LMFDB - Embedded newform 177.8.a.c.1.13

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			1.13
Root			$11.5967$ 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)

$f(q)$	$=$	$q+11.5967 q^{2} -27.0000 q^{3} +6.48306 q^{4} -401.104 q^{5} -313.110 q^{6} +213.573 q^{7} -1409.19 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+11.5967 q^{2} -27.0000 q^{3} +6.48306 q^{4} -401.104 q^{5} -313.110 q^{6} +213.573 q^{7} -1409.19 q^{8} +729.000 q^{9} -4651.48 q^{10} -4974.14 q^{11} -175.043 q^{12} -12649.9 q^{13} +2476.74 q^{14} +10829.8 q^{15} -17171.8 q^{16} +36937.0 q^{17} +8453.98 q^{18} -31065.7 q^{19} -2600.38 q^{20} -5766.47 q^{21} -57683.5 q^{22} +52594.0 q^{23} +38048.2 q^{24} +82759.6 q^{25} -146697. q^{26} -19683.0 q^{27} +1384.61 q^{28} -209912. q^{29} +125590. q^{30} -11865.2 q^{31} -18759.2 q^{32} +134302. q^{33} +428347. q^{34} -85665.0 q^{35} +4726.15 q^{36} +16919.7 q^{37} -360259. q^{38} +341549. q^{39} +565233. q^{40} +801040. q^{41} -66871.9 q^{42} +720238. q^{43} -32247.7 q^{44} -292405. q^{45} +609916. q^{46} -54403.0 q^{47} +463639. q^{48} -777930. q^{49} +959737. q^{50} -997299. q^{51} -82010.4 q^{52} -295498. q^{53} -228258. q^{54} +1.99515e6 q^{55} -300965. q^{56} +838773. q^{57} -2.43428e6 q^{58} -205379. q^{59} +70210.3 q^{60} +1.37027e6 q^{61} -137597. q^{62} +155695. q^{63} +1.98045e6 q^{64} +5.07395e6 q^{65} +1.55746e6 q^{66} +3.05207e6 q^{67} +239465. q^{68} -1.42004e6 q^{69} -993430. q^{70} -4.70310e6 q^{71} -1.02730e6 q^{72} -3.65576e6 q^{73} +196212. q^{74} -2.23451e6 q^{75} -201401. q^{76} -1.06234e6 q^{77} +3.96083e6 q^{78} +6.37313e6 q^{79} +6.88768e6 q^{80} +531441. q^{81} +9.28941e6 q^{82} -2.08701e6 q^{83} -37384.4 q^{84} -1.48156e7 q^{85} +8.35238e6 q^{86} +5.66762e6 q^{87} +7.00953e6 q^{88} +1.43644e6 q^{89} -3.39093e6 q^{90} -2.70169e6 q^{91} +340970. q^{92} +320360. q^{93} -630894. q^{94} +1.24606e7 q^{95} +506498. q^{96} -6.42693e6 q^{97} -9.02140e6 q^{98} -3.62615e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	11.5967	1.02501	0.512506	−	0.858684i	$-0.328717\pi$
$2$	11.5967	1.02501	0.512506	+	0.858684i	$0.328717\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	6.48306	0.0506489
$5$	−401.104	−1.43503	−0.717517	−	0.696541i	$-0.754721\pi$
$5$	−401.104	−1.43503	−0.717517	+	0.696541i	$0.754721\pi$
$6$	−313.110	−0.591791
$7$	213.573	0.235344	0.117672	−	0.993053i	$-0.462457\pi$
$7$	213.573	0.235344	0.117672	+	0.993053i	$0.462457\pi$
$8$	−1409.19	−0.973096
$9$	729.000	0.333333
$10$	−4651.48	−1.47093
$11$	−4974.14	−1.12679	−0.563396	−	0.826187i	$-0.690505\pi$
$11$	−4974.14	−1.12679	−0.563396	+	0.826187i	$0.690505\pi$
$12$	−175.043	−0.0292422
$13$	−12649.9	−1.59693	−0.798467	−	0.602038i	$-0.794355\pi$
$13$	−12649.9	−1.59693	−0.798467	+	0.602038i	$0.794355\pi$
$14$	2476.74	0.241230
$15$	10829.8	0.828517
$16$	−17171.8	−1.04808
$17$	36937.0	1.82344	0.911718	−	0.410816i	$-0.134756\pi$
$17$	36937.0	1.82344	0.911718	+	0.410816i	$0.134756\pi$
$18$	8453.98	0.341671
$19$	−31065.7	−1.03907	−0.519533	−	0.854451i	$-0.673894\pi$
$19$	−31065.7	−1.03907	−0.519533	+	0.854451i	$0.673894\pi$
$20$	−2600.38	−0.0726829
$21$	−5766.47	−0.135876
$22$	−57683.5	−1.15497
$23$	52594.0	0.901341	0.450670	−	0.892690i	$-0.351185\pi$
$23$	52594.0	0.901341	0.450670	+	0.892690i	$0.351185\pi$
$24$	38048.2	0.561817
$25$	82759.6	1.05932
$26$	−146697.	−1.63688
$27$	−19683.0	−0.192450
$28$	1384.61	0.0119199
$29$	−209912.	−1.59825	−0.799123	−	0.601167i	$-0.794702\pi$
$29$	−209912.	−1.59825	−0.799123	+	0.601167i	$0.794702\pi$
$30$	125590.	0.849240
$31$	−11865.2	−0.0715333	−0.0357667	−	0.999360i	$-0.511387\pi$
$31$	−11865.2	−0.0715333	−0.0357667	+	0.999360i	$0.511387\pi$
$32$	−18759.2	−0.101202
$33$	134302.	0.650553
$34$	428347.	1.86904
$35$	−85665.0	−0.337727
$36$	4726.15	0.0168830
$37$	16919.7	0.0549143	0.0274572	−	0.999623i	$-0.491259\pi$
$37$	16919.7	0.0549143	0.0274572	+	0.999623i	$0.491259\pi$
$38$	−360259.	−1.06505
$39$	341549.	0.921990
$40$	565233.	1.39643
$41$	801040.	1.81514	0.907571	−	0.419898i	$-0.137934\pi$
$41$	801040.	1.81514	0.907571	+	0.419898i	$0.137934\pi$
$42$	−66871.9	−0.139274
$43$	720238.	1.38145	0.690727	−	0.723115i	$-0.257290\pi$
$43$	720238.	1.38145	0.690727	+	0.723115i	$0.257290\pi$
$44$	−32247.7	−0.0570708
$45$	−292405.	−0.478345
$46$	609916.	0.923885
$47$	−54403.0	−0.0764329	−0.0382164	−	0.999269i	$-0.512168\pi$
$47$	−54403.0	−0.0764329	−0.0382164	+	0.999269i	$0.512168\pi$
$48$	463639.	0.605111
$49$	−777930.	−0.944613
$50$	959737.	1.08582
$51$	−997299.	−1.05276
$52$	−82010.4	−0.0808830
$53$	−295498.	−0.272639	−0.136320	−	0.990665i	$-0.543527\pi$
$53$	−295498.	−0.272639	−0.136320	+	0.990665i	$0.543527\pi$
$54$	−228258.	−0.197264
$55$	1.99515e6	1.61698
$56$	−300965.	−0.229012
$57$	838773.	0.599905
$58$	−2.43428e6	−1.63822
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	70210.3	0.0419635
$61$	1.37027e6	0.772952	0.386476	−	0.922300i	$-0.373692\pi$
$61$	1.37027e6	0.772952	0.386476	+	0.922300i	$0.373692\pi$
$62$	−137597.	−0.0733225
$63$	155695.	0.0784480
$64$	1.98045e6	0.944350
$65$	5.07395e6	2.29166
$66$	1.55746e6	0.666825
$67$	3.05207e6	1.23975	0.619873	−	0.784702i	$-0.287184\pi$
$67$	3.05207e6	1.23975	0.619873	+	0.784702i	$0.287184\pi$
$68$	239465.	0.0923551
$69$	−1.42004e6	−0.520389
$70$	−993430.	−0.346174
$71$	−4.70310e6	−1.55948	−0.779740	−	0.626104i	$-0.784649\pi$
$71$	−4.70310e6	−1.55948	−0.779740	+	0.626104i	$0.784649\pi$
$72$	−1.02730e6	−0.324365
$73$	−3.65576e6	−1.09989	−0.549943	−	0.835202i	$-0.685351\pi$
$73$	−3.65576e6	−1.09989	−0.549943	+	0.835202i	$0.685351\pi$
$74$	196212.	0.0562878
$75$	−2.23451e6	−0.611600
$76$	−201401.	−0.0526275
$77$	−1.06234e6	−0.265184
$78$	3.96083e6	0.945051
$79$	6.37313e6	1.45431	0.727157	−	0.686471i	$-0.240841\pi$
$79$	6.37313e6	1.45431	0.727157	+	0.686471i	$0.240841\pi$
$80$	6.88768e6	1.50404
$81$	531441.	0.111111
