LMFDB - Embedded newform 91.10.a.c.1.9

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:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 4752 x^{12} + 9346 x^{11} + 8576824 x^{10} - 26923636 x^{9} - 7450416552 x^{8} + \cdots - 24\!\cdots\!40 $ x^14 - x^13 - 4752x^12 + 9346x^11 + 8576824x^10 - 26923636x^9 - 7450416552x^8 + 31594524240x^7 + 3232668379296x^6 - 15784728192704x^5 - 654706244016512x^4 + 3031992312058112x^3 + 50459693673905664x^2 - 177878730644221952x - 247584423217725440
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-12.8857$ 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)

$f(q)$	$=$	$q+14.8857 q^{2} +54.8703 q^{3} -290.415 q^{4} +1171.15 q^{5} +816.786 q^{6} +2401.00 q^{7} -11944.5 q^{8} -16672.2 q^{9} +O(q^{10})$	\(q+14.8857 q^{2} +54.8703 q^{3} -290.415 q^{4} +1171.15 q^{5} +816.786 q^{6} +2401.00 q^{7} -11944.5 q^{8} -16672.2 q^{9} +17433.4 q^{10} +56032.8 q^{11} -15935.1 q^{12} -28561.0 q^{13} +35740.7 q^{14} +64261.4 q^{15} -29111.2 q^{16} +237405. q^{17} -248179. q^{18} +939826. q^{19} -340119. q^{20} +131744. q^{21} +834089. q^{22} -689962. q^{23} -655401. q^{24} -581532. q^{25} -425152. q^{26} -1.99482e6 q^{27} -697285. q^{28} +4.61836e6 q^{29} +956579. q^{30} -2.78785e6 q^{31} +5.68226e6 q^{32} +3.07454e6 q^{33} +3.53395e6 q^{34} +2.81193e6 q^{35} +4.84186e6 q^{36} +1.19418e7 q^{37} +1.39900e7 q^{38} -1.56715e6 q^{39} -1.39888e7 q^{40} +2.85832e7 q^{41} +1.96110e6 q^{42} +2.63180e7 q^{43} -1.62727e7 q^{44} -1.95257e7 q^{45} -1.02706e7 q^{46} -1.32034e7 q^{47} -1.59734e6 q^{48} +5.76480e6 q^{49} -8.65654e6 q^{50} +1.30265e7 q^{51} +8.29453e6 q^{52} -2.56595e7 q^{53} -2.96944e7 q^{54} +6.56228e7 q^{55} -2.86788e7 q^{56} +5.15686e7 q^{57} +6.87478e7 q^{58} +1.06182e8 q^{59} -1.86624e7 q^{60} +6.59672e6 q^{61} -4.14992e7 q^{62} -4.00301e7 q^{63} +9.94897e7 q^{64} -3.34492e7 q^{65} +4.57668e7 q^{66} +1.22000e8 q^{67} -6.89458e7 q^{68} -3.78584e7 q^{69} +4.18577e7 q^{70} +1.45652e8 q^{71} +1.99142e8 q^{72} -4.49426e8 q^{73} +1.77762e8 q^{74} -3.19089e7 q^{75} -2.72939e8 q^{76} +1.34535e8 q^{77} -2.33282e7 q^{78} +6.80670e8 q^{79} -3.40936e7 q^{80} +2.18703e8 q^{81} +4.25482e8 q^{82} +1.14283e8 q^{83} -3.82603e7 q^{84} +2.78037e8 q^{85} +3.91762e8 q^{86} +2.53411e8 q^{87} -6.69285e8 q^{88} +3.85818e8 q^{89} -2.90655e8 q^{90} -6.85750e7 q^{91} +2.00375e8 q^{92} -1.52970e8 q^{93} -1.96543e8 q^{94} +1.10068e9 q^{95} +3.11788e8 q^{96} -1.40755e9 q^{97} +8.58134e7 q^{98} -9.34192e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 27 q^{2} + 163 q^{3} + 2389 q^{4} + 2964 q^{5} + 471 q^{6} + 33614 q^{7} + 43263 q^{8} + 144129 q^{9}+O(q^{10}) $ 14 * q + 27 * q^2 + 163 * q^3 + 2389 * q^4 + 2964 * q^5 + 471 * q^6 + 33614 * q^7 + 43263 * q^8 + 144129 * q^9	\( 14 q + 27 q^{2} + 163 q^{3} + 2389 q^{4} + 2964 q^{5} + 471 q^{6} + 33614 q^{7} + 43263 q^{8} + 144129 q^{9} + 126524 q^{10} + 81825 q^{11} + 157399 q^{12} - 399854 q^{13} + 64827 q^{14} + 163856 q^{15} + 166361 q^{16} - 44922 q^{17} - 826396 q^{18} + 171756 q^{19} + 3899724 q^{20} + 391363 q^{21} + 917579 q^{22} + 1930479 q^{23} + 2992373 q^{24} + 8222344 q^{25} - 771147 q^{26} + 4139125 q^{27} + 5735989 q^{28} - 3799608 q^{29} - 5918004 q^{30} - 4392203 q^{31} + 3135663 q^{32} + 17499977 q^{33} - 20071132 q^{34} + 7116564 q^{35} + 2121398 q^{36} + 29198909 q^{37} - 44208366 q^{38} - 4655443 q^{39} + 134932928 q^{40} + 48410973 q^{41} + 1130871 q^{42} + 52650242 q^{43} - 14827353 q^{44} + 99215088 q^{45} - 34410455 q^{46} + 160580841 q^{47} + 227620515 q^{48} + 80707214 q^{49} + 149462949 q^{50} + 57114360 q^{51} - 68232229 q^{52} + 80753796 q^{53} + 301368833 q^{54} + 328919412 q^{55} + 103874463 q^{56} + 151101102 q^{57} + 335044204 q^{58} + 442445502 q^{59} + 561078360 q^{60} + 270199089 q^{61} + 543824517 q^{62} + 346053729 q^{63} + 223643137 q^{64} - 84654804 q^{65} + 317483345 q^{66} + 92500909 q^{67} + 255771204 q^{68} + 292017029 q^{69} + 303784124 q^{70} + 84383796 q^{71} + 1456696818 q^{72} + 367274315 q^{73} + 1091659407 q^{74} + 1154152501 q^{75} + 674789222 q^{76} + 196461825 q^{77} - 13452231 q^{78} + 434861545 q^{79} + 2644363752 q^{80} + 644207518 q^{81} + 634104331 q^{82} + 1013603934 q^{83} + 377914999 q^{84} + 1103701048 q^{85} + 2514069096 q^{86} + 1039292304 q^{87} + 1071310221 q^{88} + 1069739706 q^{89} - 1271572324 q^{90} - 960049454 q^{91} + 2301673917 q^{92} - 933838861 q^{93} + 2025486277 q^{94} + 2504029998 q^{95} - 116199027 q^{96} + 2839636281 q^{97} + 155649627 q^{98} + 5063037274 q^{99}+O(q^{100}) \) 14 * q + 27 * q^2 + 163 * q^3 + 2389 * q^4 + 2964 * q^5 + 471 * q^6 + 33614 * q^7 + 43263 * q^8 + 144129 * q^9 + 126524 * q^10 + 81825 * q^11 + 157399 * q^12 - 399854 * q^13 + 64827 * q^14 + 163856 * q^15 + 166361 * q^16 - 44922 * q^17 - 826396 * q^18 + 171756 * q^19 + 3899724 * q^20 + 391363 * q^21 + 917579 * q^22 + 1930479 * q^23 + 2992373 * q^24 + 8222344 * q^25 - 771147 * q^26 + 4139125 * q^27 + 5735989 * q^28 - 3799608 * q^29 - 5918004 * q^30 - 4392203 * q^31 + 3135663 * q^32 + 17499977 * q^33 - 20071132 * q^34 + 7116564 * q^35 + 2121398 * q^36 + 29198909 * q^37 - 44208366 * q^38 - 4655443 * q^39 + 134932928 * q^40 + 48410973 * q^41 + 1130871 * q^42 + 52650242 * q^43 - 14827353 * q^44 + 99215088 * q^45 - 34410455 * q^46 + 160580841 * q^47 + 227620515 * q^48 + 80707214 * q^49 + 149462949 * q^50 + 57114360 * q^51 - 68232229 * q^52 + 80753796 * q^53 + 301368833 * q^54 + 328919412 * q^55 + 103874463 * q^56 + 151101102 * q^57 + 335044204 * q^58 + 442445502 * q^59 + 561078360 * q^60 + 270199089 * q^61 + 543824517 * q^62 + 346053729 * q^63 + 223643137 * q^64 - 84654804 * q^65 + 317483345 * q^66 + 92500909 * q^67 + 255771204 * q^68 + 292017029 * q^69 + 303784124 * q^70 + 84383796 * q^71 + 1456696818 * q^72 + 367274315 * q^73 + 1091659407 * q^74 + 1154152501 * q^75 + 674789222 * q^76 + 196461825 * q^77 - 13452231 * q^78 + 434861545 * q^79 + 2644363752 * q^80 + 644207518 * q^81 + 634104331 * q^82 + 1013603934 * q^83 + 377914999 * q^84 + 1103701048 * q^85 + 2514069096 * q^86 + 1039292304 * q^87 + 1071310221 * q^88 + 1069739706 * q^89 - 1271572324 * q^90 - 960049454 * q^91 + 2301673917 * q^92 - 933838861 * q^93 + 2025486277 * q^94 + 2504029998 * q^95 - 116199027 * q^96 + 2839636281 * q^97 + 155649627 * q^98 + 5063037274 * 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 $

$2$	14.8857	0.657863	0.328932	−	0.944354i	$-0.393311\pi$
$2$	14.8857	0.657863	0.328932	+	0.944354i	$0.393311\pi$
$3$	54.8703	0.391104	0.195552	−	0.980693i	$-0.437350\pi$
$3$	54.8703	0.391104	0.195552	+	0.980693i	$0.437350\pi$
$4$	−290.415	−0.567216
$5$	1171.15	0.838007	0.419003	−	0.907985i	$-0.362380\pi$
$5$	1171.15	0.838007	0.419003	+	0.907985i	$0.362380\pi$
$6$	816.786	0.257293
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	−11944.5	−1.03101
$9$	−16672.2	−0.847038
$10$	17433.4	0.551294
$11$	56032.8	1.15392	0.576959	−	0.816773i	$-0.304239\pi$
$11$	56032.8	1.15392	0.576959	+	0.816773i	$0.304239\pi$
