LMFDB - Embedded newform 177.12.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,12,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, 12, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
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:	$135.996742959$
Analytic rank:	$1$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-88.8229 q^{2} +243.000 q^{3} +5841.51 q^{4} +11395.4 q^{5} -21584.0 q^{6} +23008.9 q^{7} -336951. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-88.8229 q^{2} +243.000 q^{3} +5841.51 q^{4} +11395.4 q^{5} -21584.0 q^{6} +23008.9 q^{7} -336951. q^{8} +59049.0 q^{9} -1.01218e6 q^{10} -240447. q^{11} +1.41949e6 q^{12} -2.32601e6 q^{13} -2.04372e6 q^{14} +2.76909e6 q^{15} +1.79656e7 q^{16} +1.04209e7 q^{17} -5.24491e6 q^{18} -1.05088e7 q^{19} +6.65666e7 q^{20} +5.59117e6 q^{21} +2.13572e7 q^{22} -3.94534e7 q^{23} -8.18791e7 q^{24} +8.10278e7 q^{25} +2.06603e8 q^{26} +1.43489e7 q^{27} +1.34407e8 q^{28} -9.37519e6 q^{29} -2.45959e8 q^{30} -2.38250e7 q^{31} -9.05679e8 q^{32} -5.84287e7 q^{33} -9.25614e8 q^{34} +2.62197e8 q^{35} +3.44936e8 q^{36} +3.44877e8 q^{37} +9.33424e8 q^{38} -5.65220e8 q^{39} -3.83971e9 q^{40} -1.07900e9 q^{41} -4.96624e8 q^{42} +9.52560e8 q^{43} -1.40458e9 q^{44} +6.72889e8 q^{45} +3.50437e9 q^{46} -2.34758e9 q^{47} +4.36563e9 q^{48} -1.44792e9 q^{49} -7.19713e9 q^{50} +2.53228e9 q^{51} -1.35874e10 q^{52} -1.54271e9 q^{53} -1.27451e9 q^{54} -2.74000e9 q^{55} -7.75289e9 q^{56} -2.55364e9 q^{57} +8.32732e8 q^{58} -7.14924e8 q^{59} +1.61757e10 q^{60} +5.48052e9 q^{61} +2.11620e9 q^{62} +1.35865e9 q^{63} +4.36516e10 q^{64} -2.65059e10 q^{65} +5.18981e9 q^{66} -3.63841e9 q^{67} +6.08738e10 q^{68} -9.58717e9 q^{69} -2.32891e10 q^{70} -4.43632e9 q^{71} -1.98966e10 q^{72} -1.08626e10 q^{73} -3.06330e10 q^{74} +1.96898e10 q^{75} -6.13874e10 q^{76} -5.53244e9 q^{77} +5.02045e10 q^{78} -1.30413e10 q^{79} +2.04725e11 q^{80} +3.48678e9 q^{81} +9.58401e10 q^{82} -2.78822e10 q^{83} +3.26609e10 q^{84} +1.18751e11 q^{85} -8.46092e10 q^{86} -2.27817e9 q^{87} +8.10190e10 q^{88} +3.44766e10 q^{89} -5.97680e10 q^{90} -5.35190e10 q^{91} -2.30468e11 q^{92} -5.78946e9 q^{93} +2.08519e11 q^{94} -1.19752e11 q^{95} -2.20080e11 q^{96} +1.26705e11 q^{97} +1.28608e11 q^{98} -1.41982e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) $ 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * 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 $

$2$	−88.8229	−1.96273	−0.981364	−	0.192157i	$-0.938452\pi$
$2$	−88.8229	−1.96273	−0.981364	+	0.192157i	$0.938452\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	5841.51	2.85230
$5$	11395.4	1.63078	0.815391	−	0.578911i	$-0.196522\pi$
$5$	11395.4	1.63078	0.815391	+	0.578911i	$0.196522\pi$
$6$	−21584.0	−1.13318
$7$	23008.9	0.517437	0.258718	−	0.965953i	$-0.416700\pi$
$7$	23008.9	0.517437	0.258718	+	0.965953i	$0.416700\pi$
$8$	−336951.	−3.63557
$9$	59049.0	0.333333
$10$	−1.01218e6	−3.20078
$11$	−240447.	−0.450153	−0.225077	−	0.974341i	$-0.572263\pi$
$11$	−240447.	−0.450153	−0.225077	+	0.974341i	$0.572263\pi$
$12$	1.41949e6	1.64678
$13$	−2.32601e6	−1.73749	−0.868747	−	0.495257i	$-0.835074\pi$
$13$	−2.32601e6	−1.73749	−0.868747	+	0.495257i	$0.835074\pi$
$14$	−2.04372e6	−1.01559
$15$	2.76909e6	0.941532
$16$	1.79656e7	4.28333
$17$	1.04209e7	1.78006	0.890032	−	0.455897i	$-0.150682\pi$
$17$	1.04209e7	1.78006	0.890032	+	0.455897i	$0.150682\pi$
$18$	−5.24491e6	−0.654243
$19$	−1.05088e7	−0.973663	−0.486832	−	0.873496i	$-0.661847\pi$
$19$	−1.05088e7	−0.973663	−0.486832	+	0.873496i	$0.661847\pi$
$20$	6.65666e7	4.65148
$21$	5.59117e6	0.298742
$22$	2.13572e7	0.883528
$23$	−3.94534e7	−1.27815	−0.639074	−	0.769145i	$-0.720682\pi$
$23$	−3.94534e7	−1.27815	−0.639074	+	0.769145i	$0.720682\pi$
$24$	−8.18791e7	−2.09899
$25$	8.10278e7	1.65945
$26$	2.06603e8	3.41023
$27$	1.43489e7	0.192450
$28$	1.34407e8	1.47589
$29$	−9.37519e6	−0.0848773	−0.0424386	−	0.999099i	$-0.513513\pi$
$29$	−9.37519e6	−0.0848773	−0.0424386	+	0.999099i	$0.513513\pi$
$30$	−2.45959e8	−1.84797
$31$	−2.38250e7	−0.149466	−0.0747331	−	0.997204i	$-0.523810\pi$
$31$	−2.38250e7	−0.149466	−0.0747331	+	0.997204i	$0.523810\pi$
$32$	−9.05679e8	−4.77144
$33$	−5.84287e7	−0.259896
$34$	−9.25614e8	−3.49378
$35$	2.62197e8	0.843827
$36$	3.44936e8	0.950767
$37$	3.44877e8	0.817627	0.408813	−	0.912618i	$-0.365943\pi$
$37$	3.44877e8	0.817627	0.408813	+	0.912618i	$0.365943\pi$
$38$	9.33424e8	1.91104
$39$	−5.65220e8	−1.00314
$40$	−3.83971e9	−5.92882
$41$	−1.07900e9	−1.45449	−0.727245	−	0.686378i	$-0.759200\pi$
$41$	−1.07900e9	−1.45449	−0.727245	+	0.686378i	$0.759200\pi$
$42$	−4.96624e8	−0.586350
$43$	9.52560e8	0.988134	0.494067	−	0.869424i	$-0.335510\pi$
$43$	9.52560e8	0.988134	0.494067	+	0.869424i	$0.335510\pi$
$44$	−1.40458e9	−1.28397
$45$	6.72889e8	0.543594
$46$	3.50437e9	2.50866
$47$	−2.34758e9	−1.49308	−0.746538	−	0.665342i	$-0.768286\pi$
$47$	−2.34758e9	−1.49308	−0.746538	+	0.665342i	$0.768286\pi$
$48$	4.36563e9	2.47298
$49$	−1.44792e9	−0.732259
$50$	−7.19713e9	−3.25705
$51$	2.53228e9	1.02772
$52$	−1.35874e10	−4.95586
$53$	−1.54271e9	−0.506718	−0.253359	−	0.967372i	$-0.581535\pi$
$53$	−1.54271e9	−0.506718	−0.253359	+	0.967372i	$0.581535\pi$
$54$	−1.27451e9	−0.377727
$55$	−2.74000e9	−0.734102
$56$	−7.75289e9	−1.88118
$57$	−2.55364e9	−0.562145
$58$	8.32732e8	0.166591
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	1.61757e10	2.68554
$61$	5.48052e9	0.830822	0.415411	−	0.909634i	$-0.363638\pi$
$61$	5.48052e9	0.830822	0.415411	+	0.909634i	$0.363638\pi$
$62$	2.11620e9	0.293361
$63$	1.35865e9	0.172479
$64$	4.36516e10	5.08171
$65$	−2.65059e10	−2.83347
$66$	5.18981e9	0.510105
$67$	−3.63841e9	−0.329230	−0.164615	−	0.986358i	$-0.552638\pi$
$67$	−3.63841e9	−0.329230	−0.164615	+	0.986358i	$0.552638\pi$
$68$	6.08738e10	5.07728
$69$	−9.58717e9	−0.737939
$70$	−2.32891e10	−1.65620
$71$	−4.43632e9	−0.291811	−0.145906	−	0.989299i	$-0.546610\pi$
$71$	−4.43632e9	−0.291811	−0.145906	+	0.989299i	$0.546610\pi$
$72$	−1.98966e10	−1.21186
