LMFDB - Embedded newform 177.12.a.b.1.2

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			1.2
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)

$f(q)$	$=$	$q-86.7335 q^{2} +243.000 q^{3} +5474.69 q^{4} -11727.0 q^{5} -21076.2 q^{6} +24236.6 q^{7} -297209. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-86.7335 q^{2} +243.000 q^{3} +5474.69 q^{4} -11727.0 q^{5} -21076.2 q^{6} +24236.6 q^{7} -297209. q^{8} +59049.0 q^{9} +1.01712e6 q^{10} -225721. q^{11} +1.33035e6 q^{12} -1.93565e6 q^{13} -2.10212e6 q^{14} -2.84965e6 q^{15} +1.45658e7 q^{16} -7.58845e6 q^{17} -5.12152e6 q^{18} +2.02438e7 q^{19} -6.42015e7 q^{20} +5.88949e6 q^{21} +1.95775e7 q^{22} +4.13605e6 q^{23} -7.22217e7 q^{24} +8.86937e7 q^{25} +1.67885e8 q^{26} +1.43489e7 q^{27} +1.32688e8 q^{28} +1.28733e8 q^{29} +2.47160e8 q^{30} -1.26556e8 q^{31} -6.54656e8 q^{32} -5.48501e7 q^{33} +6.58173e8 q^{34} -2.84222e8 q^{35} +3.23275e8 q^{36} +1.58528e8 q^{37} -1.75581e9 q^{38} -4.70363e8 q^{39} +3.48536e9 q^{40} +7.42011e8 q^{41} -5.10816e8 q^{42} -1.64490e8 q^{43} -1.23575e9 q^{44} -6.92466e8 q^{45} -3.58734e8 q^{46} -1.37797e9 q^{47} +3.53948e9 q^{48} -1.38992e9 q^{49} -7.69271e9 q^{50} -1.84399e9 q^{51} -1.05971e10 q^{52} +4.06680e8 q^{53} -1.24453e9 q^{54} +2.64702e9 q^{55} -7.20332e9 q^{56} +4.91924e9 q^{57} -1.11655e10 q^{58} -7.14924e8 q^{59} -1.56010e10 q^{60} +1.25207e9 q^{61} +1.09767e10 q^{62} +1.43115e9 q^{63} +2.69499e10 q^{64} +2.26993e10 q^{65} +4.75734e9 q^{66} -3.89914e9 q^{67} -4.15444e10 q^{68} +1.00506e9 q^{69} +2.46515e10 q^{70} +2.09101e10 q^{71} -1.75499e10 q^{72} +1.32307e10 q^{73} -1.37497e10 q^{74} +2.15526e10 q^{75} +1.10829e11 q^{76} -5.47069e9 q^{77} +4.07962e10 q^{78} +3.04105e10 q^{79} -1.70812e11 q^{80} +3.48678e9 q^{81} -6.43572e10 q^{82} -6.10863e10 q^{83} +3.22431e10 q^{84} +8.89895e10 q^{85} +1.42668e10 q^{86} +3.12822e10 q^{87} +6.70861e10 q^{88} +6.05385e10 q^{89} +6.00600e10 q^{90} -4.69135e10 q^{91} +2.26436e10 q^{92} -3.07532e10 q^{93} +1.19516e11 q^{94} -2.37398e11 q^{95} -1.59081e11 q^{96} -1.06180e11 q^{97} +1.20552e11 q^{98} -1.33286e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−86.7335	−1.91656	−0.958278	−	0.285837i	$-0.907728\pi$
$2$	−86.7335	−1.91656	−0.958278	+	0.285837i	$0.907728\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	5474.69	2.67319
$5$	−11727.0	−1.67823	−0.839114	−	0.543956i	$-0.816926\pi$
$5$	−11727.0	−1.67823	−0.839114	+	0.543956i	$0.816926\pi$
$6$	−21076.2	−1.10652
$7$	24236.6	0.545045	0.272522	−	0.962149i	$-0.412142\pi$
$7$	24236.6	0.545045	0.272522	+	0.962149i	$0.412142\pi$
$8$	−297209.	−3.20676
$9$	59049.0	0.333333
$10$	1.01712e6	3.21642
$11$	−225721.	−0.422582	−0.211291	−	0.977423i	$-0.567767\pi$
$11$	−225721.	−0.422582	−0.211291	+	0.977423i	$0.567767\pi$
$12$	1.33035e6	1.54337
$13$	−1.93565e6	−1.44590	−0.722950	−	0.690901i	$-0.757214\pi$
$13$	−1.93565e6	−1.44590	−0.722950	+	0.690901i	$0.757214\pi$
$14$	−2.10212e6	−1.04461
$15$	−2.84965e6	−0.968925
$16$	1.45658e7	3.47275
$17$	−7.58845e6	−1.29624	−0.648118	−	0.761540i	$-0.724444\pi$
$17$	−7.58845e6	−1.29624	−0.648118	+	0.761540i	$0.724444\pi$
$18$	−5.12152e6	−0.638852
$19$	2.02438e7	1.87563	0.937815	−	0.347136i	$-0.112846\pi$
$19$	2.02438e7	1.87563	0.937815	+	0.347136i	$0.112846\pi$
$20$	−6.42015e7	−4.48622
$21$	5.88949e6	0.314682
$22$	1.95775e7	0.809903
$23$	4.13605e6	0.133993	0.0669965	−	0.997753i	$-0.478658\pi$
$23$	4.13605e6	0.133993	0.0669965	+	0.997753i	$0.478658\pi$
$24$	−7.22217e7	−1.85142
$25$	8.86937e7	1.81645
$26$	1.67885e8	2.77115
$27$	1.43489e7	0.192450
$28$	1.32688e8	1.45701
$29$	1.28733e8	1.16547	0.582736	−	0.812662i	$-0.301982\pi$
$29$	1.28733e8	1.16547	0.582736	+	0.812662i	$0.301982\pi$
$30$	2.47160e8	1.85700
$31$	−1.26556e8	−0.793953	−0.396976	−	0.917829i	$-0.629941\pi$
$31$	−1.26556e8	−0.793953	−0.396976	+	0.917829i	$0.629941\pi$
$32$	−6.54656e8	−3.44896
$33$	−5.48501e7	−0.243978
$34$	6.58173e8	2.48431
$35$	−2.84222e8	−0.914709
$36$	3.23275e8	0.891063
$37$	1.58528e8	0.375834	0.187917	−	0.982185i	$-0.439826\pi$
$37$	1.58528e8	0.375834	0.187917	+	0.982185i	$0.439826\pi$
$38$	−1.75581e9	−3.59475
$39$	−4.70363e8	−0.834790
$40$	3.48536e9	5.38168
$41$	7.42011e8	1.00023	0.500114	−	0.865959i	$-0.333291\pi$
$41$	7.42011e8	1.00023	0.500114	+	0.865959i	$0.333291\pi$
$42$	−5.10816e8	−0.603105
$43$	−1.64490e8	−0.170633	−0.0853166	−	0.996354i	$-0.527190\pi$
$43$	−1.64490e8	−0.170633	−0.0853166	+	0.996354i	$0.527190\pi$
$44$	−1.23575e9	−1.12964
$45$	−6.92466e8	−0.559409
$46$	−3.58734e8	−0.256805
$47$	−1.37797e9	−0.876401	−0.438200	−	0.898877i	$-0.644384\pi$
$47$	−1.37797e9	−0.876401	−0.438200	+	0.898877i	$0.644384\pi$
$48$	3.53948e9	2.00499
$49$	−1.38992e9	−0.702926
$50$	−7.69271e9	−3.48132
$51$	−1.84399e9	−0.748382
$52$	−1.05971e10	−3.86516
$53$	4.06680e8	0.133578	0.0667891	−	0.997767i	$-0.478725\pi$
$53$	4.06680e8	0.133578	0.0667891	+	0.997767i	$0.478725\pi$
$54$	−1.24453e9	−0.368841
$55$	2.64702e9	0.709189
$56$	−7.20332e9	−1.74783
$57$	4.91924e9	1.08290
$58$	−1.11655e10	−2.23369
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	−1.56010e10	−2.59012
$61$	1.25207e9	0.189808	0.0949042	−	0.995486i	$-0.469746\pi$
$61$	1.25207e9	0.189808	0.0949042	+	0.995486i	$0.469746\pi$
$62$	1.09767e10	1.52166
$63$	1.43115e9	0.181682
$64$	2.69499e10	3.13738
$65$	2.26993e10	2.42655
$66$	4.75734e9	0.467598
$67$	−3.89914e9	−0.352823	−0.176412	−	0.984316i	$-0.556449\pi$
$67$	−3.89914e9	−0.352823	−0.176412	+	0.984316i	$0.556449\pi$
$68$	−4.15444e10	−3.46508
$69$	1.00506e9	0.0773609
$70$	2.46515e10	1.75309
$71$	2.09101e10	1.37542	0.687709	−	0.725986i	$-0.258617\pi$
$71$	2.09101e10	1.37542	0.687709	+	0.725986i	$0.258617\pi$
$72$	−1.75499e10	−1.06892
$73$	1.32307e10	0.746975	0.373487	−	0.927635i	$-0.378162\pi$
$73$	1.32307e10	0.746975	0.373487	+	0.927635i	$0.378162\pi$
$74$	−1.37497e10	−0.720308
$75$	2.15526e10	1.04873
$76$	1.10829e11	5.01391
$77$	−5.47069e9	−0.230326
$78$	4.07962e10	1.59992
