LMFDB - Embedded newform 14.12.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,12,Mod(1,14)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, 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("14.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	14.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:	$10.7568045278$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{352969}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 88242 $ x^2 - x - 88242
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-296.556$ of defining polynomial
Character	$\chi$	$=$	14.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+32.0000 q^{2} +419.112 q^{3} +1024.00 q^{4} +3651.34 q^{5} +13411.6 q^{6} +16807.0 q^{7} +32768.0 q^{8} -1492.18 q^{9} +O(q^{10})$	\(q+32.0000 q^{2} +419.112 q^{3} +1024.00 q^{4} +3651.34 q^{5} +13411.6 q^{6} +16807.0 q^{7} +32768.0 q^{8} -1492.18 q^{9} +116843. q^{10} +52654.1 q^{11} +429171. q^{12} +748007. q^{13} +537824. q^{14} +1.53032e6 q^{15} +1.04858e6 q^{16} +3.00372e6 q^{17} -47749.8 q^{18} +3.57665e6 q^{19} +3.73897e6 q^{20} +7.04401e6 q^{21} +1.68493e6 q^{22} -5.95295e6 q^{23} +1.37335e7 q^{24} -3.54959e7 q^{25} +2.39362e7 q^{26} -7.48698e7 q^{27} +1.72104e7 q^{28} -2.01806e8 q^{29} +4.89702e7 q^{30} -2.49368e8 q^{31} +3.35544e7 q^{32} +2.20680e7 q^{33} +9.61190e7 q^{34} +6.13680e7 q^{35} -1.52799e6 q^{36} +5.23379e8 q^{37} +1.14453e8 q^{38} +3.13499e8 q^{39} +1.19647e8 q^{40} +6.23002e8 q^{41} +2.25408e8 q^{42} -7.78742e8 q^{43} +5.39178e7 q^{44} -5.44845e6 q^{45} -1.90494e8 q^{46} -1.33304e9 q^{47} +4.39471e8 q^{48} +2.82475e8 q^{49} -1.13587e9 q^{50} +1.25889e9 q^{51} +7.65959e8 q^{52} +2.02948e9 q^{53} -2.39583e9 q^{54} +1.92258e8 q^{55} +5.50732e8 q^{56} +1.49901e9 q^{57} -6.45781e9 q^{58} -6.16234e8 q^{59} +1.56705e9 q^{60} -8.89926e9 q^{61} -7.97977e9 q^{62} -2.50791e7 q^{63} +1.07374e9 q^{64} +2.73123e9 q^{65} +7.06174e8 q^{66} +1.28503e10 q^{67} +3.07581e9 q^{68} -2.49495e9 q^{69} +1.96378e9 q^{70} +2.52870e10 q^{71} -4.88957e7 q^{72} -1.48743e10 q^{73} +1.67481e10 q^{74} -1.48767e10 q^{75} +3.66248e9 q^{76} +8.84957e8 q^{77} +1.00320e10 q^{78} +1.26801e10 q^{79} +3.82870e9 q^{80} -3.11145e10 q^{81} +1.99361e10 q^{82} +3.51486e10 q^{83} +7.21307e9 q^{84} +1.09676e10 q^{85} -2.49197e10 q^{86} -8.45795e10 q^{87} +1.72537e9 q^{88} -2.32552e10 q^{89} -1.74350e8 q^{90} +1.25718e10 q^{91} -6.09582e9 q^{92} -1.04513e11 q^{93} -4.26571e10 q^{94} +1.30595e10 q^{95} +1.40631e10 q^{96} +8.71423e10 q^{97} +9.03921e9 q^{98} -7.85693e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 64 q^{2} - 350 q^{3} + 2048 q^{4} + 3738 q^{5} - 11200 q^{6} + 33614 q^{7} + 65536 q^{8} + 412894 q^{9}+O(q^{10}) $ 2 * q + 64 * q^2 - 350 * q^3 + 2048 * q^4 + 3738 * q^5 - 11200 * q^6 + 33614 * q^7 + 65536 * q^8 + 412894 * q^9	\( 2 q + 64 q^{2} - 350 q^{3} + 2048 q^{4} + 3738 q^{5} - 11200 q^{6} + 33614 q^{7} + 65536 q^{8} + 412894 q^{9} + 119616 q^{10} + 953700 q^{11} - 358400 q^{12} - 225722 q^{13} + 1075648 q^{14} + 1463664 q^{15} + 2097152 q^{16} + 5116272 q^{17} + 13212608 q^{18} + 16531942 q^{19} + 3827712 q^{20} - 5882450 q^{21} + 30518400 q^{22} - 14101728 q^{23} - 11468800 q^{24} - 84316486 q^{25} - 7223104 q^{26} - 257333300 q^{27} + 34420736 q^{28} - 70893504 q^{29} + 46837248 q^{30} - 5164292 q^{31} + 67108864 q^{32} - 670937232 q^{33} + 163720704 q^{34} + 62824566 q^{35} + 422803456 q^{36} + 107289472 q^{37} + 529022144 q^{38} + 1062405512 q^{39} + 122486784 q^{40} + 172190088 q^{41} - 188238400 q^{42} + 878848156 q^{43} + 976588800 q^{44} + 30463986 q^{45} - 451255296 q^{46} - 1299140556 q^{47} - 367001600 q^{48} + 564950498 q^{49} - 2698127552 q^{50} - 365894100 q^{51} - 231139328 q^{52} + 7439756316 q^{53} - 8234665600 q^{54} + 270346104 q^{55} + 1101463552 q^{56} - 8465058484 q^{57} - 2268592128 q^{58} + 2219271558 q^{59} + 1498791936 q^{60} - 9739798838 q^{61} - 165257344 q^{62} + 6939509458 q^{63} + 2147483648 q^{64} + 2646838068 q^{65} - 21469991424 q^{66} + 2779087912 q^{67} + 5239062528 q^{68} + 3772375824 q^{69} + 2010386112 q^{70} + 21197540088 q^{71} + 13529710592 q^{72} - 14015230628 q^{73} + 3433263104 q^{74} + 22671773782 q^{75} + 16928708608 q^{76} + 16028835900 q^{77} + 33996976384 q^{78} - 21708444104 q^{79} + 3919577088 q^{80} + 35813079982 q^{81} + 5510082816 q^{82} + 10851702750 q^{83} - 6023628800 q^{84} + 11150672868 q^{85} + 28123140992 q^{86} - 185266159932 q^{87} + 31250841600 q^{88} - 125407177980 q^{89} + 974847552 q^{90} - 3793709654 q^{91} - 14440169472 q^{92} - 292333010968 q^{93} - 41572497792 q^{94} + 14182293696 q^{95} - 11744051200 q^{96} + 104692220416 q^{97} + 18078415936 q^{98} + 373302410100 q^{99}+O(q^{100}) \) 2 * q + 64 * q^2 - 350 * q^3 + 2048 * q^4 + 3738 * q^5 - 11200 * q^6 + 33614 * q^7 + 65536 * q^8 + 412894 * q^9 + 119616 * q^10 + 953700 * q^11 - 358400 * q^12 - 225722 * q^13 + 1075648 * q^14 + 1463664 * q^15 + 2097152 * q^16 + 5116272 * q^17 + 13212608 * q^18 + 16531942 * q^19 + 3827712 * q^20 - 5882450 * q^21 + 30518400 * q^22 - 14101728 * q^23 - 11468800 * q^24 - 84316486 * q^25 - 7223104 * q^26 - 257333300 * q^27 + 34420736 * q^28 - 70893504 * q^29 + 46837248 * q^30 - 5164292 * q^31 + 67108864 * q^32 - 670937232 * q^33 + 163720704 * q^34 + 62824566 * q^35 + 422803456 * q^36 + 107289472 * q^37 + 529022144 * q^38 + 1062405512 * q^39 + 122486784 * q^40 + 172190088 * q^41 - 188238400 * q^42 + 878848156 * q^43 + 976588800 * q^44 + 30463986 * q^45 - 451255296 * q^46 - 1299140556 * q^47 - 367001600 * q^48 + 564950498 * q^49 - 2698127552 * q^50 - 365894100 * q^51 - 231139328 * q^52 + 7439756316 * q^53 - 8234665600 * q^54 + 270346104 * q^55 + 1101463552 * q^56 - 8465058484 * q^57 - 2268592128 * q^58 + 2219271558 * q^59 + 1498791936 * q^60 - 9739798838 * q^61 - 165257344 * q^62 + 6939509458 * q^63 + 2147483648 * q^64 + 2646838068 * q^65 - 21469991424 * q^66 + 2779087912 * q^67 + 5239062528 * q^68 + 3772375824 * q^69 + 2010386112 * q^70 + 21197540088 * q^71 + 13529710592 * q^72 - 14015230628 * q^73 + 3433263104 * q^74 + 22671773782 * q^75 + 16928708608 * q^76 + 16028835900 * q^77 + 33996976384 * q^78 - 21708444104 * q^79 + 3919577088 * q^80 + 35813079982 * q^81 + 5510082816 * q^82 + 10851702750 * q^83 - 6023628800 * q^84 + 11150672868 * q^85 + 28123140992 * q^86 - 185266159932 * q^87 + 31250841600 * q^88 - 125407177980 * q^89 + 974847552 * q^90 - 3793709654 * q^91 - 14440169472 * q^92 - 292333010968 * q^93 - 41572497792 * q^94 + 14182293696 * q^95 - 11744051200 * q^96 + 104692220416 * q^97 + 18078415936 * q^98 + 373302410100 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	32.0000	0.707107
$2$	32.0000	0.707107
$3$	419.112	0.995779	0.497890	−	0.867240i	$-0.334108\pi$
$3$	419.112	0.995779	0.497890	+	0.867240i	$0.334108\pi$
$4$	1024.00	0.500000
$5$	3651.34	0.522537	0.261268	−	0.965266i	$-0.415859\pi$
$5$	3651.34	0.522537	0.261268	+	0.965266i	$0.415859\pi$
$6$	13411.6	0.704122
$7$	16807.0	0.377964
$7$	16807.0	0.377964
$8$	32768.0	0.353553
$9$	−1492.18	−0.00842340
$10$	116843.	0.369489
$11$	52654.1	0.0985762	0.0492881	−	0.998785i	$-0.484305\pi$
