LMFDB - Embedded newform 177.10.a.d.1.17

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			1.17
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)

$f(q)$	$=$	$q+26.8820 q^{2} +81.0000 q^{3} +210.640 q^{4} +1004.40 q^{5} +2177.44 q^{6} +2540.49 q^{7} -8101.16 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+26.8820 q^{2} +81.0000 q^{3} +210.640 q^{4} +1004.40 q^{5} +2177.44 q^{6} +2540.49 q^{7} -8101.16 q^{8} +6561.00 q^{9} +27000.3 q^{10} -17065.1 q^{11} +17061.8 q^{12} +177208. q^{13} +68293.3 q^{14} +81356.4 q^{15} -325622. q^{16} -49497.6 q^{17} +176373. q^{18} +560689. q^{19} +211566. q^{20} +205779. q^{21} -458742. q^{22} -659184. q^{23} -656194. q^{24} -944305. q^{25} +4.76370e6 q^{26} +531441. q^{27} +535127. q^{28} +4.93430e6 q^{29} +2.18702e6 q^{30} +7.19154e6 q^{31} -4.60558e6 q^{32} -1.38227e6 q^{33} -1.33059e6 q^{34} +2.55167e6 q^{35} +1.38201e6 q^{36} -8.70511e6 q^{37} +1.50724e7 q^{38} +1.43539e7 q^{39} -8.13681e6 q^{40} +3.16641e7 q^{41} +5.53175e6 q^{42} +7.46475e6 q^{43} -3.59458e6 q^{44} +6.58987e6 q^{45} -1.77201e7 q^{46} +9.15962e6 q^{47} -2.63754e7 q^{48} -3.38995e7 q^{49} -2.53848e7 q^{50} -4.00931e6 q^{51} +3.73270e7 q^{52} -2.75118e6 q^{53} +1.42862e7 q^{54} -1.71402e7 q^{55} -2.05809e7 q^{56} +4.54158e7 q^{57} +1.32644e8 q^{58} -1.21174e7 q^{59} +1.71369e7 q^{60} +1.29284e8 q^{61} +1.93323e8 q^{62} +1.66681e7 q^{63} +4.29118e7 q^{64} +1.77988e8 q^{65} -3.71581e7 q^{66} -2.48513e8 q^{67} -1.04262e7 q^{68} -5.33939e7 q^{69} +6.85938e7 q^{70} +2.49769e8 q^{71} -5.31517e7 q^{72} +1.10902e8 q^{73} -2.34010e8 q^{74} -7.64887e7 q^{75} +1.18103e8 q^{76} -4.33536e7 q^{77} +3.85860e8 q^{78} +6.21014e7 q^{79} -3.27055e8 q^{80} +4.30467e7 q^{81} +8.51192e8 q^{82} -1.85488e8 q^{83} +4.33453e7 q^{84} -4.97154e7 q^{85} +2.00667e8 q^{86} +3.99679e8 q^{87} +1.38247e8 q^{88} +3.17916e8 q^{89} +1.77149e8 q^{90} +4.50195e8 q^{91} -1.38850e8 q^{92} +5.82515e8 q^{93} +2.46229e8 q^{94} +5.63157e8 q^{95} -3.73052e8 q^{96} +2.93921e8 q^{97} -9.11286e8 q^{98} -1.11964e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	26.8820	1.18803	0.594013	−	0.804455i	$-0.297543\pi$
$2$	26.8820	1.18803	0.594013	+	0.804455i	$0.297543\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	210.640	0.411405
$5$	1004.40	0.718691	0.359345	−	0.933205i	$-0.383000\pi$
$5$	1004.40	0.718691	0.359345	+	0.933205i	$0.383000\pi$
$6$	2177.44	0.685907
$7$	2540.49	0.399923	0.199961	−	0.979804i	$-0.435918\pi$
$7$	2540.49	0.399923	0.199961	+	0.979804i	$0.435918\pi$
$8$	−8101.16	−0.699266
$9$	6561.00	0.333333
$10$	27000.3	0.853823
$11$	−17065.1	−0.351431	−0.175716	−	0.984441i	$-0.556224\pi$
$11$	−17065.1	−0.351431	−0.175716	+	0.984441i	$0.556224\pi$
$12$	17061.8	0.237525
$13$	177208.	1.72083	0.860416	−	0.509593i	$-0.170204\pi$
$13$	177208.	1.72083	0.860416	+	0.509593i	$0.170204\pi$
$14$	68293.3	0.475118
$15$	81356.4	0.414936
$16$	−325622.	−1.24215
$17$	−49497.6	−0.143735	−0.0718677	−	0.997414i	$-0.522896\pi$
$17$	−49497.6	−0.143735	−0.0718677	+	0.997414i	$0.522896\pi$
$18$	176373.	0.396009
$19$	560689.	0.987031	0.493516	−	0.869737i	$-0.335712\pi$
$19$	560689.	0.987031	0.493516	+	0.869737i	$0.335712\pi$
$20$	211566.	0.295673
$21$	205779.	0.230895
$22$	−458742.	−0.417510
$23$	−659184.	−0.491169	−0.245585	−	0.969375i	$-0.578980\pi$
$23$	−659184.	−0.491169	−0.245585	+	0.969375i	$0.578980\pi$
$24$	−656194.	−0.403721
$25$	−944305.	−0.483484
$26$	4.76370e6	2.04439
$27$	531441.	0.192450
$28$	535127.	0.164530
$29$	4.93430e6	1.29549	0.647746	−	0.761856i	$-0.275712\pi$
$29$	4.93430e6	1.29549	0.647746	+	0.761856i	$0.275712\pi$
$30$	2.18702e6	0.492955
$31$	7.19154e6	1.39860	0.699301	−	0.714827i	$-0.253495\pi$
$31$	7.19154e6	1.39860	0.699301	+	0.714827i	$0.253495\pi$
$32$	−4.60558e6	−0.776442
$33$	−1.38227e6	−0.202899
$34$	−1.33059e6	−0.170761
$35$	2.55167e6	0.287421
$36$	1.38201e6	0.137135
$37$	−8.70511e6	−0.763601	−0.381801	−	0.924245i	$-0.624696\pi$
$37$	−8.70511e6	−0.763601	−0.381801	+	0.924245i	$0.624696\pi$
$38$	1.50724e7	1.17262
$39$	1.43539e7	0.993523
$40$	−8.13681e6	−0.502556
$41$	3.16641e7	1.75001	0.875003	−	0.484117i	$-0.160859\pi$
$41$	3.16641e7	1.75001	0.875003	+	0.484117i	$0.160859\pi$
$42$	5.53175e6	0.274310
$43$	7.46475e6	0.332972	0.166486	−	0.986044i	$-0.446758\pi$
$43$	7.46475e6	0.332972	0.166486	+	0.986044i	$0.446758\pi$
$44$	−3.59458e6	−0.144581
$45$	6.58987e6	0.239564
$46$	−1.77201e7	−0.583522
$47$	9.15962e6	0.273802	0.136901	−	0.990585i	$-0.456286\pi$
$47$	9.15962e6	0.273802	0.136901	+	0.990585i	$0.456286\pi$
$48$	−2.63754e7	−0.717156
$49$	−3.38995e7	−0.840062
$50$	−2.53848e7	−0.574391
$51$	−4.00931e6	−0.0829857
$52$	3.73270e7	0.707959
$53$	−2.75118e6	−0.0478935	−0.0239468	−	0.999713i	$-0.507623\pi$
$53$	−2.75118e6	−0.0478935	−0.0239468	+	0.999713i	$0.507623\pi$
$54$	1.42862e7	0.228636
$55$	−1.71402e7	−0.252570
$56$	−2.05809e7	−0.279652
$57$	4.54158e7	0.569863
$58$	1.32644e8	1.53908
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	1.71369e7	0.170707
$61$	1.29284e8	1.19553	0.597765	−	0.801671i	$-0.296055\pi$
$61$	1.29284e8	1.19553	0.597765	+	0.801671i	$0.296055\pi$
$62$	1.93323e8	1.66158
$63$	1.66681e7	0.133308
$64$	4.29118e7	0.319718
$65$	1.77988e8	1.23675
$66$	−3.71581e7	−0.241049
$67$	−2.48513e8	−1.50665	−0.753324	−	0.657650i	$-0.771551\pi$
$67$	−2.48513e8	−1.50665	−0.753324	+	0.657650i	$0.771551\pi$
$68$	−1.04262e7	−0.0591336
$69$	−5.33939e7	−0.283577
$70$	6.85938e7	0.341463
$71$	2.49769e8	1.16648	0.583239	−	0.812301i	$-0.301785\pi$
$71$	2.49769e8	1.16648	0.583239	+	0.812301i	$0.301785\pi$
$72$	−5.31517e7	−0.233089
$73$	1.10902e8	0.457072	0.228536	−	0.973535i	$-0.426606\pi$
$73$	1.10902e8	0.457072	0.228536	+	0.973535i	$0.426606\pi$
$74$	−2.34010e8	−0.907178
$75$	−7.64887e7	−0.279140
$76$	1.18103e8	0.406070
$77$	−4.33536e7	−0.140545
$78$	3.85860e8	1.18033
$79$	6.21014e7	0.179382	0.0896911	−	0.995970i	$-0.471412\pi$
$79$	6.21014e7	0.179382	0.0896911	+	0.995970i	$0.471412\pi$
$80$	−3.27055e8	−0.892722
