LMFDB - Embedded newform 177.14.a.b.1.19

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			1.19
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)

$f(q)$	$=$	$q+39.4833 q^{2} -729.000 q^{3} -6633.07 q^{4} +39747.6 q^{5} -28783.4 q^{6} -539057. q^{7} -585343. q^{8} +531441. q^{9} +O(q^{10})$	\(q+39.4833 q^{2} -729.000 q^{3} -6633.07 q^{4} +39747.6 q^{5} -28783.4 q^{6} -539057. q^{7} -585343. q^{8} +531441. q^{9} +1.56937e6 q^{10} -1.01761e7 q^{11} +4.83551e6 q^{12} +1.08564e6 q^{13} -2.12838e7 q^{14} -2.89760e7 q^{15} +3.12268e7 q^{16} +1.61734e8 q^{17} +2.09831e7 q^{18} +1.53748e8 q^{19} -2.63648e8 q^{20} +3.92972e8 q^{21} -4.01786e8 q^{22} +1.08113e8 q^{23} +4.26715e8 q^{24} +3.59167e8 q^{25} +4.28647e7 q^{26} -3.87420e8 q^{27} +3.57560e9 q^{28} +5.15790e9 q^{29} -1.14407e9 q^{30} -1.74651e8 q^{31} +6.02807e9 q^{32} +7.41838e9 q^{33} +6.38579e9 q^{34} -2.14262e10 q^{35} -3.52508e9 q^{36} -2.19273e10 q^{37} +6.07049e9 q^{38} -7.91431e8 q^{39} -2.32660e10 q^{40} +3.56936e10 q^{41} +1.55159e10 q^{42} +2.18836e10 q^{43} +6.74987e10 q^{44} +2.11235e10 q^{45} +4.26868e9 q^{46} -5.63281e10 q^{47} -2.27643e10 q^{48} +1.93693e11 q^{49} +1.41811e10 q^{50} -1.17904e11 q^{51} -7.20112e9 q^{52} -2.33624e10 q^{53} -1.52967e10 q^{54} -4.04475e11 q^{55} +3.15533e11 q^{56} -1.12082e11 q^{57} +2.03651e11 q^{58} -4.21805e10 q^{59} +1.92200e11 q^{60} -6.59589e11 q^{61} -6.89579e9 q^{62} -2.86477e11 q^{63} -1.78016e10 q^{64} +4.31515e10 q^{65} +2.92902e11 q^{66} +1.98586e10 q^{67} -1.07279e12 q^{68} -7.88147e10 q^{69} -8.45978e11 q^{70} +1.48511e12 q^{71} -3.11075e11 q^{72} -2.63525e11 q^{73} -8.65764e11 q^{74} -2.61833e11 q^{75} -1.01982e12 q^{76} +5.48550e12 q^{77} -3.12483e10 q^{78} +2.47859e12 q^{79} +1.24119e12 q^{80} +2.82430e11 q^{81} +1.40930e12 q^{82} -1.76625e12 q^{83} -2.60661e12 q^{84} +6.42852e12 q^{85} +8.64037e11 q^{86} -3.76011e12 q^{87} +5.95651e12 q^{88} +1.27082e12 q^{89} +8.34026e11 q^{90} -5.85221e11 q^{91} -7.17124e11 q^{92} +1.27320e11 q^{93} -2.22402e12 q^{94} +6.11112e12 q^{95} -4.39446e12 q^{96} +3.89183e12 q^{97} +7.64765e12 q^{98} -5.40800e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	39.4833	0.436233	0.218117	−	0.975923i	$-0.430009\pi$
$2$	39.4833	0.436233	0.218117	+	0.975923i	$0.430009\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	−6633.07	−0.809700
$5$	39747.6	1.13764	0.568821	−	0.822461i	$-0.307400\pi$
$5$	39747.6	1.13764	0.568821	+	0.822461i	$0.307400\pi$
$6$	−28783.4	−0.251859
$7$	−539057.	−1.73180	−0.865899	−	0.500219i	$-0.833253\pi$
$7$	−539057.	−1.73180	−0.865899	+	0.500219i	$0.833253\pi$
$8$	−585343.	−0.789452
$9$	531441.	0.333333
$10$	1.56937e6	0.496277
$11$	−1.01761e7	−1.73192	−0.865962	−	0.500109i	$-0.833293\pi$
$11$	−1.01761e7	−1.73192	−0.865962	+	0.500109i	$0.833293\pi$
$12$	4.83551e6	0.467481
$13$	1.08564e6	0.0623812	0.0311906	−	0.999513i	$-0.490070\pi$
$13$	1.08564e6	0.0623812	0.0311906	+	0.999513i	$0.490070\pi$
$14$	−2.12838e7	−0.755468
$15$	−2.89760e7	−0.656818
$16$	3.12268e7	0.465315
$17$	1.61734e8	1.62511	0.812555	−	0.582885i	$-0.198076\pi$
$17$	1.61734e8	1.62511	0.812555	+	0.582885i	$0.198076\pi$
$18$	2.09831e7	0.145411
$19$	1.53748e8	0.749742	0.374871	−	0.927077i	$-0.377687\pi$
$19$	1.53748e8	0.749742	0.374871	+	0.927077i	$0.377687\pi$
$20$	−2.63648e8	−0.921149
$21$	3.92972e8	0.999854
$22$	−4.01786e8	−0.755523
$23$	1.08113e8	0.152282	0.0761411	−	0.997097i	$-0.475740\pi$
$23$	1.08113e8	0.152282	0.0761411	+	0.997097i	$0.475740\pi$
$24$	4.26715e8	0.455790
$25$	3.59167e8	0.294230
$26$	4.28647e7	0.0272128
$27$	−3.87420e8	−0.192450
$28$	3.57560e9	1.40224
$29$	5.15790e9	1.61022	0.805111	−	0.593124i	$-0.202106\pi$
$29$	5.15790e9	1.61022	0.805111	+	0.593124i	$0.202106\pi$
$30$	−1.14407e9	−0.286526
$31$	−1.74651e8	−0.0353443	−0.0176721	−	0.999844i	$-0.505626\pi$
$31$	−1.74651e8	−0.0353443	−0.0176721	+	0.999844i	$0.505626\pi$
$32$	6.02807e9	0.992438
$33$	7.41838e9	0.999927
$34$	6.38579e9	0.708927
$35$	−2.14262e10	−1.97017
$36$	−3.52508e9	−0.269900
$37$	−2.19273e10	−1.40499	−0.702497	−	0.711687i	$-0.747931\pi$
$37$	−2.19273e10	−1.40499	−0.702497	+	0.711687i	$0.747931\pi$
$38$	6.07049e9	0.327062
$39$	−7.91431e8	−0.0360158
$40$	−2.32660e10	−0.898114
$41$	3.56936e10	1.17353	0.586766	−	0.809757i	$-0.300401\pi$
$41$	3.56936e10	1.17353	0.586766	+	0.809757i	$0.300401\pi$
$42$	1.55159e10	0.436170
$43$	2.18836e10	0.527927	0.263963	−	0.964533i	$-0.414970\pi$
$43$	2.18836e10	0.527927	0.263963	+	0.964533i	$0.414970\pi$
$44$	6.74987e10	1.40234
$45$	2.11235e10	0.379214
$46$	4.26868e9	0.0664305
$47$	−5.63281e10	−0.762235	−0.381117	−	0.924527i	$-0.624461\pi$
$47$	−5.63281e10	−0.762235	−0.381117	+	0.924527i	$0.624461\pi$
$48$	−2.27643e10	−0.268650
$49$	1.93693e11	1.99912
$50$	1.41811e10	0.128353
$51$	−1.17904e11	−0.938257
$52$	−7.20112e9	−0.0505101
$53$	−2.33624e10	−0.144785	−0.0723925	−	0.997376i	$-0.523063\pi$
$53$	−2.33624e10	−0.144785	−0.0723925	+	0.997376i	$0.523063\pi$
$54$	−1.52967e10	−0.0839531
$55$	−4.04475e11	−1.97031
$56$	3.15533e11	1.36717
$57$	−1.12082e11	−0.432864
$58$	2.03651e11	0.702433
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	1.92200e11	0.531826
$61$	−6.59589e11	−1.63919	−0.819596	−	0.572943i	$-0.805802\pi$
$61$	−6.59589e11	−1.63919	−0.819596	+	0.572943i	$0.805802\pi$
$62$	−6.89579e9	−0.0154184
$63$	−2.86477e11	−0.577266
$64$	−1.78016e10	−0.0323809
$65$	4.31515e10	0.0709675
$66$	2.92902e11	0.436202
$67$	1.98586e10	0.0268203	0.0134101	−	0.999910i	$-0.495731\pi$
$67$	1.98586e10	0.0268203	0.0134101	+	0.999910i	$0.495731\pi$
$68$	−1.07279e12	−1.31585
$69$	−7.88147e10	−0.0879201
$70$	−8.45978e11	−0.859452
$71$	1.48511e12	1.37587	0.687937	−	0.725770i	$-0.258516\pi$
$71$	1.48511e12	1.37587	0.687937	+	0.725770i	$0.258516\pi$
$72$	−3.11075e11	−0.263151
$73$	−2.63525e11	−0.203809	−0.101905	−	0.994794i	$-0.532494\pi$
$73$	−2.63525e11	−0.203809	−0.101905	+	0.994794i	$0.532494\pi$
$74$	−8.65764e11	−0.612905
$75$	−2.61833e11	−0.169874
$76$	−1.01982e12	−0.607066
$77$	5.48550e12	2.99934
$78$	−3.12483e10	−0.0157113
