LMFDB - Embedded newform 91.10.a.d.1.6

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			1.6
Root			$-19.4300$ 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)

$f(q)$	$=$	$q-18.4300 q^{2} +260.590 q^{3} -172.335 q^{4} +266.250 q^{5} -4802.67 q^{6} -2401.00 q^{7} +12612.3 q^{8} +48224.1 q^{9} +O(q^{10})$	\(q-18.4300 q^{2} +260.590 q^{3} -172.335 q^{4} +266.250 q^{5} -4802.67 q^{6} -2401.00 q^{7} +12612.3 q^{8} +48224.1 q^{9} -4906.98 q^{10} -86941.8 q^{11} -44908.9 q^{12} +28561.0 q^{13} +44250.4 q^{14} +69382.1 q^{15} -144209. q^{16} +194111. q^{17} -888771. q^{18} +622912. q^{19} -45884.3 q^{20} -625677. q^{21} +1.60234e6 q^{22} +1.97949e6 q^{23} +3.28664e6 q^{24} -1.88224e6 q^{25} -526379. q^{26} +7.43754e6 q^{27} +413777. q^{28} +3.07074e6 q^{29} -1.27871e6 q^{30} +3.59067e6 q^{31} -3.79973e6 q^{32} -2.26562e7 q^{33} -3.57746e6 q^{34} -639266. q^{35} -8.31073e6 q^{36} -1.23557e7 q^{37} -1.14803e7 q^{38} +7.44271e6 q^{39} +3.35802e6 q^{40} -7.59440e6 q^{41} +1.15312e7 q^{42} +3.36179e7 q^{43} +1.49832e7 q^{44} +1.28397e7 q^{45} -3.64819e7 q^{46} +2.11507e7 q^{47} -3.75794e7 q^{48} +5.76480e6 q^{49} +3.46896e7 q^{50} +5.05833e7 q^{51} -4.92207e6 q^{52} -4.88511e6 q^{53} -1.37074e8 q^{54} -2.31483e7 q^{55} -3.02821e7 q^{56} +1.62325e8 q^{57} -5.65938e7 q^{58} +4.39477e7 q^{59} -1.19570e7 q^{60} -6.64849e7 q^{61} -6.61761e7 q^{62} -1.15786e8 q^{63} +1.43864e8 q^{64} +7.60437e6 q^{65} +4.17553e8 q^{66} +2.89596e8 q^{67} -3.34522e7 q^{68} +5.15835e8 q^{69} +1.17817e7 q^{70} -2.07395e7 q^{71} +6.08217e8 q^{72} +5.58821e7 q^{73} +2.27716e8 q^{74} -4.90492e8 q^{75} -1.07350e8 q^{76} +2.08747e8 q^{77} -1.37169e8 q^{78} +4.77419e8 q^{79} -3.83956e7 q^{80} +9.88951e8 q^{81} +1.39965e8 q^{82} -2.28868e8 q^{83} +1.07826e8 q^{84} +5.16820e7 q^{85} -6.19579e8 q^{86} +8.00205e8 q^{87} -1.09654e9 q^{88} +3.96890e8 q^{89} -2.36635e8 q^{90} -6.85750e7 q^{91} -3.41136e8 q^{92} +9.35694e8 q^{93} -3.89807e8 q^{94} +1.65850e8 q^{95} -9.90171e8 q^{96} +1.38384e9 q^{97} -1.06245e8 q^{98} -4.19269e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−18.4300	−0.814498	−0.407249	−	0.913317i	$-0.633512\pi$
$2$	−18.4300	−0.814498	−0.407249	+	0.913317i	$0.633512\pi$
$3$	260.590	1.85743	0.928714	−	0.370796i	$-0.120915\pi$
$3$	260.590	1.85743	0.928714	+	0.370796i	$0.120915\pi$
$4$	−172.335	−0.336593
$5$	266.250	0.190513	0.0952565	−	0.995453i	$-0.469633\pi$
$5$	266.250	0.190513	0.0952565	+	0.995453i	$0.469633\pi$
$6$	−4802.67	−1.51287
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	12612.3	1.08865
$9$	48224.1	2.45004
$10$	−4906.98	−0.155172
$11$	−86941.8	−1.79045	−0.895224	−	0.445617i	$-0.852984\pi$
$11$	−86941.8	−1.79045	−0.895224	+	0.445617i	$0.852984\pi$
$12$	−44908.9	−0.625197
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	44250.4	0.307851
$15$	69382.1	0.353864
$16$	−144209.	−0.550113
$17$	194111.	0.563676	0.281838	−	0.959462i	$-0.409056\pi$
$17$	194111.	0.563676	0.281838	+	0.959462i	$0.409056\pi$
$18$	−888771.	−1.99555
$19$	622912.	1.09657	0.548284	−	0.836292i	$-0.315281\pi$
$19$	622912.	1.09657	0.548284	+	0.836292i	$0.315281\pi$
$20$	−45884.3	−0.0641252
$21$	−625677.	−0.702042
$22$	1.60234e6	1.45832
$23$	1.97949e6	1.47495	0.737475	−	0.675374i	$-0.236018\pi$
$23$	1.97949e6	1.47495	0.737475	+	0.675374i	$0.236018\pi$
$24$	3.28664e6	2.02209
$25$	−1.88224e6	−0.963705
$26$	−526379.	−0.225901
$27$	7.43754e6	2.69335
$28$	413777.	0.127220
$29$	3.07074e6	0.806218	0.403109	−	0.915152i	$-0.367929\pi$
$29$	3.07074e6	0.806218	0.403109	+	0.915152i	$0.367929\pi$
$30$	−1.27871e6	−0.288222
$31$	3.59067e6	0.698310	0.349155	−	0.937065i	$-0.386469\pi$
$31$	3.59067e6	0.698310	0.349155	+	0.937065i	$0.386469\pi$
$32$	−3.79973e6	−0.640586
$33$	−2.26562e7	−3.32563
$34$	−3.57746e6	−0.459113
$35$	−639266.	−0.0720071
$36$	−8.31073e6	−0.824665
$37$	−1.23557e7	−1.08383	−0.541915	−	0.840433i	$-0.682301\pi$
$37$	−1.23557e7	−1.08383	−0.541915	+	0.840433i	$0.682301\pi$
$38$	−1.14803e7	−0.893153
$39$	7.44271e6	0.515158
$40$	3.35802e6	0.207402
$41$	−7.59440e6	−0.419726	−0.209863	−	0.977731i	$-0.567302\pi$
$41$	−7.59440e6	−0.419726	−0.209863	+	0.977731i	$0.567302\pi$
$42$	1.15312e7	0.571812
$43$	3.36179e7	1.49956	0.749779	−	0.661689i	$-0.230160\pi$
$43$	3.36179e7	1.49956	0.749779	+	0.661689i	$0.230160\pi$
$44$	1.49832e7	0.602651
$45$	1.28397e7	0.466764
$46$	−3.64819e7	−1.20134
$47$	2.11507e7	0.632243	0.316122	−	0.948719i	$-0.397619\pi$
$47$	2.11507e7	0.632243	0.316122	+	0.948719i	$0.397619\pi$
$48$	−3.75794e7	−1.02180
$49$	5.76480e6	0.142857
$50$	3.46896e7	0.784936
$51$	5.05833e7	1.04699
$52$	−4.92207e6	−0.0933540
$53$	−4.88511e6	−0.0850420	−0.0425210	−	0.999096i	$-0.513539\pi$
$53$	−4.88511e6	−0.0850420	−0.0425210	+	0.999096i	$0.513539\pi$
$54$	−1.37074e8	−2.19373
$55$	−2.31483e7	−0.341104
$56$	−3.02821e7	−0.411472
$57$	1.62325e8	2.03680
$58$	−5.65938e7	−0.656664
$59$	4.39477e7	0.472174	0.236087	−	0.971732i	$-0.424135\pi$
$59$	4.39477e7	0.472174	0.236087	+	0.971732i	$0.424135\pi$
$60$	−1.19570e7	−0.119108
$61$	−6.64849e7	−0.614807	−0.307404	−	0.951579i	$-0.599460\pi$
$61$	−6.64849e7	−0.614807	−0.307404	+	0.951579i	$0.599460\pi$
$62$	−6.61761e7	−0.568773
$63$	−1.15786e8	−0.926028
$64$	1.43864e8	1.07187
$65$	7.60437e6	0.0528388
$66$	4.17553e8	2.70872
$67$	2.89596e8	1.75572	0.877862	−	0.478914i	$-0.158970\pi$
$67$	2.89596e8	1.75572	0.877862	+	0.478914i	$0.158970\pi$
$68$	−3.34522e7	−0.189729
$69$	5.15835e8	2.73962
$70$	1.17817e7	0.0586497
$71$	−2.07395e7	−0.0968579	−0.0484290	−	0.998827i	$-0.515421\pi$
$71$	−2.07395e7	−0.0968579	−0.0484290	+	0.998827i	$0.515421\pi$
$72$	6.08217e8	2.66724
$73$	5.58821e7	0.230314	0.115157	−	0.993347i	$-0.463263\pi$
$73$	5.58821e7	0.230314	0.115157	+	0.993347i	$0.463263\pi$
$74$	2.27716e8	0.882778
$75$	−4.90492e8	−1.79001
$76$	−1.07350e8	−0.369097
$77$	2.08747e8	0.676726
$78$	−1.37169e8	−0.419595
$79$	4.77419e8	1.37904	0.689522	−	0.724265i	$-0.257821\pi$
$79$	4.77419e8	1.37904	0.689522	+	0.724265i	$0.257821\pi$
