LMFDB - Embedded newform 13.12.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,12,Mod(1,13)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 12, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("13.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	13.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:	$9.98846134727$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 13546x^{4} + 130998x^{3} + 49403509x^{2} - 776207317x - 22123683244 $ x^6 - x^5 - 13546x^4 + 130998x^3 + 49403509x^2 - 776207317x - 22123683244
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$73.0961$ of defining polynomial
Character	$\chi$	$=$	13.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+82.0961 q^{2} -696.954 q^{3} +4691.77 q^{4} +6795.70 q^{5} -57217.2 q^{6} +67467.4 q^{7} +217044. q^{8} +308598. q^{9} +O(q^{10})$	\(q+82.0961 q^{2} -696.954 q^{3} +4691.77 q^{4} +6795.70 q^{5} -57217.2 q^{6} +67467.4 q^{7} +217044. q^{8} +308598. q^{9} +557901. q^{10} -109439. q^{11} -3.26995e6 q^{12} -371293. q^{13} +5.53881e6 q^{14} -4.73629e6 q^{15} +8.20969e6 q^{16} -7.17536e6 q^{17} +2.53347e7 q^{18} +2.86570e6 q^{19} +3.18839e7 q^{20} -4.70217e7 q^{21} -8.98449e6 q^{22} +3.30545e7 q^{23} -1.51269e8 q^{24} -2.64658e6 q^{25} -3.04817e7 q^{26} -9.16155e7 q^{27} +3.16542e8 q^{28} +1.00760e8 q^{29} -3.88831e8 q^{30} -2.27822e8 q^{31} +2.29478e8 q^{32} +7.62738e7 q^{33} -5.89069e8 q^{34} +4.58488e8 q^{35} +1.44787e9 q^{36} -3.45962e8 q^{37} +2.35263e8 q^{38} +2.58774e8 q^{39} +1.47496e9 q^{40} -8.48231e8 q^{41} -3.86030e9 q^{42} +2.07988e7 q^{43} -5.13462e8 q^{44} +2.09714e9 q^{45} +2.71364e9 q^{46} +2.76700e8 q^{47} -5.72178e9 q^{48} +2.57452e9 q^{49} -2.17274e8 q^{50} +5.00090e9 q^{51} -1.74202e9 q^{52} -5.34414e9 q^{53} -7.52128e9 q^{54} -7.43713e8 q^{55} +1.46434e10 q^{56} -1.99726e9 q^{57} +8.27197e9 q^{58} +1.37983e9 q^{59} -2.22216e10 q^{60} +1.66734e9 q^{61} -1.87033e10 q^{62} +2.08203e10 q^{63} +2.02583e9 q^{64} -2.52320e9 q^{65} +6.26178e9 q^{66} +1.71867e10 q^{67} -3.36652e10 q^{68} -2.30374e10 q^{69} +3.76401e10 q^{70} +3.04766e9 q^{71} +6.69793e10 q^{72} -7.07528e8 q^{73} -2.84021e10 q^{74} +1.84454e9 q^{75} +1.34452e10 q^{76} -7.38354e9 q^{77} +2.12444e10 q^{78} -8.61399e9 q^{79} +5.57906e10 q^{80} +9.18455e9 q^{81} -6.96365e10 q^{82} +7.03527e9 q^{83} -2.20615e11 q^{84} -4.87616e10 q^{85} +1.70750e9 q^{86} -7.02248e10 q^{87} -2.37530e10 q^{88} -2.50144e10 q^{89} +1.72167e11 q^{90} -2.50502e10 q^{91} +1.55084e11 q^{92} +1.58782e11 q^{93} +2.27160e10 q^{94} +1.94744e10 q^{95} -1.59936e11 q^{96} -7.08836e10 q^{97} +2.11358e11 q^{98} -3.37726e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 55 q^{2} + 476 q^{3} + 15309 q^{4} + 3312 q^{5} - 57797 q^{6} - 4176 q^{7} + 158493 q^{8} + 876218 q^{9}+O(q^{10}) $ 6 * q + 55 * q^2 + 476 * q^3 + 15309 * q^4 + 3312 * q^5 - 57797 * q^6 - 4176 * q^7 + 158493 * q^8 + 876218 * q^9	\( 6 q + 55 q^{2} + 476 q^{3} + 15309 q^{4} + 3312 q^{5} - 57797 q^{6} - 4176 q^{7} + 158493 q^{8} + 876218 q^{9} + 997497 q^{10} + 275060 q^{11} + 3949049 q^{12} - 2227758 q^{13} + 6462587 q^{14} + 5951652 q^{15} + 25038945 q^{16} + 18470848 q^{17} + 1544758 q^{18} + 2382612 q^{19} + 37821799 q^{20} - 67640772 q^{21} - 52649718 q^{22} + 25001944 q^{23} - 243039615 q^{24} - 14063202 q^{25} - 20421115 q^{26} + 77250908 q^{27} - 340836927 q^{28} - 142876028 q^{29} - 838796927 q^{30} - 158397468 q^{31} + 739784589 q^{32} - 115057792 q^{33} - 668802009 q^{34} + 1377003692 q^{35} + 3099344006 q^{36} + 47994456 q^{37} + 2673019714 q^{38} - 176735468 q^{39} + 242886231 q^{40} + 112037548 q^{41} - 5282633557 q^{42} + 1399191924 q^{43} - 1571975050 q^{44} + 7736061780 q^{45} - 2701412412 q^{46} - 3383597640 q^{47} + 1090782789 q^{48} + 7189538970 q^{49} - 12848613144 q^{50} + 8959562860 q^{51} - 5684124537 q^{52} + 546961604 q^{53} - 38372021519 q^{54} - 7803526248 q^{55} - 6807872407 q^{56} + 918537576 q^{57} + 5714690406 q^{58} + 10067834260 q^{59} + 2453022955 q^{60} + 15731821572 q^{61} - 7829475572 q^{62} + 29876175732 q^{63} + 2237284569 q^{64} - 1229722416 q^{65} + 12031833058 q^{66} + 50546073444 q^{67} + 15412804265 q^{68} + 10879166680 q^{69} + 2924449065 q^{70} - 2646136112 q^{71} - 8720745402 q^{72} + 4198695060 q^{73} + 5050454541 q^{74} - 7695720336 q^{75} + 59928748062 q^{76} + 9015828840 q^{77} + 21459621521 q^{78} - 92124930312 q^{79} + 89421404931 q^{80} + 67208776622 q^{81} - 150798850248 q^{82} + 20440296092 q^{83} - 419349915667 q^{84} - 124095891228 q^{85} + 116436457677 q^{86} - 161197597808 q^{87} - 158617438842 q^{88} + 20540234076 q^{89} - 279059693450 q^{90} + 1550519568 q^{91} + 446253814012 q^{92} + 142195723000 q^{93} + 92592053391 q^{94} + 82521342544 q^{95} - 2651637759 q^{96} - 203942467020 q^{97} + 711378915442 q^{98} - 235408311580 q^{99}+O(q^{100}) \) 6 * q + 55 * q^2 + 476 * q^3 + 15309 * q^4 + 3312 * q^5 - 57797 * q^6 - 4176 * q^7 + 158493 * q^8 + 876218 * q^9 + 997497 * q^10 + 275060 * q^11 + 3949049 * q^12 - 2227758 * q^13 + 6462587 * q^14 + 5951652 * q^15 + 25038945 * q^16 + 18470848 * q^17 + 1544758 * q^18 + 2382612 * q^19 + 37821799 * q^20 - 67640772 * q^21 - 52649718 * q^22 + 25001944 * q^23 - 243039615 * q^24 - 14063202 * q^25 - 20421115 * q^26 + 77250908 * q^27 - 340836927 * q^28 - 142876028 * q^29 - 838796927 * q^30 - 158397468 * q^31 + 739784589 * q^32 - 115057792 * q^33 - 668802009 * q^34 + 1377003692 * q^35 + 3099344006 * q^36 + 47994456 * q^37 + 2673019714 * q^38 - 176735468 * q^39 + 242886231 * q^40 + 112037548 * q^41 - 5282633557 * q^42 + 1399191924 * q^43 - 1571975050 * q^44 + 7736061780 * q^45 - 2701412412 * q^46 - 3383597640 * q^47 + 1090782789 * q^48 + 7189538970 * q^49 - 12848613144 * q^50 + 8959562860 * q^51 - 5684124537 * q^52 + 546961604 * q^53 - 38372021519 * q^54 - 7803526248 * q^55 - 6807872407 * q^56 + 918537576 * q^57 + 5714690406 * q^58 + 10067834260 * q^59 + 2453022955 * q^60 + 15731821572 * q^61 - 7829475572 * q^62 + 29876175732 * q^63 + 2237284569 * q^64 - 1229722416 * q^65 + 12031833058 * q^66 + 50546073444 * q^67 + 15412804265 * q^68 + 10879166680 * q^69 + 2924449065 * q^70 - 2646136112 * q^71 - 8720745402 * q^72 + 4198695060 * q^73 + 5050454541 * q^74 - 7695720336 * q^75 + 59928748062 * q^76 + 9015828840 * q^77 + 21459621521 * q^78 - 92124930312 * q^79 + 89421404931 * q^80 + 67208776622 * q^81 - 150798850248 * q^82 + 20440296092 * q^83 - 419349915667 * q^84 - 124095891228 * q^85 + 116436457677 * q^86 - 161197597808 * q^87 - 158617438842 * q^88 + 20540234076 * q^89 - 279059693450 * q^90 + 1550519568 * q^91 + 446253814012 * q^92 + 142195723000 * q^93 + 92592053391 * q^94 + 82521342544 * q^95 - 2651637759 * q^96 - 203942467020 * q^97 + 711378915442 * q^98 - 235408311580 * 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 $

$2$	82.0961	1.81409	0.907043	−	0.421039i	$-0.138334\pi$
$2$	82.0961	1.81409	0.907043	+	0.421039i	$0.138334\pi$
$3$	−696.954	−1.65591	−0.827956	−	0.560793i	$-0.810496\pi$
$3$	−696.954	−1.65591	−0.827956	+	0.560793i	$0.810496\pi$
$4$	4691.77	2.29091
$5$	6795.70	0.972522	0.486261	−	0.873814i	$-0.338361\pi$