$11$	52654.1	0.0985762	0.0492881	+	0.998785i	$0.484305\pi$
$12$	429171.	0.497890
$13$	748007.	0.558750	0.279375	−	0.960182i	$-0.409873\pi$
$13$	748007.	0.558750	0.279375	+	0.960182i	$0.409873\pi$
$14$	537824.	0.267261
$15$	1.53032e6	0.520331
$16$	1.04858e6	0.250000
$17$	3.00372e6	0.513086	0.256543	−	0.966533i	$-0.417416\pi$
$17$	3.00372e6	0.513086	0.256543	+	0.966533i	$0.417416\pi$
$18$	−47749.8	−0.00595624
$19$	3.57665e6	0.331384	0.165692	−	0.986178i	$-0.447014\pi$
$19$	3.57665e6	0.331384	0.165692	+	0.986178i	$0.447014\pi$
$20$	3.73897e6	0.261268
$21$	7.04401e6	0.376369
$22$	1.68493e6	0.0697039
$23$	−5.95295e6	−0.192854	−0.0964270	−	0.995340i	$-0.530741\pi$
$23$	−5.95295e6	−0.192854	−0.0964270	+	0.995340i	$0.530741\pi$
$24$	1.37335e7	0.352061
$25$	−3.54959e7	−0.726955
$26$	2.39362e7	0.395096
$27$	−7.48698e7	−1.00417
$28$	1.72104e7	0.188982
$29$	−2.01806e8	−1.82703	−0.913516	−	0.406804i	$-0.866643\pi$
$29$	−2.01806e8	−1.82703	−0.913516	+	0.406804i	$0.866643\pi$
$30$	4.89702e7	0.367930
$31$	−2.49368e8	−1.56441	−0.782206	−	0.623020i	$-0.785906\pi$
$31$	−2.49368e8	−1.56441	−0.782206	+	0.623020i	$0.785906\pi$
$32$	3.35544e7	0.176777
$33$	2.20680e7	0.0981602
$34$	9.61190e7	0.362807
$35$	6.13680e7	0.197500
$36$	−1.52799e6	−0.00421170
$37$	5.23379e8	1.24082	0.620408	−	0.784280i	$-0.286967\pi$
$37$	5.23379e8	1.24082	0.620408	+	0.784280i	$0.286967\pi$
$38$	1.14453e8	0.234324
$39$	3.13499e8	0.556391
$40$	1.19647e8	0.184745
$41$	6.23002e8	0.839805	0.419902	−	0.907569i	$-0.362064\pi$
$41$	6.23002e8	0.839805	0.419902	+	0.907569i	$0.362064\pi$
$42$	2.25408e8	0.266133
$43$	−7.78742e8	−0.807824	−0.403912	−	0.914798i	$-0.632350\pi$
$43$	−7.78742e8	−0.807824	−0.403912	+	0.914798i	$0.632350\pi$
$44$	5.39178e7	0.0492881
$45$	−5.44845e6	−0.00440153
$46$	−1.90494e8	−0.136368
$47$	−1.33304e9	−0.847820	−0.423910	−	0.905704i	$-0.639343\pi$
$47$	−1.33304e9	−0.847820	−0.423910	+	0.905704i	$0.639343\pi$
$48$	4.39471e8	0.248945
$49$	2.82475e8	0.142857
$50$	−1.13587e9	−0.514035
$51$	1.25889e9	0.510921
$52$	7.65959e8	0.279375
$53$	2.02948e9	0.666604	0.333302	−	0.942820i	$-0.391837\pi$
$53$	2.02948e9	0.666604	0.333302	+	0.942820i	$0.391837\pi$
$54$	−2.39583e9	−0.710053
$55$	1.92258e8	0.0515097
$56$	5.50732e8	0.133631
$57$	1.49901e9	0.329985
$58$	−6.45781e9	−1.29191
$59$	−6.16234e8	−0.112217	−0.0561086	−	0.998425i	$-0.517869\pi$
$59$	−6.16234e8	−0.112217	−0.0561086	+	0.998425i	$0.517869\pi$
$60$	1.56705e9	0.260166
$61$	−8.89926e9	−1.34909	−0.674543	−	0.738235i	$-0.735659\pi$
$61$	−8.89926e9	−1.34909	−0.674543	+	0.738235i	$0.735659\pi$
$62$	−7.97977e9	−1.10621
$63$	−2.50791e7	−0.00318375
$64$	1.07374e9	0.125000
$65$	2.73123e9	0.291967
$66$	7.06174e8	0.0694097
$67$	1.28503e10	1.16279	0.581397	−	0.813620i	$-0.302506\pi$
$67$	1.28503e10	1.16279	0.581397	+	0.813620i	$0.302506\pi$
$68$	3.07581e9	0.256543
$69$	−2.49495e9	−0.192040
$70$	1.96378e9	0.139654
$71$	2.52870e10	1.66332	0.831660	−	0.555285i	$-0.187391\pi$
$71$	2.52870e10	1.66332	0.831660	+	0.555285i	$0.187391\pi$
$72$	−4.88957e7	−0.00297812
$73$	−1.48743e10	−0.839770	−0.419885	−	0.907577i	$-0.637930\pi$
$73$	−1.48743e10	−0.839770	−0.419885	+	0.907577i	$0.637930\pi$
$74$	1.67481e10	0.877389
$75$	−1.48767e10	−0.723887
$76$	3.66248e9	0.165692
$77$	8.84957e8	0.0372583
$78$	1.00320e10	0.393428
$79$	1.26801e10	0.463633	0.231816	−	0.972760i	$-0.425533\pi$
$79$	1.26801e10	0.463633	0.231816	+	0.972760i	$0.425533\pi$
$80$	3.82870e9	0.130634
$81$	−3.11145e10	−0.991506
$82$	1.99361e10	0.593832
$83$	3.51486e10	0.979443	0.489721	−	0.871879i	$-0.337098\pi$
$83$	3.51486e10	0.979443	0.489721	+	0.871879i	$0.337098\pi$
$84$	7.21307e9	0.188185
$85$	1.09676e10	0.268106
$86$	−2.49197e10	−0.571218
$87$	−8.45795e10	−1.81932
$88$	1.72537e9	0.0348520
$89$	−2.32552e10	−0.441442	−0.220721	−	0.975337i	$-0.570841\pi$
$89$	−2.32552e10	−0.441442	−0.220721	+	0.975337i	$0.570841\pi$
$90$	−1.74350e8	−0.00311235
$91$	1.25718e10	0.211188
$92$	−6.09582e9	−0.0964270
$93$	−1.04513e11	−1.55781
$94$	−4.26571e10	−0.599499
$95$	1.30595e10	0.173160
$96$	1.40631e10	0.176031
$97$	8.71423e10	1.03035	0.515175	−	0.857085i	$-0.327727\pi$
$97$	8.71423e10	1.03035	0.515175	+	0.857085i	$0.327727\pi$
$98$	9.03921e9	0.101015
$99$	−7.85693e7	−0.000830347 0
$100$	−3.63478e10	−0.363478
$101$	−2.04410e11	−1.93524	−0.967621	−	0.252407i	$-0.918778\pi$
$101$	−2.04410e11	−1.93524	−0.967621	+	0.252407i	$0.918778\pi$
$102$	4.02846e10	0.361275
$103$	1.64696e11	1.39984	0.699919	−	0.714222i	$-0.253219\pi$
$103$	1.64696e11	1.39984	0.699919	+	0.714222i	$0.253219\pi$
$104$	2.45107e10	0.197548
$105$	2.57201e10	0.196667
$106$	6.49434e10	0.471360
$107$	−4.50036e10	−0.310196	−0.155098	−	0.987899i	$-0.549569\pi$
$107$	−4.50036e10	−0.310196	−0.155098	+	0.987899i	$0.549569\pi$
$108$	−7.66667e10	−0.502084
$109$	2.47944e11	1.54350	0.771752	−	0.635924i	$-0.219381\pi$
$109$	2.47944e11	1.54350	0.771752	+	0.635924i	$0.219381\pi$
$110$	6.15225e9	0.0364229
$111$	2.19355e11	1.23558
$112$	1.76234e10	0.0944911
$113$	1.48530e11	0.758372	0.379186	−	0.925320i	$-0.376204\pi$
$113$	1.48530e11	0.758372	0.379186	+	0.925320i	$0.376204\pi$
$114$	4.79685e10	0.233335
$115$	−2.17362e10	−0.100773
$116$	−2.06650e11	−0.913516
$117$	−1.11616e9	−0.00470657
$118$	−1.97195e10	−0.0793496
$119$	5.04835e10	0.193928
$120$	5.01455e10	0.183965
$121$	−2.82539e11	−0.990283
$122$	−2.84776e11	−0.953948
$123$	2.61108e11	0.836261
$124$	−2.55353e11	−0.782206
$125$	−3.07895e11	−0.902398
$126$	−8.02530e8	−0.00225125
$127$	6.04769e11	1.62431	0.812155	−	0.583441i	$-0.198294\pi$
$127$	6.04769e11	1.62431	0.812155	+	0.583441i	$0.198294\pi$
$128$	3.43597e10	0.0883883
$129$	−3.26380e11	−0.804415
$130$	8.73992e10	0.206452
$131$	−5.99875e11	−1.35853	−0.679264	−	0.733894i	$-0.737701\pi$
$131$	−5.99875e11	−1.35853	−0.679264	+	0.733894i	$0.737701\pi$
$132$	2.25976e10	0.0490801
$133$	6.01127e10	0.125251
$134$	4.11210e11	0.822219
$135$	−2.73375e11	−0.524714
$136$	9.84259e10	0.181403
$137$	−6.17894e10	−0.109383	−0.0546916	−	0.998503i	$-0.517418\pi$
$137$	−6.17894e10	−0.109383	−0.0546916	+	0.998503i	$0.517418\pi$
$138$	−7.98384e10	−0.135793
$139$	2.40894e11	0.393772	0.196886	−	0.980426i	$-0.436917\pi$
$139$	2.40894e11	0.393772	0.196886	+	0.980426i	$0.436917\pi$
$140$	6.28408e10	0.0987501
$141$	−5.58691e11	−0.844241
$142$	8.09183e11	1.17615
$143$	3.93856e10	0.0550794
$144$	−1.56466e9	−0.00210585
$145$	−7.36863e11	−0.954691
$146$	−4.75977e11	−0.593807
$147$	1.18389e11	0.142254
$148$	5.35940e11	0.620408
$149$	−1.14011e12	−1.27181	−0.635907	−	0.771766i	$-0.719374\pi$
$149$	−1.14011e12	−1.27181	−0.635907	+	0.771766i	$0.719374\pi$
$150$	−4.76056e11	−0.511866
$151$	1.34036e12	1.38947	0.694735	−	0.719266i	$-0.255522\pi$
$151$	1.34036e12	1.38947	0.694735	+	0.719266i	$0.255522\pi$
$152$	1.17200e11	0.117162
$153$	−4.48209e9	−0.00432193
$154$	2.83186e10	0.0263456
$155$	−9.10526e11	−0.817463
$156$	3.21023e11	0.278196
$157$	1.37421e12	1.14975	0.574876	−	0.818240i	$-0.305050\pi$
$157$	1.37421e12	1.14975	0.574876	+	0.818240i	$0.305050\pi$
$158$	4.05764e11	0.327838
$159$	8.50580e11	0.663791
$160$	1.22518e11	0.0923723
$161$	−1.00051e11	−0.0728920
$162$	−9.95664e11	−0.701100