$79$	3.04105e10	1.11192	0.555961	−	0.831208i	$-0.312350\pi$
$79$	3.04105e10	1.11192	0.555961	+	0.831208i	$0.312350\pi$
$80$	−1.70812e11	−5.82807
$81$	3.48678e9	0.111111
$82$	−6.43572e10	−1.91699
$83$	−6.10863e10	−1.70221	−0.851107	−	0.524993i	$-0.824068\pi$
$83$	−6.10863e10	−1.70221	−0.851107	+	0.524993i	$0.824068\pi$
$84$	3.22431e10	0.841204
$85$	8.89895e10	2.17538
$86$	1.42668e10	0.327028
$87$	3.12822e10	0.672885
$88$	6.70861e10	1.35512
$89$	6.05385e10	1.14918	0.574588	−	0.818443i	$-0.305162\pi$
$89$	6.05385e10	1.14918	0.574588	+	0.818443i	$0.305162\pi$
$90$	6.00600e10	1.07214
$91$	−4.69135e10	−0.788080
$92$	2.26436e10	0.358189
$93$	−3.07532e10	−0.458389
$94$	1.19516e11	1.67967
$95$	−2.37398e11	−3.14773
$96$	−1.59081e11	−1.99126
$97$	−1.06180e11	−1.25544	−0.627720	−	0.778439i	$-0.716012\pi$
$97$	−1.06180e11	−1.25544	−0.627720	+	0.778439i	$0.716012\pi$
$98$	1.20552e11	1.34720
$99$	−1.33286e10	−0.140861
$100$	4.85571e11	4.85571
$101$	1.20010e11	1.13619	0.568094	−	0.822964i	$-0.307681\pi$
$101$	1.20010e11	1.13619	0.568094	+	0.822964i	$0.307681\pi$
$102$	1.59936e11	1.43432
$103$	8.50039e10	0.722493	0.361247	−	0.932470i	$-0.382351\pi$
$103$	8.50039e10	0.722493	0.361247	+	0.932470i	$0.382351\pi$
$104$	5.75292e11	4.63665
$105$	−6.90659e10	−0.528107
$106$	−3.52728e10	−0.256010
$107$	1.46709e11	1.01122	0.505612	−	0.862761i	$-0.331267\pi$
$107$	1.46709e11	1.01122	0.505612	+	0.862761i	$0.331267\pi$
$108$	7.85558e10	0.514455
$109$	2.04883e11	1.27544	0.637721	−	0.770267i	$-0.279877\pi$
$109$	2.04883e11	1.27544	0.637721	+	0.770267i	$0.279877\pi$
$110$	−2.29585e11	−1.35920
$111$	3.85223e10	0.216988
$112$	3.53024e11	1.89280
$113$	2.74469e10	0.140140	0.0700699	−	0.997542i	$-0.477678\pi$
$113$	2.74469e10	0.140140	0.0700699	+	0.997542i	$0.477678\pi$
$114$	−4.26663e11	−2.07543
$115$	−4.85033e10	−0.224871
$116$	7.04775e11	3.11553
$117$	−1.14298e11	−0.481966
$118$	6.20079e10	0.249514
$119$	−1.83918e11	−0.706506
$120$	8.46942e11	3.10711
$121$	−2.34362e11	−0.821424
$122$	−1.08597e11	−0.363779
$123$	1.80309e11	0.577482
$124$	−6.92857e11	−2.12239
$125$	−4.67503e11	−1.37018
$126$	−1.24128e11	−0.348203
$127$	3.40084e11	0.913411	0.456706	−	0.889618i	$-0.349029\pi$
$127$	3.40084e11	0.913411	0.456706	+	0.889618i	$0.349029\pi$
$128$	−9.96721e11	−2.56400
$129$	−3.99711e10	−0.0985151
$130$	−1.96879e12	−4.65062
$131$	−8.54131e11	−1.93434	−0.967169	−	0.254133i	$-0.918210\pi$
$131$	−8.54131e11	−1.93434	−0.967169	+	0.254133i	$0.918210\pi$
$132$	−3.00287e11	−0.652199
$133$	4.90640e11	1.02230
$134$	3.38186e11	0.676206
$135$	−1.68269e11	−0.322975
$136$	2.25535e12	4.15672
$137$	4.87116e11	0.862321	0.431161	−	0.902275i	$-0.358104\pi$
$137$	4.87116e11	0.862321	0.431161	+	0.902275i	$0.358104\pi$
$138$	−8.71722e10	−0.148267
$139$	4.36340e11	0.713253	0.356627	−	0.934247i	$-0.383927\pi$
$139$	4.36340e11	0.713253	0.356627	+	0.934247i	$0.383927\pi$
$140$	−1.55603e12	−2.44519
$141$	−3.34848e11	−0.505990
$142$	−1.81360e12	−2.63607
$143$	4.36916e11	0.611012
$144$	8.60094e11	1.15758
$145$	−1.50965e12	−1.95593
$146$	−1.14754e12	−1.43162
$147$	−3.37749e11	−0.405835
$148$	8.67892e11	1.00468
$149$	1.56344e11	0.174405	0.0872023	−	0.996191i	$-0.472207\pi$
$149$	1.56344e11	0.174405	0.0872023	+	0.996191i	$0.472207\pi$
$150$	−1.86933e12	−2.00994
$151$	−9.22244e11	−0.956032	−0.478016	−	0.878351i	$-0.658644\pi$
$151$	−9.22244e11	−0.956032	−0.478016	+	0.878351i	$0.658644\pi$
$152$	−6.01663e12	−6.01470
$153$	−4.48090e11	−0.432079
$154$	4.74492e11	0.441433
$155$	1.48412e12	1.33243
$156$	−2.57509e12	−2.23155
$157$	−1.30773e12	−1.09413	−0.547067	−	0.837089i	$-0.684256\pi$
$157$	−1.30773e12	−1.09413	−0.547067	+	0.837089i	$0.684256\pi$
$158$	−2.63761e12	−2.13106
$159$	9.88233e10	0.0771214
$160$	7.67713e12	5.78814
$161$	1.00244e11	0.0730322
$162$	−3.02421e11	−0.212951
$163$	−1.36308e12	−0.927873	−0.463937	−	0.885868i	$-0.653563\pi$
$163$	−1.36308e12	−0.927873	−0.463937	+	0.885868i	$0.653563\pi$
$164$	4.06228e12	2.67380
$165$	6.43225e11	0.409451
$166$	5.29822e12	3.26239
$167$	1.84641e12	1.09999	0.549995	−	0.835168i	$-0.314630\pi$
$167$	1.84641e12	1.09999	0.549995	+	0.835168i	$0.314630\pi$
$168$	−1.75041e12	−1.00911
$169$	1.95458e12	1.09063
$170$	−7.71837e12	−4.16924
$171$	1.19538e12	0.625210
$172$	−9.00533e11	−0.456135
$173$	1.76237e12	0.864655	0.432327	−	0.901717i	$-0.357693\pi$
$173$	1.76237e12	0.864655	0.432327	+	0.901717i	$0.357693\pi$
$174$	−2.71321e12	−1.28962
$175$	2.14963e12	0.990045
$176$	−3.28779e12	−1.46752
$177$	−1.73727e11	−0.0751646
$178$	−5.25071e12	−2.20246
$179$	4.00844e12	1.63036	0.815180	−	0.579208i	$-0.196638\pi$
$179$	4.00844e12	1.63036	0.815180	+	0.579208i	$0.196638\pi$
$180$	−3.79104e12	−1.49541
$181$	9.05666e11	0.346526	0.173263	−	0.984876i	$-0.444569\pi$
$181$	9.05666e11	0.346526	0.173263	+	0.984876i	$0.444569\pi$
$182$	4.06897e12	1.51040
$183$	3.04254e11	0.109586
$184$	−1.22927e12	−0.429684
$185$	−1.85905e12	−0.630735
$186$	2.66733e12	0.878528
$187$	1.71287e12	0.547766
$188$	−7.54398e12	−2.34278
$189$	3.47768e11	0.104894
$190$	2.05904e13	6.03281
$191$	−6.55756e12	−1.86663	−0.933316	−	0.359055i	$-0.883099\pi$
$191$	−6.55756e12	−1.86663	−0.933316	+	0.359055i	$0.883099\pi$
$192$	6.54882e12	1.81137
$193$	−6.69275e12	−1.79903	−0.899517	−	0.436885i	$-0.856082\pi$
$193$	−6.69275e12	−1.79903	−0.899517	+	0.436885i	$0.856082\pi$
$194$	9.20932e12	2.40612
$195$	5.51593e12	1.40097
$196$	−7.60936e12	−1.87906
$197$	−3.16829e12	−0.760783	−0.380391	−	0.924826i	$-0.624211\pi$
$197$	−3.16829e12	−0.760783	−0.380391	+	0.924826i	$0.624211\pi$
$198$	1.15603e12	0.269968
$199$	4.98278e12	1.13183	0.565913	−	0.824465i	$-0.308524\pi$
$199$	4.98278e12	1.13183	0.565913	+	0.824465i	$0.308524\pi$
$200$	−2.63605e13	−5.82491
$201$	−9.47490e11	−0.203703
$202$	−1.04089e13	−2.17757
$203$	3.12005e12	0.635234
$204$	−1.00953e13	−2.00057
$205$	−8.70154e12	−1.67861
$206$	−7.37268e12	−1.38470
$207$	2.44229e11	0.0446643
$208$	−2.81942e13	−5.02125
$209$	−4.56944e12	−0.792608