$73$	−1.08626e10	−0.613277	−0.306638	−	0.951826i	$-0.599204\pi$
$73$	−1.08626e10	−0.613277	−0.306638	+	0.951826i	$0.599204\pi$
$74$	−3.06330e10	−1.60478
$75$	1.96898e10	0.958084
$76$	−6.13874e10	−2.77718
$77$	−5.53244e9	−0.232926
$78$	5.02045e10	1.96890
$79$	−1.30413e10	−0.476840	−0.238420	−	0.971162i	$-0.576629\pi$
$79$	−1.30413e10	−0.476840	−0.238420	+	0.971162i	$0.576629\pi$
$80$	2.04725e11	6.98517
$81$	3.48678e9	0.111111
$82$	9.58401e10	2.85477
$83$	−2.78822e10	−0.776958	−0.388479	−	0.921458i	$-0.626999\pi$
$83$	−2.78822e10	−0.776958	−0.388479	+	0.921458i	$0.626999\pi$
$84$	3.26609e10	0.852103
$85$	1.18751e11	2.90290
$86$	−8.46092e10	−1.93944
$87$	−2.27817e9	−0.0490039
$88$	8.10190e10	1.63656
$89$	3.44766e10	0.654454	0.327227	−	0.944946i	$-0.393886\pi$
$89$	3.44766e10	0.654454	0.327227	+	0.944946i	$0.393886\pi$
$90$	−5.97680e10	−1.06693
$91$	−5.35190e10	−0.899043
$92$	−2.30468e11	−3.64566
$93$	−5.78946e9	−0.0862943
$94$	2.08519e11	2.93050
$95$	−1.19752e11	−1.58783
$96$	−2.20080e11	−2.75479
$97$	1.26705e11	1.49812	0.749062	−	0.662500i	$-0.230504\pi$
$97$	1.26705e11	1.49812	0.749062	+	0.662500i	$0.230504\pi$
$98$	1.28608e11	1.43723
$99$	−1.41982e10	−0.150051
$100$	4.73325e11	4.73325
$101$	−8.52892e10	−0.807471	−0.403735	−	0.914876i	$-0.632288\pi$
$101$	−8.52892e10	−0.807471	−0.403735	+	0.914876i	$0.632288\pi$
$102$	−2.24924e11	−2.01714
$103$	7.54733e10	0.641488	0.320744	−	0.947166i	$-0.396067\pi$
$103$	7.54733e10	0.641488	0.320744	+	0.947166i	$0.396067\pi$
$104$	7.83752e11	6.31677
$105$	6.37138e10	0.487184
$106$	1.37028e11	0.994551
$107$	−1.82905e11	−1.26071	−0.630355	−	0.776307i	$-0.717091\pi$
$107$	−1.82905e11	−1.26071	−0.630355	+	0.776307i	$0.717091\pi$
$108$	8.38194e10	0.548926
$109$	−1.01699e11	−0.633098	−0.316549	−	0.948576i	$-0.602524\pi$
$109$	−1.01699e11	−0.633098	−0.316549	+	0.948576i	$0.602524\pi$
$110$	2.43375e11	1.44084
$111$	8.38052e10	0.472057
$112$	4.13369e11	2.21635
$113$	−2.58972e11	−1.32228	−0.661138	−	0.750264i	$-0.729926\pi$
$113$	−2.58972e11	−1.32228	−0.661138	+	0.750264i	$0.729926\pi$
$114$	2.26822e11	1.10334
$115$	−4.49588e11	−2.08438
$116$	−5.47653e10	−0.242096
$117$	−1.37349e11	−0.579164
$118$	6.35017e10	0.255525
$119$	2.39774e11	0.921071
$120$	−9.33048e11	−3.42300
$121$	−2.27497e11	−0.797362
$122$	−4.86796e11	−1.63068
$123$	−2.62197e11	−0.839751
$124$	−1.39174e11	−0.426323
$125$	3.66930e11	1.07542
$126$	−1.20680e11	−0.338529
$127$	−5.59654e11	−1.50314	−0.751570	−	0.659654i	$-0.770703\pi$
$127$	−5.59654e11	−1.50314	−0.751570	+	0.659654i	$0.770703\pi$
$128$	−2.02243e12	−5.20258
$129$	2.31472e11	0.570499
$130$	2.35433e12	5.56134
$131$	1.30344e11	0.295189	0.147594	−	0.989048i	$-0.452847\pi$
$131$	1.30344e11	0.295189	0.147594	+	0.989048i	$0.452847\pi$
$132$	−3.41312e11	−0.741302
$133$	−2.41797e11	−0.503809
$134$	3.23174e11	0.646189
$135$	1.63512e11	0.313844
$136$	−3.51133e12	−6.47154
$137$	−6.33227e10	−0.112098	−0.0560488	−	0.998428i	$-0.517850\pi$
$137$	−6.33227e10	−0.112098	−0.0560488	+	0.998428i	$0.517850\pi$
$138$	8.51561e11	1.44837
$139$	−1.36820e11	−0.223650	−0.111825	−	0.993728i	$-0.535670\pi$
$139$	−1.36820e11	−0.223650	−0.111825	+	0.993728i	$0.535670\pi$
$140$	1.53163e12	2.40685
$141$	−5.70462e11	−0.862028
$142$	3.94047e11	0.572746
$143$	5.59283e11	0.782138
$144$	1.06085e12	1.42778
$145$	−1.06834e11	−0.138416
$146$	9.64845e11	1.20370
$147$	−3.51844e11	−0.422770
$148$	2.01461e12	2.33212
$149$	1.29089e12	1.44001	0.720006	−	0.693968i	$-0.244139\pi$
$149$	1.29089e12	1.44001	0.720006	+	0.693968i	$0.244139\pi$
$150$	−1.74890e12	−1.88046
$151$	−1.71851e12	−1.78147	−0.890736	−	0.454522i	$-0.849810\pi$
$151$	−1.71851e12	−1.78147	−0.890736	+	0.454522i	$0.849810\pi$
$152$	3.54096e12	3.53982
$153$	6.15343e11	0.593355
$154$	4.91407e11	0.457170
$155$	−2.71496e11	−0.243747
$156$	−3.30174e12	−2.86126
$157$	1.17133e12	0.980011	0.490005	−	0.871719i	$-0.336995\pi$
$157$	1.17133e12	0.980011	0.490005	+	0.871719i	$0.336995\pi$
$158$	1.15837e12	0.935907
$159$	−3.74878e11	−0.292554
$160$	−1.03206e13	−7.78118
$161$	−9.07780e11	−0.661361
$162$	−3.09706e11	−0.218081
$163$	1.09485e11	0.0745289	0.0372644	−	0.999305i	$-0.488136\pi$
$163$	1.09485e11	0.0745289	0.0372644	+	0.999305i	$0.488136\pi$
$164$	−6.30301e12	−4.14865
$165$	−6.65821e11	−0.423834
$166$	2.47658e12	1.52496
$167$	−1.86167e12	−1.10908	−0.554540	−	0.832157i	$-0.687106\pi$
$167$	−1.86167e12	−1.10908	−0.554540	+	0.832157i	$0.687106\pi$
$168$	−1.88395e12	−1.08610
$169$	3.61816e12	2.01888
$170$	−1.05478e13	−5.69760
$171$	−6.20535e11	−0.324554
$172$	5.56439e12	2.81846
$173$	−3.00980e11	−0.147667	−0.0738336	−	0.997271i	$-0.523523\pi$
$173$	−3.00980e11	−0.147667	−0.0738336	+	0.997271i	$0.523523\pi$
$174$	2.02354e11	0.0961813
$175$	1.86436e12	0.858660
$176$	−4.31977e12	−1.92815
$177$	−1.73727e11	−0.0751646
$178$	−3.06231e12	−1.28451
$179$	−1.70328e12	−0.692780	−0.346390	−	0.938091i	$-0.612593\pi$
$179$	−1.70328e12	−0.692780	−0.346390	+	0.938091i	$0.612593\pi$
$180$	3.93069e12	1.55049
$181$	2.80974e12	1.07506	0.537531	−	0.843244i	$-0.319357\pi$
$181$	2.80974e12	1.07506	0.537531	+	0.843244i	$0.319357\pi$
$182$	4.75372e12	1.76458
$183$	1.33177e12	0.479675
$184$	1.32939e13	4.64679
$185$	3.93003e12	1.33337
$186$	5.14237e11	0.169372
$187$	−2.50568e12	−0.801302
$188$	−1.37134e13	−4.25871
$189$	3.30153e11	0.0995808
$190$	1.06368e13	3.11648
$191$	5.15965e12	1.46871	0.734356	−	0.678764i	$-0.237484\pi$
$191$	5.15965e12	1.46871	0.734356	+	0.678764i	$0.237484\pi$
$192$	1.06073e13	2.93393
$193$	−1.39897e11	−0.0376049	−0.0188024	−	0.999823i	$-0.505985\pi$
$193$	−1.39897e11	−0.0376049	−0.0188024	+	0.999823i	$0.505985\pi$
$194$	−1.12543e13	−2.94041
$195$	−6.44093e12	−1.63591
$196$	−8.45802e12	−2.08862
$197$	−5.23182e12	−1.25629	−0.628143	−	0.778098i	$-0.716185\pi$
$197$	−5.23182e12	−1.25629	−0.628143	+	0.778098i	$0.716185\pi$
$198$	1.26112e12	0.294509
$199$	3.51930e12	0.799399	0.399700	−	0.916646i	$-0.369114\pi$
$199$	3.51930e12	0.799399	0.399700	+	0.916646i	$0.369114\pi$
