562 * q^43 - 596924 * q^44 - 231822 * q^45 - 3078663 * q^46 + 703121 * q^47 - 3759102 * q^48 + 1895082 * q^49 - 876967 * q^50 + 418689 * q^51 + 6278296 * q^52 - 1005974 * q^53 - 39366 * q^54 + 5212846 * q^55 + 3425294 * q^56 - 1406241 * q^57 + 6710166 * q^58 - 3491443 * q^59 - 19467 * q^60 + 11510749 * q^61 + 5996234 * q^62 + 2292705 * q^63 + 29496941 * q^64 + 11094180 * q^65 + 6329718 * q^66 + 14007144 * q^67 + 19688159 * q^68 - 1723221 * q^69 + 30909708 * q^70 + 5229074 * q^71 + 1716795 * q^72 + 5452211 * q^73 + 12819662 * q^74 - 5458131 * q^75 + 41929340 * q^76 + 9930777 * q^77 + 9934812 * q^78 + 15275654 * q^79 + 36576105 * q^80 + 9034497 * q^81 + 32025935 * q^82 + 7826609 * q^83 - 4922262 * q^84 + 11836945 * q^85 + 51649136 * q^86 + 13579785 * q^87 + 30223741 * q^88 - 6436185 * q^89 + 4753809 * q^90 + 11633535 * q^91 + 43357972 * q^92 - 9383337 * q^93 - 4494252 * q^94 + 23741055 * q^95 + 6585516 * q^96 + 26377540 * q^97 + 26517816 * q^98 - 1285956 * 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 $

$2$	7.49302	0.662296	0.331148	−	0.943579i	$-0.392564\pi$
$2$	7.49302	0.662296	0.331148	+	0.943579i	$0.392564\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	−71.8546	−0.561364
$5$	400.807	1.43397	0.716985	−	0.697089i	$-0.245522\pi$
$5$	400.807	1.43397	0.716985	+	0.697089i	$0.245522\pi$
$6$	−202.312	−0.382377
$7$	−272.200	−0.299948	−0.149974	−	0.988690i	$-0.547919\pi$
$7$	−272.200	−0.299948	−0.149974	+	0.988690i	$0.547919\pi$
$8$	−1497.52	−1.03408
$9$	729.000	0.333333
$10$	3003.25	0.949712
$11$	1287.50	0.291657	0.145829	−	0.989310i	$-0.453415\pi$
$11$	1287.50	0.291657	0.145829	+	0.989310i	$0.453415\pi$
$12$	1940.08	0.324104
$13$	9535.11	1.20372	0.601858	−	0.798603i	$-0.294427\pi$
$13$	9535.11	1.20372	0.601858	+	0.798603i	$0.294427\pi$
$14$	−2039.60	−0.198654
$15$	−10821.8	−0.827902
$16$	−2023.52	−0.123506
$17$	−35497.8	−1.75239	−0.876195	−	0.481957i	$-0.839926\pi$
$17$	−35497.8	−1.75239	−0.876195	+	0.481957i	$0.839926\pi$
$18$	5462.41	0.220765
$19$	−14418.3	−0.482255	−0.241128	−	0.970493i	$-0.577517\pi$
$19$	−14418.3	−0.482255	−0.241128	+	0.970493i	$0.577517\pi$
$20$	−28799.8	−0.804979
$21$	7349.41	0.173175
$22$	9647.27	0.193163
$23$	51239.1	0.878120	0.439060	−	0.898458i	$-0.355312\pi$
$23$	51239.1	0.878120	0.439060	+	0.898458i	$0.355312\pi$
$24$	40432.9	0.597029
$25$	82520.9	1.05627
$26$	71446.8	0.797216
$27$	−19683.0	−0.192450
$28$	19558.9	0.168380
$29$	−79916.8	−0.608478	−0.304239	−	0.952596i	$-0.598402\pi$
$29$	−79916.8	−0.608478	−0.304239	+	0.952596i	$0.598402\pi$
$30$	−81087.8	−0.548316
$31$	228626.	1.37835	0.689175	−	0.724595i	$-0.257973\pi$
$31$	228626.	1.37835	0.689175	+	0.724595i	$0.257973\pi$
$32$	176520.	0.952288
$33$	−34762.5	−0.168388
$34$	−265986.	−1.16060
$35$	−109100.	−0.430116
$36$	−52382.0	−0.187121
$37$	−139882.	−0.454001	−0.227000	−	0.973895i	$-0.572892\pi$
$37$	−139882.	−0.454001	−0.227000	+	0.973895i	$0.572892\pi$
$38$	−108037.	−0.319395
$39$	−257448.	−0.694966
$40$	−600214.	−1.48285
$41$	497679.	1.12773	0.563866	−	0.825866i	$-0.309314\pi$
$41$	497679.	1.12773	0.563866	+	0.825866i	$0.309314\pi$
$42$	55069.3	0.114693
$43$	299840.	0.575109	0.287554	−	0.957764i	$-0.407158\pi$
$43$	299840.	0.575109	0.287554	+	0.957764i	$0.407158\pi$
$44$	−92512.8	−0.163726
$45$	292188.	0.477990
$46$	383936.	0.581575
$47$	280623.	0.394258	0.197129	−	0.980378i	$-0.436838\pi$
$47$	280623.	0.394258	0.197129	+	0.980378i	$0.436838\pi$
$48$	54635.0	0.0713061
$49$	−749450.	−0.910031
$50$	618331.	0.699561
$51$	958441.	1.01174
$52$	−685142.	−0.675723
$53$	1.78864e6	1.65028	0.825140	−	0.564928i	$-0.191096\pi$
$53$	1.78864e6	1.65028	0.825140	+	0.564928i	$0.191096\pi$
$54$	−147485.	−0.127459
$55$	516038.	0.418228
$56$	407624.	0.310172
$57$	389294.	0.278430
$58$	−598818.	−0.402992
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	777595.	0.464755
$61$	3.36147e6	1.89616	0.948080	−	0.318033i	$-0.103022\pi$
$61$	3.36147e6	1.89616	0.948080	+	0.318033i	$0.103022\pi$
$62$	1.71310e6	0.912875
$63$	−198434.	−0.0999826
$64$	1.58168e6	0.754202
$65$	3.82174e6	1.72609
$66$	−260476.	−0.111523
$67$	−585455.	−0.237811	−0.118905	−	0.992906i	$-0.537939\pi$
$67$	−585455.	−0.237811	−0.118905	+	0.992906i	$0.537939\pi$
$68$	2.55068e6	0.983729
$69$	−1.38346e6	−0.506983
$70$	−817487.	−0.284864
$71$	2.83547e6	0.940202	0.470101	−	0.882612i	$-0.344217\pi$
$71$	2.83547e6	0.940202	0.470101	+	0.882612i	$0.344217\pi$
$72$	−1.09169e6	−0.344695
$73$	−758408.	−0.228178	−0.114089	−	0.993471i	$-0.536395\pi$
$73$	−758408.	−0.228178	−0.114089	+	0.993471i	$0.536395\pi$
$74$	−1.04814e6	−0.300683
$75$	−2.22806e6	−0.609836
$76$	1.03602e6	0.270721
$77$	−350458.	−0.0874820
$78$	−1.92906e6	−0.460273
$79$	3.27559e6	0.747471	0.373736	−	0.927535i	$-0.378077\pi$
$79$	3.27559e6	0.747471	0.373736	+	0.927535i	$0.378077\pi$
$80$	−811040.	−0.177104
$81$	531441.	0.111111
$82$	3.72912e6	0.746892
$83$	9.92122e6	1.90455	0.952273	−	0.305246i	$-0.0987388\pi$
$83$	9.92122e6	1.90455	0.952273	+	0.305246i	$0.0987388\pi$
$84$	−528089.	−0.0972142
$85$	−1.42278e7	−2.51287
$86$	2.24671e6	0.380892
$87$	2.15775e6	0.351305
$88$	−1.92805e6	−0.301598
$89$	−634907.	−0.0954652	−0.0477326	−	0.998860i	$-0.515200\pi$
$89$	−634907.	−0.0954652	−0.0477326	+	0.998860i	$0.515200\pi$
$90$	2.18937e6	0.316571
$91$	−2.59546e6	−0.361052
$92$	−3.68177e6	−0.492945
$93$	−6.17290e6	−0.795791
$94$	2.10271e6	0.261116
$95$	−5.77895e6	−0.691539
$96$	−4.76603e6	−0.549804
$97$	8.12879e6	0.904325	0.452163	−	0.891936i	$-0.350653\pi$
$97$	8.12879e6	0.904325	0.452163	+	0.891936i	$0.350653\pi$
$98$	−5.61564e6	−0.602710
$99$	938588.	0.0972191
$100$	−5.92951e6	−0.592951
$101$	4.69794e6	0.453715	0.226857	−	0.973928i	$-0.427155\pi$
$101$	4.69794e6	0.453715	0.226857	+	0.973928i	$0.427155\pi$
$102$	7.18162e6	0.670073
$103$	6.17390e6	0.556710	0.278355	−	0.960478i	$-0.410211\pi$
$103$	6.17390e6	0.556710	0.278355	+	0.960478i	$0.410211\pi$
$104$	−1.42790e7	−1.24474
$105$	2.94569e6	0.248328
$106$	1.34023e7	1.09297
$107$	−1.35523e6	−0.106948	−0.0534738	−	0.998569i	$-0.517029\pi$
$107$	−1.35523e6	−0.106948	−0.0534738	+	0.998569i	$0.517029\pi$
$108$	1.41431e6	0.108035
