LMFDB - Embedded newform 177.14.a.b.1.9

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			1.9
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)

$f(q)$	$=$	$q-80.4989 q^{2} -729.000 q^{3} -1711.93 q^{4} -19074.6 q^{5} +58683.7 q^{6} -213612. q^{7} +797255. q^{8} +531441. q^{9} +O(q^{10})$	\(q-80.4989 q^{2} -729.000 q^{3} -1711.93 q^{4} -19074.6 q^{5} +58683.7 q^{6} -213612. q^{7} +797255. q^{8} +531441. q^{9} +1.53548e6 q^{10} +8.17809e6 q^{11} +1.24800e6 q^{12} +1.28272e7 q^{13} +1.71955e7 q^{14} +1.39054e7 q^{15} -5.01540e7 q^{16} -1.73178e8 q^{17} -4.27804e7 q^{18} -1.17963e8 q^{19} +3.26545e7 q^{20} +1.55723e8 q^{21} -6.58327e8 q^{22} -4.16120e8 q^{23} -5.81199e8 q^{24} -8.56862e8 q^{25} -1.03257e9 q^{26} -3.87420e8 q^{27} +3.65690e8 q^{28} -1.55997e8 q^{29} -1.11937e9 q^{30} -3.96240e9 q^{31} -2.49378e9 q^{32} -5.96182e9 q^{33} +1.39407e10 q^{34} +4.07457e9 q^{35} -9.09792e8 q^{36} +1.91396e10 q^{37} +9.49589e9 q^{38} -9.35103e9 q^{39} -1.52073e10 q^{40} +4.39945e10 q^{41} -1.25355e10 q^{42} +5.38432e10 q^{43} -1.40003e10 q^{44} -1.01370e10 q^{45} +3.34972e10 q^{46} -9.05033e10 q^{47} +3.65622e10 q^{48} -5.12589e10 q^{49} +6.89764e10 q^{50} +1.26247e11 q^{51} -2.19593e10 q^{52} +3.89797e10 q^{53} +3.11869e10 q^{54} -1.55994e11 q^{55} -1.70303e11 q^{56} +8.59951e10 q^{57} +1.25576e10 q^{58} -4.21805e10 q^{59} -2.38051e10 q^{60} +1.44043e11 q^{61} +3.18969e11 q^{62} -1.13522e11 q^{63} +6.11608e11 q^{64} -2.44674e11 q^{65} +4.79920e11 q^{66} +3.53590e11 q^{67} +2.96470e11 q^{68} +3.03351e11 q^{69} -3.27998e11 q^{70} +8.31665e11 q^{71} +4.23694e11 q^{72} +1.24104e11 q^{73} -1.54072e12 q^{74} +6.24653e11 q^{75} +2.01945e11 q^{76} -1.74694e12 q^{77} +7.52747e11 q^{78} +1.36968e12 q^{79} +9.56668e11 q^{80} +2.82430e11 q^{81} -3.54151e12 q^{82} -2.42824e12 q^{83} -2.66588e11 q^{84} +3.30331e12 q^{85} -4.33431e12 q^{86} +1.13722e11 q^{87} +6.52002e12 q^{88} +1.71038e12 q^{89} +8.16019e11 q^{90} -2.74004e12 q^{91} +7.12370e11 q^{92} +2.88859e12 q^{93} +7.28541e12 q^{94} +2.25010e12 q^{95} +1.81796e12 q^{96} +1.14861e13 q^{97} +4.12628e12 q^{98} +4.34617e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−80.4989	−0.889395	−0.444698	−	0.895681i	$-0.646689\pi$
$2$	−80.4989	−0.889395	−0.444698	+	0.895681i	$0.646689\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	−1711.93	−0.208976
$5$	−19074.6	−0.545947	−0.272974	−	0.962022i	$-0.588007\pi$
$5$	−19074.6	−0.545947	−0.272974	+	0.962022i	$0.588007\pi$
$6$	58683.7	0.513492
$7$	−213612.	−0.686260	−0.343130	−	0.939288i	$-0.611487\pi$
$7$	−213612.	−0.686260	−0.343130	+	0.939288i	$0.611487\pi$
$8$	797255.	1.07526
$9$	531441.	0.333333
$10$	1.53548e6	0.485563
$11$	8.17809e6	1.39187	0.695936	−	0.718104i	$-0.254990\pi$
$11$	8.17809e6	1.39187	0.695936	+	0.718104i	$0.254990\pi$
$12$	1.24800e6	0.120653
$13$	1.28272e7	0.737055	0.368528	−	0.929617i	$-0.379862\pi$
$13$	1.28272e7	0.737055	0.368528	+	0.929617i	$0.379862\pi$
$14$	1.71955e7	0.610356
$15$	1.39054e7	0.315203
$16$	−5.01540e7	−0.747352
$17$	−1.73178e8	−1.74010	−0.870052	−	0.492959i	$-0.835915\pi$
$17$	−1.73178e8	−1.74010	−0.870052	+	0.492959i	$0.835915\pi$
$18$	−4.27804e7	−0.296465
$19$	−1.17963e8	−0.575238	−0.287619	−	0.957745i	$-0.592864\pi$
$19$	−1.17963e8	−0.575238	−0.287619	+	0.957745i	$0.592864\pi$
$20$	3.26545e7	0.114090
$21$	1.55723e8	0.396212
$22$	−6.58327e8	−1.23792
$23$	−4.16120e8	−0.586121	−0.293061	−	0.956094i	$-0.594674\pi$
$23$	−4.16120e8	−0.586121	−0.293061	+	0.956094i	$0.594674\pi$
$24$	−5.81199e8	−0.620800
$25$	−8.56862e8	−0.701942
$26$	−1.03257e9	−0.655533
$27$	−3.87420e8	−0.192450
$28$	3.65690e8	0.143412
$29$	−1.55997e8	−0.0487000	−0.0243500	−	0.999703i	$-0.507752\pi$
$29$	−1.55997e8	−0.0487000	−0.0243500	+	0.999703i	$0.507752\pi$
$30$	−1.11937e9	−0.280340
$31$	−3.96240e9	−0.801877	−0.400939	−	0.916105i	$-0.631316\pi$
$31$	−3.96240e9	−0.801877	−0.400939	+	0.916105i	$0.631316\pi$
$32$	−2.49378e9	−0.410566
$33$	−5.96182e9	−0.803598
$34$	1.39407e10	1.54764
$35$	4.07457e9	0.374661
$36$	−9.09792e8	−0.0696588
$37$	1.91396e10	1.22637	0.613186	−	0.789938i	$-0.289888\pi$
$37$	1.91396e10	1.22637	0.613186	+	0.789938i	$0.289888\pi$
$38$	9.49589e9	0.511614
$39$	−9.35103e9	−0.425539
$40$	−1.52073e10	−0.587034
$41$	4.39945e10	1.44645	0.723225	−	0.690613i	$-0.242659\pi$
$41$	4.39945e10	1.44645	0.723225	+	0.690613i	$0.242659\pi$
$42$	−1.25355e10	−0.352389
$43$	5.38432e10	1.29893	0.649465	−	0.760392i	$-0.274993\pi$
$43$	5.38432e10	1.29893	0.649465	+	0.760392i	$0.274993\pi$
$44$	−1.40003e10	−0.290868
$45$	−1.01370e10	−0.181982
$46$	3.34972e10	0.521293
$47$	−9.05033e10	−1.22470	−0.612348	−	0.790588i	$-0.709775\pi$
$47$	−9.05033e10	−1.22470	−0.612348	+	0.790588i	$0.709775\pi$
$48$	3.65622e10	0.431484
$49$	−5.12589e10	−0.529048
$50$	6.89764e10	0.624303
$51$	1.26247e11	1.00465
$52$	−2.19593e10	−0.154027
$53$	3.89797e10	0.241571	0.120786	−	0.992679i	$-0.461459\pi$
$53$	3.89797e10	0.241571	0.120786	+	0.992679i	$0.461459\pi$
$54$	3.11869e10	0.171164
$55$	−1.55994e11	−0.759888
$56$	−1.70303e11	−0.737906
$57$	8.59951e10	0.332114
$58$	1.25576e10	0.0433136
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	−2.38051e10	−0.0658699
$61$	1.44043e11	0.357972	0.178986	−	0.983852i	$-0.442718\pi$
$61$	1.44043e11	0.357972	0.178986	+	0.983852i	$0.442718\pi$
$62$	3.18969e11	0.713185
$63$	−1.13522e11	−0.228753
$64$	6.11608e11	1.11251
$65$	−2.44674e11	−0.402393
$66$	4.79920e11	0.714716
$67$	3.53590e11	0.477545	0.238772	−	0.971076i	$-0.423255\pi$
$67$	3.53590e11	0.477545	0.238772	+	0.971076i	$0.423255\pi$
$68$	2.96470e11	0.363641
$69$	3.03351e11	0.338397
$70$	−3.27998e11	−0.333222
$71$	8.31665e11	0.770494	0.385247	−	0.922814i	$-0.374116\pi$
$71$	8.31665e11	0.770494	0.385247	+	0.922814i	$0.374116\pi$
$72$	4.23694e11	0.358419
$73$	1.24104e11	0.0959811	0.0479905	−	0.998848i	$-0.484718\pi$
$73$	1.24104e11	0.0959811	0.0479905	+	0.998848i	$0.484718\pi$
$74$	−1.54072e12	−1.09073
$75$	6.24653e11	0.405266
$76$	2.01945e11	0.120211
$77$	−1.74694e12	−0.955185
$78$	7.52747e11	0.378472
