LMFDB - Embedded newform 177.8.a.c.1.16

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			1.16
Root			$21.5848$ 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)

$f(q)$	$=$	$q+21.5848 q^{2} -27.0000 q^{3} +337.903 q^{4} -113.334 q^{5} -582.789 q^{6} -647.523 q^{7} +4530.72 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+21.5848 q^{2} -27.0000 q^{3} +337.903 q^{4} -113.334 q^{5} -582.789 q^{6} -647.523 q^{7} +4530.72 q^{8} +729.000 q^{9} -2446.30 q^{10} +797.052 q^{11} -9123.39 q^{12} +863.046 q^{13} -13976.6 q^{14} +3060.03 q^{15} +54543.1 q^{16} +30234.1 q^{17} +15735.3 q^{18} +36679.8 q^{19} -38296.1 q^{20} +17483.1 q^{21} +17204.2 q^{22} +55059.3 q^{23} -122330. q^{24} -65280.3 q^{25} +18628.7 q^{26} -19683.0 q^{27} -218800. q^{28} +201168. q^{29} +66050.1 q^{30} -17365.2 q^{31} +597369. q^{32} -21520.4 q^{33} +652597. q^{34} +73386.6 q^{35} +246332. q^{36} -157061. q^{37} +791727. q^{38} -23302.2 q^{39} -513487. q^{40} +264460. q^{41} +377370. q^{42} +97565.6 q^{43} +269327. q^{44} -82620.8 q^{45} +1.18844e6 q^{46} +236490. q^{47} -1.47266e6 q^{48} -404257. q^{49} -1.40906e6 q^{50} -816321. q^{51} +291626. q^{52} -524092. q^{53} -424854. q^{54} -90333.5 q^{55} -2.93375e6 q^{56} -990355. q^{57} +4.34217e6 q^{58} -205379. q^{59} +1.03399e6 q^{60} +2.50976e6 q^{61} -374823. q^{62} -472044. q^{63} +5.91257e6 q^{64} -97812.8 q^{65} -464514. q^{66} -1.86827e6 q^{67} +1.02162e7 q^{68} -1.48660e6 q^{69} +1.58404e6 q^{70} -3.17472e6 q^{71} +3.30290e6 q^{72} +303181. q^{73} -3.39014e6 q^{74} +1.76257e6 q^{75} +1.23942e7 q^{76} -516110. q^{77} -502974. q^{78} +3.54094e6 q^{79} -6.18161e6 q^{80} +531441. q^{81} +5.70830e6 q^{82} +9.87483e6 q^{83} +5.90761e6 q^{84} -3.42656e6 q^{85} +2.10593e6 q^{86} -5.43154e6 q^{87} +3.61122e6 q^{88} -6.49191e6 q^{89} -1.78335e6 q^{90} -558842. q^{91} +1.86047e7 q^{92} +468859. q^{93} +5.10459e6 q^{94} -4.15709e6 q^{95} -1.61290e7 q^{96} -8435.50 q^{97} -8.72581e6 q^{98} +581051. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	21.5848	1.90784	0.953922	−	0.300054i	$-0.0970047\pi$
$2$	21.5848	1.90784	0.953922	+	0.300054i	$0.0970047\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	337.903	2.63987
$5$	−113.334	−0.405478	−0.202739	−	0.979233i	$-0.564984\pi$
$5$	−113.334	−0.405478	−0.202739	+	0.979233i	$0.564984\pi$
$6$	−582.789	−1.10149
$7$	−647.523	−0.713530	−0.356765	−	0.934194i	$-0.616120\pi$
$7$	−647.523	−0.713530	−0.356765	+	0.934194i	$0.616120\pi$
$8$	4530.72	3.12862
$9$	729.000	0.333333
$10$	−2446.30	−0.773588
$11$	797.052	0.180556	0.0902781	−	0.995917i	$-0.471224\pi$
$11$	797.052	0.180556	0.0902781	+	0.995917i	$0.471224\pi$
$12$	−9123.39	−1.52413
$13$	863.046	0.108951	0.0544756	−	0.998515i	$-0.482651\pi$
$13$	863.046	0.108951	0.0544756	+	0.998515i	$0.482651\pi$
$14$	−13976.6	−1.36130
$15$	3060.03	0.234103
$16$	54543.1	3.32905
$17$	30234.1	1.49254	0.746270	−	0.665644i	$-0.231843\pi$
$17$	30234.1	1.49254	0.746270	+	0.665644i	$0.231843\pi$
$18$	15735.3	0.635948
$19$	36679.8	1.22685	0.613423	−	0.789755i	$-0.289792\pi$
$19$	36679.8	1.22685	0.613423	+	0.789755i	$0.289792\pi$
$20$	−38296.1	−1.07041
$21$	17483.1	0.411957
$22$	17204.2	0.344473
$23$	55059.3	0.943591	0.471795	−	0.881708i	$-0.343606\pi$
$23$	55059.3	0.943591	0.471795	+	0.881708i	$0.343606\pi$
$24$	−122330.	−1.80631
$25$	−65280.3	−0.835588
$26$	18628.7	0.207862
$27$	−19683.0	−0.192450
$28$	−218800.	−1.88363
$29$	201168.	1.53167	0.765836	−	0.643036i	$-0.222325\pi$
$29$	201168.	1.53167	0.765836	+	0.643036i	$0.222325\pi$
$30$	66050.1	0.446631
$31$	−17365.2	−0.104692	−0.0523459	−	0.998629i	$-0.516670\pi$
$31$	−17365.2	−0.104692	−0.0523459	+	0.998629i	$0.516670\pi$
$32$	597369.	3.22268
$33$	−21520.4	−0.104244
$34$	652597.	2.84753
$35$	73386.6	0.289320
$36$	246332.	0.879957
$37$	−157061.	−0.509757	−0.254879	−	0.966973i	$-0.582036\pi$
$37$	−157061.	−0.509757	−0.254879	+	0.966973i	$0.582036\pi$
$38$	791727.	2.34063
$39$	−23302.2	−0.0629030
$40$	−513487.	−1.26858
$41$	264460.	0.599261	0.299630	−	0.954055i	$-0.403137\pi$
$41$	264460.	0.599261	0.299630	+	0.954055i	$0.403137\pi$
$42$	377370.	0.785949
$43$	97565.6	0.187136	0.0935680	−	0.995613i	$-0.470173\pi$
$43$	97565.6	0.187136	0.0935680	+	0.995613i	$0.470173\pi$
$44$	269327.	0.476645
$45$	−82620.8	−0.135159
$46$	1.18844e6	1.80022
$47$	236490.	0.332254	0.166127	−	0.986104i	$-0.446874\pi$
$47$	236490.	0.332254	0.166127	+	0.986104i	$0.446874\pi$
$48$	−1.47266e6	−1.92203
$49$	−404257.	−0.490876
$50$	−1.40906e6	−1.59417
$51$	−816321.	−0.861718
$52$	291626.	0.287617
$53$	−524092.	−0.483551	−0.241775	−	0.970332i	$-0.577730\pi$
$53$	−524092.	−0.483551	−0.241775	+	0.970332i	$0.577730\pi$
$54$	−424854.	−0.367165
$55$	−90333.5	−0.0732115
$56$	−2.93375e6	−2.23236
$57$	−990355.	−0.708319
$58$	4.34217e6	2.92219
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	1.03399e6	0.618001
$61$	2.50976e6	1.41572	0.707860	−	0.706353i	$-0.249661\pi$
$61$	2.50976e6	1.41572	0.707860	+	0.706353i	$0.249661\pi$
$62$	−374823.	−0.199736
$63$	−472044.	−0.237843
$64$	5.91257e6	2.81933
$65$	−97812.8	−0.0441773
$66$	−464514.	−0.198882
$67$	−1.86827e6	−0.758888	−0.379444	−	0.925215i	$-0.623885\pi$
$67$	−1.86827e6	−0.758888	−0.379444	+	0.925215i	$0.623885\pi$
$68$	1.02162e7	3.94011
$69$	−1.48660e6	−0.544782
$70$	1.58404e6	0.551978
$71$	−3.17472e6	−1.05269	−0.526345	−	0.850271i	$-0.676438\pi$
$71$	−3.17472e6	−1.05269	−0.526345	+	0.850271i	$0.676438\pi$
$72$	3.30290e6	1.04287
$73$	303181.	0.0912162	0.0456081	−	0.998959i	$-0.485477\pi$
$73$	303181.	0.0912162	0.0456081	+	0.998959i	$0.485477\pi$
$74$	−3.39014e6	−0.972538
$75$	1.76257e6	0.482427
$76$	1.23942e7	3.23871
$77$	−516110.	−0.128832
$78$	−502974.	−0.120009
$79$	3.54094e6	0.808023	0.404011	−	0.914754i	$-0.367616\pi$
$79$	3.54094e6	0.808023	0.404011	+	0.914754i	$0.367616\pi$
$80$	−6.18161e6	−1.34985
$81$	531441.	0.111111
