LMFDB - Embedded newform 177.8.a.c.1.3

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			1.3
Root			$-14.3045$ 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)

$f(q)$	$=$	$q-14.3045 q^{2} -27.0000 q^{3} +76.6177 q^{4} +348.885 q^{5} +386.221 q^{6} -1316.66 q^{7} +734.996 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-14.3045 q^{2} -27.0000 q^{3} +76.6177 q^{4} +348.885 q^{5} +386.221 q^{6} -1316.66 q^{7} +734.996 q^{8} +729.000 q^{9} -4990.62 q^{10} +4994.84 q^{11} -2068.68 q^{12} +3397.75 q^{13} +18834.2 q^{14} -9419.91 q^{15} -20320.8 q^{16} +13080.3 q^{17} -10428.0 q^{18} +8796.50 q^{19} +26730.8 q^{20} +35549.9 q^{21} -71448.5 q^{22} +107491. q^{23} -19844.9 q^{24} +43596.1 q^{25} -48603.0 q^{26} -19683.0 q^{27} -100880. q^{28} +31901.3 q^{29} +134747. q^{30} -154292. q^{31} +196599. q^{32} -134861. q^{33} -187107. q^{34} -459365. q^{35} +55854.3 q^{36} -528856. q^{37} -125829. q^{38} -91739.2 q^{39} +256430. q^{40} -480637. q^{41} -508523. q^{42} -438138. q^{43} +382693. q^{44} +254338. q^{45} -1.53760e6 q^{46} +1.23501e6 q^{47} +548661. q^{48} +910062. q^{49} -623619. q^{50} -353169. q^{51} +260328. q^{52} -1.18221e6 q^{53} +281555. q^{54} +1.74263e6 q^{55} -967743. q^{56} -237505. q^{57} -456331. q^{58} -205379. q^{59} -721732. q^{60} +873606. q^{61} +2.20706e6 q^{62} -959848. q^{63} -211175. q^{64} +1.18542e6 q^{65} +1.92911e6 q^{66} -832263. q^{67} +1.00219e6 q^{68} -2.90226e6 q^{69} +6.57097e6 q^{70} +3.15545e6 q^{71} +535812. q^{72} +2.69697e6 q^{73} +7.56500e6 q^{74} -1.17709e6 q^{75} +673968. q^{76} -6.57652e6 q^{77} +1.31228e6 q^{78} +6.93335e6 q^{79} -7.08963e6 q^{80} +531441. q^{81} +6.87525e6 q^{82} -3.14360e6 q^{83} +2.72375e6 q^{84} +4.56354e6 q^{85} +6.26733e6 q^{86} -861335. q^{87} +3.67119e6 q^{88} -470189. q^{89} -3.63816e6 q^{90} -4.47369e6 q^{91} +8.23572e6 q^{92} +4.16587e6 q^{93} -1.76661e7 q^{94} +3.06897e6 q^{95} -5.30816e6 q^{96} +1.03272e7 q^{97} -1.30179e7 q^{98} +3.64124e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−14.3045	−1.26435	−0.632174	−	0.774826i	$-0.717837\pi$
$2$	−14.3045	−1.26435	−0.632174	+	0.774826i	$0.717837\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	76.6177	0.598576
$5$	348.885	1.24821	0.624105	−	0.781340i	$-0.285464\pi$
$5$	348.885	1.24821	0.624105	+	0.781340i	$0.285464\pi$
$6$	386.221	0.729972
$7$	−1316.66	−1.45088	−0.725441	−	0.688285i	$-0.758364\pi$
$7$	−1316.66	−1.45088	−0.725441	+	0.688285i	$0.758364\pi$
$8$	734.996	0.507540
$9$	729.000	0.333333
$10$	−4990.62	−1.57817
$11$	4994.84	1.13148	0.565740	−	0.824584i	$-0.308591\pi$
$11$	4994.84	1.13148	0.565740	+	0.824584i	$0.308591\pi$
$12$	−2068.68	−0.345588
$13$	3397.75	0.428933	0.214466	−	0.976731i	$-0.431199\pi$
$13$	3397.75	0.428933	0.214466	+	0.976731i	$0.431199\pi$
$14$	18834.2	1.83442
$15$	−9419.91	−0.720655
$16$	−20320.8	−1.24028
$17$	13080.3	0.645725	0.322863	−	0.946446i	$-0.395355\pi$
$17$	13080.3	0.645725	0.322863	+	0.946446i	$0.395355\pi$
$18$	−10428.0	−0.421449
$19$	8796.50	0.294220	0.147110	−	0.989120i	$-0.453003\pi$
$19$	8796.50	0.294220	0.147110	+	0.989120i	$0.453003\pi$
$20$	26730.8	0.747149
$21$	35549.9	0.837667
$22$	−71448.5	−1.43058
$23$	107491.	1.84215	0.921075	−	0.389385i	$-0.127313\pi$
$23$	107491.	1.84215	0.921075	+	0.389385i	$0.127313\pi$
$24$	−19844.9	−0.293028
$25$	43596.1	0.558030
$26$	−48603.0	−0.542320
$27$	−19683.0	−0.192450
$28$	−100880.	−0.868462
$29$	31901.3	0.242893	0.121447	−	0.992598i	$-0.461247\pi$
$29$	31901.3	0.242893	0.121447	+	0.992598i	$0.461247\pi$
$30$	134747.	0.911158
$31$	−154292.	−0.930200	−0.465100	−	0.885258i	$-0.653982\pi$
$31$	−154292.	−0.930200	−0.465100	+	0.885258i	$0.653982\pi$
$32$	196599.	1.06061
$33$	−134861.	−0.653260
$34$	−187107.	−0.816422
$35$	−459365.	−1.81101
$36$	55854.3	0.199525
$37$	−528856.	−1.71645	−0.858225	−	0.513274i	$-0.828432\pi$
$37$	−528856.	−1.71645	−0.858225	+	0.513274i	$0.828432\pi$
$38$	−125829.	−0.371996
$39$	−91739.2	−0.247645
$40$	256430.	0.633517
$41$	−480637.	−1.08911	−0.544557	−	0.838724i	$-0.683302\pi$
$41$	−480637.	−1.08911	−0.544557	+	0.838724i	$0.683302\pi$
$42$	−508523.	−1.05910
$43$	−438138.	−0.840371	−0.420186	−	0.907438i	$-0.638035\pi$
$43$	−438138.	−0.840371	−0.420186	+	0.907438i	$0.638035\pi$
$44$	382693.	0.677277
$45$	254338.	0.416070
$46$	−1.53760e6	−2.32912
$47$	1.23501e6	1.73511	0.867555	−	0.497341i	$-0.165690\pi$
$47$	1.23501e6	1.73511	0.867555	+	0.497341i	$0.165690\pi$
$48$	548661.	0.716078
$49$	910062.	1.10506
$50$	−623619.	−0.705544
$51$	−353169.	−0.372810
$52$	260328.	0.256749
$53$	−1.18221e6	−1.09076	−0.545379	−	0.838190i	$-0.683614\pi$
$53$	−1.18221e6	−1.09076	−0.545379	+	0.838190i	$0.683614\pi$
$54$	281555.	0.243324
$55$	1.74263e6	1.41233
$56$	−967743.	−0.736380
$57$	−237505.	−0.169868
$58$	−456331.	−0.307102
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	−721732.	−0.431367
$61$	873606.	0.492789	0.246395	−	0.969170i	$-0.420754\pi$
$61$	873606.	0.492789	0.246395	+	0.969170i	$0.420754\pi$
$62$	2.20706e6	1.17610
$63$	−959848.	−0.483627
$64$	−211175.	−0.100696
$65$	1.18542e6	0.535399
$66$	1.92911e6	0.825948
$67$	−832263.	−0.338064	−0.169032	−	0.985611i	$-0.554064\pi$
$67$	−832263.	−0.338064	−0.169032	+	0.985611i	$0.554064\pi$
$68$	1.00219e6	0.386516
$69$	−2.90226e6	−1.06357
$70$	6.57097e6	2.28974
$71$	3.15545e6	1.04630	0.523152	−	0.852240i	$-0.324756\pi$
$71$	3.15545e6	1.04630	0.523152	+	0.852240i	$0.324756\pi$
$72$	535812.	0.169180
$73$	2.69697e6	0.811420	0.405710	−	0.914002i	$-0.367024\pi$
$73$	2.69697e6	0.811420	0.405710	+	0.914002i	$0.367024\pi$
$74$	7.56500e6	2.17019
$75$	−1.17709e6	−0.322179
$76$	673968.	0.176113
$77$	−6.57652e6	−1.64164
$78$	1.31228e6	0.313109
$79$	6.93335e6	1.58215	0.791076	−	0.611718i	$-0.209521\pi$
$79$	6.93335e6	1.58215	0.791076	+	0.611718i	$0.209521\pi$
$80$	−7.08963e6	−1.54813
$81$	531441.	0.111111