$81$	4.30467e7	0.111111
$82$	8.51192e8	2.07905
$83$	−1.85488e8	−0.429008	−0.214504	−	0.976723i	$-0.568814\pi$
$83$	−1.85488e8	−0.429008	−0.214504	+	0.976723i	$0.568814\pi$
$84$	4.33453e7	0.0949916
$85$	−4.97154e7	−0.103301
$86$	2.00667e8	0.395579
$87$	3.99679e8	0.747953
$88$	1.38247e8	0.245744
$89$	3.17916e8	0.537103	0.268551	−	0.963265i	$-0.413455\pi$
$89$	3.17916e8	0.537103	0.268551	+	0.963265i	$0.413455\pi$
$90$	1.77149e8	0.284608
$91$	4.50195e8	0.688199
$92$	−1.38850e8	−0.202070
$93$	5.82515e8	0.807484
$94$	2.46229e8	0.325284
$95$	5.63157e8	0.709370
$96$	−3.73052e8	−0.448279
$97$	2.93921e8	0.337100	0.168550	−	0.985693i	$-0.446092\pi$
$97$	2.93921e8	0.337100	0.168550	+	0.985693i	$0.446092\pi$
$98$	−9.11286e8	−0.998015
$99$	−1.11964e8	−0.117144
$100$	−1.98908e8	−0.198908
$101$	−7.67270e8	−0.733673	−0.366836	−	0.930286i	$-0.619559\pi$
$101$	−7.67270e8	−0.733673	−0.366836	+	0.930286i	$0.619559\pi$
$102$	−1.07778e8	−0.0985892
$103$	−9.86745e7	−0.0863848	−0.0431924	−	0.999067i	$-0.513753\pi$
$103$	−9.86745e7	−0.0863848	−0.0431924	+	0.999067i	$0.513753\pi$
$104$	−1.43559e9	−1.20332
$105$	2.06685e8	0.165942
$106$	−7.39570e7	−0.0568988
$107$	1.51051e9	1.11403	0.557013	−	0.830504i	$-0.311947\pi$
$107$	1.51051e9	1.11403	0.557013	+	0.830504i	$0.311947\pi$
$108$	1.11943e8	0.0791750
$109$	−1.72548e9	−1.17082	−0.585411	−	0.810736i	$-0.699067\pi$
$109$	−1.72548e9	−1.17082	−0.585411	+	0.810736i	$0.699067\pi$
$110$	−4.60761e8	−0.300060
$111$	−7.05114e8	−0.440865
$112$	−8.27240e8	−0.496764
$113$	2.29046e9	1.32151	0.660754	−	0.750603i	$-0.270237\pi$
$113$	2.29046e9	1.32151	0.660754	+	0.750603i	$0.270237\pi$
$114$	1.22087e9	0.677012
$115$	−6.62084e8	−0.352999
$116$	1.03936e9	0.532973
$117$	1.16266e9	0.573611
$118$	−3.25738e8	−0.154668
$119$	−1.25748e8	−0.0574831
$120$	−6.59081e8	−0.290151
$121$	−2.06673e9	−0.876496
$122$	3.47541e9	1.42032
$123$	2.56479e9	1.01037
$124$	1.51482e9	0.575393
$125$	−2.91018e9	−1.06617
$126$	4.48072e8	0.158373
$127$	4.13955e9	1.41201	0.706003	−	0.708209i	$-0.250497\pi$
$127$	4.13955e9	1.41201	0.706003	+	0.708209i	$0.250497\pi$
$128$	3.51161e9	1.15628
$129$	6.04645e8	0.192241
$130$	4.78466e9	1.46929
$131$	4.82605e8	0.143176	0.0715882	−	0.997434i	$-0.477193\pi$
$131$	4.82605e8	0.143176	0.0715882	+	0.997434i	$0.477193\pi$
$132$	−2.91161e8	−0.0834738
$133$	1.42442e9	0.394736
$134$	−6.68050e9	−1.78994
$135$	5.33780e8	0.138312
$136$	4.00988e8	0.100509
$137$	−2.53966e9	−0.615932	−0.307966	−	0.951397i	$-0.599648\pi$
$137$	−2.53966e9	−0.615932	−0.307966	+	0.951397i	$0.599648\pi$
$138$	−1.43533e9	−0.336896
$139$	−4.54412e9	−1.03248	−0.516242	−	0.856443i	$-0.672670\pi$
$139$	−4.54412e9	−1.03248	−0.516242	+	0.856443i	$0.672670\pi$
$140$	5.37482e8	0.118246
$141$	7.41930e8	0.158080
$142$	6.71429e9	1.38581
$143$	−3.02407e9	−0.604754
$144$	−2.13641e9	−0.414050
$145$	4.95602e9	0.931058
$146$	2.98125e9	0.543014
$147$	−2.74586e9	−0.485010
$148$	−1.83364e9	−0.314150
$149$	−3.49472e9	−0.580863	−0.290432	−	0.956896i	$-0.593799\pi$
$149$	−3.49472e9	−0.580863	−0.290432	+	0.956896i	$0.593799\pi$
$150$	−2.05617e9	−0.331625
$151$	−1.55298e8	−0.0243091	−0.0121546	−	0.999926i	$-0.503869\pi$
$151$	−1.55298e8	−0.0243091	−0.0121546	+	0.999926i	$0.503869\pi$
$152$	−4.54223e9	−0.690197
$153$	−3.24754e8	−0.0479118
$154$	−1.16543e9	−0.166972
$155$	7.22319e9	1.00516
$156$	3.02349e9	0.408741
$157$	2.17714e8	0.0285981	0.0142991	−	0.999898i	$-0.495448\pi$
$157$	2.17714e8	0.0285981	0.0142991	+	0.999898i	$0.495448\pi$
$158$	1.66941e9	0.213111
$159$	−2.22845e8	−0.0276513
$160$	−4.62584e9	−0.558021
$161$	−1.67465e9	−0.196430
$162$	1.15718e9	0.132003
$163$	−8.72186e9	−0.967754	−0.483877	−	0.875136i	$-0.660772\pi$
$163$	−8.72186e9	−0.967754	−0.483877	+	0.875136i	$0.660772\pi$
$164$	6.66971e9	0.719962
$165$	−1.38835e9	−0.145822
$166$	−4.98629e9	−0.509673
$167$	1.45130e10	1.44389	0.721945	−	0.691951i	$-0.243249\pi$
$167$	1.45130e10	1.44389	0.721945	+	0.691951i	$0.243249\pi$
$168$	−1.66705e9	−0.161457
$169$	2.07982e10	1.96126
$170$	−1.33645e9	−0.122725
$171$	3.67868e9	0.329010
$172$	1.57237e9	0.136986
$173$	−1.16705e10	−0.990561	−0.495280	−	0.868733i	$-0.664935\pi$
$173$	−1.16705e10	−0.990561	−0.495280	+	0.868733i	$0.664935\pi$
$174$	1.07441e10	0.888587
$175$	−2.39899e9	−0.193356
$176$	5.55677e9	0.436531
$177$	−9.81506e8	−0.0751646
$178$	8.54621e9	0.638092
$179$	2.03224e9	0.147957	0.0739787	−	0.997260i	$-0.476430\pi$
$179$	2.03224e9	0.147957	0.0739787	+	0.997260i	$0.476430\pi$
$180$	1.38809e9	0.0985577
$181$	−1.11418e10	−0.771616	−0.385808	−	0.922579i	$-0.626077\pi$
$181$	−1.11418e10	−0.771616	−0.385808	+	0.922579i	$0.626077\pi$
$182$	1.21021e10	0.817599
$183$	1.04720e10	0.690240
$184$	5.34015e9	0.343458
$185$	−8.74342e9	−0.548793
$186$	1.56591e10	0.959311
$187$	8.44679e8	0.0505132
$188$	1.92938e9	0.112644
$189$	1.35012e9	0.0769651
$190$	1.51387e10	0.842750
$191$	−1.39384e10	−0.757817	−0.378908	−	0.925434i	$-0.623700\pi$
$191$	−1.39384e10	−0.757817	−0.378908	+	0.925434i	$0.623700\pi$
$192$	3.47586e9	0.184589
$193$	1.04739e10	0.543374	0.271687	−	0.962386i	$-0.412418\pi$
$193$	1.04739e10	0.543374	0.271687	+	0.962386i	$0.412418\pi$
$194$	7.90118e9	0.400483
$195$	1.44170e10	0.714035
$196$	−7.14058e9	−0.345606
$197$	−3.70303e10	−1.75170	−0.875848	−	0.482587i	$-0.839697\pi$
$197$	−3.70303e10	−1.75170	−0.875848	+	0.482587i	$0.839697\pi$
$198$	−3.00981e9	−0.139170
$199$	9.63246e9	0.435410	0.217705	−	0.976015i	$-0.430143\pi$
$199$	9.63246e9	0.435410	0.217705	+	0.976015i	$0.430143\pi$
$200$	7.64996e9	0.338084
$201$	−2.01295e10	−0.869863
$202$	−2.06257e10	−0.871622
$203$	1.25355e10	0.518097
$204$	−8.44518e8	−0.0341408
$205$	3.18034e10	1.25771
$206$	−2.65256e9	−0.102627
$207$	−4.32490e9	−0.163723
$208$	−5.77029e10	−2.13753
$209$	−9.56819e9	−0.346874
$210$	5.55610e9	0.197144
$211$	1.24880e10	0.433732	0.216866	−	0.976201i	$-0.430416\pi$
$211$	1.24880e10	0.433732	0.216866	+	0.976201i	$0.430416\pi$
$212$	−5.79507e8	−0.0197037
$213$	2.02313e10	0.673466
