LMFDB - Embedded newform 91.10.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,10,Mod(1,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("91.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	91.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:	$46.8682610909$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 7 x^{14} - 7002 x^{13} + 56252 x^{12} + 19365525 x^{11} - 172593791 x^{10} + \cdots + 15\!\cdots\!80 $ x^15 - 7x^14 - 7002x^13 + 56252x^12 + 19365525x^11 - 172593791x^10 - 26814463634x^9 + 254652735184x^8 + 19468686934379x^7 - 187275922162581x^6 - 7114485342885046x^5 + 65109704629514532x^4 + 1131832063959701151x^3 - 8977247355614269573x^2 - 47004259937698392062x + 152144189066892720880
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-43.2539$ of defining polynomial
Character	$\chi$	$=$	91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-42.2539 q^{2} -265.754 q^{3} +1273.39 q^{4} -1521.37 q^{5} +11229.2 q^{6} -2401.00 q^{7} -32171.6 q^{8} +50942.5 q^{9} +O(q^{10})$	\(q-42.2539 q^{2} -265.754 q^{3} +1273.39 q^{4} -1521.37 q^{5} +11229.2 q^{6} -2401.00 q^{7} -32171.6 q^{8} +50942.5 q^{9} +64283.6 q^{10} +92179.5 q^{11} -338409. q^{12} +28561.0 q^{13} +101452. q^{14} +404310. q^{15} +707399. q^{16} +504568. q^{17} -2.15251e6 q^{18} +235795. q^{19} -1.93729e6 q^{20} +638077. q^{21} -3.89494e6 q^{22} +796264. q^{23} +8.54974e6 q^{24} +361433. q^{25} -1.20681e6 q^{26} -8.30734e6 q^{27} -3.05740e6 q^{28} -212839. q^{29} -1.70837e7 q^{30} -1.19427e6 q^{31} -1.34185e7 q^{32} -2.44971e7 q^{33} -2.13199e7 q^{34} +3.65280e6 q^{35} +6.48695e7 q^{36} +8.24654e6 q^{37} -9.96323e6 q^{38} -7.59021e6 q^{39} +4.89448e7 q^{40} +1.19313e7 q^{41} -2.69612e7 q^{42} +1.35929e7 q^{43} +1.17380e8 q^{44} -7.75022e7 q^{45} -3.36452e7 q^{46} +1.92154e7 q^{47} -1.87994e8 q^{48} +5.76480e6 q^{49} -1.52719e7 q^{50} -1.34091e8 q^{51} +3.63692e7 q^{52} +5.37391e7 q^{53} +3.51017e8 q^{54} -1.40239e8 q^{55} +7.72440e7 q^{56} -6.26635e7 q^{57} +8.99328e6 q^{58} +4.84812e7 q^{59} +5.14844e8 q^{60} +1.52158e8 q^{61} +5.04626e7 q^{62} -1.22313e8 q^{63} +2.04794e8 q^{64} -4.34518e7 q^{65} +1.03510e9 q^{66} -1.64100e8 q^{67} +6.42511e8 q^{68} -2.11611e8 q^{69} -1.54345e8 q^{70} +1.27188e8 q^{71} -1.63890e9 q^{72} -4.54145e8 q^{73} -3.48448e8 q^{74} -9.60524e7 q^{75} +3.00258e8 q^{76} -2.21323e8 q^{77} +3.20716e8 q^{78} +5.50026e8 q^{79} -1.07621e9 q^{80} +1.20501e9 q^{81} -5.04145e8 q^{82} +3.51638e8 q^{83} +8.12519e8 q^{84} -7.67633e8 q^{85} -5.74353e8 q^{86} +5.65630e7 q^{87} -2.96556e9 q^{88} -5.81650e7 q^{89} +3.27477e9 q^{90} -6.85750e7 q^{91} +1.01395e9 q^{92} +3.17383e8 q^{93} -8.11924e8 q^{94} -3.58730e8 q^{95} +3.56602e9 q^{96} -5.97568e8 q^{97} -2.43585e8 q^{98} +4.69585e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 22 q^{2} + q^{3} + 6402 q^{4} + 1694 q^{5} + 4189 q^{6} - 36015 q^{7} - 1704 q^{8} + 160366 q^{9}+O(q^{10}) $ 15 * q + 22 * q^2 + q^3 + 6402 * q^4 + 1694 * q^5 + 4189 * q^6 - 36015 * q^7 - 1704 * q^8 + 160366 * q^9	\( 15 q + 22 q^{2} + q^{3} + 6402 q^{4} + 1694 q^{5} + 4189 q^{6} - 36015 q^{7} - 1704 q^{8} + 160366 q^{9} - 69748 q^{10} + 23441 q^{11} + 64437 q^{12} + 428415 q^{13} - 52822 q^{14} - 68316 q^{15} + 2694730 q^{16} + 606640 q^{17} + 1242207 q^{18} + 1762528 q^{19} + 43054 q^{20} - 2401 q^{21} + 119431 q^{22} + 3649531 q^{23} + 15986883 q^{24} + 9120575 q^{25} + 628342 q^{26} - 5957633 q^{27} - 15371202 q^{28} + 18072234 q^{29} - 58091296 q^{30} - 1096937 q^{31} + 6565744 q^{32} - 18425617 q^{33} - 46741622 q^{34} - 4067294 q^{35} + 132788567 q^{36} - 34982109 q^{37} - 2819104 q^{38} + 28561 q^{39} + 2107274 q^{40} + 59341985 q^{41} - 10057789 q^{42} + 38829122 q^{43} + 202791507 q^{44} + 2955478 q^{45} + 165169119 q^{46} + 18734035 q^{47} + 340656557 q^{48} + 86472015 q^{49} + 220443888 q^{50} + 93517168 q^{51} + 182847522 q^{52} + 332415086 q^{53} + 567466451 q^{54} - 120908856 q^{55} + 4091304 q^{56} + 62932402 q^{57} + 180863580 q^{58} + 28220174 q^{59} + 467078152 q^{60} + 404536605 q^{61} + 4283245 q^{62} - 385038766 q^{63} + 1276533074 q^{64} + 48382334 q^{65} + 1696546059 q^{66} + 746448213 q^{67} + 492702034 q^{68} + 453755667 q^{69} + 167464948 q^{70} + 81316200 q^{71} + 1255645679 q^{72} + 12687907 q^{73} + 1350657501 q^{74} - 164589481 q^{75} + 679560842 q^{76} - 56281841 q^{77} + 119642029 q^{78} + 1896008477 q^{79} - 1458560390 q^{80} + 3853340295 q^{81} + 410985635 q^{82} - 753815178 q^{83} - 154713237 q^{84} - 259541636 q^{85} - 1842794378 q^{86} + 1391390932 q^{87} + 288708813 q^{88} + 1109816012 q^{89} + 1196058116 q^{90} - 1028624415 q^{91} + 2409710277 q^{92} + 3345736043 q^{93} - 1423358651 q^{94} + 4615875678 q^{95} + 11615772371 q^{96} + 1054179205 q^{97} + 126825622 q^{98} - 2512222258 q^{99}+O(q^{100}) \) 15 * q + 22 * q^2 + q^3 + 6402 * q^4 + 1694 * q^5 + 4189 * q^6 - 36015 * q^7 - 1704 * q^8 + 160366 * q^9 - 69748 * q^10 + 23441 * q^11 + 64437 * q^12 + 428415 * q^13 - 52822 * q^14 - 68316 * q^15 + 2694730 * q^16 + 606640 * q^17 + 1242207 * q^18 + 1762528 * q^19 + 43054 * q^20 - 2401 * q^21 + 119431 * q^22 + 3649531 * q^23 + 15986883 * q^24 + 9120575 * q^25 + 628342 * q^26 - 5957633 * q^27 - 15371202 * q^28 + 18072234 * q^29 - 58091296 * q^30 - 1096937 * q^31 + 6565744 * q^32 - 18425617 * q^33 - 46741622 * q^34 - 4067294 * q^35 + 132788567 * q^36 - 34982109 * q^37 - 2819104 * q^38 + 28561 * q^39 + 2107274 * q^40 + 59341985 * q^41 - 10057789 * q^42 + 38829122 * q^43 + 202791507 * q^44 + 2955478 * q^45 + 165169119 * q^46 + 18734035 * q^47 + 340656557 * q^48 + 86472015 * q^49 + 220443888 * q^50 + 93517168 * q^51 + 182847522 * q^52 + 332415086 * q^53 + 567466451 * q^54 - 120908856 * q^55 + 4091304 * q^56 + 62932402 * q^57 + 180863580 * q^58 + 28220174 * q^59 + 467078152 * q^60 + 404536605 * q^61 + 4283245 * q^62 - 385038766 * q^63 + 1276533074 * q^64 + 48382334 * q^65 + 1696546059 * q^66 + 746448213 * q^67 + 492702034 * q^68 + 453755667 * q^69 + 167464948 * q^70 + 81316200 * q^71 + 1255645679 * q^72 + 12687907 * q^73 + 1350657501 * q^74 - 164589481 * q^75 + 679560842 * q^76 - 56281841 * q^77 + 119642029 * q^78 + 1896008477 * q^79 - 1458560390 * q^80 + 3853340295 * q^81 + 410985635 * q^82 - 753815178 * q^83 - 154713237 * q^84 - 259541636 * q^85 - 1842794378 * q^86 + 1391390932 * q^87 + 288708813 * q^88 + 1109816012 * q^89 + 1196058116 * q^90 - 1028624415 * q^91 + 2409710277 * q^92 + 3345736043 * q^93 - 1423358651 * q^94 + 4615875678 * q^95 + 11615772371 * q^96 + 1054179205 * q^97 + 126825622 * q^98 - 2512222258 * 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 $

$2$	−42.2539	−1.86737	−0.933687	−	0.358090i	$-0.883428\pi$
$2$	−42.2539	−1.86737	−0.933687	+	0.358090i	$0.883428\pi$
$3$	−265.754	−1.89424	−0.947120	−	0.320880i	$-0.896021\pi$
$3$	−265.754	−1.89424	−0.947120	+	0.320880i	$0.896021\pi$
$4$	1273.39	2.48709
$5$	−1521.37	−1.08860	−0.544301	−	0.838890i	$-0.683205\pi$