$210$	5.99032e12	1.01215
$211$	4.55874e12	0.750397	0.375199	−	0.926944i	$-0.377575\pi$
$211$	4.55874e12	0.750397	0.375199	+	0.926944i	$0.377575\pi$
$212$	2.22645e12	0.357080
$213$	5.08115e12	0.794098
$214$	−1.27246e13	−1.93807
$215$	1.92897e12	0.286361
$216$	−4.26462e12	−0.617142
$217$	−3.06729e12	−0.432740
$218$	−1.77702e13	−2.44446
$219$	3.21505e12	0.431266
$220$	1.44916e13	1.89580
$221$	1.46886e13	1.87423
$222$	−3.34117e12	−0.415870
$223$	−8.99847e12	−1.09268	−0.546339	−	0.837564i	$-0.683979\pi$
$223$	−8.99847e12	−1.09268	−0.546339	+	0.837564i	$0.683979\pi$
$224$	−1.58666e13	−1.87984
$225$	5.23727e12	0.605482
$226$	−2.38056e12	−0.268586
$227$	−1.33843e12	−0.147385	−0.0736925	−	0.997281i	$-0.523478\pi$
$227$	−1.33843e12	−0.147385	−0.0736925	+	0.997281i	$0.523478\pi$
$228$	2.69313e13	2.89478
$229$	−1.15610e13	−1.21311	−0.606555	−	0.795042i	$-0.707449\pi$
$229$	−1.15610e13	−1.21311	−0.606555	+	0.795042i	$0.707449\pi$
$230$	4.20686e12	0.430978
$231$	−1.32938e12	−0.132979
$232$	−3.82606e13	−3.73739
$233$	−5.98856e12	−0.571301	−0.285650	−	0.958334i	$-0.592210\pi$
$233$	−5.98856e12	−0.571301	−0.285650	+	0.958334i	$0.592210\pi$
$234$	9.91347e12	0.923716
$235$	1.61595e13	1.47080
$236$	−3.91399e12	−0.348020
$237$	7.38975e12	0.641969
$238$	1.59519e13	1.35406
$239$	1.71328e13	1.42115	0.710576	−	0.703620i	$-0.248434\pi$
$239$	1.71328e13	1.42115	0.710576	+	0.703620i	$0.248434\pi$
$240$	−4.15074e13	−3.36484
$241$	1.29158e13	1.02336	0.511679	−	0.859177i	$-0.329024\pi$
$241$	1.29158e13	1.02336	0.511679	+	0.859177i	$0.329024\pi$
$242$	2.03270e13	1.57431
$243$	8.47289e11	0.0641500
$244$	6.85471e12	0.507394
$245$	1.62995e13	1.17967
$246$	−1.56388e13	−1.10678
$247$	−3.91849e13	−2.71197
$248$	3.76137e13	2.54602
$249$	−1.48440e13	−0.982773
$250$	4.05481e13	2.62604
$251$	−2.60915e13	−1.65308	−0.826540	−	0.562879i	$-0.809694\pi$
$251$	−2.60915e13	−1.65308	−0.826540	+	0.562879i	$0.809694\pi$
$252$	7.83508e12	0.485669
$253$	−9.33591e11	−0.0566231
$254$	−2.94967e13	−1.75060
$255$	2.16245e13	1.25596
$256$	3.12557e13	1.77668
$257$	2.28259e13	1.26998	0.634989	−	0.772521i	$-0.281005\pi$
$257$	2.28259e13	1.26998	0.634989	+	0.772521i	$0.281005\pi$
$258$	3.46683e12	0.188810
$259$	3.84218e12	0.204846
$260$	1.24272e14	6.48662
$261$	7.60157e12	0.388491
$262$	7.40818e13	3.70727
$263$	−2.36115e13	−1.15709	−0.578545	−	0.815651i	$-0.696379\pi$
$263$	−2.36115e13	−1.15709	−0.578545	+	0.815651i	$0.696379\pi$
$264$	1.63019e13	0.782379
$265$	−4.76912e12	−0.224175
$266$	−4.25549e13	−1.95930
$267$	1.47108e13	0.663477
$268$	−2.13466e13	−0.943163
$269$	−3.13089e13	−1.35528	−0.677642	−	0.735392i	$-0.736998\pi$
$269$	−3.13089e13	−1.35528	−0.677642	+	0.735392i	$0.736998\pi$
$270$	1.45946e13	0.619000
$271$	−4.19841e13	−1.74483	−0.872417	−	0.488763i	$-0.837448\pi$
$271$	−4.19841e13	−1.74483	−0.872417	+	0.488763i	$0.837448\pi$
$272$	−1.10532e14	−4.50151
$273$	−1.14000e13	−0.454998
$274$	−4.22492e13	−1.65269
$275$	−2.00200e13	−0.767599
$276$	5.50239e12	0.206800
$277$	−3.49366e13	−1.28719	−0.643595	−	0.765366i	$-0.722558\pi$
$277$	−3.49366e13	−1.28719	−0.643595	+	0.765366i	$0.722558\pi$
$278$	−3.78453e13	−1.36699
$279$	−7.47303e12	−0.264651
$280$	8.44732e13	2.93325
$281$	−5.31784e13	−1.81072	−0.905359	−	0.424647i	$-0.860398\pi$
$281$	−5.31784e13	−1.81072	−0.905359	+	0.424647i	$0.860398\pi$
$282$	2.90425e13	0.969759
$283$	−1.01159e13	−0.331267	−0.165633	−	0.986187i	$-0.552967\pi$
$283$	−1.01159e13	−0.331267	−0.165633	+	0.986187i	$0.552967\pi$
$284$	1.14476e14	3.67675
$285$	−5.76878e13	−1.81734
$286$	−3.78952e13	−1.17104
$287$	1.79838e13	0.545169
$288$	−3.86568e13	−1.14965
$289$	2.33127e13	0.680228
$290$	1.30937e14	3.74864
$291$	−2.58016e13	−0.724829
$292$	7.24338e13	1.99680
$293$	−1.50814e13	−0.408008	−0.204004	−	0.978970i	$-0.565396\pi$
$293$	−1.50814e13	−0.408008	−0.204004	+	0.978970i	$0.565396\pi$
$294$	2.92942e13	0.777805
$295$	8.38390e12	0.218487
$296$	−4.71159e13	−1.20521
$297$	−3.23884e12	−0.0813260
$298$	−1.35603e13	−0.334256
$299$	−8.00593e12	−0.193740
$300$	1.17994e14	2.80344
$301$	−3.98668e12	−0.0930027
$302$	7.99894e13	1.83229
$303$	2.91624e13	0.655978
$304$	2.94866e14	6.51359
$305$	−1.46830e13	−0.318542
$306$	3.88644e13	0.828103
$307$	1.31999e13	0.276256	0.138128	−	0.990414i	$-0.455892\pi$
$307$	1.31999e13	0.276256	0.138128	+	0.990414i	$0.455892\pi$
$308$	−2.99504e13	−0.615706
$309$	2.06559e13	0.417132
$310$	−1.28723e14	−2.55368
$311$	−5.37958e13	−1.04850	−0.524248	−	0.851566i	$-0.675653\pi$
$311$	−5.37958e13	−1.04850	−0.524248	+	0.851566i	$0.675653\pi$
$312$	1.39796e14	2.67697
$313$	2.38417e13	0.448583	0.224291	−	0.974522i	$-0.427993\pi$
$313$	2.38417e13	0.448583	0.224291	+	0.974522i	$0.427993\pi$
$314$	1.13424e14	2.09697
$315$	−1.67830e13	−0.304903
$316$	1.66488e14	2.97238
$317$	5.46736e13	0.959294	0.479647	−	0.877461i	$-0.340765\pi$
$317$	5.46736e13	0.959294	0.479647	+	0.877461i	$0.340765\pi$
$318$	−8.57128e12	−0.147808
$319$	−2.90577e13	−0.492508
$320$	−3.16041e14	−5.26524
$321$	3.56504e13	0.583830
$322$	−8.69447e12	−0.139970
$323$	−1.53619e14	−2.43126
$324$	1.90891e13	0.297021
$325$	−1.71680e14	−2.62640
$326$	1.18224e14	1.77832
$327$	4.97866e13	0.736377
$328$	−2.20532e14	−3.20749
$329$	−3.33974e13	−0.477677
$330$	−5.57892e13	−0.784735
$331$	−4.00410e13	−0.553925	−0.276962	−	0.960881i	$-0.589328\pi$
$331$	−4.00410e13	−0.553925	−0.276962	+	0.960881i	$0.589328\pi$
$332$	−3.34428e14	−4.55034
$333$	9.36092e12	0.125278
$334$	−1.60146e14	−2.10819
$335$	4.57251e13	0.592118
$336$	8.57850e13	1.09281
$337$	1.09478e14	1.37203	0.686013	−	0.727589i	$-0.259359\pi$
$337$	1.09478e14	1.37203	0.686013	+	0.727589i	$0.259359\pi$
$338$	−1.69527e14	−2.09024
$339$	6.66959e12	0.0809098
$340$	4.87190e14	5.81520
$341$	2.85664e13	0.335511
$342$	−1.03679e14	−1.19825
$343$	−8.16104e13	−0.928171
$344$	4.88879e13	0.547180
$345$	−1.17863e13	−0.129829
$346$	−1.52856e14	−1.65716
$347$	6.14955e13	0.656193	0.328096	−	0.944644i	$-0.393593\pi$
