LMFDB - Embedded newform 91.10.a.d.1.3

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			1.3
Root			$-41.6058$ 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)

$f(q)$	$=$	$q-40.6058 q^{2} +33.8931 q^{3} +1136.83 q^{4} -709.594 q^{5} -1376.25 q^{6} -2401.00 q^{7} -25371.6 q^{8} -18534.3 q^{9} +O(q^{10})$	\(q-40.6058 q^{2} +33.8931 q^{3} +1136.83 q^{4} -709.594 q^{5} -1376.25 q^{6} -2401.00 q^{7} -25371.6 q^{8} -18534.3 q^{9} +28813.6 q^{10} -61654.9 q^{11} +38530.6 q^{12} +28561.0 q^{13} +97494.4 q^{14} -24050.3 q^{15} +448177. q^{16} +371001. q^{17} +752598. q^{18} -815756. q^{19} -806686. q^{20} -81377.3 q^{21} +2.50354e6 q^{22} +843768. q^{23} -859922. q^{24} -1.44960e6 q^{25} -1.15974e6 q^{26} -1.29530e6 q^{27} -2.72952e6 q^{28} -1.17935e6 q^{29} +976582. q^{30} -5.21568e6 q^{31} -5.20830e6 q^{32} -2.08967e6 q^{33} -1.50648e7 q^{34} +1.70374e6 q^{35} -2.10703e7 q^{36} -1.21967e7 q^{37} +3.31244e7 q^{38} +968021. q^{39} +1.80035e7 q^{40} +3.76998e6 q^{41} +3.30439e6 q^{42} -3.68549e7 q^{43} -7.00909e7 q^{44} +1.31518e7 q^{45} -3.42618e7 q^{46} -4.27229e6 q^{47} +1.51901e7 q^{48} +5.76480e6 q^{49} +5.88622e7 q^{50} +1.25744e7 q^{51} +3.24689e7 q^{52} +7.43643e7 q^{53} +5.25967e7 q^{54} +4.37499e7 q^{55} +6.09172e7 q^{56} -2.76485e7 q^{57} +4.78885e7 q^{58} +4.00140e7 q^{59} -2.73411e7 q^{60} +8.72200e7 q^{61} +2.11787e8 q^{62} +4.45008e7 q^{63} -1.79794e7 q^{64} -2.02667e7 q^{65} +8.48528e7 q^{66} +5.46745e7 q^{67} +4.21764e8 q^{68} +2.85979e7 q^{69} -6.91815e7 q^{70} -2.42030e8 q^{71} +4.70244e8 q^{72} +1.94212e8 q^{73} +4.95257e8 q^{74} -4.91315e7 q^{75} -9.27374e8 q^{76} +1.48033e8 q^{77} -3.93072e7 q^{78} -5.40375e8 q^{79} -3.18024e8 q^{80} +3.20908e8 q^{81} -1.53083e8 q^{82} -5.05002e8 q^{83} -9.25120e7 q^{84} -2.63260e8 q^{85} +1.49652e9 q^{86} -3.99719e7 q^{87} +1.56428e9 q^{88} +9.65605e8 q^{89} -5.34039e8 q^{90} -6.85750e7 q^{91} +9.59218e8 q^{92} -1.76776e8 q^{93} +1.73480e8 q^{94} +5.78856e8 q^{95} -1.76526e8 q^{96} +627939. q^{97} -2.34084e8 q^{98} +1.14273e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−40.6058	−1.79454	−0.897269	−	0.441484i	$-0.854452\pi$
$2$	−40.6058	−1.79454	−0.897269	+	0.441484i	$0.854452\pi$
$3$	33.8931	0.241583	0.120791	−	0.992678i	$-0.461457\pi$
$3$	33.8931	0.241583	0.120791	+	0.992678i	$0.461457\pi$
$4$	1136.83	2.22037
$5$	−709.594	−0.507744	−0.253872	−	0.967238i	$-0.581704\pi$
$5$	−709.594	−0.507744	−0.253872	+	0.967238i	$0.581704\pi$
$6$	−1376.25	−0.433529
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	−25371.6	−2.18999
$9$	−18534.3	−0.941638
$10$	28813.6	0.911166
$11$	−61654.9	−1.26970	−0.634849	−	0.772636i	$-0.718938\pi$
$11$	−61654.9	−1.26970	−0.634849	+	0.772636i	$0.718938\pi$
$12$	38530.6	0.536402
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	97494.4	0.678272
$15$	−24050.3	−0.122662
$16$	448177.	1.70966
$17$	371001.	1.07735	0.538673	−	0.842515i	$-0.318926\pi$
$17$	371001.	1.07735	0.538673	+	0.842515i	$0.318926\pi$
$18$	752598.	1.68980
$19$	−815756.	−1.43605	−0.718024	−	0.696018i	$-0.754953\pi$
$19$	−815756.	−1.43605	−0.718024	+	0.696018i	$0.754953\pi$
$20$	−806686.	−1.12738
$21$	−81377.3	−0.0913096
$22$	2.50354e6	2.27852
$23$	843768.	0.628706	0.314353	−	0.949306i	$-0.398212\pi$
$23$	843768.	0.628706	0.314353	+	0.949306i	$0.398212\pi$
$24$	−859922.	−0.529064
$25$	−1.44960e6	−0.742196
$26$	−1.15974e6	−0.497715
$27$	−1.29530e6	−0.469066
$28$	−2.72952e6	−0.839219
$29$	−1.17935e6	−0.309637	−0.154818	−	0.987943i	$-0.549479\pi$
$29$	−1.17935e6	−0.309637	−0.154818	+	0.987943i	$0.549479\pi$
$30$	976582.	0.220122
$31$	−5.21568e6	−1.01434	−0.507170	−	0.861846i	$-0.669308\pi$
$31$	−5.21568e6	−1.01434	−0.507170	+	0.861846i	$0.669308\pi$
$32$	−5.20830e6	−0.878055
$33$	−2.08967e6	−0.306737
$34$	−1.50648e7	−1.93334
$35$	1.70374e6	0.191909
$36$	−2.10703e7	−2.09078
$37$	−1.21967e7	−1.06988	−0.534940	−	0.844890i	$-0.679666\pi$
$37$	−1.21967e7	−1.06988	−0.534940	+	0.844890i	$0.679666\pi$
$38$	3.31244e7	2.57704
$39$	968021.	0.0670029
$40$	1.80035e7	1.11196
$41$	3.76998e6	0.208359	0.104179	−	0.994559i	$-0.466778\pi$
$41$	3.76998e6	0.208359	0.104179	+	0.994559i	$0.466778\pi$
$42$	3.30439e6	0.163859
$43$	−3.68549e7	−1.64394	−0.821972	−	0.569529i	$-0.807126\pi$
$43$	−3.68549e7	−1.64394	−0.821972	+	0.569529i	$0.807126\pi$
$44$	−7.00909e7	−2.81919
$45$	1.31518e7	0.478111
$46$	−3.42618e7	−1.12824
$47$	−4.27229e6	−0.127709	−0.0638543	−	0.997959i	$-0.520339\pi$
$47$	−4.27229e6	−0.127709	−0.0638543	+	0.997959i	$0.520339\pi$
$48$	1.51901e7	0.413024
$49$	5.76480e6	0.142857
$50$	5.88622e7	1.33190
$51$	1.25744e7	0.260268
$52$	3.24689e7	0.615819
$53$	7.43643e7	1.29456	0.647281	−	0.762252i	$-0.275906\pi$
$53$	7.43643e7	1.29456	0.647281	+	0.762252i	$0.275906\pi$
$54$	5.25967e7	0.841756
$55$	4.37499e7	0.644681
$56$	6.09172e7	0.827739
$57$	−2.76485e7	−0.346924
$58$	4.78885e7	0.555655
$59$	4.00140e7	0.429910	0.214955	−	0.976624i	$-0.431039\pi$
$59$	4.00140e7	0.429910	0.214955	+	0.976624i	$0.431039\pi$
$60$	−2.73411e7	−0.272355
$61$	8.72200e7	0.806551	0.403276	−	0.915079i	$-0.367872\pi$
$61$	8.72200e7	0.806551	0.403276	+	0.915079i	$0.367872\pi$
$62$	2.11787e8	1.82027
$63$	4.45008e7	0.355906
$64$	−1.79794e7	−0.133957
$65$	−2.02667e7	−0.140823
$66$	8.48528e7	0.550451
$67$	5.46745e7	0.331473	0.165736	−	0.986170i	$-0.447000\pi$
$67$	5.46745e7	0.331473	0.165736	+	0.986170i	$0.447000\pi$
$68$	4.21764e8	2.39210
$69$	2.85979e7	0.151884
$70$	−6.91815e7	−0.344388
$71$	−2.42030e8	−1.13034	−0.565168	−	0.824976i	$-0.691189\pi$
$71$	−2.42030e8	−1.13034	−0.565168	+	0.824976i	$0.691189\pi$
$72$	4.70244e8	2.06218
$73$	1.94212e8	0.800429	0.400215	−	0.916421i	$-0.368936\pi$
$73$	1.94212e8	0.800429	0.400215	+	0.916421i	$0.368936\pi$
$74$	4.95257e8	1.91994
$75$	−4.91315e7	−0.179302
$76$	−9.27374e8	−3.18855
$77$	1.48033e8	0.479901
$78$	−3.93072e7	−0.120239
$79$	−5.40375e8	−1.56089	−0.780447	−	0.625222i	$-0.785009\pi$
$79$	−5.40375e8	−1.56089	−0.780447	+	0.625222i	$0.785009\pi$
