LMFDB - Embedded newform 177.14.a.b.1.31

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			1.31
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)

$f(q)$	$=$	$q+168.501 q^{2} -729.000 q^{3} +20200.7 q^{4} -50694.6 q^{5} -122837. q^{6} +203067. q^{7} +2.02347e6 q^{8} +531441. q^{9} +O(q^{10})$	\(q+168.501 q^{2} -729.000 q^{3} +20200.7 q^{4} -50694.6 q^{5} -122837. q^{6} +203067. q^{7} +2.02347e6 q^{8} +531441. q^{9} -8.54210e6 q^{10} -3.23415e6 q^{11} -1.47263e7 q^{12} +1.43528e7 q^{13} +3.42170e7 q^{14} +3.69563e7 q^{15} +1.75474e8 q^{16} -9.48472e7 q^{17} +8.95485e7 q^{18} -7.38001e7 q^{19} -1.02406e9 q^{20} -1.48036e8 q^{21} -5.44959e8 q^{22} +2.17725e8 q^{23} -1.47511e9 q^{24} +1.34924e9 q^{25} +2.41847e9 q^{26} -3.87420e8 q^{27} +4.10208e9 q^{28} +1.43412e9 q^{29} +6.22719e9 q^{30} -2.08317e9 q^{31} +1.29913e10 q^{32} +2.35770e9 q^{33} -1.59819e10 q^{34} -1.02944e10 q^{35} +1.07355e10 q^{36} -8.62553e9 q^{37} -1.24354e10 q^{38} -1.04632e10 q^{39} -1.02579e11 q^{40} +1.89443e10 q^{41} -2.49442e10 q^{42} -2.90685e10 q^{43} -6.53320e10 q^{44} -2.69412e10 q^{45} +3.66869e10 q^{46} +3.92325e10 q^{47} -1.27921e11 q^{48} -5.56530e10 q^{49} +2.27348e11 q^{50} +6.91436e10 q^{51} +2.89937e11 q^{52} +1.89361e10 q^{53} -6.52808e10 q^{54} +1.63954e11 q^{55} +4.10900e11 q^{56} +5.38002e10 q^{57} +2.41651e11 q^{58} -4.21805e10 q^{59} +7.46542e11 q^{60} -3.32293e11 q^{61} -3.51016e11 q^{62} +1.07918e11 q^{63} +7.51563e11 q^{64} -7.27611e11 q^{65} +3.97275e11 q^{66} +4.65879e11 q^{67} -1.91598e12 q^{68} -1.58721e11 q^{69} -1.73461e12 q^{70} -1.25103e12 q^{71} +1.07536e12 q^{72} -4.92390e11 q^{73} -1.45341e12 q^{74} -9.83593e11 q^{75} -1.49081e12 q^{76} -6.56748e11 q^{77} -1.76307e12 q^{78} -1.86849e12 q^{79} -8.89557e12 q^{80} +2.82430e11 q^{81} +3.19213e12 q^{82} -5.31370e11 q^{83} -2.99042e12 q^{84} +4.80824e12 q^{85} -4.89807e12 q^{86} -1.04547e12 q^{87} -6.54422e12 q^{88} -9.16175e12 q^{89} -4.53962e12 q^{90} +2.91458e12 q^{91} +4.39818e12 q^{92} +1.51863e12 q^{93} +6.61073e12 q^{94} +3.74126e12 q^{95} -9.47064e12 q^{96} -5.98758e12 q^{97} -9.37759e12 q^{98} -1.71876e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	168.501	1.86169	0.930846	−	0.365410i	$-0.119071\pi$
$2$	168.501	1.86169	0.930846	+	0.365410i	$0.119071\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	20200.7	2.46590
$5$	−50694.6	−1.45096	−0.725482	−	0.688242i	$-0.758383\pi$
$5$	−50694.6	−1.45096	−0.725482	+	0.688242i	$0.758383\pi$
$6$	−122837.	−1.07485
$7$	203067.	0.652381	0.326190	−	0.945304i	$-0.394235\pi$
$7$	203067.	0.652381	0.326190	+	0.945304i	$0.394235\pi$
$8$	2.02347e6	2.72906
$9$	531441.	0.333333
$10$	−8.54210e6	−2.70125
$11$	−3.23415e6	−0.550438	−0.275219	−	0.961382i	$-0.588750\pi$
$11$	−3.23415e6	−0.550438	−0.275219	+	0.961382i	$0.588750\pi$
$12$	−1.47263e7	−1.42369
$13$	1.43528e7	0.824719	0.412360	−	0.911021i	$-0.364705\pi$
$13$	1.43528e7	0.824719	0.412360	+	0.911021i	$0.364705\pi$
$14$	3.42170e7	1.21453
$15$	3.69563e7	0.837714
$16$	1.75474e8	2.61477
$17$	−9.48472e7	−0.953030	−0.476515	−	0.879166i	$-0.658100\pi$
$17$	−9.48472e7	−0.953030	−0.476515	+	0.879166i	$0.658100\pi$
$18$	8.95485e7	0.620564
$19$	−7.38001e7	−0.359880	−0.179940	−	0.983678i	$-0.557590\pi$
$19$	−7.38001e7	−0.359880	−0.179940	+	0.983678i	$0.557590\pi$
$20$	−1.02406e9	−3.57793
$21$	−1.48036e8	−0.376652
$22$	−5.44959e8	−1.02475
$23$	2.17725e8	0.306674	0.153337	−	0.988174i	$-0.450998\pi$
$23$	2.17725e8	0.306674	0.153337	+	0.988174i	$0.450998\pi$
$24$	−1.47511e9	−1.57562
$25$	1.34924e9	1.10529
$26$	2.41847e9	1.53537
$27$	−3.87420e8	−0.192450
$28$	4.10208e9	1.60871
$29$	1.43412e9	0.447712	0.223856	−	0.974622i	$-0.428135\pi$
$29$	1.43412e9	0.447712	0.223856	+	0.974622i	$0.428135\pi$
$30$	6.22719e9	1.55957
$31$	−2.08317e9	−0.421574	−0.210787	−	0.977532i	$-0.567603\pi$
$31$	−2.08317e9	−0.421574	−0.210787	+	0.977532i	$0.567603\pi$
$32$	1.29913e10	2.13883
$33$	2.35770e9	0.317795
$34$	−1.59819e10	−1.77425
$35$	−1.02944e10	−0.946581
$36$	1.07355e10	0.821967
$37$	−8.62553e9	−0.552681	−0.276341	−	0.961060i	$-0.589122\pi$
$37$	−8.62553e9	−0.552681	−0.276341	+	0.961060i	$0.589122\pi$
$38$	−1.24354e10	−0.669987
$39$	−1.04632e10	−0.476152
$40$	−1.02579e11	−3.95976
$41$	1.89443e10	0.622849	0.311425	−	0.950271i	$-0.399194\pi$
$41$	1.89443e10	0.622849	0.311425	+	0.950271i	$0.399194\pi$
$42$	−2.49442e10	−0.701211
$43$	−2.90685e10	−0.701257	−0.350629	−	0.936515i	$-0.614032\pi$
$43$	−2.90685e10	−0.701257	−0.350629	+	0.936515i	$0.614032\pi$
$44$	−6.53320e10	−1.35732
$45$	−2.69412e10	−0.483654
$46$	3.66869e10	0.570933
$47$	3.92325e10	0.530897	0.265448	−	0.964125i	$-0.414480\pi$
$47$	3.92325e10	0.530897	0.265448	+	0.964125i	$0.414480\pi$
$48$	−1.27921e11	−1.50964
$49$	−5.56530e10	−0.574399
$50$	2.27348e11	2.05772
$51$	6.91436e10	0.550232
$52$	2.89937e11	2.03368
$53$	1.89361e10	0.117354	0.0586771	−	0.998277i	$-0.481312\pi$
$53$	1.89361e10	0.117354	0.0586771	+	0.998277i	$0.481312\pi$
$54$	−6.52808e10	−0.358283
$55$	1.63954e11	0.798664
$56$	4.10900e11	1.78038
$57$	5.38002e10	0.207777
$58$	2.41651e11	0.833502
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	7.46542e11	2.06572
$61$	−3.32293e11	−0.825804	−0.412902	−	0.910775i	$-0.635485\pi$
$61$	−3.32293e11	−0.825804	−0.412902	+	0.910775i	$0.635485\pi$
$62$	−3.51016e11	−0.784841
$63$	1.07918e11	0.217460
$64$	7.51563e11	1.36709
$65$	−7.27611e11	−1.19664
$66$	3.97275e11	0.591637
$67$	4.65879e11	0.629197	0.314599	−	0.949225i	$-0.398130\pi$
$67$	4.65879e11	0.629197	0.314599	+	0.949225i	$0.398130\pi$
$68$	−1.91598e12	−2.35008
$69$	−1.58721e11	−0.177058
$70$	−1.73461e12	−1.76224
$71$	−1.25103e12	−1.15901	−0.579507	−	0.814967i	$-0.696755\pi$
$71$	−1.25103e12	−1.15901	−0.579507	+	0.814967i	$0.696755\pi$
$72$	1.07536e12	0.909686
$73$	−4.92390e11	−0.380812	−0.190406	−	0.981705i	$-0.560980\pi$
$73$	−4.92390e11	−0.380812	−0.190406	+	0.981705i	$0.560980\pi$
$74$	−1.45341e12	−1.02892
$75$	−9.83593e11	−0.638142
$76$	−1.49081e12	−0.887429
$77$	−6.56748e11	−0.359095
