LMFDB - Embedded newform 14.14.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,14,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, 14, names="a")

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

chi := DirichletCharacter("14.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 14 $
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:	$15.0123300533$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{100129}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 25032 $ x^2 - x - 25032
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-157.716$ 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)

$f(q)$	$=$	$q-64.0000 q^{2} +1108.86 q^{3} +4096.00 q^{4} +55872.4 q^{5} -70967.3 q^{6} +117649. q^{7} -262144. q^{8} -364745. q^{9} +O(q^{10})$	\(q-64.0000 q^{2} +1108.86 q^{3} +4096.00 q^{4} +55872.4 q^{5} -70967.3 q^{6} +117649. q^{7} -262144. q^{8} -364745. q^{9} -3.57583e6 q^{10} +6.34082e6 q^{11} +4.54190e6 q^{12} -3.04544e7 q^{13} -7.52954e6 q^{14} +6.19548e7 q^{15} +1.67772e7 q^{16} +1.90043e8 q^{17} +2.33437e7 q^{18} +2.23440e8 q^{19} +2.28853e8 q^{20} +1.30457e8 q^{21} -4.05813e8 q^{22} -2.75371e8 q^{23} -2.90682e8 q^{24} +1.90102e9 q^{25} +1.94908e9 q^{26} -2.17234e9 q^{27} +4.81890e8 q^{28} -1.75578e9 q^{29} -3.96511e9 q^{30} +3.31553e9 q^{31} -1.07374e9 q^{32} +7.03110e9 q^{33} -1.21628e10 q^{34} +6.57333e9 q^{35} -1.49400e9 q^{36} -6.03567e9 q^{37} -1.43001e10 q^{38} -3.37698e10 q^{39} -1.46466e10 q^{40} +3.70799e10 q^{41} -8.34923e9 q^{42} -9.97530e9 q^{43} +2.59720e10 q^{44} -2.03792e10 q^{45} +1.76237e10 q^{46} +9.22647e10 q^{47} +1.86036e10 q^{48} +1.38413e10 q^{49} -1.21665e11 q^{50} +2.10732e11 q^{51} -1.24741e11 q^{52} -1.82069e11 q^{53} +1.39030e11 q^{54} +3.54277e11 q^{55} -3.08410e10 q^{56} +2.47764e11 q^{57} +1.12370e11 q^{58} -9.53478e10 q^{59} +2.53767e11 q^{60} -1.55426e11 q^{61} -2.12194e11 q^{62} -4.29119e10 q^{63} +6.87195e10 q^{64} -1.70156e12 q^{65} -4.49991e11 q^{66} -3.27563e11 q^{67} +7.78418e11 q^{68} -3.05349e11 q^{69} -4.20693e11 q^{70} -1.50186e12 q^{71} +9.56157e10 q^{72} +6.71800e11 q^{73} +3.86283e11 q^{74} +2.10797e12 q^{75} +9.15209e11 q^{76} +7.45991e11 q^{77} +2.16126e12 q^{78} -2.82797e12 q^{79} +9.37383e11 q^{80} -1.82731e12 q^{81} -2.37312e12 q^{82} -1.88505e12 q^{83} +5.34350e11 q^{84} +1.06182e13 q^{85} +6.38419e11 q^{86} -1.94692e12 q^{87} -1.66221e12 q^{88} -7.04412e9 q^{89} +1.30427e12 q^{90} -3.58293e12 q^{91} -1.12792e12 q^{92} +3.67647e12 q^{93} -5.90494e12 q^{94} +1.24841e13 q^{95} -1.19063e12 q^{96} +1.02012e12 q^{97} -8.85842e11 q^{98} -2.31278e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 128 q^{2} + 952 q^{3} + 8192 q^{4} + 32004 q^{5} - 60928 q^{6} + 235298 q^{7} - 524288 q^{8} - 1934462 q^{9}+O(q^{10}) $ 2 * q - 128 * q^2 + 952 * q^3 + 8192 * q^4 + 32004 * q^5 - 60928 * q^6 + 235298 * q^7 - 524288 * q^8 - 1934462 * q^9	\( 2 q - 128 q^{2} + 952 q^{3} + 8192 q^{4} + 32004 q^{5} - 60928 q^{6} + 235298 q^{7} - 524288 q^{8} - 1934462 q^{9} - 2048256 q^{10} - 1352736 q^{11} + 3899392 q^{12} + 3510388 q^{13} - 15059072 q^{14} + 65698920 q^{15} + 33554432 q^{16} + 217711956 q^{17} + 123805568 q^{18} + 591335752 q^{19} + 131088384 q^{20} + 112001848 q^{21} + 86575104 q^{22} + 840735000 q^{23} - 249561088 q^{24} + 1250017766 q^{25} - 224664832 q^{26} - 1676016944 q^{27} + 963780608 q^{28} - 487623540 q^{29} - 4204730880 q^{30} + 2193076144 q^{31} - 2147483648 q^{32} + 8237940480 q^{33} - 13933565184 q^{34} + 3765238596 q^{35} - 7923556352 q^{36} + 405060268 q^{37} - 37845488128 q^{38} - 39097578952 q^{39} - 8389656576 q^{40} + 8518172628 q^{41} - 7168118272 q^{42} + 26225045296 q^{43} - 5540806656 q^{44} + 17087434308 q^{45} - 53807040000 q^{46} + 155048849760 q^{47} + 15971909632 q^{48} + 27682574402 q^{49} - 80001137024 q^{50} + 206392082208 q^{51} + 14378549248 q^{52} + 66007050492 q^{53} + 107265084416 q^{54} + 537909615936 q^{55} - 61681958912 q^{56} + 190054836824 q^{57} + 31207906560 q^{58} - 476362296984 q^{59} + 269102776320 q^{60} + 197378850004 q^{61} - 140356873216 q^{62} - 227587519838 q^{63} + 137438953472 q^{64} - 2512243760544 q^{65} - 527228190720 q^{66} - 1718732859488 q^{67} + 891748171776 q^{68} - 480424669200 q^{69} - 240975270144 q^{70} - 695543478336 q^{71} + 507107606528 q^{72} - 466085239340 q^{73} - 25923857152 q^{74} + 2210090828680 q^{75} + 2422111240192 q^{76} - 159148037664 q^{77} + 2502245052928 q^{78} - 2432016575840 q^{79} + 536938020864 q^{80} + 597475723018 q^{81} - 545163048192 q^{82} - 1743984494616 q^{83} + 458759569408 q^{84} + 9957781762488 q^{85} - 1678402898944 q^{86} - 2145843141792 q^{87} + 354611625984 q^{88} + 3022580240484 q^{89} - 1093595795712 q^{90} + 412993637812 q^{91} + 3443650560000 q^{92} + 3852541919312 q^{93} - 9923126384640 q^{94} + 3703032892440 q^{95} - 1022202216448 q^{96} + 7760062661092 q^{97} - 1771684761728 q^{98} + 9763922554848 q^{99}+O(q^{100}) \) 2 * q - 128 * q^2 + 952 * q^3 + 8192 * q^4 + 32004 * q^5 - 60928 * q^6 + 235298 * q^7 - 524288 * q^8 - 1934462 * q^9 - 2048256 * q^10 - 1352736 * q^11 + 3899392 * q^12 + 3510388 * q^13 - 15059072 * q^14 + 65698920 * q^15 + 33554432 * q^16 + 217711956 * q^17 + 123805568 * q^18 + 591335752 * q^19 + 131088384 * q^20 + 112001848 * q^21 + 86575104 * q^22 + 840735000 * q^23 - 249561088 * q^24 + 1250017766 * q^25 - 224664832 * q^26 - 1676016944 * q^27 + 963780608 * q^28 - 487623540 * q^29 - 4204730880 * q^30 + 2193076144 * q^31 - 2147483648 * q^32 + 8237940480 * q^33 - 13933565184 * q^34 + 3765238596 * q^35 - 7923556352 * q^36 + 405060268 * q^37 - 37845488128 * q^38 - 39097578952 * q^39 - 8389656576 * q^40 + 8518172628 * q^41 - 7168118272 * q^42 + 26225045296 * q^43 - 5540806656 * q^44 + 17087434308 * q^45 - 53807040000 * q^46 + 155048849760 * q^47 + 15971909632 * q^48 + 27682574402 * q^49 - 80001137024 * q^50 + 206392082208 * q^51 + 14378549248 * q^52 + 66007050492 * q^53 + 107265084416 * q^54 + 537909615936 * q^55 - 61681958912 * q^56 + 190054836824 * q^57 + 31207906560 * q^58 - 476362296984 * q^59 + 269102776320 * q^60 + 197378850004 * q^61 - 140356873216 * q^62 - 227587519838 * q^63 + 137438953472 * q^64 - 2512243760544 * q^65 - 527228190720 * q^66 - 1718732859488 * q^67 + 891748171776 * q^68 - 480424669200 * q^69 - 240975270144 * q^70 - 695543478336 * q^71 + 507107606528 * q^72 - 466085239340 * q^73 - 25923857152 * q^74 + 2210090828680 * q^75 + 2422111240192 * q^76 - 159148037664 * q^77 + 2502245052928 * q^78 - 2432016575840 * q^79 + 536938020864 * q^80 + 597475723018 * q^81 - 545163048192 * q^82 - 1743984494616 * q^83 + 458759569408 * q^84 + 9957781762488 * q^85 - 1678402898944 * q^86 - 2145843141792 * q^87 + 354611625984 * q^88 + 3022580240484 * q^89 - 1093595795712 * q^90 + 412993637812 * q^91 + 3443650560000 * q^92 + 3852541919312 * q^93 - 9923126384640 * q^94 + 3703032892440 * q^95 - 1022202216448 * q^96 + 7760062661092 * q^97 - 1771684761728 * q^98 + 9763922554848 * 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 $

$2$	−64.0000	−0.707107
$2$	−64.0000	−0.707107
$3$	1108.86	0.878193	0.439096	−	0.898440i	$-0.355299\pi$
$3$	1108.86	0.878193	0.439096	+	0.898440i	$0.355299\pi$
$4$	4096.00	0.500000
