LMFDB - Embedded newform 43.8.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,8,Mod(1,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("43.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	43.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:	$13.4325560958$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 3 x^{12} - 1279 x^{11} + 3765 x^{10} + 598742 x^{9} - 1518614 x^{8} - 124677082 x^{7} + \cdots + 1551032970660 $ x^13 - 3x^12 - 1279x^11 + 3765x^10 + 598742x^9 - 1518614x^8 - 124677082x^7 + 193428526x^6 + 11160446785x^5 + 1754605765x^4 - 349352939351x^3 - 481872751923x^2 + 2098464001560x + 1551032970660
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-20.1662$ of defining polynomial
Character	$\chi$	$=$	43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-19.1662 q^{2} -36.5899 q^{3} +239.342 q^{4} -174.722 q^{5} +701.287 q^{6} -1126.43 q^{7} -2133.99 q^{8} -848.182 q^{9} +O(q^{10})$	\(q-19.1662 q^{2} -36.5899 q^{3} +239.342 q^{4} -174.722 q^{5} +701.287 q^{6} -1126.43 q^{7} -2133.99 q^{8} -848.182 q^{9} +3348.75 q^{10} -8178.46 q^{11} -8757.47 q^{12} -13500.8 q^{13} +21589.4 q^{14} +6393.05 q^{15} +10264.6 q^{16} +37508.8 q^{17} +16256.4 q^{18} -26617.7 q^{19} -41818.2 q^{20} +41216.0 q^{21} +156750. q^{22} -20061.6 q^{23} +78082.3 q^{24} -47597.3 q^{25} +258757. q^{26} +111057. q^{27} -269602. q^{28} -27521.8 q^{29} -122530. q^{30} -184114. q^{31} +76416.8 q^{32} +299249. q^{33} -718900. q^{34} +196812. q^{35} -203005. q^{36} +301128. q^{37} +510158. q^{38} +493991. q^{39} +372855. q^{40} -507344. q^{41} -789952. q^{42} -79507.0 q^{43} -1.95745e6 q^{44} +148196. q^{45} +384503. q^{46} -137672. q^{47} -375582. q^{48} +445307. q^{49} +912256. q^{50} -1.37244e6 q^{51} -3.23129e6 q^{52} +577240. q^{53} -2.12853e6 q^{54} +1.42896e6 q^{55} +2.40379e6 q^{56} +973937. q^{57} +527487. q^{58} +1.70368e6 q^{59} +1.53012e6 q^{60} +1.24127e6 q^{61} +3.52877e6 q^{62} +955420. q^{63} -2.77849e6 q^{64} +2.35888e6 q^{65} -5.73545e6 q^{66} -1.24429e6 q^{67} +8.97742e6 q^{68} +734050. q^{69} -3.77214e6 q^{70} -3.10722e6 q^{71} +1.81001e6 q^{72} -3.60450e6 q^{73} -5.77146e6 q^{74} +1.74158e6 q^{75} -6.37071e6 q^{76} +9.21248e6 q^{77} -9.46790e6 q^{78} -3.14376e6 q^{79} -1.79346e6 q^{80} -2.20858e6 q^{81} +9.72384e6 q^{82} +347048. q^{83} +9.86470e6 q^{84} -6.55361e6 q^{85} +1.52384e6 q^{86} +1.00702e6 q^{87} +1.74527e7 q^{88} -4.60056e6 q^{89} -2.84035e6 q^{90} +1.52077e7 q^{91} -4.80156e6 q^{92} +6.73672e6 q^{93} +2.63864e6 q^{94} +4.65069e6 q^{95} -2.79608e6 q^{96} -1.55843e7 q^{97} -8.53482e6 q^{98} +6.93682e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9}+O(q^{10}) $ 13 * q + 16 * q^2 + 94 * q^3 + 922 * q^4 + 998 * q^5 + 183 * q^6 + 1360 * q^7 + 3870 * q^8 + 10011 * q^9	\( 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9} + 4667 q^{10} + 1620 q^{11} - 19681 q^{12} + 13550 q^{13} + 44160 q^{14} + 31412 q^{15} + 114026 q^{16} + 110880 q^{17} + 159267 q^{18} + 105058 q^{19} + 167251 q^{20} + 129840 q^{21} + 201504 q^{22} + 160184 q^{23} + 161289 q^{24} + 270149 q^{25} + 272104 q^{26} + 252544 q^{27} + 208172 q^{28} + 285546 q^{29} + 107580 q^{30} - 99616 q^{31} + 200126 q^{32} + 531468 q^{33} - 80941 q^{34} - 187104 q^{35} - 608975 q^{36} + 176038 q^{37} + 652165 q^{38} - 794680 q^{39} - 895387 q^{40} - 410260 q^{41} - 3413218 q^{42} - 1033591 q^{43} - 2177076 q^{44} - 1051178 q^{45} - 3975765 q^{46} - 424556 q^{47} - 2360477 q^{48} - 1561359 q^{49} - 4063801 q^{50} - 2375738 q^{51} - 4172312 q^{52} + 3992458 q^{53} - 10438626 q^{54} + 406960 q^{55} + 1559556 q^{56} - 3116152 q^{57} - 4052005 q^{58} + 2248836 q^{59} - 2911436 q^{60} + 6210394 q^{61} + 885317 q^{62} + 11622368 q^{63} - 3096318 q^{64} + 5600420 q^{65} - 2174604 q^{66} - 1993648 q^{67} + 9327135 q^{68} + 13366240 q^{69} - 1105098 q^{70} + 4978064 q^{71} + 11370663 q^{72} + 8224814 q^{73} - 3613563 q^{74} + 27115592 q^{75} + 10687121 q^{76} + 17261892 q^{77} - 15226630 q^{78} + 6945708 q^{79} + 15822799 q^{80} + 35113185 q^{81} - 508449 q^{82} + 22937328 q^{83} - 14010106 q^{84} - 575532 q^{85} - 1272112 q^{86} + 9081380 q^{87} + 11202656 q^{88} + 9291302 q^{89} + 2841402 q^{90} + 25581108 q^{91} - 14388137 q^{92} + 25930480 q^{93} - 24645805 q^{94} + 30750464 q^{95} - 22461255 q^{96} + 10001852 q^{97} - 32304856 q^{98} + 5055452 q^{99}+O(q^{100}) \) 13 * q + 16 * q^2 + 94 * q^3 + 922 * q^4 + 998 * q^5 + 183 * q^6 + 1360 * q^7 + 3870 * q^8 + 10011 * q^9 + 4667 * q^10 + 1620 * q^11 - 19681 * q^12 + 13550 * q^13 + 44160 * q^14 + 31412 * q^15 + 114026 * q^16 + 110880 * q^17 + 159267 * q^18 + 105058 * q^19 + 167251 * q^20 + 129840 * q^21 + 201504 * q^22 + 160184 * q^23 + 161289 * q^24 + 270149 * q^25 + 272104 * q^26 + 252544 * q^27 + 208172 * q^28 + 285546 * q^29 + 107580 * q^30 - 99616 * q^31 + 200126 * q^32 + 531468 * q^33 - 80941 * q^34 - 187104 * q^35 - 608975 * q^36 + 176038 * q^37 + 652165 * q^38 - 794680 * q^39 - 895387 * q^40 - 410260 * q^41 - 3413218 * q^42 - 1033591 * q^43 - 2177076 * q^44 - 1051178 * q^45 - 3975765 * q^46 - 424556 * q^47 - 2360477 * q^48 - 1561359 * q^49 - 4063801 * q^50 - 2375738 * q^51 - 4172312 * q^52 + 3992458 * q^53 - 10438626 * q^54 + 406960 * q^55 + 1559556 * q^56 - 3116152 * q^57 - 4052005 * q^58 + 2248836 * q^59 - 2911436 * q^60 + 6210394 * q^61 + 885317 * q^62 + 11622368 * q^63 - 3096318 * q^64 + 5600420 * q^65 - 2174604 * q^66 - 1993648 * q^67 + 9327135 * q^68 + 13366240 * q^69 - 1105098 * q^70 + 4978064 * q^71 + 11370663 * q^72 + 8224814 * q^73 - 