LMFDB - Embedded newform 91.10.a.b.1.5

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:	$1$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4945 x^{11} - 8694 x^{10} + 9009530 x^{9} + 27431200 x^{8} - 7320118704 x^{7} + \cdots + 20\!\cdots\!00 $ x^13 - 4945x^11 - 8694x^10 + 9009530x^9 + 27431200x^8 - 7320118704x^7 - 28566940352x^6 + 2456696387328x^5 + 11170187661056x^4 - 201778709941248x^3 - 1417840074892800x^2 - 1725123584678400*x + 2025982720512000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-8.24674$ 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)

$f(q)$	$=$	$q-10.2467 q^{2} -61.4030 q^{3} -407.004 q^{4} -1449.57 q^{5} +629.180 q^{6} -2401.00 q^{7} +9416.80 q^{8} -15912.7 q^{9} +O(q^{10})$	\(q-10.2467 q^{2} -61.4030 q^{3} -407.004 q^{4} -1449.57 q^{5} +629.180 q^{6} -2401.00 q^{7} +9416.80 q^{8} -15912.7 q^{9} +14853.4 q^{10} +81793.4 q^{11} +24991.3 q^{12} -28561.0 q^{13} +24602.4 q^{14} +89008.1 q^{15} +111895. q^{16} +420721. q^{17} +163053. q^{18} -247869. q^{19} +589983. q^{20} +147429. q^{21} -838116. q^{22} +173272. q^{23} -578219. q^{24} +148139. q^{25} +292657. q^{26} +2.18568e6 q^{27} +977217. q^{28} +4.14891e6 q^{29} -912043. q^{30} -3.12298e6 q^{31} -5.96796e6 q^{32} -5.02236e6 q^{33} -4.31101e6 q^{34} +3.48043e6 q^{35} +6.47653e6 q^{36} -1.06394e7 q^{37} +2.53985e6 q^{38} +1.75373e6 q^{39} -1.36503e7 q^{40} +1.89090e7 q^{41} -1.51066e6 q^{42} +4.40873e6 q^{43} -3.32903e7 q^{44} +2.30666e7 q^{45} -1.77548e6 q^{46} +4.89911e7 q^{47} -6.87066e6 q^{48} +5.76480e6 q^{49} -1.51794e6 q^{50} -2.58335e7 q^{51} +1.16244e7 q^{52} -4.97977e7 q^{53} -2.23961e7 q^{54} -1.18566e8 q^{55} -2.26097e7 q^{56} +1.52199e7 q^{57} -4.25129e7 q^{58} +6.54970e6 q^{59} -3.62267e7 q^{60} -1.65913e8 q^{61} +3.20003e7 q^{62} +3.82063e7 q^{63} +3.86206e6 q^{64} +4.14013e7 q^{65} +5.14628e7 q^{66} +8.11719e7 q^{67} -1.71235e8 q^{68} -1.06394e7 q^{69} -3.56630e7 q^{70} -2.87728e8 q^{71} -1.49846e8 q^{72} -6.04463e7 q^{73} +1.09019e8 q^{74} -9.09619e6 q^{75} +1.00884e8 q^{76} -1.96386e8 q^{77} -1.79700e7 q^{78} -4.42205e8 q^{79} -1.62200e8 q^{80} +1.79002e8 q^{81} -1.93755e8 q^{82} -1.80554e8 q^{83} -6.00040e7 q^{84} -6.09865e8 q^{85} -4.51751e7 q^{86} -2.54756e8 q^{87} +7.70232e8 q^{88} +6.84618e8 q^{89} -2.36358e8 q^{90} +6.85750e7 q^{91} -7.05226e7 q^{92} +1.91760e8 q^{93} -5.01999e8 q^{94} +3.59305e8 q^{95} +3.66450e8 q^{96} +3.24285e8 q^{97} -5.90704e7 q^{98} -1.30155e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 26 q^{2} + 163 q^{3} + 3286 q^{4} - 2640 q^{5} - 995 q^{6} - 31213 q^{7} - 6738 q^{8} + 94756 q^{9}+O(q^{10}) $ 13 * q - 26 * q^2 + 163 * q^3 + 3286 * q^4 - 2640 * q^5 - 995 * q^6 - 31213 * q^7 - 6738 * q^8 + 94756 * q^9	\( 13 q - 26 q^{2} + 163 q^{3} + 3286 q^{4} - 2640 q^{5} - 995 q^{6} - 31213 q^{7} - 6738 q^{8} + 94756 q^{9} + 42588 q^{10} - 107493 q^{11} + 157399 q^{12} - 371293 q^{13} + 62426 q^{14} - 469556 q^{15} + 1033802 q^{16} + 50812 q^{17} - 2994615 q^{18} + 479470 q^{19} - 1834962 q^{20} - 391363 q^{21} - 5474013 q^{22} - 984639 q^{23} - 12496965 q^{24} + 4519039 q^{25} + 742586 q^{26} + 5965117 q^{27} - 7889686 q^{28} - 3441800 q^{29} + 25168012 q^{30} - 2185751 q^{31} - 2746342 q^{32} + 34793355 q^{33} - 966694 q^{34} + 6338640 q^{35} + 23974587 q^{36} - 31532363 q^{37} - 51039796 q^{38} - 4655443 q^{39} + 27446642 q^{40} - 38029287 q^{41} + 2388995 q^{42} - 65479740 q^{43} - 64795239 q^{44} - 190647152 q^{45} - 68737615 q^{46} + 18884785 q^{47} - 43918333 q^{48} + 74942413 q^{49} - 295918964 q^{50} - 97799092 q^{51} - 93851446 q^{52} - 37670088 q^{53} - 420784337 q^{54} - 11739604 q^{55} + 16177938 q^{56} - 119447794 q^{57} - 351819004 q^{58} - 86030686 q^{59} - 1421949708 q^{60} - 413609773 q^{61} + 21747651 q^{62} - 227509156 q^{63} - 611561502 q^{64} + 75401040 q^{65} - 154290083 q^{66} + 121596783 q^{67} - 613335382 q^{68} - 1089108303 q^{69} - 102253788 q^{70} - 900222116 q^{71} - 1897573017 q^{72} - 586910355 q^{73} - 688661251 q^{74} - 1466887131 q^{75} - 180912510 q^{76} + 258090693 q^{77} + 28418195 q^{78} - 590012173 q^{79} - 1724662122 q^{80} - 58178363 q^{81} + 145984865 q^{82} + 94283256 q^{83} - 377914999 q^{84} - 1689818164 q^{85} + 13901738 q^{86} + 1073171888 q^{87} - 1814132379 q^{88} - 1154652750 q^{89} + 2671175016 q^{90} + 891474493 q^{91} + 670826733 q^{92} - 5057835587 q^{93} - 2961146369 q^{94} - 3377803464 q^{95} - 4898921405 q^{96} - 2173622401 q^{97} - 149884826 q^{98} - 4653424330 q^{99}+O(q^{100}) \) 13 * q - 26 * q^2 + 163 * q^3 + 3286 * q^4 - 2640 * q^5 - 995 * q^6 - 31213 * q^7 - 6738 * q^8 + 94756 * q^9 + 42588 * q^10 - 107493 * q^11 + 157399 * q^12 - 371293 * q^13 + 62426 * q^14 - 469556 * q^15 + 1033802 * q^16 + 50812 * q^17 - 2994615 * q^18 + 479470 * q^19 - 1834962 * q^20 - 391363 * q^21 - 5474013 * q^22 - 984639 * q^23 - 12496965 * q^24 + 4519039 * q^25 + 742586 * q^26 + 5965117 * q^27 - 7889686 * q^28 - 3441800 * q^29 + 25168012 * q^30 - 2185751 * q^31 - 2746342 * q^32 + 34793355 * q^33 - 966694 * q^34 + 6338640 * q^35 + 23974587 * q^36 - 31532363 * q^37 - 51039796 * q^38 - 4655443 * q^39 + 27446642 * q^40 - 38029287 * q^41 + 2388995 * q^42 - 65479740 * q^43 - 64795239 * q^44 - 190647152 * q^45 - 68737615 * q^46 + 18884785 * q^47 - 43918333 * q^48 + 74942413 * q^49 - 295918964 * q^50 - 97799092 * q^51 - 93851446 * q^52 - 37670088 * q^53 - 420784337 * q^54 - 11739604 * q^55 + 16177938 * q^56 - 119447794 * q^57 - 351819004 * q^58 - 86030686 * q^59 - 1421949708 * q^60 - 413609773 * q^61 + 21747651 * q^62 - 227509156 * q^63 - 611561502 * q^64 + 75401040 * q^65 - 154290083 * q^66 + 121596783 * q^67 - 613335382 * q^68 - 1089108303 * q^69 - 102253788 * q^70 - 900222116 * q^71 - 1897573017 * q^72 - 586910355 * q^73 - 688661251 * q^74 - 1466887131 * q^75 - 180912510 * q^76 + 258090693 * q^77 + 28418195 * q^78 - 590012173 * q^79 - 1724662122 * q^80 - 58178363 * q^81 + 145984865 * q^82 + 94283256 * q^83 - 377914999 * q^84 - 1689818164 * q^85 + 13901738 * q^86 + 1073171888 * q^87 - 1814132379 * q^88 - 1154652750 * q^89 + 2671175016 * q^90 + 891474493 * q^91 + 670826733 * q^92 - 5057835587 * q^93 - 2961146369 * q^94 - 3377803464 * q^95 - 4898921405 * q^96 - 2173622401 * q^97 - 149884826 * q^98 - 4653424330 * 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 $

$2$	−10.2467	−0.452846	−0.226423	−	0.974029i	$-0.572703\pi$
$2$	−10.2467	−0.452846	−0.226423	+	0.974029i	$0.572703\pi$
$3$	−61.4030	−0.437667	−0.218833	−	0.975762i	$-0.570225\pi$
$3$	−61.4030	−0.437667	−0.218833	+	0.975762i	$0.570225\pi$
$4$	−407.004	−0.794930
$5$	−1449.57	−1.03723	−0.518615	−	0.855008i	$-0.673552\pi$
$5$	−1449.57	−1.03723	−0.518615	+	0.855008i	$0.673552\pi$
$6$	629.180	0.198196
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	9416.80	0.812828
$9$	−15912.7	−0.808448
$10$	14853.4	0.469706
$11$	81793.4	1.68442	0.842211	−	0.539147i	$-0.181253\pi$
$11$	81793.4	1.68442	0.842211	+	0.539147i	$0.181253\pi$