$5$	6795.70	0.972522	0.486261	+	0.873814i	$0.338361\pi$
$6$	−57217.2	−3.00397
$7$	67467.4	1.51724	0.758620	−	0.651533i	$-0.225874\pi$
$7$	67467.4	1.51724	0.758620	+	0.651533i	$0.225874\pi$
$8$	217044.	2.34181
$9$	308598.	1.74205
$10$	557901.	1.76424
$11$	−109439.	−0.204885	−0.102443	−	0.994739i	$-0.532666\pi$
$11$	−109439.	−0.204885	−0.102443	+	0.994739i	$0.532666\pi$
$12$	−3.26995e6	−3.79354
$13$	−371293.	−0.277350
$13$	−371293.	−0.277350
$14$	5.53881e6	2.75240
$15$	−4.73629e6	−1.61041
$16$	8.20969e6	1.95734
$17$	−7.17536e6	−1.22567	−0.612837	−	0.790210i	$-0.709972\pi$
$17$	−7.17536e6	−1.22567	−0.612837	+	0.790210i	$0.709972\pi$
$18$	2.53347e7	3.16022
$19$	2.86570e6	0.265513	0.132756	−	0.991149i	$-0.457617\pi$
$19$	2.86570e6	0.265513	0.132756	+	0.991149i	$0.457617\pi$
$20$	3.18839e7	2.22795
$21$	−4.70217e7	−2.51242
$22$	−8.98449e6	−0.371680
$23$	3.30545e7	1.07085	0.535423	−	0.844584i	$-0.320152\pi$
$23$	3.30545e7	1.07085	0.535423	+	0.844584i	$0.320152\pi$
$24$	−1.51269e8	−3.87784
$25$	−2.64658e6	−0.0542019
$26$	−3.04817e7	−0.503137
$27$	−9.16155e7	−1.22876
$28$	3.16542e8	3.47585
$29$	1.00760e8	0.912215	0.456108	−	0.889925i	$-0.349243\pi$
$29$	1.00760e8	0.912215	0.456108	+	0.889925i	$0.349243\pi$
$30$	−3.88831e8	−2.92142
$31$	−2.27822e8	−1.42925	−0.714623	−	0.699510i	$-0.753402\pi$
$31$	−2.27822e8	−1.42925	−0.714623	+	0.699510i	$0.753402\pi$
$32$	2.29478e8	1.20897
$33$	7.62738e7	0.339272
$34$	−5.89069e8	−2.22348
$35$	4.58488e8	1.47555
$36$	1.44787e9	3.99086
$37$	−3.45962e8	−0.820198	−0.410099	−	0.912041i	$-0.634506\pi$
$37$	−3.45962e8	−0.820198	−0.410099	+	0.912041i	$0.634506\pi$
$38$	2.35263e8	0.481663
$39$	2.58774e8	0.459267
$40$	1.47496e9	2.27746
$41$	−8.48231e8	−1.14341	−0.571706	−	0.820458i	$-0.693718\pi$
$41$	−8.48231e8	−1.14341	−0.571706	+	0.820458i	$0.693718\pi$
$42$	−3.86030e9	−4.55774
$43$	2.07988e7	0.0215755	0.0107878	−	0.999942i	$-0.496566\pi$
$43$	2.07988e7	0.0215755	0.0107878	+	0.999942i	$0.496566\pi$
$44$	−5.13462e8	−0.469373
$45$	2.09714e9	1.69418
$46$	2.71364e9	1.94261
$47$	2.76700e8	0.175983	0.0879916	−	0.996121i	$-0.471955\pi$
$47$	2.76700e8	0.175983	0.0879916	+	0.996121i	$0.471955\pi$
$48$	−5.72178e9	−3.24119
$49$	2.57452e9	1.30202
$50$	−2.17274e8	−0.0983268
$51$	5.00090e9	2.02961
$52$	−1.74202e9	−0.635383
$53$	−5.34414e9	−1.75534	−0.877668	−	0.479269i	$-0.840902\pi$
$53$	−5.34414e9	−1.75534	−0.877668	+	0.479269i	$0.840902\pi$
$54$	−7.52128e9	−2.22908
$55$	−7.43713e8	−0.199256
$56$	1.46434e10	3.55309
$57$	−1.99726e9	−0.439666
$58$	8.27197e9	1.65484
$59$	1.37983e9	0.251270	0.125635	−	0.992077i	$-0.459903\pi$
$59$	1.37983e9	0.251270	0.125635	+	0.992077i	$0.459903\pi$
$60$	−2.22216e10	−3.68930
$61$	1.66734e9	0.252760	0.126380	−	0.991982i	$-0.459664\pi$
$61$	1.66734e9	0.252760	0.126380	+	0.991982i	$0.459664\pi$
$62$	−1.87033e10	−2.59277
$63$	2.08203e10	2.64310
$64$	2.02583e9	0.235837
$65$	−2.52320e9	−0.269729
$66$	6.26178e9	0.615469
$67$	1.71867e10	1.55519	0.777593	−	0.628768i	$-0.216441\pi$
$67$	1.71867e10	1.55519	0.777593	+	0.628768i	$0.216441\pi$
$68$	−3.36652e10	−2.80790
$69$	−2.30374e10	−1.77323
$70$	3.76401e10	2.67677
$71$	3.04766e9	0.200469	0.100234	−	0.994964i	$-0.468041\pi$
$71$	3.04766e9	0.200469	0.100234	+	0.994964i	$0.468041\pi$
$72$	6.69793e10	4.07954
$73$	−7.07528e8	−0.0399455	−0.0199728	−	0.999801i	$-0.506358\pi$
$73$	−7.07528e8	−0.0399455	−0.0199728	+	0.999801i	$0.506358\pi$
$74$	−2.84021e10	−1.48791
$75$	1.84454e9	0.0897535
$76$	1.34452e10	0.608265
$77$	−7.38354e9	−0.310861
$78$	2.12444e10	0.833150
$79$	−8.61399e9	−0.314960	−0.157480	−	0.987522i	$-0.550337\pi$
$79$	−8.61399e9	−0.314960	−0.157480	+	0.987522i	$0.550337\pi$
$80$	5.57906e10	1.90356
$81$	9.18455e9	0.292678
$82$	−6.96365e10	−2.07425
$83$	7.03527e9	0.196043	0.0980215	−	0.995184i	$-0.468749\pi$
$83$	7.03527e9	0.196043	0.0980215	+	0.995184i	$0.468749\pi$
$84$	−2.20615e11	−5.75571
$85$	−4.87616e10	−1.19199
$86$	1.70750e9	0.0391398
$87$	−7.02248e10	−1.51055
$88$	−2.37530e10	−0.479803
$89$	−2.50144e10	−0.474837	−0.237419	−	0.971407i	$-0.576301\pi$
$89$	−2.50144e10	−0.474837	−0.237419	+	0.971407i	$0.576301\pi$
$90$	1.72167e11	3.07338
$91$	−2.50502e10	−0.420807
$92$	1.55084e11	2.45321
$93$	1.58782e11	2.36670
$94$	2.27160e10	0.319249
$95$	1.94744e10	0.258217
$96$	−1.59936e11	−2.00195
$97$	−7.08836e10	−0.838111	−0.419055	−	0.907961i	$-0.637639\pi$
$97$	−7.08836e10	−0.838111	−0.419055	+	0.907961i	$0.637639\pi$
$98$	2.11358e11	2.36197
$99$	−3.37726e10	−0.356920
$100$	−1.24171e10	−0.124171
$101$	5.46688e10	0.517573	0.258787	−	0.965935i	$-0.416677\pi$
$101$	5.46688e10	0.517573	0.258787	+	0.965935i	$0.416677\pi$
$102$	4.10554e11	3.68188
$103$	−1.16418e11	−0.989500	−0.494750	−	0.869035i	$-0.664740\pi$
$103$	−1.16418e11	−0.989500	−0.494750	+	0.869035i	$0.664740\pi$
$104$	−8.05868e10	−0.649502
$105$	−3.19545e11	−2.44338
$106$	−4.38733e11	−3.18433
$107$	2.24367e11	1.54649	0.773247	−	0.634104i	$-0.218631\pi$
$107$	2.24367e11	1.54649	0.773247	+	0.634104i	$0.218631\pi$
$108$	−4.29839e11	−2.81498
$109$	3.09661e11	1.92771	0.963854	−	0.266431i	$-0.0858445\pi$
$109$	3.09661e11	1.92771	0.963854	+	0.266431i	$0.0858445\pi$
$110$	−6.10559e10	−0.361467
$111$	2.41120e11	1.35818
$112$	5.53886e11	2.96976
$113$	−1.20705e11	−0.616303	−0.308151	−	0.951337i	$-0.599710\pi$
$113$	−1.20705e11	−0.616303	−0.308151	+	0.951337i	$0.599710\pi$
$114$	−1.63967e11	−0.797591
$115$	2.24628e11	1.04142
$116$	4.72741e11	2.08980
$117$	−1.14580e11	−0.483157
$118$	1.13279e11	0.455824
$119$	−4.84103e11	−1.85964
$120$	−1.02798e12	−3.77128
$121$	−2.73335e11	−0.958022
$122$	1.36882e11	0.458529
$123$	5.91178e11	1.89339
$124$	−1.06889e12	−3.27426
$125$	−3.49807e11	−1.02523
$126$	1.70927e12	4.79481
$127$	1.33140e11	0.357591	0.178796	−	0.983886i	$-0.442780\pi$
$127$	1.33140e11	0.357591	0.178796	+	0.983886i	$0.442780\pi$
$128$	−3.03659e11	−0.781143
$129$	−1.44958e10	−0.0357271
$130$	−2.07145e11	−0.489311
$131$	−5.58494e10	−0.126481	−0.0632407	−	0.997998i	$-0.520144\pi$
$131$	−5.58494e10	−0.126481	−0.0632407	+	0.997998i	$0.520144\pi$
$132$	3.57859e11	0.777241
$133$	1.93341e11	0.402847
$134$	1.41096e12	2.82124
$135$	−6.22591e11	−1.19500
$136$	−1.55737e12	−2.87030
$137$	2.93799e11	0.520100	0.260050	−	0.965595i	$-0.416261\pi$
$137$	2.93799e11	0.520100	0.260050	+	0.965595i	$0.416261\pi$
$138$	−1.89129e12	−3.21679
$139$	−9.08612e11	−1.48524	−0.742621	−	0.669712i	$-0.766417\pi$
$139$	−9.08612e11	−1.48524	−0.742621	+	0.669712i	$0.766417\pi$
$140$	2.15112e12	3.38034
$141$	−1.92847e11	−0.291413
$142$	2.50201e11	0.363667
$143$	4.06338e10	0.0568250
$144$	2.53349e12	3.40978
$145$	6.84732e11	0.887149
$146$	−5.80853e10	−0.0724646
$147$	−1.79432e12	−2.15603
$148$	−1.62318e12	−1.87900
$149$	1.15676e12	1.29038	0.645190	−	0.764022i	$-0.276778\pi$
$149$	1.15676e12	1.29038	0.645190	+	0.764022i	$0.276778\pi$
$150$	1.51430e11	0.162821
$151$	1.13324e12	1.17476	0.587379	−	0.809312i	$-0.300160\pi$
$151$	1.13324e12	1.17476	0.587379	+	0.809312i	$0.300160\pi$
$152$	6.21981e11	0.621781
$153$	−2.21430e12	−2.13518
$154$	−6.06160e11	−0.563928
$155$	−1.54821e12	−1.38997
