LMFDB - Embedded newform 177.10.a.d.1.12

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			1.12
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)

$f(q)$	$=$	$q+1.23437 q^{2} +81.0000 q^{3} -510.476 q^{4} -1722.16 q^{5} +99.9839 q^{6} +4577.43 q^{7} -1262.11 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+1.23437 q^{2} +81.0000 q^{3} -510.476 q^{4} -1722.16 q^{5} +99.9839 q^{6} +4577.43 q^{7} -1262.11 q^{8} +6561.00 q^{9} -2125.78 q^{10} -75628.8 q^{11} -41348.6 q^{12} -128893. q^{13} +5650.24 q^{14} -139495. q^{15} +259806. q^{16} -7944.95 q^{17} +8098.70 q^{18} -291562. q^{19} +879120. q^{20} +370772. q^{21} -93353.9 q^{22} -586180. q^{23} -102231. q^{24} +1.01270e6 q^{25} -159102. q^{26} +531441. q^{27} -2.33667e6 q^{28} -4.07295e6 q^{29} -172188. q^{30} -2.85910e6 q^{31} +966899. q^{32} -6.12593e6 q^{33} -9807.01 q^{34} -7.88305e6 q^{35} -3.34924e6 q^{36} -1.13923e7 q^{37} -359895. q^{38} -1.04403e7 q^{39} +2.17356e6 q^{40} +2.10328e7 q^{41} +457669. q^{42} -1.69667e7 q^{43} +3.86067e7 q^{44} -1.12991e7 q^{45} -723563. q^{46} +2.55397e7 q^{47} +2.10443e7 q^{48} -1.94007e7 q^{49} +1.25004e6 q^{50} -643541. q^{51} +6.57969e7 q^{52} +4.62154e7 q^{53} +655995. q^{54} +1.30245e8 q^{55} -5.77724e6 q^{56} -2.36165e7 q^{57} -5.02752e6 q^{58} -1.21174e7 q^{59} +7.12087e7 q^{60} +577170. q^{61} -3.52918e6 q^{62} +3.00325e7 q^{63} -1.31827e8 q^{64} +2.21974e8 q^{65} -7.56167e6 q^{66} -1.20480e8 q^{67} +4.05571e6 q^{68} -4.74806e7 q^{69} -9.73060e6 q^{70} +2.52522e8 q^{71} -8.28073e6 q^{72} +1.25719e8 q^{73} -1.40623e7 q^{74} +8.20284e7 q^{75} +1.48835e8 q^{76} -3.46186e8 q^{77} -1.28872e7 q^{78} +1.68453e8 q^{79} -4.47426e8 q^{80} +4.30467e7 q^{81} +2.59622e7 q^{82} +2.60377e8 q^{83} -1.89270e8 q^{84} +1.36824e7 q^{85} -2.09432e7 q^{86} -3.29909e8 q^{87} +9.54522e7 q^{88} +6.26006e8 q^{89} -1.39472e7 q^{90} -5.89999e8 q^{91} +2.99231e8 q^{92} -2.31587e8 q^{93} +3.15254e7 q^{94} +5.02115e8 q^{95} +7.83188e7 q^{96} -3.81243e8 q^{97} -2.39477e7 q^{98} -4.96201e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.23437	0.0545519	0.0272760	−	0.999628i	$-0.491317\pi$
$2$	1.23437	0.0545519	0.0272760	+	0.999628i	$0.491317\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	−510.476	−0.997024
$5$	−1722.16	−1.23227	−0.616137	−	0.787639i	$-0.711303\pi$
$5$	−1722.16	−1.23227	−0.616137	+	0.787639i	$0.711303\pi$
$6$	99.9839	0.0314956
$7$	4577.43	0.720577	0.360289	−	0.932841i	$-0.382678\pi$
$7$	4577.43	0.720577	0.360289	+	0.932841i	$0.382678\pi$
$8$	−1262.11	−0.108942
$9$	6561.00	0.333333
$10$	−2125.78	−0.0672230
$11$	−75628.8	−1.55747	−0.778736	−	0.627352i	$-0.784139\pi$
$11$	−75628.8	−1.55747	−0.778736	+	0.627352i	$0.784139\pi$
$12$	−41348.6	−0.575632
$13$	−128893.	−1.25165	−0.625827	−	0.779962i	$-0.715239\pi$
$13$	−128893.	−1.25165	−0.625827	+	0.779962i	$0.715239\pi$
$14$	5650.24	0.0393089
$15$	−139495.	−0.711454
$16$	259806.	0.991081
$17$	−7944.95	−0.0230713	−0.0115356	−	0.999933i	$-0.503672\pi$
$17$	−7944.95	−0.0230713	−0.0115356	+	0.999933i	$0.503672\pi$
$18$	8098.70	0.0181840
$19$	−291562.	−0.513263	−0.256631	−	0.966509i	$-0.582613\pi$
$19$	−291562.	−0.513263	−0.256631	+	0.966509i	$0.582613\pi$
$20$	879120.	1.22861
$21$	370772.	0.416025
$22$	−93353.9	−0.0849631
$23$	−586180.	−0.436773	−0.218386	−	0.975862i	$-0.570079\pi$
$23$	−586180.	−0.436773	−0.218386	+	0.975862i	$0.570079\pi$
$24$	−102231.	−0.0628974
$25$	1.01270e6	0.518501
$26$	−159102.	−0.0682802
$27$	531441.	0.192450
$28$	−2.33667e6	−0.718433
$29$	−4.07295e6	−1.06935	−0.534673	−	0.845059i	$-0.679565\pi$
$29$	−4.07295e6	−1.06935	−0.534673	+	0.845059i	$0.679565\pi$
$30$	−172188.	−0.0388112
$31$	−2.85910e6	−0.556034	−0.278017	−	0.960576i	$-0.589677\pi$
$31$	−2.85910e6	−0.556034	−0.278017	+	0.960576i	$0.589677\pi$
$32$	966899.	0.163007
$33$	−6.12593e6	−0.899207
$34$	−9807.01	−0.00125858
$35$	−7.88305e6	−0.887949
$36$	−3.34924e6	−0.332341
$37$	−1.13923e7	−0.999318	−0.499659	−	0.866222i	$-0.666541\pi$
$37$	−1.13923e7	−0.999318	−0.499659	+	0.866222i	$0.666541\pi$
$38$	−359895.	−0.0279995
$39$	−1.04403e7	−0.722643
$40$	2.17356e6	0.134246
$41$	2.10328e7	1.16244	0.581218	−	0.813748i	$-0.302576\pi$
$41$	2.10328e7	1.16244	0.581218	+	0.813748i	$0.302576\pi$
$42$	457669.	0.0226950
$43$	−1.69667e7	−0.756814	−0.378407	−	0.925639i	$-0.623528\pi$
$43$	−1.69667e7	−0.756814	−0.378407	+	0.925639i	$0.623528\pi$
$44$	3.86067e7	1.55284
$45$	−1.12991e7	−0.410758
$46$	−723563.	−0.0238268
$47$	2.55397e7	0.763441	0.381721	−	0.924278i	$-0.375332\pi$
$47$	2.55397e7	0.763441	0.381721	+	0.924278i	$0.375332\pi$
$48$	2.10443e7	0.572201
$49$	−1.94007e7	−0.480769
$50$	1.25004e6	0.0282852
$51$	−643541.	−0.0133202
$52$	6.57969e7	1.24793
$53$	4.62154e7	0.804536	0.402268	−	0.915522i	$-0.368222\pi$
$53$	4.62154e7	0.804536	0.402268	+	0.915522i	$0.368222\pi$
$54$	655995.	0.0104985
$55$	1.30245e8	1.91923
$56$	−5.77724e6	−0.0785008
$57$	−2.36165e7	−0.296332
$58$	−5.02752e6	−0.0583349
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	7.12087e7	0.709337
$61$	577170.	0.00533727	0.00266864	−	0.999996i	$-0.499151\pi$
$61$	577170.	0.00533727	0.00266864	+	0.999996i	$0.499151\pi$
$62$	−3.52918e6	−0.0303327
$63$	3.00325e7	0.240192
$64$	−1.31827e8	−0.982189
$65$	2.21974e8	1.54238
$66$	−7.56167e6	−0.0490535
$67$	−1.20480e8	−0.730427	−0.365213	−	0.930924i	$-0.619004\pi$
$67$	−1.20480e8	−0.730427	−0.365213	+	0.930924i	$0.619004\pi$
$68$	4.05571e6	0.0230026
$69$	−4.74806e7	−0.252171
$70$	−9.73060e6	−0.0484393
$71$	2.52522e8	1.17933	0.589667	−	0.807646i	$-0.299259\pi$
$71$	2.52522e8	1.17933	0.589667	+	0.807646i	$0.299259\pi$
$72$	−8.28073e6	−0.0363138
$73$	1.25719e8	0.518140	0.259070	−	0.965859i	$-0.416584\pi$
$73$	1.25719e8	0.518140	0.259070	+	0.965859i	$0.416584\pi$
$74$	−1.40623e7	−0.0545147
$75$	8.20284e7	0.299357
$76$	1.48835e8	0.511735
$77$	−3.46186e8	−1.12228
$78$	−1.28872e7	−0.0394216
$79$	1.68453e8	0.486584	0.243292	−	0.969953i	$-0.421773\pi$
$79$	1.68453e8	0.486584	0.243292	+	0.969953i	$0.421773\pi$