$5$	55872.4	1.59916	0.799581	−	0.600559i	$-0.205055\pi$
$5$	55872.4	1.59916	0.799581	+	0.600559i	$0.205055\pi$
$6$	−70967.3	−0.620976
$7$	117649.	0.377964
$7$	117649.	0.377964
$8$	−262144.	−0.353553
$9$	−364745.	−0.228777
$10$	−3.57583e6	−1.13078
$11$	6.34082e6	1.07918	0.539589	−	0.841929i	$-0.318580\pi$
$11$	6.34082e6	1.07918	0.539589	+	0.841929i	$0.318580\pi$
$12$	4.54190e6	0.439096
$13$	−3.04544e7	−1.74992	−0.874960	−	0.484196i	$-0.839112\pi$
$13$	−3.04544e7	−1.74992	−0.874960	+	0.484196i	$0.839112\pi$
$14$	−7.52954e6	−0.267261
$15$	6.19548e7	1.40437
$16$	1.67772e7	0.250000
$17$	1.90043e8	1.90957	0.954784	−	0.297301i	$-0.0960866\pi$
$17$	1.90043e8	1.90957	0.954784	+	0.297301i	$0.0960866\pi$
$18$	2.33437e7	0.161770
$19$	2.23440e8	1.08959	0.544794	−	0.838570i	$-0.316608\pi$
$19$	2.23440e8	1.08959	0.544794	+	0.838570i	$0.316608\pi$
$20$	2.28853e8	0.799581
$21$	1.30457e8	0.331926
$22$	−4.05813e8	−0.763094
$23$	−2.75371e8	−0.387871	−0.193935	−	0.981014i	$-0.562125\pi$
$23$	−2.75371e8	−0.387871	−0.193935	+	0.981014i	$0.562125\pi$
$24$	−2.90682e8	−0.310488
$25$	1.90102e9	1.55732
$26$	1.94908e9	1.23738
$27$	−2.17234e9	−1.07910
$28$	4.81890e8	0.188982
$29$	−1.75578e9	−0.548128	−0.274064	−	0.961711i	$-0.588368\pi$
$29$	−1.75578e9	−0.548128	−0.274064	+	0.961711i	$0.588368\pi$
$30$	−3.96511e9	−0.993041
$31$	3.31553e9	0.670968	0.335484	−	0.942046i	$-0.391100\pi$
$31$	3.31553e9	0.670968	0.335484	+	0.942046i	$0.391100\pi$
$32$	−1.07374e9	−0.176777
$33$	7.03110e9	0.947726
$34$	−1.21628e10	−1.35027
$35$	6.57333e9	0.604426
$36$	−1.49400e9	−0.114389
$37$	−6.03567e9	−0.386736	−0.193368	−	0.981126i	$-0.561941\pi$
$37$	−6.03567e9	−0.386736	−0.193368	+	0.981126i	$0.561941\pi$
$38$	−1.43001e10	−0.770455
$39$	−3.37698e10	−1.53677
$40$	−1.46466e10	−0.565389
$41$	3.70799e10	1.21911	0.609556	−	0.792743i	$-0.291348\pi$
$41$	3.70799e10	1.21911	0.609556	+	0.792743i	$0.291348\pi$
$42$	−8.34923e9	−0.234707
$43$	−9.97530e9	−0.240647	−0.120324	−	0.992735i	$-0.538393\pi$
$43$	−9.97530e9	−0.240647	−0.120324	+	0.992735i	$0.538393\pi$
$44$	2.59720e10	0.539589
$45$	−2.03792e10	−0.365852
$46$	1.76237e10	0.274266
$47$	9.22647e10	1.24853	0.624266	−	0.781212i	$-0.285398\pi$
$47$	9.22647e10	1.24853	0.624266	+	0.781212i	$0.285398\pi$
$48$	1.86036e10	0.219548
$49$	1.38413e10	0.142857
$50$	−1.21665e11	−1.10119
$51$	2.10732e11	1.67697
$52$	−1.24741e11	−0.874960
$53$	−1.82069e11	−1.12835	−0.564173	−	0.825657i	$-0.690805\pi$
$53$	−1.82069e11	−1.12835	−0.564173	+	0.825657i	$0.690805\pi$
$54$	1.39030e11	0.763041
$55$	3.54277e11	1.72578
$56$	−3.08410e10	−0.133631
$57$	2.47764e11	0.956868
$58$	1.12370e11	0.387585
$59$	−9.53478e10	−0.294288	−0.147144	−	0.989115i	$-0.547008\pi$
$59$	−9.53478e10	−0.294288	−0.147144	+	0.989115i	$0.547008\pi$
$60$	2.53767e11	0.702186
$61$	−1.55426e11	−0.386260	−0.193130	−	0.981173i	$-0.561864\pi$
$61$	−1.55426e11	−0.386260	−0.193130	+	0.981173i	$0.561864\pi$
$62$	−2.12194e11	−0.474446
$63$	−4.29119e10	−0.0864697
$64$	6.87195e10	0.125000
$65$	−1.70156e12	−2.79840
$66$	−4.49991e11	−0.670144
$67$	−3.27563e11	−0.442393	−0.221197	−	0.975229i	$-0.570996\pi$
$67$	−3.27563e11	−0.442393	−0.221197	+	0.975229i	$0.570996\pi$
$68$	7.78418e11	0.954784
$69$	−3.05349e11	−0.340625
$70$	−4.20693e11	−0.427394
$71$	−1.50186e12	−1.39140	−0.695698	−	0.718334i	$-0.744905\pi$
$71$	−1.50186e12	−1.39140	−0.695698	+	0.718334i	$0.744905\pi$
$72$	9.56157e10	0.0808850
$73$	6.71800e11	0.519567	0.259783	−	0.965667i	$-0.416349\pi$
$73$	6.71800e11	0.519567	0.259783	+	0.965667i	$0.416349\pi$
$74$	3.86283e11	0.273463
$75$	2.10797e12	1.36762
$76$	9.15209e11	0.544794
$77$	7.45991e11	0.407891
$78$	2.16126e12	1.08666
$79$	−2.82797e12	−1.30888	−0.654439	−	0.756115i	$-0.727095\pi$
$79$	−2.82797e12	−1.30888	−0.654439	+	0.756115i	$0.727095\pi$
$80$	9.37383e11	0.399790
$81$	−1.82731e12	−0.718883
$82$	−2.37312e12	−0.862043
$83$	−1.88505e12	−0.632872	−0.316436	−	0.948614i	$-0.602486\pi$
$83$	−1.88505e12	−0.632872	−0.316436	+	0.948614i	$0.602486\pi$
$84$	5.34350e11	0.165963
$85$	1.06182e13	3.05371
$86$	6.38419e11	0.170163
$87$	−1.94692e12	−0.481362
$88$	−1.66221e12	−0.381547
$89$	−7.04412e9	−0.00150242	−0.000751210	−	1.00000i	$-0.500239\pi$
$89$	−7.04412e9	−0.00150242	−0.000751210		1.00000i	$0.500239\pi$
$90$	1.30427e12	0.258696
$91$	−3.58293e12	−0.661407
$92$	−1.12792e12	−0.193935
$93$	3.67647e12	0.589240
$94$	−5.90494e12	−0.882845
$95$	1.24841e13	1.74243
$96$	−1.19063e12	−0.155244
$97$	1.02012e12	0.124346	0.0621732	−	0.998065i	$-0.480197\pi$
$97$	1.02012e12	0.124346	0.0621732	+	0.998065i	$0.480197\pi$
$98$	−8.85842e11	−0.101015
$99$	−2.31278e12	−0.246892
$100$	7.78658e12	0.778658
$101$	−1.26179e13	−1.18276	−0.591382	−	0.806392i	$-0.701417\pi$
$101$	−1.26179e13	−1.18276	−0.591382	+	0.806392i	$0.701417\pi$
$102$	−1.34869e13	−1.18580
$103$	1.13875e12	0.0939698	0.0469849	−	0.998896i	$-0.485039\pi$
$103$	1.13875e12	0.0939698	0.0469849	+	0.998896i	$0.485039\pi$
$104$	7.98343e12	0.618690
$105$	7.28893e12	0.530803
$106$	1.16524e13	0.797861
$107$	−1.73535e13	−1.11788	−0.558938	−	0.829210i	$-0.688791\pi$
$107$	−1.73535e13	−1.11788	−0.558938	+	0.829210i	$0.688791\pi$
$108$	−8.89790e12	−0.539552
$109$	1.82182e13	1.04048	0.520241	−	0.854020i	$-0.325842\pi$
$109$	1.82182e13	1.04048	0.520241	+	0.854020i	$0.325842\pi$
$110$	−2.26737e13	−1.22031
$111$	−6.69273e12	−0.339629
$112$	1.97382e12	0.0944911
$113$	−2.46900e13	−1.11561	−0.557803	−	0.829973i	$-0.688356\pi$
$113$	−2.46900e13	−1.11561	−0.557803	+	0.829973i	$0.688356\pi$
$114$	−1.58569e13	−0.676608
$115$	−1.53856e13	−0.620268
$116$	−7.19166e12	−0.274064
$117$	1.11081e13	0.400342
$118$	6.10226e12	0.208093
$119$	2.23584e13	0.721749
$120$	−1.62411e13	−0.496520
$121$	5.68329e12	0.164625
$122$	9.94726e12	0.273127
$123$	4.11166e13	1.07062
$124$	1.35804e13	0.335484
$125$	3.80110e13	0.891239
$126$	2.74636e12	0.0611433
$127$	2.62824e13	0.555829	0.277915	−	0.960606i	$-0.410357\pi$
$127$	2.62824e13	0.555829	0.277915	+	0.960606i	$0.410357\pi$
$128$	−4.39805e12	−0.0883883
$129$	−1.10612e13	−0.211335
$130$	1.08900e14	1.97877
$131$	−7.53259e13	−1.30221	−0.651105	−	0.758988i	$-0.725694\pi$
$131$	−7.53259e13	−1.30221	−0.651105	+	0.758988i	$0.725694\pi$
$132$	2.87994e13	0.473863
$133$	2.62875e13	0.411825
$134$	2.09640e13	0.312819
$135$	−1.21374e14	−1.72566
$136$	−4.98188e13	−0.675134
$137$	−2.73030e12	−0.0352798	−0.0176399	−	0.999844i	$-0.505615\pi$
$137$	−2.73030e12	−0.0352798	−0.0176399	+	0.999844i	$0.505615\pi$
$138$	1.95423e13	0.240858
$139$	5.47785e13	0.644190	0.322095	−	0.946707i	$-0.395613\pi$
$139$	5.47785e13	0.644190	0.322095	+	0.946707i	$0.395613\pi$
$140$	2.69244e13	0.302213
$141$	1.02309e14	1.09645
$142$	9.61192e13	0.983866
$143$	−1.93106e14	−1.88847
$144$	−6.11941e12	−0.0571944
$145$	−9.80994e13	−0.876546
$146$	−4.29952e13	−0.367389
$147$	1.53481e13	0.125456
$148$	−2.47221e13	−0.193368
$149$	1.66164e14	1.24401	0.622007	−	0.783012i	$-0.286318\pi$
$149$	1.66164e14	1.24401	0.622007	+	0.783012i	$0.286318\pi$
$150$	−1.34910e14	−0.967056
$151$	−1.18437e14	−0.813088	−0.406544	−	0.913631i	$-0.633266\pi$
$151$	−1.18437e14	−0.813088	−0.406544	+	0.913631i	$0.633266\pi$
$152$	−5.85734e13	−0.385227
$153$	−6.93174e13	−0.436866
$154$	−4.77434e13	−0.288422
