LMFDB - Embedded newform 91.10.a.d.1.14

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			1.14
Root			$40.4230$ 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)

$f(q)$	$=$	$q+41.4230 q^{2} -119.530 q^{3} +1203.86 q^{4} +1154.28 q^{5} -4951.28 q^{6} -2401.00 q^{7} +28659.0 q^{8} -5395.62 q^{9} +O(q^{10})$	\(q+41.4230 q^{2} -119.530 q^{3} +1203.86 q^{4} +1154.28 q^{5} -4951.28 q^{6} -2401.00 q^{7} +28659.0 q^{8} -5395.62 q^{9} +47813.7 q^{10} +93082.7 q^{11} -143898. q^{12} +28561.0 q^{13} -99456.6 q^{14} -137971. q^{15} +570765. q^{16} -471086. q^{17} -223503. q^{18} +678023. q^{19} +1.38960e6 q^{20} +286991. q^{21} +3.85576e6 q^{22} +862781. q^{23} -3.42561e6 q^{24} -620761. q^{25} +1.18308e6 q^{26} +2.99764e6 q^{27} -2.89048e6 q^{28} +6.95629e6 q^{29} -5.71517e6 q^{30} +2.03805e6 q^{31} +8.96936e6 q^{32} -1.11262e7 q^{33} -1.95138e7 q^{34} -2.77143e6 q^{35} -6.49559e6 q^{36} -58119.0 q^{37} +2.80857e7 q^{38} -3.41389e6 q^{39} +3.30806e7 q^{40} -1.26460e7 q^{41} +1.18880e7 q^{42} +776152. q^{43} +1.12059e8 q^{44} -6.22806e6 q^{45} +3.57390e7 q^{46} +1.78650e7 q^{47} -6.82235e7 q^{48} +5.76480e6 q^{49} -2.57138e7 q^{50} +5.63089e7 q^{51} +3.43835e7 q^{52} +1.11399e8 q^{53} +1.24171e8 q^{54} +1.07444e8 q^{55} -6.88104e7 q^{56} -8.10440e7 q^{57} +2.88150e8 q^{58} -7.24218e7 q^{59} -1.66098e8 q^{60} -2.00653e8 q^{61} +8.44220e7 q^{62} +1.29549e7 q^{63} +7.93060e7 q^{64} +3.29674e7 q^{65} -4.60879e8 q^{66} +9.74775e7 q^{67} -5.67124e8 q^{68} -1.03128e8 q^{69} -1.14801e8 q^{70} -2.73649e8 q^{71} -1.54633e8 q^{72} +1.07735e8 q^{73} -2.40746e6 q^{74} +7.41995e7 q^{75} +8.16247e8 q^{76} -2.23492e8 q^{77} -1.41414e8 q^{78} +3.69798e8 q^{79} +6.58823e8 q^{80} -2.52106e8 q^{81} -5.23833e8 q^{82} -7.82846e6 q^{83} +3.45498e8 q^{84} -5.43766e8 q^{85} +3.21505e7 q^{86} -8.31484e8 q^{87} +2.66766e9 q^{88} +4.40756e8 q^{89} -2.57985e8 q^{90} -6.85750e7 q^{91} +1.03867e9 q^{92} -2.43608e8 q^{93} +7.40021e8 q^{94} +7.82629e8 q^{95} -1.07211e9 q^{96} -2.04701e8 q^{97} +2.38795e8 q^{98} -5.02239e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	41.4230	1.83065	0.915327	−	0.402711i	$-0.131932\pi$
$2$	41.4230	1.83065	0.915327	+	0.402711i	$0.131932\pi$
$3$	−119.530	−0.851982	−0.425991	−	0.904727i	$-0.640075\pi$
$3$	−119.530	−0.851982	−0.425991	+	0.904727i	$0.640075\pi$
$4$	1203.86	2.35130
$5$	1154.28	0.825936	0.412968	−	0.910746i	$-0.364492\pi$
$5$	1154.28	0.825936	0.412968	+	0.910746i	$0.364492\pi$
$6$	−4951.28	−1.55969
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	28659.0	2.47376
$9$	−5395.62	−0.274126
$10$	47813.7	1.51200
$11$	93082.7	1.91691	0.958455	−	0.285243i	$-0.0920743\pi$
$11$	93082.7	1.91691	0.958455	+	0.285243i	$0.0920743\pi$
$12$	−143898.	−2.00326
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	−99456.6	−0.691922
$15$	−137971.	−0.703683
$16$	570765.	2.17730
$17$	−471086.	−1.36798	−0.683991	−	0.729490i	$-0.739757\pi$
$17$	−471086.	−1.36798	−0.683991	+	0.729490i	$0.739757\pi$
$18$	−223503.	−0.501830
$19$	678023.	1.19358	0.596792	−	0.802396i	$-0.296442\pi$
$19$	678023.	1.19358	0.596792	+	0.802396i	$0.296442\pi$
$20$	1.38960e6	1.94202
$21$	286991.	0.322019
$22$	3.85576e6	3.50920
$23$	862781.	0.642873	0.321437	−	0.946931i	$-0.395834\pi$
$23$	862781.	0.642873	0.321437	+	0.946931i	$0.395834\pi$
$24$	−3.42561e6	−2.10760
$25$	−620761.	−0.317830
$26$	1.18308e6	0.507732
$27$	2.99764e6	1.08553
$28$	−2.89048e6	−0.888706
$29$	6.95629e6	1.82636	0.913180	−	0.407556i	$-0.133619\pi$
$29$	6.95629e6	1.82636	0.913180	+	0.407556i	$0.133619\pi$
$30$	−5.71517e6	−1.28820
$31$	2.03805e6	0.396357	0.198179	−	0.980166i	$-0.436497\pi$
$31$	2.03805e6	0.396357	0.198179	+	0.980166i	$0.436497\pi$
$32$	8.96936e6	1.51212
$33$	−1.11262e7	−1.63317
$34$	−1.95138e7	−2.50430
$35$	−2.77143e6	−0.312174
$36$	−6.49559e6	−0.644551
$37$	−58119.0	−0.00509812	−0.00254906	−	0.999997i	$-0.500811\pi$
$37$	−58119.0	−0.00509812	−0.00254906	+	0.999997i	$0.500811\pi$
$38$	2.80857e7	2.18504
$39$	−3.41389e6	−0.236297
$40$	3.30806e7	2.04316
$41$	−1.26460e7	−0.698915	−0.349458	−	0.936952i	$-0.613634\pi$
$41$	−1.26460e7	−0.698915	−0.349458	+	0.936952i	$0.613634\pi$
$42$	1.18880e7	0.589506
$43$	776152.	0.0346209	0.0173105	−	0.999850i	$-0.494490\pi$
$43$	776152.	0.0346209	0.0173105	+	0.999850i	$0.494490\pi$
$44$	1.12059e8	4.50722
$45$	−6.22806e6	−0.226411
$46$	3.57390e7	1.17688
$47$	1.78650e7	0.534026	0.267013	−	0.963693i	$-0.413963\pi$
$47$	1.78650e7	0.534026	0.267013	+	0.963693i	$0.413963\pi$
$48$	−6.82235e7	−1.85502
$49$	5.76480e6	0.142857
$50$	−2.57138e7	−0.581836
$51$	5.63089e7	1.16550
$52$	3.43835e7	0.652132
$53$	1.11399e8	1.93927	0.969636	−	0.244552i	$-0.0786409\pi$
$53$	1.11399e8	1.93927	0.969636	+	0.244552i	$0.0786409\pi$
$54$	1.24171e8	1.98724
$55$	1.07444e8	1.58325
$56$	−6.88104e7	−0.934992
$57$	−8.10440e7	−1.01691
$58$	2.88150e8	3.34344
$59$	−7.24218e7	−0.778100	−0.389050	−	0.921217i	$-0.627197\pi$
$59$	−7.24218e7	−0.778100	−0.389050	+	0.921217i	$0.627197\pi$
$60$	−1.66098e8	−1.65457
$61$	−2.00653e8	−1.85551	−0.927753	−	0.373196i	$-0.878262\pi$
$61$	−2.00653e8	−1.85551	−0.927753	+	0.373196i	$0.878262\pi$
$62$	8.44220e7	0.725593
$63$	1.29549e7	0.103610
$64$	7.93060e7	0.590876
$65$	3.29674e7	0.229073
$66$	−4.60879e8	−2.98978
$67$	9.74775e7	0.590973	0.295487	−	0.955347i	$-0.404518\pi$
$67$	9.74775e7	0.590973	0.295487	+	0.955347i	$0.404518\pi$
$68$	−5.67124e8	−3.21653
$69$	−1.03128e8	−0.547717
$70$	−1.14801e8	−0.571484
$71$	−2.73649e8	−1.27800	−0.639001	−	0.769206i	$-0.720652\pi$
$71$	−2.73649e8	−1.27800	−0.639001	+	0.769206i	$0.720652\pi$
$72$	−1.54633e8	−0.678121
$73$	1.07735e8	0.444022	0.222011	−	0.975044i	$-0.428738\pi$
$73$	1.07735e8	0.444022	0.222011	+	0.975044i	$0.428738\pi$
$74$	−2.40746e6	−0.00933290
$75$	7.41995e7	0.270785
$76$	8.16247e8	2.80647
$77$	−2.23492e8	−0.724524
$78$	−1.41414e8	−0.432579
$79$	3.69798e8	1.06818	0.534088	−	0.845429i	$-0.320655\pi$
$79$	3.69798e8	1.06818	0.534088	+	0.845429i	$0.320655\pi$