$82$	5.70830e6	1.14330
$83$	9.87483e6	1.89564	0.947821	−	0.318804i	$-0.103281\pi$
$83$	9.87483e6	1.89564	0.947821	+	0.318804i	$0.103281\pi$
$84$	5.90761e6	1.08751
$85$	−3.42656e6	−0.605191
$86$	2.10593e6	0.357026
$87$	−5.43154e6	−0.884311
$88$	3.61122e6	0.564891
$89$	−6.49191e6	−0.976130	−0.488065	−	0.872807i	$-0.662297\pi$
$89$	−6.49191e6	−0.976130	−0.488065	+	0.872807i	$0.662297\pi$
$90$	−1.78335e6	−0.257863
$91$	−558842.	−0.0777399
$92$	1.86047e7	2.49096
$93$	468859.	0.0604439
$94$	5.10459e6	0.633889
$95$	−4.15709e6	−0.497458
$96$	−1.61290e7	−1.86062
$97$	−8435.50	−0.000938447 0	−0.000469223	−	1.00000i	$-0.500149\pi$
$97$	−8435.50	−0.000938447 0	−0.000469223		1.00000i	$0.500149\pi$
$98$	−8.72581e6	−0.936514
$99$	581051.	0.0601854
$100$	−2.20584e7	−2.20584
$101$	3.74750e6	0.361923	0.180962	−	0.983490i	$-0.442079\pi$
$101$	3.74750e6	0.361923	0.180962	+	0.983490i	$0.442079\pi$
$102$	−1.76201e7	−1.64402
$103$	−7.16189e6	−0.645799	−0.322900	−	0.946433i	$-0.604658\pi$
$103$	−7.16189e6	−0.645799	−0.322900	+	0.946433i	$0.604658\pi$
$104$	3.91022e6	0.340867
$105$	−1.98144e6	−0.167039
$106$	−1.13124e7	−0.922539
$107$	−1.89118e7	−1.49242	−0.746208	−	0.665712i	$-0.768128\pi$
$107$	−1.89118e7	−1.49242	−0.746208	+	0.665712i	$0.768128\pi$
$108$	−6.65095e6	−0.508043
$109$	−1.60040e7	−1.18368	−0.591842	−	0.806054i	$-0.701599\pi$
$109$	−1.60040e7	−1.18368	−0.591842	+	0.806054i	$0.701599\pi$
$110$	−1.94983e6	−0.139676
$111$	4.24066e6	0.294309
$112$	−3.53179e7	−2.37537
$113$	−4.77754e6	−0.311480	−0.155740	−	0.987798i	$-0.549776\pi$
$113$	−4.77754e6	−0.311480	−0.155740	+	0.987798i	$0.549776\pi$
$114$	−2.13766e7	−1.35136
$115$	−6.24012e6	−0.382605
$116$	6.79754e7	4.04342
$117$	629160.	0.0363171
$118$	−4.43306e6	−0.248380
$119$	−1.95773e7	−1.06497
$120$	1.38641e7	0.732418
$121$	−1.88519e7	−0.967399
$122$	5.41726e7	2.70097
$123$	−7.14041e6	−0.345983
$124$	−5.86775e6	−0.276373
$125$	1.62528e7	0.744290
$126$	−1.01890e7	−0.453768
$127$	2.70787e7	1.17304	0.586522	−	0.809933i	$-0.300497\pi$
$127$	2.70787e7	1.17304	0.586522	+	0.809933i	$0.300497\pi$
$128$	5.11584e7	2.15617
$129$	−2.63427e6	−0.108043
$130$	−2.11127e6	−0.0842834
$131$	6.72224e6	0.261255	0.130627	−	0.991432i	$-0.458301\pi$
$131$	6.72224e6	0.261255	0.130627	+	0.991432i	$0.458301\pi$
$132$	−7.27182e6	−0.275191
$133$	−2.37510e7	−0.875390
$134$	−4.03262e7	−1.44784
$135$	2.23076e6	0.0780342
$136$	1.36982e8	4.66959
$137$	4.39105e7	1.45897	0.729485	−	0.683997i	$-0.239760\pi$
$137$	4.39105e7	1.45897	0.729485	+	0.683997i	$0.239760\pi$
$138$	−3.20880e7	−1.03936
$139$	8.55233e6	0.270105	0.135052	−	0.990838i	$-0.456880\pi$
$139$	8.55233e6	0.270105	0.135052	+	0.990838i	$0.456880\pi$
$140$	2.47976e7	0.763768
$141$	−6.38523e6	−0.191827
$142$	−6.85256e7	−2.00837
$143$	687893.	0.0196718
$144$	3.97619e7	1.10968
$145$	−2.27993e7	−0.621059
$146$	6.54410e6	0.174026
$147$	1.09149e7	0.283407
$148$	−5.30716e7	−1.34569
$149$	−4.40487e7	−1.09089	−0.545445	−	0.838146i	$-0.683639\pi$
$149$	−4.40487e7	−1.09089	−0.545445	+	0.838146i	$0.683639\pi$
$150$	3.80447e7	0.920395
$151$	−5.79273e7	−1.36919	−0.684596	−	0.728923i	$-0.740021\pi$
$151$	−5.79273e7	−1.36919	−0.684596	+	0.728923i	$0.740021\pi$
$152$	1.66186e8	3.83833
$153$	2.20407e7	0.497513
$154$	−1.11401e7	−0.245792
$155$	1.96807e6	0.0424502
$156$	−7.87391e6	−0.166056
$157$	−6.48864e7	−1.33815	−0.669075	−	0.743195i	$-0.733309\pi$
$157$	−6.48864e7	−1.33815	−0.669075	+	0.743195i	$0.733309\pi$
$158$	7.64304e7	1.54158
$159$	1.41505e7	0.279178
$160$	−6.77025e7	−1.30673
$161$	−3.56522e7	−0.673280
$162$	1.14710e7	0.211983
$163$	6.81238e7	1.23209	0.616045	−	0.787711i	$-0.288734\pi$
$163$	6.81238e7	1.23209	0.616045	+	0.787711i	$0.288734\pi$
$164$	8.93618e7	1.58197
$165$	2.43900e6	0.0422687
$166$	2.13146e8	3.61659
$167$	3.52225e7	0.585210	0.292605	−	0.956233i	$-0.405478\pi$
$167$	3.52225e7	0.585210	0.292605	+	0.956233i	$0.405478\pi$
$168$	7.92112e7	1.28885
$169$	−6.20037e7	−0.988130
$170$	−7.39617e7	−1.15461
$171$	2.67396e7	0.408948
$172$	3.29678e7	0.494015
$173$	−5.35823e7	−0.786792	−0.393396	−	0.919369i	$-0.628700\pi$
$173$	−5.35823e7	−0.786792	−0.393396	+	0.919369i	$0.628700\pi$
$174$	−1.17239e8	−1.68713
$175$	4.22705e7	0.596217
$176$	4.34737e7	0.601080
$177$	5.54523e6	0.0751646
$178$	−1.40127e8	−1.86230
$179$	−1.25733e8	−1.63857	−0.819283	−	0.573390i	$-0.805628\pi$
$179$	−1.25733e8	−1.63857	−0.819283	+	0.573390i	$0.805628\pi$
$180$	−2.79179e7	−0.356803
$181$	6.35900e7	0.797102	0.398551	−	0.917146i	$-0.369513\pi$
$181$	6.35900e7	0.797102	0.398551	+	0.917146i	$0.369513\pi$
$182$	−1.20625e7	−0.148316
$183$	−6.77634e7	−0.817366
$184$	2.49459e8	2.95213
$185$	1.78005e7	0.206695
$186$	1.01202e7	0.115317
$187$	2.40982e7	0.269487
$188$	7.99108e7	0.877108
$189$	1.27452e7	0.137319
$190$	−8.97299e7	−0.949073
$191$	2.21042e7	0.229540	0.114770	−	0.993392i	$-0.463387\pi$
$191$	2.21042e7	0.229540	0.114770	+	0.993392i	$0.463387\pi$
$192$	−1.59639e8	−1.62774
$193$	−2.73971e6	−0.0274318	−0.0137159	−	0.999906i	$-0.504366\pi$
$193$	−2.73971e6	−0.0274318	−0.0137159	+	0.999906i	$0.504366\pi$
$194$	−182078.	−0.00179041
$195$	2.64095e6	0.0255058
$196$	−1.36600e8	−1.29585
$197$	1.45954e7	0.136014	0.0680072	−	0.997685i	$-0.478336\pi$
$197$	1.45954e7	0.136014	0.0680072	+	0.997685i	$0.478336\pi$
$198$	1.25419e7	0.114824
$199$	−1.26330e8	−1.13637	−0.568184	−	0.822901i	$-0.692354\pi$
$199$	−1.26330e8	−1.13637	−0.568184	+	0.822901i	$0.692354\pi$
$200$	−2.95767e8	−2.61424
$201$	5.04433e7	0.438144
$202$	8.08890e7	0.690493
$203$	−1.30261e8	−1.09289
$204$	−2.75838e8	−2.27482
$205$	−2.99724e7	−0.242987
$206$	−1.54588e8	−1.23208
$207$	4.01383e7	0.314530
$208$	4.70732e7	0.362704
$209$	2.92357e7	0.221514
$210$	−4.27690e7	−0.318685
$211$	2.01964e8	1.48008	0.740041	−	0.672562i	$-0.234806\pi$
$211$	2.01964e8	1.48008	0.740041	+	0.672562i	$0.234806\pi$
