LMFDB - Embedded newform 114.12.a.f.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,12,Mod(1,114)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("114.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	114.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:	$87.5911225838$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 2999302x^{2} - 1003379071x + 558664856310 $ x^4 - 2x^3 - 2999302x^2 - 1003379071*x + 558664856310
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1839.39$ of defining polynomial
Character	$\chi$	$=$	114.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-32.0000 q^{2} +243.000 q^{3} +1024.00 q^{4} +6182.37 q^{5} -7776.00 q^{6} -34779.2 q^{7} -32768.0 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-32.0000 q^{2} +243.000 q^{3} +1024.00 q^{4} +6182.37 q^{5} -7776.00 q^{6} -34779.2 q^{7} -32768.0 q^{8} +59049.0 q^{9} -197836. q^{10} -762750. q^{11} +248832. q^{12} -1.32279e6 q^{13} +1.11293e6 q^{14} +1.50232e6 q^{15} +1.04858e6 q^{16} -7.62893e6 q^{17} -1.88957e6 q^{18} +2.47610e6 q^{19} +6.33075e6 q^{20} -8.45135e6 q^{21} +2.44080e7 q^{22} +3.21896e7 q^{23} -7.96262e6 q^{24} -1.06064e7 q^{25} +4.23292e7 q^{26} +1.43489e7 q^{27} -3.56139e7 q^{28} +1.50621e8 q^{29} -4.80741e7 q^{30} +1.16841e8 q^{31} -3.35544e7 q^{32} -1.85348e8 q^{33} +2.44126e8 q^{34} -2.15018e8 q^{35} +6.04662e7 q^{36} +5.17400e8 q^{37} -7.92352e7 q^{38} -3.21437e8 q^{39} -2.02584e8 q^{40} +1.34483e9 q^{41} +2.70443e8 q^{42} +1.14636e9 q^{43} -7.81056e8 q^{44} +3.65063e8 q^{45} -1.03007e9 q^{46} -2.69187e9 q^{47} +2.54804e8 q^{48} -7.67734e8 q^{49} +3.39405e8 q^{50} -1.85383e9 q^{51} -1.35453e9 q^{52} -1.10649e9 q^{53} -4.59165e8 q^{54} -4.71560e9 q^{55} +1.13964e9 q^{56} +6.01692e8 q^{57} -4.81986e9 q^{58} +3.43113e9 q^{59} +1.53837e9 q^{60} +9.63847e9 q^{61} -3.73890e9 q^{62} -2.05368e9 q^{63} +1.07374e9 q^{64} -8.17797e9 q^{65} +5.93114e9 q^{66} +1.42736e10 q^{67} -7.81203e9 q^{68} +7.82208e9 q^{69} +6.88057e9 q^{70} -8.56849e9 q^{71} -1.93492e9 q^{72} -1.55160e10 q^{73} -1.65568e10 q^{74} -2.57736e9 q^{75} +2.53553e9 q^{76} +2.65278e10 q^{77} +1.02860e10 q^{78} +2.14439e10 q^{79} +6.48269e9 q^{80} +3.48678e9 q^{81} -4.30345e10 q^{82} -6.22700e9 q^{83} -8.65418e9 q^{84} -4.71649e10 q^{85} -3.66835e10 q^{86} +3.66008e10 q^{87} +2.49938e10 q^{88} -1.33559e9 q^{89} -1.16820e10 q^{90} +4.60055e10 q^{91} +3.29622e10 q^{92} +2.83923e10 q^{93} +8.61398e10 q^{94} +1.53082e10 q^{95} -8.15373e9 q^{96} -1.24258e11 q^{97} +2.45675e10 q^{98} -4.50396e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 128 q^{2} + 972 q^{3} + 4096 q^{4} + 9912 q^{5} - 31104 q^{6} + 36234 q^{7} - 131072 q^{8} + 236196 q^{9}+O(q^{10}) $ 4 * q - 128 * q^2 + 972 * q^3 + 4096 * q^4 + 9912 * q^5 - 31104 * q^6 + 36234 * q^7 - 131072 * q^8 + 236196 * q^9	\( 4 q - 128 q^{2} + 972 q^{3} + 4096 q^{4} + 9912 q^{5} - 31104 q^{6} + 36234 q^{7} - 131072 q^{8} + 236196 q^{9} - 317184 q^{10} + 656548 q^{11} + 995328 q^{12} - 1328426 q^{13} - 1159488 q^{14} + 2408616 q^{15} + 4194304 q^{16} - 6116414 q^{17} - 7558272 q^{18} + 9904396 q^{19} + 10149888 q^{20} + 8804862 q^{21} - 21009536 q^{22} + 34001164 q^{23} - 31850496 q^{24} + 58663954 q^{25} + 42509632 q^{26} + 57395628 q^{27} + 37103616 q^{28} + 276975486 q^{29} - 77075712 q^{30} + 264731062 q^{31} - 134217728 q^{32} + 159541164 q^{33} + 195725248 q^{34} + 575633478 q^{35} + 241864704 q^{36} + 886797726 q^{37} - 316940672 q^{38} - 322807518 q^{39} - 324796416 q^{40} - 275275946 q^{41} - 281755584 q^{42} + 683228242 q^{43} + 672305152 q^{44} + 585293688 q^{45} - 1088037248 q^{46} - 1324778186 q^{47} + 1019215872 q^{48} - 306061098 q^{49} - 1877246528 q^{50} - 1486288602 q^{51} - 1360308224 q^{52} + 446705822 q^{53} - 1836660096 q^{54} - 12020135034 q^{55} - 1187315712 q^{56} + 2406768228 q^{57} - 8863215552 q^{58} + 6625246756 q^{59} + 2466422784 q^{60} - 6743662354 q^{61} - 8471393984 q^{62} + 2139581466 q^{63} + 4294967296 q^{64} - 3307258728 q^{65} - 5105317248 q^{66} - 33594510788 q^{67} - 6263207936 q^{68} + 8262282852 q^{69} - 18420271296 q^{70} - 7592117020 q^{71} - 7739670528 q^{72} + 6699940398 q^{73} - 28377527232 q^{74} + 14255340822 q^{75} + 10142101504 q^{76} + 47149048966 q^{77} + 10329840576 q^{78} + 8043101838 q^{79} + 10393485312 q^{80} + 13947137604 q^{81} + 8808830272 q^{82} - 16824459190 q^{83} + 9016178688 q^{84} + 66979473594 q^{85} - 21863303744 q^{86} + 67305043098 q^{87} - 21513764864 q^{88} + 9048133798 q^{89} - 18729398016 q^{90} + 158880145340 q^{91} + 34817191936 q^{92} + 64329648066 q^{93} + 42392901952 q^{94} + 24543093288 q^{95} - 32614907904 q^{96} - 96323093704 q^{97} + 9793955136 q^{98} + 38768502852 q^{99}+O(q^{100}) \) 4 * q - 128 * q^2 + 972 * q^3 + 4096 * q^4 + 9912 * q^5 - 31104 * q^6 + 36234 * q^7 - 131072 * q^8 + 236196 * q^9 - 317184 * q^10 + 656548 * q^11 + 995328 * q^12 - 1328426 * q^13 - 1159488 * q^14 + 2408616 * q^15 + 4194304 * q^16 - 6116414 * q^17 - 7558272 * q^18 + 9904396 * q^19 + 10149888 * q^20 + 8804862 * q^21 - 21009536 * q^22 + 34001164 * q^23 - 31850496 * q^24 + 58663954 * q^25 + 42509632 * q^26 + 57395628 * q^27 + 37103616 * q^28 + 276975486 * q^29 - 77075712 * q^30 + 264731062 * q^31 - 134217728 * q^32 + 159541164 * q^33 + 195725248 * q^34 + 575633478 * q^35 + 241864704 * q^36 + 886797726 * q^37 - 316940672 * q^38 - 322807518 * q^39 - 324796416 * q^40 - 275275946 * q^41 - 281755584 * q^42 + 683228242 * q^43 + 672305152 * q^44 + 585293688 * q^45 - 1088037248 * q^46 - 1324778186 * q^47 + 1019215872 * q^48 - 306061098 * q^49 - 1877246528 * q^50 - 1486288602 * q^51 - 1360308224 * q^52 + 446705822 * q^53 - 1836660096 * q^54 - 12020135034 * q^55 - 1187315712 * q^56 + 2406768228 * q^57 - 8863215552 * q^58 + 6625246756 * q^59 + 2466422784 * q^60 - 6743662354 * q^61 - 8471393984 * q^62 + 2139581466 * q^63 + 4294967296 * q^64 - 3307258728 * q^65 - 5105317248 * q^66 - 33594510788 * q^67 - 6263207936 * q^68 + 8262282852 * q^69 - 18420271296 * q^70 - 7592117020 * q^71 - 7739670528 * q^72 + 6699940398 * q^73 - 28377527232 * q^74 + 14255340822 * q^75 + 10142101504 * q^76 + 47149048966 * q^77 + 10329840576 * q^78 + 8043101838 * q^79 + 10393485312 * q^80 + 13947137604 * q^81 + 8808830272 * q^82 - 16824459190 * q^83 + 9016178688 * q^84 + 66979473594 * q^85 - 21863303744 * q^86 + 67305043098 * q^87 - 21513764864 * q^88 + 9048133798 * q^89 - 18729398016 * q^90 + 158880145340 * q^91 + 34817191936 * q^92 + 64329648066 * q^93 + 42392901952 * q^94 + 24543093288 * q^95 - 32614907904 * q^96 - 96323093704 * q^97 + 9793955136 * q^98 + 38768502852 * 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 $

$2$	−32.0000	−0.707107
$2$	−32.0000	−0.707107
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	1024.00	0.500000
$5$	6182.37	0.884749	0.442375	−	0.896830i	$-0.354136\pi$
$5$	6182.37	0.884749	0.442375	+	0.896830i	$0.354136\pi$
$6$	−7776.00	−0.408248
$7$	−34779.2	−0.782133	−0.391066	−	0.920363i	$-0.627894\pi$
$7$	−34779.2	−0.782133	−0.391066	+	0.920363i	$0.627894\pi$
$8$	−32768.0	−0.353553
