LMFDB - Embedded newform 91.10.a.d.1.11

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			1.11
Root			$25.4969$ 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)

$f(q)$	$=$	$q+26.4969 q^{2} -277.459 q^{3} +190.088 q^{4} +2398.86 q^{5} -7351.82 q^{6} -2401.00 q^{7} -8529.69 q^{8} +57300.7 q^{9} +O(q^{10})$	\(q+26.4969 q^{2} -277.459 q^{3} +190.088 q^{4} +2398.86 q^{5} -7351.82 q^{6} -2401.00 q^{7} -8529.69 q^{8} +57300.7 q^{9} +63562.4 q^{10} -76819.0 q^{11} -52741.6 q^{12} +28561.0 q^{13} -63619.2 q^{14} -665585. q^{15} -323336. q^{16} -291393. q^{17} +1.51829e6 q^{18} +459049. q^{19} +455993. q^{20} +666180. q^{21} -2.03547e6 q^{22} +711333. q^{23} +2.36664e6 q^{24} +3.80139e6 q^{25} +756779. q^{26} -1.04374e7 q^{27} -456401. q^{28} +2.48029e6 q^{29} -1.76360e7 q^{30} -108503. q^{31} -4.20020e6 q^{32} +2.13141e7 q^{33} -7.72103e6 q^{34} -5.75966e6 q^{35} +1.08922e7 q^{36} +1.04971e7 q^{37} +1.21634e7 q^{38} -7.92452e6 q^{39} -2.04615e7 q^{40} +2.35016e7 q^{41} +1.76517e7 q^{42} +1.77396e7 q^{43} -1.46024e7 q^{44} +1.37456e8 q^{45} +1.88482e7 q^{46} +2.24965e7 q^{47} +8.97125e7 q^{48} +5.76480e6 q^{49} +1.00725e8 q^{50} +8.08498e7 q^{51} +5.42910e6 q^{52} +2.78805e7 q^{53} -2.76558e8 q^{54} -1.84278e8 q^{55} +2.04798e7 q^{56} -1.27368e8 q^{57} +6.57201e7 q^{58} +9.28208e7 q^{59} -1.26520e8 q^{60} -1.75471e7 q^{61} -2.87500e6 q^{62} -1.37579e8 q^{63} +5.42553e7 q^{64} +6.85137e7 q^{65} +5.64760e8 q^{66} +7.32976e7 q^{67} -5.53903e7 q^{68} -1.97366e8 q^{69} -1.52613e8 q^{70} +3.79736e8 q^{71} -4.88757e8 q^{72} -2.09156e8 q^{73} +2.78141e8 q^{74} -1.05473e9 q^{75} +8.72597e7 q^{76} +1.84442e8 q^{77} -2.09975e8 q^{78} -2.44184e8 q^{79} -7.75636e8 q^{80} +1.76810e9 q^{81} +6.22721e8 q^{82} -3.43460e8 q^{83} +1.26633e8 q^{84} -6.99011e8 q^{85} +4.70045e8 q^{86} -6.88179e8 q^{87} +6.55242e8 q^{88} -5.92819e8 q^{89} +3.64217e9 q^{90} -6.85750e7 q^{91} +1.35216e8 q^{92} +3.01052e7 q^{93} +5.96089e8 q^{94} +1.10119e9 q^{95} +1.16539e9 q^{96} +7.56337e7 q^{97} +1.52750e8 q^{98} -4.40178e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	26.4969	1.17101	0.585505	−	0.810669i	$-0.300896\pi$
$2$	26.4969	1.17101	0.585505	+	0.810669i	$0.300896\pi$
$3$	−277.459	−1.97767	−0.988835	−	0.149017i	$-0.952389\pi$
$3$	−277.459	−1.97767	−0.988835	+	0.149017i	$0.952389\pi$
$4$	190.088	0.371265
$5$	2398.86	1.71648	0.858241	−	0.513247i	$-0.171557\pi$
$5$	2398.86	1.71648	0.858241	+	0.513247i	$0.171557\pi$
$6$	−7351.82	−2.31587
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	−8529.69	−0.736255
$9$	57300.7	2.91118
$10$	63562.4	2.01002
$11$	−76819.0	−1.58198	−0.790991	−	0.611828i	$-0.790435\pi$
$11$	−76819.0	−1.58198	−0.790991	+	0.611828i	$0.790435\pi$
$12$	−52741.6	−0.734240
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	−63619.2	−0.442600
$15$	−665585.	−3.39463
$16$	−323336.	−1.23343
$17$	−291393.	−0.846174	−0.423087	−	0.906089i	$-0.639053\pi$
$17$	−291393.	−0.846174	−0.423087	+	0.906089i	$0.639053\pi$
$18$	1.51829e6	3.40902
$19$	459049.	0.808106	0.404053	−	0.914736i	$-0.367601\pi$
$19$	459049.	0.808106	0.404053	+	0.914736i	$0.367601\pi$
$20$	455993.	0.637270
$21$	666180.	0.747489
$22$	−2.03547e6	−1.85252
$23$	711333.	0.530027	0.265013	−	0.964245i	$-0.414624\pi$
$23$	711333.	0.530027	0.265013	+	0.964245i	$0.414624\pi$
$24$	2.36664e6	1.45607
$25$	3.80139e6	1.94631
$26$	756779.	0.324780
$27$	−1.04374e7	−3.77967
$28$	−456401.	−0.140325
$29$	2.48029e6	0.651195	0.325598	−	0.945508i	$-0.394435\pi$
$29$	2.48029e6	0.651195	0.325598	+	0.945508i	$0.394435\pi$
$30$	−1.76360e7	−3.97515
$31$	−108503.	−0.0211015	−0.0105508	−	0.999944i	$-0.503358\pi$
$31$	−108503.	−0.0211015	−0.0105508	+	0.999944i	$0.503358\pi$
$32$	−4.20020e6	−0.708101
$33$	2.13141e7	3.12864
$34$	−7.72103e6	−0.990878
$35$	−5.75966e6	−0.648769
$36$	1.08922e7	1.08082
$37$	1.04971e7	0.920792	0.460396	−	0.887714i	$-0.347707\pi$
$37$	1.04971e7	0.920792	0.460396	+	0.887714i	$0.347707\pi$
$38$	1.21634e7	0.946300
$39$	−7.92452e6	−0.548507
$40$	−2.04615e7	−1.26377
$41$	2.35016e7	1.29888	0.649442	−	0.760411i	$-0.275003\pi$
$41$	2.35016e7	1.29888	0.649442	+	0.760411i	$0.275003\pi$
$42$	1.76517e7	0.875317
$43$	1.77396e7	0.791291	0.395645	−	0.918403i	$-0.370521\pi$
$43$	1.77396e7	0.791291	0.395645	+	0.918403i	$0.370521\pi$
$44$	−1.46024e7	−0.587335
$45$	1.37456e8	4.99698
$46$	1.88482e7	0.620667
$47$	2.24965e7	0.672474	0.336237	−	0.941777i	$-0.390846\pi$
$47$	2.24965e7	0.672474	0.336237	+	0.941777i	$0.390846\pi$
$48$	8.97125e7	2.43931
$49$	5.76480e6	0.142857
$50$	1.00725e8	2.27915
$51$	8.08498e7	1.67345
$52$	5.42910e6	0.102970
$53$	2.78805e7	0.485354	0.242677	−	0.970107i	$-0.421975\pi$
$53$	2.78805e7	0.485354	0.242677	+	0.970107i	$0.421975\pi$
$54$	−2.76558e8	−4.42604
$55$	−1.84278e8	−2.71544
$56$	2.04798e7	0.278278
$57$	−1.27368e8	−1.59817
$58$	6.57201e7	0.762556
$59$	9.28208e7	0.997266	0.498633	−	0.866813i	$-0.333836\pi$
$59$	9.28208e7	0.997266	0.498633	+	0.866813i	$0.333836\pi$
$60$	−1.26520e8	−1.26031
$61$	−1.75471e7	−0.162264	−0.0811319	−	0.996703i	$-0.525854\pi$
$61$	−1.75471e7	−0.162264	−0.0811319	+	0.996703i	$0.525854\pi$
$62$	−2.87500e6	−0.0247101
$63$	−1.37579e8	−1.10032
$64$	5.42553e7	0.404233
$65$	6.85137e7	0.476067
$66$	5.64760e8	3.66367
$67$	7.32976e7	0.444379	0.222189	−	0.975004i	$-0.428680\pi$
$67$	7.32976e7	0.444379	0.222189	+	0.975004i	$0.428680\pi$
$68$	−5.53903e7	−0.314155
$69$	−1.97366e8	−1.04822
$70$	−1.52613e8	−0.759716
$71$	3.79736e8	1.77345	0.886726	−	0.462295i	$-0.152974\pi$
$71$	3.79736e8	1.77345	0.886726	+	0.462295i	$0.152974\pi$
$72$	−4.88757e8	−2.14337
$73$	−2.09156e8	−0.862022	−0.431011	−	0.902347i	$-0.641843\pi$
$73$	−2.09156e8	−0.862022	−0.431011	+	0.902347i	$0.641843\pi$
$74$	2.78141e8	1.07826
$75$	−1.05473e9	−3.84916
$76$	8.72597e7	0.300022
$77$	1.84442e8	0.597933
$78$	−2.09975e8	−0.642307
$79$	−2.44184e8	−0.705335	−0.352667	−	0.935749i	$-0.614725\pi$
$79$	−2.44184e8	−0.705335	−0.352667	+	0.935749i	$0.614725\pi$
