LMFDB - Embedded newform 177.10.a.d.1.20

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			1.20
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)

$f(q)$	$=$	$q+40.5682 q^{2} +81.0000 q^{3} +1133.78 q^{4} -281.912 q^{5} +3286.03 q^{6} -11944.6 q^{7} +25224.6 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+40.5682 q^{2} +81.0000 q^{3} +1133.78 q^{4} -281.912 q^{5} +3286.03 q^{6} -11944.6 q^{7} +25224.6 q^{8} +6561.00 q^{9} -11436.7 q^{10} +38053.5 q^{11} +91836.3 q^{12} +124569. q^{13} -484571. q^{14} -22834.8 q^{15} +442820. q^{16} +483647. q^{17} +266168. q^{18} +118744. q^{19} -319626. q^{20} -967511. q^{21} +1.54376e6 q^{22} +1.81149e6 q^{23} +2.04319e6 q^{24} -1.87365e6 q^{25} +5.05356e6 q^{26} +531441. q^{27} -1.35425e7 q^{28} +1.59230e6 q^{29} -926369. q^{30} +3.75720e6 q^{31} +5.04944e6 q^{32} +3.08233e6 q^{33} +1.96207e7 q^{34} +3.36732e6 q^{35} +7.43874e6 q^{36} +1.86388e7 q^{37} +4.81725e6 q^{38} +1.00901e7 q^{39} -7.11109e6 q^{40} +223048. q^{41} -3.92502e7 q^{42} +9.66466e6 q^{43} +4.31443e7 q^{44} -1.84962e6 q^{45} +7.34889e7 q^{46} -2.98480e6 q^{47} +3.58684e7 q^{48} +1.02320e8 q^{49} -7.60107e7 q^{50} +3.91754e7 q^{51} +1.41235e8 q^{52} -3.40106e7 q^{53} +2.15596e7 q^{54} -1.07277e7 q^{55} -3.01297e8 q^{56} +9.61829e6 q^{57} +6.45968e7 q^{58} -1.21174e7 q^{59} -2.58897e7 q^{60} -1.41279e8 q^{61} +1.52423e8 q^{62} -7.83684e7 q^{63} -2.18769e7 q^{64} -3.51176e7 q^{65} +1.25045e8 q^{66} +2.24453e7 q^{67} +5.48350e8 q^{68} +1.46731e8 q^{69} +1.36606e8 q^{70} -2.18355e8 q^{71} +1.65498e8 q^{72} -2.38222e8 q^{73} +7.56143e8 q^{74} -1.51766e8 q^{75} +1.34630e8 q^{76} -4.54533e8 q^{77} +4.09339e8 q^{78} -4.97164e7 q^{79} -1.24836e8 q^{80} +4.30467e7 q^{81} +9.04867e6 q^{82} -5.31042e8 q^{83} -1.09695e9 q^{84} -1.36346e8 q^{85} +3.92078e8 q^{86} +1.28976e8 q^{87} +9.59882e8 q^{88} -1.52080e6 q^{89} -7.50359e7 q^{90} -1.48793e9 q^{91} +2.05383e9 q^{92} +3.04333e8 q^{93} -1.21088e8 q^{94} -3.34754e7 q^{95} +4.09005e8 q^{96} +1.14057e9 q^{97} +4.15092e9 q^{98} +2.49669e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	40.5682	1.79288	0.896440	−	0.443166i	$-0.146145\pi$
$2$	40.5682	1.79288	0.896440	+	0.443166i	$0.146145\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	1133.78	2.21442
$5$	−281.912	−0.201719	−0.100860	−	0.994901i	$-0.532159\pi$
$5$	−281.912	−0.201719	−0.100860	+	0.994901i	$0.532159\pi$
$6$	3286.03	1.03512
$7$	−11944.6	−1.88031	−0.940156	−	0.340744i	$-0.889321\pi$
$7$	−11944.6	−1.88031	−0.940156	+	0.340744i	$0.889321\pi$
$8$	25224.6	2.17730
$9$	6561.00	0.333333
$10$	−11436.7	−0.361659
$11$	38053.5	0.783659	0.391829	−	0.920038i	$-0.371842\pi$
$11$	38053.5	0.783659	0.391829	+	0.920038i	$0.371842\pi$
$12$	91836.3	1.27849
$13$	124569.	1.20967	0.604834	−	0.796351i	$-0.293239\pi$
$13$	124569.	1.20967	0.604834	+	0.796351i	$0.293239\pi$
$14$	−484571.	−3.37117
$15$	−22834.8	−0.116463
$16$	442820.	1.68922
$17$	483647.	1.40446	0.702228	−	0.711952i	$-0.252189\pi$
$17$	483647.	1.40446	0.702228	+	0.711952i	$0.252189\pi$
$18$	266168.	0.597626
$19$	118744.	0.209036	0.104518	−	0.994523i	$-0.466670\pi$
$19$	118744.	0.209036	0.104518	+	0.994523i	$0.466670\pi$
$20$	−319626.	−0.446691
$21$	−967511.	−1.08560
$22$	1.54376e6	1.40501
$23$	1.81149e6	1.34977	0.674886	−	0.737922i	$-0.264193\pi$
$23$	1.81149e6	1.34977	0.674886	+	0.737922i	$0.264193\pi$
$24$	2.04319e6	1.25707
$25$	−1.87365e6	−0.959309
$26$	5.05356e6	2.16879
$27$	531441.	0.192450
$28$	−1.35425e7	−4.16379
$29$	1.59230e6	0.418056	0.209028	−	0.977910i	$-0.432970\pi$
$29$	1.59230e6	0.418056	0.209028	+	0.977910i	$0.432970\pi$
$30$	−926369.	−0.208804
$31$	3.75720e6	0.730696	0.365348	−	0.930871i	$-0.380950\pi$
$31$	3.75720e6	0.730696	0.365348	+	0.930871i	$0.380950\pi$
$32$	5.04944e6	0.851272
$33$	3.08233e6	0.452446
$34$	1.96207e7	2.51802
$35$	3.36732e6	0.379296
$36$	7.43874e6	0.738139
$37$	1.86388e7	1.63497	0.817485	−	0.575950i	$-0.195368\pi$
$37$	1.86388e7	1.63497	0.817485	+	0.575950i	$0.195368\pi$
$38$	4.81725e6	0.374777
$39$	1.00901e7	0.698403
$40$	−7.11109e6	−0.439204
$41$	223048.	0.0123274	0.00616370	−	0.999981i	$-0.498038\pi$
$41$	223048.	0.0123274	0.00616370	+	0.999981i	$0.498038\pi$
$42$	−3.92502e7	−1.94635
$43$	9.66466e6	0.431101	0.215550	−	0.976493i	$-0.430845\pi$
$43$	9.66466e6	0.431101	0.215550	+	0.976493i	$0.430845\pi$
$44$	4.31443e7	1.73535
$45$	−1.84962e6	−0.0672398
$46$	7.34889e7	2.41998
$47$	−2.98480e6	−0.0892227	−0.0446113	−	0.999004i	$-0.514205\pi$
$47$	−2.98480e6	−0.0892227	−0.0446113	+	0.999004i	$0.514205\pi$
$48$	3.58684e7	0.975274
$49$	1.02320e8	2.53557
$50$	−7.60107e7	−1.71993
$51$	3.91754e7	0.810863
$52$	1.41235e8	2.67871
$53$	−3.40106e7	−0.592070	−0.296035	−	0.955177i	$-0.595664\pi$
$53$	−3.40106e7	−0.592070	−0.296035	+	0.955177i	$0.595664\pi$
$54$	2.15596e7	0.345040
$55$	−1.07277e7	−0.158079
$56$	−3.01297e8	−4.09401
$57$	9.61829e6	0.120687
$58$	6.45968e7	0.749524
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	−2.58897e7	−0.257897
$61$	−1.41279e8	−1.30645	−0.653225	−	0.757164i	$-0.726584\pi$
$61$	−1.41279e8	−1.30645	−0.653225	+	0.757164i	$0.726584\pi$
$62$	1.52423e8	1.31005
$63$	−7.83684e7	−0.626771
$64$	−2.18769e7	−0.162996
$65$	−3.51176e7	−0.244014
$66$	1.25045e8	0.811181
$67$	2.24453e7	0.136078	0.0680390	−	0.997683i	$-0.478326\pi$
$67$	2.24453e7	0.136078	0.0680390	+	0.997683i	$0.478326\pi$
$68$	5.48350e8	3.11005
$69$	1.46731e8	0.779291
$70$	1.36606e8	0.680031
$71$	−2.18355e8	−1.01977	−0.509884	−	0.860243i	$-0.670312\pi$
$71$	−2.18355e8	−1.01977	−0.509884	+	0.860243i	$0.670312\pi$
$72$	1.65498e8	0.725767
$73$	−2.38222e8	−0.981815	−0.490907	−	0.871212i	$-0.663335\pi$
$73$	−2.38222e8	−0.981815	−0.490907	+	0.871212i	$0.663335\pi$
$74$	7.56143e8	2.93130
$75$	−1.51766e8	−0.553857
$76$	1.34630e8	0.462893
$77$	−4.54533e8	−1.47352
$78$	4.09339e8	1.25215
$79$	−4.97164e7	−0.143608	−0.0718038	−	0.997419i	$-0.522876\pi$
$79$	−4.97164e7	−0.143608	−0.0718038	+	0.997419i	$0.522876\pi$