$79$	2.47859e12	1.14717	0.573585	−	0.819146i	$-0.305552\pi$
$79$	2.47859e12	1.14717	0.573585	+	0.819146i	$0.305552\pi$
$80$	1.24119e12	0.529362
$81$	2.82430e11	0.111111
$82$	1.40930e12	0.511934
$83$	−1.76625e12	−0.592988	−0.296494	−	0.955035i	$-0.595817\pi$
$83$	−1.76625e12	−0.592988	−0.296494	+	0.955035i	$0.595817\pi$
$84$	−2.60661e12	−0.809582
$85$	6.42852e12	1.84879
$86$	8.64037e11	0.230299
$87$	−3.76011e12	−0.929662
$88$	5.95651e12	1.36727
$89$	1.27082e12	0.271050	0.135525	−	0.990774i	$-0.456728\pi$
$89$	1.27082e12	0.271050	0.135525	+	0.990774i	$0.456728\pi$
$90$	8.34026e11	0.165426
$91$	−5.85221e11	−0.108032
$92$	−7.17124e11	−0.123303
$93$	1.27320e11	0.0204060
$94$	−2.22402e12	−0.332512
$95$	6.11112e12	0.852938
$96$	−4.39446e12	−0.572984
$97$	3.89183e12	0.474392	0.237196	−	0.971462i	$-0.423772\pi$
$97$	3.89183e12	0.474392	0.237196	+	0.971462i	$0.423772\pi$
$98$	7.64765e12	0.872085
$99$	−5.40800e12	−0.577308
$100$	−2.38238e12	−0.238238
$101$	1.43375e13	1.34396	0.671978	−	0.740571i	$-0.265445\pi$
$101$	1.43375e13	1.34396	0.671978	+	0.740571i	$0.265445\pi$
$102$	−4.65524e12	−0.409299
$103$	9.09071e11	0.0750163	0.0375082	−	0.999296i	$-0.488058\pi$
$103$	9.09071e11	0.0750163	0.0375082	+	0.999296i	$0.488058\pi$
$104$	−6.35471e11	−0.0492470
$105$	1.56197e13	1.13748
$106$	−9.22424e11	−0.0631600
$107$	−1.72384e13	−1.11046	−0.555230	−	0.831697i	$-0.687370\pi$
$107$	−1.72384e13	−1.11046	−0.555230	+	0.831697i	$0.687370\pi$
$108$	2.56979e12	0.155827
$109$	2.44984e13	1.39915	0.699577	−	0.714557i	$-0.253372\pi$
$109$	2.44984e13	1.39915	0.699577	+	0.714557i	$0.253372\pi$
$110$	−1.59700e13	−0.859515
$111$	1.59850e13	0.811173
$112$	−1.68330e13	−0.805832
$113$	−3.44144e13	−1.55500	−0.777499	−	0.628884i	$-0.783512\pi$
$113$	−3.44144e13	−1.55500	−0.777499	+	0.628884i	$0.783512\pi$
$114$	−4.42539e12	−0.188830
$115$	4.29725e12	0.173243
$116$	−3.42127e13	−1.30380
$117$	5.76953e11	0.0207937
$118$	−1.66543e12	−0.0567927
$119$	−8.71837e13	−2.81436
$120$	1.69609e13	0.518526
$121$	6.90303e13	1.99956
$122$	−2.60428e13	−0.715070
$123$	−2.60206e13	−0.677539
$124$	1.15847e12	0.0286183
$125$	−3.42440e13	−0.802914
$126$	−1.13111e13	−0.251823
$127$	−3.39799e13	−0.718619	−0.359309	−	0.933219i	$-0.616988\pi$
$127$	−3.39799e13	−0.718619	−0.359309	+	0.933219i	$0.616988\pi$
$128$	−5.00848e13	−1.00656
$129$	−1.59531e13	−0.304799
$130$	1.70377e12	0.0309584
$131$	−1.62272e13	−0.280530	−0.140265	−	0.990114i	$-0.544796\pi$
$131$	−1.62272e13	−0.280530	−0.140265	+	0.990114i	$0.544796\pi$
$132$	−4.92066e13	−0.809641
$133$	−8.28790e13	−1.29840
$134$	7.84085e11	0.0116999
$135$	−1.53990e13	−0.218939
$136$	−9.46697e13	−1.28295
$137$	−1.50222e14	−1.94111	−0.970557	−	0.240873i	$-0.922566\pi$
$137$	−1.50222e14	−1.94111	−0.970557	+	0.240873i	$0.922566\pi$
$138$	−3.11187e12	−0.0383537
$139$	−4.68636e12	−0.0551111	−0.0275556	−	0.999620i	$-0.508772\pi$
$139$	−4.68636e12	−0.0551111	−0.0275556	+	0.999620i	$0.508772\pi$
$140$	1.42121e14	1.59524
$141$	4.10632e13	0.440076
$142$	5.86370e13	0.600202
$143$	−1.10476e13	−0.108040
$144$	1.65952e13	0.155105
$145$	2.05014e14	1.83186
$146$	−1.04049e13	−0.0889084
$147$	−1.41202e14	−1.15420
$148$	1.45445e14	1.13762
$149$	4.80391e13	0.359654	0.179827	−	0.983698i	$-0.442446\pi$
$149$	4.80391e13	0.359654	0.179827	+	0.983698i	$0.442446\pi$
$150$	−1.03380e13	−0.0741045
$151$	7.87849e13	0.540870	0.270435	−	0.962738i	$-0.412833\pi$
$151$	7.87849e13	0.540870	0.270435	+	0.962738i	$0.412833\pi$
$152$	−8.99955e13	−0.591885
$153$	8.59519e13	0.541703
$154$	2.16586e14	1.30841
$155$	−6.94194e12	−0.0402091
$156$	5.24962e12	0.0291620
$157$	−3.02191e14	−1.61040	−0.805200	−	0.593003i	$-0.797942\pi$
$157$	−3.02191e14	−1.61040	−0.805200	+	0.593003i	$0.797942\pi$
$158$	9.78628e13	0.500434
$159$	1.70312e13	0.0835917
$160$	2.39601e14	1.12904
$161$	−5.82793e13	−0.263722
$162$	1.11513e13	0.0484704
$163$	2.22757e14	0.930278	0.465139	−	0.885238i	$-0.346004\pi$
$163$	2.22757e14	0.930278	0.465139	+	0.885238i	$0.346004\pi$
$164$	−2.36758e14	−0.950209
$165$	2.94863e14	1.13756
$166$	−6.97376e13	−0.258681
$167$	−3.81692e14	−1.36162	−0.680809	−	0.732461i	$-0.738372\pi$
$167$	−3.81692e14	−1.36162	−0.680809	+	0.732461i	$0.738372\pi$
$168$	−2.30024e14	−0.789336
$169$	−3.01696e14	−0.996109
$170$	2.53820e14	0.806505
$171$	8.17081e13	0.249914
$172$	−1.45155e14	−0.427463
$173$	4.04749e13	0.114785	0.0573926	−	0.998352i	$-0.481721\pi$
$173$	4.04749e13	0.114785	0.0573926	+	0.998352i	$0.481721\pi$
$174$	−1.48462e14	−0.405550
$175$	−1.93611e14	−0.509546
$176$	−3.17767e14	−0.805891
$177$	3.07496e13	0.0751646
$178$	5.01764e13	0.118241
$179$	−8.88689e13	−0.201932	−0.100966	−	0.994890i	$-0.532193\pi$
$179$	−8.88689e13	−0.201932	−0.100966	+	0.994890i	$0.532193\pi$
$180$	−1.40114e14	−0.307050
$181$	8.99177e13	0.190079	0.0950396	−	0.995473i	$-0.469702\pi$
$181$	8.99177e13	0.190079	0.0950396	+	0.995473i	$0.469702\pi$
$182$	−2.31065e13	−0.0471270
$183$	4.80841e14	0.946387
$184$	−6.32835e13	−0.120219
$185$	−8.71558e14	−1.59838
$186$	5.02703e12	0.00890179
$187$	−1.64582e15	−2.81457
$188$	3.73628e14	0.617182
$189$	2.08842e14	0.333285
$190$	2.41287e14	0.372080
$191$	9.77835e14	1.45730	0.728650	−	0.684887i	$-0.240148\pi$
$191$	9.77835e14	1.45730	0.728650	+	0.684887i	$0.240148\pi$
$192$	1.29774e13	0.0186951
$193$	1.24226e15	1.73017	0.865087	−	0.501622i	$-0.167263\pi$
$193$	1.24226e15	1.73017	0.865087	+	0.501622i	$0.167263\pi$
$194$	1.53662e14	0.206945
$195$	−3.14575e13	−0.0409731
$196$	−1.28478e15	−1.61869
$197$	7.37782e14	0.899286	0.449643	−	0.893208i	$-0.351551\pi$
$197$	7.37782e14	0.899286	0.449643	+	0.893208i	$0.351551\pi$
$198$	−2.13526e14	−0.251841
$199$	−6.49842e14	−0.741759	−0.370879	−	0.928681i	$-0.620944\pi$
$199$	−6.49842e14	−0.741759	−0.370879	+	0.928681i	$0.620944\pi$
$200$	−2.10236e14	−0.232280
$201$	−1.44769e13	−0.0154847
$202$	5.66093e14	0.586278
$203$	−2.78040e15	−2.78858
$204$	7.82064e14	0.759707
$205$	1.41873e15	1.33506
$206$	3.58932e13	0.0327246
$207$	5.74559e13	0.0507607
$208$	3.39010e13	0.0290269