$156$	1.21411e12	1.05214
$157$	1.76599e12	1.47755	0.738773	−	0.673955i	$-0.235406\pi$
$157$	1.76599e12	1.47755	0.738773	+	0.673955i	$0.235406\pi$
$158$	−7.07175e11	−0.571364
$159$	3.72462e12	2.90668
$160$	1.55946e12	1.17575
$161$	2.23010e12	1.62473
$162$	7.54016e11	0.530943
$163$	−5.19705e11	−0.353773	−0.176887	−	0.984231i	$-0.556603\pi$
$163$	−5.19705e11	−0.353773	−0.176887	+	0.984231i	$0.556603\pi$
$164$	−3.97971e12	−2.61945
$165$	5.18334e11	0.329950
$166$	5.77569e11	0.355639
$167$	1.88903e12	1.12538	0.562689	−	0.826668i	$-0.309767\pi$
$167$	1.88903e12	1.12538	0.562689	+	0.826668i	$0.309767\pi$
$168$	−1.02058e13	−5.88361
$169$	1.37858e11	0.0769231
$170$	−4.00314e12	−2.16238
$171$	8.84349e11	0.462535
$172$	9.75831e10	0.0494274
$173$	3.04198e12	1.49246	0.746230	−	0.665688i	$-0.231862\pi$
$173$	3.04198e12	1.49246	0.746230	+	0.665688i	$0.231862\pi$
$174$	−5.76519e12	−2.74026
$175$	−1.78557e11	−0.0822373
$176$	−8.98457e11	−0.401031
$177$	−9.61679e11	−0.416080
$178$	−2.05358e12	−0.861395
$179$	8.39824e11	0.341583	0.170792	−	0.985307i	$-0.445367\pi$
$179$	8.39824e11	0.341583	0.170792	+	0.985307i	$0.445367\pi$
$180$	9.83931e12	3.88120
$181$	−3.08672e12	−1.18104	−0.590520	−	0.807023i	$-0.701077\pi$
$181$	−3.08672e12	−1.18104	−0.590520	+	0.807023i	$0.701077\pi$
$182$	−2.05652e12	−0.763380
$183$	−1.16206e12	−0.418549
$184$	7.17426e12	2.50772
$185$	−2.35105e12	−0.797661
$186$	1.30354e13	4.29340
$187$	7.85262e11	0.251123
$188$	1.29821e12	0.403161
$189$	−6.18105e12	−1.86433
$190$	1.59877e12	0.468427
$191$	1.03365e12	0.294231	0.147115	−	0.989119i	$-0.453001\pi$
$191$	1.03365e12	0.294231	0.147115	+	0.989119i	$0.453001\pi$
$192$	−1.41191e12	−0.390526
$193$	−2.40907e12	−0.647566	−0.323783	−	0.946131i	$-0.604955\pi$
$193$	−2.40907e12	−0.647566	−0.323783	+	0.946131i	$0.604955\pi$
$194$	−5.81927e12	−1.52040
$195$	1.75855e12	0.446648
$196$	1.20791e13	2.98280
$197$	−9.82517e11	−0.235926	−0.117963	−	0.993018i	$-0.537636\pi$
$197$	−9.82517e11	−0.235926	−0.117963	+	0.993018i	$0.537636\pi$
$198$	−2.77260e12	−0.647483
$199$	2.11376e12	0.480135	0.240067	−	0.970756i	$-0.422830\pi$
$199$	2.11376e12	0.480135	0.240067	+	0.970756i	$0.422830\pi$
$200$	−5.74422e11	−0.126931
$201$	−1.19784e13	−2.57525
$202$	4.48809e12	0.938922
$203$	6.79798e12	1.38405
$204$	2.34631e13	4.64964
$205$	−5.76432e12	−1.11199
$206$	−9.55747e12	−1.79504
$207$	1.02005e13	1.86546
$208$	−3.04820e12	−0.542869
$209$	−3.13618e11	−0.0543997
$210$	−2.62334e13	−4.43250
$211$	−5.38052e12	−0.885667	−0.442834	−	0.896604i	$-0.646027\pi$
$211$	−5.38052e12	−0.885667	−0.442834	+	0.896604i	$0.646027\pi$
$212$	−2.50735e13	−4.02131
$213$	−2.12408e12	−0.331958
$214$	1.84197e13	2.80547
$215$	1.41342e11	0.0209826
$216$	−1.98846e13	−2.87753
$217$	−1.53706e13	−2.16851
$218$	2.54220e13	3.49703
$219$	4.93115e11	0.0661463
$220$	−3.48933e12	−0.456476
$221$	2.66416e12	0.339941
$222$	1.97950e13	2.46385
$223$	9.66064e12	1.17308	0.586542	−	0.809919i	$-0.300489\pi$
$223$	9.66064e12	1.17308	0.586542	+	0.809919i	$0.300489\pi$
$224$	1.54823e13	1.83430
$225$	−8.16728e11	−0.0944221
$226$	−9.90942e12	−1.11803
$227$	−5.19488e12	−0.572049	−0.286025	−	0.958222i	$-0.592334\pi$
$227$	−5.19488e12	−0.572049	−0.286025	+	0.958222i	$0.592334\pi$
$228$	−9.37069e12	−1.00723
$229$	−7.97233e12	−0.836546	−0.418273	−	0.908321i	$-0.637364\pi$
$229$	−7.97233e12	−0.836546	−0.418273	+	0.908321i	$0.637364\pi$
$230$	1.84411e13	1.88923
$231$	5.14599e12	0.514758
$232$	2.18692e13	2.13624
$233$	1.55124e13	1.47987	0.739933	−	0.672680i	$-0.234857\pi$
$233$	1.55124e13	1.47987	0.739933	+	0.672680i	$0.234857\pi$
$234$	−9.40660e12	−0.876487
$235$	1.88037e12	0.171147
$236$	6.47386e12	0.575635
$237$	6.00355e12	0.521546
$238$	−3.97430e13	−3.37355
$239$	−2.18881e13	−1.81560	−0.907798	−	0.419408i	$-0.862238\pi$
$239$	−2.18881e13	−1.81560	−0.907798	+	0.419408i	$0.862238\pi$
$240$	−3.88835e13	−3.15212
$241$	−2.63983e12	−0.209161	−0.104581	−	0.994516i	$-0.533350\pi$
$241$	−2.63983e12	−0.209161	−0.104581	+	0.994516i	$0.533350\pi$
$242$	−2.24397e13	−1.73793
$243$	9.82820e12	0.744114
$244$	7.82276e12	0.579050
$245$	1.74957e13	1.26624
$246$	4.85334e13	3.43477
$247$	−1.06401e12	−0.0736400
$248$	−4.94473e13	−3.34702
$249$	−4.90326e12	−0.324630
$250$	−2.87178e13	−1.85986
$251$	1.59678e13	1.01167	0.505835	−	0.862630i	$-0.331184\pi$
$251$	1.59678e13	1.01167	0.505835	+	0.862630i	$0.331184\pi$
$252$	9.76842e13	6.05510
$253$	−3.61744e12	−0.219401
$254$	1.09302e13	0.648701
$255$	3.39846e13	1.97384
$256$	−2.90781e13	−1.65290
$257$	−1.80561e13	−1.00460	−0.502298	−	0.864695i	$-0.667512\pi$
$257$	−1.80561e13	−1.00460	−0.502298	+	0.864695i	$0.667512\pi$
$258$	−1.19005e12	−0.0648121
$259$	−2.33411e13	−1.24444
$260$	−1.18383e13	−0.617923
$261$	3.10942e13	1.58912
$262$	−4.58502e12	−0.229448
$263$	2.73351e13	1.33957	0.669784	−	0.742556i	$-0.266387\pi$
$263$	2.73351e13	1.33957	0.669784	+	0.742556i	$0.266387\pi$
$264$	1.65547e13	0.794512
$265$	−3.63171e13	−1.70710
$266$	1.58725e13	0.730798
$267$	1.74339e13	0.786289
$268$	8.06363e13	3.56278
$269$	−3.47546e13	−1.50444	−0.752220	−	0.658912i	$-0.771017\pi$
$269$	−3.47546e13	−1.50444	−0.752220	+	0.658912i	$0.771017\pi$
$270$	−5.11123e13	−2.16783
$271$	2.85886e13	1.18812	0.594062	−	0.804419i	$-0.297523\pi$
$271$	2.85886e13	1.18812	0.594062	+	0.804419i	$0.297523\pi$
$272$	−5.89075e13	−2.39906
$273$	1.74588e13	0.696819
$274$	2.41197e13	0.943506
$275$	2.89638e11	0.0111052
$276$	−1.08086e14	−4.06230
$277$	1.58010e12	0.0582163	0.0291081	−	0.999576i	$-0.490733\pi$
$277$	1.58010e12	0.0582163	0.0291081	+	0.999576i	$0.490733\pi$
$278$	−7.45935e13	−2.69435
$279$	−7.03055e13	−2.48981
$280$	9.95119e13	3.45546
$281$	1.42258e13	0.484387	0.242194	−	0.970228i	$-0.422133\pi$
$281$	1.42258e13	0.484387	0.242194	+	0.970228i	$0.422133\pi$
$282$	−1.58320e13	−0.528648
$283$	−1.71126e13	−0.560389	−0.280195	−	0.959943i	$-0.590399\pi$
$283$	−1.71126e13	−0.560389	−0.280195	+	0.959943i	$0.590399\pi$
$284$	1.42989e13	0.459254
$285$	−1.35728e13	−0.427585
$286$	3.33588e12	0.103085
$287$	−5.72279e13	−1.73483
$288$	7.08165e13	2.10609
$289$	1.72139e13	0.502276
$290$	5.62138e13	1.60936
$291$	4.94027e13	1.38784
$292$	−3.31956e12	−0.0915114
$293$	5.11986e13	1.38512	0.692558	−	0.721362i	$-0.256484\pi$
$293$	5.11986e13	1.38512	0.692558	+	0.721362i	$0.256484\pi$
$294$	−1.47307e14	−3.91122
$295$	9.37692e12	0.244365
$296$	−7.50888e13	−1.92075
$297$	1.00263e13	0.251756
$298$	9.49653e13	2.34086
$299$	−1.22729e13	−0.296999
$300$	8.65417e12	0.205617
$301$	1.40324e12	0.0327352
$302$	9.30345e13	2.13111
$303$	−3.81016e13	−0.857056
$304$	2.35265e13	0.519699
$305$	1.13307e13	0.245815
$306$	−1.81786e14	−3.87340
$307$	−7.17394e11	−0.0150140	−0.00750701	−	0.999972i	$-0.502390\pi$
$307$	−7.17394e11	−0.0150140	−0.00750701	+	0.999972i	$0.502390\pi$
$308$	−3.46419e13	−0.712152
$309$	8.11381e13	1.63852
$310$	−1.27102e14	−2.52153
$311$	9.15272e12	0.178389	0.0891945	−	0.996014i	$-0.471571\pi$
$311$	9.15272e12	0.178389	0.0891945	+	0.996014i	$0.471571\pi$
$312$	5.61653e13	1.07552
$313$	−4.33462e13	−0.815562	−0.407781	−	0.913080i	$-0.633697\pi$