$80$	−4.47426e8	−1.22128
$81$	4.30467e7	0.111111
$82$	2.59622e7	0.0634131
$83$	2.60377e8	0.602214	0.301107	−	0.953590i	$-0.402644\pi$
$83$	2.60377e8	0.602214	0.301107	+	0.953590i	$0.402644\pi$
$84$	−1.89270e8	−0.414787
$85$	1.36824e7	0.0284301
$86$	−2.09432e7	−0.0412857
$87$	−3.29909e8	−0.617387
$88$	9.54522e7	0.169673
$89$	6.26006e8	1.05760	0.528802	−	0.848745i	$-0.322641\pi$
$89$	6.26006e8	1.05760	0.528802	+	0.848745i	$0.322641\pi$
$90$	−1.39472e7	−0.0224077
$91$	−5.89999e8	−0.901914
$92$	2.99231e8	0.435473
$93$	−2.31587e8	−0.321026
$94$	3.15254e7	0.0416472
$95$	5.02115e8	0.632480
$96$	7.83188e7	0.0941121
$97$	−3.81243e8	−0.437249	−0.218624	−	0.975809i	$-0.570157\pi$
$97$	−3.81243e8	−0.437249	−0.218624	+	0.975809i	$0.570157\pi$
$98$	−2.39477e7	−0.0262269
$99$	−4.96201e8	−0.519157
$100$	−5.16958e8	−0.516958
$101$	−1.79665e9	−1.71797	−0.858986	−	0.511999i	$-0.828905\pi$
$101$	−1.79665e9	−1.71797	−0.858986	+	0.511999i	$0.828905\pi$
$102$	−794368.	−0.000726643 0
$103$	1.89121e9	1.65567	0.827834	−	0.560973i	$-0.189573\pi$
$103$	1.89121e9	1.65567	0.827834	+	0.560973i	$0.189573\pi$
$104$	1.62678e8	0.136357
$105$	−6.38527e8	−0.512658
$106$	5.70469e7	0.0438890
$107$	3.37128e8	0.248638	0.124319	−	0.992242i	$-0.460325\pi$
$107$	3.37128e8	0.248638	0.124319	+	0.992242i	$0.460325\pi$
$108$	−2.71288e8	−0.191877
$109$	1.73641e9	1.17823	0.589117	−	0.808047i	$-0.299476\pi$
$109$	1.73641e9	1.17823	0.589117	+	0.808047i	$0.299476\pi$
$110$	1.60770e8	0.104698
$111$	−9.22776e8	−0.576956
$112$	1.18924e9	0.714150
$113$	1.15382e9	0.665708	0.332854	−	0.942978i	$-0.391988\pi$
$113$	1.15382e9	0.665708	0.332854	+	0.942978i	$0.391988\pi$
$114$	−2.91515e7	−0.0161655
$115$	1.00949e9	0.538224
$116$	2.07914e9	1.06616
$117$	−8.45668e8	−0.417218
$118$	−1.49573e7	−0.00710206
$119$	−3.63675e7	−0.0166246
$120$	1.76058e8	0.0775069
$121$	3.36177e9	1.42572
$122$	712441.	0.000291159 0
$123$	1.70365e9	0.671133
$124$	1.45950e9	0.554379
$125$	1.61956e9	0.593339
$126$	3.70712e7	0.0131030
$127$	2.16551e9	0.738660	0.369330	−	0.929298i	$-0.379587\pi$
$127$	2.16551e9	0.738660	0.369330	+	0.929298i	$0.379587\pi$
$128$	−6.57776e8	−0.216587
$129$	−1.37430e9	−0.436947
$130$	2.73998e8	0.0841400
$131$	−5.32788e8	−0.158064	−0.0790321	−	0.996872i	$-0.525183\pi$
$131$	−5.32788e8	−0.158064	−0.0790321	+	0.996872i	$0.525183\pi$
$132$	3.12714e9	0.896531
$133$	−1.33460e9	−0.369845
$134$	−1.48716e8	−0.0398462
$135$	−9.15224e8	−0.237151
$136$	1.00274e7	0.00251342
$137$	5.97504e8	0.144910	0.0724550	−	0.997372i	$-0.476917\pi$
$137$	5.97504e8	0.144910	0.0724550	+	0.997372i	$0.476917\pi$
$138$	−5.86086e7	−0.0137564
$139$	−3.68105e9	−0.836383	−0.418192	−	0.908359i	$-0.637336\pi$
$139$	−3.68105e9	−0.836383	−0.418192	+	0.908359i	$0.637336\pi$
$140$	4.02411e9	0.885306
$141$	2.06872e9	0.440773
$142$	3.11706e8	0.0643350
$143$	9.74803e9	1.94942
$144$	1.70459e9	0.330360
$145$	7.01425e9	1.31773
$146$	1.55183e8	0.0282656
$147$	−1.57146e9	−0.277572
$148$	5.81550e9	0.996344
$149$	−8.72669e9	−1.45048	−0.725239	−	0.688497i	$-0.758271\pi$
$149$	−8.72669e9	−1.45048	−0.725239	+	0.688497i	$0.758271\pi$
$150$	1.01253e8	0.0163305
$151$	3.64829e9	0.571074	0.285537	−	0.958368i	$-0.407828\pi$
$151$	3.64829e9	0.571074	0.285537	+	0.958368i	$0.407828\pi$
$152$	3.67984e8	0.0559156
$153$	−5.21268e7	−0.00769042
$154$	−4.27321e8	−0.0612225
$155$	4.92381e9	0.685186
$156$	5.32955e9	0.720493
$157$	−1.23067e10	−1.61657	−0.808283	−	0.588794i	$-0.799603\pi$
$157$	−1.23067e10	−1.61657	−0.808283	+	0.588794i	$0.799603\pi$
$158$	2.07934e8	0.0265441
$159$	3.74345e9	0.464499
$160$	−1.66515e9	−0.200869
$161$	−2.68320e9	−0.314729
$162$	5.31356e7	0.00606133
$163$	−4.00912e8	−0.0444842	−0.0222421	−	0.999753i	$-0.507080\pi$
$163$	−4.00912e8	−0.0444842	−0.0222421	+	0.999753i	$0.507080\pi$
$164$	−1.07367e10	−1.15898
$165$	1.05498e10	1.10807
$166$	3.21401e8	0.0328520
$167$	−5.01358e9	−0.498797	−0.249398	−	0.968401i	$-0.580233\pi$
$167$	−5.01358e9	−0.498797	−0.249398	+	0.968401i	$0.580233\pi$
$168$	−4.67956e8	−0.0453225
$169$	6.00894e9	0.566640
$170$	1.68892e7	0.00155092
$171$	−1.91294e9	−0.171088
$172$	8.66109e9	0.754562
$173$	−1.13828e9	−0.0966145	−0.0483072	−	0.998833i	$-0.515383\pi$
$173$	−1.13828e9	−0.0966145	−0.0483072	+	0.998833i	$0.515383\pi$
$174$	−4.07229e8	−0.0336797
$175$	4.63555e9	0.373620
$176$	−1.96488e10	−1.54358
$177$	−9.81506e8	−0.0751646
$178$	7.72723e8	0.0576944
$179$	1.74893e10	1.27331	0.636655	−	0.771149i	$-0.280318\pi$
$179$	1.74893e10	1.27331	0.636655	+	0.771149i	$0.280318\pi$
$180$	5.76791e9	0.409536
$181$	8.61457e9	0.596596	0.298298	−	0.954473i	$-0.403581\pi$
$181$	8.61457e9	0.596596	0.298298	+	0.954473i	$0.403581\pi$
$182$	−7.28277e8	−0.0492012
$183$	4.67508e7	0.00308148
$184$	7.39826e8	0.0475827
$185$	1.96193e10	1.23143
$186$	−2.85864e8	−0.0175126
$187$	6.00867e8	0.0359328
$188$	−1.30374e10	−0.761169
$189$	2.43263e9	0.138675
$190$	6.19796e8	0.0345030
$191$	1.63079e10	0.886643	0.443321	−	0.896363i	$-0.353800\pi$
$191$	1.63079e10	0.886643	0.443321	+	0.896363i	$0.353800\pi$
$192$	−1.06780e10	−0.567067
$193$	4.83203e9	0.250681	0.125340	−	0.992114i	$-0.459998\pi$
$193$	4.83203e9	0.250681	0.125340	+	0.992114i	$0.459998\pi$
$194$	−4.70594e8	−0.0238528
$195$	1.79799e10	0.890495
$196$	9.90362e9	0.479338
$197$	7.60149e9	0.359585	0.179792	−	0.983705i	$-0.442457\pi$
$197$	7.60149e9	0.359585	0.179792	+	0.983705i	$0.442457\pi$
$198$	−6.12495e8	−0.0283210
$199$	−2.00563e10	−0.906593	−0.453296	−	0.891360i	$-0.649752\pi$
$199$	−2.00563e10	−0.906593	−0.453296	+	0.891360i	$0.649752\pi$
$200$	−1.27814e9	−0.0564863
$201$	−9.75884e9	−0.421712
$202$	−2.21772e9	−0.0937187
$203$	−1.86436e10	−0.770546
$204$	3.28513e8	0.0132806
$205$	−3.62217e10	−1.43244
$206$	2.33446e9	0.0903199
$207$	−3.84593e9	−0.145591
$208$	−3.34872e10	−1.24049
$209$	2.20505e10	0.799392
$210$	−7.88178e8	−0.0279665
$211$	−3.43734e10	−1.19386	−0.596928	−	0.802295i	$-0.703612\pi$
$211$	−3.43734e10	−1.19386	−0.596928	+	0.802295i	$0.703612\pi$
$212$	−2.35919e10	−0.802141