$78$	−1.76307e12	−0.886449
$79$	−1.86849e12	−0.864797	−0.432398	−	0.901683i	$-0.642333\pi$
$79$	−1.86849e12	−0.864797	−0.432398	+	0.901683i	$0.642333\pi$
$80$	−8.89557e12	−3.79393
$81$	2.82430e11	0.111111
$82$	3.19213e12	1.15955
$83$	−5.31370e11	−0.178398	−0.0891990	−	0.996014i	$-0.528431\pi$
$83$	−5.31370e11	−0.178398	−0.0891990	+	0.996014i	$0.528431\pi$
$84$	−2.99042e12	−0.928787
$85$	4.80824e12	1.38281
$86$	−4.89807e12	−1.30553
$87$	−1.04547e12	−0.258487
$88$	−6.54422e12	−1.50218
$89$	−9.16175e12	−1.95408	−0.977042	−	0.213046i	$-0.931661\pi$
$89$	−9.16175e12	−1.95408	−0.977042	+	0.213046i	$0.931661\pi$
$90$	−4.53962e12	−0.900416
$91$	2.91458e12	0.538031
$92$	4.39818e12	0.756228
$93$	1.51863e12	0.243396
$94$	6.61073e12	0.988367
$95$	3.74126e12	0.522173
$96$	−9.47064e12	−1.23486
$97$	−5.98758e12	−0.729853	−0.364926	−	0.931036i	$-0.618906\pi$
$97$	−5.98758e12	−0.729853	−0.364926	+	0.931036i	$0.618906\pi$
$98$	−9.37759e12	−1.06935
$99$	−1.71876e12	−0.183479
$100$	2.72554e13	2.72554
$101$	−1.88584e12	−0.176773	−0.0883863	−	0.996086i	$-0.528171\pi$
$101$	−1.88584e12	−0.176773	−0.0883863	+	0.996086i	$0.528171\pi$
$102$	1.16508e13	1.02436
$103$	−2.09376e13	−1.72776	−0.863881	−	0.503696i	$-0.831973\pi$
$103$	−2.09376e13	−1.72776	−0.863881	+	0.503696i	$0.831973\pi$
$104$	2.90426e13	2.25071
$105$	7.50460e12	0.546509
$106$	3.19076e12	0.218477
$107$	9.27640e10	0.00597564	0.00298782	−	0.999996i	$-0.499049\pi$
$107$	9.27640e10	0.00597564	0.00298782	+	0.999996i	$0.499049\pi$
$108$	−7.82615e12	−0.474563
$109$	−1.05607e13	−0.603143	−0.301571	−	0.953444i	$-0.597511\pi$
$109$	−1.05607e13	−0.603143	−0.301571	+	0.953444i	$0.597511\pi$
$110$	2.76264e13	1.48687
$111$	6.28801e12	0.319091
$112$	3.56329e13	1.70582
$113$	1.77414e13	0.801638	0.400819	−	0.916157i	$-0.368726\pi$
$113$	1.77414e13	0.801638	0.400819	+	0.916157i	$0.368726\pi$
$114$	9.06541e12	0.386817
$115$	−1.10375e13	−0.444973
$116$	2.89702e13	1.10401
$117$	7.62769e12	0.274906
$118$	−7.10747e12	−0.242372
$119$	−1.92603e13	−0.621739
$120$	7.47802e13	2.28617
$121$	−2.40630e13	−0.697019
$122$	−5.59917e13	−1.53739
$123$	−1.38104e13	−0.359602
$124$	−4.20814e13	−1.03956
$125$	−6.51590e12	−0.152777
$126$	1.81843e13	0.404844
$127$	−4.01863e13	−0.849873	−0.424937	−	0.905223i	$-0.639704\pi$
$127$	−4.01863e13	−0.849873	−0.424937	+	0.905223i	$0.639704\pi$
$128$	2.02148e13	0.406260
$129$	2.11909e13	0.404871
$130$	−1.22603e14	−2.22777
$131$	−1.11722e14	−1.93142	−0.965711	−	0.259621i	$-0.916402\pi$
$131$	−1.11722e14	−1.93142	−0.965711	+	0.259621i	$0.916402\pi$
$132$	4.76270e13	0.783652
$133$	−1.49863e13	−0.234779
$134$	7.85012e13	1.17137
$135$	1.96401e13	0.279238
$136$	−1.91921e14	−2.60087
$137$	1.29279e14	1.67049	0.835243	−	0.549881i	$-0.185327\pi$
$137$	1.29279e14	1.67049	0.835243	+	0.549881i	$0.185327\pi$
$138$	−2.67447e13	−0.329628
$139$	−7.77542e13	−0.914382	−0.457191	−	0.889368i	$-0.651144\pi$
$139$	−7.77542e13	−0.914382	−0.457191	+	0.889368i	$0.651144\pi$
$140$	−2.07953e14	−2.33417
$141$	−2.86005e13	−0.306514
$142$	−2.10800e14	−2.15773
$143$	−4.64193e13	−0.453956
$144$	9.32540e13	0.871588
$145$	−7.27021e13	−0.649613
$146$	−8.29684e13	−0.708956
$147$	4.05710e13	0.331630
$148$	−1.74241e14	−1.36286
$149$	1.16204e14	0.869980	0.434990	−	0.900435i	$-0.356752\pi$
$149$	1.16204e14	0.869980	0.434990	+	0.900435i	$0.356752\pi$
$150$	−1.65737e14	−1.18802
$151$	−5.32989e13	−0.365905	−0.182952	−	0.983122i	$-0.558565\pi$
$151$	−5.32989e13	−0.365905	−0.182952	+	0.983122i	$0.558565\pi$
$152$	−1.49332e14	−0.982134
$153$	−5.04057e13	−0.317677
$154$	−1.10663e14	−0.668524
$155$	1.05605e14	0.611688
$156$	−2.11364e14	−1.17414
$157$	1.36296e14	0.726330	0.363165	−	0.931725i	$-0.381696\pi$
$157$	1.36296e14	0.726330	0.363165	+	0.931725i	$0.381696\pi$
$158$	−3.14842e14	−1.60999
$159$	−1.38045e13	−0.0677545
$160$	−6.58587e14	−3.10337
$161$	4.42126e13	0.200068
$162$	4.75897e13	0.206855
$163$	−1.20959e14	−0.505149	−0.252575	−	0.967577i	$-0.581277\pi$
$163$	−1.20959e14	−0.505149	−0.252575	+	0.967577i	$0.581277\pi$
$164$	3.82687e14	1.53588
$165$	−1.19522e14	−0.461109
$166$	−8.95366e13	−0.332122
$167$	3.87286e14	1.38158	0.690788	−	0.723057i	$-0.257264\pi$
$167$	3.87286e14	1.38158	0.690788	+	0.723057i	$0.257264\pi$
$168$	−2.99546e14	−1.02791
$169$	−9.68710e13	−0.319838
$170$	8.10194e14	2.57437
$171$	−3.92204e13	−0.119960
$172$	−5.87202e14	−1.72923
$173$	8.26140e13	0.234290	0.117145	−	0.993115i	$-0.462626\pi$
$173$	8.26140e13	0.234290	0.117145	+	0.993115i	$0.462626\pi$
$174$	−1.76164e14	−0.481223
$175$	2.73985e14	0.721073
$176$	−5.67509e14	−1.43926
$177$	3.07496e13	0.0751646
$178$	−1.54377e15	−3.63790
$179$	−3.40633e14	−0.774001	−0.387001	−	0.922079i	$-0.626489\pi$
$179$	−3.40633e14	−0.774001	−0.387001	+	0.922079i	$0.626489\pi$
$180$	−5.44229e14	−1.19264
$181$	−7.04001e14	−1.48820	−0.744102	−	0.668066i	$-0.767122\pi$
$181$	−7.04001e14	−1.48820	−0.744102	+	0.668066i	$0.767122\pi$
$182$	4.91111e14	1.00165
$183$	2.42241e14	0.476778
$184$	4.40560e14	0.836931
$185$	4.37268e14	0.801920
$186$	2.55891e14	0.453128
$187$	3.06750e14	0.524584
$188$	7.92523e14	1.30914
$189$	−7.86722e13	−0.125551
$190$	6.30407e14	0.972126
$191$	8.25015e14	1.22955	0.614774	−	0.788704i	$-0.289247\pi$
$191$	8.25015e14	1.22955	0.614774	+	0.788704i	$0.289247\pi$
$192$	−5.47890e14	−0.789287
$193$	7.28555e14	1.01471	0.507353	−	0.861739i	$-0.330624\pi$
$193$	7.28555e14	1.01471	0.507353	+	0.861739i	$0.330624\pi$
$194$	−1.00892e15	−1.35876
$195$	5.30428e14	0.690879
$196$	−1.12423e15	−1.41641
$197$	−1.94460e14	−0.237028	−0.118514	−	0.992952i	$-0.537813\pi$
$197$	−1.94460e14	−0.237028	−0.118514	+	0.992952i	$0.537813\pi$
$198$	−2.89613e14	−0.341582
$199$	−1.44168e15	−1.64560	−0.822800	−	0.568331i	$-0.807589\pi$
$199$	−1.44168e15	−1.64560	−0.822800	+	0.568331i	$0.807589\pi$
$200$	2.73014e15	3.01641
$201$	−3.39626e14	−0.363267
$202$	−3.17766e14	−0.329096
$203$	2.91222e14	0.292079
$204$	1.39675e15	1.35682
$205$	−9.60372e14	−0.903731
$206$	−3.52800e15	−3.21656