$79$	1.36968e12	0.633932	0.316966	−	0.948437i	$-0.397336\pi$
$79$	1.36968e12	0.633932	0.316966	+	0.948437i	$0.397336\pi$
$80$	9.56668e11	0.408015
$81$	2.82430e11	0.111111
$82$	−3.54151e12	−1.28646
$83$	−2.42824e12	−0.815237	−0.407618	−	0.913152i	$-0.633641\pi$
$83$	−2.42824e12	−0.815237	−0.407618	+	0.913152i	$0.633641\pi$
$84$	−2.66588e11	−0.0827990
$85$	3.30331e12	0.950005
$86$	−4.33431e12	−1.15526
$87$	1.13722e11	0.0281170
$88$	6.52002e12	1.49662
$89$	1.71038e12	0.364802	0.182401	−	0.983224i	$-0.441613\pi$
$89$	1.71038e12	0.364802	0.182401	+	0.983224i	$0.441613\pi$
$90$	8.16019e11	0.161854
$91$	−2.74004e12	−0.505811
$92$	7.12370e11	0.122486
$93$	2.88859e12	0.462964
$94$	7.28541e12	1.08924
$95$	2.25010e12	0.314050
$96$	1.81796e12	0.237040
$97$	1.14861e13	1.40009	0.700045	−	0.714098i	$-0.253163\pi$
$97$	1.14861e13	1.40009	0.700045	+	0.714098i	$0.253163\pi$
$98$	4.12628e12	0.470532
$99$	4.34617e12	0.463957
$100$	1.46689e12	0.146689
$101$	2.63942e12	0.247411	0.123706	−	0.992319i	$-0.460522\pi$
$101$	2.63942e12	0.247411	0.123706	+	0.992319i	$0.460522\pi$
$102$	−1.01627e13	−0.893531
$103$	−3.88934e12	−0.320948	−0.160474	−	0.987040i	$-0.551302\pi$
$103$	−3.88934e12	−0.320948	−0.160474	+	0.987040i	$0.551302\pi$
$104$	1.02266e13	0.792524
$105$	−2.97036e12	−0.216311
$106$	−3.13782e12	−0.214852
$107$	−1.65551e13	−1.06644	−0.533222	−	0.845975i	$-0.679019\pi$
$107$	−1.65551e13	−1.06644	−0.533222	+	0.845975i	$0.679019\pi$
$108$	6.63239e11	0.0402175
$109$	−1.37664e13	−0.786228	−0.393114	−	0.919490i	$-0.628602\pi$
$109$	−1.37664e13	−0.786228	−0.393114	+	0.919490i	$0.628602\pi$
$110$	1.25573e13	0.675841
$111$	−1.39528e13	−0.708046
$112$	1.07135e13	0.512878
$113$	−1.07861e13	−0.487363	−0.243682	−	0.969855i	$-0.578355\pi$
$113$	−1.07861e13	−0.487363	−0.243682	+	0.969855i	$0.578355\pi$
$114$	−6.92251e12	−0.295380
$115$	7.93732e12	0.319991
$116$	2.67057e11	0.0101772
$117$	6.81690e12	0.245685
$118$	3.39548e12	0.115789
$119$	3.69930e13	1.19416
$120$	1.10861e13	0.338924
$121$	3.23584e13	0.937307
$122$	−1.15953e13	−0.318379
$123$	−3.20720e13	−0.835108
$124$	6.78338e12	0.167573
$125$	3.96288e13	0.929170
$126$	9.13841e12	0.203452
$127$	2.31937e13	0.490509	0.245254	−	0.969459i	$-0.421129\pi$
$127$	2.31937e13	0.490509	0.245254	+	0.969459i	$0.421129\pi$
$128$	−2.88047e13	−0.578893
$129$	−3.92517e13	−0.749938
$130$	1.96960e13	0.357887
$131$	−1.11690e13	−0.193086	−0.0965429	−	0.995329i	$-0.530778\pi$
$131$	−1.11690e13	−0.193086	−0.0965429	+	0.995329i	$0.530778\pi$
$132$	1.02063e13	0.167933
$133$	2.51983e13	0.394763
$134$	−2.84636e13	−0.424726
$135$	7.38989e12	0.105068
$136$	−1.38067e14	−1.87106
$137$	1.20494e14	1.55697	0.778485	−	0.627663i	$-0.215989\pi$
$137$	1.20494e14	1.55697	0.778485	+	0.627663i	$0.215989\pi$
$138$	−2.44194e13	−0.300969
$139$	1.61914e14	1.90410	0.952048	−	0.305947i	$-0.0989732\pi$
$139$	1.61914e14	1.90410	0.952048	+	0.305947i	$0.0989732\pi$
$140$	−6.97539e12	−0.0782954
$141$	6.59769e13	0.707079
$142$	−6.69481e13	−0.685273
$143$	1.04902e14	1.02589
$144$	−2.66539e13	−0.249117
$145$	2.97558e12	0.0265877
$146$	−9.99019e12	−0.0853651
$147$	3.73678e13	0.305446
$148$	−3.27658e13	−0.256283
$149$	−9.37466e11	−0.00701850	−0.00350925	−	0.999994i	$-0.501117\pi$
$149$	−9.37466e11	−0.00701850	−0.00350925	+	0.999994i	$0.501117\pi$
$150$	−5.02838e13	−0.360442
$151$	−1.24838e14	−0.857030	−0.428515	−	0.903535i	$-0.640963\pi$
$151$	−1.24838e14	−0.857030	−0.428515	+	0.903535i	$0.640963\pi$
$152$	−9.40467e13	−0.618529
$153$	−9.20340e13	−0.580035
$154$	1.40626e14	0.849537
$155$	7.55813e13	0.437783
$156$	1.60084e13	0.0889276
$157$	−2.14585e14	−1.14354	−0.571771	−	0.820413i	$-0.693744\pi$
$157$	−2.14585e14	−1.14354	−0.571771	+	0.820413i	$0.693744\pi$
$158$	−1.10258e14	−0.563816
$159$	−2.84162e13	−0.139471
$160$	4.75679e13	0.224147
$161$	8.88882e13	0.402231
$162$	−2.27353e13	−0.0988217
$163$	2.45085e14	1.02352	0.511761	−	0.859128i	$-0.328993\pi$
$163$	2.45085e14	1.02352	0.511761	+	0.859128i	$0.328993\pi$
$164$	−7.53157e13	−0.302274
$165$	1.13719e14	0.438722
$166$	1.95470e14	0.725068
$167$	−1.53043e14	−0.545955	−0.272977	−	0.962020i	$-0.588008\pi$
$167$	−1.53043e14	−0.545955	−0.272977	+	0.962020i	$0.588008\pi$
$168$	1.24151e14	0.426030
$169$	−1.38338e14	−0.456749
$170$	−2.65913e14	−0.844930
$171$	−6.26904e13	−0.191746
$172$	−9.21760e13	−0.271446
$173$	5.15002e14	1.46053	0.730264	−	0.683166i	$-0.239397\pi$
$173$	5.15002e14	1.46053	0.730264	+	0.683166i	$0.239397\pi$
$174$	−9.15448e12	−0.0250071
$175$	1.83036e14	0.481714
$176$	−4.10164e14	−1.04022
$177$	3.07496e13	0.0751646
$178$	−1.37684e14	−0.324453
$179$	6.31949e14	1.43594	0.717972	−	0.696072i	$-0.245071\pi$
$179$	6.31949e14	1.43594	0.717972	+	0.696072i	$0.245071\pi$
$180$	1.73539e13	0.0380300
$181$	−4.63932e13	−0.0980717	−0.0490359	−	0.998797i	$-0.515615\pi$
$181$	−4.63932e13	−0.0980717	−0.0490359	+	0.998797i	$0.515615\pi$
$182$	2.20570e14	0.449866
$183$	−1.05008e14	−0.206675
$184$	−3.31754e14	−0.630231
$185$	−3.65081e14	−0.669534
$186$	−2.32528e14	−0.411758
$187$	−1.41627e15	−2.42200
$188$	1.54936e14	0.255933
$189$	8.27577e13	0.132071
$190$	−1.81130e14	−0.279314
$191$	6.06776e14	0.904298	0.452149	−	0.891942i	$-0.350658\pi$
$191$	6.06776e14	0.904298	0.452149	+	0.891942i	$0.350658\pi$
$192$	−4.45862e14	−0.642307
$193$	−2.92079e14	−0.406797	−0.203398	−	0.979096i	$-0.565199\pi$
$193$	−2.92079e14	−0.406797	−0.203398	+	0.979096i	$0.565199\pi$
$194$	−9.24617e14	−1.24523
$195$	1.78367e14	0.232322
$196$	8.77519e13	0.110559
$197$	8.20582e14	1.00021	0.500106	−	0.865964i	$-0.333295\pi$
$197$	8.20582e14	1.00021	0.500106	+	0.865964i	$0.333295\pi$
$198$	−3.49862e14	−0.412641
$199$	−8.75439e14	−0.999266	−0.499633	−	0.866237i	$-0.666532\pi$
$199$	−8.75439e14	−0.999266	−0.499633	+	0.866237i	$0.666532\pi$
$200$	−6.83138e14	−0.754768
$201$	−2.57767e14	−0.275711
$202$	−2.12470e14	−0.220046
$203$	3.33228e13	0.0334209
$204$	−2.16127e14	−0.209948
$205$	−8.39178e14	−0.789685
$206$	3.13088e14	0.285449
$207$	−2.21143e14	−0.195374
