LMFDB - Embedded newform 177.8.a.a.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:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + \cdots - 23\!\cdots\!32 $ x^16 - 6x^15 - 1493x^14 + 8791x^13 + 890490x^12 - 5107725x^11 - 269092298x^10 + 1488374176x^9 + 42885295136x^8 - 226132003872x^7 - 3353576629440x^6 + 16796366777600x^5 + 99470801612800x^4 - 494039551757568x^3 - 493048066650624x^2 + 3193975642099712*x - 2385018853548032
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$16.2952$ 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)

$f(q)$	$=$	$q-16.2952 q^{2} -27.0000 q^{3} +137.534 q^{4} +495.569 q^{5} +439.971 q^{6} +565.301 q^{7} -155.363 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-16.2952 q^{2} -27.0000 q^{3} +137.534 q^{4} +495.569 q^{5} +439.971 q^{6} +565.301 q^{7} -155.363 q^{8} +729.000 q^{9} -8075.41 q^{10} -826.834 q^{11} -3713.43 q^{12} +11479.1 q^{13} -9211.71 q^{14} -13380.4 q^{15} -15072.7 q^{16} -23564.6 q^{17} -11879.2 q^{18} -53546.6 q^{19} +68157.8 q^{20} -15263.1 q^{21} +13473.4 q^{22} -87155.1 q^{23} +4194.81 q^{24} +167464. q^{25} -187055. q^{26} -19683.0 q^{27} +77748.3 q^{28} +26745.6 q^{29} +218036. q^{30} -231681. q^{31} +265500. q^{32} +22324.5 q^{33} +383990. q^{34} +280146. q^{35} +100263. q^{36} +409893. q^{37} +872554. q^{38} -309936. q^{39} -76993.4 q^{40} +189635. q^{41} +248716. q^{42} -849460. q^{43} -113718. q^{44} +361270. q^{45} +1.42021e6 q^{46} -902990. q^{47} +406963. q^{48} -503977. q^{49} -2.72886e6 q^{50} +636244. q^{51} +1.57877e6 q^{52} -324949. q^{53} +320739. q^{54} -409753. q^{55} -87827.2 q^{56} +1.44576e6 q^{57} -435826. q^{58} +205379. q^{59} -1.84026e6 q^{60} -1.58592e6 q^{61} +3.77529e6 q^{62} +412105. q^{63} -2.39707e6 q^{64} +5.68870e6 q^{65} -363783. q^{66} -2.57819e6 q^{67} -3.24094e6 q^{68} +2.35319e6 q^{69} -4.56504e6 q^{70} -678037. q^{71} -113260. q^{72} +2.50036e6 q^{73} -6.67930e6 q^{74} -4.52153e6 q^{75} -7.36449e6 q^{76} -467410. q^{77} +5.05048e6 q^{78} -7.33035e6 q^{79} -7.46957e6 q^{80} +531441. q^{81} -3.09015e6 q^{82} +3.91602e6 q^{83} -2.09920e6 q^{84} -1.16779e7 q^{85} +1.38421e7 q^{86} -722131. q^{87} +128460. q^{88} +3.80382e6 q^{89} -5.88698e6 q^{90} +6.48916e6 q^{91} -1.19868e7 q^{92} +6.25539e6 q^{93} +1.47144e7 q^{94} -2.65361e7 q^{95} -7.16849e6 q^{96} -7.68854e6 q^{97} +8.21243e6 q^{98} -602762. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 432 q^{3} + 974 q^{4} - 68 q^{5} + 162 q^{6} - 2343 q^{7} + 819 q^{8} + 11664 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 - 432 * q^3 + 974 * q^4 - 68 * q^5 + 162 * q^6 - 2343 * q^7 + 819 * q^8 + 11664 * q^9	\( 16 q - 6 q^{2} - 432 q^{3} + 974 q^{4} - 68 q^{5} + 162 q^{6} - 2343 q^{7} + 819 q^{8} + 11664 q^{9} - 3479 q^{10} + 898 q^{11} - 26298 q^{12} - 8172 q^{13} - 13315 q^{14} + 1836 q^{15} + 3138 q^{16} - 44985 q^{17} - 4374 q^{18} - 40137 q^{19} + 130657 q^{20} + 63261 q^{21} + 109394 q^{22} - 2833 q^{23} - 22113 q^{24} + 285746 q^{25} - 129420 q^{26} - 314928 q^{27} + 112890 q^{28} + 144375 q^{29} + 93933 q^{30} - 141759 q^{31} - 36224 q^{32} - 24246 q^{33} - 341332 q^{34} - 78859 q^{35} + 710046 q^{36} - 297971 q^{37} + 329075 q^{38} + 220644 q^{39} - 203048 q^{40} + 659077 q^{41} + 359505 q^{42} - 1431608 q^{43} + 254916 q^{44} - 49572 q^{45} + 873113 q^{46} - 1574073 q^{47} - 84726 q^{48} + 1893545 q^{49} + 302533 q^{50} + 1214595 q^{51} - 4972548 q^{52} + 587736 q^{53} + 118098 q^{54} - 4624036 q^{55} - 5798506 q^{56} + 1083699 q^{57} - 6991380 q^{58} + 3286064 q^{59} - 3527739 q^{60} - 6117131 q^{61} - 11570258 q^{62} - 1708047 q^{63} - 19063011 q^{64} - 5335514 q^{65} - 2953638 q^{66} - 16518710 q^{67} - 17284669 q^{68} + 76491 q^{69} - 39189486 q^{70} - 10882582 q^{71} + 597051 q^{72} - 21097441 q^{73} - 16717030 q^{74} - 7715142 q^{75} - 40864952 q^{76} - 3404601 q^{77} + 3494340 q^{78} - 3784458 q^{79} - 27466195 q^{80} + 8503056 q^{81} - 24990117 q^{82} - 1951425 q^{83} - 3048030 q^{84} - 23238675 q^{85} - 35910572 q^{86} - 3898125 q^{87} - 27843055 q^{88} + 10499443 q^{89} - 2536191 q^{90} + 699217 q^{91} - 20062766 q^{92} + 3827493 q^{93} - 59358988 q^{94} - 29236333 q^{95} + 978048 q^{96} - 25158976 q^{97} + 2120460 q^{98} + 654642 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 432 * q^3 + 974 * q^4 - 68 * q^5 + 162 * q^6 - 2343 * q^7 + 819 * q^8 + 11664 * q^9 - 3479 * q^10 + 898 * q^11 - 26298 * q^12 - 8172 * q^13 - 13315 * q^14 + 1836 * q^15 + 3138 * q^16 - 44985 * q^17 - 4374 * q^18 - 40137 * q^19 + 130657 * q^20 + 63261 * q^21 + 109394 * q^22 - 2833 * q^23 - 22113 * q^24 + 285746 * q^25 - 129420 * q^26 - 314928 * q^27 + 112890 * q^28 + 144375 * q^29 + 93933 * q^30 - 141759 * q^31 - 36224 * q^32 - 24246 * q^33 - 341332 * q^34 - 78859 * q^35 + 710046 * q^36 - 297971 * q^37 + 329075 * q^38 + 220644 * q^39 - 203048 * q^40 + 659077 * q^41 + 359505 * q^42 - 1431608 * q^43 + 254916 * q^44 - 49572 * q^45 + 873113 * q^46 - 1574073 * q^47 - 84726 * q^48 + 1893545 * q^49 + 302533 * q^50 + 1214595 * q^51 - 4972548 * q^52 + 587736 * q^53 + 118098 * q^54 - 4624036 * q^55 - 5798506 * q^56 + 1083699 * q^57 - 6991380 * q^58 + 3286064 * q^59 - 3527739 * q^60 - 6117131 * q^61 - 11570258 * q^62 - 1708047 * q^63 - 19063011 * q^64 - 5335514 * q^65 - 2953638 * q^66 - 16518710 * q^67 - 17284669 * q^68 + 76491 * q^69 - 39189486 * q^70 - 10882582 * q^71 + 597051 * q^72 - 21097441 * q^73 - 16717030 * q^74 - 7715142 * q^75 - 40864952 * q^76 - 3404601 * q^77 + 3494340 * q^78 - 3784458 * q^79 - 27466195 * q^80 + 8503056 * q^81 - 24990117 * q^82 - 1951425 * q^83 - 3048030 * q^84 - 23238675 * q^85 - 35910572 * q^86 - 3898125 * q^87 - 27843055 * q^88 + 10499443 * q^89 - 2536191 * q^90 + 699217 * q^91 - 20062766 * q^92 + 3827493 * q^93 - 59358988 * q^94 - 29236333 * q^95 + 978048 * q^96 - 25158976 * q^97 + 2120460 * q^98 + 654642 * 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 $

$2$	−16.2952	−1.44031	−0.720154	−	0.693814i	$-0.755929\pi$
$2$	−16.2952	−1.44031	−0.720154	+	0.693814i	$0.755929\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	137.534	1.07449
$5$	495.569	1.77300	0.886502	−	0.462726i	$-0.153128\pi$
$5$	495.569	1.77300	0.886502	+	0.462726i	$0.153128\pi$
$6$	439.971	0.831562
$7$	565.301	0.622927	0.311463	−	0.950258i	$-0.399181\pi$
$7$	565.301	0.622927	0.311463	+	0.950258i	$0.399181\pi$
$8$	−155.363	−0.107284
$9$	729.000	0.333333
$10$	−8075.41	−2.55367
$11$	−826.834	−0.187303	−0.0936513	−	0.995605i	$-0.529854\pi$
$11$	−826.834	−0.187303	−0.0936513	+	0.995605i	$0.529854\pi$
$12$	−3713.43	−0.620355
$13$	11479.1	1.44913	0.724564	−	0.689207i	$-0.242041\pi$
$13$	11479.1	1.44913	0.724564	+	0.689207i	$0.242041\pi$
$14$	−9211.71	−0.897206
$15$	−13380.4	−1.02364
$16$	−15072.7	−0.919965
