LMFDB - Embedded newform 177.12.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,12,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, 12, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
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:	$135.996742959$
Analytic rank:	$1$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-68.7593 q^{2} +243.000 q^{3} +2679.84 q^{4} +7324.59 q^{5} -16708.5 q^{6} -63928.8 q^{7} -43445.2 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-68.7593 q^{2} +243.000 q^{3} +2679.84 q^{4} +7324.59 q^{5} -16708.5 q^{6} -63928.8 q^{7} -43445.2 q^{8} +59049.0 q^{9} -503634. q^{10} -307718. q^{11} +651202. q^{12} -1.14204e6 q^{13} +4.39570e6 q^{14} +1.77988e6 q^{15} -2.50106e6 q^{16} +1.41880e6 q^{17} -4.06017e6 q^{18} +4.00245e6 q^{19} +1.96288e7 q^{20} -1.55347e7 q^{21} +2.11585e7 q^{22} +4.77119e7 q^{23} -1.05572e7 q^{24} +4.82151e6 q^{25} +7.85260e7 q^{26} +1.43489e7 q^{27} -1.71319e8 q^{28} +1.63918e8 q^{29} -1.22383e8 q^{30} +1.17737e8 q^{31} +2.60947e8 q^{32} -7.47754e7 q^{33} -9.75560e7 q^{34} -4.68252e8 q^{35} +1.58242e8 q^{36} -5.45888e8 q^{37} -2.75206e8 q^{38} -2.77516e8 q^{39} -3.18218e8 q^{40} -5.77402e8 q^{41} +1.06815e9 q^{42} -1.16727e9 q^{43} -8.24635e8 q^{44} +4.32510e8 q^{45} -3.28064e9 q^{46} -3.29117e8 q^{47} -6.07758e8 q^{48} +2.10956e9 q^{49} -3.31524e8 q^{50} +3.44769e8 q^{51} -3.06049e9 q^{52} +5.23739e9 q^{53} -9.86621e8 q^{54} -2.25391e9 q^{55} +2.77740e9 q^{56} +9.72596e8 q^{57} -1.12709e10 q^{58} -7.14924e8 q^{59} +4.76979e9 q^{60} +6.69141e9 q^{61} -8.09555e9 q^{62} -3.77493e9 q^{63} -1.28204e10 q^{64} -8.36499e9 q^{65} +5.14151e9 q^{66} -1.09510e10 q^{67} +3.80217e9 q^{68} +1.15940e10 q^{69} +3.21967e10 q^{70} -1.13733e10 q^{71} -2.56539e9 q^{72} -1.17767e10 q^{73} +3.75349e10 q^{74} +1.17163e9 q^{75} +1.07259e10 q^{76} +1.96720e10 q^{77} +1.90818e10 q^{78} +4.67627e10 q^{79} -1.83192e10 q^{80} +3.48678e9 q^{81} +3.97018e10 q^{82} -4.41617e9 q^{83} -4.16305e10 q^{84} +1.03922e10 q^{85} +8.02607e10 q^{86} +3.98320e10 q^{87} +1.33688e10 q^{88} +2.79794e9 q^{89} -2.97391e10 q^{90} +7.30093e10 q^{91} +1.27861e11 q^{92} +2.86102e10 q^{93} +2.26299e10 q^{94} +2.93163e10 q^{95} +6.34101e10 q^{96} -1.07713e11 q^{97} -1.45052e11 q^{98} -1.81704e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) $ 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * 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 $

$2$	−68.7593	−1.51938	−0.759690	−	0.650285i	$-0.774649\pi$
$2$	−68.7593	−1.51938	−0.759690	+	0.650285i	$0.774649\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	2679.84	1.30852
$5$	7324.59	1.04821	0.524105	−	0.851654i	$-0.324400\pi$
$5$	7324.59	1.04821	0.524105	+	0.851654i	$0.324400\pi$
$6$	−16708.5	−0.877215
$7$	−63928.8	−1.43766	−0.718832	−	0.695184i	$-0.755323\pi$
$7$	−63928.8	−1.43766	−0.718832	+	0.695184i	$0.755323\pi$
$8$	−43445.2	−0.468756
$9$	59049.0	0.333333
$10$	−503634.	−1.59263
$11$	−307718.	−0.576093	−0.288047	−	0.957616i	$-0.593006\pi$
$11$	−307718.	−0.576093	−0.288047	+	0.957616i	$0.593006\pi$
$12$	651202.	0.755473
$13$	−1.14204e6	−0.853088	−0.426544	−	0.904467i	$-0.640269\pi$
$13$	−1.14204e6	−0.853088	−0.426544	+	0.904467i	$0.640269\pi$
$14$	4.39570e6	2.18436
$15$	1.77988e6	0.605184
$16$	−2.50106e6	−0.596299
$17$	1.41880e6	0.242356	0.121178	−	0.992631i	$-0.461333\pi$
$17$	1.41880e6	0.242356	0.121178	+	0.992631i	$0.461333\pi$
$18$	−4.06017e6	−0.506460
$19$	4.00245e6	0.370836	0.185418	−	0.982660i	$-0.440636\pi$
$19$	4.00245e6	0.370836	0.185418	+	0.982660i	$0.440636\pi$
$20$	1.96288e7	1.37160
$21$	−1.55347e7	−0.830035
$22$	2.11585e7	0.875305
$23$	4.77119e7	1.54570	0.772848	−	0.634591i	$-0.218832\pi$
$23$	4.77119e7	1.54570	0.772848	+	0.634591i	$0.218832\pi$
$24$	−1.05572e7	−0.270636
$25$	4.82151e6	0.0987445
$26$	7.85260e7	1.29616
$27$	1.43489e7	0.192450
$28$	−1.71319e8	−1.88121
$29$	1.63918e8	1.48401	0.742006	−	0.670393i	$-0.233875\pi$
$29$	1.63918e8	1.48401	0.742006	+	0.670393i	$0.233875\pi$
$30$	−1.22383e8	−0.919505
$31$	1.17737e8	0.738627	0.369314	−	0.929305i	$-0.379593\pi$
$31$	1.17737e8	0.738627	0.369314	+	0.929305i	$0.379593\pi$
$32$	2.60947e8	1.37476
$33$	−7.47754e7	−0.332608
$34$	−9.75560e7	−0.368231
$35$	−4.68252e8	−1.50697
$36$	1.58242e8	0.436173
$37$	−5.45888e8	−1.29418	−0.647089	−	0.762414i	$-0.724014\pi$
$37$	−5.45888e8	−1.29418	−0.647089	+	0.762414i	$0.724014\pi$
$38$	−2.75206e8	−0.563440
$39$	−2.77516e8	−0.492530
$40$	−3.18218e8	−0.491354
$41$	−5.77402e8	−0.778336	−0.389168	−	0.921167i	$-0.627237\pi$
$41$	−5.77402e8	−0.778336	−0.389168	+	0.921167i	$0.627237\pi$
$42$	1.06815e9	1.26114
$43$	−1.16727e9	−1.21086	−0.605431	−	0.795897i	$-0.706999\pi$
$43$	−1.16727e9	−1.21086	−0.605431	+	0.795897i	$0.706999\pi$
$44$	−8.24635e8	−0.753828
$45$	4.32510e8	0.349403
$46$	−3.28064e9	−2.34850
$47$	−3.29117e8	−0.209321	−0.104660	−	0.994508i	$-0.533376\pi$
$47$	−3.29117e8	−0.209321	−0.104660	+	0.994508i	$0.533376\pi$
$48$	−6.07758e8	−0.344274
$49$	2.10956e9	1.06688
$50$	−3.31524e8	−0.150030
$51$	3.44769e8	0.139924
$52$	−3.06049e9	−1.11628
$53$	5.23739e9	1.72027	0.860137	−	0.510063i	$-0.170378\pi$
$53$	5.23739e9	1.72027	0.860137	+	0.510063i	$0.170378\pi$
$54$	−9.86621e8	−0.292405
$55$	−2.25391e9	−0.603867
$56$	2.77740e9	0.673913
$57$	9.72596e8	0.214102
$58$	−1.12709e10	−2.25478
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	4.76979e9	0.791894
$61$	6.69141e9	1.01439	0.507193	−	0.861832i	$-0.330683\pi$
$61$	6.69141e9	1.01439	0.507193	+	0.861832i	$0.330683\pi$
$62$	−8.09555e9	−1.12226
$63$	−3.77493e9	−0.479221
$64$	−1.28204e10	−1.49249
$65$	−8.36499e9	−0.894215
$66$	5.14151e9	0.505357
$67$	−1.09510e10	−0.990930	−0.495465	−	0.868628i	$-0.665002\pi$
$67$	−1.09510e10	−0.990930	−0.495465	+	0.868628i	$0.665002\pi$
$68$	3.80217e9	0.317127
$69$	1.15940e10	0.892408
$70$	3.21967e10	2.28967
$71$	−1.13733e10	−0.748109	−0.374055	−	0.927407i	$-0.622033\pi$
$71$	−1.13733e10	−0.748109	−0.374055	+	0.927407i	$0.622033\pi$
$72$	−2.56539e9	−0.156252