$347$	6.14955e13	0.656193	0.328096	+	0.944644i	$0.393593\pi$
$348$	1.71260e14	1.79875
$349$	−1.61145e14	−1.66601	−0.833005	−	0.553266i	$-0.813381\pi$
$349$	−1.61145e14	−1.66601	−0.833005	+	0.553266i	$0.813381\pi$
$350$	−1.86445e14	−1.89748
$351$	−2.77744e13	−0.278263
$352$	1.47769e14	1.45747
$353$	−5.18807e13	−0.503785	−0.251892	−	0.967755i	$-0.581053\pi$
$353$	−5.18807e13	−0.503785	−0.251892	+	0.967755i	$0.581053\pi$
$354$	1.50679e13	0.144057
$355$	−2.45212e14	−2.30826
$356$	3.31429e14	3.07196
$357$	−4.46921e13	−0.407902
$358$	−3.47665e14	−3.12468
$359$	−2.44194e13	−0.216130	−0.108065	−	0.994144i	$-0.534466\pi$
$359$	−2.44194e13	−0.216130	−0.108065	+	0.994144i	$0.534466\pi$
$360$	2.05807e14	1.79389
$361$	2.93321e14	2.51799
$362$	−7.85515e13	−0.664137
$363$	−5.69499e13	−0.474249
$364$	−2.56837e14	−2.10669
$365$	−1.55156e14	−1.25359
$366$	−2.63890e13	−0.210028
$367$	1.30968e14	1.02684	0.513418	−	0.858139i	$-0.328379\pi$
$367$	1.30968e14	1.02684	0.513418	+	0.858139i	$0.328379\pi$
$368$	6.02447e13	0.465324
$369$	4.38150e13	0.333409
$370$	1.61242e14	1.20884
$371$	9.85653e12	0.0728061
$372$	−1.68364e14	−1.22536
$373$	2.23070e14	1.59972	0.799858	−	0.600189i	$-0.204908\pi$
$373$	2.23070e14	1.59972	0.799858	+	0.600189i	$0.204908\pi$
$374$	−1.48563e14	−1.04983
$375$	−1.13603e14	−0.791076
$376$	4.09546e14	2.81041
$377$	−2.49182e14	−1.68515
$378$	−3.01632e13	−0.201035
$379$	9.13403e13	0.599994	0.299997	−	0.953940i	$-0.403014\pi$
$379$	9.13403e13	0.599994	0.299997	+	0.953940i	$0.403014\pi$
$380$	−1.29968e15	−8.41449
$381$	8.26405e13	0.527358
$382$	5.68760e14	3.57751
$383$	−1.79938e14	−1.11565	−0.557826	−	0.829958i	$-0.688364\pi$
$383$	−1.79938e14	−1.11565	−0.557826	+	0.829958i	$0.688364\pi$
$384$	−2.42203e14	−1.48033
$385$	6.41547e13	0.386540
$386$	5.80485e14	3.44795
$387$	−9.71298e12	−0.0568777
$388$	−5.81300e14	−3.35603
$389$	−2.49341e14	−1.41929	−0.709643	−	0.704561i	$-0.751144\pi$
$389$	−2.49341e14	−1.41929	−0.709643	+	0.704561i	$0.751144\pi$
$390$	−4.78416e14	−2.68503
$391$	−3.13862e13	−0.173687
$392$	4.13095e14	2.25412
$393$	−2.07554e14	−1.11679
$394$	2.74797e14	1.45808
$395$	−3.56623e14	−1.86606
$396$	−7.29698e13	−0.376548
$397$	2.47278e14	1.25845	0.629226	−	0.777222i	$-0.283372\pi$
$397$	2.47278e14	1.25845	0.629226	+	0.777222i	$0.283372\pi$
$398$	−4.32174e14	−2.16921
$399$	1.19226e14	0.590226
$400$	1.29189e15	6.30807
$401$	3.49823e13	0.168483	0.0842413	−	0.996445i	$-0.473153\pi$
$401$	3.49823e13	0.168483	0.0842413	+	0.996445i	$0.473153\pi$
$402$	8.21791e13	0.390407
$403$	2.44969e14	1.14798
$404$	6.57018e14	3.03724
$405$	−4.08894e13	−0.186470
$406$	−2.70613e14	−1.21746
$407$	−3.57830e13	−0.158821
$408$	5.48051e14	2.39988
$409$	−2.42776e14	−1.04888	−0.524441	−	0.851447i	$-0.675726\pi$
$409$	−2.42776e14	−1.04888	−0.524441	+	0.851447i	$0.675726\pi$
$410$	7.54715e14	3.21715
$411$	1.18369e14	0.497861
$412$	4.65370e14	1.93136
$413$	−1.73273e13	−0.0709588
$414$	−2.11829e13	−0.0856017
$415$	7.16357e14	2.85670
$416$	1.26718e15	4.98685
$417$	1.06031e14	0.411797
$418$	3.96323e14	1.51908
$419$	1.65501e14	0.626069	0.313035	−	0.949742i	$-0.398654\pi$
$419$	1.65501e14	0.626069	0.313035	+	0.949742i	$0.398654\pi$
$420$	−3.78114e14	−1.41173
$421$	−5.33194e14	−1.96487	−0.982435	−	0.186604i	$-0.940252\pi$
$421$	−5.33194e14	−1.96487	−0.982435	+	0.186604i	$0.940252\pi$
$422$	−3.95395e14	−1.43818
$423$	−8.13680e13	−0.292134
$424$	−1.20869e14	−0.428353
$425$	−6.73048e14	−2.35454
$426$	−4.40706e14	−1.52193
$427$	3.03460e13	0.103454
$428$	8.03189e14	2.70319
$429$	1.06171e14	0.352768
$430$	−1.67306e14	−0.548828
$431$	2.86684e14	0.928494	0.464247	−	0.885706i	$-0.346325\pi$
$431$	2.86684e14	0.928494	0.464247	+	0.885706i	$0.346325\pi$
$432$	2.09003e14	0.668331
$433$	3.80518e14	1.20141	0.600706	−	0.799470i	$-0.294886\pi$
$433$	3.80518e14	1.20141	0.600706	+	0.799470i	$0.294886\pi$
$434$	2.66037e14	0.829370
$435$	−3.66845e14	−1.12925
$436$	1.12167e15	3.40950
$437$	8.37293e13	0.251321
$438$	−2.78852e14	−0.826546
$439$	−4.85503e14	−1.42114	−0.710570	−	0.703626i	$-0.751563\pi$
$439$	−4.85503e14	−1.42114	−0.710570	+	0.703626i	$0.751563\pi$
$440$	−7.86717e14	−2.27420
$441$	−8.20731e13	−0.234309
$442$	−1.27399e15	−3.59206
$443$	6.11464e14	1.70275	0.851373	−	0.524560i	$-0.175770\pi$
$443$	6.11464e14	1.70275	0.851373	+	0.524560i	$0.175770\pi$
$444$	2.10898e14	0.580050
$445$	−7.09933e14	−1.92858
$446$	7.80468e14	2.09418
$447$	3.79917e13	0.100693
$448$	6.53173e14	1.71001
$449$	−3.00652e14	−0.777516	−0.388758	−	0.921340i	$-0.627096\pi$
$449$	−3.00652e14	−0.777516	−0.388758	+	0.921340i	$0.627096\pi$
$450$	−4.54247e14	−1.16044
$451$	−1.67487e14	−0.422679
$452$	1.50263e14	0.374620
$453$	−2.24105e14	−0.551965
$454$	1.16087e14	0.282472
$455$	5.50153e14	1.32258
$456$	−1.46204e15	−3.47259
$457$	8.18072e12	0.0191979	0.00959893	−	0.999954i	$-0.496945\pi$
$457$	8.18072e12	0.0191979	0.00959893	+	0.999954i	$0.496945\pi$
$458$	1.00272e15	2.32499
$459$	−1.08886e14	−0.249461
$460$	−2.65541e14	−0.601122
$461$	−3.92650e14	−0.878316	−0.439158	−	0.898410i	$-0.644723\pi$
$461$	−3.92650e14	−0.878316	−0.439158	+	0.898410i	$0.644723\pi$
$462$	1.15302e14	0.254862
$463$	−4.44783e13	−0.0971522	−0.0485761	−	0.998819i	$-0.515468\pi$
$463$	−4.44783e13	−0.0971522	−0.0485761	+	0.998819i	$0.515468\pi$
$464$	1.87510e15	4.04739
$465$	3.60642e14	0.769281
$466$	5.19408e14	1.09493
$467$	−1.85784e14	−0.387048	−0.193524	−	0.981096i	$-0.561992\pi$
$467$	−1.85784e14	−0.387048	−0.193524	+	0.981096i	$0.561992\pi$
$468$	−6.25747e14	−1.28839
$469$	−9.45017e13	−0.192304
$470$	−1.40157e15	−2.81887
$471$	−3.17779e14	−0.631698
$472$	2.12482e14	0.417485
$473$	3.71288e13	0.0721066
$474$	−6.40939e14	−1.23037
$475$	1.79550e15	3.40698
$476$	−1.00689e15	−1.88863
$477$	2.40141e13	0.0445261
$478$	−1.48599e15	−2.72372
$479$	−4.25471e14	−0.770948	−0.385474	−	0.922719i	$-0.625962\pi$
$479$	−4.25471e14	−0.770948	−0.385474	+	0.922719i	$0.625962\pi$
$480$	1.86554e15	3.34179
$481$	−3.06854e14	−0.543419