$12$	24991.3	0.347915
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	24602.4	0.171160
$15$	89008.1	0.453961
$16$	111895.	0.426844
$17$	420721.	1.22173	0.610863	−	0.791737i	$-0.290823\pi$
$17$	420721.	1.22173	0.610863	+	0.791737i	$0.290823\pi$
$18$	163053.	0.366103
$19$	−247869.	−0.436347	−0.218173	−	0.975910i	$-0.570010\pi$
$19$	−247869.	−0.436347	−0.218173	+	0.975910i	$0.570010\pi$
$20$	589983.	0.824526
$21$	147429.	0.165423
$22$	−838116.	−0.762785
$23$	173272.	0.129108	0.0645542	−	0.997914i	$-0.479437\pi$
$23$	173272.	0.129108	0.0645542	+	0.997914i	$0.479437\pi$
$24$	−578219.	−0.355748
$25$	148139.	0.0758473
$26$	292657.	0.125597
$27$	2.18568e6	0.791498
$28$	977217.	0.300455
$29$	4.14891e6	1.08929	0.544645	−	0.838667i	$-0.316664\pi$
$29$	4.14891e6	1.08929	0.544645	+	0.838667i	$0.316664\pi$
$30$	−912043.	−0.205575
$31$	−3.12298e6	−0.607353	−0.303677	−	0.952775i	$-0.598214\pi$
$31$	−3.12298e6	−0.607353	−0.303677	+	0.952775i	$0.598214\pi$
$32$	−5.96796e6	−1.00612
$33$	−5.02236e6	−0.737216
$34$	−4.31101e6	−0.553254
$35$	3.48043e6	0.392036
$36$	6.47653e6	0.642660
$37$	−1.06394e7	−0.933272	−0.466636	−	0.884450i	$-0.654534\pi$
$37$	−1.06394e7	−0.933272	−0.466636	+	0.884450i	$0.654534\pi$
$38$	2.53985e6	0.197598
$39$	1.75373e6	0.121387
$40$	−1.36503e7	−0.843090
$41$	1.89090e7	1.04506	0.522529	−	0.852622i	$-0.324989\pi$
$41$	1.89090e7	1.04506	0.522529	+	0.852622i	$0.324989\pi$
$42$	−1.51066e6	−0.0749110
$43$	4.40873e6	0.196655	0.0983276	−	0.995154i	$-0.468651\pi$
$43$	4.40873e6	0.196655	0.0983276	+	0.995154i	$0.468651\pi$
$44$	−3.32903e7	−1.33900
$45$	2.30666e7	0.838547
$46$	−1.77548e6	−0.0584662
$47$	4.89911e7	1.46446	0.732229	−	0.681058i	$-0.238480\pi$
$47$	4.89911e7	1.46446	0.732229	+	0.681058i	$0.238480\pi$
$48$	−6.87066e6	−0.186816
$49$	5.76480e6	0.142857
$50$	−1.51794e6	−0.0343472
$51$	−2.58335e7	−0.534709
$52$	1.16244e7	0.220474
$53$	−4.97977e7	−0.866897	−0.433449	−	0.901178i	$-0.642703\pi$
$53$	−4.97977e7	−0.866897	−0.433449	+	0.901178i	$0.642703\pi$
$54$	−2.23961e7	−0.358427
$55$	−1.18566e8	−1.74713
$56$	−2.26097e7	−0.307220
$57$	1.52199e7	0.190974
$58$	−4.25129e7	−0.493281
$59$	6.54970e6	0.0703699	0.0351850	−	0.999381i	$-0.488798\pi$
$59$	6.54970e6	0.0703699	0.0351850	+	0.999381i	$0.488798\pi$
$60$	−3.62267e7	−0.360868
$61$	−1.65913e8	−1.53425	−0.767127	−	0.641495i	$-0.778314\pi$
$61$	−1.65913e8	−1.53425	−0.767127	+	0.641495i	$0.778314\pi$
$62$	3.20003e7	0.275038
$63$	3.82063e7	0.305565
$64$	3.86206e6	0.0287746
$65$	4.14013e7	0.287676
$66$	5.14628e7	0.333846
$67$	8.11719e7	0.492118	0.246059	−	0.969255i	$-0.420864\pi$
$67$	8.11719e7	0.492118	0.246059	+	0.969255i	$0.420864\pi$
$68$	−1.71235e8	−0.971186
$69$	−1.06394e7	−0.0565064
$70$	−3.56630e7	−0.177532
$71$	−2.87728e8	−1.34375	−0.671876	−	0.740664i	$-0.734511\pi$
$71$	−2.87728e8	−1.34375	−0.671876	+	0.740664i	$0.734511\pi$
$72$	−1.49846e8	−0.657129
$73$	−6.04463e7	−0.249125	−0.124562	−	0.992212i	$-0.539753\pi$
$73$	−6.04463e7	−0.249125	−0.124562	+	0.992212i	$0.539753\pi$
$74$	1.09019e8	0.422629
$75$	−9.09619e6	−0.0331958
$76$	1.00884e8	0.346865
$77$	−1.96386e8	−0.636652
$78$	−1.79700e7	−0.0549696
$79$	−4.42205e8	−1.27732	−0.638662	−	0.769487i	$-0.720512\pi$
$79$	−4.42205e8	−1.27732	−0.638662	+	0.769487i	$0.720512\pi$
$80$	−1.62200e8	−0.442736
$81$	1.79002e8	0.462035
$82$	−1.93755e8	−0.473250
$83$	−1.80554e8	−0.417594	−0.208797	−	0.977959i	$-0.566955\pi$
$83$	−1.80554e8	−0.417594	−0.208797	+	0.977959i	$0.566955\pi$
$84$	−6.00040e7	−0.131499
$85$	−6.09865e8	−1.26721
$86$	−4.51751e7	−0.0890545
$87$	−2.54756e8	−0.476746
$88$	7.70232e8	1.36915
$89$	6.84618e8	1.15663	0.578313	−	0.815815i	$-0.303711\pi$
$89$	6.84618e8	1.15663	0.578313	+	0.815815i	$0.303711\pi$
$90$	−2.36358e8	−0.379733
$91$	6.85750e7	0.104828
$92$	−7.05226e7	−0.102632
$93$	1.91760e8	0.265818
$94$	−5.01999e8	−0.663175
$95$	3.59305e8	0.452592
$96$	3.66450e8	0.440346
$97$	3.24285e8	0.371924	0.185962	−	0.982557i	$-0.440460\pi$
$97$	3.24285e8	0.371924	0.185962	+	0.982557i	$0.440460\pi$
$98$	−5.90704e7	−0.0646923
$99$	−1.30155e9	−1.36177
$100$	−6.02933e7	−0.0602933
$101$	1.30859e9	1.25129	0.625647	−	0.780107i	$-0.284835\pi$
$101$	1.30859e9	1.25129	0.625647	+	0.780107i	$0.284835\pi$
$102$	2.64709e8	0.242141
$103$	−1.25909e9	−1.10227	−0.551137	−	0.834415i	$-0.685806\pi$
$103$	−1.25909e9	−1.10227	−0.551137	+	0.834415i	$0.685806\pi$
$104$	−2.68953e8	−0.225438
$105$	−2.13709e8	−0.171581
$106$	5.10264e8	0.392571
$107$	−4.65525e8	−0.343333	−0.171667	−	0.985155i	$-0.554915\pi$
$107$	−4.65525e8	−0.343333	−0.171667	+	0.985155i	$0.554915\pi$
$108$	−8.89581e8	−0.629185
$109$	1.51111e9	1.02536	0.512681	−	0.858579i	$-0.328652\pi$
$109$	1.51111e9	1.02536	0.512681	+	0.858579i	$0.328652\pi$
$110$	1.21491e9	0.791184
$111$	6.53289e8	0.408462
$112$	−2.68659e8	−0.161332
$113$	−2.71866e9	−1.56856	−0.784282	−	0.620404i	$-0.786968\pi$
$113$	−2.71866e9	−1.56856	−0.784282	+	0.620404i	$0.786968\pi$
$114$	−1.55955e8	−0.0864821
$115$	−2.51171e8	−0.133915
$116$	−1.68863e9	−0.865910
$117$	4.54482e8	0.224223
$118$	−6.71131e7	−0.0318668
$119$	−1.01015e9	−0.461769
$120$	8.38172e8	0.368992
$121$	4.33221e9	1.83728
$122$	1.70007e9	0.694781
$123$	−1.16107e9	−0.457387
$124$	1.27107e9	0.482803
$125$	2.61646e9	0.958559
$126$	−3.91490e8	−0.138374
$127$	3.88225e9	1.32424	0.662121	−	0.749397i	$-0.269657\pi$
$127$	3.88225e9	1.32424	0.662121	+	0.749397i	$0.269657\pi$
$128$	3.01602e9	0.993092
$129$	−2.70709e8	−0.0860694
$130$	−4.24228e8	−0.130273
$131$	7.06737e8	0.209670	0.104835	−	0.994490i	$-0.466568\pi$
$131$	7.06737e8	0.209670	0.104835	+	0.994490i	$0.466568\pi$
$132$	2.04412e9	0.586035
$133$	5.95134e8	0.164924
$134$	−8.31748e8	−0.222854
$135$	−3.16830e9	−0.820966
$136$	3.96184e9	0.993052
$137$	6.03175e9	1.46285	0.731427	−	0.681920i	$-0.238855\pi$
$137$	6.03175e9	1.46285	0.731427	+	0.681920i	$0.238855\pi$
$138$	1.09020e8	0.0255887
$139$	−1.76014e9	−0.399928	−0.199964	−	0.979803i	$-0.564083\pi$
$139$	−1.76014e9	−0.399928	−0.199964	+	0.979803i	$0.564083\pi$
$140$	−1.41655e9	−0.311642
$141$	−3.00820e9	−0.640945
$142$	2.94827e9	0.608513
$143$	−2.33610e9	−0.467175
$144$	−1.78054e9	−0.345081
$145$	−6.01416e9	−1.12984
$146$	6.19378e8	0.112815
$147$	−3.53976e8	−0.0625238
$148$	4.33027e9	0.741886
$149$	−2.31163e9	−0.384221	−0.192110	−	0.981373i	$-0.561533\pi$
$149$	−2.31163e9	−0.384221	−0.192110	+	0.981373i	$0.561533\pi$
$150$	9.32063e7	0.0150326
$151$	−3.19601e9	−0.500279	−0.250139	−	0.968210i	$-0.580476\pi$
$151$	−3.19601e9	−0.500279	−0.250139	+	0.968210i	$0.580476\pi$
$152$	−2.33414e9	−0.354675
$153$	−6.69479e9	−0.987701
$154$	2.01232e9	0.288306
$155$	4.52699e9	0.629965
$156$	−7.13776e8	−0.0964942
$157$	1.01862e10	1.33802	0.669009	−	0.743254i	$-0.266719\pi$
$157$	1.01862e10	1.33802	0.669009	+	0.743254i	$0.266719\pi$
$158$	4.53116e9	0.578432
$159$	3.05772e9	0.379412
$160$	8.65099e9	1.04358
$161$	−4.16027e8	−0.0487984
$162$	−1.83419e9	−0.209231
$163$	−9.70447e9	−1.07678	−0.538391	−	0.842695i	$-0.680968\pi$