$200$	−2.73024e13	−6.03304
$201$	−8.84132e11	−0.190081
$202$	7.57564e12	1.58485
$203$	−2.15713e11	−0.0439186
$204$	1.47923e13	2.93137
$205$	−1.22957e13	−2.37196
$206$	−6.70376e12	−1.25907
$207$	−2.32968e12	−0.426049
$208$	−4.17881e13	−7.44225
$209$	2.52682e12	0.438298
$210$	−5.65925e12	−0.956209
$211$	6.22111e12	1.02403	0.512017	−	0.858975i	$-0.328898\pi$
$211$	6.22111e12	1.02403	0.512017	+	0.858975i	$0.328898\pi$
$212$	−9.01176e12	−1.44531
$213$	−1.07803e12	−0.168477
$214$	1.62462e13	2.47443
$215$	1.08548e13	1.61143
$216$	−4.83488e12	−0.699665
$217$	−5.48187e11	−0.0773393
$218$	9.03321e12	1.24260
$219$	−2.63960e12	−0.354076
$220$	−1.60058e13	−2.09388
$221$	−2.42391e13	−3.09285
$222$	−7.44382e12	−0.926520
$223$	8.46778e12	1.02824	0.514118	−	0.857720i	$-0.328119\pi$
$223$	8.46778e12	1.02824	0.514118	+	0.857720i	$0.328119\pi$
$224$	−2.08387e13	−2.46892
$225$	4.78461e12	0.553150
$226$	2.30027e13	2.59527
$227$	−7.90846e12	−0.870863	−0.435432	−	0.900222i	$-0.643404\pi$
$227$	−7.90846e12	−0.870863	−0.435432	+	0.900222i	$0.643404\pi$
$228$	−1.49171e13	−1.60341
$229$	−1.50654e13	−1.58083	−0.790413	−	0.612574i	$-0.790134\pi$
$229$	−1.50654e13	−1.58083	−0.790413	+	0.612574i	$0.790134\pi$
$230$	3.99338e13	4.09107
$231$	−1.34438e12	−0.134480
$232$	3.15898e12	0.308577
$233$	6.84441e12	0.652948	0.326474	−	0.945206i	$-0.394139\pi$
$233$	6.84441e12	0.652948	0.326474	+	0.945206i	$0.394139\pi$
$234$	1.21997e13	1.13674
$235$	−2.67517e13	−2.43488
$236$	−4.17624e12	−0.371338
$237$	−3.16904e12	−0.275304
$238$	−2.12974e13	−1.80781
$239$	−1.26859e13	−1.05229	−0.526143	−	0.850396i	$-0.676362\pi$
$239$	−1.26859e13	−1.05229	−0.526143	+	0.850396i	$0.676362\pi$
$240$	4.97483e13	4.03289
$241$	1.47735e13	1.17055	0.585273	−	0.810836i	$-0.300987\pi$
$241$	1.47735e13	1.17055	0.585273	+	0.810836i	$0.300987\pi$
$242$	2.02069e13	1.56501
$243$	8.47289e11	0.0641500
$244$	3.20146e13	2.36976
$245$	−1.64996e13	−1.19416
$246$	2.32891e13	1.64820
$247$	2.44436e13	1.69173
$248$	8.02785e12	0.543394
$249$	−6.77538e12	−0.448577
$250$	−3.25918e13	−2.11076
$251$	9.62805e11	0.0610004	0.0305002	−	0.999535i	$-0.490290\pi$
$251$	9.62805e11	0.0610004	0.0305002	+	0.999535i	$0.490290\pi$
$252$	7.93660e12	0.491962
$253$	9.48646e12	0.575362
$254$	4.97101e13	2.95025
$255$	2.88564e13	1.67599
$256$	9.02398e13	5.12954
$257$	−6.84840e12	−0.381028	−0.190514	−	0.981684i	$-0.561015\pi$
$257$	−6.84840e12	−0.381028	−0.190514	+	0.981684i	$0.561015\pi$
$258$	−2.05600e13	−1.11973
$259$	7.93526e12	0.423070
$260$	−1.54835e14	−8.08192
$261$	−5.53596e11	−0.0282924
$262$	−1.15776e13	−0.579376
$263$	−9.94610e12	−0.487412	−0.243706	−	0.969849i	$-0.578363\pi$
$263$	−9.94610e12	−0.487412	−0.243706	+	0.969849i	$0.578363\pi$
$264$	1.96876e13	0.944869
$265$	−1.75798e13	−0.826347
$266$	2.14771e13	0.988841
$267$	8.37780e12	0.377849
$268$	−2.12538e13	−0.939064
$269$	2.96879e13	1.28511	0.642557	−	0.766238i	$-0.277874\pi$
$269$	2.96879e13	1.28511	0.642557	+	0.766238i	$0.277874\pi$
$270$	−1.45236e13	−0.615991
$271$	1.68982e13	0.702277	0.351139	−	0.936323i	$-0.385795\pi$
$271$	1.68982e13	0.702277	0.351139	+	0.936323i	$0.385795\pi$
$272$	1.87217e14	7.62460
$273$	−1.30051e13	−0.519063
$274$	5.62451e12	0.220017
$275$	−1.94829e13	−0.747007
$276$	−5.60036e13	−2.10483
$277$	2.76547e13	1.01890	0.509449	−	0.860501i	$-0.329849\pi$
$277$	2.76547e13	1.01890	0.509449	+	0.860501i	$0.329849\pi$
$278$	1.21528e13	0.438964
$279$	−1.40684e12	−0.0498220
$280$	−8.83475e13	−3.06779
$281$	−6.84594e12	−0.233103	−0.116552	−	0.993185i	$-0.537184\pi$
$281$	−6.84594e12	−0.233103	−0.116552	+	0.993185i	$0.537184\pi$
$282$	5.06701e13	1.69193
$283$	2.56673e13	0.840533	0.420267	−	0.907401i	$-0.361937\pi$
$283$	2.56673e13	0.840533	0.420267	+	0.907401i	$0.361937\pi$
$284$	−2.59148e13	−0.832333
$285$	−2.90999e13	−0.916736
$286$	−4.96772e13	−1.53512
$287$	−2.48267e13	−0.752607
$288$	−5.34794e13	−1.59048
$289$	7.43231e13	2.16863
$290$	9.48935e12	0.271674
$291$	3.07892e13	0.864943
$292$	−6.34538e13	−1.74925
$293$	−6.78053e13	−1.83439	−0.917195	−	0.398439i	$-0.869552\pi$
$293$	−6.78053e13	−1.83439	−0.917195	+	0.398439i	$0.869552\pi$
$294$	3.12518e13	0.829783
$295$	−8.14687e12	−0.212310
$296$	−1.16207e14	−2.97254
$297$	−3.45016e12	−0.0866320
$298$	−1.14661e14	−2.82635
$299$	9.17689e13	2.22077
$300$	1.15018e14	2.73274
$301$	2.19174e13	0.511297
$302$	1.52643e14	3.49654
$303$	−2.07253e13	−0.466193
$304$	−1.88797e14	−4.17052
$305$	6.24530e13	1.35489
$306$	−5.46566e13	−1.16459
$307$	4.73650e13	0.991280	0.495640	−	0.868528i	$-0.334933\pi$
$307$	4.73650e13	0.991280	0.495640	+	0.868528i	$0.334933\pi$
$308$	−3.23178e13	−0.664375
$309$	1.83400e13	0.370363
$310$	2.41151e13	0.478408
$311$	8.09067e13	1.57689	0.788447	−	0.615103i	$-0.210885\pi$
$311$	8.09067e13	1.57689	0.788447	+	0.615103i	$0.210885\pi$
$312$	1.90452e14	3.64699
$313$	−7.41330e13	−1.39482	−0.697410	−	0.716673i	$-0.745664\pi$
$313$	−7.41330e13	−1.39482	−0.697410	+	0.716673i	$0.745664\pi$
$314$	−1.04041e14	−1.92350
$315$	1.54825e13	0.281276
$316$	−7.61811e13	−1.36009
$317$	−8.33862e13	−1.46308	−0.731540	−	0.681799i	$-0.761198\pi$
$317$	−8.33862e13	−1.46308	−0.731540	+	0.681799i	$0.761198\pi$
$318$	3.32978e13	0.574204
$319$	2.25424e12	0.0382078
$320$	4.97429e14	8.28716
$321$	−4.44459e13	−0.727871
$322$	8.06317e13	1.29807
$323$	−1.09511e14	−1.73318
$324$	2.03681e13	0.316922
$325$	−1.88472e14	−2.88328
$326$	−9.72482e12	−0.146280
$327$	−2.47129e13	−0.365520
$328$	3.63571e14	5.28790
$329$	−5.40153e13	−0.772573
$330$	5.91401e13	0.831870
$331$	−1.37867e14	−1.90725	−0.953624	−	0.301000i	$-0.902680\pi$
$331$	−1.37867e14	−1.90725	−0.953624	+	0.301000i	$0.902680\pi$
$332$	−1.62874e14	−2.21612
$333$	2.03647e13	0.272542
$334$	1.65359e14	2.17682
$335$	−4.14612e13	−0.536903
$336$	1.00449e14	1.27961
$337$	8.41270e13	1.05432	0.527158	−	0.849767i	$-0.323258\pi$
$337$	8.41270e13	1.05432	0.527158	+	0.849767i	$0.323258\pi$
$338$	−3.21376e14	−3.96252
$339$	−6.29303e13	−0.763416
$340$	6.93683e14	8.27994
