LMFDB - Embedded newform 177.12.a.b.1.10

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			1.10
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)

$f(q)$	$=$	$q-45.6492 q^{2} +243.000 q^{3} +35.8459 q^{4} -2292.40 q^{5} -11092.7 q^{6} +55379.8 q^{7} +91853.1 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-45.6492 q^{2} +243.000 q^{3} +35.8459 q^{4} -2292.40 q^{5} -11092.7 q^{6} +55379.8 q^{7} +91853.1 q^{8} +59049.0 q^{9} +104646. q^{10} +946706. q^{11} +8710.56 q^{12} +853793. q^{13} -2.52804e6 q^{14} -557052. q^{15} -4.26643e6 q^{16} -1.00374e7 q^{17} -2.69554e6 q^{18} -6.49611e6 q^{19} -82173.0 q^{20} +1.34573e7 q^{21} -4.32163e7 q^{22} -3.83400e7 q^{23} +2.23203e7 q^{24} -4.35730e7 q^{25} -3.89749e7 q^{26} +1.43489e7 q^{27} +1.98514e6 q^{28} +8.96507e7 q^{29} +2.54290e7 q^{30} -1.71742e8 q^{31} +6.64378e6 q^{32} +2.30049e8 q^{33} +4.58198e8 q^{34} -1.26952e8 q^{35} +2.11667e6 q^{36} +4.13912e8 q^{37} +2.96542e8 q^{38} +2.07472e8 q^{39} -2.10564e8 q^{40} -1.94788e8 q^{41} -6.14314e8 q^{42} -4.76784e8 q^{43} +3.39355e7 q^{44} -1.35364e8 q^{45} +1.75019e9 q^{46} -1.06462e9 q^{47} -1.03674e9 q^{48} +1.08959e9 q^{49} +1.98907e9 q^{50} -2.43909e9 q^{51} +3.06050e7 q^{52} -3.74273e8 q^{53} -6.55016e8 q^{54} -2.17022e9 q^{55} +5.08681e9 q^{56} -1.57856e9 q^{57} -4.09248e9 q^{58} -7.14924e8 q^{59} -1.99680e7 q^{60} +8.62006e9 q^{61} +7.83988e9 q^{62} +3.27012e9 q^{63} +8.43437e9 q^{64} -1.95723e9 q^{65} -1.05016e10 q^{66} -2.01539e10 q^{67} -3.59799e8 q^{68} -9.31661e9 q^{69} +5.79527e9 q^{70} -8.96176e9 q^{71} +5.42384e9 q^{72} -1.78559e10 q^{73} -1.88948e10 q^{74} -1.05883e10 q^{75} -2.32859e8 q^{76} +5.24283e10 q^{77} -9.47091e9 q^{78} -1.08063e10 q^{79} +9.78035e9 q^{80} +3.48678e9 q^{81} +8.89193e9 q^{82} -5.12155e10 q^{83} +4.82389e8 q^{84} +2.30097e10 q^{85} +2.17648e10 q^{86} +2.17851e10 q^{87} +8.69579e10 q^{88} +2.09557e9 q^{89} +6.17924e9 q^{90} +4.72829e10 q^{91} -1.37433e9 q^{92} -4.17333e10 q^{93} +4.85992e10 q^{94} +1.48917e10 q^{95} +1.61444e9 q^{96} -8.78726e10 q^{97} -4.97390e10 q^{98} +5.59020e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−45.6492	−1.00871	−0.504357	−	0.863495i	$-0.668270\pi$
$2$	−45.6492	−1.00871	−0.504357	+	0.863495i	$0.668270\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	35.8459	0.0175029
$5$	−2292.40	−0.328061	−0.164030	−	0.986455i	$-0.552450\pi$
$5$	−2292.40	−0.328061	−0.164030	+	0.986455i	$0.552450\pi$
$6$	−11092.7	−0.582381
$7$	55379.8	1.24541	0.622704	−	0.782457i	$-0.286034\pi$
$7$	55379.8	1.24541	0.622704	+	0.782457i	$0.286034\pi$
$8$	91853.1	0.991058
$9$	59049.0	0.333333
$10$	104646.	0.330919
$11$	946706.	1.77237	0.886187	−	0.463328i	$-0.153345\pi$
$11$	946706.	1.77237	0.886187	+	0.463328i	$0.153345\pi$
$12$	8710.56	0.0101053
$13$	853793.	0.637770	0.318885	−	0.947793i	$-0.396692\pi$
$13$	853793.	0.637770	0.318885	+	0.947793i	$0.396692\pi$
$14$	−2.52804e6	−1.25626
$15$	−557052.	−0.189406
$16$	−4.26643e6	−1.01720
$17$	−1.00374e7	−1.71456	−0.857278	−	0.514854i	$-0.827846\pi$
$17$	−1.00374e7	−1.71456	−0.857278	+	0.514854i	$0.827846\pi$
$18$	−2.69554e6	−0.336238
$19$	−6.49611e6	−0.601878	−0.300939	−	0.953643i	$-0.597300\pi$
$19$	−6.49611e6	−0.601878	−0.300939	+	0.953643i	$0.597300\pi$
$20$	−82173.0	−0.00574201
$21$	1.34573e7	0.719037
$22$	−4.32163e7	−1.78782
$23$	−3.83400e7	−1.24208	−0.621039	−	0.783780i	$-0.713289\pi$
$23$	−3.83400e7	−1.24208	−0.621039	+	0.783780i	$0.713289\pi$
$24$	2.23203e7	0.572188
$25$	−4.35730e7	−0.892376
$26$	−3.89749e7	−0.643327
$27$	1.43489e7	0.192450
$28$	1.98514e6	0.0217983
$29$	8.96507e7	0.811642	0.405821	−	0.913953i	$-0.366986\pi$
$29$	8.96507e7	0.811642	0.405821	+	0.913953i	$0.366986\pi$
$30$	2.54290e7	0.191056
$31$	−1.71742e8	−1.07743	−0.538713	−	0.842489i	$-0.681089\pi$
$31$	−1.71742e8	−1.07743	−0.538713	+	0.842489i	$0.681089\pi$
$32$	6.64378e6	0.0350018
$33$	2.30049e8	1.02328
$34$	4.58198e8	1.72950
$35$	−1.26952e8	−0.408570
$36$	2.11667e6	0.00583430
$37$	4.13912e8	0.981294	0.490647	−	0.871359i	$-0.336761\pi$
$37$	4.13912e8	0.981294	0.490647	+	0.871359i	$0.336761\pi$
$38$	2.96542e8	0.607123
$39$	2.07472e8	0.368217
$40$	−2.10564e8	−0.325127
$41$	−1.94788e8	−0.262574	−0.131287	−	0.991344i	$-0.541911\pi$
$41$	−1.94788e8	−0.262574	−0.131287	+	0.991344i	$0.541911\pi$
$42$	−6.14314e8	−0.725303
$43$	−4.76784e8	−0.494590	−0.247295	−	0.968940i	$-0.579542\pi$
$43$	−4.76784e8	−0.494590	−0.247295	+	0.968940i	$0.579542\pi$
$44$	3.39355e7	0.0310216
$45$	−1.35364e8	−0.109354
$46$	1.75019e9	1.25290
$47$	−1.06462e9	−0.677108	−0.338554	−	0.940947i	$-0.609938\pi$
$47$	−1.06462e9	−0.677108	−0.338554	+	0.940947i	$0.609938\pi$
$48$	−1.03674e9	−0.587279
$49$	1.08959e9	0.551043
$50$	1.98907e9	0.900152
$51$	−2.43909e9	−0.989899
$52$	3.06050e7	0.0111628
$53$	−3.74273e8	−0.122934	−0.0614669	−	0.998109i	$-0.519578\pi$
$53$	−3.74273e8	−0.122934	−0.0614669	+	0.998109i	$0.519578\pi$
$54$	−6.55016e8	−0.194127
$55$	−2.17022e9	−0.581446
$56$	5.08681e9	1.23427
$57$	−1.57856e9	−0.347495
$58$	−4.09248e9	−0.818714
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	−1.99680e7	−0.00331515
$61$	8.62006e9	1.30676	0.653381	−	0.757029i	$-0.273350\pi$
$61$	8.62006e9	1.30676	0.653381	+	0.757029i	$0.273350\pi$
$62$	7.83988e9	1.08681
$63$	3.27012e9	0.415136
$64$	8.43437e9	0.981890
$65$	−1.95723e9	−0.209227
$66$	−1.05016e10	−1.03220
$67$	−2.01539e10	−1.82367	−0.911837	−	0.410552i	$-0.865336\pi$
$67$	−2.01539e10	−1.82367	−0.911837	+	0.410552i	$0.865336\pi$
$68$	−3.59799e8	−0.0300097
$69$	−9.31661e9	−0.717114
$70$	5.79527e9	0.412130
$71$	−8.96176e9	−0.589485	−0.294742	−	0.955577i	$-0.595234\pi$
$71$	−8.96176e9	−0.589485	−0.294742	+	0.955577i	$0.595234\pi$
$72$	5.42384e9	0.330353
$73$	−1.78559e10	−1.00810	−0.504052	−	0.863673i	$-0.668158\pi$
$73$	−1.78559e10	−1.00810	−0.504052	+	0.863673i	$0.668158\pi$
$74$	−1.88948e10	−0.989844
$75$	−1.05883e10	−0.515214
$76$	−2.32859e8	−0.0105346
$77$	5.24283e10	2.20733
$78$	−9.47091e9	−0.371425
$79$	−1.08063e10	−0.395120	−0.197560	−	0.980291i	$-0.563302\pi$