$5$	−1521.37	−1.08860	−0.544301	+	0.838890i	$0.683205\pi$
$6$	11229.2	3.53725
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	−32171.6	−2.77695
$9$	50942.5	2.58814
$10$	64283.6	2.03283
$11$	92179.5	1.89831	0.949155	−	0.314808i	$-0.101940\pi$
$11$	92179.5	1.89831	0.949155	+	0.314808i	$0.101940\pi$
$12$	−338409.	−4.71114
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	101452.	0.705801
$15$	404310.	2.06207
$16$	707399.	2.69851
$17$	504568.	1.46521	0.732604	−	0.680655i	$-0.238305\pi$
$17$	504568.	1.46521	0.732604	+	0.680655i	$0.238305\pi$
$18$	−2.15251e6	−4.83303
$19$	235795.	0.415090	0.207545	−	0.978225i	$-0.433453\pi$
$19$	235795.	0.415090	0.207545	+	0.978225i	$0.433453\pi$
$20$	−1.93729e6	−2.70745
$21$	638077.	0.715955
$22$	−3.89494e6	−3.54486
$23$	796264.	0.593310	0.296655	−	0.954985i	$-0.404129\pi$
$23$	796264.	0.593310	0.296655	+	0.954985i	$0.404129\pi$
$24$	8.54974e6	5.26020
$25$	361433.	0.185054
$26$	−1.20681e6	−0.517916
$27$	−8.30734e6	−3.00833
$28$	−3.05740e6	−0.940030
$29$	−212839.	−0.0558805	−0.0279403	−	0.999610i	$-0.508895\pi$
$29$	−212839.	−0.0558805	−0.0279403	+	0.999610i	$0.508895\pi$
$30$	−1.70837e7	−3.85066
$31$	−1.19427e6	−0.232261	−0.116130	−	0.993234i	$-0.537049\pi$
$31$	−1.19427e6	−0.232261	−0.116130	+	0.993234i	$0.537049\pi$
$32$	−1.34185e7	−2.26218
$33$	−2.44971e7	−3.59586
$34$	−2.13199e7	−2.73609
$35$	3.65280e6	0.411453
$36$	6.48695e7	6.43694
$37$	8.24654e6	0.723376	0.361688	−	0.932299i	$-0.382201\pi$
$37$	8.24654e6	0.723376	0.361688	+	0.932299i	$0.382201\pi$
$38$	−9.96323e6	−0.775129
$39$	−7.59021e6	−0.525368
$40$	4.89448e7	3.02299
$41$	1.19313e7	0.659420	0.329710	−	0.944082i	$-0.393049\pi$
$41$	1.19313e7	0.659420	0.329710	+	0.944082i	$0.393049\pi$
$42$	−2.69612e7	−1.33696
$43$	1.35929e7	0.606324	0.303162	−	0.952939i	$-0.401958\pi$
$43$	1.35929e7	0.606324	0.303162	+	0.952939i	$0.401958\pi$
$44$	1.17380e8	4.72126
$45$	−7.75022e7	−2.81746
$46$	−3.36452e7	−1.10793
$47$	1.92154e7	0.574393	0.287196	−	0.957872i	$-0.407277\pi$
$47$	1.92154e7	0.574393	0.287196	+	0.957872i	$0.407277\pi$
$48$	−1.87994e8	−5.11163
$49$	5.76480e6	0.142857
$50$	−1.52719e7	−0.345564
$51$	−1.34091e8	−2.77546
$52$	3.63692e7	0.689794
$53$	5.37391e7	0.935511	0.467756	−	0.883858i	$-0.345063\pi$
$53$	5.37391e7	0.935511	0.467756	+	0.883858i	$0.345063\pi$
$54$	3.51017e8	5.61767
$55$	−1.40239e8	−2.06650
$56$	7.72440e7	1.04959
$57$	−6.26635e7	−0.786280
$58$	8.99328e6	0.104350
$59$	4.84812e7	0.520882	0.260441	−	0.965490i	$-0.416132\pi$
$59$	4.84812e7	0.520882	0.260441	+	0.965490i	$0.416132\pi$
$60$	5.14844e8	5.12855
$61$	1.52158e8	1.40705	0.703526	−	0.710670i	$-0.251608\pi$
$61$	1.52158e8	1.40705	0.703526	+	0.710670i	$0.251608\pi$
$62$	5.04626e7	0.433717
$63$	−1.22313e8	−0.978227
$64$	2.04794e8	1.52583
$65$	−4.34518e7	−0.301924
$66$	1.03510e9	6.71481
$67$	−1.64100e8	−0.994880	−0.497440	−	0.867498i	$-0.665727\pi$
$67$	−1.64100e8	−0.994880	−0.497440	+	0.867498i	$0.665727\pi$
$68$	6.42511e8	3.64410
$69$	−2.11611e8	−1.12387
$70$	−1.54345e8	−0.768336
$71$	1.27188e8	0.593994	0.296997	−	0.954878i	$-0.404015\pi$
$71$	1.27188e8	0.593994	0.296997	+	0.954878i	$0.404015\pi$
$72$	−1.63890e9	−7.18714
$73$	−4.54145e8	−1.87172	−0.935861	−	0.352369i	$-0.885376\pi$
$73$	−4.54145e8	−1.87172	−0.935861	+	0.352369i	$0.885376\pi$
$74$	−3.48448e8	−1.35081
$75$	−9.60524e7	−0.350536
$76$	3.00258e8	1.03237
$77$	−2.21323e8	−0.717494
$78$	3.20716e8	0.981058
$79$	5.50026e8	1.58877	0.794386	−	0.607413i	$-0.207793\pi$
$79$	5.50026e8	1.58877	0.794386	+	0.607413i	$0.207793\pi$
$80$	−1.07621e9	−2.93760
$81$	1.20501e9	3.11035
$82$	−5.04145e8	−1.23138
$83$	3.51638e8	0.813288	0.406644	−	0.913587i	$-0.366699\pi$
$83$	3.51638e8	0.813288	0.406644	+	0.913587i	$0.366699\pi$
$84$	8.12519e8	1.78064
$85$	−7.67633e8	−1.59503
$86$	−5.74353e8	−1.13223
$87$	5.65630e7	0.105851
$88$	−2.96556e9	−5.27151
$89$	−5.81650e7	−0.0982667	−0.0491334	−	0.998792i	$-0.515646\pi$
$89$	−5.81650e7	−0.0982667	−0.0491334	+	0.998792i	$0.515646\pi$
$90$	3.27477e9	5.26125
$91$	−6.85750e7	−0.104828
$92$	1.01395e9	1.47561
$93$	3.17383e8	0.439957
$94$	−8.11924e8	−1.07261
$95$	−3.58730e8	−0.451868
$96$	3.56602e9	4.28512
$97$	−5.97568e8	−0.685354	−0.342677	−	0.939453i	$-0.611334\pi$
$97$	−5.97568e8	−0.685354	−0.342677	+	0.939453i	$0.611334\pi$
$98$	−2.43585e8	−0.266768
$99$	4.69585e9	4.91310
$100$	4.60244e8	0.460244
$101$	5.42898e8	0.519125	0.259563	−	0.965726i	$-0.416422\pi$
$101$	5.42898e8	0.519125	0.259563	+	0.965726i	$0.416422\pi$
$102$	5.66587e9	5.18282
$103$	−1.09200e9	−0.955996	−0.477998	−	0.878361i	$-0.658637\pi$
$103$	−1.09200e9	−0.955996	−0.477998	+	0.878361i	$0.658637\pi$
$104$	−9.18853e8	−0.770186
$105$	−9.70749e8	−0.779390
$106$	−2.27068e9	−1.74695
$107$	2.45875e8	0.181337	0.0906686	−	0.995881i	$-0.471100\pi$
$107$	2.45875e8	0.181337	0.0906686	+	0.995881i	$0.471100\pi$
$108$	−1.05785e10	−7.48197
$109$	−8.52204e8	−0.578261	−0.289131	−	0.957290i	$-0.593366\pi$
$109$	−8.52204e8	−0.578261	−0.289131	+	0.957290i	$0.593366\pi$
$110$	5.92563e9	3.85894
$111$	−2.19155e9	−1.37025
$112$	−1.69846e9	−1.01994
$113$	2.21450e9	1.27768	0.638841	−	0.769338i	$-0.279414\pi$
$113$	2.21450e9	1.27768	0.638841	+	0.769338i	$0.279414\pi$
$114$	2.64777e9	1.46828
$115$	−1.21141e9	−0.645879
$116$	−2.71027e8	−0.138980
$117$	1.45497e9	0.717822
$118$	−2.04852e9	−0.972682
$119$	−1.21147e9	−0.553797
$120$	−1.30073e10	−5.72627
$121$	6.13911e9	2.60358
$122$	−6.42925e9	−2.62749
$123$	−3.17081e9	−1.24910
$124$	−1.52077e9	−0.577652
$125$	2.42155e9	0.887152
$126$	5.16819e9	1.82672
$127$	−2.05832e9	−0.702095	−0.351048	−	0.936358i	$-0.614175\pi$
$127$	−2.05832e9	−0.702095	−0.351048	+	0.936358i	$0.614175\pi$
$128$	−1.78308e9	−0.587117
$129$	−3.61238e9	−1.14852
$130$	1.83600e9	0.563805
$131$	−4.88433e9	−1.44905	−0.724527	−	0.689247i	$-0.757942\pi$
$131$	−4.88433e9	−1.44905	−0.724527	+	0.689247i	$0.757942\pi$
$132$	−3.11943e10	−8.94320
$133$	−5.66143e8	−0.156889
$134$	6.93384e9	1.85781
$135$	1.26385e10	3.27487
$136$	−1.62327e10	−4.06881
$137$	−5.64442e8	−0.136892	−0.0684458	−	0.997655i	$-0.521804\pi$
$137$	−5.64442e8	−0.136892	−0.0684458	+	0.997655i	$0.521804\pi$
$138$	8.94137e9	2.09869
$139$	−3.07059e9	−0.697678	−0.348839	−	0.937183i	$-0.613424\pi$
$139$	−3.07059e9	−0.697678	−0.348839	+	0.937183i	$0.613424\pi$
$140$	4.65144e9	1.02332
$141$	−5.10658e9	−1.08804
$142$	−5.37416e9	−1.10921
$143$	2.63274e9	0.526497
$144$	3.60366e10	6.98414
$145$	3.23807e8	0.0608317
$146$	1.91894e10	3.49521
$147$	−1.53202e9	−0.270606
$148$	1.05010e10	1.79910
$149$	−4.75629e9	−0.790551	−0.395275	−	0.918563i	$-0.629351\pi$
$149$	−4.75629e9	−0.790551	−0.395275	+	0.918563i	$0.629351\pi$
$150$	4.05859e9	0.654582
$151$	2.03670e9	0.318809	0.159404	−	0.987213i	$-0.449043\pi$
$151$	2.03670e9	0.318809	0.159404	+	0.987213i	$0.449043\pi$
$152$	−7.58588e9	−1.15268
$153$	2.57039e10	3.79217
$154$	9.35175e9	1.33983
$155$	1.81693e9	0.252839
$156$	−9.66529e9	−1.30663
$157$	3.37544e9	0.443385	0.221693	−	0.975117i	$-0.428842\pi$