$80$	−3.18024e8	−0.868069
$81$	3.20908e8	0.828320
$82$	−1.53083e8	−0.373908
$83$	−5.05002e8	−1.16800	−0.583998	−	0.811755i	$-0.698513\pi$
$83$	−5.05002e8	−1.16800	−0.583998	+	0.811755i	$0.698513\pi$
$84$	−9.25120e7	−0.202741
$85$	−2.63260e8	−0.547016
$86$	1.49652e9	2.95012
$87$	−3.99719e7	−0.0748029
$88$	1.56428e9	2.78063
$89$	9.65605e8	1.63134	0.815670	−	0.578517i	$-0.196368\pi$
$89$	9.65605e8	1.63134	0.815670	+	0.578517i	$0.196368\pi$
$90$	−5.34039e8	−0.857988
$91$	−6.85750e7	−0.104828
$92$	9.59218e8	1.39596
$93$	−1.76776e8	−0.245047
$94$	1.73480e8	0.229178
$95$	5.78856e8	0.729145
$96$	−1.76526e8	−0.212123
$97$	627939.	0.000720186 0	0.000360093	−	1.00000i	$-0.499885\pi$
$97$	627939.	0.000720186 0	0.000360093		1.00000i	$0.499885\pi$
$98$	−2.34084e8	−0.256363
$99$	1.14273e9	1.19560
$100$	−1.64795e9	−1.64795
$101$	−1.27119e9	−1.21553	−0.607763	−	0.794118i	$-0.707933\pi$
$101$	−1.27119e9	−1.21553	−0.607763	+	0.794118i	$0.707933\pi$
$102$	−5.10592e8	−0.467061
$103$	1.76784e9	1.54766	0.773830	−	0.633394i	$-0.218339\pi$
$103$	1.76784e9	1.54766	0.773830	+	0.633394i	$0.218339\pi$
$104$	−7.24638e8	−0.607395
$105$	5.77449e7	0.0463619
$106$	−3.01962e9	−2.32314
$107$	7.00570e8	0.516684	0.258342	−	0.966054i	$-0.416824\pi$
$107$	7.00570e8	0.516684	0.258342	+	0.966054i	$0.416824\pi$
$108$	−1.47253e9	−1.04150
$109$	1.40031e9	0.950177	0.475089	−	0.879938i	$-0.342416\pi$
$109$	1.40031e9	0.950177	0.475089	+	0.879938i	$0.342416\pi$
$110$	−1.77650e9	−1.15691
$111$	−4.13384e8	−0.258464
$112$	−1.07607e9	−0.646190
$113$	−1.65111e8	−0.0952627	−0.0476313	−	0.998865i	$-0.515167\pi$
$113$	−1.65111e8	−0.0952627	−0.0476313	+	0.998865i	$0.515167\pi$
$114$	1.12269e9	0.622569
$115$	−5.98733e8	−0.319222
$116$	−1.34072e9	−0.687507
$117$	−5.29357e8	−0.261163
$118$	−1.62480e9	−0.771490
$119$	−8.90774e8	−0.407199
$120$	6.10195e8	0.268629
$121$	1.44337e9	0.612132
$122$	−3.54164e9	−1.44739
$123$	1.27776e8	0.0503359
$124$	−5.92933e9	−2.25221
$125$	2.41455e9	0.884590
$126$	−1.80699e9	−0.638686
$127$	−2.36464e9	−0.806583	−0.403292	−	0.915072i	$-0.632134\pi$
$127$	−2.36464e9	−0.806583	−0.403292	+	0.915072i	$0.632134\pi$
$128$	3.39672e9	1.11844
$129$	−1.24913e9	−0.397148
$130$	8.22945e8	0.252712
$131$	5.38916e9	1.59882	0.799411	−	0.600785i	$-0.205145\pi$
$131$	5.38916e9	1.59882	0.799411	+	0.600785i	$0.205145\pi$
$132$	−2.37560e9	−0.681068
$133$	1.95863e9	0.542775
$134$	−2.22010e9	−0.594841
$135$	9.19138e8	0.238165
$136$	−9.41289e9	−2.35938
$137$	−4.27464e8	−0.103671	−0.0518355	−	0.998656i	$-0.516507\pi$
$137$	−4.27464e8	−0.103671	−0.0518355	+	0.998656i	$0.516507\pi$
$138$	−1.16124e9	−0.272562
$139$	8.22347e9	1.86848	0.934240	−	0.356646i	$-0.116080\pi$
$139$	8.22347e9	1.86848	0.934240	+	0.356646i	$0.116080\pi$
$140$	1.93685e9	0.426109
$141$	−1.44801e8	−0.0308522
$142$	9.82783e9	2.02843
$143$	−1.76092e9	−0.352151
$144$	−8.30662e9	−1.60988
$145$	8.36862e8	0.157216
$146$	−7.88612e9	−1.43640
$147$	1.95387e8	0.0345118
$148$	−1.38656e10	−2.37553
$149$	2.21094e9	0.367484	0.183742	−	0.982974i	$-0.441179\pi$
$149$	2.21094e9	0.367484	0.183742	+	0.982974i	$0.441179\pi$
$150$	1.99502e9	0.321763
$151$	1.23320e10	1.93035	0.965175	−	0.261606i	$-0.0842520\pi$
$151$	1.23320e10	1.93035	0.965175	+	0.261606i	$0.0842520\pi$
$152$	2.06970e10	3.14494
$153$	−6.87623e9	−1.01447
$154$	−6.01100e9	−0.861200
$155$	3.70102e9	0.515025
$156$	1.10047e9	0.148771
$157$	9.87941e9	1.29772	0.648862	−	0.760906i	$-0.275245\pi$
$157$	9.87941e9	1.29772	0.648862	+	0.760906i	$0.275245\pi$
$158$	2.19423e10	2.80108
$159$	2.52043e9	0.312744
$160$	3.69578e9	0.445827
$161$	−2.02589e9	−0.237629
$162$	−1.30307e10	−1.48645
$163$	−1.00264e10	−1.11250	−0.556252	−	0.831014i	$-0.687761\pi$
$163$	−1.00264e10	−1.11250	−0.556252	+	0.831014i	$0.687761\pi$
$164$	4.28582e9	0.462633
$165$	1.48282e9	0.155744
$166$	2.05060e10	2.09601
$167$	−6.64322e9	−0.660929	−0.330464	−	0.943818i	$-0.607205\pi$
$167$	−6.64322e9	−0.660929	−0.330464	+	0.943818i	$0.607205\pi$
$168$	2.06467e9	0.199967
$169$	8.15731e8	0.0769231
$170$	1.06899e10	0.981641
$171$	1.51194e10	1.35224
$172$	−4.18976e10	−3.65016
$173$	−5.07748e9	−0.430963	−0.215482	−	0.976508i	$-0.569132\pi$
$173$	−5.07748e9	−0.430963	−0.215482	+	0.976508i	$0.569132\pi$
$174$	1.62309e9	0.134237
$175$	3.48049e9	0.280524
$176$	−2.76323e10	−2.17075
$177$	1.35620e9	0.103859
$178$	−3.92091e10	−2.92750
$179$	1.95364e10	1.42235	0.711174	−	0.703016i	$-0.248164\pi$
$179$	1.95364e10	1.42235	0.711174	+	0.703016i	$0.248164\pi$
$180$	1.49513e10	1.06158
$181$	2.51685e9	0.174302	0.0871512	−	0.996195i	$-0.472224\pi$
$181$	2.51685e9	0.174302	0.0871512	+	0.996195i	$0.472224\pi$
$182$	2.78454e9	0.188119
$183$	2.95616e9	0.194849
$184$	−2.14077e10	−1.37686
$185$	8.65472e9	0.543225
$186$	7.17811e9	0.439746
$187$	−2.28740e10	−1.36790
$188$	−4.85686e9	−0.283560
$189$	3.11002e9	0.177290
$190$	−2.35049e10	−1.30848
$191$	−7.79784e9	−0.423959	−0.211980	−	0.977274i	$-0.567991\pi$
$191$	−7.79784e9	−0.423959	−0.211980	+	0.977274i	$0.567991\pi$
$192$	−6.09376e8	−0.0323616
$193$	−3.40382e10	−1.76587	−0.882934	−	0.469498i	$-0.844435\pi$
$193$	−3.40382e10	−1.76587	−0.882934	+	0.469498i	$0.844435\pi$
$194$	−2.54979e7	−0.00129240
$195$	−6.86902e8	−0.0340204
$196$	6.55358e9	0.317195
$197$	2.19161e9	0.103673	0.0518366	−	0.998656i	$-0.483493\pi$
$197$	2.19161e9	0.103673	0.0518366	+	0.998656i	$0.483493\pi$
$198$	−4.64013e10	−2.14554
$199$	9.72696e9	0.439682	0.219841	−	0.975536i	$-0.429446\pi$
$199$	9.72696e9	0.439682	0.219841	+	0.975536i	$0.429446\pi$
$200$	3.67787e10	1.62540
$201$	1.85309e9	0.0800781
$202$	5.16176e10	2.18131
$203$	2.83163e9	0.117032
$204$	1.42949e10	0.577890
$205$	−2.67516e9	−0.105793
$206$	−7.17845e10	−2.77733
$207$	−1.56386e10	−0.592013
$208$	1.28004e10	0.474174
$209$	5.02953e10	1.82335
$210$	−2.34477e9	−0.0831982
$211$	−3.20181e10	−1.11205	−0.556025	−	0.831166i	$-0.687674\pi$
$211$	−3.20181e10	−1.11205	−0.556025	+	0.831166i	$0.687674\pi$
$212$	8.45393e10	2.87440
