LMFDB - Embedded newform 13.12.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,12,Mod(1,13)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("13.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	13.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:	$9.98846134727$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6448x^{3} - 12116x^{2} + 9682560x + 66650112 $ x^5 - x^4 - 6448x^3 - 12116x^2 + 9682560*x + 66650112
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$63.7031$ of defining polynomial
Character	$\chi$	$=$	13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-71.7031 q^{2} -710.121 q^{3} +3093.33 q^{4} +10598.3 q^{5} +50917.9 q^{6} -48491.8 q^{7} -74953.5 q^{8} +327125. q^{9} +O(q^{10})$	\(q-71.7031 q^{2} -710.121 q^{3} +3093.33 q^{4} +10598.3 q^{5} +50917.9 q^{6} -48491.8 q^{7} -74953.5 q^{8} +327125. q^{9} -759930. q^{10} +262047. q^{11} -2.19664e6 q^{12} +371293. q^{13} +3.47701e6 q^{14} -7.52607e6 q^{15} -960748. q^{16} -3.38243e6 q^{17} -2.34559e7 q^{18} +1.62735e7 q^{19} +3.27840e7 q^{20} +3.44351e7 q^{21} -1.87896e7 q^{22} -4.23017e7 q^{23} +5.32260e7 q^{24} +6.34957e7 q^{25} -2.66229e7 q^{26} -1.06503e8 q^{27} -1.50001e8 q^{28} -1.00743e8 q^{29} +5.39643e8 q^{30} -1.57832e8 q^{31} +2.22393e8 q^{32} -1.86085e8 q^{33} +2.42531e8 q^{34} -5.13931e8 q^{35} +1.01191e9 q^{36} +4.48631e8 q^{37} -1.16686e9 q^{38} -2.63663e8 q^{39} -7.94379e8 q^{40} -6.99273e8 q^{41} -2.46910e9 q^{42} -7.52629e8 q^{43} +8.10599e8 q^{44} +3.46697e9 q^{45} +3.03316e9 q^{46} -2.38590e9 q^{47} +6.82248e8 q^{48} +3.74131e8 q^{49} -4.55284e9 q^{50} +2.40194e9 q^{51} +1.14853e9 q^{52} +3.56840e9 q^{53} +7.63656e9 q^{54} +2.77725e9 q^{55} +3.63463e9 q^{56} -1.15561e10 q^{57} +7.22360e9 q^{58} +9.83493e8 q^{59} -2.32806e10 q^{60} -1.15375e8 q^{61} +1.13171e10 q^{62} -1.58629e10 q^{63} -1.39787e10 q^{64} +3.93507e9 q^{65} +1.33429e10 q^{66} -5.86589e9 q^{67} -1.04630e10 q^{68} +3.00393e10 q^{69} +3.68504e10 q^{70} -9.81075e9 q^{71} -2.45192e10 q^{72} -3.41836e9 q^{73} -3.21682e10 q^{74} -4.50896e10 q^{75} +5.03392e10 q^{76} -1.27071e10 q^{77} +1.89054e10 q^{78} -1.00965e10 q^{79} -1.01823e10 q^{80} +1.76805e10 q^{81} +5.01400e10 q^{82} -4.51697e10 q^{83} +1.06519e11 q^{84} -3.58480e10 q^{85} +5.39658e10 q^{86} +7.15399e10 q^{87} -1.96413e10 q^{88} -7.46127e9 q^{89} -2.48592e11 q^{90} -1.80047e10 q^{91} -1.30853e11 q^{92} +1.12080e11 q^{93} +1.71076e11 q^{94} +1.72471e11 q^{95} -1.57926e11 q^{96} -6.53631e10 q^{97} -2.68263e10 q^{98} +8.57222e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 41 q^{2} - 496 q^{3} + 2993 q^{4} - 2542 q^{5} + 35441 q^{6} - 36296 q^{7} - 200037 q^{8} + 172645 q^{9}+O(q^{10}) $ 5 * q - 41 * q^2 - 496 * q^3 + 2993 * q^4 - 2542 * q^5 + 35441 * q^6 - 36296 * q^7 - 200037 * q^8 + 172645 * q^9	\( 5 q - 41 q^{2} - 496 q^{3} + 2993 q^{4} - 2542 q^{5} + 35441 q^{6} - 36296 q^{7} - 200037 q^{8} + 172645 q^{9} - 1004055 q^{10} - 1718912 q^{11} - 3670067 q^{12} + 1856465 q^{13} - 3264661 q^{14} - 15356636 q^{15} - 9077455 q^{16} - 6022762 q^{17} - 25785896 q^{18} - 6984968 q^{19} + 38011501 q^{20} + 30001972 q^{21} + 35725110 q^{22} - 26355744 q^{23} + 88388907 q^{24} + 159029879 q^{25} - 15223013 q^{26} + 112641236 q^{27} + 56979871 q^{28} - 81933754 q^{29} + 564471025 q^{30} - 13953380 q^{31} + 399845123 q^{32} - 703422928 q^{33} - 86504907 q^{34} - 754497044 q^{35} + 70511186 q^{36} - 417857846 q^{37} - 903900222 q^{38} - 184161328 q^{39} - 1116423525 q^{40} - 2690154174 q^{41} - 1731320681 q^{42} - 2194005968 q^{43} + 2402296286 q^{44} + 953635766 q^{45} + 4518855072 q^{46} - 4632149016 q^{47} + 5192309977 q^{48} + 2068996185 q^{49} + 2031214610 q^{50} + 4379956420 q^{51} + 1111279949 q^{52} + 3964085286 q^{53} + 12032576291 q^{54} + 3173729472 q^{55} + 10863941385 q^{56} - 15850418664 q^{57} + 16463234370 q^{58} - 6213900336 q^{59} - 4723327387 q^{60} - 13653194690 q^{61} + 7267753516 q^{62} - 29514629404 q^{63} - 17414214535 q^{64} - 943826806 q^{65} + 12784796606 q^{66} - 11630839736 q^{67} - 29781833135 q^{68} - 10491265752 q^{69} + 22288071195 q^{70} - 55420684056 q^{71} - 8164244886 q^{72} - 10807393382 q^{73} - 24555721283 q^{74} - 7282468148 q^{75} + 86244951178 q^{76} - 29595239248 q^{77} + 13158995213 q^{78} - 4898325368 q^{79} - 19551386423 q^{80} + 67432983205 q^{81} + 101980594164 q^{82} - 17839206992 q^{83} + 115847226287 q^{84} + 74975179056 q^{85} - 6756156273 q^{86} + 166439707672 q^{87} - 5163165966 q^{88} + 65706244882 q^{89} - 197230060630 q^{90} - 13476450728 q^{91} - 91088158752 q^{92} + 189811093880 q^{93} + 152425406559 q^{94} + 51462465912 q^{95} - 181515906965 q^{96} - 66619160654 q^{97} - 394227632340 q^{98} - 35714076944 q^{99}+O(q^{100}) \) 5 * q - 41 * q^2 - 496 * q^3 + 2993 * q^4 - 2542 * q^5 + 35441 * q^6 - 36296 * q^7 - 200037 * q^8 + 172645 * q^9 - 1004055 * q^10 - 1718912 * q^11 - 3670067 * q^12 + 1856465 * q^13 - 3264661 * q^14 - 15356636 * q^15 - 9077455 * q^16 - 6022762 * q^17 - 25785896 * q^18 - 6984968 * q^19 + 38011501 * q^20 + 30001972 * q^21 + 35725110 * q^22 - 26355744 * q^23 + 88388907 * q^24 + 159029879 * q^25 - 15223013 * q^26 + 112641236 * q^27 + 56979871 * q^28 - 81933754 * q^29 + 564471025 * q^30 - 13953380 * q^31 + 399845123 * q^32 - 703422928 * q^33 - 86504907 * q^34 - 754497044 * q^35 + 70511186 * q^36 - 417857846 * q^37 - 903900222 * q^38 - 184161328 * q^39 - 1116423525 * q^40 - 2690154174 * q^41 - 1731320681 * q^42 - 2194005968 * q^43 + 2402296286 * q^44 + 953635766 * q^45 + 4518855072 * q^46 - 4632149016 * q^47 + 5192309977 * q^48 + 2068996185 * q^49 + 2031214610 * q^50 + 4379956420 * q^51 + 1111279949 * q^52 + 3964085286 * q^53 + 12032576291 * q^54 + 3173729472 * q^55 + 10863941385 * q^56 - 15850418664 * q^57 + 16463234370 * q^58 - 6213900336 * q^59 - 4723327387 * q^60 - 13653194690 * q^61 + 7267753516 * q^62 - 29514629404 * q^63 - 17414214535 * q^64 - 943826806 * q^65 + 12784796606 * q^66 - 11630839736 * q^67 - 29781833135 * q^68 - 10491265752 * q^69 + 22288071195 * q^70 - 55420684056 * q^71 - 8164244886 * q^72 - 10807393382 * q^73 - 24555721283 * q^74 - 7282468148 * q^75 + 86244951178 * q^76 - 29595239248 * q^77 + 13158995213 * q^78 - 4898325368 * q^79 - 19551386423 * q^80 + 67432983205 * q^81 + 101980594164 * q^82 - 17839206992 * q^83 + 115847226287 * q^84 + 74975179056 * q^85 - 6756156273 * q^86 + 166439707672 * q^87 - 5163165966 * q^88 + 65706244882 * q^89 - 197230060630 * q^90 - 13476450728 * q^91 - 91088158752 * q^92 + 189811093880 * q^93 + 152425406559 * q^94 + 51462465912 * q^95 - 181515906965 * q^96 - 66619160654 * q^97 - 394227632340 * q^98 - 35714076944 * 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 $

$2$	−71.7031	−1.58443	−0.792215	−	0.610243i	$-0.791072\pi$
$2$	−71.7031	−1.58443	−0.792215	+	0.610243i	$0.791072\pi$
$3$	−710.121	−1.68720	−0.843598	−	0.536975i	$-0.819567\pi$
$3$	−710.121	−1.68720	−0.843598	+	0.536975i	$0.819567\pi$
$4$	3093.33	1.51042
$5$	10598.3	1.51670	0.758352	−	0.651845i	$-0.226005\pi$
$5$	10598.3	1.51670	0.758352	+	0.651845i	$0.226005\pi$
