LMFDB - Embedded newform 177.8.a.d.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,8,Mod(1,177)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$55.2921495107$
Analytic rank:	$0$
Dimension:	$18$
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			1.16
Root			$17.9457$ 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)

$f(q)$	$=$	$q+18.9457 q^{2} +27.0000 q^{3} +230.941 q^{4} +260.561 q^{5} +511.535 q^{6} +254.948 q^{7} +1950.29 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+18.9457 q^{2} +27.0000 q^{3} +230.941 q^{4} +260.561 q^{5} +511.535 q^{6} +254.948 q^{7} +1950.29 q^{8} +729.000 q^{9} +4936.51 q^{10} -3600.84 q^{11} +6235.40 q^{12} +10076.4 q^{13} +4830.18 q^{14} +7035.14 q^{15} +7389.22 q^{16} +4423.02 q^{17} +13811.4 q^{18} +16970.9 q^{19} +60174.1 q^{20} +6883.60 q^{21} -68220.5 q^{22} +63177.4 q^{23} +52657.8 q^{24} -10233.2 q^{25} +190906. q^{26} +19683.0 q^{27} +58877.9 q^{28} -27436.7 q^{29} +133286. q^{30} -22223.7 q^{31} -109643. q^{32} -97222.6 q^{33} +83797.4 q^{34} +66429.5 q^{35} +168356. q^{36} +111541. q^{37} +321525. q^{38} +272064. q^{39} +508168. q^{40} +87545.8 q^{41} +130415. q^{42} -454839. q^{43} -831580. q^{44} +189949. q^{45} +1.19694e6 q^{46} -747408. q^{47} +199509. q^{48} -758544. q^{49} -193875. q^{50} +119422. q^{51} +2.32706e6 q^{52} +1.10581e6 q^{53} +372909. q^{54} -938236. q^{55} +497223. q^{56} +458213. q^{57} -519807. q^{58} +205379. q^{59} +1.62470e6 q^{60} -227215. q^{61} -421044. q^{62} +185857. q^{63} -3.02308e6 q^{64} +2.62552e6 q^{65} -1.84195e6 q^{66} +1.66699e6 q^{67} +1.02146e6 q^{68} +1.70579e6 q^{69} +1.25856e6 q^{70} +1.63889e6 q^{71} +1.42176e6 q^{72} -379956. q^{73} +2.11322e6 q^{74} -276295. q^{75} +3.91926e6 q^{76} -918027. q^{77} +5.15445e6 q^{78} -1.69232e6 q^{79} +1.92534e6 q^{80} +531441. q^{81} +1.65862e6 q^{82} +3.64673e6 q^{83} +1.58970e6 q^{84} +1.15247e6 q^{85} -8.61726e6 q^{86} -740790. q^{87} -7.02267e6 q^{88} -7.90873e6 q^{89} +3.59872e6 q^{90} +2.56897e6 q^{91} +1.45902e7 q^{92} -600040. q^{93} -1.41602e7 q^{94} +4.42194e6 q^{95} -2.96035e6 q^{96} -905108. q^{97} -1.43712e7 q^{98} -2.62501e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	18.9457	1.67458	0.837291	−	0.546758i	$-0.184138\pi$
$2$	18.9457	1.67458	0.837291	+	0.546758i	$0.184138\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	230.941	1.80422
$5$	260.561	0.932210	0.466105	−	0.884729i	$-0.345657\pi$
$5$	260.561	0.932210	0.466105	+	0.884729i	$0.345657\pi$
$6$	511.535	0.966820
$7$	254.948	0.280937	0.140468	−	0.990085i	$-0.455139\pi$
$7$	254.948	0.280937	0.140468	+	0.990085i	$0.455139\pi$
$8$	1950.29	1.34674
$9$	729.000	0.333333
$10$	4936.51	1.56106
$11$	−3600.84	−0.815697	−0.407849	−	0.913050i	$-0.633721\pi$
$11$	−3600.84	−0.815697	−0.407849	+	0.913050i	$0.633721\pi$
$12$	6235.40	1.04167
$13$	10076.4	1.27205	0.636027	−	0.771667i	$-0.280577\pi$
$13$	10076.4	1.27205	0.636027	+	0.771667i	$0.280577\pi$
$14$	4830.18	0.470452
$15$	7035.14	0.538212
$16$	7389.22	0.451002
$17$	4423.02	0.218347	0.109174	−	0.994023i	$-0.465180\pi$
$17$	4423.02	0.218347	0.109174	+	0.994023i	$0.465180\pi$
$18$	13811.4	0.558194
$19$	16970.9	0.567631	0.283815	−	0.958879i	$-0.408400\pi$
$19$	16970.9	0.567631	0.283815	+	0.958879i	$0.408400\pi$
$20$	60174.1	1.68192
$21$	6883.60	0.162199
$22$	−68220.5	−1.36595
$23$	63177.4	1.08272	0.541358	−	0.840792i	$-0.317910\pi$
$23$	63177.4	1.08272	0.541358	+	0.840792i	$0.317910\pi$
$24$	52657.8	0.777541
$25$	−10233.2	−0.130984
$26$	190906.	2.13016
$27$	19683.0	0.192450
$28$	58877.9	0.506873
$29$	−27436.7	−0.208900	−0.104450	−	0.994530i	$-0.533308\pi$
$29$	−27436.7	−0.208900	−0.104450	+	0.994530i	$0.533308\pi$
$30$	133286.	0.901280
$31$	−22223.7	−0.133983	−0.0669916	−	0.997754i	$-0.521340\pi$
$31$	−22223.7	−0.133983	−0.0669916	+	0.997754i	$0.521340\pi$
$32$	−109643.	−0.591500
$33$	−97222.6	−0.470943
$34$	83797.4	0.365641
$35$	66429.5	0.261892
$36$	168356.	0.601408
$37$	111541.	0.362016	0.181008	−	0.983482i	$-0.442064\pi$
$37$	111541.	0.362016	0.181008	+	0.983482i	$0.442064\pi$
$38$	321525.	0.950544
$39$	272064.	0.734421
$40$	508168.	1.25544
$41$	87545.8	0.198377	0.0991886	−	0.995069i	$-0.468375\pi$
$41$	87545.8	0.198377	0.0991886	+	0.995069i	$0.468375\pi$
$42$	130415.	0.271616
$43$	−454839.	−0.872405	−0.436202	−	0.899849i	$-0.643677\pi$
$43$	−454839.	−0.872405	−0.436202	+	0.899849i	$0.643677\pi$
$44$	−831580.	−1.47170
$45$	189949.	0.310737
$46$	1.19694e6	1.81310
$47$	−747408.	−1.05006	−0.525031	−	0.851083i	$-0.675946\pi$
$47$	−747408.	−1.05006	−0.525031	+	0.851083i	$0.675946\pi$
$48$	199509.	0.260386
$49$	−758544.	−0.921074
$50$	−193875.	−0.219344
$51$	119422.	0.126063
$52$	2.32706e6	2.29507
$53$	1.10581e6	1.02027	0.510136	−	0.860094i	$-0.329595\pi$
$53$	1.10581e6	1.02027	0.510136	+	0.860094i	$0.329595\pi$
$54$	372909.	0.322273
$55$	−938236.	−0.760401
$56$	497223.	0.378349
$57$	458213.	0.327722
$58$	−519807.	−0.349820
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	1.62470e6	0.971055
$61$	−227215.	−0.128169	−0.0640844	−	0.997944i	$-0.520413\pi$
$61$	−227215.	−0.128169	−0.0640844	+	0.997944i	$0.520413\pi$
$62$	−421044.	−0.224366
$63$	185857.	0.0936457
$64$	−3.02308e6	−1.44152
$65$	2.62552e6	1.18582
$66$	−1.84195e6	−0.788633
$67$	1.66699e6	0.677128	0.338564	−	0.940943i	$-0.390059\pi$
$67$	1.66699e6	0.677128	0.338564	+	0.940943i	$0.390059\pi$
$68$	1.02146e6	0.393948
$69$	1.70579e6	0.625106
$70$	1.25856e6	0.438560
$71$	1.63889e6	0.543432	0.271716	−	0.962377i	$-0.412409\pi$
$71$	1.63889e6	0.543432	0.271716	+	0.962377i	$0.412409\pi$
$72$	1.42176e6	0.448913
$73$	−379956.	−0.114315	−0.0571575	−	0.998365i	$-0.518204\pi$
$73$	−379956.	−0.114315	−0.0571575	+	0.998365i	$0.518204\pi$
$74$	2.11322e6	0.606225
$75$	−276295.	−0.0756239
$76$	3.91926e6	1.02413
$77$	−918027.	−0.229159
$78$	5.15445e6	1.22985
