LMFDB - Embedded newform 177.10.a.d.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,10,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, 10, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 10 $
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:	$91.1613430010$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+35.4666 q^{2} +81.0000 q^{3} +745.883 q^{4} +1622.90 q^{5} +2872.80 q^{6} +5254.11 q^{7} +8295.05 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+35.4666 q^{2} +81.0000 q^{3} +745.883 q^{4} +1622.90 q^{5} +2872.80 q^{6} +5254.11 q^{7} +8295.05 q^{8} +6561.00 q^{9} +57558.7 q^{10} +63201.2 q^{11} +60416.5 q^{12} -93199.3 q^{13} +186346. q^{14} +131455. q^{15} -87694.6 q^{16} +312651. q^{17} +232697. q^{18} +295079. q^{19} +1.21049e6 q^{20} +425583. q^{21} +2.24154e6 q^{22} -660434. q^{23} +671899. q^{24} +680669. q^{25} -3.30547e6 q^{26} +531441. q^{27} +3.91895e6 q^{28} -1.79623e6 q^{29} +4.66226e6 q^{30} +900850. q^{31} -7.35730e6 q^{32} +5.11930e6 q^{33} +1.10887e7 q^{34} +8.52688e6 q^{35} +4.89374e6 q^{36} +4.38437e6 q^{37} +1.04655e7 q^{38} -7.54914e6 q^{39} +1.34620e7 q^{40} +1.15498e7 q^{41} +1.50940e7 q^{42} -6.76278e6 q^{43} +4.71407e7 q^{44} +1.06478e7 q^{45} -2.34234e7 q^{46} -3.09203e7 q^{47} -7.10326e6 q^{48} -1.27480e7 q^{49} +2.41411e7 q^{50} +2.53248e7 q^{51} -6.95158e7 q^{52} +1.17476e7 q^{53} +1.88484e7 q^{54} +1.02569e8 q^{55} +4.35831e7 q^{56} +2.39014e7 q^{57} -6.37062e7 q^{58} -1.21174e7 q^{59} +9.80498e7 q^{60} -3.57264e7 q^{61} +3.19501e7 q^{62} +3.44722e7 q^{63} -2.16039e8 q^{64} -1.51253e8 q^{65} +1.81564e8 q^{66} +2.25795e8 q^{67} +2.33201e8 q^{68} -5.34952e7 q^{69} +3.02420e8 q^{70} -1.64241e8 q^{71} +5.44238e7 q^{72} -2.45097e8 q^{73} +1.55499e8 q^{74} +5.51342e7 q^{75} +2.20095e8 q^{76} +3.32066e8 q^{77} -2.67743e8 q^{78} +2.30240e8 q^{79} -1.42319e8 q^{80} +4.30467e7 q^{81} +4.09632e8 q^{82} +3.71689e8 q^{83} +3.17435e8 q^{84} +5.07401e8 q^{85} -2.39853e8 q^{86} -1.45494e8 q^{87} +5.24257e8 q^{88} +2.06997e8 q^{89} +3.77643e8 q^{90} -4.89679e8 q^{91} -4.92607e8 q^{92} +7.29688e7 q^{93} -1.09664e9 q^{94} +4.78883e8 q^{95} -5.95941e8 q^{96} +8.17254e8 q^{97} -4.52127e8 q^{98} +4.14663e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9}+O(q^{10}) $ 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9} + 45337 q^{10} + 111769 q^{11} + 483894 q^{12} + 189121 q^{13} + 251053 q^{14} + 468666 q^{15} + 2311074 q^{16} + 1113841 q^{17} + 301806 q^{18} + 476068 q^{19} - 42495 q^{20} + 618921 q^{21} - 2252022 q^{22} + 7103062 q^{23} + 4972995 q^{24} + 10628442 q^{25} + 6871048 q^{26} + 11691702 q^{27} + 8112650 q^{28} + 15279316 q^{29} + 3672297 q^{30} + 17610338 q^{31} + 32378276 q^{32} + 9053289 q^{33} + 29339436 q^{34} + 7134904 q^{35} + 39195414 q^{36} + 21961411 q^{37} + 65195131 q^{38} + 15318801 q^{39} + 75185084 q^{40} + 52781575 q^{41} + 20335293 q^{42} + 76191313 q^{43} + 61127768 q^{44} + 37961946 q^{45} + 290208769 q^{46} + 160572396 q^{47} + 187196994 q^{48} + 156292703 q^{49} + 169504821 q^{50} + 90221121 q^{51} + 65465920 q^{52} - 8762038 q^{53} + 24446286 q^{54} + 147125140 q^{55} + 9671794 q^{56} + 38561508 q^{57} - 37665424 q^{58} - 266581942 q^{59} - 3442095 q^{60} + 120750754 q^{61} - 152465186 q^{62} + 50132601 q^{63} - 40658803 q^{64} + 331055798 q^{65} - 182413782 q^{66} + 41371828 q^{67} + 145606631 q^{68} + 575348022 q^{69} - 920887614 q^{70} + 261018751 q^{71} + 402812595 q^{72} + 178388 q^{73} - 303908734 q^{74} + 860903802 q^{75} - 94541144 q^{76} + 299640561 q^{77} + 556554888 q^{78} - 905381353 q^{79} + 939128289 q^{80} + 947027862 q^{81} - 551739753 q^{82} + 1173257869 q^{83} + 657124650 q^{84} - 1546633210 q^{85} + 1384869460 q^{86} + 1237624596 q^{87} + 189740713 q^{88} + 898004974 q^{89} + 297456057 q^{90} + 591272339 q^{91} + 4328210270 q^{92} + 1426437378 q^{93} + 122568068 q^{94} + 2487967134 q^{95} + 2622640356 q^{96} + 3175709684 q^{97} + 5095778404 q^{98} + 733316409 q^{99}+O(q^{100}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9 + 45337 * q^10 + 111769 * q^11 + 483894 * q^12 + 189121 * q^13 + 251053 * q^14 + 468666 * q^15 + 2311074 * q^16 + 1113841 * q^17 + 301806 * q^18 + 476068 * q^19 - 42495 * q^20 + 618921 * q^21 - 2252022 * q^22 + 7103062 * q^23 + 4972995 * q^24 + 10628442 * q^25 + 6871048 * q^26 + 11691702 * q^27 + 8112650 * q^28 + 15279316 * q^29 + 3672297 * q^30 + 17610338 * q^31 + 32378276 * q^32 + 9053289 * q^33 + 29339436 * q^34 + 7134904 * q^35 + 39195414 * q^36 + 21961411 * q^37 + 65195131 * q^38 + 15318801 * q^39 + 75185084 * q^40 + 52781575 * q^41 + 20335293 * q^42 + 76191313 * q^43 + 61127768 * q^44 + 37961946 * q^45 + 290208769 * q^46 + 160572396 * q^47 + 187196994 * q^48 + 156292703 * q^49 + 169504821 * q^50 + 90221121 * q^51 + 65465920 * q^52 - 8762038 * q^53 + 24446286 * q^54 + 147125140 * q^55 + 9671794 * q^56 + 38561508 * q^57 - 37665424 * q^58 - 266581942 * q^59 - 3442095 * q^60 + 120750754 * q^61 - 152465186 * q^62 + 50132601 * q^63 - 40658803 * q^64 + 331055798 * q^65 - 182413782 * q^66 + 41371828 * q^67 + 145606631 * q^68 + 575348022 * q^69 - 920887614 * q^70 + 261018751 * q^71 + 402812595 * q^72 + 178388 * q^73 - 303908734 * q^74 + 860903802 * q^75 - 94541144 * q^76 + 299640561 * q^77 + 556554888 * q^78 - 905381353 * q^79 + 939128289 * q^80 + 947027862 * q^81 - 551739753 * q^82 + 1173257869 * q^83 + 657124650 * q^84 - 1546633210 * q^85 + 1384869460 * q^86 + 1237624596 * q^87 + 189740713 * q^88 + 898004974 * q^89 + 297456057 * q^90 + 591272339 * q^91 + 4328210270 * q^92 + 1426437378 * q^93 + 122568068 * q^94 + 2487967134 * q^95 + 2622640356 * q^96 + 3175709684 * q^97 + 5095778404 * q^98 + 733316409 * 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 $

$2$	35.4666	1.56742	0.783710	−	0.621127i	$-0.213325\pi$
$2$	35.4666	1.56742	0.783710	+	0.621127i	$0.213325\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	745.883	1.45680
$5$	1622.90	1.16125	0.580625	−	0.814171i	$-0.302808\pi$
$5$	1622.90	1.16125	0.580625	+	0.814171i	$0.302808\pi$
$6$	2872.80	0.904950
$7$	5254.11	0.827100	0.413550	−	0.910481i	$-0.364289\pi$
$7$	5254.11	0.827100	0.413550	+	0.910481i	$0.364289\pi$
$8$	8295.05	0.716002
$9$	6561.00	0.333333
$10$	57558.7	1.82017
$11$	63201.2	1.30154	0.650772	−	0.759274i	$-0.274446\pi$
$11$	63201.2	1.30154	0.650772	+	0.759274i	$0.274446\pi$
$12$	60416.5	0.841086
$13$	−93199.3	−0.905039	−0.452520	−	0.891754i	$-0.649475\pi$
$13$	−93199.3	−0.905039	−0.452520	+	0.891754i	$0.649475\pi$
$14$	186346.	1.29641
$15$	131455.	0.670448
$16$	−87694.6	−0.334528
$17$	312651.	0.907905	0.453952	−	0.891026i	$-0.350014\pi$
$17$	312651.	0.907905	0.453952	+	0.891026i	$0.350014\pi$
$18$	232697.	0.522473
$19$	295079.	0.519455	0.259727	−	0.965682i	$-0.416367\pi$
$19$	295079.	0.519455	0.259727	+	0.965682i	$0.416367\pi$
