LMFDB - Embedded newform 177.14.a.b.1.18

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			1.18
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)

$f(q)$	$=$	$q+32.0352 q^{2} -729.000 q^{3} -7165.75 q^{4} +52348.2 q^{5} -23353.7 q^{6} +485703. q^{7} -491988. q^{8} +531441. q^{9} +O(q^{10})$	\(q+32.0352 q^{2} -729.000 q^{3} -7165.75 q^{4} +52348.2 q^{5} -23353.7 q^{6} +485703. q^{7} -491988. q^{8} +531441. q^{9} +1.67699e6 q^{10} +7.71041e6 q^{11} +5.22383e6 q^{12} -1.68471e7 q^{13} +1.55596e7 q^{14} -3.81619e7 q^{15} +4.29408e7 q^{16} +1.67050e7 q^{17} +1.70248e7 q^{18} -1.60720e8 q^{19} -3.75114e8 q^{20} -3.54078e8 q^{21} +2.47005e8 q^{22} -7.81810e8 q^{23} +3.58660e8 q^{24} +1.51963e9 q^{25} -5.39701e8 q^{26} -3.87420e8 q^{27} -3.48042e9 q^{28} -4.88831e9 q^{29} -1.22252e9 q^{30} -5.16656e9 q^{31} +5.40599e9 q^{32} -5.62089e9 q^{33} +5.35148e8 q^{34} +2.54257e10 q^{35} -3.80817e9 q^{36} -1.18340e10 q^{37} -5.14870e9 q^{38} +1.22816e10 q^{39} -2.57547e10 q^{40} +3.96298e10 q^{41} -1.13429e10 q^{42} -4.22888e10 q^{43} -5.52509e10 q^{44} +2.78200e10 q^{45} -2.50454e10 q^{46} -1.14604e11 q^{47} -3.13039e10 q^{48} +1.39018e11 q^{49} +4.86818e10 q^{50} -1.21779e10 q^{51} +1.20722e11 q^{52} -1.15968e11 q^{53} -1.24111e10 q^{54} +4.03626e11 q^{55} -2.38960e11 q^{56} +1.17165e11 q^{57} -1.56598e11 q^{58} -4.21805e10 q^{59} +2.73458e11 q^{60} -1.57307e11 q^{61} -1.65512e11 q^{62} +2.58123e11 q^{63} -1.78589e11 q^{64} -8.81918e11 q^{65} -1.80066e11 q^{66} -1.15507e12 q^{67} -1.19704e11 q^{68} +5.69939e11 q^{69} +8.14517e11 q^{70} +1.50486e12 q^{71} -2.61463e11 q^{72} +1.68360e12 q^{73} -3.79106e11 q^{74} -1.10781e12 q^{75} +1.15168e12 q^{76} +3.74497e12 q^{77} +3.93442e11 q^{78} +1.28585e12 q^{79} +2.24788e12 q^{80} +2.82430e11 q^{81} +1.26955e12 q^{82} +3.33442e12 q^{83} +2.53723e12 q^{84} +8.74477e11 q^{85} -1.35473e12 q^{86} +3.56358e12 q^{87} -3.79343e12 q^{88} -6.70262e12 q^{89} +8.91219e11 q^{90} -8.18271e12 q^{91} +5.60225e12 q^{92} +3.76642e12 q^{93} -3.67135e12 q^{94} -8.41341e12 q^{95} -3.94097e12 q^{96} -4.23961e12 q^{97} +4.45348e12 q^{98} +4.09763e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	32.0352	0.353942	0.176971	−	0.984216i	$-0.443370\pi$
$2$	32.0352	0.353942	0.176971	+	0.984216i	$0.443370\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	−7165.75	−0.874725
$5$	52348.2	1.49829	0.749147	−	0.662404i	$-0.230464\pi$
$5$	52348.2	1.49829	0.749147	+	0.662404i	$0.230464\pi$
$6$	−23353.7	−0.204349
$7$	485703.	1.56039	0.780196	−	0.625535i	$-0.215119\pi$
$7$	485703.	1.56039	0.780196	+	0.625535i	$0.215119\pi$
$8$	−491988.	−0.663544
$9$	531441.	0.333333
$10$	1.67699e6	0.530309
$11$	7.71041e6	1.31228	0.656138	−	0.754641i	$-0.272189\pi$
$11$	7.71041e6	1.31228	0.656138	+	0.754641i	$0.272189\pi$
$12$	5.22383e6	0.505023
$13$	−1.68471e7	−0.968042	−0.484021	−	0.875056i	$-0.660824\pi$
$13$	−1.68471e7	−0.968042	−0.484021	+	0.875056i	$0.660824\pi$
$14$	1.55596e7	0.552289
$15$	−3.81619e7	−0.865040
$16$	4.29408e7	0.639868
$17$	1.67050e7	0.167853	0.0839264	−	0.996472i	$-0.473254\pi$
$17$	1.67050e7	0.167853	0.0839264	+	0.996472i	$0.473254\pi$
$18$	1.70248e7	0.117981
$19$	−1.60720e8	−0.783740	−0.391870	−	0.920021i	$-0.628172\pi$
$19$	−1.60720e8	−0.783740	−0.391870	+	0.920021i	$0.628172\pi$
$20$	−3.75114e8	−1.31059
$21$	−3.54078e8	−0.900892
$22$	2.47005e8	0.464470
$23$	−7.81810e8	−1.10121	−0.550605	−	0.834766i	$-0.685603\pi$
$23$	−7.81810e8	−1.10121	−0.550605	+	0.834766i	$0.685603\pi$
$24$	3.58660e8	0.383098
$25$	1.51963e9	1.24488
$26$	−5.39701e8	−0.342631
$27$	−3.87420e8	−0.192450
$28$	−3.48042e9	−1.36491
$29$	−4.88831e9	−1.52606	−0.763031	−	0.646362i	$-0.776289\pi$
$29$	−4.88831e9	−1.52606	−0.763031	+	0.646362i	$0.776289\pi$
$30$	−1.22252e9	−0.306174
$31$	−5.16656e9	−1.04556	−0.522782	−	0.852467i	$-0.675106\pi$
$31$	−5.16656e9	−1.04556	−0.522782	+	0.852467i	$0.675106\pi$
$32$	5.40599e9	0.890021
$33$	−5.62089e9	−0.757643
$34$	5.35148e8	0.0594102
$35$	2.54257e10	2.33792
$36$	−3.80817e9	−0.291575
$37$	−1.18340e10	−0.758267	−0.379133	−	0.925342i	$-0.623778\pi$
$37$	−1.18340e10	−0.758267	−0.379133	+	0.925342i	$0.623778\pi$
$38$	−5.14870e9	−0.277399
$39$	1.22816e10	0.558899
$40$	−2.57547e10	−0.994184
$41$	3.96298e10	1.30295	0.651473	−	0.758672i	$-0.274151\pi$
$41$	3.96298e10	1.30295	0.651473	+	0.758672i	$0.274151\pi$
$42$	−1.13429e10	−0.318864
$43$	−4.22888e10	−1.02019	−0.510094	−	0.860119i	$-0.670389\pi$
$43$	−4.22888e10	−1.02019	−0.510094	+	0.860119i	$0.670389\pi$
$44$	−5.52509e10	−1.14788
$45$	2.78200e10	0.499431
$46$	−2.50454e10	−0.389765
$47$	−1.14604e11	−1.55083	−0.775413	−	0.631455i	$-0.782458\pi$
$47$	−1.14604e11	−1.55083	−0.775413	+	0.631455i	$0.782458\pi$
$48$	−3.13039e10	−0.369428
$49$	1.39018e11	1.43482
$50$	4.86818e10	0.440617
$51$	−1.21779e10	−0.0969099
$52$	1.20722e11	0.846771
$53$	−1.15968e11	−0.718695	−0.359347	−	0.933204i	$-0.617001\pi$
$53$	−1.15968e11	−0.718695	−0.359347	+	0.933204i	$0.617001\pi$
$54$	−1.24111e10	−0.0681162
$55$	4.03626e11	1.96617
$56$	−2.38960e11	−1.03539
$57$	1.17165e11	0.452492
$58$	−1.56598e11	−0.540138
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	2.73458e11	0.756672
$61$	−1.57307e11	−0.390934	−0.195467	−	0.980710i	$-0.562622\pi$
$61$	−1.57307e11	−0.390934	−0.195467	+	0.980710i	$0.562622\pi$
$62$	−1.65512e11	−0.370069
$63$	2.58123e11	0.520131
$64$	−1.78589e11	−0.324852
$65$	−8.81918e11	−1.45041
$66$	−1.80066e11	−0.268162
$67$	−1.15507e12	−1.55999	−0.779996	−	0.625784i	$-0.784779\pi$
$67$	−1.15507e12	−1.55999	−0.779996	+	0.625784i	$0.784779\pi$
$68$	−1.19704e11	−0.146825
$69$	5.69939e11	0.635784
$70$	8.14517e11	0.827490
$71$	1.50486e12	1.39417	0.697085	−	0.716988i	$-0.254480\pi$
$71$	1.50486e12	1.39417	0.697085	+	0.716988i	$0.254480\pi$
$72$	−2.61463e11	−0.221181
$73$	1.68360e12	1.30209	0.651043	−	0.759041i	$-0.274332\pi$
$73$	1.68360e12	1.30209	0.651043	+	0.759041i	$0.274332\pi$
$74$	−3.79106e11	−0.268383
$75$	−1.10781e12	−0.718734
$76$	1.15168e12	0.685557
$77$	3.74497e12	2.04766
