LMFDB - Embedded newform 15.12.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,12,Mod(1,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, 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("15.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	15.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:	$11.5251477084$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{1609}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 402 $ x^2 - x - 402
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-19.5562$ of defining polynomial
Character	$\chi$	$=$	15.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+29.1123 q^{2} +243.000 q^{3} -1200.47 q^{4} -3125.00 q^{5} +7074.30 q^{6} -56615.3 q^{7} -94570.6 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+29.1123 q^{2} +243.000 q^{3} -1200.47 q^{4} -3125.00 q^{5} +7074.30 q^{6} -56615.3 q^{7} -94570.6 q^{8} +59049.0 q^{9} -90976.1 q^{10} +235631. q^{11} -291715. q^{12} -1.14372e6 q^{13} -1.64821e6 q^{14} -759375. q^{15} -294606. q^{16} -1.19311e6 q^{17} +1.71905e6 q^{18} -1.61391e7 q^{19} +3.75147e6 q^{20} -1.37575e7 q^{21} +6.85976e6 q^{22} +9.03374e6 q^{23} -2.29807e7 q^{24} +9.76562e6 q^{25} -3.32964e7 q^{26} +1.43489e7 q^{27} +6.79651e7 q^{28} +8.87785e7 q^{29} -2.21072e7 q^{30} +1.93921e8 q^{31} +1.85104e8 q^{32} +5.72582e7 q^{33} -3.47341e7 q^{34} +1.76923e8 q^{35} -7.08866e7 q^{36} -2.44095e8 q^{37} -4.69846e8 q^{38} -2.77924e8 q^{39} +2.95533e8 q^{40} -1.12810e9 q^{41} -4.00514e8 q^{42} +1.52618e9 q^{43} -2.82868e8 q^{44} -1.84528e8 q^{45} +2.62993e8 q^{46} -2.98238e9 q^{47} -7.15894e7 q^{48} +1.22797e9 q^{49} +2.84300e8 q^{50} -2.89925e8 q^{51} +1.37300e9 q^{52} +9.38353e7 q^{53} +4.17730e8 q^{54} -7.36346e8 q^{55} +5.35415e9 q^{56} -3.92180e9 q^{57} +2.58455e9 q^{58} -8.60858e9 q^{59} +9.11608e8 q^{60} +7.84161e9 q^{61} +5.64549e9 q^{62} -3.34308e9 q^{63} +5.99216e9 q^{64} +3.57413e9 q^{65} +1.66692e9 q^{66} -9.98768e9 q^{67} +1.43229e9 q^{68} +2.19520e9 q^{69} +5.15064e9 q^{70} +1.24227e10 q^{71} -5.58430e9 q^{72} -1.51300e10 q^{73} -7.10618e9 q^{74} +2.37305e9 q^{75} +1.93745e10 q^{76} -1.33403e10 q^{77} -8.09103e9 q^{78} -4.32508e10 q^{79} +9.20645e8 q^{80} +3.48678e9 q^{81} -3.28415e10 q^{82} -5.08621e10 q^{83} +1.65155e10 q^{84} +3.72846e9 q^{85} +4.44305e10 q^{86} +2.15732e10 q^{87} -2.22837e10 q^{88} +2.35863e10 q^{89} -5.37205e9 q^{90} +6.47522e10 q^{91} -1.08447e10 q^{92} +4.71228e10 q^{93} -8.68240e10 q^{94} +5.04346e10 q^{95} +4.49803e10 q^{96} -8.52916e10 q^{97} +3.57491e10 q^{98} +1.39137e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 22 q^{2} + 486 q^{3} - 636 q^{4} - 6250 q^{5} - 5346 q^{6} - 10864 q^{7} - 18744 q^{8} + 118098 q^{9}+O(q^{10}) $ 2 * q - 22 * q^2 + 486 * q^3 - 636 * q^4 - 6250 * q^5 - 5346 * q^6 - 10864 * q^7 - 18744 * q^8 + 118098 * q^9	\( 2 q - 22 q^{2} + 486 q^{3} - 636 q^{4} - 6250 q^{5} - 5346 q^{6} - 10864 q^{7} - 18744 q^{8} + 118098 q^{9} + 68750 q^{10} - 361792 q^{11} - 154548 q^{12} - 2133732 q^{13} - 3986664 q^{14} - 1518750 q^{15} - 5326320 q^{16} - 7804588 q^{17} - 1299078 q^{18} - 15562224 q^{19} + 1987500 q^{20} - 2639952 q^{21} + 37395424 q^{22} - 37450248 q^{23} - 4554792 q^{24} + 19531250 q^{25} + 17305364 q^{26} + 28697814 q^{27} + 93790448 q^{28} - 70320668 q^{29} + 16706250 q^{30} + 298584872 q^{31} + 286993696 q^{32} - 87915456 q^{33} + 303194188 q^{34} + 33950000 q^{35} - 37555164 q^{36} + 236000956 q^{37} - 499330888 q^{38} - 518496876 q^{39} + 58575000 q^{40} - 464942588 q^{41} - 968759352 q^{42} - 242208600 q^{43} - 620095808 q^{44} - 369056250 q^{45} + 2638898832 q^{46} - 4375796920 q^{47} - 1294295760 q^{48} + 1343830130 q^{49} - 214843750 q^{50} - 1896514884 q^{51} + 814171912 q^{52} - 2189541388 q^{53} - 315675954 q^{54} + 1130600000 q^{55} + 8823318240 q^{56} - 3781620432 q^{57} + 10716478004 q^{58} - 5480385856 q^{59} + 482962500 q^{60} + 14557903980 q^{61} + 295874592 q^{62} - 641508336 q^{63} + 11089288256 q^{64} + 6667912500 q^{65} + 9087088032 q^{66} - 15918388888 q^{67} - 2299702856 q^{68} - 9100410264 q^{69} + 12458325000 q^{70} + 1120561024 q^{71} - 1106814456 q^{72} - 24521574348 q^{73} - 31645012364 q^{74} + 4746093750 q^{75} + 19700124976 q^{76} - 40673194368 q^{77} + 4205203452 q^{78} - 79243055560 q^{79} + 16644750000 q^{80} + 6973568802 q^{81} - 66736852348 q^{82} + 9245226696 q^{83} + 22791078864 q^{84} + 24389337500 q^{85} + 134816793608 q^{86} - 17087922324 q^{87} - 67584257664 q^{88} + 22117321236 q^{89} + 4059618750 q^{90} + 19457850112 q^{91} - 37083635424 q^{92} + 72556123896 q^{93} - 15603010256 q^{94} + 48631950000 q^{95} + 69739468128 q^{96} - 160363673468 q^{97} + 29827277722 q^{98} - 21363455808 q^{99}+O(q^{100}) \) 2 * q - 22 * q^2 + 486 * q^3 - 636 * q^4 - 6250 * q^5 - 5346 * q^6 - 10864 * q^7 - 18744 * q^8 + 118098 * q^9 + 68750 * q^10 - 361792 * q^11 - 154548 * q^12 - 2133732 * q^13 - 3986664 * q^14 - 1518750 * q^15 - 5326320 * q^16 - 7804588 * q^17 - 1299078 * q^18 - 15562224 * q^19 + 1987500 * q^20 - 2639952 * q^21 + 37395424 * q^22 - 37450248 * q^23 - 4554792 * q^24 + 19531250 * q^25 + 17305364 * q^26 + 28697814 * q^27 + 93790448 * q^28 - 70320668 * q^29 + 16706250 * q^30 + 298584872 * q^31 + 286993696 * q^32 - 87915456 * q^33 + 303194188 * q^34 + 33950000 * q^35 - 37555164 * q^36 + 236000956 * q^37 - 499330888 * q^38 - 518496876 * q^39 + 58575000 * q^40 - 464942588 * q^41 - 968759352 * q^42 - 242208600 * q^43 - 620095808 * q^44 - 369056250 * q^45 + 2638898832 * q^46 - 4375796920 * q^47 - 1294295760 * q^48 + 1343830130 * q^49 - 214843750 * q^50 - 1896514884 * q^51 + 814171912 * q^52 - 2189541388 * q^53 - 315675954 * q^54 + 1130600000 * q^55 + 8823318240 * q^56 - 3781620432 * q^57 + 10716478004 * q^58 - 5480385856 * q^59 + 482962500 * q^60 + 14557903980 * q^61 + 295874592 * q^62 - 641508336 * q^63 + 11089288256 * q^64 + 6667912500 * q^65 + 9087088032 * q^66 - 15918388888 * q^67 - 2299702856 * q^68 - 9100410264 * q^69 + 12458325000 * q^70 + 1120561024 * q^71 - 1106814456 * q^72 - 24521574348 * q^73 - 31645012364 * q^74 + 4746093750 * q^75 + 19700124976 * q^76 - 40673194368 * q^77 + 4205203452 * q^78 - 79243055560 * q^79 + 16644750000 * q^80 + 6973568802 * q^81 - 66736852348 * q^82 + 9245226696 * q^83 + 22791078864 * q^84 + 24389337500 * q^85 + 134816793608 * q^86 - 17087922324 * q^87 - 67584257664 * q^88 + 22117321236 * q^89 + 4059618750 * q^90 + 19457850112 * q^91 - 37083635424 * q^92 + 72556123896 * q^93 - 15603010256 * q^94 + 48631950000 * q^95 + 69739468128 * q^96 - 160363673468 * q^97 + 29827277722 * q^98 - 21363455808 * 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 $

$2$	29.1123	0.643298	0.321649	−	0.946859i	$-0.395763\pi$
$2$	29.1123	0.643298	0.321649	+	0.946859i	$0.395763\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	−1200.47	−0.586168
$5$	−3125.00	−0.447214
$5$	−3125.00	−0.447214
$6$	7074.30	0.371408
$7$	−56615.3	−1.27320	−0.636598	−	0.771196i	$-0.719659\pi$
$7$	−56615.3	−1.27320	−0.636598	+	0.771196i	$0.719659\pi$
$8$	−94570.6	−1.02038
$9$	59049.0	0.333333
$10$	−90976.1	−0.287692
$11$	235631.	0.441135	0.220568	−	0.975372i	$-0.429209\pi$