$20$	1.21049e6	1.69171
$21$	425583.	0.477526
$22$	2.24154e6	2.04006
$23$	−660434.	−0.492101	−0.246050	−	0.969257i	$-0.579133\pi$
$23$	−660434.	−0.492101	−0.246050	+	0.969257i	$0.579133\pi$
$24$	671899.	0.413384
$25$	680669.	0.348503
$26$	−3.30547e6	−1.41858
$27$	531441.	0.192450
$28$	3.91895e6	1.20492
$29$	−1.79623e6	−0.471596	−0.235798	−	0.971802i	$-0.575770\pi$
$29$	−1.79623e6	−0.471596	−0.235798	+	0.971802i	$0.575770\pi$
$30$	4.66226e6	1.05087
$31$	900850.	0.175196	0.0875981	−	0.996156i	$-0.472081\pi$
$31$	900850.	0.175196	0.0875981	+	0.996156i	$0.472081\pi$
$32$	−7.35730e6	−1.24035
$33$	5.11930e6	0.751446
$34$	1.10887e7	1.42307
$35$	8.52688e6	0.960470
$36$	4.89374e6	0.485601
$37$	4.38437e6	0.384591	0.192296	−	0.981337i	$-0.438407\pi$
$37$	4.38437e6	0.384591	0.192296	+	0.981337i	$0.438407\pi$
$38$	1.04655e7	0.814203
$39$	−7.54914e6	−0.522525
$40$	1.34620e7	0.831457
$41$	1.15498e7	0.638331	0.319165	−	0.947699i	$-0.396597\pi$
$41$	1.15498e7	0.638331	0.319165	+	0.947699i	$0.396597\pi$
$42$	1.50940e7	0.748484
$43$	−6.76278e6	−0.301660	−0.150830	−	0.988560i	$-0.548195\pi$
$43$	−6.76278e6	−0.301660	−0.150830	+	0.988560i	$0.548195\pi$
$44$	4.71407e7	1.89609
$45$	1.06478e7	0.387083
$46$	−2.34234e7	−0.771328
$47$	−3.09203e7	−0.924279	−0.462140	−	0.886807i	$-0.652918\pi$
$47$	−3.09203e7	−0.924279	−0.462140	+	0.886807i	$0.652918\pi$
$48$	−7.10326e6	−0.193140
$49$	−1.27480e7	−0.315906
$50$	2.41411e7	0.546250
$51$	2.53248e7	0.524179
$52$	−6.95158e7	−1.31846
$53$	1.17476e7	0.204506	0.102253	−	0.994758i	$-0.467395\pi$
$53$	1.17476e7	0.204506	0.102253	+	0.994758i	$0.467395\pi$
$54$	1.88484e7	0.301650
$55$	1.02569e8	1.51142
$56$	4.35831e7	0.592205
$57$	2.39014e7	0.299907
$58$	−6.37062e7	−0.739189
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	9.80498e7	0.976711
$61$	−3.57264e7	−0.330374	−0.165187	−	0.986262i	$-0.552823\pi$
$61$	−3.57264e7	−0.330374	−0.165187	+	0.986262i	$0.552823\pi$
$62$	3.19501e7	0.274606
$63$	3.44722e7	0.275700
$64$	−2.16039e8	−1.60962
$65$	−1.51253e8	−1.05098
$66$	1.81564e8	1.17783
$67$	2.25795e8	1.36892	0.684460	−	0.729051i	$-0.260038\pi$
$67$	2.25795e8	1.36892	0.684460	+	0.729051i	$0.260038\pi$
$68$	2.33201e8	1.32264
$69$	−5.34952e7	−0.284115
$70$	3.02420e8	1.50546
$71$	−1.64241e8	−0.767040	−0.383520	−	0.923533i	$-0.625288\pi$
$71$	−1.64241e8	−0.767040	−0.383520	+	0.923533i	$0.625288\pi$
$72$	5.44238e7	0.238667
$73$	−2.45097e8	−1.01015	−0.505074	−	0.863076i	$-0.668535\pi$
$73$	−2.45097e8	−1.01015	−0.505074	+	0.863076i	$0.668535\pi$
$74$	1.55499e8	0.602815
$75$	5.51342e7	0.201208
$76$	2.20095e8	0.756743
$77$	3.32066e8	1.07651
$78$	−2.67743e8	−0.819015
$79$	2.30240e8	0.665056	0.332528	−	0.943093i	$-0.392098\pi$
$79$	2.30240e8	0.665056	0.332528	+	0.943093i	$0.392098\pi$
$80$	−1.42319e8	−0.388471
$81$	4.30467e7	0.111111
$82$	4.09632e8	1.00053
$83$	3.71689e8	0.859663	0.429831	−	0.902909i	$-0.358573\pi$
$83$	3.71689e8	0.859663	0.429831	+	0.902909i	$0.358573\pi$
$84$	3.17435e8	0.695662
$85$	5.07401e8	1.05430
$86$	−2.39853e8	−0.472827
$87$	−1.45494e8	−0.272276
$88$	5.24257e8	0.931907
$89$	2.06997e8	0.349711	0.174856	−	0.984594i	$-0.444054\pi$
$89$	2.06997e8	0.349711	0.174856	+	0.984594i	$0.444054\pi$
$90$	3.77643e8	0.606722
$91$	−4.89679e8	−0.748558
$92$	−4.92607e8	−0.716894
$93$	7.29688e7	0.101150
$94$	−1.09664e9	−1.44873
$95$	4.78883e8	0.603217
$96$	−5.95941e8	−0.716115
$97$	8.17254e8	0.937312	0.468656	−	0.883381i	$-0.344738\pi$
$97$	8.17254e8	0.937312	0.468656	+	0.883381i	$0.344738\pi$
$98$	−4.52127e8	−0.495157
$99$	4.14663e8	0.433848
$100$	5.07700e8	0.507700
$101$	−1.12280e8	−0.107363	−0.0536816	−	0.998558i	$-0.517096\pi$
$101$	−1.12280e8	−0.107363	−0.0536816	+	0.998558i	$0.517096\pi$
$102$	8.98185e8	0.821608
$103$	−1.53844e9	−1.34683	−0.673417	−	0.739263i	$-0.735174\pi$
$103$	−1.53844e9	−1.34683	−0.673417	+	0.739263i	$0.735174\pi$
$104$	−7.73092e8	−0.648010
$105$	6.90677e8	0.554528
$106$	4.16647e8	0.320547
$107$	6.12766e8	0.451927	0.225963	−	0.974136i	$-0.427447\pi$
$107$	6.12766e8	0.451927	0.225963	+	0.974136i	$0.427447\pi$
$108$	3.96393e8	0.280362
$109$	2.44993e9	1.66240	0.831199	−	0.555975i	$-0.187655\pi$
$109$	2.44993e9	1.66240	0.831199	+	0.555975i	$0.187655\pi$
$110$	3.63778e9	2.36902
$111$	3.55134e8	0.222044
$112$	−4.60757e8	−0.276688
$113$	−5.34351e8	−0.308300	−0.154150	−	0.988047i	$-0.549264\pi$
$113$	−5.34351e8	−0.308300	−0.154150	+	0.988047i	$0.549264\pi$
$114$	8.47703e8	0.470080
$115$	−1.07182e9	−0.571452
$116$	−1.33978e9	−0.687023
$117$	−6.11480e8	−0.301680
$118$	−4.29762e8	−0.204061
$119$	1.64270e9	0.750928
$120$	1.09042e9	0.480042
$121$	1.63645e9	0.694014
$122$	−1.26710e9	−0.517834
$123$	9.35531e8	0.368541
$124$	6.71928e8	0.255226
$125$	−2.06506e9	−0.756552
$126$	1.22261e9	0.432137
$127$	−2.91038e9	−0.992734	−0.496367	−	0.868113i	$-0.665333\pi$
$127$	−2.91038e9	−0.992734	−0.496367	+	0.868113i	$0.665333\pi$
$128$	−3.89524e9	−1.28260
$129$	−5.47785e8	−0.174163
$130$	−5.36443e9	−1.64732
$131$	2.39475e8	0.0710460	0.0355230	−	0.999369i	$-0.488690\pi$
$131$	2.39475e8	0.0710460	0.0355230	+	0.999369i	$0.488690\pi$
$132$	3.81840e9	1.09471
$133$	1.55038e9	0.429641
$134$	8.00819e9	2.14567
$135$	8.62474e8	0.223483
$136$	2.59346e9	0.650061
$137$	−3.30216e9	−0.800857	−0.400429	−	0.916328i	$-0.631139\pi$
$137$	−3.30216e9	−0.800857	−0.400429	+	0.916328i	$0.631139\pi$
$138$	−1.89729e9	−0.445327
$139$	−3.90848e9	−0.888057	−0.444029	−	0.896013i	$-0.646451\pi$
$139$	−3.90848e9	−0.888057	−0.444029	+	0.896013i	$0.646451\pi$
$140$	6.36005e9	1.39922
$141$	−2.50454e9	−0.533633
$142$	−5.82506e9	−1.20227
$143$	−5.89031e9	−1.17795
$144$	−5.75364e8	−0.111509
$145$	−2.91509e9	−0.547642
$146$	−8.69277e9	−1.58333
$147$	−1.03258e9	−0.182388
$148$	3.27023e9	0.560273
$149$	−8.32395e8	−0.138354	−0.0691770	−	0.997604i	$-0.522037\pi$
$149$	−8.32395e8	−0.138354	−0.0691770	+	0.997604i	$0.522037\pi$
$150$	1.95543e9	0.315377
$151$	2.24607e9	0.351582	0.175791	−	0.984427i	$-0.443752\pi$
$151$	2.24607e9	0.351582	0.175791	+	0.984427i	$0.443752\pi$
$152$	2.44770e9	0.371930
$153$	2.05131e9	0.302635
$154$	1.17773e10	1.68734
$155$	1.46199e9	0.203447
$156$	−5.63078e9	−0.761216
$157$	−5.86686e7	−0.00770650	−0.00385325	−	0.999993i	$-0.501227\pi$
$157$	−5.86686e7	−0.00770650	−0.00385325	+	0.999993i	$0.501227\pi$
$158$	8.16583e9	1.04242
$159$	9.51553e8	0.118072
$160$	−1.19401e10	−1.44035
$161$	−3.46999e9	−0.407017
$162$	1.52672e9	0.174158
$163$	1.23008e10	1.36486	0.682432	−	0.730949i	$-0.260922\pi$
$163$	1.23008e10	1.36486	0.682432	+	0.730949i	$0.260922\pi$
$164$	8.61478e9	0.929922
$165$	8.30810e9	0.872617
$166$	1.31826e10	1.34745
$167$	−1.62627e10	−1.61796	−0.808980	−	0.587836i	$-0.799980\pi$
$167$	−1.62627e10	−1.61796	−0.808980	+	0.587836i	$0.799980\pi$
$168$	3.53023e9	0.341910
$169$	−1.91839e9	−0.180904
$170$	1.79958e10	1.65254
$171$	1.93602e9	0.173152