$163$	−9.70447e9	−1.07678	−0.538391	+	0.842695i	$0.680968\pi$
$164$	−7.69602e9	−0.830748
$165$	7.28028e9	0.764663
$166$	1.85009e9	0.189106
$167$	−8.77508e9	−0.873025	−0.436513	−	0.899698i	$-0.643787\pi$
$167$	−8.77508e9	−0.873025	−0.436513	+	0.899698i	$0.643787\pi$
$168$	1.38830e9	0.134460
$169$	8.15731e8	0.0769231
$170$	6.24913e9	0.573852
$171$	3.94427e9	0.352763
$172$	−1.79437e9	−0.156327
$173$	9.46154e9	0.803072	0.401536	−	0.915843i	$-0.368476\pi$
$173$	9.46154e9	0.803072	0.401536	+	0.915843i	$0.368476\pi$
$174$	2.61042e9	0.215893
$175$	−3.55682e8	−0.0286676
$176$	9.15224e9	0.718986
$177$	−4.02171e8	−0.0307986
$178$	−7.01510e9	−0.523774
$179$	5.80250e9	0.422451	0.211225	−	0.977437i	$-0.432255\pi$
$179$	5.80250e9	0.422451	0.211225	+	0.977437i	$0.432255\pi$
$180$	−9.38820e9	−0.666586
$181$	−2.68001e10	−1.85602	−0.928009	−	0.372557i	$-0.878481\pi$
$181$	−2.68001e10	−1.85602	−0.928009	+	0.372557i	$0.878481\pi$
$182$	−7.02670e8	−0.0474712
$183$	1.01876e10	0.671492
$184$	1.63167e9	0.104943
$185$	1.54225e10	0.968018
$186$	−1.96492e9	−0.120375
$187$	3.44122e10	2.05790
$188$	−1.99396e10	−1.16414
$189$	−5.24782e9	−0.299158
$190$	−3.68171e9	−0.204955
$191$	−7.00346e9	−0.380770	−0.190385	−	0.981710i	$-0.560974\pi$
$191$	−7.00346e9	−0.380770	−0.190385	+	0.981710i	$0.560974\pi$
$192$	−2.37142e8	−0.0125937
$193$	−1.27543e10	−0.661683	−0.330841	−	0.943686i	$-0.607333\pi$
$193$	−1.27543e10	−0.661683	−0.330841	+	0.943686i	$0.607333\pi$
$194$	−3.32287e9	−0.168425
$195$	−2.54216e9	−0.125906
$196$	−2.34630e9	−0.113561
$197$	−3.07552e10	−1.45486	−0.727428	−	0.686184i	$-0.759284\pi$
$197$	−3.07552e10	−1.45486	−0.727428	+	0.686184i	$0.759284\pi$
$198$	1.33367e10	0.616672
$199$	−1.99961e10	−0.903873	−0.451937	−	0.892050i	$-0.649267\pi$
$199$	−1.99961e10	−0.903873	−0.451937	+	0.892050i	$0.649267\pi$
$200$	1.39500e9	0.0616508
$201$	−4.98420e9	−0.215384
$202$	−1.34088e10	−0.566643
$203$	−9.96154e9	−0.411713
$204$	1.05143e10	0.425056
$205$	−2.74099e10	−1.08397
$206$	1.29016e10	0.499161
$207$	−2.75723e9	−0.104377
$208$	−3.19582e9	−0.118385
$209$	−2.02741e10	−0.734992
$210$	2.18982e9	0.0777000
$211$	−5.14227e9	−0.178601	−0.0893005	−	0.996005i	$-0.528463\pi$
$211$	−5.14227e9	−0.178601	−0.0893005	+	0.996005i	$0.528463\pi$
$212$	2.02679e10	0.689123
$213$	1.76673e10	0.588116
$214$	4.77011e9	0.155477
$215$	−6.39078e9	−0.203977
$216$	2.05821e10	0.643351
$217$	7.49827e9	0.229558
$218$	−1.54840e10	−0.464332
$219$	3.71158e9	0.109034
$220$	4.82567e10	1.38885
$221$	−1.20162e10	−0.338846
$222$	−6.69408e9	−0.184971
$223$	−6.15565e10	−1.66687	−0.833435	−	0.552617i	$-0.813629\pi$
$223$	−6.15565e10	−1.66687	−0.833435	+	0.552617i	$0.813629\pi$
$224$	1.43291e10	0.380279
$225$	−2.35729e9	−0.0613186
$226$	2.78574e10	0.710319
$227$	2.74278e10	0.685605	0.342802	−	0.939408i	$-0.388624\pi$
$227$	2.74278e10	0.685605	0.342802	+	0.939408i	$0.388624\pi$
$228$	−6.19457e9	−0.151811
$229$	−1.73167e10	−0.416109	−0.208054	−	0.978117i	$-0.566713\pi$
$229$	−1.73167e10	−0.416109	−0.208054	+	0.978117i	$0.566713\pi$
$230$	2.57369e9	0.0606430
$231$	1.20587e10	0.278641
$232$	3.90695e10	0.885405
$233$	−7.38084e10	−1.64060	−0.820302	−	0.571930i	$-0.806195\pi$
$233$	−7.38084e10	−1.64060	−0.820302	+	0.571930i	$0.806195\pi$
$234$	−4.65696e9	−0.101539
$235$	−7.10162e10	−1.51898
$236$	−2.66575e9	−0.0559392
$237$	2.71527e10	0.559043
$238$	1.03507e10	0.209110
$239$	4.94536e10	0.980409	0.490205	−	0.871607i	$-0.336922\pi$
$239$	4.94536e10	0.980409	0.490205	+	0.871607i	$0.336922\pi$
$240$	9.95953e9	0.193771
$241$	−5.86364e10	−1.11967	−0.559835	−	0.828604i	$-0.689136\pi$
$241$	−5.86364e10	−1.11967	−0.559835	+	0.828604i	$0.689136\pi$
$242$	−4.43911e10	−0.832006
$243$	−5.40120e10	−0.993715
$244$	6.75275e10	1.21962
$245$	−8.35650e9	−0.148176
$246$	1.18971e10	0.207126
$247$	7.07940e9	0.121021
$248$	−2.94085e10	−0.493673
$249$	1.10865e10	0.182767
$250$	−2.68102e10	−0.434080
$251$	−3.27988e10	−0.521587	−0.260794	−	0.965395i	$-0.583984\pi$
$251$	−3.27988e10	−0.521587	−0.260794	+	0.965395i	$0.583984\pi$
$252$	−1.55501e10	−0.242902
$253$	1.41725e10	0.217473
$254$	−3.97804e10	−0.599678
$255$	3.74475e10	0.554616
$256$	−3.28818e10	−0.478493
$257$	3.62476e10	0.518298	0.259149	−	0.965837i	$-0.416558\pi$
$257$	3.62476e10	0.518298	0.259149	+	0.965837i	$0.416558\pi$
$258$	2.77388e9	0.0389762
$259$	2.55451e10	0.352744
$260$	−1.68505e10	−0.228682
$261$	−6.60203e10	−0.880634
$262$	−7.24175e9	−0.0949485
$263$	−5.84230e10	−0.752979	−0.376490	−	0.926421i	$-0.622869\pi$
$263$	−5.84230e10	−0.752979	−0.376490	+	0.926421i	$0.622869\pi$
$264$	−4.72945e10	−0.599230
$265$	7.21854e10	0.899172
$266$	−6.09819e9	−0.0746850
$267$	−4.20376e10	−0.506217
$268$	−3.30373e10	−0.391200
$269$	2.56418e10	0.298582	0.149291	−	0.988793i	$-0.452301\pi$
$269$	2.56418e10	0.298582	0.149291	+	0.988793i	$0.452301\pi$
$270$	3.24648e10	0.371771
$271$	−6.66993e10	−0.751207	−0.375603	−	0.926781i	$-0.622564\pi$
$271$	−6.66993e10	−0.751207	−0.375603	+	0.926781i	$0.622564\pi$
$272$	4.70764e10	0.521486
$273$	−4.21071e9	−0.0458800
$274$	−6.18058e10	−0.662448
$275$	1.21168e10	0.127759
$276$	4.33030e9	0.0449187
$277$	5.98833e10	0.611149	0.305574	−	0.952168i	$-0.401152\pi$
$277$	5.98833e10	0.611149	0.305574	+	0.952168i	$0.401152\pi$
$278$	1.80357e10	0.181106
$279$	4.96949e10	0.491013
$280$	3.27745e10	0.318658
$281$	1.37750e11	1.31799	0.658995	−	0.752147i	$-0.270982\pi$
$281$	1.37750e11	1.31799	0.658995	+	0.752147i	$0.270982\pi$
$282$	3.08242e10	0.290250
$283$	−9.24250e9	−0.0856545	−0.0428273	−	0.999082i	$-0.513637\pi$
$283$	−9.24250e9	−0.0856545	−0.0428273	+	0.999082i	$0.513637\pi$
$284$	1.17106e11	1.06819
$285$	−2.20624e10	−0.198085
$286$	2.39374e10	0.211558
$287$	−4.54004e10	−0.394995
$288$	9.49662e10	0.813397
$289$	5.84179e10	0.492613
$290$	6.16255e10	0.511646
$291$	−1.99121e10	−0.162779
$292$	2.46019e10	0.198037
$293$	−4.46177e10	−0.353674	−0.176837	−	0.984240i	$-0.556587\pi$
$293$	−4.46177e10	−0.353674	−0.176837	+	0.984240i	$0.556587\pi$
$294$	3.62710e9	0.0283137
$295$	−9.49427e9	−0.0729898
$296$	−1.00189e11	−0.758589
$297$	1.78774e11	1.33322
$298$	2.36867e10	0.173993
$299$	−4.94883e9	−0.0358082
$300$	3.70219e9	0.0263884
$301$	−1.05854e10	−0.0743286
$302$	3.27487e10	0.226549
$303$	−8.03516e10	−0.547650
$304$	−2.77353e10	−0.186252
$305$	2.40504e11	1.59138
$306$	6.85998e10	0.447277
$307$	−3.29677e10	−0.211820	−0.105910	−	0.994376i	$-0.533775\pi$
$307$	−3.29677e10	−0.211820	−0.105910	+	0.994376i	$0.533775\pi$
$308$	7.99299e10	0.506094
$309$	7.73119e10	0.482429
$310$	−4.63869e10	−0.285277
$311$	1.82385e11	1.10552	0.552760	−	0.833340i	$-0.313575\pi$
$311$	1.82385e11	1.10552	0.552760	+	0.833340i	$0.313575\pi$
$312$	1.65145e10	0.0986667
$313$	2.09605e11	1.23439	0.617196	−	0.786810i	$-0.288269\pi$
$313$	2.09605e11	1.23439	0.617196	+	0.786810i	$0.288269\pi$
$314$	−1.04375e11	−0.605917
$315$	−5.53829e10	−0.316941
$316$	1.79979e11	1.01538
$317$	−2.77659e11	−1.54435	−0.772175	−	0.635410i	$-0.780831\pi$