$11$	235631.	0.441135	0.220568	+	0.975372i	$0.429209\pi$
$12$	−291715.	−0.338424
$13$	−1.14372e6	−0.854342	−0.427171	−	0.904171i	$-0.640490\pi$
$13$	−1.14372e6	−0.854342	−0.427171	+	0.904171i	$0.640490\pi$
$14$	−1.64821e6	−0.819044
$15$	−759375.	−0.258199
$16$	−294606.	−0.0702396
$17$	−1.19311e6	−0.203803	−0.101901	−	0.994795i	$-0.532493\pi$
$17$	−1.19311e6	−0.203803	−0.101901	+	0.994795i	$0.532493\pi$
$18$	1.71905e6	0.214433
$19$	−1.61391e7	−1.49532	−0.747660	−	0.664082i	$-0.768823\pi$
$19$	−1.61391e7	−1.49532	−0.747660	+	0.664082i	$0.768823\pi$
$20$	3.75147e6	0.262142
$21$	−1.37575e7	−0.735080
$22$	6.85976e6	0.283781
$23$	9.03374e6	0.292661	0.146330	−	0.989236i	$-0.453254\pi$
$23$	9.03374e6	0.292661	0.146330	+	0.989236i	$0.453254\pi$
$24$	−2.29807e7	−0.589116
$25$	9.76562e6	0.200000
$26$	−3.32964e7	−0.549596
$27$	1.43489e7	0.192450
$28$	6.79651e7	0.746306
$29$	8.87785e7	0.803746	0.401873	−	0.915695i	$-0.368359\pi$
$29$	8.87785e7	0.803746	0.401873	+	0.915695i	$0.368359\pi$
$30$	−2.21072e7	−0.166099
$31$	1.93921e8	1.21657	0.608283	−	0.793721i	$-0.291859\pi$
$31$	1.93921e8	1.21657	0.608283	+	0.793721i	$0.291859\pi$
$32$	1.85104e8	0.975193
$33$	5.72582e7	0.254690
$34$	−3.47341e7	−0.131106
$35$	1.76923e8	0.569390
$36$	−7.08866e7	−0.195389
$37$	−2.44095e8	−0.578695	−0.289347	−	0.957224i	$-0.593438\pi$
$37$	−2.44095e8	−0.578695	−0.289347	+	0.957224i	$0.593438\pi$
$38$	−4.69846e8	−0.961936
$39$	−2.77924e8	−0.493255
$40$	2.95533e8	0.456327
$41$	−1.12810e9	−1.52067	−0.760335	−	0.649531i	$-0.774965\pi$
$41$	−1.12810e9	−1.52067	−0.760335	+	0.649531i	$0.774965\pi$
$42$	−4.00514e8	−0.472875
$43$	1.52618e9	1.58317	0.791586	−	0.611058i	$-0.209256\pi$
$43$	1.52618e9	1.58317	0.791586	+	0.611058i	$0.209256\pi$
$44$	−2.82868e8	−0.258579
$45$	−1.84528e8	−0.149071
$46$	2.62993e8	0.188268
$47$	−2.98238e9	−1.89681	−0.948406	−	0.317058i	$-0.897305\pi$
$47$	−2.98238e9	−1.89681	−0.948406	+	0.317058i	$0.897305\pi$
$48$	−7.15894e7	−0.0405529
$49$	1.22797e9	0.621026
$50$	2.84300e8	0.128660
$51$	−2.89925e8	−0.117666
$52$	1.37300e9	0.500788
$53$	9.38353e7	0.0308212	0.0154106	−	0.999881i	$-0.495094\pi$
$53$	9.38353e7	0.0308212	0.0154106	+	0.999881i	$0.495094\pi$
$54$	4.17730e8	0.123803
$55$	−7.36346e8	−0.197282
$56$	5.35415e9	1.29914
$57$	−3.92180e9	−0.863323
$58$	2.58455e9	0.517048
$59$	−8.60858e9	−1.56764	−0.783819	−	0.620990i	$-0.786731\pi$
$59$	−8.60858e9	−1.56764	−0.783819	+	0.620990i	$0.786731\pi$
$60$	9.11608e8	0.151348
$61$	7.84161e9	1.18875	0.594375	−	0.804188i	$-0.297399\pi$
$61$	7.84161e9	1.18875	0.594375	+	0.804188i	$0.297399\pi$
$62$	5.64549e9	0.782614
$63$	−3.34308e9	−0.424398
$64$	5.99216e9	0.697580
$65$	3.57413e9	0.382073
$66$	1.66692e9	0.163841
$67$	−9.98768e9	−0.903760	−0.451880	−	0.892079i	$-0.649246\pi$
$67$	−9.98768e9	−0.903760	−0.451880	+	0.892079i	$0.649246\pi$
$68$	1.43229e9	0.119463
$69$	2.19520e9	0.168968
$70$	5.15064e9	0.366288
$71$	1.24227e10	0.817138	0.408569	−	0.912727i	$-0.366028\pi$
$71$	1.24227e10	0.817138	0.408569	+	0.912727i	$0.366028\pi$
$72$	−5.58430e9	−0.340126
$73$	−1.51300e10	−0.854206	−0.427103	−	0.904203i	$-0.640466\pi$
$73$	−1.51300e10	−0.854206	−0.427103	+	0.904203i	$0.640466\pi$
$74$	−7.10618e9	−0.372273
$75$	2.37305e9	0.115470
$76$	1.93745e10	0.876508
$77$	−1.33403e10	−0.561651
$78$	−8.09103e9	−0.317310
$79$	−4.32508e10	−1.58141	−0.790706	−	0.612195i	$-0.790287\pi$
$79$	−4.32508e10	−1.58141	−0.790706	+	0.612195i	$0.790287\pi$
$80$	9.20645e8	0.0314121
$81$	3.48678e9	0.111111
$82$	−3.28415e10	−0.978244
$83$	−5.08621e10	−1.41731	−0.708655	−	0.705555i	$-0.750698\pi$
$83$	−5.08621e10	−1.41731	−0.708655	+	0.705555i	$0.750698\pi$
$84$	1.65155e10	0.430880
$85$	3.72846e9	0.0911434
$86$	4.44305e10	1.01845
$87$	2.15732e10	0.464043
$88$	−2.22837e10	−0.450125
$89$	2.35863e10	0.447729	0.223865	−	0.974620i	$-0.428133\pi$
$89$	2.35863e10	0.447729	0.223865	+	0.974620i	$0.428133\pi$
$90$	−5.37205e9	−0.0958972
$91$	6.47522e10	1.08774
$92$	−1.08447e10	−0.171548
$93$	4.71228e10	0.702384
$94$	−8.68240e10	−1.22022
$95$	5.04346e10	0.668727
$96$	4.49803e10	0.563028
$97$	−8.52916e10	−1.00847	−0.504233	−	0.863567i	$-0.668225\pi$
$97$	−8.52916e10	−1.00847	−0.504233	+	0.863567i	$0.668225\pi$
$98$	3.57491e10	0.399505
$99$	1.39137e10	0.147045
$100$	−1.17234e10	−0.117234
$101$	6.04095e10	0.571923	0.285961	−	0.958241i	$-0.407687\pi$
$101$	6.04095e10	0.571923	0.285961	+	0.958241i	$0.407687\pi$
$102$	−8.44039e9	−0.0756940
$103$	2.21592e11	1.88343	0.941715	−	0.336412i	$-0.109213\pi$
$103$	2.21592e11	1.88343	0.941715	+	0.336412i	$0.109213\pi$
$104$	1.08162e11	0.871752
$105$	4.29923e10	0.328738
$106$	2.73177e9	0.0198272
$107$	−2.28431e11	−1.57451	−0.787253	−	0.616631i	$-0.788497\pi$
$107$	−2.28431e11	−1.57451	−0.787253	+	0.616631i	$0.788497\pi$
$108$	−1.72255e10	−0.112808
$109$	−5.19217e10	−0.323224	−0.161612	−	0.986854i	$-0.551669\pi$
$109$	−5.19217e10	−0.323224	−0.161612	+	0.986854i	$0.551669\pi$
$110$	−2.14367e10	−0.126911
$111$	−5.93151e10	−0.334110
$112$	1.66792e10	0.0894288
$113$	1.54627e10	0.0789505	0.0394753	−	0.999221i	$-0.487431\pi$
$113$	1.54627e10	0.0789505	0.0394753	+	0.999221i	$0.487431\pi$
$114$	−1.14173e11	−0.555374
$115$	−2.82304e10	−0.130882
$116$	−1.06576e11	−0.471130
$117$	−6.75356e10	−0.284781
$118$	−2.50616e11	−1.00846
$119$	6.75481e10	0.259481
$120$	7.18146e10	0.263461
$121$	−2.29790e11	−0.805400
$122$	2.28287e11	0.764721
$123$	−2.74127e11	−0.877959
$124$	−2.32797e11	−0.713111
$125$	−3.05176e10	−0.0894427
$126$	−9.73249e10	−0.273015
$127$	4.49563e11	1.20745	0.603726	−	0.797192i	$-0.293682\pi$
$127$	4.49563e11	1.20745	0.603726	+	0.797192i	$0.293682\pi$
$128$	−2.04647e11	−0.526442
$129$	3.70861e11	0.914044
$130$	1.04051e11	0.245787
$131$	4.29593e10	0.0972892	0.0486446	−	0.998816i	$-0.484510\pi$
$131$	4.29593e10	0.0972892	0.0486446	+	0.998816i	$0.484510\pi$
$132$	−6.87369e10	−0.149291
$133$	9.13720e11	1.90383
$134$	−2.90765e11	−0.581387
$135$	−4.48403e10	−0.0860663
$136$	1.12833e11	0.207956
$137$	−7.31652e10	−0.129521	−0.0647607	−	0.997901i	$-0.520628\pi$
$137$	−7.31652e10	−0.129521	−0.0647607	+	0.997901i	$0.520628\pi$
$138$	6.39074e10	0.108697
$139$	5.61519e11	0.917873	0.458937	−	0.888469i	$-0.348230\pi$
$139$	5.61519e11	0.917873	0.458937	+	0.888469i	$0.348230\pi$
$140$	−2.12391e11	−0.333758
$141$	−7.24718e11	−1.09512
$142$	3.61654e11	0.525663
$143$	−2.69496e11	−0.376880
$144$	−1.73962e10	−0.0234132
$145$	−2.77433e11	−0.359446
$146$	−4.40469e11	−0.549509
$147$	2.98397e11	0.358549
$148$	2.93029e11	0.339212
$149$	3.84637e11	0.429068	0.214534	−	0.976716i	$-0.431177\pi$
$149$	3.84637e11	0.429068	0.214534	+	0.976716i	$0.431177\pi$
$150$	6.90850e10	0.0742816
$151$	5.29991e11	0.549408	0.274704	−	0.961529i	$-0.411420\pi$
$151$	5.29991e11	0.549408	0.274704	+	0.961529i	$0.411420\pi$
$152$	1.52628e12	1.52579
$153$	−7.04517e10	−0.0679343
$154$	−3.88368e11	−0.361309
$155$	−6.06003e11	−0.544065
$156$	3.33640e11	0.289130
$157$	4.36979e11	0.365605	0.182802	−	0.983150i	$-0.441483\pi$
$157$	4.36979e11	0.365605	0.182802	+	0.983150i	$0.441483\pi$
$158$	−1.25913e12	−1.01732
$159$	2.28020e10	0.0177946
$160$	−5.78450e11	−0.436120
$161$	−5.11448e11	−0.372614