$73$	−1.17767e10	−0.664886	−0.332443	−	0.943123i	$-0.607873\pi$
$73$	−1.17767e10	−0.664886	−0.332443	+	0.943123i	$0.607873\pi$
$74$	3.75349e10	1.96635
$75$	1.17163e9	0.0570102
$76$	1.07259e10	0.485245
$77$	1.96720e10	0.828228
$78$	1.90818e10	0.748341
$79$	4.67627e10	1.70982	0.854910	−	0.518776i	$-0.173612\pi$
$79$	4.67627e10	1.70982	0.854910	+	0.518776i	$0.173612\pi$
$80$	−1.83192e10	−0.625047
$81$	3.48678e9	0.111111
$82$	3.97018e10	1.18259
$83$	−4.41617e9	−0.123060	−0.0615299	−	0.998105i	$-0.519598\pi$
$83$	−4.41617e9	−0.123060	−0.0615299	+	0.998105i	$0.519598\pi$
$84$	−4.16305e10	−1.08612
$85$	1.03922e10	0.254040
$86$	8.02607e10	1.83976
$87$	3.98320e10	0.856795
$88$	1.33688e10	0.270047
$89$	2.79794e9	0.0531121	0.0265561	−	0.999647i	$-0.491546\pi$
$89$	2.79794e9	0.0531121	0.0265561	+	0.999647i	$0.491546\pi$
$90$	−2.97391e10	−0.530877
$91$	7.30093e10	1.22645
$92$	1.27861e11	2.02257
$93$	2.86102e10	0.426447
$94$	2.26299e10	0.318038
$95$	2.93163e10	0.388714
$96$	6.34101e10	0.793719
$97$	−1.07713e11	−1.27357	−0.636783	−	0.771043i	$-0.719735\pi$
$97$	−1.07713e11	−1.27357	−0.636783	+	0.771043i	$0.719735\pi$
$98$	−1.45052e11	−1.62099
$99$	−1.81704e10	−0.192031
$100$	1.29209e10	0.129209
$101$	1.21405e11	1.14939	0.574695	−	0.818368i	$-0.305121\pi$
$101$	1.21405e11	1.14939	0.574695	+	0.818368i	$0.305121\pi$
$102$	−2.37061e10	−0.212598
$103$	1.13157e11	0.961784	0.480892	−	0.876780i	$-0.340313\pi$
$103$	1.13157e11	0.961784	0.480892	+	0.876780i	$0.340313\pi$
$104$	4.96162e10	0.399890
$105$	−1.13785e11	−0.870051
$106$	−3.60119e11	−2.61375
$107$	−9.86871e10	−0.680220	−0.340110	−	0.940386i	$-0.610464\pi$
$107$	−9.86871e10	−0.680220	−0.340110	+	0.940386i	$0.610464\pi$
$108$	3.84528e10	0.251824
$109$	−1.67870e11	−1.04503	−0.522514	−	0.852631i	$-0.675006\pi$
$109$	−1.67870e11	−1.04503	−0.522514	+	0.852631i	$0.675006\pi$
$110$	1.54977e11	0.917503
$111$	−1.32651e11	−0.747194
$112$	1.59890e11	0.857278
$113$	8.34253e10	0.425958	0.212979	−	0.977057i	$-0.431683\pi$
$113$	8.34253e10	0.425958	0.212979	+	0.977057i	$0.431683\pi$
$114$	−6.68750e10	−0.325302
$115$	3.49470e11	1.62021
$116$	4.39274e11	1.94186
$117$	−6.74364e10	−0.284363
$118$	4.91577e10	0.197807
$119$	−9.07024e10	−0.348426
$120$	−7.73270e10	−0.283684
$121$	−1.90621e11	−0.668117
$122$	−4.60097e11	−1.54124
$123$	−1.40309e11	−0.449372
$124$	3.15518e11	0.966506
$125$	−3.22330e11	−0.944705
$126$	2.59562e11	0.728119
$127$	3.84746e11	1.03336	0.516682	−	0.856177i	$-0.327167\pi$
$127$	3.84746e11	1.03336	0.516682	+	0.856177i	$0.327167\pi$
$128$	3.47100e11	0.892894
$129$	−2.83647e11	−0.699092
$130$	5.75171e11	1.35865
$131$	−4.26964e11	−0.966939	−0.483470	−	0.875361i	$-0.660624\pi$
$131$	−4.26964e11	−0.966939	−0.483470	+	0.875361i	$0.660624\pi$
$132$	−2.00386e11	−0.435223
$133$	−2.55872e11	−0.533137
$134$	7.52985e11	1.50560
$135$	1.05100e11	0.201728
$136$	−6.16402e10	−0.113606
$137$	3.05982e11	0.541668	0.270834	−	0.962626i	$-0.412701\pi$
$137$	3.05982e11	0.541668	0.270834	+	0.962626i	$0.412701\pi$
$138$	−7.97196e11	−1.35591
$139$	−9.62226e11	−1.57288	−0.786440	−	0.617666i	$-0.788078\pi$
$139$	−9.62226e11	−1.57288	−0.786440	+	0.617666i	$0.788078\pi$
$140$	−1.25484e12	−1.97190
$141$	−7.99755e10	−0.120851
$142$	7.82019e11	1.13666
$143$	3.51427e11	0.491458
$144$	−1.47685e11	−0.198766
$145$	1.20063e12	1.55556
$146$	8.09756e11	1.01021
$147$	5.12623e11	0.615961
$148$	−1.46289e12	−1.69346
$149$	−1.17212e12	−1.30752	−0.653761	−	0.756701i	$-0.726810\pi$
$149$	−1.17212e12	−1.30752	−0.653761	+	0.756701i	$0.726810\pi$
$150$	−8.05602e10	−0.0866201
$151$	9.13900e11	0.947382	0.473691	−	0.880691i	$-0.342921\pi$
$151$	9.13900e11	0.947382	0.473691	+	0.880691i	$0.342921\pi$
$152$	−1.73887e11	−0.173831
$153$	8.37790e10	0.0807853
$154$	−1.35263e12	−1.25839
$155$	8.62378e11	0.774236
$156$	−7.43700e11	−0.644485
$157$	2.00126e12	1.67439	0.837193	−	0.546908i	$-0.184195\pi$
$157$	2.00126e12	1.67439	0.837193	+	0.546908i	$0.184195\pi$
$158$	−3.21537e12	−2.59787
$159$	1.27269e12	0.993201
$160$	1.91133e12	1.44104
$161$	−3.05017e12	−2.22219
$162$	−2.39749e11	−0.168820
$163$	−2.90005e12	−1.97412	−0.987059	−	0.160355i	$-0.948736\pi$
$163$	−2.90005e12	−1.97412	−0.987059	+	0.160355i	$0.948736\pi$
$164$	−1.54735e12	−1.01847
$165$	−5.47699e11	−0.348643
$166$	3.03653e11	0.186975
$167$	−1.12393e11	−0.0669577	−0.0334788	−	0.999439i	$-0.510659\pi$
$167$	−1.12393e11	−0.0669577	−0.0334788	+	0.999439i	$0.510659\pi$
$168$	6.74907e11	0.389084
$169$	−4.87900e11	−0.272242
$170$	−7.14558e11	−0.385983
$171$	2.36341e11	0.123612
$172$	−3.12810e12	−1.58444
$173$	−1.78076e12	−0.873677	−0.436839	−	0.899540i	$-0.643902\pi$
$173$	−1.78076e12	−0.873677	−0.436839	+	0.899540i	$0.643902\pi$
$174$	−2.73882e12	−1.30180
$175$	−3.08233e11	−0.141961
$176$	7.69621e11	0.343524
$177$	−1.73727e11	−0.0751646
$178$	−1.92385e11	−0.0806976
$179$	−2.97323e12	−1.20931	−0.604654	−	0.796488i	$-0.706689\pi$
$179$	−2.97323e12	−1.20931	−0.604654	+	0.796488i	$0.706689\pi$
$180$	1.15906e12	0.457200
$181$	2.21255e12	0.846568	0.423284	−	0.905997i	$-0.360877\pi$
$181$	2.21255e12	0.846568	0.423284	+	0.905997i	$0.360877\pi$
$182$	−5.02007e12	−1.86345
$183$	1.62601e12	0.585657
$184$	−2.07285e12	−0.724553
$185$	−3.99841e12	−1.35657
$186$	−1.96722e12	−0.647935
$187$	−4.36591e11	−0.139620
$188$	−8.81983e11	−0.273900
$189$	−9.17308e11	−0.276678
$190$	−2.01577e12	−0.590604
$191$	9.71854e11	0.276642	0.138321	−	0.990387i	$-0.455829\pi$
$191$	9.71854e11	0.276642	0.138321	+	0.990387i	$0.455829\pi$
$192$	−3.11535e12	−0.861687
$193$	−1.87888e12	−0.505050	−0.252525	−	0.967590i	$-0.581261\pi$
$193$	−1.87888e12	−0.505050	−0.252525	+	0.967590i	$0.581261\pi$
$194$	7.40624e12	1.93503
$195$	−2.03269e12	−0.516275
$196$	5.65329e12	1.39602
$197$	−2.04544e12	−0.491159	−0.245579	−	0.969376i	$-0.578978\pi$
$197$	−2.04544e12	−0.491159	−0.245579	+	0.969376i	$0.578978\pi$
$198$	1.24939e12	0.291768
$199$	3.90343e12	0.886654	0.443327	−	0.896360i	$-0.353798\pi$
$199$	3.90343e12	0.886654	0.443327	+	0.896360i	$0.353798\pi$
$200$	−2.09471e11	−0.0462870
$201$	−2.66110e12	−0.572114