$213$	−8.20316e9	−0.273069
$214$	−2.84472e10	−0.927208
$215$	2.61520e10	0.834703
$216$	3.28638e10	1.02725
$217$	1.25229e10	0.383384
$218$	−5.68606e10	−1.70513
$219$	6.58244e9	0.193370
$220$	4.97361e10	1.43143
$221$	1.05962e10	0.298802
$222$	1.67858e10	0.463824
$223$	−6.80744e9	−0.184337	−0.0921684	−	0.995743i	$-0.529380\pi$
$223$	−6.80744e9	−0.184337	−0.0921684	+	0.995743i	$0.529380\pi$
$224$	1.25051e10	0.331873
$225$	2.68673e10	0.698880
$226$	6.70445e9	0.170953
$227$	4.32119e10	1.08016	0.540078	−	0.841615i	$-0.318395\pi$
$227$	4.32119e10	1.08016	0.540078	+	0.841615i	$0.318395\pi$
$228$	−3.14316e10	−0.770299
$229$	−1.25697e10	−0.302040	−0.151020	−	0.988531i	$-0.548256\pi$
$229$	−1.25697e10	−0.302040	−0.151020	+	0.988531i	$0.548256\pi$
$230$	2.43120e10	0.572856
$231$	5.01731e9	0.115936
$232$	2.99220e10	0.678102
$233$	6.04307e10	1.34325	0.671624	−	0.740892i	$-0.265597\pi$
$233$	6.04307e10	1.34325	0.671624	+	0.740892i	$0.265597\pi$
$234$	2.14949e10	0.468668
$235$	3.03159e9	0.0648433
$236$	4.54890e10	0.954558
$237$	−1.83150e10	−0.377085
$238$	3.61706e10	0.730733
$239$	−5.49474e10	−1.08932	−0.544662	−	0.838656i	$-0.683342\pi$
$239$	−5.49474e10	−1.08932	−0.544662	+	0.838656i	$0.683342\pi$
$240$	−1.07788e10	−0.209710
$241$	−4.99349e10	−0.953516	−0.476758	−	0.879035i	$-0.658188\pi$
$241$	−4.99349e10	−0.953516	−0.476758	+	0.879035i	$0.658188\pi$
$242$	−5.86093e10	−1.09849
$243$	3.63720e10	0.669173
$244$	9.91541e10	1.79084
$245$	−4.09067e9	−0.0725349
$246$	−5.18845e9	−0.0903296
$247$	−2.32988e10	−0.398288
$248$	1.32330e11	2.22140
$249$	−1.71161e10	−0.282168
$250$	−9.80448e10	−1.58743
$251$	9.21851e10	1.46598	0.732992	−	0.680238i	$-0.238123\pi$
$251$	9.21851e10	1.46598	0.732992	+	0.680238i	$0.238123\pi$
$252$	5.05897e10	0.790241
$253$	−5.20224e10	−0.798267
$254$	9.60182e10	1.44744
$255$	−8.92271e9	−0.132150
$256$	−1.28721e11	−1.87313
$257$	−5.56416e10	−0.795611	−0.397805	−	0.917470i	$-0.630228\pi$
$257$	−5.56416e10	−0.795611	−0.397805	+	0.917470i	$0.630228\pi$
$258$	5.07217e10	0.712697
$259$	2.92843e10	0.404377
$260$	−2.30398e10	−0.312678
$261$	2.18584e10	0.291566
$262$	−2.18831e11	−2.86914
$263$	−9.98465e10	−1.28686	−0.643431	−	0.765504i	$-0.722490\pi$
$263$	−9.98465e10	−1.28686	−0.643431	+	0.765504i	$0.722490\pi$
$264$	5.30183e10	0.671751
$265$	−5.27684e10	−0.657306
$266$	−7.95317e10	−0.974031
$267$	3.27274e10	0.394103
$268$	6.21555e10	0.735991
$269$	−4.67267e10	−0.544101	−0.272051	−	0.962283i	$-0.587702\pi$
$269$	−4.67267e10	−0.544101	−0.272051	+	0.962283i	$0.587702\pi$
$270$	−3.73223e10	−0.427397
$271$	−1.55746e10	−0.175411	−0.0877053	−	0.996146i	$-0.527953\pi$
$271$	−1.55746e10	−0.175411	−0.0877053	+	0.996146i	$0.527953\pi$
$272$	1.66274e11	1.84189
$273$	−2.32422e9	−0.0253247
$274$	1.73575e10	0.186042
$275$	8.93750e10	0.942364
$276$	3.25109e10	0.337239
$277$	4.35353e9	0.0444306	0.0222153	−	0.999753i	$-0.492928\pi$
$277$	4.35353e9	0.0444306	0.0222153	+	0.999753i	$0.492928\pi$
$278$	−3.33920e11	−3.35306
$279$	9.66688e10	0.955141
$280$	−4.32265e10	−0.420280
$281$	3.61757e10	0.346130	0.173065	−	0.984910i	$-0.444633\pi$
$281$	3.61757e10	0.346130	0.173065	+	0.984910i	$0.444633\pi$
$282$	5.87976e9	0.0553654
$283$	7.91411e10	0.733437	0.366719	−	0.930332i	$-0.380481\pi$
$283$	7.91411e10	0.733437	0.366719	+	0.930332i	$0.380481\pi$
$284$	−2.75147e11	−2.50976
$285$	1.96192e10	0.176149
$286$	7.15037e10	0.631948
$287$	−9.05173e9	−0.0787522
$288$	9.65321e10	0.826809
$289$	1.90541e10	0.160675
$290$	−3.39814e10	−0.282131
$291$	2.12828e7	0.000173984 0
$292$	2.20785e11	1.77725
$293$	2.46593e9	0.0195468	0.00977341	−	0.999952i	$-0.496889\pi$
$293$	2.46593e9	0.0195468	0.00977341	+	0.999952i	$0.496889\pi$
$294$	−7.93383e9	−0.0619327
$295$	−2.83937e10	−0.218284
$296$	3.09450e11	2.34303
$297$	7.98616e10	0.595572
$298$	−8.97769e10	−0.659465
$299$	2.40989e10	0.174372
$300$	−5.58540e10	−0.398115
$301$	8.84885e10	0.621352
$302$	−5.00749e11	−3.46409
$303$	−4.30846e10	−0.293650
$304$	−3.65603e11	−2.45515
$305$	−6.18908e10	−0.409522
$306$	2.79215e11	1.82050
$307$	1.65418e11	1.06282	0.531412	−	0.847114i	$-0.321662\pi$
$307$	1.65418e11	1.06282	0.531412	+	0.847114i	$0.321662\pi$
$308$	1.68288e11	1.06555
$309$	5.99176e10	0.373887
$310$	−1.50283e11	−0.924232
$311$	−1.94108e11	−1.17658	−0.588292	−	0.808649i	$-0.700199\pi$
$311$	−1.94108e11	−1.17658	−0.588292	+	0.808649i	$0.700199\pi$
$312$	−2.45602e10	−0.146736
$313$	−1.84767e11	−1.08811	−0.544057	−	0.839048i	$-0.683112\pi$
$313$	−1.84767e11	−1.08811	−0.544057	+	0.839048i	$0.683112\pi$
$314$	−4.01161e11	−2.32881
$315$	−3.15775e10	−0.180709
$316$	−6.14313e11	−3.46576
$317$	−7.28506e10	−0.405197	−0.202599	−	0.979262i	$-0.564939\pi$
$317$	−7.28506e10	−0.405197	−0.202599	+	0.979262i	$0.564939\pi$
$318$	−1.02344e11	−0.561230
$319$	7.27128e10	0.393145
$320$	1.27580e10	0.0680157
$321$	2.37445e10	0.124822
$322$	8.22626e10	0.426433
$323$	−3.02647e11	−1.54712
$324$	3.64817e11	1.83917
$325$	−4.14021e10	−0.205848
$326$	4.07130e11	1.99643
$327$	4.74608e10	0.229546
$328$	−9.56504e10	−0.456304
$329$	1.02578e10	0.0482693
$330$	−6.02110e10	−0.279488
$331$	−3.20841e11	−1.46914	−0.734571	−	0.678532i	$-0.762617\pi$
$331$	−3.20841e11	−1.46914	−0.734571	+	0.678532i	$0.762617\pi$
$332$	−5.74100e11	−2.59338
$333$	2.26057e11	1.00744
$334$	2.69753e11	1.18606
$335$	−3.87967e10	−0.168303
$336$	−3.64714e10	−0.156108
$337$	2.00897e11	0.848473	0.424236	−	0.905551i	$-0.360543\pi$
$337$	2.00897e11	0.848473	0.424236	+	0.905551i	$0.360543\pi$
$338$	−3.31234e10	−0.138041
$339$	−5.59612e9	−0.0230138
$340$	−2.99282e11	−1.21458
$341$	3.21572e11	1.28790
$342$	−6.13936e11	−2.42664
$343$	−1.38413e10	−0.0539949
$344$	9.35066e11	3.60022
$345$	−2.02929e10	−0.0771184
$346$	2.06175e11	0.773380
$347$	1.64839e11	0.610347	0.305173	−	0.952297i	$-0.401286\pi$
$347$	1.64839e11	0.610347	0.305173	+	0.952297i	$0.401286\pi$
$348$	−4.54412e10	−0.166090
$349$	−5.14886e10	−0.185779	−0.0928895	−	0.995676i	$-0.529610\pi$