$78$	3.93442e11	0.197818
$79$	1.28585e12	0.595135	0.297568	−	0.954701i	$-0.403825\pi$
$79$	1.28585e12	0.595135	0.297568	+	0.954701i	$0.403825\pi$
$80$	2.24788e12	0.958711
$81$	2.82430e11	0.111111
$82$	1.26955e12	0.461168
$83$	3.33442e12	1.11947	0.559736	−	0.828671i	$-0.310903\pi$
$83$	3.33442e12	1.11947	0.559736	+	0.828671i	$0.310903\pi$
$84$	2.53723e12	0.788033
$85$	8.74477e11	0.251493
$86$	−1.35473e12	−0.361087
$87$	3.56358e12	0.881072
$88$	−3.79343e12	−0.870753
$89$	−6.70262e12	−1.42958	−0.714792	−	0.699337i	$-0.753479\pi$
$89$	−6.70262e12	−1.42958	−0.714792	+	0.699337i	$0.753479\pi$
$90$	8.91219e11	0.176770
$91$	−8.18271e12	−1.51052
$92$	5.60225e12	0.963256
$93$	3.76642e12	0.603656
$94$	−3.67135e12	−0.548903
$95$	−8.41341e12	−1.17427
$96$	−3.94097e12	−0.513854
$97$	−4.23961e12	−0.516784	−0.258392	−	0.966040i	$-0.583193\pi$
$97$	−4.23961e12	−0.516784	−0.258392	+	0.966040i	$0.583193\pi$
$98$	4.45348e12	0.507844
$99$	4.09763e12	0.437425
$100$	−1.08893e13	−1.08893
$101$	1.56745e13	1.46928	0.734642	−	0.678455i	$-0.237350\pi$
$101$	1.56745e13	1.46928	0.734642	+	0.678455i	$0.237350\pi$
$102$	−3.90123e11	−0.0343005
$103$	1.97494e13	1.62971	0.814856	−	0.579663i	$-0.196816\pi$
$103$	1.97494e13	1.62971	0.814856	+	0.579663i	$0.196816\pi$
$104$	8.28860e12	0.642339
$105$	−1.85353e13	−1.34980
$106$	−3.71505e12	−0.254376
$107$	−2.33565e13	−1.50457	−0.752286	−	0.658836i	$-0.771049\pi$
$107$	−2.33565e13	−1.50457	−0.752286	+	0.658836i	$0.771049\pi$
$108$	2.77616e12	0.168341
$109$	−2.58309e13	−1.47525	−0.737627	−	0.675209i	$-0.764053\pi$
$109$	−2.58309e13	−1.47525	−0.737627	+	0.675209i	$0.764053\pi$
$110$	1.29303e13	0.695912
$111$	8.62702e12	0.437786
$112$	2.08565e13	0.998445
$113$	−4.19797e13	−1.89683	−0.948417	−	0.317027i	$-0.897315\pi$
$113$	−4.19797e13	−1.89683	−0.948417	+	0.317027i	$0.897315\pi$
$114$	3.75340e12	0.160156
$115$	−4.09264e13	−1.64994
$116$	3.50284e13	1.33488
$117$	−8.95326e12	−0.322681
$118$	−1.35126e12	−0.0460794
$119$	8.11367e12	0.261916
$120$	1.87752e13	0.573993
$121$	2.49278e13	0.722068
$122$	−5.03935e12	−0.138368
$123$	−2.88901e13	−0.752256
$124$	3.70222e13	0.914580
$125$	1.56484e13	0.366907
$126$	8.26901e12	0.184096
$127$	−8.77420e13	−1.85560	−0.927798	−	0.373083i	$-0.878301\pi$
$127$	−8.77420e13	−1.85560	−0.927798	+	0.373083i	$0.878301\pi$
$128$	−5.00070e13	−1.00500
$129$	3.08285e13	0.589005
$130$	−2.82524e13	−0.513362
$131$	3.42417e13	0.591960	0.295980	−	0.955194i	$-0.404354\pi$
$131$	3.42417e13	0.591960	0.295980	+	0.955194i	$0.404354\pi$
$132$	4.02779e13	0.662729
$133$	−7.80623e13	−1.22294
$134$	−3.70029e13	−0.552147
$135$	−2.02808e13	−0.288347
$136$	−8.21867e12	−0.111378
$137$	−2.06259e13	−0.266520	−0.133260	−	0.991081i	$-0.542544\pi$
$137$	−2.06259e13	−0.266520	−0.133260	+	0.991081i	$0.542544\pi$
$138$	1.82581e13	0.225031
$139$	9.83229e13	1.15627	0.578134	−	0.815942i	$-0.303781\pi$
$139$	9.83229e13	1.15627	0.578134	+	0.815942i	$0.303781\pi$
$140$	−1.82194e14	−2.04504
$141$	8.35461e13	0.895369
$142$	4.82084e13	0.493456
$143$	−1.29898e14	−1.27034
$144$	2.28205e13	0.213289
$145$	−2.55894e14	−2.28649
$146$	5.39344e13	0.460863
$147$	−1.01344e14	−0.828395
$148$	8.47998e13	0.663275
$149$	−9.26359e13	−0.693535	−0.346768	−	0.937951i	$-0.612721\pi$
$149$	−9.26359e13	−0.693535	−0.346768	+	0.937951i	$0.612721\pi$
$150$	−3.54890e13	−0.254390
$151$	3.43768e13	0.236002	0.118001	−	0.993013i	$-0.462351\pi$
$151$	3.43768e13	0.236002	0.118001	+	0.993013i	$0.462351\pi$
$152$	7.90725e13	0.520046
$153$	8.87772e12	0.0559509
$154$	1.19971e14	0.724755
$155$	−2.70460e14	−1.56656
$156$	−8.80066e13	−0.488883
$157$	3.42941e13	0.182756	0.0913779	−	0.995816i	$-0.470873\pi$
$157$	3.42941e13	0.182756	0.0913779	+	0.995816i	$0.470873\pi$
$158$	4.11926e13	0.210643
$159$	8.45406e13	0.414939
$160$	2.82994e14	1.33351
$161$	−3.79727e14	−1.71832
$162$	9.04769e12	0.0393269
$163$	−3.18781e13	−0.133129	−0.0665645	−	0.997782i	$-0.521204\pi$
$163$	−3.18781e13	−0.133129	−0.0665645	+	0.997782i	$0.521204\pi$
$164$	−2.83977e14	−1.13972
$165$	−2.94244e14	−1.13517
$166$	1.06819e14	0.396229
$167$	1.46800e14	0.523684	0.261842	−	0.965111i	$-0.415670\pi$
$167$	1.46800e14	0.523684	0.261842	+	0.965111i	$0.415670\pi$
$168$	1.74202e14	0.597782
$169$	−1.90491e13	−0.0628941
$170$	2.80141e13	0.0890139
$171$	−8.54133e13	−0.261247
$172$	3.03030e14	0.892383
$173$	−2.52855e14	−0.717087	−0.358543	−	0.933513i	$-0.616727\pi$
$173$	−2.52855e14	−0.717087	−0.358543	+	0.933513i	$0.616727\pi$
$174$	1.14160e14	0.311849
$175$	7.38090e14	1.94251
$176$	3.31092e14	0.839684
$177$	3.07496e13	0.0751646
$178$	−2.14720e14	−0.505990
$179$	−8.22155e14	−1.86814	−0.934069	−	0.357092i	$-0.883768\pi$
$179$	−8.22155e14	−1.86814	−0.934069	+	0.357092i	$0.883768\pi$
$180$	−1.99351e14	−0.436865
$181$	8.34518e14	1.76411	0.882054	−	0.471148i	$-0.156160\pi$
$181$	8.34518e14	1.76411	0.882054	+	0.471148i	$0.156160\pi$
$182$	−2.62135e14	−0.534639
$183$	1.14677e14	0.225706
$184$	3.84641e14	0.730702
$185$	−6.19491e14	−1.13611
$186$	1.20658e14	0.213660
$187$	1.28802e14	0.220269
$188$	8.21221e14	1.35655
$189$	−1.88171e14	−0.300297
$190$	−2.69525e14	−0.415625
$191$	−5.01005e14	−0.746664	−0.373332	−	0.927698i	$-0.621785\pi$
$191$	−5.01005e14	−0.746664	−0.373332	+	0.927698i	$0.621785\pi$
$192$	1.30192e14	0.187554
$193$	−1.51823e14	−0.211454	−0.105727	−	0.994395i	$-0.533717\pi$
$193$	−1.51823e14	−0.211454	−0.105727	+	0.994395i	$0.533717\pi$
$194$	−1.35817e14	−0.182912
$195$	6.42918e14	0.837395
$196$	−9.96171e14	−1.25507
$197$	1.40464e15	1.71212	0.856062	−	0.516873i	$-0.172904\pi$
$197$	1.40464e15	1.71212	0.856062	+	0.516873i	$0.172904\pi$
$198$	1.31268e14	0.154823
$199$	3.32481e14	0.379508	0.189754	−	0.981832i	$-0.439231\pi$
$199$	3.32481e14	0.379508	0.189754	+	0.981832i	$0.439231\pi$
$200$	−7.47642e14	−0.826035
$201$	8.42047e14	0.900662
$202$	5.02137e14	0.520042
$203$	−2.37427e15	−2.38125
$204$	8.72641e13	0.0847695
$205$	2.07455e15	1.95220
$206$	6.32675e14	0.576824
$207$	−4.15486e14	−0.367070
$208$	−7.23430e14	−0.619420