$17$	−23564.6	−1.16329	−0.581646	−	0.813442i	$-0.697591\pi$
$17$	−23564.6	−1.16329	−0.581646	+	0.813442i	$0.697591\pi$
$18$	−11879.2	−0.480103
$19$	−53546.6	−1.79099	−0.895497	−	0.445067i	$-0.853180\pi$
$19$	−53546.6	−1.79099	−0.895497	+	0.445067i	$0.853180\pi$
$20$	68157.8	1.90507
$21$	−15263.1	−0.359647
$22$	13473.4	0.269773
$23$	−87155.1	−1.49364	−0.746819	−	0.665028i	$-0.768420\pi$
$23$	−87155.1	−1.49364	−0.746819	+	0.665028i	$0.768420\pi$
$24$	4194.81	0.0619403
$25$	167464.	2.14354
$26$	−187055.	−2.08719
$27$	−19683.0	−0.192450
$28$	77748.3	0.669326
$29$	26745.6	0.203638	0.101819	−	0.994803i	$-0.467534\pi$
$29$	26745.6	0.203638	0.101819	+	0.994803i	$0.467534\pi$
$30$	218036.	1.47436
$31$	−231681.	−1.39677	−0.698384	−	0.715723i	$-0.746097\pi$
$31$	−231681.	−1.39677	−0.698384	+	0.715723i	$0.746097\pi$
$32$	265500.	1.43232
$33$	22324.5	0.108139
$34$	383990.	1.67550
$35$	280146.	1.10445
$36$	100263.	0.358162
$37$	409893.	1.33035	0.665173	−	0.746689i	$-0.268358\pi$
$37$	409893.	1.33035	0.665173	+	0.746689i	$0.268358\pi$
$38$	872554.	2.57958
$39$	−309936.	−0.836655
$40$	−76993.4	−0.190214
$41$	189635.	0.429710	0.214855	−	0.976646i	$-0.431072\pi$
$41$	189635.	0.429710	0.214855	+	0.976646i	$0.431072\pi$
$42$	248716.	0.518002
$43$	−849460.	−1.62931	−0.814654	−	0.579947i	$-0.803073\pi$
$43$	−849460.	−1.62931	−0.814654	+	0.579947i	$0.803073\pi$
$44$	−113718.	−0.201254
$45$	361270.	0.591001
$46$	1.42021e6	2.15130
$47$	−902990.	−1.26865	−0.634323	−	0.773068i	$-0.718721\pi$
$47$	−902990.	−1.26865	−0.634323	+	0.773068i	$0.718721\pi$
$48$	406963.	0.531142
$49$	−503977.	−0.611963
$50$	−2.72886e6	−3.08736
$51$	636244.	0.671627
$52$	1.57877e6	1.55707
$53$	−324949.	−0.299812	−0.149906	−	0.988700i	$-0.547897\pi$
$53$	−324949.	−0.299812	−0.149906	+	0.988700i	$0.547897\pi$
$54$	320739.	0.277187
$55$	−409753.	−0.332088
$56$	−87827.2	−0.0668299
$57$	1.44576e6	1.03403
$58$	−435826.	−0.293302
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	−1.84026e6	−1.09989
$61$	−1.58592e6	−0.894598	−0.447299	−	0.894384i	$-0.647614\pi$
$61$	−1.58592e6	−0.894598	−0.447299	+	0.894384i	$0.647614\pi$
$62$	3.77529e6	2.01178
$63$	412105.	0.207642
$64$	−2.39707e6	−1.14301
$65$	5.68870e6	2.56931
$66$	−363783.	−0.155754
$67$	−2.57819e6	−1.04726	−0.523629	−	0.851947i	$-0.675422\pi$
$67$	−2.57819e6	−1.04726	−0.523629	+	0.851947i	$0.675422\pi$
$68$	−3.24094e6	−1.24994
$69$	2.35319e6	0.862352
$70$	−4.56504e6	−1.59075
$71$	−678037.	−0.224827	−0.112414	−	0.993661i	$-0.535858\pi$
$71$	−678037.	−0.224827	−0.112414	+	0.993661i	$0.535858\pi$
$72$	−113260.	−0.0357613
$73$	2.50036e6	0.752269	0.376135	−	0.926565i	$-0.377253\pi$
$73$	2.50036e6	0.752269	0.376135	+	0.926565i	$0.377253\pi$
$74$	−6.67930e6	−1.91611
$75$	−4.52153e6	−1.23757
$76$	−7.36449e6	−1.92440
$77$	−467410.	−0.116676
$78$	5.05048e6	1.20504
$79$	−7.33035e6	−1.67275	−0.836373	−	0.548161i	$-0.815328\pi$
$79$	−7.33035e6	−1.67275	−0.836373	+	0.548161i	$0.815328\pi$
$80$	−7.46957e6	−1.63110
$81$	531441.	0.111111
$82$	−3.09015e6	−0.618914
$83$	3.91602e6	0.751747	0.375874	−	0.926671i	$-0.377343\pi$
$83$	3.91602e6	0.751747	0.375874	+	0.926671i	$0.377343\pi$
$84$	−2.09920e6	−0.386436
$85$	−1.16779e7	−2.06252
$86$	1.38421e7	2.34670
$87$	−722131.	−0.117571
$88$	128460.	0.0200945
$89$	3.80382e6	0.571946	0.285973	−	0.958238i	$-0.407683\pi$
$89$	3.80382e6	0.571946	0.285973	+	0.958238i	$0.407683\pi$
$90$	−5.88698e6	−0.851223
$91$	6.48916e6	0.902700
$92$	−1.19868e7	−1.60489
$93$	6.25539e6	0.806425
$94$	1.47144e7	1.82724
$95$	−2.65361e7	−3.17544
$96$	−7.16849e6	−0.826948
$97$	−7.68854e6	−0.855348	−0.427674	−	0.903933i	$-0.640667\pi$
$97$	−7.68854e6	−0.855348	−0.427674	+	0.903933i	$0.640667\pi$
$98$	8.21243e6	0.881414
$99$	−602762.	−0.0624342
$100$	2.30321e7	2.30321
$101$	−1.11320e7	−1.07510	−0.537551	−	0.843231i	$-0.680650\pi$
$101$	−1.11320e7	−1.07510	−0.537551	+	0.843231i	$0.680650\pi$
$102$	−1.03677e7	−0.967349
$103$	9.10836e6	0.821315	0.410658	−	0.911790i	$-0.365299\pi$
$103$	9.10836e6	0.821315	0.410658	+	0.911790i	$0.365299\pi$
$104$	−1.78344e6	−0.155468
$105$	−7.56394e6	−0.637655
$106$	5.29511e6	0.431822
$107$	2.43881e7	1.92458	0.962289	−	0.272029i	$-0.0876945\pi$
$107$	2.43881e7	1.92458	0.962289	+	0.272029i	$0.0876945\pi$
$108$	−2.70709e6	−0.206785
$109$	−1.92554e7	−1.42416	−0.712080	−	0.702098i	$-0.752247\pi$
$109$	−1.92554e7	−1.42416	−0.712080	+	0.702098i	$0.752247\pi$
$110$	6.67702e6	0.478309
$111$	−1.10671e7	−0.768076
$112$	−8.52062e6	−0.573071
$113$	9.40627e6	0.613258	0.306629	−	0.951829i	$-0.400799\pi$
$113$	9.40627e6	0.613258	0.306629	+	0.951829i	$0.400799\pi$
$114$	−2.35590e7	−1.48932
$115$	−4.31914e7	−2.64822
$116$	3.67844e6	0.218807
$117$	8.36828e6	0.483043
$118$	−3.34670e6	−0.187512
$119$	−1.33211e7	−0.724645
$120$	2.07882e6	0.109820
$121$	−1.88035e7	−0.964918
$122$	2.58430e7	1.28850
$123$	−5.12015e6	−0.248093
$124$	−3.18641e7	−1.50081
$125$	4.42737e7	2.02750
$126$	−6.71534e6	−0.299069
$127$	2.55998e7	1.10898	0.554490	−	0.832190i	$-0.312913\pi$
$127$	2.55998e7	1.10898	0.554490	+	0.832190i	$0.312913\pi$
$128$	5.07683e6	0.213972
$129$	2.29354e7	0.940681
$130$	−9.26986e7	−3.70060
$131$	2.04746e7	0.795729	0.397865	−	0.917444i	$-0.369751\pi$
$131$	2.04746e7	0.795729	0.397865	+	0.917444i	$0.369751\pi$
$132$	3.07039e6	0.116194
$133$	−3.02700e7	−1.11566
$134$	4.20122e7	1.50837
$135$	−9.75429e6	−0.341215
$136$	3.66108e6	0.124802
$137$	1.13505e6	0.0377132	0.0188566	−	0.999822i	$-0.493997\pi$
$137$	1.13505e6	0.0377132	0.0188566	+	0.999822i	$0.493997\pi$
$138$	−3.83457e7	−1.24205
$139$	−1.44843e7	−0.457453	−0.228726	−	0.973491i	$-0.573456\pi$
$139$	−1.44843e7	−0.457453	−0.228726	+	0.973491i	$0.573456\pi$
$140$	3.85297e7	1.18672
$141$	2.43807e7	0.732453
$142$	1.10488e7	0.323821
$143$	−9.49132e6	−0.271425
$144$	−1.09880e7	−0.306655
$145$	1.32543e7	0.361051
$146$	−4.07440e7	−1.08350
$147$	1.36074e7	0.353317
$148$	5.63744e7	1.42944
$149$	6.91223e7	1.71185	0.855926	−	0.517098i	$-0.172988\pi$
$149$	6.91223e7	1.71185	0.855926	+	0.517098i	$0.172988\pi$
$150$	7.36793e7	1.78249
$151$	5.36019e7	1.26695	0.633477	−	0.773762i	$-0.281627\pi$
$151$	5.36019e7	1.26695	0.633477	+	0.773762i	$0.281627\pi$
$152$	8.31919e6	0.192145
$153$	−1.71786e7	−0.387764
$154$	7.61655e6	0.168049
$155$	−1.14814e8	−2.47648
$156$	−4.26269e7	−0.898974
$157$	−8.33413e7	−1.71874	−0.859372	−	0.511350i	$-0.829145\pi$
$157$	−8.33413e7	−1.71874	−0.859372	+	0.511350i	$0.829145\pi$
$158$	1.19450e8	2.40927
$159$	8.77361e6	0.173097
$160$	1.31574e8	2.53950
$161$	−4.92689e7	−0.930426
$162$	−8.65995e6	−0.160034
$163$	−5.74632e6	−0.103928	−0.0519641	−	0.998649i	$-0.516548\pi$
$163$	−5.74632e6	−0.103928	−0.0519641	+	0.998649i	$0.516548\pi$
$164$	2.60813e7	0.461717
$165$	1.10633e7	0.191731