$80$	−3.83956e7	−0.104804
$81$	9.88951e8	2.55266
$82$	1.39965e8	0.341866
$83$	−2.28868e8	−0.529339	−0.264670	−	0.964339i	$-0.585263\pi$
$83$	−2.28868e8	−0.529339	−0.264670	+	0.964339i	$0.585263\pi$
$84$	1.07826e8	0.236302
$85$	5.16820e7	0.107388
$86$	−6.19579e8	−1.22139
$87$	8.00205e8	1.49749
$88$	−1.09654e9	−1.94918
$89$	3.96890e8	0.670525	0.335262	−	0.942125i	$-0.391175\pi$
$89$	3.96890e8	0.670525	0.335262	+	0.942125i	$0.391175\pi$
$90$	−2.36635e8	−0.380179
$91$	−6.85750e7	−0.104828
$92$	−3.41136e8	−0.496457
$93$	9.35694e8	1.29706
$94$	−3.89807e8	−0.514961
$95$	1.65850e8	0.208910
$96$	−9.90171e8	−1.18984
$97$	1.38384e9	1.58713	0.793567	−	0.608483i	$-0.208222\pi$
$97$	1.38384e9	1.58713	0.793567	+	0.608483i	$0.208222\pi$
$98$	−1.06245e8	−0.116357
$99$	−4.19269e9	−4.38667
$100$	3.24376e8	0.324376
$101$	1.26754e8	0.121204	0.0606019	−	0.998162i	$-0.480698\pi$
$101$	1.26754e8	0.121204	0.0606019	+	0.998162i	$0.480698\pi$
$102$	−9.32251e8	−0.852770
$103$	1.45250e9	1.27159	0.635797	−	0.771856i	$-0.280672\pi$
$103$	1.45250e9	1.27159	0.635797	+	0.771856i	$0.280672\pi$
$104$	3.60220e8	0.301938
$105$	−1.66586e8	−0.133748
$106$	9.00326e7	0.0692665
$107$	−2.84571e7	−0.0209877	−0.0104938	−	0.999945i	$-0.503340\pi$
$107$	−2.84571e7	−0.0209877	−0.0104938	+	0.999945i	$0.503340\pi$
$108$	−1.28175e9	−0.906560
$109$	−1.52649e8	−0.103579	−0.0517897	−	0.998658i	$-0.516493\pi$
$109$	−1.52649e8	−0.103579	−0.0517897	+	0.998658i	$0.516493\pi$
$110$	4.26622e8	0.277828
$111$	−3.21978e9	−2.01314
$112$	3.46245e8	0.207923
$113$	−1.99192e9	−1.14926	−0.574631	−	0.818412i	$-0.694855\pi$
$113$	−1.99192e9	−1.14926	−0.574631	+	0.818412i	$0.694855\pi$
$114$	−2.99164e9	−1.65897
$115$	5.27038e8	0.280997
$116$	−5.29198e8	−0.271367
$117$	1.37733e9	0.679519
$118$	−8.09956e8	−0.384585
$119$	−4.66060e8	−0.213050
$120$	8.75067e8	0.385235
$121$	5.20093e9	2.20570
$122$	1.22532e9	0.500760
$123$	−1.97902e9	−0.779611
$124$	−6.18800e8	−0.235046
$125$	−1.02116e9	−0.374111
$126$	2.13394e9	0.754248
$127$	−1.40834e9	−0.480387	−0.240193	−	0.970725i	$-0.577211\pi$
$127$	−1.40834e9	−0.480387	−0.240193	+	0.970725i	$0.577211\pi$
$128$	−7.05949e8	−0.232450
$129$	8.76050e9	2.78532
$130$	−1.40148e8	−0.0430371
$131$	5.47011e9	1.62284	0.811420	−	0.584464i	$-0.198695\pi$
$131$	5.47011e9	1.62284	0.811420	+	0.584464i	$0.198695\pi$
$132$	3.90446e9	1.11938
$133$	−1.49561e9	−0.414464
$134$	−5.33725e9	−1.43003
$135$	1.98024e9	0.513117
$136$	2.44818e9	0.613647
$137$	−3.03456e9	−0.735957	−0.367979	−	0.929834i	$-0.619950\pi$
$137$	−3.03456e9	−0.735957	−0.367979	+	0.929834i	$0.619950\pi$
$138$	−9.50683e9	−2.23141
$139$	−2.44660e9	−0.555899	−0.277950	−	0.960596i	$-0.589655\pi$
$139$	−2.44660e9	−0.555899	−0.277950	+	0.960596i	$0.589655\pi$
$140$	1.10168e8	0.0242371
$141$	5.51166e9	1.17435
$142$	3.82228e8	0.0788906
$143$	−2.48315e9	−0.496581
$144$	−6.95435e9	−1.34780
$145$	8.17586e8	0.153595
$146$	−1.02991e9	−0.187590
$147$	1.50225e9	0.265347
$148$	2.12933e9	0.364809
$149$	−6.40011e9	−1.06377	−0.531887	−	0.846815i	$-0.678517\pi$
$149$	−6.40011e9	−1.06377	−0.531887	+	0.846815i	$0.678517\pi$
$150$	9.03976e9	1.45796
$151$	−8.63642e9	−1.35188	−0.675939	−	0.736958i	$-0.736262\pi$
$151$	−8.63642e9	−1.35188	−0.675939	+	0.736958i	$0.736262\pi$
$152$	7.85635e9	1.19378
$153$	9.36083e9	1.38103
$154$	−3.84721e9	−0.551192
$155$	9.56017e8	0.133037
$156$	−1.28264e9	−0.173398
$157$	−7.19428e9	−0.945015	−0.472508	−	0.881327i	$-0.656651\pi$
$157$	−7.19428e9	−0.945015	−0.472508	+	0.881327i	$0.656651\pi$
$158$	−8.79883e9	−1.12323
$159$	−1.27301e9	−0.157959
$160$	−1.01168e9	−0.122040
$161$	−4.75275e9	−0.557479
$162$	−1.82264e10	−2.07913
$163$	−1.41361e10	−1.56851	−0.784253	−	0.620441i	$-0.786953\pi$
$163$	−1.41361e10	−1.56851	−0.784253	+	0.620441i	$0.786953\pi$
$164$	1.30878e9	0.141277
$165$	−6.03220e9	−0.633575
$166$	4.21804e9	0.431146
$167$	3.38285e9	0.336557	0.168278	−	0.985740i	$-0.446179\pi$
$167$	3.38285e9	0.336557	0.168278	+	0.985740i	$0.446179\pi$
$168$	−7.89122e9	−0.764280
$169$	8.15731e8	0.0769231
$170$	−9.52499e8	−0.0874670
$171$	3.00394e10	2.68664
$172$	−5.79356e9	−0.504740
$173$	2.03042e10	1.72337	0.861687	−	0.507440i	$-0.169408\pi$
$173$	2.03042e10	1.72337	0.861687	+	0.507440i	$0.169408\pi$
$174$	−1.47478e10	−1.21971
$175$	4.51925e9	0.364246
$176$	1.25378e10	0.984948
$177$	1.14523e10	0.877029
$178$	−7.31467e9	−0.546141
$179$	1.66035e10	1.20882	0.604410	−	0.796674i	$-0.293409\pi$
$179$	1.66035e10	1.20882	0.604410	+	0.796674i	$0.293409\pi$
$180$	−2.21273e9	−0.157109
$181$	−2.14730e10	−1.48710	−0.743548	−	0.668683i	$-0.766859\pi$
$181$	−2.14730e10	−1.48710	−0.743548	+	0.668683i	$0.766859\pi$
$182$	1.26384e9	0.0853826
$183$	−1.73253e10	−1.14196
$184$	2.49659e10	1.60571
$185$	−3.28972e9	−0.206484
$186$	−1.72448e10	−1.05645
$187$	−1.68764e10	−1.00923
$188$	−3.64501e9	−0.212808
$189$	−1.78575e10	−1.01799
$190$	−3.05662e9	−0.170157
$191$	1.16618e10	0.634040	0.317020	−	0.948419i	$-0.397318\pi$
$191$	1.16618e10	0.634040	0.317020	+	0.948419i	$0.397318\pi$
$192$	3.74895e10	1.99092
$193$	−2.10821e10	−1.09372	−0.546859	−	0.837225i	$-0.684176\pi$
$193$	−2.10821e10	−1.09372	−0.546859	+	0.837225i	$0.684176\pi$
$194$	−2.55042e10	−1.29272
$195$	1.98162e9	0.0981443
$196$	−9.93479e8	−0.0480846
$197$	1.27166e10	0.601552	0.300776	−	0.953695i	$-0.402754\pi$
$197$	1.27166e10	0.601552	0.300776	+	0.953695i	$0.402754\pi$
$198$	7.72713e10	3.57293
$199$	−2.98207e10	−1.34797	−0.673984	−	0.738746i	$-0.735418\pi$
$199$	−2.98207e10	−1.34797	−0.673984	+	0.738746i	$0.735418\pi$
$200$	−2.37393e10	−1.04914
$201$	7.54658e10	3.26113
$202$	−2.33608e9	−0.0987204
$203$	−7.37286e9	−0.304722
$204$	−8.71730e9	−0.352408
$205$	−2.02201e9	−0.0799633
$206$	−2.67696e10	−1.03571
$207$	9.54591e10	3.61369
$208$	−4.11875e9	−0.152574
$209$	−5.41571e10	−1.96335
$210$	3.07019e9	0.108938
$211$	−5.08654e10	−1.76665	−0.883327	−	0.468758i	$-0.844702\pi$
$211$	−5.08654e10	−1.76665	−0.883327	+	0.468758i	$0.844702\pi$
