LMFDB - Embedded newform 177.14.a.b.1.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,14,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, 14, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 14 $
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:	$189.798744245$
Analytic rank:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.29
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)

$f(q)$	$=$	$q+151.084 q^{2} -729.000 q^{3} +14634.3 q^{4} +68332.2 q^{5} -110140. q^{6} -303969. q^{7} +973330. q^{8} +531441. q^{9} +O(q^{10})$	\(q+151.084 q^{2} -729.000 q^{3} +14634.3 q^{4} +68332.2 q^{5} -110140. q^{6} -303969. q^{7} +973330. q^{8} +531441. q^{9} +1.03239e7 q^{10} -7.32254e6 q^{11} -1.06684e7 q^{12} +3.60461e6 q^{13} -4.59248e7 q^{14} -4.98142e7 q^{15} +2.71700e7 q^{16} -1.04313e7 q^{17} +8.02921e7 q^{18} -3.54358e7 q^{19} +9.99996e8 q^{20} +2.21593e8 q^{21} -1.10632e9 q^{22} -7.59499e8 q^{23} -7.09557e8 q^{24} +3.44859e9 q^{25} +5.44598e8 q^{26} -3.87420e8 q^{27} -4.44838e9 q^{28} -3.30386e9 q^{29} -7.52612e9 q^{30} -8.30419e9 q^{31} -3.86857e9 q^{32} +5.33813e9 q^{33} -1.57600e9 q^{34} -2.07709e10 q^{35} +7.77728e9 q^{36} -3.43380e9 q^{37} -5.35377e9 q^{38} -2.62776e9 q^{39} +6.65098e10 q^{40} -3.61714e10 q^{41} +3.34792e10 q^{42} -1.31238e10 q^{43} -1.07160e11 q^{44} +3.63146e10 q^{45} -1.14748e11 q^{46} +1.29148e11 q^{47} -1.98069e10 q^{48} -4.49198e9 q^{49} +5.21027e11 q^{50} +7.60440e9 q^{51} +5.27510e10 q^{52} +6.61956e10 q^{53} -5.85330e10 q^{54} -5.00366e11 q^{55} -2.95862e11 q^{56} +2.58327e10 q^{57} -4.99160e11 q^{58} -4.21805e10 q^{59} -7.28997e11 q^{60} +7.54376e10 q^{61} -1.25463e12 q^{62} -1.61541e11 q^{63} -8.07054e11 q^{64} +2.46311e11 q^{65} +8.06505e11 q^{66} -9.97258e11 q^{67} -1.52655e11 q^{68} +5.53675e11 q^{69} -3.13814e12 q^{70} +1.02263e11 q^{71} +5.17267e11 q^{72} +4.69620e11 q^{73} -5.18791e11 q^{74} -2.51402e12 q^{75} -5.18578e11 q^{76} +2.22582e12 q^{77} -3.97012e11 q^{78} -7.23078e11 q^{79} +1.85659e12 q^{80} +2.82430e11 q^{81} -5.46492e12 q^{82} +4.73183e12 q^{83} +3.24287e12 q^{84} -7.12792e11 q^{85} -1.98279e12 q^{86} +2.40852e12 q^{87} -7.12724e12 q^{88} -2.71198e12 q^{89} +5.48654e12 q^{90} -1.09569e12 q^{91} -1.11147e13 q^{92} +6.05376e12 q^{93} +1.95122e13 q^{94} -2.42141e12 q^{95} +2.82018e12 q^{96} +6.53982e12 q^{97} -6.78666e11 q^{98} -3.89150e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9}+O(q^{10}) $ 31 * q - 52 * q^2 - 22599 * q^3 + 126886 * q^4 + 33486 * q^5 + 37908 * q^6 - 1135539 * q^7 - 1519749 * q^8 + 16474671 * q^9	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9} - 3854663 q^{10} + 3943968 q^{11} - 92499894 q^{12} - 48510022 q^{13} - 51427459 q^{14} - 24411294 q^{15} + 370110498 q^{16} + 83288419 q^{17} - 27634932 q^{18} - 180425297 q^{19} + 753620445 q^{20} + 827807931 q^{21} + 2300196142 q^{22} - 1305810279 q^{23} + 1107897021 q^{24} + 8070954867 q^{25} + 464550322 q^{26} - 12010035159 q^{27} - 9887169562 q^{28} + 6248352277 q^{29} + 2810049327 q^{30} - 26730150789 q^{31} - 24001343230 q^{32} - 2875152672 q^{33} - 36571033348 q^{34} + 10255900979 q^{35} + 67432422726 q^{36} - 43284776933 q^{37} - 36293696947 q^{38} + 35363806038 q^{39} - 105980683856 q^{40} - 9961079285 q^{41} + 37490617611 q^{42} - 51755851288 q^{43} - 59623729442 q^{44} + 17795833326 q^{45} - 202287132683 q^{46} - 82747063727 q^{47} - 269810553042 q^{48} + 535277836542 q^{49} + 526974390461 q^{50} - 60717257451 q^{51} + 544982341446 q^{52} + 561701818494 q^{53} + 20145865428 q^{54} - 521861534450 q^{55} - 228056576664 q^{56} + 131530041513 q^{57} + 10555409160 q^{58} - 1307596542871 q^{59} - 549389304405 q^{60} + 618193248201 q^{61} - 1486611437386 q^{62} - 603471981699 q^{63} + 679062548045 q^{64} - 1130583307122 q^{65} - 1676842987518 q^{66} - 4137387490592 q^{67} - 3901389300295 q^{68} + 951935693391 q^{69} - 819291947844 q^{70} - 3766439869810 q^{71} - 807656928309 q^{72} - 2386775553523 q^{73} + 3060770694642 q^{74} - 5883726098043 q^{75} - 847741068784 q^{76} + 1650423006137 q^{77} - 338657184738 q^{78} + 787155757766 q^{79} + 13999832121779 q^{80} + 8755315630911 q^{81} + 10083281915577 q^{82} + 8743877051639 q^{83} + 7207746610698 q^{84} + 15373177520565 q^{85} + 18939443838984 q^{86} - 4555048809933 q^{87} + 39713314506713 q^{88} + 11026795445259 q^{89} - 2048525959383 q^{90} + 23285721962531 q^{91} + 40411079823254 q^{92} + 19486279925181 q^{93} + 35237377585624 q^{94} + 13730236994039 q^{95} + 17496979214670 q^{96} + 10134565481560 q^{97} + 70916776240976 q^{98} + 2095986297888 q^{99}+O(q^{100}) \) 31 * q - 52 * q^2 - 22599 * q^3 + 126886 * q^4 + 33486 * q^5 + 37908 * q^6 - 1135539 * q^7 - 1519749 * q^8 + 16474671 * q^9 - 3854663 * q^10 + 3943968 * q^11 - 92499894 * q^12 - 48510022 * q^13 - 51427459 * q^14 - 24411294 * q^15 + 370110498 * q^16 + 83288419 * q^17 - 27634932 * q^18 - 180425297 * q^19 + 753620445 * q^20 + 827807931 * q^21 + 2300196142 * q^22 - 1305810279 * q^23 + 1107897021 * q^24 + 8070954867 * q^25 + 464550322 * q^26 - 12010035159 * q^27 - 9887169562 * q^28 + 6248352277 * q^29 + 2810049327 * q^30 - 26730150789 * q^31 - 24001343230 * q^32 - 2875152672 * q^33 - 36571033348 * q^34 + 10255900979 * q^35 + 67432422726 * q^36 - 43284776933 * q^37 - 36293696947 * q^38 + 35363806038 * q^39 - 105980683856 * q^40 - 9961079285 * q^41 + 37490617611 * q^42 - 51755851288 * q^43 - 59623729442 * q^44 + 17795833326 * q^45 - 202287132683 * q^46 - 82747063727 * q^47 - 269810553042 * q^48 + 535277836542 * q^49 + 526974390461 * q^50 - 60717257451 * q^51 + 544982341446 * q^52 + 561701818494 * q^53 + 20145865428 * q^54 - 521861534450 * q^55 - 228056576664 * q^56 + 131530041513 * q^57 + 10555409160 * q^58 - 1307596542871 * q^59 - 549389304405 * q^60 + 618193248201 * q^61 - 1486611437386 * q^62 - 603471981699 * q^63 + 679062548045 * q^64 - 1130583307122 * q^65 - 1676842987518 * q^66 - 4137387490592 * q^67 - 3901389300295 * q^68 + 951935693391 * q^69 - 819291947844 * q^70 - 3766439869810 * q^71 - 807656928309 * q^72 - 2386775553523 * q^73 + 3060770694642 * q^74 - 5883726098043 * q^75 - 847741068784 * q^76 + 1650423006137 * q^77 - 338657184738 * q^78 + 787155757766 * q^79 + 13999832121779 * q^80 + 8755315630911 * q^81 + 10083281915577 * q^82 + 8743877051639 * q^83 + 7207746610698 * q^84 + 15373177520565 * q^85 + 18939443838984 * q^86 - 4555048809933 * q^87 + 39713314506713 * q^88 + 11026795445259 * q^89 - 2048525959383 * q^90 + 23285721962531 * q^91 + 40411079823254 * q^92 + 19486279925181 * q^93 + 35237377585624 * q^94 + 13730236994039 * q^95 + 17496979214670 * q^96 + 10134565481560 * q^97 + 70916776240976 * q^98 + 2095986297888 * 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 $

$2$	151.084	1.66926	0.834628	−	0.550814i	$-0.185683\pi$
$2$	151.084	1.66926	0.834628	+	0.550814i	$0.185683\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	14634.3	1.78642
$5$	68332.2	1.95578	0.977892	−	0.209113i	$-0.0670576\pi$
$5$	68332.2	1.95578	0.977892	+	0.209113i	$0.0670576\pi$
$6$	−110140.	−0.963745
$7$	−303969.	−0.976544	−0.488272	−	0.872692i	$-0.662373\pi$