$157$	3.37544e9	0.443385	0.221693	+	0.975117i	$0.428842\pi$
$158$	−2.32407e10	−2.96683
$159$	−1.42814e10	−1.77208
$160$	2.04144e10	2.46262
$161$	−1.91183e9	−0.224250
$162$	−5.09164e10	−5.80818
$163$	9.41744e9	1.04493	0.522467	−	0.852660i	$-0.325012\pi$
$163$	9.41744e9	1.04493	0.522467	+	0.852660i	$0.325012\pi$
$164$	1.51932e10	1.64003
$165$	3.72691e10	3.91445
$166$	−1.48581e10	−1.51871
$167$	−1.84160e10	−1.83219	−0.916096	−	0.400960i	$-0.868677\pi$
$167$	−1.84160e10	−1.83219	−0.916096	+	0.400960i	$0.868677\pi$
$168$	−2.05279e10	−1.98817
$169$	8.15731e8	0.0769231
$170$	3.24355e10	2.97852
$171$	1.20120e10	1.07431
$172$	1.73091e10	1.50798
$173$	3.56058e9	0.302213	0.151107	−	0.988517i	$-0.451716\pi$
$173$	3.56058e9	0.302213	0.151107	+	0.988517i	$0.451716\pi$
$174$	−2.39000e9	−0.197664
$175$	−8.67801e8	−0.0699437
$176$	6.52077e10	5.12261
$177$	−1.28841e10	−0.986676
$178$	2.45769e9	0.183501
$179$	8.71624e9	0.634586	0.317293	−	0.948328i	$-0.397226\pi$
$179$	8.71624e9	0.634586	0.317293	+	0.948328i	$0.397226\pi$
$180$	−9.86903e10	−7.00726
$181$	−2.47627e10	−1.71492	−0.857461	−	0.514549i	$-0.827959\pi$
$181$	−2.47627e10	−1.71492	−0.857461	+	0.514549i	$0.827959\pi$
$182$	2.89756e9	0.195754
$183$	−4.04366e10	−2.66529
$184$	−2.56171e10	−1.64759
$185$	−1.25460e10	−0.787468
$186$	−1.34107e10	−0.821565
$187$	4.65108e10	2.78142
$188$	2.44687e10	1.42856
$189$	1.99459e10	1.13704
$190$	1.51577e10	0.843806
$191$	2.79463e10	1.51940	0.759702	−	0.650271i	$-0.225345\pi$
$191$	2.79463e10	1.51940	0.759702	+	0.650271i	$0.225345\pi$
$192$	−5.44249e10	−2.89029
$193$	1.29922e10	0.674026	0.337013	−	0.941500i	$-0.390583\pi$
$193$	1.29922e10	0.674026	0.337013	+	0.941500i	$0.390583\pi$
$194$	2.52496e10	1.27981
$195$	1.15475e10	0.571916
$196$	7.34083e9	0.355298
$197$	2.63181e10	1.24497	0.622483	−	0.782634i	$-0.286124\pi$
$197$	2.63181e10	1.24497	0.622483	+	0.782634i	$0.286124\pi$
$198$	−1.98418e11	−9.17460
$199$	−6.10195e9	−0.275822	−0.137911	−	0.990445i	$-0.544039\pi$
$199$	−6.10195e9	−0.275822	−0.137911	+	0.990445i	$0.544039\pi$
$200$	−1.16279e10	−0.513884
$201$	4.36102e10	1.88454
$202$	−2.29395e10	−0.969401
$203$	5.11027e8	0.0211209
$204$	−1.70750e11	−6.90280
$205$	−1.81520e10	−0.717846
$206$	4.61413e10	1.78520
$207$	4.05637e10	1.53557
$208$	2.02040e10	0.748432
$209$	2.17354e10	0.787970
$210$	4.10179e10	1.45541
$211$	8.48412e9	0.294670	0.147335	−	0.989087i	$-0.452930\pi$
$211$	8.48412e9	0.294670	0.147335	+	0.989087i	$0.452930\pi$
$212$	6.84308e10	2.32670
$213$	−3.38007e10	−1.12517
$214$	−1.03892e10	−0.338624
$215$	−2.06798e10	−0.660045
$216$	2.67260e11	8.35396
$217$	2.86745e9	0.0877862
$218$	3.60089e10	1.07983
$219$	1.20691e11	3.54549
$220$	−1.78579e11	−5.13957
$221$	1.44110e10	0.406376
$222$	9.26016e10	2.55876
$223$	−2.86781e10	−0.776568	−0.388284	−	0.921540i	$-0.626932\pi$
$223$	−2.86781e10	−0.776568	−0.388284	+	0.921540i	$0.626932\pi$
$224$	3.22177e10	0.855025
$225$	1.84123e10	0.478946
$226$	−9.35712e10	−2.38591
$227$	−2.97078e10	−0.742597	−0.371299	−	0.928513i	$-0.621087\pi$
$227$	−2.97078e10	−0.742597	−0.371299	+	0.928513i	$0.621087\pi$
$228$	−7.97949e10	−1.95555
$229$	5.52746e10	1.32821	0.664104	−	0.747640i	$-0.268813\pi$
$229$	5.52746e10	1.32821	0.664104	+	0.747640i	$0.268813\pi$
$230$	5.11868e10	1.20610
$231$	5.88176e10	1.35911
$232$	6.84737e9	0.155177
$233$	1.61587e10	0.359174	0.179587	−	0.983742i	$-0.442524\pi$
$233$	1.61587e10	0.359174	0.179587	+	0.983742i	$0.442524\pi$
$234$	−6.14780e10	−1.34044
$235$	−2.92337e10	−0.625285
$236$	6.17354e10	1.29548
$237$	−1.46172e11	−3.00952
$238$	5.11892e10	1.03415
$239$	−6.58517e10	−1.30550	−0.652749	−	0.757574i	$-0.726384\pi$
$239$	−6.58517e10	−1.30550	−0.652749	+	0.757574i	$0.726384\pi$
$240$	2.86008e11	5.56453
$241$	−5.07195e10	−0.968497	−0.484248	−	0.874931i	$-0.660907\pi$
$241$	−5.07195e10	−0.968497	−0.484248	+	0.874931i	$0.660907\pi$
$242$	−2.59401e11	−4.86186
$243$	−1.56724e11	−2.88342
$244$	1.93756e11	3.49946
$245$	−8.77038e9	−0.155515
$246$	1.33979e11	2.33254
$247$	6.73453e9	0.115125
$248$	3.84216e10	0.644975
$249$	−9.34494e10	−1.54056
$250$	−1.02320e11	−1.65664
$251$	−1.00611e11	−1.59998	−0.799989	−	0.600015i	$-0.795161\pi$
$251$	−1.00611e11	−1.59998	−0.799989	+	0.600015i	$0.795161\pi$
$252$	−1.55752e11	−2.43293
$253$	7.33992e10	1.12629
$254$	8.69720e10	1.31107
$255$	2.04002e11	3.02137
$256$	−2.95127e10	−0.429466
$257$	5.74989e9	0.0822167	0.0411084	−	0.999155i	$-0.486911\pi$
$257$	5.74989e9	0.0822167	0.0411084	+	0.999155i	$0.486911\pi$
$258$	1.52637e11	2.14472
$259$	−1.97999e10	−0.273410
$260$	−5.53310e10	−0.750911
$261$	−1.08426e10	−0.144627
$262$	2.06382e11	2.70593
$263$	−7.74295e10	−0.997943	−0.498971	−	0.866619i	$-0.666289\pi$
$263$	−7.74295e10	−0.997943	−0.498971	+	0.866619i	$0.666289\pi$
$264$	7.88111e11	9.98550
$265$	−8.17569e10	−1.01840
$266$	2.39217e10	0.292971
$267$	1.54576e10	0.186141
$268$	−2.08962e11	−2.47435
$269$	7.28267e10	0.848019	0.424009	−	0.905658i	$-0.360622\pi$
$269$	7.28267e10	0.848019	0.424009	+	0.905658i	$0.360622\pi$
$270$	−5.34026e11	−6.11541
$271$	3.24058e9	0.0364973	0.0182487	−	0.999833i	$-0.494191\pi$
$271$	3.24058e9	0.0364973	0.0182487	+	0.999833i	$0.494191\pi$
$272$	3.56931e11	3.95388
$273$	1.82241e10	0.198570
$274$	2.38498e10	0.255628
$275$	3.33167e10	0.351289
$276$	−2.69463e11	−2.79517
$277$	3.78083e10	0.385858	0.192929	−	0.981213i	$-0.438201\pi$
$277$	3.78083e10	0.385858	0.192929	+	0.981213i	$0.438201\pi$
$278$	1.29744e11	1.30283
$279$	−6.08391e10	−0.601124
$280$	−1.17516e11	−1.14258
$281$	−1.76918e11	−1.69276	−0.846379	−	0.532581i	$-0.821222\pi$
$281$	−1.76918e11	−1.69276	−0.846379	+	0.532581i	$0.821222\pi$
$282$	2.15773e11	2.03177
$283$	1.08504e11	1.00556	0.502778	−	0.864415i	$-0.332311\pi$
$283$	1.08504e11	1.00556	0.502778	+	0.864415i	$0.332311\pi$
$284$	1.61959e11	1.47731
$285$	9.53341e10	0.855946
$286$	−1.11243e11	−0.983166
$287$	−2.86472e10	−0.249237
$288$	−6.83570e11	−5.85486
$289$	1.36001e11	1.14684
$290$	−1.36821e10	−0.113595
$291$	1.58806e11	1.29822
$292$	−5.78303e11	−4.65513
$293$	1.04264e11	0.826478	0.413239	−	0.910623i	$-0.364397\pi$
$293$	1.04264e11	0.826478	0.413239	+	0.910623i	$0.364397\pi$
$294$	6.47338e10	0.505322
$295$	−7.37577e10	−0.567033
$296$	−2.65304e11	−2.00878
$297$	−7.65766e11	−5.71074
$298$	2.00971e11	1.47625
$299$	2.27421e10	0.164555
$300$	−1.22312e11	−0.871813
$301$	−3.26366e10	−0.229169
$302$	−8.60583e10	−0.595335
$303$	−1.44278e11	−0.983348
$304$	1.66801e11	1.12013
$305$	−2.31488e11	−1.53172
$306$	−1.08609e12	−7.08140
$307$	1.78992e11	1.15004	0.575019	−	0.818140i	$-0.304995\pi$
$307$	1.78992e11	1.15004	0.575019	+	0.818140i	$0.304995\pi$
$308$	−2.81830e11	−1.78447
$309$	2.90205e11	1.81089
$310$	−7.67721e10	−0.472145
$311$	−2.55157e10	−0.154663	−0.0773314	−	0.997005i	$-0.524640\pi$
$311$	−2.55157e10	−0.154663	−0.0773314	+	0.997005i	$0.524640\pi$
$312$	2.44189e11	1.45892
$313$	3.13590e10	0.184677	0.0923386	−	0.995728i	$-0.470566\pi$