$79$	−1.08063e10	−0.395120	−0.197560	+	0.980291i	$0.563302\pi$
$80$	9.78035e9	0.333702
$81$	3.48678e9	0.111111
$82$	8.89193e9	0.264862
$83$	−5.12155e10	−1.42716	−0.713579	−	0.700574i	$-0.752927\pi$
$83$	−5.12155e10	−1.42716	−0.713579	+	0.700574i	$0.752927\pi$
$84$	4.82389e8	0.0125852
$85$	2.30097e10	0.562479
$86$	2.17648e10	0.498900
$87$	2.17851e10	0.468602
$88$	8.69579e10	1.75652
$89$	2.09557e9	0.0397792	0.0198896	−	0.999802i	$-0.493669\pi$
$89$	2.09557e9	0.0397792	0.0198896	+	0.999802i	$0.493669\pi$
$90$	6.17924e9	0.110306
$91$	4.72829e10	0.794285
$92$	−1.37433e9	−0.0217399
$93$	−4.17333e10	−0.622052
$94$	4.85992e10	0.683008
$95$	1.48917e10	0.197453
$96$	1.61444e9	0.0202083
$97$	−8.78726e10	−1.03898	−0.519492	−	0.854475i	$-0.673879\pi$
$97$	−8.78726e10	−1.03898	−0.519492	+	0.854475i	$0.673879\pi$
$98$	−4.97390e10	−0.555845
$99$	5.59020e10	0.590791
$100$	−1.56192e9	−0.0156192
$101$	7.75387e10	0.734093	0.367046	−	0.930203i	$-0.380369\pi$
$101$	7.75387e10	0.734093	0.367046	+	0.930203i	$0.380369\pi$
$102$	1.11342e11	0.998525
$103$	2.15361e11	1.83047	0.915236	−	0.402918i	$-0.132004\pi$
$103$	2.15361e11	1.83047	0.915236	+	0.402918i	$0.132004\pi$
$104$	7.84236e10	0.632067
$105$	−3.08494e10	−0.235888
$106$	1.70853e10	0.124005
$107$	−2.57466e11	−1.77463	−0.887317	−	0.461160i	$-0.847434\pi$
$107$	−2.57466e11	−1.77463	−0.887317	+	0.461160i	$0.847434\pi$
$108$	5.14350e8	0.00336843
$109$	1.97013e11	1.22645	0.613223	−	0.789910i	$-0.289873\pi$
$109$	1.97013e11	1.22645	0.613223	+	0.789910i	$0.289873\pi$
$110$	9.90689e10	0.586513
$111$	1.00581e11	0.566550
$112$	−2.36274e11	−1.26683
$113$	1.72211e11	0.879286	0.439643	−	0.898173i	$-0.355105\pi$
$113$	1.72211e11	0.879286	0.439643	+	0.898173i	$0.355105\pi$
$114$	7.20597e10	0.350523
$115$	8.78903e10	0.407477
$116$	3.21361e9	0.0142061
$117$	5.04156e10	0.212590
$118$	3.26357e10	0.131323
$119$	−5.55868e11	−2.13532
$120$	−5.11670e10	−0.187712
$121$	6.10940e11	2.14131
$122$	−3.93499e11	−1.31815
$123$	−4.73336e10	−0.151597
$124$	−6.15625e9	−0.0188581
$125$	2.11820e11	0.620815
$126$	−1.49278e11	−0.418754
$127$	−3.52150e11	−0.945817	−0.472909	−	0.881112i	$-0.656796\pi$
$127$	−3.52150e11	−0.945817	−0.472909	+	0.881112i	$0.656796\pi$
$128$	−3.98628e11	−1.02545
$129$	−1.15859e11	−0.285552
$130$	8.93460e10	0.211051
$131$	9.90148e9	0.0224237	0.0112119	−	0.999937i	$-0.496431\pi$
$131$	9.90148e9	0.0224237	0.0112119	+	0.999937i	$0.496431\pi$
$132$	8.24633e9	0.0179104
$133$	−3.59753e11	−0.749585
$134$	9.20008e11	1.83956
$135$	−3.28934e10	−0.0631354
$136$	−9.21966e11	−1.69922
$137$	−9.04183e11	−1.60064	−0.800319	−	0.599575i	$-0.795336\pi$
$137$	−9.04183e11	−1.60064	−0.800319	+	0.599575i	$0.795336\pi$
$138$	4.25295e11	0.723362
$139$	−7.81431e11	−1.27735	−0.638674	−	0.769477i	$-0.720517\pi$
$139$	−7.81431e11	−1.27735	−0.638674	+	0.769477i	$0.720517\pi$
$140$	−4.55072e9	−0.00715115
$141$	−2.58704e11	−0.390929
$142$	4.09097e11	0.594621
$143$	8.08291e11	1.13037
$144$	−2.51929e11	−0.339066
$145$	−2.05515e11	−0.266268
$146$	8.15105e11	1.01689
$147$	2.64771e11	0.318145
$148$	1.48371e10	0.0171755
$149$	−5.21209e10	−0.0581417	−0.0290708	−	0.999577i	$-0.509255\pi$
$149$	−5.21209e10	−0.0581417	−0.0290708	+	0.999577i	$0.509255\pi$
$150$	4.83345e11	0.519703
$151$	1.29241e12	1.33976	0.669881	−	0.742469i	$-0.266345\pi$
$151$	1.29241e12	1.33976	0.669881	+	0.742469i	$0.266345\pi$
$152$	−5.96688e11	−0.596497
$153$	−5.92698e11	−0.571519
$154$	−2.39331e12	−2.22656
$155$	3.93701e11	0.353461
$156$	7.43701e9	0.00644486
$157$	−3.75275e10	−0.0313979	−0.0156990	−	0.999877i	$-0.504997\pi$
$157$	−3.75275e10	−0.0313979	−0.0156990	+	0.999877i	$0.504997\pi$
$158$	4.93299e11	0.398562
$159$	−9.09484e10	−0.0709759
$160$	−1.52302e10	−0.0114827
$161$	−2.12326e12	−1.54689
$162$	−1.59169e11	−0.112079
$163$	−1.37415e12	−0.935412	−0.467706	−	0.883884i	$-0.654919\pi$
$163$	−1.37415e12	−0.935412	−0.467706	+	0.883884i	$0.654919\pi$
$164$	−6.98237e9	−0.00459581
$165$	−5.27364e11	−0.335698
$166$	2.33795e12	1.43959
$167$	1.14860e12	0.684272	0.342136	−	0.939651i	$-0.388850\pi$
$167$	1.14860e12	0.684272	0.342136	+	0.939651i	$0.388850\pi$
$168$	1.23609e12	0.712608
$169$	−1.06320e12	−0.593249
$170$	−1.05037e12	−0.567380
$171$	−3.83589e11	−0.200626
$172$	−1.70908e10	−0.00865676
$173$	−3.02808e12	−1.48564	−0.742819	−	0.669492i	$-0.766512\pi$
$173$	−3.02808e12	−1.48564	−0.742819	+	0.669492i	$0.766512\pi$
$174$	−9.94472e11	−0.472685
$175$	−2.41307e12	−1.11137
$176$	−4.03905e12	−1.80285
$177$	−1.73727e11	−0.0751646
$178$	−9.56608e10	−0.0401258
$179$	−3.88051e12	−1.57833	−0.789164	−	0.614183i	$-0.789486\pi$
$179$	−3.88051e12	−1.57833	−0.789164	+	0.614183i	$0.789486\pi$
$180$	−4.85223e9	−0.00191400
$181$	1.77990e12	0.681027	0.340514	−	0.940240i	$-0.389399\pi$
$181$	1.77990e12	0.681027	0.340514	+	0.940240i	$0.389399\pi$
$182$	−2.15842e12	−0.801206
$183$	2.09468e12	0.754459
$184$	−3.52165e12	−1.23097
$185$	−9.48851e11	−0.321924
$186$	1.90509e12	0.627472
$187$	−9.50245e12	−3.03883
$188$	−3.81624e10	−0.0118514
$189$	7.94639e11	0.239679
$190$	−6.79792e11	−0.199173
$191$	−7.72387e11	−0.219863	−0.109931	−	0.993939i	$-0.535063\pi$
$191$	−7.72387e11	−0.219863	−0.109931	+	0.993939i	$0.535063\pi$
$192$	2.04955e12	0.566894
$193$	−1.25262e12	−0.336709	−0.168355	−	0.985727i	$-0.553845\pi$
$193$	−1.25262e12	−0.336709	−0.168355	+	0.985727i	$0.553845\pi$
$194$	4.01131e12	1.04804
$195$	−4.75607e11	−0.120798
$196$	3.90575e10	0.00964485
$197$	1.52926e12	0.367211	0.183606	−	0.983000i	$-0.441223\pi$
$197$	1.52926e12	0.367211	0.183606	+	0.983000i	$0.441223\pi$
$198$	−2.55188e12	−0.595939
$199$	2.01035e12	0.456646	0.228323	−	0.973585i	$-0.426676\pi$
$199$	2.01035e12	0.456646	0.228323	+	0.973585i	$0.426676\pi$
$200$	−4.00232e12	−0.884396
$201$	−4.89739e12	−1.05290
$202$	−3.53958e12	−0.740489
$203$	4.96483e12	1.01083
$204$	−8.74313e10	−0.0173261
$205$	4.46532e11	0.0861403
$206$	−9.83107e12	−1.84642
$207$	−2.26394e12	−0.414026
$208$	−3.64265e12	−0.648738
$209$	−6.14991e12	−1.06675
$210$	1.40825e12	0.237943