$155$	1.85247e14	1.07299
$156$	−1.38321e14	−0.768383
$157$	−2.71247e14	−1.44550	−0.722748	−	0.691112i	$-0.757121\pi$
$157$	−2.71247e14	−1.44550	−0.722748	+	0.691112i	$0.757121\pi$
$158$	1.80990e14	0.925517
$159$	−2.01889e14	−0.990905
$160$	−5.99925e13	−0.282694
$161$	−3.23971e13	−0.146601
$162$	1.16948e14	0.508327
$163$	−7.81791e13	−0.326491	−0.163246	−	0.986585i	$-0.552196\pi$
$163$	−7.81791e13	−0.326491	−0.163246	+	0.986585i	$0.552196\pi$
$164$	1.51879e14	0.609556
$165$	3.92845e14	1.51557
$166$	1.20643e14	0.447508
$167$	6.76059e13	0.241173	0.120586	−	0.992703i	$-0.461523\pi$
$167$	6.76059e13	0.241173	0.120586	+	0.992703i	$0.461523\pi$
$168$	−3.41984e13	−0.117353
$169$	6.24594e14	2.06222
$170$	−6.79564e14	−2.15930
$171$	−8.14986e13	−0.249273
$172$	−4.08588e13	−0.120324
$173$	1.85549e14	0.526210	0.263105	−	0.964767i	$-0.415253\pi$
$173$	1.85549e14	0.526210	0.263105	+	0.964767i	$0.415253\pi$
$174$	1.24603e14	0.340375
$175$	2.23653e14	0.588610
$176$	1.06381e14	0.269794
$177$	−1.05728e14	−0.258442
$178$	4.50824e11	0.00106237
$179$	−3.23863e14	−0.735895	−0.367948	−	0.929846i	$-0.619939\pi$
$179$	−3.23863e14	−0.735895	−0.367948	+	0.929846i	$0.619939\pi$
$180$	−8.34731e13	−0.182926
$181$	7.86138e14	1.66183	0.830917	−	0.556396i	$-0.187816\pi$
$181$	7.86138e14	1.66183	0.830917	+	0.556396i	$0.187816\pi$
$182$	2.29307e14	0.467686
$183$	−1.72346e14	−0.339211
$184$	7.21868e13	0.137133
$185$	−3.37227e14	−0.618453
$186$	−2.35294e14	−0.416655
$187$	1.20503e15	2.06076
$188$	3.77916e14	0.624266
$189$	−2.55573e14	−0.407863
$190$	−7.98983e14	−1.23208
$191$	−8.58152e14	−1.27893	−0.639466	−	0.768820i	$-0.720844\pi$
$191$	−8.58152e14	−1.27893	−0.639466	+	0.768820i	$0.720844\pi$
$192$	7.62005e13	0.109774
$193$	7.04074e14	0.980608	0.490304	−	0.871551i	$-0.336886\pi$
$193$	7.04074e14	0.980608	0.490304	+	0.871551i	$0.336886\pi$
$194$	−6.52874e13	−0.0879262
$195$	−1.88680e15	−2.45754
$196$	5.66939e13	0.0714286
$197$	−2.73556e13	−0.0333439	−0.0166719	−	0.999861i	$-0.505307\pi$
$197$	−2.73556e13	−0.0333439	−0.0166719	+	0.999861i	$0.505307\pi$
$198$	1.48018e14	0.174579
$199$	−4.93047e14	−0.562787	−0.281393	−	0.959593i	$-0.590797\pi$
$199$	−4.93047e14	−0.562787	−0.281393	+	0.959593i	$0.590797\pi$
$200$	−4.98341e14	−0.550594
$201$	−3.63223e14	−0.388507
$202$	8.07545e14	0.836340
$203$	−2.06565e14	−0.207173
$204$	8.63159e14	0.838484
$205$	2.07174e15	1.94956
$206$	−7.28803e13	−0.0664467
$207$	1.00440e14	0.0887361
$208$	−5.10940e14	−0.437480
$209$	1.41679e15	1.17586
$210$	−4.66491e14	−0.375334
$211$	−1.37682e15	−1.07409	−0.537045	−	0.843553i	$-0.680460\pi$
$211$	−1.37682e15	−1.07409	−0.537045	+	0.843553i	$0.680460\pi$
$212$	−7.45753e14	−0.564173
$213$	−1.66536e15	−1.22191
$214$	1.11063e15	0.790457
$215$	−5.57344e14	−0.384834
$216$	5.69466e14	0.381521
$217$	3.90069e14	0.253602
$218$	−1.16597e15	−0.735731
$219$	7.44935e14	0.456280
$220$	1.45112e15	0.862890
$221$	−5.78766e15	−3.34159
$222$	4.28335e14	0.240154
$223$	−3.05737e15	−1.66482	−0.832410	−	0.554161i	$-0.813039\pi$
$223$	−3.05737e15	−1.66482	−0.832410	+	0.554161i	$0.813039\pi$
$224$	−1.26325e14	−0.0668153
$225$	−6.93388e14	−0.356279
$226$	1.58016e15	0.788853
$227$	3.76865e15	1.82817	0.914086	−	0.405519i	$-0.132909\pi$
$227$	3.76865e15	1.82817	0.914086	+	0.405519i	$0.132909\pi$
$228$	1.01484e15	0.478434
$229$	4.38879e14	0.201101	0.100550	−	0.994932i	$-0.467940\pi$
$229$	4.38879e14	0.201101	0.100550	+	0.994932i	$0.467940\pi$
$230$	9.84680e14	0.438596
$231$	8.27202e14	0.358207
$232$	4.60266e14	0.193793
$233$	3.81449e15	1.56179	0.780897	−	0.624660i	$-0.214763\pi$
$233$	3.81449e15	1.56179	0.780897	+	0.624660i	$0.214763\pi$
$234$	−7.10918e14	−0.283085
$235$	5.15505e15	1.99660
$236$	−3.90544e14	−0.147144
$237$	−3.13584e15	−1.14945
$238$	−1.43094e15	−0.510353
$239$	3.03165e15	1.05219	0.526093	−	0.850427i	$-0.323657\pi$
$239$	3.03165e15	1.05219	0.526093	+	0.850427i	$0.323657\pi$
$240$	1.03943e15	0.351093
$241$	5.30965e15	1.74564	0.872820	−	0.488042i	$-0.162289\pi$
$241$	5.30965e15	1.74564	0.872820	+	0.488042i	$0.162289\pi$
$242$	−3.63731e14	−0.116407
$243$	1.43718e15	0.447785
$244$	−6.36625e14	−0.193130
$245$	7.73346e14	0.228452
$246$	−2.63146e15	−0.757040
$247$	−6.80472e15	−1.90669
$248$	−8.69146e14	−0.237223
$249$	−2.09026e15	−0.555783
$250$	−2.43270e15	−0.630201
$251$	−9.81501e14	−0.247749	−0.123874	−	0.992298i	$-0.539532\pi$
$251$	−9.81501e14	−0.247749	−0.123874	+	0.992298i	$0.539532\pi$
$252$	−1.75767e14	−0.0432349
$253$	−1.74608e15	−0.418581
$254$	−1.68208e15	−0.393030
$255$	1.17741e16	2.68174
$256$	2.81475e14	0.0625000
$257$	−3.48312e15	−0.754055	−0.377027	−	0.926202i	$-0.623054\pi$
$257$	−3.48312e15	−0.754055	−0.377027	+	0.926202i	$0.623054\pi$
$258$	7.07920e14	0.149436
$259$	−7.10091e14	−0.146172
$260$	−6.96959e15	−1.39920
$261$	6.40411e14	0.125399
$262$	4.82086e15	0.920801
$263$	−8.12086e15	−1.51318	−0.756588	−	0.653892i	$-0.773135\pi$
$263$	−8.12086e15	−1.51318	−0.756588	+	0.653892i	$0.773135\pi$
$264$	−1.84316e15	−0.335072
$265$	−1.01726e16	−1.80441
$266$	−1.68240e15	−0.291205
$267$	−7.81096e12	−0.00131942
$268$	−1.34170e15	−0.221197
$269$	−1.25931e15	−0.202648	−0.101324	−	0.994853i	$-0.532308\pi$
$269$	−1.25931e15	−0.202648	−0.101324	+	0.994853i	$0.532308\pi$
$270$	7.76792e15	1.22023
$271$	3.82818e15	0.587073	0.293537	−	0.955948i	$-0.405168\pi$
$271$	3.82818e15	0.587073	0.293537	+	0.955948i	$0.405168\pi$
$272$	3.18840e15	0.477392
$273$	−3.97298e15	−0.580843
$274$	1.74739e14	0.0249466
$275$	1.20540e16	1.68062
$276$	−1.25071e15	−0.170313
$277$	−2.49089e15	−0.331312	−0.165656	−	0.986184i	$-0.552974\pi$
$277$	−2.49089e15	−0.331312	−0.165656	+	0.986184i	$0.552974\pi$
$278$	−3.50583e15	−0.455511
$279$	−1.20932e15	−0.153502
$280$	−1.72316e15	−0.213697
$281$	−1.29262e15	−0.156632	−0.0783161	−	0.996929i	$-0.524954\pi$
$281$	−1.29262e15	−0.156632	−0.0783161	+	0.996929i	$0.524954\pi$
$282$	−6.54777e15	−0.775308
$283$	−1.37587e16	−1.59209	−0.796043	−	0.605239i	$-0.793077\pi$
$283$	−1.37587e16	−1.59209	−0.796043	+	0.605239i	$0.793077\pi$
$284$	−6.15163e15	−0.695698
$285$	1.38432e16	1.53019
$286$	1.23588e16	1.33535
$287$	4.36242e15	0.460781
$288$	3.91642e14	0.0404425
$289$	2.62119e16	2.64645
$290$	6.27836e15	0.619811
$291$	1.13117e15	0.109200
$292$	2.75169e15	0.259783
$293$	3.99822e15	0.369171	0.184585	−	0.982816i	$-0.440906\pi$
$293$	3.99822e15	0.369171	0.184585	+	0.982816i	$0.440906\pi$
$294$	−9.82278e14	−0.0887109
$295$	−5.32731e15	−0.470614
$296$	1.58221e15	0.136732
$297$	−1.37744e16	−1.16454
$298$	−1.06345e16	−0.879651
$299$	8.38625e15	0.678742
$300$	8.63425e15	0.683812
$301$	−1.17358e15	−0.0909562
$302$	7.57997e15	0.574940
$303$	−1.39915e16	−1.03869
$304$	3.74870e15	0.272397
$305$	−8.68402e15	−0.617692
$306$	4.43632e15	0.308911
$307$	−1.22582e16	−0.835654	−0.417827	−	0.908527i	$-0.637208\pi$
$307$	−1.22582e16	−0.835654	−0.417827	+	0.908527i	$0.637208\pi$
$308$	3.05558e15	0.203945
$309$	1.26272e15	0.0825236
$310$	−1.18558e16	−0.758716
$311$	2.81809e16	1.76609	0.883044	−	0.469290i	$-0.155490\pi$
$311$	2.81809e16	1.76609	0.883044	+	0.469290i	$0.155490\pi$
$312$	8.85254e15	0.543329
$313$	−1.30138e16	−0.782290	−0.391145	−	0.920329i	$-0.627921\pi$
$313$	−1.30138e16	−0.782290	−0.391145	+	0.920329i	$0.627921\pi$