$9$	59049.0	0.333333
$10$	−197836.	−0.625612
$11$	−762750.	−1.42798	−0.713990	−	0.700156i	$-0.753114\pi$
$11$	−762750.	−1.42798	−0.713990	+	0.700156i	$0.753114\pi$
$12$	248832.	0.288675
$13$	−1.32279e6	−0.988102	−0.494051	−	0.869433i	$-0.664484\pi$
$13$	−1.32279e6	−0.988102	−0.494051	+	0.869433i	$0.664484\pi$
$14$	1.11293e6	0.553051
$15$	1.50232e6	0.510810
$16$	1.04858e6	0.250000
$17$	−7.62893e6	−1.30315	−0.651575	−	0.758584i	$-0.725892\pi$
$17$	−7.62893e6	−1.30315	−0.651575	+	0.758584i	$0.725892\pi$
$18$	−1.88957e6	−0.235702
$19$	2.47610e6	0.229416
$19$	2.47610e6	0.229416
$20$	6.33075e6	0.442375
$21$	−8.45135e6	−0.451564
$22$	2.44080e7	1.00973
$23$	3.21896e7	1.04283	0.521414	−	0.853304i	$-0.325405\pi$
$23$	3.21896e7	1.04283	0.521414	+	0.853304i	$0.325405\pi$
$24$	−7.96262e6	−0.204124
$25$	−1.06064e7	−0.217219
$26$	4.23292e7	0.698693
$27$	1.43489e7	0.192450
$28$	−3.56139e7	−0.391066
$29$	1.50621e8	1.36363	0.681814	−	0.731526i	$-0.261191\pi$
$29$	1.50621e8	1.36363	0.681814	+	0.731526i	$0.261191\pi$
$30$	−4.80741e7	−0.361197
$31$	1.16841e8	0.733002	0.366501	−	0.930418i	$-0.380556\pi$
$31$	1.16841e8	0.733002	0.366501	+	0.930418i	$0.380556\pi$
$32$	−3.35544e7	−0.176777
$33$	−1.85348e8	−0.824445
$34$	2.44126e8	0.921467
$35$	−2.15018e8	−0.691991
$36$	6.04662e7	0.166667
$37$	5.17400e8	1.22664	0.613320	−	0.789835i	$-0.289834\pi$
$37$	5.17400e8	1.22664	0.613320	+	0.789835i	$0.289834\pi$
$38$	−7.92352e7	−0.162221
$39$	−3.21437e8	−0.570481
$40$	−2.02584e8	−0.312806
$41$	1.34483e9	1.81282	0.906412	−	0.422394i	$-0.138810\pi$
$41$	1.34483e9	1.81282	0.906412	+	0.422394i	$0.138810\pi$
$42$	2.70443e8	0.319304
$43$	1.14636e9	1.18917	0.594585	−	0.804033i	$-0.297316\pi$
$43$	1.14636e9	1.18917	0.594585	+	0.804033i	$0.297316\pi$
$44$	−7.81056e8	−0.713990
$45$	3.65063e8	0.294916
$46$	−1.03007e9	−0.737391
$47$	−2.69187e9	−1.71205	−0.856023	−	0.516937i	$-0.827072\pi$
$47$	−2.69187e9	−1.71205	−0.856023	+	0.516937i	$0.827072\pi$
$48$	2.54804e8	0.144338
$49$	−7.67734e8	−0.388269
$50$	3.39405e8	0.153597
$51$	−1.85383e9	−0.752374
$52$	−1.35453e9	−0.494051
$53$	−1.10649e9	−0.363439	−0.181719	−	0.983350i	$-0.558166\pi$
$53$	−1.10649e9	−0.363439	−0.181719	+	0.983350i	$0.558166\pi$
$54$	−4.59165e8	−0.136083
$55$	−4.71560e9	−1.26340
$56$	1.13964e9	0.276526
$57$	6.01692e8	0.132453
$58$	−4.81986e9	−0.964230
$59$	3.43113e9	0.624814	0.312407	−	0.949948i	$-0.398865\pi$
$59$	3.43113e9	0.624814	0.312407	+	0.949948i	$0.398865\pi$
$60$	1.53837e9	0.255405
$61$	9.63847e9	1.46115	0.730574	−	0.682834i	$-0.239253\pi$
$61$	9.63847e9	1.46115	0.730574	+	0.682834i	$0.239253\pi$
$62$	−3.73890e9	−0.518310
$63$	−2.05368e9	−0.260711
$64$	1.07374e9	0.125000
$65$	−8.17797e9	−0.874222
$66$	5.93114e9	0.582971
$67$	1.42736e10	1.29158	0.645791	−	0.763514i	$-0.276528\pi$
$67$	1.42736e10	1.29158	0.645791	+	0.763514i	$0.276528\pi$
$68$	−7.81203e9	−0.651575
$69$	7.82208e9	0.602077
$70$	6.88057e9	0.489312
$71$	−8.56849e9	−0.563616	−0.281808	−	0.959471i	$-0.590934\pi$
$71$	−8.56849e9	−0.563616	−0.281808	+	0.959471i	$0.590934\pi$
$72$	−1.93492e9	−0.117851
$73$	−1.55160e10	−0.876001	−0.438000	−	0.898975i	$-0.644313\pi$
$73$	−1.55160e10	−0.876001	−0.438000	+	0.898975i	$0.644313\pi$
$74$	−1.65568e10	−0.867365
$75$	−2.57736e9	−0.125412
$76$	2.53553e9	0.114708
$77$	2.65278e10	1.11687
$78$	1.02860e10	0.403391
$79$	2.14439e10	0.784069	0.392034	−	0.919951i	$-0.371771\pi$
$79$	2.14439e10	0.784069	0.392034	+	0.919951i	$0.371771\pi$
$80$	6.48269e9	0.221187
$81$	3.48678e9	0.111111
$82$	−4.30345e10	−1.28186
$83$	−6.22700e9	−0.173520	−0.0867599	−	0.996229i	$-0.527651\pi$
$83$	−6.22700e9	−0.173520	−0.0867599	+	0.996229i	$0.527651\pi$
$84$	−8.65418e9	−0.225782
$85$	−4.71649e10	−1.15296
$86$	−3.66835e10	−0.840870
$87$	3.66008e10	0.787291
$88$	2.49938e10	0.504867
$89$	−1.33559e9	−0.0253529	−0.0126764	−	0.999920i	$-0.504035\pi$
$89$	−1.33559e9	−0.0253529	−0.0126764	+	0.999920i	$0.504035\pi$
$90$	−1.16820e10	−0.208537
$91$	4.60055e10	0.772827
$92$	3.29622e10	0.521414
$93$	2.83923e10	0.423199
$94$	8.61398e10	1.21060
$95$	1.53082e10	0.202975
$96$	−8.15373e9	−0.102062
$97$	−1.24258e11	−1.46920	−0.734598	−	0.678502i	$-0.762629\pi$
$97$	−1.24258e11	−1.46920	−0.734598	+	0.678502i	$0.762629\pi$
$98$	2.45675e10	0.274547
$99$	−4.50396e10	−0.475993
$100$	−1.08610e10	−0.108610
$101$	7.67814e10	0.726923	0.363462	−	0.931609i	$-0.381595\pi$
$101$	7.67814e10	0.726923	0.363462	+	0.931609i	$0.381595\pi$
$102$	5.93226e10	0.532009
$103$	5.76828e10	0.490277	0.245138	−	0.969488i	$-0.421167\pi$
$103$	5.76828e10	0.490277	0.245138	+	0.969488i	$0.421167\pi$
$104$	4.33451e10	0.349347
$105$	−5.22494e10	−0.399521
$106$	3.54077e10	0.256990
$107$	2.64622e11	1.82396	0.911981	−	0.410232i	$-0.134552\pi$
$107$	2.64622e11	1.82396	0.911981	+	0.410232i	$0.134552\pi$
$108$	1.46933e10	0.0962250
$109$	−1.08611e10	−0.0676125	−0.0338062	−	0.999428i	$-0.510763\pi$
$109$	−1.08611e10	−0.0676125	−0.0338062	+	0.999428i	$0.510763\pi$
$110$	1.50899e11	0.893362
$111$	1.25728e11	0.708201
$112$	−3.64686e10	−0.195533
$113$	2.60514e11	1.33014	0.665072	−	0.746779i	$-0.268401\pi$
$113$	2.60514e11	1.33014	0.665072	+	0.746779i	$0.268401\pi$
$114$	−1.92541e10	−0.0936586
$115$	1.99008e11	0.922641
$116$	1.54236e11	0.681814
$117$	−7.81093e10	−0.329367
$118$	−1.09796e11	−0.441810
$119$	2.65328e11	1.01924
$120$	−4.92279e10	−0.180599
$121$	2.96475e11	1.03913
$122$	−3.08431e11	−1.03319
$123$	3.26793e11	1.04663
$124$	1.19645e11	0.366501
$125$	−3.67446e11	−1.07693
$126$	6.57177e10	0.184350
$127$	−1.19542e11	−0.321071	−0.160535	−	0.987030i	$-0.551322\pi$
$127$	−1.19542e11	−0.321071	−0.160535	+	0.987030i	$0.551322\pi$
$128$	−3.43597e10	−0.0883883
$129$	2.78565e11	0.686568
$130$	2.61695e11	0.618168
$131$	8.33882e11	1.88848	0.944241	−	0.329256i	$-0.106798\pi$
$131$	8.33882e11	1.88848	0.944241	+	0.329256i	$0.106798\pi$
$132$	−1.89797e11	−0.412222
$133$	−8.61167e10	−0.179434
$134$	−4.56755e11	−0.913287
$135$	8.87103e10	0.170270
$136$	2.49985e11	0.460733
$137$	3.24912e11	0.575178	0.287589	−	0.957754i	$-0.407146\pi$
$137$	3.24912e11	0.575178	0.287589	+	0.957754i	$0.407146\pi$
$138$	−2.50307e11	−0.425733
$139$	2.66422e11	0.435501	0.217750	−	0.976005i	$-0.430128\pi$
$139$	2.66422e11	0.435501	0.217750	+	0.976005i	$0.430128\pi$
$140$	−2.20178e11	−0.345996
$141$	−6.54124e11	−0.988450
$142$	2.74192e11	0.398537
$143$	1.00896e12	1.41099
$144$	6.19174e10	0.0833333
$145$	9.31194e11	1.20647
$146$	4.96513e11	0.619426
$147$	−1.86559e11	−0.224167
$148$	5.29818e11	0.613320
$149$	1.19447e12	1.33245	0.666225	−	0.745750i	$-0.267909\pi$
$149$	1.19447e12	1.33245	0.666225	+	0.745750i	$0.267909\pi$
$150$	8.24754e10	0.0886793
$151$	−1.24213e12	−1.28763	−0.643817	−	0.765179i	$-0.722650\pi$
$151$	−1.24213e12	−1.28763	−0.643817	+	0.765179i	$0.722650\pi$
$152$	−8.11368e10	−0.0811107
$153$	−4.50481e11	−0.434384
$154$	−8.48890e11	−0.789746
$155$	7.22353e11	0.648522
$156$	−3.29152e11	−0.285240
$157$	−8.02487e11	−0.671413	−0.335707	−	0.941967i	$-0.608975\pi$
$157$	−8.02487e11	−0.671413	−0.335707	+	0.941967i	$0.608975\pi$
$158$	−6.86204e11	−0.554420