$82$	6.87525e6	1.37702
$83$	−3.14360e6	−0.603468	−0.301734	−	0.953392i	$-0.597565\pi$
$83$	−3.14360e6	−0.603468	−0.301734	+	0.953392i	$0.597565\pi$
$84$	2.72375e6	0.501407
$85$	4.56354e6	0.806001
$86$	6.26733e6	1.06252
$87$	−861335.	−0.140235
$88$	3.67119e6	0.574271
$89$	−470189.	−0.0706980	−0.0353490	−	0.999375i	$-0.511254\pi$
$89$	−470189.	−0.0706980	−0.0353490	+	0.999375i	$0.511254\pi$
$90$	−3.63816e6	−0.526058
$91$	−4.47369e6	−0.622331
$92$	8.23572e6	1.10267
$93$	4.16587e6	0.537051
$94$	−1.76661e7	−2.19378
$95$	3.06897e6	0.367249
$96$	−5.30816e6	−0.612343
$97$	1.03272e7	1.14890	0.574448	−	0.818541i	$-0.305217\pi$
$97$	1.03272e7	1.14890	0.574448	+	0.818541i	$0.305217\pi$
$98$	−1.30179e7	−1.39718
$99$	3.64124e6	0.377160
$100$	3.34023e6	0.334023
$101$	−1.36297e7	−1.31632	−0.658159	−	0.752879i	$-0.728664\pi$
$101$	−1.36297e7	−1.31632	−0.658159	+	0.752879i	$0.728664\pi$
$102$	5.05190e6	0.471361
$103$	−1.58162e6	−0.142618	−0.0713088	−	0.997454i	$-0.522718\pi$
$103$	−1.58162e6	−0.142618	−0.0713088	+	0.997454i	$0.522718\pi$
$104$	2.49733e6	0.217701
$105$	1.24029e7	1.04558
$106$	1.69109e7	1.37910
$107$	1.70106e7	1.34238	0.671191	−	0.741284i	$-0.265783\pi$
$107$	1.70106e7	1.34238	0.671191	+	0.741284i	$0.265783\pi$
$108$	−1.50807e6	−0.115196
$109$	−5.78972e6	−0.428218	−0.214109	−	0.976810i	$-0.568685\pi$
$109$	−5.78972e6	−0.428218	−0.214109	+	0.976810i	$0.568685\pi$
$110$	−2.49273e7	−1.78567
$111$	1.42791e7	0.990993
$112$	2.67557e7	1.79950
$113$	2.12637e7	1.38632	0.693161	−	0.720783i	$-0.256217\pi$
$113$	2.12637e7	1.38632	0.693161	+	0.720783i	$0.256217\pi$
$114$	3.39739e6	0.214772
$115$	3.75021e7	2.29939
$116$	2.44421e6	0.145390
$117$	2.47696e6	0.142978
$118$	2.93784e6	0.164604
$119$	−1.72224e7	−0.936871
$120$	−6.92360e6	−0.365761
$121$	5.46122e6	0.280247
$122$	−1.24965e7	−0.623057
$123$	1.29772e7	0.628801
$124$	−1.18215e7	−0.556795
$125$	−1.20466e7	−0.551672
$126$	1.37301e7	0.611473
$127$	1.24454e7	0.539132	0.269566	−	0.962982i	$-0.413120\pi$
$127$	1.24454e7	0.539132	0.269566	+	0.962982i	$0.413120\pi$
$128$	−2.21439e7	−0.933294
$129$	1.18297e7	0.485189
$130$	−1.69569e7	−0.676930
$131$	8.16356e6	0.317271	0.158635	−	0.987337i	$-0.449291\pi$
$131$	8.16356e6	0.317271	0.158635	+	0.987337i	$0.449291\pi$
$132$	−1.03327e7	−0.391026
$133$	−1.15820e7	−0.426878
$134$	1.19051e7	0.427430
$135$	−6.86711e6	−0.240218
$136$	9.61400e6	0.327731
$137$	4.91255e7	1.63224	0.816122	−	0.577880i	$-0.196120\pi$
$137$	4.91255e7	1.63224	0.816122	+	0.577880i	$0.196120\pi$
$138$	4.15153e7	1.34472
$139$	−2.62822e6	−0.0830060	−0.0415030	−	0.999138i	$-0.513215\pi$
$139$	−2.62822e6	−0.0830060	−0.0415030	+	0.999138i	$0.513215\pi$
$140$	−3.51955e7	−1.08402
$141$	−3.33452e7	−1.00177
$142$	−4.51371e7	−1.32289
$143$	1.69712e7	0.485329
$144$	−1.48139e7	−0.413428
$145$	1.11299e7	0.303182
$146$	−3.85787e7	−1.02592
$147$	−2.45717e7	−0.638005
$148$	−4.05197e7	−1.02743
$149$	−1.97981e7	−0.490311	−0.245156	−	0.969484i	$-0.578839\pi$
$149$	−1.97981e7	−0.490311	−0.245156	+	0.969484i	$0.578839\pi$
$150$	1.68377e7	0.407346
$151$	1.33779e7	0.316205	0.158103	−	0.987423i	$-0.449462\pi$
$151$	1.33779e7	0.316205	0.158103	+	0.987423i	$0.449462\pi$
$152$	6.46539e6	0.149328
$153$	9.53557e6	0.215242
$154$	9.40736e7	2.07561
$155$	−5.38301e7	−1.16109
$156$	−7.02885e6	−0.148234
$157$	−2.96493e7	−0.611457	−0.305728	−	0.952119i	$-0.598900\pi$
$157$	−2.96493e7	−0.611457	−0.305728	+	0.952119i	$0.598900\pi$
$158$	−9.91778e7	−2.00039
$159$	3.19196e7	0.629749
$160$	6.85904e7	1.32386
$161$	−1.41530e8	−2.67274
$162$	−7.60198e6	−0.140483
$163$	−5.91942e7	−1.07059	−0.535294	−	0.844666i	$-0.679799\pi$
$163$	−5.91942e7	−1.07059	−0.535294	+	0.844666i	$0.679799\pi$
$164$	−3.68253e7	−0.651918
$165$	−4.70509e7	−0.815406
$166$	4.49675e7	0.762993
$167$	1.03566e8	1.72071	0.860357	−	0.509692i	$-0.170241\pi$
$167$	1.03566e8	1.72071	0.860357	+	0.509692i	$0.170241\pi$
$168$	2.61291e7	0.425149
$169$	−5.12038e7	−0.816017
$170$	−6.52790e7	−1.01907
$171$	6.41265e6	0.0980733
$172$	−3.35691e7	−0.503026
$173$	7.49114e7	1.09998	0.549992	−	0.835170i	$-0.314631\pi$
$173$	7.49114e7	1.09998	0.549992	+	0.835170i	$0.314631\pi$
$174$	1.23209e7	0.177305
$175$	−5.74014e7	−0.809635
$176$	−1.01499e8	−1.40336
$177$	5.54523e6	0.0751646
$178$	6.72580e6	0.0893869
$179$	1.39539e8	1.81849	0.909244	−	0.416263i	$-0.136661\pi$
$179$	1.39539e8	1.81849	0.909244	+	0.416263i	$0.136661\pi$
$180$	1.94868e7	0.249050
$181$	1.39686e7	0.175096	0.0875480	−	0.996160i	$-0.472097\pi$
$181$	1.39686e7	0.175096	0.0875480	+	0.996160i	$0.472097\pi$
$182$	6.39938e7	0.786843
$183$	−2.35874e7	−0.284512
$184$	7.90055e7	0.934965
$185$	−1.84510e8	−2.14249
$186$	−5.95906e7	−0.679019
$187$	6.53342e7	0.730625
$188$	9.46235e7	1.03860
$189$	2.59159e7	0.279222
$190$	−4.39000e7	−0.464330
$191$	−3.81975e7	−0.396660	−0.198330	−	0.980135i	$-0.563552\pi$
$191$	−3.81975e7	−0.396660	−0.198330	+	0.980135i	$0.563552\pi$
$192$	5.70174e6	0.0581370
$193$	−3.69244e7	−0.369711	−0.184856	−	0.982766i	$-0.559182\pi$
$193$	−3.69244e7	−0.369711	−0.184856	+	0.982766i	$0.559182\pi$
$194$	−1.47725e8	−1.45260
$195$	−3.20065e7	−0.309113
$196$	6.97268e7	0.661460
$197$	1.04700e8	0.975695	0.487847	−	0.872929i	$-0.337782\pi$
$197$	1.04700e8	0.975695	0.487847	+	0.872929i	$0.337782\pi$
$198$	−5.20859e7	−0.476861
$199$	−1.24096e8	−1.11628	−0.558138	−	0.829748i	$-0.688484\pi$
$199$	−1.24096e8	−1.11628	−0.558138	+	0.829748i	$0.688484\pi$
$200$	3.20430e7	0.283222
$201$	2.24711e7	0.195181
$202$	1.94965e8	1.66428
$203$	−4.20033e7	−0.352409
$204$	−2.70590e7	−0.223155
$205$	−1.67687e8	−1.35944
$206$	2.26243e7	0.180318
$207$	7.83610e7	0.614050
$208$	−6.90449e7	−0.531998
$209$	4.39371e7	0.332904
$210$	−1.77416e8	−1.32198
$211$	−8.39750e7	−0.615406	−0.307703	−	0.951483i	$-0.599560\pi$
$211$	−8.39750e7	−0.615406	−0.307703	+	0.951483i	$0.599560\pi$