$172$	−5.04424e9	−0.439459
$173$	6.36406e9	0.540166	0.270083	−	0.962837i	$-0.412949\pi$
$173$	6.36406e9	0.540166	0.270083	+	0.962837i	$0.412949\pi$
$174$	−5.16020e9	−0.426771
$175$	3.57631e9	0.288246
$176$	−5.54241e9	−0.435403
$177$	−9.81506e8	−0.0751646
$178$	7.34150e9	0.548144
$179$	−2.20122e10	−1.60260	−0.801299	−	0.598264i	$-0.795857\pi$
$179$	−2.20122e10	−1.60260	−0.801299	+	0.598264i	$0.795857\pi$
$180$	7.94203e9	0.563904
$181$	2.40644e10	1.66656	0.833280	−	0.552851i	$-0.186460\pi$
$181$	2.40644e10	1.66656	0.833280	+	0.552851i	$0.186460\pi$
$182$	−1.73673e10	−1.17330
$183$	−2.89384e9	−0.190741
$184$	−5.47833e9	−0.352345
$185$	7.11538e9	0.446607
$186$	2.58796e9	0.158544
$187$	1.97600e10	1.18168
$188$	−2.30629e10	−1.34649
$189$	2.79225e9	0.159175
$190$	1.69844e10	0.945494
$191$	−7.26972e9	−0.395246	−0.197623	−	0.980278i	$-0.563322\pi$
$191$	−7.26972e9	−0.395246	−0.197623	+	0.980278i	$0.563322\pi$
$192$	−1.74992e10	−0.929312
$193$	−1.10884e9	−0.0575254	−0.0287627	−	0.999586i	$-0.509157\pi$
$193$	−1.10884e9	−0.0575254	−0.0287627	+	0.999586i	$0.509157\pi$
$194$	2.89853e10	1.46916
$195$	−1.22515e10	−0.606782
$196$	−9.50848e9	−0.460213
$197$	4.82622e9	0.228302	0.114151	−	0.993463i	$-0.463585\pi$
$197$	4.82622e9	0.228302	0.114151	+	0.993463i	$0.463585\pi$
$198$	1.47067e10	0.680021
$199$	3.18609e10	1.44019	0.720094	−	0.693877i	$-0.244099\pi$
$199$	3.18609e10	1.44019	0.720094	+	0.693877i	$0.244099\pi$
$200$	5.64618e9	0.249528
$201$	1.82894e10	0.790346
$202$	−3.98219e9	−0.168283
$203$	−9.43758e9	−0.390057
$204$	1.88893e10	0.763626
$205$	1.87441e10	0.741262
$206$	−5.45634e10	−2.11105
$207$	−4.33311e9	−0.164034
$208$	8.17307e9	0.302761
$209$	1.86494e10	0.676092
$210$	2.44960e10	0.869177
$211$	−4.20930e10	−1.46197	−0.730986	−	0.682393i	$-0.760939\pi$
$211$	−4.20930e10	−1.46197	−0.730986	+	0.682393i	$0.760939\pi$
$212$	8.76232e9	0.297925
$213$	−1.33035e10	−0.442851
$214$	2.17328e10	0.708358
$215$	−1.09753e10	−0.350302
$216$	4.40833e9	0.137795
$217$	4.73316e9	0.144905
$218$	8.68909e10	2.60567
$219$	−1.98528e10	−0.583209
$220$	7.65046e10	2.20184
$221$	−2.91389e10	−0.821690
$222$	1.25954e10	0.348036
$223$	−5.31108e9	−0.143817	−0.0719087	−	0.997411i	$-0.522909\pi$
$223$	−5.31108e9	−0.143817	−0.0719087	+	0.997411i	$0.522909\pi$
$224$	−3.86560e10	−1.02589
$225$	4.46587e9	0.116168
$226$	−1.89516e10	−0.483236
$227$	−1.59250e10	−0.398073	−0.199037	−	0.979992i	$-0.563781\pi$
$227$	−1.59250e10	−0.398073	−0.199037	+	0.979992i	$0.563781\pi$
$228$	1.78277e10	0.436906
$229$	1.69346e10	0.406926	0.203463	−	0.979083i	$-0.434780\pi$
$229$	1.69346e10	0.406926	0.203463	+	0.979083i	$0.434780\pi$
$230$	−3.80137e10	−0.895706
$231$	2.68974e10	0.621521
$232$	−1.48998e10	−0.337664
$233$	1.13183e9	0.0251582	0.0125791	−	0.999921i	$-0.495996\pi$
$233$	1.13183e9	0.0251582	0.0125791	+	0.999921i	$0.495996\pi$
$234$	−2.16872e10	−0.472859
$235$	−5.01805e10	−1.07332
$236$	−9.03813e9	−0.189660
$237$	1.86494e10	0.383970
$238$	5.82612e10	1.17702
$239$	−3.09052e10	−0.612691	−0.306346	−	0.951920i	$-0.599106\pi$
$239$	−3.09052e10	−0.612691	−0.306346	+	0.951920i	$0.599106\pi$
$240$	−1.15279e10	−0.224284
$241$	−2.09082e10	−0.399245	−0.199623	−	0.979873i	$-0.563972\pi$
$241$	−2.09082e10	−0.399245	−0.199623	+	0.979873i	$0.563972\pi$
$242$	5.80394e10	1.08781
$243$	3.48678e9	0.0641500
$244$	−2.66477e10	−0.481289
$245$	−2.06886e10	−0.366846
$246$	3.31802e10	0.577657
$247$	−2.75012e10	−0.470127
$248$	7.47259e9	0.125441
$249$	3.01068e10	0.496327
$250$	−7.32409e10	−1.18583
$251$	−1.16586e11	−1.85402	−0.927008	−	0.375042i	$-0.877628\pi$
$251$	−1.16586e11	−1.85402	−0.927008	+	0.375042i	$0.877628\pi$
$252$	2.57122e10	0.401640
$253$	−4.17403e10	−0.640491
$254$	−1.03221e11	−1.55603
$255$	4.10995e10	0.608703
$256$	−2.75393e10	−0.400749
$257$	−1.22111e11	−1.74605	−0.873024	−	0.487677i	$-0.837844\pi$
$257$	−1.22111e11	−1.74605	−0.873024	+	0.487677i	$0.837844\pi$
$258$	−1.94281e10	−0.272987
$259$	2.30359e10	0.318095
$260$	−1.12817e11	−1.53107
$261$	−1.17851e10	−0.157199
$262$	8.49339e9	0.111359
$263$	1.12528e10	0.145031	0.0725154	−	0.997367i	$-0.476897\pi$
$263$	1.12528e10	0.145031	0.0725154	+	0.997367i	$0.476897\pi$
$264$	4.24648e10	0.538037
$265$	1.90651e10	0.237483
$266$	5.49867e10	0.673427
$267$	1.67668e10	0.201906
$268$	1.68417e11	1.99425
$269$	8.53058e10	0.993330	0.496665	−	0.867942i	$-0.334558\pi$
$269$	8.53058e10	0.993330	0.496665	+	0.867942i	$0.334558\pi$
$270$	3.05891e10	0.350291
$271$	1.03784e10	0.116887	0.0584436	−	0.998291i	$-0.481386\pi$
$271$	1.03784e10	0.116887	0.0584436	+	0.998291i	$0.481386\pi$
$272$	−2.74178e10	−0.303720
$273$	−3.96640e10	−0.432180
$274$	−1.17116e11	−1.25528
$275$	4.30191e10	0.453591
$276$	−3.99011e10	−0.413899
$277$	−6.80045e9	−0.0694030	−0.0347015	−	0.999398i	$-0.511048\pi$
$277$	−6.80045e9	−0.0694030	−0.0347015	+	0.999398i	$0.511048\pi$
$278$	−1.38621e11	−1.39196
$279$	5.91047e9	0.0583987
$280$	7.07308e10	0.687698
$281$	−1.22009e11	−1.16738	−0.583690	−	0.811977i	$-0.698392\pi$
$281$	−1.22009e11	−1.16738	−0.583690	+	0.811977i	$0.698392\pi$
$282$	−8.88278e10	−0.836427
$283$	−6.75009e9	−0.0625562	−0.0312781	−	0.999511i	$-0.509958\pi$
$283$	−6.75009e9	−0.0625562	−0.0312781	+	0.999511i	$0.509958\pi$
$284$	−1.22504e11	−1.11743
$285$	3.87895e10	0.348267
$286$	−2.08910e11	−1.84634
$287$	6.06837e10	0.527963
$288$	−4.82712e10	−0.413449
$289$	−2.08369e10	−0.175709
$290$	−1.03389e11	−0.858384
$291$	6.61976e10	0.541157
$292$	−1.82814e11	−1.47159
$293$	−1.83585e9	−0.0145523	−0.00727616	−	0.999974i	$-0.502316\pi$
$293$	−1.83585e9	−0.0145523	−0.00727616	+	0.999974i	$0.502316\pi$
$294$	−3.66223e10	−0.285879
$295$	−1.96652e10	−0.151182
$296$	3.63685e10	0.275368
$297$	3.35877e10	0.250482
$298$	−2.95223e10	−0.216859
$299$	6.15520e10	0.445371
$300$	4.11237e10	0.293121
$301$	−3.55324e10	−0.249503
$302$	7.96605e10	0.551077
$303$	−9.09466e9	−0.0619862
$304$	−2.58769e10	−0.173772
$305$	−5.79803e10	−0.383647
$306$	7.27530e10	0.474356
$307$	−2.58774e11	−1.66264	−0.831319	−	0.555796i	$-0.812414\pi$
$307$	−2.58774e11	−1.66264	−0.831319	+	0.555796i	$0.812414\pi$
$308$	2.47683e11	1.56826
$309$	−1.24614e11	−0.777595
$310$	5.18517e10	0.318886
$311$	−1.59772e11	−0.968453	−0.484227	−	0.874943i	$-0.660899\pi$
$311$	−1.59772e11	−0.968453	−0.484227	+	0.874943i	$0.660899\pi$
$312$	−6.26205e10	−0.374129
$313$	−2.57777e11	−1.51808	−0.759039	−	0.651046i	$-0.774331\pi$
$313$	−2.57777e11	−1.51808	−0.759039	+	0.651046i	$0.774331\pi$
$314$	−2.08078e9	−0.0120793
$315$	5.59448e10	0.320157
$316$	1.71732e11	0.968856
$317$	6.14218e9	0.0341630	0.0170815	−	0.999854i	$-0.494563\pi$
$317$	6.14218e9	0.0341630	0.0170815	+	0.999854i	$0.494563\pi$
$318$	3.37484e10	0.185068
$319$	−1.13524e11	−0.613803
$320$	−3.50609e11	−1.86917
$321$	4.96341e10	0.260920
$322$	−1.23069e11	−0.637966
$323$	9.22570e10	0.471615