$202$	−8.34769e12	−1.74636
$203$	−1.04791e13	−2.13351
$204$	9.23928e11	0.183093
$205$	−4.22923e12	−0.815860
$206$	−7.78061e12	−1.46132
$207$	2.81734e12	0.515232
$208$	2.85632e12	0.508696
$209$	−1.23163e12	−0.213636
$210$	7.82380e12	1.32194
$211$	4.79581e12	0.789421	0.394711	−	0.918805i	$-0.370845\pi$
$211$	4.79581e12	0.789421	0.394711	+	0.918805i	$0.370845\pi$
$212$	1.40354e13	2.25101
$213$	−2.76371e12	−0.431921
$214$	6.78566e12	1.03351
$215$	−8.54978e12	−1.26924
$216$	−6.23391e11	−0.0902121
$217$	−7.52681e12	−1.06190
$218$	1.15426e13	1.58780
$219$	−2.86173e12	−0.383872
$220$	−6.04012e12	−0.790170
$221$	−1.62033e12	−0.206751
$222$	9.12098e12	1.13527
$223$	−5.10096e12	−0.619405	−0.309703	−	0.950833i	$-0.600230\pi$
$223$	−5.10096e12	−0.619405	−0.309703	+	0.950833i	$0.600230\pi$
$224$	−1.66820e13	−1.97644
$225$	2.84705e11	0.0329148
$226$	−5.73627e12	−0.647192
$227$	−1.38386e13	−1.52387	−0.761937	−	0.647651i	$-0.775752\pi$
$227$	−1.38386e13	−1.52387	−0.761937	+	0.647651i	$0.775752\pi$
$228$	2.60641e12	0.280156
$229$	−3.00157e12	−0.314959	−0.157479	−	0.987522i	$-0.550337\pi$
$229$	−3.00157e12	−0.314959	−0.157479	+	0.987522i	$0.550337\pi$
$230$	−2.40293e13	−2.46172
$231$	4.78030e12	0.478178
$232$	−7.12144e12	−0.695639
$233$	−2.94172e12	−0.280636	−0.140318	−	0.990106i	$-0.544812\pi$
$233$	−2.94172e12	−0.280636	−0.140318	+	0.990106i	$0.544812\pi$
$234$	4.63688e12	0.432055
$235$	−2.41065e12	−0.219412
$236$	−1.91589e12	−0.170354
$237$	1.13633e13	0.987165
$238$	6.23664e12	0.529392
$239$	−1.24328e13	−1.03129	−0.515646	−	0.856802i	$-0.672448\pi$
$239$	−1.24328e13	−1.03129	−0.515646	+	0.856802i	$0.672448\pi$
$240$	−4.45158e12	−0.360871
$241$	4.39171e11	0.0347969	0.0173984	−	0.999849i	$-0.494462\pi$
$241$	4.39171e11	0.0347969	0.0173984	+	0.999849i	$0.494462\pi$
$242$	1.31070e13	1.01512
$243$	8.47289e11	0.0641500
$244$	1.79319e13	1.32734
$245$	1.54517e13	1.11831
$246$	9.64753e12	0.682768
$247$	−4.57097e12	−0.316355
$248$	−5.11512e12	−0.346236
$249$	−1.07313e12	−0.0710486
$250$	2.21632e13	1.43537
$251$	2.10997e13	1.33681	0.668405	−	0.743797i	$-0.266977\pi$
$251$	2.10997e13	1.33681	0.668405	+	0.743797i	$0.266977\pi$
$252$	−1.01162e13	−0.627069
$253$	−1.46818e13	−0.890465
$254$	−2.64548e13	−1.57007
$255$	2.52530e12	0.146670
$256$	2.38974e12	0.135841
$257$	9.06650e11	0.0504438	0.0252219	−	0.999682i	$-0.491971\pi$
$257$	9.06650e11	0.0504438	0.0252219	+	0.999682i	$0.491971\pi$
$258$	1.95034e13	1.06219
$259$	3.48980e13	1.86059
$260$	−2.24169e13	−1.17010
$261$	9.67919e12	0.494671
$262$	2.93578e13	1.46915
$263$	−5.28789e12	−0.259135	−0.129567	−	0.991571i	$-0.541359\pi$
$263$	−5.28789e12	−0.259135	−0.129567	+	0.991571i	$0.541359\pi$
$264$	3.24863e12	0.155912
$265$	3.83617e13	1.80321
$266$	1.75936e13	0.810037
$267$	6.79900e11	0.0306643
$268$	−2.93470e13	−1.29665
$269$	−6.36340e12	−0.275455	−0.137728	−	0.990470i	$-0.543980\pi$
$269$	−6.36340e12	−0.275455	−0.137728	+	0.990470i	$0.543980\pi$
$270$	−7.22660e12	−0.306502
$271$	−2.73829e13	−1.13802	−0.569008	−	0.822332i	$-0.692673\pi$
$271$	−2.73829e13	−1.13802	−0.569008	+	0.822332i	$0.692673\pi$
$272$	−3.54852e12	−0.144517
$273$	1.77413e13	0.708093
$274$	−2.10391e13	−0.823000
$275$	−1.48366e12	−0.0568860
$276$	3.10701e13	1.16773
$277$	−1.41836e13	−0.522573	−0.261287	−	0.965261i	$-0.584147\pi$
$277$	−1.41836e13	−0.522573	−0.261287	+	0.965261i	$0.584147\pi$
$278$	6.61620e13	2.38980
$279$	6.95228e12	0.246209
$280$	2.03433e13	0.706402
$281$	2.12548e13	0.723722	0.361861	−	0.932232i	$-0.382142\pi$
$281$	2.12548e13	0.723722	0.361861	+	0.932232i	$0.382142\pi$
$282$	5.49906e12	0.183619
$283$	−1.55797e13	−0.510192	−0.255096	−	0.966916i	$-0.582107\pi$
$283$	−1.55797e13	−0.510192	−0.255096	+	0.966916i	$0.582107\pi$
$284$	−3.04786e13	−0.978914
$285$	7.12387e12	0.224424
$286$	−2.41638e13	−0.746712
$287$	3.69126e13	1.11898
$288$	1.54087e13	0.458254
$289$	−3.22589e13	−0.941264
$290$	−8.25546e13	−2.36348
$291$	−2.61741e13	−0.735294
$292$	−3.15596e13	−0.870014
$293$	6.97384e13	1.88669	0.943345	−	0.331815i	$-0.107661\pi$
$293$	6.97384e13	1.88669	0.943345	+	0.331815i	$0.107661\pi$
$294$	−3.52476e13	−0.935879
$295$	−5.23653e12	−0.136465
$296$	2.37162e13	0.606653
$297$	−4.41541e12	−0.110869
$298$	8.05945e13	1.98662
$299$	−5.44890e13	−1.31861
$300$	3.13978e12	0.0745988
$301$	7.46222e13	1.74081
$302$	−6.28391e13	−1.43943
$303$	2.95013e13	0.663600
$304$	−1.00104e13	−0.221129
$305$	4.90118e13	1.06329
$306$	−5.76059e12	−0.122744
$307$	−8.59060e12	−0.179789	−0.0898944	−	0.995951i	$-0.528653\pi$
$307$	−8.59060e12	−0.179789	−0.0898944	+	0.995951i	$0.528653\pi$
$308$	5.27179e13	1.08375
$309$	2.74972e13	0.555286
$310$	−5.92966e13	−1.17636
$311$	−1.43460e13	−0.279608	−0.139804	−	0.990179i	$-0.544647\pi$
$311$	−1.43460e13	−0.279608	−0.139804	+	0.990179i	$0.544647\pi$
$312$	1.20567e13	0.230876
$313$	−4.78260e13	−0.899850	−0.449925	−	0.893066i	$-0.648549\pi$
$313$	−4.78260e13	−0.899850	−0.449925	+	0.893066i	$0.648549\pi$
$314$	−1.37605e14	−2.54403
$315$	−2.76498e13	−0.502324
$316$	1.25317e14	2.23733
$317$	3.44196e13	0.603920	0.301960	−	0.953321i	$-0.402359\pi$
$317$	3.44196e13	0.603920	0.301960	+	0.953321i	$0.402359\pi$
$318$	−8.75090e13	−1.50905
$319$	−5.04404e13	−0.854929
$320$	−9.39039e13	−1.56444
$321$	−2.39810e13	−0.392725
$322$	2.09727e14	3.37635
$323$	5.67870e12	0.0898742
$324$	9.34404e12	0.145391
$325$	−5.50636e12	−0.0842377
$326$	1.99405e14	2.99944
$327$	−4.07925e13	−0.603348
$328$	2.50853e13	0.364849
$329$	2.10401e13	0.300933
$330$	3.76594e13	0.529721
$331$	6.96318e13	0.963282	0.481641	−	0.876369i	$-0.340041\pi$
$331$	6.96318e13	0.963282	0.481641	+	0.876369i	$0.340041\pi$
$332$	−1.18346e13	−0.161026
$333$	−3.22341e13	−0.431393
$334$	7.72810e12	0.101734
$335$	−8.02117e13	−1.03870
$336$	3.88532e13	0.494949
$337$	−5.62053e13	−0.704389	−0.352195	−	0.935927i	$-0.614564\pi$
$337$	−5.62053e13	−0.704389	−0.352195	+	0.935927i	$0.614564\pi$
$338$	3.35477e13	0.413639
$339$	2.02723e13	0.245927
$340$	2.78494e13	0.332416
$341$	−3.62299e13	−0.425518
$342$	−1.62506e13	−0.187813