$109$	1.04846e7	0.775457	0.387729	−	0.921774i	$-0.373260\pi$
$109$	1.04846e7	0.775457	0.387729	+	0.921774i	$0.373260\pi$
$110$	3.86669e6	0.276990
$111$	3.77682e6	0.262118
$112$	550803.	0.0370453
$113$	−7.14003e6	−0.465506	−0.232753	−	0.972536i	$-0.574773\pi$
$113$	−7.14003e6	−0.465506	−0.232753	+	0.972536i	$0.574773\pi$
$114$	2.91699e6	0.184403
$115$	2.05370e7	1.25920
$116$	5.74239e6	0.341578
$117$	6.95110e6	0.401239
$118$	−1.53891e6	−0.0862236
$119$	9.66253e6	0.525625
$120$	1.62058e7	0.856121
$121$	−1.78295e7	−0.914936
$122$	2.51876e7	1.25582
$123$	−1.34373e7	−0.651096
$124$	−1.64278e7	−0.773756
$125$	1.76189e6	0.0806854
$126$	−1.48687e6	−0.0662181
$127$	−7.91805e6	−0.343009	−0.171504	−	0.985183i	$-0.554863\pi$
$127$	−7.91805e6	−0.343009	−0.171504	+	0.985183i	$0.554863\pi$
$128$	−1.07430e7	−0.452783
$129$	−8.09568e6	−0.332039
$130$	2.86363e7	1.14318
$131$	−2.93961e7	−1.14246	−0.571230	−	0.820790i	$-0.693534\pi$
$131$	−2.93961e7	−1.14246	−0.571230	+	0.820790i	$0.693534\pi$
$132$	2.49785e6	0.0945273
$133$	3.92467e6	0.144651
$134$	−4.38683e6	−0.157501
$135$	−7.88907e6	−0.275967
$136$	5.31585e7	1.81212
$137$	9.93494e6	0.330098	0.165049	−	0.986285i	$-0.447222\pi$
$137$	9.93494e6	0.330098	0.165049	+	0.986285i	$0.447222\pi$
$138$	−1.03663e7	−0.335773
$139$	2.35079e7	0.742440	0.371220	−	0.928545i	$-0.378939\pi$
$139$	2.35079e7	0.742440	0.371220	+	0.928545i	$0.378939\pi$
$140$	7.83932e6	0.241452
$141$	−7.57682e6	−0.227625
$142$	2.12463e7	0.622692
$143$	1.22765e7	0.351073
$144$	−1.47515e6	−0.0411686
$145$	−3.20312e7	−0.872539
$146$	−5.68277e6	−0.151121
$147$	2.02351e7	0.525407
$148$	1.00512e7	0.254860
$149$	−2.98820e7	−0.740044	−0.370022	−	0.929023i	$-0.620650\pi$
$149$	−2.98820e7	−0.740044	−0.370022	+	0.929023i	$0.620650\pi$
$150$	−1.66949e7	−0.403892
$151$	−3.58463e7	−0.847277	−0.423639	−	0.905831i	$-0.639247\pi$
$151$	−3.58463e7	−0.847277	−0.423639	+	0.905831i	$0.639247\pi$
$152$	2.15916e7	0.498693
$153$	−2.58779e7	−0.584130
$154$	−2.62599e6	−0.0579389
$155$	9.16347e7	1.97651
$156$	1.84988e7	0.390129
$157$	−6.40578e7	−1.32106	−0.660531	−	0.750799i	$-0.729669\pi$
$157$	−6.40578e7	−1.32106	−0.660531	+	0.750799i	$0.729669\pi$
$158$	2.45440e7	0.495047
$159$	−4.82933e7	−0.952790
$160$	7.07502e7	1.36555
$161$	−1.39473e7	−0.263390
$162$	3.98210e6	0.0735884
$163$	−4.23392e7	−0.765749	−0.382874	−	0.923800i	$-0.625066\pi$
$163$	−4.23392e7	−0.765749	−0.382874	+	0.923800i	$0.625066\pi$
$164$	−3.57605e7	−0.633068
$165$	−1.39330e7	−0.241464
$166$	7.43399e7	1.26137
$167$	6.08959e7	1.01177	0.505883	−	0.862602i	$-0.331167\pi$
$167$	6.08959e7	1.01177	0.505883	+	0.862602i	$0.331167\pi$
$168$	−1.10059e7	−0.179078
$169$	2.81699e7	0.448933
$170$	−1.06609e8	−1.66426
$171$	−1.05109e7	−0.160752
$172$	−2.15449e7	−0.322845
$173$	−1.00814e8	−1.48033	−0.740165	−	0.672425i	$-0.765253\pi$
$173$	−1.00814e8	−1.48033	−0.740165	+	0.672425i	$0.765253\pi$
$174$	1.61681e7	0.232668
$175$	−2.24622e7	−0.316825
$176$	−2.60528e6	−0.0360214
$177$	5.54523e6	0.0751646
$178$	−4.75737e6	−0.0632262
$179$	1.28687e8	1.67707	0.838533	−	0.544851i	$-0.183414\pi$
$179$	1.28687e8	1.67707	0.838533	+	0.544851i	$0.183414\pi$
$180$	−2.09951e7	−0.268326
$181$	−7.12899e7	−0.893620	−0.446810	−	0.894629i	$-0.647440\pi$
$181$	−7.12899e7	−0.893620	−0.446810	+	0.894629i	$0.647440\pi$
$182$	−1.94479e7	−0.239123
$183$	−9.07597e7	−1.09475
$184$	−7.67313e7	−0.908051
$185$	−5.60657e7	−0.651023
$186$	−4.62537e7	−0.527049
$187$	−4.57035e7	−0.511097
$188$	−2.01641e7	−0.221322
$189$	5.35772e6	0.0577250
$190$	−4.33018e7	−0.458003
$191$	7.68302e7	0.797839	0.398920	−	0.916986i	$-0.369385\pi$
$191$	7.68302e7	0.797839	0.398920	+	0.916986i	$0.369385\pi$
$192$	−4.27053e7	−0.435439
$193$	1.34702e8	1.34873	0.674364	−	0.738399i	$-0.264418\pi$
$193$	1.34702e8	1.34873	0.674364	+	0.738399i	$0.264418\pi$
$194$	6.09092e7	0.598931
$195$	−1.03187e8	−0.996560
$196$	5.38514e7	0.510859
$197$	1.09326e8	1.01881	0.509405	−	0.860527i	$-0.329866\pi$
$197$	1.09326e8	1.01881	0.509405	+	0.860527i	$0.329866\pi$
$198$	7.03286e6	0.0643878
$199$	−5.09514e7	−0.458322	−0.229161	−	0.973389i	$-0.573598\pi$
$199$	−5.09514e7	−0.458322	−0.229161	+	0.973389i	$0.573598\pi$
$200$	−1.23576e8	−1.09227
$201$	1.58073e7	0.137300
$202$	3.52018e7	0.300493
$203$	2.17534e7	0.182512
$204$	−6.88685e7	−0.567956
$205$	1.99473e8	1.61713
$206$	4.62612e7	0.368707
$207$	3.73533e7	0.292707
$208$	−1.92945e7	−0.148666
$209$	−1.85636e7	−0.140653
$210$	2.20721e7	0.164466
$211$	−1.44274e8	−1.05730	−0.528651	−	0.848839i	$-0.677302\pi$
$211$	−1.44274e8	−1.05730	−0.528651	+	0.848839i	$0.677302\pi$
$212$	−1.28522e8	−0.926408
$213$	−7.65578e7	−0.542826
$214$	−1.01548e7	−0.0708310
$215$	1.20178e8	0.824688
$216$	2.94756e7	0.199010
$217$	−6.22321e7	−0.413433
$218$	7.85611e7	0.513582
$219$	2.04770e7	0.131738
$220$	−3.70798e7	−0.234778
$221$	−3.38476e8	−2.10938
$222$	2.82998e7	0.173599
$223$	1.97785e8	1.19433	0.597167	−	0.802117i	$-0.296293\pi$
$223$	1.97785e8	1.19433	0.597167	+	0.802117i	$0.296293\pi$
$224$	−4.80487e7	−0.285637
$225$	6.01577e7	0.352089
$226$	−5.35004e7	−0.308303
$227$	−3.33997e8	−1.89519	−0.947593	−	0.319479i	$-0.896492\pi$
$227$	−3.33997e8	−1.89519	−0.947593	+	0.319479i	$0.896492\pi$
$228$	−2.79726e7	−0.156301
$229$	−5.10139e7	−0.280714	−0.140357	−	0.990101i	$-0.544825\pi$
$229$	−5.10139e7	−0.280714	−0.140357	+	0.990101i	$0.544825\pi$
$230$	1.53884e8	0.833961
$231$	9.46237e6	0.0505077
$232$	1.19677e8	0.629218
$233$	−1.21435e8	−0.628923	−0.314461	−	0.949270i	$-0.601824\pi$
$233$	−1.21435e8	−0.628923	−0.314461	+	0.949270i	$0.601824\pi$
$234$	5.20847e7	0.265739
$235$	1.12476e8	0.565354
$236$	1.47574e7	0.0730834
$237$	−8.84409e7	−0.431553
$238$	7.24015e7	0.348119
$239$	2.41270e7	0.114317	0.0571585	−	0.998365i	$-0.481796\pi$
$239$	2.41270e7	0.114317	0.0571585	+	0.998365i	$0.481796\pi$
$240$	2.18981e7	0.102251
$241$	−5.58221e7	−0.256890	−0.128445	−	0.991717i	$-0.540999\pi$
$241$	−5.58221e7	−0.256890	−0.128445	+	0.991717i	$0.540999\pi$
$242$	−1.33597e8	−0.605958
$243$	−1.43489e7	−0.0641500
$244$	−2.41537e8	−1.06444
$245$	−3.00384e8	−1.30496
$246$	−1.00686e8	−0.431218
$247$	−1.37480e8	−0.580498
$248$	−3.42371e8	−1.42533