$212$	−9.05781e7	−0.652901
$213$	−8.51973e7	−0.604084
$214$	−2.43327e8	−1.69724
$215$	−1.52860e8	−1.04896
$216$	−1.44669e7	−0.0976761
$217$	2.03150e8	1.34961
$218$	8.28188e7	0.541416
$219$	−7.28181e7	−0.468474
$220$	1.33516e8	0.845384
$221$	4.44437e7	0.276973
$222$	−2.04255e8	−1.25296
$223$	2.55405e8	1.54227	0.771137	−	0.636669i	$-0.219688\pi$
$223$	2.55405e8	1.54227	0.771137	+	0.636669i	$0.219688\pi$
$224$	−2.58854e8	−1.53882
$225$	3.17815e7	0.186010
$226$	−3.04166e8	−1.75279
$227$	2.94977e8	1.67377	0.836887	−	0.547375i	$-0.184373\pi$
$227$	2.94977e8	1.67377	0.836887	+	0.547375i	$0.184373\pi$
$228$	−1.81971e7	−0.101679
$229$	3.95841e7	0.217819	0.108910	−	0.994052i	$-0.465264\pi$
$229$	3.95841e7	0.217819	0.108910	+	0.994052i	$0.465264\pi$
$230$	−5.36447e8	−2.90723
$231$	1.77566e8	0.947803
$232$	2.34473e7	0.123278
$233$	−1.72426e7	−0.0893009	−0.0446505	−	0.999003i	$-0.514217\pi$
$233$	−1.72426e7	−0.0893009	−0.0446505	+	0.999003i	$0.514217\pi$
$234$	−3.54316e7	−0.180773
$235$	4.30876e8	2.16578
$236$	−1.57357e7	−0.0779279
$237$	−1.87200e8	−0.913456
$238$	2.46357e8	1.18453
$239$	3.47868e6	0.0164824	0.00824121	−	0.999966i	$-0.497377\pi$
$239$	3.47868e6	0.0164824	0.00824121	+	0.999966i	$0.497377\pi$
$240$	1.91420e8	0.893816
$241$	2.24809e8	1.03456	0.517279	−	0.855817i	$-0.326945\pi$
$241$	2.24809e8	1.03456	0.517279	+	0.855817i	$0.326945\pi$
$242$	−7.81198e7	−0.354330
$243$	−1.43489e7	−0.0641500
$244$	6.69337e7	0.294972
$245$	3.17507e8	1.37934
$246$	−1.85632e8	−0.795023
$247$	2.98883e7	0.126201
$248$	−1.13404e8	−0.472113
$249$	8.48772e7	0.348412
$250$	1.72321e8	0.697505
$251$	4.20064e8	1.67671	0.838354	−	0.545127i	$-0.183519\pi$
$251$	4.20064e8	1.67671	0.838354	+	0.545127i	$0.183519\pi$
$252$	−7.35414e7	−0.289487
$253$	5.36900e8	2.08436
$254$	−1.78024e8	−0.681650
$255$	−1.23216e8	−0.465345
$256$	3.43787e8	1.28070
$257$	1.99799e8	0.734221	0.367111	−	0.930177i	$-0.380347\pi$
$257$	1.99799e8	0.734221	0.367111	+	0.930177i	$0.380347\pi$
$258$	−1.69218e8	−0.613447
$259$	6.96325e8	2.49036
$260$	9.08245e7	0.320477
$261$	2.32561e7	0.0809644
$262$	−1.16775e8	−0.401141
$263$	5.10505e8	1.73043	0.865216	−	0.501399i	$-0.167181\pi$
$263$	5.10505e8	1.73043	0.865216	+	0.501399i	$0.167181\pi$
$264$	−9.91220e7	−0.331556
$265$	−4.12455e8	−1.36150
$266$	1.65675e8	0.539723
$267$	1.26951e7	0.0408175
$268$	−6.37661e7	−0.202357
$269$	−6.12082e8	−1.91724	−0.958621	−	0.284686i	$-0.908111\pi$
$269$	−6.12082e8	−1.91724	−0.958621	+	0.284686i	$0.908111\pi$
$270$	9.82304e7	0.303719
$271$	1.95076e8	0.595404	0.297702	−	0.954659i	$-0.403780\pi$
$271$	1.95076e8	0.595404	0.297702	+	0.954659i	$0.403780\pi$
$272$	−2.65803e8	−0.800882
$273$	1.20790e8	0.359303
$274$	−7.02714e8	−2.06372
$275$	2.17755e8	0.631400
$276$	−2.22364e8	−0.636625
$277$	−4.11429e8	−1.16310	−0.581548	−	0.813512i	$-0.697553\pi$
$277$	−4.11429e8	−1.16310	−0.581548	+	0.813512i	$0.697553\pi$
$278$	3.75953e7	0.104949
$279$	−1.12479e8	−0.310067
$280$	−3.37632e8	−0.919157
$281$	−1.45356e8	−0.390805	−0.195403	−	0.980723i	$-0.562601\pi$
$281$	−1.45356e8	−0.390805	−0.195403	+	0.980723i	$0.562601\pi$
$282$	4.76985e8	1.26658
$283$	−7.33769e8	−1.92445	−0.962226	−	0.272252i	$-0.912232\pi$
$283$	−7.33769e8	−1.92445	−0.962226	+	0.272252i	$0.912232\pi$
$284$	2.41764e8	0.626292
$285$	−8.28622e7	−0.212031
$286$	−2.42764e8	−0.613625
$287$	6.32837e8	1.58018
$288$	1.43320e8	0.353536
$289$	−2.39243e8	−0.583039
$290$	−1.59207e8	−0.383328
$291$	−2.78834e8	−0.663315
$292$	2.06635e8	0.485696
$293$	−3.59570e8	−0.835117	−0.417558	−	0.908650i	$-0.637114\pi$
$293$	−3.59570e8	−0.835117	−0.417558	+	0.908650i	$0.637114\pi$
$294$	3.51484e8	0.806660
$295$	−7.16538e7	−0.162503
$296$	−3.88707e8	−0.871167
$297$	−9.83134e7	−0.217753
$298$	2.83202e8	0.619924
$299$	3.65228e8	0.790159
$300$	−9.01862e7	−0.192848
$301$	5.76880e8	1.21928
$302$	−1.91364e8	−0.399794
$303$	3.68001e8	0.759976
$304$	−1.78752e8	−0.364916
$305$	3.04788e8	0.615105
$306$	−1.36401e8	−0.272141
$307$	−2.59711e8	−0.512278	−0.256139	−	0.966640i	$-0.582450\pi$
$307$	−2.59711e8	−0.512278	−0.256139	+	0.966640i	$0.582450\pi$
$308$	−5.03878e8	−0.982648
$309$	4.27039e7	0.0823403
$310$	7.70010e8	1.46802
$311$	4.42793e8	0.834717	0.417359	−	0.908742i	$-0.362956\pi$
$311$	4.42793e8	0.834717	0.417359	+	0.908742i	$0.362956\pi$
$312$	−6.74280e7	−0.125689
$313$	4.37731e7	0.0806867	0.0403433	−	0.999186i	$-0.487155\pi$
$313$	4.37731e7	0.0806867	0.0403433	+	0.999186i	$0.487155\pi$
$314$	4.24117e8	0.773094
$315$	−3.34877e8	−0.603668
$316$	5.31217e8	0.947038
$317$	1.74353e8	0.307413	0.153706	−	0.988117i	$-0.450879\pi$
$317$	1.74353e8	0.307413	0.153706	+	0.988117i	$0.450879\pi$
$318$	−4.56593e8	−0.796222
$319$	1.59342e8	0.274829
$320$	−7.36761e7	−0.125690
$321$	−4.59286e8	−0.775025
$322$	2.02451e9	3.37927
$323$	1.15061e8	0.189985
$324$	4.07178e7	0.0665084
$325$	1.48128e8	0.239357
$326$	8.46741e8	1.35360
$327$	1.56322e8	0.247232
$328$	−3.53266e8	−0.552769
$329$	−1.62609e9	−2.51744
$330$	6.73038e8	1.03096
$331$	4.19111e8	0.635231	0.317615	−	0.948220i	$-0.397118\pi$
$331$	4.19111e8	0.635231	0.317615	+	0.948220i	$0.397118\pi$
$332$	−2.40856e8	−0.361221
$333$	−3.85536e8	−0.572150
$334$	−1.48145e9	−2.17558
$335$	−2.90364e8	−0.421975
$336$	−7.22403e8	−1.03894
$337$	−5.81583e8	−0.827765	−0.413882	−	0.910330i	$-0.635827\pi$
$337$	−5.81583e8	−0.827765	−0.413882	+	0.910330i	$0.635827\pi$
$338$	7.32443e8	1.03173
$339$	−5.74120e8	−0.800393
$340$	3.49648e8	0.482453
$341$	−7.70661e8	−1.05250
$342$	−9.17295e7	−0.123999
$343$	−1.13916e8	−0.152425
$344$	−3.22030e8	−0.426522
$345$	−1.01256e9	−1.32755
$346$	−1.07157e9	−1.39076
$347$	6.12801e8	0.787347	0.393673	−	0.919250i	$-0.371204\pi$
$347$	6.12801e8	0.787347	0.393673	+	0.919250i	$0.371204\pi$
$348$	−6.59935e7	−0.0839410
$349$	5.26220e8	0.662642	0.331321	−	0.943518i	$-0.392506\pi$