$80$	−1.24836e8	−0.340749
$81$	4.30467e7	0.111111
$82$	9.04867e6	0.0221015
$83$	−5.31042e8	−1.22822	−0.614112	−	0.789219i	$-0.710486\pi$
$83$	−5.31042e8	−1.22822	−0.614112	+	0.789219i	$0.710486\pi$
$84$	−1.09695e9	−2.40397
$85$	−1.36346e8	−0.283306
$86$	3.92078e8	0.772912
$87$	1.28976e8	0.241365
$88$	9.59882e8	1.70626
$89$	−1.52080e6	−0.00256931	−0.00128466	−	0.999999i	$-0.500409\pi$
$89$	−1.52080e6	−0.00256931	−0.00128466	+	0.999999i	$0.500409\pi$
$90$	−7.50359e7	−0.120553
$91$	−1.48793e9	−2.27455
$92$	2.05383e9	2.98896
$93$	3.04333e8	0.421867
$94$	−1.21088e8	−0.159966
$95$	−3.34754e7	−0.0421667
$96$	4.09005e8	0.491482
$97$	1.14057e9	1.30812	0.654061	−	0.756442i	$-0.273064\pi$
$97$	1.14057e9	1.30812	0.654061	+	0.756442i	$0.273064\pi$
$98$	4.15092e9	4.54598
$99$	2.49669e8	0.261220
$100$	−2.12431e9	−2.12431
$101$	4.02295e8	0.384679	0.192340	−	0.981328i	$-0.438392\pi$
$101$	4.02295e8	0.384679	0.192340	+	0.981328i	$0.438392\pi$
$102$	1.58928e9	1.45378
$103$	1.17667e9	1.03012	0.515058	−	0.857155i	$-0.327770\pi$
$103$	1.17667e9	1.03012	0.515058	+	0.857155i	$0.327770\pi$
$104$	3.14221e9	2.63381
$105$	2.72753e8	0.218986
$106$	−1.37975e9	−1.06151
$107$	1.91003e8	0.140869	0.0704343	−	0.997516i	$-0.477561\pi$
$107$	1.91003e8	0.140869	0.0704343	+	0.997516i	$0.477561\pi$
$108$	6.02538e8	0.426165
$109$	−1.51121e9	−1.02543	−0.512715	−	0.858559i	$-0.671360\pi$
$109$	−1.51121e9	−1.02543	−0.512715	+	0.858559i	$0.671360\pi$
$110$	−4.35204e8	−0.283417
$111$	1.50974e9	0.943951
$112$	−5.28930e9	−3.17627
$113$	2.19941e8	0.126897	0.0634487	−	0.997985i	$-0.479790\pi$
$113$	2.19941e8	0.126897	0.0634487	+	0.997985i	$0.479790\pi$
$114$	3.90197e8	0.216377
$115$	−5.10679e8	−0.272275
$116$	1.80532e9	0.925750
$117$	8.17300e8	0.403223
$118$	−4.91580e8	−0.233413
$119$	−5.77696e9	−2.64082
$120$	−5.75999e8	−0.253575
$121$	−9.09882e8	−0.385879
$122$	−5.73143e9	−2.34231
$123$	1.80669e7	0.00711723
$124$	4.25984e9	1.61807
$125$	1.07881e9	0.395231
$126$	−3.17927e9	−1.12372
$127$	3.82328e9	1.30413	0.652063	−	0.758165i	$-0.273904\pi$
$127$	3.82328e9	1.30413	0.652063	+	0.758165i	$0.273904\pi$
$128$	−3.47282e9	−1.14350
$129$	7.82838e8	0.248896
$130$	−1.42466e9	−0.437487
$131$	−9.03851e7	−0.0268149	−0.0134074	−	0.999910i	$-0.504268\pi$
$131$	−9.03851e7	−0.0268149	−0.0134074	+	0.999910i	$0.504268\pi$
$132$	3.49469e9	1.00190
$133$	−1.41835e9	−0.393053
$134$	9.10565e8	0.243972
$135$	−1.49819e8	−0.0388209
$136$	1.21998e10	3.05793
$137$	−6.57593e9	−1.59483	−0.797416	−	0.603430i	$-0.793800\pi$
$137$	−6.57593e9	−1.59483	−0.797416	+	0.603430i	$0.793800\pi$
$138$	5.95260e9	1.39717
$139$	−4.80391e9	−1.09151	−0.545756	−	0.837944i	$-0.683757\pi$
$139$	−4.80391e9	−1.09151	−0.545756	+	0.837944i	$0.683757\pi$
$140$	3.81780e9	0.839918
$141$	−2.41769e8	−0.0515127
$142$	−8.85829e9	−1.82832
$143$	4.74030e9	0.947968
$144$	2.90534e9	0.563075
$145$	−4.48888e8	−0.0843300
$146$	−9.66426e9	−1.76028
$147$	8.28788e9	1.46391
$148$	2.11323e10	3.62051
$149$	3.61683e9	0.601159	0.300580	−	0.953757i	$-0.402820\pi$
$149$	3.61683e9	0.601159	0.300580	+	0.953757i	$0.402820\pi$
$150$	−6.15687e9	−0.993000
$151$	1.27313e10	1.99286	0.996429	−	0.0844386i	$-0.0269097\pi$
$151$	1.27313e10	1.99286	0.996429	+	0.0844386i	$0.0269097\pi$
$152$	2.99527e9	0.455135
$153$	3.17321e9	0.468152
$154$	−1.84396e10	−2.64185
$155$	−1.05920e9	−0.147396
$156$	1.14400e10	1.54655
$157$	−1.14915e10	−1.50948	−0.754739	−	0.656026i	$-0.772236\pi$
$157$	−1.14915e10	−1.50948	−0.754739	+	0.656026i	$0.772236\pi$
$158$	−2.01690e9	−0.257471
$159$	−2.75486e9	−0.341832
$160$	−1.42350e9	−0.171718
$161$	−2.16375e10	−2.53799
$162$	1.74633e9	0.199209
$163$	−9.49867e9	−1.05395	−0.526973	−	0.849882i	$-0.676673\pi$
$163$	−9.49867e9	−1.05395	−0.526973	+	0.849882i	$0.676673\pi$
$164$	2.52888e8	0.0272980
$165$	−8.68944e8	−0.0912671
$166$	−2.15434e10	−2.20206
$167$	−9.02614e9	−0.898004	−0.449002	−	0.893531i	$-0.648220\pi$
$167$	−9.02614e9	−0.898004	−0.449002	+	0.893531i	$0.648220\pi$
$168$	−2.44051e10	−2.36368
$169$	4.91305e9	0.463299
$170$	−5.53130e9	−0.507934
$171$	7.79081e8	0.0696787
$172$	1.09576e10	0.954636
$173$	6.93115e9	0.588299	0.294150	−	0.955759i	$-0.404964\pi$
$173$	6.93115e9	0.588299	0.294150	+	0.955759i	$0.404964\pi$
$174$	5.23234e9	0.432738
$175$	2.23800e10	1.80380
$176$	1.68508e10	1.32378
$177$	−9.81506e8	−0.0751646
$178$	−6.16962e7	−0.00460647
$179$	1.90308e10	1.38554	0.692769	−	0.721160i	$-0.256391\pi$
$179$	1.90308e10	1.38554	0.692769	+	0.721160i	$0.256391\pi$
$180$	−2.09707e9	−0.148897
$181$	1.08861e10	0.753906	0.376953	−	0.926232i	$-0.376972\pi$
$181$	1.08861e10	0.753906	0.376953	+	0.926232i	$0.376972\pi$
$182$	−6.03627e10	−4.07800
$183$	−1.14436e10	−0.754279
$184$	4.56940e10	2.93886
$185$	−5.25449e9	−0.329805
$186$	1.23463e10	0.756358
$187$	1.84044e10	1.10061
$188$	−3.38411e9	−0.197576
$189$	−6.34784e9	−0.361866
$190$	−1.35804e9	−0.0755998
$191$	2.02801e10	1.10261	0.551303	−	0.834305i	$-0.314131\pi$
$191$	2.02801e10	1.10261	0.551303	+	0.834305i	$0.314131\pi$
$192$	−1.77203e9	−0.0941056
$193$	3.01806e9	0.156574	0.0782869	−	0.996931i	$-0.475055\pi$
$193$	3.01806e9	0.156574	0.0782869	+	0.996931i	$0.475055\pi$
$194$	4.62708e10	2.34530
$195$	−2.84452e9	−0.140881
$196$	1.16008e11	5.61481
$197$	−2.02898e10	−0.959797	−0.479899	−	0.877324i	$-0.659327\pi$
$197$	−2.02898e10	−0.959797	−0.479899	+	0.877324i	$0.659327\pi$
$198$	1.01286e10	0.468335
$199$	−1.10122e10	−0.497777	−0.248888	−	0.968532i	$-0.580065\pi$
$199$	−1.10122e10	−0.497777	−0.248888	+	0.968532i	$0.580065\pi$
$200$	−4.72620e10	−2.08871
$201$	1.81807e9	0.0785647
$202$	1.63204e10	0.689684
$203$	−1.90194e10	−0.786075
$204$	4.44163e10	1.79559
$205$	−6.28799e7	−0.00248668
$206$	4.77353e10	1.84688
$207$	1.18852e10	0.449924
$208$	5.51618e10	2.04340
$209$	4.51863e9	0.163813
$210$	1.10651e10	0.392616
$211$	3.97643e10	1.38109	0.690546	−	0.723289i	$-0.257371\pi$
$211$	3.97643e10	1.38109	0.690546	+	0.723289i	$0.257371\pi$