$80$	6.58823e8	1.79831
$81$	−2.52106e8	−0.650729
$82$	−5.23833e8	−1.27947
$83$	−7.82846e6	−0.0181061	−0.00905305	−	0.999959i	$-0.502882\pi$
$83$	−7.82846e6	−0.0181061	−0.00905305	+	0.999959i	$0.502882\pi$
$84$	3.45498e8	0.757162
$85$	−5.43766e8	−1.12987
$86$	3.21505e7	0.0633790
$87$	−8.31484e8	−1.55603
$88$	2.66766e9	4.74197
$89$	4.40756e8	0.744635	0.372317	−	0.928105i	$-0.378563\pi$
$89$	4.40756e8	0.744635	0.372317	+	0.928105i	$0.378563\pi$
$90$	−2.57985e8	−0.414479
$91$	−6.85750e7	−0.104828
$92$	1.03867e9	1.51158
$93$	−2.43608e8	−0.337689
$94$	7.40021e8	0.977617
$95$	7.82629e8	0.985825
$96$	−1.07211e9	−1.28830
$97$	−2.04701e8	−0.234772	−0.117386	−	0.993086i	$-0.537451\pi$
$97$	−2.04701e8	−0.234772	−0.117386	+	0.993086i	$0.537451\pi$
$98$	2.38795e8	0.261522
$99$	−5.02239e8	−0.525475
$100$	−7.47312e8	−0.747312
$101$	−1.46536e9	−1.40119	−0.700597	−	0.713557i	$-0.747083\pi$
$101$	−1.46536e9	−1.40119	−0.700597	+	0.713557i	$0.747083\pi$
$102$	2.33248e9	2.13362
$103$	−1.61129e9	−1.41061	−0.705303	−	0.708906i	$-0.749189\pi$
$103$	−1.61129e9	−1.41061	−0.705303	+	0.708906i	$0.749189\pi$
$104$	8.18531e8	0.686096
$105$	3.31268e8	0.265967
$106$	4.61447e9	3.55014
$107$	−1.61415e9	−1.19047	−0.595233	−	0.803553i	$-0.702940\pi$
$107$	−1.61415e9	−1.19047	−0.595233	+	0.803553i	$0.702940\pi$
$108$	3.60875e9	2.55241
$109$	−1.62958e9	−1.10575	−0.552875	−	0.833264i	$-0.686469\pi$
$109$	−1.62958e9	−1.10575	−0.552875	+	0.833264i	$0.686469\pi$
$110$	4.45063e9	2.89838
$111$	6.94695e6	0.00434351
$112$	−1.37041e9	−0.822941
$113$	−1.91345e9	−1.10399	−0.551994	−	0.833848i	$-0.686133\pi$
$113$	−1.91345e9	−1.10399	−0.551994	+	0.833848i	$0.686133\pi$
$114$	−3.35708e9	−1.86162
$115$	9.95891e8	0.530972
$116$	8.37442e9	4.29431
$117$	−1.54104e8	−0.0760289
$118$	−2.99993e9	−1.42443
$119$	1.13108e9	0.517049
$120$	−3.95412e9	−1.74074
$121$	6.30644e9	2.67455
$122$	−8.31166e9	−3.39679
$123$	1.51157e9	0.595463
$124$	2.45353e9	0.931953
$125$	−2.97099e9	−1.08844
$126$	5.36630e8	0.189674
$127$	−4.91659e9	−1.67705	−0.838527	−	0.544860i	$-0.816583\pi$
$127$	−4.91659e9	−1.67705	−0.838527	+	0.544860i	$0.816583\pi$
$128$	−1.30722e9	−0.430432
$129$	−9.27733e7	−0.0294964
$130$	1.36561e9	0.419354
$131$	−4.75773e8	−0.141149	−0.0705746	−	0.997507i	$-0.522483\pi$
$131$	−4.75773e8	−0.141149	−0.0705746	+	0.997507i	$0.522483\pi$
$132$	−1.33944e10	−3.84008
$133$	−1.62793e9	−0.451133
$134$	4.03781e9	1.08187
$135$	3.46012e9	0.896581
$136$	−1.35009e10	−3.38405
$137$	−1.37787e9	−0.334168	−0.167084	−	0.985943i	$-0.553435\pi$
$137$	−1.37787e9	−0.334168	−0.167084	+	0.985943i	$0.553435\pi$
$138$	−4.27187e9	−1.00268
$139$	−6.45599e9	−1.46689	−0.733443	−	0.679751i	$-0.762088\pi$
$139$	−6.45599e9	−1.46689	−0.733443	+	0.679751i	$0.762088\pi$
$140$	−3.33642e9	−0.734015
$141$	−2.13540e9	−0.454981
$142$	−1.13354e10	−2.33958
$143$	2.65853e9	0.531655
$144$	−3.07963e9	−0.596853
$145$	8.02951e9	1.50846
$146$	4.46271e9	0.812852
$147$	−6.89066e8	−0.121712
$148$	−6.99673e7	−0.0119872
$149$	−1.18631e9	−0.197178	−0.0985892	−	0.995128i	$-0.531433\pi$
$149$	−1.18631e9	−0.197178	−0.0985892	+	0.995128i	$0.531433\pi$
$150$	3.07356e9	0.495714
$151$	6.46165e9	1.01146	0.505728	−	0.862693i	$-0.331224\pi$
$151$	6.46165e9	1.01146	0.505728	+	0.862693i	$0.331224\pi$
$152$	1.94315e10	2.95264
$153$	2.54180e9	0.374999
$154$	−9.25769e9	−1.32635
$155$	2.35248e9	0.327366
$156$	−4.10986e9	−0.555605
$157$	2.71307e9	0.356379	0.178190	−	0.983996i	$-0.442976\pi$
$157$	2.71307e9	0.356379	0.178190	+	0.983996i	$0.442976\pi$
$158$	1.53181e10	1.95546
$159$	−1.33155e10	−1.65223
$160$	1.03532e10	1.24892
$161$	−2.07154e9	−0.242983
$162$	−1.04430e10	−1.19126
$163$	−5.75836e9	−0.638932	−0.319466	−	0.947598i	$-0.603504\pi$
$163$	−5.75836e9	−0.638932	−0.319466	+	0.947598i	$0.603504\pi$
$164$	−1.52240e10	−1.64336
$165$	−1.28427e10	−1.34890
$166$	−3.24278e8	−0.0331460
$167$	6.33803e8	0.0630565	0.0315283	−	0.999503i	$-0.489963\pi$
$167$	6.33803e8	0.0630565	0.0315283	+	0.999503i	$0.489963\pi$
$168$	8.22489e9	0.796597
$169$	8.15731e8	0.0769231
$170$	−2.25244e10	−2.06839
$171$	−3.65836e9	−0.327193
$172$	9.34381e8	0.0814041
$173$	−1.33833e10	−1.13594	−0.567971	−	0.823049i	$-0.692271\pi$
$173$	−1.33833e10	−1.13594	−0.567971	+	0.823049i	$0.692271\pi$
$174$	−3.44425e10	−2.84855
$175$	1.49045e9	0.120128
$176$	5.31284e10	4.17368
$177$	8.65657e9	0.662928
$178$	1.82574e10	1.36317
$179$	1.68011e10	1.22320	0.611601	−	0.791166i	$-0.290526\pi$
$179$	1.68011e10	1.22320	0.611601	+	0.791166i	$0.290526\pi$
$180$	−7.49774e9	−0.532358
$181$	1.98933e10	1.37769	0.688847	−	0.724906i	$-0.258117\pi$
$181$	1.98933e10	1.37769	0.688847	+	0.724906i	$0.258117\pi$
$182$	−2.84058e9	−0.191905
$183$	2.39841e10	1.58086
$184$	2.47265e10	1.59031
$185$	−6.70856e7	−0.00421072
$186$	−1.00910e10	−0.618193
$187$	−4.38500e10	−2.62230
$188$	2.15070e10	1.25565
$189$	−7.19734e9	−0.410293
$190$	3.24188e10	1.80470
$191$	1.52261e10	0.827824	0.413912	−	0.910317i	$-0.364162\pi$
$191$	1.52261e10	0.827824	0.413912	+	0.910317i	$0.364162\pi$
$192$	−9.47943e9	−0.503416
$193$	1.77927e10	0.923067	0.461534	−	0.887123i	$-0.347299\pi$
$193$	1.77927e10	0.923067	0.461534	+	0.887123i	$0.347299\pi$
$194$	−8.47931e9	−0.429787
$195$	−3.94059e9	−0.195167
$196$	6.94003e9	0.335899
$197$	2.04364e10	0.966731	0.483366	−	0.875419i	$-0.339414\pi$
$197$	2.04364e10	0.966731	0.483366	+	0.875419i	$0.339414\pi$
$198$	−2.08042e10	−0.961963
$199$	−2.02290e10	−0.914399	−0.457199	−	0.889364i	$-0.651147\pi$
$199$	−2.02290e10	−0.914399	−0.457199	+	0.889364i	$0.651147\pi$
$200$	−1.77904e10	−0.786233
$201$	−1.16515e10	−0.503499
$202$	−6.06996e10	−2.56510
$203$	−1.67020e10	−0.690299
$204$	6.77882e10	2.74043
$205$	−1.45970e10	−0.577259
$206$	−6.67444e10	−2.58233
$207$	−4.65524e9	−0.176228
$208$	1.63016e10	0.603873
$209$	6.31122e10	2.28800
$210$	1.37221e10	0.486894
$211$	6.37244e9	0.221327	0.110664	−	0.993858i	$-0.464702\pi$
$211$	6.37244e9	0.221327	0.110664	+	0.993858i	$0.464702\pi$