$166$	−6.38125e7	−1.08275
$167$	−5.42463e7	−0.901286	−0.450643	−	0.892704i	$-0.648805\pi$
$167$	−5.42463e7	−0.901286	−0.450643	+	0.892704i	$0.648805\pi$
$168$	2.37133e6	0.0385843
$169$	6.90217e7	1.09997
$170$	1.90294e8	2.97066
$171$	−3.90355e7	−0.596998
$172$	−1.16830e8	−1.75067
$173$	−1.02709e8	−1.50816	−0.754081	−	0.656781i	$-0.771918\pi$
$173$	−1.02709e8	−1.50816	−0.754081	+	0.656781i	$0.771918\pi$
$174$	1.17673e7	0.169338
$175$	9.46676e7	1.33527
$176$	1.24626e7	0.172312
$177$	−5.54523e6	−0.0751646
$178$	−6.19841e7	−0.823779
$179$	1.18297e8	1.54166	0.770828	−	0.637043i	$-0.219843\pi$
$179$	1.18297e8	1.54166	0.770828	+	0.637043i	$0.219843\pi$
$180$	4.96870e7	0.635023
$181$	−7.54155e7	−0.945334	−0.472667	−	0.881241i	$-0.656709\pi$
$181$	−7.54155e7	−0.945334	−0.472667	+	0.881241i	$0.656709\pi$
$182$	−1.05742e8	−1.30017
$183$	4.28199e7	0.516496
$184$	1.35407e7	0.160243
$185$	2.03131e8	2.35871
$186$	−1.01933e8	−1.16150
$187$	1.94840e7	0.217888
$188$	−1.24192e8	−1.36314
$189$	−1.11268e7	−0.119882
$190$	4.32411e8	4.57361
$191$	5.67288e7	0.589097	0.294548	−	0.955637i	$-0.404831\pi$
$191$	5.67288e7	0.589097	0.294548	+	0.955637i	$0.404831\pi$
$192$	6.47209e7	0.659918
$193$	1.56586e7	0.156784	0.0783920	−	0.996923i	$-0.475021\pi$
$193$	1.56586e7	0.156784	0.0783920	+	0.996923i	$0.475021\pi$
$194$	1.25286e8	1.23196
$195$	−1.53595e8	−1.48339
$196$	−6.93142e7	−0.657546
$197$	1.95180e6	0.0181888	0.00909440	−	0.999959i	$-0.497105\pi$
$197$	1.95180e6	0.0181888	0.00909440	+	0.999959i	$0.497105\pi$
$198$	9.82214e6	0.0899244
$199$	4.03128e7	0.362624	0.181312	−	0.983426i	$-0.441966\pi$
$199$	4.03128e7	0.362624	0.181312	+	0.983426i	$0.441966\pi$
$200$	−2.60178e7	−0.229967
$201$	6.96112e7	0.604634
$202$	1.81399e8	1.54848
$203$	1.51193e7	0.126852
$204$	8.75054e7	0.721654
$205$	9.39774e7	0.761877
$206$	−1.48423e8	−1.18295
$207$	−6.35360e7	−0.497879
$208$	−1.73021e8	−1.33315
$209$	4.42741e7	0.335458
$210$	1.23256e8	0.918419
$211$	1.16617e8	0.854620	0.427310	−	0.904105i	$-0.359461\pi$
$211$	1.16617e8	0.854620	0.427310	+	0.904105i	$0.359461\pi$
$212$	−4.46916e7	−0.322144
$213$	1.83070e7	0.129804
$214$	−3.97410e8	−2.77199
$215$	−4.20966e8	−2.88877
$216$	3.05802e6	0.0206468
$217$	−1.30970e8	−0.870084
$218$	3.13770e8	2.05123
$219$	−6.75098e7	−0.434323
$220$	−5.63552e7	−0.356824
$221$	−2.70501e8	−1.68576
$222$	1.80341e8	1.10627
$223$	1.52043e8	0.918121	0.459060	−	0.888405i	$-0.348186\pi$
$223$	1.52043e8	0.918121	0.459060	+	0.888405i	$0.348186\pi$
$224$	1.50087e8	0.892228
$225$	1.22081e8	0.714513
$226$	−1.53277e8	−0.883280
$227$	−2.19156e8	−1.24355	−0.621774	−	0.783197i	$-0.713588\pi$
$227$	−2.19156e8	−1.24355	−0.621774	+	0.783197i	$0.713588\pi$
$228$	1.98841e8	1.11105
$229$	−1.50483e8	−0.828061	−0.414030	−	0.910263i	$-0.635879\pi$
$229$	−1.50483e8	−0.828061	−0.414030	+	0.910263i	$0.635879\pi$
$230$	7.03813e8	3.81426
$231$	1.26201e7	0.0673628
$232$	−4.15529e6	−0.0218471
$233$	1.05923e8	0.548586	0.274293	−	0.961646i	$-0.411556\pi$
$233$	1.05923e8	0.548586	0.274293	+	0.961646i	$0.411556\pi$
$234$	−1.36363e8	−0.695730
$235$	−4.47494e8	−2.24931
$236$	2.82467e7	0.139886
$237$	1.97919e8	0.965760
$238$	2.17070e8	1.04371
$239$	−2.39069e8	−1.13274	−0.566370	−	0.824151i	$-0.691653\pi$
$239$	−2.39069e8	−1.13274	−0.566370	+	0.824151i	$0.691653\pi$
$240$	2.01678e8	0.941717
$241$	−6.39780e7	−0.294422	−0.147211	−	0.989105i	$-0.547030\pi$
$241$	−6.39780e7	−0.294422	−0.147211	+	0.989105i	$0.547030\pi$
$242$	3.06408e8	1.38978
$243$	−1.43489e7	−0.0641500
$244$	−2.18119e8	−0.961234
$245$	−2.49756e8	−1.08501
$246$	8.34340e7	0.357330
$247$	−6.14668e8	−2.59538
$248$	3.59948e7	0.149851
$249$	−1.05733e8	−0.434022
$250$	−7.21450e8	−2.92022
$251$	1.43897e8	0.574373	0.287186	−	0.957875i	$-0.407280\pi$
$251$	1.43897e8	0.574373	0.287186	+	0.957875i	$0.407280\pi$
$252$	5.66785e7	0.223109
$253$	7.20627e7	0.279762
$254$	−4.17155e8	−1.59727
$255$	3.15303e8	1.19080
$256$	2.24097e8	0.834826
$257$	−1.50715e8	−0.553849	−0.276925	−	0.960892i	$-0.589315\pi$
$257$	−1.50715e8	−0.553849	−0.276925	+	0.960892i	$0.589315\pi$
$258$	−3.73738e8	−1.35487
$259$	2.31713e8	0.828708
$260$	7.82391e8	2.76069
$261$	1.94975e7	0.0678794
$262$	−3.33638e8	−1.14609
$263$	−5.02309e8	−1.70265	−0.851325	−	0.524638i	$-0.824201\pi$
$263$	−5.02309e8	−1.70265	−0.851325	+	0.524638i	$0.824201\pi$
$264$	−3.46841e6	−0.0116016
$265$	−1.61035e8	−0.531568
$266$	4.93256e8	1.60689
$267$	−1.02703e8	−0.330213
$268$	−3.54590e8	−1.12526
$269$	−2.76426e8	−0.865858	−0.432929	−	0.901428i	$-0.642520\pi$
$269$	−2.76426e8	−0.865858	−0.432929	+	0.901428i	$0.642520\pi$
$270$	1.58948e8	0.491454
$271$	1.17995e8	0.360139	0.180069	−	0.983654i	$-0.442368\pi$
$271$	1.17995e8	0.360139	0.180069	+	0.983654i	$0.442368\pi$
$272$	3.55182e8	1.07019
$273$	−1.75207e8	−0.521174
$274$	−1.84959e7	−0.0543186
$275$	−1.38465e8	−0.401491
$276$	3.23644e8	0.926586
$277$	−6.34905e7	−0.179485	−0.0897427	−	0.995965i	$-0.528604\pi$
$277$	−6.34905e7	−0.179485	−0.0897427	+	0.995965i	$0.528604\pi$
$278$	2.36025e8	0.658872
$279$	−1.68895e8	−0.465590
$280$	−4.35245e7	−0.118490
$281$	3.92031e8	1.05402	0.527009	−	0.849860i	$-0.323313\pi$
$281$	3.92031e8	1.05402	0.527009	+	0.849860i	$0.323313\pi$
$282$	−3.97290e8	−1.05496
$283$	3.91102e8	1.02574	0.512871	−	0.858466i	$-0.328582\pi$
$283$	3.91102e8	1.02574	0.512871	+	0.858466i	$0.328582\pi$
$284$	−9.32533e7	−0.241574
$285$	7.16474e8	1.83334
$286$	1.54663e8	0.390936
$287$	1.07201e8	0.267678
$288$	1.93549e8	0.477439
$289$	1.44951e8	0.353248
$290$	−2.15982e8	−0.520025
$291$	2.07590e8	0.493835
$292$	3.43886e8	0.808303
$293$	−3.95594e8	−0.918783	−0.459392	−	0.888234i	$-0.651933\pi$
$293$	−3.95594e8	−0.918783	−0.459392	+	0.888234i	$0.651933\pi$
$294$	−2.21735e8	−0.508885
$295$	1.01780e8	0.230825
$296$	−6.36824e7	−0.142725
$297$	1.62746e7	0.0360464
$298$	−1.12636e9	−2.46559
$299$	−1.00046e9	−2.16447
$300$	−6.21865e8	−1.32976
$301$	−4.80201e8	−1.01494
$302$	−8.73455e8	−1.82480
$303$	3.00565e8	0.620710
$304$	8.07092e8	1.64765
$305$	−7.85935e8	−1.58612
$306$	2.79929e8	0.558499
$307$	−3.74974e8	−0.739634	−0.369817	−	0.929105i	$-0.620580\pi$
$307$	−3.74974e8	−0.739634	−0.369817	+	0.929105i	$0.620580\pi$
$308$	−6.42849e7	−0.125367
$309$	−2.45926e8	−0.474187
$310$	1.87092e9	3.56689
$311$	5.67572e8	1.06994	0.534970	−	0.844871i	$-0.320323\pi$
$311$	5.67572e8	1.06994	0.534970	+	0.844871i	$0.320323\pi$
$312$	4.81528e7	0.0897594
$313$	−9.61191e8	−1.77176	−0.885879	−	0.463916i	$-0.846444\pi$
$313$	−9.61191e8	−1.77176	−0.885879	+	0.463916i	$0.846444\pi$
$314$	1.35806e9	2.47552
$315$	2.04226e8	0.368150
$316$	−1.00817e9	−1.79734
$317$	1.03762e8	0.182950	0.0914748	−	0.995807i	$-0.470842\pi$
$317$	1.03762e8	0.182950	0.0914748	+	0.995807i	$0.470842\pi$
$318$	−1.42968e8	−0.249312