$212$	−1.77092e8	−1.27651
$213$	8.57173e7	0.607771
$214$	−4.08208e8	−2.84730
$215$	−1.10575e7	−0.0758795
$216$	−8.91782e7	−0.602103
$217$	1.12443e7	0.0747007
$218$	−3.45443e8	−2.25829
$219$	−8.18588e6	−0.0526637
$220$	−3.05240e7	−0.193269
$221$	2.60934e7	0.162614
$222$	9.15337e7	0.561495
$223$	−2.44131e8	−1.47420	−0.737100	−	0.675784i	$-0.763805\pi$
$223$	−2.44131e8	−1.47420	−0.737100	+	0.675784i	$0.763805\pi$
$224$	−3.86810e8	−2.29948
$225$	−4.75893e7	−0.278529
$226$	−1.03122e8	−0.594255
$227$	6.69826e7	0.380077	0.190038	−	0.981777i	$-0.439139\pi$
$227$	6.69826e7	0.380077	0.190038	+	0.981777i	$0.439139\pi$
$228$	−3.34644e8	−1.86987
$229$	−5.42627e6	−0.0298591	−0.0149296	−	0.999889i	$-0.504752\pi$
$229$	−5.42627e6	−0.0298591	−0.0149296	+	0.999889i	$0.504752\pi$
$230$	−1.34692e8	−0.729951
$231$	1.39350e7	0.0743813
$232$	9.11436e8	4.79202
$233$	−1.14071e8	−0.590784	−0.295392	−	0.955376i	$-0.595450\pi$
$233$	−1.14071e8	−0.590784	−0.295392	+	0.955376i	$0.595450\pi$
$234$	1.35803e7	0.0692873
$235$	−2.68025e7	−0.134722
$236$	−6.93983e7	−0.343682
$237$	−9.56053e7	−0.466512
$238$	−4.22571e8	−2.03180
$239$	2.35111e8	1.11399	0.556993	−	0.830517i	$-0.311955\pi$
$239$	2.35111e8	1.11399	0.556993	+	0.830517i	$0.311955\pi$
$240$	1.66903e8	0.779338
$241$	−2.14221e8	−0.985830	−0.492915	−	0.870078i	$-0.664069\pi$
$241$	−2.14221e8	−0.985830	−0.492915	+	0.870078i	$0.664069\pi$
$242$	−4.06914e8	−1.84565
$243$	−1.43489e7	−0.0641500
$244$	8.48055e8	3.73732
$245$	4.58163e7	0.199039
$246$	−1.54124e8	−0.660082
$247$	3.16564e7	0.133666
$248$	−7.86767e7	−0.327541
$249$	−2.66620e8	−1.09445
$250$	3.50813e8	1.41999
$251$	−1.53834e8	−0.614036	−0.307018	−	0.951704i	$-0.599331\pi$
$251$	−1.53834e8	−0.614036	−0.307018	+	0.951704i	$0.599331\pi$
$252$	−1.59505e8	−0.627875
$253$	4.38852e7	0.170371
$254$	5.84488e8	2.23799
$255$	9.25173e7	0.349407
$256$	3.47435e8	1.29430
$257$	4.74131e8	1.74234	0.871169	−	0.490984i	$-0.163363\pi$
$257$	4.74131e8	1.74234	0.871169	+	0.490984i	$0.163363\pi$
$258$	−5.68602e7	−0.206129
$259$	1.01701e8	0.363727
$260$	−3.30513e7	−0.116622
$261$	1.46651e8	0.510557
$262$	1.45098e8	0.498434
$263$	−1.50757e8	−0.511014	−0.255507	−	0.966807i	$-0.582242\pi$
$263$	−1.50757e8	−0.511014	−0.255507	+	0.966807i	$0.582242\pi$
$264$	−9.75030e7	−0.326140
$265$	5.93977e7	0.196069
$266$	−5.12661e8	−1.67011
$267$	1.75282e8	0.563569
$268$	−6.31295e8	−2.00337
$269$	5.50062e8	1.72297	0.861486	−	0.507781i	$-0.169534\pi$
$269$	5.50062e8	1.72297	0.861486	+	0.507781i	$0.169534\pi$
$270$	4.81505e7	0.148877
$271$	4.96505e8	1.51541	0.757707	−	0.652595i	$-0.226319\pi$
$271$	4.96505e8	1.51541	0.757707	+	0.652595i	$0.226319\pi$
$272$	1.64906e9	4.96873
$273$	1.50887e7	0.0448832
$274$	9.47799e8	2.78349
$275$	−5.20318e7	−0.150871
$276$	−5.02328e8	−1.43815
$277$	1.08273e8	0.306083	0.153041	−	0.988220i	$-0.451093\pi$
$277$	1.08273e8	0.306083	0.153041	+	0.988220i	$0.451093\pi$
$278$	1.84600e8	0.515318
$279$	−1.26592e7	−0.0348973
$280$	3.32495e8	0.905173
$281$	−6.35664e8	−1.70905	−0.854527	−	0.519407i	$-0.826153\pi$
$281$	−6.35664e8	−1.70905	−0.854527	+	0.519407i	$0.826153\pi$
$282$	−1.37824e8	−0.365976
$283$	1.82266e8	0.478027	0.239014	−	0.971016i	$-0.423176\pi$
$283$	1.82266e8	0.478027	0.239014	+	0.971016i	$0.423176\pi$
$284$	−1.07275e9	−2.77897
$285$	1.12241e8	0.287208
$286$	1.48480e7	0.0375308
$287$	−1.71244e8	−0.427590
$288$	4.35482e8	1.07423
$289$	5.03762e8	1.22767
$290$	−4.92117e8	−1.18488
$291$	227758.	0.000541812 0
$292$	1.02446e8	0.240799
$293$	−2.94539e8	−0.684080	−0.342040	−	0.939685i	$-0.611118\pi$
$293$	−2.94539e8	−0.684080	−0.342040	+	0.939685i	$0.611118\pi$
$294$	2.35597e8	0.540697
$295$	2.32765e7	0.0527887
$296$	−7.11602e8	−1.59484
$297$	−1.56884e7	−0.0347481
$298$	−9.50782e8	−2.08125
$299$	4.75187e7	0.102805
$300$	5.95578e8	1.27354
$301$	−6.31760e7	−0.133527
$302$	−1.25035e9	−2.61220
$303$	−1.01182e8	−0.208957
$304$	2.00063e9	4.08422
$305$	−2.84442e8	−0.574042
$306$	4.75743e8	0.949178
$307$	−6.80308e8	−1.34190	−0.670952	−	0.741501i	$-0.734114\pi$
$307$	−6.80308e8	−1.34190	−0.670952	+	0.741501i	$0.734114\pi$
$308$	−1.74395e8	−0.340100
$309$	1.93371e8	0.372852
$310$	4.24804e7	0.0809884
$311$	−1.83957e8	−0.346780	−0.173390	−	0.984853i	$-0.555472\pi$
$311$	−1.83957e8	−0.346780	−0.173390	+	0.984853i	$0.555472\pi$
$312$	−1.05576e8	−0.196800
$313$	−4.45917e8	−0.821956	−0.410978	−	0.911645i	$-0.634813\pi$
$313$	−4.45917e8	−0.821956	−0.410978	+	0.911645i	$0.634813\pi$
$314$	−1.40056e9	−2.55298
$315$	5.34989e7	0.0964401
$316$	1.19650e9	2.13308
$317$	−5.41308e8	−0.954414	−0.477207	−	0.878791i	$-0.658351\pi$
$317$	−5.41308e8	−0.954414	−0.477207	+	0.878791i	$0.658351\pi$
$318$	3.05435e8	0.532628
$319$	1.60341e8	0.276553
$320$	−6.70098e8	−1.14318
$321$	5.10619e8	0.861647
$322$	−7.69545e8	−1.28451
$323$	1.10898e9	1.83111
$324$	1.79576e8	0.293319
$325$	−5.63399e7	−0.0910383
$326$	1.47044e9	2.35063
$327$	4.32108e8	0.683401
$328$	1.19819e9	1.87486
$329$	−1.53133e8	−0.237073
$330$	5.26454e7	0.0806420
$331$	3.83779e7	0.0581679	0.0290839	−	0.999577i	$-0.490741\pi$
$331$	3.83779e7	0.0581679	0.0290839	+	0.999577i	$0.490741\pi$
$332$	3.33674e9	5.00425
$333$	−1.14498e8	−0.169919
$334$	7.60270e8	1.11649
$335$	2.11739e8	0.307712
$336$	9.53583e8	1.37142
$337$	8.56217e8	1.21865	0.609325	−	0.792920i	$-0.291440\pi$
$337$	8.56217e8	1.21865	0.609325	+	0.792920i	$0.291440\pi$
$338$	−1.33834e9	−1.88520
$339$	1.28994e8	0.179833
$340$	−1.15785e9	−1.59763
$341$	−1.38409e7	−0.0189028
$342$	5.77169e8	0.780210
$343$	7.95029e8	1.06378
$344$	4.42043e8	0.585477
$345$	1.68483e8	0.220897
$346$	−1.15656e9	−1.50108
$347$	−2.36529e8	−0.303901	−0.151950	−	0.988388i	$-0.548555\pi$
$347$	−2.36529e8	−0.303901	−0.151950	+	0.988388i	$0.548555\pi$
$348$	−1.83533e9	−2.33447
$349$	−2.69181e8	−0.338966	−0.169483	−	0.985533i	$-0.554210\pi$
$349$	−2.69181e8	−0.338966	−0.169483	+	0.985533i	$0.554210\pi$