$212$	8.41878e8	0.0286245
$213$	−5.40450e9	−0.179907
$214$	5.24465e8	0.0170944
$215$	8.95078e9	0.285685
$216$	9.38044e10	2.93212
$217$	−8.62121e9	−0.263936
$218$	2.81331e9	0.0843653
$219$	1.45623e10	0.427792
$220$	3.98926e9	0.114813
$221$	5.54400e9	0.156336
$222$	5.93406e10	1.63970
$223$	5.27484e10	1.42836	0.714180	−	0.699962i	$-0.246800\pi$
$223$	5.27484e10	1.42836	0.714180	+	0.699962i	$0.246800\pi$
$224$	9.12315e9	0.242119
$225$	−9.07692e10	−2.36112
$226$	3.67111e10	0.936072
$227$	8.50814e8	0.0212676	0.0106338	−	0.999943i	$-0.496615\pi$
$227$	8.50814e8	0.0212676	0.0106338	+	0.999943i	$0.496615\pi$
$228$	−2.79743e10	−0.685571
$229$	−5.27092e10	−1.26656	−0.633282	−	0.773921i	$-0.718293\pi$
$229$	−5.27092e10	−1.26656	−0.633282	+	0.773921i	$0.718293\pi$
$230$	−9.71331e9	−0.228872
$231$	5.43975e10	1.25697
$232$	3.87291e10	0.877692
$233$	−6.77840e10	−1.50670	−0.753348	−	0.657622i	$-0.771562\pi$
$233$	−6.77840e10	−1.50670	−0.753348	+	0.657622i	$0.771562\pi$
$234$	−2.53842e10	−0.553467
$235$	5.63137e9	0.120450
$236$	−7.57374e9	−0.158930
$237$	1.24411e11	2.56147
$238$	8.58949e9	0.173529
$239$	−7.25670e10	−1.43863	−0.719315	−	0.694684i	$-0.755544\pi$
$239$	−7.25670e10	−1.43863	−0.719315	+	0.694684i	$0.755544\pi$
$240$	−1.00055e10	−0.194665
$241$	7.52918e10	1.43771	0.718854	−	0.695161i	$-0.244667\pi$
$241$	7.52918e10	1.43771	0.718854	+	0.695161i	$0.244667\pi$
$242$	−9.58532e10	−1.79654
$243$	1.11318e11	2.04803
$244$	1.14577e10	0.206940
$245$	1.53488e9	0.0272161
$246$	3.64734e10	0.634992
$247$	1.77910e10	0.304133
$248$	4.52867e10	0.760217
$249$	−5.96408e10	−0.983210
$250$	1.88201e10	0.304713
$251$	−5.75365e10	−0.914980	−0.457490	−	0.889215i	$-0.651251\pi$
$251$	−5.75365e10	−0.914980	−0.457490	+	0.889215i	$0.651251\pi$
$252$	1.99541e10	0.311694
$253$	−1.72100e11	−2.64082
$254$	2.59557e10	0.391274
$255$	1.34678e10	0.199465
$256$	−6.06477e10	−0.882540
$257$	5.56117e10	0.795183	0.397591	−	0.917563i	$-0.369846\pi$
$257$	5.56117e10	0.795183	0.397591	+	0.917563i	$0.369846\pi$
$258$	−1.61456e11	−2.26864
$259$	2.96662e10	0.409649
$260$	−1.31050e9	−0.0177851
$261$	1.48084e11	1.97527
$262$	−1.00814e11	−1.32180
$263$	9.14565e10	1.17873	0.589364	−	0.807868i	$-0.299378\pi$
$263$	9.14565e10	1.17873	0.589364	+	0.807868i	$0.299378\pi$
$264$	−2.85746e11	−3.62045
$265$	−1.30066e9	−0.0162016
$266$	2.75641e10	0.337580
$267$	1.03425e11	1.24545
$268$	−4.99077e10	−0.590963
$269$	9.52028e10	1.10857	0.554287	−	0.832326i	$-0.312991\pi$
$269$	9.52028e10	1.10857	0.554287	+	0.832326i	$0.312991\pi$
$270$	−3.64959e10	−0.417933
$271$	−1.48867e11	−1.67663	−0.838316	−	0.545184i	$-0.816460\pi$
$271$	−1.48867e11	−1.67663	−0.838316	+	0.545184i	$0.816460\pi$
$272$	−2.79925e10	−0.310086
$273$	−1.78699e10	−0.194711
$274$	5.59269e10	0.599436
$275$	1.63645e11	1.72546
$276$	−8.88965e10	−0.922134
$277$	7.63272e10	0.778969	0.389484	−	0.921033i	$-0.372653\pi$
$277$	7.63272e10	0.778969	0.389484	+	0.921033i	$0.372653\pi$
$278$	4.50908e10	0.452779
$279$	1.73157e11	1.71089
$280$	−8.06261e9	−0.0783907
$281$	−8.42293e10	−0.805907	−0.402953	−	0.915221i	$-0.632016\pi$
$281$	−8.42293e10	−0.805907	−0.402953	+	0.915221i	$0.632016\pi$
$282$	−1.01580e11	−0.956503
$283$	2.87261e10	0.266219	0.133109	−	0.991101i	$-0.457504\pi$
$283$	2.87261e10	0.266219	0.133109	+	0.991101i	$0.457504\pi$
$284$	3.57415e9	0.0326017
$285$	4.32189e10	0.388036
$286$	4.57644e10	0.404464
$287$	1.82342e10	0.158642
$288$	−1.83239e11	−1.56946
$289$	−8.09088e10	−0.682269
$290$	−1.50681e10	−0.125103
$291$	3.60615e11	2.94799
$292$	−9.63047e9	−0.0775219
$293$	6.78680e10	0.537973	0.268987	−	0.963144i	$-0.413311\pi$
$293$	6.78680e10	0.537973	0.268987	+	0.963144i	$0.413311\pi$
$294$	−2.76864e10	−0.216125
$295$	1.17011e10	0.0899553
$296$	−1.55834e11	−1.17991
$297$	−6.46633e11	−4.82229
$298$	1.17954e11	0.866442
$299$	5.65361e10	0.409078
$300$	8.45291e10	0.602505
$301$	−8.07167e10	−0.566780
$302$	1.59169e11	1.10110
$303$	3.30309e10	0.225128
$304$	−8.98294e10	−0.603236
$305$	−1.77016e10	−0.117129
$306$	−1.72520e11	−1.12485
$307$	−1.02595e11	−0.659177	−0.329588	−	0.944125i	$-0.606910\pi$
$307$	−1.02595e11	−0.659177	−0.329588	+	0.944125i	$0.606910\pi$
$308$	−3.59745e10	−0.227781
$309$	3.78507e11	2.36189
$310$	−1.76194e10	−0.108359
$311$	−2.07507e11	−1.25780	−0.628898	−	0.777488i	$-0.716494\pi$
$311$	−2.07507e11	−1.25780	−0.628898	+	0.777488i	$0.716494\pi$
$312$	9.38697e10	0.560828
$313$	1.49508e11	0.880471	0.440235	−	0.897882i	$-0.354895\pi$
$313$	1.49508e11	0.880471	0.440235	+	0.897882i	$0.354895\pi$
$314$	1.32591e11	0.769713
$315$	−3.08281e10	−0.176420
$316$	−8.22762e10	−0.464176
$317$	1.52968e11	0.850811	0.425406	−	0.905003i	$-0.360131\pi$
$317$	1.52968e11	0.850811	0.425406	+	0.905003i	$0.360131\pi$
$318$	2.34616e10	0.128658
$319$	−2.66976e11	−1.44349
$320$	3.83037e10	0.204205
$321$	−7.41565e9	−0.0389831
$322$	8.75931e10	0.454066
$323$	1.20914e11	0.618109
$324$	−1.70431e11	−0.859205
$325$	−5.37585e10	−0.267284
$326$	2.60529e11	1.27755
$327$	−3.97787e10	−0.192391
$328$	−9.57828e10	−0.456936
$329$	−5.07828e10	−0.238965
$330$	1.11173e11	0.516046
$331$	−3.83608e11	−1.75656	−0.878278	−	0.478150i	$-0.841308\pi$
$331$	−3.83608e11	−1.75656	−0.878278	+	0.478150i	$0.841308\pi$
$332$	3.94421e10	0.178172
$333$	−5.95845e11	−2.65543
$334$	−6.23458e10	−0.274125
$335$	7.71049e10	0.334488
$336$	9.02281e10	0.386202
$337$	−1.26571e11	−0.534565	−0.267282	−	0.963618i	$-0.586126\pi$
$337$	−1.26571e11	−0.534565	−0.267282	+	0.963618i	$0.586126\pi$
$338$	−1.50339e10	−0.0626537
$339$	−5.19075e11	−2.13467
$340$	−8.90664e9	−0.0361459
$341$	−3.12180e11	−1.25029
$342$	−5.53626e11	−2.18826
$343$	−1.38413e10	−0.0539949
$344$	4.24000e11	1.63250
$345$	1.37341e11	0.521932
$346$	−3.74207e11	−1.40368
$347$	1.02147e11	0.378220	0.189110	−	0.981956i	$-0.439440\pi$
$347$	1.02147e11	0.378220	0.189110	+	0.981956i	$0.439440\pi$
$348$	−1.37904e11	−0.504045
$349$	4.69365e11	1.69354	0.846772	−	0.531956i	$-0.178543\pi$
