LMFDB - Embedded newform 13.14.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,14,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, 14, names="a")

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

chi := DirichletCharacter("13.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 14 $
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:	$13.9400207637$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 35596x^{5} + 594856x^{4} + 263632368x^{3} + 252644208x^{2} - 410033371968x - 5442114981888 $ x^7 - x^6 - 35596x^5 + 594856x^4 + 263632368x^3 + 252644208x^2 - 410033371968*x - 5442114981888
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-37.9195$ 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)

$f(q)$	$=$	$q-19.9195 q^{2} +1765.94 q^{3} -7795.21 q^{4} +53134.3 q^{5} -35176.8 q^{6} +17946.1 q^{7} +318458. q^{8} +1.52424e6 q^{9} +O(q^{10})$	\(q-19.9195 q^{2} +1765.94 q^{3} -7795.21 q^{4} +53134.3 q^{5} -35176.8 q^{6} +17946.1 q^{7} +318458. q^{8} +1.52424e6 q^{9} -1.05841e6 q^{10} -2.53214e6 q^{11} -1.37659e7 q^{12} +4.82681e6 q^{13} -357478. q^{14} +9.38323e7 q^{15} +5.75148e7 q^{16} +1.75912e8 q^{17} -3.03621e7 q^{18} +1.32818e8 q^{19} -4.14193e8 q^{20} +3.16919e7 q^{21} +5.04391e7 q^{22} +4.27752e8 q^{23} +5.62379e8 q^{24} +1.60255e9 q^{25} -9.61478e7 q^{26} -1.23768e8 q^{27} -1.39894e8 q^{28} -4.88778e9 q^{29} -1.86909e9 q^{30} +3.62897e9 q^{31} -3.75448e9 q^{32} -4.47162e9 q^{33} -3.50408e9 q^{34} +9.53555e8 q^{35} -1.18817e10 q^{36} +1.50255e9 q^{37} -2.64568e9 q^{38} +8.52388e9 q^{39} +1.69210e10 q^{40} -4.24390e10 q^{41} -6.31287e8 q^{42} +5.08716e10 q^{43} +1.97386e10 q^{44} +8.09893e10 q^{45} -8.52062e9 q^{46} -1.35808e11 q^{47} +1.01568e11 q^{48} -9.65669e10 q^{49} -3.19221e10 q^{50} +3.10650e11 q^{51} -3.76260e10 q^{52} +9.15092e10 q^{53} +2.46541e9 q^{54} -1.34544e11 q^{55} +5.71508e9 q^{56} +2.34550e11 q^{57} +9.73623e10 q^{58} +1.42653e10 q^{59} -7.31442e11 q^{60} -4.42539e11 q^{61} -7.22874e10 q^{62} +2.73541e10 q^{63} -3.96374e11 q^{64} +2.56469e11 q^{65} +8.90726e10 q^{66} -4.38938e11 q^{67} -1.37127e12 q^{68} +7.55386e11 q^{69} -1.89944e10 q^{70} +1.91886e12 q^{71} +4.85405e11 q^{72} -1.13428e12 q^{73} -2.99300e10 q^{74} +2.83002e12 q^{75} -1.03535e12 q^{76} -4.54421e10 q^{77} -1.69792e11 q^{78} -5.18308e10 q^{79} +3.05601e12 q^{80} -2.64869e12 q^{81} +8.45365e11 q^{82} -2.30732e12 q^{83} -2.47045e11 q^{84} +9.34695e12 q^{85} -1.01334e12 q^{86} -8.63154e12 q^{87} -8.06380e11 q^{88} +4.55938e12 q^{89} -1.61327e12 q^{90} +8.66225e10 q^{91} -3.33442e12 q^{92} +6.40856e12 q^{93} +2.70523e12 q^{94} +7.05721e12 q^{95} -6.63020e12 q^{96} +1.12066e12 q^{97} +1.92357e12 q^{98} -3.85958e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 127 q^{2} + 728 q^{3} + 16153 q^{4} + 34886 q^{5} + 83045 q^{6} + 131864 q^{7} + 127671 q^{8} + 2466055 q^{9}+O(q^{10}) $ 7 * q + 127 * q^2 + 728 * q^3 + 16153 * q^4 + 34886 * q^5 + 83045 * q^6 + 131864 * q^7 + 127671 * q^8 + 2466055 * q^9	\( 7 q + 127 q^{2} + 728 q^{3} + 16153 q^{4} + 34886 q^{5} + 83045 q^{6} + 131864 q^{7} + 127671 q^{8} + 2466055 q^{9} + 3335529 q^{10} + 8912632 q^{11} + 25360909 q^{12} + 33787663 q^{13} + 67318187 q^{14} + 78942892 q^{15} + 159240961 q^{16} + 222199706 q^{17} + 596088532 q^{18} + 652665968 q^{19} + 935513953 q^{20} + 1217880580 q^{21} + 1374511830 q^{22} + 1794723984 q^{23} + 1895354895 q^{24} + 246154813 q^{25} + 613004743 q^{26} - 1915909876 q^{27} - 1789780165 q^{28} - 4735865782 q^{29} - 9918164303 q^{30} - 9436127356 q^{31} - 17224649401 q^{32} - 25638368752 q^{33} - 29930612727 q^{34} - 20876359292 q^{35} - 31714020118 q^{36} - 14832967330 q^{37} - 7473991662 q^{38} + 3513916952 q^{39} + 10553061291 q^{40} + 59907995430 q^{41} + 69292649863 q^{42} + 72489466184 q^{43} + 82565539934 q^{44} + 60104811962 q^{45} + 118453633200 q^{46} + 195641345592 q^{47} + 69842813569 q^{48} + 55402933947 q^{49} + 87739798742 q^{50} + 142246774012 q^{51} + 77967445777 q^{52} + 409286178474 q^{53} - 46365876001 q^{54} + 418486272912 q^{55} - 217713137127 q^{56} + 243297441528 q^{57} - 1099013150598 q^{58} - 160361676600 q^{59} - 1108676787295 q^{60} - 147184998046 q^{61} - 2220407254292 q^{62} + 256048021580 q^{63} - 2276361582767 q^{64} + 168388058774 q^{65} - 2841576718138 q^{66} + 1533110763584 q^{67} - 1734599536391 q^{68} + 1341159298056 q^{69} - 1953936478521 q^{70} + 1288841132520 q^{71} - 1858742324166 q^{72} + 4340518042046 q^{73} - 2522725784507 q^{74} + 3488845434748 q^{75} + 792218810282 q^{76} + 3260905865264 q^{77} + 400842353405 q^{78} + 6986884509272 q^{79} + 2848664165317 q^{80} + 9402260691943 q^{81} + 3785376233100 q^{82} + 9485774126680 q^{83} + 2428655741171 q^{84} + 9239892384264 q^{85} - 1372999514421 q^{86} + 5364161696536 q^{87} - 2985250612134 q^{88} - 1338832432586 q^{89} - 13443400684582 q^{90} + 636482341976 q^{91} - 8786066700672 q^{92} - 12529067281768 q^{93} - 18098521583937 q^{94} - 119505100680 q^{95} - 29672968067657 q^{96} + 1532637634742 q^{97} - 14020062796872 q^{98} - 17432744537624 q^{99}+O(q^{100}) \) 7 * q + 127 * q^2 + 728 * q^3 + 16153 * q^4 + 34886 * q^5 + 83045 * q^6 + 131864 * q^7 + 127671 * q^8 + 2466055 * q^9 + 3335529 * q^10 + 8912632 * q^11 + 25360909 * q^12 + 33787663 * q^13 + 67318187 * q^14 + 78942892 * q^15 + 159240961 * q^16 + 222199706 * q^17 + 596088532 * q^18 + 652665968 * q^19 + 935513953 * q^20 + 1217880580 * q^21 + 1374511830 * q^22 + 1794723984 * q^23 + 1895354895 * q^24 + 246154813 * q^25 + 613004743 * q^26 - 1915909876 * q^27 - 1789780165 * q^28 - 4735865782 * q^29 - 9918164303 * q^30 - 9436127356 * q^31 - 17224649401 * q^32 - 25638368752 * q^33 - 29930612727 * q^34 - 20876359292 * q^35 - 31714020118 * q^36 - 14832967330 * q^37 - 7473991662 * q^38 + 3513916952 * q^39 + 10553061291 * q^40 + 59907995430 * q^41 + 69292649863 * q^42 + 72489466184 * q^43 + 82565539934 * q^44 + 60104811962 * q^45 + 118453633200 * q^46 + 195641345592 * q^47 + 69842813569 * q^48 + 55402933947 * q^49 + 87739798742 * q^50 + 142246774012 * q^51 + 77967445777 * q^52 + 409286178474 * q^53 - 46365876001 * q^54 + 418486272912 * q^55 - 217713137127 * q^56 + 243297441528 * q^57 - 1099013150598 * q^58 - 160361676600 * q^59 - 1108676787295 * q^60 - 147184998046 * q^61 - 2220407254292 * q^62 + 256048021580 * q^63 - 2276361582767 * q^64 + 168388058774 * q^65 - 2841576718138 * q^66 + 1533110763584 * q^67 - 1734599536391 * q^68 + 1341159298056 * q^69 - 1953936478521 * q^70 + 1288841132520 * q^71 - 1858742324166 * q^72 + 4340518042046 * q^73 - 2522725784507 * q^74 + 3488845434748 * q^75 + 792218810282 * q^76 + 3260905865264 * q^77 + 400842353405 * q^78 + 6986884509272 * q^79 + 2848664165317 * q^80 + 9402260691943 * q^81 + 3785376233100 * q^82 + 9485774126680 * q^83 + 2428655741171 * q^84 + 9239892384264 * q^85 - 1372999514421 * q^86 + 5364161696536 * q^87 - 2985250612134 * q^88 - 1338832432586 * q^89 - 13443400684582 * q^90 + 636482341976 * q^91 - 8786066700672 * q^92 - 12529067281768 * q^93 - 18098521583937 * q^94 - 119505100680 * q^95 - 29672968067657 * q^96 + 1532637634742 * q^97 - 14020062796872 * q^98 - 17432744537624 * 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 $