$212$	1.34109e11	4.55980
$213$	3.27093e10	1.08884
$214$	−6.68629e10	−2.17933
$215$	8.95898e8	0.0285947
$216$	8.59096e10	2.68534
$217$	−4.89335e9	−0.149809
$218$	−6.75022e10	−2.02425
$219$	−1.28776e10	−0.378299
$220$	1.29347e11	3.72268
$221$	−1.34547e10	−0.379410
$222$	2.87763e8	0.00795147
$223$	−1.18037e10	−0.319629	−0.159815	−	0.987147i	$-0.551090\pi$
$223$	−1.18037e10	−0.319629	−0.159815	+	0.987147i	$0.551090\pi$
$224$	−2.15354e10	−0.571528
$225$	3.34939e9	0.0871254
$226$	−7.92608e10	−2.02102
$227$	−2.58044e10	−0.645026	−0.322513	−	0.946565i	$-0.604528\pi$
$227$	−2.58044e10	−0.645026	−0.322513	+	0.946565i	$0.604528\pi$
$228$	−9.75659e10	−2.39106
$229$	4.84817e10	1.16498	0.582490	−	0.812838i	$-0.302079\pi$
$229$	4.84817e10	1.16498	0.582490	+	0.812838i	$0.302079\pi$
$230$	4.12528e10	0.972026
$231$	2.67139e10	0.617282
$232$	1.99361e11	4.51797
$233$	1.14279e10	0.254019	0.127009	−	0.991902i	$-0.459462\pi$
$233$	1.14279e10	0.254019	0.127009	+	0.991902i	$0.459462\pi$
$234$	−6.38346e9	−0.139183
$235$	2.06212e10	0.441071
$236$	−8.71860e10	−1.82954
$237$	−4.42019e10	−0.910066
$238$	4.68526e10	0.946538
$239$	−2.33498e10	−0.462906	−0.231453	−	0.972846i	$-0.574348\pi$
$239$	−2.33498e10	−0.462906	−0.231453	+	0.972846i	$0.574348\pi$
$240$	−7.87490e10	−1.53213
$241$	9.32784e10	1.78117	0.890583	−	0.454821i	$-0.150297\pi$
$241$	9.32784e10	1.78117	0.890583	+	0.454821i	$0.150297\pi$
$242$	2.61232e11	4.89617
$243$	−2.88685e10	−0.531123
$244$	−2.41559e11	−4.36284
$245$	6.65420e9	0.117991
$246$	6.26137e10	1.09009
$247$	1.93650e10	0.331041
$248$	5.84085e10	0.980491
$249$	9.35735e8	0.0154261
$250$	−1.23067e11	−1.99256
$251$	−6.12148e10	−0.973474	−0.486737	−	0.873548i	$-0.661813\pi$
$251$	−6.12148e10	−0.973474	−0.486737	+	0.873548i	$0.661813\pi$
$252$	1.55959e10	0.243617
$253$	8.03100e10	1.23233
$254$	−2.03660e11	−3.07011
$255$	6.49963e10	0.962626
$256$	−9.47537e10	−1.37885
$257$	−1.88665e10	−0.269769	−0.134884	−	0.990861i	$-0.543066\pi$
$257$	−1.88665e10	−0.269769	−0.134884	+	0.990861i	$0.543066\pi$
$258$	−3.84295e9	−0.0539978
$259$	1.39544e8	0.00192691
$260$	3.96883e10	0.538619
$261$	−3.75335e10	−0.500653
$262$	−1.97079e10	−0.258396
$263$	−7.47237e10	−0.963069	−0.481535	−	0.876427i	$-0.659920\pi$
$263$	−7.47237e10	−0.963069	−0.481535	+	0.876427i	$0.659920\pi$
$264$	−3.18865e11	−4.04007
$265$	1.28585e11	1.60171
$266$	−6.74339e10	−0.825868
$267$	−5.26835e10	−0.634416
$268$	1.17350e11	1.38955
$269$	3.04476e10	0.354542	0.177271	−	0.984162i	$-0.443273\pi$
$269$	3.04476e10	0.354542	0.177271	+	0.984162i	$0.443273\pi$
$270$	1.43329e11	1.64133
$271$	1.03927e11	1.17049	0.585244	−	0.810857i	$-0.300999\pi$
$271$	1.03927e11	1.17049	0.585244	+	0.810857i	$0.300999\pi$
$272$	−2.68880e11	−2.97850
$273$	8.19675e9	0.0893120
$274$	−5.70754e10	−0.611746
$275$	−5.77821e10	−0.609251
$276$	−1.24152e11	−1.28784
$277$	7.39534e10	0.754743	0.377371	−	0.926062i	$-0.376828\pi$
$277$	7.39534e10	0.754743	0.377371	+	0.926062i	$0.376828\pi$
$278$	−2.67426e11	−2.68536
$279$	−1.09965e10	−0.108652
$280$	−7.94265e10	−0.772243
$281$	−2.89136e10	−0.276646	−0.138323	−	0.990387i	$-0.544171\pi$
$281$	−2.89136e10	−0.276646	−0.138323	+	0.990387i	$0.544171\pi$
$282$	−8.84546e10	−0.832913
$283$	8.71847e10	0.807981	0.403991	−	0.914763i	$-0.367623\pi$
$283$	8.71847e10	0.807981	0.403991	+	0.914763i	$0.367623\pi$
$284$	−3.29436e11	−3.00496
$285$	−9.35475e10	−0.839905
$286$	1.10124e11	0.973277
$287$	3.03629e10	0.264165
$288$	−4.83953e10	−0.414512
$289$	1.03335e11	0.871375
$290$	3.32606e11	2.76146
$291$	2.44678e10	0.200022
$292$	1.29699e11	1.04403
$293$	8.97563e10	0.711477	0.355738	−	0.934586i	$-0.384229\pi$
$293$	8.97563e10	0.711477	0.355738	+	0.934586i	$0.384229\pi$
$294$	−2.85432e10	−0.222812
$295$	−8.35951e10	−0.642661
$296$	−1.66563e9	−0.0126115
$297$	2.79029e11	2.08087
$298$	−4.91404e10	−0.360966
$299$	2.46419e10	0.178301
$300$	8.93260e10	0.636696
$301$	−1.86354e9	−0.0130855
$302$	2.67661e11	1.85163
$303$	1.75154e11	1.19379
$304$	3.86992e11	2.59879
$305$	−2.31610e11	−1.53253
$306$	1.05289e11	0.686494
$307$	2.01869e11	1.29702	0.648511	−	0.761205i	$-0.275392\pi$
$307$	2.01869e11	1.29702	0.648511	+	0.761205i	$0.275392\pi$
$308$	−2.69053e11	−1.70357
$309$	1.92597e11	1.20181
$310$	9.74467e10	0.599294
$311$	−7.80273e10	−0.472961	−0.236480	−	0.971636i	$-0.575994\pi$
$311$	−7.80273e10	−0.472961	−0.236480	+	0.971636i	$0.575994\pi$
$312$	−9.78389e10	−0.584542
$313$	−1.01428e11	−0.597322	−0.298661	−	0.954359i	$-0.596540\pi$
$313$	−1.01428e11	−0.597322	−0.298661	+	0.954359i	$0.596540\pi$
$314$	1.12383e11	0.652408
$315$	1.49536e10	0.0855751
$316$	4.45186e11	2.51160
$317$	−1.04204e11	−0.579588	−0.289794	−	0.957089i	$-0.593587\pi$
$317$	−1.04204e11	−0.579588	−0.289794	+	0.957089i	$0.593587\pi$
$318$	−5.51566e11	−3.02465
$319$	6.47510e11	3.50097
$320$	9.15414e10	0.488026
$321$	1.92939e11	1.01426
$322$	−8.58092e10	−0.444818
$323$	−3.19407e11	−1.63280
$324$	−3.03501e11	−1.53006
$325$	−1.77296e10	−0.0881501
$326$	−2.38529e11	−1.16966
$327$	1.94784e11	0.942080
$328$	−3.62421e11	−1.72895
$329$	−4.28938e10	−0.201843
$330$	−5.31983e11	−2.46936
$331$	−7.75166e10	−0.354952	−0.177476	−	0.984125i	$-0.556793\pi$
$331$	−7.75166e10	−0.354952	−0.177476	+	0.984125i	$0.556793\pi$
$332$	−9.42440e9	−0.0425728
$333$	3.13588e8	0.00139753
$334$	2.62540e10	0.115435
$335$	1.12516e11	0.488106
$336$	1.63805e11	0.701131
$337$	2.82258e10	0.119210	0.0596048	−	0.998222i	$-0.481016\pi$
$337$	2.82258e10	0.119210	0.0596048	+	0.998222i	$0.481016\pi$
$338$	3.37900e10	0.140820
$339$	2.28714e11	0.940578
$340$	−6.54620e11	−2.65665
$341$	1.89707e11	0.759781
$342$	−1.51540e11	−0.598977
$343$	−1.38413e10	−0.0539949
$344$	2.22438e10	0.0856438
$345$	−1.19039e11	−0.452379
$346$	−5.54377e11	−2.07952
$347$	−2.05429e11	−0.760638	−0.380319	−	0.924855i	$-0.624186\pi$
$347$	−2.05429e11	−0.760638	−0.380319	+	0.924855i	$0.624186\pi$
$348$	−1.00099e12	−3.65868
$349$	−6.69793e10	−0.241672	−0.120836	−	0.992672i	$-0.538557\pi$