$349$	4.69365e11	1.69354	0.846772	+	0.531956i	$0.178543\pi$
$350$	−8.32897e10	−0.296678
$351$	2.12423e11	0.747000
$352$	3.30355e11	1.14694
$353$	3.04327e11	1.04317	0.521584	−	0.853200i	$-0.325341\pi$
$353$	3.04327e11	1.04317	0.521584	+	0.853200i	$0.325341\pi$
$354$	−2.11066e11	−0.714339
$355$	−5.52188e9	−0.0184527
$356$	−6.83981e10	−0.225694
$357$	−1.21451e11	−0.395724
$358$	−3.06003e11	−0.984582
$359$	−2.46205e11	−0.782298	−0.391149	−	0.920327i	$-0.627922\pi$
$359$	−2.46205e11	−0.782298	−0.391149	+	0.920327i	$0.627922\pi$
$360$	1.61938e11	0.508144
$361$	6.53319e10	0.202462
$362$	3.95747e11	1.21124
$363$	1.35531e12	4.09694
$364$	1.18179e10	0.0352845
$365$	1.48786e10	0.0438778
$366$	3.19305e11	0.930125
$367$	−2.83285e11	−0.815129	−0.407565	−	0.913176i	$-0.633622\pi$
$367$	−2.83285e11	−0.815129	−0.407565	+	0.913176i	$0.633622\pi$
$368$	−2.85460e11	−0.811389
$369$	−3.66233e11	−1.02835
$370$	6.06295e10	0.168181
$371$	1.17292e10	0.0321428
$372$	−1.61253e11	−0.436581
$373$	4.13621e11	1.10640	0.553201	−	0.833048i	$-0.313406\pi$
$373$	4.13621e11	1.10640	0.553201	+	0.833048i	$0.313406\pi$
$374$	3.11031e11	0.822018
$375$	−2.66105e11	−0.694885
$376$	2.66759e11	0.688293
$377$	8.77035e10	0.223605
$378$	3.29114e11	0.829150
$379$	−4.17983e11	−1.04060	−0.520298	−	0.853984i	$-0.674179\pi$
$379$	−4.17983e11	−1.04060	−0.520298	+	0.853984i	$0.674179\pi$
$380$	−2.85819e10	−0.0703177
$381$	−3.66999e11	−0.892284
$382$	−2.14927e11	−0.516424
$383$	1.65980e11	0.394150	0.197075	−	0.980388i	$-0.436856\pi$
$383$	1.65980e11	0.394150	0.197075	+	0.980388i	$0.436856\pi$
$384$	−1.83963e11	−0.431758
$385$	5.55790e10	0.128925
$386$	3.88542e11	0.890831
$387$	1.62120e12	3.67398
$388$	−2.38485e11	−0.534218
$389$	−4.65454e9	−0.0103063	−0.00515316	−	0.999987i	$-0.501640\pi$
$389$	−4.65454e9	−0.0103063	−0.00515316	+	0.999987i	$0.501640\pi$
$390$	−3.65213e10	−0.0799383
$391$	3.84240e11	0.831395
$392$	7.27074e10	0.155522
$393$	1.42546e12	3.01431
$394$	−2.34367e11	−0.489963
$395$	1.27113e11	0.262726
$396$	7.22550e11	1.47652
$397$	7.04502e11	1.42339	0.711697	−	0.702487i	$-0.247927\pi$
$397$	7.04502e11	1.42339	0.711697	+	0.702487i	$0.247927\pi$
$398$	5.49596e11	1.09792
$399$	−3.89742e11	−0.769837
$400$	2.71435e11	0.530146
$401$	−7.21232e11	−1.39292	−0.696458	−	0.717597i	$-0.745242\pi$
$401$	−7.21232e11	−1.39292	−0.696458	+	0.717597i	$0.745242\pi$
$402$	−1.39083e12	−2.65619
$403$	1.02553e11	0.193676
$404$	−2.18443e10	−0.0407963
$405$	2.63308e11	0.486314
$406$	1.35882e11	0.248195
$407$	1.07423e12	1.94054
$408$	6.37972e11	1.13981
$409$	−3.94792e11	−0.697612	−0.348806	−	0.937195i	$-0.613413\pi$
$409$	−3.94792e11	−0.697612	−0.348806	+	0.937195i	$0.613413\pi$
$410$	3.72656e10	0.0651300
$411$	−7.90775e11	−1.36699
$412$	−2.50317e11	−0.428009
$413$	−1.05518e11	−0.178465
$414$	−1.75931e12	−2.94334
$415$	−6.09362e10	−0.100846
$416$	−1.08524e11	−0.177667
$417$	−6.37559e11	−1.03254
$418$	9.98115e11	1.59914
$419$	1.04154e11	0.165087	0.0825433	−	0.996587i	$-0.473696\pi$
$419$	1.04154e11	0.165087	0.0825433	+	0.996587i	$0.473696\pi$
$420$	2.87087e10	0.0450186
$421$	−8.06888e11	−1.25183	−0.625913	−	0.779893i	$-0.715273\pi$
$421$	−8.06888e11	−1.25183	−0.625913	+	0.779893i	$0.715273\pi$
$422$	9.37449e11	1.43894
$423$	1.01997e12	1.54902
$424$	−6.16125e10	−0.0925812
$425$	−3.65362e11	−0.543217
$426$	9.96049e10	0.146534
$427$	1.59630e11	0.232375
$428$	4.90417e9	0.00706430
$429$	−6.47083e11	−0.922363
$430$	−1.64963e11	−0.232690
$431$	−2.36372e11	−0.329950	−0.164975	−	0.986298i	$-0.552754\pi$
$431$	−2.36372e11	−0.329950	−0.164975	+	0.986298i	$0.552754\pi$
$432$	−1.07256e12	−1.48164
$433$	1.33826e11	0.182956	0.0914778	−	0.995807i	$-0.470841\pi$
$433$	1.33826e11	0.182956	0.0914778	+	0.995807i	$0.470841\pi$
$434$	1.58889e11	0.214976
$435$	2.13055e11	0.285292
$436$	2.63068e10	0.0348641
$437$	1.23305e12	1.61738
$438$	−2.68384e11	−0.348435
$439$	9.01393e11	1.15831	0.579154	−	0.815218i	$-0.303383\pi$
$439$	9.01393e11	1.15831	0.579154	+	0.815218i	$0.303383\pi$
$440$	−2.91953e11	−0.371343
$441$	2.78003e11	0.350006
$442$	−1.02176e11	−0.127335
$443$	4.08744e11	0.504237	0.252119	−	0.967696i	$-0.418873\pi$
$443$	4.08744e11	0.504237	0.252119	+	0.967696i	$0.418873\pi$
$444$	5.54883e11	0.677607
$445$	1.05672e11	0.127744
$446$	−9.72153e11	−1.16340
$447$	−1.66780e12	−1.97588
$448$	−3.45417e11	−0.405129
$449$	−6.48766e11	−0.753320	−0.376660	−	0.926352i	$-0.622928\pi$
$449$	−6.48766e11	−0.753320	−0.376660	+	0.926352i	$0.622928\pi$
$450$	1.67288e12	1.92312
$451$	6.60271e11	0.751498
$452$	3.43279e11	0.386833
$453$	−2.25056e12	−2.51102
$454$	−1.56805e10	−0.0173224
$455$	−1.82581e10	−0.0199712
$456$	2.04729e12	2.21736
$457$	−1.04213e12	−1.11763	−0.558815	−	0.829292i	$-0.688744\pi$
$457$	−1.04213e12	−1.11763	−0.558815	+	0.829292i	$0.688744\pi$
$458$	9.71430e11	1.03161
$459$	1.44371e12	1.51817
$460$	−9.08274e10	−0.0945816
$461$	1.20969e12	1.24744	0.623719	−	0.781649i	$-0.285621\pi$
$461$	1.20969e12	1.24744	0.623719	+	0.781649i	$0.285621\pi$
$462$	−1.00254e12	−1.02380
$463$	−8.87937e11	−0.897982	−0.448991	−	0.893536i	$-0.648217\pi$
$463$	−8.87937e11	−0.897982	−0.448991	+	0.893536i	$0.648217\pi$
$464$	−4.42828e11	−0.443511
$465$	2.49128e11	0.247107
$466$	1.24926e12	1.22720
$467$	−1.00195e12	−0.974812	−0.487406	−	0.873175i	$-0.662057\pi$
$467$	−1.00195e12	−0.974812	−0.487406	+	0.873175i	$0.662057\pi$
$468$	−2.37363e11	−0.228721
$469$	−6.95320e11	−0.663601
$470$	−1.03786e11	−0.0981067
$471$	−1.87476e12	−1.75530
$472$	5.54281e11	0.514033
$473$	−2.92281e12	−2.68488
$474$	−2.29289e12	−2.08632
$475$	−1.17247e12	−1.05677
$476$	8.03187e10	0.0717109
$477$	−2.35580e11	−0.208356
$478$	1.33741e12	1.17176
$479$	1.10385e12	0.958076	0.479038	−	0.877794i	$-0.340986\pi$
$479$	1.10385e12	0.958076	0.479038	+	0.877794i	$0.340986\pi$
$480$	−2.63633e11	−0.226681
$481$	−3.52893e11	−0.300600
$482$	−1.38763e12	−1.17101
$483$	−1.23852e12	−1.03548
$484$	−8.96305e11	−0.742423
$485$	3.68448e11	0.302370