$162$	1.01508e11	0.0714776
$163$	−2.07051e11	−0.140944	−0.0704718	−	0.997514i	$-0.522450\pi$
$163$	−2.07051e11	−0.140944	−0.0704718	+	0.997514i	$0.522450\pi$
$164$	1.35425e12	0.891368
$165$	−1.78932e11	−0.113901
$166$	−1.48072e12	−0.911753
$167$	5.81321e11	0.346318	0.173159	−	0.984894i	$-0.444603\pi$
$167$	5.81321e11	0.346318	0.173159	+	0.984894i	$0.444603\pi$
$168$	1.30106e12	0.750059
$169$	−4.84062e11	−0.270100
$170$	1.08544e11	0.0586323
$171$	−9.52997e11	−0.498440
$172$	−1.83213e12	−0.928004
$173$	−2.95650e12	−1.45052	−0.725260	−	0.688475i	$-0.758281\pi$
$173$	−2.95650e12	−1.45052	−0.725260	+	0.688475i	$0.758281\pi$
$174$	6.28045e11	0.298518
$175$	−5.52884e11	−0.254639
$176$	−6.94183e10	−0.0309852
$177$	−2.09189e12	−0.905076
$178$	6.86654e11	0.288023
$179$	1.44075e12	0.586001	0.293000	−	0.956112i	$-0.405346\pi$
$179$	1.44075e12	0.586001	0.293000	+	0.956112i	$0.405346\pi$
$180$	2.21521e11	0.0873807
$181$	−4.50305e12	−1.72296	−0.861479	−	0.507793i	$-0.830462\pi$
$181$	−4.50305e12	−1.72296	−0.861479	+	0.507793i	$0.830462\pi$
$182$	1.88509e12	0.699744
$183$	1.90551e12	0.686326
$184$	−8.54326e11	−0.298625
$185$	7.62797e11	0.258800
$186$	1.37185e12	0.451842
$187$	−2.81132e11	−0.0899046
$188$	3.58026e12	1.11185
$189$	−8.12368e11	−0.245027
$190$	1.46827e12	0.430191
$191$	6.14801e12	1.75005	0.875026	−	0.484077i	$-0.160844\pi$
$191$	6.14801e12	1.75005	0.875026	+	0.484077i	$0.160844\pi$
$192$	1.45610e12	0.402748
$193$	1.10484e12	0.296985	0.148493	−	0.988914i	$-0.452558\pi$
$193$	1.10484e12	0.296985	0.148493	+	0.988914i	$0.452558\pi$
$194$	−2.48304e12	−0.648744
$195$	8.68513e11	0.220590
$196$	−1.47414e12	−0.364025
$197$	−5.21168e11	−0.125145	−0.0625725	−	0.998040i	$-0.519930\pi$
$197$	−5.21168e11	−0.125145	−0.0625725	+	0.998040i	$0.519930\pi$
$198$	4.05062e11	0.0945938
$199$	3.29687e12	0.748876	0.374438	−	0.927252i	$-0.377836\pi$
$199$	3.29687e12	0.748876	0.374438	+	0.927252i	$0.377836\pi$
$200$	−9.23541e11	−0.204076
$201$	−2.42701e12	−0.521786
$202$	1.75866e12	0.367917
$203$	−5.02622e12	−1.02333
$204$	3.48047e11	0.0689718
$205$	3.52530e12	0.680064
$206$	6.45106e12	1.21161
$207$	5.33433e11	0.0975536
$208$	3.36948e11	0.0600087
$209$	−3.80286e12	−0.659638
$210$	1.25161e12	0.211476
$211$	4.23413e12	0.696965	0.348483	−	0.937315i	$-0.386697\pi$
$211$	4.23413e12	0.696965	0.348483	+	0.937315i	$0.386697\pi$
$212$	−1.12647e11	−0.0180664
$213$	3.01872e12	0.471775
$214$	−6.65016e12	−1.01288
$215$	−4.76930e12	−0.708016
$216$	−1.35698e12	−0.196372
$217$	−1.09789e13	−1.54892
$218$	−1.51156e12	−0.207929
$219$	−3.67658e12	−0.493176
$220$	8.83962e11	0.115640
$221$	1.36458e12	0.174117
$222$	−1.72680e12	−0.214932
$223$	−4.39253e11	−0.0533381	−0.0266690	−	0.999644i	$-0.508490\pi$
$223$	−4.39253e11	−0.0533381	−0.0266690	+	0.999644i	$0.508490\pi$
$224$	−1.04797e13	−1.24161
$225$	5.76650e11	0.0666667
$226$	4.50157e11	0.0507887
$227$	−6.69904e12	−0.737685	−0.368842	−	0.929492i	$-0.620246\pi$
$227$	−6.69904e12	−0.737685	−0.368842	+	0.929492i	$0.620246\pi$
$228$	4.70800e12	0.506052
$229$	1.58290e13	1.66095	0.830477	−	0.557053i	$-0.188068\pi$
$229$	1.58290e13	1.66095	0.830477	+	0.557053i	$0.188068\pi$
$230$	−8.21854e11	−0.0841960
$231$	−3.24169e12	−0.324270
$232$	−8.39583e12	−0.820125
$233$	−1.05341e13	−1.00494	−0.502468	−	0.864596i	$-0.667574\pi$
$233$	−1.05341e13	−1.00494	−0.502468	+	0.864596i	$0.667574\pi$
$234$	−1.96612e12	−0.183199
$235$	9.31993e12	0.848280
$236$	1.03344e13	0.918899
$237$	−1.05099e13	−0.913029
$238$	1.96648e12	0.166923
$239$	1.58200e13	1.31226	0.656128	−	0.754650i	$-0.272193\pi$
$239$	1.58200e13	1.31226	0.656128	+	0.754650i	$0.272193\pi$
$240$	2.23717e11	0.0181358
$241$	2.00225e13	1.58644	0.793220	−	0.608935i	$-0.208403\pi$
$241$	2.00225e13	1.58644	0.793220	+	0.608935i	$0.208403\pi$
$242$	−6.68972e12	−0.518112
$243$	8.47289e11	0.0641500
$244$	−9.41362e12	−0.696807
$245$	−3.83741e12	−0.277731
$246$	−7.98049e12	−0.564789
$247$	1.84586e13	1.27751
$248$	−1.83392e13	−1.24136
$249$	−1.23595e13	−0.818285
$250$	−8.88438e11	−0.0575383
$251$	2.93717e13	1.86090	0.930452	−	0.366414i	$-0.119415\pi$
$251$	2.93717e13	1.86090	0.930452	+	0.366414i	$0.119415\pi$
$252$	4.01327e12	0.248769
$253$	2.12863e12	0.129103
$254$	1.30878e13	0.776752
$255$	9.06015e11	0.0526217
$256$	−1.82297e13	−1.03624
$257$	1.59208e13	0.885793	0.442896	−	0.896573i	$-0.353951\pi$
$257$	1.59208e13	0.885793	0.442896	+	0.896573i	$0.353951\pi$
$258$	1.07966e13	0.588003
$259$	1.38195e13	0.736791
$260$	−4.29064e12	−0.223959
$261$	5.24228e12	0.267915
$262$	1.25064e12	0.0625860
$263$	−3.12857e13	−1.53317	−0.766584	−	0.642144i	$-0.778045\pi$
$263$	−3.12857e13	−1.53317	−0.766584	+	0.642144i	$0.778045\pi$
$264$	−5.41495e12	−0.259880
$265$	−2.93235e11	−0.0137836
$266$	2.66005e13	1.22473
$267$	5.73148e12	0.258497
$268$	1.19899e13	0.529755
$269$	−9.67137e12	−0.418650	−0.209325	−	0.977846i	$-0.567127\pi$
$269$	−9.67137e12	−0.418650	−0.209325	+	0.977846i	$0.567127\pi$
$270$	−1.30541e12	−0.0553663
$271$	−3.56423e13	−1.48127	−0.740636	−	0.671906i	$-0.765476\pi$
$271$	−3.56423e13	−1.48127	−0.740636	+	0.671906i	$0.765476\pi$
$272$	3.51497e11	0.0143150
$273$	1.57348e13	0.628009
$274$	−2.13001e12	−0.0833208
$275$	2.30108e12	0.0882271
$276$	−2.63527e12	−0.0990435
$277$	−2.81442e13	−1.03693	−0.518466	−	0.855098i	$-0.673497\pi$
$277$	−2.81442e13	−1.03693	−0.518466	+	0.855098i	$0.673497\pi$
$278$	1.63471e13	0.590466
$279$	1.14508e13	0.405522
$280$	−1.67317e13	−0.580993
$281$	−5.26905e13	−1.79410	−0.897052	−	0.441925i	$-0.854296\pi$
$281$	−5.26905e13	−1.79410	−0.897052	+	0.441925i	$0.854296\pi$
$282$	−2.10982e13	−0.704492
$283$	2.10244e13	0.688491	0.344246	−	0.938880i	$-0.388135\pi$
$283$	2.10244e13	0.688491	0.344246	+	0.938880i	$0.388135\pi$
$284$	−1.49131e13	−0.478980
$285$	1.22556e13	0.386090
$286$	−7.84565e12	−0.242446
$287$	6.38676e13	1.93611
$288$	1.09302e13	0.325064
$289$	−3.28484e13	−0.958464
$290$	−8.07672e12	−0.231231
$291$	−2.07258e13	−0.582238
$292$	1.81631e13	0.500708
$293$	−4.08584e13	−1.10537	−0.552687	−	0.833389i	$-0.686398\pi$
$293$	−4.08584e13	−1.10537	−0.552687	+	0.833389i	$0.686398\pi$
$294$	8.68703e12	0.230654
$295$	2.69018e13	0.701069
$296$	2.30842e13	0.590488
$297$	3.38104e12	0.0848965
$298$	1.11977e13	0.276019
$299$	−1.03321e13	−0.250032
$300$	−2.84878e12	−0.0676848
$301$	−8.64050e13	−2.01569
$302$	1.54293e13	0.353433
$303$	1.46795e13	0.330200
$304$	4.75468e12	0.105031
$305$	−2.45050e13	−0.531626
$306$	−2.05102e12	−0.0437020
$307$	−4.54646e12	−0.0951508	−0.0475754	−	0.998868i	$-0.515149\pi$
$307$	−4.54646e12	−0.0951508	−0.0475754	+	0.998868i	$0.515149\pi$
$308$	1.60147e13	0.329222
$309$	5.38469e13	1.08740
$310$	−1.76422e13	−0.349996
$311$	−1.77869e13	−0.346672	−0.173336	−	0.984863i	$-0.555455\pi$
$311$	−1.77869e13	−0.346672	−0.173336	+	0.984863i	$0.555455\pi$
$312$	2.62835e13	0.503306
$313$	−4.83939e13	−0.910536	−0.455268	−	0.890354i	$-0.650457\pi$
$313$	−4.83939e13	−0.910536	−0.455268	+	0.890354i	$0.650457\pi$
$314$	1.27215e13	0.235193
$315$	1.04471e13	0.189797
$316$	5.19214e13	0.926973
$317$	−2.22739e12	−0.0390814	−0.0195407	−	0.999809i	$-0.506220\pi$
$317$	−2.22739e12	−0.0390814	−0.0195407	+	0.999809i	$0.506220\pi$