$319$	−2.21142e7	−0.0381420
$320$	−1.18791e9	−2.02656
$321$	−6.58480e8	−1.11116
$322$	8.02847e8	1.34010
$323$	1.26180e9	2.08345
$324$	7.30914e7	0.119387
$325$	1.92234e9	3.10626
$326$	9.36376e7	0.149689
$327$	5.19895e8	0.822240
$328$	−2.94624e7	−0.0461009
$329$	−5.10462e8	−0.790273
$330$	−1.80280e8	−0.276152
$331$	−4.86499e8	−0.737367	−0.368684	−	0.929555i	$-0.620191\pi$
$331$	−4.86499e8	−0.737367	−0.368684	+	0.929555i	$0.620191\pi$
$332$	5.38587e8	0.807743
$333$	2.98812e8	0.443449
$334$	8.83956e8	1.29813
$335$	−1.27767e9	−1.85679
$336$	2.30057e8	0.330862
$337$	−2.32747e8	−0.331269	−0.165634	−	0.986187i	$-0.552967\pi$
$337$	−2.32747e8	−0.331269	−0.165634	+	0.986187i	$0.552967\pi$
$338$	−1.12472e9	−1.58430
$339$	−2.53969e8	−0.354064
$340$	−1.60611e9	−2.21615
$341$	1.91562e8	0.261618
$342$	6.36092e8	0.859861
$343$	−7.50449e8	−1.00413
$344$	1.31975e8	0.174798
$345$	1.16617e9	1.52895
$346$	1.67367e9	2.17222
$347$	−1.12320e8	−0.144312	−0.0721560	−	0.997393i	$-0.522988\pi$
$347$	−1.12320e8	−0.144312	−0.0721560	+	0.997393i	$0.522988\pi$
$348$	−9.93178e7	−0.126328
$349$	1.23358e9	1.55338	0.776688	−	0.629885i	$-0.216898\pi$
$349$	1.23358e9	1.55338	0.776688	+	0.629885i	$0.216898\pi$
$350$	−1.54263e9	−1.92320
$351$	−2.25943e8	−0.278885
$352$	−2.19524e8	−0.268277
$353$	1.25683e9	1.52078	0.760390	−	0.649466i	$-0.225008\pi$
$353$	1.25683e9	1.52078	0.760390	+	0.649466i	$0.225008\pi$
$354$	9.03608e7	0.108260
$355$	−3.36014e8	−0.398619
$356$	5.23156e8	0.614549
$357$	3.59669e8	0.418374
$358$	−1.92767e9	−2.22046
$359$	1.53369e8	0.174947	0.0874735	−	0.996167i	$-0.472121\pi$
$359$	1.53369e8	0.174947	0.0874735	+	0.996167i	$0.472121\pi$
$360$	−5.61282e7	−0.0634048
$361$	1.97337e9	2.20766
$362$	1.22891e9	1.36157
$363$	5.07695e8	0.557096
$364$	8.92482e8	0.969940
$365$	1.23910e9	1.33378
$366$	−6.97761e8	−0.743914
$367$	−9.10830e8	−0.961847	−0.480924	−	0.876762i	$-0.659699\pi$
$367$	−9.10830e8	−0.961847	−0.480924	+	0.876762i	$0.659699\pi$
$368$	1.31366e9	1.37409
$369$	1.38244e8	0.143237
$370$	−3.31006e9	−3.39727
$371$	−1.83694e8	−0.186761
$372$	8.60330e8	0.866493
$373$	−8.48680e8	−0.846766	−0.423383	−	0.905951i	$-0.639157\pi$
$373$	−8.48680e8	−0.846766	−0.423383	+	0.905951i	$0.639157\pi$
$374$	−3.17496e8	−0.313825
$375$	−1.19539e9	−1.17058
$376$	1.40292e8	0.136105
$377$	3.07016e8	0.295098
$378$	1.81314e8	0.172667
$379$	1.11369e9	1.05082	0.525410	−	0.850849i	$-0.323912\pi$
$379$	1.11369e9	1.05082	0.525410	+	0.850849i	$0.323912\pi$
$380$	−3.64962e9	−3.41197
$381$	−6.91195e8	−0.640270
$382$	−9.24408e8	−0.848481
$383$	−1.24305e9	−1.13056	−0.565279	−	0.824900i	$-0.691232\pi$
$383$	−1.24305e9	−1.13056	−0.565279	+	0.824900i	$0.691232\pi$
$384$	−1.37074e8	−0.123537
$385$	−2.31634e8	−0.206866
$386$	−2.55160e8	−0.225817
$387$	−6.19256e8	−0.543103
$388$	−1.05744e9	−0.919060
$389$	3.31934e8	0.285909	0.142955	−	0.989729i	$-0.454340\pi$
$389$	3.31934e8	0.285909	0.142955	+	0.989729i	$0.454340\pi$
$390$	2.50286e9	2.13654
$391$	2.05377e9	1.73754
$392$	7.82997e7	0.0656536
$393$	−5.52813e8	−0.459414
$394$	−3.18051e7	−0.0261975
$395$	−3.63270e9	−2.96578
$396$	−8.29004e7	−0.0670847
$397$	−2.50412e8	−0.200858	−0.100429	−	0.994944i	$-0.532021\pi$
$397$	−2.50412e8	−0.200858	−0.100429	+	0.994944i	$0.532021\pi$
$398$	−6.56906e8	−0.522291
$399$	8.17289e8	0.644126
$400$	−2.52414e9	−1.97198
$401$	1.57100e9	1.21666	0.608332	−	0.793683i	$-0.291839\pi$
$401$	1.57100e9	1.21666	0.608332	+	0.793683i	$0.291839\pi$
$402$	−1.13433e9	−0.870859
$403$	−2.65949e9	−2.02410
$404$	−1.53104e9	−1.15518
$405$	2.63366e8	0.197000
$406$	−2.46373e8	−0.182705
$407$	−3.38914e8	−0.249177
$408$	−9.88491e7	−0.0720546
$409$	−2.37344e8	−0.171532	−0.0857661	−	0.996315i	$-0.527334\pi$
$409$	−2.37344e8	−0.171532	−0.0857661	+	0.996315i	$0.527334\pi$
$410$	−1.53138e9	−1.09734
$411$	−3.06464e7	−0.0217737
$412$	1.25271e9	0.882492
$413$	1.16101e8	0.0810981
$414$	1.03533e9	0.717099
$415$	1.94066e9	1.33285
$416$	3.04770e9	2.07561
$417$	3.91076e8	0.264110
$418$	−7.21457e8	−0.483163
$419$	−1.61768e9	−1.07435	−0.537173	−	0.843472i	$-0.680508\pi$
$419$	−1.61768e9	−1.07435	−0.537173	+	0.843472i	$0.680508\pi$
$420$	−1.04030e9	−0.685152
$421$	−1.17270e9	−0.765946	−0.382973	−	0.923759i	$-0.625100\pi$
$421$	−1.17270e9	−0.765946	−0.382973	+	0.923759i	$0.625100\pi$
$422$	−1.90030e9	−1.23092
$423$	−6.58280e8	−0.422882
$424$	5.04852e7	0.0321650
$425$	−3.94622e9	−2.49356
$426$	−2.98317e8	−0.186958
$427$	−8.96525e8	−0.557269
$428$	3.35421e9	2.06793
$429$	2.56266e8	0.156708
$430$	6.85974e9	4.16071
$431$	2.74618e9	1.65219	0.826094	−	0.563533i	$-0.190558\pi$
$431$	2.74618e9	1.65219	0.826094	+	0.563533i	$0.190558\pi$
$432$	2.96676e8	0.177047
$433$	1.44724e8	0.0856709	0.0428355	−	0.999082i	$-0.486361\pi$
$433$	1.44724e8	0.0856709	0.0428355	+	0.999082i	$0.486361\pi$
$434$	2.13418e9	1.25319
$435$	−3.57866e8	−0.208453
$436$	−2.64827e9	−1.53024
$437$	4.66686e9	2.67510
$438$	1.10009e9	0.625559
$439$	−2.83060e8	−0.159681	−0.0798403	−	0.996808i	$-0.525441\pi$
$439$	−2.83060e8	−0.159681	−0.0798403	+	0.996808i	$0.525441\pi$
$440$	6.36607e7	0.0356276
$441$	−3.67400e8	−0.203988
$442$	4.40787e9	2.42801
$443$	−6.58269e8	−0.359741	−0.179871	−	0.983690i	$-0.557568\pi$
$443$	−6.58269e8	−0.359741	−0.179871	+	0.983690i	$0.557568\pi$
$444$	−1.52211e9	−0.825287
$445$	1.88506e9	1.01406
$446$	−2.47758e9	−1.32238
$447$	−1.86630e9	−0.988339
$448$	−1.35507e9	−0.712012
$449$	2.96392e9	1.54527	0.772636	−	0.634850i	$-0.218938\pi$
$449$	2.96392e9	1.54527	0.772636	+	0.634850i	$0.218938\pi$
$450$	−1.98934e9	−1.02912
$451$	−1.56797e8	−0.0804857
$452$	1.29368e9	0.658937
$453$	−1.44725e9	−0.731476
$454$	3.57119e9	1.79109
$455$	3.21583e9	1.60049
$456$	−2.24618e8	−0.110935
$457$	−2.62985e8	−0.128891	−0.0644456	−	0.997921i	$-0.520528\pi$
$457$	−2.62985e8	−0.128891	−0.0644456	+	0.997921i	$0.520528\pi$
$458$	2.45215e9	1.19266
$459$	4.63822e8	0.223876
$460$	−5.94030e9	−2.84548
$461$	7.39703e8	0.351645	0.175822	−	0.984422i	$-0.443742\pi$
$461$	7.39703e8	0.351645	0.175822	+	0.984422i	$0.443742\pi$
$462$	−2.05647e8	−0.0970231
$463$	−8.00108e8	−0.374641	−0.187320	−	0.982299i	$-0.559980\pi$
$463$	−8.00108e8	−0.374641	−0.187320	+	0.982299i	$0.559980\pi$
$464$	−4.03129e8	−0.187340
$465$	3.09998e9	1.42979
$466$	−1.72604e9	−0.790132
$467$	3.44400e9	1.56478	0.782392	−	0.622786i	$-0.213999\pi$
$467$	3.44400e9	1.56478	0.782392	+	0.622786i	$0.213999\pi$
$468$	1.15093e9	0.519023
$469$	−1.45745e9	−0.652364
$470$	7.29202e9	3.23970
$471$	2.25021e9	0.992318
$472$	−3.19084e7	−0.0139672
$473$	7.02362e8	0.305174
$474$	−3.22514e9	−1.39099
$475$	−8.96713e9	−3.83907
$476$	−1.83211e9	−0.778622
$477$	−2.36888e8	−0.0999374
$478$	3.89568e9	1.63149
$479$	−2.17648e9	−0.904857	−0.452429	−	0.891801i	$-0.649442\pi$