$324$	3.21078e10	0.161867
$325$	−6.34379e10	−0.315409
$326$	4.36268e11	2.13931
$327$	1.98445e11	0.959786
$328$	9.58059e10	0.457046
$329$	−1.62459e11	−0.764471
$330$	2.94660e11	1.36776
$331$	−1.87466e11	−0.858415	−0.429207	−	0.903206i	$-0.641207\pi$
$331$	−1.87466e11	−0.858415	−0.429207	+	0.903206i	$0.641207\pi$
$332$	2.77236e11	1.25236
$333$	2.87658e10	0.128197
$334$	−5.76783e11	−2.53602
$335$	3.66442e11	1.58966
$336$	−3.73213e10	−0.159746
$337$	−1.68990e11	−0.713717	−0.356858	−	0.934159i	$-0.616152\pi$
$337$	−1.68990e11	−0.713717	−0.356858	+	0.934159i	$0.616152\pi$
$338$	−6.80390e10	−0.283552
$339$	−4.32824e10	−0.177997
$340$	3.78462e11	1.53591
$341$	5.69348e10	0.228025
$342$	6.86640e10	0.271401
$343$	−2.79001e11	−1.08839
$344$	−5.60976e10	−0.215989
$345$	−8.68171e10	−0.329928
$346$	2.25712e11	0.846666
$347$	1.40470e11	0.520116	0.260058	−	0.965593i	$-0.416258\pi$
$347$	1.40470e11	0.520116	0.260058	+	0.965593i	$0.416258\pi$
$348$	−1.08522e11	−0.396653
$349$	−1.59703e11	−0.576232	−0.288116	−	0.957596i	$-0.593029\pi$
$349$	−1.59703e11	−0.576232	−0.288116	+	0.957596i	$0.593029\pi$
$350$	1.26840e11	0.451803
$351$	−4.95299e10	−0.174175
$352$	−4.64990e11	−1.61437
$353$	1.13039e11	0.387474	0.193737	−	0.981054i	$-0.437939\pi$
$353$	1.13039e11	0.387474	0.193737	+	0.981054i	$0.437939\pi$
$354$	−3.48107e10	−0.117814
$355$	−2.66545e11	−0.890725
$356$	1.54396e11	0.509461
$357$	1.33059e11	0.433548
$358$	−7.80698e11	−2.51194
$359$	2.28065e11	0.724658	0.362329	−	0.932050i	$-0.381982\pi$
$359$	2.28065e11	0.724658	0.362329	+	0.932050i	$0.381982\pi$
$360$	8.83242e10	0.277152
$361$	−2.35616e11	−0.730167
$362$	8.53483e11	2.61220
$363$	1.32552e11	0.400689
$364$	−3.65243e11	−1.09050
$365$	−3.97767e11	−1.17303
$366$	−1.02635e11	−0.298972
$367$	6.25844e11	1.80081	0.900407	−	0.435048i	$-0.143269\pi$
$367$	6.25844e11	1.80081	0.900407	+	0.435048i	$0.143269\pi$
$368$	5.79165e10	0.164622
$369$	7.57780e10	0.212777
$370$	2.52359e11	0.700020
$371$	6.17230e10	0.169147
$372$	5.44262e10	0.147355
$373$	6.76899e10	0.181065	0.0905324	−	0.995894i	$-0.471143\pi$
$373$	6.76899e10	0.181065	0.0905324	+	0.995894i	$0.471143\pi$
$374$	7.00820e11	1.85218
$375$	−1.67270e11	−0.436795
$376$	−2.56485e11	−0.661786
$377$	1.67407e11	0.426813
$378$	9.90317e10	0.249495
$379$	2.61371e11	0.650700	0.325350	−	0.945594i	$-0.394518\pi$
$379$	2.61371e11	0.650700	0.325350	+	0.945594i	$0.394518\pi$
$380$	3.57191e11	0.878768
$381$	−2.35741e11	−0.573155
$382$	−2.57833e11	−0.619517
$383$	−1.12750e11	−0.267745	−0.133873	−	0.990999i	$-0.542741\pi$
$383$	−1.12750e11	−0.267745	−0.133873	+	0.990999i	$0.542741\pi$
$384$	−3.15515e11	−0.740507
$385$	5.38909e11	1.25009
$386$	−3.93267e10	−0.0901664
$387$	−4.43706e10	−0.100553
$388$	6.09576e11	1.36548
$389$	5.33391e11	1.18106	0.590531	−	0.807015i	$-0.298918\pi$
$389$	5.33391e11	1.18106	0.590531	+	0.807015i	$0.298918\pi$
$390$	−4.34519e11	−0.951082
$391$	−2.06486e11	−0.446781
$392$	−1.05745e11	−0.226189
$393$	1.93975e10	0.0410184
$394$	1.71170e11	0.357844
$395$	3.73655e11	0.772297
$396$	3.09290e11	0.632031
$397$	8.56941e11	1.73139	0.865693	−	0.500576i	$-0.166878\pi$
$397$	8.56941e11	1.73139	0.865693	+	0.500576i	$0.166878\pi$
$398$	1.13000e12	2.25738
$399$	1.25581e11	0.248053
$400$	−5.96910e10	−0.116584
$401$	1.29537e11	0.250176	0.125088	−	0.992146i	$-0.460079\pi$
$401$	1.29537e11	0.250176	0.125088	+	0.992146i	$0.460079\pi$
$402$	6.48664e11	1.23880
$403$	−8.39585e10	−0.158559
$404$	−8.37476e10	−0.156407
$405$	6.98604e10	0.129028
$406$	−3.34719e11	−0.611383
$407$	2.77097e11	0.500562
$408$	2.10070e11	0.375313
$409$	−2.39667e11	−0.423501	−0.211750	−	0.977324i	$-0.567916\pi$
$409$	−2.39667e11	−0.423501	−0.211750	+	0.977324i	$0.567916\pi$
$410$	6.64790e11	1.16187
$411$	−2.67475e11	−0.462375
$412$	−1.14750e12	−1.96207
$413$	−6.36659e10	−0.107679
$414$	−1.53681e11	−0.257109
$415$	6.03213e11	0.998284
$416$	6.85695e11	1.12256
$417$	−3.16587e11	−0.512720
$418$	6.61431e11	1.05972
$419$	7.69914e11	1.22033	0.610167	−	0.792272i	$-0.291102\pi$
$419$	7.69914e11	1.22033	0.610167	+	0.792272i	$0.291102\pi$
$420$	5.15164e11	0.807837
$421$	1.58818e11	0.246394	0.123197	−	0.992382i	$-0.460685\pi$
$421$	1.58818e11	0.246394	0.123197	+	0.992382i	$0.460685\pi$
$422$	−1.49290e12	−2.29152
$423$	−2.02868e11	−0.308093
$424$	9.74467e10	0.146427
$425$	2.12812e11	0.316407
$426$	−4.71830e11	−0.694132
$427$	−1.87711e11	−0.273252
$428$	4.57052e11	0.658368
$429$	−4.77115e11	−0.680088
$430$	−3.89257e11	−0.549071
$431$	6.16553e11	0.860642	0.430321	−	0.902676i	$-0.358400\pi$
$431$	6.16553e11	0.860642	0.430321	+	0.902676i	$0.358400\pi$
$432$	−4.66045e10	−0.0643800
$433$	1.91051e11	0.261189	0.130594	−	0.991436i	$-0.458311\pi$
$433$	1.91051e11	0.261189	0.130594	+	0.991436i	$0.458311\pi$
$434$	1.67869e11	0.227126
$435$	−2.36123e11	−0.316181
$436$	1.82736e12	2.42179
$437$	−1.94880e11	−0.255624
$438$	−7.04114e11	−0.914133
$439$	3.59506e11	0.461973	0.230986	−	0.972957i	$-0.425805\pi$
$439$	3.59506e11	0.461973	0.230986	+	0.972957i	$0.425805\pi$
$440$	8.50816e11	1.08218
$441$	−8.36393e10	−0.105302
$442$	−1.03346e12	−1.28793
$443$	2.77924e11	0.342854	0.171427	−	0.985197i	$-0.445162\pi$
$443$	2.77924e11	0.342854	0.171427	+	0.985197i	$0.445162\pi$
$444$	2.64888e11	0.323474
$445$	3.35935e11	0.406103
$446$	−1.88366e11	−0.225422
$447$	−6.74240e10	−0.0798787
$448$	−1.13509e12	−1.33131
$449$	−5.78433e11	−0.671653	−0.335826	−	0.941924i	$-0.609016\pi$
$449$	−5.78433e11	−0.671653	−0.335826	+	0.941924i	$0.609016\pi$
$450$	1.58389e11	0.182083
$451$	7.29960e11	0.830815
$452$	−3.98564e11	−0.449133
$453$	1.81932e11	0.202986
$454$	−5.64806e11	−0.623947
$455$	−7.94699e11	−0.869263
$456$	1.98263e11	0.214734
$457$	1.39805e12	1.49933	0.749667	−	0.661815i	$-0.230214\pi$
$457$	1.39805e12	1.49933	0.749667	+	0.661815i	$0.230214\pi$
$458$	6.00613e11	0.637823
$459$	1.66156e11	0.174726
$460$	−7.99450e11	−0.832494
$461$	−1.30225e12	−1.34289	−0.671445	−	0.741054i	$-0.734326\pi$
$461$	−1.30225e12	−1.34289	−0.671445	+	0.741054i	$0.734326\pi$
$462$	9.53959e11	0.974184
$463$	1.77308e12	1.79313	0.896567	−	0.442908i	$-0.146053\pi$
$463$	1.77308e12	1.79313	0.896567	+	0.442908i	$0.146053\pi$
$464$	1.57519e11	0.157762
$465$	1.18421e11	0.117460
$466$	4.01422e10	0.0394334
$467$	−5.78947e11	−0.563265	−0.281632	−	0.959522i	$-0.590876\pi$
$467$	−5.78947e11	−0.563265	−0.281632	+	0.959522i	$0.590876\pi$
$468$	−4.56093e11	−0.439488
$469$	1.18635e12	1.13223
$470$	−1.77973e12	−1.68234
$471$	−4.75216e9	−0.00444935
$472$	−1.00514e11	−0.0932155
$473$	−4.27416e11	−0.392623
$474$	6.61432e11	0.601842
$475$	2.00851e11	0.181031
$476$	1.22527e12	1.09395
$477$	7.70758e10	0.0681688
$478$	−1.09611e12	−0.960344
$479$	2.87330e10	0.0249385	0.0124693	−	0.999922i	$-0.496031\pi$
$479$	2.87330e10	0.0249385	0.0124693	+	0.999922i	$0.496031\pi$
$480$	−9.67151e11	−0.831589