$318$	6.63819e11	0.0114472
$319$	2.09189e13	0.354561
$320$	−1.87255e13	−0.311967
$321$	−5.55087e13	−0.909041
$322$	−1.48895e13	−0.239702
$323$	1.92556e13	0.304750
$324$	−4.18579e12	−0.0651297
$325$	−1.11692e13	−0.170868
$326$	−6.02774e12	−0.0906688
$327$	−1.26170e13	−0.186613
$328$	1.06685e14	1.55166
$329$	1.68848e14	2.41501
$330$	−5.20913e12	−0.0732721
$331$	1.19438e13	0.165231	0.0826153	−	0.996582i	$-0.473673\pi$
$331$	1.19438e13	0.165231	0.0826153	+	0.996582i	$0.473673\pi$
$332$	6.10586e13	0.830782
$333$	−1.44136e13	−0.192898
$334$	1.69236e13	0.222786
$335$	3.12115e13	0.404174
$336$	4.05306e12	0.0516317
$337$	1.78353e13	0.223520	0.111760	−	0.993735i	$-0.464351\pi$
$337$	1.78353e13	0.223520	0.111760	+	0.993735i	$0.464351\pi$
$338$	−1.40922e13	−0.173755
$339$	3.75745e12	0.0455821
$340$	−4.47591e12	−0.0534253
$341$	4.56937e13	0.536670
$342$	−2.77440e13	−0.320645
$343$	4.24250e13	0.482508
$344$	−1.44331e14	−1.61543
$345$	−6.86000e12	−0.0755647
$346$	−8.60705e13	−0.933117
$347$	−3.45314e13	−0.368469	−0.184235	−	0.982882i	$-0.558981\pi$
$347$	−3.45314e13	−0.368469	−0.184235	+	0.982882i	$0.558981\pi$
$348$	−2.58980e13	−0.272007
$349$	−7.72313e13	−0.798461	−0.399230	−	0.916851i	$-0.630723\pi$
$349$	−7.72313e13	−0.798461	−0.399230	+	0.916851i	$0.630723\pi$
$350$	−1.60958e13	−0.163809
$351$	−1.64111e13	−0.164418
$352$	4.36161e13	0.430192
$353$	−1.99859e14	−1.94072	−0.970361	−	0.241660i	$-0.922308\pi$
$353$	−1.99859e14	−1.94072	−0.970361	+	0.241660i	$0.922308\pi$
$354$	−6.08997e13	−0.582234
$355$	−3.88210e13	−0.365435
$356$	−2.83147e13	−0.262444
$357$	1.64142e13	0.149811
$358$	4.19437e13	0.376973
$359$	4.15248e13	0.367526	0.183763	−	0.982971i	$-0.441172\pi$
$359$	4.15248e13	0.367526	0.183763	+	0.982971i	$0.441172\pi$
$360$	1.74509e13	0.152109
$361$	1.43980e14	1.23598
$362$	−1.31094e14	−1.10838
$363$	−5.58389e13	−0.464998
$364$	−7.77331e13	−0.637600
$365$	4.72812e13	0.382012
$366$	5.54739e13	0.441512
$367$	3.32070e13	0.260355	0.130178	−	0.991491i	$-0.458445\pi$
$367$	3.32070e13	0.260355	0.130178	+	0.991491i	$0.458445\pi$
$368$	−2.66140e12	−0.0205564
$369$	−6.66129e13	−0.506890
$370$	2.22068e13	0.166486
$371$	−5.31252e12	−0.0392414
$372$	−5.65696e13	−0.411715
$373$	−1.32283e14	−0.948646	−0.474323	−	0.880351i	$-0.657307\pi$
$373$	−1.32283e14	−0.948646	−0.474323	+	0.880351i	$0.657307\pi$
$374$	−8.18442e12	−0.0578355
$375$	−7.41577e12	−0.0516398
$376$	2.82045e14	1.93547
$377$	−1.01538e14	−0.686674
$378$	−2.36499e13	−0.157625
$379$	−8.61298e12	−0.0565767	−0.0282884	−	0.999600i	$-0.509006\pi$
$379$	−8.61298e12	−0.0565767	−0.0282884	+	0.999600i	$0.509006\pi$
$380$	−6.05453e13	−0.391986
$381$	1.09244e14	0.697123
$382$	1.78983e14	1.12580
$383$	9.02294e13	0.559441	0.279721	−	0.960081i	$-0.409758\pi$
$383$	9.02294e13	0.559441	0.279721	+	0.960081i	$0.409758\pi$
$384$	−4.97292e13	−0.303941
$385$	4.16885e13	0.251178
$386$	3.21645e13	0.191050
$387$	9.01191e13	0.527724
$388$	1.02390e14	0.591131
$389$	9.40791e13	0.535513	0.267757	−	0.963487i	$-0.413718\pi$
$389$	9.40791e13	0.535513	0.267757	+	0.963487i	$0.413718\pi$
$390$	2.52845e13	0.141905
$391$	−1.07782e13	−0.0596451
$392$	−1.16130e14	−0.633681
$393$	1.04391e13	0.0561700
$394$	−1.51724e13	−0.0805056
$395$	1.35159e14	0.707229
$396$	−1.67031e13	−0.0861931
$397$	−1.61469e14	−0.821753	−0.410877	−	0.911691i	$-0.634777\pi$
$397$	−1.61469e14	−0.821753	−0.410877	+	0.911691i	$0.634777\pi$
$398$	9.59796e13	0.481750
$399$	2.22034e14	1.09918
$400$	−2.87702e12	−0.0140479
$401$	1.09960e14	0.529592	0.264796	−	0.964304i	$-0.414695\pi$
$401$	1.09960e14	0.529592	0.264796	+	0.964304i	$0.414695\pi$
$402$	−7.06558e13	−0.335664
$403$	−2.21792e14	−1.03936
$404$	−7.25199e13	−0.335243
$405$	−1.08962e13	−0.0496904
$406$	−1.46325e14	−0.658303
$407$	−5.75163e13	−0.255283
$408$	2.74184e13	0.120063
$409$	1.49361e14	0.645296	0.322648	−	0.946519i	$-0.395427\pi$
$409$	1.49361e14	0.645296	0.322648	+	0.946519i	$0.395427\pi$
$410$	1.02630e14	0.437484
$411$	−1.77791e13	−0.0747792
$412$	−2.66015e14	−1.10401
$413$	4.87378e14	1.99591
$414$	1.55295e13	0.0627560
$415$	1.58944e14	0.633841
$416$	−2.11707e14	−0.833149
$417$	1.36449e14	0.529934
$418$	−1.10710e14	−0.424344
$419$	−3.37386e14	−1.27629	−0.638147	−	0.769915i	$-0.720299\pi$
$419$	−3.37386e14	−1.27629	−0.638147	+	0.769915i	$0.720299\pi$
$420$	−5.16110e13	−0.192695
$421$	1.85109e14	0.682144	0.341072	−	0.940037i	$-0.389210\pi$
$421$	1.85109e14	0.682144	0.341072	+	0.940037i	$0.389210\pi$
$422$	1.23266e14	0.448356
$423$	−1.76106e14	−0.632271
$424$	−8.87407e12	−0.0314493
$425$	−1.16514e13	−0.0407606
$426$	8.78820e13	0.303492
$427$	−4.43955e14	−1.51351
$428$	2.74225e14	0.922924
$429$	−6.54875e13	−0.217592
$430$	−1.38845e14	−0.455465
$431$	2.44075e13	0.0790495	0.0395248	−	0.999219i	$-0.487416\pi$
$431$	2.44075e13	0.0790495	0.0395248	+	0.999219i	$0.487416\pi$
$432$	−4.22728e12	−0.0135176
$433$	−1.15877e14	−0.365858	−0.182929	−	0.983126i	$-0.558558\pi$
$433$	−1.15877e14	−0.365858	−0.182929	+	0.983126i	$0.558558\pi$
$434$	−3.19622e14	−0.996420
$435$	−6.74161e13	−0.207526
$436$	6.23305e13	0.189463
$437$	−1.45796e14	−0.437621
$438$	−1.07034e14	−0.317259
$439$	8.13540e12	0.0238135	0.0119068	−	0.999929i	$-0.496210\pi$
$439$	8.13540e12	0.0238135	0.0119068	+	0.999929i	$0.496210\pi$
$440$	6.96366e13	0.201302
$441$	7.25105e13	0.207009
$442$	3.97262e13	0.112009
$443$	8.68327e11	0.00241804	0.00120902	−	0.999999i	$-0.499615\pi$
$443$	8.68327e11	0.00241804	0.00120902	+	0.999999i	$0.499615\pi$
$444$	7.12061e13	0.195844
$445$	−7.37073e13	−0.200231
$446$	−1.27877e13	−0.0343123
$447$	9.34668e13	0.247723
$448$	−3.39248e14	−0.888155
$449$	5.97599e14	1.54545	0.772726	−	0.634740i	$-0.218893\pi$
$449$	5.97599e14	1.54545	0.772726	+	0.634740i	$0.218893\pi$
$450$	1.67876e13	0.0428865
$451$	−2.65814e14	−0.670821
$452$	−1.85626e13	−0.0462782
$453$	1.28788e14	0.317201
$454$	−1.95025e14	−0.474551
$455$	−2.02351e14	−0.486454
$456$	3.70887e14	0.880916
$457$	1.39757e14	0.327971	0.163985	−	0.986463i	$-0.447565\pi$
$457$	1.39757e14	0.327971	0.163985	+	0.986463i	$0.447565\pi$
$458$	4.60818e14	1.06849
$459$	−1.71198e13	−0.0392219
$460$	3.38898e13	0.0767187
$461$	−7.80055e14	−1.74490	−0.872449	−	0.488705i	$-0.837469\pi$
$461$	−7.80055e14	−1.74490	−0.872449	+	0.488705i	$0.837469\pi$
$462$	−9.43733e13	−0.208602
$463$	−4.16977e14	−0.910786	−0.455393	−	0.890291i	$-0.650501\pi$
$463$	−4.16977e14	−0.910786	−0.455393	+	0.890291i	$0.650501\pi$
$464$	−2.61547e13	−0.0564548
$465$	−1.47259e14	−0.314116
$466$	−3.06671e14	−0.646473
$467$	2.97874e14	0.620569	0.310285	−	0.950644i	$-0.399576\pi$
$467$	2.97874e14	0.620569	0.310285	+	0.950644i	$0.399576\pi$
$468$	8.10746e13	0.166929
$469$	5.65456e14	1.15066
$470$	2.71325e14	0.545697
$471$	1.06186e14	0.211082
$472$	8.14119e14	1.59958
$473$	3.59614e14	0.698393
$474$	−3.05969e14	−0.587350
$475$	−1.57608e14	−0.299064
$476$	−8.10896e13	−0.152099
$477$	5.54088e12	0.0102737
$478$	4.60558e14	0.844171
$479$	−7.31950e14	−1.32628	−0.663141	−	0.748494i	$-0.730777\pi$
$479$	−7.31950e14	−1.32628	−0.663141	+	0.748494i	$0.730777\pi$
$480$	−1.40563e14	−0.251794
$481$	2.79177e14	0.494403
$482$	5.82900e14	1.02055