$80$	−7.75636e8	−2.11716
$81$	1.76810e9	4.56377
$82$	6.22721e8	1.52101
$83$	−3.43460e8	−0.794372	−0.397186	−	0.917738i	$-0.630013\pi$
$83$	−3.43460e8	−0.794372	−0.397186	+	0.917738i	$0.630013\pi$
$84$	1.26633e8	0.277517
$85$	−6.99011e8	−1.45244
$86$	4.70045e8	0.926610
$87$	−6.88179e8	−1.28785
$88$	6.55242e8	1.16474
$89$	−5.92819e8	−1.00154	−0.500769	−	0.865581i	$-0.666949\pi$
$89$	−5.92819e8	−1.00154	−0.500769	+	0.865581i	$0.666949\pi$
$90$	3.64217e9	5.85152
$91$	−6.85750e7	−0.104828
$92$	1.35216e8	0.196781
$93$	3.01052e7	0.0417319
$94$	5.96089e8	0.787474
$95$	1.10119e9	1.38710
$96$	1.16539e9	1.40039
$97$	7.56337e7	0.0867446	0.0433723	−	0.999059i	$-0.486190\pi$
$97$	7.56337e7	0.0867446	0.0433723	+	0.999059i	$0.486190\pi$
$98$	1.52750e8	0.167287
$99$	−4.40178e9	−4.60543
$100$	7.22598e8	0.722598
$101$	−6.85104e8	−0.655104	−0.327552	−	0.944833i	$-0.606224\pi$
$101$	−6.85104e8	−0.655104	−0.327552	+	0.944833i	$0.606224\pi$
$102$	2.14227e9	1.95963
$103$	6.50294e8	0.569302	0.284651	−	0.958631i	$-0.408122\pi$
$103$	6.50294e8	0.569302	0.284651	+	0.958631i	$0.408122\pi$
$104$	−2.43616e8	−0.204200
$105$	1.59807e9	1.28305
$106$	7.38747e8	0.568354
$107$	−5.07743e8	−0.374470	−0.187235	−	0.982315i	$-0.559953\pi$
$107$	−5.07743e8	−0.374470	−0.187235	+	0.982315i	$0.559953\pi$
$108$	−1.98402e9	−1.40326
$109$	1.50664e9	1.02233	0.511164	−	0.859483i	$-0.329215\pi$
$109$	1.50664e9	1.02233	0.511164	+	0.859483i	$0.329215\pi$
$110$	−4.88280e9	−3.17981
$111$	−2.91252e9	−1.82102
$112$	7.76329e8	0.466192
$113$	1.80858e9	1.04348	0.521740	−	0.853105i	$-0.325283\pi$
$113$	1.80858e9	1.04348	0.521740	+	0.853105i	$0.325283\pi$
$114$	−3.37485e9	−1.87147
$115$	1.70639e9	0.909782
$116$	4.71473e8	0.241766
$117$	1.63656e9	0.807415
$118$	2.45947e9	1.16781
$119$	6.99635e8	0.319824
$120$	5.67723e9	2.49932
$121$	3.54321e9	1.50267
$122$	−4.64945e8	−0.190013
$123$	−6.52074e9	−2.56876
$124$	−2.06251e7	−0.00783427
$125$	4.43372e9	1.62433
$126$	−3.64542e9	−1.28849
$127$	−1.90701e9	−0.650482	−0.325241	−	0.945631i	$-0.605445\pi$
$127$	−1.90701e9	−0.650482	−0.325241	+	0.945631i	$0.605445\pi$
$128$	3.58810e9	1.18146
$129$	−4.92202e9	−1.56491
$130$	1.81540e9	0.557479
$131$	−2.39027e9	−0.709130	−0.354565	−	0.935031i	$-0.615371\pi$
$131$	−2.39027e9	−0.709130	−0.354565	+	0.935031i	$0.615371\pi$
$132$	4.05156e9	1.16155
$133$	−1.10218e9	−0.305435
$134$	1.94216e9	0.520372
$135$	−2.50378e10	−6.48774
$136$	2.48549e9	0.622999
$137$	1.84094e9	0.446474	0.223237	−	0.974764i	$-0.428338\pi$
$137$	1.84094e9	0.446474	0.223237	+	0.974764i	$0.428338\pi$
$138$	−5.22960e9	−1.22747
$139$	8.26362e9	1.87760	0.938802	−	0.344457i	$-0.111937\pi$
$139$	8.26362e9	1.87760	0.938802	+	0.344457i	$0.111937\pi$
$140$	−1.09484e9	−0.240865
$141$	−6.24187e9	−1.32993
$142$	1.00618e10	2.07673
$143$	−2.19403e9	−0.438763
$144$	−1.85273e10	−3.59072
$145$	5.94986e9	1.11777
$146$	−5.54200e9	−1.00944
$147$	−1.59950e9	−0.282524
$148$	1.99537e9	0.341858
$149$	2.80217e9	0.465754	0.232877	−	0.972506i	$-0.425186\pi$
$149$	2.80217e9	0.465754	0.232877	+	0.972506i	$0.425186\pi$
$150$	−2.79471e10	−4.50741
$151$	2.12154e9	0.332089	0.166044	−	0.986118i	$-0.446901\pi$
$151$	2.12154e9	0.332089	0.166044	+	0.986118i	$0.446901\pi$
$152$	−3.91555e9	−0.594972
$153$	−1.66970e10	−2.46336
$154$	4.88716e9	0.700186
$155$	−2.60283e8	−0.0362204
$156$	−1.50635e9	−0.203642
$157$	−1.32649e10	−1.74243	−0.871217	−	0.490899i	$-0.836669\pi$
$157$	−1.32649e10	−1.74243	−0.871217	+	0.490899i	$0.836669\pi$
$158$	−6.47013e9	−0.825954
$159$	−7.73569e9	−0.959869
$160$	−1.00757e10	−1.21544
$161$	−1.70791e9	−0.200331
$162$	4.68492e10	5.34422
$163$	1.20868e10	1.34112	0.670561	−	0.741855i	$-0.266054\pi$
$163$	1.20868e10	1.34112	0.670561	+	0.741855i	$0.266054\pi$
$164$	4.46737e9	0.482231
$165$	5.11296e10	5.37025
$166$	−9.10063e9	−0.930218
$167$	8.10121e9	0.805983	0.402992	−	0.915204i	$-0.367970\pi$
$167$	8.10121e9	0.805983	0.402992	+	0.915204i	$0.367970\pi$
$168$	−5.68231e9	−0.550342
$169$	8.15731e8	0.0769231
$170$	−1.85216e10	−1.70082
$171$	2.63038e10	2.35254
$172$	3.37208e9	0.293779
$173$	6.17802e9	0.524375	0.262187	−	0.965017i	$-0.415556\pi$
$173$	6.17802e9	0.524375	0.262187	+	0.965017i	$0.415556\pi$
$174$	−1.82346e10	−1.50808
$175$	−9.12713e9	−0.735636
$176$	2.48383e10	1.95126
$177$	−2.57540e10	−1.97226
$178$	−1.57079e10	−1.17281
$179$	8.89717e9	0.647759	0.323879	−	0.946098i	$-0.395013\pi$
$179$	8.89717e9	0.647759	0.323879	+	0.946098i	$0.395013\pi$
$180$	2.61287e10	1.85521
$181$	1.03368e10	0.715868	0.357934	−	0.933747i	$-0.383481\pi$
$181$	1.03368e10	0.715868	0.357934	+	0.933747i	$0.383481\pi$
$182$	−1.81703e9	−0.122755
$183$	4.86862e9	0.320904
$184$	−6.06745e9	−0.390235
$185$	2.51810e10	1.58052
$186$	7.97695e8	0.0488685
$187$	2.23845e10	1.33863
$188$	4.27632e9	0.249666
$189$	2.50601e10	1.42858
$190$	2.91783e10	1.62431
$191$	1.12240e9	0.0610238	0.0305119	−	0.999534i	$-0.490286\pi$
$191$	1.12240e9	0.0610238	0.0305119	+	0.999534i	$0.490286\pi$
$192$	−1.50536e10	−0.799440
$193$	−1.30436e10	−0.676692	−0.338346	−	0.941022i	$-0.609867\pi$
$193$	−1.30436e10	−0.676692	−0.338346	+	0.941022i	$0.609867\pi$
$194$	2.00406e9	0.101579
$195$	−1.90098e10	−0.941502
$196$	1.09582e9	0.0530379
$197$	2.00026e10	0.946212	0.473106	−	0.881005i	$-0.343133\pi$
$197$	2.00026e10	0.946212	0.473106	+	0.881005i	$0.343133\pi$
$198$	−1.16634e11	−5.39300
$199$	−1.18798e10	−0.536995	−0.268497	−	0.963280i	$-0.586527\pi$
$199$	−1.18798e10	−0.536995	−0.268497	+	0.963280i	$0.586527\pi$
$200$	−3.24247e10	−1.43298
$201$	−2.03371e10	−0.878834
$202$	−1.81532e10	−0.767134
$203$	−5.95517e9	−0.246129
$204$	1.53686e10	0.621294
$205$	5.63770e10	2.22951
$206$	1.72308e10	0.666658
$207$	4.07599e10	1.54300
$208$	−9.23479e9	−0.342091
$209$	−3.52637e10	−1.27841
$210$	4.23440e10	1.50247
$211$	−3.92872e10	−1.36452	−0.682260	−	0.731110i	$-0.739003\pi$
$211$	−3.92872e10	−1.36452	−0.682260	+	0.731110i	$0.739003\pi$
$212$	5.29973e9	0.180195