$349$	−6.69793e10	−0.241672	−0.120836	+	0.992672i	$0.538557\pi$
$350$	6.17388e10	0.219913
$351$	8.56157e10	0.301073
$352$	8.34892e11	2.89860
$353$	−3.05476e11	−1.04711	−0.523553	−	0.851993i	$-0.675394\pi$
$353$	−3.05476e11	−1.04711	−0.523553	+	0.851993i	$0.675394\pi$
$354$	3.58581e11	1.21359
$355$	−3.15868e11	−1.05555
$356$	5.30610e11	1.75086
$357$	−1.35198e11	−0.440516
$358$	6.95950e11	2.23926
$359$	2.30751e11	0.733194	0.366597	−	0.930380i	$-0.380523\pi$
$359$	2.30751e11	0.733194	0.366597	+	0.930380i	$0.380523\pi$
$360$	−1.78490e11	−0.560084
$361$	1.37028e11	0.424645
$362$	8.24039e11	2.52208
$363$	−7.53808e11	−2.27867
$364$	−8.25549e10	−0.246483
$365$	1.24357e11	0.366734
$366$	9.93491e11	2.89400
$367$	−4.61420e11	−1.32770	−0.663849	−	0.747867i	$-0.731078\pi$
$367$	−4.61420e11	−1.32770	−0.663849	+	0.747867i	$0.731078\pi$
$368$	4.92445e11	1.39973
$369$	6.82328e10	0.191591
$370$	−2.77889e9	−0.00770838
$371$	−2.67468e11	−0.732976
$372$	−2.93270e11	−0.794008
$373$	−4.67350e11	−1.25012	−0.625061	−	0.780576i	$-0.714926\pi$
$373$	−4.67350e11	−1.25012	−0.625061	+	0.780576i	$0.714926\pi$
$374$	−1.81640e12	−4.80052
$375$	3.55122e11	0.927334
$376$	5.11994e11	1.32105
$377$	1.98679e11	0.506541
$378$	−2.98135e11	−0.751104
$379$	2.03513e11	0.506659	0.253330	−	0.967380i	$-0.418474\pi$
$379$	2.03513e11	0.506659	0.253330	+	0.967380i	$0.418474\pi$
$380$	9.42178e11	2.31797
$381$	5.87679e11	1.42882
$382$	6.30709e11	1.51546
$383$	2.39166e10	0.0567944	0.0283972	−	0.999597i	$-0.490960\pi$
$383$	2.39166e10	0.0567944	0.0283972	+	0.999597i	$0.490960\pi$
$384$	1.56252e11	0.366721
$385$	−2.57972e11	−0.598411
$386$	7.37026e11	1.68982
$387$	−4.18782e9	−0.00949050
$388$	−2.46432e11	−0.552019
$389$	−4.68934e11	−1.03834	−0.519169	−	0.854672i	$-0.673758\pi$
$389$	−4.68934e11	−1.03834	−0.519169	+	0.854672i	$0.673758\pi$
$390$	−1.63231e11	−0.357283
$391$	−4.06444e11	−0.879439
$392$	1.65214e11	0.353394
$393$	5.68690e10	0.120257
$394$	8.46535e11	1.76975
$395$	4.26851e11	0.882244
$396$	−6.04627e11	−1.23555
$397$	2.25132e11	0.454862	0.227431	−	0.973794i	$-0.426967\pi$
$397$	2.25132e11	0.454862	0.227431	+	0.973794i	$0.426967\pi$
$398$	−8.37946e11	−1.67395
$399$	1.94587e11	0.384357
$400$	−3.54309e11	−0.692009
$401$	−6.88246e11	−1.32921	−0.664606	−	0.747194i	$-0.731401\pi$
$401$	−6.88246e11	−1.32921	−0.664606	+	0.747194i	$0.731401\pi$
$402$	−4.82639e11	−0.921733
$403$	5.82087e10	0.109930
$404$	−1.76409e12	−3.29462
$405$	−2.91001e11	−0.537461
$406$	−6.91849e11	−1.26370
$407$	−5.40987e9	−0.00977264
$408$	1.61376e12	2.88315
$409$	8.00632e11	1.41474	0.707372	−	0.706841i	$-0.249881\pi$
$409$	8.00632e11	1.41474	0.707372	+	0.706841i	$0.249881\pi$
$410$	−6.04651e11	−1.05676
$411$	1.64696e11	0.284705
$412$	−1.93977e12	−3.31675
$413$	1.73885e11	0.294094
$414$	−1.92834e11	−0.322613
$415$	−9.03624e9	−0.0149545
$416$	2.56174e11	0.419387
$417$	7.71683e11	1.24976
$418$	2.61430e12	4.18853
$419$	5.66782e11	0.898365	0.449183	−	0.893440i	$-0.351715\pi$
$419$	5.66782e11	0.898365	0.449183	+	0.893440i	$0.351715\pi$
$420$	3.98802e11	0.625368
$421$	−4.86833e11	−0.755284	−0.377642	−	0.925952i	$-0.623265\pi$
$421$	−4.86833e11	−0.755284	−0.377642	+	0.925952i	$0.623265\pi$
$422$	2.63965e11	0.405173
$423$	−9.63927e10	−0.146390
$424$	3.19258e12	4.79729
$425$	2.92432e11	0.434785
$426$	1.35491e12	1.99328
$427$	4.81769e11	0.701315
$428$	−1.94322e12	−2.79914
$429$	−3.17774e11	−0.452961
$430$	3.71107e10	0.0523470
$431$	−2.52866e11	−0.352974	−0.176487	−	0.984303i	$-0.556473\pi$
$431$	−2.52866e11	−0.352974	−0.176487	+	0.984303i	$0.556473\pi$
$432$	1.71095e12	2.36353
$433$	−1.14119e11	−0.156013	−0.0780067	−	0.996953i	$-0.524856\pi$
$433$	−1.14119e11	−0.156013	−0.0780067	+	0.996953i	$0.524856\pi$
$434$	−2.02697e11	−0.274248
$435$	−9.59766e11	−1.28518
$436$	−1.96179e12	−2.59995
$437$	5.84985e11	0.767324
$438$	−5.33427e11	−0.692535
$439$	−1.29634e11	−0.166583	−0.0832913	−	0.996525i	$-0.526543\pi$
$439$	−1.29634e11	−0.166583	−0.0832913	+	0.996525i	$0.526543\pi$
$440$	3.07923e12	3.91656
$441$	−3.11047e10	−0.0391608
$442$	−5.57334e11	−0.694569
$443$	−1.25590e12	−1.54931	−0.774654	−	0.632385i	$-0.782076\pi$
$443$	−1.25590e12	−1.54931	−0.774654	+	0.632385i	$0.782076\pi$
$444$	8.36318e9	0.0102129
$445$	5.08756e11	0.615021
$446$	−4.88945e11	−0.585131
$447$	1.41799e11	0.167993
$448$	−1.90414e11	−0.223330
$449$	4.85816e10	0.0564109	0.0282055	−	0.999602i	$-0.491021\pi$
$449$	4.85816e10	0.0564109	0.0282055	+	0.999602i	$0.491021\pi$
$450$	1.38742e11	0.159496
$451$	−1.17712e12	−1.33976
$452$	−2.30353e12	−2.59580
$453$	−7.72360e11	−0.861743
$454$	−1.06890e12	−1.18082
$455$	−7.91548e10	−0.0865816
$456$	−2.32264e12	−2.51560
$457$	1.56610e12	1.67956	0.839781	−	0.542925i	$-0.182683\pi$
$457$	1.56610e12	1.67956	0.839781	+	0.542925i	$0.182683\pi$
$458$	2.00826e12	2.13268
$459$	−1.41215e12	−1.48499
$460$	1.19892e12	1.24847
$461$	1.64286e12	1.69413	0.847065	−	0.531489i	$-0.178367\pi$
$461$	1.64286e12	1.69413	0.847065	+	0.531489i	$0.178367\pi$
$462$	1.10657e12	1.13003
$463$	−1.28749e12	−1.30205	−0.651026	−	0.759055i	$-0.725661\pi$
$463$	−1.28749e12	−1.30205	−0.651026	+	0.759055i	$0.725661\pi$
$464$	3.97041e12	3.97653
$465$	−2.81192e11	−0.278910
$466$	4.73379e11	0.465020
$467$	3.68943e11	0.358949	0.179475	−	0.983763i	$-0.442560\pi$
$467$	3.68943e11	0.358949	0.179475	+	0.983763i	$0.442560\pi$
$468$	−1.85521e11	−0.178766
$469$	−2.34044e11	−0.223367
$470$	8.54192e11	0.807449
$471$	−3.24293e11	−0.303629
$472$	−2.07554e12	−1.92483
$473$	7.22463e10	0.0663652
$474$	−1.83097e12	−1.66602
$475$	−4.20890e11	−0.379357
$476$	1.36166e12	1.21573
$477$	−6.01065e11	−0.531605
$478$	−9.67218e11	−0.847420
$479$	1.99863e12	1.73469	0.867346	−	0.497706i	$-0.165824\pi$
$479$	1.99863e12	1.73469	0.867346	+	0.497706i	$0.165824\pi$
$480$	−1.23751e12	−1.06405
$481$	−1.65994e9	−0.00141396
$482$	3.86387e12	3.26070
$483$	2.47610e11	0.207017
$484$	7.59209e12	6.28865
$485$	−2.36282e11	−0.193907
$486$	−1.19582e12	−0.972303