$211$	1.15333e13	1.89845	0.949226	−	0.314596i	$-0.101869\pi$
$211$	1.15333e13	1.89845	0.949226	+	0.314596i	$0.101869\pi$
$212$	−1.34162e10	−0.00215170
$213$	−2.17771e12	−0.340339
$214$	1.17531e13	1.79010
$215$	1.09298e12	0.162256
$216$	1.31799e12	0.190729
$217$	−9.51104e12	−1.34184
$218$	−8.99346e12	−1.23713
$219$	−4.33897e12	−0.582029
$220$	−7.77936e10	−0.0101770
$221$	−8.56985e12	−1.09349
$222$	−4.59143e12	−0.571487
$223$	−3.82932e12	−0.464992	−0.232496	−	0.972597i	$-0.574689\pi$
$223$	−3.82932e12	−0.464992	−0.232496	+	0.972597i	$0.574689\pi$
$224$	3.67931e11	0.0435915
$225$	−2.57294e12	−0.297459
$226$	−7.86130e12	−0.886948
$227$	3.99728e12	0.440171	0.220086	−	0.975481i	$-0.429366\pi$
$227$	3.99728e12	0.440171	0.220086	+	0.975481i	$0.429366\pi$
$228$	−5.65848e10	−0.00608216
$229$	1.28159e13	1.34479	0.672395	−	0.740192i	$-0.265265\pi$
$229$	1.28159e13	1.34479	0.672395	+	0.740192i	$0.265265\pi$
$230$	−4.01212e12	−0.411028
$231$	1.27401e13	1.27440
$232$	8.23470e12	0.804384
$233$	1.68344e13	1.60598	0.802990	−	0.595993i	$-0.203241\pi$
$233$	1.68344e13	1.60598	0.802990	+	0.595993i	$0.203241\pi$
$234$	−2.30143e12	−0.214442
$235$	2.44054e12	0.222133
$236$	−2.56271e10	−0.00227868
$237$	−2.62593e12	−0.228122
$238$	2.53749e13	2.15393
$239$	1.59953e13	1.32679	0.663396	−	0.748269i	$-0.269115\pi$
$239$	1.59953e13	1.32679	0.663396	+	0.748269i	$0.269115\pi$
$240$	2.37662e12	0.192663
$241$	4.50987e12	0.357331	0.178666	−	0.983910i	$-0.442822\pi$
$241$	4.50987e12	0.357331	0.178666	+	0.983910i	$0.442822\pi$
$242$	−2.78889e13	−2.15997
$243$	8.47289e11	0.0641500
$244$	3.08994e11	0.0228721
$245$	−2.49778e12	−0.180776
$246$	2.16074e12	0.152918
$247$	−5.54634e12	−0.383860
$248$	−1.57751e13	−1.06779
$249$	−1.24454e13	−0.823971
$250$	−9.66941e12	−0.626224
$251$	−4.00229e12	−0.253573	−0.126786	−	0.991930i	$-0.540466\pi$
$251$	−4.00229e12	−0.253573	−0.126786	+	0.991930i	$0.540466\pi$
$252$	1.17220e11	0.00726608
$253$	−3.62967e13	−2.20142
$254$	1.60753e13	0.954058
$255$	5.59135e12	0.324747
$256$	9.23461e11	0.0524927
$257$	4.14560e12	0.230651	0.115325	−	0.993328i	$-0.463209\pi$
$257$	4.14560e12	0.230651	0.115325	+	0.993328i	$0.463209\pi$
$258$	5.28885e12	0.288040
$259$	2.29224e13	1.22211
$260$	−7.01587e10	−0.00366208
$261$	5.29378e12	0.270547
$262$	−4.51994e11	−0.0226191
$263$	−2.60341e13	−1.27581	−0.637904	−	0.770116i	$-0.720198\pi$
$263$	−2.60341e13	−1.27581	−0.637904	+	0.770116i	$0.720198\pi$
$264$	2.11308e13	1.01413
$265$	8.57982e11	0.0403298
$266$	1.64224e13	0.756116
$267$	5.09222e11	0.0229665
$268$	−7.22434e11	−0.0319196
$269$	2.33894e12	0.101247	0.0506234	−	0.998718i	$-0.483879\pi$
$269$	2.33894e12	0.101247	0.0506234	+	0.998718i	$0.483879\pi$
$270$	1.50155e12	0.0636855
$271$	−7.38151e12	−0.306771	−0.153385	−	0.988166i	$-0.549018\pi$
$271$	−7.38151e12	−0.306771	−0.153385	+	0.988166i	$0.549018\pi$
$272$	4.28238e13	1.74404
$273$	1.14897e13	0.458580
$274$	4.12752e13	1.61458
$275$	−4.12508e13	−1.58162
$276$	−3.33962e11	−0.0125516
$277$	−8.75117e9	−0.000322424 0	−0.000161212	−	1.00000i	$-0.500051\pi$
$277$	−8.75117e9	−0.000322424 0	−0.000161212		1.00000i	$0.500051\pi$
$278$	3.56717e13	1.28848
$279$	−1.01412e13	−0.359142
$280$	−1.16610e13	−0.404917
$281$	−3.35223e13	−1.14143	−0.570714	−	0.821149i	$-0.693334\pi$
$281$	−3.35223e13	−1.14143	−0.570714	+	0.821149i	$0.693334\pi$
$282$	1.18096e13	0.394335
$283$	8.53267e12	0.279421	0.139711	−	0.990192i	$-0.455383\pi$
$283$	8.53267e12	0.279421	0.139711	+	0.990192i	$0.455383\pi$
$284$	−3.21243e11	−0.0103177
$285$	3.61867e12	0.113999
$286$	−3.68978e13	−1.14022
$287$	−1.07873e13	−0.327012
$288$	3.92308e11	0.0116673
$289$	6.64773e13	1.93970
$290$	9.38158e12	0.268588
$291$	−2.13530e13	−0.599858
$292$	−6.40060e11	−0.0176447
$293$	−5.45014e13	−1.47447	−0.737235	−	0.675636i	$-0.763869\pi$
$293$	−5.45014e13	−1.47447	−0.737235	+	0.675636i	$0.763869\pi$
$294$	−1.20866e13	−0.320917
$295$	1.63889e12	0.0427099
$296$	3.80192e13	0.972519
$297$	1.35842e13	0.341093
$298$	2.37928e12	0.0586483
$299$	−3.27344e13	−0.792160
$300$	−3.79546e11	−0.00901772
$301$	−2.64042e13	−0.615967
$302$	−5.89975e13	−1.35144
$303$	1.88419e13	0.423829
$304$	2.77152e13	0.612229
$305$	−1.97606e13	−0.428697
$306$	2.70562e13	0.576499
$307$	7.80827e13	1.63416	0.817078	−	0.576527i	$-0.195592\pi$
$307$	7.80827e13	1.63416	0.817078	+	0.576527i	$0.195592\pi$
$308$	1.87934e12	0.0386346
$309$	5.23328e13	1.05682
$310$	−1.79721e13	−0.356541
$311$	−4.62993e13	−0.902386	−0.451193	−	0.892427i	$-0.649001\pi$
$311$	−4.62993e13	−0.902386	−0.451193	+	0.892427i	$0.649001\pi$
$312$	1.90569e13	0.364924
$313$	−2.52505e13	−0.475090	−0.237545	−	0.971376i	$-0.576343\pi$
$313$	−2.52505e13	−0.475090	−0.237545	+	0.971376i	$0.576343\pi$
$314$	1.71310e12	0.0316715
$315$	−7.49641e12	−0.136190
$316$	−3.87362e11	−0.00691573
$317$	−4.06043e13	−0.712436	−0.356218	−	0.934403i	$-0.615934\pi$
$317$	−4.06043e13	−0.712436	−0.356218	+	0.934403i	$0.615934\pi$
$318$	4.15172e12	0.0715943
$319$	8.48728e13	1.43853
$320$	−1.93349e13	−0.322120
$321$	−6.25642e13	−1.02459
$322$	9.69250e13	1.56037
$323$	6.52040e13	1.03195
$324$	1.24987e11	0.00194477
$325$	−3.72024e13	−0.569131
$326$	6.27289e13	0.943562
$327$	4.78741e13	0.708089
$328$	−1.78919e13	−0.260226
$329$	−5.89587e13	−0.843277
$330$	2.40737e13	0.338623
$331$	−2.51913e13	−0.348494	−0.174247	−	0.984702i	$-0.555749\pi$
$331$	−2.51913e13	−0.348494	−0.174247	+	0.984702i	$0.555749\pi$
$332$	−1.83587e12	−0.0249794
$333$	2.44411e13	0.327098
$334$	−5.24327e13	−0.690234
$335$	4.62007e13	0.598276
$336$	−5.74146e13	−0.731402
$337$	−8.31760e13	−1.04240	−0.521199	−	0.853435i	$-0.674515\pi$
$337$	−8.31760e13	−1.04240	−0.521199	+	0.853435i	$0.674515\pi$
$338$	4.85341e13	0.598418
$339$	4.18473e13	0.507656
$340$	8.24802e11	0.00984500
$341$	−1.62589e14	−1.90960
$342$	1.75105e13	0.202374
$343$	−4.91625e13	−0.559135
$344$	−4.37942e13	−0.490168
$345$	2.13574e13	0.235257
$346$	1.38229e14	1.49858
$347$	−1.29687e14	−1.38383	−0.691915	−	0.721979i	$-0.743233\pi$
$347$	−1.29687e14	−1.38383	−0.691915	+	0.721979i	$0.743233\pi$
