LMFDB - Embedded newform 177.8.a.d.1.17

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:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 1798 x^{16} + 11087 x^{15} + 1326765 x^{14} - 8403720 x^{13} - 518334228 x^{12} + \cdots + 51\!\cdots\!48 $ x^18 - 6x^17 - 1798x^16 + 11087x^15 + 1326765x^14 - 8403720x^13 - 518334228x^12 + 3375594921x^11 + 115310342333x^10 - 774932111214x^9 - 14600047830166x^8 + 102185027148481x^7 + 988557475638619x^6 - 7379206238519716x^5 - 30152342836849520x^4 + 260578770749067175x^3 + 182609347488069978x^2 - 3481290425710753600*x + 5164646074739714048
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Root			$19.9328$ 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)

$f(q)$	$=$	$q+20.9328 q^{2} +27.0000 q^{3} +310.183 q^{4} -149.882 q^{5} +565.186 q^{6} +1201.09 q^{7} +3813.60 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+20.9328 q^{2} +27.0000 q^{3} +310.183 q^{4} -149.882 q^{5} +565.186 q^{6} +1201.09 q^{7} +3813.60 q^{8} +729.000 q^{9} -3137.45 q^{10} +3090.18 q^{11} +8374.94 q^{12} -9762.44 q^{13} +25142.2 q^{14} -4046.82 q^{15} +40126.1 q^{16} +774.830 q^{17} +15260.0 q^{18} +42295.3 q^{19} -46490.9 q^{20} +32429.5 q^{21} +64686.2 q^{22} +19299.9 q^{23} +102967. q^{24} -55660.4 q^{25} -204355. q^{26} +19683.0 q^{27} +372558. q^{28} -148022. q^{29} -84711.3 q^{30} -77522.7 q^{31} +351811. q^{32} +83434.9 q^{33} +16219.4 q^{34} -180022. q^{35} +226123. q^{36} +381041. q^{37} +885360. q^{38} -263586. q^{39} -571591. q^{40} +313892. q^{41} +678840. q^{42} +86822.9 q^{43} +958522. q^{44} -109264. q^{45} +404002. q^{46} +1.09797e6 q^{47} +1.08340e6 q^{48} +619078. q^{49} -1.16513e6 q^{50} +20920.4 q^{51} -3.02814e6 q^{52} -1.35146e6 q^{53} +412021. q^{54} -463163. q^{55} +4.58049e6 q^{56} +1.14197e6 q^{57} -3.09852e6 q^{58} +205379. q^{59} -1.25525e6 q^{60} -1.17823e6 q^{61} -1.62277e6 q^{62} +875596. q^{63} +2.22825e6 q^{64} +1.46321e6 q^{65} +1.74653e6 q^{66} -2.20281e6 q^{67} +240339. q^{68} +521098. q^{69} -3.76837e6 q^{70} +64342.9 q^{71} +2.78012e6 q^{72} -1.88910e6 q^{73} +7.97626e6 q^{74} -1.50283e6 q^{75} +1.31193e7 q^{76} +3.71159e6 q^{77} -5.51760e6 q^{78} -267273. q^{79} -6.01418e6 q^{80} +531441. q^{81} +6.57065e6 q^{82} -9.61801e6 q^{83} +1.00591e7 q^{84} -116133. q^{85} +1.81745e6 q^{86} -3.99660e6 q^{87} +1.17847e7 q^{88} +1.26033e7 q^{89} -2.28720e6 q^{90} -1.17256e7 q^{91} +5.98651e6 q^{92} -2.09311e6 q^{93} +2.29835e7 q^{94} -6.33931e6 q^{95} +9.49889e6 q^{96} -7.21193e6 q^{97} +1.29590e7 q^{98} +2.25274e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9}+O(q^{10}) $ 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9	\( 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9} + 3609 q^{10} + 15070 q^{11} + 36666 q^{12} + 13662 q^{13} + 20861 q^{14} + 18306 q^{15} + 60482 q^{16} + 71919 q^{17} + 17496 q^{18} + 56231 q^{19} + 143053 q^{20} + 83187 q^{21} + 274198 q^{22} + 150029 q^{23} + 110889 q^{24} + 399672 q^{25} + 182846 q^{26} + 354294 q^{27} + 434150 q^{28} + 591285 q^{29} + 97443 q^{30} + 426733 q^{31} + 1205630 q^{32} + 406890 q^{33} + 403548 q^{34} + 912879 q^{35} + 989982 q^{36} + 7703 q^{37} - 417859 q^{38} + 368874 q^{39} + 618020 q^{40} + 770959 q^{41} + 563247 q^{42} + 793050 q^{43} + 2591274 q^{44} + 494262 q^{45} - 4068019 q^{46} + 1410373 q^{47} + 1633014 q^{48} + 1637427 q^{49} + 1021549 q^{50} + 1941813 q^{51} - 3749190 q^{52} + 1037934 q^{53} + 472392 q^{54} + 331974 q^{55} - 391748 q^{56} + 1518237 q^{57} + 653724 q^{58} + 3696822 q^{59} + 3862431 q^{60} - 1374623 q^{61} + 5251718 q^{62} + 2246049 q^{63} + 5077197 q^{64} + 3257170 q^{65} + 7403346 q^{66} - 2436904 q^{67} + 14119909 q^{68} + 4050783 q^{69} + 5185580 q^{70} + 14289172 q^{71} + 2994003 q^{72} + 5482515 q^{73} + 14934154 q^{74} + 10791144 q^{75} + 3822912 q^{76} + 23157109 q^{77} + 4936842 q^{78} + 19786414 q^{79} + 31978143 q^{80} + 9565938 q^{81} + 9749509 q^{82} + 30227337 q^{83} + 11722050 q^{84} + 9946981 q^{85} + 44295864 q^{86} + 15964695 q^{87} + 39970897 q^{88} + 31061677 q^{89} + 2630961 q^{90} + 26377785 q^{91} + 4719698 q^{92} + 11521791 q^{93} + 44488296 q^{94} + 15534599 q^{95} + 32552010 q^{96} + 12084118 q^{97} + 42274744 q^{98} + 10986030 q^{99}+O(q^{100}) \) 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9 + 3609 * q^10 + 15070 * q^11 + 36666 * q^12 + 13662 * q^13 + 20861 * q^14 + 18306 * q^15 + 60482 * q^16 + 71919 * q^17 + 17496 * q^18 + 56231 * q^19 + 143053 * q^20 + 83187 * q^21 + 274198 * q^22 + 150029 * q^23 + 110889 * q^24 + 399672 * q^25 + 182846 * q^26 + 354294 * q^27 + 434150 * q^28 + 591285 * q^29 + 97443 * q^30 + 426733 * q^31 + 1205630 * q^32 + 406890 * q^33 + 403548 * q^34 + 912879 * q^35 + 989982 * q^36 + 7703 * q^37 - 417859 * q^38 + 368874 * q^39 + 618020 * q^40 + 770959 * q^41 + 563247 * q^42 + 793050 * q^43 + 2591274 * q^44 + 494262 * q^45 - 4068019 * q^46 + 1410373 * q^47 + 1633014 * q^48 + 1637427 * q^49 + 1021549 * q^50 + 1941813 * q^51 - 3749190 * q^52 + 1037934 * q^53 + 472392 * q^54 + 331974 * q^55 - 391748 * q^56 + 1518237 * q^57 + 653724 * q^58 + 3696822 * q^59 + 3862431 * q^60 - 1374623 * q^61 + 5251718 * q^62 + 2246049 * q^63 + 5077197 * q^64 + 3257170 * q^65 + 7403346 * q^66 - 2436904 * q^67 + 14119909 * q^68 + 4050783 * q^69 + 5185580 * q^70 + 14289172 * q^71 + 2994003 * q^72 + 5482515 * q^73 + 14934154 * q^74 + 10791144 * q^75 + 3822912 * q^76 + 23157109 * q^77 + 4936842 * q^78 + 19786414 * q^79 + 31978143 * q^80 + 9565938 * q^81 + 9749509 * q^82 + 30227337 * q^83 + 11722050 * q^84 + 9946981 * q^85 + 44295864 * q^86 + 15964695 * q^87 + 39970897 * q^88 + 31061677 * q^89 + 2630961 * q^90 + 26377785 * q^91 + 4719698 * q^92 + 11521791 * q^93 + 44488296 * q^94 + 15534599 * q^95 + 32552010 * q^96 + 12084118 * q^97 + 42274744 * q^98 + 10986030 * 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 $

$2$	20.9328	1.85022	0.925109	−	0.379702i	$-0.123974\pi$
$2$	20.9328	1.85022	0.925109	+	0.379702i	$0.123974\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	310.183	2.42330
$5$	−149.882	−0.536234	−0.268117	−	0.963386i	$-0.586401\pi$
$5$	−149.882	−0.536234	−0.268117	+	0.963386i	$0.586401\pi$
$6$	565.186	1.06822
$7$	1201.09	1.32353	0.661764	−	0.749712i	$-0.269808\pi$
$7$	1201.09	1.32353	0.661764	+	0.749712i	$0.269808\pi$
$8$	3813.60	2.63342
$9$	729.000	0.333333
$10$	−3137.45	−0.992150
$11$	3090.18	0.700019	0.350009	−	0.936746i	$-0.386178\pi$
$11$	3090.18	0.700019	0.350009	+	0.936746i	$0.386178\pi$
$12$	8374.94	1.39910
$13$	−9762.44	−1.23241	−0.616207	−	0.787584i	$-0.711332\pi$
$13$	−9762.44	−1.23241	−0.616207	+	0.787584i	$0.711332\pi$
$14$	25142.2	2.44881
$15$	−4046.82	−0.309595
$16$	40126.1	2.44910