$12$	−15935.1	−0.221840
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	35740.7	0.248649
$15$	64261.4	0.327747
$16$	−29111.2	−0.111050
$17$	237405.	0.689397	0.344698	−	0.938713i	$-0.387981\pi$
$17$	237405.	0.689397	0.344698	+	0.938713i	$0.387981\pi$
$18$	−248179.	−0.557235
$19$	939826.	1.65446	0.827230	−	0.561863i	$-0.189915\pi$
$19$	939826.	1.65446	0.827230	+	0.561863i	$0.189915\pi$
$20$	−340119.	−0.475331
$21$	131744.	0.147823
$22$	834089.	0.759120
$23$	−689962.	−0.514103	−0.257051	−	0.966398i	$-0.582751\pi$
$23$	−689962.	−0.514103	−0.257051	+	0.966398i	$0.582751\pi$
$24$	−655401.	−0.403233
$25$	−581532.	−0.297745
$26$	−425152.	−0.182458
$27$	−1.99482e6	−0.722383
$28$	−697285.	−0.214387
$29$	4.61836e6	1.21254	0.606271	−	0.795258i	$-0.292665\pi$
$29$	4.61836e6	1.21254	0.606271	+	0.795258i	$0.292665\pi$
$30$	956579.	0.215613
$31$	−2.78785e6	−0.542177	−0.271089	−	0.962554i	$-0.587384\pi$
$31$	−2.78785e6	−0.542177	−0.271089	+	0.962554i	$0.587384\pi$
$32$	5.68226e6	0.957958
$33$	3.07454e6	0.451301
$34$	3.53395e6	0.453529
$35$	2.81193e6	0.316737
$36$	4.84186e6	0.480453
$37$	1.19418e7	1.04752	0.523759	−	0.851866i	$-0.324529\pi$
$37$	1.19418e7	1.04752	0.523759	+	0.851866i	$0.324529\pi$
$38$	1.39900e7	1.08841
$39$	−1.56715e6	−0.108473
$40$	−1.39888e7	−0.863997
$41$	2.85832e7	1.57973	0.789866	−	0.613279i	$-0.210150\pi$
$41$	2.85832e7	1.57973	0.789866	+	0.613279i	$0.210150\pi$
$42$	1.96110e6	0.0972475
$43$	2.63180e7	1.17394	0.586968	−	0.809610i	$-0.300322\pi$
$43$	2.63180e7	1.17394	0.586968	+	0.809610i	$0.300322\pi$
$44$	−1.62727e7	−0.654520
$45$	−1.95257e7	−0.709824
$46$	−1.02706e7	−0.338209
$47$	−1.32034e7	−0.394681	−0.197340	−	0.980335i	$-0.563230\pi$
$47$	−1.32034e7	−0.394681	−0.197340	+	0.980335i	$0.563230\pi$
$48$	−1.59734e6	−0.0434322
$49$	5.76480e6	0.142857
$50$	−8.65654e6	−0.195875
$51$	1.30265e7	0.269626
$52$	8.29453e6	0.157317
$53$	−2.56595e7	−0.446690	−0.223345	−	0.974739i	$-0.571698\pi$
$53$	−2.56595e7	−0.446690	−0.223345	+	0.974739i	$0.571698\pi$
$54$	−2.96944e7	−0.475229
$55$	6.56228e7	0.966991
$56$	−2.86788e7	−0.389687
$57$	5.15686e7	0.647065
$58$	6.87478e7	0.797687
$59$	1.06182e8	1.14082	0.570411	−	0.821360i	$-0.306784\pi$
$59$	1.06182e8	1.14082	0.570411	+	0.821360i	$0.306784\pi$
$60$	−1.86624e7	−0.185904
$61$	6.59672e6	0.0610019	0.0305010	−	0.999535i	$-0.490290\pi$
$61$	6.59672e6	0.0610019	0.0305010	+	0.999535i	$0.490290\pi$
$62$	−4.14992e7	−0.356679
$63$	−4.00301e7	−0.320150
$64$	9.94897e7	0.741256
$65$	−3.34492e7	−0.232421
$66$	4.57668e7	0.296895
$67$	1.22000e8	0.739642	0.369821	−	0.929103i	$-0.379419\pi$
$67$	1.22000e8	0.739642	0.369821	+	0.929103i	$0.379419\pi$
$68$	−6.89458e7	−0.391037
$69$	−3.78584e7	−0.201067
$70$	4.18577e7	0.208370
$71$	1.45652e8	0.680229	0.340115	−	0.940384i	$-0.389534\pi$
$71$	1.45652e8	0.680229	0.340115	+	0.940384i	$0.389534\pi$
$72$	1.99142e8	0.873308
$73$	−4.49426e8	−1.85227	−0.926137	−	0.377187i	$-0.876891\pi$
$73$	−4.49426e8	−1.85227	−0.926137	+	0.377187i	$0.876891\pi$
$74$	1.77762e8	0.689124
$75$	−3.19089e7	−0.116449
$76$	−2.72939e8	−0.938436
$77$	1.34535e8	0.436140
$78$	−2.33282e7	−0.0713602
$79$	6.80670e8	1.96614	0.983071	−	0.183227i	$-0.0586544\pi$
$79$	6.80670e8	1.96614	0.983071	+	0.183227i	$0.0586544\pi$
$80$	−3.40936e7	−0.0930609
$81$	2.18703e8	0.564511
$82$	4.25482e8	1.03925
$83$	1.14283e8	0.264320	0.132160	−	0.991228i	$-0.457809\pi$
$83$	1.14283e8	0.264320	0.132160	+	0.991228i	$0.457809\pi$
$84$	−3.82603e7	−0.0838477
$85$	2.78037e8	0.577719
$86$	3.91762e8	0.772289
$87$	2.53411e8	0.474230
$88$	−6.69285e8	−1.18971
$89$	3.85818e8	0.651819	0.325910	−	0.945401i	$-0.394329\pi$
$89$	3.85818e8	0.651819	0.325910	+	0.945401i	$0.394329\pi$
$90$	−2.90655e8	−0.466967
$91$	−6.85750e7	−0.104828
$92$	2.00375e8	0.291607
$93$	−1.52970e8	−0.212048
$94$	−1.96543e8	−0.259646
$95$	1.10068e9	1.38645
$96$	3.11788e8	0.374661
$97$	−1.40755e9	−1.61432	−0.807161	−	0.590332i	$-0.798997\pi$
$97$	−1.40755e9	−1.61432	−0.807161	+	0.590332i	$0.798997\pi$
$98$	8.58134e7	0.0939805
$99$	−9.34192e8	−0.977412
$100$	1.68885e8	0.168885
$101$	−6.99791e8	−0.669148	−0.334574	−	0.942370i	$-0.608592\pi$
$101$	−6.99791e8	−0.669148	−0.334574	+	0.942370i	$0.608592\pi$
$102$	1.93909e8	0.177377
$103$	−1.92214e8	−0.168274	−0.0841370	−	0.996454i	$-0.526813\pi$
$103$	−1.92214e8	−0.168274	−0.0841370	+	0.996454i	$0.526813\pi$
$104$	3.41148e8	0.285952
$105$	1.54292e8	0.123877
$106$	−3.81960e8	−0.293861
$107$	−1.31731e9	−0.971538	−0.485769	−	0.874087i	$-0.661460\pi$
$107$	−1.31731e9	−0.971538	−0.485769	+	0.874087i	$0.661460\pi$
$108$	5.79326e8	0.409747
$109$	1.30529e9	0.885700	0.442850	−	0.896596i	$-0.353967\pi$
$109$	1.30529e9	0.885700	0.442850	+	0.896596i	$0.353967\pi$
$110$	9.76844e8	0.636148
$111$	6.55250e8	0.409688
$112$	−6.98959e7	−0.0419731
$113$	−1.46263e9	−0.843879	−0.421940	−	0.906624i	$-0.638651\pi$
$113$	−1.46263e9	−0.843879	−0.421940	+	0.906624i	$0.638651\pi$
$114$	7.67636e8	0.425681
$115$	−8.08049e8	−0.430822
$116$	−1.34124e9	−0.687773
$117$	4.76176e8	0.234926
$118$	1.58060e9	0.750504
$119$	5.70009e8	0.260567
$120$	−7.67573e8	−0.337912
$121$	7.81722e8	0.331526
$122$	9.81971e7	0.0401309
$123$	1.56837e9	0.617839
$124$	8.09631e8	0.307532
$125$	−2.96846e9	−1.08752
$126$	−5.95877e8	−0.210615
$127$	1.47190e9	0.502066	0.251033	−	0.967979i	$-0.419230\pi$
$127$	1.47190e9	0.502066	0.251033	+	0.967979i	$0.419230\pi$
$128$	−1.42834e9	−0.470313
$129$	1.44407e9	0.459130
$130$	−4.97917e8	−0.152901
$131$	1.89756e8	0.0562956	0.0281478	−	0.999604i	$-0.491039\pi$
$131$	1.89756e8	0.0562956	0.0281478	+	0.999604i	$0.491039\pi$
$132$	−8.92890e8	−0.255985
$133$	2.25652e9	0.625327
$134$	1.81606e9	0.486584
$135$	−2.33624e9	−0.605362
$136$	−2.83569e9	−0.710778
$137$	−7.03563e9	−1.70632	−0.853160	−	0.521650i	$-0.825317\pi$
$137$	−7.03563e9	−1.70632	−0.853160	+	0.521650i	$0.825317\pi$
$138$	−5.63551e8	−0.132275
$139$	4.54245e8	0.103210	0.0516052	−	0.998668i	$-0.483566\pi$
$139$	4.54245e8	0.103210	0.0516052	+	0.998668i	$0.483566\pi$
$140$	−8.16626e8	−0.179658
$141$	−7.24476e8	−0.154361
$142$	2.16815e9	0.447498
$143$	−1.60035e9	−0.320039
$144$	4.85349e8	0.0940638
$145$	5.40879e9	1.01612
$146$	−6.69004e9	−1.21854
$147$	3.16316e8	0.0558719
$148$	−3.46807e9	−0.594169
$149$	−8.48666e9	−1.41058	−0.705291	−	0.708918i	$-0.749184\pi$
$149$	−8.48666e9	−1.41058	−0.705291	+	0.708918i	$0.749184\pi$
$150$	−4.74987e8	−0.0766075
$151$	−1.45264e9	−0.227384	−0.113692	−	0.993516i	$-0.536268\pi$
$151$	−1.45264e9	−0.227384	−0.113692	+	0.993516i	$0.536268\pi$
$152$	−1.12258e10	−1.70577
$153$	−3.95807e9	−0.583945
$154$	2.00265e9	0.286920
$155$	−3.26499e9	−0.454348
$156$	4.55123e8	0.0615274
$157$	−1.15445e10	−1.51644	−0.758221	−	0.651997i	$-0.773931\pi$
$157$	−1.15445e10	−1.51644	−0.758221	+	0.651997i	$0.773931\pi$
$158$	1.01323e10	1.29345
$159$	−1.40794e9	−0.174702
$160$	6.65478e9	0.802775
$161$	−1.65660e9	−0.194313
$162$	3.25556e9	0.371371
$163$	−6.24652e9	−0.693097	−0.346548	−	0.938032i	$-0.612646\pi$