$350$	9.12400e8	1.13749
$351$	−1.69873e7	−0.0209677
$352$	4.76134e8	0.581875
$353$	−4.00304e8	−0.484371	−0.242186	−	0.970230i	$-0.577864\pi$
$353$	−4.00304e8	−0.484371	−0.242186	+	0.970230i	$0.577864\pi$
$354$	1.19693e8	0.143402
$355$	3.59805e8	0.426842
$356$	−2.19364e9	−2.57686
$357$	5.28586e8	0.614861
$358$	−2.71392e9	−3.12613
$359$	−6.09817e8	−0.695615	−0.347808	−	0.937566i	$-0.613074\pi$
$359$	−6.09817e8	−0.695615	−0.347808	+	0.937566i	$0.613074\pi$
$360$	−3.74332e8	−0.422862
$361$	4.51538e8	0.505149
$362$	1.37258e9	1.52075
$363$	5.09001e8	0.558528
$364$	−1.88835e8	−0.205223
$365$	−3.43608e7	−0.0369861
$366$	−1.46266e9	−1.55941
$367$	−3.65526e8	−0.386000	−0.193000	−	0.981199i	$-0.561822\pi$
$367$	−3.65526e8	−0.386000	−0.193000	+	0.981199i	$0.561822\pi$
$368$	3.00311e9	3.14126
$369$	1.92791e8	0.199754
$370$	3.84219e8	0.394342
$371$	3.39361e8	0.345028
$372$	1.58429e8	0.159564
$373$	−1.64569e9	−1.64198	−0.820990	−	0.570942i	$-0.806578\pi$
$373$	−1.64569e9	−1.64198	−0.820990	+	0.570942i	$0.806578\pi$
$374$	5.20154e8	0.514140
$375$	−4.38825e8	−0.429716
$376$	1.07147e9	1.03950
$377$	1.73617e8	0.166878
$378$	2.75102e8	0.261983
$379$	1.32916e9	1.25412	0.627062	−	0.778969i	$-0.284257\pi$
$379$	1.32916e9	1.25412	0.627062	+	0.778969i	$0.284257\pi$
$380$	−1.40469e9	−1.31323
$381$	−7.31124e8	−0.677257
$382$	4.77115e8	0.437927
$383$	1.43631e9	1.30633	0.653163	−	0.757217i	$-0.273442\pi$
$383$	1.43631e9	1.30633	0.653163	+	0.757217i	$0.273442\pi$
$384$	−1.38128e9	−1.24486
$385$	5.84930e7	0.0522386
$386$	−5.91360e7	−0.0523355
$387$	7.11254e7	0.0623787
$388$	−2.85038e6	−0.00247738
$389$	1.62608e9	1.40062	0.700309	−	0.713840i	$-0.253046\pi$
$389$	1.62608e9	1.40062	0.700309	+	0.713840i	$0.253046\pi$
$390$	5.70043e7	0.0486610
$391$	1.66467e9	1.40835
$392$	−1.83158e9	−1.53576
$393$	−1.81500e8	−0.150836
$394$	3.15039e8	0.259494
$395$	−4.01310e8	−0.327635
$396$	1.96339e8	0.158882
$397$	1.66052e9	1.33192	0.665958	−	0.745989i	$-0.268023\pi$
$397$	1.66052e9	1.33192	0.665958	+	0.745989i	$0.268023\pi$
$398$	−2.72680e9	−2.16802
$399$	6.41278e8	0.505407
$400$	−3.56059e9	−2.78171
$401$	1.65806e9	1.28409	0.642045	−	0.766667i	$-0.278086\pi$
$401$	1.65806e9	1.28409	0.642045	+	0.766667i	$0.278086\pi$
$402$	1.08881e9	0.835911
$403$	−1.49869e7	−0.0114063
$404$	1.26629e9	0.955431
$405$	−6.02306e7	−0.0450531
$406$	−2.81165e9	−2.08507
$407$	−1.25186e8	−0.0920398
$408$	−3.69852e9	−2.69599
$409$	2.60200e9	1.88051	0.940256	−	0.340468i	$-0.110585\pi$
$409$	2.60200e9	1.88051	0.940256	+	0.340468i	$0.110585\pi$
$410$	−6.46947e8	−0.463581
$411$	−1.18558e9	−0.842337
$412$	−2.42003e9	−1.70483
$413$	1.32988e8	0.0928936
$414$	8.66376e8	0.600075
$415$	−1.11916e9	−0.768640
$416$	5.15557e8	0.351115
$417$	−2.30913e8	−0.155945
$418$	6.31047e8	0.422615
$419$	−1.66480e9	−1.10564	−0.552819	−	0.833302i	$-0.686448\pi$
$419$	−1.66480e9	−1.10564	−0.552819	+	0.833302i	$0.686448\pi$
$420$	−6.69535e8	−0.440962
$421$	2.00138e9	1.30720	0.653601	−	0.756839i	$-0.273257\pi$
$421$	2.00138e9	1.30720	0.653601	+	0.756839i	$0.273257\pi$
$422$	4.35936e9	2.82377
$423$	1.72401e8	0.110751
$424$	−2.37451e9	−1.51284
$425$	−1.97369e9	−1.24715
$426$	1.85019e9	1.15953
$427$	−1.62512e9	−1.01016
$428$	−6.39037e9	−3.93979
$429$	−1.85731e7	−0.0113575
$430$	−2.38675e8	−0.144766
$431$	4.72430e8	0.284228	0.142114	−	0.989850i	$-0.454610\pi$
$431$	4.72430e8	0.284228	0.142114	+	0.989850i	$0.454610\pi$
$432$	−1.07357e9	−0.640675
$433$	6.77203e8	0.400877	0.200439	−	0.979706i	$-0.435763\pi$
$433$	6.77203e8	0.400877	0.200439	+	0.979706i	$0.435763\pi$
$434$	2.42707e8	0.142517
$435$	6.15580e8	0.358568
$436$	−5.40781e9	−3.12477
$437$	2.01957e9	1.15764
$438$	−1.76691e8	−0.100474
$439$	1.96136e9	1.10645	0.553224	−	0.833033i	$-0.313397\pi$
$439$	1.96136e9	1.10645	0.553224	+	0.833033i	$0.313397\pi$
$440$	−4.09276e8	−0.229051
$441$	−2.94703e8	−0.163625
$442$	5.63221e8	0.310242
$443$	7.15483e7	0.0391008	0.0195504	−	0.999809i	$-0.493777\pi$
$443$	7.15483e7	0.0391008	0.0195504	+	0.999809i	$0.493777\pi$
$444$	1.43293e9	0.776936
$445$	7.35757e8	0.395799
$446$	−5.26952e9	−2.81254
$447$	1.18932e9	0.629826
$448$	−3.82853e9	−2.01168
$449$	−2.36841e9	−1.23479	−0.617397	−	0.786652i	$-0.711813\pi$
$449$	−2.36841e9	−1.23479	−0.617397	+	0.786652i	$0.711813\pi$
$450$	−1.02721e9	−0.531391
$451$	2.10788e8	0.108200
$452$	−1.61435e9	−0.822266
$453$	1.56404e9	0.790503
$454$	1.44580e9	0.725127
$455$	6.33360e7	0.0315218
$456$	−4.48703e9	−2.21606
$457$	9.23556e8	0.452644	0.226322	−	0.974053i	$-0.427330\pi$
$457$	9.23556e8	0.452644	0.226322	+	0.974053i	$0.427330\pi$
$458$	−1.17125e8	−0.0569666
$459$	−5.95098e8	−0.287239
$460$	−2.10856e9	−1.01003
$461$	−2.95040e8	−0.140258	−0.0701289	−	0.997538i	$-0.522341\pi$
$461$	−2.95040e8	−0.140258	−0.0701289	+	0.997538i	$0.522341\pi$
$462$	3.00783e8	0.141908
$463$	2.57536e9	1.20588	0.602940	−	0.797787i	$-0.293996\pi$
$463$	2.57536e9	1.20588	0.602940	+	0.797787i	$0.293996\pi$
$464$	1.09723e10	5.09901
$465$	−5.31379e7	−0.0245086
$466$	−2.46219e9	−1.12712
$467$	−9.62315e8	−0.437228	−0.218614	−	0.975811i	$-0.570154\pi$
$467$	−9.62315e8	−0.437228	−0.218614	+	0.975811i	$0.570154\pi$
$468$	2.12595e8	0.0958724
$469$	1.20975e9	0.541489
$470$	−5.78526e8	−0.257028
$471$	1.75193e9	0.772581
$472$	−9.30515e8	−0.407311
$473$	7.77649e7	0.0337886
$474$	−2.06362e9	−0.890032
$475$	−2.39447e9	−1.02514
$476$	−6.61523e9	−2.81139
$477$	−3.82063e8	−0.161184
$478$	5.07482e9	2.12531
$479$	−1.04097e9	−0.432777	−0.216389	−	0.976307i	$-0.569428\pi$
$479$	−1.04097e9	−0.432777	−0.216389	+	0.976307i	$0.569428\pi$
$480$	1.82797e9	0.754439
$481$	−1.35551e8	−0.0555387
$482$	−4.62391e9	−1.88081
$483$	9.62609e8	0.388718
$484$	−6.37011e9	−2.55381
$485$	956032.	0.000380519 0
$486$	−3.09718e8	−0.122388
$487$	1.54301e9	0.605365	0.302683	−	0.953091i	$-0.402118\pi$