$313$	−4.33462e13	−0.815562	−0.407781	+	0.913080i	$0.633697\pi$
$314$	1.44981e14	2.68039
$315$	1.41489e14	2.57047
$316$	−4.04149e13	−0.721543
$317$	3.50067e13	0.614222	0.307111	−	0.951674i	$-0.400638\pi$
$317$	3.50067e13	0.614222	0.307111	+	0.951674i	$0.400638\pi$
$318$	3.05777e14	5.27297
$319$	−1.10270e13	−0.186900
$320$	1.37669e13	0.229357
$321$	−1.56374e14	−2.56086
$322$	1.83082e14	2.94740
$323$	−2.05624e13	−0.325432
$324$	4.30918e13	0.670498
$325$	9.82655e11	0.0150329
$326$	−4.26658e13	−0.641775
$327$	−2.15820e14	−3.19212
$328$	−1.84103e14	−2.67766
$329$	1.86682e13	0.267009
$330$	4.25532e13	0.598557
$331$	−3.72355e13	−0.515113	−0.257557	−	0.966263i	$-0.582917\pi$
$331$	−3.72355e13	−0.515113	−0.257557	+	0.966263i	$0.582917\pi$
$332$	3.30079e13	0.449116
$333$	−1.06763e14	−1.42882
$334$	1.55082e14	2.04153
$335$	1.16796e14	1.51245
$336$	−3.86033e14	−4.91766
$337$	−1.58067e14	−1.98096	−0.990482	−	0.137640i	$-0.956048\pi$
$337$	−1.58067e14	−1.98096	−0.990482	+	0.137640i	$0.956048\pi$
$338$	1.13176e13	0.139545
$339$	8.41259e13	1.02054
$340$	−2.28778e14	−2.73075
$341$	2.49326e13	0.292832
$342$	7.26016e13	0.839079
$343$	4.02909e13	0.458236
$344$	4.51424e12	0.0505258
$345$	−1.56556e14	−1.72450
$346$	2.49735e14	2.70745
$347$	1.01968e13	0.108806	0.0544028	−	0.998519i	$-0.482674\pi$
$347$	1.01968e13	0.108806	0.0544028	+	0.998519i	$0.482674\pi$
$348$	−3.29479e14	−3.46052
$349$	1.53612e14	1.58813	0.794065	−	0.607833i	$-0.207961\pi$
$349$	1.53612e14	1.58813	0.794065	+	0.607833i	$0.207961\pi$
$350$	−1.46589e13	−0.149185
$351$	3.40162e13	0.340798
$352$	−2.51138e13	−0.247701
$353$	1.82004e14	1.76734	0.883668	−	0.468114i	$-0.155066\pi$
$353$	1.82004e14	1.76734	0.883668	+	0.468114i	$0.155066\pi$
$354$	−7.89501e13	−0.754805
$355$	2.07110e13	0.194960
$356$	−1.17362e14	−1.08781
$357$	3.37397e14	3.07940
$358$	6.89463e13	0.619661
$359$	−4.67311e13	−0.413606	−0.206803	−	0.978383i	$-0.566306\pi$
$359$	−4.67311e13	−0.413606	−0.206803	+	0.978383i	$0.566306\pi$
$360$	4.55171e14	3.96744
$361$	−1.08278e14	−0.929503
$362$	−2.53407e14	−2.14251
$363$	1.90502e14	1.58640
$364$	−1.17530e14	−0.964029
$365$	−4.80815e12	−0.0388479
$366$	−9.54003e13	−0.759283
$367$	1.32042e14	1.03526	0.517628	−	0.855606i	$-0.326815\pi$
$367$	1.32042e14	1.03526	0.517628	+	0.855606i	$0.326815\pi$
$368$	2.71367e14	2.09601
$369$	−2.61763e14	−1.99188
$370$	−1.93012e14	−1.44702
$371$	−3.60555e14	−2.66327
$372$	7.44968e14	5.42190
$373$	−1.70225e14	−1.22074	−0.610371	−	0.792116i	$-0.708980\pi$
$373$	−1.70225e14	−1.22074	−0.610371	+	0.792116i	$0.708980\pi$
$374$	6.44670e13	0.455558
$375$	2.43799e14	1.69770
$376$	6.00560e13	0.412120
$377$	−3.74113e13	−0.253003
$378$	−5.07441e14	−3.38205
$379$	−2.68131e14	−1.76129	−0.880647	−	0.473773i	$-0.842892\pi$
$379$	−2.68131e14	−1.76129	−0.880647	+	0.473773i	$0.842892\pi$
$380$	9.13696e13	0.591550
$381$	−9.27922e13	−0.592139
$382$	8.48583e13	0.533759
$383$	4.56858e13	0.283262	0.141631	−	0.989920i	$-0.454765\pi$
$383$	4.56858e13	0.283262	0.141631	+	0.989920i	$0.454765\pi$
$384$	2.11636e14	1.29351
$385$	−5.01763e13	−0.302319
$386$	−1.97775e14	−1.17474
$387$	6.41846e12	0.0375855
$388$	−3.32570e14	−1.92003
$389$	2.10412e14	1.19770	0.598849	−	0.800862i	$-0.295625\pi$
$389$	2.10412e14	1.19770	0.598849	+	0.800862i	$0.295625\pi$
$390$	1.44370e14	0.810257
$391$	−2.37178e14	−1.31251
$392$	5.58783e14	3.04909
$393$	3.89245e13	0.209442
$394$	−8.06609e13	−0.427990
$395$	−5.85381e13	−0.306305
$396$	−1.58453e14	−0.817670
$397$	2.30485e14	1.17299	0.586497	−	0.809952i	$-0.300507\pi$
$397$	2.30485e14	1.17299	0.586497	+	0.809952i	$0.300507\pi$
$398$	1.73531e14	0.871006
$399$	−1.34750e14	−0.667079
$400$	−2.17276e13	−0.106092
$401$	−2.41254e13	−0.116193	−0.0580967	−	0.998311i	$-0.518503\pi$
$401$	−2.41254e13	−0.116193	−0.0580967	+	0.998311i	$0.518503\pi$
$402$	−9.83378e14	−4.67172
$403$	8.45888e13	0.396401
$404$	2.56493e14	1.18571
$405$	6.24155e13	0.284636
$406$	5.58088e14	2.51079
$407$	3.78616e13	0.168047
$408$	1.08541e15	4.75296
$409$	−2.40310e14	−1.03823	−0.519115	−	0.854704i	$-0.673738\pi$
$409$	−2.40310e14	−1.03823	−0.519115	+	0.854704i	$0.673738\pi$
$410$	−4.73229e14	−2.01725
$411$	−2.04764e14	−0.861240
$412$	−5.46207e14	−2.26685
$413$	9.30936e13	0.381236
$414$	8.37425e14	3.38411
$415$	4.78096e13	0.190656
$416$	−8.52036e13	−0.335309
$417$	6.33261e14	2.45943
$418$	−2.57468e13	−0.0986857
$419$	1.06044e14	0.401153	0.200577	−	0.979678i	$-0.435718\pi$
$419$	1.06044e14	0.401153	0.200577	+	0.979678i	$0.435718\pi$
$420$	−1.49923e15	−5.59755
$421$	3.01588e14	1.11138	0.555691	−	0.831389i	$-0.312454\pi$
$421$	3.01588e14	1.11138	0.555691	+	0.831389i	$0.312454\pi$
$422$	−4.41720e14	−1.60668
$423$	8.53892e13	0.306571
$424$	−1.15991e15	−4.11067
$425$	1.89901e13	0.0664338
$426$	−1.74379e14	−0.602201
$427$	1.12491e14	0.383498
$428$	1.05268e15	3.54287
$429$	−2.83199e13	−0.0940972
$430$	1.16036e13	0.0380643
$431$	−3.04035e14	−0.984689	−0.492345	−	0.870400i	$-0.663860\pi$
$431$	−3.04035e14	−0.984689	−0.492345	+	0.870400i	$0.663860\pi$
$432$	−7.52134e14	−2.40511
$433$	2.24012e14	0.707275	0.353638	−	0.935383i	$-0.384945\pi$
$433$	2.24012e14	0.707275	0.353638	+	0.935383i	$0.384945\pi$
$434$	−1.26186e15	−3.93386
$435$	−4.77227e14	−1.46904
$436$	1.45286e15	4.41620
$437$	9.47241e13	0.284323
$438$	4.04828e13	0.119995
$439$	1.45392e14	0.425585	0.212792	−	0.977097i	$-0.431744\pi$
$439$	1.45392e14	0.425585	0.212792	+	0.977097i	$0.431744\pi$
$440$	−1.61418e14	−0.466619
$441$	7.94492e14	2.26818
$442$	2.18717e14	0.616681
$443$	−6.66106e13	−0.185491	−0.0927456	−	0.995690i	$-0.529564\pi$
$443$	−6.66106e13	−0.185491	−0.0927456	+	0.995690i	$0.529564\pi$
$444$	1.13128e15	3.11145
$445$	−1.69990e14	−0.461789
$446$	7.93101e14	2.12807
$447$	−8.06207e14	−2.13676
$448$	1.36677e14	0.357822
$449$	−9.99847e13	−0.258570	−0.129285	−	0.991607i	$-0.541268\pi$
$449$	−9.99847e13	−0.258570	−0.129285	+	0.991607i	$0.541268\pi$
$450$	−6.70502e13	−0.171290
$451$	9.28293e13	0.234269
$452$	−5.66321e14	−1.41189
$453$	−7.89816e14	−1.94530
$454$	−4.26480e14	−1.03775
$455$	−1.70233e14	−0.409244
$456$	−4.33492e14	−1.02961
$457$	−1.96992e14	−0.462285	−0.231143	−	0.972920i	$-0.574246\pi$
$457$	−1.96992e14	−0.462285	−0.231143	+	0.972920i	$0.574246\pi$
$458$	−6.54497e14	−1.51757
$459$	6.57374e14	1.50606
$460$	1.05390e15	2.38580
$461$	8.20721e14	1.83586	0.917932	−	0.396737i	$-0.129858\pi$
$461$	8.20721e14	1.83586	0.917932	+	0.396737i	$0.129858\pi$
$462$	4.22466e14	0.933815
$463$	5.69797e14	1.24459	0.622293	−	0.782784i	$-0.286201\pi$
$463$	5.69797e14	1.24459	0.622293	+	0.782784i	$0.286201\pi$
$464$	8.27205e14	1.78552
$465$	1.07903e15	2.30167
$466$	1.27351e15	2.68460
$467$	8.85101e14	1.84395	0.921977	−	0.387245i	$-0.126573\pi$
$467$	8.85101e14	1.84395	0.921977	+	0.387245i	$0.126573\pi$
$468$	−5.37585e14	−1.10687
$469$	1.15954e15	2.35959
$470$	1.54371e14	0.310476
$471$	−1.23082e15	−2.44669
$472$	2.99484e14	0.588426
$473$	−2.27619e12	−0.00442051
$474$	4.92868e14	0.946129
$475$	−7.58428e12	−0.0143913
$476$	−2.27130e15	−4.26026
$477$	−1.64919e15	−3.05788
$478$	−1.79693e15	−3.29365