$213$	2.04543e10	0.680889
$214$	4.16141e8	0.0135637
$215$	2.92193e10	0.932603
$216$	−6.70739e8	−0.0209658
$217$	−1.30873e10	−0.400665
$218$	2.14337e9	0.0642750
$219$	1.01832e10	0.299148
$220$	−6.64868e10	−1.91352
$221$	1.02405e9	0.0288772
$222$	−1.13905e9	−0.0314741
$223$	1.85618e10	0.502631	0.251315	−	0.967905i	$-0.419137\pi$
$223$	1.85618e10	0.502631	0.251315	+	0.967905i	$0.419137\pi$
$224$	4.42591e9	0.117459
$225$	6.64430e9	0.172834
$226$	1.42424e9	0.0363157
$227$	2.95817e10	0.739447	0.369724	−	0.929142i	$-0.379452\pi$
$227$	2.95817e10	0.739447	0.369724	+	0.929142i	$0.379452\pi$
$228$	1.20557e10	0.295450
$229$	−7.00551e9	−0.168337	−0.0841686	−	0.996452i	$-0.526823\pi$
$229$	−7.00551e9	−0.168337	−0.0841686	+	0.996452i	$0.526823\pi$
$230$	1.24609e9	0.0293612
$231$	−2.80410e10	−0.647948
$232$	5.14052e9	0.116496
$233$	7.20100e10	1.60063	0.800315	−	0.599580i	$-0.204666\pi$
$233$	7.20100e10	1.60063	0.800315	+	0.599580i	$0.204666\pi$
$234$	−1.04387e9	−0.0227601
$235$	−4.39834e10	−0.940769
$236$	6.18563e9	0.129801
$237$	1.36447e10	0.280929
$238$	−4.48909e7	−0.000906905 0
$239$	−4.52370e10	−0.896816	−0.448408	−	0.893829i	$-0.648009\pi$
$239$	−4.52370e10	−0.896816	−0.448408	+	0.893829i	$0.648009\pi$
$240$	−3.62415e10	−0.705109
$241$	−4.81152e10	−0.918767	−0.459384	−	0.888238i	$-0.651930\pi$
$241$	−4.81152e10	−0.918767	−0.459384	+	0.888238i	$0.651930\pi$
$242$	4.14967e9	0.0777758
$243$	3.48678e9	0.0641500
$244$	−2.94632e8	−0.00532139
$245$	3.34111e10	0.592439
$246$	2.10294e9	0.0366116
$247$	3.75803e10	0.642428
$248$	3.60851e9	0.0605752
$249$	2.10905e10	0.347689
$250$	1.99914e9	0.0323678
$251$	−3.37349e10	−0.536472	−0.268236	−	0.963353i	$-0.586441\pi$
$251$	−3.37349e10	−0.536472	−0.268236	+	0.963353i	$0.586441\pi$
$252$	−1.53309e10	−0.239478
$253$	4.43321e10	0.680262
$254$	2.67305e9	0.0402953
$255$	1.10828e9	0.0164141
$256$	6.66836e10	0.970374
$257$	4.88383e10	0.698331	0.349165	−	0.937061i	$-0.386465\pi$
$257$	4.88383e10	0.698331	0.349165	+	0.937061i	$0.386465\pi$
$258$	−1.69640e9	−0.0238363
$259$	−5.21475e10	−0.720086
$260$	−1.13313e11	−1.53779
$261$	−2.67226e10	−0.356448
$262$	−6.57657e8	−0.00862271
$263$	−5.73393e10	−0.739012	−0.369506	−	0.929228i	$-0.620473\pi$
$263$	−5.73393e10	−0.739012	−0.369506	+	0.929228i	$0.620473\pi$
$264$	7.73163e9	0.0979610
$265$	−7.95901e10	−0.991409
$266$	−1.64739e9	−0.0201758
$267$	5.07065e10	0.610609
$268$	6.15020e10	0.728253
$269$	5.33586e10	0.621326	0.310663	−	0.950520i	$-0.399449\pi$
$269$	5.33586e10	0.621326	0.310663	+	0.950520i	$0.399449\pi$
$270$	−1.12973e9	−0.0129371
$271$	−4.34358e10	−0.489199	−0.244600	−	0.969624i	$-0.578656\pi$
$271$	−4.34358e10	−0.489199	−0.244600	+	0.969624i	$0.578656\pi$
$272$	−2.06415e9	−0.0228655
$273$	−4.77899e10	−0.520720
$274$	7.37541e8	0.00790512
$275$	−7.65891e10	−0.807550
$276$	2.42377e10	0.251420
$277$	4.32531e10	0.441427	0.220713	−	0.975339i	$-0.429161\pi$
$277$	4.32531e10	0.441427	0.220713	+	0.975339i	$0.429161\pi$
$278$	−4.54378e9	−0.0456263
$279$	−1.87585e10	−0.185345
$280$	9.94930e9	0.0967345
$281$	−7.68788e10	−0.735577	−0.367789	−	0.929909i	$-0.619885\pi$
$281$	−7.68788e10	−0.735577	−0.367789	+	0.929909i	$0.619885\pi$
$282$	2.55356e9	0.0240450
$283$	6.08362e10	0.563797	0.281899	−	0.959444i	$-0.409036\pi$
$283$	6.08362e10	0.563797	0.281899	+	0.959444i	$0.409036\pi$
$284$	−1.28907e11	−1.17582
$285$	4.06713e10	0.365163
$286$	1.20327e10	0.106345
$287$	9.62760e10	0.837625
$288$	6.34382e9	0.0543357
$289$	−1.18525e11	−0.999468
$290$	8.65818e9	0.0718846
$291$	−3.08806e10	−0.252446
$292$	−6.41765e10	−0.516598
$293$	−1.08229e11	−0.857905	−0.428952	−	0.903327i	$-0.641117\pi$
$293$	−1.08229e11	−0.857905	−0.428952	+	0.903327i	$0.641117\pi$
$294$	−1.93976e9	−0.0151421
$295$	2.08680e10	0.160428
$296$	1.43784e10	0.108867
$297$	−4.01923e10	−0.299736
$298$	−1.07720e10	−0.0791264
$299$	7.55546e10	0.546689
$300$	−4.18736e10	−0.298466
$301$	−7.76638e10	−0.545343
$302$	4.50333e9	0.0311532
$303$	−1.45528e11	−0.991872
$304$	−7.57495e10	−0.508685
$305$	−9.93977e8	−0.00657699
$306$	−6.43438e7	−0.000419527 0
$307$	−1.72665e11	−1.10938	−0.554691	−	0.832056i	$-0.687164\pi$
$307$	−1.72665e11	−1.10938	−0.554691	+	0.832056i	$0.687164\pi$
$308$	1.76720e11	1.11894
$309$	1.53188e11	0.955900
$310$	6.07780e9	0.0373783
$311$	−1.81316e10	−0.109904	−0.0549520	−	0.998489i	$-0.517501\pi$
$311$	−1.81316e10	−0.109904	−0.0549520	+	0.998489i	$0.517501\pi$
$312$	1.31769e10	0.0787259
$313$	−3.00247e11	−1.76819	−0.884095	−	0.467308i	$-0.845224\pi$
$313$	−3.00247e11	−1.76819	−0.884095	+	0.467308i	$0.845224\pi$
$314$	−1.51910e10	−0.0881868
$315$	−5.17207e10	−0.295983
$316$	−8.59914e10	−0.485136
$317$	−3.28029e11	−1.82451	−0.912254	−	0.409625i	$-0.865660\pi$
$317$	−3.28029e11	−1.82451	−0.912254	+	0.409625i	$0.865660\pi$
$318$	4.62080e9	0.0253393
$319$	3.08032e11	1.66548
$320$	2.27027e11	1.21033
$321$	2.73074e10	0.143551
$322$	−3.31206e9	−0.0171691
$323$	2.31645e9	0.0118416
$324$	−2.19743e10	−0.110780
$325$	−1.30530e11	−0.648984
$326$	−4.94874e8	−0.00242670
$327$	1.40649e11	0.680254
$328$	−2.65457e10	−0.126638
$329$	1.16906e11	0.550118
$330$	1.30224e10	0.0604474
$331$	−4.20956e11	−1.92757	−0.963787	−	0.266672i	$-0.914076\pi$
$331$	−4.20956e11	−1.92757	−0.963787	+	0.266672i	$0.914076\pi$
$332$	−1.32916e11	−0.600422
$333$	−7.47449e10	−0.333106
$334$	−6.18860e9	−0.0272103
$335$	2.07485e11	0.900087
$336$	9.63287e10	0.412315
$337$	1.86450e11	0.787458	0.393729	−	0.919226i	$-0.371185\pi$
$337$	1.86450e11	0.787458	0.393729	+	0.919226i	$0.371185\pi$
$338$	7.41725e9	0.0309113
$339$	9.34592e10	0.384347
$340$	−6.98457e9	−0.0283455
$341$	2.16230e11	0.866007
$342$	−2.36127e9	−0.00933316
$343$	−2.73521e11	−1.06701
$344$	2.14139e10	0.0824485
$345$	8.17690e10	0.310744
$346$	−1.40506e9	−0.00527051
$347$	−3.20207e11	−1.18563	−0.592814	−	0.805339i	$-0.701983\pi$
$347$	−3.20207e11	−1.18563	−0.592814	+	0.805339i	$0.701983\pi$
$348$	1.68411e11	0.615550
$349$	4.15903e11	1.50065	0.750323	−	0.661072i	$-0.229898\pi$