$209$	−1.23922e15	−1.02848
$210$	−5.93783e14	−0.477752
$211$	−1.06679e14	−0.0832230	−0.0416115	−	0.999134i	$-0.513249\pi$
$211$	−1.06679e14	−0.0832230	−0.0416115	+	0.999134i	$0.513249\pi$
$212$	8.30996e14	0.628660
$213$	−1.09704e15	−0.804924
$214$	−7.48230e14	−0.532532
$215$	−2.21374e15	−1.52854
$216$	1.90606e14	0.127699
$217$	−2.50941e15	−1.63149
$218$	−8.27497e14	−0.522155
$219$	−1.22734e15	−0.751760
$220$	−2.89228e15	−1.71986
$221$	−2.81432e14	−0.162489
$222$	2.76368e14	0.154951
$223$	5.46831e14	0.297764	0.148882	−	0.988855i	$-0.452433\pi$
$223$	5.46831e14	0.297764	0.148882	+	0.988855i	$0.452433\pi$
$224$	2.62571e15	1.38878
$225$	8.07595e14	0.414961
$226$	−1.34483e15	−0.671369
$227$	−3.30107e14	−0.160135	−0.0800675	−	0.996789i	$-0.525514\pi$
$227$	−3.30107e14	−0.160135	−0.0800675	+	0.996789i	$0.525514\pi$
$228$	−8.39575e14	−0.395806
$229$	3.25892e15	1.49329	0.746644	−	0.665224i	$-0.231664\pi$
$229$	3.25892e15	1.49329	0.746644	+	0.665224i	$0.231664\pi$
$230$	−1.31108e15	−0.583982
$231$	−2.73008e15	−1.18222
$232$	2.40499e15	1.01261
$233$	−1.08294e15	−0.443396	−0.221698	−	0.975115i	$-0.571160\pi$
$233$	−1.08294e15	−0.443396	−0.221698	+	0.975115i	$0.571160\pi$
$234$	−2.86819e14	−0.114210
$235$	−5.99930e15	−2.32359
$236$	3.02255e14	0.113879
$237$	−9.37388e14	−0.343601
$238$	2.59923e14	0.0927032
$239$	−2.83994e15	−0.985650	−0.492825	−	0.870129i	$-0.664036\pi$
$239$	−2.83994e15	−0.985650	−0.492825	+	0.870129i	$0.664036\pi$
$240$	−1.63870e15	−0.553512
$241$	1.55768e15	0.512114	0.256057	−	0.966662i	$-0.417577\pi$
$241$	1.55768e15	0.512114	0.256057	+	0.966662i	$0.417577\pi$
$242$	7.98566e14	0.255571
$243$	−2.05891e14	−0.0641500
$244$	1.12722e15	0.341960
$245$	7.27737e15	2.14978
$246$	−9.25500e14	−0.266255
$247$	2.70767e15	0.758693
$248$	2.54189e15	0.693778
$249$	−2.43080e15	−0.646327
$250$	5.01301e14	0.129864
$251$	1.40586e15	0.354865	0.177433	−	0.984133i	$-0.443221\pi$
$251$	1.40586e15	0.354865	0.177433	+	0.984133i	$0.443221\pi$
$252$	−1.84964e15	−0.454971
$253$	−6.02808e15	−1.44509
$254$	−2.81083e15	−0.656774
$255$	−6.37494e14	−0.145199
$256$	−1.38980e14	−0.0308597
$257$	−6.93421e15	−1.50118	−0.750588	−	0.660771i	$-0.770230\pi$
$257$	−6.93421e15	−1.50118	−0.750588	+	0.660771i	$0.770230\pi$
$258$	9.87597e14	0.208474
$259$	−5.74783e15	−1.18319
$260$	6.31960e15	1.26871
$261$	−2.59785e15	−0.508687
$262$	1.09694e15	0.209520
$263$	−8.75842e15	−1.63197	−0.815987	−	0.578070i	$-0.803806\pi$
$263$	−8.75842e15	−1.63197	−0.815987	+	0.578070i	$0.803806\pi$
$264$	2.76541e15	0.502730
$265$	−6.07071e15	−1.07682
$266$	−2.50074e15	−0.432851
$267$	4.88621e15	0.825371
$268$	8.27695e15	1.36456
$269$	1.04083e15	0.167490	0.0837450	−	0.996487i	$-0.473312\pi$
$269$	1.04083e15	0.167490	0.0837450	+	0.996487i	$0.473312\pi$
$270$	−6.49699e14	−0.102058
$271$	3.55084e15	0.544541	0.272270	−	0.962221i	$-0.412225\pi$
$271$	3.55084e15	0.544541	0.272270	+	0.962221i	$0.412225\pi$
$272$	7.17327e14	0.107404
$273$	5.96519e15	0.872102
$274$	−6.60755e14	−0.0943325
$275$	1.17170e16	1.63363
$276$	−4.08404e15	−0.556136
$277$	4.83555e15	0.643172	0.321586	−	0.946880i	$-0.395784\pi$
$277$	4.83555e15	0.643172	0.321586	+	0.946880i	$0.395784\pi$
$278$	3.14979e15	0.409252
$279$	−2.74572e15	−0.348521
$280$	−1.25091e16	−1.55132
$281$	7.71208e15	0.934502	0.467251	−	0.884125i	$-0.345244\pi$
$281$	7.71208e15	0.934502	0.467251	+	0.884125i	$0.345244\pi$
$282$	2.67642e15	0.316909
$283$	1.30634e16	1.51163	0.755815	−	0.654785i	$-0.227241\pi$
$283$	1.30634e16	1.51163	0.755815	+	0.654785i	$0.227241\pi$
$284$	−1.07834e16	−1.21952
$285$	6.13338e15	0.677966
$286$	−4.16132e15	−0.449627
$287$	1.92483e16	2.03311
$288$	2.87296e15	0.296674
$289$	−9.62552e15	−0.971825
$290$	−8.19763e15	−0.809285
$291$	3.09067e15	0.298365
$292$	−1.20642e16	−1.13897
$293$	−1.22226e16	−1.12856	−0.564278	−	0.825585i	$-0.690845\pi$
$293$	−1.22226e16	−1.12856	−0.564278	+	0.825585i	$0.690845\pi$
$294$	−3.24659e15	−0.293204
$295$	−2.20808e15	−0.195061
$296$	5.82221e15	0.503144
$297$	−2.98717e15	−0.252548
$298$	−2.96761e15	−0.245471
$299$	1.31713e16	1.06602
$300$	7.93830e15	0.628694
$301$	−2.05398e16	−1.59189
$302$	1.10127e15	0.0835310
$303$	−1.14267e16	−0.848292
$304$	−6.90146e15	−0.501490
$305$	−8.23472e15	−0.585734
$306$	2.84400e14	0.0198034
$307$	1.24361e16	0.847780	0.423890	−	0.905714i	$-0.360664\pi$
$307$	1.24361e16	0.847780	0.423890	+	0.905714i	$0.360664\pi$
$308$	−2.68355e16	−1.79114
$309$	−1.43973e16	−0.940915
$310$	−8.66425e15	−0.554472
$311$	1.87158e16	1.17291	0.586456	−	0.809981i	$-0.300523\pi$
$311$	1.87158e16	1.17291	0.586456	+	0.809981i	$0.300523\pi$
$312$	−6.04239e15	−0.370855
$313$	−1.73461e16	−1.04271	−0.521355	−	0.853340i	$-0.674573\pi$
$313$	−1.73461e16	−1.04271	−0.521355	+	0.853340i	$0.674573\pi$
$314$	1.09862e15	0.0646850
$315$	1.35123e16	0.779308
$316$	−9.21410e15	−0.520579
$317$	−9.81312e15	−0.543153	−0.271576	−	0.962417i	$-0.587545\pi$
$317$	−9.81312e15	−0.543153	−0.271576	+	0.962417i	$0.587545\pi$
$318$	2.70827e15	0.146864
$319$	−3.76909e16	−2.00261
$320$	−9.34884e15	−0.486724
$321$	1.70269e16	0.868665
$322$	−1.21646e16	−0.608186
$323$	−2.68483e15	−0.131553
$324$	−2.02382e15	−0.0971916
$325$	−2.56015e16	−1.20510
$326$	−1.02122e15	−0.0471200
$327$	1.88307e16	0.851738
$328$	−1.94974e16	−0.864563
$329$	−5.56634e16	−2.41989
$330$	−9.42615e15	−0.401785
$331$	9.73826e15	0.407005	0.203502	−	0.979074i	$-0.434768\pi$
$331$	9.73826e15	0.407005	0.203502	+	0.979074i	$0.434768\pi$
$332$	−2.38936e16	−0.979230
$333$	−6.28910e15	−0.252756
$334$	4.70277e15	0.185354
$335$	−6.04659e16	−2.33733
$336$	−1.52044e16	−0.576453
$337$	7.79523e15	0.289891	0.144945	−	0.989440i	$-0.453699\pi$
$337$	7.79523e15	0.289891	0.144945	+	0.989440i	$0.453699\pi$
$338$	−6.10241e14	−0.0222609
$339$	3.06032e16	1.09514
$340$	−6.26628e15	−0.219987
$341$	−3.98363e16	−1.37207
$342$	−2.73623e15	−0.0924662
$343$	2.04624e16	0.678492
$344$	2.08056e16	0.676940
$345$	2.98353e16	0.952591
$346$	−8.10026e15	−0.253807
$347$	−9.26264e15	−0.284835	−0.142418	−	0.989807i	$-0.545488\pi$