$82$	9.28941e6	1.86054
$83$	−2.08701e6	−0.400636	−0.200318	−	0.979731i	$-0.564198\pi$
$83$	−2.08701e6	−0.400636	−0.200318	+	0.979731i	$0.564198\pi$
$84$	−37384.4	−0.00688197
$85$	−1.48156e7	−2.61669
$86$	8.35238e6	1.41601
$87$	5.66762e6	0.922748
$88$	7.00953e6	1.09648
$89$	1.43644e6	0.215984	0.107992	−	0.994152i	$-0.465558\pi$
$89$	1.43644e6	0.215984	0.107992	+	0.994152i	$0.465558\pi$
$90$	−3.39093e6	−0.490309
$91$	−2.70169e6	−0.375829
$92$	340970.	0.0456519
$93$	320360.	0.0412998
$94$	−630894.	−0.0783446
$95$	1.24606e7	1.49109
$96$	506498.	0.0584290
$97$	−6.42693e6	−0.714994	−0.357497	−	0.933914i	$-0.616370\pi$
$97$	−6.42693e6	−0.714994	−0.357497	+	0.933914i	$0.616370\pi$
$98$	−9.02140e6	−0.968240
$99$	−3.62615e6	−0.375597
$100$	536536.	0.0536536
$101$	1.06724e6	0.103071	0.0515356	−	0.998671i	$-0.483588\pi$
$101$	1.06724e6	0.103071	0.0515356	+	0.998671i	$0.483588\pi$
$102$	−1.15654e7	−1.07909
$103$	−9.80605e6	−0.884227	−0.442113	−	0.896959i	$-0.645771\pi$
$103$	−9.80605e6	−0.884227	−0.442113	+	0.896959i	$0.645771\pi$
$104$	1.78262e7	1.55397
$105$	2.31295e6	0.194987
$106$	−3.42679e6	−0.279459
$107$	−1.96135e7	−1.54779	−0.773895	−	0.633314i	$-0.781694\pi$
$107$	−1.96135e7	−1.54779	−0.773895	+	0.633314i	$0.781694\pi$
$108$	−127606.	−0.00974739
$109$	2.55432e7	1.88922	0.944610	−	0.328194i	$-0.106440\pi$
$109$	2.55432e7	1.88922	0.944610	+	0.328194i	$0.106440\pi$
$110$	2.31371e7	1.65743
$111$	−456831.	−0.0317048
$112$	−3.66743e6	−0.246660
$113$	−1.24785e7	−0.813559	−0.406780	−	0.913526i	$-0.633348\pi$
$113$	−1.24785e7	−0.813559	−0.406780	+	0.913526i	$0.633348\pi$
$114$	9.72698e6	0.614909
$115$	−2.10957e7	−1.29345
$116$	−1.36087e6	−0.0809494
$117$	−9.22181e6	−0.532311
$118$	−2.38172e6	−0.133445
$119$	7.88875e6	0.429135
$120$	−1.52613e7	−0.806227
$121$	5.25490e6	0.269659
$122$	1.58906e7	0.792284
$123$	−2.16281e7	−1.04797
$124$	−76922.7	−0.00362308
$125$	−1.85896e6	−0.0851305
$126$	1.80554e6	0.0804101
$127$	−1.73455e7	−0.751403	−0.375701	−	0.926741i	$-0.622598\pi$
$127$	−1.73455e7	−0.751403	−0.375701	+	0.926741i	$0.622598\pi$
$128$	2.53678e7	1.06917
$129$	−1.94464e7	−0.797583
$130$	5.88410e7	2.34897
$131$	−1.36249e7	−0.529520	−0.264760	−	0.964314i	$-0.585293\pi$
$131$	−1.36249e7	−0.529520	−0.264760	+	0.964314i	$0.585293\pi$
$132$	870687.	0.0329498
$133$	−6.63478e6	−0.244538
$134$	3.53939e7	1.27075
$135$	7.89493e6	0.276172
$136$	−5.20514e7	−1.77438
$137$	−1.67308e7	−0.555898	−0.277949	−	0.960596i	$-0.589655\pi$
$137$	−1.67308e7	−0.555898	−0.277949	+	0.960596i	$0.589655\pi$
$138$	−1.64677e7	−0.533405
$139$	1.17094e7	0.369813	0.184907	−	0.982756i	$-0.440802\pi$
$139$	1.17094e7	0.369813	0.184907	+	0.982756i	$0.440802\pi$
$140$	−555371.	−0.0171055
$141$	1.46888e6	0.0441285
$142$	−5.45403e7	−1.59848
$143$	6.29226e7	1.79941
$144$	−1.25182e7	−0.349361
$145$	8.41965e7	2.29354
$146$	−4.23947e7	−1.12740
$147$	2.10041e7	0.545373
$148$	109691.	0.00278135
$149$	153329.	0.00379728	0.00189864	−	0.999998i	$-0.499396\pi$
$149$	153329.	0.00379728	0.00189864	+	0.999998i	$0.499396\pi$
$150$	−2.59129e7	−0.626898
$151$	7.64791e7	1.80769	0.903843	−	0.427863i	$-0.140734\pi$
$151$	7.64791e7	1.80769	0.903843	+	0.427863i	$0.140734\pi$
$152$	4.37775e7	1.01111
$153$	2.69271e7	0.607812
$154$	−1.23196e7	−0.271816
$155$	4.75917e6	0.102653
$156$	2.21428e6	0.0466978
$157$	−6.86729e6	−0.141624	−0.0708119	−	0.997490i	$-0.522559\pi$
$157$	−6.86729e6	−0.141624	−0.0708119	+	0.997490i	$0.522559\pi$
$158$	7.39072e7	1.49069
$159$	7.97844e6	0.157408
$160$	7.52439e6	0.145228
$161$	1.12327e7	0.212125
$162$	6.16295e6	0.113890
$163$	−1.89828e7	−0.343323	−0.171662	−	0.985156i	$-0.554914\pi$
$163$	−1.89828e7	−0.343323	−0.171662	+	0.985156i	$0.554914\pi$
$164$	5.19319e6	0.0919350
$165$	−5.38690e7	−0.933566
$166$	−2.42024e7	−0.410657
$167$	−1.70383e7	−0.283085	−0.141543	−	0.989932i	$-0.545206\pi$
$167$	−1.70383e7	−0.283085	−0.141543	+	0.989932i	$0.545206\pi$
$168$	8.12607e6	0.132220
$169$	9.72727e7	1.55020
$170$	−1.71812e8	−2.68214
$171$	−2.26469e7	−0.346355
$172$	4.66935e6	0.0699692
$173$	−8.07641e6	−0.118592	−0.0592962	−	0.998240i	$-0.518886\pi$
$173$	−8.07641e6	−0.118592	−0.0592962	+	0.998240i	$0.518886\pi$
$174$	6.57255e7	0.945827
$175$	1.76752e7	0.249305
$176$	8.54149e7	1.18097
$177$	5.54523e6	0.0751646
$178$	1.66579e7	0.221386
$179$	4.99947e7	0.651536	0.325768	−	0.945450i	$-0.394377\pi$
$179$	4.99947e7	0.651536	0.325768	+	0.945450i	$0.394377\pi$
$180$	−1.89568e6	−0.0242276
$181$	7.07416e7	0.886747	0.443373	−	0.896337i	$-0.353782\pi$
$181$	7.07416e7	0.886747	0.443373	+	0.896337i	$0.353782\pi$
$182$	−3.13306e7	−0.385229
$183$	−3.69973e7	−0.446264
$184$	−7.41151e7	−0.877091
$185$	−6.78655e6	−0.0788039
$186$	3.71511e6	0.0423327
$187$	−1.83730e8	−2.05463
$188$	−352698.	−0.00387124
$189$	−4.20375e6	−0.0452920
$190$	1.44501e8	1.52839
$191$	−1.40226e8	−1.45617	−0.728086	−	0.685486i	$-0.759590\pi$
$191$	−1.40226e8	−1.45617	−0.728086	+	0.685486i	$0.759590\pi$
$192$	−5.34721e7	−0.545221
$193$	−5.81729e7	−0.582465	−0.291233	−	0.956652i	$-0.594065\pi$
$193$	−5.81729e7	−0.582465	−0.291233	+	0.956652i	$0.594065\pi$
$194$	−7.45311e7	−0.732878
$195$	−1.36997e8	−1.32309
$196$	−5.04337e6	−0.0478436
$197$	6.06171e7	0.564889	0.282445	−	0.959284i	$-0.408855\pi$
$197$	6.06171e7	0.564889	0.282445	+	0.959284i	$0.408855\pi$
$198$	−4.20513e7	−0.384992
$199$	234342.	0.00210797	0.00105398	−	0.999999i	$-0.499665\pi$
$199$	234342.	0.00210797	0.00105398	+	0.999999i	$0.499665\pi$
$200$	−1.16624e8	−1.03082
$201$	−8.24059e7	−0.715768
$202$	1.23765e7	0.105649
$203$	−4.48314e7	−0.376137
$204$	−6.46555e6	−0.0533212
$205$	−3.21300e8	−2.60479
$206$	−1.13718e8	−0.906343
$207$	3.83410e7	0.300447
$208$	2.17222e8	1.67372
$209$	1.54525e8	1.17081
$210$	2.68226e7	0.199863
$211$	−2.04520e8	−1.49881	−0.749406	−	0.662111i	$-0.769661\pi$
$211$	−2.04520e8	−1.49881	−0.749406	+	0.662111i	$0.769661\pi$