$479$	−2.17648e9	−0.904857	−0.452429	+	0.891801i	$0.649442\pi$
$480$	−3.55248e9	−1.46618
$481$	4.70521e9	1.92784
$482$	1.04254e9	0.424059
$483$	1.33026e9	0.537182
$484$	−2.58613e9	−1.03679
$485$	−3.81020e9	−1.51653
$486$	2.33819e8	0.0923958
$487$	1.73782e9	0.681796	0.340898	−	0.940100i	$-0.389269\pi$
$487$	1.73782e9	0.681796	0.340898	+	0.940100i	$0.389269\pi$
$488$	2.46395e8	0.0959758
$489$	1.55151e8	0.0600030
$490$	4.06983e9	1.56275
$491$	−7.21828e8	−0.275200	−0.137600	−	0.990488i	$-0.543939\pi$
$491$	−7.21828e8	−0.275200	−0.137600	+	0.990488i	$0.543939\pi$
$492$	−7.04196e8	−0.266573
$493$	−6.30249e8	−0.236891
$494$	1.00161e10	3.73815
$495$	−2.98710e8	−0.110696
$496$	3.49206e9	1.28498
$497$	−3.83295e8	−0.140051
$498$	1.72294e9	0.625125
$499$	−1.78127e9	−0.641769	−0.320885	−	0.947118i	$-0.603980\pi$
$499$	−1.78127e9	−0.641769	−0.320885	+	0.947118i	$0.603980\pi$
$500$	6.08915e9	2.17852
$501$	1.46465e9	0.520358
$502$	−2.34483e9	−0.827273
$503$	1.72676e9	0.604986	0.302493	−	0.953152i	$-0.402181\pi$
$503$	1.72676e9	0.604986	0.302493	+	0.953152i	$0.402181\pi$
$504$	−6.40260e7	−0.0222766
$505$	−5.51669e9	−1.90616
$506$	−1.17428e9	−0.402944
$507$	−1.86358e9	−0.635069
$508$	3.52085e9	1.19158
$509$	1.96038e8	0.0658912	0.0329456	−	0.999457i	$-0.489511\pi$
$509$	1.96038e8	0.0658912	0.0329456	+	0.999457i	$0.489511\pi$
$510$	−5.13793e9	−1.71511
$511$	1.41346e9	0.468608
$512$	−4.30154e9	−1.41638
$513$	1.05396e9	0.344677
$514$	2.45594e9	0.797713
$515$	4.51383e9	1.45619
$516$	3.15441e9	1.01075
$517$	7.46623e8	0.237621
$518$	−3.77582e9	−1.19359
$519$	2.77315e9	0.870738
$520$	−8.83816e8	−0.275645
$521$	−2.84883e9	−0.882540	−0.441270	−	0.897374i	$-0.645472\pi$
$521$	−2.84883e9	−0.882540	−0.441270	+	0.897374i	$0.645472\pi$
$522$	−3.17717e8	−0.0977673
$523$	−3.08000e9	−0.941445	−0.470722	−	0.882281i	$-0.656007\pi$
$523$	−3.08000e9	−0.941445	−0.470722	+	0.882281i	$0.656007\pi$
$524$	2.81596e9	0.855000
$525$	−2.55603e9	−0.770917
$526$	8.18523e9	2.45234
$527$	5.45947e9	1.62485
$528$	−3.36491e8	−0.0994843
$529$	4.19118e9	1.23095
$530$	2.62410e9	0.765621
$531$	1.49721e8	0.0433963
$532$	−4.16316e9	−1.19876
$533$	2.17684e9	0.622705
$534$	1.67357e9	0.475609
$535$	1.20860e10	3.41228
$536$	4.00557e8	0.112354
$537$	−3.19402e9	−0.890076
$538$	4.50443e9	1.24710
$539$	4.16706e8	0.114622
$540$	−1.34155e9	−0.366631
$541$	3.69807e9	1.00412	0.502060	−	0.864833i	$-0.332576\pi$
$541$	3.69807e9	1.00412	0.502060	+	0.864833i	$0.332576\pi$
$542$	−1.92275e9	−0.518711
$543$	2.03622e9	0.545789
$544$	−6.25639e9	−1.66620
$545$	−9.54237e9	−2.52504
$546$	2.85504e9	0.750651
$547$	−1.21521e9	−0.317464	−0.158732	−	0.987322i	$-0.550741\pi$
$547$	−1.21521e9	−0.317464	−0.158732	+	0.987322i	$0.550741\pi$
$548$	1.56108e8	0.0405223
$549$	−1.15614e9	−0.298199
$550$	2.25632e9	0.578270
$551$	−1.43214e9	−0.364715
$552$	−3.65599e8	−0.0925163
$553$	−4.14386e9	−1.04200
$554$	1.03459e9	0.258514
$555$	−5.48453e9	−1.36180
$556$	−1.99209e9	−0.491527
$557$	−6.35497e9	−1.55819	−0.779095	−	0.626906i	$-0.784321\pi$
$557$	−6.35497e9	−1.55819	−0.779095	+	0.626906i	$0.784321\pi$
$558$	2.75219e9	0.670592
$559$	−9.75105e9	−2.36108
$560$	−4.22256e9	−1.01606
$561$	−5.26068e8	−0.125797
$562$	−6.38823e9	−1.51811
$563$	2.41689e9	0.570791	0.285395	−	0.958410i	$-0.407875\pi$
$563$	2.41689e9	0.570791	0.285395	+	0.958410i	$0.407875\pi$
$564$	3.35319e9	0.787011
$565$	4.66146e9	1.08731
$566$	−6.37310e9	−1.47738
$567$	3.00424e8	0.0692141
$568$	1.05342e8	0.0241203
$569$	2.02038e9	0.459769	0.229884	−	0.973218i	$-0.426165\pi$
$569$	2.02038e9	0.459769	0.229884	+	0.973218i	$0.426165\pi$
$570$	−1.16751e10	−2.64057
$571$	−5.09913e9	−1.14622	−0.573112	−	0.819477i	$-0.694264\pi$
$571$	−5.09913e9	−1.14622	−0.573112	+	0.819477i	$0.694264\pi$
$572$	−1.30538e9	−0.291643
$573$	−1.53168e9	−0.340115
$574$	−1.74686e9	−0.385538
$575$	−1.45953e10	−3.20167
$576$	−1.74746e9	−0.381004
$577$	−5.65588e9	−1.22570	−0.612851	−	0.790199i	$-0.709977\pi$
$577$	−5.65588e9	−1.22570	−0.612851	+	0.790199i	$0.709977\pi$
$578$	−2.36201e9	−0.508785
$579$	−4.22782e8	−0.0905193
$580$	1.82292e9	0.387945
$581$	2.21373e9	0.468283
$582$	−3.38273e9	−0.711275
$583$	2.68678e8	0.0561556
$584$	−3.88465e8	−0.0807063
$585$	4.14706e9	0.856436
$586$	6.44629e9	1.32333
$587$	8.74088e9	1.78370	0.891850	−	0.452331i	$-0.149407\pi$
$587$	8.74088e9	1.78370	0.891850	+	0.452331i	$0.149407\pi$
$588$	1.87148e9	0.379634
$589$	1.24057e10	2.50161
$590$	−1.65852e9	−0.332460
$591$	−5.26987e7	−0.0105013
$592$	−6.17820e9	−1.22387
$593$	−7.16535e9	−1.41106	−0.705531	−	0.708679i	$-0.749291\pi$
$593$	−7.16535e9	−1.41106	−0.705531	+	0.708679i	$0.749291\pi$
$594$	−2.65198e8	−0.0519179
$595$	−6.60153e9	−1.28480
$596$	9.50669e9	1.83936
$597$	−1.08845e9	−0.209361
$598$	1.63028e10	3.11751
$599$	−1.12486e8	−0.0213847	−0.0106923	−	0.999943i	$-0.503404\pi$
$599$	−1.12486e8	−0.0213847	−0.0106923	+	0.999943i	$0.503404\pi$
$600$	7.02481e8	0.132772
$601$	2.43804e9	0.458121	0.229061	−	0.973412i	$-0.426435\pi$
$601$	2.43804e9	0.458121	0.229061	+	0.973412i	$0.426435\pi$
$602$	7.82498e9	1.46182
$603$	−1.87950e9	−0.349086
$604$	7.37210e9	1.36132
$605$	−9.31845e9	−1.71080
$606$	−4.89777e9	−0.894014
$607$	3.37659e9	0.612800	0.306400	−	0.951903i	$-0.400876\pi$
$607$	3.37659e9	0.612800	0.306400	+	0.951903i	$0.400876\pi$
$608$	−1.42166e10	−2.56527
$609$	−4.08222e8	−0.0732379
$610$	1.28070e10	2.28451
$611$	−1.03655e10	−1.83843
$612$	−2.36264e9	−0.416647
$613$	−3.64627e9	−0.639348	−0.319674	−	0.947528i	$-0.603573\pi$
$613$	−3.64627e9	−0.639348	−0.319674	+	0.947528i	$0.603573\pi$
$614$	6.11029e9	1.06530
$615$	−2.53739e9	−0.439870
$616$	7.26184e7	0.0125174
$617$	−2.27884e8	−0.0390585	−0.0195293	−	0.999809i	$-0.506217\pi$
$617$	−2.27884e8	−0.0390585	−0.0195293	+	0.999809i	$0.506217\pi$
$618$	4.00741e9	0.682975
$619$	2.30512e9	0.390640	0.195320	−	0.980740i	$-0.437426\pi$
$619$	2.30512e9	0.390640	0.195320	+	0.980740i	$0.437426\pi$
$620$	−1.57909e10	−2.66094
$621$	1.71547e9	0.287451
$622$	−9.24870e9	−1.54104
$623$	2.15031e9	0.356280
$624$	4.67158e9	0.769693
$625$	8.85757e9	1.45122
$626$	1.56628e10	2.55188
$627$	−1.19540e9	−0.193677
$628$	−1.14623e10	−1.84677
$629$	−9.65897e9	−1.54758
$630$	−3.32792e9	−0.530250
$631$	5.67126e9	0.898622	0.449311	−	0.893375i	$-0.351670\pi$
$631$	5.67126e9	0.898622	0.449311	+	0.893375i	$0.351670\pi$
$632$	1.13887e9	0.179458
$633$	−3.14866e9	−0.493415
$634$	−1.69083e9	−0.263504
$635$	1.26865e10	1.96623
$636$	1.20667e9	0.185990
$637$	−5.78522e9	−0.886812
$638$	3.60355e8	0.0549362
$639$	−4.94289e8	−0.0749424
$640$	2.51592e9	0.379373
$641$	−8.04557e9	−1.20657	−0.603287	−	0.797524i	$-0.706142\pi$
$641$	−8.04557e9	−1.20657	−0.603287	+	0.797524i	$0.706142\pi$
$642$	1.07301e10	1.60041
$643$	6.95787e9	1.03214	0.516069	−	0.856547i	$-0.327395\pi$