$213$	−1.05361e11	−3.50730
$214$	−1.34536e10	−0.438508
$215$	4.25548e10	1.35824
$216$	8.90275e10	2.78280
$217$	2.60516e8	0.00797563
$218$	3.99213e10	1.19716
$219$	5.80324e10	1.70479
$220$	−3.50290e10	−1.00815
$221$	−8.32248e9	−0.234686
$222$	−7.71728e10	−2.13244
$223$	−6.01989e10	−1.63011	−0.815054	−	0.579384i	$-0.803293\pi$
$223$	−6.01989e10	−1.63011	−0.815054	+	0.579384i	$0.803293\pi$
$224$	1.00847e10	0.267637
$225$	2.17822e11	5.66605
$226$	4.79217e10	1.22192
$227$	−4.01885e10	−1.00458	−0.502291	−	0.864699i	$-0.667509\pi$
$227$	−4.01885e10	−1.00458	−0.502291	+	0.864699i	$0.667509\pi$
$228$	−2.42110e10	−0.593344
$229$	−1.10241e10	−0.264900	−0.132450	−	0.991190i	$-0.542284\pi$
$229$	−1.10241e10	−0.264900	−0.132450	+	0.991190i	$0.542284\pi$
$230$	4.52140e10	1.06536
$231$	−5.11753e10	−1.18251
$232$	−2.11561e10	−0.479446
$233$	−1.12011e10	−0.248977	−0.124489	−	0.992221i	$-0.539729\pi$
$233$	−1.12011e10	−0.248977	−0.124489	+	0.992221i	$0.539729\pi$
$234$	4.33640e10	0.945491
$235$	5.39660e10	1.15429
$236$	1.76441e10	0.370250
$237$	6.77511e10	1.39492
$238$	1.85382e10	0.374517
$239$	−7.26906e10	−1.44108	−0.720540	−	0.693414i	$-0.756106\pi$
$239$	−7.26906e10	−1.44108	−0.720540	+	0.693414i	$0.756106\pi$
$240$	2.15207e11	4.18703
$241$	2.78685e10	0.532154	0.266077	−	0.963952i	$-0.414272\pi$
$241$	2.78685e10	0.532154	0.266077	+	0.963952i	$0.414272\pi$
$242$	9.38842e10	1.75964
$243$	−2.85136e11	−5.24595
$244$	−3.33550e9	−0.0602429
$245$	1.38289e10	0.245212
$246$	−1.72780e11	−3.00805
$247$	1.31109e10	0.224128
$248$	9.25497e8	0.0155361
$249$	9.52960e10	1.57101
$250$	1.17480e11	1.90210
$251$	−7.50781e10	−1.19394	−0.596968	−	0.802265i	$-0.703628\pi$
$251$	−7.50781e10	−1.19394	−0.596968	+	0.802265i	$0.703628\pi$
$252$	−2.61521e10	−0.408511
$253$	−5.46439e10	−0.838493
$254$	−5.05298e10	−0.761721
$255$	1.93947e11	2.87245
$256$	6.72950e10	0.979272
$257$	−9.16533e10	−1.31054	−0.655268	−	0.755396i	$-0.727444\pi$
$257$	−9.16533e10	−1.31054	−0.655268	+	0.755396i	$0.727444\pi$
$258$	−1.30418e11	−1.83253
$259$	−2.52035e10	−0.348027
$260$	1.30236e10	0.176747
$261$	1.42122e11	1.89574
$262$	−6.33348e10	−0.830398
$263$	4.94093e10	0.636807	0.318404	−	0.947955i	$-0.396853\pi$
$263$	4.94093e10	0.636807	0.318404	+	0.947955i	$0.396853\pi$
$264$	−1.81803e11	−2.30347
$265$	6.68812e10	0.833101
$266$	−2.92043e10	−0.357668
$267$	1.64483e11	1.98071
$268$	1.39330e10	0.164982
$269$	−1.57496e10	−0.183394	−0.0916968	−	0.995787i	$-0.529229\pi$
$269$	−1.57496e10	−0.183394	−0.0916968	+	0.995787i	$0.529229\pi$
$270$	−6.63424e11	−7.59721
$271$	1.36371e11	1.53589	0.767946	−	0.640514i	$-0.221279\pi$
$271$	1.36371e11	1.53589	0.767946	+	0.640514i	$0.221279\pi$
$272$	9.42178e10	1.04369
$273$	1.90268e10	0.207316
$274$	4.87792e10	0.522826
$275$	−2.92019e11	−3.07903
$276$	−3.75169e10	−0.389167
$277$	4.56765e10	0.466159	0.233079	−	0.972458i	$-0.425120\pi$
$277$	4.56765e10	0.466159	0.233079	+	0.972458i	$0.425120\pi$
$278$	2.18961e11	2.19869
$279$	−6.21730e9	−0.0614303
$280$	4.91281e10	0.477660
$281$	−1.26483e11	−1.21019	−0.605095	−	0.796153i	$-0.706865\pi$
$281$	−1.26483e11	−1.21019	−0.605095	+	0.796153i	$0.706865\pi$
$282$	−1.65391e11	−1.55736
$283$	1.06887e11	0.990572	0.495286	−	0.868730i	$-0.335063\pi$
$283$	1.06887e11	0.990572	0.495286	+	0.868730i	$0.335063\pi$
$284$	7.21832e10	0.658421
$285$	−3.05537e11	−2.74322
$286$	−5.81350e10	−0.513796
$287$	−5.64274e10	−0.490932
$288$	−2.40674e11	−2.06141
$289$	−3.36778e10	−0.283990
$290$	1.57653e11	1.30891
$291$	−2.09853e10	−0.171552
$292$	−3.97581e10	−0.320039
$293$	1.88608e11	1.49505	0.747525	−	0.664234i	$-0.231242\pi$
$293$	1.88608e11	1.49505	0.747525	+	0.664234i	$0.231242\pi$
$294$	−4.23818e10	−0.330839
$295$	2.22664e11	1.71179
$296$	−8.95370e10	−0.677938
$297$	8.01789e11	5.97938
$298$	7.42489e10	0.545402
$299$	2.03164e10	0.147003
$300$	−2.00491e11	−1.42906
$301$	−4.25928e10	−0.299080
$302$	5.62142e10	0.388879
$303$	1.90089e11	1.29558
$304$	−1.48427e11	−0.996740
$305$	−4.20931e10	−0.278523
$306$	−4.42420e11	−2.88462
$307$	−1.56897e11	−1.00807	−0.504035	−	0.863683i	$-0.668152\pi$
$307$	−1.56897e11	−1.00807	−0.504035	+	0.863683i	$0.668152\pi$
$308$	3.50603e10	0.221992
$309$	−1.80430e11	−1.12589
$310$	−6.89671e9	−0.0424145
$311$	3.09817e11	1.87795	0.938974	−	0.343989i	$-0.111778\pi$
$311$	3.09817e11	1.87795	0.938974	+	0.343989i	$0.111778\pi$
$312$	6.75936e10	0.403841
$313$	7.61815e10	0.448642	0.224321	−	0.974515i	$-0.427984\pi$
$313$	7.61815e10	0.448642	0.224321	+	0.974515i	$0.427984\pi$
$314$	−3.51480e11	−2.04041
$315$	−3.30032e11	−1.88868
$316$	−4.64164e10	−0.261866
$317$	−1.55190e11	−0.863170	−0.431585	−	0.902072i	$-0.642046\pi$
$317$	−1.55190e11	−0.863170	−0.431585	+	0.902072i	$0.642046\pi$
$318$	−2.04972e11	−1.12402
$319$	−1.90533e11	−1.03018
$320$	1.30151e11	0.693859
$321$	1.40878e11	0.740578
$322$	−4.52544e10	−0.234590
$323$	−1.33764e11	−0.683798
$324$	3.36094e11	1.69437
$325$	1.08571e11	0.539810
$326$	3.20264e11	1.57047
$327$	−4.18031e11	−2.02183
$328$	−2.00461e11	−0.956310
$329$	−5.40142e10	−0.254171
$330$	1.35478e12	6.28862
$331$	−3.05827e10	−0.140039	−0.0700195	−	0.997546i	$-0.522306\pi$
$331$	−3.05827e10	−0.140039	−0.0700195	+	0.997546i	$0.522306\pi$
$332$	−6.52875e10	−0.294923
$333$	6.01491e11	2.68059
$334$	2.14657e11	0.943814
$335$	1.75831e11	0.762768
$336$	−2.15400e11	−0.921973
$337$	−2.62984e11	−1.11070	−0.555348	−	0.831618i	$-0.687415\pi$
$337$	−2.62984e11	−1.11070	−0.555348	+	0.831618i	$0.687415\pi$
$338$	2.16144e10	0.0900777
$339$	−5.01806e11	−2.06366
$340$	−1.32873e11	−0.539241
$341$	8.33509e9	0.0333823
$342$	6.96971e11	2.75485
$343$	−1.38413e10	−0.0539949
$344$	−1.51313e11	−0.582592
$345$	−4.73453e11	−1.79925
$346$	1.63699e11	0.614048
$347$	1.11251e11	0.411928	0.205964	−	0.978560i	$-0.433967\pi$
$347$	1.11251e11	0.411928	0.205964	+	0.978560i	$0.433967\pi$
$348$	−1.30814e11	−0.478134
$349$	3.04891e11	1.10009	0.550047	−	0.835134i	$-0.314610\pi$