$2$	−19.9195	−0.220082	−0.110041	−	0.993927i	$-0.535098\pi$
$2$	−19.9195	−0.220082	−0.110041	+	0.993927i	$0.535098\pi$
$3$	1765.94	1.39859	0.699293	−	0.714836i	$-0.253498\pi$
$3$	1765.94	1.39859	0.699293	+	0.714836i	$0.253498\pi$
$4$	−7795.21	−0.951564
$5$	53134.3	1.52079	0.760396	−	0.649459i	$-0.225005\pi$
$5$	53134.3	1.52079	0.760396	+	0.649459i	$0.225005\pi$
$6$	−35176.8	−0.307803
$7$	17946.1	0.0576545	0.0288273	−	0.999584i	$-0.490823\pi$
$7$	17946.1	0.0576545	0.0288273	+	0.999584i	$0.490823\pi$
$8$	318458.	0.429504
$9$	1.52424e6	0.956040
$10$	−1.05841e6	−0.334699
$11$	−2.53214e6	−0.430958	−0.215479	−	0.976508i	$-0.569131\pi$
$11$	−2.53214e6	−0.430958	−0.215479	+	0.976508i	$0.569131\pi$
$12$	−1.37659e7	−1.33084
$13$	4.82681e6	0.277350
$13$	4.82681e6	0.277350
$14$	−357478.	−0.0126887
$15$	9.38323e7	2.12696
$16$	5.75148e7	0.857038
$17$	1.75912e8	1.76757	0.883785	−	0.467893i	$-0.154987\pi$
$17$	1.75912e8	1.76757	0.883785	+	0.467893i	$0.154987\pi$
$18$	−3.03621e7	−0.210407
$19$	1.32818e8	0.647679	0.323839	−	0.946112i	$-0.395026\pi$
$19$	1.32818e8	0.647679	0.323839	+	0.946112i	$0.395026\pi$
$20$	−4.14193e8	−1.44713
$21$	3.16919e7	0.0806347
$22$	5.04391e7	0.0948461
$23$	4.27752e8	0.602506	0.301253	−	0.953544i	$-0.402595\pi$
$23$	4.27752e8	0.602506	0.301253	+	0.953544i	$0.402595\pi$
$24$	5.62379e8	0.600698
$25$	1.60255e9	1.31281
$26$	−9.61478e7	−0.0610397
$27$	−1.23768e8	−0.0614816
$28$	−1.39894e8	−0.0548620
$29$	−4.88778e9	−1.52589	−0.762947	−	0.646461i	$-0.776248\pi$
$29$	−4.88778e9	−1.52589	−0.762947	+	0.646461i	$0.776248\pi$
$30$	−1.86909e9	−0.468105
$31$	3.62897e9	0.734400	0.367200	−	0.930142i	$-0.380317\pi$
$31$	3.62897e9	0.734400	0.367200	+	0.930142i	$0.380317\pi$
$32$	−3.75448e9	−0.618122
$33$	−4.47162e9	−0.602732
$34$	−3.50408e9	−0.389010
$35$	9.53555e8	0.0876806
$36$	−1.18817e10	−0.909733
$37$	1.50255e9	0.0962757	0.0481378	−	0.998841i	$-0.484671\pi$
$37$	1.50255e9	0.0962757	0.0481378	+	0.998841i	$0.484671\pi$
$38$	−2.64568e9	−0.142542
$39$	8.52388e9	0.387898
$40$	1.69210e10	0.653186
$41$	−4.24390e10	−1.39531	−0.697653	−	0.716435i	$-0.745772\pi$
$41$	−4.24390e10	−1.39531	−0.697653	+	0.716435i	$0.745772\pi$
$42$	−6.31287e8	−0.0177462
$43$	5.08716e10	1.22724	0.613622	−	0.789600i	$-0.289712\pi$
$43$	5.08716e10	1.22724	0.613622	+	0.789600i	$0.289712\pi$
$44$	1.97386e10	0.410084
$45$	8.09893e10	1.45394
$46$	−8.52062e9	−0.132601
$47$	−1.35808e11	−1.83776	−0.918881	−	0.394534i	$-0.870906\pi$
$47$	−1.35808e11	−1.83776	−0.918881	+	0.394534i	$0.870906\pi$
$48$	1.01568e11	1.19864
$49$	−9.65669e10	−0.996676
$50$	−3.19221e10	−0.288926
$51$	3.10650e11	2.47210
$52$	−3.76260e10	−0.263916
$53$	9.15092e10	0.567115	0.283558	−	0.958955i	$-0.408485\pi$
$53$	9.15092e10	0.567115	0.283558	+	0.958955i	$0.408485\pi$
$54$	2.46541e9	0.0135310
$55$	−1.34544e11	−0.655398
$56$	5.71508e9	0.0247628
$57$	2.34550e11	0.905834
$58$	9.73623e10	0.335822
$59$	1.42653e10	0.0440294	0.0220147	−	0.999758i	$-0.492992\pi$
$59$	1.42653e10	0.0440294	0.0220147	+	0.999758i	$0.492992\pi$
$60$	−7.31442e11	−2.02394
$61$	−4.42539e11	−1.09979	−0.549893	−	0.835235i	$-0.685331\pi$
$61$	−4.42539e11	−1.09979	−0.549893	+	0.835235i	$0.685331\pi$
$62$	−7.22874e10	−0.161628
$63$	2.73541e10	0.0551200
$64$	−3.96374e11	−0.721000
$65$	2.56469e11	0.421792
$66$	8.90726e10	0.132650
$67$	−4.38938e11	−0.592812	−0.296406	−	0.955062i	$-0.595788\pi$
$67$	−4.38938e11	−0.592812	−0.296406	+	0.955062i	$0.595788\pi$
$68$	−1.37127e12	−1.68196
$69$	7.55386e11	0.842655
$70$	−1.89944e10	−0.0192969
$71$	1.91886e12	1.77772	0.888861	−	0.458177i	$-0.151498\pi$
$71$	1.91886e12	1.77772	0.888861	+	0.458177i	$0.151498\pi$
$72$	4.85405e11	0.410623
$73$	−1.13428e12	−0.877247	−0.438624	−	0.898671i	$-0.644534\pi$
$73$	−1.13428e12	−0.877247	−0.438624	+	0.898671i	$0.644534\pi$
$74$	−2.99300e10	−0.0211885
$75$	2.83002e12	1.83608
$76$	−1.03535e12	−0.616308
$77$	−4.54421e10	−0.0248467
$78$	−1.69792e11	−0.0853692
$79$	−5.18308e10	−0.0239890	−0.0119945	−	0.999928i	$-0.503818\pi$
$79$	−5.18308e10	−0.0239890	−0.0119945	+	0.999928i	$0.503818\pi$
$80$	3.05601e12	1.30338
$81$	−2.64869e12	−1.04203
$82$	8.45365e11	0.307082
$83$	−2.30732e12	−0.774639	−0.387320	−	0.921946i	$-0.626599\pi$
$83$	−2.30732e12	−0.774639	−0.387320	+	0.921946i	$0.626599\pi$
$84$	−2.47045e11	−0.0767291
$85$	9.34695e12	2.68811
$86$	−1.01334e12	−0.270094
$87$	−8.63154e12	−2.13409
$88$	−8.06380e11	−0.185098
$89$	4.55938e12	0.972458	0.486229	−	0.873831i	$-0.338372\pi$
$89$	4.55938e12	0.972458	0.486229	+	0.873831i	$0.338372\pi$
$90$	−1.61327e12	−0.319986
$91$	8.66225e10	0.0159905
$92$	−3.33442e12	−0.573323
$93$	6.40856e12	1.02712
$94$	2.70523e12	0.404458
$95$	7.05721e12	0.984985
$96$	−6.63020e12	−0.864497
$97$	1.12066e12	0.136602	0.0683009	−	0.997665i	$-0.478242\pi$
$97$	1.12066e12	0.136602	0.0683009	+	0.997665i	$0.478242\pi$
$98$	1.92357e12	0.219350
$99$	−3.85958e12	−0.412013
$100$	−1.24922e13	−1.24922
$101$	−6.96106e12	−0.652509	−0.326255	−	0.945282i	$-0.605787\pi$
$101$	−6.96106e12	−0.652509	−0.326255	+	0.945282i	$0.605787\pi$
$102$	−6.18801e12	−0.544064
$103$	−2.26391e13	−1.86817	−0.934086	−	0.357048i	$-0.883783\pi$
$103$	−2.26391e13	−1.86817	−0.934086	+	0.357048i	$0.883783\pi$
$104$	1.53714e12	0.119123
$105$	1.68392e12	0.122629
$106$	−1.82282e12	−0.124812
$107$	−1.22617e13	−0.789868	−0.394934	−	0.918710i	$-0.629233\pi$
$107$	−1.22617e13	−0.789868	−0.394934	+	0.918710i	$0.629233\pi$
$108$	9.64800e11	0.0585037
$109$	3.08194e13	1.76016	0.880079	−	0.474827i	$-0.157490\pi$
$109$	3.08194e13	1.76016	0.880079	+	0.474827i	$0.157490\pi$
$110$	2.68004e12	0.144241
$111$	2.65341e12	0.134650
$112$	1.03217e12	0.0494121
$113$	1.67781e13	0.758111	0.379055	−	0.925374i	$-0.376249\pi$
$113$	1.67781e13	0.758111	0.379055	+	0.925374i	$0.376249\pi$
$114$	−4.67212e12	−0.199358
$115$	2.27283e13	0.916286
$116$	3.81013e13	1.45199
$117$	7.35720e12	0.265158
$118$	−2.84158e11	−0.00969008
$119$	3.15693e12	0.101908
$120$	2.98816e13	0.913537
$121$	−2.81110e13	−0.814275
$122$	8.81518e12	0.242043
$123$	−7.49449e13	−1.95146
$124$	−2.82886e13	−0.698828
$125$	2.02893e13	0.475721
$126$	−5.44882e11	−0.0121309
$127$	−6.62313e13	−1.40068	−0.700341	−	0.713809i	$-0.746969\pi$
$127$	−6.62313e13	−1.40068	−0.700341	+	0.713809i	$0.746969\pi$
$128$	3.86523e13	0.776801
$129$	8.98365e13	1.71640
$130$	−5.10875e12	−0.0928288
$131$	−1.83818e13	−0.317779	−0.158889	−	0.987296i	$-0.550791\pi$
$131$	−1.83818e13	−0.317779	−0.158889	+	0.987296i	$0.550791\pi$
$132$	3.48572e13	0.573538
$133$	2.38357e12	0.0373416
$134$	8.74344e12	0.130467
$135$	−6.57635e12	−0.0935008
$136$	5.60205e13	0.759178
$137$	−5.52606e13	−0.714056	−0.357028	−	0.934094i	$-0.616210\pi$
$137$	−5.52606e13	−0.714056	−0.357028	+	0.934094i	$0.616210\pi$
$138$	−1.50469e13	−0.185453
$139$	8.83524e13	1.03902	0.519508	−	0.854466i	$-0.326115\pi$
$139$	8.83524e13	1.03902	0.519508	+	0.854466i	$0.326115\pi$
$140$	−7.43316e12	−0.0834337
$141$	−2.39829e14	−2.57027
$142$	−3.82228e13	−0.391244
$143$	−1.22222e13	−0.119526
$144$	8.76662e13	0.819363
$145$	−2.59709e14	−2.32057
$146$	2.25944e13	0.193066
$147$	−1.70532e14	−1.39394
$148$	−1.17127e13	−0.0916125
$149$	2.08741e13	0.156278	0.0781388	−	0.996942i	$-0.475102\pi$
$149$	2.08741e13	0.156278	0.0781388	+	0.996942i	$0.475102\pi$