$482$	−1.12023e15	−1.96132
$483$	2.43592e13	0.0421652
$484$	−1.28306e15	−2.19582
$485$	1.24516e15	2.10692
$486$	−7.34883e13	−0.122947
$487$	−4.34881e12	−0.00719385	−0.00359692	−	0.999994i	$-0.501145\pi$
$487$	−4.34881e12	−0.00719385	−0.00359692	+	0.999994i	$0.501145\pi$
$488$	−3.72127e14	−0.608670
$489$	−3.31228e14	−0.535708
$490$	−1.41371e15	−2.26090
$491$	−1.49931e14	−0.237107	−0.118553	−	0.992948i	$-0.537826\pi$
$491$	−1.49931e14	−0.237107	−0.118553	+	0.992948i	$0.537826\pi$
$492$	9.87134e14	1.54372
$493$	−9.76886e14	−1.51073
$494$	3.39864e15	5.19765
$495$	1.56304e14	0.236396
$496$	−1.84339e15	−2.75720
$497$	5.06789e14	0.749664
$498$	1.28747e15	1.88354
$499$	6.62725e14	0.958916	0.479458	−	0.877565i	$-0.340833\pi$
$499$	6.62725e14	0.958916	0.479458	+	0.877565i	$0.340833\pi$
$500$	−2.55943e15	−3.66276
$501$	4.48679e14	0.635079
$502$	2.26301e15	3.16822
$503$	−1.25716e15	−1.74087	−0.870433	−	0.492286i	$-0.836161\pi$
$503$	−1.25716e15	−1.74087	−0.870433	+	0.492286i	$0.836161\pi$
$504$	−4.25349e14	−0.582609
$505$	−1.40735e15	−1.90678
$506$	8.09735e13	0.108521
$507$	4.74962e14	0.629673
$508$	1.86186e15	2.44172
$509$	−7.08145e14	−0.918702	−0.459351	−	0.888255i	$-0.651918\pi$
$509$	−7.08145e14	−0.918702	−0.459351	+	0.888255i	$0.651918\pi$
$510$	−1.87556e15	−2.40711
$511$	3.20666e14	0.407134
$512$	−6.69628e14	−0.841102
$513$	2.90476e14	0.360965
$514$	−1.97977e15	−2.43398
$515$	−9.96838e14	−1.21251
$516$	−2.18829e14	−0.263349
$517$	3.11037e14	0.370351
$518$	−3.33245e14	−0.392600
$519$	4.28255e14	0.499209
$520$	−6.74643e15	−7.78136
$521$	1.38595e15	1.58176	0.790881	−	0.611971i	$-0.209623\pi$
$521$	1.38595e15	1.58176	0.790881	+	0.611971i	$0.209623\pi$
$522$	−6.59310e14	−0.744564
$523$	−3.11808e14	−0.348440	−0.174220	−	0.984707i	$-0.555740\pi$
$523$	−3.11808e14	−0.348440	−0.174220	+	0.984707i	$0.555740\pi$
$524$	−4.67611e15	−5.17085
$525$	5.22361e14	0.571603
$526$	2.04791e15	2.21763
$527$	9.60367e14	1.02915
$528$	−7.98934e14	−0.847275
$529$	−9.35703e14	−0.982046
$530$	4.13643e14	0.429643
$531$	−4.22156e13	−0.0433963
$532$	2.68610e15	2.73281
$533$	−1.43627e15	−1.44623
$534$	−1.27592e15	−1.27159
$535$	−1.72046e15	−1.69706
$536$	1.15886e15	1.13142
$537$	9.74050e14	0.941288
$538$	2.71553e15	2.59748
$539$	3.13732e14	0.297044
$540$	−9.21222e14	−0.863373
$541$	−1.49757e15	−1.38932	−0.694660	−	0.719338i	$-0.744445\pi$
$541$	−1.49757e15	−1.38932	−0.694660	+	0.719338i	$0.744445\pi$
$542$	3.64143e15	3.34407
$543$	2.20077e14	0.200067
$544$	4.96783e15	4.47067
$545$	−2.40266e15	−2.14048
$546$	9.88760e14	0.872029
$547$	3.15839e14	0.275762	0.137881	−	0.990449i	$-0.455971\pi$
$547$	3.15839e14	0.275762	0.137881	+	0.990449i	$0.455971\pi$
$548$	2.66681e15	2.30515
$549$	7.39337e13	0.0632695
$550$	1.73640e15	1.47115
$551$	2.60605e15	2.18599
$552$	−2.98712e14	−0.248078
$553$	7.37047e14	0.606048
$554$	3.03018e15	2.46697
$555$	−4.51750e14	−0.364155
$556$	2.38883e15	1.90666
$557$	−8.63856e14	−0.682712	−0.341356	−	0.939934i	$-0.610886\pi$
$557$	−8.63856e14	−0.682712	−0.341356	+	0.939934i	$0.610886\pi$
$558$	6.48162e14	0.507219
$559$	3.18395e14	0.246718
$560$	−4.13991e15	−3.17656
$561$	4.16227e14	0.316253
$562$	4.61235e15	3.47034
$563$	2.02055e15	1.50548	0.752739	−	0.658319i	$-0.228732\pi$
$563$	2.02055e15	1.50548	0.752739	+	0.658319i	$0.228732\pi$
$564$	−1.83319e15	−1.35261
$565$	−3.21869e14	−0.235187
$566$	8.77385e14	0.634892
$567$	8.45077e13	0.0605605
$568$	−6.21466e15	−4.41064
$569$	−8.80440e14	−0.618846	−0.309423	−	0.950925i	$-0.600136\pi$
$569$	−8.80440e14	−0.618846	−0.309423	+	0.950925i	$0.600136\pi$
$570$	5.00346e15	3.48304
$571$	−1.19192e15	−0.821767	−0.410883	−	0.911688i	$-0.634780\pi$
$571$	−1.19192e15	−0.821767	−0.410883	+	0.911688i	$0.634780\pi$
$572$	2.39198e15	1.63335
$573$	−1.59349e15	−1.07770
$574$	−1.55980e15	−1.04485
$575$	3.66841e14	0.243391
$576$	1.59136e15	1.04579
$577$	2.00994e14	0.130832	0.0654162	−	0.997858i	$-0.479162\pi$
$577$	2.00994e14	0.130832	0.0654162	+	0.997858i	$0.479162\pi$
$578$	−2.02199e15	−1.30370
$579$	−1.62634e15	−1.03867
$580$	−8.26487e15	−5.22856
$581$	−1.48052e15	−0.927782
$582$	2.23786e15	1.38918
$583$	−9.17960e13	−0.0564478
$584$	−3.93227e15	−2.39537
$585$	1.34037e15	0.808849
$586$	1.30806e15	0.781971
$587$	−9.19761e14	−0.544710	−0.272355	−	0.962197i	$-0.587803\pi$
$587$	−9.19761e14	−0.544710	−0.272355	+	0.962197i	$0.587803\pi$
$588$	−1.84907e15	−1.08487
$589$	−2.56198e15	−1.48916
$590$	−7.27164e14	−0.418742
$591$	−7.69894e14	−0.439238
$592$	2.30908e15	1.30518
$593$	7.80639e14	0.437169	0.218585	−	0.975818i	$-0.429856\pi$
$593$	7.80639e14	0.437169	0.218585	+	0.975818i	$0.429856\pi$
$594$	2.80916e14	0.155866
$595$	2.15680e15	1.18568
$596$	8.55937e14	0.466216
$597$	1.21082e15	0.653460
$598$	6.94382e14	0.371315
$599$	−5.49675e14	−0.291245	−0.145622	−	0.989340i	$-0.546518\pi$
$599$	−5.49675e14	−0.291245	−0.145622	+	0.989340i	$0.546518\pi$
$600$	−6.40561e15	−3.36302
$601$	−1.50512e15	−0.783000	−0.391500	−	0.920178i	$-0.628044\pi$
$601$	−1.50512e15	−0.783000	−0.391500	+	0.920178i	$0.628044\pi$
$602$	3.45778e14	0.178245
$603$	−2.30240e14	−0.117608
$604$	−5.04900e15	−2.55565
$605$	2.74836e15	1.37854
$606$	−2.52936e15	−1.25722
$607$	−2.78314e15	−1.37087	−0.685436	−	0.728133i	$-0.740388\pi$
$607$	−2.78314e15	−1.37087	−0.685436	+	0.728133i	$0.740388\pi$
$608$	−1.32527e16	−6.46898
$609$	7.58173e14	0.366753
$610$	1.27351e15	0.610503
$611$	2.66727e15	1.26719
$612$	−2.45316e15	−1.15503
$613$	−1.81488e15	−0.846868	−0.423434	−	0.905927i	$-0.639175\pi$
$613$	−1.81488e15	−0.846868	−0.423434	+	0.905927i	$0.639175\pi$
$614$	−1.14488e15	−0.529460
$615$	−2.11447e15	−0.969146
$616$	1.62594e15	0.738601
$617$	2.32132e15	1.04512	0.522559	−	0.852603i	$-0.324977\pi$
$617$	2.32132e15	1.04512	0.522559	+	0.852603i	$0.324977\pi$
$618$	−1.79156e15	−0.799457
$619$	1.23097e15	0.544440	0.272220	−	0.962235i	$-0.412242\pi$
$619$	1.23097e15	0.544440	0.272220	+	0.962235i	$0.412242\pi$
$620$	8.12512e15	3.56185