$349$	4.15903e11	1.50065	0.750323	+	0.661072i	$0.229898\pi$
$350$	5.72198e9	0.0203817
$351$	−6.84991e10	−0.240881
$352$	−7.31254e10	−0.253879
$353$	2.67923e10	0.0918382	0.0459191	−	0.998945i	$-0.485378\pi$
$353$	2.67923e10	0.0918382	0.0459191	+	0.998945i	$0.485378\pi$
$354$	−1.21154e9	−0.00410038
$355$	−4.34883e11	−1.45326
$356$	−3.19561e11	−1.05446
$357$	−2.94576e9	−0.00959823
$358$	2.15883e10	0.0694615
$359$	1.06956e11	0.339845	0.169922	−	0.985457i	$-0.445648\pi$
$359$	1.06956e11	0.339845	0.169922	+	0.985457i	$0.445648\pi$
$360$	1.42607e10	0.0447486
$361$	−2.37679e11	−0.736562
$362$	1.06336e10	0.0325455
$363$	2.72303e11	0.823139
$364$	3.01181e11	0.899230
$365$	−2.16507e11	−0.638491
$366$	5.77077e7	0.000168101 0
$367$	−1.72987e11	−0.497755	−0.248877	−	0.968535i	$-0.580062\pi$
$367$	−1.72987e11	−0.497755	−0.248877	+	0.968535i	$0.580062\pi$
$368$	−1.52293e11	−0.432877
$369$	1.37996e11	0.387479
$370$	2.42175e10	0.0671771
$371$	2.11548e11	0.579730
$372$	1.18220e11	0.320071
$373$	5.37786e11	1.43853	0.719267	−	0.694734i	$-0.244478\pi$
$373$	5.37786e11	1.43853	0.719267	+	0.694734i	$0.244478\pi$
$374$	7.41693e8	0.00196021
$375$	1.31185e11	0.342565
$376$	−3.22340e10	−0.0831705
$377$	5.24975e11	1.33845
$378$	3.00277e9	0.00756500
$379$	−3.86868e11	−0.963134	−0.481567	−	0.876409i	$-0.659932\pi$
$379$	−3.86868e11	−0.963134	−0.481567	+	0.876409i	$0.659932\pi$
$380$	−2.56318e11	−0.630598
$381$	1.75407e11	0.426465
$382$	2.01300e10	0.0483681
$383$	−5.21091e11	−1.23742	−0.618712	−	0.785618i	$-0.712345\pi$
$383$	−5.21091e11	−1.23742	−0.618712	+	0.785618i	$0.712345\pi$
$384$	−5.32798e10	−0.125047
$385$	5.96186e11	1.38296
$386$	5.96451e9	0.0136751
$387$	−1.11318e11	−0.252271
$388$	1.94615e11	0.435947
$389$	8.11858e11	1.79766	0.898829	−	0.438300i	$-0.144419\pi$
$389$	8.11858e11	1.79766	0.898829	+	0.438300i	$0.144419\pi$
$390$	2.21938e10	0.0485782
$391$	4.65717e9	0.0100769
$392$	2.44859e10	0.0523757
$393$	−4.31558e10	−0.0912584
$394$	9.38305e9	0.0196160
$395$	−2.90103e11	−0.599605
$396$	2.53299e11	0.517612
$397$	2.98669e11	0.603438	0.301719	−	0.953397i	$-0.402440\pi$
$397$	2.98669e11	0.603438	0.301719	+	0.953397i	$0.402440\pi$
$398$	−2.47569e10	−0.0494564
$399$	−1.08103e11	−0.213530
$400$	2.63105e11	0.513876
$401$	7.14419e11	1.37976	0.689879	−	0.723924i	$-0.257664\pi$
$401$	7.14419e11	1.37976	0.689879	+	0.723924i	$0.257664\pi$
$402$	−1.20460e10	−0.0230052
$403$	3.68518e11	0.695963
$404$	9.17145e11	1.71286
$405$	−7.41332e10	−0.136919
$406$	−2.30131e10	−0.0420348
$407$	8.61586e11	1.55641
$408$	8.12222e8	0.00145112
$409$	7.98601e10	0.141116	0.0705578	−	0.997508i	$-0.477522\pi$
$409$	7.98601e10	0.141116	0.0705578	+	0.997508i	$0.477522\pi$
$410$	−4.47110e10	−0.0781424
$411$	4.83978e10	0.0836638
$412$	−9.65420e11	−1.65074
$413$	−5.54664e10	−0.0938112
$414$	−4.74729e9	−0.00794227
$415$	−4.48410e11	−0.742094
$416$	−1.24627e11	−0.204028
$417$	−2.98165e11	−0.482886
$418$	2.72184e10	0.0436084
$419$	3.18506e11	0.504841	0.252420	−	0.967618i	$-0.418773\pi$
$419$	3.18506e11	0.504841	0.252420	+	0.967618i	$0.418773\pi$
$420$	3.25953e11	0.511132
$421$	9.50164e11	1.47411	0.737054	−	0.675834i	$-0.236216\pi$
$421$	9.50164e11	1.47411	0.737054	+	0.675834i	$0.236216\pi$
$422$	−4.24295e10	−0.0651271
$423$	1.67566e11	0.254480
$424$	−5.83291e10	−0.0876473
$425$	−8.04583e9	−0.0119625
$426$	2.52482e10	0.0371438
$427$	2.64196e9	0.00384592
$428$	−1.72096e11	−0.247898
$429$	7.89591e11	1.12550
$430$	3.60674e10	0.0508753
$431$	1.08204e11	0.151041	0.0755203	−	0.997144i	$-0.475938\pi$
$431$	1.08204e11	0.151041	0.0755203	+	0.997144i	$0.475938\pi$
$432$	1.38072e11	0.190734
$433$	−8.27119e11	−1.13076	−0.565382	−	0.824829i	$-0.691271\pi$
$433$	−8.27119e11	−1.13076	−0.565382	+	0.824829i	$0.691271\pi$
$434$	−1.61546e10	−0.0218571
$435$	5.68155e11	0.760790
$436$	−8.86394e11	−1.17473
$437$	1.70908e11	0.224179
$438$	1.25699e10	0.0163191
$439$	1.41581e11	0.181935	0.0909674	−	0.995854i	$-0.471004\pi$
$439$	1.41581e11	0.181935	0.0909674	+	0.995854i	$0.471004\pi$
$440$	−1.64384e11	−0.209084
$441$	−1.27288e11	−0.160256
$442$	1.26406e9	0.00157531
$443$	1.32265e12	1.63165	0.815826	−	0.578297i	$-0.196283\pi$
$443$	1.32265e12	1.63165	0.815826	+	0.578297i	$0.196283\pi$
$444$	4.71055e11	0.575239
$445$	−1.07808e12	−1.30326
$446$	2.29122e10	0.0274195
$447$	−7.06862e11	−0.837434
$448$	−6.03429e11	−0.707743
$449$	5.50408e11	0.639110	0.319555	−	0.947568i	$-0.396467\pi$
$449$	5.50408e11	0.639110	0.319555	+	0.947568i	$0.396467\pi$
$450$	8.20153e9	0.00942841
$451$	−1.59068e12	−1.81046
$452$	−5.88996e11	−0.663727
$453$	2.95511e11	0.329710
$454$	3.65148e10	0.0403383
$455$	1.01607e12	1.11141
$456$	2.98067e10	0.0322829
$457$	8.90772e11	0.955309	0.477654	−	0.878548i	$-0.341487\pi$
$457$	8.90772e11	0.955309	0.477654	+	0.878548i	$0.341487\pi$
$458$	−8.64739e9	−0.00918312
$459$	−4.22227e9	−0.00444006
$460$	−5.15322e11	−0.536622
$461$	5.40229e11	0.557088	0.278544	−	0.960423i	$-0.410148\pi$
$461$	5.40229e11	0.557088	0.278544	+	0.960423i	$0.410148\pi$
$462$	−3.46130e10	−0.0353468
$463$	−1.15861e12	−1.17172	−0.585859	−	0.810413i	$-0.699243\pi$
$463$	−1.15861e12	−1.17172	−0.585859	+	0.810413i	$0.699243\pi$
$464$	−1.05818e12	−1.05981
$465$	3.98829e11	0.395593
$466$	8.88869e10	0.0873175
$467$	3.39246e11	0.330057	0.165029	−	0.986289i	$-0.447228\pi$
$467$	3.39246e11	0.330057	0.165029	+	0.986289i	$0.447228\pi$
$468$	4.31693e11	0.415977
$469$	−5.51487e11	−0.526329
$470$	−5.42917e10	−0.0513208
$471$	−9.96843e11	−0.933325
$472$	1.52935e10	0.0141830
$473$	1.28317e12	1.17872
$474$	1.68426e10	0.0153252
$475$	−2.95264e11	−0.266127
$476$	1.85647e10	0.0165751
$477$	3.03219e11	0.268179
$478$	−5.58392e10	−0.0489231
$479$	−7.35605e10	−0.0638461	−0.0319231	−	0.999490i	$-0.510163\pi$
$479$	−7.35605e10	−0.0638461	−0.0319231	+	0.999490i	$0.510163\pi$
$480$	−1.34877e11	−0.115972
$481$	1.46839e12	1.25080
$482$	−5.93919e10	−0.0501206
$483$	−2.17339e11	−0.181709
$484$	−1.71610e12	−1.42148
$485$	6.56559e11	0.538810
$486$	4.30398e9	0.00349951