$163$	−6.24652e9	−0.693097	−0.346548	+	0.938032i	$0.612646\pi$
$164$	−8.30098e9	−0.896050
$165$	3.60074e9	0.378194
$166$	1.70119e9	0.173887
$167$	2.46109e9	0.244851	0.122426	−	0.992478i	$-0.460933\pi$
$167$	2.46109e9	0.244851	0.122426	+	0.992478i	$0.460933\pi$
$168$	−1.57362e9	−0.152408
$169$	8.15731e8	0.0769231
$170$	4.13878e9	0.380060
$171$	−1.56690e10	−1.40139
$172$	−7.64312e9	−0.665875
$173$	−2.68513e9	−0.227907	−0.113953	−	0.993486i	$-0.536351\pi$
$173$	−2.68513e9	−0.227907	−0.113953	+	0.993486i	$0.536351\pi$
$174$	3.77221e9	0.311978
$175$	−1.39626e9	−0.112537
$176$	−1.63118e9	−0.128143
$177$	5.82625e9	0.446179
$178$	5.74319e9	0.428808
$179$	1.67166e10	1.21705	0.608527	−	0.793533i	$-0.291761\pi$
$179$	1.67166e10	1.21705	0.608527	+	0.793533i	$0.291761\pi$
$180$	5.67055e9	0.402623
$181$	1.74871e10	1.21105	0.605526	−	0.795825i	$-0.292963\pi$
$181$	1.74871e10	1.21105	0.605526	+	0.795825i	$0.292963\pi$
$182$	−1.02079e9	−0.0689628
$183$	3.61964e8	0.0238581
$184$	8.24128e9	0.530047
$185$	1.39856e10	0.877827
$186$	−2.27707e9	−0.139498
$187$	1.33024e10	0.795507
$188$	3.83446e9	0.223869
$189$	−4.78957e9	−0.273035
$190$	1.63844e10	0.912094
$191$	−6.56421e9	−0.356888	−0.178444	−	0.983950i	$-0.557106\pi$
$191$	−6.56421e9	−0.356888	−0.178444	+	0.983950i	$0.557106\pi$
$192$	5.45903e9	0.289908
$193$	9.32012e9	0.483519	0.241759	−	0.970336i	$-0.422276\pi$
$193$	9.32012e9	0.483519	0.241759	+	0.970336i	$0.422276\pi$
$194$	−2.09524e10	−1.06200
$195$	−1.83537e9	−0.0909008
$196$	−1.67418e9	−0.0810308
$197$	−3.37115e10	−1.59470	−0.797351	−	0.603516i	$-0.793766\pi$
$197$	−3.37115e10	−1.59470	−0.797351	+	0.603516i	$0.793766\pi$
$198$	−1.39061e10	−0.643004
$199$	2.85426e10	1.29020	0.645098	−	0.764100i	$-0.276817\pi$
$199$	2.85426e10	1.29020	0.645098	+	0.764100i	$0.276817\pi$
$200$	6.94614e9	0.306979
$201$	6.69416e9	0.289277
$202$	−1.04169e10	−0.440208
$203$	1.10887e10	0.458298
$204$	−3.78308e9	−0.152936
$205$	3.34752e10	1.32383
$206$	−2.86125e9	−0.110701
$207$	1.15032e10	0.435465
$208$	8.31444e8	0.0307998
$209$	5.26610e10	1.90911
$210$	2.29675e9	0.0814941
$211$	−1.78417e10	−0.619678	−0.309839	−	0.950789i	$-0.600275\pi$
$211$	−1.78417e10	−0.619678	−0.309839	+	0.950789i	$0.600275\pi$
$212$	7.45188e9	0.253370
$213$	7.99200e9	0.266040
$214$	−1.96091e10	−0.639139
$215$	3.08223e10	0.983766
$216$	2.38273e10	0.744787
$217$	−6.69362e9	−0.204924
$218$	1.94302e10	0.582670
$219$	−2.46601e10	−0.724431
$220$	−1.90578e10	−0.548493
$221$	−6.78052e9	−0.191204
$222$	9.75388e9	0.269519
$223$	9.09759e9	0.246351	0.123175	−	0.992385i	$-0.460692\pi$
$223$	9.09759e9	0.246351	0.123175	+	0.992385i	$0.460692\pi$
$224$	1.36431e10	0.362074
$225$	9.69545e9	0.252201
$226$	−2.17723e10	−0.555157
$227$	−5.05192e10	−1.26282	−0.631408	−	0.775451i	$-0.717523\pi$
$227$	−5.05192e10	−1.26282	−0.631408	+	0.775451i	$0.717523\pi$
$228$	−1.49763e10	−0.367026
$229$	7.77315e10	1.86783	0.933915	−	0.357496i	$-0.116369\pi$
$229$	7.77315e10	1.86783	0.933915	+	0.357496i	$0.116369\pi$
$230$	−1.20284e10	−0.283422
$231$	7.38196e9	0.170576
$232$	−5.51642e10	−1.25015
$233$	5.85104e10	1.30056	0.650281	−	0.759694i	$-0.274651\pi$
$233$	5.85104e10	1.30056	0.650281	+	0.759694i	$0.274651\pi$
$234$	7.08824e9	0.154549
$235$	−1.54632e10	−0.330745
$236$	−3.08368e10	−0.647092
$237$	3.73486e10	0.768965
$238$	8.48501e9	0.171418
$239$	−3.17529e10	−0.629496	−0.314748	−	0.949175i	$-0.601920\pi$
$239$	−3.17529e10	−0.629496	−0.314748	+	0.949175i	$0.601920\pi$
$240$	−1.87072e9	−0.0363965
$241$	2.99027e9	0.0570998	0.0285499	−	0.999592i	$-0.490911\pi$
$241$	2.99027e9	0.0570998	0.0285499	+	0.999592i	$0.490911\pi$
$242$	1.16365e10	0.218099
$243$	5.12644e10	0.943166
$244$	−1.91578e9	−0.0346013
$245$	6.75145e9	0.119715
$246$	2.33464e10	0.406454
$247$	−2.68424e10	−0.458865
$248$	3.32996e10	0.558992
$249$	6.27075e9	0.103377
$250$	−4.41878e10	−0.715439
$251$	−2.67070e10	−0.424711	−0.212355	−	0.977193i	$-0.568113\pi$
$251$	−2.67070e10	−0.424711	−0.212355	+	0.977193i	$0.568113\pi$
$252$	1.16253e10	0.181594
$253$	−3.86605e10	−0.593232
$254$	2.19103e10	0.330291
$255$	1.52560e10	0.225948
$256$	−7.22006e10	−1.05066
$257$	−6.64620e10	−0.950329	−0.475165	−	0.879897i	$-0.657612\pi$
$257$	−6.64620e10	−0.950329	−0.475165	+	0.879897i	$0.657612\pi$
$258$	2.14961e10	0.302045
$259$	2.86722e10	0.395925
$260$	9.71414e9	0.131833
$261$	−7.69985e10	−1.02707
$262$	2.82466e9	0.0370348
$263$	−2.91030e10	−0.375091	−0.187546	−	0.982256i	$-0.560053\pi$
$263$	−2.91030e10	−0.375091	−0.187546	+	0.982256i	$0.560053\pi$
$264$	−3.67239e10	−0.465298
$265$	−3.00511e10	−0.374329
$266$	3.35900e10	0.411380
$267$	2.11699e10	0.254929
$268$	−3.54305e10	−0.419537
$269$	9.44614e10	1.09994	0.549970	−	0.835184i	$-0.314639\pi$
$269$	9.44614e10	1.09994	0.549970	+	0.835184i	$0.314639\pi$
$270$	−3.47767e10	−0.398245
$271$	−1.40552e10	−0.158298	−0.0791491	−	0.996863i	$-0.525220\pi$
$271$	−1.40552e10	−0.158298	−0.0791491	+	0.996863i	$0.525220\pi$
$272$	−6.91113e9	−0.0765577
$273$	−3.76273e9	−0.0409988
$274$	−1.04731e11	−1.12252
$275$	−3.25849e10	−0.343573
$276$	1.09946e10	0.114049
$277$	1.80248e11	1.83955	0.919775	−	0.392447i	$-0.128371\pi$
$277$	1.80248e11	1.83955	0.919775	+	0.392447i	$0.128371\pi$
$278$	6.76178e9	0.0678984
$279$	4.64797e10	0.459245
$280$	−3.35872e10	−0.326560
$281$	−4.59798e10	−0.439935	−0.219968	−	0.975507i	$-0.570595\pi$
$281$	−4.59798e10	−0.439935	−0.219968	+	0.975507i	$0.570595\pi$
$282$	−1.07844e10	−0.101548
$283$	−7.59488e10	−0.703853	−0.351926	−	0.936028i	$-0.614473\pi$
$283$	−7.59488e10	−0.703853	−0.351926	+	0.936028i	$0.614473\pi$
$284$	−4.22996e10	−0.385837
$285$	6.03945e10	0.542245
$286$	−2.38224e10	−0.210542
$287$	6.86283e10	0.597083
$288$	−9.47361e10	−0.811427
$289$	−6.22269e10	−0.524732
$290$	8.05140e10	0.668467
$291$	−7.72326e10	−0.631367
$292$	1.30520e11	1.05064
$293$	−1.13072e11	−0.896294	−0.448147	−	0.893960i	$-0.647916\pi$
$293$	−1.13072e11	−0.896294	−0.448147	+	0.893960i	$0.647916\pi$
$294$	4.70861e9	0.0367561
$295$	1.24355e11	0.956016
$296$	−1.42639e11	−1.08001
$297$	−1.11775e11	−0.833571
$298$	−1.26330e11	−0.927971
$299$	1.97060e10	0.142586
$300$	9.26680e9	0.0660517
$301$	6.31894e10	0.443706
$302$	−2.16236e10	−0.149588
$303$	−3.83977e10	−0.261706
$304$	−2.73594e10	−0.183728
$305$	7.72575e9	0.0511200
$306$	−5.89188e10	−0.384156
$307$	−8.58576e10	−0.551640	−0.275820	−	0.961209i	$-0.588949\pi$
$307$	−8.58576e10	−0.551640	−0.275820	+	0.961209i	$0.588949\pi$
$308$	−3.90708e10	−0.247385
$309$	−1.05468e10	−0.0658126
$310$	−4.86018e10	−0.298899
$311$	1.38901e11	0.841947	0.420974	−	0.907073i	$-0.361689\pi$
$311$	1.38901e11	0.841947	0.420974	+	0.907073i	$0.361689\pi$
$312$	1.87189e10	0.111837
$313$	2.19944e11	1.29527	0.647637	−	0.761949i	$-0.275757\pi$
$313$	2.19944e11	1.29527	0.647637	+	0.761949i	$0.275757\pi$
$314$	−1.71848e11	−0.997612
$315$	−4.68812e10	−0.268288
$316$	−1.97676e11	−1.11523
$317$	2.56324e11	1.42568	0.712841	−	0.701326i	$-0.247408\pi$
