LMFDB - Embedded newform 13.12.a.b.1.3

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			1.3
Root			$-15.2405$ 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)

$f(q)$	$=$	$q-6.24050 q^{2} -573.204 q^{3} -2009.06 q^{4} -3613.82 q^{5} +3577.08 q^{6} +14401.4 q^{7} +25318.0 q^{8} +151416. q^{9} +O(q^{10})$	\(q-6.24050 q^{2} -573.204 q^{3} -2009.06 q^{4} -3613.82 q^{5} +3577.08 q^{6} +14401.4 q^{7} +25318.0 q^{8} +151416. q^{9} +22552.1 q^{10} +11559.7 q^{11} +1.15160e6 q^{12} -371293. q^{13} -89871.6 q^{14} +2.07146e6 q^{15} +3.95655e6 q^{16} +4.40705e6 q^{17} -944911. q^{18} +178584. q^{19} +7.26038e6 q^{20} -8.25492e6 q^{21} -72138.4 q^{22} -3.48688e7 q^{23} -1.45124e7 q^{24} -3.57684e7 q^{25} +2.31705e6 q^{26} +1.47491e7 q^{27} -2.89331e7 q^{28} -2.10941e7 q^{29} -1.29269e7 q^{30} +1.38525e8 q^{31} -7.65422e7 q^{32} -6.62608e6 q^{33} -2.75022e7 q^{34} -5.20440e7 q^{35} -3.04203e8 q^{36} +4.63353e8 q^{37} -1.11445e6 q^{38} +2.12827e8 q^{39} -9.14950e7 q^{40} +1.31776e9 q^{41} +5.15148e7 q^{42} +1.34993e9 q^{43} -2.32241e7 q^{44} -5.47191e8 q^{45} +2.17599e8 q^{46} -1.53087e9 q^{47} -2.26791e9 q^{48} -1.76993e9 q^{49} +2.23213e8 q^{50} -2.52614e9 q^{51} +7.45949e8 q^{52} +1.23580e9 q^{53} -9.20415e7 q^{54} -4.17748e7 q^{55} +3.64614e8 q^{56} -1.02365e8 q^{57} +1.31638e8 q^{58} +9.72295e9 q^{59} -4.16168e9 q^{60} -7.93576e9 q^{61} -8.64464e8 q^{62} +2.18060e9 q^{63} -7.62535e9 q^{64} +1.34179e9 q^{65} +4.13500e7 q^{66} +1.80370e10 q^{67} -8.85401e9 q^{68} +1.99870e10 q^{69} +3.24780e8 q^{70} +1.78981e10 q^{71} +3.83356e9 q^{72} -2.12821e10 q^{73} -2.89155e9 q^{74} +2.05026e10 q^{75} -3.58784e8 q^{76} +1.66476e8 q^{77} -1.32814e9 q^{78} -1.34997e10 q^{79} -1.42983e10 q^{80} -3.52771e10 q^{81} -8.22348e9 q^{82} -2.37731e10 q^{83} +1.65846e10 q^{84} -1.59263e10 q^{85} -8.42424e9 q^{86} +1.20912e10 q^{87} +2.92670e8 q^{88} -1.12535e10 q^{89} +3.41474e9 q^{90} -5.34712e9 q^{91} +7.00535e10 q^{92} -7.94030e10 q^{93} +9.55342e9 q^{94} -6.45370e8 q^{95} +4.38743e10 q^{96} -2.21465e10 q^{97} +1.10452e10 q^{98} +1.75033e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−6.24050	−0.137897	−0.0689484	−	0.997620i	$-0.521964\pi$
$2$	−6.24050	−0.137897	−0.0689484	+	0.997620i	$0.521964\pi$
$3$	−573.204	−1.36189	−0.680946	−	0.732334i	$-0.738431\pi$
$3$	−573.204	−1.36189	−0.680946	+	0.732334i	$0.738431\pi$
$4$	−2009.06	−0.980984
$5$	−3613.82	−0.517168	−0.258584	−	0.965989i	$-0.583256\pi$
$5$	−3613.82	−0.517168	−0.258584	+	0.965989i	$0.583256\pi$
$6$	3577.08	0.187800
$7$	14401.4	0.323865	0.161933	−	0.986802i	$-0.448227\pi$
$7$	14401.4	0.323865	0.161933	+	0.986802i	$0.448227\pi$
$8$	25318.0	0.273171
$9$	151416.	0.854748
$10$	22552.1	0.0713159
$11$	11559.7	0.0216415	0.0108208	−	0.999941i	$-0.496556\pi$
$11$	11559.7	0.0216415	0.0108208	+	0.999941i	$0.496556\pi$
$12$	1.15160e6	1.33599
$13$	−371293.	−0.277350
$13$	−371293.	−0.277350
$14$	−89871.6	−0.0446600
$15$	2.07146e6	0.704327
$16$	3.95655e6	0.943315
$17$	4.40705e6	0.752799	0.376399	−	0.926457i	$-0.377162\pi$
$17$	4.40705e6	0.752799	0.376399	+	0.926457i	$0.377162\pi$
$18$	−944911.	−0.117867
$19$	178584.	0.0165461	0.00827307	−	0.999966i	$-0.497367\pi$
$19$	178584.	0.0165461	0.00827307	+	0.999966i	$0.497367\pi$
$20$	7.26038e6	0.507334
$21$	−8.25492e6	−0.441069
$22$	−72138.4	−0.00298430
$23$	−3.48688e7	−1.12963	−0.564813	−	0.825219i	$-0.691052\pi$
$23$	−3.48688e7	−1.12963	−0.564813	+	0.825219i	$0.691052\pi$
$24$	−1.45124e7	−0.372030
$25$	−3.57684e7	−0.732537
$26$	2.31705e6	0.0382457
$27$	1.47491e7	0.197817
$28$	−2.89331e7	−0.317707
$29$	−2.10941e7	−0.190973	−0.0954867	−	0.995431i	$-0.530441\pi$
$29$	−2.10941e7	−0.190973	−0.0954867	+	0.995431i	$0.530441\pi$
$30$	−1.29269e7	−0.0971245
$31$	1.38525e8	0.869037	0.434519	−	0.900663i	$-0.356918\pi$
$31$	1.38525e8	0.869037	0.434519	+	0.900663i	$0.356918\pi$
$32$	−7.65422e7	−0.403251
$33$	−6.62608e6	−0.0294734
$34$	−2.75022e7	−0.103809
$35$	−5.20440e7	−0.167493
$36$	−3.04203e8	−0.838495
$37$	4.63353e8	1.09851	0.549253	−	0.835656i	$-0.314912\pi$
$37$	4.63353e8	1.09851	0.549253	+	0.835656i	$0.314912\pi$
$38$	−1.11445e6	−0.00228166
$39$	2.12827e8	0.377721
$40$	−9.14950e7	−0.141276
$41$	1.31776e9	1.77634	0.888169	−	0.459517i	$-0.151978\pi$
$41$	1.31776e9	1.77634	0.888169	+	0.459517i	$0.151978\pi$
$42$	5.15148e7	0.0608220
$43$	1.34993e9	1.40035	0.700173	−	0.713974i	$-0.253106\pi$
$43$	1.34993e9	1.40035	0.700173	+	0.713974i	$0.253106\pi$
$44$	−2.32241e7	−0.0212300
$45$	−5.47191e8	−0.442049
$46$	2.17599e8	0.155772
$47$	−1.53087e9	−0.973647	−0.486823	−	0.873500i	$-0.661844\pi$
$47$	−1.53087e9	−0.973647	−0.486823	+	0.873500i	$0.661844\pi$
$48$	−2.26791e9	−1.28469
$49$	−1.76993e9	−0.895111
$50$	2.23213e8	0.101014
$51$	−2.52614e9	−1.02523
$52$	7.45949e8	0.272076
$53$	1.23580e9	0.405910	0.202955	−	0.979188i	$-0.434945\pi$
$53$	1.23580e9	0.405910	0.202955	+	0.979188i	$0.434945\pi$
$54$	−9.20415e7	−0.0272784
$55$	−4.17748e7	−0.0111923
$56$	3.64614e8	0.0884707
$57$	−1.02365e8	−0.0225340
$58$	1.31638e8	0.0263346
$59$	9.72295e9	1.77057	0.885283	−	0.465053i	$-0.153965\pi$
$59$	9.72295e9	1.77057	0.885283	+	0.465053i	$0.153965\pi$
$60$	−4.16168e9	−0.690934
$61$	−7.93576e9	−1.20302	−0.601512	−	0.798864i	$-0.705435\pi$
$61$	−7.93576e9	−1.20302	−0.601512	+	0.798864i	$0.705435\pi$
$62$	−8.64464e8	−0.119837
$63$	2.18060e9	0.276823
$64$	−7.62535e9	−0.887708
$65$	1.34179e9	0.143437
$66$	4.13500e7	0.00406429
$67$	1.80370e10	1.63212	0.816061	−	0.577966i	$-0.196153\pi$
$67$	1.80370e10	1.63212	0.816061	+	0.577966i	$0.196153\pi$
$68$	−8.85401e9	−0.738484
$69$	1.99870e10	1.53843
$70$	3.24780e8	0.0230967
$71$	1.78981e10	1.17729	0.588647	−	0.808390i	$-0.299661\pi$
$71$	1.78981e10	1.17729	0.588647	+	0.808390i	$0.299661\pi$
$72$	3.83356e9	0.233493
$73$	−2.12821e10	−1.20154	−0.600770	−	0.799422i	$-0.705139\pi$
$73$	−2.12821e10	−1.20154	−0.600770	+	0.799422i	$0.705139\pi$
$74$	−2.89155e9	−0.151480
$75$	2.05026e10	0.997635
$76$	−3.58784e8	−0.0162315
$77$	1.66476e8	0.00700893
$78$	−1.32814e9	−0.0520865
$79$	−1.34997e10	−0.493601	−0.246800	−	0.969066i	$-0.579379\pi$