$159$	−2.68878e11	−0.209831
$160$	−2.07446e11	−0.156403
$161$	−1.11953e12	−0.815630
$162$	−1.11577e11	−0.0785674
$163$	−1.50766e12	−1.02629	−0.513147	−	0.858300i	$-0.671521\pi$
$163$	−1.50766e12	−1.02629	−0.513147	+	0.858300i	$0.671521\pi$
$164$	1.37710e12	0.906412
$165$	−1.14589e12	−0.729427
$166$	1.99264e11	0.122697
$167$	−1.78331e12	−1.06240	−0.531199	−	0.847247i	$-0.678258\pi$
$167$	−1.78331e12	−1.06240	−0.531199	+	0.847247i	$0.678258\pi$
$168$	2.76934e11	0.159652
$169$	−4.23933e10	−0.0236548
$170$	1.50928e12	0.815267
$171$	1.46211e11	0.0764719
$172$	1.17387e12	0.594585
$173$	1.70998e12	0.838953	0.419477	−	0.907766i	$-0.362214\pi$
$173$	1.70998e12	0.838953	0.419477	+	0.907766i	$0.362214\pi$
$174$	−1.17123e12	−0.556699
$175$	3.68882e11	0.169894
$176$	−7.99801e11	−0.356995
$177$	8.33764e11	0.360736
$178$	4.27388e10	0.0179272
$179$	3.26377e12	1.32748	0.663740	−	0.747964i	$-0.268968\pi$
$179$	3.26377e12	1.32748	0.663740	+	0.747964i	$0.268968\pi$
$180$	3.73824e11	0.147458
$181$	−3.56516e12	−1.36410	−0.682051	−	0.731305i	$-0.738912\pi$
$181$	−3.56516e12	−1.36410	−0.682051	+	0.731305i	$0.738912\pi$
$182$	−1.47218e12	−0.546471
$183$	2.34215e12	0.843594
$184$	−1.05479e12	−0.368695
$185$	3.19876e12	1.08527
$186$	−9.08553e11	−0.299247
$187$	5.81896e12	1.86087
$188$	−2.75647e12	−0.856023
$189$	−4.99043e11	−0.150521
$190$	−4.89861e11	−0.143525
$191$	−5.80921e12	−1.65361	−0.826805	−	0.562488i	$-0.809844\pi$
$191$	−5.80921e12	−1.65361	−0.826805	+	0.562488i	$0.809844\pi$
$192$	2.60919e11	0.0721688
$193$	−9.57010e11	−0.257248	−0.128624	−	0.991693i	$-0.541056\pi$
$193$	−9.57010e11	−0.257248	−0.128624	+	0.991693i	$0.541056\pi$
$194$	3.97626e12	1.03888
$195$	−1.98725e12	−0.504732
$196$	−7.86160e11	−0.194134
$197$	−4.52143e12	−1.08570	−0.542852	−	0.839829i	$-0.682655\pi$
$197$	−4.52143e12	−1.08570	−0.542852	+	0.839829i	$0.682655\pi$
$198$	1.44127e12	0.336578
$199$	−3.10573e12	−0.705459	−0.352729	−	0.935725i	$-0.614746\pi$
$199$	−3.10573e12	−0.705459	−0.352729	+	0.935725i	$0.614746\pi$
$200$	3.47551e11	0.0767985
$201$	3.46849e12	0.745696
$202$	−2.45700e12	−0.514012
$203$	−5.23847e12	−1.06654
$204$	−1.89832e12	−0.376187
$205$	8.31423e12	1.60389
$206$	−1.84585e12	−0.346678
$207$	1.90077e12	0.347609
$208$	−1.38704e12	−0.247025
$209$	−1.88864e12	−0.327601
$210$	1.67198e12	0.282504
$211$	1.02998e12	0.169542	0.0847708	−	0.996400i	$-0.472984\pi$
$211$	1.02998e12	0.169542	0.0847708	+	0.996400i	$0.472984\pi$
$212$	−1.13305e12	−0.181719
$213$	−2.08214e12	−0.325404
$214$	−8.46792e12	−1.28974
$215$	7.08721e12	1.05212
$216$	−4.70185e11	−0.0680414
$217$	−4.06363e12	−0.573304
$218$	3.47554e11	0.0478092
$219$	−3.77039e12	−0.505759
$220$	−4.82878e12	−0.631702
$221$	1.00915e13	1.28765
$222$	−4.02330e12	−0.500773
$223$	1.13844e13	1.38240	0.691201	−	0.722663i	$-0.257082\pi$
$223$	1.13844e13	1.38240	0.691201	+	0.722663i	$0.257082\pi$
$224$	1.16700e12	0.138263
$225$	−6.26297e11	−0.0724064
$226$	−8.33643e12	−0.940554
$227$	−5.00646e12	−0.551301	−0.275651	−	0.961258i	$-0.588893\pi$
$227$	−5.00646e12	−0.551301	−0.275651	+	0.961258i	$0.588893\pi$
$228$	6.16133e11	0.0662266
$229$	−1.05791e13	−1.11008	−0.555042	−	0.831823i	$-0.687298\pi$
$229$	−1.05791e13	−1.11008	−0.555042	+	0.831823i	$0.687298\pi$
$230$	−6.36826e12	−0.652406
$231$	6.44626e12	0.644825
$232$	−4.93554e12	−0.482115
$233$	1.33358e13	1.27221	0.636107	−	0.771601i	$-0.280544\pi$
$233$	1.33358e13	1.27221	0.636107	+	0.771601i	$0.280544\pi$
$234$	2.49950e12	0.232898
$235$	−1.66421e13	−1.51473
$236$	3.51347e12	0.312407
$237$	5.21086e12	0.452682
$238$	−8.49050e12	−0.720709
$239$	1.81741e13	1.50752	0.753762	−	0.657148i	$-0.228237\pi$
$239$	1.81741e13	1.50752	0.753762	+	0.657148i	$0.228237\pi$
$240$	1.57529e12	0.127703
$241$	6.86013e12	0.543549	0.271774	−	0.962361i	$-0.412390\pi$
$241$	6.86013e12	0.543549	0.271774	+	0.962361i	$0.412390\pi$
$242$	−9.48721e12	−0.734774
$243$	8.47289e11	0.0641500
$244$	9.86979e12	0.730574
$245$	−4.74642e12	−0.343520
$246$	−1.04574e13	−0.740083
$247$	−3.27535e12	−0.226686
$248$	−3.82864e12	−0.259155
$249$	−1.51316e12	−0.100182
$250$	1.17583e13	0.761507
$251$	2.47745e13	1.56964	0.784818	−	0.619727i	$-0.212757\pi$
$251$	2.47745e13	1.56964	0.784818	+	0.619727i	$0.212757\pi$
$252$	−2.10297e12	−0.130355
$253$	−2.45526e13	−1.48914
$254$	3.82535e12	0.227031
$255$	−1.14611e13	−0.665662
$256$	1.09951e12	0.0625000
$257$	−2.57967e13	−1.43526	−0.717632	−	0.696422i	$-0.754774\pi$
$257$	−2.57967e13	−1.43526	−0.717632	+	0.696422i	$0.754774\pi$
$258$	−8.91408e12	−0.485477
$259$	−1.79948e13	−0.959395
$260$	−8.37424e12	−0.437111
$261$	8.89401e12	0.454543
$262$	−2.66842e13	−1.33536
$263$	−6.94608e12	−0.340395	−0.170198	−	0.985410i	$-0.554441\pi$
$263$	−6.94608e12	−0.340395	−0.170198	+	0.985410i	$0.554441\pi$
$264$	6.07349e12	0.291485
$265$	−6.84075e12	−0.321552
$266$	2.75574e12	0.126879
$267$	−3.24548e11	−0.0146375
$268$	1.46162e13	0.645791
$269$	3.68020e13	1.59307	0.796534	−	0.604594i	$-0.206665\pi$
$269$	3.68020e13	1.59307	0.796534	+	0.604594i	$0.206665\pi$
$270$	−2.83873e12	−0.120399
$271$	2.21988e13	0.922569	0.461285	−	0.887252i	$-0.347389\pi$
$271$	2.21988e13	0.922569	0.461285	+	0.887252i	$0.347389\pi$
$272$	−7.99951e12	−0.325788
$273$	1.11793e13	0.446192
$274$	−1.03972e13	−0.406712
$275$	8.09003e12	0.310185
$276$	8.00981e12	0.301039
$277$	−4.99134e13	−1.83899	−0.919493	−	0.393105i	$-0.871401\pi$
$277$	−4.99134e13	−1.83899	−0.919493	+	0.393105i	$0.871401\pi$
$278$	−8.52551e12	−0.307945
$279$	6.89933e12	0.244334
$280$	7.04571e12	0.244656
$281$	−1.13170e13	−0.385343	−0.192671	−	0.981263i	$-0.561715\pi$
$281$	−1.13170e13	−0.385343	−0.192671	+	0.981263i	$0.561715\pi$
$282$	2.09320e13	0.698940
$283$	5.82715e13	1.90823	0.954115	−	0.299441i	$-0.0968001\pi$
$283$	5.82715e13	1.90823	0.954115	+	0.299441i	$0.0968001\pi$
$284$	−8.77413e12	−0.281808
$285$	3.71988e12	0.117188
$286$	−3.22866e13	−0.997721
$287$	−4.67721e13	−1.41787
$288$	−1.98136e12	−0.0589256
$289$	2.39287e13	0.698201
$290$	−2.97982e13	−0.853102
$291$	−3.01947e13	−0.848241
$292$	−1.58884e13	−0.438000
$293$	5.76723e13	1.56026	0.780128	−	0.625621i	$-0.215154\pi$
$293$	5.76723e13	1.56026	0.780128	+	0.625621i	$0.215154\pi$
$294$	5.96990e12	0.158510
$295$	2.12125e13	0.552803
$296$	−1.69542e13	−0.433683
$297$	−1.09446e13	−0.274815
$298$	−3.82231e13	−0.942185
$299$	−4.25800e13	−1.03042
$300$	−2.63921e12	−0.0627058
$301$	−3.98694e13	−0.930088
$302$	3.97480e13	0.910495
$303$	1.86579e13	0.419689
$304$	2.59638e12	0.0573539
$305$	5.95886e13	1.29275
$306$	1.44154e13	0.307156
$307$	−1.67296e13	−0.350127	−0.175063	−	0.984557i	$-0.556013\pi$
$307$	−1.67296e13	−0.350127	−0.175063	+	0.984557i	$0.556013\pi$
$308$	2.71645e13	0.558435
$309$	1.40169e13	0.283061
$310$	−2.31153e13	−0.458575
$311$	−4.38185e13	−0.854034	−0.427017	−	0.904244i	$-0.640436\pi$
$311$	−4.38185e13	−0.854034	−0.427017	+	0.904244i	$0.640436\pi$
$312$	1.05329e13	0.201695
$313$	1.18988e13	0.223877	0.111938	−	0.993715i	$-0.464294\pi$
$313$	1.18988e13	0.223877	0.111938	+	0.993715i	$0.464294\pi$
$314$	2.56796e13	0.474761
$315$	−1.26966e13	−0.230664