$487$	−1.42738e12	−1.14990	−0.574948	−	0.818190i	$-0.694978\pi$
$487$	−1.42738e12	−1.14990	−0.574948	+	0.818190i	$0.694978\pi$
$488$	−7.28454e8	−0.000581451 0
$489$	−3.24739e10	−0.0256829
$490$	4.12417e10	0.0323187
$491$	1.94184e12	1.50781	0.753906	−	0.656982i	$-0.228167\pi$
$491$	1.94184e12	1.50781	0.753906	+	0.656982i	$0.228167\pi$
$492$	−8.69675e11	−0.669135
$493$	3.23594e10	0.0246711
$494$	4.63880e10	0.0350457
$495$	8.54535e11	0.639744
$496$	−7.42810e11	−0.551075
$497$	1.15590e12	0.849802
$498$	2.60335e10	0.0189671
$499$	−2.56548e12	−1.85232	−0.926159	−	0.377134i	$-0.876910\pi$
$499$	−2.56548e12	−1.85232	−0.926159	+	0.377134i	$0.876910\pi$
$500$	−8.26749e11	−0.591574
$501$	−4.06100e11	−0.287980
$502$	−4.16413e10	−0.0292656
$503$	5.93035e11	0.413071	0.206535	−	0.978439i	$-0.433781\pi$
$503$	5.93035e11	0.413071	0.206535	+	0.978439i	$0.433781\pi$
$504$	−3.79044e10	−0.0261669
$505$	3.09410e12	2.11701
$506$	5.47222e10	0.0371096
$507$	4.86724e11	0.327150
$508$	−1.10544e12	−0.736462
$509$	1.72608e12	1.13981	0.569904	−	0.821711i	$-0.306980\pi$
$509$	1.72608e12	1.13981	0.569904	+	0.821711i	$0.306980\pi$
$510$	1.36803e9	0.000895423 0
$511$	5.75469e11	0.373360
$512$	4.19093e11	0.269523
$513$	−1.54948e11	−0.0987774
$514$	6.02845e10	0.0380953
$515$	−3.25697e12	−2.04024
$516$	7.01549e11	0.435646
$517$	−1.93154e12	−1.18904
$518$	−6.43692e10	−0.0392821
$519$	−9.22008e10	−0.0557804
$520$	−2.80157e11	−0.168030
$521$	−5.35237e10	−0.0318256	−0.0159128	−	0.999873i	$-0.505065\pi$
$521$	−5.35237e10	−0.0318256	−0.0159128	+	0.999873i	$0.505065\pi$
$522$	−3.29856e10	−0.0194450
$523$	8.66933e11	0.506673	0.253337	−	0.967378i	$-0.418472\pi$
$523$	8.66933e11	0.506673	0.253337	+	0.967378i	$0.418472\pi$
$524$	2.71976e11	0.157594
$525$	3.75479e11	0.215710
$526$	−7.07779e10	−0.0403145
$527$	2.27154e10	0.0128284
$528$	−1.59155e12	−0.891187
$529$	−1.45755e12	−0.809229
$530$	−9.82436e10	−0.0540833
$531$	−7.95020e10	−0.0433963
$532$	6.81284e11	0.368745
$533$	−2.71098e12	−1.45497
$534$	6.25905e10	0.0333099
$535$	−5.80587e11	−0.306391
$536$	1.52059e11	0.0795738
$537$	1.41663e12	0.735146
$538$	6.58643e10	0.0338945
$539$	1.46726e12	0.748784
$540$	4.67200e11	0.236446
$541$	3.04212e12	1.52682	0.763411	−	0.645913i	$-0.223523\pi$
$541$	3.04212e12	1.52682	0.763411	+	0.645913i	$0.223523\pi$
$542$	−5.36158e10	−0.0266868
$543$	6.97781e11	0.344445
$544$	−7.68197e9	−0.00376077
$545$	−2.99036e12	−1.45191
$546$	−5.89904e10	−0.0284063
$547$	3.02958e12	1.44691	0.723453	−	0.690374i	$-0.242554\pi$
$547$	3.02958e12	1.44691	0.723453	+	0.690374i	$0.242554\pi$
$548$	−3.05012e11	−0.144479
$549$	3.78681e9	0.00177909
$550$	−9.45392e10	−0.0440534
$551$	1.18752e12	0.548855
$552$	5.99259e10	0.0274719
$553$	7.71083e11	0.350621
$554$	5.33903e10	0.0240807
$555$	1.58916e12	0.710969
$556$	1.87909e12	0.833894
$557$	−2.52749e12	−1.11261	−0.556303	−	0.830979i	$-0.687781\pi$
$557$	−2.52749e12	−1.11261	−0.556303	+	0.830979i	$0.687781\pi$
$558$	−2.31550e10	−0.0101109
$559$	2.18689e12	0.947270
$560$	−2.04806e12	−0.880029
$561$	4.86703e10	0.0207458
$562$	−9.48969e10	−0.0401272
$563$	1.94482e12	0.815816	0.407908	−	0.913023i	$-0.366258\pi$
$563$	1.94482e12	0.815816	0.407908	+	0.913023i	$0.366258\pi$
$564$	−1.05603e12	−0.439461
$565$	−1.98705e12	−0.820335
$566$	7.50943e10	0.0307562
$567$	1.97043e11	0.0800641
$568$	−3.18712e11	−0.128479
$569$	1.76979e12	0.707808	0.353904	−	0.935282i	$-0.384854\pi$
$569$	1.76979e12	0.707808	0.353904	+	0.935282i	$0.384854\pi$
$570$	5.02034e10	0.0199203
$571$	−2.23937e12	−0.881584	−0.440792	−	0.897609i	$-0.645302\pi$
$571$	−2.23937e12	−0.881584	−0.440792	+	0.897609i	$0.645302\pi$
$572$	−4.97614e12	−1.94362
$573$	1.32094e12	0.511903
$574$	1.18840e11	0.0456941
$575$	−5.93623e11	−0.226467
$576$	−8.64918e11	−0.327396
$577$	3.11152e12	1.16864	0.584322	−	0.811522i	$-0.301361\pi$
$577$	3.11152e12	1.16864	0.584322	+	0.811522i	$0.301361\pi$
$578$	−1.46303e11	−0.0545229
$579$	3.91394e11	0.144731
$580$	−3.58061e12	−1.31381
$581$	1.19186e12	0.433942
$582$	−3.81181e10	−0.0137714
$583$	−3.49522e12	−1.25304
$584$	−1.58671e11	−0.0564470
$585$	1.45637e12	0.514128
$586$	−1.33595e11	−0.0468004
$587$	−3.40126e12	−1.18241	−0.591206	−	0.806521i	$-0.701348\pi$
$587$	−3.40126e12	−1.18241	−0.591206	+	0.806521i	$0.701348\pi$
$588$	8.02193e11	0.276746
$589$	8.33604e11	0.285391
$590$	2.57588e10	0.00875169
$591$	6.15721e11	0.207606
$592$	−2.95979e12	−0.990405
$593$	−1.25239e12	−0.415904	−0.207952	−	0.978139i	$-0.566680\pi$
$593$	−1.25239e12	−0.415904	−0.207952	+	0.978139i	$0.566680\pi$
$594$	−4.96121e10	−0.0163512
$595$	6.26305e10	0.0204861
$596$	4.45477e12	1.44616
$597$	−1.62456e12	−0.523422
$598$	9.32622e10	0.0298229
$599$	−2.25023e12	−0.714178	−0.357089	−	0.934070i	$-0.616231\pi$
$599$	−2.25023e12	−0.714178	−0.357089	+	0.934070i	$0.616231\pi$
$600$	−1.03529e11	−0.0326124
$601$	4.24405e12	1.32692	0.663462	−	0.748210i	$-0.269087\pi$
$601$	4.24405e12	1.32692	0.663462	+	0.748210i	$0.269087\pi$
$602$	−9.58659e10	−0.0297495
$603$	−7.90466e11	−0.243476
$604$	−1.86236e12	−0.569375
$605$	−5.78949e12	−1.75688
$606$	−1.79636e11	−0.0541085
$607$	−3.86858e12	−1.15665	−0.578326	−	0.815806i	$-0.696294\pi$
$607$	−3.86858e12	−1.15665	−0.578326	+	0.815806i	$0.696294\pi$
$608$	−2.81911e11	−0.0836654
$609$	−1.51013e12	−0.444875
$610$	−1.22693e9	−0.000358787 0
$611$	−3.29189e12	−0.955565
$612$	2.66095e10	0.00766753
$613$	−1.24759e12	−0.356862	−0.178431	−	0.983952i	$-0.557102\pi$
$613$	−1.24759e12	−0.356862	−0.178431	+	0.983952i	$0.557102\pi$
$614$	−2.13132e11	−0.0605190
$615$	−2.93396e12	−0.827020
$616$	4.36926e11	0.122263
$617$	−6.58800e12	−1.83008	−0.915040	−	0.403363i	$-0.867841\pi$
$617$	−6.58800e12	−1.83008	−0.915040	+	0.403363i	$0.867841\pi$
$618$	1.89091e11	0.0521462
$619$	−6.62001e12	−1.81238	−0.906192	−	0.422866i	$-0.861024\pi$
$619$	−6.62001e12	−1.81238	−0.906192	+	0.422866i	$0.861024\pi$
$620$	−2.51349e12	−0.683147
$621$	−3.11520e11	−0.0840570
$622$	−2.23810e10	−0.00599547
$623$	2.86550e12	0.762086
$624$	−2.71246e12	−0.716198