$343$	−8.45354e12	−0.0961437
$344$	5.07123e13	0.567599
$345$	8.49213e13	0.935431
$346$	1.22444e14	1.32745
$347$	−4.96603e13	−0.529904	−0.264952	−	0.964262i	$-0.585356\pi$
$347$	−4.96603e13	−0.529904	−0.264952	+	0.964262i	$0.585356\pi$
$348$	1.06744e14	1.12113
$349$	−3.32863e13	−0.344133	−0.172066	−	0.985085i	$-0.555044\pi$
$349$	−3.32863e13	−0.344133	−0.172066	+	0.985085i	$0.555044\pi$
$350$	2.11939e13	0.215693
$351$	−1.63871e13	−0.164177
$352$	−8.02980e13	−0.791991
$353$	−1.82488e14	−1.77204	−0.886021	−	0.463646i	$-0.846541\pi$
$353$	−1.82488e14	−1.77204	−0.886021	+	0.463646i	$0.846541\pi$
$354$	1.19453e13	0.114204
$355$	−8.33047e13	−0.784176
$356$	7.49805e12	0.0694982
$357$	−2.20407e13	−0.201164
$358$	2.04437e14	1.83740
$359$	−2.06373e14	−1.82655	−0.913277	−	0.407339i	$-0.866457\pi$
$359$	−2.06373e14	−1.82655	−0.913277	+	0.407339i	$0.866457\pi$
$360$	−1.87905e13	−0.163785
$361$	−1.00471e14	−0.862481
$362$	−1.52134e14	−1.28626
$363$	−4.63210e13	−0.385737
$364$	1.95654e14	1.60483
$365$	−8.62593e13	−0.696940
$366$	−1.11804e14	−0.889835
$367$	8.31297e13	0.651768	0.325884	−	0.945410i	$-0.394338\pi$
$367$	8.31297e13	0.651768	0.325884	+	0.945410i	$0.394338\pi$
$368$	−1.19330e14	−0.921697
$369$	−3.40950e13	−0.259445
$370$	2.74928e14	2.06115
$371$	−3.34820e14	−2.47317
$372$	7.66709e13	0.558013
$373$	−2.44630e14	−1.75433	−0.877164	−	0.480192i	$-0.840567\pi$
$373$	−2.44630e14	−1.75433	−0.877164	+	0.480192i	$0.840567\pi$
$374$	3.00197e13	0.212135
$375$	−7.83263e13	−0.545426
$376$	1.42986e13	0.0981203
$377$	−1.87201e14	−1.26599
$378$	6.30735e13	0.420380
$379$	−9.15400e13	−0.601306	−0.300653	−	0.953734i	$-0.597205\pi$
$379$	−9.15400e13	−0.601306	−0.300653	+	0.953734i	$0.597205\pi$
$380$	7.85632e13	0.508639
$381$	9.34932e13	0.596613
$382$	−6.68240e13	−0.420324
$383$	−3.80408e13	−0.235861	−0.117931	−	0.993022i	$-0.537626\pi$
$383$	−3.80408e13	−0.235861	−0.117931	+	0.993022i	$0.537626\pi$
$384$	8.43453e13	0.515512
$385$	1.44089e14	0.868157
$386$	1.29191e14	0.767363
$387$	−6.89262e13	−0.403621
$388$	−2.88653e14	−1.66648
$389$	1.69152e14	0.962841	0.481420	−	0.876490i	$-0.340121\pi$
$389$	1.69152e14	0.962841	0.481420	+	0.876490i	$0.340121\pi$
$390$	1.39767e14	0.784419
$391$	6.76939e13	0.374608
$392$	−9.16502e13	−0.500104
$393$	−1.03752e14	−0.558263
$394$	1.40643e14	0.746257
$395$	3.42518e14	1.79225
$396$	−4.86939e13	−0.251276
$397$	2.92592e14	1.48907	0.744535	−	0.667583i	$-0.232671\pi$
$397$	2.92592e14	1.48907	0.744535	+	0.667583i	$0.232671\pi$
$398$	−2.68397e14	−1.34717
$399$	−6.21769e13	−0.307807
$400$	−1.20589e13	−0.0588813
$401$	1.76860e14	0.851798	0.425899	−	0.904771i	$-0.359958\pi$
$401$	1.76860e14	0.851798	0.425899	+	0.904771i	$0.359958\pi$
$402$	1.82975e14	0.869259
$403$	−1.34461e14	−0.630114
$404$	3.25345e14	1.50400
$405$	2.55393e13	0.116468
$406$	7.20534e14	3.24161
$407$	1.67979e14	0.745567
$408$	−1.49786e13	−0.0655903
$409$	−9.26772e13	−0.400401	−0.200200	−	0.979755i	$-0.564159\pi$
$409$	−9.26772e13	−0.400401	−0.200200	+	0.979755i	$0.564159\pi$
$410$	2.90799e14	1.23960
$411$	7.43537e13	0.312732
$412$	3.03244e14	1.25851
$413$	4.57042e13	0.187168
$414$	−1.93719e14	−0.782833
$415$	−3.23466e13	−0.128993
$416$	−2.98012e14	−1.17279
$417$	−2.33821e14	−0.908103
$418$	8.46857e13	0.324594
$419$	3.72528e12	0.0140923	0.00704614	−	0.999975i	$-0.497757\pi$
$419$	3.72528e12	0.0140923	0.00704614	+	0.999975i	$0.497757\pi$
$420$	−3.04927e14	−1.13848
$421$	4.18454e14	1.54204	0.771022	−	0.636809i	$-0.219746\pi$
$421$	4.18454e14	1.54204	0.771022	+	0.636809i	$0.219746\pi$
$422$	−3.29757e14	−1.19943
$423$	−1.94340e13	−0.0697736
$424$	−2.27539e14	−0.806388
$425$	6.84078e12	0.0239313
$426$	1.90031e14	0.656252
$427$	−4.27774e14	−1.45835
$428$	−2.64466e14	−0.890080
$429$	8.53966e13	0.283743
$430$	5.87877e14	1.92846
$431$	−3.15215e14	−1.02090	−0.510448	−	0.859909i	$-0.670520\pi$
$431$	−3.15215e14	−1.02090	−0.510448	+	0.859909i	$0.670520\pi$
$432$	−3.58875e13	−0.114758
$433$	−6.15459e14	−1.94319	−0.971596	−	0.236644i	$-0.923953\pi$
$433$	−6.15459e14	−1.94319	−0.971596	+	0.236644i	$0.923953\pi$
$434$	5.17538e14	1.61343
$435$	2.91753e14	0.898101
$436$	−4.49866e14	−1.36744
$437$	1.90965e14	0.573199
$438$	1.96771e14	0.583248
$439$	−5.68329e14	−1.66358	−0.831792	−	0.555087i	$-0.812685\pi$
$439$	−5.68329e14	−1.66358	−0.831792	+	0.555087i	$0.812685\pi$
$440$	9.79213e13	0.283066
$441$	1.24567e14	0.355625
$442$	1.11413e14	0.314133
$443$	−1.07083e14	−0.298195	−0.149097	−	0.988823i	$-0.547637\pi$
$443$	−1.07083e14	−0.298195	−0.149097	+	0.988823i	$0.547637\pi$
$444$	−3.55483e14	−0.977717
$445$	2.04938e13	0.0556727
$446$	3.50738e14	0.941113
$447$	−2.84826e14	−0.754899
$448$	8.19590e14	2.14569
$449$	−1.43883e14	−0.372097	−0.186048	−	0.982541i	$-0.559568\pi$
$449$	−1.43883e14	−0.372097	−0.186048	+	0.982541i	$0.559568\pi$
$450$	−1.95761e13	−0.0500102
$451$	1.77677e14	0.448394
$452$	2.23567e14	0.557373
$453$	2.22078e14	0.546971
$454$	9.51531e14	2.31535
$455$	5.34764e14	1.28558
$456$	−4.22546e13	−0.100362
$457$	−5.29269e14	−1.24204	−0.621022	−	0.783793i	$-0.713282\pi$
$457$	−5.29269e14	−1.24204	−0.621022	+	0.783793i	$0.713282\pi$
$458$	2.06386e14	0.478542
$459$	2.03583e13	0.0466414
$460$	9.36526e14	2.12008
$461$	3.99873e14	0.894473	0.447236	−	0.894416i	$-0.352408\pi$
$461$	3.99873e14	0.894473	0.447236	+	0.894416i	$0.352408\pi$
$462$	−3.28690e14	−0.726534
$463$	−7.10906e14	−1.55280	−0.776402	−	0.630237i	$-0.782958\pi$
$463$	−7.10906e14	−1.55280	−0.776402	+	0.630237i	$0.782958\pi$
$464$	−4.09969e14	−0.884915
$465$	2.09558e14	0.447006
$466$	2.02270e14	0.426393
$467$	8.69930e13	0.181235	0.0906174	−	0.995886i	$-0.471116\pi$
$467$	8.69930e13	0.181235	0.0906174	+	0.995886i	$0.471116\pi$
$468$	−1.80719e14	−0.372093
$469$	7.00085e14	1.42462
$470$	1.65755e14	0.333371
$471$	4.86306e14	0.966707
$472$	3.10600e13	0.0610268
$473$	3.59190e14	0.697570
$474$	−7.81335e14	−1.49988
$475$	1.92979e13	0.0366180
$476$	−2.43068e14	−0.455922
$477$	3.09263e14	0.573425
$478$	8.54873e14	1.56692