$214$	4.06054e10	1.32349
$215$	7.49760e9	0.239304
$216$	−4.30529e9	−0.134574
$217$	1.82700e10	0.559333
$218$	−4.63843e10	−1.39097
$219$	8.98303e9	0.263891
$220$	−3.61039e9	−0.103909
$221$	−8.77137e9	−0.247345
$222$	−1.89548e10	−0.523759
$223$	−3.24581e10	−0.878923	−0.439462	−	0.898261i	$-0.644831\pi$
$223$	−3.24581e10	−0.878923	−0.439462	+	0.898261i	$0.644831\pi$
$224$	−1.17004e10	−0.310517
$225$	−6.19558e9	−0.161161
$226$	6.15720e10	1.56998
$227$	4.82276e10	1.20553	0.602766	−	0.797918i	$-0.294065\pi$
$227$	4.82276e10	1.20553	0.602766	+	0.797918i	$0.294065\pi$
$228$	9.56637e9	0.234445
$229$	6.50235e10	1.56247	0.781233	−	0.624240i	$-0.214591\pi$
$229$	6.50235e10	1.56247	0.781233	+	0.624240i	$0.214591\pi$
$230$	−1.77981e10	−0.419372
$231$	−3.51164e9	−0.0811439
$232$	−3.99736e10	−0.905893
$233$	−2.95164e10	−0.656087	−0.328043	−	0.944663i	$-0.606389\pi$
$233$	−2.95164e10	−0.656087	−0.328043	+	0.944663i	$0.606389\pi$
$234$	3.12546e10	0.681464
$235$	9.19993e9	0.196779
$236$	−2.55240e9	−0.0535604
$237$	5.03021e9	0.103566
$238$	−3.38035e9	−0.0682914
$239$	7.31519e9	0.145022	0.0725112	−	0.997368i	$-0.476899\pi$
$239$	7.31519e9	0.145022	0.0725112	+	0.997368i	$0.476899\pi$
$240$	−2.64915e10	−0.515413
$241$	−6.99742e10	−1.33617	−0.668085	−	0.744085i	$-0.732886\pi$
$241$	−6.99742e10	−1.33617	−0.668085	+	0.744085i	$0.732886\pi$
$242$	−5.55578e10	−1.04130
$243$	3.48678e9	0.0641500
$244$	2.72323e10	0.491848
$245$	−3.40487e10	−0.603745
$246$	6.89466e10	1.20034
$247$	9.93586e10	1.69851
$248$	−5.82598e10	−0.977995
$249$	−1.50246e10	−0.247688
$250$	−7.82313e10	−1.26663
$251$	−9.97303e10	−1.58597	−0.792985	−	0.609241i	$-0.791474\pi$
$251$	−9.97303e10	−1.58597	−0.792985	+	0.609241i	$0.791474\pi$
$252$	3.51097e9	0.0548434
$253$	1.12490e10	0.172612
$254$	1.11279e11	1.67750
$255$	−4.02695e9	−0.0596410
$256$	7.24280e10	1.05397
$257$	2.72429e9	0.0389542	0.0194771	−	0.999810i	$-0.493800\pi$
$257$	2.72429e9	0.0389542	0.0194771	+	0.999810i	$0.493800\pi$
$258$	1.62540e10	0.228388
$259$	−2.21152e10	−0.305381
$260$	3.74913e10	0.508804
$261$	3.23740e10	0.431831
$262$	1.29734e10	0.170097
$263$	−1.08091e11	−1.39312	−0.696559	−	0.717500i	$-0.745287\pi$
$263$	−1.08091e11	−1.39312	−0.696559	+	0.717500i	$0.745287\pi$
$264$	1.11980e10	0.141880
$265$	−2.76328e9	−0.0344206
$266$	3.82913e10	0.468957
$267$	2.57512e10	0.310097
$268$	−5.23466e10	−0.619843
$269$	−1.39793e11	−1.62780	−0.813901	−	0.581004i	$-0.802660\pi$
$269$	−1.39793e11	−1.62780	−0.813901	+	0.581004i	$0.802660\pi$
$270$	1.43490e10	0.164318
$271$	−1.32949e11	−1.49735	−0.748675	−	0.662938i	$-0.769309\pi$
$271$	−1.32949e11	−1.49735	−0.748675	+	0.662938i	$0.769309\pi$
$272$	1.61175e10	0.178541
$273$	3.64658e10	0.397332
$274$	−6.82710e10	−0.731743
$275$	1.61146e10	0.169911
$276$	−1.12469e10	−0.116665
$277$	−1.69080e11	−1.72558	−0.862789	−	0.505565i	$-0.831284\pi$
$277$	−1.69080e11	−1.72558	−0.862789	+	0.505565i	$0.831284\pi$
$278$	−1.22155e11	−1.22662
$279$	4.71837e10	0.466201
$280$	−2.06715e10	−0.200983
$281$	−1.57003e11	−1.50221	−0.751104	−	0.660184i	$-0.770478\pi$
$281$	−1.57003e11	−1.50221	−0.751104	+	0.660184i	$0.770478\pi$
$282$	1.99445e10	0.187803
$283$	−1.41256e11	−1.30908	−0.654541	−	0.756026i	$-0.727138\pi$
$283$	−1.41256e11	−1.30908	−0.654541	+	0.756026i	$0.727138\pi$
$284$	5.26113e10	0.479895
$285$	4.56157e10	0.409555
$286$	−8.12928e10	−0.718464
$287$	8.04422e10	0.699867
$288$	−3.02172e10	−0.258814
$289$	−1.16138e11	−0.979340
$290$	1.33227e11	1.10612
$291$	2.38076e10	0.194625
$292$	2.33603e10	0.188042
$293$	−7.72906e10	−0.612664	−0.306332	−	0.951925i	$-0.599102\pi$
$293$	−7.72906e10	−0.612664	−0.306332	+	0.951925i	$0.599102\pi$
$294$	−7.38141e10	−0.576204
$295$	−1.21707e10	−0.0935655
$296$	7.05215e10	0.533960
$297$	−9.06907e9	−0.0676330
$298$	−9.39448e10	−0.690080
$299$	−1.16813e11	−0.845220
$300$	−1.61115e10	−0.114840
$301$	1.89641e10	0.133163
$302$	−4.17471e9	−0.0288799
$303$	−6.21489e10	−0.423586
$304$	−1.82573e11	−1.22604
$305$	1.29853e11	0.859216
$306$	−8.73002e9	−0.0569205
$307$	1.33175e10	0.0855656	0.0427828	−	0.999084i	$-0.486378\pi$
$307$	1.33175e10	0.0855656	0.0427828	+	0.999084i	$0.486378\pi$
$308$	−9.13198e9	−0.0578211
$309$	−7.99263e9	−0.0498743
$310$	1.94173e11	1.19416
$311$	3.71351e10	0.225093	0.112547	−	0.993646i	$-0.464099\pi$
$311$	3.71351e10	0.225093	0.112547	+	0.993646i	$0.464099\pi$
$312$	−1.16283e11	−0.694736
$313$	−2.77950e10	−0.163688	−0.0818440	−	0.996645i	$-0.526081\pi$
$313$	−2.77950e10	−0.163688	−0.0818440	+	0.996645i	$0.526081\pi$
$314$	5.85258e9	0.0339753
$315$	1.67415e10	0.0958068
$316$	1.30810e10	0.0737988
$317$	9.28132e10	0.516230	0.258115	−	0.966114i	$-0.416899\pi$
$317$	9.28132e10	0.516230	0.258115	+	0.966114i	$0.416899\pi$
$318$	−5.99052e9	−0.0328505
$319$	−8.42042e10	−0.455277
$320$	4.31006e10	0.229778
$321$	1.22351e11	0.643184
$322$	−4.50178e10	−0.233364
$323$	−2.77528e10	−0.141871
$324$	9.06734e9	0.0457117
$325$	−1.67338e11	−0.831994
$326$	−2.34461e11	−1.14972
$327$	−1.39764e11	−0.675975
$328$	−2.56516e11	−1.22372
$329$	2.32699e10	0.109500
$330$	−3.73216e10	−0.173240
$331$	−1.33057e10	−0.0609271	−0.0304636	−	0.999536i	$-0.509698\pi$
$331$	−1.33057e10	−0.0609271	−0.0304636	+	0.999536i	$0.509698\pi$
$332$	−3.90712e10	−0.176496
$333$	−5.71142e10	−0.254534
$334$	3.90138e11	1.71538
$335$	−2.49606e11	−1.08281
$336$	−6.70064e10	−0.286807
$337$	−2.49443e11	−1.05351	−0.526754	−	0.850018i	$-0.676591\pi$
$337$	−2.49443e11	−1.05351	−0.526754	+	0.850018i	$0.676591\pi$
$338$	5.59096e11	2.33003
$339$	1.85527e11	0.762972
$340$	−1.04720e10	−0.0424987
$341$	−1.22724e11	−0.491513
$342$	9.88902e10	0.390873
$343$	−1.88639e11	−0.735882
$344$	−6.04731e10	−0.232836
$345$	−5.36288e10	−0.203804
$346$	−3.13725e11	−1.17681
$347$	3.58966e11	1.32914	0.664570	−	0.747226i	$-0.268615\pi$
$347$	3.58966e11	1.32914	0.664570	+	0.747226i	$0.268615\pi$
$348$	8.41881e10	0.307712
$349$	1.63254e11	0.589045	0.294522	−	0.955645i	$-0.404839\pi$