$625$	−4.76707e12	−1.24966
$626$	−3.70615e11	−0.0964582
$627$	1.78609e12	0.461529
$628$	6.28228e12	1.61176
$629$	9.05113e10	0.0230555
$630$	−6.38424e10	−0.0161464
$631$	7.31068e12	1.83580	0.917900	−	0.396811i	$-0.129883\pi$
$631$	7.31068e12	1.83580	0.917900	+	0.396811i	$0.129883\pi$
$632$	−2.12607e11	−0.0530092
$633$	−2.78425e12	−0.689273
$634$	−4.04909e11	−0.0995305
$635$	−3.72935e12	−0.910232
$636$	−1.91094e12	−0.463116
$637$	2.50062e12	0.601756
$638$	3.80226e11	0.0908549
$639$	1.65680e12	0.393112
$640$	1.13279e12	0.266895
$641$	−1.91229e12	−0.447397	−0.223698	−	0.974658i	$-0.571813\pi$
$641$	−1.91229e12	−0.447397	−0.223698	+	0.974658i	$0.571813\pi$
$642$	3.37074e10	0.00783101
$643$	−2.85686e12	−0.659082	−0.329541	−	0.944141i	$-0.606894\pi$
$643$	−2.85686e12	−0.659082	−0.329541	+	0.944141i	$0.606894\pi$
$644$	1.36971e12	0.313792
$645$	2.36676e12	0.538438
$646$	2.85935e9	0.000645983 0
$647$	6.56091e12	1.47196	0.735978	−	0.677005i	$-0.236723\pi$
$647$	6.56091e12	1.47196	0.735978	+	0.677005i	$0.236723\pi$
$648$	−5.43299e10	−0.0121046
$649$	9.16422e11	0.202766
$650$	−1.61122e11	−0.0354033
$651$	−1.06007e12	−0.231324
$652$	2.04656e11	0.0443518
$653$	7.12775e12	1.53406	0.767031	−	0.641610i	$-0.221733\pi$
$653$	7.12775e12	1.53406	0.767031	+	0.641610i	$0.221733\pi$
$654$	1.73613e11	0.0371092
$655$	9.17544e11	0.194779
$656$	5.46444e12	1.15207
$657$	8.24841e11	0.172713
$658$	1.44305e11	0.0300100
$659$	4.89769e12	1.01160	0.505798	−	0.862652i	$-0.331198\pi$
$659$	4.89769e12	1.01160	0.505798	+	0.862652i	$0.331198\pi$
$660$	−5.38543e12	−1.10477
$661$	5.75298e12	1.17216	0.586080	−	0.810253i	$-0.300671\pi$
$661$	5.75298e12	1.17216	0.586080	+	0.810253i	$0.300671\pi$
$662$	−5.19616e11	−0.105153
$663$	8.29480e10	0.0166723
$664$	−3.28625e11	−0.0656062
$665$	2.29840e12	0.455751
$666$	−9.22628e10	−0.0181716
$667$	2.38748e12	0.467061
$668$	2.55931e12	0.497312
$669$	1.50351e12	0.290194
$670$	2.56113e11	0.0491015
$671$	−4.36507e10	−0.00831266
$672$	3.58499e11	0.0678150
$673$	4.61673e12	0.867494	0.433747	−	0.901035i	$-0.357191\pi$
$673$	4.61673e12	0.867494	0.433747	+	0.901035i	$0.357191\pi$
$674$	2.30148e11	0.0429574
$675$	5.38189e11	0.0997855
$676$	−3.06742e12	−0.564954
$677$	−8.67156e12	−1.58653	−0.793265	−	0.608877i	$-0.791620\pi$
$677$	−8.67156e12	−1.58653	−0.793265	+	0.608877i	$0.791620\pi$
$678$	1.15363e11	0.0209669
$679$	−1.74511e12	−0.315071
$680$	−1.72688e10	−0.00309722
$681$	2.39612e12	0.426920
$682$	2.66908e11	0.0472424
$683$	7.15878e12	1.25877	0.629385	−	0.777094i	$-0.283307\pi$
$683$	7.15878e12	1.25877	0.629385	+	0.777094i	$0.283307\pi$
$684$	9.76509e11	0.170578
$685$	−1.02900e12	−0.178569
$686$	−3.37626e11	−0.0582074
$687$	−5.67446e11	−0.0971895
$688$	−4.40805e12	−0.750064
$689$	−5.95685e12	−1.00700
$690$	1.00933e11	0.0169517
$691$	9.45943e12	1.57839	0.789194	−	0.614144i	$-0.210499\pi$
$691$	9.45943e12	1.57839	0.789194	+	0.614144i	$0.210499\pi$
$692$	5.81066e11	0.0963270
$693$	−2.27132e12	−0.374093
$694$	−3.95254e11	−0.0646783
$695$	6.33935e12	1.03065
$696$	4.16382e11	0.0672591
$697$	−1.67104e11	−0.0268189
$698$	5.13378e11	0.0818631
$699$	5.83281e12	0.924124
$700$	−2.36634e12	−0.372508
$701$	−2.18884e12	−0.342360	−0.171180	−	0.985240i	$-0.554758\pi$
$701$	−2.18884e12	−0.342360	−0.171180	+	0.985240i	$0.554758\pi$
$702$	−8.45532e10	−0.0131405
$703$	3.32156e12	0.512912
$704$	9.96993e12	1.52973
$705$	−3.56265e12	−0.543153
$706$	3.30716e10	0.00500995
$707$	−8.22402e12	−1.23793
$708$	5.01036e11	0.0749409
$709$	−6.30577e12	−0.937195	−0.468597	−	0.883412i	$-0.655241\pi$
$709$	−6.30577e12	−0.937195	−0.468597	+	0.883412i	$0.655241\pi$
$710$	−5.36806e11	−0.0792784
$711$	1.10522e12	0.162195
$712$	−7.90091e11	−0.115217
$713$	1.67595e12	0.242861
$714$	−3.63616e9	−0.000523602 0
$715$	−1.67876e13	−2.40222
$716$	−8.92788e12	−1.26952
$717$	−3.66420e12	−0.517777
$718$	1.32023e11	0.0185392
$719$	1.65166e12	0.230483	0.115242	−	0.993337i	$-0.463236\pi$
$719$	1.65166e12	0.230483	0.115242	+	0.993337i	$0.463236\pi$
$720$	−2.93556e12	−0.407095
$721$	8.65690e12	1.19304
$722$	−2.93384e11	−0.0401809
$723$	−3.89733e12	−0.530451
$724$	−4.39754e12	−0.594820
$725$	−4.12466e12	−0.554456
$726$	3.36123e11	0.0449039
$727$	1.12273e13	1.49064	0.745319	−	0.666708i	$-0.232297\pi$
$727$	1.12273e13	1.49064	0.745319	+	0.666708i	$0.232297\pi$
$728$	7.44646e11	0.0982559
$729$	2.82430e11	0.0370370
$730$	−2.67250e11	−0.0348309
$731$	1.34800e11	0.0174606
$732$	−2.38652e10	−0.00307231
$733$	5.92897e12	0.758598	0.379299	−	0.925274i	$-0.376165\pi$
$733$	5.92897e12	0.758598	0.379299	+	0.925274i	$0.376165\pi$
$734$	−2.13529e11	−0.0271535
$735$	2.70630e12	0.342045
$736$	−5.66777e11	−0.0711970
$737$	9.11173e12	1.13762
$738$	1.70338e11	0.0211377
$739$	−6.19162e11	−0.0763667	−0.0381834	−	0.999271i	$-0.512157\pi$
$739$	−6.19162e11	−0.0763667	−0.0381834	+	0.999271i	$0.512157\pi$
$740$	−1.00152e13	−1.22777
$741$	3.04401e12	0.370906
$742$	2.61128e11	0.0316254
$743$	6.89752e12	0.830316	0.415158	−	0.909749i	$-0.363726\pi$
$743$	6.89752e12	0.830316	0.415158	+	0.909749i	$0.363726\pi$
$744$	2.92289e11	0.0349731
$745$	1.50287e13	1.78739
$746$	6.63827e11	0.0784748
$747$	1.70833e12	0.200738
$748$	−3.06729e11	−0.0358259
$749$	1.54318e12	0.179163
$750$	1.61930e11	0.0186876
$751$	1.12380e13	1.28916	0.644581	−	0.764536i	$-0.277032\pi$
$751$	1.12380e13	1.28916	0.644581	+	0.764536i	$0.277032\pi$
$752$	6.63537e12	0.756632
$753$	−2.73252e12	−0.309732
$754$	6.48013e11	0.0730151
$755$	−6.28292e12	−0.703720
$756$	−1.24180e12	−0.138262
$757$	−7.11433e11	−0.0787413	−0.0393707	−	0.999225i	$-0.512535\pi$
$757$	−7.11433e11	−0.0787413	−0.0393707	+	0.999225i	$0.512535\pi$
$758$	−4.77539e11	−0.0525408
$759$	3.59090e12	0.392749
$760$	−6.33726e11	−0.0689034
$761$	7.84301e12	0.847719	0.423859	−	0.905728i	$-0.360675\pi$
$761$	7.84301e12	0.847719	0.423859	+	0.905728i	$0.360675\pi$
$762$	2.16517e11	0.0232645
$763$	7.94827e12	0.849009
$764$	−8.32481e12	−0.884004
$765$	8.97706e10	0.00947671
$766$	−6.43218e11	−0.0675039