$481$	−4.08620e11	−0.348070
$482$	−7.41543e11	−0.625785
$483$	−2.81069e11	−0.234991
$484$	1.22060e12	1.01104
$485$	1.32632e12	1.08845
$486$	1.23665e11	0.100550
$487$	−4.24889e11	−0.342291	−0.171145	−	0.985246i	$-0.554747\pi$
$487$	−4.24889e11	−0.342291	−0.171145	+	0.985246i	$0.554747\pi$
$488$	−2.96352e11	−0.236548
$489$	9.96366e11	0.788005
$490$	−7.33756e11	−0.575002
$491$	2.40381e12	1.86652	0.933261	−	0.359199i	$-0.116950\pi$
$491$	2.40381e12	1.86652	0.933261	+	0.359199i	$0.116950\pi$
$492$	6.97797e11	0.536891
$493$	−5.61593e11	−0.428165
$494$	−9.75375e11	−0.736886
$495$	6.72956e11	0.503806
$496$	−7.89996e10	−0.0586081
$497$	−8.62938e11	−0.634418
$498$	1.06779e12	0.777952
$499$	−2.16393e12	−1.56240	−0.781199	−	0.624283i	$-0.785391\pi$
$499$	−2.16393e12	−1.56240	−0.781199	+	0.624283i	$0.785391\pi$
$500$	−1.54030e12	−1.10215
$501$	−1.31728e12	−0.934130
$502$	−4.13490e12	−2.90602
$503$	−4.78087e10	−0.0333005	−0.0166503	−	0.999861i	$-0.505300\pi$
$503$	−4.78087e10	−0.0333005	−0.0166503	+	0.999861i	$0.505300\pi$
$504$	2.85949e11	0.197402
$505$	−1.82219e11	−0.124676
$506$	−1.48039e12	−1.00392
$507$	−1.55390e11	−0.104445
$508$	−2.17080e12	−1.44622
$509$	6.59076e11	0.435216	0.217608	−	0.976036i	$-0.430175\pi$
$509$	6.59076e11	0.435216	0.217608	+	0.976036i	$0.430175\pi$
$510$	1.45766e12	0.954093
$511$	−1.28777e12	−0.835493
$512$	1.01764e12	0.654454
$513$	1.56817e11	0.0999691
$514$	−4.33087e12	−2.73679
$515$	−2.49673e12	−1.56401
$516$	−4.08584e11	−0.253722
$517$	−1.95420e12	−1.20299
$518$	8.17008e11	0.498588
$519$	5.15489e11	0.311865
$520$	−1.25465e12	−0.752501
$521$	−9.54421e11	−0.567505	−0.283753	−	0.958897i	$-0.591579\pi$
$521$	−9.54421e11	−0.567505	−0.283753	+	0.958897i	$0.591579\pi$
$522$	−4.17976e11	−0.246396
$523$	−3.29305e12	−1.92460	−0.962300	−	0.271992i	$-0.912318\pi$
$523$	−3.29305e12	−1.92460	−0.962300	+	0.271992i	$0.912318\pi$
$524$	1.78621e11	0.103500
$525$	2.89681e11	0.166419
$526$	3.99100e11	0.227324
$527$	2.81652e11	0.159061
$528$	−4.48935e11	−0.251380
$529$	−1.36498e12	−0.757837
$530$	6.76175e11	0.372236
$531$	−7.95020e10	−0.0433963
$532$	1.15640e12	0.625902
$533$	−1.07643e12	−0.577715
$534$	5.94662e11	0.316471
$535$	9.94457e11	0.524800
$536$	1.87298e12	0.980148
$537$	−1.78299e12	−0.925260
$538$	3.02551e12	1.55696
$539$	−8.05686e11	−0.411165
$540$	6.43305e11	0.325570
$541$	8.28435e11	0.415787	0.207893	−	0.978151i	$-0.433339\pi$
$541$	8.28435e11	0.415787	0.207893	+	0.978151i	$0.433339\pi$
$542$	3.68086e11	0.183211
$543$	1.94921e12	0.962189
$544$	−2.30027e12	−1.12612
$545$	3.97599e12	1.93046
$546$	−1.40675e12	−0.677407
$547$	2.61365e12	1.24826	0.624130	−	0.781320i	$-0.285453\pi$
$547$	2.61365e12	1.24826	0.624130	+	0.781320i	$0.285453\pi$
$548$	−2.46302e12	−1.16669
$549$	−2.34401e11	−0.110125
$550$	1.52574e12	0.710967
$551$	−5.30030e11	−0.244973
$552$	−4.43745e11	−0.203427
$553$	1.20970e12	0.550068
$554$	−2.41189e11	−0.108784
$555$	5.76345e11	0.257848
$556$	−2.91527e12	−1.29372
$557$	3.51699e12	1.54819	0.774093	−	0.633072i	$-0.218206\pi$
$557$	3.51699e12	1.54819	0.774093	+	0.633072i	$0.218206\pi$
$558$	2.09625e11	0.0915353
$559$	6.30286e11	0.273014
$560$	−7.47761e11	−0.321304
$561$	1.60056e12	0.682242
$562$	−4.32724e12	−1.82977
$563$	2.45632e12	1.03038	0.515190	−	0.857076i	$-0.327721\pi$
$563$	2.45632e12	1.03038	0.515190	+	0.857076i	$0.327721\pi$
$564$	−1.86810e12	−0.777398
$565$	−8.67197e11	−0.358014
$566$	−2.39403e11	−0.0980518
$567$	2.26172e11	0.0919000
$568$	−1.36238e12	−0.549202
$569$	1.66431e12	0.665624	0.332812	−	0.942993i	$-0.392003\pi$
$569$	1.66431e12	0.665624	0.332812	+	0.942993i	$0.392003\pi$
$570$	1.37574e12	0.545881
$571$	−2.28653e12	−0.900150	−0.450075	−	0.892991i	$-0.648603\pi$
$571$	−2.28653e12	−0.900150	−0.450075	+	0.892991i	$0.648603\pi$
$572$	−4.39348e12	−1.71604
$573$	−5.88848e11	−0.228196
$574$	2.15225e12	0.827540
$575$	−4.49537e11	−0.171498
$576$	−1.41743e12	−0.536539
$577$	4.56676e12	1.71521	0.857604	−	0.514310i	$-0.171952\pi$
$577$	4.56676e12	1.71521	0.857604	+	0.514310i	$0.171952\pi$
$578$	−7.39016e11	−0.275409
$579$	−8.98157e10	−0.0332123
$580$	−2.17432e12	−0.797806
$581$	1.95289e12	0.711027
$582$	2.34781e12	0.848221
$583$	7.42461e11	0.266174
$584$	−2.03309e12	−0.723267
$585$	−9.92370e11	−0.350326
$586$	−6.51113e10	−0.0228096
$587$	4.67076e12	1.62374	0.811870	−	0.583838i	$-0.198450\pi$
$587$	4.67076e12	1.62374	0.811870	+	0.583838i	$0.198450\pi$
$588$	−7.70187e11	−0.265704
$589$	2.65822e11	0.0910065
$590$	−6.97460e11	−0.236965
$591$	3.90924e11	0.131810
$592$	−3.84485e11	−0.128657
$593$	1.37887e12	0.457907	0.228954	−	0.973437i	$-0.426470\pi$
$593$	1.37887e12	0.457907	0.228954	+	0.973437i	$0.426470\pi$
$594$	1.19124e12	0.392610
$595$	2.66594e12	0.872015
$596$	−6.20870e11	−0.201554
$597$	2.58073e12	0.831493
$598$	2.18304e12	0.698083
$599$	3.94924e12	1.25341	0.626705	−	0.779257i	$-0.284403\pi$
$599$	3.94924e12	1.25341	0.626705	+	0.779257i	$0.284403\pi$
$600$	4.57341e11	0.144065
$601$	3.41758e12	1.06852	0.534261	−	0.845319i	$-0.320590\pi$
$601$	3.41758e12	1.06852	0.534261	+	0.845319i	$0.320590\pi$
$602$	−1.26021e12	−0.391075
$603$	1.48144e12	0.456306
$604$	1.67530e12	0.512186
$605$	2.65579e12	0.805925
$606$	−3.22557e11	−0.0971583
$607$	3.04748e12	0.911154	0.455577	−	0.890196i	$-0.349433\pi$
$607$	3.04748e12	0.911154	0.455577	+	0.890196i	$0.349433\pi$
$608$	−2.17099e12	−0.644304
$609$	−7.64444e11	−0.225200
$610$	−2.05637e12	−0.601335
$611$	2.88175e12	0.836509
$612$	1.53003e12	0.440879
$613$	2.00612e12	0.573833	0.286916	−	0.957956i	$-0.407370\pi$
$613$	2.00612e12	0.573833	0.286916	+	0.957956i	$0.407370\pi$
$614$	−9.17784e12	−2.60605
$615$	1.51827e12	0.427968
$616$	2.75450e12	0.770780
$617$	5.13085e12	1.42530	0.712650	−	0.701520i	$-0.247495\pi$
$617$	5.13085e12	1.42530	0.712650	+	0.701520i	$0.247495\pi$
$618$	−4.41964e12	−1.21882
$619$	5.80716e12	1.58985	0.794924	−	0.606709i	$-0.207511\pi$
$619$	5.80716e12	1.58985	0.794924	+	0.606709i	$0.207511\pi$
$620$	1.09047e12	0.296382
$621$	−3.50982e11	−0.0947049
$622$	−5.66657e12	−1.51797
$623$	1.08759e12	0.289246
$624$	6.62019e11	0.174799
$625$	−4.68082e12	−1.22705
$626$	−9.14247e12	−2.37946
$627$	1.51060e12	0.390342
$628$	−4.37599e10	−0.0112269
$629$	1.37078e12	0.349172
$630$	1.98418e12	0.501820
$631$	5.78092e11	0.145166	0.0725830	−	0.997362i	$-0.476876\pi$
$631$	5.78092e11	0.145166	0.0725830	+	0.997362i	$0.476876\pi$
$632$	1.90985e12	0.476181
$633$	−3.40953e12	−0.844070
$634$	2.17842e11	0.0535477
$635$	−4.72325e12	−1.15281
$636$	7.09748e11	0.172007
$637$	1.18810e12	0.285907
$638$	−4.02631e12	−0.962087
$639$	−1.07758e12	−0.255680
$640$	−6.32158e12	−1.48942
$641$	1.17584e12	0.275097	0.137548	−	0.990495i	$-0.456078\pi$
$641$	1.17584e12	0.275097	0.137548	+	0.990495i	$0.456078\pi$
$642$	1.76035e12	0.408971
$643$	−4.79162e12	−1.10543	−0.552717	−	0.833369i	$-0.686409\pi$