$313$	3.13590e10	0.184677	0.0923386	+	0.995728i	$0.470566\pi$
$314$	−1.42625e11	−0.827966
$315$	1.86083e11	1.06490
$316$	7.00397e11	3.95141
$317$	−9.21312e9	−0.0512436	−0.0256218	−	0.999672i	$-0.508157\pi$
$317$	−9.21312e9	−0.0512436	−0.0256218	+	0.999672i	$0.508157\pi$
$318$	6.03445e11	3.30914
$319$	−1.96194e10	−0.106079
$320$	−3.11567e11	−1.66102
$321$	−6.53423e10	−0.343496
$322$	8.07822e10	0.418759
$323$	1.18974e11	0.608194
$324$	1.53445e12	7.73570
$325$	1.03229e10	0.0513247
$326$	−3.97923e11	−1.95128
$327$	2.26477e11	1.09537
$328$	−3.83850e11	−1.83117
$329$	−4.61362e10	−0.217100
$330$	−1.57476e12	−7.30975
$331$	−2.77410e11	−1.27027	−0.635135	−	0.772401i	$-0.719055\pi$
$331$	−2.77410e11	−1.27027	−0.635135	+	0.772401i	$0.719055\pi$
$332$	4.47772e11	2.02272
$333$	4.20099e11	1.87220
$334$	7.78146e11	3.42139
$335$	2.49656e11	1.08303
$336$	4.51374e11	1.93201
$337$	2.94414e11	1.24344	0.621720	−	0.783240i	$-0.286434\pi$
$337$	2.94414e11	1.24344	0.621720	+	0.783240i	$0.286434\pi$
$338$	−3.44678e10	−0.143644
$339$	−5.88514e11	−2.42024
$340$	−9.77495e11	−3.96697
$341$	−1.10087e11	−0.440903
$342$	−5.07551e11	−2.00615
$343$	−1.38413e10	−0.0539949
$344$	−4.37306e11	−1.68373
$345$	3.21938e11	1.22345
$346$	−1.50448e11	−0.564345
$347$	2.12665e11	0.787433	0.393717	−	0.919232i	$-0.371189\pi$
$347$	2.12665e11	0.787433	0.393717	+	0.919232i	$0.371189\pi$
$348$	7.20266e10	0.263261
$349$	2.10067e11	0.757956	0.378978	−	0.925406i	$-0.376276\pi$
$349$	2.10067e11	0.757956	0.378978	+	0.925406i	$0.376276\pi$
$350$	3.66679e10	0.130611
$351$	−2.37266e11	−0.834360
$352$	−1.23691e12	−4.29433
$353$	4.17640e10	0.143158	0.0715791	−	0.997435i	$-0.477196\pi$
$353$	4.17640e10	0.143158	0.0715791	+	0.997435i	$0.477196\pi$
$354$	5.44403e11	1.84249
$355$	−1.93499e11	−0.646623
$356$	−7.40666e10	−0.244398
$357$	3.21953e11	1.04902
$358$	−3.68295e11	−1.18501
$359$	−1.40197e11	−0.445465	−0.222733	−	0.974880i	$-0.571498\pi$
$359$	−1.40197e11	−0.445465	−0.222733	+	0.974880i	$0.571498\pi$
$360$	2.49337e12	7.82393
$361$	−2.67089e11	−0.827700
$362$	1.04632e12	3.20240
$363$	−1.63150e12	−4.93181
$364$	−8.73225e10	−0.260717
$365$	6.90921e11	2.03756
$366$	1.70860e12	4.97710
$367$	2.93329e11	0.844030	0.422015	−	0.906589i	$-0.361323\pi$
$367$	2.93329e11	0.844030	0.422015	+	0.906589i	$0.361323\pi$
$368$	5.63276e11	1.60106
$369$	6.07812e11	1.70667
$370$	5.30117e11	1.47050
$371$	−1.29028e11	−0.353590
$372$	4.04152e11	1.09421
$373$	6.03328e11	1.61385	0.806926	−	0.590652i	$-0.201129\pi$
$373$	6.03328e11	1.61385	0.806926	+	0.590652i	$0.201129\pi$
$374$	−1.96526e12	−5.19395
$375$	−6.43537e11	−1.68048
$376$	−6.18190e11	−1.59506
$377$	−6.07890e9	−0.0154985
$378$	−8.42792e11	−2.12328
$379$	−7.59539e11	−1.89092	−0.945461	−	0.325734i	$-0.894389\pi$
$379$	−7.59539e11	−1.89092	−0.945461	+	0.325734i	$0.894389\pi$
$380$	−4.56803e11	−1.12383
$381$	5.47008e11	1.32994
$382$	−1.18084e12	−2.83730
$383$	−7.94740e10	−0.188726	−0.0943628	−	0.995538i	$-0.530081\pi$
$383$	−7.94740e10	−0.188726	−0.0943628	+	0.995538i	$0.530081\pi$
$384$	4.73860e11	1.11214
$385$	3.36714e11	0.781065
$386$	−5.48973e11	−1.25866
$387$	6.92456e11	1.56925
$388$	−7.60936e11	−1.70453
$389$	8.34373e11	1.84751	0.923755	−	0.382983i	$-0.125103\pi$
$389$	8.34373e11	1.84751	0.923755	+	0.382983i	$0.125103\pi$
$390$	−4.87926e11	−1.06798
$391$	4.01769e11	0.869324
$392$	−1.85463e11	−0.396707
$393$	1.29803e12	2.74486
$394$	−1.11204e12	−2.32482
$395$	−8.36792e11	−1.72954
$396$	5.97964e12	12.2193
$397$	6.35325e11	1.28363	0.641813	−	0.766861i	$-0.278182\pi$
$397$	6.35325e11	1.28363	0.641813	+	0.766861i	$0.278182\pi$
$398$	2.57831e11	0.515064
$399$	1.50455e11	0.297186
$400$	2.55677e11	0.499370
$401$	6.62258e11	1.27902	0.639511	−	0.768782i	$-0.279137\pi$
$401$	6.62258e11	1.27902	0.639511	+	0.768782i	$0.279137\pi$
$402$	−1.84270e12	−3.51915
$403$	−3.41096e10	−0.0644175
$404$	6.91320e11	1.29111
$405$	−1.83327e12	−3.38593
$406$	−2.15929e10	−0.0394405
$407$	7.60162e11	1.37319
$408$	4.31393e12	7.70729
$409$	2.93543e11	0.518700	0.259350	−	0.965783i	$-0.416492\pi$
$409$	2.93543e11	0.518700	0.259350	+	0.965783i	$0.416492\pi$
$410$	7.66990e11	1.34049
$411$	1.50003e11	0.259305
$412$	−1.39054e12	−2.37764
$413$	−1.16403e11	−0.196875
$414$	−1.71397e12	−2.86749
$415$	−5.34971e11	−0.885347
$416$	−3.83245e11	−0.627417
$417$	8.16022e11	1.32157
$418$	−9.18405e11	−1.47144
$419$	6.65783e11	1.05529	0.527643	−	0.849466i	$-0.323076\pi$
$419$	6.65783e11	1.05529	0.527643	+	0.849466i	$0.323076\pi$
$420$	−1.23614e12	−1.93841
$421$	−5.66598e11	−0.879034	−0.439517	−	0.898234i	$-0.644850\pi$
$421$	−5.66598e11	−0.879034	−0.439517	+	0.898234i	$0.644850\pi$
$422$	−3.58487e11	−0.550259
$423$	9.78879e11	1.48661
$424$	−1.72887e12	−2.59787
$425$	1.82368e11	0.271142
$426$	1.42821e12	2.10111
$427$	−3.65331e11	−0.531816
$428$	3.13094e11	0.451001
$429$	−6.99662e11	−0.997311
$430$	8.73802e11	1.23255
$431$	−2.86933e11	−0.400528	−0.200264	−	0.979742i	$-0.564180\pi$
$431$	−2.86933e11	−0.400528	−0.200264	+	0.979742i	$0.564180\pi$
$432$	−5.87660e12	−8.11801
$433$	−4.09172e11	−0.559384	−0.279692	−	0.960090i	$-0.590232\pi$
$433$	−4.09172e11	−0.559384	−0.279692	+	0.960090i	$0.590232\pi$
$434$	−1.21161e11	−0.163930
$435$	−8.60531e10	−0.115230
$436$	−1.08519e12	−1.43819
$437$	1.87755e11	0.246277
$438$	−5.09966e12	−6.62076
$439$	4.17558e11	0.536570	0.268285	−	0.963340i	$-0.413543\pi$
$439$	4.17558e11	0.536570	0.268285	+	0.963340i	$0.413543\pi$
$440$	4.51171e12	5.73857
$441$	2.93673e11	0.369735
$442$	−6.08919e11	−0.758856
$443$	−4.53986e11	−0.560049	−0.280024	−	0.959993i	$-0.590343\pi$
$443$	−4.53986e11	−0.560049	−0.280024	+	0.959993i	$0.590343\pi$
$444$	−2.79070e12	−3.40792
$445$	8.84903e10	0.106973
$446$	1.21176e12	1.45014
$447$	1.26400e12	1.49749
$448$	−4.91710e11	−0.576711
$449$	2.38218e11	0.276609	0.138304	−	0.990390i	$-0.455835\pi$
$449$	2.38218e11	0.276609	0.138304	+	0.990390i	$0.455835\pi$
$450$	−7.77990e11	−0.894371
$451$	1.09983e12	1.25178
$452$	2.81992e12	3.17771
$453$	−5.41261e11	−0.603900
$454$	1.25527e12	1.38671
$455$	1.04328e11	0.114116
$456$	2.01598e12	2.18346
$457$	−4.92704e11	−0.528400	−0.264200	−	0.964468i	$-0.585108\pi$
$457$	−4.92704e11	−0.528400	−0.264200	+	0.964468i	$0.585108\pi$
$458$	−2.33556e12	−2.48026
$459$	−4.19162e12	−4.40783
$460$	−1.54260e12	−1.60636
$461$	1.76600e11	0.182111	0.0910556	−	0.995846i	$-0.470976\pi$
$461$	1.76600e11	0.182111	0.0910556	+	0.995846i	$0.470976\pi$
$462$	−2.48527e12	−2.53796
$463$	7.27640e11	0.735871	0.367936	−	0.929851i	$-0.380065\pi$
$463$	7.27640e11	0.735871	0.367936	+	0.929851i	$0.380065\pi$
$464$	−1.50562e11	−0.150794
$465$	−4.82856e11	−0.478938
$466$	−6.82768e11	−0.670712
$467$	1.95594e12	1.90296	0.951478	−	0.307717i	$-0.0995649\pi$
$467$	1.95594e12	1.90296	0.951478	+	0.307717i	$0.0995649\pi$
$468$	1.85274e12	1.78529
$469$	3.94003e11	0.376029
$470$	1.23523e12	1.16764
$471$	−8.97037e11	−0.839878
$472$	−1.55972e12	−1.44646
$473$	1.25299e12	1.15099