$150$	−5.63727e13	−0.404087
$151$	2.42588e14	1.66540	0.832702	−	0.553722i	$-0.186793\pi$
$151$	2.42588e14	1.66540	0.832702	+	0.553722i	$0.186793\pi$
$152$	4.22970e13	0.278180
$153$	2.68131e14	1.68987
$154$	9.05185e11	0.00546831
$155$	1.92823e14	1.11687
$156$	−6.64454e13	−0.369109
$157$	−2.48765e14	−1.32569	−0.662845	−	0.748757i	$-0.730651\pi$
$157$	−2.48765e14	−1.32569	−0.662845	+	0.748757i	$0.730651\pi$
$158$	1.03245e12	0.00527954
$159$	1.61600e14	0.793159
$160$	−1.99491e14	−0.940036
$161$	7.67649e12	0.0347372
$162$	5.27607e13	0.229331
$163$	2.73886e14	1.14380	0.571900	−	0.820323i	$-0.306207\pi$
$163$	2.73886e14	1.14380	0.571900	+	0.820323i	$0.306207\pi$
$164$	3.30821e14	1.32772
$165$	−2.37596e14	−0.916630
$166$	4.59607e13	0.170484
$167$	1.84501e14	0.658175	0.329088	−	0.944299i	$-0.393259\pi$
$167$	1.84501e14	0.658175	0.329088	+	0.944299i	$0.393259\pi$
$168$	1.00925e13	0.0346329
$169$	2.32981e13	0.0769231
$170$	−1.86187e14	−0.591604
$171$	2.02447e14	0.619207
$172$	−3.96555e14	−1.16780
$173$	3.22855e14	0.915604	0.457802	−	0.889054i	$-0.348637\pi$
$173$	3.22855e14	0.915604	0.457802	+	0.889054i	$0.348637\pi$
$174$	1.71936e14	0.469675
$175$	2.87596e13	0.0756895
$176$	−1.45636e14	−0.369348
$177$	2.51917e13	0.0615789
$178$	−9.08208e13	−0.214020
$179$	1.73745e14	0.394792	0.197396	−	0.980324i	$-0.436751\pi$
$179$	1.73745e14	0.394792	0.197396	+	0.980324i	$0.436751\pi$
$180$	−6.31329e14	−1.38352
$181$	3.53209e13	0.0746657	0.0373328	−	0.999303i	$-0.488114\pi$
$181$	3.53209e13	0.0746657	0.0373328	+	0.999303i	$0.488114\pi$
$182$	−1.72548e12	−0.00351922
$183$	−7.81500e14	−1.53814
$184$	1.36221e14	0.258778
$185$	7.98368e13	0.146415
$186$	−1.27656e14	−0.226051
$187$	−4.45433e14	−0.761749
$188$	1.05865e15	1.74875
$189$	−2.22116e12	−0.00354469
$190$	−1.40576e14	−0.216777
$191$	−1.24224e14	−0.185135	−0.0925674	−	0.995706i	$-0.529507\pi$
$191$	−1.24224e14	−0.185135	−0.0925674	+	0.995706i	$0.529507\pi$
$192$	−6.99975e14	−1.00838
$193$	−7.57888e14	−1.05556	−0.527780	−	0.849381i	$-0.676975\pi$
$193$	−7.57888e14	−1.05556	−0.527780	+	0.849381i	$0.676975\pi$
$194$	−2.23230e13	−0.0300636
$195$	4.52910e14	0.589912
$196$	7.52760e14	0.948401
$197$	2.08104e14	0.253659	0.126829	−	0.991925i	$-0.459520\pi$
$197$	2.08104e14	0.253659	0.126829	+	0.991925i	$0.459520\pi$
$198$	7.68811e13	0.0906767
$199$	1.17228e15	1.33809	0.669046	−	0.743221i	$-0.266703\pi$
$199$	1.17228e15	1.33809	0.669046	+	0.743221i	$0.266703\pi$
$200$	5.10345e14	0.563857
$201$	−7.75140e14	−0.829098
$202$	1.38661e14	0.143605
$203$	−8.77167e13	−0.0879747
$204$	−2.42158e15	−2.35236
$205$	−2.25497e15	−2.12197
$206$	4.50960e14	0.411151
$207$	6.51995e14	0.576020
$208$	2.77613e14	0.237700
$209$	−3.36315e14	−0.279122
$210$	−3.35430e13	−0.0269884
$211$	2.82774e14	0.220599	0.110299	−	0.993898i	$-0.464819\pi$
$211$	2.82774e14	0.220599	0.110299	+	0.993898i	$0.464819\pi$
$212$	−7.13333e14	−0.539647
$213$	3.38860e15	2.48629
$214$	2.44246e14	0.173836
$215$	2.70303e15	1.86638
$216$	−3.94150e13	−0.0264066
$217$	6.51259e13	0.0423415
$218$	−6.13908e14	−0.387379
$219$	−2.00308e15	−1.22691
$220$	1.04880e15	0.623653
$221$	8.49092e14	0.490236
$222$	−5.28547e13	−0.0296340
$223$	2.44917e15	1.33363	0.666817	−	0.745221i	$-0.267656\pi$
$223$	2.44917e15	1.33363	0.666817	+	0.745221i	$0.267656\pi$
$224$	−6.73783e13	−0.0356375
$225$	2.44267e15	1.25510
$226$	−3.34212e14	−0.166846
$227$	1.73690e15	0.842573	0.421286	−	0.906928i	$-0.361579\pi$
$227$	1.73690e15	0.842573	0.421286	+	0.906928i	$0.361579\pi$
$228$	−1.82837e15	−0.861959
$229$	−6.86566e14	−0.314595	−0.157297	−	0.987551i	$-0.550278\pi$
$229$	−6.86566e14	−0.314595	−0.157297	+	0.987551i	$0.550278\pi$
$230$	−4.52737e14	−0.201658
$231$	−8.02482e13	−0.0347502
$232$	−1.55655e15	−0.655377
$233$	9.42058e14	0.385713	0.192856	−	0.981227i	$-0.438225\pi$
$233$	9.42058e14	0.385713	0.192856	+	0.981227i	$0.438225\pi$
$234$	−1.46552e14	−0.0583564
$235$	−7.21607e15	−2.79486
$236$	−1.11201e14	−0.0418968
$237$	−9.15304e13	−0.0335507
$238$	−6.28846e13	−0.0224282
$239$	−1.59733e15	−0.554379	−0.277190	−	0.960815i	$-0.589403\pi$
$239$	−1.59733e15	−0.554379	−0.277190	+	0.960815i	$0.589403\pi$
$240$	5.39675e15	1.82288
$241$	−2.97324e15	−0.977504	−0.488752	−	0.872423i	$-0.662548\pi$
$241$	−2.97324e15	−0.977504	−0.488752	+	0.872423i	$0.662548\pi$
$242$	5.59958e14	0.179207
$243$	−4.48012e15	−1.39588
$244$	3.44969e15	1.04652
$245$	−5.13102e15	−1.51574
$246$	1.49287e15	0.429480
$247$	6.41089e14	0.179634
$248$	1.15567e15	0.315427
$249$	−4.07459e15	−1.08340
$250$	−4.04154e14	−0.104698
$251$	−5.38123e15	−1.35832	−0.679160	−	0.733990i	$-0.737656\pi$
$251$	−5.38123e15	−1.35832	−0.679160	+	0.733990i	$0.737656\pi$
$252$	−2.13231e14	−0.0524502
$253$	−1.08313e15	−0.259655
$254$	1.31930e15	0.308265
$255$	1.65062e16	3.75955
$256$	2.47716e15	0.550041
$257$	−1.18241e15	−0.255977	−0.127989	−	0.991776i	$-0.540852\pi$
$257$	−1.18241e15	−0.255977	−0.127989	+	0.991776i	$0.540852\pi$
$258$	−1.78950e15	−0.377749
$259$	2.69649e13	0.00555073
$260$	−1.99923e15	−0.401362
$261$	−7.45013e15	−1.45882
$262$	3.66157e14	0.0699373
$263$	1.37843e15	0.256846	0.128423	−	0.991719i	$-0.459009\pi$
$263$	1.37843e15	0.256846	0.128423	+	0.991719i	$0.459009\pi$
$264$	−1.42402e15	−0.258876
$265$	4.86228e15	0.862465
$266$	−4.74797e13	−0.00821821
$267$	8.05162e15	1.36007
$268$	3.42162e15	0.564099
$269$	−4.80377e15	−0.773023	−0.386512	−	0.922285i	$-0.626320\pi$
$269$	−4.80377e15	−0.773023	−0.386512	+	0.922285i	$0.626320\pi$
$270$	1.30998e14	0.0205778
$271$	−6.06795e15	−0.930555	−0.465277	−	0.885165i	$-0.654045\pi$
$271$	−6.06795e15	−0.930555	−0.465277	+	0.885165i	$0.654045\pi$
$272$	1.01175e16	1.51487
$273$	1.52971e14	0.0223641
$274$	1.10077e15	0.157151
$275$	−4.05789e15	−0.565767
$276$	−5.88840e15	−0.801840
$277$	−4.55294e15	−0.605583	−0.302791	−	0.953057i	$-0.597919\pi$
$277$	−4.55294e15	−0.605583	−0.302791	+	0.953057i	$0.597919\pi$
$278$	−1.75994e15	−0.228668
$279$	5.53141e15	0.702116
$280$	3.03667e14	0.0376591
$281$	5.44622e15	0.659940	0.329970	−	0.943991i	$-0.392961\pi$
$281$	5.44622e15	0.659940	0.329970	+	0.943991i	$0.392961\pi$
$282$	4.77729e15	0.565669
$283$	4.37961e15	0.506785	0.253392	−	0.967364i	$-0.418454\pi$
$283$	4.37961e15	0.506785	0.253392	+	0.967364i	$0.418454\pi$
$284$	−1.49579e16	−1.69162
$285$	1.24626e16	1.37759
$286$	2.43460e14	0.0263056
$287$	−7.61615e14	−0.0804457
$288$	−5.72271e15	−0.590950
$289$	2.10403e16	2.12431
$290$	5.17328e15	0.510715
$291$	1.97902e15	0.191049
$292$	8.84196e15	0.834757
$293$	−2.15079e16	−1.98590	−0.992951	−	0.118523i	$-0.962184\pi$
$293$	−2.15079e16	−1.98590	−0.992951	+	0.118523i	$0.962184\pi$
$294$	3.39692e15	0.306780
$295$	7.57977e14	0.0669596
$296$	4.78498e14	0.0413508
$297$	3.13399e14	0.0264960
$298$	−4.15802e14	−0.0343939
$299$	2.06468e15	0.167105
$300$	−2.20606e16	−1.74715
$301$	9.12948e14	0.0707561
$302$	−4.83224e15	−0.366525
$303$	−1.22929e16	−0.912590
$304$	7.63903e15	0.555085
$305$	−2.35140e16	−1.67255
$306$	−5.34105e15	−0.371909
$307$	6.00393e15	0.409295	0.204648	−	0.978836i	$-0.434395\pi$
$307$	6.00393e15	0.409295	0.204648	+	0.978836i	$0.434395\pi$
$308$	3.54231e14	0.0236432
$309$	−3.99794e16	−2.61280
$310$	−3.84094e15	−0.245803
$311$	5.72056e15	0.358506	0.179253	−	0.983803i	$-0.442632\pi$