$349$	1.63254e11	0.589045	0.294522	+	0.955645i	$0.404839\pi$
$350$	−6.44896e10	−0.229712
$351$	9.41756e10	0.331174
$352$	7.85944e10	0.272866
$353$	4.68374e11	1.60549	0.802744	−	0.596324i	$-0.203373\pi$
$353$	4.68374e11	1.60549	0.802744	+	0.596324i	$0.203373\pi$
$354$	−2.63848e10	−0.0892975
$355$	2.50868e11	0.838336
$356$	6.69657e10	0.220967
$357$	−1.01856e10	−0.0331879
$358$	5.46306e10	0.175777
$359$	−1.51162e10	−0.0480307	−0.0240153	−	0.999712i	$-0.507645\pi$
$359$	−1.51162e10	−0.0480307	−0.0240153	+	0.999712i	$0.507645\pi$
$360$	−5.33856e10	−0.167519
$361$	−8.31533e9	−0.0257690
$362$	−2.99513e11	−0.916700
$363$	−1.67405e11	−0.506045
$364$	9.48288e10	0.283129
$365$	1.11390e11	0.328493
$366$	2.81508e11	0.820023
$367$	−5.96213e11	−1.71555	−0.857776	−	0.514024i	$-0.828154\pi$
$367$	−5.96213e11	−1.71555	−0.857776	+	0.514024i	$0.828154\pi$
$368$	2.14645e11	0.610106
$369$	2.07748e11	0.583335
$370$	−2.35040e11	−0.651980
$371$	−6.98933e9	−0.0191537
$372$	1.22701e11	0.332203
$373$	3.43289e11	0.918270	0.459135	−	0.888367i	$-0.348160\pi$
$373$	3.43289e11	0.918270	0.459135	+	0.888367i	$0.348160\pi$
$374$	2.27066e10	0.0600110
$375$	−2.35725e11	−0.615551
$376$	−7.42036e10	−0.191461
$377$	8.74398e11	2.22932
$378$	3.62938e10	0.0914366
$379$	−3.16105e11	−0.786965	−0.393482	−	0.919332i	$-0.628730\pi$
$379$	−3.16105e11	−0.786965	−0.393482	+	0.919332i	$0.628730\pi$
$380$	1.18623e11	0.291839
$381$	3.35304e11	0.815222
$382$	−3.74693e11	−0.900306
$383$	1.76185e11	0.418383	0.209192	−	0.977875i	$-0.432917\pi$
$383$	1.76185e11	0.418383	0.209192	+	0.977875i	$0.432917\pi$
$384$	2.84440e11	0.667576
$385$	−4.35443e10	−0.101009
$386$	2.81558e11	0.645542
$387$	4.89762e10	0.110991
$388$	6.19115e10	0.138685
$389$	8.21100e11	1.81812	0.909061	−	0.416664i	$-0.136801\pi$
$389$	8.21100e11	1.81812	0.909061	+	0.416664i	$0.136801\pi$
$390$	3.87558e11	0.848292
$391$	3.26280e10	0.0705985
$392$	2.74625e11	0.587426
$393$	3.90910e10	0.0826629
$394$	−9.95446e11	−2.08106
$395$	6.23746e10	0.128920
$396$	−2.35840e10	−0.0481936
$397$	−2.79061e11	−0.563821	−0.281911	−	0.959441i	$-0.590968\pi$
$397$	−2.79061e11	−0.563821	−0.281911	+	0.959441i	$0.590968\pi$
$398$	2.58939e11	0.517278
$399$	1.15378e11	0.227901
$400$	3.07487e11	0.600560
$401$	7.21122e11	1.39270	0.696352	−	0.717700i	$-0.254805\pi$
$401$	7.21122e11	1.39270	0.696352	+	0.717700i	$0.254805\pi$
$402$	−5.41121e11	−1.03342
$403$	1.27440e12	2.40676
$404$	−1.61618e11	−0.301837
$405$	4.32361e10	0.0798545
$406$	3.36980e11	0.615512
$407$	1.48553e11	0.268353
$408$	3.24800e10	0.0580291
$409$	−5.40997e11	−0.955960	−0.477980	−	0.878371i	$-0.658631\pi$
$409$	−5.40997e11	−0.955960	−0.477980	+	0.878371i	$0.658631\pi$
$410$	8.54938e11	1.49420
$411$	−2.05712e11	−0.355609
$412$	−2.07847e10	−0.0355392
$413$	−3.07840e10	−0.0520655
$414$	−1.16262e11	−0.194507
$415$	−1.86305e11	−0.308324
$416$	−8.16145e11	−1.33613
$417$	−3.68074e11	−0.596105
$418$	−2.57212e11	−0.412095
$419$	−4.35766e11	−0.690701	−0.345350	−	0.938474i	$-0.612240\pi$
$419$	−4.35766e11	−0.690701	−0.345350	+	0.938474i	$0.612240\pi$
$420$	4.35360e10	0.0682696
$421$	5.04248e11	0.782303	0.391151	−	0.920326i	$-0.372077\pi$
$421$	5.04248e11	0.782303	0.391151	+	0.920326i	$0.372077\pi$
$422$	3.35702e11	0.515285
$423$	6.00963e10	0.0912675
$424$	2.22877e10	0.0334903
$425$	4.67408e10	0.0694938
$426$	5.43857e11	0.800095
$427$	3.28444e11	0.478120
$428$	3.18172e11	0.458317
$429$	−2.44949e11	−0.349155
$430$	2.01550e11	0.284299
$431$	8.09773e11	1.13036	0.565179	−	0.824969i	$-0.308807\pi$
$431$	8.09773e11	1.13036	0.565179	+	0.824969i	$0.308807\pi$
$432$	−1.73049e11	−0.239052
$433$	5.81362e11	0.794787	0.397394	−	0.917648i	$-0.369915\pi$
$433$	5.81362e11	0.794787	0.397394	+	0.917648i	$0.369915\pi$
$434$	4.91134e11	0.664502
$435$	4.01437e11	0.537547
$436$	−3.63455e11	−0.481683
$437$	−3.69597e11	−0.484800
$438$	2.41481e11	0.313509
$439$	4.32577e11	0.555870	0.277935	−	0.960600i	$-0.410350\pi$
$439$	4.32577e11	0.555870	0.277935	+	0.960600i	$0.410350\pi$
$440$	1.38855e11	0.176614
$441$	−2.22415e11	−0.280021
$442$	−2.35792e11	−0.293852
$443$	1.47115e12	1.81484	0.907422	−	0.420220i	$-0.138047\pi$
$443$	1.47115e12	1.81484	0.907422	+	0.420220i	$0.138047\pi$
$444$	−1.48525e11	−0.181374
$445$	3.19315e11	0.386011
$446$	−8.72537e11	−1.04418
$447$	−2.83072e11	−0.335361
$448$	1.09017e11	0.127862
$449$	−1.70596e12	−1.98089	−0.990444	−	0.137916i	$-0.955960\pi$
$449$	−1.70596e12	−1.98089	−0.990444	+	0.137916i	$0.955960\pi$
$450$	−1.66549e11	−0.191464
$451$	−5.40349e11	−0.615007
$452$	4.82461e11	0.543675
$453$	−1.25791e10	−0.0140349
$454$	1.29645e12	1.43220
$455$	4.52176e11	0.494602
$456$	−3.67921e11	−0.398485
$457$	−6.16875e10	−0.0661568	−0.0330784	−	0.999453i	$-0.510531\pi$
$457$	−6.16875e10	−0.0661568	−0.0330784	+	0.999453i	$0.510531\pi$
$458$	1.74796e12	1.85625
$459$	−2.63051e10	−0.0276619
$460$	−1.39461e11	−0.145226
$461$	6.66518e11	0.687318	0.343659	−	0.939094i	$-0.388334\pi$
$461$	6.66518e11	0.687318	0.343659	+	0.939094i	$0.388334\pi$
$462$	−9.43997e10	−0.0964011
$463$	−6.86095e11	−0.693857	−0.346928	−	0.937892i	$-0.612775\pi$
$463$	−6.86095e11	−0.693857	−0.346928	+	0.937892i	$0.612775\pi$
$464$	−1.60672e12	−1.60920
$465$	5.85078e11	0.580331
$466$	−7.93458e11	−0.779448
$467$	8.37390e11	0.814707	0.407354	−	0.913271i	$-0.366452\pi$
$467$	8.37390e11	0.814707	0.407354	+	0.913271i	$0.366452\pi$
$468$	2.44903e11	0.235986
$469$	−6.31343e11	−0.602542
$470$	2.47312e11	0.233779
$471$	1.76348e10	0.0165111
$472$	9.81647e10	0.0910366
$473$	−1.27386e11	−0.117017
$474$	1.35222e11	0.123039
$475$	−5.29461e11	−0.477214
$476$	−2.64875e10	−0.0236488
$477$	−1.80505e10	−0.0159645
$478$	1.96647e11	0.172290
$479$	−6.38652e11	−0.554313	−0.277156	−	0.960825i	$-0.589392\pi$
$479$	−6.38652e11	−0.554313	−0.277156	+	0.960825i	$0.589392\pi$
$480$	−3.74693e11	−0.322174
$481$	−1.54262e12	−1.31403
$482$	−1.88104e12	−1.58740
$483$	−1.35646e11	−0.113409
$484$	−4.35335e11	−0.360595
$485$	2.95215e11	0.242270
$486$	9.37316e10	0.0762119