$474$	6.17633e12	5.61989
$475$	8.52239e10	0.0768140
$476$	−1.54267e12	−1.37734
$477$	2.73760e12	2.42124
$478$	2.78249e12	2.43785
$479$	−7.77801e11	−0.675086	−0.337543	−	0.941310i	$-0.609596\pi$
$479$	−7.77801e11	−0.675086	−0.337543	+	0.941310i	$0.609596\pi$
$480$	−5.42522e12	−4.66479
$481$	2.35529e11	0.200628
$482$	2.14309e12	1.80855
$483$	5.08078e11	0.424784
$484$	7.81747e12	6.47534
$485$	9.09121e11	0.746077
$486$	6.62220e12	5.38442
$487$	−2.05221e12	−1.65326	−0.826631	−	0.562745i	$-0.809745\pi$
$487$	−2.05221e12	−1.65326	−0.826631	+	0.562745i	$0.809745\pi$
$488$	−4.89516e12	−3.90731
$489$	−2.50273e12	−1.97936
$490$	3.70582e11	0.290404
$491$	−1.31197e12	−1.01872	−0.509362	−	0.860553i	$-0.670118\pi$
$491$	−1.31197e12	−1.01872	−0.509362	+	0.860553i	$0.670118\pi$
$492$	−4.03767e12	−3.10662
$493$	−1.07392e11	−0.0818767
$494$	−2.84560e11	−0.214982
$495$	−7.14411e12	−5.34841
$496$	−8.44826e11	−0.626758
$497$	−3.05377e11	−0.224509
$498$	3.94860e12	2.87681
$499$	−1.87607e12	−1.35455	−0.677277	−	0.735728i	$-0.736840\pi$
$499$	−1.87607e12	−1.35455	−0.677277	+	0.735728i	$0.736840\pi$
$500$	3.08357e12	2.20642
$501$	4.89413e12	3.47061
$502$	4.25120e12	2.98776
$503$	−1.12118e11	−0.0780941	−0.0390470	−	0.999237i	$-0.512432\pi$
$503$	−1.12118e11	−0.0780941	−0.0390470	+	0.999237i	$0.512432\pi$
$504$	3.93500e12	2.71648
$505$	−8.25948e11	−0.565121
$506$	−3.10140e12	−2.10320
$507$	−2.16784e11	−0.145711
$508$	−2.62104e12	−1.74617
$509$	−2.52041e11	−0.166434	−0.0832169	−	0.996531i	$-0.526519\pi$
$509$	−2.52041e11	−0.166434	−0.0832169	+	0.996531i	$0.526519\pi$
$510$	−8.61987e12	−5.64202
$511$	1.09040e12	0.707445
$512$	2.15996e12	1.38909
$513$	−1.95883e12	−1.24873
$514$	−2.42955e11	−0.153529
$515$	1.66134e12	1.04070
$516$	−4.59996e12	−2.85647
$517$	1.77127e12	1.09038
$518$	8.36624e11	0.510559
$519$	−9.46240e11	−0.572464
$520$	1.39791e12	0.838426
$521$	2.34370e12	1.39358	0.696789	−	0.717276i	$-0.254611\pi$
$521$	2.34370e12	1.39358	0.696789	+	0.717276i	$0.254611\pi$
$522$	4.58140e11	0.270073
$523$	−1.42413e12	−0.832326	−0.416163	−	0.909290i	$-0.636625\pi$
$523$	−1.42413e12	−0.832326	−0.416163	+	0.909290i	$0.636625\pi$
$524$	−6.21965e12	−3.60392
$525$	2.30622e11	0.132490
$526$	3.27169e12	1.86353
$527$	−6.02591e11	−0.340310
$528$	−1.73292e13	−9.70346
$529$	−1.16712e12	−0.647983
$530$	3.45455e12	1.90173
$531$	2.46975e12	1.34812
$532$	−7.20919e11	−0.390197
$533$	3.40771e11	0.182890
$534$	−6.53143e11	−0.347594
$535$	−3.74066e11	−0.197404
$536$	5.27934e12	2.76273
$537$	−2.31638e12	−1.20206
$538$	−3.07721e12	−1.58357
$539$	5.31396e11	0.271187
$540$	1.60937e13	8.14488
$541$	2.60997e11	0.130993	0.0654965	−	0.997853i	$-0.479137\pi$
$541$	2.60997e11	0.130993	0.0654965	+	0.997853i	$0.479137\pi$
$542$	−1.36927e11	−0.0681541
$543$	6.58080e12	3.24847
$544$	−6.77053e12	−3.31457
$545$	1.29651e12	0.629496
$546$	−7.70039e11	−0.370805
$547$	2.29603e12	1.09657	0.548283	−	0.836293i	$-0.315282\pi$
$547$	2.29603e12	1.09657	0.548283	+	0.836293i	$0.315282\pi$
$548$	−7.18753e11	−0.340461
$549$	7.75129e12	3.64165
$550$	−1.40776e12	−0.655989
$551$	−5.01863e10	−0.0231955
$552$	6.80785e12	3.12093
$553$	−1.32061e12	−0.600499
$554$	−1.59754e12	−0.720542
$555$	3.33416e12	1.49165
$556$	−3.91005e12	−1.73518
$557$	−7.44642e11	−0.327793	−0.163896	−	0.986478i	$-0.552406\pi$
$557$	−7.44642e11	−0.327793	−0.163896	+	0.986478i	$0.552406\pi$
$558$	2.57069e12	1.12252
$559$	3.88227e11	0.168164
$560$	2.58399e12	1.11031
$561$	−1.23605e13	−5.26868
$562$	7.47549e12	3.16101
$563$	−2.14797e12	−0.901031	−0.450516	−	0.892769i	$-0.648760\pi$
$563$	−2.14797e12	−0.901031	−0.450516	+	0.892769i	$0.648760\pi$
$564$	−6.50265e12	−2.70604
$565$	−3.36907e12	−1.39089
$566$	−4.58471e12	−1.87775
$567$	−2.89324e12	−1.17560
$568$	−4.09182e12	−1.64949
$569$	−1.35212e12	−0.540766	−0.270383	−	0.962753i	$-0.587150\pi$
$569$	−1.35212e12	−0.540766	−0.270383	+	0.962753i	$0.587150\pi$
$570$	−4.02823e12	−1.59837
$571$	−5.18107e11	−0.203966	−0.101983	−	0.994786i	$-0.532519\pi$
$571$	−5.18107e11	−0.203966	−0.101983	+	0.994786i	$0.532519\pi$
$572$	3.35250e12	1.30944
$573$	−7.42684e12	−2.87812
$574$	1.21045e12	0.465419
$575$	2.87796e11	0.109794
$576$	1.04327e13	3.94908
$577$	−1.48947e12	−0.559423	−0.279712	−	0.960084i	$-0.590239\pi$
$577$	−1.48947e12	−0.559423	−0.279712	+	0.960084i	$0.590239\pi$
$578$	−5.74656e12	−2.14157
$579$	−3.45275e12	−1.27677
$580$	4.12331e11	0.151294
$581$	−8.44283e11	−0.307394
$582$	−6.71018e12	−2.42427
$583$	4.95364e12	1.77589
$584$	1.46106e13	5.19767
$585$	−2.21354e12	−0.781422
$586$	−4.40557e12	−1.54334
$587$	−3.73783e12	−1.29941	−0.649707	−	0.760184i	$-0.725109\pi$
$587$	−3.73783e12	−1.29941	−0.649707	+	0.760184i	$0.725109\pi$
$588$	−1.95086e12	−0.673020
$589$	−2.81603e11	−0.0964091
$590$	3.11655e12	1.05886
$591$	−6.99417e12	−2.35826
$592$	5.83359e12	1.95204
$593$	4.86635e11	0.161606	0.0808029	−	0.996730i	$-0.474252\pi$
$593$	4.86635e11	0.161606	0.0808029	+	0.996730i	$0.474252\pi$
$594$	3.23566e13	10.6641
$595$	1.84309e12	0.602864
$596$	−6.05660e12	−1.96617
$597$	1.62162e12	0.522474
$598$	−9.60942e11	−0.307285
$599$	2.00543e12	0.636483	0.318241	−	0.948010i	$-0.396908\pi$
$599$	2.00543e12	0.636483	0.318241	+	0.948010i	$0.396908\pi$
$600$	3.09016e12	0.973420
$601$	2.62118e12	0.819525	0.409762	−	0.912192i	$-0.365612\pi$
$601$	2.62118e12	0.819525	0.409762	+	0.912192i	$0.365612\pi$
$602$	1.37902e12	0.427944
$603$	−8.35963e12	−2.57489
$604$	2.59350e12	0.792904
$605$	−9.33984e12	−2.83427
$606$	6.09629e12	1.83628
$607$	−2.98552e12	−0.892630	−0.446315	−	0.894876i	$-0.647264\pi$
$607$	−2.98552e12	−0.892630	−0.446315	+	0.894876i	$0.647264\pi$
$608$	−3.16400e12	−0.939011
$609$	−1.35808e11	−0.0400080
$610$	9.78126e12	2.86029
$611$	5.48811e11	0.159308
$612$	3.27311e13	9.43146
$613$	6.01869e12	1.72159	0.860796	−	0.508951i	$-0.169966\pi$
$613$	6.01869e12	1.72159	0.860796	+	0.508951i	$0.169966\pi$
$614$	−7.56312e12	−2.14755
$615$	4.82397e12	1.35977
$616$	7.12031e12	1.99244
$617$	−3.53176e12	−0.981088	−0.490544	−	0.871417i	$-0.663202\pi$
$617$	−3.53176e12	−0.981088	−0.490544	+	0.871417i	$0.663202\pi$
$618$	−1.22623e13	−3.38160
$619$	−5.78882e11	−0.158483	−0.0792414	−	0.996855i	$-0.525250\pi$
$619$	−5.78882e11	−0.158483	−0.0792414	+	0.996855i	$0.525250\pi$
$620$	2.31365e12	0.628833
$621$	−6.61484e12	−1.78487
$622$	1.07814e12	0.288813
$623$	1.39654e11	0.0371413
$624$	−5.36931e12	−1.41771
$625$	−4.38999e12	−1.15081
$626$	−1.32504e12	−0.344861
$627$	−5.77629e12	−1.49260
$628$	4.29824e12	1.10274
$629$	4.16094e12	1.05990
$630$	−7.86271e12	−1.98857
$631$	−3.23617e12	−0.812641	−0.406321	−	0.913731i	$-0.633188\pi$
$631$	−3.23617e12	−0.812641	−0.406321	+	0.913731i	$0.633188\pi$
$632$	−1.76952e13	−4.41194
$633$	−2.25469e12	−0.558175
$634$	3.89290e11	0.0956910
$635$	3.13146e12	0.764302
$636$	−1.81858e13	−4.40732
$637$	1.64648e11	0.0396214
$638$	8.28996e11	0.198088
$639$	6.47925e12	1.53734
$640$	2.71271e12	0.639137