$311$	5.72056e15	0.358506	0.179253	+	0.983803i	$0.442632\pi$
$312$	2.71450e15	0.166604
$313$	6.93862e15	0.417095	0.208548	−	0.978012i	$-0.433126\pi$
$313$	6.93862e15	0.417095	0.208548	+	0.978012i	$0.433126\pi$
$314$	4.95529e15	0.291760
$315$	1.45344e15	0.0838262
$316$	4.04032e14	0.0228271
$317$	2.56464e16	1.41952	0.709760	−	0.704443i	$-0.248803\pi$
$317$	2.56464e16	1.41952	0.709760	+	0.704443i	$0.248803\pi$
$318$	−3.21900e15	−0.174560
$319$	1.23765e16	0.657597
$320$	−2.10611e16	−1.09649
$321$	−2.16534e16	−1.10470
$322$	−1.52912e14	−0.00764502
$323$	2.33643e16	1.14482
$324$	2.06471e16	0.991556
$325$	7.73522e15	0.364108
$326$	−5.45568e15	−0.251730
$327$	5.44253e16	2.46173
$328$	−1.35150e16	−0.599290
$329$	−2.43723e15	−0.105955
$330$	4.73281e15	0.201734
$331$	1.25289e16	0.523639	0.261819	−	0.965117i	$-0.415677\pi$
$331$	1.25289e16	0.523639	0.261819	+	0.965117i	$0.415677\pi$
$332$	1.79860e16	0.737119
$333$	2.29024e15	0.0920434
$334$	−3.67517e15	−0.144852
$335$	−2.33227e16	−0.901544
$336$	1.82275e15	0.0691070
$337$	−3.11810e16	−1.15957	−0.579783	−	0.814771i	$-0.696863\pi$
$337$	−3.11810e16	−1.15957	−0.579783	+	0.814771i	$0.696863\pi$
$338$	−4.64087e14	−0.0169294
$339$	2.96292e16	1.06028
$340$	−7.28614e16	−2.55791
$341$	−9.18906e15	−0.316496
$342$	−4.03264e15	−0.136276
$343$	−3.47178e15	−0.115117
$344$	1.62005e16	0.527106
$345$	4.01369e16	1.28150
$346$	−6.43112e15	−0.201508
$347$	−4.63138e16	−1.42419	−0.712096	−	0.702082i	$-0.752254\pi$
$347$	−4.63138e16	−1.42419	−0.712096	+	0.702082i	$0.752254\pi$
$348$	6.72847e16	2.03073
$349$	−2.21612e16	−0.656490	−0.328245	−	0.944593i	$-0.606457\pi$
$349$	−2.21612e16	−0.656490	−0.328245	+	0.944593i	$0.606457\pi$
$350$	−5.72878e14	−0.0166579
$351$	−5.97406e14	−0.0170519
$352$	9.50686e15	0.266385
$353$	5.20027e16	1.43051	0.715254	−	0.698864i	$-0.246311\pi$
$353$	5.20027e16	1.43051	0.715254	+	0.698864i	$0.246311\pi$
$354$	−5.01808e14	−0.0135524
$355$	1.01957e17	2.70355
$356$	−3.55414e16	−0.925356
$357$	5.57497e15	0.142528
$358$	−3.46093e15	−0.0868866
$359$	9.08524e14	0.0223987	0.0111993	−	0.999937i	$-0.496435\pi$
$359$	9.08524e14	0.0223987	0.0111993	+	0.999937i	$0.496435\pi$
$360$	2.57917e16	0.624472
$361$	−2.44123e16	−0.580512
$362$	−7.03576e14	−0.0164326
$363$	−4.96424e16	−1.13883
$364$	−6.75241e14	−0.0152160
$365$	−6.02693e16	−1.33411
$366$	1.55671e16	0.338517
$367$	6.82845e14	0.0145879	0.00729395	−	0.999973i	$-0.497678\pi$
$367$	6.82845e14	0.0145879	0.00729395	+	0.999973i	$0.497678\pi$
$368$	2.46021e16	0.516370
$369$	−6.46870e16	−1.33397
$370$	−1.59031e15	−0.0322234
$371$	1.64223e15	0.0326968
$372$	−4.99561e16	−0.977371
$373$	−1.54002e16	−0.296087	−0.148043	−	0.988981i	$-0.547298\pi$
$373$	−1.54002e16	−0.296087	−0.148043	+	0.988981i	$0.547298\pi$
$374$	8.87282e15	0.167647
$375$	3.58298e16	0.665336
$376$	−4.32491e16	−0.789326
$377$	−2.35924e16	−0.423207
$378$	4.42445e13	0.000780122 0
$379$	1.98983e16	0.344875	0.172437	−	0.985020i	$-0.444836\pi$
$379$	1.98983e16	0.344875	0.172437	+	0.985020i	$0.444836\pi$
$380$	−5.50125e16	−0.937276
$381$	−1.16961e17	−1.95897
$382$	2.47448e15	0.0407448
$383$	−2.92604e16	−0.473684	−0.236842	−	0.971548i	$-0.576112\pi$
$383$	−2.92604e16	−0.473684	−0.236842	+	0.971548i	$0.576112\pi$
$384$	6.82577e16	1.08642
$385$	−2.41453e15	−0.0377867
$386$	1.50968e16	0.232309
$387$	7.75404e16	1.17329
$388$	−8.73576e15	−0.129985
$389$	3.68657e16	0.539448	0.269724	−	0.962938i	$-0.413068\pi$
$389$	3.68657e16	0.539448	0.269724	+	0.962938i	$0.413068\pi$
$390$	−9.02176e15	−0.129829
$391$	7.52466e16	1.06497
$392$	−3.07525e16	−0.428076
$393$	−3.24612e16	−0.444440
$394$	−4.14533e15	−0.0558256
$395$	−2.75400e15	−0.0364823
$396$	3.00863e16	0.392057
$397$	−1.38554e17	−1.77615	−0.888075	−	0.459699i	$-0.847957\pi$
$397$	−1.38554e17	−1.77615	−0.888075	+	0.459699i	$0.847957\pi$
$398$	−2.33513e16	−0.294490
$399$	4.20926e15	0.0522254
$400$	9.21706e16	1.12513
$401$	1.48348e17	1.78174	0.890868	−	0.454263i	$-0.150097\pi$
$401$	1.48348e17	1.78174	0.890868	+	0.454263i	$0.150097\pi$
$402$	1.54404e16	0.182469
$403$	1.75163e16	0.203686
$404$	5.42630e16	0.620904
$405$	−1.40737e17	−1.58471
$406$	1.74727e15	0.0193616
$407$	−3.80466e15	−0.0414908
$408$	9.89290e16	1.06178
$409$	7.13621e16	0.753817	0.376908	−	0.926251i	$-0.376987\pi$
$409$	7.13621e16	0.753817	0.376908	+	0.926251i	$0.376987\pi$
$410$	4.49179e16	0.467008
$411$	−9.75872e16	−0.998668
$412$	1.76476e17	1.77769
$413$	2.56007e14	0.00253849
$414$	−1.29874e16	−0.126771
$415$	−1.22598e17	−1.17807
$416$	−1.81221e16	−0.171436
$417$	1.56025e17	1.45315
$418$	6.69923e15	0.0614298
$419$	1.65137e17	1.49091	0.745457	−	0.666553i	$-0.232231\pi$
$419$	1.65137e17	1.49091	0.745457	+	0.666553i	$0.232231\pi$
$420$	−1.31266e16	−0.116689
$421$	−1.44519e17	−1.26500	−0.632501	−	0.774559i	$-0.717972\pi$
$421$	−1.44519e17	−1.26500	−0.632501	+	0.774559i	$0.717972\pi$
$422$	−5.63272e15	−0.0485498
$423$	−2.07004e17	−1.75697
$424$	2.91418e16	0.243578
$425$	2.81908e17	2.32049
$426$	−6.74993e16	−0.547188
$427$	−7.94186e15	−0.0634076
$428$	9.55822e16	0.751610
$429$	−2.15836e16	−0.167168
$430$	−5.38431e16	−0.410757
$431$	1.53951e16	0.115686	0.0578429	−	0.998326i	$-0.481578\pi$
$431$	1.53951e16	0.115686	0.0578429	+	0.998326i	$0.481578\pi$
$432$	−7.11852e15	−0.0526921
$433$	4.79206e16	0.349422	0.174711	−	0.984620i	$-0.444101\pi$
$433$	4.79206e16	0.349422	0.174711	+	0.984620i	$0.444101\pi$
$434$	−1.29728e15	−0.00931859
$435$	−4.58631e17	−3.24551
$436$	−2.40244e17	−1.67490
$437$	5.68133e16	0.390230
$438$	3.99004e16	0.270020
$439$	−1.91983e17	−1.28010	−0.640050	−	0.768333i	$-0.721087\pi$
$439$	−1.91983e17	−1.28010	−0.640050	+	0.768333i	$0.721087\pi$
$440$	−4.28464e16	−0.281496
$441$	−1.47191e17	−0.952862
$442$	−1.69135e16	−0.107892
$443$	1.81731e17	1.14236	0.571181	−	0.820824i	$-0.306485\pi$
$443$	1.81731e17	1.14236	0.571181	+	0.820824i	$0.306485\pi$
$444$	−2.06839e16	−0.128128
$445$	2.42260e17	1.47891
$446$	−4.87863e16	−0.293509
$447$	3.68625e16	0.218568
$448$	−7.11338e15	−0.0415689
$449$	1.50266e17	0.865487	0.432744	−	0.901517i	$-0.357546\pi$
$449$	1.50266e17	0.865487	0.432744	+	0.901517i	$0.357546\pi$
$450$	−4.86568e16	−0.276225
$451$	1.07461e17	0.601319
$452$	−1.30789e17	−0.721391
$453$	4.28397e17	2.32921
$454$	−3.45983e16	−0.185435
$455$	4.60263e15	0.0243182
$456$	7.46942e16	0.389059
$457$	−7.84771e16	−0.402984	−0.201492	−	0.979490i	$-0.564579\pi$
$457$	−7.84771e16	−0.402984	−0.201492	+	0.979490i	$0.564579\pi$
$458$	1.36761e16	0.0692366
$459$	−2.17723e16	−0.108673
$460$	−1.77172e17	−0.871905
$461$	−2.73044e17	−1.32488	−0.662440	−	0.749115i	$-0.730479\pi$
$461$	−2.73044e17	−1.32488	−0.662440	+	0.749115i	$0.730479\pi$
$462$	1.59851e15	0.00764789
$463$	−2.18949e17	−1.03292	−0.516459	−	0.856312i	$-0.672750\pi$
$463$	−2.18949e17	−1.03292	−0.516459	+	0.856312i	$0.672750\pi$
$464$	−2.81120e17	−1.30775
$465$	3.40515e17	1.56204
$466$	−1.87654e16	−0.0848884
$467$	1.67968e17	0.749317	0.374658	−	0.927163i	$-0.377760\pi$
$467$	1.67968e17	0.749317	0.374658	+	0.927163i	$0.377760\pi$
$468$	−5.73509e16	−0.252315
$469$	−7.87724e15	−0.0341783
$470$	1.43741e17	0.615097
$471$	−4.39306e17	−1.85409
$472$	4.54290e15	0.0189108
$473$	−1.28814e17	−0.528891
$474$	1.82324e15	0.00738389
$475$	2.12848e17	0.850280