$487$	4.45800e11	0.359137	0.179568	−	0.983745i	$-0.442530\pi$
$487$	4.45800e11	0.359137	0.179568	+	0.983745i	$0.442530\pi$
$488$	−1.04735e12	−0.835993
$489$	−7.06471e11	−0.558733
$490$	−9.15296e11	−0.717264
$491$	7.33856e10	0.0569829	0.0284914	−	0.999594i	$-0.490930\pi$
$491$	7.33856e10	0.0569829	0.0284914	+	0.999594i	$0.490930\pi$
$492$	5.40246e11	0.415670
$493$	−2.44236e11	−0.186208
$494$	2.67095e12	2.01788
$495$	−1.12457e11	−0.0841902
$496$	−2.34173e12	−1.73728
$497$	6.34536e11	0.466501
$498$	−4.03890e11	−0.294260
$499$	9.92890e11	0.716884	0.358442	−	0.933552i	$-0.383308\pi$
$499$	9.92890e11	0.716884	0.358442	+	0.933552i	$0.383308\pi$
$500$	−6.12999e11	−0.438626
$501$	1.17556e12	0.833630
$502$	−2.68094e12	−1.88417
$503$	−2.24824e12	−1.56598	−0.782989	−	0.622035i	$-0.786306\pi$
$503$	−2.24824e12	−1.56598	−0.782989	+	0.622035i	$0.786306\pi$
$504$	−1.35031e11	−0.0932173
$505$	−7.70647e11	−0.527283
$506$	3.02395e11	0.205068
$507$	1.68465e12	1.13233
$508$	8.71953e11	0.580907
$509$	−1.49442e12	−0.986829	−0.493414	−	0.869794i	$-0.664251\pi$
$509$	−1.49442e12	−0.986829	−0.493414	+	0.869794i	$0.664251\pi$
$510$	−1.08252e11	−0.0708551
$511$	2.81744e11	0.182793
$512$	1.49064e11	0.0958647
$513$	2.97973e11	0.189954
$514$	7.32342e10	0.0462786
$515$	−9.91087e10	−0.0620839
$516$	1.27362e11	0.0790891
$517$	−1.56310e11	−0.0962228
$518$	−5.94500e11	−0.362801
$519$	−9.45309e11	−0.571901
$520$	−1.44191e12	−0.864813
$521$	3.29635e10	0.0196003	0.00980017	−	0.999952i	$-0.496880\pi$
$521$	3.29635e10	0.0196003	0.00980017	+	0.999952i	$0.496880\pi$
$522$	8.70276e11	0.513026
$523$	2.00057e12	1.16922	0.584609	−	0.811315i	$-0.301248\pi$
$523$	2.00057e12	1.16922	0.584609	+	0.811315i	$0.301248\pi$
$524$	1.01656e11	0.0589035
$525$	−1.94319e11	−0.111634
$526$	−2.90569e12	−1.65506
$527$	−3.55964e11	−0.201029
$528$	4.50098e11	0.252031
$529$	−1.36663e12	−0.758753
$530$	−7.42824e10	−0.0408926
$531$	−7.95020e10	−0.0433963
$532$	3.00040e11	0.162397
$533$	5.61113e12	3.01147
$534$	6.92243e11	0.368403
$535$	1.51715e12	0.800640
$536$	2.01324e12	1.05355
$537$	1.64612e11	0.0854232
$538$	−3.75792e12	−1.93387
$539$	5.78497e11	0.295224
$540$	1.12435e11	0.0569023
$541$	−1.86300e12	−0.935028	−0.467514	−	0.883986i	$-0.654850\pi$
$541$	−1.86300e12	−0.935028	−0.467514	+	0.883986i	$0.654850\pi$
$542$	−3.57393e12	−1.77889
$543$	−9.02485e11	−0.445493
$544$	2.27965e11	0.111602
$545$	−1.73308e12	−0.841459
$546$	9.80272e11	0.472041
$547$	−3.94348e11	−0.188338	−0.0941688	−	0.995556i	$-0.530019\pi$
$547$	−3.94348e11	−0.188338	−0.0941688	+	0.995556i	$0.530019\pi$
$548$	−5.34953e11	−0.253398
$549$	8.48233e11	0.398510
$550$	4.33192e11	0.201859
$551$	2.76661e12	1.27869
$552$	4.32552e11	0.198295
$553$	1.57768e11	0.0717390
$554$	−4.54521e12	−2.05003
$555$	−7.08217e11	−0.316846
$556$	−9.57172e11	−0.424770
$557$	−8.18991e11	−0.360521	−0.180261	−	0.983619i	$-0.557694\pi$
$557$	−8.18991e11	−0.360521	−0.180261	+	0.983619i	$0.557694\pi$
$558$	1.26839e12	0.553859
$559$	1.32281e12	0.572988
$560$	−8.30880e11	−0.357020
$561$	6.84190e10	0.0291638
$562$	−4.22055e12	−1.78466
$563$	2.58923e12	1.08613	0.543066	−	0.839690i	$-0.317264\pi$
$563$	2.58923e12	1.08613	0.543066	+	0.839690i	$0.317264\pi$
$564$	1.56280e11	0.0650349
$565$	2.30054e12	0.949755
$566$	−3.79723e12	−1.55522
$567$	1.09360e11	0.0444358
$568$	−2.02342e12	−0.815678
$569$	4.71689e11	0.188647	0.0943237	−	0.995542i	$-0.469931\pi$
$569$	4.71689e11	0.188647	0.0943237	+	0.995542i	$0.469931\pi$
$570$	1.22624e12	0.486562
$571$	3.68890e12	1.45223	0.726113	−	0.687576i	$-0.241325\pi$
$571$	3.68890e12	1.45223	0.726113	+	0.687576i	$0.241325\pi$
$572$	−6.36988e11	−0.248799
$573$	−1.12901e12	−0.437526
$574$	2.16244e12	0.831460
$575$	6.22470e11	0.237472
$576$	2.81544e11	0.106573
$577$	2.54528e12	0.955969	0.477985	−	0.878368i	$-0.341368\pi$
$577$	2.54528e12	0.955969	0.477985	+	0.878368i	$0.341368\pi$
$578$	−3.12201e12	−1.16348
$579$	8.48382e11	0.313717
$580$	1.04393e12	0.383042
$581$	−4.71231e11	−0.171570
$582$	6.39996e11	0.231219
$583$	4.69490e10	0.0168313
$584$	−8.98431e11	−0.319615
$585$	1.16778e12	0.412248
$586$	−2.07772e12	−0.727861
$587$	6.08590e11	0.211570	0.105785	−	0.994389i	$-0.466265\pi$
$587$	6.08590e11	0.211570	0.105785	+	0.994389i	$0.466265\pi$
$588$	−5.78387e11	−0.199536
$589$	4.03222e12	1.38046
$590$	−3.27172e11	−0.111158
$591$	−2.99945e12	−1.01134
$592$	2.83458e12	0.948508
$593$	5.29940e12	1.75987	0.879936	−	0.475093i	$-0.157585\pi$
$593$	5.29940e12	1.75987	0.879936	+	0.475093i	$0.157585\pi$
$594$	−2.43794e11	−0.0803498
$595$	−1.26301e11	−0.0413125
$596$	−7.36126e11	−0.238970
$597$	7.80229e11	0.251384
$598$	−3.14015e12	−1.00414
$599$	−1.40023e12	−0.444404	−0.222202	−	0.975001i	$-0.571324\pi$
$599$	−1.40023e12	−0.444404	−0.222202	+	0.975001i	$0.571324\pi$
$600$	6.19647e11	0.195193
$601$	−5.15838e12	−1.61279	−0.806396	−	0.591376i	$-0.798585\pi$
$601$	−5.15838e12	−1.61279	−0.806396	+	0.591376i	$0.798585\pi$
$602$	5.09792e11	0.158201
$603$	−1.63049e12	−0.502216
$604$	−3.27119e10	−0.0100009
$605$	−2.07583e12	−0.629929
$606$	−1.67068e12	−0.503231
$607$	−1.84609e11	−0.0551954	−0.0275977	−	0.999619i	$-0.508786\pi$
$607$	−1.84609e11	−0.0551954	−0.0275977	+	0.999619i	$0.508786\pi$
$608$	−2.58230e12	−0.766373
$609$	1.01538e12	0.299123
$610$	3.49070e12	1.02077
$611$	1.62316e12	0.471168
$612$	−6.84060e10	−0.0197112
$613$	2.95650e12	0.845678	0.422839	−	0.906205i	$-0.361033\pi$
$613$	2.95650e12	0.845678	0.422839	+	0.906205i	$0.361033\pi$
$614$	3.58000e11	0.101654
$615$	2.57608e12	0.726141
$616$	3.51214e11	0.0982785
$617$	5.12873e12	1.42471	0.712355	−	0.701819i	$-0.247629\pi$
$617$	5.12873e12	1.42471	0.712355	+	0.701819i	$0.247629\pi$
$618$	−2.14858e11	−0.0592519
$619$	−3.52031e12	−0.963769	−0.481884	−	0.876235i	$-0.660047\pi$
$619$	−3.52031e12	−0.963769	−0.481884	+	0.876235i	$0.660047\pi$
$620$	1.52149e12	0.413529
$621$	−3.50317e11	−0.0945256
$622$	9.98264e11	0.267417
$623$	8.07662e11	0.214800
$624$	−4.67394e12	−1.23411