$349$	−5.14886e10	−0.185779	−0.0928895	+	0.995676i	$0.529610\pi$
$350$	−1.41328e11	−0.503410
$351$	−3.69951e10	−0.130095
$352$	3.21117e11	1.11486
$353$	−3.59174e11	−1.23117	−0.615586	−	0.788070i	$-0.711081\pi$
$353$	−3.59174e11	−1.23117	−0.615586	+	0.788070i	$0.711081\pi$
$354$	−5.50694e10	−0.186379
$355$	1.71743e11	0.573921
$356$	1.09773e12	3.62217
$357$	−3.01911e10	−0.0983721
$358$	−7.93290e11	−2.55246
$359$	−4.47119e11	−1.42069	−0.710344	−	0.703855i	$-0.751460\pi$
$359$	−4.47119e11	−1.42069	−0.710344	+	0.703855i	$0.751460\pi$
$360$	−3.33682e11	−1.04706
$361$	3.42770e11	1.06224
$362$	−1.02198e11	−0.312792
$363$	4.89204e10	0.147880
$364$	−7.79579e10	−0.232758
$365$	−1.37812e11	−0.406413
$366$	−1.20037e11	−0.349663
$367$	−1.19896e11	−0.344992	−0.172496	−	0.985010i	$-0.555183\pi$
$367$	−1.19896e11	−0.344992	−0.172496	+	0.985010i	$0.555183\pi$
$368$	3.78157e11	1.07487
$369$	−6.98738e10	−0.196199
$370$	−3.51431e11	−0.974839
$371$	−1.78549e11	−0.489298
$372$	−2.00963e11	−0.544094
$373$	4.34640e9	0.0116263	0.00581313	−	0.999983i	$-0.498150\pi$
$373$	4.34640e9	0.0116263	0.00581313	+	0.999983i	$0.498150\pi$
$374$	9.28817e11	2.45476
$375$	8.18367e10	0.213701
$376$	1.08395e11	0.279681
$377$	−3.36835e10	−0.0858778
$378$	−1.26285e11	−0.318154
$379$	5.66745e11	1.41095	0.705474	−	0.708736i	$-0.250734\pi$
$379$	5.66745e11	1.41095	0.705474	+	0.708736i	$0.250734\pi$
$380$	6.58059e11	1.61897
$381$	−8.01451e10	−0.194856
$382$	3.16637e11	0.760811
$383$	7.11023e11	1.68845	0.844227	−	0.535986i	$-0.180060\pi$
$383$	7.11023e11	1.68845	0.844227	+	0.535986i	$0.180060\pi$
$384$	1.15125e11	0.270197
$385$	−1.05044e11	−0.243667
$386$	1.38214e12	3.16892
$387$	6.83078e11	1.54800
$388$	7.13858e8	0.00159908
$389$	−1.33143e10	−0.0294812	−0.0147406	−	0.999891i	$-0.504692\pi$
$389$	−1.33143e10	−0.0294812	−0.0147406	+	0.999891i	$0.504692\pi$
$390$	2.78922e10	0.0610508
$391$	3.13039e11	0.677334
$392$	−1.46262e11	−0.312856
$393$	1.82655e11	0.386247
$394$	−8.89922e10	−0.186045
$395$	3.83447e11	0.792535
$396$	1.29908e12	2.65466
$397$	2.34010e11	0.472801	0.236400	−	0.971656i	$-0.424032\pi$
$397$	2.34010e11	0.472801	0.236400	+	0.971656i	$0.424032\pi$
$398$	−3.94971e11	−0.789026
$399$	6.63840e10	0.131125
$400$	−6.49678e11	−1.26890
$401$	5.22538e11	1.00918	0.504589	−	0.863360i	$-0.331644\pi$
$401$	5.22538e11	1.00918	0.504589	+	0.863360i	$0.331644\pi$
$402$	−7.52460e10	−0.143703
$403$	−1.48965e11	−0.281327
$404$	−1.44512e12	−2.69891
$405$	−2.27714e11	−0.420575
$406$	−1.14980e11	−0.210018
$407$	7.51987e11	1.35842
$408$	−3.19032e11	−0.569985
$409$	3.65238e11	0.645388	0.322694	−	0.946503i	$-0.395412\pi$
$409$	3.65238e11	0.645388	0.322694	+	0.946503i	$0.395412\pi$
$410$	1.08627e11	0.189849
$411$	−1.44881e10	−0.0250451
$412$	2.00973e12	3.43637
$413$	−9.60736e10	−0.162491
$414$	6.35018e11	1.06239
$415$	3.58346e11	0.593043
$416$	−1.48754e11	−0.243529
$417$	2.78719e11	0.451392
$418$	−2.04228e12	−3.27207
$419$	−6.14337e11	−0.973741	−0.486871	−	0.873474i	$-0.661862\pi$
$419$	−6.14337e11	−0.973741	−0.486871	+	0.873474i	$0.661862\pi$
$420$	6.56459e10	0.102940
$421$	−1.71623e11	−0.266261	−0.133130	−	0.991099i	$-0.542503\pi$
$421$	−1.71623e11	−0.266261	−0.133130	+	0.991099i	$0.542503\pi$
$422$	1.30012e12	1.99562
$423$	7.91837e10	0.120255
$424$	−1.88674e12	−2.83508
$425$	−5.37804e11	−0.799602
$426$	3.33095e11	0.490033
$427$	−2.09415e11	−0.304848
$428$	7.96427e11	1.14723
$429$	−5.96832e10	−0.0850735
$430$	−1.06192e12	−1.49791
$431$	4.32317e11	0.603468	0.301734	−	0.953392i	$-0.402435\pi$
$431$	4.32317e11	0.603468	0.301734	+	0.953392i	$0.402435\pi$
$432$	−5.80524e11	−0.801943
$433$	−1.18821e12	−1.62442	−0.812211	−	0.583363i	$-0.801736\pi$
$433$	−1.18821e12	−1.62442	−0.812211	+	0.583363i	$0.801736\pi$
$434$	−5.08500e11	−0.687998
$435$	2.83638e10	0.0379807
$436$	1.59191e12	2.10974
$437$	−6.88309e11	−0.902852
$438$	−2.67285e11	−0.347009
$439$	−5.34711e11	−0.687114	−0.343557	−	0.939132i	$-0.611632\pi$
$439$	−5.34711e11	−0.687114	−0.343557	+	0.939132i	$0.611632\pi$
$440$	−1.11000e12	−1.41185
$441$	−1.06846e11	−0.134520
$442$	−4.30265e11	−0.536212
$443$	−1.01296e12	−1.24961	−0.624805	−	0.780781i	$-0.714822\pi$
$443$	−1.01296e12	−1.24961	−0.624805	+	0.780781i	$0.714822\pi$
$444$	−4.69947e11	−0.573886
$445$	−6.85188e11	−0.828304
$446$	2.76421e11	0.330799
$447$	7.49356e10	0.0887778
$448$	4.31684e10	0.0506309
$449$	−3.44166e11	−0.399631	−0.199815	−	0.979834i	$-0.564034\pi$
$449$	−3.44166e11	−0.399631	−0.199815	+	0.979834i	$0.564034\pi$
$450$	−1.09097e12	−1.25417
$451$	−2.32438e11	−0.264553
$452$	−1.87703e11	−0.211518
$453$	4.17968e11	0.466339
$454$	−1.75465e12	−1.93838
$455$	4.86604e10	0.0532261
$456$	7.01486e11	0.759762
$457$	1.33688e12	1.43374	0.716869	−	0.697208i	$-0.245575\pi$
$457$	1.33688e12	1.43374	0.716869	+	0.697208i	$0.245575\pi$
$458$	5.10402e11	0.542023
$459$	−4.80558e11	−0.505346
$460$	−6.80656e11	−0.708789
$461$	1.82738e12	1.88441	0.942203	−	0.335041i	$-0.108750\pi$
$461$	1.82738e12	1.88441	0.942203	+	0.335041i	$0.108750\pi$
$462$	−2.03732e11	−0.208051
$463$	−3.19475e11	−0.323089	−0.161544	−	0.986865i	$-0.551647\pi$
$463$	−3.19475e11	−0.323089	−0.161544	+	0.986865i	$0.551647\pi$
$464$	−5.28558e11	−0.529373
$465$	1.25439e11	0.124421
$466$	−2.45384e12	−2.41051
$467$	1.05679e12	1.02817	0.514084	−	0.857740i	$-0.328132\pi$
$467$	1.05679e12	1.02817	0.514084	+	0.857740i	$0.328132\pi$
$468$	−6.01787e11	−0.579878
$469$	−1.31273e11	−0.125285
$470$	−1.23100e11	−0.116364
$471$	3.34844e11	0.313508
$472$	−1.01522e12	−0.941500
$473$	2.27228e12	2.08731
$474$	7.43694e11	0.676693
$475$	1.18252e12	1.06583
$476$	−1.01266e12	−0.904130
$477$	−1.37829e12	−1.21901
$478$	2.23118e12	1.95483
$479$	−1.09109e11	−0.0947006	−0.0473503	−	0.998878i	$-0.515078\pi$
$479$	−1.09109e11	−0.0947006	−0.0473503	+	0.998878i	$0.515078\pi$
$480$	1.25261e11	0.107704
$481$	−3.48350e11	−0.296731
$482$	2.02765e12	1.71112
$483$	−6.86636e10	−0.0574069
$484$	1.64087e12	1.35916
$485$	−4.45582e8	−0.000365670 0