$249$	−2.67873e8	−1.09959
$250$	1.32019e7	0.0534376
$251$	1.85785e8	0.741570	0.370785	−	0.928719i	$-0.379089\pi$
$251$	1.85785e8	0.741570	0.370785	+	0.928719i	$0.379089\pi$
$252$	1.42584e7	0.0561267
$253$	6.59703e7	0.256110
$254$	−5.93301e7	−0.227173
$255$	3.84150e8	1.45081
$256$	−2.82952e8	−1.05408
$257$	−4.53248e8	−1.66560	−0.832799	−	0.553575i	$-0.813263\pi$
$257$	−4.53248e8	−1.66560	−0.832799	+	0.553575i	$0.813263\pi$
$258$	−6.06611e7	−0.219908
$259$	3.80760e7	0.136177
$260$	−2.74609e8	−0.968966
$261$	−5.82593e7	−0.202826
$262$	−2.20266e8	−0.756646
$263$	4.28480e8	1.45240	0.726199	−	0.687485i	$-0.241285\pi$
$263$	4.28480e8	1.45240	0.726199	+	0.687485i	$0.241285\pi$
$264$	5.20574e7	0.174128
$265$	7.16899e8	2.36645
$266$	2.94076e7	0.0958020
$267$	1.71425e7	0.0551169
$268$	4.20677e7	0.133499
$269$	−2.65173e7	−0.0830609	−0.0415305	−	0.999137i	$-0.513223\pi$
$269$	−2.65173e7	−0.0830609	−0.0415305	+	0.999137i	$0.513223\pi$
$270$	−5.91130e7	−0.182772
$271$	1.36921e8	0.417905	0.208952	−	0.977926i	$-0.432995\pi$
$271$	1.36921e8	0.417905	0.208952	+	0.977926i	$0.432995\pi$
$272$	7.18305e7	0.216430
$273$	7.00775e7	0.208453
$274$	7.44427e7	0.218623
$275$	1.06246e8	0.308068
$276$	9.94077e7	0.284602
$277$	4.27728e8	1.20917	0.604586	−	0.796540i	$-0.293338\pi$
$277$	4.27728e8	1.20917	0.604586	+	0.796540i	$0.293338\pi$
$278$	1.76145e8	0.491715
$279$	1.66668e8	0.459450
$280$	1.63378e8	0.444776
$281$	−3.52657e8	−0.948157	−0.474079	−	0.880482i	$-0.657219\pi$
$281$	−3.52657e8	−0.948157	−0.474079	+	0.880482i	$0.657219\pi$
$282$	−5.67733e7	−0.150755
$283$	5.10806e8	1.33969	0.669844	−	0.742502i	$-0.266361\pi$
$283$	5.10806e8	1.33969	0.669844	+	0.742502i	$0.266361\pi$
$284$	−2.03742e8	−0.527796
$285$	1.56032e8	0.399260
$286$	9.19878e7	0.232514
$287$	−1.35468e8	−0.338261
$288$	1.28683e8	0.317429
$289$	8.49757e8	2.07087
$290$	−2.40010e8	−0.577879
$291$	−2.19477e8	−0.522112
$292$	5.44952e7	0.128091
$293$	1.53209e8	0.355835	0.177917	−	0.984045i	$-0.443064\pi$
$293$	1.53209e8	0.355835	0.177917	+	0.984045i	$0.443064\pi$
$294$	1.51622e8	0.347975
$295$	−8.23172e7	−0.186687
$296$	2.09476e8	0.469476
$297$	−2.53419e7	−0.0561295
$298$	−2.23906e8	−0.490128
$299$	4.88570e8	1.05701
$300$	1.60097e8	0.342340
$301$	−8.16165e7	−0.172503
$302$	−2.68597e8	−0.561148
$303$	−1.26844e8	−0.261952
$304$	2.91757e7	0.0595613
$305$	1.34730e9	2.71903
$306$	−1.93904e8	−0.386867
$307$	7.83772e8	1.54598	0.772992	−	0.634415i	$-0.218759\pi$
$307$	7.83772e8	1.54598	0.772992	+	0.634415i	$0.218759\pi$
$308$	2.51820e7	0.0491093
$309$	−1.66695e8	−0.321417
$310$	6.86621e8	1.30903
$311$	−7.44813e7	−0.140406	−0.0702030	−	0.997533i	$-0.522365\pi$
$311$	−7.44813e7	−0.140406	−0.0702030	+	0.997533i	$0.522365\pi$
$312$	3.85532e8	0.718654
$313$	4.78847e8	0.882657	0.441328	−	0.897346i	$-0.354507\pi$
$313$	4.78847e8	0.882657	0.441328	+	0.897346i	$0.354507\pi$
$314$	−4.79986e8	−0.874934
$315$	−7.95337e7	−0.143372
$316$	−2.35366e8	−0.419604
$317$	−3.22619e8	−0.568829	−0.284415	−	0.958701i	$-0.591799\pi$
$317$	−3.22619e8	−0.568829	−0.284415	+	0.958701i	$0.591799\pi$
$318$	−3.61863e8	−0.631029
$319$	−1.02893e8	−0.177467
$320$	6.33946e8	1.08150
$321$	3.65913e7	0.0617462
$322$	−1.04507e8	−0.174442
$323$	5.11819e8	0.845099
$324$	−3.81865e7	−0.0623738
$325$	7.86846e8	1.27145
$326$	−3.17249e8	−0.507152
$327$	−2.83083e8	−0.447710
$328$	−7.45282e8	−1.16617
$329$	−7.63857e7	−0.118257
$330$	−1.04401e8	−0.159920
$331$	1.02925e9	1.56000	0.779998	−	0.625782i	$-0.215220\pi$
$331$	1.02925e9	1.56000	0.779998	+	0.625782i	$0.215220\pi$
$332$	−7.12885e8	−1.06914
$333$	−1.01974e8	−0.151334
$334$	4.56294e8	0.670089
$335$	−2.34654e8	−0.341014
$336$	−1.48717e7	−0.0213881
$337$	3.61784e7	0.0514926	0.0257463	−	0.999669i	$-0.491804\pi$
$337$	3.61784e7	0.0514926	0.0257463	+	0.999669i	$0.491804\pi$
$338$	2.11077e8	0.297326
$339$	1.92781e8	0.268760
$340$	1.02233e9	1.41064
$341$	2.94356e8	0.402006
$342$	−7.87588e7	−0.106465
$343$	4.28169e8	0.572910
$344$	−4.49015e8	−0.594711
$345$	−5.54498e8	−0.726998
$346$	−7.55400e8	−0.980417
$347$	1.13436e9	1.45746	0.728729	−	0.684802i	$-0.240111\pi$
$347$	1.13436e9	1.45746	0.728729	+	0.684802i	$0.240111\pi$
$348$	−1.55044e8	−0.197210
$349$	−3.76547e8	−0.474166	−0.237083	−	0.971489i	$-0.576191\pi$
$349$	−3.76547e8	−0.474166	−0.237083	+	0.971489i	$0.576191\pi$
$350$	−1.68310e8	−0.209832
$351$	−1.87680e8	−0.231655
$352$	2.27269e8	0.277742
$353$	−1.14395e9	−1.38419	−0.692097	−	0.721805i	$-0.743313\pi$
$353$	−1.14395e9	−1.38419	−0.692097	+	0.721805i	$0.743313\pi$
$354$	4.15505e7	0.0497812
$355$	1.13648e9	1.34822
$356$	4.56210e7	0.0535908
$357$	−2.60888e8	−0.303470
$358$	9.64257e8	1.11071
$359$	−1.69002e9	−1.92780	−0.963900	−	0.266265i	$-0.914210\pi$
$359$	−1.69002e9	−1.92780	−0.963900	+	0.266265i	$0.914210\pi$
$360$	−4.37556e8	−0.494282
$361$	−6.85984e8	−0.767430
$362$	−5.34177e8	−0.591841
$363$	4.81397e8	0.528239
$364$	1.86496e8	0.202682
$365$	−3.03975e8	−0.327200
$366$	−6.80064e8	−0.725047
$367$	−1.11560e9	−1.17809	−0.589046	−	0.808100i	$-0.700496\pi$
$367$	−1.11560e9	−1.17809	−0.589046	+	0.808100i	$0.700496\pi$
$368$	−1.03683e8	−0.108453
$369$	3.62808e8	0.375911
$370$	−4.20102e8	−0.431170
$371$	−4.86869e8	−0.494998
$372$	4.43551e8	0.446728
$373$	−1.06668e9	−1.06427	−0.532134	−	0.846660i	$-0.678610\pi$
$373$	−1.06668e9	−1.06427	−0.532134	+	0.846660i	$0.678610\pi$
$374$	−3.42457e8	−0.338497
$375$	−4.75712e7	−0.0465837
$376$	−4.20237e8	−0.407697
$377$	−7.62015e8	−0.732435
$378$	4.01455e7	0.0382310
$379$	9.06012e7	0.0854864	0.0427432	−	0.999086i	$-0.486390\pi$
$379$	9.06012e7	0.0854864	0.0427432	+	0.999086i	$0.486390\pi$
$380$	4.15245e8	0.388205
$381$	2.13787e8	0.198036
$382$	5.75691e8	0.528406
$383$	1.02770e9	0.934700	0.467350	−	0.884072i	$-0.345209\pi$
$383$	1.02770e9	0.934700	0.467350	+	0.884072i	$0.345209\pi$
$384$	2.90061e8	0.261414
$385$	−1.40466e8	−0.125446
$386$	1.00933e9	0.893257
$387$	2.18583e8	0.191703
$388$	−5.84091e8	−0.507656
$389$	1.62652e9	1.40099	0.700495	−	0.713657i	$-0.252962\pi$
$389$	1.62652e9	1.40099	0.700495	+	0.713657i	$0.252962\pi$
$390$	−7.73181e8	−0.660017
$391$	−1.81888e9	−1.53881
$392$	1.12231e9	0.941050