$643$	6.95787e9	1.03214	0.516069	+	0.856547i	$0.327395\pi$
$644$	−6.77616e9	−0.999731
$645$	1.13661e10	1.66783
$646$	−2.05614e10	−3.00081
$647$	−1.50113e9	−0.217898	−0.108949	−	0.994047i	$-0.534748\pi$
$647$	−1.50113e9	−0.217898	−0.108949	+	0.994047i	$0.534748\pi$
$648$	−8.25665e7	−0.0119204
$649$	−1.69814e8	−0.0243847
$650$	−3.13250e10	−4.47398
$651$	3.53618e9	0.502343
$652$	−7.90316e8	−0.111669
$653$	−1.05745e9	−0.148616	−0.0743078	−	0.997235i	$-0.523675\pi$
$653$	−1.05745e9	−0.148616	−0.0743078	+	0.997235i	$0.523675\pi$
$654$	−8.47180e9	−1.18428
$655$	1.01466e10	1.41083
$656$	−2.85831e9	−0.395318
$657$	1.82277e9	0.250756
$658$	8.31808e9	1.13824
$659$	−1.27158e10	−1.73079	−0.865396	−	0.501088i	$-0.832933\pi$
$659$	−1.27158e10	−1.73079	−0.865396	+	0.501088i	$0.832933\pi$
$660$	1.52159e9	0.206013
$661$	−1.38832e10	−1.86976	−0.934878	−	0.354968i	$-0.884492\pi$
$661$	−1.38832e10	−1.86976	−0.934878	+	0.354968i	$0.884492\pi$
$662$	7.92761e9	1.06204
$663$	7.30352e9	0.973273
$664$	−6.08407e8	−0.0806503
$665$	−1.50009e10	−1.97807
$666$	−4.86921e9	−0.638703
$667$	−2.33101e9	−0.304162
$668$	−7.46073e9	−0.968420
$669$	−4.10516e9	−0.530077
$670$	2.08200e10	2.67435
$671$	1.31130e9	0.167560
$672$	−4.05236e9	−0.515128
$673$	8.66625e9	1.09592	0.547960	−	0.836505i	$-0.315405\pi$
$673$	8.66625e9	1.09592	0.547960	+	0.836505i	$0.315405\pi$
$674$	3.79267e9	0.477129
$675$	−3.29620e9	−0.412524
$676$	9.49284e9	1.18191
$677$	−1.30940e10	−1.62186	−0.810929	−	0.585144i	$-0.801038\pi$
$677$	−1.30940e10	−1.62186	−0.810929	+	0.585144i	$0.801038\pi$
$678$	4.13849e9	0.509962
$679$	−4.34634e9	−0.532819
$680$	1.81432e9	0.221275
$681$	5.91721e9	0.717963
$682$	−3.12154e9	−0.376811
$683$	5.07430e9	0.609402	0.304701	−	0.952448i	$-0.401443\pi$
$683$	5.07430e9	0.609402	0.304701	+	0.952448i	$0.401443\pi$
$684$	−5.36872e9	−0.641467
$685$	5.62496e8	0.0668656
$686$	1.22287e10	1.44626
$687$	4.06303e9	0.478081
$688$	1.28037e10	1.49891
$689$	−3.73012e9	−0.434466
$690$	−1.90030e10	−2.20216
$691$	7.09480e9	0.818026	0.409013	−	0.912529i	$-0.365873\pi$
$691$	7.09480e9	0.818026	0.409013	+	0.912529i	$0.365873\pi$
$692$	−1.41260e10	−1.62050
$693$	−3.40742e8	−0.0388919
$694$	1.83027e9	0.207854
$695$	−7.17798e9	−0.811065
$696$	1.12193e8	0.0126134
$697$	−4.46867e9	−0.499878
$698$	−2.01014e10	−2.23734
$699$	−2.85992e9	−0.316726
$700$	1.30200e10	1.43473
$701$	5.74769e9	0.630203	0.315101	−	0.949058i	$-0.397961\pi$
$701$	5.74769e9	0.630203	0.315101	+	0.949058i	$0.397961\pi$
$702$	3.68180e9	0.401680
$703$	−2.19484e10	−2.38264
$704$	1.98198e9	0.214089
$705$	1.20823e10	1.29864
$706$	−2.04804e10	−2.19039
$707$	−6.29295e9	−0.669709
$708$	−7.62660e8	−0.0807634
$709$	−5.47895e9	−0.577345	−0.288672	−	0.957428i	$-0.593214\pi$
$709$	−5.47895e9	−0.577345	−0.288672	+	0.957428i	$0.593214\pi$
$710$	5.47543e9	0.574135
$711$	−5.34383e9	−0.557582
$712$	−5.90975e8	−0.0613605
$713$	2.01922e10	2.08627
$714$	−5.86089e9	−0.602588
$715$	−4.70361e9	−0.481238
$716$	1.62699e10	1.65649
$717$	6.45486e9	0.653988
$718$	−2.49918e9	−0.251978
$719$	1.62636e10	1.63179	0.815895	−	0.578200i	$-0.196245\pi$
$719$	1.62636e10	1.63179	0.815895	+	0.578200i	$0.196245\pi$
$720$	−5.44532e9	−0.543700
$721$	5.14897e9	0.511619
$722$	−3.21565e10	−3.17971
$723$	1.72741e9	0.169985
$724$	−1.03722e10	−1.01575
$725$	4.47893e9	0.436507
$726$	−8.27300e9	−0.802389
$727$	−2.55116e9	−0.246245	−0.123122	−	0.992391i	$-0.539291\pi$
$727$	−2.55116e9	−0.246245	−0.123122	+	0.992391i	$0.539291\pi$
$728$	−1.00818e9	−0.0968451
$729$	3.87420e8	0.0370370
$730$	−2.01915e10	−1.92105
$731$	2.00172e10	1.89536
$732$	5.88921e9	0.554968
$733$	1.41305e10	1.32524	0.662619	−	0.748957i	$-0.269445\pi$
$733$	1.41305e10	1.32524	0.662619	+	0.748957i	$0.269445\pi$
$734$	1.48422e10	1.38536
$735$	6.74341e9	0.626432
$736$	−2.31396e10	−2.13936
$737$	2.13174e9	0.196154
$738$	−2.25272e9	−0.206305
$739$	1.92246e10	1.75227	0.876136	−	0.482064i	$-0.160113\pi$
$739$	1.92246e10	1.75227	0.876136	+	0.482064i	$0.160113\pi$
$740$	2.79374e10	2.53440
$741$	1.65960e10	1.49844
$742$	2.99333e9	0.268993
$743$	5.89705e9	0.527441	0.263721	−	0.964599i	$-0.415050\pi$
$743$	5.89705e9	0.527441	0.263721	+	0.964599i	$0.415050\pi$
$744$	−9.71859e8	−0.0865163
$745$	3.42549e10	3.03512
$746$	1.38294e10	1.21960
$747$	2.85478e9	0.250582
$748$	2.67972e9	0.234117
$749$	1.37867e10	1.19887
$750$	1.94791e10	1.68599
$751$	−3.11911e9	−0.268715	−0.134357	−	0.990933i	$-0.542897\pi$
$751$	−3.11911e9	−0.268715	−0.134357	+	0.990933i	$0.542897\pi$
$752$	1.36105e10	1.16711
$753$	−3.88522e9	−0.331614
$754$	−5.00289e9	−0.425032
$755$	2.65635e10	2.24631
$756$	−1.53032e9	−0.128812
$757$	−1.03709e10	−0.868921	−0.434461	−	0.900691i	$-0.643061\pi$
$757$	−1.03709e10	−0.868921	−0.434461	+	0.900691i	$0.643061\pi$
$758$	−1.81479e10	−1.51350
$759$	−1.94569e9	−0.161521
$760$	4.12273e9	0.340673
$761$	1.48892e9	0.122468	0.0612342	−	0.998123i	$-0.480496\pi$
$761$	1.48892e9	0.122468	0.0612342	+	0.998123i	$0.480496\pi$
$762$	1.12632e10	0.922186
$763$	−1.08851e10	−0.887147
$764$	7.80215e9	0.632977
$765$	−8.51318e9	−0.687507
$766$	2.02558e10	1.62835
$767$	2.35757e9	0.188660
$768$	−6.05062e9	−0.481987
$769$	1.76503e10	1.39962	0.699809	−	0.714330i	$-0.253268\pi$
$769$	1.76503e10	1.39962	0.699809	+	0.714330i	$0.253268\pi$
$770$	3.77453e9	0.297951
$771$	4.06931e9	0.319765
$772$	2.15359e9	0.168462
$773$	−6.95196e8	−0.0541351	−0.0270676	−	0.999634i	$-0.508617\pi$
$773$	−6.95196e8	−0.0541351	−0.0270676	+	0.999634i	$0.508617\pi$
$774$	1.00909e10	0.782235
$775$	−3.87982e10	−2.99403
$776$	1.19452e9	0.0917649
$777$	−6.25626e9	−0.478455
$778$	−5.40894e9	−0.411798
$779$	−1.01543e10	−0.769608
$780$	−2.11246e10	−1.59388
$781$	5.60624e8	0.0421107
$782$	−3.34667e10	−2.50259
$783$	−5.26434e8	−0.0391902
$784$	7.59631e9	0.562984
$785$	−4.13014e10	−3.04734
$786$	9.00822e9	0.661698
$787$	−7.19358e8	−0.0526058	−0.0263029	−	0.999654i	$-0.508373\pi$
$787$	−7.19358e8	−0.0526058	−0.0263029	+	0.999654i	$0.508373\pi$
$788$	2.68440e8	0.0195436
$789$	1.35623e10	0.983026
$790$	5.91956e10	4.27164
$791$	5.31738e9	0.382014
$792$	9.36471e7	0.00669817
$793$	−1.82050e10	−1.29639
$794$	4.08052e9	0.289297
$795$	4.34793e9	0.306901
$796$	5.54439e9	0.389635
$797$	4.07407e9	0.285052	0.142526	−	0.989791i	$-0.454477\pi$
$797$	4.07407e9	0.285052	0.142526	+	0.989791i	$0.454477\pi$
$798$	−1.33179e10	−0.927739
$799$	2.12786e10	1.47581
$800$	4.44616e10	3.07023
$801$	2.77299e9	0.190649
$802$	−2.55998e10	−1.75237
$803$	−2.06739e9	−0.140902
$804$	9.57392e9	0.649671
$805$	−2.44161e10	−1.64965
$806$	4.33371e10	2.91532
$807$	7.46351e9	0.499903
$808$	1.72951e9	0.115341
$809$	−1.12391e10	−0.746296	−0.373148	−	0.927772i	$-0.621722\pi$
$809$	−1.12391e10	−0.746296	−0.373148	+	0.927772i	$0.621722\pi$
$810$	−4.29161e9	−0.283741