$476$	−2.46090e16	−0.0969724
$477$	1.39482e17	0.542185
$478$	3.18180e16	0.122009
$479$	6.58544e16	0.249117	0.124559	−	0.992212i	$-0.460248\pi$
$479$	6.58544e16	0.249117	0.124559	+	0.992212i	$0.460248\pi$
$480$	−3.52291e17	−1.31472
$481$	7.25250e15	0.0267021
$482$	5.92255e16	0.215131
$483$	1.35563e16	0.0485829
$484$	2.19131e17	0.774835
$485$	5.95453e16	0.207743
$486$	8.92419e16	0.307208
$487$	5.63030e17	1.91246	0.956232	−	0.292610i	$-0.0945238\pi$
$487$	5.63030e17	1.91246	0.956232	+	0.292610i	$0.0945238\pi$
$488$	−1.40930e17	−0.472362
$489$	4.83667e17	1.59970
$490$	1.02208e17	0.333586
$491$	1.95910e17	0.630998	0.315499	−	0.948926i	$-0.397828\pi$
$491$	1.95910e17	0.630998	0.315499	+	0.948926i	$0.397828\pi$
$492$	5.84211e17	1.85693
$493$	−8.59817e17	−2.69713
$494$	−1.27702e16	−0.0395341
$495$	−2.05076e17	−0.626587
$496$	2.08720e17	0.629408
$497$	3.44361e16	0.102494
$498$	8.11640e16	0.238436
$499$	8.71241e16	0.252630	0.126315	−	0.991990i	$-0.459685\pi$
$499$	8.71241e16	0.252630	0.126315	+	0.991990i	$0.459685\pi$
$500$	−1.58159e17	−0.452679
$501$	3.25818e17	0.920514
$502$	1.07192e17	0.298942
$503$	−7.42132e16	−0.204310	−0.102155	−	0.994769i	$-0.532574\pi$
$503$	−7.42132e16	−0.204310	−0.102155	+	0.994769i	$0.532574\pi$
$504$	8.71114e15	0.0236743
$505$	−3.69871e17	−0.992331
$506$	2.15754e16	0.0571453
$507$	4.11431e16	0.107583
$508$	5.16287e17	1.33284
$509$	2.22746e17	0.567733	0.283867	−	0.958864i	$-0.408383\pi$
$509$	2.22746e17	0.567733	0.283867	+	0.958864i	$0.408383\pi$
$510$	−3.28796e17	−0.827408
$511$	−2.03559e16	−0.0505773
$512$	−3.65983e17	−0.897855
$513$	−1.64387e16	−0.0398203
$514$	2.35530e16	0.0563360
$515$	−1.20291e18	−2.84110
$516$	−7.00294e17	−1.63327
$517$	3.43885e17	0.791999
$518$	−5.37128e14	−0.00122161
$519$	5.70144e17	1.28055
$520$	8.16746e16	0.181161
$521$	−6.13203e17	−1.34326	−0.671628	−	0.740889i	$-0.734405\pi$
$521$	−6.13203e17	−1.34326	−0.671628	+	0.740889i	$0.734405\pi$
$522$	1.48403e17	0.321059
$523$	−2.10537e17	−0.449851	−0.224925	−	0.974376i	$-0.572214\pi$
$523$	−2.10537e17	−0.449851	−0.224925	+	0.974376i	$0.572214\pi$
$524$	1.43290e17	0.302387
$525$	5.07879e16	0.105858
$526$	−2.74577e16	−0.0565271
$527$	6.38378e17	1.29810
$528$	−2.57184e17	−0.516564
$529$	−3.21065e17	−0.636987
$530$	−9.68543e16	−0.189813
$531$	2.17437e16	0.0420939
$532$	−1.85805e16	−0.0355329
$533$	−2.04845e17	−0.386989
$534$	−1.60384e17	−0.299326
$535$	−6.51515e17	−1.20123
$536$	−1.39783e17	−0.254615
$537$	3.06825e17	0.552151
$538$	9.56889e16	0.170128
$539$	2.44521e17	0.429526
$540$	5.12640e16	0.0889720
$541$	−4.79284e17	−0.821884	−0.410942	−	0.911662i	$-0.634800\pi$
$541$	−4.79284e17	−0.821884	−0.410942	+	0.911662i	$0.634800\pi$
$542$	1.20871e17	0.204798
$543$	6.23747e16	0.104426
$544$	−6.60456e17	−1.09257
$545$	1.63757e18	2.67684
$546$	−3.04710e15	−0.00492192
$547$	6.61511e17	1.05589	0.527946	−	0.849278i	$-0.322962\pi$
$547$	6.61511e17	1.05589	0.527946	+	0.849278i	$0.322962\pi$
$548$	4.30768e17	0.679470
$549$	−6.74535e17	−1.05144
$550$	8.08312e16	0.124515
$551$	−6.49186e17	−0.988289
$552$	2.40559e17	0.361924
$553$	−9.30162e14	−0.00138307
$554$	9.06925e16	0.133278
$555$	1.40987e17	0.204774
$556$	−6.88725e17	−0.988690
$557$	−2.15737e17	−0.306102	−0.153051	−	0.988218i	$-0.548910\pi$
$557$	−2.15737e17	−0.306102	−0.153051	+	0.988218i	$0.548910\pi$
$558$	−1.10183e17	−0.154523
$559$	2.45548e17	0.340376
$560$	5.48436e16	0.0751456
$561$	−7.86610e17	−1.06537
$562$	−1.08486e17	−0.145241
$563$	−1.55483e17	−0.205768	−0.102884	−	0.994693i	$-0.532807\pi$
$563$	−1.55483e17	−0.205768	−0.102884	+	0.994693i	$0.532807\pi$
$564$	1.86952e18	2.44577
$565$	8.91492e17	1.15293
$566$	−8.72398e16	−0.111534
$567$	−4.75338e16	−0.0600776
$568$	6.11076e17	0.763538
$569$	−8.13314e17	−1.00468	−0.502341	−	0.864670i	$-0.667528\pi$
$569$	−8.13314e17	−1.00468	−0.502341	+	0.864670i	$0.667528\pi$
$570$	−2.48250e17	−0.303182
$571$	−5.17049e17	−0.624305	−0.312153	−	0.950032i	$-0.601050\pi$
$571$	−5.17049e17	−0.624305	−0.312153	+	0.950032i	$0.601050\pi$
$572$	9.52743e16	0.113737
$573$	−2.19372e17	−0.258927
$574$	1.51710e16	0.0177046
$575$	6.85495e17	0.790976
$576$	−6.04168e17	−0.689305
$577$	7.19201e17	0.811348	0.405674	−	0.914018i	$-0.367037\pi$
$577$	7.19201e17	0.811348	0.405674	+	0.914018i	$0.367037\pi$
$578$	−4.19114e17	−0.467521
$579$	−1.33839e18	−1.47629
$580$	2.02448e18	2.20817
$581$	−4.14074e16	−0.0446614
$582$	−3.94211e16	−0.0420465
$583$	−2.31714e17	−0.244403
$584$	−3.61221e17	−0.376781
$585$	3.90920e17	0.403250
$586$	4.28427e17	0.437061
$587$	−2.38814e16	−0.0240942	−0.0120471	−	0.999927i	$-0.503835\pi$
$587$	−2.38814e16	−0.0240942	−0.0120471	+	0.999927i	$0.503835\pi$
$588$	1.32933e18	1.32642
$589$	4.81994e17	0.475655
$590$	−1.50986e16	−0.0147366
$591$	3.67500e17	0.354763
$592$	8.64187e16	0.0825119
$593$	9.73073e17	0.918946	0.459473	−	0.888192i	$-0.348038\pi$
$593$	9.73073e17	0.918946	0.459473	+	0.888192i	$0.348038\pi$
$594$	−6.24276e15	−0.00583129
$595$	1.67741e17	0.154982
$596$	−1.62718e17	−0.148708
$597$	2.07018e18	1.87144
$598$	−4.11274e16	−0.0367768
$599$	−2.06208e18	−1.82402	−0.912011	−	0.410165i	$-0.865471\pi$
$599$	−2.06208e18	−1.82402	−0.912011	+	0.410165i	$0.865471\pi$
$600$	9.01242e17	0.788602
$601$	3.33319e17	0.288520	0.144260	−	0.989540i	$-0.453920\pi$
$601$	3.33319e17	0.288520	0.144260	+	0.989540i	$0.453920\pi$
$602$	−1.81855e16	−0.0155721
$603$	−6.69046e17	−0.566752
$604$	−1.89103e18	−1.58474
$605$	−1.49366e18	−1.23834
$606$	2.44868e17	0.200844
$607$	−5.34991e17	−0.434130	−0.217065	−	0.976157i	$-0.569648\pi$
$607$	−5.34991e17	−0.434130	−0.217065	+	0.976157i	$0.569648\pi$
$608$	−4.98663e17	−0.400345
$609$	−1.54903e17	−0.123040
$610$	4.68388e17	0.368097
$611$	−6.55519e17	−0.509704
$612$	−2.09014e18	−1.60802
$613$	−1.22167e18	−0.929951	−0.464975	−	0.885324i	$-0.653937\pi$
$613$	−1.22167e18	−0.929951	−0.464975	+	0.885324i	$0.653937\pi$
$614$	−1.19596e17	−0.0900784
$615$	−3.98214e18	−2.96776
$616$	−1.44714e16	−0.0106717
$617$	9.06226e17	0.661277	0.330638	−	0.943758i	$-0.392736\pi$
$617$	9.06226e17	0.661277	0.330638	+	0.943758i	$0.392736\pi$
$618$	7.96370e17	0.575029
$619$	2.03399e18	1.45332	0.726658	−	0.687000i	$-0.241073\pi$
$619$	2.03399e18	1.45332	0.726658	+	0.687000i	$0.241073\pi$
$620$	−1.50310e18	−1.06277
$621$	−5.29421e16	−0.0370430
$622$	−1.13951e17	−0.0789006
$623$	8.18232e16	0.0560666
$624$	4.90249e17	0.332443
$625$	−8.78182e17	−0.589338
$626$	−1.38214e17	−0.0917950
$627$	−5.93913e17	−0.390377
$628$	1.93918e18	1.26148
$629$	2.64315e17	0.170174
$630$	−2.89519e16	−0.0184486
$631$	1.85727e18	1.17135	0.585673	−	0.810547i	$-0.300830\pi$
$631$	1.85727e18	1.17135	0.585673	+	0.810547i	$0.300830\pi$
$632$	−1.65059e16	−0.0103034
$633$	4.99362e17	0.308526
$634$	−5.10865e17	−0.312411
$635$	−3.51916e18	−2.13015
$636$	−1.25971e18	−0.754742
$637$	−4.66110e17	−0.276428
$638$	−2.46535e17	−0.144725
$639$	2.92479e18	1.69957
$640$	2.05376e18	1.18135
$641$	2.00871e18	1.14377	0.571887	−	0.820333i	$-0.306212\pi$
$641$	2.00871e18	1.14377	0.571887	+	0.820333i	$0.306212\pi$
$642$	4.31326e17	0.243124
$643$	8.62302e17	0.481158	0.240579	−	0.970630i	$-0.422663\pi$
$643$	8.62302e17	0.481158	0.240579	+	0.970630i	$0.422663\pi$
$644$	−5.98399e16	−0.0330546
$645$	4.77340e18	2.61030