$17$	774.830	0.0382503	0.0191252	−	0.999817i	$-0.493912\pi$
$17$	774.830	0.0382503	0.0191252	+	0.999817i	$0.493912\pi$
$18$	15260.0	0.616739
$19$	42295.3	1.41467	0.707334	−	0.706879i	$-0.249898\pi$
$19$	42295.3	1.41467	0.707334	+	0.706879i	$0.249898\pi$
$20$	−46490.9	−1.29946
$21$	32429.5	0.764139
$22$	64686.2	1.29519
$23$	19299.9	0.330756	0.165378	−	0.986230i	$-0.447116\pi$
$23$	19299.9	0.330756	0.165378	+	0.986230i	$0.447116\pi$
$24$	102967.	1.52041
$25$	−55660.4	−0.712453
$26$	−204355.	−2.28023
$27$	19683.0	0.192450
$28$	372558.	3.20731
$29$	−148022.	−1.12703	−0.563513	−	0.826107i	$-0.690551\pi$
$29$	−148022.	−1.12703	−0.563513	+	0.826107i	$0.690551\pi$
$30$	−84711.3	−0.572818
$31$	−77522.7	−0.467372	−0.233686	−	0.972312i	$-0.575079\pi$
$31$	−77522.7	−0.467372	−0.233686	+	0.972312i	$0.575079\pi$
$32$	351811.	1.89795
$33$	83434.9	0.404156
$34$	16219.4	0.0707714
$35$	−180022.	−0.709721
$36$	226123.	0.807768
$37$	381041.	1.23670	0.618352	−	0.785901i	$-0.287801\pi$
$37$	381041.	1.23670	0.618352	+	0.785901i	$0.287801\pi$
$38$	885360.	2.61744
$39$	−263586.	−0.711535
$40$	−571591.	−1.41213
$41$	313892.	0.711274	0.355637	−	0.934624i	$-0.384264\pi$
$41$	313892.	0.711274	0.355637	+	0.934624i	$0.384264\pi$
$42$	678840.	1.41382
$43$	86822.9	0.166531	0.0832654	−	0.996527i	$-0.473465\pi$
$43$	86822.9	0.166531	0.0832654	+	0.996527i	$0.473465\pi$
$44$	958522.	1.69636
$45$	−109264.	−0.178745
$46$	404002.	0.611971
$47$	1.09797e6	1.54258	0.771288	−	0.636486i	$-0.219613\pi$
$47$	1.09797e6	1.54258	0.771288	+	0.636486i	$0.219613\pi$
$48$	1.08340e6	1.41399
$49$	619078.	0.751725
$50$	−1.16513e6	−1.31819
$51$	20920.4	0.0220838
$52$	−3.02814e6	−2.98652
$53$	−1.35146e6	−1.24692	−0.623458	−	0.781857i	$-0.714273\pi$
$53$	−1.35146e6	−1.24692	−0.623458	+	0.781857i	$0.714273\pi$
$54$	412021.	0.356075
$55$	−463163.	−0.375374
$56$	4.58049e6	3.48541
$57$	1.14197e6	0.816759
$58$	−3.09852e6	−2.08524
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	−1.25525e6	−0.750243
$61$	−1.17823e6	−0.664622	−0.332311	−	0.943170i	$-0.607828\pi$
$61$	−1.17823e6	−0.664622	−0.332311	+	0.943170i	$0.607828\pi$
$62$	−1.62277e6	−0.864741
$63$	875596.	0.441176
$64$	2.22825e6	1.06251
$65$	1.46321e6	0.660863
$66$	1.74653e6	0.747776
$67$	−2.20281e6	−0.894777	−0.447389	−	0.894340i	$-0.647646\pi$
$67$	−2.20281e6	−0.894777	−0.447389	+	0.894340i	$0.647646\pi$
$68$	240339.	0.0926922
$69$	521098.	0.190962
$70$	−3.76837e6	−1.31314
$71$	64342.9	0.0213352	0.0106676	−	0.999943i	$-0.496604\pi$
$71$	64342.9	0.0213352	0.0106676	+	0.999943i	$0.496604\pi$
$72$	2.78012e6	0.877808
$73$	−1.88910e6	−0.568363	−0.284181	−	0.958771i	$-0.591722\pi$
$73$	−1.88910e6	−0.568363	−0.284181	+	0.958771i	$0.591722\pi$
$74$	7.97626e6	2.28817
$75$	−1.50283e6	−0.411335
$76$	1.31193e7	3.42817
$77$	3.71159e6	0.926494
$78$	−5.51760e6	−1.31649
$79$	−267273.	−0.0609902	−0.0304951	−	0.999535i	$-0.509708\pi$
$79$	−267273.	−0.0609902	−0.0304951	+	0.999535i	$0.509708\pi$
$80$	−6.01418e6	−1.31329
$81$	531441.	0.111111
$82$	6.57065e6	1.31601
$83$	−9.61801e6	−1.84634	−0.923170	−	0.384391i	$-0.874411\pi$
$83$	−9.61801e6	−1.84634	−0.923170	+	0.384391i	$0.874411\pi$
$84$	1.00591e7	1.85174
$85$	−116133.	−0.0205111
$86$	1.81745e6	0.308118
$87$	−3.99660e6	−0.650689
$88$	1.17847e7	1.84345
$89$	1.26033e7	1.89505	0.947523	−	0.319687i	$-0.103578\pi$
$89$	1.26033e7	1.89505	0.947523	+	0.319687i	$0.103578\pi$
$90$	−2.28720e6	−0.330717
$91$	−1.17256e7	−1.63113
$92$	5.98651e6	0.801523
$93$	−2.09311e6	−0.269838
$94$	2.29835e7	2.85410
$95$	−6.33931e6	−0.758594
$96$	9.49889e6	1.09578
$97$	−7.21193e6	−0.802325	−0.401162	−	0.916007i	$-0.631394\pi$
$97$	−7.21193e6	−0.802325	−0.401162	+	0.916007i	$0.631394\pi$
$98$	1.29590e7	1.39085
$99$	2.25274e6	0.233340
$100$	−1.72649e7	−1.72649
$101$	−3.44100e6	−0.332322	−0.166161	−	0.986099i	$-0.553137\pi$
$101$	−3.44100e6	−0.332322	−0.166161	+	0.986099i	$0.553137\pi$
$102$	437923.	0.0408599
$103$	−8.00277e6	−0.721623	−0.360811	−	0.932639i	$-0.617500\pi$
$103$	−8.00277e6	−0.721623	−0.360811	+	0.932639i	$0.617500\pi$
$104$	−3.72301e7	−3.24547
$105$	−4.86060e6	−0.409758
$106$	−2.82899e7	−2.30707
$107$	−1.89058e7	−1.49194	−0.745972	−	0.665978i	$-0.768015\pi$
$107$	−1.89058e7	−1.49194	−0.745972	+	0.665978i	$0.768015\pi$
$108$	6.10533e6	0.466365
$109$	−1.48351e7	−1.09723	−0.548613	−	0.836076i	$-0.684844\pi$
$109$	−1.48351e7	−1.09723	−0.548613	+	0.836076i	$0.684844\pi$
$110$	−9.69530e6	−0.694524
$111$	1.02881e7	0.714011
$112$	4.81951e7	3.24145
$113$	1.51244e7	0.986061	0.493030	−	0.870012i	$-0.335889\pi$
$113$	1.51244e7	0.986061	0.493030	+	0.870012i	$0.335889\pi$
$114$	2.39047e7	1.51118
$115$	−2.89271e6	−0.177363
$116$	−4.59140e7	−2.73113
$117$	−7.11682e6	−0.410805
$118$	4.29916e6	0.240878
$119$	930642.	0.0506254
$120$	−1.54330e7	−0.815295
$121$	−9.93795e6	−0.509974
$122$	−2.46636e7	−1.22970
$123$	8.47509e6	0.410654
$124$	−2.40462e7	−1.13259
$125$	2.00520e7	0.918276
$126$	1.83287e7	0.816271
$127$	3.60355e7	1.56105	0.780527	−	0.625122i	$-0.214951\pi$
$127$	3.60355e7	1.56105	0.780527	+	0.625122i	$0.214951\pi$
$128$	1.61184e6	0.0679339
$129$	2.34422e6	0.0961466
$130$	3.06292e7	1.22274
$131$	1.15356e7	0.448321	0.224161	−	0.974552i	$-0.428036\pi$
$131$	1.15356e7	0.448321	0.224161	+	0.974552i	$0.428036\pi$
$132$	2.58801e7	0.979393
$133$	5.08005e7	1.87235
$134$	−4.61110e7	−1.65553
$135$	−2.95013e6	−0.103198
$136$	2.95490e6	0.100729
$137$	−3.77725e7	−1.25503	−0.627515	−	0.778605i	$-0.715928\pi$
$137$	−3.77725e7	−1.25503	−0.627515	+	0.778605i	$0.715928\pi$
$138$	1.09080e7	0.353322
$139$	−3.71316e6	−0.117271	−0.0586357	−	0.998279i	$-0.518675\pi$
$139$	−3.71316e6	−0.117271	−0.0586357	+	0.998279i	$0.518675\pi$
$140$	−5.58398e7	−1.71987
$141$	2.96451e7	0.890607
$142$	1.34688e6	0.0394747
$143$	−3.01677e7	−0.862713
$144$	2.92519e7	0.816367
$145$	2.21859e7	0.604350
$146$	−3.95442e7	−1.05159
$147$	1.67151e7	0.434009
$148$	1.18192e8	2.99691
$149$	−6.47154e7	−1.60271	−0.801357	−	0.598187i	$-0.795888\pi$
$149$	−6.47154e7	−1.60271	−0.801357	+	0.598187i	$0.795888\pi$
$150$	−3.14585e7	−0.761059
$151$	2.42807e7	0.573907	0.286953	−	0.957945i	$-0.407358\pi$
$151$	2.42807e7	0.573907	0.286953	+	0.957945i	$0.407358\pi$
$152$	1.61298e8	3.72542
$153$	564851.	0.0127501
$154$	7.76941e7	1.71422
$155$	1.16193e7	0.250621
$156$	−8.17599e7	−1.72427
$157$	4.14110e7	0.854018	0.427009	−	0.904247i	$-0.359567\pi$
$157$	4.14110e7	0.854018	0.427009	+	0.904247i	$0.359567\pi$
$158$	−5.59477e6	−0.112845
$159$	−3.64894e7	−0.719908
$160$	−5.27301e7	−1.01774
$161$	2.31810e7	0.437765
$162$	1.11246e7	0.205580
$163$	−8.91039e7	−1.61154	−0.805769	−	0.592231i	$-0.798247\pi$
$163$	−8.91039e7	−1.61154	−0.805769	+	0.592231i	$0.798247\pi$
$164$	9.73640e7	1.72363