$212$	−3.85606e10	−1.31109
$213$	−1.76868e10	−0.588763
$214$	7.74867e9	0.252560
$215$	−2.72458e9	−0.0869614
$216$	1.34054e10	0.419022
$217$	−4.48782e10	−1.37394
$218$	−6.13072e10	−1.83847
$219$	−1.92960e10	−0.566851
$220$	−1.21629e10	−0.350053
$221$	6.02476e10	1.69893
$222$	6.12475e10	1.69239
$223$	7.26492e10	1.96725	0.983624	−	0.180234i	$-0.0576854\pi$
$223$	7.26492e10	1.96725	0.983624	+	0.180234i	$0.0576854\pi$
$224$	−6.03135e10	−1.60066
$225$	−1.22930e10	−0.319770
$226$	8.92260e9	0.227512
$227$	2.91674e10	0.729092	0.364546	−	0.931185i	$-0.381224\pi$
$227$	2.91674e10	0.729092	0.364546	+	0.931185i	$0.381224\pi$
$228$	1.09050e10	0.267252
$229$	−7.04501e10	−1.69286	−0.846432	−	0.532497i	$-0.821254\pi$
$229$	−7.04501e10	−1.69286	−0.846432	+	0.532497i	$0.821254\pi$
$230$	−2.07174e10	−0.488157
$231$	−3.68172e10	−0.850739
$232$	4.01651e10	0.910234
$233$	−2.66720e10	−0.592863	−0.296432	−	0.955054i	$-0.595797\pi$
$233$	−2.66720e10	−0.592863	−0.296432	+	0.955054i	$0.595797\pi$
$234$	3.31564e10	0.722930
$235$	8.41450e8	0.0179980
$236$	−1.37384e10	−0.288292
$237$	−4.02703e9	−0.0829119
$238$	−2.34361e11	−4.73467
$239$	−5.20140e10	−1.03117	−0.515584	−	0.856839i	$-0.672425\pi$
$239$	−5.20140e10	−1.03117	−0.515584	+	0.856839i	$0.672425\pi$
$240$	−1.01117e10	−0.196732
$241$	9.31533e10	1.77878	0.889389	−	0.457152i	$-0.151130\pi$
$241$	9.31533e10	1.77878	0.889389	+	0.457152i	$0.151130\pi$
$242$	−3.69123e10	−0.691834
$243$	3.48678e9	0.0641500
$244$	−1.60179e11	−2.89302
$245$	−2.88451e10	−0.511474
$246$	7.32942e8	0.0127603
$247$	1.47919e10	0.252865
$248$	9.47737e10	1.59095
$249$	−4.30144e10	−0.709116
$250$	4.37655e10	0.708601
$251$	1.01318e10	0.161122	0.0805612	−	0.996750i	$-0.474329\pi$
$251$	1.01318e10	0.161122	0.0805612	+	0.996750i	$0.474329\pi$
$252$	−8.88526e10	−1.38793
$253$	6.89334e10	1.05776
$254$	1.55104e11	2.33814
$255$	−1.10440e10	−0.163567
$256$	−1.29685e11	−1.88717
$257$	−9.92179e10	−1.41870	−0.709351	−	0.704856i	$-0.751012\pi$
$257$	−9.92179e10	−1.41870	−0.709351	+	0.704856i	$0.751012\pi$
$258$	3.17583e10	0.446241
$259$	−2.22633e11	−3.07425
$260$	−3.98156e10	−0.540348
$261$	1.04471e10	0.139352
$262$	−3.66676e9	−0.0480759
$263$	−1.04898e11	−1.35197	−0.675983	−	0.736917i	$-0.736281\pi$
$263$	−1.04898e11	−1.35197	−0.675983	+	0.736917i	$0.736281\pi$
$264$	7.77504e10	0.985111
$265$	9.58798e9	0.119432
$266$	−5.75400e10	−0.704697
$267$	−1.23185e8	−0.00148339
$268$	2.54480e10	0.301334
$269$	−1.39602e11	−1.62557	−0.812785	−	0.582563i	$-0.802050\pi$
$269$	−1.39602e11	−1.62557	−0.812785	+	0.582563i	$0.802050\pi$
$270$	−6.07791e9	−0.0696012
$271$	−4.91722e10	−0.553807	−0.276903	−	0.960898i	$-0.589308\pi$
$271$	−4.91722e10	−0.553807	−0.276903	+	0.960898i	$0.589308\pi$
$272$	2.14168e11	2.37244
$273$	−1.20522e11	−1.31321
$274$	−2.66774e11	−2.85934
$275$	−7.12989e10	−0.751771
$276$	1.66360e11	1.72567
$277$	−3.34988e10	−0.341878	−0.170939	−	0.985282i	$-0.554680\pi$
$277$	−3.34988e10	−0.341878	−0.170939	+	0.985282i	$0.554680\pi$
$278$	−1.94886e11	−1.95695
$279$	2.46510e10	0.243565
$280$	8.49391e10	0.825841
$281$	1.83976e11	1.76028	0.880140	−	0.474714i	$-0.157449\pi$
$281$	1.83976e11	1.76028	0.880140	+	0.474714i	$0.157449\pi$
$282$	−9.80814e9	−0.0923561
$283$	−9.61863e10	−0.891404	−0.445702	−	0.895181i	$-0.647046\pi$
$283$	−9.61863e10	−0.891404	−0.445702	+	0.895181i	$0.647046\pi$
$284$	−2.47567e11	−2.25819
$285$	−2.71151e9	−0.0243449
$286$	1.92306e11	1.69959
$287$	−2.66422e9	−0.0231794
$288$	3.31294e10	0.283757
$289$	1.15327e11	0.972498
$290$	−1.82106e10	−0.151194
$291$	9.23859e10	0.755244
$292$	−2.70092e11	−2.17415
$293$	−2.03250e11	−1.61111	−0.805556	−	0.592519i	$-0.798134\pi$
$293$	−2.03250e11	−1.61111	−0.805556	+	0.592519i	$0.798134\pi$
$294$	3.36225e11	2.62462
$295$	3.41602e9	0.0262616
$296$	4.70155e11	3.55982
$297$	2.02232e10	0.150815
$298$	1.46728e11	1.07781
$299$	2.25656e11	1.63278
$300$	−1.72069e11	−1.22647
$301$	−1.15440e11	−0.810604
$302$	5.16486e11	3.57295
$303$	3.25859e10	0.222095
$304$	5.25823e10	0.353109
$305$	3.98281e10	0.263536
$306$	1.28731e11	0.839340
$307$	7.47524e10	0.480289	0.240144	−	0.970737i	$-0.422805\pi$
$307$	7.47524e10	0.480289	0.240144	+	0.970737i	$0.422805\pi$
$308$	−5.15341e11	−3.26299
$309$	9.53101e10	0.594738
$310$	−4.29698e10	−0.264263
$311$	−1.42843e11	−0.865841	−0.432921	−	0.901432i	$-0.642517\pi$
$311$	−1.42843e11	−0.865841	−0.432921	+	0.901432i	$0.642517\pi$
$312$	2.54519e11	1.52063
$313$	3.18510e11	1.87574	0.937871	−	0.346984i	$-0.112794\pi$
$313$	3.18510e11	1.87574	0.937871	+	0.346984i	$0.112794\pi$
$314$	−4.66188e11	−2.70631
$315$	2.20930e10	0.126432
$316$	−5.63675e10	−0.318007
$317$	−1.73974e11	−0.967647	−0.483823	−	0.875166i	$-0.660752\pi$
$317$	−1.73974e11	−0.967647	−0.483823	+	0.875166i	$0.660752\pi$
$318$	−1.11760e11	−0.612863
$319$	6.05926e10	0.327613
$320$	6.16735e9	0.0328794
$321$	1.54713e10	0.0813305
$322$	−8.77794e11	−4.55031
$323$	5.74303e10	0.293582
$324$	4.88056e10	0.246046
$325$	−2.33400e11	−1.16045
$326$	−3.85344e11	−1.88960
$327$	−1.22408e11	−0.592032
$328$	5.62629e9	0.0268405
$329$	3.56522e10	0.167766
$330$	−3.52515e10	−0.163631
$331$	1.01046e11	0.462692	0.231346	−	0.972872i	$-0.425687\pi$
$331$	1.01046e11	0.462692	0.231346	+	0.972872i	$0.425687\pi$
$332$	−6.02086e11	−2.71980
$333$	1.22289e11	0.544990
$334$	−3.66175e11	−1.61001
$335$	−6.32758e9	−0.0274496
$336$	−4.28433e11	−1.83382
$337$	−2.47111e11	−1.04366	−0.521828	−	0.853051i	$-0.674750\pi$
$337$	−2.47111e11	−1.04366	−0.521828	+	0.853051i	$0.674750\pi$
$338$	1.99314e11	0.830639
$339$	1.78152e10	0.0732642
$340$	−1.54586e11	−0.627358
$341$	1.42974e11	0.572616
$342$	3.16060e10	0.124926
$343$	−7.40157e11	−2.88736
$344$	2.43787e11	0.938636
$345$	−4.13650e10	−0.157198
$346$	2.81185e11	1.05475
$347$	−1.26269e11	−0.467536	−0.233768	−	0.972292i	$-0.575106\pi$
$347$	−1.26269e11	−0.467536	−0.233768	+	0.972292i	$0.575106\pi$
$348$	1.46231e11	0.534482