3613563 * q^74 + 27115592 * q^75 + 10687121 * q^76 + 17261892 * q^77 - 15226630 * q^78 + 6945708 * q^79 + 15822799 * q^80 + 35113185 * q^81 - 508449 * q^82 + 22937328 * q^83 - 14010106 * q^84 - 575532 * q^85 - 1272112 * q^86 + 9081380 * q^87 + 11202656 * q^88 + 9291302 * q^89 + 2841402 * q^90 + 25581108 * q^91 - 14388137 * q^92 + 25930480 * q^93 - 24645805 * q^94 + 30750464 * q^95 - 22461255 * q^96 + 10001852 * q^97 - 32304856 * q^98 + 5055452 * 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 $

$2$	−19.1662	−1.69406	−0.847032	−	0.531541i	$-0.821613\pi$
$2$	−19.1662	−1.69406	−0.847032	+	0.531541i	$0.821613\pi$
$3$	−36.5899	−0.782414	−0.391207	−	0.920303i	$-0.627942\pi$
$3$	−36.5899	−0.782414	−0.391207	+	0.920303i	$0.627942\pi$
$4$	239.342	1.86986
$5$	−174.722	−0.625104	−0.312552	−	0.949901i	$-0.601184\pi$
$5$	−174.722	−0.625104	−0.312552	+	0.949901i	$0.601184\pi$
$6$	701.287	1.32546
$7$	−1126.43	−1.24126	−0.620629	−	0.784104i	$-0.713123\pi$
$7$	−1126.43	−1.24126	−0.620629	+	0.784104i	$0.713123\pi$
$8$	−2133.99	−1.47359
$9$	−848.182	−0.387829
$10$	3348.75	1.05897
$11$	−8178.46	−1.85267	−0.926333	−	0.376705i	$-0.877057\pi$
$11$	−8178.46	−1.85267	−0.926333	+	0.376705i	$0.877057\pi$
$12$	−8757.47	−1.46300
$13$	−13500.8	−1.70434	−0.852170	−	0.523265i	$-0.824714\pi$
$13$	−13500.8	−1.70434	−0.852170	+	0.523265i	$0.824714\pi$
$14$	21589.4	2.10277
$15$	6393.05	0.489090
$16$	10264.6	0.626504
$17$	37508.8	1.85166	0.925832	−	0.377935i	$-0.123366\pi$
$17$	37508.8	1.85166	0.925832	+	0.377935i	$0.123366\pi$
$18$	16256.4	0.657008
$19$	−26617.7	−0.890292	−0.445146	−	0.895458i	$-0.646848\pi$
$19$	−26617.7	−0.890292	−0.445146	+	0.895458i	$0.646848\pi$
$20$	−41818.2	−1.16885
$21$	41216.0	0.971177
$22$	156750.	3.13854
$23$	−20061.6	−0.343809	−0.171905	−	0.985114i	$-0.554992\pi$
$23$	−20061.6	−0.343809	−0.171905	+	0.985114i	$0.554992\pi$
$24$	78082.3	1.15296
$25$	−47597.3	−0.609245
$26$	258757.	2.88726
$27$	111057.	1.08586
$28$	−269602.	−2.32097
$29$	−27521.8	−0.209548	−0.104774	−	0.994496i	$-0.533412\pi$
$29$	−27521.8	−0.209548	−0.104774	+	0.994496i	$0.533412\pi$
$30$	−122530.	−0.828550
$31$	−184114.	−1.11000	−0.554999	−	0.831851i	$-0.687281\pi$
$31$	−184114.	−1.11000	−0.554999	+	0.831851i	$0.687281\pi$
$32$	76416.8	0.412253
$33$	299249.	1.44955
$34$	−718900.	−3.13684
$35$	196812.	0.775915
$36$	−203005.	−0.725184
$37$	301128.	0.977338	0.488669	−	0.872469i	$-0.337483\pi$
$37$	301128.	0.977338	0.488669	+	0.872469i	$0.337483\pi$
$38$	510158.	1.50821
$39$	493991.	1.33350
$40$	372855.	0.921148
$41$	−507344.	−1.14963	−0.574817	−	0.818282i	$-0.694927\pi$
$41$	−507344.	−1.14963	−0.574817	+	0.818282i	$0.694927\pi$
$42$	−789952.	−1.64524
$43$	−79507.0	−0.152499
$43$	−79507.0	−0.152499
$44$	−1.95745e6	−3.46422