$208$	−6.43335e14	−0.550840
$209$	−9.64712e14	−0.800658
$210$	2.39110e14	0.192386
$211$	−3.01341e14	−0.235083	−0.117542	−	0.993068i	$-0.537501\pi$
$211$	−3.01341e14	−0.235083	−0.117542	+	0.993068i	$0.537501\pi$
$212$	−6.67306e13	−0.0504827
$213$	−6.06284e14	−0.444845
$214$	1.33267e15	0.948490
$215$	−1.02704e15	−0.709147
$216$	−3.08873e14	−0.206933
$217$	8.46417e14	0.550296
$218$	1.10818e15	0.699267
$219$	−9.04715e13	−0.0554147
$220$	2.67051e14	0.158799
$221$	−2.22139e15	−1.28255
$222$	1.12318e15	0.629733
$223$	7.48486e14	0.407570	0.203785	−	0.979016i	$-0.434676\pi$
$223$	7.48486e14	0.407570	0.203785	+	0.979016i	$0.434676\pi$
$224$	5.32701e14	0.281755
$225$	−4.55372e14	−0.233981
$226$	8.68265e14	0.433458
$227$	−1.73311e15	−0.840731	−0.420365	−	0.907355i	$-0.638098\pi$
$227$	−1.73311e15	−0.840731	−0.420365	+	0.907355i	$0.638098\pi$
$228$	−1.47218e14	−0.0694040
$229$	−1.83370e15	−0.840231	−0.420116	−	0.907471i	$-0.638010\pi$
$229$	−1.83370e15	−0.840231	−0.420116	+	0.907471i	$0.638010\pi$
$230$	−6.38945e14	−0.284599
$231$	1.27352e15	0.551476
$232$	−1.24369e14	−0.0523651
$233$	−1.82157e15	−0.745818	−0.372909	−	0.927868i	$-0.621640\pi$
$233$	−1.82157e15	−0.745818	−0.372909	+	0.927868i	$0.621640\pi$
$234$	−5.48753e14	−0.218511
$235$	1.72632e15	0.668620
$236$	7.22103e13	0.0272064
$237$	−9.98496e14	−0.366001
$238$	−2.97789e15	−1.06208
$239$	4.32444e15	1.50087	0.750435	−	0.660944i	$-0.229844\pi$
$239$	4.32444e15	1.50087	0.750435	+	0.660944i	$0.229844\pi$
$240$	−6.97411e14	−0.235568
$241$	2.79473e15	0.918818	0.459409	−	0.888225i	$-0.348061\pi$
$241$	2.79473e15	0.918818	0.459409	+	0.888225i	$0.348061\pi$
$242$	−2.60481e15	−0.833636
$243$	−2.05891e14	−0.0641500
$244$	−2.46593e14	−0.0748078
$245$	9.77744e14	0.288832
$246$	2.58176e15	0.742741
$247$	−1.51314e15	−0.423982
$248$	−3.15905e15	−0.862224
$249$	1.77019e15	0.470677
$250$	−3.19007e15	−0.826399
$251$	1.43836e15	0.363068	0.181534	−	0.983385i	$-0.441894\pi$
$251$	1.43836e15	0.363068	0.181534	+	0.983385i	$0.441894\pi$
$252$	1.94343e14	0.0478040
$253$	−3.40306e15	−0.815806
$254$	−1.86707e15	−0.436256
$255$	−2.40811e15	−0.548486
$256$	−2.69155e15	−0.597643
$257$	−4.98081e15	−1.07829	−0.539143	−	0.842214i	$-0.681252\pi$
$257$	−4.98081e15	−1.07829	−0.539143	+	0.842214i	$0.681252\pi$
$258$	3.15971e15	0.666991
$259$	−4.08845e15	−0.841610
$260$	4.18866e14	0.0840907
$261$	−8.29032e13	−0.0162333
$262$	8.99090e14	0.171730
$263$	−6.11475e14	−0.113937	−0.0569687	−	0.998376i	$-0.518144\pi$
$263$	−6.11475e14	−0.113937	−0.0569687	+	0.998376i	$0.518144\pi$
$264$	−4.75310e15	−0.864074
$265$	−7.43522e14	−0.131885
$266$	−2.02844e15	−0.351100
$267$	−1.24687e15	−0.210619
$268$	−6.05323e14	−0.0997956
$269$	−1.10305e16	−1.77502	−0.887512	−	0.460785i	$-0.847568\pi$
$269$	−1.10305e16	−1.77502	−0.887512	+	0.460785i	$0.847568\pi$
$270$	−5.94878e14	−0.0934466
$271$	−4.71700e15	−0.723378	−0.361689	−	0.932299i	$-0.617800\pi$
$271$	−4.71700e15	−0.723378	−0.361689	+	0.932299i	$0.617800\pi$
$272$	8.68558e15	1.30047
$273$	1.99749e15	0.292030
$274$	−9.69959e15	−1.38476
$275$	−7.00749e15	−0.977013
$276$	−5.19318e14	−0.0707170
$277$	−7.70626e15	−1.02500	−0.512502	−	0.858686i	$-0.671281\pi$
$277$	−7.70626e15	−1.02500	−0.512502	+	0.858686i	$0.671281\pi$
$278$	−1.30339e16	−1.69349
$279$	−2.10578e15	−0.267292
$280$	3.24847e15	0.402858
$281$	1.10133e15	0.133453	0.0667263	−	0.997771i	$-0.478745\pi$
$281$	1.10133e15	0.133453	0.0667263	+	0.997771i	$0.478745\pi$
$282$	−5.31107e15	−0.628872
$283$	1.00903e16	1.16760	0.583798	−	0.811899i	$-0.301566\pi$
$283$	1.00903e16	1.16760	0.583798	+	0.811899i	$0.301566\pi$
$284$	−1.42376e15	−0.161015
$285$	−1.64032e15	−0.181317
$286$	−8.44449e15	−0.912418
$287$	−9.39775e15	−0.992640
$288$	−1.32530e15	−0.136855
$289$	2.00861e16	2.02797
$290$	−2.39531e14	−0.0236469
$291$	−8.37336e15	−0.808343
$292$	−2.12457e14	−0.0200578
$293$	4.10282e14	0.0378829	0.0189415	−	0.999821i	$-0.493970\pi$
$293$	4.10282e14	0.0378829	0.0189415	+	0.999821i	$0.493970\pi$
$294$	−3.00806e15	−0.271662
$295$	8.04577e14	0.0710763
$296$	1.52592e16	1.31867
$297$	−3.16836e15	−0.267866
$298$	7.54649e13	0.00624222
$299$	−5.33765e15	−0.432004
$300$	−1.06936e15	−0.0846911
$301$	−1.15016e16	−0.891403
$302$	1.00493e16	0.762238
$303$	−1.92413e15	−0.142843
$304$	5.91632e15	0.429906
$305$	−2.74757e15	−0.195434
$306$	7.40863e15	0.515880
$307$	−9.89210e15	−0.674356	−0.337178	−	0.941441i	$-0.609472\pi$
$307$	−9.89210e15	−0.674356	−0.337178	+	0.941441i	$0.609472\pi$
$308$	2.99064e15	0.199611
$309$	2.83533e15	0.185299
$310$	−6.08421e15	−0.389362
$311$	2.68530e16	1.68287	0.841434	−	0.540360i	$-0.181712\pi$
$311$	2.68530e16	1.68287	0.841434	+	0.540360i	$0.181712\pi$
$312$	−7.45516e15	−0.457564
$313$	−2.91390e15	−0.175161	−0.0875803	−	0.996157i	$-0.527913\pi$
$313$	−2.91390e15	−0.175161	−0.0875803	+	0.996157i	$0.527913\pi$
$314$	1.72739e16	1.01706
$315$	2.16539e15	0.124887
$316$	−2.34480e15	−0.132477
$317$	−1.30073e16	−0.719948	−0.359974	−	0.932962i	$-0.617214\pi$
$317$	−1.30073e16	−0.719948	−0.359974	+	0.932962i	$0.617214\pi$
$318$	2.28747e15	0.124045
$319$	−1.27576e15	−0.0677842
$320$	−1.16662e16	−0.607371
$321$	1.20687e16	0.615712
$322$	−7.15540e15	−0.357743
$323$	2.04286e16	1.00097
$324$	−4.83501e14	−0.0232196
$325$	−1.09911e16	−0.517370
$326$	−1.97290e16	−0.910315
$327$	1.00357e16	0.453929
$328$	3.50748e16	1.55531
$329$	1.93326e16	0.840460
$330$	−9.15429e15	−0.390197
$331$	8.56049e15	0.357780	0.178890	−	0.983869i	$-0.442749\pi$
$331$	8.56049e15	0.357780	0.178890	+	0.983869i	$0.442749\pi$
$332$	4.15699e15	0.170365
$333$	1.01716e16	0.408791
$334$	1.23198e16	0.485569
$335$	−6.74460e15	−0.260714
$336$	−7.81014e15	−0.296110
$337$	−4.26634e15	−0.158658	−0.0793289	−	0.996848i	$-0.525278\pi$
$337$	−4.26634e15	−0.158658	−0.0793289	+	0.996848i	$0.525278\pi$
$338$	1.11361e16	0.406231
$339$	7.86303e15	0.281379
$340$	−5.65505e15	−0.198529
$341$	−3.24049e16	−1.11611
$342$	5.04651e15	0.170538
$343$	3.16462e16	1.04932
$344$	4.29268e16	1.39668
$345$	−5.78631e15	−0.184747
$346$	−4.14571e16	−1.29899