$625$	−1.07864e12	−0.282759
$626$	−7.47183e11	−0.194466
$627$	−7.75024e11	−0.200268
$628$	4.58592e10	0.0117654
$629$	4.30882e11	0.109757
$630$	4.50044e11	0.113821
$631$	7.39205e12	1.85624	0.928118	−	0.372287i	$-0.121426\pi$
$631$	7.39205e12	1.85624	0.928118	+	0.372287i	$0.121426\pi$
$632$	−5.03093e11	−0.125436
$633$	1.01153e12	0.250415
$634$	2.49500e12	0.613295
$635$	4.15777e12	1.01479
$636$	−4.69400e10	−0.0113759
$637$	−6.00727e12	−1.44561
$638$	−2.26357e12	−0.540881
$639$	1.63874e12	0.388826
$640$	3.52706e12	0.831004
$641$	−4.35042e11	−0.101782	−0.0508908	−	0.998704i	$-0.516206\pi$
$641$	−4.35042e11	−0.101782	−0.0508908	+	0.998704i	$0.516206\pi$
$642$	3.28903e12	0.764119
$643$	4.15366e12	0.958256	0.479128	−	0.877745i	$-0.340953\pi$
$643$	4.15366e12	0.958256	0.479128	+	0.877745i	$0.340953\pi$
$644$	−3.52747e11	−0.0808122
$645$	6.07306e11	0.138162
$646$	−7.46049e11	−0.168547
$647$	6.51804e11	0.146234	0.0731169	−	0.997323i	$-0.476705\pi$
$647$	6.51804e11	0.146234	0.0731169	+	0.997323i	$0.476705\pi$
$648$	−3.48728e11	−0.0776962
$649$	2.06783e11	0.0457525
$650$	−4.49838e12	−0.988431
$651$	1.47987e12	0.322931
$652$	−1.83717e12	−0.398139
$653$	−3.91543e12	−0.842695	−0.421347	−	0.906899i	$-0.638443\pi$
$653$	−3.91543e12	−0.842695	−0.421347	+	0.906899i	$0.638443\pi$
$654$	−3.75713e12	−0.803076
$655$	4.84729e11	0.102899
$656$	−1.03105e13	−2.17377
$657$	7.27625e11	0.152357
$658$	6.25541e11	0.130089
$659$	1.01878e12	0.210425	0.105212	−	0.994450i	$-0.466448\pi$
$659$	1.01878e12	0.210425	0.105212	+	0.994450i	$0.466448\pi$
$660$	−2.92442e11	−0.0599918
$661$	9.61179e11	0.195838	0.0979192	−	0.995194i	$-0.468781\pi$
$661$	9.61179e11	0.195838	0.0979192	+	0.995194i	$0.468781\pi$
$662$	−3.57682e11	−0.0723830
$663$	−7.10481e11	−0.142804
$664$	1.50267e12	0.299991
$665$	1.43069e12	0.283693
$666$	−1.53534e12	−0.302393
$667$	−3.25261e12	−0.636306
$668$	3.05702e12	0.594024
$669$	−2.62911e12	−0.507447
$670$	−6.70990e12	−1.28641
$671$	−2.20624e12	−0.420147
$672$	−9.47733e11	−0.179277
$673$	5.32563e12	1.00070	0.500350	−	0.865823i	$-0.333205\pi$
$673$	5.32563e12	1.00070	0.500350	+	0.865823i	$0.333205\pi$
$674$	−6.70553e12	−1.25159
$675$	−5.01842e11	−0.0930465
$676$	4.38092e12	0.806874
$677$	1.50186e12	0.274777	0.137388	−	0.990517i	$-0.456129\pi$
$677$	1.50186e12	0.274777	0.137388	+	0.990517i	$0.456129\pi$
$678$	4.98733e12	0.906431
$679$	7.46704e11	0.134814
$680$	4.02752e11	0.0722351
$681$	3.90643e12	0.696015
$682$	−3.29906e12	−0.583930
$683$	−2.94350e12	−0.517572	−0.258786	−	0.965935i	$-0.583323\pi$
$683$	−2.94350e12	−0.517572	−0.258786	+	0.965935i	$0.583323\pi$
$684$	7.74876e11	0.135357
$685$	−2.55084e12	−0.442665
$686$	−5.07099e12	−0.874247
$687$	5.26690e12	0.902090
$688$	−2.43069e12	−0.413601
$689$	−4.87531e11	−0.0824167
$690$	−1.44165e12	−0.242124
$691$	−5.59771e12	−0.934026	−0.467013	−	0.884250i	$-0.654670\pi$
$691$	−5.59771e12	−0.934026	−0.467013	+	0.884250i	$0.654670\pi$
$692$	−2.45826e12	−0.407522
$693$	−2.84443e11	−0.0468485
$694$	9.64971e12	1.57905
$695$	−4.56412e12	−0.742037
$696$	−3.23786e12	−0.523018
$697$	−1.56730e12	−0.251538
$698$	4.38858e12	0.699800
$699$	−2.39083e12	−0.378792
$700$	−5.05323e11	−0.0795478
$701$	−1.22684e12	−0.191892	−0.0959459	−	0.995387i	$-0.530588\pi$
$701$	−1.22684e12	−0.191892	−0.0959459	+	0.995387i	$0.530588\pi$
$702$	2.53163e12	0.393444
$703$	−4.88086e12	−0.753698
$704$	−7.32293e11	−0.112359
$705$	7.45194e11	0.113611
$706$	1.25908e13	1.90736
$707$	−1.94924e12	−0.293412
$708$	−2.06744e11	−0.0309231
$709$	1.14374e13	1.69989	0.849943	−	0.526875i	$-0.176637\pi$
$709$	1.14374e13	1.69989	0.849943	+	0.526875i	$0.176637\pi$
$710$	6.74383e12	0.995965
$711$	4.07447e11	0.0597941
$712$	−2.57549e12	−0.375578
$713$	−4.74055e12	−0.686951
$714$	−2.73809e11	−0.0394280
$715$	−3.03737e12	−0.434631
$716$	4.28070e11	0.0608705
$717$	5.92530e11	0.0837287
$718$	−4.06354e11	−0.0570617
$719$	−5.07223e10	−0.00707813	−0.00353907	−	0.999994i	$-0.501127\pi$
$719$	−5.07223e10	−0.00707813	−0.00353907	+	0.999994i	$0.501127\pi$
$720$	−2.14581e12	−0.297574
$721$	−2.50681e11	−0.0345472
$722$	−2.23532e11	−0.0306142
$723$	−5.66791e12	−0.771438
$724$	−2.34690e12	−0.317447
$725$	−4.65949e12	−0.626350
$726$	−4.50018e12	−0.601195
$727$	−1.25047e13	−1.66024	−0.830118	−	0.557588i	$-0.811727\pi$
$727$	−1.25047e13	−1.66024	−0.830118	+	0.557588i	$0.811727\pi$
$728$	−3.64710e12	−0.481234
$729$	2.82430e11	0.0370370
$730$	2.99437e12	0.390259
$731$	−3.69487e11	−0.0478598
$732$	2.20582e12	0.283968
$733$	−4.88939e12	−0.625586	−0.312793	−	0.949821i	$-0.601265\pi$
$733$	−4.88939e12	−0.625586	−0.312793	+	0.949821i	$0.601265\pi$
$734$	−1.60274e13	−2.03812
$735$	−2.75795e12	−0.348572
$736$	3.03592e12	0.381364
$737$	4.24088e12	0.529483
$738$	5.58467e12	0.693017
$739$	−1.41341e13	−1.74328	−0.871641	−	0.490146i	$-0.836944\pi$
$739$	−1.41341e13	−1.74328	−0.871641	+	0.490146i	$0.836944\pi$
$740$	−1.84171e12	−0.225776
$741$	8.04805e12	0.980638
$742$	−1.87887e11	−0.0227551
$743$	6.49246e12	0.781555	0.390778	−	0.920485i	$-0.372206\pi$
$743$	6.49246e12	0.781555	0.390778	+	0.920485i	$0.372206\pi$
$744$	−4.71904e12	−0.564646
$745$	−3.51009e12	−0.417461
$746$	9.22828e12	1.09093
$747$	−1.21699e12	−0.143003
$748$	1.77923e11	0.0207814
$749$	3.83742e12	0.445524
$750$	−6.33674e12	−0.731291
$751$	1.27660e13	1.46445	0.732227	−	0.681060i	$-0.238481\pi$
$751$	1.27660e13	1.46445	0.732227	+	0.681060i	$0.238481\pi$
$752$	−2.98258e12	−0.340104
$753$	−8.07815e12	−0.915661
$754$	2.35055e13	2.64849
$755$	−1.55981e11	−0.0174707
$756$	2.84389e11	0.0316639
$757$	1.98458e12	0.219653	0.109827	−	0.993951i	$-0.464970\pi$
$757$	1.98458e12	0.219653	0.109827	+	0.993951i	$0.464970\pi$
$758$	−8.49753e12	−0.934934
$759$	9.11170e11	0.0996578
$760$	−4.56222e12	−0.496038
$761$	1.71578e13	1.85451	0.927257	−	0.374426i	$-0.122160\pi$
$761$	1.71578e13	1.85451	0.927257	+	0.374426i	$0.122160\pi$
$762$	9.01362e12	0.968504
$763$	−4.38357e12	−0.468238
$764$	−2.93599e12	−0.311770
$765$	−3.26183e11	−0.0344338