$341$	5.72865e12	0.0672826
$342$	5.51177e13	0.637012
$343$	−7.88112e13	−0.896335
$344$	−3.20966e14	−3.59242
$345$	−1.09250e14	−1.20342
$346$	2.67339e13	0.289831
$347$	−1.54945e13	−0.165335	−0.0826676	−	0.996577i	$-0.526344\pi$
$347$	−1.54945e13	−0.165335	−0.0826676	+	0.996577i	$0.526344\pi$
$348$	−1.33080e13	−0.139774
$349$	1.51619e14	1.56752	0.783762	−	0.621061i	$-0.213298\pi$
$349$	1.51619e14	1.56752	0.783762	+	0.621061i	$0.213298\pi$
$350$	−1.65598e14	−1.68532
$351$	−3.33757e13	−0.334381
$352$	2.17768e14	2.14788
$353$	1.58801e14	1.54203	0.771014	−	0.636818i	$-0.219750\pi$
$353$	1.58801e14	1.54203	0.771014	+	0.636818i	$0.219750\pi$
$354$	1.54309e13	0.147528
$355$	−5.05538e13	−0.475880
$356$	2.01395e14	1.86670
$357$	5.82650e13	0.531781
$358$	1.51291e14	1.35974
$359$	−1.05114e14	−0.930341	−0.465171	−	0.885221i	$-0.654007\pi$
$359$	−1.05114e14	−0.930341	−0.465171	+	0.885221i	$0.654007\pi$
$360$	−2.26731e14	−1.97627
$361$	−6.05513e12	−0.0519798
$362$	−2.49569e14	−2.11005
$363$	−5.52817e13	−0.460357
$364$	−3.12632e14	−2.56434
$365$	−1.23784e14	−1.00012
$366$	−1.18292e14	−0.941472
$367$	−1.98072e14	−1.55295	−0.776477	−	0.630145i	$-0.782995\pi$
$367$	−1.98072e14	−1.55295	−0.776477	+	0.630145i	$0.782995\pi$
$368$	−7.08802e14	−5.47472
$369$	−6.37140e13	−0.484830
$370$	−3.49077e14	−2.61705
$371$	−3.54961e13	−0.262195
$372$	−3.38192e13	−0.246137
$373$	−1.78362e14	−1.27910	−0.639548	−	0.768751i	$-0.720879\pi$
$373$	−1.78362e14	−1.27910	−0.639548	+	0.768751i	$0.720879\pi$
$374$	2.22561e14	1.57274
$375$	8.91639e13	0.620894
$376$	7.91020e14	5.42818
$377$	2.18068e13	0.147474
$378$	−2.93252e13	−0.195450
$379$	−1.86888e14	−1.22762	−0.613811	−	0.789453i	$-0.710364\pi$
$379$	−1.86888e14	−1.22762	−0.613811	+	0.789453i	$0.710364\pi$
$380$	−6.99536e14	−4.52898
$381$	−1.35996e14	−0.867838
$382$	−4.58295e14	−2.88268
$383$	−1.15566e14	−0.716533	−0.358266	−	0.933619i	$-0.616632\pi$
$383$	−1.15566e14	−0.716533	−0.358266	+	0.933619i	$0.616632\pi$
$384$	−4.91451e14	−3.00371
$385$	−6.30445e13	−0.379851
$386$	1.24261e13	0.0738082
$387$	5.62477e13	0.329378
$388$	7.40147e14	4.27310
$389$	5.04611e13	0.287233	0.143616	−	0.989633i	$-0.454127\pi$
$389$	5.04611e13	0.287233	0.143616	+	0.989633i	$0.454127\pi$
$390$	5.72103e14	3.21084
$391$	−4.11139e14	−2.27519
$392$	4.87877e14	2.66218
$393$	3.16737e13	0.170427
$394$	4.64706e14	2.46575
$395$	−1.48612e14	−0.777622
$396$	−8.29389e13	−0.427991
$397$	−2.93044e14	−1.49137	−0.745685	−	0.666299i	$-0.767877\pi$
$397$	−2.93044e14	−1.49137	−0.745685	+	0.666299i	$0.767877\pi$
$398$	−3.12594e14	−1.56900
$399$	−5.87566e13	−0.290874
$400$	1.45571e15	7.10796
$401$	−2.54837e14	−1.22735	−0.613676	−	0.789558i	$-0.710310\pi$
$401$	−2.54837e14	−1.22735	−0.613676	+	0.789558i	$0.710310\pi$
$402$	7.85312e13	0.373078
$403$	5.54171e13	0.259696
$404$	−4.98218e14	−2.30315
$405$	3.97334e13	0.181198
$406$	1.91603e13	0.0862003
$407$	−8.29248e13	−0.368057
$408$	−8.53254e14	−3.73635
$409$	3.55207e14	1.53463	0.767314	−	0.641271i	$-0.221593\pi$
$409$	3.55207e14	1.53463	0.767314	+	0.641271i	$0.221593\pi$
$410$	1.09214e15	4.65551
$411$	−1.53874e13	−0.0647196
$412$	4.40879e14	1.82972
$413$	−1.64496e13	−0.0673645
$414$	2.06929e14	0.836219
$415$	−3.17730e14	−1.26705
$416$	2.10662e15	8.29034
$417$	−3.32473e13	−0.129124
$418$	−2.24439e14	−0.860259
$419$	1.32237e14	0.500236	0.250118	−	0.968215i	$-0.419531\pi$
$419$	1.32237e14	0.500236	0.250118	+	0.968215i	$0.419531\pi$
$420$	3.72185e14	1.38959
$421$	−3.26349e14	−1.20263	−0.601314	−	0.799013i	$-0.705356\pi$
$421$	−3.26349e14	−1.20263	−0.601314	+	0.799013i	$0.705356\pi$
$422$	−5.52578e14	−2.00990
$423$	−1.38622e14	−0.497692
$424$	5.19818e14	1.84221
$425$	8.44382e14	2.95393
$426$	9.57534e13	0.330675
$427$	1.26101e14	0.429898
$428$	−1.06844e15	−3.59593
$429$	1.35906e14	0.451568
$430$	−9.64158e14	−3.16280
$431$	3.23418e14	1.04747	0.523733	−	0.851883i	$-0.324539\pi$
$431$	3.23418e14	1.04747	0.523733	+	0.851883i	$0.324539\pi$
$432$	2.57786e14	0.824326
$433$	2.43979e14	0.770316	0.385158	−	0.922851i	$-0.374147\pi$
$433$	2.43979e14	0.770316	0.385158	+	0.922851i	$0.374147\pi$
$434$	4.86916e13	0.151796
$435$	−2.59608e13	−0.0799147
$436$	−5.94077e14	−1.80579
$437$	4.14608e14	1.24449
$438$	2.34457e14	0.694954
$439$	−5.42131e14	−1.58690	−0.793449	−	0.608637i	$-0.791717\pi$
$439$	−5.42131e14	−1.58690	−0.793449	+	0.608637i	$0.791717\pi$
$440$	9.23247e14	2.66887
$441$	−8.54980e13	−0.244086
$442$	2.15299e15	6.07042
$443$	1.28812e14	0.358703	0.179352	−	0.983785i	$-0.442600\pi$
$443$	1.28812e14	0.358703	0.179352	+	0.983785i	$0.442600\pi$
$444$	4.89549e14	1.34645
$445$	3.92875e14	1.06727
$446$	−7.52133e14	−2.01815
$447$	3.13687e14	0.831391
$448$	1.00438e15	2.62946
$449$	−6.51432e13	−0.168467	−0.0842334	−	0.996446i	$-0.526844\pi$
$449$	−6.51432e13	−0.168467	−0.0842334	+	0.996446i	$0.526844\pi$
$450$	−4.24983e14	−1.08568
$451$	2.59443e14	0.654744
$452$	−1.51279e15	−3.77153
$453$	−4.17598e14	−1.02853
$454$	7.02453e14	1.70927
$455$	−6.09872e14	−1.46614
$456$	8.60452e14	2.04371
$457$	−4.29850e14	−1.00874	−0.504369	−	0.863488i	$-0.668275\pi$
$457$	−4.29850e14	−1.00874	−0.504369	+	0.863488i	$0.668275\pi$
$458$	1.33815e15	3.10273
$459$	1.49528e14	0.342574
$460$	−2.62628e15	−5.94528
$461$	1.02578e14	0.229456	0.114728	−	0.993397i	$-0.463400\pi$
$461$	1.02578e14	0.229456	0.114728	+	0.993397i	$0.463400\pi$
$462$	1.19412e14	0.263947
$463$	1.89958e14	0.414919	0.207459	−	0.978244i	$-0.433481\pi$
$463$	1.89958e14	0.414919	0.207459	+	0.978244i	$0.433481\pi$
$464$	−1.68431e14	−0.363557
$465$	−6.59735e13	−0.140727
$466$	−6.07941e14	−1.28156
$467$	−7.59612e14	−1.58252	−0.791260	−	0.611480i	$-0.790575\pi$
$467$	−7.59612e14	−1.58252	−0.791260	+	0.611480i	$0.790575\pi$
$468$	−8.02324e14	−1.65195
$469$	−8.37158e13	−0.170356
$470$	2.37616e15	4.77901
$471$	2.84633e14	0.565810
$472$	2.40895e14	0.473310
$473$	−2.29040e14	−0.444811
$474$	2.81484e14	0.540346
$475$	−8.51506e14	−1.61575
$476$	1.40064e15	2.62717
$477$	−9.10954e13	−0.168906
$478$	1.12680e15	2.06535