$349$	3.04891e11	1.10009	0.550047	+	0.835134i	$0.314610\pi$
$350$	−2.41841e11	−0.861438
$351$	−2.98102e11	−1.04829
$352$	3.22655e11	1.12020
$353$	−5.08802e11	−1.74407	−0.872033	−	0.489448i	$-0.837198\pi$
$353$	−5.08802e11	−1.74407	−0.872033	+	0.489448i	$0.837198\pi$
$354$	−6.82402e11	−2.30954
$355$	9.10933e11	3.04410
$356$	−1.12688e11	−0.371836
$357$	−1.94120e11	−0.632505
$358$	2.35748e11	0.758532
$359$	4.65758e11	1.47991	0.739955	−	0.672656i	$-0.234847\pi$
$359$	4.65758e11	1.47991	0.739955	+	0.672656i	$0.234847\pi$
$360$	−1.17246e12	−3.67905
$361$	−1.11961e11	−0.346965
$362$	2.73894e11	0.838289
$363$	−9.83097e11	−2.97178
$364$	−1.30353e10	−0.0389192
$365$	−5.01736e11	−1.47964
$366$	1.29003e11	0.375782
$367$	3.53772e11	1.01795	0.508975	−	0.860781i	$-0.330024\pi$
$367$	3.53772e11	1.01795	0.508975	+	0.860781i	$0.330024\pi$
$368$	−2.29999e11	−0.653750
$369$	1.34666e12	3.78128
$370$	6.67220e11	1.85081
$371$	−6.69410e10	−0.183447
$372$	5.72263e9	0.0154936
$373$	2.71566e11	0.726415	0.363208	−	0.931708i	$-0.381682\pi$
$373$	2.71566e11	0.726415	0.363208	+	0.931708i	$0.381682\pi$
$374$	5.93122e11	1.56755
$375$	−1.23018e12	−3.21238
$376$	−1.91888e11	−0.495112
$377$	7.08395e10	0.180609
$378$	6.64017e11	1.67288
$379$	2.57514e11	0.641097	0.320548	−	0.947232i	$-0.396133\pi$
$379$	2.57514e11	0.641097	0.320548	+	0.947232i	$0.396133\pi$
$380$	2.09324e11	0.514982
$381$	5.29116e11	1.28644
$382$	2.97403e10	0.0714595
$383$	6.05972e10	0.143899	0.0719496	−	0.997408i	$-0.477078\pi$
$383$	6.05972e10	0.143899	0.0719496	+	0.997408i	$0.477078\pi$
$384$	−9.95553e11	−2.33654
$385$	4.42451e11	1.02634
$386$	−3.45617e11	−0.792413
$387$	1.01649e12	2.30359
$388$	1.43770e10	0.0322053
$389$	1.65406e11	0.366250	0.183125	−	0.983090i	$-0.441379\pi$
$389$	1.65406e11	0.366250	0.183125	+	0.983090i	$0.441379\pi$
$390$	−5.03701e11	−1.10251
$391$	−2.07278e11	−0.448495
$392$	−4.91720e10	−0.105179
$393$	6.63202e11	1.40242
$394$	5.30008e11	1.10802
$395$	−5.85762e11	−1.21069
$396$	−8.36725e11	−1.70984
$397$	−4.13695e11	−0.835840	−0.417920	−	0.908484i	$-0.637241\pi$
$397$	−4.13695e11	−0.835840	−0.417920	+	0.908484i	$0.637241\pi$
$398$	−3.14778e11	−0.628827
$399$	3.05810e11	0.604050
$400$	−1.22912e12	−2.40063
$401$	5.58295e11	1.07824	0.539118	−	0.842230i	$-0.318758\pi$
$401$	5.58295e11	1.07824	0.539118	+	0.842230i	$0.318758\pi$
$402$	−5.38871e11	−1.02912
$403$	−3.09895e9	−0.00585252
$404$	−1.30230e11	−0.243217
$405$	4.24141e12	7.83363
$406$	−1.57794e11	−0.288219
$407$	−8.06377e11	−1.45668
$408$	−6.89623e11	−1.23209
$409$	−5.70882e11	−1.00877	−0.504384	−	0.863480i	$-0.668280\pi$
$409$	−5.70882e11	−1.00877	−0.504384	+	0.863480i	$0.668280\pi$
$410$	1.49382e12	2.61078
$411$	−5.10785e11	−0.882979
$412$	1.23613e11	0.211362
$413$	−2.22863e11	−0.376931
$414$	1.08001e12	1.80687
$415$	−8.23910e11	−1.36353
$416$	−1.19962e11	−0.196392
$417$	−2.29282e12	−3.71328
$418$	−9.34381e11	−1.49703
$419$	−8.23728e11	−1.30563	−0.652816	−	0.757517i	$-0.726412\pi$
$419$	−8.23728e11	−1.30563	−0.652816	+	0.757517i	$0.726412\pi$
$420$	3.03774e11	0.476352
$421$	4.81803e11	0.747481	0.373741	−	0.927533i	$-0.378075\pi$
$421$	4.81803e11	0.747481	0.373741	+	0.927533i	$0.378075\pi$
$422$	−1.04099e12	−1.59787
$423$	1.28907e12	1.95769
$424$	−2.37812e11	−0.357344
$425$	−1.10770e12	−1.64692
$426$	−2.79175e12	−4.10709
$427$	4.21307e10	0.0613300
$428$	−9.65158e10	−0.139028
$429$	6.08753e11	0.867728
$430$	1.12757e12	1.59051
$431$	2.96390e11	0.413729	0.206865	−	0.978370i	$-0.433674\pi$
$431$	2.96390e11	0.413729	0.206865	+	0.978370i	$0.433674\pi$
$432$	3.37477e12	4.66195
$433$	1.61523e11	0.220820	0.110410	−	0.993886i	$-0.464784\pi$
$433$	1.61523e11	0.220820	0.110410	+	0.993886i	$0.464784\pi$
$434$	6.90287e9	0.00933955
$435$	−1.65084e12	−2.21057
$436$	2.86394e11	0.379555
$437$	3.26537e11	0.428318
$438$	1.53768e12	1.99633
$439$	8.16317e11	1.04898	0.524491	−	0.851416i	$-0.324256\pi$
$439$	8.16317e11	1.04898	0.524491	+	0.851416i	$0.324256\pi$
$440$	1.57183e12	1.99926
$441$	3.30327e11	0.415882
$442$	−2.20520e11	−0.274820
$443$	5.85838e11	0.722704	0.361352	−	0.932429i	$-0.382315\pi$
$443$	5.85838e11	0.722704	0.361352	+	0.932429i	$0.382315\pi$
$444$	−5.53634e11	−0.676082
$445$	−1.42209e12	−1.71912
$446$	−1.59509e12	−1.90887
$447$	−7.77488e11	−0.921107
$448$	−1.30267e11	−0.152786
$449$	−4.39931e10	−0.0510830	−0.0255415	−	0.999674i	$-0.508131\pi$
$449$	−4.39931e10	−0.0510830	−0.0255415	+	0.999674i	$0.508131\pi$
$450$	5.77162e12	6.63501
$451$	−1.80537e12	−2.05481
$452$	3.43788e11	0.387408
$453$	−5.88640e11	−0.656762
$454$	−1.06487e12	−1.17638
$455$	−1.64502e11	−0.179936
$456$	1.08641e12	1.17666
$457$	1.31992e12	1.41555	0.707776	−	0.706437i	$-0.249699\pi$
$457$	1.31992e12	1.41555	0.707776	+	0.706437i	$0.249699\pi$
$458$	−2.92104e11	−0.310200
$459$	3.04138e12	3.19826
$460$	3.24363e11	0.337770
$461$	1.22900e12	1.26735	0.633677	−	0.773598i	$-0.281545\pi$
$461$	1.22900e12	1.26735	0.633677	+	0.773598i	$0.281545\pi$
$462$	−1.35599e12	−1.38474
$463$	−1.27424e12	−1.28866	−0.644328	−	0.764750i	$-0.722863\pi$
$463$	−1.27424e12	−1.28866	−0.644328	+	0.764750i	$0.722863\pi$
$464$	−8.01966e11	−0.803202
$465$	7.22180e10	0.0716320
$466$	−2.96795e11	−0.291555
$467$	−1.29483e12	−1.25976	−0.629880	−	0.776692i	$-0.716896\pi$
$467$	−1.29483e12	−1.25976	−0.629880	+	0.776692i	$0.716896\pi$
$468$	3.11091e11	0.299765
$469$	−1.75988e11	−0.167959
$470$	1.42993e12	1.35168
$471$	3.68048e12	3.44596
$472$	−7.91732e11	−0.734242
$473$	−1.36274e12	−1.25181
$474$	1.79520e12	1.63346
$475$	1.74503e12	1.57283
$476$	1.32992e11	0.118739
$477$	1.59757e12	1.41295
$478$	−1.92608e12	−1.68752
$479$	2.12991e11	0.184864	0.0924318	−	0.995719i	$-0.470536\pi$
$479$	2.12991e11	0.184864	0.0924318	+	0.995719i	$0.470536\pi$
$480$	2.79559e12	2.40374
$481$	2.99808e11	0.255382
$482$	7.38431e11	0.623158
$483$	4.73876e11	0.396189
$484$	6.73521e11	0.557888
$485$	1.81434e11	0.148896
$486$	−7.55524e12	−6.14306