$79$	−1.69232e6	−0.386179	−0.193090	−	0.981181i	$-0.561851\pi$
$79$	−1.69232e6	−0.386179	−0.193090	+	0.981181i	$0.561851\pi$
$80$	1.92534e6	0.420429
$81$	531441.	0.111111
$82$	1.65862e6	0.332199
$83$	3.64673e6	0.700052	0.350026	−	0.936740i	$-0.386173\pi$
$83$	3.64673e6	0.700052	0.350026	+	0.936740i	$0.386173\pi$
$84$	1.58970e6	0.292644
$85$	1.15247e6	0.203546
$86$	−8.61726e6	−1.46091
$87$	−740790.	−0.120608
$88$	−7.02267e6	−1.09853
$89$	−7.90873e6	−1.18916	−0.594582	−	0.804035i	$-0.702682\pi$
$89$	−7.90873e6	−1.18916	−0.594582	+	0.804035i	$0.702682\pi$
$90$	3.59872e6	0.520354
$91$	2.56897e6	0.357367
$92$	1.45902e7	1.95346
$93$	−600040.	−0.0773552
$94$	−1.41602e7	−1.75842
$95$	4.42194e6	0.529151
$96$	−2.96035e6	−0.341503
$97$	−905108.	−0.100693	−0.0503465	−	0.998732i	$-0.516033\pi$
$97$	−905108.	−0.100693	−0.0503465	+	0.998732i	$0.516033\pi$
$98$	−1.43712e7	−1.54241
$99$	−2.62501e6	−0.271899
$100$	−2.36325e6	−0.236325
$101$	−5.51628e6	−0.532748	−0.266374	−	0.963870i	$-0.585826\pi$
$101$	−5.51628e6	−0.532748	−0.266374	+	0.963870i	$0.585826\pi$
$102$	2.26253e6	0.211103
$103$	−8.52758e6	−0.768945	−0.384473	−	0.923136i	$-0.625617\pi$
$103$	−8.52758e6	−0.768945	−0.384473	+	0.923136i	$0.625617\pi$
$104$	1.96520e7	1.71313
$105$	1.79360e6	0.151204
$106$	2.09504e7	1.70853
$107$	6.00654e6	0.474003	0.237001	−	0.971509i	$-0.423835\pi$
$107$	6.00654e6	0.474003	0.237001	+	0.971509i	$0.423835\pi$
$108$	4.54561e6	0.347223
$109$	−4.33355e6	−0.320517	−0.160258	−	0.987075i	$-0.551233\pi$
$109$	−4.33355e6	−0.320517	−0.160258	+	0.987075i	$0.551233\pi$
$110$	−1.77756e7	−1.27335
$111$	3.01160e6	0.209010
$112$	1.88387e6	0.126703
$113$	−2.30765e7	−1.50451	−0.752255	−	0.658872i	$-0.771034\pi$
$113$	−2.30765e7	−1.50451	−0.752255	+	0.658872i	$0.771034\pi$
$114$	8.68118e6	0.548797
$115$	1.64615e7	1.00932
$116$	−6.33624e6	−0.376902
$117$	7.34573e6	0.424018
$118$	3.89106e6	0.218012
$119$	1.12764e6	0.0613419
$120$	1.37205e7	0.724831
$121$	−6.52115e6	−0.334638
$122$	−4.30475e6	−0.214629
$123$	2.36374e6	0.114533
$124$	−5.13236e6	−0.241736
$125$	−2.30227e7	−1.05432
$126$	3.52120e6	0.156817
$127$	8.51811e6	0.369003	0.184502	−	0.982832i	$-0.440933\pi$
$127$	8.51811e6	0.369003	0.184502	+	0.982832i	$0.440933\pi$
$128$	−4.32402e7	−1.82244
$129$	−1.22807e7	−0.503683
$130$	4.97425e7	1.98576
$131$	−2.97734e7	−1.15712	−0.578560	−	0.815640i	$-0.696385\pi$
$131$	−2.97734e7	−1.15712	−0.578560	+	0.815640i	$0.696385\pi$
$132$	−2.24527e7	−0.849687
$133$	4.32669e6	0.159469
$134$	3.15823e7	1.13391
$135$	5.12861e6	0.179404
$136$	8.62617e6	0.294057
$137$	1.89565e7	0.629849	0.314924	−	0.949117i	$-0.398021\pi$
$137$	1.89565e7	0.629849	0.314924	+	0.949117i	$0.398021\pi$
$138$	3.23174e7	1.04679
$139$	2.62226e7	0.828177	0.414088	−	0.910237i	$-0.364100\pi$
$139$	2.62226e7	0.828177	0.414088	+	0.910237i	$0.364100\pi$
$140$	1.53413e7	0.472512
$141$	−2.01800e7	−0.606254
$142$	3.10500e7	0.910022
$143$	−3.62836e7	−1.03761
$144$	5.38674e6	0.150334
$145$	−7.14891e6	−0.194739
$146$	−7.19854e6	−0.191430
$147$	−2.04807e7	−0.531783
$148$	2.57593e7	0.653158
$149$	−2.30589e7	−0.571066	−0.285533	−	0.958369i	$-0.592171\pi$
$149$	−2.30589e7	−0.571066	−0.285533	+	0.958369i	$0.592171\pi$
$150$	−5.23462e6	−0.126638
$151$	4.51544e7	1.06728	0.533642	−	0.845710i	$-0.320823\pi$
$151$	4.51544e7	1.06728	0.533642	+	0.845710i	$0.320823\pi$
$152$	3.30981e7	0.764451
$153$	3.22438e6	0.0727825
$154$	−1.73927e7	−0.383746
$155$	−5.79062e6	−0.124900
$156$	6.28307e7	1.32506
$157$	−3.09695e7	−0.638684	−0.319342	−	0.947640i	$-0.603462\pi$
$157$	−3.09695e7	−0.638684	−0.319342	+	0.947640i	$0.603462\pi$
$158$	−3.20623e7	−0.646689
$159$	2.98569e7	0.589054
$160$	−2.85686e7	−0.551402
$161$	1.61070e7	0.304175
$162$	1.00685e7	0.186065
$163$	8.52913e7	1.54258	0.771290	−	0.636483i	$-0.219612\pi$
$163$	8.52913e7	1.54258	0.771290	+	0.636483i	$0.219612\pi$
$164$	2.02179e7	0.357917
$165$	−2.53324e7	−0.439018
$166$	6.90900e7	1.17229
$167$	−4.10631e7	−0.682250	−0.341125	−	0.940018i	$-0.610808\pi$
$167$	−4.10631e7	−0.682250	−0.341125	+	0.940018i	$0.610808\pi$
$168$	1.34250e7	0.218440
$169$	3.87862e7	0.618122
$170$	2.18343e7	0.340854
$171$	1.23718e7	0.189210
$172$	−1.05041e8	−1.57401
$173$	3.80863e7	0.559252	0.279626	−	0.960109i	$-0.409790\pi$
$173$	3.80863e7	0.559252	0.279626	+	0.960109i	$0.409790\pi$
$174$	−1.40348e7	−0.201969
$175$	−2.60893e6	−0.0367984
$176$	−2.66074e7	−0.367881
$177$	5.54523e6	0.0751646
$178$	−1.49837e8	−1.99135
$179$	2.59663e7	0.338395	0.169198	−	0.985582i	$-0.445882\pi$
$179$	2.59663e7	0.338395	0.169198	+	0.985582i	$0.445882\pi$
$180$	4.38669e7	0.560639
$181$	−4.28031e6	−0.0536537	−0.0268269	−	0.999640i	$-0.508540\pi$
$181$	−4.28031e6	−0.0536537	−0.0268269	+	0.999640i	$0.508540\pi$
$182$	4.86711e7	0.598440
$183$	−6.13480e6	−0.0739983
$184$	1.23214e8	1.45814
$185$	2.90631e7	0.337475
$186$	−1.13682e7	−0.129538
$187$	−1.59266e7	−0.178105
$188$	−1.72607e8	−1.89455
$189$	5.01815e6	0.0540663
$190$	8.37768e7	0.886107
$191$	6.15146e6	0.0638795	0.0319398	−	0.999490i	$-0.489832\pi$
$191$	6.15146e6	0.0638795	0.0319398	+	0.999490i	$0.489832\pi$
$192$	−8.16232e7	−0.832261
$193$	−1.33350e8	−1.33519	−0.667594	−	0.744525i	$-0.732676\pi$
$193$	−1.33350e8	−1.33519	−0.667594	+	0.744525i	$0.732676\pi$
$194$	−1.71479e7	−0.168619
$195$	7.08892e7	0.684634
$196$	−1.75179e8	−1.66183
$197$	−1.28756e8	−1.19987	−0.599936	−	0.800048i	$-0.704807\pi$
$197$	−1.28756e8	−1.19987	−0.599936	+	0.800048i	$0.704807\pi$
$198$	−4.97327e7	−0.455317
$199$	−1.66821e8	−1.50060	−0.750301	−	0.661096i	$-0.770092\pi$
$199$	−1.66821e8	−1.50060	−0.750301	+	0.661096i	$0.770092\pi$
$200$	−1.99576e7	−0.176402
$201$	4.50087e7	0.390940
$202$	−1.04510e8	−0.892130
$203$	−6.99493e6	−0.0586877
$204$	2.75793e7	0.227446
$205$	2.28110e7	0.184929
$206$	−1.61561e8	−1.28766
$207$	4.60563e7	0.360905
$208$	7.44570e7	0.573699