$483$	−1.24282e14	−0.215129
$484$	2.75856e14	0.472099
$485$	2.66536e14	0.451000
$486$	2.46666e13	0.0412676
$487$	7.75754e14	1.28326	0.641630	−	0.767014i	$-0.278258\pi$
$487$	7.75754e14	1.28326	0.641630	+	0.767014i	$0.278258\pi$
$488$	−7.41585e14	−1.21298
$489$	−5.03134e13	−0.0813739
$490$	−1.11716e14	−0.178664
$491$	−9.48333e14	−1.49973	−0.749865	−	0.661591i	$-0.769881\pi$
$491$	−9.48333e14	−1.49973	−0.749865	+	0.661591i	$0.769881\pi$
$492$	3.29082e14	0.514631
$493$	−1.05922e14	−0.163806
$494$	5.37373e14	0.821822
$495$	−4.34805e13	−0.0657606
$496$	−5.71304e13	−0.0854511
$497$	−7.03316e14	−1.04038
$498$	−3.59814e14	−0.526401
$499$	6.44054e14	0.931901	0.465950	−	0.884811i	$-0.345713\pi$
$499$	6.44054e14	0.931901	0.465950	+	0.884811i	$0.345713\pi$
$500$	3.66355e13	0.0524284
$501$	1.41261e14	0.199947
$502$	8.55080e14	1.19712
$503$	−4.01173e13	−0.0555531	−0.0277765	−	0.999614i	$-0.508843\pi$
$503$	−4.01173e13	−0.0555531	−0.0277765	+	0.999614i	$0.508843\pi$
$504$	3.16157e14	0.433047
$505$	−1.88780e14	−0.255772
$506$	6.19693e13	0.0830517
$507$	−1.17627e14	−0.155942
$508$	−5.39688e14	−0.707770
$509$	2.27943e14	0.295718	0.147859	−	0.989008i	$-0.452762\pi$
$509$	2.27943e14	0.295718	0.147859	+	0.989008i	$0.452762\pi$
$510$	2.63762e13	0.0338514
$511$	8.56589e14	1.08757
$512$	−1.11592e14	−0.140168
$513$	−2.31578e14	−0.287774
$514$	4.63491e14	0.569829
$515$	−6.92475e14	−0.842296
$516$	−4.45208e14	−0.535783
$517$	−7.02739e14	−0.836751
$518$	4.02319e14	0.473976
$519$	−7.18429e14	−0.837458
$520$	−3.38008e14	−0.389859
$521$	−7.39422e14	−0.843888	−0.421944	−	0.906622i	$-0.638652\pi$
$521$	−7.39422e14	−0.843888	−0.421944	+	0.906622i	$0.638652\pi$
$522$	1.52615e14	0.172349
$523$	−1.18627e14	−0.132563	−0.0662815	−	0.997801i	$-0.521114\pi$
$523$	−1.18627e14	−0.132563	−0.0662815	+	0.997801i	$0.521114\pi$
$524$	−5.15714e13	−0.0570278
$525$	−1.34351e14	−0.147016
$526$	−9.10801e14	−0.986283
$527$	−2.31368e14	−0.247939
$528$	−1.68686e13	−0.0178893
$529$	−8.71201e14	−0.914350
$530$	−8.53677e12	−0.00886699
$531$	−5.08328e14	−0.522546
$532$	−1.09689e15	−1.11597
$533$	1.29023e15	1.29917
$534$	1.66857e14	0.166290
$535$	7.13847e14	0.704140
$536$	9.44541e14	0.922177
$537$	3.50103e14	0.338328
$538$	−2.81556e14	−0.269316
$539$	2.89347e14	0.273956
$540$	5.38295e13	0.0504493
$541$	1.57725e14	0.146324	0.0731622	−	0.997320i	$-0.476691\pi$
$541$	1.57725e14	0.146324	0.0731622	+	0.997320i	$0.476691\pi$
$542$	−1.03763e15	−0.952900
$543$	−1.09424e15	−0.994751
$544$	−2.20849e14	−0.198747
$545$	1.62255e14	0.144550
$546$	4.58076e14	0.403997
$547$	1.19330e15	1.04188	0.520941	−	0.853592i	$-0.325581\pi$
$547$	1.19330e15	1.04188	0.520941	+	0.853592i	$0.325581\pi$
$548$	8.78327e13	0.0759212
$549$	4.63039e14	0.396250
$550$	6.69898e13	0.0567563
$551$	−1.43280e15	−1.20186
$552$	−2.07601e14	−0.172411
$553$	2.44866e15	2.01345
$554$	−8.19344e14	−0.667057
$555$	1.85360e14	0.149418
$556$	−6.74087e14	−0.538028
$557$	1.44342e15	1.14074	0.570372	−	0.821386i	$-0.306799\pi$
$557$	1.44342e15	1.14074	0.570372	+	0.821386i	$0.306799\pi$
$558$	3.33361e14	0.260871
$559$	−1.74552e15	−1.35257
$560$	−5.21226e13	−0.0399938
$561$	−6.83152e13	−0.0519065
$562$	−1.53394e15	−1.15414
$563$	1.95149e15	1.45402	0.727009	−	0.686628i	$-0.240910\pi$
$563$	1.95149e15	1.45402	0.727009	+	0.686628i	$0.240910\pi$
$564$	8.70003e14	0.641927
$565$	−4.83211e13	−0.0353077
$566$	6.12070e14	0.442905
$567$	−1.97406e14	−0.141466
$568$	−1.17482e15	−0.833790
$569$	2.96647e14	0.208508	0.104254	−	0.994551i	$-0.466755\pi$
$569$	2.96647e14	0.208508	0.104254	+	0.994551i	$0.466755\pi$
$570$	3.56790e14	0.248371
$571$	2.67753e15	1.84601	0.923007	−	0.384782i	$-0.125723\pi$
$571$	2.67753e15	1.84601	0.923007	+	0.384782i	$0.125723\pi$
$572$	3.23522e14	0.220915
$573$	1.49397e15	1.01039
$574$	1.85933e15	1.24550
$575$	8.82201e13	0.0585322
$576$	3.53831e14	0.232527
$577$	−2.57076e14	−0.167338	−0.0836691	−	0.996494i	$-0.526664\pi$
$577$	−2.57076e14	−0.167338	−0.0836691	+	0.996494i	$0.526664\pi$
$578$	−9.56294e14	−0.616578
$579$	2.68476e14	0.171464
$580$	3.33050e14	0.210696
$581$	2.87958e15	1.80451
$582$	−6.03378e14	−0.374553
$583$	2.21105e13	0.0135963
$584$	1.43085e15	0.871613
$585$	2.11049e14	0.127358
$586$	−1.18948e15	−0.711085
$587$	−9.31911e14	−0.551906	−0.275953	−	0.961171i	$-0.588993\pi$
$587$	−9.31911e14	−0.551906	−0.275953	+	0.961171i	$0.588993\pi$
$588$	−3.58217e14	−0.210170
$589$	−3.12971e15	−1.81915
$590$	7.83175e14	0.450996
$591$	−1.26644e14	−0.0722525
$592$	7.19120e13	0.0406473
$593$	−3.24439e15	−1.81690	−0.908452	−	0.417989i	$-0.862735\pi$
$593$	−3.24439e15	−1.81690	−0.908452	+	0.417989i	$0.862735\pi$
$594$	9.84300e13	0.0546138
$595$	−2.11088e14	−0.116043
$596$	−4.61746e14	−0.251506
$597$	8.01139e14	0.432364
$598$	−3.00791e14	−0.160845
$599$	−9.95808e14	−0.527628	−0.263814	−	0.964574i	$-0.584981\pi$
$599$	−9.95808e14	−0.527628	−0.263814	+	0.964574i	$0.584981\pi$
$600$	−2.24421e14	−0.117823
$601$	−8.44194e14	−0.439170	−0.219585	−	0.975593i	$-0.570470\pi$
$601$	−8.44194e14	−0.439170	−0.219585	+	0.975593i	$0.570470\pi$
$602$	−2.51545e15	−1.29669
$603$	−5.89762e14	−0.301253
$604$	−6.36239e14	−0.322045
$605$	7.18093e14	0.360186
$606$	4.27355e14	0.212417
$607$	−1.02571e15	−0.505226	−0.252613	−	0.967567i	$-0.581290\pi$
$607$	−1.02571e15	−0.505226	−0.252613	+	0.967567i	$0.581290\pi$
$608$	−2.98741e15	−1.45823
$609$	−1.22137e15	−0.590817
$610$	−7.13398e14	−0.341994
$611$	3.41101e15	1.62053
$612$	8.45753e13	0.0398209
$613$	1.14237e15	0.533059	0.266529	−	0.963827i	$-0.414123\pi$
$613$	1.14237e15	0.533059	0.266529	+	0.963827i	$0.414123\pi$
$614$	−1.32358e14	−0.0612103
$615$	8.56648e14	0.392635
$616$	1.26160e15	0.573097
$617$	−4.41494e14	−0.198773	−0.0993863	−	0.995049i	$-0.531688\pi$
$617$	−4.41494e14	−0.198773	−0.0993863	+	0.995049i	$0.531688\pi$
$618$	1.56761e15	0.699521
$619$	−6.66698e14	−0.294870	−0.147435	−	0.989072i	$-0.547102\pi$
$619$	−6.66698e14	−0.294870	−0.147435	+	0.989072i	$0.547102\pi$
$620$	7.27489e14	0.318913
$621$	1.29624e14	0.0563226
$622$	−5.17819e14	−0.223013
$623$	−1.33535e15	−0.570047
$624$	8.18783e13	0.0346460
$625$	9.53674e13	0.0400000
$626$	−1.40886e15	−0.585746
$627$	−9.24095e14	−0.380842
$628$	−5.24580e14	−0.214306
$629$	2.91231e14	0.117940
$630$	3.04140e14	0.122096
$631$	−9.96905e14	−0.396728	−0.198364	−	0.980128i	$-0.563563\pi$
$631$	−9.96905e14	−0.396728	−0.198364	+	0.980128i	$0.563563\pi$
$632$	4.09026e15	1.61364
$633$	1.02889e15	0.402393
$634$	−6.48445e13	−0.0251410
$635$	−1.40488e15	−0.539989
$636$	−2.73731e13	−0.0104306
$637$	−1.40446e15	−0.530568
$638$	6.08999e14	0.228088
$639$	7.33549e14	0.272379
$640$	6.39522e14	0.235432
$641$	2.57562e15	0.940076	0.470038	−	0.882646i	$-0.344240\pi$
$641$	2.57562e15	0.940076	0.470038	+	0.882646i	$0.344240\pi$
$642$	−1.61599e15	−0.584784
$643$	2.38099e15	0.854273	0.427137	−	0.904187i	$-0.359522\pi$
$643$	2.38099e15	0.854273	0.427137	+	0.904187i	$0.359522\pi$
$644$	6.13979e14	0.218414
$645$	−1.15894e15	−0.408773
$646$	5.60577e14	0.196045
$647$	2.00022e15	0.693594	0.346797	−	0.937940i	$-0.387269\pi$
$647$	2.00022e15	0.693594	0.346797	+	0.937940i	$0.387269\pi$
$648$	−3.29747e14	−0.113375