$347$	−9.26264e15	−0.284835	−0.142418	+	0.989807i	$0.545488\pi$
$348$	−2.55357e16	−0.770695
$349$	−3.21933e16	−0.953675	−0.476837	−	0.878992i	$-0.658217\pi$
$349$	−3.21933e16	−0.953675	−0.476837	+	0.878992i	$0.658217\pi$
$350$	2.36449e16	0.687535
$351$	6.52693e15	0.186300
$352$	4.16824e16	1.16795
$353$	−1.62281e16	−0.446407	−0.223204	−	0.974772i	$-0.571651\pi$
$353$	−1.62281e16	−0.446407	−0.223204	+	0.974772i	$0.571651\pi$
$354$	9.85070e14	0.0266039
$355$	7.87766e16	2.08888
$356$	4.80293e16	1.25049
$357$	−5.91487e15	−0.151217
$358$	−2.63379e16	−0.661213
$359$	3.32964e16	0.820887	0.410444	−	0.911886i	$-0.365374\pi$
$359$	3.32964e16	0.820887	0.410444	+	0.911886i	$0.365374\pi$
$360$	−1.36871e16	−0.331395
$361$	−1.62220e16	−0.385752
$362$	2.67340e16	0.624392
$363$	−1.81723e16	−0.416886
$364$	5.86352e16	1.32129
$365$	8.81333e16	1.95091
$366$	3.67369e15	0.0798868
$367$	−7.77449e16	−1.66090	−0.830448	−	0.557097i	$-0.811915\pi$
$367$	−7.77449e16	−1.66090	−0.830448	+	0.557097i	$0.811915\pi$
$368$	−3.35716e16	−0.704630
$369$	2.10609e16	0.434315
$370$	−1.98455e16	−0.402116
$371$	−5.63259e16	−1.12145
$372$	−2.69892e16	−0.528033
$373$	6.08101e16	1.16915	0.584573	−	0.811341i	$-0.301262\pi$
$373$	6.08101e16	1.16915	0.584573	+	0.811341i	$0.301262\pi$
$374$	4.12621e15	0.0779626
$375$	−1.14077e16	−0.211834
$376$	5.63837e16	1.02904
$377$	8.23541e16	1.47729
$378$	−6.02811e15	−0.106288
$379$	8.97513e16	1.55556	0.777778	−	0.628539i	$-0.216347\pi$
$379$	8.97513e16	1.55556	0.777778	+	0.628539i	$0.216347\pi$
$380$	6.02884e16	1.02717
$381$	6.39639e16	1.07133
$382$	−1.60498e16	−0.264276
$383$	−6.99155e16	−1.13183	−0.565915	−	0.824464i	$-0.691477\pi$
$383$	−6.99155e16	−1.13183	−0.565915	+	0.824464i	$0.691477\pi$
$384$	3.64551e16	0.580237
$385$	1.96043e17	3.06800
$386$	−4.86369e15	−0.0748426
$387$	−2.24740e16	−0.340062
$388$	3.03799e16	0.452044
$389$	4.80283e16	0.702788	0.351394	−	0.936228i	$-0.385708\pi$
$389$	4.80283e16	0.702788	0.351394	+	0.936228i	$0.385708\pi$
$390$	2.05960e16	0.296390
$391$	−1.30601e16	−0.184841
$392$	−6.83955e16	−0.952068
$393$	−2.49622e16	−0.341768
$394$	4.49980e16	0.605993
$395$	6.73122e16	0.891687
$396$	−2.93626e16	−0.382627
$397$	−2.88338e16	−0.369626	−0.184813	−	0.982774i	$-0.559168\pi$
$397$	−2.88338e16	−0.369626	−0.184813	+	0.982774i	$0.559168\pi$
$398$	1.06511e16	0.134324
$399$	5.69074e16	0.706065
$400$	6.52543e16	0.796561
$401$	−5.84467e16	−0.701975	−0.350988	−	0.936380i	$-0.614154\pi$
$401$	−5.84467e16	−0.701975	−0.350988	+	0.936380i	$0.614154\pi$
$402$	2.69751e16	0.318782
$403$	8.70417e16	1.01215
$404$	−1.12320e17	−1.28522
$405$	1.47847e16	0.166477
$406$	−7.60602e16	−0.842826
$407$	−9.12454e16	−0.995055
$408$	5.99141e15	0.0643040
$409$	−1.86398e16	−0.196897	−0.0984486	−	0.995142i	$-0.531388\pi$
$409$	−1.86398e16	−0.196897	−0.0984486	+	0.995142i	$0.531388\pi$
$410$	6.64586e16	0.690965
$411$	1.50363e16	0.153875
$412$	−1.41519e17	−1.42555
$413$	−2.04872e16	−0.203146
$414$	−1.33102e16	−0.129922
$415$	1.74551e17	1.67730
$416$	−9.10754e16	−0.861578
$417$	−7.16774e16	−0.667572
$418$	−3.96986e16	−0.364024
$419$	2.92711e16	0.264270	0.132135	−	0.991232i	$-0.457817\pi$
$419$	2.92711e16	0.264270	0.132135	+	0.991232i	$0.457817\pi$
$420$	1.32819e17	1.18070
$421$	−1.93762e17	−1.69603	−0.848017	−	0.529969i	$-0.822204\pi$
$421$	−1.93762e17	−1.69603	−0.848017	+	0.529969i	$0.822204\pi$
$422$	−3.41749e15	−0.0294561
$423$	−6.09051e16	−0.516942
$424$	5.70548e16	0.476886
$425$	2.53855e16	0.208957
$426$	−3.51439e16	−0.284897
$427$	−7.64043e16	−0.610010
$428$	1.67367e17	1.31609
$429$	9.46959e16	0.733430
$430$	−7.09176e16	−0.541015
$431$	3.77201e16	0.283446	0.141723	−	0.989906i	$-0.454736\pi$
$431$	3.77201e16	0.283446	0.141723	+	0.989906i	$0.454736\pi$
$432$	−1.66362e16	−0.123143
$433$	−2.20311e17	−1.60644	−0.803221	−	0.595682i	$-0.796882\pi$
$433$	−2.20311e17	−1.60644	−0.803221	+	0.595682i	$0.796882\pi$
$434$	−8.03896e16	−0.577453
$435$	1.86547e17	1.32010
$436$	1.85097e17	1.29044
$437$	1.25653e17	0.863062
$438$	−3.93182e16	−0.266080
$439$	2.31477e17	1.54344	0.771718	−	0.635965i	$-0.219398\pi$
$439$	2.31477e17	1.54344	0.771718	+	0.635965i	$0.219398\pi$
$440$	−1.98580e17	−1.30464
$441$	7.38801e16	0.478274
$442$	−9.01572e15	−0.0575116
$443$	−5.29852e16	−0.333066	−0.166533	−	0.986036i	$-0.553257\pi$
$443$	−5.29852e16	−0.333066	−0.166533	+	0.986036i	$0.553257\pi$
$444$	−6.18190e16	−0.382942
$445$	−3.50870e17	−2.14194
$446$	1.75178e16	0.105391
$447$	6.75315e16	0.400413
$448$	−8.67414e16	−0.506897
$449$	2.43564e17	1.40285	0.701427	−	0.712741i	$-0.252547\pi$
$449$	2.43564e17	1.40285	0.701427	+	0.712741i	$0.252547\pi$
$450$	2.58715e16	0.146872
$451$	3.05562e17	1.70982
$452$	3.00816e17	1.65921
$453$	−2.50607e16	−0.136256
$454$	−1.05750e16	−0.0566785
$455$	−4.28350e17	−2.26321
$456$	−5.76438e16	−0.300249
$457$	1.71174e17	0.878988	0.439494	−	0.898245i	$-0.355158\pi$
$457$	1.71174e17	0.878988	0.439494	+	0.898245i	$0.355158\pi$
$458$	1.04400e17	0.528538
$459$	−6.47186e15	−0.0323033
$460$	2.93268e17	1.44324
$461$	2.62111e17	1.27183	0.635916	−	0.771759i	$-0.280623\pi$
$461$	2.62111e17	1.27183	0.635916	+	0.771759i	$0.280623\pi$
$462$	−8.74588e16	−0.418438
$463$	1.98787e17	0.937801	0.468900	−	0.883251i	$-0.344650\pi$
$463$	1.98787e17	0.937801	0.468900	+	0.883251i	$0.344650\pi$
$464$	−2.09908e17	−0.976478
$465$	1.97165e17	0.904454
$466$	−3.46923e16	−0.156937
$467$	3.01014e17	1.34285	0.671425	−	0.741073i	$-0.265683\pi$
$467$	3.01014e17	1.34285	0.671425	+	0.741073i	$0.265683\pi$
$468$	6.41568e16	0.282257
$469$	−5.61022e17	−2.43420
$470$	−1.92189e17	−0.822417
$471$	−2.50004e16	−0.105514
$472$	2.07523e16	0.0863861
$473$	−3.26064e17	−1.33877
$474$	−3.00294e16	−0.121615
$475$	−2.44236e17	−0.975665
$476$	−5.81405e16	−0.229105
$477$	−6.16301e16	−0.239565
$478$	−9.09780e16	−0.348863
$479$	2.50277e17	0.946759	0.473379	−	0.880859i	$-0.343034\pi$
$479$	2.50277e17	0.946759	0.473379	+	0.880859i	$0.343034\pi$
$480$	−2.06303e17	−0.769904
$481$	1.99370e17	0.734034