$209$	−1.56456e15	−1.29850
$210$	6.16718e14	0.496205
$211$	−3.09358e13	−0.0241337	−0.0120669	−	0.999927i	$-0.503841\pi$
$211$	−3.09358e13	−0.0241337	−0.0120669	+	0.999927i	$0.503841\pi$
$212$	1.54964e14	0.117232
$213$	−1.08264e15	−0.794361
$214$	−6.80630e14	−0.484419
$215$	8.69820e14	0.600592
$216$	2.26774e14	0.151930
$217$	9.41466e13	0.0612092
$218$	9.67279e14	0.610358
$219$	1.92110e14	0.117669
$220$	2.68291e15	1.59536
$221$	1.75585e14	0.101376
$222$	6.31142e14	0.353861
$223$	−6.13798e14	−0.334229	−0.167114	−	0.985938i	$-0.553445\pi$
$223$	−6.13798e14	−0.334229	−0.167114	+	0.985938i	$0.553445\pi$
$224$	−3.24947e15	−1.71870
$225$	1.90876e14	0.0980765
$226$	−1.35879e15	−0.678342
$227$	−2.02574e15	−0.982686	−0.491343	−	0.870966i	$-0.663494\pi$
$227$	−2.02574e15	−0.982686	−0.491343	+	0.870966i	$0.663494\pi$
$228$	7.43451e14	0.350490
$229$	2.82538e14	0.129463	0.0647315	−	0.997903i	$-0.479381\pi$
$229$	2.82538e14	0.129463	0.0647315	+	0.997903i	$0.479381\pi$
$230$	1.69670e14	0.0755742
$231$	−3.99893e15	−1.73167
$232$	−3.01914e15	−1.27119
$233$	−2.28292e15	−0.934709	−0.467354	−	0.884070i	$-0.654793\pi$
$233$	−2.28292e15	−0.934709	−0.467354	+	0.884070i	$0.654793\pi$
$234$	2.27800e13	0.00907092
$235$	−2.23890e15	−0.867150
$236$	2.79786e14	0.105414
$237$	−1.80689e15	−0.662319
$238$	−3.44230e15	−1.22772
$239$	−2.57641e15	−0.894187	−0.447094	−	0.894487i	$-0.647541\pi$
$239$	−2.57641e15	−0.894187	−0.447094	+	0.894487i	$0.647541\pi$
$240$	−9.04827e14	−0.305627
$241$	−7.04715e14	−0.231688	−0.115844	−	0.993267i	$-0.536957\pi$
$241$	−7.04715e14	−0.231688	−0.115844	+	0.993267i	$0.536957\pi$
$242$	2.72555e15	0.872276
$243$	−2.05891e14	−0.0641500
$244$	4.37510e15	1.32725
$245$	7.69884e15	2.27429
$246$	−1.02738e15	−0.295565
$247$	1.66915e14	0.0467698
$248$	1.02231e14	0.0279026
$249$	1.28760e15	0.342362
$250$	−1.35207e15	−0.350258
$251$	2.49900e15	0.630793	0.315397	−	0.948960i	$-0.397862\pi$
$251$	2.49900e15	0.630793	0.315397	+	0.948960i	$0.397862\pi$
$252$	1.90022e15	0.467413
$253$	−1.10017e15	−0.263741
$254$	−1.34164e15	−0.313485
$255$	−4.68639e15	−1.06740
$256$	−1.83168e15	−0.406716
$257$	−9.37515e14	−0.202961	−0.101481	−	0.994838i	$-0.532358\pi$
$257$	−9.37515e14	−0.202961	−0.101481	+	0.994838i	$0.532358\pi$
$258$	−6.29883e14	−0.132963
$259$	1.18201e16	2.43316
$260$	−2.86227e14	−0.0574624
$261$	2.74112e15	0.536741
$262$	−6.40704e14	−0.122377
$263$	8.60213e15	1.60285	0.801427	−	0.598093i	$-0.204075\pi$
$263$	8.60213e15	1.60285	0.801427	+	0.598093i	$0.204075\pi$
$264$	−4.34230e15	−0.789394
$265$	−9.28597e14	−0.164714
$266$	−3.27234e15	−0.566406
$267$	−9.26430e14	−0.156491
$268$	−1.31724e14	−0.0217164
$269$	−1.09969e16	−1.76962	−0.884809	−	0.465955i	$-0.845711\pi$
$269$	−1.09969e16	−1.76962	−0.884809	+	0.465955i	$0.845711\pi$
$270$	−6.08005e14	−0.0955086
$271$	−1.98040e15	−0.303705	−0.151852	−	0.988403i	$-0.548524\pi$
$271$	−1.98040e15	−0.303705	−0.151852	+	0.988403i	$0.548524\pi$
$272$	5.05042e15	0.756188
$273$	4.26626e14	0.0623721
$274$	−5.93128e15	−0.846778
$275$	−3.65492e15	−0.509583
$276$	5.22783e14	0.0711890
$277$	−1.29200e16	−1.71848	−0.859238	−	0.511577i	$-0.829062\pi$
$277$	−1.29200e16	−1.71848	−0.859238	+	0.511577i	$0.829062\pi$
$278$	−1.85033e14	−0.0240413
$279$	−9.28165e13	−0.0117814
$280$	1.25417e16	1.55535
$281$	−1.58154e15	−0.191641	−0.0958207	−	0.995399i	$-0.530548\pi$
$281$	−1.58154e15	−0.191641	−0.0958207	+	0.995399i	$0.530548\pi$
$282$	1.62131e15	0.191976
$283$	−7.97822e14	−0.0923197	−0.0461598	−	0.998934i	$-0.514698\pi$
$283$	−7.97822e14	−0.0923197	−0.0461598	+	0.998934i	$0.514698\pi$
$284$	−9.85082e15	−1.11405
$285$	−4.45501e15	−0.492444
$286$	−4.36195e14	−0.0471305
$287$	−1.92409e16	−2.03232
$288$	3.20356e15	0.330813
$289$	1.62532e16	1.64098
$290$	8.09464e15	0.799117
$291$	−2.83714e15	−0.273890
$292$	1.74798e15	0.165024
$293$	2.88481e15	0.266365	0.133182	−	0.991092i	$-0.457480\pi$
$293$	2.88481e15	0.266365	0.133182	+	0.991092i	$0.457480\pi$
$294$	−5.57514e15	−0.503498
$295$	−1.67657e15	−0.148108
$296$	1.28350e16	1.10917
$297$	3.94243e15	0.333309
$298$	1.89675e15	0.156893
$299$	1.17372e14	0.00949954
$300$	1.73675e15	0.137547
$301$	−1.17965e16	−0.914262
$302$	3.11069e15	0.235945
$303$	−1.04520e16	−0.775933
$304$	4.80106e15	0.348866
$305$	−2.62171e16	−1.86481
$306$	3.39367e15	0.236309
$307$	−2.70735e16	−1.84563	−0.922815	−	0.385242i	$-0.874118\pi$
$307$	−2.70735e16	−1.84563	−0.922815	+	0.385242i	$0.874118\pi$
$308$	−3.63857e16	−2.42857
$309$	−6.62713e14	−0.0433107
$310$	−2.74091e14	−0.0175406
$311$	−1.50598e16	−0.943790	−0.471895	−	0.881655i	$-0.656430\pi$
$311$	−1.50598e16	−0.943790	−0.471895	+	0.881655i	$0.656430\pi$
$312$	4.63259e14	0.0284327
$313$	2.92034e16	1.75548	0.877739	−	0.479139i	$-0.159051\pi$
$313$	2.92034e16	1.75548	0.877739	+	0.479139i	$0.159051\pi$
$314$	−1.19315e16	−0.702510
$315$	−1.13868e16	−0.656722
$316$	−1.64406e16	−0.928864
$317$	1.21142e16	0.670516	0.335258	−	0.942126i	$-0.391177\pi$
$317$	1.21142e16	0.670516	0.335258	+	0.942126i	$0.391177\pi$
$318$	6.72447e14	0.0364655
$319$	−5.24873e16	−2.78878
$320$	−7.07570e14	−0.0368379
$321$	1.25668e16	0.641124
$322$	−2.30106e15	−0.115044
$323$	2.48663e16	1.21841
$324$	−1.87337e15	−0.0899667
$325$	3.89926e14	0.0183544
$326$	8.79521e15	0.405818
$327$	−1.78593e16	−0.807802
$328$	−2.08930e16	−0.926446
$329$	3.03640e16	1.32004
$330$	1.16422e16	0.496241
$331$	−1.29603e16	−0.541667	−0.270833	−	0.962626i	$-0.587299\pi$
$331$	−1.29603e16	−0.541667	−0.270833	+	0.962626i	$0.587299\pi$
$332$	1.17157e16	0.480142
$333$	−1.16531e16	−0.468331
$334$	−1.50705e16	−0.593984
$335$	7.89333e14	0.0305119
$336$	1.22713e16	0.465247
$337$	2.54197e16	0.945315	0.472658	−	0.881246i	$-0.343295\pi$
$337$	2.54197e16	0.945315	0.472658	+	0.881246i	$0.343295\pi$
$338$	−1.19120e16	−0.434536
$339$	2.50881e16	0.897779
$340$	−4.26408e16	−1.49697
$341$	1.77726e15	0.0612136
$342$	3.22611e15	0.109021
$343$	−5.21829e16	−1.73028
$344$	−1.28094e16	−0.416773
$345$	−3.13269e15	−0.100022
$346$	1.59808e15	0.0500731
$347$	5.45411e16	1.67719	0.838595	−	0.544756i	$-0.183378\pi$