$646$	−4.65406e17	−0.251954
$647$	1.40723e18	0.754202	0.377101	−	0.926172i	$-0.376921\pi$
$647$	1.40723e18	0.754202	0.377101	+	0.926172i	$0.376921\pi$
$648$	−8.43497e17	−0.447555
$649$	−3.61217e16	−0.0189748
$650$	−1.54082e17	−0.0801336
$651$	1.15009e17	0.0592181
$652$	−2.13500e18	−1.08840
$653$	2.13760e18	1.07892	0.539461	−	0.842011i	$-0.318628\pi$
$653$	2.13760e18	1.07892	0.539461	+	0.842011i	$0.318628\pi$
$654$	−1.08413e18	−0.541782
$655$	−9.76704e17	−0.483275
$656$	−2.44087e18	−1.19583
$657$	−1.72891e18	−0.838684
$658$	4.85484e16	0.0233188
$659$	−6.21802e16	−0.0295731	−0.0147866	−	0.999891i	$-0.504707\pi$
$659$	−6.21802e16	−0.0295731	−0.0147866	+	0.999891i	$0.504707\pi$
$660$	1.85211e18	0.872232
$661$	−1.24487e18	−0.580514	−0.290257	−	0.956949i	$-0.593741\pi$
$661$	−1.24487e18	−0.580514	−0.290257	+	0.956949i	$0.593741\pi$
$662$	−2.49570e17	−0.115243
$663$	1.49945e18	0.685636
$664$	−7.34783e17	−0.332710
$665$	1.26650e17	0.0567888
$666$	−4.56204e16	−0.0202571
$667$	−2.09076e18	−0.919360
$668$	−1.43822e18	−0.626296
$669$	4.32509e18	1.86520
$670$	4.64577e17	0.198414
$671$	1.12057e18	0.473962
$672$	−1.18986e17	−0.0498421
$673$	−3.50588e18	−1.45445	−0.727226	−	0.686399i	$-0.759191\pi$
$673$	−3.50588e18	−1.45445	−0.727226	+	0.686399i	$0.759191\pi$
$674$	6.21111e17	0.255199
$675$	−1.98345e17	−0.0807137
$676$	−1.81614e17	−0.0731972
$677$	2.22894e18	0.889760	0.444880	−	0.895590i	$-0.353246\pi$
$677$	2.22894e18	0.889760	0.444880	+	0.895590i	$0.353246\pi$
$678$	−5.90199e17	−0.233349
$679$	2.01114e16	0.00787571
$680$	2.97661e18	1.15455
$681$	3.06727e18	1.17841
$682$	1.83042e17	0.0696549
$683$	2.91738e18	1.09966	0.549830	−	0.835277i	$-0.314693\pi$
$683$	2.91738e18	1.09966	0.549830	+	0.835277i	$0.314693\pi$
$684$	−1.57811e18	−0.589215
$685$	−2.93624e18	−1.08593
$686$	6.91563e16	0.0253352
$687$	−1.21244e18	−0.439987
$688$	2.92587e18	1.05179
$689$	4.41697e17	0.157290
$690$	−7.99509e17	−0.282036
$691$	9.55445e17	0.333886	0.166943	−	0.985967i	$-0.446610\pi$
$691$	9.55445e17	0.333886	0.166943	+	0.985967i	$0.446610\pi$
$692$	−2.51672e18	−0.871256
$693$	−6.92645e16	−0.0237544
$694$	9.22549e17	0.313439
$695$	4.69454e18	1.58013
$696$	−2.74878e18	−0.916601
$697$	−7.46551e18	−2.46630
$698$	4.41441e17	0.144481
$699$	1.66362e18	0.539452
$700$	−2.24187e17	−0.0720234
$701$	2.60156e18	0.828069	0.414034	−	0.910261i	$-0.364119\pi$
$701$	2.60156e18	0.828069	0.414034	+	0.910261i	$0.364119\pi$
$702$	1.19001e16	0.00375282
$703$	1.99566e17	0.0623557
$704$	1.00367e18	0.310721
$705$	−1.27432e19	−3.90884
$706$	−1.03587e18	−0.314829
$707$	−1.24924e17	−0.0376201
$708$	−1.96375e17	−0.0585962
$709$	3.86217e18	1.14191	0.570954	−	0.820982i	$-0.306573\pi$
$709$	3.86217e18	1.14191	0.570954	+	0.820982i	$0.306573\pi$
$710$	−2.03094e18	−0.595001
$711$	−7.90025e16	−0.0229344
$712$	1.45197e18	0.417675
$713$	1.55230e18	0.442480
$714$	−1.11051e17	−0.0313677
$715$	−6.49416e17	−0.181775
$716$	−1.35438e18	−0.375670
$717$	−2.82079e18	−0.775347
$718$	−1.80974e16	−0.00492954
$719$	1.43745e18	0.388021	0.194011	−	0.980999i	$-0.437850\pi$
$719$	1.43745e18	0.388021	0.194011	+	0.980999i	$0.437850\pi$
$720$	4.65809e18	1.24608
$721$	−4.06284e17	−0.107709
$722$	4.86281e17	0.127760
$723$	−5.25057e18	−1.36712
$724$	−2.75334e17	−0.0710491
$725$	−7.83292e18	−2.00321
$726$	9.88854e17	0.250636
$727$	2.80298e18	0.704120	0.352060	−	0.935977i	$-0.385481\pi$
$727$	2.80298e18	0.704120	0.352060	+	0.935977i	$0.385481\pi$
$728$	2.75856e16	0.00686797
$729$	−3.68877e18	−0.910233
$730$	1.20054e18	0.293614
$731$	8.94891e18	2.16924
$732$	6.09196e18	1.46364
$733$	−4.14808e18	−0.987805	−0.493903	−	0.869517i	$-0.664430\pi$
$733$	−4.14808e18	−0.987805	−0.493903	+	0.869517i	$0.664430\pi$
$734$	−1.36020e16	−0.00321053
$735$	−9.06109e18	−2.11989
$736$	−1.60598e18	−0.372422
$737$	1.11145e18	0.255477
$738$	1.28854e18	0.293582
$739$	3.38096e18	0.763575	0.381787	−	0.924250i	$-0.375309\pi$
$739$	3.38096e18	0.763575	0.381787	+	0.924250i	$0.375309\pi$
$740$	−6.22344e17	−0.139324
$741$	1.13213e18	0.251233
$742$	−3.27126e16	−0.00719596
$743$	2.25678e18	0.492109	0.246054	−	0.969256i	$-0.420866\pi$
$743$	2.25678e18	0.492109	0.246054	+	0.969256i	$0.420866\pi$
$744$	2.04086e18	0.441152
$745$	1.10913e18	0.237666
$746$	3.06765e17	0.0651634
$747$	−3.51690e18	−0.740586
$748$	3.47224e18	0.724853
$749$	−2.20049e17	−0.0455394
$750$	−7.13713e17	−0.146428
$751$	3.14987e18	0.640668	0.320334	−	0.947305i	$-0.396205\pi$
$751$	3.14987e18	0.640668	0.320334	+	0.947305i	$0.396205\pi$
$752$	−7.81098e18	−1.57503
$753$	−9.50295e18	−1.89973
$754$	4.69949e17	0.0931402
$755$	1.28898e19	2.53273
$756$	1.73144e16	0.00337300
$757$	−1.03300e18	−0.199515	−0.0997577	−	0.995012i	$-0.531807\pi$
$757$	−1.03300e18	−0.199515	−0.0997577	+	0.995012i	$0.531807\pi$
$758$	−3.96365e17	−0.0759007
$759$	−1.91274e18	−0.363149
$760$	2.24742e18	0.423055
$761$	8.32025e18	1.55287	0.776437	−	0.630195i	$-0.217025\pi$
$761$	8.32025e18	1.55287	0.776437	+	0.630195i	$0.217025\pi$
$762$	2.32981e18	0.431134
$763$	5.53088e17	0.101481
$764$	9.68351e17	0.176168
$765$	1.42470e19	2.56994
$766$	5.82854e17	0.104249
$767$	6.88559e16	0.0122116
$768$	4.37453e18	0.769279
$769$	−4.05855e18	−0.707701	−0.353850	−	0.935302i	$-0.615128\pi$
$769$	−4.05855e18	−0.707701	−0.353850	+	0.935302i	$0.615128\pi$
$770$	4.80964e16	0.00831616
$771$	−2.08806e18	−0.358006
$772$	5.90790e18	1.00443
$773$	−8.41350e17	−0.141844	−0.0709218	−	0.997482i	$-0.522594\pi$
$773$	−8.41350e17	−0.141844	−0.0709218	+	0.997482i	$0.522594\pi$
$774$	−1.54457e18	−0.258221
$775$	5.81562e18	0.964128
$776$	3.56882e17	0.0586710
$777$	4.76185e16	0.00776316
$778$	−7.34347e17	−0.118723
$779$	−5.63667e18	−0.903710
$780$	−3.53053e18	−0.561339
$781$	−4.85882e18	−0.766124
$782$	−1.49888e18	−0.234381
$783$	6.04952e17	0.0938144
$784$	−5.55403e18	−0.854189
$785$	−1.32180e19	−2.01610
$786$	6.46613e17	0.0978133
$787$	9.28081e18	1.39236	0.696178	−	0.717869i	$-0.254882\pi$
$787$	9.28081e18	1.39236	0.696178	+	0.717869i	$0.254882\pi$
$788$	−1.62221e18	−0.241372
$789$	2.43423e18	0.359221
$790$	5.48583e16	0.00802909
$791$	3.01102e17	0.0437085
$792$	−1.22911e18	−0.176961
$793$	−2.13605e18	−0.305026
$794$	2.75992e18	0.390898
$795$	8.58651e18	1.20623
$796$	−9.13817e18	−1.27328
$797$	−4.52728e18	−0.625689	−0.312845	−	0.949804i	$-0.601282\pi$
$797$	−4.52728e18	−0.625689	−0.312845	+	0.949804i	$0.601282\pi$
$798$	−8.38465e16	−0.0114939
$799$	−2.38902e19	−3.24837
$800$	−6.01674e18	−0.811478
$801$	6.94958e18	0.929709
$802$	−2.95502e18	−0.392128
$803$	2.87216e18	0.378057
$804$	6.04238e18	0.788940
$805$	4.07885e17	0.0528280
$806$	−3.48918e17	−0.0448276
$807$	−8.48320e18	−1.08114
$808$	−2.21681e18	−0.280255
$809$	9.99346e18	1.25329	0.626643	−	0.779306i	$-0.284428\pi$
$809$	9.99346e18	1.25329	0.626643	+	0.779306i	$0.284428\pi$
$810$	2.80341e18	0.348765
$811$	−4.81481e18	−0.594215	−0.297107	−	0.954844i	$-0.596022\pi$
$811$	−4.81481e18	−0.594215	−0.297107	+	0.954844i	$0.596022\pi$
$812$	6.83770e17	0.0837136
$813$	−1.07157e19	−1.30146
$814$	7.57870e16	0.00913137
$815$	1.45527e19	1.73948
$816$	1.78670e19	2.11868
$817$	6.75668e18	0.794859
$818$	−1.42150e18	−0.165901
$819$	1.32033e17	0.0152875
$820$	1.75779e19	2.01919
$821$	7.59026e18	0.865020	0.432510	−	0.901629i	$-0.357628\pi$