$316$	2.19585e13	0.392034
$317$	3.82734e13	0.671539	0.335769	−	0.941944i	$-0.391004\pi$
$317$	3.82734e13	0.671539	0.335769	+	0.941944i	$0.391004\pi$
$318$	8.60408e12	0.148373
$319$	−1.14886e14	−1.94723
$320$	6.63827e12	0.110594
$321$	6.43033e13	1.05307
$322$	3.58249e13	0.576737
$323$	−1.88900e13	−0.298963
$324$	3.57047e12	0.0555556
$325$	1.40300e13	0.214635
$326$	4.82452e13	0.725700
$327$	−2.63924e12	−0.0390361
$328$	−4.40674e13	−0.640930
$329$	9.36210e13	1.33905
$330$	3.66685e13	0.515783
$331$	6.15189e13	0.851049	0.425524	−	0.904947i	$-0.360090\pi$
$331$	6.15189e13	0.851049	0.425524	+	0.904947i	$0.360090\pi$
$332$	−6.37645e12	−0.0867599
$333$	3.05520e13	0.408880
$334$	5.70661e13	0.751229
$335$	8.82447e13	1.14273
$336$	−8.86188e12	−0.112891
$337$	3.10968e13	0.389719	0.194860	−	0.980831i	$-0.437575\pi$
$337$	3.10968e13	0.389719	0.194860	+	0.980831i	$0.437575\pi$
$338$	1.35658e12	0.0167265
$339$	6.33048e13	0.767959
$340$	−4.82968e13	−0.576481
$341$	−8.91202e13	−1.04671
$342$	−4.67876e12	−0.0540738
$343$	9.54710e13	1.08581
$344$	−3.75639e13	−0.420435
$345$	4.83590e13	0.532687
$346$	−5.47194e13	−0.593229
$347$	−5.34366e13	−0.570199	−0.285100	−	0.958498i	$-0.592027\pi$
$347$	−5.34366e13	−0.570199	−0.285100	+	0.958498i	$0.592027\pi$
$348$	3.74793e13	0.393645
$349$	6.61616e13	0.684016	0.342008	−	0.939697i	$-0.388893\pi$
$349$	6.61616e13	0.684016	0.342008	+	0.939697i	$0.388893\pi$
$350$	−1.18042e13	−0.120133
$351$	−1.89806e13	−0.190160
$352$	2.55936e13	0.252434
$353$	1.16202e14	1.12838	0.564189	−	0.825646i	$-0.309189\pi$
$353$	1.16202e14	1.12838	0.564189	+	0.825646i	$0.309189\pi$
$354$	−2.66804e13	−0.255079
$355$	−5.29736e13	−0.498659
$356$	−1.36764e12	−0.0126764
$357$	6.44747e13	0.588456
$358$	−1.04441e14	−0.938670
$359$	3.56394e12	0.0315436	0.0157718	−	0.999876i	$-0.494979\pi$
$359$	3.56394e12	0.0315436	0.0157718	+	0.999876i	$0.494979\pi$
$360$	−1.19624e13	−0.104269
$361$	6.13107e12	0.0526316
$362$	1.14085e14	0.964565
$363$	7.20435e13	0.599941
$364$	4.71096e13	0.386413
$365$	−9.59258e13	−0.775041
$366$	−7.49488e13	−0.596511
$367$	1.36823e14	1.07274	0.536371	−	0.843982i	$-0.319795\pi$
$367$	1.36823e14	1.07274	0.536371	+	0.843982i	$0.319795\pi$
$368$	3.37533e13	0.260707
$369$	7.94108e13	0.604275
$370$	−1.02360e14	−0.767400
$371$	3.84829e13	0.284257
$372$	2.90737e13	0.211599
$373$	−1.51716e14	−1.08801	−0.544006	−	0.839081i	$-0.683093\pi$
$373$	−1.51716e14	−1.08801	−0.544006	+	0.839081i	$0.683093\pi$
$374$	−1.86207e14	−1.31584
$375$	−8.92895e13	−0.621768
$376$	8.82071e13	0.605300
$377$	−1.99239e14	−1.34740
$378$	1.59694e13	0.106435
$379$	−2.25370e14	−1.48040	−0.740202	−	0.672384i	$-0.765270\pi$
$379$	−2.25370e14	−1.48040	−0.740202	+	0.672384i	$0.765270\pi$
$380$	1.56756e13	0.101488
$381$	−2.90488e13	−0.185370
$382$	1.85895e14	1.16928
$383$	2.84364e14	1.76312	0.881560	−	0.472072i	$-0.156494\pi$
$383$	2.84364e14	1.76312	0.881560	+	0.472072i	$0.156494\pi$
$384$	−8.34942e12	−0.0510310
$385$	1.64005e14	0.988150
$386$	3.06243e13	0.181901
$387$	6.76913e13	0.396390
$388$	−1.27240e14	−0.734598
$389$	−1.20447e14	−0.685606	−0.342803	−	0.939407i	$-0.611376\pi$
$389$	−1.20447e14	−0.685606	−0.342803	+	0.939407i	$0.611376\pi$
$390$	6.35919e13	0.356900
$391$	−2.45572e14	−1.35896
$392$	2.51571e13	0.137274
$393$	2.02633e14	1.09032
$394$	1.44686e14	0.767708
$395$	1.32574e14	0.693704
$396$	−4.61206e13	−0.237997
$397$	3.45050e14	1.75604	0.878019	−	0.478625i	$-0.158865\pi$
$397$	3.45050e14	1.75604	0.878019	+	0.478625i	$0.158865\pi$
$398$	9.93833e13	0.498835
$399$	−2.09264e13	−0.103596
$400$	−1.11216e13	−0.0543048
$401$	2.18946e13	0.105449	0.0527245	−	0.998609i	$-0.483209\pi$
$401$	2.18946e13	0.105449	0.0527245	+	0.998609i	$0.483209\pi$
$402$	−1.10992e14	−0.527287
$403$	−1.54555e14	−0.724280
$404$	7.86241e13	0.363462
$405$	2.15566e13	0.0983055
$406$	1.67631e14	0.754156
$407$	−3.94647e14	−1.75162
$408$	6.07463e13	0.266004
$409$	−2.25595e14	−0.974654	−0.487327	−	0.873220i	$-0.662028\pi$
$409$	−2.25595e14	−0.974654	−0.487327	+	0.873220i	$0.662028\pi$
$410$	−2.66055e14	−1.13413
$411$	7.89535e13	0.332079
$412$	5.90671e13	0.245138
$413$	−1.19332e14	−0.488687
$414$	−6.08245e13	−0.245797
$415$	−3.84976e13	−0.153522
$416$	4.43854e13	0.174673
$417$	6.47406e13	0.251436
$418$	6.04366e13	0.231649
$419$	−8.34144e13	−0.315547	−0.157773	−	0.987475i	$-0.550432\pi$
$419$	−8.34144e13	−0.315547	−0.157773	+	0.987475i	$0.550432\pi$
$420$	−5.35033e13	−0.199761
$421$	−2.55832e13	−0.0942766	−0.0471383	−	0.998888i	$-0.515010\pi$
$421$	−2.55832e13	−0.0942766	−0.0471383	+	0.998888i	$0.515010\pi$
$422$	−3.29594e13	−0.119884
$423$	−1.58952e14	−0.570682
$424$	3.62575e13	0.128495
$425$	8.09155e13	0.283069
$426$	6.66286e13	0.230095
$427$	−3.35218e14	−1.14281
$428$	2.70973e14	0.911981
$429$	2.45176e14	0.814635
$430$	−2.26791e14	−0.743959
$431$	1.79500e14	0.581352	0.290676	−	0.956822i	$-0.406120\pi$
$431$	1.79500e14	0.581352	0.290676	+	0.956822i	$0.406120\pi$
$432$	1.50459e13	0.0481125
$433$	−5.38373e14	−1.69981	−0.849905	−	0.526937i	$-0.823341\pi$
$433$	−5.38373e14	−1.69981	−0.849905	+	0.526937i	$0.823341\pi$
$434$	1.30036e14	0.405387
$435$	2.26280e14	0.696555
$436$	−1.11217e13	−0.0338062
$437$	7.97047e13	0.239241
$438$	1.20653e14	0.357626
$439$	2.24250e14	0.656415	0.328207	−	0.944606i	$-0.393556\pi$
$439$	2.24250e14	0.656415	0.328207	+	0.944606i	$0.393556\pi$
$440$	1.54521e14	0.446681
$441$	−4.53339e13	−0.129423
$442$	−3.22927e14	−0.910503
$443$	5.79019e14	1.61240	0.806200	−	0.591643i	$-0.201521\pi$
$443$	5.79019e14	1.61240	0.806200	+	0.591643i	$0.201521\pi$
$444$	1.28746e14	0.354100
$445$	−8.25710e12	−0.0224310
$446$	−3.64301e14	−0.977506
$447$	2.90256e14	0.769291
$448$	−3.73439e13	−0.0977666
$449$	1.62520e14	0.420292	0.210146	−	0.977670i	$-0.432606\pi$
$449$	1.62520e14	0.420292	0.210146	+	0.977670i	$0.432606\pi$
$450$	2.00415e13	0.0511990
$451$	−1.02577e15	−2.58868
$452$	2.66766e14	0.665072
$453$	−3.01837e14	−0.743416
$454$	1.60207e14	0.389829
$455$	2.84423e14	0.683758
$456$	−1.97162e13	−0.0468293
$457$	−7.95211e14	−1.86614	−0.933068	−	0.359699i	$-0.882879\pi$
$457$	−7.95211e14	−1.86614	−0.933068	+	0.359699i	$0.882879\pi$
$458$	3.38533e14	0.784947
$459$	−1.09467e14	−0.250791
$460$	2.03784e14	0.461321
$461$	8.14212e13	0.182130	0.0910652	−	0.995845i	$-0.470973\pi$
$461$	8.14212e13	0.182130	0.0910652	+	0.995845i	$0.470973\pi$
$462$	−2.06280e14	−0.455960
$463$	−1.50187e14	−0.328048	−0.164024	−	0.986456i	$-0.552447\pi$
$463$	−1.50187e14	−0.328048	−0.164024	+	0.986456i	$0.552447\pi$
$464$	1.57937e14	0.340907
$465$	1.75532e14	0.374425
$466$	−4.26744e14	−0.899591
$467$	−9.02732e14	−1.88068	−0.940342	−	0.340230i	$-0.889495\pi$
$467$	−9.02732e14	−1.88068	−0.940342	+	0.340230i	$0.889495\pi$
$468$	−7.99839e13	−0.164684
$469$	−4.96425e14	−1.01019
$470$	5.32548e14	1.07108
$471$	−1.95004e14	−0.387641
$472$	−1.12431e14	−0.220905
$473$	−8.74384e14	−1.69811
$474$	−1.66748e14	−0.320095
$475$	−2.62625e13	−0.0498335
$476$	2.71696e14	0.509618
$477$	−6.53373e13	−0.121146
$478$	−5.81571e14	−1.06598
$479$	5.90924e14	1.07075	0.535373	−	0.844616i	$-0.320171\pi$