$45$	148196.	0.242434
$46$	384503.	0.582435
$47$	−137672.	−0.193420	−0.0967102	−	0.995313i	$-0.530832\pi$
$47$	−137672.	−0.193420	−0.0967102	+	0.995313i	$0.530832\pi$
$48$	−375582.	−0.490185
$49$	445307.	0.540721
$50$	912256.	1.03210
$51$	−1.37244e6	−1.44877
$52$	−3.23129e6	−3.18687
$53$	577240.	0.532588	0.266294	−	0.963892i	$-0.414201\pi$
$53$	577240.	0.532588	0.266294	+	0.963892i	$0.414201\pi$
$54$	−2.12853e6	−1.83951
$55$	1.42896e6	1.15811
$56$	2.40379e6	1.82911
$57$	973937.	0.696577
$58$	527487.	0.354988
$59$	1.70368e6	1.07995	0.539977	−	0.841680i	$-0.318433\pi$
$59$	1.70368e6	1.07995	0.539977	+	0.841680i	$0.318433\pi$
$60$	1.53012e6	0.914527
$61$	1.24127e6	0.700182	0.350091	−	0.936716i	$-0.386151\pi$
$61$	1.24127e6	0.700182	0.350091	+	0.936716i	$0.386151\pi$
$62$	3.52877e6	1.88041
$63$	955420.	0.481396
$64$	−2.77849e6	−1.32489
$65$	2.35888e6	1.06539
$66$	−5.73545e6	−2.45563
$67$	−1.24429e6	−0.505430	−0.252715	−	0.967541i	$-0.581323\pi$
$67$	−1.24429e6	−0.505430	−0.252715	+	0.967541i	$0.581323\pi$
$68$	8.97742e6	3.46234
$69$	734050.	0.269001
$70$	−3.77214e6	−1.31445
$71$	−3.10722e6	−1.03031	−0.515154	−	0.857098i	$-0.672265\pi$
$71$	−3.10722e6	−1.03031	−0.515154	+	0.857098i	$0.672265\pi$
$72$	1.81001e6	0.571502
$73$	−3.60450e6	−1.08446	−0.542232	−	0.840229i	$-0.682421\pi$
$73$	−3.60450e6	−1.08446	−0.542232	+	0.840229i	$0.682421\pi$
$74$	−5.77146e6	−1.65567
$75$	1.74158e6	0.476681
$76$	−6.37071e6	−1.66472
$77$	9.21248e6	2.29964
$78$	−9.46790e6	−2.25903
$79$	−3.14376e6	−0.717390	−0.358695	−	0.933455i	$-0.616778\pi$
$79$	−3.14376e6	−0.717390	−0.358695	+	0.933455i	$0.616778\pi$
$80$	−1.79346e6	−0.391630
$81$	−2.20858e6	−0.461760
$82$	9.72384e6	1.94755
$83$	347048.	0.0666218	0.0333109	−	0.999445i	$-0.489395\pi$
$83$	347048.	0.0666218	0.0333109	+	0.999445i	$0.489395\pi$
$84$	9.86470e6	1.81596
$85$	−6.55361e6	−1.15748
$86$	1.52384e6	0.258342
$87$	1.00702e6	0.163953
$88$	1.74527e7	2.73007
$89$	−4.60056e6	−0.691745	−0.345872	−	0.938282i	$-0.612417\pi$
$89$	−4.60056e6	−0.691745	−0.345872	+	0.938282i	$0.612417\pi$
$90$	−2.84035e6	−0.410698
$91$	1.52077e7	2.11553
$92$	−4.80156e6	−0.642873
$93$	6.73672e6	0.868477
$94$	2.63864e6	0.327667
$95$	4.65069e6	0.556525
$96$	−2.79608e6	−0.322552
$97$	−1.55843e7	−1.73375	−0.866875	−	0.498526i	$-0.833875\pi$
$97$	−1.55843e7	−1.73375	−0.866875	+	0.498526i	$0.833875\pi$
$98$	−8.53482e6	−0.916016
$99$	6.93682e6	0.718518
$100$	−1.13920e7	−1.13920
$101$	−9.18925e6	−0.887474	−0.443737	−	0.896157i	$-0.646348\pi$
$101$	−9.18925e6	−0.887474	−0.443737	+	0.896157i	$0.646348\pi$
$102$	2.63044e7	2.45431
$103$	−1.58567e7	−1.42982	−0.714910	−	0.699216i	$-0.753533\pi$
$103$	−1.58567e7	−1.42982	−0.714910	+	0.699216i	$0.753533\pi$
$104$	2.88104e7	2.51150
$105$	−7.20134e6	−0.607087