$314$	1.73598e16	1.02212
$315$	−2.39759e15	−0.138279
$316$	−1.15834e16	−0.654439
$317$	−1.63712e16	−0.906142	−0.453071	−	0.891474i	$-0.649672\pi$
$317$	−1.63712e16	−0.906142	−0.453071	+	0.891474i	$0.649672\pi$
$318$	1.29209e16	0.700676
$319$	−1.11331e16	−0.591528
$320$	3.83952e15	0.199895
$321$	−1.92427e16	−0.981710
$322$	2.07341e15	0.103663
$323$	4.24633e16	2.08064
$324$	−7.48464e15	−0.359442
$325$	−5.78944e16	−2.72518
$326$	5.00346e15	0.230864
$327$	2.02015e16	0.913743
$328$	−9.72028e15	−0.431021
$329$	1.08549e16	0.471901
$330$	−2.51421e16	−1.07167
$331$	2.06113e16	0.861439	0.430719	−	0.902486i	$-0.358260\pi$
$331$	2.06113e16	0.861439	0.430719	+	0.902486i	$0.358260\pi$
$332$	−7.72117e15	−0.316436
$333$	2.20148e15	0.0884764
$334$	−4.32678e15	−0.170535
$335$	−1.83017e16	−0.707458
$336$	2.18870e15	0.0829814
$337$	−2.21434e16	−0.823475	−0.411737	−	0.911303i	$-0.635078\pi$
$337$	−2.21434e16	−0.823475	−0.411737	+	0.911303i	$0.635078\pi$
$338$	−3.99740e16	−1.45821
$339$	−2.73778e16	−0.979718
$340$	4.34921e16	1.52685
$341$	2.10232e16	0.724094
$342$	5.21591e15	0.176263
$343$	1.62841e15	0.0539949
$344$	2.61497e15	0.0850817
$345$	−1.70606e16	−0.544715
$346$	−1.18751e16	−0.372087
$347$	2.13643e16	0.656974	0.328487	−	0.944509i	$-0.393461\pi$
$347$	2.13643e16	0.656974	0.328487	+	0.944509i	$0.393461\pi$
$348$	−7.97457e15	−0.240681
$349$	4.24274e16	1.25684	0.628422	−	0.777873i	$-0.283701\pi$
$349$	4.24274e16	1.25684	0.628422	+	0.777873i	$0.283701\pi$
$350$	−1.43138e16	−0.416210
$351$	6.61572e16	1.88834
$352$	−6.80840e15	−0.190773
$353$	3.03468e16	0.834791	0.417395	−	0.908725i	$-0.362943\pi$
$353$	3.03468e16	0.834791	0.417395	+	0.908725i	$0.362943\pi$
$354$	6.76657e15	0.182746
$355$	−8.39127e16	−2.22507
$356$	−2.88527e13	−0.000751210 0
$357$	2.47924e16	0.633834
$358$	2.07272e16	0.520357
$359$	2.09778e16	0.517185	0.258593	−	0.965986i	$-0.416741\pi$
$359$	2.09778e16	0.517185	0.258593	+	0.965986i	$0.416741\pi$
$360$	5.34228e15	0.129348
$361$	7.87237e15	0.187201
$362$	−5.03128e16	−1.17509
$363$	6.30200e15	0.144572
$364$	−1.46757e16	−0.330704
$365$	3.75351e16	0.830871
$366$	1.10302e16	0.239858
$367$	−2.26892e16	−0.484719	−0.242359	−	0.970187i	$-0.577921\pi$
$367$	−2.26892e16	−0.484719	−0.242359	+	0.970187i	$0.577921\pi$
$368$	−4.61996e15	−0.0969677
$369$	−1.35247e16	−0.278905
$370$	2.15826e16	0.437312
$371$	−2.14202e16	−0.426475
$372$	1.50588e16	0.294620
$373$	−3.52414e15	−0.0677557	−0.0338778	−	0.999426i	$-0.510786\pi$
$373$	−3.52414e15	−0.0677557	−0.0338778	+	0.999426i	$0.510786\pi$
$374$	−7.71220e16	−1.45718
$375$	4.21490e16	0.782679
$376$	−2.41866e16	−0.441423
$377$	5.34711e16	0.959181
$378$	1.63567e16	0.288403
$379$	4.66091e16	0.807822	0.403911	−	0.914798i	$-0.367650\pi$
$379$	4.66091e16	0.807822	0.403911	+	0.914798i	$0.367650\pi$
$380$	5.11349e16	0.871213
$381$	2.91436e16	0.488125
$382$	5.49217e16	0.904341
$383$	−7.45938e16	−1.20757	−0.603783	−	0.797149i	$-0.706341\pi$
$383$	−7.45938e16	−1.20757	−0.603783	+	0.797149i	$0.706341\pi$
$384$	−4.87683e15	−0.0776220
$385$	4.16803e16	0.652283
$386$	−4.50607e16	−0.693395
$387$	3.63844e15	0.0550547
$388$	4.17840e15	0.0621732
$389$	1.81977e16	0.266283	0.133141	−	0.991097i	$-0.457494\pi$
$389$	1.81977e16	0.266283	0.133141	+	0.991097i	$0.457494\pi$
$390$	1.20755e17	1.73774
$391$	−5.23324e16	−0.740665
$392$	−3.62841e15	−0.0505076
$393$	−8.35261e16	−1.14359
$394$	1.75076e15	0.0235777
$395$	−1.58006e17	−2.09311
$396$	−9.47316e15	−0.123446
$397$	3.11021e16	0.398704	0.199352	−	0.979928i	$-0.436116\pi$
$397$	3.11021e16	0.398704	0.199352	+	0.979928i	$0.436116\pi$
$398$	3.15550e16	0.397950
$399$	2.91492e16	0.361662
$400$	3.18938e16	0.389329
$401$	−2.57328e16	−0.309064	−0.154532	−	0.987988i	$-0.549387\pi$
$401$	−2.57328e16	−0.309064	−0.154532	+	0.987988i	$0.549387\pi$
$402$	2.32462e16	0.274716
$403$	−1.00972e17	−1.17414
$404$	−5.16829e16	−0.591382
$405$	−1.02096e17	−1.14961
$406$	1.32202e16	0.146493
$407$	−3.82711e16	−0.417357
$408$	−5.52422e16	−0.592898
$409$	9.43441e16	0.996582	0.498291	−	0.867010i	$-0.333961\pi$
$409$	9.43441e16	0.996582	0.498291	+	0.867010i	$0.333961\pi$
$410$	−1.32592e17	−1.37855
$411$	−3.02753e15	−0.0309825
$412$	4.66434e15	0.0469849
$413$	−1.12176e16	−0.111230
$414$	−6.42817e15	−0.0627459
$415$	−1.05322e17	−1.01206
$416$	3.27001e16	0.309345
$417$	6.07419e16	0.565723
$418$	−9.06747e16	−0.831458
$419$	−3.91699e16	−0.353640	−0.176820	−	0.984243i	$-0.556581\pi$
$419$	−3.91699e16	−0.353640	−0.176820	+	0.984243i	$0.556581\pi$
$420$	2.98554e16	0.265401
$421$	−6.64825e16	−0.581934	−0.290967	−	0.956733i	$-0.593977\pi$
$421$	−6.64825e16	−0.581934	−0.290967	+	0.956733i	$0.593977\pi$
$422$	8.81164e16	0.759497
$423$	−3.36531e16	−0.285636
$424$	4.77282e16	0.398930
$425$	3.61277e17	2.97380
$426$	1.06583e17	0.864024
$427$	−1.82857e16	−0.145993
$428$	−7.10801e16	−0.558938
$429$	−2.14128e17	−1.65844
$430$	3.56700e16	0.272119
$431$	2.22144e17	1.66929	0.834646	−	0.550787i	$-0.185672\pi$
$431$	2.22144e17	1.66929	0.834646	+	0.550787i	$0.185672\pi$
$432$	−3.64458e16	−0.269776
$433$	4.53695e16	0.330821	0.165410	−	0.986225i	$-0.447105\pi$
$433$	4.53695e16	0.330821	0.165410	+	0.986225i	$0.447105\pi$
$434$	−2.49644e16	−0.179324
$435$	−1.08779e17	−0.769776
$436$	7.46219e16	0.520241
$437$	−6.15288e16	−0.422619
$438$	−4.76758e16	−0.322639
$439$	6.48405e16	0.432342	0.216171	−	0.976356i	$-0.430643\pi$
$439$	6.48405e16	0.432342	0.216171	+	0.976356i	$0.430643\pi$
$440$	−9.28715e16	−0.610155
$441$	−5.04854e15	−0.0326825
$442$	3.70410e17	2.36286
$443$	2.17048e17	1.36437	0.682183	−	0.731181i	$-0.261031\pi$
$443$	2.17048e17	1.36437	0.682183	+	0.731181i	$0.261031\pi$
$444$	−2.74134e16	−0.169814
$445$	−3.93572e14	−0.00240261
$446$	1.95672e17	1.17720
$447$	1.84253e17	1.09248
$448$	8.08478e15	0.0472456
$449$	−1.96759e16	−0.113327	−0.0566635	−	0.998393i	$-0.518046\pi$
$449$	−1.96759e16	−0.113327	−0.0566635	+	0.998393i	$0.518046\pi$
$450$	4.43768e16	0.251927
$451$	2.35117e17	1.31564
$452$	−1.01130e17	−0.557803
$453$	−1.31331e17	−0.714048
$454$	−2.41193e17	−1.29271
$455$	−2.00187e17	−1.05770
$456$	−6.49499e16	−0.338304
$457$	3.87963e17	1.99221	0.996105	−	0.0881765i	$-0.0281039\pi$
$457$	3.87963e17	1.99221	0.996105	+	0.0881765i	$0.0281039\pi$
$458$	−2.80882e16	−0.142200
$459$	−4.12839e17	−2.06062
$460$	−6.30195e16	−0.310134
$461$	−5.56368e15	−0.0269964	−0.0134982	−	0.999909i	$-0.504297\pi$
$461$	−5.56368e15	−0.0269964	−0.0134982	+	0.999909i	$0.504297\pi$
$462$	−5.29409e16	−0.253290
$463$	1.93151e16	0.0911216	0.0455608	−	0.998962i	$-0.485493\pi$
$463$	1.93151e16	0.0911216	0.0455608	+	0.998962i	$0.485493\pi$
$464$	−2.94570e16	−0.137032
$465$	2.05413e17	0.942289
$466$	−2.44128e17	−1.10435
$467$	−3.86375e17	−1.72365	−0.861826	−	0.507204i	$-0.830679\pi$
$467$	−3.86375e17	−1.72365	−0.861826	+	0.507204i	$0.830679\pi$
$468$	4.54987e16	0.200171
$469$	−3.85375e16	−0.167209
$470$	−3.29923e17	−1.41181
$471$	−3.00775e17	−1.26942
$472$	2.49948e16	0.104046
$473$	−6.32516e16	−0.259701
$474$	2.00693e17	0.812782
$475$	4.24764e17	1.69683
$476$	9.15801e16	0.360874
$477$	6.64087e16	0.258140
$478$	−1.94025e17	−0.744007
$479$	4.21069e17	1.59284	0.796420	−	0.604744i	$-0.206724\pi$
$479$	4.21069e17	1.59284	0.796420	+	0.604744i	$0.206724\pi$