$209$	−6.11093e7	−0.463015
$210$	3.39810e7	0.253203
$211$	2.09952e7	0.153862	0.0769310	−	0.997036i	$-0.475488\pi$
$211$	2.09952e7	0.153862	0.0769310	+	0.997036i	$0.475488\pi$
$212$	2.55377e8	1.84080
$213$	4.42500e7	0.313751
$214$	1.13798e8	0.793757
$215$	−1.18513e8	−0.813265
$216$	3.83875e7	0.259180
$217$	−5.66589e6	−0.0376408
$218$	−8.21022e7	−0.536732
$219$	−1.02588e7	−0.0659998
$220$	−2.16677e8	−1.37193
$221$	4.45684e7	0.277750
$222$	5.70570e7	0.350004
$223$	−1.74632e8	−1.05453	−0.527263	−	0.849702i	$-0.676782\pi$
$223$	−1.74632e8	−1.05453	−0.527263	+	0.849702i	$0.676782\pi$
$224$	−2.79532e7	−0.166174
$225$	−7.45997e6	−0.0436615
$226$	−4.37201e8	−2.51942
$227$	−3.02436e8	−1.71610	−0.858051	−	0.513565i	$-0.828324\pi$
$227$	−3.02436e8	−1.71610	−0.858051	+	0.513565i	$0.828324\pi$
$228$	1.05820e8	0.591284
$229$	−1.49255e8	−0.821307	−0.410653	−	0.911792i	$-0.634699\pi$
$229$	−1.49255e8	−0.821307	−0.410653	+	0.911792i	$0.634699\pi$
$230$	3.11876e8	1.69019
$231$	−2.47867e7	−0.132305
$232$	−5.35094e7	−0.281334
$233$	−2.80934e8	−1.45499	−0.727493	−	0.686115i	$-0.759314\pi$
$233$	−2.80934e8	−1.45499	−0.727493	+	0.686115i	$0.759314\pi$
$234$	1.39170e8	0.710053
$235$	−1.94745e8	−0.978879
$236$	4.74304e7	0.234890
$237$	−4.56928e7	−0.222961
$238$	2.13640e7	0.102722
$239$	9.57324e6	0.0453593	0.0226796	−	0.999743i	$-0.492780\pi$
$239$	9.57324e6	0.0453593	0.0226796	+	0.999743i	$0.492780\pi$
$240$	5.19842e7	0.242735
$241$	7.63167e7	0.351204	0.175602	−	0.984461i	$-0.443813\pi$
$241$	7.63167e7	0.351204	0.175602	+	0.984461i	$0.443813\pi$
$242$	−1.23548e8	−0.560379
$243$	1.43489e7	0.0641500
$244$	−5.24732e7	−0.231245
$245$	−1.97647e8	−0.858635
$246$	4.47827e7	0.191795
$247$	1.71006e8	0.722057
$248$	−4.33426e7	−0.180441
$249$	9.84617e7	0.404175
$250$	−4.36181e8	−1.76554
$251$	3.07061e8	1.22565	0.612825	−	0.790218i	$-0.290033\pi$
$251$	3.07061e8	1.22565	0.612825	+	0.790218i	$0.290033\pi$
$252$	4.29220e7	0.168958
$253$	−2.27492e8	−0.883168
$254$	1.61382e8	0.617926
$255$	3.11166e7	0.117517
$256$	−4.32263e8	−1.61031
$257$	3.52469e8	1.29525	0.647626	−	0.761958i	$-0.275762\pi$
$257$	3.52469e8	1.29525	0.647626	+	0.761958i	$0.275762\pi$
$258$	−2.32666e8	−0.843459
$259$	2.84371e7	0.101704
$260$	6.06341e8	2.13949
$261$	−2.00013e7	−0.0696333
$262$	−5.64078e8	−1.93769
$263$	3.39887e8	1.15210	0.576048	−	0.817416i	$-0.304594\pi$
$263$	3.39887e8	1.15210	0.576048	+	0.817416i	$0.304594\pi$
$264$	−1.89612e8	−0.634238
$265$	2.88131e8	0.951107
$266$	8.19723e7	0.267043
$267$	−2.13536e8	−0.686564
$268$	3.84975e8	1.22169
$269$	4.31047e8	1.35018	0.675090	−	0.737735i	$-0.264105\pi$
$269$	4.31047e8	1.35018	0.675090	+	0.737735i	$0.264105\pi$
$270$	9.71654e7	0.300427
$271$	−1.49089e8	−0.455044	−0.227522	−	0.973773i	$-0.573062\pi$
$271$	−1.49089e8	−0.455044	−0.227522	+	0.973773i	$0.573062\pi$
$272$	3.26827e7	0.0984752
$273$	6.93622e7	0.206326
$274$	3.59145e8	1.05473
$275$	3.68479e7	0.106844
$276$	3.93936e8	1.12783
$277$	3.21914e8	0.910041	0.455020	−	0.890481i	$-0.349632\pi$
$277$	3.21914e8	0.910041	0.455020	+	0.890481i	$0.349632\pi$
$278$	4.96805e8	1.38685
$279$	−1.62011e7	−0.0446611
$280$	1.29557e8	0.352701
$281$	6.09518e8	1.63876	0.819378	−	0.573253i	$-0.194319\pi$
$281$	6.09518e8	1.63876	0.819378	+	0.573253i	$0.194319\pi$
$282$	−3.82325e8	−1.01522
$283$	−4.38418e8	−1.14984	−0.574918	−	0.818211i	$-0.694966\pi$
$283$	−4.38418e8	−1.14984	−0.574918	+	0.818211i	$0.694966\pi$
$284$	3.78486e8	0.980474
$285$	1.19392e8	0.305506
$286$	−6.87420e8	−1.73756
$287$	2.23196e7	0.0557315
$288$	−7.99295e7	−0.197167
$289$	−3.90776e8	−0.952324
$290$	−1.35441e8	−0.326106
$291$	−2.44379e7	−0.0581351
$292$	−8.77473e7	−0.206250
$293$	−4.48586e7	−0.104186	−0.0520930	−	0.998642i	$-0.516589\pi$
$293$	−4.48586e7	−0.104186	−0.0520930	+	0.998642i	$0.516589\pi$
$294$	−3.88022e8	−0.890513
$295$	5.35137e7	0.121363
$296$	2.17537e8	0.487541
$297$	−7.08753e7	−0.156981
$298$	−4.36868e8	−0.956297
$299$	6.36604e8	1.37727
$300$	−6.38078e7	−0.136442
$301$	−1.15960e8	−0.245091
$302$	8.55482e8	1.78726
$303$	−1.48940e8	−0.307582
$304$	1.25401e8	0.256003
$305$	−5.92032e7	−0.119480
$306$	6.10883e7	0.121880
$307$	7.78794e7	0.153617	0.0768083	−	0.997046i	$-0.475527\pi$
$307$	7.78794e7	0.153617	0.0768083	+	0.997046i	$0.475527\pi$
$308$	−2.12010e8	−0.413455
$309$	−2.30245e8	−0.443951
$310$	−1.09708e8	−0.209156
$311$	4.98982e8	0.940640	0.470320	−	0.882496i	$-0.344139\pi$
$311$	4.98982e8	0.940640	0.470320	+	0.882496i	$0.344139\pi$
$312$	5.30603e8	0.989074
$313$	3.57809e8	0.659547	0.329774	−	0.944060i	$-0.393028\pi$
$313$	3.57809e8	0.659547	0.329774	+	0.944060i	$0.393028\pi$
$314$	−5.86741e8	−1.06953
$315$	4.84271e7	0.0872974
$316$	−3.90827e8	−0.696754
$317$	1.30653e8	0.230363	0.115181	−	0.993344i	$-0.463255\pi$
$317$	1.30653e8	0.230363	0.115181	+	0.993344i	$0.463255\pi$
$318$	5.65661e8	0.986419
$319$	9.87949e7	0.170399
$320$	−7.87696e8	−1.34380
$321$	1.62176e8	0.273666
$322$	3.05158e8	0.509366
$323$	7.50625e7	0.123941
$324$	1.22731e8	0.200469
$325$	−1.03114e8	−0.166619
$326$	1.61591e9	2.58318
$327$	−1.17006e8	−0.185050
$328$	1.70739e8	0.267162
$329$	−1.90550e8	−0.295001
$330$	−4.79940e8	−0.735171
$331$	9.92186e8	1.50382	0.751909	−	0.659267i	$-0.229133\pi$
$331$	9.92186e8	1.50382	0.751909	+	0.659267i	$0.229133\pi$
$332$	8.42179e8	1.26305
$333$	8.13132e7	0.120672
$334$	−7.77970e8	−1.14248
$335$	4.34351e8	0.631225
$336$	5.08644e7	0.0731521
$337$	−2.68966e7	−0.0382818	−0.0191409	−	0.999817i	$-0.506093\pi$
$337$	−2.68966e7	−0.0382818	−0.0191409	+	0.999817i	$0.506093\pi$
$338$	7.34833e8	1.03510
$339$	−6.23065e8	−0.868629
$340$	2.66151e8	0.367242
$341$	8.00239e7	0.109290
$342$	2.34392e8	0.316848
$343$	−4.03350e8	−0.539701
$344$	−8.87067e8	−1.17490
$345$	4.44462e8	0.582730
$346$	7.21573e8	0.936513
$347$	1.17341e9	1.50764	0.753821	−	0.657080i	$-0.228209\pi$