$6$	50917.9	2.67324
$7$	−48491.8	−1.09051	−0.545255	−	0.838270i	$-0.683567\pi$
$7$	−48491.8	−1.09051	−0.545255	+	0.838270i	$0.683567\pi$
$8$	−74953.5	−0.808717
$9$	327125.	1.84663
$10$	−759930.	−2.40311
$11$	262047.	0.490591	0.245296	−	0.969448i	$-0.421115\pi$
$11$	262047.	0.490591	0.245296	+	0.969448i	$0.421115\pi$
$12$	−2.19664e6	−2.54837
$13$	371293.	0.277350
$13$	371293.	0.277350
$14$	3.47701e6	1.72783
$15$	−7.52607e6	−2.55898
$16$	−960748.	−0.229060
$17$	−3.38243e6	−0.577777	−0.288888	−	0.957363i	$-0.593286\pi$
$17$	−3.38243e6	−0.577777	−0.288888	+	0.957363i	$0.593286\pi$
$18$	−2.34559e7	−2.92585
$19$	1.62735e7	1.50777	0.753886	−	0.657006i	$-0.228177\pi$
$19$	1.62735e7	1.50777	0.753886	+	0.657006i	$0.228177\pi$
$20$	3.27840e7	2.29085
$21$	3.44351e7	1.83990
$22$	−1.87896e7	−0.777307
$23$	−4.23017e7	−1.37042	−0.685211	−	0.728344i	$-0.740290\pi$
$23$	−4.23017e7	−1.37042	−0.685211	+	0.728344i	$0.740290\pi$
$24$	5.32260e7	1.36446
$25$	6.34957e7	1.30039
$26$	−2.66229e7	−0.439442
$27$	−1.06503e8	−1.42843
$28$	−1.50001e8	−1.64712
$29$	−1.00743e8	−0.912068	−0.456034	−	0.889962i	$-0.650730\pi$
$29$	−1.00743e8	−0.912068	−0.456034	+	0.889962i	$0.650730\pi$
$30$	5.39643e8	4.05452
$31$	−1.57832e8	−0.990162	−0.495081	−	0.868847i	$-0.664862\pi$
$31$	−1.57832e8	−0.990162	−0.495081	+	0.868847i	$0.664862\pi$
$32$	2.22393e8	1.17165
$33$	−1.86085e8	−0.827723
$34$	2.42531e8	0.915447
$35$	−5.13931e8	−1.65398
$36$	1.01191e9	2.78918
$37$	4.48631e8	1.06360	0.531802	−	0.846869i	$-0.321515\pi$
$37$	4.48631e8	1.06360	0.531802	+	0.846869i	$0.321515\pi$
$38$	−1.16686e9	−2.38896
$39$	−2.63663e8	−0.467944
$40$	−7.94379e8	−1.22659
$41$	−6.99273e8	−0.942618	−0.471309	−	0.881968i	$-0.656218\pi$
$41$	−6.99273e8	−0.942618	−0.471309	+	0.881968i	$0.656218\pi$
$42$	−2.46910e9	−2.91520
$43$	−7.52629e8	−0.780737	−0.390368	−	0.920659i	$-0.627652\pi$
$43$	−7.52629e8	−0.780737	−0.390368	+	0.920659i	$0.627652\pi$
$44$	8.10599e8	0.740996
$45$	3.46697e9	2.80079
$46$	3.03316e9	2.17134
$47$	−2.38590e9	−1.51745	−0.758723	−	0.651414i	$-0.774176\pi$
$47$	−2.38590e9	−1.51745	−0.758723	+	0.651414i	$0.774176\pi$
$48$	6.82248e8	0.386470
$49$	3.74131e8	0.189210
$50$	−4.55284e9	−2.06038
$51$	2.40194e9	0.974823
$52$	1.14853e9	0.418914
$53$	3.56840e9	1.17208	0.586038	−	0.810283i	$-0.300687\pi$
$53$	3.56840e9	1.17208	0.586038	+	0.810283i	$0.300687\pi$
$54$	7.63656e9	2.26325
$55$	2.77725e9	0.744082
$56$	3.63463e9	0.881914
$57$	−1.15561e10	−2.54391
$58$	7.22360e9	1.44511
$59$	9.83493e8	0.179096	0.0895479	−	0.995983i	$-0.471458\pi$
$59$	9.83493e8	0.179096	0.0895479	+	0.995983i	$0.471458\pi$
$60$	−2.32806e10	−3.86512
$61$	−1.15375e8	−0.0174903	−0.00874514	−	0.999962i	$-0.502784\pi$
$61$	−1.15375e8	−0.0174903	−0.00874514	+	0.999962i	$0.502784\pi$
$62$	1.13171e10	1.56884
$63$	−1.58629e10	−2.01377
$64$	−1.39787e10	−1.62733
$65$	3.93507e9	0.420658
$66$	1.33429e10	1.31147
$67$	−5.86589e9	−0.530789	−0.265395	−	0.964140i	$-0.585502\pi$
$67$	−5.86589e9	−0.530789	−0.265395	+	0.964140i	$0.585502\pi$
$68$	−1.04630e10	−0.872683
$69$	3.00393e10	2.31217
$70$	3.68504e10	2.62061
$71$	−9.81075e9	−0.645329	−0.322665	−	0.946513i	$-0.604579\pi$
$71$	−9.81075e9	−0.645329	−0.322665	+	0.946513i	$0.604579\pi$
$72$	−2.45192e10	−1.49340
$73$	−3.41836e9	−0.192993	−0.0964965	−	0.995333i	$-0.530764\pi$
$73$	−3.41836e9	−0.192993	−0.0964965	+	0.995333i	$0.530764\pi$
$74$	−3.21682e10	−1.68520
$75$	−4.50896e10	−2.19402
$76$	5.03392e10	2.27736
$77$	−1.27071e10	−0.534994
$78$	1.89054e10	0.741424
$79$	−1.00965e10	−0.369167	−0.184584	−	0.982817i	$-0.559094\pi$
$79$	−1.00965e10	−0.369167	−0.184584	+	0.982817i	$0.559094\pi$
$80$	−1.01823e10	−0.347417
$81$	1.76805e10	0.563413
$82$	5.01400e10	1.49351
$83$	−4.51697e10	−1.25869	−0.629344	−	0.777127i	$-0.716676\pi$
$83$	−4.51697e10	−1.25869	−0.629344	+	0.777127i	$0.716676\pi$
$84$	1.06519e11	2.77902
$85$	−3.58480e10	−0.876317
$86$	5.39658e10	1.23702
$87$	7.15399e10	1.53884
$88$	−1.96413e10	−0.396750
$89$	−7.46127e9	−0.141634	−0.0708170	−	0.997489i	$-0.522561\pi$
$89$	−7.46127e9	−0.141634	−0.0708170	+	0.997489i	$0.522561\pi$
$90$	−2.48592e11	−4.43766
$91$	−1.80047e10	−0.302453
$92$	−1.30853e11	−2.06991
$93$	1.12080e11	1.67060
$94$	1.71076e11	2.40429
$95$	1.72471e11	2.28684
$96$	−1.57926e11	−1.97680
$97$	−6.53631e10	−0.772838	−0.386419	−	0.922323i	$-0.626288\pi$
$97$	−6.53631e10	−0.772838	−0.386419	+	0.922323i	$0.626288\pi$
$98$	−2.68263e10	−0.299791
$99$	8.57222e10	0.905940
$100$	1.96413e11	1.96413
$101$	−4.13120e10	−0.391119	−0.195560	−	0.980692i	$-0.562652\pi$
$101$	−4.13120e10	−0.391119	−0.195560	+	0.980692i	$0.562652\pi$
$102$	−1.72226e11	−1.54454
$103$	1.29627e10	0.110177	0.0550886	−	0.998481i	$-0.482456\pi$
$103$	1.29627e10	0.110177	0.0550886	+	0.998481i	$0.482456\pi$
$104$	−2.78297e10	−0.224298
$105$	3.64953e11	2.79059
$106$	−2.55865e11	−1.85707
$107$	−4.49354e10	−0.309726	−0.154863	−	0.987936i	$-0.549494\pi$
$107$	−4.49354e10	−0.309726	−0.154863	+	0.987936i	$0.549494\pi$
$108$	−3.29448e11	−2.15752
$109$	5.48066e10	0.341183	0.170591	−	0.985342i	$-0.445432\pi$
$109$	5.48066e10	0.341183	0.170591	+	0.985342i	$0.445432\pi$
$110$	−1.99138e11	−1.17894
$111$	−3.18582e11	−1.79451
$112$	4.65885e10	0.249792
$113$	−1.24124e11	−0.633762	−0.316881	−	0.948465i	$-0.602636\pi$
$113$	−1.24124e11	−0.633762	−0.316881	+	0.948465i	$0.602636\pi$
$114$	8.28611e11	4.03064
$115$	−4.48326e11	−2.07853
$116$	−3.11632e11	−1.37760
$117$	1.21459e11	0.512163
$118$	−7.05195e10	−0.283765
$119$	1.64020e11	0.630071
$120$	5.64105e11	2.06949
$121$	−2.16643e11	−0.759320
$122$	8.27272e9	0.0277121
$123$	4.96569e11	1.59038
$124$	−4.88227e11	−1.49556
$125$	1.55451e11	0.455606
$126$	1.13742e12	3.19067
$127$	2.00782e11	0.539267	0.269633	−	0.962963i	$-0.413097\pi$
$127$	2.00782e11	0.539267	0.269633	+	0.962963i	$0.413097\pi$
$128$	5.46852e11	1.40674
$129$	5.34458e11	1.31726
$130$	−2.82157e11	−0.666503
$131$	4.49222e11	1.01735	0.508674	−	0.860959i	$-0.330136\pi$
$131$	4.49222e11	1.01735	0.508674	+	0.860959i	$0.330136\pi$
$132$	−5.75623e11	−1.25021
$133$	−7.89130e11	−1.64424
$134$	4.20602e11	0.840998
$135$	−1.12875e12	−2.16651
$136$	2.53525e11	0.467258
$137$	−8.55705e11	−1.51482	−0.757410	−	0.652939i	$-0.773536\pi$
$137$	−8.55705e11	−1.51482	−0.757410	+	0.652939i	$0.773536\pi$
$138$	−2.15391e12	−3.66347
$139$	3.52641e11	0.576437	0.288218	−	0.957565i	$-0.406937\pi$
$139$	3.52641e11	0.576437	0.288218	+	0.957565i	$0.406937\pi$
$140$	−1.58976e12	−2.49820
$141$	1.69427e12	2.56023
$142$	7.03461e11	1.02248
$143$	9.72963e10	0.136065
$144$	−3.14285e11	−0.422990
$145$	−1.06771e12	−1.38334
$146$	2.45107e11	0.305784
$147$	−2.65678e11	−0.319235
$148$	1.38776e12	1.60648
$149$	−1.64190e12	−1.83157	−0.915784	−	0.401672i	$-0.868429\pi$
$149$	−1.64190e12	−1.83157	−0.915784	+	0.401672i	$0.868429\pi$
$150$	3.23307e12	3.47626
$151$	1.45068e12	1.50382	0.751912	−	0.659263i	$-0.229132\pi$
$151$	1.45068e12	1.50382	0.751912	+	0.659263i	$0.229132\pi$
$152$	−1.21975e12	−1.21936
$153$	−1.10648e12	−1.06694
$154$	9.11141e11	0.847660
$155$	−1.67275e12	−1.50178
$156$	−8.15597e11	−0.706790