$349$	4.17641e11	1.50692	0.753458	−	0.657496i	$-0.228384\pi$
$349$	4.17641e11	1.50692	0.753458	+	0.657496i	$0.228384\pi$
$350$	9.07916e11	3.23400
$351$	6.62013e10	0.232801
$352$	1.92149e11	0.667107
$353$	3.55099e10	0.121720	0.0608602	−	0.998146i	$-0.480616\pi$
$353$	3.55099e10	0.121720	0.0608602	+	0.998146i	$0.480616\pi$
$354$	−3.98180e10	−0.134761
$355$	6.15569e10	0.205707
$356$	−1.72426e9	−0.00568953
$357$	−4.67934e11	−1.52468
$358$	7.72045e11	2.48410
$359$	3.59038e11	1.14082	0.570408	−	0.821362i	$-0.306785\pi$
$359$	3.59038e11	1.14082	0.570408	+	0.821362i	$0.306785\pi$
$360$	−4.66559e10	−0.146401
$361$	−3.08587e11	−0.956304
$362$	4.41628e11	1.35166
$363$	−7.37004e10	−0.222787
$364$	−1.68699e12	−5.03681
$365$	6.71576e10	0.198051
$366$	−4.64246e11	−1.35233
$367$	1.15361e11	0.331941	0.165971	−	0.986131i	$-0.446924\pi$
$367$	1.15361e11	0.331941	0.165971	+	0.986131i	$0.446924\pi$
$368$	8.02163e11	2.28007
$369$	1.46342e9	0.00410913
$370$	−2.13165e11	−0.591301
$371$	4.06242e11	1.11328
$372$	3.45047e11	0.934190
$373$	−4.98354e11	−1.33306	−0.666528	−	0.745480i	$-0.732220\pi$
$373$	−4.98354e11	−1.33306	−0.666528	+	0.745480i	$0.732220\pi$
$374$	7.46636e11	1.97327
$375$	8.73838e10	0.228187
$376$	−7.52904e10	−0.194265
$377$	1.98352e11	0.505709
$378$	−2.57521e11	−0.648782
$379$	3.12014e11	0.776780	0.388390	−	0.921495i	$-0.373031\pi$
$379$	3.12014e11	0.776780	0.388390	+	0.921495i	$0.373031\pi$
$380$	−3.79538e10	−0.0933746
$381$	3.09686e11	0.752937
$382$	8.22728e11	1.97684
$383$	2.71390e11	0.644466	0.322233	−	0.946660i	$-0.395567\pi$
$383$	2.71390e11	0.644466	0.322233	+	0.946660i	$0.395567\pi$
$384$	−2.81298e11	−0.660202
$385$	1.28138e11	0.297238
$386$	1.22437e11	0.280718
$387$	6.34099e10	0.143700
$388$	1.29315e12	2.89673
$389$	−4.06550e11	−0.900204	−0.450102	−	0.892977i	$-0.648612\pi$
$389$	−4.06550e11	−0.900204	−0.450102	+	0.892977i	$0.648612\pi$
$390$	−1.15397e11	−0.252583
$391$	8.76121e11	1.89570
$392$	2.58096e12	5.52071
$393$	−7.32119e9	−0.0154816
$394$	−8.23121e11	−1.72080
$395$	1.40156e10	0.0289685
$396$	2.83070e11	0.578449
$397$	−2.24286e11	−0.453153	−0.226576	−	0.973993i	$-0.572753\pi$
$397$	−2.24286e11	−0.453153	−0.226576	+	0.973993i	$0.572753\pi$
$398$	−4.46745e11	−0.892454
$399$	−1.14886e11	−0.226929
$400$	−8.29690e11	−1.62049
$401$	2.88476e11	0.557135	0.278568	−	0.960417i	$-0.410140\pi$
$401$	2.88476e11	0.557135	0.278568	+	0.960417i	$0.410140\pi$
$402$	7.37558e10	0.140857
$403$	4.68032e11	0.883900
$404$	4.56115e11	0.851840
$405$	−1.21354e10	−0.0224133
$406$	−7.71583e11	−1.40934
$407$	7.09270e11	1.28126
$408$	9.88182e11	1.76549
$409$	−7.08376e11	−1.25173	−0.625863	−	0.779933i	$-0.715253\pi$
$409$	−7.08376e11	−1.25173	−0.625863	+	0.779933i	$0.715253\pi$
$410$	−2.55092e9	−0.00445831
$411$	−5.32650e11	−0.920776
$412$	1.33408e12	2.28111
$413$	1.44737e11	0.244796
$414$	4.82161e11	0.806659
$415$	1.49707e11	0.247757
$416$	6.29006e11	1.02976
$417$	−3.89117e11	−0.630184
$418$	1.83313e11	0.293697
$419$	−2.04860e11	−0.324709	−0.162355	−	0.986732i	$-0.551909\pi$
$419$	−2.04860e11	−0.324709	−0.162355	+	0.986732i	$0.551909\pi$
$420$	3.09242e11	0.484927
$421$	−2.91573e11	−0.452353	−0.226176	−	0.974086i	$-0.572623\pi$
$421$	−2.91573e11	−0.452353	−0.226176	+	0.974086i	$0.572623\pi$
$422$	1.61317e12	2.47613
$423$	−1.95833e10	−0.0297409
$424$	−8.57902e11	−1.28911
$425$	−9.06186e11	−1.34731
$426$	−7.17522e11	−1.05558
$427$	1.68752e12	2.45653
$428$	2.16556e11	0.311942
$429$	3.83964e11	0.547309
$430$	−1.10531e11	−0.155911
$431$	−1.09016e12	−1.52175	−0.760874	−	0.648900i	$-0.775229\pi$
$431$	−1.09016e12	−1.52175	−0.760874	+	0.648900i	$0.775229\pi$
$432$	2.35333e11	0.325091
$433$	−1.27445e12	−1.74232	−0.871162	−	0.490997i	$-0.836633\pi$
$433$	−1.27445e12	−1.74232	−0.871162	+	0.490997i	$0.836633\pi$
$434$	−1.82063e12	−2.46330
$435$	−3.63599e10	−0.0486879
$436$	−1.71338e12	−2.27073
$437$	2.15104e11	0.282151
$438$	−7.82805e11	−1.01630
$439$	3.76534e11	0.483853	0.241926	−	0.970295i	$-0.422221\pi$
$439$	3.76534e11	0.483853	0.241926	+	0.970295i	$0.422221\pi$
$440$	−2.70602e11	−0.344186
$441$	6.71318e11	0.845191
$442$	2.44414e12	3.04597
$443$	−9.96474e11	−1.22928	−0.614638	−	0.788810i	$-0.710698\pi$
$443$	−9.96474e11	−1.22928	−0.614638	+	0.788810i	$0.710698\pi$
$444$	1.71172e12	2.09030
$445$	4.28731e8	0.000518281 0
$446$	2.94725e12	3.52704
$447$	2.92963e11	0.347079
$448$	2.61311e11	0.306483
$449$	1.48027e11	0.171883	0.0859416	−	0.996300i	$-0.472610\pi$
$449$	1.48027e11	0.171883	0.0859416	+	0.996300i	$0.472610\pi$
$450$	−4.98706e11	−0.573309
$451$	8.48776e9	0.00966047
$452$	2.49365e11	0.281004
$453$	1.03123e12	1.15058
$454$	1.18327e12	1.30717
$455$	4.19465e11	0.458822
$456$	2.42617e11	0.262772
$457$	−8.19298e11	−0.878657	−0.439328	−	0.898327i	$-0.644784\pi$
$457$	−8.19298e11	−0.878657	−0.439328	+	0.898327i	$0.644784\pi$
$458$	−2.85804e12	−3.03510
$459$	2.57030e11	0.270288
$460$	−5.78999e11	−0.602931
$461$	1.53125e12	1.57904	0.789518	−	0.613727i	$-0.210331\pi$
$461$	1.53125e12	1.57904	0.789518	+	0.613727i	$0.210331\pi$
$462$	−1.49361e12	−1.52527
$463$	−5.77069e11	−0.583598	−0.291799	−	0.956480i	$-0.594254\pi$
$463$	−5.77069e11	−0.583598	−0.291799	+	0.956480i	$0.594254\pi$
$464$	7.05103e11	0.706190
$465$	−8.57950e10	−0.0850989
$466$	−1.08204e12	−1.06293
$467$	−4.88015e11	−0.474796	−0.237398	−	0.971412i	$-0.576295\pi$
$467$	−4.88015e11	−0.474796	−0.237398	+	0.971412i	$0.576295\pi$
$468$	9.26640e11	0.892904
$469$	−2.68099e11	−0.255869
$470$	3.41362e10	0.0322682
$471$	−9.30808e11	−0.871497
$472$	−3.05655e11	−0.283461
$473$	3.67774e11	0.337836
$474$	−1.63369e11	−0.148651
$475$	−2.22485e11	−0.200530
$476$	−6.54981e12	−5.84787
$477$	−2.23144e11	−0.197357
$478$	−2.11011e12	−1.84876
$479$	2.02874e12	1.76083	0.880413	−	0.474207i	$-0.157265\pi$
$479$	2.02874e12	1.76083	0.880413	+	0.474207i	$0.157265\pi$
$480$	−1.15303e11	−0.0991415
$481$	2.32182e12	1.97777
$482$	3.77906e12	3.18913
$483$	−1.75264e12	−1.46531
$484$	−1.03161e12	−0.854496