$766$	4.73620e12	0.497050
$767$	−2.14729e12	−0.224033
$768$	5.86667e12	0.608508
$769$	1.34721e13	1.38921	0.694606	−	0.719391i	$-0.255579\pi$
$769$	1.34721e13	1.38921	0.694606	+	0.719391i	$0.255579\pi$
$770$	−1.17056e12	−0.120001
$771$	2.20667e11	0.0224902
$772$	2.20621e12	0.223547
$773$	−9.26209e12	−0.933042	−0.466521	−	0.884510i	$-0.654493\pi$
$773$	−9.26209e12	−0.933042	−0.466521	+	0.884510i	$0.654493\pi$
$774$	1.31658e12	0.131860
$775$	−6.79101e12	−0.676202
$776$	−2.38110e12	−0.235722
$777$	−1.79133e12	−0.176312
$778$	2.20728e13	2.15998
$779$	1.77537e13	1.72731
$780$	3.03679e12	0.293758
$781$	−4.26233e12	−0.409937
$782$	8.77105e11	0.0838728
$783$	2.62229e12	0.249318
$784$	1.10384e13	1.04348
$785$	2.18672e11	0.0205532
$786$	1.05084e12	0.0982057
$787$	1.57166e13	1.46040	0.730201	−	0.683232i	$-0.239426\pi$
$787$	1.57166e13	1.46040	0.730201	+	0.683232i	$0.239426\pi$
$788$	−7.80004e12	−0.720657
$789$	−8.75535e12	−0.804317
$790$	1.67675e12	0.153161
$791$	5.81888e12	0.528500
$792$	9.07037e11	0.0819146
$793$	2.29102e13	2.05731
$794$	−7.50170e12	−0.669834
$795$	−2.23826e11	−0.0198728
$796$	2.02898e12	0.179130
$797$	1.84624e13	1.62078	0.810391	−	0.585890i	$-0.199255\pi$
$797$	1.84624e13	1.62078	0.810391	+	0.585890i	$0.199255\pi$
$798$	3.10160e12	0.270752
$799$	−4.53379e11	−0.0393551
$800$	4.34907e12	0.375397
$801$	2.08585e12	0.179034
$802$	1.93852e13	1.65457
$803$	−1.89254e12	−0.160630
$804$	−4.24007e12	−0.357867
$805$	−1.68202e12	−0.141172
$806$	3.42583e13	2.85929
$807$	−1.13233e13	−0.939812
$808$	6.21578e12	0.513032
$809$	4.37858e12	0.359389	0.179695	−	0.983722i	$-0.442489\pi$
$809$	4.37858e12	0.359389	0.179695	+	0.983722i	$0.442489\pi$
$810$	1.16227e12	0.0948692
$811$	−3.85768e11	−0.0313135	−0.0156568	−	0.999877i	$-0.504984\pi$
$811$	−3.85768e11	−0.0313135	−0.0156568	+	0.999877i	$0.504984\pi$
$812$	2.64048e12	0.213148
$813$	−1.07689e13	−0.864495
$814$	3.99340e12	0.318811
$815$	−8.76024e12	−0.695516
$816$	1.30552e12	0.103081
$817$	4.18541e12	0.328654
$818$	−1.45430e13	−1.13570
$819$	2.95373e12	0.229400
$820$	6.69906e12	0.517430
$821$	−1.46865e13	−1.12817	−0.564083	−	0.825718i	$-0.690770\pi$
$821$	−1.46865e13	−1.12817	−0.564083	+	0.825718i	$0.690770\pi$
$822$	−5.52995e12	−0.422472
$823$	−1.51766e13	−1.15313	−0.576563	−	0.817053i	$-0.695606\pi$
$823$	−1.51766e13	−1.15313	−0.576563	+	0.817053i	$0.695606\pi$
$824$	7.99377e11	0.0604059
$825$	1.30528e12	0.0980984
$826$	−8.27534e11	−0.0618551
$827$	−1.74238e13	−1.29529	−0.647646	−	0.761941i	$-0.724246\pi$
$827$	−1.74238e13	−1.29529	−0.647646	+	0.761941i	$0.724246\pi$
$828$	−9.10996e11	−0.0673566
$829$	−1.91002e13	−1.40457	−0.702284	−	0.711897i	$-0.747836\pi$
$829$	−1.91002e13	−1.40457	−0.702284	+	0.711897i	$0.747836\pi$
$830$	−5.00823e12	−0.366297
$831$	−1.36955e13	−0.996263
$832$	7.60432e12	0.550181
$833$	1.67795e12	0.120747
$834$	−9.89455e12	−0.708188
$835$	1.45769e13	1.03771
$836$	−2.01544e12	−0.142706
$837$	3.82188e12	0.269161
$838$	−1.17142e13	−0.820570
$839$	−5.97560e12	−0.416345	−0.208172	−	0.978092i	$-0.566751\pi$
$839$	−5.97560e12	−0.416345	−0.208172	+	0.978092i	$0.566751\pi$
$840$	−1.67439e12	−0.116038
$841$	9.84020e12	0.678301
$842$	1.35552e13	0.929396
$843$	−1.27173e13	−0.867300
$844$	2.63047e12	0.178440
$845$	2.08897e13	1.40954
$846$	1.61551e12	0.108428
$847$	−5.25051e12	−0.350530
$848$	8.95845e11	0.0594910
$849$	−1.14417e13	−0.755799
$850$	1.25648e12	0.0825604
$851$	5.73827e12	0.375057
$852$	4.26151e12	0.277068
$853$	−9.12291e12	−0.590014	−0.295007	−	0.955495i	$-0.595322\pi$
$853$	−9.12291e12	−0.590014	−0.295007	+	0.955495i	$0.595322\pi$
$854$	8.82923e12	0.568018
$855$	3.69487e12	0.236457
$856$	−1.22369e13	−0.779001
$857$	−4.11601e12	−0.260653	−0.130326	−	0.991471i	$-0.541603\pi$
$857$	−4.11601e12	−0.260653	−0.130326	+	0.991471i	$0.541603\pi$
$858$	−6.58472e12	−0.414805
$859$	4.94399e11	0.0309819	0.0154910	−	0.999880i	$-0.495069\pi$
$859$	4.94399e11	0.0309819	0.0154910	+	0.999880i	$0.495069\pi$
$860$	1.57929e12	0.0984508
$861$	6.51582e12	0.404068
$862$	2.17683e13	1.34289
$863$	1.22015e13	0.748797	0.374398	−	0.927268i	$-0.377849\pi$
$863$	1.22015e13	0.748797	0.374398	+	0.927268i	$0.377849\pi$
$864$	−2.44759e12	−0.149426
$865$	−1.17218e13	−0.711907
$866$	1.56281e13	0.944228
$867$	−9.40717e12	−0.565422
$868$	3.84839e12	0.230113
$869$	−1.05976e12	−0.0630405
$870$	1.07914e13	0.638619
$871$	−4.40384e13	−2.59269
$872$	1.39784e13	0.818716
$873$	1.92842e12	0.112367
$874$	−9.93550e12	−0.575954
$875$	−7.39327e12	−0.426384
$876$	1.89218e12	0.108566
$877$	−2.66821e13	−1.52308	−0.761539	−	0.648120i	$-0.775556\pi$
$877$	−2.66821e13	−1.52308	−0.761539	+	0.648120i	$0.775556\pi$
$878$	1.16285e13	0.660388
$879$	−6.26054e12	−0.353722
$880$	5.58122e12	0.313731
$881$	−4.84046e12	−0.270704	−0.135352	−	0.990798i	$-0.543217\pi$
$881$	−4.84046e12	−0.270704	−0.135352	+	0.990798i	$0.543217\pi$
$882$	−5.97895e12	−0.332672
$883$	−9.59584e12	−0.531202	−0.265601	−	0.964083i	$-0.585570\pi$
$883$	−9.59584e12	−0.531202	−0.265601	+	0.964083i	$0.585570\pi$
$884$	−1.84760e12	−0.101759
$885$	−9.85825e11	−0.0540201
$886$	3.95473e13	2.15608
$887$	−1.61306e13	−0.874973	−0.437486	−	0.899225i	$-0.644131\pi$
$887$	−1.61306e13	−0.874973	−0.437486	+	0.899225i	$0.644131\pi$
$888$	5.71224e12	0.308282
$889$	1.05165e13	0.564693
$890$	8.58381e12	0.458591
$891$	−7.34595e11	−0.0390479
$892$	−6.83696e12	−0.361594
$893$	5.13570e12	0.270252
$894$	−7.60953e12	−0.398418
$895$	2.04118e12	0.106336
$896$	8.92120e12	0.462420
$897$	−9.46183e12	−0.487988
$898$	−4.58595e13	−2.35335
$899$	3.54852e13	1.81188
$900$	−1.30503e12	−0.0663026
$901$	1.36177e11	0.00688400
$902$	−1.45256e13	−0.730644
$903$	1.53609e12	0.0768816
$904$	−1.85554e13	−0.924084
$905$	−1.11908e13	−0.554553
$906$	−3.38151e11	−0.0166738
$907$	1.76304e13	0.865029	0.432514	−	0.901627i	$-0.357626\pi$
$907$	1.76304e13	0.865029	0.432514	+	0.901627i	$0.357626\pi$
$908$	1.01586e13	0.495963
$909$	−5.03406e12	−0.244558
$910$	1.21554e13	0.587600