$212$	−1.91573e6	−0.0138089
$213$	1.26984e8	0.900366
$214$	−2.27452e8	−1.58650
$215$	−2.88891e8	−1.98243
$216$	2.77372e7	0.187272
$217$	−2.53408e6	−0.0168349
$218$	2.96216e8	1.93647
$219$	9.87055e7	0.635019
$220$	1.29347e7	0.0818985
$221$	−4.67251e8	−2.91191
$222$	−5.29772e6	−0.0324978
$223$	2.44062e8	1.47378	0.736892	−	0.676011i	$-0.236293\pi$
$223$	2.44062e8	1.47378	0.736892	+	0.676011i	$0.236293\pi$
$224$	−4.00645e6	−0.0238173
$225$	6.03318e7	0.353108
$226$	−1.44710e8	−0.833908
$227$	−1.77415e8	−1.00670	−0.503350	−	0.864083i	$-0.667899\pi$
$227$	−1.77415e8	−1.00670	−0.503350	+	0.864083i	$0.667899\pi$
$228$	5.43781e6	0.0303845
$229$	2.17580e8	1.19728	0.598638	−	0.801020i	$-0.295709\pi$
$229$	2.17580e8	1.19728	0.598638	+	0.801020i	$0.295709\pi$
$230$	−2.44640e8	−1.32581
$231$	2.86832e7	0.153104
$232$	2.95806e8	1.55525
$233$	−3.27814e8	−1.69778	−0.848890	−	0.528570i	$-0.822728\pi$
$233$	−3.27814e8	−1.69778	−0.848890	+	0.528570i	$0.822728\pi$
$234$	−1.06942e8	−0.545625
$235$	2.18213e7	0.109684
$236$	−1.33148e6	−0.00659393
$237$	−1.72075e8	−0.839648
$238$	9.14833e7	0.439868
$239$	2.79462e8	1.32413	0.662064	−	0.749448i	$-0.269681\pi$
$239$	2.79462e8	1.32413	0.662064	+	0.749448i	$0.269681\pi$
$240$	−1.85967e8	−0.868355
$241$	3.83280e8	1.76383	0.881915	−	0.471409i	$-0.156254\pi$
$241$	3.83280e8	1.76383	0.881915	+	0.471409i	$0.156254\pi$
$242$	6.09394e7	0.276404
$243$	−1.43489e7	−0.0641500
$244$	8.88356e6	0.0391492
$245$	3.12031e8	1.35555
$246$	−2.50814e8	−1.07418
$247$	3.92979e8	1.65932
$248$	1.67203e7	0.0696088
$249$	5.63492e7	0.231308
$250$	−2.15578e7	−0.0872598
$251$	−4.23948e8	−1.69221	−0.846106	−	0.533014i	$-0.821059\pi$
$251$	−4.23948e8	−1.69221	−0.846106	+	0.533014i	$0.821059\pi$
$252$	1.00938e6	0.00397330
$253$	−2.61610e8	−1.01562
$254$	−2.01150e8	−0.770196
$255$	4.00021e8	1.51075
$256$	4.06850e7	0.151564
$257$	1.80864e8	0.664638	0.332319	−	0.943167i	$-0.392169\pi$
$257$	1.80864e8	0.664638	0.332319	+	0.943167i	$0.392169\pi$
$258$	−2.25514e8	−0.817532
$259$	3.61358e6	0.0129237
$260$	3.28947e7	0.116070
$261$	−1.53026e8	−0.532749
$262$	−1.58003e8	−0.542764
$263$	4.23691e8	1.43616	0.718082	−	0.695958i	$-0.245020\pi$
$263$	4.23691e8	1.43616	0.718082	+	0.695958i	$0.245020\pi$
$264$	−1.89257e8	−0.633051
$265$	1.18525e8	0.391247
$266$	−7.69415e7	−0.250654
$267$	−3.87838e7	−0.124699
$268$	1.97868e7	0.0627918
$269$	3.48418e8	1.09136	0.545679	−	0.837994i	$-0.316272\pi$
$269$	3.48418e8	1.09136	0.545679	+	0.837994i	$0.316272\pi$
$270$	9.15551e7	0.283080
$271$	−1.26441e8	−0.385918	−0.192959	−	0.981207i	$-0.561809\pi$
$271$	−1.26441e8	−0.385918	−0.192959	+	0.981207i	$0.561809\pi$
$272$	−6.34275e8	−1.91111
$273$	7.29455e7	0.216985
$274$	−1.94022e8	−0.569802
$275$	−4.11658e8	−1.19364
$276$	−9.20620e6	−0.0263571
$277$	−2.22094e8	−0.627852	−0.313926	−	0.949447i	$-0.601644\pi$
$277$	−2.22094e8	−0.627852	−0.313926	+	0.949447i	$0.601644\pi$
$278$	1.35790e8	0.379063
$279$	−8.64971e6	−0.0238444
$280$	1.20719e8	0.328640
$281$	−3.20287e8	−0.861128	−0.430564	−	0.902560i	$-0.641685\pi$
$281$	−3.20287e8	−0.861128	−0.430564	+	0.902560i	$0.641685\pi$
$282$	1.70341e7	0.0452323
$283$	2.46262e8	0.645870	0.322935	−	0.946421i	$-0.395331\pi$
$283$	2.46262e8	0.645870	0.322935	+	0.946421i	$0.395331\pi$
$284$	−3.04905e7	−0.0789860
$285$	−3.36435e8	−0.860884
$286$	7.29694e8	1.84442
$287$	1.71080e8	0.427183
$288$	−1.36754e7	−0.0337340
$289$	9.54005e8	2.32492
$290$	9.76400e8	2.35090
$291$	1.73527e8	0.412802
$292$	−2.37005e7	−0.0557080
$293$	2.26005e8	0.524905	0.262453	−	0.964945i	$-0.415469\pi$
$293$	2.26005e8	0.524905	0.262453	+	0.964945i	$0.415469\pi$
$294$	2.43578e8	0.559013
$295$	8.23784e7	0.186826
$296$	−2.38431e7	−0.0534369
$297$	9.79060e7	0.216851
$298$	1.77811e6	0.00389226
$299$	−6.65312e8	−1.43938
$300$	−1.44865e7	−0.0309769
$301$	1.53823e8	0.325117
$302$	8.86903e8	1.85290
$303$	−2.88155e7	−0.0595082
$304$	5.33453e8	1.08903
$305$	−5.49622e8	−1.10921
$306$	3.12265e8	0.623015
$307$	5.53693e8	1.09216	0.546078	−	0.837734i	$-0.316120\pi$
$307$	5.53693e8	1.09216	0.546078	+	0.837734i	$0.316120\pi$
$308$	−6.88722e6	−0.0134313
$309$	2.64763e8	0.510509
$310$	5.51906e7	0.105220
$311$	8.72060e8	1.64394	0.821968	−	0.569534i	$-0.192876\pi$
$311$	8.72060e8	1.64394	0.821968	+	0.569534i	$0.192876\pi$
$312$	−4.81308e8	−0.897185
$313$	3.27729e8	0.604102	0.302051	−	0.953292i	$-0.402329\pi$
$313$	3.27729e8	0.604102	0.302051	+	0.953292i	$0.402329\pi$
$314$	−7.96378e7	−0.145166
$315$	−6.24498e7	−0.112576
$316$	4.13174e7	0.0736594
$317$	1.07872e9	1.90196	0.950982	−	0.309246i	$-0.100077\pi$
$317$	1.07872e9	1.90196	0.950982	+	0.309246i	$0.100077\pi$
$318$	9.25234e7	0.161345
$319$	1.04413e9	1.80089
$320$	−7.94365e8	−1.35518
$321$	5.29564e8	0.893616
$322$	1.30262e8	0.217431
$323$	−1.14747e9	−1.89467
$324$	3.44536e6	0.00562766
$325$	−1.04690e9	−1.69167
$326$	−2.20137e8	−0.351910
$327$	−6.89667e8	−1.09074
$328$	−1.12882e9	−1.76631
$329$	−1.16190e7	−0.0179880
$330$	−6.24702e8	−0.956916
$331$	1.91834e8	0.290755	0.145378	−	0.989376i	$-0.453560\pi$
$331$	1.91834e8	0.290755	0.145378	+	0.989376i	$0.453560\pi$
$332$	−1.35302e7	−0.0202918
$333$	1.23344e7	0.0183048
$334$	−1.97587e8	−0.290166
$335$	−1.22420e9	−1.77908
$336$	9.90206e7	0.142409
$337$	4.73052e8	0.673294	0.336647	−	0.941631i	$-0.390707\pi$
$337$	4.73052e8	0.673294	0.336647	+	0.941631i	$0.390707\pi$
$338$	1.12804e9	1.58897
$339$	3.36921e8	0.469709
$340$	−9.60504e7	−0.132533
$341$	5.90190e7	0.0806031
$342$	−2.62628e8	−0.355018
$343$	−3.42031e8	−0.457653
$344$	−1.01496e9	−1.34429
$345$	5.69583e8	0.746776
$346$	−9.36596e7	−0.121559
$347$	−2.39433e8	−0.307631	−0.153815	−	0.988100i	$-0.549156\pi$
$347$	−2.39433e8	−0.307631	−0.153815	+	0.988100i	$0.549156\pi$
$348$	3.67435e7	0.0467362
$349$	2.55293e8	0.321477	0.160738	−	0.986997i	$-0.448612\pi$
$349$	2.55293e8	0.321477	0.160738	+	0.986997i	$0.448612\pi$
$350$	2.04974e8	0.255541