$7$	−303969.	−0.976544	−0.488272	+	0.872692i	$0.662373\pi$
$8$	973330.	1.31273
$9$	531441.	0.333333
$10$	1.03239e7	3.26470
$11$	−7.32254e6	−1.24626	−0.623131	−	0.782118i	$-0.714140\pi$
$11$	−7.32254e6	−1.24626	−0.623131	+	0.782118i	$0.714140\pi$
$12$	−1.06684e7	−1.03139
$13$	3.60461e6	0.207122	0.103561	−	0.994623i	$-0.466976\pi$
$13$	3.60461e6	0.207122	0.103561	+	0.994623i	$0.466976\pi$
$14$	−4.59248e7	−1.63010
$15$	−4.98142e7	−1.12917
$16$	2.71700e7	0.404865
$17$	−1.04313e7	−0.104814	−0.0524070	−	0.998626i	$-0.516689\pi$
$17$	−1.04313e7	−0.104814	−0.0524070	+	0.998626i	$0.516689\pi$
$18$	8.02921e7	0.556419
$19$	−3.54358e7	−0.172800	−0.0863999	−	0.996261i	$-0.527536\pi$
$19$	−3.54358e7	−0.172800	−0.0863999	+	0.996261i	$0.527536\pi$
$20$	9.99996e8	3.49384
$21$	2.21593e8	0.563808
$22$	−1.10632e9	−2.08033
$23$	−7.59499e8	−1.06978	−0.534892	−	0.844920i	$-0.679648\pi$
$23$	−7.59499e8	−1.06978	−0.534892	+	0.844920i	$0.679648\pi$
$24$	−7.09557e8	−0.757904
$25$	3.44859e9	2.82509
$26$	5.44598e8	0.345740
$27$	−3.87420e8	−0.192450
$28$	−4.44838e9	−1.74451
$29$	−3.30386e9	−1.03142	−0.515710	−	0.856763i	$-0.672472\pi$
$29$	−3.30386e9	−1.03142	−0.515710	+	0.856763i	$0.672472\pi$
$30$	−7.52612e9	−1.88488
$31$	−8.30419e9	−1.68053	−0.840265	−	0.542175i	$-0.817601\pi$
$31$	−8.30419e9	−1.68053	−0.840265	+	0.542175i	$0.817601\pi$
$32$	−3.86857e9	−0.636906
$33$	5.33813e9	0.719529
$34$	−1.57600e9	−0.174961
$35$	−2.07709e10	−1.90991
$36$	7.77728e9	0.595472
$37$	−3.43380e9	−0.220021	−0.110010	−	0.993930i	$-0.535088\pi$
$37$	−3.43380e9	−0.220021	−0.110010	+	0.993930i	$0.535088\pi$
$38$	−5.35377e9	−0.288447
$39$	−2.62776e9	−0.119582
$40$	6.65098e10	2.56741
$41$	−3.61714e10	−1.18924	−0.594621	−	0.804006i	$-0.702698\pi$
$41$	−3.61714e10	−1.18924	−0.594621	+	0.804006i	$0.702698\pi$
$42$	3.34792e10	0.941140
$43$	−1.31238e10	−0.316603	−0.158301	−	0.987391i	$-0.550602\pi$
$43$	−1.31238e10	−0.316603	−0.158301	+	0.987391i	$0.550602\pi$
$44$	−1.07160e11	−2.22634
$45$	3.63146e10	0.651928
$46$	−1.14748e11	−1.78574
$47$	1.29148e11	1.74764	0.873821	−	0.486247i	$-0.161635\pi$
$47$	1.29148e11	1.74764	0.873821	+	0.486247i	$0.161635\pi$
$48$	−1.98069e10	−0.233749
$49$	−4.49198e9	−0.0463621
$50$	5.21027e11	4.71579
$51$	7.60440e9	0.0605144
$52$	5.27510e10	0.370006
$53$	6.61956e10	0.410238	0.205119	−	0.978737i	$-0.434242\pi$
$53$	6.61956e10	0.410238	0.205119	+	0.978737i	$0.434242\pi$
$54$	−5.85330e10	−0.321248
$55$	−5.00366e11	−2.43742
$56$	−2.95862e11	−1.28194
$57$	2.58327e10	0.0997661
$58$	−4.99160e11	−1.72170
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	−7.28997e11	−2.01717
$61$	7.54376e10	0.187475	0.0937376	−	0.995597i	$-0.470119\pi$
$61$	7.54376e10	0.187475	0.0937376	+	0.995597i	$0.470119\pi$
$62$	−1.25463e12	−2.80524
$63$	−1.61541e11	−0.325515
$64$	−8.07054e11	−1.46802
$65$	2.46311e11	0.405086
$66$	8.06505e11	1.20108
$67$	−9.97258e11	−1.34686	−0.673428	−	0.739253i	$-0.735179\pi$
$67$	−9.97258e11	−1.34686	−0.673428	+	0.739253i	$0.735179\pi$
$68$	−1.52655e11	−0.187241
$69$	5.53675e11	0.617640
$70$	−3.13814e12	−3.18813
$71$	1.02263e11	0.0947411	0.0473706	−	0.998877i	$-0.484916\pi$
$71$	1.02263e11	0.0947411	0.0473706	+	0.998877i	$0.484916\pi$
$72$	5.17267e11	0.437576
$73$	4.69620e11	0.363202	0.181601	−	0.983372i	$-0.441872\pi$
$73$	4.69620e11	0.363202	0.181601	+	0.983372i	$0.441872\pi$
$74$	−5.18791e11	−0.367271
$75$	−2.51402e12	−1.63107
$76$	−5.18578e11	−0.308692
$77$	2.22582e12	1.21703
$78$	−3.97012e11	−0.199613
$79$	−7.23078e11	−0.334664	−0.167332	−	0.985901i	$-0.553515\pi$
$79$	−7.23078e11	−0.334664	−0.167332	+	0.985901i	$0.553515\pi$
$80$	1.85659e12	0.791828
$81$	2.82430e11	0.111111
$82$	−5.46492e12	−1.98515
$83$	4.73183e12	1.58863	0.794313	−	0.607509i	$-0.207831\pi$
$83$	4.73183e12	1.58863	0.794313	+	0.607509i	$0.207831\pi$
$84$	3.24287e12	1.00720
$85$	−7.12792e11	−0.204993
$86$	−1.98279e12	−0.528491
$87$	2.40852e12	0.595490
$88$	−7.12724e12	−1.63600
$89$	−2.71198e12	−0.578430	−0.289215	−	0.957264i	$-0.593394\pi$
$89$	−2.71198e12	−0.578430	−0.289215	+	0.957264i	$0.593394\pi$
$90$	5.48654e12	1.08823
$91$	−1.09569e12	−0.202264
$92$	−1.11147e13	−1.91108
$93$	6.05376e12	0.970255
$94$	1.95122e13	2.91726
$95$	−2.42141e12	−0.337959
$96$	2.82018e12	0.367718
$97$	6.53982e12	0.797167	0.398583	−	0.917132i	$-0.369502\pi$
$97$	6.53982e12	0.797167	0.398583	+	0.917132i	$0.369502\pi$
$98$	−6.78666e11	−0.0773903
$99$	−3.89150e12	−0.415421
$100$	5.04678e13	5.04678
$101$	−6.43289e11	−0.0603000	−0.0301500	−	0.999545i	$-0.509598\pi$
$101$	−6.43289e11	−0.0603000	−0.0301500	+	0.999545i	$0.509598\pi$
$102$	1.14890e12	0.101014
$103$	1.12198e13	0.925859	0.462929	−	0.886395i	$-0.346798\pi$
$103$	1.12198e13	0.925859	0.462929	+	0.886395i	$0.346798\pi$
$104$	3.50847e12	0.271895
$105$	1.51420e13	1.10269
$106$	1.00011e13	0.684792
$107$	8.41834e12	0.542290	0.271145	−	0.962538i	$-0.412598\pi$
$107$	8.41834e12	0.542290	0.271145	+	0.962538i	$0.412598\pi$
$108$	−5.66963e12	−0.343796
$109$	−1.32612e13	−0.757376	−0.378688	−	0.925524i	$-0.623625\pi$
$109$	−1.32612e13	−0.757376	−0.378688	+	0.925524i	$0.623625\pi$
$110$	−7.55971e13	−4.06867
$111$	2.50324e12	0.127029
$112$	−8.25884e12	−0.395368
$113$	−2.91333e13	−1.31637	−0.658187	−	0.752854i	$-0.728677\pi$
$113$	−2.91333e13	−1.31637	−0.658187	+	0.752854i	$0.728677\pi$
$114$	3.90290e12	0.166535
$115$	−5.18983e13	−2.09227
$116$	−4.83498e13	−1.84254
$117$	1.91564e12	0.0690407
$118$	−6.37280e12	−0.217319
$119$	3.17078e12	0.102355
$120$	−4.84856e13	−1.48230
$121$	1.90969e13	0.553168
$122$	1.13974e13	0.312944
$123$	2.63690e13	0.686610
$124$	−1.21526e14	−3.00213
$125$	1.52237e14	3.56948
$126$	−2.44063e13	−0.543367
$127$	8.97810e13	1.89872	0.949358	−	0.314195i	$-0.101735\pi$
$127$	8.97810e13	1.89872	0.949358	+	0.314195i	$0.101735\pi$
$128$	−9.02416e13	−1.81360
$129$	9.56725e12	0.182791
$130$	3.72136e13	0.676192
$131$	−9.74934e13	−1.68543	−0.842717	−	0.538356i	$-0.819045\pi$
$131$	−9.74934e13	−1.68543	−0.842717	+	0.538356i	$0.819045\pi$
$132$	7.81199e13	1.28538
$133$	1.07714e13	0.168747
$134$	−1.50670e14	−2.24825
$135$	−2.64733e13	−0.376391
$136$	−1.01531e13	−0.137592
$137$	−5.24271e12	−0.0677442	−0.0338721	−	0.999426i	$-0.510784\pi$
$137$	−5.24271e12	−0.0677442	−0.0338721	+	0.999426i	$0.510784\pi$
$138$	8.36513e13	1.03100
$139$	−1.36329e14	−1.60322	−0.801609	−	0.597849i	$-0.796022\pi$
$139$	−1.36329e14	−1.60322	−0.801609	+	0.597849i	$0.796022\pi$
$140$	−3.03967e14	−3.41189
$141$	−9.41491e13	−1.00900
$142$	1.54503e13	0.158147
$143$	−2.63949e13	−0.258128
$144$	1.44393e13	0.134955
$145$	−2.25760e14	−2.01723
$146$	7.09519e13	0.606276
$147$	3.27465e12	0.0267672
$148$	−5.02513e13	−0.393048
$149$	2.16406e14	1.62017	0.810083	−	0.586315i	$-0.199422\pi$
$149$	2.16406e14	1.62017	0.810083	+	0.586315i	$0.199422\pi$
$150$	−3.79828e14	−2.72267
$151$	−2.57652e14	−1.76882	−0.884409	−	0.466712i	$-0.845438\pi$
$151$	−2.57652e14	−1.76882	−0.884409	+	0.466712i	$0.845438\pi$
$152$	−3.44907e13	−0.226839
$153$	−5.54361e12	−0.0349380
$154$	3.36286e14	2.03153
$155$	−5.67444e14	−3.28675
$156$	−3.84555e13	−0.213623