$347$	5.45411e16	1.67719	0.838595	+	0.544756i	$0.183378\pi$
$348$	2.49410e16	0.752748
$349$	6.05705e16	1.79430	0.897151	−	0.441724i	$-0.145633\pi$
$349$	6.05705e16	1.79430	0.897151	+	0.441724i	$0.145633\pi$
$350$	−7.64442e15	−0.222281
$351$	−4.20599e14	−0.0120053
$352$	−6.13422e16	−1.71883
$353$	−4.09890e16	−1.12754	−0.563770	−	0.825932i	$-0.690649\pi$
$353$	−4.09890e16	−1.12754	−0.563770	+	0.825932i	$0.690649\pi$
$354$	1.21410e15	0.0327893
$355$	5.90294e16	1.56525
$356$	−8.42946e15	−0.219470
$357$	6.35569e16	1.62487
$358$	−3.50884e15	−0.0880895
$359$	−6.30612e16	−1.55471	−0.777353	−	0.629065i	$-0.783438\pi$
$359$	−6.30612e16	−1.55471	−0.777353	+	0.629065i	$0.783438\pi$
$360$	−1.23645e16	−0.299371
$361$	−1.84145e16	−0.437887
$362$	3.55025e15	0.0829189
$363$	−5.03231e16	−1.15445
$364$	3.88181e15	0.0874733
$365$	−1.04745e16	−0.231862
$366$	1.89852e16	0.412846
$367$	−1.03944e16	−0.222060	−0.111030	−	0.993817i	$-0.535415\pi$
$367$	−1.03944e16	−0.222060	−0.111030	+	0.993817i	$0.535415\pi$
$368$	3.37604e15	0.0708592
$369$	1.89690e16	0.391177
$370$	−3.44120e16	−0.697267
$371$	1.25936e16	0.250738
$372$	−8.44524e14	−0.0165228
$373$	8.47541e15	0.162950	0.0814748	−	0.996675i	$-0.474037\pi$
$373$	8.47541e15	0.162950	0.0814748	+	0.996675i	$0.474037\pi$
$374$	−6.49824e16	−1.22781
$375$	2.49639e16	0.463563
$376$	3.29712e16	0.601748
$377$	5.59962e15	0.100448
$378$	8.24576e15	0.145390
$379$	−5.81147e16	−1.00724	−0.503618	−	0.863926i	$-0.667998\pi$
$379$	−5.81147e16	−1.00724	−0.503618	+	0.863926i	$0.667998\pi$
$380$	−4.05355e16	−0.690624
$381$	2.47714e16	0.414895
$382$	3.86082e16	0.635723
$383$	−3.72322e16	−0.602735	−0.301368	−	0.953508i	$-0.597443\pi$
$383$	−3.72322e16	−0.602735	−0.301368	+	0.953508i	$0.597443\pi$
$384$	3.65118e16	0.581140
$385$	2.18035e17	3.41218
$386$	4.90486e16	0.754760
$387$	1.16298e16	0.175976
$388$	−2.58147e16	−0.384115
$389$	8.98330e16	1.31451	0.657254	−	0.753669i	$-0.271718\pi$
$389$	8.98330e16	1.31451	0.657254	+	0.753669i	$0.271718\pi$
$390$	−1.24205e15	−0.0178738
$391$	1.74856e16	0.247475
$392$	−1.13377e17	−1.57821
$393$	1.18296e16	0.161964
$394$	2.91301e16	0.392298
$395$	9.85178e16	1.30507
$396$	3.58716e16	0.467447
$397$	−4.90872e16	−0.629259	−0.314630	−	0.949215i	$-0.601880\pi$
$397$	−4.90872e16	−0.629259	−0.314630	+	0.949215i	$0.601880\pi$
$398$	−2.56579e16	−0.323580
$399$	6.04188e16	0.749633
$400$	1.12156e16	0.136910
$401$	−7.31157e16	−0.878157	−0.439078	−	0.898449i	$-0.644695\pi$
$401$	−7.31157e16	−0.878157	−0.439078	+	0.898449i	$0.644695\pi$
$402$	−5.71598e14	−0.00675494
$403$	−1.89608e14	−0.00220482
$404$	−9.51017e16	−1.08820
$405$	1.12259e16	0.126405
$406$	−1.09779e17	−1.21647
$407$	2.23135e17	2.43334
$408$	6.90142e16	0.740709
$409$	8.27643e16	0.874262	0.437131	−	0.899398i	$-0.355995\pi$
$409$	8.27643e16	0.874262	0.437131	+	0.899398i	$0.355995\pi$
$410$	5.60163e16	0.582397
$411$	1.09512e17	1.12070
$412$	−6.02993e15	−0.0607408
$413$	2.27377e16	0.225461
$414$	2.26855e15	0.0221435
$415$	−7.02043e16	−0.674608
$416$	6.54431e15	0.0619095
$417$	3.41636e15	0.0318184
$418$	−6.17740e16	−0.566447
$419$	7.63073e16	0.688929	0.344465	−	0.938799i	$-0.388060\pi$
$419$	7.63073e16	0.688929	0.344465	+	0.938799i	$0.388060\pi$
$420$	−1.03607e17	−0.921015
$421$	1.51693e17	1.32780	0.663901	−	0.747821i	$-0.268900\pi$
$421$	1.51693e17	1.32780	0.663901	+	0.747821i	$0.268900\pi$
$422$	−1.22145e15	−0.0105279
$423$	−2.99350e16	−0.254078
$424$	1.36750e16	0.114301
$425$	5.80894e16	0.478155
$426$	−4.27464e16	−0.346527
$427$	3.55556e17	2.83875
$428$	1.14344e17	0.899140
$429$	8.05368e15	0.0623767
$430$	3.43434e16	0.261998
$431$	−1.95964e17	−1.47256	−0.736281	−	0.676676i	$-0.763420\pi$
$431$	−1.95964e17	−1.47256	−0.736281	+	0.676676i	$0.763420\pi$
$432$	−1.20979e16	−0.0895500
$433$	1.94301e17	1.41678	0.708392	−	0.705819i	$-0.249421\pi$
$433$	1.94301e17	1.41678	0.708392	+	0.705819i	$0.249421\pi$
$434$	3.71722e15	0.0267015
$435$	−1.49455e17	−1.05762
$436$	−1.62500e17	−1.13290
$437$	1.66223e16	0.114172
$438$	7.58514e15	0.0513313
$439$	1.99015e17	1.32699	0.663494	−	0.748182i	$-0.269073\pi$
$439$	1.99015e17	1.32699	0.663494	+	0.748182i	$0.269073\pi$
$440$	2.36757e17	1.55546
$441$	1.02937e17	0.666375
$442$	6.93266e15	0.0442237
$443$	−7.49549e15	−0.0471168	−0.0235584	−	0.999722i	$-0.507500\pi$
$443$	−7.49549e15	−0.0471168	−0.0235584	+	0.999722i	$0.507500\pi$
$444$	−1.06030e17	−0.656807
$445$	5.05122e16	0.308358
$446$	−2.42348e16	−0.145802
$447$	−3.50205e16	−0.207646
$448$	9.59606e15	0.0560772
$449$	−2.82724e17	−1.62840	−0.814201	−	0.580583i	$-0.802825\pi$
$449$	−2.82724e17	−1.62840	−0.814201	+	0.580583i	$0.802825\pi$
$450$	7.53642e15	0.0427843
$451$	−3.63221e17	−2.03247
$452$	2.28273e17	1.25908
$453$	−5.74342e16	−0.312271
$454$	−7.99828e16	−0.428680
$455$	−2.32611e16	−0.122901
$456$	6.56067e16	0.341725
$457$	1.30903e17	0.672196	0.336098	−	0.941827i	$-0.390893\pi$
$457$	1.30903e17	0.672196	0.336098	+	0.941827i	$0.390893\pi$
$458$	1.11555e16	0.0564761
$459$	−6.26590e16	−0.312752
$460$	−2.85039e16	−0.140275
$461$	−2.79235e17	−1.35492	−0.677459	−	0.735560i	$-0.736919\pi$
$461$	−2.79235e17	−1.35492	−0.677459	+	0.735560i	$0.736919\pi$
$462$	−1.57891e17	−0.755413
$463$	−2.05969e17	−0.971685	−0.485843	−	0.874046i	$-0.661487\pi$
$463$	−2.05969e17	−0.971685	−0.485843	+	0.874046i	$0.661487\pi$
$464$	1.61065e17	0.749261
$465$	5.06068e15	0.0232148
$466$	−9.01371e16	−0.407751
$467$	1.82294e17	0.813230	0.406615	−	0.913600i	$-0.366709\pi$
$467$	1.82294e17	0.813230	0.406615	+	0.913600i	$0.366709\pi$
$468$	−3.82697e15	−0.0168367
$469$	−1.07049e16	−0.0464473
$470$	−8.83994e16	−0.378280
$471$	2.20297e17	0.929765
$472$	2.46901e16	0.102778
$473$	−2.22690e17	−0.914329
$474$	−7.13420e16	−0.288926
$475$	5.52213e16	0.220596
$476$	5.78295e17	2.27879
$477$	−1.24157e16	−0.0482617
$478$	−1.01725e17	−0.390074
$479$	−1.74764e17	−0.661108	−0.330554	−	0.943787i	$-0.607236\pi$
$479$	−1.74764e17	−0.661108	−0.330554	+	0.943787i	$0.607236\pi$
$480$	−1.74669e17	−0.651851
$481$	−2.38052e16	−0.0876452