$317$	−2.77659e11	−1.54435	−0.772175	+	0.635410i	$0.780831\pi$
$318$	−3.13317e10	−0.171815
$319$	3.39354e11	1.83482
$320$	−5.59834e9	−0.0298459
$321$	2.85846e10	0.150266
$322$	4.26292e9	0.0220982
$323$	−1.04284e11	−0.533096
$324$	−7.28546e10	−0.367286
$325$	−4.23100e9	−0.0210363
$326$	9.94392e10	0.487617
$327$	−9.27867e10	−0.448767
$328$	1.78062e11	0.849451
$329$	−1.17628e11	−0.553513
$330$	−7.45991e10	−0.346275
$331$	2.44542e11	1.11976	0.559882	−	0.828572i	$-0.310846\pi$
$331$	2.44542e11	1.11976	0.559882	+	0.828572i	$0.310846\pi$
$332$	7.34861e10	0.331958
$333$	1.69301e11	0.754501
$334$	8.99159e10	0.395346
$335$	−1.17665e11	−0.510440
$336$	1.64965e10	0.0706097
$337$	−3.47235e11	−1.46652	−0.733262	−	0.679946i	$-0.762003\pi$
$337$	−3.47235e11	−1.46652	−0.733262	+	0.679946i	$0.762003\pi$
$338$	−8.35858e9	−0.0348343
$339$	1.66934e11	0.686509
$340$	2.48218e11	1.00734
$341$	−2.55439e11	−1.02304
$342$	−4.04159e10	−0.159748
$343$	−1.38413e10	−0.0539949
$344$	4.15161e10	0.159847
$345$	1.54227e10	0.0586102
$346$	−9.69500e10	−0.363668
$347$	−3.16486e11	−1.17185	−0.585924	−	0.810366i	$-0.699268\pi$
$347$	−3.16486e11	−1.17185	−0.585924	+	0.810366i	$0.699268\pi$
$348$	1.03687e11	0.378980
$349$	−5.77775e10	−0.208471	−0.104235	−	0.994553i	$-0.533239\pi$
$349$	−5.77775e10	−0.208471	−0.104235	+	0.994553i	$0.533239\pi$
$350$	3.64458e9	0.0129820
$351$	−6.24252e10	−0.219522
$352$	−4.88139e11	−1.69474
$353$	−4.21664e11	−1.44538	−0.722688	−	0.691175i	$-0.757093\pi$
$353$	−4.21664e11	−1.44538	−0.722688	+	0.691175i	$0.757093\pi$
$354$	4.12094e9	0.0139470
$355$	4.17083e11	1.39378
$356$	−2.78642e11	−0.919437
$357$	6.20262e10	0.202101
$358$	−5.94567e10	−0.191305
$359$	−4.95868e11	−1.57558	−0.787791	−	0.615942i	$-0.788775\pi$
$359$	−4.95868e11	−1.57558	−0.787791	+	0.615942i	$0.788775\pi$
$360$	2.17214e11	0.681594
$361$	−2.61248e11	−0.809602
$362$	2.74613e11	0.840491
$363$	−2.66011e11	−0.804117
$364$	−2.79103e10	−0.0833313
$365$	8.76214e10	0.258400
$366$	−1.04389e11	−0.304083
$367$	−8.64291e9	−0.0248692	−0.0124346	−	0.999923i	$-0.503958\pi$
$367$	−8.64291e9	−0.0248692	−0.0124346	+	0.999923i	$0.503958\pi$
$368$	1.93883e10	0.0551091
$369$	−3.00892e11	−0.844874
$370$	−1.58031e11	−0.438363
$371$	1.19564e11	0.327656
$372$	−7.80472e10	−0.211307
$373$	−2.46680e10	−0.0659849	−0.0329925	−	0.999456i	$-0.510504\pi$
$373$	−2.46680e10	−0.0659849	−0.0329925	+	0.999456i	$0.510504\pi$
$374$	−3.52613e11	−0.931913
$375$	−1.60658e11	−0.419530
$376$	4.61340e11	1.19035
$377$	−1.18497e11	−0.302115
$378$	5.37730e10	0.135473
$379$	2.13643e11	0.531879	0.265939	−	0.963990i	$-0.414318\pi$
$379$	2.13643e11	0.531879	0.265939	+	0.963990i	$0.414318\pi$
$380$	−1.46239e11	−0.359779
$381$	−2.38382e11	−0.579576
$382$	7.17626e10	0.172430
$383$	−7.39737e10	−0.175664	−0.0878320	−	0.996135i	$-0.527994\pi$
$383$	−7.39737e10	−0.175664	−0.0878320	+	0.996135i	$0.527994\pi$
$384$	−1.85193e11	−0.434643
$385$	2.84676e11	0.660355
$386$	1.30690e11	0.299641
$387$	−7.01547e10	−0.158985
$388$	−1.31986e11	−0.295654
$389$	−3.56938e11	−0.790351	−0.395176	−	0.918606i	$-0.629316\pi$
$389$	−3.56938e11	−0.790351	−0.395176	+	0.918606i	$0.629316\pi$
$390$	2.60489e10	0.0570162
$391$	7.28993e10	0.157735
$392$	5.42860e10	0.116118
$393$	−4.33958e10	−0.0917658
$394$	3.15140e11	0.658826
$395$	6.41008e11	1.32488
$396$	5.29737e11	1.08251
$397$	6.65369e11	1.34433	0.672164	−	0.740402i	$-0.265365\pi$
$397$	6.65369e11	1.34433	0.672164	+	0.740402i	$0.265365\pi$
$398$	2.04895e11	0.409316
$399$	−3.65430e10	−0.0721816
$400$	1.65760e10	0.0323750
$401$	−3.39728e11	−0.656118	−0.328059	−	0.944657i	$-0.606394\pi$
$401$	−3.39728e11	−0.656118	−0.328059	+	0.944657i	$0.606394\pi$
$402$	5.10718e10	0.0975357
$403$	8.91954e10	0.168449
$404$	−5.32604e11	−0.994691
$405$	−2.59477e11	−0.479237
$406$	1.02073e11	0.186443
$407$	−8.70230e11	−1.57202
$408$	−2.43269e11	−0.434626
$409$	4.05110e11	0.715843	0.357921	−	0.933752i	$-0.383486\pi$
$409$	4.05110e11	0.715843	0.357921	+	0.933752i	$0.383486\pi$
$410$	2.80862e11	0.490870
$411$	−3.70368e11	−0.640243
$412$	5.12455e11	0.876231
$413$	−1.57258e10	−0.0265973
$414$	2.82526e10	0.0472669
$415$	2.61726e11	0.433142
$416$	1.70451e11	0.279048
$417$	1.08078e11	0.175035
$418$	2.07743e11	0.332839
$419$	−9.66341e11	−1.53168	−0.765838	−	0.643033i	$-0.777676\pi$
$419$	−9.66341e11	−1.53168	−0.765838	+	0.643033i	$0.777676\pi$
$420$	8.69803e10	0.136395
$421$	−1.18381e12	−1.83659	−0.918296	−	0.395894i	$-0.870435\pi$
$421$	−1.18381e12	−1.83659	−0.918296	+	0.395894i	$0.870435\pi$
$422$	5.26915e10	0.0808788
$423$	−7.79580e11	−1.18394
$424$	−4.68935e11	−0.704638
$425$	6.23252e10	0.0926645
$426$	−1.81033e11	−0.266326
$427$	3.98358e11	0.579894
$428$	1.89471e11	0.272926
$429$	1.43444e11	0.204467
$430$	6.54846e10	0.0923701
$431$	−4.57374e11	−0.638446	−0.319223	−	0.947680i	$-0.603422\pi$
$431$	−4.57374e11	−0.638446	−0.319223	+	0.947680i	$0.603422\pi$
$432$	2.44566e11	0.337846
$433$	1.61007e11	0.220115	0.110057	−	0.993925i	$-0.464897\pi$
$433$	1.61007e11	0.220115	0.110057	+	0.993925i	$0.464897\pi$
$434$	−7.68328e10	−0.103954
$435$	3.69287e11	0.494496
$436$	−6.15029e11	−0.815091
$437$	−4.29489e10	−0.0563360
$438$	−3.80316e10	−0.0493755
$439$	2.72959e10	0.0350758	0.0175379	−	0.999846i	$-0.494417\pi$
$439$	2.72959e10	0.0350758	0.0175379	+	0.999846i	$0.494417\pi$
$440$	−1.11651e12	−1.42012
$441$	−9.17334e10	−0.115493
$442$	1.23127e11	0.153445
$443$	6.25625e11	0.771787	0.385893	−	0.922543i	$-0.373893\pi$
$443$	6.25625e11	0.771787	0.385893	+	0.922543i	$0.373893\pi$
$444$	−2.65891e11	−0.324699
$445$	−9.92404e11	−1.19969
$446$	6.30753e11	0.754836
$447$	1.41941e11	0.168161
$448$	−9.27280e9	−0.0108758
$449$	−1.25497e12	−1.45722	−0.728610	−	0.684929i	$-0.759833\pi$
$449$	−1.25497e12	−1.45722	−0.728610	+	0.684929i	$0.759833\pi$
$450$	2.41546e10	0.0277679
$451$	1.54663e12	1.76032
$452$	1.10651e12	1.24690
$453$	1.96245e11	0.218956
$454$	−2.81045e11	−0.310474
$455$	−9.94045e10	−0.108731
$456$	1.43323e11	0.155229
$457$	−1.72935e12	−1.85465	−0.927323	−	0.374263i	$-0.877896\pi$
$457$	−1.72935e12	−1.85465	−0.927323	+	0.374263i	$0.877896\pi$
$458$	1.77440e11	0.188433
$459$	9.19560e11	0.966993
$460$	1.02228e11	0.106453
$461$	−4.95257e11	−0.510712	−0.255356	−	0.966847i	$-0.582193\pi$
$461$	−4.95257e11	−0.510712	−0.255356	+	0.966847i	$0.582193\pi$
$462$	−1.23562e11	−0.126182
$463$	9.30361e11	0.940887	0.470443	−	0.882430i	$-0.344094\pi$
$463$	9.30361e11	0.940887	0.470443	+	0.882430i	$0.344094\pi$
$464$	4.64241e11	0.464957
$465$	−2.77970e11	−0.275715
$466$	7.56295e11	0.742942
$467$	1.44637e12	1.40719	0.703597	−	0.710599i	$-0.251576\pi$
$467$	1.44637e12	1.40719	0.703597	+	0.710599i	$0.251576\pi$
$468$	−1.84976e11	−0.178242
$469$	−1.94894e11	−0.186003
$470$	7.27685e11	0.687865
$471$	−6.25461e11	−0.585607
$472$	6.16772e10	0.0571986
$473$	3.60605e11	0.331250
$474$	−2.78226e11	−0.253160
$475$	−3.67192e10	−0.0330957
$476$	4.11135e11	0.367074
$477$	7.92414e11	0.700841
$478$	−5.06738e11	−0.443975