$163$	1.47870e12	1.00658	0.503289	−	0.864118i	$-0.332123\pi$
$163$	1.47870e12	1.00658	0.503289	+	0.864118i	$0.332123\pi$
$164$	6.37954e11	0.419902
$165$	8.05775e10	0.0512923
$166$	1.12476e12	0.692571
$167$	2.15824e12	1.28576	0.642878	−	0.765969i	$-0.277740\pi$
$167$	2.15824e12	1.28576	0.642878	+	0.765969i	$0.277740\pi$
$168$	2.30818e11	0.133067
$169$	−1.23265e12	−0.687799
$170$	3.50963e11	0.189580
$171$	−5.33700e9	−0.00279138
$172$	−7.97432e11	−0.403912
$173$	−6.17569e11	−0.302992	−0.151496	−	0.988458i	$-0.548409\pi$
$173$	−6.17569e11	−0.302992	−0.151496	+	0.988458i	$0.548409\pi$
$174$	−2.70654e12	−1.28645
$175$	−5.96579e11	−0.274763
$176$	5.52118e10	0.0246441
$177$	−2.58271e11	−0.111744
$178$	−7.44165e11	−0.312147
$179$	−4.10512e12	−1.66968	−0.834842	−	0.550489i	$-0.814441\pi$
$179$	−4.10512e12	−1.66968	−0.834842	+	0.550489i	$0.814441\pi$
$180$	−5.57921e9	−0.00220077
$181$	1.60660e12	0.614719	0.307360	−	0.951593i	$-0.400555\pi$
$181$	1.60660e12	0.614719	0.307360	+	0.951593i	$0.400555\pi$
$182$	4.02296e11	0.149332
$183$	−3.72979e12	−1.34339
$184$	−1.95066e11	−0.0681842
$185$	1.91103e12	0.648371
$186$	−3.34442e12	−1.10154
$187$	1.58158e11	0.0505781
$188$	−1.36503e12	−0.423910
$189$	−1.25834e12	−0.379540
$190$	4.17905e11	0.122443
$191$	2.13707e12	0.608326	0.304163	−	0.952620i	$-0.401623\pi$
$191$	2.13707e12	0.608326	0.304163	+	0.952620i	$0.401623\pi$
$192$	4.50018e11	0.124472
$193$	1.15529e11	0.0310546	0.0155273	−	0.999879i	$-0.495057\pi$
$193$	1.15529e11	0.0310546	0.0155273	+	0.999879i	$0.495057\pi$
$194$	2.78855e12	0.728567
$195$	1.14469e12	0.290735
$196$	2.89255e11	0.0714286
$197$	2.99021e12	0.718021	0.359011	−	0.933333i	$-0.383114\pi$
$197$	2.99021e12	0.718021	0.359011	+	0.933333i	$0.383114\pi$
$198$	−2.51422e9	−0.000587144 0
$199$	2.02024e12	0.458893	0.229446	−	0.973321i	$-0.426308\pi$
$199$	2.02024e12	0.458893	0.229446	+	0.973321i	$0.426308\pi$
$200$	−1.16313e12	−0.257018
$201$	5.38572e12	1.15789
$202$	−6.54113e12	−1.36842
$203$	−3.39176e12	−0.690553
$204$	1.28911e12	0.255460
$205$	2.27479e12	0.438829
$206$	5.27027e12	0.989835
$207$	8.88286e9	0.00162449
$208$	7.84342e11	0.139687
$209$	1.88325e11	0.0326666
$210$	8.23042e11	0.139064
$211$	−4.31868e12	−0.710883	−0.355441	−	0.934699i	$-0.615669\pi$
$211$	−4.31868e12	−0.710883	−0.355441	+	0.934699i	$0.615669\pi$
$212$	2.07819e12	0.333302
$213$	1.05981e13	1.65630
$214$	−1.44011e12	−0.219342
$215$	−2.84345e12	−0.422118
$216$	−2.45333e12	−0.355027
$217$	−4.19113e12	−0.591292
$218$	7.93421e12	1.09142
$219$	−6.23399e12	−0.836226
$220$	1.96872e11	0.0257548
$221$	2.24680e12	0.286687
$222$	7.01935e12	0.873686
$223$	−1.64662e12	−0.199948	−0.0999741	−	0.994990i	$-0.531876\pi$
$223$	−1.64662e12	−0.199948	−0.0999741	+	0.994990i	$0.531876\pi$
$224$	5.63949e11	0.0668153
$225$	5.29662e10	0.00612344
$226$	4.75296e12	0.536250
$227$	−2.77710e12	−0.305809	−0.152904	−	0.988241i	$-0.548863\pi$
$227$	−2.77710e12	−0.305809	−0.152904	+	0.988241i	$0.548863\pi$
$228$	1.53499e12	0.164993
$229$	−1.18625e13	−1.24475	−0.622374	−	0.782720i	$-0.713832\pi$
$229$	−1.18625e13	−1.24475	−0.622374	+	0.782720i	$0.713832\pi$
$230$	−6.95558e11	−0.0712575
$231$	3.70896e11	0.0371011
$232$	−6.61279e12	−0.645953
$233$	−1.08598e13	−1.03601	−0.518005	−	0.855378i	$-0.673325\pi$
$233$	−1.08598e13	−1.03601	−0.518005	+	0.855378i	$0.673325\pi$
$234$	−3.57172e10	−0.00332805
$235$	−4.86736e12	−0.443017
$236$	−6.31023e11	−0.0561086
$237$	5.31439e12	0.461676
$238$	1.61547e12	0.137128
$239$	−1.88146e13	−1.56066	−0.780328	−	0.625370i	$-0.784948\pi$
$239$	−1.88146e13	−1.56066	−0.780328	+	0.625370i	$0.784948\pi$
$240$	1.60466e12	0.130083
$241$	5.67490e12	0.449639	0.224820	−	0.974400i	$-0.427821\pi$
$241$	5.67490e12	0.449639	0.224820	+	0.974400i	$0.427821\pi$
$242$	−9.04126e12	−0.700236
$243$	2.22505e11	0.0168463
$244$	−9.11284e12	−0.674543
$245$	1.03141e12	0.0746481
$246$	8.35545e12	0.591325
$247$	2.67536e12	0.185161
$248$	−8.17129e12	−0.553103
$249$	1.47312e13	0.975309
$250$	−9.85265e12	−0.638091
$251$	2.54378e13	1.61166	0.805830	−	0.592147i	$-0.201719\pi$
$251$	2.54378e13	1.61166	0.805830	+	0.592147i	$0.201719\pi$
$252$	−2.56810e10	−0.00159187
$253$	−3.13447e11	−0.0190108
$254$	1.93526e13	1.14856
$255$	4.59665e12	0.266975
$256$	1.09951e12	0.0625000
$257$	−5.86280e12	−0.326192	−0.163096	−	0.986610i	$-0.552148\pi$
$257$	−5.86280e12	−0.326192	−0.163096	+	0.986610i	$0.552148\pi$
$258$	−1.04442e13	−0.568807
$259$	8.79644e12	0.468984
$260$	2.79677e12	0.145984
$261$	3.01131e11	0.0153898
$262$	−1.91960e13	−0.960625
$263$	4.11390e12	0.201603	0.100802	−	0.994907i	$-0.467859\pi$
$263$	4.11390e12	0.201603	0.100802	+	0.994907i	$0.467859\pi$
$264$	7.23123e11	0.0347049
$265$	7.41032e12	0.348325
$266$	1.92361e12	0.0885660
$267$	−9.74651e12	−0.439579
$268$	1.31587e13	0.581397
$269$	−1.20987e13	−0.523722	−0.261861	−	0.965106i	$-0.584336\pi$
$269$	−1.20987e13	−0.523722	−0.261861	+	0.965106i	$0.584336\pi$
$270$	−8.74799e12	−0.371029
$271$	5.65012e12	0.234815	0.117408	−	0.993084i	$-0.462542\pi$
$271$	5.65012e12	0.234815	0.117408	+	0.993084i	$0.462542\pi$
$272$	3.14963e12	0.128272
$273$	5.26897e12	0.210296
$274$	−1.97726e12	−0.0773456
$275$	−1.86900e12	−0.0716605
$276$	−2.55483e12	−0.0960200
$277$	3.04100e13	1.12041	0.560206	−	0.828354i	$-0.310722\pi$
$277$	3.04100e13	1.12041	0.560206	+	0.828354i	$0.310722\pi$
$278$	7.70862e12	0.278439
$279$	3.72102e11	0.0131777
$280$	2.01091e12	0.0698269
$281$	2.99116e13	1.01849	0.509243	−	0.860623i	$-0.329926\pi$
$281$	2.99116e13	1.01849	0.509243	+	0.860623i	$0.329926\pi$
$282$	−1.78781e13	−0.596969
$283$	−2.91560e13	−0.954780	−0.477390	−	0.878692i	$-0.658417\pi$
$283$	−2.91560e13	−0.954780	−0.477390	+	0.878692i	$0.658417\pi$
$284$	2.58939e13	0.831660
$285$	5.47341e12	0.172429
$286$	1.26034e12	0.0389470
$287$	1.04708e13	0.317416
$288$	−5.00692e10	−0.00148906
$289$	−2.52496e13	−0.736743
$290$	−2.35796e13	−0.675068
$291$	3.65224e13	1.02600
$292$	−1.52313e13	−0.419885
$293$	−1.26752e13	−0.342913	−0.171456	−	0.985192i	$-0.554847\pi$
$293$	−1.26752e13	−0.342913	−0.171456	+	0.985192i	$0.554847\pi$
$294$	3.78844e12	0.100589
$295$	−2.25008e12	−0.0586376
$296$	1.71501e13	0.438694
$297$	−3.94220e12	−0.0989870
$298$	−3.64836e13	−0.899309
$299$	−4.45285e12	−0.107757
$300$	−1.52338e13	−0.361944
$301$	−1.30883e13	−0.305329
$302$	4.28916e13	0.982503
$303$	−8.56708e13	−1.92707
$304$	3.75038e12	0.0828459
$305$	−3.24942e13	−0.704947
$306$	−1.43427e11	−0.00305607
$307$	2.70252e13	0.565598	0.282799	−	0.959179i	$-0.408737\pi$
$307$	2.70252e13	0.565598	0.282799	+	0.959179i	$0.408737\pi$
$308$	9.06196e11	0.0186292
$309$	6.90260e13	1.39393
$310$	−2.91368e13	−0.578034
$311$	−7.37241e13	−1.43690	−0.718452	−	0.695577i	$-0.755149\pi$
$311$	−7.37241e13	−1.43690	−0.718452	+	0.695577i	$0.755149\pi$
$312$	1.02727e13	0.196714
$313$	−9.43928e13	−1.77601	−0.888004	−	0.459835i	$-0.847909\pi$
$313$	−9.43928e13	−1.77601	−0.888004	+	0.459835i	$0.847909\pi$
$314$	4.39747e13	0.812998
$315$	−9.15721e10	−0.00166362
$316$	1.29844e13	0.231816
$317$	−2.42073e13	−0.424737	−0.212368	−	0.977190i	$-0.568118\pi$
$317$	−2.42073e13	−0.424737	−0.212368	+	0.977190i	$0.568118\pi$
$318$	2.72186e13	0.469371