$621$	5.93477e13	0.0257870
$622$	4.66590e15	2.00950
$623$	1.46725e15	0.626352
$624$	−6.85120e15	−2.89902
$625$	1.15164e15	0.483033
$626$	−2.06787e15	−0.859735
$627$	−1.11037e15	−0.457612
$628$	−7.15942e15	−2.92483
$629$	−1.20298e15	−0.487170
$630$	1.45565e15	0.584364
$631$	1.68636e15	0.671101	0.335551	−	0.942022i	$-0.391078\pi$
$631$	1.68636e15	0.671101	0.335551	+	0.942022i	$0.391078\pi$
$632$	−9.03827e15	−3.56567
$633$	1.10777e15	0.433242
$634$	−4.74203e15	−1.83854
$635$	−3.98816e15	−1.53291
$636$	5.41027e14	0.206160
$637$	2.69039e15	1.01636
$638$	2.52028e15	0.943919
$639$	1.23472e15	0.458473
$640$	1.16885e16	4.30298
$641$	1.29835e15	0.473885	0.236943	−	0.971524i	$-0.423855\pi$
$641$	1.29835e15	0.473885	0.236943	+	0.971524i	$0.423855\pi$
$642$	−3.09208e15	−1.11894
$643$	−2.08702e15	−0.748800	−0.374400	−	0.927267i	$-0.622151\pi$
$643$	−2.08702e15	−0.748800	−0.374400	+	0.927267i	$0.622151\pi$
$644$	5.48803e14	0.195229
$645$	4.68740e14	0.165331
$646$	1.33239e16	4.65964
$647$	−4.43825e15	−1.53900	−0.769499	−	0.638649i	$-0.779494\pi$
$647$	−4.43825e15	−1.53900	−0.769499	+	0.638649i	$0.779494\pi$
$648$	−1.03630e15	−0.356307
$649$	1.61373e14	0.0550155
$650$	1.48904e16	5.03364
$651$	−7.45352e14	−0.249842
$652$	−7.46243e15	−2.48038
$653$	−2.02446e15	−0.667247	−0.333624	−	0.942706i	$-0.608271\pi$
$653$	−2.02446e15	−0.667247	−0.333624	+	0.942706i	$0.608271\pi$
$654$	−4.31817e15	−1.41131
$655$	1.00164e16	3.24626
$656$	1.08080e16	3.47354
$657$	7.81257e14	0.248992
$658$	2.89667e15	0.915496
$659$	5.05072e15	1.58301	0.791504	−	0.611164i	$-0.209298\pi$
$659$	5.05072e15	1.58301	0.791504	+	0.611164i	$0.209298\pi$
$660$	3.52146e15	1.09454
$661$	−5.90345e15	−1.81969	−0.909845	−	0.414947i	$-0.863800\pi$
$661$	−5.90345e15	−1.81969	−0.909845	+	0.414947i	$0.863800\pi$
$662$	3.47289e15	1.06163
$663$	3.56932e15	1.08209
$664$	1.81554e16	5.45859
$665$	−5.75372e15	−1.71565
$666$	−8.11905e14	−0.240103
$667$	5.32447e14	0.156165
$668$	1.01086e16	2.94048
$669$	−2.18663e15	−0.630858
$670$	−3.96589e15	−1.13483
$671$	−2.82619e14	−0.0802097
$672$	−3.85559e15	−1.08533
$673$	−2.41929e15	−0.675470	−0.337735	−	0.941241i	$-0.609661\pi$
$673$	−2.41929e15	−0.675470	−0.337735	+	0.941241i	$0.609661\pi$
$674$	−9.49541e15	−2.62957
$675$	1.27266e15	0.349575
$676$	1.07007e16	2.91545
$677$	−4.11801e15	−1.11288	−0.556442	−	0.830887i	$-0.687834\pi$
$677$	−4.11801e15	−1.11288	−0.556442	+	0.830887i	$0.687834\pi$
$678$	−5.78477e14	−0.155068
$679$	−2.57343e15	−0.684271
$680$	−2.64485e16	−6.97592
$681$	−3.25238e14	−0.0850928
$682$	−2.47766e15	−0.643025
$683$	−1.64718e15	−0.424059	−0.212029	−	0.977263i	$-0.568007\pi$
$683$	−1.64718e15	−0.424059	−0.212029	+	0.977263i	$0.568007\pi$
$684$	6.54431e15	1.67130
$685$	−5.71239e15	−1.44717
$686$	7.07835e15	1.77889
$687$	−2.80932e15	−0.700389
$688$	−2.39593e15	−0.592566
$689$	−7.87190e14	−0.193141
$690$	1.02227e15	0.248825
$691$	−8.24714e14	−0.199147	−0.0995736	−	0.995030i	$-0.531748\pi$
$691$	−8.24714e14	−0.199147	−0.0995736	+	0.995030i	$0.531748\pi$
$692$	9.64841e15	2.31139
$693$	−3.23039e14	−0.0767754
$694$	−5.33372e15	−1.25763
$695$	−5.11695e15	−1.19700
$696$	−9.29734e15	−2.15778
$697$	−5.63071e15	−1.29653
$698$	1.39767e16	3.19300
$699$	−1.45522e15	−0.329841
$700$	1.17686e16	2.64658
$701$	6.73359e14	0.150244	0.0751221	−	0.997174i	$-0.476065\pi$
$701$	6.73359e14	0.150244	0.0751221	+	0.997174i	$0.476065\pi$
$702$	2.40897e15	0.533308
$703$	3.20921e15	0.704926
$704$	−6.08314e15	−1.32580
$705$	3.92675e15	0.849166
$706$	4.49979e15	0.965532
$707$	2.90863e15	0.619273
$708$	−9.51100e14	−0.200929
$709$	−2.01792e15	−0.423008	−0.211504	−	0.977377i	$-0.567836\pi$
$709$	−2.01792e15	−0.423008	−0.211504	+	0.977377i	$0.567836\pi$
$710$	2.12681e16	4.42392
$711$	1.79571e15	0.370641
$712$	−1.79926e16	−3.68513
$713$	−5.23443e14	−0.106384
$714$	3.87630e15	0.781767
$715$	−5.12370e15	−1.02542
$716$	2.19449e16	4.35826
$717$	4.16328e15	0.820502
$718$	2.11798e15	0.414226
$719$	3.13698e15	0.608839	0.304419	−	0.952538i	$-0.401538\pi$
$719$	3.13698e15	0.608839	0.304419	+	0.952538i	$0.401538\pi$
$720$	−1.00863e16	−1.94269
$721$	2.06020e15	0.393791
$722$	−2.54407e16	−4.82586
$723$	3.13854e15	0.590836
$724$	4.95824e15	0.926329
$725$	1.14178e16	2.11702
$726$	4.93946e15	0.908926
$727$	9.93240e15	1.81391	0.906953	−	0.421231i	$-0.138402\pi$
$727$	9.93240e15	1.81391	0.906953	+	0.421231i	$0.138402\pi$
$728$	1.39431e16	2.52718
$729$	2.05891e14	0.0370370
$730$	1.34572e16	2.40258
$731$	1.24823e15	0.221181
$732$	1.66570e15	0.292944
$733$	−5.38590e15	−0.940127	−0.470064	−	0.882633i	$-0.655769\pi$
$733$	−5.38590e15	−0.940127	−0.470064	+	0.882633i	$0.655769\pi$
$734$	−1.13593e16	−1.96799
$735$	3.96078e15	0.681083
$736$	−2.70769e15	−0.462137
$737$	8.80115e14	0.149097
$738$	−3.80023e15	−0.638998
$739$	8.41325e15	1.40417	0.702085	−	0.712094i	$-0.252253\pi$
$739$	8.41325e15	1.40417	0.702085	+	0.712094i	$0.252253\pi$
$740$	−1.01777e16	−1.68608
$741$	−9.52192e15	−1.56576
$742$	−8.54891e14	−0.139537
$743$	−9.16171e15	−1.48436	−0.742178	−	0.670203i	$-0.766207\pi$
$743$	−9.16171e15	−1.48436	−0.742178	+	0.670203i	$0.766207\pi$
$744$	9.14012e15	1.46994
$745$	−1.83345e15	−0.292691
$746$	−1.93476e16	−3.06595
$747$	−3.60708e15	−0.567405
$748$	9.37743e15	1.46428
$749$	3.55573e15	0.551162
$750$	9.85319e15	1.51614
$751$	5.67309e15	0.866563	0.433281	−	0.901259i	$-0.357356\pi$
$751$	5.67309e15	0.866563	0.433281	+	0.901259i	$0.357356\pi$
$752$	−2.00712e16	−3.04352
$753$	−6.34024e15	−0.954406
$754$	2.16124e16	3.22969
$755$	1.08151e16	1.60444
$756$	1.90392e15	0.280401
$757$	5.88431e13	0.00860337	0.00430168	−	0.999991i	$-0.498631\pi$
$757$	5.88431e13	0.00860337	0.00430168	+	0.999991i	$0.498631\pi$
$758$	−7.92226e15	−1.14992
$759$	−2.26863e14	−0.0326914
$760$	7.05569e16	10.0940
$761$	−1.03107e16	−1.46444	−0.732222	−	0.681066i	$-0.761517\pi$
$761$	−1.03107e16	−1.46444	−0.732222	+	0.681066i	$0.761517\pi$
$762$	−7.16770e15	−1.01071
$763$	4.96567e15	0.695173