$486$	−1.47691e12	−1.20086
$487$	1.06599e12	0.858759	0.429379	−	0.903124i	$-0.358732\pi$
$487$	1.06599e12	0.858759	0.429379	+	0.903124i	$0.358732\pi$
$488$	−2.21291e12	−1.76634
$489$	−3.39826e11	−0.268762
$490$	1.66105e11	0.130167
$491$	1.13836e12	0.883924	0.441962	−	0.897034i	$-0.354283\pi$
$491$	1.13836e12	0.883924	0.441962	+	0.897034i	$0.354283\pi$
$492$	1.45260e11	0.111764
$493$	−4.37541e11	−0.333586
$494$	9.46066e11	0.714743
$495$	−8.10872e11	−0.607056
$496$	−2.33755e12	−1.73418
$497$	5.81115e11	0.427227
$498$	6.95011e11	0.506360
$499$	−2.06496e12	−1.49094	−0.745469	−	0.666540i	$-0.767774\pi$
$499$	−2.06496e12	−1.49094	−0.745469	+	0.666540i	$0.767774\pi$
$500$	2.74493e12	1.96411
$501$	−2.25159e11	−0.159669
$502$	−3.74325e12	−2.63076
$503$	−1.28977e12	−0.898370	−0.449185	−	0.893439i	$-0.648286\pi$
$503$	−1.28977e12	−0.898370	−0.449185	+	0.893439i	$0.648286\pi$
$504$	−1.12905e12	−0.779431
$505$	9.02029e11	0.617176
$506$	2.11241e12	1.43252
$507$	2.76476e10	0.0185833
$508$	−2.68819e12	−1.79091
$509$	−1.72563e12	−1.13951	−0.569754	−	0.821815i	$-0.692962\pi$
$509$	−1.72563e12	−1.13951	−0.569754	+	0.821815i	$0.692962\pi$
$510$	3.62313e11	0.237147
$511$	−4.66303e11	−0.302534
$512$	3.48769e12	2.24297
$513$	1.05665e12	0.673601
$514$	2.25937e12	1.42775
$515$	−1.25445e12	−0.785815
$516$	−1.42004e12	−0.881814
$517$	2.63407e11	0.162151
$518$	−1.18911e12	−0.725669
$519$	−1.72091e11	−0.104113
$520$	5.14199e11	0.308401
$521$	2.96237e12	1.76145	0.880723	−	0.473632i	$-0.157057\pi$
$521$	2.96237e12	1.76145	0.880723	+	0.473632i	$0.157057\pi$
$522$	−8.87578e11	−0.523226
$523$	−1.07185e12	−0.626437	−0.313218	−	0.949681i	$-0.601407\pi$
$523$	−1.07185e12	−0.626437	−0.313218	+	0.949681i	$0.601407\pi$
$524$	6.12654e12	3.54997
$525$	1.17965e11	0.0677696
$526$	4.05434e12	2.30932
$527$	−1.93503e12	−1.09280
$528$	−9.36543e11	−0.524415
$529$	−1.08921e12	−0.604729
$530$	2.14270e12	1.17956
$531$	−7.41629e11	−0.404820
$532$	2.22662e12	1.20516
$533$	1.07674e11	0.0577883
$534$	−1.32892e12	−0.707233
$535$	−4.97120e11	−0.262343
$536$	−1.38718e12	−0.725923
$537$	6.62149e11	0.343615
$538$	1.89737e12	0.976410
$539$	−3.55428e11	−0.181385
$540$	1.04490e12	0.528814
$541$	−9.63542e11	−0.483596	−0.241798	−	0.970327i	$-0.577737\pi$
$541$	−9.63542e11	−0.483596	−0.241798	+	0.970327i	$0.577737\pi$
$542$	6.32419e11	0.314781
$543$	8.53037e10	0.0421084
$544$	−1.93229e12	−0.945969
$545$	−9.93651e11	−0.482447
$546$	9.43766e10	0.0454462
$547$	−3.76643e11	−0.179882	−0.0899408	−	0.995947i	$-0.528668\pi$
$547$	−3.76643e11	−0.179882	−0.0899408	+	0.995947i	$0.528668\pi$
$548$	−4.85953e11	−0.230188
$549$	−1.61656e12	−0.759479
$550$	−3.62914e12	−1.69111
$551$	9.62064e11	0.444654
$552$	−7.25574e11	−0.332626
$553$	1.29744e12	0.589963
$554$	−1.76778e11	−0.0797324
$555$	2.93335e11	0.131234
$556$	9.34866e12	4.14871
$557$	−3.53961e11	−0.155814	−0.0779072	−	0.996961i	$-0.524824\pi$
$557$	−3.53961e11	−0.155814	−0.0779072	+	0.996961i	$0.524824\pi$
$558$	−3.92531e12	−1.71404
$559$	−1.05261e12	−0.455948
$560$	7.63575e11	0.328099
$561$	−7.75272e11	−0.330462
$562$	−1.46894e12	−0.621143
$563$	−1.12126e12	−0.470347	−0.235173	−	0.971953i	$-0.575566\pi$
$563$	−1.12126e12	−0.470347	−0.235173	+	0.971953i	$0.575566\pi$
$564$	−1.64614e11	−0.0685031
$565$	1.17162e11	0.0483691
$566$	−3.21358e12	−1.31618
$567$	−7.70500e11	−0.313075
$568$	6.14069e12	2.47543
$569$	−3.66365e12	−1.46524	−0.732619	−	0.680638i	$-0.761702\pi$
$569$	−3.66365e12	−1.46524	−0.732619	+	0.680638i	$0.761702\pi$
$570$	−7.96653e11	−0.316106
$571$	1.44171e12	0.567563	0.283782	−	0.958889i	$-0.408411\pi$
$571$	1.44171e12	0.567563	0.283782	+	0.958889i	$0.408411\pi$
$572$	−2.00187e12	−0.781903
$573$	−2.64293e11	−0.102421
$574$	3.67552e11	0.141324
$575$	−1.22313e12	−0.466623
$576$	3.33234e11	0.126139
$577$	−1.04095e12	−0.390964	−0.195482	−	0.980707i	$-0.562627\pi$
$577$	−1.04095e12	−0.390964	−0.195482	+	0.980707i	$0.562627\pi$
$578$	−7.73706e11	−0.288337
$579$	−1.15366e12	−0.426603
$580$	9.51367e11	0.349078
$581$	1.21251e12	0.441461
$582$	−8.64204e8	−0.000312221 0
$583$	−4.58492e12	−1.64370
$584$	−4.92746e12	−1.75293
$585$	3.75629e11	0.132604
$586$	−1.00131e11	−0.0350775
$587$	−5.30726e12	−1.84501	−0.922505	−	0.385984i	$-0.873862\pi$
$587$	−5.30726e12	−1.84501	−0.922505	+	0.385984i	$0.873862\pi$
$588$	2.22121e11	0.0766288
$589$	4.25472e12	1.45664
$590$	1.15295e12	0.391720
$591$	7.42806e10	0.0250456
$592$	−5.46629e12	−1.82913
$593$	4.70325e12	1.56190	0.780948	−	0.624596i	$-0.214736\pi$
$593$	4.70325e12	1.56190	0.780948	+	0.624596i	$0.214736\pi$
$594$	−3.24284e12	−1.06878
$595$	6.32088e11	0.206753
$596$	2.51346e12	0.815950
$597$	3.29677e11	0.106219
$598$	−9.78552e11	−0.312917
$599$	2.30279e12	0.730860	0.365430	−	0.930839i	$-0.380922\pi$
$599$	2.30279e12	0.730860	0.365430	+	0.930839i	$0.380922\pi$
$600$	1.24654e12	0.392669
$601$	4.70264e12	1.47030	0.735151	−	0.677903i	$-0.237111\pi$
$601$	4.70264e12	1.47030	0.735151	+	0.677903i	$0.237111\pi$
$602$	−3.59314e12	−1.11504
$603$	−1.01335e12	−0.312127
$604$	1.40193e13	4.28608
$605$	−1.02421e12	−0.310806
$606$	1.74948e12	0.526966
$607$	−2.00350e12	−0.599019	−0.299509	−	0.954093i	$-0.596823\pi$
$607$	−2.00350e12	−0.599019	−0.299509	+	0.954093i	$0.596823\pi$
$608$	4.24871e12	1.26093
$609$	9.59725e10	0.0282728
$610$	2.51312e12	0.734902
$611$	−1.22021e11	−0.0354200
$612$	−7.81709e12	−2.25249
$613$	−1.93266e12	−0.552819	−0.276409	−	0.961040i	$-0.589145\pi$
$613$	−1.93266e12	−0.552819	−0.276409	+	0.961040i	$0.589145\pi$
$614$	−6.71694e12	−1.90728
$615$	−9.06693e10	−0.0255577
$616$	−3.75584e12	−1.05098
$617$	−5.12476e12	−1.42361	−0.711804	−	0.702378i	$-0.752122\pi$
$617$	−5.12476e12	−1.42361	−0.711804	+	0.702378i	$0.752122\pi$
$618$	−2.43300e12	−0.670955
$619$	2.81193e12	0.769834	0.384917	−	0.922951i	$-0.374230\pi$
$619$	2.81193e12	0.769834	0.384917	+	0.922951i	$0.374230\pi$
$620$	4.20742e12	1.14354
$621$	−1.09293e12	−0.294905
$622$	7.88192e12	2.11142
$623$	−2.31842e12	−0.616589