$319$	−1.06259e13	−0.180102
$320$	3.92059e12	0.0653171
$321$	−1.88615e13	−0.308887
$322$	−3.20164e12	−0.0515424
$323$	1.07432e13	0.170028
$324$	−3.18612e13	−0.495753
$325$	−2.65512e13	−0.406186
$326$	4.73183e13	0.711758
$327$	1.03916e14	1.53699
$328$	2.04145e13	0.296916
$329$	−2.24043e13	−0.320446
$330$	2.57848e12	0.0362691
$331$	1.31244e14	1.81562	0.907812	−	0.419377i	$-0.137751\pi$
$331$	1.31244e14	1.81562	0.907812	+	0.419377i	$0.137751\pi$
$332$	3.59922e13	0.489721
$333$	−7.80976e11	−0.0104519
$334$	6.90636e13	0.909166
$335$	4.69208e13	0.607602
$336$	7.38618e12	0.0940923
$337$	6.83728e13	0.856877	0.428439	−	0.903571i	$-0.359064\pi$
$337$	6.83728e13	0.856877	0.428439	+	0.903571i	$0.359064\pi$
$338$	−3.94447e13	−0.486347
$339$	6.22506e13	0.755171
$340$	1.12308e13	0.134053
$341$	−1.31302e13	−0.154214
$342$	−1.70784e11	−0.00197380
$343$	4.74756e12	0.0539949
$344$	−2.55178e13	−0.285609
$345$	−9.10990e12	−0.100348
$346$	−1.97622e13	−0.214248
$347$	8.54214e12	0.0911496	0.0455748	−	0.998961i	$-0.485488\pi$
$347$	8.54214e12	0.0911496	0.0455748	+	0.998961i	$0.485488\pi$
$348$	−8.66094e13	−0.909660
$349$	−3.19725e12	−0.0330550	−0.0165275	−	0.999863i	$-0.505261\pi$
$349$	−3.19725e12	−0.0330550	−0.0165275	+	0.999863i	$0.505261\pi$
$350$	−1.90905e13	−0.194287
$351$	−5.60032e13	−0.561078
$352$	1.76678e12	0.0174260
$353$	−1.84044e14	−1.78715	−0.893576	−	0.448912i	$-0.851812\pi$
$353$	−1.84044e14	−1.78715	−0.893576	+	0.448912i	$0.851812\pi$
$354$	−8.26467e12	−0.0790147
$355$	9.23312e13	0.869146
$356$	−2.38133e13	−0.220721
$357$	2.11582e13	0.193110
$358$	−1.31364e14	−1.18065
$359$	1.31039e14	1.15980	0.579898	−	0.814689i	$-0.303093\pi$
$359$	1.31039e14	1.15980	0.579898	+	0.814689i	$0.303093\pi$
$360$	−1.78535e11	−0.00155618
$361$	−1.03698e14	−0.890185
$362$	5.14113e13	0.434672
$363$	−1.18416e14	−0.986103
$364$	1.28735e13	0.105594
$365$	−5.43110e13	−0.438811
$366$	−1.19353e14	−0.949922
$367$	1.39676e14	1.09511	0.547556	−	0.836769i	$-0.315558\pi$
$367$	1.39676e14	1.09511	0.547556	+	0.836769i	$0.315558\pi$
$368$	−6.24212e12	−0.0482135
$369$	−9.29631e11	−0.00707401
$370$	6.11531e13	0.458468
$371$	3.41095e13	0.251953
$372$	−1.07021e14	−0.778905
$373$	1.41141e14	1.01217	0.506085	−	0.862484i	$-0.331092\pi$
$373$	1.41141e14	1.01217	0.506085	+	0.862484i	$0.331092\pi$
$374$	5.06106e12	0.0357641
$375$	−1.29043e14	−0.898589
$376$	−4.36809e13	−0.299750
$377$	−1.50953e14	−1.02085
$378$	−4.02668e13	−0.268375
$379$	−1.92190e13	−0.126245	−0.0631227	−	0.998006i	$-0.520106\pi$
$379$	−1.92190e13	−0.126245	−0.0631227	+	0.998006i	$0.520106\pi$
$380$	1.33730e13	0.0865801
$381$	2.53466e14	1.61746
$382$	6.83864e13	0.430151
$383$	−8.68659e13	−0.538587	−0.269294	−	0.963058i	$-0.586790\pi$
$383$	−8.68659e13	−0.538587	−0.269294	+	0.963058i	$0.586790\pi$
$384$	1.44006e13	0.0880153
$385$	3.23128e12	0.0194688
$386$	3.69693e12	0.0219589
$387$	1.16202e12	0.00680463
$388$	8.92337e13	0.515175
$389$	8.55263e12	0.0486829	0.0243415	−	0.999704i	$-0.492251\pi$
$389$	8.55263e12	0.0486829	0.0243415	+	0.999704i	$0.492251\pi$
$390$	3.66301e13	0.205581
$391$	−1.78810e13	−0.0989508
$392$	9.25615e12	0.0505076
$393$	−2.51415e14	−1.35279
$394$	9.56867e13	0.507718
$395$	4.62994e13	0.242265
$396$	−8.04550e10	−0.000415173 0
$397$	1.28779e14	0.655384	0.327692	−	0.944785i	$-0.393729\pi$
$397$	1.28779e14	0.655384	0.327692	+	0.944785i	$0.393729\pi$
$398$	6.46477e13	0.324486
$399$	2.51939e13	0.124723
$400$	−3.72201e13	−0.181739
$401$	1.21493e14	0.585138	0.292569	−	0.956244i	$-0.405490\pi$
$401$	1.21493e14	0.585138	0.292569	+	0.956244i	$0.405490\pi$
$402$	1.72343e14	0.818749
$403$	−1.86529e14	−0.874115
$404$	−2.09316e14	−0.967621
$405$	−1.13609e14	−0.518098
$406$	−1.08536e14	−0.488295
$407$	2.75581e13	0.122315
$408$	4.12515e13	0.180638
$409$	2.97650e14	1.28596	0.642981	−	0.765882i	$-0.277697\pi$
$409$	2.97650e14	1.28596	0.642981	+	0.765882i	$0.277697\pi$
$410$	7.27933e13	0.310299
$411$	−2.58967e13	−0.108922
$412$	1.68649e14	0.699919
$413$	−1.03570e13	−0.0424141
$414$	2.84252e11	0.00114869
$415$	1.28340e14	0.511795
$416$	2.50990e13	0.0987739
$417$	1.00962e14	0.392110
$418$	6.02640e12	0.0230987
$419$	−2.12109e14	−0.802382	−0.401191	−	0.915994i	$-0.631404\pi$
$419$	−2.12109e14	−0.802382	−0.401191	+	0.915994i	$0.631404\pi$
$420$	2.63373e13	0.0983334
$421$	4.01743e14	1.48046	0.740230	−	0.672354i	$-0.234717\pi$
$421$	4.01743e14	1.48046	0.740230	+	0.672354i	$0.234717\pi$
$422$	−1.38198e14	−0.502670
$423$	1.98913e12	0.00714152
$424$	6.65021e13	0.235680
$425$	−1.06620e14	−0.372991
$426$	3.39138e14	1.17118
$427$	−1.49570e14	−0.509907
$428$	−4.60837e13	−0.155098
$429$	1.65070e13	0.0548470
$430$	−9.09903e13	−0.298482
$431$	8.24644e13	0.267080	0.133540	−	0.991043i	$-0.457366\pi$
$431$	8.24644e13	0.267080	0.133540	+	0.991043i	$0.457366\pi$
$432$	−7.85067e13	−0.251042
$433$	−4.65721e14	−1.47042	−0.735212	−	0.677837i	$-0.762918\pi$
$433$	−4.65721e14	−1.47042	−0.735212	+	0.677837i	$0.762918\pi$
$434$	−1.34116e14	−0.418107
$435$	−3.08828e14	−0.950661
$436$	2.53895e14	0.771752
$437$	−2.12916e13	−0.0639087
$438$	−1.99488e14	−0.591301
$439$	−5.69191e12	−0.0166611	−0.00833055	−	0.999965i	$-0.502652\pi$
$439$	−5.69191e12	−0.0166611	−0.00833055	+	0.999965i	$0.502652\pi$
$440$	6.29990e12	0.0182114
$441$	−4.21504e11	−0.00120334
$442$	7.18977e13	0.202718
$443$	−3.81071e14	−1.06117	−0.530586	−	0.847631i	$-0.678028\pi$
$443$	−3.81071e14	−1.06117	−0.530586	+	0.847631i	$0.678028\pi$
$444$	2.24619e14	0.617789
$445$	−8.49124e13	−0.230670
$446$	−5.26919e13	−0.141385
$447$	−4.77835e14	−1.26645
$448$	1.80464e13	0.0472456
$449$	1.41481e14	0.365884	0.182942	−	0.983124i	$-0.441438\pi$
$449$	1.41481e14	0.365884	0.182942	+	0.983124i	$0.441438\pi$
$450$	1.69492e12	0.00432992
$451$	3.28036e13	0.0827848
$452$	1.52095e14	0.379186
$453$	5.61762e14	1.38360
$454$	−8.88673e13	−0.216239
$455$	4.59037e13	0.110353
$456$	4.91197e13	0.116667
$457$	−4.19190e14	−0.983721	−0.491861	−	0.870674i	$-0.663683\pi$
$457$	−4.19190e14	−0.983721	−0.491861	+	0.870674i	$0.663683\pi$
$458$	−3.79600e14	−0.880170
$459$	−2.24888e14	−0.515224
$460$	−2.22579e13	−0.0503867
$461$	7.97169e14	1.78318	0.891590	−	0.452844i	$-0.149590\pi$
$461$	7.97169e14	1.78318	0.891590	+	0.452844i	$0.149590\pi$
$462$	1.18687e13	0.0262344
$463$	1.11913e14	0.244447	0.122224	−	0.992503i	$-0.460998\pi$
$463$	1.11913e14	0.244447	0.122224	+	0.992503i	$0.460998\pi$
$464$	−2.11609e14	−0.456758
$465$	−3.81612e14	−0.814013
$466$	−3.47513e14	−0.732569
$467$	1.54057e14	0.320951	0.160475	−	0.987040i	$-0.448697\pi$
$467$	1.54057e14	0.320951	0.160475	+	0.987040i	$0.448697\pi$
$468$	−1.14295e12	−0.00235329
$469$	2.15975e14	0.439495
$470$	−1.55756e14	−0.313260
$471$	5.75947e14	1.14490
$472$	−2.01928e13	−0.0396748
$473$	−4.10039e13	−0.0796323
$474$	1.70060e14	0.326454
$475$	−1.26956e14	−0.240901
$476$	5.16951e13	0.0969642
$477$	−3.02835e12	−0.00561507
$478$	−6.02068e14	−1.10355
$479$	−3.59556e13	−0.0651511	−0.0325755	−	0.999469i	$-0.510371\pi$
$479$	−3.59556e13	−0.0651511	−0.0325755	+	0.999469i	$0.510371\pi$
$480$	5.13490e13	0.0919824
$481$	3.91492e14	0.693305
$482$	1.81597e14	0.317943
$483$	−4.19326e13	−0.0725843