$487$	4.56414e11	0.367688	0.183844	−	0.982955i	$-0.441146\pi$
$487$	4.56414e11	0.367688	0.183844	+	0.982955i	$0.441146\pi$
$488$	1.49672e11	0.119468
$489$	−3.35360e12	−2.65230
$490$	3.66424e11	0.287145
$491$	2.93744e11	0.228088	0.114044	−	0.993476i	$-0.463620\pi$
$491$	2.93744e11	0.228088	0.114044	+	0.993476i	$0.463620\pi$
$492$	−1.23951e12	−0.953693
$493$	−7.22740e11	−0.551024
$494$	3.47399e11	0.262457
$495$	−1.05592e13	−7.90514
$496$	3.50829e10	0.0260272
$497$	−9.11747e11	−0.670302
$498$	2.52505e12	1.83966
$499$	1.32402e12	0.955962	0.477981	−	0.878370i	$-0.341369\pi$
$499$	1.32402e12	0.955962	0.477981	+	0.878370i	$0.341369\pi$
$500$	8.42796e11	0.603056
$501$	−2.24776e12	−1.59397
$502$	−1.98934e12	−1.39811
$503$	−6.97884e11	−0.486102	−0.243051	−	0.970014i	$-0.578148\pi$
$503$	−6.97884e11	−0.486102	−0.243051	+	0.970014i	$0.578148\pi$
$504$	1.17351e12	0.810117
$505$	−1.64347e12	−1.12447
$506$	−1.44790e12	−0.981884
$507$	−2.26332e11	−0.152128
$508$	−3.62498e11	−0.241501
$509$	−1.38012e11	−0.0911355	−0.0455678	−	0.998961i	$-0.514510\pi$
$509$	−1.38012e11	−0.0911355	−0.0455678	+	0.998961i	$0.514510\pi$
$510$	5.13900e12	3.36367
$511$	5.02184e11	0.325814
$512$	−5.39961e10	−0.0347254
$513$	−4.79127e12	−3.05438
$514$	−2.42853e12	−1.53465
$515$	1.55996e12	0.977196
$516$	−9.35616e11	−0.580997
$517$	−1.72816e12	−1.06384
$518$	−6.67817e11	−0.407543
$519$	−1.71415e12	−1.03704
$520$	−5.84401e11	−0.350506
$521$	1.16892e12	0.695050	0.347525	−	0.937671i	$-0.387022\pi$
$521$	1.16892e12	0.695050	0.347525	+	0.937671i	$0.387022\pi$
$522$	3.76580e12	2.21994
$523$	1.56229e12	0.913068	0.456534	−	0.889706i	$-0.349091\pi$
$523$	1.56229e12	0.913068	0.456534	+	0.889706i	$0.349091\pi$
$524$	−4.54361e11	−0.263275
$525$	2.53241e12	1.45485
$526$	1.30920e12	0.745708
$527$	3.16171e10	0.0178556
$528$	−6.89162e12	−3.85895
$529$	−1.29516e12	−0.719072
$530$	1.77215e12	0.975570
$531$	5.31869e12	2.90322
$532$	−2.09511e11	−0.113398
$533$	6.71230e11	0.360246
$534$	4.35830e12	2.31943
$535$	−1.21800e12	−0.642771
$536$	−6.25206e11	−0.327176
$537$	−2.46860e12	−1.28105
$538$	−4.17316e11	−0.214756
$539$	−4.42846e11	−0.225997
$540$	−4.75937e12	−2.40867
$541$	−1.98015e12	−0.993827	−0.496914	−	0.867800i	$-0.665533\pi$
$541$	−1.98015e12	−0.993827	−0.496914	+	0.867800i	$0.665533\pi$
$542$	3.61342e12	1.79855
$543$	−2.86805e12	−1.41575
$544$	1.22391e12	0.599177
$545$	3.61421e12	1.75481
$546$	5.04151e11	0.242769
$547$	2.69781e12	1.28845	0.644226	−	0.764835i	$-0.277180\pi$
$547$	2.69781e12	1.28845	0.644226	+	0.764835i	$0.277180\pi$
$548$	3.49940e11	0.165760
$549$	−1.00546e12	−0.472379
$550$	−7.73761e12	−3.60558
$551$	1.13858e12	0.526235
$552$	1.68347e12	0.771756
$553$	5.86286e11	0.266591
$554$	1.21029e12	0.545877
$555$	−6.98671e12	−3.12575
$556$	1.57081e12	0.697089
$557$	−1.98888e12	−0.875509	−0.437754	−	0.899095i	$-0.644226\pi$
$557$	−1.98888e12	−0.875509	−0.437754	+	0.899095i	$0.644226\pi$
$558$	−1.64739e11	−0.0719355
$559$	5.06661e11	0.219465
$560$	1.86230e12	0.800210
$561$	−6.21080e12	−2.64737
$562$	−3.35141e12	−1.41714
$563$	2.31950e12	0.972986	0.486493	−	0.873685i	$-0.338276\pi$
$563$	2.31950e12	0.972986	0.486493	+	0.873685i	$0.338276\pi$
$564$	−1.18650e12	−0.493757
$565$	4.33852e12	1.79111
$566$	2.83218e12	1.15997
$567$	−4.24520e12	−1.72494
$568$	−3.23903e12	−1.30571
$569$	3.73307e12	1.49300	0.746502	−	0.665383i	$-0.231732\pi$
$569$	3.73307e12	1.49300	0.746502	+	0.665383i	$0.231732\pi$
$570$	−8.09578e12	−3.21234
$571$	5.07920e11	0.199955	0.0999777	−	0.994990i	$-0.468123\pi$
$571$	5.07920e11	0.199955	0.0999777	+	0.994990i	$0.468123\pi$
$572$	−4.17058e11	−0.162897
$573$	−3.11421e11	−0.120685
$574$	−1.49515e12	−0.574887
$575$	2.70405e12	1.03160
$576$	3.10886e12	1.17679
$577$	−1.32703e12	−0.498412	−0.249206	−	0.968451i	$-0.580170\pi$
$577$	−1.32703e12	−0.498412	−0.249206	+	0.968451i	$0.580170\pi$
$578$	−8.92359e11	−0.332556
$579$	3.61908e12	1.33827
$580$	1.13100e12	0.414987
$581$	8.24646e11	0.300245
$582$	−5.56046e11	−0.200889
$583$	−2.14175e12	−0.767821
$584$	1.78404e12	0.634668
$585$	3.92588e12	1.38591
$586$	4.99753e12	1.75072
$587$	1.49468e12	0.519607	0.259804	−	0.965661i	$-0.416342\pi$
$587$	1.49468e12	0.519607	0.259804	+	0.965661i	$0.416342\pi$
$588$	−3.04045e11	−0.104891
$589$	−4.98083e10	−0.0170523
$590$	5.89991e12	2.00452
$591$	−5.54991e12	−1.87130
$592$	−3.39409e12	−1.13573
$593$	5.13938e12	1.70673	0.853364	−	0.521316i	$-0.174559\pi$
$593$	5.13938e12	1.70673	0.853364	+	0.521316i	$0.174559\pi$
$594$	2.12449e13	7.00191
$595$	1.67832e12	0.548971
$596$	5.32658e11	0.172918
$597$	3.29616e12	1.06200
$598$	5.38322e11	0.172142
$599$	5.91186e12	1.87631	0.938153	−	0.346222i	$-0.112536\pi$
$599$	5.91186e12	1.87631	0.938153	+	0.346222i	$0.112536\pi$
$600$	8.99652e12	2.83396
$601$	−2.59431e12	−0.811123	−0.405561	−	0.914068i	$-0.632924\pi$
$601$	−2.59431e12	−0.811123	−0.405561	+	0.914068i	$0.632924\pi$
$602$	−1.12858e12	−0.350226
$603$	4.20000e12	1.29366
$604$	4.03278e11	0.123293
$605$	8.49966e12	2.57930
$606$	5.03676e12	1.51714
$607$	−9.72998e11	−0.290913	−0.145456	−	0.989365i	$-0.546465\pi$
$607$	−9.72998e11	−0.290913	−0.145456	+	0.989365i	$0.546465\pi$
$608$	−1.92810e12	−0.572221
$609$	1.65232e12	0.486761
$610$	−1.11534e12	−0.326153
$611$	6.42524e11	0.186511
$612$	−3.17390e12	−0.914560
$613$	−3.42096e12	−0.978535	−0.489267	−	0.872134i	$-0.662736\pi$
$613$	−3.42096e12	−0.978535	−0.489267	+	0.872134i	$0.662736\pi$
$614$	−4.15728e12	−1.18046
$615$	−1.56423e13	−4.40924
$616$	−1.57324e12	−0.440231
$617$	3.21416e12	0.892863	0.446431	−	0.894818i	$-0.352695\pi$
$617$	3.21416e12	0.892863	0.446431	+	0.894818i	$0.352695\pi$
$618$	−4.78085e12	−1.31843
$619$	6.18766e12	1.69402	0.847010	−	0.531577i	$-0.178400\pi$
$619$	6.18766e12	1.69402	0.847010	+	0.531577i	$0.178400\pi$
$620$	−4.94767e10	−0.0134474
$621$	−7.42445e12	−2.00333
$622$	8.20920e12	2.19910
$623$	1.42336e12	0.378545
$624$	2.56228e12	0.676543
$625$	3.21127e12	0.841816