$624$	4.33844e11	0.114552
$625$	1.11790e12	0.293051
$626$	7.50259e12	1.95266
$627$	1.70466e12	0.440489
$628$	1.12312e13	2.88142
$629$	−4.52500e12	−1.15263
$630$	1.28223e12	0.324289
$631$	−2.52915e12	−0.635099	−0.317550	−	0.948242i	$-0.602860\pi$
$631$	−2.52915e12	−0.635099	−0.317550	+	0.948242i	$0.602860\pi$
$632$	1.37102e13	3.41835
$633$	−1.08519e12	−0.268652
$634$	2.95815e12	0.727141
$635$	1.67794e12	0.409538
$636$	2.86530e12	0.694405
$637$	1.64648e11	0.0396214
$638$	−2.95256e12	−0.705514
$639$	4.48585e12	1.06437
$640$	−2.41029e12	−0.567884
$641$	−4.73006e12	−1.10664	−0.553319	−	0.832970i	$-0.686639\pi$
$641$	−4.73006e12	−1.10664	−0.553319	+	0.832970i	$0.686639\pi$
$642$	−9.64163e11	−0.223997
$643$	−2.44664e12	−0.564444	−0.282222	−	0.959349i	$-0.591072\pi$
$643$	−2.44664e12	−0.564444	−0.282222	+	0.959349i	$0.591072\pi$
$644$	−2.30308e12	−0.527622
$645$	8.86372e11	0.201650
$646$	1.22892e13	2.77637
$647$	−2.61870e12	−0.587512	−0.293756	−	0.955880i	$-0.594905\pi$
$647$	−2.61870e12	−0.587512	−0.293756	+	0.955880i	$0.594905\pi$
$648$	−8.14195e12	−1.81401
$649$	−2.46706e12	−0.545856
$650$	1.68116e12	0.369402
$651$	4.24438e11	0.0926190
$652$	−1.13983e13	−2.47017
$653$	2.58375e12	0.556085	0.278043	−	0.960569i	$-0.410314\pi$
$653$	2.58375e12	0.556085	0.278043	+	0.960569i	$0.410314\pi$
$654$	−1.92718e12	−0.411930
$655$	−3.82411e12	−0.811792
$656$	1.68962e12	0.356222
$657$	−3.59957e12	−0.753714
$658$	−4.16524e11	−0.0866211
$659$	5.71019e12	1.17941	0.589707	−	0.807617i	$-0.299243\pi$
$659$	5.71019e12	1.17941	0.589707	+	0.807617i	$0.299243\pi$
$660$	1.68571e12	0.345808
$661$	−7.45062e12	−1.51805	−0.759024	−	0.651062i	$-0.774324\pi$
$661$	−7.45062e12	−1.51805	−0.759024	+	0.651062i	$0.774324\pi$
$662$	1.30280e13	2.63643
$663$	3.59137e11	0.0721854
$664$	1.28127e13	2.55790
$665$	−1.38983e12	−0.275591
$666$	−9.17922e12	−1.80789
$667$	−9.95100e11	−0.194671
$668$	−7.55220e12	−1.46750
$669$	−2.30725e11	−0.0445326
$670$	1.57537e12	0.302027
$671$	−5.37754e12	−1.02408
$672$	4.23838e11	0.0801748
$673$	−8.21134e11	−0.154293	−0.0771465	−	0.997020i	$-0.524581\pi$
$673$	−8.21134e11	−0.154293	−0.0771465	+	0.997020i	$0.524581\pi$
$674$	−8.15756e12	−1.52262
$675$	1.87767e12	0.348139
$676$	9.27345e11	0.170797
$677$	−8.02643e11	−0.146850	−0.0734249	−	0.997301i	$-0.523393\pi$
$677$	−8.02643e11	−0.146850	−0.0734249	+	0.997301i	$0.523393\pi$
$678$	2.27235e11	0.0412991
$679$	−1.50768e9	−0.000272205 0
$680$	6.67933e12	1.19796
$681$	1.46458e12	0.260947
$682$	−1.30577e13	−2.31119
$683$	9.21743e12	1.62075	0.810376	−	0.585910i	$-0.199263\pi$
$683$	9.21743e12	1.62075	0.810376	+	0.585910i	$0.199263\pi$
$684$	1.71882e13	3.00246
$685$	3.03326e11	0.0526383
$686$	5.62036e11	0.0968959
$687$	−4.26026e11	−0.0729676
$688$	−1.65175e13	−2.81058
$689$	2.12392e12	0.359047
$690$	8.24009e11	0.138392
$691$	−8.09015e12	−1.34991	−0.674956	−	0.737858i	$-0.735837\pi$
$691$	−8.09015e12	−1.34991	−0.674956	+	0.737858i	$0.735837\pi$
$692$	−5.77221e12	−0.956897
$693$	−2.74369e12	−0.451892
$694$	−6.69340e12	−1.09529
$695$	−5.83532e12	−0.948710
$696$	1.01415e12	0.163818
$697$	1.39867e12	0.224475
$698$	2.09073e12	0.333387
$699$	2.04818e12	0.324505
$700$	3.95672e12	0.622865
$701$	1.34474e12	0.210333	0.105167	−	0.994455i	$-0.466462\pi$
$701$	1.34474e12	0.210333	0.105167	+	0.994455i	$0.466462\pi$
$702$	1.50221e12	0.233461
$703$	9.94955e12	1.53640
$704$	1.10852e12	0.170084
$705$	1.02750e11	0.0156650
$706$	1.45845e13	2.20938
$707$	3.05213e12	0.459426
$708$	1.54176e12	0.230605
$709$	1.07046e13	1.59098	0.795488	−	0.605969i	$-0.207215\pi$
$709$	1.07046e13	1.59098	0.795488	+	0.605969i	$0.207215\pi$
$710$	−6.97377e12	−1.02992
$711$	1.00155e13	1.46980
$712$	−2.44989e13	−3.57262
$713$	−4.40082e12	−0.637722
$714$	1.22593e12	0.176532
$715$	1.24954e12	0.178802
$716$	2.22095e13	3.15813
$717$	−1.86234e12	−0.263162
$718$	1.81556e13	2.54948
$719$	7.34609e12	1.02512	0.512561	−	0.858651i	$-0.328697\pi$
$719$	7.34609e12	1.02512	0.512561	+	0.858651i	$0.328697\pi$
$720$	5.89433e12	0.817407
$721$	−4.24458e12	−0.584960
$722$	−1.39184e13	−1.90622
$723$	−1.69245e12	−0.230353
$724$	2.86122e12	0.387015
$725$	1.70959e12	0.229811
$726$	−1.98645e12	−0.265377
$727$	4.69938e12	0.623930	0.311965	−	0.950094i	$-0.399013\pi$
$727$	4.69938e12	0.623930	0.311965	+	0.950094i	$0.399013\pi$
$728$	1.73986e12	0.229574
$729$	−5.08367e12	−0.666659
$730$	5.59594e12	0.729324
$731$	−1.36732e13	−1.77110
$732$	3.36064e12	0.432635
$733$	1.48734e13	1.90302	0.951510	−	0.307618i	$-0.0995320\pi$
$733$	1.48734e13	1.90302	0.951510	+	0.307618i	$0.0995320\pi$
$734$	4.86848e12	0.619101
$735$	−1.38645e11	−0.0175232
$736$	−4.39460e12	−0.552038
$737$	−3.37095e12	−0.420870
$738$	2.83728e12	0.352086
$739$	−1.37566e13	−1.69672	−0.848359	−	0.529422i	$-0.822409\pi$
$739$	−1.37566e13	−1.69672	−0.848359	+	0.529422i	$0.822409\pi$
$740$	9.83892e12	1.20616
$741$	−7.89669e11	−0.0962195
$742$	7.25010e12	0.878064
$743$	−6.92448e12	−0.833562	−0.416781	−	0.909007i	$-0.636842\pi$
$743$	−6.92448e12	−0.833562	−0.416781	+	0.909007i	$0.636842\pi$
$744$	4.48508e12	0.536651
$745$	−1.56887e12	−0.186588
$746$	−1.76489e11	−0.0208638
$747$	9.35983e12	1.09983
$748$	−2.60038e13	−3.03725
$749$	−1.68207e12	−0.195288
$750$	−3.32304e12	−0.383495
$751$	1.29506e13	1.48563	0.742815	−	0.669497i	$-0.233490\pi$
$751$	1.29506e13	1.48563	0.742815	+	0.669497i	$0.233490\pi$
$752$	−1.91474e12	−0.218338
$753$	3.12444e12	0.354156
$754$	1.36774e12	0.154111
$755$	−8.75069e12	−0.980124
$756$	3.53555e12	0.393649
$757$	−9.22531e12	−1.02106	−0.510528	−	0.859861i	$-0.670550\pi$
$757$	−9.22531e12	−1.02106	−0.510528	+	0.859861i	$0.670550\pi$
$758$	−2.30131e13	−2.53200
$759$	−1.76320e12	−0.192847
$760$	−1.46865e13	−1.59682
$761$	1.04542e13	1.12995	0.564977	−	0.825106i	$-0.308885\pi$
$761$	1.04542e13	1.12995	0.564977	+	0.825106i	$0.308885\pi$
$762$	3.25435e12	0.349677
$763$	−3.36214e12	−0.359133
$764$	−8.86480e12	−0.941345
$765$	4.87933e12	0.515091
$766$	−2.88716e13	−3.02999