$79$	−1.34997e10	−0.493601	−0.246800	+	0.969066i	$0.579379\pi$
$80$	−1.42983e10	−0.487853
$81$	−3.52771e10	−1.12415
$82$	−8.22348e9	−0.244951
$83$	−2.37731e10	−0.662455	−0.331228	−	0.943551i	$-0.607463\pi$
$83$	−2.37731e10	−0.662455	−0.331228	+	0.943551i	$0.607463\pi$
$84$	1.65846e10	0.432682
$85$	−1.59263e10	−0.389324
$86$	−8.42424e9	−0.193103
$87$	1.20912e10	0.260085
$88$	2.92670e8	0.00591184
$89$	−1.12535e10	−0.213620	−0.106810	−	0.994279i	$-0.534064\pi$
$89$	−1.12535e10	−0.213620	−0.106810	+	0.994279i	$0.534064\pi$
$90$	3.41474e9	0.0609571
$91$	−5.34712e9	−0.0898240
$92$	7.00535e10	1.10814
$93$	−7.94030e10	−1.18353
$94$	9.55342e9	0.134263
$95$	−6.45370e8	−0.00855714
$96$	4.38743e10	0.549185
$97$	−2.21465e10	−0.261854	−0.130927	−	0.991392i	$-0.541795\pi$
$97$	−2.21465e10	−0.261854	−0.130927	+	0.991392i	$0.541795\pi$
$98$	1.10452e10	0.123433
$99$	1.75033e9	0.0184980
$100$	7.18607e10	0.718607
$101$	1.16629e10	0.110417	0.0552087	−	0.998475i	$-0.482418\pi$
$101$	1.16629e10	0.110417	0.0552087	+	0.998475i	$0.482418\pi$
$102$	1.57644e10	0.141376
$103$	1.65563e10	0.140721	0.0703605	−	0.997522i	$-0.477585\pi$
$103$	1.65563e10	0.140721	0.0703605	+	0.997522i	$0.477585\pi$
$104$	−9.40041e9	−0.0757641
$105$	2.98318e10	0.228107
$106$	−7.71199e9	−0.0559737
$107$	2.18025e11	1.50278	0.751389	−	0.659860i	$-0.229384\pi$
$107$	2.18025e11	1.50278	0.751389	+	0.659860i	$0.229384\pi$
$108$	−2.96317e10	−0.194056
$109$	−1.35166e11	−0.841440	−0.420720	−	0.907191i	$-0.638222\pi$
$109$	−1.35166e11	−0.841440	−0.420720	+	0.907191i	$0.638222\pi$
$110$	2.60696e8	0.00154338
$111$	−2.65596e11	−1.49605
$112$	5.69797e10	0.305507
$113$	3.10746e11	1.58663	0.793313	−	0.608813i	$-0.208354\pi$
$113$	3.10746e11	1.58663	0.793313	+	0.608813i	$0.208354\pi$
$114$	6.38807e8	0.00310737
$115$	1.26010e11	0.584207
$116$	4.23793e10	0.187342
$117$	−5.62197e10	−0.237064
$118$	−6.06760e10	−0.244155
$119$	6.34675e10	0.243805
$120$	5.24453e10	0.192402
$121$	−2.85178e11	−0.999532
$122$	4.95231e10	0.165893
$123$	−7.55346e11	−2.41918
$124$	−2.78304e11	−0.852512
$125$	3.05717e11	0.896013
$126$	−1.36080e10	−0.0381730
$127$	−1.45272e10	−0.0390176	−0.0195088	−	0.999810i	$-0.506210\pi$
$127$	−1.45272e10	−0.0390176	−0.0195088	+	0.999810i	$0.506210\pi$
$128$	2.04344e11	0.525664
$129$	−7.73786e11	−1.90712
$130$	−8.37342e9	−0.0197795
$131$	2.90831e11	0.658640	0.329320	−	0.944218i	$-0.393181\pi$
$131$	2.90831e11	0.658640	0.329320	+	0.944218i	$0.393181\pi$
$132$	1.33122e10	0.0289129
$133$	2.57185e9	0.00535872
$134$	−1.12560e11	−0.225064
$135$	−5.33006e10	−0.102305
$136$	1.11578e11	0.205643
$137$	5.99207e11	1.06075	0.530376	−	0.847763i	$-0.322051\pi$
$137$	5.99207e11	1.06075	0.530376	+	0.847763i	$0.322051\pi$
$138$	−1.24729e11	−0.212144
$139$	3.36082e11	0.549368	0.274684	−	0.961535i	$-0.411427\pi$
$139$	3.36082e11	0.549368	0.274684	+	0.961535i	$0.411427\pi$
$140$	1.04559e11	0.164308
$141$	8.77504e11	1.32600
$142$	−1.11693e11	−0.162345
$143$	−4.29204e9	−0.00600228
$144$	5.99085e11	0.806297
$145$	7.62305e10	0.0987654
$146$	1.32811e11	0.165689
$147$	1.01453e12	1.21904
$148$	−9.30902e11	−1.07762
$149$	−1.75790e11	−0.196097	−0.0980483	−	0.995182i	$-0.531260\pi$
$149$	−1.75790e11	−0.196097	−0.0980483	+	0.995182i	$0.531260\pi$
$150$	−1.27946e11	−0.137571
$151$	−1.21465e12	−1.25915	−0.629577	−	0.776938i	$-0.716772\pi$
$151$	−1.21465e12	−1.25915	−0.629577	+	0.776938i	$0.716772\pi$
$152$	4.52138e9	0.00451993
$153$	6.67298e11	0.643453
$154$	−1.03889e9	−0.000966509 0
$155$	−5.00605e11	−0.449439
$156$	−4.27581e11	−0.370538
$157$	1.02369e12	0.856483	0.428242	−	0.903664i	$-0.359133\pi$
$157$	1.02369e12	0.856483	0.428242	+	0.903664i	$0.359133\pi$
$158$	8.42449e10	0.0680659
$159$	−7.08364e11	−0.552806
$160$	2.76610e11	0.208549
$161$	−5.02159e11	−0.365846
$162$	2.20147e11	0.155017
$163$	8.00937e11	0.545214	0.272607	−	0.962126i	$-0.412114\pi$
$163$	8.00937e11	0.545214	0.272607	+	0.962126i	$0.412114\pi$
$164$	−2.64746e12	−1.74256
$165$	2.39455e10	0.0152427
$166$	1.48356e11	0.0913504
$167$	2.88718e12	1.72002	0.860009	−	0.510280i	$-0.170458\pi$
$167$	2.88718e12	1.72002	0.860009	+	0.510280i	$0.170458\pi$
$168$	−2.08998e11	−0.120487
$169$	1.37858e11	0.0769231
$170$	9.93881e10	0.0536865
$171$	2.70404e10	0.0141428
$172$	−2.71209e12	−1.37372
$173$	2.61065e11	0.128084	0.0640421	−	0.997947i	$-0.479601\pi$
$173$	2.61065e11	0.128084	0.0640421	+	0.997947i	$0.479601\pi$
$174$	−7.54554e10	−0.0358649
$175$	−5.15114e11	−0.237243
$176$	4.57366e10	0.0204148
$177$	−5.57324e12	−2.41132
$178$	7.02272e10	0.0294575
$179$	9.18848e11	0.373725	0.186862	−	0.982386i	$-0.440168\pi$
$179$	9.18848e11	0.373725	0.186862	+	0.982386i	$0.440168\pi$
$180$	1.09934e12	0.433643
$181$	−3.29723e12	−1.26159	−0.630793	−	0.775951i	$-0.717270\pi$
$181$	−3.29723e12	−1.26159	−0.630793	+	0.775951i	$0.717270\pi$
$182$	3.33687e10	0.0123864
$183$	4.54881e12	1.63839
$184$	−8.82811e11	−0.308581
$185$	−1.67448e12	−0.568113
$186$	4.95514e11	0.163206
$187$	5.09443e10	0.0162917
$188$	3.07561e12	0.955132
$189$	2.12407e11	0.0640661
$190$	4.02743e9	0.00118000
$191$	3.38423e12	0.963332	0.481666	−	0.876355i	$-0.340032\pi$
$191$	3.38423e12	0.963332	0.481666	+	0.876355i	$0.340032\pi$
$192$	4.37088e12	1.20896
$193$	4.32682e12	1.16306	0.581531	−	0.813524i	$-0.302454\pi$
$193$	4.32682e12	1.16306	0.581531	+	0.813524i	$0.302454\pi$
$194$	1.38205e11	0.0361089
$195$	−7.69118e11	−0.195345
$196$	3.55588e12	0.878090
$197$	1.53085e12	0.367595	0.183797	−	0.982964i	$-0.441161\pi$
$197$	1.53085e12	0.367595	0.183797	+	0.982964i	$0.441161\pi$
$198$	−1.09229e10	−0.00255082
$199$	1.69509e12	0.385036	0.192518	−	0.981293i	$-0.438335\pi$
$199$	1.69509e12	0.385036	0.192518	+	0.981293i	$0.438335\pi$
$200$	−9.05586e11	−0.200108
$201$	−1.03389e13	−2.22277
$202$	−7.27820e10	−0.0152262
$203$	−3.03784e11	−0.0618496
$204$	5.07516e12	1.00574
$205$	−4.76216e12	−0.918666
$206$	−1.03320e11	−0.0194050
$207$	−5.27970e12	−0.965545
$208$	−1.46904e12	−0.261629
$209$	2.06438e9	0.000358083 0
$210$	−1.86165e11	−0.0314552
$211$	1.00323e13	1.65138	0.825690	−	0.564125i	$-0.190786\pi$