$626$	2.01858e12	0.525364
$627$	9.78425e12	2.52827
$628$	−2.52150e12	−0.646905
$629$	−3.05878e12	−0.779150
$630$	−8.74484e12	−2.21167
$631$	−1.41212e12	−0.354601	−0.177301	−	0.984157i	$-0.556737\pi$
$631$	−1.41212e12	−0.354601	−0.177301	+	0.984157i	$0.556737\pi$
$632$	2.08281e12	0.519306
$633$	1.09006e13	2.69857
$634$	−4.11205e12	−1.01078
$635$	−4.57463e12	−1.11654
$636$	−1.47046e12	−0.356366
$637$	1.64648e11	0.0396214
$638$	−5.04855e12	−1.20635
$639$	2.17591e13	5.16283
$640$	8.60735e12	2.02796
$641$	−2.12051e12	−0.496110	−0.248055	−	0.968746i	$-0.579791\pi$
$641$	−2.12051e12	−0.496110	−0.248055	+	0.968746i	$0.579791\pi$
$642$	3.73284e12	0.867224
$643$	−4.00523e12	−0.924012	−0.462006	−	0.886877i	$-0.652870\pi$
$643$	−4.00523e12	−0.924012	−0.462006	+	0.886877i	$0.652870\pi$
$644$	−3.24653e11	−0.0743761
$645$	−1.18072e13	−2.68614
$646$	−3.54434e12	−0.800734
$647$	−5.78356e12	−1.29755	−0.648777	−	0.760978i	$-0.724719\pi$
$647$	−5.78356e12	−1.29755	−0.648777	+	0.760978i	$0.724719\pi$
$648$	−1.50813e13	−3.36010
$649$	−7.13040e12	−1.57766
$650$	2.87681e12	0.632123
$651$	−7.22825e10	−0.0157732
$652$	2.29756e12	0.497912
$653$	−8.00952e12	−1.72384	−0.861920	−	0.507044i	$-0.830738\pi$
$653$	−8.00952e12	−1.72384	−0.861920	+	0.507044i	$0.830738\pi$
$654$	−1.10765e13	−2.36758
$655$	−5.73391e12	−1.21721
$656$	−7.59891e12	−1.60208
$657$	−1.19848e13	−2.50950
$658$	−1.43121e12	−0.297637
$659$	−1.35625e11	−0.0280127	−0.0140063	−	0.999902i	$-0.504459\pi$
$659$	−1.35625e11	−0.0280127	−0.0140063	+	0.999902i	$0.504459\pi$
$660$	9.71911e12	1.99379
$661$	8.30109e12	1.69133	0.845666	−	0.533713i	$-0.179204\pi$
$661$	8.30109e12	1.69133	0.845666	+	0.533713i	$0.179204\pi$
$662$	−8.10347e11	−0.163987
$663$	2.30915e12	0.464132
$664$	2.92960e12	0.584861
$665$	−2.64397e12	−0.524274
$666$	1.59377e13	3.13900
$667$	1.76431e12	0.345151
$668$	1.53994e12	0.299233
$669$	1.67027e13	3.22382
$670$	4.65897e12	0.893210
$671$	1.34795e12	0.256699
$672$	−2.79809e12	−0.529298
$673$	1.36269e12	0.256053	0.128027	−	0.991771i	$-0.459136\pi$
$673$	1.36269e12	0.256053	0.128027	+	0.991771i	$0.459136\pi$
$674$	−6.96828e12	−1.30064
$675$	−3.96765e13	−7.35642
$676$	1.55060e11	0.0285589
$677$	4.36285e12	0.798218	0.399109	−	0.916904i	$-0.369320\pi$
$677$	4.36285e12	0.798218	0.399109	+	0.916904i	$0.369320\pi$
$678$	−1.32963e13	−2.41656
$679$	−1.81597e11	−0.0327864
$680$	5.96234e12	1.06937
$681$	1.11507e13	1.98673
$682$	2.20854e11	0.0390910
$683$	−3.17805e12	−0.558815	−0.279408	−	0.960173i	$-0.590138\pi$
$683$	−3.17805e12	−0.558815	−0.279408	+	0.960173i	$0.590138\pi$
$684$	5.00004e12	0.873416
$685$	4.41615e12	0.766365
$686$	−3.66752e11	−0.0632286
$687$	3.05873e12	0.523884
$688$	−5.73585e12	−0.976000
$689$	7.96294e11	0.134613
$690$	−1.25451e13	−2.10694
$691$	−1.03260e13	−1.72299	−0.861494	−	0.507768i	$-0.830471\pi$
$691$	−1.03260e13	−1.72299	−0.861494	+	0.507768i	$0.830471\pi$
$692$	1.17437e12	0.194682
$693$	1.05687e13	1.74069
$694$	2.94781e12	0.482372
$695$	1.98233e13	3.22287
$696$	5.86995e12	0.948185
$697$	−6.84821e12	−1.09908
$698$	8.07867e12	1.28822
$699$	3.10785e12	0.492394
$700$	−1.73496e12	−0.273116
$701$	−6.94497e12	−1.08627	−0.543137	−	0.839644i	$-0.682764\pi$
$701$	−6.94497e12	−1.08627	−0.543137	+	0.839644i	$0.682764\pi$
$702$	−7.89879e12	−1.22756
$703$	4.81869e12	0.744097
$704$	−4.16784e12	−0.639490
$705$	−1.49734e13	−2.28280
$706$	−1.34817e13	−2.04232
$707$	1.64494e12	0.247606
$708$	−4.89552e12	−0.732233
$709$	9.72796e12	1.44582	0.722909	−	0.690943i	$-0.242805\pi$
$709$	9.72796e12	1.44582	0.722909	+	0.690943i	$0.242805\pi$
$710$	2.41369e13	3.56467
$711$	−1.39919e13	−2.05335
$712$	5.05656e12	0.737387
$713$	−7.71818e10	−0.0111844
$714$	−5.14360e12	−0.740670
$715$	−5.26316e12	−0.753129
$716$	1.69124e12	0.240490
$717$	2.01687e13	2.84998
$718$	1.23412e13	1.73299
$719$	8.85585e12	1.23581	0.617903	−	0.786254i	$-0.287982\pi$
$719$	8.85585e12	1.23581	0.617903	+	0.786254i	$0.287982\pi$
$720$	−4.44445e13	−6.16341
$721$	−1.56136e12	−0.215176
$722$	−2.96663e12	−0.406299
$723$	−7.73239e12	−1.05243
$724$	1.96490e12	0.265777
$725$	9.42854e12	1.26743
$726$	−2.60491e13	−3.47998
$727$	−6.27985e12	−0.833767	−0.416883	−	0.908960i	$-0.636878\pi$
$727$	−6.27985e12	−0.833767	−0.416883	+	0.908960i	$0.636878\pi$
$728$	5.84923e11	0.0771805
$729$	4.43123e13	5.81099
$730$	−1.32945e13	−1.73268
$731$	−5.16920e12	−0.669569
$732$	9.25464e11	0.119141
$733$	5.07216e12	0.648970	0.324485	−	0.945891i	$-0.394809\pi$
$733$	5.07216e12	0.648970	0.324485	+	0.945891i	$0.394809\pi$
$734$	9.37389e12	1.19203
$735$	−3.83697e12	−0.484948
$736$	−2.98774e12	−0.375313
$737$	−5.63065e12	−0.702999
$738$	3.56823e13	4.42792
$739$	1.32468e13	1.63385	0.816923	−	0.576747i	$-0.195678\pi$
$739$	1.32468e13	1.63385	0.816923	+	0.576747i	$0.195678\pi$
$740$	4.78661e12	0.586793
$741$	−3.63774e12	−0.443252
$742$	−1.77373e12	−0.214818
$743$	−2.80783e12	−0.338003	−0.169002	−	0.985616i	$-0.554054\pi$
$743$	−2.80783e12	−0.338003	−0.169002	+	0.985616i	$0.554054\pi$
$744$	−2.56788e11	−0.0307253
$745$	6.72200e12	0.799458
$746$	7.19566e12	0.850640
$747$	−1.96805e13	−2.31256
$748$	4.25503e12	0.496987
$749$	1.21909e12	0.141536
$750$	−3.25959e13	−3.76173
$751$	7.26416e12	0.833309	0.416654	−	0.909065i	$-0.363203\pi$
$751$	7.26416e12	0.833309	0.416654	+	0.909065i	$0.363203\pi$
$752$	−7.27393e12	−0.829448
$753$	2.08311e13	2.36121
$754$	1.87703e12	0.211495
$755$	5.08926e12	0.570024
$756$	4.76363e12	0.530383
$757$	−3.92411e12	−0.434320	−0.217160	−	0.976136i	$-0.569679\pi$
$757$	−3.92411e12	−0.434320	−0.217160	+	0.976136i	$0.569679\pi$
$758$	6.82332e12	0.750731
$759$	1.51615e13	1.65826
$760$	−9.39284e12	−1.02126
$761$	−1.38205e13	−1.49380	−0.746901	−	0.664935i	$-0.768459\pi$
$761$	−1.38205e13	−1.49380	−0.746901	+	0.664935i	$0.768459\pi$
$762$	1.40200e13	1.50643
$763$	−3.61744e12	−0.386404
$764$	2.13355e11	0.0226560
$765$	−4.00538e13	−4.22831
$766$	1.60564e12	0.168507
$767$	2.65105e12	0.276592