$347$	1.84443e16	0.567178	0.283589	−	0.958946i	$-0.408475\pi$
$347$	1.84443e16	0.567178	0.283589	+	0.958946i	$0.408475\pi$
$348$	−1.94684e14	−0.00587579
$349$	1.37643e16	0.407744	0.203872	−	0.978998i	$-0.434647\pi$
$349$	1.37643e16	0.407744	0.203872	+	0.978998i	$0.434647\pi$
$350$	−1.47342e16	−0.428434
$351$	−4.96952e15	−0.141846
$352$	−2.03943e16	−0.571455
$353$	1.10794e16	0.304775	0.152388	−	0.988321i	$-0.451304\pi$
$353$	1.10794e16	0.304775	0.152388	+	0.988321i	$0.451304\pi$
$354$	−2.47531e15	−0.0668510
$355$	−1.58637e16	−0.420649
$356$	−2.92806e15	−0.0762351
$357$	−2.69679e16	−0.689451
$358$	−5.08712e16	−1.27712
$359$	7.87950e16	1.94261	0.971304	−	0.237843i	$-0.0764405\pi$
$359$	7.87950e16	1.94261	0.971304	+	0.237843i	$0.0764405\pi$
$360$	−8.08180e15	−0.195678
$361$	−2.81377e16	−0.669101
$362$	3.73460e15	0.0872245
$363$	−2.35893e16	−0.541154
$364$	4.69078e15	0.105703
$365$	−2.36723e15	−0.0524006
$366$	8.45300e15	0.183816
$367$	−5.97301e16	−1.27604	−0.638019	−	0.770020i	$-0.720246\pi$
$367$	−5.97301e16	−1.27604	−0.638019	+	0.770020i	$0.720246\pi$
$368$	2.08701e16	0.438039
$369$	2.33805e16	0.482150
$370$	2.93886e16	0.595481
$371$	−8.32652e15	−0.165780
$372$	−4.94508e15	−0.0967485
$373$	−2.86827e16	−0.551458	−0.275729	−	0.961235i	$-0.588919\pi$
$373$	−2.86827e16	−0.551458	−0.275729	+	0.961235i	$0.588919\pi$
$374$	1.14008e17	2.15412
$375$	−2.88894e16	−0.536457
$376$	−7.21543e16	−1.31686
$377$	−2.00101e15	−0.0358946
$378$	−6.66190e15	−0.117463
$379$	5.49980e16	0.953218	0.476609	−	0.879115i	$-0.341866\pi$
$379$	5.49980e16	0.953218	0.476609	+	0.879115i	$0.341866\pi$
$380$	−3.85202e15	−0.0656290
$381$	−1.69082e16	−0.283195
$382$	−4.88448e16	−0.804278
$383$	−2.75953e16	−0.446729	−0.223364	−	0.974735i	$-0.571704\pi$
$383$	−2.75953e16	−0.446729	−0.223364	+	0.974735i	$0.571704\pi$
$384$	2.09986e16	0.334224
$385$	3.33221e16	0.521481
$386$	2.35120e16	0.361803
$387$	2.86145e16	0.432977
$388$	−1.96634e16	−0.292586
$389$	−3.35993e14	−0.00491652	−0.00245826	−	0.999997i	$-0.500782\pi$
$389$	−3.35993e14	−0.00491652	−0.00245826	+	0.999997i	$0.500782\pi$
$390$	−1.43584e16	−0.206626
$391$	7.20629e16	1.01991
$392$	−4.08664e16	−0.568863
$393$	8.14219e15	0.111478
$394$	−6.60559e16	−0.889583
$395$	−2.61261e16	−0.346093
$396$	−7.44036e15	−0.0969561
$397$	−9.99384e16	−1.28113	−0.640566	−	0.767903i	$-0.721300\pi$
$397$	−9.99384e16	−1.28113	−0.640566	+	0.767903i	$0.721300\pi$
$398$	7.04719e16	0.888742
$399$	−1.83696e16	−0.227916
$400$	4.29751e16	0.524598
$401$	1.36815e17	1.64322	0.821610	−	0.570050i	$-0.193076\pi$
$401$	1.36815e17	1.64322	0.821610	+	0.570050i	$0.193076\pi$
$402$	2.07500e16	0.245216
$403$	−5.08266e16	−0.591028
$404$	−4.51851e15	−0.0517031
$405$	−5.38723e15	−0.0606608
$406$	−2.68245e15	−0.0297244
$407$	1.56526e17	1.70695
$408$	1.00651e17	1.08026
$409$	6.83409e16	0.721904	0.360952	−	0.932584i	$-0.382452\pi$
$409$	6.83409e16	0.721904	0.360952	+	0.932584i	$0.382452\pi$
$410$	6.75528e16	0.702342
$411$	−8.78398e16	−0.898917
$412$	6.65830e15	0.0670705
$413$	9.01027e15	0.0893434
$414$	1.78018e16	0.173764
$415$	4.63177e16	0.445076
$416$	−3.19882e16	−0.302610
$417$	−1.18036e17	−1.09933
$418$	7.76582e16	0.712101
$419$	−8.94425e16	−0.807519	−0.403759	−	0.914865i	$-0.632297\pi$
$419$	−8.94425e16	−0.807519	−0.403759	+	0.914865i	$0.632297\pi$
$420$	5.08506e15	0.0452039
$421$	−7.32844e16	−0.641472	−0.320736	−	0.947169i	$-0.603930\pi$
$421$	−7.32844e16	−0.641472	−0.320736	+	0.947169i	$0.603930\pi$
$422$	2.42576e16	0.209082
$423$	−4.80972e16	−0.408232
$424$	3.10767e16	0.259751
$425$	1.48390e17	1.22145
$426$	4.88051e16	0.395643
$427$	−3.07694e16	−0.245662
$428$	2.83413e16	0.222862
$429$	−7.64735e16	−0.592296
$430$	8.26754e16	0.630712
$431$	−1.36306e17	−1.02426	−0.512132	−	0.858907i	$-0.671144\pi$
$431$	−1.36306e17	−1.02426	−0.512132	+	0.858907i	$0.671144\pi$
$432$	1.94307e16	0.143828
$433$	1.44267e17	1.05195	0.525976	−	0.850500i	$-0.323700\pi$
$433$	1.44267e17	1.05195	0.525976	+	0.850500i	$0.323700\pi$
$434$	−6.81356e16	−0.489430
$435$	−2.16920e15	−0.0153504
$436$	2.35672e16	0.164303
$437$	4.90868e16	0.337159
$438$	7.28285e15	0.0492856
$439$	−2.35753e17	−1.57195	−0.785975	−	0.618259i	$-0.787838\pi$
$439$	−2.35753e17	−1.57195	−0.785975	+	0.618259i	$0.787838\pi$
$440$	−1.24367e17	−0.817076
$441$	−2.72411e16	−0.176349
$442$	1.78820e17	1.14070
$443$	−2.55727e17	−1.60750	−0.803752	−	0.594964i	$-0.797166\pi$
$443$	−2.55727e17	−1.60750	−0.803752	+	0.594964i	$0.797166\pi$
$444$	2.38863e16	0.147965
$445$	−3.26248e16	−0.199163
$446$	−6.02522e16	−0.362490
$447$	6.83412e14	0.00405214
$448$	−1.30647e17	−0.763469
$449$	2.25571e16	0.129922	0.0649609	−	0.997888i	$-0.479308\pi$
$449$	2.25571e16	0.129922	0.0649609	+	0.997888i	$0.479308\pi$
$450$	3.66569e16	0.208101
$451$	3.59791e17	2.01327
$452$	1.84650e16	0.101847
$453$	9.10068e16	0.494806
$454$	1.39513e17	0.747742
$455$	5.22653e16	0.276146
$456$	6.85600e16	0.357108
$457$	−9.18133e16	−0.471466	−0.235733	−	0.971818i	$-0.575749\pi$
$457$	−9.18133e16	−0.471466	−0.235733	+	0.971818i	$0.575749\pi$
$458$	1.47611e17	0.747297
$459$	6.70928e16	0.334883
$460$	−1.35882e16	−0.0668706
$461$	1.21412e17	0.589125	0.294562	−	0.955632i	$-0.404826\pi$
$461$	1.21412e17	0.589125	0.294562	+	0.955632i	$0.404826\pi$
$462$	−1.02517e17	−0.490480
$463$	−1.82524e17	−0.861081	−0.430541	−	0.902571i	$-0.641677\pi$
$463$	−1.82524e17	−0.861081	−0.430541	+	0.902571i	$0.641677\pi$
$464$	7.82387e15	0.0363961
$465$	−5.50988e16	−0.252754
$466$	1.46635e17	0.663327
$467$	7.60620e16	0.339319	0.169659	−	0.985503i	$-0.445733\pi$
$467$	7.60620e16	0.339319	0.169659	+	0.985503i	$0.445733\pi$
$468$	−1.16701e16	−0.0513424
$469$	−7.55311e16	−0.327720
$470$	−1.38966e17	−0.594667
$471$	1.56433e17	0.660225
$472$	−3.36287e16	−0.139987
$473$	4.40334e17	1.80794
$474$	8.03778e16	0.325519
$475$	1.01078e17	0.403784
$476$	−6.33295e16	−0.249552
$477$	2.07154e16	0.0805237
$478$	−3.48112e17	−1.33487
$479$	6.08627e16	0.230235	0.115117	−	0.993352i	$-0.463276\pi$