$106$	−1.10635e7	−0.902238
$107$	−833526.	−0.0657773	−0.0328886	−	0.999459i	$-0.510471\pi$
$107$	−833526.	−0.0657773	−0.0328886	+	0.999459i	$0.510471\pi$
$108$	2.65805e7	2.03039
$109$	7.34548e6	0.543285	0.271642	−	0.962398i	$-0.412433\pi$
$109$	7.34548e6	0.543285	0.271642	+	0.962398i	$0.412433\pi$
$110$	−2.73876e7	−1.96191
$111$	−1.10182e7	−0.764683
$112$	−1.15624e7	−0.777653
$113$	3.08279e6	0.200988	0.100494	−	0.994938i	$-0.467958\pi$
$113$	3.08279e6	0.200988	0.100494	+	0.994938i	$0.467958\pi$
$114$	−1.86666e7	−1.18005
$115$	3.50519e6	0.214916
$116$	−6.58710e6	−0.391824
$117$	1.14511e7	0.660993
$118$	−3.26530e7	−1.82951
$119$	−4.22512e7	−2.29839
$120$	−1.36427e7	−0.720719
$121$	4.74000e7	2.43237
$122$	−2.37903e7	−1.18615
$123$	1.85637e7	0.899489
$124$	−4.40662e7	−2.07553
$125$	2.19664e7	1.00595
$126$	−1.83117e7	−0.815516
$127$	−1.91611e6	−0.0830057	−0.0415028	−	0.999138i	$-0.513215\pi$
$127$	−1.91611e6	−0.0830057	−0.0415028	+	0.999138i	$0.513215\pi$
$128$	4.34716e7	1.83219
$129$	2.90915e6	0.119317
$130$	−4.52106e7	−1.80484
$131$	−2.07138e7	−0.805026	−0.402513	−	0.915414i	$-0.631863\pi$
$131$	−2.07138e7	−0.805026	−0.402513	+	0.915414i	$0.631863\pi$
$132$	7.16226e7	2.71045
$133$	2.99830e7	1.10508
$134$	2.38483e7	0.856231
$135$	−1.94041e7	−0.678773
$136$	−8.00434e7	−2.72860
$137$	−3.16796e7	−1.05259	−0.526294	−	0.850303i	$-0.676419\pi$
$137$	−3.16796e7	−1.05259	−0.526294	+	0.850303i	$0.676419\pi$
$138$	−1.40689e7	−0.455705
$139$	−4.90696e7	−1.54975	−0.774873	−	0.632117i	$-0.782186\pi$
$139$	−4.90696e7	−1.54975	−0.774873	+	0.632117i	$0.782186\pi$
$140$	4.71054e7	1.45085
$141$	5.03739e6	0.151335
$142$	5.95534e7	1.74541
$143$	1.10415e8	3.15757
$144$	−8.70629e6	−0.242976
$145$	4.80866e6	0.130989
$146$	6.90844e7	1.83715
$147$	−1.62937e7	−0.423067
$148$	7.20724e7	1.82748
$149$	8.04857e6	0.199327	0.0996637	−	0.995021i	$-0.468223\pi$
$149$	8.04857e6	0.199327	0.0996637	+	0.995021i	$0.468223\pi$
$150$	−3.33793e7	−0.807529
$151$	−9.45579e6	−0.223500	−0.111750	−	0.993736i	$-0.535646\pi$
$151$	−9.45579e6	−0.223500	−0.111750	+	0.993736i	$0.535646\pi$
$152$	5.68018e7	1.31193
$153$	−3.18143e7	−0.718129
$154$	−1.76568e8	−3.89573
$155$	3.21688e7	0.693864
$156$	1.18232e8	2.49345
$157$	5.50699e7	1.13571	0.567853	−	0.823130i	$-0.307774\pi$
$157$	5.50699e7	1.13571	0.567853	+	0.823130i	$0.307774\pi$
$158$	6.02539e7	1.21530
$159$	−2.11211e7	−0.416704
$160$	−1.33517e7	−0.257701
$161$	2.25980e7	0.426756
$162$	4.23300e7	0.782251
$163$	3.56380e7	0.644551	0.322275	−	0.946646i	$-0.395552\pi$
$163$	3.56380e7	0.644551	0.322275	+	0.946646i	$0.395552\pi$
$164$	−1.21429e8	−2.14965
$165$	−5.22853e7	−0.906120
$166$	−6.65158e6	−0.112862
$167$	−4.96680e7	−0.825218	−0.412609	−	0.910908i	$-0.635382\pi$
$167$	−4.96680e7	−0.825218	−0.412609	+	0.910908i	$0.635382\pi$