$479$	−7.89655e14	−1.43084	−0.715422	−	0.698693i	$-0.753765\pi$
$479$	−7.89655e14	−1.43084	−0.715422	+	0.698693i	$0.753765\pi$
$480$	4.64453e14	0.831984
$481$	6.23427e14	1.10405
$482$	−3.01971e13	−0.0528697
$483$	−7.41190e14	−1.28298
$484$	−5.10836e14	−0.874242
$485$	−7.88950e14	−1.33497
$486$	−5.82590e13	−0.0974683
$487$	−6.74215e14	−1.11529	−0.557647	−	0.830078i	$-0.688296\pi$
$487$	−6.74215e14	−1.11529	−0.557647	+	0.830078i	$0.688296\pi$
$488$	−2.90709e14	−0.475500
$489$	−7.04712e14	−1.13976
$490$	−1.06245e15	−1.69914
$491$	−5.64669e14	−0.892988	−0.446494	−	0.894787i	$-0.647328\pi$
$491$	−5.64669e14	−0.892988	−0.446494	+	0.894787i	$0.647328\pi$
$492$	−3.76005e14	−0.588012
$493$	2.32567e14	0.359659
$494$	3.14297e14	0.480664
$495$	−1.33091e14	−0.201289
$496$	−2.94468e14	−0.440443
$497$	7.27080e14	1.07553
$498$	7.37876e13	0.107950
$499$	−4.45620e14	−0.644780	−0.322390	−	0.946607i	$-0.604486\pi$
$499$	−4.45620e14	−0.644780	−0.322390	+	0.946607i	$0.604486\pi$
$500$	−8.63795e14	−1.23616
$501$	−2.73116e13	−0.0386580
$502$	−1.45080e15	−2.03112
$503$	3.31592e14	0.459177	0.229588	−	0.973288i	$-0.426262\pi$
$503$	3.31592e14	0.459177	0.229588	+	0.973288i	$0.426262\pi$
$504$	1.64002e14	0.224638
$505$	8.89238e14	1.20480
$506$	1.00951e15	1.35295
$507$	−1.18560e14	−0.157179
$508$	1.03106e15	1.35217
$509$	−4.37985e14	−0.568214	−0.284107	−	0.958793i	$-0.591697\pi$
$509$	−4.37985e14	−0.568214	−0.284107	+	0.958793i	$0.591697\pi$
$510$	−1.73638e14	−0.222848
$511$	7.52868e14	0.955881
$512$	−8.75178e14	−1.09929
$513$	5.74308e13	0.0713673
$514$	−6.23407e13	−0.0766433
$515$	8.28830e14	1.00815
$516$	−7.60129e14	−0.914774
$517$	1.01275e14	0.120588
$518$	−2.39956e15	−2.82695
$519$	−4.32724e14	−0.504418
$520$	3.63418e14	0.419168
$521$	1.25952e15	1.43746	0.718732	−	0.695287i	$-0.244723\pi$
$521$	1.25952e15	1.43746	0.718732	+	0.695287i	$0.244723\pi$
$522$	−6.65534e14	−0.751593
$523$	−7.52673e14	−0.841099	−0.420550	−	0.907270i	$-0.638163\pi$
$523$	−7.52673e14	−0.841099	−0.420550	+	0.907270i	$0.638163\pi$
$524$	−1.14420e15	−1.26526
$525$	−7.49006e13	−0.0819614
$526$	3.63592e14	0.393724
$527$	1.67046e14	0.179011
$528$	1.87018e14	0.198334
$529$	1.32362e15	1.38917
$530$	−2.63773e15	−2.73976
$531$	−4.22156e13	−0.0433963
$532$	−6.85697e14	−0.697619
$533$	6.59417e14	0.663989
$534$	−4.67495e13	−0.0465908
$535$	−7.22843e14	−0.713014
$536$	4.75769e14	0.464504
$537$	−7.22495e14	−0.698194
$538$	4.37543e14	0.418522
$539$	−6.49149e14	−0.614619
$540$	2.81651e14	0.263965
$541$	−1.77185e15	−1.64378	−0.821888	−	0.569649i	$-0.807079\pi$
$541$	−1.77185e15	−1.64378	−0.821888	+	0.569649i	$0.807079\pi$
$542$	1.88283e15	1.72908
$543$	5.37651e14	0.488766
$544$	3.70233e14	0.333181
$545$	−1.22958e15	−1.09541
$546$	−1.21988e15	−1.07586
$547$	5.08668e14	0.444124	0.222062	−	0.975033i	$-0.428721\pi$
$547$	5.08668e14	0.444124	0.222062	+	0.975033i	$0.428721\pi$
$548$	8.19985e14	0.708782
$549$	3.95121e14	0.338129
$550$	1.02016e14	0.0864315
$551$	6.56074e14	0.550324
$552$	−5.03703e14	−0.418321
$553$	−2.98948e15	−2.45815
$554$	9.75254e14	0.793988
$555$	−9.71613e14	−0.783217
$556$	−2.57862e15	−2.05814
$557$	5.44481e14	0.430307	0.215154	−	0.976580i	$-0.430975\pi$
$557$	5.44481e14	0.430307	0.215154	+	0.976580i	$0.430975\pi$
$558$	−4.78034e14	−0.374085
$559$	1.33307e15	1.03297
$560$	1.17113e15	0.898607
$561$	−1.06092e14	−0.0806094
$562$	−1.46146e15	−1.09961
$563$	−1.32189e15	−0.984919	−0.492459	−	0.870335i	$-0.663902\pi$
$563$	−1.32189e15	−0.984919	−0.492459	+	0.870335i	$0.663902\pi$
$564$	−2.14322e14	−0.158136
$565$	6.11056e14	0.446493
$566$	1.07125e15	0.775177
$567$	−2.22906e14	−0.159740
$568$	4.94114e14	0.350680
$569$	1.85007e15	1.30038	0.650191	−	0.759771i	$-0.274689\pi$
$569$	1.85007e15	1.30038	0.650191	+	0.759771i	$0.274689\pi$
$570$	−4.89832e14	−0.340985
$571$	−1.66054e15	−1.14486	−0.572429	−	0.819954i	$-0.693999\pi$
$571$	−1.66054e15	−1.14486	−0.572429	+	0.819954i	$0.693999\pi$
$572$	9.41768e14	0.643081
$573$	2.36161e14	0.159719
$574$	−2.53809e15	−1.70016
$575$	2.30043e14	0.152629
$576$	−7.57029e14	−0.497495
$577$	2.32812e15	1.51544	0.757721	−	0.652579i	$-0.226313\pi$
$577$	2.32812e15	1.51544	0.757721	+	0.652579i	$0.226313\pi$
$578$	2.21810e15	1.43014
$579$	−4.56568e14	−0.291591
$580$	3.21751e15	2.03547
$581$	2.82320e14	0.176919
$582$	1.79972e15	1.11719
$583$	−1.61164e15	−0.991038
$584$	5.11640e14	0.311669
$585$	−4.93944e14	−0.298072
$586$	−4.79517e15	−2.86660
$587$	1.56510e15	0.926898	0.463449	−	0.886124i	$-0.346612\pi$
$587$	1.56510e15	0.926898	0.463449	+	0.886124i	$0.346612\pi$
$588$	1.37375e15	0.805995
$589$	4.71238e14	0.273909
$590$	3.60060e14	0.207343
$591$	−4.97041e14	−0.283571
$592$	1.36530e15	0.771718
$593$	−5.65084e14	−0.316455	−0.158227	−	0.987403i	$-0.550578\pi$
$593$	−5.65084e14	−0.316455	−0.158227	+	0.987403i	$0.550578\pi$
$594$	3.03601e14	0.168452
$595$	−6.64358e14	−0.365224
$596$	−3.14111e15	−1.71092
$597$	9.48533e14	0.511910
$598$	3.74663e15	2.00348
$599$	1.21451e15	0.643507	0.321753	−	0.946824i	$-0.395728\pi$
$599$	1.21451e15	0.643507	0.321753	+	0.946824i	$0.395728\pi$
$600$	−5.09015e13	−0.0267238
$601$	−1.08552e15	−0.564716	−0.282358	−	0.959309i	$-0.591117\pi$
$601$	−1.08552e15	−0.564716	−0.282358	+	0.959309i	$0.591117\pi$
$602$	−5.13097e15	−2.64496
$603$	−6.46647e14	−0.330310
$604$	2.44911e15	1.23967
$605$	−1.39622e15	−0.700327
$606$	−2.02849e15	−1.00826
$607$	−1.50458e15	−0.741102	−0.370551	−	0.928812i	$-0.620831\pi$
$607$	−1.50458e15	−0.741102	−0.370551	+	0.928812i	$0.620831\pi$
$608$	1.04443e15	0.509810
$609$	−2.54641e15	−1.23178
$610$	−3.37002e15	−1.61554
$611$	3.75866e14	0.178569
$612$	2.24515e14	0.105709
$613$	−7.91295e14	−0.369237	−0.184619	−	0.982810i	$-0.559105\pi$
$613$	−7.91295e14	−0.369237	−0.184619	+	0.982810i	$0.559105\pi$
$614$	5.90684e14	0.273168
$615$	−1.02770e15	−0.471037
$616$	−8.54654e14	−0.388236
$617$	1.66604e15	0.750096	0.375048	−	0.927005i	$-0.377626\pi$
$617$	1.66604e15	0.750096	0.375048	+	0.927005i	$0.377626\pi$
$618$	−1.89069e15	−0.843691
$619$	3.78034e15	1.67198	0.835992	−	0.548741i	$-0.184893\pi$