$165$	−1.25054e7	−0.216722
$166$	−2.01332e8	−3.41613
$167$	5.76977e7	0.958630	0.479315	−	0.877643i	$-0.340885\pi$
$167$	5.76977e7	0.958630	0.479315	+	0.877643i	$0.340885\pi$
$168$	1.23673e8	2.01230
$169$	3.25568e7	0.518845
$170$	−2.43099e6	−0.0379501
$171$	3.08333e7	0.471556
$172$	2.69310e7	0.403555
$173$	1.70091e7	0.249759	0.124880	−	0.992172i	$-0.460146\pi$
$173$	1.70091e7	0.249759	0.124880	+	0.992172i	$0.460146\pi$
$174$	−8.36601e7	−1.20392
$175$	−6.68532e7	−0.942951
$176$	1.23997e8	1.71442
$177$	5.54523e6	0.0751646
$178$	2.63823e8	3.50625
$179$	−3.67383e7	−0.478777	−0.239388	−	0.970924i	$-0.576947\pi$
$179$	−3.67383e7	−0.478777	−0.239388	+	0.970924i	$0.576947\pi$
$180$	−3.38918e7	−0.433153
$181$	1.07531e7	0.134791	0.0673954	−	0.997726i	$-0.478531\pi$
$181$	1.07531e7	0.134791	0.0673954	+	0.997726i	$0.478531\pi$
$182$	−2.45450e8	−3.01795
$183$	−3.18121e7	−0.383720
$184$	7.36023e7	0.871021
$185$	−5.71112e7	−0.663163
$186$	−4.38148e7	−0.499258
$187$	2.39437e6	0.0267759
$188$	3.40571e8	3.73813
$189$	2.36411e7	0.254713
$190$	−1.32700e8	−1.40356
$191$	−4.65850e7	−0.483759	−0.241880	−	0.970306i	$-0.577764\pi$
$191$	−4.65850e7	−0.483759	−0.241880	+	0.970306i	$0.577764\pi$
$192$	6.01628e7	0.613442
$193$	−6.10866e7	−0.611639	−0.305820	−	0.952089i	$-0.598930\pi$
$193$	−6.10866e7	−0.611639	−0.305820	+	0.952089i	$0.598930\pi$
$194$	−1.50966e8	−1.48448
$195$	3.95068e7	0.381549
$196$	1.92027e8	1.82166
$197$	7.42960e7	0.692363	0.346181	−	0.938168i	$-0.387478\pi$
$197$	7.42960e7	0.692363	0.346181	+	0.938168i	$0.387478\pi$
$198$	4.71563e7	0.431729
$199$	−1.79787e8	−1.61723	−0.808617	−	0.588335i	$-0.799784\pi$
$199$	−1.79787e8	−1.61723	−0.808617	+	0.588335i	$0.799784\pi$
$200$	−2.12267e8	−1.87619
$201$	−5.94758e7	−0.516600
$202$	−7.20298e7	−0.614869
$203$	−1.77788e8	−1.49165
$204$	6.48916e6	0.0535159
$205$	−4.70468e7	−0.381410
$206$	−1.67521e8	−1.33516
$207$	1.40696e7	0.110252
$208$	−3.91729e8	−3.01831
$209$	1.30700e8	0.990294
$210$	−1.01746e8	−0.758141
$211$	−1.70096e8	−1.24654	−0.623269	−	0.782008i	$-0.714196\pi$
$211$	−1.70096e8	−1.24654	−0.623269	+	0.782008i	$0.714196\pi$
$212$	−4.19200e8	−3.02166
$213$	1.73726e6	0.0123179
$214$	−3.95752e8	−2.76042
$215$	−1.30132e7	−0.0892996
$216$	7.50632e7	0.506803
$217$	−9.31119e7	−0.618580
$218$	−3.10540e8	−2.03011
$219$	−5.10058e7	−0.328144
$220$	−1.43665e8	−0.909646
$221$	−7.56423e6	−0.0471402
$222$	2.15359e8	1.32108
$223$	−1.26142e8	−0.761713	−0.380857	−	0.924634i	$-0.624371\pi$
$223$	−1.26142e8	−0.761713	−0.380857	+	0.924634i	$0.624371\pi$
$224$	4.22557e8	2.51199
$225$	−4.05764e7	−0.237484
$226$	3.16596e8	1.82443
$227$	1.79611e8	1.01916	0.509579	−	0.860424i	$-0.329801\pi$
$227$	1.79611e8	1.01916	0.509579	+	0.860424i	$0.329801\pi$
$228$	3.54221e8	1.97926
$229$	3.37131e8	1.85513	0.927564	−	0.373664i	$-0.121899\pi$
$229$	3.37131e8	1.85513	0.927564	+	0.373664i	$0.121899\pi$
$230$	−6.05526e7	−0.328160
$231$	1.00213e8	0.534912
$232$	−5.64498e8	−2.96794
$233$	2.03401e8	1.05343	0.526716	−	0.850041i	$-0.323423\pi$
$233$	2.03401e8	1.05343	0.526716	+	0.850041i	$0.323423\pi$
$234$	−1.48975e8	−0.760078
$235$	−1.64565e8	−0.827182
$236$	6.37051e7	0.315487
$237$	−7.21636e6	−0.0352127
$238$	1.94810e7	0.0936679
$239$	2.40718e8	1.14056	0.570278	−	0.821452i	$-0.306836\pi$
$239$	2.40718e8	1.14056	0.570278	+	0.821452i	$0.306836\pi$
$240$	−1.62383e8	−0.758230
$241$	6.28354e7	0.289164	0.144582	−	0.989493i	$-0.453816\pi$
$241$	6.28354e7	0.289164	0.144582	+	0.989493i	$0.453816\pi$
$242$	−2.08029e8	−0.943563
$243$	1.43489e7	0.0641500
$244$	−3.65466e8	−1.61058
$245$	−9.27887e7	−0.403101
$246$	1.77408e8	0.759800
$247$	−4.12905e8	−1.74346
$248$	−2.95641e8	−1.23079
$249$	−2.59686e8	−1.06599
$250$	4.19746e8	1.69901
$251$	1.10247e8	0.440058	0.220029	−	0.975493i	$-0.429385\pi$
$251$	1.10247e8	0.440058	0.220029	+	0.975493i	$0.429385\pi$
$252$	2.71595e8	1.06910
$253$	5.96403e7	0.231536
$254$	7.54326e8	2.88829
$255$	−3.13559e6	−0.0118421
$256$	−2.51476e8	−0.936821
$257$	−8.00040e7	−0.293999	−0.146999	−	0.989137i	$-0.546962\pi$
$257$	−8.00040e7	−0.293999	−0.146999	+	0.989137i	$0.546962\pi$
$258$	4.90711e7	0.177892
$259$	4.57665e8	1.63681
$260$	4.53864e8	1.60147
$261$	−1.07908e8	−0.375675
$262$	2.41472e8	0.829492
$263$	−1.42844e8	−0.484190	−0.242095	−	0.970253i	$-0.577835\pi$
$263$	−1.42844e8	−0.484190	−0.242095	+	0.970253i	$0.577835\pi$
$264$	3.18188e8	1.06431
$265$	2.02559e8	0.668639
$266$	1.06340e9	3.46426
$267$	3.40290e8	1.09411
$268$	−6.83274e8	−2.16832
$269$	−1.90832e8	−0.597747	−0.298873	−	0.954293i	$-0.596611\pi$
$269$	−1.90832e8	−0.597747	−0.298873	+	0.954293i	$0.596611\pi$
$270$	−6.17545e7	−0.190939
$271$	1.37623e8	0.420048	0.210024	−	0.977696i	$-0.432646\pi$
$271$	1.37623e8	0.420048	0.210024	+	0.977696i	$0.432646\pi$
$272$	3.10909e7	0.0936789
$273$	−3.16591e8	−0.941736
$274$	−7.90685e8	−2.32208
$275$	−1.72001e8	−0.498730
$276$	1.61636e8	0.462760
$277$	1.18249e8	0.334286	0.167143	−	0.985933i	$-0.446546\pi$
$277$	1.18249e8	0.334286	0.167143	+	0.985933i	$0.446546\pi$
$278$	−7.77269e7	−0.216978
$279$	−5.65141e7	−0.155791
$280$	−6.86533e8	−1.86900
$281$	−1.62690e8	−0.437411	−0.218705	−	0.975791i	$-0.570183\pi$
$281$	−1.62690e8	−0.437411	−0.218705	+	0.975791i	$0.570183\pi$
$282$	6.20555e8	1.64782
$283$	−4.15031e8	−1.08850	−0.544249	−	0.838924i	$-0.683185\pi$
$283$	−4.15031e8	−1.08850	−0.544249	+	0.838924i	$0.683185\pi$
$284$	1.99581e7	0.0517016
$285$	−1.71161e8	−0.437974
$286$	−6.31495e8	−1.59621
$287$	3.77013e8	0.941391
$288$	2.56470e8	0.632649
$289$	−4.09738e8	−0.998537
$290$	4.64413e8	1.11818
$291$	−1.94722e8	−0.463222
$292$	−5.85968e8	−1.37732
$293$	4.61387e8	1.07159	0.535796	−	0.844348i	$-0.320012\pi$
$293$	4.61387e8	1.07159	0.535796	+	0.844348i	$0.320012\pi$
$294$	3.49894e8	0.803010
$295$	−3.07826e7	−0.0698118
$296$	1.45314e9	3.25676
$297$	6.08240e7	0.134719
$298$	−1.35468e9	−2.96537
$299$	−1.88414e8	−0.407629
$300$	−4.66152e8	−0.996790
$301$	1.04282e8	0.220408
$302$	5.08263e8	1.06185
$303$	−9.29070e7	−0.191866
$304$	1.69714e9	3.46467
$305$	1.76595e8	0.356393
$306$	1.18239e7	0.0235905
$307$	7.27720e8	1.43542	0.717712	−	0.696340i	$-0.245189\pi$
$307$	7.27720e8	1.43542	0.717712	+	0.696340i	$0.245189\pi$
$308$	1.15127e9	2.24518
$309$	−2.16075e8	−0.416629
$310$	2.43224e8	0.463704
$311$	−1.57441e8	−0.296794	−0.148397	−	0.988928i	$-0.547411\pi$
$311$	−1.57441e8	−0.296794	−0.148397	+	0.988928i	$0.547411\pi$
$312$	−1.00521e9	−1.87377
$313$	−1.78754e8	−0.329497	−0.164748	−	0.986336i	$-0.552681\pi$
$313$	−1.78754e8	−0.329497	−0.164748	+	0.986336i	$0.552681\pi$
$314$	8.66850e8	1.58012
$315$	−1.31236e8	−0.236574
$316$	−8.29035e7	−0.147798
$317$	5.72794e8	1.00993	0.504965	−	0.863140i	$-0.331505\pi$