$317$	2.56324e11	1.42568	0.712841	+	0.701326i	$0.247408\pi$
$318$	−2.09583e10	−0.114930
$319$	2.58780e11	1.39917
$320$	1.16517e11	0.621177
$321$	−7.22810e10	−0.379972
$322$	−2.46597e10	−0.127831
$323$	2.23119e11	1.14058
$324$	−6.35146e10	−0.320200
$325$	1.66091e10	0.0825795
$326$	−9.29841e10	−0.455963
$327$	7.16215e10	0.346401
$328$	−3.41413e11	−1.62873
$329$	−3.17014e10	−0.149175
$330$	5.35997e10	0.248800
$331$	3.35041e11	1.53416	0.767081	−	0.641550i	$-0.221708\pi$
$331$	3.35041e11	1.53416	0.767081	+	0.641550i	$0.221708\pi$
$332$	−3.31895e10	−0.149927
$333$	−1.99096e11	−0.887288
$334$	3.66351e10	0.161079
$335$	1.42880e11	0.619825
$336$	−3.83521e9	−0.0164158
$337$	−2.74242e10	−0.115824	−0.0579122	−	0.998322i	$-0.518444\pi$
$337$	−2.74242e10	−0.115824	−0.0579122	+	0.998322i	$0.518444\pi$
$338$	1.21428e10	0.0506049
$339$	−8.02547e10	−0.330044
$340$	−8.07459e10	−0.327691
$341$	−1.56211e11	−0.625628
$342$	−2.33245e11	−0.921923
$343$	1.38413e10	0.0539949
$344$	−3.14356e11	−1.21034
$345$	−4.43379e10	−0.168496
$346$	−3.99701e10	−0.149931
$347$	−9.41807e10	−0.348722	−0.174361	−	0.984682i	$-0.555786\pi$
$347$	−9.41807e10	−0.348722	−0.174361	+	0.984682i	$0.555786\pi$
$348$	−7.35942e10	−0.268991
$349$	3.68602e11	1.32997	0.664986	−	0.746855i	$-0.268437\pi$
$349$	3.68602e11	1.32997	0.664986	+	0.746855i	$0.268437\pi$
$350$	−2.07844e10	−0.0740339
$351$	5.69742e10	0.200353
$352$	3.18393e11	1.10540
$353$	6.04311e9	0.0207145	0.0103572	−	0.999946i	$-0.496703\pi$
$353$	6.04311e9	0.0207145	0.0103572	+	0.999946i	$0.496703\pi$
$354$	8.67281e10	0.293525
$355$	1.70581e11	0.570037
$356$	−1.12047e11	−0.369722
$357$	3.12766e10	0.101909
$358$	2.48839e11	0.800655
$359$	−3.58417e11	−1.13884	−0.569421	−	0.822046i	$-0.692833\pi$
$359$	−3.58417e11	−1.13884	−0.569421	+	0.822046i	$0.692833\pi$
$360$	2.33226e11	0.731838
$361$	5.60585e11	1.73724
$362$	2.60308e11	0.796707
$363$	4.28933e10	0.129661
$364$	1.99152e10	0.0594604
$365$	−5.26345e11	−1.55222
$366$	5.38810e9	0.0156954
$367$	−2.98511e11	−0.858941	−0.429471	−	0.903081i	$-0.641300\pi$
$367$	−2.98511e11	−0.858941	−0.429471	+	0.903081i	$0.641300\pi$
$368$	2.00856e10	0.0570913
$369$	−4.76546e11	−1.33809
$370$	2.08187e11	0.577490
$371$	−6.16084e10	−0.168833
$372$	4.44247e10	0.120277
$373$	−3.35261e11	−0.896795	−0.448397	−	0.893834i	$-0.648005\pi$
$373$	−3.35261e11	−0.896795	−0.448397	+	0.893834i	$0.648005\pi$
$374$	1.98017e11	0.523335
$375$	−1.62881e11	−0.425333
$376$	1.57709e11	0.406921
$377$	−1.31905e11	−0.336299
$378$	−7.12964e10	−0.179620
$379$	−5.80929e11	−1.44626	−0.723130	−	0.690711i	$-0.757297\pi$
$379$	−5.80929e11	−1.44626	−0.723130	+	0.690711i	$0.757297\pi$
$380$	−3.19653e11	−0.786416
$381$	8.07635e10	0.196360
$382$	−9.77131e10	−0.234784
$383$	7.71579e11	1.83226	0.916128	−	0.400886i	$-0.131298\pi$
$383$	7.71579e11	1.83226	0.916128	+	0.400886i	$0.131298\pi$
$384$	−7.83735e10	−0.183941
$385$	1.57560e11	0.365488
$386$	1.38737e11	0.318089
$387$	−4.38779e11	−0.994368
$388$	4.08772e11	0.915669
$389$	3.01688e11	0.668012	0.334006	−	0.942571i	$-0.391599\pi$
$389$	3.01688e11	0.668012	0.334006	+	0.942571i	$0.391599\pi$
$390$	−2.73208e10	−0.0598003
$391$	−1.63800e11	−0.354421
$392$	−6.88579e10	−0.147288
$393$	1.04120e10	0.0220174
$394$	−5.01820e11	−1.04910
$395$	7.97167e11	1.64764
$396$	2.71303e11	0.554404
$397$	−4.86957e10	−0.0983860	−0.0491930	−	0.998789i	$-0.515665\pi$
$397$	−4.86957e10	−0.0983860	−0.0491930	+	0.998789i	$0.515665\pi$
$398$	4.24879e11	0.848772
$399$	1.23816e11	0.244568
$400$	1.69291e10	0.0330646
$401$	2.59434e10	0.0501046	0.0250523	−	0.999686i	$-0.492025\pi$
$401$	2.59434e10	0.0501046	0.0250523	+	0.999686i	$0.492025\pi$
$402$	9.96475e10	0.190305
$403$	7.96237e10	0.150373
$404$	2.03229e11	0.379551
$405$	2.56134e11	0.473064
$406$	1.65063e11	0.301497
$407$	6.69131e11	1.20875
$408$	−1.55595e11	−0.277988
$409$	2.51042e11	0.443599	0.221800	−	0.975092i	$-0.428807\pi$
$409$	2.51042e11	0.443599	0.221800	+	0.975092i	$0.428807\pi$
$410$	4.98304e11	0.870897
$411$	−3.86047e11	−0.667348
$412$	5.58217e10	0.0954477
$413$	2.54943e11	0.431190
$414$	1.71234e11	0.286476
$415$	1.33843e11	0.221502
$416$	−1.62291e11	−0.265690
$417$	2.49246e10	0.0403660
$418$	7.83899e11	1.25593
$419$	1.53427e11	0.243187	0.121593	−	0.992580i	$-0.461200\pi$
$419$	1.53427e11	0.243187	0.121593	+	0.992580i	$0.461200\pi$
$420$	−4.48085e10	−0.0702649
$421$	−1.06293e12	−1.64905	−0.824524	−	0.565827i	$-0.808557\pi$
$421$	−1.06293e12	−1.64905	−0.824524	+	0.565827i	$0.808557\pi$
$422$	−2.65588e11	−0.407664
$423$	2.20131e11	0.334310
$424$	3.06491e11	0.460544
$425$	−1.38059e11	−0.205264
$426$	1.18967e11	0.175018
$427$	1.58387e10	0.0230566
$428$	3.82565e11	0.551072
$429$	−8.78118e10	−0.125168
$430$	4.58813e11	0.647183
$431$	4.60835e10	0.0643276	0.0321638	−	0.999483i	$-0.489760\pi$
$431$	4.60835e10	0.0643276	0.0321638	+	0.999483i	$0.489760\pi$
$432$	5.80717e10	0.0802209
$433$	2.79528e11	0.382147	0.191073	−	0.981576i	$-0.438803\pi$
$433$	2.79528e11	0.382147	0.191073	+	0.981576i	$0.438803\pi$
$434$	−9.96396e10	−0.134812
$435$	2.96782e11	0.397408
$436$	−3.79074e11	−0.502383
$437$	−6.48444e11	−0.850562
$438$	−3.67085e11	−0.476577
$439$	−2.28845e11	−0.294070	−0.147035	−	0.989131i	$-0.546973\pi$
$439$	−2.28845e11	−0.294070	−0.147035	+	0.989131i	$0.546973\pi$
$440$	−7.83834e11	−0.996981
$441$	−9.61122e10	−0.121005
$442$	−1.00933e11	−0.125786
$443$	−8.34045e11	−1.02890	−0.514450	−	0.857521i	$-0.672004\pi$
$443$	−8.34045e11	−1.02890	−0.514450	+	0.857521i	$0.672004\pi$
$444$	−1.90294e11	−0.232382
$445$	4.51850e11	0.546229
$446$	1.35424e11	0.162065
$447$	−4.65666e11	−0.551684
$448$	2.38875e11	0.280168
$449$	1.18958e12	1.38129	0.690643	−	0.723196i	$-0.257328\pi$
$449$	1.18958e12	1.38129	0.690643	+	0.723196i	$0.257328\pi$
$450$	1.44324e11	0.165914
$451$	1.60160e12	1.82288
$452$	4.24768e11	0.478662
$453$	−7.97066e10	−0.0889309
$454$	−7.52016e11	−0.830760
$455$	−8.03116e10	−0.0878470
$456$	−6.15963e11	−0.667133
$457$	−1.15025e12	−1.23358	−0.616792	−	0.787126i	$-0.711568\pi$
$457$	−1.15025e12	−1.23358	−0.616792	+	0.787126i	$0.711568\pi$
$458$	1.15709e12	1.22878
$459$	−4.73581e11	−0.498009
$460$	2.34669e11	0.244369
$461$	−1.55958e12	−1.60825	−0.804125	−	0.594460i	$-0.797366\pi$
$461$	−1.55958e12	−1.60825	−0.804125	+	0.594460i	$0.797366\pi$
$462$	1.09886e11	0.112216
$463$	−6.08544e11	−0.615429	−0.307714	−	0.951479i	$-0.599564\pi$
$463$	−6.08544e11	−0.615429	−0.307714	+	0.951479i	$0.599564\pi$
$464$	−1.34446e11	−0.134653
$465$	−1.79151e11	−0.177697
$466$	8.70971e11	0.855592
$467$	9.13553e11	0.888808	0.444404	−	0.895827i	$-0.353416\pi$
$467$	9.13553e11	0.888808	0.444404	+	0.895827i	$0.353416\pi$
$468$	−1.38288e11	−0.133254
$469$	2.92921e11	0.279559
$470$	−2.30181e11	−0.217585
$471$	−6.33449e11	−0.593086
$472$	−1.26830e12	−1.17620
$473$	1.47467e12	1.35462
$474$	5.55962e11	0.505874
$475$	−5.46539e11	−0.492607
$476$	−1.65539e11	−0.147798
$477$	4.27801e11	0.378363
$478$	−4.72666e11	−0.414123