$482$	−2.78245e16	−0.101070
$483$	4.24856e16	0.152260
$484$	−4.57883e17	−1.61905
$485$	1.54691e17	0.539688
$486$	−8.12927e15	−0.0279844
$487$	−3.30318e16	−0.112200	−0.0561002	−	0.998425i	$-0.517867\pi$
$487$	−3.30318e16	−0.112200	−0.0561002	+	0.998425i	$0.517867\pi$
$488$	3.86086e17	1.29406
$489$	−1.62390e17	−0.537096
$490$	3.03976e17	0.992120
$491$	−5.07135e17	−1.63341	−0.816703	−	0.577058i	$-0.804201\pi$
$491$	−5.07135e17	−1.63341	−0.816703	+	0.577058i	$0.804201\pi$
$492$	1.72596e17	0.548603
$493$	8.34206e17	2.61679
$494$	6.59037e15	0.0204026
$495$	−2.14955e17	−0.656770
$496$	−5.45378e15	−0.0164462
$497$	−8.00558e17	−2.38274
$498$	5.08387e16	0.149350
$499$	−2.64604e17	−0.767261	−0.383630	−	0.923487i	$-0.625326\pi$
$499$	−2.64604e17	−0.767261	−0.383630	+	0.923487i	$0.625326\pi$
$500$	2.27143e17	0.650120
$501$	2.78253e17	0.786131
$502$	9.86688e16	0.275173
$503$	−2.50951e17	−0.690870	−0.345435	−	0.938443i	$-0.612269\pi$
$503$	−2.50951e17	−0.690870	−0.345435	+	0.938443i	$0.612269\pi$
$504$	1.67687e17	0.455724
$505$	5.69881e17	1.52894
$506$	−4.34385e16	−0.115053
$507$	2.19937e17	0.575104
$508$	2.25391e17	0.581866
$509$	4.29578e17	1.09491	0.547453	−	0.836836i	$-0.315597\pi$
$509$	4.29578e17	1.09491	0.547453	+	0.836836i	$0.315597\pi$
$510$	−1.85034e17	−0.465636
$511$	1.42055e17	0.352956
$512$	3.37974e17	0.829140
$513$	−5.95652e16	−0.144288
$514$	−3.70162e16	−0.0885384
$515$	3.61334e16	0.0853417
$516$	1.05818e17	0.246796
$517$	5.73200e17	1.32013
$518$	4.66696e17	1.06143
$519$	−2.95062e16	−0.0662712
$520$	−2.52585e16	−0.0560254
$521$	−2.44624e17	−0.535862	−0.267931	−	0.963438i	$-0.586340\pi$
$521$	−2.44624e17	−0.535862	−0.267931	+	0.963438i	$0.586340\pi$
$522$	1.08229e17	0.234144
$523$	5.77350e17	1.23361	0.616805	−	0.787116i	$-0.288427\pi$
$523$	5.77350e17	1.23361	0.616805	+	0.787116i	$0.288427\pi$
$524$	1.07636e17	0.227146
$525$	1.41143e17	0.294187
$526$	3.39641e17	0.699218
$527$	−2.82469e16	−0.0574383
$528$	2.31652e17	0.465281
$529$	−4.92348e17	−0.976810
$530$	−3.66641e16	−0.0718535
$531$	−2.24165e16	−0.0433963
$532$	5.49742e17	1.05132
$533$	3.87503e16	0.0732063
$534$	−3.65786e16	−0.0682666
$535$	−6.85185e17	−1.26331
$536$	−1.16241e16	−0.0211733
$537$	6.47854e16	0.116586
$538$	−4.34193e17	−0.771966
$539$	−1.97104e18	−3.46233
$540$	1.02143e17	0.177275
$541$	−2.66477e16	−0.0456959	−0.0228480	−	0.999739i	$-0.507273\pi$
$541$	−2.66477e16	−0.0456959	−0.0228480	+	0.999739i	$0.507273\pi$
$542$	−7.81927e16	−0.132486
$543$	−6.55500e16	−0.109742
$544$	9.74942e17	1.61282
$545$	9.73752e17	1.59174
$546$	1.68446e16	0.0272088
$547$	−4.19740e17	−0.669981	−0.334991	−	0.942221i	$-0.608733\pi$
$547$	−4.19740e17	−0.669981	−0.334991	+	0.942221i	$0.608733\pi$
$548$	9.96435e17	1.57172
$549$	−3.50533e17	−0.546397
$550$	−1.44308e17	−0.222297
$551$	7.93018e17	1.20725
$552$	4.61337e16	0.0694087
$553$	−1.33610e18	−1.98667
$554$	−5.10124e17	−0.749656
$555$	6.35366e17	0.922825
$556$	3.10849e16	0.0446235
$557$	1.02642e18	1.45635	0.728173	−	0.685393i	$-0.240370\pi$
$557$	1.02642e18	1.45635	0.728173	+	0.685393i	$0.240370\pi$
$558$	−3.66471e15	−0.00513945
$559$	2.37577e16	0.0329327
$560$	−6.69071e17	−0.916749
$561$	1.19980e18	1.62499
$562$	−6.24445e16	−0.0836003
$563$	−3.37558e17	−0.446729	−0.223364	−	0.974735i	$-0.571704\pi$
$563$	−3.37558e17	−0.446729	−0.223364	+	0.974735i	$0.571704\pi$
$564$	−2.72375e17	−0.356330
$565$	−1.36789e18	−1.76903
$566$	−3.15007e16	−0.0402729
$567$	−1.52246e17	−0.192422
$568$	−8.69298e17	−1.08619
$569$	2.22383e17	0.274708	0.137354	−	0.990522i	$-0.456140\pi$
$569$	2.22383e17	0.274708	0.137354	+	0.990522i	$0.456140\pi$
$570$	−1.75899e17	−0.214821
$571$	9.51406e17	1.14877	0.574383	−	0.818587i	$-0.305242\pi$
$571$	9.51406e17	1.14877	0.574383	+	0.818587i	$0.305242\pi$
$572$	7.32793e16	0.0874797
$573$	−7.12842e17	−0.841372
$574$	−7.59693e17	−0.886565
$575$	3.88308e16	0.0448059
$576$	−9.46049e15	−0.0107936
$577$	8.05161e15	0.00908322	0.00454161	−	0.999990i	$-0.498554\pi$
$577$	8.05161e15	0.00908322	0.00454161	+	0.999990i	$0.498554\pi$
$578$	6.41731e17	0.715850
$579$	−9.05607e17	−0.998917
$580$	−1.35987e18	−1.48326
$581$	9.52111e17	1.02693
$582$	−1.12020e17	−0.119480
$583$	2.37738e17	0.250757
$584$	1.54253e17	0.160898
$585$	2.29325e16	0.0236558
$586$	1.13902e17	0.116197
$587$	−7.16555e17	−0.722939	−0.361469	−	0.932384i	$-0.617725\pi$
$587$	−7.16555e17	−0.722939	−0.361469	+	0.932384i	$0.617725\pi$
$588$	9.36604e17	0.934552
$589$	−2.68522e16	−0.0264991
$590$	−6.61967e16	−0.0646098
$591$	−5.37843e17	−0.519203
$592$	−6.84720e17	−0.653765
$593$	1.49489e18	1.41173	0.705866	−	0.708345i	$-0.250558\pi$
$593$	1.49489e18	1.41173	0.705866	+	0.708345i	$0.250558\pi$
$594$	1.55660e17	0.145401
$595$	−3.46534e18	−3.20174
$596$	−3.18647e17	−0.291212
$597$	4.73735e17	0.428255
$598$	4.63425e15	0.00414402
$599$	1.51378e18	1.33902	0.669512	−	0.742801i	$-0.266503\pi$
$599$	1.51378e18	1.33902	0.669512	+	0.742801i	$0.266503\pi$
$600$	1.53262e17	0.134107
$601$	−2.90568e17	−0.251515	−0.125758	−	0.992061i	$-0.540136\pi$
$601$	−2.90568e17	−0.251515	−0.125758	+	0.992061i	$0.540136\pi$
$602$	−4.65765e17	−0.398832
$603$	1.05537e16	0.00894009
$604$	−5.22585e17	−0.437942
$605$	2.74379e18	2.27479
$606$	−4.12682e17	−0.338488
$607$	3.89647e17	0.316188	0.158094	−	0.987424i	$-0.449465\pi$
$607$	3.89647e17	0.316188	0.158094	+	0.987424i	$0.449465\pi$
$608$	9.26805e17	0.744072
$609$	2.02691e18	1.60999
$610$	−1.03514e18	−0.813494
$611$	−6.11520e16	−0.0475491
$612$	−5.70125e17	−0.438617
$613$	3.31013e17	0.251972	0.125986	−	0.992032i	$-0.459791\pi$
$613$	3.31013e17	0.251972	0.125986	+	0.992032i	$0.459791\pi$
$614$	−1.06895e18	−0.805126
$615$	−1.03426e18	−0.770797
$616$	−3.21090e18	−2.36784
$617$	−2.30491e18	−1.68190	−0.840952	−	0.541109i	$-0.818004\pi$
$617$	−2.30491e18	−1.68190	−0.840952	+	0.541109i	$0.818004\pi$
$618$	−2.61661e16	−0.0188936
$619$	1.02217e17	0.0730352	0.0365176	−	0.999333i	$-0.488373\pi$
$619$	1.02217e17	0.0730352	0.0365176	+	0.999333i	$0.488373\pi$
$620$	4.60464e16	0.0325574