$157$	2.61413e14	1.39309	0.696544	−	0.717514i	$-0.254720\pi$
$157$	2.61413e14	1.39309	0.696544	+	0.717514i	$0.254720\pi$
$158$	−1.09245e14	−0.558640
$159$	−4.82566e13	−0.236851
$160$	−2.64348e14	−1.24565
$161$	2.30864e14	1.04469
$162$	4.26705e13	0.185473
$163$	2.54617e12	0.0106333	0.00531665	−	0.999986i	$-0.498308\pi$
$163$	2.54617e12	0.0106333	0.00531665	+	0.999986i	$0.498308\pi$
$164$	−5.29344e14	−2.12448
$165$	3.64766e14	1.40724
$166$	7.14903e14	2.65182
$167$	2.91090e13	0.103841	0.0519206	−	0.998651i	$-0.483466\pi$
$167$	2.91090e13	0.103841	0.0519206	+	0.998651i	$0.483466\pi$
$168$	2.15683e14	0.740127
$169$	−2.89882e14	−0.957100
$170$	−1.07691e14	−0.342187
$171$	−1.88320e13	−0.0576000
$172$	−1.92058e14	−0.565584
$173$	1.12116e14	0.317956	0.158978	−	0.987282i	$-0.449180\pi$
$173$	1.12116e14	0.317956	0.158978	+	0.987282i	$0.449180\pi$
$174$	3.63888e14	0.994025
$175$	−1.04826e15	−2.75882
$176$	−1.98954e14	−0.504568
$177$	3.07496e13	0.0751646
$178$	−4.09736e14	−0.965548
$179$	−4.78140e14	−1.08645	−0.543226	−	0.839586i	$-0.682797\pi$
$179$	−4.78140e14	−1.08645	−0.543226	+	0.839586i	$0.682797\pi$
$180$	5.31439e14	1.16461
$181$	−5.60778e14	−1.18544	−0.592721	−	0.805408i	$-0.701946\pi$
$181$	−5.60778e14	−1.18544	−0.592721	+	0.805408i	$0.701946\pi$
$182$	−1.65541e14	−0.337630
$183$	−5.49940e13	−0.108239
$184$	−7.39243e14	−1.40434
$185$	−2.34639e14	−0.430313
$186$	9.14625e14	1.61960
$187$	7.63834e13	0.130626
$188$	1.89000e15	3.12202
$189$	1.17764e14	0.187936
$190$	−3.65835e14	−0.564140
$191$	−1.00942e15	−1.50437	−0.752185	−	0.658952i	$-0.771000\pi$
$191$	−1.00942e15	−1.50437	−0.752185	+	0.658952i	$0.771000\pi$
$192$	5.88343e14	0.847564
$193$	−2.93200e14	−0.408358	−0.204179	−	0.978934i	$-0.565452\pi$
$193$	−2.93200e14	−0.408358	−0.204179	+	0.978934i	$0.565452\pi$
$194$	9.88060e14	1.33068
$195$	−1.79561e14	−0.233876
$196$	−6.57371e13	−0.0828220
$197$	−1.82305e13	−0.0222213	−0.0111106	−	0.999938i	$-0.503537\pi$
$197$	−1.82305e13	−0.0222213	−0.0111106	+	0.999938i	$0.503537\pi$
$198$	−5.87942e14	−0.693443
$199$	1.32856e14	0.151648	0.0758239	−	0.997121i	$-0.475841\pi$
$199$	1.32856e14	0.151648	0.0758239	+	0.997121i	$0.475841\pi$
$200$	3.35662e15	3.70857
$201$	7.27001e14	0.777608
$202$	−9.71905e13	−0.100656
$203$	1.00427e15	1.00723
$204$	1.11285e14	0.108104
$205$	−2.47167e15	−2.32590
$206$	1.69514e15	1.54550
$207$	−4.03629e14	−0.356595
$208$	9.79373e13	0.0838565
$209$	2.59480e14	0.215354
$210$	2.28771e15	1.84066
$211$	−9.90408e14	−0.772642	−0.386321	−	0.922364i	$-0.626254\pi$
$211$	−9.90408e14	−0.772642	−0.386321	+	0.922364i	$0.626254\pi$
$212$	9.68727e14	0.732855
$213$	−7.45496e13	−0.0546988
$214$	1.27187e15	0.905221
$215$	−8.96778e14	−0.619206
$216$	−3.77088e14	−0.252635
$217$	2.52422e15	1.64111
$218$	−2.00356e15	−1.26425
$219$	−3.42353e14	−0.209695
$220$	−7.32251e15	−4.35424
$221$	−3.76007e13	−0.0217093
$222$	3.78199e14	0.212044
$223$	1.56676e15	0.853143	0.426572	−	0.904454i	$-0.359721\pi$
$223$	1.56676e15	0.853143	0.426572	+	0.904454i	$0.359721\pi$
$224$	1.17592e15	0.621966
$225$	1.83272e15	0.941696
$226$	−4.40157e15	−2.19737
$227$	−3.45205e15	−1.67459	−0.837297	−	0.546748i	$-0.815865\pi$
$227$	−3.45205e15	−1.67459	−0.837297	+	0.546748i	$0.815865\pi$
$228$	3.78044e14	0.178224
$229$	6.80391e14	0.311766	0.155883	−	0.987776i	$-0.450178\pi$
$229$	6.80391e14	0.311766	0.155883	+	0.987776i	$0.450178\pi$
$230$	−7.84099e15	−3.49253
$231$	−1.62263e15	−0.702652
$232$	−3.21575e15	−1.35397
$233$	−2.28715e15	−0.936444	−0.468222	−	0.883611i	$-0.655105\pi$
$233$	−2.28715e15	−0.936444	−0.468222	+	0.883611i	$0.655105\pi$
$234$	2.89422e14	0.115247
$235$	8.82499e15	3.41801
$236$	−6.17283e14	−0.232571
$237$	5.27124e14	0.193218
$238$	4.79054e14	0.170857
$239$	3.87762e15	1.34580	0.672898	−	0.739736i	$-0.265049\pi$
$239$	3.87762e15	1.34580	0.672898	+	0.739736i	$0.265049\pi$
$240$	−1.35345e15	−0.457162
$241$	3.00004e15	0.986316	0.493158	−	0.869940i	$-0.335842\pi$
$241$	3.00004e15	0.986316	0.493158	+	0.869940i	$0.335842\pi$
$242$	2.88523e15	0.923379
$243$	−2.05891e14	−0.0641500
$244$	1.10398e15	0.334909
$245$	−3.06947e14	−0.0906743
$246$	3.98392e15	1.14613
$247$	−1.27732e14	−0.0357907
$248$	−8.08272e15	−2.20608
$249$	−3.44950e15	−0.917193
$250$	2.30005e16	5.95837
$251$	−1.64227e15	−0.414539	−0.207270	−	0.978284i	$-0.566458\pi$
$251$	−1.64227e15	−0.414539	−0.207270	+	0.978284i	$0.566458\pi$
$252$	−2.36405e15	−0.581504
$253$	5.56146e15	1.33323
$254$	1.35645e16	3.16944
$255$	5.19626e14	0.118353
$256$	−7.02265e15	−1.55934
$257$	−4.88298e15	−1.05711	−0.528554	−	0.848900i	$-0.677266\pi$
$257$	−4.88298e15	−1.05711	−0.528554	+	0.848900i	$0.677266\pi$
$258$	1.44546e15	0.305124
$259$	1.04377e15	0.214860
$260$	3.60459e15	0.723652
$261$	−1.75581e15	−0.343806
$262$	−1.47297e16	−2.81342
$263$	2.16700e15	0.403782	0.201891	−	0.979408i	$-0.435291\pi$
$263$	2.16700e15	0.403782	0.201891	+	0.979408i	$0.435291\pi$
$264$	5.19576e15	0.944547
$265$	4.52329e15	0.802336
$266$	1.62738e15	0.281681
$267$	1.97703e15	0.333957
$268$	−1.45942e16	−2.40605
$269$	1.03616e16	1.66739	0.833697	−	0.552222i	$-0.186220\pi$
$269$	1.03616e16	1.66739	0.833697	+	0.552222i	$0.186220\pi$
$270$	−3.99969e15	−0.628292
$271$	7.12222e15	1.09223	0.546116	−	0.837710i	$-0.316106\pi$
$271$	7.12222e15	1.09223	0.546116	+	0.837710i	$0.316106\pi$
$272$	−2.83418e14	−0.0424355
$273$	7.98757e14	0.116777
$274$	−7.92089e14	−0.113082
$275$	−2.52525e16	−3.52080
$276$	8.10265e15	1.10336
$277$	−7.05365e15	−0.938200	−0.469100	−	0.883145i	$-0.655422\pi$
$277$	−7.05365e15	−0.938200	−0.469100	+	0.883145i	$0.655422\pi$
$278$	−2.05971e16	−2.67618
$279$	−4.41319e15	−0.560177
$280$	−2.02169e16	−2.50719
$281$	8.85668e15	1.07320	0.536599	−	0.843837i	$-0.319709\pi$
$281$	8.85668e15	1.07320	0.536599	+	0.843837i	$0.319709\pi$
$282$	−1.42244e16	−1.68428
$283$	−1.23333e15	−0.142714	−0.0713570	−	0.997451i	$-0.522733\pi$
$283$	−1.23333e15	−0.142714	−0.0713570	+	0.997451i	$0.522733\pi$
$284$	1.49655e15	0.169247
$285$	1.76520e15	0.195121
$286$	−3.98784e15	−0.430882
$287$	1.09950e16	1.16135
$288$	−2.05591e15	−0.212302
$289$	−9.79577e15	−0.989014
$290$	−3.41088e16	−3.36728
$291$	−4.76753e15	−0.460245
$292$	6.87256e15	0.648829
$293$	−3.37497e15	−0.311624	−0.155812	−	0.987787i	$-0.549799\pi$
$293$	−3.37497e15	−0.311624	−0.155812	+	0.987787i	$0.549799\pi$
$294$	4.94747e14	0.0446813
$295$	−2.88229e15	−0.254621
$296$	−3.34222e15	−0.288828
$297$	2.83690e15	0.239843
$298$	3.26955e16	2.70447
$299$	−2.73770e15	−0.221576
$300$	−3.67910e16	−2.91376
$301$	3.98922e15	0.309176
$302$	−3.89270e16	−2.95261
$303$	4.68957e14	0.0348142
$304$	−9.62791e14	−0.0699606
$305$	5.15482e15	0.366661
$306$	−8.37549e14	−0.0583205
$307$	5.59260e15	0.381254	0.190627	−	0.981663i	$-0.438948\pi$
$307$	5.59260e15	0.381254	0.190627	+	0.981663i	$0.438948\pi$
$308$	3.25734e16	2.17412
$309$	−8.17926e15	−0.534545
$310$	−8.57316e16	−5.48643
$311$	−1.83007e16	−1.14690	−0.573449	−	0.819241i	$-0.694395\pi$
$311$	−1.83007e16	−1.14690	−0.573449	+	0.819241i	$0.694395\pi$
$312$	−2.55768e15	−0.156979
$313$	1.42887e16	0.858926	0.429463	−	0.903085i	$-0.358703\pi$