$479$	3.77438e14	0.683912	0.341956	−	0.939716i	$-0.388911\pi$
$479$	3.77438e14	0.683912	0.341956	+	0.939716i	$0.388911\pi$
$480$	−2.50791e15	−4.49246
$481$	−8.02188e14	−1.42062
$482$	−1.31222e15	−2.29746
$483$	−2.20591e14	−0.381837
$484$	−1.32893e15	−2.27432
$485$	1.44385e15	2.44311
$486$	−7.52587e13	−0.125909
$487$	6.56935e14	1.08671	0.543354	−	0.839503i	$-0.317154\pi$
$487$	6.56935e14	1.08671	0.543354	+	0.839503i	$0.317154\pi$
$488$	−1.84667e15	−3.02051
$489$	2.66050e13	0.0430293
$490$	1.46555e15	2.34380
$491$	−4.51043e14	−0.713297	−0.356648	−	0.934239i	$-0.616081\pi$
$491$	−4.51043e14	−0.713297	−0.356648	+	0.934239i	$0.616081\pi$
$492$	−1.53163e15	−2.39522
$493$	−9.76979e13	−0.151087
$494$	−2.17115e15	−3.32041
$495$	−1.61794e14	−0.244701
$496$	−4.28029e14	−0.640212
$497$	−1.02075e14	−0.150994
$498$	6.01809e14	0.880435
$499$	7.01153e13	0.101452	0.0507259	−	0.998713i	$-0.483847\pi$
$499$	7.01153e13	0.101452	0.0507259	+	0.998713i	$0.483847\pi$
$500$	2.14343e15	3.06742
$501$	−4.52387e14	−0.640328
$502$	−8.55192e13	−0.119727
$503$	−1.06161e15	−1.47009	−0.735043	−	0.678021i	$-0.762838\pi$
$503$	−1.06161e15	−1.47009	−0.735043	+	0.678021i	$0.762838\pi$
$504$	−4.57800e14	−0.627058
$505$	−9.71908e14	−1.31681
$506$	−8.42615e14	−1.12928
$507$	8.79213e14	1.16560
$508$	−3.26923e15	−4.28741
$509$	7.42466e14	0.963227	0.481614	−	0.876384i	$-0.340051\pi$
$509$	7.42466e14	0.963227	0.481614	+	0.876384i	$0.340051\pi$
$510$	−2.56311e15	−3.28951
$511$	−2.49936e14	−0.317332
$512$	−3.87343e15	−4.86531
$513$	−1.50790e14	−0.187382
$514$	6.08295e14	0.747854
$515$	8.60051e14	1.04613
$516$	1.35215e15	1.62724
$517$	5.64469e14	0.672113
$518$	−7.04833e14	−0.830372
$519$	−7.31381e13	−0.0852557
$520$	8.93119e15	10.3013
$521$	1.13056e15	1.29029	0.645145	−	0.764061i	$-0.276797\pi$
$521$	1.13056e15	1.29029	0.645145	+	0.764061i	$0.276797\pi$
$522$	4.91720e13	0.0555303
$523$	6.85320e14	0.765834	0.382917	−	0.923783i	$-0.374920\pi$
$523$	6.85320e14	0.765834	0.382917	+	0.923783i	$0.374920\pi$
$524$	7.61408e14	0.841968
$525$	4.53040e14	0.495748
$526$	8.83442e14	0.956658
$527$	−2.48277e14	−0.266059
$528$	−1.04970e15	−1.11322
$529$	6.03759e14	0.633662
$530$	1.56149e15	1.62190
$531$	−4.22156e13	−0.0433963
$532$	−1.41246e15	−1.43702
$533$	2.50977e15	2.52717
$534$	−7.44141e14	−0.741615
$535$	−2.08428e15	−2.05594
$536$	1.22596e15	1.19694
$537$	−4.13898e14	−0.399977
$538$	−2.63696e15	−2.52233
$539$	3.48147e14	0.329629
$540$	9.55158e14	0.895178
$541$	−1.17281e15	−1.08803	−0.544017	−	0.839074i	$-0.683097\pi$
$541$	−1.17281e15	−1.08803	−0.544017	+	0.839074i	$0.683097\pi$
$542$	−1.50095e15	−1.37838
$543$	6.82766e14	0.620687
$544$	−9.43798e15	−8.49347
$545$	−1.15891e15	−1.03245
$546$	1.15515e15	1.01878
$547$	1.75059e15	1.52846	0.764228	−	0.644946i	$-0.223120\pi$
$547$	1.75059e15	1.52846	0.764228	+	0.644946i	$0.223120\pi$
$548$	−3.69900e14	−0.319736
$549$	3.23620e14	0.276941
$550$	1.73053e15	1.46617
$551$	9.85222e13	0.0826419
$552$	3.23041e15	2.68283
$553$	−3.00067e14	−0.246735
$554$	−2.45638e15	−1.99982
$555$	9.54997e14	0.769822
$556$	−7.99237e14	−0.637917
$557$	5.14429e14	0.406557	0.203279	−	0.979121i	$-0.434840\pi$
$557$	5.14429e14	0.406557	0.203279	+	0.979121i	$0.434840\pi$
$558$	1.24960e14	0.0977871
$559$	−2.21566e15	−1.71688
$560$	4.71052e15	3.61438
$561$	−6.08879e14	−0.462632
$562$	6.08077e14	0.457518
$563$	−5.38082e14	−0.400915	−0.200458	−	0.979702i	$-0.564243\pi$
$563$	−5.38082e14	−0.400915	−0.200458	+	0.979702i	$0.564243\pi$
$564$	−3.33236e15	−2.45877
$565$	−2.95110e15	−2.15634
$566$	−2.27985e15	−1.64974
$567$	8.02272e13	0.0574930
$568$	1.49482e15	1.06090
$569$	−2.65655e14	−0.186724	−0.0933620	−	0.995632i	$-0.529761\pi$
$569$	−2.65655e14	−0.186724	−0.0933620	+	0.995632i	$0.529761\pi$
$570$	2.58473e15	1.79930
$571$	−1.72754e15	−1.19105	−0.595525	−	0.803337i	$-0.703056\pi$
$571$	−1.72754e15	−1.19105	−0.595525	+	0.803337i	$0.703056\pi$
$572$	3.26706e15	2.23089
$573$	1.25380e15	0.847962
$574$	2.20518e15	1.47716
$575$	−3.19682e15	−2.12102
$576$	2.57758e15	1.69390
$577$	−6.32164e13	−0.0411494	−0.0205747	−	0.999788i	$-0.506550\pi$
$577$	−6.32164e13	−0.0411494	−0.0205747	+	0.999788i	$0.506550\pi$
$578$	−6.60160e15	−4.25643
$579$	−3.39951e13	−0.0217112
$580$	−6.24075e14	−0.394805
$581$	−6.41540e14	−0.402027
$582$	−2.73479e15	−1.69765
$583$	3.70940e14	0.228101
$584$	3.66015e15	2.22961
$585$	−1.56515e15	−0.944491
$586$	6.02266e15	3.60041
$587$	5.95482e14	0.352663	0.176331	−	0.984331i	$-0.443577\pi$
$587$	5.95482e14	0.352663	0.176331	+	0.984331i	$0.443577\pi$
$588$	−2.05530e15	−1.20587
$589$	2.50372e14	0.145530
$590$	7.23629e14	0.416706
$591$	−1.27133e15	−0.725317
$592$	6.19592e15	3.50216
$593$	1.66761e15	0.933885	0.466943	−	0.884288i	$-0.345355\pi$
$593$	1.66761e15	0.933885	0.466943	+	0.884288i	$0.345355\pi$
$594$	3.06453e14	0.170035
$595$	2.73232e15	1.50207
$596$	7.54078e15	4.10735
$597$	8.55189e14	0.461533
$598$	−8.15119e15	−4.35877
$599$	−2.02609e15	−1.07352	−0.536761	−	0.843734i	$-0.680353\pi$
$599$	−2.02609e15	−1.07352	−0.536761	+	0.843734i	$0.680353\pi$
$600$	−6.63449e15	−3.48318
$601$	−1.52237e15	−0.791975	−0.395988	−	0.918256i	$-0.629598\pi$
$601$	−1.52237e15	−0.791975	−0.395988	+	0.918256i	$0.629598\pi$
$602$	−1.94677e15	−1.00354
$603$	−2.14844e14	−0.109743
$604$	−1.00387e16	−5.08129
$605$	−2.59242e15	−1.30032
$606$	1.84088e15	0.915011
$607$	2.77705e15	1.36788	0.683938	−	0.729540i	$-0.260266\pi$
$607$	2.77705e15	1.36788	0.683938	+	0.729540i	$0.260266\pi$
$608$	9.51761e15	4.64577
$609$	−5.24183e13	−0.0253564
$610$	−5.54726e15	−2.65928
$611$	5.46049e15	2.59421
$612$	3.59454e15	1.69243
$613$	−4.11696e15	−1.92107	−0.960537	−	0.278153i	$-0.910278\pi$
$613$	−4.11696e15	−1.92107	−0.960537	+	0.278153i	$0.910278\pi$
$614$	−4.20710e15	−1.94561
$615$	−2.98785e15	−1.36945
$616$	1.86416e15	0.846817
$617$	8.99302e14	0.404890	0.202445	−	0.979294i	$-0.435111\pi$
$617$	8.99302e14	0.404890	0.202445	+	0.979294i	$0.435111\pi$
$618$	−1.62901e15	−0.726923