$168$	−8.79545e7	−1.43112
$169$	1.19522e8	1.90477
$170$	1.25608e8	1.96085
$171$	2.25766e7	0.345281
$172$	−1.90293e7	−0.285150
$173$	5.97290e7	0.877049	0.438524	−	0.898719i	$-0.355501\pi$
$173$	5.97290e7	0.877049	0.438524	+	0.898719i	$0.355501\pi$
$174$	−1.93007e7	−0.277747
$175$	5.36151e7	0.756230
$176$	−8.39490e7	−1.16070
$177$	−6.23373e7	−0.844971
$178$	8.81751e7	1.17186
$179$	−5.19556e6	−0.0677090	−0.0338545	−	0.999427i	$-0.510778\pi$
$179$	−5.19556e6	−0.0677090	−0.0338545	+	0.999427i	$0.510778\pi$
$180$	3.54695e7	0.453316
$181$	9.47873e6	0.118816	0.0594080	−	0.998234i	$-0.481079\pi$
$181$	9.47873e6	0.118816	0.0594080	+	0.998234i	$0.481079\pi$
$182$	−2.91473e8	−3.58384
$183$	−4.54178e7	−0.547832
$184$	4.28111e7	0.506634
$185$	−5.26136e7	−0.610938
$186$	−1.29117e8	−1.47126
$187$	−3.06764e8	−3.43052
$188$	−3.29506e7	−0.361668
$189$	−1.25098e8	−1.34783
$190$	−8.91359e7	−0.942790
$191$	1.10607e8	1.14859	0.574295	−	0.818648i	$-0.305276\pi$
$191$	1.10607e8	1.14859	0.574295	+	0.818648i	$0.305276\pi$
$192$	1.01665e8	1.03661
$193$	−8.62108e7	−0.863199	−0.431599	−	0.902065i	$-0.642051\pi$
$193$	−8.62108e7	−0.863199	−0.431599	+	0.902065i	$0.642051\pi$
$194$	2.98691e8	2.93708
$195$	−8.63110e7	−0.833575
$196$	1.06580e8	1.01107
$197$	−1.14482e8	−1.06686	−0.533429	−	0.845845i	$-0.679097\pi$
$197$	−1.14482e8	−1.06686	−0.533429	+	0.845845i	$0.679097\pi$
$198$	−1.32952e8	−1.21722
$199$	−3.94085e7	−0.354490	−0.177245	−	0.984167i	$-0.556719\pi$
$199$	−3.94085e7	−0.354490	−0.177245	+	0.984167i	$0.556719\pi$
$200$	1.01572e8	0.897778
$201$	4.55285e7	0.395455
$202$	1.76123e8	1.50344
$203$	3.10014e7	0.260103
$204$	−3.28482e8	−2.70899
$205$	8.86442e7	0.718640
$206$	3.03911e8	2.42221
$207$	1.70159e7	0.133339
$208$	−1.38580e8	−1.06778
$209$	2.17692e8	1.64941
$210$	1.38022e8	1.02844
$211$	−1.39696e8	−1.02375	−0.511876	−	0.859059i	$-0.671049\pi$
$211$	−1.39696e8	−1.02375	−0.511876	+	0.859059i	$0.671049\pi$
$212$	1.38158e8	0.995862
$213$	1.13693e8	0.806127
$214$	1.59755e7	0.111431
$215$	1.38916e7	0.0953275
$216$	−2.36994e8	−1.60011
$217$	2.07393e8	1.37779
$218$	−1.40785e8	−0.920360
$219$	1.31888e8	0.848499
$220$	3.42009e8	2.16550
$221$	−5.06397e8	−3.15586
$222$	2.11177e8	1.29542
$223$	−1.20926e8	−0.730218	−0.365109	−	0.930965i	$-0.618968\pi$
$223$	−1.20926e8	−0.730218	−0.365109	+	0.930965i	$0.618968\pi$
$224$	−8.60784e7	−0.511712
$225$	4.03711e7	0.236283
$226$	−5.90852e7	−0.340486
$227$	−1.15625e8	−0.656084	−0.328042	−	0.944663i	$-0.606389\pi$
$227$	−1.15625e8	−0.656084	−0.328042	+	0.944663i	$0.606389\pi$
$228$	2.33104e8	1.30250
$229$	−1.39236e8	−0.766175	−0.383087	−	0.923712i	$-0.625139\pi$
$229$	−1.39236e8	−0.766175	−0.383087	+	0.923712i	$0.625139\pi$
$230$	−6.71811e7	−0.364082