$313$	1.42887e16	0.858926	0.429463	+	0.903085i	$0.358703\pi$
$314$	3.94952e16	2.32542
$315$	−1.10385e16	−0.636636
$316$	−1.05818e16	−0.597849
$317$	5.98419e15	0.331222	0.165611	−	0.986191i	$-0.447040\pi$
$317$	5.98419e15	0.331222	0.165611	+	0.986191i	$0.447040\pi$
$318$	−7.29079e15	−0.395365
$319$	2.41927e16	1.28542
$320$	−5.51478e16	−2.87114
$321$	−6.13697e15	−0.313091
$322$	3.48798e16	1.74386
$323$	3.69640e14	0.0181118
$324$	4.13316e15	0.198491
$325$	1.24308e16	0.585138
$326$	3.84685e14	0.0177497
$327$	9.66743e15	0.437271
$328$	−3.52067e16	−1.56115
$329$	−3.92570e16	−1.70665
$330$	5.51103e16	2.34905
$331$	−1.93032e16	−0.806766	−0.403383	−	0.915031i	$-0.632166\pi$
$331$	−1.93032e16	−0.806766	−0.403383	+	0.915031i	$0.632166\pi$
$332$	6.92471e16	2.83795
$333$	−1.82486e15	−0.0733403
$334$	4.39789e15	0.173338
$335$	−6.81449e16	−2.63416
$336$	6.02069e15	0.228266
$337$	−4.09179e15	−0.152167	−0.0760833	−	0.997101i	$-0.524241\pi$
$337$	−4.09179e15	−0.152167	−0.0760833	+	0.997101i	$0.524241\pi$
$338$	−4.37965e16	−1.59765
$339$	2.12382e16	0.760009
$340$	−1.04312e16	−0.366203
$341$	6.08078e16	2.09438
$342$	−2.84521e15	−0.0961491
$343$	3.08167e16	1.02182
$344$	−1.27738e16	−0.415613
$345$	3.78338e16	1.20797
$346$	1.69389e16	0.530749
$347$	5.34494e16	1.64362	0.821809	−	0.569763i	$-0.192965\pi$
$347$	5.34494e16	1.64362	0.821809	+	0.569763i	$0.192965\pi$
$348$	3.52470e16	1.06379
$349$	1.33988e16	0.396919	0.198459	−	0.980109i	$-0.436406\pi$
$349$	1.33988e16	0.396919	0.198459	+	0.980109i	$0.436406\pi$
$350$	−1.58376e17	−4.60518
$351$	−1.39650e15	−0.0398607
$352$	2.83277e16	0.793751
$353$	4.59257e16	1.26334	0.631670	−	0.775237i	$-0.282370\pi$
$353$	4.59257e16	1.26334	0.631670	+	0.775237i	$0.282370\pi$
$354$	4.64577e15	0.125469
$355$	6.98785e15	0.185293
$356$	−3.96879e16	−1.03332
$357$	−2.31150e15	−0.0590950
$358$	−7.22393e16	−1.81357
$359$	−2.00344e16	−0.493928	−0.246964	−	0.969025i	$-0.579433\pi$
$359$	−2.00344e16	−0.493928	−0.246964	+	0.969025i	$0.579433\pi$
$360$	3.53460e16	0.855804
$361$	−4.07973e16	−0.970140
$362$	−8.47245e16	−1.97881
$363$	−1.39216e16	−0.319372
$364$	−1.60347e16	−0.361327
$365$	3.20902e16	0.710343
$366$	−8.30870e15	−0.180678
$367$	−1.55611e16	−0.332438	−0.166219	−	0.986089i	$-0.553156\pi$
$367$	−1.55611e16	−0.332438	−0.166219	+	0.986089i	$0.553156\pi$
$368$	−2.06356e16	−0.433118
$369$	−1.92230e16	−0.396414
$370$	−3.54502e16	−0.718302
$371$	−2.01214e16	−0.400615
$372$	8.85926e16	1.73328
$373$	8.13182e16	1.56344	0.781719	−	0.623631i	$-0.214343\pi$
$373$	8.13182e16	1.56344	0.781719	+	0.623631i	$0.214343\pi$
$374$	1.15403e16	0.218048
$375$	−1.10981e17	−2.06084
$376$	1.25704e17	2.29418
$377$	−1.19091e16	−0.213630
$378$	1.77922e16	0.313713
$379$	8.84513e16	1.53303	0.766513	−	0.642229i	$-0.221990\pi$
$379$	8.84513e16	1.53303	0.766513	+	0.642229i	$0.221990\pi$
$380$	−3.54356e16	−0.603735
$381$	−6.54503e16	−1.09622
$382$	−1.52507e17	−2.51118
$383$	5.94766e16	0.962840	0.481420	−	0.876490i	$-0.340121\pi$
$383$	5.94766e16	0.962840	0.481420	+	0.876490i	$0.340121\pi$
$384$	6.57861e16	1.04708
$385$	1.52095e17	2.38024
$386$	−4.42977e16	−0.681654
$387$	−6.97452e15	−0.105534
$388$	9.57057e16	1.42407
$389$	−4.00773e16	−0.586444	−0.293222	−	0.956044i	$-0.594727\pi$
$389$	−4.00773e16	−0.586444	−0.293222	+	0.956044i	$0.594727\pi$
$390$	−2.71287e16	−0.390400
$391$	7.92254e15	0.112128
$392$	−4.37218e15	−0.0608609
$393$	7.10727e16	0.973086
$394$	−2.75434e15	−0.0370930
$395$	−4.94095e16	−0.654530
$396$	−5.69494e16	−0.742114
$397$	1.21223e17	1.55398	0.776990	−	0.629513i	$-0.216745\pi$
$397$	1.21223e17	1.55398	0.776990	+	0.629513i	$0.216745\pi$
$398$	2.00724e16	0.253139
$399$	−7.85233e15	−0.0974259
$400$	9.36984e16	1.14378
$401$	−7.69992e16	−0.924800	−0.462400	−	0.886671i	$-0.653012\pi$
$401$	−7.69992e16	−0.924800	−0.462400	+	0.886671i	$0.653012\pi$
$402$	1.09838e17	1.29803
$403$	−2.99334e16	−0.348075
$404$	−9.41409e15	−0.107721
$405$	1.92990e16	0.217309
$406$	1.51729e17	1.68132
$407$	2.51441e16	0.274203
$408$	7.40159e15	0.0794390
$409$	1.23840e17	1.30816	0.654078	−	0.756427i	$-0.273057\pi$
$409$	1.23840e17	1.30816	0.654078	+	0.756427i	$0.273057\pi$
$410$	−3.73430e17	−3.88252
$411$	3.82194e15	0.0391121
$412$	1.64195e17	1.65397
$413$	1.28216e16	0.127135
$414$	−6.09818e16	−0.595248
$415$	3.23337e17	3.10701
$416$	−1.39447e16	−0.131917
$417$	9.93839e16	0.925618
$418$	3.92032e16	0.359481
$419$	1.58445e17	1.43050	0.715251	−	0.698867i	$-0.246312\pi$
$419$	1.58445e17	1.43050	0.715251	+	0.698867i	$0.246312\pi$
$420$	2.21592e17	1.96986
$421$	−3.87729e16	−0.339386	−0.169693	−	0.985497i	$-0.554278\pi$
$421$	−3.87729e16	−0.339386	−0.169693	+	0.985497i	$0.554278\pi$
$422$	−1.49635e17	−1.28974
$423$	6.86347e16	0.582547
$424$	6.44301e16	0.538531
$425$	−3.59732e16	−0.296109
$426$	−1.12632e16	−0.0913063
$427$	−2.29307e16	−0.183078
$428$	1.23197e17	0.968756
$429$	1.92419e16	0.149030
$430$	−1.35489e17	−1.03361
$431$	−2.01605e17	−1.51495	−0.757477	−	0.652862i	$-0.773568\pi$
$431$	−2.01605e17	−1.51495	−0.757477	+	0.652862i	$0.773568\pi$
$432$	−1.05262e16	−0.0779163
$433$	8.53145e16	0.622087	0.311044	−	0.950396i	$-0.399321\pi$
$433$	8.53145e16	0.622087	0.311044	+	0.950396i	$0.399321\pi$
$434$	3.81368e17	2.73944
$435$	1.64579e17	1.16465
$436$	−1.94069e17	−1.35299
$437$	2.69134e16	0.184859
$438$	−5.17240e16	−0.350034
$439$	2.09947e17	1.39988	0.699940	−	0.714201i	$-0.253210\pi$
$439$	2.09947e17	1.39988	0.699940	+	0.714201i	$0.253210\pi$
$440$	−4.87021e17	−3.19967
$441$	−2.38722e15	−0.0154540
$442$	−5.68085e15	−0.0362384
$443$	−2.47473e17	−1.55562	−0.777810	−	0.628499i	$-0.783670\pi$
$443$	−2.47473e17	−1.55562	−0.777810	+	0.628499i	$0.783670\pi$
$444$	3.66332e16	0.226927
$445$	−1.85315e17	−1.13128
$446$	2.36713e17	1.42411
$447$	−1.57760e17	−0.935403
$448$	2.45319e17	1.43359
$449$	−9.78404e16	−0.563530	−0.281765	−	0.959483i	$-0.590920\pi$
$449$	−9.78404e16	−0.563530	−0.281765	+	0.959483i	$0.590920\pi$
$450$	2.76895e17	1.57193
$451$	2.64867e17	1.48211
$452$	−4.26346e17	−2.35159
$453$	1.87828e17	1.02123
$454$	−5.21550e17	−2.79533
$455$	−7.48709e16	−0.395584
$456$	2.51437e16	0.130966
$457$	7.80402e16	0.400740	0.200370	−	0.979720i	$-0.435786\pi$
$457$	7.80402e16	0.400740	0.200370	+	0.979720i	$0.435786\pi$
$458$	1.02796e17	0.520416
$459$	4.04129e15	0.0201715
$460$	−7.59496e17	−3.73766
$461$	2.08645e17	1.01240	0.506199	−	0.862417i	$-0.331050\pi$
$461$	2.08645e17	1.01240	0.506199	+	0.862417i	$0.331050\pi$
$462$	−2.45152e17	−1.17291
$463$	−2.40097e17	−1.13269	−0.566345	−	0.824168i	$-0.691643\pi$
$463$	−2.40097e17	−1.13269	−0.566345	+	0.824168i	$0.691643\pi$
$464$	−8.97661e16	−0.417585
$465$	4.13667e17	1.89761
$466$	−3.45552e17	−1.56316
$467$	−1.76154e17	−0.785838	−0.392919	−	0.919573i	$-0.628535\pi$
$467$	−1.76154e17	−0.785838	−0.392919	+	0.919573i	$0.628535\pi$
$468$	2.80340e16	0.123335
$469$	3.03135e17	1.31526
$470$	1.33331e18	5.70553
$471$	−1.90570e17	−0.804300
$472$	−4.10556e16	−0.170903
$473$	9.60995e16	0.394570
$474$	7.96399e16	0.322531
$475$	−1.22204e17	−0.488175
$476$	4.64022e16	0.182849
$477$	3.51790e16	0.136746
$478$	5.85846e17	2.24648