$479$	6.08627e16	0.230235	0.115117	+	0.993352i	$0.463276\pi$
$480$	−3.46770e16	−0.129412
$481$	2.45508e17	0.903904
$482$	−2.24973e17	−0.817192
$483$	−6.47995e16	−0.232228
$484$	−5.53954e16	−0.195875
$485$	−2.19093e17	−0.764376
$486$	1.65740e16	0.0570547
$487$	−1.79972e17	−0.611317	−0.305659	−	0.952141i	$-0.598877\pi$
$487$	−1.79972e17	−0.611317	−0.305659	+	0.952141i	$0.598877\pi$
$488$	1.14839e17	0.384913
$489$	−1.78667e17	−0.590930
$490$	−7.87073e16	−0.256886
$491$	−3.07934e17	−0.991809	−0.495905	−	0.868377i	$-0.665163\pi$
$491$	−3.07934e17	−0.991809	−0.495905	+	0.868377i	$0.665163\pi$
$492$	5.49051e16	0.174518
$493$	2.70153e16	0.0847432
$494$	1.21806e17	0.377088
$495$	−8.29015e16	−0.253296
$496$	1.98730e17	0.599285
$497$	−1.77654e17	−0.528759
$498$	−1.42498e17	−0.418618
$499$	−3.50911e17	−1.01752	−0.508760	−	0.860908i	$-0.669896\pi$
$499$	−3.50911e17	−1.01752	−0.508760	+	0.860908i	$0.669896\pi$
$500$	−6.78418e16	−0.194175
$501$	1.11568e17	0.315207
$502$	−1.15786e17	−0.322911
$503$	3.57981e17	0.985526	0.492763	−	0.870164i	$-0.335987\pi$
$503$	3.57981e17	0.985526	0.492763	+	0.870164i	$0.335987\pi$
$504$	−9.05062e16	−0.245969
$505$	−5.03458e16	−0.135073
$506$	2.73943e17	0.725574
$507$	1.00848e17	0.263704
$508$	−3.97062e16	−0.102505
$509$	4.62471e17	1.17874	0.589371	−	0.807863i	$-0.299376\pi$
$509$	4.62471e17	1.17874	0.589371	+	0.807863i	$0.299376\pi$
$510$	1.93850e17	0.487821
$511$	−2.65100e16	−0.0658679
$512$	4.52634e17	1.11043
$513$	4.57013e16	0.110705
$514$	4.00949e17	0.959023
$515$	7.41877e16	0.175221
$516$	6.71963e16	0.156719
$517$	−7.40144e17	−1.70462
$518$	3.29116e17	0.748524
$519$	−3.75437e17	−0.843236
$520$	−1.95068e17	−0.432676
$521$	4.25083e17	0.931170	0.465585	−	0.885003i	$-0.345844\pi$
$521$	4.25083e17	0.931170	0.465585	+	0.885003i	$0.345844\pi$
$522$	6.67361e15	0.0144379
$523$	1.34418e17	0.287208	0.143604	−	0.989635i	$-0.454131\pi$
$523$	1.34418e17	0.287208	0.143604	+	0.989635i	$0.454131\pi$
$524$	1.91206e16	0.0403504
$525$	−1.33433e17	−0.278118
$526$	4.92230e16	0.101335
$527$	6.86202e17	1.39535
$528$	2.99009e17	0.600571
$529$	−3.30881e17	−0.656462
$530$	5.98527e16	0.117298
$531$	−2.24165e16	−0.0433963
$532$	−4.31379e16	−0.0824961
$533$	5.64326e17	1.06611
$534$	1.00371e17	0.187323
$535$	3.15783e17	0.582222
$536$	2.81902e17	0.513484
$537$	−4.60691e17	−0.829042
$538$	8.87940e17	1.57870
$539$	−4.19200e17	−0.736367
$540$	−1.26510e16	−0.0219566
$541$	−1.30229e17	−0.223320	−0.111660	−	0.993746i	$-0.535617\pi$
$541$	−1.30229e17	−0.223320	−0.111660	+	0.993746i	$0.535617\pi$
$542$	3.79713e17	0.643369
$543$	3.38207e16	0.0566217
$544$	4.31868e17	0.714428
$545$	2.62589e17	0.429239
$546$	−1.60796e17	−0.259730
$547$	−1.28017e17	−0.204339	−0.102169	−	0.994767i	$-0.532578\pi$
$547$	−1.28017e17	−0.204339	−0.102169	+	0.994767i	$0.532578\pi$
$548$	−2.06277e17	−0.325370
$549$	7.65506e16	0.119324
$550$	5.64095e17	0.868950
$551$	1.84019e16	0.0280141
$552$	2.41849e17	0.363864
$553$	−2.92580e17	−0.435042
$554$	6.20345e17	0.911633
$555$	2.66144e17	0.386556
$556$	−2.77187e17	−0.397911
$557$	6.55367e17	0.929878	0.464939	−	0.885343i	$-0.346076\pi$
$557$	6.55367e17	0.929878	0.464939	+	0.885343i	$0.346076\pi$
$558$	1.69513e17	0.237728
$559$	6.90657e17	0.957383
$560$	−2.04356e17	−0.280004
$561$	1.03246e18	1.39834
$562$	−8.86560e16	−0.118692
$563$	−5.69437e16	−0.0753600	−0.0376800	−	0.999290i	$-0.511997\pi$
$563$	−5.69437e16	−0.0753600	−0.0376800	+	0.999290i	$0.511997\pi$
$564$	−1.12948e17	−0.147763
$565$	2.05740e17	0.266074
$566$	−8.12259e17	−1.03845
$567$	−6.03303e16	−0.0762511
$568$	6.63049e17	0.828479
$569$	−3.58343e17	−0.442659	−0.221329	−	0.975199i	$-0.571040\pi$
$569$	−3.58343e17	−0.442659	−0.221329	+	0.975199i	$0.571040\pi$
$570$	1.32044e17	0.161262
$571$	−1.30154e18	−1.57153	−0.785766	−	0.618524i	$-0.787731\pi$
$571$	−1.30154e18	−1.57153	−0.785766	+	0.618524i	$0.787731\pi$
$572$	−1.79585e17	−0.214386
$573$	−4.42340e17	−0.522097
$574$	7.56508e17	0.882849
$575$	3.56557e17	0.411423
$576$	3.25033e17	0.370836
$577$	−1.26412e18	−1.42609	−0.713043	−	0.701120i	$-0.752684\pi$
$577$	−1.26412e18	−1.42609	−0.713043	+	0.701120i	$0.752684\pi$
$578$	−1.61691e18	−1.80366
$579$	2.12926e17	0.234864
$580$	−5.09400e15	−0.00555619
$581$	5.18701e17	0.559464
$582$	6.74046e17	0.718936
$583$	3.18779e17	0.336236
$584$	9.89422e16	0.103204
$585$	−1.30030e17	−0.134131
$586$	−3.30273e16	−0.0336929
$587$	−1.20369e18	−1.21442	−0.607210	−	0.794542i	$-0.707711\pi$
$587$	−1.20369e18	−1.21442	−0.607210	+	0.794542i	$0.707711\pi$
$588$	−6.39711e16	−0.0638310
$589$	4.67417e17	0.461270
$590$	−6.47675e16	−0.0632149
$591$	−5.98205e17	−0.577472
$592$	−9.59928e17	−0.916532
$593$	−1.50625e18	−1.42247	−0.711234	−	0.702956i	$-0.751863\pi$
$593$	−1.50625e18	−1.42247	−0.711234	+	0.702956i	$0.751863\pi$
$594$	2.55049e17	0.238239
$595$	−7.05626e17	−0.651950
$596$	1.60488e15	0.00146670
$597$	6.38195e17	0.576926
$598$	4.29675e17	0.384222
$599$	−5.52771e17	−0.488957	−0.244479	−	0.969655i	$-0.578617\pi$
$599$	−5.52771e17	−0.488957	−0.244479	+	0.969655i	$0.578617\pi$
$600$	4.98008e17	0.435766
$601$	−1.44492e18	−1.25072	−0.625360	−	0.780337i	$-0.715048\pi$
$601$	−1.44492e18	−1.25072	−0.625360	+	0.780337i	$0.715048\pi$
$602$	9.25862e17	0.792810
$603$	1.87912e17	0.159182
$604$	2.13714e17	0.179099
$605$	−6.17223e17	−0.511720
$606$	1.54891e17	0.127044
$607$	7.08095e17	0.574600	0.287300	−	0.957841i	$-0.407242\pi$
$607$	7.08095e17	0.574600	0.287300	+	0.957841i	$0.407242\pi$
$608$	2.94174e17	0.236173
$609$	−2.42923e16	−0.0192955
$610$	2.21176e17	0.173818
$611$	−1.16090e18	−0.902669
$612$	1.57556e17	0.121214
$613$	4.16918e17	0.317364	0.158682	−	0.987330i	$-0.449276\pi$
$613$	4.16918e17	0.317364	0.158682	+	0.987330i	$0.449276\pi$
$614$	7.96303e17	0.599769
$615$	6.11761e17	0.455925
$616$	−1.39276e18	−1.02707
$617$	−1.42371e18	−1.03889	−0.519444	−	0.854505i	$-0.673861\pi$
$617$	−1.42371e18	−1.03889	−0.519444	+	0.854505i	$0.673861\pi$
$618$	−2.28241e17	−0.164804
$619$	−2.13246e17	−0.152367	−0.0761836	−	0.997094i	$-0.524274\pi$