$231$	−3.37083e8	−1.79927
$232$	5.87311e7	0.308788
$233$	−3.66295e7	−0.189708	−0.0948539	−	0.995491i	$-0.530238\pi$
$233$	−3.66295e7	−0.189708	−0.0948539	+	0.995491i	$0.530238\pi$
$234$	−2.19473e8	−1.11976
$235$	2.40543e7	0.120908
$236$	4.07761e8	2.01936
$237$	1.15030e8	0.561295
$238$	8.09792e8	3.89363
$239$	−3.71440e7	−0.175993	−0.0879967	−	0.996121i	$-0.528046\pi$
$239$	−3.71440e7	−0.175993	−0.0879967	+	0.996121i	$0.528046\pi$
$240$	6.56224e7	0.306417
$241$	3.96773e7	0.182592	0.0912962	−	0.995824i	$-0.470899\pi$
$241$	3.96773e7	0.182592	0.0912962	+	0.995824i	$0.470899\pi$
$242$	−9.08477e8	−4.12060
$243$	−1.62070e8	−0.724569
$244$	2.97087e8	1.30924
$245$	−7.78049e7	−0.338007
$246$	−3.55794e8	−1.52379
$247$	3.59359e8	1.51736
$248$	3.92898e8	1.63568
$249$	−1.26984e7	−0.0521258
$250$	−4.21012e8	−1.70414
$251$	6.08382e7	0.242839	0.121419	−	0.992601i	$-0.461255\pi$
$251$	6.08382e7	0.242839	0.121419	+	0.992601i	$0.461255\pi$
$252$	2.28672e8	0.900141
$253$	1.64073e8	0.636963
$254$	3.67245e7	0.140617
$255$	2.39796e8	0.905630
$256$	−4.77537e8	−1.77896
$257$	9.91857e7	0.364488	0.182244	−	0.983253i	$-0.441664\pi$
$257$	9.91857e7	0.364488	0.182244	+	0.983253i	$0.441664\pi$
$258$	−5.57572e7	−0.202131
$259$	−3.39200e8	−1.21313
$260$	5.64577e8	1.99212
$261$	2.33435e7	0.0812688
$262$	3.97004e8	1.36377
$263$	−2.73541e8	−0.927209	−0.463605	−	0.886042i	$-0.653444\pi$
$263$	−2.73541e8	−0.927209	−0.463605	+	0.886042i	$0.653444\pi$
$264$	−6.38593e8	−2.13605
$265$	−1.00857e8	−0.332923
$266$	−5.74659e8	−1.87208
$267$	1.68334e8	0.541231
$268$	−2.97811e8	−0.945081
$269$	2.75672e8	0.863494	0.431747	−	0.901995i	$-0.357897\pi$
$269$	2.75672e8	0.863494	0.431747	+	0.901995i	$0.357897\pi$
$270$	3.71901e8	1.14989
$271$	4.75651e8	1.45176	0.725882	−	0.687819i	$-0.241432\pi$
$271$	4.75651e8	1.45176	0.725882	+	0.687819i	$0.241432\pi$
$272$	3.85015e8	1.16008
$273$	−5.56447e8	−1.65522
$274$	6.07177e8	1.78315
$275$	3.89272e8	1.12873
$276$	1.75689e8	0.502993
$277$	2.38870e8	0.675279	0.337639	−	0.941276i	$-0.390372\pi$
$277$	2.38870e8	0.675279	0.337639	+	0.941276i	$0.390372\pi$
$278$	9.40475e8	2.62537
$279$	1.56163e8	0.430489
$280$	−4.19995e8	−1.14338
$281$	−5.54874e8	−1.49184	−0.745920	−	0.666036i	$-0.767990\pi$
$281$	−5.54874e8	−1.49184	−0.745920	+	0.666036i	$0.767990\pi$
$282$	−9.65474e7	−0.256371
$283$	−2.03982e7	−0.0534981	−0.0267491	−	0.999642i	$-0.508516\pi$
$283$	−2.03982e7	−0.0534981	−0.0267491	+	0.999642i	$0.508516\pi$
$284$	−7.43686e8	−1.92653
$285$	−1.70168e8	−0.435433
$286$	−2.11624e9	−5.34913
$287$	5.71489e8	1.42699
$288$	−6.48154e7	−0.159884
$289$	9.96573e8	2.42866
$290$	−9.21635e7	−0.221904
$291$	5.70228e8	1.35651
$292$	−8.62707e8	−2.02779
$293$	2.34109e8	0.543728	0.271864	−	0.962336i	$-0.412360\pi$