$487$	1.54301e9	0.605365	0.302683	+	0.953091i	$0.402118\pi$
$488$	1.13710e10	4.42924
$489$	−1.83934e9	−0.711347
$490$	9.88934e8	0.379736
$491$	8.27706e8	0.315566	0.157783	−	0.987474i	$-0.449565\pi$
$491$	8.27706e8	0.315566	0.157783	+	0.987474i	$0.449565\pi$
$492$	−2.41277e9	−0.913351
$493$	6.08213e9	2.28608
$494$	6.83296e8	0.255014
$495$	−6.58531e7	−0.0244038
$496$	−9.47149e8	−0.348524
$497$	2.05570e9	0.751126
$498$	−5.75494e9	−2.08804
$499$	−5.08912e9	−1.83354	−0.916771	−	0.399413i	$-0.869214\pi$
$499$	−5.08912e9	−1.83354	−0.916771	+	0.399413i	$0.869214\pi$
$500$	5.49186e9	1.96483
$501$	−9.51006e8	−0.337871
$502$	−3.32047e9	−1.17149
$503$	1.24283e9	0.435434	0.217717	−	0.976012i	$-0.430139\pi$
$503$	1.24283e9	0.435434	0.217717	+	0.976012i	$0.430139\pi$
$504$	−2.13870e9	−0.744120
$505$	−4.24721e8	−0.146752
$506$	9.47252e8	0.325042
$507$	1.67410e9	0.570497
$508$	9.14997e9	3.09668
$509$	−3.51527e9	−1.18154	−0.590768	−	0.806842i	$-0.701175\pi$
$509$	−3.51527e9	−1.18154	−0.590768	+	0.806842i	$0.701175\pi$
$510$	1.99697e9	0.666615
$511$	−1.96317e8	−0.0650854
$512$	9.51036e8	0.313150
$513$	−7.21969e8	−0.236106
$514$	1.02340e10	3.32411
$515$	8.11689e8	0.261857
$516$	−8.90130e8	−0.285220
$517$	1.88495e8	0.0599905
$518$	2.19519e9	0.693934
$519$	1.44672e9	0.454255
$520$	−4.43163e8	−0.138214
$521$	−4.15959e9	−1.28860	−0.644301	−	0.764772i	$-0.722852\pi$
$521$	−4.15959e9	−1.28860	−0.644301	+	0.764772i	$0.722852\pi$
$522$	3.16544e9	0.974064
$523$	−9.27018e8	−0.283356	−0.141678	−	0.989913i	$-0.545250\pi$
$523$	−9.27018e8	−0.283356	−0.141678	+	0.989913i	$0.545250\pi$
$524$	2.27147e9	0.689679
$525$	−1.14130e9	−0.344226
$526$	−3.25406e9	−0.974936
$527$	−5.25020e8	−0.156257
$528$	−1.17379e9	−0.347034
$529$	−3.73295e8	−0.109637
$530$	1.28209e9	0.374069
$531$	−1.49721e8	−0.0433963
$532$	−8.02555e9	−2.31092
$533$	2.28241e8	0.0652902
$534$	3.78342e9	1.07520
$535$	2.14336e9	0.605142
$536$	−8.46461e9	−2.37427
$537$	3.39479e9	0.946026
$538$	1.18730e10	3.28716
$539$	−3.22214e8	−0.0886306
$540$	7.53782e8	0.206000
$541$	−6.33596e9	−1.72037	−0.860186	−	0.509981i	$-0.829652\pi$
$541$	−6.33596e9	−1.72037	−0.860186	+	0.509981i	$0.829652\pi$
$542$	1.07170e10	2.89118
$543$	−1.71693e9	−0.460207
$544$	1.80609e10	4.80998
$545$	1.81381e9	0.479958
$546$	3.25687e8	0.0856301
$547$	2.00352e9	0.523406	0.261703	−	0.965148i	$-0.415716\pi$
$547$	2.00352e9	0.523406	0.261703	+	0.965148i	$0.415716\pi$
$548$	1.48375e10	3.85149
$549$	1.82961e9	0.471906
$550$	−1.12310e9	−0.287838
$551$	7.37881e9	1.87912
$552$	−6.73538e9	−1.70442
$553$	−2.29284e9	−0.576548
$554$	2.33704e9	0.583959
$555$	−4.80613e8	−0.119336
$556$	2.88986e9	0.713042
$557$	−4.93285e9	−1.20950	−0.604748	−	0.796417i	$-0.706726\pi$
$557$	−4.93285e9	−1.20950	−0.604748	+	0.796417i	$0.706726\pi$
$558$	−2.73246e8	−0.0665786
$559$	8.42036e7	0.0203887
$560$	4.00273e9	0.963160
$561$	−6.50650e8	−0.155589
$562$	−1.37207e10	−3.26061
$563$	4.64054e9	1.09595	0.547973	−	0.836496i	$-0.315400\pi$
$563$	4.64054e9	1.09595	0.547973	+	0.836496i	$0.315400\pi$
$564$	−2.15759e9	−0.506398
$565$	5.41460e8	0.126298
$566$	3.93417e9	0.912001
$567$	−3.44120e8	−0.0792811
$568$	−1.43838e10	−3.29347
$569$	−4.82571e9	−1.09817	−0.549083	−	0.835768i	$-0.685023\pi$
$569$	−4.82571e9	−1.09817	−0.549083	+	0.835768i	$0.685023\pi$
$570$	2.42271e9	0.547947
$571$	−6.84565e9	−1.53882	−0.769410	−	0.638755i	$-0.779450\pi$
$571$	−6.84565e9	−1.53882	−0.769410	+	0.638755i	$0.779450\pi$
$572$	2.32441e8	0.0519310
$573$	−5.96814e8	−0.132525
$574$	−3.69626e9	−0.815775
$575$	−3.59429e9	−0.788453
$576$	4.31026e9	0.939778
$577$	−3.78107e9	−0.819407	−0.409704	−	0.912219i	$-0.634368\pi$
$577$	−3.78107e9	−0.819407	−0.409704	+	0.912219i	$0.634368\pi$
$578$	1.08736e10	2.34221
$579$	7.39721e7	0.0158377
$580$	−7.70395e9	−1.63951
$581$	−6.39418e9	−1.35260
$582$	4.91612e6	0.00103369
$583$	−4.17729e8	−0.0873080
$584$	1.37363e9	0.285381
$585$	−7.13055e7	−0.0147258
$586$	−6.35757e9	−1.30512
$587$	4.65957e9	0.950852	0.475426	−	0.879756i	$-0.342294\pi$
$587$	4.65957e9	0.950852	0.475426	+	0.879756i	$0.342294\pi$
$588$	3.68820e9	0.748158
$589$	−6.36951e8	−0.128441
$590$	5.02419e8	0.100713
$591$	−3.94076e8	−0.0785279
$592$	−8.56661e9	−1.69701
$593$	−7.46187e9	−1.46945	−0.734727	−	0.678363i	$-0.762690\pi$
$593$	−7.46187e9	−1.46945	−0.734727	+	0.678363i	$0.762690\pi$
$594$	−3.38630e8	−0.0662939
$595$	2.21878e9	0.431822
$596$	−1.48842e10	−2.87981
$597$	3.41090e9	0.656083
$598$	1.02568e9	0.196137
$599$	−4.56957e9	−0.868723	−0.434362	−	0.900739i	$-0.643026\pi$
$599$	−4.56957e9	−0.868723	−0.434362	+	0.900739i	$0.643026\pi$
$600$	7.98571e9	1.50933
$601$	−3.26243e9	−0.613028	−0.306514	−	0.951866i	$-0.599163\pi$
$601$	−3.26243e9	−0.613028	−0.306514	+	0.951866i	$0.599163\pi$
$602$	−1.36364e9	−0.254749
$603$	−1.36197e9	−0.252963
$604$	−1.95738e10	−3.61449
$605$	2.13657e9	0.392259
$606$	−2.18400e9	−0.398657
$607$	7.83444e9	1.42183	0.710915	−	0.703278i	$-0.248281\pi$
$607$	7.83444e9	1.42183	0.710915	+	0.703278i	$0.248281\pi$
$608$	2.19114e10	3.95373
$609$	3.51704e9	0.630982
$610$	−6.13962e9	−1.09518
$611$	2.04102e8	0.0361995
$612$	7.44761e9	1.31337
$613$	1.83847e9	0.322363	0.161181	−	0.986925i	$-0.448470\pi$
$613$	1.83847e9	0.322363	0.161181	+	0.986925i	$0.448470\pi$
$614$	−1.46843e10	−2.56014
$615$	8.09254e8	0.140288
$616$	−2.33835e9	−0.403067
$617$	−7.28601e9	−1.24880	−0.624399	−	0.781106i	$-0.714656\pi$
$617$	−7.28601e9	−1.24880	−0.624399	+	0.781106i	$0.714656\pi$
$618$	4.17388e9	0.711344
$619$	2.62525e8	0.0444891	0.0222446	−	0.999753i	$-0.492919\pi$
$619$	2.62525e8	0.0444891	0.0222446	+	0.999753i	$0.492919\pi$
$620$	6.65018e8	0.112063
$621$	−1.08373e9	−0.181594
$622$	−3.97067e9	−0.661603
$623$	4.20366e9	0.696497
$624$	−1.27098e9	−0.209407
$625$	3.25803e9	0.533795
$626$	−9.62502e9	−1.56816
$627$	−7.89365e8	−0.127891
$628$	−2.19253e10	−3.53254
$629$	−4.74861e9	−0.760833