$349$	5.26220e8	0.662642	0.331321	+	0.943518i	$0.392506\pi$
$350$	8.21096e8	1.02366
$351$	−6.68779e7	−0.0825482
$352$	9.81978e8	1.20006
$353$	7.42142e8	0.897999	0.448999	−	0.893532i	$-0.351781\pi$
$353$	7.42142e8	0.897999	0.448999	+	0.893532i	$0.351781\pi$
$354$	−7.93216e7	−0.0950342
$355$	1.10089e9	1.30601
$356$	−3.60248e7	−0.0423181
$357$	4.65005e8	0.540903
$358$	−1.99603e9	−2.29920
$359$	4.68258e8	0.534139	0.267070	−	0.963677i	$-0.413945\pi$
$359$	4.68258e8	0.534139	0.267070	+	0.963677i	$0.413945\pi$
$360$	1.86937e8	0.211172
$361$	−8.16493e8	−0.913435
$362$	−1.99813e8	−0.221382
$363$	−1.47453e8	−0.161801
$364$	−3.42764e8	−0.372512
$365$	9.40933e8	1.01282
$366$	3.37405e8	0.359722
$367$	4.07678e8	0.430513	0.215257	−	0.976558i	$-0.430941\pi$
$367$	4.07678e8	0.430513	0.215257	+	0.976558i	$0.430941\pi$
$368$	−2.18430e9	−2.28479
$369$	−3.50384e8	−0.363038
$370$	2.63932e9	2.70885
$371$	1.55657e9	1.58256
$372$	3.19180e8	0.321466
$373$	1.76997e9	1.76598	0.882989	−	0.469393i	$-0.155527\pi$
$373$	1.76997e9	1.76598	0.882989	+	0.469393i	$0.155527\pi$
$374$	−9.34570e8	−0.923765
$375$	3.25259e8	0.318508
$376$	9.07726e8	0.880638
$377$	1.08393e8	0.104185
$378$	−3.70713e8	−0.353034
$379$	−2.03436e8	−0.191951	−0.0959757	−	0.995384i	$-0.530597\pi$
$379$	−2.03436e8	−0.191951	−0.0959757	+	0.995384i	$0.530597\pi$
$380$	2.35137e8	0.219826
$381$	−3.36025e8	−0.311268
$382$	5.46395e8	0.501516
$383$	−1.58998e9	−1.44609	−0.723044	−	0.690802i	$-0.757258\pi$
$383$	−1.58998e9	−1.44609	−0.723044	+	0.690802i	$0.757258\pi$
$384$	5.97884e8	0.538838
$385$	−2.29445e9	−2.04912
$386$	5.28184e8	0.467444
$387$	−3.19402e8	−0.280124
$388$	7.91244e8	0.687701
$389$	−6.10709e8	−0.526030	−0.263015	−	0.964792i	$-0.584717\pi$
$389$	−6.10709e8	−0.526030	−0.263015	+	0.964792i	$0.584717\pi$
$390$	4.57835e8	0.390826
$391$	1.40602e9	1.18952
$392$	6.68892e8	0.560860
$393$	−2.20416e8	−0.183176
$394$	−1.49767e9	−1.23362
$395$	2.41894e9	1.97486
$396$	2.78983e8	0.225759
$397$	1.32027e8	0.105900	0.0529501	−	0.998597i	$-0.483138\pi$
$397$	1.32027e8	0.105900	0.0529501	+	0.998597i	$0.483138\pi$
$398$	1.77513e9	1.41136
$399$	3.12715e8	0.246458
$400$	−8.85907e8	−0.692115
$401$	6.34337e8	0.491263	0.245632	−	0.969363i	$-0.421005\pi$
$401$	6.34337e8	0.491263	0.245632	+	0.969363i	$0.421005\pi$
$402$	−3.21437e8	−0.246777
$403$	−5.24244e8	−0.398993
$404$	−1.04427e9	−0.787916
$405$	1.85412e8	0.138690
$406$	6.00835e8	0.445568
$407$	−2.64155e9	−1.94213
$408$	−2.59578e8	−0.189216
$409$	9.45727e8	0.683493	0.341746	−	0.939792i	$-0.388982\pi$
$409$	9.45727e8	0.683493	0.341746	+	0.939792i	$0.388982\pi$
$410$	2.39868e9	1.71881
$411$	−1.32639e9	−0.942376
$412$	−1.21180e8	−0.0853675
$413$	2.70415e8	0.188889
$414$	−1.12091e9	−0.776373
$415$	−1.09676e9	−0.753255
$416$	6.67992e8	0.454930
$417$	7.09619e7	0.0479236
$418$	−6.28496e8	−0.420907
$419$	−1.99014e9	−1.32170	−0.660852	−	0.750517i	$-0.729805\pi$
$419$	−1.99014e9	−1.32170	−0.660852	+	0.750517i	$0.729805\pi$
$420$	9.50278e8	0.625862
$421$	2.39417e8	0.156375	0.0781875	−	0.996939i	$-0.475087\pi$
$421$	2.39417e8	0.156375	0.0781875	+	0.996939i	$0.475087\pi$
$422$	1.20122e9	0.778087
$423$	9.00321e8	0.578370
$424$	−8.68918e8	−0.553603
$425$	5.70252e8	0.360334
$426$	1.21870e9	0.763772
$427$	−1.15025e9	−0.714979
$428$	1.30331e9	0.803518
$429$	−4.58222e8	−0.280205
$430$	2.18658e9	1.32625
$431$	−1.41644e9	−0.852171	−0.426086	−	0.904683i	$-0.640108\pi$
$431$	−1.41644e9	−0.852171	−0.426086	+	0.904683i	$0.640108\pi$
$432$	3.99974e8	0.238693
$433$	2.49096e9	1.47455	0.737273	−	0.675595i	$-0.236113\pi$
$433$	2.49096e9	1.47455	0.737273	+	0.675595i	$0.236113\pi$
$434$	−2.90595e9	−1.70638
$435$	−3.00507e8	−0.175042
$436$	−4.43595e8	−0.256321
$437$	9.45545e8	0.541997
$438$	1.04162e9	0.592314
$439$	1.29699e9	0.731661	0.365831	−	0.930681i	$-0.380785\pi$
$439$	1.29699e9	0.731661	0.365831	+	0.930681i	$0.380785\pi$
$440$	1.28082e9	0.716811
$441$	6.63435e8	0.368352
$442$	−6.35743e8	−0.350190
$443$	−4.26015e8	−0.232815	−0.116408	−	0.993202i	$-0.537138\pi$
$443$	−4.26015e8	−0.232815	−0.116408	+	0.993202i	$0.537138\pi$
$444$	1.09403e9	0.593184
$445$	−1.64042e8	−0.0882460
$446$	−3.65343e9	−1.94997
$447$	5.34549e8	0.283081
$448$	2.78047e8	0.146098
$449$	3.29234e9	1.71649	0.858247	−	0.513236i	$-0.171554\pi$
$449$	3.29234e9	1.71649	0.858247	+	0.513236i	$0.171554\pi$
$450$	−4.54618e8	−0.235181
$451$	−2.40070e9	−1.23231
$452$	1.62918e9	0.829819
$453$	−3.61204e8	−0.182561
$454$	−4.21948e9	−2.11623
$455$	−1.56081e9	−0.776800
$456$	−1.74566e8	−0.0862148
$457$	−4.28524e8	−0.210024	−0.105012	−	0.994471i	$-0.533488\pi$
$457$	−4.28524e8	−0.210024	−0.105012	+	0.994471i	$0.533488\pi$
$458$	−5.66229e8	−0.275399
$459$	−2.57460e8	−0.124270
$460$	2.87332e9	1.37636
$461$	−2.18183e9	−1.03721	−0.518605	−	0.855014i	$-0.673548\pi$
$461$	−2.18183e9	−1.03721	−0.518605	+	0.855014i	$0.673548\pi$
$462$	−2.53999e9	−1.19835
$463$	−3.49857e9	−1.63816	−0.819082	−	0.573677i	$-0.805517\pi$
$463$	−3.49857e9	−1.63816	−0.819082	+	0.573677i	$0.805517\pi$
$464$	−6.48260e8	−0.301256
$465$	1.45341e9	0.670353
$466$	2.46646e8	0.112907
$467$	5.99769e8	0.272505	0.136253	−	0.990674i	$-0.456494\pi$
$467$	5.99769e8	0.272505	0.136253	+	0.990674i	$0.456494\pi$
$468$	1.89779e8	0.0855830
$469$	1.09581e9	0.490490
$470$	−6.16345e9	−2.73830
$471$	8.00531e8	0.353025
$472$	−1.50953e8	−0.0660761
$473$	−2.18843e9	−0.950863
$474$	2.67780e9	1.15493
$475$	3.83493e8	0.164184
$476$	−1.31954e9	−0.560788
$477$	−8.61830e8	−0.363586
$478$	−4.97606e7	−0.0208395
$479$	1.04242e9	0.433381	0.216691	−	0.976240i	$-0.430474\pi$
$479$	1.04242e9	0.433381	0.216691	+	0.976240i	$0.430474\pi$
$480$	−1.85194e9	−0.764333
$481$	−1.79692e9	−0.736242
$482$	−3.21578e9	−1.30804
$483$	3.82130e9	1.54311
$484$	4.18426e8	0.167749
$485$	3.60300e9	1.43406
$486$	2.05253e8	0.0811080
$487$	4.49609e9	1.76394	0.881970	−	0.471305i	$-0.156217\pi$