$480$	−6.65235e16	−0.248260
$481$	1.83813e17	0.676756
$482$	−3.39817e17	−1.23435
$483$	−3.59240e16	−0.128744
$484$	2.32788e16	0.0823124
$485$	5.69963e16	0.198850
$486$	−9.19794e16	−0.316632
$487$	−7.57529e16	−0.257312	−0.128656	−	0.991689i	$-0.541066\pi$
$487$	−7.57529e16	−0.257312	−0.128656	+	0.991689i	$0.541066\pi$
$488$	4.07440e16	0.136564
$489$	−8.66900e16	−0.286722
$490$	−4.94941e16	−0.161540
$491$	1.98609e17	0.639689	0.319844	−	0.947470i	$-0.396369\pi$
$491$	1.98609e17	0.639689	0.319844	+	0.947470i	$0.396369\pi$
$492$	1.68413e17	0.535308
$493$	−3.33674e17	−1.04669
$494$	4.35502e17	1.34823
$495$	−1.29221e17	−0.394819
$496$	5.56254e16	0.167742
$497$	−1.76693e17	−0.525898
$498$	1.33777e17	0.392998
$499$	−6.49296e16	−0.188274	−0.0941368	−	0.995559i	$-0.530009\pi$
$499$	−6.49296e16	−0.188274	−0.0941368	+	0.995559i	$0.530009\pi$
$500$	1.55693e17	0.445619
$501$	7.49658e16	0.211796
$502$	6.28161e16	0.175185
$503$	−6.28854e17	−1.73124	−0.865622	−	0.500699i	$-0.833076\pi$
$503$	−6.28854e17	−1.73124	−0.865622	+	0.500699i	$0.833076\pi$
$504$	1.12491e16	0.0305717
$505$	−7.04992e17	−1.89143
$506$	1.11749e17	0.295982
$507$	6.92590e17	1.81102
$508$	1.07653e17	0.277915
$509$	−3.65504e17	−0.931593	−0.465797	−	0.884892i	$-0.654232\pi$
$509$	−3.65504e17	−0.931593	−0.465797	+	0.884892i	$0.654232\pi$
$510$	−7.53543e17	−1.89628
$511$	7.90366e16	0.196378
$512$	−1.80144e16	−0.0441942
$513$	−4.85387e17	−1.17578
$514$	2.22920e17	0.533197
$515$	6.36249e16	0.150273
$516$	−4.53069e16	−0.105667
$517$	5.85034e17	1.34739
$518$	4.54458e16	0.103359
$519$	2.05749e17	0.462114
$520$	4.46054e17	0.989385
$521$	5.48448e17	1.20141	0.600704	−	0.799471i	$-0.294887\pi$
$521$	5.48448e17	1.20141	0.600704	+	0.799471i	$0.294887\pi$
$522$	−4.09863e16	−0.0886708
$523$	6.93718e17	1.48225	0.741126	−	0.671366i	$-0.234292\pi$
$523$	6.93718e17	1.48225	0.741126	+	0.671366i	$0.234292\pi$
$524$	−3.08535e17	−0.651105
$525$	2.48001e17	0.516913
$526$	5.19735e17	1.06998
$527$	6.30095e17	1.28126
$528$	1.17962e17	0.236932
$529$	−4.28207e17	−0.849556
$530$	6.51047e17	1.27591
$531$	3.47776e16	0.0673264
$532$	1.07673e17	0.205913
$533$	−1.12925e18	−2.13335
$534$	4.99902e14	0.000932967 0
$535$	−9.69583e17	−1.78766
$536$	8.58687e16	0.156410
$537$	−3.59119e17	−0.646258
$538$	8.05959e16	0.143294
$539$	8.77651e16	0.154168
$540$	−4.97147e17	−0.862830
$541$	3.00935e17	0.516048	0.258024	−	0.966138i	$-0.416929\pi$
$541$	3.00935e17	0.516048	0.258024	+	0.966138i	$0.416929\pi$
$542$	−2.45004e17	−0.415124
$543$	8.71719e17	1.45941
$544$	−2.04058e17	−0.337567
$545$	1.01790e18	1.66390
$546$	2.54271e17	0.410718
$547$	−6.18059e17	−0.986534	−0.493267	−	0.869878i	$-0.664197\pi$
$547$	−6.18059e17	−0.986534	−0.493267	+	0.869878i	$0.664197\pi$
$548$	−1.11833e16	−0.0176399
$549$	5.66909e16	0.0883676
$550$	−7.71458e17	−1.18838
$551$	−3.92310e17	−0.597234
$552$	8.00453e16	0.120429
$553$	−3.32708e17	−0.494709
$554$	1.59417e17	0.234273
$555$	−3.73939e17	−0.543121
$556$	2.24373e17	0.322095
$557$	−4.15372e17	−0.589357	−0.294678	−	0.955596i	$-0.595213\pi$
$557$	−4.15372e17	−0.589357	−0.294678	+	0.955596i	$0.595213\pi$
$558$	7.73967e16	0.108543
$559$	3.03792e17	0.421114
$560$	1.10282e17	0.151107
$561$	1.33622e18	1.80975
$562$	8.27279e16	0.110756
$563$	−4.52551e17	−0.598911	−0.299456	−	0.954110i	$-0.596805\pi$
$563$	−4.52551e17	−0.598911	−0.299456	+	0.954110i	$0.596805\pi$
$564$	4.19058e17	0.548226
$565$	−1.37949e18	−1.78404
$566$	8.80559e17	1.12578
$567$	−2.14981e17	−0.271712
$568$	3.93704e17	0.491933
$569$	5.95211e17	0.735260	0.367630	−	0.929972i	$-0.380169\pi$
$569$	5.95211e17	0.735260	0.367630	+	0.929972i	$0.380169\pi$
$570$	−8.85963e17	−1.08200
$571$	1.47206e18	1.77743	0.888713	−	0.458464i	$-0.151600\pi$
$571$	1.47206e18	1.77743	0.888713	+	0.458464i	$0.151600\pi$
$572$	−7.90961e17	−0.944237
$573$	−9.51573e17	−1.12315
$574$	−2.79195e17	−0.325822
$575$	−5.23486e17	−0.604037
$576$	−2.50651e16	−0.0285972
$577$	−9.62048e17	−1.08531	−0.542655	−	0.839956i	$-0.682581\pi$
$577$	−9.62048e17	−1.08531	−0.542655	+	0.839956i	$0.682581\pi$
$578$	−1.67756e18	−1.87132
$579$	7.80722e17	0.861163
$580$	−4.01815e17	−0.438273
$581$	−2.21774e17	−0.239203
$582$	−7.23949e16	−0.0772162
$583$	−1.15446e18	−1.21769
$584$	−1.76108e17	−0.183695
$585$	6.20635e17	0.640211
$586$	−2.55886e17	−0.261043
$587$	−9.29322e15	−0.00937602	−0.00468801	−	0.999989i	$-0.501492\pi$
$587$	−9.29322e15	−0.00937602	−0.00468801	+	0.999989i	$0.501492\pi$
$588$	6.28658e16	0.0627281
$589$	7.40821e17	0.731079
$590$	3.40948e17	0.332774
$591$	−3.03337e16	−0.0292824
$592$	−1.01262e17	−0.0966839
$593$	1.86928e17	0.176531	0.0882653	−	0.996097i	$-0.471868\pi$
$593$	1.86928e17	0.176531	0.0882653	+	0.996097i	$0.471868\pi$
$594$	8.81562e17	0.823457
$595$	1.24922e18	1.15419
$596$	6.80606e17	0.622007
$597$	−5.46722e17	−0.494235
$598$	−5.36720e17	−0.479943
$599$	−3.07346e17	−0.271865	−0.135932	−	0.990718i	$-0.543403\pi$
$599$	−3.07346e17	−0.271865	−0.135932	+	0.990718i	$0.543403\pi$
$600$	−5.52592e17	−0.483528
$601$	1.82771e17	0.158206	0.0791029	−	0.996866i	$-0.474794\pi$
$601$	1.82771e17	0.158206	0.0791029	+	0.996866i	$0.474794\pi$
$602$	7.51094e16	0.0643157
$603$	1.19477e17	0.101210
$604$	−4.85118e17	−0.406544
$605$	3.17539e17	0.263262
$606$	8.95457e17	0.734468
$607$	1.64727e18	1.33672	0.668358	−	0.743840i	$-0.266998\pi$
$607$	1.64727e18	1.33672	0.668358	+	0.743840i	$0.266998\pi$
$608$	−2.39917e17	−0.192614
$609$	−2.29053e17	−0.181938
$610$	5.55777e17	0.436774
$611$	−2.80987e18	−2.18483
$612$	−2.83924e17	−0.218433
$613$	7.43288e17	0.565801	0.282901	−	0.959149i	$-0.408703\pi$
$613$	7.43288e17	0.565801	0.282901	+	0.959149i	$0.408703\pi$
$614$	7.84523e17	0.590896
$615$	2.29728e18	1.71209
$616$	−1.95557e17	−0.144211
$617$	2.15022e18	1.56902	0.784511	−	0.620115i	$-0.212914\pi$
$617$	2.15022e18	1.56902	0.784511	+	0.620115i	$0.212914\pi$
$618$	−8.08143e16	−0.0583530
$619$	−7.03308e17	−0.502524	−0.251262	−	0.967919i	$-0.580846\pi$
$619$	−7.03308e17	−0.502524	−0.251262	+	0.967919i	$0.580846\pi$
$620$	7.58770e17	0.536493
$621$	5.98199e17	0.418553
$622$	−1.80358e18	−1.24881
$623$	−8.28733e14	−0.000567862 0
$624$	−5.66562e17	−0.384192
$625$	−1.96818e17	−0.132082
$626$	8.32886e17	0.553162
$627$	1.57103e18	1.03263
$628$	−1.11103e18	−0.722748
$629$	−1.14704e18	−0.738498
$630$	1.53446e17	0.0977780
$631$	1.69976e18	1.07201	0.536003	−	0.844216i	$-0.319933\pi$
$631$	1.69976e18	1.07201	0.536003	+	0.844216i	$0.319933\pi$
$632$	7.41336e17	0.462758
$633$	−1.52670e18	−0.943259
$634$	1.04776e18	0.640739
$635$	1.46846e18	0.888860
$636$	−8.26939e17	−0.495452
$637$	−4.21528e17	−0.249988
$638$	7.12516e17	0.418273
$639$	5.47797e17	0.318320
$640$	−2.45729e17	−0.141347
$641$	−3.06814e17	−0.174702	−0.0873511	−	0.996178i	$-0.527840\pi$
$641$	−3.06814e17	−0.174702	−0.0873511	+	0.996178i	$0.527840\pi$
$642$	1.23153e18	0.694174
$643$	−1.87966e18	−1.04884	−0.524419	−	0.851461i	$-0.675717\pi$
$643$	−1.87966e18	−1.04884	−0.524419	+	0.851461i	$0.675717\pi$
$644$	−1.32699e17	−0.0733007
$645$	−6.18018e17	−0.337958
$646$	−2.71765e18	−1.47124
$647$	2.01268e18	1.07869	0.539347	−	0.842084i	$-0.318671\pi$
$647$	2.01268e18	1.07869	0.539347	+	0.842084i	$0.318671\pi$
$648$	4.79017e17	0.254164