$393$	7.93696e8	0.659599
$394$	8.19184e8	0.674753
$395$	1.31288e9	1.07185
$396$	−6.74419e7	−0.0545753
$397$	−1.41716e8	−0.113672	−0.0568359	−	0.998384i	$-0.518101\pi$
$397$	−1.41716e8	−0.113672	−0.0568359	+	0.998384i	$0.518101\pi$
$398$	−3.81780e8	−0.303545
$399$	−1.05966e8	−0.0835145
$400$	−1.66983e8	−0.130455
$401$	−1.70702e9	−1.32200	−0.661002	−	0.750384i	$-0.729868\pi$
$401$	−1.70702e9	−1.32200	−0.661002	+	0.750384i	$0.729868\pi$
$402$	1.18444e8	0.0909333
$403$	2.17997e9	1.65914
$404$	−3.37569e8	−0.254699
$405$	2.13005e8	0.159330
$406$	1.62999e8	0.120877
$407$	−1.80099e8	−0.132413
$408$	−1.43528e9	−1.04623
$409$	−1.96299e9	−1.41869	−0.709345	−	0.704862i	$-0.751009\pi$
$409$	−1.96299e9	−1.41869	−0.709345	+	0.704862i	$0.751009\pi$
$410$	1.49466e9	1.07102
$411$	−2.68243e8	−0.190582
$412$	−4.43623e8	−0.312517
$413$	5.59043e7	0.0390499
$414$	2.79889e8	0.193858
$415$	3.97649e9	2.73106
$416$	1.68313e9	1.14628
$417$	−6.34713e8	−0.428648
$418$	−1.39097e8	−0.0931540
$419$	2.45844e9	1.63271	0.816357	−	0.577547i	$-0.195990\pi$
$419$	2.45844e9	1.63271	0.816357	+	0.577547i	$0.195990\pi$
$420$	−2.11662e8	−0.139402
$421$	6.57370e8	0.429361	0.214681	−	0.976684i	$-0.431129\pi$
$421$	6.57370e8	0.429361	0.214681	+	0.976684i	$0.431129\pi$
$422$	−1.08105e9	−0.700247
$423$	2.04574e8	0.131419
$424$	−2.67852e9	−1.70653
$425$	−2.92931e9	−1.85099
$426$	−5.73649e8	−0.359511
$427$	−9.14994e8	−0.568749
$428$	9.73799e7	0.0600366
$429$	−3.31464e8	−0.202692
$430$	9.00495e8	0.546187
$431$	−1.65546e9	−0.995976	−0.497988	−	0.867184i	$-0.665928\pi$
$431$	−1.65546e9	−0.995976	−0.497988	+	0.867184i	$0.665928\pi$
$432$	3.98289e7	0.0237687
$433$	−1.96267e9	−1.16182	−0.580910	−	0.813968i	$-0.697303\pi$
$433$	−1.96267e9	−1.16182	−0.580910	+	0.813968i	$0.697303\pi$
$434$	−4.66306e8	−0.273815
$435$	8.64841e8	0.503760
$436$	−7.53365e8	−0.435314
$437$	−7.38781e8	−0.423478
$438$	1.53435e8	0.0872498
$439$	6.65374e8	0.375353	0.187677	−	0.982231i	$-0.439904\pi$
$439$	6.65374e8	0.375353	0.187677	+	0.982231i	$0.439904\pi$
$440$	−7.72775e8	−0.432483
$441$	−5.46349e8	−0.303344
$442$	−2.53621e9	−1.39703
$443$	2.45181e8	0.133991	0.0669953	−	0.997753i	$-0.478659\pi$
$443$	2.45181e8	0.133991	0.0669953	+	0.997753i	$0.478659\pi$
$444$	−2.71382e8	−0.147143
$445$	−2.54475e8	−0.136894
$446$	1.48201e9	0.791003
$447$	8.06813e8	0.427264
$448$	−4.30533e8	−0.226221
$449$	1.56613e9	0.816516	0.408258	−	0.912867i	$-0.366136\pi$
$449$	1.56613e9	0.816516	0.408258	+	0.912867i	$0.366136\pi$
$450$	4.50763e8	0.233187
$451$	6.40762e8	0.328911
$452$	5.13044e8	0.261318
$453$	9.67851e8	0.489176
$454$	−2.50265e9	−1.25517
$455$	−1.04028e9	−0.517737
$456$	−5.82974e8	−0.287920
$457$	2.77494e9	1.36002	0.680012	−	0.733201i	$-0.261974\pi$
$457$	2.77494e9	1.36002	0.680012	+	0.733201i	$0.261974\pi$
$458$	−3.82249e8	−0.185916
$459$	6.98704e8	0.337247
$460$	−1.47568e9	−0.706868
$461$	1.84492e9	0.877051	0.438525	−	0.898719i	$-0.355501\pi$
$461$	1.84492e9	0.877051	0.438525	+	0.898719i	$0.355501\pi$
$462$	7.09017e7	0.0334511
$463$	−1.44653e9	−0.677322	−0.338661	−	0.940908i	$-0.609974\pi$
$463$	−1.44653e9	−0.677322	−0.338661	+	0.940908i	$0.609974\pi$
$464$	1.61713e8	0.0751506
$465$	−2.47414e9	−1.14114
$466$	−9.09914e8	−0.416533
$467$	−1.95804e9	−0.889636	−0.444818	−	0.895621i	$-0.646732\pi$
$467$	−1.95804e9	−0.889636	−0.444818	+	0.895621i	$0.646732\pi$
$468$	−4.99469e8	−0.225241
$469$	1.59361e8	0.0713309
$470$	8.42782e8	0.374432
$471$	1.72956e9	0.762715
$472$	3.07558e8	0.134626
$473$	3.86044e8	0.167735
$474$	−6.62689e8	−0.285815
$475$	−1.18981e9	−0.509390
$476$	−6.94297e8	−0.295067
$477$	1.30392e9	0.550093
$478$	1.80784e8	0.0757116
$479$	−3.02650e9	−1.25825	−0.629124	−	0.777305i	$-0.716586\pi$
$479$	−3.02650e9	−1.25825	−0.629124	+	0.777305i	$0.716586\pi$
$480$	−1.91026e9	−0.788401
$481$	−1.33379e9	−0.546488
$482$	−4.18277e8	−0.170137
$483$	3.76577e8	0.152068
$484$	1.28113e9	0.513612
$485$	3.25807e9	1.29677
$486$	−1.07517e8	−0.0424863
$487$	−1.90649e9	−0.747967	−0.373983	−	0.927435i	$-0.622008\pi$
$487$	−1.90649e9	−0.747967	−0.373983	+	0.927435i	$0.622008\pi$
$488$	−5.03385e9	−1.96079
$489$	1.14316e9	0.442105
$490$	−2.25079e9	−0.864267
$491$	2.37779e9	0.906544	0.453272	−	0.891372i	$-0.350257\pi$
$491$	2.37779e9	0.906544	0.453272	+	0.891372i	$0.350257\pi$
$492$	9.65534e8	0.365502
$493$	2.83687e9	1.06629
$494$	−1.03014e9	−0.384462
$495$	3.76192e8	0.139409
$496$	−4.62629e8	−0.170234
$497$	−7.71817e8	−0.282012
$498$	−2.00718e9	−0.728254
$499$	−1.25478e9	−0.452081	−0.226041	−	0.974118i	$-0.572578\pi$
$499$	−1.25478e9	−0.452081	−0.226041	+	0.974118i	$0.572578\pi$
$500$	−1.26600e8	−0.0452939
$501$	−1.64419e9	−0.584144
$502$	1.39209e9	0.491139
$503$	−1.13501e9	−0.397660	−0.198830	−	0.980034i	$-0.563714\pi$
$503$	−1.13501e9	−0.397660	−0.198830	+	0.980034i	$0.563714\pi$
$504$	2.97158e8	0.103391
$505$	1.88297e9	0.650613
$506$	4.94317e8	0.169621
$507$	−7.60586e8	−0.259191
$508$	5.68949e8	0.192553
$509$	−4.34255e9	−1.45960	−0.729798	−	0.683663i	$-0.760386\pi$
$509$	−4.34255e9	−1.45960	−0.729798	+	0.683663i	$0.760386\pi$
$510$	2.87844e9	0.960864
$511$	2.06439e8	0.0684414
$512$	−7.45063e8	−0.245329
$513$	2.83796e8	0.0928100
$514$	−3.39620e9	−1.10312
$515$	2.47454e9	0.798305
$516$	5.81712e8	0.186395
$517$	3.61302e8	0.114988
$518$	2.85305e8	0.0901892
$519$	2.72197e9	0.854669
$520$	−5.72311e9	−1.78493
$521$	1.60678e9	0.497764	0.248882	−	0.968534i	$-0.419937\pi$
$521$	1.60678e9	0.497764	0.248882	+	0.968534i	$0.419937\pi$
$522$	−4.36538e8	−0.134331
$523$	−1.33872e9	−0.409198	−0.204599	−	0.978846i	$-0.565589\pi$
$523$	−1.33872e9	−0.409198	−0.204599	+	0.978846i	$0.565589\pi$
$524$	2.11225e9	0.641336
$525$	6.06480e8	0.182919
$526$	3.21061e9	0.961917
$527$	−8.11572e9	−2.41541
$528$	7.03426e7	0.0207970
$529$	−7.79382e8	−0.228905
$530$	5.37174e9	1.56729
$531$	−1.49721e8	−0.0433963
$532$	−2.82006e8	−0.0812021
$533$	4.74542e9	1.35747
$534$	1.28449e8	0.0365037
$535$	−5.43187e8	−0.153360
$536$	8.76728e8	0.245917
$537$	−3.47456e9	−0.968255
$538$	−1.98695e8	−0.0550109
$539$	−9.64917e8	−0.265417
$540$	5.66867e8	0.154918
$541$	2.04184e9	0.554410	0.277205	−	0.960811i	$-0.410592\pi$