$348$	7.80907e11	0.00820188
$349$	1.52157e14	1.57308	0.786541	−	0.617538i	$-0.211870\pi$
$349$	1.52157e14	1.57308	0.786541	+	0.617538i	$0.211870\pi$
$350$	1.10154e14	1.12106
$351$	1.22510e13	0.122739
$352$	6.28970e12	0.0620362
$353$	7.62557e13	0.740477	0.370238	−	0.928937i	$-0.379276\pi$
$353$	7.62557e13	0.740477	0.370238	+	0.928937i	$0.379276\pi$
$354$	7.93047e12	0.0758195
$355$	2.05439e13	0.193387
$356$	7.51175e10	0.000696251 0
$357$	−1.35076e14	−1.23283
$358$	1.77142e14	1.59208
$359$	−1.21029e14	−1.07119	−0.535597	−	0.844474i	$-0.679913\pi$
$359$	−1.21029e14	−1.07119	−0.535597	+	0.844474i	$0.679913\pi$
$360$	−1.24336e13	−0.108376
$361$	−7.42908e13	−0.637742
$362$	−8.12511e13	−0.686961
$363$	1.48458e14	1.23628
$364$	1.69490e12	0.0139023
$365$	4.09327e13	0.330719
$366$	−9.56202e13	−0.761033
$367$	9.61873e12	0.0754144	0.0377072	−	0.999289i	$-0.487995\pi$
$367$	9.61873e12	0.0754144	0.0377072	+	0.999289i	$0.487995\pi$
$368$	1.63575e14	1.26344
$369$	−1.15021e13	−0.0875247
$370$	4.33143e13	0.324729
$371$	−2.07272e13	−0.153103
$372$	−1.49597e12	−0.0108877
$373$	6.11511e13	0.438537	0.219268	−	0.975665i	$-0.429633\pi$
$373$	6.11511e13	0.438537	0.219268	+	0.975665i	$0.429633\pi$
$374$	4.33779e14	3.06531
$375$	5.14723e13	0.358427
$376$	−9.77891e13	−0.671054
$377$	7.65431e13	0.517641
$378$	−3.62746e13	−0.241768
$379$	−2.49856e14	−1.64124	−0.820622	−	0.571471i	$-0.806373\pi$
$379$	−2.49856e14	−1.64124	−0.820622	+	0.571471i	$0.806373\pi$
$380$	5.33805e11	0.00345599
$381$	−8.55724e13	−0.546068
$382$	3.52588e13	0.221778
$383$	−1.81282e14	−1.12399	−0.561995	−	0.827141i	$-0.689966\pi$
$383$	−1.81282e14	−1.12399	−0.561995	+	0.827141i	$0.689966\pi$
$384$	−9.68667e13	−0.592042
$385$	−1.20186e14	−0.724139
$386$	5.71811e13	0.339643
$387$	−2.81536e13	−0.164863
$388$	−3.14987e12	−0.0181852
$389$	−3.10316e14	−1.76637	−0.883185	−	0.469025i	$-0.844605\pi$
$389$	−3.10316e14	−1.76637	−0.883185	+	0.469025i	$0.844605\pi$
$390$	2.17111e13	0.121850
$391$	3.84833e14	2.12961
$392$	1.00083e14	0.546116
$393$	2.40606e12	0.0129463
$394$	−6.98092e13	−0.370411
$395$	2.47723e13	0.129623
$396$	2.00386e12	0.0103405
$397$	1.60268e14	0.815642	0.407821	−	0.913062i	$-0.366289\pi$
$397$	1.60268e14	0.815642	0.407821	+	0.913062i	$0.366289\pi$
$398$	−9.17708e13	−0.460625
$399$	−8.74201e13	−0.432773
$400$	1.85901e14	0.907722
$401$	−2.08875e14	−1.00599	−0.502993	−	0.864291i	$-0.667768\pi$
$401$	−2.08875e14	−1.00599	−0.502993	+	0.864291i	$0.667768\pi$
$402$	2.23562e14	1.06207
$403$	−1.46632e14	−0.687150
$404$	2.77945e12	0.0128487
$405$	−7.99309e12	−0.0364512
$406$	−2.26641e14	−1.01963
$407$	3.91853e14	1.73922
$408$	−2.24038e14	−0.981048
$409$	2.18943e14	0.945917	0.472958	−	0.881085i	$-0.343186\pi$
$409$	2.18943e14	0.945917	0.472958	+	0.881085i	$0.343186\pi$
$410$	−2.03838e13	−0.0868909
$411$	−2.19716e14	−0.924129
$412$	7.71983e12	0.0320386
$413$	−3.95923e13	−0.162138
$414$	1.03347e14	0.417633
$415$	1.17406e14	0.468195
$416$	5.67241e12	0.0223231
$417$	−1.89888e14	−0.737478
$418$	2.80738e14	1.07605
$419$	−9.83765e13	−0.372147	−0.186073	−	0.982536i	$-0.559576\pi$
$419$	−9.83765e13	−0.372147	−0.186073	+	0.982536i	$0.559576\pi$
$420$	−1.10583e12	−0.00412872
$421$	−9.72533e13	−0.358387	−0.179194	−	0.983814i	$-0.557349\pi$
$421$	−9.72533e13	−0.358387	−0.179194	+	0.983814i	$0.557349\pi$
$422$	−5.26485e14	−1.91499
$423$	−6.28650e13	−0.225703
$424$	−3.43782e13	−0.121835
$425$	4.37360e14	1.53003
$426$	9.94105e13	0.343305
$427$	4.77377e14	1.62745
$428$	−9.22910e12	−0.0310612
$429$	1.96415e14	0.652618
$430$	−4.98936e13	−0.163670
$431$	2.09361e14	0.678063	0.339031	−	0.940775i	$-0.389901\pi$
$431$	2.09361e14	0.678063	0.339031	+	0.940775i	$0.389901\pi$
$432$	−6.12186e13	−0.195760
$433$	5.48395e14	1.73145	0.865726	−	0.500519i	$-0.166857\pi$
$433$	5.48395e14	1.73145	0.865726	+	0.500519i	$0.166857\pi$
$434$	4.34171e14	1.35353
$435$	−4.99401e13	−0.153730
$436$	7.06210e12	0.0214663
$437$	2.49061e14	0.747580
$438$	1.98071e14	0.587100
$439$	3.87623e14	1.13463	0.567315	−	0.823501i	$-0.307982\pi$
$439$	3.87623e14	1.13463	0.567315	+	0.823501i	$0.307982\pi$
$440$	−1.99342e14	−0.576247
$441$	6.43394e13	0.183681
$442$	3.91207e14	1.10302
$443$	−1.78451e14	−0.496934	−0.248467	−	0.968640i	$-0.579927\pi$
$443$	−1.78451e14	−0.496934	−0.248467	+	0.968640i	$0.579927\pi$
$444$	3.60541e12	0.00991626
$445$	−4.80387e12	−0.0130500
$446$	1.74805e14	0.469043
$447$	−1.26654e13	−0.0335681
$448$	4.67093e14	1.22285
$449$	−4.36198e14	−1.12805	−0.564025	−	0.825758i	$-0.690748\pi$
$449$	−4.36198e14	−1.12805	−0.564025	+	0.825758i	$0.690748\pi$
$450$	1.17453e14	0.300051
$451$	−1.84407e14	−0.465379
$452$	6.17307e12	0.0153900
$453$	3.14056e14	0.773512
$454$	−1.82472e14	−0.444007
$455$	−1.08391e14	−0.260574
$456$	−1.44995e14	−0.344387
$457$	8.18828e14	1.92156	0.960779	−	0.277315i	$-0.0894446\pi$
$457$	8.18828e14	1.92156	0.960779	+	0.277315i	$0.0894446\pi$
$458$	−5.85036e14	−1.35651
$459$	−1.44026e14	−0.329966
$460$	3.15051e12	0.00713202
$461$	−7.92188e14	−1.77204	−0.886019	−	0.463648i	$-0.846540\pi$
$461$	−7.92188e14	−1.77204	−0.886019	+	0.463648i	$0.846540\pi$
$462$	−5.81574e14	−1.28551
$463$	3.66634e14	0.800825	0.400412	−	0.916335i	$-0.368867\pi$
$463$	3.66634e14	0.800825	0.400412	+	0.916335i	$0.368867\pi$
$464$	−3.82488e14	−0.825600
$465$	9.56693e13	0.204071
$466$	−7.68476e14	−1.61997
$467$	−1.80916e13	−0.0376906	−0.0188453	−	0.999822i	$-0.505999\pi$
$467$	−1.80916e13	−0.0376906	−0.0188453	+	0.999822i	$0.505999\pi$
$468$	1.80719e12	0.00372094
$469$	−1.11612e15	−2.27122
$470$	−1.11409e14	−0.224068
$471$	−9.11917e12	−0.0181276
$472$	−6.56680e13	−0.129025
$473$	−4.51375e14	−0.876599
$474$	1.19872e14	0.230110
$475$	2.83055e14	0.537102
$476$	−1.99256e13	−0.0373743
$477$	−2.21005e13	−0.0409779
$478$	−7.30170e14	−1.33835
$479$	−1.42483e14	−0.258178	−0.129089	−	0.991633i	$-0.541205\pi$
$479$	−1.42483e14	−0.258178	−0.129089	+	0.991633i	$0.541205\pi$
$480$	−3.70093e12	−0.00662955
$481$	3.53396e14	0.625840
$482$	−2.05872e14	−0.360445