$485$	−3.21539e11	−0.263874
$486$	1.41453e11	0.115013
$487$	−3.85405e11	−0.310482	−0.155241	−	0.987877i	$-0.549615\pi$
$487$	−3.85405e11	−0.310482	−0.155241	+	0.987877i	$0.549615\pi$
$488$	−3.56370e12	−2.84454
$489$	−7.69392e11	−0.608496
$490$	−1.17019e12	−0.917012
$491$	−5.78610e11	−0.449282	−0.224641	−	0.974442i	$-0.572121\pi$
$491$	−5.78610e11	−0.449282	−0.224641	+	0.974442i	$0.572121\pi$
$492$	2.04839e10	0.0157605
$493$	7.70112e11	0.587141
$494$	6.00082e11	0.453356
$495$	−7.03845e10	−0.0526931
$496$	1.66376e12	1.23431
$497$	2.60816e12	1.91748
$498$	−1.74502e12	−1.27136
$499$	−2.53831e12	−1.83271	−0.916353	−	0.400372i	$-0.868881\pi$
$499$	−2.53831e12	−1.83271	−0.916353	+	0.400372i	$0.868881\pi$
$500$	1.22314e12	0.875206
$501$	−7.31118e11	−0.518463
$502$	4.11030e11	0.288873
$503$	2.31730e12	1.61409	0.807043	−	0.590492i	$-0.201066\pi$
$503$	2.31730e12	1.61409	0.807043	+	0.590492i	$0.201066\pi$
$504$	−1.97681e12	−1.36467
$505$	−1.13412e11	−0.0775973
$506$	2.79651e12	1.89644
$507$	3.97957e11	0.267486
$508$	4.33476e12	2.88788
$509$	1.52851e12	1.00934	0.504671	−	0.863312i	$-0.331614\pi$
$509$	1.52851e12	1.00934	0.504671	+	0.863312i	$0.331614\pi$
$510$	−4.48035e11	−0.293256
$511$	2.84547e12	1.84612
$512$	−3.48301e12	−2.23996
$513$	6.31056e10	0.0402290
$514$	−4.02509e12	−2.54356
$515$	−3.31716e11	−0.207795
$516$	8.87567e11	0.551160
$517$	−1.13582e11	−0.0699202
$518$	−9.03181e12	−5.51177
$519$	5.61424e11	0.339655
$520$	−8.85825e11	−0.531292
$521$	−5.49591e11	−0.326791	−0.163396	−	0.986561i	$-0.552245\pi$
$521$	−5.49591e11	−0.326791	−0.163396	+	0.986561i	$0.552245\pi$
$522$	4.23820e11	0.249841
$523$	−1.21125e12	−0.707905	−0.353953	−	0.935263i	$-0.615163\pi$
$523$	−1.21125e12	−0.707905	−0.353953	+	0.935263i	$0.615163\pi$
$524$	−1.02477e11	−0.0593793
$525$	1.81278e12	1.04142
$526$	−4.25552e12	−2.42391
$527$	1.81716e12	1.02623
$528$	1.36492e12	0.764282
$529$	1.48034e12	0.821884
$530$	3.88967e11	0.214127
$531$	−7.95020e10	−0.0433963
$532$	−1.60810e12	−0.870384
$533$	2.77850e10	0.0149121
$534$	−4.99739e9	−0.00265955
$535$	−5.38461e10	−0.0284159
$536$	5.66172e11	0.296283
$537$	1.54149e12	0.799940
$538$	−5.66340e12	−2.91445
$539$	3.89361e12	1.98702
$540$	−1.69862e11	−0.0859657
$541$	−1.18365e12	−0.594067	−0.297033	−	0.954867i	$-0.595997\pi$
$541$	−1.18365e12	−0.594067	−0.297033	+	0.954867i	$0.595997\pi$
$542$	−1.99483e12	−0.992908
$543$	8.81771e11	0.435268
$544$	2.44215e12	1.19557
$545$	4.26028e11	0.206849
$546$	−4.88938e12	−2.35444
$547$	−1.81035e12	−0.864609	−0.432305	−	0.901728i	$-0.642300\pi$
$547$	−1.81035e12	−0.864609	−0.432305	+	0.901728i	$0.642300\pi$
$548$	−7.45567e12	−3.53162
$549$	−9.26930e11	−0.435483
$550$	−2.89247e12	−1.34784
$551$	1.89077e11	0.0873888
$552$	3.70121e12	1.69675
$553$	5.93841e11	0.270027
$554$	−1.35899e12	−0.612946
$555$	−4.25614e11	−0.190413
$556$	−5.44658e12	−2.41706
$557$	2.97827e12	1.31104	0.655519	−	0.755178i	$-0.272450\pi$
$557$	2.97827e12	1.31104	0.655519	+	0.755178i	$0.272450\pi$
$558$	1.00005e12	0.436683
$559$	1.20392e12	0.521489
$560$	1.49111e12	0.640715
$561$	1.49076e12	0.635440
$562$	7.46356e12	3.15597
$563$	1.21487e12	0.509616	0.254808	−	0.966992i	$-0.417988\pi$
$563$	1.21487e12	0.509616	0.254808	+	0.966992i	$0.417988\pi$
$564$	−2.74113e11	−0.114071
$565$	−6.20038e10	−0.0255977
$566$	−3.90211e12	−1.59818
$567$	−5.14175e11	−0.208924
$568$	−5.50792e12	−2.22034
$569$	4.43625e12	1.77423	0.887116	−	0.461546i	$-0.152705\pi$
$569$	4.43625e12	1.77423	0.887116	+	0.461546i	$0.152705\pi$
$570$	−1.10001e11	−0.0436476
$571$	−7.36560e11	−0.289965	−0.144983	−	0.989434i	$-0.546313\pi$
$571$	−7.36560e11	−0.289965	−0.144983	+	0.989434i	$0.546313\pi$
$572$	5.37446e12	2.09920
$573$	1.64269e12	0.636590
$574$	−1.08083e11	−0.0415578
$575$	−3.39410e12	−1.29485
$576$	−1.43534e11	−0.0543319
$577$	−3.15376e12	−1.18451	−0.592253	−	0.805752i	$-0.701761\pi$
$577$	−3.15376e12	−1.18451	−0.592253	+	0.805752i	$0.701761\pi$
$578$	4.67859e12	1.74357
$579$	2.44462e11	0.0903980
$580$	−5.08941e11	−0.186742
$581$	6.34308e12	2.30945
$582$	3.74793e12	1.35406
$583$	−1.29422e12	−0.463981
$584$	−6.00905e12	−2.13771
$585$	−2.30406e11	−0.0813379
$586$	−8.24549e12	−2.88853
$587$	−5.09156e12	−1.77002	−0.885012	−	0.465567i	$-0.845850\pi$
$587$	−5.09156e12	−1.77002	−0.885012	+	0.465567i	$0.845850\pi$
$588$	9.39664e12	3.24171
$589$	4.46146e11	0.152742
$590$	1.38582e11	0.0470840
$591$	−1.64347e12	−0.554139
$592$	8.25362e12	2.76183
$593$	3.55550e12	1.18074	0.590371	−	0.807132i	$-0.298982\pi$
$593$	3.55550e12	1.18074	0.590371	+	0.807132i	$0.298982\pi$
$594$	8.20418e11	0.270394
$595$	1.62859e12	0.532704
$596$	4.10069e12	1.33122
$597$	−8.91987e11	−0.287392
$598$	9.15447e12	2.92737
$599$	−2.80603e12	−0.890576	−0.445288	−	0.895387i	$-0.646899\pi$
$599$	−2.80603e12	−0.890576	−0.445288	+	0.895387i	$0.646899\pi$
$600$	−3.82822e12	−1.20591
$601$	3.34060e12	1.04446	0.522228	−	0.852806i	$-0.325101\pi$
$601$	3.34060e12	1.04446	0.522228	+	0.852806i	$0.325101\pi$
$602$	−4.68321e12	−1.45331
$603$	1.47263e11	0.0453594
$604$	1.44345e13	4.41302
$605$	2.56506e11	0.0778393
$606$	1.32195e12	0.398189
$607$	5.25103e12	1.56998	0.784992	−	0.619506i	$-0.212667\pi$
$607$	5.25103e12	1.56998	0.784992	+	0.619506i	$0.212667\pi$
$608$	5.99592e11	0.177947
$609$	−1.54057e12	−0.453841
$610$	1.61576e12	0.472489
$611$	−3.71815e11	−0.107930
$612$	3.59772e12	1.03668
$613$	−3.05318e11	−0.0873335	−0.0436668	−	0.999046i	$-0.513904\pi$
$613$	−3.05318e11	−0.0873335	−0.0436668	+	0.999046i	$0.513904\pi$
$614$	3.03257e12	0.861100
$615$	−5.09327e9	−0.00143568
$616$	−1.14654e13	−3.20831
$617$	−3.46151e12	−0.961572	−0.480786	−	0.876838i	$-0.659649\pi$
$617$	−3.46151e12	−0.961572	−0.480786	+	0.876838i	$0.659649\pi$
$618$	3.86656e12	1.06629
$619$	4.23333e11	0.115897	0.0579487	−	0.998320i	$-0.481544\pi$
$619$	4.23333e11	0.115897	0.0579487	+	0.998320i	$0.481544\pi$
$620$	−1.20090e12	−0.326395
$621$	9.62699e11	0.259764