$619$	−2.13246e17	−0.152367	−0.0761836	+	0.997094i	$0.524274\pi$
$620$	−1.29390e17	−0.0914862
$621$	1.61213e17	0.112799
$622$	−2.16163e18	−1.49673
$623$	−3.65358e17	−0.250349
$624$	4.68991e17	0.318028
$625$	2.90072e17	0.194664
$626$	2.34566e17	0.155787
$627$	7.03275e17	0.462260
$628$	3.67356e17	0.238973
$629$	−3.31457e18	−2.13402
$630$	−1.74312e17	−0.111074
$631$	−1.54439e18	−0.974013	−0.487007	−	0.873398i	$-0.661911\pi$
$631$	−1.54439e18	−0.974013	−0.487007	+	0.873398i	$0.661911\pi$
$632$	1.09198e18	0.681640
$633$	2.19677e17	0.135725
$634$	1.04707e18	0.640318
$635$	−4.42412e17	−0.267792
$636$	4.86466e16	0.0291462
$637$	−6.57508e17	−0.389937
$638$	1.02697e17	0.0602869
$639$	4.41981e17	0.256831
$640$	5.49438e17	0.316045
$641$	1.32543e18	0.754707	0.377354	−	0.926069i	$-0.376834\pi$
$641$	1.32543e18	0.754707	0.377354	+	0.926069i	$0.376834\pi$
$642$	−9.71516e17	−0.547611
$643$	−2.70013e18	−1.50665	−0.753326	−	0.657647i	$-0.771552\pi$
$643$	−2.70013e18	−1.50665	−0.753326	+	0.657647i	$0.771552\pi$
$644$	−1.52171e17	−0.0840569
$645$	7.48710e17	0.409426
$646$	−1.64448e18	−0.890262
$647$	−1.72588e18	−0.924983	−0.462491	−	0.886624i	$-0.653044\pi$
$647$	−1.72588e18	−0.924983	−0.462491	+	0.886624i	$0.653044\pi$
$648$	2.25168e17	0.119473
$649$	−3.44956e17	−0.181206
$650$	8.84775e17	0.460146
$651$	−6.17038e17	−0.317713
$652$	−4.19569e17	−0.213892
$653$	−6.14833e17	−0.310329	−0.155164	−	0.987889i	$-0.549591\pi$
$653$	−6.14833e17	−0.310329	−0.155164	+	0.987889i	$0.549591\pi$
$654$	−8.07863e17	−0.403722
$655$	2.13044e17	0.105415
$656$	−2.20650e18	−1.08101
$657$	6.59537e16	0.0319937
$658$	−1.55625e18	−0.747501
$659$	−4.49875e17	−0.213962	−0.106981	−	0.994261i	$-0.534118\pi$
$659$	−4.49875e17	−0.213962	−0.106981	+	0.994261i	$0.534118\pi$
$660$	−1.94680e17	−0.0916825
$661$	−8.57866e17	−0.400046	−0.200023	−	0.979791i	$-0.564102\pi$
$661$	−8.57866e17	−0.400046	−0.200023	+	0.979791i	$0.564102\pi$
$662$	−6.89109e17	−0.318208
$663$	1.61940e18	0.740483
$664$	−1.93593e18	−0.876590
$665$	−4.80648e17	−0.215520
$666$	−8.18801e17	−0.363576
$667$	6.49135e16	0.0285441
$668$	2.62000e17	0.114092
$669$	−5.45646e17	−0.235310
$670$	5.42932e17	0.231878
$671$	1.17800e18	0.498252
$672$	−3.88339e17	−0.162671
$673$	2.84588e18	1.18064	0.590321	−	0.807168i	$-0.299001\pi$
$673$	2.84588e18	1.18064	0.590321	+	0.807168i	$0.299001\pi$
$674$	3.43436e17	0.141109
$675$	3.31966e17	0.135089
$676$	2.36826e17	0.0954499
$677$	9.37510e17	0.374239	0.187120	−	0.982337i	$-0.440085\pi$
$677$	9.37510e17	0.374239	0.187120	+	0.982337i	$0.440085\pi$
$678$	−6.32965e17	−0.250257
$679$	−2.45357e18	−0.960826
$680$	2.63358e18	1.02150
$681$	1.26343e18	0.485396
$682$	2.60856e18	0.992663
$683$	1.83395e18	0.691279	0.345639	−	0.938367i	$-0.387662\pi$
$683$	1.83395e18	0.691279	0.345639	+	0.938367i	$0.387662\pi$
$684$	1.07322e17	0.0400704
$685$	−2.29837e18	−0.850023
$686$	−2.54748e18	−0.933263
$687$	1.33677e18	0.485108
$688$	−2.70045e18	−0.970758
$689$	5.00000e17	0.178051
$690$	4.65791e17	0.164313
$691$	−5.18222e18	−1.81096	−0.905479	−	0.424391i	$-0.860488\pi$
$691$	−5.18222e18	−1.81096	−0.905479	+	0.424391i	$0.860488\pi$
$692$	−8.81651e17	−0.305216
$693$	−9.28394e17	−0.318395
$694$	−1.48474e18	−0.504446
$695$	−3.08845e18	−1.03954
$696$	9.06653e16	0.0302330
$697$	−7.61889e18	−2.51697
$698$	−1.10801e18	−0.362646
$699$	1.32793e18	0.430598
$700$	−3.13346e17	−0.100667
$701$	−2.74774e18	−0.874598	−0.437299	−	0.899316i	$-0.644065\pi$
$701$	−2.74774e18	−0.874598	−0.437299	+	0.899316i	$0.644065\pi$
$702$	4.00041e17	0.126157
$703$	−2.25777e18	−0.705456
$704$	5.00178e18	1.54847
$705$	−1.25848e18	−0.386028
$706$	−8.91877e17	−0.271066
$707$	−5.63811e17	−0.169788
$708$	−5.26413e16	−0.0157076
$709$	1.84861e18	0.546569	0.273284	−	0.961933i	$-0.411890\pi$
$709$	1.84861e18	0.546569	0.273284	+	0.961933i	$0.411890\pi$
$710$	1.27701e18	0.374123
$711$	7.27903e17	0.211311
$712$	1.36361e18	0.392256
$713$	1.64884e18	0.469997
$714$	2.17088e18	0.613194
$715$	−2.00096e18	−0.560080
$716$	−1.08186e18	−0.300078
$717$	−3.15251e18	−0.866528
$718$	−6.34291e18	−1.72775
$719$	−1.08067e18	−0.291713	−0.145856	−	0.989306i	$-0.546594\pi$
$719$	−1.08067e18	−0.291713	−0.145856	+	0.989306i	$0.546594\pi$
$720$	5.08412e17	0.136005
$721$	8.30810e17	0.220253
$722$	2.26505e18	0.595095
$723$	−2.03736e18	−0.530480
$724$	7.94222e16	0.0204947
$725$	1.33668e17	0.0341846
$726$	1.89891e18	0.481300
$727$	5.54684e18	1.39339	0.696694	−	0.717368i	$-0.254654\pi$
$727$	5.54684e18	1.39339	0.696694	+	0.717368i	$0.254654\pi$
$728$	−2.18451e18	−0.543877
$729$	1.50095e17	0.0370370
$730$	1.90559e17	0.0466048
$731$	−9.32447e18	−2.26027
$732$	1.79766e17	0.0431903
$733$	1.45102e18	0.345539	0.172770	−	0.984962i	$-0.444728\pi$
$733$	1.45102e18	0.345539	0.172770	+	0.984962i	$0.444728\pi$
$734$	4.80820e18	1.13490
$735$	−7.12775e17	−0.166757
$736$	1.03771e18	0.240642
$737$	2.89169e18	0.664681
$738$	−1.88210e18	−0.428822
$739$	1.54915e18	0.349868	0.174934	−	0.984580i	$-0.444029\pi$
$739$	1.54915e18	0.349868	0.174934	+	0.984580i	$0.444029\pi$
$740$	6.24995e17	0.139917
$741$	1.10308e18	0.244786
$742$	6.70276e17	0.147444
$743$	1.60773e18	0.350579	0.175289	−	0.984517i	$-0.443914\pi$
$743$	1.60773e18	0.350579	0.175289	+	0.984517i	$0.443914\pi$
$744$	2.30295e18	0.497806
$745$	1.78818e16	0.00383173
$746$	2.30893e18	0.490464
$747$	−1.29047e18	−0.271746
$748$	2.42456e18	0.506141
$749$	3.53637e18	0.731857
$750$	2.32556e18	0.477122
$751$	1.29902e17	0.0264214	0.0132107	−	0.999913i	$-0.495795\pi$
$751$	1.29902e17	0.0264214	0.0132107	+	0.999913i	$0.495795\pi$
$752$	4.53910e18	0.915280
$753$	−1.04856e18	−0.209617
$754$	1.61079e17	0.0319245
$755$	2.38123e18	0.467893
$756$	−1.41676e17	−0.0275997
$757$	−3.65956e18	−0.706815	−0.353407	−	0.935470i	$-0.614977\pi$
$757$	−3.65956e18	−0.706815	−0.353407	+	0.935470i	$0.614977\pi$
$758$	−4.42728e18	−0.847787
$759$	2.48083e18	0.471006
$760$	1.79390e18	0.337684
$761$	−3.82973e18	−0.714772	−0.357386	−	0.933957i	$-0.616332\pi$
$761$	−3.82973e18	−0.714772	−0.357386	+	0.933957i	$0.616332\pi$