$157$	1.27471e12	1.06651	0.533253	−	0.845956i	$-0.320969\pi$
$157$	1.27471e12	1.06651	0.533253	+	0.845956i	$0.320969\pi$
$158$	7.23952e11	0.584919
$159$	−2.53399e12	−1.97752
$160$	2.35699e12	1.77704
$161$	2.05129e12	1.49446
$162$	−1.26775e12	−0.892688
$163$	1.67659e12	1.14129	0.570644	−	0.821198i	$-0.306694\pi$
$163$	1.67659e12	1.14129	0.570644	+	0.821198i	$0.306694\pi$
$164$	−2.16308e12	−1.42374
$165$	−1.97219e12	−1.25541
$166$	3.23881e12	1.99430
$167$	2.56880e11	0.153035	0.0765173	−	0.997068i	$-0.475620\pi$
$167$	2.56880e11	0.153035	0.0765173	+	0.997068i	$0.475620\pi$
$168$	−2.58103e12	−1.48796
$169$	1.37858e11	0.0769231
$170$	2.57041e12	1.38846
$171$	5.32346e12	2.78430
$172$	−2.32813e12	−1.17924
$173$	−9.74191e11	−0.477959	−0.238980	−	0.971025i	$-0.576813\pi$
$173$	−9.74191e11	−0.477959	−0.238980	+	0.971025i	$0.576813\pi$
$174$	−5.12963e12	−2.43818
$175$	−3.07902e12	−1.41809
$176$	−2.51761e11	−0.112375
$177$	−6.98399e11	−0.302170
$178$	5.34996e11	0.224409
$179$	−1.69954e12	−0.691257	−0.345629	−	0.938371i	$-0.612334\pi$
$179$	−1.69954e12	−0.691257	−0.345629	+	0.938371i	$0.612334\pi$
$180$	1.07245e13	4.23036
$181$	1.42278e12	0.544384	0.272192	−	0.962243i	$-0.412251\pi$
$181$	1.42278e12	0.544384	0.272192	+	0.962243i	$0.412251\pi$
$182$	1.29099e12	0.479215
$183$	8.19300e10	0.0295095
$184$	3.17066e12	1.10828
$185$	4.75472e12	1.61317
$186$	−8.03648e12	−2.64694
$187$	−8.86357e11	−0.283452
$188$	−7.38036e12	−2.29197
$189$	5.16450e12	1.55772
$190$	−1.23667e13	−3.62334
$191$	−3.82549e12	−1.08894	−0.544469	−	0.838781i	$-0.683269\pi$
$191$	−3.82549e12	−1.08894	−0.544469	+	0.838781i	$0.683269\pi$
$192$	9.92655e12	2.74563
$193$	−5.23619e11	−0.140751	−0.0703753	−	0.997521i	$-0.522420\pi$
$193$	−5.23619e11	−0.140751	−0.0703753	+	0.997521i	$0.522420\pi$
$194$	4.68674e12	1.22451
$195$	−2.79438e12	−0.709733
$196$	1.15731e12	0.285786
$197$	4.46908e12	1.07313	0.536567	−	0.843858i	$-0.319721\pi$
$197$	4.46908e12	1.07313	0.536567	+	0.843858i	$0.319721\pi$
$198$	−6.14654e12	−1.43540
$199$	−5.49722e12	−1.24868	−0.624340	−	0.781153i	$-0.714632\pi$
$199$	−5.49722e12	−1.24868	−0.624340	+	0.781153i	$0.714632\pi$
$200$	−4.75922e12	−1.05165
$201$	4.16549e12	0.895546
$202$	2.96220e12	0.619701
$203$	4.88523e12	0.994618
$204$	7.42999e12	1.47239
$205$	−7.41110e12	−1.42967
$206$	−9.29468e11	−0.174568
$207$	−1.38379e13	−2.53066
$208$	−3.56719e11	−0.0635299
$209$	4.26442e12	0.739699
$210$	−2.61683e13	−4.42149
$211$	9.75594e12	1.60589	0.802945	−	0.596054i	$-0.203266\pi$
$211$	9.75594e12	1.60589	0.802945	+	0.596054i	$0.203266\pi$
$212$	1.10382e13	1.77032
$213$	6.96682e12	1.08880
$214$	3.22200e12	0.490739
$215$	−7.97659e12	−1.18415
$216$	7.98273e12	1.15520
$217$	7.65357e12	1.07978
$218$	−3.92980e12	−0.540580
$219$	2.42745e12	0.325617
$220$	8.59096e12	1.12387
$221$	−1.25587e12	−0.160246
$222$	2.28433e13	2.84327
$223$	−9.83688e12	−1.19448	−0.597242	−	0.802061i	$-0.703737\pi$
$223$	−9.83688e12	−1.19448	−0.597242	+	0.802061i	$0.703737\pi$
$224$	−1.07843e13	−1.27769
$225$	2.07710e13	2.40134
$226$	8.90011e12	1.00415
$227$	−3.46700e12	−0.381778	−0.190889	−	0.981612i	$-0.561137\pi$
$227$	−3.46700e12	−0.381778	−0.190889	+	0.981612i	$0.561137\pi$
$228$	−3.57470e13	−3.84235
$229$	−1.83855e13	−1.92921	−0.964606	−	0.263696i	$-0.915058\pi$
$229$	−1.83855e13	−1.92921	−0.964606	+	0.263696i	$0.915058\pi$
$230$	3.21463e13	3.29328
$231$	9.02361e12	0.902640
$232$	7.55106e12	0.737605
$233$	8.62270e12	0.822594	0.411297	−	0.911501i	$-0.365076\pi$
$233$	8.62270e12	0.822594	0.411297	+	0.911501i	$0.365076\pi$
$234$	−8.70900e12	−0.811486
$235$	−2.52864e13	−2.30152
$236$	3.04227e12	0.270509
$237$	7.16976e12	0.622857
$238$	−1.17608e13	−0.998303
$239$	−1.40284e13	−1.16364	−0.581820	−	0.813318i	$-0.697659\pi$
$239$	−1.40284e13	−1.16364	−0.581820	+	0.813318i	$0.697659\pi$
$240$	7.23066e12	0.586160
$241$	3.78064e12	0.299552	0.149776	−	0.988720i	$-0.452145\pi$
$241$	3.78064e12	0.299552	0.149776	+	0.988720i	$0.452145\pi$
$242$	1.55340e13	1.20309
$243$	6.31131e12	0.477843
$244$	−3.56892e11	−0.0264176
$245$	3.96515e12	0.286976
$246$	−3.56055e13	−2.51985
$247$	6.04223e12	0.418180
$248$	1.18301e13	0.800761
$249$	3.20760e13	2.12365
$250$	−1.11463e13	−0.721875
$251$	−1.47327e13	−0.933421	−0.466711	−	0.884410i	$-0.654561\pi$
$251$	−1.47327e13	−0.933421	−0.466711	+	0.884410i	$0.654561\pi$
$252$	−4.90692e13	−3.04163
$253$	−1.10850e13	−0.672317
$254$	−1.43967e13	−0.854430
$255$	2.54564e13	1.47852
$256$	−1.05827e13	−0.601555
$257$	−9.18701e12	−0.511142	−0.255571	−	0.966790i	$-0.582264\pi$
$257$	−9.18701e12	−0.511142	−0.255571	+	0.966790i	$0.582264\pi$
$258$	−3.83223e13	−2.08710
$259$	−2.17549e13	−1.15987
$260$	1.21725e13	0.635369
$261$	−3.29556e13	−1.68425
$262$	−3.22106e13	−1.61191
$263$	3.19550e13	1.56597	0.782983	−	0.622043i	$-0.213697\pi$
$263$	3.19550e13	1.56597	0.782983	+	0.622043i	$0.213697\pi$
$264$	1.39477e13	0.669394
$265$	3.78189e13	1.77769
$266$	5.65831e13	2.60518
$267$	5.29840e12	0.238964
$268$	−1.81451e13	−0.801713
$269$	2.56582e13	1.11068	0.555339	−	0.831624i	$-0.312588\pi$
$269$	2.56582e13	1.11068	0.555339	+	0.831624i	$0.312588\pi$
$270$	8.09345e13	3.43268
$271$	4.12454e12	0.171413	0.0857067	−	0.996320i	$-0.472685\pi$
$271$	4.12454e12	0.171413	0.0857067	+	0.996320i	$0.472685\pi$
$272$	3.24967e12	0.132346
$273$	1.27855e13	0.510297
$274$	6.13567e13	2.40013
$275$	1.66389e13	0.637961
$276$	9.29216e13	3.49234
$277$	−1.56779e13	−0.577631	−0.288815	−	0.957385i	$-0.593261\pi$
$277$	−1.56779e13	−0.577631	−0.288815	+	0.957385i	$0.593261\pi$
$278$	−2.52854e13	−0.913323
$279$	−5.16309e13	−1.82846
$280$	3.85209e13	1.33760
$281$	−4.68152e13	−1.59405	−0.797026	−	0.603945i	$-0.793595\pi$
$281$	−4.68152e13	−1.59405	−0.797026	+	0.603945i	$0.793595\pi$
$282$	−1.21485e14	−4.05650
$283$	−5.79825e13	−1.89877	−0.949383	−	0.314120i	$-0.898290\pi$
$283$	−5.79825e13	−1.89877	−0.949383	+	0.314120i	$0.898290\pi$
$284$	−3.03479e13	−0.974715
$285$	−1.22475e14	−3.85835
$286$	−6.97644e12	−0.215586
$287$	3.39090e13	1.02793
$288$	7.27504e13	2.16360
$289$	−2.28310e13	−0.666174
$290$	7.65579e13	2.19180
$291$	4.64158e13	1.30393
$292$	−1.05741e13	−0.291500
$293$	−7.94028e12	−0.214815	−0.107407	−	0.994215i	$-0.534255\pi$
$293$	−7.94028e12	−0.214815	−0.107407	+	0.994215i	$0.534255\pi$
$294$	1.90499e13	0.505805
$295$	1.04234e13	0.271635
$296$	−3.36264e13	−0.860155
$297$	−2.79087e13	−0.700776
$298$	1.17729e14	2.90199
$299$	−1.57063e13	−0.380087
$300$	−1.39477e14	−3.31388
$301$	3.64964e13	0.851401
$302$	−1.04018e14	−2.38270
$303$	2.93366e13	0.659895
$304$	−1.56347e13	−0.345370
$305$	−1.22278e12	−0.0265276
$306$	7.93379e13	1.69049
$307$	8.03311e13	1.68121	0.840607	−	0.541646i	$-0.182199\pi$
$307$	8.03311e13	1.68121	0.840607	+	0.541646i	$0.182199\pi$
$308$	−3.93074e13	−0.808063
$309$	−9.20511e12	−0.185891
$310$	1.19941e14	2.37947
$311$	9.70268e13	1.89108	0.945539	−	0.325509i	$-0.105536\pi$
$311$	9.70268e13	1.89108	0.945539	+	0.325509i	$0.105536\pi$
$312$	1.97625e13	0.378434
$313$	−1.73007e12	−0.0325514	−0.0162757	−	0.999868i	$-0.505181\pi$
$313$	−1.73007e12	−0.0325514	−0.0162757	+	0.999868i	$0.505181\pi$