$622$	−5.79490e12	−1.55235
$623$	1.81653e10	0.00483111
$624$	4.46811e12	1.17976
$625$	3.35534e12	0.879583
$626$	1.29214e13	3.36298
$627$	3.66009e11	0.0945775
$628$	−1.30288e13	−3.34261
$629$	9.01459e12	2.29624
$630$	8.96272e11	0.226677
$631$	5.83317e12	1.46478	0.732390	−	0.680886i	$-0.238405\pi$
$631$	5.83317e12	1.46478	0.732390	+	0.680886i	$0.238405\pi$
$632$	−1.25407e12	−0.312677
$633$	3.22091e12	0.797373
$634$	−7.05780e12	−1.73487
$635$	−1.07783e12	−0.263068
$636$	−3.12341e12	−0.756957
$637$	1.27459e13	3.06720
$638$	2.45813e12	0.587371
$639$	−1.43263e12	−0.339923
$640$	9.79028e11	0.230667
$641$	−3.63777e12	−0.851087	−0.425543	−	0.904938i	$-0.639917\pi$
$641$	−3.63777e12	−0.851087	−0.425543	+	0.904938i	$0.639917\pi$
$642$	6.27642e11	0.145816
$643$	4.65808e12	1.07463	0.537313	−	0.843383i	$-0.319439\pi$
$643$	4.65808e12	1.07463	0.537313	+	0.843383i	$0.319439\pi$
$644$	−2.45322e13	−5.62017
$645$	−2.20691e11	−0.0502072
$646$	2.32985e12	0.526358
$647$	3.10601e11	0.0696841	0.0348421	−	0.999393i	$-0.488907\pi$
$647$	3.10601e11	0.0696841	0.0348421	+	0.999393i	$0.488907\pi$
$648$	1.08583e12	0.241922
$649$	−4.61108e11	−0.102024
$650$	−9.46861e12	−2.08054
$651$	−3.63513e12	−0.793242
$652$	−1.07694e13	−2.33388
$653$	−3.77027e12	−0.811452	−0.405726	−	0.913995i	$-0.632981\pi$
$653$	−3.77027e12	−0.811452	−0.405726	+	0.913995i	$0.632981\pi$
$654$	−4.96588e12	−1.06144
$655$	2.54806e10	0.00540908
$656$	9.87702e10	0.0208237
$657$	−1.56298e12	−0.327272
$658$	1.44635e12	0.300785
$659$	−7.34637e12	−1.51736	−0.758680	−	0.651463i	$-0.774155\pi$
$659$	−7.34637e12	−1.51736	−0.758680	+	0.651463i	$0.774155\pi$
$660$	−9.85193e11	−0.202103
$661$	−1.83465e12	−0.373806	−0.186903	−	0.982378i	$-0.559845\pi$
$661$	−1.83465e12	−0.373806	−0.186903	+	0.982378i	$0.559845\pi$
$662$	4.09924e12	0.829550
$663$	4.88006e12	0.980876
$664$	−1.33953e13	−2.67422
$665$	3.99850e11	0.0792865
$666$	4.96105e12	0.977102
$667$	2.88444e12	0.564280
$668$	−1.02337e13	−1.98855
$669$	5.88459e12	1.13579
$670$	−2.56699e11	−0.0492138
$671$	−5.37615e12	−1.02381
$672$	−4.88539e12	−0.924140
$673$	−5.91558e12	−1.11155	−0.555776	−	0.831332i	$-0.687579\pi$
$673$	−5.91558e12	−1.11155	−0.555776	+	0.831332i	$0.687579\pi$
$674$	−1.00248e13	−1.87115
$675$	−9.95735e11	−0.184619
$676$	5.57033e12	1.02594
$677$	2.97452e12	0.544212	0.272106	−	0.962267i	$-0.412280\pi$
$677$	2.97452e12	0.544212	0.272106	+	0.962267i	$0.412280\pi$
$678$	7.22731e11	0.131354
$679$	−1.36236e13	−2.45968
$680$	−3.43926e12	−0.616843
$681$	2.36256e12	0.420941
$682$	5.80022e12	1.02663
$683$	1.10993e13	1.95166	0.975830	−	0.218529i	$-0.0701259\pi$
$683$	1.10993e13	1.95166	0.975830	+	0.218529i	$0.0701259\pi$
$684$	8.83308e11	0.154298
$685$	1.85383e12	0.321709
$686$	−3.00269e13	−5.17668
$687$	−5.70646e12	−0.977375
$688$	4.27970e12	0.728225
$689$	−4.23668e12	−0.716208
$690$	−1.67811e12	−0.281837
$691$	1.92510e12	0.321219	0.160609	−	0.987018i	$-0.448654\pi$
$691$	1.92510e12	0.321219	0.160609	+	0.987018i	$0.448654\pi$
$692$	7.85841e12	1.30274
$693$	−2.98219e12	−0.491174
$694$	−5.12252e12	−0.838236
$695$	1.35428e12	0.220179
$696$	3.25337e12	0.525524
$697$	1.07877e11	0.0173133
$698$	1.69430e13	2.70172
$699$	−2.16043e12	−0.342290
$700$	2.53740e13	3.99437
$701$	8.67559e12	1.35696	0.678481	−	0.734618i	$-0.262639\pi$
$701$	8.67559e12	1.35696	0.678481	+	0.734618i	$0.262639\pi$
$702$	2.68567e12	0.417384
$703$	2.21325e12	0.341768
$704$	−8.32492e11	−0.127733
$705$	6.81575e10	0.0103911
$706$	1.44057e12	0.218230
$707$	−4.80525e12	−0.723317
$708$	−1.11281e12	−0.166446
$709$	−8.64020e11	−0.128415	−0.0642075	−	0.997937i	$-0.520452\pi$
$709$	−8.64020e11	−0.128415	−0.0642075	+	0.997937i	$0.520452\pi$
$710$	2.49725e12	0.368808
$711$	−3.26189e11	−0.0478692
$712$	−3.83615e10	−0.00559417
$713$	6.80612e12	0.986273
$714$	−1.89833e13	−2.73356
$715$	−1.33634e12	−0.191224
$716$	2.15768e13	3.06816
$717$	−4.21313e12	−0.595345
$718$	1.45655e13	2.04534
$719$	−1.29472e13	−1.80674	−0.903369	−	0.428864i	$-0.858914\pi$
$719$	−1.29472e13	−1.80674	−0.903369	+	0.428864i	$0.858914\pi$
$720$	−8.19049e11	−0.113583
$721$	−1.40548e13	−1.93694
$722$	−1.25188e13	−1.71454
$723$	7.54542e12	1.02698
$724$	1.23424e13	1.66946
$725$	−2.98342e12	−0.401045
$726$	−2.98990e12	−0.399431
$727$	−8.51037e11	−0.112991	−0.0564955	−	0.998403i	$-0.517993\pi$
$727$	−8.51037e11	−0.112991	−0.0564955	+	0.998403i	$0.517993\pi$
$728$	−3.75324e13	−4.95239
$729$	2.82430e11	0.0370370
$730$	2.72447e12	0.355082
$731$	4.67429e12	0.605462
$732$	−1.29745e13	−1.67029
$733$	7.42264e12	0.949709	0.474855	−	0.880064i	$-0.342501\pi$
$733$	7.42264e12	0.949709	0.474855	+	0.880064i	$0.342501\pi$
$734$	4.67999e12	0.595131
$735$	−2.33645e12	−0.295300
$736$	9.14700e12	1.14902
$737$	8.54120e11	0.106639
$738$	5.93683e10	0.00736718
$739$	5.31381e12	0.655399	0.327700	−	0.944782i	$-0.393727\pi$
$739$	5.31381e12	0.655399	0.327700	+	0.944782i	$0.393727\pi$
$740$	−5.95744e12	−0.730326
$741$	1.19815e12	0.145991
$742$	1.64805e13	1.99597
$743$	1.03262e13	1.24306	0.621529	−	0.783391i	$-0.286512\pi$
$743$	1.03262e13	1.24306	0.621529	+	0.783391i	$0.286512\pi$
$744$	7.67667e12	0.918533
$745$	−1.01963e12	−0.121266
$746$	−2.02174e13	−2.39001
$747$	−3.48417e12	−0.409408
$748$	2.08666e13	2.43722
$749$	−2.28146e12	−0.264877
$750$	3.54501e12	0.409111
$751$	−9.37694e12	−1.07568	−0.537838	−	0.843048i	$-0.680759\pi$
$751$	−9.37694e12	−1.07568	−0.537838	+	0.843048i	$0.680759\pi$
$752$	−1.32173e12	−0.150717
$753$	8.20677e11	0.0930240
$754$	8.04679e12	0.906675
$755$	−3.58910e12	−0.401998
$756$	−7.19706e12	−0.801322
$757$	−1.35880e13	−1.50392	−0.751960	−	0.659208i	$-0.770892\pi$
$757$	−1.35880e13	−1.50392	−0.751960	+	0.659208i	$0.770892\pi$
$758$	1.26579e13	1.39267
$759$	5.58361e12	0.610698
$760$	−8.44402e11	−0.0918096
$761$	2.78203e12	0.300698	0.150349	−	0.988633i	$-0.451960\pi$
$761$	2.78203e12	0.300698	0.150349	+	0.988633i	$0.451960\pi$
$762$	1.25634e13	1.34993
$763$	1.80508e13	1.92813