$630$	1.15476e9	0.183993
$631$	1.62131e9	0.256899	0.128450	−	0.991716i	$-0.459000\pi$
$631$	1.62131e9	0.256899	0.128450	+	0.991716i	$0.459000\pi$
$632$	1.60430e10	2.52799
$633$	−5.45303e9	−0.854526
$634$	−1.16840e10	−1.82087
$635$	−3.06895e9	−0.475643
$636$	4.78150e9	0.736994
$637$	−3.48892e8	−0.0534815
$638$	3.46094e9	0.527620
$639$	−2.31437e9	−0.350897
$640$	−5.79801e9	−0.874277
$641$	1.50371e9	0.225508	0.112754	−	0.993623i	$-0.464033\pi$
$641$	1.50371e9	0.225508	0.112754	+	0.993623i	$0.464033\pi$
$642$	1.10216e10	1.64389
$643$	7.26580e9	1.07782	0.538908	−	0.842365i	$-0.318837\pi$
$643$	7.26580e9	1.07782	0.538908	+	0.842365i	$0.318837\pi$
$644$	−1.20470e10	−1.77737
$645$	2.98554e8	0.0438090
$646$	2.39371e10	3.49348
$647$	−1.31988e10	−1.91588	−0.957942	−	0.286962i	$-0.907355\pi$
$647$	−1.31988e10	−1.91588	−0.957942	+	0.286962i	$0.907355\pi$
$648$	2.40781e9	0.347624
$649$	−1.63698e8	−0.0235064
$650$	−1.21609e9	−0.173687
$651$	−3.03597e8	−0.0431285
$652$	2.30193e10	3.25256
$653$	−1.08050e10	−1.51855	−0.759276	−	0.650768i	$-0.774447\pi$
$653$	−1.08050e10	−1.51855	−0.759276	+	0.650768i	$0.774447\pi$
$654$	9.32697e9	1.30382
$655$	−7.61861e8	−0.105933
$656$	1.44244e10	1.99497
$657$	2.21019e8	0.0304054
$658$	−3.30534e9	−0.452299
$659$	−1.38422e10	−1.88411	−0.942053	−	0.335464i	$-0.891107\pi$
$659$	−1.38422e10	−1.88411	−0.942053	+	0.335464i	$0.891107\pi$
$660$	8.24148e8	0.111584
$661$	1.08222e10	1.45751	0.728756	−	0.684773i	$-0.240099\pi$
$661$	1.08222e10	1.45751	0.728756	+	0.684773i	$0.240099\pi$
$662$	8.28379e8	0.110975
$663$	−7.04522e8	−0.0938852
$664$	4.47401e10	5.93074
$665$	2.69181e9	0.354951
$666$	−2.47141e9	−0.324179
$667$	1.10762e10	1.44527
$668$	1.19018e10	1.54488
$669$	6.59154e9	0.851130
$670$	4.57035e9	0.587067
$671$	2.00041e9	0.255617
$672$	1.04439e10	1.32761
$673$	−7.77779e9	−0.983566	−0.491783	−	0.870718i	$-0.663655\pi$
$673$	−7.77779e9	−0.983566	−0.491783	+	0.870718i	$0.663655\pi$
$674$	1.84813e10	2.32500
$675$	1.28491e9	0.160809
$676$	−2.09513e10	−2.60853
$677$	−9.88602e9	−1.22451	−0.612253	−	0.790662i	$-0.709737\pi$
$677$	−9.88602e9	−1.22451	−0.612253	+	0.790662i	$0.709737\pi$
$678$	2.78430e9	0.343093
$679$	5.46218e6	0.000669610 0
$680$	−1.55248e10	−1.89341
$681$	−1.80853e9	−0.219437
$682$	−2.98754e8	−0.0360635
$683$	1.44552e10	1.73601	0.868003	−	0.496559i	$-0.165403\pi$
$683$	1.44552e10	1.73601	0.868003	+	0.496559i	$0.165403\pi$
$684$	9.03540e9	1.07957
$685$	−4.97657e9	−0.591580
$686$	1.71605e10	2.02953
$687$	1.46509e8	0.0172392
$688$	5.32153e9	0.622984
$689$	−4.52315e8	−0.0526834
$690$	3.63668e9	0.421437
$691$	−9.78421e9	−1.12811	−0.564056	−	0.825736i	$-0.690760\pi$
$691$	−9.78421e9	−1.12811	−0.564056	+	0.825736i	$0.690760\pi$
$692$	−1.81056e10	−2.07703
$693$	−3.76244e8	−0.0429441
$694$	−5.10544e9	−0.579795
$695$	−9.69273e8	−0.109521
$696$	−2.46088e10	−2.76667
$697$	7.99570e9	0.894420
$698$	−5.81022e9	−0.646694
$699$	3.07991e9	0.341089
$700$	1.42833e10	1.57393
$701$	−1.39642e7	−0.00153110	−0.000765548	−	1.00000i	$-0.500244\pi$
$701$	−1.39642e7	−0.00153110	−0.000765548		1.00000i	$0.500244\pi$
$702$	−3.66668e8	−0.0400031
$703$	−5.76099e9	−0.625393
$704$	4.71263e9	0.509048
$705$	7.23667e8	0.0777815
$706$	−8.64047e9	−0.924105
$707$	−2.42659e9	−0.258243
$708$	1.87375e9	0.198425
$709$	1.10083e10	1.16000	0.580002	−	0.814615i	$-0.303052\pi$
$709$	1.10083e10	1.16000	0.580002	+	0.814615i	$0.303052\pi$
$710$	7.76631e9	0.814349
$711$	2.58134e9	0.269341
$712$	−2.94130e10	−3.05394
$713$	−9.56114e8	−0.0987862
$714$	1.14094e10	1.17306
$715$	−7.79619e7	−0.00797648
$716$	−4.24856e10	−4.32560
$717$	−6.34799e9	−0.643161
$718$	−1.31628e10	−1.32713
$719$	−1.00251e10	−1.00586	−0.502932	−	0.864326i	$-0.667746\pi$
$719$	−1.00251e10	−1.00586	−0.502932	+	0.864326i	$0.667746\pi$
$720$	−4.50639e9	−0.449951
$721$	4.63749e9	0.460797
$722$	9.74636e9	0.963745
$723$	5.78396e9	0.569169
$724$	2.14873e10	2.10425
$725$	−1.31323e10	−1.27985
$726$	1.09867e10	1.06559
$727$	1.36958e9	0.132195	0.0660977	−	0.997813i	$-0.478945\pi$
$727$	1.36958e9	0.132195	0.0660977	+	0.997813i	$0.478945\pi$
$728$	−2.53196e9	−0.243219
$729$	3.87420e8	0.0370370
$730$	−7.41672e8	−0.0705637
$731$	2.94981e9	0.279308
$732$	−2.28975e10	−2.15774
$733$	−2.47923e9	−0.232516	−0.116258	−	0.993219i	$-0.537090\pi$
$733$	−2.47923e9	−0.232516	−0.116258	+	0.993219i	$0.537090\pi$
$734$	−7.88981e9	−0.736428
$735$	−1.23704e9	−0.114915
$736$	3.28907e10	3.04089
$737$	−1.48911e9	−0.137022
$738$	4.16135e9	0.381099
$739$	−4.61946e9	−0.421052	−0.210526	−	0.977588i	$-0.567518\pi$
$739$	−4.61946e9	−0.421052	−0.210526	+	0.977588i	$0.567518\pi$
$740$	6.01484e9	0.545649
$741$	−8.54722e8	−0.0771723
$742$	7.32505e9	0.658259
$743$	−1.55272e10	−1.38878	−0.694389	−	0.719600i	$-0.744325\pi$
$743$	−1.55272e10	−1.38878	−0.694389	+	0.719600i	$0.744325\pi$
$744$	2.12427e9	0.189106
$745$	4.99224e9	0.442332
$746$	−3.55220e10	−3.13264
$747$	7.19875e9	0.631880
$748$	8.14285e9	0.711411
$749$	1.22458e10	1.06488
$750$	−9.47194e9	−0.819831
$751$	−5.50391e9	−0.474167	−0.237084	−	0.971489i	$-0.576192\pi$
$751$	−5.50391e9	−0.474167	−0.237084	+	0.971489i	$0.576192\pi$
$752$	1.28989e10	1.10609
$753$	4.15352e9	0.354514
$754$	3.74749e9	0.318376
$755$	6.56516e9	0.555177
$756$	4.30664e9	0.362504
$757$	−1.57056e10	−1.31589	−0.657946	−	0.753065i	$-0.728574\pi$
$757$	−1.57056e10	−1.31589	−0.657946	+	0.753065i	$0.728574\pi$
$758$	2.86897e10	2.39268
$759$	−1.18490e9	−0.0983638
$760$	−1.88346e10	−1.55636
$761$	−1.80765e10	−1.48685	−0.743427	−	0.668817i	$-0.766801\pi$
$761$	−1.80765e10	−1.48685	−0.743427	+	0.668817i	$0.766801\pi$
$762$	−1.57812e10	−1.29210
$763$	1.03630e10	0.844594
$764$	7.46910e9	0.605956
$765$	−2.49797e9	−0.201730
$766$	3.10024e10	2.49227
$767$	−1.77251e8	−0.0141842
$768$	−9.38075e9	−0.747262
$769$	−1.35958e10	−1.07811	−0.539053	−	0.842272i	$-0.681218\pi$