$486$	−2.05159e12	−1.66812
$487$	−7.17522e11	−0.578036	−0.289018	−	0.957324i	$-0.593329\pi$
$487$	−7.17522e11	−0.578036	−0.289018	+	0.957324i	$0.593329\pi$
$488$	−8.38528e11	−0.669312
$489$	−3.68373e12	−2.91339
$490$	−2.82878e10	−0.0221675
$491$	2.63934e11	0.204941	0.102471	−	0.994736i	$-0.467325\pi$
$491$	2.63934e11	0.204941	0.102471	+	0.994736i	$0.467325\pi$
$492$	3.41056e11	0.262411
$493$	5.96065e11	0.454446
$494$	−3.27888e11	−0.247716
$495$	−1.11630e12	−0.835717
$496$	−5.17807e11	−0.384150
$497$	4.97955e10	0.0366089
$498$	1.09918e12	0.800823
$499$	1.47329e12	1.06374	0.531870	−	0.846826i	$-0.321489\pi$
$499$	1.47329e12	1.06374	0.531870	+	0.846826i	$0.321489\pi$
$500$	1.75983e11	0.125923
$501$	8.81536e11	0.625130
$502$	1.06040e12	0.745249
$503$	2.54685e12	1.77398	0.886989	−	0.461791i	$-0.152793\pi$
$503$	2.54685e12	1.77398	0.886989	+	0.461791i	$0.152793\pi$
$504$	−1.46033e12	−1.00812
$505$	3.37483e10	0.0230909
$506$	3.17181e12	2.15095
$507$	2.12571e11	0.142879
$508$	2.42707e11	0.161695
$509$	1.29023e12	0.851994	0.425997	−	0.904725i	$-0.359923\pi$
$509$	1.29023e12	0.851994	0.425997	+	0.904725i	$0.359923\pi$
$510$	−2.48212e11	−0.162464
$511$	−1.34173e11	−0.0870505
$512$	1.47918e12	0.951277
$513$	4.63293e12	2.95344
$514$	−1.02492e12	−0.647675
$515$	3.86728e11	0.242255
$516$	−1.50974e12	−0.937518
$517$	−1.83888e12	−1.13200
$518$	−5.46747e11	−0.333659
$519$	5.29108e12	3.20104
$520$	9.59085e10	0.0575231
$521$	−2.54691e12	−1.51441	−0.757206	−	0.653176i	$-0.773436\pi$
$521$	−2.54691e12	−1.51441	−0.757206	+	0.653176i	$0.773436\pi$
$522$	−2.72919e12	−1.60885
$523$	7.57135e11	0.442503	0.221251	−	0.975217i	$-0.428986\pi$
$523$	7.57135e11	0.442503	0.221251	+	0.975217i	$0.428986\pi$
$524$	−9.42694e11	−0.546236
$525$	1.17767e12	0.676561
$526$	−1.68554e12	−0.960072
$527$	6.96989e11	0.393621
$528$	3.26722e12	1.82947
$529$	2.11722e12	1.17548
$530$	2.39712e10	0.0131962
$531$	2.11934e12	1.15685
$532$	2.57747e11	0.139505
$533$	−2.16904e11	−0.116411
$534$	−1.90613e12	−1.01442
$535$	−7.57671e9	−0.00399842
$536$	3.65247e12	1.91137
$537$	4.32671e12	2.24530
$538$	−1.75459e12	−0.902931
$539$	−5.01202e11	−0.255778
$540$	−3.41266e11	−0.172711
$541$	2.99576e11	0.150355	0.0751777	−	0.997170i	$-0.476048\pi$
$541$	2.99576e11	0.150355	0.0751777	+	0.997170i	$0.476048\pi$
$542$	2.74363e12	1.36561
$543$	−5.59565e12	−2.76217
$544$	−7.37569e11	−0.361083
$545$	−4.06427e10	−0.0197332
$546$	3.29343e11	0.158592
$547$	5.37896e11	0.256895	0.128447	−	0.991716i	$-0.459001\pi$
$547$	5.37896e11	0.256895	0.128447	+	0.991716i	$0.459001\pi$
$548$	5.22961e11	0.247718
$549$	−3.20618e12	−1.50630
$550$	−3.01598e12	−1.40539
$551$	1.91280e12	0.884073
$552$	6.50586e12	2.98249
$553$	−1.14628e12	−0.521229
$554$	−1.40671e12	−0.634469
$555$	−8.57267e11	−0.383529
$556$	4.21635e11	0.187111
$557$	−1.48988e12	−0.655847	−0.327923	−	0.944704i	$-0.606349\pi$
$557$	−1.48988e12	−0.655847	−0.327923	+	0.944704i	$0.606349\pi$
$558$	−3.19129e12	−1.39352
$559$	9.60162e11	0.415902
$560$	9.21878e10	0.0396121
$561$	−4.39781e12	−1.87458
$562$	1.55235e12	0.656410
$563$	−2.52767e11	−0.106031	−0.0530155	−	0.998594i	$-0.516883\pi$
$563$	−2.52767e11	−0.106031	−0.0530155	+	0.998594i	$0.516883\pi$
$564$	−9.49853e11	−0.395276
$565$	−5.30349e11	−0.218949
$566$	−5.29422e11	−0.216835
$567$	−2.37447e12	−0.964813
$568$	−2.61572e11	−0.105445
$569$	1.07299e12	0.429133	0.214566	−	0.976709i	$-0.431166\pi$
$569$	1.07299e12	0.429133	0.214566	+	0.976709i	$0.431166\pi$
$570$	−7.96525e11	−0.316055
$571$	−3.03285e12	−1.19395	−0.596977	−	0.802258i	$-0.703632\pi$
$571$	−3.03285e12	−1.19395	−0.596977	+	0.802258i	$0.703632\pi$
$572$	4.27934e11	0.167145
$573$	3.03896e12	1.17768
$574$	−3.36055e11	−0.129213
$575$	−3.72586e12	−1.42142
$576$	6.93771e12	2.62612
$577$	−3.02746e12	−1.13707	−0.568536	−	0.822658i	$-0.692490\pi$
$577$	−3.02746e12	−1.13707	−0.568536	+	0.822658i	$0.692490\pi$
$578$	1.49115e12	0.555707
$579$	−5.49377e12	−2.03150
$580$	−1.40899e11	−0.0516989
$581$	5.49513e11	0.200072
$582$	−6.64614e12	−2.40113
$583$	4.24721e11	0.152263
$584$	7.04802e11	0.250732
$585$	3.66714e11	0.129457
$586$	−1.25081e12	−0.438178
$587$	−3.37734e12	−1.17410	−0.587048	−	0.809552i	$-0.699710\pi$
$587$	−3.37734e12	−1.17410	−0.587048	+	0.809552i	$0.699710\pi$
$588$	−2.58891e11	−0.0893138
$589$	2.23668e12	0.765745
$590$	−2.15651e11	−0.0732684
$591$	3.31382e12	1.11734
$592$	1.78181e12	0.596229
$593$	1.70205e12	0.565231	0.282616	−	0.959233i	$-0.408798\pi$
$593$	1.70205e12	0.565231	0.282616	+	0.959233i	$0.408798\pi$
$594$	1.19174e13	3.92775
$595$	−1.24089e11	−0.0405887
$596$	1.10297e12	0.358058
$597$	−7.77099e12	−2.50375
$598$	−1.04196e12	−0.333193
$599$	−2.78063e12	−0.882516	−0.441258	−	0.897380i	$-0.645468\pi$
$599$	−2.78063e12	−0.882516	−0.441258	+	0.897380i	$0.645468\pi$
$600$	−6.18623e12	−1.94870
$601$	−2.37673e12	−0.743096	−0.371548	−	0.928414i	$-0.621173\pi$
$601$	−2.37673e12	−0.743096	−0.371548	+	0.928414i	$0.621173\pi$
$602$	1.48761e12	0.461641
$603$	1.39655e13	4.30159
$604$	1.48836e12	0.455032
$605$	1.38475e12	0.420215
$606$	−6.08759e11	−0.183366
$607$	6.14838e11	0.183828	0.0919140	−	0.995767i	$-0.470702\pi$
$607$	6.14838e11	0.183828	0.0919140	+	0.995767i	$0.470702\pi$
$608$	−2.36690e12	−0.702447
$609$	−1.92129e12	−0.565999
$610$	3.26241e11	0.0954012
$611$	6.04085e11	0.175353
$612$	−1.61320e12	−0.464844
$613$	1.91630e12	0.548139	0.274069	−	0.961710i	$-0.411630\pi$
$613$	1.91630e12	0.548139	0.274069	+	0.961710i	$0.411630\pi$
$614$	1.89082e12	0.536898
$615$	−5.26915e11	−0.148526
$616$	2.63278e12	0.736719
$617$	4.45574e11	0.123776	0.0618880	−	0.998083i	$-0.480288\pi$
$617$	4.45574e11	0.123776	0.0618880	+	0.998083i	$0.480288\pi$
$618$	−6.97588e12	−1.92376
$619$	−2.21371e12	−0.606056	−0.303028	−	0.952982i	$-0.597998\pi$
$619$	−2.21371e12	−0.606056	−0.303028	+	0.952982i	$0.597998\pi$
$620$	−1.64756e11	−0.0447793
$621$	1.47225e13	3.97255
$622$	3.82434e12	1.02447
$623$	−9.52932e11	−0.253435
$624$	−1.07330e12	−0.283395