$479$	−2.33098e17	−0.881775	−0.440887	−	0.897562i	$-0.645336\pi$
$479$	−2.33098e17	−0.881775	−0.440887	+	0.897562i	$0.645336\pi$
$480$	1.92710e17	0.719176
$481$	−1.23775e16	−0.0455711
$482$	4.53257e17	1.64641
$483$	−1.68300e17	−0.603153
$484$	2.79469e17	0.988188
$485$	4.46880e17	1.55909
$486$	−3.11068e16	−0.107083
$487$	−3.41148e17	−1.15879	−0.579395	−	0.815047i	$-0.696711\pi$
$487$	−3.41148e17	−1.15879	−0.579395	+	0.815047i	$0.696711\pi$
$488$	7.34256e16	0.246104
$489$	−1.85616e15	−0.00613914
$490$	−4.63747e16	−0.151359
$491$	−6.05547e16	−0.195038	−0.0975188	−	0.995234i	$-0.531091\pi$
$491$	−6.05547e16	−0.195038	−0.0975188	+	0.995234i	$0.531091\pi$
$492$	3.85892e17	1.22657
$493$	3.44635e16	0.108107
$494$	−1.92982e16	−0.0597438
$495$	−2.65915e17	−0.812472
$496$	−2.25625e17	−0.680388
$497$	−3.10847e16	−0.0925188
$498$	−5.21164e17	−1.53103
$499$	−3.07505e17	−0.891659	−0.445829	−	0.895118i	$-0.647091\pi$
$499$	−3.07505e17	−0.891659	−0.445829	+	0.895118i	$0.647091\pi$
$500$	2.22788e18	6.37657
$501$	−2.12204e16	−0.0599527
$502$	−2.48120e17	−0.691972
$503$	−4.30993e17	−1.18653	−0.593264	−	0.805008i	$-0.702161\pi$
$503$	−4.30993e17	−1.18653	−0.593264	+	0.805008i	$0.702161\pi$
$504$	−1.57233e17	−0.427312
$505$	−4.39574e16	−0.117934
$506$	8.40246e17	2.22550
$507$	2.11324e17	0.552582
$508$	1.31388e18	3.39190
$509$	3.07897e17	0.784765	0.392383	−	0.919802i	$-0.371651\pi$
$509$	3.07897e17	0.784765	0.392383	+	0.919802i	$0.371651\pi$
$510$	7.85070e16	0.197561
$511$	−1.42750e17	−0.354682
$512$	−3.21750e17	−0.789339
$513$	1.37285e16	0.0332554
$514$	−7.37739e17	−1.76458
$515$	7.66677e17	1.81078
$516$	1.40010e17	0.326540
$517$	−9.45693e17	−2.17802
$518$	1.57696e17	0.358656
$519$	−8.17323e16	−0.183572
$520$	2.39742e17	0.531768
$521$	−2.18771e17	−0.479231	−0.239615	−	0.970868i	$-0.577021\pi$
$521$	−2.18771e17	−0.479231	−0.239615	+	0.970868i	$0.577021\pi$
$522$	−2.65274e17	−0.573901
$523$	−9.65435e16	−0.206282	−0.103141	−	0.994667i	$-0.532889\pi$
$523$	−9.65435e16	−0.206282	−0.103141	+	0.994667i	$0.532889\pi$
$524$	−1.42675e18	−3.01089
$525$	7.64185e17	1.59281
$526$	3.27399e17	0.674016
$527$	8.66233e16	0.176143
$528$	1.45037e17	0.291312
$529$	7.28020e16	0.144438
$530$	6.83396e17	1.33930
$531$	−2.24165e16	−0.0433963
$532$	1.57632e17	0.301452
$533$	−1.30384e17	−0.246318
$534$	2.98697e17	0.557459
$535$	5.75244e17	1.06060
$536$	−9.70661e17	−1.76806
$537$	3.48564e17	0.627264
$538$	1.56547e18	2.78331
$539$	3.28927e16	0.0577793
$540$	−3.87419e17	−0.672390
$541$	−5.01805e17	−0.860504	−0.430252	−	0.902709i	$-0.641575\pi$
$541$	−5.01805e17	−0.860504	−0.430252	+	0.902709i	$0.641575\pi$
$542$	1.07605e18	1.82321
$543$	4.08807e17	0.684416
$544$	4.03541e16	0.0667566
$545$	−9.06169e17	−1.48126
$546$	1.20679e17	0.194931
$547$	−1.01850e17	−0.162571	−0.0812857	−	0.996691i	$-0.525903\pi$
$547$	−1.01850e17	−0.162571	−0.0812857	+	0.996691i	$0.525903\pi$
$548$	−7.67235e16	−0.121019
$549$	4.00906e16	0.0624917
$550$	−3.81524e18	−5.87711
$551$	1.17075e17	0.178229
$552$	5.38908e17	0.810794
$553$	2.19793e17	0.326814
$554$	−1.06569e18	−1.56610
$555$	1.71052e17	0.248441
$556$	−1.99508e18	−2.86401
$557$	7.48543e17	1.06208	0.531041	−	0.847346i	$-0.321801\pi$
$557$	7.48543e17	1.06208	0.531041	+	0.847346i	$0.321801\pi$
$558$	−6.66761e17	−0.935079
$559$	−4.73061e16	−0.0655754
$560$	−5.64345e17	−0.773255
$561$	−5.56835e16	−0.0754168
$562$	1.33810e18	1.79144
$563$	−7.05070e17	−0.933099	−0.466549	−	0.884495i	$-0.654503\pi$
$563$	−7.05070e17	−0.933099	−0.466549	+	0.884495i	$0.654503\pi$
$564$	−1.37781e18	−1.80250
$565$	−1.99074e18	−2.57454
$566$	−1.86336e17	−0.238226
$567$	−8.58498e16	−0.108505
$568$	9.95354e16	0.124369
$569$	−3.93985e17	−0.486687	−0.243343	−	0.969940i	$-0.578244\pi$
$569$	−3.93985e17	−0.486687	−0.243343	+	0.969940i	$0.578244\pi$
$570$	2.66694e17	0.325707
$571$	3.60010e16	0.0434690	0.0217345	−	0.999764i	$-0.493081\pi$
$571$	3.60010e16	0.0434690	0.0217345	+	0.999764i	$0.493081\pi$
$572$	−3.86271e17	−0.461124
$573$	7.35866e17	0.868548
$574$	1.66116e18	1.93859
$575$	−2.61920e18	−3.02223
$576$	−4.28902e17	−0.489341
$577$	−1.02172e18	−1.15262	−0.576311	−	0.817230i	$-0.695508\pi$
$577$	−1.02172e18	−1.15262	−0.576311	+	0.817230i	$0.695508\pi$
$578$	−1.47998e18	−1.65092
$579$	2.13743e17	0.235766
$580$	−3.30385e18	−3.60361
$581$	−1.43833e18	−1.55136
$582$	−7.20296e17	−0.768266
$583$	−4.84720e17	−0.511264
$584$	4.57095e17	0.476785
$585$	1.30900e17	0.135029
$586$	−5.09903e17	−0.520179
$587$	8.92720e17	0.900674	0.450337	−	0.892859i	$-0.351304\pi$
$587$	8.92720e17	0.900674	0.450337	+	0.892859i	$0.351304\pi$
$588$	4.79223e16	0.0478173
$589$	2.94265e17	0.290396
$590$	−4.35467e17	−0.425028
$591$	1.32901e16	0.0128295
$592$	−9.32964e16	−0.0890787
$593$	1.38547e17	0.130840	0.0654202	−	0.997858i	$-0.479161\pi$
$593$	1.38547e17	0.130840	0.0654202	+	0.997858i	$0.479161\pi$
$594$	4.28610e17	0.400360
$595$	2.16667e17	0.200185
$596$	3.16696e18	2.89429
$597$	−9.68520e16	−0.0875539
$598$	−4.13621e17	−0.369867
$599$	−1.25548e18	−1.11054	−0.555270	−	0.831670i	$-0.687385\pi$
$599$	−1.25548e18	−1.11054	−0.555270	+	0.831670i	$0.687385\pi$
$600$	−2.44697e18	−2.14115
$601$	−2.03541e17	−0.176184	−0.0880921	−	0.996112i	$-0.528077\pi$
$601$	−2.03541e17	−0.176184	−0.0880921	+	0.996112i	$0.528077\pi$
$602$	6.02707e17	0.516094
$603$	−5.29984e17	−0.448952
$604$	−3.77056e18	−3.15984
$605$	1.30493e18	1.08188
$606$	7.08519e16	0.0581138
$607$	1.44952e18	1.17625	0.588124	−	0.808771i	$-0.299867\pi$
$607$	1.44952e18	1.17625	0.588124	+	0.808771i	$0.299867\pi$
$608$	1.37086e17	0.110057
$609$	−7.32114e17	−0.581522
$610$	7.78810e17	0.612051
$611$	4.65529e17	0.361975
$612$	−8.11269e16	−0.0624138
$613$	1.84372e18	1.40346	0.701732	−	0.712441i	$-0.252410\pi$
$613$	1.84372e18	1.40346	0.701732	+	0.712441i	$0.252410\pi$
$614$	8.44952e17	0.636411
$615$	1.80185e18	1.34286
$616$	2.16646e18	1.59763
$617$	1.06316e18	0.775794	0.387897	−	0.921703i	$-0.373202\pi$
$617$	1.06316e18	0.775794	0.387897	+	0.921703i	$0.373202\pi$
$618$	−1.23575e18	−0.892292
$619$	1.08826e18	0.777580	0.388790	−	0.921326i	$-0.372893\pi$
$619$	1.08826e18	0.777580	0.388790	+	0.921326i	$0.372893\pi$
$620$	−8.30416e18	−5.87151
$621$	2.94245e17	0.205880
$622$	−2.76494e18	−1.91447
$623$	8.24356e17	0.564862
$624$	−7.13963e16	−0.0484145
$625$	6.19297e18	4.15603
$626$	2.15880e18	1.43377
$627$	−1.89161e17	−0.124335
$628$	3.82560e18	2.48864
$629$	3.58189e16	0.0230613
$630$	−1.66774e18	−1.06271
$631$	2.82063e18	1.77891	0.889456	−	0.457021i	$-0.151083\pi$
$631$	2.82063e18	1.77891	0.889456	+	0.457021i	$0.151083\pi$
$632$	−7.03793e17	−0.439323
$633$	7.22007e17	0.446085
$634$	9.04113e17	0.552895
$635$	6.13494e18	3.71348
$636$	−7.06202e17	−0.423114
$637$	−1.61918e16	−0.00960262
$638$	3.65512e18	2.14569
$639$	5.43466e16	0.0315804
$640$	−6.16641e18	−3.54701
$641$	1.42226e18	0.809847	0.404924	−	0.914350i	$-0.367298\pi$
$641$	1.42226e18	0.809847	0.404924	+	0.914350i	$0.367298\pi$
$642$	−9.27197e17	−0.522630
$643$	2.37408e18	1.32472	0.662361	−	0.749185i	$-0.269555\pi$
$643$	2.37408e18	1.32472	0.662361	+	0.749185i	$0.269555\pi$
$644$	3.37854e18	1.86625
$645$	6.53751e17	0.357499