$641$	2.43868e12	0.570550	0.285275	−	0.958446i	$-0.407915\pi$
$641$	2.43868e12	0.570550	0.285275	+	0.958446i	$0.407915\pi$
$642$	2.76096e12	0.641436
$643$	4.69897e12	1.08406	0.542030	−	0.840359i	$-0.317656\pi$
$643$	4.69897e12	1.08406	0.542030	+	0.840359i	$0.317656\pi$
$644$	−2.43450e12	−0.557730
$645$	5.49575e12	1.25028
$646$	−5.02712e12	−1.13573
$647$	1.96791e12	0.441504	0.220752	−	0.975330i	$-0.429149\pi$
$647$	1.96791e12	0.441504	0.220752	+	0.975330i	$0.429149\pi$
$648$	−3.87672e13	−8.63727
$649$	4.46898e12	0.988796
$650$	−4.36182e11	−0.0958423
$651$	−7.62037e11	−0.166288
$652$	1.19921e13	2.59884
$653$	3.77005e12	0.811405	0.405703	−	0.914005i	$-0.367027\pi$
$653$	3.77005e12	0.811405	0.405703	+	0.914005i	$0.367027\pi$
$654$	−9.56953e12	−2.04546
$655$	7.43086e12	1.57744
$656$	8.44022e12	1.77945
$657$	−2.31352e13	−4.84429
$658$	1.94943e12	0.405407
$659$	3.41820e12	0.706014	0.353007	−	0.935621i	$-0.385159\pi$
$659$	3.41820e12	0.706014	0.353007	+	0.935621i	$0.385159\pi$
$660$	4.74580e13	9.73559
$661$	3.57369e12	0.728132	0.364066	−	0.931373i	$-0.381388\pi$
$661$	3.57369e12	0.728132	0.364066	+	0.931373i	$0.381388\pi$
$662$	1.17216e13	2.37207
$663$	−3.82978e12	−0.769773
$664$	−1.13128e13	−2.25846
$665$	8.61311e11	0.170790
$666$	−1.77508e13	−3.49610
$667$	−1.69476e11	−0.0331545
$668$	−2.34507e13	−4.55682
$669$	7.62135e12	1.47101
$670$	−1.05489e13	−2.02242
$671$	1.40258e13	2.67102
$672$	−8.56201e12	−1.61962
$673$	−7.62482e12	−1.43272	−0.716361	−	0.697730i	$-0.754194\pi$
$673$	−7.62482e12	−1.43272	−0.716361	+	0.697730i	$0.754194\pi$
$674$	−1.24401e13	−2.32197
$675$	−3.00255e12	−0.556702
$676$	1.03874e12	0.191314
$677$	2.22730e12	0.407502	0.203751	−	0.979023i	$-0.434687\pi$
$677$	2.22730e12	0.407502	0.203751	+	0.979023i	$0.434687\pi$
$678$	2.48670e13	4.51949
$679$	1.43476e12	0.259039
$680$	2.46960e13	4.42931
$681$	7.89497e12	1.40666
$682$	4.65161e12	0.823330
$683$	−4.80474e12	−0.844844	−0.422422	−	0.906399i	$-0.638820\pi$
$683$	−4.80474e12	−0.844844	−0.422422	+	0.906399i	$0.638820\pi$
$684$	1.52959e13	2.67191
$685$	8.58723e11	0.149020
$686$	5.84848e11	0.100829
$687$	−1.46895e13	−2.51594
$688$	9.61561e12	1.63617
$689$	1.53484e12	0.259464
$690$	−1.36031e13	−2.28464
$691$	−2.34843e12	−0.391857	−0.195928	−	0.980618i	$-0.562772\pi$
$691$	−2.34843e12	−0.391857	−0.195928	+	0.980618i	$0.562772\pi$
$692$	4.53400e12	0.751630
$693$	−1.12747e13	−1.85698
$694$	−8.98593e12	−1.47043
$695$	4.67149e12	0.759493
$696$	−1.81972e12	−0.293943
$697$	6.02018e12	0.966188
$698$	−8.87615e12	−1.41539
$699$	−4.29425e12	−0.680362
$700$	−1.10505e12	−0.173956
$701$	2.35718e12	0.368691	0.184345	−	0.982862i	$-0.440983\pi$
$701$	2.35718e12	0.368691	0.184345	+	0.982862i	$0.440983\pi$
$702$	1.00254e13	1.55806
$703$	1.94449e12	0.300266
$704$	1.88778e13	2.89651
$705$	7.76898e12	1.18444
$706$	−1.76469e12	−0.267330
$707$	−1.30350e12	−0.196211
$708$	−1.64065e13	−2.45395
$709$	−2.76736e11	−0.0411299	−0.0205650	−	0.999789i	$-0.506546\pi$
$709$	−2.76736e11	−0.0411299	−0.0205650	+	0.999789i	$0.506546\pi$
$710$	8.17608e12	1.20749
$711$	2.80197e13	4.11197
$712$	1.87126e12	0.272881
$713$	−9.50956e11	−0.137803
$714$	−1.36038e13	−1.95892
$715$	−4.00536e12	−0.573145
$716$	1.10992e13	1.57827
$717$	1.75004e13	2.47293
$718$	5.92387e12	0.831850
$719$	−7.46859e12	−1.04222	−0.521109	−	0.853490i	$-0.674482\pi$
$719$	−7.46859e12	−1.04222	−0.521109	+	0.853490i	$0.674482\pi$
$720$	−5.48249e13	−7.60295
$721$	2.62190e12	0.361333
$722$	1.12855e13	1.54563
$723$	1.34789e13	1.83456
$724$	−3.15325e13	−4.26516
$725$	−7.69271e10	−0.0103409
$726$	6.89370e13	9.20954
$727$	8.74373e12	1.16089	0.580446	−	0.814299i	$-0.302878\pi$
$727$	8.74373e12	1.16089	0.580446	+	0.814299i	$0.302878\pi$
$728$	2.20617e12	0.291103
$729$	1.79319e13	2.35154
$730$	−2.91941e13	−3.80489
$731$	6.85855e12	0.888391
$732$	−5.14915e13	−6.62881
$733$	4.93746e12	0.631736	0.315868	−	0.948803i	$-0.397704\pi$
$733$	4.93746e12	0.631736	0.315868	+	0.948803i	$0.397704\pi$
$734$	−1.23943e13	−1.57612
$735$	2.33077e12	0.294582
$736$	−1.06846e13	−1.34218
$737$	−1.51266e13	−1.88859
$738$	−2.56824e13	−3.18700
$739$	−1.16731e13	−1.43975	−0.719875	−	0.694103i	$-0.755801\pi$
$739$	−1.16731e13	−1.43975	−0.719875	+	0.694103i	$0.755801\pi$
$740$	−1.59759e13	−1.95850
$741$	−1.78973e12	−0.218075
$742$	5.45191e12	0.660285
$743$	−8.08011e12	−0.972675	−0.486337	−	0.873771i	$-0.661667\pi$
$743$	−8.08011e12	−0.972675	−0.486337	+	0.873771i	$0.661667\pi$
$744$	−1.02107e13	−1.22174
$745$	7.23606e12	0.860595
$746$	−2.54929e13	−3.01367
$747$	1.79133e13	2.10491
$748$	5.92263e13	6.91763
$749$	−5.90345e11	−0.0685390
$750$	2.71919e13	3.13808
$751$	−1.28077e13	−1.46924	−0.734619	−	0.678480i	$-0.762639\pi$
$751$	−1.28077e13	−1.46924	−0.734619	+	0.678480i	$0.762639\pi$
$752$	1.35929e13	1.55001
$753$	2.67378e13	3.03074
$754$	2.56857e11	0.0289415
$755$	−3.09856e12	−0.347056
$756$	2.53989e13	2.82792
$757$	−6.67668e12	−0.738974	−0.369487	−	0.929236i	$-0.620467\pi$
$757$	−6.67668e12	−0.738974	−0.369487	+	0.929236i	$0.620467\pi$
$758$	3.20935e13	3.53106
$759$	−1.95062e13	−2.13346
$760$	1.15409e13	1.25481
$761$	−6.69033e12	−0.723130	−0.361565	−	0.932347i	$-0.617757\pi$
$761$	−6.69033e12	−0.723130	−0.361565	+	0.932347i	$0.617757\pi$
$762$	−2.31132e13	−2.48349
$763$	2.04614e12	0.218562
$764$	3.55864e13	3.77889
$765$	−3.91051e13	−4.12817
$766$	3.35808e12	0.352421
$767$	1.38467e12	0.144467
$768$	7.84313e12	0.813512
$769$	−4.93825e12	−0.509219	−0.254609	−	0.967044i	$-0.581947\pi$
$769$	−4.93825e12	−0.509219	−0.254609	+	0.967044i	$0.581947\pi$
$770$	−1.42274e13	−1.45854
$771$	−1.52806e12	−0.155738
$772$	1.65442e13	1.67636
$773$	−1.15674e13	−1.16528	−0.582638	−	0.812732i	$-0.697980\pi$
$773$	−1.15674e13	−1.16528	−0.582638	+	0.812732i	$0.697980\pi$
$774$	−2.92590e13	−2.93038
$775$	−4.31649e11	−0.0429807
$776$	1.92247e13	1.90319
$777$	5.26192e12	0.517905
$778$	−3.52555e13	−3.44999
$779$	2.81335e12	0.273719
$780$	1.47045e13	1.42240
$781$	1.17241e13	1.12758
$782$	−1.69763e13	−1.62335
$783$	1.76813e12	0.168107
$784$	4.07801e12	0.385502
$785$	−5.13528e12	−0.482670
$786$	−5.48469e13	−5.12567
$787$	1.93217e13	1.79539	0.897694	−	0.440620i	$-0.145241\pi$
$787$	1.93217e13	1.79539	0.897694	+	0.440620i	$0.145241\pi$
$788$	3.35132e13	3.09634
$789$	2.05772e13	1.89034
$790$	3.53577e13	3.22970
$791$	−5.31702e12	−0.482919
$792$	−1.51073e14	−13.6434
$793$	4.34578e12	0.390246
$794$	−2.68449e13	−2.39701
$795$	2.17273e13	1.92909
$796$	−7.77015e12	−0.685994
$797$	−1.56002e13	−1.36952	−0.684761	−	0.728768i	$-0.740093\pi$
$797$	−1.56002e13	−1.36952	−0.684761	+	0.728768i	$0.740093\pi$
$798$	−6.35730e12	−0.554958
$799$	9.69547e12	0.841605
$800$	−4.84988e12	−0.418626
$801$	−2.96307e12	−0.254329
$802$	−2.79830e13	−2.38841
$803$	−4.18628e13	−3.55311
$804$	5.55327e13	4.68702
$805$	2.90860e12	0.244119
$806$	1.44126e12	0.120292
$807$	−1.93540e13	−1.60635
$808$	−1.74659e13	−1.44158
$809$	5.58929e12	0.458763	0.229381	−	0.973337i	$-0.426330\pi$