$479$	8.56092e11	0.743037	0.371519	−	0.928425i	$-0.378837\pi$
$479$	8.56092e11	0.743037	0.371519	+	0.928425i	$0.378837\pi$
$480$	−5.31197e11	−0.456741
$481$	3.03871e11	0.258843
$482$	6.00832e11	0.507039
$483$	2.55453e10	0.0213574
$484$	−1.76323e12	−1.46051
$485$	−4.70076e11	−0.385771
$486$	5.53447e11	0.450000
$487$	4.12919e11	0.332647	0.166324	−	0.986071i	$-0.446810\pi$
$487$	4.12919e11	0.332647	0.166324	+	0.986071i	$0.446810\pi$
$488$	−1.56237e12	−1.24708
$489$	5.95883e11	0.471272
$490$	8.56270e10	0.0671009
$491$	1.92383e12	1.49382	0.746912	−	0.664923i	$-0.231536\pi$
$491$	1.92383e12	1.49382	0.746912	+	0.664923i	$0.231536\pi$
$492$	4.72559e11	0.363591
$493$	1.74553e12	1.33081
$494$	−7.25408e10	−0.0548038
$495$	1.88670e12	1.41247
$496$	−3.49444e11	−0.259245
$497$	6.90834e11	0.507891
$498$	−1.13601e11	−0.0827655
$499$	1.37323e11	0.0991495	0.0495747	−	0.998770i	$-0.484213\pi$
$499$	1.37323e11	0.0991495	0.0495747	+	0.998770i	$0.484213\pi$
$500$	−1.06491e12	−0.761988
$501$	5.38816e11	0.382094
$502$	3.36081e11	0.236199
$503$	−1.09450e12	−0.762361	−0.381180	−	0.924501i	$-0.624482\pi$
$503$	−1.09450e12	−0.762361	−0.381180	+	0.924501i	$0.624482\pi$
$504$	3.59781e11	0.248371
$505$	−1.89690e12	−1.29788
$506$	−1.45222e11	−0.0984818
$507$	−5.00883e10	−0.0336667
$508$	−1.58009e12	−1.05268
$509$	1.89558e12	1.25173	0.625867	−	0.779930i	$-0.284745\pi$
$509$	1.89558e12	1.25173	0.625867	+	0.779930i	$0.284745\pi$
$510$	−3.83715e11	−0.251156
$511$	1.45132e11	0.0941604
$512$	−1.20727e12	−0.776408
$513$	−5.41763e11	−0.345367
$514$	−3.71419e11	−0.234709
$515$	1.82514e12	1.14331
$516$	1.10180e11	0.0684192
$517$	4.00715e12	2.46677
$518$	−2.61754e11	−0.159739
$519$	−5.80967e11	−0.351478
$520$	3.89868e11	0.233831
$521$	2.34308e12	1.39321	0.696607	−	0.717453i	$-0.254692\pi$
$521$	2.34308e12	1.39321	0.696607	+	0.717453i	$0.254692\pi$
$522$	6.76493e11	0.398792
$523$	1.99525e12	1.16611	0.583054	−	0.812433i	$-0.301857\pi$
$523$	1.99525e12	1.16611	0.583054	+	0.812433i	$0.301857\pi$
$524$	−2.87645e11	−0.166673
$525$	2.18399e10	0.0125468
$526$	5.98645e11	0.340984
$527$	−1.31390e12	−0.742019
$528$	−5.61975e11	−0.314676
$529$	−1.77113e12	−0.983331
$530$	−7.39665e11	−0.407187
$531$	−1.04223e11	−0.0568904
$532$	−2.42222e11	−0.131103
$533$	−5.40059e11	−0.289847
$534$	4.30748e11	0.229239
$535$	6.74813e11	0.356116
$536$	7.64380e11	0.400007
$537$	−3.56290e11	−0.184893
$538$	−2.62745e11	−0.135212
$539$	4.71523e11	0.240632
$540$	1.28951e12	0.652610
$541$	−1.67570e12	−0.841026	−0.420513	−	0.907287i	$-0.638150\pi$
$541$	−1.67570e12	−0.841026	−0.420513	+	0.907287i	$0.638150\pi$
$542$	6.83450e11	0.340181
$543$	1.64560e12	0.812318
$544$	−2.51084e12	−1.22921
$545$	−2.19047e12	−1.06354
$546$	4.31460e10	0.0207766
$547$	−2.36001e12	−1.12712	−0.563561	−	0.826074i	$-0.690569\pi$
$547$	−2.36001e12	−1.12712	−0.563561	+	0.826074i	$0.690569\pi$
$548$	−2.45495e12	−1.16287
$549$	2.64013e12	1.24036
$550$	−1.24158e11	−0.0578551
$551$	−1.02839e12	−0.475308
$552$	−1.00189e11	−0.0459300
$553$	1.06173e12	0.482783
$554$	−6.13609e11	−0.276756
$555$	−9.46990e11	−0.423669
$556$	7.16386e11	0.317915
$557$	−4.06129e12	−1.78778	−0.893892	−	0.448282i	$-0.852036\pi$
$557$	−4.06129e12	−1.78778	−0.893892	+	0.448282i	$0.852036\pi$
$558$	−5.09211e11	−0.222354
$559$	−1.25918e11	−0.0545423
$560$	3.89441e11	0.167338
$561$	−2.11301e12	−0.900675
$562$	−1.41149e12	−0.596847
$563$	4.29229e12	1.80053	0.900266	−	0.435340i	$-0.143372\pi$
$563$	4.29229e12	1.80053	0.900266	+	0.435340i	$0.143372\pi$
$564$	1.22435e12	0.509506
$565$	3.94090e12	1.62696
$566$	9.47055e10	0.0387883
$567$	−4.29784e11	−0.174633
$568$	−2.70947e12	−1.09224
$569$	−3.83530e12	−1.53389	−0.766944	−	0.641714i	$-0.778224\pi$
$569$	−3.83530e12	−1.53389	−0.766944	+	0.641714i	$0.778224\pi$
$570$	2.26068e11	0.0897019
$571$	−1.08620e12	−0.427610	−0.213805	−	0.976876i	$-0.568586\pi$
$571$	−1.08620e12	−0.427610	−0.213805	+	0.976876i	$0.568586\pi$
$572$	9.50803e11	0.371371
$573$	4.30033e11	0.166650
$574$	4.65206e11	0.178872
$575$	2.56684e10	0.00979251
$576$	−6.14557e10	−0.0232627
$577$	4.22680e12	1.58753	0.793763	−	0.608228i	$-0.208119\pi$
$577$	4.22680e12	1.58753	0.793763	+	0.608228i	$0.208119\pi$
$578$	−5.98593e11	−0.223078
$579$	7.83154e11	0.289597
$580$	2.44779e12	0.898148
$581$	4.33509e11	0.157836
$582$	2.04034e11	0.0737138
$583$	−4.07312e12	−1.46022
$584$	−5.69211e11	−0.202496
$585$	−6.58805e11	−0.232571
$586$	4.57186e11	0.160160
$587$	−7.50196e11	−0.260797	−0.130399	−	0.991462i	$-0.541626\pi$
$587$	−7.50196e11	−0.260797	−0.130399	+	0.991462i	$0.541626\pi$
$588$	1.44070e11	0.0497021
$589$	7.74090e11	0.265016
$590$	9.72853e10	0.0330532
$591$	1.88846e12	0.636742
$592$	−1.19049e12	−0.398362
$593$	−7.15112e11	−0.237480	−0.118740	−	0.992925i	$-0.537886\pi$
$593$	−7.15112e11	−0.237480	−0.118740	+	0.992925i	$0.537886\pi$
$594$	−1.83185e12	−0.603742
$595$	1.46429e12	0.478961
$596$	9.40845e11	0.305429
$597$	1.22782e12	0.395595
$598$	5.07094e10	0.0162156
$599$	3.48919e11	0.110740	0.0553699	−	0.998466i	$-0.482366\pi$
$599$	3.48919e11	0.110740	0.0553699	+	0.998466i	$0.482366\pi$
$600$	−8.56570e10	−0.0269825
$601$	5.66112e12	1.76997	0.884987	−	0.465616i	$-0.154167\pi$
$601$	5.66112e12	1.76997	0.884987	+	0.465616i	$0.154167\pi$
$602$	1.08465e11	0.0336595
$603$	−1.29166e12	−0.397852
$604$	1.30079e12	0.397687
$605$	−6.27986e12	−1.90568
$606$	8.23342e11	0.248001
$607$	4.30458e12	1.28701	0.643505	−	0.765442i	$-0.277480\pi$
$607$	4.30458e12	1.28701	0.643505	+	0.765442i	$0.277480\pi$
$608$	1.47927e12	0.439018
$609$	6.11668e11	0.180193
$610$	−2.46438e12	−0.720648
$611$	−1.39924e12	−0.406168
$612$	2.72481e12	0.785153
$613$	4.62524e11	0.132301	0.0661504	−	0.997810i	$-0.478928\pi$
$613$	4.62524e11	0.132301	0.0661504	+	0.997810i	$0.478928\pi$
$614$	3.37812e11	0.0959218
$615$	1.68305e12	0.474416
$616$	−1.84933e12	−0.517488
$617$	−1.95536e12	−0.543179	−0.271590	−	0.962413i	$-0.587549\pi$
$617$	−1.95536e12	−0.543179	−0.271590	+	0.962413i	$0.587549\pi$
$618$	−7.92195e11	−0.218466
$619$	−4.01169e12	−1.09830	−0.549148	−	0.835725i	$-0.685048\pi$
$619$	−4.01169e12	−1.09830	−0.549148	+	0.835725i	$0.685048\pi$
$620$	−1.84250e12	−0.500778
$621$	3.78718e11	0.102189
$622$	−1.86885e12	−0.500631
$623$	−1.64377e12	−0.437164
$624$	1.96233e11	0.0518133
$625$	−4.08209e12	−1.07009
$626$	−2.14777e12	−0.558990
$627$	1.24489e12	0.321682
$628$	−4.14581e12	−1.06363
$629$	−4.47620e12	−1.14020
$630$	5.67494e11	0.143526
$631$	4.93570e12	1.23941	0.619707	−	0.784833i	$-0.287251\pi$
$631$	4.93570e12	1.23941	0.619707	+	0.784833i	$0.287251\pi$
$632$	−4.16415e12	−1.03824
$633$	3.15751e11	0.0781677
$634$	2.84510e12	0.699353
$635$	−5.62761e12	−1.37354
$636$	−1.24451e12	−0.301606
$637$	−1.64648e11	−0.0396214
$638$	−3.47727e12	−0.830894
$639$	4.57852e12	1.08635
$640$	−4.37194e12	−1.03007
$641$	7.99451e12	1.87038	0.935192	−	0.354142i	$-0.115227\pi$
$641$	7.99451e12	1.87038	0.935192	+	0.354142i	$0.115227\pi$
$642$	−2.92899e11	−0.0680472