$211$	1.00323e13	1.65138	0.825690	+	0.564125i	$0.190786\pi$
$212$	−2.48279e12	−0.398192
$213$	−1.02592e13	−1.60335
$214$	−1.36058e12	−0.207228
$215$	−4.87841e12	−0.724214
$216$	3.73418e11	0.0540380
$217$	1.99495e12	0.281451
$218$	8.43506e11	0.116032
$219$	1.21990e13	1.63637
$220$	8.39280e10	0.0109795
$221$	−1.63631e12	−0.208789
$222$	1.65745e12	0.206300
$223$	3.93274e12	0.477550	0.238775	−	0.971075i	$-0.423254\pi$
$223$	3.93274e12	0.477550	0.238775	+	0.971075i	$0.423254\pi$
$224$	−1.10231e12	−0.130599
$225$	−5.41591e12	−0.626134
$226$	−1.93921e12	−0.218791
$227$	−1.60625e13	−1.76877	−0.884383	−	0.466761i	$-0.845421\pi$
$227$	−1.60625e13	−1.76877	−0.884383	+	0.466761i	$0.845421\pi$
$228$	2.05657e11	0.0221055
$229$	7.96324e12	0.835593	0.417796	−	0.908541i	$-0.362803\pi$
$229$	7.96324e12	0.835593	0.417796	+	0.908541i	$0.362803\pi$
$230$	−7.86364e11	−0.0805602
$231$	−9.54246e10	−0.00954541
$232$	−5.34062e11	−0.0521684
$233$	−1.62136e13	−1.54676	−0.773380	−	0.633943i	$-0.781435\pi$
$233$	−1.62136e13	−1.54676	−0.773380	+	0.633943i	$0.781435\pi$
$234$	3.50839e11	0.0326904
$235$	5.53231e12	0.503539
$236$	−1.95340e13	−1.73690
$237$	7.73810e12	0.672230
$238$	−3.96069e11	−0.0336200
$239$	1.00650e13	0.834884	0.417442	−	0.908704i	$-0.362927\pi$
$239$	1.00650e13	0.834884	0.417442	+	0.908704i	$0.362927\pi$
$240$	8.19583e12	0.664403
$241$	−1.54238e13	−1.22207	−0.611036	−	0.791603i	$-0.709247\pi$
$241$	−1.54238e13	−1.22207	−0.611036	+	0.791603i	$0.709247\pi$
$242$	1.77965e12	0.137832
$243$	1.76082e13	1.33316
$244$	1.59434e13	1.18015
$245$	6.39621e12	0.462923
$246$	4.71374e12	0.333597
$247$	−6.63068e10	−0.00458907
$248$	3.50718e12	0.237396
$249$	1.36268e13	0.902192
$250$	−1.90783e12	−0.123557
$251$	−5.71938e12	−0.362363	−0.181181	−	0.983450i	$-0.557992\pi$
$251$	−5.71938e12	−0.362363	−0.181181	+	0.983450i	$0.557992\pi$
$252$	−4.38094e12	−0.271559
$253$	−4.03074e11	−0.0244468
$254$	9.06568e10	0.00538040
$255$	9.12903e12	0.530217
$256$	1.43415e13	0.815221
$257$	−9.83805e12	−0.547365	−0.273682	−	0.961820i	$-0.588242\pi$
$257$	−9.83805e12	−0.547365	−0.273682	+	0.961820i	$0.588242\pi$
$258$	4.82881e12	0.262985
$259$	6.67291e12	0.355768
$260$	−2.69573e12	−0.140709
$261$	−3.19399e12	−0.163234
$262$	−1.81493e12	−0.0908243
$263$	7.10760e12	0.348311	0.174155	−	0.984718i	$-0.444281\pi$
$263$	7.10760e12	0.348311	0.174155	+	0.984718i	$0.444281\pi$
$264$	−1.67759e11	−0.00805129
$265$	−4.46596e12	−0.209924
$266$	−1.60496e10	−0.000738950 0
$267$	6.45053e12	0.290927
$268$	−3.62373e13	−1.60109
$269$	−2.58593e13	−1.11938	−0.559692	−	0.828701i	$-0.689081\pi$
$269$	−2.58593e13	−1.11938	−0.559692	+	0.828701i	$0.689081\pi$
$270$	3.32622e11	0.0141075
$271$	−2.16466e13	−0.899617	−0.449809	−	0.893125i	$-0.648508\pi$
$271$	−2.16466e13	−0.899617	−0.449809	+	0.893125i	$0.648508\pi$
$272$	1.74367e13	0.710127
$273$	3.06499e12	0.122331
$274$	−3.73935e12	−0.146274
$275$	−4.13473e11	−0.0158532
$276$	−4.01549e13	−1.50917
$277$	3.51482e13	1.29498	0.647492	−	0.762072i	$-0.275818\pi$
$277$	3.51482e13	1.29498	0.647492	+	0.762072i	$0.275818\pi$
$278$	−2.09732e12	−0.0757561
$279$	2.09749e13	0.742808
$280$	−1.31765e12	−0.0457543
$281$	−2.46676e13	−0.839929	−0.419965	−	0.907541i	$-0.637957\pi$
$281$	−2.46676e13	−0.839929	−0.419965	+	0.907541i	$0.637957\pi$
$282$	−5.47606e12	−0.182851
$283$	−1.07416e13	−0.351756	−0.175878	−	0.984412i	$-0.556276\pi$
$283$	−1.07416e13	−0.351756	−0.175878	+	0.984412i	$0.556276\pi$
$284$	−3.59582e13	−1.15491
$285$	3.69929e11	0.0116539
$286$	2.67845e10	0.000827695 0
$287$	1.89776e13	0.575294
$288$	−1.15897e13	−0.344678
$289$	−1.48498e13	−0.433294
$290$	−4.75716e11	−0.0136194
$291$	1.26944e13	0.356617
$292$	4.27569e13	1.17869
$293$	5.79404e13	1.56751	0.783754	−	0.621071i	$-0.213302\pi$
$293$	5.79404e13	1.56751	0.783754	+	0.621071i	$0.213302\pi$
$294$	−6.33117e12	−0.168102
$295$	−3.51370e13	−0.915681
$296$	1.17312e13	0.300080
$297$	1.70495e11	0.00428106
$298$	1.09702e12	0.0270411
$299$	1.29466e13	0.313302
$300$	−4.11909e13	−0.978665
$301$	1.94408e13	0.453523
$302$	7.58004e12	0.173633
$303$	−6.68520e12	−0.150376
$304$	7.06575e11	0.0156082
$305$	2.86785e13	0.622166
$306$	−4.16427e12	−0.0887302
$307$	4.55086e13	0.952428	0.476214	−	0.879329i	$-0.342009\pi$
$307$	4.55086e13	0.952428	0.476214	+	0.879329i	$0.342009\pi$
$308$	−3.34459e11	−0.00687566
$309$	−9.49014e12	−0.191647
$310$	3.12402e12	0.0619762
$311$	−2.24000e13	−0.436582	−0.218291	−	0.975884i	$-0.570048\pi$
$311$	−2.24000e13	−0.436582	−0.218291	+	0.975884i	$0.570048\pi$
$312$	5.38836e12	0.103182
$313$	−3.12722e13	−0.588390	−0.294195	−	0.955745i	$-0.595051\pi$
$313$	−3.12722e13	−0.588390	−0.294195	+	0.955745i	$0.595051\pi$
$314$	−6.38831e12	−0.118106
$315$	−7.88030e12	−0.143164
$316$	2.71217e13	0.484215
$317$	7.11792e13	1.24890	0.624449	−	0.781065i	$-0.285323\pi$
$317$	7.11792e13	1.24890	0.624449	+	0.781065i	$0.285323\pi$
$318$	4.42054e12	0.0762301
$319$	−2.43842e11	−0.00413295
$320$	2.75567e13	0.459095
$321$	−1.24973e14	−2.04662
$322$	3.13372e12	0.0504490
$323$	7.87027e11	0.0124559
$324$	7.08737e13	1.10278
$325$	1.32806e13	0.203169
$326$	−4.99825e12	−0.0751832
$327$	7.74780e13	1.14595
$328$	3.33631e13	0.485245
$329$	−2.20467e13	−0.315330
$330$	−1.49432e11	−0.00210192
$331$	−6.50834e13	−0.900360	−0.450180	−	0.892938i	$-0.648640\pi$
$331$	−6.50834e13	−0.900360	−0.450180	+	0.892938i	$0.648640\pi$
$332$	4.77615e13	0.649858
$333$	7.01591e13	0.938946
$334$	−1.80174e13	−0.237185
$335$	−6.51825e13	−0.844082
$336$	−3.26610e13	−0.416067
$337$	2.07245e13	0.259728	0.129864	−	0.991532i	$-0.458546\pi$
$337$	2.07245e13	0.259728	0.129864	+	0.991532i	$0.458546\pi$
$338$	−8.60305e11	−0.0106074
$339$	−1.78121e14	−2.16081
$340$	3.19968e13	0.381921
$341$	1.60131e12	0.0188073
$342$	−1.68746e11	−0.00195024
$343$	−5.39656e13	−0.613761
$344$	3.41776e13	0.382534
$345$	−7.22294e13	−0.795626
$346$	−1.62918e12	−0.0176624
$347$	3.33365e13	0.355720	0.177860	−	0.984056i	$-0.443083\pi$
$347$	3.33365e13	0.355720	0.177860	+	0.984056i	$0.443083\pi$
$348$	−2.42920e13	−0.255139
$349$	−1.83167e14	−1.89369	−0.946843	−	0.321695i	$-0.895748\pi$