$619$	3.53814e15	1.56486	0.782431	−	0.622737i	$-0.213980\pi$
$619$	3.53814e15	1.56486	0.782431	+	0.622737i	$0.213980\pi$
$620$	−1.58595e15	−0.695239
$621$	−5.66113e14	−0.245980
$622$	−7.18637e15	−3.09501
$623$	7.93269e14	0.338638
$624$	−1.01545e16	−4.29678
$625$	2.24887e14	0.0943244
$626$	6.58471e15	2.73765
$627$	6.14016e14	0.253051
$628$	6.84234e15	2.79529
$629$	3.59393e15	1.45543
$630$	−1.37520e15	−0.552067
$631$	1.08963e15	0.433630	0.216815	−	0.976213i	$-0.430433\pi$
$631$	1.08963e15	0.433630	0.216815	+	0.976213i	$0.430433\pi$
$632$	4.39429e15	1.73358
$633$	1.51173e15	0.591227
$634$	7.40660e15	2.87163
$635$	−6.37750e15	−2.45129
$636$	−2.18986e15	−0.834453
$637$	3.36787e15	1.27230
$638$	−2.00228e14	−0.0749914
$639$	−2.61960e14	−0.0972704
$640$	−2.30465e16	−8.48427
$641$	2.66708e15	0.973457	0.486728	−	0.873553i	$-0.338190\pi$
$641$	2.66708e15	0.973457	0.486728	+	0.873553i	$0.338190\pi$
$642$	3.94782e15	1.42861
$643$	1.95524e14	0.0701518	0.0350759	−	0.999385i	$-0.488833\pi$
$643$	1.95524e14	0.0701518	0.0350759	+	0.999385i	$0.488833\pi$
$644$	−5.30281e15	−1.88640
$645$	2.63772e15	0.930360
$646$	9.72711e15	3.40177
$647$	3.70613e14	0.128513	0.0642565	−	0.997933i	$-0.479532\pi$
$647$	3.70613e14	0.128513	0.0642565	+	0.997933i	$0.479532\pi$
$648$	−1.17488e15	−0.403952
$649$	1.71902e14	0.0586049
$650$	1.67406e16	5.65910
$651$	−1.33209e14	−0.0446518
$652$	6.39561e14	0.212579
$653$	5.59755e14	0.184491	0.0922456	−	0.995736i	$-0.470596\pi$
$653$	5.59755e14	0.184491	0.0922456	+	0.995736i	$0.470596\pi$
$654$	2.19507e15	0.717416
$655$	1.48533e15	0.481389
$656$	−1.93849e16	−6.23006
$657$	−6.41424e14	−0.204426
$658$	4.79780e15	1.51635
$659$	2.30893e15	0.723670	0.361835	−	0.932242i	$-0.382150\pi$
$659$	2.30893e15	0.723670	0.361835	+	0.932242i	$0.382150\pi$
$660$	−3.88940e15	−1.20890
$661$	1.89110e15	0.582916	0.291458	−	0.956584i	$-0.405860\pi$
$661$	1.89110e15	0.582916	0.291458	+	0.956584i	$0.405860\pi$
$662$	1.22458e16	3.74341
$663$	−5.89010e15	−1.78566
$664$	9.39494e15	2.82468
$665$	−2.75538e15	−0.821603
$666$	−1.80885e15	−0.534926
$667$	3.69883e14	0.108486
$668$	−1.08750e16	−3.16343
$669$	2.05767e15	0.593652
$670$	3.68271e15	1.05379
$671$	−1.31778e15	−0.373997
$672$	−5.06380e15	−1.42543
$673$	2.18803e15	0.610900	0.305450	−	0.952208i	$-0.401193\pi$
$673$	2.18803e15	0.610900	0.305450	+	0.952208i	$0.401193\pi$
$674$	−7.47241e15	−2.06934
$675$	1.16266e15	0.319361
$676$	2.11355e16	5.75846
$677$	−4.32264e15	−1.16819	−0.584093	−	0.811687i	$-0.698550\pi$
$677$	−4.32264e15	−1.16819	−0.584093	+	0.811687i	$0.698550\pi$
$678$	5.58965e15	1.49838
$679$	2.91534e15	0.775185
$680$	−4.00132e16	−10.5537
$681$	−1.92176e15	−0.502793
$682$	−5.08835e14	−0.132058
$683$	2.53936e15	0.653747	0.326873	−	0.945068i	$-0.394005\pi$
$683$	2.53936e15	0.653747	0.326873	+	0.945068i	$0.394005\pi$
$684$	−3.62486e15	−0.925727
$685$	−7.21590e14	−0.182807
$686$	7.00024e15	1.75926
$687$	−3.66088e15	−0.912691
$688$	1.71133e16	4.23250
$689$	3.58836e15	0.880420
$690$	9.70391e15	2.36198
$691$	−2.88128e15	−0.695756	−0.347878	−	0.937540i	$-0.613098\pi$
$691$	−2.88128e15	−0.695756	−0.347878	+	0.937540i	$0.613098\pi$
$692$	−1.75818e15	−0.421191
$693$	−3.26685e14	−0.0776419
$694$	1.37627e15	0.324508
$695$	−1.55913e15	−0.364724
$696$	7.67633e14	0.178157
$697$	−1.12442e16	−2.58909
$698$	−1.34673e16	−3.07662
$699$	1.66319e15	0.376980
$700$	1.08907e16	2.44916
$701$	−2.44431e15	−0.545389	−0.272695	−	0.962101i	$-0.587915\pi$
$701$	−2.44431e15	−0.545389	−0.272695	+	0.962101i	$0.587915\pi$
$702$	2.96453e15	0.656298
$703$	−3.62425e15	−0.796093
$704$	−1.04959e16	−2.28755
$705$	−6.50066e15	−1.40578
$706$	−1.41052e16	−3.02658
$707$	−1.96241e15	−0.417815
$708$	−1.01483e15	−0.214392
$709$	7.69783e15	1.61367	0.806834	−	0.590779i	$-0.201179\pi$
$709$	7.69783e15	1.61367	0.806834	+	0.590779i	$0.201179\pi$
$710$	4.49034e15	0.934024
$711$	−7.70077e14	−0.158947
$712$	−1.16169e16	−2.37931
$713$	9.39975e14	0.191040
$714$	−5.17527e15	−1.04374
$715$	6.37327e15	1.27550
$716$	−9.94976e15	−1.97602
$717$	−3.08268e15	−0.607538
$718$	9.33656e15	1.82601
$719$	5.87465e15	1.14018	0.570090	−	0.821583i	$-0.306908\pi$
$719$	5.87465e15	1.14018	0.570090	+	0.821583i	$0.306908\pi$
$720$	1.20888e16	2.32839
$721$	1.73656e15	0.331930
$722$	5.37835e14	0.102022
$723$	3.58995e15	0.675815
$724$	1.64131e16	3.06640
$725$	−7.59652e14	−0.140850
$726$	4.91028e15	0.903556
$727$	−1.37032e15	−0.250255	−0.125128	−	0.992141i	$-0.539934\pi$
$727$	−1.37032e15	−0.250255	−0.125128	+	0.992141i	$0.539934\pi$
$728$	1.80333e16	3.26853
$729$	2.05891e14	0.0370370
$730$	1.09948e16	1.96297
$731$	9.92652e15	1.75894
$732$	7.77954e15	1.36818
$733$	−2.97135e15	−0.518659	−0.259330	−	0.965789i	$-0.583502\pi$
$733$	−2.97135e15	−0.518659	−0.259330	+	0.965789i	$0.583502\pi$
$734$	1.75933e16	3.04803
$735$	−4.00941e15	−0.689446
$736$	3.57321e16	6.09860
$737$	8.74845e14	0.148204
$738$	5.65926e15	0.951590
$739$	4.90213e14	0.0818164	0.0409082	−	0.999163i	$-0.486975\pi$
$739$	4.90213e14	0.0818164	0.0409082	+	0.999163i	$0.486975\pi$
$740$	2.29573e16	3.80318
$741$	5.93979e15	0.976723
$742$	3.15287e15	0.514617
$743$	−1.22261e16	−1.98084	−0.990419	−	0.138094i	$-0.955902\pi$
$743$	−1.22261e16	−1.98084	−0.990419	+	0.138094i	$0.955902\pi$
$744$	1.95077e15	0.313729
$745$	1.47103e16	2.34835
$746$	1.58426e16	2.51052
$747$	−1.64642e15	−0.258986
$748$	−1.46369e16	−2.28555
$749$	−4.20845e15	−0.652338
$750$	−7.91980e15	−1.21865
$751$	1.46728e15	0.224126	0.112063	−	0.993701i	$-0.464254\pi$
$751$	1.46728e15	0.224126	0.112063	+	0.993701i	$0.464254\pi$
$752$	−4.21756e16	−6.39533
$753$	2.33962e14	0.0352186
$754$	−1.93694e15	−0.289451
$755$	−1.95832e16	−2.90519
$756$	1.92859e15	0.284034
$757$	−6.98997e15	−1.02199	−0.510996	−	0.859583i	$-0.670723\pi$
$757$	−6.98997e15	−1.02199	−0.510996	+	0.859583i	$0.670723\pi$
$758$	1.65999e16	2.40949
$759$	2.30521e15	0.332186
$760$	4.03507e16	5.77267
$761$	2.23176e15	0.316980	0.158490	−	0.987361i	$-0.449337\pi$
$761$	2.23176e15	0.316980	0.158490	+	0.987361i	$0.449337\pi$