$484$	−2.89320e14	−0.495141
$485$	3.18186e14	0.538395
$486$	7.12017e12	0.0119122
$487$	−2.69322e14	−0.445515	−0.222757	−	0.974874i	$-0.571506\pi$
$487$	−2.69322e14	−0.445515	−0.222757	+	0.974874i	$0.571506\pi$
$488$	−2.91611e14	−0.476974
$489$	6.19740e14	1.00233
$490$	3.30052e13	0.0527842
$491$	1.11111e15	1.75715	0.878577	−	0.477601i	$-0.158493\pi$
$491$	1.11111e15	1.75715	0.878577	+	0.477601i	$0.158493\pi$
$492$	2.67374e14	0.418130
$493$	−6.06170e14	−0.937425
$494$	8.56114e13	0.130928
$495$	−2.86883e11	−0.000433887 0
$496$	−2.61481e14	−0.391103
$497$	4.24998e14	0.628676
$498$	4.71399e14	0.689648
$499$	−3.12674e14	−0.452417	−0.226209	−	0.974079i	$-0.572633\pi$
$499$	−3.12674e14	−0.452417	−0.226209	+	0.974079i	$0.572633\pi$
$500$	−3.15285e14	−0.451199
$501$	9.04542e14	1.28033
$502$	8.14009e14	1.13962
$503$	9.41365e14	1.30357	0.651785	−	0.758404i	$-0.274021\pi$
$503$	9.41365e14	1.30357	0.651785	+	0.758404i	$0.274021\pi$
$504$	−8.21791e11	−0.00112562
$505$	−7.46371e14	−1.01124
$506$	−1.00303e13	−0.0134427
$507$	−5.16616e14	−0.684896
$508$	6.19284e14	0.812155
$509$	−1.34027e14	−0.173877	−0.0869387	−	0.996214i	$-0.527708\pi$
$509$	−1.34027e14	−0.173877	−0.0869387	+	0.996214i	$0.527708\pi$
$510$	1.47093e14	0.188780
$511$	−2.49992e14	−0.317403
$512$	3.51844e13	0.0441942
$513$	−2.67783e14	−0.332765
$514$	−1.87610e14	−0.230652
$515$	6.01360e14	0.731467
$516$	−3.34213e14	−0.402207
$517$	−7.01897e13	−0.0835749
$518$	2.81486e14	0.331622
$519$	−2.58830e14	−0.301713
$520$	8.94968e13	0.103226
$521$	−1.42533e15	−1.62670	−0.813351	−	0.581773i	$-0.802359\pi$
$521$	−1.42533e15	−1.62670	−0.813351	+	0.581773i	$0.802359\pi$
$522$	9.63621e12	0.0108822
$523$	−1.54699e15	−1.72874	−0.864368	−	0.502859i	$-0.832281\pi$
$523$	−1.54699e15	−1.72874	−0.864368	+	0.502859i	$0.832281\pi$
$524$	−6.14272e14	−0.679264
$525$	−2.50033e14	−0.273604
$526$	1.31645e14	0.142555
$527$	−7.49031e14	−0.802679
$528$	2.31399e13	0.0245400
$529$	−9.17372e14	−0.962807
$530$	2.37130e14	0.246303
$531$	9.19532e11	0.000945250 0
$532$	6.15554e13	0.0626256
$533$	4.66010e14	0.469241
$534$	−3.11888e14	−0.310830
$535$	−1.64323e14	−0.162089
$536$	4.21079e14	0.411110
$537$	−1.72051e15	−1.66264
$538$	−3.87158e14	−0.370327
$539$	1.48735e13	0.0140823
$540$	−2.79936e14	−0.262357
$541$	−9.82068e12	−0.00911081	−0.00455540	−	0.999990i	$-0.501450\pi$
$541$	−9.82068e12	−0.00911081	−0.00455540	+	0.999990i	$0.501450\pi$
$542$	1.80804e14	0.166039
$543$	6.73347e14	0.612125
$544$	1.00788e14	0.0907017
$545$	9.05327e14	0.806537
$546$	1.68607e14	0.148702
$547$	2.98190e14	0.260353	0.130177	−	0.991491i	$-0.458446\pi$
$547$	2.98190e14	0.260353	0.130177	+	0.991491i	$0.458446\pi$
$548$	−6.32723e13	−0.0546916
$549$	1.32793e13	0.0113639
$550$	−5.98081e13	−0.0506716
$551$	−7.21790e14	−0.605448
$552$	−8.17545e13	−0.0678964
$553$	2.13115e14	0.175237
$554$	9.73119e14	0.792250
$555$	8.00937e14	0.645635
$556$	2.46676e14	0.196886
$557$	1.78336e15	1.40940	0.704700	−	0.709505i	$-0.251082\pi$
$557$	1.78336e15	1.40940	0.704700	+	0.709505i	$0.251082\pi$
$558$	1.19073e13	0.00931802
$559$	−5.82505e14	−0.451372
$560$	6.43490e13	0.0493751
$561$	6.62859e13	0.0503646
$562$	9.57171e14	0.720178
$563$	2.18552e15	1.62839	0.814194	−	0.580593i	$-0.197179\pi$
$563$	2.18552e15	1.62839	0.814194	+	0.580593i	$0.197179\pi$
$564$	−5.72100e14	−0.422121
$565$	5.42332e14	0.396277
$566$	−9.32994e14	−0.675131
$567$	−5.22941e14	−0.374754
$568$	8.28604e14	0.588073
$569$	−1.82764e15	−1.28462	−0.642309	−	0.766446i	$-0.722023\pi$
$569$	−1.82764e15	−1.28462	−0.642309	+	0.766446i	$0.722023\pi$
$570$	1.75149e14	0.121926
$571$	4.69262e14	0.323531	0.161766	−	0.986829i	$-0.448281\pi$
$571$	4.69262e14	0.323531	0.161766	+	0.986829i	$0.448281\pi$
$572$	4.03309e13	0.0275397
$573$	8.95673e14	0.605758
$574$	3.35066e14	0.224447
$575$	2.11305e14	0.140196
$576$	−1.60222e12	−0.00105292
$577$	−3.78595e14	−0.246438	−0.123219	−	0.992379i	$-0.539322\pi$
$577$	−3.78595e14	−0.246438	−0.123219	+	0.992379i	$0.539322\pi$
$578$	−8.07986e14	−0.520956
$579$	4.84196e13	0.0309235
$580$	−7.54548e14	−0.477345
$581$	5.90743e14	0.370195
$582$	1.16872e15	0.725492
$583$	1.06861e14	0.0657113
$584$	−4.87400e14	−0.296903
$585$	−4.07548e12	−0.00245936
$586$	−4.05607e14	−0.242476
$587$	−1.28152e14	−0.0758957	−0.0379479	−	0.999280i	$-0.512082\pi$
$587$	−1.28152e14	−0.0758957	−0.0379479	+	0.999280i	$0.512082\pi$
$588$	1.21230e14	0.0711271
$589$	−8.91901e14	−0.518421
$590$	−7.20025e13	−0.0414631
$591$	1.25323e15	0.714991
$592$	5.48803e14	0.310204
$593$	7.40481e13	0.0414680	0.0207340	−	0.999785i	$-0.493400\pi$
$593$	7.40481e13	0.0414680	0.0207340	+	0.999785i	$0.493400\pi$
$594$	−1.26150e14	−0.0699944
$595$	1.84332e14	0.101335
$596$	−1.16748e15	−0.635907
$597$	8.46707e14	0.456956
$598$	−1.42491e14	−0.0761958
$599$	−8.95710e14	−0.474592	−0.237296	−	0.971437i	$-0.576261\pi$
$599$	−8.95710e14	−0.474592	−0.237296	+	0.971437i	$0.576261\pi$
$600$	−4.87481e14	−0.255933
$601$	−3.89019e14	−0.202377	−0.101188	−	0.994867i	$-0.532265\pi$
$601$	−3.89019e14	−0.202377	−0.101188	+	0.994867i	$0.532265\pi$
$602$	−4.18826e14	−0.215900
$603$	−1.91750e13	−0.00979467
$604$	1.37253e15	0.694735
$605$	−1.03165e15	−0.517459
$606$	−2.74147e15	−1.36265
$607$	2.65623e15	1.30836	0.654181	−	0.756338i	$-0.273013\pi$
$607$	2.65623e15	1.30836	0.654181	+	0.756338i	$0.273013\pi$
$608$	1.20012e14	0.0585809
$609$	−1.42153e15	−0.687638
$610$	−1.03981e15	−0.498473
$611$	−9.97120e14	−0.473719
$612$	−4.58966e12	−0.00216097
$613$	2.36184e14	0.110209	0.0551047	−	0.998481i	$-0.482451\pi$
$613$	2.36184e14	0.110209	0.0551047	+	0.998481i	$0.482451\pi$
$614$	8.64806e14	0.399938
$615$	9.53392e14	0.436977
$616$	2.89983e13	0.0131728
$617$	−3.44029e15	−1.54891	−0.774457	−	0.632627i	$-0.781977\pi$
$617$	−3.44029e15	−1.54891	−0.774457	+	0.632627i	$0.781977\pi$
$618$	2.20883e15	0.985657
$619$	4.35026e15	1.92405	0.962026	−	0.272956i	$-0.0880014\pi$
$619$	4.35026e15	1.92405	0.962026	+	0.272956i	$0.0880014\pi$
$620$	−9.32379e14	−0.408731
$621$	4.45696e14	0.193658
$622$	−2.35917e15	−1.01604
$623$	−3.90849e14	−0.166850
$624$	3.28727e14	0.139098
$625$	6.08968e14	0.255420
$626$	−3.02057e15	−1.25583
$627$	7.89292e13	0.0325287
$628$	1.40719e15	0.574876
$629$	1.57208e15	0.636645
$630$	−2.93031e12	−0.00117636
$631$	−3.08396e15	−1.22729	−0.613646	−	0.789581i	$-0.710298\pi$
$631$	−3.08396e15	−1.22729	−0.613646	+	0.789581i	$0.710298\pi$
$632$	4.15502e14	0.163919
$633$	−1.81001e15	−0.707882
$634$	−7.74633e14	−0.300334
$635$	2.20822e15	0.848762
$636$	8.70994e14	0.331895
$637$	2.11294e14	0.0798214
$638$	−3.40030e14	−0.127351
$639$	−3.77327e13	−0.0140108
$640$	1.25459e14	0.0461862
$641$	−2.65356e15	−0.968524	−0.484262	−	0.874923i	$-0.660912\pi$
$641$	−2.65356e15	−0.968524	−0.484262	+	0.874923i	$0.660912\pi$
$642$	−6.03569e14	−0.218416
$643$	2.23849e14	0.0803147	0.0401574	−	0.999193i	$-0.487214\pi$
$643$	2.23849e14	0.0803147	0.0401574	+	0.999193i	$0.487214\pi$
$644$	−1.02452e14	−0.0364460
$645$	−1.19172e15	−0.420336
$646$	3.43784e14	0.120228
$647$	1.78413e15	0.618660	0.309330	−	0.950955i	$-0.399895\pi$
$647$	1.78413e15	0.618660	0.309330	+	0.950955i	$0.399895\pi$