$769$	−1.35958e10	−1.07811	−0.539053	+	0.842272i	$0.681218\pi$
$770$	1.26256e9	0.0996630
$771$	−1.28015e10	−1.00594
$772$	−9.25757e8	−0.0724163
$773$	1.25983e9	0.0981032	0.0490516	−	0.998796i	$-0.484380\pi$
$773$	1.25983e9	0.0981032	0.0490516	+	0.998796i	$0.484380\pi$
$774$	1.53523e9	0.119009
$775$	1.13360e9	0.0874792
$776$	−3.82189e7	−0.00293604
$777$	−2.74592e9	−0.209998
$778$	3.50987e10	2.67216
$779$	9.70033e9	0.735200
$780$	8.92385e8	0.0673319
$781$	−2.53041e9	−0.190070
$782$	3.59316e10	2.68691
$783$	−3.95959e9	−0.294770
$784$	−2.20494e10	−1.63415
$785$	7.35386e9	0.542590
$786$	−3.91765e9	−0.287771
$787$	1.93512e10	1.41513	0.707566	−	0.706647i	$-0.249793\pi$
$787$	1.93512e10	1.41513	0.707566	+	0.706647i	$0.249793\pi$
$788$	4.93184e9	0.359060
$789$	4.07045e9	0.295034
$790$	−8.66220e9	−0.625077
$791$	3.09357e9	0.222250
$792$	2.63258e9	0.188297
$793$	2.16603e9	0.154244
$794$	3.58420e10	2.54109
$795$	−1.60374e9	−0.113200
$796$	−4.26872e10	−2.99987
$797$	1.07925e10	0.755122	0.377561	−	0.925985i	$-0.376763\pi$
$797$	1.07925e10	0.755122	0.377561	+	0.925985i	$0.376763\pi$
$798$	1.38419e10	0.964238
$799$	7.15006e9	0.495902
$800$	−3.89964e10	−2.69284
$801$	−4.73260e9	−0.325377
$802$	3.57890e10	2.44985
$803$	2.41651e8	0.0164696
$804$	1.70450e10	1.15664
$805$	4.04062e9	0.273000
$806$	−3.23490e8	−0.0217615
$807$	−1.48517e10	−0.994759
$808$	1.69789e10	1.13232
$809$	−4.14105e9	−0.274973	−0.137487	−	0.990504i	$-0.543902\pi$
$809$	−4.14105e9	−0.274973	−0.137487	+	0.990504i	$0.543902\pi$
$810$	−1.30006e9	−0.0859542
$811$	3.15148e9	0.207463	0.103732	−	0.994605i	$-0.466922\pi$
$811$	3.15148e9	0.207463	0.103732	+	0.994605i	$0.466922\pi$
$812$	−4.40156e10	−2.88510
$813$	−1.34056e10	−0.874925
$814$	−2.70212e9	−0.175598
$815$	−7.72077e9	−0.499585
$816$	−4.45247e10	−2.86870
$817$	3.57869e9	0.229587
$818$	5.61637e10	3.58773
$819$	−4.07396e8	−0.0259133
$820$	−1.01278e10	−0.641454
$821$	−3.16518e10	−1.99617	−0.998085	−	0.0618543i	$-0.980299\pi$
$821$	−3.16518e10	−1.99617	−0.998085	+	0.0618543i	$0.980299\pi$
$822$	−2.55906e10	−1.60705
$823$	−2.99731e9	−0.187427	−0.0937135	−	0.995599i	$-0.529874\pi$
$823$	−2.99731e9	−0.187427	−0.0937135	+	0.995599i	$0.529874\pi$
$824$	−3.24485e10	−2.02046
$825$	1.40486e9	0.0871052
$826$	2.87051e9	0.177227
$827$	−6.29398e9	−0.386951	−0.193475	−	0.981105i	$-0.561976\pi$
$827$	−6.29398e9	−0.386951	−0.193475	+	0.981105i	$0.561976\pi$
$828$	1.35629e10	0.830319
$829$	1.29264e10	0.788018	0.394009	−	0.919107i	$-0.371088\pi$
$829$	1.29264e10	0.788018	0.394009	+	0.919107i	$0.371088\pi$
$830$	−2.41568e10	−1.46645
$831$	−2.92336e9	−0.176717
$832$	5.10282e9	0.307170
$833$	−1.22223e10	−0.732651
$834$	−4.98421e9	−0.297519
$835$	−3.99192e9	−0.237290
$836$	9.87886e9	0.584769
$837$	3.41798e8	0.0201480
$838$	−3.59343e10	−2.10938
$839$	2.72788e9	0.159462	0.0797312	−	0.996816i	$-0.474594\pi$
$839$	2.72788e9	0.159462	0.0797312	+	0.996816i	$0.474594\pi$
$840$	−8.97735e9	−0.522602
$841$	2.32187e10	1.34602
$842$	4.31994e10	2.49394
$843$	1.71629e10	0.986723
$844$	6.82444e10	3.90722
$845$	7.02715e9	0.400664
$846$	3.72125e9	0.211296
$847$	1.22070e10	0.690268
$848$	−2.85856e10	−1.60976
$849$	−4.92118e9	−0.275989
$850$	−4.26017e10	−2.37936
$851$	−8.64770e9	−0.481002
$852$	2.89642e10	1.60444
$853$	−1.22649e10	−0.676618	−0.338309	−	0.941035i	$-0.609855\pi$
$853$	−1.22649e10	−0.676618	−0.338309	+	0.941035i	$0.609855\pi$
$854$	−3.50780e10	−1.92722
$855$	−3.03052e9	−0.165819
$856$	−8.56842e10	−4.66920
$857$	−3.61684e10	−1.96289	−0.981447	−	0.191732i	$-0.938589\pi$
$857$	−3.61684e10	−1.96289	−0.981447	+	0.191732i	$0.938589\pi$
$858$	−4.00897e8	−0.0216684
$859$	−9.13867e9	−0.491934	−0.245967	−	0.969278i	$-0.579106\pi$
$859$	−9.13867e9	−0.491934	−0.245967	+	0.969278i	$0.579106\pi$
$860$	−3.73638e9	−0.200312
$861$	4.62358e9	0.246869
$862$	1.01973e10	0.542262
$863$	2.82611e10	1.49676	0.748378	−	0.663272i	$-0.230833\pi$
$863$	2.82611e10	1.49676	0.748378	+	0.663272i	$0.230833\pi$
$864$	−1.17580e10	−0.620206
$865$	6.07272e9	0.319027
$866$	1.46173e10	0.764811
$867$	−1.36016e10	−0.708798
$868$	3.79950e9	0.197200
$869$	2.82231e9	0.145893
$870$	1.32872e10	0.684093
$871$	−1.61240e9	−0.0826818
$872$	−7.25097e10	−3.70330
$873$	−6.14948e6	−0.000312816 0
$874$	4.35919e10	2.20860
$875$	−1.05240e10	−0.531073
$876$	−2.76604e9	−0.139025
$877$	−8.41638e9	−0.421334	−0.210667	−	0.977558i	$-0.567564\pi$
$877$	−8.41638e9	−0.421334	−0.210667	+	0.977558i	$0.567564\pi$
$878$	4.23355e10	2.11093
$879$	7.95257e9	0.394954
$880$	−4.92707e9	−0.243724
$881$	2.07127e10	1.02052	0.510259	−	0.860021i	$-0.329550\pi$
$881$	2.07127e10	1.02052	0.510259	+	0.860021i	$0.329550\pi$
$882$	−6.36111e9	−0.312171
$883$	−1.60168e10	−0.782910	−0.391455	−	0.920197i	$-0.628028\pi$
$883$	−1.60168e10	−0.782910	−0.391455	+	0.920197i	$0.628028\pi$
$884$	8.81705e9	0.429280
$885$	−6.28466e8	−0.0304776
$886$	1.54435e9	0.0745983
$887$	2.24851e10	1.08184	0.540920	−	0.841074i	$-0.318076\pi$
$887$	2.24851e10	1.08184	0.540920	+	0.841074i	$0.318076\pi$
$888$	1.92132e10	0.920779
$889$	−1.75341e10	−0.837002
$890$	1.58812e10	0.755122
$891$	4.23586e8	0.0200618
$892$	−8.24928e10	−3.89170
$893$	8.67441e9	0.407624
$894$	2.56711e10	1.20161
$895$	1.42499e10	0.664402
$896$	−3.31263e10	−1.53849
$897$	−1.28301e9	−0.0593547
$898$	−5.11216e10	−2.35580
$899$	−3.49331e9	−0.160354
$900$	−1.60806e10	−0.735281
$901$	−1.58454e10	−0.721718
$902$	4.54982e9	0.206429
$903$	1.70575e9	0.0770919
$904$	−2.16457e10	−0.974501
$905$	−7.20694e9	−0.323207
$906$	3.37594e10	1.50816
$907$	1.63521e10	0.727693	0.363847	−	0.931459i	$-0.381463\pi$
$907$	1.63521e10	0.727693	0.363847	+	0.931459i	$0.381463\pi$
$908$	2.26336e10	1.00335
$909$	2.73193e9	0.120641
$910$	1.36710e9	0.0601387
$911$	5.02950e9	0.220399	0.110200	−	0.993909i	$-0.464851\pi$
$911$	5.02950e9	0.220399	0.110200	+	0.993909i	$0.464851\pi$
$912$	−5.40170e10	−2.35803