$643$	−4.79162e12	−1.10543	−0.552717	+	0.833369i	$0.686409\pi$
$644$	−2.58821e12	−0.592943
$645$	−8.88999e11	−0.202247
$646$	3.27205e12	0.739219
$647$	−6.93263e11	−0.155535	−0.0777676	−	0.996972i	$-0.524779\pi$
$647$	−6.93263e11	−0.155535	−0.0777676	+	0.996972i	$0.524779\pi$
$648$	3.57075e11	0.0795557
$649$	−7.65832e11	−0.169446
$650$	−2.24993e12	−0.494377
$651$	3.83386e11	0.0836608
$652$	9.17497e12	1.98834
$653$	6.48149e12	1.39497	0.697486	−	0.716598i	$-0.254302\pi$
$653$	6.48149e12	1.39497	0.697486	+	0.716598i	$0.254302\pi$
$654$	7.03816e12	1.50439
$655$	3.88644e11	0.0825022
$656$	−1.01285e12	−0.213540
$657$	−1.60808e12	−0.336716
$658$	−5.76186e12	−1.19825
$659$	−2.34935e12	−0.485248	−0.242624	−	0.970120i	$-0.578008\pi$
$659$	−2.34935e12	−0.485248	−0.242624	+	0.970120i	$0.578008\pi$
$660$	6.19687e12	1.27123
$661$	7.15134e12	1.45707	0.728536	−	0.685007i	$-0.240201\pi$
$661$	7.15134e12	1.45707	0.728536	+	0.685007i	$0.240201\pi$
$662$	−6.64880e12	−1.34550
$663$	−2.36025e12	−0.474403
$664$	3.08318e12	0.615520
$665$	2.51610e12	0.498920
$666$	1.02023e12	0.200938
$667$	1.18629e12	0.232073
$668$	−1.21301e13	−2.35705
$669$	−4.30198e11	−0.0830330
$670$	1.29965e13	2.49166
$671$	−2.25795e12	−0.429995
$672$	−3.13114e12	−0.592299
$673$	−1.03521e13	−1.94518	−0.972592	−	0.232519i	$-0.925303\pi$
$673$	−1.03521e13	−1.94518	−0.972592	+	0.232519i	$0.925303\pi$
$674$	−5.99350e12	−1.11869
$675$	3.61736e11	0.0670694
$676$	−1.43090e12	−0.263541
$677$	−4.12518e12	−0.754733	−0.377367	−	0.926064i	$-0.623170\pi$
$677$	−4.12518e12	−0.754733	−0.377367	+	0.926064i	$0.623170\pi$
$678$	−1.53508e12	−0.278996
$679$	4.29394e12	0.775251
$680$	4.20892e12	0.754884
$681$	−1.28992e12	−0.229828
$682$	2.01929e12	0.357411
$683$	7.10900e12	1.25002	0.625008	−	0.780618i	$-0.285096\pi$
$683$	7.10900e12	1.25002	0.625008	+	0.780618i	$0.285096\pi$
$684$	1.44404e12	0.252248
$685$	−5.35906e12	−0.929996
$686$	−9.89524e12	−1.70596
$687$	1.37170e12	0.234939
$688$	5.93059e11	0.100914
$689$	−1.09487e12	−0.185086
$690$	−3.07911e12	−0.517136
$691$	−5.47912e12	−0.914239	−0.457119	−	0.889405i	$-0.651119\pi$
$691$	−5.47912e12	−0.914239	−0.457119	+	0.889405i	$0.651119\pi$
$692$	4.74685e12	0.786915
$693$	2.17869e12	0.358835
$694$	4.98199e12	0.815239
$695$	−6.34306e12	−1.03126
$696$	−1.20688e12	−0.194950
$697$	3.61105e12	0.579544
$698$	−5.66411e12	−0.903197
$699$	9.16781e10	0.0145251
$700$	2.66751e12	0.419918
$701$	−3.79491e12	−0.593568	−0.296784	−	0.954945i	$-0.595914\pi$
$701$	−3.79491e12	−0.593568	−0.296784	+	0.954945i	$0.595914\pi$
$702$	−1.75666e12	−0.273005
$703$	1.29374e12	0.199778
$704$	−1.36539e13	−2.09498
$705$	−4.06462e12	−0.619682
$706$	4.00912e12	0.607334
$707$	−5.89930e11	−0.0888001
$708$	−7.32089e11	−0.109500
$709$	−3.93622e12	−0.585021	−0.292510	−	0.956262i	$-0.594491\pi$
$709$	−3.93622e12	−0.585021	−0.292510	+	0.956262i	$0.594491\pi$
$710$	−9.45347e12	−1.39614
$711$	1.51060e12	0.221685
$712$	1.71705e12	0.250394
$713$	−5.94952e11	−0.0862142
$714$	4.71916e12	0.679552
$715$	−9.55937e12	−1.36789
$716$	−1.64185e13	−2.33467
$717$	−2.50332e12	−0.353737
$718$	8.08869e12	1.13584
$719$	3.83409e12	0.535036	0.267518	−	0.963553i	$-0.413797\pi$
$719$	3.83409e12	0.535036	0.267518	+	0.963553i	$0.413797\pi$
$720$	−9.33757e11	−0.129490
$721$	−8.08315e12	−1.11397
$722$	−8.35651e12	−1.14448
$723$	−1.69356e12	−0.230504
$724$	1.79492e13	2.42785
$725$	−1.22264e12	−0.164353
$726$	4.70119e12	0.628048
$727$	−1.18819e13	−1.57754	−0.788769	−	0.614689i	$-0.789281\pi$
$727$	−1.18819e13	−1.57754	−0.788769	+	0.614689i	$0.789281\pi$
$728$	−4.06191e12	−0.535969
$729$	2.82430e11	0.0370370
$730$	−1.41075e13	−1.83864
$731$	−2.11439e12	−0.273878
$732$	−2.15847e12	−0.277872
$733$	7.50616e12	0.960395	0.480198	−	0.877160i	$-0.340565\pi$
$733$	7.50616e12	0.960395	0.480198	+	0.877160i	$0.340565\pi$
$734$	2.21966e13	2.82263
$735$	−1.67578e12	−0.211799
$736$	4.85901e12	0.610376
$737$	1.42705e13	1.78171
$738$	2.68759e12	0.333511
$739$	−1.28013e13	−1.57890	−0.789452	−	0.613812i	$-0.789635\pi$
$739$	−1.28013e13	−1.57890	−0.789452	+	0.613812i	$0.789635\pi$
$740$	5.30724e12	0.650618
$741$	−2.22760e12	−0.271428
$742$	2.18911e12	0.265124
$743$	1.22654e13	1.47649	0.738246	−	0.674531i	$-0.235654\pi$
$743$	1.22654e13	1.47649	0.738246	+	0.674531i	$0.235654\pi$
$744$	6.05280e11	0.0724233
$745$	−1.35089e12	−0.160664
$746$	2.40073e12	0.283804
$747$	2.43865e12	0.286554
$748$	1.47386e13	1.72147
$749$	3.21954e12	0.373788
$750$	−5.93251e12	−0.684641
$751$	−3.60774e11	−0.0413862	−0.0206931	−	0.999786i	$-0.506587\pi$
$751$	−3.60774e11	−0.0413862	−0.0206931	+	0.999786i	$0.506587\pi$
$752$	2.71154e12	0.309198
$753$	−9.44344e12	−1.07042
$754$	5.93737e12	0.668995
$755$	3.64514e12	0.408275
$756$	2.08269e12	0.231887
$757$	1.08258e13	1.19820	0.599101	−	0.800674i	$-0.295525\pi$
$757$	1.08258e13	1.19820	0.599101	+	0.800674i	$0.295525\pi$
$758$	9.26995e12	1.01992
$759$	−3.38096e12	−0.369787
$760$	3.97236e12	0.431904
$761$	−4.20431e12	−0.454426	−0.227213	−	0.973845i	$-0.572961\pi$
$761$	−4.20431e12	−0.454426	−0.227213	+	0.973845i	$0.572961\pi$
$762$	−8.36094e12	−0.898375
$763$	1.28722e13	1.37497
$764$	−5.42236e12	−0.575796
$765$	3.32906e12	0.351435
$766$	−3.99886e12	−0.419669
$767$	1.12933e12	0.117826
$768$	−2.23068e12	−0.231373
$769$	1.45302e12	0.149831	0.0749155	−	0.997190i	$-0.476131\pi$
$769$	1.45302e12	0.149831	0.0749155	+	0.997190i	$0.476131\pi$
$770$	1.91133e13	1.95942
$771$	−9.89100e12	−1.00808
$772$	−8.27062e11	−0.0838031
$773$	7.94784e12	0.800648	0.400324	−	0.916374i	$-0.368898\pi$
$773$	7.94784e12	0.800648	0.400324	+	0.916374i	$0.368898\pi$
$774$	−1.57368e12	−0.157609
$775$	6.13181e11	0.0610563
$776$	6.77916e12	0.671117
$777$	1.86591e12	0.183652
$778$	1.89176e13	1.85122
$779$	3.40810e12	0.331584
$780$	−9.13817e12	−0.883962
$781$	−1.03802e13	−0.998335
$782$	−7.32336e12	−0.700293
$783$	−9.54589e11	−0.0907588
$784$	1.11793e12	0.105680
$785$	−9.52131e10	−0.00894918
$786$	6.87964e11	0.0642931
$787$	−8.30103e12	−0.771340	−0.385670	−	0.922637i	$-0.626030\pi$
$787$	−8.30103e12	−0.771340	−0.385670	+	0.922637i	$0.626030\pi$
$788$	3.59979e12	0.332590
$789$	9.11478e11	0.0837336
$790$	1.32523e13	1.21051
$791$	−2.80754e12	−0.254995
$792$	3.43965e12	0.310636
$793$	3.32968e12	0.299001
$794$	3.03928e13	2.71381
$795$	1.54427e12	0.137111
$796$	2.37645e13	2.09807
$797$	−8.52949e12	−0.748791	−0.374396	−	0.927269i	$-0.622150\pi$
$797$	−8.52949e12	−0.748791	−0.374396	+	0.927269i	$0.622150\pi$
$798$	4.45393e12	0.388803
$799$	−9.66728e12	−0.839158
$800$	−5.00789e12	−0.432264
$801$	1.35811e12	0.116570
$802$	4.59425e12	0.392130
$803$	−1.54904e13	−1.31475
$804$	1.36418e13	1.15138
$805$	−5.63144e12	−0.472648
$806$	−2.97773e12	−0.248529
$807$	6.90977e12	0.573499
$808$	−9.31366e11	−0.0768722
$809$	5.02024e12	0.412056	0.206028	−	0.978546i	$-0.433946\pi$