$349$	−1.83167e14	−1.89369	−0.946843	+	0.321695i	$0.895748\pi$
$350$	3.21456e12	0.0327151
$351$	−5.47623e12	−0.0548646
$352$	−8.84806e11	−0.00872697
$353$	−7.59854e13	−0.737852	−0.368926	−	0.929459i	$-0.620274\pi$
$353$	−7.59854e13	−0.737852	−0.368926	+	0.929459i	$0.620274\pi$
$354$	3.47798e13	0.332513
$355$	−6.46804e13	−0.608859
$356$	2.26088e13	0.209558
$357$	−3.63799e13	−0.332036
$358$	−5.73406e12	−0.0515354
$359$	2.14518e14	1.89865	0.949325	−	0.314297i	$-0.101769\pi$
$359$	2.14518e14	1.89865	0.949325	+	0.314297i	$0.101769\pi$
$360$	−1.38538e13	−0.120755
$361$	−1.16458e14	−0.999726
$362$	2.05763e13	0.173969
$363$	1.63465e14	1.36125
$364$	1.07427e13	0.0881160
$365$	7.69097e13	0.621399
$366$	−2.83868e13	−0.225929
$367$	1.68049e14	1.31756	0.658782	−	0.752334i	$-0.271072\pi$
$367$	1.68049e14	1.31756	0.658782	+	0.752334i	$0.271072\pi$
$368$	−1.37960e14	−1.06559
$369$	1.99530e14	1.51832
$370$	1.04496e13	0.0783409
$371$	1.77972e13	0.131460
$372$	1.59525e14	1.16103
$373$	1.35311e14	0.970366	0.485183	−	0.874413i	$-0.338753\pi$
$373$	1.35311e14	0.970366	0.485183	+	0.874413i	$0.338753\pi$
$374$	−3.17918e11	−0.00224657
$375$	−1.75238e14	−1.22027
$376$	−3.87588e13	−0.265972
$377$	7.83210e12	0.0529665
$378$	−1.32552e12	−0.00883451
$379$	−1.33936e14	−0.879792	−0.439896	−	0.898049i	$-0.644985\pi$
$379$	−1.33936e14	−0.879792	−0.439896	+	0.898049i	$0.644985\pi$
$380$	1.29658e12	0.00839442
$381$	8.32704e12	0.0531378
$382$	−2.11193e13	−0.132840
$383$	3.83252e13	0.237624	0.118812	−	0.992917i	$-0.462091\pi$
$383$	3.83252e13	0.237624	0.118812	+	0.992917i	$0.462091\pi$
$384$	−1.17131e14	−0.715897
$385$	−6.01614e11	−0.00362480
$386$	−2.70015e13	−0.160383
$387$	2.04401e14	1.19694
$388$	4.44935e13	0.256875
$389$	2.50937e14	1.42837	0.714187	−	0.699955i	$-0.246797\pi$
$389$	2.50937e14	1.42837	0.714187	+	0.699955i	$0.246797\pi$
$390$	4.79968e12	0.0269375
$391$	−1.53669e14	−0.850381
$392$	−4.48111e13	−0.244519
$393$	−1.66705e14	−0.896996
$394$	−9.55328e12	−0.0506901
$395$	4.87856e13	0.255275
$396$	−3.51651e12	−0.0181463
$397$	−2.47041e13	−0.125725	−0.0628625	−	0.998022i	$-0.520023\pi$
$397$	−2.47041e13	−0.125725	−0.0628625	+	0.998022i	$0.520023\pi$
$398$	−1.05782e13	−0.0530952
$399$	−1.47419e12	−0.00729799
$400$	−1.41519e14	−0.691013
$401$	−4.25752e13	−0.205051	−0.102526	−	0.994730i	$-0.532692\pi$
$401$	−4.25752e13	−0.205051	−0.102526	+	0.994730i	$0.532692\pi$
$402$	6.45197e13	0.306513
$403$	−5.14333e13	−0.241028
$404$	−2.34313e13	−0.108318
$405$	1.27485e14	0.581377
$406$	1.89576e12	0.00852886
$407$	5.35623e12	0.0237733
$408$	−6.39569e13	−0.280064
$409$	3.74827e14	1.61939	0.809697	−	0.586848i	$-0.199631\pi$
$409$	3.74827e14	1.61939	0.809697	+	0.586848i	$0.199631\pi$
$410$	2.97182e13	0.126681
$411$	−3.43468e14	−1.44463
$412$	−3.32625e13	−0.138045
$413$	1.40024e14	0.573425
$414$	3.29480e13	0.133146
$415$	8.59119e13	0.342601
$416$	2.84196e13	0.111842
$417$	−1.92644e14	−0.748180
$418$	−1.28827e10	−4.93786e−5 0
$419$	−1.75893e14	−0.665381	−0.332691	−	0.943036i	$-0.607956\pi$
$419$	−1.75893e14	−0.665381	−0.332691	+	0.943036i	$0.607956\pi$
$420$	−5.99338e13	−0.223770
$421$	−1.84327e14	−0.679262	−0.339631	−	0.940559i	$-0.610302\pi$
$421$	−1.84327e14	−0.679262	−0.339631	+	0.940559i	$0.610302\pi$
$422$	−6.26065e13	−0.227720
$423$	−2.31799e14	−0.832223
$424$	3.12880e13	0.110883
$425$	−1.57633e14	−0.551453
$426$	6.40227e13	0.221096
$427$	−1.14286e14	−0.389618
$428$	−4.38024e14	−1.47420
$429$	2.46022e12	0.00817445
$430$	3.04437e13	0.0998668
$431$	−3.82824e14	−1.23986	−0.619932	−	0.784655i	$-0.712840\pi$
$431$	−3.82824e14	−1.23986	−0.619932	+	0.784655i	$0.712840\pi$
$432$	5.83554e13	0.186604
$433$	5.04919e14	1.59418	0.797092	−	0.603858i	$-0.206371\pi$
$433$	5.04919e14	1.59418	0.797092	+	0.603858i	$0.206371\pi$
$434$	−1.24495e13	−0.0388112
$435$	−4.36956e13	−0.134508
$436$	2.71557e14	0.825439
$437$	−6.22700e12	−0.0186909
$438$	−7.61277e13	−0.225650
$439$	2.53930e14	0.743291	0.371645	−	0.928375i	$-0.378794\pi$
$439$	2.53930e14	0.743291	0.371645	+	0.928375i	$0.378794\pi$
$440$	−1.05766e12	−0.00305742
$441$	−2.67995e14	−0.765095
$442$	1.02114e13	0.0287913
$443$	6.33332e14	1.76364	0.881822	−	0.471582i	$-0.156317\pi$
$443$	6.33332e14	1.76364	0.881822	+	0.471582i	$0.156317\pi$
$444$	5.33597e14	1.46760
$445$	4.06681e13	0.110477
$446$	−2.45422e13	−0.0658525
$447$	1.00764e14	0.267062
$448$	−1.09815e14	−0.287498
$449$	7.39380e14	1.91211	0.956055	−	0.293187i	$-0.0947160\pi$
$449$	7.39380e14	1.91211	0.956055	+	0.293187i	$0.0947160\pi$
$450$	3.37980e13	0.0863419
$451$	1.52330e13	0.0384426
$452$	−6.24307e14	−1.55646
$453$	6.96244e14	1.71483
$454$	1.00238e14	0.243907
$455$	1.93236e13	0.0464542
$456$	−2.59168e12	−0.00615565
$457$	2.97334e14	0.697759	0.348879	−	0.937168i	$-0.386562\pi$
$457$	2.97334e14	0.697759	0.348879	+	0.937168i	$0.386562\pi$
$458$	−4.96946e13	−0.115226
$459$	6.49999e13	0.148917
$460$	−2.53161e14	−0.573098
$461$	2.70662e13	0.0605442	0.0302721	−	0.999542i	$-0.490363\pi$
$461$	2.70662e13	0.0605442	0.0302721	+	0.999542i	$0.490363\pi$
$462$	5.95497e11	0.00131628
$463$	−7.66302e14	−1.67380	−0.836902	−	0.547353i	$-0.815636\pi$
$463$	−7.66302e14	−1.67380	−0.836902	+	0.547353i	$0.815636\pi$
$464$	−8.34600e13	−0.180148
$465$	2.86949e14	0.612087
$466$	1.01181e14	0.213293
$467$	−8.24785e14	−1.71830	−0.859148	−	0.511728i	$-0.829006\pi$
$467$	−8.24785e14	−1.71830	−0.859148	+	0.511728i	$0.829006\pi$
$468$	1.12949e14	0.232557
$469$	2.59757e14	0.528587
$470$	−3.45244e13	−0.0694365
$471$	−5.86781e14	−1.16644
$472$	2.46166e14	0.483668
$473$	1.56048e13	0.0303056
$474$	−4.82896e13	−0.0926984
$475$	−6.38765e12	−0.0121207
$476$	−1.27510e14	−0.239169
$477$	1.87120e14	0.346951
$478$	−6.28107e13	−0.115128
$479$	−3.40423e14	−0.616841	−0.308421	−	0.951250i	$-0.599800\pi$
$479$	−3.40423e14	−0.616841	−0.308421	+	0.951250i	$0.599800\pi$
$480$	−1.58554e14	−0.284021
$481$	−1.72040e14	−0.304671
$482$	9.62520e13	0.168520
$483$	2.87840e14	0.498243
$484$	5.72939e14	0.980525
$485$	8.00334e13	0.135423
$486$	−1.09884e14	−0.183838
$487$	−7.74101e14	−1.28053	−0.640263	−	0.768156i	$-0.721175\pi$