$811$	1.57592e10	1.03744	0.518719	−	0.854945i	$-0.326409\pi$
$811$	1.57592e10	1.03744	0.518719	+	0.854945i	$0.326409\pi$
$812$	2.07943e9	0.136300
$813$	−3.18586e9	−0.207926
$814$	5.52267e9	0.358892
$815$	−2.84770e9	−0.184265
$816$	−9.58992e9	−0.617873
$817$	4.54857e10	2.91808
$818$	3.86757e9	0.247059
$819$	4.73060e9	0.300900
$820$	1.29251e10	0.818627
$821$	−1.83331e10	−1.15621	−0.578103	−	0.815964i	$-0.696207\pi$
$821$	−1.83331e10	−1.15621	−0.578103	+	0.815964i	$0.696207\pi$
$822$	4.99389e8	0.0313608
$823$	3.71121e9	0.232069	0.116034	−	0.993245i	$-0.462982\pi$
$823$	3.71121e9	0.232069	0.116034	+	0.993245i	$0.462982\pi$
$824$	−1.41511e9	−0.0881138
$825$	3.73855e9	0.231801
$826$	−1.89189e9	−0.116806
$827$	3.00461e9	0.184722	0.0923610	−	0.995726i	$-0.470559\pi$
$827$	3.00461e9	0.184722	0.0923610	+	0.995726i	$0.470559\pi$
$828$	−8.73838e9	−0.534964
$829$	1.97799e10	1.20582	0.602912	−	0.797808i	$-0.294007\pi$
$829$	1.97799e10	1.20582	0.602912	+	0.797808i	$0.294007\pi$
$830$	−3.16235e10	−1.91971
$831$	1.71424e9	0.103626
$832$	−2.75162e10	−1.65637
$833$	1.18760e10	0.711891
$834$	−6.37268e9	−0.380400
$835$	−2.68828e10	−1.59798
$836$	6.08921e9	0.360445
$837$	4.56018e9	0.268808
$838$	2.63605e10	1.54739
$839$	−7.17247e9	−0.419278	−0.209639	−	0.977779i	$-0.567229\pi$
$839$	−7.17247e9	−0.419278	−0.209639	+	0.977779i	$0.567229\pi$
$840$	1.17516e9	0.0684100
$841$	−1.65345e10	−0.958531
$842$	1.91094e10	1.10320
$843$	−1.05848e10	−0.608538
$844$	1.60388e10	0.918278
$845$	3.42050e10	1.95025
$846$	1.07268e10	0.609080
$847$	−1.06297e10	−0.601073
$848$	4.89786e9	0.275817
$849$	−1.05598e10	−0.592212
$850$	6.43046e10	3.59150
$851$	−3.57243e10	−1.98706
$852$	2.51784e9	0.139473
$853$	−2.70770e9	−0.149375	−0.0746877	−	0.997207i	$-0.523796\pi$
$853$	−2.70770e9	−0.149375	−0.0746877	+	0.997207i	$0.523796\pi$
$854$	1.46091e10	0.802639
$855$	−1.93448e10	−1.05848
$856$	−3.78903e9	−0.206476
$857$	−1.93553e10	−1.05043	−0.525215	−	0.850969i	$-0.676015\pi$
$857$	−1.93553e10	−1.05043	−0.525215	+	0.850969i	$0.676015\pi$
$858$	−4.17591e9	−0.225707
$859$	−3.02146e10	−1.62645	−0.813224	−	0.581951i	$-0.802290\pi$
$859$	−3.02146e10	−1.62645	−0.813224	+	0.581951i	$0.802290\pi$
$860$	−5.78973e10	−3.10394
$861$	−2.89443e9	−0.154544
$862$	−4.47497e10	−2.37966
$863$	4.20793e9	0.222859	0.111430	−	0.993772i	$-0.464457\pi$
$863$	4.20793e9	0.222859	0.111430	+	0.993772i	$0.464457\pi$
$864$	−5.22583e9	−0.275649
$865$	−5.08996e10	−2.67398
$866$	−2.35831e9	−0.123393
$867$	−3.91368e9	−0.203948
$868$	−1.80128e10	−0.934894
$869$	6.06098e9	0.313310
$870$	5.83151e9	0.300237
$871$	−2.95954e10	−1.51761
$872$	2.99158e9	0.152789
$873$	−5.60494e9	−0.285116
$874$	−7.60475e10	−3.85296
$875$	2.50280e10	1.26298
$876$	−9.28492e9	−0.466674
$877$	−1.97999e10	−0.991206	−0.495603	−	0.868549i	$-0.665053\pi$
$877$	−1.97999e10	−0.991206	−0.495603	+	0.868549i	$0.665053\pi$
$878$	4.61252e9	0.229989
$879$	1.06810e10	0.530460
$880$	6.17609e9	0.305509
$881$	5.47108e9	0.269561	0.134781	−	0.990875i	$-0.456967\pi$
$881$	5.47108e9	0.269561	0.134781	+	0.990875i	$0.456967\pi$
$882$	5.98686e9	0.293805
$883$	1.99701e10	0.976153	0.488076	−	0.872801i	$-0.337699\pi$
$883$	1.99701e10	0.976153	0.488076	+	0.872801i	$0.337699\pi$
$884$	−3.72031e10	−1.81133
$885$	−2.74805e9	−0.133267
$886$	1.07266e10	0.518138
$887$	−6.76780e9	−0.325623	−0.162811	−	0.986657i	$-0.552056\pi$
$887$	−6.76780e9	−0.325623	−0.162811	+	0.986657i	$0.552056\pi$
$888$	1.71943e9	0.0824021
$889$	1.44716e10	0.690813
$890$	−3.07174e10	−1.46056
$891$	−4.39413e8	−0.0208114
$892$	2.09111e10	0.986508
$893$	4.83521e10	2.27214
$894$	3.04118e10	1.42351
$895$	5.86243e10	2.73336
$896$	2.86994e9	0.133289
$897$	2.70125e10	1.24966
$898$	−4.82978e10	−2.22567
$899$	−6.19645e9	−0.284436
$900$	1.67904e10	0.767735
$901$	7.65728e9	0.348769
$902$	2.55504e9	0.115924
$903$	1.29654e10	0.585975
$904$	−1.46139e9	−0.0657926
$905$	−3.73736e10	−1.67608
$906$	2.35833e10	1.05355
$907$	−2.47127e10	−1.09975	−0.549877	−	0.835246i	$-0.685325\pi$
$907$	−2.47127e10	−1.09975	−0.549877	+	0.835246i	$0.685325\pi$
$908$	−3.01414e10	−1.33618
$909$	−8.11525e9	−0.358367
$910$	−5.24027e10	−2.30520
$911$	−3.74402e9	−0.164068	−0.0820340	−	0.996630i	$-0.526142\pi$
$911$	−3.74402e9	−0.164068	−0.0820340	+	0.996630i	$0.526142\pi$
$912$	−2.17915e10	−0.951273
$913$	−3.23790e9	−0.140804
$914$	4.28539e9	0.185643
$915$	2.12203e10	0.915750
$916$	−2.06965e10	−0.889740
$917$	1.15743e10	0.495681
$918$	−7.55808e9	−0.322450
$919$	−3.76618e9	−0.160065	−0.0800326	−	0.996792i	$-0.525502\pi$
$919$	−3.76618e9	−0.160065	−0.0800326	+	0.996792i	$0.525502\pi$
$920$	6.71036e9	0.284111
$921$	1.01243e10	0.427028
$922$	−1.20536e10	−0.506477
$923$	−7.78326e9	−0.325804
$924$	1.73569e9	0.0723804
$925$	6.86424e10	2.85165
$926$	1.30379e10	0.539598
$927$	6.63999e9	0.273772
$928$	7.10095e9	0.291675
$929$	3.28415e10	1.34390	0.671952	−	0.740595i	$-0.265456\pi$
$929$	3.28415e10	1.34390	0.671952	+	0.740595i	$0.265456\pi$
$930$	−5.05149e10	−2.05934
$931$	2.69863e10	1.09602
$932$	1.45680e10	0.589448
$933$	−1.53244e10	−0.617730
$934$	−5.61208e10	−2.25377
$935$	9.65567e9	0.386315
$936$	−1.30012e9	−0.0518226
$937$	−3.67023e10	−1.45749	−0.728744	−	0.684787i	$-0.759895\pi$
$937$	−3.67023e10	−1.45749	−0.728744	+	0.684787i	$0.759895\pi$
$938$	2.37496e10	0.939605
$939$	2.59522e10	1.02293
$940$	−6.15458e10	−2.41686
$941$	2.52107e10	0.986329	0.493165	−	0.869936i	$-0.335840\pi$
$941$	2.52107e10	0.986329	0.493165	+	0.869936i	$0.335840\pi$
$942$	−3.66677e10	−1.42924
$943$	−1.65277e10	−0.641831
$944$	−3.09562e9	−0.119769
$945$	−5.51411e9	−0.212552
$946$	−1.14451e10	−0.439544
$947$	8.87956e9	0.339755	0.169878	−	0.985465i	$-0.445663\pi$
$947$	8.87956e9	0.339755	0.169878	+	0.985465i	$0.445663\pi$
$948$	2.72207e10	1.03770
$949$	2.87020e10	1.09013
$950$	1.46121e11	5.52944
$951$	−2.80158e9	−0.105626
$952$	2.06961e9	0.0777427
$953$	1.58158e10	0.591925	0.295962	−	0.955200i	$-0.404360\pi$
$953$	1.58158e10	0.591925	0.295962	+	0.955200i	$0.404360\pi$
$954$	3.86014e9	0.143941
$955$	2.81131e10	1.04447
$956$	−3.28802e10	−1.21711
$957$	5.97082e8	0.0220213
$958$	3.54662e10	1.30327
$959$	6.41645e8	0.0234925
$960$	3.20737e10	1.17004
$961$	2.61635e10	0.950963
$962$	−7.66725e10	−2.77669
$963$	1.77790e10	0.641526
$964$	−8.79917e9	−0.316353
$965$	7.75992e9	0.277979
$966$	−2.16769e10	−0.773707
$967$	5.18915e10	1.84546	0.922728	−	0.385451i	$-0.125954\pi$
$967$	5.18915e10	1.84546	0.922728	+	0.385451i	$0.125954\pi$
$968$	2.92138e9	0.103520
$969$	−3.40687e10	−1.20288
$970$	6.20881e10	2.18428
$971$	−1.69159e10	−0.592963	−0.296481	−	0.955039i	$-0.595813\pi$
$971$	−1.69159e10	−0.592963	−0.296481	+	0.955039i	$0.595813\pi$
$972$	−1.97347e9	−0.0689284
$973$	−8.18800e9	−0.284959
$974$	−2.83182e10	−0.981996