$762$	1.20796e16	1.70333
$763$	−2.33999e15	−0.327588
$764$	3.01402e16	4.18921
$765$	7.01210e15	0.967633
$766$	1.02649e16	1.40636
$767$	1.66292e15	0.226202
$768$	2.19283e16	2.96154
$769$	−5.22092e15	−0.700087	−0.350044	−	0.936733i	$-0.613833\pi$
$769$	−5.22092e15	−0.700087	−0.350044	+	0.936733i	$0.613833\pi$
$770$	5.59980e15	0.745545
$771$	−1.66416e15	−0.219987
$772$	−8.17212e14	−0.107261
$773$	−1.43588e15	−0.187124	−0.0935622	−	0.995613i	$-0.529825\pi$
$773$	−1.43588e15	−0.187124	−0.0935622	+	0.995613i	$0.529825\pi$
$774$	−4.99609e15	−0.646479
$775$	−1.93048e15	−0.248032
$776$	−4.26933e16	−5.44653
$777$	1.92827e15	0.244260
$778$	−4.48211e15	−0.563760
$779$	1.13390e16	1.41618
$780$	−3.76248e16	−4.66610
$781$	1.06670e15	0.131360
$782$	3.65186e16	4.46557
$783$	−1.34524e14	−0.0163346
$784$	−2.60126e16	−3.13650
$785$	1.33478e16	1.59818
$786$	−2.81335e15	−0.334503
$787$	2.85594e15	0.337200	0.168600	−	0.985685i	$-0.446075\pi$
$787$	2.85594e15	0.337200	0.168600	+	0.985685i	$0.446075\pi$
$788$	−3.05618e16	−3.58331
$789$	−2.41690e15	−0.281408
$790$	1.32001e16	1.52626
$791$	−5.95868e15	−0.684194
$792$	4.78409e15	0.545520
$793$	−1.27478e16	−1.44355
$794$	2.60290e16	2.92715
$795$	−4.27190e15	−0.477092
$796$	2.05580e16	2.28013
$797$	1.02947e15	0.113395	0.0566974	−	0.998391i	$-0.481943\pi$
$797$	1.02947e15	0.113395	0.0566974	+	0.998391i	$0.481943\pi$
$798$	5.21893e15	0.570907
$799$	−2.44639e16	−2.65777
$800$	−7.33852e16	−7.91796
$801$	2.03581e15	0.218151
$802$	2.26354e16	2.40896
$803$	2.61187e15	0.276069
$804$	−5.16467e15	−0.542169
$805$	−1.03446e16	−1.07854
$806$	−4.92231e15	−0.509713
$807$	7.21415e15	0.741960
$808$	2.87383e16	2.93561
$809$	−4.09115e15	−0.415077	−0.207538	−	0.978227i	$-0.566545\pi$
$809$	−4.09115e15	−0.415077	−0.207538	+	0.978227i	$0.566545\pi$
$810$	−3.52924e15	−0.355642
$811$	−4.62714e15	−0.463124	−0.231562	−	0.972820i	$-0.574384\pi$
$811$	−4.62714e15	−0.463124	−0.231562	+	0.972820i	$0.574384\pi$
$812$	−1.26009e15	−0.125269
$813$	4.10626e15	0.405460
$814$	7.36563e15	0.722396
$815$	1.24763e15	0.121540
$816$	4.54938e16	4.40206
$817$	−1.00103e16	−0.962109
$818$	−3.15505e16	−3.01206
$819$	−3.16024e15	−0.299681
$820$	−7.18255e16	−6.76554
$821$	−3.20316e15	−0.299703	−0.149851	−	0.988709i	$-0.547880\pi$
$821$	−3.20316e15	−0.299703	−0.149851	+	0.988709i	$0.547880\pi$
$822$	1.36676e15	0.127027
$823$	5.02055e15	0.463503	0.231751	−	0.972775i	$-0.425554\pi$
$823$	5.02055e15	0.463503	0.231751	+	0.972775i	$0.425554\pi$
$824$	−2.54308e16	−2.33217
$825$	−4.73435e15	−0.431284
$826$	1.46111e15	0.132218
$827$	−5.59661e15	−0.503089	−0.251545	−	0.967846i	$-0.580939\pi$
$827$	−5.59661e15	−0.503089	−0.251545	+	0.967846i	$0.580939\pi$
$828$	−1.36089e16	−1.21522
$829$	1.80300e16	1.59935	0.799677	−	0.600430i	$-0.205004\pi$
$829$	1.80300e16	1.59935	0.799677	+	0.600430i	$0.205004\pi$
$830$	2.82217e16	2.48687
$831$	6.72010e15	0.588261
$832$	−1.01534e17	−8.82944
$833$	−1.50886e16	−1.30347
$834$	2.95312e15	0.253436
$835$	−2.12146e16	−1.80867
$836$	1.47604e16	1.25016
$837$	−3.41862e14	−0.0287648
$838$	−1.17457e16	−0.981827
$839$	1.29962e16	1.07926	0.539628	−	0.841903i	$-0.318565\pi$
$839$	1.29962e16	1.07926	0.539628	+	0.841903i	$0.318565\pi$
$840$	−2.14684e16	−1.77119
$841$	−1.21126e16	−0.992796
$842$	2.89873e16	2.36043
$843$	−1.66356e15	−0.134582
$844$	3.63407e16	2.92086
$845$	4.12305e16	3.29236
$846$	1.23128e16	0.976835
$847$	−5.23446e15	−0.412585
$848$	−2.77156e16	−2.17044
$849$	6.23715e15	0.485282
$850$	−7.50005e16	−5.79776
$851$	−1.36066e16	−1.04505
$852$	−6.29730e15	−0.480548
$853$	8.73059e15	0.661948	0.330974	−	0.943640i	$-0.392623\pi$
$853$	8.73059e15	0.661948	0.330974	+	0.943640i	$0.392623\pi$
$854$	−1.12007e16	−0.843773
$855$	−7.07126e15	−0.529278
$856$	6.16301e16	4.58339
$857$	3.42182e15	0.252850	0.126425	−	0.991976i	$-0.459650\pi$
$857$	3.42182e15	0.252850	0.126425	+	0.991976i	$0.459650\pi$
$858$	−1.20715e16	−0.886304
$859$	1.24428e15	0.0907730	0.0453865	−	0.998970i	$-0.485548\pi$
$859$	1.24428e15	0.0907730	0.0453865	+	0.998970i	$0.485548\pi$
$860$	6.34087e16	4.59629
$861$	−6.03288e15	−0.434518
$862$	−2.87270e16	−2.05589
$863$	−8.73742e15	−0.621332	−0.310666	−	0.950519i	$-0.600552\pi$
$863$	−8.73742e15	−0.621332	−0.310666	+	0.950519i	$0.600552\pi$
$864$	−1.29955e16	−0.918264
$865$	−3.42980e15	−0.240813
$866$	−2.16709e16	−1.51192
$867$	1.80605e16	1.25206
$868$	−3.20224e15	−0.220595
$869$	3.13575e15	0.214651
$870$	2.30591e15	0.156851
$871$	8.46297e15	0.572035
$872$	3.42676e16	2.30167
$873$	7.48178e15	0.499375
$874$	−3.68267e16	−2.44259
$875$	8.44266e15	0.556461
$876$	−1.54193e16	−1.00993
$877$	−5.54899e15	−0.361174	−0.180587	−	0.983559i	$-0.557800\pi$
$877$	−5.54899e15	−0.361174	−0.180587	+	0.983559i	$0.557800\pi$
$878$	4.81536e16	3.11465
$879$	−1.64767e16	−1.05909
$880$	−4.92257e16	−3.14440
$881$	3.77264e14	0.0239485	0.0119742	−	0.999928i	$-0.496188\pi$
$881$	3.77264e14	0.0239485	0.0119742	+	0.999928i	$0.496188\pi$
$882$	7.59418e15	0.479075
$883$	−1.26882e16	−0.795455	−0.397728	−	0.917504i	$-0.630201\pi$
$883$	−1.26882e16	−0.795455	−0.397728	+	0.917504i	$0.630201\pi$
$884$	−1.41593e17	−8.82174
$885$	−1.97969e15	−0.122577
$886$	−1.14414e16	−0.704037
$887$	−1.05798e16	−0.646989	−0.323494	−	0.946230i	$-0.604858\pi$
$887$	−1.05798e16	−0.646989	−0.323494	+	0.946230i	$0.604858\pi$
$888$	−2.82383e16	−1.71619
$889$	−1.28770e16	−0.777780
$890$	−3.48963e16	−2.09476
$891$	−8.38388e14	−0.0500170
$892$	4.94647e16	2.93284
$893$	2.46703e16	1.45375
$894$	−2.78626e16	−1.63180
$895$	−1.94097e16	−1.12977
$896$	−4.65340e16	−2.69201
$897$	2.22999e16	1.28216
$898$	5.78621e15	0.330655
$899$	2.23364e14	0.0126863
$900$	2.79494e16	1.57775
$901$	−1.60764e16	−0.901992
$902$	−2.30445e16	−1.28508
$903$	5.32592e15	0.295197
$904$	8.72611e16	4.80722
$905$	3.20182e16	1.75319
$906$	3.70923e16	2.01873
$907$	2.55994e16	1.38481	0.692404	−	0.721510i	$-0.256552\pi$
$907$	2.55994e16	1.38481	0.692404	+	0.721510i	$0.256552\pi$
$908$	−4.61974e16	−2.48396