$643$	−1.89073e12	−0.436195	−0.218098	−	0.975927i	$-0.569985\pi$
$643$	−1.89073e12	−0.436195	−0.218098	+	0.975927i	$0.569985\pi$
$644$	1.69325e11	0.0387913
$645$	3.92413e11	0.0892738
$646$	1.06857e12	0.241410
$647$	−8.06830e12	−1.81014	−0.905071	−	0.425260i	$-0.860183\pi$
$647$	−8.06830e12	−1.81014	−0.905071	+	0.425260i	$0.860183\pi$
$648$	1.68563e12	0.375555
$649$	5.35722e11	0.118533
$650$	4.33540e10	0.00952619
$651$	−4.60416e11	−0.100470
$652$	3.94976e12	0.855966
$653$	2.62737e12	0.565473	0.282736	−	0.959198i	$-0.408758\pi$
$653$	2.62737e12	0.565473	0.282736	+	0.959198i	$0.408758\pi$
$654$	9.50762e11	0.203223
$655$	−1.02447e12	−0.217477
$656$	2.11581e12	0.446077
$657$	9.61863e11	0.201404
$658$	1.20530e12	0.250656
$659$	6.49743e12	1.34201	0.671007	−	0.741451i	$-0.265862\pi$
$659$	6.49743e12	1.34201	0.671007	+	0.741451i	$0.265862\pi$
$660$	−2.96310e12	−0.607854
$661$	−4.43215e12	−0.903041	−0.451520	−	0.892261i	$-0.649118\pi$
$661$	−4.43215e12	−0.903041	−0.451520	+	0.892261i	$0.649118\pi$
$662$	−2.50575e12	−0.507081
$663$	7.37830e11	0.148302
$664$	−1.70024e12	−0.339432
$665$	−8.62691e11	−0.171064
$666$	−1.73478e12	−0.341673
$667$	7.18892e11	0.140636
$668$	3.57149e12	0.693994
$669$	3.77975e12	0.729534
$670$	1.20568e12	0.231151
$671$	−1.35706e13	−2.58433
$672$	−8.79847e11	−0.166435
$673$	5.41615e12	1.01771	0.508853	−	0.860853i	$-0.330070\pi$
$673$	5.41615e12	1.01771	0.508853	+	0.860853i	$0.330070\pi$
$674$	3.55803e12	0.664110
$675$	3.23785e11	0.0600329
$676$	−3.32006e11	−0.0611485
$677$	5.93170e12	1.08525	0.542625	−	0.839975i	$-0.317430\pi$
$677$	5.93170e12	1.08525	0.542625	+	0.839975i	$0.317430\pi$
$678$	−1.71053e12	−0.310883
$679$	−7.78609e11	−0.140574
$680$	−5.74298e12	−1.03002
$681$	−1.68415e12	−0.300067
$682$	2.61742e12	0.463280
$683$	−4.12202e12	−0.724798	−0.362399	−	0.932023i	$-0.618042\pi$
$683$	−4.12202e12	−0.724798	−0.362399	+	0.932023i	$0.618042\pi$
$684$	−1.60533e12	−0.280422
$685$	−8.74347e12	−1.51732
$686$	1.41828e11	0.0244514
$687$	1.06330e12	0.182117
$688$	4.93313e11	0.0839411
$689$	1.42227e12	0.240434
$690$	−1.58032e11	−0.0265414
$691$	−3.05293e12	−0.509409	−0.254704	−	0.967019i	$-0.581978\pi$
$691$	−3.05293e12	−0.509409	−0.254704	+	0.967019i	$0.581978\pi$
$692$	−3.85089e12	−0.638386
$693$	3.12503e12	0.514700
$694$	3.24295e12	0.530667
$695$	2.55146e12	0.414817
$696$	−2.39898e12	−0.387512
$697$	7.95538e12	1.27677
$698$	5.92032e11	0.0944051
$699$	4.53205e12	0.718038
$700$	1.44764e11	0.0227887
$701$	−1.05964e13	−1.65740	−0.828698	−	0.559697i	$-0.810918\pi$
$701$	−1.05964e13	−1.65740	−0.828698	+	0.559697i	$0.810918\pi$
$702$	6.39655e11	0.0994097
$703$	2.63717e12	0.407230
$704$	3.15891e11	0.0484686
$705$	4.36061e12	0.664808
$706$	4.32069e12	0.654533
$707$	−3.14194e12	−0.472944
$708$	1.63685e11	0.0244827
$709$	−4.91500e12	−0.730491	−0.365246	−	0.930911i	$-0.619015\pi$
$709$	−4.91500e12	−0.730491	−0.365246	+	0.930911i	$0.619015\pi$
$710$	−4.27374e12	−0.631169
$711$	7.03666e12	1.03265
$712$	6.44691e12	0.940138
$713$	−5.41126e11	−0.0784143
$714$	−6.35567e11	−0.0915206
$715$	3.38635e12	0.484568
$716$	−2.36164e12	−0.335819
$717$	−3.03660e12	−0.429093
$718$	5.08103e12	0.713497
$719$	−6.94267e12	−0.968827	−0.484414	−	0.874839i	$-0.660967\pi$
$719$	−6.94267e12	−0.968827	−0.484414	+	0.874839i	$0.660967\pi$
$720$	2.58103e12	0.357929
$721$	3.02308e12	0.416620
$722$	2.67695e12	0.366625
$723$	3.60045e12	0.490043
$724$	1.09077e13	1.47541
$725$	6.14617e11	0.0826197
$726$	2.72574e12	0.364141
$727$	−4.15143e12	−0.551179	−0.275589	−	0.961275i	$-0.588873\pi$
$727$	−4.15143e12	−0.551179	−0.275589	+	0.961275i	$0.588873\pi$
$728$	6.45757e11	0.0852075
$729$	−2.06800e11	−0.0271192
$730$	−8.97834e11	−0.117015
$731$	1.85484e12	0.240259
$732$	−4.14639e12	−0.533789
$733$	2.46735e12	0.315692	0.157846	−	0.987464i	$-0.449545\pi$
$733$	2.46735e12	0.315692	0.157846	+	0.987464i	$0.449545\pi$
$734$	8.85616e10	0.0112619
$735$	5.13114e11	0.0648516
$736$	−1.03408e12	−0.129899
$737$	6.63933e12	0.828935
$738$	3.08316e12	0.382598
$739$	−7.46399e12	−0.920600	−0.460300	−	0.887763i	$-0.652258\pi$
$739$	−7.46399e12	−0.920600	−0.460300	+	0.887763i	$0.652258\pi$
$740$	−6.27704e12	−0.769507
$741$	−4.34696e11	−0.0529668
$742$	−1.22514e12	−0.148378
$743$	1.40726e13	1.69405	0.847023	−	0.531557i	$-0.178393\pi$
$743$	1.40726e13	1.69405	0.847023	+	0.531557i	$0.178393\pi$
$744$	1.80577e12	0.216064
$745$	3.35088e12	0.398526
$746$	2.52767e11	0.0298810
$747$	2.87309e12	0.337603
$748$	−1.40059e13	−1.63589
$749$	1.11773e12	0.129768
$750$	1.64623e12	0.189982
$751$	−9.37923e12	−1.07594	−0.537969	−	0.842965i	$-0.680808\pi$
$751$	−9.37923e12	−1.07594	−0.537969	+	0.842965i	$0.680808\pi$
$752$	5.48184e12	0.625096
$753$	2.01395e12	0.228281
$754$	1.21421e12	0.136812
$755$	4.63286e12	0.518905
$756$	2.13588e12	0.237810
$757$	1.15093e13	1.27385	0.636926	−	0.770925i	$-0.280206\pi$
$757$	1.15093e13	1.27385	0.636926	+	0.770925i	$0.280206\pi$
$758$	−2.18915e12	−0.240859
$759$	−8.70236e11	−0.0951807
$760$	3.38350e12	0.367879
$761$	−1.38249e13	−1.49428	−0.747141	−	0.664666i	$-0.768574\pi$
$761$	−1.38249e13	−1.49428	−0.747141	+	0.664666i	$0.768574\pi$
$762$	2.44264e12	0.262459
$763$	−3.62818e12	−0.387551
$764$	2.85044e12	0.302685
$765$	9.70459e12	1.02447
$766$	7.57989e11	0.0795488
$767$	−1.87066e11	−0.0195171
$768$	2.01904e12	0.209420
$769$	5.68069e12	0.585777	0.292889	−	0.956147i	$-0.405383\pi$
$769$	5.68069e12	0.585777	0.292889	+	0.956147i	$0.405383\pi$
$770$	−2.91700e12	−0.299039
$771$	−2.22571e12	−0.226842
$772$	5.19107e12	0.525992
$773$	5.99086e12	0.603506	0.301753	−	0.953386i	$-0.402428\pi$
$773$	5.99086e12	0.603506	0.301753	+	0.953386i	$0.402428\pi$
$774$	7.18857e11	0.0719959
$775$	−4.62635e11	−0.0460661
$776$	3.05373e12	0.302310
$777$	−1.56855e12	−0.154384
$778$	3.65746e12	0.357908
$779$	−4.68695e12	−0.456007
$780$	1.03467e12	0.100087
$781$	−2.35342e13	−2.26345
$782$	−7.46980e11	−0.0714297
$783$	9.06820e12	0.862170
$784$	6.45050e11	0.0609777
$785$	−1.47656e13	−1.38783
$786$	4.44665e11	0.0415558
$787$	−9.11119e12	−0.846620	−0.423310	−	0.905985i	$-0.639132\pi$
$787$	−9.11119e12	−0.846620	−0.423310	+	0.905985i	$0.639132\pi$
$788$	1.25175e13	1.15651
$789$	3.58734e12	0.329554
$790$	−6.56825e12	−0.599967
$791$	6.52751e12	0.592862
$792$	−1.22565e13	−1.10688
$793$	4.73865e12	0.425526
$794$	−6.81786e12	−0.608774
$795$	−4.43240e12	−0.393538
$796$	8.13852e12	0.718516
$797$	8.66441e12	0.760635	0.380318	−	0.924856i	$-0.375815\pi$
$797$	8.66441e12	0.760635	0.380318	+	0.924856i	$0.375815\pi$
$798$	3.74447e11	0.0326872
$799$	2.06116e13	1.78917
$800$	−8.84089e11	−0.0763116
$801$	−1.08941e13	−0.935072
$802$	3.48111e12	0.297121
$803$	−4.94411e12	−0.419632
$804$	2.02859e12	0.171215
$805$	6.03062e11	0.0506151
$806$	−9.13962e11	−0.0762817
$807$	−1.57448e12	−0.130679
$808$	1.23228e13	1.01709
$809$	2.59933e12	0.213350	0.106675	−	0.994294i	$-0.465980\pi$
$809$	2.59933e12	0.213350	0.106675	+	0.994294i	$0.465980\pi$
$810$	2.65879e12	0.217021