$317$	5.72794e8	1.00993	0.504965	+	0.863140i	$0.331505\pi$
$318$	−7.63826e8	−1.33199
$319$	−4.57416e8	−0.788939
$320$	−3.33975e8	−0.569756
$321$	−5.10457e8	−0.861374
$322$	4.85243e8	0.809961
$323$	3.27717e7	0.0541115
$324$	1.64844e8	0.269256
$325$	5.43381e8	0.878037
$326$	−1.86520e9	−2.98169
$327$	−4.00547e8	−0.633484
$328$	1.19706e9	1.87309
$329$	1.31876e9	2.04164
$330$	−2.61773e8	−0.400983
$331$	2.90899e8	0.440905	0.220452	−	0.975398i	$-0.429247\pi$
$331$	2.90899e8	0.440905	0.220452	+	0.975398i	$0.429247\pi$
$332$	−2.98334e9	−4.47425
$333$	2.77779e8	0.412235
$334$	1.20778e9	1.77367
$335$	3.30162e8	0.479810
$336$	1.30127e9	1.87145
$337$	1.34379e9	1.91261	0.956304	−	0.292374i	$-0.0944453\pi$
$337$	1.34379e9	1.91261	0.956304	+	0.292374i	$0.0944453\pi$
$338$	6.81505e8	0.959976
$339$	4.08359e8	0.569302
$340$	−3.60225e7	−0.0497047
$341$	−2.39559e8	−0.327169
$342$	6.45428e8	0.872481
$343$	−2.45581e8	−0.328599
$344$	3.31108e8	0.438546
$345$	−7.81032e7	−0.102401
$346$	3.56049e8	0.462109
$347$	2.97139e8	0.381774	0.190887	−	0.981612i	$-0.438864\pi$
$347$	2.97139e8	0.381774	0.190887	+	0.981612i	$0.438864\pi$
$348$	−1.23968e9	−1.57682
$349$	1.52383e9	1.91888	0.959440	−	0.281912i	$-0.0909687\pi$
$349$	1.52383e9	1.91888	0.959440	+	0.281912i	$0.0909687\pi$
$350$	−1.39943e9	−1.74466
$351$	−1.92154e8	−0.237178
$352$	1.08716e9	1.32860
$353$	−5.87541e8	−0.710930	−0.355465	−	0.934690i	$-0.615677\pi$
$353$	−5.87541e8	−0.710930	−0.355465	+	0.934690i	$0.615677\pi$
$354$	1.16077e8	0.139071
$355$	−9.64384e6	−0.0114407
$356$	3.90934e9	4.59228
$357$	2.51273e7	0.0292286
$358$	−7.69036e8	−0.885841
$359$	1.34525e9	1.53452	0.767262	−	0.641334i	$-0.221619\pi$
$359$	1.34525e9	1.53452	0.767262	+	0.641334i	$0.221619\pi$
$360$	−4.16690e8	−0.470711
$361$	8.95021e8	1.00129
$362$	2.25094e8	0.249392
$363$	−2.68325e8	−0.294434
$364$	−3.63708e9	−3.95274
$365$	2.83143e8	0.304776
$366$	−6.65918e8	−0.709965
$367$	1.37516e9	1.45218	0.726090	−	0.687600i	$-0.241336\pi$
$367$	1.37516e9	1.45218	0.726090	+	0.687600i	$0.241336\pi$
$368$	7.74430e8	0.810056
$369$	2.28827e8	0.237091
$370$	−1.19550e9	−1.22700
$371$	−1.62323e9	−1.65033
$372$	−6.49248e8	−0.653899
$373$	−1.95269e8	−0.194829	−0.0974143	−	0.995244i	$-0.531057\pi$
$373$	−1.95269e8	−0.194829	−0.0974143	+	0.995244i	$0.531057\pi$
$374$	5.01208e7	0.0495413
$375$	5.41405e8	0.530167
$376$	4.18721e9	4.06226
$377$	1.44506e9	1.38896
$378$	4.94875e8	0.471274
$379$	−1.78491e9	−1.68414	−0.842071	−	0.539367i	$-0.818664\pi$
$379$	−1.78491e9	−1.68414	−0.842071	+	0.539367i	$0.818664\pi$
$380$	−1.96635e9	−1.83830
$381$	9.72960e8	0.901275
$382$	−9.75155e8	−0.895059
$383$	1.02371e9	0.931072	0.465536	−	0.885029i	$-0.345862\pi$
$383$	1.02371e9	0.931072	0.465536	+	0.885029i	$0.345862\pi$
$384$	4.35196e7	0.0392216
$385$	−5.56301e8	−0.496818
$386$	−1.27872e9	−1.13167
$387$	6.32939e7	0.0555103
$388$	−2.23702e9	−1.94428
$389$	5.45849e8	0.470163	0.235082	−	0.971976i	$-0.424464\pi$
$389$	5.45849e8	0.470163	0.235082	+	0.971976i	$0.424464\pi$
$390$	8.26989e8	0.705949
$391$	1.49542e7	0.0126515
$392$	2.36092e9	1.97961
$393$	3.11460e8	0.258838
$394$	1.55522e9	1.28102
$395$	4.00594e7	0.0327050
$396$	6.98762e8	0.565453
$397$	1.54111e9	1.23614	0.618070	−	0.786123i	$-0.287915\pi$
$397$	1.54111e9	1.23614	0.618070	+	0.786123i	$0.287915\pi$
$398$	−3.76345e9	−2.99224
$399$	1.37161e9	1.08100
$400$	−2.23343e9	−1.74487
$401$	−1.87893e9	−1.45514	−0.727570	−	0.686034i	$-0.759350\pi$
$401$	−1.87893e9	−1.45514	−0.727570	+	0.686034i	$0.759350\pi$
$402$	−1.24500e9	−0.955822
$403$	7.56811e8	0.575996
$404$	−1.06734e9	−0.805319
$405$	−7.96535e7	−0.0595816
$406$	−3.72161e9	−2.75988
$407$	1.17749e9	0.865716
$408$	7.97822e7	0.0581561
$409$	−1.97782e9	−1.42941	−0.714703	−	0.699428i	$-0.753438\pi$
$409$	−1.97782e9	−1.42941	−0.714703	+	0.699428i	$0.753438\pi$
$410$	−9.84822e8	−0.705691
$411$	−1.01986e9	−0.724592
$412$	−2.48232e9	−1.74871
$413$	2.46679e8	0.172309
$414$	2.94517e8	0.203990
$415$	1.44157e9	0.990071
$416$	−3.43453e9	−2.33906
$417$	−1.00255e8	−0.0677066
$418$	2.73592e9	1.83226
$419$	1.09100e9	0.724561	0.362280	−	0.932069i	$-0.381998\pi$
$419$	1.09100e9	0.724561	0.362280	+	0.932069i	$0.381998\pi$
$420$	−1.50767e9	−0.992968
$421$	1.23434e9	0.806211	0.403105	−	0.915154i	$-0.367931\pi$
$421$	1.23434e9	0.806211	0.403105	+	0.915154i	$0.367931\pi$
$422$	−3.56059e9	−2.30637
$423$	8.00417e8	0.514192
$424$	−5.15393e9	−3.28366
$425$	−4.31273e7	−0.0272515
$426$	3.63657e7	0.0227907
$427$	−1.41516e9	−0.879645
$428$	−5.86426e9	−3.61543
$429$	−8.14528e8	−0.498088
$430$	−2.72403e8	−0.165224
$431$	2.37469e8	0.142869	0.0714343	−	0.997445i	$-0.477242\pi$
$431$	2.37469e8	0.142869	0.0714343	+	0.997445i	$0.477242\pi$
$432$	7.89802e8	0.471330
$433$	2.89301e9	1.71255	0.856274	−	0.516522i	$-0.172774\pi$
$433$	2.89301e9	1.71255	0.856274	+	0.516522i	$0.172774\pi$
$434$	−1.94909e9	−1.14451
$435$	5.99019e8	0.348922
$436$	−4.60158e9	−2.65892
$437$	8.16296e8	0.467910
$438$	−1.06769e9	−0.607138
$439$	−1.35570e9	−0.764781	−0.382391	−	0.924001i	$-0.624899\pi$
$439$	−1.35570e9	−0.764781	−0.382391	+	0.924001i	$0.624899\pi$
$440$	−1.76632e9	−0.988519
$441$	4.51308e8	0.250575
$442$	−1.58341e8	−0.0872197
$443$	1.36994e9	0.748664	0.374332	−	0.927295i	$-0.377872\pi$
$443$	1.36994e9	0.748664	0.374332	+	0.927295i	$0.377872\pi$
$444$	3.19120e9	1.73027
$445$	−1.88901e9	−1.01619
$446$	−2.64050e9	−1.40934
$447$	−1.74732e9	−0.925327
$448$	2.67633e9	1.40627
$449$	3.56894e9	1.86070	0.930352	−	0.366669i	$-0.119502\pi$
$449$	3.56894e9	1.86070	0.930352	+	0.366669i	$0.119502\pi$
$450$	−8.49379e8	−0.439397
$451$	9.69984e8	0.497905
$452$	4.69133e9	2.38953
$453$	6.55578e8	0.331345
$454$	3.75976e9	1.88566
$455$	1.75746e9	0.874670
$456$	4.35503e9	2.15087
$457$	−1.58612e9	−0.777374	−0.388687	−	0.921370i	$-0.627071\pi$
$457$	−1.58612e9	−0.777374	−0.388687	+	0.921370i	$0.627071\pi$
$458$	7.05709e9	3.43239
$459$	1.52510e7	0.00736128
$460$	−8.97270e8	−0.429804
$461$	−2.42902e9	−1.15472	−0.577361	−	0.816489i	$-0.695917\pi$
$461$	−2.42902e9	−1.15472	−0.577361	+	0.816489i	$0.695917\pi$
$462$	2.09774e9	0.989703
$463$	−2.06490e9	−0.966865	−0.483432	−	0.875382i	$-0.660610\pi$
$463$	−2.06490e9	−0.966865	−0.483432	+	0.875382i	$0.660610\pi$
$464$	−5.93955e9	−2.76020
$465$	3.13720e8	0.144696
$466$	4.25775e9	1.94908
$467$	−2.28871e9	−1.03988	−0.519938	−	0.854204i	$-0.674045\pi$
$467$	−2.28871e9	−1.03988	−0.519938	+	0.854204i	$0.674045\pi$
$468$	−2.20752e9	−0.995505
$469$	−2.64578e9	−1.18426
$470$	−3.44482e9	−1.53047
$471$	1.11810e9	0.493068
$472$	7.83234e8	0.342843
$473$	2.68299e8	0.116575
$474$	−1.51059e8	−0.0651511
$475$	−2.35417e9	−1.00788
$476$	2.88669e8	0.122681
$477$	−9.85214e8	−0.415639
$478$	5.03891e9	2.11028
$479$	−9.59752e8	−0.399011	−0.199505	−	0.979897i	$-0.563934\pi$