$621$	−4.18854e16	−0.0293067
$622$	−5.94609e17	−0.411713
$623$	−6.85046e17	−0.469405
$624$	−2.47138e16	−0.0167587
$625$	−1.79955e18	−1.20766
$626$	1.15305e18	0.765798
$627$	1.14056e18	0.749687
$628$	2.00445e18	1.30394
$629$	−3.54639e18	−2.28327
$630$	−4.49587e17	−0.286484
$631$	−2.06481e18	−1.30224	−0.651119	−	0.758976i	$-0.725700\pi$
$631$	−2.06481e18	−1.30224	−0.651119	+	0.758976i	$0.725700\pi$
$632$	−1.45082e18	−0.905635
$633$	2.25522e16	0.0139336
$634$	4.78309e17	0.292501
$635$	−1.35062e18	−0.817531
$636$	−1.12969e17	−0.0676842
$637$	2.10281e17	0.124708
$638$	−2.07237e18	−1.21656
$639$	7.89247e17	0.458625
$640$	−1.99075e18	−1.14511
$641$	2.74428e18	1.56261	0.781306	−	0.624149i	$-0.214554\pi$
$641$	2.74428e18	1.56261	0.781306	+	0.624149i	$0.214554\pi$
$642$	4.96179e17	0.279680
$643$	5.66233e17	0.315954	0.157977	−	0.987443i	$-0.449503\pi$
$643$	5.66233e17	0.315954	0.157977	+	0.987443i	$0.449503\pi$
$644$	3.86571e17	0.213536
$645$	−6.34099e17	−0.346752
$646$	9.81804e17	0.531512
$647$	−1.70444e18	−0.913491	−0.456745	−	0.889597i	$-0.650985\pi$
$647$	−1.70444e18	−0.913491	−0.456745	+	0.889597i	$0.650985\pi$
$648$	−1.65318e17	−0.0877169
$649$	4.29233e17	0.225477
$650$	1.53956e16	0.00800680
$651$	−6.86329e16	−0.0353391
$652$	−1.47757e18	−0.753247
$653$	1.24185e18	0.626804	0.313402	−	0.949620i	$-0.398531\pi$
$653$	1.24185e18	0.626804	0.313402	+	0.949620i	$0.398531\pi$
$654$	−7.05146e17	−0.352390
$655$	−6.44991e17	−0.319143
$656$	1.11459e18	0.546062
$657$	−1.40048e17	−0.0679364
$658$	1.19887e18	0.575844
$659$	2.19988e18	1.04627	0.523134	−	0.852250i	$-0.324763\pi$
$659$	2.19988e18	1.04627	0.523134	+	0.852250i	$0.324763\pi$
$660$	−1.95584e18	−0.921082
$661$	1.41911e18	0.661770	0.330885	−	0.943671i	$-0.392653\pi$
$661$	1.41911e18	0.661770	0.330885	+	0.943671i	$0.392653\pi$
$662$	−5.11715e17	−0.236293
$663$	−1.28001e17	−0.0585296
$664$	1.03386e18	0.468135
$665$	−3.29424e18	−1.47712
$666$	−4.60102e17	−0.204302
$667$	5.57638e17	0.245208
$668$	2.53179e18	1.10250
$669$	4.47459e17	0.192967
$670$	3.11655e16	0.0133103
$671$	6.71205e18	2.83896
$672$	2.36886e18	0.992293
$673$	−3.61377e18	−1.49921	−0.749605	−	0.661885i	$-0.769756\pi$
$673$	−3.61377e18	−1.49921	−0.749605	+	0.661885i	$0.769756\pi$
$674$	1.00366e18	0.412378
$675$	−1.39149e17	−0.0566245
$676$	2.00117e18	0.806550
$677$	−1.28727e18	−0.513858	−0.256929	−	0.966430i	$-0.582711\pi$
$677$	−1.28727e18	−0.513858	−0.256929	+	0.966430i	$0.582711\pi$
$678$	9.90561e17	0.391641
$679$	−2.09792e18	−0.821551
$680$	−3.76289e18	−1.45953
$681$	1.47676e18	0.567354
$682$	7.01723e16	0.0267034
$683$	−1.78382e17	−0.0672384	−0.0336192	−	0.999435i	$-0.510703\pi$
$683$	−1.78382e17	−0.0672384	−0.0336192	+	0.999435i	$0.510703\pi$
$684$	−5.41975e17	−0.202355
$685$	−5.97097e18	−2.20829
$686$	−2.06036e18	−0.754807
$687$	−2.05970e17	−0.0747455
$688$	6.83354e17	0.245652
$689$	−2.53631e16	−0.00903186
$690$	−1.23689e17	−0.0436328
$691$	−3.98126e18	−1.39127	−0.695637	−	0.718393i	$-0.744878\pi$
$691$	−3.98126e18	−1.39127	−0.695637	+	0.718393i	$0.744878\pi$
$692$	−2.68472e17	−0.0929416
$693$	2.91522e18	0.999781
$694$	2.15346e18	0.731646
$695$	−1.86271e17	−0.0626967
$696$	2.20095e18	0.733924
$697$	5.77285e18	1.90712
$698$	2.39152e18	0.782735
$699$	1.66425e18	0.539654
$700$	1.28424e18	0.412580
$701$	−2.72040e18	−0.865895	−0.432947	−	0.901419i	$-0.642526\pi$
$701$	−2.72040e18	−0.865895	−0.432947	+	0.901419i	$0.642526\pi$
$702$	−1.66066e16	−0.00523710
$703$	−3.37129e18	−1.05338
$704$	1.81151e17	0.0560813
$705$	1.63216e18	0.500650
$706$	−1.61838e18	−0.491870
$707$	−7.72873e18	−2.32746
$708$	−2.03964e17	−0.0608608
$709$	3.78329e18	1.11859	0.559293	−	0.828970i	$-0.311073\pi$
$709$	3.78329e18	1.11859	0.559293	+	0.828970i	$0.311073\pi$
$710$	2.33068e18	0.682815
$711$	1.31722e18	0.382390
$712$	−7.43868e17	−0.213981
$713$	−1.88821e16	−0.00538230
$714$	2.50944e18	0.708823
$715$	−4.39114e17	−0.122910
$716$	5.89473e17	0.163504
$717$	1.87820e18	0.516259
$718$	−2.48987e18	−0.678215
$719$	−5.92790e18	−1.60016	−0.800079	−	0.599895i	$-0.795209\pi$
$719$	−5.92790e18	−1.60016	−0.800079	+	0.599895i	$0.795209\pi$
$720$	6.59619e17	0.176454
$721$	−4.90041e17	−0.129913
$722$	−7.27064e17	−0.191021
$723$	5.13737e17	0.133765
$724$	−5.96430e17	−0.153907
$725$	1.85255e18	0.473775
$726$	−1.98692e18	−0.503609
$727$	−1.64674e18	−0.413669	−0.206834	−	0.978376i	$-0.566316\pi$
$727$	−1.64674e18	−0.413669	−0.206834	+	0.978376i	$0.566316\pi$
$728$	3.42555e17	0.0852858
$729$	1.50095e17	0.0370370
$730$	−4.13568e17	−0.101146
$731$	3.53931e18	0.857939
$732$	−3.18945e18	−0.766290
$733$	3.18011e18	0.757296	0.378648	−	0.925541i	$-0.376389\pi$
$733$	3.18011e18	0.757296	0.378648	+	0.925541i	$0.376389\pi$
$734$	−4.10406e17	−0.0968699
$735$	−5.61245e18	−1.31306
$736$	6.51715e17	0.151131
$737$	−2.02084e17	−0.0464507
$738$	7.48960e17	0.170645
$739$	−4.55441e18	−1.02859	−0.514296	−	0.857613i	$-0.671947\pi$
$739$	−4.55441e18	−1.02859	−0.514296	+	0.857613i	$0.671947\pi$
$740$	5.78110e18	1.29421
$741$	−1.21681e17	−0.0270026
$742$	4.97239e17	0.109380
$743$	−4.15267e17	−0.0905525	−0.0452762	−	0.998975i	$-0.514417\pi$
$743$	−4.15267e17	−0.0905525	−0.0452762	+	0.998975i	$0.514417\pi$
$744$	−7.45261e16	−0.0161096
$745$	1.90944e18	0.409157
$746$	3.34638e17	0.0710841
$747$	−9.38660e17	−0.197663
$748$	1.09168e19	2.27896
$749$	9.29248e18	1.92309
$750$	9.85656e17	0.202221
$751$	−3.75814e18	−0.764386	−0.382193	−	0.924082i	$-0.624831\pi$
$751$	−3.75814e18	−0.764386	−0.382193	+	0.924082i	$0.624831\pi$
$752$	−1.75894e18	−0.354680
$753$	−1.82177e18	−0.364189
$754$	2.21092e17	0.0438186
$755$	3.13151e18	0.615316
$756$	−1.38526e18	−0.269861
$757$	−7.53010e18	−1.45438	−0.727190	−	0.686436i	$-0.759174\pi$
$757$	−7.53010e18	−1.45438	−0.727190	+	0.686436i	$0.759174\pi$
$758$	−2.29456e18	−0.439390
$759$	8.02027e17	0.152271
$760$	−3.57710e18	−0.673353
$761$	3.68111e17	0.0687035	0.0343518	−	0.999410i	$-0.489063\pi$
$761$	3.68111e17	0.0687035	0.0343518	+	0.999410i	$0.489063\pi$
$762$	9.78057e17	0.180991
$763$	−1.32060e19	−2.42305