$811$	1.66938e13	1.35507	0.677536	−	0.735490i	$-0.263048\pi$
$811$	1.66938e13	1.35507	0.677536	+	0.735490i	$0.263048\pi$
$812$	4.05439e12	0.327283
$813$	4.09553e12	0.328778
$814$	8.91702e12	0.711885
$815$	1.40673e13	1.11687
$816$	−2.89063e12	−0.228237
$817$	−1.09279e12	−0.0858098
$818$	−4.15105e12	−0.324167
$819$	−1.09121e12	−0.0847483
$820$	1.11560e13	0.861677
$821$	−2.40385e13	−1.84656	−0.923278	−	0.384131i	$-0.874501\pi$
$821$	−2.40385e13	−1.84656	−0.923278	+	0.384131i	$0.874501\pi$
$822$	3.79506e12	0.289932
$823$	8.43615e12	0.640981	0.320490	−	0.947252i	$-0.396152\pi$
$823$	8.43615e12	0.640981	0.320490	+	0.947252i	$0.396152\pi$
$824$	−1.18566e13	−0.895958
$825$	−7.44008e11	−0.0559158
$826$	1.61138e11	0.0120445
$827$	−6.59645e11	−0.0490383	−0.0245192	−	0.999699i	$-0.507805\pi$
$827$	−6.59645e11	−0.0490383	−0.0245192	+	0.999699i	$0.507805\pi$
$828$	1.12220e12	0.0829727
$829$	−1.97186e13	−1.45005	−0.725023	−	0.688725i	$-0.758171\pi$
$829$	−1.97186e13	−1.45005	−0.725023	+	0.688725i	$0.758171\pi$
$830$	−2.68184e12	−0.196147
$831$	−3.67701e12	−0.267480
$832$	−1.10304e11	−0.00798063
$833$	2.42537e12	0.174532
$834$	−1.10745e12	−0.0792640
$835$	1.27201e13	0.905528
$836$	8.25164e12	0.584268
$837$	−6.82583e12	−0.480718
$838$	9.90184e12	0.693614
$839$	9.45081e12	0.658477	0.329238	−	0.944247i	$-0.393208\pi$
$839$	9.45081e12	0.658477	0.329238	+	0.944247i	$0.393208\pi$
$840$	−2.01245e12	−0.139466
$841$	2.70635e12	0.186553
$842$	1.21302e13	0.831694
$843$	−8.45824e12	−0.576841
$844$	2.09293e12	0.141975
$845$	−1.18246e12	−0.0797870
$846$	7.98815e12	0.536142
$847$	−1.04016e13	−0.694427
$848$	−5.57209e12	−0.370030
$849$	5.67517e11	0.0374882
$850$	−6.38630e11	−0.0419628
$851$	−1.84351e12	−0.120493
$852$	−7.19068e12	−0.467511
$853$	3.15676e12	0.204160	0.102080	−	0.994776i	$-0.467450\pi$
$853$	3.15676e12	0.204160	0.102080	+	0.994776i	$0.467450\pi$
$854$	−4.08187e12	−0.262603
$855$	−5.71750e12	−0.365897
$856$	−4.38376e12	−0.279071
$857$	−1.85749e13	−1.17628	−0.588142	−	0.808757i	$-0.700141\pi$
$857$	−1.85749e13	−1.17628	−0.588142	+	0.808757i	$0.700141\pi$
$858$	−1.46983e12	−0.0925921
$859$	−1.81850e13	−1.13958	−0.569788	−	0.821792i	$-0.692975\pi$
$859$	−1.81850e13	−1.13958	−0.569788	+	0.821792i	$0.692975\pi$
$860$	2.60107e12	0.162147
$861$	2.78772e12	0.172876
$862$	4.68660e12	0.289118
$863$	−2.80435e13	−1.72101	−0.860505	−	0.509442i	$-0.829852\pi$
$863$	−2.80435e13	−1.72101	−0.860505	+	0.509442i	$0.829852\pi$
$864$	−1.30440e13	−0.796343
$865$	−1.37152e13	−0.832971
$866$	−1.64980e12	−0.0996782
$867$	−3.58703e12	−0.215600
$868$	−3.05183e12	−0.182482
$869$	−3.61694e13	−2.15155
$870$	−3.78399e12	−0.223931
$871$	−2.31835e12	−0.136489
$872$	1.42298e13	0.833443
$873$	−5.16025e12	−0.300681
$874$	4.40087e11	0.0255115
$875$	−6.28212e12	−0.362301
$876$	−1.51063e12	−0.0866742
$877$	−1.44199e12	−0.0823121	−0.0411561	−	0.999153i	$-0.513104\pi$
$877$	−1.44199e12	−0.0823121	−0.0411561	+	0.999153i	$0.513104\pi$
$878$	−2.79694e11	−0.0158839
$879$	2.73966e12	0.154791
$880$	−1.32669e13	−0.745754
$881$	1.33604e13	0.747187	0.373594	−	0.927592i	$-0.378125\pi$
$881$	1.33604e13	0.747187	0.373594	+	0.927592i	$0.378125\pi$
$882$	9.39969e11	0.0523004
$883$	−6.27202e12	−0.347204	−0.173602	−	0.984816i	$-0.555541\pi$
$883$	−6.27202e12	−0.347204	−0.173602	+	0.984816i	$0.555541\pi$
$884$	4.89064e12	0.269359
$885$	5.82976e11	0.0319452
$886$	−6.41062e12	−0.349501
$887$	3.15484e13	1.71128	0.855641	−	0.517570i	$-0.173163\pi$
$887$	3.15484e13	1.71128	0.855641	+	0.517570i	$0.173163\pi$
$888$	6.15189e12	0.332009
$889$	−9.32129e12	−0.500516
$890$	1.01689e13	0.543274
$891$	1.46412e13	0.778263
$892$	2.50538e13	1.32505
$893$	−1.21434e13	−0.639011
$894$	−1.45444e12	−0.0761510
$895$	−8.41115e12	−0.438179
$896$	−7.24147e12	−0.375353
$897$	3.03873e11	0.0156721
$898$	1.28594e13	0.659896
$899$	−1.29570e13	−0.661584
$900$	9.59428e11	0.0487440
$901$	−2.09509e13	−1.05911
$902$	−1.58479e13	−0.797154
$903$	6.49972e11	0.0325312
$904$	−2.56011e13	−1.27497
$905$	3.88487e13	1.92512
$906$	−2.01087e12	−0.0991532
$907$	−1.88281e13	−0.923792	−0.461896	−	0.886934i	$-0.652831\pi$
$907$	−1.88281e13	−0.923792	−0.461896	+	0.886934i	$0.652831\pi$
$908$	−1.11632e13	−0.545008
$909$	−2.08232e13	−1.01161
$910$	1.01857e12	0.0492386
$911$	7.59224e12	0.365206	0.182603	−	0.983187i	$-0.441548\pi$
$911$	7.59224e12	0.365206	0.182603	+	0.983187i	$0.441548\pi$
$912$	1.70303e12	0.0815164
$913$	−1.47681e13	−0.703406
$914$	1.77202e13	0.839869
$915$	−1.47676e13	−0.696492
$916$	7.04799e12	0.330777
$917$	−1.69688e12	−0.0792480
$918$	−9.42250e12	−0.437899
$919$	2.68060e13	1.23969	0.619844	−	0.784725i	$-0.287196\pi$
$919$	2.68060e13	1.23969	0.619844	+	0.784725i	$0.287196\pi$
$920$	−2.36523e12	−0.108850
$921$	2.02432e12	0.0927065
$922$	5.07477e12	0.231274
$923$	8.21779e12	0.372690
$924$	−4.90793e12	−0.221501
$925$	−1.57611e12	−0.0707861
$926$	−9.53317e12	−0.426077
$927$	2.00355e13	0.891131
$928$	−2.47605e13	−1.09596
$929$	−4.09064e13	−1.80186	−0.900928	−	0.433969i	$-0.857113\pi$
$929$	−4.09064e13	−1.80186	−0.900928	+	0.433969i	$0.857113\pi$
$930$	2.84829e12	0.124856
$931$	−1.42892e12	−0.0623352
$932$	3.00403e13	1.30417
$933$	−1.11990e13	−0.483850
$934$	−1.48206e13	−0.637243
$935$	−4.98830e13	−2.13452
$936$	4.27977e12	0.182255
$937$	1.13309e12	0.0480215	0.0240108	−	0.999712i	$-0.492356\pi$
$937$	1.13309e12	0.0480215	0.0240108	+	0.999712i	$0.492356\pi$
$938$	1.99703e12	0.0842308
$939$	−1.28704e13	−0.540252
$940$	2.89039e13	1.20748
$941$	−3.52057e11	−0.0146372	−0.00731862	−	0.999973i	$-0.502330\pi$
$941$	−3.52057e11	−0.0146372	−0.00731862	+	0.999973i	$0.502330\pi$
$942$	6.40893e12	0.265190
$943$	3.27640e12	0.134926
$944$	7.32876e11	0.0300370
$945$	7.60710e12	0.310296
$946$	−3.69502e12	−0.150006
$947$	4.48335e12	0.181146	0.0905729	−	0.995890i	$-0.471130\pi$
$947$	4.48335e12	0.181146	0.0905729	+	0.995890i	$0.471130\pi$
$948$	−1.10513e13	−0.444400
$949$	1.72641e12	0.0690948
$950$	3.76252e11	0.0149873
$951$	1.70491e13	0.675911
$952$	−9.51238e12	−0.375338
$953$	3.48212e13	1.36749	0.683747	−	0.729720i	$-0.260349\pi$
$953$	3.48212e13	1.36749	0.683747	+	0.729720i	$0.260349\pi$
$954$	−8.11966e12	−0.317373
$955$	1.01520e13	0.394946
$956$	−2.01278e13	−0.779357
$957$	−2.08373e13	−0.803042
$958$	−8.77215e12	−0.336482
$959$	−1.44822e13	−0.552907
$960$	3.43755e11	0.0130625
$961$	−1.66866e13	−0.631122
$962$	−3.11369e12	−0.117216
$963$	7.40775e12	0.277567
$964$	2.38652e13	0.890060
$965$	1.84883e13	0.686318
$966$	−2.61756e11	−0.00967163
$967$	4.32458e13	1.59047	0.795233	−	0.606304i	$-0.207349\pi$
$967$	4.32458e13	1.59047	0.795233	+	0.606304i	$0.207349\pi$
$968$	4.07956e13	1.49339
$969$	6.40333e12	0.233318
$970$	4.81674e12	0.174695
$971$	−2.45954e13	−0.887908	−0.443954	−	0.896050i	$-0.646425\pi$
$971$	−2.45954e13	−0.887908	−0.443954	+	0.896050i	$0.646425\pi$
$972$	2.19831e13	0.789934
$973$	4.22611e12	0.151159
$974$	−4.23107e12	−0.150638
$975$	2.59796e11	0.00920687
$976$	−1.85648e13	−0.654888