$207$	1.15708e14	0.102225
$208$	2.51855e15	2.15645
$209$	2.38681e14	0.198092
$210$	1.26453e15	1.01743
$211$	−3.90316e14	−0.304495	−0.152248	−	0.988342i	$-0.548651\pi$
$211$	−3.90316e14	−0.304495	−0.152248	+	0.988342i	$0.548651\pi$
$212$	3.82523e14	0.289384
$213$	9.12002e14	0.669157
$214$	1.56308e13	0.0111248
$215$	1.47361e15	1.01750
$216$	−7.83935e14	−0.525207
$217$	−4.23022e14	−0.275027
$218$	−1.77949e15	−1.12287
$219$	3.58953e14	0.219862
$220$	3.31198e15	1.96943
$221$	−1.36133e15	−0.785982
$222$	1.05954e15	0.594049
$223$	2.33569e15	1.27185	0.635923	−	0.771753i	$-0.280620\pi$
$223$	2.33569e15	1.27185	0.635923	+	0.771753i	$0.280620\pi$
$224$	2.63809e15	1.39533
$225$	7.17039e14	0.368431
$226$	2.98945e15	1.49240
$227$	9.74913e14	0.472931	0.236465	−	0.971640i	$-0.424011\pi$
$227$	9.74913e14	0.472931	0.236465	+	0.971640i	$0.424011\pi$
$228$	1.08680e15	0.512358
$229$	3.10294e15	1.42181	0.710907	−	0.703286i	$-0.248285\pi$
$229$	3.10294e15	1.42181	0.710907	+	0.703286i	$0.248285\pi$
$230$	−1.85983e15	−0.828402
$231$	4.78769e14	0.207324
$232$	2.90190e15	1.22183
$233$	1.91674e15	0.784783	0.392392	−	0.919798i	$-0.371648\pi$
$233$	1.91674e15	0.784783	0.392392	+	0.919798i	$0.371648\pi$
$234$	1.28527e15	0.511791
$235$	−1.98888e15	−0.770312
$236$	−8.52075e14	−0.321033
$237$	1.36213e15	0.499291
$238$	−3.24538e15	−1.15749
$239$	5.00132e15	1.73579	0.867896	−	0.496745i	$-0.165472\pi$
$239$	5.00132e15	1.73579	0.867896	+	0.496745i	$0.165472\pi$
$240$	6.48487e15	2.19043
$241$	3.09755e14	0.101837	0.0509187	−	0.998703i	$-0.483785\pi$
$241$	3.09755e14	0.101837	0.0509187	+	0.998703i	$0.483785\pi$
$242$	−4.05464e15	−1.29763
$243$	−2.05891e14	−0.0641500
$244$	−6.71253e15	−2.03635
$245$	2.82130e15	0.833432
$246$	−2.32707e15	−0.669469
$247$	−1.05924e15	−0.296800
$248$	−4.21524e15	−1.15050
$249$	3.87369e14	0.102998
$250$	−1.09794e15	−0.284425
$251$	5.03608e15	1.27120	0.635599	−	0.772020i	$-0.280753\pi$
$251$	5.03608e15	1.27120	0.635599	+	0.772020i	$0.280753\pi$
$252$	2.18001e15	0.536235
$253$	−7.04155e14	−0.168805
$254$	−6.77145e15	−1.58220
$255$	−3.50521e15	−0.798367
$256$	−2.75059e15	−0.610753
$257$	−1.51105e15	−0.327125	−0.163562	−	0.986533i	$-0.552299\pi$
$257$	−1.51105e15	−0.327125	−0.163562	+	0.986533i	$0.552299\pi$
$258$	3.57069e15	0.753745
$259$	−1.75156e15	−0.360559
$260$	−1.46982e16	−2.95079
$261$	7.62150e14	0.149237
$262$	−1.88254e16	−3.59571
$263$	2.81323e15	0.524194	0.262097	−	0.965041i	$-0.415586\pi$
$263$	2.81323e15	0.524194	0.262097	+	0.965041i	$0.415586\pi$
$264$	4.77074e15	0.867281
$265$	−9.59960e14	−0.170277
$266$	−2.52521e15	−0.437087
$267$	6.67891e15	1.12819
$268$	9.41106e15	1.55154
$269$	−4.93370e15	−0.793931	−0.396965	−	0.917834i	$-0.629937\pi$
$269$	−4.93370e15	−0.793931	−0.396965	+	0.917834i	$0.629937\pi$
$270$	3.30938e15	0.519855
$271$	−3.42205e15	−0.524791	−0.262395	−	0.964960i	$-0.584512\pi$
$271$	−3.42205e15	−0.524791	−0.262395	+	0.964960i	$0.584512\pi$
$272$	−1.66432e16	−2.49195
$273$	−2.12473e15	−0.310632
$274$	2.17836e16	3.10993
$275$	−4.36363e15	−0.608395
$276$	−3.20628e15	−0.436608
$277$	−2.62060e15	−0.348564	−0.174282	−	0.984696i	$-0.555760\pi$
$277$	−2.62060e15	−0.348564	−0.174282	+	0.984696i	$0.555760\pi$
$278$	−1.31017e16	−1.70230
$279$	−1.10708e15	−0.140525
$280$	−2.08304e16	−2.58327
$281$	−3.48170e15	−0.421891	−0.210946	−	0.977498i	$-0.567654\pi$
$281$	−3.48170e15	−0.421891	−0.210946	+	0.977498i	$0.567654\pi$
$282$	−4.81922e15	−0.570634
$283$	−2.94322e15	−0.340574	−0.170287	−	0.985395i	$-0.554469\pi$
$283$	−2.94322e15	−0.340574	−0.170287	+	0.985395i	$0.554469\pi$
$284$	−2.52717e16	−2.85801
$285$	−2.72738e15	−0.301477
$286$	−7.82170e15	−0.845127
$287$	3.84695e15	0.406335
$288$	6.90410e15	0.712944
$289$	−9.08579e14	−0.0917332
$290$	−1.22504e16	−1.20938
$291$	4.36495e15	0.421381
$292$	−9.94661e15	−0.939045
$293$	−1.05756e15	−0.0976485	−0.0488243	−	0.998807i	$-0.515547\pi$
$293$	−1.05756e15	−0.0976485	−0.0488243	+	0.998807i	$0.515547\pi$
$294$	6.83627e15	0.617392
$295$	2.13832e15	0.188899
$296$	−1.74535e16	−1.50830
$297$	1.25298e15	0.105932
$298$	1.95805e16	1.61964
$299$	3.12497e15	0.252920
$300$	−1.98692e16	−1.57359
$301$	−5.90284e15	−0.457487
$302$	−8.98093e15	−0.681203
$303$	1.37477e15	0.102060
$304$	−1.29500e16	−0.941003
$305$	1.68454e16	1.19821
$306$	−8.49342e15	−0.591417
$307$	−6.67626e15	−0.455129	−0.227564	−	0.973763i	$-0.573076\pi$
$307$	−6.67626e15	−0.455129	−0.227564	+	0.973763i	$0.573076\pi$
$308$	−1.32667e16	−0.885492
$309$	1.52635e16	0.997524
$310$	1.77946e16	1.13877
$311$	1.32241e16	0.828751	0.414375	−	0.910106i	$-0.364000\pi$
$311$	1.32241e16	0.828751	0.414375	+	0.910106i	$0.364000\pi$
$312$	−2.11721e16	−1.29945
$313$	−1.55866e16	−0.936942	−0.468471	−	0.883479i	$-0.655195\pi$
$313$	−1.55866e16	−0.936942	−0.468471	+	0.883479i	$0.655195\pi$
$314$	2.29660e16	1.35220
$315$	−5.47085e15	−0.315527
$316$	−3.77447e16	−2.13250
$317$	2.55252e16	1.41281	0.706405	−	0.707808i	$-0.250316\pi$
$317$	2.55252e16	1.41281	0.706405	+	0.707808i	$0.250316\pi$
$318$	−2.32607e15	−0.126138
$319$	−4.63816e15	−0.246437
$320$	−3.81002e16	−1.98359
$321$	−6.76249e13	−0.00345004
$322$	7.44988e15	0.372466
$323$	6.99973e15	0.342977
$324$	5.70526e15	0.273989
$325$	1.93654e16	0.911557
$326$	−2.03818e16	−0.940433
$327$	7.69874e15	0.348225
$328$	3.83332e16	1.69979
$329$	7.96682e15	0.346347
$330$	−2.01397e16	−0.858444
$331$	4.24193e16	1.77289	0.886443	−	0.462837i	$-0.153168\pi$
$331$	4.24193e16	1.77289	0.886443	+	0.462837i	$0.153168\pi$
$332$	−1.07340e16	−0.439912
$333$	−4.58396e15	−0.184227
$334$	6.52582e16	2.57207
$335$	−2.36175e16	−0.912942
$336$	−2.59764e16	−0.984857
$337$	−3.01032e15	−0.111948	−0.0559742	−	0.998432i	$-0.517826\pi$
$337$	−3.01032e15	−0.111948	−0.0559742	+	0.998432i	$0.517826\pi$
$338$	−1.63229e16	−0.595440
$339$	−1.29335e16	−0.462826
$340$	9.71296e16	3.40988
$341$	6.73729e15	0.232050
$342$	−6.60868e15	−0.223329
$343$	−3.09762e16	−1.02711
$344$	−5.88193e16	−1.91377
$345$	8.04631e15	0.256905
$346$	1.39206e16	0.436176