$762$	1.36109e18	0.251873
$763$	2.94067e18	0.539556
$764$	−1.03876e18	−0.188977
$765$	1.75551e18	0.316668
$766$	2.22139e18	0.397318
$767$	−5.41058e17	−0.0959564
$768$	1.96214e18	0.345050
$769$	−3.84684e18	−0.670785	−0.335392	−	0.942079i	$-0.608869\pi$
$769$	−3.84684e18	−0.670785	−0.335392	+	0.942079i	$0.608869\pi$
$770$	−2.68239e18	−0.463802
$771$	3.63101e18	0.622549
$772$	5.00020e17	0.0850110
$773$	3.24278e18	0.546702	0.273351	−	0.961914i	$-0.411868\pi$
$773$	3.24278e18	0.546702	0.273351	+	0.961914i	$0.411868\pi$
$774$	−2.30343e18	−0.385087
$775$	3.39524e18	0.562871
$776$	9.15735e18	1.50546
$777$	2.98048e18	0.485904
$778$	2.70471e16	0.00437273
$779$	−5.18973e18	−0.832053
$780$	−3.05353e17	−0.0485498
$781$	6.80143e18	1.07243
$782$	−5.80098e18	−0.907105
$783$	6.04364e16	0.00937233
$784$	2.57084e18	0.395385
$785$	4.09313e18	0.624314
$786$	−6.55437e17	−0.0991481
$787$	1.66449e18	0.249716	0.124858	−	0.992175i	$-0.460152\pi$
$787$	1.66449e18	0.249716	0.124858	+	0.992175i	$0.460152\pi$
$788$	−1.40478e18	−0.209021
$789$	4.45765e17	0.0657818
$790$	2.10312e18	0.307814
$791$	2.30403e18	0.334458
$792$	3.46501e18	0.498874
$793$	1.84767e18	0.263845
$794$	8.04493e18	1.13943
$795$	5.42027e17	0.0761439
$796$	1.49870e18	0.208823
$797$	−7.59643e18	−1.04986	−0.524929	−	0.851146i	$-0.675908\pi$
$797$	−7.59643e18	−1.04986	−0.524929	+	0.851146i	$0.675908\pi$
$798$	1.47873e18	0.202708
$799$	1.56732e19	2.13110
$800$	2.13683e18	0.288193
$801$	9.08966e17	0.121601
$802$	−1.10135e19	−1.46147
$803$	1.01493e18	0.133593
$804$	4.41281e17	0.0576170
$805$	−1.69551e18	−0.219597
$806$	4.09148e18	0.525657
$807$	8.04121e18	1.02481
$808$	2.10429e18	0.266031
$809$	−8.74663e17	−0.109692	−0.0548460	−	0.998495i	$-0.517467\pi$
$809$	−8.74663e17	−0.109692	−0.0548460	+	0.998495i	$0.517467\pi$
$810$	4.33666e17	0.0539514
$811$	−1.26322e19	−1.55899	−0.779495	−	0.626409i	$-0.784524\pi$
$811$	−1.26322e19	−1.55899	−0.779495	+	0.626409i	$0.784524\pi$
$812$	−5.70465e16	−0.00698417
$813$	3.43869e18	0.417642
$814$	−1.26001e19	−1.51816
$815$	−4.67490e18	−0.558789
$816$	−6.33179e18	−0.750828
$817$	−6.35151e18	−0.747194
$818$	−5.50136e18	−0.642057
$819$	−1.45617e18	−0.168604
$820$	1.43662e18	0.165026
$821$	8.64806e18	0.985572	0.492786	−	0.870151i	$-0.335979\pi$
$821$	8.64806e18	0.985572	0.492786	+	0.870151i	$0.335979\pi$
$822$	7.07100e18	0.799492
$823$	−1.67852e19	−1.88291	−0.941453	−	0.337144i	$-0.890539\pi$
$823$	−1.67852e19	−1.88291	−0.941453	+	0.337144i	$0.890539\pi$
$824$	−3.10080e18	−0.345102
$825$	5.10846e18	0.564079
$826$	−7.25316e17	−0.0794616
$827$	−3.84411e18	−0.417840	−0.208920	−	0.977933i	$-0.566995\pi$
$827$	−3.84411e18	−0.417840	−0.208920	+	0.977933i	$0.566995\pi$
$828$	3.78583e17	0.0408285
$829$	2.24354e17	0.0240065	0.0120033	−	0.999928i	$-0.496179\pi$
$829$	2.24354e17	0.0240065	0.0120033	+	0.999928i	$0.496179\pi$
$830$	−3.72852e18	−0.395849
$831$	5.61786e18	0.591786
$832$	7.84521e18	0.819980
$833$	8.87693e18	0.920599
$834$	9.50172e18	0.977739
$835$	2.91924e18	0.298062
$836$	1.65152e18	0.167319
$837$	1.53512e18	0.154321
$838$	7.20002e18	0.718203
$839$	1.12129e19	1.10985	0.554927	−	0.831899i	$-0.312746\pi$
$839$	1.12129e19	1.10985	0.554927	+	0.831899i	$0.312746\pi$
$840$	−2.36813e18	−0.232590
$841$	−1.02363e19	−0.997628
$842$	5.89931e18	0.570522
$843$	−8.02871e17	−0.0770489
$844$	5.15875e17	0.0491269
$845$	2.63874e18	0.249361
$846$	3.87177e18	0.363080
$847$	−6.91214e18	−0.643236
$848$	−1.95499e18	−0.180539
$849$	−7.35584e18	−0.674112
$850$	−1.19452e19	−1.08635
$851$	−7.96438e18	−0.718803
$852$	1.03792e18	0.0929621
$853$	8.41030e18	0.747554	0.373777	−	0.927519i	$-0.378063\pi$
$853$	8.41030e18	0.747554	0.373777	+	0.927519i	$0.378063\pi$
$854$	2.47690e18	0.218491
$855$	1.19580e18	0.104683
$856$	−1.31987e19	−1.14670
$857$	1.58581e19	1.36734	0.683668	−	0.729793i	$-0.260384\pi$
$857$	1.58581e19	1.36734	0.683668	+	0.729793i	$0.260384\pi$
$858$	6.15603e18	0.526785
$859$	1.82988e19	1.55406	0.777029	−	0.629465i	$-0.216726\pi$
$859$	1.82988e19	1.55406	0.777029	+	0.629465i	$0.216726\pi$
$860$	1.75822e18	0.148195
$861$	6.85096e18	0.573101
$862$	1.09724e19	0.910975
$863$	2.15593e18	0.177650	0.0888250	−	0.996047i	$-0.471689\pi$
$863$	2.15593e18	0.177650	0.0888250	+	0.996047i	$0.471689\pi$
$864$	9.66141e17	0.0790135
$865$	−9.82347e18	−0.797371
$866$	−1.16133e19	−0.935600
$867$	−1.46428e19	−1.17085
$868$	−1.44901e18	−0.114999
$869$	1.12014e19	0.882352
$870$	1.74618e17	0.0136526
$871$	4.53557e18	0.351977
$872$	−1.09753e19	−0.845397
$873$	6.10418e18	0.466697
$874$	−3.95143e18	−0.299868
$875$	−8.46518e18	−0.637652
$876$	1.54881e17	0.0115804
$877$	−1.47003e19	−1.09101	−0.545505	−	0.838108i	$-0.683662\pi$
$877$	−1.47003e19	−1.09101	−0.545505	+	0.838108i	$0.683662\pi$
$878$	1.89779e19	1.39808
$879$	−2.99096e17	−0.0218717
$880$	7.82371e18	0.567905
$881$	2.66615e19	1.92106	0.960531	−	0.278174i	$-0.0897292\pi$
$881$	2.66615e19	1.92106	0.960531	+	0.278174i	$0.0897292\pi$
$882$	2.19288e18	0.156844
$883$	1.91984e19	1.36308	0.681538	−	0.731783i	$-0.261312\pi$
$883$	1.91984e19	1.36308	0.681538	+	0.731783i	$0.261312\pi$
$884$	3.80288e18	0.268023
$885$	−5.86537e17	−0.0410359
$886$	2.05857e19	1.42971
$887$	−2.08261e19	−1.43583	−0.717916	−	0.696130i	$-0.754904\pi$
$887$	−2.08261e19	−1.43583	−0.717916	+	0.696130i	$0.754904\pi$
$888$	−1.11239e19	−0.761332
$889$	−4.95446e18	−0.336616
$890$	2.62626e18	0.177134
$891$	2.30973e18	0.154652
$892$	−1.28136e18	−0.0851724
$893$	1.06761e19	0.704492
$894$	−5.50139e16	−0.00360395
$895$	−1.20542e19	−0.783949
$896$	6.15303e18	0.397271
$897$	3.89115e18	0.249418
$898$	−1.81582e18	−0.115552
$899$	6.18123e17	0.0390514
$900$	7.79567e17	0.0488964
$901$	−6.75043e18	−0.420359
$902$	−2.89627e19	−1.79059
$903$	8.38463e18	0.514652
$904$	−8.59924e18	−0.524041
$905$	8.84933e17	0.0535420
$906$	−7.32594e18	−0.440078
$907$	7.30186e18	0.435498	0.217749	−	0.976005i	$-0.430129\pi$
$907$	7.30186e18	0.435498	0.217749	+	0.976005i	$0.430129\pi$
$908$	2.96696e18	0.175693
$909$	1.40269e18	0.0824703
$910$	−4.20729e18	−0.245603