$351$	2.48989e8	0.307330
$352$	9.33108e7	0.114034
$353$	9.16807e8	1.10934	0.554672	−	0.832069i	$-0.312844\pi$
$353$	9.16807e8	1.10934	0.554672	+	0.832069i	$0.312844\pi$
$354$	6.43063e7	0.0770446
$355$	1.88643e9	2.23791
$356$	9.31252e6	0.0109394
$357$	−2.12996e8	−0.247761
$358$	5.79773e8	0.667832
$359$	−1.06121e8	−0.121051	−0.0605256	−	0.998167i	$-0.519278\pi$
$359$	−1.06121e8	−0.121051	−0.0605256	+	0.998167i	$0.519278\pi$
$360$	4.12055e8	0.465475
$361$	7.12032e7	0.0796570
$362$	8.20368e8	0.908926
$363$	−1.41882e8	−0.155688
$364$	−1.75152e7	−0.0190353
$365$	1.46634e9	1.57837
$366$	−4.29046e8	−0.457426
$367$	1.13340e9	1.19689	0.598444	−	0.801164i	$-0.295786\pi$
$367$	1.13340e9	1.19689	0.598444	+	0.801164i	$0.295786\pi$
$368$	−9.03134e8	−0.944680
$369$	5.83958e8	0.605047
$370$	−7.87014e7	−0.0807749
$371$	−6.31103e7	−0.0641640
$372$	2.07691e6	0.00209179
$373$	3.48649e8	0.347863	0.173931	−	0.984758i	$-0.444353\pi$
$373$	3.48649e8	0.347863	0.173931	+	0.984758i	$0.444353\pi$
$374$	−2.13066e9	−2.10602
$375$	5.01920e7	0.0491501
$376$	7.66643e7	0.0743765
$377$	2.65537e9	2.55229
$378$	−4.87496e7	−0.0464248
$379$	−1.97757e8	−0.186592	−0.0932962	−	0.995638i	$-0.529740\pi$
$379$	−1.97757e8	−0.186592	−0.0932962	+	0.995638i	$0.529740\pi$
$380$	8.07826e7	0.0755223
$381$	4.68327e8	0.433822
$382$	−1.62616e9	−1.49259
$383$	−1.60320e9	−1.45811	−0.729056	−	0.684454i	$-0.760041\pi$
$383$	−1.60320e9	−1.45811	−0.729056	+	0.684454i	$0.760041\pi$
$384$	−6.84930e8	−0.617287
$385$	4.26110e8	0.380547
$386$	−6.74613e8	−0.597034
$387$	5.25054e8	0.460485
$388$	−4.16662e7	−0.0362137
$389$	−7.74392e8	−0.667018	−0.333509	−	0.942747i	$-0.608233\pi$
$389$	−7.74392e8	−0.667018	−0.333509	+	0.942747i	$0.608233\pi$
$390$	−1.58871e9	−1.35618
$391$	1.94267e9	1.64354
$392$	1.09625e9	0.919199
$393$	3.67871e8	0.305718
$394$	7.02957e8	0.579018
$395$	−2.55629e9	−2.08699
$396$	−2.35085e7	−0.0190236
$397$	−1.24932e9	−1.00209	−0.501044	−	0.865422i	$-0.667050\pi$
$397$	−1.24932e9	−1.00209	−0.501044	+	0.865422i	$0.667050\pi$
$398$	2.71759e6	0.00216069
$399$	1.79139e8	0.141184
$400$	−1.42113e9	−1.11026
$401$	−2.10043e9	−1.62668	−0.813341	−	0.581788i	$-0.802353\pi$
$401$	−2.10043e9	−1.62668	−0.813341	+	0.581788i	$0.802353\pi$
$402$	−9.55635e8	−0.733670
$403$	1.50094e8	0.114234
$404$	6.91899e6	0.00522045
$405$	−2.13163e8	−0.159448
$406$	−5.19896e8	−0.385545
$407$	−8.41607e7	−0.0618770
$408$	1.40539e9	1.02444
$409$	2.09675e9	1.51535	0.757677	−	0.652629i	$-0.226334\pi$
$409$	2.09675e9	1.51535	0.757677	+	0.652629i	$0.226334\pi$
$410$	−3.72602e9	−2.66994
$411$	4.51732e8	0.320948
$412$	−6.35732e7	−0.0447851
$413$	−4.38634e7	−0.0306392
$414$	4.44629e8	0.307962
$415$	8.37107e8	0.574927
$416$	2.37303e8	0.161613
$417$	−3.16153e8	−0.213512
$418$	1.79198e9	1.20009
$419$	−7.54525e8	−0.501100	−0.250550	−	0.968104i	$-0.580612\pi$
$419$	−7.54525e8	−0.501100	−0.250550	+	0.968104i	$0.580612\pi$
$420$	1.49950e7	0.00987585
$421$	−1.83091e8	−0.119586	−0.0597931	−	0.998211i	$-0.519044\pi$
$421$	−1.83091e8	−0.119586	−0.0597931	+	0.998211i	$0.519044\pi$
$422$	−2.37175e9	−1.53630
$423$	−3.96598e7	−0.0254776
$424$	4.16413e8	0.265304
$425$	3.05689e9	1.93161
$426$	1.47259e9	0.922886
$427$	2.92653e8	0.181909
$428$	−1.27155e8	−0.0783938
$429$	−1.69891e9	−1.03889
$430$	−3.35017e9	−2.03202
$431$	2.72495e8	0.163941	0.0819706	−	0.996635i	$-0.473879\pi$
$431$	2.72495e8	0.163941	0.0819706	+	0.996635i	$0.473879\pi$
$432$	3.37993e8	0.201704
$433$	−9.06889e8	−0.536842	−0.268421	−	0.963302i	$-0.586502\pi$
$433$	−9.06889e8	−0.536842	−0.268421	+	0.963302i	$0.586502\pi$
$434$	−2.93869e7	−0.0172560
$435$	−2.27330e9	−1.32417
$436$	1.65598e8	0.0956870
$437$	−1.63387e9	−0.936552
$438$	1.14466e9	0.650902
$439$	−6.54375e7	−0.0369148	−0.0184574	−	0.999830i	$-0.505876\pi$
$439$	−6.54375e7	−0.0369148	−0.0184574	+	0.999830i	$0.505876\pi$
$440$	−2.81155e9	−1.57348
$441$	−5.67111e8	−0.314871
$442$	−5.41857e9	−2.98474
$443$	2.60048e9	1.42115	0.710575	−	0.703621i	$-0.248435\pi$
$443$	2.60048e9	1.42115	0.710575	+	0.703621i	$0.248435\pi$
$444$	−2.96166e6	−0.00160581
$445$	−5.76162e8	−0.309945
$446$	2.83031e9	1.51065
$447$	−4.13989e6	−0.00219236
$448$	4.22970e8	0.222247
$449$	2.52865e9	1.31834	0.659168	−	0.751996i	$-0.270909\pi$
$449$	2.52865e9	1.31834	0.659168	+	0.751996i	$0.270909\pi$
$450$	6.99648e8	0.361939
$451$	−3.98448e9	−2.04529
$452$	−8.08992e7	−0.0412059
$453$	−2.06493e9	−1.04367
$454$	−2.05742e9	−1.03188
$455$	1.08366e9	0.539327
$456$	−1.18199e9	−0.583765
$457$	−1.26888e9	−0.621888	−0.310944	−	0.950428i	$-0.600645\pi$
$457$	−1.26888e9	−0.621888	−0.310944	+	0.950428i	$0.600645\pi$
$458$	2.52320e9	1.22722
$459$	−7.27031e8	−0.350920
$460$	−1.36765e8	−0.0655121
$461$	6.17722e8	0.293656	0.146828	−	0.989162i	$-0.453094\pi$
$461$	6.17722e8	0.293656	0.146828	+	0.989162i	$0.453094\pi$
$462$	3.32630e8	0.156933
$463$	1.76885e9	0.828241	0.414120	−	0.910222i	$-0.364089\pi$
$463$	1.76885e9	0.828241	0.414120	+	0.910222i	$0.364089\pi$
$464$	3.60456e9	1.67510
$465$	−1.28498e8	−0.0592666
$466$	−3.80155e9	−1.74024
$467$	2.09197e9	0.950489	0.475244	−	0.879854i	$-0.342360\pi$
$467$	2.09197e9	0.950489	0.475244	+	0.879854i	$0.342360\pi$
$468$	−5.97856e7	−0.0269610
$469$	6.51839e8	0.291767
$470$	2.53054e8	0.112427
$471$	1.85417e8	0.0817666
$472$	2.89419e8	0.126686
$473$	−3.58257e9	−1.55661
$474$	−1.99549e9	−0.860649
$475$	−2.57098e9	−1.10071
$476$	5.11432e7	0.0217352
$477$	−2.15418e8	−0.0908798
$478$	3.24083e9	1.35725
$479$	−7.21973e8	−0.300156	−0.150078	−	0.988674i	$-0.547952\pi$
$479$	−7.21973e8	−0.300156	−0.150078	+	0.988674i	$0.547952\pi$
$480$	−2.03158e8	−0.0838476
$481$	−2.14033e8	−0.0876945
$482$	4.44478e9	1.80795
$483$	−3.03282e8	−0.122470
$484$	3.40678e7	0.0136580
$485$	2.57787e9	1.02604
$486$	−1.66400e8	−0.0657545
$487$	2.53074e9	0.992878	0.496439	−	0.868072i	$-0.334641\pi$
$487$	2.53074e9	0.992878	0.496439	+	0.868072i	$0.334641\pi$