$911$	1.71264e13	0.823824	0.411912	−	0.911224i	$-0.364861\pi$
$911$	1.71264e13	0.823824	0.411912	+	0.911224i	$0.364861\pi$
$912$	−1.47884e13	−0.707856
$913$	3.16537e12	0.150767
$914$	−1.65828e12	−0.0785959
$915$	1.05181e13	0.496069
$916$	1.36965e13	0.642807
$917$	1.22605e12	0.0572595
$918$	−7.07131e11	−0.0328631
$919$	2.33347e13	1.07915	0.539576	−	0.841937i	$-0.318584\pi$
$919$	2.33347e13	1.07915	0.539576	+	0.841937i	$0.318584\pi$
$920$	5.36365e12	0.246840
$921$	1.07872e12	0.0494013
$922$	1.79173e13	0.816552
$923$	4.42611e13	2.00731
$924$	−7.39690e11	−0.0333830
$925$	8.22028e12	0.369189
$926$	−1.84436e13	−0.824319
$927$	−6.47403e11	−0.0287949
$928$	−2.27253e13	−1.00587
$929$	4.53635e12	0.199819	0.0999094	−	0.994997i	$-0.468145\pi$
$929$	4.53635e12	0.199819	0.0999094	+	0.994997i	$0.468145\pi$
$930$	1.57280e13	0.689448
$931$	−1.90071e13	−0.829168
$932$	−6.21731e12	−0.269918
$933$	3.00794e12	0.129958
$934$	2.25107e13	0.967893
$935$	8.48396e11	0.0363033
$936$	−9.41891e12	−0.401106
$937$	5.78059e12	0.244987	0.122494	−	0.992469i	$-0.460911\pi$
$937$	5.78059e12	0.244987	0.122494	+	0.992469i	$0.460911\pi$
$938$	−1.69717e13	−0.715836
$939$	−2.25139e12	−0.0945053
$940$	1.93787e12	0.0809560
$941$	−4.12365e13	−1.71446	−0.857231	−	0.514932i	$-0.827817\pi$
$941$	−4.12365e13	−1.71446	−0.857231	+	0.514932i	$0.827817\pi$
$942$	4.74059e11	0.0196157
$943$	−2.08724e13	−0.859549
$944$	3.94568e12	0.161714
$945$	1.35606e12	0.0553141
$946$	−3.42440e12	−0.139019
$947$	5.25224e12	0.212212	0.106106	−	0.994355i	$-0.466162\pi$
$947$	5.25224e12	0.212212	0.106106	+	0.994355i	$0.466162\pi$
$948$	1.05956e12	0.0426078
$949$	1.96526e13	0.786544
$950$	−1.42330e13	−0.566942
$951$	7.51787e12	0.298046
$952$	1.01870e12	0.0401959
$953$	−3.07823e13	−1.20888	−0.604440	−	0.796651i	$-0.706603\pi$
$953$	−3.07823e13	−1.20888	−0.604440	+	0.796651i	$0.706603\pi$
$954$	−4.85232e11	−0.0189663
$955$	−1.39998e13	−0.544636
$956$	1.54087e12	0.0596630
$957$	−6.82054e12	−0.262854
$958$	−1.71682e13	−0.658538
$959$	−6.45197e12	−0.246325
$960$	3.49115e12	0.132663
$961$	2.52786e13	0.956089
$962$	−4.14685e13	−1.56110
$963$	9.91043e12	0.371342
$964$	−1.47393e13	−0.549707
$965$	1.05199e13	0.390518
$966$	−3.64644e12	−0.134732
$967$	−4.21928e13	−1.55174	−0.775871	−	0.630892i	$-0.782689\pi$
$967$	−4.21928e13	−1.55174	−0.775871	+	0.630892i	$0.782689\pi$
$968$	1.67429e13	0.612903
$969$	−2.24797e12	−0.0819095
$970$	7.93595e12	0.287823
$971$	1.49247e13	0.538791	0.269395	−	0.963030i	$-0.413176\pi$
$971$	1.49247e13	0.538791	0.269395	+	0.963030i	$0.413176\pi$
$972$	7.34455e11	0.0263917
$973$	−1.15443e13	−0.412914
$974$	1.19840e13	0.426664
$975$	−1.35544e13	−0.480352
$976$	−4.20978e13	−1.48503
$977$	1.00619e13	0.353309	0.176654	−	0.984273i	$-0.443473\pi$
$977$	1.00619e13	0.353309	0.176654	+	0.984273i	$0.443473\pi$
$978$	−1.89913e13	−0.663789
$979$	−5.42526e12	−0.188755
$980$	−7.17201e12	−0.248384
$981$	−1.13209e13	−0.390274
$982$	1.97275e12	0.0676971
$983$	−1.70566e13	−0.582641	−0.291321	−	0.956626i	$-0.594095\pi$
$983$	−1.70566e13	−0.582641	−0.291321	+	0.956626i	$0.594095\pi$
$984$	−2.07778e13	−0.706514
$985$	−3.71932e13	−1.25893
$986$	−6.56555e12	−0.221220
$987$	1.88486e12	0.0632197
$988$	2.09289e13	0.698778
$989$	−4.92064e12	−0.163545
$990$	−3.02305e12	−0.100020
$991$	4.73012e13	1.55791	0.778953	−	0.627083i	$-0.215751\pi$
$991$	4.73012e13	1.55791	0.778953	+	0.627083i	$0.215751\pi$
$992$	−3.31212e13	−1.08593
$993$	−1.07776e12	−0.0351763
$994$	1.70576e13	0.554215
$995$	9.67484e12	0.312925
$996$	−3.16477e12	−0.101900
$997$	3.88932e13	1.24665	0.623326	−	0.781962i	$-0.285781\pi$
$997$	3.88932e13	1.24665	0.623326	+	0.781962i	$0.285781\pi$
$998$	2.66908e13	0.851676
$999$	−4.62625e12	−0.146955

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.d.1.17	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.d.1.17	✓	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)

\(f(q)\)	\(=\)	\(q+26.8820 q^{2} +81.0000 q^{3} +210.640 q^{4} +1004.40 q^{5} +2177.44 q^{6} +2540.49 q^{7} -8101.16 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+26.8820 q^{2} +81.0000 q^{3} +210.640 q^{4} +1004.40 q^{5} +2177.44 q^{6} +2540.49 q^{7} -8101.16 q^{8} +6561.00 q^{9} +27000.3 q^{10} -17065.1 q^{11} +17061.8 q^{12} +177208. q^{13} +68293.3 q^{14} +81356.4 q^{15} -325622. q^{16} -49497.6 q^{17} +176373. q^{18} +560689. q^{19} +211566. q^{20} +205779. q^{21} -458742. q^{22} -659184. q^{23} -656194. q^{24} -944305. q^{25} +4.76370e6 q^{26} +531441. q^{27} +535127. q^{28} +4.93430e6 q^{29} +2.18702e6 q^{30} +7.19154e6 q^{31} -4.60558e6 q^{32} -1.38227e6 q^{33} -1.33059e6 q^{34} +2.55167e6 q^{35} +1.38201e6 q^{36} -8.70511e6 q^{37} +1.50724e7 q^{38} +1.43539e7 q^{39} -8.13681e6 q^{40} +3.16641e7 q^{41} +5.53175e6 q^{42} +7.46475e6 q^{43} -3.59458e6 q^{44} +6.58987e6 q^{45} -1.77201e7 q^{46} +9.15962e6 q^{47} -2.63754e7 q^{48} -3.38995e7 q^{49} -2.53848e7 q^{50} -4.00931e6 q^{51} +3.73270e7 q^{52} -2.75118e6 q^{53} +1.42862e7 q^{54} -1.71402e7 q^{55} -2.05809e7 q^{56} +4.54158e7 q^{57} +1.32644e8 q^{58} -1.21174e7 q^{59} +1.71369e7 q^{60} +1.29284e8 q^{61} +1.93323e8 q^{62} +1.66681e7 q^{63} +4.29118e7 q^{64} +1.77988e8 q^{65} -3.71581e7 q^{66} -2.48513e8 q^{67} -1.04262e7 q^{68} -5.33939e7 q^{69} +6.85938e7 q^{70} +2.49769e8 q^{71} -5.31517e7 q^{72} +1.10902e8 q^{73} -2.34010e8 q^{74} -7.64887e7 q^{75} +1.18103e8 q^{76} -4.33536e7 q^{77} +3.85860e8 q^{78} +6.21014e7 q^{79} -3.27055e8 q^{80} +4.30467e7 q^{81} +8.51192e8 q^{82} -1.85488e8 q^{83} +4.33453e7 q^{84} -4.97154e7 q^{85} +2.00667e8 q^{86} +3.99679e8 q^{87} +1.38247e8 q^{88} +3.17916e8 q^{89} +1.77149e8 q^{90} +4.50195e8 q^{91} -1.38850e8 q^{92} +5.82515e8 q^{93} +2.46229e8 q^{94} +5.63157e8 q^{95} -3.73052e8 q^{96} +2.93921e8 q^{97} -9.11286e8 q^{98} -1.11964e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9}+O(q^{10}) \) 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

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