$479$	−9.59752e8	−0.399011	−0.199505	+	0.979897i	$0.563934\pi$
$480$	−1.42371e9	−0.587595
$481$	−3.71989e9	−1.52413
$482$	1.31532e9	0.535017
$483$	6.25886e8	0.252744
$484$	−3.08258e9	−1.23582
$485$	1.08094e9	0.430234
$486$	3.00363e8	0.118692
$487$	8.78521e8	0.344668	0.172334	−	0.985039i	$-0.444869\pi$
$487$	8.78521e8	0.344668	0.172334	+	0.985039i	$0.444869\pi$
$488$	−4.49329e9	−1.75023
$489$	−2.40581e9	−0.930421
$490$	−1.94233e9	−0.745824
$491$	1.17143e9	0.446612	0.223306	−	0.974748i	$-0.428315\pi$
$491$	1.17143e9	0.446612	0.223306	+	0.974748i	$0.428315\pi$
$492$	2.62883e9	0.995140
$493$	−1.14692e8	−0.0431091
$494$	−8.64328e9	−3.22578
$495$	−3.37646e8	−0.125125
$496$	−3.11068e9	−1.14464
$497$	7.72817e7	0.0282377
$498$	−5.43597e9	−1.97230
$499$	3.72675e9	1.34270	0.671349	−	0.741142i	$-0.265715\pi$
$499$	3.72675e9	1.34270	0.671349	+	0.741142i	$0.265715\pi$
$500$	6.21980e9	2.22526
$501$	1.55784e9	0.553465
$502$	2.30778e9	0.814202
$503$	5.09523e9	1.78516	0.892578	−	0.450894i	$-0.148895\pi$
$503$	5.09523e9	1.78516	0.892578	+	0.450894i	$0.148895\pi$
$504$	3.33918e9	1.16180
$505$	5.15744e8	0.178203
$506$	1.24844e9	0.428391
$507$	8.79032e8	0.299555
$508$	1.11776e10	3.78291
$509$	3.59219e9	1.20739	0.603693	−	0.797217i	$-0.293695\pi$
$509$	3.59219e9	1.20739	0.603693	+	0.797217i	$0.293695\pi$
$510$	−6.56368e7	−0.0219105
$511$	−2.26899e9	−0.752244
$512$	−5.47042e9	−1.80126
$513$	8.32499e8	0.272253
$514$	−1.67471e9	−0.543962
$515$	1.19947e9	0.386959
$516$	7.27137e8	0.232993
$517$	3.39292e9	1.07983
$518$	9.58022e9	3.02846
$519$	4.59247e8	0.144198
$520$	5.58012e9	1.74033
$521$	5.07000e9	1.57064	0.785318	−	0.619092i	$-0.212499\pi$
$521$	5.07000e9	1.57064	0.785318	+	0.619092i	$0.212499\pi$
$522$	−2.25882e9	−0.695081
$523$	4.99855e8	0.152788	0.0763938	−	0.997078i	$-0.475659\pi$
$523$	4.99855e8	0.152788	0.0763938	+	0.997078i	$0.475659\pi$
$524$	3.57814e9	1.08642
$525$	−1.80504e9	−0.544413
$526$	−2.99012e9	−0.895856
$527$	−6.00669e7	−0.0178771
$528$	3.34792e9	0.989819
$529$	−3.03234e9	−0.890600
$530$	4.24014e9	1.23713
$531$	1.49721e8	0.0433963
$532$	1.57575e10	4.53728
$533$	−3.06435e9	−0.876584
$534$	7.12322e9	2.02433
$535$	2.83364e9	0.800031
$536$	−8.40064e9	−2.35633
$537$	−9.91933e8	−0.276422
$538$	−3.99464e9	−1.10596
$539$	1.91306e9	0.526222
$540$	−9.15080e8	−0.250081
$541$	5.11313e9	1.38834	0.694171	−	0.719810i	$-0.255771\pi$
$541$	5.11313e9	1.38834	0.694171	+	0.719810i	$0.255771\pi$
$542$	2.88084e9	0.777181
$543$	2.90335e8	0.0778215
$544$	2.72593e8	0.0725971
$545$	2.22351e9	0.588371
$546$	−6.62714e9	−1.74242
$547$	−3.84269e8	−0.100387	−0.0501937	−	0.998739i	$-0.515984\pi$
$547$	−3.84269e8	−0.100387	−0.0501937	+	0.998739i	$0.515984\pi$
$548$	−1.17164e10	−3.04132
$549$	−8.58928e8	−0.221541
$550$	−3.60046e9	−0.922759
$551$	−6.26065e9	−1.59437
$552$	1.98726e9	0.502884
$553$	−3.21019e8	−0.0807222
$554$	2.47528e9	0.618501
$555$	−1.54200e9	−0.382877
$556$	−1.15176e9	−0.284184
$557$	5.07247e9	1.24373	0.621866	−	0.783124i	$-0.286375\pi$
$557$	5.07247e9	1.24373	0.621866	+	0.783124i	$0.286375\pi$
$558$	−1.18300e9	−0.288247
$559$	−8.47604e8	−0.205235
$560$	−7.22358e9	−1.73818
$561$	6.46479e7	0.0154591
$562$	−3.40557e9	−0.809305
$563$	−8.25453e8	−0.194945	−0.0974727	−	0.995238i	$-0.531076\pi$
$563$	−8.25453e8	−0.194945	−0.0974727	+	0.995238i	$0.531076\pi$
$564$	9.19540e9	2.15821
$565$	−2.26688e9	−0.528760
$566$	−8.68776e9	−2.01396
$567$	6.38309e8	0.147059
$568$	2.45378e8	0.0561845
$569$	4.84625e9	1.10284	0.551420	−	0.834228i	$-0.314086\pi$
$569$	4.84625e9	1.10284	0.551420	+	0.834228i	$0.314086\pi$
$570$	−3.58289e9	−0.810348
$571$	2.06740e9	0.464728	0.232364	−	0.972629i	$-0.425354\pi$
$571$	2.06740e9	0.464728	0.232364	+	0.972629i	$0.425354\pi$
$572$	−9.35751e9	−2.09062
$573$	−1.25779e9	−0.279298
$574$	7.89195e9	1.74178
$575$	−1.07424e9	−0.235648
$576$	1.62440e9	0.354171
$577$	5.23872e9	1.13530	0.567649	−	0.823270i	$-0.307853\pi$
$577$	5.23872e9	1.13530	0.567649	+	0.823270i	$0.307853\pi$
$578$	−8.57698e9	−1.84751
$579$	−1.64934e9	−0.353130
$580$	6.88169e9	1.46453
$581$	−1.15521e10	−2.44368
$582$	−4.07608e9	−0.857062
$583$	−4.17625e9	−0.872865
$584$	−7.20429e9	−1.49674
$585$	1.06668e9	0.220288
$586$	9.65814e9	1.98268
$587$	−5.79577e9	−1.18271	−0.591355	−	0.806411i	$-0.701407\pi$
$587$	−5.79577e9	−1.18271	−0.591355	+	0.806411i	$0.701407\pi$
$588$	5.18474e9	1.05174
$589$	−3.27885e9	−0.661177
$590$	−6.44367e8	−0.129167
$591$	2.00599e9	0.399736
$592$	1.52897e10	3.02881
$593$	6.07221e8	0.119579	0.0597896	−	0.998211i	$-0.480957\pi$
$593$	6.07221e8	0.119579	0.0597896	+	0.998211i	$0.480957\pi$
$594$	1.27322e9	0.249259
$595$	−1.39486e8	−0.0271471
$596$	−2.00736e10	−3.88386
$597$	−4.85426e9	−0.933711
$598$	−3.94404e9	−0.754202
$599$	7.83137e9	1.48883	0.744413	−	0.667720i	$-0.232730\pi$
$599$	7.83137e9	1.48883	0.744413	+	0.667720i	$0.232730\pi$
$600$	−5.73120e9	−1.08322
$601$	−9.69564e9	−1.82186	−0.910932	−	0.412556i	$-0.864636\pi$
$601$	−9.69564e9	−1.82186	−0.910932	+	0.412556i	$0.864636\pi$
$602$	2.18292e9	0.407803
$603$	−1.60585e9	−0.298259
$604$	7.53145e9	1.39075
$605$	1.48952e9	0.273466
$606$	−1.94480e9	−0.354995
$607$	2.75108e9	0.499278	0.249639	−	0.968339i	$-0.419688\pi$
$607$	2.75108e9	0.499278	0.249639	+	0.968339i	$0.419688\pi$
$608$	1.48799e10	2.68497
$609$	−4.80028e9	−0.861205
$610$	3.69663e9	0.659405
$611$	−1.07188e10	−1.90109
$612$	1.75207e8	0.0308974
$613$	−1.06940e10	−1.87511	−0.937557	−	0.347832i	$-0.886918\pi$
$613$	−1.06940e10	−1.87511	−0.937557	+	0.347832i	$0.886918\pi$
$614$	1.52332e10	2.65585
$615$	−1.27026e9	−0.220207
$616$	1.41545e10	2.43985
$617$	3.67080e9	0.629162	0.314581	−	0.949231i	$-0.398136\pi$
$617$	3.67080e9	0.629162	0.314581	+	0.949231i	$0.398136\pi$
$618$	−4.52306e9	−0.770854
$619$	−7.09568e9	−1.20248	−0.601238	−	0.799070i	$-0.705326\pi$
$619$	−7.09568e9	−1.20248	−0.601238	+	0.799070i	$0.705326\pi$
$620$	3.60410e9	0.607331
$621$	3.79880e8	0.0636541
$622$	−3.29568e9	−0.549134
$623$	1.51377e10	2.50815
$624$	−1.05767e10	−1.74262
$625$	1.34303e9	0.220042
$626$	−3.74183e9	−0.609640
$627$	3.52890e9	0.571747
$628$	1.28450e10	2.06955
$629$	2.95242e8	0.0473043
$630$	−2.74714e9	−0.437713
$631$	−1.14862e10	−1.82000	−0.910001	−	0.414606i	$-0.863919\pi$
$631$	−1.14862e10	−1.82000	−0.910001	+	0.414606i	$0.863919\pi$
$632$	−1.01927e9	−0.160613
$633$	−4.59259e9	−0.719689
$634$	1.19902e10	1.86859
$635$	−5.40108e9	−0.837091
$636$	−1.13184e10	−1.74456
$637$	−6.04371e9	−0.926437
$638$	−9.57500e9	−1.45971
$639$	4.69059e7	0.00711172
$640$	−2.41586e8	−0.0364285
$641$	−7.81739e9	−1.17235	−0.586177	−	0.810183i	$-0.699367\pi$
$641$	−7.81739e9	−1.17235	−0.586177	+	0.810183i	$0.699367\pi$
$642$	−1.06853e10	−1.59373