$649$	−6.04583e17	−0.317589
$650$	3.70524e18	1.92699
$651$	4.32533e17	0.222712
$652$	−3.20222e17	−0.163246
$653$	−1.11480e18	−0.562679	−0.281339	−	0.959608i	$-0.590779\pi$
$653$	−1.11480e18	−0.562679	−0.281339	+	0.959608i	$0.590779\pi$
$654$	−1.29290e18	−0.646114
$655$	−4.20864e18	−2.08244
$656$	6.22098e17	0.304778
$657$	−2.45036e17	−0.118865
$658$	−6.94711e17	−0.333684
$659$	−3.53771e17	−0.168255	−0.0841273	−	0.996455i	$-0.526810\pi$
$659$	−3.53771e17	−0.168255	−0.0841273	+	0.996455i	$0.526810\pi$
$660$	1.60909e18	0.757783
$661$	−2.70797e18	−1.26280	−0.631400	−	0.775457i	$-0.717519\pi$
$661$	−2.70797e18	−1.26280	−0.631400	+	0.775457i	$0.717519\pi$
$662$	−1.31913e18	−0.609129
$663$	−6.41772e18	−2.93456
$664$	4.94155e17	0.223754
$665$	1.46874e18	0.658575
$666$	−1.40895e17	−0.0625623
$667$	4.83490e17	0.212603
$668$	2.76914e17	0.120586
$669$	−3.39021e18	−1.46203
$670$	1.17131e18	0.500249
$671$	−9.85528e17	−0.416843
$672$	−1.40077e17	−0.0586767
$673$	2.69775e18	1.11919	0.559594	−	0.828767i	$-0.310957\pi$
$673$	2.69775e18	1.11919	0.559594	+	0.828767i	$0.310957\pi$
$674$	1.41718e18	0.582285
$675$	−4.12966e18	−1.68051
$676$	2.55834e18	1.03111
$677$	−7.06744e17	−0.282121	−0.141061	−	0.990001i	$-0.545051\pi$
$677$	−7.06744e17	−0.282121	−0.141061	+	0.990001i	$0.545051\pi$
$678$	1.75218e18	0.692765
$679$	1.20016e17	0.0469985
$680$	−2.78349e18	−1.07965
$681$	4.17891e18	1.60549
$682$	−1.34548e18	−0.512012
$683$	−2.88707e18	−1.08824	−0.544118	−	0.839009i	$-0.683136\pi$
$683$	−2.88707e18	−1.08824	−0.544118	+	0.839009i	$0.683136\pi$
$684$	−3.33818e17	−0.124637
$685$	−1.52548e17	−0.0564181
$686$	−1.04218e17	−0.0381802
$687$	4.86657e17	0.176605
$688$	−1.67358e17	−0.0601618
$689$	5.54479e18	1.97451
$690$	1.09188e18	0.385171
$691$	2.77646e18	0.970252	0.485126	−	0.874444i	$-0.338774\pi$
$691$	2.77646e18	0.970252	0.485126	+	0.874444i	$0.338774\pi$
$692$	7.60009e17	0.263105
$693$	−2.72097e17	−0.0933162
$694$	−1.36732e18	−0.464550
$695$	3.06061e18	1.03016
$696$	5.10372e17	0.170187
$697$	7.04680e18	2.32798
$698$	−2.71535e18	−0.888723
$699$	4.22975e18	1.37156
$700$	9.16084e17	0.294305
$701$	−4.76671e18	−1.51723	−0.758615	−	0.651540i	$-0.774123\pi$
$701$	−4.76671e18	−1.51723	−0.758615	+	0.651540i	$0.774123\pi$
$702$	−4.23406e18	−1.33526
$703$	−1.34861e18	−0.421383
$704$	4.35738e17	0.134897
$705$	5.71625e18	1.75340
$706$	−1.94220e18	−0.590286
$707$	−1.48448e18	−0.447043
$708$	−4.33060e17	−0.129221
$709$	3.00386e18	0.888134	0.444067	−	0.895994i	$-0.353535\pi$
$709$	3.00386e18	0.888134	0.444067	+	0.895994i	$0.353535\pi$
$710$	5.37041e18	1.57336
$711$	1.03149e18	0.299442
$712$	1.84657e15	0.000531186 0
$713$	−9.13000e17	−0.260249
$714$	−1.58672e18	−0.448189
$715$	−1.07893e19	−3.01997
$716$	−1.32654e18	−0.367948
$717$	3.36168e18	0.924022
$718$	−1.34258e18	−0.365705
$719$	−2.43787e18	−0.658071	−0.329036	−	0.944317i	$-0.606724\pi$
$719$	−2.43787e18	−0.658071	−0.329036	+	0.944317i	$0.606724\pi$
$720$	−3.41906e17	−0.0914630
$721$	1.33973e17	0.0355172
$722$	−5.03832e17	−0.132371
$723$	5.88767e18	1.53301
$724$	3.22002e18	0.830917
$725$	−3.33777e18	−0.853609
$726$	−4.03328e17	−0.102228
$727$	−4.13756e18	−1.03937	−0.519685	−	0.854358i	$-0.673951\pi$
$727$	−4.13756e18	−1.03937	−0.519685	+	0.854358i	$0.673951\pi$
$728$	9.39243e17	0.233843
$729$	4.50695e18	1.11213
$730$	−2.40225e18	−0.587515
$731$	−1.89574e18	−0.459532
$732$	−7.05930e17	−0.169605
$733$	2.05309e18	0.488915	0.244457	−	0.969660i	$-0.421390\pi$
$733$	2.05309e18	0.488915	0.244457	+	0.969660i	$0.421390\pi$
$734$	1.45211e18	0.342748
$735$	8.57535e17	0.200625
$736$	2.95677e17	0.0685665
$737$	−2.07702e18	−0.477421
$738$	8.65582e17	0.197216
$739$	1.49427e18	0.337474	0.168737	−	0.985661i	$-0.446031\pi$
$739$	1.49427e18	0.337474	0.168737	+	0.985661i	$0.446031\pi$
$740$	−1.38128e18	−0.309226
$741$	−7.54551e18	−1.67444
$742$	1.37089e18	0.301563
$743$	7.20473e18	1.57105	0.785526	−	0.618829i	$-0.212393\pi$
$743$	7.20473e18	1.57105	0.785526	+	0.618829i	$0.212393\pi$
$744$	−9.63765e17	−0.208328
$745$	9.28396e18	1.98938
$746$	2.25545e17	0.0479105
$747$	6.87563e17	0.144787
$748$	4.93581e18	1.03038
$749$	−2.04163e18	−0.422517
$750$	−2.69753e18	−0.553438
$751$	−5.98230e17	−0.121677	−0.0608385	−	0.998148i	$-0.519377\pi$
$751$	−5.98230e17	−0.121677	−0.0608385	+	0.998148i	$0.519377\pi$
$752$	1.54795e18	0.312133
$753$	−1.08835e18	−0.217571
$754$	−3.42215e18	−0.678243
$755$	−6.61736e18	−1.30026
$756$	−1.04683e18	−0.203931
$757$	5.19543e18	1.00346	0.501728	−	0.865025i	$-0.332698\pi$
$757$	5.19543e18	1.00346	0.501728	+	0.865025i	$0.332698\pi$
$758$	−2.98298e18	−0.571217
$759$	−1.93616e18	−0.367595
$760$	−3.27264e18	−0.616041
$761$	−1.96107e18	−0.366009	−0.183005	−	0.983112i	$-0.558582\pi$
$761$	−1.96107e18	−0.366009	−0.183005	+	0.983112i	$0.558582\pi$
$762$	−1.86519e18	−0.345157
$763$	2.14336e18	0.393265
$764$	−3.51499e18	−0.639466
$765$	−3.87293e18	−0.698619
$766$	4.77400e18	0.853878
$767$	2.90376e18	0.514980
$768$	3.12117e17	0.0548870
$769$	−8.41483e18	−1.46732	−0.733659	−	0.679518i	$-0.762189\pi$
$769$	−8.41483e18	−1.46732	−0.733659	+	0.679518i	$0.762189\pi$
$770$	−2.66754e18	−0.461234
$771$	−3.86230e18	−0.662205
$772$	2.88389e18	0.490304
$773$	9.01252e18	1.51943	0.759713	−	0.650259i	$-0.225340\pi$
$773$	9.01252e18	1.51943	0.759713	+	0.650259i	$0.225340\pi$
$774$	−2.32860e17	−0.0389295
$775$	6.30289e18	1.04491
$776$	−2.67417e17	−0.0439631
$777$	−7.87393e17	−0.128368
$778$	−1.16465e18	−0.188290
$779$	8.28513e18	1.32833
$780$	−7.72832e18	−1.22877
$781$	−9.52304e18	−1.50156
$782$	3.34928e18	0.523729
$783$	3.81414e18	0.591487
$784$	2.32218e17	0.0357143
$785$	−1.51552e19	−2.31158
$786$	5.34567e18	0.808641
$787$	−6.52810e18	−0.979379	−0.489689	−	0.871897i	$-0.662890\pi$
$787$	−6.52810e18	−0.979379	−0.489689	+	0.871897i	$0.662890\pi$
$788$	−1.12049e17	−0.0166719
$789$	−9.00492e18	−1.32886
$790$	1.01124e19	1.48005
$791$	−2.90475e18	−0.421660
$792$	6.06282e17	0.0872893
$793$	4.73340e18	0.675924
$794$	−1.99053e18	−0.281927
$795$	−1.12800e19	−1.58462
$796$	−2.01952e18	−0.281393
$797$	−7.28998e17	−0.100751	−0.0503753	−	0.998730i	$-0.516042\pi$
$797$	−7.28998e17	−0.100751	−0.0503753	+	0.998730i	$0.516042\pi$
$798$	−1.86555e18	−0.255734
$799$	1.75343e19	2.38416
$800$	−2.04121e18	−0.275297
$801$	2.56931e15	0.000343720 0
$802$	1.64690e18	0.218541
$803$	4.25976e18	0.560705
$804$	−1.48776e18	−0.194253
$805$	−1.81010e18	−0.234439
$806$	6.46224e18	0.830243
$807$	−1.39640e18	−0.177964
$808$	3.30771e18	0.418170
$809$	−5.95710e17	−0.0747084	−0.0373542	−	0.999302i	$-0.511893\pi$
$809$	−5.95710e17	−0.0747084	−0.0373542	+	0.999302i	$0.511893\pi$
$810$	6.53414e18	0.812897
$811$	6.43308e18	0.793932	0.396966	−	0.917833i	$-0.370063\pi$
$811$	6.43308e18	0.793932	0.396966	+	0.917833i	$0.370063\pi$
$812$	−8.46092e17	−0.103587
$813$	4.24493e18	0.515564
$814$	2.44935e18	0.295116
$815$	−4.36805e18	−0.522112
$816$	3.53550e18	0.419242
$817$	−2.22888e18	−0.262206
$818$	−6.03802e18	−0.704690
$819$	1.30686e18	0.151315
$820$	8.48586e18	0.974779
$821$	−8.28256e18	−0.943917	−0.471959	−	0.881621i	$-0.656453\pi$
$821$	−8.28256e18	−0.943917	−0.471959	+	0.881621i	$0.656453\pi$
$822$	1.93762e17	0.0219079
$823$	6.45598e18	0.724208	0.362104	−	0.932138i	$-0.382058\pi$