$487$	4.49609e9	1.76394	0.881970	+	0.471305i	$0.156217\pi$
$488$	6.42097e8	0.250110
$489$	1.59824e9	0.618104
$490$	−4.54177e9	−1.74397
$491$	−3.34941e9	−1.27698	−0.638489	−	0.769631i	$-0.720440\pi$
$491$	−3.34941e9	−1.27698	−0.638489	+	0.769631i	$0.720440\pi$
$492$	9.94283e8	0.376385
$493$	4.17280e8	0.156842
$494$	−4.27536e8	−0.159562
$495$	1.27037e9	0.470775
$496$	3.13533e9	1.15371
$497$	−4.15467e9	−1.51806
$498$	−1.21412e9	−0.440514
$499$	−2.53248e9	−0.912419	−0.456209	−	0.889872i	$-0.650793\pi$
$499$	−2.53248e9	−0.912419	−0.456209	+	0.889872i	$0.650793\pi$
$500$	−9.22986e8	−0.330217
$501$	−2.79628e9	−0.993455
$502$	−6.00879e9	−2.11994
$503$	−2.14316e9	−0.750874	−0.375437	−	0.926848i	$-0.622507\pi$
$503$	−2.14316e9	−0.750874	−0.375437	+	0.926848i	$0.622507\pi$
$504$	−7.05485e8	−0.245460
$505$	−4.75520e9	−1.64304
$506$	−7.68007e9	−2.63535
$507$	1.38250e9	0.471127
$508$	9.53536e8	0.322711
$509$	3.85176e9	1.29463	0.647316	−	0.762222i	$-0.275891\pi$
$509$	3.85176e9	1.29463	0.647316	+	0.762222i	$0.275891\pi$
$510$	1.76253e9	0.588358
$511$	−3.55100e9	−1.17727
$512$	−2.08327e9	−0.685962
$513$	−1.73141e8	−0.0566227
$514$	−2.85801e9	−0.928311
$515$	−5.51806e8	−0.178017
$516$	9.06366e8	0.290422
$517$	6.16866e9	1.96324
$518$	−9.96056e9	−3.14869
$519$	−2.02261e9	−0.635076
$520$	8.71283e8	0.271736
$521$	−4.67938e9	−1.44963	−0.724814	−	0.688945i	$-0.758074\pi$
$521$	−4.67938e9	−1.44963	−0.724814	+	0.688945i	$0.758074\pi$
$522$	−3.32665e8	−0.102367
$523$	3.37502e9	1.03162	0.515810	−	0.856703i	$-0.327491\pi$
$523$	3.37502e9	1.03162	0.515810	+	0.856703i	$0.327491\pi$
$524$	6.25474e8	0.189911
$525$	1.54984e9	0.467443
$526$	−7.30250e9	−2.18787
$527$	−2.01819e9	−0.600654
$528$	2.74047e9	0.810228
$529$	8.14951e9	2.39352
$530$	5.89995e9	1.72140
$531$	−1.49721e8	−0.0433963
$532$	−8.87389e8	−0.255519
$533$	−1.63308e9	−0.467157
$534$	−1.81596e8	−0.0516075
$535$	5.93475e9	1.67558
$536$	−6.11710e8	−0.171581
$537$	−3.76756e9	−1.04990
$538$	8.75551e9	2.42406
$539$	4.54561e9	1.25035
$540$	−5.26142e8	−0.143789
$541$	3.20625e9	0.870576	0.435288	−	0.900291i	$-0.356647\pi$
$541$	3.20625e9	0.870576	0.435288	+	0.900291i	$0.356647\pi$
$542$	−2.79046e9	−0.752798
$543$	−3.77151e8	−0.101092
$544$	2.57158e9	0.684862
$545$	−2.01995e9	−0.534506
$546$	−1.72783e9	−0.454284
$547$	−4.82907e8	−0.126156	−0.0630779	−	0.998009i	$-0.520092\pi$
$547$	−4.82907e8	−0.126156	−0.0630779	+	0.998009i	$0.520092\pi$
$548$	3.76388e9	0.977022
$549$	6.36859e8	0.164263
$550$	−3.11487e9	−0.798309
$551$	2.80620e8	0.0714641
$552$	−2.13315e9	−0.539802
$553$	−9.12889e9	−2.29551
$554$	5.88527e9	1.47056
$555$	4.98177e9	1.23697
$556$	−2.01368e8	−0.0496854
$557$	−3.29285e9	−0.807380	−0.403690	−	0.914896i	$-0.632273\pi$
$557$	−3.29285e9	−0.807380	−0.403690	+	0.914896i	$0.632273\pi$
$558$	1.60895e9	0.392032
$559$	−1.48868e9	−0.360463
$560$	9.33466e9	2.24616
$561$	−1.76402e9	−0.421827
$562$	2.07924e9	0.494114
$563$	1.67347e9	0.395220	0.197610	−	0.980281i	$-0.436682\pi$
$563$	1.67347e9	0.395220	0.197610	+	0.980281i	$0.436682\pi$
$564$	−2.55483e9	−0.599633
$565$	7.41859e9	1.73042
$566$	1.04962e10	2.43318
$567$	−6.99729e8	−0.161209
$568$	2.31925e9	0.531041
$569$	5.59667e9	1.27361	0.636805	−	0.771025i	$-0.280255\pi$
$569$	5.59667e9	1.27361	0.636805	+	0.771025i	$0.280255\pi$
$570$	1.18530e9	0.268081
$571$	−6.50267e9	−1.46172	−0.730862	−	0.682525i	$-0.760882\pi$
$571$	−6.50267e9	−1.46172	−0.730862	+	0.682525i	$0.760882\pi$
$572$	1.30029e9	0.290506
$573$	1.03133e9	0.229012
$574$	−9.05240e9	−1.99789
$575$	4.68619e9	1.02797
$576$	−1.53947e8	−0.0335654
$577$	−4.50802e9	−0.976945	−0.488473	−	0.872579i	$-0.662446\pi$
$577$	−4.50802e9	−0.976945	−0.488473	+	0.872579i	$0.662446\pi$
$578$	3.42225e9	0.737164
$579$	9.96959e8	0.213453
$580$	8.52748e8	0.181477
$581$	4.13907e9	0.875560
$582$	3.98857e9	0.838661
$583$	−5.90494e9	−1.23417
$584$	1.98226e9	0.411828
$585$	8.64175e8	0.178466
$586$	5.14346e9	1.05588
$587$	6.96930e9	1.42218	0.711092	−	0.703099i	$-0.248201\pi$
$587$	6.96930e9	1.42218	0.711092	+	0.703099i	$0.248201\pi$
$588$	−1.88262e9	−0.381894
$589$	−1.35723e9	−0.273683
$590$	1.02497e9	0.205461
$591$	−2.82689e9	−0.563318
$592$	1.07468e10	2.12888
$593$	1.72102e9	0.338917	0.169459	−	0.985537i	$-0.445798\pi$
$593$	1.72102e9	0.338917	0.169459	+	0.985537i	$0.445798\pi$
$594$	1.40632e9	0.275316
$595$	−6.00865e9	−1.16941
$596$	−1.51689e9	−0.293489
$597$	3.35059e9	0.644483
$598$	−5.22438e9	−0.999036
$599$	4.56819e9	0.868460	0.434230	−	0.900802i	$-0.357021\pi$
$599$	4.56819e9	0.868460	0.434230	+	0.900802i	$0.357021\pi$
$600$	−8.65160e8	−0.163518
$601$	−2.34532e9	−0.440698	−0.220349	−	0.975421i	$-0.570720\pi$
$601$	−2.34532e9	−0.440698	−0.220349	+	0.975421i	$0.570720\pi$
$602$	−8.25197e9	−1.54159
$603$	−6.06720e8	−0.112688
$604$	1.02499e9	0.189273
$605$	1.90534e9	0.349807
$606$	−5.26406e9	−0.960875
$607$	3.67032e9	0.666107	0.333053	−	0.942908i	$-0.391921\pi$
$607$	3.67032e9	0.666107	0.333053	+	0.942908i	$0.391921\pi$
$608$	1.72938e9	0.312052
$609$	1.13409e9	0.203464
$610$	−4.35984e9	−0.777706
$611$	4.19624e9	0.744246
$612$	7.30593e8	0.128839
$613$	3.62973e9	0.636447	0.318223	−	0.948016i	$-0.396914\pi$
$613$	3.62973e9	0.636447	0.318223	+	0.948016i	$0.396914\pi$
$614$	3.71502e9	0.647697
$615$	4.52756e9	0.784876
$616$	−4.83372e9	−0.833199
$617$	4.89208e9	0.838486	0.419243	−	0.907874i	$-0.362296\pi$
$617$	4.89208e9	0.838486	0.419243	+	0.907874i	$0.362296\pi$
$618$	−6.10856e8	−0.104107
$619$	−8.57865e9	−1.45379	−0.726895	−	0.686749i	$-0.759037\pi$
$619$	−8.57865e9	−1.45379	−0.726895	+	0.686749i	$0.759037\pi$
$620$	−4.12434e9	−0.694997
$621$	−2.11575e9	−0.354522
$622$	−6.33392e9	−1.05537
$623$	6.19080e8	0.102574
$624$	1.86421e9	0.307149
$625$	−7.60884e9	−1.24663
$626$	−6.26150e8	−0.102016
$627$	−1.18630e9	−0.192202
$628$	−2.27166e9	−0.366003
$629$	−6.91761e9	−1.10836