$483$	−5.15952e14	−0.893100
$484$	2.18997e13	0.0374791
$485$	2.01439e14	0.340850
$486$	−3.86780e13	−0.0647090
$487$	−5.62723e13	−0.0930862	−0.0465431	−	0.998916i	$-0.514820\pi$
$487$	−5.62723e13	−0.0930862	−0.0465431	+	0.998916i	$0.514820\pi$
$488$	7.91780e14	1.29508
$489$	−3.33919e14	−0.540060
$490$	1.14021e14	0.182351
$491$	3.83123e14	0.605885	0.302942	−	0.953009i	$-0.402031\pi$
$491$	3.83123e14	0.605885	0.302942	+	0.953009i	$0.402031\pi$
$492$	−1.69672e12	−0.00265339
$493$	−8.99859e14	−1.39161
$494$	2.53186e14	0.387205
$495$	−1.28150e14	−0.193815
$496$	7.32726e14	1.09595
$497$	−4.96300e14	−0.734149
$498$	5.68121e14	0.831150
$499$	−8.22669e14	−1.19034	−0.595172	−	0.803598i	$-0.702916\pi$
$499$	−8.22669e14	−1.19034	−0.595172	+	0.803598i	$0.702916\pi$
$500$	7.59288e12	0.0108660
$501$	2.79110e14	0.395064
$502$	1.82701e14	0.255782
$503$	9.04428e14	1.25242	0.626210	−	0.779654i	$-0.284605\pi$
$503$	9.04428e14	1.25242	0.626210	+	0.779654i	$0.284605\pi$
$504$	3.00371e14	0.411424
$505$	−1.77749e14	−0.240827
$506$	1.65691e15	2.22061
$507$	−2.58357e14	−0.342513
$508$	−1.26231e13	−0.0165545
$509$	9.07252e14	1.17701	0.588505	−	0.808494i	$-0.299717\pi$
$509$	9.07252e14	1.17701	0.588505	+	0.808494i	$0.299717\pi$
$510$	−2.55240e14	−0.327577
$511$	−9.88854e14	−1.25550
$512$	7.74236e14	0.972497
$513$	−9.32121e13	−0.115832
$514$	−1.89243e14	−0.232661
$515$	−4.93694e14	−0.600507
$516$	−4.15306e12	−0.00499798
$517$	−1.00789e15	−1.20009
$518$	−1.04639e15	−1.23276
$519$	−7.35822e14	−0.857734
$520$	−1.79778e14	−0.207357
$521$	−3.79217e14	−0.432793	−0.216396	−	0.976306i	$-0.569430\pi$
$521$	−3.79217e14	−0.432793	−0.216396	+	0.976306i	$0.569430\pi$
$522$	−2.41657e14	−0.272905
$523$	−5.94956e14	−0.664853	−0.332426	−	0.943129i	$-0.607867\pi$
$523$	−5.94956e14	−0.664853	−0.332426	+	0.943129i	$0.607867\pi$
$524$	3.54927e11	0.000392480 0
$525$	−5.86375e14	−0.641652
$526$	1.18843e15	1.28692
$527$	1.72384e15	1.84731
$528$	−9.81490e14	−1.04088
$529$	5.17143e14	0.542756
$530$	−3.91662e13	−0.0406812
$531$	−4.22156e13	−0.0433963
$532$	−1.28957e13	−0.0131199
$533$	−1.66309e14	−0.167462
$534$	−2.32456e13	−0.0231667
$535$	5.90214e14	0.582188
$536$	−1.85120e15	−1.80737
$537$	−9.42964e14	−0.911248
$538$	−1.06771e14	−0.102129
$539$	1.03152e15	0.976655
$540$	−1.17909e12	−0.00110505
$541$	−1.96976e14	−0.182738	−0.0913688	−	0.995817i	$-0.529124\pi$
$541$	−1.96976e14	−0.182738	−0.0913688	+	0.995817i	$0.529124\pi$
$542$	3.36960e14	0.309444
$543$	4.32517e14	0.393191
$544$	−6.66862e13	−0.0600125
$545$	−4.51631e14	−0.402349
$546$	−5.24497e14	−0.462576
$547$	−1.09754e15	−0.958271	−0.479135	−	0.877741i	$-0.659050\pi$
$547$	−1.09754e15	−0.958271	−0.479135	+	0.877741i	$0.659050\pi$
$548$	−3.24113e13	−0.0280158
$549$	5.09006e14	0.435587
$550$	1.88307e15	1.59540
$551$	−5.82381e14	−0.488510
$552$	−8.55760e14	−0.710701
$553$	−5.98451e14	−0.492086
$554$	3.99484e11	0.000325233 0
$555$	−2.30571e14	−0.185863
$556$	−2.80111e13	−0.0223573
$557$	−1.50745e15	−1.19135	−0.595675	−	0.803226i	$-0.703115\pi$
$557$	−1.50745e15	−1.19135	−0.595675	+	0.803226i	$0.703115\pi$
$558$	4.62937e14	0.362271
$559$	−4.07075e14	−0.315435
$560$	5.41633e14	0.415596
$561$	−2.30910e15	−1.75447
$562$	1.53026e15	1.15137
$563$	4.37573e14	0.326028	0.163014	−	0.986624i	$-0.447878\pi$
$563$	4.37573e14	0.326028	0.163014	+	0.986624i	$0.447878\pi$
$564$	−9.27347e12	−0.00684238
$565$	−3.94776e14	−0.288459
$566$	−3.89509e14	−0.281856
$567$	1.93097e14	0.138379
$568$	−8.23166e14	−0.584213
$569$	1.56835e15	1.10236	0.551182	−	0.834385i	$-0.314177\pi$
$569$	1.56835e15	1.10236	0.551182	+	0.834385i	$0.314177\pi$
$570$	−1.65189e14	−0.114993
$571$	5.15698e14	0.355547	0.177773	−	0.984071i	$-0.443111\pi$
$571$	5.15698e14	0.355547	0.177773	+	0.984071i	$0.443111\pi$
$572$	2.89739e13	0.0197847
$573$	−1.87690e14	−0.126938
$574$	4.92433e14	0.329862
$575$	1.67059e15	1.10840
$576$	4.98041e14	0.327297
$577$	−4.83873e13	−0.0314967	−0.0157483	−	0.999876i	$-0.505013\pi$
$577$	−4.83873e13	−0.0314967	−0.0157483	+	0.999876i	$0.505013\pi$
$578$	−3.03463e15	−1.95660
$579$	−3.04387e14	−0.194399
$580$	−7.36686e12	−0.00466046
$581$	−2.83631e15	−1.77740
$582$	9.74748e14	0.605084
$583$	−3.54326e14	−0.217885
$584$	−1.64012e15	−0.999089
$585$	−1.15573e14	−0.0697425
$586$	2.48795e15	1.48732
$587$	−2.20013e15	−1.30298	−0.651492	−	0.758655i	$-0.725857\pi$
$587$	−2.20013e15	−1.30298	−0.651492	+	0.758655i	$0.725857\pi$
$588$	9.49096e12	0.00556846
$589$	1.11566e15	0.648480
$590$	−7.48139e13	−0.0430820
$591$	3.71609e14	0.212009
$592$	−1.76593e15	−0.998169
$593$	−7.70185e14	−0.431315	−0.215657	−	0.976469i	$-0.569189\pi$
$593$	−7.70185e14	−0.431315	−0.215657	+	0.976469i	$0.569189\pi$
$594$	−6.20107e14	−0.344065
$595$	1.27427e15	0.700516
$596$	−1.86832e12	−0.00101765
$597$	4.88515e14	0.263645
$598$	1.49430e15	0.799062
$599$	2.28431e15	1.21034	0.605171	−	0.796096i	$-0.293105\pi$
$599$	2.28431e15	1.21034	0.605171	+	0.796096i	$0.293105\pi$
$600$	−9.72564e14	−0.510607
$601$	−2.38115e15	−1.23873	−0.619366	−	0.785102i	$-0.712610\pi$
$601$	−2.38115e15	−1.23873	−0.619366	+	0.785102i	$0.712610\pi$
$602$	1.20533e15	0.621334
$603$	−1.19007e15	−0.607891
$604$	4.63277e13	0.0234497
$605$	−1.40052e15	−0.702479
$606$	−8.60117e14	−0.427522
$607$	6.17573e13	0.0304194	0.0152097	−	0.999884i	$-0.495158\pi$
$607$	6.17573e13	0.0304194	0.0152097	+	0.999884i	$0.495158\pi$
$608$	−4.31587e13	−0.0210668
$609$	1.20645e15	0.583601
$610$	9.02054e14	0.432433
$611$	−9.08969e14	−0.431840
$612$	−2.12458e13	−0.0100032
$613$	−1.42374e15	−0.664350	−0.332175	−	0.943218i	$-0.607782\pi$
$613$	−1.42374e15	−0.664350	−0.332175	+	0.943218i	$0.607782\pi$
$614$	−3.56441e15	−1.64840
$615$	1.08507e14	0.0497331
$616$	4.81571e15	2.18759
$617$	2.11352e15	0.951563	0.475781	−	0.879564i	$-0.342165\pi$
$617$	2.11352e15	0.951563	0.475781	+	0.879564i	$0.342165\pi$
$618$	−2.38895e15	−1.06603
$619$	−1.87457e15	−0.829095	−0.414547	−	0.910028i	$-0.636060\pi$
$619$	−1.87457e15	−0.829095	−0.414547	+	0.910028i	$0.636060\pi$
$620$	1.41126e13	0.00618659