$479$	−3.43450e14	−0.622326	−0.311163	−	0.950357i	$-0.600718\pi$
$479$	−3.43450e14	−0.622326	−0.311163	+	0.950357i	$0.600718\pi$
$480$	−1.08688e15	−1.94694
$481$	1.28453e14	0.227482
$482$	−2.16720e14	−0.379437
$483$	−1.55428e15	−2.69041
$484$	−1.28243e15	−2.19474
$485$	−4.81704e14	−0.815081
$486$	8.06857e14	1.34989
$487$	1.33167e14	0.220286	0.110143	−	0.993916i	$-0.464869\pi$
$487$	1.33167e14	0.220286	0.110143	+	0.993916i	$0.464869\pi$
$488$	3.61884e14	0.591917
$489$	3.62211e14	0.585818
$490$	1.43633e15	2.29707
$491$	1.67050e14	0.264179	0.132090	−	0.991238i	$-0.457831\pi$
$491$	1.67050e14	0.264179	0.132090	+	0.991238i	$0.457831\pi$
$492$	2.77367e15	4.33758
$493$	−7.22987e14	−1.11808
$494$	−8.73514e13	−0.133589
$495$	−2.29508e14	−0.347112
$496$	−1.87035e15	−2.79752
$497$	2.05618e14	0.304159
$498$	−4.02539e14	−0.588907
$499$	4.40710e13	0.0637675	0.0318838	−	0.999492i	$-0.489849\pi$
$499$	4.40710e13	0.0637675	0.0318838	+	0.999492i	$0.489849\pi$
$500$	−1.64121e15	−2.34871
$501$	−1.31657e15	−1.86353
$502$	1.31089e15	1.83526
$503$	2.57167e14	0.356116	0.178058	−	0.984020i	$-0.443019\pi$
$503$	2.57167e14	0.356116	0.178058	+	0.984020i	$0.443019\pi$
$504$	4.51891e15	6.18965
$505$	3.71513e14	0.503351
$506$	−2.96978e14	−0.398012
$507$	−9.60811e13	−0.127378
$508$	6.24661e14	0.819207
$509$	−1.50592e14	−0.195368	−0.0976838	−	0.995217i	$-0.531143\pi$
$509$	−1.50592e14	−0.195368	−0.0976838	+	0.995217i	$0.531143\pi$
$510$	2.79001e15	3.58071
$511$	−4.77351e13	−0.0606070
$512$	−1.76531e15	−2.21735
$513$	−2.62542e14	−0.326252
$514$	−1.48233e15	−1.82242
$515$	−7.91142e14	−0.962310
$516$	−6.80109e13	−0.0818475
$517$	−3.02817e13	−0.0360564
$518$	−1.91622e15	−2.25752
$519$	−2.12012e15	−2.47138
$520$	−5.47644e14	−0.631655
$521$	−8.86211e14	−1.01142	−0.505708	−	0.862705i	$-0.668769\pi$
$521$	−8.86211e14	−1.01142	−0.505708	+	0.862705i	$0.668769\pi$
$522$	2.55272e15	2.88280
$523$	2.90292e14	0.324396	0.162198	−	0.986758i	$-0.448142\pi$
$523$	2.90292e14	0.324396	0.162198	+	0.986758i	$0.448142\pi$
$524$	−2.62033e14	−0.289757
$525$	1.24446e14	0.136178
$526$	2.24411e15	2.43009
$527$	1.63471e15	1.75179
$528$	6.26184e14	0.664072
$529$	1.39788e14	0.146711
$530$	−2.98150e15	−3.09683
$531$	4.25813e14	0.437723
$532$	9.07112e14	0.922884
$533$	3.14942e14	0.317126
$534$	1.43125e15	1.42639
$535$	1.52473e15	1.50400
$536$	3.73027e15	3.64195
$537$	−5.85319e14	−0.565632
$538$	−2.85322e15	−2.72918
$539$	−2.81752e14	−0.266765
$540$	−2.92106e15	−2.73763
$541$	−5.54814e14	−0.514710	−0.257355	−	0.966317i	$-0.582851\pi$
$541$	−5.54814e14	−0.514710	−0.257355	+	0.966317i	$0.582851\pi$
$542$	2.34701e15	2.15536
$543$	2.15130e15	1.95570
$544$	−1.64659e15	−1.48181
$545$	2.10437e15	1.87474
$546$	1.43330e15	1.26409
$547$	−6.93334e14	−0.605358	−0.302679	−	0.953093i	$-0.597881\pi$
$547$	−6.93334e14	−0.605358	−0.302679	+	0.953093i	$0.597881\pi$
$548$	1.37844e15	1.19150
$549$	5.14537e14	0.440320
$550$	2.37781e13	0.0201457
$551$	2.88746e14	0.242205
$552$	−5.00013e15	−4.15256
$553$	−5.81163e14	−0.477870
$554$	1.29720e14	0.105609
$555$	1.63858e15	1.32086
$556$	−4.26300e15	−3.40255
$557$	−3.66222e14	−0.289428	−0.144714	−	0.989474i	$-0.546226\pi$
$557$	−3.66222e14	−0.289428	−0.144714	+	0.989474i	$0.546226\pi$
$558$	−5.77181e15	−4.51673
$559$	−7.72243e12	−0.00598397
$560$	3.76404e15	2.88815
$561$	−5.47292e14	−0.415837
$562$	1.16789e15	0.878720
$563$	2.15143e15	1.60299	0.801494	−	0.598003i	$-0.204039\pi$
$563$	2.15143e15	1.60299	0.801494	+	0.598003i	$0.204039\pi$
$564$	−9.04796e14	−0.667599
$565$	−8.20276e14	−0.599368
$566$	−1.40488e15	−1.01659
$567$	6.19657e14	0.444063
$568$	6.61476e14	0.469460
$569$	1.79364e14	0.126071	0.0630357	−	0.998011i	$-0.479922\pi$
$569$	1.79364e14	0.126071	0.0630357	+	0.998011i	$0.479922\pi$
$570$	−1.11427e15	−0.775675
$571$	−9.51254e14	−0.655840	−0.327920	−	0.944706i	$-0.606348\pi$
$571$	−9.51254e14	−0.655840	−0.327920	+	0.944706i	$0.606348\pi$
$572$	1.90645e14	0.130181
$573$	−7.20403e14	−0.487220
$574$	−4.69819e15	−3.14713
$575$	−8.74811e13	−0.0580418
$576$	6.25167e14	0.410839
$577$	1.75001e15	1.13913	0.569564	−	0.821947i	$-0.307112\pi$
$577$	1.75001e15	1.13913	0.569564	+	0.821947i	$0.307112\pi$
$578$	1.41320e15	0.911171
$579$	1.67901e15	1.07231
$580$	3.21261e15	2.03237
$581$	4.74651e14	0.297444
$582$	4.05577e15	2.51766
$583$	5.84855e14	0.359643
$584$	−1.53564e14	−0.0935449
$585$	−7.78654e14	−0.469880
$586$	4.20321e15	2.51272
$587$	1.25955e15	0.745945	0.372972	−	0.927842i	$-0.378339\pi$
$587$	1.25955e15	0.745945	0.372972	+	0.927842i	$0.378339\pi$
$588$	−8.41855e15	−4.93926
$589$	−6.52869e14	−0.379483
$590$	7.69809e14	0.443299
$591$	6.84770e14	0.390673
$592$	−2.84024e15	−1.60541
$593$	−2.78196e14	−0.155794	−0.0778968	−	0.996961i	$-0.524820\pi$
$593$	−2.78196e14	−0.155794	−0.0778968	+	0.996961i	$0.524820\pi$
$594$	8.23119e14	0.456706
$595$	−3.28982e15	−1.80854
$596$	5.42725e15	2.95614
$597$	−1.47319e15	−0.795061
$598$	−1.00756e15	−0.538782
$599$	−2.95447e15	−1.56543	−0.782713	−	0.622383i	$-0.786164\pi$
$599$	−2.95447e15	−1.56543	−0.782713	+	0.622383i	$0.786164\pi$
$600$	4.00346e14	0.210186
$601$	3.43552e15	1.78724	0.893620	−	0.448824i	$-0.148157\pi$
$601$	3.43552e15	1.78724	0.893620	+	0.448824i	$0.148157\pi$
$602$	1.15200e14	0.0593845
$603$	5.30380e15	2.70920
$604$	5.31690e15	2.69126
$605$	−1.85750e15	−0.931697
$606$	−3.12800e15	−1.55477
$607$	−2.48359e15	−1.22333	−0.611663	−	0.791118i	$-0.709499\pi$
$607$	−2.48359e15	−1.22333	−0.611663	+	0.791118i	$0.709499\pi$
$608$	6.57615e14	0.320998
$609$	−4.73788e15	−2.29187
$610$	9.30207e14	0.445929
$611$	−1.02737e14	−0.0488090
$612$	−1.03890e16	−4.89149
$613$	1.70259e15	0.794469	0.397234	−	0.917717i	$-0.369970\pi$
$613$	1.70259e15	0.794469	0.397234	+	0.917717i	$0.369970\pi$
$614$	−5.88953e13	−0.0272367
$615$	4.01747e15	1.84136
$616$	−1.60255e15	−0.727977
$617$	−7.79487e13	−0.0350946	−0.0175473	−	0.999846i	$-0.505586\pi$
$617$	−7.79487e13	−0.0350946	−0.0175473	+	0.999846i	$0.505586\pi$
$618$	6.66112e15	2.97242
$619$	−3.08345e15	−1.36376	−0.681880	−	0.731464i	$-0.738837\pi$
$619$	−3.08345e15	−1.36376	−0.681880	+	0.731464i	$0.738837\pi$
$620$	−7.26386e15	−3.18429
$621$	−3.02830e15	−1.31582
$622$	7.51403e14	0.323613
$623$	−1.68765e15	−0.720442
$624$	2.12446e15	0.898943
$625$	−2.24795e15	−0.942860
$626$	−3.55855e15	−1.47950
$627$	2.18577e14	0.0900812
$628$	8.28564e15	3.38492
$629$	2.48240e15	1.00530
$630$	1.16157e16	4.66306
$631$	−3.96634e15	−1.57844	−0.789220	−	0.614111i	$-0.789515\pi$
$631$	−3.96634e15	−1.57844	−0.789220	+	0.614111i	$0.789515\pi$
$632$	−1.86961e15	−0.737577
$633$	3.74998e15	1.46659
$634$	2.87391e15	1.11425
$635$	9.04777e14	0.347765
$636$	1.74751e16	6.65893
$637$	−9.55900e14	−0.361115
$638$	−9.05274e14	−0.339052
$639$	9.40504e14	0.349225
$640$	−2.06357e15	−0.759679
$641$	−2.83446e15	−1.03455	−0.517274	−	0.855820i	$-0.673053\pi$
$641$	−2.83446e15	−1.03455	−0.517274	+	0.855820i	$0.673053\pi$
$642$	−1.28377e16	−4.64562
$643$	−1.61281e15	−0.578658	−0.289329	−	0.957230i	$-0.593432\pi$
$643$	−1.61281e15	−0.578658	−0.289329	+	0.957230i	$0.593432\pi$
$644$	1.04631e16	3.72211
$645$	−9.85090e13	−0.0347454