$764$	2.29932e13	2.44163
$765$	−8.94564e11	−0.0944354
$766$	1.10098e13	1.15545
$767$	−1.50945e12	−0.157485
$768$	−1.05045e13	−1.08956
$769$	−1.13304e13	−1.16836	−0.584180	−	0.811624i	$-0.698584\pi$
$769$	−1.13304e13	−1.16836	−0.584180	+	0.811624i	$0.698584\pi$
$770$	5.19833e12	0.532912
$771$	−8.03665e12	−0.819087
$772$	3.42181e12	0.346720
$773$	2.73666e12	0.275685	0.137842	−	0.990454i	$-0.455983\pi$
$773$	2.73666e12	0.275685	0.137842	+	0.990454i	$0.455983\pi$
$774$	2.57243e12	0.257637
$775$	−7.03968e12	−0.700963
$776$	2.87703e13	2.84818
$777$	−1.80332e13	−1.77492
$778$	−1.64930e13	−1.61396
$779$	2.64857e10	0.00257687
$780$	−3.22507e12	−0.311970
$781$	−8.30918e12	−0.799150
$782$	3.55427e13	3.39875
$783$	8.46214e11	0.0804549
$784$	4.53091e13	4.28315
$785$	3.23957e12	0.304491
$786$	−2.97008e11	−0.0277566
$787$	3.43999e12	0.319647	0.159824	−	0.987146i	$-0.448907\pi$
$787$	3.43999e12	0.319647	0.159824	+	0.987146i	$0.448907\pi$
$788$	−2.30042e13	−2.12539
$789$	−8.49673e12	−0.780558
$790$	5.68589e11	0.0519369
$791$	−2.62710e12	−0.238607
$792$	6.29778e12	0.568754
$793$	−1.75990e13	−1.58037
$794$	−9.09888e12	−0.812448
$795$	7.76626e11	0.0689541
$796$	−1.24854e13	−1.10229
$797$	1.68943e13	1.48313	0.741564	−	0.670882i	$-0.234084\pi$
$797$	1.68943e13	1.48313	0.741564	+	0.670882i	$0.234084\pi$
$798$	−4.66074e12	−0.406857
$799$	−1.44359e12	−0.125309
$800$	−9.46089e12	−0.816633
$801$	−9.97798e9	−0.000856438 0
$802$	1.17030e13	0.998876
$803$	−9.06518e12	−0.769408
$804$	2.06129e12	0.173975
$805$	6.09985e12	0.511962
$806$	1.89872e13	1.58473
$807$	−1.13077e13	−0.938524
$808$	1.01477e13	0.837563
$809$	−7.90565e12	−0.648887	−0.324444	−	0.945905i	$-0.605177\pi$
$809$	−7.90565e12	−0.648887	−0.324444	+	0.945905i	$0.605177\pi$
$810$	−4.92310e11	−0.0401843
$811$	−1.91135e13	−1.55148	−0.775740	−	0.631053i	$-0.782623\pi$
$811$	−1.91135e13	−1.55148	−0.775740	+	0.631053i	$0.782623\pi$
$812$	−2.15638e13	−1.74070
$813$	−3.98295e12	−0.319740
$814$	2.87738e13	2.29714
$815$	2.67778e12	0.212601
$816$	1.73476e13	1.36973
$817$	1.14762e12	0.0901157
$818$	−2.87376e13	−2.24419
$819$	−9.76231e12	−0.758185
$820$	−7.12920e10	−0.00550654
$821$	2.51585e10	0.00193260	0.000966298	−	1.00000i	$-0.499692\pi$
$821$	2.51585e10	0.00193260	0.000966298		1.00000i	$0.499692\pi$
$822$	−2.16087e13	−1.65084
$823$	6.43524e12	0.488951	0.244475	−	0.969655i	$-0.421384\pi$
$823$	6.43524e12	0.488951	0.244475	+	0.969655i	$0.421384\pi$
$824$	2.96809e13	2.24288
$825$	−5.77521e12	−0.434035
$826$	5.87172e12	0.438889
$827$	1.22657e13	0.911841	0.455920	−	0.890021i	$-0.349310\pi$
$827$	1.22657e13	0.911841	0.455920	+	0.890021i	$0.349310\pi$
$828$	1.34752e13	0.996319
$829$	5.05540e12	0.371758	0.185879	−	0.982573i	$-0.440487\pi$
$829$	5.05540e12	0.371758	0.185879	+	0.982573i	$0.440487\pi$
$830$	6.07335e12	0.444198
$831$	−2.71341e12	−0.197383
$832$	−2.72519e12	−0.197171
$833$	4.94865e13	3.56110
$834$	−1.57858e13	−1.12984
$835$	2.54457e12	0.181145
$836$	5.12314e12	0.362750
$837$	1.99673e12	0.140622
$838$	−8.31081e12	−0.582164
$839$	−1.26668e13	−0.882550	−0.441275	−	0.897372i	$-0.645474\pi$
$839$	−1.26668e13	−0.882550	−0.441275	+	0.897372i	$0.645474\pi$
$840$	6.88007e12	0.476800
$841$	−1.19717e13	−0.825229
$842$	−1.18286e13	−0.811014
$843$	1.49020e13	1.01630
$844$	4.50840e13	3.05831
$845$	−1.38505e12	−0.0934564
$846$	−7.94460e11	−0.0533218
$847$	1.08682e13	0.725572
$848$	−1.50606e13	−1.00014
$849$	−7.79109e12	−0.514652
$850$	−3.67623e13	−2.41556
$851$	3.37639e13	2.20684
$852$	−2.00529e13	−1.30377
$853$	2.09793e13	1.35681	0.678406	−	0.734687i	$-0.262671\pi$
$853$	2.09793e13	1.35681	0.678406	+	0.734687i	$0.262671\pi$
$854$	6.84596e13	4.40427
$855$	−2.19632e11	−0.0140556
$856$	4.81798e12	0.306714
$857$	−2.21766e13	−1.40437	−0.702186	−	0.711993i	$-0.747793\pi$
$857$	−2.21766e13	−1.40437	−0.702186	+	0.711993i	$0.747793\pi$
$858$	1.55767e13	0.981260
$859$	−3.66631e12	−0.229753	−0.114876	−	0.993380i	$-0.536647\pi$
$859$	−3.66631e12	−0.229753	−0.114876	+	0.993380i	$0.536647\pi$
$860$	−3.08908e12	−0.192569
$861$	−2.15802e11	−0.0133826
$862$	−4.42259e13	−2.72831
$863$	−6.55735e12	−0.402420	−0.201210	−	0.979548i	$-0.564487\pi$
$863$	−6.55735e12	−0.402420	−0.201210	+	0.979548i	$0.564487\pi$
$864$	2.68348e12	0.163827
$865$	−1.95397e12	−0.118671
$866$	−5.17023e13	−3.12378
$867$	9.34145e12	0.561472
$868$	−5.08821e13	−3.04247
$869$	−1.89188e12	−0.112539
$870$	−1.47506e12	−0.0872916
$871$	2.79600e12	0.164609
$872$	−3.81196e13	−2.23267
$873$	7.48326e12	0.436040
$874$	8.72639e12	0.505863
$875$	−1.28860e13	−0.743157
$876$	−2.18774e13	−1.25524
$877$	9.97574e12	0.569438	0.284719	−	0.958611i	$-0.408100\pi$
$877$	9.97574e12	0.569438	0.284719	+	0.958611i	$0.408100\pi$
$878$	1.52753e13	0.867490
$879$	−1.64632e13	−0.930177
$880$	−4.75044e12	−0.267031
$881$	2.65054e12	0.148232	0.0741160	−	0.997250i	$-0.476386\pi$
$881$	2.65054e12	0.148232	0.0741160	+	0.997250i	$0.476386\pi$
$882$	2.72342e13	1.51533
$883$	−2.56410e13	−1.41942	−0.709710	−	0.704494i	$-0.751174\pi$
$883$	−2.56410e13	−1.41942	−0.709710	+	0.704494i	$0.751174\pi$
$884$	6.83076e13	3.76213
$885$	2.76698e11	0.0151622
$886$	−4.04252e13	−2.20394
$887$	−2.79022e13	−1.51350	−0.756748	−	0.653706i	$-0.773213\pi$
$887$	−2.79022e13	−1.51350	−0.756748	+	0.653706i	$0.773213\pi$
$888$	3.80826e13	2.05527
$889$	−4.56675e13	−2.45216
$890$	1.73929e10	0.000929215 0
$891$	1.63808e12	0.0870732
$892$	8.23683e13	4.35631
$893$	−3.54428e11	−0.0186508
$894$	1.18850e13	0.622272
$895$	−5.36500e12	−0.279490
$896$	4.14814e13	2.15014
$897$	1.82781e13	0.942684
$898$	6.00521e12	0.308166
$899$	5.98259e12	0.305472
$900$	−1.39376e13	−0.708103
$901$	−1.64491e13	−0.831536
$902$	3.44333e11	0.0173201
$903$	−9.35067e12	−0.468002
$904$	5.54791e12	0.276294
$905$	−3.06891e12	−0.152078
$906$	4.18354e13	2.06285
$907$	3.50674e12	0.172056	0.0860282	−	0.996293i	$-0.472582\pi$
$907$	3.50674e12	0.172056	0.0860282	+	0.996293i	$0.472582\pi$
$908$	3.30695e13	1.61451