$347$	−9.80771e15	−0.301596	−0.150798	−	0.988565i	$-0.548184\pi$
$347$	−9.80771e15	−0.301596	−0.150798	+	0.988565i	$0.548184\pi$
$348$	−2.11193e16	−0.637402
$349$	4.35415e16	1.28985	0.644924	−	0.764247i	$-0.276889\pi$
$349$	4.35415e16	1.28985	0.644924	+	0.764247i	$0.276889\pi$
$350$	4.61667e16	1.34242
$351$	−5.56059e15	−0.158717
$352$	−4.20158e16	−1.17729
$353$	−8.84246e15	−0.243241	−0.121621	−	0.992577i	$-0.538809\pi$
$353$	−8.84246e15	−0.243241	−0.121621	+	0.992577i	$0.538809\pi$
$354$	5.18135e15	0.139933
$355$	6.34205e16	1.68169
$356$	−1.85073e17	−4.81858
$357$	1.40408e16	0.358961
$358$	−5.73970e16	−1.44095
$359$	−4.29788e16	−1.05960	−0.529798	−	0.848124i	$-0.677732\pi$
$359$	−4.29788e16	−1.05960	−0.529798	+	0.848124i	$0.677732\pi$
$360$	−5.45147e16	−1.31992
$361$	−3.66065e16	−0.870486
$362$	−1.18625e17	−2.77058
$363$	1.75419e16	0.402424
$364$	5.88765e16	1.32673
$365$	2.49615e16	0.552545
$366$	4.08180e16	0.887614
$367$	−7.07028e16	−1.51045	−0.755226	−	0.655464i	$-0.772473\pi$
$367$	−7.07028e16	−1.51045	−0.755226	+	0.655464i	$0.772473\pi$
$368$	3.82050e16	0.801881
$369$	1.00678e16	0.207616
$370$	7.36801e16	1.49293
$371$	3.84530e15	0.0765596
$372$	3.06773e16	0.600190
$373$	−2.64667e16	−0.508854	−0.254427	−	0.967092i	$-0.581887\pi$
$373$	−2.64667e16	−0.508854	−0.254427	+	0.967092i	$0.581887\pi$
$374$	5.16878e16	0.976614
$375$	4.75009e15	0.0882061
$376$	7.93860e16	1.44885
$377$	2.05837e16	0.369237
$378$	−1.32564e16	−0.233737
$379$	7.60516e16	1.31812	0.659058	−	0.752093i	$-0.270955\pi$
$379$	7.60516e16	1.31812	0.659058	+	0.752093i	$0.270955\pi$
$380$	7.55759e16	1.28763
$381$	2.92958e16	0.490675
$382$	1.39016e17	2.28904
$383$	1.51514e16	0.245279	0.122639	−	0.992451i	$-0.460864\pi$
$383$	1.51514e16	0.245279	0.122639	+	0.992451i	$0.460864\pi$
$384$	−1.47366e16	−0.234555
$385$	3.32936e16	0.521033
$386$	1.22762e17	1.88907
$387$	−1.54482e16	−0.233752
$388$	−1.20953e17	−1.79974
$389$	5.58564e15	0.0817336	0.0408668	−	0.999165i	$-0.486988\pi$
$389$	5.58564e15	0.0817336	0.0408668	+	0.999165i	$0.486988\pi$
$390$	8.93778e16	1.28620
$391$	−2.06506e16	−0.292270
$392$	−1.12612e17	−1.56757
$393$	8.14457e16	1.11511
$394$	−3.27668e16	−0.441274
$395$	9.47221e16	1.25479
$396$	−3.47201e16	−0.452441
$397$	−1.10559e17	−1.41729	−0.708643	−	0.705567i	$-0.750692\pi$
$397$	−1.10559e17	−1.41729	−0.708643	+	0.705567i	$0.750692\pi$
$398$	−2.42925e17	−3.06360
$399$	1.09250e16	0.135550
$400$	2.36756e17	2.89008
$401$	−7.58411e16	−0.910891	−0.455446	−	0.890264i	$-0.650520\pi$
$401$	−7.58411e16	−0.910891	−0.455446	+	0.890264i	$0.650520\pi$
$402$	−5.72274e16	−0.676292
$403$	−2.98994e16	−0.347680
$404$	−3.80951e16	−0.435904
$405$	−1.43176e16	−0.161218
$406$	4.90712e16	0.543761
$407$	2.78963e16	0.304217
$408$	1.39910e17	1.50162
$409$	−8.74110e15	−0.0923346	−0.0461673	−	0.998934i	$-0.514701\pi$
$409$	−8.74110e15	−0.0923346	−0.0461673	+	0.998934i	$0.514701\pi$
$410$	−1.61824e17	−1.68247
$411$	−9.42441e16	−0.964456
$412$	−4.22952e17	−4.26049
$413$	−8.56546e15	−0.0849328
$414$	1.94969e16	0.190311
$415$	2.69376e16	0.258849
$416$	1.86462e17	1.76394
$417$	5.66828e16	0.527919
$418$	4.02180e16	0.368786
$419$	−1.60247e17	−1.44677	−0.723383	−	0.690447i	$-0.757414\pi$
$419$	−1.60247e17	−1.44677	−0.723383	+	0.690447i	$0.757414\pi$
$420$	1.51598e17	1.34764
$421$	9.57202e16	0.837857	0.418928	−	0.908019i	$-0.362406\pi$
$421$	9.57202e16	0.837857	0.418928	+	0.908019i	$0.362406\pi$
$422$	−6.57688e16	−0.566877
$423$	2.08498e16	0.176966
$424$	3.83168e16	0.320266
$425$	−1.27971e17	−1.05338
$426$	1.53673e17	1.24577
$427$	−6.74776e16	−0.538739
$428$	1.87389e15	0.0147353
$429$	3.38397e16	0.262092
$430$	2.48306e17	1.89427
$431$	−4.18322e16	−0.314346	−0.157173	−	0.987571i	$-0.550238\pi$
$431$	−4.18322e16	−0.314346	−0.157173	+	0.987571i	$0.550238\pi$
$432$	−6.79822e16	−0.503212
$433$	−1.73552e17	−1.26549	−0.632745	−	0.774360i	$-0.718072\pi$
$433$	−1.73552e17	−1.26549	−0.632745	+	0.774360i	$0.718072\pi$
$434$	−7.12797e16	−0.512015
$435$	5.29998e16	0.375054
$436$	−2.13333e17	−1.48729
$437$	−1.60681e16	−0.110366
$438$	6.04839e16	0.409316
$439$	−6.85968e14	−0.00457388	−0.00228694	−	0.999997i	$-0.500728\pi$
$439$	−6.85968e14	−0.00457388	−0.00228694	+	0.999997i	$0.500728\pi$
$440$	3.31756e17	2.17960
$441$	−2.95763e16	−0.191466
$442$	−2.29385e17	−1.46326
$443$	3.64824e16	0.229329	0.114665	−	0.993404i	$-0.463421\pi$
$443$	3.64824e16	0.229329	0.114665	+	0.993404i	$0.463421\pi$
$444$	1.27022e17	0.786846
$445$	4.64451e17	2.83530
$446$	3.93567e17	2.36779
$447$	−8.47125e16	−0.502283
$448$	1.52617e17	0.891861
$449$	3.45449e17	1.98968	0.994840	−	0.101454i	$-0.0323496\pi$
$449$	3.45449e17	1.98968	0.994840	+	0.101454i	$0.0323496\pi$
$450$	1.20822e17	0.685906
$451$	−6.12687e16	−0.342840
$452$	3.58388e17	1.97676
$453$	3.88549e16	0.211255
$454$	1.64274e17	0.880452
$455$	−1.47754e17	−0.780663
$456$	1.08863e17	0.567035
$457$	1.22558e17	0.629340	0.314670	−	0.949201i	$-0.398106\pi$
$457$	1.22558e17	0.629340	0.314670	+	0.949201i	$0.398106\pi$
$458$	5.22849e17	2.64698
$459$	3.67458e16	0.183411
$460$	−2.22964e17	−1.09726
$461$	−2.19140e17	−1.06332	−0.531661	−	0.846957i	$-0.678432\pi$
$461$	−2.19140e17	−1.06332	−0.531661	+	0.846957i	$0.678432\pi$
$462$	8.06732e16	0.385973
$463$	1.68050e17	0.792796	0.396398	−	0.918079i	$-0.370260\pi$
$463$	1.68050e17	0.792796	0.396398	+	0.918079i	$0.370260\pi$
$464$	2.51651e17	1.17066
$465$	−7.69863e16	−0.353158
$466$	3.22973e17	1.46103
$467$	−2.11796e17	−0.944840	−0.472420	−	0.881373i	$-0.656620\pi$
$467$	−2.11796e17	−0.944840	−0.472420	+	0.881373i	$0.656620\pi$
$468$	1.54084e17	0.677892
$469$	9.46045e16	0.410476
$470$	−3.35128e17	−1.43408
$471$	−9.93595e16	−0.419347
$472$	−8.53512e16	−0.355293
$473$	9.40119e16	0.385998
$474$	2.29520e17	0.929526
$475$	−9.95737e16	−0.397774
$476$	−3.89071e17	−1.53315
$477$	1.00634e16	0.0391181
$478$	8.42728e17	3.23151
$479$	3.53685e17	1.33794	0.668969	−	0.743290i	$-0.266736\pi$
$479$	3.53685e17	1.33794	0.668969	+	0.743290i	$0.266736\pi$