$823$	6.45598e18	0.724208	0.362104	+	0.932138i	$0.382058\pi$
$824$	−2.98518e17	−0.0332233
$825$	1.33663e19	1.47591
$826$	7.17924e17	0.0786518
$827$	−1.92987e18	−0.209770	−0.104885	−	0.994484i	$-0.533447\pi$
$827$	−1.92987e18	−0.209770	−0.104885	+	0.994484i	$0.533447\pi$
$828$	4.11403e17	0.0443680
$829$	9.56289e18	1.02326	0.511628	−	0.859207i	$-0.329042\pi$
$829$	9.56289e18	1.02326	0.511628	+	0.859207i	$0.329042\pi$
$830$	6.74063e18	0.715637
$831$	−2.76206e18	−0.290956
$832$	−2.09281e18	−0.218740
$833$	2.63045e18	0.272795
$834$	−3.88748e18	−0.400027
$835$	3.77731e18	0.385674
$836$	5.80318e18	0.587929
$837$	−7.20246e18	−0.724044
$838$	2.50688e18	0.250061
$839$	−6.90871e18	−0.683824	−0.341912	−	0.939732i	$-0.611074\pi$
$839$	−6.90871e18	−0.683824	−0.341912	+	0.939732i	$0.611074\pi$
$840$	−1.91075e18	−0.187667
$841$	−7.17788e18	−0.699555
$842$	4.25488e18	0.411489
$843$	−1.43334e18	−0.137553
$844$	−5.63945e18	−0.537045
$845$	3.48976e19	3.29782
$846$	2.15380e18	0.201975
$847$	6.68634e17	0.0622223
$848$	−3.05461e18	−0.282086
$849$	−1.52566e19	−1.39816
$850$	−2.31217e19	−2.10279
$851$	1.66205e18	0.150003
$852$	−6.82132e18	−0.610957
$853$	−1.00043e19	−0.889242	−0.444621	−	0.895719i	$-0.646662\pi$
$853$	−1.00043e19	−0.889242	−0.444621	+	0.895719i	$0.646662\pi$
$854$	1.17029e18	0.103232
$855$	−4.55352e18	−0.398628
$856$	4.54912e18	0.395229
$857$	−1.99771e19	−1.72249	−0.861244	−	0.508192i	$-0.830314\pi$
$857$	−1.99771e19	−1.72249	−0.861244	+	0.508192i	$0.830314\pi$
$858$	1.37042e19	1.17270
$859$	−4.91261e18	−0.417212	−0.208606	−	0.978000i	$-0.566893\pi$
$859$	−4.91261e18	−0.417212	−0.208606	+	0.978000i	$0.566893\pi$
$860$	−2.28288e18	−0.192417
$861$	4.83732e18	0.404655
$862$	−1.42172e19	−1.18037
$863$	−2.09882e19	−1.72944	−0.864718	−	0.502258i	$-0.832503\pi$
$863$	−2.09882e19	−1.72944	−0.864718	+	0.502258i	$0.832503\pi$
$864$	2.33253e18	0.190760
$865$	1.03671e19	0.841495
$866$	−2.90365e18	−0.233926
$867$	2.90655e19	2.32409
$868$	1.59772e18	0.126801
$869$	−1.79317e19	−1.41251
$870$	6.96185e18	0.544314
$871$	9.97573e18	0.774153
$872$	−4.77580e18	−0.367866
$873$	−3.72082e17	−0.0284477
$874$	3.93784e18	0.298837
$875$	4.47195e18	0.336856
$876$	3.05125e18	0.228140
$877$	−7.25903e18	−0.538742	−0.269371	−	0.963036i	$-0.586816\pi$
$877$	−7.25903e18	−0.538742	−0.269371	+	0.963036i	$0.586816\pi$
$878$	−4.14980e18	−0.305712
$879$	4.43348e18	0.324203
$880$	5.94378e18	0.431445
$881$	3.60512e18	0.259762	0.129881	−	0.991530i	$-0.458540\pi$
$881$	3.60512e18	0.259762	0.129881	+	0.991530i	$0.458540\pi$
$882$	3.23107e17	0.0231100
$883$	2.23424e19	1.58630	0.793151	−	0.609025i	$-0.208439\pi$
$883$	2.23424e19	1.58630	0.793151	+	0.609025i	$0.208439\pi$
$884$	−2.37062e19	−1.67079
$885$	−5.90726e18	−0.413290
$886$	−1.38911e19	−0.964753
$887$	−1.65027e19	−1.13776	−0.568882	−	0.822419i	$-0.692624\pi$
$887$	−1.65027e19	−1.13776	−0.568882	+	0.822419i	$0.692624\pi$
$888$	1.75446e18	0.120077
$889$	3.09210e18	0.210084
$890$	2.51886e16	0.00169890
$891$	−1.15866e19	−0.775803
$892$	−1.25230e19	−0.832410
$893$	2.06156e19	1.36038
$894$	−1.17922e19	−0.772503
$895$	−1.80950e19	−1.17682
$896$	−5.17426e17	−0.0334077
$897$	9.29920e18	0.596067
$898$	1.25926e18	0.0801343
$899$	−5.82133e18	−0.367777
$900$	−2.84012e18	−0.178139
$901$	−3.46010e19	−2.15465
$902$	−1.50475e19	−0.930297
$903$	−1.30134e18	−0.0798771
$904$	6.47234e18	0.394427
$905$	4.39234e19	2.65754
$906$	8.40515e18	0.504908
$907$	9.57981e18	0.571360	0.285680	−	0.958325i	$-0.407781\pi$
$907$	9.57981e18	0.571360	0.285680	+	0.958325i	$0.407781\pi$
$908$	1.54364e19	0.914086
$909$	4.60232e18	0.270590
$910$	1.28120e19	0.747905
$911$	2.49206e19	1.44441	0.722204	−	0.691680i	$-0.243129\pi$
$911$	2.49206e19	1.44441	0.722204	+	0.691680i	$0.243129\pi$
$912$	4.15679e18	0.239217
$913$	−1.19528e19	−0.682981
$914$	−2.48296e19	−1.40871
$915$	−9.62939e18	−0.542453
$916$	1.79765e18	0.100550
$917$	−8.86201e18	−0.492189
$918$	2.64217e19	1.45708
$919$	−1.31856e19	−0.722019	−0.361009	−	0.932562i	$-0.617568\pi$
$919$	−1.31856e19	−0.722019	−0.361009	+	0.932562i	$0.617568\pi$
$920$	4.03325e18	0.219298
$921$	−1.35926e19	−0.733865
$922$	3.56075e17	0.0190893
$923$	4.57383e19	2.43483
$924$	3.38822e18	0.179103
$925$	−1.14739e19	−0.602270
$926$	−1.23617e18	−0.0644327
$927$	−4.15355e17	−0.0214982
$928$	1.88525e18	0.0968963
$929$	1.38234e19	0.705527	0.352763	−	0.935713i	$-0.385242\pi$
$929$	1.38234e19	0.705527	0.352763	+	0.935713i	$0.385242\pi$
$930$	−1.31464e19	−0.666299
$931$	3.09269e18	0.155655
$932$	1.56242e19	0.780897
$933$	3.12488e19	1.55097
$934$	2.47280e19	1.21881
$935$	6.73280e19	3.29549
$936$	−2.91192e18	−0.141542
$937$	−2.19986e19	−1.06191	−0.530955	−	0.847400i	$-0.678167\pi$
$937$	−2.19986e19	−1.06191	−0.530955	+	0.847400i	$0.678167\pi$
$938$	2.46640e18	0.118235
$939$	−1.44306e19	−0.687001
$940$	2.11151e19	0.998302
$941$	−2.18800e19	−1.02734	−0.513670	−	0.857988i	$-0.671715\pi$
$941$	−2.18800e19	−1.02734	−0.513670	+	0.857988i	$0.671715\pi$
$942$	1.92496e19	0.897618
$943$	−1.02107e19	−0.472858
$944$	−1.59967e18	−0.0735720
$945$	−1.42795e19	−0.652238
$946$	4.04810e18	0.183637
$947$	4.96128e18	0.223521	0.111761	−	0.993735i	$-0.464351\pi$
$947$	4.96128e18	0.223521	0.111761	+	0.993735i	$0.464351\pi$
$948$	−1.28444e19	−0.574724
$949$	−2.04593e19	−0.909200
$950$	−2.71849e19	−1.19984
$951$	−1.81535e19	−0.795767
$952$	−5.86113e18	−0.255177
$953$	−7.56115e18	−0.326952	−0.163476	−	0.986547i	$-0.552271\pi$
$953$	−7.56115e18	−0.326952	−0.163476	+	0.986547i	$0.552271\pi$
$954$	−4.25015e18	−0.182533
$955$	−4.79470e19	−2.04522
$956$	1.24176e19	0.526093
$957$	−1.23450e19	−0.519476
$958$	−2.69484e19	−1.12631
$959$	−3.21217e17	−0.0133345
$960$	4.25750e18	0.175546
$961$	−1.34248e19	−0.549802
$962$	−1.17640e19	−0.478539
$963$	6.32962e18	0.255745
$964$	2.17483e19	0.872820
$965$	3.93383e19	1.56815
$966$	2.29913e18	0.0910359
$967$	1.65832e19	0.652225	0.326112	−	0.945331i	$-0.394261\pi$
$967$	1.65832e19	0.652225	0.326112	+	0.945331i	$0.394261\pi$
$968$	−1.48984e18	−0.0582037
$969$	4.70860e19	1.82720
$970$	−3.64777e18	−0.140608
$971$	−1.93339e19	−0.740278	−0.370139	−	0.928976i	$-0.620690\pi$
$971$	−1.93339e19	−0.740278	−0.370139	+	0.928976i	$0.620690\pi$
$972$	5.88668e18	0.223893
$973$	6.44464e18	0.243481
$974$	4.84818e18	0.181947
$975$	−6.41970e19	−2.39323
$976$	−2.60762e18	−0.0965650
$977$	−6.44980e18	−0.237264	−0.118632	−	0.992938i	$-0.537851\pi$
$977$	−6.44980e18	−0.237264	−0.118632	+	0.992938i	$0.537851\pi$
$978$	5.54816e18	0.202743
$979$	−4.46655e16	−0.00162138
$980$	3.16762e18	0.114226
$981$	−6.64501e18	−0.238039
$982$	−1.27110e19	−0.452328
$983$	1.39114e19	0.491781	0.245891	−	0.969298i	$-0.420920\pi$
$983$	1.39114e19	0.491781	0.245891	+	0.969298i	$0.420920\pi$
$984$	−1.07785e19	−0.378520
$985$	−1.52842e18	−0.0533223
$986$	2.13551e19	0.740120
$987$	1.20365e19	0.414420
$988$	−2.78721e19	−0.953345
$989$	2.74691e18	0.0933401
$990$	8.27013e18	0.279179
$991$	−2.16705e19	−0.726760	−0.363380	−	0.931641i	$-0.618377\pi$
$991$	−2.16705e19	−0.726760	−0.363380	+	0.931641i	$0.618377\pi$
$992$	−3.56002e18	−0.118612
$993$	2.28552e19	0.756509
$994$	1.13083e19	0.371866
$995$	−2.75477e19	−0.899986
$996$	−8.56173e18	−0.277892