$643$	2.34946e9	0.348522	0.174261	−	0.984699i	$-0.444246\pi$
$643$	2.34946e9	0.348522	0.174261	+	0.984699i	$0.444246\pi$
$644$	7.19034e9	1.06084
$645$	−3.51356e8	−0.0515571
$646$	6.86003e8	0.100118
$647$	7.89807e9	1.14645	0.573226	−	0.819397i	$-0.305692\pi$
$647$	7.89807e9	1.14645	0.573226	+	0.819397i	$0.305692\pi$
$648$	2.02671e9	0.292603
$649$	6.34658e8	0.0911347
$650$	1.13745e10	1.62456
$651$	−2.51402e9	−0.357137
$652$	−2.76385e10	−3.90525
$653$	6.38444e8	0.0897277	0.0448639	−	0.998993i	$-0.485715\pi$
$653$	6.38444e8	0.0897277	0.0448639	+	0.998993i	$0.485715\pi$
$654$	−8.38457e9	−1.17208
$655$	−1.72897e9	−0.240405
$656$	1.25953e10	1.74198
$657$	−1.37716e9	−0.189454
$658$	2.76053e10	3.77748
$659$	8.08275e9	1.10017	0.550085	−	0.835108i	$-0.314595\pi$
$659$	8.08275e9	1.10017	0.550085	+	0.835108i	$0.314595\pi$
$660$	−3.87896e9	−0.525184
$661$	9.43857e9	1.27116	0.635581	−	0.772034i	$-0.280761\pi$
$661$	9.43857e9	1.27116	0.635581	+	0.772034i	$0.280761\pi$
$662$	6.08934e9	0.815770
$663$	−2.04234e8	−0.0272164
$664$	−3.66793e10	−4.86220
$665$	−7.61409e9	−1.00402
$666$	5.81470e9	0.762724
$667$	−2.85682e9	−0.372771
$668$	1.78969e10	2.32305
$669$	−3.40583e9	−0.439775
$670$	6.91121e9	0.887754
$671$	−3.64094e9	−0.465248
$672$	1.14090e10	1.45030
$673$	−1.08913e10	−1.37730	−0.688649	−	0.725095i	$-0.741796\pi$
$673$	−1.08913e10	−1.37730	−0.688649	+	0.725095i	$0.741796\pi$
$674$	2.81293e10	3.53874
$675$	−1.09556e9	−0.137112
$676$	1.00986e10	1.25732
$677$	−1.25627e10	−1.55604	−0.778021	−	0.628238i	$-0.783777\pi$
$677$	−1.25627e10	−1.55604	−0.778021	+	0.628238i	$0.783777\pi$
$678$	8.54810e9	1.05333
$679$	−8.66218e9	−1.06190
$680$	−4.42886e8	−0.0540145
$681$	4.84949e9	0.588411
$682$	−5.01465e9	−0.605335
$683$	−1.74046e9	−0.209022	−0.104511	−	0.994524i	$-0.533328\pi$
$683$	−1.74046e9	−0.209022	−0.104511	+	0.994524i	$0.533328\pi$
$684$	9.56396e9	1.14272
$685$	5.66142e9	0.672990
$686$	−5.14071e9	−0.607979
$687$	9.10253e9	1.07106
$688$	3.48386e9	0.407851
$689$	1.31935e10	1.53672
$690$	−1.63492e9	−0.189463
$691$	−1.58954e10	−1.83272	−0.916362	−	0.400351i	$-0.868888\pi$
$691$	−1.58954e10	−1.83272	−0.916362	+	0.400351i	$0.868888\pi$
$692$	5.27595e9	0.605242
$693$	2.70575e9	0.308831
$694$	6.21995e9	0.706364
$695$	5.56536e8	0.0628849
$696$	−1.52415e10	−1.71354
$697$	2.43213e8	0.0272065
$698$	3.18981e10	3.55035
$699$	5.49182e9	0.608200
$700$	−2.07367e10	−2.28506
$701$	1.64503e10	1.80369	0.901844	−	0.432062i	$-0.142214\pi$
$701$	1.64503e10	1.80369	0.901844	+	0.432062i	$0.142214\pi$
$702$	−4.02233e9	−0.438831
$703$	1.61162e10	1.74953
$704$	6.88570e9	0.743779
$705$	−4.44327e9	−0.477574
$706$	−1.22989e10	−1.31538
$707$	−4.13295e9	−0.439838
$708$	1.72004e9	0.182147
$709$	−8.21342e9	−0.865491	−0.432745	−	0.901516i	$-0.642455\pi$
$709$	−8.21342e9	−0.865491	−0.432745	+	0.901516i	$0.642455\pi$
$710$	−2.01873e8	−0.0211677
$711$	−1.94842e8	−0.0203301
$712$	4.80641e10	4.99046
$713$	−1.49618e9	−0.154586
$714$	5.25986e8	0.0540792
$715$	4.52160e9	0.462616
$716$	−1.13956e10	−1.16022
$717$	6.49939e9	0.658500
$718$	2.81600e10	2.83920
$719$	−9.47920e9	−0.951088	−0.475544	−	0.879692i	$-0.657749\pi$
$719$	−9.47920e9	−0.951088	−0.475544	+	0.879692i	$0.657749\pi$
$720$	−4.38434e9	−0.437764
$721$	−9.61206e9	−0.955087
$722$	1.87353e10	1.85260
$723$	1.69655e9	0.166949
$724$	3.33544e9	0.326639
$725$	8.23897e9	0.802953
$726$	−5.61679e9	−0.544766
$727$	−1.39173e10	−1.34333	−0.671667	−	0.740853i	$-0.734421\pi$
$727$	−1.39173e10	−1.34333	−0.671667	+	0.740853i	$0.734421\pi$
$728$	−4.47168e10	−4.29547
$729$	3.87420e8	0.0370370
$730$	5.92697e9	0.563901
$731$	6.72730e7	0.00636986
$732$	−9.86759e9	−0.929870
$733$	−1.17895e10	−1.10569	−0.552843	−	0.833286i	$-0.686457\pi$
$733$	−1.17895e10	−1.10569	−0.552843	+	0.833286i	$0.686457\pi$
$734$	2.87859e10	2.68685
$735$	−2.50529e9	−0.232730
$736$	6.78992e9	0.627758
$737$	−6.80708e9	−0.626361
$738$	4.79000e9	0.438671
$739$	−4.71766e9	−0.430003	−0.215001	−	0.976614i	$-0.568976\pi$
$739$	−4.71766e9	−0.430003	−0.215001	+	0.976614i	$0.568976\pi$
$740$	−1.77149e10	−1.60705
$741$	−1.11484e10	−1.00659
$742$	−3.39787e10	−3.05347
$743$	−8.49980e8	−0.0760235	−0.0380118	−	0.999277i	$-0.512102\pi$
$743$	−8.49980e8	−0.0760235	−0.0380118	+	0.999277i	$0.512102\pi$
$744$	−7.98231e9	−0.710597
$745$	9.69968e9	0.859430
$746$	−4.08753e9	−0.360475
$747$	−7.01153e9	−0.615447
$748$	7.42691e8	0.0648863
$749$	−2.27076e10	−1.97463
$750$	1.13331e10	0.980924
$751$	1.12483e9	0.0969050	0.0484525	−	0.998825i	$-0.484571\pi$
$751$	1.12483e9	0.0969050	0.0484525	+	0.998825i	$0.484571\pi$
$752$	4.40571e10	3.77793
$753$	2.97667e9	0.254067
$754$	3.02492e10	2.56988
$755$	−3.63924e9	−0.307748
$756$	7.33306e9	0.617247
$757$	−2.61362e9	−0.218981	−0.109491	−	0.993988i	$-0.534922\pi$
$757$	−2.61362e9	−0.218981	−0.109491	+	0.993988i	$0.534922\pi$
$758$	−3.73632e10	−3.11603
$759$	1.61029e9	0.133677
$760$	−2.41756e10	−1.99770
$761$	1.20945e10	0.994817	0.497408	−	0.867516i	$-0.334285\pi$
$761$	1.20945e10	0.994817	0.497408	+	0.867516i	$0.334285\pi$
$762$	2.03668e10	1.66756
$763$	−1.78183e10	−1.45221
$764$	−1.44499e10	−1.17230
$765$	−8.46610e7	−0.00683705
$766$	2.14292e10	1.72269
$767$	−2.00500e9	−0.160447
$768$	−6.78985e9	−0.540874
$769$	3.67326e9	0.291279	0.145639	−	0.989338i	$-0.453476\pi$
$769$	3.67326e9	0.291279	0.145639	+	0.989338i	$0.453476\pi$
$770$	−1.16449e10	−0.919221
$771$	−2.16011e9	−0.169740
$772$	−1.89480e10	−1.48219
$773$	−2.06426e10	−1.60744	−0.803721	−	0.595007i	$-0.797149\pi$
$773$	−2.06426e10	−1.60744	−0.803721	+	0.595007i	$0.797149\pi$
$774$	1.32492e9	0.102706
$775$	4.31494e9	0.332981
$776$	−2.75034e10	−2.11286
$777$	1.23570e10	0.945013
$778$	1.14262e10	0.869904
$779$	1.32762e10	1.00622
$780$	1.22543e10	0.924610
$781$	1.98831e8	0.0149350
$782$	3.13033e8	0.0234081
$783$	−2.91352e9	−0.216896
$784$	2.48412e10	1.84105
$785$	−6.20677e9	−0.457954
$786$	6.51974e9	0.478907
$787$	8.84372e7	0.00646731	0.00323365	−	0.999995i	$-0.498971\pi$
$787$	8.84372e7	0.00646731	0.00323365	+	0.999995i	$0.498971\pi$
$788$	2.30454e10	1.67781
$789$	−3.85678e9	−0.279547
$790$	8.38556e8	0.0605114
$791$	1.81658e10	1.30508
$792$	8.59107e9	0.614482
$793$	1.15024e10	0.819090
$794$	3.22598e10	2.28713
$795$	5.46911e9	0.386039
$796$	−5.57670e10	−3.91905
$797$	1.12406e10	0.786478	0.393239	−	0.919436i	$-0.371354\pi$
$797$	1.12406e10	0.786478	0.393239	+	0.919436i	$0.371354\pi$
$798$	2.87118e10	2.00009
$799$	8.50737e8	0.0590040
$800$	−1.95819e10	−1.35220
$801$	9.18782e9	0.631682
$802$	−3.93312e10	−2.69232
$803$	−5.83767e9	−0.397864
$804$	−1.84484e10	−1.25188
$805$	−3.47441e9	−0.234745
$806$	1.58422e10	1.06572
$807$	−5.15245e9	−0.345109
$808$	−1.31226e10	−0.875146
$809$	2.81091e10	1.86650	0.933249	−	0.359230i	$-0.116961\pi$