$479$	5.90924e14	1.07075	0.535373	+	0.844616i	$0.320171\pi$
$480$	−5.04094e13	−0.0902993
$481$	−6.84410e14	−1.21204
$482$	−2.19524e14	−0.384347
$483$	−2.72046e14	−0.470904
$484$	3.03591e14	0.519564
$485$	−7.68210e14	−1.29987
$486$	−2.71132e13	−0.0453609
$487$	−5.81492e14	−0.961910	−0.480955	−	0.876745i	$-0.659710\pi$
$487$	−5.81492e14	−0.961910	−0.480955	+	0.876745i	$0.659710\pi$
$488$	−3.15833e14	−0.516594
$489$	−3.66362e14	−0.592532
$490$	1.51885e14	0.242906
$491$	−5.41407e14	−0.856201	−0.428101	−	0.903731i	$-0.640817\pi$
$491$	−5.41407e14	−0.856201	−0.428101	+	0.903731i	$0.640817\pi$
$492$	3.34636e14	0.523317
$493$	−1.14908e15	−1.77701
$494$	1.04811e14	0.160291
$495$	−2.78452e14	−0.421135
$496$	1.22516e14	0.183250
$497$	2.98005e14	0.440822
$498$	4.84211e13	0.0708392
$499$	1.00306e14	0.145136	0.0725680	−	0.997363i	$-0.476881\pi$
$499$	1.00306e14	0.145136	0.0725680	+	0.997363i	$0.476881\pi$
$500$	−3.76265e14	−0.538467
$501$	−4.33346e14	−0.613376
$502$	−7.92783e14	−1.10990
$503$	−2.74363e14	−0.379929	−0.189964	−	0.981791i	$-0.560837\pi$
$503$	−2.74363e14	−0.379929	−0.189964	+	0.981791i	$0.560837\pi$
$504$	6.72949e13	0.0921752
$505$	4.74691e14	0.643144
$506$	7.85684e14	1.05298
$507$	−1.03016e13	−0.0136571
$508$	−1.22411e14	−0.160535
$509$	3.20687e14	0.416039	0.208019	−	0.978125i	$-0.433298\pi$
$509$	3.20687e14	0.416039	0.208019	+	0.978125i	$0.433298\pi$
$510$	3.66754e14	0.470694
$511$	5.39635e14	0.685149
$512$	−3.51844e13	−0.0441942
$513$	3.55293e13	0.0441511
$514$	8.25494e14	1.01489
$515$	3.56616e14	0.433772
$516$	2.85251e14	0.343284
$517$	2.05322e15	2.44477
$518$	5.75832e14	0.678394
$519$	4.15525e14	0.484370
$520$	2.67976e14	0.309084
$521$	3.16135e12	0.00360799	0.00180399	−	0.999998i	$-0.499426\pi$
$521$	3.16135e12	0.00360799	0.00180399	+	0.999998i	$0.499426\pi$
$522$	−2.84608e14	−0.321410
$523$	−9.48613e12	−0.0106006	−0.00530029	−	0.999986i	$-0.501687\pi$
$523$	−9.48613e12	−0.0106006	−0.00530029	+	0.999986i	$0.501687\pi$
$524$	8.53896e14	0.944241
$525$	8.96384e13	0.0980884
$526$	2.22275e14	0.240696
$527$	−8.91370e14	−0.955211
$528$	−1.94352e14	−0.206111
$529$	8.33622e13	0.0874910
$530$	2.18904e14	0.227372
$531$	2.02605e14	0.208271
$532$	−8.81835e13	−0.0897168
$533$	−1.77892e15	−1.79126
$534$	1.03855e13	0.0103503
$535$	1.63599e15	1.61375
$536$	−4.67718e14	−0.456644
$537$	7.93096e14	0.766421
$538$	−1.17766e15	−1.12647
$539$	5.85589e14	0.554440
$540$	9.08393e13	0.0851350
$541$	1.40499e15	1.30343	0.651717	−	0.758462i	$-0.274049\pi$
$541$	1.40499e15	1.30343	0.651717	+	0.758462i	$0.274049\pi$
$542$	−7.10362e14	−0.652355
$543$	−8.66333e14	−0.787564
$544$	2.55984e14	0.230367
$545$	−6.71472e13	−0.0598201
$546$	−3.57739e14	−0.315505
$547$	8.06780e14	0.704409	0.352204	−	0.935923i	$-0.385432\pi$
$547$	8.06780e14	0.704409	0.352204	+	0.935923i	$0.385432\pi$
$548$	3.32709e14	0.287589
$549$	5.69142e14	0.487049
$550$	−2.58881e14	−0.219334
$551$	3.72952e14	0.312838
$552$	−2.56314e14	−0.212866
$553$	−7.45801e14	−0.613246
$554$	1.59723e15	1.30036
$555$	7.77298e14	0.626580
$556$	2.72816e14	0.217750
$557$	6.53934e14	0.516809	0.258404	−	0.966037i	$-0.416803\pi$
$557$	6.53934e14	0.516809	0.258404	+	0.966037i	$0.416803\pi$
$558$	−2.20778e14	−0.172770
$559$	−1.51639e15	−1.17502
$560$	−2.25463e14	−0.172998
$561$	1.41401e15	1.07438
$562$	3.62145e14	0.272478
$563$	1.91051e15	1.42349	0.711744	−	0.702439i	$-0.247906\pi$
$563$	1.91051e15	1.42349	0.711744	+	0.702439i	$0.247906\pi$
$564$	−6.69823e14	−0.494225
$565$	1.61059e15	1.17684
$566$	−1.86469e15	−1.34932
$567$	−1.21268e14	−0.0869036
$568$	2.80772e14	0.199268
$569$	6.72470e14	0.472667	0.236333	−	0.971672i	$-0.424054\pi$
$569$	6.72470e14	0.472667	0.236333	+	0.971672i	$0.424054\pi$
$570$	−1.19036e14	−0.0828643
$571$	1.27487e15	0.878959	0.439480	−	0.898253i	$-0.355163\pi$
$571$	1.27487e15	0.878959	0.439480	+	0.898253i	$0.355163\pi$
$572$	1.03317e15	0.705495
$573$	−1.41164e15	−0.954712
$574$	1.49671e15	1.00258
$575$	−3.41416e14	−0.226522
$576$	6.34034e13	0.0416667
$577$	−2.16114e15	−1.40674	−0.703372	−	0.710822i	$-0.748323\pi$
$577$	−2.16114e15	−1.40674	−0.703372	+	0.710822i	$0.748323\pi$
$578$	−7.65718e14	−0.493703
$579$	−2.32553e14	−0.148522
$580$	9.53542e14	0.603234
$581$	2.16570e14	0.135716
$582$	9.66231e14	0.599797
$583$	8.43976e14	0.518983
$584$	5.08429e14	0.309713
$585$	−4.82901e14	−0.291407
$586$	−1.84551e15	−1.10327
$587$	1.14499e14	0.0678096	0.0339048	−	0.999425i	$-0.489206\pi$
$587$	1.14499e14	0.0678096	0.0339048	+	0.999425i	$0.489206\pi$
$588$	−1.91037e14	−0.112084
$589$	2.89309e14	0.168162
$590$	−6.78800e14	−0.390891
$591$	−1.09871e15	−0.626831
$592$	5.42533e14	0.306660
$593$	−5.50718e14	−0.308410	−0.154205	−	0.988039i	$-0.549282\pi$
$593$	−5.50718e14	−0.308410	−0.154205	+	0.988039i	$0.549282\pi$
$594$	3.50228e14	0.194324
$595$	1.64036e15	0.901769
$596$	1.22314e15	0.666225
$597$	−7.54692e14	−0.407297
$598$	1.36256e15	0.728617
$599$	−2.20014e15	−1.16574	−0.582872	−	0.812564i	$-0.698071\pi$
$599$	−2.20014e15	−1.16574	−0.582872	+	0.812564i	$0.698071\pi$
$600$	8.44548e13	0.0443397
$601$	1.58493e15	0.824520	0.412260	−	0.911066i	$-0.364740\pi$
$601$	1.58493e15	0.824520	0.412260	+	0.911066i	$0.364740\pi$
$602$	1.27582e15	0.657672
$603$	8.42842e14	0.430528
$604$	−1.27194e15	−0.643817
$605$	1.83292e15	0.919367
$606$	−5.97052e14	−0.296765
$607$	1.70205e15	0.838368	0.419184	−	0.907901i	$-0.362316\pi$
$607$	1.70205e15	0.838368	0.419184	+	0.907901i	$0.362316\pi$
$608$	−8.30841e13	−0.0405554
$609$	−1.27295e15	−0.615766
$610$	−1.90684e15	−0.914112
$611$	3.56077e15	1.69168
$612$	−4.61292e14	−0.217192
$613$	1.95548e15	0.912474	0.456237	−	0.889858i	$-0.349197\pi$
$613$	1.95548e15	0.912474	0.456237	+	0.889858i	$0.349197\pi$
$614$	5.35348e14	0.247577
$615$	2.02036e15	0.926009
$616$	−8.69264e14	−0.394873
$617$	−1.66830e15	−0.751114	−0.375557	−	0.926799i	$-0.622549\pi$
$617$	−1.66830e15	−0.751114	−0.375557	+	0.926799i	$0.622549\pi$
$618$	−4.48541e14	−0.200155
$619$	−7.70896e14	−0.340955	−0.170477	−	0.985362i	$-0.554531\pi$
$619$	−7.70896e14	−0.340955	−0.170477	+	0.985362i	$0.554531\pi$
$620$	7.39689e14	0.324261
$621$	4.61886e14	0.200692
$622$	1.40219e15	0.603893
$623$	4.64507e13	0.0198293
$624$	−3.37052e14	−0.142620
$625$	−1.75380e15	−0.735597
$626$	−3.80762e14	−0.158305
$627$	−4.58940e14	−0.189141
$628$	−8.21747e14	−0.335707
$629$	−3.94721e15	−1.59850
$630$	4.06291e14	0.163104
$631$	−1.46829e15	−0.584320	−0.292160	−	0.956369i	$-0.594374\pi$
$631$	−1.46829e15	−0.584320	−0.292160	+	0.956369i	$0.594374\pi$
$632$	−7.02673e14	−0.277210
$633$	2.50286e14	0.0978848
$634$	−1.22475e15	−0.474850
$635$	−7.39055e14	−0.284067
$636$	−2.75331e14	−0.104916
$637$	1.01555e15	0.383649
$638$	3.67635e15	1.37690
$639$	−5.05961e14	−0.187872
$640$	−2.12425e14	−0.0782015
$641$	−3.30106e15	−1.20485	−0.602426	−	0.798174i	$-0.705799\pi$
$641$	−3.30106e15	−1.20485	−0.602426	+	0.798174i	$0.705799\pi$
$642$	−2.05770e15	−0.744630
$643$	4.30595e15	1.54493	0.772464	−	0.635058i	$-0.219024\pi$
$643$	4.30595e15	1.54493	0.772464	+	0.635058i	$0.219024\pi$