$821$	7.59026e18	0.865020	0.432510	+	0.901629i	$0.357628\pi$
$822$	1.94389e18	0.219789
$823$	−1.43058e19	−1.60477	−0.802387	−	0.596804i	$-0.796437\pi$
$823$	−1.43058e19	−1.60477	−0.802387	+	0.596804i	$0.796437\pi$
$824$	−7.20959e18	−0.802387
$825$	−7.16600e18	−0.791273
$826$	−5.09954e15	−0.000558677 0
$827$	−5.83779e18	−0.634545	−0.317272	−	0.948334i	$-0.602767\pi$
$827$	−5.83779e18	−0.634545	−0.317272	+	0.948334i	$0.602767\pi$
$828$	−5.08244e18	−0.548119
$829$	−1.60285e19	−1.71509	−0.857547	−	0.514405i	$-0.828013\pi$
$829$	−1.60285e19	−1.71509	−0.857547	+	0.514405i	$0.828013\pi$
$830$	2.44209e18	0.259271
$831$	−8.04024e18	−0.846959
$832$	−1.91322e18	−0.199970
$833$	−1.69873e19	−1.76169
$834$	−3.10795e18	−0.319812
$835$	9.80333e18	1.00095
$836$	2.62164e18	0.265603
$837$	−4.49152e17	−0.0451521
$838$	−3.28945e18	−0.328123
$839$	−5.95087e18	−0.589017	−0.294508	−	0.955649i	$-0.595156\pi$
$839$	−5.95087e18	−0.589017	−0.294508	+	0.955649i	$0.595156\pi$
$840$	5.36259e17	0.0526695
$841$	1.36297e19	1.32835
$842$	2.87875e18	0.278404
$843$	9.61772e18	0.922982
$844$	−2.20428e18	−0.209914
$845$	1.23793e18	0.116984
$846$	4.12342e18	0.386678
$847$	−5.04483e17	−0.0469466
$848$	5.26314e18	0.486040
$849$	7.73415e18	0.708781
$850$	−5.61547e18	−0.510697
$851$	6.42717e17	0.0580066
$852$	−2.64148e19	−2.36587
$853$	1.05197e19	0.935048	0.467524	−	0.883980i	$-0.345146\pi$
$853$	1.05197e19	0.935048	0.467524	+	0.883980i	$0.345146\pi$
$854$	1.58198e17	0.0139549
$855$	1.07569e19	0.941685
$856$	−3.90482e18	−0.339251
$857$	−1.09051e19	−0.940276	−0.470138	−	0.882593i	$-0.655796\pi$
$857$	−1.09051e19	−0.940276	−0.470138	+	0.882593i	$0.655796\pi$
$858$	4.29936e17	0.0367906
$859$	2.11688e19	1.79780	0.898899	−	0.438157i	$-0.144369\pi$
$859$	2.11688e19	1.79780	0.898899	+	0.438157i	$0.144369\pi$
$860$	−2.10707e19	−1.77598
$861$	−1.34497e18	−0.112510
$862$	−3.06663e17	−0.0254604
$863$	1.52934e19	1.26019	0.630093	−	0.776520i	$-0.283017\pi$
$863$	1.52934e19	1.26019	0.630093	+	0.776520i	$0.283017\pi$
$864$	4.64685e17	0.0380031
$865$	1.71547e19	1.39244
$866$	−9.54556e17	−0.0769015
$867$	3.71561e19	2.97102
$868$	−5.07671e17	−0.0402906
$869$	1.31243e17	0.0103383
$870$	9.13572e18	0.714279
$871$	−2.11867e18	−0.164416
$872$	9.81467e18	0.755995
$873$	1.70815e18	0.130597
$874$	−1.13169e18	−0.0858825
$875$	3.64114e17	0.0274275
$876$	1.56144e19	1.16748
$877$	1.89659e19	1.40759	0.703794	−	0.710404i	$-0.251488\pi$
$877$	1.89659e19	1.40759	0.703794	+	0.710404i	$0.251488\pi$
$878$	3.82422e18	0.281727
$879$	−3.79817e19	−2.77745
$880$	−7.73825e18	−0.561701
$881$	−7.76141e18	−0.559238	−0.279619	−	0.960111i	$-0.590208\pi$
$881$	−7.76141e18	−0.559238	−0.279619	+	0.960111i	$0.590208\pi$
$882$	2.93197e18	0.209708
$883$	2.00139e19	1.42098	0.710489	−	0.703709i	$-0.248474\pi$
$883$	2.00139e19	1.42098	0.710489	+	0.703709i	$0.248474\pi$
$884$	−6.61885e18	−0.466491
$885$	1.33855e18	0.0936487
$886$	−3.61999e18	−0.251413
$887$	−1.96278e19	−1.35322	−0.676611	−	0.736341i	$-0.736552\pi$
$887$	−1.96278e19	−1.35322	−0.676611	+	0.736341i	$0.736552\pi$
$888$	8.45000e17	0.0578326
$889$	−1.18860e18	−0.0807556
$890$	−4.82570e18	−0.325481
$891$	6.70686e18	0.449070
$892$	−1.90918e19	−1.26904
$893$	−1.80378e19	−1.19028
$894$	−7.34283e17	−0.0481027
$895$	9.23184e18	0.600397
$896$	6.93658e17	0.0447861
$897$	3.64610e18	0.233711
$898$	−2.99324e18	−0.190478
$899$	−1.77376e19	−1.12062
$900$	−1.90411e19	−1.19431
$901$	1.60975e19	1.00242
$902$	−2.14058e18	−0.132339
$903$	1.61222e18	0.0989584
$904$	5.34311e18	0.325611
$905$	1.87675e18	0.113551
$906$	−8.53347e18	−0.512616
$907$	−1.95445e19	−1.16567	−0.582836	−	0.812590i	$-0.698057\pi$
$907$	−1.95445e19	−1.16567	−0.582836	+	0.812590i	$0.698057\pi$
$908$	−1.35395e19	−0.801762
$909$	−1.06103e19	−0.623825
$910$	−9.16822e16	−0.00535200
$911$	2.24766e19	1.30275	0.651376	−	0.758755i	$-0.274192\pi$
$911$	2.24766e19	1.30275	0.651376	+	0.758755i	$0.274192\pi$
$912$	1.34901e19	0.776334
$913$	5.84245e18	0.333837
$914$	1.56323e18	0.0886895
$915$	−4.15245e19	−2.33920
$916$	5.35192e18	0.299357
$917$	−3.29882e17	−0.0183214
$918$	4.33694e17	0.0239170
$919$	1.25273e18	0.0685971	0.0342985	−	0.999412i	$-0.489080\pi$
$919$	1.25273e18	0.0685971	0.0342985	+	0.999412i	$0.489080\pi$
$920$	7.23801e18	0.393548
$921$	1.06026e19	0.572434
$922$	5.43891e18	0.291582
$923$	9.26196e18	0.493051
$924$	6.25552e17	0.0330670
$925$	2.40791e18	0.126392
$926$	4.36135e18	0.227326
$927$	−3.45073e19	−1.78605
$928$	1.83510e19	0.943189
$929$	7.14662e18	0.364753	0.182376	−	0.983229i	$-0.441621\pi$
$929$	7.14662e18	0.364753	0.182376	+	0.983229i	$0.441621\pi$
$930$	−6.78289e18	−0.343776
$931$	−1.28259e19	−0.645526
$932$	−7.34354e18	−0.367031
$933$	1.01022e19	0.501400
$934$	−3.34583e18	−0.164911
$935$	−2.36678e19	−1.15846
$936$	2.34296e18	0.113886
$937$	−3.14622e19	−1.51874	−0.759368	−	0.650661i	$-0.774492\pi$
$937$	−3.14622e19	−1.51874	−0.759368	+	0.650661i	$0.774492\pi$
$938$	1.56911e17	0.00752202
$939$	1.22532e19	0.583343
$940$	5.62508e19	2.65948
$941$	−4.59649e17	−0.0215821	−0.0107910	−	0.999942i	$-0.503435\pi$
$941$	−4.59649e17	−0.0215821	−0.0107910	+	0.999942i	$0.503435\pi$
$942$	8.75077e18	0.408052
$943$	−1.81534e19	−0.840680
$944$	8.20467e17	0.0377349
$945$	−1.18020e17	−0.00539074
$946$	2.56592e18	0.116399
$947$	1.94287e18	0.0875324	0.0437662	−	0.999042i	$-0.486064\pi$
$947$	1.94287e18	0.0875324	0.0437662	+	0.999042i	$0.486064\pi$
$948$	7.13499e17	0.0319256
$949$	−5.47496e18	−0.243305
$950$	−4.23984e18	−0.187131
$951$	4.52902e19	1.98532
$952$	1.00535e18	0.0437700
$953$	1.83193e19	0.792146	0.396073	−	0.918219i	$-0.370373\pi$
$953$	1.83193e19	0.792146	0.396073	+	0.918219i	$0.370373\pi$
$954$	−2.77841e18	−0.119325
$955$	−6.60055e18	−0.281552
$956$	1.24515e19	0.527527
$957$	2.18563e19	0.919705
$958$	−1.31179e18	−0.0548262
$959$	−9.91714e17	−0.0411685
$960$	−3.71927e19	−1.53354
$961$	−1.12481e19	−0.460657
$962$	−1.44466e17	−0.00587664
$963$	−1.86897e19	−0.755145
$964$	2.31770e19	0.930157
$965$	−4.02699e19	−1.60529
$966$	−2.70034e17	−0.0106922
$967$	−2.48735e19	−0.978283	−0.489142	−	0.872204i	$-0.662690\pi$
$967$	−2.48735e19	−0.978283	−0.489142	+	0.872204i	$0.662690\pi$
$968$	−8.95216e18	−0.349734
$969$	4.12600e19	1.60112
$970$	−1.18612e18	−0.0457205
$971$	−2.08613e19	−0.798761	−0.399380	−	0.916785i	$-0.630775\pi$
$971$	−2.08613e19	−0.798761	−0.399380	+	0.916785i	$0.630775\pi$
$972$	3.49235e19	1.32827
$973$	1.58558e18	0.0599039
$974$	−1.12153e19	−0.420899
$975$	1.36600e19	0.509236
$976$	−2.54526e19	−0.942558
$977$	−1.82655e19	−0.671917	−0.335959	−	0.941877i	$-0.609060\pi$
$977$	−1.82655e19	−0.671917	−0.335959	+	0.941877i	$0.609060\pi$
$978$	−9.63442e18	−0.352065
$979$	−1.15450e19	−0.419089
$980$	3.99974e19	1.44232
$981$	4.69760e19	1.68278
$982$	−3.90244e18	−0.138871
$983$	2.80949e18	0.0993185	0.0496592	−	0.998766i	$-0.484186\pi$
$983$	2.80949e18	0.0993185	0.0496592	+	0.998766i	$0.484186\pi$
$984$	−2.38668e19	−0.838158
$985$	1.10575e19	0.385762
$986$	1.71272e19	0.593588
$987$	−4.30401e18	−0.148188
$988$	−4.99742e18	−0.170933
$989$	2.17604e19	0.739421
$990$	4.08502e18	0.137900
$991$	1.09815e19	0.368286	0.184143	−	0.982899i	$-0.441049\pi$
$991$	1.09815e19	0.368286	0.184143	+	0.982899i	$0.441049\pi$