$913$	7.87075e9	0.342270
$914$	1.99348e10	0.863574
$915$	7.67993e9	0.331424
$916$	−1.83356e9	−0.0788243
$917$	−4.35280e9	−0.186413
$918$	−1.28451e10	−0.548008
$919$	−2.98229e10	−1.26749	−0.633746	−	0.773541i	$-0.718483\pi$
$919$	−2.98229e10	−1.26749	−0.633746	+	0.773541i	$0.718483\pi$
$920$	−2.82723e10	−1.19702
$921$	1.83683e10	0.774749
$922$	−6.36837e9	−0.267590
$923$	−2.73993e9	−0.114692
$924$	4.70867e9	0.196357
$925$	1.02530e10	0.425947
$926$	5.55885e10	2.30063
$927$	−5.22102e9	−0.215266
$928$	1.20172e11	4.93610
$929$	1.92466e10	0.787589	0.393794	−	0.919199i	$-0.371162\pi$
$929$	1.92466e10	0.787589	0.393794	+	0.919199i	$0.371162\pi$
$930$	−1.14697e9	−0.0467587
$931$	−1.48281e10	−0.602228
$932$	−3.85449e10	−1.55959
$933$	4.96683e9	0.200214
$934$	−2.07714e10	−0.834164
$935$	−2.73115e9	−0.109271
$936$	2.85055e9	0.113622
$937$	2.73206e10	1.08493	0.542465	−	0.840078i	$-0.317491\pi$
$937$	2.73206e10	1.08493	0.542465	+	0.840078i	$0.317491\pi$
$938$	2.61121e10	1.03308
$939$	1.20397e10	0.474556
$940$	−9.05664e9	−0.355648
$941$	4.38771e10	1.71662	0.858309	−	0.513132i	$-0.171515\pi$
$941$	4.38771e10	1.71662	0.858309	+	0.513132i	$0.171515\pi$
$942$	3.78151e10	1.47396
$943$	1.45610e10	0.565457
$944$	−1.12020e10	−0.433405
$945$	−1.44447e9	−0.0556797
$946$	1.67854e9	0.0644633
$947$	−7.76685e9	−0.297180	−0.148590	−	0.988899i	$-0.547474\pi$
$947$	−7.76685e9	−0.297180	−0.148590	+	0.988899i	$0.547474\pi$
$948$	−3.23054e10	−1.23153
$949$	2.61659e8	0.00993811
$950$	−5.16842e10	−1.95580
$951$	1.46153e10	0.551031
$952$	−8.86992e10	−3.33189
$953$	−8.96167e9	−0.335401	−0.167700	−	0.985838i	$-0.553634\pi$
$953$	−8.96167e9	−0.335401	−0.167700	+	0.985838i	$0.553634\pi$
$954$	−8.24675e9	−0.307513
$955$	−2.50517e9	−0.0930734
$956$	7.94448e10	2.94078
$957$	−4.32922e9	−0.159668
$958$	−2.24692e10	−0.825672
$959$	−2.84331e10	−1.04102
$960$	1.80926e10	0.660013
$961$	−2.72111e10	−0.989040
$962$	−2.92585e9	−0.105959
$963$	−1.37867e10	−0.497472
$964$	−7.23859e10	−2.60246
$965$	3.10503e8	0.0111230
$966$	2.07777e10	0.741614
$967$	3.13646e10	1.11544	0.557721	−	0.830029i	$-0.311676\pi$
$967$	3.13646e10	1.11544	0.557721	+	0.830029i	$0.311676\pi$
$968$	−8.54126e10	−3.02662
$969$	−2.99425e10	−1.05719
$970$	2.06358e7	0.000725971 0
$971$	−3.71209e10	−1.30122	−0.650611	−	0.759411i	$-0.725487\pi$
$971$	−3.71209e10	−1.30122	−0.650611	+	0.759411i	$0.725487\pi$
$972$	−4.84854e9	−0.169348
$973$	−5.53783e9	−0.192728
$974$	3.33056e10	1.15494
$975$	1.52118e9	0.0525610
$976$	1.36890e11	4.71299
$977$	3.64354e10	1.24995	0.624975	−	0.780644i	$-0.285109\pi$
$977$	3.64354e10	1.24995	0.624975	+	0.780644i	$0.285109\pi$
$978$	−3.97018e10	−1.35714
$979$	−5.17439e9	−0.176246
$980$	1.54815e10	0.525437
$981$	−1.16669e10	−0.394562
$982$	1.78659e10	0.602052
$983$	−4.88356e9	−0.163983	−0.0819915	−	0.996633i	$-0.526128\pi$
$983$	−4.88356e9	−0.163983	−0.0819915	+	0.996633i	$0.526128\pi$
$984$	−3.23512e10	−1.08245
$985$	−1.65416e9	−0.0551508
$986$	1.31282e11	4.36149
$987$	4.13458e9	0.136874
$988$	1.06968e10	0.352862
$989$	5.37190e9	0.176580
$990$	−1.42143e9	−0.0465587
$991$	2.89018e10	0.943336	0.471668	−	0.881776i	$-0.343652\pi$
$991$	2.89018e10	0.943336	0.471668	+	0.881776i	$0.343652\pi$
$992$	−1.03734e10	−0.337389
$993$	−1.03620e9	−0.0335832
$994$	4.43719e10	1.43303
$995$	1.43175e10	0.460772
$996$	−9.00919e10	−2.88920
$997$	−8.79812e9	−0.281162	−0.140581	−	0.990069i	$-0.544897\pi$
$997$	−8.79812e9	−0.281162	−0.140581	+	0.990069i	$0.544897\pi$
$998$	−1.09848e11	−3.49811
$999$	3.09144e9	0.0981028

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.c.1.16	✓	17
3.2	odd	2		531.8.a.c.1.2		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.16	✓	17	1.1	even	1	trivial
531.8.a.c.1.2		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)

\(f(q)\)	\(=\)	\(q+21.5848 q^{2} -27.0000 q^{3} +337.903 q^{4} -113.334 q^{5} -582.789 q^{6} -647.523 q^{7} +4530.72 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+21.5848 q^{2} -27.0000 q^{3} +337.903 q^{4} -113.334 q^{5} -582.789 q^{6} -647.523 q^{7} +4530.72 q^{8} +729.000 q^{9} -2446.30 q^{10} +797.052 q^{11} -9123.39 q^{12} +863.046 q^{13} -13976.6 q^{14} +3060.03 q^{15} +54543.1 q^{16} +30234.1 q^{17} +15735.3 q^{18} +36679.8 q^{19} -38296.1 q^{20} +17483.1 q^{21} +17204.2 q^{22} +55059.3 q^{23} -122330. q^{24} -65280.3 q^{25} +18628.7 q^{26} -19683.0 q^{27} -218800. q^{28} +201168. q^{29} +66050.1 q^{30} -17365.2 q^{31} +597369. q^{32} -21520.4 q^{33} +652597. q^{34} +73386.6 q^{35} +246332. q^{36} -157061. q^{37} +791727. q^{38} -23302.2 q^{39} -513487. q^{40} +264460. q^{41} +377370. q^{42} +97565.6 q^{43} +269327. q^{44} -82620.8 q^{45} +1.18844e6 q^{46} +236490. q^{47} -1.47266e6 q^{48} -404257. q^{49} -1.40906e6 q^{50} -816321. q^{51} +291626. q^{52} -524092. q^{53} -424854. q^{54} -90333.5 q^{55} -2.93375e6 q^{56} -990355. q^{57} +4.34217e6 q^{58} -205379. q^{59} +1.03399e6 q^{60} +2.50976e6 q^{61} -374823. q^{62} -472044. q^{63} +5.91257e6 q^{64} -97812.8 q^{65} -464514. q^{66} -1.86827e6 q^{67} +1.02162e7 q^{68} -1.48660e6 q^{69} +1.58404e6 q^{70} -3.17472e6 q^{71} +3.30290e6 q^{72} +303181. q^{73} -3.39014e6 q^{74} +1.76257e6 q^{75} +1.23942e7 q^{76} -516110. q^{77} -502974. q^{78} +3.54094e6 q^{79} -6.18161e6 q^{80} +531441. q^{81} +5.70830e6 q^{82} +9.87483e6 q^{83} +5.90761e6 q^{84} -3.42656e6 q^{85} +2.10593e6 q^{86} -5.43154e6 q^{87} +3.61122e6 q^{88} -6.49191e6 q^{89} -1.78335e6 q^{90} -558842. q^{91} +1.86047e7 q^{92} +468859. q^{93} +5.10459e6 q^{94} -4.15709e6 q^{95} -1.61290e7 q^{96} -8435.50 q^{97} -8.72581e6 q^{98} +581051. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 2 q^{2} - 459 q^{3} + 1166 q^{4} - 318 q^{5} - 54 q^{6} + 3145 q^{7} + 2355 q^{8} + 12393 q^{9}+O(q^{10}) \) 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

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