$625$	3.40436e12	0.892432
$626$	−2.75543e12	−0.717142
$627$	−1.41128e13	−3.64678
$628$	1.23983e12	0.318085
$629$	−2.39839e12	−0.610929
$630$	5.68161e11	0.143694
$631$	−9.98175e11	−0.250654	−0.125327	−	0.992115i	$-0.539998\pi$
$631$	−9.98175e11	−0.250654	−0.125327	+	0.992115i	$0.539998\pi$
$632$	6.02135e12	1.50130
$633$	−1.32550e13	−3.28143
$634$	−2.81920e12	−0.692985
$635$	−3.74971e11	−0.0915199
$636$	2.19385e11	0.0531680
$637$	1.64648e11	0.0396214
$638$	4.92037e12	1.17572
$639$	−1.00014e12	−0.237306
$640$	−1.87959e11	−0.0442846
$641$	3.11756e12	0.729380	0.364690	−	0.931129i	$-0.381175\pi$
$641$	3.11756e12	0.729380	0.364690	+	0.931129i	$0.381175\pi$
$642$	1.36670e11	0.0317517
$643$	2.31010e11	0.0532943	0.0266472	−	0.999645i	$-0.491517\pi$
$643$	2.31010e11	0.0532943	0.0266472	+	0.999645i	$0.491517\pi$
$644$	8.19067e11	0.187643
$645$	2.33248e12	0.530640
$646$	−2.22844e12	−0.503449
$647$	1.23306e11	0.0276640	0.0138320	−	0.999904i	$-0.495597\pi$
$647$	1.23306e11	0.0276640	0.0138320	+	0.999904i	$0.495597\pi$
$648$	1.24729e13	2.77896
$649$	−3.82089e12	−0.845403
$650$	9.90770e11	0.217702
$651$	−2.24660e12	−0.490243
$652$	2.43615e12	0.527947
$653$	4.43164e10	0.00953794	0.00476897	−	0.999989i	$-0.498482\pi$
$653$	4.43164e10	0.00953794	0.00476897	+	0.999989i	$0.498482\pi$
$654$	7.33121e11	0.156702
$655$	1.45642e12	0.309172
$656$	1.09518e12	0.230897
$657$	2.69487e12	0.564278
$658$	9.35926e11	0.194637
$659$	−7.71107e12	−1.59269	−0.796343	−	0.604845i	$-0.793235\pi$
$659$	−7.71107e12	−1.59269	−0.796343	+	0.604845i	$0.793235\pi$
$660$	1.03956e12	0.213257
$661$	8.28640e12	1.68834	0.844169	−	0.536077i	$-0.180094\pi$
$661$	8.28640e12	1.68834	0.844169	+	0.536077i	$0.180094\pi$
$662$	7.06990e12	1.43071
$663$	1.44471e12	0.290382
$664$	−2.88656e12	−0.576267
$665$	−3.98207e11	−0.0789607
$666$	1.09814e13	2.16284
$667$	6.07850e12	1.18913
$668$	−5.82984e11	−0.113282
$669$	1.37457e13	2.65308
$670$	−1.42104e12	−0.272440
$671$	5.78032e12	1.10078
$672$	2.37740e12	0.449718
$673$	3.42473e12	0.643515	0.321758	−	0.946822i	$-0.395726\pi$
$673$	3.42473e12	0.643515	0.321758	+	0.946822i	$0.395726\pi$
$674$	2.33271e12	0.435402
$675$	−1.39992e13	−2.59559
$676$	−1.40579e11	−0.0258917
$677$	7.30751e12	1.33697	0.668483	−	0.743728i	$-0.266944\pi$
$677$	7.30751e12	1.33697	0.668483	+	0.743728i	$0.266944\pi$
$678$	9.56655e12	1.73869
$679$	−3.32260e12	−0.599880
$680$	6.51829e11	0.116908
$681$	2.21714e11	0.0395030
$682$	5.75347e12	1.01836
$683$	4.51786e12	0.794400	0.397200	−	0.917732i	$-0.369982\pi$
$683$	4.51786e12	0.794400	0.397200	+	0.917732i	$0.369982\pi$
$684$	−5.17685e12	−0.904302
$685$	−8.07951e11	−0.140209
$686$	2.55095e11	0.0439788
$687$	−1.37355e13	−2.35255
$688$	−4.84800e12	−0.824926
$689$	−1.39524e11	−0.0235864
$690$	−2.53119e12	−0.425113
$691$	−6.25383e12	−1.04351	−0.521753	−	0.853097i	$-0.674722\pi$
$691$	−6.25383e12	−1.04351	−0.521753	+	0.853097i	$0.674722\pi$
$692$	−3.49914e12	−0.580075
$693$	1.00667e13	1.65801
$694$	−1.88258e12	−0.308060
$695$	−6.51407e11	−0.105906
$696$	1.00924e13	1.63025
$697$	−1.47416e12	−0.236590
$698$	−8.65039e12	−1.37939
$699$	−1.76638e13	−2.79858
$700$	−7.78826e11	−0.122603
$701$	3.41266e12	0.533780	0.266890	−	0.963727i	$-0.414004\pi$
$701$	3.41266e12	0.533780	0.266890	+	0.963727i	$0.414004\pi$
$702$	−3.91496e12	−0.608430
$703$	−7.69655e12	−1.18849
$704$	−1.25078e13	−1.91913
$705$	1.46748e12	0.223728
$706$	−5.60874e12	−0.849659
$707$	−3.04337e11	−0.0458108
$708$	−1.97364e12	−0.295202
$709$	−5.34391e12	−0.794238	−0.397119	−	0.917767i	$-0.629990\pi$
$709$	−5.34391e12	−0.794238	−0.397119	+	0.917767i	$0.629990\pi$
$710$	1.01768e11	0.0150297
$711$	2.30231e13	3.37871
$712$	5.00569e12	0.729968
$713$	7.10770e12	1.02997
$714$	2.23833e12	0.322317
$715$	−6.61137e11	−0.0946051
$716$	−2.86137e12	−0.406880
$717$	−1.89102e13	−2.67215
$718$	4.53756e12	0.637181
$719$	−1.43452e12	−0.200183	−0.100091	−	0.994978i	$-0.531914\pi$
$719$	−1.43452e12	−0.200183	−0.100091	+	0.994978i	$0.531914\pi$
$720$	−1.85159e12	−0.256773
$721$	−3.48745e12	−0.480617
$722$	−1.20407e12	−0.164905
$723$	1.96203e13	2.67044
$724$	3.70056e12	0.500545
$725$	−5.77987e12	−0.776957
$726$	−2.49784e13	−3.33695
$727$	−1.27420e13	−1.69174	−0.845868	−	0.533393i	$-0.820917\pi$
$727$	−1.27420e13	−1.69174	−0.845868	+	0.533393i	$0.820917\pi$
$728$	−8.64888e11	−0.114122
$729$	9.54278e12	1.25141
$730$	−2.74213e11	−0.0357384
$731$	6.52561e12	0.845265
$732$	2.98576e12	0.384375
$733$	1.30437e12	0.166891	0.0834454	−	0.996512i	$-0.473408\pi$
$733$	1.30437e12	0.166891	0.0834454	+	0.996512i	$0.473408\pi$
$734$	5.22094e12	0.663922
$735$	3.99974e11	0.0505520
$736$	−7.52151e12	−0.944833
$737$	−2.51780e13	−3.14353
$738$	6.74968e12	0.837586
$739$	−5.62918e12	−0.694296	−0.347148	−	0.937810i	$-0.612850\pi$
$739$	−5.62918e12	−0.694296	−0.347148	+	0.937810i	$0.612850\pi$
$740$	5.66935e11	0.0695009
$741$	4.63616e12	0.564906
$742$	−2.16168e11	−0.0261803
$743$	1.31651e13	1.58480	0.792401	−	0.610001i	$-0.208831\pi$
$743$	1.31651e13	1.58480	0.792401	+	0.610001i	$0.208831\pi$
$744$	1.18012e13	1.41205
$745$	−1.70403e12	−0.202663
$746$	−7.62303e12	−0.901162
$747$	−1.10370e13	−1.29690
$748$	2.90839e12	0.339700
$749$	6.83256e10	0.00793260
$750$	4.90432e12	0.565982
$751$	−4.24370e12	−0.486816	−0.243408	−	0.969924i	$-0.578265\pi$
$751$	−4.24370e12	−0.486816	−0.243408	+	0.969924i	$0.578265\pi$
$752$	−3.05011e12	−0.347805
$753$	−1.49934e13	−1.69951
$754$	−1.61638e12	−0.182126
$755$	−2.29945e12	−0.257550
$756$	3.07748e12	0.342647
$757$	−3.79624e12	−0.420167	−0.210084	−	0.977683i	$-0.567374\pi$
$757$	−3.79624e12	−0.420167	−0.210084	+	0.977683i	$0.567374\pi$
$758$	7.70343e12	0.847564
$759$	−4.48476e13	−4.90514
$760$	2.09175e12	0.227431
$761$	1.29706e13	1.40194	0.700971	−	0.713190i	$-0.252750\pi$
$761$	1.29706e13	1.40194	0.700971	+	0.713190i	$0.252750\pi$
$762$	6.76380e12	0.726764
$763$	3.66509e11	0.0391494
$764$	−2.00975e12	−0.213413
$765$	2.49232e12	0.263104
$766$	−3.05901e12	−0.321034