$621$	−5.50137e14	−0.239038
$622$	2.11352e15	0.910248
$623$	1.16052e14	0.0495414
$624$	−8.85164e14	−0.374549
$625$	1.64202e15	0.688711
$626$	1.15266e15	0.479230
$627$	−1.49443e15	−0.615890
$628$	−1.34521e12	−0.000549555 0
$629$	−4.15460e15	−1.68248
$630$	3.42205e14	0.137377
$631$	3.36702e15	1.33994	0.669968	−	0.742390i	$-0.266308\pi$
$631$	3.36702e15	1.33994	0.669968	+	0.742390i	$0.266308\pi$
$632$	−9.92594e14	−0.391586
$633$	2.80259e15	1.09607
$634$	1.85355e15	0.718644
$635$	8.07267e14	0.310286
$636$	−3.26013e12	−0.00124228
$637$	9.30287e14	0.351439
$638$	−3.87437e15	−1.45107
$639$	−5.29183e14	−0.196495
$640$	9.13814e14	0.336409
$641$	−4.16406e15	−1.51984	−0.759920	−	0.650017i	$-0.774762\pi$
$641$	−4.16406e15	−1.51984	−0.759920	+	0.650017i	$0.774762\pi$
$642$	2.85600e15	1.03351
$643$	−2.00066e15	−0.717816	−0.358908	−	0.933373i	$-0.616851\pi$
$643$	−2.00066e15	−0.717816	−0.358908	+	0.933373i	$0.616851\pi$
$644$	−7.61101e13	−0.0270751
$645$	2.65594e14	0.0936784
$646$	−2.97651e15	−1.04095
$647$	−4.89568e15	−1.69762	−0.848809	−	0.528700i	$-0.822680\pi$
$647$	−4.89568e15	−1.69762	−0.848809	+	0.528700i	$0.822680\pi$
$648$	3.20272e14	0.110118
$649$	−6.76823e14	−0.230743
$650$	1.69826e15	0.574090
$651$	−2.31118e15	−0.774709
$652$	−4.92577e13	−0.0163724
$653$	4.83871e15	1.59480	0.797402	−	0.603449i	$-0.206207\pi$
$653$	4.83871e15	1.59480	0.797402	+	0.603449i	$0.206207\pi$
$654$	−2.18541e15	−0.714258
$655$	−2.26981e13	−0.00735635
$656$	8.31052e14	0.267090
$657$	−1.05437e15	−0.336034
$658$	2.69141e15	0.850625
$659$	−1.44327e15	−0.452352	−0.226176	−	0.974086i	$-0.572622\pi$
$659$	−1.44327e15	−0.452352	−0.226176	+	0.974086i	$0.572622\pi$
$660$	−1.89039e13	−0.00587569
$661$	4.10129e15	1.26419	0.632095	−	0.774891i	$-0.282195\pi$
$661$	4.10129e15	1.26419	0.632095	+	0.774891i	$0.282195\pi$
$662$	1.14996e15	0.351531
$663$	−2.08247e15	−0.631328
$664$	−4.70431e15	−1.41440
$665$	8.24697e14	0.245909
$666$	−1.11572e15	−0.329948
$667$	−3.43720e15	−1.00812
$668$	4.11726e13	0.0119767
$669$	−9.30525e14	−0.268463
$670$	−2.10902e15	−0.603489
$671$	8.16066e15	2.31607
$672$	8.94072e13	0.0251676
$673$	6.68396e15	1.86617	0.933085	−	0.359656i	$-0.117106\pi$
$673$	6.68396e15	1.86617	0.933085	+	0.359656i	$0.117106\pi$
$674$	3.79692e15	1.05148
$675$	−6.25226e14	−0.171738
$676$	−3.81113e13	−0.0103836
$677$	1.83931e15	0.497071	0.248535	−	0.968623i	$-0.420051\pi$
$677$	1.83931e15	0.497071	0.248535	+	0.968623i	$0.420051\pi$
$678$	−1.91030e15	−0.512080
$679$	−4.86636e15	−1.29396
$680$	2.11351e15	0.557449
$681$	9.71338e14	0.254133
$682$	7.42206e15	1.92624
$683$	1.20792e15	0.310975	0.155487	−	0.987838i	$-0.450305\pi$
$683$	1.20792e15	0.310975	0.155487	+	0.987838i	$0.450305\pi$
$684$	−1.37501e13	−0.00351154
$685$	2.07274e15	0.525107
$686$	2.24423e15	0.564007
$687$	3.11427e15	0.776415
$688$	2.03417e15	0.503096
$689$	−3.19552e14	−0.0784035
$690$	−9.74945e14	−0.237307
$691$	1.74426e15	0.421193	0.210597	−	0.977573i	$-0.432459\pi$
$691$	1.74426e15	0.421193	0.210597	+	0.977573i	$0.432459\pi$
$692$	−1.08544e14	−0.0260030
$693$	3.09584e15	0.735776
$694$	5.92008e15	1.39589
$695$	1.79135e15	0.419048
$696$	2.00103e15	0.464412
$697$	1.95517e15	0.450198
$698$	−6.94583e15	−1.58679
$699$	4.09076e15	0.927213
$700$	−8.64985e13	−0.0194522
$701$	−4.82894e15	−1.07746	−0.538732	−	0.842477i	$-0.681096\pi$
$701$	−4.82894e15	−1.07746	−0.538732	+	0.842477i	$0.681096\pi$
$702$	−5.59248e14	−0.123808
$703$	−2.68882e15	−0.590620
$704$	7.98486e15	1.74028
$705$	5.93051e14	0.128248
$706$	−3.48101e15	−0.746929
$707$	4.29408e15	0.914246
$708$	−6.22739e12	−0.00131560
$709$	−1.00902e15	−0.211518	−0.105759	−	0.994392i	$-0.533727\pi$
$709$	−1.00902e15	−0.211518	−0.105759	+	0.994392i	$0.533727\pi$
$710$	−9.37812e14	−0.195072
$711$	−6.38102e14	−0.131707
$712$	1.92484e14	0.0394235
$713$	6.58459e15	1.33825
$714$	6.16611e15	1.24357
$715$	−1.85292e15	−0.370829
$716$	−1.39100e14	−0.0276253
$717$	3.88685e15	0.766023
$718$	5.52485e15	1.08053
$719$	5.37134e15	1.04250	0.521248	−	0.853405i	$-0.325467\pi$
$719$	5.37134e15	1.04250	0.521248	+	0.853405i	$0.325467\pi$
$720$	5.77520e14	0.111234
$721$	1.19267e16	2.27969
$722$	3.39131e15	0.643299
$723$	1.09590e15	0.206305
$724$	6.38023e13	0.0119199
$725$	−3.90635e15	−0.724290
$726$	−6.77700e15	−1.24706
$727$	−1.01159e15	−0.184742	−0.0923712	−	0.995725i	$-0.529445\pi$
$727$	−1.01159e15	−0.184742	−0.0923712	+	0.995725i	$0.529445\pi$
$728$	4.34308e15	0.787182
$729$	2.05891e14	0.0370370
$730$	−1.86854e15	−0.333601
$731$	4.78567e15	0.848003
$732$	7.50855e13	0.0132052
$733$	9.27668e15	1.61928	0.809638	−	0.586929i	$-0.199663\pi$
$733$	9.27668e15	1.61928	0.809638	+	0.586929i	$0.199663\pi$
$734$	−4.39087e14	−0.0760716
$735$	−6.06960e14	−0.104371
$736$	−2.54722e14	−0.0434749
$737$	−1.90798e16	−3.23223
$738$	5.25059e14	0.0882874
$739$	−5.39464e15	−0.900365	−0.450182	−	0.892937i	$-0.648641\pi$
$739$	−5.39464e15	−0.900365	−0.450182	+	0.892937i	$0.648641\pi$
$740$	−3.40124e13	−0.00563460
$741$	−1.34776e15	−0.221622
$742$	9.46177e14	0.154437
$743$	5.12721e15	0.830697	0.415349	−	0.909662i	$-0.363660\pi$
$743$	5.12721e15	0.830697	0.415349	+	0.909662i	$0.363660\pi$
$744$	−3.83334e15	−0.616490
$745$	1.19482e14	0.0190740
$746$	−2.79150e15	−0.442358
$747$	−3.02423e15	−0.475720
$748$	−3.40624e14	−0.0531884
$749$	−1.42584e16	−2.21015
$750$	−2.34967e15	−0.361551
$751$	−5.16172e15	−0.788451	−0.394225	−	0.919014i	$-0.628987\pi$
$751$	−5.16172e15	−0.788451	−0.394225	+	0.919014i	$0.628987\pi$
$752$	4.54215e15	0.688752
$753$	−9.72556e14	−0.146400
$754$	−3.49413e15	−0.522152
$755$	−2.96272e15	−0.439523
$756$	2.84846e13	0.00419508
$757$	1.03746e15	0.151685	0.0758426	−	0.997120i	$-0.475835\pi$
$757$	1.03746e15	0.151685	0.0758426	+	0.997120i	$0.475835\pi$
$758$	1.14057e16	1.65555
$759$	−8.82009e15	−1.27099
$760$	1.36785e15	0.195687
$761$	9.01004e15	1.27971	0.639855	−	0.768496i	$-0.278995\pi$
$761$	9.01004e15	1.27971	0.639855	+	0.768496i	$0.278995\pi$
$762$	3.90631e15	0.550826
$763$	1.09105e16	1.52743
$764$	−2.76869e13	−0.00384823