$347$	1.17341e9	1.50764	0.753821	+	0.657080i	$0.228209\pi$
$348$	−1.71079e8	−0.217605
$349$	1.13126e9	1.42454	0.712269	−	0.701907i	$-0.247668\pi$
$349$	1.13126e9	1.42454	0.712269	+	0.701907i	$0.247668\pi$
$350$	−4.94280e7	−0.0616219
$351$	1.98335e8	0.244807
$352$	3.94805e8	0.482485
$353$	1.22377e9	1.48078	0.740389	−	0.672179i	$-0.234641\pi$
$353$	1.22377e9	1.48078	0.740389	+	0.672179i	$0.234641\pi$
$354$	1.05058e8	0.125869
$355$	4.27030e8	0.506593
$356$	−1.82645e9	−2.14552
$357$	3.04463e7	0.0354157
$358$	4.91950e8	0.566670
$359$	−6.37571e7	−0.0727274	−0.0363637	−	0.999339i	$-0.511577\pi$
$359$	−6.37571e7	−0.0727274	−0.0363637	+	0.999339i	$0.511577\pi$
$360$	3.70455e8	0.418482
$361$	−6.05862e8	−0.677795
$362$	−8.10936e7	−0.0898476
$363$	−1.76071e8	−0.193203
$364$	5.93280e8	0.644770
$365$	−9.90015e7	−0.106566
$366$	−1.16228e8	−0.123916
$367$	1.18246e9	1.24870	0.624348	−	0.781147i	$-0.285365\pi$
$367$	1.18246e9	1.24870	0.624348	+	0.781147i	$0.285365\pi$
$368$	4.66832e8	0.488307
$369$	6.38209e7	0.0661257
$370$	5.50622e8	0.565129
$371$	2.81925e8	0.286632
$372$	−1.38574e8	−0.139566
$373$	5.09652e8	0.508502	0.254251	−	0.967138i	$-0.418171\pi$
$373$	5.09652e8	0.508502	0.254251	+	0.967138i	$0.418171\pi$
$374$	−3.01741e8	−0.298252
$375$	−6.21612e8	−0.608709
$376$	−1.45766e9	−1.41416
$377$	−2.76464e8	−0.265732
$378$	9.50725e7	0.0905385
$379$	5.82373e8	0.549496	0.274748	−	0.961516i	$-0.411406\pi$
$379$	5.82373e8	0.549496	0.274748	+	0.961516i	$0.411406\pi$
$380$	1.02121e9	0.954708
$381$	2.29989e8	0.213044
$382$	1.16544e8	0.106971
$383$	−2.95800e8	−0.269031	−0.134515	−	0.990912i	$-0.542948\pi$
$383$	−2.95800e8	−0.269031	−0.134515	+	0.990912i	$0.542948\pi$
$384$	−1.16749e9	−1.05219
$385$	−2.39202e8	−0.213625
$386$	−2.52641e9	−2.23588
$387$	−3.31578e8	−0.290802
$388$	−2.09026e8	−0.181673
$389$	−1.67193e9	−1.44011	−0.720055	−	0.693917i	$-0.755884\pi$
$389$	−1.67193e9	−1.44011	−0.720055	+	0.693917i	$0.755884\pi$
$390$	1.34305e9	1.14648
$391$	2.79435e8	0.236408
$392$	−1.47938e9	−1.24045
$393$	−8.03881e8	−0.668064
$394$	−2.43937e9	−2.00928
$395$	−4.40953e8	−0.360000
$396$	−6.06222e8	−0.490567
$397$	3.26565e7	0.0261940	0.0130970	−	0.999914i	$-0.495831\pi$
$397$	3.26565e7	0.0261940	0.0130970	+	0.999914i	$0.495831\pi$
$398$	−3.16055e9	−2.51288
$399$	1.16821e8	0.0920692
$400$	−7.56150e7	−0.0590742
$401$	2.13725e7	0.0165520	0.00827600	−	0.999966i	$-0.497366\pi$
$401$	2.13725e7	0.0165520	0.00827600	+	0.999966i	$0.497366\pi$
$402$	8.52722e8	0.654661
$403$	−2.23936e8	−0.170434
$404$	−1.27393e9	−0.961197
$405$	1.38473e8	0.103579
$406$	−1.32524e8	−0.0982773
$407$	−4.01640e8	−0.295295
$408$	2.32907e8	0.169774
$409$	7.70641e8	0.556955	0.278478	−	0.960443i	$-0.410170\pi$
$409$	7.70641e8	0.556955	0.278478	+	0.960443i	$0.410170\pi$
$410$	4.32171e8	0.309679
$411$	5.11826e8	0.363643
$412$	−1.96937e9	−1.38735
$413$	5.23610e7	0.0365749
$414$	8.72571e8	0.604365
$415$	9.50195e8	0.652596
$416$	−1.10481e9	−0.752420
$417$	7.08009e8	0.478148
$418$	−1.15776e9	−0.775356
$419$	1.32286e9	0.878547	0.439274	−	0.898353i	$-0.355236\pi$
$419$	1.32286e9	0.878547	0.439274	+	0.898353i	$0.355236\pi$
$420$	4.14214e8	0.272805
$421$	−5.11479e8	−0.334073	−0.167036	−	0.985951i	$-0.553420\pi$
$421$	−5.11479e8	−0.334073	−0.167036	+	0.985951i	$0.553420\pi$
$422$	3.97769e8	0.257655
$423$	−5.44860e8	−0.350021
$424$	2.15665e9	1.37404
$425$	−4.52615e7	−0.0286001
$426$	8.38349e8	0.525402
$427$	−5.79280e7	−0.0360073
$428$	1.38715e9	0.855208
$429$	−9.79658e8	−0.599065
$430$	−2.24532e9	−1.36188
$431$	−1.38021e8	−0.0830374	−0.0415187	−	0.999138i	$-0.513220\pi$
$431$	−1.38021e8	−0.0830374	−0.0415187	+	0.999138i	$0.513220\pi$
$432$	1.45442e8	0.0867954
$433$	−1.42354e9	−0.842680	−0.421340	−	0.906903i	$-0.638440\pi$
$433$	−1.42354e9	−0.842680	−0.421340	+	0.906903i	$0.638440\pi$
$434$	−1.07344e8	−0.0630326
$435$	−1.93021e8	−0.112432
$436$	−1.00079e9	−0.578284
$437$	1.07217e9	0.614583
$438$	−1.94361e8	−0.110522
$439$	−6.95019e8	−0.392077	−0.196038	−	0.980596i	$-0.562808\pi$
$439$	−6.95019e8	−0.392077	−0.196038	+	0.980596i	$0.562808\pi$
$440$	−1.82983e9	−1.02406
$441$	−5.52979e8	−0.307025
$442$	8.44380e8	0.465115
$443$	2.52605e9	1.38047	0.690237	−	0.723583i	$-0.257506\pi$
$443$	2.52605e9	1.38047	0.690237	+	0.723583i	$0.257506\pi$
$444$	6.95501e8	0.377101
$445$	−2.06070e9	−1.10855
$446$	−3.30853e9	−1.76589
$447$	−6.22590e8	−0.329705
$448$	−7.70729e8	−0.404976
$449$	1.92004e9	1.00103	0.500517	−	0.865727i	$-0.333143\pi$
$449$	1.92004e9	1.00103	0.500517	+	0.865727i	$0.333143\pi$
$450$	−1.41335e8	−0.0731147
$451$	−3.15238e8	−0.161816
$452$	−5.32930e9	−2.71447
$453$	1.21917e9	0.616197
$454$	−5.72987e9	−2.87375
$455$	6.69373e8	0.333141
$456$	8.93647e8	0.441356
$457$	2.28317e9	1.11900	0.559502	−	0.828829i	$-0.310992\pi$
$457$	2.28317e9	1.11900	0.559502	+	0.828829i	$0.310992\pi$
$458$	−2.82775e9	−1.37535
$459$	8.70584e7	0.0420210
$460$	3.80164e9	1.82104
$461$	8.39344e8	0.399013	0.199506	−	0.979897i	$-0.436066\pi$
$461$	8.39344e8	0.399013	0.199506	+	0.979897i	$0.436066\pi$
$462$	−4.69603e8	−0.221556
$463$	−1.31128e9	−0.613990	−0.306995	−	0.951711i	$-0.599323\pi$
$463$	−1.31128e9	−0.613990	−0.306995	+	0.951711i	$0.599323\pi$
$464$	−2.02735e8	−0.0942143
$465$	−1.56347e8	−0.0721113
$466$	−5.32250e9	−2.43649
$467$	2.02299e9	0.919145	0.459572	−	0.888140i	$-0.348003\pi$
$467$	2.02299e9	0.919145	0.459572	+	0.888140i	$0.348003\pi$
$468$	1.69643e9	0.765024
$469$	4.24996e8	0.190230
$470$	−3.68959e9	−1.63921
$471$	−8.36178e8	−0.368744
$472$	4.00548e8	0.175331
$473$	1.63780e9	0.711618
$474$	−8.65683e8	−0.373366
$475$	−1.73665e8	−0.0743508
$476$	2.60419e8	0.110675
$477$	8.06137e8	0.340091
$478$	1.81372e8	0.0759578
$479$	1.74780e9	0.726635	0.363318	−	0.931665i	$-0.381644\pi$
$479$	1.74780e9	0.726635	0.363318	+	0.931665i	$0.381644\pi$
$480$	−7.71352e8	−0.318352
$481$	1.12393e9	0.460504