$314$	−9.14006e13	−1.68980
$315$	−1.68120e14	−3.05429
$316$	−3.12319e13	−0.557596
$317$	2.13977e13	0.375440	0.187720	−	0.982223i	$-0.439890\pi$
$317$	2.13977e13	0.375440	0.187720	+	0.982223i	$0.439890\pi$
$318$	1.81695e14	3.13324
$319$	−2.63995e13	−0.447452
$320$	−1.48150e14	−2.46818
$321$	3.19095e13	0.522568
$322$	−1.47084e14	−2.36786
$323$	−5.50439e13	−0.871155
$324$	5.46916e13	0.850988
$325$	2.35755e13	0.360664
$326$	−1.20217e14	−1.80829
$327$	−3.89193e13	−0.575642
$328$	5.24129e13	0.762311
$329$	1.15696e14	1.65479
$330$	1.41412e14	1.98911
$331$	−6.32407e13	−0.874868	−0.437434	−	0.899251i	$-0.644113\pi$
$331$	−6.32407e13	−0.874868	−0.437434	+	0.899251i	$0.644113\pi$
$332$	−1.39725e14	−1.90114
$333$	1.46758e14	1.96408
$334$	−1.84191e13	−0.242473
$335$	−6.21684e13	−0.805051
$336$	−3.30834e13	−0.421449
$337$	7.60121e13	0.952616	0.476308	−	0.879278i	$-0.341975\pi$
$337$	7.60121e13	0.952616	0.476308	+	0.879278i	$0.341975\pi$
$338$	−9.88488e12	−0.121879
$339$	8.81434e13	1.06928
$340$	−1.10890e14	−1.32360
$341$	−4.13595e13	−0.485765
$342$	−3.81708e14	−4.41152
$343$	7.77419e13	0.884174
$344$	5.64122e13	0.631395
$345$	3.18366e14	3.50688
$346$	6.98525e13	0.757292
$347$	8.56776e13	0.914230	0.457115	−	0.889408i	$-0.348883\pi$
$347$	8.56776e13	0.914230	0.457115	+	0.889408i	$0.348883\pi$
$348$	2.21297e14	2.32428
$349$	−6.68352e13	−0.690980	−0.345490	−	0.938422i	$-0.612287\pi$
$349$	−6.68352e13	−0.690980	−0.345490	+	0.938422i	$0.612287\pi$
$350$	2.20775e14	2.24686
$351$	−3.95437e13	−0.396176
$352$	5.82775e13	0.574800
$353$	5.72345e13	0.555773	0.277886	−	0.960614i	$-0.410366\pi$
$353$	5.72345e13	0.555773	0.277886	+	0.960614i	$0.410366\pi$
$354$	5.00774e13	0.478766
$355$	−1.03977e14	−0.978774
$356$	−2.30802e13	−0.213926
$357$	−1.16474e14	−1.06305
$358$	1.21862e14	1.09525
$359$	−1.08068e14	−0.956482	−0.478241	−	0.878229i	$-0.658726\pi$
$359$	−1.08068e14	−0.956482	−0.478241	+	0.878229i	$0.658726\pi$
$360$	−2.59861e14	−2.26505
$361$	1.48336e14	1.27337
$362$	−1.02018e14	−0.862537
$363$	1.53843e14	1.28112
$364$	−5.56944e13	−0.456830
$365$	−3.62287e13	−0.292713
$366$	−5.87464e12	−0.0467557
$367$	1.10470e14	0.866122	0.433061	−	0.901364i	$-0.357433\pi$
$367$	1.10470e14	0.866122	0.433061	+	0.901364i	$0.357433\pi$
$368$	4.06413e13	0.313909
$369$	−2.28750e14	−1.74067
$370$	−3.40928e14	−2.55596
$371$	−1.73038e14	−1.27816
$372$	3.46700e14	2.52330
$373$	−2.31892e14	−1.66298	−0.831492	−	0.555537i	$-0.812513\pi$
$373$	−2.31892e14	−1.66298	−0.831492	+	0.555537i	$0.812513\pi$
$374$	6.35545e13	0.449110
$375$	−1.10389e14	−0.768696
$376$	1.78831e14	1.22718
$377$	−3.74053e13	−0.252962
$378$	−3.70311e14	−2.46809
$379$	1.78075e14	1.16973	0.584867	−	0.811129i	$-0.301147\pi$
$379$	1.78075e14	1.16973	0.584867	+	0.811129i	$0.301147\pi$
$380$	5.33510e14	3.45408
$381$	−1.42579e14	−0.909849
$382$	2.74299e14	1.72535
$383$	8.44570e13	0.523652	0.261826	−	0.965115i	$-0.415675\pi$
$383$	8.44570e13	0.523652	0.261826	+	0.965115i	$0.415675\pi$
$384$	−3.88331e14	−2.37345
$385$	−1.34674e14	−0.811428
$386$	3.75451e13	0.223009
$387$	−2.46204e14	−1.44173
$388$	−2.02190e14	−1.16731
$389$	−1.98191e14	−1.12813	−0.564067	−	0.825729i	$-0.690764\pi$
$389$	−1.98191e14	−1.12813	−0.564067	+	0.825729i	$0.690764\pi$
$390$	2.00365e14	1.12452
$391$	1.43083e14	0.791799
$392$	−2.80424e13	−0.153018
$393$	−3.19002e14	−1.71646
$394$	−3.20447e14	−1.70030
$395$	−1.07006e14	−0.559917
$396$	2.65167e14	1.36835
$397$	2.11044e14	1.07405	0.537027	−	0.843565i	$-0.319547\pi$
$397$	2.11044e14	1.07405	0.537027	+	0.843565i	$0.319547\pi$
$398$	3.94167e14	1.97844
$399$	5.60378e14	2.77415
$400$	−6.10034e13	−0.297868
$401$	−1.50555e14	−0.725107	−0.362553	−	0.931963i	$-0.618095\pi$
$401$	−1.50555e14	−0.725107	−0.362553	+	0.931963i	$0.618095\pi$
$402$	−2.98678e14	−1.41893
$403$	−5.86020e13	−0.274622
$404$	−1.27792e14	−0.590752
$405$	1.87383e14	0.854531
$406$	−3.50286e14	−1.57590
$407$	1.17562e14	0.521794
$408$	−1.80034e14	−0.788356
$409$	1.66799e14	0.720636	0.360318	−	0.932830i	$-0.382668\pi$
$409$	1.66799e14	0.720636	0.360318	+	0.932830i	$0.382668\pi$
$410$	5.31399e14	2.26521
$411$	6.07654e14	2.55580
$412$	4.00980e13	0.166413
$413$	−4.76914e13	−0.195306
$414$	9.92223e14	4.00966
$415$	−4.78722e14	−1.90906
$416$	8.25731e13	0.324956
$417$	−2.50418e14	−0.972561
$418$	−3.05772e14	−1.17200
$419$	4.82067e12	0.0182360	0.00911801	−	0.999958i	$-0.497098\pi$
$419$	4.82067e12	0.0182360	0.00911801	+	0.999958i	$0.497098\pi$
$420$	1.12892e15	4.21495
$421$	4.30990e14	1.58824	0.794119	−	0.607762i	$-0.207932\pi$
$421$	4.30990e14	1.58824	0.794119	+	0.607762i	$0.207932\pi$
$422$	−6.99531e14	−2.54442
$423$	−7.80486e14	−2.80216
$424$	−2.67464e14	−0.947879
$425$	−2.14770e14	−0.751336
$426$	−4.99542e14	−1.72512
$427$	5.59473e12	0.0190733
$428$	−1.39000e14	−0.467815
$429$	−6.90921e13	−0.229569
$430$	5.71946e14	1.87620
$431$	4.24318e14	1.37425	0.687127	−	0.726537i	$-0.258872\pi$
$431$	4.24318e14	1.37425	0.687127	+	0.726537i	$0.258872\pi$
$432$	1.02322e14	0.327197
$433$	2.24669e13	0.0709348	0.0354674	−	0.999371i	$-0.488708\pi$
$433$	2.24669e13	0.0709348	0.0354674	+	0.999371i	$0.488708\pi$
$434$	−5.48785e14	−1.71084
$435$	7.58201e14	2.33396
$436$	1.69535e14	0.515328
$437$	−6.88395e14	−2.06628
$438$	−1.74055e14	−0.515917
$439$	−4.19885e13	−0.122907	−0.0614534	−	0.998110i	$-0.519574\pi$
$439$	−4.19885e13	−0.122907	−0.0614534	+	0.998110i	$0.519574\pi$
$440$	−2.08165e14	−0.601752
$441$	1.22388e14	0.349402
$442$	9.00500e13	0.253899
$443$	−3.39749e14	−0.946100	−0.473050	−	0.881036i	$-0.656847\pi$
$443$	−3.39749e14	−0.946100	−0.473050	+	0.881036i	$0.656847\pi$
$444$	−9.85481e14	−2.71045
$445$	−7.90767e13	−0.214817
$446$	7.05334e14	1.89258
$447$	1.16595e15	3.09021
$448$	6.77851e14	1.77462
$449$	−4.29182e14	−1.10991	−0.554954	−	0.831881i	$-0.687264\pi$
$449$	−4.29182e14	−1.10991	−0.554954	+	0.831881i	$0.687264\pi$
$450$	−1.48935e15	−3.80476
$451$	−1.83243e14	−0.462440
$452$	−3.83958e14	−0.957244
$453$	−1.03016e15	−2.53725
$454$	2.48594e14	0.604901
$455$	−1.90819e14	−0.458732
$456$	8.66172e14	2.05730
$457$	2.26508e13	0.0531551	0.0265776	−	0.999647i	$-0.491539\pi$
$457$	2.26508e13	0.0531551	0.0265776	+	0.999647i	$0.491539\pi$
$458$	1.31830e15	3.05670
$459$	3.60238e14	0.825314
$460$	−1.38682e15	−3.13944
$461$	2.37498e14	0.531257	0.265628	−	0.964076i	$-0.414421\pi$
$461$	2.37498e14	0.531257	0.265628	+	0.964076i	$0.414421\pi$
$462$	−6.47021e14	−1.43017
$463$	−3.25706e14	−0.711426	−0.355713	−	0.934595i	$-0.615762\pi$
$463$	−3.25706e14	−0.711426	−0.355713	+	0.934595i	$0.615762\pi$
$464$	9.67889e13	0.208918
$465$	1.18786e15	2.53380
$466$	−6.18274e14	−1.30334
$467$	−4.71136e14	−0.981530	−0.490765	−	0.871292i	$-0.663283\pi$
$467$	−4.71136e14	−0.981530	−0.490765	+	0.871292i	$0.663283\pi$
$468$	3.75714e14	0.773579
$469$	2.84448e14	0.578831
$470$	1.81311e15	3.64659
$471$	−9.05198e14	−1.79940
$472$	−7.37162e13	−0.144838
$473$	−1.97224e14	−0.383022
$474$	−5.14094e14	−0.986873
$475$	1.03330e15	1.96069
$476$	5.07369e14	0.951669
$477$	1.16731e15	2.16439
$478$	1.00588e15	1.84370