$648$	−1.01956e15	−0.350550
$649$	−3.24472e13	−0.0110620
$650$	−8.49637e14	−0.287217
$651$	−1.75655e15	−0.588797
$652$	1.51419e15	0.503289
$653$	−3.07168e15	−1.01240	−0.506202	−	0.862415i	$-0.668951\pi$
$653$	−3.07168e15	−1.01240	−0.506202	+	0.862415i	$0.668951\pi$
$654$	3.32532e15	1.08682
$655$	−2.19035e15	−0.709881
$656$	6.53265e14	0.209951
$657$	2.21951e13	0.00707372
$658$	−7.16938e14	−0.226589
$659$	−1.76526e15	−0.553273	−0.276637	−	0.960975i	$-0.589220\pi$
$659$	−1.76526e15	−0.553273	−0.276637	+	0.960975i	$0.589220\pi$
$660$	8.25114e13	0.0256461
$661$	2.69734e15	0.831434	0.415717	−	0.909494i	$-0.363531\pi$
$661$	2.69734e15	0.831434	0.415717	+	0.909494i	$0.363531\pi$
$662$	4.19981e15	1.28384
$663$	9.41662e14	0.285477
$664$	1.15175e15	0.346285
$665$	2.19492e14	0.0654484
$666$	−2.49912e13	−0.00739060
$667$	1.20134e15	0.352350
$668$	2.21003e15	0.642878
$669$	−6.90119e14	−0.199104
$670$	1.50147e15	0.429640
$671$	−4.68582e14	−0.132988
$672$	2.36358e14	0.0665333
$673$	6.48757e15	1.81134	0.905668	−	0.423987i	$-0.139370\pi$
$673$	6.48757e15	1.81134	0.905668	+	0.423987i	$0.139370\pi$
$674$	2.18793e15	0.605904
$675$	2.65757e15	0.729985
$676$	−1.26223e15	−0.343899
$677$	−1.39346e15	−0.376580	−0.188290	−	0.982113i	$-0.560294\pi$
$677$	−1.39346e15	−0.376580	−0.188290	+	0.982113i	$0.560294\pi$
$678$	1.99202e15	0.533987
$679$	1.46460e15	0.389436
$680$	3.59386e14	0.0947899
$681$	−1.16392e15	−0.304518
$682$	−4.20168e14	−0.109046
$683$	−1.54689e15	−0.398240	−0.199120	−	0.979975i	$-0.563808\pi$
$683$	−1.54689e15	−0.398240	−0.199120	+	0.979975i	$0.563808\pi$
$684$	−5.46509e12	−0.00139569
$685$	−2.25614e14	−0.0571567
$686$	1.51922e14	0.0381802
$687$	−4.97172e15	−1.23949
$688$	−8.16570e14	−0.201956
$689$	1.51807e15	0.372465
$690$	−2.91517e14	−0.0709567
$691$	−8.91113e14	−0.215181	−0.107590	−	0.994195i	$-0.534314\pi$
$691$	−8.91113e14	−0.215181	−0.107590	+	0.994195i	$0.534314\pi$
$692$	−6.32390e14	−0.151496
$693$	−1.32051e12	−0.000313842 0
$694$	2.73349e14	0.0644525
$695$	8.79586e14	0.205760
$696$	−2.77150e15	−0.643227
$697$	1.87132e15	0.430892
$698$	−1.02312e14	−0.0233734
$699$	−4.55147e15	−1.03164
$700$	−6.10897e14	−0.137382
$701$	4.50934e15	1.00615	0.503076	−	0.864242i	$-0.332202\pi$
$701$	4.50934e15	1.00615	0.503076	+	0.864242i	$0.332202\pi$
$702$	−1.79210e15	−0.396742
$703$	1.87194e15	0.411186
$704$	5.65369e13	0.0123220
$705$	−2.03997e15	−0.441147
$706$	−5.88942e15	−1.26371
$707$	−3.43552e15	−0.731453
$708$	−2.64469e14	−0.0558718
$709$	4.09560e15	0.858545	0.429273	−	0.903175i	$-0.358770\pi$
$709$	4.09560e15	0.858545	0.429273	+	0.903175i	$0.358770\pi$
$710$	2.95460e15	0.614579
$711$	−1.89210e13	−0.00390537
$712$	−7.62025e14	−0.156073
$713$	1.48447e15	0.301703
$714$	6.77064e14	0.136549
$715$	1.43810e14	0.0287810
$716$	−4.20364e15	−0.834842
$717$	−7.88544e15	−1.55407
$718$	4.19325e15	0.820099
$719$	−4.39047e15	−0.852123	−0.426061	−	0.904694i	$-0.640099\pi$
$719$	−4.39047e15	−0.852123	−0.426061	+	0.904694i	$0.640099\pi$
$720$	−5.71311e12	−0.00110038
$721$	2.76804e15	0.529089
$722$	−3.31833e15	−0.629456
$723$	2.37842e15	0.447742
$724$	1.64516e15	0.307360
$725$	7.16329e15	1.32817
$726$	−3.78930e15	−0.697280
$727$	−8.89360e15	−1.62420	−0.812098	−	0.583521i	$-0.801674\pi$
$727$	−8.89360e15	−1.62420	−0.812098	+	0.583521i	$0.801674\pi$
$728$	4.11951e14	0.0746661
$729$	5.60509e15	1.00828
$730$	−1.73795e15	−0.310286
$731$	−2.33912e15	−0.414484
$732$	−3.81930e15	−0.671696
$733$	−2.05689e15	−0.359037	−0.179519	−	0.983755i	$-0.557454\pi$
$733$	−2.05689e15	−0.359037	−0.179519	+	0.983755i	$0.557454\pi$
$734$	4.46963e15	0.774361
$735$	4.32277e14	0.0743330
$736$	−1.99748e14	−0.0340921
$737$	6.76622e14	0.114624
$738$	−2.97482e13	−0.00500208
$739$	−8.64792e15	−1.44334	−0.721668	−	0.692240i	$-0.756624\pi$
$739$	−8.64792e15	−1.44334	−0.721668	+	0.692240i	$0.756624\pi$
$740$	1.95690e15	0.324186
$741$	1.12127e15	0.184379
$742$	1.09150e15	0.178157
$743$	−3.17198e15	−0.513915	−0.256958	−	0.966423i	$-0.582720\pi$
$743$	−3.17198e15	−0.513915	−0.256958	+	0.966423i	$0.582720\pi$
$744$	−3.42468e15	−0.550769
$745$	−4.16294e15	−0.664570
$746$	4.51650e15	0.715712
$747$	−5.24481e13	−0.00825024
$748$	1.61954e14	0.0252891
$749$	−7.56375e14	−0.117243
$750$	−4.12936e15	−0.635398
$751$	8.11260e15	1.23920	0.619599	−	0.784919i	$-0.287295\pi$
$751$	8.11260e15	1.23920	0.619599	+	0.784919i	$0.287295\pi$
$752$	−1.39779e15	−0.211955
$753$	1.06613e16	1.60486
$754$	−4.83048e15	−0.721852
$755$	4.89411e15	0.726049
$756$	−1.28854e15	−0.189770
$757$	7.59054e15	1.10980	0.554901	−	0.831916i	$-0.312756\pi$
$757$	7.59054e15	1.10980	0.554901	+	0.831916i	$0.312756\pi$
$758$	−6.15009e14	−0.0892690
$759$	−1.31369e14	−0.0189306
$760$	4.27935e14	0.0612213
$761$	−1.49003e15	−0.211631	−0.105815	−	0.994386i	$-0.533745\pi$
$761$	−1.49003e15	−0.211631	−0.105815	+	0.994386i	$0.533745\pi$
$762$	8.11091e15	1.14371
$763$	4.16719e15	0.583390
$764$	2.18836e15	0.304163
$765$	−1.63656e13	−0.00225837
$766$	−2.77971e15	−0.380839
$767$	−4.60947e14	−0.0627013
$768$	4.60818e14	0.0622362
$769$	4.09607e15	0.549253	0.274626	−	0.961551i	$-0.411446\pi$
$769$	4.09607e15	0.549253	0.274626	+	0.961551i	$0.411446\pi$
$770$	1.03401e14	0.0137665
$771$	−2.45717e15	−0.324815
$772$	1.18302e14	0.0155273
$773$	−7.00690e15	−0.913142	−0.456571	−	0.889687i	$-0.650923\pi$
$773$	−7.00690e15	−0.913142	−0.456571	+	0.889687i	$0.650923\pi$
$774$	3.71847e13	0.00481160
$775$	8.85153e15	1.13726
$776$	2.85548e15	0.364284
$777$	3.68669e15	0.467005
$778$	2.73684e14	0.0344240
$779$	2.22826e15	0.278298
$780$	1.17216e15	0.145367
$781$	1.33146e15	0.163964
$782$	−5.72191e14	−0.0699688
$783$	1.51092e16	1.83464
$784$	2.96197e14	0.0357143
$785$	5.01769e15	0.600788
$786$	−8.04527e15	−0.956570
$787$	−1.41659e16	−1.67257	−0.836283	−	0.548298i	$-0.815276\pi$
$787$	−1.41659e16	−1.67257	−0.836283	+	0.548298i	$0.815276\pi$
$788$	3.06197e15	0.359011
$789$	1.72419e15	0.200752
$790$	1.48158e15	0.171307
$791$	2.49634e15	0.286638
$792$	−2.57456e12	−0.000293572 0
$793$	−6.65671e15	−0.753802
$794$	4.12091e15	0.463427
$795$	3.10575e15	0.346855
$796$	2.06873e15	0.229446
$797$	−1.24720e16	−1.37378	−0.686890	−	0.726762i	$-0.741024\pi$
$797$	−1.24720e16	−1.37378	−0.686890	+	0.726762i	$0.741024\pi$
$798$	8.06206e14	0.0881922
$799$	−4.00407e15	−0.435005
$800$	−1.19104e15	−0.128509
$801$	3.47009e13	0.00371845
$802$	3.88779e15	0.413755
$803$	−7.83192e14	−0.0827813
$804$	5.51498e15	0.578943
$805$	−3.65320e14	−0.0380887
$806$	−5.96893e15	−0.618093
$807$	−5.07070e15	−0.521511
$808$	−6.69812e15	−0.684211
$809$	−1.18730e16	−1.20461	−0.602303	−	0.798268i	$-0.705750\pi$
$809$	−1.18730e16	−1.20461	−0.602303	+	0.798268i	$0.705750\pi$
$810$	−3.63550e15	−0.366351
$811$	−1.53598e16	−1.53734	−0.768672	−	0.639644i	$-0.779082\pi$
$811$	−1.53598e16	−1.53734	−0.768672	+	0.639644i	$0.779082\pi$
$812$	−3.47316e15	−0.345276
$813$	2.36803e15	0.233824
$814$	8.81858e14	0.0864897
$815$	5.39922e15	0.525974
$816$	1.32005e15	0.127730
$817$	−2.78528e15	−0.267700
$818$	9.52481e15	0.909312
$819$	−1.87593e13	−0.00177892
$820$	2.32939e15	0.219414
$821$	−1.83050e16	−1.71271	−0.856353	−	0.516392i	$-0.827275\pi$