$809$	5.02024e12	0.412056	0.206028	+	0.978546i	$0.433946\pi$
$810$	2.47771e12	0.202241
$811$	−1.87975e11	−0.0152583	−0.00762917	−	0.999971i	$-0.502428\pi$
$811$	−1.87975e11	−0.0152583	−0.00762917	+	0.999971i	$0.502428\pi$
$812$	−7.03933e12	−0.568237
$813$	8.40647e11	0.0674849
$814$	9.82772e12	0.784590
$815$	1.99629e13	1.58495
$816$	−2.22085e12	−0.175353
$817$	−1.99556e12	−0.156698
$818$	−8.50020e12	−0.663803
$819$	−3.21278e12	−0.249519
$820$	1.39809e13	1.07987
$821$	−2.48419e13	−1.90827	−0.954135	−	0.299375i	$-0.903222\pi$
$821$	−2.48419e13	−1.90827	−0.954135	+	0.299375i	$0.903222\pi$
$822$	−9.48643e12	−0.724736
$823$	2.43389e13	1.84928	0.924638	−	0.380848i	$-0.124368\pi$
$823$	2.43389e13	1.84928	0.924638	+	0.380848i	$0.124368\pi$
$824$	−1.27615e13	−0.964335
$825$	3.48455e12	0.261881
$826$	−2.25802e12	−0.168778
$827$	1.01862e13	0.757248	0.378624	−	0.925551i	$-0.376397\pi$
$827$	1.01862e13	0.757248	0.378624	+	0.925551i	$0.376397\pi$
$828$	−3.23199e12	−0.238965
$829$	1.02130e13	0.751029	0.375514	−	0.926817i	$-0.377466\pi$
$829$	1.02130e13	0.751029	0.375514	+	0.926817i	$0.377466\pi$
$830$	2.13939e13	1.56473
$831$	−5.50836e11	−0.0400699
$832$	2.01347e13	1.45677
$833$	−3.98567e12	−0.286813
$834$	−1.12283e13	−0.803647
$835$	−2.63926e13	−1.87886
$836$	1.39103e13	0.984933
$837$	4.78748e11	0.0337165
$838$	2.73063e13	1.91278
$839$	−1.79221e13	−1.24870	−0.624352	−	0.781143i	$-0.714637\pi$
$839$	−1.79221e13	−1.24870	−0.624352	+	0.781143i	$0.714637\pi$
$840$	5.72920e12	0.397043
$841$	−1.12807e13	−0.777597
$842$	5.63274e12	0.386203
$843$	−9.88270e12	−0.673987
$844$	−3.13965e13	−2.12980
$845$	−3.11335e12	−0.210075
$846$	−7.19505e12	−0.482911
$847$	8.59808e12	0.574019
$848$	−1.03020e12	−0.0684132
$849$	−5.46757e11	−0.0361169
$850$	7.54774e12	0.495943
$851$	−2.89559e12	−0.189258
$852$	−9.92284e12	−0.645146
$853$	−1.03449e13	−0.669048	−0.334524	−	0.942387i	$-0.608575\pi$
$853$	−1.03449e13	−0.669048	−0.334524	+	0.942387i	$0.608575\pi$
$854$	−6.65746e12	−0.428300
$855$	3.14195e12	0.201072
$856$	5.08293e12	0.323580
$857$	1.72812e12	0.109436	0.0547179	−	0.998502i	$-0.482574\pi$
$857$	1.72812e12	0.109436	0.0547179	+	0.998502i	$0.482574\pi$
$858$	−1.69217e13	−1.06598
$859$	1.43047e13	0.896416	0.448208	−	0.893929i	$-0.352062\pi$
$859$	1.43047e13	0.896416	0.448208	+	0.893929i	$0.352062\pi$
$860$	−8.18629e12	−0.510322
$861$	4.91538e12	0.304820
$862$	2.18671e13	1.34899
$863$	−6.54341e12	−0.401565	−0.200782	−	0.979636i	$-0.564348\pi$
$863$	−6.54341e12	−0.401565	−0.200782	+	0.979636i	$0.564348\pi$
$864$	−3.90997e12	−0.238705
$865$	1.03282e13	0.627267
$866$	6.77595e12	0.409392
$867$	−1.68779e12	−0.101445
$868$	3.53039e12	0.211098
$869$	1.45514e13	0.865599
$870$	−8.37447e12	−0.495588
$871$	−2.10439e13	−1.23893
$872$	2.03223e13	1.19028
$873$	5.36200e12	0.312437
$874$	−6.91176e12	−0.400670
$875$	−1.08501e13	−0.625744
$876$	−1.48079e13	−0.849621
$877$	−1.57637e13	−0.899830	−0.449915	−	0.893071i	$-0.648546\pi$
$877$	−1.57637e13	−0.899830	−0.449915	+	0.893071i	$0.648546\pi$
$878$	1.27505e13	0.724105
$879$	−1.48704e11	−0.00840178
$880$	−8.99476e12	−0.505612
$881$	−2.36603e13	−1.32321	−0.661606	−	0.749852i	$-0.730125\pi$
$881$	−2.36603e13	−1.32321	−0.661606	+	0.749852i	$0.730125\pi$
$882$	−2.96641e12	−0.165052
$883$	7.82639e12	0.433250	0.216625	−	0.976255i	$-0.430495\pi$
$883$	7.82639e12	0.433250	0.216625	+	0.976255i	$0.430495\pi$
$884$	−2.17342e13	−1.19704
$885$	−1.59288e12	−0.0872849
$886$	9.85703e12	0.537396
$887$	1.92636e13	1.04492	0.522458	−	0.852665i	$-0.325015\pi$
$887$	1.92636e13	1.04492	0.522458	+	0.852665i	$0.325015\pi$
$888$	2.94585e12	0.158984
$889$	−1.52915e13	−0.821090
$890$	1.19145e13	0.636533
$891$	2.72061e12	0.144616
$892$	−3.96145e12	−0.209514
$893$	−9.12394e12	−0.480121
$894$	−2.39130e12	−0.125203
$895$	−3.57235e13	−1.86102
$896$	−2.04660e13	−1.06083
$897$	4.98571e12	0.257135
$898$	−2.05151e13	−1.05276
$899$	−1.61813e12	−0.0826219
$900$	3.33102e12	0.169233
$901$	3.67290e12	0.185672
$902$	2.58892e13	1.30224
$903$	−2.87812e12	−0.144050
$904$	−4.43247e12	−0.220743
$905$	3.90540e13	1.93529
$906$	6.45250e12	0.318164
$907$	−3.54971e13	−1.74165	−0.870824	−	0.491595i	$-0.836414\pi$
$907$	−3.54971e13	−1.74165	−0.870824	+	0.491595i	$0.836414\pi$
$908$	−1.18782e13	−0.579914
$909$	−7.36668e11	−0.0357877
$910$	−2.81853e13	−1.36250
$911$	−2.79806e13	−1.34593	−0.672967	−	0.739672i	$-0.734981\pi$
$911$	−2.79806e13	−1.34593	−0.672967	+	0.739672i	$0.734981\pi$
$912$	−2.09603e12	−0.100327
$913$	2.34912e13	1.11889
$914$	4.95840e13	2.35008
$915$	−4.69641e12	−0.221498
$916$	1.26312e13	0.592811
$917$	1.25823e12	0.0587622
$918$	5.89299e12	0.273869
$919$	5.86841e12	0.271394	0.135697	−	0.990750i	$-0.456673\pi$
$919$	5.86841e12	0.271394	0.135697	+	0.990750i	$0.456673\pi$
$920$	−8.89077e12	−0.409161
$921$	−2.09607e13	−0.959925
$922$	−4.61865e13	−2.10487
$923$	1.53071e13	0.694201
$924$	2.00623e13	0.905433
$925$	2.98430e12	0.134031
$926$	6.28850e13	2.81059
$927$	−1.00937e13	−0.448945
$928$	1.32154e13	0.584944
$929$	3.20314e12	0.141093	0.0705464	−	0.997508i	$-0.477526\pi$
$929$	3.20314e12	0.141093	0.0705464	+	0.997508i	$0.477526\pi$
$930$	4.19999e12	0.184109
$931$	−3.76166e12	−0.164099
$932$	8.44212e11	0.0366505
$933$	−1.29415e13	−0.559137
$934$	−2.05333e13	−0.882872
$935$	3.20684e13	1.37222
$936$	−5.07226e12	−0.216003
$937$	2.84740e13	1.20676	0.603380	−	0.797454i	$-0.293820\pi$
$937$	2.84740e13	1.20676	0.603380	+	0.797454i	$0.293820\pi$
$938$	4.20759e13	1.77468
$939$	−2.08799e13	−0.876462
$940$	−3.74287e13	−1.56362
$941$	4.06774e13	1.69122	0.845609	−	0.533803i	$-0.179238\pi$
$941$	4.06774e13	1.69122	0.845609	+	0.533803i	$0.179238\pi$
$942$	−1.68543e11	−0.00697400
$943$	−7.62786e12	−0.314123
$944$	1.06263e12	0.0435519
$945$	4.53153e12	0.184843
$946$	−1.51590e13	−0.615405
$947$	−6.71090e11	−0.0271148	−0.0135574	−	0.999908i	$-0.504316\pi$
$947$	−6.71090e11	−0.0271148	−0.0135574	+	0.999908i	$0.504316\pi$
$948$	1.39103e13	0.559369
$949$	2.28429e13	0.914224
$950$	7.12353e12	0.283752
$951$	4.97516e11	0.0197240
$952$	1.36263e13	0.537665
$953$	2.85607e13	1.12163	0.560816	−	0.827941i	$-0.310488\pi$
$953$	2.85607e13	1.12163	0.560816	+	0.827941i	$0.310488\pi$
$954$	2.73362e12	0.106849
$955$	−1.17980e13	−0.458980
$956$	−2.30517e13	−0.892570
$957$	−9.19543e12	−0.354379
$958$	1.01906e12	0.0390892
$959$	−1.73499e13	−0.662389
$960$	−2.83993e13	−1.07916
$961$	−2.56281e13	−0.969306
$962$	−1.44924e13	−0.545572
$963$	4.02036e12	0.150642
$964$	−1.55951e13	−0.581621
$965$	−1.79953e12	−0.0668013
$966$	−9.96859e12	−0.368330
$967$	−1.66612e13	−0.612756	−0.306378	−	0.951910i	$-0.599117\pi$
$967$	−1.66612e13	−0.612756	−0.306378	+	0.951910i	$0.599117\pi$
$968$	1.35744e13	0.496915
$969$	7.47282e12	0.272287
$970$	4.70401e13	1.70606
$971$	−4.12487e13	−1.48910	−0.744551	−	0.667566i	$-0.767336\pi$