$479$	−7.60005e11	−0.659640	−0.329820	−	0.944044i	$-0.606988\pi$
$479$	−7.60005e11	−0.659640	−0.329820	+	0.944044i	$0.606988\pi$
$480$	3.65150e11	0.313968
$481$	−3.41069e11	−0.290529
$482$	4.45125e10	0.0375638
$483$	−9.08981e10	−0.0759964
$484$	−2.27023e11	−0.188047
$485$	−1.64845e12	−1.35281
$486$	7.63109e11	0.620474
$487$	1.31990e12	1.06331	0.531655	−	0.846961i	$-0.321570\pi$
$487$	1.31990e12	1.06331	0.531655	+	0.846961i	$0.321570\pi$
$488$	−7.87947e10	−0.0628938
$489$	−3.42748e11	−0.271073
$490$	1.00500e11	0.0787563
$491$	2.39571e12	1.86023	0.930117	−	0.367264i	$-0.119705\pi$
$491$	2.39571e12	1.86023	0.930117	+	0.367264i	$0.119705\pi$
$492$	−4.55477e11	−0.350448
$493$	1.09642e12	0.835923
$494$	−3.99569e11	−0.301870
$495$	−1.09408e12	−0.819078
$496$	8.11575e10	0.0602090
$497$	3.49712e11	0.257102
$498$	9.33448e10	0.0680077
$499$	−1.51885e12	−1.09663	−0.548317	−	0.836271i	$-0.684731\pi$
$499$	−1.51885e12	−1.09663	−0.548317	+	0.836271i	$0.684731\pi$
$500$	8.62085e11	0.616858
$501$	1.35041e11	0.0957623
$502$	−3.97553e11	−0.279402
$503$	−9.62029e11	−0.670089	−0.335044	−	0.942202i	$-0.608751\pi$
$503$	−9.62029e11	−0.670089	−0.335044	+	0.942202i	$0.608751\pi$
$504$	4.78141e11	0.330079
$505$	−8.19560e11	−0.560750
$506$	−5.75490e11	−0.390266
$507$	4.47594e10	0.0300849
$508$	−4.27460e11	−0.284780
$509$	−1.57085e12	−1.03730	−0.518649	−	0.854987i	$-0.673565\pi$
$509$	−1.57085e12	−1.03730	−0.518649	+	0.854987i	$0.673565\pi$
$510$	2.27096e11	0.148643
$511$	−1.07907e12	−0.700094
$512$	−3.43450e11	−0.220876
$513$	−1.87479e12	−1.19515
$514$	−9.89336e11	−0.625187
$515$	−2.25111e11	−0.141015
$516$	−4.19380e11	−0.260426
$517$	−7.39824e11	−0.455429
$518$	4.26808e11	0.260464
$519$	−1.47334e11	−0.0891351
$520$	3.99536e11	0.239630
$521$	1.76338e12	1.04852	0.524260	−	0.851558i	$-0.324342\pi$
$521$	1.76338e12	1.04852	0.524260	+	0.851558i	$0.324342\pi$
$522$	−1.14618e12	−0.675671
$523$	−2.05406e12	−1.20048	−0.600240	−	0.799820i	$-0.704928\pi$
$523$	−2.05406e12	−1.20048	−0.600240	+	0.799820i	$0.704928\pi$
$524$	−5.51079e10	−0.0319318
$525$	−7.66132e10	−0.0440136
$526$	−4.33220e11	−0.246759
$527$	−6.61848e11	−0.373775
$528$	−8.95033e10	−0.0501172
$529$	−1.32511e12	−0.735698
$530$	−4.47333e11	−0.246258
$531$	−1.77030e12	−0.966319
$532$	−6.55327e11	−0.354695
$533$	−8.16365e11	−0.438139
$534$	3.15130e11	0.167708
$535$	−1.54276e12	−0.814156
$536$	−1.45723e12	−0.762582
$537$	9.17246e11	0.475994
$538$	1.40613e12	0.723611
$539$	3.23018e11	0.164845
$540$	6.78478e11	0.343371
$541$	−1.75672e12	−0.881687	−0.440843	−	0.897584i	$-0.645321\pi$
$541$	−1.75672e12	−0.881687	−0.440843	+	0.897584i	$0.645321\pi$
$542$	−2.09223e11	−0.104139
$543$	9.59520e11	0.473647
$544$	1.34900e12	0.660413
$545$	1.52869e12	0.742223
$546$	−5.60110e10	−0.0269716
$547$	1.86146e12	0.889016	0.444508	−	0.895775i	$-0.353378\pi$
$547$	1.86146e12	0.889016	0.444508	+	0.895775i	$0.353378\pi$
$548$	2.04325e12	0.967851
$549$	−1.09982e11	−0.0516709
$550$	−4.85050e11	−0.226024
$551$	4.34046e12	2.00610
$552$	4.52202e11	0.207303
$553$	1.63429e12	0.743132
$554$	2.68313e12	1.21017
$555$	7.67396e11	0.343322
$556$	−1.31919e11	−0.0585426
$557$	−3.36261e12	−1.48022	−0.740112	−	0.672483i	$-0.765228\pi$
$557$	−3.36261e12	−1.48022	−0.740112	+	0.672483i	$0.765228\pi$
$558$	6.91885e11	0.302120
$559$	−7.51667e11	−0.325591
$560$	−8.18586e10	−0.0351737
$561$	7.29909e11	0.311126
$562$	−6.84444e11	−0.289417
$563$	1.67643e12	0.703230	0.351615	−	0.936145i	$-0.385633\pi$
$563$	1.67643e12	0.703230	0.351615	+	0.936145i	$0.385633\pi$
$564$	2.10398e11	0.0875560
$565$	−1.71295e12	−0.707176
$566$	−1.13055e12	−0.463039
$567$	5.25106e11	0.213365
$568$	−1.73975e12	−0.701326
$569$	−4.15585e11	−0.166209	−0.0831045	−	0.996541i	$-0.526484\pi$
$569$	−4.15585e11	−0.166209	−0.0831045	+	0.996541i	$0.526484\pi$
$570$	8.99018e11	0.356723
$571$	1.29715e12	0.510654	0.255327	−	0.966855i	$-0.417817\pi$
$571$	1.29715e12	0.510654	0.255327	+	0.966855i	$0.417817\pi$
$572$	4.64765e11	0.181531
$573$	−3.60180e11	−0.139580
$574$	1.02158e12	0.392799
$575$	4.01235e11	0.153071
$576$	−1.65872e12	−0.627872
$577$	2.21887e12	0.833374	0.416687	−	0.909050i	$-0.363191\pi$
$577$	2.21887e12	0.833374	0.416687	+	0.909050i	$0.363191\pi$
$578$	−9.26293e11	−0.345202
$579$	5.11398e11	0.189106
$580$	−1.57079e12	−0.576359
$581$	2.74394e11	0.0999037
$582$	−1.14966e12	−0.415353
$583$	−1.43777e12	−0.515444
$584$	5.36819e12	1.90972
$585$	5.57674e11	0.196870
$586$	−1.68316e12	−0.589639
$587$	−3.31465e12	−1.15230	−0.576151	−	0.817343i	$-0.695446\pi$
$587$	−3.31465e12	−1.15230	−0.576151	+	0.817343i	$0.695446\pi$
$588$	−9.18629e10	−0.0316915
$589$	−2.62009e12	−0.897011
$590$	1.85112e12	0.628928
$591$	−1.84976e12	−0.623694
$592$	−3.47639e11	−0.116327
$593$	3.44047e12	1.14254	0.571270	−	0.820762i	$-0.306451\pi$
$593$	3.44047e12	1.14254	0.571270	+	0.820762i	$0.306451\pi$
$594$	−1.66386e12	−0.548376
$595$	6.67566e11	0.218357
$596$	2.46465e12	0.800105
$597$	1.56614e12	0.504600
$598$	2.93339e11	0.0938024
$599$	8.31093e11	0.263772	0.131886	−	0.991265i	$-0.457897\pi$
$599$	8.31093e11	0.263772	0.131886	+	0.991265i	$0.457897\pi$
$600$	3.81137e11	0.120061
$601$	−4.29929e12	−1.34419	−0.672097	−	0.740463i	$-0.734606\pi$
$601$	−4.29929e12	−1.34419	−0.672097	+	0.740463i	$0.734606\pi$
$602$	9.40622e11	0.291898
$603$	−2.03401e12	−0.626505
$604$	4.21867e11	0.128976
$605$	9.15514e11	0.277821
$606$	−5.71579e11	−0.172167
$607$	1.93368e12	0.578144	0.289072	−	0.957307i	$-0.406653\pi$
$607$	1.93368e12	0.578144	0.289072	+	0.957307i	$0.406653\pi$
$608$	5.34034e12	1.58490
$609$	6.08440e11	0.179242
$610$	1.15003e11	0.0336300
$611$	3.77103e11	0.109465
$612$	1.14948e12	0.331223
$613$	6.29773e12	1.80141	0.900704	−	0.434433i	$-0.143051\pi$
$613$	6.29773e12	1.80141	0.900704	+	0.434433i	$0.143051\pi$
$614$	−1.27805e12	−0.362904
$615$	1.83680e12	0.517753
$616$	−1.60695e12	−0.449666
$617$	5.26115e12	1.46150	0.730748	−	0.682647i	$-0.239172\pi$
$617$	5.26115e12	1.46150	0.730748	+	0.682647i	$0.239172\pi$
$618$	−1.56997e11	−0.0432957
$619$	−6.49007e12	−1.77681	−0.888407	−	0.459057i	$-0.848187\pi$
$619$	−6.49007e12	−1.77681	−0.888407	+	0.459057i	$0.848187\pi$
$620$	9.48200e11	0.257714
$621$	1.37635e12	0.371379
$622$	2.06765e12	0.553886
$623$	9.26348e11	0.246365
$624$	4.56216e10	0.0120459
$625$	−2.34071e12	−0.613604
$626$	3.27403e12	0.852114
$627$	2.88953e12	0.746660
$628$	3.35269e12	0.860150
$629$	2.83504e12	0.722156
$630$	−6.97862e11	−0.176497
$631$	−3.97065e12	−0.997080	−0.498540	−	0.866867i	$-0.666130\pi$
$631$	−3.97065e12	−0.997080	−0.498540	+	0.866867i	$0.666130\pi$
$632$	−8.13029e12	−2.02712
$633$	−9.78982e11	−0.242358
$634$	3.81557e12	0.937904
$635$	1.72381e12	0.420735
$636$	4.08887e11	0.0990938
$637$	−1.64648e11	−0.0396214
$638$	3.85213e12	0.920465
$639$	−2.42835e12	−0.576180
$640$	−1.67280e12	−0.394125
$641$	−3.26111e12	−0.762964	−0.381482	−	0.924376i	$-0.624586\pi$
$641$	−3.26111e12	−0.762964	−0.381482	+	0.924376i	$0.624586\pi$
$642$	−1.07596e12	−0.249970