$909$	2.63946e12	0.128226
$910$	1.70169e13	0.822612
$911$	2.04657e13	0.984452	0.492226	−	0.870467i	$-0.336183\pi$
$911$	2.04657e13	0.984452	0.492226	+	0.870467i	$0.336183\pi$
$912$	4.25917e12	0.203868
$913$	−2.02080e13	−0.962509
$914$	−3.32375e13	−1.57533
$915$	3.22608e12	0.152153
$916$	−7.98750e13	−3.74870
$917$	1.07961e12	0.0504203
$918$	1.04272e13	0.484593
$919$	2.10812e13	0.974935	0.487468	−	0.873141i	$-0.337921\pi$
$919$	2.10812e13	0.974935	0.487468	+	0.873141i	$0.337921\pi$
$920$	−1.28817e13	−0.592825
$921$	6.05494e12	0.277295
$922$	6.21201e13	2.83102
$923$	−2.72004e13	−1.23358
$924$	−4.17426e13	−1.88389
$925$	−3.49226e13	−1.56844
$926$	−2.34107e13	−1.04632
$927$	7.72012e12	0.343372
$928$	8.04023e12	0.355879
$929$	2.79571e13	1.23146	0.615731	−	0.787956i	$-0.288861\pi$
$929$	2.79571e13	1.23146	0.615731	+	0.787956i	$0.288861\pi$
$930$	−3.48055e12	−0.152572
$931$	1.21499e13	0.530027
$932$	−3.02402e13	−1.31285
$933$	−1.15703e13	−0.499894
$934$	−1.97979e13	−0.851252
$935$	−5.18842e12	−0.222015
$936$	2.06160e13	0.877938
$937$	−1.17695e13	−0.498804	−0.249402	−	0.968400i	$-0.580234\pi$
$937$	−1.17695e13	−0.498804	−0.249402	+	0.968400i	$0.580234\pi$
$938$	−1.08763e13	−0.458743
$939$	2.57993e13	1.08296
$940$	9.54021e11	0.0398550
$941$	3.95533e13	1.64448	0.822242	−	0.569137i	$-0.192723\pi$
$941$	3.95533e13	1.64448	0.822242	+	0.569137i	$0.192723\pi$
$942$	−3.77612e13	−1.56249
$943$	4.04049e11	0.0166392
$944$	−5.36581e12	−0.219918
$945$	1.78953e12	0.0729955
$946$	1.49199e13	0.605699
$947$	2.61668e13	1.05724	0.528622	−	0.848857i	$-0.322709\pi$
$947$	2.61668e13	1.05724	0.528622	+	0.848857i	$0.322709\pi$
$948$	−4.56577e12	−0.183601
$949$	−2.96752e13	−1.18767
$950$	−9.02584e12	−0.359527
$951$	−1.40919e13	−0.558671
$952$	−1.45721e14	−5.74986
$953$	−4.58939e13	−1.80234	−0.901170	−	0.433466i	$-0.857290\pi$
$953$	−4.58939e13	−1.80234	−0.901170	+	0.433466i	$0.857290\pi$
$954$	−9.05254e12	−0.353836
$955$	−5.71720e12	−0.222417
$956$	−5.89725e13	−2.28344
$957$	4.90800e12	0.189148
$958$	8.23024e13	3.15695
$959$	7.85468e13	2.99878
$960$	4.99556e11	0.0189829
$961$	−1.23231e13	−0.466083
$962$	9.41923e13	3.54591
$963$	1.25317e12	0.0469562
$964$	1.05615e14	3.93895
$965$	−8.50825e11	−0.0315840
$966$	−7.11013e13	−2.62712
$967$	−3.95626e13	−1.45501	−0.727505	−	0.686102i	$-0.759320\pi$
$967$	−3.95626e13	−1.45501	−0.727505	+	0.686102i	$0.759320\pi$
$968$	−2.29514e13	−0.840175
$969$	4.65186e12	0.169500
$970$	−1.30443e13	−0.473093
$971$	−4.07858e13	−1.47239	−0.736195	−	0.676770i	$-0.763379\pi$
$971$	−4.07858e13	−1.47239	−0.736195	+	0.676770i	$0.763379\pi$
$972$	3.95325e12	0.142055
$973$	5.73807e13	2.05238
$974$	−1.56352e13	−0.556657
$975$	−1.89054e13	−0.669984
$976$	−6.25611e13	−2.20689
$977$	1.36935e13	0.480828	0.240414	−	0.970670i	$-0.422717\pi$
$977$	1.36935e13	0.480828	0.240414	+	0.970670i	$0.422717\pi$
$978$	−3.12129e13	−1.09096
$979$	−5.78717e10	−0.00201347
$980$	−3.27040e13	−1.13262
$981$	−9.91506e12	−0.341810
$982$	−2.34732e13	−0.805509
$983$	3.07077e13	1.04895	0.524477	−	0.851424i	$-0.324261\pi$
$983$	3.07077e13	1.04895	0.524477	+	0.851424i	$0.324261\pi$
$984$	4.55730e11	0.0154964
$985$	5.71993e12	0.193610
$986$	3.12421e13	1.05267
$987$	2.88783e12	0.0968600
$988$	1.67708e13	0.559948
$989$	1.75074e13	0.581888
$990$	−2.85537e12	−0.0944723
$991$	7.26101e12	0.239147	0.119574	−	0.992825i	$-0.461847\pi$
$991$	7.26101e12	0.239147	0.119574	+	0.992825i	$0.461847\pi$
$992$	1.89718e13	0.622021
$993$	8.18470e12	0.267135
$994$	1.05809e14	3.43781
$995$	3.10446e12	0.100411
$996$	−4.87690e13	−1.57028
$997$	3.20796e13	1.02826	0.514128	−	0.857714i	$-0.328116\pi$
$997$	3.20796e13	1.02826	0.514128	+	0.857714i	$0.328116\pi$
$998$	−1.02975e14	−3.28582
$999$	9.90542e12	0.314650

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.d.1.20	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.d.1.20	✓	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)

\(f(q)\)	\(=\)	\(q+40.5682 q^{2} +81.0000 q^{3} +1133.78 q^{4} -281.912 q^{5} +3286.03 q^{6} -11944.6 q^{7} +25224.6 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+40.5682 q^{2} +81.0000 q^{3} +1133.78 q^{4} -281.912 q^{5} +3286.03 q^{6} -11944.6 q^{7} +25224.6 q^{8} +6561.00 q^{9} -11436.7 q^{10} +38053.5 q^{11} +91836.3 q^{12} +124569. q^{13} -484571. q^{14} -22834.8 q^{15} +442820. q^{16} +483647. q^{17} +266168. q^{18} +118744. q^{19} -319626. q^{20} -967511. q^{21} +1.54376e6 q^{22} +1.81149e6 q^{23} +2.04319e6 q^{24} -1.87365e6 q^{25} +5.05356e6 q^{26} +531441. q^{27} -1.35425e7 q^{28} +1.59230e6 q^{29} -926369. q^{30} +3.75720e6 q^{31} +5.04944e6 q^{32} +3.08233e6 q^{33} +1.96207e7 q^{34} +3.36732e6 q^{35} +7.43874e6 q^{36} +1.86388e7 q^{37} +4.81725e6 q^{38} +1.00901e7 q^{39} -7.11109e6 q^{40} +223048. q^{41} -3.92502e7 q^{42} +9.66466e6 q^{43} +4.31443e7 q^{44} -1.84962e6 q^{45} +7.34889e7 q^{46} -2.98480e6 q^{47} +3.58684e7 q^{48} +1.02320e8 q^{49} -7.60107e7 q^{50} +3.91754e7 q^{51} +1.41235e8 q^{52} -3.40106e7 q^{53} +2.15596e7 q^{54} -1.07277e7 q^{55} -3.01297e8 q^{56} +9.61829e6 q^{57} +6.45968e7 q^{58} -1.21174e7 q^{59} -2.58897e7 q^{60} -1.41279e8 q^{61} +1.52423e8 q^{62} -7.83684e7 q^{63} -2.18769e7 q^{64} -3.51176e7 q^{65} +1.25045e8 q^{66} +2.24453e7 q^{67} +5.48350e8 q^{68} +1.46731e8 q^{69} +1.36606e8 q^{70} -2.18355e8 q^{71} +1.65498e8 q^{72} -2.38222e8 q^{73} +7.56143e8 q^{74} -1.51766e8 q^{75} +1.34630e8 q^{76} -4.54533e8 q^{77} +4.09339e8 q^{78} -4.97164e7 q^{79} -1.24836e8 q^{80} +4.30467e7 q^{81} +9.04867e6 q^{82} -5.31042e8 q^{83} -1.09695e9 q^{84} -1.36346e8 q^{85} +3.92078e8 q^{86} +1.28976e8 q^{87} +9.59882e8 q^{88} -1.52080e6 q^{89} -7.50359e7 q^{90} -1.48793e9 q^{91} +2.05383e9 q^{92} +3.04333e8 q^{93} -1.21088e8 q^{94} -3.34754e7 q^{95} +4.09005e8 q^{96} +1.14057e9 q^{97} +4.15092e9 q^{98} +2.49669e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9}+O(q^{10}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more