$764$	−3.59006e16	−4.98986
$765$	5.25474e15	0.725126
$766$	1.56066e16	2.13821
$767$	1.38384e15	0.188240
$768$	7.59513e15	1.02577
$769$	2.13146e15	0.285813	0.142906	−	0.989736i	$-0.454355\pi$
$769$	2.13146e15	0.285813	0.142906	+	0.989736i	$0.454355\pi$
$770$	−5.56436e15	−0.740825
$771$	5.54670e15	0.733222
$772$	−3.66407e16	−4.80916
$773$	−1.93099e15	−0.251648	−0.125824	−	0.992053i	$-0.540157\pi$
$773$	−1.93099e15	−0.251648	−0.125824	+	0.992053i	$0.540157\pi$
$774$	8.42440e14	0.109009
$775$	−1.12248e16	−1.44217
$776$	3.15575e16	4.02590
$777$	9.33649e14	0.118268
$778$	2.16262e16	2.72014
$779$	1.50211e16	1.87606
$780$	3.01980e16	3.74505
$781$	−4.71983e15	−0.581227
$782$	2.72223e15	0.332880
$783$	1.84718e15	0.224295
$784$	−2.02452e16	−2.44109
$785$	1.53357e16	1.83621
$786$	1.80019e16	2.14039
$787$	−3.71511e15	−0.438642	−0.219321	−	0.975653i	$-0.570384\pi$
$787$	−3.71511e15	−0.438642	−0.219321	+	0.975653i	$0.570384\pi$
$788$	−1.73454e16	−2.03372
$789$	−5.73759e15	−0.668046
$790$	3.09312e16	3.57641
$791$	6.65219e14	0.0763825
$792$	3.96137e15	0.451707
$793$	−2.42357e15	−0.274444
$794$	−2.14472e16	−2.41190
$795$	−1.15890e15	−0.129427
$796$	2.72792e16	3.02559
$797$	7.65519e15	0.843209	0.421604	−	0.906780i	$-0.361467\pi$
$797$	7.65519e15	0.843209	0.421604	+	0.906780i	$0.361467\pi$
$798$	−1.03408e16	−1.13120
$799$	1.04567e16	1.13602
$800$	−5.80639e16	−6.26486
$801$	3.57474e15	0.383059
$802$	−3.03414e15	−0.322906
$803$	−2.98643e15	−0.315658
$804$	−5.18722e15	−0.544535
$805$	−1.17555e15	−0.122565
$806$	−2.12470e16	−2.20016
$807$	−7.60807e15	−0.782474
$808$	−3.56680e16	−3.64348
$809$	1.66989e16	1.69422	0.847111	−	0.531416i	$-0.178340\pi$
$809$	1.66989e16	1.69422	0.847111	+	0.531416i	$0.178340\pi$
$810$	3.54648e15	0.357380
$811$	7.06461e15	0.707088	0.353544	−	0.935418i	$-0.384976\pi$
$811$	7.06461e15	0.707088	0.353544	+	0.935418i	$0.384976\pi$
$812$	1.70813e16	1.69810
$813$	−1.02021e16	−1.00738
$814$	3.10358e15	0.304389
$815$	1.59848e16	1.55718
$816$	−2.68592e16	−2.59895
$817$	−3.32990e15	−0.320045
$818$	2.10568e16	2.01024
$819$	−2.77020e15	−0.262693
$820$	−4.76383e16	−4.48724
$821$	6.78885e15	0.635197	0.317599	−	0.948225i	$-0.397124\pi$
$821$	6.78885e15	0.635197	0.317599	+	0.948225i	$0.397124\pi$
$822$	−1.02666e16	−0.954179
$823$	−1.37578e15	−0.127014	−0.0635068	−	0.997981i	$-0.520228\pi$
$823$	−1.37578e15	−0.127014	−0.0635068	+	0.997981i	$0.520228\pi$
$824$	−2.52639e16	−2.31686
$825$	−4.86486e15	−0.443173
$826$	1.50286e15	0.135996
$827$	1.88493e16	1.69439	0.847196	−	0.531280i	$-0.178289\pi$
$827$	1.88493e16	1.69439	0.847196	+	0.531280i	$0.178289\pi$
$828$	1.33708e15	0.119396
$829$	7.56471e15	0.671031	0.335515	−	0.942035i	$-0.391090\pi$
$829$	7.56471e15	0.671031	0.335515	+	0.942035i	$0.391090\pi$
$830$	−6.21321e16	−5.47503
$831$	−8.48961e15	−0.743159
$832$	−5.21655e16	−4.53634
$833$	1.05473e16	0.911158
$834$	−9.19640e15	−0.789232
$835$	−2.16529e16	−1.84603
$836$	−2.50163e16	−2.11879
$837$	−1.81595e15	−0.152796
$838$	−1.43544e16	−1.19990
$839$	1.36055e16	1.12986	0.564928	−	0.825140i	$-0.308904\pi$
$839$	1.36055e16	1.12986	0.564928	+	0.825140i	$0.308904\pi$
$840$	2.05270e16	1.69351
$841$	4.37174e15	0.358324
$842$	4.62458e16	3.76579
$843$	−1.29224e16	−1.04542
$844$	2.49577e16	2.00595
$845$	−2.29212e16	−1.83032
$846$	7.05732e15	0.559890
$847$	−5.68013e15	−0.447713
$848$	5.92361e15	0.463884
$849$	−2.45816e15	−0.191257
$850$	5.83758e16	4.51262
$851$	6.55679e14	0.0503592
$852$	2.78177e16	2.12277
$853$	−7.49852e15	−0.568533	−0.284267	−	0.958745i	$-0.591750\pi$
$853$	−7.49852e15	−0.568533	−0.284267	+	0.958745i	$0.591750\pi$
$854$	−2.63201e15	−0.198276
$855$	−1.40181e16	−1.04924
$856$	−4.36033e16	−3.24275
$857$	1.40143e16	1.03557	0.517783	−	0.855512i	$-0.326757\pi$
$857$	1.40143e16	1.03557	0.517783	+	0.855512i	$0.326757\pi$
$858$	−9.20854e15	−0.676099
$859$	−1.43539e16	−1.04715	−0.523575	−	0.851980i	$-0.675402\pi$
$859$	−1.43539e16	−1.04715	−0.523575	+	0.851980i	$0.675402\pi$
$860$	1.05605e16	0.765498
$861$	4.37007e15	0.314754
$862$	−2.48651e16	−1.77951
$863$	−2.01996e16	−1.43643	−0.718213	−	0.695823i	$-0.755040\pi$
$863$	−2.01996e16	−1.43643	−0.718213	+	0.695823i	$0.755040\pi$
$864$	−9.39360e15	−0.663753
$865$	−2.06672e16	−1.45109
$866$	−3.30037e16	−2.30257
$867$	5.66499e15	0.392730
$868$	−1.67925e16	−1.15680
$869$	−6.86428e15	−0.469879
$870$	3.18177e16	2.16428
$871$	7.54736e15	0.510147
$872$	−6.08931e16	−4.09004
$873$	−6.26980e15	−0.418480
$874$	−7.26213e15	−0.481672
$875$	−1.13307e16	−0.746811
$876$	1.76014e16	1.15286
$877$	−1.06436e16	−0.692774	−0.346387	−	0.938092i	$-0.612592\pi$
$877$	−1.06436e16	−0.692774	−0.346387	+	0.938092i	$0.612592\pi$
$878$	4.21094e16	2.72370
$879$	−3.66477e15	−0.235564
$880$	3.85559e16	2.46284
$881$	−6.05995e15	−0.384682	−0.192341	−	0.981328i	$-0.561608\pi$
$881$	−6.05995e15	−0.384682	−0.192341	+	0.981328i	$0.561608\pi$
$882$	7.11848e15	0.449066
$883$	3.73590e15	0.234213	0.117107	−	0.993119i	$-0.462638\pi$
$883$	3.73590e15	0.234213	0.117107	+	0.993119i	$0.462638\pi$
$884$	8.04154e16	5.01016
$885$	2.03729e15	0.126143
$886$	−5.30343e16	−3.26341
$887$	1.30168e16	0.796023	0.398011	−	0.917380i	$-0.369700\pi$
$887$	1.30168e16	0.796023	0.398011	+	0.917380i	$0.369700\pi$
$888$	−1.14492e16	−0.695829
$889$	8.24248e15	0.497850
$890$	6.15749e16	3.69623
$891$	−7.87039e14	−0.0469536
$892$	−4.92638e16	−2.92093
$893$	−2.78954e16	−1.64380
$894$	−3.29515e15	−0.192983
$895$	−4.70068e16	−2.73611
$896$	−2.41571e16	−1.39750
$897$	−1.94544e15	−0.111856
$898$	2.60766e16	1.49015
$899$	−1.62920e16	−0.925330
$900$	2.86725e16	1.61857
$901$	−3.08607e15	−0.173149
$902$	1.45267e16	0.810088
$903$	−9.68763e14	−0.0536951
$904$	−8.15746e15	−0.449395
$905$	−1.06207e16	−0.581549
$906$	1.94374e16	1.05787
$907$	3.18539e16	1.72315	0.861575	−	0.507631i	$-0.169479\pi$
$907$	3.18539e16	1.72315	0.861575	+	0.507631i	$0.169479\pi$
$908$	−7.32749e15	−0.393988
$909$	7.08647e15	0.378729
$910$	−4.77167e16	−2.53479