$480$	4.80110e17	1.79173
$481$	−1.23801e17	−0.455807
$482$	5.21941e16	0.189590
$483$	−3.22310e16	−0.115509
$484$	−4.86088e17	−1.71878
$485$	3.03538e17	1.05899
$486$	−3.46929e16	−0.119428
$487$	3.13755e17	1.06574	0.532871	−	0.846197i	$-0.321113\pi$
$487$	3.13755e17	1.06574	0.532871	+	0.846197i	$0.321113\pi$
$488$	−6.72386e17	−2.25367
$489$	8.81793e16	0.291648
$490$	4.75393e17	1.55159
$491$	5.52074e16	0.177815	0.0889074	−	0.996040i	$-0.471662\pi$
$491$	5.52074e16	0.177815	0.0889074	+	0.996040i	$0.471662\pi$
$492$	−2.78979e17	−0.886743
$493$	−1.36022e17	−0.426683
$494$	−1.78483e17	−0.552551
$495$	8.71318e16	0.266221
$496$	−3.65542e17	−1.10232
$497$	−2.54043e17	−0.756119
$498$	6.52722e16	0.191751
$499$	3.27144e17	0.948605	0.474303	−	0.880362i	$-0.342700\pi$
$499$	3.27144e17	0.948605	0.474303	+	0.880362i	$0.342700\pi$
$500$	−1.31625e17	−0.376734
$501$	−2.82331e17	−0.797653
$502$	8.48585e17	2.36658
$503$	1.28398e17	0.353482	0.176741	−	0.984257i	$-0.443444\pi$
$503$	1.28398e17	0.353482	0.176741	+	0.984257i	$0.443444\pi$
$504$	2.18369e17	0.593462
$505$	9.56016e16	0.256491
$506$	−1.18651e17	−0.314263
$507$	7.06190e16	0.184659
$508$	−8.11790e17	−2.09570
$509$	4.84991e17	1.23614	0.618070	−	0.786123i	$-0.287915\pi$
$509$	4.84991e17	1.23614	0.618070	+	0.786123i	$0.287915\pi$
$510$	−5.90632e17	−1.48631
$511$	−9.99880e16	−0.248435
$512$	−6.29077e17	−1.54330
$513$	2.85917e16	0.0692590
$514$	−2.54614e17	−0.609006
$515$	1.06142e18	2.50692
$516$	4.28070e17	0.998371
$517$	−1.26884e17	−0.292226
$518$	−2.95140e17	−0.671250
$519$	−6.02256e16	−0.135267
$520$	−1.47230e18	−3.26569
$521$	5.77233e17	1.26446	0.632231	−	0.774780i	$-0.282139\pi$
$521$	5.77233e17	1.26446	0.632231	+	0.774780i	$0.282139\pi$
$522$	1.28423e17	0.277834
$523$	6.55441e17	1.40047	0.700233	−	0.713915i	$-0.253080\pi$
$523$	6.55441e17	1.40047	0.700233	+	0.713915i	$0.253080\pi$
$524$	−2.25687e18	−4.76269
$525$	−1.99735e17	−0.416311
$526$	4.74032e17	0.975889
$527$	1.97583e17	0.401772
$528$	4.13714e17	0.830960
$529$	−4.56632e17	−0.905951
$530$	−1.61754e17	−0.317003
$531$	−2.24165e16	−0.0433963
$532$	−3.02734e17	−0.578942
$533$	2.71904e17	0.513676
$534$	1.12541e18	2.10035
$535$	−4.70263e15	−0.00867044
$536$	9.42694e17	1.71712
$537$	2.48321e17	0.446870
$538$	−8.31334e17	−1.47806
$539$	1.79990e17	0.316171
$540$	3.96743e17	0.688573
$541$	−4.27201e17	−0.732571	−0.366286	−	0.930502i	$-0.619371\pi$
$541$	−4.27201e17	−0.732571	−0.366286	+	0.930502i	$0.619371\pi$
$542$	−5.76620e17	−0.977000
$543$	5.13216e17	0.859215
$544$	−1.23219e18	−2.03837
$545$	5.35369e17	0.875138
$546$	−3.58020e17	−0.578302
$547$	1.55294e17	0.247877	0.123938	−	0.992290i	$-0.460447\pi$
$547$	1.55294e17	0.247877	0.123938	+	0.992290i	$0.460447\pi$
$548$	2.61151e18	4.11925
$549$	−1.76594e17	−0.275268
$550$	−7.35278e17	−1.13264
$551$	−1.05838e17	−0.161123
$552$	−3.21168e17	−0.483202
$553$	−3.79427e17	−0.564177
$554$	−4.41575e17	−0.648920
$555$	−3.18768e17	−0.462989
$556$	−1.57069e18	−2.25478
$557$	2.85238e17	0.404714	0.202357	−	0.979312i	$-0.435140\pi$
$557$	2.85238e17	0.404714	0.202357	+	0.979312i	$0.435140\pi$
$558$	−1.86545e17	−0.261614
$559$	−4.17215e17	−0.578340
$560$	−1.80639e18	−2.47509
$561$	−2.23621e17	−0.302869
$562$	−5.86671e17	−0.785432
$563$	2.82389e17	0.373718	0.186859	−	0.982387i	$-0.440169\pi$
$563$	2.82389e17	0.373718	0.186859	+	0.982387i	$0.440169\pi$
$564$	−5.77749e17	−0.755832
$565$	−8.99393e17	−1.16315
$566$	−4.95937e17	−0.634044
$567$	5.73520e16	0.0724868
$568$	−2.53143e18	−3.16302
$569$	−8.21356e17	−1.01462	−0.507308	−	0.861765i	$-0.669359\pi$
$569$	−8.21356e17	−1.01462	−0.507308	+	0.861765i	$0.669359\pi$
$570$	−4.59567e17	−0.561257
$571$	1.18849e18	1.43503	0.717516	−	0.696542i	$-0.245279\pi$
$571$	1.18849e18	1.43503	0.717516	+	0.696542i	$0.245279\pi$
$572$	−9.37700e17	−1.11941
$573$	−6.01436e17	−0.709879
$574$	6.48216e17	0.756471
$575$	2.93762e17	0.338965
$576$	3.99412e17	0.455695
$577$	1.29563e18	1.46163	0.730817	−	0.682574i	$-0.239139\pi$
$577$	1.29563e18	1.46163	0.730817	+	0.682574i	$0.239139\pi$
$578$	−1.53097e17	−0.170779
$579$	−5.31117e17	−0.585840
$580$	−1.46863e18	−1.60188
$581$	−1.07904e17	−0.116383
$582$	7.35499e17	0.784482
$583$	−6.12424e16	−0.0645961
$584$	−9.96339e17	−1.03926
$585$	−3.86682e17	−0.398879
$586$	−1.78200e17	−0.181792
$587$	−1.14786e18	−1.15809	−0.579043	−	0.815297i	$-0.696574\pi$
$587$	−1.14786e18	−1.15809	−0.579043	+	0.815297i	$0.696574\pi$
$588$	8.19561e17	0.817765
$589$	1.53738e17	0.151716
$590$	3.60310e17	0.351672
$591$	1.41762e17	0.136848
$592$	−1.51356e18	−1.44513
$593$	3.09596e17	0.292375	0.146188	−	0.989257i	$-0.453300\pi$
$593$	3.09596e17	0.292375	0.146188	+	0.989257i	$0.453300\pi$
$594$	2.11128e17	0.197212
$595$	9.76393e17	0.902120
$596$	2.34739e18	2.14528
$597$	1.05099e18	0.950087
$598$	5.26561e17	0.470859
$599$	1.50875e18	1.33457	0.667287	−	0.744801i	$-0.267456\pi$
$599$	1.50875e18	1.33457	0.667287	+	0.744801i	$0.267456\pi$
$600$	−1.99027e18	−1.74152
$601$	−1.17624e18	−1.01815	−0.509077	−	0.860721i	$-0.670013\pi$
$601$	−1.17624e18	−1.01815	−0.509077	+	0.860721i	$0.670013\pi$
$602$	−9.94635e17	−0.851700
$603$	2.47587e17	0.209732
$604$	−1.07667e18	−0.902285
$605$	1.21986e18	1.01135
$606$	2.31651e17	0.190004
$607$	−3.05776e17	−0.248128	−0.124064	−	0.992274i	$-0.539593\pi$
$607$	−3.05776e17	−0.248128	−0.124064	+	0.992274i	$0.539593\pi$
$608$	−9.58757e17	−0.769724
$609$	−2.12301e17	−0.168632
$610$	2.83848e18	2.23070
$611$	5.63098e17	0.437841
$612$	−1.01823e18	−0.783359
$613$	1.67048e18	1.27159	0.635797	−	0.771856i	$-0.280672\pi$
$613$	1.67048e18	1.27159	0.635797	+	0.771856i	$0.280672\pi$
$614$	−1.12496e18	−0.847310
$615$	7.00111e17	0.521770
$616$	−1.32891e18	−0.979990
$617$	−1.87006e18	−1.36459	−0.682294	−	0.731078i	$-0.739017\pi$
$617$	−1.87006e18	−1.36459	−0.682294	+	0.731078i	$0.739017\pi$
$618$	2.57191e18	1.85708
$619$	2.29756e18	1.64164	0.820819	−	0.571188i	$-0.193517\pi$
$619$	2.29756e18	1.64164	0.820819	+	0.571188i	$0.193517\pi$
$620$	2.13330e18	1.50836