$649$	−2.02845e15	−0.691540
$650$	−3.25160e14	−0.109919
$651$	−2.66787e15	−0.894272
$652$	2.48559e14	0.0826166
$653$	−4.59960e15	−1.51600	−0.757998	−	0.652257i	$-0.773822\pi$
$653$	−4.59960e15	−1.51600	−0.757998	+	0.652257i	$0.773822\pi$
$654$	−3.67310e14	−0.120048
$655$	−1.34248e14	−0.0435091
$656$	3.32344e14	0.106811
$657$	−8.93410e14	−0.284735
$658$	4.91557e15	1.55357
$659$	−4.62481e14	−0.144952	−0.0724760	−	0.997370i	$-0.523090\pi$
$659$	−4.62481e14	−0.144952	−0.0724760	+	0.997370i	$0.523090\pi$
$660$	2.14803e14	0.0667649
$661$	3.62076e15	1.11607	0.558036	−	0.829817i	$-0.311555\pi$
$661$	3.62076e15	1.11607	0.558036	+	0.829817i	$0.311555\pi$
$662$	3.47713e14	0.106292
$663$	3.31593e14	0.100527
$664$	4.81006e15	1.44619
$665$	−2.85537e15	−0.851420
$666$	−4.19613e14	−0.124091
$667$	8.02002e14	0.235225
$668$	−6.97859e14	−0.203001
$669$	−1.06738e14	−0.0307948
$670$	9.08640e14	0.260004
$671$	1.84772e15	0.524400
$672$	−2.54657e15	−0.716845
$673$	−3.29629e15	−0.920327	−0.460164	−	0.887834i	$-0.652209\pi$
$673$	−3.29629e15	−0.920327	−0.460164	+	0.887834i	$0.652209\pi$
$674$	5.19227e14	0.143790
$675$	1.40126e14	0.0384900
$676$	5.81103e14	0.158324
$677$	−5.06076e14	−0.136766	−0.0683830	−	0.997659i	$-0.521784\pi$
$677$	−5.06076e14	−0.136766	−0.0683830	+	0.997659i	$0.521784\pi$
$678$	1.09388e14	0.0293229
$679$	4.82881e15	1.28397
$680$	−3.52603e14	−0.0930007
$681$	−1.62787e15	−0.425902
$682$	1.33025e15	0.345239
$683$	3.02204e15	0.778011	0.389005	−	0.921235i	$-0.372819\pi$
$683$	3.02204e15	0.778011	0.389005	+	0.921235i	$0.372819\pi$
$684$	1.14405e15	0.292169
$685$	2.28641e14	0.0579237
$686$	1.23509e15	0.310396
$687$	3.84644e15	0.958952
$688$	−4.49621e14	−0.111201
$689$	−1.07321e14	−0.0263318
$690$	−1.99711e14	−0.0486106
$691$	−3.72816e15	−0.900255	−0.450128	−	0.892964i	$-0.648622\pi$
$691$	−3.72816e15	−0.900255	−0.450128	+	0.892964i	$0.648622\pi$
$692$	3.54919e15	0.850248
$693$	−7.87732e14	−0.187217
$694$	−1.00529e15	−0.237036
$695$	−1.75475e15	−0.410485
$696$	−2.04019e15	−0.473499
$697$	1.34594e15	0.309917
$698$	−2.24838e15	−0.513648
$699$	−2.55978e15	−0.580200
$700$	6.63722e14	0.149261
$701$	−3.09794e15	−0.691232	−0.345616	−	0.938376i	$-0.612330\pi$
$701$	−3.09794e15	−0.691232	−0.345616	+	0.938376i	$0.612330\pi$
$702$	−4.77767e14	−0.105770
$703$	3.93947e15	0.865333
$704$	1.41194e15	0.307727
$705$	2.26474e15	0.489755
$706$	−5.81837e15	−1.24846
$707$	−3.42010e15	−0.728170
$708$	2.51125e15	0.530526
$709$	−3.32378e15	−0.696752	−0.348376	−	0.937355i	$-0.613267\pi$
$709$	−3.32378e15	−0.696752	−0.348376	+	0.937355i	$0.613267\pi$
$710$	−1.13017e15	−0.235084
$711$	−2.55392e15	−0.527138
$712$	−2.23057e15	−0.456853
$713$	1.75183e15	0.356041
$714$	4.77856e14	0.0963733
$715$	8.42174e14	0.168546
$716$	−1.72958e15	−0.343495
$717$	3.84426e15	0.757631
$718$	1.20888e15	0.236429
$719$	−8.91970e15	−1.73118	−0.865588	−	0.500756i	$-0.833055\pi$
$719$	−8.91970e15	−1.73118	−0.865588	+	0.500756i	$0.833055\pi$
$720$	5.43632e13	0.0104707
$721$	−1.25455e16	−2.39797
$722$	4.19158e15	0.795104
$723$	4.86546e15	0.915931
$724$	5.40579e15	1.00994
$725$	8.66977e14	0.160749
$726$	−1.62560e15	−0.299132
$727$	7.27742e15	1.32904	0.664520	−	0.747270i	$-0.268636\pi$
$727$	7.27742e15	1.32904	0.664520	+	0.747270i	$0.268636\pi$
$728$	−6.12365e15	−1.10991
$729$	2.05891e14	0.0370370
$730$	1.37647e15	0.245748
$731$	−1.82089e15	−0.322655
$732$	−2.28751e15	−0.402302
$733$	−7.13370e15	−1.24521	−0.622605	−	0.782536i	$-0.713926\pi$
$733$	−7.13370e15	−1.24521	−0.622605	+	0.782536i	$0.713926\pi$
$734$	9.66734e14	0.167486
$735$	−9.32490e14	−0.160348
$736$	1.67218e15	0.285401
$737$	−2.35340e15	−0.398681
$738$	−1.93926e15	−0.326081
$739$	6.29983e15	1.05144	0.525720	−	0.850658i	$-0.323796\pi$
$739$	6.29983e15	1.05144	0.525720	+	0.850658i	$0.323796\pi$
$740$	−9.15716e14	−0.151700
$741$	4.48544e15	0.737573
$742$	−1.54660e14	−0.0252439
$743$	2.75042e15	0.445615	0.222808	−	0.974862i	$-0.428478\pi$
$743$	2.75042e15	0.445615	0.222808	+	0.974862i	$0.428478\pi$
$744$	−4.45643e15	−0.716698
$745$	−1.20199e15	−0.191885
$746$	−3.85106e15	−0.610262
$747$	−3.00336e15	−0.472437
$748$	3.37491e14	0.0526992
$749$	1.29327e16	2.00465
$750$	−2.15890e14	−0.0332198
$751$	−4.87884e15	−0.745241	−0.372621	−	0.927984i	$-0.621541\pi$
$751$	−4.87884e15	−0.745241	−0.372621	+	0.927984i	$0.621541\pi$
$752$	8.78627e14	0.133231
$753$	7.13733e15	1.07439
$754$	−2.95600e15	−0.441736
$755$	−1.65622e15	−0.245703
$756$	9.75225e14	0.143627
$757$	−1.73534e15	−0.253722	−0.126861	−	0.991921i	$-0.540490\pi$
$757$	−1.73534e15	−0.253722	−0.126861	+	0.991921i	$0.540490\pi$
$758$	−2.50744e14	−0.0363957
$759$	5.17256e14	0.0745377
$760$	−4.76963e15	−0.682355
$761$	1.02876e16	1.46116	0.730578	−	0.682829i	$-0.239251\pi$
$761$	1.02876e16	1.46116	0.730578	+	0.682829i	$0.239251\pi$
$762$	3.18034e15	0.448458
$763$	2.93957e15	0.411527
$764$	−7.38051e15	−1.02582
$765$	2.20162e14	0.0303811
$766$	2.62679e15	0.359888
$767$	9.84582e15	1.33930
$768$	−4.42982e15	−0.598273
$769$	−1.23019e16	−1.64959	−0.824796	−	0.565430i	$-0.808710\pi$
$769$	−1.23019e16	−1.64959	−0.824796	+	0.565430i	$0.808710\pi$
$770$	1.21365e15	0.161582
$771$	3.86875e15	0.511413
$772$	−1.32633e15	−0.174083
$773$	2.35957e15	0.307500	0.153750	−	0.988110i	$-0.450865\pi$
$773$	2.35957e15	0.307500	0.153750	+	0.988110i	$0.450865\pi$
$774$	2.62358e15	0.339484
$775$	1.89376e15	0.243313
$776$	8.06608e15	1.02902
$777$	3.35815e15	0.425387
$778$	2.73886e15	0.344495
$779$	1.82064e16	2.27389
$780$	−1.04263e15	−0.129303
$781$	2.92717e15	0.360469
$782$	−3.13779e14	−0.0383696
$783$	1.27387e15	0.154681
$784$	−3.61768e14	−0.0436206
$785$	−1.36556e15	−0.163503
$786$	3.03907e14	0.0361340
$787$	−1.02145e15	−0.120603	−0.0603014	−	0.998180i	$-0.519206\pi$
$787$	−1.02145e15	−0.120603	−0.0603014	+	0.998180i	$0.519206\pi$
$788$	6.25648e14	0.0733560
$789$	−7.60243e15	−0.885175
$790$	3.93479e15	0.454959
$791$	−8.75428e14	−0.100519
$792$	−1.31583e15	−0.150042
$793$	−8.96861e15	−1.01560
$794$	−4.70074e15	−0.528632
$795$	−7.12562e13	−0.00795799
$796$	−3.95780e15	−0.438967
$797$	−1.03317e16	−1.13802	−0.569012	−	0.822329i	$-0.692674\pi$
$797$	−1.03317e16	−1.13802	−0.569012	+	0.822329i	$0.692674\pi$
$798$	6.46393e15	0.707099
$799$	3.55829e15	0.386576
$800$	1.80766e15	0.195039
$801$	1.39275e15	0.149243
$802$	3.20120e15	0.340685
$803$	−3.56508e15	−0.376820
$804$	2.91355e15	0.305854
$805$	1.59828e15	0.166638
$806$	−6.45687e15	−0.668620
$807$	−2.35014e15	−0.241707
$808$	−5.71296e15	−0.583578
$809$	−1.79260e15	−0.181872	−0.0909359	−	0.995857i	$-0.528986\pi$
$809$	−1.79260e15	−0.181872	−0.0909359	+	0.995857i	$0.528986\pi$
$810$	−3.17214e14	−0.0319657
$811$	1.31722e16	1.31839	0.659196	−	0.751971i	$-0.270897\pi$
$811$	1.31722e16	1.31839	0.659196	+	0.751971i	$0.270897\pi$
$812$	6.03384e15	0.599840
$813$	−8.66109e15	−0.855213
$814$	−1.67443e15	−0.164223
$815$	6.47035e14	0.0630319
$816$	8.54137e13	0.00826479
$817$	−2.46311e16	−2.36735
$818$	4.34825e15	0.415118
$819$	3.82355e15	0.362581
$820$	−4.23202e15	−0.398632
$821$	1.05900e15	0.0990856	0.0495428	−	0.998772i	$-0.484224\pi$
$821$	1.05900e15	0.0990856	0.0495428	+	0.998772i	$0.484224\pi$