$487$	−7.74101e14	−1.28053	−0.640263	+	0.768156i	$0.721175\pi$
$488$	−2.00918e14	−0.328632
$489$	−4.59101e14	−0.742522
$490$	−3.99155e13	−0.0638356
$491$	9.84879e13	0.155752	0.0778762	−	0.996963i	$-0.475186\pi$
$491$	9.84879e13	0.155752	0.0778762	+	0.996963i	$0.475186\pi$
$492$	1.51753e15	2.37318
$493$	−9.29629e13	−0.143765
$494$	4.13787e11	0.000632818 0
$495$	−6.32538e12	−0.00956661
$496$	5.48081e14	0.819776
$497$	2.57756e14	0.381284
$498$	−8.50383e13	−0.124409
$499$	−1.67726e14	−0.242687	−0.121344	−	0.992611i	$-0.538720\pi$
$499$	−1.67726e14	−0.242687	−0.121344	+	0.992611i	$0.538720\pi$
$500$	−6.14203e14	−0.878975
$501$	−1.65494e15	−2.34248
$502$	3.56918e13	0.0499687
$503$	3.93736e14	0.545232	0.272616	−	0.962123i	$-0.412111\pi$
$503$	3.93736e14	0.545232	0.272616	+	0.962123i	$0.412111\pi$
$504$	5.52085e13	0.0756202
$505$	−4.21475e13	−0.0571044
$506$	2.51538e12	0.00337114
$507$	−7.90211e13	−0.104761
$508$	2.91859e13	0.0382757
$509$	−1.26888e15	−1.64617	−0.823083	−	0.567920i	$-0.807748\pi$
$509$	−1.26888e15	−1.64617	−0.823083	+	0.567920i	$0.807748\pi$
$510$	−5.69697e13	−0.0731152
$511$	−3.06491e14	−0.389137
$512$	−5.07995e14	−0.638080
$513$	2.63394e12	0.00327311
$514$	6.13943e13	0.0754798
$515$	−5.98316e13	−0.0727764
$516$	1.55458e15	1.87085
$517$	−1.76965e13	−0.0210712
$518$	−4.16423e13	−0.0490592
$519$	−1.49644e14	−0.174437
$520$	3.39714e13	0.0391828
$521$	1.20140e15	1.37114	0.685568	−	0.728009i	$-0.259554\pi$
$521$	1.20140e15	1.37114	0.685568	+	0.728009i	$0.259554\pi$
$522$	1.99321e13	0.0225095
$523$	2.66330e14	0.297620	0.148810	−	0.988866i	$-0.452456\pi$
$523$	2.66330e14	0.297620	0.148810	+	0.988866i	$0.452456\pi$
$524$	−5.84295e14	−0.646116
$525$	2.95265e14	0.323099
$526$	−4.43550e13	−0.0480309
$527$	6.10486e14	0.654210
$528$	−2.62164e13	−0.0278027
$529$	2.63026e14	0.276053
$530$	2.78698e13	0.0289478
$531$	1.47221e15	1.51339
$532$	−5.16698e12	−0.00525682
$533$	−4.89275e14	−0.492667
$534$	−4.02545e13	−0.0401179
$535$	−7.87902e14	−0.777189
$536$	4.56661e14	0.445849
$537$	−5.26687e14	−0.508972
$538$	1.61375e14	0.154359
$539$	−2.04599e13	−0.0193716
$540$	1.07084e14	0.100359
$541$	7.14248e14	0.662619	0.331310	−	0.943522i	$-0.392510\pi$
$541$	7.14248e14	0.662619	0.331310	+	0.943522i	$0.392510\pi$
$542$	1.35085e14	0.124054
$543$	1.88998e15	1.71814
$544$	−3.37325e14	−0.303567
$545$	4.88468e14	0.435166
$546$	−1.91271e13	−0.0168690
$547$	1.69672e15	1.48142	0.740711	−	0.671823i	$-0.234489\pi$
$547$	1.69672e15	1.48142	0.740711	+	0.671823i	$0.234489\pi$
$548$	−1.20384e15	−1.04058
$549$	−1.20160e15	−1.02828
$550$	2.58028e12	0.00218611
$551$	−3.76706e12	−0.00315987
$552$	5.06031e14	0.420254
$553$	−1.94414e14	−0.159860
$554$	−2.19342e14	−0.178574
$555$	9.59817e14	0.773708
$556$	−6.75207e14	−0.538922
$557$	−8.05244e14	−0.636391	−0.318195	−	0.948025i	$-0.603077\pi$
$557$	−8.05244e14	−0.636391	−0.318195	+	0.948025i	$0.603077\pi$
$558$	−1.30894e14	−0.102431
$559$	−5.01220e14	−0.388386
$560$	−2.05915e14	−0.157999
$561$	−2.92015e13	−0.0221875
$562$	1.53938e14	0.115824
$563$	8.27301e14	0.616407	0.308203	−	0.951321i	$-0.400272\pi$
$563$	8.27301e14	0.616407	0.308203	+	0.951321i	$0.400272\pi$
$564$	−1.76295e15	−1.30079
$565$	−1.12298e15	−0.820553
$566$	6.70326e13	0.0485060
$567$	−5.08039e14	−0.364074
$568$	4.53144e14	0.321603
$569$	5.99743e14	0.421548	0.210774	−	0.977535i	$-0.432402\pi$
$569$	5.99743e14	0.421548	0.210774	+	0.977535i	$0.432402\pi$
$570$	−2.30854e12	−0.00160703
$571$	5.36156e14	0.369652	0.184826	−	0.982771i	$-0.440828\pi$
$571$	5.36156e14	0.369652	0.184826	+	0.982771i	$0.440828\pi$
$572$	8.62296e12	0.00588814
$573$	−1.93985e15	−1.31195
$574$	−1.18429e14	−0.0793312
$575$	1.24720e15	0.827492
$576$	−1.15460e15	−0.758767
$577$	−8.84192e14	−0.575545	−0.287773	−	0.957699i	$-0.592915\pi$
$577$	−8.84192e14	−0.575545	−0.287773	+	0.957699i	$0.592915\pi$
$578$	9.26701e13	0.0597498
$579$	−2.48015e15	−1.58397
$580$	−1.53151e14	−0.0968873
$581$	−3.42365e14	−0.214546
$582$	−7.92196e13	−0.0491764
$583$	1.42855e13	0.00878451
$584$	−5.38821e14	−0.328226
$585$	2.03168e14	0.122602
$586$	−3.61577e14	−0.216154
$587$	2.40239e15	1.42277	0.711385	−	0.702803i	$-0.248068\pi$
$587$	2.40239e15	1.42277	0.711385	+	0.702803i	$0.248068\pi$
$588$	−2.03825e15	−1.19586
$589$	2.47383e13	0.0143792
$590$	2.19273e14	0.126269
$591$	−8.77491e14	−0.500624
$592$	1.83328e15	1.03624
$593$	1.08816e15	0.609384	0.304692	−	0.952451i	$-0.401446\pi$
$593$	1.08816e15	0.609384	0.304692	+	0.952451i	$0.401446\pi$
$594$	−1.06397e12	−0.000590345 0
$595$	−2.29360e14	−0.126088
$596$	3.53172e14	0.192368
$597$	−9.71633e14	−0.524377
$598$	−8.07929e13	−0.0432033
$599$	1.01546e15	0.538039	0.269019	−	0.963135i	$-0.413300\pi$
$599$	1.01546e15	0.538039	0.269019	+	0.963135i	$0.413300\pi$
$600$	5.19086e14	0.272525
$601$	4.73017e14	0.246075	0.123038	−	0.992402i	$-0.460736\pi$
$601$	4.73017e14	0.246075	0.123038	+	0.992402i	$0.460736\pi$
$602$	−1.21320e14	−0.0625394
$603$	2.73109e15	1.39505
$604$	2.44031e15	1.23521
$605$	1.03058e15	0.516926
$606$	4.17190e13	0.0207364
$607$	−2.98775e15	−1.47166	−0.735829	−	0.677167i	$-0.763207\pi$
$607$	−2.98775e15	−1.47166	−0.735829	+	0.677167i	$0.763207\pi$
$608$	−1.36692e13	−0.00667225
$609$	1.74130e14	0.0842325
$610$	−1.78968e14	−0.0857947
$611$	5.68403e14	0.270041
$612$	−1.34064e15	−0.631218
$613$	−1.04143e14	−0.0485956	−0.0242978	−	0.999705i	$-0.507735\pi$
$613$	−1.04143e14	−0.0485956	−0.0242978	+	0.999705i	$0.507735\pi$
$614$	−2.83996e14	−0.131337
$615$	2.72969e15	1.25112
$616$	4.21484e12	0.00191464
$617$	−1.84676e14	−0.0831462	−0.0415731	−	0.999135i	$-0.513237\pi$
$617$	−1.84676e14	−0.0831462	−0.0415731	+	0.999135i	$0.513237\pi$
$618$	5.92232e13	0.0264274
$619$	−2.82249e15	−1.24834	−0.624171	−	0.781287i	$-0.714563\pi$
$619$	−2.82249e15	−1.24834	−0.624171	+	0.781287i	$0.714563\pi$
$620$	1.00574e15	0.440892
$621$	−5.14283e14	−0.223459
$622$	1.39787e14	0.0602033
$623$	−1.62065e14	−0.0691840
$624$	8.42060e14	0.356310
$625$	6.41696e14	0.269147
$626$	1.95154e14	0.0811370
$627$	−1.18331e12	−0.000487671 0
$628$	−2.05664e15	−0.840197
$629$	2.04202e15	0.826954