$911$	4.37440e15	0.230976	0.115488	−	0.993309i	$-0.463157\pi$
$911$	4.37440e15	0.230976	0.115488	+	0.993309i	$0.463157\pi$
$912$	7.16526e16	3.76063
$913$	1.37884e16	0.719325
$914$	−7.09542e14	−0.0367938
$915$	−3.56797e15	−0.183910
$916$	−6.32929e16	−3.24287
$917$	−2.07012e16	−1.05430
$918$	9.44406e15	0.478106
$919$	1.89945e16	0.955858	0.477929	−	0.878399i	$-0.341388\pi$
$919$	1.89945e16	0.955858	0.477929	+	0.878399i	$0.341388\pi$
$920$	1.44156e16	0.721107
$921$	3.20759e15	0.159496
$922$	3.40559e16	1.68334
$923$	−4.04746e16	−1.98872
$924$	−7.27794e15	−0.355478
$925$	1.40604e16	0.682683
$926$	3.85776e15	0.186198
$927$	5.01939e15	0.240831
$928$	−8.42760e16	−4.01967
$929$	3.75792e16	1.78181	0.890904	−	0.454191i	$-0.150072\pi$
$929$	3.75792e16	1.78181	0.890904	+	0.454191i	$0.150072\pi$
$930$	−3.12797e16	−1.47437
$931$	−2.81372e16	−1.31843
$932$	−3.27855e16	−1.52719
$933$	−1.30724e16	−0.605349
$934$	1.61137e16	0.741799
$935$	−2.00868e16	−0.919277
$936$	3.39704e16	1.54555
$937$	1.34406e16	0.607928	0.303964	−	0.952684i	$-0.401690\pi$
$937$	1.34406e16	0.607928	0.303964	+	0.952684i	$0.401690\pi$
$938$	8.19646e15	0.368562
$939$	5.79353e15	0.258989
$940$	8.84680e16	3.93172
$941$	−8.15918e15	−0.360499	−0.180249	−	0.983621i	$-0.557690\pi$
$941$	−8.15918e15	−0.360499	−0.180249	+	0.983621i	$0.557690\pi$
$942$	2.75620e16	1.21069
$943$	3.06899e15	0.134024
$944$	−1.04134e16	−0.452114
$945$	−4.07827e15	−0.176036
$946$	−3.22031e15	−0.138196
$947$	−2.94524e15	−0.125660	−0.0628298	−	0.998024i	$-0.520013\pi$
$947$	−2.94524e15	−0.125660	−0.0628298	+	0.998024i	$0.520013\pi$
$948$	4.04566e16	1.71610
$949$	−2.56099e16	−1.08005
$950$	−1.55730e17	−6.52967
$951$	1.32857e16	0.553849
$952$	5.46621e16	2.26560
$953$	−4.33689e16	−1.78718	−0.893588	−	0.448889i	$-0.851820\pi$
$953$	−4.33689e16	−1.78718	−0.893588	+	0.448889i	$0.851820\pi$
$954$	−2.08282e15	−0.0853367
$955$	7.69003e16	3.13263
$956$	9.37969e16	3.79901
$957$	−7.06103e15	−0.284349
$958$	3.69026e16	1.47757
$959$	1.18060e16	0.470004
$960$	−7.67979e16	−3.03989
$961$	−9.39196e15	−0.369639
$962$	2.66145e16	1.04149
$963$	8.66305e15	0.337075
$964$	7.07100e16	2.73563
$965$	7.84857e16	3.01919
$966$	−2.11276e15	−0.0808119
$967$	−3.73342e16	−1.41991	−0.709957	−	0.704246i	$-0.751285\pi$
$967$	−3.73342e16	−1.41991	−0.709957	+	0.704246i	$0.751285\pi$
$968$	6.96544e16	2.63411
$969$	−3.73294e16	−1.40369
$970$	−1.07997e17	−4.03802
$971$	−2.32292e15	−0.0863632	−0.0431816	−	0.999067i	$-0.513749\pi$
$971$	−2.32292e15	−0.0863632	−0.0431816	+	0.999067i	$0.513749\pi$
$972$	4.63864e15	0.171485
$973$	1.05754e16	0.388755
$974$	3.77187e14	0.0137874
$975$	−4.17182e16	−1.51635
$976$	1.82374e16	0.659157
$977$	−3.64377e16	−1.30958	−0.654789	−	0.755812i	$-0.727242\pi$
$977$	−3.64377e16	−1.30958	−0.654789	+	0.755812i	$0.727242\pi$
$978$	2.87285e16	1.02671
$979$	−1.36648e16	−0.485621
$980$	8.92347e16	3.15348
$981$	1.20982e16	0.425147
$982$	1.30041e16	0.454429
$983$	1.95246e16	0.678480	0.339240	−	0.940700i	$-0.389830\pi$
$983$	1.95246e16	0.678480	0.339240	+	0.940700i	$0.389830\pi$
$984$	−5.35893e16	−1.85185
$985$	3.71544e16	1.27677
$986$	8.47287e16	2.89539
$987$	−8.11556e15	−0.275787
$988$	−2.14525e17	−7.24961
$989$	−6.80339e14	−0.0228637
$990$	−1.35568e16	−0.453067
$991$	−5.04520e16	−1.67677	−0.838384	−	0.545080i	$-0.816499\pi$
$991$	−5.04520e16	−1.67677	−0.838384	+	0.545080i	$0.816499\pi$
$992$	8.28509e16	2.73831
$993$	−9.72996e15	−0.319809
$994$	−4.39555e16	−1.43677
$995$	−5.84329e16	−1.89946
$996$	−8.12661e16	−2.62714
$997$	−4.06996e16	−1.30848	−0.654239	−	0.756288i	$-0.727011\pi$
$997$	−4.06996e16	−1.30848	−0.654239	+	0.756288i	$0.727011\pi$
$998$	−5.74804e16	−1.83782
$999$	2.27470e15	0.0723293

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.b.1.2	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.b.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-86.7335 q^{2} +243.000 q^{3} +5474.69 q^{4} -11727.0 q^{5} -21076.2 q^{6} +24236.6 q^{7} -297209. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-86.7335 q^{2} +243.000 q^{3} +5474.69 q^{4} -11727.0 q^{5} -21076.2 q^{6} +24236.6 q^{7} -297209. q^{8} +59049.0 q^{9} +1.01712e6 q^{10} -225721. q^{11} +1.33035e6 q^{12} -1.93565e6 q^{13} -2.10212e6 q^{14} -2.84965e6 q^{15} +1.45658e7 q^{16} -7.58845e6 q^{17} -5.12152e6 q^{18} +2.02438e7 q^{19} -6.42015e7 q^{20} +5.88949e6 q^{21} +1.95775e7 q^{22} +4.13605e6 q^{23} -7.22217e7 q^{24} +8.86937e7 q^{25} +1.67885e8 q^{26} +1.43489e7 q^{27} +1.32688e8 q^{28} +1.28733e8 q^{29} +2.47160e8 q^{30} -1.26556e8 q^{31} -6.54656e8 q^{32} -5.48501e7 q^{33} +6.58173e8 q^{34} -2.84222e8 q^{35} +3.23275e8 q^{36} +1.58528e8 q^{37} -1.75581e9 q^{38} -4.70363e8 q^{39} +3.48536e9 q^{40} +7.42011e8 q^{41} -5.10816e8 q^{42} -1.64490e8 q^{43} -1.23575e9 q^{44} -6.92466e8 q^{45} -3.58734e8 q^{46} -1.37797e9 q^{47} +3.53948e9 q^{48} -1.38992e9 q^{49} -7.69271e9 q^{50} -1.84399e9 q^{51} -1.05971e10 q^{52} +4.06680e8 q^{53} -1.24453e9 q^{54} +2.64702e9 q^{55} -7.20332e9 q^{56} +4.91924e9 q^{57} -1.11655e10 q^{58} -7.14924e8 q^{59} -1.56010e10 q^{60} +1.25207e9 q^{61} +1.09767e10 q^{62} +1.43115e9 q^{63} +2.69499e10 q^{64} +2.26993e10 q^{65} +4.75734e9 q^{66} -3.89914e9 q^{67} -4.15444e10 q^{68} +1.00506e9 q^{69} +2.46515e10 q^{70} +2.09101e10 q^{71} -1.75499e10 q^{72} +1.32307e10 q^{73} -1.37497e10 q^{74} +2.15526e10 q^{75} +1.10829e11 q^{76} -5.47069e9 q^{77} +4.07962e10 q^{78} +3.04105e10 q^{79} -1.70812e11 q^{80} +3.48678e9 q^{81} -6.43572e10 q^{82} -6.10863e10 q^{83} +3.22431e10 q^{84} +8.89895e10 q^{85} +1.42668e10 q^{86} +3.12822e10 q^{87} +6.70861e10 q^{88} +6.05385e10 q^{89} +6.00600e10 q^{90} -4.69135e10 q^{91} +2.26436e10 q^{92} -3.07532e10 q^{93} +1.19516e11 q^{94} -2.37398e11 q^{95} -1.59081e11 q^{96} -1.06180e11 q^{97} +1.20552e11 q^{98} -1.33286e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) \) 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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