$992$	−1.36249e19	−0.453949
$993$	2.21254e19	0.732354
$994$	−6.85950e17	−0.0225570
$995$	6.22883e19	2.03496
$996$	3.17623e19	1.03092
$997$	−4.57598e19	−1.47559	−0.737795	−	0.675025i	$-0.764133\pi$
$997$	−4.57598e19	−1.47559	−0.737795	+	0.675025i	$0.764133\pi$
$998$	−1.73547e18	−0.0555992
$999$	−1.85968e17	−0.00591918

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.14.a.b.1.3	✓	7
3.2	odd	2		117.14.a.d.1.5		7
13.12	even	2		169.14.a.b.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.14.a.b.1.3	✓	7	1.1	even	1	trivial
117.14.a.d.1.5		7	3.2	odd	2
169.14.a.b.1.5		7	13.12	even	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:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	13.a (trivial)

\(f(q)\)	\(=\)	\(q-19.9195 q^{2} +1765.94 q^{3} -7795.21 q^{4} +53134.3 q^{5} -35176.8 q^{6} +17946.1 q^{7} +318458. q^{8} +1.52424e6 q^{9} +O(q^{10})\)	\(q-19.9195 q^{2} +1765.94 q^{3} -7795.21 q^{4} +53134.3 q^{5} -35176.8 q^{6} +17946.1 q^{7} +318458. q^{8} +1.52424e6 q^{9} -1.05841e6 q^{10} -2.53214e6 q^{11} -1.37659e7 q^{12} +4.82681e6 q^{13} -357478. q^{14} +9.38323e7 q^{15} +5.75148e7 q^{16} +1.75912e8 q^{17} -3.03621e7 q^{18} +1.32818e8 q^{19} -4.14193e8 q^{20} +3.16919e7 q^{21} +5.04391e7 q^{22} +4.27752e8 q^{23} +5.62379e8 q^{24} +1.60255e9 q^{25} -9.61478e7 q^{26} -1.23768e8 q^{27} -1.39894e8 q^{28} -4.88778e9 q^{29} -1.86909e9 q^{30} +3.62897e9 q^{31} -3.75448e9 q^{32} -4.47162e9 q^{33} -3.50408e9 q^{34} +9.53555e8 q^{35} -1.18817e10 q^{36} +1.50255e9 q^{37} -2.64568e9 q^{38} +8.52388e9 q^{39} +1.69210e10 q^{40} -4.24390e10 q^{41} -6.31287e8 q^{42} +5.08716e10 q^{43} +1.97386e10 q^{44} +8.09893e10 q^{45} -8.52062e9 q^{46} -1.35808e11 q^{47} +1.01568e11 q^{48} -9.65669e10 q^{49} -3.19221e10 q^{50} +3.10650e11 q^{51} -3.76260e10 q^{52} +9.15092e10 q^{53} +2.46541e9 q^{54} -1.34544e11 q^{55} +5.71508e9 q^{56} +2.34550e11 q^{57} +9.73623e10 q^{58} +1.42653e10 q^{59} -7.31442e11 q^{60} -4.42539e11 q^{61} -7.22874e10 q^{62} +2.73541e10 q^{63} -3.96374e11 q^{64} +2.56469e11 q^{65} +8.90726e10 q^{66} -4.38938e11 q^{67} -1.37127e12 q^{68} +7.55386e11 q^{69} -1.89944e10 q^{70} +1.91886e12 q^{71} +4.85405e11 q^{72} -1.13428e12 q^{73} -2.99300e10 q^{74} +2.83002e12 q^{75} -1.03535e12 q^{76} -4.54421e10 q^{77} -1.69792e11 q^{78} -5.18308e10 q^{79} +3.05601e12 q^{80} -2.64869e12 q^{81} +8.45365e11 q^{82} -2.30732e12 q^{83} -2.47045e11 q^{84} +9.34695e12 q^{85} -1.01334e12 q^{86} -8.63154e12 q^{87} -8.06380e11 q^{88} +4.55938e12 q^{89} -1.61327e12 q^{90} +8.66225e10 q^{91} -3.33442e12 q^{92} +6.40856e12 q^{93} +2.70523e12 q^{94} +7.05721e12 q^{95} -6.63020e12 q^{96} +1.12066e12 q^{97} +1.92357e12 q^{98} -3.85958e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 127 q^{2} + 728 q^{3} + 16153 q^{4} + 34886 q^{5} + 83045 q^{6} + 131864 q^{7} + 127671 q^{8} + 2466055 q^{9}+O(q^{10}) \) 7 * q + 127 * q^2 + 728 * q^3 + 16153 * q^4 + 34886 * q^5 + 83045 * q^6 + 131864 * q^7 + 127671 * q^8 + 2466055 * q^9	\( 7 q + 127 q^{2} + 728 q^{3} + 16153 q^{4} + 34886 q^{5} + 83045 q^{6} + 131864 q^{7} + 127671 q^{8} + 2466055 q^{9} + 3335529 q^{10} + 8912632 q^{11} + 25360909 q^{12} + 33787663 q^{13} + 67318187 q^{14} + 78942892 q^{15} + 159240961 q^{16} + 222199706 q^{17} + 596088532 q^{18} + 652665968 q^{19} + 935513953 q^{20} + 1217880580 q^{21} + 1374511830 q^{22} + 1794723984 q^{23} + 1895354895 q^{24} + 246154813 q^{25} + 613004743 q^{26} - 1915909876 q^{27} - 1789780165 q^{28} - 4735865782 q^{29} - 9918164303 q^{30} - 9436127356 q^{31} - 17224649401 q^{32} - 25638368752 q^{33} - 29930612727 q^{34} - 20876359292 q^{35} - 31714020118 q^{36} - 14832967330 q^{37} - 7473991662 q^{38} + 3513916952 q^{39} + 10553061291 q^{40} + 59907995430 q^{41} + 69292649863 q^{42} + 72489466184 q^{43} + 82565539934 q^{44} + 60104811962 q^{45} + 118453633200 q^{46} + 195641345592 q^{47} + 69842813569 q^{48} + 55402933947 q^{49} + 87739798742 q^{50} + 142246774012 q^{51} + 77967445777 q^{52} + 409286178474 q^{53} - 46365876001 q^{54} + 418486272912 q^{55} - 217713137127 q^{56} + 243297441528 q^{57} - 1099013150598 q^{58} - 160361676600 q^{59} - 1108676787295 q^{60} - 147184998046 q^{61} - 2220407254292 q^{62} + 256048021580 q^{63} - 2276361582767 q^{64} + 168388058774 q^{65} - 2841576718138 q^{66} + 1533110763584 q^{67} - 1734599536391 q^{68} + 1341159298056 q^{69} - 1953936478521 q^{70} + 1288841132520 q^{71} - 1858742324166 q^{72} + 4340518042046 q^{73} - 2522725784507 q^{74} + 3488845434748 q^{75} + 792218810282 q^{76} + 3260905865264 q^{77} + 400842353405 q^{78} + 6986884509272 q^{79} + 2848664165317 q^{80} + 9402260691943 q^{81} + 3785376233100 q^{82} + 9485774126680 q^{83} + 2428655741171 q^{84} + 9239892384264 q^{85} - 1372999514421 q^{86} + 5364161696536 q^{87} - 2985250612134 q^{88} - 1338832432586 q^{89} - 13443400684582 q^{90} + 636482341976 q^{91} - 8786066700672 q^{92} - 12529067281768 q^{93} - 18098521583937 q^{94} - 119505100680 q^{95} - 29672968067657 q^{96} + 1532637634742 q^{97} - 14020062796872 q^{98} - 17432744537624 q^{99}+O(q^{100}) \) 7 * q + 127 * q^2 + 728 * q^3 + 16153 * q^4 + 34886 * q^5 + 83045 * q^6 + 131864 * q^7 + 127671 * q^8 + 2466055 * q^9 + 3335529 * q^10 + 8912632 * q^11 + 25360909 * q^12 + 33787663 * q^13 + 67318187 * q^14 + 78942892 * q^15 + 159240961 * q^16 + 222199706 * q^17 + 596088532 * q^18 + 652665968 * q^19 + 935513953 * q^20 + 1217880580 * q^21 + 1374511830 * q^22 + 1794723984 * q^23 + 1895354895 * q^24 + 246154813 * q^25 + 613004743 * q^26 - 1915909876 * q^27 - 1789780165 * q^28 - 4735865782 * q^29 - 9918164303 * q^30 - 9436127356 * q^31 - 17224649401 * q^32 - 25638368752 * q^33 - 29930612727 * q^34 - 20876359292 * q^35 - 31714020118 * q^36 - 14832967330 * q^37 - 7473991662 * q^38 + 3513916952 * q^39 + 10553061291 * q^40 + 59907995430 * q^41 + 69292649863 * q^42 + 72489466184 * q^43 + 82565539934 * q^44 + 60104811962 * q^45 + 118453633200 * q^46 + 195641345592 * q^47 + 69842813569 * q^48 + 55402933947 * q^49 + 87739798742 * q^50 + 142246774012 * q^51 + 77967445777 * q^52 + 409286178474 * q^53 - 46365876001 * q^54 + 418486272912 * q^55 - 217713137127 * q^56 + 243297441528 * q^57 - 1099013150598 * q^58 - 160361676600 * q^59 - 1108676787295 * q^60 - 147184998046 * q^61 - 2220407254292 * q^62 + 256048021580 * q^63 - 2276361582767 * q^64 + 168388058774 * q^65 - 2841576718138 * q^66 + 1533110763584 * q^67 - 1734599536391 * q^68 + 1341159298056 * q^69 - 1953936478521 * q^70 + 1288841132520 * q^71 - 1858742324166 * q^72 + 4340518042046 * q^73 - 2522725784507 * q^74 + 3488845434748 * q^75 + 792218810282 * q^76 + 3260905865264 * q^77 + 400842353405 * q^78 + 6986884509272 * q^79 + 2848664165317 * q^80 + 9402260691943 * q^81 + 3785376233100 * q^82 + 9485774126680 * q^83 + 2428655741171 * q^84 + 9239892384264 * q^85 - 1372999514421 * q^86 + 5364161696536 * q^87 - 2985250612134 * q^88 - 1338832432586 * q^89 - 13443400684582 * q^90 + 636482341976 * q^91 - 8786066700672 * q^92 - 12529067281768 * q^93 - 18098521583937 * q^94 - 119505100680 * q^95 - 29672968067657 * q^96 + 1532637634742 * q^97 - 14020062796872 * q^98 - 17432744537624 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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