$643$	−6.17325e12	−1.42418	−0.712089	−	0.702089i	$-0.752251\pi$
$643$	−6.17325e12	−1.42418	−0.712089	+	0.702089i	$0.752251\pi$
$644$	4.81100e11	0.110217
$645$	1.69123e12	0.384754
$646$	3.32130e12	0.750345
$647$	8.40009e11	0.188458	0.0942290	−	0.995551i	$-0.469961\pi$
$647$	8.40009e11	0.188458	0.0942290	+	0.995551i	$0.469961\pi$
$648$	−2.61231e12	−0.582019
$649$	5.94968e12	1.31641
$650$	2.47240e11	0.0543260
$651$	−3.67281e11	−0.0801464
$652$	1.81408e12	0.393135
$653$	1.80435e10	0.00388340	0.00194170	−	0.999998i	$-0.499382\pi$
$653$	1.80435e10	0.00388340	0.00194170	+	0.999998i	$0.499382\pi$
$654$	1.06614e12	0.227884
$655$	2.22233e11	0.0471761
$656$	−8.32091e11	−0.175430
$657$	7.49294e12	1.56895
$658$	−4.71899e11	−0.0981369
$659$	−8.02016e12	−1.65653	−0.828263	−	0.560339i	$-0.810671\pi$
$659$	−8.02016e12	−1.65653	−0.828263	+	0.560339i	$0.810671\pi$
$660$	−1.04571e12	−0.214517
$661$	6.09192e12	1.24122	0.620608	−	0.784121i	$-0.286886\pi$
$661$	6.09192e12	1.24122	0.620608	+	0.784121i	$0.286886\pi$
$662$	4.98733e12	1.00927
$663$	−3.72049e11	−0.0747807
$664$	−1.36506e12	−0.272518
$665$	2.64273e12	0.524028
$666$	−2.96370e12	−0.583714
$667$	−3.18649e12	−0.623371
$668$	−7.14735e11	−0.138884
$669$	4.99187e11	0.0963488
$670$	2.12687e12	0.407760
$671$	3.69632e11	0.0703912
$672$	7.48602e11	0.141608
$673$	−6.40005e12	−1.20258	−0.601292	−	0.799029i	$-0.705347\pi$
$673$	−6.40005e12	−1.20258	−0.601292	+	0.799029i	$0.705347\pi$
$674$	−4.08230e11	−0.0761966
$675$	1.16005e12	0.215086
$676$	−2.36900e11	−0.0436320
$677$	3.06063e12	0.559967	0.279984	−	0.960005i	$-0.409671\pi$
$677$	3.06063e12	0.559967	0.279984	+	0.960005i	$0.409671\pi$
$678$	−1.19465e12	−0.217124
$679$	−3.37952e12	−0.610156
$680$	−3.32102e12	−0.595636
$681$	−2.77200e12	−0.493892
$682$	−2.32531e12	−0.411578
$683$	9.87164e12	1.73579	0.867893	−	0.496751i	$-0.165474\pi$
$683$	9.87164e12	1.73579	0.867893	+	0.496751i	$0.165474\pi$
$684$	4.55051e12	0.794891
$685$	−8.23977e12	−1.42991
$686$	2.06038e11	0.0355213
$687$	4.26515e12	0.730515
$688$	−7.66147e11	−0.130366
$689$	7.32860e11	0.123890
$690$	−6.60003e11	−0.110847
$691$	−1.05865e13	−1.76645	−0.883224	−	0.468952i	$-0.844632\pi$
$691$	−1.05865e13	−1.76645	−0.883224	+	0.468952i	$0.844632\pi$
$692$	7.79799e11	0.129272
$693$	−2.24299e12	−0.369427
$694$	−1.40195e12	−0.229411
$695$	5.31989e11	0.0864911
$696$	−3.02688e12	−0.488937
$697$	6.78579e12	1.08906
$698$	5.48691e12	0.874940
$699$	3.21048e12	0.508655
$700$	4.05494e11	0.0638327
$701$	−9.47927e12	−1.48267	−0.741334	−	0.671136i	$-0.765807\pi$
$701$	−9.47927e12	−1.48267	−0.741334	+	0.671136i	$0.765807\pi$
$702$	8.48103e11	0.131805
$703$	1.12232e13	1.73308
$704$	5.57468e12	0.855348
$705$	−8.48470e11	−0.129356
$706$	8.99562e10	0.0136273
$707$	−1.68020e12	−0.252914
$708$	−1.69203e12	−0.253080
$709$	8.81424e12	1.31002	0.655009	−	0.755621i	$-0.272665\pi$
$709$	8.81424e12	1.31002	0.655009	+	0.755621i	$0.272665\pi$
$710$	2.53922e12	0.375006
$711$	−1.13483e13	−1.66540
$712$	−4.60842e12	−0.672035
$713$	1.92351e12	0.278735
$714$	4.65575e11	0.0670421
$715$	−1.87425e12	−0.268195
$716$	−4.85475e12	−0.690332
$717$	−1.74229e12	−0.246198
$718$	−5.33530e12	−0.749202
$719$	−5.68210e12	−0.792919	−0.396460	−	0.918052i	$-0.629761\pi$
$719$	−5.68210e12	−0.792919	−0.396460	+	0.918052i	$0.629761\pi$
$720$	5.68416e11	0.0788261
$721$	−4.61505e11	−0.0636016
$722$	8.34473e12	1.14287
$723$	1.64077e11	0.0223319
$724$	−5.07849e12	−0.686928
$725$	−2.68573e12	−0.361028
$726$	6.38499e11	0.0852993
$727$	−1.05081e13	−1.39515	−0.697574	−	0.716513i	$-0.745737\pi$
$727$	−1.05081e13	−1.39515	−0.697574	+	0.716513i	$0.745737\pi$
$728$	8.19096e11	0.108080
$729$	−1.49184e12	−0.195636
$730$	−7.83504e12	−1.02115
$731$	6.24801e12	0.809307
$732$	−1.05120e11	−0.0135327
$733$	1.97777e12	0.253051	0.126526	−	0.991963i	$-0.459617\pi$
$733$	1.97777e12	0.253051	0.126526	+	0.991963i	$0.459617\pi$
$734$	−4.44356e12	−0.565066
$735$	3.70454e11	0.0468211
$736$	−3.92055e12	−0.492489
$737$	6.83597e12	0.853487
$738$	−7.09375e12	−0.880283
$739$	−4.32925e12	−0.533965	−0.266982	−	0.963701i	$-0.586027\pi$
$739$	−4.32925e12	−0.533965	−0.266982	+	0.963701i	$0.586027\pi$
$740$	−4.06163e12	−0.497918
$741$	−1.47285e12	−0.179464
$742$	−9.17087e11	−0.111069
$743$	−4.04814e12	−0.487311	−0.243655	−	0.969862i	$-0.578347\pi$
$743$	−4.04814e12	−0.487311	−0.243655	+	0.969862i	$0.578347\pi$
$744$	1.82716e12	0.218624
$745$	−9.93915e12	−1.18208
$746$	−4.99061e12	−0.589968
$747$	−1.90536e12	−0.223889
$748$	−3.86322e12	−0.451224
$749$	−3.16285e12	−0.367207
$750$	−2.42460e12	−0.279811
$751$	5.88905e12	0.675563	0.337781	−	0.941225i	$-0.390324\pi$
$751$	5.88905e12	0.675563	0.337781	+	0.941225i	$0.390324\pi$
$752$	3.84367e11	0.0438294
$753$	−1.46542e12	−0.166106
$754$	−1.96350e12	−0.221239
$755$	−1.70126e12	−0.190550
$756$	1.39096e12	0.154870
$757$	−8.08632e12	−0.894992	−0.447496	−	0.894286i	$-0.647684\pi$
$757$	−8.08632e12	−0.894992	−0.447496	+	0.894286i	$0.647684\pi$
$758$	−8.64756e12	−0.951442
$759$	−2.12131e12	−0.232015
$760$	−1.31471e13	−1.42945
$761$	1.54427e13	1.66914	0.834568	−	0.550904i	$-0.185717\pi$
$761$	1.54427e13	1.66914	0.834568	+	0.550904i	$0.185717\pi$
$762$	1.20222e12	0.129178
$763$	3.13399e12	0.334763
$764$	1.90634e12	0.202433
$765$	−4.63550e12	−0.489350
$766$	1.14855e13	1.20537
$767$	−3.03267e12	−0.316407
$768$	−3.96167e12	−0.410916
$769$	1.24931e13	1.28825	0.644126	−	0.764919i	$-0.277221\pi$
$769$	1.24931e13	1.28825	0.644126	+	0.764919i	$0.277221\pi$
$770$	2.34540e12	0.240441
$771$	−3.64679e12	−0.371677
$772$	−2.70670e12	−0.274260
$773$	−7.55861e12	−0.761438	−0.380719	−	0.924691i	$-0.624323\pi$
$773$	−7.55861e12	−0.761438	−0.380719	+	0.924691i	$0.624323\pi$
$774$	−6.53156e12	−0.654158
$775$	1.62122e12	0.161430
$776$	1.68125e13	1.66439
$777$	1.57325e12	0.154848
$778$	4.49085e12	0.439461
$779$	2.68632e13	2.61360
$780$	5.33018e11	0.0515604
$781$	8.16131e12	0.784929
$782$	−2.43829e12	−0.233160
$783$	−9.21282e12	−0.875920
$784$	−1.67820e11	−0.0158643
$785$	−1.35203e13	−1.27079
$786$	1.54990e11	0.0144845
$787$	−3.00895e12	−0.279594	−0.139797	−	0.990180i	$-0.544645\pi$
$787$	−3.00895e12	−0.279594	−0.139797	+	0.990180i	$0.544645\pi$
$788$	9.79029e12	0.904540
$789$	−1.59689e12	−0.146700
$790$	1.18664e13	1.08392
$791$	−3.51176e12	−0.318956
$792$	1.11585e13	1.00773
$793$	−1.88409e11	−0.0169189
$794$	−7.24872e11	−0.0647245
$795$	−1.64891e12	−0.146402
$796$	−8.28920e12	−0.731819
$797$	1.55967e13	1.36921	0.684606	−	0.728913i	$-0.259974\pi$
$797$	1.55967e13	1.36921	0.684606	+	0.728913i	$0.259974\pi$
$798$	1.84310e12	0.160892
$799$	−3.13455e12	−0.272092
$800$	−3.30442e12	−0.285227
$801$	−6.43245e12	−0.552116
$802$	3.86187e11	0.0329620
$803$	−2.51826e13	−2.13737
$804$	−1.94408e12	−0.164082
$805$	−1.94013e12	−0.162835
$806$	1.18526e12	0.0989248
$807$	5.18313e12	0.430191
$808$	8.35868e12	0.689901
$809$	9.70928e12	0.796927	0.398464	−	0.917184i	$-0.369544\pi$
$809$	9.70928e12	0.796927	0.398464	+	0.917184i	$0.369544\pi$