$541$	2.04184e9	0.554410	0.277205	+	0.960811i	$0.410592\pi$
$542$	1.02595e9	0.276777
$543$	1.92483e9	0.515932
$544$	−6.26606e9	−1.66878
$545$	4.20228e9	1.11198
$546$	5.25092e8	0.138058
$547$	4.97747e9	1.30033	0.650164	−	0.759794i	$-0.274700\pi$
$547$	4.97747e9	1.30033	0.650164	+	0.759794i	$0.274700\pi$
$548$	−7.13871e8	−0.185305
$549$	2.45051e9	0.632053
$550$	7.96101e8	0.204032
$551$	1.15226e9	0.293442
$552$	2.07175e9	0.524263
$553$	−8.91616e8	−0.224202
$554$	3.20497e9	0.800830
$555$	1.51378e9	0.375869
$556$	−1.68915e9	−0.416780
$557$	4.71080e9	1.15505	0.577526	−	0.816372i	$-0.304018\pi$
$557$	4.71080e9	1.15505	0.577526	+	0.816372i	$0.304018\pi$
$558$	1.24885e9	0.304292
$559$	2.85901e9	0.692267
$560$	2.20765e8	0.0531218
$561$	1.23399e9	0.295082
$562$	−2.64247e9	−0.627961
$563$	−4.24894e9	−1.00346	−0.501731	−	0.865024i	$-0.667303\pi$
$563$	−4.24894e9	−1.00346	−0.501731	+	0.865024i	$0.667303\pi$
$564$	5.44430e8	0.127781
$565$	−2.86177e9	−0.667521
$566$	3.82748e9	0.887269
$567$	−1.44658e8	−0.0333275
$568$	−4.24616e9	−0.972249
$569$	5.26230e9	1.19752	0.598759	−	0.800929i	$-0.295661\pi$
$569$	5.26230e9	1.19752	0.598759	+	0.800929i	$0.295661\pi$
$570$	1.16915e9	0.264428
$571$	−3.29668e9	−0.741056	−0.370528	−	0.928821i	$-0.620823\pi$
$571$	−3.29668e9	−0.741056	−0.370528	+	0.928821i	$0.620823\pi$
$572$	−8.82120e8	−0.197080
$573$	−2.07442e9	−0.460633
$574$	−1.01507e9	−0.224029
$575$	4.22829e9	0.927529
$576$	1.15304e9	0.251401
$577$	−3.50100e9	−0.758713	−0.379356	−	0.925251i	$-0.623855\pi$
$577$	−3.50100e9	−0.758713	−0.379356	+	0.925251i	$0.623855\pi$
$578$	6.36725e9	1.37153
$579$	−3.63696e9	−0.778688
$580$	2.30159e9	0.489812
$581$	−2.70056e9	−0.571265
$582$	−1.64455e9	−0.345793
$583$	2.30288e9	0.481316
$584$	1.13573e9	0.235955
$585$	2.78605e9	0.575364
$586$	1.14800e9	0.235668
$587$	−3.06924e9	−0.626322	−0.313161	−	0.949700i	$-0.601388\pi$
$587$	−3.06924e9	−0.626322	−0.313161	+	0.949700i	$0.601388\pi$
$588$	−1.45399e9	−0.294945
$589$	−3.29640e9	−0.664716
$590$	−6.16805e8	−0.123642
$591$	−2.95181e9	−0.588210
$592$	2.83055e8	0.0560718
$593$	−9.06218e9	−1.78460	−0.892300	−	0.451442i	$-0.850910\pi$
$593$	−9.06218e9	−1.78460	−0.892300	+	0.451442i	$0.850910\pi$
$594$	−1.89887e8	−0.0371743
$595$	3.87280e9	0.753730
$596$	2.14716e9	0.415434
$597$	1.37569e9	0.264612
$598$	3.66087e9	0.700052
$599$	5.53085e9	1.05147	0.525736	−	0.850648i	$-0.323790\pi$
$599$	5.53085e9	1.05147	0.525736	+	0.850648i	$0.323790\pi$
$600$	3.33656e9	0.630622
$601$	2.64790e9	0.497555	0.248777	−	0.968561i	$-0.419971\pi$
$601$	2.64790e9	0.497555	0.248777	+	0.968561i	$0.419971\pi$
$602$	−6.11555e8	−0.114248
$603$	−4.26797e8	−0.0792703
$604$	2.57573e9	0.475631
$605$	−7.14619e9	−1.31199
$606$	−9.50448e8	−0.173490
$607$	1.49005e9	0.270421	0.135210	−	0.990817i	$-0.456829\pi$
$607$	1.49005e9	0.270421	0.135210	+	0.990817i	$0.456829\pi$
$608$	−2.54512e9	−0.459246
$609$	−5.87341e8	−0.105373
$610$	1.00953e10	1.80080
$611$	2.67577e9	0.474575
$612$	1.85945e9	0.327910
$613$	6.01176e9	1.05412	0.527060	−	0.849828i	$-0.323294\pi$
$613$	6.01176e9	1.05412	0.527060	+	0.849828i	$0.323294\pi$
$614$	5.87282e9	1.02390
$615$	−5.38577e9	−0.933652
$616$	5.24816e8	0.0904638
$617$	1.06578e10	1.82671	0.913356	−	0.407161i	$-0.133481\pi$
$617$	1.06578e10	1.82671	0.913356	+	0.407161i	$0.133481\pi$
$618$	−1.24905e9	−0.212873
$619$	−3.27736e9	−0.555401	−0.277700	−	0.960668i	$-0.589572\pi$
$619$	−3.27736e9	−0.555401	−0.277700	+	0.960668i	$0.589572\pi$
$620$	−6.58438e9	−1.10954
$621$	−1.00854e9	−0.168994
$622$	−5.58090e8	−0.0929903
$623$	1.72822e8	0.0286346
$624$	5.20951e8	0.0858323
$625$	−5.74076e9	−0.940567
$626$	3.58801e9	0.584580
$627$	5.01217e8	0.0812062
$628$	4.60285e9	0.741597
$629$	4.96552e9	0.795586
$630$	−5.95948e8	−0.0949546
$631$	−5.83790e9	−0.925026	−0.462513	−	0.886613i	$-0.653052\pi$
$631$	−5.83790e9	−0.925026	−0.462513	+	0.886613i	$0.653052\pi$
$632$	−4.90524e9	−0.772949
$633$	3.89540e9	0.610434
$634$	−2.41739e9	−0.376733
$635$	−3.17361e9	−0.491864
$636$	3.47010e9	0.534862
$637$	−7.14609e9	−1.09542
$638$	−7.70978e8	−0.117536
$639$	2.06706e9	0.313401
$640$	−4.30586e9	−0.649277
$641$	−9.30439e9	−1.39536	−0.697678	−	0.716412i	$-0.745783\pi$
$641$	−9.30439e9	−1.39536	−0.697678	+	0.716412i	$0.745783\pi$
$642$	2.74180e8	0.0408943
$643$	7.27839e9	1.07969	0.539843	−	0.841766i	$-0.318484\pi$
$643$	7.27839e9	1.07969	0.539843	+	0.841766i	$0.318484\pi$
$644$	1.00218e9	0.147858
$645$	−3.24480e9	−0.476134
$646$	3.83507e9	0.559705
$647$	−8.75508e9	−1.27085	−0.635426	−	0.772162i	$-0.719176\pi$
$647$	−8.75508e9	−1.27085	−0.635426	+	0.772162i	$0.719176\pi$
$648$	−7.95841e8	−0.114898
$649$	−2.64425e8	−0.0379705
$650$	5.89585e9	0.842073
$651$	1.68027e9	0.238696
$652$	3.04227e9	0.429864
$653$	5.51167e8	0.0774617	0.0387308	−	0.999250i	$-0.487669\pi$
$653$	5.51167e8	0.0774617	0.0387308	+	0.999250i	$0.487669\pi$
$654$	−2.12115e9	−0.296517
$655$	−1.17822e10	−1.63825
$656$	−1.00706e9	−0.139281
$657$	−5.52880e8	−0.0760592
$658$	−5.72360e8	−0.0783210
$659$	2.23902e8	0.0304761	0.0152381	−	0.999884i	$-0.495149\pi$
$659$	2.23902e8	0.0304761	0.0152381	+	0.999884i	$0.495149\pi$
$660$	1.00115e9	0.135549
$661$	1.42160e10	1.91458	0.957288	−	0.289137i	$-0.0933682\pi$
$661$	1.42160e10	1.91458	0.957288	+	0.289137i	$0.0933682\pi$
$662$	7.71221e9	1.03318
$663$	9.13885e9	1.21785
$664$	−1.48572e10	−1.96946
$665$	1.57303e9	0.207426
$666$	−7.64095e8	−0.100228
$667$	−4.09486e9	−0.534317
$668$	−4.37565e9	−0.567970
$669$	−5.34019e9	−0.689550
$670$	−1.75827e9	−0.225852
$671$	4.32789e9	0.553029
$672$	1.29732e9	0.164912
$673$	−1.15239e10	−1.45730	−0.728648	−	0.684888i	$-0.759851\pi$
$673$	−1.15239e10	−1.45730	−0.728648	+	0.684888i	$0.759851\pi$
$674$	2.71085e8	0.0341033
$675$	−1.62426e9	−0.203279
$676$	−2.02414e9	−0.252015
$677$	−1.31983e10	−1.63477	−0.817385	−	0.576092i	$-0.804577\pi$
$677$	−1.31983e10	−1.63477	−0.817385	+	0.576092i	$0.804577\pi$
$678$	1.44451e9	0.177999
$679$	−2.21266e9	−0.271250
$680$	2.13063e10	2.59852
$681$	9.01792e9	1.09419
$682$	2.20561e9	0.266247
$683$	−1.04211e10	−1.25153	−0.625766	−	0.780010i	$-0.715214\pi$
$683$	−1.04211e10	−1.25153	−0.625766	+	0.780010i	$0.715214\pi$