$767$	1.25519e12	0.130957
$768$	−1.58042e13	−1.63925
$769$	1.25118e13	1.29018	0.645091	−	0.764105i	$-0.276819\pi$
$769$	1.25118e13	1.29018	0.645091	+	0.764105i	$0.276819\pi$
$770$	−1.02432e12	−0.105009
$771$	1.44918e13	1.47699
$772$	3.63318e12	0.368137
$773$	1.16278e13	1.17135	0.585677	−	0.810544i	$-0.300829\pi$
$773$	1.16278e13	1.17135	0.585677	+	0.810544i	$0.300829\pi$
$774$	−2.98786e13	−2.99245
$775$	−6.75850e12	−0.672965
$776$	1.74534e13	1.72784
$777$	7.73070e12	0.760894
$778$	8.57831e10	0.00839448
$779$	−4.73064e12	−0.460258
$780$	−3.41503e11	−0.0330346
$781$	1.80313e12	0.173419
$782$	−7.08154e12	−0.677169
$783$	2.28388e13	2.17142
$784$	−8.31335e11	−0.0785876
$785$	−1.91548e12	−0.180038
$786$	−2.62712e13	−2.45515
$787$	−1.99090e12	−0.184996	−0.0924980	−	0.995713i	$-0.529485\pi$
$787$	−1.99090e12	−0.184996	−0.0924980	+	0.995713i	$0.529485\pi$
$788$	−2.19152e12	−0.202478
$789$	2.38326e13	2.18940
$790$	−2.34269e12	−0.213990
$791$	4.78260e12	0.434380
$792$	−5.28795e13	−4.77556
$793$	−1.89888e12	−0.170517
$794$	−1.29840e13	−1.15935
$795$	−3.38939e11	−0.0300933
$796$	5.13917e12	0.453716
$797$	−1.41122e13	−1.23889	−0.619446	−	0.785039i	$-0.712643\pi$
$797$	−1.41122e13	−1.23889	−0.619446	+	0.785039i	$0.712643\pi$
$798$	7.18293e12	0.627031
$799$	4.10558e12	0.356380
$800$	7.15199e12	0.617336
$801$	1.91397e13	1.64281
$802$	1.32923e13	1.13453
$803$	−4.85849e12	−0.412365
$804$	−1.30054e13	−1.09767
$805$	−1.26542e12	−0.106207
$806$	−1.89006e12	−0.157749
$807$	2.48089e13	2.05909
$808$	1.59866e12	0.131949
$809$	5.35373e12	0.439428	0.219714	−	0.975564i	$-0.429488\pi$
$809$	5.35373e12	0.439428	0.219714	+	0.975564i	$0.429488\pi$
$810$	−4.85277e12	−0.396102
$811$	−1.92141e13	−1.55965	−0.779825	−	0.625998i	$-0.784692\pi$
$811$	−1.92141e13	−1.55965	−0.779825	+	0.625998i	$0.784692\pi$
$812$	1.27060e12	0.102567
$813$	−3.87934e13	−3.11423
$814$	−1.97981e13	−1.58057
$815$	−3.76374e12	−0.298821
$816$	−7.29456e12	−0.575962
$817$	2.09410e13	1.64437
$818$	7.27602e12	0.568203
$819$	−3.30697e12	−0.256834
$820$	3.48464e11	0.0269150
$821$	2.47213e13	1.89901	0.949504	−	0.313754i	$-0.101587\pi$
$821$	2.47213e13	1.89901	0.949504	+	0.313754i	$0.101587\pi$
$822$	1.45740e13	1.11341
$823$	−5.39843e12	−0.410174	−0.205087	−	0.978744i	$-0.565748\pi$
$823$	−5.39843e12	−0.410174	−0.205087	+	0.978744i	$0.565748\pi$
$824$	1.83194e13	1.38432
$825$	4.26443e13	3.20492
$826$	1.94470e12	0.145359
$827$	2.23707e12	0.166305	0.0831524	−	0.996537i	$-0.473501\pi$
$827$	2.23707e12	0.166305	0.0831524	+	0.996537i	$0.473501\pi$
$828$	−1.64510e13	−1.21634
$829$	1.81720e13	1.33631	0.668155	−	0.744022i	$-0.267084\pi$
$829$	1.81720e13	1.33631	0.668155	+	0.744022i	$0.267084\pi$
$830$	1.12305e12	0.0821389
$831$	1.98901e13	1.44688
$832$	4.10890e12	0.297283
$833$	1.11901e12	0.0805252
$834$	1.17502e13	0.841004
$835$	9.00682e11	0.0641184
$836$	9.33319e12	0.660848
$837$	2.67058e13	1.88079
$838$	−1.91955e12	−0.134463
$839$	1.34400e13	0.936417	0.468209	−	0.883618i	$-0.344900\pi$
$839$	1.34400e13	0.936417	0.468209	+	0.883618i	$0.344900\pi$
$840$	−2.10104e12	−0.145605
$841$	−5.07767e12	−0.350012
$842$	1.48709e13	1.01961
$843$	−2.19493e13	−1.49691
$844$	8.76590e12	0.594642
$845$	2.17188e11	0.0146548
$846$	−1.87981e13	−1.26167
$847$	−1.24874e13	−0.833677
$848$	7.04477e11	0.0467827
$849$	7.48574e12	0.494482
$850$	6.73363e12	0.442450
$851$	−2.44581e13	−1.59860
$852$	9.31386e11	0.0605552
$853$	−1.27527e13	−0.824768	−0.412384	−	0.911010i	$-0.635304\pi$
$853$	−1.27527e13	−0.824768	−0.412384	+	0.911010i	$0.635304\pi$
$854$	−2.94199e12	−0.189269
$855$	7.99799e12	0.511839
$856$	−3.58910e11	−0.0228483
$857$	2.54279e13	1.61026	0.805131	−	0.593097i	$-0.202095\pi$
$857$	2.54279e13	1.61026	0.805131	+	0.593097i	$0.202095\pi$
$858$	1.19257e13	0.751263
$859$	8.72407e12	0.546701	0.273351	−	0.961914i	$-0.411868\pi$
$859$	8.72407e12	0.546701	0.273351	+	0.961914i	$0.411868\pi$
$860$	−1.54254e12	−0.0961595
$861$	4.75164e12	0.294665
$862$	4.35633e12	0.268744
$863$	1.41413e13	0.867840	0.433920	−	0.900951i	$-0.357130\pi$
$863$	1.41413e13	0.867840	0.433920	+	0.900951i	$0.357130\pi$
$864$	−2.82606e13	−1.72532
$865$	5.40601e12	0.328325
$866$	−2.46642e12	−0.149017
$867$	−2.10840e13	−1.26727
$868$	1.48574e12	0.0888390
$869$	−4.15077e13	−2.46910
$870$	−3.92660e12	−0.232370
$871$	8.27115e12	0.486950
$872$	−1.92525e12	−0.112762
$873$	6.67346e13	3.88854
$874$	−2.27250e13	−1.31736
$875$	2.45182e12	0.141401
$876$	−2.50960e12	−0.143991
$877$	−6.34472e12	−0.362171	−0.181086	−	0.983467i	$-0.557961\pi$
$877$	−6.34472e12	−0.362171	−0.181086	+	0.983467i	$0.557961\pi$
$878$	−1.66127e13	−0.943439
$879$	1.76857e13	0.999247
$880$	3.33818e12	0.187645
$881$	−5.58201e12	−0.312175	−0.156088	−	0.987743i	$-0.549888\pi$
$881$	−5.58201e12	−0.312175	−0.156088	+	0.987743i	$0.549888\pi$
$882$	−5.12359e12	−0.285079
$883$	1.95146e13	1.08028	0.540139	−	0.841576i	$-0.318372\pi$
$883$	1.95146e13	1.08028	0.540139	+	0.841576i	$0.318372\pi$
$884$	−9.55427e11	−0.0526214
$885$	3.04918e12	0.167085
$886$	−7.53315e12	−0.410700
$887$	2.11461e13	1.14703	0.573513	−	0.819196i	$-0.305580\pi$
$887$	2.11461e13	1.14703	0.573513	+	0.819196i	$0.305580\pi$
$888$	−4.06089e13	−2.19161
$889$	3.38143e12	0.181569
$890$	−1.94753e12	−0.104047
$891$	−8.59812e13	−4.57040
$892$	−9.09042e12	−0.480775
$893$	1.31750e13	0.693298
$894$	3.07376e13	1.60935
$895$	4.42069e12	0.230296
$896$	1.69498e12	0.0878577
$897$	1.47328e13	0.759833
$898$	1.19568e13	0.613578
$899$	1.10260e13	0.562991
$900$	1.56427e13	0.794734
$901$	−9.48254e11	−0.0479361
$902$	−1.21688e13	−0.612094
$903$	−2.10340e13	−1.05275
$904$	−2.51227e13	−1.25115
$905$	−5.71718e12	−0.283311
$906$	4.14779e13	2.04522
$907$	−2.65739e13	−1.30383	−0.651917	−	0.758290i	$-0.726035\pi$
$907$	−2.65739e13	−1.30383	−0.651917	+	0.758290i	$0.726035\pi$
$908$	−1.46625e11	−0.00715851
$909$	6.11262e12	0.296954
$910$	3.36496e11	0.0162665
$911$	1.59962e12	0.0769459	0.0384729	−	0.999260i	$-0.487751\pi$