$810$	3.81275e12	0.311212
$811$	5.49187e12	0.445786	0.222893	−	0.974843i	$-0.428450\pi$
$811$	5.49187e12	0.445786	0.222893	+	0.974843i	$0.428450\pi$
$812$	−3.22032e12	−0.259954
$813$	−7.71215e11	−0.0619110
$814$	9.96052e12	0.795192
$815$	−7.31561e12	−0.580820
$816$	−3.79216e11	−0.0299420
$817$	2.47343e13	1.94223
$818$	3.73694e12	0.291828
$819$	1.14330e12	0.0887937
$820$	−9.72169e12	−0.750896
$821$	2.51924e13	1.93520	0.967598	−	0.252495i	$-0.0812511\pi$
$821$	2.51924e13	1.93520	0.967598	+	0.252495i	$0.0812511\pi$
$822$	−5.74660e12	−0.439023
$823$	−2.09373e13	−1.59082	−0.795409	−	0.606073i	$-0.792744\pi$
$823$	−2.09373e13	−1.59082	−0.795409	+	0.606073i	$0.792744\pi$
$824$	2.29590e12	0.173493
$825$	−1.78794e12	−0.134373
$826$	3.79502e12	0.283664
$827$	7.38108e12	0.548713	0.274357	−	0.961628i	$-0.411535\pi$
$827$	7.38108e12	0.548713	0.274357	+	0.961628i	$0.411535\pi$
$828$	−3.34070e12	−0.247002
$829$	−4.87072e12	−0.358177	−0.179089	−	0.983833i	$-0.557315\pi$
$829$	−4.87072e12	−0.358177	−0.179089	+	0.983833i	$0.557315\pi$
$830$	1.99235e12	0.145718
$831$	9.89027e12	0.719455
$832$	−2.84152e12	−0.205587
$833$	1.36859e12	0.0984853
$834$	3.71021e11	0.0265553
$835$	2.88230e12	0.205187
$836$	−1.52935e13	−1.08288
$837$	5.56127e12	0.391660
$838$	2.28388e12	0.159984
$839$	1.76148e13	1.22729	0.613647	−	0.789581i	$-0.289702\pi$
$839$	1.76148e13	1.22729	0.613647	+	0.789581i	$0.289702\pi$
$840$	−1.84294e12	−0.127719
$841$	6.82212e12	0.470259
$842$	−1.58224e13	−1.08485
$843$	−2.52293e12	−0.172060
$844$	5.18150e12	0.351491
$845$	9.55343e11	0.0644621
$846$	3.27681e12	0.219930
$847$	1.87691e12	0.125305
$848$	7.46977e11	0.0496051
$849$	−4.16733e12	−0.275279
$850$	−2.05510e12	−0.135036
$851$	−8.23938e12	−0.538532
$852$	−2.32099e12	−0.150902
$853$	−3.97201e12	−0.256886	−0.128443	−	0.991717i	$-0.540998\pi$
$853$	−3.97201e12	−0.256886	−0.128443	+	0.991717i	$0.540998\pi$
$854$	2.35771e11	0.0151681
$855$	−1.83508e13	−1.17437
$856$	1.57346e13	1.00167
$857$	−1.12250e12	−0.0710843	−0.0355421	−	0.999368i	$-0.511316\pi$
$857$	−1.12250e12	−0.0710843	−0.0355421	+	0.999368i	$0.511316\pi$
$858$	−1.30714e12	−0.0823438
$859$	−2.94640e13	−1.84639	−0.923194	−	0.384333i	$-0.874431\pi$
$859$	−2.94640e13	−1.84639	−0.923194	+	0.384333i	$0.874431\pi$
$860$	−8.95124e12	−0.558007
$861$	3.76566e12	0.233521
$862$	6.85987e11	0.0423188
$863$	4.73520e12	0.290596	0.145298	−	0.989388i	$-0.453586\pi$
$863$	4.73520e12	0.290596	0.145298	+	0.989388i	$0.453586\pi$
$864$	−1.13351e13	−0.692013
$865$	−3.14469e12	−0.190987
$866$	4.16099e12	0.251400
$867$	−3.41441e12	−0.205225
$868$	1.94393e12	0.116236
$869$	3.81398e13	2.26877
$870$	4.41783e12	0.261440
$871$	−3.48443e12	−0.205140
$872$	−1.55911e13	−0.913169
$873$	2.34670e13	1.36739
$874$	−9.65258e12	−0.559554
$875$	−7.12728e12	−0.411043
$876$	7.16166e12	0.410909
$877$	−2.40776e13	−1.37440	−0.687202	−	0.726467i	$-0.741161\pi$
$877$	−2.40776e13	−1.37440	−0.687202	+	0.726467i	$0.741161\pi$
$878$	−3.40652e12	−0.193458
$879$	−6.20429e12	−0.350544
$880$	−1.91036e12	−0.107385
$881$	−2.90030e13	−1.62200	−0.811000	−	0.585045i	$-0.801077\pi$
$881$	−2.90030e13	−1.62200	−0.811000	+	0.585045i	$0.801077\pi$
$882$	−1.43070e12	−0.0796050
$883$	2.62484e13	1.45305	0.726524	−	0.687141i	$-0.241135\pi$
$883$	2.62484e13	1.45305	0.726524	+	0.687141i	$0.241135\pi$
$884$	1.96916e12	0.108454
$885$	6.82341e12	0.373901
$886$	−1.24154e13	−0.676875
$887$	1.89179e12	0.102616	0.0513081	−	0.998683i	$-0.483661\pi$
$887$	1.89179e12	0.102616	0.0513081	+	0.998683i	$0.483661\pi$
$888$	−7.82666e12	−0.422394
$889$	3.53403e12	0.189763
$890$	6.72613e12	0.359344
$891$	1.22545e13	0.651400
$892$	−2.64207e12	−0.139734
$893$	−1.24089e13	−0.652983
$894$	−6.93178e12	−0.362933
$895$	1.95777e13	1.01990
$896$	−3.42945e12	−0.177762
$897$	1.08127e12	0.0557661
$898$	1.77077e13	0.908698
$899$	−1.28753e13	−0.657413
$900$	−2.81570e12	−0.143052
$901$	−6.09168e12	−0.307947
$902$	2.38410e13	1.19921
$903$	3.46722e12	0.173535
$904$	1.74704e13	0.870051
$905$	2.04800e13	1.01487
$906$	−1.18649e12	−0.0585043
$907$	3.39514e13	1.66581	0.832905	−	0.553416i	$-0.186676\pi$
$907$	3.39514e13	1.66581	0.832905	+	0.553416i	$0.186676\pi$
$908$	1.46715e13	0.716289
$909$	1.16671e13	0.566794
$910$	−1.19550e12	−0.0577913
$911$	−2.32607e13	−1.11889	−0.559447	−	0.828866i	$-0.688987\pi$
$911$	−2.32607e13	−1.11889	−0.559447	+	0.828866i	$0.688987\pi$
$912$	−1.50122e12	−0.0718568
$913$	6.40360e12	0.305004
$914$	−1.71223e13	−0.811529
$915$	4.23914e11	0.0199932
$916$	−2.25743e13	−1.05946
$917$	4.55604e11	0.0212777
$918$	−7.04960e12	−0.327622
$919$	7.28082e12	0.336714	0.168357	−	0.985726i	$-0.446154\pi$
$919$	7.28082e12	0.336714	0.168357	+	0.985726i	$0.446154\pi$
$920$	9.65178e12	0.444183
$921$	−4.71103e12	−0.215749
$922$	−2.32155e13	−1.05801
$923$	−4.15998e12	−0.188662
$924$	−2.14383e12	−0.0967534
$925$	−6.94454e12	−0.311893
$926$	−9.05863e12	−0.404868
$927$	3.20464e12	0.142534
$928$	2.62427e13	1.16156
$929$	2.26901e13	0.999463	0.499731	−	0.866180i	$-0.333432\pi$
$929$	2.26901e13	0.999463	0.499731	+	0.866180i	$0.333432\pi$
$930$	−2.66680e12	−0.116901
$931$	5.41791e12	0.236351
$932$	−1.69923e13	−0.737700
$933$	7.62156e12	0.329289
$934$	1.35989e13	0.584714
$935$	1.55792e13	0.666640
$936$	−5.68770e12	−0.242212
$937$	6.55727e12	0.277904	0.138952	−	0.990299i	$-0.455627\pi$
$937$	6.55727e12	0.277904	0.138952	+	0.990299i	$0.455627\pi$
$938$	4.36035e12	0.183911
$939$	1.20684e13	0.506587
$940$	4.49073e12	0.187604
$941$	2.49853e13	1.03880	0.519400	−	0.854531i	$-0.326156\pi$
$941$	2.49853e13	1.03880	0.519400	+	0.854531i	$0.326156\pi$
$942$	−9.42937e12	−0.390170
$943$	−1.97213e13	−0.812145
$944$	−3.09109e12	−0.126689
$945$	−5.60931e12	−0.228805
$946$	2.19515e13	0.891158
$947$	5.45603e12	0.220446	0.110223	−	0.993907i	$-0.464844\pi$
$947$	5.45603e12	0.220446	0.110223	+	0.993907i	$0.464844\pi$
$948$	−1.08466e13	−0.436169
$949$	1.28361e13	0.513728
$950$	−8.13565e12	−0.324068
$951$	1.40646e13	0.557589
$952$	−6.80849e12	−0.268649
$953$	2.01712e13	0.792159	0.396080	−	0.918216i	$-0.370370\pi$
$953$	2.01712e13	0.792159	0.396080	+	0.918216i	$0.370370\pi$
$954$	6.36814e12	0.248911
$955$	−7.68767e12	−0.299075
$956$	9.22151e12	0.357060
$957$	1.41993e13	0.547222
$958$	−1.13132e13	−0.433953
$959$	−1.68925e13	−0.644928
$960$	6.39334e12	0.242945
$961$	−1.86675e13	−0.706044
$962$	−5.07707e12	−0.191129
$963$	2.19625e13	0.822930
$964$	−8.68419e11	−0.0323879
$965$	1.09153e13	0.405192
$966$	−1.35309e12	−0.0499952
$967$	1.10731e13	0.407238	0.203619	−	0.979050i	$-0.434730\pi$
$967$	1.10731e13	0.407238	0.203619	+	0.979050i	$0.434730\pi$
$968$	−9.33731e12	−0.341808
$969$	1.22426e13	0.446085
$970$	−2.45384e13	−0.889966
$971$	−2.51589e13	−0.908251	−0.454125	−	0.890938i	$-0.650048\pi$
$971$	−2.51589e13	−0.908251	−0.454125	+	0.890938i	$0.650048\pi$
$972$	−1.48879e13	−0.534979
$973$	1.09064e12	0.0390099
$974$	1.96477e13	0.699512
$975$	9.11349e11	0.0322971
$976$	−1.92038e11	−0.00677428
$977$	7.22965e12	0.253859	0.126929	−	0.991912i	$-0.459488\pi$