$630$	4.79024e9	0.763247
$631$	5.81549e9	0.921475	0.460737	−	0.887537i	$-0.347585\pi$
$631$	5.81549e9	0.921475	0.460737	+	0.887537i	$0.347585\pi$
$632$	5.09598e9	0.803005
$633$	2.26733e9	0.355305
$634$	−2.49403e9	−0.388677
$635$	4.34201e9	0.672950
$636$	2.44561e9	0.376953
$637$	3.09216e9	0.473995
$638$	−2.27930e9	−0.347479
$639$	2.30033e9	0.348768
$640$	−7.72567e9	−1.16495
$641$	−1.97168e6	−0.000295688 0	−0.000147844	−	1.00000i	$-0.500047\pi$
$641$	−1.97168e6	−0.000295688 0	−0.000147844		1.00000i	$0.500047\pi$
$642$	6.56984e9	0.979901
$643$	−5.68675e9	−0.843580	−0.421790	−	0.906694i	$-0.638598\pi$
$643$	−5.68675e9	−0.843580	−0.421790	+	0.906694i	$0.638598\pi$
$644$	−1.08437e10	−1.59984
$645$	4.12722e9	0.605618
$646$	−1.64589e9	−0.240208
$647$	8.00900e9	1.16256	0.581278	−	0.813705i	$-0.302553\pi$
$647$	8.00900e9	1.16256	0.581278	+	0.813705i	$0.302553\pi$
$648$	3.90607e8	0.0563933
$649$	−1.02583e9	−0.147306
$650$	−2.11890e9	−0.302631
$651$	−5.48505e9	−0.779197
$652$	−4.53532e9	−0.640828
$653$	4.57134e9	0.642462	0.321231	−	0.947001i	$-0.395903\pi$
$653$	4.57134e9	0.642462	0.321231	+	0.947001i	$0.395903\pi$
$654$	−2.23611e9	−0.312587
$655$	2.84815e9	0.396021
$656$	9.76692e9	1.35081
$657$	1.96609e9	0.270473
$658$	2.32604e10	3.18292
$659$	1.31699e10	1.79260	0.896298	−	0.443452i	$-0.146246\pi$
$659$	1.31699e10	1.79260	0.896298	+	0.443452i	$0.146246\pi$
$660$	−3.60493e9	−0.488083
$661$	−7.04155e9	−0.948338	−0.474169	−	0.880434i	$-0.657251\pi$
$661$	−7.04155e9	−0.948338	−0.474169	+	0.880434i	$0.657251\pi$
$662$	−5.99517e9	−0.803153
$663$	−1.19998e9	−0.159910
$664$	−2.31053e9	−0.306284
$665$	−4.04080e9	−0.532834
$666$	5.51488e9	0.723397
$667$	3.42911e9	0.447446
$668$	7.93497e9	1.02998
$669$	−6.89592e9	−0.890433
$670$	4.15351e9	0.533523
$671$	4.36352e9	0.557581
$672$	6.98907e9	0.888437
$673$	8.33165e8	0.105361	0.0526803	−	0.998611i	$-0.483224\pi$
$673$	8.33165e8	0.105361	0.0526803	+	0.998611i	$0.483224\pi$
$674$	8.31923e9	1.04658
$675$	−8.58102e8	−0.107393
$676$	−3.92312e9	−0.488448
$677$	1.49936e10	1.85715	0.928573	−	0.371150i	$-0.121036\pi$
$677$	1.49936e10	1.85715	0.928573	+	0.371150i	$0.121036\pi$
$678$	8.21247e9	1.01198
$679$	−1.35974e10	−1.66691
$680$	3.35419e9	0.409078
$681$	−7.96437e9	−0.966354
$682$	1.10239e10	1.33073
$683$	6.61866e9	0.794873	0.397436	−	0.917630i	$-0.369900\pi$
$683$	6.61866e9	0.794873	0.397436	+	0.917630i	$0.369900\pi$
$684$	4.91322e8	0.0587043
$685$	1.71392e10	2.03738
$686$	1.62951e9	0.192718
$687$	−1.06877e9	−0.125758
$688$	8.90331e9	1.04230
$689$	−4.01684e9	−0.467862
$690$	1.44841e10	1.67849
$691$	7.24311e9	0.835125	0.417563	−	0.908648i	$-0.362884\pi$
$691$	7.24311e9	0.835125	0.417563	+	0.908648i	$0.362884\pi$
$692$	5.73954e9	0.658424
$693$	−4.79428e9	−0.547214
$694$	−8.76579e9	−0.995480
$695$	−9.16947e8	−0.103609
$696$	−6.33078e8	−0.0711746
$697$	−6.28689e9	−0.703269
$698$	−7.52730e9	−0.837810
$699$	4.65549e8	0.0515579
$700$	−4.39796e9	−0.484628
$701$	−2.33354e9	−0.255860	−0.127930	−	0.991783i	$-0.540833\pi$
$701$	−2.33354e9	−0.255860	−0.127930	+	0.991783i	$0.540833\pi$
$702$	9.56652e8	0.104370
$703$	−4.65208e9	−0.505014
$704$	−1.05479e9	−0.113936
$705$	−1.16337e10	−1.25042
$706$	−1.06160e10	−1.13538
$707$	1.79457e10	1.90982
$708$	4.24863e8	0.0449917
$709$	4.23075e9	0.445816	0.222908	−	0.974839i	$-0.428445\pi$
$709$	4.23075e9	0.445816	0.222908	+	0.974839i	$0.428445\pi$
$710$	−1.57477e10	−1.65125
$711$	5.05441e9	0.527384
$712$	−3.45587e8	−0.0358820
$713$	−1.65850e10	−1.71357
$714$	−6.65165e9	−0.683889
$715$	5.92100e9	0.605793
$716$	1.06912e10	1.08850
$717$	−9.39242e7	−0.00951614
$718$	−6.69818e9	−0.675338
$719$	−1.25609e10	−1.26029	−0.630143	−	0.776479i	$-0.717004\pi$
$719$	−1.25609e10	−1.26029	−0.630143	+	0.776479i	$0.717004\pi$
$720$	−5.16834e9	−0.516045
$721$	2.08247e9	0.206921
$722$	1.16795e10	1.15490
$723$	−6.06985e9	−0.597302
$724$	1.07024e9	0.104808
$725$	1.39077e9	0.135542
$726$	2.10924e9	0.204572
$727$	9.77361e9	0.943375	0.471688	−	0.881766i	$-0.343645\pi$
$727$	9.77361e9	0.943375	0.471688	+	0.881766i	$0.343645\pi$
$728$	−3.28815e9	−0.315858
$729$	3.87420e8	0.0370370
$730$	−1.34595e10	−1.28056
$731$	−5.73099e9	−0.542649
$732$	−1.80721e9	−0.170302
$733$	−4.89324e9	−0.458915	−0.229458	−	0.973319i	$-0.573695\pi$
$733$	−4.89324e9	−0.458915	−0.229458	+	0.973319i	$0.573695\pi$
$734$	−5.83162e9	−0.544318
$735$	−8.57270e9	−0.796364
$736$	2.11326e10	1.95380
$737$	−4.15702e9	−0.382512
$738$	5.01206e9	0.459007
$739$	−1.16838e10	−1.06495	−0.532473	−	0.846447i	$-0.678737\pi$
$739$	−1.16838e10	−1.06495	−0.532473	+	0.846447i	$0.678737\pi$
$740$	−1.41367e10	−1.28244
$741$	−8.06984e8	−0.0728620
$742$	−2.22659e10	−2.00091
$743$	−2.02352e9	−0.180987	−0.0904934	−	0.995897i	$-0.528844\pi$
$743$	−2.02352e9	−0.180987	−0.0904934	+	0.995897i	$0.528844\pi$
$744$	3.06190e9	0.272575
$745$	−6.90728e9	−0.612012
$746$	−2.53185e10	−2.23281
$747$	−2.29169e9	−0.201156
$748$	5.00575e9	0.437335
$749$	−2.23972e10	−1.94764
$750$	−4.65266e9	−0.402705
$751$	−5.88364e8	−0.0506881	−0.0253441	−	0.999679i	$-0.508068\pi$
$751$	−5.88364e8	−0.0506881	−0.0253441	+	0.999679i	$0.508068\pi$
$752$	−2.50963e10	−2.15203
$753$	−1.13417e10	−0.968047
$754$	−1.55050e9	−0.131726
$755$	4.66736e9	0.394691
$756$	1.98562e9	0.167136
$757$	−1.84565e10	−1.54637	−0.773185	−	0.634181i	$-0.781337\pi$
$757$	−1.84565e10	−1.54637	−0.773185	+	0.634181i	$0.781337\pi$
$758$	2.91005e9	0.242693
$759$	−1.44963e10	−1.20340
$760$	2.25568e9	0.186393
$761$	1.56129e10	1.28421	0.642105	−	0.766617i	$-0.278061\pi$
$761$	1.56129e10	1.28421	0.642105	+	0.766617i	$0.278061\pi$
$762$	4.80666e9	0.393551
$763$	7.62311e9	0.621293
$764$	−2.92660e9	−0.237431
$765$	3.32682e9	0.268667
$766$	2.27438e10	1.82836
$767$	−6.97826e8	−0.0558423
$768$	−9.28224e9	−0.739415
$769$	2.12983e10	1.68889	0.844446	−	0.535641i	$-0.179930\pi$