$911$	1.59962e12	0.0769459	0.0384729	+	0.999260i	$0.487751\pi$
$912$	−2.34086e13	−1.12047
$913$	1.98982e13	0.947755
$914$	1.92064e13	0.910308
$915$	−4.61286e12	−0.217558
$916$	9.08366e12	0.426316
$917$	−1.31337e13	−0.613376
$918$	−2.66075e13	−1.23655
$919$	1.93105e13	0.893045	0.446522	−	0.894773i	$-0.352662\pi$
$919$	1.93105e13	0.893045	0.446522	+	0.894773i	$0.352662\pi$
$920$	6.64716e12	0.305908
$921$	−2.67351e13	−1.22437
$922$	−2.22945e13	−1.01604
$923$	−5.92340e11	−0.0268636
$924$	−9.37461e12	−0.423087
$925$	2.32564e13	1.04449
$926$	1.63647e13	0.731405
$927$	7.00455e13	3.11546
$928$	−1.16680e13	−0.516452
$929$	−2.65045e13	−1.16748	−0.583740	−	0.811941i	$-0.698411\pi$
$929$	−2.65045e13	−1.16748	−0.583740	+	0.811941i	$0.698411\pi$
$930$	−4.59144e12	−0.201268
$931$	3.59096e12	0.156653
$932$	1.16816e13	0.507143
$933$	−5.40741e13	−2.33626
$934$	1.84660e13	0.793983
$935$	−4.49333e12	−0.192272
$936$	1.73713e13	0.739760
$937$	2.13515e13	0.904900	0.452450	−	0.891790i	$-0.350550\pi$
$937$	2.13515e13	0.904900	0.452450	+	0.891790i	$0.350550\pi$
$938$	1.28147e13	0.540502
$939$	3.89603e13	1.63541
$940$	−9.70484e11	−0.0405427
$941$	2.69960e13	1.12239	0.561197	−	0.827682i	$-0.310341\pi$
$941$	2.69960e13	1.12239	0.561197	+	0.827682i	$0.310341\pi$
$942$	3.45518e13	1.42969
$943$	−1.50330e13	−0.619075
$944$	−6.33764e12	−0.259749
$945$	−4.75456e12	−0.193940
$946$	5.38673e13	2.18683
$947$	−2.66652e13	−1.07738	−0.538690	−	0.842504i	$-0.681081\pi$
$947$	−2.66652e13	−1.07738	−0.538690	+	0.842504i	$0.681081\pi$
$948$	−2.14404e13	−0.862173
$949$	1.59605e12	0.0638776
$950$	2.16086e13	0.860736
$951$	3.98619e13	1.58032
$952$	−5.87809e12	−0.231937
$953$	−7.84200e12	−0.307970	−0.153985	−	0.988073i	$-0.549211\pi$
$953$	−7.84200e12	−0.307970	−0.153985	+	0.988073i	$0.549211\pi$
$954$	4.34175e12	0.169706
$955$	3.10496e12	0.120793
$956$	1.25059e13	0.484232
$957$	−6.95713e13	−2.68118
$958$	−2.03439e13	−0.780351
$959$	7.28597e12	0.278166
$960$	9.98157e12	0.379296
$961$	−1.35467e13	−0.512363
$962$	6.50381e12	0.244839
$963$	−1.37232e12	−0.0514207
$964$	−1.29754e13	−0.483922
$965$	−5.61310e12	−0.208367
$966$	2.28259e13	0.843394
$967$	−2.16665e13	−0.796839	−0.398419	−	0.917203i	$-0.630441\pi$
$967$	−2.16665e13	−0.796839	−0.398419	+	0.917203i	$0.630441\pi$
$968$	6.55957e13	2.40124
$969$	3.15090e13	1.14809
$970$	−6.79049e12	−0.246280
$971$	4.19208e13	1.51336	0.756682	−	0.653783i	$-0.226819\pi$
$971$	4.19208e13	1.51336	0.756682	+	0.653783i	$0.226819\pi$
$972$	−1.91840e13	−0.689352
$973$	5.87428e12	0.210110
$974$	1.32239e13	0.470809
$975$	−1.40089e13	−0.496460
$976$	9.58772e12	0.338214
$977$	−5.96219e11	−0.0209353	−0.0104677	−	0.999945i	$-0.503332\pi$
$977$	−5.96219e11	−0.0209353	−0.0104677	+	0.999945i	$0.503332\pi$
$978$	6.78912e13	2.37295
$979$	−3.45063e13	−1.20054
$980$	−2.64514e11	−0.00916075
$981$	−7.36135e12	−0.253774
$982$	−4.86430e12	−0.166924
$983$	2.86282e13	0.977918	0.488959	−	0.872307i	$-0.337377\pi$
$983$	2.86282e13	0.977918	0.488959	+	0.872307i	$0.337377\pi$
$984$	−2.49600e13	−0.848726
$985$	3.38579e12	0.114603
$986$	−1.09855e13	−0.370146
$987$	−1.32335e13	−0.443861
$988$	−3.06602e12	−0.102369
$989$	6.65463e13	2.21177
$990$	2.05735e13	0.680690
$991$	−1.17922e13	−0.388385	−0.194192	−	0.980963i	$-0.562209\pi$
$991$	−1.17922e13	−0.388385	−0.194192	+	0.980963i	$0.562209\pi$
$992$	−1.36436e13	−0.447328
$993$	−9.99645e13	−3.26268
$994$	−9.17730e11	−0.0298179
$995$	−7.93977e12	−0.256805
$996$	1.02782e13	0.330941
$997$	4.50363e13	1.44356	0.721779	−	0.692124i	$-0.243325\pi$
$997$	4.50363e13	1.44356	0.721779	+	0.692124i	$0.243325\pi$
$998$	−2.71527e13	−0.866415
$999$	−9.18963e13	−2.91913

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.d.1.6	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.d.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-18.4300 q^{2} +260.590 q^{3} -172.335 q^{4} +266.250 q^{5} -4802.67 q^{6} -2401.00 q^{7} +12612.3 q^{8} +48224.1 q^{9} +O(q^{10})\)	\(q-18.4300 q^{2} +260.590 q^{3} -172.335 q^{4} +266.250 q^{5} -4802.67 q^{6} -2401.00 q^{7} +12612.3 q^{8} +48224.1 q^{9} -4906.98 q^{10} -86941.8 q^{11} -44908.9 q^{12} +28561.0 q^{13} +44250.4 q^{14} +69382.1 q^{15} -144209. q^{16} +194111. q^{17} -888771. q^{18} +622912. q^{19} -45884.3 q^{20} -625677. q^{21} +1.60234e6 q^{22} +1.97949e6 q^{23} +3.28664e6 q^{24} -1.88224e6 q^{25} -526379. q^{26} +7.43754e6 q^{27} +413777. q^{28} +3.07074e6 q^{29} -1.27871e6 q^{30} +3.59067e6 q^{31} -3.79973e6 q^{32} -2.26562e7 q^{33} -3.57746e6 q^{34} -639266. q^{35} -8.31073e6 q^{36} -1.23557e7 q^{37} -1.14803e7 q^{38} +7.44271e6 q^{39} +3.35802e6 q^{40} -7.59440e6 q^{41} +1.15312e7 q^{42} +3.36179e7 q^{43} +1.49832e7 q^{44} +1.28397e7 q^{45} -3.64819e7 q^{46} +2.11507e7 q^{47} -3.75794e7 q^{48} +5.76480e6 q^{49} +3.46896e7 q^{50} +5.05833e7 q^{51} -4.92207e6 q^{52} -4.88511e6 q^{53} -1.37074e8 q^{54} -2.31483e7 q^{55} -3.02821e7 q^{56} +1.62325e8 q^{57} -5.65938e7 q^{58} +4.39477e7 q^{59} -1.19570e7 q^{60} -6.64849e7 q^{61} -6.61761e7 q^{62} -1.15786e8 q^{63} +1.43864e8 q^{64} +7.60437e6 q^{65} +4.17553e8 q^{66} +2.89596e8 q^{67} -3.34522e7 q^{68} +5.15835e8 q^{69} +1.17817e7 q^{70} -2.07395e7 q^{71} +6.08217e8 q^{72} +5.58821e7 q^{73} +2.27716e8 q^{74} -4.90492e8 q^{75} -1.07350e8 q^{76} +2.08747e8 q^{77} -1.37169e8 q^{78} +4.77419e8 q^{79} -3.83956e7 q^{80} +9.88951e8 q^{81} +1.39965e8 q^{82} -2.28868e8 q^{83} +1.07826e8 q^{84} +5.16820e7 q^{85} -6.19579e8 q^{86} +8.00205e8 q^{87} -1.09654e9 q^{88} +3.96890e8 q^{89} -2.36635e8 q^{90} -6.85750e7 q^{91} -3.41136e8 q^{92} +9.35694e8 q^{93} -3.89807e8 q^{94} +1.65850e8 q^{95} -9.90171e8 q^{96} +1.38384e9 q^{97} -1.06245e8 q^{98} -4.19269e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 22 q^{2} + q^{3} + 6402 q^{4} + 1694 q^{5} + 4189 q^{6} - 36015 q^{7} - 1704 q^{8} + 160366 q^{9}+O(q^{10}) \) 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

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