$479$	8.05360e14	1.45930	0.729650	−	0.683821i	$-0.239683\pi$
$479$	8.05360e14	1.45930	0.729650	+	0.683821i	$0.239683\pi$
$480$	−1.67375e15	−2.99822
$481$	1.66574e14	0.294991
$482$	−2.71084e14	−0.474619
$483$	−1.45666e15	−2.52144
$484$	−6.70148e14	−1.14689
$485$	−6.92738e14	−1.17217
$486$	−4.52541e14	−0.757108
$487$	5.26958e14	0.871700	0.435850	−	0.900019i	$-0.356448\pi$
$487$	5.26958e14	0.871700	0.435850	+	0.900019i	$0.356448\pi$
$488$	8.64773e12	0.0141447
$489$	−1.19058e15	−1.92558
$490$	−2.84313e14	−0.454694
$491$	6.41795e14	1.01496	0.507479	−	0.861664i	$-0.330577\pi$
$491$	6.41795e14	1.01496	0.507479	+	0.861664i	$0.330577\pi$
$492$	1.53605e15	2.40214
$493$	3.40757e14	0.526972
$494$	−4.33246e14	−0.662577
$495$	9.08509e14	1.37404
$496$	1.51637e14	0.226807
$497$	4.75741e14	0.703737
$498$	−2.29995e15	−3.36478
$499$	−4.41020e14	−0.638125	−0.319062	−	0.947734i	$-0.603368\pi$
$499$	−4.41020e14	−0.638125	−0.319062	+	0.947734i	$0.603368\pi$
$500$	4.80862e14	0.688154
$501$	−1.82416e14	−0.258199
$502$	1.05638e15	1.47894
$503$	−2.37981e14	−0.329547	−0.164774	−	0.986331i	$-0.552689\pi$
$503$	−2.37981e14	−0.329547	−0.164774	+	0.986331i	$0.552689\pi$
$504$	1.18898e15	1.62857
$505$	−4.37837e14	−0.593212
$506$	7.94831e14	1.06524
$507$	−9.78962e13	−0.129784
$508$	6.21084e14	0.814517
$509$	−7.92262e14	−1.02783	−0.513915	−	0.857841i	$-0.671805\pi$
$509$	−7.92262e14	−1.02783	−0.513915	+	0.857841i	$0.671805\pi$
$510$	−1.82530e15	−2.34261
$511$	1.65762e14	0.210461
$512$	−3.61143e14	−0.453623
$513$	−1.73317e15	−2.15375
$514$	6.58737e14	0.809869
$515$	1.37383e14	0.167106
$516$	1.65326e15	1.98960
$517$	−6.25217e14	−0.744445
$518$	1.55990e15	1.83773
$519$	6.91794e14	0.806411
$520$	−2.94947e14	−0.340193
$521$	−8.57294e14	−0.978413	−0.489207	−	0.872168i	$-0.662714\pi$
$521$	−8.57294e14	−0.978413	−0.489207	+	0.872168i	$0.662714\pi$
$522$	2.36302e15	2.66858
$523$	1.20397e15	1.34542	0.672710	−	0.739907i	$-0.265130\pi$
$523$	1.20397e15	1.34542	0.672710	+	0.739907i	$0.265130\pi$
$524$	1.38959e15	1.53662
$525$	2.18648e15	2.39259
$526$	−2.29127e15	−2.48116
$527$	5.33857e14	0.572093
$528$	1.78781e14	0.189599
$529$	8.36623e14	0.878058
$530$	−2.71173e15	−2.81663
$531$	3.21725e14	0.330724
$532$	−2.44104e15	−2.48348
$533$	−2.59635e14	−0.261435
$534$	−3.79912e14	−0.378622
$535$	−4.76238e14	−0.469762
$536$	4.39668e14	0.429259
$537$	1.20688e15	1.16629
$538$	−1.83977e15	−1.75979
$539$	9.80399e13	0.0928250
$540$	−3.49158e15	−3.27233
$541$	2.09479e15	1.94337	0.971687	−	0.236273i	$-0.0759259\pi$
$541$	2.09479e15	1.94337	0.971687	+	0.236273i	$0.0759259\pi$
$542$	−2.95742e14	−0.271592
$543$	−1.01035e15	−0.918482
$544$	−7.52231e14	−0.676951
$545$	5.80856e14	0.517473
$546$	−9.16760e14	−0.808530
$547$	−6.45840e14	−0.563890	−0.281945	−	0.959431i	$-0.590980\pi$
$547$	−6.45840e14	−0.563890	−0.281945	+	0.959431i	$0.590980\pi$
$548$	−2.64698e15	−2.28801
$549$	−3.77420e13	−0.0322981
$550$	−1.19306e15	−1.01080
$551$	−1.63944e15	−1.37519
$552$	−2.25155e15	−1.86989
$553$	4.89599e14	0.402580
$554$	1.12416e15	0.915215
$555$	−3.37643e15	−2.72174
$556$	1.09084e15	0.870659
$557$	−3.36710e14	−0.266105	−0.133052	−	0.991109i	$-0.542478\pi$
$557$	−3.36710e14	−0.266105	−0.133052	+	0.991109i	$0.542478\pi$
$558$	3.70209e15	2.89707
$559$	−2.79446e14	−0.216537
$560$	4.93758e14	0.378861
$561$	6.29421e14	0.478239
$562$	3.35680e15	2.52566
$563$	1.02311e15	0.762301	0.381151	−	0.924513i	$-0.375528\pi$
$563$	1.02311e15	0.762301	0.381151	+	0.924513i	$0.375528\pi$
$564$	5.24095e15	3.86701
$565$	−1.31551e15	−0.961229
$566$	4.15752e15	3.00846
$567$	−8.57360e14	−0.614407
$568$	7.35350e14	0.521889
$569$	−4.81815e14	−0.338659	−0.169330	−	0.985559i	$-0.554160\pi$
$569$	−4.81815e14	−0.338659	−0.169330	+	0.985559i	$0.554160\pi$
$570$	8.78186e15	6.11329
$571$	−1.40014e15	−0.965326	−0.482663	−	0.875806i	$-0.660330\pi$
$571$	−1.40014e15	−0.965326	−0.482663	+	0.875806i	$0.660330\pi$
$572$	3.00970e14	0.205515
$573$	2.71656e15	1.83725
$574$	−2.43138e15	−1.62869
$575$	−2.68597e15	−1.78209
$576$	−4.57277e15	−3.00508
$577$	−2.12075e14	−0.138046	−0.0690229	−	0.997615i	$-0.521988\pi$
$577$	−2.12075e14	−0.138046	−0.0690229	+	0.997615i	$0.521988\pi$
$578$	1.63706e15	1.05551
$579$	3.71833e14	0.237474
$580$	−3.30277e15	−2.08941
$581$	2.19036e15	1.37261
$582$	−3.32815e15	−2.06598
$583$	9.35088e14	0.575010
$584$	2.56218e14	0.156077
$585$	1.28726e15	0.776800
$586$	5.69342e14	0.340359
$587$	1.19355e15	0.706858	0.353429	−	0.935461i	$-0.385016\pi$
$587$	1.19355e15	0.706858	0.353429	+	0.935461i	$0.385016\pi$
$588$	−8.21831e14	−0.482178
$589$	−2.56848e15	−1.49294
$590$	−7.47386e14	−0.430387
$591$	−3.17359e15	−1.81059
$592$	−4.31021e14	−0.243629
$593$	−1.20930e15	−0.677224	−0.338612	−	0.940926i	$-0.609957\pi$
$593$	−1.20930e15	−0.677224	−0.338612	+	0.940926i	$0.609957\pi$
$594$	2.00114e15	1.11033
$595$	1.73834e15	0.955631
$596$	−5.07895e15	−2.76643
$597$	3.90369e15	2.10677
$598$	1.12619e15	0.602221
$599$	7.10412e14	0.376412	0.188206	−	0.982130i	$-0.439733\pi$
$599$	7.10412e14	0.376412	0.188206	+	0.982130i	$0.439733\pi$
$600$	3.37962e15	1.77434
$601$	1.65916e15	0.863133	0.431567	−	0.902081i	$-0.357961\pi$
$601$	1.65916e15	0.863133	0.431567	+	0.902081i	$0.357961\pi$
$602$	−2.61690e15	−1.34898
$603$	−1.91888e15	−0.980172
$604$	4.48742e15	2.27140
$605$	−2.29605e15	−1.15166
$606$	−2.10352e15	−1.04556
$607$	−1.36722e14	−0.0673441	−0.0336720	−	0.999433i	$-0.510720\pi$
$607$	−1.36722e14	−0.0673441	−0.0336720	+	0.999433i	$0.510720\pi$
$608$	3.61911e15	1.76658
$609$	−3.46910e15	−1.67812
$610$	8.76767e13	0.0420311
$611$	−8.85866e14	−0.420864
$612$	−3.42270e15	−1.61152
$613$	3.14315e15	1.46667	0.733335	−	0.679867i	$-0.237962\pi$
$613$	3.14315e15	1.46667	0.733335	+	0.679867i	$0.237962\pi$
$614$	−5.75999e15	−2.66376
$615$	5.26278e15	2.41214
$616$	9.52445e14	0.432659
$617$	−3.31924e15	−1.49441	−0.747206	−	0.664592i	$-0.768605\pi$
$617$	−3.31924e15	−1.49441	−0.747206	+	0.664592i	$0.768605\pi$
$618$	6.60035e14	0.294531
$619$	5.78448e13	0.0255838	0.0127919	−	0.999918i	$-0.495928\pi$
$619$	5.78448e13	0.0255838	0.0127919	+	0.999918i	$0.495928\pi$
$620$	−5.17438e15	−2.26832
$621$	4.50524e15	1.95755
$622$	−6.95712e15	−2.99628
$623$	3.61811e14	0.154453
$624$	2.53314e14	0.107187
$625$	−1.45286e15	−0.609373
$626$	1.24051e14	0.0515754
$627$	−3.02825e15	−1.24802
$628$	3.94310e15	1.61087
$629$	−1.51746e15	−0.614526
$630$	1.20547e16	4.83931
$631$	−1.39291e15	−0.554321	−0.277160	−	0.960824i	$-0.589393\pi$
$631$	−1.39291e15	−0.554321	−0.277160	+	0.960824i	$0.589393\pi$
$632$	7.56770e14	0.298552
$633$	−6.92790e15	−2.70945
$634$	−1.53428e15	−0.594859
$635$	2.12794e15	0.817908
$636$	−7.83848e15	−2.98688
$637$	1.38912e14	0.0524775
$638$	1.89292e15	0.708956
$639$	−3.20934e15	−1.19168
$640$	5.79570e15	2.13362
$641$	1.87986e15	0.686131	0.343066	−	0.939311i	$-0.388535\pi$
$641$	1.87986e15	0.686131	0.343066	+	0.939311i	$0.388535\pi$
$642$	−2.28801e15	−0.827972
$643$	−2.65724e15	−0.953389	−0.476694	−	0.879069i	$-0.658165\pi$
$643$	−2.65724e15	−0.953389	−0.476694	+	0.879069i	$0.658165\pi$
$644$	6.34531e15	2.25725