$911$	1.45485e19	0.843235	0.421618	−	0.906774i	$-0.361462\pi$
$911$	1.45485e19	0.843235	0.421618	+	0.906774i	$0.361462\pi$
$912$	−4.31300e18	−0.248206
$913$	−1.98583e19	−1.13471
$914$	7.39086e18	0.419319
$915$	2.00298e18	0.112834
$916$	3.13918e18	0.175588
$917$	2.38583e18	0.132507
$918$	−5.40089e18	−0.297844
$919$	3.07202e19	1.68218	0.841091	−	0.540893i	$-0.181914\pi$
$919$	3.07202e19	1.68218	0.841091	+	0.540893i	$0.181914\pi$
$920$	6.32807e18	0.344073
$921$	7.21134e18	0.389339
$922$	−9.77357e18	−0.523965
$923$	1.06679e19	0.567897
$924$	−2.18018e18	−0.115246
$925$	−1.64000e19	−0.860842
$926$	1.46930e19	0.765841
$927$	−2.06696e18	−0.106983
$928$	3.89022e17	0.0199946
$929$	3.14728e19	1.60633	0.803163	−	0.595759i	$-0.203149\pi$
$929$	3.14728e19	1.60633	0.803163	+	0.595759i	$0.203149\pi$
$930$	4.43539e18	0.224798
$931$	6.04666e18	0.304328
$932$	3.11841e18	0.155858
$933$	−1.95758e19	−0.971604
$934$	−6.12290e18	−0.301789
$935$	2.70147e19	1.32229
$936$	5.43481e18	0.264175
$937$	−3.26697e19	−1.57702	−0.788511	−	0.615021i	$-0.789147\pi$
$937$	−3.26697e19	−1.57702	−0.788511	+	0.615021i	$0.789147\pi$
$938$	6.08017e18	0.291472
$939$	2.12423e18	0.101129
$940$	−2.95534e18	−0.139726
$941$	−8.38611e18	−0.393757	−0.196878	−	0.980428i	$-0.563080\pi$
$941$	−8.38611e18	−0.393757	−0.196878	+	0.980428i	$0.563080\pi$
$942$	−1.25927e19	−0.587201
$943$	−1.83070e19	−0.847795
$944$	2.11552e18	0.0972970
$945$	−1.57857e18	−0.0721036
$946$	−3.54464e19	−1.60798
$947$	6.26802e18	0.282394	0.141197	−	0.989982i	$-0.454905\pi$
$947$	6.26802e18	0.282394	0.141197	+	0.989982i	$0.454905\pi$
$948$	1.70936e18	0.0764855
$949$	1.59190e18	0.0707434
$950$	−8.13667e18	−0.359123
$951$	9.48230e18	0.415662
$952$	2.94928e19	1.28403
$953$	3.46589e19	1.49869	0.749343	−	0.662183i	$-0.230370\pi$
$953$	3.46589e19	1.49869	0.749343	+	0.662183i	$0.230370\pi$
$954$	−1.66757e18	−0.0716174
$955$	−1.15740e19	−0.493699
$956$	−7.40315e18	−0.313646
$957$	9.30027e17	0.0391352
$958$	−4.89938e18	−0.204769
$959$	−2.57389e19	−1.06849
$960$	8.50464e18	0.350666
$961$	−8.71690e18	−0.356993
$962$	−1.97631e19	−0.803928
$963$	−8.79808e18	−0.355481
$964$	−4.78440e18	−0.192011
$965$	5.57129e18	0.222090
$966$	5.21629e18	0.206543
$967$	4.76538e18	0.187424	0.0937121	−	0.995599i	$-0.470127\pi$
$967$	4.76538e18	0.187424	0.0937121	+	0.995599i	$0.470127\pi$
$968$	2.57979e19	1.00785
$969$	−1.48925e19	−0.577913
$970$	1.76367e19	0.679832
$971$	−4.11037e19	−1.57382	−0.786912	−	0.617066i	$-0.788321\pi$
$971$	−4.11037e19	−1.57382	−0.786912	+	0.617066i	$0.788321\pi$
$972$	3.52472e17	0.0134058
$973$	−3.45868e19	−1.30670
$974$	1.44875e19	0.543703
$975$	8.01254e18	0.298704
$976$	−7.22435e18	−0.267532
$977$	1.21988e19	0.448747	0.224373	−	0.974503i	$-0.427966\pi$
$977$	1.21988e19	0.448747	0.224373	+	0.974503i	$0.427966\pi$
$978$	1.43825e19	0.525571
$979$	1.39876e19	0.507758
$980$	−1.67383e18	−0.0603591
$981$	−7.31603e18	−0.262076
$982$	2.47883e19	0.882110
$983$	4.85533e19	1.71641	0.858204	−	0.513309i	$-0.171580\pi$
$983$	4.85533e19	1.71641	0.858204	+	0.513309i	$0.171580\pi$
$984$	−2.55696e19	−0.897956
$985$	−1.56523e19	−0.546063
$986$	−2.17470e18	−0.0753702
$987$	−1.40935e19	−0.485240
$988$	2.59039e18	0.0886023
$989$	−2.24052e19	−0.761330
$990$	6.67348e18	0.225280
$991$	−1.09206e19	−0.366242	−0.183121	−	0.983090i	$-0.558620\pi$
$991$	−1.09206e19	−0.366242	−0.183121	+	0.983090i	$0.558620\pi$
$992$	9.88136e18	0.329224
$993$	−6.24060e18	−0.206565
$994$	1.43009e19	0.470275
$995$	1.66987e19	0.545546
$996$	−3.03044e18	−0.0983604
$997$	−1.56931e19	−0.506046	−0.253023	−	0.967460i	$-0.581425\pi$
$997$	−1.56931e19	−0.506046	−0.253023	+	0.967460i	$0.581425\pi$
$998$	2.82479e19	0.904978
$999$	−7.41508e18	−0.236015

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.b.1.9	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.b.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-80.4989 q^{2} -729.000 q^{3} -1711.93 q^{4} -19074.6 q^{5} +58683.7 q^{6} -213612. q^{7} +797255. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-80.4989 q^{2} -729.000 q^{3} -1711.93 q^{4} -19074.6 q^{5} +58683.7 q^{6} -213612. q^{7} +797255. q^{8} +531441. q^{9} +1.53548e6 q^{10} +8.17809e6 q^{11} +1.24800e6 q^{12} +1.28272e7 q^{13} +1.71955e7 q^{14} +1.39054e7 q^{15} -5.01540e7 q^{16} -1.73178e8 q^{17} -4.27804e7 q^{18} -1.17963e8 q^{19} +3.26545e7 q^{20} +1.55723e8 q^{21} -6.58327e8 q^{22} -4.16120e8 q^{23} -5.81199e8 q^{24} -8.56862e8 q^{25} -1.03257e9 q^{26} -3.87420e8 q^{27} +3.65690e8 q^{28} -1.55997e8 q^{29} -1.11937e9 q^{30} -3.96240e9 q^{31} -2.49378e9 q^{32} -5.96182e9 q^{33} +1.39407e10 q^{34} +4.07457e9 q^{35} -9.09792e8 q^{36} +1.91396e10 q^{37} +9.49589e9 q^{38} -9.35103e9 q^{39} -1.52073e10 q^{40} +4.39945e10 q^{41} -1.25355e10 q^{42} +5.38432e10 q^{43} -1.40003e10 q^{44} -1.01370e10 q^{45} +3.34972e10 q^{46} -9.05033e10 q^{47} +3.65622e10 q^{48} -5.12589e10 q^{49} +6.89764e10 q^{50} +1.26247e11 q^{51} -2.19593e10 q^{52} +3.89797e10 q^{53} +3.11869e10 q^{54} -1.55994e11 q^{55} -1.70303e11 q^{56} +8.59951e10 q^{57} +1.25576e10 q^{58} -4.21805e10 q^{59} -2.38051e10 q^{60} +1.44043e11 q^{61} +3.18969e11 q^{62} -1.13522e11 q^{63} +6.11608e11 q^{64} -2.44674e11 q^{65} +4.79920e11 q^{66} +3.53590e11 q^{67} +2.96470e11 q^{68} +3.03351e11 q^{69} -3.27998e11 q^{70} +8.31665e11 q^{71} +4.23694e11 q^{72} +1.24104e11 q^{73} -1.54072e12 q^{74} +6.24653e11 q^{75} +2.01945e11 q^{76} -1.74694e12 q^{77} +7.52747e11 q^{78} +1.36968e12 q^{79} +9.56668e11 q^{80} +2.82430e11 q^{81} -3.54151e12 q^{82} -2.42824e12 q^{83} -2.66588e11 q^{84} +3.30331e12 q^{85} -4.33431e12 q^{86} +1.13722e11 q^{87} +6.52002e12 q^{88} +1.71038e12 q^{89} +8.16019e11 q^{90} -2.74004e12 q^{91} +7.12370e11 q^{92} +2.88859e12 q^{93} +7.28541e12 q^{94} +2.25010e12 q^{95} +1.81796e12 q^{96} +1.14861e13 q^{97} +4.12628e12 q^{98} +4.34617e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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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