$482$	4.99005e16	0.181259
$483$	2.76821e17	0.992072
$484$	−1.78626e17	−0.631611
$485$	−2.21936e17	−0.774294
$486$	−6.59576e15	−0.0227054
$487$	4.96787e16	0.168745	0.0843727	−	0.996434i	$-0.473111\pi$
$487$	4.96787e16	0.168745	0.0843727	+	0.996434i	$0.473111\pi$
$488$	7.73931e16	0.259402
$489$	2.32391e16	0.0768620
$490$	2.33132e17	0.760900
$491$	7.49828e16	0.241508	0.120754	−	0.992682i	$-0.461469\pi$
$491$	7.49828e16	0.241508	0.120754	+	0.992682i	$0.461469\pi$
$492$	2.07019e17	0.658017
$493$	−8.16593e16	−0.256154
$494$	8.67409e16	0.268534
$495$	2.14504e17	0.655392
$496$	−2.21856e17	−0.669023
$497$	7.30913e17	2.17545
$498$	−7.78710e16	−0.228763
$499$	−2.43010e17	−0.704646	−0.352323	−	0.935879i	$-0.614608\pi$
$499$	−2.43010e17	−0.704646	−0.352323	+	0.935879i	$0.614608\pi$
$500$	−1.12133e17	−0.320943
$501$	−1.07017e17	−0.302349
$502$	4.50371e16	0.125602
$503$	−4.48131e17	−1.23371	−0.616855	−	0.787077i	$-0.711594\pi$
$503$	−4.48131e17	−1.23371	−0.616855	+	0.787077i	$0.711594\pi$
$504$	−1.26993e17	−0.345130
$505$	8.20534e17	2.20142
$506$	−1.93111e17	−0.511479
$507$	1.38868e16	0.0363119
$508$	6.28737e17	1.62314
$509$	4.56958e17	1.16469	0.582345	−	0.812941i	$-0.302135\pi$
$509$	4.56958e17	1.16469	0.582345	+	0.812941i	$0.302135\pi$
$510$	−2.04222e16	−0.0513922
$511$	8.17728e17	2.03176
$512$	4.05205e17	0.994077
$513$	6.22663e16	0.150831
$514$	−2.22139e17	−0.531330
$515$	1.03384e18	2.44179
$516$	−2.20909e17	−0.515218
$517$	−8.83642e17	−2.03511
$518$	−1.84133e17	−0.418782
$519$	1.84331e17	0.414010
$520$	4.33893e17	0.962412
$521$	9.57048e16	0.209647	0.104823	−	0.994491i	$-0.466572\pi$
$521$	9.57048e16	0.209647	0.104823	+	0.994491i	$0.466572\pi$
$522$	−8.32226e16	−0.180046
$523$	−6.12717e17	−1.30918	−0.654589	−	0.755985i	$-0.727158\pi$
$523$	−6.12717e17	−1.30918	−0.654589	+	0.755985i	$0.727158\pi$
$524$	−2.45368e17	−0.517802
$525$	−5.38068e17	−1.12151
$526$	−2.80578e17	−0.577625
$527$	−8.63074e16	−0.175501
$528$	−2.41366e17	−0.484792
$529$	1.07190e17	0.212664
$530$	−1.94476e17	−0.381131
$531$	−2.24165e16	−0.0433963
$532$	5.59374e17	1.06974
$533$	−6.67648e17	−1.26131
$534$	1.56531e17	0.292134
$535$	−1.22267e18	−2.25429
$536$	5.68282e17	1.03512
$537$	5.99351e17	1.07857
$538$	3.33431e16	0.0592818
$539$	1.07189e18	1.88288
$540$	1.45327e17	0.252224
$541$	2.14986e16	0.0368661	0.0184331	−	0.999830i	$-0.494132\pi$
$541$	2.14986e16	0.0368661	0.0184331	+	0.999830i	$0.494132\pi$
$542$	1.13752e17	0.192736
$543$	−6.08364e17	−1.01851
$544$	9.03071e16	0.149393
$545$	−1.35220e18	−2.21036
$546$	1.91096e17	0.308674
$547$	−3.63252e17	−0.579816	−0.289908	−	0.957054i	$-0.593625\pi$
$547$	−3.63252e17	−0.579816	−0.289908	+	0.957054i	$0.593625\pi$
$548$	1.47800e17	0.233131
$549$	−8.35992e16	−0.130311
$550$	3.75356e17	0.578211
$551$	7.85650e17	1.19604
$552$	−2.80404e17	−0.421871
$553$	6.24543e17	0.928644
$554$	1.54908e17	0.227646
$555$	4.51609e17	0.655931
$556$	−7.04557e17	−1.01142
$557$	−2.48805e17	−0.353021	−0.176511	−	0.984299i	$-0.556481\pi$
$557$	−2.48805e17	−0.353021	−0.176511	+	0.984299i	$0.556481\pi$
$558$	−8.79597e16	−0.123356
$559$	7.12444e17	0.987585
$560$	1.09180e18	1.49596
$561$	−9.38970e16	−0.127172
$562$	2.47058e17	0.330760
$563$	−4.54008e17	−0.600840	−0.300420	−	0.953807i	$-0.597127\pi$
$563$	−4.54008e17	−0.600840	−0.300420	+	0.953807i	$0.597127\pi$
$564$	−5.98670e17	−0.783202
$565$	−2.19756e18	−2.84201
$566$	4.18490e17	0.535030
$567$	1.37177e17	0.173377
$568$	−7.40372e17	−0.925094
$569$	−4.33355e17	−0.535321	−0.267660	−	0.963513i	$-0.586251\pi$
$569$	−4.33355e17	−0.535321	−0.267660	+	0.963513i	$0.586251\pi$
$570$	1.96484e17	0.239961
$571$	−7.27408e17	−0.878301	−0.439151	−	0.898413i	$-0.644721\pi$
$571$	−7.27408e17	−0.878301	−0.439151	+	0.898413i	$0.644721\pi$
$572$	9.30819e17	1.11120
$573$	3.65233e17	0.431087
$574$	6.16623e17	0.719602
$575$	−1.18806e18	−1.37088
$576$	−9.49097e16	−0.108284
$577$	−1.52093e17	−0.171579	−0.0857897	−	0.996313i	$-0.527341\pi$
$577$	−1.52093e17	−0.171579	−0.0857897	+	0.996313i	$0.527341\pi$
$578$	−3.08356e17	−0.343970
$579$	1.10679e17	0.122083
$580$	1.83367e18	2.00005
$581$	1.61954e18	1.74681
$582$	9.90103e16	0.105604
$583$	−8.94160e17	−0.943126
$584$	−8.28310e17	−0.863992
$585$	−4.68687e17	−0.483470
$586$	−3.91552e17	−0.399443
$587$	−2.29539e17	−0.231584	−0.115792	−	0.993273i	$-0.536941\pi$
$587$	−2.29539e17	−0.231584	−0.115792	+	0.993273i	$0.536941\pi$
$588$	7.26209e17	0.724617
$589$	8.30370e17	0.819450
$590$	−7.07362e16	−0.0690404
$591$	−1.02398e18	−0.988495
$592$	−5.08164e17	−0.485191
$593$	2.48505e17	0.234682	0.117341	−	0.993092i	$-0.462563\pi$
$593$	2.48505e17	0.234682	0.117341	+	0.993092i	$0.462563\pi$
$594$	−9.56947e16	−0.0893873
$595$	4.24736e17	0.392427
$596$	6.63805e17	0.606652
$597$	−2.42378e17	−0.219109
$598$	4.21944e17	0.377309
$599$	−1.43267e18	−1.26728	−0.633638	−	0.773630i	$-0.718439\pi$
$599$	−1.43267e18	−1.26728	−0.633638	+	0.773630i	$0.718439\pi$
$600$	5.45031e17	0.476912
$601$	4.76099e17	0.412110	0.206055	−	0.978540i	$-0.433937\pi$
$601$	4.76099e17	0.412110	0.206055	+	0.978540i	$0.433937\pi$
$602$	−6.57996e17	−0.563438
$603$	−6.13852e17	−0.519997
$604$	−2.46335e17	−0.206437
$605$	1.30492e18	1.08187
$606$	−3.66058e17	−0.300246
$607$	−2.45086e16	−0.0198880	−0.00994401	−	0.999951i	$-0.503165\pi$
$607$	−2.45086e16	−0.0198880	−0.00994401	+	0.999951i	$0.503165\pi$
$608$	−8.68851e17	−0.697545
$609$	1.73084e18	1.37482
$610$	−2.63801e17	−0.207316
$611$	1.93075e18	1.50126
$612$	−6.36155e16	−0.0489417
$613$	1.78818e18	1.36119	0.680593	−	0.732662i	$-0.261722\pi$
$613$	1.78818e18	1.36119	0.680593	+	0.732662i	$0.261722\pi$
$614$	3.98391e17	0.300065
$615$	−1.51235e18	−1.12710
$616$	−1.84248e18	−1.35872
$617$	−2.36700e18	−1.72721	−0.863603	−	0.504173i	$-0.831797\pi$
$617$	−2.36700e18	−1.72721	−0.863603	+	0.504173i	$0.831797\pi$
$618$	−4.61220e17	−0.333030
$619$	−1.72699e18	−1.23396	−0.616978	−	0.786981i	$-0.711643\pi$
$619$	−1.72699e18	−1.23396	−0.616978	+	0.786981i	$0.711643\pi$
$620$	1.93805e18	1.37031