$767$	1.56184e12	0.162952
$768$	5.40137e12	0.560245
$769$	−1.61297e13	−1.66325	−0.831627	−	0.555335i	$-0.812590\pi$
$769$	−1.61297e13	−1.66325	−0.831627	+	0.555335i	$0.812590\pi$
$770$	7.35913e11	0.0754429
$771$	3.95590e12	0.403181
$772$	−2.46663e12	−0.249935
$773$	2.75113e12	0.277142	0.138571	−	0.990352i	$-0.455749\pi$
$773$	2.75113e12	0.277142	0.138571	+	0.990352i	$0.455749\pi$
$774$	−1.37408e11	−0.0137619
$775$	−2.89540e12	−0.288304
$776$	4.81171e11	0.0476346
$777$	−4.22394e12	−0.415742
$778$	1.00213e12	0.0980657
$779$	−6.13235e12	−0.596635
$780$	−9.17831e12	−0.887845
$781$	−1.90980e13	−1.83678
$782$	5.74867e9	0.000549714 0
$783$	−2.16453e12	−0.205796
$784$	−5.04043e12	−0.476481
$785$	2.11941e13	1.99205
$786$	−5.32703e10	−0.00497833
$787$	6.57985e12	0.611406	0.305703	−	0.952127i	$-0.401108\pi$
$787$	6.57985e12	0.611406	0.305703	+	0.952127i	$0.401108\pi$
$788$	−3.88038e12	−0.358514
$789$	−4.64448e12	−0.426669
$790$	−3.58094e11	−0.0327096
$791$	5.28152e12	0.479694
$792$	6.26262e11	0.0565578
$793$	−7.43932e10	−0.00668043
$794$	3.68668e11	0.0329187
$795$	−6.44680e12	−0.572390
$796$	1.02383e13	0.903895
$797$	−1.64506e13	−1.44418	−0.722088	−	0.691801i	$-0.756817\pi$
$797$	−1.64506e13	−1.44418	−0.722088	+	0.691801i	$0.756817\pi$
$798$	−1.33439e11	−0.0116485
$799$	−2.02912e11	−0.0176135
$800$	9.79175e11	0.0845192
$801$	4.10723e12	0.352535
$802$	8.81857e11	0.0752685
$803$	−9.50796e12	−0.806989
$804$	4.98166e12	0.420457
$805$	4.62088e12	0.387832
$806$	4.54887e11	0.0379661
$807$	4.32205e12	0.358723
$808$	2.26757e12	0.187159
$809$	1.93194e13	1.58572	0.792859	−	0.609405i	$-0.208592\pi$
$809$	1.93194e13	1.58572	0.792859	+	0.609405i	$0.208592\pi$
$810$	−9.15077e10	−0.00746922
$811$	2.50823e12	0.203598	0.101799	−	0.994805i	$-0.467540\pi$
$811$	2.50823e12	0.203598	0.101799	+	0.994805i	$0.467540\pi$
$812$	9.51714e12	0.768253
$813$	−3.51830e12	−0.282439
$814$	1.06352e12	0.0849052
$815$	6.90434e11	0.0548167
$816$	−1.67196e11	−0.0132014
$817$	4.94684e12	0.388444
$818$	9.85768e10	0.00769813
$819$	−3.87098e12	−0.300638
$820$	1.84903e13	1.42818
$821$	2.08249e13	1.59970	0.799850	−	0.600200i	$-0.204912\pi$
$821$	2.08249e13	1.59970	0.799850	+	0.600200i	$0.204912\pi$
$822$	5.97408e10	0.00456402
$823$	−1.22807e13	−0.933091	−0.466545	−	0.884497i	$-0.654502\pi$
$823$	−1.22807e13	−0.933091	−0.466545	+	0.884497i	$0.654502\pi$
$824$	−2.38693e12	−0.180371
$825$	−6.20371e12	−0.466239
$826$	−6.84660e10	−0.00511758
$827$	−2.51636e11	−0.0187068	−0.00935338	−	0.999956i	$-0.502977\pi$
$827$	−2.51636e11	−0.0187068	−0.00935338	+	0.999956i	$0.502977\pi$
$828$	1.96325e12	0.145158
$829$	−1.55316e12	−0.114214	−0.0571072	−	0.998368i	$-0.518188\pi$
$829$	−1.55316e12	−0.114214	−0.0571072	+	0.998368i	$0.518188\pi$
$830$	−5.53503e11	−0.0404826
$831$	3.50350e12	0.254858
$832$	1.69916e13	1.22936
$833$	1.54138e11	0.0110919
$834$	−3.68046e11	−0.0263424
$835$	8.63416e12	0.614654
$836$	−1.12562e13	−0.797013
$837$	−1.51944e12	−0.107009
$838$	3.93154e11	0.0275400
$839$	−1.81673e12	−0.126579	−0.0632895	−	0.997995i	$-0.520159\pi$
$839$	−1.81673e12	−0.126579	−0.0632895	+	0.997995i	$0.520159\pi$
$840$	8.05894e11	0.0558497
$841$	2.08177e12	0.143499
$842$	1.17285e12	0.0804154
$843$	−6.22719e12	−0.424686
$844$	1.75468e13	1.19030
$845$	−1.03483e13	−0.698256
$846$	2.06838e11	0.0138824
$847$	1.53883e13	1.02734
$848$	1.20070e13	0.797360
$849$	4.92773e12	0.325509
$850$	−9.93153e9	−0.000652576 0
$851$	6.67794e12	0.436475
$852$	−1.04414e13	−0.678863
$853$	2.04844e13	1.32481	0.662403	−	0.749148i	$-0.269537\pi$
$853$	2.04844e13	1.32481	0.662403	+	0.749148i	$0.269537\pi$
$854$	3.26115e9	0.000209802 0
$855$	3.29438e12	0.210827
$856$	−4.25494e11	−0.0270870
$857$	−1.32055e13	−0.836263	−0.418131	−	0.908387i	$-0.637315\pi$
$857$	−1.32055e13	−0.836263	−0.418131	+	0.908387i	$0.637315\pi$
$858$	9.74647e11	0.0613980
$859$	1.73514e13	1.08734	0.543670	−	0.839299i	$-0.317034\pi$
$859$	1.73514e13	1.08734	0.543670	+	0.839299i	$0.317034\pi$
$860$	−1.49158e13	−0.929827
$861$	7.79836e12	0.483603
$862$	1.33563e11	0.00823956
$863$	−1.87435e13	−1.15028	−0.575138	−	0.818056i	$-0.695052\pi$
$863$	−1.87435e13	−1.15028	−0.575138	+	0.818056i	$0.695052\pi$
$864$	5.13850e11	0.0313707
$865$	1.96030e12	0.119056
$866$	−1.02097e12	−0.0616854
$867$	−9.60051e12	−0.577043
$868$	6.68076e12	0.399473
$869$	−1.27399e13	−0.757841
$870$	7.01313e11	0.0415026
$871$	1.55290e13	0.914242
$872$	−2.19154e12	−0.128359
$873$	−2.50133e12	−0.145750
$874$	2.10963e11	0.0122294
$875$	7.41344e12	0.427547
$876$	−5.19829e12	−0.298258
$877$	4.56616e12	0.260647	0.130323	−	0.991472i	$-0.458398\pi$
$877$	4.56616e12	0.260647	0.130323	+	0.991472i	$0.458398\pi$
$878$	1.74764e11	0.00992490
$879$	−8.76654e12	−0.495312
$880$	3.38383e13	1.90212
$881$	−4.31027e12	−0.241053	−0.120527	−	0.992710i	$-0.538458\pi$
$881$	−4.31027e12	−0.241053	−0.120527	+	0.992710i	$0.538458\pi$
$882$	−1.57121e11	−0.00874229
$883$	−1.02590e13	−0.567914	−0.283957	−	0.958837i	$-0.591647\pi$
$883$	−1.02590e13	−0.567914	−0.283957	+	0.958837i	$0.591647\pi$
$884$	−5.22753e11	−0.0287913
$885$	1.69031e12	0.0926234
$886$	1.63264e12	0.0890098
$887$	−1.22517e13	−0.664569	−0.332285	−	0.943179i	$-0.607819\pi$
$887$	−1.22517e13	−0.664569	−0.332285	+	0.943179i	$0.607819\pi$
$888$	1.16465e12	0.0628545
$889$	9.91249e12	0.532261
$890$	−1.33075e12	−0.0710954
$891$	−3.25557e12	−0.173052
$892$	−9.47538e12	−0.501135
$893$	−7.44641e12	−0.391846
$894$	−8.72529e11	−0.0456837
$895$	−3.01193e13	−1.56907
$896$	−3.01092e12	−0.156068
$897$	6.11992e12	0.315631
$898$	6.79406e11	0.0348647
$899$	1.16450e13	0.594592
$900$	−3.39176e12	−0.172319
$901$	−3.67179e11	−0.0185616
$902$	−1.96349e12	−0.0987642
$903$	−6.29077e12	−0.314854
$904$	−1.45625e12	−0.0725233
$905$	−1.48356e13	−0.735170
$906$	3.64770e11	0.0179863
$907$	4.04322e12	0.198378	0.0991892	−	0.995069i	$-0.468375\pi$
$907$	4.04322e12	0.198378	0.0991892	+	0.995069i	$0.468375\pi$
$908$	−1.51008e13	−0.737247
$909$	−1.17878e13	−0.572657
$910$	1.25421e12	0.0606293