$646$	−1.68809e15	−0.590361
$647$	3.55855e15	1.23395	0.616977	−	0.786981i	$-0.288357\pi$
$647$	3.55855e15	1.23395	0.616977	+	0.786981i	$0.288357\pi$
$648$	1.99345e15	0.685397
$649$	−1.51007e14	−0.0514815
$650$	8.06722e13	0.0272709
$651$	1.07126e16	3.59086
$652$	−2.43834e15	−0.810461
$653$	−5.14164e14	−0.169465	−0.0847324	−	0.996404i	$-0.527004\pi$
$653$	−5.14164e14	−0.169465	−0.0847324	+	0.996404i	$0.527004\pi$
$654$	−1.77180e16	−5.79077
$655$	−3.79536e14	−0.123006
$656$	−6.96371e15	−2.23805
$657$	−2.18342e14	−0.0695869
$658$	1.53259e15	0.484377
$659$	−4.51339e15	−1.41460	−0.707299	−	0.706914i	$-0.750087\pi$
$659$	−4.51339e15	−1.41460	−0.707299	+	0.706914i	$0.750087\pi$
$660$	2.43190e15	0.755884
$661$	−3.48339e15	−1.07373	−0.536863	−	0.843669i	$-0.680391\pi$
$661$	−3.48339e15	−1.07373	−0.536863	+	0.843669i	$0.680391\pi$
$662$	−3.05689e15	−0.934460
$663$	−1.85680e15	−0.562912
$664$	1.52696e15	0.459096
$665$	1.31389e15	0.391777
$666$	−8.76485e15	−2.59201
$667$	3.33055e15	0.976842
$668$	8.86291e15	2.57814
$669$	−6.73302e15	−1.94252
$670$	9.58850e15	2.74372
$671$	−1.82471e14	−0.0517869
$672$	−1.07904e16	−3.03744
$673$	−2.32777e14	−0.0649916	−0.0324958	−	0.999472i	$-0.510346\pi$
$673$	−2.32777e14	−0.0649916	−0.0324958	+	0.999472i	$0.510346\pi$
$674$	−1.29767e16	−3.59364
$675$	2.42467e14	0.0666012
$676$	6.46801e14	0.176223
$677$	4.09898e15	1.10774	0.553870	−	0.832603i	$-0.313150\pi$
$677$	4.09898e15	1.10774	0.553870	+	0.832603i	$0.313150\pi$
$678$	6.90641e15	1.85135
$679$	−4.78233e15	−1.27162
$680$	−1.05834e16	−2.79143
$681$	3.62060e15	0.947264
$682$	2.04687e15	0.531221
$683$	5.02973e15	1.29488	0.647442	−	0.762115i	$-0.275839\pi$
$683$	5.02973e15	1.29488	0.647442	+	0.762115i	$0.275839\pi$
$684$	4.14916e15	1.05962
$685$	1.99657e15	0.505809
$686$	3.30773e15	0.831280
$687$	5.55635e15	1.38525
$688$	1.70751e14	0.0422306
$689$	1.98424e15	0.486843
$690$	−1.28526e16	−3.12839
$691$	−1.61781e15	−0.390658	−0.195329	−	0.980738i	$-0.562578\pi$
$691$	−1.61781e15	−0.390658	−0.195329	+	0.980738i	$0.562578\pi$
$692$	1.42723e16	3.41908
$693$	−2.27855e15	−0.541533
$694$	8.37117e14	0.197383
$695$	−6.17465e15	−1.44443
$696$	−1.52418e16	−3.53742
$697$	6.08637e15	1.40145
$698$	1.26110e16	2.88100
$699$	−1.08115e16	−2.45053
$700$	−8.37751e14	−0.188398
$701$	1.19401e15	0.266415	0.133208	−	0.991088i	$-0.457472\pi$
$701$	1.19401e15	0.266415	0.133208	+	0.991088i	$0.457472\pi$
$702$	2.79260e15	0.618236
$703$	−9.91422e14	−0.217773
$704$	−2.21704e14	−0.0483196
$705$	−1.31053e15	−0.283405
$706$	1.49418e16	3.20610
$707$	3.68836e15	0.785283
$708$	−4.51198e15	−0.953201
$709$	7.68395e15	1.61076	0.805379	−	0.592760i	$-0.201962\pi$
$709$	7.68395e15	1.61076	0.805379	+	0.592760i	$0.201962\pi$
$710$	1.70029e15	0.353674
$711$	−2.65826e15	−0.548674
$712$	−5.42921e15	−1.11198
$713$	−7.53054e15	−1.53050
$714$	2.76990e16	5.58630
$715$	2.76135e14	0.0552635
$716$	3.94027e15	0.782535
$717$	1.52550e16	3.00647
$718$	−3.83644e15	−0.750316
$719$	−3.58422e15	−0.695641	−0.347821	−	0.937561i	$-0.613078\pi$
$719$	−3.58422e15	−0.695641	−0.347821	+	0.937561i	$0.613078\pi$
$720$	1.72169e16	3.31608
$721$	−7.85442e15	−1.50131
$722$	−8.88921e15	−1.68620
$723$	1.83984e15	0.346353
$724$	−1.44822e16	−2.70565
$725$	−2.66668e14	−0.0494438
$726$	1.56395e16	2.87787
$727$	−8.52679e15	−1.55721	−0.778603	−	0.627516i	$-0.784072\pi$
$727$	−8.52679e15	−1.55721	−0.778603	+	0.627516i	$0.784072\pi$
$728$	−5.43698e15	−0.985451
$729$	−8.47682e15	−1.52487
$730$	−3.94730e14	−0.0704733
$731$	−1.49239e14	−0.0264445
$732$	−5.45211e15	−0.958856
$733$	−3.82726e15	−0.668061	−0.334030	−	0.942562i	$-0.608409\pi$
$733$	−3.82726e15	−0.668061	−0.334030	+	0.942562i	$0.608409\pi$
$734$	1.08401e16	1.87804
$735$	−1.21937e16	−2.09679
$736$	7.58528e15	1.29462
$737$	−1.88089e15	−0.318635
$738$	−2.14897e16	−3.61344
$739$	6.74971e15	1.12652	0.563262	−	0.826278i	$-0.309546\pi$
$739$	6.74971e15	1.12652	0.563262	+	0.826278i	$0.309546\pi$
$740$	−1.10306e16	−1.82736
$741$	7.41568e14	0.121941
$742$	−2.96001e16	−4.83139
$743$	−8.79793e13	−0.0142542	−0.00712709	−	0.999975i	$-0.502269\pi$
$743$	−8.79793e13	−0.0142542	−0.00712709	+	0.999975i	$0.502269\pi$
$744$	3.44625e16	5.54238
$745$	7.86098e15	1.25492
$746$	−1.39748e16	−2.21453
$747$	2.17107e15	0.341516
$748$	3.68427e15	0.575298
$749$	1.51375e16	2.34640
$750$	2.00150e16	3.07977
$751$	2.12764e15	0.324997	0.162498	−	0.986709i	$-0.448045\pi$
$751$	2.12764e15	0.324997	0.162498	+	0.986709i	$0.448045\pi$
$752$	2.27162e15	0.344459
$753$	−1.11288e16	−1.67524
$754$	−3.07133e15	−0.458969
$755$	7.70115e15	1.14248
$756$	−2.90001e16	−4.27100
$757$	−1.24899e16	−1.82613	−0.913067	−	0.407810i	$-0.866293\pi$
$757$	−1.24899e16	−1.82613	−0.913067	+	0.407810i	$0.866293\pi$
$758$	−2.20125e16	−3.19514
$759$	2.52119e15	0.363308
$760$	4.22680e15	0.604695
$761$	1.01304e16	1.43884	0.719418	−	0.694578i	$-0.244409\pi$
$761$	1.01304e16	1.43884	0.719418	+	0.694578i	$0.244409\pi$
$762$	−7.61788e15	−1.07419
$763$	2.08920e16	2.92480
$764$	4.84963e15	0.674055
$765$	−1.50477e16	−2.07651
$766$	3.75062e15	0.513861
$767$	−5.12322e14	−0.0696896
$768$	2.02661e16	2.73705
$769$	−1.07902e16	−1.44689	−0.723445	−	0.690382i	$-0.757442\pi$
$769$	−1.07902e16	−1.44689	−0.723445	+	0.690382i	$0.757442\pi$
$770$	−4.11928e15	−0.548432
$771$	1.25843e16	1.66352
$772$	−1.13028e16	−1.48351
$773$	3.19078e15	0.415824	0.207912	−	0.978148i	$-0.433333\pi$
$773$	3.19078e15	0.415824	0.207912	+	0.978148i	$0.433333\pi$
$774$	5.26931e14	0.0681833
$775$	6.02949e14	0.0774677
$776$	−1.53848e16	−1.96270
$777$	1.62677e16	2.06068
$778$	1.72740e16	2.17273
$779$	−2.43077e15	−0.303591
$780$	8.25073e15	1.02323
$781$	−3.33532e14	−0.0410731
$782$	−1.94714e16	−2.38100
$783$	−9.23114e15	−1.12090
$784$	2.11360e16	2.54850
$785$	1.20012e16	1.43694
$786$	3.19555e15	0.379946
$787$	−1.41309e16	−1.66843	−0.834214	−	0.551441i	$-0.814078\pi$
$787$	−1.41309e16	−1.66843	−0.834214	+	0.551441i	$0.814078\pi$
$788$	−4.60975e15	−0.540484
$789$	−1.90513e16	−2.21821
$790$	−4.80575e15	−0.555664
$791$	−8.14366e15	−0.935080
$792$	−7.33012e15	−0.835839
$793$	−6.19070e14	−0.0701031
$794$	1.89220e16	2.12791
$795$	2.53114e16	2.82681
$796$	9.91727e15	1.09994
$797$	3.02733e15	0.333457	0.166728	−	0.986003i	$-0.446680\pi$
$797$	3.02733e15	0.333457	0.166728	+	0.986003i	$0.446680\pi$
$798$	−1.10624e16	−1.21014
$799$	−1.98542e15	−0.215698
$800$	−6.07331e14	−0.0655286
$801$	−7.71939e15	−0.827188
$802$	−1.98061e15	−0.210785
$803$	7.74310e13	0.00818425
$804$	−5.61998e16	−5.89966
$805$	1.51551e16	1.58009
$806$	6.94441e15	0.719106
$807$	2.42224e16	2.49122
$808$	1.18655e16	1.21206
$809$	−3.38779e15	−0.343715	−0.171858	−	0.985122i	$-0.554977\pi$
$809$	−3.38779e15	−0.343715	−0.171858	+	0.985122i	$0.554977\pi$
$810$	5.12407e15	0.516354
$811$	−1.03239e16	−1.03330	−0.516652	−	0.856195i	$-0.672822\pi$
$811$	−1.03239e16	−1.03330	−0.516652	+	0.856195i	$0.672822\pi$
$812$	3.18946e16	3.17073
$813$	−1.99250e16	−1.96743
$814$	3.10829e15	0.304851
$815$	−3.53176e15	−0.344052
$816$	4.10558e16	3.97264
$817$	5.96029e13	0.00572857
$818$	−1.97285e16	−1.88344
$819$	−7.73043e15	−0.733065