$621$	3.02889e17	0.211928
$622$	5.99564e17	0.415143
$623$	−3.25549e18	−2.23071
$624$	5.27381e17	0.357622
$625$	−1.03585e18	−0.695149
$626$	−5.55685e17	−0.369059
$627$	9.03391e17	0.593795
$628$	−2.45743e17	−0.159861
$629$	−1.97688e17	−0.127277
$630$	4.32868e17	0.275830
$631$	−1.39038e18	−0.876884	−0.438442	−	0.898759i	$-0.644470\pi$
$631$	−1.39038e18	−0.876884	−0.438442	+	0.898759i	$0.644470\pi$
$632$	−6.32625e17	−0.394899
$633$	7.77691e16	0.0480488
$634$	−3.14365e17	−0.192245
$635$	−4.59314e18	−2.78023
$636$	−6.05796e17	−0.362957
$637$	−2.34206e18	−1.38897
$638$	−1.20744e18	−0.708810
$639$	7.99742e17	0.464723
$640$	−2.61778e18	−1.50578
$641$	−2.31193e17	−0.131643	−0.0658214	−	0.997831i	$-0.520967\pi$
$641$	−2.31193e17	−0.131643	−0.0658214	+	0.997831i	$0.520967\pi$
$642$	5.45460e17	0.307457
$643$	−2.50596e18	−1.39831	−0.699155	−	0.714971i	$-0.746440\pi$
$643$	−2.50596e18	−1.39831	−0.699155	+	0.714971i	$0.746440\pi$
$644$	2.72103e18	1.50306
$645$	1.61382e18	0.882503
$646$	−8.60091e16	−0.0465622
$647$	9.43881e17	0.505871	0.252935	−	0.967483i	$-0.418604\pi$
$647$	9.43881e17	0.505871	0.252935	+	0.967483i	$0.418604\pi$
$648$	−1.38952e17	−0.0737272
$649$	−3.25229e17	−0.170844
$650$	−8.20148e17	−0.426536
$651$	1.82936e18	0.941940
$652$	2.28430e17	0.116451
$653$	−1.51419e18	−0.764266	−0.382133	−	0.924107i	$-0.624810\pi$
$653$	−1.51419e18	−0.764266	−0.382133	+	0.924107i	$0.624810\pi$
$654$	6.03245e17	0.301466
$655$	1.79249e18	0.886930
$656$	1.70174e18	0.833714
$657$	8.94733e17	0.434029
$658$	−1.78319e18	−0.856503
$659$	6.65290e17	0.316414	0.158207	−	0.987406i	$-0.449429\pi$
$659$	6.65290e17	0.316414	0.158207	+	0.987406i	$0.449429\pi$
$660$	2.10848e18	0.992963
$661$	−1.48382e17	−0.0691945	−0.0345973	−	0.999401i	$-0.511015\pi$
$661$	−1.48382e17	−0.0691945	−0.0345973	+	0.999401i	$0.511015\pi$
$662$	3.11967e17	0.144056
$663$	2.05164e17	0.0938128
$664$	−1.64050e18	−0.742819
$665$	−4.08642e18	−1.83232
$666$	−2.01472e17	−0.0894609
$667$	3.82173e18	1.68051
$668$	−1.05193e18	−0.458079
$669$	−3.98640e17	−0.171914
$670$	−1.93704e18	−0.827279
$671$	−1.21290e18	−0.513013
$672$	−1.91414e18	−0.801813
$673$	−4.26382e18	−1.76889	−0.884446	−	0.466643i	$-0.845463\pi$
$673$	−4.26382e18	−1.76889	−0.884446	+	0.466643i	$0.845463\pi$
$674$	2.49722e17	0.102605
$675$	−5.88737e17	−0.239578
$676$	1.36501e17	0.0550150
$677$	3.08939e18	1.23324	0.616618	−	0.787263i	$-0.288502\pi$
$677$	3.08939e18	1.23324	0.616618	+	0.787263i	$0.288502\pi$
$678$	9.80379e17	0.387615
$679$	−2.05919e18	−0.806386
$680$	−4.30233e17	−0.166877
$681$	2.40648e17	0.0924539
$682$	−1.27616e18	−0.485633
$683$	7.57376e17	0.285481	0.142740	−	0.989760i	$-0.454409\pi$
$683$	7.57376e17	0.285481	0.142740	+	0.989760i	$0.454409\pi$
$684$	6.12050e17	0.228519
$685$	−1.07973e18	−0.399324
$686$	6.55517e17	0.240147
$687$	−2.37575e18	−0.862150
$688$	−1.81591e18	−0.652786
$689$	1.95373e18	0.695727
$690$	9.55780e17	0.337162
$691$	−2.28803e18	−0.799564	−0.399782	−	0.916610i	$-0.630914\pi$
$691$	−2.28803e18	−0.799564	−0.399782	+	0.916610i	$0.630914\pi$
$692$	1.81189e18	0.627254
$693$	1.99023e18	0.682555
$694$	−2.96731e17	−0.100815
$695$	5.14703e18	1.73243
$696$	−1.75324e18	−0.584630
$697$	6.62015e17	0.218703
$698$	−1.03132e18	−0.337546
$699$	7.89465e17	0.255995
$700$	−5.28897e18	−1.69916
$701$	2.55032e18	0.811761	0.405881	−	0.913926i	$-0.366965\pi$
$701$	2.55032e18	0.811761	0.405881	+	0.913926i	$0.366965\pi$
$702$	2.09091e17	0.0659394
$703$	1.90197e18	0.594284
$704$	−1.37700e18	−0.426296
$705$	4.37349e18	1.34153
$706$	−5.19869e17	−0.158002
$707$	7.61317e18	2.29266
$708$	−2.20344e17	−0.0657483
$709$	1.33695e18	0.395288	0.197644	−	0.980274i	$-0.436671\pi$
$709$	1.33695e18	0.395288	0.197644	+	0.980274i	$0.436671\pi$
$710$	2.52362e18	0.739342
$711$	6.83356e17	0.198378
$712$	3.29761e18	0.948593
$713$	4.03927e18	1.15139
$714$	−1.89484e17	−0.0535222
$715$	−6.79995e18	−1.90334
$716$	5.89135e18	1.63411
$717$	2.07031e18	0.569065
$718$	1.06666e18	0.290547
$719$	−2.11011e18	−0.569595	−0.284798	−	0.958588i	$-0.591926\pi$
$719$	−2.11011e18	−0.569595	−0.284798	+	0.958588i	$0.591926\pi$
$720$	1.19461e18	0.319570
$721$	9.59232e18	2.54299
$722$	−5.19675e17	−0.136534
$723$	−1.13555e18	−0.295669
$724$	−5.97995e18	−1.54311
$725$	−7.42844e18	−1.89977
$726$	−5.82154e17	−0.147554
$727$	−1.12546e18	−0.282720	−0.141360	−	0.989958i	$-0.545148\pi$
$727$	−1.12546e18	−0.282720	−0.141360	+	0.989958i	$0.545148\pi$
$728$	4.02580e18	1.00230
$729$	1.50095e17	0.0370370
$730$	2.82337e18	0.690508
$731$	−7.06434e17	−0.171241
$732$	−8.21743e17	−0.197430
$733$	−2.41198e18	−0.574378	−0.287189	−	0.957874i	$-0.592721\pi$
$733$	−2.41198e18	−0.574378	−0.287189	+	0.957874i	$0.592721\pi$
$734$	−2.49057e18	−0.587861
$735$	−5.30520e18	−1.24118
$736$	−4.22646e18	−0.980100
$737$	−8.90608e18	−2.04714
$738$	6.74690e17	0.153723
$739$	4.14722e17	0.0936631	0.0468315	−	0.998903i	$-0.485088\pi$
$739$	4.14722e17	0.0936631	0.0468315	+	0.998903i	$0.485088\pi$
$740$	4.43912e18	0.993780
$741$	−1.97389e18	−0.438032
$742$	−1.80441e18	−0.396927
$743$	3.39730e18	0.740809	0.370405	−	0.928871i	$-0.379219\pi$
$743$	3.39730e18	0.740809	0.370405	+	0.928871i	$0.379219\pi$
$744$	−1.85304e18	−0.400553
$745$	−4.84932e18	−1.03912
$746$	1.94806e18	0.413810
$747$	1.77205e18	0.373157
$748$	−9.22966e17	−0.192675
$749$	−1.13443e19	−2.34772
$750$	−3.65449e17	−0.0749770
$751$	−1.32835e18	−0.270181	−0.135090	−	0.990833i	$-0.543132\pi$
$751$	−1.32835e18	−0.270181	−0.135090	+	0.990833i	$0.543132\pi$
$752$	−4.92118e18	−0.992324
$753$	−1.02487e18	−0.204882
$754$	2.63823e18	0.522876
$755$	1.79956e18	0.353600
$756$	1.34839e18	0.262678
$757$	1.99577e16	0.00385467	0.00192733	−	0.999998i	$-0.499387\pi$
$757$	1.99577e16	0.00385467	0.00192733	+	0.999998i	$0.499387\pi$
$758$	2.87520e18	0.550577
$759$	4.39447e18	0.834324
$760$	4.13930e18	0.779182
$761$	4.42416e18	0.825715	0.412858	−	0.910796i	$-0.364531\pi$
$761$	4.42416e18	0.825715	0.412858	+	0.910796i	$0.364531\pi$
$762$	2.04910e18	0.379189
$763$	−1.25461e19	−2.30197