$630$	4.91770e13	0.0197419
$631$	3.87072e15	1.54039	0.770194	−	0.637809i	$-0.220159\pi$
$631$	3.87072e15	1.54039	0.770194	+	0.637809i	$0.220159\pi$
$632$	−3.41786e14	−0.134838
$633$	−5.75055e15	−2.24900
$634$	−4.44193e14	−0.172219
$635$	5.24987e13	0.0201787
$636$	1.42314e15	0.542294
$637$	6.57162e14	0.248259
$638$	1.52170e12	0.000569921 0
$639$	2.71005e15	1.00629
$640$	−7.38465e14	−0.271857
$641$	3.82598e15	1.39644	0.698222	−	0.715881i	$-0.253975\pi$
$641$	3.82598e15	1.39644	0.698222	+	0.715881i	$0.253975\pi$
$642$	7.79891e14	0.282222
$643$	−8.89867e14	−0.319275	−0.159637	−	0.987176i	$-0.551033\pi$
$643$	−8.89867e14	−0.319275	−0.159637	+	0.987176i	$0.551033\pi$
$644$	1.00887e15	0.358890
$645$	2.79633e15	0.986301
$646$	−4.91144e12	−0.00171763
$647$	−4.51101e15	−1.56423	−0.782115	−	0.623135i	$-0.785859\pi$
$647$	−4.51101e15	−1.56423	−0.782115	+	0.623135i	$0.785859\pi$
$648$	−8.93148e14	−0.307087
$649$	1.12395e14	0.0383177
$650$	−8.28772e13	−0.0280164
$651$	−1.14351e15	−0.383306
$652$	−1.60913e15	−0.534846
$653$	2.98348e15	0.983333	0.491667	−	0.870784i	$-0.336388\pi$
$653$	2.98348e15	0.983333	0.491667	+	0.870784i	$0.336388\pi$
$654$	−4.83501e14	−0.158023
$655$	−1.05101e15	−0.340628
$656$	5.21379e15	1.67565
$657$	−3.22245e15	−1.02701
$658$	1.37582e14	0.0434830
$659$	−8.77436e14	−0.275008	−0.137504	−	0.990501i	$-0.543908\pi$
$659$	−8.77436e14	−0.275008	−0.137504	+	0.990501i	$0.543908\pi$
$660$	−4.81079e13	−0.0149529
$661$	−5.50906e15	−1.69812	−0.849062	−	0.528293i	$-0.822832\pi$
$661$	−5.50906e15	−1.69812	−0.849062	+	0.528293i	$0.822832\pi$
$662$	4.06153e14	0.124157
$663$	9.37938e14	0.284348
$664$	−6.01889e14	−0.180964
$665$	−9.29420e12	−0.00277136
$666$	−4.37827e14	−0.129478
$667$	7.35528e14	0.215728
$668$	−5.80050e15	−1.68731
$669$	−2.25426e15	−0.650371
$670$	4.06771e14	0.116396
$671$	−9.17352e13	−0.0260353
$672$	6.31850e14	0.177862
$673$	−4.53240e15	−1.26545	−0.632725	−	0.774376i	$-0.718064\pi$
$673$	−4.53240e15	−1.26545	−0.632725	+	0.774376i	$0.718064\pi$
$674$	−1.29331e14	−0.0358157
$675$	−5.27551e14	−0.144908
$676$	−2.76965e14	−0.0754603
$677$	−6.61896e15	−1.78876	−0.894380	−	0.447309i	$-0.852382\pi$
$677$	−6.61896e15	−1.78876	−0.894380	+	0.447309i	$0.852382\pi$
$678$	1.11156e15	0.297969
$679$	−3.18939e14	−0.0848055
$680$	−4.03223e14	−0.106352
$681$	9.20708e15	2.40887
$682$	−9.99296e12	−0.00259346
$683$	−1.23373e15	−0.317619	−0.158809	−	0.987309i	$-0.550766\pi$
$683$	−1.23373e15	−0.317619	−0.158809	+	0.987309i	$0.550766\pi$
$684$	−5.43257e13	−0.0138738
$685$	−2.16543e15	−0.548587
$686$	3.36772e14	0.0846356
$687$	−4.56456e15	−1.13799
$688$	5.34107e15	1.32097
$689$	−4.58843e14	−0.112579
$690$	4.50747e14	0.109714
$691$	−3.92078e14	−0.0946767	−0.0473383	−	0.998879i	$-0.515074\pi$
$691$	−3.92078e14	−0.0946767	−0.0473383	+	0.998879i	$0.515074\pi$
$692$	−5.24495e14	−0.125649
$693$	2.52071e13	0.00599087
$694$	−2.08036e14	−0.0490526
$695$	−1.21454e15	−0.284116
$696$	3.06127e14	0.0710478
$697$	5.80744e15	1.33722
$698$	1.14305e15	0.261133
$699$	9.29372e15	2.10652
$700$	1.03489e15	0.232732
$701$	5.03380e15	1.12317	0.561587	−	0.827418i	$-0.310191\pi$
$701$	5.03380e15	1.12317	0.561587	+	0.827418i	$0.310191\pi$
$702$	3.41744e13	0.00756565
$703$	8.27472e13	0.0181760
$704$	−8.81470e13	−0.0192113
$705$	−3.17115e15	−0.685766
$706$	4.74186e14	0.101747
$707$	1.67961e14	0.0357603
$708$	1.11969e16	2.36547
$709$	−1.87543e14	−0.0393139	−0.0196570	−	0.999807i	$-0.506257\pi$
$709$	−1.87543e14	−0.0393139	−0.0196570	+	0.999807i	$0.506257\pi$
$710$	4.03638e14	0.0839597
$711$	−2.04407e15	−0.421904
$712$	−2.84916e14	−0.0583548
$713$	−4.83020e15	−0.981687
$714$	2.27028e14	0.0457868
$715$	1.55107e13	0.00310419
$716$	−1.84602e15	−0.366618
$717$	−5.76931e15	−1.13702
$718$	−1.33870e15	−0.261818
$719$	−5.31583e15	−1.03172	−0.515860	−	0.856673i	$-0.672528\pi$
$719$	−5.31583e15	−1.03172	−0.515860	+	0.856673i	$0.672528\pi$
$720$	−2.16499e15	−0.416991
$721$	2.38433e14	0.0455746
$722$	7.26758e14	0.137859
$723$	8.84097e15	1.66433
$724$	6.62432e15	1.23760
$725$	7.54503e14	0.139895
$726$	−1.02010e15	−0.187712
$727$	−2.60429e15	−0.475609	−0.237804	−	0.971313i	$-0.576428\pi$
$727$	−2.60429e15	−0.475609	−0.237804	+	0.971313i	$0.576428\pi$
$728$	−1.35379e14	−0.0245374
$729$	−3.84388e15	−0.691463
$730$	−4.79955e14	−0.0856889
$731$	5.94921e15	1.05418
$732$	−9.13882e15	−1.60723
$733$	6.22703e15	1.08695	0.543474	−	0.839426i	$-0.317109\pi$
$733$	6.22703e15	1.08695	0.543474	+	0.839426i	$0.317109\pi$
$734$	−1.04871e15	−0.181688
$735$	−3.66633e15	−0.630451
$736$	2.66894e15	0.455523
$737$	2.08503e14	0.0353216
$738$	−1.24517e15	−0.209372
$739$	6.60610e14	0.110256	0.0551278	−	0.998479i	$-0.482443\pi$
$739$	6.60610e14	0.110256	0.0551278	+	0.998479i	$0.482443\pi$
$740$	3.36412e15	0.557310
$741$	3.80073e13	0.00624982
$742$	−1.11063e14	−0.0181279
$743$	−3.75701e15	−0.608700	−0.304350	−	0.952560i	$-0.598439\pi$
$743$	−3.75701e15	−0.608700	−0.304350	+	0.952560i	$0.598439\pi$
$744$	−2.01033e15	−0.323308
$745$	6.35275e14	0.101415
$746$	−8.44410e14	−0.133810
$747$	−3.59963e15	−0.566232
$748$	−1.02350e14	−0.0159819
$749$	3.13985e15	0.486697
$750$	1.09357e15	0.168272
$751$	5.10177e15	0.779294	0.389647	−	0.920964i	$-0.372597\pi$
$751$	5.10177e15	0.779294	0.389647	+	0.920964i	$0.372597\pi$
$752$	−6.05698e15	−0.918456
$753$	3.27837e15	0.493499
$754$	−4.88762e13	−0.00730391
$755$	4.38954e15	0.651195
$756$	−4.26737e14	−0.0628478
$757$	1.00960e16	1.47613	0.738063	−	0.674732i	$-0.235741\pi$
$757$	1.00960e16	1.47613	0.738063	+	0.674732i	$0.235741\pi$
$758$	8.35824e14	0.121320
$759$	2.31044e14	0.0332939
$760$	−1.63395e13	−0.00233757
$761$	−5.02354e15	−0.713500	−0.356750	−	0.934200i	$-0.616115\pi$
$761$	−5.02354e15	−0.713500	−0.356750	+	0.934200i	$0.616115\pi$
$762$	−5.19649e13	−0.00732753
$763$	−1.94658e15	−0.272513
$764$	−6.79911e15	−0.945014
$765$	−2.41150e15	−0.332774
$766$	−2.39168e14	−0.0327676
$767$	−3.61006e15	−0.491067
$768$	−8.22062e15	−1.11024
$769$	2.44929e15	0.328432	0.164216	−	0.986424i	$-0.447491\pi$
$769$	2.44929e15	0.328432	0.164216	+	0.986424i	$0.447491\pi$