$619$	3.78034e15	1.67198	0.835992	+	0.548741i	$0.184893\pi$
$620$	2.31104e15	1.01310
$621$	6.84614e14	0.297469
$622$	9.86422e14	0.424830
$623$	−1.78869e14	−0.0763574
$624$	6.94085e14	0.293696
$625$	−2.59636e15	−1.08899
$626$	3.28848e15	1.36721
$627$	−2.99285e14	−0.123343
$628$	5.36306e15	2.19096
$629$	−7.74508e14	−0.313652
$630$	1.90118e15	0.763222
$631$	−9.43582e14	−0.375507	−0.187753	−	0.982216i	$-0.560121\pi$
$631$	−9.43582e14	−0.375507	−0.187753	+	0.982216i	$0.560121\pi$
$632$	−2.03161e15	−0.801488
$633$	1.16538e15	0.455773
$634$	−2.36667e15	−0.917585
$635$	2.81810e15	1.08318
$636$	3.41060e15	1.29962
$637$	−2.40921e15	−0.910138
$638$	3.46825e15	1.29896
$639$	−6.71581e14	−0.249370
$640$	2.54237e15	0.935940
$641$	1.91334e15	0.698350	0.349175	−	0.937058i	$-0.386462\pi$
$641$	1.91334e15	0.698350	0.349175	+	0.937058i	$0.386462\pi$
$642$	1.64891e15	0.596699
$643$	1.55238e15	0.556977	0.278489	−	0.960440i	$-0.410167\pi$
$643$	1.55238e15	0.556977	0.278489	+	0.960440i	$0.410167\pi$
$644$	−8.17397e15	−2.90777
$645$	−2.07760e15	−0.732795
$646$	−3.90463e14	−0.136553
$647$	−1.34109e15	−0.465034	−0.232517	−	0.972592i	$-0.574696\pi$
$647$	−1.34109e15	−0.465034	−0.232517	+	0.972592i	$0.574696\pi$
$648$	−1.51484e14	−0.0520840
$649$	2.19995e14	0.0750009
$650$	3.78614e14	0.127989
$651$	−1.82901e15	−0.613086
$652$	−7.77168e15	−2.58317
$653$	−1.19942e15	−0.395319	−0.197659	−	0.980271i	$-0.563334\pi$
$653$	−1.19942e15	−0.395319	−0.197659	+	0.980271i	$0.563334\pi$
$654$	2.80486e15	0.916715
$655$	−3.12734e15	−1.01356
$656$	1.44412e15	0.464121
$657$	−6.95401e14	−0.221629
$658$	−1.44670e15	−0.457231
$659$	−4.29128e15	−1.34498	−0.672492	−	0.740104i	$-0.734776\pi$
$659$	−4.29128e15	−1.34498	−0.672492	+	0.740104i	$0.734776\pi$
$660$	−1.46775e15	−0.456205
$661$	2.71996e15	0.838406	0.419203	−	0.907893i	$-0.362310\pi$
$661$	2.71996e15	0.838406	0.419203	+	0.907893i	$0.362310\pi$
$662$	−4.78783e15	−1.46359
$663$	−3.93741e14	−0.119368
$664$	1.91861e14	0.0576850
$665$	−1.87416e15	−0.558839
$666$	2.21640e15	0.655450
$667$	7.82084e15	2.29383
$668$	−3.01197e14	−0.0876153
$669$	−1.23953e15	−0.357614
$670$	5.51530e15	1.57819
$671$	−2.05907e15	−0.584381
$672$	−4.05373e15	−1.14110
$673$	4.33839e15	1.21128	0.605641	−	0.795738i	$-0.292917\pi$
$673$	4.33839e15	1.21128	0.605641	+	0.795738i	$0.292917\pi$
$674$	3.86464e15	1.07024
$675$	6.91834e13	0.0190034
$676$	−1.30750e15	−0.356233
$677$	−4.29274e15	−1.16010	−0.580052	−	0.814580i	$-0.696968\pi$
$677$	−4.29274e15	−1.16010	−0.580052	+	0.814580i	$0.696968\pi$
$678$	−1.39391e15	−0.373656
$679$	6.88593e15	1.83096
$680$	−4.51489e14	−0.119083
$681$	−3.36277e15	−0.879809
$682$	2.49114e15	0.646524
$683$	1.80140e15	0.463763	0.231881	−	0.972744i	$-0.425512\pi$
$683$	1.80140e15	0.463763	0.231881	+	0.972744i	$0.425512\pi$
$684$	6.33356e14	0.161748
$685$	2.24119e15	0.567782
$686$	5.81260e14	0.146079
$687$	−7.29382e14	−0.181841
$688$	2.91941e15	0.722037
$689$	−5.98132e15	−1.46754
$690$	−5.83913e15	−1.42128
$691$	5.96668e15	1.44080	0.720399	−	0.693560i	$-0.243959\pi$
$691$	5.96668e15	1.44080	0.720399	+	0.693560i	$0.243959\pi$
$692$	−4.77215e15	−1.14322
$693$	1.16161e15	0.276076
$694$	3.41461e15	0.805126
$695$	−7.04791e15	−1.64871
$696$	−1.73051e15	−0.401627
$697$	−8.19221e14	−0.188634
$698$	2.28875e15	0.522869
$699$	−7.14837e14	−0.162025
$700$	−8.26016e14	−0.185759
$701$	−4.27057e15	−0.952876	−0.476438	−	0.879208i	$-0.658072\pi$
$701$	−4.27057e15	−0.952876	−0.476438	+	0.879208i	$0.658072\pi$
$702$	1.12676e15	0.249447
$703$	−2.18489e15	−0.479927
$704$	3.94505e15	0.859811
$705$	−5.85788e14	−0.126678
$706$	1.25478e16	2.69241
$707$	−7.76124e15	−1.65244
$708$	−4.65560e14	−0.0983542
$709$	6.74401e15	1.41372	0.706861	−	0.707353i	$-0.250111\pi$
$709$	6.74401e15	1.41372	0.706861	+	0.707353i	$0.250111\pi$
$710$	5.72797e15	1.19146
$711$	2.76129e15	0.569940
$712$	−1.21557e14	−0.0248966
$713$	5.61748e15	1.14169
$714$	1.51550e15	0.305644
$715$	2.57406e15	0.515151
$716$	−7.96780e15	−1.58240
$717$	−3.02118e15	−0.595416
$718$	1.41900e16	2.77523
$719$	6.94235e15	1.34740	0.673702	−	0.739003i	$-0.264703\pi$
$719$	6.94235e15	1.34740	0.673702	+	0.739003i	$0.264703\pi$
$720$	−1.08173e15	−0.208349
$721$	−7.23400e15	−1.38272
$722$	6.90829e15	1.31044
$723$	1.06719e14	0.0200900
$724$	5.92930e15	1.10775
$725$	7.90331e14	0.146538
$726$	3.18500e15	0.586082
$727$	−1.32393e15	−0.241783	−0.120892	−	0.992666i	$-0.538575\pi$
$727$	−1.32393e15	−0.241783	−0.120892	+	0.992666i	$0.538575\pi$
$728$	−3.17190e15	−0.574906
$729$	2.05891e14	0.0370370
$730$	5.93113e15	1.05892
$731$	−1.65613e15	−0.293460
$732$	4.35746e15	0.766342
$733$	6.09764e15	1.06436	0.532182	−	0.846630i	$-0.321372\pi$
$733$	6.09764e15	1.06436	0.532182	+	0.846630i	$0.321372\pi$
$734$	−5.71594e15	−0.990283
$735$	3.75476e15	0.645656
$736$	1.24503e16	2.12496
$737$	3.36982e15	0.570868
$738$	2.34435e15	0.394196
$739$	3.04358e15	0.507972	0.253986	−	0.967208i	$-0.418258\pi$
$739$	3.04358e15	0.507972	0.253986	+	0.967208i	$0.418258\pi$
$740$	−1.07151e16	−1.77510
$741$	−1.11075e15	−0.182648
$742$	2.30220e16	3.75769
$743$	−1.38530e15	−0.224442	−0.112221	−	0.993683i	$-0.535796\pi$
$743$	−1.38530e15	−0.224442	−0.112221	+	0.993683i	$0.535796\pi$
$744$	−1.24297e15	−0.199899
$745$	−8.58533e15	−1.37056
$746$	1.68206e16	2.66549
$747$	−2.60770e14	−0.0410199
$748$	−1.17000e15	−0.182695
$749$	6.30894e15	0.977927
$750$	5.38566e15	0.828709
$751$	−3.49866e15	−0.534419	−0.267209	−	0.963638i	$-0.586102\pi$
$751$	−3.49866e15	−0.534419	−0.267209	+	0.963638i	$0.586102\pi$
$752$	8.23142e14	0.124818
$753$	5.12721e15	0.771808
$754$	1.28718e16	1.92352
$755$	6.69394e15	0.993056
$756$	−2.45824e15	−0.362039
$757$	7.88002e15	1.15213	0.576063	−	0.817405i	$-0.304588\pi$
$757$	7.88002e15	1.15213	0.576063	+	0.817405i	$0.304588\pi$
$758$	6.29423e15	0.913612
$759$	−3.56768e15	−0.514110
$760$	−1.27365e15	−0.182212
$761$	8.78969e15	1.24841	0.624206	−	0.781260i	$-0.285422\pi$
$761$	8.78969e15	1.24841	0.624206	+	0.781260i	$0.285422\pi$
$762$	−6.42853e15	−0.906482