$646$	5.58466e16	0.0302333
$647$	−3.16196e18	−1.69464	−0.847321	−	0.531081i	$-0.821786\pi$
$647$	−3.16196e18	−1.69464	−0.847321	+	0.531081i	$0.821786\pi$
$648$	2.74897e17	0.145859
$649$	3.08869e17	0.162249
$650$	1.87810e18	0.976745
$651$	−1.84015e18	−0.947496
$652$	3.72615e16	0.0189955
$653$	7.71439e17	0.389373	0.194687	−	0.980866i	$-0.437631\pi$
$653$	7.71439e17	0.389373	0.194687	+	0.980866i	$0.437631\pi$
$654$	1.46059e18	0.729917
$655$	−6.66195e18	−3.29634
$656$	−9.82778e17	−0.481483
$657$	2.49575e17	0.121067
$658$	−5.93110e18	−2.84883
$659$	−2.89278e17	−0.137582	−0.0687909	−	0.997631i	$-0.521914\pi$
$659$	−2.89278e17	−0.137582	−0.0687909	+	0.997631i	$0.521914\pi$
$660$	5.33811e18	2.51392
$661$	−3.56846e17	−0.166407	−0.0832034	−	0.996533i	$-0.526515\pi$
$661$	−3.56846e17	−0.166407	−0.0832034	+	0.996533i	$0.526515\pi$
$662$	−2.91640e18	−1.34670
$663$	2.74109e16	0.0125339
$664$	4.60563e18	2.08543
$665$	7.36032e17	0.330032
$666$	−2.75707e17	−0.122424
$667$	2.50928e18	1.10340
$668$	4.25990e17	0.185504
$669$	−1.14217e18	−0.492563
$670$	−1.02956e19	−4.39709
$671$	−5.52395e17	−0.233643
$672$	−8.57248e17	−0.359092
$673$	−6.71732e17	−0.278675	−0.139337	−	0.990245i	$-0.544497\pi$
$673$	−6.71732e17	−0.278675	−0.139337	+	0.990245i	$0.544497\pi$
$674$	−6.18203e17	−0.254005
$675$	−1.33606e18	−0.543688
$676$	−4.24222e18	−1.70978
$677$	1.51755e18	0.605783	0.302892	−	0.953025i	$-0.402048\pi$
$677$	1.51755e18	0.605783	0.302892	+	0.953025i	$0.402048\pi$
$678$	3.20874e18	1.26865
$679$	−1.98790e18	−0.778468
$680$	−6.93782e17	−0.269101
$681$	2.51655e18	0.966827
$682$	9.18707e18	3.49606
$683$	1.66018e16	0.00625779	0.00312890	−	0.999995i	$-0.499004\pi$
$683$	1.66018e16	0.00625779	0.00312890	+	0.999995i	$0.499004\pi$
$684$	−2.75594e17	−0.102897
$685$	−3.58246e17	−0.132493
$686$	4.65590e18	1.70568
$687$	−4.96005e17	−0.179998
$688$	−3.56574e17	−0.128181
$689$	2.38609e17	0.0849693
$690$	5.71608e18	2.01641
$691$	2.35708e18	0.823695	0.411848	−	0.911253i	$-0.364884\pi$
$691$	2.35708e18	0.823695	0.411848	+	0.911253i	$0.364884\pi$
$692$	1.64074e18	0.568001
$693$	1.18289e18	0.405676
$694$	8.07533e18	2.74362
$695$	−9.31567e18	−3.13554
$696$	2.34428e18	0.781717
$697$	3.77314e17	0.124649
$698$	2.02435e18	0.662559
$699$	1.66733e18	0.540656
$700$	−1.53406e19	−4.92840
$701$	2.18888e18	0.696715	0.348358	−	0.937362i	$-0.386740\pi$
$701$	2.18888e18	0.696715	0.348358	+	0.937362i	$0.386740\pi$
$702$	−2.10988e17	−0.0665376
$703$	1.21679e17	0.0380196
$704$	5.90969e18	1.82954
$705$	−6.43342e18	−1.97339
$706$	6.93863e18	2.10884
$707$	1.95540e17	0.0588856
$708$	4.49999e17	0.134275
$709$	1.57558e18	0.465844	0.232922	−	0.972495i	$-0.425171\pi$
$709$	1.57558e18	0.465844	0.232922	+	0.972495i	$0.425171\pi$
$710$	1.05575e18	0.309302
$711$	−3.84273e17	−0.111555
$712$	−2.63965e18	−0.759322
$713$	6.30702e18	1.79781
$714$	−3.49230e17	−0.0986446
$715$	−1.80362e18	−0.504843
$716$	−6.99726e18	−1.94086
$717$	−2.82679e18	−0.776995
$718$	−3.02688e18	−0.824492
$719$	3.07681e18	0.830545	0.415272	−	0.909697i	$-0.363686\pi$
$719$	3.07681e18	0.830545	0.415272	+	0.909697i	$0.363686\pi$
$720$	9.86668e17	0.263943
$721$	−3.41048e18	−0.904142
$722$	−6.16381e18	−1.61941
$723$	−2.18703e18	−0.569450
$724$	−8.20661e18	−2.11769
$725$	−1.13937e19	−2.91385
$726$	−2.10333e18	−0.533113
$727$	−1.81146e18	−0.455046	−0.227523	−	0.973773i	$-0.573063\pi$
$727$	−1.81146e18	−0.455046	−0.227523	+	0.973773i	$0.573063\pi$
$728$	−1.06647e18	−0.265517
$729$	1.50095e17	0.0370370
$730$	4.84830e18	1.18575
$731$	1.36898e17	0.0331844
$732$	−8.04800e17	−0.193360
$733$	4.85626e18	1.15645	0.578224	−	0.815878i	$-0.303746\pi$
$733$	4.85626e18	1.15645	0.578224	+	0.815878i	$0.303746\pi$
$734$	−2.35103e18	−0.554924
$735$	2.23764e17	0.0523508
$736$	2.93817e18	0.681352
$737$	7.30246e18	1.67854
$738$	−2.90428e18	−0.661717
$739$	−2.71902e18	−0.614079	−0.307039	−	0.951697i	$-0.599338\pi$
$739$	−2.71902e18	−0.614079	−0.307039	+	0.951697i	$0.599338\pi$
$740$	−3.43378e18	−0.768718
$741$	9.31167e16	0.0206637
$742$	−3.04002e18	−0.668729
$743$	5.63791e18	1.22939	0.614697	−	0.788763i	$-0.289278\pi$
$743$	5.63791e18	1.22939	0.614697	+	0.788763i	$0.289278\pi$
$744$	5.89230e18	1.27368
$745$	1.47875e19	3.16869
$746$	1.22859e19	2.60978
$747$	2.51469e18	0.529542
$748$	1.11782e18	0.233352
$749$	−2.55891e18	−0.529570
$750$	−1.67674e19	−3.44007
$751$	−9.79672e18	−1.99260	−0.996302	−	0.0859227i	$-0.972616\pi$
$751$	−9.79672e18	−1.99260	−0.996302	+	0.0859227i	$0.972616\pi$
$752$	3.50896e18	0.707559
$753$	1.19722e18	0.239334
$754$	−1.79928e18	−0.356603
$755$	−1.76059e19	−3.45943
$756$	1.72339e18	0.335732
$757$	−1.00554e19	−1.94212	−0.971058	−	0.238845i	$-0.923231\pi$
$757$	−1.00554e19	−1.94212	−0.971058	+	0.238845i	$0.923231\pi$
$758$	1.33636e19	2.55901
$759$	−4.05430e18	−0.769741
$760$	−2.35683e18	−0.443649
$761$	−2.04547e18	−0.381762	−0.190881	−	0.981613i	$-0.561134\pi$
$761$	−2.04547e18	−0.381762	−0.190881	+	0.981613i	$0.561134\pi$
$762$	−9.88849e18	−1.82988
$763$	4.03100e18	0.739610
$764$	−1.47722e19	−2.68743
$765$	−3.78807e17	−0.0683311
$766$	8.98595e18	1.60723
$767$	−1.52044e17	−0.0269650
$768$	5.11951e18	0.900286
$769$	1.70629e17	0.0297530	0.0148765	−	0.999889i	$-0.495264\pi$
$769$	1.70629e17	0.0297530	0.0148765	+	0.999889i	$0.495264\pi$
$770$	2.29792e19	3.97324
$771$	3.55969e18	0.610321
$772$	−4.29078e18	−0.729497
$773$	1.74614e18	0.294383	0.147192	−	0.989108i	$-0.452977\pi$
$773$	1.74614e18	0.294383	0.147192	+	0.989108i	$0.452977\pi$
$774$	−1.05374e18	−0.176164
$775$	−2.86378e19	−4.74765
$776$	6.36540e18	1.04646
$777$	−7.60907e17	−0.124049
$778$	−6.05503e18	−0.978925
$779$	1.28176e18	0.205501
$780$	−2.62775e18	−0.417800
$781$	−7.48823e17	−0.118072
$782$	1.19697e18	0.187171
$783$	1.27998e18	0.198497
$784$	−1.22047e17	−0.0187704
$785$	1.78629e19	2.72458
$786$	1.07379e19	1.62433
$787$	−4.09038e18	−0.613660	−0.306830	−	0.951764i	$-0.599268\pi$
$787$	−4.09038e18	−0.613660	−0.306830	+	0.951764i	$0.599268\pi$
$788$	−2.66792e17	−0.0396965
$789$	−1.57975e18	−0.233124
$790$	−7.46498e18	−1.09258
$791$	8.85561e18	1.28550
$792$	−3.78771e18	−0.545334
$793$	2.71923e17	0.0388302
$794$	1.83148e19	2.59399
$795$	−3.29748e18	−0.463229
$796$	1.94426e18	0.270906
$797$	1.13959e18	0.157496	0.0787480	−	0.996895i	$-0.474908\pi$
$797$	1.13959e18	0.157496	0.0787480	+	0.996895i	$0.474908\pi$
$798$	−1.18636e18	−0.162629
$799$	−1.34718e18	−0.183177
$800$	−1.33411e19	−1.79931
$801$	−1.44126e18	−0.192810
$802$	−1.16333e19	−1.54373
$803$	−3.43881e18	−0.452644
$804$	1.06392e19	1.38913
$805$	1.57755e19	2.04319
$806$	−4.52245e18	−0.581026
$807$	−7.55363e18	−0.962671
$808$	−6.26132e17	−0.0791575
$809$	−1.51245e19	−1.89678	−0.948389	−	0.317111i	$-0.897287\pi$
$809$	−1.51245e19	−1.89678	−0.948389	+	0.317111i	$0.897287\pi$
$810$	2.91577e18	0.362745
$811$	−7.40863e18	−0.914329	−0.457164	−	0.889382i	$-0.651135\pi$
$811$	−7.40863e18	−0.914329	−0.457164	+	0.889382i	$0.651135\pi$
$812$	1.46968e19	1.79932
$813$	−5.19209e18	−0.630600
$814$	3.79887e18	0.457716
$815$	1.73986e17	0.0207964
$816$	2.06612e17	0.0245002
$817$	4.65052e17	0.0547089