$822$	−5.17592e14	−0.0481053
$823$	1.36816e15	0.126310	0.0631550	−	0.998004i	$-0.479884\pi$
$823$	1.36816e15	0.126310	0.0631550	+	0.998004i	$0.479884\pi$
$824$	−2.09561e16	−1.92181
$825$	5.59162e14	0.0509379
$826$	1.41887e16	1.28396
$827$	−2.16177e16	−1.94325	−0.971626	−	0.236522i	$-0.923993\pi$
$827$	−2.16177e16	−1.94325	−0.971626	+	0.236522i	$0.923993\pi$
$828$	−6.40372e14	−0.0571828
$829$	1.05105e16	0.932337	0.466169	−	0.884696i	$-0.345634\pi$
$829$	1.05105e16	0.932337	0.466169	+	0.884696i	$0.345634\pi$
$830$	4.62724e15	0.407748
$831$	−6.83905e15	−0.598673
$832$	−6.85336e15	−0.595972
$833$	−1.46510e15	−0.126567
$834$	3.97235e15	0.340906
$835$	−1.81663e15	−0.154878
$836$	4.56523e15	0.386659
$837$	2.78255e15	0.234128
$838$	−9.82211e15	−0.821037
$839$	2.60531e15	0.216356	0.108178	−	0.994132i	$-0.465498\pi$
$839$	2.60531e15	0.216356	0.108178	+	0.994132i	$0.465498\pi$
$840$	−4.06581e15	−0.335437
$841$	−4.31889e15	−0.353993
$842$	5.38895e15	0.438822
$843$	−1.28038e16	−1.03583
$844$	−5.08296e15	−0.408539
$845$	1.51269e15	0.120792
$846$	−5.12687e15	−0.406738
$847$	1.30096e16	1.02543
$848$	−2.76445e13	−0.00216487
$849$	5.10893e15	0.397501
$850$	−3.39200e14	−0.0262212
$851$	−2.20509e15	−0.169361
$852$	−3.62389e15	−0.276539
$853$	5.98728e15	0.453952	0.226976	−	0.973900i	$-0.427116\pi$
$853$	5.98728e15	0.453952	0.226976	+	0.973900i	$0.427116\pi$
$854$	−1.29246e16	−0.973639
$855$	2.97811e15	0.222909
$856$	2.16029e16	1.60659
$857$	5.81347e15	0.429577	0.214788	−	0.976661i	$-0.431094\pi$
$857$	5.81347e15	0.429577	0.214788	+	0.976661i	$0.431094\pi$
$858$	−1.90649e15	−0.139977
$859$	1.33730e16	0.975587	0.487793	−	0.872959i	$-0.337802\pi$
$859$	1.33730e16	0.975587	0.487793	+	0.872959i	$0.337802\pi$
$860$	5.72541e15	0.415016
$861$	1.55198e16	1.11781
$862$	7.10561e14	0.0508524
$863$	−1.71805e15	−0.122173	−0.0610865	−	0.998132i	$-0.519457\pi$
$863$	−1.71805e15	−0.122173	−0.0610865	+	0.998132i	$0.519457\pi$
$864$	2.65604e15	0.187676
$865$	9.23905e15	0.648692
$866$	−3.37345e15	−0.235356
$867$	−7.98216e15	−0.553370
$868$	1.31799e16	0.907930
$869$	−1.01912e16	−0.697617
$870$	−1.96264e15	−0.133501
$871$	1.14231e16	0.772120
$872$	4.91027e15	0.329811
$873$	−5.03638e15	−0.336156
$874$	−4.24447e15	−0.281521
$875$	1.72776e15	0.113878
$876$	4.41363e15	0.289084
$877$	2.73327e16	1.77904	0.889519	−	0.456899i	$-0.151040\pi$
$877$	2.73327e16	1.77904	0.889519	+	0.456899i	$0.151040\pi$
$878$	2.36840e14	0.0153192
$879$	−9.92859e15	−0.638188
$880$	2.16932e14	0.0138570
$881$	−1.65865e16	−1.05290	−0.526450	−	0.850206i	$-0.676477\pi$
$881$	−1.65865e16	−1.05290	−0.526450	+	0.850206i	$0.676477\pi$
$882$	2.11095e15	0.133168
$883$	−4.38792e15	−0.275090	−0.137545	−	0.990496i	$-0.543921\pi$
$883$	−4.38792e15	−0.275090	−0.137545	+	0.990496i	$0.543921\pi$
$884$	−1.63814e15	−0.102062
$885$	6.53714e15	0.404762
$886$	2.52790e13	0.00155552
$887$	−2.92614e16	−1.78943	−0.894717	−	0.446634i	$-0.852623\pi$
$887$	−2.92614e16	−1.78943	−0.894717	+	0.446634i	$0.852623\pi$
$888$	5.60947e15	0.340918
$889$	−2.54522e16	−1.53732
$890$	−2.14579e15	−0.128808
$891$	8.21593e14	0.0490150
$892$	5.27310e14	0.0312651
$893$	4.81328e16	2.83634
$894$	2.72104e15	0.159360
$895$	−4.50235e15	−0.262067
$896$	1.15862e16	0.670263
$897$	−2.51070e15	−0.144356
$898$	1.73975e16	0.994186
$899$	1.72160e16	0.977809
$900$	−6.92252e14	−0.0390778
$901$	−1.11956e14	−0.00628144
$902$	−7.73847e15	−0.431538
$903$	−2.09964e16	−1.16376
$904$	−1.46232e15	−0.0805594
$905$	1.40720e16	0.770531
$906$	3.74931e15	0.204055
$907$	1.95252e15	0.105622	0.0528112	−	0.998605i	$-0.483182\pi$
$907$	1.95252e15	0.105622	0.0528112	+	0.998605i	$0.483182\pi$
$908$	8.04201e15	0.432407
$909$	3.56712e15	0.190641
$910$	−5.89090e15	−0.312935
$911$	−2.94345e16	−1.55420	−0.777098	−	0.629380i	$-0.783309\pi$
$911$	−2.94345e16	−1.55420	−0.777098	+	0.629380i	$0.783309\pi$
$912$	1.15539e15	0.0606395
$913$	−1.19847e16	−0.625226
$914$	4.06866e15	0.210983
$915$	−5.95472e15	−0.306934
$916$	−1.90022e16	−0.973597
$917$	−2.43215e15	−0.123868
$918$	−4.98397e14	−0.0252313
$919$	−1.24630e16	−0.627171	−0.313585	−	0.949560i	$-0.601530\pi$
$919$	−1.24630e16	−0.627171	−0.313585	+	0.949560i	$0.601530\pi$
$920$	2.66977e15	0.133549
$921$	−1.10479e15	−0.0549353
$922$	−2.27092e16	−1.12249
$923$	−1.42081e16	−0.698116
$924$	3.89156e15	0.190076
$925$	−2.38374e15	−0.115739
$926$	−1.21392e16	−0.585907
$927$	1.30848e16	0.627810
$928$	1.64332e16	0.783807
$929$	2.58205e16	1.22427	0.612136	−	0.790752i	$-0.290310\pi$
$929$	2.58205e16	1.22427	0.612136	+	0.790752i	$0.290310\pi$
$930$	−4.28705e15	−0.202070
$931$	−1.98183e16	−0.928632
$932$	1.26458e16	0.589061
$933$	−4.32222e15	−0.200151
$934$	8.67182e15	0.399211
$935$	8.78539e14	0.0402066
$936$	6.38688e15	0.290584
$937$	4.20770e15	0.190317	0.0951583	−	0.995462i	$-0.469664\pi$
$937$	4.20770e15	0.190317	0.0951583	+	0.995462i	$0.469664\pi$
$938$	1.64617e16	0.740219
$939$	−1.17597e16	−0.525698
$940$	−1.11883e16	−0.497234
$941$	3.22624e15	0.142545	0.0712727	−	0.997457i	$-0.477294\pi$
$941$	3.22624e15	0.142545	0.0712727	+	0.997457i	$0.477294\pi$
$942$	3.09132e15	0.135789
$943$	−1.01909e16	−0.445040
$944$	2.53614e15	0.110110
$945$	2.53865e15	0.109579
$946$	1.04692e16	0.449275
$947$	8.32429e14	0.0355159	0.0177579	−	0.999842i	$-0.494347\pi$
$947$	8.32429e14	0.0355159	0.0177579	+	0.999842i	$0.494347\pi$
$948$	1.26169e16	0.535188
$949$	1.73045e16	0.729784
$950$	−4.58834e15	−0.192387
$951$	−5.41255e14	−0.0225637
$952$	−6.38807e15	−0.264769
$953$	−3.30399e16	−1.36153	−0.680766	−	0.732501i	$-0.738353\pi$
$953$	−3.30399e16	−1.36153	−0.680766	+	0.732501i	$0.738353\pi$
$954$	1.61308e14	0.00660907
$955$	−1.92125e16	−0.782647
$956$	−1.89915e16	−0.769202
$957$	5.08330e15	0.204706
$958$	−2.13088e16	−0.853195
$959$	4.14227e15	0.164906
$960$	−4.55030e15	−0.180114
$961$	1.21969e16	0.480031
$962$	8.12749e15	0.318049
$963$	−1.34886e16	−0.524835
$964$	−2.40364e16	−0.929920
$965$	−3.45263e15	−0.132816
$966$	−3.61814e15	−0.138392
$967$	4.42983e16	1.68477	0.842386	−	0.538875i	$-0.181151\pi$
$967$	4.42983e16	1.68477	0.842386	+	0.538875i	$0.181151\pi$
$968$	2.17314e16	0.821812
$969$	4.67912e15	0.175948
$970$	7.75949e15	0.290127
$971$	−2.59210e16	−0.963709	−0.481855	−	0.876251i	$-0.660037\pi$
$971$	−2.59210e16	−0.963709	−0.481855	+	0.876251i	$0.660037\pi$
$972$	−1.01715e15	−0.0376027
$973$	−3.17906e16	−1.16863
$974$	2.25840e16	0.825519
$975$	−2.71410e15	−0.0986509
$976$	−2.31019e15	−0.0834974
$977$	−2.85417e16	−1.02579	−0.512896	−	0.858451i	$-0.671427\pi$
$977$	−2.85417e16	−1.02579	−0.512896	+	0.858451i	$0.671427\pi$
$978$	−1.46474e15	−0.0523476
$979$	5.55766e15	0.197509
$980$	4.60670e15	0.162797
$981$	−3.06593e15	−0.107741
$982$	−2.76082e16	−0.964773
$983$	1.27482e16	0.443000	0.221500	−	0.975160i	$-0.428905\pi$
$983$	1.27482e16	0.443000	0.221500	+	0.975160i	$0.428905\pi$
$984$	2.59244e16	0.895851
$985$	1.62865e15	0.0559666
$986$	−3.08364e15	−0.105376
$987$	4.10301e16	1.39431
$988$	−2.21590e16	−0.748838
$989$	1.37871e16	0.463332
$990$	−1.26582e15	−0.0423036
$991$	−2.28656e16	−0.759937	−0.379968	−	0.924999i	$-0.624065\pi$
$991$	−2.28656e16	−0.759937	−0.379968	+	0.924999i	$0.624065\pi$