$768$	−1.86716e13	−1.93668
$769$	−4.53896e12	−0.468045	−0.234023	−	0.972231i	$-0.575189\pi$
$769$	−4.53896e12	−0.468045	−0.234023	+	0.972231i	$0.575189\pi$
$770$	1.17236e13	1.20186
$771$	2.54301e13	2.59181
$772$	−2.47944e12	−0.251232
$773$	−1.40549e13	−1.41586	−0.707931	−	0.706281i	$-0.750371\pi$
$773$	−1.40549e13	−1.41586	−0.707931	+	0.706281i	$0.750371\pi$
$774$	2.69339e13	2.69752
$775$	−4.12462e11	−0.0410702
$776$	−6.45132e11	−0.0638662
$777$	6.99296e12	0.688282
$778$	4.38274e12	0.428882
$779$	1.07884e13	1.04964
$780$	−3.61353e12	−0.349547
$781$	−2.91710e13	−2.80557
$782$	−5.49223e12	−0.525192
$783$	−2.58877e13	−2.46131
$784$	−1.86397e12	−0.176204
$785$	−3.18206e13	−2.99086
$786$	1.75728e13	1.64225
$787$	−1.34638e13	−1.25107	−0.625536	−	0.780195i	$-0.715120\pi$
$787$	−1.34638e13	−1.25107	−0.625536	+	0.780195i	$0.715120\pi$
$788$	3.80225e12	0.351296
$789$	−1.37091e13	−1.25939
$790$	−1.55209e13	−1.41774
$791$	−4.34239e12	−0.394398
$792$	3.75458e13	3.39077
$793$	−5.01164e11	−0.0450039
$794$	−1.09617e13	−0.978777
$795$	−1.85568e13	−1.64760
$796$	−2.25820e12	−0.199368
$797$	−1.42488e13	−1.25088	−0.625439	−	0.780273i	$-0.715080\pi$
$797$	−1.42488e13	−1.25088	−0.625439	+	0.780273i	$0.715080\pi$
$798$	8.10302e12	0.707349
$799$	−6.55534e12	−0.569029
$800$	−1.59666e13	−1.37819
$801$	−3.39689e13	−2.91565
$802$	1.47931e13	1.26263
$803$	1.60672e13	1.36370
$804$	−3.86584e12	−0.326281
$805$	−4.09703e12	−0.343865
$806$	−8.21128e10	−0.00685336
$807$	4.36987e12	0.362692
$808$	5.84372e12	0.482324
$809$	6.34414e12	0.520720	0.260360	−	0.965512i	$-0.416159\pi$
$809$	6.34414e12	0.520720	0.260360	+	0.965512i	$0.416159\pi$
$810$	1.12384e14	9.17326
$811$	2.31379e13	1.87815	0.939073	−	0.343719i	$-0.111687\pi$
$811$	2.31379e13	1.87815	0.939073	+	0.343719i	$0.111687\pi$
$812$	−1.13201e12	−0.0913790
$813$	−3.78375e13	−3.03749
$814$	−2.13665e13	−1.70578
$815$	2.89946e13	2.30201
$816$	−2.61416e13	−2.06408
$817$	8.14336e12	0.639447
$818$	−1.51266e13	−1.18128
$819$	−3.92939e12	−0.305174
$820$	1.07166e13	0.827740
$821$	9.70997e12	0.745888	0.372944	−	0.927854i	$-0.378348\pi$
$821$	9.70997e12	0.745888	0.372944	+	0.927854i	$0.378348\pi$
$822$	−1.35343e13	−1.03398
$823$	−5.67650e12	−0.431302	−0.215651	−	0.976471i	$-0.569187\pi$
$823$	−5.67650e12	−0.431302	−0.215651	+	0.976471i	$0.569187\pi$
$824$	−5.54681e12	−0.419151
$825$	8.10234e13	6.08930
$826$	−5.90518e12	−0.441390
$827$	8.76966e12	0.651941	0.325970	−	0.945380i	$-0.394309\pi$
$827$	8.76966e12	0.651941	0.325970	+	0.945380i	$0.394309\pi$
$828$	7.74796e12	0.572863
$829$	−9.89738e12	−0.727821	−0.363911	−	0.931434i	$-0.618559\pi$
$829$	−9.89738e12	−0.727821	−0.363911	+	0.931434i	$0.618559\pi$
$830$	−2.18311e13	−1.59670
$831$	−1.26734e13	−0.921908
$832$	1.54959e12	0.112114
$833$	−1.67982e12	−0.120882
$834$	−6.07527e13	−4.34829
$835$	1.94336e13	1.38346
$836$	−6.70320e12	−0.474629
$837$	1.13249e12	0.0797570
$838$	−2.18263e13	−1.52891
$839$	5.43436e12	0.378634	0.189317	−	0.981916i	$-0.439373\pi$
$839$	5.43436e12	0.378634	0.189317	+	0.981916i	$0.439373\pi$
$840$	−1.36310e13	−0.944653
$841$	−8.35531e12	−0.575945
$842$	1.27663e13	0.875308
$843$	3.50939e13	2.39336
$844$	−7.46801e12	−0.506599
$845$	1.95682e12	0.132037
$846$	3.41563e13	2.29247
$847$	−8.50725e12	−0.567955
$848$	−9.01474e12	−0.598649
$849$	−2.96568e13	−1.95902
$850$	−2.93506e13	−1.92856
$851$	7.46694e12	0.488044
$852$	−2.00279e13	−1.30214
$853$	−5.85034e12	−0.378364	−0.189182	−	0.981942i	$-0.560584\pi$
$853$	−5.85034e12	−0.378364	−0.189182	+	0.981942i	$0.560584\pi$
$854$	1.11633e12	0.0718180
$855$	6.30992e13	4.03809
$856$	4.33089e12	0.275705
$857$	2.25901e13	1.43056	0.715278	−	0.698840i	$-0.246300\pi$
$857$	2.25901e13	1.43056	0.715278	+	0.698840i	$0.246300\pi$
$858$	1.61301e13	1.01612
$859$	−2.68487e13	−1.68249	−0.841246	−	0.540652i	$-0.818178\pi$
$859$	−2.68487e13	−1.68249	−0.841246	+	0.540652i	$0.818178\pi$
$860$	8.08915e12	0.504266
$861$	1.56563e13	0.970901
$862$	7.85343e12	0.484481
$863$	1.71044e13	1.04968	0.524842	−	0.851199i	$-0.324124\pi$
$863$	1.71044e13	1.04968	0.524842	+	0.851199i	$0.324124\pi$
$864$	4.38391e13	2.67639
$865$	1.48202e13	0.900080
$866$	4.27985e12	0.258582
$867$	9.34422e12	0.561639
$868$	4.95209e10	0.00296108
$869$	1.87580e13	1.11583
$870$	−4.37423e13	−2.58860
$871$	2.09345e12	0.123249
$872$	−1.28512e13	−0.752694
$873$	4.33386e12	0.252529
$874$	8.65224e12	0.501565
$875$	−1.06454e13	−0.613938
$876$	1.10312e13	0.632931
$877$	9.99257e12	0.570400	0.285200	−	0.958468i	$-0.407940\pi$
$877$	9.99257e12	0.570400	0.285200	+	0.958468i	$0.407940\pi$
$878$	2.16299e13	1.22837
$879$	−5.23310e13	−2.95671
$880$	5.95836e13	3.34930
$881$	−2.34044e13	−1.30890	−0.654449	−	0.756106i	$-0.727100\pi$
$881$	−2.34044e13	−1.30890	−0.654449	+	0.756106i	$0.727100\pi$
$882$	8.75265e12	0.487002
$883$	2.46363e13	1.36381	0.681904	−	0.731442i	$-0.261152\pi$
$883$	2.46363e13	1.36381	0.681904	+	0.731442i	$0.261152\pi$
$884$	−1.58200e12	−0.0871309
$885$	−6.17801e13	−3.38535
$886$	1.55229e13	0.846294
$887$	−1.97388e12	−0.107069	−0.0535346	−	0.998566i	$-0.517049\pi$
$887$	−1.97388e12	−0.107069	−0.0535346	+	0.998566i	$0.517049\pi$
$888$	2.48429e13	1.34074
$889$	4.57872e12	0.245859
$890$	−3.76810e13	−2.01311
$891$	−1.35823e14	−7.21980
$892$	−1.14431e13	−0.605203
$893$	1.03270e13	0.543430
$894$	−2.06011e13	−1.07863
$895$	2.13430e13	1.11187
$896$	−8.61504e12	−0.446551
$897$	−5.63697e12	−0.290723
$898$	−1.16568e12	−0.0598187
$899$	−2.69119e11	−0.0137412
$900$	4.14053e13	2.10361
$901$	−8.12418e12	−0.410694
$902$	−4.78368e13	−2.40621
$903$	1.18178e13	0.591481
$904$	−1.54266e13	−0.768267
$905$	2.47965e13	1.22878
$906$	−1.55972e13	−0.769075
$907$	−2.09991e13	−1.03031	−0.515156	−	0.857097i	$-0.672266\pi$
$907$	−2.09991e13	−1.03031	−0.515156	+	0.857097i	$0.672266\pi$
$908$	−7.63934e12	−0.372966
$909$	−3.92569e13	−1.90712
$910$	−4.35879e12	−0.210707
$911$	3.25895e12	0.156764	0.0783818	−	0.996923i	$-0.475025\pi$