$975$	−5.19032e10	−1.79340
$976$	2.39042e10	0.822999
$977$	8.24427e9	0.282827	0.141414	−	0.989951i	$-0.454835\pi$
$977$	8.24427e9	0.282827	0.141414	+	0.989951i	$0.454835\pi$
$978$	−2.52821e9	−0.0864227
$979$	−3.14513e9	−0.107127
$980$	−3.43500e10	−1.16583
$981$	−1.40372e10	−0.474720
$982$	1.17623e10	0.396373
$983$	−4.10669e9	−0.137897	−0.0689484	−	0.997620i	$-0.521964\pi$
$983$	−4.10669e9	−0.137897	−0.0689484	+	0.997620i	$0.521964\pi$
$984$	7.95484e8	0.0266164
$985$	9.67254e8	0.0322488
$986$	1.02701e10	0.341196
$987$	1.37825e10	0.456265
$988$	−8.45379e10	−2.78870
$989$	7.40347e10	2.43359
$990$	4.86755e9	0.159436
$991$	−1.53943e9	−0.0502460	−0.0251230	−	0.999684i	$-0.507998\pi$
$991$	−1.53943e9	−0.0502460	−0.0251230	+	0.999684i	$0.507998\pi$
$992$	−6.15112e10	−2.00062
$993$	1.31355e10	0.425719
$994$	6.24588e9	0.201716
$995$	1.99778e10	0.642934
$996$	−1.45419e10	−0.466350
$997$	−2.17704e10	−0.695717	−0.347858	−	0.937547i	$-0.613091\pi$
$997$	−2.17704e10	−0.695717	−0.347858	+	0.937547i	$0.613091\pi$
$998$	2.90263e10	0.924345
$999$	−8.06793e9	−0.256025

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.a.1.3	✓	16
3.2	odd	2		531.8.a.b.1.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.a.1.3	✓	16	1.1	even	1	trivial
531.8.a.b.1.14		16	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)

\(f(q)\)	\(=\)	\(q-16.2952 q^{2} -27.0000 q^{3} +137.534 q^{4} +495.569 q^{5} +439.971 q^{6} +565.301 q^{7} -155.363 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-16.2952 q^{2} -27.0000 q^{3} +137.534 q^{4} +495.569 q^{5} +439.971 q^{6} +565.301 q^{7} -155.363 q^{8} +729.000 q^{9} -8075.41 q^{10} -826.834 q^{11} -3713.43 q^{12} +11479.1 q^{13} -9211.71 q^{14} -13380.4 q^{15} -15072.7 q^{16} -23564.6 q^{17} -11879.2 q^{18} -53546.6 q^{19} +68157.8 q^{20} -15263.1 q^{21} +13473.4 q^{22} -87155.1 q^{23} +4194.81 q^{24} +167464. q^{25} -187055. q^{26} -19683.0 q^{27} +77748.3 q^{28} +26745.6 q^{29} +218036. q^{30} -231681. q^{31} +265500. q^{32} +22324.5 q^{33} +383990. q^{34} +280146. q^{35} +100263. q^{36} +409893. q^{37} +872554. q^{38} -309936. q^{39} -76993.4 q^{40} +189635. q^{41} +248716. q^{42} -849460. q^{43} -113718. q^{44} +361270. q^{45} +1.42021e6 q^{46} -902990. q^{47} +406963. q^{48} -503977. q^{49} -2.72886e6 q^{50} +636244. q^{51} +1.57877e6 q^{52} -324949. q^{53} +320739. q^{54} -409753. q^{55} -87827.2 q^{56} +1.44576e6 q^{57} -435826. q^{58} +205379. q^{59} -1.84026e6 q^{60} -1.58592e6 q^{61} +3.77529e6 q^{62} +412105. q^{63} -2.39707e6 q^{64} +5.68870e6 q^{65} -363783. q^{66} -2.57819e6 q^{67} -3.24094e6 q^{68} +2.35319e6 q^{69} -4.56504e6 q^{70} -678037. q^{71} -113260. q^{72} +2.50036e6 q^{73} -6.67930e6 q^{74} -4.52153e6 q^{75} -7.36449e6 q^{76} -467410. q^{77} +5.05048e6 q^{78} -7.33035e6 q^{79} -7.46957e6 q^{80} +531441. q^{81} -3.09015e6 q^{82} +3.91602e6 q^{83} -2.09920e6 q^{84} -1.16779e7 q^{85} +1.38421e7 q^{86} -722131. q^{87} +128460. q^{88} +3.80382e6 q^{89} -5.88698e6 q^{90} +6.48916e6 q^{91} -1.19868e7 q^{92} +6.25539e6 q^{93} +1.47144e7 q^{94} -2.65361e7 q^{95} -7.16849e6 q^{96} -7.68854e6 q^{97} +8.21243e6 q^{98} -602762. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 432 q^{3} + 974 q^{4} - 68 q^{5} + 162 q^{6} - 2343 q^{7} + 819 q^{8} + 11664 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 - 432 * q^3 + 974 * q^4 - 68 * q^5 + 162 * q^6 - 2343 * q^7 + 819 * q^8 + 11664 * q^9	\( 16 q - 6 q^{2} - 432 q^{3} + 974 q^{4} - 68 q^{5} + 162 q^{6} - 2343 q^{7} + 819 q^{8} + 11664 q^{9} - 3479 q^{10} + 898 q^{11} - 26298 q^{12} - 8172 q^{13} - 13315 q^{14} + 1836 q^{15} + 3138 q^{16} - 44985 q^{17} - 4374 q^{18} - 40137 q^{19} + 130657 q^{20} + 63261 q^{21} + 109394 q^{22} - 2833 q^{23} - 22113 q^{24} + 285746 q^{25} - 129420 q^{26} - 314928 q^{27} + 112890 q^{28} + 144375 q^{29} + 93933 q^{30} - 141759 q^{31} - 36224 q^{32} - 24246 q^{33} - 341332 q^{34} - 78859 q^{35} + 710046 q^{36} - 297971 q^{37} + 329075 q^{38} + 220644 q^{39} - 203048 q^{40} + 659077 q^{41} + 359505 q^{42} - 1431608 q^{43} + 254916 q^{44} - 49572 q^{45} + 873113 q^{46} - 1574073 q^{47} - 84726 q^{48} + 1893545 q^{49} + 302533 q^{50} + 1214595 q^{51} - 4972548 q^{52} + 587736 q^{53} + 118098 q^{54} - 4624036 q^{55} - 5798506 q^{56} + 1083699 q^{57} - 6991380 q^{58} + 3286064 q^{59} - 3527739 q^{60} - 6117131 q^{61} - 11570258 q^{62} - 1708047 q^{63} - 19063011 q^{64} - 5335514 q^{65} - 2953638 q^{66} - 16518710 q^{67} - 17284669 q^{68} + 76491 q^{69} - 39189486 q^{70} - 10882582 q^{71} + 597051 q^{72} - 21097441 q^{73} - 16717030 q^{74} - 7715142 q^{75} - 40864952 q^{76} - 3404601 q^{77} + 3494340 q^{78} - 3784458 q^{79} - 27466195 q^{80} + 8503056 q^{81} - 24990117 q^{82} - 1951425 q^{83} - 3048030 q^{84} - 23238675 q^{85} - 35910572 q^{86} - 3898125 q^{87} - 27843055 q^{88} + 10499443 q^{89} - 2536191 q^{90} + 699217 q^{91} - 20062766 q^{92} + 3827493 q^{93} - 59358988 q^{94} - 29236333 q^{95} + 978048 q^{96} - 25158976 q^{97} + 2120460 q^{98} + 654642 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 432 * q^3 + 974 * q^4 - 68 * q^5 + 162 * q^6 - 2343 * q^7 + 819 * q^8 + 11664 * q^9 - 3479 * q^10 + 898 * q^11 - 26298 * q^12 - 8172 * q^13 - 13315 * q^14 + 1836 * q^15 + 3138 * q^16 - 44985 * q^17 - 4374 * q^18 - 40137 * q^19 + 130657 * q^20 + 63261 * q^21 + 109394 * q^22 - 2833 * q^23 - 22113 * q^24 + 285746 * q^25 - 129420 * q^26 - 314928 * q^27 + 112890 * q^28 + 144375 * q^29 + 93933 * q^30 - 141759 * q^31 - 36224 * q^32 - 24246 * q^33 - 341332 * q^34 - 78859 * q^35 + 710046 * q^36 - 297971 * q^37 + 329075 * q^38 + 220644 * q^39 - 203048 * q^40 + 659077 * q^41 + 359505 * q^42 - 1431608 * q^43 + 254916 * q^44 - 49572 * q^45 + 873113 * q^46 - 1574073 * q^47 - 84726 * q^48 + 1893545 * q^49 + 302533 * q^50 + 1214595 * q^51 - 4972548 * q^52 + 587736 * q^53 + 118098 * q^54 - 4624036 * q^55 - 5798506 * q^56 + 1083699 * q^57 - 6991380 * q^58 + 3286064 * q^59 - 3527739 * q^60 - 6117131 * q^61 - 11570258 * q^62 - 1708047 * q^63 - 19063011 * q^64 - 5335514 * q^65 - 2953638 * q^66 - 16518710 * q^67 - 17284669 * q^68 + 76491 * q^69 - 39189486 * q^70 - 10882582 * q^71 + 597051 * q^72 - 21097441 * q^73 - 16717030 * q^74 - 7715142 * q^75 - 40864952 * q^76 - 3404601 * q^77 + 3494340 * q^78 - 3784458 * q^79 - 27466195 * q^80 + 8503056 * q^81 - 24990117 * q^82 - 1951425 * q^83 - 3048030 * q^84 - 23238675 * q^85 - 35910572 * q^86 - 3898125 * q^87 - 27843055 * q^88 + 10499443 * q^89 - 2536191 * q^90 + 699217 * q^91 - 20062766 * q^92 + 3827493 * q^93 - 59358988 * q^94 - 29236333 * q^95 + 978048 * q^96 - 25158976 * q^97 + 2120460 * q^98 + 654642 * q^99

Introduction

L-functions

Modular forms

Varieties

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