$645$	5.66434e15	1.99789
$646$	3.94682e15	1.38028
$647$	1.07083e15	0.371320	0.185660	−	0.982614i	$-0.440558\pi$
$647$	1.07083e15	0.371320	0.185660	+	0.982614i	$0.440558\pi$
$648$	−1.32521e15	−0.455642
$649$	2.57722e14	0.0878628
$650$	−1.69044e15	−0.571446
$651$	−5.43496e15	−1.82180
$652$	5.18625e15	1.72382
$653$	4.38634e15	1.44571	0.722853	−	0.691002i	$-0.242830\pi$
$653$	4.38634e15	1.44571	0.722853	+	0.691002i	$0.242830\pi$
$654$	2.79064e15	0.912064
$655$	4.76099e15	1.54301
$656$	6.71826e14	0.215916
$657$	−1.11823e15	−0.356387
$658$	−8.29579e15	−2.62190
$659$	−1.21741e15	−0.381564	−0.190782	−	0.981632i	$-0.561102\pi$
$659$	−1.21741e15	−0.381564	−0.190782	+	0.981632i	$0.561102\pi$
$660$	−6.10062e15	−1.89619
$661$	−3.68678e15	−1.13642	−0.568211	−	0.822883i	$-0.692364\pi$
$661$	−3.68678e15	−1.13642	−0.568211	+	0.822883i	$0.692364\pi$
$662$	4.53455e15	1.38617
$663$	8.91823e14	0.270367
$664$	3.38563e15	1.01792
$665$	−8.36344e15	−2.49382
$666$	−1.05230e16	−3.11195
$667$	4.26161e15	1.24992
$668$	7.94615e14	0.231146
$669$	6.98537e15	2.01533
$670$	4.45766e15	1.27555
$671$	−3.02336e13	−0.00858057
$672$	7.65813e15	2.15572
$673$	4.16992e15	1.16425	0.582123	−	0.813101i	$-0.302222\pi$
$673$	4.16992e15	1.16425	0.582123	+	0.813101i	$0.302222\pi$
$674$	−5.45030e15	−1.50935
$675$	−6.76245e15	−1.85752
$676$	4.26442e14	0.116186
$677$	5.84385e15	1.57929	0.789644	−	0.613565i	$-0.210265\pi$
$677$	5.84385e15	1.57929	0.789644	+	0.613565i	$0.210265\pi$
$678$	−6.32015e15	−1.69420
$679$	3.16958e15	0.842787
$680$	2.68693e15	0.708693
$681$	2.46199e15	0.644135
$682$	2.96560e15	0.769660
$683$	−4.43795e15	−1.14253	−0.571266	−	0.820765i	$-0.693548\pi$
$683$	−4.43795e15	−1.14253	−0.571266	+	0.820765i	$0.693548\pi$
$684$	1.64672e16	4.20544
$685$	−9.06902e15	−2.29753
$686$	−5.57433e15	−1.40091
$687$	1.30559e16	3.25496
$688$	7.23087e14	0.178836
$689$	1.32492e15	0.325076
$690$	−2.28278e16	−5.55640
$691$	4.95399e15	1.19626	0.598130	−	0.801399i	$-0.295911\pi$
$691$	4.95399e15	1.19626	0.598130	+	0.801399i	$0.295911\pi$
$692$	−3.01350e15	−0.721917
$693$	−4.15683e15	−0.987936
$694$	−6.14335e15	−1.44853
$695$	3.73739e15	0.874284
$696$	−5.36217e15	−1.24448
$697$	2.36524e15	0.544623
$698$	4.79229e15	1.09481
$699$	−6.12316e15	−1.38788
$700$	−9.52444e15	−2.14190
$701$	−8.15244e15	−1.81902	−0.909512	−	0.415678i	$-0.863544\pi$
$701$	−8.15244e15	−1.81902	−0.909512	+	0.415678i	$0.863544\pi$
$702$	2.83540e15	0.627712
$703$	7.30078e15	1.60367
$704$	−3.66307e15	−0.798354
$705$	1.79564e16	3.88311
$706$	−4.10389e15	−0.880582
$707$	2.00330e15	0.426519
$708$	−2.16038e15	−0.456402
$709$	−7.73818e15	−1.62213	−0.811063	−	0.584959i	$-0.801110\pi$
$709$	−7.73818e15	−1.62213	−0.811063	+	0.584959i	$0.801110\pi$
$710$	7.45549e15	1.55080
$711$	−3.30283e15	−0.681715
$712$	5.59248e14	0.114542
$713$	6.67657e15	1.35694
$714$	8.35157e15	1.68433
$715$	1.03117e15	0.206371
$716$	−5.25724e15	−1.04409
$717$	9.96184e15	1.96329
$718$	7.74880e15	1.51548
$719$	5.64043e15	1.09472	0.547360	−	0.836897i	$-0.315633\pi$
$719$	5.64043e15	1.09472	0.547360	+	0.836897i	$0.315633\pi$
$720$	−3.33088e15	−0.641550
$721$	−6.28587e14	−0.120149
$722$	−1.06361e16	−2.01757
$723$	−2.68472e15	−0.505403
$724$	4.40113e15	0.822246
$725$	−6.39676e15	−1.18605
$726$	−1.10310e16	−2.02985
$727$	2.80771e15	0.512759	0.256380	−	0.966576i	$-0.417470\pi$
$727$	2.80771e15	0.512759	0.256380	+	0.966576i	$0.417470\pi$
$728$	1.34951e15	0.244599
$729$	−7.61384e15	−1.36963
$730$	2.59771e15	0.463784
$731$	2.54572e15	0.451092
$732$	2.53437e14	0.0445716
$733$	−2.26331e15	−0.395068	−0.197534	−	0.980296i	$-0.563293\pi$
$733$	−2.26331e15	−0.395068	−0.197534	+	0.980296i	$0.563293\pi$
$734$	−7.92101e15	−1.37231
$735$	−2.81574e15	−0.484185
$736$	−9.40761e15	−1.60565
$737$	−1.53714e15	−0.260401
$738$	1.64021e16	2.75796
$739$	−1.11460e16	−1.86026	−0.930131	−	0.367227i	$-0.880307\pi$
$739$	−1.11460e16	−1.86026	−0.930131	+	0.367227i	$0.880307\pi$
$740$	1.47079e16	2.43656
$741$	−4.29071e15	−0.705552
$742$	1.24074e16	2.02515
$743$	−1.03772e16	−1.68128	−0.840641	−	0.541593i	$-0.817821\pi$
$743$	−1.03772e16	−1.68128	−0.840641	+	0.541593i	$0.817821\pi$
$744$	−8.40078e15	−1.35104
$745$	−1.74014e16	−2.77795
$746$	1.66274e16	2.63488
$747$	−1.47762e16	−2.32433
$748$	−2.74180e15	−0.428131
$749$	2.17900e15	0.337759
$750$	7.91524e15	1.21794
$751$	−7.70122e15	−1.17636	−0.588180	−	0.808730i	$-0.700155\pi$
$751$	−7.70122e15	−1.17636	−0.588180	+	0.808730i	$0.700155\pi$
$752$	2.29225e15	0.347587
$753$	1.04620e16	1.57486
$754$	2.68207e15	0.400800
$755$	1.53747e16	2.28086
$756$	1.59755e16	2.35280
$757$	−8.79465e15	−1.28585	−0.642926	−	0.765928i	$-0.722280\pi$
$757$	−8.79465e15	−1.28585	−0.642926	+	0.765928i	$0.722280\pi$
$758$	−1.27685e16	−1.85336
$759$	7.87172e15	1.13433
$760$	−1.29273e16	−1.84941
$761$	1.31811e16	1.87213	0.936066	−	0.351824i	$-0.114438\pi$
$761$	1.31811e16	1.87213	0.936066	+	0.351824i	$0.114438\pi$
$762$	1.02234e16	1.44159
$763$	−2.65767e15	−0.372063
$764$	−1.18335e16	−1.64475
$765$	−1.17268e16	−1.61823
$766$	−6.05583e15	−0.829689
$767$	3.65164e14	0.0496722
$768$	7.51498e15	1.01494
$769$	2.93001e15	0.392893	0.196446	−	0.980515i	$-0.437060\pi$
$769$	2.93001e15	0.392893	0.196446	+	0.980515i	$0.437060\pi$
$770$	9.65654e15	1.28565
$771$	6.52389e15	0.862397
$772$	−1.61973e15	−0.212592
$773$	−8.98653e14	−0.117113	−0.0585565	−	0.998284i	$-0.518650\pi$
$773$	−8.98653e14	−0.117113	−0.0585565	+	0.998284i	$0.518650\pi$
$774$	1.76536e16	2.28432
$775$	−1.00217e16	−1.28760
$776$	4.89919e15	0.625007
$777$	1.54486e16	1.95693
$778$	1.42109e16	1.78745
$779$	−1.13796e16	−1.42125
$780$	−8.64394e15	−1.07199
$781$	−2.57088e15	−0.316593
$782$	−1.02595e16	−1.25455
$783$	1.07294e16	1.30283
$784$	−3.59446e14	−0.0433406
$785$	1.35098e16	1.61757
$786$	2.28734e16	2.71962
$787$	4.06131e15	0.479519	0.239759	−	0.970832i	$-0.422931\pi$
$787$	4.06131e15	0.479519	0.239759	+	0.970832i	$0.422931\pi$
$788$	1.38243e16	1.62088
$789$	−2.26919e16	−2.64209
$790$	7.67266e15	0.887150
$791$	6.01902e15	0.691123
$792$	−6.42517e15	−0.732650
$793$	−4.28378e13	−0.00485093
$794$	−1.51325e16	−1.70176
$795$	−2.68560e16	−2.99932
$796$	−1.70047e16	−1.88602
$797$	5.81392e15	0.640395	0.320198	−	0.947351i	$-0.396251\pi$
$797$	5.81392e15	0.640395	0.320198	+	0.947351i	$0.396251\pi$
$798$	−4.01808e16	−4.39545
$799$	8.07013e15	0.876745
$800$	1.41210e16	1.52360
$801$	−2.44077e15	−0.261546
$802$	1.07953e16	1.14888
$803$	−8.95771e14	−0.0946807
$804$	1.28852e16	1.35265
$805$	2.17401e16	2.26665
$806$	4.20194e15	0.435118
$807$	−1.82204e16	−1.87393
$808$	3.09648e15	0.316305
$809$	−6.61270e15	−0.670907	−0.335453	−	0.942057i	$-0.608889\pi$
$809$	−6.61270e15	−0.670907	−0.335453	+	0.942057i	$0.608889\pi$
$810$	−1.34359e16	−1.35394
$811$	−4.22461e15	−0.422836	−0.211418	−	0.977396i	$-0.567808\pi$
$811$	−4.22461e15	−0.422836	−0.211418	+	0.977396i	$0.567808\pi$
$812$	1.51116e16	1.50229
$813$	−2.92893e15	−0.289208
$814$	−8.42959e15	−0.826746
$815$	1.77690e16	1.73100
$816$	−2.30766e15	−0.223293
$817$	−1.22479e16	−1.17717
$818$	−1.19600e16	−1.14180
$819$	−5.88978e15	−0.558519