$977$	1.45203e12	0.0509858	0.0254929	−	0.999675i	$-0.491884\pi$
$977$	1.45203e12	0.0509858	0.0254929	+	0.999675i	$0.491884\pi$
$978$	−6.10586e12	−0.213414
$979$	5.59972e13	1.94825
$980$	3.40113e12	0.117789
$981$	−2.40458e13	−0.828952
$982$	−1.97130e13	−0.676473
$983$	5.12156e13	1.74949	0.874746	−	0.484582i	$-0.161028\pi$
$983$	5.12156e13	1.74949	0.874746	+	0.484582i	$0.161028\pi$
$984$	−1.09335e13	−0.371777
$985$	4.45819e13	1.50902
$986$	−1.78860e13	−0.602654
$987$	7.22269e12	0.242254
$988$	−2.88134e12	−0.0962031
$989$	7.63911e11	0.0253898
$990$	−1.93325e13	−0.639631
$991$	−5.11988e13	−1.68628	−0.843138	−	0.537698i	$-0.819294\pi$
$991$	−5.11988e13	−1.68628	−0.843138	+	0.537698i	$0.819294\pi$
$992$	1.86378e13	0.611071
$993$	−1.50156e13	−0.490084
$994$	−7.07880e12	−0.229996
$995$	2.89859e13	0.937525
$996$	−4.51226e12	−0.145287
$997$	−1.78453e13	−0.571998	−0.285999	−	0.958230i	$-0.592325\pi$
$997$	−1.78453e13	−0.571998	−0.285999	+	0.958230i	$0.592325\pi$
$998$	−1.40711e12	−0.0448995
$999$	−2.32543e13	−0.738682

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.b.1.5	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.b.1.5	✓	13	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)

\(f(q)\)	\(=\)	\(q-10.2467 q^{2} -61.4030 q^{3} -407.004 q^{4} -1449.57 q^{5} +629.180 q^{6} -2401.00 q^{7} +9416.80 q^{8} -15912.7 q^{9} +O(q^{10})\)	\(q-10.2467 q^{2} -61.4030 q^{3} -407.004 q^{4} -1449.57 q^{5} +629.180 q^{6} -2401.00 q^{7} +9416.80 q^{8} -15912.7 q^{9} +14853.4 q^{10} +81793.4 q^{11} +24991.3 q^{12} -28561.0 q^{13} +24602.4 q^{14} +89008.1 q^{15} +111895. q^{16} +420721. q^{17} +163053. q^{18} -247869. q^{19} +589983. q^{20} +147429. q^{21} -838116. q^{22} +173272. q^{23} -578219. q^{24} +148139. q^{25} +292657. q^{26} +2.18568e6 q^{27} +977217. q^{28} +4.14891e6 q^{29} -912043. q^{30} -3.12298e6 q^{31} -5.96796e6 q^{32} -5.02236e6 q^{33} -4.31101e6 q^{34} +3.48043e6 q^{35} +6.47653e6 q^{36} -1.06394e7 q^{37} +2.53985e6 q^{38} +1.75373e6 q^{39} -1.36503e7 q^{40} +1.89090e7 q^{41} -1.51066e6 q^{42} +4.40873e6 q^{43} -3.32903e7 q^{44} +2.30666e7 q^{45} -1.77548e6 q^{46} +4.89911e7 q^{47} -6.87066e6 q^{48} +5.76480e6 q^{49} -1.51794e6 q^{50} -2.58335e7 q^{51} +1.16244e7 q^{52} -4.97977e7 q^{53} -2.23961e7 q^{54} -1.18566e8 q^{55} -2.26097e7 q^{56} +1.52199e7 q^{57} -4.25129e7 q^{58} +6.54970e6 q^{59} -3.62267e7 q^{60} -1.65913e8 q^{61} +3.20003e7 q^{62} +3.82063e7 q^{63} +3.86206e6 q^{64} +4.14013e7 q^{65} +5.14628e7 q^{66} +8.11719e7 q^{67} -1.71235e8 q^{68} -1.06394e7 q^{69} -3.56630e7 q^{70} -2.87728e8 q^{71} -1.49846e8 q^{72} -6.04463e7 q^{73} +1.09019e8 q^{74} -9.09619e6 q^{75} +1.00884e8 q^{76} -1.96386e8 q^{77} -1.79700e7 q^{78} -4.42205e8 q^{79} -1.62200e8 q^{80} +1.79002e8 q^{81} -1.93755e8 q^{82} -1.80554e8 q^{83} -6.00040e7 q^{84} -6.09865e8 q^{85} -4.51751e7 q^{86} -2.54756e8 q^{87} +7.70232e8 q^{88} +6.84618e8 q^{89} -2.36358e8 q^{90} +6.85750e7 q^{91} -7.05226e7 q^{92} +1.91760e8 q^{93} -5.01999e8 q^{94} +3.59305e8 q^{95} +3.66450e8 q^{96} +3.24285e8 q^{97} -5.90704e7 q^{98} -1.30155e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 26 q^{2} + 163 q^{3} + 3286 q^{4} - 2640 q^{5} - 995 q^{6} - 31213 q^{7} - 6738 q^{8} + 94756 q^{9}+O(q^{10}) \) 13 * q - 26 * q^2 + 163 * q^3 + 3286 * q^4 - 2640 * q^5 - 995 * q^6 - 31213 * q^7 - 6738 * q^8 + 94756 * q^9	\( 13 q - 26 q^{2} + 163 q^{3} + 3286 q^{4} - 2640 q^{5} - 995 q^{6} - 31213 q^{7} - 6738 q^{8} + 94756 q^{9} + 42588 q^{10} - 107493 q^{11} + 157399 q^{12} - 371293 q^{13} + 62426 q^{14} - 469556 q^{15} + 1033802 q^{16} + 50812 q^{17} - 2994615 q^{18} + 479470 q^{19} - 1834962 q^{20} - 391363 q^{21} - 5474013 q^{22} - 984639 q^{23} - 12496965 q^{24} + 4519039 q^{25} + 742586 q^{26} + 5965117 q^{27} - 7889686 q^{28} - 3441800 q^{29} + 25168012 q^{30} - 2185751 q^{31} - 2746342 q^{32} + 34793355 q^{33} - 966694 q^{34} + 6338640 q^{35} + 23974587 q^{36} - 31532363 q^{37} - 51039796 q^{38} - 4655443 q^{39} + 27446642 q^{40} - 38029287 q^{41} + 2388995 q^{42} - 65479740 q^{43} - 64795239 q^{44} - 190647152 q^{45} - 68737615 q^{46} + 18884785 q^{47} - 43918333 q^{48} + 74942413 q^{49} - 295918964 q^{50} - 97799092 q^{51} - 93851446 q^{52} - 37670088 q^{53} - 420784337 q^{54} - 11739604 q^{55} + 16177938 q^{56} - 119447794 q^{57} - 351819004 q^{58} - 86030686 q^{59} - 1421949708 q^{60} - 413609773 q^{61} + 21747651 q^{62} - 227509156 q^{63} - 611561502 q^{64} + 75401040 q^{65} - 154290083 q^{66} + 121596783 q^{67} - 613335382 q^{68} - 1089108303 q^{69} - 102253788 q^{70} - 900222116 q^{71} - 1897573017 q^{72} - 586910355 q^{73} - 688661251 q^{74} - 1466887131 q^{75} - 180912510 q^{76} + 258090693 q^{77} + 28418195 q^{78} - 590012173 q^{79} - 1724662122 q^{80} - 58178363 q^{81} + 145984865 q^{82} + 94283256 q^{83} - 377914999 q^{84} - 1689818164 q^{85} + 13901738 q^{86} + 1073171888 q^{87} - 1814132379 q^{88} - 1154652750 q^{89} + 2671175016 q^{90} + 891474493 q^{91} + 670826733 q^{92} - 5057835587 q^{93} - 2961146369 q^{94} - 3377803464 q^{95} - 4898921405 q^{96} - 2173622401 q^{97} - 149884826 q^{98} - 4653424330 q^{99}+O(q^{100}) \) 13 * q - 26 * q^2 + 163 * q^3 + 3286 * q^4 - 2640 * q^5 - 995 * q^6 - 31213 * q^7 - 6738 * q^8 + 94756 * q^9 + 42588 * q^10 - 107493 * q^11 + 157399 * q^12 - 371293 * q^13 + 62426 * q^14 - 469556 * q^15 + 1033802 * q^16 + 50812 * q^17 - 2994615 * q^18 + 479470 * q^19 - 1834962 * q^20 - 391363 * q^21 - 5474013 * q^22 - 984639 * q^23 - 12496965 * q^24 + 4519039 * q^25 + 742586 * q^26 + 5965117 * q^27 - 7889686 * q^28 - 3441800 * q^29 + 25168012 * q^30 - 2185751 * q^31 - 2746342 * q^32 + 34793355 * q^33 - 966694 * q^34 + 6338640 * q^35 + 23974587 * q^36 - 31532363 * q^37 - 51039796 * q^38 - 4655443 * q^39 + 27446642 * q^40 - 38029287 * q^41 + 2388995 * q^42 - 65479740 * q^43 - 64795239 * q^44 - 190647152 * q^45 - 68737615 * q^46 + 18884785 * q^47 - 43918333 * q^48 + 74942413 * q^49 - 295918964 * q^50 - 97799092 * q^51 - 93851446 * q^52 - 37670088 * q^53 - 420784337 * q^54 - 11739604 * q^55 + 16177938 * q^56 - 119447794 * q^57 - 351819004 * q^58 - 86030686 * q^59 - 1421949708 * q^60 - 413609773 * q^61 + 21747651 * q^62 - 227509156 * q^63 - 611561502 * q^64 + 75401040 * q^65 - 154290083 * q^66 + 121596783 * q^67 - 613335382 * q^68 - 1089108303 * q^69 - 102253788 * q^70 - 900222116 * q^71 - 1897573017 * q^72 - 586910355 * q^73 - 688661251 * q^74 - 1466887131 * q^75 - 180912510 * q^76 + 258090693 * q^77 + 28418195 * q^78 - 590012173 * q^79 - 1724662122 * q^80 - 58178363 * q^81 + 145984865 * q^82 + 94283256 * q^83 - 377914999 * q^84 - 1689818164 * q^85 + 13901738 * q^86 + 1073171888 * q^87 - 1814132379 * q^88 - 1154652750 * q^89 + 2671175016 * q^90 + 891474493 * q^91 + 670826733 * q^92 - 5057835587 * q^93 - 2961146369 * q^94 - 3377803464 * q^95 - 4898921405 * q^96 - 2173622401 * q^97 - 149884826 * q^98 - 4653424330 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more