$764$	3.59008e18	0.653126
$765$	4.64733e17	0.0838309
$766$	−2.23976e18	−0.400602
$767$	7.10621e17	0.126028
$768$	1.01316e17	0.0178169
$769$	5.45929e18	0.951951	0.475976	−	0.879458i	$-0.342095\pi$
$769$	5.45929e18	0.951951	0.475976	+	0.879458i	$0.342095\pi$
$770$	6.28026e18	1.08590
$771$	5.05504e18	0.866704
$772$	1.08793e18	0.184964
$773$	5.23841e18	0.883147	0.441573	−	0.897225i	$-0.354420\pi$
$773$	5.23841e18	0.883147	0.441573	+	0.897225i	$0.354420\pi$
$774$	−7.19958e17	−0.120362
$775$	−7.85127e18	−1.30160
$776$	2.08584e18	0.342909
$777$	4.19017e18	0.683117
$778$	1.53860e18	0.248747
$779$	−6.36930e18	−1.02117
$780$	−4.60699e18	−0.732491
$781$	1.16031e19	1.82954
$782$	−4.18384e17	−0.0654231
$783$	1.89383e18	0.293691
$784$	5.96957e18	0.918097
$785$	1.79523e18	0.273822
$786$	−7.99670e17	−0.120966
$787$	1.09536e19	1.64331	0.821656	−	0.569984i	$-0.193050\pi$
$787$	1.09536e19	1.64331	0.821656	+	0.569984i	$0.193050\pi$
$788$	−1.00653e19	−1.49764
$789$	6.38489e18	0.942221
$790$	2.15636e18	0.315606
$791$	−2.03897e19	−2.95980
$792$	−2.01599e18	−0.290251
$793$	2.65017e18	0.378440
$794$	−9.23695e17	−0.130826
$795$	4.42555e18	0.621700
$796$	−2.38247e18	−0.331965
$797$	1.74637e18	0.241355	0.120678	−	0.992692i	$-0.461493\pi$
$797$	1.74637e18	0.241355	0.120678	+	0.992692i	$0.461493\pi$
$798$	1.82304e18	0.249906
$799$	−1.91446e18	−0.260310
$800$	8.21512e18	1.10797
$801$	−3.56205e18	−0.476528
$802$	−1.87235e18	−0.248459
$803$	1.29812e19	1.70870
$804$	−6.03389e18	−0.787831
$805$	−1.98781e19	−2.57455
$806$	2.78840e18	0.358243
$807$	−7.58763e17	−0.0967004
$808$	−7.71169e18	−0.974935
$809$	1.32134e19	1.65710	0.828549	−	0.559916i	$-0.189167\pi$
$809$	1.32134e19	1.65710	0.828549	+	0.559916i	$0.189167\pi$
$810$	4.73630e17	0.0589233
$811$	−3.58558e18	−0.442510	−0.221255	−	0.975216i	$-0.571015\pi$
$811$	−3.58558e18	−0.442510	−0.221255	+	0.975216i	$0.571015\pi$
$812$	1.70134e19	2.08294
$813$	−2.58856e18	−0.314391
$814$	−2.92306e18	−0.352192
$815$	−1.66876e18	−0.199466
$816$	−5.22931e17	−0.0620096
$817$	6.79666e18	0.799562
$818$	−5.97129e17	−0.0696902
$819$	−4.34863e18	−0.503508
$820$	−1.48657e19	−1.70763
$821$	1.45956e18	0.166338	0.0831688	−	0.996535i	$-0.473496\pi$
$821$	1.45956e18	0.166338	0.0831688	+	0.996535i	$0.473496\pi$
$822$	4.81690e17	0.0544629
$823$	−8.13681e18	−0.912757	−0.456379	−	0.889786i	$-0.650854\pi$
$823$	−8.13681e18	−0.912757	−0.456379	+	0.889786i	$0.650854\pi$
$824$	−9.71646e18	−1.08139
$825$	−8.54169e18	−0.943177
$826$	−6.56312e17	−0.0719019
$827$	4.53647e18	0.493097	0.246548	−	0.969130i	$-0.420704\pi$
$827$	4.53647e18	0.493097	0.246548	+	0.969130i	$0.420704\pi$
$828$	2.97727e18	0.321085
$829$	−2.08028e18	−0.222596	−0.111298	−	0.993787i	$-0.535501\pi$
$829$	−2.08028e18	−0.222596	−0.111298	+	0.993787i	$0.535501\pi$
$830$	5.59178e18	0.593667
$831$	−3.52511e18	−0.371335
$832$	3.00872e18	0.314471
$833$	2.32230e18	0.240839
$834$	−2.29620e18	−0.236282
$835$	7.68472e18	0.784632
$836$	8.87993e18	0.899640
$837$	2.00163e18	0.201219
$838$	9.37706e17	0.0935364
$839$	−1.65818e19	−1.64126	−0.820632	−	0.571457i	$-0.806378\pi$
$839$	−1.65818e19	−1.64126	−0.820632	+	0.571457i	$0.806378\pi$
$840$	9.11917e18	0.895653
$841$	1.36350e19	1.32886
$842$	−6.20720e18	−0.600298
$843$	−5.62211e18	−0.539535
$844$	7.64435e17	0.0727972
$845$	−9.97184e17	−0.0942338
$846$	−1.95111e18	−0.182968
$847$	1.21075e19	1.12671
$848$	−4.97976e18	−0.459870
$849$	−9.52324e18	−0.872740
$850$	8.13229e17	0.0739588
$851$	9.25197e18	0.835011
$852$	7.86111e18	0.704087
$853$	1.58201e19	1.40617	0.703087	−	0.711103i	$-0.251804\pi$
$853$	1.58201e19	1.40617	0.703087	+	0.711103i	$0.251804\pi$
$854$	−2.44763e18	−0.215908
$855$	−4.47123e18	−0.391424
$856$	1.14911e19	0.998351
$857$	−1.07971e19	−0.930960	−0.465480	−	0.885059i	$-0.654118\pi$
$857$	−1.07971e19	−0.930960	−0.465480	+	0.885059i	$0.654118\pi$
$858$	3.03360e18	0.259592
$859$	−1.35604e19	−1.15164	−0.575821	−	0.817576i	$-0.695317\pi$
$859$	−1.35604e19	−1.15164	−0.575821	+	0.817576i	$0.695317\pi$
$860$	1.58631e19	1.33705
$861$	−1.40320e19	−1.17381
$862$	1.20837e18	0.100324
$863$	3.42847e18	0.282507	0.141254	−	0.989973i	$-0.454887\pi$
$863$	3.42847e18	0.282507	0.141254	+	0.989973i	$0.454887\pi$
$864$	−2.09439e18	−0.171285
$865$	−1.32365e19	−1.07441
$866$	−7.05771e18	−0.568588
$867$	7.01700e18	0.561084
$868$	1.79818e19	1.42710
$869$	9.91447e18	0.780982
$870$	5.97607e18	0.467241
$871$	1.94596e19	1.51014
$872$	1.27085e19	0.978896
$873$	−2.25310e18	−0.172261
$874$	4.02531e18	0.305474
$875$	7.60050e18	0.572519
$876$	8.79482e18	0.657583
$877$	−1.50516e19	−1.11708	−0.558541	−	0.829477i	$-0.688639\pi$
$877$	−1.50516e19	−1.11708	−0.558541	+	0.829477i	$0.688639\pi$
$878$	7.41541e18	0.546287
$879$	8.91025e18	0.651572
$880$	1.73321e19	1.25809
$881$	−5.85836e18	−0.422117	−0.211058	−	0.977473i	$-0.567691\pi$
$881$	−5.85836e18	−0.422117	−0.211058	+	0.977473i	$0.567691\pi$
$882$	2.36676e18	0.169281
$883$	1.29408e19	0.918790	0.459395	−	0.888232i	$-0.348066\pi$
$883$	1.29408e19	0.918790	0.459395	+	0.888232i	$0.348066\pi$
$884$	2.01667e18	0.142133
$885$	1.60969e18	0.112619
$886$	−1.69739e18	−0.117886
$887$	−5.97829e18	−0.412167	−0.206083	−	0.978534i	$-0.566072\pi$
$887$	−5.97829e18	−0.412167	−0.206083	+	0.978534i	$0.566072\pi$
$888$	−4.24439e18	−0.290490
$889$	−4.26166e19	−2.89546
$890$	−1.12402e19	−0.758122
$891$	2.17765e18	0.145808
$892$	−3.91845e18	−0.260461
$893$	1.84191e19	1.21544
$894$	2.16339e18	0.141723
$895$	−4.30384e19	−2.79902
$896$	−2.42886e19	−1.56819
$897$	−9.60185e18	−0.615466
$898$	7.80263e18	0.496529
$899$	2.52558e19	1.59559
$900$	−5.78702e18	−0.362977
$901$	−1.93724e18	−0.120635
$902$	9.78874e18	0.605179
$903$	1.49735e19	0.919079
$904$	2.06535e19	1.25863
$905$	4.36856e19	2.64315
$906$	−8.02824e17	−0.0482266
$907$	8.69133e18	0.518369	0.259185	−	0.965828i	$-0.416546\pi$
$907$	8.69133e18	0.518369	0.259185	+	0.965828i	$0.416546\pi$
$908$	2.36546e18	0.140074
$909$	8.33009e18	0.489761
$910$	−1.37223e19	−0.801046
$911$	−3.39930e19	−1.97024	−0.985122	−	0.171858i	$-0.945023\pi$