$482$	1.44588e9	0.588120
$483$	4.34888e8	0.175615
$484$	−1.50600e9	−0.603762
$485$	−2.35836e8	−0.0938671
$486$	2.71851e8	0.107424
$487$	−2.38890e8	−0.0937231	−0.0468616	−	0.998901i	$-0.514922\pi$
$487$	−2.38890e8	−0.0937231	−0.0468616	+	0.998901i	$0.514922\pi$
$488$	−4.43134e8	−0.172610
$489$	2.30286e9	0.890609
$490$	−3.74456e9	−1.43785
$491$	2.15282e9	0.820772	0.410386	−	0.911912i	$-0.365394\pi$
$491$	2.15282e9	0.820772	0.410386	+	0.911912i	$0.365394\pi$
$492$	5.45883e8	0.206643
$493$	−1.21353e8	−0.0456128
$494$	3.23983e9	1.20914
$495$	−6.83974e8	−0.253467
$496$	−1.64216e8	−0.0604267
$497$	4.17832e8	0.152670
$498$	1.86543e9	0.676825
$499$	9.90364e8	0.356815	0.178407	−	0.983957i	$-0.442906\pi$
$499$	9.90364e8	0.356815	0.178407	+	0.983957i	$0.442906\pi$
$500$	−5.31687e9	−1.90222
$501$	−1.10870e9	−0.393897
$502$	5.81750e9	2.05245
$503$	1.94133e9	0.680161	0.340080	−	0.940396i	$-0.389546\pi$
$503$	1.94133e9	0.680161	0.340080	+	0.940396i	$0.389546\pi$
$504$	3.62475e8	0.126116
$505$	−1.43733e9	−0.496633
$506$	−4.30999e9	−1.47894
$507$	1.04723e9	0.356873
$508$	1.96718e9	0.665764
$509$	1.30601e9	0.438970	0.219485	−	0.975616i	$-0.429562\pi$
$509$	1.30601e9	0.438970	0.219485	+	0.975616i	$0.429562\pi$
$510$	5.89526e8	0.196792
$511$	−9.68690e7	−0.0321153
$512$	−2.65480e9	−0.874150
$513$	3.34037e8	0.109241
$514$	6.67778e9	2.16901
$515$	−2.22195e9	−0.716818
$516$	−2.83610e9	−0.908758
$517$	2.69129e9	0.856533
$518$	5.38762e8	0.170311
$519$	1.02833e9	0.322884
$520$	5.12053e9	1.59699
$521$	4.39027e9	1.36006	0.680031	−	0.733183i	$-0.261966\pi$
$521$	4.39027e9	1.36006	0.680031	+	0.733183i	$0.261966\pi$
$522$	−3.78940e8	−0.116607
$523$	3.06969e9	0.938293	0.469146	−	0.883120i	$-0.344562\pi$
$523$	3.06969e9	0.938293	0.469146	+	0.883120i	$0.344562\pi$
$524$	−6.87589e9	−2.08771
$525$	−7.04410e7	−0.0212455
$526$	6.43940e9	1.92928
$527$	−9.82959e7	−0.0292549
$528$	−7.18399e8	−0.212396
$529$	5.86560e8	0.172273
$530$	5.45885e9	1.59271
$531$	1.49721e8	0.0433963
$532$	9.99209e8	0.287717
$533$	8.82150e8	0.252346
$534$	−4.04559e9	−1.14971
$535$	1.56507e9	0.441870
$536$	3.25111e9	0.911915
$537$	7.01089e8	0.195372
$538$	8.16650e9	2.26099
$539$	2.73139e9	0.751318
$540$	1.18441e9	0.323685
$541$	−7.85502e7	−0.0213283	−0.0106642	−	0.999943i	$-0.503395\pi$
$541$	−7.85502e7	−0.0213283	−0.0106642	+	0.999943i	$0.503395\pi$
$542$	−2.82460e9	−0.762009
$543$	−1.15568e8	−0.0309770
$544$	−4.84952e8	−0.129153
$545$	−1.12915e9	−0.298789
$546$	1.31412e9	0.345510
$547$	−6.56046e9	−1.71387	−0.856937	−	0.515422i	$-0.827635\pi$
$547$	−6.56046e9	−1.71387	−0.856937	+	0.515422i	$0.827635\pi$
$548$	4.37783e9	1.13639
$549$	−1.65640e8	−0.0427229
$550$	6.98111e8	0.178918
$551$	−4.65623e8	−0.118578
$552$	3.32678e9	0.841856
$553$	−4.31455e8	−0.108492
$554$	6.09890e9	1.52394
$555$	7.84704e8	0.194841
$556$	6.05586e9	1.49422
$557$	−5.79150e9	−1.42003	−0.710015	−	0.704186i	$-0.751312\pi$
$557$	−5.79150e9	−1.42003	−0.710015	+	0.704186i	$0.751312\pi$
$558$	−3.06941e8	−0.0747886
$559$	−4.58316e9	−1.10975
$560$	4.90862e8	0.118114
$561$	−4.30018e8	−0.102829
$562$	1.15478e10	2.74423
$563$	1.04570e9	0.246961	0.123480	−	0.992347i	$-0.460594\pi$
$563$	1.04570e9	0.246961	0.123480	+	0.992347i	$0.460594\pi$
$564$	−4.66039e9	−1.09382
$565$	−6.01282e9	−1.40252
$566$	−8.30614e9	−1.92549
$567$	1.35490e8	0.0312152
$568$	3.19631e9	0.731862
$569$	7.96871e8	0.181341	0.0906704	−	0.995881i	$-0.471099\pi$
$569$	7.96871e8	0.181341	0.0906704	+	0.995881i	$0.471099\pi$
$570$	2.26197e9	0.511594
$571$	1.01872e9	0.228996	0.114498	−	0.993423i	$-0.463474\pi$
$571$	1.01872e9	0.228996	0.114498	+	0.993423i	$0.463474\pi$
$572$	−8.37937e9	−1.87208
$573$	1.66089e8	0.0368808
$574$	4.22862e8	0.0933269
$575$	−6.46504e8	−0.141819
$576$	−2.20383e9	−0.480506
$577$	−1.71883e9	−0.372492	−0.186246	−	0.982503i	$-0.559632\pi$
$577$	−1.71883e9	−0.372492	−0.186246	+	0.982503i	$0.559632\pi$
$578$	−7.40353e9	−1.59475
$579$	−3.60045e9	−0.770872
$580$	−1.65098e9	−0.351352
$581$	9.29728e8	0.196671
$582$	−4.62994e8	−0.0973521
$583$	−3.98185e9	−0.832233
$584$	−7.41023e8	−0.153953
$585$	1.91401e9	0.395274
$586$	−8.49879e8	−0.174468
$587$	−4.84773e9	−0.989249	−0.494624	−	0.869107i	$-0.664694\pi$
$587$	−4.84773e9	−0.989249	−0.494624	+	0.869107i	$0.664694\pi$
$588$	−4.72983e9	−0.959455
$589$	−3.77155e8	−0.0760530
$590$	1.01386e9	0.203233
$591$	−3.47641e9	−0.692747
$592$	8.24199e8	0.163270
$593$	−6.50386e9	−1.28080	−0.640398	−	0.768043i	$-0.721230\pi$
$593$	−6.50386e9	−1.28080	−0.640398	+	0.768043i	$0.721230\pi$
$594$	−1.34278e9	−0.262878
$595$	2.93819e8	0.0571835
$596$	−5.32524e9	−1.03033
$597$	−4.50418e9	−0.866373
$598$	1.20609e10	2.30636
$599$	3.67574e9	0.698797	0.349398	−	0.936974i	$-0.386386\pi$
$599$	3.67574e9	0.698797	0.349398	+	0.936974i	$0.386386\pi$
$600$	−5.38855e8	−0.101846
$601$	2.39919e9	0.450821	0.225410	−	0.974264i	$-0.427628\pi$
$601$	2.39919e9	0.450821	0.225410	+	0.974264i	$0.427628\pi$
$602$	−2.19695e9	−0.410425
$603$	1.21523e9	0.225709
$604$	1.04280e10	1.92562
$605$	−1.69916e9	−0.311953
$606$	−2.82177e9	−0.515072
$607$	−6.08714e9	−1.10472	−0.552361	−	0.833605i	$-0.686273\pi$
$607$	−6.08714e9	−1.10472	−0.552361	+	0.833605i	$0.686273\pi$
$608$	−1.86073e9	−0.335754
$609$	−1.88863e8	−0.0338834
$610$	−1.12165e9	−0.200079
$611$	−7.53121e9	−1.33574
$612$	7.44642e8	0.131316
$613$	9.32738e9	1.63549	0.817745	−	0.575581i	$-0.195224\pi$
$613$	9.32738e9	1.63549	0.817745	+	0.575581i	$0.195224\pi$
$614$	1.47548e9	0.257244
$615$	6.15896e8	0.106769
$616$	−1.79042e9	−0.308618
$617$	6.37210e9	1.09216	0.546078	−	0.837734i	$-0.316120\pi$
$617$	6.37210e9	1.09216	0.546078	+	0.837734i	$0.316120\pi$
$618$	−4.36215e9	−0.743432
$619$	−4.05521e9	−0.687220	−0.343610	−	0.939112i	$-0.611650\pi$
$619$	−4.05521e9	−0.687220	−0.343610	+	0.939112i	$0.611650\pi$
$620$	−1.33729e9	−0.225348
$621$	1.24352e9	0.208369