$765$	1.35870e15	0.187493
$766$	8.27539e15	1.13378
$767$	−6.10397e14	−0.0830306
$768$	2.24401e14	0.0303067
$769$	−1.31431e16	−1.76239	−0.881196	−	0.472751i	$-0.843261\pi$
$769$	−1.31431e16	−1.76239	−0.881196	+	0.472751i	$0.843261\pi$
$770$	5.48641e15	0.730448
$771$	1.00738e15	0.133166
$772$	−4.49014e13	−0.00589338
$773$	−3.73422e15	−0.486646	−0.243323	−	0.969945i	$-0.578237\pi$
$773$	−3.73422e15	−0.486646	−0.243323	+	0.969945i	$0.578237\pi$
$774$	1.28519e15	0.166300
$775$	7.48333e15	0.961469
$776$	−8.07137e15	−1.02969
$777$	5.57014e15	0.705587
$778$	1.41657e16	1.78176
$779$	1.26537e15	0.158038
$780$	−1.70486e13	−0.00211431
$781$	−8.48415e15	−1.04479
$782$	−1.75673e16	−2.14817
$783$	1.28639e15	0.156201
$784$	−4.64867e15	−0.560519
$785$	8.60278e13	0.0103004
$786$	−1.09835e14	−0.0130592
$787$	−6.18378e15	−0.730118	−0.365059	−	0.930984i	$-0.618951\pi$
$787$	−6.18378e15	−0.730118	−0.365059	+	0.930984i	$0.618951\pi$
$788$	5.48176e13	0.00642725
$789$	−6.32627e15	−0.736588
$790$	−1.13084e15	−0.130753
$791$	9.53702e15	1.09507
$792$	5.13478e15	0.585508
$793$	7.35975e15	0.833414
$794$	−7.31611e15	−0.822749
$795$	2.08490e14	0.0232844
$796$	7.20628e13	0.00799263
$797$	−7.49422e15	−0.825478	−0.412739	−	0.910849i	$-0.635428\pi$
$797$	−7.49422e15	−0.825478	−0.412739	+	0.910849i	$0.635428\pi$
$798$	3.99065e15	0.436544
$799$	1.06861e16	1.16094
$800$	−2.89490e14	−0.0312347
$801$	1.23741e14	0.0132597
$802$	9.53496e15	1.01475
$803$	−1.69042e16	−1.78674
$804$	−1.75552e14	−0.0184288
$805$	4.86735e15	0.507475
$806$	6.69364e15	0.693138
$807$	5.68363e14	0.0584549
$808$	7.12218e15	0.727529
$809$	−5.07971e15	−0.515374	−0.257687	−	0.966228i	$-0.582960\pi$
$809$	−5.07971e15	−0.515374	−0.257687	+	0.966228i	$0.582960\pi$
$810$	3.64878e14	0.0367688
$811$	4.13943e15	0.414311	0.207155	−	0.978308i	$-0.433579\pi$
$811$	4.13943e15	0.414311	0.207155	+	0.978308i	$0.433579\pi$
$812$	1.77969e14	0.0176924
$813$	−1.79371e15	−0.177114
$814$	−1.78878e16	−1.75437
$815$	3.15010e15	0.306872
$816$	1.04062e16	1.00692
$817$	3.09725e15	0.297683
$818$	−9.99457e15	−0.954159
$819$	2.79201e15	0.264762
$820$	1.60064e13	0.00150770
$821$	1.31830e16	1.23347	0.616735	−	0.787171i	$-0.288455\pi$
$821$	1.31830e16	1.23347	0.616735	+	0.787171i	$0.288455\pi$
$822$	1.00299e16	0.932181
$823$	−3.65311e15	−0.337259	−0.168630	−	0.985679i	$-0.553934\pi$
$823$	−3.65311e15	−0.337259	−0.168630	+	0.985679i	$0.553934\pi$
$824$	1.97816e16	1.81410
$825$	−1.00240e16	−0.913151
$826$	1.80736e15	0.163551
$827$	−4.28535e15	−0.385217	−0.192609	−	0.981276i	$-0.561695\pi$
$827$	−4.28535e15	−0.385217	−0.192609	+	0.981276i	$0.561695\pi$
$828$	−8.11529e13	−0.00724665
$829$	−9.68218e14	−0.0858862	−0.0429431	−	0.999078i	$-0.513673\pi$
$829$	−9.68218e14	−0.0858862	−0.0429431	+	0.999078i	$0.513673\pi$
$830$	−5.35950e15	−0.472275
$831$	−2.12653e12	−0.000186152 0
$832$	7.20121e15	0.626220
$833$	−1.09367e16	−0.944795
$834$	8.66822e15	0.743904
$835$	−2.63305e15	−0.224483
$836$	−2.20449e14	−0.0186713
$837$	−2.46431e15	−0.207351
$838$	4.49080e15	0.375389
$839$	−6.92947e15	−0.575452	−0.287726	−	0.957713i	$-0.592899\pi$
$839$	−6.92947e15	−0.575452	−0.287726	+	0.957713i	$0.592899\pi$
$840$	−2.83362e15	−0.233779
$841$	−4.16327e15	−0.341237
$842$	4.43953e15	0.361510
$843$	−8.14591e15	−0.659004
$844$	4.13421e14	0.0332284
$845$	2.43727e15	0.194622
$846$	2.86974e15	0.227669
$847$	3.38337e16	2.66680
$848$	1.59681e15	0.125048
$849$	2.07344e15	0.161324
$850$	−1.99651e16	−1.54336
$851$	−1.58694e16	−1.21884
$852$	−7.80619e13	−0.00595692
$853$	−8.53570e14	−0.0647172	−0.0323586	−	0.999476i	$-0.510302\pi$
$853$	−8.53570e14	−0.0647172	−0.0323586	+	0.999476i	$0.510302\pi$
$854$	−2.17919e16	−1.64163
$855$	8.79338e14	0.0658176
$856$	−2.36491e16	−1.75877
$857$	−1.33844e16	−0.989019	−0.494510	−	0.869172i	$-0.664652\pi$
$857$	−1.33844e16	−0.989019	−0.494510	+	0.869172i	$0.664652\pi$
$858$	−8.96616e15	−0.658304
$859$	−8.83485e15	−0.644520	−0.322260	−	0.946651i	$-0.604443\pi$
$859$	−8.83485e15	−0.644520	−0.322260	+	0.946651i	$0.604443\pi$
$860$	3.91788e13	0.00283994
$861$	−2.62132e15	−0.188801
$862$	−9.55714e15	−0.683971
$863$	2.00425e16	1.42525	0.712626	−	0.701544i	$-0.247506\pi$
$863$	2.00425e16	1.42525	0.712626	+	0.701544i	$0.247506\pi$
$864$	9.53309e13	0.00673610
$865$	6.94155e15	0.487380
$866$	−2.50338e16	−1.74654
$867$	1.61540e16	1.11989
$868$	−3.40932e14	−0.0234860
$869$	−1.02304e16	−0.700299
$870$	2.27972e15	0.155069
$871$	−1.72072e16	−1.16308
$872$	1.80962e16	1.21548
$873$	−5.18879e15	−0.346328
$874$	−1.13694e16	−0.754094
$875$	1.17305e16	0.773168
$876$	−1.55534e14	−0.0101872
$877$	−4.19319e15	−0.272927	−0.136463	−	0.990645i	$-0.543574\pi$
$877$	−4.19319e15	−0.272927	−0.136463	+	0.990645i	$0.543574\pi$
$878$	−1.76946e16	−1.14452
$879$	−1.32439e16	−0.851286
$880$	9.25911e15	0.591445
$881$	−2.40393e16	−1.52600	−0.763000	−	0.646399i	$-0.776274\pi$
$881$	−2.40393e16	−1.52600	−0.763000	+	0.646399i	$0.776274\pi$
$882$	−2.93704e15	−0.185282
$883$	−6.12735e15	−0.384139	−0.192070	−	0.981381i	$-0.561520\pi$
$883$	−6.12735e15	−0.384139	−0.192070	+	0.981381i	$0.561520\pi$
$884$	−3.07194e14	−0.0191393
$885$	3.98250e14	0.0246586
$886$	8.14614e15	0.501264
$887$	−1.15893e16	−0.708724	−0.354362	−	0.935108i	$-0.615302\pi$
$887$	−1.15893e16	−0.708724	−0.354362	+	0.935108i	$0.615302\pi$
$888$	9.23866e15	0.561484
$889$	−1.95020e16	−1.17793
$890$	2.19292e14	0.0131637
$891$	3.30096e15	0.196930
$892$	−1.37266e14	−0.00813870
$893$	6.91592e15	0.407537
$894$	5.78164e14	0.0338606
$895$	8.89566e15	0.517788
$896$	−2.20759e16	−1.27710
$897$	−7.95446e15	−0.457354
$898$	1.99121e16	1.13788
$899$	−1.53968e16	−0.874484
$900$	−9.22296e13	−0.00520639
$901$	3.75672e15	0.210777
$902$	8.41804e15	0.469434
$903$	−6.41623e15	−0.355629
$904$	1.58181e16	0.871424
$905$	−4.08024e15	−0.223418
$906$	−1.43364e16	−0.780252
$907$	3.52662e15	0.190774	0.0953868	−	0.995440i	$-0.469591\pi$
$907$	3.52662e15	0.190774	0.0953868	+	0.995440i	$0.469591\pi$
$908$	1.43286e14	0.00770427
$909$	4.57858e15	0.244698