$909$	−5.03624e15	−0.269157
$910$	5.41707e16	2.87764
$911$	−2.75529e16	−1.45485	−0.727423	−	0.686189i	$-0.759282\pi$
$911$	−2.75529e16	−1.45485	−0.727423	+	0.686189i	$0.759282\pi$
$912$	−4.58776e16	−2.40785
$913$	6.70420e15	0.349750
$914$	3.81806e16	1.97988
$915$	1.51761e16	0.782246
$916$	−8.80045e16	−4.50899
$917$	2.99908e15	0.152742
$918$	−1.32816e16	−0.672379
$919$	5.89532e15	0.296669	0.148335	−	0.988937i	$-0.452609\pi$
$919$	5.89532e15	0.296669	0.148335	+	0.988937i	$0.452609\pi$
$920$	1.51489e17	7.57790
$921$	1.15097e16	0.572316
$922$	−9.11128e15	−0.450359
$923$	1.03189e16	0.507020
$924$	−7.85323e15	−0.383577
$925$	2.79447e16	1.35681
$926$	−1.68727e16	−0.814373
$927$	4.45662e15	0.213829
$928$	8.49091e15	0.404987
$929$	8.28063e15	0.392624	0.196312	−	0.980541i	$-0.437103\pi$
$929$	8.28063e15	0.392624	0.196312	+	0.980541i	$0.437103\pi$
$930$	5.85996e15	0.276209
$931$	1.52159e16	0.712974
$932$	3.99818e16	1.86241
$933$	1.96603e16	0.910420
$934$	6.74710e16	3.10606
$935$	−2.85533e16	−1.30675
$936$	4.62798e16	2.10559
$937$	−2.43077e16	−1.09945	−0.549725	−	0.835346i	$-0.685268\pi$
$937$	−2.43077e16	−1.09945	−0.549725	+	0.835346i	$0.685268\pi$
$938$	7.43589e15	0.334362
$939$	−1.80143e16	−0.805299
$940$	−1.56270e17	−6.94502
$941$	1.84021e16	0.813063	0.406531	−	0.913637i	$-0.366738\pi$
$941$	1.84021e16	0.813063	0.406531	+	0.913637i	$0.366738\pi$
$942$	−2.52819e16	−1.11053
$943$	4.25703e16	1.85905
$944$	−1.28440e16	−0.557641
$945$	3.76224e15	0.162395
$946$	2.03440e16	0.873044
$947$	−3.43633e16	−1.46612	−0.733061	−	0.680163i	$-0.761909\pi$
$947$	−3.43633e16	−1.46612	−0.733061	+	0.680163i	$0.761909\pi$
$948$	−1.85120e16	−0.785249
$949$	2.52664e16	1.06556
$950$	7.56333e16	3.17127
$951$	−2.02628e16	−0.844709
$952$	−8.07920e16	−3.34861
$953$	−8.61832e15	−0.355150	−0.177575	−	0.984107i	$-0.556825\pi$
$953$	−8.61832e15	−0.355150	−0.177575	+	0.984107i	$0.556825\pi$
$954$	8.09136e15	0.331517
$955$	5.87965e16	2.39515
$956$	−7.41051e16	−3.00144
$957$	5.47781e14	0.0220593
$958$	−3.35251e16	−1.34233
$959$	−1.45699e15	−0.0580034
$960$	1.20875e17	4.78460
$961$	−2.48408e16	−0.977660
$962$	7.12527e16	2.78829
$963$	−1.08004e16	−0.420237
$964$	8.62994e16	3.33875
$965$	−1.59419e15	−0.0613254
$966$	1.95935e16	0.749442
$967$	−4.27912e15	−0.162745	−0.0813727	−	0.996684i	$-0.525930\pi$
$967$	−4.27912e15	−0.162745	−0.0813727	+	0.996684i	$0.525930\pi$
$968$	7.66553e16	2.89886
$969$	−2.66112e16	−1.00065
$970$	−1.28247e17	−4.79517
$971$	−1.14410e16	−0.425362	−0.212681	−	0.977122i	$-0.568220\pi$
$971$	−1.14410e16	−0.425362	−0.212681	+	0.977122i	$0.568220\pi$
$972$	4.94945e15	0.182975
$973$	−3.14809e15	−0.115725
$974$	−5.83509e16	−2.13291
$975$	−4.57986e16	−1.66466
$976$	9.84607e16	3.55868
$977$	−1.57282e16	−0.565273	−0.282636	−	0.959227i	$-0.591209\pi$
$977$	−1.57282e16	−0.565273	−0.282636	+	0.959227i	$0.591209\pi$
$978$	−2.36313e15	−0.0844548
$979$	−8.28980e15	−0.294604
$980$	−9.63828e16	−3.40609
$981$	−6.00523e15	−0.211033
$982$	4.00630e16	1.40001
$983$	4.00337e16	1.39117	0.695587	−	0.718442i	$-0.255145\pi$
$983$	4.00337e16	1.39117	0.695587	+	0.718442i	$0.255145\pi$
$984$	8.83477e16	3.05297
$985$	−5.96189e16	−2.04873
$986$	8.67781e15	0.296543
$987$	−1.31257e16	−0.446045
$988$	1.42788e17	4.82533
$989$	−3.75817e16	−1.26298
$990$	1.43711e16	0.480281
$991$	2.40351e15	0.0798806	0.0399403	−	0.999202i	$-0.487283\pi$
$991$	2.40351e15	0.0798806	0.0399403	+	0.999202i	$0.487283\pi$
$992$	2.15778e16	0.713168
$993$	−3.35018e16	−1.10115
$994$	9.06660e15	0.296360
$995$	4.01039e16	1.30365
$996$	−3.95785e16	−1.27948
$997$	−3.36628e16	−1.08225	−0.541124	−	0.840943i	$-0.682001\pi$
$997$	−3.36628e16	−1.08225	−0.541124	+	0.840943i	$0.682001\pi$
$998$	−6.22785e15	−0.199122
$999$	4.94861e15	0.157352

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.b.1.1	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.b.1.1	✓	27	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-88.8229 q^{2} +243.000 q^{3} +5841.51 q^{4} +11395.4 q^{5} -21584.0 q^{6} +23008.9 q^{7} -336951. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-88.8229 q^{2} +243.000 q^{3} +5841.51 q^{4} +11395.4 q^{5} -21584.0 q^{6} +23008.9 q^{7} -336951. q^{8} +59049.0 q^{9} -1.01218e6 q^{10} -240447. q^{11} +1.41949e6 q^{12} -2.32601e6 q^{13} -2.04372e6 q^{14} +2.76909e6 q^{15} +1.79656e7 q^{16} +1.04209e7 q^{17} -5.24491e6 q^{18} -1.05088e7 q^{19} +6.65666e7 q^{20} +5.59117e6 q^{21} +2.13572e7 q^{22} -3.94534e7 q^{23} -8.18791e7 q^{24} +8.10278e7 q^{25} +2.06603e8 q^{26} +1.43489e7 q^{27} +1.34407e8 q^{28} -9.37519e6 q^{29} -2.45959e8 q^{30} -2.38250e7 q^{31} -9.05679e8 q^{32} -5.84287e7 q^{33} -9.25614e8 q^{34} +2.62197e8 q^{35} +3.44936e8 q^{36} +3.44877e8 q^{37} +9.33424e8 q^{38} -5.65220e8 q^{39} -3.83971e9 q^{40} -1.07900e9 q^{41} -4.96624e8 q^{42} +9.52560e8 q^{43} -1.40458e9 q^{44} +6.72889e8 q^{45} +3.50437e9 q^{46} -2.34758e9 q^{47} +4.36563e9 q^{48} -1.44792e9 q^{49} -7.19713e9 q^{50} +2.53228e9 q^{51} -1.35874e10 q^{52} -1.54271e9 q^{53} -1.27451e9 q^{54} -2.74000e9 q^{55} -7.75289e9 q^{56} -2.55364e9 q^{57} +8.32732e8 q^{58} -7.14924e8 q^{59} +1.61757e10 q^{60} +5.48052e9 q^{61} +2.11620e9 q^{62} +1.35865e9 q^{63} +4.36516e10 q^{64} -2.65059e10 q^{65} +5.18981e9 q^{66} -3.63841e9 q^{67} +6.08738e10 q^{68} -9.58717e9 q^{69} -2.32891e10 q^{70} -4.43632e9 q^{71} -1.98966e10 q^{72} -1.08626e10 q^{73} -3.06330e10 q^{74} +1.96898e10 q^{75} -6.13874e10 q^{76} -5.53244e9 q^{77} +5.02045e10 q^{78} -1.30413e10 q^{79} +2.04725e11 q^{80} +3.48678e9 q^{81} +9.58401e10 q^{82} -2.78822e10 q^{83} +3.26609e10 q^{84} +1.18751e11 q^{85} -8.46092e10 q^{86} -2.27817e9 q^{87} +8.10190e10 q^{88} +3.44766e10 q^{89} -5.97680e10 q^{90} -5.35190e10 q^{91} -2.30468e11 q^{92} -5.78946e9 q^{93} +2.08519e11 q^{94} -1.19752e11 q^{95} -2.20080e11 q^{96} +1.26705e11 q^{97} +1.28608e11 q^{98} -1.41982e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * q^99

Introduction

L-functions

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