$488$	−1.93098e9	−0.752156
$489$	5.12535e8	0.198218
$490$	3.61852e9	1.38946
$491$	4.02112e9	1.53307	0.766535	−	0.642203i	$-0.221979\pi$
$491$	4.02112e9	1.53307	0.766535	+	0.642203i	$0.221979\pi$
$492$	−1.40216e8	−0.0530787
$493$	−7.75351e9	−2.91430
$494$	4.55725e9	1.70082
$495$	1.45446e9	0.538995
$496$	2.03746e8	0.0749729
$497$	−1.00445e9	−0.367014
$498$	6.53463e8	0.237093
$499$	−1.21528e9	−0.437849	−0.218924	−	0.975742i	$-0.570255\pi$
$499$	−1.21528e9	−0.437849	−0.218924	+	0.975742i	$0.570255\pi$
$500$	−1.20518e7	−0.00431177
$501$	4.60033e8	0.163439
$502$	−4.91640e9	−1.73454
$503$	4.23068e9	1.48225	0.741126	−	0.671366i	$-0.234292\pi$
$503$	4.23068e9	1.48225	0.741126	+	0.671366i	$0.234292\pi$
$504$	−2.19404e8	−0.0763374
$505$	−4.28075e8	−0.147911
$506$	−3.03381e9	−1.04103
$507$	−2.62636e9	−0.895008
$508$	−1.12452e8	−0.0380577
$509$	5.89664e9	1.98195	0.990974	−	0.134052i	$-0.0427989\pi$
$509$	5.89664e9	1.98195	0.990974	+	0.134052i	$0.0427989\pi$
$510$	4.63892e9	1.54853
$511$	−7.80771e8	−0.258851
$512$	−2.77526e9	−0.913818
$513$	6.11465e8	0.199968
$514$	2.09742e9	0.681262
$515$	3.93325e9	1.26890
$516$	−1.26072e8	−0.0403967
$517$	2.70608e8	0.0861239
$518$	4.19055e7	0.0132470
$519$	2.18063e8	0.0684694
$520$	−7.15017e9	−2.23000
$521$	−3.53847e8	−0.109618	−0.0548092	−	0.998497i	$-0.517455\pi$
$521$	−3.53847e8	−0.109618	−0.0548092	+	0.998497i	$0.517455\pi$
$522$	−1.77459e9	−0.546074
$523$	1.49203e9	0.456059	0.228029	−	0.973654i	$-0.426772\pi$
$523$	1.49203e9	0.456059	0.228029	+	0.973654i	$0.426772\pi$
$524$	−8.83307e7	−0.0268196
$525$	−4.77231e8	−0.143936
$526$	4.91341e9	1.47209
$527$	−4.38264e8	−0.130436
$528$	−2.30620e9	−0.681834
$529$	−6.38695e8	−0.187585
$530$	1.37450e9	0.401033
$531$	−1.49721e8	−0.0433963
$532$	−4.30137e7	−0.0123856
$533$	−1.01331e10	−2.89866
$534$	−4.49764e8	−0.127817
$535$	7.86706e9	2.22113
$536$	−4.30096e9	−1.20639
$537$	−1.34986e9	−0.376164
$538$	4.04049e9	1.11866
$539$	3.86953e9	1.06438
$540$	5.11833e7	0.0139878
$541$	−2.13831e9	−0.580603	−0.290302	−	0.956935i	$-0.593756\pi$
$541$	−2.13831e9	−0.580603	−0.290302	+	0.956935i	$0.593756\pi$
$542$	−1.46630e9	−0.395571
$543$	−1.91002e9	−0.511964
$544$	−6.92908e8	−0.184535
$545$	−1.02455e10	−2.71110
$546$	8.45926e8	0.222412
$547$	−2.11049e9	−0.551351	−0.275676	−	0.961251i	$-0.588902\pi$
$547$	−2.11049e9	−0.551351	−0.275676	+	0.961251i	$0.588902\pi$
$548$	−1.08467e8	−0.0281556
$549$	9.98928e8	0.257651
$550$	−4.77387e9	−1.22349
$551$	6.52104e9	1.66068
$552$	2.00111e9	0.506389
$553$	1.36113e9	0.342264
$554$	−2.57555e9	−0.643556
$555$	1.83237e8	0.0454975
$556$	7.59126e7	0.0187306
$557$	−5.51882e9	−1.35317	−0.676586	−	0.736364i	$-0.736541\pi$
$557$	−5.51882e9	−1.35317	−0.676586	+	0.736364i	$0.736541\pi$
$558$	−1.00308e8	−0.0244408
$559$	−9.11098e9	−2.20609
$560$	1.47102e9	0.353966
$561$	4.96071e9	1.18624
$562$	−3.71427e9	−0.882666
$563$	−3.94126e8	−0.0930798	−0.0465399	−	0.998916i	$-0.514819\pi$
$563$	−3.94126e8	−0.0930798	−0.0465399	+	0.998916i	$0.514819\pi$
$564$	9.52284e6	0.00223506
$565$	5.00520e9	1.16749
$566$	2.85582e9	0.662024
$567$	1.13501e8	0.0261493
$568$	6.62757e9	1.51752
$569$	−5.23096e9	−1.19039	−0.595194	−	0.803582i	$-0.702925\pi$
$569$	−5.23096e9	−1.19039	−0.595194	+	0.803582i	$0.702925\pi$
$570$	−3.90153e9	−0.882416
$571$	3.54290e9	0.796401	0.398201	−	0.917298i	$-0.369635\pi$
$571$	3.54290e9	0.796401	0.398201	+	0.917298i	$0.369635\pi$
$572$	4.07931e8	0.0911383
$573$	3.78611e9	0.840721
$574$	1.98397e9	0.437867
$575$	4.35266e9	0.954811
$576$	1.44375e9	0.314783
$577$	−5.36264e8	−0.116215	−0.0581077	−	0.998310i	$-0.518507\pi$
$577$	−5.36264e8	−0.116215	−0.0581077	+	0.998310i	$0.518507\pi$
$578$	1.10633e10	2.38307
$579$	1.57067e9	0.336286
$580$	5.45851e8	0.116165
$581$	−4.45728e8	−0.0942873
$582$	2.01234e9	0.423127
$583$	1.46985e9	0.307208
$584$	5.15167e9	1.07029
$585$	3.69891e9	0.763885
$586$	2.62090e9	0.538034
$587$	−1.65503e9	−0.337733	−0.168867	−	0.985639i	$-0.554011\pi$
$587$	−1.65503e9	−0.337733	−0.168867	+	0.985639i	$0.554011\pi$
$588$	1.36171e8	0.0276225
$589$	3.68599e8	0.0743278
$590$	9.55316e8	0.191498
$591$	−1.63666e9	−0.326139
$592$	−2.90541e8	−0.0575548
$593$	−8.05027e9	−1.58533	−0.792664	−	0.609659i	$-0.791307\pi$
$593$	−8.05027e9	−1.58533	−0.792664	+	0.609659i	$0.791307\pi$
$594$	1.13538e9	0.222275
$595$	−3.16421e9	−0.615823
$596$	994042.	0.000192328 0
$597$	−6.32723e6	−0.00121704
$598$	−7.71541e9	−1.47538
$599$	−2.91923e7	−0.00554976	−0.00277488	−	0.999996i	$-0.500883\pi$
$599$	−2.91923e7	−0.00554976	−0.00277488	+	0.999996i	$0.500883\pi$
$600$	3.14886e9	0.595146
$601$	−5.20322e9	−0.977713	−0.488856	−	0.872364i	$-0.662586\pi$
$601$	−5.20322e9	−0.977713	−0.488856	+	0.872364i	$0.662586\pi$
$602$	1.78384e9	0.333249
$603$	2.22496e9	0.413249
$604$	4.95818e8	0.0915574
$605$	−2.10776e9	−0.386970
$606$	−3.34164e8	−0.0609966
$607$	7.88385e9	1.43080	0.715398	−	0.698717i	$-0.246245\pi$
$607$	7.88385e9	1.43080	0.715398	+	0.698717i	$0.246245\pi$
$608$	5.82766e8	0.105155
$609$	1.21045e9	0.217163
$610$	−6.37379e9	−1.13696
$611$	6.88195e8	0.122058
$612$	1.74570e8	0.0307850
$613$	−3.27886e9	−0.574926	−0.287463	−	0.957792i	$-0.592812\pi$
$613$	−3.27886e9	−0.574926	−0.287463	+	0.957792i	$0.592812\pi$
$614$	6.42100e9	1.11947
$615$	8.67511e9	1.50388
$616$	1.49704e9	0.258049
$617$	1.20684e9	0.206848	0.103424	−	0.994637i	$-0.467020\pi$
$617$	1.20684e9	0.206848	0.103424	+	0.994637i	$0.467020\pi$
$618$	3.07038e9	0.523277
$619$	−4.26264e9	−0.722372	−0.361186	−	0.932494i	$-0.617628\pi$
$619$	−4.26264e9	−0.722372	−0.361186	+	0.932494i	$0.617628\pi$
$620$	3.08540e7	0.00519925
$621$	−1.03521e9	−0.173463
$622$	1.01130e10	1.68505
$623$	3.06784e8	0.0508306
$624$	−5.86501e9	−0.966323
$625$	−5.71996e9	−0.937158
$626$	3.80057e9	0.619211
$627$	−4.17217e9	−0.675968
$628$	−4.45210e7	−0.00717310
$629$	6.24962e8	0.100133