$911$	6.23447e12	0.299893	0.149947	−	0.988694i	$-0.452090\pi$
$911$	6.23447e12	0.299893	0.149947	+	0.988694i	$0.452090\pi$
$912$	−6.13571e12	−0.293689
$913$	−1.96920e13	−0.937932
$914$	1.09954e12	0.0521139
$915$	−8.05121e10	−0.00379723
$916$	3.57615e12	0.167836
$917$	−2.43880e12	−0.113897
$918$	−5.21185e9	−0.000242214 0
$919$	1.21666e13	0.562663	0.281332	−	0.959611i	$-0.409224\pi$
$919$	1.21666e13	0.562663	0.281332	+	0.959611i	$0.409224\pi$
$920$	−1.27410e12	−0.0586350
$921$	−1.39859e13	−0.640502
$922$	6.66842e11	0.0303902
$923$	−3.25484e13	−1.47612
$924$	1.43143e13	0.646020
$925$	−1.15369e13	−0.518147
$926$	−1.43015e12	−0.0639195
$927$	1.24083e13	0.551889
$928$	−3.93813e12	−0.174311
$929$	1.94095e13	0.854955	0.427477	−	0.904026i	$-0.359402\pi$
$929$	1.94095e13	0.854955	0.427477	+	0.904026i	$0.359402\pi$
$930$	4.92302e11	0.0215803
$931$	5.65652e12	0.246760
$932$	−3.67594e13	−1.59587
$933$	−1.46866e12	−0.0634531
$934$	4.18756e11	0.0180053
$935$	−1.03479e12	−0.0442791
$936$	1.06733e12	0.0454524
$937$	3.80869e13	1.61416	0.807082	−	0.590439i	$-0.201046\pi$
$937$	3.80869e13	1.61416	0.807082	+	0.590439i	$0.201046\pi$
$938$	−6.80738e11	−0.0287123
$939$	−2.43200e13	−1.02086
$940$	2.24525e13	0.937970
$941$	−3.84217e13	−1.59743	−0.798717	−	0.601707i	$-0.794488\pi$
$941$	−3.84217e13	−1.59743	−0.798717	+	0.601707i	$0.794488\pi$
$942$	−1.23047e12	−0.0509147
$943$	−1.23290e13	−0.507720
$944$	−3.14816e12	−0.129028
$945$	−4.18938e12	−0.170886
$946$	1.58391e12	0.0643013
$947$	−2.26959e13	−0.917008	−0.458504	−	0.888692i	$-0.651615\pi$
$947$	−2.26959e13	−0.917008	−0.458504	+	0.888692i	$0.651615\pi$
$948$	−6.96531e12	−0.280093
$949$	−1.62043e13	−0.648533
$950$	−3.64465e11	−0.0145177
$951$	−2.65704e13	−1.05338
$952$	4.58999e10	0.00181111
$953$	−2.81368e13	−1.10498	−0.552492	−	0.833518i	$-0.686323\pi$
$953$	−2.81368e13	−1.10498	−0.552492	+	0.833518i	$0.686323\pi$
$954$	3.74285e11	0.0146297
$955$	−2.80848e13	−1.09259
$956$	2.30924e13	0.894147
$957$	2.49506e13	0.961563
$958$	−9.08008e10	−0.00348293
$959$	2.73503e12	0.104419
$960$	1.83892e13	0.698782
$961$	−1.82652e13	−0.690826
$962$	1.81253e12	0.0682336
$963$	2.21190e12	0.0828794
$964$	2.45617e13	0.916033
$965$	−8.32150e12	−0.308908
$966$	−2.68277e11	−0.00991256
$967$	−3.29680e13	−1.21248	−0.606238	−	0.795283i	$-0.707322\pi$
$967$	−3.29680e13	−1.21248	−0.606238	+	0.795283i	$0.707322\pi$
$968$	−4.24294e12	−0.155320
$969$	1.87632e11	0.00683676
$970$	8.10437e11	0.0293932
$971$	−3.55036e12	−0.128170	−0.0640849	−	0.997944i	$-0.520413\pi$
$971$	−3.55036e12	−0.128170	−0.0640849	+	0.997944i	$0.520413\pi$
$972$	−1.77992e12	−0.0639591
$973$	−1.68498e13	−0.602679
$974$	−1.76191e12	−0.0627291
$975$	−1.05729e13	−0.374691
$976$	1.49952e11	0.00528967
$977$	−2.31998e13	−0.814625	−0.407313	−	0.913289i	$-0.633534\pi$
$977$	−2.31998e13	−0.814625	−0.407313	+	0.913289i	$0.633534\pi$
$978$	−4.00848e10	−0.00140105
$979$	−4.73441e13	−1.64719
$980$	−1.70556e13	−0.590676
$981$	1.13926e13	0.392745
$982$	2.39695e12	0.0822541
$983$	5.95029e12	0.203258	0.101629	−	0.994822i	$-0.467595\pi$
$983$	5.95029e12	0.203258	0.101629	+	0.994822i	$0.467595\pi$
$984$	−2.15021e12	−0.0731142
$985$	−1.30910e13	−0.443107
$986$	3.99434e10	0.00134586
$987$	9.46940e12	0.317611
$988$	−1.91839e13	−0.640516
$989$	9.94553e12	0.330556
$990$	1.05481e12	0.0348993
$991$	3.98196e13	1.31149	0.655745	−	0.754982i	$-0.272355\pi$
$991$	3.98196e13	1.31149	0.655745	+	0.754982i	$0.272355\pi$
$992$	−2.76446e12	−0.0906374
$993$	−3.40975e13	−1.11289
$994$	1.42681e12	0.0463583
$995$	3.45401e13	1.11717
$996$	−1.07662e13	−0.346654
$997$	1.10377e13	0.353793	0.176897	−	0.984229i	$-0.443394\pi$
$997$	1.10377e13	0.353793	0.176897	+	0.984229i	$0.443394\pi$
$998$	−3.16674e12	−0.101048
$999$	−6.05434e12	−0.192319

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.d.1.12	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.d.1.12	✓	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)

\(f(q)\)	\(=\)	\(q+1.23437 q^{2} +81.0000 q^{3} -510.476 q^{4} -1722.16 q^{5} +99.9839 q^{6} +4577.43 q^{7} -1262.11 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+1.23437 q^{2} +81.0000 q^{3} -510.476 q^{4} -1722.16 q^{5} +99.9839 q^{6} +4577.43 q^{7} -1262.11 q^{8} +6561.00 q^{9} -2125.78 q^{10} -75628.8 q^{11} -41348.6 q^{12} -128893. q^{13} +5650.24 q^{14} -139495. q^{15} +259806. q^{16} -7944.95 q^{17} +8098.70 q^{18} -291562. q^{19} +879120. q^{20} +370772. q^{21} -93353.9 q^{22} -586180. q^{23} -102231. q^{24} +1.01270e6 q^{25} -159102. q^{26} +531441. q^{27} -2.33667e6 q^{28} -4.07295e6 q^{29} -172188. q^{30} -2.85910e6 q^{31} +966899. q^{32} -6.12593e6 q^{33} -9807.01 q^{34} -7.88305e6 q^{35} -3.34924e6 q^{36} -1.13923e7 q^{37} -359895. q^{38} -1.04403e7 q^{39} +2.17356e6 q^{40} +2.10328e7 q^{41} +457669. q^{42} -1.69667e7 q^{43} +3.86067e7 q^{44} -1.12991e7 q^{45} -723563. q^{46} +2.55397e7 q^{47} +2.10443e7 q^{48} -1.94007e7 q^{49} +1.25004e6 q^{50} -643541. q^{51} +6.57969e7 q^{52} +4.62154e7 q^{53} +655995. q^{54} +1.30245e8 q^{55} -5.77724e6 q^{56} -2.36165e7 q^{57} -5.02752e6 q^{58} -1.21174e7 q^{59} +7.12087e7 q^{60} +577170. q^{61} -3.52918e6 q^{62} +3.00325e7 q^{63} -1.31827e8 q^{64} +2.21974e8 q^{65} -7.56167e6 q^{66} -1.20480e8 q^{67} +4.05571e6 q^{68} -4.74806e7 q^{69} -9.73060e6 q^{70} +2.52522e8 q^{71} -8.28073e6 q^{72} +1.25719e8 q^{73} -1.40623e7 q^{74} +8.20284e7 q^{75} +1.48835e8 q^{76} -3.46186e8 q^{77} -1.28872e7 q^{78} +1.68453e8 q^{79} -4.47426e8 q^{80} +4.30467e7 q^{81} +2.59622e7 q^{82} +2.60377e8 q^{83} -1.89270e8 q^{84} +1.36824e7 q^{85} -2.09432e7 q^{86} -3.29909e8 q^{87} +9.54522e7 q^{88} +6.26006e8 q^{89} -1.39472e7 q^{90} -5.89999e8 q^{91} +2.99231e8 q^{92} -2.31587e8 q^{93} +3.15254e7 q^{94} +5.02115e8 q^{95} +7.83188e7 q^{96} -3.81243e8 q^{97} -2.39477e7 q^{98} -4.96201e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9}+O(q^{10}) \) 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

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