$763$	1.07317e16	1.50240
$764$	2.60442e15	0.361990
$765$	6.13647e14	0.0846800
$766$	2.61566e15	0.358363
$767$	8.16474e14	0.111063
$768$	5.80707e14	0.0784279
$769$	−6.36504e15	−0.853505	−0.426752	−	0.904369i	$-0.640342\pi$
$769$	−6.36504e15	−0.853505	−0.426752	+	0.904369i	$0.640342\pi$
$770$	−9.90749e15	−1.31906
$771$	2.20316e14	0.0291237
$772$	−5.03511e15	−0.660866
$773$	−7.57190e15	−0.986774	−0.493387	−	0.869810i	$-0.664241\pi$
$773$	−7.57190e15	−0.986774	−0.493387	+	0.869810i	$0.664241\pi$
$774$	4.73932e15	0.613254
$775$	5.67672e14	0.0729353
$776$	4.67959e15	0.596991
$777$	8.48020e15	1.07421
$778$	−1.16308e16	−1.46292
$779$	−2.31102e15	−0.288635
$780$	−5.44730e15	−0.675555
$781$	3.49976e15	0.430981
$782$	−4.65459e15	−0.569173
$783$	2.35204e15	0.285598
$784$	−5.27614e15	−0.636177
$785$	1.46584e16	1.75511
$786$	7.13393e15	0.848213
$787$	−1.79619e14	−0.0212075	−0.0106038	−	0.999944i	$-0.503375\pi$
$787$	−1.79619e14	−0.0212075	−0.0106038	+	0.999944i	$0.503375\pi$
$788$	−5.48145e15	−0.642690
$789$	−1.28496e15	−0.149612
$790$	−2.35513e16	−2.72311
$791$	−5.33328e15	−0.612383
$792$	7.89417e14	0.0900156
$793$	−7.64187e15	−0.865361
$794$	−2.01185e16	−2.26246
$795$	9.32190e15	1.04108
$796$	1.04606e16	1.16020
$797$	1.68156e15	0.185221	0.0926106	−	0.995702i	$-0.470479\pi$
$797$	1.68156e15	0.185221	0.0926106	+	0.995702i	$0.470479\pi$
$798$	4.27524e15	0.467675
$799$	−4.66953e14	−0.0507301
$800$	1.25816e15	0.135750
$801$	1.65216e14	0.0177040
$802$	−1.21608e16	−1.29420
$803$	3.62389e15	0.383036
$804$	−7.13133e15	−0.748621
$805$	−2.23412e16	−2.32932
$806$	9.24545e15	0.957382
$807$	−1.54631e15	−0.159034
$808$	−5.27444e15	−0.538783
$809$	−6.94771e15	−0.704896	−0.352448	−	0.935831i	$-0.614651\pi$
$809$	−6.94771e15	−0.704896	−0.352448	+	0.935831i	$0.614651\pi$
$810$	−1.75606e15	−0.176959
$811$	−5.93624e15	−0.594151	−0.297076	−	0.954854i	$-0.596011\pi$
$811$	−5.93624e15	−0.594151	−0.297076	+	0.954854i	$0.596011\pi$
$812$	−2.80823e16	−2.79173
$813$	−6.65405e15	−0.657034
$814$	−1.15502e16	−1.13280
$815$	−2.12417e16	−2.06929
$816$	−8.62289e14	−0.0834367
$817$	−4.67194e15	−0.449031
$818$	6.37242e15	0.608361
$819$	4.31113e15	0.408818
$820$	−1.13337e16	−1.06757
$821$	1.57327e16	1.47203	0.736015	−	0.676965i	$-0.236705\pi$
$821$	1.57327e16	1.47203	0.736015	+	0.676965i	$0.236705\pi$
$822$	−5.11251e15	−0.475159
$823$	−1.40061e16	−1.29306	−0.646528	−	0.762890i	$-0.723780\pi$
$823$	−1.40061e16	−1.29306	−0.646528	+	0.762890i	$0.723780\pi$
$824$	−4.91613e15	−0.450842
$825$	−3.60530e14	−0.0328432
$826$	−3.14259e15	−0.284379
$827$	7.21399e15	0.648478	0.324239	−	0.945975i	$-0.394892\pi$
$827$	7.21399e15	0.648478	0.324239	+	0.945975i	$0.394892\pi$
$828$	7.55004e15	0.674190
$829$	1.09885e16	0.974739	0.487369	−	0.873196i	$-0.337957\pi$
$829$	1.09885e16	0.974739	0.487369	+	0.873196i	$0.337957\pi$
$830$	2.22413e15	0.195989
$831$	−3.44661e15	−0.301708
$832$	1.46414e16	1.27322
$833$	2.99305e15	0.258563
$834$	1.60774e16	1.37975
$835$	−8.23236e14	−0.0701857
$836$	−3.30056e15	−0.279546
$837$	1.68940e15	0.142149
$838$	−2.56148e14	−0.0214116
$839$	−1.66430e16	−1.38210	−0.691051	−	0.722806i	$-0.742852\pi$
$839$	−1.66430e16	−1.38210	−0.691051	+	0.722806i	$0.742852\pi$
$840$	4.94342e15	0.407841
$841$	1.46686e16	1.20229
$842$	−2.87726e16	−2.34295
$843$	5.16491e15	0.417841
$844$	1.28520e16	1.03297
$845$	−3.57367e15	−0.285366
$846$	1.33627e15	0.106013
$847$	1.21862e16	0.960527
$848$	−1.30990e16	−1.02580
$849$	−3.78587e15	−0.294560
$850$	−4.70367e14	−0.0363608
$851$	−2.60454e16	−2.00041
$852$	−7.40631e15	−0.565176
$853$	−2.43050e16	−1.84279	−0.921394	−	0.388630i	$-0.872948\pi$
$853$	−2.43050e16	−1.84279	−0.921394	+	0.388630i	$0.872948\pi$
$854$	2.94134e16	2.21578
$855$	1.73110e15	0.129571
$856$	4.28748e15	0.318857
$857$	−1.40484e15	−0.103808	−0.0519042	−	0.998652i	$-0.516529\pi$
$857$	−1.40484e15	−0.103808	−0.0519042	+	0.998652i	$0.516529\pi$
$858$	−5.87182e15	−0.431114
$859$	−9.01491e15	−0.657656	−0.328828	−	0.944390i	$-0.606654\pi$
$859$	−9.01491e15	−0.657656	−0.328828	+	0.944390i	$0.606654\pi$
$860$	−2.29121e16	−1.66082
$861$	8.96976e15	0.646046
$862$	2.16739e16	1.55113
$863$	−1.45313e16	−1.03334	−0.516672	−	0.856183i	$-0.672829\pi$
$863$	−1.45313e16	−1.03334	−0.516672	+	0.856183i	$0.672829\pi$
$864$	3.74430e15	0.264573
$865$	−1.30433e16	−0.915797
$866$	4.23186e16	2.95245
$867$	−7.83891e15	−0.543439
$868$	−2.01707e16	−1.38951
$869$	−1.43897e16	−0.985016
$870$	−2.00608e16	−1.36456
$871$	1.25065e16	0.845350
$872$	7.29315e15	0.489863
$873$	−6.36032e15	−0.424522
$874$	−1.31306e16	−0.870907
$875$	2.06062e16	1.35817
$876$	−7.66899e15	−0.502303
$877$	−1.53984e16	−1.00225	−0.501127	−	0.865374i	$-0.667081\pi$
$877$	−1.53984e16	−1.00225	−0.501127	+	0.865374i	$0.667081\pi$
$878$	3.90779e16	2.52762
$879$	1.69464e16	1.08928
$880$	5.63716e15	0.360085
$881$	−7.14900e15	−0.453814	−0.226907	−	0.973916i	$-0.572861\pi$
$881$	−7.14900e15	−0.453814	−0.226907	+	0.973916i	$0.572861\pi$
$882$	−8.56517e15	−0.540330
$883$	−2.60603e16	−1.63379	−0.816893	−	0.576789i	$-0.804305\pi$
$883$	−2.60603e16	−1.63379	−0.816893	+	0.576789i	$0.804305\pi$
$884$	−4.34224e15	−0.270537
$885$	−1.27248e15	−0.0787883
$886$	7.36296e15	0.453072
$887$	−1.95473e16	−1.19538	−0.597690	−	0.801727i	$-0.703915\pi$
$887$	−1.95473e16	−1.19538	−0.597690	+	0.801727i	$0.703915\pi$
$888$	5.76304e15	0.350251
$889$	−2.45963e16	−1.48563
$890$	−1.40914e15	−0.0845880
$891$	−1.07295e15	−0.0640103
$892$	−1.36698e16	−0.810503
$893$	−1.31728e15	−0.0776236
$894$	1.95845e16	1.14698
$895$	−2.17777e16	−1.26761
$896$	−2.21897e16	−1.28368
$897$	−1.32408e16	−0.761302
$898$	9.89332e15	0.565356
$899$	1.92993e16	1.09613
$900$	7.62966e14	0.0430696
$901$	7.43083e15	0.416918
$902$	−1.22169e16	−0.681281
$903$	1.81332e16	1.00506
$904$	−3.62443e15	−0.199670
$905$	1.62061e16	0.887381
$906$	−1.52699e16	−0.831058
$907$	−8.30930e15	−0.449495	−0.224747	−	0.974417i	$-0.572156\pi$
$907$	−8.30930e15	−0.449495	−0.224747	+	0.974417i	$0.572156\pi$
$908$	−3.70852e16	−1.99402
$909$	7.16882e15	0.383130