$630$	−7.24210e8	−0.115391
$631$	−3.40983e9	−0.540294	−0.270147	−	0.962819i	$-0.587072\pi$
$631$	−3.40983e9	−0.540294	−0.270147	+	0.962819i	$0.587072\pi$
$632$	−8.98098e9	−1.41519
$633$	5.52204e9	0.865339
$634$	1.25096e10	1.94954
$635$	6.95733e9	1.07829
$636$	5.17247e7	0.00797257
$637$	9.84077e9	1.50849
$638$	1.21084e10	1.84593
$639$	−3.42856e9	−0.519827
$640$	−1.01751e10	−1.53430
$641$	−7.05809e9	−1.05848	−0.529242	−	0.848471i	$-0.677524\pi$
$641$	−7.05809e9	−1.05848	−0.529242	+	0.848471i	$0.677524\pi$
$642$	6.14119e9	0.915967
$643$	9.53642e9	1.41464	0.707322	−	0.706892i	$-0.249903\pi$
$643$	9.53642e9	1.41464	0.707322	+	0.706892i	$0.249903\pi$
$644$	7.28220e7	0.0107439
$645$	7.80005e9	1.14456
$646$	−1.33069e10	−1.94206
$647$	1.17077e10	1.69945	0.849723	−	0.527230i	$-0.176769\pi$
$647$	1.17077e10	1.69945	0.849723	+	0.527230i	$0.176769\pi$
$648$	−7.48903e8	−0.108122
$649$	1.02158e9	0.146696
$650$	−1.21406e10	−1.73398
$651$	6.84202e7	0.00971965
$652$	−1.23066e8	−0.0173889
$653$	−1.32050e9	−0.185584	−0.0927921	−	0.995686i	$-0.529579\pi$
$653$	−1.32050e9	−0.185584	−0.0927921	+	0.995686i	$0.529579\pi$
$654$	−7.99784e9	−1.11802
$655$	5.46499e9	0.759879
$656$	−1.37553e10	−1.90242
$657$	−2.66505e9	−0.366629
$658$	−1.34742e8	−0.0184379
$659$	−2.98482e9	−0.406275	−0.203137	−	0.979150i	$-0.565114\pi$
$659$	−2.98482e9	−0.406275	−0.203137	+	0.979150i	$0.565114\pi$
$660$	−3.49236e8	−0.0472841
$661$	−1.22973e10	−1.65617	−0.828087	−	0.560600i	$-0.810571\pi$
$661$	−1.22973e10	−1.65617	−0.828087	+	0.560600i	$0.810571\pi$
$662$	2.22464e9	0.298027
$663$	1.26158e10	1.68119
$664$	2.94100e9	0.389858
$665$	2.66124e9	0.350920
$666$	1.43038e8	0.0187626
$667$	−1.10401e10	−1.44056
$668$	−1.10460e8	−0.0143380
$669$	−6.58968e9	−0.850889
$670$	−1.41966e10	−1.82358
$671$	−6.81592e9	−0.870955
$672$	1.08174e8	0.0137509
$673$	−7.89633e9	−0.998557	−0.499278	−	0.866442i	$-0.666401\pi$
$673$	−7.89633e9	−0.998557	−0.499278	+	0.866442i	$0.666401\pi$
$674$	5.48584e9	0.690134
$675$	−1.62896e9	−0.203867
$676$	6.30625e8	0.0785159
$677$	−1.34037e9	−0.166021	−0.0830106	−	0.996549i	$-0.526454\pi$
$677$	−1.34037e9	−0.166021	−0.0830106	+	0.996549i	$0.526454\pi$
$678$	3.90716e9	0.481457
$679$	−1.37262e9	−0.168270
$680$	2.08780e10	2.54629
$681$	4.79020e9	0.581218
$682$	6.84425e8	0.0826191
$683$	−6.85009e9	−0.822667	−0.411333	−	0.911485i	$-0.634937\pi$
$683$	−6.85009e9	−0.822667	−0.411333	+	0.911485i	$0.634937\pi$
$684$	−1.46821e8	−0.0175425
$685$	6.71080e9	0.797732
$686$	−3.96643e9	−0.469100
$687$	−5.87465e9	−0.691247
$688$	−1.23678e10	−1.44788
$689$	3.73803e9	0.435387
$690$	6.60528e9	0.765454
$691$	1.48604e10	1.71340	0.856698	−	0.515818i	$-0.172512\pi$
$691$	1.48604e10	1.71340	0.856698	+	0.515818i	$0.172512\pi$
$692$	−5.23599e7	−0.00600658
$693$	−7.74447e8	−0.0883945
$694$	−2.77662e9	−0.315325
$695$	−4.69668e9	−0.530694
$696$	−7.98677e9	−0.897922
$697$	2.95880e10	3.30980
$698$	2.96055e9	0.329518
$699$	8.85097e9	0.980214
$700$	1.14589e8	0.0126270
$701$	−1.54673e10	−1.69590	−0.847952	−	0.530073i	$-0.822164\pi$
$701$	−1.54673e10	−1.69590	−0.847952	+	0.530073i	$0.822164\pi$
$702$	2.88745e9	0.315017
$703$	−5.25620e8	−0.0570596
$704$	−9.85102e9	−1.06409
$705$	−5.89174e8	−0.0633260
$706$	1.06319e10	1.13709
$707$	2.27934e8	0.0242572
$708$	3.59501e7	0.00380701
$709$	2.09686e9	0.220957	0.110478	−	0.993879i	$-0.464762\pi$
$709$	2.09686e9	0.220957	0.110478	+	0.993879i	$0.464762\pi$
$710$	2.18764e10	2.29388
$711$	4.64601e9	0.484771
$712$	−2.02422e9	−0.210173
$713$	−6.24037e8	−0.0644759
$714$	−2.47005e9	−0.253958
$715$	−2.52385e10	−2.58222
$716$	3.24119e8	0.0329996
$717$	−7.54547e9	−0.764485
$718$	−1.23065e9	−0.124079
$719$	−1.96050e10	−1.96705	−0.983527	−	0.180761i	$-0.942144\pi$
$719$	−1.96050e10	−1.96705	−0.983527	+	0.180761i	$0.942144\pi$
$720$	5.02112e9	0.501345
$721$	−2.09431e9	−0.208097
$722$	8.25721e8	0.0816494
$723$	−1.03486e10	−1.01835
$724$	4.58622e8	0.0449128
$725$	−1.73722e10	−1.69306
$726$	−1.64536e9	−0.159582
$727$	−1.11617e10	−1.07735	−0.538677	−	0.842513i	$-0.681075\pi$
$727$	−1.11617e10	−1.07735	−0.538677	+	0.842513i	$0.681075\pi$
$728$	3.80720e9	0.365717
$729$	3.87420e8	0.0370370
$730$	1.70047e10	1.61785
$731$	2.66035e10	2.51899
$732$	−2.39856e8	−0.0226028
$733$	1.37783e10	1.29221	0.646103	−	0.763250i	$-0.276397\pi$
$733$	1.37783e10	1.29221	0.646103	+	0.763250i	$0.276397\pi$
$734$	1.31437e10	1.22683
$735$	−8.42483e9	−0.782628
$736$	−9.86621e8	−0.0912175
$737$	−1.51814e10	−1.39694
$738$	6.77198e9	0.620181
$739$	3.03220e9	0.276377	0.138189	−	0.990406i	$-0.455872\pi$
$739$	3.03220e9	0.276377	0.138189	+	0.990406i	$0.455872\pi$
$740$	−4.39976e7	−0.00399133
$741$	−1.06104e10	−0.958008
$742$	−7.31870e8	−0.0657689
$743$	−1.93427e9	−0.173004	−0.0865020	−	0.996252i	$-0.527569\pi$
$743$	−1.93427e9	−0.173004	−0.0865020	+	0.996252i	$0.527569\pi$
$744$	−4.51449e8	−0.0401886
$745$	−6.15009e7	−0.00544923
$746$	4.04318e9	0.356563
$747$	−1.52143e9	−0.133545
$748$	−1.19113e9	−0.104065
$749$	−4.18891e9	−0.364263
$750$	5.82060e8	0.0503795
$751$	5.54431e9	0.477647	0.238824	−	0.971063i	$-0.423238\pi$
$751$	5.54431e9	0.477647	0.238824	+	0.971063i	$0.423238\pi$
$752$	9.34197e8	0.0801081
$753$	1.14466e10	0.977000
$754$	3.07935e10	2.61613
$755$	−3.06761e10	−2.59409
$756$	−2.72532e7	−0.00229399
$757$	1.76557e10	1.47927	0.739637	−	0.673006i	$-0.234997\pi$
$757$	1.76557e10	1.47927	0.739637	+	0.673006i	$0.234997\pi$
$758$	−2.29332e9	−0.191259
$759$	7.06347e9	0.586370
$760$	−1.75593e10	−1.45098
$761$	2.32983e9	0.191636	0.0958180	−	0.995399i	$-0.469453\pi$
$761$	2.32983e9	0.191636	0.0958180	+	0.995399i	$0.469453\pi$
$762$	5.43104e9	0.444673
$763$	5.45534e9	0.444617
$764$	−9.09095e8	−0.0737535
$765$	−1.08006e10	−0.872231
$766$	−1.85918e10	−1.49458
$767$	2.59803e9	0.207903
$768$	−1.09850e9	−0.0875052
$769$	8.88822e9	0.704811	0.352405	−	0.935847i	$-0.385364\pi$