$621$	−8.43510e16	−0.0590194
$622$	2.22828e18	1.54288
$623$	−1.86044e18	−1.27481
$624$	−1.83602e18	−1.24503
$625$	−1.31670e18	−0.883619
$626$	−2.62636e18	−1.74430
$627$	−1.73998e17	−0.114368
$628$	2.75326e18	1.79106
$629$	8.18108e17	0.526722
$630$	−9.21845e17	−0.587414
$631$	−8.46114e17	−0.533627	−0.266814	−	0.963748i	$-0.585971\pi$
$631$	−8.46114e17	−0.533627	−0.266814	+	0.963748i	$0.585971\pi$
$632$	−3.78083e18	−2.36008
$633$	2.84541e17	0.175801
$634$	4.30102e18	2.63022
$635$	2.03723e18	1.23313
$636$	−2.78859e17	−0.167076
$637$	−7.98778e17	−0.473718
$638$	−7.81536e17	−0.458791
$639$	−6.64849e17	−0.386338
$640$	−1.02478e18	−0.589469
$641$	3.97297e17	0.226224	0.113112	−	0.993582i	$-0.463918\pi$
$641$	3.97297e17	0.226224	0.113112	+	0.993582i	$0.463918\pi$
$642$	−1.13949e16	−0.00642291
$643$	1.52471e18	0.850776	0.425388	−	0.905011i	$-0.360138\pi$
$643$	1.52471e18	0.850776	0.425388	+	0.905011i	$0.360138\pi$
$644$	8.93124e17	0.493348
$645$	−1.07426e18	−0.587453
$646$	1.17946e18	0.638518
$647$	−1.96552e18	−1.05341	−0.526707	−	0.850047i	$-0.676573\pi$
$647$	−1.96552e18	−1.05341	−0.526707	+	0.850047i	$0.676573\pi$
$648$	5.71489e17	0.303229
$649$	1.36418e17	0.0716609
$650$	3.26309e18	1.69704
$651$	3.08383e17	0.158787
$652$	−2.44346e18	−1.24565
$653$	−1.60312e18	−0.809153	−0.404577	−	0.914504i	$-0.632581\pi$
$653$	−1.60312e18	−0.809153	−0.404577	+	0.914504i	$0.632581\pi$
$654$	1.29725e18	0.648287
$655$	5.66372e18	2.80242
$656$	3.32423e18	1.62860
$657$	−2.61676e17	−0.126937
$658$	1.34242e18	0.644792
$659$	−3.10546e18	−1.47696	−0.738482	−	0.674273i	$-0.764457\pi$
$659$	−3.10546e18	−1.47696	−0.738482	+	0.674273i	$0.764457\pi$
$660$	−2.41443e18	−1.13705
$661$	−4.80564e17	−0.224100	−0.112050	−	0.993703i	$-0.535742\pi$
$661$	−4.80564e17	−0.224100	−0.112050	+	0.993703i	$0.535742\pi$
$662$	7.14770e18	3.30057
$663$	9.92408e17	0.453787
$664$	−1.07521e18	−0.486858
$665$	7.59725e17	0.340656
$666$	−7.72403e17	−0.342974
$667$	3.12244e17	0.137302
$668$	7.82343e18	3.40683
$669$	−1.70272e18	−0.734300
$670$	−3.97958e18	−1.69962
$671$	1.07469e18	0.454553
$672$	−1.92317e18	−0.805596
$673$	1.10529e18	0.458541	0.229270	−	0.973363i	$-0.426366\pi$
$673$	1.10529e18	0.458541	0.229270	+	0.973363i	$0.426366\pi$
$674$	−5.07242e17	−0.208414
$675$	−5.22722e17	−0.212714
$676$	−1.95686e18	−0.788689
$677$	−7.00092e17	−0.279466	−0.139733	−	0.990189i	$-0.544624\pi$
$677$	−7.00092e17	−0.279466	−0.139733	+	0.990189i	$0.544624\pi$
$678$	−2.17931e18	−0.861639
$679$	−1.21588e18	−0.476142
$680$	9.72935e18	3.77377
$681$	−7.10711e17	−0.273047
$682$	1.13524e18	0.432006
$683$	1.58894e17	0.0598925	0.0299463	−	0.999552i	$-0.490466\pi$
$683$	1.58894e17	0.0598925	0.0299463	+	0.999552i	$0.490466\pi$
$684$	−7.92277e17	−0.295810
$685$	−6.55372e18	−2.42381
$686$	−5.21952e18	−1.91216
$687$	−2.26204e18	−0.820885
$688$	−5.10076e18	−1.83362
$689$	2.71788e17	0.0967842
$690$	1.35581e18	0.478278
$691$	−3.01116e18	−1.05227	−0.526135	−	0.850401i	$-0.676359\pi$
$691$	−3.01116e18	−1.05227	−0.526135	+	0.850401i	$0.676359\pi$
$692$	1.66886e18	0.577736
$693$	−3.49023e17	−0.119698
$694$	−1.65261e18	−0.561480
$695$	3.94172e18	1.32674
$696$	−2.11549e18	−0.705425
$697$	−1.79681e18	−0.593594
$698$	7.33680e18	2.40130
$699$	−1.39730e18	−0.453095
$700$	5.53467e18	1.77809
$701$	1.56773e18	0.499003	0.249502	−	0.968374i	$-0.419733\pi$
$701$	1.56773e18	0.499003	0.249502	+	0.968374i	$0.419733\pi$
$702$	−9.36965e17	−0.295483
$703$	6.36565e17	0.198899
$704$	−2.43067e18	−0.752495
$705$	1.44989e18	0.444740
$706$	−1.48997e18	−0.452841
$707$	−3.82950e17	−0.115323
$708$	6.21162e17	0.185348
$709$	1.14764e18	0.339318	0.169659	−	0.985503i	$-0.445733\pi$
$709$	1.14764e18	0.339318	0.169659	+	0.985503i	$0.445733\pi$
$710$	1.06864e19	3.13078
$711$	−9.92990e17	−0.288266
$712$	−1.85386e19	−5.33281
$713$	−4.53558e17	−0.129286
$714$	2.36589e18	0.668275
$715$	2.35321e18	0.658674
$716$	−6.88100e18	−1.90861
$717$	−3.64596e18	−1.00216
$718$	−7.24197e18	−1.97264
$719$	−2.77376e18	−0.748740	−0.374370	−	0.927279i	$-0.622141\pi$
$719$	−2.77376e18	−0.748740	−0.374370	+	0.927279i	$0.622141\pi$
$720$	−4.72747e18	−1.26464
$721$	−4.25172e18	−1.12716
$722$	−6.16825e18	−1.62058
$723$	−2.25811e17	−0.0587959
$724$	−1.42213e19	−3.66976
$725$	1.93497e18	0.494853
$726$	2.95583e18	0.749190
$727$	3.98253e18	1.00043	0.500214	−	0.865902i	$-0.333255\pi$
$727$	3.98253e18	1.00043	0.500214	+	0.865902i	$0.333255\pi$
$728$	5.89758e18	1.46832
$729$	1.50095e17	0.0370370
$730$	4.20605e18	1.02867
$731$	2.75706e18	0.668319
$732$	4.89344e18	1.17569
$733$	−5.00781e18	−1.19254	−0.596268	−	0.802785i	$-0.703351\pi$
$733$	−5.00781e18	−1.19254	−0.596268	+	0.802785i	$0.703351\pi$
$734$	−1.19135e19	−2.81200
$735$	−2.05673e18	−0.481182
$736$	2.82852e18	0.655925
$737$	−1.50672e18	−0.346334
$738$	1.69643e18	0.386518
$739$	5.41074e17	0.122199	0.0610996	−	0.998132i	$-0.480539\pi$
$739$	5.41074e17	0.122199	0.0610996	+	0.998132i	$0.480539\pi$
$740$	8.83309e18	1.97746
$741$	7.72186e17	0.171358
$742$	6.47938e17	0.142530
$743$	6.47739e18	1.41245	0.706224	−	0.707988i	$-0.250397\pi$
$743$	6.47739e18	1.41245	0.706224	+	0.707988i	$0.250397\pi$
$744$	3.07291e18	0.664241
$745$	−5.89090e18	−1.26231
$746$	−4.45968e18	−0.947330
$747$	−2.82392e17	−0.0594660
$748$	6.19656e18	1.29357
$749$	1.88373e16	0.00389840
$750$	8.00396e17	0.164213
$751$	−4.28870e18	−0.872301	−0.436150	−	0.899874i	$-0.643658\pi$
$751$	−4.28870e18	−0.872301	−0.436150	+	0.899874i	$0.643658\pi$
$752$	6.88429e18	1.38817
$753$	−3.67130e18	−0.733926
$754$	3.46838e18	0.687405
$755$	2.70197e18	0.530915
$756$	−1.58923e18	−0.309596
$757$	−2.31077e18	−0.446306	−0.223153	−	0.974783i	$-0.571635\pi$
$757$	−2.31077e18	−0.446306	−0.223153	+	0.974783i	$0.571635\pi$
$758$	1.28148e19	2.45393
$759$	5.13329e17	0.0974595
$760$	7.57034e18	1.42504
$761$	−4.11661e18	−0.768315	−0.384157	−	0.923268i	$-0.625508\pi$
$761$	−4.11661e18	−0.768315	−0.384157	+	0.923268i	$0.625508\pi$
$762$	4.93638e18	0.913485
$763$	−2.14452e18	−0.393479