$622$	9.45358e9	1.57518
$623$	−2.01632e9	−0.334080
$624$	2.01034e9	0.331225
$625$	−5.19933e9	−0.851859
$626$	6.77895e9	1.10447
$627$	−1.64995e9	−0.267322
$628$	−7.15213e9	−1.15233
$629$	4.93347e8	0.0790452
$630$	9.17487e8	0.146187
$631$	−8.06865e9	−1.27849	−0.639246	−	0.769002i	$-0.720754\pi$
$631$	−8.06865e9	−1.27849	−0.639246	+	0.769002i	$0.720754\pi$
$632$	−3.30052e9	−0.520083
$633$	5.66870e8	0.0888323
$634$	2.47532e9	0.385762
$635$	2.21948e9	0.343988
$636$	6.89518e9	1.06279
$637$	−7.64343e9	−1.17166
$638$	1.87174e9	0.285347
$639$	1.19475e9	0.181144
$640$	−1.12667e10	−1.69890
$641$	−3.59478e9	−0.539100	−0.269550	−	0.962986i	$-0.586875\pi$
$641$	−3.59478e9	−0.539100	−0.269550	+	0.962986i	$0.586875\pi$
$642$	3.07255e9	0.458276
$643$	−7.51354e9	−1.11457	−0.557283	−	0.830322i	$-0.688156\pi$
$643$	−7.51354e9	−1.11457	−0.557283	+	0.830322i	$0.688156\pi$
$644$	3.71976e9	0.548800
$645$	−3.19985e9	−0.469539
$646$	1.42211e9	0.207549
$647$	1.51619e9	0.220084	0.110042	−	0.993927i	$-0.464901\pi$
$647$	1.51619e9	0.220084	0.110042	+	0.993927i	$0.464901\pi$
$648$	1.03646e9	0.149638
$649$	−7.39536e8	−0.106195
$650$	−1.95357e9	−0.279018
$651$	−1.52979e8	−0.0217319
$652$	1.96972e10	2.78316
$653$	1.30271e10	1.83084	0.915421	−	0.402497i	$-0.131858\pi$
$653$	1.30271e10	1.83084	0.915421	+	0.402497i	$0.131858\pi$
$654$	−2.21676e9	−0.309882
$655$	−7.75777e9	−1.07868
$656$	6.46895e8	0.0894685
$657$	−2.76988e8	−0.0381050
$658$	−3.61011e9	−0.494004
$659$	8.76958e8	0.119366	0.0596829	−	0.998217i	$-0.480991\pi$
$659$	8.76958e8	0.119366	0.0596829	+	0.998217i	$0.480991\pi$
$660$	−5.85028e9	−0.792087
$661$	−9.86047e9	−1.32798	−0.663991	−	0.747740i	$-0.731139\pi$
$661$	−9.86047e9	−1.32798	−0.663991	+	0.747740i	$0.731139\pi$
$662$	1.87977e10	2.51827
$663$	1.20335e9	0.160359
$664$	7.11218e9	0.942788
$665$	1.12736e9	0.148658
$666$	1.54054e9	0.202075
$667$	−1.73338e9	−0.226179
$668$	−9.48314e9	−1.23093
$669$	−4.71507e9	−0.608831
$670$	8.22910e9	1.05704
$671$	8.18163e8	0.104547
$672$	−7.54737e8	−0.0959408
$673$	5.88788e9	0.744571	0.372286	−	0.928118i	$-0.378574\pi$
$673$	5.88788e9	0.744571	0.372286	+	0.928118i	$0.378574\pi$
$674$	−5.09576e8	−0.0641061
$675$	−2.01419e8	−0.0252080
$676$	8.95732e9	1.11523
$677$	2.79927e9	0.346724	0.173362	−	0.984858i	$-0.444537\pi$
$677$	2.79927e9	0.346724	0.173362	+	0.984858i	$0.444537\pi$
$678$	−1.18044e10	−1.45459
$679$	−2.30756e8	−0.0282884
$680$	2.24764e9	0.274123
$681$	−8.16577e9	−0.990792
$682$	1.51611e9	0.183015
$683$	2.69530e9	0.323694	0.161847	−	0.986816i	$-0.448255\pi$
$683$	2.69530e9	0.323694	0.161847	+	0.986816i	$0.448255\pi$
$684$	2.85714e9	0.341378
$685$	4.93932e9	0.587152
$686$	−7.64177e9	−0.903773
$687$	−4.02989e9	−0.474182
$688$	−3.36090e9	−0.393456
$689$	1.11427e10	1.29784
$690$	8.42065e9	0.975830
$691$	−6.92452e9	−0.798393	−0.399196	−	0.916865i	$-0.630711\pi$
$691$	−6.92452e9	−0.798393	−0.399196	+	0.916865i	$0.630711\pi$
$692$	8.79568e9	1.00902
$693$	−6.69242e8	−0.0763865
$694$	2.22312e10	2.52467
$695$	6.83256e9	0.772035
$696$	−1.44475e9	−0.162428
$697$	3.87217e8	0.0433151
$698$	2.14326e10	2.38551
$699$	−7.58522e9	−0.840036
$700$	−6.02507e8	−0.0663925
$701$	−1.39420e10	−1.52867	−0.764333	−	0.644822i	$-0.776932\pi$
$701$	−1.39420e10	−1.52867	−0.764333	+	0.644822i	$0.776932\pi$
$702$	3.75760e9	0.409949
$703$	1.89294e9	0.205491
$704$	1.08856e10	1.17584
$705$	−5.25811e9	−0.565156
$706$	2.31853e10	2.47968
$707$	−1.40637e9	−0.149669
$708$	1.28062e9	0.135614
$709$	1.10083e10	1.16000	0.579998	−	0.814618i	$-0.303053\pi$
$709$	1.10083e10	1.16000	0.579998	+	0.814618i	$0.303053\pi$
$710$	8.09040e9	0.848332
$711$	−1.23370e9	−0.128726
$712$	−1.54243e10	−1.60149
$713$	−1.40404e9	−0.145066
$714$	5.76828e8	0.0593066
$715$	−9.45408e9	−0.967271
$716$	5.99667e9	0.610541
$717$	2.58477e8	0.0261882
$718$	−1.20793e9	−0.121788
$719$	5.92255e9	0.594234	0.297117	−	0.954841i	$-0.403975\pi$
$719$	5.92255e9	0.594234	0.297117	+	0.954841i	$0.403975\pi$
$720$	1.40357e9	0.140143
$721$	−2.17409e9	−0.216025
$722$	−1.14785e10	−1.13502
$723$	2.06055e9	0.202768
$724$	−9.88498e8	−0.0968034
$725$	2.80764e8	0.0273626
$726$	−3.33580e9	−0.323535
$727$	2.95171e9	0.284907	0.142453	−	0.989802i	$-0.454501\pi$
$727$	2.95171e9	0.284907	0.142453	+	0.989802i	$0.454501\pi$
$728$	5.01024e9	0.481281
$729$	3.87420e8	0.0370370
$730$	−1.87566e9	−0.178453
$731$	−2.01176e9	−0.190487
$732$	−1.41678e9	−0.133510
$733$	1.40788e9	0.132038	0.0660192	−	0.997818i	$-0.478970\pi$
$733$	1.40788e9	0.132038	0.0660192	+	0.997818i	$0.478970\pi$
$734$	2.24026e10	2.09104
$735$	−5.33646e9	−0.495733
$736$	−6.92694e9	−0.640427
$737$	−6.00255e9	−0.552331
$738$	1.20913e9	0.110733
$739$	1.57441e10	1.43504	0.717518	−	0.696540i	$-0.245278\pi$
$739$	1.57441e10	1.43504	0.717518	+	0.696540i	$0.245278\pi$
$740$	6.71186e9	0.608880
$741$	4.61716e9	0.416880
$742$	5.34127e9	0.479989
$743$	−1.31118e10	−1.17274	−0.586369	−	0.810044i	$-0.699443\pi$
$743$	−1.31118e10	−1.17274	−0.586369	+	0.810044i	$0.699443\pi$
$744$	−1.17025e9	−0.104177
$745$	−6.00824e9	−0.532354
$746$	9.65572e9	0.851528
$747$	2.65847e9	0.233351
$748$	−3.67810e9	−0.321342
$749$	1.53136e9	0.133165
$750$	−1.17769e10	−1.01933
$751$	−1.05574e10	−0.909532	−0.454766	−	0.890611i	$-0.650277\pi$
$751$	−1.05574e10	−0.909532	−0.454766	+	0.890611i	$0.650277\pi$
$752$	−5.52276e9	−0.473580
$753$	8.29065e9	0.707630
$754$	−5.23781e9	−0.444990
$755$	1.17654e10	0.994934
$756$	1.15889e9	0.0975478
$757$	7.96333e8	0.0667205	0.0333602	−	0.999443i	$-0.489379\pi$
$757$	7.96333e8	0.0667205	0.0333602	+	0.999443i	$0.489379\pi$
$758$	1.10335e10	0.920175
$759$	−6.14227e9	−0.509897
$760$	8.62405e9	0.712629
$761$	2.66159e9	0.218925	0.109462	−	0.993991i	$-0.465087\pi$
$761$	2.66159e9	0.218925	0.109462	+	0.993991i	$0.465087\pi$
$762$	4.35731e9	0.356760
$763$	−1.10483e9	−0.0900450
$764$	1.42062e9	0.115253