$911$	−3.39930e19	−1.97024	−0.985122	+	0.171858i	$0.945023\pi$
$912$	5.03116e18	0.289536
$913$	2.57098e19	1.46906
$914$	5.48360e18	0.311111
$915$	6.00311e18	0.338173
$916$	−2.33526e19	−1.30622
$917$	1.66313e19	0.923689
$918$	−2.07327e17	−0.0114335
$919$	−9.37352e18	−0.513277	−0.256639	−	0.966507i	$-0.582615\pi$
$919$	−9.37352e18	−0.513277	−0.256639	+	0.966507i	$0.582615\pi$
$920$	2.01353e19	1.09481
$921$	−9.06588e18	−0.489466
$922$	8.39678e18	0.450155
$923$	−2.53525e19	−1.34962
$924$	1.95631e19	1.03412
$925$	−1.79834e19	−0.943954
$926$	6.36817e18	0.331927
$927$	1.04956e19	0.543238
$928$	−2.64262e19	−1.35823
$929$	−5.54495e18	−0.283006	−0.141503	−	0.989938i	$-0.545194\pi$
$929$	−5.54495e18	−0.283006	−0.141503	+	0.989938i	$0.545194\pi$
$930$	6.31624e18	0.320125
$931$	−2.23431e19	−1.12453
$932$	7.76009e18	0.387849
$933$	−1.36438e19	−0.677181
$934$	9.64306e18	0.475291
$935$	6.74258e18	0.330028
$936$	4.40490e18	0.214113
$937$	−1.72390e19	−0.832157	−0.416079	−	0.909329i	$-0.636596\pi$
$937$	−1.72390e19	−0.832157	−0.416079	+	0.909329i	$0.636596\pi$
$938$	−1.79724e19	−0.861566
$939$	1.26453e19	0.602008
$940$	4.29895e19	2.03250
$941$	−2.51439e18	−0.118060	−0.0590298	−	0.998256i	$-0.518801\pi$
$941$	−2.51439e18	−0.118060	−0.0590298	+	0.998256i	$0.518801\pi$
$942$	−8.00892e17	−0.0373459
$943$	−3.09829e19	−1.43482
$944$	−1.81127e18	−0.0833038
$945$	−9.85043e18	−0.449934
$946$	−1.04455e19	−0.473846
$947$	−1.89103e19	−0.851969	−0.425985	−	0.904730i	$-0.640072\pi$
$947$	−1.89103e19	−0.851969	−0.425985	+	0.904730i	$0.640072\pi$
$948$	6.71708e18	0.300557
$949$	−2.83638e19	−1.26047
$950$	−7.82414e18	−0.345329
$951$	7.15376e18	0.313589
$952$	−3.99183e18	−0.173793
$953$	2.77370e18	0.119938	0.0599688	−	0.998200i	$-0.480900\pi$
$953$	2.77370e18	0.119938	0.0599688	+	0.998200i	$0.480900\pi$
$954$	−1.97433e18	−0.0847921
$955$	−2.62267e19	−1.11872
$956$	2.03503e19	0.862172
$957$	2.74767e19	1.15621
$958$	8.01766e18	0.335098
$959$	−1.00181e19	−0.415875
$960$	6.81530e18	0.281010
$961$	2.27579e18	0.0932029
$962$	6.38685e18	0.259806
$963$	−1.24126e19	−0.501524
$964$	−1.11619e19	−0.447959
$965$	−7.94769e18	−0.316820
$966$	8.86803e18	0.351136
$967$	4.35158e19	1.71149	0.855747	−	0.517395i	$-0.173098\pi$
$967$	4.35158e19	1.71149	0.855747	+	0.517395i	$0.173098\pi$
$968$	−1.22642e19	−0.479124
$969$	1.95724e18	0.0759521
$970$	−7.10976e18	−0.274056
$971$	1.11305e19	0.426175	0.213088	−	0.977033i	$-0.431648\pi$
$971$	1.11305e19	0.426175	0.213088	+	0.977033i	$0.431648\pi$
$972$	1.47536e18	0.0561136
$973$	4.77557e19	1.80423
$974$	1.59147e18	0.0597261
$975$	1.86635e19	0.695765
$976$	−6.75488e18	−0.250146
$977$	1.68696e19	0.620568	0.310284	−	0.950644i	$-0.399576\pi$
$977$	1.68696e19	0.620568	0.310284	+	0.950644i	$0.399576\pi$
$978$	7.44470e17	0.0272047
$979$	−5.16800e19	−1.87601
$980$	−5.21478e19	−1.88047
$981$	−1.37276e19	−0.491751
$982$	2.40209e18	0.0854800
$983$	2.33001e18	0.0823681	0.0411841	−	0.999152i	$-0.486887\pi$
$983$	2.33001e18	0.0823681	0.0411841	+	0.999152i	$0.486887\pi$
$984$	1.42136e19	0.499155
$985$	7.35305e19	2.56526
$986$	−2.61597e18	−0.0906636
$987$	4.05786e19	1.39713
$988$	−1.94025e19	−0.663648
$989$	3.30618e19	1.12344
$990$	6.87167e18	0.231971
$991$	3.77599e19	1.26635	0.633173	−	0.774010i	$-0.281752\pi$
$991$	3.77599e19	1.26635	0.633173	+	0.774010i	$0.281752\pi$
$992$	−2.79304e19	−0.930573
$993$	−7.09919e18	−0.234984
$994$	2.34150e19	0.769984
$995$	1.74048e19	0.568615
$996$	1.74185e19	0.565359
$997$	6.10950e19	1.97009	0.985047	−	0.172287i	$-0.0551158\pi$
$997$	6.10950e19	1.97009	0.985047	+	0.172287i	$0.0551158\pi$
$998$	−7.78488e18	−0.249404
$999$	4.58475e18	0.145929

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.b.1.18	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.b.1.18	✓	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)

\(f(q)\)	\(=\)	\(q+32.0352 q^{2} -729.000 q^{3} -7165.75 q^{4} +52348.2 q^{5} -23353.7 q^{6} +485703. q^{7} -491988. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+32.0352 q^{2} -729.000 q^{3} -7165.75 q^{4} +52348.2 q^{5} -23353.7 q^{6} +485703. q^{7} -491988. q^{8} +531441. q^{9} +1.67699e6 q^{10} +7.71041e6 q^{11} +5.22383e6 q^{12} -1.68471e7 q^{13} +1.55596e7 q^{14} -3.81619e7 q^{15} +4.29408e7 q^{16} +1.67050e7 q^{17} +1.70248e7 q^{18} -1.60720e8 q^{19} -3.75114e8 q^{20} -3.54078e8 q^{21} +2.47005e8 q^{22} -7.81810e8 q^{23} +3.58660e8 q^{24} +1.51963e9 q^{25} -5.39701e8 q^{26} -3.87420e8 q^{27} -3.48042e9 q^{28} -4.88831e9 q^{29} -1.22252e9 q^{30} -5.16656e9 q^{31} +5.40599e9 q^{32} -5.62089e9 q^{33} +5.35148e8 q^{34} +2.54257e10 q^{35} -3.80817e9 q^{36} -1.18340e10 q^{37} -5.14870e9 q^{38} +1.22816e10 q^{39} -2.57547e10 q^{40} +3.96298e10 q^{41} -1.13429e10 q^{42} -4.22888e10 q^{43} -5.52509e10 q^{44} +2.78200e10 q^{45} -2.50454e10 q^{46} -1.14604e11 q^{47} -3.13039e10 q^{48} +1.39018e11 q^{49} +4.86818e10 q^{50} -1.21779e10 q^{51} +1.20722e11 q^{52} -1.15968e11 q^{53} -1.24111e10 q^{54} +4.03626e11 q^{55} -2.38960e11 q^{56} +1.17165e11 q^{57} -1.56598e11 q^{58} -4.21805e10 q^{59} +2.73458e11 q^{60} -1.57307e11 q^{61} -1.65512e11 q^{62} +2.58123e11 q^{63} -1.78589e11 q^{64} -8.81918e11 q^{65} -1.80066e11 q^{66} -1.15507e12 q^{67} -1.19704e11 q^{68} +5.69939e11 q^{69} +8.14517e11 q^{70} +1.50486e12 q^{71} -2.61463e11 q^{72} +1.68360e12 q^{73} -3.79106e11 q^{74} -1.10781e12 q^{75} +1.15168e12 q^{76} +3.74497e12 q^{77} +3.93442e11 q^{78} +1.28585e12 q^{79} +2.24788e12 q^{80} +2.82430e11 q^{81} +1.26955e12 q^{82} +3.33442e12 q^{83} +2.53723e12 q^{84} +8.74477e11 q^{85} -1.35473e12 q^{86} +3.56358e12 q^{87} -3.79343e12 q^{88} -6.70262e12 q^{89} +8.91219e11 q^{90} -8.18271e12 q^{91} +5.60225e12 q^{92} +3.76642e12 q^{93} -3.67135e12 q^{94} -8.41341e12 q^{95} -3.94097e12 q^{96} -4.23961e12 q^{97} +4.45348e12 q^{98} +4.09763e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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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