$809$	5.58929e12	0.458763	0.229381	+	0.973337i	$0.426330\pi$
$810$	7.74626e13	6.32280
$811$	−1.32416e12	−0.107485	−0.0537423	−	0.998555i	$-0.517115\pi$
$811$	−1.32416e12	−0.107485	−0.0537423	+	0.998555i	$0.517115\pi$
$812$	6.50736e11	0.0525294
$813$	−8.61198e11	−0.0691346
$814$	−3.21198e13	−2.56426
$815$	−1.43274e13	−1.13752
$816$	−9.48559e13	−7.48960
$817$	3.20513e12	0.251679
$818$	−1.24033e13	−0.968608
$819$	−3.49338e12	−0.271311
$820$	−2.31145e13	−1.78534
$821$	−1.37805e13	−1.05858	−0.529288	−	0.848442i	$-0.677541\pi$
$821$	−1.37805e13	−1.05858	−0.529288	+	0.848442i	$0.677541\pi$
$822$	−6.33820e12	−0.484220
$823$	9.94834e12	0.755878	0.377939	−	0.925831i	$-0.376633\pi$
$823$	9.94834e12	0.755878	0.377939	+	0.925831i	$0.376633\pi$
$824$	3.51314e13	2.65475
$825$	−8.85407e12	−0.665426
$826$	4.91849e12	0.367639
$827$	−2.08704e13	−1.55152	−0.775759	−	0.631030i	$-0.782633\pi$
$827$	−2.08704e13	−1.55152	−0.775759	+	0.631030i	$0.782633\pi$
$828$	5.16533e13	3.81910
$829$	1.60649e13	1.18136	0.590681	−	0.806905i	$-0.298859\pi$
$829$	1.60649e13	1.18136	0.590681	+	0.806905i	$0.298859\pi$
$830$	2.26046e13	1.65327
$831$	−1.00477e13	−0.730908
$832$	5.84912e12	0.423190
$833$	2.90873e12	0.209316
$834$	−3.44801e13	−2.46786
$835$	2.80175e13	1.99453
$836$	2.76776e13	1.95975
$837$	9.92122e12	0.698716
$838$	−2.81319e13	−1.97061
$839$	4.05933e12	0.282830	0.141415	−	0.989950i	$-0.454835\pi$
$839$	4.05933e12	0.282830	0.141415	+	0.989950i	$0.454835\pi$
$840$	3.12305e13	2.16432
$841$	−1.44618e13	−0.996877
$842$	2.39410e13	1.64149
$843$	4.70169e13	3.20649
$844$	1.08036e13	0.732869
$845$	−1.24103e12	−0.0837386
$846$	−4.13614e13	−2.77606
$847$	−1.47400e13	−0.984062
$848$	3.80150e13	2.52449
$849$	−2.88354e13	−1.90476
$850$	−7.70573e12	−0.506324
$851$	6.56642e12	0.429186
$852$	−4.30414e13	−2.79839
$853$	−6.93359e12	−0.448422	−0.224211	−	0.974541i	$-0.571981\pi$
$853$	−6.93359e12	−0.448422	−0.224211	+	0.974541i	$0.571981\pi$
$854$	1.54366e13	0.993099
$855$	−1.82746e13	−1.16950
$856$	−7.91018e12	−0.503564
$857$	−9.04986e12	−0.573097	−0.286549	−	0.958066i	$-0.592508\pi$
$857$	−9.04986e12	−0.573097	−0.286549	+	0.958066i	$0.592508\pi$
$858$	2.95634e13	1.86235
$859$	2.85007e13	1.78602	0.893011	−	0.450035i	$-0.148588\pi$
$859$	2.85007e13	1.78602	0.893011	+	0.450035i	$0.148588\pi$
$860$	−2.63334e13	−1.64159
$861$	7.61311e12	0.472115
$862$	1.21240e13	0.747936
$863$	2.89918e13	1.77921	0.889604	−	0.456732i	$-0.150980\pi$
$863$	2.89918e13	1.77921	0.889604	+	0.456732i	$0.150980\pi$
$864$	1.11472e14	6.80539
$865$	−5.41695e12	−0.328990
$866$	1.72891e13	1.04458
$867$	−3.61429e13	−2.17238
$868$	3.65137e12	0.218332
$869$	5.07012e13	3.01598
$870$	3.63607e12	0.215177
$871$	−4.68685e12	−0.275930
$872$	2.74167e13	1.60580
$873$	−3.04416e13	−1.77379
$874$	−7.93336e12	−0.459892
$875$	−5.81414e12	−0.335312
$876$	1.53687e14	8.81794
$877$	−6.18353e12	−0.352970	−0.176485	−	0.984303i	$-0.556473\pi$
$877$	−6.18353e12	−0.352970	−0.176485	+	0.984303i	$0.556473\pi$
$878$	−1.76434e13	−1.00198
$879$	−2.77087e13	−1.56555
$880$	−9.92048e13	−5.57649
$881$	2.40374e13	1.34430	0.672148	−	0.740417i	$-0.265372\pi$
$881$	2.40374e13	1.34430	0.672148	+	0.740417i	$0.265372\pi$
$882$	−1.24088e13	−0.690434
$883$	1.92639e13	1.06640	0.533200	−	0.845989i	$-0.320989\pi$
$883$	1.92639e13	1.06640	0.533200	+	0.845989i	$0.320989\pi$
$884$	1.83508e13	1.01069
$885$	1.96015e13	1.07410
$886$	1.91827e13	1.04582
$887$	5.38879e12	0.292304	0.146152	−	0.989262i	$-0.453311\pi$
$887$	5.38879e12	0.292304	0.146152	+	0.989262i	$0.453311\pi$
$888$	7.05058e13	3.80510
$889$	4.94203e12	0.265367
$890$	−3.73906e12	−0.199759
$891$	1.11077e14	5.90441
$892$	−3.65184e13	−1.93139
$893$	4.53088e12	0.238425
$894$	−5.34091e13	−2.79638
$895$	−1.32606e13	−0.690811
$896$	4.28116e12	0.221909
$897$	−6.04382e12	−0.311706
$898$	−1.00656e13	−0.516532
$899$	2.54188e11	0.0129788
$900$	2.34460e13	1.19118
$901$	2.71150e13	1.37072
$902$	−4.64719e13	−2.33755
$903$	8.67332e12	0.434101
$904$	−7.12440e13	−3.54806
$905$	3.76731e13	1.86687
$906$	2.28704e13	1.12771
$907$	−2.85846e13	−1.40249	−0.701245	−	0.712921i	$-0.747372\pi$
$907$	−2.85846e13	−1.40249	−0.701245	+	0.712921i	$0.747372\pi$
$908$	−3.78295e13	−1.84690
$909$	2.76566e13	1.34357
$910$	−4.40825e12	−0.213098
$911$	−6.05294e12	−0.291161	−0.145581	−	0.989346i	$-0.546505\pi$
$911$	−6.05294e12	−0.291161	−0.145581	+	0.989346i	$0.546505\pi$
$912$	−4.43280e13	−2.12179
$913$	3.24138e13	1.54387
$914$	2.08186e13	0.986721
$915$	6.15190e13	2.90144
$916$	7.03860e13	3.30337
$917$	1.17273e13	0.547691
$918$	1.77112e14	8.23106
$919$	2.20989e13	1.02200	0.510999	−	0.859581i	$-0.329276\pi$
$919$	2.20989e13	1.02200	0.510999	+	0.859581i	$0.329276\pi$
$920$	3.89730e13	1.79357
$921$	−4.75680e13	−2.17845
$922$	−7.46204e12	−0.340070
$923$	3.63260e12	0.164744
$924$	7.48976e13	3.38021
$925$	2.98057e12	0.133863
$926$	−3.07456e13	−1.37415
$927$	−5.56293e13	−2.47426
$928$	2.85598e12	0.126412
$929$	1.00382e13	0.442167	0.221084	−	0.975255i	$-0.429041\pi$
$929$	1.00382e13	0.442167	0.221084	+	0.975255i	$0.429041\pi$
$930$	2.04025e13	0.894357
$931$	1.35931e12	0.0592986
$932$	2.05763e13	0.893297
$933$	6.78091e12	0.292968
$934$	−8.26459e13	−3.55353
$935$	−7.07600e13	−3.02786
$936$	−4.68086e13	−1.99335
$937$	−4.36496e13	−1.84991	−0.924957	−	0.380071i	$-0.875899\pi$
$937$	−4.36496e13	−1.84991	−0.924957	+	0.380071i	$0.875899\pi$
$938$	−1.66481e13	−0.702188
$939$	−8.33380e12	−0.349823
$940$	−3.72258e13	−1.55514
$941$	−5.58108e12	−0.232041	−0.116021	−	0.993247i	$-0.537014\pi$
$941$	−5.58108e12	−0.232041	−0.116021	+	0.993247i	$0.537014\pi$
$942$	3.79033e13	1.56837
$943$	9.50051e12	0.391241
$944$	3.42956e13	1.40561
$945$	−3.03451e13	−1.23778
$946$	−5.29436e13	−2.14933
$947$	1.97381e13	0.797498	0.398749	−	0.917060i	$-0.369444\pi$
$947$	1.97381e13	0.797498	0.398749	+	0.917060i	$0.369444\pi$
$948$	−1.86134e14	−7.48493
$949$	−1.29708e13	−0.519122
$950$	−3.60104e12	−0.143440
$951$	2.44843e12	0.0970677
$952$	3.89748e13	1.53786
$953$	2.27998e13	0.895393	0.447696	−	0.894186i	$-0.352245\pi$
$953$	2.27998e13	0.895393	0.447696	+	0.894186i	$0.352245\pi$
$954$	−1.15674e14	−4.52136
$955$	−4.25165e13	−1.65403
$956$	−8.38547e13	−3.24689
$957$	5.21395e12	0.200938
$958$	3.28651e13	1.26064
$959$	1.35522e12	0.0517401
$960$	8.28002e13	3.14638
$961$	−2.50133e13	−0.946055
$962$	−9.95202e12	−0.374648
$963$	1.25255e13	0.469327
$964$	−6.45856e13	−2.40873
$965$	−1.97660e13	−0.733745
$966$	−2.14682e13	−0.793230
$967$	−2.32794e13	−0.856155	−0.428077	−	0.903742i	$-0.640809\pi$
$967$	−2.32794e13	−0.856155	−0.428077	+	0.903742i	$0.640809\pi$
$968$	−1.97505e14	−7.23001
$969$	−3.16180e13	−1.15206
$970$	−3.84138e13	−1.39321
$971$	−2.97354e13	−1.07346	−0.536732	−	0.843753i	$-0.680341\pi$
$971$	−2.97354e13	−1.07346	−0.536732	+	0.843753i	$0.680341\pi$
$972$	−1.99571e14	−7.17131
$973$	7.37248e12	0.263697
$974$	8.67138e13	3.08726
$975$	−2.74335e12	−0.0972212
$976$	1.07636e14	3.79695
$977$	3.33093e13	1.16961	0.584804	−	0.811175i	$-0.301172\pi$