$644$	−1.14640e15	−0.407815
$645$	1.72219e15	0.607440
$646$	6.04480e14	0.211399
$647$	−2.18330e15	−0.757078	−0.378539	−	0.925585i	$-0.623573\pi$
$647$	−2.18330e15	−0.757078	−0.378539	+	0.925585i	$0.623573\pi$
$648$	−1.14255e14	−0.0392837
$649$	−2.61709e15	−0.892222
$650$	−4.48961e14	−0.151770
$651$	−9.87461e14	−0.330997
$652$	−1.54385e15	−0.513147
$653$	1.21070e15	0.399037	0.199518	−	0.979894i	$-0.436062\pi$
$653$	1.21070e15	0.399037	0.199518	+	0.979894i	$0.436062\pi$
$654$	8.44557e13	0.0276027
$655$	5.15537e15	1.67083
$656$	1.41016e15	0.453206
$657$	−9.16205e14	−0.292000
$658$	−2.99587e15	−0.946849
$659$	2.20512e15	0.691133	0.345566	−	0.938394i	$-0.387687\pi$
$659$	2.20512e15	0.691133	0.345566	+	0.938394i	$0.387687\pi$
$660$	−1.17339e15	−0.364713
$661$	−5.96381e14	−0.183830	−0.0919148	−	0.995767i	$-0.529299\pi$
$661$	−5.96381e14	−0.183830	−0.0919148	+	0.995767i	$0.529299\pi$
$662$	−1.96860e15	−0.601783
$663$	2.45222e15	0.743422
$664$	2.04046e14	0.0613485
$665$	−5.32406e14	−0.158754
$666$	−9.77662e14	−0.289122
$667$	4.84843e15	1.42203
$668$	−1.82611e15	−0.531199
$669$	2.76641e15	0.798130
$670$	−2.82383e15	−0.808030
$671$	−7.35174e15	−2.08649
$672$	2.83580e14	0.0798261
$673$	−2.96526e14	−0.0827903	−0.0413952	−	0.999143i	$-0.513180\pi$
$673$	−2.96526e14	−0.0827903	−0.0413952	+	0.999143i	$0.513180\pi$
$674$	−9.95099e14	−0.275573
$675$	−1.52190e14	−0.0418038
$676$	−4.34107e13	−0.0118274
$677$	1.19420e15	0.322731	0.161366	−	0.986895i	$-0.448410\pi$
$677$	1.19420e15	0.322731	0.161366	+	0.986895i	$0.448410\pi$
$678$	−2.02575e15	−0.543029
$679$	4.32160e15	1.14911
$680$	1.54550e15	0.407633
$681$	−1.21657e15	−0.318294
$682$	2.85185e15	0.740137
$683$	1.67849e15	0.432121	0.216060	−	0.976380i	$-0.430679\pi$
$683$	1.67849e15	0.432121	0.216060	+	0.976380i	$0.430679\pi$
$684$	1.49720e14	0.0382360
$685$	2.00872e15	0.508888
$686$	−3.05507e15	−0.767784
$687$	−2.57073e15	−0.640907
$688$	1.20204e15	0.297292
$689$	1.46365e15	0.359114
$690$	−1.54749e15	−0.376667
$691$	6.10838e15	1.47502	0.737508	−	0.675338i	$-0.236002\pi$
$691$	6.10838e15	1.47502	0.737508	+	0.675338i	$0.236002\pi$
$692$	1.75102e15	0.419477
$693$	1.56644e15	0.372290
$694$	1.70997e15	0.403192
$695$	1.64712e15	0.385309
$696$	−1.19934e15	−0.278349
$697$	−1.02596e16	−2.36238
$698$	−2.11717e15	−0.483672
$699$	3.24059e15	0.734513
$700$	3.77735e14	0.0849471
$701$	−8.71614e14	−0.194480	−0.0972401	−	0.995261i	$-0.531001\pi$
$701$	−8.71614e14	−0.194480	−0.0972401	+	0.995261i	$0.531001\pi$
$702$	6.07378e14	0.134464
$703$	1.28113e15	0.281410
$704$	−8.18996e14	−0.178498
$705$	−4.04404e15	−0.874531
$706$	−3.71848e15	−0.797883
$707$	−2.67040e15	−0.568550
$708$	8.53774e14	0.180368
$709$	7.44379e14	0.156041	0.0780207	−	0.996952i	$-0.475140\pi$
$709$	7.44379e14	0.156041	0.0780207	+	0.996952i	$0.475140\pi$
$710$	1.69515e15	0.352605
$711$	1.26624e15	0.261356
$712$	4.37646e13	0.00896360
$713$	3.76106e15	0.764395
$714$	−2.06319e15	−0.416102
$715$	6.23774e15	1.24837
$716$	3.34210e15	0.663740
$717$	4.41630e15	0.870369
$718$	−1.14046e14	−0.0223047
$719$	−3.40554e15	−0.660963	−0.330482	−	0.943812i	$-0.607211\pi$
$719$	−3.40554e15	−0.660963	−0.330482	+	0.943812i	$0.607211\pi$
$720$	3.82796e14	0.0737291
$721$	−2.00616e15	−0.383461
$722$	−1.96194e14	−0.0372161
$723$	1.66701e15	0.313818
$724$	−3.65072e15	−0.682051
$725$	−1.59754e15	−0.296206
$726$	−2.30539e15	−0.424222
$727$	1.85446e15	0.338671	0.169335	−	0.985558i	$-0.445838\pi$
$727$	1.85446e15	0.338671	0.169335	+	0.985558i	$0.445838\pi$
$728$	−1.50751e15	−0.273235
$729$	2.05891e14	0.0370370
$730$	3.06963e15	0.548037
$731$	−8.74549e15	−1.54967
$732$	2.39836e15	0.421797
$733$	−5.60062e15	−0.977607	−0.488803	−	0.872394i	$-0.662566\pi$
$733$	−5.60062e15	−0.977607	−0.488803	+	0.872394i	$0.662566\pi$
$734$	−4.37834e15	−0.758544
$735$	−1.15338e15	−0.198332
$736$	−1.08010e15	−0.184348
$737$	−1.08872e16	−1.84436
$738$	−2.54115e15	−0.427287
$739$	2.80953e15	0.468910	0.234455	−	0.972127i	$-0.424670\pi$
$739$	2.80953e15	0.468910	0.234455	+	0.972127i	$0.424670\pi$
$740$	3.27553e15	0.542634
$741$	−7.95911e14	−0.130877
$742$	−1.23145e15	−0.201000
$743$	−1.43920e15	−0.233175	−0.116588	−	0.993180i	$-0.537196\pi$
$743$	−1.43920e15	−0.233175	−0.116588	+	0.993180i	$0.537196\pi$
$744$	−9.30359e14	−0.149623
$745$	7.38466e15	1.17888
$746$	4.85493e15	0.769341
$747$	−3.67698e14	−0.0578400
$748$	5.95862e15	0.930437
$749$	−9.20336e15	−1.42658
$750$	2.85726e15	0.439656
$751$	2.87436e15	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$751$	2.87436e15	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$752$	−2.82263e15	−0.428012
$753$	6.02020e15	0.906230
$754$	6.37566e15	0.952758
$755$	−7.67929e15	−1.13923
$756$	−5.11021e14	−0.0752607
$757$	3.91091e15	0.571808	0.285904	−	0.958258i	$-0.407706\pi$
$757$	3.91091e15	0.571808	0.285904	+	0.958258i	$0.407706\pi$
$758$	7.21184e15	1.04680
$759$	−5.96629e15	−0.859754
$760$	−5.01618e14	−0.0717626
$761$	1.28588e16	1.82636	0.913179	−	0.407558i	$-0.133620\pi$
$761$	1.28588e16	1.82636	0.913179	+	0.407558i	$0.133620\pi$
$762$	9.29560e14	0.131077
$763$	3.77739e14	0.0528819
$764$	−5.94863e15	−0.826805
$765$	−2.78504e15	−0.384320
$766$	−9.09966e15	−1.24671
$767$	−4.53865e15	−0.617380
$768$	2.67181e14	0.0360844
$769$	8.86152e14	0.118827	0.0594133	−	0.998233i	$-0.481077\pi$
$769$	8.86152e14	0.118827	0.0594133	+	0.998233i	$0.481077\pi$
$770$	−5.24816e15	−0.698727
$771$	−6.26860e15	−0.828650
$772$	−9.79978e14	−0.128624
$773$	1.11477e15	0.145277	0.0726386	−	0.997358i	$-0.476858\pi$
$773$	1.11477e15	0.145277	0.0726386	+	0.997358i	$0.476858\pi$
$774$	−2.16612e15	−0.280290
$775$	−1.23926e15	−0.159222
$776$	4.07169e15	0.519440
$777$	−4.37273e15	−0.553907
$778$	3.85432e15	0.484796
$779$	3.32993e15	0.415891
$780$	−2.03494e15	−0.252366
$781$	6.53561e15	0.804833
$782$	7.85832e15	0.960932
$783$	2.16124e15	0.262430
$784$	−8.05028e14	−0.0970672
$785$	−4.96127e15	−0.594032
$786$	−6.48427e15	−0.770969
$787$	−5.95332e15	−0.702907	−0.351454	−	0.936205i	$-0.614313\pi$
$787$	−5.95332e15	−0.702907	−0.351454	+	0.936205i	$0.614313\pi$
$788$	−4.62994e15	−0.542852
$789$	−1.68790e15	−0.196527
$790$	−4.24237e15	−0.490523
$791$	−9.06045e15	−1.04035
$792$	1.47586e15	0.168289
$793$	−1.27497e16	−1.44376
$794$	−1.10416e16	−1.24171
$795$	−1.66230e15	−0.185648
$796$	−3.18027e15	−0.352729
$797$	9.51738e15	1.04833	0.524163	−	0.851618i	$-0.324378\pi$
$797$	9.51738e15	1.04833	0.524163	+	0.851618i	$0.324378\pi$
$798$	6.69644e14	0.0732534
$799$	2.05361e16	2.23105
$800$	3.55892e14	0.0383993
$801$	−7.88652e13	−0.00845097
$802$	−7.00626e14	−0.0745637
$803$	1.18348e16	1.25091
$804$	3.55173e15	0.372848
$805$	−6.92135e15	−0.721628
$806$	4.94577e15	0.512143
$807$	8.94289e15	0.919758
$808$	−2.51597e15	−0.257006
$809$	−1.61171e16	−1.63520	−0.817600	−	0.575786i	$-0.804696\pi$
$809$	−1.61171e16	−1.63520	−0.817600	+	0.575786i	$0.804696\pi$
$810$	−6.89811e14	−0.0695125
$811$	−1.78320e15	−0.178478	−0.0892391	−	0.996010i	$-0.528444\pi$
$811$	−1.78320e15	−0.178478	−0.0892391	+	0.996010i	$0.528444\pi$
$812$	−5.36419e15	−0.533269
$813$	5.39431e15	0.532645