$821$	−1.83050e16	−1.71271	−0.856353	+	0.516392i	$0.827275\pi$
$822$	−8.28693e14	−0.0770191
$823$	−1.48673e16	−1.37257	−0.686284	−	0.727333i	$-0.740759\pi$
$823$	−1.48673e16	−1.37257	−0.686284	+	0.727333i	$0.740759\pi$
$824$	5.39675e15	0.494918
$825$	−7.83321e14	−0.0713581
$826$	−3.31425e14	−0.0299913
$827$	−4.51455e15	−0.405821	−0.202910	−	0.979197i	$-0.565040\pi$
$827$	−4.51455e15	−0.405821	−0.202910	+	0.979197i	$0.565040\pi$
$828$	9.09605e12	0.000812243 0
$829$	−2.17763e16	−1.93168	−0.965839	−	0.259142i	$-0.916560\pi$
$829$	−2.17763e16	−1.93168	−0.965839	+	0.259142i	$0.916560\pi$
$830$	4.10686e15	0.361894
$831$	1.27452e16	1.11568
$832$	8.03167e14	0.0698437
$833$	8.48477e14	0.0732980
$834$	3.23077e15	0.277264
$835$	7.88044e15	0.671854
$836$	1.92845e14	0.0163333
$837$	1.86701e16	1.57093
$838$	−6.78748e15	−0.567370
$839$	1.09104e15	0.0906049	0.0453024	−	0.998973i	$-0.485575\pi$
$839$	1.09104e15	0.0906049	0.0453024	+	0.998973i	$0.485575\pi$
$840$	8.42795e14	0.0695322
$841$	2.85253e16	2.33804
$842$	1.28558e16	1.04684
$843$	1.25363e16	1.01419
$844$	−4.42233e15	−0.355441
$845$	−4.50080e15	−0.359400
$846$	6.36521e13	0.00504982
$847$	−4.74864e15	−0.374292
$848$	2.12807e15	0.166651
$849$	−1.22196e16	−0.950750
$850$	−3.41183e15	−0.263744
$851$	−3.11565e15	−0.239296
$852$	1.08524e16	0.828150
$853$	−1.42690e16	−1.08187	−0.540935	−	0.841064i	$-0.681930\pi$
$853$	−1.42690e16	−1.08187	−0.540935	+	0.841064i	$0.681930\pi$
$854$	−4.78624e15	−0.360559
$855$	−1.94872e13	−0.00145860
$856$	−1.47468e15	−0.109671
$857$	3.76432e13	0.00278159	0.00139079	−	0.999999i	$-0.499557\pi$
$857$	3.76432e13	0.00278159	0.00139079	+	0.999999i	$0.499557\pi$
$858$	5.28224e14	0.0387827
$859$	4.07641e15	0.297382	0.148691	−	0.988884i	$-0.452494\pi$
$859$	4.07641e15	0.297382	0.148691	+	0.988884i	$0.452494\pi$
$860$	−2.91169e15	−0.211059
$861$	4.38844e15	0.316077
$862$	2.63886e15	0.188854
$863$	1.64808e16	1.17197	0.585987	−	0.810320i	$-0.300707\pi$
$863$	1.64808e16	1.17197	0.585987	+	0.810320i	$0.300707\pi$
$864$	−2.51221e15	−0.177513
$865$	−2.25495e15	−0.158325
$866$	−1.49031e16	−1.03975
$867$	−1.05824e16	−0.733633
$868$	−4.29171e15	−0.295646
$869$	6.67660e14	0.0457032
$870$	−9.88250e15	−0.672219
$871$	9.61213e15	0.649710
$872$	8.12463e15	0.545711
$873$	−1.30032e14	−0.00867905
$874$	−6.81330e14	−0.0451903
$875$	−5.17480e15	−0.341074
$876$	−6.38361e15	−0.418113
$877$	6.27123e15	0.408183	0.204092	−	0.978952i	$-0.434576\pi$
$877$	6.27123e15	0.408183	0.204092	+	0.978952i	$0.434576\pi$
$878$	−1.82141e14	−0.0117812
$879$	−5.31234e15	−0.341465
$880$	2.01597e14	0.0128774
$881$	2.12067e16	1.34619	0.673094	−	0.739557i	$-0.264965\pi$
$881$	2.12067e16	1.34619	0.673094	+	0.739557i	$0.264965\pi$
$882$	−1.34881e13	−0.000850892 0
$883$	9.83103e15	0.616333	0.308166	−	0.951332i	$-0.400285\pi$
$883$	9.83103e15	0.616333	0.308166	+	0.951332i	$0.400285\pi$
$884$	2.30073e15	0.143343
$885$	−9.43034e14	−0.0583901
$886$	−1.21943e16	−0.750362
$887$	1.23667e16	0.756263	0.378131	−	0.925752i	$-0.376567\pi$
$887$	1.23667e16	0.756263	0.378131	+	0.925752i	$0.376567\pi$
$888$	7.18781e15	0.436843
$889$	1.01644e16	0.613932
$890$	−2.71720e15	−0.163108
$891$	−1.63831e15	−0.0977389
$892$	−1.68614e15	−0.0999741
$893$	−4.76780e15	−0.280954
$894$	−1.52907e16	−0.895513
$895$	−1.49892e16	−0.872471
$896$	5.77484e14	0.0334077
$897$	−1.86624e15	−0.107302
$898$	4.52739e15	0.258719
$899$	5.03240e16	2.85823
$900$	5.42374e13	0.00306172
$901$	6.09600e15	0.342025
$902$	1.04972e15	0.0585377
$903$	−5.48547e15	−0.304040
$904$	4.86703e15	0.268125
$905$	5.86625e15	0.321213
$906$	1.79764e16	0.978356
$907$	−2.23775e15	−0.121052	−0.0605258	−	0.998167i	$-0.519278\pi$
$907$	−2.23775e15	−0.121052	−0.0605258	+	0.998167i	$0.519278\pi$
$908$	−2.84375e15	−0.152904
$909$	3.05017e14	0.0163013
$910$	1.46892e15	0.0780315
$911$	−2.04505e16	−1.07982	−0.539912	−	0.841721i	$-0.681543\pi$
$911$	−2.04505e16	−1.07982	−0.539912	+	0.841721i	$0.681543\pi$
$912$	1.57183e15	0.0824963
$913$	1.85072e15	0.0965498
$914$	−1.34141e16	−0.695596
$915$	−1.36187e16	−0.701972
$916$	−1.21472e16	−0.622374
$917$	−1.00821e16	−0.513476
$918$	−7.19641e15	−0.364319
$919$	2.11108e16	1.06235	0.531177	−	0.847261i	$-0.321750\pi$
$919$	2.11108e16	1.06235	0.531177	+	0.847261i	$0.321750\pi$
$920$	−7.12252e14	−0.0356287
$921$	1.13266e16	0.563211
$922$	2.55094e16	1.26090
$923$	1.89148e16	0.929380
$924$	3.79798e14	0.0185505
$925$	−1.85778e16	−0.902017
$926$	3.58121e15	0.172850
$927$	−2.45756e14	−0.0117914
$928$	−6.77150e15	−0.322977
$929$	−2.15943e16	−1.02389	−0.511945	−	0.859018i	$-0.671075\pi$
$929$	−2.15943e16	−1.02389	−0.511945	+	0.859018i	$0.671075\pi$
$930$	−1.22116e16	−0.575594
$931$	1.01031e15	0.0473405
$932$	−1.11204e16	−0.518005
$933$	−3.08987e16	−1.43084
$934$	4.92982e15	0.226946
$935$	5.77488e14	0.0264289
$936$	−3.65744e13	−0.00166402
$937$	−1.01361e16	−0.458463	−0.229231	−	0.973372i	$-0.573621\pi$
$937$	−1.01361e16	−0.458463	−0.229231	+	0.973372i	$0.573621\pi$
$938$	6.91121e15	0.310770
$939$	−3.95612e16	−1.76851
$940$	−4.98418e15	−0.221508
$941$	−1.11347e16	−0.491965	−0.245983	−	0.969274i	$-0.579111\pi$
$941$	−1.11347e16	−0.491965	−0.245983	+	0.969274i	$0.579111\pi$
$942$	1.84303e16	0.809566
$943$	−3.70870e15	−0.161960
$944$	−6.46168e14	−0.0280543
$945$	−4.59461e15	−0.198323
$946$	−1.31213e15	−0.0563085
$947$	2.23167e16	0.952148	0.476074	−	0.879405i	$-0.342059\pi$
$947$	2.23167e16	0.952148	0.476074	+	0.879405i	$0.342059\pi$
$948$	5.44193e15	0.230838
$949$	−1.11261e16	−0.469221
$950$	−4.06260e15	−0.170343
$951$	−1.01456e16	−0.422944
$952$	1.65424e15	0.0685640
$953$	−3.20406e16	−1.32035	−0.660175	−	0.751112i	$-0.729518\pi$
$953$	−3.20406e16	−1.32035	−0.660175	+	0.751112i	$0.729518\pi$
$954$	−9.69073e13	−0.00397046
$955$	7.80317e15	0.317872
$956$	−1.92662e16	−0.780328
$957$	−4.45345e15	−0.179342
$958$	−1.15058e15	−0.0460688
$959$	−1.03849e15	−0.0413430
$960$	1.64317e15	0.0650414
$961$	3.67759e16	1.44739
$962$	1.25277e16	0.490241
$963$	6.71534e13	0.00261291
$964$	5.81110e15	0.224820
$965$	4.21835e14	0.0162272
$966$	−1.34184e15	−0.0513249
$967$	−8.82937e15	−0.335803	−0.167901	−	0.985804i	$-0.553699\pi$
$967$	−8.82937e15	−0.335803	−0.167901	+	0.985804i	$0.553699\pi$
$968$	−9.25825e15	−0.350118
$969$	4.50262e15	0.169311
$970$	1.01819e16	0.380703
$971$	3.30146e16	1.22744	0.613720	−	0.789524i	$-0.289672\pi$
$971$	3.30146e16	1.22744	0.613720	+	0.789524i	$0.289672\pi$
$972$	2.27845e14	0.00842317
$973$	4.04871e15	0.148832
$974$	−8.61829e15	−0.315026
$975$	−1.11279e16	−0.404472
$976$	−9.33155e15	−0.337272
$977$	2.94492e15	0.105841	0.0529205	−	0.998599i	$-0.483147\pi$
$977$	2.94492e15	0.105841	0.0529205	+	0.998599i	$0.483147\pi$
$978$	1.98317e16	0.708754
$979$	−1.22448e15	−0.0435157
$980$	1.05617e15	0.0373240
$981$	−3.69977e14	−0.0130016
$982$	3.55556e16	1.24250
$983$	3.30745e16	1.14934	0.574670	−	0.818385i	$-0.305130\pi$
$983$	3.30745e16	1.14934	0.574670	+	0.818385i	$0.305130\pi$
$984$	8.55598e15	0.295663
$985$	1.09183e16	0.375192
$986$	−1.93974e16	−0.662859
$987$	−9.38992e15	−0.319093
$988$	2.73957e15	0.0925803
$989$	4.63581e15	0.155792
$990$	−9.18026e12	−0.000306804 0
$991$	−9.36467e15	−0.311234	−0.155617	−	0.987817i	$-0.549737\pi$