$767$	1.14284e12	0.119236
$768$	−4.36275e12	−0.452517
$769$	1.46960e13	1.51541	0.757704	−	0.652599i	$-0.226321\pi$
$769$	1.46960e13	1.51541	0.757704	+	0.652599i	$0.226321\pi$
$770$	4.26537e12	0.437269
$771$	−1.88587e12	−0.192206
$772$	−3.86955e13	−3.92087
$773$	−5.53470e11	−0.0557553	−0.0278777	−	0.999611i	$-0.508875\pi$
$773$	−5.53470e11	−0.0557553	−0.0278777	+	0.999611i	$0.508875\pi$
$774$	−2.77369e13	−2.77794
$775$	7.56066e12	0.752839
$776$	−1.59318e10	−0.00157720
$777$	9.92536e11	0.0976904
$778$	5.40637e11	0.0529051
$779$	−3.07539e12	−0.299213
$780$	−7.80889e11	−0.0755376
$781$	1.49224e13	1.43518
$782$	−1.27112e13	−1.21550
$783$	1.52762e12	0.145240
$784$	2.58365e12	0.244237
$785$	−7.01037e12	−0.658912
$786$	−7.41685e12	−0.693135
$787$	1.24173e13	1.15382	0.576912	−	0.816806i	$-0.304257\pi$
$787$	1.24173e13	1.15382	0.576912	+	0.816806i	$0.304257\pi$
$788$	2.49149e12	0.230192
$789$	−3.38411e12	−0.310884
$790$	−1.55702e13	−1.42223
$791$	3.96431e11	0.0360059
$792$	−2.89928e13	−2.61834
$793$	2.49109e12	0.223697
$794$	−9.50217e12	−0.848458
$795$	−1.78849e12	−0.158794
$796$	1.10579e13	0.976254
$797$	2.10900e13	1.85146	0.925731	−	0.378182i	$-0.123451\pi$
$797$	2.10900e13	1.85146	0.925731	+	0.378182i	$0.123451\pi$
$798$	−2.69557e12	−0.235309
$799$	−1.58503e12	−0.137586
$800$	7.54997e12	0.651688
$801$	−1.78968e13	−1.53613
$802$	−2.12180e13	−1.81101
$803$	−1.19741e13	−1.01630
$804$	2.10664e12	0.177803
$805$	1.43756e12	0.120655
$806$	6.04884e12	0.504852
$807$	−1.58371e12	−0.131445
$808$	3.22521e13	2.66199
$809$	2.61400e12	0.214554	0.107277	−	0.994229i	$-0.465787\pi$
$809$	2.61400e12	0.214554	0.107277	+	0.994229i	$0.465787\pi$
$810$	9.24652e12	0.754737
$811$	−6.89470e12	−0.559657	−0.279828	−	0.960050i	$-0.590278\pi$
$811$	−6.89470e12	−0.559657	−0.279828	+	0.960050i	$0.590278\pi$
$812$	3.21907e12	0.259853
$813$	−5.27872e11	−0.0423761
$814$	−3.05350e13	−2.43774
$815$	7.11469e12	0.564868
$816$	5.63555e12	0.444970
$817$	3.00646e13	2.36078
$818$	−1.48308e13	−1.15817
$819$	1.27099e12	0.0987105
$820$	−3.04119e12	−0.234899
$821$	2.04486e13	1.57080	0.785399	−	0.618990i	$-0.212458\pi$
$821$	2.04486e13	1.57080	0.785399	+	0.618990i	$0.212458\pi$
$822$	5.88300e11	0.0449444
$823$	1.75050e13	1.33003	0.665017	−	0.746828i	$-0.268424\pi$
$823$	1.75050e13	1.33003	0.665017	+	0.746828i	$0.268424\pi$
$824$	−4.48529e13	−3.38936
$825$	3.02919e12	0.227659
$826$	3.90114e12	0.291596
$827$	2.19160e13	1.62925	0.814623	−	0.579991i	$-0.196944\pi$
$827$	2.19160e13	1.62925	0.814623	+	0.579991i	$0.196944\pi$
$828$	−1.77784e13	−1.31449
$829$	−6.37917e12	−0.469103	−0.234552	−	0.972104i	$-0.575362\pi$
$829$	−6.37917e12	−0.469103	−0.234552	+	0.972104i	$0.575362\pi$
$830$	−1.45509e13	−1.06424
$831$	1.47555e11	0.0107337
$832$	−5.13509e11	−0.0371529
$833$	2.13875e12	0.153907
$834$	−1.13176e13	−0.810040
$835$	4.71399e12	0.335583
$836$	5.71771e13	4.04850
$837$	6.75588e12	0.475792
$838$	2.49456e13	1.74742
$839$	−3.60279e12	−0.251021	−0.125510	−	0.992092i	$-0.540057\pi$
$839$	−3.60279e12	−0.251021	−0.125510	+	0.992092i	$0.540057\pi$
$840$	−1.46508e12	−0.101532
$841$	−1.31163e13	−0.904125
$842$	6.96890e12	0.477815
$843$	1.22611e12	0.0836189
$844$	−3.63990e13	−2.46916
$845$	−5.78838e11	−0.0390572
$846$	−3.21531e12	−0.215803
$847$	−3.46554e12	−0.231364
$848$	3.33283e13	2.21326
$849$	2.68234e12	0.177186
$850$	2.18379e13	1.43492
$851$	−1.02912e13	−0.672640
$852$	−9.32558e12	−0.606314
$853$	−1.10813e12	−0.0716671	−0.0358336	−	0.999358i	$-0.511409\pi$
$853$	−1.10813e12	−0.0716671	−0.0358336	+	0.999358i	$0.511409\pi$
$854$	8.50347e12	0.547061
$855$	−1.07287e13	−0.686591
$856$	−1.77746e13	−1.13153
$857$	−2.77327e12	−0.175622	−0.0878109	−	0.996137i	$-0.527987\pi$
$857$	−2.77327e12	−0.175622	−0.0878109	+	0.996137i	$0.527987\pi$
$858$	2.42348e12	0.152668
$859$	−2.38978e13	−1.49758	−0.748789	−	0.662809i	$-0.769364\pi$
$859$	−2.38978e13	−1.49758	−0.748789	+	0.662809i	$0.769364\pi$
$860$	2.97303e13	1.85335
$861$	−3.06791e11	−0.0190252
$862$	−1.75545e13	−1.08295
$863$	2.70310e13	1.65888	0.829438	−	0.558598i	$-0.188661\pi$
$863$	2.70310e13	1.65888	0.829438	+	0.558598i	$0.188661\pi$
$864$	6.74632e12	0.411865
$865$	3.60295e12	0.218819
$866$	4.82483e13	2.91509
$867$	6.45803e11	0.0388163
$868$	1.42363e13	0.851254
$869$	3.33168e13	1.98186
$870$	−1.15173e12	−0.0681578
$871$	1.56156e12	0.0919341
$872$	−3.55281e13	−2.08088
$873$	−1.16384e10	−0.000678154 0
$874$	2.79493e13	1.62020
$875$	−5.79734e12	−0.334344
$876$	7.48310e12	0.429352
$877$	1.42466e13	0.813230	0.406615	−	0.913600i	$-0.366709\pi$
$877$	1.42466e13	0.813230	0.406615	+	0.913600i	$0.366709\pi$
$878$	2.17124e13	1.23305
$879$	8.35779e10	0.00472217
$880$	1.96077e13	1.10219
$881$	−1.77814e13	−0.994431	−0.497216	−	0.867627i	$-0.665644\pi$
$881$	−1.77814e13	−0.994431	−0.497216	+	0.867627i	$0.665644\pi$
$882$	4.33858e12	0.241401
$883$	−7.06774e12	−0.391253	−0.195626	−	0.980678i	$-0.562674\pi$
$883$	−7.06774e12	−0.391253	−0.195626	+	0.980678i	$0.562674\pi$
$884$	1.20460e13	0.663450
$885$	−9.62350e11	−0.0527337
$886$	4.11319e13	2.24247
$887$	−2.11211e13	−1.14567	−0.572835	−	0.819670i	$-0.694157\pi$
$887$	−2.11211e13	−1.14567	−0.572835	+	0.819670i	$0.694157\pi$
$888$	1.04882e13	0.566035
$889$	5.67751e12	0.304860
$890$	2.78226e13	1.48642
$891$	−1.97855e13	−1.05172
$892$	−7.73889e12	−0.409295
$893$	3.48515e12	0.183396
$894$	−3.04282e12	−0.159315
$895$	−1.38629e13	−0.722189
$896$	−8.15552e12	−0.422732
$897$	8.16785e11	0.0421252
$898$	1.39751e13	0.717152
$899$	6.15113e12	0.314077
$900$	3.05435e13	1.55177
$901$	2.75892e13	1.39469
$902$	9.43831e12	0.474750
$903$	2.99915e12	0.150108
$904$	4.18913e12	0.208625
$905$	−1.78594e12	−0.0885010
$906$	−1.69719e13	−0.836863
$907$	1.72848e12	0.0848068	0.0424034	−	0.999101i	$-0.486499\pi$
$907$	1.72848e12	0.0848068	0.0424034	+	0.999101i	$0.486499\pi$
$908$	4.91244e13	2.39834
$909$	2.35606e13	1.14459
$910$	−1.97589e12	−0.0955162
$911$	1.22908e13	0.591216	0.295608	−	0.955309i	$-0.404478\pi$