$820$	−2.29250e16	−2.15940
$821$	1.23031e16	1.15114	0.575568	−	0.817754i	$-0.304781\pi$
$821$	1.23031e16	1.15114	0.575568	+	0.817754i	$0.304781\pi$
$822$	−4.35707e16	−4.04948
$823$	1.00189e15	0.0924960	0.0462480	−	0.998930i	$-0.485274\pi$
$823$	1.00189e15	0.0924960	0.0462480	+	0.998930i	$0.485274\pi$
$824$	−9.71602e14	−0.0891023
$825$	−1.18156e16	−1.07636
$826$	3.41962e15	0.309448
$827$	−5.55561e15	−0.499404	−0.249702	−	0.968323i	$-0.580333\pi$
$827$	−5.55561e15	−0.499404	−0.249702	+	0.968323i	$0.580333\pi$
$828$	−4.28053e16	−3.82235
$829$	−4.21733e15	−0.374100	−0.187050	−	0.982350i	$-0.559893\pi$
$829$	−4.21733e15	−0.374100	−0.187050	+	0.982350i	$0.559893\pi$
$830$	3.43259e16	3.02477
$831$	1.11332e16	0.974576
$832$	−5.19018e15	−0.451341
$833$	−1.26547e15	−0.109321
$834$	1.79557e16	1.54095
$835$	2.72249e15	0.232108
$836$	1.31913e16	1.11725
$837$	1.68095e16	1.41438
$838$	−3.45657e14	−0.0288937
$839$	−1.17805e16	−0.978301	−0.489150	−	0.872199i	$-0.662693\pi$
$839$	−1.17805e16	−0.978301	−0.489150	+	0.872199i	$0.662693\pi$
$840$	−2.73545e16	−2.25680
$841$	−2.05130e15	−0.168132
$842$	−3.09033e16	−2.51645
$843$	3.32445e16	2.68948
$844$	3.01783e16	2.42556
$845$	1.46106e15	0.116670
$846$	5.59632e16	4.43983
$847$	1.05054e16	0.828046
$848$	−3.42833e15	−0.268476
$849$	4.11746e16	3.20359
$850$	1.53997e16	1.19044
$851$	−1.89778e16	−1.45759
$852$	2.15507e16	1.64454
$853$	−1.09828e16	−0.832710	−0.416355	−	0.909202i	$-0.636693\pi$
$853$	−1.09828e16	−0.832710	−0.416355	+	0.909202i	$0.636693\pi$
$854$	−4.01159e14	−0.0302203
$855$	5.64196e16	4.22295
$856$	3.36806e15	0.250481
$857$	−1.23775e16	−0.914616	−0.457308	−	0.889308i	$-0.651186\pi$
$857$	−1.23775e16	−0.914616	−0.457308	+	0.889308i	$0.651186\pi$
$858$	4.95412e15	0.363736
$859$	2.15114e16	1.56930	0.784650	−	0.619939i	$-0.212842\pi$
$859$	2.15114e16	1.56930	0.784650	+	0.619939i	$0.212842\pi$
$860$	−2.46742e16	−1.78855
$861$	−2.40795e16	−1.73433
$862$	−3.04249e16	−2.17741
$863$	−2.30641e16	−1.64012	−0.820061	−	0.572276i	$-0.806061\pi$
$863$	−2.30641e16	−1.64012	−0.820061	+	0.572276i	$0.806061\pi$
$864$	−2.36855e16	−1.67362
$865$	−1.03248e16	−0.724923
$866$	−1.61094e15	−0.112391
$867$	1.62128e16	1.12397
$868$	2.36750e16	1.63092
$869$	−2.64577e15	−0.181110
$870$	−5.43654e16	−3.69800
$871$	−2.17796e15	−0.147214
$872$	−4.10794e15	−0.275920
$873$	−2.13819e16	−1.42715
$874$	4.93601e16	3.27388
$875$	−7.53811e15	−0.496842
$876$	7.50890e15	0.491817
$877$	1.80153e16	1.17258	0.586292	−	0.810100i	$-0.300587\pi$
$877$	1.80153e16	1.17258	0.586292	+	0.810100i	$0.300587\pi$
$878$	3.01071e15	0.194737
$879$	5.63856e15	0.362434
$880$	−2.66824e15	−0.170440
$881$	−4.65647e15	−0.295590	−0.147795	−	0.989018i	$-0.547218\pi$
$881$	−4.65647e15	−0.295590	−0.147795	+	0.989018i	$0.547218\pi$
$882$	−8.77557e15	−0.553602
$883$	1.65932e16	1.04027	0.520135	−	0.854084i	$-0.325882\pi$
$883$	1.65932e16	1.04027	0.520135	+	0.854084i	$0.325882\pi$
$884$	−3.88483e15	−0.242039
$885$	−7.40184e15	−0.458302
$886$	2.43610e16	1.49903
$887$	−1.72665e16	−1.05590	−0.527952	−	0.849274i	$-0.677040\pi$
$887$	−1.72665e16	−1.05590	−0.527952	+	0.849274i	$0.677040\pi$
$888$	2.38788e16	1.45125
$889$	−9.73627e15	−0.588075
$890$	5.67004e15	0.340362
$891$	4.63312e15	0.276405
$892$	−3.04287e16	−1.80417
$893$	−3.88268e16	−2.28796
$894$	−8.36022e16	−4.89622
$895$	−1.80122e16	−1.04843
$896$	−2.65179e16	−1.53407
$897$	1.11534e16	0.641281
$898$	3.07737e16	1.75857
$899$	1.59005e16	0.903095
$900$	6.42517e16	3.62703
$901$	−1.20699e16	−0.677199
$902$	1.31391e16	0.732703
$903$	−2.59168e16	−1.43648
$904$	9.30356e15	0.512534
$905$	1.50790e16	0.825669
$906$	7.38653e16	4.02009
$907$	2.65125e16	1.43420	0.717102	−	0.696968i	$-0.245468\pi$
$907$	2.65125e16	1.43420	0.717102	+	0.696968i	$0.245468\pi$
$908$	−1.07246e16	−0.576644
$909$	−1.35142e16	−0.722252
$910$	1.36823e16	0.726828
$911$	1.80324e16	0.952142	0.476071	−	0.879407i	$-0.342061\pi$
$911$	1.80324e16	0.952142	0.476071	+	0.879407i	$0.342061\pi$
$912$	1.11025e16	0.582708
$913$	−1.18366e16	−0.617501
$914$	−1.62413e15	−0.0842205
$915$	8.68318e14	0.0447572
$916$	−5.68724e16	−2.91391
$917$	−2.17836e16	−1.10943
$918$	−2.58302e16	−1.30765
$919$	3.17845e16	1.59948	0.799742	−	0.600343i	$-0.204969\pi$
$919$	3.17845e16	1.59948	0.799742	+	0.600343i	$0.204969\pi$
$920$	3.36036e16	1.68094
$921$	−5.70448e16	−2.83654
$922$	−1.70293e16	−0.841738
$923$	−3.64266e15	−0.178982
$924$	2.79130e16	1.36336
$925$	2.84861e16	1.38310
$926$	2.33541e16	1.12720
$927$	4.24044e15	0.203457
$928$	−2.24046e16	−1.06862
$929$	3.36906e16	1.59743	0.798716	−	0.601709i	$-0.205513\pi$
$929$	3.36906e16	1.59743	0.798716	+	0.601709i	$0.205513\pi$
$930$	−8.51730e16	−4.01463
$931$	6.08841e15	0.285286
$932$	2.66729e16	1.24246
$933$	−6.89008e16	−3.19062
$934$	3.37819e16	1.55516
$935$	−9.39387e15	−0.429913
$936$	−9.10379e15	−0.414195
$937$	−1.72813e16	−0.781642	−0.390821	−	0.920467i	$-0.627809\pi$
$937$	−1.72813e16	−0.781642	−0.390821	+	0.920467i	$0.627809\pi$
$938$	−2.03958e16	−0.917116
$939$	1.22856e15	0.0549206
$940$	−7.82193e16	−3.47625
$941$	1.50567e16	0.665254	0.332627	−	0.943058i	$-0.392065\pi$
$941$	1.50567e16	0.665254	0.332627	+	0.943058i	$0.392065\pi$
$942$	6.49055e16	2.85103
$943$	2.95804e16	1.29178
$944$	−9.44890e14	−0.0410237
$945$	5.47349e16	2.36260
$946$	1.41416e16	0.606872
$947$	1.81073e16	0.772555	0.386277	−	0.922383i	$-0.373761\pi$
$947$	1.81073e16	0.772555	0.386277	+	0.922383i	$0.373761\pi$
$948$	2.21784e16	0.940774
$949$	−1.26921e15	−0.0535266
$950$	−7.40905e16	−3.10658
$951$	−1.51950e16	−0.633442
$952$	−1.22939e16	−0.509549
$953$	2.46794e16	1.01700	0.508502	−	0.861061i	$-0.330199\pi$
$953$	2.46794e16	1.01700	0.508502	+	0.861061i	$0.330199\pi$
$954$	−8.36999e16	−3.42933
$955$	−4.05436e16	−1.65160
$956$	−4.33944e16	−1.75758
$957$	1.87468e16	0.754940
$958$	−5.77468e16	−2.31216
$959$	4.14947e16	1.65193
$960$	1.05204e17	4.16430
$961$	−4.97480e14	−0.0195793
$962$	−1.19438e16	−0.467392
$963$	−1.46995e16	−0.571949
$964$	1.16948e16	0.452448
$965$	−5.54947e15	−0.213477
$966$	1.04447e17	3.99505
$967$	3.88722e15	0.147841	0.0739203	−	0.997264i	$-0.476449\pi$
$967$	3.88722e15	0.147841	0.0739203	+	0.997264i	$0.476449\pi$
$968$	1.62381e16	0.614076
$969$	3.90879e16	1.46981
$970$	4.96714e16	1.85721
$971$	1.32536e16	0.492753	0.246377	−	0.969174i	$-0.420760\pi$
$971$	1.32536e16	0.492753	0.246377	+	0.969174i	$0.420760\pi$
$972$	1.95230e16	0.721742
$973$	−1.71002e16	−0.628609
$974$	−3.77845e16	−1.38115
$975$	−1.67415e16	−0.608511
$976$	1.10846e14	0.00400633
$977$	−4.94295e16	−1.77650	−0.888252	−	0.459357i	$-0.848080\pi$
$977$	−4.94295e16	−1.77650	−0.888252	+	0.459357i	$0.848080\pi$
$978$	8.53684e16	3.05094
$979$	−1.95520e15	−0.0694844
$980$	1.22655e16	0.433453
$981$	1.79286e16	0.630038
$982$	−4.60187e16	−1.60813
$983$	3.12934e16	1.08745	0.543724	−	0.839264i	$-0.317014\pi$
$983$	3.12934e16	1.08745	0.543724	+	0.839264i	$0.317014\pi$
$984$	−3.72195e16	−1.28617
$985$	4.73646e16	1.62763
$986$	−2.44334e16	−0.834949
$987$	−8.21585e16	−2.79195
$988$	1.86906e16	0.631626
$989$	3.18375e16	1.06994
$990$	−6.51429e16	−2.17707