$487$	−4.72373e11	−0.380544	−0.190272	−	0.981731i	$-0.560937\pi$
$487$	−4.72373e11	−0.380544	−0.190272	+	0.981731i	$0.560937\pi$
$488$	−5.75053e12	−4.59007
$489$	6.88296e11	0.544359
$490$	2.75637e11	0.216001
$491$	−1.46196e12	−1.13519	−0.567594	−	0.823309i	$-0.692126\pi$
$491$	−1.46196e12	−1.13519	−0.567594	+	0.823309i	$0.692126\pi$
$492$	1.81972e12	1.40011
$493$	−3.27701e12	−2.49843
$494$	8.02157e11	0.606021
$495$	−5.79725e11	−0.434009
$496$	1.16325e12	0.862987
$497$	6.57032e11	0.483040
$498$	3.87609e10	0.0282398
$499$	5.28519e11	0.381600	0.190800	−	0.981629i	$-0.438892\pi$
$499$	5.28519e11	0.381600	0.190800	+	0.981629i	$0.438892\pi$
$500$	−3.57666e12	−2.55925
$501$	−7.57584e10	−0.0537231
$502$	−2.53570e12	−1.78210
$503$	−1.34909e12	−0.939691	−0.469846	−	0.882749i	$-0.655690\pi$
$503$	−1.34909e12	−0.939691	−0.469846	+	0.882749i	$0.655690\pi$
$504$	3.71275e11	0.256306
$505$	−1.69144e12	−1.15730
$506$	3.32668e12	2.25597
$507$	−9.75041e10	−0.0655371
$508$	−5.91890e12	−3.94325
$509$	3.62094e10	0.0239107	0.0119553	−	0.999929i	$-0.496194\pi$
$509$	3.62094e10	0.0239107	0.0119553	+	0.999929i	$0.496194\pi$
$510$	2.69234e12	1.76224
$511$	−2.58672e11	−0.167825
$512$	−3.25568e12	−2.09376
$513$	2.03247e12	1.29568
$514$	−7.81506e11	−0.493853
$515$	−1.85988e12	−1.16507
$516$	−1.11686e11	−0.0693548
$517$	1.66292e12	1.02368
$518$	5.78031e9	0.00352750
$519$	1.59971e12	0.967803
$520$	9.44815e11	0.566672
$521$	6.91577e11	0.411217	0.205608	−	0.978634i	$-0.434083\pi$
$521$	6.91577e11	0.411217	0.205608	+	0.978634i	$0.434083\pi$
$522$	−1.55475e12	−0.916522
$523$	−8.74451e11	−0.511067	−0.255534	−	0.966800i	$-0.582251\pi$
$523$	−8.74451e11	−0.511067	−0.255534	+	0.966800i	$0.582251\pi$
$524$	−5.72765e11	−0.331884
$525$	−1.78153e11	−0.102347
$526$	−3.09528e12	−1.76305
$527$	−9.60097e11	−0.542210
$528$	−6.35042e12	−3.55590
$529$	−1.05676e12	−0.586714
$530$	5.32639e12	2.93219
$531$	3.90761e11	0.213297
$532$	−1.95981e12	−1.06075
$533$	−3.61181e11	−0.193844
$534$	−2.18231e12	−1.16140
$535$	−1.86318e12	−0.983249
$536$	2.79361e12	1.46192
$537$	−2.00823e12	−1.04215
$538$	1.26123e12	0.649043
$539$	5.36603e11	0.273844
$540$	4.16551e12	2.10813
$541$	5.85792e11	0.294006	0.147003	−	0.989136i	$-0.453037\pi$
$541$	5.85792e11	0.294006	0.147003	+	0.989136i	$0.453037\pi$
$542$	4.30497e12	2.14276
$543$	−2.37784e12	−1.17377
$544$	−4.22535e12	−2.06856
$545$	−1.88100e12	−0.913279
$546$	3.39534e11	0.163499
$547$	−5.66898e11	−0.270746	−0.135373	−	0.990795i	$-0.543223\pi$
$547$	−5.66898e11	−0.270746	−0.135373	+	0.990795i	$0.543223\pi$
$548$	−1.65876e12	−0.785728
$549$	1.08265e12	0.508642
$550$	−2.39351e12	−1.11533
$551$	4.71652e12	2.17992
$552$	−2.95555e12	−1.35492
$553$	−8.87885e11	−0.403732
$554$	3.06337e12	1.38167
$555$	8.01873e9	0.00358746
$556$	−7.77213e12	−3.44908
$557$	−2.59415e12	−1.14195	−0.570975	−	0.820967i	$-0.693435\pi$
$557$	−2.59415e12	−1.14195	−0.570975	+	0.820967i	$0.693435\pi$
$558$	−4.55509e11	−0.198904
$559$	2.21677e10	0.00960212
$560$	−1.58183e12	−0.679696
$561$	5.24138e12	2.23415
$562$	−1.19769e12	−0.506443
$563$	3.87524e12	1.62559	0.812794	−	0.582551i	$-0.197945\pi$
$563$	3.87524e12	1.62559	0.812794	+	0.582551i	$0.197945\pi$
$564$	−2.57073e12	−1.06979
$565$	−2.20866e12	−0.911823
$566$	3.61145e12	1.47913
$567$	6.05306e11	0.245952
$568$	−7.84253e12	−3.16147
$569$	−4.49189e12	−1.79649	−0.898243	−	0.439500i	$-0.855156\pi$
$569$	−4.49189e12	−1.79649	−0.898243	+	0.439500i	$0.855156\pi$
$570$	−3.87502e12	−1.53758
$571$	1.36541e12	0.537527	0.268763	−	0.963206i	$-0.413385\pi$
$571$	1.36541e12	0.537527	0.268763	+	0.963206i	$0.413385\pi$
$572$	3.20051e12	1.25008
$573$	−1.81997e12	−0.705291
$574$	1.25772e12	0.483595
$575$	−5.35581e11	−0.204324
$576$	−4.27905e11	−0.161974
$577$	−1.23383e12	−0.463408	−0.231704	−	0.972786i	$-0.574430\pi$
$577$	−1.23383e12	−0.463408	−0.231704	+	0.972786i	$0.574430\pi$
$578$	4.28043e12	1.59519
$579$	−2.12676e12	−0.786437
$580$	9.66643e12	3.54683
$581$	1.87961e10	0.00684346
$582$	1.01353e12	0.366171
$583$	1.03693e13	3.71741
$584$	3.08759e12	1.09840
$585$	−1.77880e11	−0.0627950
$586$	3.71797e12	1.30247
$587$	4.13748e12	1.43835	0.719176	−	0.694828i	$-0.244520\pi$
$587$	4.13748e12	1.43835	0.719176	+	0.694828i	$0.244520\pi$
$588$	−8.29541e11	−0.286180
$589$	1.38184e12	0.473086
$590$	−3.46276e12	−1.17649
$591$	−2.44276e12	−0.823638
$592$	−3.31723e10	−0.0111001
$593$	−4.18821e12	−1.39086	−0.695428	−	0.718596i	$-0.744785\pi$
$593$	−4.18821e12	−1.39086	−0.695428	+	0.718596i	$0.744785\pi$
$594$	1.15582e13	3.80935
$595$	1.30558e12	0.427049
$596$	−1.42815e12	−0.463625
$597$	2.41797e12	0.779052
$598$	1.02074e12	0.326407
$599$	1.98063e12	0.628611	0.314306	−	0.949322i	$-0.398228\pi$
$599$	1.98063e12	0.628611	0.314306	+	0.949322i	$0.398228\pi$
$600$	2.12649e12	0.669857
$601$	−1.56144e12	−0.488191	−0.244095	−	0.969751i	$-0.578491\pi$
$601$	−1.56144e12	−0.488191	−0.244095	+	0.969751i	$0.578491\pi$
$602$	−7.71934e10	−0.0239550
$603$	−5.25952e11	−0.162001
$604$	7.77895e12	2.37823
$605$	7.27940e12	2.20900
$606$	7.25541e12	2.18542
$607$	−2.47993e12	−0.741465	−0.370732	−	0.928740i	$-0.620893\pi$
$607$	−2.47993e12	−0.741465	−0.370732	+	0.928740i	$0.620893\pi$
$608$	6.08144e12	1.80485
$609$	1.99639e12	0.588123
$610$	−9.59399e12	−2.80553
$611$	5.10242e11	0.148112
$612$	3.05999e12	0.881735
$613$	9.65163e11	0.276076	0.138038	−	0.990427i	$-0.455920\pi$
$613$	9.65163e11	0.276076	0.138038	+	0.990427i	$0.455920\pi$
$614$	8.36203e12	2.37440
$615$	1.74478e12	0.491815
$616$	−6.40505e12	−1.79230
$617$	7.49399e11	0.208176	0.104088	−	0.994568i	$-0.466808\pi$
$617$	7.49399e11	0.208176	0.104088	+	0.994568i	$0.466808\pi$
$618$	7.97795e12	2.20010
$619$	2.58762e12	0.708423	0.354212	−	0.935165i	$-0.384749\pi$
$619$	2.58762e12	0.708423	0.354212	+	0.935165i	$0.384749\pi$
$620$	2.83206e12	0.769734
$621$	2.58631e12	0.697860
$622$	−3.23212e12	−0.865828
$623$	−1.05826e12	−0.281446
$624$	−1.94853e12	−0.514490
$625$	−2.21693e12	−0.581155