$820$	−2.70449e16	−2.54747
$821$	−3.57921e15	−0.334888	−0.167444	−	0.985882i	$-0.553551\pi$
$821$	−3.57921e15	−0.334888	−0.167444	+	0.985882i	$0.553551\pi$
$822$	−1.68104e16	−1.56236
$823$	2.41391e15	0.222855	0.111427	−	0.993773i	$-0.464458\pi$
$823$	2.41391e15	0.222855	0.111427	+	0.993773i	$0.464458\pi$
$824$	−2.52678e16	−2.31722
$825$	−2.01864e14	−0.0183892
$826$	7.64262e15	0.691595
$827$	2.17301e15	0.195336	0.0976680	−	0.995219i	$-0.468862\pi$
$827$	2.17301e15	0.195336	0.0976680	+	0.995219i	$0.468862\pi$
$828$	4.78587e16	4.27360
$829$	1.49764e16	1.32849	0.664243	−	0.747516i	$-0.268754\pi$
$829$	1.49764e16	1.32849	0.664243	+	0.747516i	$0.268754\pi$
$830$	3.92498e15	0.345866
$831$	−1.10125e15	−0.0964011
$832$	−7.52175e14	−0.0654095
$833$	−1.84731e16	−1.59585
$834$	5.19883e16	4.46161
$835$	1.28373e16	1.09446
$836$	−1.47143e15	−0.124625
$837$	2.08720e16	1.75620
$838$	8.70583e15	0.727726
$839$	8.53924e15	0.709134	0.354567	−	0.935031i	$-0.384628\pi$
$839$	8.53924e15	0.709134	0.354567	+	0.935031i	$0.384628\pi$
$840$	−6.93552e16	−5.72194
$841$	−2.04801e15	−0.167863
$842$	2.47592e16	2.01614
$843$	−9.91475e15	−0.802103
$844$	−2.52442e16	−2.02898
$845$	9.36845e14	0.0748093
$846$	7.01012e15	0.556146
$847$	−1.84412e16	−1.45355
$848$	−4.38737e16	−3.43579
$849$	1.19267e16	0.927955
$850$	1.55902e15	0.120517
$851$	−1.14356e16	−0.878306
$852$	−9.96571e15	−0.760485
$853$	−6.90612e15	−0.523618	−0.261809	−	0.965120i	$-0.584319\pi$
$853$	−6.90612e15	−0.523618	−0.261809	+	0.965120i	$0.584319\pi$
$854$	9.23505e15	0.695698
$855$	6.00977e15	0.449826
$856$	4.86974e16	3.62160
$857$	1.64744e16	1.21735	0.608674	−	0.793420i	$-0.291702\pi$
$857$	1.64744e16	1.21735	0.608674	+	0.793420i	$0.291702\pi$
$858$	−2.32496e15	−0.170700
$859$	−1.10353e16	−0.805051	−0.402526	−	0.915409i	$-0.631868\pi$
$859$	−1.10353e16	−0.805051	−0.402526	+	0.915409i	$0.631868\pi$
$860$	6.63145e14	0.0480692
$861$	3.98852e16	2.87273
$862$	−2.49601e16	−1.78631
$863$	−2.66251e15	−0.189336	−0.0946678	−	0.995509i	$-0.530179\pi$
$863$	−2.66251e15	−0.189336	−0.0946678	+	0.995509i	$0.530179\pi$
$864$	−2.10237e16	−1.48554
$865$	2.06724e16	1.45145
$866$	1.83905e16	1.28306
$867$	−1.19973e16	−0.831724
$868$	−7.21152e16	−4.96785
$869$	9.42703e14	0.0645307
$870$	−3.91785e16	−2.66497
$871$	−6.38132e15	−0.431331
$872$	6.72100e16	4.51433
$873$	−2.18746e16	−1.46003
$874$	7.77648e15	0.515787
$875$	−2.36005e16	−1.55553
$876$	2.31358e15	0.151535
$877$	2.54870e16	1.65891	0.829453	−	0.558577i	$-0.188652\pi$
$877$	2.54870e16	1.65891	0.829453	+	0.558577i	$0.188652\pi$
$878$	1.19361e16	0.772047
$879$	−3.56831e16	−2.29363
$880$	−6.10565e15	−0.390011
$881$	−1.31560e16	−0.835135	−0.417567	−	0.908646i	$-0.637117\pi$
$881$	−1.31560e16	−0.835135	−0.417567	+	0.908646i	$0.637117\pi$
$882$	6.52247e16	4.11467
$883$	−1.81916e16	−1.14048	−0.570238	−	0.821480i	$-0.693149\pi$
$883$	−1.81916e16	−1.14048	−0.570238	+	0.821480i	$0.693149\pi$
$884$	1.24996e16	0.778772
$885$	−6.53528e15	−0.404647
$886$	−5.46848e15	−0.336497
$887$	−1.01100e16	−0.618261	−0.309131	−	0.951020i	$-0.600038\pi$
$887$	−1.01100e16	−0.618261	−0.309131	+	0.951020i	$0.600038\pi$
$888$	5.23335e16	3.18059
$889$	8.98257e15	0.542552
$890$	−1.39555e16	−0.837725
$891$	−1.00515e15	−0.0599655
$892$	4.53255e16	2.68742
$893$	7.92939e14	0.0467258
$894$	−6.61865e16	−3.87626
$895$	5.70719e15	0.332197
$896$	−2.04870e16	−1.18518
$897$	8.55364e15	0.491805
$898$	−8.20836e15	−0.469069
$899$	−2.29553e16	−1.30378
$900$	−3.83190e15	−0.216312
$901$	3.83461e16	2.15147
$902$	7.62093e15	0.424983
$903$	−9.77992e14	−0.0542067
$904$	−2.61983e16	−1.44327
$905$	−2.09764e16	−1.14859
$906$	−6.48408e16	−3.52893
$907$	1.05641e16	0.571471	0.285736	−	0.958308i	$-0.407762\pi$
$907$	1.05641e16	0.571471	0.285736	+	0.958308i	$0.407762\pi$
$908$	−2.43732e16	−1.31051
$909$	1.68707e16	0.901636
$910$	−1.39755e16	−0.742403
$911$	−2.50140e16	−1.32078	−0.660392	−	0.750921i	$-0.729610\pi$
$911$	−2.50140e16	−1.32078	−0.660392	+	0.750921i	$0.729610\pi$
$912$	−1.63969e16	−0.860576
$913$	−7.69931e14	−0.0401664
$914$	−1.61723e16	−0.838625
$915$	−7.89699e15	−0.407048
$916$	−3.74044e16	−1.91645
$917$	−3.76801e15	−0.191903
$918$	5.39679e16	2.73213
$919$	3.28732e16	1.65427	0.827137	−	0.562001i	$-0.189968\pi$
$919$	3.28732e16	1.65427	0.827137	+	0.562001i	$0.189968\pi$
$920$	4.87541e16	2.43881
$921$	4.99991e14	0.0248619
$922$	6.73780e16	3.33041
$923$	−1.13158e15	−0.0556000
$924$	2.41438e16	1.17926
$925$	9.15614e14	0.0444563
$926$	4.67781e16	2.25778
$927$	−3.59264e16	−1.72375
$928$	2.31221e16	1.10284
$929$	−3.32890e16	−1.57839	−0.789194	−	0.614144i	$-0.789502\pi$
$929$	−3.32890e16	−1.57839	−0.789194	+	0.614144i	$0.789502\pi$
$930$	8.85844e16	4.17543
$931$	7.37779e15	0.345703
$932$	7.27809e16	3.39023
$933$	−6.37903e15	−0.295397
$934$	7.26634e16	3.34509
$935$	5.33641e15	0.244222
$936$	−2.48689e16	−1.13146
$937$	−1.90953e16	−0.863691	−0.431845	−	0.901948i	$-0.642137\pi$
$937$	−1.90953e16	−0.863691	−0.431845	+	0.901948i	$0.642137\pi$
$938$	9.51941e16	4.28050
$939$	3.02103e16	1.35050
$940$	8.82228e15	0.392083
$941$	4.07150e15	0.179892	0.0899460	−	0.995947i	$-0.471331\pi$
$941$	4.07150e15	0.179892	0.0899460	+	0.995947i	$0.471331\pi$
$942$	−1.01045e17	−4.43850
$943$	−2.80378e16	−1.22442
$944$	1.13280e16	0.491820
$945$	−4.20046e16	−1.81310
$946$	−1.86866e14	−0.00801918
$947$	4.49034e16	1.91582	0.957909	−	0.287070i	$-0.0926814\pi$
$947$	4.49034e16	1.91582	0.957909	+	0.287070i	$0.0926814\pi$
$948$	2.81673e16	1.19481
$949$	2.62700e14	0.0110789
$950$	−6.22640e14	−0.0261070
$951$	−2.43981e16	−1.01710
$952$	−1.05071e17	−4.35493
$953$	1.09355e16	0.450639	0.225319	−	0.974285i	$-0.427657\pi$
$953$	1.09355e16	0.450639	0.225319	+	0.974285i	$0.427657\pi$
$954$	−1.35392e17	−5.54725
$955$	7.02434e15	0.286146
$956$	−1.02694e17	−4.15936
$957$	7.68531e15	0.309490
$958$	−2.81959e16	−1.12895
$959$	1.98218e16	0.789117
$960$	−9.59491e15	−0.379795
$961$	2.64945e16	1.04274
$962$	1.05455e16	0.412672
$963$	6.92393e16	2.69406
$964$	−1.23855e16	−0.479169
$965$	−1.63713e16	−0.629772
$966$	−1.27600e17	−4.88064
$967$	3.10026e16	1.17910	0.589552	−	0.807730i	$-0.299304\pi$
$967$	3.10026e16	1.17910	0.589552	+	0.807730i	$0.299304\pi$
$968$	−5.93256e16	−2.24351
$969$	1.43311e16	0.538887
$970$	−3.95460e16	−1.47863
$971$	−1.86317e16	−0.692703	−0.346351	−	0.938105i	$-0.612579\pi$
$971$	−1.86317e16	−0.692703	−0.346351	+	0.938105i	$0.612579\pi$
$972$	4.61117e16	1.70469
$973$	−6.13016e16	−2.25347
$974$	1.09325e16	0.399617
$975$	−6.84865e14	−0.0248932
$976$	1.36883e16	0.494738
$977$	1.62270e15	0.0583200	0.0291600	−	0.999575i	$-0.490717\pi$
$977$	1.62270e15	0.0583200	0.0291600	+	0.999575i	$0.490717\pi$
$978$	2.97361e16	1.06272
$979$	2.73754e15	0.0972872
$980$	8.20857e16	2.90084
$981$	9.55609e16	3.35816
$982$	1.37142e16	0.479243
$983$	−2.46306e16	−0.855914	−0.427957	−	0.903799i	$-0.640767\pi$
$983$	−2.46306e16	−0.855914	−0.427957	+	0.903799i	$0.640767\pi$
$984$	1.28311e17	4.43397
$985$	−6.67689e15	−0.229443
$986$	−5.93544e16	−2.02829
$987$	−1.30109e16	−0.442143
$988$	−4.99211e15	−0.168702
$989$	6.87492e14	0.0231040