$764$	−6.48605e18	−1.17998
$765$	3.41638e18	0.616264
$766$	−1.47005e18	−0.262933
$767$	−4.57929e16	−0.00812134
$768$	1.33530e18	0.234817
$769$	9.13345e18	1.59263	0.796313	−	0.604885i	$-0.206781\pi$
$769$	9.13345e18	1.59263	0.796313	+	0.604885i	$0.206781\pi$
$770$	8.60876e18	1.48851
$771$	6.83448e17	0.117180
$772$	−8.23999e18	−1.40092
$773$	−3.94572e18	−0.665212	−0.332606	−	0.943066i	$-0.607928\pi$
$773$	−3.94572e18	−0.665212	−0.332606	+	0.943066i	$0.607928\pi$
$774$	4.59185e17	0.0767664
$775$	−6.27288e16	−0.0103993
$776$	−2.27805e18	−0.374509
$777$	−8.61683e18	−1.40479
$778$	3.54690e18	0.573432
$779$	5.48782e18	0.879846
$780$	2.08660e17	0.0331759
$781$	−1.51126e19	−2.38291
$782$	6.90390e17	0.107957
$783$	−1.99828e18	−0.309887
$784$	6.04842e18	0.930223
$785$	−1.20114e19	−1.83206
$786$	4.67073e17	0.0706542
$787$	4.37670e18	0.656615	0.328308	−	0.944571i	$-0.393522\pi$
$787$	4.37670e18	0.656615	0.328308	+	0.944571i	$0.393522\pi$
$788$	−4.89376e18	−0.728152
$789$	−6.27095e18	−0.925408
$790$	3.88981e18	0.569315
$791$	1.85513e19	2.69294
$792$	3.16553e18	0.455757
$793$	−7.16076e17	−0.102255
$794$	−1.93813e18	−0.274504
$795$	6.76947e17	0.0950974
$796$	4.31044e18	0.600602
$797$	1.39323e18	0.192550	0.0962751	−	0.995355i	$-0.469307\pi$
$797$	1.39323e18	0.192550	0.0962751	+	0.995355i	$0.469307\pi$
$798$	2.38554e18	0.327015
$799$	−9.11015e18	−1.23871
$800$	2.16508e18	0.292005
$801$	6.75368e17	0.0903502
$802$	−2.88685e18	−0.383081
$803$	2.68166e18	0.352982
$804$	9.60266e16	0.0125380
$805$	−2.31646e18	−0.300021
$806$	−7.48634e15	−0.000961816 0
$807$	8.01672e18	1.02169
$808$	−8.39236e18	−1.06099
$809$	1.51208e19	1.89631	0.948154	−	0.317813i	$-0.102948\pi$
$809$	1.51208e19	1.89631	0.948154	+	0.317813i	$0.102948\pi$
$810$	4.43236e17	0.0551419
$811$	1.55860e19	1.92352	0.961762	−	0.273885i	$-0.0883089\pi$
$811$	1.55860e19	1.92352	0.961762	+	0.273885i	$0.0883089\pi$
$812$	1.84426e19	2.25791
$813$	1.44371e18	0.175344
$814$	8.81010e18	1.06151
$815$	8.85407e18	1.05832
$816$	−3.68176e18	−0.436586
$817$	3.36456e18	0.395809
$818$	3.26781e18	0.381382
$819$	−3.11011e17	−0.0360106
$820$	−9.41055e18	−1.08100
$821$	2.41807e18	0.275574	0.137787	−	0.990462i	$-0.456001\pi$
$821$	2.41807e18	0.275574	0.137787	+	0.990462i	$0.456001\pi$
$822$	4.32390e18	0.488888
$823$	−3.48773e18	−0.391241	−0.195621	−	0.980680i	$-0.562672\pi$
$823$	−3.48773e18	−0.391241	−0.195621	+	0.980680i	$0.562672\pi$
$824$	−5.32118e17	−0.0592218
$825$	2.66444e18	0.294208
$826$	8.97760e17	0.0983536
$827$	−1.15041e19	−1.25045	−0.625223	−	0.780446i	$-0.714992\pi$
$827$	−1.15041e19	−1.25045	−0.625223	+	0.780446i	$0.714992\pi$
$828$	−3.81109e17	−0.0411010
$829$	2.18971e18	0.234305	0.117153	−	0.993114i	$-0.462623\pi$
$829$	2.18971e18	0.234305	0.117153	+	0.993114i	$0.462623\pi$
$830$	−2.77190e18	−0.294286
$831$	9.41866e18	0.992162
$832$	−1.93261e16	−0.00201996
$833$	3.13267e19	3.24880
$834$	1.34889e17	0.0138803
$835$	−1.51713e19	−1.54904
$836$	1.03778e19	1.05139
$837$	6.76632e16	0.00680201
$838$	3.01286e18	0.300534
$839$	7.57490e18	0.749763	0.374882	−	0.927073i	$-0.377683\pi$
$839$	7.57490e18	0.749763	0.374882	+	0.927073i	$0.377683\pi$
$840$	−9.14288e18	−0.897982
$841$	1.63433e19	1.59282
$842$	5.98936e18	0.579231
$843$	1.15294e18	0.110644
$844$	2.05199e17	0.0195411
$845$	−1.19917e19	−1.13322
$846$	−1.18194e18	−0.110837
$847$	−3.72113e19	−3.46284
$848$	−7.29531e17	−0.0673707
$849$	5.81612e17	0.0533008
$850$	2.29356e18	0.208587
$851$	−2.37064e18	−0.213955
$852$	7.18125e18	0.643195
$853$	−8.81050e18	−0.783127	−0.391563	−	0.920151i	$-0.628066\pi$
$853$	−8.81050e18	−0.783127	−0.391563	+	0.920151i	$0.628066\pi$
$854$	1.40385e19	1.23836
$855$	3.24770e18	0.284313
$856$	1.00904e19	0.876654
$857$	−1.14302e19	−0.985547	−0.492773	−	0.870158i	$-0.664017\pi$
$857$	−1.14302e19	−0.985547	−0.492773	+	0.870158i	$0.664017\pi$
$858$	3.17986e17	0.0272108
$859$	−2.00379e19	−1.70175	−0.850876	−	0.525366i	$-0.823928\pi$
$859$	−2.00379e19	−1.70175	−0.850876	+	0.525366i	$0.823928\pi$
$860$	−5.76957e18	−0.486299
$861$	1.40266e19	1.17336
$862$	−7.73730e18	−0.642380
$863$	−9.43378e18	−0.777349	−0.388674	−	0.921375i	$-0.627067\pi$
$863$	−9.43378e18	−0.777349	−0.388674	+	0.921375i	$0.627067\pi$
$864$	−2.33540e18	−0.190995
$865$	1.60878e18	0.130584
$866$	7.67165e18	0.618049
$867$	−1.18486e19	−0.947421
$868$	−6.24481e17	−0.0495611
$869$	−2.52223e19	−1.98681
$870$	−5.90099e18	−0.461370
$871$	2.15593e16	0.00167308
$872$	−1.43400e19	−1.10456
$873$	2.06828e18	0.158131
$874$	6.56302e17	0.0498058
$875$	1.84594e19	1.39049
$876$	−1.27428e18	−0.0952769
$877$	−9.99454e18	−0.741764	−0.370882	−	0.928680i	$-0.620944\pi$
$877$	−9.99454e18	−0.741764	−0.370882	+	0.928680i	$0.620944\pi$
$878$	7.85778e18	0.578876
$879$	−2.10302e18	−0.153786
$880$	−1.26305e19	−0.916816
$881$	−1.65985e19	−1.19598	−0.597991	−	0.801503i	$-0.704034\pi$
$881$	−1.65985e19	−1.19598	−0.597991	+	0.801503i	$0.704034\pi$
$882$	4.06428e18	0.290695
$883$	−2.07107e19	−1.47045	−0.735223	−	0.677825i	$-0.762923\pi$
$883$	−2.07107e19	−1.47045	−0.735223	+	0.677825i	$0.762923\pi$
$884$	−1.16466e18	−0.0820844
$885$	1.22222e18	0.0855104
$886$	−2.95947e17	−0.0205539
$887$	−2.46265e18	−0.169785	−0.0848925	−	0.996390i	$-0.527055\pi$
$887$	−2.46265e18	−0.169785	−0.0848925	+	0.996390i	$0.527055\pi$
$888$	−9.35672e18	−0.640382
$889$	1.83171e19	1.24450
$890$	1.99439e18	0.134516
$891$	−2.87403e18	−0.192436
$892$	4.07136e18	0.270625
$893$	−8.66034e18	−0.571479
$894$	−1.38273e18	−0.0905822
$895$	−3.53232e18	−0.229726
$896$	2.69985e19	1.74316
$897$	−8.55644e16	−0.00548456
$898$	−1.11629e19	−0.710363
$899$	−9.00831e17	−0.0569122
$900$	−1.26609e18	−0.0794126
$901$	−3.77848e18	−0.235291
$902$	−1.43412e19	−0.886630
$903$	8.59965e18	0.527850
$904$	2.01442e19	1.22760
$905$	3.57401e18	0.216242
$906$	−2.26769e18	−0.136223
$907$	9.10587e18	0.543093	0.271546	−	0.962425i	$-0.412465\pi$
$907$	9.10587e18	0.543093	0.271546	+	0.962425i	$0.412465\pi$
$908$	1.34368e19	0.795681
$909$	7.61954e18	0.447985
$910$	−9.18427e17	−0.0536137