$626$	−4.20145e12	−1.09349
$627$	−7.54379e12	−1.94933
$628$	3.26617e12	0.837954
$629$	2.73791e10	0.00697414
$630$	6.19422e11	0.156658
$631$	5.67671e11	0.142549	0.0712746	−	0.997457i	$-0.477293\pi$
$631$	5.67671e11	0.142549	0.0712746	+	0.997457i	$0.477293\pi$
$632$	1.05981e13	2.64240
$633$	−7.61696e11	−0.188567
$634$	−4.31646e12	−1.06102
$635$	−5.67512e12	−1.38514
$636$	−1.60300e13	−3.88487
$637$	1.64648e11	0.0396214
$638$	2.68218e13	6.40907
$639$	1.47651e12	0.350334
$640$	−1.50890e12	−0.355509
$641$	6.66948e12	1.56038	0.780191	−	0.625541i	$-0.215122\pi$
$641$	6.66948e12	1.56038	0.780191	+	0.625541i	$0.215122\pi$
$642$	7.99212e12	1.85675
$643$	−4.04542e12	−0.933285	−0.466643	−	0.884446i	$-0.654537\pi$
$643$	−4.04542e12	−0.933285	−0.466643	+	0.884446i	$0.654537\pi$
$644$	−2.49385e12	−0.571325
$645$	−1.07086e11	−0.0243622
$646$	−1.32308e13	−2.98910
$647$	−1.03670e12	−0.232587	−0.116293	−	0.993215i	$-0.537101\pi$
$647$	−1.03670e12	−0.232587	−0.116293	+	0.993215i	$0.537101\pi$
$648$	−7.22511e12	−1.60974
$649$	−6.74122e12	−1.49155
$650$	−7.34411e11	−0.161372
$651$	5.84902e11	0.127635
$652$	−6.93228e12	−1.50232
$653$	−4.28943e12	−0.923188	−0.461594	−	0.887091i	$-0.652722\pi$
$653$	−4.28943e12	−0.923188	−0.461594	+	0.887091i	$0.652722\pi$
$654$	8.06852e12	1.72462
$655$	−5.49175e11	−0.116580
$656$	−7.21787e12	−1.52175
$657$	−5.81298e11	−0.121718
$658$	−1.77679e12	−0.369504
$659$	−3.56971e12	−0.737308	−0.368654	−	0.929567i	$-0.620181\pi$
$659$	−3.56971e12	−0.737308	−0.368654	+	0.929567i	$0.620181\pi$
$660$	−1.54609e13	−3.17166
$661$	3.93426e12	0.801598	0.400799	−	0.916166i	$-0.368733\pi$
$661$	3.93426e12	0.801598	0.400799	+	0.916166i	$0.368733\pi$
$662$	−3.21097e12	−0.649794
$663$	1.60824e12	0.323251
$664$	−2.24356e11	−0.0447901
$665$	−1.87909e12	−0.372607
$666$	1.29897e10	0.00255839
$667$	6.00175e12	1.17412
$668$	7.63012e11	0.148265
$669$	1.41089e12	0.272318
$670$	4.66077e12	0.893554
$671$	−1.86774e13	−3.55684
$672$	2.57413e12	0.486932
$673$	7.94225e12	1.49237	0.746183	−	0.665740i	$-0.231884\pi$
$673$	7.94225e12	1.49237	0.746183	+	0.665740i	$0.231884\pi$
$674$	1.16920e12	0.218232
$675$	−1.86082e12	−0.345015
$676$	9.82028e11	0.180869
$677$	−1.99514e12	−0.365027	−0.182513	−	0.983203i	$-0.558423\pi$
$677$	−1.99514e12	−0.365027	−0.182513	+	0.983203i	$0.558423\pi$
$678$	9.47403e12	1.72187
$679$	4.91486e11	0.0887355
$680$	−1.55838e13	−2.79501
$681$	3.08440e12	0.549551
$682$	7.85823e12	1.39090
$683$	7.31175e12	1.28567	0.642833	−	0.766006i	$-0.277759\pi$
$683$	7.31175e12	1.28567	0.642833	+	0.766006i	$0.277759\pi$
$684$	−4.40416e12	−0.769327
$685$	−1.59045e12	−0.276001
$686$	−5.73347e11	−0.0988461
$687$	−5.79501e12	−0.992542
$688$	4.43001e11	0.0753801
$689$	3.18166e12	0.537857
$690$	−4.93094e12	−0.828149
$691$	1.01826e13	1.69906	0.849528	−	0.527544i	$-0.176887\pi$
$691$	1.01826e13	1.69906	0.849528	+	0.527544i	$0.176887\pi$
$692$	−1.61117e13	−2.67094
$693$	1.20588e12	0.198611
$694$	−8.50946e12	−1.39247
$695$	−7.45202e12	−1.21155
$696$	−2.38295e13	−3.84923
$697$	5.95734e12	0.956103
$698$	−2.77448e12	−0.442418
$699$	−1.36598e12	−0.216419
$700$	1.79430e12	0.282457
$701$	1.13009e13	1.76759	0.883797	−	0.467871i	$-0.154979\pi$
$701$	1.13009e13	1.76759	0.883797	+	0.467871i	$0.154979\pi$
$702$	3.54646e12	0.551160
$703$	−3.94060e10	−0.00608504
$704$	7.38202e12	1.13266
$705$	−2.46485e12	−0.375785
$706$	−1.26537e13	−1.91689
$707$	3.51833e12	0.529601
$708$	1.04213e13	1.55874
$709$	−1.08206e13	−1.60821	−0.804107	−	0.594485i	$-0.797356\pi$
$709$	−1.08206e13	−1.60821	−0.804107	+	0.594485i	$0.797356\pi$
$710$	−1.30842e13	−1.93234
$711$	−1.99529e12	−0.292815
$712$	1.26317e13	1.84204
$713$	1.75839e12	0.254807
$714$	−5.60029e12	−0.806433
$715$	3.06870e12	0.439113
$716$	2.02262e13	2.87611
$717$	2.79100e12	0.394387
$718$	9.55840e12	1.34222
$719$	−9.86894e12	−1.37718	−0.688590	−	0.725151i	$-0.741770\pi$
$719$	−9.86894e12	−1.37718	−0.688590	+	0.725151i	$0.741770\pi$
$720$	−3.55476e12	−0.492963
$721$	3.86871e12	0.533159
$722$	5.67609e12	0.777378
$723$	−1.11495e13	−1.51752
$724$	2.39488e13	3.23937
$725$	−4.31819e12	−0.580472
$726$	−3.12250e13	−4.17145
$727$	1.39733e13	1.85521	0.927606	−	0.373561i	$-0.121863\pi$
$727$	1.39733e13	1.85521	0.927606	+	0.373561i	$0.121863\pi$
$728$	−1.96529e12	−0.259320
$729$	8.41284e12	1.10324
$730$	5.15123e12	0.671363
$731$	−3.65635e11	−0.0473608
$732$	2.88735e13	3.71706
$733$	−5.01453e12	−0.641597	−0.320799	−	0.947147i	$-0.603951\pi$
$733$	−5.01453e12	−0.641597	−0.320799	+	0.947147i	$0.603951\pi$
$734$	−1.91134e13	−2.43056
$735$	−7.95375e11	−0.100526
$736$	7.73860e12	0.972102
$737$	9.07347e12	1.13284
$738$	2.82641e12	0.350736
$739$	1.61807e12	0.199571	0.0997855	−	0.995009i	$-0.468184\pi$
$739$	1.61807e12	0.199571	0.0997855	+	0.995009i	$0.468184\pi$
$740$	−8.07619e10	−0.00990065
$741$	−2.31470e12	−0.282041
$742$	−1.10793e13	−1.34183
$743$	−9.22713e12	−1.11075	−0.555376	−	0.831600i	$-0.687426\pi$
$743$	−9.22713e12	−1.11075	−0.555376	+	0.831600i	$0.687426\pi$
$744$	−6.98156e12	−0.835361
$745$	−1.36933e12	−0.162857
$746$	−1.93590e13	−2.28854
$747$	4.22394e10	0.00496335
$748$	−5.27894e13	−6.16580
$749$	3.87558e12	0.449954
$750$	1.47102e13	1.69763
$751$	1.18742e13	1.36215	0.681077	−	0.732212i	$-0.261512\pi$
$751$	1.18742e13	1.36215	0.681077	+	0.732212i	$0.261512\pi$
$752$	1.01967e13	1.16273
$753$	7.31699e12	0.829383
$754$	8.22986e12	0.927302
$755$	7.45856e12	0.835399
$756$	−8.66462e12	−0.964720
$757$	−1.24740e13	−1.38062	−0.690311	−	0.723513i	$-0.742526\pi$
$757$	−1.24740e13	−1.38062	−0.690311	+	0.723513i	$0.742526\pi$
$758$	8.43012e12	0.927518
$759$	−9.59944e12	−1.04992
$760$	2.24294e13	2.43869
$761$	−4.00014e11	−0.0432358	−0.0216179	−	0.999766i	$-0.506882\pi$
$761$	−4.00014e11	−0.0432358	−0.0216179	+	0.999766i	$0.506882\pi$
$762$	2.43434e13	2.61568
$763$	3.91263e12	0.417934
$764$	1.83301e13	1.94646
$765$	2.93396e12	0.309726
$766$	9.90698e11	0.103971
$767$	−2.06844e12	−0.215806
$768$	1.13259e13	1.17475