$764$	1.66659e19	3.03194
$765$	2.55530e18	0.460937
$766$	2.55302e18	0.456633
$767$	−6.05411e17	−0.107369
$768$	2.00518e18	0.352619
$769$	4.01220e18	0.699619	0.349810	−	0.936821i	$-0.386246\pi$
$769$	4.01220e18	0.699619	0.349810	+	0.936821i	$0.386246\pi$
$770$	5.61001e18	0.970004
$771$	1.10156e18	0.188866
$772$	1.47173e19	2.50216
$773$	−1.86034e18	−0.313636	−0.156818	−	0.987628i	$-0.550124\pi$
$773$	−1.86034e18	−0.313636	−0.156818	+	0.987628i	$0.550124\pi$
$774$	−2.60304e18	−0.435175
$775$	−2.81069e18	−0.465963
$776$	−1.21157e19	−1.99181
$777$	1.27689e18	0.208169
$778$	9.41187e17	0.152163
$779$	−1.39809e18	−0.224151
$780$	1.07150e19	1.70364
$781$	4.04602e18	0.637965
$782$	−3.47965e18	−0.544116
$783$	−5.55608e17	−0.0861622
$784$	−9.76565e18	−1.50192
$785$	−6.90945e18	−1.05388
$786$	1.37237e19	2.07599
$787$	1.83007e18	0.274556	0.137278	−	0.990533i	$-0.456165\pi$
$787$	1.83007e18	0.274556	0.137278	+	0.990533i	$0.456165\pi$
$788$	−3.92823e18	−0.584489
$789$	−2.05084e18	−0.302644
$790$	1.59608e19	2.33603
$791$	3.60269e18	0.522973
$792$	−3.47787e18	−0.500725
$793$	−4.76935e18	−0.681056
$794$	−1.86294e19	−2.63855
$795$	6.99811e17	0.0983092
$796$	−2.91229e19	−4.05789
$797$	6.39343e18	0.883598	0.441799	−	0.897114i	$-0.354340\pi$
$797$	6.39343e18	0.883598	0.441799	+	0.897114i	$0.354340\pi$
$798$	1.84088e18	0.252352
$799$	−3.72110e18	−0.505961
$800$	1.75283e19	2.36404
$801$	−4.86893e18	−0.651361
$802$	−1.27793e19	−1.69580
$803$	1.59247e18	0.209613
$804$	−6.86067e18	−0.895781
$805$	−2.24134e18	−0.290292
$806$	−5.03808e18	−0.647273
$807$	3.59666e18	0.458376
$808$	−3.81594e18	−0.482423
$809$	−5.16947e18	−0.648306	−0.324153	−	0.946005i	$-0.605079\pi$
$809$	−5.16947e18	−0.648306	−0.324153	+	0.946005i	$0.605079\pi$
$810$	−2.41254e18	−0.300139
$811$	−1.20596e19	−1.48832	−0.744162	−	0.667999i	$-0.767151\pi$
$811$	−1.20596e19	−1.48832	−0.744162	+	0.667999i	$0.767151\pi$
$812$	5.88287e18	0.720237
$813$	2.49468e18	0.302988
$814$	4.70056e18	0.566358
$815$	6.13198e18	0.732953
$816$	1.21329e19	1.43873
$817$	2.14525e18	0.252369
$818$	−1.47289e18	−0.171899
$819$	1.54893e18	0.179344
$820$	−1.94001e19	−2.22851
$821$	1.22480e19	1.39584	0.697921	−	0.716175i	$-0.254109\pi$
$821$	1.22480e19	1.39584	0.697921	+	0.716175i	$0.254109\pi$
$822$	−1.58802e19	−1.79552
$823$	1.38823e19	1.55727	0.778634	−	0.627478i	$-0.215913\pi$
$823$	1.38823e19	1.55727	0.778634	+	0.627478i	$0.215913\pi$
$824$	−4.23666e19	−4.71516
$825$	3.18109e18	0.351257
$826$	−1.44329e18	−0.158119
$827$	3.69663e18	0.401809	0.200904	−	0.979611i	$-0.435612\pi$
$827$	3.69663e18	0.401809	0.200904	+	0.979611i	$0.435612\pi$
$828$	2.33738e18	0.252076
$829$	−1.35887e19	−1.45403	−0.727015	−	0.686622i	$-0.759093\pi$
$829$	−1.35887e19	−1.45403	−0.727015	+	0.686622i	$0.759093\pi$
$830$	4.53902e18	0.481897
$831$	1.91042e18	0.201244
$832$	1.07871e19	1.12746
$833$	5.27853e18	0.547420
$834$	9.55113e18	0.982823
$835$	−1.96333e19	−2.00462
$836$	4.82151e18	0.488474
$837$	8.07062e17	0.0811319
$838$	−2.70018e19	−2.69343
$839$	−5.71064e18	−0.565239	−0.282620	−	0.959232i	$-0.591203\pi$
$839$	−5.71064e18	−0.565239	−0.282620	+	0.959232i	$0.591203\pi$
$840$	1.51854e19	1.49145
$841$	−8.20393e18	−0.799554
$842$	1.61290e19	1.55983
$843$	2.53816e18	0.243579
$844$	−7.88465e18	−0.750856
$845$	4.91083e18	0.464073
$846$	3.51321e18	0.329456
$847$	−4.88639e18	−0.454722
$848$	3.32280e18	0.306854
$849$	2.14561e18	0.196630
$850$	−2.15633e19	−1.96107
$851$	−1.87799e18	−0.169493
$852$	1.84230e19	1.65008
$853$	1.94405e19	1.72798	0.863991	−	0.503508i	$-0.167957\pi$
$853$	1.94405e19	1.72798	0.863991	+	0.503508i	$0.167957\pi$
$854$	−1.13700e19	−1.00297
$855$	1.98826e18	0.174058
$856$	1.87705e17	0.0163079
$857$	−1.34658e19	−1.16107	−0.580535	−	0.814236i	$-0.697156\pi$
$857$	−1.34658e19	−1.16107	−0.580535	+	0.814236i	$0.697156\pi$
$858$	5.70202e18	0.487935
$859$	4.08083e18	0.346572	0.173286	−	0.984872i	$-0.444562\pi$
$859$	4.08083e18	0.346572	0.173286	+	0.984872i	$0.444562\pi$
$860$	2.97680e19	2.50905
$861$	−2.80443e18	−0.234598
$862$	−7.04877e18	−0.585216
$863$	−1.43244e19	−1.18034	−0.590169	−	0.807279i	$-0.700939\pi$
$863$	−1.43244e19	−1.18034	−0.590169	+	0.807279i	$0.700939\pi$
$864$	−5.03309e18	−0.411619
$865$	−4.18808e18	−0.339946
$866$	−2.92437e19	−2.35595
$867$	6.62354e17	0.0529622
$868$	−8.54532e18	−0.678188
$869$	6.04297e18	0.476016
$870$	8.93054e18	0.698236
$871$	6.68669e18	0.518911
$872$	−2.13693e19	−1.64601
$873$	−3.18205e18	−0.243284
$874$	−2.70749e18	−0.205468
$875$	−1.32316e18	−0.0996690
$876$	7.25108e18	0.542158
$877$	1.22567e19	0.909657	0.454829	−	0.890579i	$-0.349701\pi$
$877$	1.22567e19	0.909657	0.454829	+	0.890579i	$0.349701\pi$
$878$	−1.15586e17	−0.00851515
$879$	7.70962e17	0.0563774
$880$	2.87696e19	2.08832
$881$	−1.92714e19	−1.38858	−0.694288	−	0.719697i	$-0.744281\pi$
$881$	−1.92714e19	−1.38858	−0.694288	+	0.719697i	$0.744281\pi$
$882$	−4.98364e18	−0.356452
$883$	−1.50698e19	−1.06995	−0.534975	−	0.844868i	$-0.679679\pi$
$883$	−1.50698e19	−1.06995	−0.534975	+	0.844868i	$0.679679\pi$
$884$	−2.74997e19	−1.93815
$885$	−1.55884e18	−0.109061
$886$	6.14733e18	0.426940
$887$	8.90505e18	0.613950	0.306975	−	0.951718i	$-0.400683\pi$
$887$	8.90505e18	0.613950	0.306975	+	0.951718i	$0.400683\pi$
$888$	1.27236e19	0.870817
$889$	−8.16050e18	−0.554441
$890$	7.82605e19	5.27847
$891$	−9.13420e17	−0.0611597
$892$	4.71825e19	3.13624
$893$	−2.89536e18	−0.191059
$894$	−1.42742e19	−0.935097
$895$	1.72682e19	1.12305
$896$	4.10495e18	0.265037
$897$	−2.27810e18	−0.146023
$898$	5.82087e19	3.70417
$899$	−2.98751e18	−0.188744
$900$	1.44847e19	0.908515
$901$	−1.79604e18	−0.111842
$902$	−1.03238e19	−0.638262
$903$	4.30317e18	0.264130
$904$	3.58993e19	2.18771
$905$	3.56890e19	2.15933
$906$	6.54710e18	0.393293
$907$	1.82157e19	1.08642	0.543212	−	0.839596i	$-0.317208\pi$
$907$	1.82157e19	1.08642	0.543212	+	0.839596i	$0.317208\pi$
$908$	1.96939e19	1.16620
$909$	−1.00221e18	−0.0589242
$910$	−2.48966e19	−1.45336
$911$	−2.82471e19	−1.63721	−0.818605	−	0.574358i	$-0.805252\pi$