$770$	3.75437e12	0.000499848 0
$771$	5.63921e15	0.745451
$772$	−8.69282e15	−1.14095
$773$	−4.47498e15	−0.583182	−0.291591	−	0.956543i	$-0.594185\pi$
$773$	−4.47498e15	−0.583182	−0.291591	+	0.956543i	$0.594185\pi$
$774$	−1.27557e15	−0.165054
$775$	−4.95481e15	−0.636602
$776$	−5.60705e14	−0.0715311
$777$	−3.82494e15	−0.484517
$778$	−1.56597e15	−0.196968
$779$	2.35330e14	0.0293915
$780$	1.54520e15	0.191631
$781$	2.06897e14	0.0254784
$782$	9.58969e14	0.117265
$783$	−3.11119e14	−0.0377778
$784$	−7.00281e15	−0.844372
$785$	−3.69942e15	−0.442946
$786$	1.04032e15	0.123693
$787$	4.34376e15	0.512867	0.256433	−	0.966562i	$-0.417453\pi$
$787$	4.34376e15	0.512867	0.256433	+	0.966562i	$0.417453\pi$
$788$	−3.07557e15	−0.360605
$789$	−4.07411e15	−0.474361
$790$	−3.04446e14	−0.0352016
$791$	4.47517e15	0.513853
$792$	4.43149e13	0.00505314
$793$	2.94649e15	0.333659
$794$	1.54166e14	0.0173371
$795$	2.55990e15	0.285894
$796$	−3.40553e15	−0.377714
$797$	1.05653e16	1.16376	0.581879	−	0.813275i	$-0.302318\pi$
$797$	1.05653e16	1.16376	0.581879	+	0.813275i	$0.302318\pi$
$798$	9.19969e12	0.00100637
$799$	−6.74664e15	−0.732960
$800$	2.73779e15	0.295397
$801$	−1.70396e15	−0.182591
$802$	2.65690e14	0.0282759
$803$	−2.46015e14	−0.0260032
$804$	2.07714e16	2.18050
$805$	1.81471e15	0.189204
$806$	3.20969e14	0.0332369
$807$	1.48227e16	1.52448
$808$	2.95281e14	0.0301629
$809$	−4.64538e15	−0.471308	−0.235654	−	0.971837i	$-0.575723\pi$
$809$	−4.64538e15	−0.471308	−0.235654	+	0.971837i	$0.575723\pi$
$810$	−7.95572e14	−0.0801700
$811$	1.48481e16	1.48613	0.743064	−	0.669220i	$-0.233372\pi$
$811$	1.48481e16	1.48613	0.743064	+	0.669220i	$0.233372\pi$
$812$	6.10320e14	0.0606735
$813$	1.24079e16	1.22518
$814$	−3.34255e13	−0.00327827
$815$	−2.89445e15	−0.281967
$816$	−9.99480e15	−0.967115
$817$	2.41075e14	0.0231703
$818$	−2.33911e15	−0.223309
$819$	−8.09641e14	−0.0767769
$820$	9.56744e15	0.901197
$821$	1.16458e16	1.08963	0.544817	−	0.838555i	$-0.316599\pi$
$821$	1.16458e16	1.08963	0.544817	+	0.838555i	$0.316599\pi$
$822$	2.14341e15	0.199210
$823$	4.25435e15	0.392766	0.196383	−	0.980527i	$-0.437080\pi$
$823$	4.25435e15	0.392766	0.196383	+	0.980527i	$0.437080\pi$
$824$	4.19173e14	0.0384409
$825$	2.37004e14	0.0215903
$826$	−8.73818e14	−0.0790734
$827$	−1.20663e16	−1.08466	−0.542331	−	0.840165i	$-0.682458\pi$
$827$	−1.20663e16	−1.08466	−0.542331	+	0.840165i	$0.682458\pi$
$828$	1.06072e16	0.947185
$829$	8.05530e15	0.714549	0.357274	−	0.933999i	$-0.383706\pi$
$829$	8.05530e15	0.714549	0.357274	+	0.933999i	$0.383706\pi$
$830$	−5.36133e14	−0.0472436
$831$	−2.01471e16	−1.76363
$832$	2.83124e15	0.246206
$833$	−7.80016e15	−0.673839
$834$	1.20219e15	0.103172
$835$	−1.04338e16	−0.889539
$836$	−4.14745e12	−0.000351274 0
$837$	2.04311e15	0.171911
$838$	1.09766e15	0.0917539
$839$	−1.88926e16	−1.56892	−0.784462	−	0.620177i	$-0.787061\pi$
$839$	−1.88926e16	−1.56892	−0.784462	+	0.620177i	$0.787061\pi$
$840$	7.55284e14	0.0623123
$841$	−1.17555e16	−0.963529
$842$	1.15029e15	0.0936681
$843$	1.41396e16	1.14389
$844$	−2.01554e16	−1.61998
$845$	−4.98196e14	−0.0397822
$846$	1.44654e15	0.114761
$847$	−4.10695e15	−0.323714
$848$	4.88949e15	0.382901
$849$	6.15710e15	0.479054
$850$	9.83709e14	0.0760436
$851$	−1.61566e16	−1.24090
$852$	2.06114e16	1.57286
$853$	−1.37629e16	−1.04349	−0.521746	−	0.853101i	$-0.674719\pi$
$853$	−1.37629e16	−1.04349	−0.521746	+	0.853101i	$0.674719\pi$
$854$	7.13200e14	0.0537270
$855$	−9.77193e13	−0.00731420
$856$	5.51995e15	0.410516
$857$	9.59561e15	0.709052	0.354526	−	0.935046i	$-0.384642\pi$
$857$	9.59561e15	0.709052	0.354526	+	0.935046i	$0.384642\pi$
$858$	−1.53530e13	−0.00112723
$859$	6.17707e15	0.450630	0.225315	−	0.974286i	$-0.427659\pi$
$859$	6.17707e15	0.450630	0.225315	+	0.974286i	$0.427659\pi$
$860$	9.80101e15	0.710443
$861$	−1.08780e16	−0.783488
$862$	2.38901e15	0.170973
$863$	−1.22575e16	−0.871652	−0.435826	−	0.900031i	$-0.643544\pi$
$863$	−1.22575e16	−0.871652	−0.435826	+	0.900031i	$0.643544\pi$
$864$	−1.12893e15	−0.0797701
$865$	−9.43445e14	−0.0662411
$866$	−3.15095e15	−0.219833
$867$	8.51197e15	0.590099
$868$	−4.00796e15	−0.276099
$869$	−1.56053e14	−0.0106823
$870$	2.72682e14	0.0185482
$871$	−6.69701e15	−0.452669
$872$	−3.42215e15	−0.229857
$873$	−3.35333e15	−0.223820
$874$	3.88596e13	0.00257742
$875$	4.40274e15	0.290188
$876$	−2.45084e16	−1.60525
$877$	2.60797e16	1.69748	0.848740	−	0.528811i	$-0.177362\pi$
$877$	2.60797e16	1.69748	0.848740	+	0.528811i	$0.177362\pi$
$878$	−1.58465e15	−0.102497
$879$	−3.32117e16	−2.13478
$880$	−1.65284e14	−0.0105579
$881$	2.06261e16	1.30933	0.654666	−	0.755918i	$-0.272809\pi$
$881$	2.06261e16	1.30933	0.654666	+	0.755918i	$0.272809\pi$
$882$	1.67242e15	0.105504
$883$	−1.04889e16	−0.657575	−0.328788	−	0.944404i	$-0.606640\pi$
$883$	−1.04889e16	−0.657575	−0.328788	+	0.944404i	$0.606640\pi$
$884$	3.28743e15	0.204819
$885$	2.01407e16	1.24706
$886$	−3.95231e15	−0.243201
$887$	−1.14953e16	−0.702978	−0.351489	−	0.936192i	$-0.614325\pi$
$887$	−1.14953e16	−0.702978	−0.351489	+	0.936192i	$0.614325\pi$
$888$	−6.72437e15	−0.408677
$889$	−2.09211e14	−0.0126365
$890$	−2.53789e14	−0.0152345
$891$	−4.07794e14	−0.0243284
$892$	−7.90110e15	−0.468469
$893$	−2.73389e14	−0.0161101
$894$	−6.28815e14	−0.0368270
$895$	−3.32055e15	−0.193279
$896$	2.94284e15	0.170244
$897$	−7.42102e15	−0.426683
$898$	−4.61410e15	−0.263674
$899$	−2.92206e15	−0.165963
$900$	1.08809e16	0.614228
$901$	5.44622e15	0.305569
$902$	−9.50612e13	−0.00530112
$903$	−1.11436e16	−0.617649
$904$	7.86749e15	0.433421
$905$	1.19156e16	0.652452
$906$	−4.34491e15	−0.236470
$907$	1.81111e16	0.979724	0.489862	−	0.871800i	$-0.337047\pi$
$907$	1.81111e16	0.979724	0.489862	+	0.871800i	$0.337047\pi$
$908$	3.22704e16	1.73513
$909$	1.76594e15	0.0943790
$910$	−1.20589e14	−0.00640588
$911$	1.83058e16	0.966582	0.483291	−	0.875460i	$-0.339441\pi$
$911$	1.83058e16	0.966582	0.483291	+	0.875460i	$0.339441\pi$
$912$	−4.05012e14	−0.0212567
$913$	−2.74811e14	−0.0143365
$914$	−1.85551e15	−0.0962187
$915$	−1.64386e16	−0.847323
$916$	−1.59986e16	−0.819703
$917$	4.18836e15	0.213311
$918$	−4.05632e14	−0.0205351