$684$	7.55260e8	0.0902403
$685$	3.98199e9	0.473351
$686$	3.20828e9	0.379436
$687$	1.37738e9	0.162071
$688$	−6.06732e8	−0.0710292
$689$	1.70549e10	1.98647
$690$	−4.15486e9	−0.481488
$691$	1.27099e10	1.46544	0.732721	−	0.680529i	$-0.238250\pi$
$691$	1.27099e10	1.46544	0.732721	+	0.680529i	$0.238250\pi$
$692$	7.24394e9	0.831005
$693$	−2.55484e8	−0.0291607
$694$	8.49976e9	0.965269
$695$	9.42211e9	1.06464
$696$	−3.23127e9	−0.363279
$697$	−1.76665e10	−1.97622
$698$	−2.82148e9	−0.314038
$699$	3.27874e9	0.363109
$700$	1.61401e9	0.177854
$701$	−9.44240e9	−1.03531	−0.517654	−	0.855590i	$-0.673194\pi$
$701$	−9.44240e9	−1.03531	−0.517654	+	0.855590i	$0.673194\pi$
$702$	−1.40629e9	−0.153424
$703$	2.01687e9	0.218944
$704$	2.03641e9	0.219968
$705$	−3.03684e9	−0.326407
$706$	−8.57167e9	−0.916745
$707$	−1.27878e9	−0.136091
$708$	−3.98451e8	−0.0421947
$709$	5.62595e9	0.592835	0.296417	−	0.955058i	$-0.404208\pi$
$709$	5.62595e9	0.592835	0.296417	+	0.955058i	$0.404208\pi$
$710$	8.51564e9	0.892921
$711$	2.38790e9	0.249157
$712$	9.50783e8	0.0987191
$713$	1.17146e10	1.21036
$714$	−1.95484e9	−0.200987
$715$	4.92049e9	0.503427
$716$	−9.24678e9	−0.941445
$717$	−6.51429e8	−0.0660009
$718$	−1.26634e10	−1.27677
$719$	1.77080e9	0.177672	0.0888360	−	0.996046i	$-0.471685\pi$
$719$	1.77080e9	0.177672	0.0888360	+	0.996046i	$0.471685\pi$
$720$	−5.91248e8	−0.0590345
$721$	−1.68054e9	−0.166984
$722$	−5.14009e9	−0.508266
$723$	1.50720e9	0.148315
$724$	5.12251e9	0.501647
$725$	−6.59480e9	−0.642715
$726$	3.60712e9	0.349850
$727$	−2.42657e9	−0.234219	−0.117110	−	0.993119i	$-0.537363\pi$
$727$	−2.42657e9	−0.234219	−0.117110	+	0.993119i	$0.537363\pi$
$728$	3.88674e9	0.373359
$729$	3.87420e8	0.0370370
$730$	−2.27769e9	−0.216703
$731$	−1.06437e10	−1.00781
$732$	6.52150e9	0.614552
$733$	7.37181e9	0.691370	0.345685	−	0.938351i	$-0.387647\pi$
$733$	7.37181e9	0.691370	0.345685	+	0.938351i	$0.387647\pi$
$734$	−8.35925e9	−0.780245
$735$	8.11038e9	0.753417
$736$	9.04471e9	0.836223
$737$	−7.53774e8	−0.0693593
$738$	2.71853e9	0.248964
$739$	−1.11711e6	−0.000101822 0	−5.09108e−5	−	1.00000i	$-0.500016\pi$
$739$	−1.11711e6	−0.000101822 0	−5.09108e−5		1.00000i	$0.500016\pi$
$740$	4.02858e9	0.365461
$741$	3.71197e9	0.335151
$742$	−3.64812e9	−0.327835
$743$	−6.56798e9	−0.587450	−0.293725	−	0.955890i	$-0.594895\pi$
$743$	−6.56798e9	−0.587450	−0.293725	+	0.955890i	$0.594895\pi$
$744$	9.24401e9	0.822915
$745$	−1.19769e10	−1.06120
$746$	−7.99262e9	−0.704861
$747$	7.23257e9	0.634849
$748$	3.28401e9	0.286912
$749$	3.68895e8	0.0320787
$750$	−3.56452e8	−0.0308522
$751$	5.66489e9	0.488036	0.244018	−	0.969771i	$-0.421534\pi$
$751$	5.66489e9	0.488036	0.244018	+	0.969771i	$0.421534\pi$
$752$	−5.67846e8	−0.0486932
$753$	−5.01619e9	−0.428146
$754$	−5.70980e9	−0.485088
$755$	−1.43674e10	−1.21497
$756$	−3.84977e8	−0.0324047
$757$	−8.32870e9	−0.697817	−0.348908	−	0.937157i	$-0.613448\pi$
$757$	−8.32870e9	−0.697817	−0.348908	+	0.937157i	$0.613448\pi$
$758$	6.78877e8	0.0566173
$759$	−1.78120e9	−0.147865
$760$	8.65407e9	0.715110
$761$	−1.51950e10	−1.24984	−0.624918	−	0.780690i	$-0.714868\pi$
$761$	−1.51950e10	−1.24984	−0.624918	+	0.780690i	$0.714868\pi$
$762$	1.60191e9	0.131159
$763$	−2.85390e9	−0.232597
$764$	−5.52061e9	−0.447878
$765$	−1.03720e10	−0.837624
$766$	7.70060e9	0.619048
$767$	−1.95831e9	−0.156711
$768$	7.63970e9	0.608572
$769$	5.04268e9	0.399871	0.199935	−	0.979809i	$-0.435927\pi$
$769$	5.04268e9	0.399871	0.199935	+	0.979809i	$0.435927\pi$
$770$	−1.05251e9	−0.0830826
$771$	1.22377e10	0.961634
$772$	−9.67898e9	−0.757128
$773$	8.09728e9	0.630537	0.315269	−	0.949002i	$-0.397905\pi$
$773$	8.09728e9	0.630537	0.315269	+	0.949002i	$0.397905\pi$
$774$	1.63785e9	0.126964
$775$	1.88664e10	1.45591
$776$	−1.21730e10	−0.935149
$777$	−1.02805e9	−0.0786216
$778$	1.21875e10	0.927870
$779$	−7.17569e9	−0.543854
$780$	7.41445e9	0.559433
$781$	3.65067e9	0.274217
$782$	−1.36289e10	−1.01915
$783$	1.57300e9	0.117102
$784$	1.51653e9	0.112394
$785$	−2.56748e10	−1.89436
$786$	5.94718e9	0.436850
$787$	−1.32475e10	−0.968773	−0.484387	−	0.874854i	$-0.660957\pi$
$787$	−1.32475e10	−0.968773	−0.484387	+	0.874854i	$0.660957\pi$
$788$	−7.85560e9	−0.571923
$789$	−1.15690e10	−0.838542
$790$	9.83741e9	0.709882
$791$	1.94352e9	0.139628
$792$	−1.40555e9	−0.100533
$793$	3.20520e10	2.28244
$794$	−1.06188e9	−0.0752843
$795$	−1.93563e10	−1.36627
$796$	3.66110e9	0.257286
$797$	−1.25069e10	−0.875076	−0.437538	−	0.899200i	$-0.644149\pi$
$797$	−1.25069e10	−0.875076	−0.437538	+	0.899200i	$0.644149\pi$
$798$	−7.94006e8	−0.0553113
$799$	−9.96151e9	−0.690894
$800$	1.45666e10	1.00587
$801$	−4.62847e8	−0.0318217
$802$	−1.27907e10	−0.875557
$803$	−9.76451e8	−0.0665497
$804$	−1.13583e9	−0.0770754
$805$	−5.59017e9	−0.377693
$806$	1.63346e10	1.09884
$807$	7.15968e8	0.0479552
$808$	−7.03524e9	−0.469179
$809$	2.07620e10	1.37864	0.689319	−	0.724458i	$-0.257910\pi$
$809$	2.07620e10	1.37864	0.689319	+	0.724458i	$0.257910\pi$
$810$	1.59605e9	0.105524
$811$	−8.31574e8	−0.0547429	−0.0273715	−	0.999625i	$-0.508714\pi$
$811$	−8.31574e8	−0.0547429	−0.0273715	+	0.999625i	$0.508714\pi$
$812$	−1.56308e9	−0.102456
$813$	−3.69687e9	−0.241277
$814$	−1.34948e9	−0.0876964
$815$	−1.69698e10	−1.09806
$816$	−1.93942e9	−0.124956
$817$	−4.32318e9	−0.277349
$818$	−1.47088e10	−0.939592
$819$	−1.89209e9	−0.120351
$820$	−1.43331e10	−0.907800
$821$	−7.46166e9	−0.470581	−0.235290	−	0.971925i	$-0.575604\pi$
$821$	−7.46166e9	−0.470581	−0.235290	+	0.971925i	$0.575604\pi$
$822$	−2.00995e9	−0.126222
$823$	−1.83123e10	−1.14510	−0.572550	−	0.819870i	$-0.694046\pi$
$823$	−1.83123e10	−1.14510	−0.572550	+	0.819870i	$0.694046\pi$
$824$	−9.24551e9	−0.575686
$825$	−2.86863e9	−0.177863
$826$	4.18892e8	0.0258626
$827$	2.57787e10	1.58487	0.792433	−	0.609960i	$-0.208814\pi$
$827$	2.57787e10	1.58487	0.792433	+	0.609960i	$0.208814\pi$
$828$	−2.68401e9	−0.164315
$829$	−2.26603e10	−1.38142	−0.690710	−	0.723132i	$-0.742702\pi$
$829$	−2.26603e10	−1.38142	−0.690710	+	0.723132i	$0.742702\pi$
$830$	2.97959e10	1.80877
$831$	−1.15487e10	−0.698116
$832$	1.50815e10	0.907845
$833$	2.66038e10	1.59473
$834$	−4.75592e9	−0.283892
$835$	2.44075e10	1.45084