$911$	−2.82471e19	−1.63721	−0.818605	+	0.574358i	$0.805252\pi$
$912$	9.44054e18	0.543288
$913$	1.71853e18	0.0981969
$914$	2.06511e19	1.17164
$915$	−1.22803e19	−0.691787
$916$	6.26814e19	3.50605
$917$	−2.26871e19	−1.26002
$918$	6.19171e18	0.341455
$919$	−1.82541e19	−0.999563	−0.499781	−	0.866152i	$-0.666586\pi$
$919$	−1.82541e19	−0.999563	−0.499781	+	0.866152i	$0.666586\pi$
$920$	−2.23340e19	−1.21436
$921$	4.86700e18	0.262769
$922$	−3.69253e19	−1.97958
$923$	−1.79559e19	−0.955861
$924$	9.67146e18	0.511239
$925$	−1.16379e19	−0.610875
$926$	2.83166e19	1.47594
$927$	−1.11271e19	−0.575921
$928$	1.86311e19	0.957581
$929$	1.22411e18	0.0624769	0.0312385	−	0.999512i	$-0.490055\pi$
$929$	1.22411e18	0.0624769	0.0312385	+	0.999512i	$0.490055\pi$
$930$	−1.29723e19	−0.657472
$931$	4.10719e18	0.206715
$932$	3.87194e19	1.93520
$933$	−9.64038e18	−0.478480
$934$	−3.56879e19	−1.75900
$935$	−1.55506e19	−0.761151
$936$	1.54344e19	0.750235
$937$	−4.94198e18	−0.238558	−0.119279	−	0.992861i	$-0.538058\pi$
$937$	−4.94198e18	−0.238558	−0.119279	+	0.992861i	$0.538058\pi$
$938$	1.59410e19	0.764181
$939$	1.13626e19	0.540944
$940$	−4.01766e19	−1.89951
$941$	−4.08948e19	−1.92015	−0.960076	−	0.279740i	$-0.909752\pi$
$941$	−4.08948e19	−1.92015	−0.960076	+	0.279740i	$0.909752\pi$
$942$	−1.67422e19	−0.780695
$943$	4.12464e18	0.191012
$944$	−7.40158e18	−0.340413
$945$	3.98825e18	0.182170
$946$	1.58411e19	0.718610
$947$	−1.06679e19	−0.480624	−0.240312	−	0.970696i	$-0.577250\pi$
$947$	−1.06679e19	−0.480624	−0.240312	+	0.970696i	$0.577250\pi$
$948$	2.75159e19	1.23120
$949$	−7.06720e18	−0.314063
$950$	−1.67783e19	−0.740532
$951$	−1.86079e19	−0.815686
$952$	−3.89727e19	−1.69676
$953$	−1.53246e19	−0.662651	−0.331326	−	0.943516i	$-0.607496\pi$
$953$	−1.53246e19	−0.662651	−0.331326	+	0.943516i	$0.607496\pi$
$954$	1.69570e18	0.0728258
$955$	−4.18238e19	−1.78403
$956$	1.01030e20	4.28029
$957$	3.38122e18	0.142281
$958$	5.95964e19	2.49083
$959$	2.62522e19	1.08979
$960$	2.77750e19	1.14523
$961$	−2.00780e19	−0.822276
$962$	−2.08606e19	−0.848572
$963$	4.92986e16	0.00199188
$964$	6.25726e18	0.251121
$965$	−3.69338e19	−1.47230
$966$	−5.43096e18	−0.215043
$967$	1.63923e19	0.644713	0.322357	−	0.946618i	$-0.395525\pi$
$967$	1.63923e19	0.644713	0.322357	+	0.946618i	$0.395525\pi$
$968$	−4.86908e19	−1.90220
$969$	−5.10280e18	−0.198018
$970$	5.11465e19	1.97151
$971$	−4.67670e19	−1.79067	−0.895333	−	0.445398i	$-0.853062\pi$
$971$	−4.67670e19	−1.79067	−0.895333	+	0.445398i	$0.853062\pi$
$972$	−4.15914e18	−0.158188
$973$	−1.57893e19	−0.596526
$974$	5.28680e19	1.98408
$975$	−1.41174e19	−0.526288
$976$	−5.83087e19	−2.15928
$977$	−1.63943e19	−0.603085	−0.301543	−	0.953453i	$-0.597502\pi$
$977$	−1.63943e19	−0.603085	−0.301543	+	0.953453i	$0.597502\pi$
$978$	1.48583e19	0.542959
$979$	2.96305e19	1.07560
$980$	5.69922e19	2.05516
$981$	−5.61238e18	−0.201048
$982$	9.30252e18	0.331037
$983$	2.50792e19	0.886575	0.443288	−	0.896379i	$-0.353812\pi$
$983$	2.50792e19	0.886575	0.443288	+	0.896379i	$0.353812\pi$
$984$	−2.79449e19	−0.981375
$985$	9.85808e18	0.343920
$986$	−2.29199e19	−0.794353
$987$	−5.80781e18	−0.199964
$988$	−2.13974e19	−0.731880
$989$	−6.32893e18	−0.215057
$990$	1.46818e19	0.495623
$991$	−1.11771e19	−0.374843	−0.187422	−	0.982280i	$-0.560013\pi$
$991$	−1.11771e19	−0.374843	−0.187422	+	0.982280i	$0.560013\pi$
$992$	−2.70630e19	−0.901676
$993$	−3.09236e19	−1.02358
$994$	−4.28065e19	−1.40766
$995$	7.30854e19	2.38770
$996$	7.82511e18	0.253983
$997$	2.72837e19	0.879803	0.439901	−	0.898046i	$-0.355013\pi$
$997$	2.72837e19	0.879803	0.439901	+	0.898046i	$0.355013\pi$
$998$	5.51242e19	1.76601
$999$	3.34171e18	0.106364

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.b.1.31	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.b.1.31	✓	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)

\(f(q)\)	\(=\)	\(q+168.501 q^{2} -729.000 q^{3} +20200.7 q^{4} -50694.6 q^{5} -122837. q^{6} +203067. q^{7} +2.02347e6 q^{8} +531441. q^{9} +O(q^{10})\)	\(q+168.501 q^{2} -729.000 q^{3} +20200.7 q^{4} -50694.6 q^{5} -122837. q^{6} +203067. q^{7} +2.02347e6 q^{8} +531441. q^{9} -8.54210e6 q^{10} -3.23415e6 q^{11} -1.47263e7 q^{12} +1.43528e7 q^{13} +3.42170e7 q^{14} +3.69563e7 q^{15} +1.75474e8 q^{16} -9.48472e7 q^{17} +8.95485e7 q^{18} -7.38001e7 q^{19} -1.02406e9 q^{20} -1.48036e8 q^{21} -5.44959e8 q^{22} +2.17725e8 q^{23} -1.47511e9 q^{24} +1.34924e9 q^{25} +2.41847e9 q^{26} -3.87420e8 q^{27} +4.10208e9 q^{28} +1.43412e9 q^{29} +6.22719e9 q^{30} -2.08317e9 q^{31} +1.29913e10 q^{32} +2.35770e9 q^{33} -1.59819e10 q^{34} -1.02944e10 q^{35} +1.07355e10 q^{36} -8.62553e9 q^{37} -1.24354e10 q^{38} -1.04632e10 q^{39} -1.02579e11 q^{40} +1.89443e10 q^{41} -2.49442e10 q^{42} -2.90685e10 q^{43} -6.53320e10 q^{44} -2.69412e10 q^{45} +3.66869e10 q^{46} +3.92325e10 q^{47} -1.27921e11 q^{48} -5.56530e10 q^{49} +2.27348e11 q^{50} +6.91436e10 q^{51} +2.89937e11 q^{52} +1.89361e10 q^{53} -6.52808e10 q^{54} +1.63954e11 q^{55} +4.10900e11 q^{56} +5.38002e10 q^{57} +2.41651e11 q^{58} -4.21805e10 q^{59} +7.46542e11 q^{60} -3.32293e11 q^{61} -3.51016e11 q^{62} +1.07918e11 q^{63} +7.51563e11 q^{64} -7.27611e11 q^{65} +3.97275e11 q^{66} +4.65879e11 q^{67} -1.91598e12 q^{68} -1.58721e11 q^{69} -1.73461e12 q^{70} -1.25103e12 q^{71} +1.07536e12 q^{72} -4.92390e11 q^{73} -1.45341e12 q^{74} -9.83593e11 q^{75} -1.49081e12 q^{76} -6.56748e11 q^{77} -1.76307e12 q^{78} -1.86849e12 q^{79} -8.89557e12 q^{80} +2.82430e11 q^{81} +3.19213e12 q^{82} -5.31370e11 q^{83} -2.99042e12 q^{84} +4.80824e12 q^{85} -4.89807e12 q^{86} -1.04547e12 q^{87} -6.54422e12 q^{88} -9.16175e12 q^{89} -4.53962e12 q^{90} +2.91458e12 q^{91} +4.39818e12 q^{92} +1.51863e12 q^{93} +6.61073e12 q^{94} +3.74126e12 q^{95} -9.47064e12 q^{96} -5.98758e12 q^{97} -9.37759e12 q^{98} -1.71876e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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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