$991$	−5.12694e16	−1.70393	−0.851967	−	0.523595i	$-0.824590\pi$
$991$	−5.12694e16	−1.70393	−0.851967	+	0.523595i	$0.824590\pi$
$992$	−3.51008e16	−1.16012
$993$	4.49085e16	1.47607
$994$	−3.41121e16	−1.11502
$995$	−5.82611e16	−1.89388
$996$	9.92217e16	3.20760
$997$	8.43943e14	0.0271325	0.0135662	−	0.999908i	$-0.495682\pi$
$997$	8.43943e14	0.0271325	0.0135662	+	0.999908i	$0.495682\pi$
$998$	3.16225e16	1.01106
$999$	−4.77803e16	−1.51928

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.12.a.a.1.1	✓	5
3.2	odd	2		117.12.a.b.1.5		5
4.3	odd	2		208.12.a.f.1.5		5
13.12	even	2		169.12.a.b.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.12.a.a.1.1	✓	5	1.1	even	1	trivial
117.12.a.b.1.5		5	3.2	odd	2
169.12.a.b.1.5		5	13.12	even	2
208.12.a.f.1.5		5	4.3	odd	2

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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	13.a (trivial)

\(f(q)\)	\(=\)	\(q-71.7031 q^{2} -710.121 q^{3} +3093.33 q^{4} +10598.3 q^{5} +50917.9 q^{6} -48491.8 q^{7} -74953.5 q^{8} +327125. q^{9} +O(q^{10})\)	\(q-71.7031 q^{2} -710.121 q^{3} +3093.33 q^{4} +10598.3 q^{5} +50917.9 q^{6} -48491.8 q^{7} -74953.5 q^{8} +327125. q^{9} -759930. q^{10} +262047. q^{11} -2.19664e6 q^{12} +371293. q^{13} +3.47701e6 q^{14} -7.52607e6 q^{15} -960748. q^{16} -3.38243e6 q^{17} -2.34559e7 q^{18} +1.62735e7 q^{19} +3.27840e7 q^{20} +3.44351e7 q^{21} -1.87896e7 q^{22} -4.23017e7 q^{23} +5.32260e7 q^{24} +6.34957e7 q^{25} -2.66229e7 q^{26} -1.06503e8 q^{27} -1.50001e8 q^{28} -1.00743e8 q^{29} +5.39643e8 q^{30} -1.57832e8 q^{31} +2.22393e8 q^{32} -1.86085e8 q^{33} +2.42531e8 q^{34} -5.13931e8 q^{35} +1.01191e9 q^{36} +4.48631e8 q^{37} -1.16686e9 q^{38} -2.63663e8 q^{39} -7.94379e8 q^{40} -6.99273e8 q^{41} -2.46910e9 q^{42} -7.52629e8 q^{43} +8.10599e8 q^{44} +3.46697e9 q^{45} +3.03316e9 q^{46} -2.38590e9 q^{47} +6.82248e8 q^{48} +3.74131e8 q^{49} -4.55284e9 q^{50} +2.40194e9 q^{51} +1.14853e9 q^{52} +3.56840e9 q^{53} +7.63656e9 q^{54} +2.77725e9 q^{55} +3.63463e9 q^{56} -1.15561e10 q^{57} +7.22360e9 q^{58} +9.83493e8 q^{59} -2.32806e10 q^{60} -1.15375e8 q^{61} +1.13171e10 q^{62} -1.58629e10 q^{63} -1.39787e10 q^{64} +3.93507e9 q^{65} +1.33429e10 q^{66} -5.86589e9 q^{67} -1.04630e10 q^{68} +3.00393e10 q^{69} +3.68504e10 q^{70} -9.81075e9 q^{71} -2.45192e10 q^{72} -3.41836e9 q^{73} -3.21682e10 q^{74} -4.50896e10 q^{75} +5.03392e10 q^{76} -1.27071e10 q^{77} +1.89054e10 q^{78} -1.00965e10 q^{79} -1.01823e10 q^{80} +1.76805e10 q^{81} +5.01400e10 q^{82} -4.51697e10 q^{83} +1.06519e11 q^{84} -3.58480e10 q^{85} +5.39658e10 q^{86} +7.15399e10 q^{87} -1.96413e10 q^{88} -7.46127e9 q^{89} -2.48592e11 q^{90} -1.80047e10 q^{91} -1.30853e11 q^{92} +1.12080e11 q^{93} +1.71076e11 q^{94} +1.72471e11 q^{95} -1.57926e11 q^{96} -6.53631e10 q^{97} -2.68263e10 q^{98} +8.57222e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 41 q^{2} - 496 q^{3} + 2993 q^{4} - 2542 q^{5} + 35441 q^{6} - 36296 q^{7} - 200037 q^{8} + 172645 q^{9}+O(q^{10}) \) 5 * q - 41 * q^2 - 496 * q^3 + 2993 * q^4 - 2542 * q^5 + 35441 * q^6 - 36296 * q^7 - 200037 * q^8 + 172645 * q^9	\( 5 q - 41 q^{2} - 496 q^{3} + 2993 q^{4} - 2542 q^{5} + 35441 q^{6} - 36296 q^{7} - 200037 q^{8} + 172645 q^{9} - 1004055 q^{10} - 1718912 q^{11} - 3670067 q^{12} + 1856465 q^{13} - 3264661 q^{14} - 15356636 q^{15} - 9077455 q^{16} - 6022762 q^{17} - 25785896 q^{18} - 6984968 q^{19} + 38011501 q^{20} + 30001972 q^{21} + 35725110 q^{22} - 26355744 q^{23} + 88388907 q^{24} + 159029879 q^{25} - 15223013 q^{26} + 112641236 q^{27} + 56979871 q^{28} - 81933754 q^{29} + 564471025 q^{30} - 13953380 q^{31} + 399845123 q^{32} - 703422928 q^{33} - 86504907 q^{34} - 754497044 q^{35} + 70511186 q^{36} - 417857846 q^{37} - 903900222 q^{38} - 184161328 q^{39} - 1116423525 q^{40} - 2690154174 q^{41} - 1731320681 q^{42} - 2194005968 q^{43} + 2402296286 q^{44} + 953635766 q^{45} + 4518855072 q^{46} - 4632149016 q^{47} + 5192309977 q^{48} + 2068996185 q^{49} + 2031214610 q^{50} + 4379956420 q^{51} + 1111279949 q^{52} + 3964085286 q^{53} + 12032576291 q^{54} + 3173729472 q^{55} + 10863941385 q^{56} - 15850418664 q^{57} + 16463234370 q^{58} - 6213900336 q^{59} - 4723327387 q^{60} - 13653194690 q^{61} + 7267753516 q^{62} - 29514629404 q^{63} - 17414214535 q^{64} - 943826806 q^{65} + 12784796606 q^{66} - 11630839736 q^{67} - 29781833135 q^{68} - 10491265752 q^{69} + 22288071195 q^{70} - 55420684056 q^{71} - 8164244886 q^{72} - 10807393382 q^{73} - 24555721283 q^{74} - 7282468148 q^{75} + 86244951178 q^{76} - 29595239248 q^{77} + 13158995213 q^{78} - 4898325368 q^{79} - 19551386423 q^{80} + 67432983205 q^{81} + 101980594164 q^{82} - 17839206992 q^{83} + 115847226287 q^{84} + 74975179056 q^{85} - 6756156273 q^{86} + 166439707672 q^{87} - 5163165966 q^{88} + 65706244882 q^{89} - 197230060630 q^{90} - 13476450728 q^{91} - 91088158752 q^{92} + 189811093880 q^{93} + 152425406559 q^{94} + 51462465912 q^{95} - 181515906965 q^{96} - 66619160654 q^{97} - 394227632340 q^{98} - 35714076944 q^{99}+O(q^{100}) \) 5 * q - 41 * q^2 - 496 * q^3 + 2993 * q^4 - 2542 * q^5 + 35441 * q^6 - 36296 * q^7 - 200037 * q^8 + 172645 * q^9 - 1004055 * q^10 - 1718912 * q^11 - 3670067 * q^12 + 1856465 * q^13 - 3264661 * q^14 - 15356636 * q^15 - 9077455 * q^16 - 6022762 * q^17 - 25785896 * q^18 - 6984968 * q^19 + 38011501 * q^20 + 30001972 * q^21 + 35725110 * q^22 - 26355744 * q^23 + 88388907 * q^24 + 159029879 * q^25 - 15223013 * q^26 + 112641236 * q^27 + 56979871 * q^28 - 81933754 * q^29 + 564471025 * q^30 - 13953380 * q^31 + 399845123 * q^32 - 703422928 * q^33 - 86504907 * q^34 - 754497044 * q^35 + 70511186 * q^36 - 417857846 * q^37 - 903900222 * q^38 - 184161328 * q^39 - 1116423525 * q^40 - 2690154174 * q^41 - 1731320681 * q^42 - 2194005968 * q^43 + 2402296286 * q^44 + 953635766 * q^45 + 4518855072 * q^46 - 4632149016 * q^47 + 5192309977 * q^48 + 2068996185 * q^49 + 2031214610 * q^50 + 4379956420 * q^51 + 1111279949 * q^52 + 3964085286 * q^53 + 12032576291 * q^54 + 3173729472 * q^55 + 10863941385 * q^56 - 15850418664 * q^57 + 16463234370 * q^58 - 6213900336 * q^59 - 4723327387 * q^60 - 13653194690 * q^61 + 7267753516 * q^62 - 29514629404 * q^63 - 17414214535 * q^64 - 943826806 * q^65 + 12784796606 * q^66 - 11630839736 * q^67 - 29781833135 * q^68 - 10491265752 * q^69 + 22288071195 * q^70 - 55420684056 * q^71 - 8164244886 * q^72 - 10807393382 * q^73 - 24555721283 * q^74 - 7282468148 * q^75 + 86244951178 * q^76 - 29595239248 * q^77 + 13158995213 * q^78 - 4898325368 * q^79 - 19551386423 * q^80 + 67432983205 * q^81 + 101980594164 * q^82 - 17839206992 * q^83 + 115847226287 * q^84 + 74975179056 * q^85 - 6756156273 * q^86 + 166439707672 * q^87 - 5163165966 * q^88 + 65706244882 * q^89 - 197230060630 * q^90 - 13476450728 * q^91 - 91088158752 * q^92 + 189811093880 * q^93 + 152425406559 * q^94 + 51462465912 * q^95 - 181515906965 * q^96 - 66619160654 * q^97 - 394227632340 * q^98 - 35714076944 * q^99

Introduction

L-functions

Modular forms

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