$836$	1.33388e9	0.0789577
$837$	−4.50004e9	−0.265264
$838$	1.84211e10	1.08134
$839$	−9.57948e9	−0.559983	−0.279992	−	0.960002i	$-0.590332\pi$
$839$	−9.57948e9	−0.559983	−0.279992	+	0.960002i	$0.590332\pi$
$840$	−4.41122e9	−0.256792
$841$	−1.08632e10	−0.629755
$842$	4.92569e9	0.284364
$843$	9.52174e9	0.547419
$844$	1.03668e10	0.593532
$845$	1.12907e10	0.643756
$846$	1.53288e9	0.0870385
$847$	4.85320e9	0.274433
$848$	−3.61935e9	−0.203819
$849$	−1.37918e10	−0.773469
$850$	−2.19494e10	−1.22590
$851$	−7.16744e9	−0.398667
$852$	5.50103e9	0.304723
$853$	2.74400e10	1.51378	0.756889	−	0.653544i	$-0.226718\pi$
$853$	2.74400e10	1.51378	0.756889	+	0.653544i	$0.226718\pi$
$854$	−6.85607e9	−0.376680
$855$	−4.21286e9	−0.230513
$856$	2.02948e9	0.110593
$857$	−1.29104e10	−0.700657	−0.350329	−	0.936627i	$-0.613930\pi$
$857$	−1.29104e10	−0.700657	−0.350329	+	0.936627i	$0.613930\pi$
$858$	−2.48367e9	−0.134242
$859$	2.65615e10	1.42981	0.714903	−	0.699224i	$-0.246471\pi$
$859$	2.65615e10	1.42981	0.714903	+	0.699224i	$0.246471\pi$
$860$	−8.63533e9	−0.462950
$861$	3.65765e9	0.195295
$862$	−1.24044e10	−0.659631
$863$	1.29749e10	0.687173	0.343586	−	0.939121i	$-0.388358\pi$
$863$	1.29749e10	0.687173	0.343586	+	0.939121i	$0.388358\pi$
$864$	−3.47444e9	−0.183268
$865$	−4.04068e10	−2.12275
$866$	−1.47063e10	−0.769469
$867$	−2.29434e10	−1.19562
$868$	4.47166e9	0.232087
$869$	4.21732e9	0.218005
$870$	6.48027e9	0.333638
$871$	−5.58238e9	−0.286257
$872$	−1.57008e10	−0.801889
$873$	5.92588e9	0.301442
$874$	−5.53570e9	−0.280468
$875$	−4.79588e8	−0.0242014
$876$	−1.47137e9	−0.0739533
$877$	−1.08321e10	−0.542270	−0.271135	−	0.962541i	$-0.587399\pi$
$877$	−1.08321e10	−0.542270	−0.271135	+	0.962541i	$0.587399\pi$
$878$	4.98566e9	0.248595
$879$	−4.13665e9	−0.205441
$880$	−1.04421e9	−0.0516535
$881$	1.78817e10	0.881034	0.440517	−	0.897744i	$-0.354795\pi$
$881$	1.78817e10	0.881034	0.440517	+	0.897744i	$0.354795\pi$
$882$	−4.09380e9	−0.200903
$883$	2.05428e9	0.100415	0.0502073	−	0.998739i	$-0.484012\pi$
$883$	2.05428e9	0.100415	0.0502073	+	0.998739i	$0.484012\pi$
$884$	2.43211e10	1.18413
$885$	2.22257e9	0.107784
$886$	1.83715e9	0.0887414
$887$	2.26672e10	1.09060	0.545299	−	0.838242i	$-0.316416\pi$
$887$	2.26672e10	1.09060	0.545299	+	0.838242i	$0.316416\pi$
$888$	−5.65585e9	−0.271052
$889$	2.15530e9	0.102885
$890$	−1.90679e9	−0.0906644
$891$	6.84230e8	0.0324064
$892$	−1.42118e10	−0.670457
$893$	−4.04611e9	−0.190133
$894$	6.04547e9	0.282975
$895$	5.15787e10	2.40486
$896$	2.92424e9	0.135811
$897$	−1.31914e10	−0.610264
$898$	1.17350e10	0.540775
$899$	−1.82710e10	−0.838695
$900$	−4.32261e9	−0.197650
$901$	−6.34929e10	−2.89193
$902$	4.80124e9	0.217836
$903$	2.20365e9	0.0995944
$904$	1.06923e10	0.481373
$905$	−2.85735e10	−1.28142
$906$	7.25213e9	0.323979
$907$	−3.69882e10	−1.64603	−0.823015	−	0.568020i	$-0.807710\pi$
$907$	−3.69882e10	−1.64603	−0.823015	+	0.568020i	$0.807710\pi$
$908$	2.39992e10	1.06389
$909$	3.42480e9	0.151238
$910$	−7.79483e9	−0.342895
$911$	−3.70589e10	−1.62397	−0.811986	−	0.583677i	$-0.801613\pi$
$911$	−3.70589e10	−1.62397	−0.811986	+	0.583677i	$0.801613\pi$
$912$	−7.87745e8	−0.0343877
$913$	1.27736e10	0.555475
$914$	2.07927e10	0.900739
$915$	−3.63771e10	−1.56983
$916$	3.66559e9	0.157583
$917$	8.00164e9	0.342678
$918$	5.23540e9	0.223358
$919$	−3.58106e10	−1.52197	−0.760986	−	0.648768i	$-0.775285\pi$
$919$	−3.58106e10	−1.52197	−0.760986	+	0.648768i	$0.775285\pi$
$920$	−3.07544e10	−1.30212
$921$	−2.11618e10	−0.892575
$922$	1.38240e10	0.580867
$923$	2.70366e10	1.13174
$924$	−6.79915e8	−0.0283532
$925$	−1.15432e10	−0.479546
$926$	−1.08389e10	−0.448587
$927$	4.50077e9	0.185570
$928$	−1.41069e10	−0.579446
$929$	−3.54484e10	−1.45058	−0.725291	−	0.688443i	$-0.758295\pi$
$929$	−3.54484e10	−1.45058	−0.725291	+	0.688443i	$0.758295\pi$
$930$	−1.85388e10	−0.755772
$931$	1.08058e10	0.438867
$932$	8.72565e9	0.353055
$933$	2.01099e9	0.0810634
$934$	−1.46716e10	−0.589202
$935$	−1.83182e10	−0.732897
$936$	−1.04094e10	−0.414915
$937$	3.58282e10	1.42278	0.711388	−	0.702800i	$-0.248067\pi$
$937$	3.58282e10	1.42278	0.711388	+	0.702800i	$0.248067\pi$
$938$	1.19410e9	0.0472421
$939$	−1.29289e10	−0.509602
$940$	−8.08189e9	−0.317370
$941$	−5.81166e9	−0.227372	−0.113686	−	0.993517i	$-0.536266\pi$
$941$	−5.81166e9	−0.227372	−0.113686	+	0.993517i	$0.536266\pi$
$942$	1.29596e10	0.505143
$943$	2.55006e10	0.990284
$944$	4.15588e8	0.0160791
$945$	2.14741e9	0.0827758
$946$	2.89264e9	0.111090
$947$	3.32826e10	1.27348	0.636740	−	0.771079i	$-0.280283\pi$
$947$	3.32826e10	1.27348	0.636740	+	0.771079i	$0.280283\pi$
$948$	6.35489e9	0.242258
$949$	−7.23151e9	−0.274661
$950$	−8.91528e9	−0.337367
$951$	8.71070e9	0.328414
$952$	−1.44698e10	−0.543541
$953$	−1.73227e9	−0.0648322	−0.0324161	−	0.999474i	$-0.510320\pi$
$953$	−1.73227e9	−0.0648322	−0.0324161	+	0.999474i	$0.510320\pi$
$954$	9.77030e9	0.364324
$955$	3.07941e10	1.14408
$956$	−1.73364e9	−0.0641735
$957$	2.77811e9	0.102461
$958$	−2.26776e10	−0.833332
$959$	−2.70429e9	−0.0990122
$960$	−1.71165e10	−0.624406
$961$	2.47572e10	0.899848
$962$	−9.99415e9	−0.361937
$963$	−9.87966e8	−0.0356492
$964$	4.01108e9	0.144209
$965$	5.39895e10	1.93403
$966$	2.82170e9	0.100714
$967$	3.35118e10	1.19180	0.595902	−	0.803057i	$-0.296795\pi$
$967$	3.35118e10	1.19180	0.595902	+	0.803057i	$0.296795\pi$
$968$	2.67000e10	0.946122
$969$	−1.38191e10	−0.487918
$970$	2.44128e10	0.858848
$971$	−2.03751e10	−0.714219	−0.357110	−	0.934063i	$-0.616238\pi$
$971$	−2.03751e10	−0.714219	−0.357110	+	0.934063i	$0.616238\pi$
$972$	1.03104e9	0.0360115
$973$	−6.39885e9	−0.222693
$974$	−1.42853e10	−0.495375
$975$	−2.12448e10	−0.734070
$976$	−6.80200e9	−0.234187
$977$	4.03720e10	1.38500	0.692498	−	0.721419i	$-0.256510\pi$
$977$	4.03720e10	1.38500	0.692498	+	0.721419i	$0.256510\pi$
$978$	8.56572e9	0.292805
$979$	−8.17443e8	−0.0278431
$980$	2.15840e10	0.732556
$981$	7.64325e9	0.258486
$982$	1.78169e10	0.600400
$983$	1.10528e10	0.371139	0.185569	−	0.982631i	$-0.440587\pi$
$983$	1.10528e10	0.371139	0.185569	+	0.982631i	$0.440587\pi$
$984$	2.01226e10	0.673289
$985$	4.38187e10	1.46094
$986$	2.12567e10	0.706199
$987$	2.06241e9	0.0682756