$809$	2.81091e10	1.86650	0.933249	+	0.359230i	$0.116961\pi$
$810$	−1.66737e9	−0.110239
$811$	2.83599e8	0.0186695	0.00933474	−	0.999956i	$-0.497029\pi$
$811$	2.83599e8	0.0186695	0.00933474	+	0.999956i	$0.497029\pi$
$812$	−5.51469e10	−3.61472
$813$	3.71583e9	0.242515
$814$	2.46481e10	1.60176
$815$	1.33551e10	0.864162
$816$	8.39454e8	0.0540856
$817$	3.67220e9	0.235586
$818$	−4.14014e10	−2.64471
$819$	−8.54795e9	−0.543711
$820$	−1.45931e10	−0.924272
$821$	−1.71158e10	−1.07943	−0.539717	−	0.841846i	$-0.681469\pi$
$821$	−1.71158e10	−1.07943	−0.539717	+	0.841846i	$0.681469\pi$
$822$	−2.13485e10	−1.34065
$823$	−1.08622e10	−0.679235	−0.339618	−	0.940564i	$-0.610298\pi$
$823$	−1.08622e10	−0.679235	−0.339618	+	0.940564i	$0.610298\pi$
$824$	−3.05194e10	−1.90034
$825$	−4.64402e9	−0.287942
$826$	5.16369e9	0.318808
$827$	1.34081e10	0.824321	0.412161	−	0.911111i	$-0.364774\pi$
$827$	1.34081e10	0.824321	0.412161	+	0.911111i	$0.364774\pi$
$828$	4.36416e9	0.267174
$829$	1.85211e10	1.12908	0.564542	−	0.825404i	$-0.309053\pi$
$829$	1.85211e10	1.12908	0.564542	+	0.825404i	$0.309053\pi$
$830$	3.01761e10	1.83185
$831$	3.19272e9	0.193000
$832$	−2.17532e10	−1.30946
$833$	4.79680e8	0.0287537
$834$	−2.09863e9	−0.125272
$835$	−8.64785e9	−0.514050
$836$	4.05410e10	2.39978
$837$	−1.52588e9	−0.0899459
$838$	2.28377e10	1.34059
$839$	−3.61962e9	−0.211591	−0.105795	−	0.994388i	$-0.533739\pi$
$839$	−3.61962e9	−0.211591	−0.105795	+	0.994388i	$0.533739\pi$
$840$	−1.85364e10	−1.07907
$841$	4.66072e9	0.270189
$842$	2.58383e10	1.49167
$843$	−4.39264e9	−0.252539
$844$	−5.27609e10	−3.02074
$845$	−4.87967e9	−0.278223
$846$	1.67550e10	0.951367
$847$	−1.19364e10	−0.674965
$848$	−5.42288e10	−3.05383
$849$	−1.12058e10	−0.628444
$850$	−9.02776e8	−0.0504213
$851$	7.35406e9	0.409047
$852$	5.38868e8	0.0298499
$853$	−1.71198e10	−0.944448	−0.472224	−	0.881478i	$-0.656549\pi$
$853$	−1.71198e10	−0.944448	−0.472224	+	0.881478i	$0.656549\pi$
$854$	−2.96233e10	−1.62754
$855$	−4.62136e9	−0.252865
$856$	−7.20993e10	−3.92892
$857$	−1.15451e10	−0.626565	−0.313282	−	0.949660i	$-0.601429\pi$
$857$	−1.15451e10	−0.626565	−0.313282	+	0.949660i	$0.601429\pi$
$858$	−1.70504e10	−0.921570
$859$	4.99390e9	0.268821	0.134411	−	0.990926i	$-0.457086\pi$
$859$	4.99390e9	0.268821	0.134411	+	0.990926i	$0.457086\pi$
$860$	−4.03647e9	−0.216400
$861$	1.01794e10	0.543512
$862$	4.97090e9	0.264338
$863$	−1.41398e9	−0.0748867	−0.0374434	−	0.999299i	$-0.511921\pi$
$863$	−1.41398e9	−0.0748867	−0.0374434	+	0.999299i	$0.511921\pi$
$864$	6.92469e9	0.365260
$865$	−2.54937e9	−0.133929
$866$	6.05589e10	3.16859
$867$	−1.10629e10	−0.576506
$868$	−2.88817e10	−1.49901
$869$	−8.25921e8	−0.0426943
$870$	1.25392e10	0.645581
$871$	2.15048e10	1.10274
$872$	−5.65750e10	−2.88946
$873$	−5.25749e9	−0.267442
$874$	1.70874e10	0.865736
$875$	2.40843e10	1.21536
$876$	−1.58211e10	−0.795194
$877$	−4.65935e9	−0.233253	−0.116626	−	0.993176i	$-0.537208\pi$
$877$	−4.65935e9	−0.233253	−0.116626	+	0.993176i	$0.537208\pi$
$878$	−2.83786e10	−1.41501
$879$	1.24575e10	0.618683
$880$	−1.85849e10	−0.919329
$881$	3.44643e10	1.69806	0.849031	−	0.528342i	$-0.177186\pi$
$881$	3.44643e10	1.69806	0.849031	+	0.528342i	$0.177186\pi$
$882$	9.44715e9	0.463618
$883$	−1.49854e10	−0.732498	−0.366249	−	0.930517i	$-0.619358\pi$
$883$	−1.49854e10	−0.732498	−0.366249	+	0.930517i	$0.619358\pi$
$884$	−2.34630e9	−0.114235
$885$	−8.31131e8	−0.0403058
$886$	2.86766e10	1.38519
$887$	2.02649e10	0.975015	0.487508	−	0.873119i	$-0.337906\pi$
$887$	2.02649e10	0.975015	0.487508	+	0.873119i	$0.337906\pi$
$888$	3.92348e10	1.88029
$889$	4.32820e10	2.06610
$890$	−3.95423e10	−1.88017
$891$	1.64225e9	0.0777798
$892$	−3.91270e10	−1.84586
$893$	4.64388e10	2.18223
$894$	−3.65763e10	−1.71206
$895$	5.50641e9	0.256737
$896$	1.93596e9	0.0899123
$897$	−5.08719e9	−0.235345
$898$	7.47080e10	3.44271
$899$	1.14751e10	0.526741
$900$	−1.25861e10	−0.575497
$901$	−1.04715e9	−0.0476950
$902$	2.03045e10	0.921233
$903$	2.81562e9	0.127253
$904$	5.76785e10	2.59672
$905$	−1.61170e9	−0.0722795
$906$	1.37231e10	0.613061
$907$	2.55043e10	1.13498	0.567491	−	0.823380i	$-0.307914\pi$
$907$	2.55043e10	1.13498	0.567491	+	0.823380i	$0.307914\pi$
$908$	5.57122e10	2.46973
$909$	−2.50849e9	−0.110774
$910$	3.67885e10	1.61833
$911$	−3.56300e10	−1.56135	−0.780677	−	0.624935i	$-0.785126\pi$
$911$	−3.56300e10	−1.56135	−0.780677	+	0.624935i	$0.785126\pi$
$912$	4.58229e10	2.00033
$913$	−2.97214e10	−1.29247
$914$	−3.32020e10	−1.43831
$915$	4.76807e9	0.205764
$916$	1.04572e11	4.49554
$917$	1.38553e10	0.593366
$918$	3.19246e8	0.0136200
$919$	−2.41602e10	−1.02682	−0.513412	−	0.858143i	$-0.671619\pi$
$919$	−2.41602e10	−1.02682	−0.513412	+	0.858143i	$0.671619\pi$
$920$	−1.10317e10	−0.467072
$921$	1.96485e10	0.828742
$922$	−5.08462e10	−2.13649
$923$	−6.28143e8	−0.0262938
$924$	3.10844e10	1.29625
$925$	−2.12089e10	−0.881093
$926$	−4.32242e10	−1.78891
$927$	−5.83402e9	−0.240541
$928$	−5.20758e10	−2.13904
$929$	1.41353e9	0.0578427	0.0289214	−	0.999582i	$-0.490793\pi$
$929$	1.41353e9	0.0578427	0.0289214	+	0.999582i	$0.490793\pi$
$930$	6.56705e9	0.267719
$931$	2.61841e10	1.06344
$932$	6.30915e10	2.55279
$933$	−4.25090e9	−0.171354
$934$	−4.79091e10	−1.92400
$935$	−3.58872e8	−0.0143582
$936$	−2.71407e10	−1.08182
$937$	3.20821e10	1.27402	0.637008	−	0.770857i	$-0.280172\pi$
$937$	3.20821e10	1.27402	0.637008	+	0.770857i	$0.280172\pi$
$938$	−5.53835e10	−2.19114
$939$	−4.82636e9	−0.190235
$940$	−5.10454e10	−2.00451
$941$	−4.82625e10	−1.88819	−0.944096	−	0.329671i	$-0.893062\pi$
$941$	−4.82625e10	−1.88819	−0.944096	+	0.329671i	$0.893062\pi$
$942$	2.34049e10	0.912282
$943$	6.05809e9	0.235258
$944$	8.24105e9	0.318846
$945$	−3.54337e9	−0.136586
$946$	5.61625e9	0.215689
$947$	3.71988e9	0.142333	0.0711663	−	0.997464i	$-0.477328\pi$
$947$	3.71988e9	0.142333	0.0711663	+	0.997464i	$0.477328\pi$
$948$	−2.23839e9	−0.0853311
$949$	1.84423e10	0.700458
$950$	−4.92795e10	−1.86480
$951$	1.54654e10	0.583083
$952$	3.54910e9	0.133318
$953$	−3.84659e10	−1.43963	−0.719814	−	0.694167i	$-0.755773\pi$
$953$	−3.84659e10	−1.43963	−0.719814	+	0.694167i	$0.755773\pi$
$954$	−2.06233e10	−0.769022
$955$	6.98225e9	0.259408
$956$	7.46667e10	2.76391
$957$	−1.23502e10	−0.455494
$958$	−2.00903e10	−0.738257
$959$	−4.53682e10	−1.66107
$960$	−9.01733e9	−0.328949
$961$	−2.15028e10	−0.781563
$962$	−7.78678e10	−2.81997
$963$	−1.37823e10	−0.497314
$964$	1.94905e10	0.700733
$965$	9.15579e9	0.327982
$966$	1.31016e10	0.467631
$967$	−1.01210e10	−0.359942	−0.179971	−	0.983672i	$-0.557600\pi$
$967$	−1.01210e10	−0.359942	−0.179971	+	0.983672i	$0.557600\pi$
$968$	−3.78994e10	−1.34298
$969$	8.84835e8	0.0312413
$970$	2.26271e10	0.796027