$997$	2.53678e19	0.818021	0.409010	−	0.912530i	$-0.365874\pi$
$997$	2.53678e19	0.818021	0.409010	+	0.912530i	$0.365874\pi$
$998$	4.15549e18	0.133129
$999$	1.31115e19	0.417328

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.14.a.c.1.2	✓	2
3.2	odd	2		126.14.a.l.1.1		2
4.3	odd	2		112.14.a.d.1.1		2
7.2	even	3		98.14.c.l.67.1		4
7.3	odd	6		98.14.c.m.79.2		4
7.4	even	3		98.14.c.l.79.1		4
7.5	odd	6		98.14.c.m.67.2		4
7.6	odd	2		98.14.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.14.a.c.1.2	✓	2	1.1	even	1	trivial
98.14.a.e.1.1		2	7.6	odd	2
98.14.c.l.67.1		4	7.2	even	3
98.14.c.l.79.1		4	7.4	even	3
98.14.c.m.67.2		4	7.5	odd	6
98.14.c.m.79.2		4	7.3	odd	6
112.14.a.d.1.1		2	4.3	odd	2
126.14.a.l.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:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)

\(f(q)\)	\(=\)	\(q-64.0000 q^{2} +1108.86 q^{3} +4096.00 q^{4} +55872.4 q^{5} -70967.3 q^{6} +117649. q^{7} -262144. q^{8} -364745. q^{9} +O(q^{10})\)	\(q-64.0000 q^{2} +1108.86 q^{3} +4096.00 q^{4} +55872.4 q^{5} -70967.3 q^{6} +117649. q^{7} -262144. q^{8} -364745. q^{9} -3.57583e6 q^{10} +6.34082e6 q^{11} +4.54190e6 q^{12} -3.04544e7 q^{13} -7.52954e6 q^{14} +6.19548e7 q^{15} +1.67772e7 q^{16} +1.90043e8 q^{17} +2.33437e7 q^{18} +2.23440e8 q^{19} +2.28853e8 q^{20} +1.30457e8 q^{21} -4.05813e8 q^{22} -2.75371e8 q^{23} -2.90682e8 q^{24} +1.90102e9 q^{25} +1.94908e9 q^{26} -2.17234e9 q^{27} +4.81890e8 q^{28} -1.75578e9 q^{29} -3.96511e9 q^{30} +3.31553e9 q^{31} -1.07374e9 q^{32} +7.03110e9 q^{33} -1.21628e10 q^{34} +6.57333e9 q^{35} -1.49400e9 q^{36} -6.03567e9 q^{37} -1.43001e10 q^{38} -3.37698e10 q^{39} -1.46466e10 q^{40} +3.70799e10 q^{41} -8.34923e9 q^{42} -9.97530e9 q^{43} +2.59720e10 q^{44} -2.03792e10 q^{45} +1.76237e10 q^{46} +9.22647e10 q^{47} +1.86036e10 q^{48} +1.38413e10 q^{49} -1.21665e11 q^{50} +2.10732e11 q^{51} -1.24741e11 q^{52} -1.82069e11 q^{53} +1.39030e11 q^{54} +3.54277e11 q^{55} -3.08410e10 q^{56} +2.47764e11 q^{57} +1.12370e11 q^{58} -9.53478e10 q^{59} +2.53767e11 q^{60} -1.55426e11 q^{61} -2.12194e11 q^{62} -4.29119e10 q^{63} +6.87195e10 q^{64} -1.70156e12 q^{65} -4.49991e11 q^{66} -3.27563e11 q^{67} +7.78418e11 q^{68} -3.05349e11 q^{69} -4.20693e11 q^{70} -1.50186e12 q^{71} +9.56157e10 q^{72} +6.71800e11 q^{73} +3.86283e11 q^{74} +2.10797e12 q^{75} +9.15209e11 q^{76} +7.45991e11 q^{77} +2.16126e12 q^{78} -2.82797e12 q^{79} +9.37383e11 q^{80} -1.82731e12 q^{81} -2.37312e12 q^{82} -1.88505e12 q^{83} +5.34350e11 q^{84} +1.06182e13 q^{85} +6.38419e11 q^{86} -1.94692e12 q^{87} -1.66221e12 q^{88} -7.04412e9 q^{89} +1.30427e12 q^{90} -3.58293e12 q^{91} -1.12792e12 q^{92} +3.67647e12 q^{93} -5.90494e12 q^{94} +1.24841e13 q^{95} -1.19063e12 q^{96} +1.02012e12 q^{97} -8.85842e11 q^{98} -2.31278e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 128 q^{2} + 952 q^{3} + 8192 q^{4} + 32004 q^{5} - 60928 q^{6} + 235298 q^{7} - 524288 q^{8} - 1934462 q^{9}+O(q^{10}) \) 2 * q - 128 * q^2 + 952 * q^3 + 8192 * q^4 + 32004 * q^5 - 60928 * q^6 + 235298 * q^7 - 524288 * q^8 - 1934462 * q^9	\( 2 q - 128 q^{2} + 952 q^{3} + 8192 q^{4} + 32004 q^{5} - 60928 q^{6} + 235298 q^{7} - 524288 q^{8} - 1934462 q^{9} - 2048256 q^{10} - 1352736 q^{11} + 3899392 q^{12} + 3510388 q^{13} - 15059072 q^{14} + 65698920 q^{15} + 33554432 q^{16} + 217711956 q^{17} + 123805568 q^{18} + 591335752 q^{19} + 131088384 q^{20} + 112001848 q^{21} + 86575104 q^{22} + 840735000 q^{23} - 249561088 q^{24} + 1250017766 q^{25} - 224664832 q^{26} - 1676016944 q^{27} + 963780608 q^{28} - 487623540 q^{29} - 4204730880 q^{30} + 2193076144 q^{31} - 2147483648 q^{32} + 8237940480 q^{33} - 13933565184 q^{34} + 3765238596 q^{35} - 7923556352 q^{36} + 405060268 q^{37} - 37845488128 q^{38} - 39097578952 q^{39} - 8389656576 q^{40} + 8518172628 q^{41} - 7168118272 q^{42} + 26225045296 q^{43} - 5540806656 q^{44} + 17087434308 q^{45} - 53807040000 q^{46} + 155048849760 q^{47} + 15971909632 q^{48} + 27682574402 q^{49} - 80001137024 q^{50} + 206392082208 q^{51} + 14378549248 q^{52} + 66007050492 q^{53} + 107265084416 q^{54} + 537909615936 q^{55} - 61681958912 q^{56} + 190054836824 q^{57} + 31207906560 q^{58} - 476362296984 q^{59} + 269102776320 q^{60} + 197378850004 q^{61} - 140356873216 q^{62} - 227587519838 q^{63} + 137438953472 q^{64} - 2512243760544 q^{65} - 527228190720 q^{66} - 1718732859488 q^{67} + 891748171776 q^{68} - 480424669200 q^{69} - 240975270144 q^{70} - 695543478336 q^{71} + 507107606528 q^{72} - 466085239340 q^{73} - 25923857152 q^{74} + 2210090828680 q^{75} + 2422111240192 q^{76} - 159148037664 q^{77} + 2502245052928 q^{78} - 2432016575840 q^{79} + 536938020864 q^{80} + 597475723018 q^{81} - 545163048192 q^{82} - 1743984494616 q^{83} + 458759569408 q^{84} + 9957781762488 q^{85} - 1678402898944 q^{86} - 2145843141792 q^{87} + 354611625984 q^{88} + 3022580240484 q^{89} - 1093595795712 q^{90} + 412993637812 q^{91} + 3443650560000 q^{92} + 3852541919312 q^{93} - 9923126384640 q^{94} + 3703032892440 q^{95} - 1022202216448 q^{96} + 7760062661092 q^{97} - 1771684761728 q^{98} + 9763922554848 q^{99}+O(q^{100}) \) 2 * q - 128 * q^2 + 952 * q^3 + 8192 * q^4 + 32004 * q^5 - 60928 * q^6 + 235298 * q^7 - 524288 * q^8 - 1934462 * q^9 - 2048256 * q^10 - 1352736 * q^11 + 3899392 * q^12 + 3510388 * q^13 - 15059072 * q^14 + 65698920 * q^15 + 33554432 * q^16 + 217711956 * q^17 + 123805568 * q^18 + 591335752 * q^19 + 131088384 * q^20 + 112001848 * q^21 + 86575104 * q^22 + 840735000 * q^23 - 249561088 * q^24 + 1250017766 * q^25 - 224664832 * q^26 - 1676016944 * q^27 + 963780608 * q^28 - 487623540 * q^29 - 4204730880 * q^30 + 2193076144 * q^31 - 2147483648 * q^32 + 8237940480 * q^33 - 13933565184 * q^34 + 3765238596 * q^35 - 7923556352 * q^36 + 405060268 * q^37 - 37845488128 * q^38 - 39097578952 * q^39 - 8389656576 * q^40 + 8518172628 * q^41 - 7168118272 * q^42 + 26225045296 * q^43 - 5540806656 * q^44 + 17087434308 * q^45 - 53807040000 * q^46 + 155048849760 * q^47 + 15971909632 * q^48 + 27682574402 * q^49 - 80001137024 * q^50 + 206392082208 * q^51 + 14378549248 * q^52 + 66007050492 * q^53 + 107265084416 * q^54 + 537909615936 * q^55 - 61681958912 * q^56 + 190054836824 * q^57 + 31207906560 * q^58 - 476362296984 * q^59 + 269102776320 * q^60 + 197378850004 * q^61 - 140356873216 * q^62 - 227587519838 * q^63 + 137438953472 * q^64 - 2512243760544 * q^65 - 527228190720 * q^66 - 1718732859488 * q^67 + 891748171776 * q^68 - 480424669200 * q^69 - 240975270144 * q^70 - 695543478336 * q^71 + 507107606528 * q^72 - 466085239340 * q^73 - 25923857152 * q^74 + 2210090828680 * q^75 + 2422111240192 * q^76 - 159148037664 * q^77 + 2502245052928 * q^78 - 2432016575840 * q^79 + 536938020864 * q^80 + 597475723018 * q^81 - 545163048192 * q^82 - 1743984494616 * q^83 + 458759569408 * q^84 + 9957781762488 * q^85 - 1678402898944 * q^86 - 2145843141792 * q^87 + 354611625984 * q^88 + 3022580240484 * q^89 - 1093595795712 * q^90 + 412993637812 * q^91 + 3443650560000 * q^92 + 3852541919312 * q^93 - 9923126384640 * q^94 + 3703032892440 * q^95 - 1022202216448 * q^96 + 7760062661092 * q^97 - 1771684761728 * q^98 + 9763922554848 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more