$769$	−2.75083e12	−0.283658	−0.141829	−	0.989891i	$-0.545298\pi$
$769$	−2.75083e12	−0.283658	−0.141829	+	0.989891i	$0.545298\pi$
$770$	−1.06860e13	−1.09548
$771$	2.25511e12	0.229838
$772$	2.14199e13	2.17040
$773$	−6.91331e11	−0.0696432	−0.0348216	−	0.999394i	$-0.511086\pi$
$773$	−6.91331e11	−0.0696432	−0.0348216	+	0.999394i	$0.511086\pi$
$774$	−1.73472e11	−0.0173738
$775$	−1.26514e12	−0.125974
$776$	−5.86653e12	−0.580769
$777$	−1.66796e10	−0.00164169
$778$	−1.94247e13	−1.90084
$779$	−8.57425e12	−0.834214
$780$	−4.74393e12	−0.458894
$781$	−2.54720e13	−2.44982
$782$	−1.68361e13	−1.60995
$783$	2.08525e13	1.98257
$784$	3.29035e12	0.311042
$785$	3.13165e12	0.294347
$786$	2.35568e12	0.220148
$787$	7.26241e11	0.0674830	0.0337415	−	0.999431i	$-0.489258\pi$
$787$	7.26241e11	0.0674830	0.0337415	+	0.999431i	$0.489258\pi$
$788$	2.46026e13	2.27307
$789$	8.93171e12	0.820518
$790$	1.76814e13	1.61508
$791$	4.59420e12	0.417268
$792$	−1.43937e13	−1.29990
$793$	−5.73086e12	−0.514625
$794$	9.32564e12	0.832696
$795$	−1.53698e13	−1.36463
$796$	−2.43530e13	−2.15002
$797$	7.48570e12	0.657158	0.328579	−	0.944476i	$-0.393430\pi$
$797$	7.48570e12	0.657158	0.328579	+	0.944476i	$0.393430\pi$
$798$	8.06036e12	0.703625
$799$	−8.41595e12	−0.730538
$800$	−5.56783e12	−0.480597
$801$	−2.37815e12	−0.204124
$802$	−2.85092e13	−2.43333
$803$	1.00283e13	0.851151
$804$	−1.40268e13	−1.18387
$805$	−2.39113e12	−0.200689
$806$	2.41118e12	0.201243
$807$	−3.63939e12	−0.302063
$808$	−4.19958e13	−3.46621
$809$	−1.07267e13	−0.880437	−0.440218	−	0.897891i	$-0.645099\pi$
$809$	−1.07267e13	−0.880437	−0.440218	+	0.897891i	$0.645099\pi$
$810$	−1.20541e13	−0.983905
$811$	−1.39897e13	−1.13557	−0.567786	−	0.823176i	$-0.692200\pi$
$811$	−1.39897e13	−1.13557	−0.567786	+	0.823176i	$0.692200\pi$
$812$	−2.01070e13	−1.62310
$813$	−1.24224e13	−0.997236
$814$	−2.24093e11	−0.0178903
$815$	−6.64677e12	−0.527717
$816$	3.21391e13	2.53763
$817$	5.26249e11	0.0413230
$818$	3.31646e13	2.58991
$819$	3.70005e11	0.0287362
$820$	−1.75728e13	−1.35731
$821$	−8.45248e12	−0.649292	−0.324646	−	0.945836i	$-0.605245\pi$
$821$	−8.45248e12	−0.649292	−0.324646	+	0.945836i	$0.605245\pi$
$822$	6.82221e12	0.521197
$823$	6.38827e12	0.485382	0.242691	−	0.970104i	$-0.421970\pi$
$823$	6.38827e12	0.485382	0.242691	+	0.970104i	$0.421970\pi$
$824$	−4.61780e13	−3.48950
$825$	6.90668e12	0.519071
$826$	7.20283e12	0.538385
$827$	1.49407e13	1.11070	0.555349	−	0.831617i	$-0.312585\pi$
$827$	1.49407e13	1.11070	0.555349	+	0.831617i	$0.312585\pi$
$828$	−5.60427e12	−0.414365
$829$	−9.83457e12	−0.723202	−0.361601	−	0.932333i	$-0.617770\pi$
$829$	−9.83457e12	−0.723202	−0.361601	+	0.932333i	$0.617770\pi$
$830$	−3.74308e11	−0.0273765
$831$	−8.83963e12	−0.643028
$832$	2.26506e12	0.163879
$833$	−2.71572e12	−0.195426
$834$	3.19654e13	2.28788
$835$	7.31586e11	0.0520807
$836$	7.59785e13	5.37975
$837$	6.10934e12	0.430259
$838$	2.34778e13	1.64460
$839$	1.92563e13	1.34167	0.670833	−	0.741608i	$-0.265937\pi$
$839$	1.92563e13	1.34167	0.670833	+	0.741608i	$0.265937\pi$
$840$	9.49383e12	0.657938
$841$	3.38828e13	2.33559
$842$	−2.01661e13	−1.38266
$843$	3.45604e12	0.235697
$844$	7.67154e12	0.520405
$845$	9.41582e11	0.0635335
$846$	−3.99287e12	−0.267990
$847$	−1.51418e13	−1.01088
$848$	6.35825e13	4.22237
$849$	−1.04212e13	−0.688386
$850$	1.21134e13	0.795942
$851$	−5.01439e10	−0.00327745
$852$	3.93775e13	2.56018
$853$	−2.73353e13	−1.76788	−0.883941	−	0.467598i	$-0.845119\pi$
$853$	−2.73353e13	−1.76788	−0.883941	+	0.467598i	$0.845119\pi$
$854$	1.99563e13	1.28387
$855$	−4.22277e12	−0.270240
$856$	−4.62600e13	−2.94492
$857$	2.91625e13	1.84676	0.923382	−	0.383881i	$-0.125413\pi$
$857$	2.91625e13	1.84676	0.923382	+	0.383881i	$0.125413\pi$
$858$	−1.31632e13	−0.829215
$859$	−9.86832e12	−0.618406	−0.309203	−	0.950996i	$-0.600062\pi$
$859$	−9.86832e12	−0.618406	−0.309203	+	0.950996i	$0.600062\pi$
$860$	1.07854e12	0.0672346
$861$	−3.62928e12	−0.225064
$862$	−1.04745e13	−0.646173
$863$	−1.26771e13	−0.777985	−0.388993	−	0.921241i	$-0.627177\pi$
$863$	−1.26771e13	−0.777985	−0.388993	+	0.921241i	$0.627177\pi$
$864$	2.68870e13	1.64146
$865$	−1.54481e13	−0.938216
$866$	−4.72714e12	−0.285607
$867$	−1.23516e13	−0.742397
$868$	−5.89093e12	−0.352245
$869$	3.44218e13	2.04760
$870$	−3.97564e13	−2.35272
$871$	2.78406e12	0.163907
$872$	−4.67023e13	−2.73536
$873$	1.10449e12	0.0643571
$874$	2.42318e13	1.40470
$875$	7.13334e12	0.411393
$876$	−1.55028e13	−0.889494
$877$	2.80233e13	1.59963	0.799817	−	0.600244i	$-0.204930\pi$
$877$	2.80233e13	1.59963	0.799817	+	0.600244i	$0.204930\pi$
$878$	−5.36984e12	−0.304955
$879$	−1.07286e13	−0.606166
$880$	6.13250e13	3.44719
$881$	−1.12496e13	−0.629135	−0.314568	−	0.949235i	$-0.601860\pi$
$881$	−1.12496e13	−0.629135	−0.314568	+	0.949235i	$0.601860\pi$
$882$	−1.28845e12	−0.0716900
$883$	6.74794e11	0.0373549	0.0186775	−	0.999826i	$-0.494054\pi$
$883$	6.74794e11	0.0373549	0.0186775	+	0.999826i	$0.494054\pi$
$884$	−1.61976e13	−0.892105
$885$	9.99211e12	0.547536
$886$	−5.20231e13	−2.83625
$887$	1.52798e13	0.828821	0.414410	−	0.910090i	$-0.363988\pi$
$887$	1.52798e13	0.828821	0.414410	+	0.910090i	$0.363988\pi$
$888$	1.99093e11	0.0107448
$889$	1.18047e13	0.633867
$890$	2.10742e13	1.12589
$891$	−2.34667e13	−1.24739
$892$	−1.42100e13	−0.751543
$893$	1.21129e13	0.637405
$894$	5.87375e12	0.307536
$895$	1.93931e13	1.01029
$896$	3.13864e12	0.162688
$897$	−2.94544e12	−0.151909
$898$	2.01240e12	0.103269
$899$	1.41773e13	0.723891
$900$	4.03221e12	0.204857
$901$	−5.24784e13	−2.65289
$902$	−4.87598e13	−2.45263
$903$	2.22749e11	0.0111486
$904$	−5.48377e13	−2.73100
$905$	2.29624e13	1.13789
$906$	−3.19935e13	−1.57755
$907$	−5.96609e12	−0.292723	−0.146362	−	0.989231i	$-0.546756\pi$
$907$	−5.96609e12	−0.292723	−0.146362	+	0.989231i	$0.546756\pi$
$908$	−3.10650e13	−1.51665
$909$	7.90653e12	0.384104
$910$	−3.27883e12	−0.158501
$911$	1.31326e13	0.631712	0.315856	−	0.948807i	$-0.397708\pi$