$814$	1.26287e16	1.23858
$815$	−9.32093e15	−0.908013
$816$	−1.94388e15	−0.188094
$817$	2.83850e15	0.272814
$818$	7.21903e15	0.689184
$819$	2.71658e15	0.257609
$820$	8.51377e15	0.801947
$821$	−5.81735e15	−0.544300	−0.272150	−	0.962255i	$-0.587735\pi$
$821$	−5.81735e15	−0.544300	−0.272150	+	0.962255i	$0.587735\pi$
$822$	−2.52651e15	−0.234815
$823$	−4.41879e15	−0.407948	−0.203974	−	0.978976i	$-0.565386\pi$
$823$	−4.41879e15	−0.407948	−0.203974	+	0.978976i	$0.565386\pi$
$824$	−1.89015e15	−0.173339
$825$	1.96588e15	0.179085
$826$	3.81862e15	0.345554
$827$	−1.58364e16	−1.42356	−0.711778	−	0.702404i	$-0.752110\pi$
$827$	−1.58364e16	−1.42356	−0.711778	+	0.702404i	$0.752110\pi$
$828$	1.94638e15	0.173805
$829$	9.18914e15	0.815127	0.407563	−	0.913177i	$-0.366379\pi$
$829$	9.18914e15	0.815127	0.407563	+	0.913177i	$0.366379\pi$
$830$	1.23192e15	0.108556
$831$	−1.21290e16	−1.06174
$832$	−1.42033e15	−0.123513
$833$	5.85699e15	0.505973
$834$	−2.07170e15	−0.177792
$835$	−1.10251e16	−0.939956
$836$	−1.93397e15	−0.163801
$837$	1.67654e15	0.141066
$838$	2.66926e15	0.223125
$839$	−3.31613e15	−0.275385	−0.137693	−	0.990475i	$-0.543969\pi$
$839$	−3.31613e15	−0.275385	−0.137693	+	0.990475i	$0.543969\pi$
$840$	1.71211e15	0.141252
$841$	1.04861e16	0.859481
$842$	8.18663e14	0.0666636
$843$	−2.75004e15	−0.222478
$844$	1.05470e15	0.0847708
$845$	−2.62091e14	−0.0209286
$846$	5.08647e15	0.403533
$847$	−1.03112e16	−0.812736
$848$	−1.16024e15	−0.0908596
$849$	1.41600e16	1.10172
$850$	−2.58930e15	−0.200160
$851$	1.66549e16	1.27917
$852$	−2.13211e15	−0.162702
$853$	−1.31702e16	−0.998557	−0.499278	−	0.866442i	$-0.666401\pi$
$853$	−1.31702e16	−0.998557	−0.499278	+	0.866442i	$0.666401\pi$
$854$	1.07270e16	0.808089
$855$	9.03932e14	0.0676585
$856$	−8.67115e15	−0.644868
$857$	1.61740e16	1.19515	0.597576	−	0.801812i	$-0.296130\pi$
$857$	1.61740e16	1.19515	0.597576	+	0.801812i	$0.296130\pi$
$858$	−7.84564e15	−0.576034
$859$	1.22110e15	0.0890816	0.0445408	−	0.999008i	$-0.485818\pi$
$859$	1.22110e15	0.0890816	0.0445408	+	0.999008i	$0.485818\pi$
$860$	7.25731e15	0.526058
$861$	−1.13656e16	−0.818607
$862$	−5.74399e15	−0.411078
$863$	1.12405e16	0.799332	0.399666	−	0.916661i	$-0.369126\pi$
$863$	1.12405e16	0.799332	0.399666	+	0.916661i	$0.369126\pi$
$864$	−4.81469e14	−0.0340207
$865$	1.05717e16	0.742263
$866$	1.72280e16	1.20195
$867$	5.81467e15	0.403107
$868$	−4.16115e15	−0.286652
$869$	−1.63563e16	−1.11963
$870$	−7.24096e15	−0.492539
$871$	−1.88809e16	−1.27622
$872$	3.55896e14	0.0239046
$873$	−7.33731e15	−0.489732
$874$	−2.55055e15	−0.169169
$875$	1.27795e16	0.842305
$876$	−3.86088e15	−0.252880
$877$	−1.59596e16	−1.03878	−0.519391	−	0.854537i	$-0.673841\pi$
$877$	−1.59596e16	−1.03878	−0.519391	+	0.854537i	$0.673841\pi$
$878$	−7.17601e15	−0.464155
$879$	1.40144e16	0.900814
$880$	−4.94467e15	−0.315851
$881$	1.67785e15	0.106509	0.0532544	−	0.998581i	$-0.483041\pi$
$881$	1.67785e15	0.106509	0.0532544	+	0.998581i	$0.483041\pi$
$882$	1.45069e15	0.0915158
$883$	2.70866e15	0.169813	0.0849066	−	0.996389i	$-0.472941\pi$
$883$	2.70866e15	0.169813	0.0849066	+	0.996389i	$0.472941\pi$
$884$	1.03337e16	0.643823
$885$	5.15464e15	0.319161
$886$	−1.85286e16	−1.14014
$887$	1.94458e16	1.18917	0.594586	−	0.804032i	$-0.297316\pi$
$887$	1.94458e16	1.18917	0.594586	+	0.804032i	$0.297316\pi$
$888$	−4.11986e15	−0.250387
$889$	4.15758e15	0.251120
$890$	2.64227e14	0.0158611
$891$	−2.65954e15	−0.158664
$892$	1.16576e16	0.691201
$893$	−6.66533e15	−0.392770
$894$	−9.28821e15	−0.543971
$895$	2.01778e16	1.17449
$896$	1.19500e15	0.0691314
$897$	−1.03469e16	−0.594914
$898$	−5.20063e15	−0.297192
$899$	1.75986e16	0.999541
$900$	−6.41329e14	−0.0362032
$901$	8.44135e15	0.473615
$902$	3.28246e16	1.83047
$903$	−9.68827e15	−0.536987
$904$	−8.53651e15	−0.470277
$905$	−2.20411e16	−1.20689
$906$	9.65878e15	0.525675
$907$	1.63333e16	0.883558	0.441779	−	0.897124i	$-0.354348\pi$
$907$	1.63333e16	0.883558	0.441779	+	0.897124i	$0.354348\pi$
$908$	−5.12662e15	−0.275651
$909$	4.53386e15	0.242308
$910$	−9.10154e15	−0.483490
$911$	−1.57092e16	−0.829475	−0.414737	−	0.909941i	$-0.636127\pi$
$911$	−1.57092e16	−0.829475	−0.414737	+	0.909941i	$0.636127\pi$
$912$	6.30920e14	0.0331133
$913$	4.74964e15	0.247783
$914$	2.54468e16	1.31956
$915$	1.44800e16	0.746369
$916$	−1.08330e16	−0.555042
$917$	−2.90018e16	−1.47704
$918$	3.50294e15	0.177336
$919$	8.85481e15	0.445599	0.222799	−	0.974864i	$-0.428481\pi$
$919$	8.85481e15	0.445599	0.222799	+	0.974864i	$0.428481\pi$
$920$	−6.52110e15	−0.326203
$921$	−4.06530e15	−0.202146
$922$	−2.60548e15	−0.128786
$923$	1.13343e16	0.556910
$924$	6.60097e15	0.322413
$925$	−5.48775e15	−0.266450
$926$	4.80599e15	0.231965
$927$	3.40611e15	0.163426
$928$	−5.05399e15	−0.241058
$929$	−2.58244e16	−1.22446	−0.612228	−	0.790681i	$-0.709727\pi$
$929$	−2.58244e16	−1.22446	−0.612228	+	0.790681i	$0.709727\pi$
$930$	−5.61702e15	−0.264758
$931$	−1.90099e15	−0.0890750
$932$	1.36558e16	0.636107
$933$	−1.06479e16	−0.493077
$934$	2.88874e16	1.32984
$935$	3.59750e16	1.64641
$936$	2.55949e15	0.116449
$937$	−1.33587e16	−0.604221	−0.302111	−	0.953273i	$-0.597691\pi$
$937$	−1.33587e16	−0.604221	−0.302111	+	0.953273i	$0.597691\pi$
$938$	1.58856e16	0.714311
$939$	2.89141e15	0.129255
$940$	−1.70415e16	−0.757366
$941$	1.11508e16	0.492677	0.246339	−	0.969184i	$-0.420772\pi$
$941$	1.11508e16	0.492677	0.246339	+	0.969184i	$0.420772\pi$
$942$	6.24014e15	0.274103
$943$	4.32895e16	1.89046
$944$	3.59780e15	0.156203
$945$	−3.08527e15	−0.133174
$946$	2.79803e16	1.20075
$947$	4.11547e16	1.75588	0.877938	−	0.478774i	$-0.158919\pi$
$947$	4.11547e16	1.75588	0.877938	+	0.478774i	$0.158919\pi$
$948$	5.33592e15	0.226341
$949$	2.05244e16	0.865578
$950$	8.40400e14	0.0352376
$951$	9.30043e15	0.387713
$952$	−8.69427e15	−0.360355
$953$	1.82521e16	0.752144	0.376072	−	0.926590i	$-0.377274\pi$
$953$	1.82521e16	0.752144	0.376072	+	0.926590i	$0.377274\pi$
$954$	2.09079e15	0.0856633
$955$	−3.59147e16	−1.46303
$956$	1.86103e16	0.753762
$957$	−2.79173e16	−1.12424
$958$	−1.89096e16	−0.757131
$959$	−1.13002e16	−0.449865
$960$	1.61310e15	0.0638513
$961$	−1.17567e16	−0.462709
$962$	2.19011e16	0.857045
$963$	1.56257e16	0.607987
$964$	7.02477e15	0.271774
$965$	−5.91659e15	−0.227600
$966$	8.70546e15	0.332980
$967$	−7.18935e14	−0.0273429	−0.0136714	−	0.999907i	$-0.504352\pi$
$967$	−7.18935e14	−0.0273429	−0.0136714	+	0.999907i	$0.504352\pi$
$968$	−9.71490e15	−0.367387
$969$	−4.59027e15	−0.172607
$970$	2.45827e16	0.919147
$971$	−4.78065e16	−1.77739	−0.888693	−	0.458504i	$-0.848386\pi$
$971$	−4.78065e16	−1.77739	−0.888693	+	0.458504i	$0.848386\pi$
$972$	8.67624e14	0.0320750
$973$	−9.26595e15	−0.340619
$974$	1.86077e16	0.680173
$975$	3.40929e15	0.123919
$976$	1.01067e16	0.365287
$977$	2.61294e16	0.939094	0.469547	−	0.882908i	$-0.344417\pi$
$977$	2.61294e16	0.939094	0.469547	+	0.882908i	$0.344417\pi$
$978$	1.17236e16	0.418983
$979$	1.01872e15	0.0362034
$980$	−4.86033e15	−0.171760
$981$	−6.41335e14	−0.0225375
$982$	1.73250e16	0.605426
$983$	−1.55444e16	−0.540168	−0.270084	−	0.962837i	$-0.587051\pi$