$919$	2.66729e16	1.34225	0.671127	−	0.741342i	$-0.265811\pi$
$919$	2.66729e16	1.34225	0.671127	+	0.741342i	$0.265811\pi$
$920$	3.19032e15	0.159589
$921$	−2.60857e16	−1.29710
$922$	−1.68907e14	−0.00834885
$923$	−6.64542e15	−0.326523
$924$	1.91713e14	0.00936390
$925$	−1.65734e16	−0.804696
$926$	4.78210e15	0.230812
$927$	2.50689e15	0.120281
$928$	1.61459e15	0.0770103
$929$	7.59728e15	0.360223	0.180112	−	0.983646i	$-0.442354\pi$
$929$	7.59728e15	0.360223	0.180112	+	0.983646i	$0.442354\pi$
$930$	−1.79070e15	−0.0844048
$931$	−3.16080e14	−0.0148106
$932$	3.25741e16	1.51735
$933$	1.28398e16	0.594577
$934$	5.14707e15	0.236947
$935$	−1.84104e14	−0.00842556
$936$	−1.42337e15	−0.0647592
$937$	1.10440e16	0.499528	0.249764	−	0.968307i	$-0.419647\pi$
$937$	1.10440e16	0.499528	0.249764	+	0.968307i	$0.419647\pi$
$938$	−1.62101e15	−0.0728905
$939$	1.79254e16	0.801323
$940$	−1.11147e16	−0.493964
$941$	2.58156e16	1.14062	0.570309	−	0.821430i	$-0.306824\pi$
$941$	2.58156e16	1.14062	0.570309	+	0.821430i	$0.306824\pi$
$942$	3.66181e15	0.160848
$943$	−4.59488e16	−2.00660
$944$	3.84693e16	1.67020
$945$	−7.67601e14	−0.0331330
$946$	−9.73819e13	−0.00417904
$947$	2.82738e16	1.20631	0.603156	−	0.797624i	$-0.293910\pi$
$947$	2.82738e16	1.20631	0.603156	+	0.797624i	$0.293910\pi$
$948$	−1.55463e16	−0.659448
$949$	7.90189e15	0.333247
$950$	3.98621e13	0.00167140
$951$	−4.08002e16	−1.70086
$952$	1.60687e15	0.0666006
$953$	−2.64812e16	−1.09126	−0.545628	−	0.838028i	$-0.683709\pi$
$953$	−2.64812e16	−1.09126	−0.545628	+	0.838028i	$0.683709\pi$
$954$	−1.16772e15	−0.0478434
$955$	−1.22300e16	−0.498205
$956$	−2.02212e16	−0.819008
$957$	1.39771e14	0.00562863
$958$	2.12441e15	0.0850604
$959$	8.62940e15	0.343541
$960$	−1.57956e16	−0.625237
$961$	−6.21934e15	−0.244774
$962$	1.07361e15	0.0420131
$963$	3.30124e16	1.28450
$964$	3.09872e16	1.19883
$965$	−1.56364e16	−0.601500
$966$	−1.79626e15	−0.0687061
$967$	−2.70727e16	−1.02964	−0.514820	−	0.857298i	$-0.672141\pi$
$967$	−2.70727e16	−1.02964	−0.514820	+	0.857298i	$0.672141\pi$
$968$	−7.22015e15	−0.273043
$969$	−4.51127e14	−0.0169636
$970$	−4.99448e14	−0.0186744
$971$	3.38359e16	1.25798	0.628988	−	0.777415i	$-0.283469\pi$
$971$	3.38359e16	1.25798	0.628988	+	0.777415i	$0.283469\pi$
$972$	−3.53760e16	−1.30781
$973$	4.84003e15	0.177921
$974$	4.83077e15	0.176580
$975$	−7.61247e15	−0.276694
$976$	−3.13982e16	−1.13483
$977$	−1.47719e16	−0.530903	−0.265452	−	0.964124i	$-0.585521\pi$
$977$	−1.47719e16	−0.530903	−0.265452	+	0.964124i	$0.585521\pi$
$978$	2.86502e15	0.102391
$979$	−1.30087e14	−0.00462305
$980$	−1.28503e16	−0.454121
$981$	−2.04664e16	−0.719219
$982$	−6.14613e14	−0.0214778
$983$	2.86329e15	0.0994994	0.0497497	−	0.998762i	$-0.484158\pi$
$983$	2.86329e15	0.0994994	0.0497497	+	0.998762i	$0.484158\pi$
$984$	−1.91239e16	−0.660850
$985$	−5.53223e15	−0.190108
$986$	5.80135e14	0.0198247
$987$	1.26372e16	0.429446
$988$	1.33214e14	0.00450181
$989$	−4.70705e16	−1.58187
$990$	3.94735e13	0.00131920
$991$	1.87290e15	0.0622459	0.0311229	−	0.999516i	$-0.490092\pi$
$991$	1.87290e15	0.0622459	0.0311229	+	0.999516i	$0.490092\pi$
$992$	−1.06030e16	−0.350441
$993$	3.73061e16	1.22619
$994$	−1.60853e15	−0.0525779
$995$	−6.12576e15	−0.199128
$996$	−2.73771e16	−0.885036
$997$	−1.00274e16	−0.322377	−0.161189	−	0.986924i	$-0.551533\pi$
$997$	−1.00274e16	−0.322377	−0.161189	+	0.986924i	$0.551533\pi$
$998$	1.04669e15	0.0334658
$999$	6.83402e15	0.217303

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.12.a.b.1.3	✓	6
3.2	odd	2		117.12.a.d.1.4		6
4.3	odd	2		208.12.a.h.1.5		6
13.12	even	2		169.12.a.c.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.12.a.b.1.3	✓	6	1.1	even	1	trivial
117.12.a.d.1.4		6	3.2	odd	2
169.12.a.c.1.4		6	13.12	even	2
208.12.a.h.1.5		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)

\(f(q)\)	\(=\)	\(q-6.24050 q^{2} -573.204 q^{3} -2009.06 q^{4} -3613.82 q^{5} +3577.08 q^{6} +14401.4 q^{7} +25318.0 q^{8} +151416. q^{9} +O(q^{10})\)	\(q-6.24050 q^{2} -573.204 q^{3} -2009.06 q^{4} -3613.82 q^{5} +3577.08 q^{6} +14401.4 q^{7} +25318.0 q^{8} +151416. q^{9} +22552.1 q^{10} +11559.7 q^{11} +1.15160e6 q^{12} -371293. q^{13} -89871.6 q^{14} +2.07146e6 q^{15} +3.95655e6 q^{16} +4.40705e6 q^{17} -944911. q^{18} +178584. q^{19} +7.26038e6 q^{20} -8.25492e6 q^{21} -72138.4 q^{22} -3.48688e7 q^{23} -1.45124e7 q^{24} -3.57684e7 q^{25} +2.31705e6 q^{26} +1.47491e7 q^{27} -2.89331e7 q^{28} -2.10941e7 q^{29} -1.29269e7 q^{30} +1.38525e8 q^{31} -7.65422e7 q^{32} -6.62608e6 q^{33} -2.75022e7 q^{34} -5.20440e7 q^{35} -3.04203e8 q^{36} +4.63353e8 q^{37} -1.11445e6 q^{38} +2.12827e8 q^{39} -9.14950e7 q^{40} +1.31776e9 q^{41} +5.15148e7 q^{42} +1.34993e9 q^{43} -2.32241e7 q^{44} -5.47191e8 q^{45} +2.17599e8 q^{46} -1.53087e9 q^{47} -2.26791e9 q^{48} -1.76993e9 q^{49} +2.23213e8 q^{50} -2.52614e9 q^{51} +7.45949e8 q^{52} +1.23580e9 q^{53} -9.20415e7 q^{54} -4.17748e7 q^{55} +3.64614e8 q^{56} -1.02365e8 q^{57} +1.31638e8 q^{58} +9.72295e9 q^{59} -4.16168e9 q^{60} -7.93576e9 q^{61} -8.64464e8 q^{62} +2.18060e9 q^{63} -7.62535e9 q^{64} +1.34179e9 q^{65} +4.13500e7 q^{66} +1.80370e10 q^{67} -8.85401e9 q^{68} +1.99870e10 q^{69} +3.24780e8 q^{70} +1.78981e10 q^{71} +3.83356e9 q^{72} -2.12821e10 q^{73} -2.89155e9 q^{74} +2.05026e10 q^{75} -3.58784e8 q^{76} +1.66476e8 q^{77} -1.32814e9 q^{78} -1.34997e10 q^{79} -1.42983e10 q^{80} -3.52771e10 q^{81} -8.22348e9 q^{82} -2.37731e10 q^{83} +1.65846e10 q^{84} -1.59263e10 q^{85} -8.42424e9 q^{86} +1.20912e10 q^{87} +2.92670e8 q^{88} -1.12535e10 q^{89} +3.41474e9 q^{90} -5.34712e9 q^{91} +7.00535e10 q^{92} -7.94030e10 q^{93} +9.55342e9 q^{94} -6.45370e8 q^{95} +4.38743e10 q^{96} -2.21465e10 q^{97} +1.10452e10 q^{98} +1.75033e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 55 q^{2} + 476 q^{3} + 15309 q^{4} + 3312 q^{5} - 57797 q^{6} - 4176 q^{7} + 158493 q^{8} + 876218 q^{9}+O(q^{10}) \) 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

Fields

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Groups

Database

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