$769$	2.12983e10	1.68889	0.844446	+	0.535641i	$0.179930\pi$
$770$	3.28209e10	2.59080
$771$	−5.39457e9	−0.423903
$772$	−2.82906e9	−0.221300
$773$	1.58105e10	1.23116	0.615582	−	0.788073i	$-0.288921\pi$
$773$	1.58105e10	1.23116	0.615582	+	0.788073i	$0.288921\pi$
$774$	4.56888e9	0.354174
$775$	−6.72651e9	−0.519079
$776$	7.59043e9	0.583110
$777$	−1.88008e10	−1.43781
$778$	8.73587e9	0.665086
$779$	−4.22792e9	−0.320439
$780$	−2.45226e9	−0.185027
$781$	1.57610e10	1.18387
$782$	−2.01124e10	−1.50397
$783$	−6.27913e8	−0.0467448
$784$	−1.84932e10	−1.37058
$785$	−1.03442e10	−0.763227
$786$	3.15294e9	0.231599
$787$	2.69394e9	0.197005	0.0985024	−	0.995137i	$-0.468595\pi$
$787$	2.69394e9	0.197005	0.0985024	+	0.995137i	$0.468595\pi$
$788$	8.02186e9	0.584027
$789$	−1.37836e10	−0.999066
$790$	−3.46017e10	−2.49691
$791$	−2.79971e10	−2.01139
$792$	2.67629e9	0.191424
$793$	2.96829e9	0.211374
$794$	−1.88858e9	−0.133895
$795$	1.11363e10	0.786060
$796$	−9.50795e9	−0.668176
$797$	5.54182e9	0.387747	0.193873	−	0.981027i	$-0.437895\pi$
$797$	5.54182e9	0.387747	0.193873	+	0.981027i	$0.437895\pi$
$798$	−4.47322e9	−0.311609
$799$	1.61543e10	1.12040
$800$	8.57093e9	0.591852
$801$	−3.42767e8	−0.0235660
$802$	−9.07385e9	−0.621128
$803$	1.34709e10	0.918106
$804$	1.72168e9	0.116831
$805$	−4.93776e10	−3.33614
$806$	7.49903e9	0.504466
$807$	1.65262e10	1.10692
$808$	−1.00178e10	−0.668084
$809$	1.56002e10	1.03589	0.517943	−	0.855415i	$-0.326698\pi$
$809$	1.56002e10	1.03589	0.517943	+	0.855415i	$0.326698\pi$
$810$	−2.65222e9	−0.175353
$811$	−7.79846e9	−0.513377	−0.256688	−	0.966494i	$-0.582631\pi$
$811$	−7.79846e9	−0.513377	−0.256688	+	0.966494i	$0.582631\pi$
$812$	−3.21820e9	−0.210944
$813$	−5.26706e9	−0.343757
$814$	3.77859e10	2.45553
$815$	−2.06520e10	−1.33632
$816$	7.17668e9	0.462390
$817$	−3.85408e9	−0.247254
$818$	−1.35281e10	−0.864173
$819$	−3.26132e9	−0.207444
$820$	−1.28478e10	−0.813731
$821$	5.49348e9	0.346455	0.173227	−	0.984882i	$-0.444580\pi$
$821$	5.49348e9	0.346455	0.173227	+	0.984882i	$0.444580\pi$
$822$	1.89733e10	1.19149
$823$	2.49423e10	1.55969	0.779843	−	0.625976i	$-0.215299\pi$
$823$	2.49423e10	1.55969	0.779843	+	0.625976i	$0.215299\pi$
$824$	−1.16249e9	−0.0723841
$825$	−5.87939e9	−0.364539
$826$	−3.86814e9	−0.238821
$827$	−3.09149e10	−1.90063	−0.950317	−	0.311285i	$-0.899241\pi$
$827$	−3.09149e10	−1.90063	−0.950317	+	0.311285i	$0.899241\pi$
$828$	6.00384e9	0.367555
$829$	−7.17903e8	−0.0437648	−0.0218824	−	0.999761i	$-0.506966\pi$
$829$	−7.17903e8	−0.0437648	−0.0218824	+	0.999761i	$0.506966\pi$
$830$	1.56885e10	0.952376
$831$	1.11086e10	0.671514
$832$	−7.17521e8	−0.0431920
$833$	1.19039e10	0.713563
$834$	−1.01507e9	−0.0605921
$835$	3.61326e10	2.14781
$836$	3.36636e9	0.199268
$837$	3.03692e9	0.179017
$838$	2.84678e10	1.67109
$839$	−1.00495e10	−0.587460	−0.293730	−	0.955888i	$-0.594897\pi$
$839$	−1.00495e10	−0.587460	−0.293730	+	0.955888i	$0.594897\pi$
$840$	9.11605e9	0.530676
$841$	−1.62322e10	−0.941003
$842$	−3.42473e9	−0.197713
$843$	3.92461e9	0.225631
$844$	−6.43397e9	−0.368367
$845$	−1.78643e10	−1.01856
$846$	−1.28786e10	−0.731261
$847$	−7.19059e9	−0.406605
$848$	2.40234e10	1.35285
$849$	1.98118e10	1.11108
$850$	−8.15714e9	−0.455588
$851$	−5.68473e10	−3.16196
$852$	−6.52762e9	−0.361590
$853$	7.41016e9	0.408795	0.204398	−	0.978888i	$-0.434476\pi$
$853$	7.41016e9	0.408795	0.204398	+	0.978888i	$0.434476\pi$
$854$	1.64536e10	0.903982
$855$	2.23728e9	0.122416
$856$	1.25027e10	0.681313
$857$	1.81207e10	0.983429	0.491714	−	0.870757i	$-0.336370\pi$
$857$	1.81207e10	0.983429	0.491714	+	0.870757i	$0.336370\pi$
$858$	6.55462e9	0.354276
$859$	1.04208e10	0.560953	0.280477	−	0.959861i	$-0.409508\pi$
$859$	1.04208e10	0.560953	0.280477	+	0.959861i	$0.409508\pi$
$860$	−1.17118e10	−0.627882
$861$	−1.70866e10	−0.912315
$862$	2.02614e10	1.07744
$863$	−2.49924e10	−1.32364	−0.661821	−	0.749662i	$-0.730216\pi$
$863$	−2.49924e10	−1.32364	−0.661821	+	0.749662i	$0.730216\pi$
$864$	−3.86965e9	−0.204114
$865$	2.61355e10	1.37301
$866$	−3.56318e10	−1.86434
$867$	6.45957e9	0.336618
$868$	1.55649e10	0.807843
$869$	3.46309e10	1.79017
$870$	4.29860e9	0.221314
$871$	−2.82782e9	−0.145007
$872$	−4.25542e9	−0.217337
$873$	7.52851e9	0.382965
$874$	−1.35255e10	−0.685273
$875$	1.58614e10	0.800410
$876$	−5.57916e9	−0.280417
$877$	−1.00470e10	−0.502964	−0.251482	−	0.967862i	$-0.580918\pi$
$877$	−1.00470e10	−0.502964	−0.251482	+	0.967862i	$0.580918\pi$
$878$	−1.85527e10	−0.925075
$879$	9.70840e9	0.482155
$880$	−3.54115e10	−1.75168
$881$	−3.06184e10	−1.50858	−0.754288	−	0.656544i	$-0.772018\pi$
$881$	−3.06184e10	−1.50858	−0.754288	+	0.656544i	$0.772018\pi$
$882$	−9.49008e9	−0.465725
$883$	5.86608e9	0.286738	0.143369	−	0.989669i	$-0.454206\pi$
$883$	5.86608e9	0.286738	0.143369	+	0.989669i	$0.454206\pi$
$884$	3.40517e9	0.165789
$885$	1.93465e9	0.0938213
$886$	6.09391e9	0.294359
$887$	1.17203e9	0.0563905	0.0281953	−	0.999602i	$-0.491024\pi$
$887$	1.17203e9	0.0563905	0.0281953	+	0.999602i	$0.491024\pi$
$888$	1.04951e10	0.502968
$889$	−1.63864e10	−0.782217
$890$	2.34653e9	0.111574
$891$	2.65446e9	0.125720
$892$	1.95685e10	0.923168
$893$	1.08637e10	0.510504
$894$	−7.64644e9	−0.357913
$895$	4.86832e10	2.26986
$896$	2.91560e10	1.35410
$897$	−9.86114e9	−0.456198
$898$	−4.70952e10	−2.17025
$899$	−4.92210e9	−0.225939
$900$	2.43503e9	0.111341
$901$	−1.54637e10	−0.704330
$902$	3.43408e10	1.55807
$903$	−1.55758e10	−0.703951
$904$	1.56287e10	0.703614
$905$	4.87342e9	0.218557
$906$	5.16683e9	0.230821
$907$	1.61777e10	0.719932	0.359966	−	0.932965i	$-0.382788\pi$
$907$	1.61777e10	0.719932	0.359966	+	0.932965i	$0.382788\pi$
$908$	2.26004e10	1.00188
$909$	−9.93603e9	−0.438773
$910$	2.23265e10	0.982145
$911$	−1.77685e10	−0.778637	−0.389319	−	0.921103i	$-0.627290\pi$
$911$	−1.77685e10	−0.778637	−0.389319	+	0.921103i	$0.627290\pi$
$912$	4.82630e9	0.210684
$913$	−1.57018e10	−0.682812