$977$	7.22965e12	0.253859	0.126929	+	0.991912i	$0.459488\pi$
$978$	−5.10207e12	−0.178329
$979$	2.16184e13	0.752146
$980$	−1.96072e12	−0.0679044
$981$	−2.17621e13	−0.750222
$982$	3.56619e13	1.22378
$983$	9.16711e12	0.313142	0.156571	−	0.987667i	$-0.449956\pi$
$983$	9.16711e12	0.313142	0.156571	+	0.987667i	$0.449956\pi$
$984$	−1.87335e13	−0.637001
$985$	−3.94812e13	−1.33637
$986$	1.63210e13	0.549923
$987$	−1.73947e12	−0.0583430
$988$	7.79541e12	0.260275
$989$	−1.81584e13	−0.603523
$990$	−1.62862e13	−0.538841
$991$	−5.71417e12	−0.188201	−0.0941005	−	0.995563i	$-0.529997\pi$
$991$	−5.71417e12	−0.188201	−0.0941005	+	0.995563i	$0.529997\pi$
$992$	−1.58413e13	−0.519383
$993$	1.83838e13	0.600017
$994$	5.20572e12	0.169138
$995$	3.34277e13	1.08119
$996$	−1.82112e12	−0.0586369
$997$	−3.62859e13	−1.16308	−0.581540	−	0.813518i	$-0.697549\pi$
$997$	−3.62859e13	−1.16308	−0.581540	+	0.813518i	$0.697549\pi$
$998$	−2.26092e13	−0.721435
$999$	−2.38218e13	−0.756710

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.c.1.9	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.c.1.9	✓	14	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)

\(f(q)\)	\(=\)	\(q+14.8857 q^{2} +54.8703 q^{3} -290.415 q^{4} +1171.15 q^{5} +816.786 q^{6} +2401.00 q^{7} -11944.5 q^{8} -16672.2 q^{9} +O(q^{10})\)	\(q+14.8857 q^{2} +54.8703 q^{3} -290.415 q^{4} +1171.15 q^{5} +816.786 q^{6} +2401.00 q^{7} -11944.5 q^{8} -16672.2 q^{9} +17433.4 q^{10} +56032.8 q^{11} -15935.1 q^{12} -28561.0 q^{13} +35740.7 q^{14} +64261.4 q^{15} -29111.2 q^{16} +237405. q^{17} -248179. q^{18} +939826. q^{19} -340119. q^{20} +131744. q^{21} +834089. q^{22} -689962. q^{23} -655401. q^{24} -581532. q^{25} -425152. q^{26} -1.99482e6 q^{27} -697285. q^{28} +4.61836e6 q^{29} +956579. q^{30} -2.78785e6 q^{31} +5.68226e6 q^{32} +3.07454e6 q^{33} +3.53395e6 q^{34} +2.81193e6 q^{35} +4.84186e6 q^{36} +1.19418e7 q^{37} +1.39900e7 q^{38} -1.56715e6 q^{39} -1.39888e7 q^{40} +2.85832e7 q^{41} +1.96110e6 q^{42} +2.63180e7 q^{43} -1.62727e7 q^{44} -1.95257e7 q^{45} -1.02706e7 q^{46} -1.32034e7 q^{47} -1.59734e6 q^{48} +5.76480e6 q^{49} -8.65654e6 q^{50} +1.30265e7 q^{51} +8.29453e6 q^{52} -2.56595e7 q^{53} -2.96944e7 q^{54} +6.56228e7 q^{55} -2.86788e7 q^{56} +5.15686e7 q^{57} +6.87478e7 q^{58} +1.06182e8 q^{59} -1.86624e7 q^{60} +6.59672e6 q^{61} -4.14992e7 q^{62} -4.00301e7 q^{63} +9.94897e7 q^{64} -3.34492e7 q^{65} +4.57668e7 q^{66} +1.22000e8 q^{67} -6.89458e7 q^{68} -3.78584e7 q^{69} +4.18577e7 q^{70} +1.45652e8 q^{71} +1.99142e8 q^{72} -4.49426e8 q^{73} +1.77762e8 q^{74} -3.19089e7 q^{75} -2.72939e8 q^{76} +1.34535e8 q^{77} -2.33282e7 q^{78} +6.80670e8 q^{79} -3.40936e7 q^{80} +2.18703e8 q^{81} +4.25482e8 q^{82} +1.14283e8 q^{83} -3.82603e7 q^{84} +2.78037e8 q^{85} +3.91762e8 q^{86} +2.53411e8 q^{87} -6.69285e8 q^{88} +3.85818e8 q^{89} -2.90655e8 q^{90} -6.85750e7 q^{91} +2.00375e8 q^{92} -1.52970e8 q^{93} -1.96543e8 q^{94} +1.10068e9 q^{95} +3.11788e8 q^{96} -1.40755e9 q^{97} +8.58134e7 q^{98} -9.34192e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 27 q^{2} + 163 q^{3} + 2389 q^{4} + 2964 q^{5} + 471 q^{6} + 33614 q^{7} + 43263 q^{8} + 144129 q^{9}+O(q^{10}) \) 14 * q + 27 * q^2 + 163 * q^3 + 2389 * q^4 + 2964 * q^5 + 471 * q^6 + 33614 * q^7 + 43263 * q^8 + 144129 * q^9	\( 14 q + 27 q^{2} + 163 q^{3} + 2389 q^{4} + 2964 q^{5} + 471 q^{6} + 33614 q^{7} + 43263 q^{8} + 144129 q^{9} + 126524 q^{10} + 81825 q^{11} + 157399 q^{12} - 399854 q^{13} + 64827 q^{14} + 163856 q^{15} + 166361 q^{16} - 44922 q^{17} - 826396 q^{18} + 171756 q^{19} + 3899724 q^{20} + 391363 q^{21} + 917579 q^{22} + 1930479 q^{23} + 2992373 q^{24} + 8222344 q^{25} - 771147 q^{26} + 4139125 q^{27} + 5735989 q^{28} - 3799608 q^{29} - 5918004 q^{30} - 4392203 q^{31} + 3135663 q^{32} + 17499977 q^{33} - 20071132 q^{34} + 7116564 q^{35} + 2121398 q^{36} + 29198909 q^{37} - 44208366 q^{38} - 4655443 q^{39} + 134932928 q^{40} + 48410973 q^{41} + 1130871 q^{42} + 52650242 q^{43} - 14827353 q^{44} + 99215088 q^{45} - 34410455 q^{46} + 160580841 q^{47} + 227620515 q^{48} + 80707214 q^{49} + 149462949 q^{50} + 57114360 q^{51} - 68232229 q^{52} + 80753796 q^{53} + 301368833 q^{54} + 328919412 q^{55} + 103874463 q^{56} + 151101102 q^{57} + 335044204 q^{58} + 442445502 q^{59} + 561078360 q^{60} + 270199089 q^{61} + 543824517 q^{62} + 346053729 q^{63} + 223643137 q^{64} - 84654804 q^{65} + 317483345 q^{66} + 92500909 q^{67} + 255771204 q^{68} + 292017029 q^{69} + 303784124 q^{70} + 84383796 q^{71} + 1456696818 q^{72} + 367274315 q^{73} + 1091659407 q^{74} + 1154152501 q^{75} + 674789222 q^{76} + 196461825 q^{77} - 13452231 q^{78} + 434861545 q^{79} + 2644363752 q^{80} + 644207518 q^{81} + 634104331 q^{82} + 1013603934 q^{83} + 377914999 q^{84} + 1103701048 q^{85} + 2514069096 q^{86} + 1039292304 q^{87} + 1071310221 q^{88} + 1069739706 q^{89} - 1271572324 q^{90} - 960049454 q^{91} + 2301673917 q^{92} - 933838861 q^{93} + 2025486277 q^{94} + 2504029998 q^{95} - 116199027 q^{96} + 2839636281 q^{97} + 155649627 q^{98} + 5063037274 q^{99}+O(q^{100}) \) 14 * q + 27 * q^2 + 163 * q^3 + 2389 * q^4 + 2964 * q^5 + 471 * q^6 + 33614 * q^7 + 43263 * q^8 + 144129 * q^9 + 126524 * q^10 + 81825 * q^11 + 157399 * q^12 - 399854 * q^13 + 64827 * q^14 + 163856 * q^15 + 166361 * q^16 - 44922 * q^17 - 826396 * q^18 + 171756 * q^19 + 3899724 * q^20 + 391363 * q^21 + 917579 * q^22 + 1930479 * q^23 + 2992373 * q^24 + 8222344 * q^25 - 771147 * q^26 + 4139125 * q^27 + 5735989 * q^28 - 3799608 * q^29 - 5918004 * q^30 - 4392203 * q^31 + 3135663 * q^32 + 17499977 * q^33 - 20071132 * q^34 + 7116564 * q^35 + 2121398 * q^36 + 29198909 * q^37 - 44208366 * q^38 - 4655443 * q^39 + 134932928 * q^40 + 48410973 * q^41 + 1130871 * q^42 + 52650242 * q^43 - 14827353 * q^44 + 99215088 * q^45 - 34410455 * q^46 + 160580841 * q^47 + 227620515 * q^48 + 80707214 * q^49 + 149462949 * q^50 + 57114360 * q^51 - 68232229 * q^52 + 80753796 * q^53 + 301368833 * q^54 + 328919412 * q^55 + 103874463 * q^56 + 151101102 * q^57 + 335044204 * q^58 + 442445502 * q^59 + 561078360 * q^60 + 270199089 * q^61 + 543824517 * q^62 + 346053729 * q^63 + 223643137 * q^64 - 84654804 * q^65 + 317483345 * q^66 + 92500909 * q^67 + 255771204 * q^68 + 292017029 * q^69 + 303784124 * q^70 + 84383796 * q^71 + 1456696818 * q^72 + 367274315 * q^73 + 1091659407 * q^74 + 1154152501 * q^75 + 674789222 * q^76 + 196461825 * q^77 - 13452231 * q^78 + 434861545 * q^79 + 2644363752 * q^80 + 644207518 * q^81 + 634104331 * q^82 + 1013603934 * q^83 + 377914999 * q^84 + 1103701048 * q^85 + 2514069096 * q^86 + 1039292304 * q^87 + 1071310221 * q^88 + 1069739706 * q^89 - 1271572324 * q^90 - 960049454 * q^91 + 2301673917 * q^92 - 933838861 * q^93 + 2025486277 * q^94 + 2504029998 * q^95 - 116199027 * q^96 + 2839636281 * q^97 + 155649627 * q^98 + 5063037274 * q^99

Introduction

L-functions

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