$971$	3.40438e10	1.19336	0.596679	−	0.802480i	$-0.296487\pi$
$971$	3.40438e10	1.19336	0.596679	+	0.802480i	$0.296487\pi$
$972$	4.45079e9	0.155455
$973$	−4.45985e9	−0.155212
$974$	1.83899e10	0.637710
$975$	1.46713e10	0.506935
$976$	−4.72776e10	−1.62773
$977$	−1.56624e10	−0.537314	−0.268657	−	0.963236i	$-0.586580\pi$
$977$	−1.56624e10	−0.537314	−0.268657	+	0.963236i	$0.586580\pi$
$978$	−5.03603e10	−1.72148
$979$	3.89465e10	1.32657
$980$	−2.87815e10	−0.976836
$981$	−1.08148e10	−0.365742
$982$	2.45213e10	0.826330
$983$	−3.86584e10	−1.29810	−0.649048	−	0.760747i	$-0.724833\pi$
$983$	−3.86584e10	−1.29810	−0.649048	+	0.760747i	$0.724833\pi$
$984$	3.23206e10	1.08143
$985$	−1.11356e10	−0.371269
$986$	−2.40083e9	−0.0797613
$987$	3.56065e10	1.17874
$988$	−1.28076e11	−4.22493
$989$	1.67568e9	0.0550811
$990$	−7.06788e9	−0.231508
$991$	1.35643e10	0.442731	0.221365	−	0.975191i	$-0.428949\pi$
$991$	1.35643e10	0.442731	0.221365	+	0.975191i	$0.428949\pi$
$992$	−2.72733e10	−0.887048
$993$	7.85428e9	0.254556
$994$	1.61772e9	0.0522459
$995$	2.69469e10	0.867217
$996$	−8.05503e10	−2.58321
$997$	−4.26350e10	−1.36249	−0.681245	−	0.732055i	$-0.738561\pi$
$997$	−4.26350e10	−1.36249	−0.681245	+	0.732055i	$0.738561\pi$
$998$	7.80113e10	2.48428
$999$	7.50003e9	0.238004

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.d.1.17	✓	18
3.2	odd	2		531.8.a.e.1.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.d.1.17	✓	18	1.1	even	1	trivial
531.8.a.e.1.2		18	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)

\(f(q)\)	\(=\)	\(q+20.9328 q^{2} +27.0000 q^{3} +310.183 q^{4} -149.882 q^{5} +565.186 q^{6} +1201.09 q^{7} +3813.60 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+20.9328 q^{2} +27.0000 q^{3} +310.183 q^{4} -149.882 q^{5} +565.186 q^{6} +1201.09 q^{7} +3813.60 q^{8} +729.000 q^{9} -3137.45 q^{10} +3090.18 q^{11} +8374.94 q^{12} -9762.44 q^{13} +25142.2 q^{14} -4046.82 q^{15} +40126.1 q^{16} +774.830 q^{17} +15260.0 q^{18} +42295.3 q^{19} -46490.9 q^{20} +32429.5 q^{21} +64686.2 q^{22} +19299.9 q^{23} +102967. q^{24} -55660.4 q^{25} -204355. q^{26} +19683.0 q^{27} +372558. q^{28} -148022. q^{29} -84711.3 q^{30} -77522.7 q^{31} +351811. q^{32} +83434.9 q^{33} +16219.4 q^{34} -180022. q^{35} +226123. q^{36} +381041. q^{37} +885360. q^{38} -263586. q^{39} -571591. q^{40} +313892. q^{41} +678840. q^{42} +86822.9 q^{43} +958522. q^{44} -109264. q^{45} +404002. q^{46} +1.09797e6 q^{47} +1.08340e6 q^{48} +619078. q^{49} -1.16513e6 q^{50} +20920.4 q^{51} -3.02814e6 q^{52} -1.35146e6 q^{53} +412021. q^{54} -463163. q^{55} +4.58049e6 q^{56} +1.14197e6 q^{57} -3.09852e6 q^{58} +205379. q^{59} -1.25525e6 q^{60} -1.17823e6 q^{61} -1.62277e6 q^{62} +875596. q^{63} +2.22825e6 q^{64} +1.46321e6 q^{65} +1.74653e6 q^{66} -2.20281e6 q^{67} +240339. q^{68} +521098. q^{69} -3.76837e6 q^{70} +64342.9 q^{71} +2.78012e6 q^{72} -1.88910e6 q^{73} +7.97626e6 q^{74} -1.50283e6 q^{75} +1.31193e7 q^{76} +3.71159e6 q^{77} -5.51760e6 q^{78} -267273. q^{79} -6.01418e6 q^{80} +531441. q^{81} +6.57065e6 q^{82} -9.61801e6 q^{83} +1.00591e7 q^{84} -116133. q^{85} +1.81745e6 q^{86} -3.99660e6 q^{87} +1.17847e7 q^{88} +1.26033e7 q^{89} -2.28720e6 q^{90} -1.17256e7 q^{91} +5.98651e6 q^{92} -2.09311e6 q^{93} +2.29835e7 q^{94} -6.33931e6 q^{95} +9.49889e6 q^{96} -7.21193e6 q^{97} +1.29590e7 q^{98} +2.25274e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9}+O(q^{10}) \) 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9	\( 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9} + 3609 q^{10} + 15070 q^{11} + 36666 q^{12} + 13662 q^{13} + 20861 q^{14} + 18306 q^{15} + 60482 q^{16} + 71919 q^{17} + 17496 q^{18} + 56231 q^{19} + 143053 q^{20} + 83187 q^{21} + 274198 q^{22} + 150029 q^{23} + 110889 q^{24} + 399672 q^{25} + 182846 q^{26} + 354294 q^{27} + 434150 q^{28} + 591285 q^{29} + 97443 q^{30} + 426733 q^{31} + 1205630 q^{32} + 406890 q^{33} + 403548 q^{34} + 912879 q^{35} + 989982 q^{36} + 7703 q^{37} - 417859 q^{38} + 368874 q^{39} + 618020 q^{40} + 770959 q^{41} + 563247 q^{42} + 793050 q^{43} + 2591274 q^{44} + 494262 q^{45} - 4068019 q^{46} + 1410373 q^{47} + 1633014 q^{48} + 1637427 q^{49} + 1021549 q^{50} + 1941813 q^{51} - 3749190 q^{52} + 1037934 q^{53} + 472392 q^{54} + 331974 q^{55} - 391748 q^{56} + 1518237 q^{57} + 653724 q^{58} + 3696822 q^{59} + 3862431 q^{60} - 1374623 q^{61} + 5251718 q^{62} + 2246049 q^{63} + 5077197 q^{64} + 3257170 q^{65} + 7403346 q^{66} - 2436904 q^{67} + 14119909 q^{68} + 4050783 q^{69} + 5185580 q^{70} + 14289172 q^{71} + 2994003 q^{72} + 5482515 q^{73} + 14934154 q^{74} + 10791144 q^{75} + 3822912 q^{76} + 23157109 q^{77} + 4936842 q^{78} + 19786414 q^{79} + 31978143 q^{80} + 9565938 q^{81} + 9749509 q^{82} + 30227337 q^{83} + 11722050 q^{84} + 9946981 q^{85} + 44295864 q^{86} + 15964695 q^{87} + 39970897 q^{88} + 31061677 q^{89} + 2630961 q^{90} + 26377785 q^{91} + 4719698 q^{92} + 11521791 q^{93} + 44488296 q^{94} + 15534599 q^{95} + 32552010 q^{96} + 12084118 q^{97} + 42274744 q^{98} + 10986030 q^{99}+O(q^{100}) \) 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9 + 3609 * q^10 + 15070 * q^11 + 36666 * q^12 + 13662 * q^13 + 20861 * q^14 + 18306 * q^15 + 60482 * q^16 + 71919 * q^17 + 17496 * q^18 + 56231 * q^19 + 143053 * q^20 + 83187 * q^21 + 274198 * q^22 + 150029 * q^23 + 110889 * q^24 + 399672 * q^25 + 182846 * q^26 + 354294 * q^27 + 434150 * q^28 + 591285 * q^29 + 97443 * q^30 + 426733 * q^31 + 1205630 * q^32 + 406890 * q^33 + 403548 * q^34 + 912879 * q^35 + 989982 * q^36 + 7703 * q^37 - 417859 * q^38 + 368874 * q^39 + 618020 * q^40 + 770959 * q^41 + 563247 * q^42 + 793050 * q^43 + 2591274 * q^44 + 494262 * q^45 - 4068019 * q^46 + 1410373 * q^47 + 1633014 * q^48 + 1637427 * q^49 + 1021549 * q^50 + 1941813 * q^51 - 3749190 * q^52 + 1037934 * q^53 + 472392 * q^54 + 331974 * q^55 - 391748 * q^56 + 1518237 * q^57 + 653724 * q^58 + 3696822 * q^59 + 3862431 * q^60 - 1374623 * q^61 + 5251718 * q^62 + 2246049 * q^63 + 5077197 * q^64 + 3257170 * q^65 + 7403346 * q^66 - 2436904 * q^67 + 14119909 * q^68 + 4050783 * q^69 + 5185580 * q^70 + 14289172 * q^71 + 2994003 * q^72 + 5482515 * q^73 + 14934154 * q^74 + 10791144 * q^75 + 3822912 * q^76 + 23157109 * q^77 + 4936842 * q^78 + 19786414 * q^79 + 31978143 * q^80 + 9565938 * q^81 + 9749509 * q^82 + 30227337 * q^83 + 11722050 * q^84 + 9946981 * q^85 + 44295864 * q^86 + 15964695 * q^87 + 39970897 * q^88 + 31061677 * q^89 + 2630961 * q^90 + 26377785 * q^91 + 4719698 * q^92 + 11521791 * q^93 + 44488296 * q^94 + 15534599 * q^95 + 32552010 * q^96 + 12084118 * q^97 + 42274744 * q^98 + 10986030 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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