$818$	1.87102e19	2.18365
$819$	−5.82294e17	−0.0674212
$820$	−3.61713e19	−4.15502
$821$	−1.12362e19	−1.28053	−0.640263	−	0.768156i	$-0.721174\pi$
$821$	−1.12362e19	−1.28053	−0.640263	+	0.768156i	$0.721174\pi$
$822$	5.77433e17	0.0652882
$823$	−3.53355e18	−0.396381	−0.198190	−	0.980164i	$-0.563506\pi$
$823$	−3.53355e18	−0.396381	−0.198190	+	0.980164i	$0.563506\pi$
$824$	1.09206e19	1.21540
$825$	1.84090e19	2.03273
$826$	1.93713e18	0.212221
$827$	−1.68840e19	−1.83523	−0.917615	−	0.397471i	$-0.869888\pi$
$827$	−1.68840e19	−1.83523	−0.917615	+	0.397471i	$0.869888\pi$
$828$	−5.90683e18	−0.637026
$829$	−2.61390e18	−0.279695	−0.139847	−	0.990173i	$-0.544661\pi$
$829$	−2.61390e18	−0.279695	−0.139847	+	0.990173i	$0.544661\pi$
$830$	4.88509e19	5.18639
$831$	5.14211e18	0.541670
$832$	−2.90912e18	−0.304060
$833$	4.68571e16	0.00485940
$834$	1.50153e19	1.54509
$835$	1.98908e18	0.203091
$836$	3.79731e18	0.384711
$837$	3.21721e18	0.323418
$838$	2.39385e19	2.38788
$839$	1.28790e19	1.27476	0.637379	−	0.770550i	$-0.280019\pi$
$839$	1.28790e19	1.27476	0.637379	+	0.770550i	$0.280019\pi$
$840$	1.47381e19	1.44753
$841$	6.54890e17	0.0638255
$842$	−5.85795e18	−0.566523
$843$	−6.45652e18	−0.619611
$844$	−1.44939e19	−1.38026
$845$	−1.98083e19	−1.87188
$846$	1.03696e19	0.972421
$847$	−5.80485e18	−0.540193
$848$	1.79854e18	0.166091
$849$	8.99095e17	0.0823959
$850$	−5.43497e18	−0.494281
$851$	2.60797e18	0.235375
$852$	−1.09098e18	−0.0977148
$853$	9.92352e18	0.882058	0.441029	−	0.897493i	$-0.354614\pi$
$853$	9.92352e18	0.882058	0.441029	+	0.897493i	$0.354614\pi$
$854$	−3.46445e18	−0.305604
$855$	−1.28683e18	−0.112653
$856$	8.19382e18	0.711880
$857$	9.41154e18	0.811494	0.405747	−	0.913985i	$-0.367011\pi$
$857$	9.41154e18	0.811494	0.405747	+	0.913985i	$0.367011\pi$
$858$	2.90713e18	0.248770
$859$	6.11517e18	0.519341	0.259671	−	0.965697i	$-0.416386\pi$
$859$	6.11517e18	0.519341	0.259671	+	0.965697i	$0.416386\pi$
$860$	−1.31237e19	−1.10616
$861$	−8.01534e18	−0.670504
$862$	−3.04593e19	−2.52885
$863$	1.43388e19	1.18153	0.590764	−	0.806845i	$-0.298827\pi$
$863$	1.43388e19	1.18153	0.590764	+	0.806845i	$0.298827\pi$
$864$	1.49876e18	0.122573
$865$	7.66111e18	0.621852
$866$	1.28896e19	1.03842
$867$	7.14111e18	0.571008
$868$	3.69402e19	2.93171
$869$	5.29477e18	0.417079
$870$	2.48653e19	1.94410
$871$	−3.59472e18	−0.278964
$872$	−1.29075e19	−0.994229
$873$	3.47553e18	0.265722
$874$	4.06618e18	0.308576
$875$	−4.62752e19	−3.48575
$876$	−5.01010e18	−0.374602
$877$	1.29415e18	0.0960474	0.0480237	−	0.998846i	$-0.484708\pi$
$877$	1.29415e18	0.0960474	0.0480237	+	0.998846i	$0.484708\pi$
$878$	3.17196e19	2.33676
$879$	2.46035e18	0.179916
$880$	−1.35949e19	−0.986825
$881$	−2.44875e19	−1.76442	−0.882209	−	0.470859i	$-0.843944\pi$
$881$	−2.44875e19	−1.76442	−0.882209	+	0.470859i	$0.843944\pi$
$882$	−3.60671e17	−0.0257968
$883$	1.32558e19	0.941156	0.470578	−	0.882358i	$-0.344045\pi$
$883$	1.32558e19	0.941156	0.470578	+	0.882358i	$0.344045\pi$
$884$	−5.50260e17	−0.0387818
$885$	2.10119e18	0.147006
$886$	−3.73892e19	−2.59673
$887$	9.94982e18	0.685980	0.342990	−	0.939339i	$-0.388560\pi$
$887$	9.94982e18	0.685980	0.342990	+	0.939339i	$0.388560\pi$
$888$	2.43648e18	0.166755
$889$	−2.72906e19	−1.85418
$890$	−2.79982e19	−1.88840
$891$	−2.06810e18	−0.138474
$892$	2.29285e19	1.52407
$893$	−4.57647e18	−0.301992
$894$	−2.38350e19	−1.56143
$895$	−3.26724e19	−2.12487
$896$	2.74306e19	1.77106
$897$	1.99578e18	0.127927
$898$	−1.47821e19	−0.940676
$899$	2.74359e19	1.73333
$900$	2.68207e19	1.68226
$901$	−6.90504e17	−0.0429987
$902$	4.00170e19	2.47402
$903$	−2.90814e18	−0.178503
$904$	−2.83563e19	−1.72804
$905$	−3.83192e19	−2.31847
$906$	2.83778e19	1.70469
$907$	−1.60163e19	−0.955246	−0.477623	−	0.878565i	$-0.658501\pi$
$907$	−1.60163e19	−0.955246	−0.477623	+	0.878565i	$0.658501\pi$
$908$	−5.05185e19	−2.99152
$909$	−3.41870e17	−0.0201000
$910$	−1.13118e19	−0.660331
$911$	6.27404e18	0.363645	0.181823	−	0.983331i	$-0.441800\pi$
$911$	6.27404e18	0.363645	0.181823	+	0.983331i	$0.441800\pi$
$912$	7.01874e17	0.0403918
$913$	−3.46490e19	−1.97984
$914$	1.17906e19	0.668938
$915$	−3.75786e18	−0.211692
$916$	9.95706e18	0.556943
$917$	2.96350e19	1.64590
$918$	6.10573e17	0.0336713
$919$	−6.31635e16	−0.00345872	−0.00172936	−	0.999999i	$-0.500550\pi$
$919$	−6.31635e16	−0.00345872	−0.00172936	+	0.999999i	$0.500550\pi$
$920$	−5.05141e19	−2.74658
$921$	−4.07701e18	−0.220117
$922$	3.15228e19	1.68995
$923$	3.68617e17	0.0196230
$924$	−2.37460e19	−1.25523
$925$	−1.18418e19	−0.621578
$926$	−3.62748e19	−1.89075
$927$	5.96268e18	0.308620
$928$	1.27812e19	0.656917
$929$	1.02660e19	0.523963	0.261981	−	0.965073i	$-0.415624\pi$
$929$	1.02660e19	0.523963	0.261981	+	0.965073i	$0.415624\pi$
$930$	6.24984e19	3.16759
$931$	1.59177e17	0.00801137
$932$	−3.34709e19	−1.67288
$933$	1.33412e19	0.662162
$934$	−2.66140e19	−1.31176
$935$	5.21945e18	0.255475
$936$	1.86455e18	0.0906317
$937$	2.86257e19	1.38181	0.690905	−	0.722945i	$-0.257212\pi$
$937$	2.86257e19	1.38181	0.690905	+	0.722945i	$0.257212\pi$
$938$	4.57988e19	2.19551
$939$	−1.04165e19	−0.495901
$940$	1.29148e20	6.10598
$941$	8.66342e18	0.406778	0.203389	−	0.979098i	$-0.434804\pi$
$941$	8.66342e18	0.406778	0.203389	+	0.979098i	$0.434804\pi$
$942$	−2.87920e19	−1.34258
$943$	2.74721e19	1.27223
$944$	−1.14605e18	−0.0527089
$945$	8.04706e18	0.367562
$946$	1.45191e19	0.658638
$947$	−3.55050e19	−1.59961	−0.799807	−	0.600257i	$-0.795065\pi$
$947$	−3.55050e19	−1.59961	−0.799807	+	0.600257i	$0.795065\pi$
$948$	7.71410e18	0.345168
$949$	1.69280e18	0.0752270
$950$	−1.84630e19	−0.814889
$951$	−4.36247e18	−0.191231
$952$	3.08622e18	0.134365
$953$	1.83165e19	0.792024	0.396012	−	0.918245i	$-0.370394\pi$
$953$	1.83165e19	0.792024	0.396012	+	0.918245i	$0.370394\pi$
$954$	5.31498e18	0.228264
$955$	−6.89759e19	−2.94222
$956$	5.67463e19	2.40415
$957$	−1.76365e19	−0.742136
$958$	−3.52173e19	−1.47191
$959$	1.59362e18	0.0661552
$960$	4.02028e19	1.65765
$961$	4.45421e19	1.82418
$962$	−1.87004e18	−0.0760699
$963$	4.47385e18	0.180763
$964$	4.39035e19	1.76197
$965$	−2.00350e19	−0.798659
$966$	−2.54274e19	−1.00682
$967$	4.04599e19	1.59130	0.795650	−	0.605756i	$-0.207129\pi$
$967$	4.04599e19	1.59130	0.795650	+	0.605756i	$0.207129\pi$
$968$	1.85875e19	0.726159
$969$	−2.69468e17	−0.0104569
$970$	6.75164e19	2.60251
$971$	1.18780e19	0.454797	0.227399	−	0.973802i	$-0.426978\pi$
$971$	1.18780e19	0.454797	0.227399	+	0.973802i	$0.426978\pi$
$972$	−3.01308e18	−0.114599
$973$	4.14398e19	1.56561
$974$	−5.15420e19	−1.93432
$975$	−9.06207e18	−0.337830
$976$	2.04964e18	0.0759021
$977$	−3.26518e19	−1.20114	−0.600568	−	0.799574i	$-0.705059\pi$
$977$	−3.26518e19	−1.20114	−0.600568	+	0.799574i	$0.705059\pi$
$978$	−2.80436e17	−0.0102478
$979$	1.98586e19	0.720875
$980$	−4.49196e18	−0.161982
$981$	−7.04756e18	−0.252459
$982$	−9.14884e18	−0.325568
$983$	−1.99889e19	−0.706630	−0.353315	−	0.935505i	$-0.614946\pi$
$983$	−1.99889e19	−0.706630	−0.353315	+	0.935505i	$0.614946\pi$
$984$	2.56657e19	0.901332
$985$	−1.24573e18	−0.0434600
$986$	5.20688e18	0.180459
$987$	2.86184e19	0.985334
$988$	−1.86927e18	−0.0639370