$911$	1.22908e13	0.591216	0.295608	+	0.955309i	$0.404478\pi$
$912$	−1.23914e13	−0.593122
$913$	3.11358e13	1.48300
$914$	−5.42850e13	−2.57290
$915$	−2.09767e12	−0.0989333
$916$	−1.42896e13	−0.670640
$917$	−1.29394e13	−0.604298
$918$	1.95134e13	0.906863
$919$	−2.12225e13	−0.981469	−0.490734	−	0.871309i	$-0.663271\pi$
$919$	−2.12225e13	−0.981469	−0.490734	+	0.871309i	$0.663271\pi$
$920$	1.51908e13	0.699094
$921$	5.60654e12	0.256760
$922$	−7.42021e13	−3.38164
$923$	−6.91263e12	−0.313499
$924$	5.70381e12	0.257419
$925$	1.76804e13	0.794061
$926$	1.29725e13	0.579795
$927$	−3.27656e13	−1.45733
$928$	6.14243e12	0.271878
$929$	6.84565e12	0.301539	0.150770	−	0.988569i	$-0.451825\pi$
$929$	6.84565e12	0.301539	0.150770	+	0.988569i	$0.451825\pi$
$930$	−5.09354e12	−0.223278
$931$	−4.70267e12	−0.205150
$932$	6.86993e13	2.98250
$933$	−6.57894e12	−0.284242
$934$	−4.29119e13	−1.84509
$935$	1.62313e13	0.694545
$936$	1.34306e13	0.571946
$937$	−1.49515e13	−0.633662	−0.316831	−	0.948482i	$-0.602619\pi$
$937$	−1.49515e13	−0.633662	−0.316831	+	0.948482i	$0.602619\pi$
$938$	5.33046e12	0.224829
$939$	−6.26232e12	−0.262869
$940$	3.44640e12	0.143976
$941$	1.07007e12	0.0444897	0.0222448	−	0.999753i	$-0.492919\pi$
$941$	1.07007e12	0.0444897	0.0222448	+	0.999753i	$0.492919\pi$
$942$	−1.35966e13	−0.562601
$943$	3.18099e12	0.130996
$944$	1.79333e13	0.735000
$945$	−2.20685e12	−0.0900181
$946$	−9.22677e13	−3.74576
$947$	−2.38549e13	−0.963836	−0.481918	−	0.876216i	$-0.660060\pi$
$947$	−2.38549e13	−0.963836	−0.481918	+	0.876216i	$0.660060\pi$
$948$	−2.08210e13	−0.837267
$949$	5.54689e12	0.221999
$950$	−4.80172e13	−1.91267
$951$	−2.46913e12	−0.0978885
$952$	2.26004e13	0.891762
$953$	6.91612e12	0.271609	0.135805	−	0.990736i	$-0.456638\pi$
$953$	6.91612e12	0.271609	0.135805	+	0.990736i	$0.456638\pi$
$954$	5.59664e13	2.18756
$955$	5.53330e12	0.215263
$956$	−6.24657e13	−2.41870
$957$	2.46446e12	0.0949770
$958$	4.43047e12	0.169944
$959$	1.02634e12	0.0391840
$960$	4.32410e11	0.0164314
$961$	7.63719e11	0.0288854
$962$	1.41450e13	0.532496
$963$	−1.29845e13	−0.486529
$964$	−5.67674e13	−2.11715
$965$	2.41533e13	0.896609
$966$	2.78814e12	0.103019
$967$	−2.38295e13	−0.876385	−0.438193	−	0.898881i	$-0.644381\pi$
$967$	−2.38295e13	−0.876385	−0.438193	+	0.898881i	$0.644381\pi$
$968$	−3.66207e13	−1.34056
$969$	−1.02576e13	−0.373758
$970$	1.80932e10	0.000656209 0
$971$	1.41849e13	0.512082	0.256041	−	0.966666i	$-0.417582\pi$
$971$	1.41849e13	0.512082	0.256041	+	0.966666i	$0.417582\pi$
$972$	4.13487e13	1.48581
$973$	−1.97445e13	−0.706219
$974$	−4.32852e13	−1.54108
$975$	−1.40324e12	−0.0497293
$976$	3.90900e13	1.37893
$977$	7.51215e12	0.263778	0.131889	−	0.991264i	$-0.457896\pi$
$977$	7.51215e12	0.263778	0.131889	+	0.991264i	$0.457896\pi$
$978$	1.37989e13	0.482303
$979$	−5.95343e13	−2.07131
$980$	−4.65038e12	−0.161054
$981$	−2.59537e13	−0.894723
$982$	−4.62242e13	−1.58623
$983$	−3.50360e13	−1.19681	−0.598403	−	0.801195i	$-0.704198\pi$
$983$	−3.50360e13	−1.19681	−0.598403	+	0.801195i	$0.704198\pi$
$984$	−3.24189e12	−0.110235
$985$	−1.55516e12	−0.0526394
$986$	1.77667e13	0.598633
$987$	3.47667e11	0.0116610
$988$	−2.64867e13	−0.884346
$989$	−3.10969e13	−1.03356
$990$	3.29261e13	1.08939
$991$	5.40121e13	1.77893	0.889467	−	0.456999i	$-0.151076\pi$
$991$	5.40121e13	1.77893	0.889467	+	0.456999i	$0.151076\pi$
$992$	2.71649e13	0.890646
$993$	−1.08743e13	−0.354919
$994$	−2.35966e13	−0.766674
$995$	−6.90220e12	−0.223246
$996$	−1.94580e13	−0.626515
$997$	−1.67272e13	−0.536161	−0.268080	−	0.963397i	$-0.586389\pi$
$997$	−1.67272e13	−0.536161	−0.268080	+	0.963397i	$0.586389\pi$
$998$	8.38493e13	2.67554
$999$	1.57984e13	0.501844

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.d.1.3	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.d.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-40.6058 q^{2} +33.8931 q^{3} +1136.83 q^{4} -709.594 q^{5} -1376.25 q^{6} -2401.00 q^{7} -25371.6 q^{8} -18534.3 q^{9} +O(q^{10})\)	\(q-40.6058 q^{2} +33.8931 q^{3} +1136.83 q^{4} -709.594 q^{5} -1376.25 q^{6} -2401.00 q^{7} -25371.6 q^{8} -18534.3 q^{9} +28813.6 q^{10} -61654.9 q^{11} +38530.6 q^{12} +28561.0 q^{13} +97494.4 q^{14} -24050.3 q^{15} +448177. q^{16} +371001. q^{17} +752598. q^{18} -815756. q^{19} -806686. q^{20} -81377.3 q^{21} +2.50354e6 q^{22} +843768. q^{23} -859922. q^{24} -1.44960e6 q^{25} -1.15974e6 q^{26} -1.29530e6 q^{27} -2.72952e6 q^{28} -1.17935e6 q^{29} +976582. q^{30} -5.21568e6 q^{31} -5.20830e6 q^{32} -2.08967e6 q^{33} -1.50648e7 q^{34} +1.70374e6 q^{35} -2.10703e7 q^{36} -1.21967e7 q^{37} +3.31244e7 q^{38} +968021. q^{39} +1.80035e7 q^{40} +3.76998e6 q^{41} +3.30439e6 q^{42} -3.68549e7 q^{43} -7.00909e7 q^{44} +1.31518e7 q^{45} -3.42618e7 q^{46} -4.27229e6 q^{47} +1.51901e7 q^{48} +5.76480e6 q^{49} +5.88622e7 q^{50} +1.25744e7 q^{51} +3.24689e7 q^{52} +7.43643e7 q^{53} +5.25967e7 q^{54} +4.37499e7 q^{55} +6.09172e7 q^{56} -2.76485e7 q^{57} +4.78885e7 q^{58} +4.00140e7 q^{59} -2.73411e7 q^{60} +8.72200e7 q^{61} +2.11787e8 q^{62} +4.45008e7 q^{63} -1.79794e7 q^{64} -2.02667e7 q^{65} +8.48528e7 q^{66} +5.46745e7 q^{67} +4.21764e8 q^{68} +2.85979e7 q^{69} -6.91815e7 q^{70} -2.42030e8 q^{71} +4.70244e8 q^{72} +1.94212e8 q^{73} +4.95257e8 q^{74} -4.91315e7 q^{75} -9.27374e8 q^{76} +1.48033e8 q^{77} -3.93072e7 q^{78} -5.40375e8 q^{79} -3.18024e8 q^{80} +3.20908e8 q^{81} -1.53083e8 q^{82} -5.05002e8 q^{83} -9.25120e7 q^{84} -2.63260e8 q^{85} +1.49652e9 q^{86} -3.99719e7 q^{87} +1.56428e9 q^{88} +9.65605e8 q^{89} -5.34039e8 q^{90} -6.85750e7 q^{91} +9.59218e8 q^{92} -1.76776e8 q^{93} +1.73480e8 q^{94} +5.78856e8 q^{95} -1.76526e8 q^{96} +627939. q^{97} -2.34084e8 q^{98} +1.14273e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 22 q^{2} + q^{3} + 6402 q^{4} + 1694 q^{5} + 4189 q^{6} - 36015 q^{7} - 1704 q^{8} + 160366 q^{9}+O(q^{10}) \) 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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