$769$	8.88822e9	0.704811	0.352405	+	0.935847i	$0.385364\pi$
$770$	4.94146e9	0.390066
$771$	−4.88332e9	−0.383729
$772$	−3.77138e8	−0.0295012
$773$	−1.51855e9	−0.118250	−0.0591251	−	0.998251i	$-0.518831\pi$
$773$	−1.51855e9	−0.118250	−0.0591251	+	0.998251i	$0.518831\pi$
$774$	6.08888e9	0.472002
$775$	−9.81957e8	−0.0757769
$776$	9.05679e9	0.695758
$777$	−9.75667e7	−0.00746153
$778$	−8.98038e9	−0.683701
$779$	−2.48848e10	−1.88605
$780$	−8.88157e8	−0.0670130
$781$	2.33939e10	1.75721
$782$	2.25285e10	1.68464
$783$	4.13169e9	0.307583
$784$	1.33585e10	0.990034
$785$	2.75450e9	0.203235
$786$	4.26608e9	0.313365
$787$	5.14294e9	0.376097	0.188048	−	0.982160i	$-0.439784\pi$
$787$	5.14294e9	0.376097	0.188048	+	0.982160i	$0.439784\pi$
$788$	3.92984e8	0.0286110
$789$	−1.14397e10	−0.829170
$790$	−2.96445e10	−2.13919
$791$	−2.66508e9	−0.191466
$792$	5.10994e9	0.365492
$793$	−1.73339e10	−1.23435
$794$	−1.44879e10	−1.02715
$795$	−3.20019e9	−0.225886
$796$	1.51925e6	0.000106766 0
$797$	2.31164e10	1.61739	0.808697	−	0.588225i	$-0.200173\pi$
$797$	2.31164e10	1.61739	0.808697	+	0.588225i	$0.200173\pi$
$798$	2.07742e9	0.144715
$799$	−2.00948e9	−0.139371
$800$	−1.55250e9	−0.107206
$801$	1.04716e9	0.0719947
$802$	−2.43580e10	−1.66737
$803$	1.81843e10	1.23934
$804$	−5.34243e8	−0.0362529
$805$	−4.50547e9	−0.304407
$806$	1.74059e9	0.117091
$807$	−9.40729e9	−0.630096
$808$	−1.50395e9	−0.100298
$809$	2.29952e10	1.52692	0.763462	−	0.645853i	$-0.223498\pi$
$809$	2.29952e10	1.52692	0.763462	+	0.645853i	$0.223498\pi$
$810$	−2.47199e9	−0.163436
$811$	−2.76002e9	−0.181694	−0.0908468	−	0.995865i	$-0.528957\pi$
$811$	−2.76002e9	−0.181694	−0.0908468	+	0.995865i	$0.528957\pi$
$812$	−2.90645e8	−0.0190510
$813$	3.41391e9	0.222810
$814$	−9.75985e8	−0.0634246
$815$	7.61407e9	0.492680
$816$	1.71254e10	1.10338
$817$	−2.23747e10	−1.43542
$818$	2.43153e10	1.55326
$819$	−1.96953e9	−0.125276
$820$	−2.08301e9	−0.131930
$821$	5.67826e9	0.358108	0.179054	−	0.983839i	$-0.442696\pi$
$821$	5.67826e9	0.358108	0.179054	+	0.983839i	$0.442696\pi$
$822$	5.23859e9	0.328975
$823$	−2.56662e7	−0.00160495	−0.000802475	−	1.00000i	$-0.500255\pi$
$823$	−2.56662e7	−0.00160495	−0.000802475		1.00000i	$0.500255\pi$
$824$	1.38186e10	0.860437
$825$	1.11148e10	0.689146
$826$	−5.08670e8	−0.0314055
$827$	−2.08817e10	−1.28380	−0.641899	−	0.766789i	$-0.721853\pi$
$827$	−2.08817e10	−1.28380	−0.641899	+	0.766789i	$0.721853\pi$
$828$	2.48567e8	0.0152173
$829$	−2.54198e10	−1.54964	−0.774821	−	0.632180i	$-0.782160\pi$
$829$	−2.54198e10	−1.54964	−0.774821	+	0.632180i	$0.782160\pi$
$830$	9.70767e9	0.589307
$831$	5.99654e9	0.362491
$832$	−2.50525e10	−1.50807
$833$	−2.87344e10	−1.72244
$834$	−3.66633e9	−0.218852
$835$	6.83412e9	0.406237
$836$	1.00179e9	0.0593003
$837$	2.33542e8	0.0137666
$838$	−8.74999e9	−0.513634
$839$	−3.56300e9	−0.208281	−0.104140	−	0.994563i	$-0.533209\pi$
$839$	−3.56300e9	−0.208281	−0.104140	+	0.994563i	$0.533209\pi$
$840$	−3.25940e9	−0.189741
$841$	2.68130e10	1.55439
$842$	−2.12325e9	−0.122577
$843$	8.64776e9	0.497172
$844$	−1.32592e9	−0.0759132
$845$	−3.90165e10	−2.22459
$846$	−4.59922e8	−0.0261149
$847$	1.12230e9	0.0634627
$848$	5.07423e9	0.285749
$849$	−6.64908e9	−0.372893
$850$	3.54498e10	1.97992
$851$	8.89873e8	0.0494965
$852$	8.23243e8	0.0456026
$853$	2.29229e10	1.26458	0.632291	−	0.774731i	$-0.282115\pi$
$853$	2.29229e10	1.26458	0.632291	+	0.774731i	$0.282115\pi$
$854$	3.39380e9	0.186459
$855$	9.08375e9	0.497031
$856$	2.76392e10	1.50615
$857$	−1.48684e10	−0.806924	−0.403462	−	0.914996i	$-0.632193\pi$
$857$	−1.48684e10	−0.806924	−0.403462	+	0.914996i	$0.632193\pi$
$858$	−1.97017e10	−1.06488
$859$	−2.17432e10	−1.17043	−0.585217	−	0.810877i	$-0.698991\pi$
$859$	−2.17432e10	−1.17043	−0.585217	+	0.810877i	$0.698991\pi$
$860$	−1.87290e9	−0.100408
$861$	−4.61917e9	−0.246634
$862$	3.16004e9	0.168042
$863$	−1.50753e10	−0.798414	−0.399207	−	0.916861i	$-0.630715\pi$
$863$	−1.50753e10	−0.798414	−0.399207	+	0.916861i	$0.630715\pi$
$864$	3.69237e8	0.0194763
$865$	3.23948e9	0.170184
$866$	−1.05169e10	−0.550269
$867$	−2.57581e10	−1.34229
$868$	−1.64286e7	−0.000852671 0
$869$	−3.17009e10	−1.63871
$870$	−2.63628e10	−1.35729
$871$	−3.86085e10	−1.97979
$872$	−3.59953e10	−1.83839
$873$	−4.68523e9	−0.238331
$874$	−1.89474e10	−0.959977
$875$	−3.97024e8	−0.0200350
$876$	6.39914e8	0.0321630
$877$	−1.29162e10	−0.646598	−0.323299	−	0.946297i	$-0.604792\pi$
$877$	−1.29162e10	−0.646598	−0.323299	+	0.946297i	$0.604792\pi$
$878$	−7.58858e8	−0.0378381
$879$	−6.10213e9	−0.303054
$880$	−3.42603e10	−1.69473
$881$	−2.47400e10	−1.21895	−0.609473	−	0.792807i	$-0.708619\pi$
$881$	−2.47400e10	−1.21895	−0.609473	+	0.792807i	$0.708619\pi$
$882$	−6.57660e9	−0.322747
$883$	2.21032e10	1.08042	0.540211	−	0.841530i	$-0.318345\pi$
$883$	2.21032e10	1.08042	0.540211	+	0.841530i	$0.318345\pi$
$884$	−3.02922e9	−0.147485
$885$	−2.22422e9	−0.107864
$886$	3.01569e10	1.45670
$887$	−8.79294e9	−0.423060	−0.211530	−	0.977372i	$-0.567845\pi$
$887$	−8.79294e9	−0.423060	−0.211530	+	0.977372i	$0.567845\pi$
$888$	6.43763e8	0.0308518
$889$	−3.70452e9	−0.176838
$890$	−6.68156e9	−0.317697
$891$	−2.64346e9	−0.125199
$892$	1.58227e9	0.0746455
$893$	1.69006e9	0.0794188
$894$	−4.80089e7	−0.00224719
$895$	−2.00531e10	−0.934976
$896$	5.41787e9	0.251623
$897$	1.79634e10	0.831027
$898$	2.93239e10	1.35131
$899$	2.49064e9	0.114328
$900$	3.91134e8	0.0178845
$901$	−1.09148e10	−0.497141
$902$	−4.62068e10	−2.09644
$903$	−4.15323e9	−0.187706
$904$	1.75847e10	0.791671
$905$	−2.83747e10	−1.27251
$906$	−2.39464e10	−1.06977
$907$	−6.78075e8	−0.0301753	−0.0150877	−	0.999886i	$-0.504803\pi$
$907$	−6.78075e8	−0.0301753	−0.0150877	+	0.999886i	$0.504803\pi$
$908$	−1.15019e9	−0.0509882
$909$	7.78019e8	0.0343571
$910$	1.25668e10	0.552817
$911$	1.87905e10	0.823424	0.411712	−	0.911314i	$-0.364931\pi$
$911$	1.87905e10	0.823424	0.411712	+	0.911314i	$0.364931\pi$
$912$	−1.44032e10	−0.628750