$989$	9.96751e18	0.338696
$990$	−4.01754e19	−1.35622
$991$	−2.12002e19	−0.710986	−0.355493	−	0.934679i	$-0.615687\pi$
$991$	−2.12002e19	−0.710986	−0.355493	+	0.934679i	$0.615687\pi$
$992$	3.21253e19	1.07034
$993$	1.40720e19	0.465786
$994$	−4.69639e18	−0.154438
$995$	9.07835e18	0.296590
$996$	−5.04811e19	−1.63849
$997$	−5.05073e19	−1.62868	−0.814339	−	0.580389i	$-0.802901\pi$
$997$	−5.05073e19	−1.62868	−0.814339	+	0.580389i	$0.802901\pi$
$998$	−4.64590e19	−1.48841
$999$	1.33032e18	0.0423430

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.b.1.29	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.b.1.29	✓	31	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:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+151.084 q^{2} -729.000 q^{3} +14634.3 q^{4} +68332.2 q^{5} -110140. q^{6} -303969. q^{7} +973330. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+151.084 q^{2} -729.000 q^{3} +14634.3 q^{4} +68332.2 q^{5} -110140. q^{6} -303969. q^{7} +973330. q^{8} +531441. q^{9} +1.03239e7 q^{10} -7.32254e6 q^{11} -1.06684e7 q^{12} +3.60461e6 q^{13} -4.59248e7 q^{14} -4.98142e7 q^{15} +2.71700e7 q^{16} -1.04313e7 q^{17} +8.02921e7 q^{18} -3.54358e7 q^{19} +9.99996e8 q^{20} +2.21593e8 q^{21} -1.10632e9 q^{22} -7.59499e8 q^{23} -7.09557e8 q^{24} +3.44859e9 q^{25} +5.44598e8 q^{26} -3.87420e8 q^{27} -4.44838e9 q^{28} -3.30386e9 q^{29} -7.52612e9 q^{30} -8.30419e9 q^{31} -3.86857e9 q^{32} +5.33813e9 q^{33} -1.57600e9 q^{34} -2.07709e10 q^{35} +7.77728e9 q^{36} -3.43380e9 q^{37} -5.35377e9 q^{38} -2.62776e9 q^{39} +6.65098e10 q^{40} -3.61714e10 q^{41} +3.34792e10 q^{42} -1.31238e10 q^{43} -1.07160e11 q^{44} +3.63146e10 q^{45} -1.14748e11 q^{46} +1.29148e11 q^{47} -1.98069e10 q^{48} -4.49198e9 q^{49} +5.21027e11 q^{50} +7.60440e9 q^{51} +5.27510e10 q^{52} +6.61956e10 q^{53} -5.85330e10 q^{54} -5.00366e11 q^{55} -2.95862e11 q^{56} +2.58327e10 q^{57} -4.99160e11 q^{58} -4.21805e10 q^{59} -7.28997e11 q^{60} +7.54376e10 q^{61} -1.25463e12 q^{62} -1.61541e11 q^{63} -8.07054e11 q^{64} +2.46311e11 q^{65} +8.06505e11 q^{66} -9.97258e11 q^{67} -1.52655e11 q^{68} +5.53675e11 q^{69} -3.13814e12 q^{70} +1.02263e11 q^{71} +5.17267e11 q^{72} +4.69620e11 q^{73} -5.18791e11 q^{74} -2.51402e12 q^{75} -5.18578e11 q^{76} +2.22582e12 q^{77} -3.97012e11 q^{78} -7.23078e11 q^{79} +1.85659e12 q^{80} +2.82430e11 q^{81} -5.46492e12 q^{82} +4.73183e12 q^{83} +3.24287e12 q^{84} -7.12792e11 q^{85} -1.98279e12 q^{86} +2.40852e12 q^{87} -7.12724e12 q^{88} -2.71198e12 q^{89} +5.48654e12 q^{90} -1.09569e12 q^{91} -1.11147e13 q^{92} +6.05376e12 q^{93} +1.95122e13 q^{94} -2.42141e12 q^{95} +2.82018e12 q^{96} +6.53982e12 q^{97} -6.78666e11 q^{98} -3.89150e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9}+O(q^{10}) \) 31 * q - 52 * q^2 - 22599 * q^3 + 126886 * q^4 + 33486 * q^5 + 37908 * q^6 - 1135539 * q^7 - 1519749 * q^8 + 16474671 * q^9	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9} - 3854663 q^{10} + 3943968 q^{11} - 92499894 q^{12} - 48510022 q^{13} - 51427459 q^{14} - 24411294 q^{15} + 370110498 q^{16} + 83288419 q^{17} - 27634932 q^{18} - 180425297 q^{19} + 753620445 q^{20} + 827807931 q^{21} + 2300196142 q^{22} - 1305810279 q^{23} + 1107897021 q^{24} + 8070954867 q^{25} + 464550322 q^{26} - 12010035159 q^{27} - 9887169562 q^{28} + 6248352277 q^{29} + 2810049327 q^{30} - 26730150789 q^{31} - 24001343230 q^{32} - 2875152672 q^{33} - 36571033348 q^{34} + 10255900979 q^{35} + 67432422726 q^{36} - 43284776933 q^{37} - 36293696947 q^{38} + 35363806038 q^{39} - 105980683856 q^{40} - 9961079285 q^{41} + 37490617611 q^{42} - 51755851288 q^{43} - 59623729442 q^{44} + 17795833326 q^{45} - 202287132683 q^{46} - 82747063727 q^{47} - 269810553042 q^{48} + 535277836542 q^{49} + 526974390461 q^{50} - 60717257451 q^{51} + 544982341446 q^{52} + 561701818494 q^{53} + 20145865428 q^{54} - 521861534450 q^{55} - 228056576664 q^{56} + 131530041513 q^{57} + 10555409160 q^{58} - 1307596542871 q^{59} - 549389304405 q^{60} + 618193248201 q^{61} - 1486611437386 q^{62} - 603471981699 q^{63} + 679062548045 q^{64} - 1130583307122 q^{65} - 1676842987518 q^{66} - 4137387490592 q^{67} - 3901389300295 q^{68} + 951935693391 q^{69} - 819291947844 q^{70} - 3766439869810 q^{71} - 807656928309 q^{72} - 2386775553523 q^{73} + 3060770694642 q^{74} - 5883726098043 q^{75} - 847741068784 q^{76} + 1650423006137 q^{77} - 338657184738 q^{78} + 787155757766 q^{79} + 13999832121779 q^{80} + 8755315630911 q^{81} + 10083281915577 q^{82} + 8743877051639 q^{83} + 7207746610698 q^{84} + 15373177520565 q^{85} + 18939443838984 q^{86} - 4555048809933 q^{87} + 39713314506713 q^{88} + 11026795445259 q^{89} - 2048525959383 q^{90} + 23285721962531 q^{91} + 40411079823254 q^{92} + 19486279925181 q^{93} + 35237377585624 q^{94} + 13730236994039 q^{95} + 17496979214670 q^{96} + 10134565481560 q^{97} + 70916776240976 q^{98} + 2095986297888 q^{99}+O(q^{100}) \) 31 * q - 52 * q^2 - 22599 * q^3 + 126886 * q^4 + 33486 * q^5 + 37908 * q^6 - 1135539 * q^7 - 1519749 * q^8 + 16474671 * q^9 - 3854663 * q^10 + 3943968 * q^11 - 92499894 * q^12 - 48510022 * q^13 - 51427459 * q^14 - 24411294 * q^15 + 370110498 * q^16 + 83288419 * q^17 - 27634932 * q^18 - 180425297 * q^19 + 753620445 * q^20 + 827807931 * q^21 + 2300196142 * q^22 - 1305810279 * q^23 + 1107897021 * q^24 + 8070954867 * q^25 + 464550322 * q^26 - 12010035159 * q^27 - 9887169562 * q^28 + 6248352277 * q^29 + 2810049327 * q^30 - 26730150789 * q^31 - 24001343230 * q^32 - 2875152672 * q^33 - 36571033348 * q^34 + 10255900979 * q^35 + 67432422726 * q^36 - 43284776933 * q^37 - 36293696947 * q^38 + 35363806038 * q^39 - 105980683856 * q^40 - 9961079285 * q^41 + 37490617611 * q^42 - 51755851288 * q^43 - 59623729442 * q^44 + 17795833326 * q^45 - 202287132683 * q^46 - 82747063727 * q^47 - 269810553042 * q^48 + 535277836542 * q^49 + 526974390461 * q^50 - 60717257451 * q^51 + 544982341446 * q^52 + 561701818494 * q^53 + 20145865428 * q^54 - 521861534450 * q^55 - 228056576664 * q^56 + 131530041513 * q^57 + 10555409160 * q^58 - 1307596542871 * q^59 - 549389304405 * q^60 + 618193248201 * q^61 - 1486611437386 * q^62 - 603471981699 * q^63 + 679062548045 * q^64 - 1130583307122 * q^65 - 1676842987518 * q^66 - 4137387490592 * q^67 - 3901389300295 * q^68 + 951935693391 * q^69 - 819291947844 * q^70 - 3766439869810 * q^71 - 807656928309 * q^72 - 2386775553523 * q^73 + 3060770694642 * q^74 - 5883726098043 * q^75 - 847741068784 * q^76 + 1650423006137 * q^77 - 338657184738 * q^78 + 787155757766 * q^79 + 13999832121779 * q^80 + 8755315630911 * q^81 + 10083281915577 * q^82 + 8743877051639 * q^83 + 7207746610698 * q^84 + 15373177520565 * q^85 + 18939443838984 * q^86 - 4555048809933 * q^87 + 39713314506713 * q^88 + 11026795445259 * q^89 - 2048525959383 * q^90 + 23285721962531 * q^91 + 40411079823254 * q^92 + 19486279925181 * q^93 + 35237377585624 * q^94 + 13730236994039 * q^95 + 17496979214670 * q^96 + 10134565481560 * q^97 + 70916776240976 * q^98 + 2095986297888 * q^99

Introduction

L-functions

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