$914$	6.12981e9	0.265543
$915$	−8.22929e9	−0.355131
$916$	3.03284e9	0.130381
$917$	−1.07487e10	−0.460322
$918$	3.68283e9	0.157120
$919$	2.24473e10	0.954024	0.477012	−	0.878897i	$-0.341720\pi$
$919$	2.24473e10	0.954024	0.477012	+	0.878897i	$0.341720\pi$
$920$	2.75639e10	1.16703
$921$	7.01219e9	0.295764
$922$	3.12098e10	1.31139
$923$	1.07214e10	0.448794
$924$	1.36047e10	0.567332
$925$	−2.30560e10	−0.957830
$926$	5.00452e10	2.07121
$927$	−1.15300e9	−0.0475392
$928$	6.27175e9	0.257615
$929$	−2.97565e10	−1.21766	−0.608831	−	0.793300i	$-0.708361\pi$
$929$	−2.97565e10	−1.21766	−0.608831	+	0.793300i	$0.708361\pi$
$930$	−2.07903e10	−0.847559
$931$	8.00535e9	0.325130
$932$	−1.32109e9	−0.0534534
$933$	−1.19554e10	−0.481924
$934$	−8.57937e9	−0.344541
$935$	2.27941e10	0.911974
$936$	1.82055e9	0.0725669
$937$	2.60896e9	0.103605	0.0518023	−	0.998657i	$-0.483503\pi$
$937$	2.60896e9	0.103605	0.0518023	+	0.998657i	$0.483503\pi$
$938$	−1.56750e10	−0.620151
$939$	−1.18187e9	−0.0465845
$940$	3.30127e10	1.29639
$941$	3.46382e10	1.35516	0.677582	−	0.735447i	$-0.263028\pi$
$941$	3.46382e10	1.35516	0.677582	+	0.735447i	$0.263028\pi$
$942$	−1.14512e10	−0.446346
$943$	−5.16642e10	−2.00631
$944$	4.17346e9	0.161471
$945$	9.04168e9	0.348528
$946$	3.13043e10	1.20222
$947$	−4.81487e10	−1.84230	−0.921149	−	0.389209i	$-0.872748\pi$
$947$	−4.81487e10	−1.84230	−0.921149	+	0.389209i	$0.872748\pi$
$948$	−1.43429e10	−0.546772
$949$	9.16362e9	0.348045
$950$	−5.48566e9	−0.207585
$951$	−4.70753e9	−0.177485
$952$	−1.26584e10	−0.475499
$953$	−1.99375e9	−0.0746182	−0.0373091	−	0.999304i	$-0.511879\pi$
$953$	−1.99375e9	−0.0746182	−0.0373091	+	0.999304i	$0.511879\pi$
$954$	1.23280e10	0.459699
$955$	−1.33266e10	−0.495115
$956$	2.66528e8	0.00986598
$957$	−4.30223e9	−0.158673
$958$	−1.49113e10	−0.547945
$959$	−6.46818e10	−2.36819
$960$	1.98925e9	0.0725673
$961$	−3.70674e9	−0.134729
$962$	2.57039e10	0.930866
$963$	1.24007e10	0.447461
$964$	1.72244e10	0.619261
$965$	−1.28824e10	−0.461478
$966$	−5.46617e10	−1.95103
$967$	−7.83920e9	−0.278791	−0.139396	−	0.990237i	$-0.544516\pi$
$967$	−7.83920e9	−0.278791	−0.139396	+	0.990237i	$0.544516\pi$
$968$	4.01398e9	0.142237
$969$	−3.10665e9	−0.109688
$970$	−5.15390e10	−1.81315
$971$	−4.89013e10	−1.71417	−0.857084	−	0.515177i	$-0.827726\pi$
$971$	−4.89013e10	−1.71417	−0.857084	+	0.515177i	$0.827726\pi$
$972$	−1.09938e9	−0.0383987
$973$	3.46048e9	0.120432
$974$	−6.43142e10	−2.23023
$975$	−3.99947e9	−0.138193
$976$	−1.77524e10	−0.611198
$977$	−2.82603e10	−0.969494	−0.484747	−	0.874654i	$-0.661088\pi$
$977$	−2.82603e10	−0.969494	−0.484747	+	0.874654i	$0.661088\pi$
$978$	−2.28620e10	−0.781499
$979$	−2.34852e9	−0.0799934
$980$	2.43267e10	0.825642
$981$	−4.22070e9	−0.142739
$982$	4.79115e10	1.61454
$983$	4.62408e10	1.55270	0.776351	−	0.630301i	$-0.217068\pi$
$983$	4.62408e10	1.55270	0.776351	+	0.630301i	$0.217068\pi$
$984$	9.53819e9	0.319141
$985$	3.65282e10	1.21787
$986$	−5.96897e9	−0.198303
$987$	4.39044e10	1.45344
$988$	2.28997e9	0.0755407
$989$	−4.70959e10	−1.54809
$990$	−1.81720e10	−0.595224
$991$	1.15771e10	0.377870	0.188935	−	0.981990i	$-0.439497\pi$
$991$	1.15771e10	0.377870	0.188935	+	0.981990i	$0.439497\pi$
$992$	−3.03335e10	−0.986578
$993$	−1.13160e10	−0.366751
$994$	5.94304e10	1.91936
$995$	−4.32953e10	−1.39335
$996$	6.50310e9	0.208551
$997$	4.71011e9	0.150521	0.0752607	−	0.997164i	$-0.476021\pi$
$997$	4.71011e9	0.150521	0.0752607	+	0.997164i	$0.476021\pi$
$998$	3.62258e10	1.15361
$999$	1.04095e10	0.330331

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.c.1.3	✓	17
3.2	odd	2		531.8.a.c.1.15		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.3	✓	17	1.1	even	1	trivial
531.8.a.c.1.15		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)

\(f(q)\)	\(=\)	\(q-14.3045 q^{2} -27.0000 q^{3} +76.6177 q^{4} +348.885 q^{5} +386.221 q^{6} -1316.66 q^{7} +734.996 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-14.3045 q^{2} -27.0000 q^{3} +76.6177 q^{4} +348.885 q^{5} +386.221 q^{6} -1316.66 q^{7} +734.996 q^{8} +729.000 q^{9} -4990.62 q^{10} +4994.84 q^{11} -2068.68 q^{12} +3397.75 q^{13} +18834.2 q^{14} -9419.91 q^{15} -20320.8 q^{16} +13080.3 q^{17} -10428.0 q^{18} +8796.50 q^{19} +26730.8 q^{20} +35549.9 q^{21} -71448.5 q^{22} +107491. q^{23} -19844.9 q^{24} +43596.1 q^{25} -48603.0 q^{26} -19683.0 q^{27} -100880. q^{28} +31901.3 q^{29} +134747. q^{30} -154292. q^{31} +196599. q^{32} -134861. q^{33} -187107. q^{34} -459365. q^{35} +55854.3 q^{36} -528856. q^{37} -125829. q^{38} -91739.2 q^{39} +256430. q^{40} -480637. q^{41} -508523. q^{42} -438138. q^{43} +382693. q^{44} +254338. q^{45} -1.53760e6 q^{46} +1.23501e6 q^{47} +548661. q^{48} +910062. q^{49} -623619. q^{50} -353169. q^{51} +260328. q^{52} -1.18221e6 q^{53} +281555. q^{54} +1.74263e6 q^{55} -967743. q^{56} -237505. q^{57} -456331. q^{58} -205379. q^{59} -721732. q^{60} +873606. q^{61} +2.20706e6 q^{62} -959848. q^{63} -211175. q^{64} +1.18542e6 q^{65} +1.92911e6 q^{66} -832263. q^{67} +1.00219e6 q^{68} -2.90226e6 q^{69} +6.57097e6 q^{70} +3.15545e6 q^{71} +535812. q^{72} +2.69697e6 q^{73} +7.56500e6 q^{74} -1.17709e6 q^{75} +673968. q^{76} -6.57652e6 q^{77} +1.31228e6 q^{78} +6.93335e6 q^{79} -7.08963e6 q^{80} +531441. q^{81} +6.87525e6 q^{82} -3.14360e6 q^{83} +2.72375e6 q^{84} +4.56354e6 q^{85} +6.26733e6 q^{86} -861335. q^{87} +3.67119e6 q^{88} -470189. q^{89} -3.63816e6 q^{90} -4.47369e6 q^{91} +8.23572e6 q^{92} +4.16587e6 q^{93} -1.76661e7 q^{94} +3.06897e6 q^{95} -5.30816e6 q^{96} +1.03272e7 q^{97} -1.30179e7 q^{98} +3.64124e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 2 q^{2} - 459 q^{3} + 1166 q^{4} - 318 q^{5} - 54 q^{6} + 3145 q^{7} + 2355 q^{8} + 12393 q^{9}+O(q^{10}) \) 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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