$911$	3.25895e12	0.156764	0.0783818	+	0.996923i	$0.475025\pi$
$912$	4.11825e13	1.97122
$913$	2.63842e13	1.25668
$914$	3.49739e13	1.65763
$915$	1.16791e13	0.550827
$916$	−2.09554e12	−0.0983481
$917$	5.73903e12	0.268026
$918$	8.05873e13	3.74520
$919$	−3.55979e13	−1.64628	−0.823142	−	0.567835i	$-0.807781\pi$
$919$	−3.55979e13	−1.64628	−0.823142	+	0.567835i	$0.807781\pi$
$920$	−1.45549e13	−0.669831
$921$	4.35324e13	1.99363
$922$	3.25648e13	1.48408
$923$	1.08456e13	0.491867
$924$	−9.72779e12	−0.439026
$925$	3.99036e13	1.79215
$926$	−3.37635e13	−1.50903
$927$	3.72623e13	1.65734
$928$	−1.04177e13	−0.461112
$929$	−1.74409e12	−0.0768244	−0.0384122	−	0.999262i	$-0.512230\pi$
$929$	−1.74409e12	−0.0768244	−0.0384122	+	0.999262i	$0.512230\pi$
$930$	1.91356e12	0.0838818
$931$	2.64633e12	0.115444
$932$	−2.12919e12	−0.0924366
$933$	−8.59616e13	−3.71396
$934$	−3.43091e13	−1.47519
$935$	5.36973e13	2.29774
$936$	−1.39594e13	−0.594463
$937$	6.94275e12	0.294241	0.147121	−	0.989119i	$-0.452999\pi$
$937$	6.94275e12	0.294241	0.147121	+	0.989119i	$0.452999\pi$
$938$	−4.66313e12	−0.196682
$939$	−2.11373e13	−0.887266
$940$	1.02583e13	0.428547
$941$	−9.17701e12	−0.381547	−0.190773	−	0.981634i	$-0.561100\pi$
$941$	−9.17701e12	−0.381547	−0.190773	+	0.981634i	$0.561100\pi$
$942$	9.75213e13	4.03525
$943$	1.67175e13	0.688443
$944$	−3.00123e13	−1.23006
$945$	6.01157e13	2.45214
$946$	−3.61084e13	−1.46588
$947$	3.03420e13	1.22594	0.612971	−	0.790105i	$-0.289974\pi$
$947$	3.03420e13	1.22594	0.612971	+	0.790105i	$0.289974\pi$
$948$	1.28787e13	0.517885
$949$	−5.97371e12	−0.239082
$950$	4.62378e13	1.84180
$951$	4.30588e13	1.70707
$952$	−5.96767e12	−0.235472
$953$	2.76636e13	1.08640	0.543201	−	0.839603i	$-0.317212\pi$
$953$	2.76636e13	1.08640	0.543201	+	0.839603i	$0.317212\pi$
$954$	4.23307e13	1.65458
$955$	2.69249e12	0.104746
$956$	−1.38176e13	−0.535023
$957$	5.28652e13	2.03735
$958$	5.64361e12	0.216477
$959$	−4.42009e12	−0.168751
$960$	−3.61115e13	−1.37222
$961$	−2.64278e13	−0.999555
$962$	7.94399e12	0.299055
$963$	−2.90940e13	−1.09015
$964$	5.29747e12	0.197570
$965$	−3.12898e13	−1.16153
$966$	1.25563e13	0.463942
$967$	6.69223e12	0.246123	0.123061	−	0.992399i	$-0.460729\pi$
$967$	6.69223e12	0.246123	0.123061	+	0.992399i	$0.460729\pi$
$968$	−3.02225e13	−1.10635
$969$	3.71141e13	1.35233
$970$	4.80746e12	0.174358
$971$	−2.87538e13	−1.03803	−0.519013	−	0.854766i	$-0.673701\pi$
$971$	−2.87538e13	−1.03803	−0.519013	+	0.854766i	$0.673701\pi$
$972$	−5.42009e13	−1.94764
$973$	−1.98410e13	−0.709668
$974$	1.20936e13	0.430566
$975$	−3.01242e13	−1.06756
$976$	5.67361e12	0.200141
$977$	−1.71791e13	−0.603219	−0.301609	−	0.953432i	$-0.597524\pi$
$977$	−1.71791e13	−0.603219	−0.301609	+	0.953432i	$0.597524\pi$
$978$	−8.88602e13	−3.10587
$979$	4.55398e13	1.58441
$980$	2.62871e12	0.0910386
$981$	8.63315e13	2.97618
$982$	7.78332e12	0.267093
$983$	−4.52401e13	−1.54537	−0.772685	−	0.634789i	$-0.781087\pi$
$983$	−4.52401e13	−1.54537	−0.772685	+	0.634789i	$0.781087\pi$
$984$	5.56199e13	1.89126
$985$	4.79834e13	1.62416
$986$	−1.91504e13	−0.645255
$987$	1.49867e13	0.502667
$988$	2.49222e12	0.0832110
$989$	1.26188e13	0.419405
$990$	−2.79788e14	−9.25700
$991$	−4.49657e13	−1.48098	−0.740491	−	0.672066i	$-0.765407\pi$
$991$	−4.49657e13	−1.48098	−0.740491	+	0.672066i	$0.765407\pi$
$992$	4.55735e11	0.0149420
$993$	8.48544e12	0.276951
$994$	−2.41585e13	−0.784930
$995$	−2.84979e13	−0.921742
$996$	1.81146e13	0.583260
$997$	4.39312e13	1.40814	0.704069	−	0.710132i	$-0.251365\pi$
$997$	4.39312e13	1.40814	0.704069	+	0.710132i	$0.251365\pi$
$998$	3.50824e13	1.11944
$999$	−1.09562e14	−3.48029

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.d.1.11	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.d.1.11	✓	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)

\(f(q)\)	\(=\)	\(q+26.4969 q^{2} -277.459 q^{3} +190.088 q^{4} +2398.86 q^{5} -7351.82 q^{6} -2401.00 q^{7} -8529.69 q^{8} +57300.7 q^{9} +O(q^{10})\)	\(q+26.4969 q^{2} -277.459 q^{3} +190.088 q^{4} +2398.86 q^{5} -7351.82 q^{6} -2401.00 q^{7} -8529.69 q^{8} +57300.7 q^{9} +63562.4 q^{10} -76819.0 q^{11} -52741.6 q^{12} +28561.0 q^{13} -63619.2 q^{14} -665585. q^{15} -323336. q^{16} -291393. q^{17} +1.51829e6 q^{18} +459049. q^{19} +455993. q^{20} +666180. q^{21} -2.03547e6 q^{22} +711333. q^{23} +2.36664e6 q^{24} +3.80139e6 q^{25} +756779. q^{26} -1.04374e7 q^{27} -456401. q^{28} +2.48029e6 q^{29} -1.76360e7 q^{30} -108503. q^{31} -4.20020e6 q^{32} +2.13141e7 q^{33} -7.72103e6 q^{34} -5.75966e6 q^{35} +1.08922e7 q^{36} +1.04971e7 q^{37} +1.21634e7 q^{38} -7.92452e6 q^{39} -2.04615e7 q^{40} +2.35016e7 q^{41} +1.76517e7 q^{42} +1.77396e7 q^{43} -1.46024e7 q^{44} +1.37456e8 q^{45} +1.88482e7 q^{46} +2.24965e7 q^{47} +8.97125e7 q^{48} +5.76480e6 q^{49} +1.00725e8 q^{50} +8.08498e7 q^{51} +5.42910e6 q^{52} +2.78805e7 q^{53} -2.76558e8 q^{54} -1.84278e8 q^{55} +2.04798e7 q^{56} -1.27368e8 q^{57} +6.57201e7 q^{58} +9.28208e7 q^{59} -1.26520e8 q^{60} -1.75471e7 q^{61} -2.87500e6 q^{62} -1.37579e8 q^{63} +5.42553e7 q^{64} +6.85137e7 q^{65} +5.64760e8 q^{66} +7.32976e7 q^{67} -5.53903e7 q^{68} -1.97366e8 q^{69} -1.52613e8 q^{70} +3.79736e8 q^{71} -4.88757e8 q^{72} -2.09156e8 q^{73} +2.78141e8 q^{74} -1.05473e9 q^{75} +8.72597e7 q^{76} +1.84442e8 q^{77} -2.09975e8 q^{78} -2.44184e8 q^{79} -7.75636e8 q^{80} +1.76810e9 q^{81} +6.22721e8 q^{82} -3.43460e8 q^{83} +1.26633e8 q^{84} -6.99011e8 q^{85} +4.70045e8 q^{86} -6.88179e8 q^{87} +6.55242e8 q^{88} -5.92819e8 q^{89} +3.64217e9 q^{90} -6.85750e7 q^{91} +1.35216e8 q^{92} +3.01052e7 q^{93} +5.96089e8 q^{94} +1.10119e9 q^{95} +1.16539e9 q^{96} +7.56337e7 q^{97} +1.52750e8 q^{98} -4.40178e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 22 q^{2} + q^{3} + 6402 q^{4} + 1694 q^{5} + 4189 q^{6} - 36015 q^{7} - 1704 q^{8} + 160366 q^{9}+O(q^{10}) \) 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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