$911$	1.31326e13	0.631712	0.315856	+	0.948807i	$0.397708\pi$
$912$	−4.62571e13	−2.21412
$913$	−7.28694e11	−0.0347078
$914$	6.48725e13	3.07470
$915$	2.76843e13	1.30569
$916$	5.83654e13	2.73921
$917$	1.14233e12	0.0533494
$918$	−5.84954e13	−2.71850
$919$	−3.57823e13	−1.65481	−0.827405	−	0.561606i	$-0.810184\pi$
$919$	−3.57823e13	−1.65481	−0.827405	+	0.561606i	$0.810184\pi$
$920$	2.85413e13	1.31350
$921$	−2.41294e13	−1.10504
$922$	6.80522e13	3.10137
$923$	−7.81570e12	−0.354454
$924$	3.21599e13	1.45141
$925$	3.60780e10	0.00162033
$926$	−5.33316e13	−2.38361
$927$	8.69391e12	0.386684
$928$	6.23935e13	2.76168
$929$	−3.83566e12	−0.168954	−0.0844772	−	0.996425i	$-0.526922\pi$
$929$	−3.83566e12	−0.168954	−0.0844772	+	0.996425i	$0.526922\pi$
$930$	−1.16478e13	−0.510588
$931$	3.90867e12	0.170512
$932$	1.37577e13	0.597273
$933$	9.32659e12	0.402954
$934$	1.52827e13	0.657112
$935$	−5.06152e13	−2.16585
$936$	−4.41648e12	−0.188077
$937$	3.40750e13	1.44414	0.722068	−	0.691822i	$-0.243192\pi$
$937$	3.40750e13	1.44414	0.722068	+	0.691822i	$0.243192\pi$
$938$	−9.69478e12	−0.408908
$939$	1.21237e13	0.508907
$940$	2.48251e13	1.03709
$941$	4.31077e13	1.79226	0.896131	−	0.443789i	$-0.146366\pi$
$941$	4.31077e13	1.79226	0.896131	+	0.443789i	$0.146366\pi$
$942$	−1.34332e13	−0.555840
$943$	−1.09107e13	−0.449314
$944$	−4.13359e13	−1.69415
$945$	−8.30775e12	−0.338876
$946$	2.99266e12	0.121492
$947$	−2.52967e12	−0.102209	−0.0511046	−	0.998693i	$-0.516274\pi$
$947$	−2.52967e12	−0.102209	−0.0511046	+	0.998693i	$0.516274\pi$
$948$	−5.32130e13	−2.13984
$949$	3.07703e12	0.123150
$950$	−1.74345e13	−0.694471
$951$	1.24555e13	0.493799
$952$	3.24156e13	1.27905
$953$	−4.28646e13	−1.68337	−0.841686	−	0.539967i	$-0.818437\pi$
$953$	−4.28646e13	−1.68337	−0.841686	+	0.539967i	$0.818437\pi$
$954$	−2.48979e13	−0.973185
$955$	1.75752e13	0.683729
$956$	−2.81100e13	−1.08843
$957$	−7.73968e13	−2.98276
$958$	8.27892e13	3.17562
$959$	3.30826e12	0.126304
$960$	−1.09419e13	−0.415789
$961$	−2.22860e13	−0.842901
$962$	−6.87595e10	−0.00258848
$963$	8.70935e12	0.326338
$964$	1.12294e14	4.18805
$965$	2.05377e13	0.762394
$966$	1.02568e13	0.378977
$967$	6.30345e12	0.231825	0.115912	−	0.993259i	$-0.463021\pi$
$967$	6.30345e12	0.231825	0.115912	+	0.993259i	$0.463021\pi$
$968$	1.80737e14	6.61617
$969$	3.81787e13	1.39112
$970$	−9.78751e12	−0.354976
$971$	−6.75585e12	−0.243890	−0.121945	−	0.992537i	$-0.538913\pi$
$971$	−6.75585e12	−0.243890	−0.121945	+	0.992537i	$0.538913\pi$
$972$	−3.47537e13	−1.24883
$973$	1.55008e13	0.554431
$974$	−1.95671e13	−0.696645
$975$	2.11921e12	0.0751023
$976$	−1.14526e14	−4.03998
$977$	2.97208e13	1.04360	0.521802	−	0.853067i	$-0.325260\pi$
$977$	2.97208e13	1.04360	0.521802	+	0.853067i	$0.325260\pi$
$978$	2.85113e13	0.996533
$979$	4.10268e13	1.42740
$980$	8.01075e12	0.277431
$981$	8.79261e12	0.303115
$982$	−6.05586e13	−2.07814
$983$	−1.44667e12	−0.0494171	−0.0247086	−	0.999695i	$-0.507866\pi$
$983$	−1.44667e12	−0.0494171	−0.0247086	+	0.999695i	$0.507866\pi$
$984$	4.33201e13	1.47303
$985$	2.35893e13	0.798458
$986$	−1.35744e14	−4.57376
$987$	5.12709e12	0.171967
$988$	2.33128e13	0.778375
$989$	6.69649e11	0.0222569
$990$	−2.40139e13	−0.794520
$991$	−7.39505e12	−0.243562	−0.121781	−	0.992557i	$-0.538861\pi$
$991$	−7.39505e12	−0.243562	−0.121781	+	0.992557i	$0.538861\pi$
$992$	1.82800e13	0.599340
$993$	9.26555e12	0.302412
$994$	2.72162e13	0.884279
$995$	−2.33500e13	−0.755235
$996$	1.12650e12	0.0362713
$997$	−1.75280e13	−0.561828	−0.280914	−	0.959733i	$-0.590638\pi$
$997$	−1.75280e13	−0.561828	−0.280914	+	0.959733i	$0.590638\pi$
$998$	2.18928e13	0.698577
$999$	−1.74220e11	−0.00553418

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.d.1.14	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.d.1.14	✓	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)

\(f(q)\)	\(=\)	\(q+41.4230 q^{2} -119.530 q^{3} +1203.86 q^{4} +1154.28 q^{5} -4951.28 q^{6} -2401.00 q^{7} +28659.0 q^{8} -5395.62 q^{9} +O(q^{10})\)	\(q+41.4230 q^{2} -119.530 q^{3} +1203.86 q^{4} +1154.28 q^{5} -4951.28 q^{6} -2401.00 q^{7} +28659.0 q^{8} -5395.62 q^{9} +47813.7 q^{10} +93082.7 q^{11} -143898. q^{12} +28561.0 q^{13} -99456.6 q^{14} -137971. q^{15} +570765. q^{16} -471086. q^{17} -223503. q^{18} +678023. q^{19} +1.38960e6 q^{20} +286991. q^{21} +3.85576e6 q^{22} +862781. q^{23} -3.42561e6 q^{24} -620761. q^{25} +1.18308e6 q^{26} +2.99764e6 q^{27} -2.89048e6 q^{28} +6.95629e6 q^{29} -5.71517e6 q^{30} +2.03805e6 q^{31} +8.96936e6 q^{32} -1.11262e7 q^{33} -1.95138e7 q^{34} -2.77143e6 q^{35} -6.49559e6 q^{36} -58119.0 q^{37} +2.80857e7 q^{38} -3.41389e6 q^{39} +3.30806e7 q^{40} -1.26460e7 q^{41} +1.18880e7 q^{42} +776152. q^{43} +1.12059e8 q^{44} -6.22806e6 q^{45} +3.57390e7 q^{46} +1.78650e7 q^{47} -6.82235e7 q^{48} +5.76480e6 q^{49} -2.57138e7 q^{50} +5.63089e7 q^{51} +3.43835e7 q^{52} +1.11399e8 q^{53} +1.24171e8 q^{54} +1.07444e8 q^{55} -6.88104e7 q^{56} -8.10440e7 q^{57} +2.88150e8 q^{58} -7.24218e7 q^{59} -1.66098e8 q^{60} -2.00653e8 q^{61} +8.44220e7 q^{62} +1.29549e7 q^{63} +7.93060e7 q^{64} +3.29674e7 q^{65} -4.60879e8 q^{66} +9.74775e7 q^{67} -5.67124e8 q^{68} -1.03128e8 q^{69} -1.14801e8 q^{70} -2.73649e8 q^{71} -1.54633e8 q^{72} +1.07735e8 q^{73} -2.40746e6 q^{74} +7.41995e7 q^{75} +8.16247e8 q^{76} -2.23492e8 q^{77} -1.41414e8 q^{78} +3.69798e8 q^{79} +6.58823e8 q^{80} -2.52106e8 q^{81} -5.23833e8 q^{82} -7.82846e6 q^{83} +3.45498e8 q^{84} -5.43766e8 q^{85} +3.21505e7 q^{86} -8.31484e8 q^{87} +2.66766e9 q^{88} +4.40756e8 q^{89} -2.57985e8 q^{90} -6.85750e7 q^{91} +1.03867e9 q^{92} -2.43608e8 q^{93} +7.40021e8 q^{94} +7.82629e8 q^{95} -1.07211e9 q^{96} -2.04701e8 q^{97} +2.38795e8 q^{98} -5.02239e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 22 q^{2} + q^{3} + 6402 q^{4} + 1694 q^{5} + 4189 q^{6} - 36015 q^{7} - 1704 q^{8} + 160366 q^{9}+O(q^{10}) \) 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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