$765$	8.40148e8	0.0678486
$766$	−5.60414e9	−0.450514
$767$	2.06949e9	0.165607
$768$	−1.16711e10	−0.929711
$769$	3.74953e9	0.297327	0.148664	−	0.988888i	$-0.452503\pi$
$769$	3.74953e9	0.297327	0.148664	+	0.988888i	$0.452503\pi$
$770$	−4.53185e9	−0.357732
$771$	9.51665e9	0.747815
$772$	−3.07960e10	−2.40898
$773$	−2.17332e10	−1.69237	−0.846187	−	0.532886i	$-0.821107\pi$
$773$	−2.17332e10	−1.69237	−0.846187	+	0.532886i	$0.821107\pi$
$774$	−6.28198e9	−0.486971
$775$	2.27419e8	0.0175497
$776$	−1.76522e9	−0.135607
$777$	7.67802e8	0.0587186
$778$	−3.16760e10	−2.41158
$779$	1.48573e9	0.112605
$780$	1.63712e10	1.23523
$781$	−5.90137e9	−0.443276
$782$	5.29411e9	0.395885
$783$	−5.40036e8	−0.0402028
$784$	−5.60505e9	−0.415406
$785$	−8.06944e9	−0.595388
$786$	−1.52301e10	−1.11873
$787$	−5.76067e9	−0.421271	−0.210636	−	0.977565i	$-0.567553\pi$
$787$	−5.76067e9	−0.421271	−0.210636	+	0.977565i	$0.567553\pi$
$788$	−2.97350e10	−2.16484
$789$	9.17694e9	0.665163
$790$	−8.35418e9	−0.602850
$791$	−5.88331e9	−0.422672
$792$	−5.11952e9	−0.366177
$793$	−2.28952e9	−0.163038
$794$	6.18701e8	0.0438641
$795$	7.77954e9	0.549122
$796$	−3.85258e10	−2.70742
$797$	−1.81058e9	−0.126682	−0.0633409	−	0.997992i	$-0.520176\pi$
$797$	−1.81058e9	−0.126682	−0.0633409	+	0.997992i	$0.520176\pi$
$798$	2.21325e9	0.154177
$799$	−3.30580e9	−0.229278
$800$	1.12199e9	0.0774773
$801$	−5.76546e9	−0.396388
$802$	4.04918e8	0.0277177
$803$	1.36816e9	0.0932464
$804$	1.03943e10	0.705343
$805$	4.19684e9	0.283555
$806$	−4.24263e9	−0.285405
$807$	1.16383e10	0.779527
$808$	−1.07583e10	−0.717473
$809$	−1.38975e10	−0.922823	−0.461411	−	0.887186i	$-0.652657\pi$
$809$	−1.38975e10	−0.922823	−0.461411	+	0.887186i	$0.652657\pi$
$810$	2.62346e9	0.173451
$811$	2.46372e10	1.62188	0.810940	−	0.585129i	$-0.198956\pi$
$811$	2.46372e10	1.62188	0.810940	+	0.585129i	$0.198956\pi$
$812$	−1.61541e9	−0.105886
$813$	−4.02541e9	−0.262720
$814$	−7.60936e9	−0.494496
$815$	2.22235e10	1.43801
$816$	8.82433e8	0.0568547
$817$	−7.71900e9	−0.495204
$818$	1.46004e10	0.932667
$819$	1.87278e9	0.119122
$820$	5.26798e9	0.333654
$821$	−6.82682e8	−0.0430544	−0.0215272	−	0.999768i	$-0.506853\pi$
$821$	−6.82682e8	−0.0430544	−0.0215272	+	0.999768i	$0.506853\pi$
$822$	9.69691e9	0.608951
$823$	−2.59117e10	−1.62030	−0.810151	−	0.586222i	$-0.800615\pi$
$823$	−2.59117e10	−1.62030	−0.810151	+	0.586222i	$0.800615\pi$
$824$	−1.66312e10	−1.03557
$825$	9.94894e8	0.0616862
$826$	9.92018e8	0.0612476
$827$	−1.70204e10	−1.04641	−0.523203	−	0.852208i	$-0.675263\pi$
$827$	−1.70204e10	−1.04641	−0.523203	+	0.852208i	$0.675263\pi$
$828$	1.06363e10	0.651154
$829$	−1.88349e10	−1.14821	−0.574107	−	0.818780i	$-0.694651\pi$
$829$	−1.88349e10	−1.14821	−0.574107	+	0.818780i	$0.694651\pi$
$830$	1.80021e10	1.09283
$831$	8.69168e9	0.525412
$832$	−3.04619e10	−1.83369
$833$	−3.35506e9	−0.201114
$834$	1.34137e10	0.800698
$835$	−1.06994e10	−0.636001
$836$	−1.41126e10	−0.835383
$837$	−4.37429e8	−0.0257851
$838$	2.50626e10	1.47120
$839$	8.65181e9	0.505755	0.252877	−	0.967498i	$-0.418623\pi$
$839$	8.65181e9	0.505755	0.252877	+	0.967498i	$0.418623\pi$
$840$	3.49803e9	0.203632
$841$	−1.64971e10	−0.956361
$842$	−9.69035e9	−0.559432
$843$	1.64570e10	0.946136
$844$	4.84865e9	0.277602
$845$	1.01062e10	0.576219
$846$	−1.03228e10	−0.586138
$847$	−1.66256e9	−0.0940122
$848$	8.17109e9	0.460145
$849$	−1.18373e10	−0.663858
$850$	−8.57512e8	−0.0478932
$851$	7.04685e9	0.391960
$852$	1.02191e10	0.566077
$853$	1.84081e10	1.01552	0.507758	−	0.861500i	$-0.330474\pi$
$853$	1.84081e10	1.01552	0.507758	+	0.861500i	$0.330474\pi$
$854$	−1.09749e9	−0.0602973
$855$	3.22359e9	0.176384
$856$	1.17145e10	0.638359
$857$	2.23324e10	1.21200	0.605999	−	0.795466i	$-0.292774\pi$
$857$	2.23324e10	1.21200	0.605999	+	0.795466i	$0.292774\pi$
$858$	−1.85603e10	−1.00318
$859$	1.81305e10	0.975966	0.487983	−	0.872853i	$-0.337733\pi$
$859$	1.81305e10	0.975966	0.487983	+	0.872853i	$0.337733\pi$
$860$	−2.73695e10	−1.46731
$861$	6.02630e8	0.0321766
$862$	−2.61490e9	−0.139053
$863$	−9.25181e8	−0.0489992	−0.0244996	−	0.999700i	$-0.507799\pi$
$863$	−9.25181e8	−0.0489992	−0.0244996	+	0.999700i	$0.507799\pi$
$864$	−2.15810e9	−0.113834
$865$	9.92379e9	0.521340
$866$	−2.69700e10	−1.41114
$867$	−1.05509e10	−0.549825
$868$	−1.30849e9	−0.0679125
$869$	6.09378e9	0.315005
$870$	−3.65692e9	−0.188277
$871$	1.67973e10	0.861343
$872$	−8.45167e9	−0.431653
$873$	−6.59824e8	−0.0335643
$874$	2.03131e10	1.02917
$875$	−5.86959e9	−0.296196
$876$	−2.36918e9	−0.119078
$877$	−9.58624e9	−0.479899	−0.239949	−	0.970785i	$-0.577131\pi$
$877$	−9.58624e9	−0.479899	−0.239949	+	0.970785i	$0.577131\pi$
$878$	−1.31676e10	−0.656565
$879$	−1.21118e9	−0.0601518
$880$	−6.93283e9	−0.342942
$881$	1.89685e9	0.0934583	0.0467291	−	0.998908i	$-0.485120\pi$
$881$	1.89685e9	0.0934583	0.0467291	+	0.998908i	$0.485120\pi$
$882$	−1.04766e10	−0.514138
$883$	3.26755e10	1.59720	0.798600	−	0.601862i	$-0.205574\pi$
$883$	3.26755e10	1.59720	0.798600	+	0.601862i	$0.205574\pi$
$884$	1.02927e10	0.501123
$885$	1.44487e9	0.0700692
$886$	4.78578e10	2.31172
$887$	2.36089e10	1.13591	0.567955	−	0.823060i	$-0.307735\pi$
$887$	2.36089e10	1.13591	0.567955	+	0.823060i	$0.307735\pi$
$888$	5.87349e9	0.281482
$889$	2.17168e9	0.103667
$890$	−3.90415e10	−1.85636
$891$	−1.91363e9	−0.0906330
$892$	−4.03297e10	−1.90260
$893$	−1.26841e10	−0.596048
$894$	−1.17954e10	−0.552119
$895$	6.76579e9	0.315455
$896$	−1.10240e10	−0.511991
$897$	1.71883e10	0.795169
$898$	3.63766e10	1.67631
$899$	6.09744e8	0.0279891
$900$	−1.72281e9	−0.0787751
$901$	4.89103e9	0.222774
$902$	−5.97241e9	−0.270974
$903$	−3.13093e9	−0.141503
$904$	−4.50058e10	−2.02618
$905$	−1.11528e9	−0.0500166
$906$	2.30980e10	1.03187
$907$	−1.15848e10	−0.515540	−0.257770	−	0.966206i	$-0.582988\pi$
$907$	−1.15848e10	−0.515540	−0.257770	+	0.966206i	$0.582988\pi$
$908$	−6.98448e10	−3.09623