$971$	−4.12487e13	−1.48910	−0.744551	+	0.667566i	$0.767336\pi$
$972$	2.60073e12	0.0934539
$973$	−2.05356e13	−0.734512
$974$	−1.50694e13	−0.536513
$975$	−5.13847e12	−0.182101
$976$	3.13301e12	0.110519
$977$	3.51543e13	1.23439	0.617197	−	0.786809i	$-0.288268\pi$
$977$	3.51543e13	1.23439	0.617197	+	0.786809i	$0.288268\pi$
$978$	3.53377e13	1.23513
$979$	1.30825e13	0.455165
$980$	−1.54313e13	−0.534422
$981$	1.60740e13	0.554132
$982$	8.52550e13	2.92562
$983$	−6.62406e12	−0.226273	−0.113137	−	0.993579i	$-0.536090\pi$
$983$	−6.62406e12	−0.226273	−0.113137	+	0.993579i	$0.536090\pi$
$984$	7.76028e12	0.263876
$985$	7.83246e12	0.265115
$986$	−1.99178e13	−0.671114
$987$	−1.31591e13	−0.441368
$988$	−2.05127e13	−0.684882
$989$	4.46637e12	0.148447
$990$	2.38675e13	0.789675
$991$	−1.87240e12	−0.0616690	−0.0308345	−	0.999525i	$-0.509816\pi$
$991$	−1.87240e12	−0.0616690	−0.0308345	+	0.999525i	$0.509816\pi$
$992$	−6.62782e12	−0.217304
$993$	−1.51848e13	−0.495606
$994$	−3.06055e13	−0.994399
$995$	5.17069e13	1.67242
$996$	2.24562e13	0.723050
$997$	7.06126e12	0.226336	0.113168	−	0.993576i	$-0.463900\pi$
$997$	7.06126e12	0.226336	0.113168	+	0.993576i	$0.463900\pi$
$998$	−7.67475e13	−2.44893
$999$	2.33003e12	0.0740146

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.d.1.18	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.d.1.18	✓	22	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+35.4666 q^{2} +81.0000 q^{3} +745.883 q^{4} +1622.90 q^{5} +2872.80 q^{6} +5254.11 q^{7} +8295.05 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+35.4666 q^{2} +81.0000 q^{3} +745.883 q^{4} +1622.90 q^{5} +2872.80 q^{6} +5254.11 q^{7} +8295.05 q^{8} +6561.00 q^{9} +57558.7 q^{10} +63201.2 q^{11} +60416.5 q^{12} -93199.3 q^{13} +186346. q^{14} +131455. q^{15} -87694.6 q^{16} +312651. q^{17} +232697. q^{18} +295079. q^{19} +1.21049e6 q^{20} +425583. q^{21} +2.24154e6 q^{22} -660434. q^{23} +671899. q^{24} +680669. q^{25} -3.30547e6 q^{26} +531441. q^{27} +3.91895e6 q^{28} -1.79623e6 q^{29} +4.66226e6 q^{30} +900850. q^{31} -7.35730e6 q^{32} +5.11930e6 q^{33} +1.10887e7 q^{34} +8.52688e6 q^{35} +4.89374e6 q^{36} +4.38437e6 q^{37} +1.04655e7 q^{38} -7.54914e6 q^{39} +1.34620e7 q^{40} +1.15498e7 q^{41} +1.50940e7 q^{42} -6.76278e6 q^{43} +4.71407e7 q^{44} +1.06478e7 q^{45} -2.34234e7 q^{46} -3.09203e7 q^{47} -7.10326e6 q^{48} -1.27480e7 q^{49} +2.41411e7 q^{50} +2.53248e7 q^{51} -6.95158e7 q^{52} +1.17476e7 q^{53} +1.88484e7 q^{54} +1.02569e8 q^{55} +4.35831e7 q^{56} +2.39014e7 q^{57} -6.37062e7 q^{58} -1.21174e7 q^{59} +9.80498e7 q^{60} -3.57264e7 q^{61} +3.19501e7 q^{62} +3.44722e7 q^{63} -2.16039e8 q^{64} -1.51253e8 q^{65} +1.81564e8 q^{66} +2.25795e8 q^{67} +2.33201e8 q^{68} -5.34952e7 q^{69} +3.02420e8 q^{70} -1.64241e8 q^{71} +5.44238e7 q^{72} -2.45097e8 q^{73} +1.55499e8 q^{74} +5.51342e7 q^{75} +2.20095e8 q^{76} +3.32066e8 q^{77} -2.67743e8 q^{78} +2.30240e8 q^{79} -1.42319e8 q^{80} +4.30467e7 q^{81} +4.09632e8 q^{82} +3.71689e8 q^{83} +3.17435e8 q^{84} +5.07401e8 q^{85} -2.39853e8 q^{86} -1.45494e8 q^{87} +5.24257e8 q^{88} +2.06997e8 q^{89} +3.77643e8 q^{90} -4.89679e8 q^{91} -4.92607e8 q^{92} +7.29688e7 q^{93} -1.09664e9 q^{94} +4.78883e8 q^{95} -5.95941e8 q^{96} +8.17254e8 q^{97} -4.52127e8 q^{98} +4.14663e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9}+O(q^{10}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9} + 45337 q^{10} + 111769 q^{11} + 483894 q^{12} + 189121 q^{13} + 251053 q^{14} + 468666 q^{15} + 2311074 q^{16} + 1113841 q^{17} + 301806 q^{18} + 476068 q^{19} - 42495 q^{20} + 618921 q^{21} - 2252022 q^{22} + 7103062 q^{23} + 4972995 q^{24} + 10628442 q^{25} + 6871048 q^{26} + 11691702 q^{27} + 8112650 q^{28} + 15279316 q^{29} + 3672297 q^{30} + 17610338 q^{31} + 32378276 q^{32} + 9053289 q^{33} + 29339436 q^{34} + 7134904 q^{35} + 39195414 q^{36} + 21961411 q^{37} + 65195131 q^{38} + 15318801 q^{39} + 75185084 q^{40} + 52781575 q^{41} + 20335293 q^{42} + 76191313 q^{43} + 61127768 q^{44} + 37961946 q^{45} + 290208769 q^{46} + 160572396 q^{47} + 187196994 q^{48} + 156292703 q^{49} + 169504821 q^{50} + 90221121 q^{51} + 65465920 q^{52} - 8762038 q^{53} + 24446286 q^{54} + 147125140 q^{55} + 9671794 q^{56} + 38561508 q^{57} - 37665424 q^{58} - 266581942 q^{59} - 3442095 q^{60} + 120750754 q^{61} - 152465186 q^{62} + 50132601 q^{63} - 40658803 q^{64} + 331055798 q^{65} - 182413782 q^{66} + 41371828 q^{67} + 145606631 q^{68} + 575348022 q^{69} - 920887614 q^{70} + 261018751 q^{71} + 402812595 q^{72} + 178388 q^{73} - 303908734 q^{74} + 860903802 q^{75} - 94541144 q^{76} + 299640561 q^{77} + 556554888 q^{78} - 905381353 q^{79} + 939128289 q^{80} + 947027862 q^{81} - 551739753 q^{82} + 1173257869 q^{83} + 657124650 q^{84} - 1546633210 q^{85} + 1384869460 q^{86} + 1237624596 q^{87} + 189740713 q^{88} + 898004974 q^{89} + 297456057 q^{90} + 591272339 q^{91} + 4328210270 q^{92} + 1426437378 q^{93} + 122568068 q^{94} + 2487967134 q^{95} + 2622640356 q^{96} + 3175709684 q^{97} + 5095778404 q^{98} + 733316409 q^{99}+O(q^{100}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9 + 45337 * q^10 + 111769 * q^11 + 483894 * q^12 + 189121 * q^13 + 251053 * q^14 + 468666 * q^15 + 2311074 * q^16 + 1113841 * q^17 + 301806 * q^18 + 476068 * q^19 - 42495 * q^20 + 618921 * q^21 - 2252022 * q^22 + 7103062 * q^23 + 4972995 * q^24 + 10628442 * q^25 + 6871048 * q^26 + 11691702 * q^27 + 8112650 * q^28 + 15279316 * q^29 + 3672297 * q^30 + 17610338 * q^31 + 32378276 * q^32 + 9053289 * q^33 + 29339436 * q^34 + 7134904 * q^35 + 39195414 * q^36 + 21961411 * q^37 + 65195131 * q^38 + 15318801 * q^39 + 75185084 * q^40 + 52781575 * q^41 + 20335293 * q^42 + 76191313 * q^43 + 61127768 * q^44 + 37961946 * q^45 + 290208769 * q^46 + 160572396 * q^47 + 187196994 * q^48 + 156292703 * q^49 + 169504821 * q^50 + 90221121 * q^51 + 65465920 * q^52 - 8762038 * q^53 + 24446286 * q^54 + 147125140 * q^55 + 9671794 * q^56 + 38561508 * q^57 - 37665424 * q^58 - 266581942 * q^59 - 3442095 * q^60 + 120750754 * q^61 - 152465186 * q^62 + 50132601 * q^63 - 40658803 * q^64 + 331055798 * q^65 - 182413782 * q^66 + 41371828 * q^67 + 145606631 * q^68 + 575348022 * q^69 - 920887614 * q^70 + 261018751 * q^71 + 402812595 * q^72 + 178388 * q^73 - 303908734 * q^74 + 860903802 * q^75 - 94541144 * q^76 + 299640561 * q^77 + 556554888 * q^78 - 905381353 * q^79 + 939128289 * q^80 + 947027862 * q^81 - 551739753 * q^82 + 1173257869 * q^83 + 657124650 * q^84 - 1546633210 * q^85 + 1384869460 * q^86 + 1237624596 * q^87 + 189740713 * q^88 + 898004974 * q^89 + 297456057 * q^90 + 591272339 * q^91 + 4328210270 * q^92 + 1426437378 * q^93 + 122568068 * q^94 + 2487967134 * q^95 + 2622640356 * q^96 + 3175709684 * q^97 + 5095778404 * q^98 + 733316409 * q^99

Introduction

L-functions

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