$911$	1.08145e19	0.626813	0.313407	−	0.949619i	$-0.398530\pi$
$911$	1.08145e19	0.626813	0.313407	+	0.949619i	$0.398530\pi$
$912$	−3.49998e18	−0.201418
$913$	1.79736e19	1.02701
$914$	5.16851e18	0.293234
$915$	1.91122e19	1.07665
$916$	−1.87409e18	−0.104826
$917$	8.74738e18	0.485822
$918$	−2.47398e18	−0.136433
$919$	−6.28434e18	−0.344119	−0.172060	−	0.985087i	$-0.555042\pi$
$919$	−6.28434e18	−0.344119	−0.172060	+	0.985087i	$0.555042\pi$
$920$	−2.51537e18	−0.136767
$921$	1.97366e19	1.06558
$922$	−1.10251e19	−0.591060
$923$	1.61229e18	0.0858287
$924$	2.65251e19	1.40214
$925$	−7.87557e18	−0.413391
$926$	−8.13234e18	−0.423881
$927$	4.83118e17	0.0250054
$928$	3.10922e19	1.59805
$929$	−2.70811e19	−1.38218	−0.691090	−	0.722769i	$-0.742869\pi$
$929$	−2.70811e19	−1.38218	−0.691090	+	0.722769i	$0.742869\pi$
$930$	1.99812e17	0.0101271
$931$	2.97800e19	1.49883
$932$	1.51427e19	0.756834
$933$	1.09786e19	0.544898
$934$	7.19759e18	0.354758
$935$	−6.54173e19	−3.20197
$936$	−3.37716e17	−0.0164157
$937$	2.81216e18	0.135748	0.0678738	−	0.997694i	$-0.478378\pi$
$937$	2.81216e18	0.135748	0.0678738	+	0.997694i	$0.478378\pi$
$938$	−4.22667e17	−0.0202619
$939$	−2.12893e19	−1.01353
$940$	1.48508e19	0.702132
$941$	−5.77022e18	−0.270932	−0.135466	−	0.990782i	$-0.543253\pi$
$941$	−5.77022e18	−0.270932	−0.135466	+	0.990782i	$0.543253\pi$
$942$	8.69807e18	0.405595
$943$	3.85895e18	0.178708
$944$	−1.31716e18	−0.0605789
$945$	8.30095e18	0.379159
$946$	−8.79253e18	−0.398861
$947$	3.28036e19	1.47791	0.738953	−	0.673757i	$-0.235320\pi$
$947$	3.28036e19	1.47791	0.738953	+	0.673757i	$0.235320\pi$
$948$	1.19852e19	0.536280
$949$	−2.86093e17	−0.0127139
$950$	2.18032e18	0.0962315
$951$	−8.83124e18	−0.387123
$952$	5.10323e19	2.22180
$953$	−2.07704e19	−0.898133	−0.449066	−	0.893498i	$-0.648243\pi$
$953$	−2.07704e19	−0.898133	−0.449066	+	0.893498i	$0.648243\pi$
$954$	−4.90214e17	−0.0210533
$955$	3.88666e19	1.65789
$956$	1.70895e19	0.724024
$957$	3.82632e19	1.61010
$958$	−6.90028e18	−0.288397
$959$	8.09784e19	3.36162
$960$	5.15818e17	0.0212684
$961$	−2.43870e19	−0.998751
$962$	−9.39907e17	−0.0382338
$963$	−9.16120e18	−0.370153
$964$	4.67442e18	0.187598
$965$	4.93768e19	1.96832
$966$	1.67747e18	0.0664208
$967$	3.81385e19	1.50000	0.750000	−	0.661438i	$-0.230053\pi$
$967$	3.81385e19	1.50000	0.750000	+	0.661438i	$0.230053\pi$
$968$	−4.04064e19	−1.57856
$969$	−1.81275e19	−0.703451
$970$	6.10770e18	0.235430
$971$	−4.46309e19	−1.70888	−0.854439	−	0.519553i	$-0.826099\pi$
$971$	−4.46309e19	−1.70888	−0.854439	+	0.519553i	$0.826099\pi$
$972$	1.36569e18	0.0519423
$973$	2.52621e18	0.0954414
$974$	−1.30421e18	−0.0489455
$975$	−2.84256e17	−0.0105969
$976$	−2.05968e19	−0.762741
$977$	−3.29520e19	−1.21218	−0.606089	−	0.795397i	$-0.707263\pi$
$977$	−3.29520e19	−1.21218	−0.606089	+	0.795397i	$0.707263\pi$
$978$	−6.41171e18	−0.234299
$979$	−1.29320e19	−0.469439
$980$	−5.10669e19	−1.84149
$981$	1.30195e19	0.466385
$982$	−2.00234e19	−0.712546
$983$	−6.62960e18	−0.234363	−0.117182	−	0.993111i	$-0.537386\pi$
$983$	−6.62960e18	−0.234363	−0.117182	+	0.993111i	$0.537386\pi$
$984$	1.52310e19	0.534884
$985$	2.93251e19	1.02307
$986$	3.29372e19	1.14153
$987$	−2.21354e19	−0.762124
$988$	−1.10716e18	−0.0378695
$989$	2.36591e18	0.0803938
$990$	−8.48713e18	−0.286505
$991$	1.82552e19	0.612221	0.306110	−	0.951996i	$-0.400972\pi$
$991$	1.82552e19	0.612221	0.306110	+	0.951996i	$0.400972\pi$
$992$	−1.05281e18	−0.0350770
$993$	9.44804e18	0.312731
$994$	−3.16087e19	−1.03943
$995$	−2.58296e19	−0.843856
$996$	−8.54073e18	−0.277210
$997$	2.75990e19	0.889968	0.444984	−	0.895538i	$-0.353209\pi$
$997$	2.75990e19	0.889968	0.444984	+	0.895538i	$0.353209\pi$
$998$	−1.04474e19	−0.334705
$999$	8.49509e18	0.270391

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.b.1.19	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.b.1.19	✓	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)

\(f(q)\)	\(=\)	\(q+39.4833 q^{2} -729.000 q^{3} -6633.07 q^{4} +39747.6 q^{5} -28783.4 q^{6} -539057. q^{7} -585343. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+39.4833 q^{2} -729.000 q^{3} -6633.07 q^{4} +39747.6 q^{5} -28783.4 q^{6} -539057. q^{7} -585343. q^{8} +531441. q^{9} +1.56937e6 q^{10} -1.01761e7 q^{11} +4.83551e6 q^{12} +1.08564e6 q^{13} -2.12838e7 q^{14} -2.89760e7 q^{15} +3.12268e7 q^{16} +1.61734e8 q^{17} +2.09831e7 q^{18} +1.53748e8 q^{19} -2.63648e8 q^{20} +3.92972e8 q^{21} -4.01786e8 q^{22} +1.08113e8 q^{23} +4.26715e8 q^{24} +3.59167e8 q^{25} +4.28647e7 q^{26} -3.87420e8 q^{27} +3.57560e9 q^{28} +5.15790e9 q^{29} -1.14407e9 q^{30} -1.74651e8 q^{31} +6.02807e9 q^{32} +7.41838e9 q^{33} +6.38579e9 q^{34} -2.14262e10 q^{35} -3.52508e9 q^{36} -2.19273e10 q^{37} +6.07049e9 q^{38} -7.91431e8 q^{39} -2.32660e10 q^{40} +3.56936e10 q^{41} +1.55159e10 q^{42} +2.18836e10 q^{43} +6.74987e10 q^{44} +2.11235e10 q^{45} +4.26868e9 q^{46} -5.63281e10 q^{47} -2.27643e10 q^{48} +1.93693e11 q^{49} +1.41811e10 q^{50} -1.17904e11 q^{51} -7.20112e9 q^{52} -2.33624e10 q^{53} -1.52967e10 q^{54} -4.04475e11 q^{55} +3.15533e11 q^{56} -1.12082e11 q^{57} +2.03651e11 q^{58} -4.21805e10 q^{59} +1.92200e11 q^{60} -6.59589e11 q^{61} -6.89579e9 q^{62} -2.86477e11 q^{63} -1.78016e10 q^{64} +4.31515e10 q^{65} +2.92902e11 q^{66} +1.98586e10 q^{67} -1.07279e12 q^{68} -7.88147e10 q^{69} -8.45978e11 q^{70} +1.48511e12 q^{71} -3.11075e11 q^{72} -2.63525e11 q^{73} -8.65764e11 q^{74} -2.61833e11 q^{75} -1.01982e12 q^{76} +5.48550e12 q^{77} -3.12483e10 q^{78} +2.47859e12 q^{79} +1.24119e12 q^{80} +2.82430e11 q^{81} +1.40930e12 q^{82} -1.76625e12 q^{83} -2.60661e12 q^{84} +6.42852e12 q^{85} +8.64037e11 q^{86} -3.76011e12 q^{87} +5.95651e12 q^{88} +1.27082e12 q^{89} +8.34026e11 q^{90} -5.85221e11 q^{91} -7.17124e11 q^{92} +1.27320e11 q^{93} -2.22402e12 q^{94} +6.11112e12 q^{95} -4.39446e12 q^{96} +3.89183e12 q^{97} +7.64765e12 q^{98} -5.40800e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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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