$988$	9.87859e9	0.325871
$989$	1.53635e10	0.505014
$990$	2.81881e9	0.0923301
$991$	3.39895e10	1.10940	0.554699	−	0.832051i	$-0.312833\pi$
$991$	3.39895e10	1.10940	0.554699	+	0.832051i	$0.312833\pi$
$992$	4.03570e10	1.31259
$993$	−2.77898e10	−0.900664
$994$	−5.78324e9	−0.186775
$995$	−2.04217e10	−0.657219
$996$	1.92479e10	0.617271
$997$	5.14554e10	1.64436	0.822182	−	0.569225i	$-0.192757\pi$
$997$	5.14554e10	1.64436	0.822182	+	0.569225i	$0.192757\pi$
$998$	−9.40211e9	−0.299412
$999$	2.75330e9	0.0873725

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.c.1.11	✓	17
3.2	odd	2		531.8.a.c.1.7		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.11	✓	17	1.1	even	1	trivial
531.8.a.c.1.7		17	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+7.49302 q^{2} -27.0000 q^{3} -71.8546 q^{4} +400.807 q^{5} -202.312 q^{6} -272.200 q^{7} -1497.52 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+7.49302 q^{2} -27.0000 q^{3} -71.8546 q^{4} +400.807 q^{5} -202.312 q^{6} -272.200 q^{7} -1497.52 q^{8} +729.000 q^{9} +3003.25 q^{10} +1287.50 q^{11} +1940.08 q^{12} +9535.11 q^{13} -2039.60 q^{14} -10821.8 q^{15} -2023.52 q^{16} -35497.8 q^{17} +5462.41 q^{18} -14418.3 q^{19} -28799.8 q^{20} +7349.41 q^{21} +9647.27 q^{22} +51239.1 q^{23} +40432.9 q^{24} +82520.9 q^{25} +71446.8 q^{26} -19683.0 q^{27} +19558.9 q^{28} -79916.8 q^{29} -81087.8 q^{30} +228626. q^{31} +176520. q^{32} -34762.5 q^{33} -265986. q^{34} -109100. q^{35} -52382.0 q^{36} -139882. q^{37} -108037. q^{38} -257448. q^{39} -600214. q^{40} +497679. q^{41} +55069.3 q^{42} +299840. q^{43} -92512.8 q^{44} +292188. q^{45} +383936. q^{46} +280623. q^{47} +54635.0 q^{48} -749450. q^{49} +618331. q^{50} +958441. q^{51} -685142. q^{52} +1.78864e6 q^{53} -147485. q^{54} +516038. q^{55} +407624. q^{56} +389294. q^{57} -598818. q^{58} -205379. q^{59} +777595. q^{60} +3.36147e6 q^{61} +1.71310e6 q^{62} -198434. q^{63} +1.58168e6 q^{64} +3.82174e6 q^{65} -260476. q^{66} -585455. q^{67} +2.55068e6 q^{68} -1.38346e6 q^{69} -817487. q^{70} +2.83547e6 q^{71} -1.09169e6 q^{72} -758408. q^{73} -1.04814e6 q^{74} -2.22806e6 q^{75} +1.03602e6 q^{76} -350458. q^{77} -1.92906e6 q^{78} +3.27559e6 q^{79} -811040. q^{80} +531441. q^{81} +3.72912e6 q^{82} +9.92122e6 q^{83} -528089. q^{84} -1.42278e7 q^{85} +2.24671e6 q^{86} +2.15775e6 q^{87} -1.92805e6 q^{88} -634907. q^{89} +2.18937e6 q^{90} -2.59546e6 q^{91} -3.68177e6 q^{92} -6.17290e6 q^{93} +2.10271e6 q^{94} -5.77895e6 q^{95} -4.76603e6 q^{96} +8.12879e6 q^{97} -5.61564e6 q^{98} +938588. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 2 q^{2} - 459 q^{3} + 1166 q^{4} - 318 q^{5} - 54 q^{6} + 3145 q^{7} + 2355 q^{8} + 12393 q^{9}+O(q^{10}) \) 17 * q + 2 * q^2 - 459 * q^3 + 1166 * q^4 - 318 * q^5 - 54 * q^6 + 3145 * q^7 + 2355 * q^8 + 12393 * q^9	\( 17 q + 2 q^{2} - 459 q^{3} + 1166 q^{4} - 318 q^{5} - 54 q^{6} + 3145 q^{7} + 2355 q^{8} + 12393 q^{9} + 6521 q^{10} - 1764 q^{11} - 31482 q^{12} + 18192 q^{13} - 7827 q^{14} + 8586 q^{15} + 139226 q^{16} - 15507 q^{17} + 1458 q^{18} + 52083 q^{19} + 721 q^{20} - 84915 q^{21} - 234434 q^{22} + 63823 q^{23} - 63585 q^{24} + 202153 q^{25} - 367956 q^{26} - 334611 q^{27} + 182306 q^{28} - 502955 q^{29} - 176067 q^{30} + 347531 q^{31} - 243908 q^{32} + 47628 q^{33} - 330872 q^{34} + 92641 q^{35} + 850014 q^{36} + 447615 q^{37} + 775669 q^{38} - 491184 q^{39} + 2203270 q^{40} + 940335 q^{41} + 211329 q^{42} + 478562 q^{43} - 596924 q^{44} - 231822 q^{45} - 3078663 q^{46} + 703121 q^{47} - 3759102 q^{48} + 1895082 q^{49} - 876967 q^{50} + 418689 q^{51} + 6278296 q^{52} - 1005974 q^{53} - 39366 q^{54} + 5212846 q^{55} + 3425294 q^{56} - 1406241 q^{57} + 6710166 q^{58} - 3491443 q^{59} - 19467 q^{60} + 11510749 q^{61} + 5996234 q^{62} + 2292705 q^{63} + 29496941 q^{64} + 11094180 q^{65} + 6329718 q^{66} + 14007144 q^{67} + 19688159 q^{68} - 1723221 q^{69} + 30909708 q^{70} + 5229074 q^{71} + 1716795 q^{72} + 5452211 q^{73} + 12819662 q^{74} - 5458131 q^{75} + 41929340 q^{76} + 9930777 q^{77} + 9934812 q^{78} + 15275654 q^{79} + 36576105 q^{80} + 9034497 q^{81} + 32025935 q^{82} + 7826609 q^{83} - 4922262 q^{84} + 11836945 q^{85} + 51649136 q^{86} + 13579785 q^{87} + 30223741 q^{88} - 6436185 q^{89} + 4753809 q^{90} + 11633535 q^{91} + 43357972 q^{92} - 9383337 q^{93} - 4494252 q^{94} + 23741055 q^{95} + 6585516 q^{96} + 26377540 q^{97} + 26517816 q^{98} - 1285956 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 - 459 * q^3 + 1166 * q^4 - 318 * q^5 - 54 * q^6 + 3145 * q^7 + 2355 * q^8 + 12393 * q^9 + 6521 * q^10 - 1764 * q^11 - 31482 * q^12 + 18192 * q^13 - 7827 * q^14 + 8586 * q^15 + 139226 * q^16 - 15507 * q^17 + 1458 * q^18 + 52083 * q^19 + 721 * q^20 - 84915 * q^21 - 234434 * q^22 + 63823 * q^23 - 63585 * q^24 + 202153 * q^25 - 367956 * q^26 - 334611 * q^27 + 182306 * q^28 - 502955 * q^29 - 176067 * q^30 + 347531 * q^31 - 243908 * q^32 + 47628 * q^33 - 330872 * q^34 + 92641 * q^35 + 850014 * q^36 + 447615 * q^37 + 775669 * q^38 - 491184 * q^39 + 2203270 * q^40 + 940335 * q^41 + 211329 * q^42 + 478562 * q^43 - 596924 * q^44 - 231822 * q^45 - 3078663 * q^46 + 703121 * q^47 - 3759102 * q^48 + 1895082 * q^49 - 876967 * q^50 + 418689 * q^51 + 6278296 * q^52 - 1005974 * q^53 - 39366 * q^54 + 5212846 * q^55 + 3425294 * q^56 - 1406241 * q^57 + 6710166 * q^58 - 3491443 * q^59 - 19467 * q^60 + 11510749 * q^61 + 5996234 * q^62 + 2292705 * q^63 + 29496941 * q^64 + 11094180 * q^65 + 6329718 * q^66 + 14007144 * q^67 + 19688159 * q^68 - 1723221 * q^69 + 30909708 * q^70 + 5229074 * q^71 + 1716795 * q^72 + 5452211 * q^73 + 12819662 * q^74 - 5458131 * q^75 + 41929340 * q^76 + 9930777 * q^77 + 9934812 * q^78 + 15275654 * q^79 + 36576105 * q^80 + 9034497 * q^81 + 32025935 * q^82 + 7826609 * q^83 - 4922262 * q^84 + 11836945 * q^85 + 51649136 * q^86 + 13579785 * q^87 + 30223741 * q^88 - 6436185 * q^89 + 4753809 * q^90 + 11633535 * q^91 + 43357972 * q^92 - 9383337 * q^93 - 4494252 * q^94 + 23741055 * q^95 + 6585516 * q^96 + 26377540 * q^97 + 26517816 * q^98 - 1285956 * q^99

Introduction

L-functions

Modular forms

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