$910$	−3.67700e16	−1.95329
$911$	1.50691e16	0.795675	0.397837	−	0.917456i	$-0.369761\pi$
$911$	1.50691e16	0.795675	0.397837	+	0.917456i	$0.369761\pi$
$912$	−2.43252e15	−0.127669
$913$	1.35893e15	0.0708939
$914$	3.63922e16	1.88714
$915$	1.19099e16	0.613891
$916$	−8.04374e15	−0.412129
$917$	2.72953e16	1.39013
$918$	−1.39982e15	−0.0708660
$919$	1.38543e16	0.697188	0.348594	−	0.937274i	$-0.386659\pi$
$919$	1.38543e16	0.697188	0.348594	+	0.937274i	$0.386659\pi$
$920$	−1.51828e16	−0.759484
$921$	−2.08752e15	−0.103801
$922$	−2.74950e16	−1.35904
$923$	1.29888e16	0.638203
$924$	1.28105e16	0.625704
$925$	−2.63200e15	−0.127793
$926$	4.88814e16	2.35930
$927$	6.68182e15	0.320595
$928$	4.27739e16	2.04016
$929$	−3.12674e16	−1.48254	−0.741269	−	0.671208i	$-0.765776\pi$
$929$	−3.12674e16	−1.48254	−0.741269	+	0.671208i	$0.765776\pi$
$930$	−1.44091e16	−0.679172
$931$	8.44342e15	0.395635
$932$	−7.88334e15	−0.367217
$933$	−3.48608e15	−0.161432
$934$	−5.98158e15	−0.275365
$935$	−3.19785e15	−0.146351
$936$	2.92979e15	0.133297
$937$	−3.08797e16	−1.39671	−0.698354	−	0.715753i	$-0.746084\pi$
$937$	−3.08797e16	−1.39671	−0.698354	+	0.715753i	$0.746084\pi$
$938$	−4.81374e16	−2.16455
$939$	−1.16217e16	−0.519529
$940$	−6.46016e15	−0.287105
$941$	1.21992e16	0.538999	0.269499	−	0.963001i	$-0.413142\pi$
$941$	1.21992e16	0.538999	0.269499	+	0.963001i	$0.413142\pi$
$942$	−3.34381e16	−1.46880
$943$	−2.75490e16	−1.20307
$944$	1.78807e15	0.0776316
$945$	−6.71891e15	−0.290017
$946$	−2.46976e16	−1.05987
$947$	−4.47461e15	−0.190911	−0.0954554	−	0.995434i	$-0.530431\pi$
$947$	−4.47461e15	−0.190911	−0.0954554	+	0.995434i	$0.530431\pi$
$948$	3.04520e16	1.29172
$949$	1.34495e16	0.567206
$950$	−1.32691e15	−0.0556366
$951$	8.36396e15	0.348674
$952$	3.94058e15	0.163327
$953$	4.43753e16	1.82865	0.914325	−	0.404981i	$-0.132722\pi$
$953$	4.43753e16	1.82865	0.914325	+	0.404981i	$0.132722\pi$
$954$	−2.12647e16	−0.871250
$955$	7.11843e15	0.289979
$956$	−3.33180e16	−1.34946
$957$	−1.22570e16	−0.493594
$958$	5.42961e16	2.17400
$959$	−1.95611e16	−0.778736
$960$	−2.28186e16	−0.903229
$961$	−1.15464e16	−0.454430
$962$	−4.28664e16	−1.67747
$963$	−5.82737e15	−0.226740
$964$	1.17691e15	0.0455323
$965$	−1.37620e16	−0.529398
$966$	5.09637e16	1.94934
$967$	3.87053e16	1.47206	0.736029	−	0.676950i	$-0.236699\pi$
$967$	3.87053e16	1.47206	0.736029	+	0.676950i	$0.236699\pi$
$968$	8.28158e15	0.313183
$969$	1.37992e15	0.0518889
$970$	5.42477e16	2.02832
$971$	1.17311e16	0.436146	0.218073	−	0.975932i	$-0.430023\pi$
$971$	1.17311e16	0.436146	0.218073	+	0.975932i	$0.430023\pi$
$972$	2.27060e15	0.0839414
$973$	6.15139e16	2.26127
$974$	4.63586e16	1.69456
$975$	−1.33805e15	−0.0486347
$976$	−1.67356e16	−0.604878
$977$	2.66043e16	0.956161	0.478081	−	0.878316i	$-0.341333\pi$
$977$	2.66043e16	0.956161	0.478081	+	0.878316i	$0.341333\pi$
$978$	4.84555e16	1.73173
$979$	−8.60977e14	−0.0305975
$980$	4.14081e16	1.46333
$981$	−9.91257e15	−0.348343
$982$	3.88263e16	1.35679
$983$	1.81683e16	0.631350	0.315675	−	0.948867i	$-0.397769\pi$
$983$	1.81683e16	0.631350	0.315675	+	0.948867i	$0.397769\pi$
$984$	6.09573e15	0.210646
$985$	−1.49820e16	−0.514838
$986$	−1.59912e16	−0.546459
$987$	5.11273e15	0.173744
$988$	−1.22495e16	−0.413956
$989$	−5.56927e16	−1.87163
$990$	9.15124e15	0.305834
$991$	2.95832e16	0.983196	0.491598	−	0.870822i	$-0.336413\pi$
$991$	2.95832e16	0.983196	0.491598	+	0.870822i	$0.336413\pi$
$992$	3.07232e16	1.01544
$993$	1.69205e16	0.556151
$994$	−4.99935e16	−1.63414
$995$	2.85910e16	0.929400
$996$	−2.87582e15	−0.0929683
$997$	2.06404e16	0.663582	0.331791	−	0.943353i	$-0.392347\pi$
$997$	2.06404e16	0.663582	0.331791	+	0.943353i	$0.392347\pi$
$998$	3.06405e16	0.979667
$999$	−7.83290e15	−0.249065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.b.1.5	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.b.1.5	✓	27	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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-68.7593 q^{2} +243.000 q^{3} +2679.84 q^{4} +7324.59 q^{5} -16708.5 q^{6} -63928.8 q^{7} -43445.2 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-68.7593 q^{2} +243.000 q^{3} +2679.84 q^{4} +7324.59 q^{5} -16708.5 q^{6} -63928.8 q^{7} -43445.2 q^{8} +59049.0 q^{9} -503634. q^{10} -307718. q^{11} +651202. q^{12} -1.14204e6 q^{13} +4.39570e6 q^{14} +1.77988e6 q^{15} -2.50106e6 q^{16} +1.41880e6 q^{17} -4.06017e6 q^{18} +4.00245e6 q^{19} +1.96288e7 q^{20} -1.55347e7 q^{21} +2.11585e7 q^{22} +4.77119e7 q^{23} -1.05572e7 q^{24} +4.82151e6 q^{25} +7.85260e7 q^{26} +1.43489e7 q^{27} -1.71319e8 q^{28} +1.63918e8 q^{29} -1.22383e8 q^{30} +1.17737e8 q^{31} +2.60947e8 q^{32} -7.47754e7 q^{33} -9.75560e7 q^{34} -4.68252e8 q^{35} +1.58242e8 q^{36} -5.45888e8 q^{37} -2.75206e8 q^{38} -2.77516e8 q^{39} -3.18218e8 q^{40} -5.77402e8 q^{41} +1.06815e9 q^{42} -1.16727e9 q^{43} -8.24635e8 q^{44} +4.32510e8 q^{45} -3.28064e9 q^{46} -3.29117e8 q^{47} -6.07758e8 q^{48} +2.10956e9 q^{49} -3.31524e8 q^{50} +3.44769e8 q^{51} -3.06049e9 q^{52} +5.23739e9 q^{53} -9.86621e8 q^{54} -2.25391e9 q^{55} +2.77740e9 q^{56} +9.72596e8 q^{57} -1.12709e10 q^{58} -7.14924e8 q^{59} +4.76979e9 q^{60} +6.69141e9 q^{61} -8.09555e9 q^{62} -3.77493e9 q^{63} -1.28204e10 q^{64} -8.36499e9 q^{65} +5.14151e9 q^{66} -1.09510e10 q^{67} +3.80217e9 q^{68} +1.15940e10 q^{69} +3.21967e10 q^{70} -1.13733e10 q^{71} -2.56539e9 q^{72} -1.17767e10 q^{73} +3.75349e10 q^{74} +1.17163e9 q^{75} +1.07259e10 q^{76} +1.96720e10 q^{77} +1.90818e10 q^{78} +4.67627e10 q^{79} -1.83192e10 q^{80} +3.48678e9 q^{81} +3.97018e10 q^{82} -4.41617e9 q^{83} -4.16305e10 q^{84} +1.03922e10 q^{85} +8.02607e10 q^{86} +3.98320e10 q^{87} +1.33688e10 q^{88} +2.79794e9 q^{89} -2.97391e10 q^{90} +7.30093e10 q^{91} +1.27861e11 q^{92} +2.86102e10 q^{93} +2.26299e10 q^{94} +2.93163e10 q^{95} +6.34101e10 q^{96} -1.07713e11 q^{97} -1.45052e11 q^{98} -1.81704e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * q^99

Introduction

L-functions

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