$983$	−1.55444e16	−0.540168	−0.270084	+	0.962837i	$0.587051\pi$
$984$	−1.07084e16	−0.370041
$985$	−2.79531e16	−0.960575
$986$	3.67704e16	1.25654
$987$	2.27499e16	0.773099
$988$	−3.35396e15	−0.113343
$989$	3.69008e16	1.24010
$990$	8.91045e15	0.297787
$991$	−2.36795e16	−0.786986	−0.393493	−	0.919328i	$-0.628733\pi$
$991$	−2.36795e16	−0.786986	−0.393493	+	0.919328i	$0.628733\pi$
$992$	−3.92052e15	−0.129578
$993$	1.49491e16	0.491353
$994$	−9.53617e15	−0.311709
$995$	−1.92008e16	−0.624154
$996$	−1.54948e15	−0.0500909
$997$	1.19598e16	0.384504	0.192252	−	0.981346i	$-0.438421\pi$
$997$	1.19598e16	0.384504	0.192252	+	0.981346i	$0.438421\pi$
$998$	−3.20980e15	−0.102627
$999$	7.42412e15	0.236067

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.12.a.f.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.12.a.f.1.3	✓	4	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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	114.a (trivial)

\(f(q)\)	\(=\)	\(q-32.0000 q^{2} +243.000 q^{3} +1024.00 q^{4} +6182.37 q^{5} -7776.00 q^{6} -34779.2 q^{7} -32768.0 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-32.0000 q^{2} +243.000 q^{3} +1024.00 q^{4} +6182.37 q^{5} -7776.00 q^{6} -34779.2 q^{7} -32768.0 q^{8} +59049.0 q^{9} -197836. q^{10} -762750. q^{11} +248832. q^{12} -1.32279e6 q^{13} +1.11293e6 q^{14} +1.50232e6 q^{15} +1.04858e6 q^{16} -7.62893e6 q^{17} -1.88957e6 q^{18} +2.47610e6 q^{19} +6.33075e6 q^{20} -8.45135e6 q^{21} +2.44080e7 q^{22} +3.21896e7 q^{23} -7.96262e6 q^{24} -1.06064e7 q^{25} +4.23292e7 q^{26} +1.43489e7 q^{27} -3.56139e7 q^{28} +1.50621e8 q^{29} -4.80741e7 q^{30} +1.16841e8 q^{31} -3.35544e7 q^{32} -1.85348e8 q^{33} +2.44126e8 q^{34} -2.15018e8 q^{35} +6.04662e7 q^{36} +5.17400e8 q^{37} -7.92352e7 q^{38} -3.21437e8 q^{39} -2.02584e8 q^{40} +1.34483e9 q^{41} +2.70443e8 q^{42} +1.14636e9 q^{43} -7.81056e8 q^{44} +3.65063e8 q^{45} -1.03007e9 q^{46} -2.69187e9 q^{47} +2.54804e8 q^{48} -7.67734e8 q^{49} +3.39405e8 q^{50} -1.85383e9 q^{51} -1.35453e9 q^{52} -1.10649e9 q^{53} -4.59165e8 q^{54} -4.71560e9 q^{55} +1.13964e9 q^{56} +6.01692e8 q^{57} -4.81986e9 q^{58} +3.43113e9 q^{59} +1.53837e9 q^{60} +9.63847e9 q^{61} -3.73890e9 q^{62} -2.05368e9 q^{63} +1.07374e9 q^{64} -8.17797e9 q^{65} +5.93114e9 q^{66} +1.42736e10 q^{67} -7.81203e9 q^{68} +7.82208e9 q^{69} +6.88057e9 q^{70} -8.56849e9 q^{71} -1.93492e9 q^{72} -1.55160e10 q^{73} -1.65568e10 q^{74} -2.57736e9 q^{75} +2.53553e9 q^{76} +2.65278e10 q^{77} +1.02860e10 q^{78} +2.14439e10 q^{79} +6.48269e9 q^{80} +3.48678e9 q^{81} -4.30345e10 q^{82} -6.22700e9 q^{83} -8.65418e9 q^{84} -4.71649e10 q^{85} -3.66835e10 q^{86} +3.66008e10 q^{87} +2.49938e10 q^{88} -1.33559e9 q^{89} -1.16820e10 q^{90} +4.60055e10 q^{91} +3.29622e10 q^{92} +2.83923e10 q^{93} +8.61398e10 q^{94} +1.53082e10 q^{95} -8.15373e9 q^{96} -1.24258e11 q^{97} +2.45675e10 q^{98} -4.50396e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 128 q^{2} + 972 q^{3} + 4096 q^{4} + 9912 q^{5} - 31104 q^{6} + 36234 q^{7} - 131072 q^{8} + 236196 q^{9}+O(q^{10}) \) 4 * q - 128 * q^2 + 972 * q^3 + 4096 * q^4 + 9912 * q^5 - 31104 * q^6 + 36234 * q^7 - 131072 * q^8 + 236196 * q^9	\( 4 q - 128 q^{2} + 972 q^{3} + 4096 q^{4} + 9912 q^{5} - 31104 q^{6} + 36234 q^{7} - 131072 q^{8} + 236196 q^{9} - 317184 q^{10} + 656548 q^{11} + 995328 q^{12} - 1328426 q^{13} - 1159488 q^{14} + 2408616 q^{15} + 4194304 q^{16} - 6116414 q^{17} - 7558272 q^{18} + 9904396 q^{19} + 10149888 q^{20} + 8804862 q^{21} - 21009536 q^{22} + 34001164 q^{23} - 31850496 q^{24} + 58663954 q^{25} + 42509632 q^{26} + 57395628 q^{27} + 37103616 q^{28} + 276975486 q^{29} - 77075712 q^{30} + 264731062 q^{31} - 134217728 q^{32} + 159541164 q^{33} + 195725248 q^{34} + 575633478 q^{35} + 241864704 q^{36} + 886797726 q^{37} - 316940672 q^{38} - 322807518 q^{39} - 324796416 q^{40} - 275275946 q^{41} - 281755584 q^{42} + 683228242 q^{43} + 672305152 q^{44} + 585293688 q^{45} - 1088037248 q^{46} - 1324778186 q^{47} + 1019215872 q^{48} - 306061098 q^{49} - 1877246528 q^{50} - 1486288602 q^{51} - 1360308224 q^{52} + 446705822 q^{53} - 1836660096 q^{54} - 12020135034 q^{55} - 1187315712 q^{56} + 2406768228 q^{57} - 8863215552 q^{58} + 6625246756 q^{59} + 2466422784 q^{60} - 6743662354 q^{61} - 8471393984 q^{62} + 2139581466 q^{63} + 4294967296 q^{64} - 3307258728 q^{65} - 5105317248 q^{66} - 33594510788 q^{67} - 6263207936 q^{68} + 8262282852 q^{69} - 18420271296 q^{70} - 7592117020 q^{71} - 7739670528 q^{72} + 6699940398 q^{73} - 28377527232 q^{74} + 14255340822 q^{75} + 10142101504 q^{76} + 47149048966 q^{77} + 10329840576 q^{78} + 8043101838 q^{79} + 10393485312 q^{80} + 13947137604 q^{81} + 8808830272 q^{82} - 16824459190 q^{83} + 9016178688 q^{84} + 66979473594 q^{85} - 21863303744 q^{86} + 67305043098 q^{87} - 21513764864 q^{88} + 9048133798 q^{89} - 18729398016 q^{90} + 158880145340 q^{91} + 34817191936 q^{92} + 64329648066 q^{93} + 42392901952 q^{94} + 24543093288 q^{95} - 32614907904 q^{96} - 96323093704 q^{97} + 9793955136 q^{98} + 38768502852 q^{99}+O(q^{100}) \) 4 * q - 128 * q^2 + 972 * q^3 + 4096 * q^4 + 9912 * q^5 - 31104 * q^6 + 36234 * q^7 - 131072 * q^8 + 236196 * q^9 - 317184 * q^10 + 656548 * q^11 + 995328 * q^12 - 1328426 * q^13 - 1159488 * q^14 + 2408616 * q^15 + 4194304 * q^16 - 6116414 * q^17 - 7558272 * q^18 + 9904396 * q^19 + 10149888 * q^20 + 8804862 * q^21 - 21009536 * q^22 + 34001164 * q^23 - 31850496 * q^24 + 58663954 * q^25 + 42509632 * q^26 + 57395628 * q^27 + 37103616 * q^28 + 276975486 * q^29 - 77075712 * q^30 + 264731062 * q^31 - 134217728 * q^32 + 159541164 * q^33 + 195725248 * q^34 + 575633478 * q^35 + 241864704 * q^36 + 886797726 * q^37 - 316940672 * q^38 - 322807518 * q^39 - 324796416 * q^40 - 275275946 * q^41 - 281755584 * q^42 + 683228242 * q^43 + 672305152 * q^44 + 585293688 * q^45 - 1088037248 * q^46 - 1324778186 * q^47 + 1019215872 * q^48 - 306061098 * q^49 - 1877246528 * q^50 - 1486288602 * q^51 - 1360308224 * q^52 + 446705822 * q^53 - 1836660096 * q^54 - 12020135034 * q^55 - 1187315712 * q^56 + 2406768228 * q^57 - 8863215552 * q^58 + 6625246756 * q^59 + 2466422784 * q^60 - 6743662354 * q^61 - 8471393984 * q^62 + 2139581466 * q^63 + 4294967296 * q^64 - 3307258728 * q^65 - 5105317248 * q^66 - 33594510788 * q^67 - 6263207936 * q^68 + 8262282852 * q^69 - 18420271296 * q^70 - 7592117020 * q^71 - 7739670528 * q^72 + 6699940398 * q^73 - 28377527232 * q^74 + 14255340822 * q^75 + 10142101504 * q^76 + 47149048966 * q^77 + 10329840576 * q^78 + 8043101838 * q^79 + 10393485312 * q^80 + 13947137604 * q^81 + 8808830272 * q^82 - 16824459190 * q^83 + 9016178688 * q^84 + 66979473594 * q^85 - 21863303744 * q^86 + 67305043098 * q^87 - 21513764864 * q^88 + 9048133798 * q^89 - 18729398016 * q^90 + 158880145340 * q^91 + 34817191936 * q^92 + 64329648066 * q^93 + 42392901952 * q^94 + 24543093288 * q^95 - 32614907904 * q^96 - 96323093704 * q^97 + 9793955136 * q^98 + 38768502852 * q^99

Introduction

L-functions

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