$913$	1.03811e10	0.451434
$914$	−1.47148e10	−0.637443
$915$	1.48398e10	0.640404
$916$	1.41058e9	0.0606407
$917$	−2.90990e9	−0.124619
$918$	−8.43115e9	−0.359698
$919$	3.67497e10	1.56189	0.780943	−	0.624603i	$-0.214739\pi$
$919$	3.67497e10	1.56189	0.780943	+	0.624603i	$0.214739\pi$
$920$	2.97279e10	1.25866
$921$	−1.49497e10	−0.630557
$922$	7.16352e9	0.301001
$923$	5.94939e10	2.49039
$924$	1.85955e8	0.00775454
$925$	1.40026e9	0.0581720
$926$	2.05128e10	0.848957
$927$	−7.14861e9	−0.294742
$928$	3.93777e9	0.161746
$929$	5.36643e9	0.219599	0.109800	−	0.993954i	$-0.464979\pi$
$929$	5.36643e9	0.219599	0.109800	+	0.993954i	$0.464979\pi$
$930$	−1.49015e9	−0.0607489
$931$	2.41669e10	0.981515
$932$	−2.12524e9	−0.0859907
$933$	−2.35456e10	−0.949127
$934$	2.42599e10	0.974262
$935$	7.36948e10	2.94847
$936$	1.29953e10	0.517990
$937$	−2.19515e10	−0.871717	−0.435859	−	0.900015i	$-0.643555\pi$
$937$	−2.19515e10	−0.871717	−0.435859	+	0.900015i	$0.643555\pi$
$938$	7.55918e9	0.299064
$939$	−8.84869e9	−0.348778
$940$	1.41469e8	0.00555537
$941$	2.82488e10	1.10519	0.552595	−	0.833450i	$-0.313638\pi$
$941$	2.82488e10	1.10519	0.552595	+	0.833450i	$0.313638\pi$
$942$	2.15022e9	0.0838117
$943$	4.21299e10	1.63606
$944$	3.52673e9	0.136449
$945$	1.68614e9	0.0649955
$946$	−4.15459e10	−1.59554
$947$	2.51489e10	0.962264	0.481132	−	0.876648i	$-0.340226\pi$
$947$	2.51489e10	0.962264	0.481132	+	0.876648i	$0.340226\pi$
$948$	−1.11557e9	−0.0425273
$949$	4.62452e10	1.75645
$950$	−2.98149e10	−1.12824
$951$	−2.91255e10	−1.09810
$952$	−1.11168e10	−0.417589
$953$	−4.09484e10	−1.53254	−0.766269	−	0.642519i	$-0.777889\pi$
$953$	−4.09484e10	−1.53254	−0.766269	+	0.642519i	$0.777889\pi$
$954$	−2.49813e9	−0.0931529
$955$	5.62453e10	2.08966
$956$	1.81177e9	0.0670656
$957$	−2.81915e10	−1.03974
$958$	−8.37249e9	−0.307663
$959$	−3.57325e9	−0.130827
$960$	2.14479e10	0.782411
$961$	−2.73718e10	−0.994883
$962$	−2.48207e9	−0.0898879
$963$	−1.42982e10	−0.515930
$964$	2.48483e9	0.0893360
$965$	2.33334e10	0.835858
$966$	−3.51706e9	−0.125534
$967$	−5.25463e10	−1.86874	−0.934372	−	0.356299i	$-0.884038\pi$
$967$	−5.25463e10	−1.86874	−0.934372	+	0.356299i	$0.884038\pi$
$968$	−7.40517e9	−0.262404
$969$	3.09818e10	1.09389
$970$	2.98947e10	1.05170
$971$	−2.49973e9	−0.0876246	−0.0438123	−	0.999040i	$-0.513950\pi$
$971$	−2.49973e9	−0.0876246	−0.0438123	+	0.999040i	$0.513950\pi$
$972$	−9.30248e7	−0.00324913
$973$	2.50081e9	0.0870332
$974$	2.93482e10	1.01771
$975$	2.82664e10	0.976686
$976$	−2.35300e10	−0.810118
$977$	−2.71796e10	−0.932420	−0.466210	−	0.884674i	$-0.654381\pi$
$977$	−2.71796e10	−0.932420	−0.466210	+	0.884674i	$0.654381\pi$
$978$	5.94370e9	0.203175
$979$	−7.14505e9	−0.243369
$980$	2.02292e9	0.0686573
$981$	1.86210e10	0.629740
$982$	4.66316e10	1.57141
$983$	3.97905e9	0.133611	0.0668055	−	0.997766i	$-0.478719\pi$
$983$	3.97905e9	0.133611	0.0668055	+	0.997766i	$0.478719\pi$
$984$	3.04781e10	1.01978
$985$	−2.43138e10	−0.810635
$986$	−8.99150e10	−2.98719
$987$	3.13713e8	0.0103854
$988$	2.54771e9	0.0840427
$989$	3.78802e10	1.24516
$990$	1.68670e10	0.552476
$991$	−2.12813e9	−0.0694610	−0.0347305	−	0.999397i	$-0.511057\pi$
$991$	−2.12813e9	−0.0694610	−0.0347305	+	0.999397i	$0.511057\pi$
$992$	2.22581e8	0.00723931
$993$	−5.17951e9	−0.167867
$994$	−1.16483e10	−0.376194
$995$	−9.39956e7	−0.00302501
$996$	3.65315e8	0.0117155
$997$	−1.59834e8	−0.00510784	−0.00255392	−	0.999997i	$-0.500813\pi$
$997$	−1.59834e8	−0.00510784	−0.00255392	+	0.999997i	$0.500813\pi$
$998$	−1.40932e10	−0.448800
$999$	−3.33030e8	−0.0105683

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.c.1.13	✓	17
3.2	odd	2		531.8.a.c.1.5		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.13	✓	17	1.1	even	1	trivial
531.8.a.c.1.5		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)

\(f(q)\)	\(=\)	\(q+11.5967 q^{2} -27.0000 q^{3} +6.48306 q^{4} -401.104 q^{5} -313.110 q^{6} +213.573 q^{7} -1409.19 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+11.5967 q^{2} -27.0000 q^{3} +6.48306 q^{4} -401.104 q^{5} -313.110 q^{6} +213.573 q^{7} -1409.19 q^{8} +729.000 q^{9} -4651.48 q^{10} -4974.14 q^{11} -175.043 q^{12} -12649.9 q^{13} +2476.74 q^{14} +10829.8 q^{15} -17171.8 q^{16} +36937.0 q^{17} +8453.98 q^{18} -31065.7 q^{19} -2600.38 q^{20} -5766.47 q^{21} -57683.5 q^{22} +52594.0 q^{23} +38048.2 q^{24} +82759.6 q^{25} -146697. q^{26} -19683.0 q^{27} +1384.61 q^{28} -209912. q^{29} +125590. q^{30} -11865.2 q^{31} -18759.2 q^{32} +134302. q^{33} +428347. q^{34} -85665.0 q^{35} +4726.15 q^{36} +16919.7 q^{37} -360259. q^{38} +341549. q^{39} +565233. q^{40} +801040. q^{41} -66871.9 q^{42} +720238. q^{43} -32247.7 q^{44} -292405. q^{45} +609916. q^{46} -54403.0 q^{47} +463639. q^{48} -777930. q^{49} +959737. q^{50} -997299. q^{51} -82010.4 q^{52} -295498. q^{53} -228258. q^{54} +1.99515e6 q^{55} -300965. q^{56} +838773. q^{57} -2.43428e6 q^{58} -205379. q^{59} +70210.3 q^{60} +1.37027e6 q^{61} -137597. q^{62} +155695. q^{63} +1.98045e6 q^{64} +5.07395e6 q^{65} +1.55746e6 q^{66} +3.05207e6 q^{67} +239465. q^{68} -1.42004e6 q^{69} -993430. q^{70} -4.70310e6 q^{71} -1.02730e6 q^{72} -3.65576e6 q^{73} +196212. q^{74} -2.23451e6 q^{75} -201401. q^{76} -1.06234e6 q^{77} +3.96083e6 q^{78} +6.37313e6 q^{79} +6.88768e6 q^{80} +531441. q^{81} +9.28941e6 q^{82} -2.08701e6 q^{83} -37384.4 q^{84} -1.48156e7 q^{85} +8.35238e6 q^{86} +5.66762e6 q^{87} +7.00953e6 q^{88} +1.43644e6 q^{89} -3.39093e6 q^{90} -2.70169e6 q^{91} +340970. q^{92} +320360. q^{93} -630894. q^{94} +1.24606e7 q^{95} +506498. q^{96} -6.42693e6 q^{97} -9.02140e6 q^{98} -3.62615e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 2 q^{2} - 459 q^{3} + 1166 q^{4} - 318 q^{5} - 54 q^{6} + 3145 q^{7} + 2355 q^{8} + 12393 q^{9}+O(q^{10}) \) 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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