$992$	3.58955e16	1.18639
$993$	2.90235e15	0.0953959
$994$	−2.04752e16	−0.669272
$995$	−1.03027e16	−0.334907
$996$	1.48372e16	0.479652
$997$	2.28135e16	0.733446	0.366723	−	0.930330i	$-0.380480\pi$
$997$	2.28135e16	0.733446	0.366723	+	0.930330i	$0.380480\pi$
$998$	1.87499e16	0.599490
$999$	−3.50250e15	−0.111370

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.12.a.b.1.2	✓	2
3.2	odd	2		45.12.a.e.1.1		2
4.3	odd	2		240.12.a.j.1.2		2
5.2	odd	4		75.12.b.c.49.3		4
5.3	odd	4		75.12.b.c.49.2		4
5.4	even	2		75.12.a.d.1.1		2
15.2	even	4		225.12.b.h.199.2		4
15.8	even	4		225.12.b.h.199.3		4
15.14	odd	2		225.12.a.g.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.12.a.b.1.2	✓	2	1.1	even	1	trivial
45.12.a.e.1.1		2	3.2	odd	2
75.12.a.d.1.1		2	5.4	even	2
75.12.b.c.49.2		4	5.3	odd	4
75.12.b.c.49.3		4	5.2	odd	4
225.12.a.g.1.2		2	15.14	odd	2
225.12.b.h.199.2		4	15.2	even	4
225.12.b.h.199.3		4	15.8	even	4
240.12.a.j.1.2		2	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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	15.a (trivial)

\(f(q)\)	\(=\)	\(q+29.1123 q^{2} +243.000 q^{3} -1200.47 q^{4} -3125.00 q^{5} +7074.30 q^{6} -56615.3 q^{7} -94570.6 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+29.1123 q^{2} +243.000 q^{3} -1200.47 q^{4} -3125.00 q^{5} +7074.30 q^{6} -56615.3 q^{7} -94570.6 q^{8} +59049.0 q^{9} -90976.1 q^{10} +235631. q^{11} -291715. q^{12} -1.14372e6 q^{13} -1.64821e6 q^{14} -759375. q^{15} -294606. q^{16} -1.19311e6 q^{17} +1.71905e6 q^{18} -1.61391e7 q^{19} +3.75147e6 q^{20} -1.37575e7 q^{21} +6.85976e6 q^{22} +9.03374e6 q^{23} -2.29807e7 q^{24} +9.76562e6 q^{25} -3.32964e7 q^{26} +1.43489e7 q^{27} +6.79651e7 q^{28} +8.87785e7 q^{29} -2.21072e7 q^{30} +1.93921e8 q^{31} +1.85104e8 q^{32} +5.72582e7 q^{33} -3.47341e7 q^{34} +1.76923e8 q^{35} -7.08866e7 q^{36} -2.44095e8 q^{37} -4.69846e8 q^{38} -2.77924e8 q^{39} +2.95533e8 q^{40} -1.12810e9 q^{41} -4.00514e8 q^{42} +1.52618e9 q^{43} -2.82868e8 q^{44} -1.84528e8 q^{45} +2.62993e8 q^{46} -2.98238e9 q^{47} -7.15894e7 q^{48} +1.22797e9 q^{49} +2.84300e8 q^{50} -2.89925e8 q^{51} +1.37300e9 q^{52} +9.38353e7 q^{53} +4.17730e8 q^{54} -7.36346e8 q^{55} +5.35415e9 q^{56} -3.92180e9 q^{57} +2.58455e9 q^{58} -8.60858e9 q^{59} +9.11608e8 q^{60} +7.84161e9 q^{61} +5.64549e9 q^{62} -3.34308e9 q^{63} +5.99216e9 q^{64} +3.57413e9 q^{65} +1.66692e9 q^{66} -9.98768e9 q^{67} +1.43229e9 q^{68} +2.19520e9 q^{69} +5.15064e9 q^{70} +1.24227e10 q^{71} -5.58430e9 q^{72} -1.51300e10 q^{73} -7.10618e9 q^{74} +2.37305e9 q^{75} +1.93745e10 q^{76} -1.33403e10 q^{77} -8.09103e9 q^{78} -4.32508e10 q^{79} +9.20645e8 q^{80} +3.48678e9 q^{81} -3.28415e10 q^{82} -5.08621e10 q^{83} +1.65155e10 q^{84} +3.72846e9 q^{85} +4.44305e10 q^{86} +2.15732e10 q^{87} -2.22837e10 q^{88} +2.35863e10 q^{89} -5.37205e9 q^{90} +6.47522e10 q^{91} -1.08447e10 q^{92} +4.71228e10 q^{93} -8.68240e10 q^{94} +5.04346e10 q^{95} +4.49803e10 q^{96} -8.52916e10 q^{97} +3.57491e10 q^{98} +1.39137e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 22 q^{2} + 486 q^{3} - 636 q^{4} - 6250 q^{5} - 5346 q^{6} - 10864 q^{7} - 18744 q^{8} + 118098 q^{9}+O(q^{10}) \) 2 * q - 22 * q^2 + 486 * q^3 - 636 * q^4 - 6250 * q^5 - 5346 * q^6 - 10864 * q^7 - 18744 * q^8 + 118098 * q^9	\( 2 q - 22 q^{2} + 486 q^{3} - 636 q^{4} - 6250 q^{5} - 5346 q^{6} - 10864 q^{7} - 18744 q^{8} + 118098 q^{9} + 68750 q^{10} - 361792 q^{11} - 154548 q^{12} - 2133732 q^{13} - 3986664 q^{14} - 1518750 q^{15} - 5326320 q^{16} - 7804588 q^{17} - 1299078 q^{18} - 15562224 q^{19} + 1987500 q^{20} - 2639952 q^{21} + 37395424 q^{22} - 37450248 q^{23} - 4554792 q^{24} + 19531250 q^{25} + 17305364 q^{26} + 28697814 q^{27} + 93790448 q^{28} - 70320668 q^{29} + 16706250 q^{30} + 298584872 q^{31} + 286993696 q^{32} - 87915456 q^{33} + 303194188 q^{34} + 33950000 q^{35} - 37555164 q^{36} + 236000956 q^{37} - 499330888 q^{38} - 518496876 q^{39} + 58575000 q^{40} - 464942588 q^{41} - 968759352 q^{42} - 242208600 q^{43} - 620095808 q^{44} - 369056250 q^{45} + 2638898832 q^{46} - 4375796920 q^{47} - 1294295760 q^{48} + 1343830130 q^{49} - 214843750 q^{50} - 1896514884 q^{51} + 814171912 q^{52} - 2189541388 q^{53} - 315675954 q^{54} + 1130600000 q^{55} + 8823318240 q^{56} - 3781620432 q^{57} + 10716478004 q^{58} - 5480385856 q^{59} + 482962500 q^{60} + 14557903980 q^{61} + 295874592 q^{62} - 641508336 q^{63} + 11089288256 q^{64} + 6667912500 q^{65} + 9087088032 q^{66} - 15918388888 q^{67} - 2299702856 q^{68} - 9100410264 q^{69} + 12458325000 q^{70} + 1120561024 q^{71} - 1106814456 q^{72} - 24521574348 q^{73} - 31645012364 q^{74} + 4746093750 q^{75} + 19700124976 q^{76} - 40673194368 q^{77} + 4205203452 q^{78} - 79243055560 q^{79} + 16644750000 q^{80} + 6973568802 q^{81} - 66736852348 q^{82} + 9245226696 q^{83} + 22791078864 q^{84} + 24389337500 q^{85} + 134816793608 q^{86} - 17087922324 q^{87} - 67584257664 q^{88} + 22117321236 q^{89} + 4059618750 q^{90} + 19457850112 q^{91} - 37083635424 q^{92} + 72556123896 q^{93} - 15603010256 q^{94} + 48631950000 q^{95} + 69739468128 q^{96} - 160363673468 q^{97} + 29827277722 q^{98} - 21363455808 q^{99}+O(q^{100}) \) 2 * q - 22 * q^2 + 486 * q^3 - 636 * q^4 - 6250 * q^5 - 5346 * q^6 - 10864 * q^7 - 18744 * q^8 + 118098 * q^9 + 68750 * q^10 - 361792 * q^11 - 154548 * q^12 - 2133732 * q^13 - 3986664 * q^14 - 1518750 * q^15 - 5326320 * q^16 - 7804588 * q^17 - 1299078 * q^18 - 15562224 * q^19 + 1987500 * q^20 - 2639952 * q^21 + 37395424 * q^22 - 37450248 * q^23 - 4554792 * q^24 + 19531250 * q^25 + 17305364 * q^26 + 28697814 * q^27 + 93790448 * q^28 - 70320668 * q^29 + 16706250 * q^30 + 298584872 * q^31 + 286993696 * q^32 - 87915456 * q^33 + 303194188 * q^34 + 33950000 * q^35 - 37555164 * q^36 + 236000956 * q^37 - 499330888 * q^38 - 518496876 * q^39 + 58575000 * q^40 - 464942588 * q^41 - 968759352 * q^42 - 242208600 * q^43 - 620095808 * q^44 - 369056250 * q^45 + 2638898832 * q^46 - 4375796920 * q^47 - 1294295760 * q^48 + 1343830130 * q^49 - 214843750 * q^50 - 1896514884 * q^51 + 814171912 * q^52 - 2189541388 * q^53 - 315675954 * q^54 + 1130600000 * q^55 + 8823318240 * q^56 - 3781620432 * q^57 + 10716478004 * q^58 - 5480385856 * q^59 + 482962500 * q^60 + 14557903980 * q^61 + 295874592 * q^62 - 641508336 * q^63 + 11089288256 * q^64 + 6667912500 * q^65 + 9087088032 * q^66 - 15918388888 * q^67 - 2299702856 * q^68 - 9100410264 * q^69 + 12458325000 * q^70 + 1120561024 * q^71 - 1106814456 * q^72 - 24521574348 * q^73 - 31645012364 * q^74 + 4746093750 * q^75 + 19700124976 * q^76 - 40673194368 * q^77 + 4205203452 * q^78 - 79243055560 * q^79 + 16644750000 * q^80 + 6973568802 * q^81 - 66736852348 * q^82 + 9245226696 * q^83 + 22791078864 * q^84 + 24389337500 * q^85 + 134816793608 * q^86 - 17087922324 * q^87 - 67584257664 * q^88 + 22117321236 * q^89 + 4059618750 * q^90 + 19457850112 * q^91 - 37083635424 * q^92 + 72556123896 * q^93 - 15603010256 * q^94 + 48631950000 * q^95 + 69739468128 * q^96 - 160363673468 * q^97 + 29827277722 * q^98 - 21363455808 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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