$991$	−9.36467e15	−0.311234	−0.155617	+	0.987817i	$0.549737\pi$
$992$	−8.36740e15	−0.276552
$993$	5.50060e16	1.80796
$994$	1.35999e16	0.444541
$995$	7.37657e15	0.239788
$996$	1.50848e16	0.487655
$997$	−4.81675e16	−1.54857	−0.774284	−	0.632838i	$-0.781890\pi$
$997$	−4.81675e16	−1.54857	−0.774284	+	0.632838i	$0.781890\pi$
$998$	−1.00056e16	−0.319907
$999$	−3.91853e16	−1.24599

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.12.a.d.1.2	✓	2
3.2	odd	2		126.12.a.i.1.1		2
4.3	odd	2		112.12.a.e.1.1		2
7.2	even	3		98.12.c.h.67.1		4
7.3	odd	6		98.12.c.e.79.2		4
7.4	even	3		98.12.c.h.79.1		4
7.5	odd	6		98.12.c.e.67.2		4
7.6	odd	2		98.12.a.g.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.12.a.d.1.2	✓	2	1.1	even	1	trivial
98.12.a.g.1.1		2	7.6	odd	2
98.12.c.e.67.2		4	7.5	odd	6
98.12.c.e.79.2		4	7.3	odd	6
98.12.c.h.67.1		4	7.2	even	3
98.12.c.h.79.1		4	7.4	even	3
112.12.a.e.1.1		2	4.3	odd	2
126.12.a.i.1.1		2	3.2	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:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)

\(f(q)\)	\(=\)	\(q+32.0000 q^{2} +419.112 q^{3} +1024.00 q^{4} +3651.34 q^{5} +13411.6 q^{6} +16807.0 q^{7} +32768.0 q^{8} -1492.18 q^{9} +O(q^{10})\)	\(q+32.0000 q^{2} +419.112 q^{3} +1024.00 q^{4} +3651.34 q^{5} +13411.6 q^{6} +16807.0 q^{7} +32768.0 q^{8} -1492.18 q^{9} +116843. q^{10} +52654.1 q^{11} +429171. q^{12} +748007. q^{13} +537824. q^{14} +1.53032e6 q^{15} +1.04858e6 q^{16} +3.00372e6 q^{17} -47749.8 q^{18} +3.57665e6 q^{19} +3.73897e6 q^{20} +7.04401e6 q^{21} +1.68493e6 q^{22} -5.95295e6 q^{23} +1.37335e7 q^{24} -3.54959e7 q^{25} +2.39362e7 q^{26} -7.48698e7 q^{27} +1.72104e7 q^{28} -2.01806e8 q^{29} +4.89702e7 q^{30} -2.49368e8 q^{31} +3.35544e7 q^{32} +2.20680e7 q^{33} +9.61190e7 q^{34} +6.13680e7 q^{35} -1.52799e6 q^{36} +5.23379e8 q^{37} +1.14453e8 q^{38} +3.13499e8 q^{39} +1.19647e8 q^{40} +6.23002e8 q^{41} +2.25408e8 q^{42} -7.78742e8 q^{43} +5.39178e7 q^{44} -5.44845e6 q^{45} -1.90494e8 q^{46} -1.33304e9 q^{47} +4.39471e8 q^{48} +2.82475e8 q^{49} -1.13587e9 q^{50} +1.25889e9 q^{51} +7.65959e8 q^{52} +2.02948e9 q^{53} -2.39583e9 q^{54} +1.92258e8 q^{55} +5.50732e8 q^{56} +1.49901e9 q^{57} -6.45781e9 q^{58} -6.16234e8 q^{59} +1.56705e9 q^{60} -8.89926e9 q^{61} -7.97977e9 q^{62} -2.50791e7 q^{63} +1.07374e9 q^{64} +2.73123e9 q^{65} +7.06174e8 q^{66} +1.28503e10 q^{67} +3.07581e9 q^{68} -2.49495e9 q^{69} +1.96378e9 q^{70} +2.52870e10 q^{71} -4.88957e7 q^{72} -1.48743e10 q^{73} +1.67481e10 q^{74} -1.48767e10 q^{75} +3.66248e9 q^{76} +8.84957e8 q^{77} +1.00320e10 q^{78} +1.26801e10 q^{79} +3.82870e9 q^{80} -3.11145e10 q^{81} +1.99361e10 q^{82} +3.51486e10 q^{83} +7.21307e9 q^{84} +1.09676e10 q^{85} -2.49197e10 q^{86} -8.45795e10 q^{87} +1.72537e9 q^{88} -2.32552e10 q^{89} -1.74350e8 q^{90} +1.25718e10 q^{91} -6.09582e9 q^{92} -1.04513e11 q^{93} -4.26571e10 q^{94} +1.30595e10 q^{95} +1.40631e10 q^{96} +8.71423e10 q^{97} +9.03921e9 q^{98} -7.85693e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 64 q^{2} - 350 q^{3} + 2048 q^{4} + 3738 q^{5} - 11200 q^{6} + 33614 q^{7} + 65536 q^{8} + 412894 q^{9}+O(q^{10}) \) 2 * q + 64 * q^2 - 350 * q^3 + 2048 * q^4 + 3738 * q^5 - 11200 * q^6 + 33614 * q^7 + 65536 * q^8 + 412894 * q^9	\( 2 q + 64 q^{2} - 350 q^{3} + 2048 q^{4} + 3738 q^{5} - 11200 q^{6} + 33614 q^{7} + 65536 q^{8} + 412894 q^{9} + 119616 q^{10} + 953700 q^{11} - 358400 q^{12} - 225722 q^{13} + 1075648 q^{14} + 1463664 q^{15} + 2097152 q^{16} + 5116272 q^{17} + 13212608 q^{18} + 16531942 q^{19} + 3827712 q^{20} - 5882450 q^{21} + 30518400 q^{22} - 14101728 q^{23} - 11468800 q^{24} - 84316486 q^{25} - 7223104 q^{26} - 257333300 q^{27} + 34420736 q^{28} - 70893504 q^{29} + 46837248 q^{30} - 5164292 q^{31} + 67108864 q^{32} - 670937232 q^{33} + 163720704 q^{34} + 62824566 q^{35} + 422803456 q^{36} + 107289472 q^{37} + 529022144 q^{38} + 1062405512 q^{39} + 122486784 q^{40} + 172190088 q^{41} - 188238400 q^{42} + 878848156 q^{43} + 976588800 q^{44} + 30463986 q^{45} - 451255296 q^{46} - 1299140556 q^{47} - 367001600 q^{48} + 564950498 q^{49} - 2698127552 q^{50} - 365894100 q^{51} - 231139328 q^{52} + 7439756316 q^{53} - 8234665600 q^{54} + 270346104 q^{55} + 1101463552 q^{56} - 8465058484 q^{57} - 2268592128 q^{58} + 2219271558 q^{59} + 1498791936 q^{60} - 9739798838 q^{61} - 165257344 q^{62} + 6939509458 q^{63} + 2147483648 q^{64} + 2646838068 q^{65} - 21469991424 q^{66} + 2779087912 q^{67} + 5239062528 q^{68} + 3772375824 q^{69} + 2010386112 q^{70} + 21197540088 q^{71} + 13529710592 q^{72} - 14015230628 q^{73} + 3433263104 q^{74} + 22671773782 q^{75} + 16928708608 q^{76} + 16028835900 q^{77} + 33996976384 q^{78} - 21708444104 q^{79} + 3919577088 q^{80} + 35813079982 q^{81} + 5510082816 q^{82} + 10851702750 q^{83} - 6023628800 q^{84} + 11150672868 q^{85} + 28123140992 q^{86} - 185266159932 q^{87} + 31250841600 q^{88} - 125407177980 q^{89} + 974847552 q^{90} - 3793709654 q^{91} - 14440169472 q^{92} - 292333010968 q^{93} - 41572497792 q^{94} + 14182293696 q^{95} - 11744051200 q^{96} + 104692220416 q^{97} + 18078415936 q^{98} + 373302410100 q^{99}+O(q^{100}) \) 2 * q + 64 * q^2 - 350 * q^3 + 2048 * q^4 + 3738 * q^5 - 11200 * q^6 + 33614 * q^7 + 65536 * q^8 + 412894 * q^9 + 119616 * q^10 + 953700 * q^11 - 358400 * q^12 - 225722 * q^13 + 1075648 * q^14 + 1463664 * q^15 + 2097152 * q^16 + 5116272 * q^17 + 13212608 * q^18 + 16531942 * q^19 + 3827712 * q^20 - 5882450 * q^21 + 30518400 * q^22 - 14101728 * q^23 - 11468800 * q^24 - 84316486 * q^25 - 7223104 * q^26 - 257333300 * q^27 + 34420736 * q^28 - 70893504 * q^29 + 46837248 * q^30 - 5164292 * q^31 + 67108864 * q^32 - 670937232 * q^33 + 163720704 * q^34 + 62824566 * q^35 + 422803456 * q^36 + 107289472 * q^37 + 529022144 * q^38 + 1062405512 * q^39 + 122486784 * q^40 + 172190088 * q^41 - 188238400 * q^42 + 878848156 * q^43 + 976588800 * q^44 + 30463986 * q^45 - 451255296 * q^46 - 1299140556 * q^47 - 367001600 * q^48 + 564950498 * q^49 - 2698127552 * q^50 - 365894100 * q^51 - 231139328 * q^52 + 7439756316 * q^53 - 8234665600 * q^54 + 270346104 * q^55 + 1101463552 * q^56 - 8465058484 * q^57 - 2268592128 * q^58 + 2219271558 * q^59 + 1498791936 * q^60 - 9739798838 * q^61 - 165257344 * q^62 + 6939509458 * q^63 + 2147483648 * q^64 + 2646838068 * q^65 - 21469991424 * q^66 + 2779087912 * q^67 + 5239062528 * q^68 + 3772375824 * q^69 + 2010386112 * q^70 + 21197540088 * q^71 + 13529710592 * q^72 - 14015230628 * q^73 + 3433263104 * q^74 + 22671773782 * q^75 + 16928708608 * q^76 + 16028835900 * q^77 + 33996976384 * q^78 - 21708444104 * q^79 + 3919577088 * q^80 + 35813079982 * q^81 + 5510082816 * q^82 + 10851702750 * q^83 - 6023628800 * q^84 + 11150672868 * q^85 + 28123140992 * q^86 - 185266159932 * q^87 + 31250841600 * q^88 - 125407177980 * q^89 + 974847552 * q^90 - 3793709654 * q^91 - 14440169472 * q^92 - 292333010968 * q^93 - 41572497792 * q^94 + 14182293696 * q^95 - 11744051200 * q^96 + 104692220416 * q^97 + 18078415936 * q^98 + 373302410100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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