$990$	−1.88418e16	−0.629691
$991$	−3.11494e16	−1.03525	−0.517624	−	0.855608i	$-0.673183\pi$
$991$	−3.11494e16	−1.03525	−0.517624	+	0.855608i	$0.673183\pi$
$992$	−5.22802e16	−1.72792
$993$	2.59514e16	0.852983
$994$	1.68804e16	0.551770
$995$	1.43645e16	0.466942
$996$	−2.30050e16	−0.743697
$997$	−2.29811e16	−0.738836	−0.369418	−	0.929263i	$-0.620443\pi$
$997$	−2.29811e16	−0.738836	−0.369418	+	0.929263i	$0.620443\pi$
$998$	3.61806e15	0.115680
$999$	3.16955e16	1.00783

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.12.a.b.1.5	✓	6
3.2	odd	2		117.12.a.d.1.2		6
4.3	odd	2		208.12.a.h.1.6		6
13.12	even	2		169.12.a.c.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.12.a.b.1.5	✓	6	1.1	even	1	trivial
117.12.a.d.1.2		6	3.2	odd	2
169.12.a.c.1.2		6	13.12	even	2
208.12.a.h.1.6		6	4.3	odd	2

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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	13.a (trivial)

\(f(q)\)	\(=\)	\(q+82.0961 q^{2} -696.954 q^{3} +4691.77 q^{4} +6795.70 q^{5} -57217.2 q^{6} +67467.4 q^{7} +217044. q^{8} +308598. q^{9} +O(q^{10})\)	\(q+82.0961 q^{2} -696.954 q^{3} +4691.77 q^{4} +6795.70 q^{5} -57217.2 q^{6} +67467.4 q^{7} +217044. q^{8} +308598. q^{9} +557901. q^{10} -109439. q^{11} -3.26995e6 q^{12} -371293. q^{13} +5.53881e6 q^{14} -4.73629e6 q^{15} +8.20969e6 q^{16} -7.17536e6 q^{17} +2.53347e7 q^{18} +2.86570e6 q^{19} +3.18839e7 q^{20} -4.70217e7 q^{21} -8.98449e6 q^{22} +3.30545e7 q^{23} -1.51269e8 q^{24} -2.64658e6 q^{25} -3.04817e7 q^{26} -9.16155e7 q^{27} +3.16542e8 q^{28} +1.00760e8 q^{29} -3.88831e8 q^{30} -2.27822e8 q^{31} +2.29478e8 q^{32} +7.62738e7 q^{33} -5.89069e8 q^{34} +4.58488e8 q^{35} +1.44787e9 q^{36} -3.45962e8 q^{37} +2.35263e8 q^{38} +2.58774e8 q^{39} +1.47496e9 q^{40} -8.48231e8 q^{41} -3.86030e9 q^{42} +2.07988e7 q^{43} -5.13462e8 q^{44} +2.09714e9 q^{45} +2.71364e9 q^{46} +2.76700e8 q^{47} -5.72178e9 q^{48} +2.57452e9 q^{49} -2.17274e8 q^{50} +5.00090e9 q^{51} -1.74202e9 q^{52} -5.34414e9 q^{53} -7.52128e9 q^{54} -7.43713e8 q^{55} +1.46434e10 q^{56} -1.99726e9 q^{57} +8.27197e9 q^{58} +1.37983e9 q^{59} -2.22216e10 q^{60} +1.66734e9 q^{61} -1.87033e10 q^{62} +2.08203e10 q^{63} +2.02583e9 q^{64} -2.52320e9 q^{65} +6.26178e9 q^{66} +1.71867e10 q^{67} -3.36652e10 q^{68} -2.30374e10 q^{69} +3.76401e10 q^{70} +3.04766e9 q^{71} +6.69793e10 q^{72} -7.07528e8 q^{73} -2.84021e10 q^{74} +1.84454e9 q^{75} +1.34452e10 q^{76} -7.38354e9 q^{77} +2.12444e10 q^{78} -8.61399e9 q^{79} +5.57906e10 q^{80} +9.18455e9 q^{81} -6.96365e10 q^{82} +7.03527e9 q^{83} -2.20615e11 q^{84} -4.87616e10 q^{85} +1.70750e9 q^{86} -7.02248e10 q^{87} -2.37530e10 q^{88} -2.50144e10 q^{89} +1.72167e11 q^{90} -2.50502e10 q^{91} +1.55084e11 q^{92} +1.58782e11 q^{93} +2.27160e10 q^{94} +1.94744e10 q^{95} -1.59936e11 q^{96} -7.08836e10 q^{97} +2.11358e11 q^{98} -3.37726e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 55 q^{2} + 476 q^{3} + 15309 q^{4} + 3312 q^{5} - 57797 q^{6} - 4176 q^{7} + 158493 q^{8} + 876218 q^{9}+O(q^{10}) \) 6 * q + 55 * q^2 + 476 * q^3 + 15309 * q^4 + 3312 * q^5 - 57797 * q^6 - 4176 * q^7 + 158493 * q^8 + 876218 * q^9	\( 6 q + 55 q^{2} + 476 q^{3} + 15309 q^{4} + 3312 q^{5} - 57797 q^{6} - 4176 q^{7} + 158493 q^{8} + 876218 q^{9} + 997497 q^{10} + 275060 q^{11} + 3949049 q^{12} - 2227758 q^{13} + 6462587 q^{14} + 5951652 q^{15} + 25038945 q^{16} + 18470848 q^{17} + 1544758 q^{18} + 2382612 q^{19} + 37821799 q^{20} - 67640772 q^{21} - 52649718 q^{22} + 25001944 q^{23} - 243039615 q^{24} - 14063202 q^{25} - 20421115 q^{26} + 77250908 q^{27} - 340836927 q^{28} - 142876028 q^{29} - 838796927 q^{30} - 158397468 q^{31} + 739784589 q^{32} - 115057792 q^{33} - 668802009 q^{34} + 1377003692 q^{35} + 3099344006 q^{36} + 47994456 q^{37} + 2673019714 q^{38} - 176735468 q^{39} + 242886231 q^{40} + 112037548 q^{41} - 5282633557 q^{42} + 1399191924 q^{43} - 1571975050 q^{44} + 7736061780 q^{45} - 2701412412 q^{46} - 3383597640 q^{47} + 1090782789 q^{48} + 7189538970 q^{49} - 12848613144 q^{50} + 8959562860 q^{51} - 5684124537 q^{52} + 546961604 q^{53} - 38372021519 q^{54} - 7803526248 q^{55} - 6807872407 q^{56} + 918537576 q^{57} + 5714690406 q^{58} + 10067834260 q^{59} + 2453022955 q^{60} + 15731821572 q^{61} - 7829475572 q^{62} + 29876175732 q^{63} + 2237284569 q^{64} - 1229722416 q^{65} + 12031833058 q^{66} + 50546073444 q^{67} + 15412804265 q^{68} + 10879166680 q^{69} + 2924449065 q^{70} - 2646136112 q^{71} - 8720745402 q^{72} + 4198695060 q^{73} + 5050454541 q^{74} - 7695720336 q^{75} + 59928748062 q^{76} + 9015828840 q^{77} + 21459621521 q^{78} - 92124930312 q^{79} + 89421404931 q^{80} + 67208776622 q^{81} - 150798850248 q^{82} + 20440296092 q^{83} - 419349915667 q^{84} - 124095891228 q^{85} + 116436457677 q^{86} - 161197597808 q^{87} - 158617438842 q^{88} + 20540234076 q^{89} - 279059693450 q^{90} + 1550519568 q^{91} + 446253814012 q^{92} + 142195723000 q^{93} + 92592053391 q^{94} + 82521342544 q^{95} - 2651637759 q^{96} - 203942467020 q^{97} + 711378915442 q^{98} - 235408311580 q^{99}+O(q^{100}) \) 6 * q + 55 * q^2 + 476 * q^3 + 15309 * q^4 + 3312 * q^5 - 57797 * q^6 - 4176 * q^7 + 158493 * q^8 + 876218 * q^9 + 997497 * q^10 + 275060 * q^11 + 3949049 * q^12 - 2227758 * q^13 + 6462587 * q^14 + 5951652 * q^15 + 25038945 * q^16 + 18470848 * q^17 + 1544758 * q^18 + 2382612 * q^19 + 37821799 * q^20 - 67640772 * q^21 - 52649718 * q^22 + 25001944 * q^23 - 243039615 * q^24 - 14063202 * q^25 - 20421115 * q^26 + 77250908 * q^27 - 340836927 * q^28 - 142876028 * q^29 - 838796927 * q^30 - 158397468 * q^31 + 739784589 * q^32 - 115057792 * q^33 - 668802009 * q^34 + 1377003692 * q^35 + 3099344006 * q^36 + 47994456 * q^37 + 2673019714 * q^38 - 176735468 * q^39 + 242886231 * q^40 + 112037548 * q^41 - 5282633557 * q^42 + 1399191924 * q^43 - 1571975050 * q^44 + 7736061780 * q^45 - 2701412412 * q^46 - 3383597640 * q^47 + 1090782789 * q^48 + 7189538970 * q^49 - 12848613144 * q^50 + 8959562860 * q^51 - 5684124537 * q^52 + 546961604 * q^53 - 38372021519 * q^54 - 7803526248 * q^55 - 6807872407 * q^56 + 918537576 * q^57 + 5714690406 * q^58 + 10067834260 * q^59 + 2453022955 * q^60 + 15731821572 * q^61 - 7829475572 * q^62 + 29876175732 * q^63 + 2237284569 * q^64 - 1229722416 * q^65 + 12031833058 * q^66 + 50546073444 * q^67 + 15412804265 * q^68 + 10879166680 * q^69 + 2924449065 * q^70 - 2646136112 * q^71 - 8720745402 * q^72 + 4198695060 * q^73 + 5050454541 * q^74 - 7695720336 * q^75 + 59928748062 * q^76 + 9015828840 * q^77 + 21459621521 * q^78 - 92124930312 * q^79 + 89421404931 * q^80 + 67208776622 * q^81 - 150798850248 * q^82 + 20440296092 * q^83 - 419349915667 * q^84 - 124095891228 * q^85 + 116436457677 * q^86 - 161197597808 * q^87 - 158617438842 * q^88 + 20540234076 * q^89 - 279059693450 * q^90 + 1550519568 * q^91 + 446253814012 * q^92 + 142195723000 * q^93 + 92592053391 * q^94 + 82521342544 * q^95 - 2651637759 * q^96 - 203942467020 * q^97 + 711378915442 * q^98 - 235408311580 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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