$909$	−4.02137e9	−0.177583
$910$	1.26818e10	0.557872
$911$	4.24123e10	1.85856	0.929281	−	0.369373i	$-0.120427\pi$
$911$	4.24123e10	1.85856	0.929281	+	0.369373i	$0.120427\pi$
$912$	3.38584e9	0.147803
$913$	−1.31313e10	−0.571031
$914$	4.32564e10	1.87386
$915$	−1.59849e9	−0.0689819
$916$	−3.44691e10	−1.48182
$917$	−7.59067e9	−0.325078
$918$	1.64939e9	0.0703676
$919$	−1.45194e10	−0.617085	−0.308543	−	0.951211i	$-0.599841\pi$
$919$	−1.45194e10	−0.617085	−0.308543	+	0.951211i	$0.599841\pi$
$920$	3.21048e10	1.35929
$921$	2.10274e9	0.0886906
$922$	1.59020e10	0.668180
$923$	1.65142e10	0.691275
$924$	−5.72426e9	−0.238708
$925$	−1.14141e9	−0.0474184
$926$	−2.48431e10	−1.02818
$927$	−6.21660e9	−0.256315
$928$	3.00823e9	0.123564
$929$	1.76962e9	0.0724145	0.0362072	−	0.999344i	$-0.488472\pi$
$929$	1.76962e9	0.0724145	0.0362072	+	0.999344i	$0.488472\pi$
$930$	−2.96210e9	−0.120756
$931$	−1.28731e10	−0.522830
$932$	−6.48791e10	−2.62512
$933$	1.34725e10	0.543079
$934$	3.83270e10	1.53918
$935$	−4.14984e9	−0.166032
$936$	1.43263e10	0.571042
$937$	2.29343e10	0.910747	0.455373	−	0.890301i	$-0.349506\pi$
$937$	2.29343e10	0.910747	0.455373	+	0.890301i	$0.349506\pi$
$938$	8.05185e9	0.318556
$939$	9.66084e9	0.380790
$940$	−4.49746e10	−1.76612
$941$	−1.81317e10	−0.709375	−0.354687	−	0.934985i	$-0.615413\pi$
$941$	−1.81317e10	−0.709375	−0.354687	+	0.934985i	$0.615413\pi$
$942$	−1.58420e10	−0.617493
$943$	5.53091e9	0.214786
$944$	1.51759e9	0.0587155
$945$	1.30753e9	0.0504012
$946$	3.10293e10	1.19166
$947$	−4.46859e10	−1.70980	−0.854901	−	0.518791i	$-0.826382\pi$
$947$	−4.46859e10	−1.70980	−0.854901	+	0.518791i	$0.826382\pi$
$948$	−1.05523e10	−0.402271
$949$	−3.82860e9	−0.145415
$950$	−3.29022e9	−0.124507
$951$	3.52764e9	0.133000
$952$	2.19923e9	0.0826116
$953$	−4.37413e10	−1.63707	−0.818534	−	0.574458i	$-0.805213\pi$
$953$	−4.37413e10	−1.63707	−0.818534	+	0.574458i	$0.805213\pi$
$954$	1.52729e10	0.569509
$955$	1.60283e9	0.0595491
$956$	2.21085e9	0.0818383
$957$	2.66746e9	0.0983799
$958$	3.31133e10	1.21681
$959$	4.83293e9	0.176948
$960$	−2.12678e10	−0.775842
$961$	−2.70187e10	−0.982049
$962$	2.12938e10	0.771151
$963$	4.37877e9	0.158001
$964$	1.76246e10	0.633652
$965$	−3.47458e10	−1.24468
$966$	8.23928e9	0.294082
$967$	−1.87281e10	−0.666042	−0.333021	−	0.942919i	$-0.608068\pi$
$967$	−1.87281e10	−0.666042	−0.333021	+	0.942919i	$0.608068\pi$
$968$	−1.27181e10	−0.450671
$969$	2.02669e9	0.0715572
$970$	−4.46808e9	−0.157188
$971$	4.41287e10	1.54687	0.773434	−	0.633877i	$-0.218537\pi$
$971$	4.41287e10	1.54687	0.773434	+	0.633877i	$0.218537\pi$
$972$	3.31375e9	0.115741
$973$	6.68539e9	0.232666
$974$	−4.52595e9	−0.156947
$975$	−2.78407e9	−0.0961977
$976$	−1.67894e9	−0.0578044
$977$	2.33709e10	0.801762	0.400881	−	0.916130i	$-0.368704\pi$
$977$	2.33709e10	0.801762	0.400881	+	0.916130i	$0.368704\pi$
$978$	4.36294e10	1.49140
$979$	2.84780e10	0.969997
$980$	−4.56447e10	−1.54917
$981$	−3.15916e9	−0.106839
$982$	4.07868e10	1.37445
$983$	1.07329e10	0.360396	0.180198	−	0.983630i	$-0.442326\pi$
$983$	1.07329e10	0.360396	0.180198	+	0.983630i	$0.442326\pi$
$984$	4.60996e9	0.154246
$985$	−3.35487e10	−1.11853
$986$	−2.29912e9	−0.0763823
$987$	−5.14486e9	−0.170319
$988$	3.94922e10	1.30275
$989$	−2.87355e10	−0.944566
$990$	−1.29584e10	−0.424451
$991$	2.64397e10	0.862975	0.431488	−	0.902119i	$-0.357989\pi$
$991$	2.64397e10	0.862975	0.431488	+	0.902119i	$0.357989\pi$
$992$	2.43667e9	0.0792511
$993$	2.67890e10	0.868230
$994$	7.91614e9	0.255659
$995$	−4.34671e10	−1.39888
$996$	2.27388e10	0.729223
$997$	−3.85050e10	−1.23051	−0.615253	−	0.788330i	$-0.710946\pi$
$997$	−3.85050e10	−1.23051	−0.615253	+	0.788330i	$0.710946\pi$
$998$	1.87632e10	0.597516
$999$	2.19546e9	0.0696700

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.d.1.16	✓	18
3.2	odd	2		531.8.a.e.1.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.d.1.16	✓	18	1.1	even	1	trivial
531.8.a.e.1.3		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)

\(f(q)\)	\(=\)	\(q+18.9457 q^{2} +27.0000 q^{3} +230.941 q^{4} +260.561 q^{5} +511.535 q^{6} +254.948 q^{7} +1950.29 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+18.9457 q^{2} +27.0000 q^{3} +230.941 q^{4} +260.561 q^{5} +511.535 q^{6} +254.948 q^{7} +1950.29 q^{8} +729.000 q^{9} +4936.51 q^{10} -3600.84 q^{11} +6235.40 q^{12} +10076.4 q^{13} +4830.18 q^{14} +7035.14 q^{15} +7389.22 q^{16} +4423.02 q^{17} +13811.4 q^{18} +16970.9 q^{19} +60174.1 q^{20} +6883.60 q^{21} -68220.5 q^{22} +63177.4 q^{23} +52657.8 q^{24} -10233.2 q^{25} +190906. q^{26} +19683.0 q^{27} +58877.9 q^{28} -27436.7 q^{29} +133286. q^{30} -22223.7 q^{31} -109643. q^{32} -97222.6 q^{33} +83797.4 q^{34} +66429.5 q^{35} +168356. q^{36} +111541. q^{37} +321525. q^{38} +272064. q^{39} +508168. q^{40} +87545.8 q^{41} +130415. q^{42} -454839. q^{43} -831580. q^{44} +189949. q^{45} +1.19694e6 q^{46} -747408. q^{47} +199509. q^{48} -758544. q^{49} -193875. q^{50} +119422. q^{51} +2.32706e6 q^{52} +1.10581e6 q^{53} +372909. q^{54} -938236. q^{55} +497223. q^{56} +458213. q^{57} -519807. q^{58} +205379. q^{59} +1.62470e6 q^{60} -227215. q^{61} -421044. q^{62} +185857. q^{63} -3.02308e6 q^{64} +2.62552e6 q^{65} -1.84195e6 q^{66} +1.66699e6 q^{67} +1.02146e6 q^{68} +1.70579e6 q^{69} +1.25856e6 q^{70} +1.63889e6 q^{71} +1.42176e6 q^{72} -379956. q^{73} +2.11322e6 q^{74} -276295. q^{75} +3.91926e6 q^{76} -918027. q^{77} +5.15445e6 q^{78} -1.69232e6 q^{79} +1.92534e6 q^{80} +531441. q^{81} +1.65862e6 q^{82} +3.64673e6 q^{83} +1.58970e6 q^{84} +1.15247e6 q^{85} -8.61726e6 q^{86} -740790. q^{87} -7.02267e6 q^{88} -7.90873e6 q^{89} +3.59872e6 q^{90} +2.56897e6 q^{91} +1.45902e7 q^{92} -600040. q^{93} -1.41602e7 q^{94} +4.42194e6 q^{95} -2.96035e6 q^{96} -905108. q^{97} -1.43712e7 q^{98} -2.62501e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more