$977$	3.33093e13	1.16961	0.584804	+	0.811175i	$0.301172\pi$
$978$	1.05750e14	3.69620
$979$	−5.36162e12	−0.186541
$980$	−1.11681e13	−0.386778
$981$	−4.34133e13	−1.49662
$982$	5.54357e13	1.90234
$983$	1.44610e13	0.493978	0.246989	−	0.969018i	$-0.420559\pi$
$983$	1.44610e13	0.493978	0.246989	+	0.969018i	$0.420559\pi$
$984$	1.02010e14	3.46868
$985$	−4.00396e13	−1.35527
$986$	4.53772e12	0.152894
$987$	1.22609e13	0.411239
$988$	8.57567e12	0.286327
$989$	1.08236e13	0.359738
$990$	3.01866e14	9.98749
$991$	5.82083e13	1.91714	0.958569	−	0.284859i	$-0.0919468\pi$
$991$	5.82083e13	1.91714	0.958569	+	0.284859i	$0.0919468\pi$
$992$	1.60253e13	0.525416
$993$	7.37229e13	2.40620
$994$	1.29034e13	0.419242
$995$	9.28330e12	0.300261
$996$	−1.18997e14	−3.83151
$997$	−2.01153e13	−0.644762	−0.322381	−	0.946610i	$-0.604483\pi$
$997$	−2.01153e13	−0.644762	−0.322381	+	0.946610i	$0.604483\pi$
$998$	7.92712e13	2.52946
$999$	−6.85068e13	−2.17615

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.d.1.1	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.d.1.1	✓	15	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	91.a (trivial)

\(f(q)\)	\(=\)	\(q-42.2539 q^{2} -265.754 q^{3} +1273.39 q^{4} -1521.37 q^{5} +11229.2 q^{6} -2401.00 q^{7} -32171.6 q^{8} +50942.5 q^{9} +O(q^{10})\)	\(q-42.2539 q^{2} -265.754 q^{3} +1273.39 q^{4} -1521.37 q^{5} +11229.2 q^{6} -2401.00 q^{7} -32171.6 q^{8} +50942.5 q^{9} +64283.6 q^{10} +92179.5 q^{11} -338409. q^{12} +28561.0 q^{13} +101452. q^{14} +404310. q^{15} +707399. q^{16} +504568. q^{17} -2.15251e6 q^{18} +235795. q^{19} -1.93729e6 q^{20} +638077. q^{21} -3.89494e6 q^{22} +796264. q^{23} +8.54974e6 q^{24} +361433. q^{25} -1.20681e6 q^{26} -8.30734e6 q^{27} -3.05740e6 q^{28} -212839. q^{29} -1.70837e7 q^{30} -1.19427e6 q^{31} -1.34185e7 q^{32} -2.44971e7 q^{33} -2.13199e7 q^{34} +3.65280e6 q^{35} +6.48695e7 q^{36} +8.24654e6 q^{37} -9.96323e6 q^{38} -7.59021e6 q^{39} +4.89448e7 q^{40} +1.19313e7 q^{41} -2.69612e7 q^{42} +1.35929e7 q^{43} +1.17380e8 q^{44} -7.75022e7 q^{45} -3.36452e7 q^{46} +1.92154e7 q^{47} -1.87994e8 q^{48} +5.76480e6 q^{49} -1.52719e7 q^{50} -1.34091e8 q^{51} +3.63692e7 q^{52} +5.37391e7 q^{53} +3.51017e8 q^{54} -1.40239e8 q^{55} +7.72440e7 q^{56} -6.26635e7 q^{57} +8.99328e6 q^{58} +4.84812e7 q^{59} +5.14844e8 q^{60} +1.52158e8 q^{61} +5.04626e7 q^{62} -1.22313e8 q^{63} +2.04794e8 q^{64} -4.34518e7 q^{65} +1.03510e9 q^{66} -1.64100e8 q^{67} +6.42511e8 q^{68} -2.11611e8 q^{69} -1.54345e8 q^{70} +1.27188e8 q^{71} -1.63890e9 q^{72} -4.54145e8 q^{73} -3.48448e8 q^{74} -9.60524e7 q^{75} +3.00258e8 q^{76} -2.21323e8 q^{77} +3.20716e8 q^{78} +5.50026e8 q^{79} -1.07621e9 q^{80} +1.20501e9 q^{81} -5.04145e8 q^{82} +3.51638e8 q^{83} +8.12519e8 q^{84} -7.67633e8 q^{85} -5.74353e8 q^{86} +5.65630e7 q^{87} -2.96556e9 q^{88} -5.81650e7 q^{89} +3.27477e9 q^{90} -6.85750e7 q^{91} +1.01395e9 q^{92} +3.17383e8 q^{93} -8.11924e8 q^{94} -3.58730e8 q^{95} +3.56602e9 q^{96} -5.97568e8 q^{97} -2.43585e8 q^{98} +4.69585e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 22 q^{2} + q^{3} + 6402 q^{4} + 1694 q^{5} + 4189 q^{6} - 36015 q^{7} - 1704 q^{8} + 160366 q^{9}+O(q^{10}) \) 15 * q + 22 * q^2 + q^3 + 6402 * q^4 + 1694 * q^5 + 4189 * q^6 - 36015 * q^7 - 1704 * q^8 + 160366 * q^9	\( 15 q + 22 q^{2} + q^{3} + 6402 q^{4} + 1694 q^{5} + 4189 q^{6} - 36015 q^{7} - 1704 q^{8} + 160366 q^{9} - 69748 q^{10} + 23441 q^{11} + 64437 q^{12} + 428415 q^{13} - 52822 q^{14} - 68316 q^{15} + 2694730 q^{16} + 606640 q^{17} + 1242207 q^{18} + 1762528 q^{19} + 43054 q^{20} - 2401 q^{21} + 119431 q^{22} + 3649531 q^{23} + 15986883 q^{24} + 9120575 q^{25} + 628342 q^{26} - 5957633 q^{27} - 15371202 q^{28} + 18072234 q^{29} - 58091296 q^{30} - 1096937 q^{31} + 6565744 q^{32} - 18425617 q^{33} - 46741622 q^{34} - 4067294 q^{35} + 132788567 q^{36} - 34982109 q^{37} - 2819104 q^{38} + 28561 q^{39} + 2107274 q^{40} + 59341985 q^{41} - 10057789 q^{42} + 38829122 q^{43} + 202791507 q^{44} + 2955478 q^{45} + 165169119 q^{46} + 18734035 q^{47} + 340656557 q^{48} + 86472015 q^{49} + 220443888 q^{50} + 93517168 q^{51} + 182847522 q^{52} + 332415086 q^{53} + 567466451 q^{54} - 120908856 q^{55} + 4091304 q^{56} + 62932402 q^{57} + 180863580 q^{58} + 28220174 q^{59} + 467078152 q^{60} + 404536605 q^{61} + 4283245 q^{62} - 385038766 q^{63} + 1276533074 q^{64} + 48382334 q^{65} + 1696546059 q^{66} + 746448213 q^{67} + 492702034 q^{68} + 453755667 q^{69} + 167464948 q^{70} + 81316200 q^{71} + 1255645679 q^{72} + 12687907 q^{73} + 1350657501 q^{74} - 164589481 q^{75} + 679560842 q^{76} - 56281841 q^{77} + 119642029 q^{78} + 1896008477 q^{79} - 1458560390 q^{80} + 3853340295 q^{81} + 410985635 q^{82} - 753815178 q^{83} - 154713237 q^{84} - 259541636 q^{85} - 1842794378 q^{86} + 1391390932 q^{87} + 288708813 q^{88} + 1109816012 q^{89} + 1196058116 q^{90} - 1028624415 q^{91} + 2409710277 q^{92} + 3345736043 q^{93} - 1423358651 q^{94} + 4615875678 q^{95} + 11615772371 q^{96} + 1054179205 q^{97} + 126825622 q^{98} - 2512222258 q^{99}+O(q^{100}) \) 15 * q + 22 * q^2 + q^3 + 6402 * q^4 + 1694 * q^5 + 4189 * q^6 - 36015 * q^7 - 1704 * q^8 + 160366 * q^9 - 69748 * q^10 + 23441 * q^11 + 64437 * q^12 + 428415 * q^13 - 52822 * q^14 - 68316 * q^15 + 2694730 * q^16 + 606640 * q^17 + 1242207 * q^18 + 1762528 * q^19 + 43054 * q^20 - 2401 * q^21 + 119431 * q^22 + 3649531 * q^23 + 15986883 * q^24 + 9120575 * q^25 + 628342 * q^26 - 5957633 * q^27 - 15371202 * q^28 + 18072234 * q^29 - 58091296 * q^30 - 1096937 * q^31 + 6565744 * q^32 - 18425617 * q^33 - 46741622 * q^34 - 4067294 * q^35 + 132788567 * q^36 - 34982109 * q^37 - 2819104 * q^38 + 28561 * q^39 + 2107274 * q^40 + 59341985 * q^41 - 10057789 * q^42 + 38829122 * q^43 + 202791507 * q^44 + 2955478 * q^45 + 165169119 * q^46 + 18734035 * q^47 + 340656557 * q^48 + 86472015 * q^49 + 220443888 * q^50 + 93517168 * q^51 + 182847522 * q^52 + 332415086 * q^53 + 567466451 * q^54 - 120908856 * q^55 + 4091304 * q^56 + 62932402 * q^57 + 180863580 * q^58 + 28220174 * q^59 + 467078152 * q^60 + 404536605 * q^61 + 4283245 * q^62 - 385038766 * q^63 + 1276533074 * q^64 + 48382334 * q^65 + 1696546059 * q^66 + 746448213 * q^67 + 492702034 * q^68 + 453755667 * q^69 + 167464948 * q^70 + 81316200 * q^71 + 1255645679 * q^72 + 12687907 * q^73 + 1350657501 * q^74 - 164589481 * q^75 + 679560842 * q^76 - 56281841 * q^77 + 119642029 * q^78 + 1896008477 * q^79 - 1458560390 * q^80 + 3853340295 * q^81 + 410985635 * q^82 - 753815178 * q^83 - 154713237 * q^84 - 259541636 * q^85 - 1842794378 * q^86 + 1391390932 * q^87 + 288708813 * q^88 + 1109816012 * q^89 + 1196058116 * q^90 - 1028624415 * q^91 + 2409710277 * q^92 + 3345736043 * q^93 - 1423358651 * q^94 + 4615875678 * q^95 + 11615772371 * q^96 + 1054179205 * q^97 + 126825622 * q^98 - 2512222258 * q^99

Introduction

L-functions

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