$910$	4.94796e15	0.262844
$911$	−4.46644e14	−0.0235836	−0.0117918	−	0.999930i	$-0.503754\pi$
$911$	−4.46644e14	−0.0235836	−0.0117918	+	0.999930i	$0.503754\pi$
$912$	6.73480e15	0.353470
$913$	−4.84860e16	−2.52946
$914$	−3.73788e16	−1.93830
$915$	−4.80182e15	−0.247509
$916$	4.59398e14	0.0235377
$917$	5.48342e14	0.0279267
$918$	6.57465e15	0.332842
$919$	−2.41299e16	−1.21429	−0.607143	−	0.794593i	$-0.707684\pi$
$919$	−2.41299e16	−1.21429	−0.607143	+	0.794593i	$0.707684\pi$
$920$	8.07300e15	0.403833
$921$	1.89741e16	0.943480
$922$	3.61627e16	1.78748
$923$	−7.65149e15	−0.375956
$924$	4.56680e14	0.0223057
$925$	−1.80354e16	−0.875683
$926$	−1.67365e16	−0.807803
$927$	1.27169e16	0.610158
$928$	5.95619e14	0.0284089
$929$	−5.21221e15	−0.247136	−0.123568	−	0.992336i	$-0.539434\pi$
$929$	−5.21221e15	−0.247136	−0.123568	+	0.992336i	$0.539434\pi$
$930$	−4.36722e15	−0.205849
$931$	−7.07812e15	−0.331661
$932$	6.03444e14	0.0281093
$933$	−1.12507e16	−0.520993
$934$	8.25865e14	0.0380191
$935$	2.17834e16	0.996922
$936$	4.63083e15	0.210689
$937$	−3.76736e16	−1.70400	−0.852000	−	0.523541i	$-0.824611\pi$
$937$	−3.76736e16	−1.70400	−0.852000	+	0.523541i	$0.824611\pi$
$938$	5.09498e16	2.29101
$939$	−6.13587e15	−0.274294
$940$	8.74834e13	0.00388797
$941$	2.55617e16	1.12940	0.564698	−	0.825298i	$-0.308993\pi$
$941$	2.55617e16	1.12940	0.564698	+	0.825298i	$0.308993\pi$
$942$	4.16283e14	0.0182856
$943$	7.46818e15	0.326137
$944$	3.05018e15	0.132428
$945$	−1.82163e15	−0.0786293
$946$	2.06049e16	0.884237
$947$	1.81337e13	0.000773681 0	0.000386840	−	1.00000i	$-0.499877\pi$
$947$	1.81337e13	0.000773681 0	0.000386840		1.00000i	$0.499877\pi$
$948$	−9.41290e13	−0.00399280
$949$	−1.52452e16	−0.642938
$950$	−1.29212e16	−0.541782
$951$	−9.86684e15	−0.411325
$952$	−5.10583e16	−2.11623
$953$	4.71702e16	1.94382	0.971912	−	0.235344i	$-0.0756218\pi$
$953$	4.71702e16	1.94382	0.971912	+	0.235344i	$0.0756218\pi$
$954$	1.00887e15	0.0413350
$955$	1.77062e15	0.0721284
$956$	5.73364e14	0.0232227
$957$	2.06241e16	0.830537
$958$	6.50424e15	0.260427
$959$	−5.00734e16	−1.99345
$960$	−4.69838e15	−0.185976
$961$	4.08687e15	0.160847
$962$	−1.61322e16	−0.631293
$963$	−1.52031e16	−0.591545
$964$	1.61661e14	0.00625432
$965$	2.87150e15	0.110461
$966$	2.35528e16	0.900882
$967$	7.07719e15	0.269163	0.134581	−	0.990903i	$-0.457031\pi$
$967$	7.07719e15	0.269163	0.134581	+	0.990903i	$0.457031\pi$
$968$	5.61167e16	2.12216
$969$	1.58446e16	0.595799
$970$	−9.19551e15	−0.343820
$971$	2.78049e16	1.03375	0.516875	−	0.856061i	$-0.327095\pi$
$971$	2.78049e16	1.03375	0.516875	+	0.856061i	$0.327095\pi$
$972$	3.03718e13	0.00112281
$973$	−4.32755e16	−1.59082
$974$	2.56878e15	0.0938973
$975$	−9.04018e15	−0.328588
$976$	−3.67769e16	−1.32923
$977$	3.67508e14	0.0132083	0.00660415	−	0.999978i	$-0.497898\pi$
$977$	3.67508e14	0.0132083	0.00660415	+	0.999978i	$0.497898\pi$
$978$	1.52431e16	0.544766
$979$	1.98388e15	0.0705036
$980$	−8.95351e13	−0.00316410
$981$	1.16334e16	0.408815
$982$	−1.74892e16	−0.611164
$983$	1.64787e16	0.572635	0.286317	−	0.958135i	$-0.407569\pi$
$983$	1.64787e16	0.572635	0.286317	+	0.958135i	$0.407569\pi$
$984$	−4.34774e15	−0.150242
$985$	−3.50566e15	−0.120468
$986$	4.10778e16	1.40373
$987$	−1.43270e16	−0.486866
$988$	−1.98814e14	−0.00671866
$989$	1.82799e16	0.614319
$990$	5.84992e15	0.195504
$991$	−7.53912e15	−0.250562	−0.125281	−	0.992121i	$-0.539983\pi$
$991$	−7.53912e15	−0.250562	−0.125281	+	0.992121i	$0.539983\pi$
$992$	−1.14102e15	−0.0377118
$993$	−6.12147e15	−0.201203
$994$	2.26557e16	0.740546
$995$	−4.60852e15	−0.149808
$996$	−4.46116e14	−0.0144219
$997$	9.66084e15	0.310593	0.155296	−	0.987868i	$-0.450367\pi$
$997$	9.66084e15	0.310593	0.155296	+	0.987868i	$0.450367\pi$
$998$	3.75542e16	1.20072
$999$	5.93919e15	0.188850

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.b.1.10	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.b.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-45.6492 q^{2} +243.000 q^{3} +35.8459 q^{4} -2292.40 q^{5} -11092.7 q^{6} +55379.8 q^{7} +91853.1 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-45.6492 q^{2} +243.000 q^{3} +35.8459 q^{4} -2292.40 q^{5} -11092.7 q^{6} +55379.8 q^{7} +91853.1 q^{8} +59049.0 q^{9} +104646. q^{10} +946706. q^{11} +8710.56 q^{12} +853793. q^{13} -2.52804e6 q^{14} -557052. q^{15} -4.26643e6 q^{16} -1.00374e7 q^{17} -2.69554e6 q^{18} -6.49611e6 q^{19} -82173.0 q^{20} +1.34573e7 q^{21} -4.32163e7 q^{22} -3.83400e7 q^{23} +2.23203e7 q^{24} -4.35730e7 q^{25} -3.89749e7 q^{26} +1.43489e7 q^{27} +1.98514e6 q^{28} +8.96507e7 q^{29} +2.54290e7 q^{30} -1.71742e8 q^{31} +6.64378e6 q^{32} +2.30049e8 q^{33} +4.58198e8 q^{34} -1.26952e8 q^{35} +2.11667e6 q^{36} +4.13912e8 q^{37} +2.96542e8 q^{38} +2.07472e8 q^{39} -2.10564e8 q^{40} -1.94788e8 q^{41} -6.14314e8 q^{42} -4.76784e8 q^{43} +3.39355e7 q^{44} -1.35364e8 q^{45} +1.75019e9 q^{46} -1.06462e9 q^{47} -1.03674e9 q^{48} +1.08959e9 q^{49} +1.98907e9 q^{50} -2.43909e9 q^{51} +3.06050e7 q^{52} -3.74273e8 q^{53} -6.55016e8 q^{54} -2.17022e9 q^{55} +5.08681e9 q^{56} -1.57856e9 q^{57} -4.09248e9 q^{58} -7.14924e8 q^{59} -1.99680e7 q^{60} +8.62006e9 q^{61} +7.83988e9 q^{62} +3.27012e9 q^{63} +8.43437e9 q^{64} -1.95723e9 q^{65} -1.05016e10 q^{66} -2.01539e10 q^{67} -3.59799e8 q^{68} -9.31661e9 q^{69} +5.79527e9 q^{70} -8.96176e9 q^{71} +5.42384e9 q^{72} -1.78559e10 q^{73} -1.88948e10 q^{74} -1.05883e10 q^{75} -2.32859e8 q^{76} +5.24283e10 q^{77} -9.47091e9 q^{78} -1.08063e10 q^{79} +9.78035e9 q^{80} +3.48678e9 q^{81} +8.89193e9 q^{82} -5.12155e10 q^{83} +4.82389e8 q^{84} +2.30097e10 q^{85} +2.17648e10 q^{86} +2.17851e10 q^{87} +8.69579e10 q^{88} +2.09557e9 q^{89} +6.17924e9 q^{90} +4.72829e10 q^{91} -1.37433e9 q^{92} -4.17333e10 q^{93} +4.85992e10 q^{94} +1.48917e10 q^{95} +1.61444e9 q^{96} -8.78726e10 q^{97} -4.97390e10 q^{98} +5.59020e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) \) 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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