$293$	2.34109e8	0.543728	0.271864	+	0.962336i	$0.412360\pi$
$294$	3.12288e8	0.716704
$295$	−2.97670e8	−0.675084
$296$	−6.42603e8	−1.44020
$297$	−9.08274e8	−2.01173
$298$	−1.54260e8	−0.337673
$299$	2.70846e8	0.585967
$300$	4.16832e8	0.891325
$301$	8.95593e7	0.189290
$302$	1.81231e8	0.378624
$303$	3.36234e8	0.694371
$304$	−2.73221e8	−0.557772
$305$	−2.16877e8	−0.437687
$306$	6.09758e8	1.21656
$307$	3.42975e8	0.676515	0.338258	−	0.941054i	$-0.390162\pi$
$307$	3.42975e8	0.676515	0.338258	+	0.941054i	$0.390162\pi$
$308$	2.20493e9	4.29999
$309$	5.80193e8	1.11871
$310$	−6.16553e8	−1.17545
$311$	−7.24592e8	−1.36594	−0.682971	−	0.730446i	$-0.739312\pi$
$311$	−7.24592e8	−1.36594	−0.682971	+	0.730446i	$0.739312\pi$
$312$	−1.05417e9	−1.96503
$313$	2.90144e8	0.534820	0.267410	−	0.963583i	$-0.413832\pi$
$313$	2.90144e8	0.534820	0.267410	+	0.963583i	$0.413832\pi$
$314$	−1.05548e9	−1.92396
$315$	−1.66933e8	−0.300923
$316$	−7.52433e8	−1.34141
$317$	6.90711e8	1.21784	0.608918	−	0.793233i	$-0.291604\pi$
$317$	6.90711e8	1.21784	0.608918	+	0.793233i	$0.291604\pi$
$318$	4.04811e8	0.705923
$319$	2.25086e8	0.388222
$320$	4.85463e8	0.828193
$321$	3.04986e7	0.0514650
$322$	−4.33117e8	−0.722952
$323$	−9.98398e8	−1.64852
$324$	−5.28605e8	−0.863424
$325$	6.42599e8	1.03836
$326$	−6.83044e8	−1.09191
$327$	−2.68770e8	−0.425073
$328$	1.08267e9	1.69409
$329$	1.55078e8	0.240085
$330$	1.00211e9	1.53503
$331$	−1.29514e9	−1.96300	−0.981498	−	0.191470i	$-0.938675\pi$
$331$	−1.29514e9	−1.96300	−0.981498	+	0.191470i	$0.938675\pi$
$332$	8.30630e7	0.124573
$333$	−2.55411e8	−0.379040
$334$	9.51944e8	1.39797
$335$	2.17405e8	0.315946
$336$	4.23068e8	0.608446
$337$	−4.49309e8	−0.639500	−0.319750	−	0.947502i	$-0.603599\pi$
$337$	−4.49309e8	−0.639500	−0.319750	+	0.947502i	$0.603599\pi$
$338$	−2.29077e9	−3.22681
$339$	−1.12799e8	−0.157255
$340$	−1.56855e9	−2.16433
$341$	1.50577e9	2.05645
$342$	−4.32707e8	−0.584929
$343$	4.26057e8	0.570084
$344$	1.69667e8	0.224721
$345$	−1.28255e8	−0.168154
$346$	−1.14477e9	−1.48578
$347$	6.18982e7	0.0795288	0.0397644	−	0.999209i	$-0.487339\pi$
$347$	6.18982e7	0.0795288	0.0397644	+	0.999209i	$0.487339\pi$
$348$	2.41021e8	0.306569
$349$	7.40278e8	0.932193	0.466096	−	0.884734i	$-0.345660\pi$
$349$	7.40278e8	0.932193	0.466096	+	0.884734i	$0.345660\pi$
$350$	−1.02760e9	−1.28110
$351$	−1.49935e9	−1.85067
$352$	−6.24972e8	−0.763767
$353$	1.53714e9	1.85995	0.929976	−	0.367620i	$-0.119827\pi$
$353$	1.53714e9	1.85995	0.929976	+	0.367620i	$0.119827\pi$
$354$	1.19477e9	1.43144
$355$	5.42899e8	0.644050
$356$	−1.10111e9	−1.29346
$357$	1.54596e9	1.79829
$358$	9.95789e7	0.114704
$359$	−1.14737e9	−1.30880	−0.654400	−	0.756149i	$-0.727079\pi$
$359$	−1.14737e9	−1.30880	−0.654400	+	0.756149i	$0.727079\pi$
$360$	−3.16249e8	−0.357248
$361$	−1.85371e8	−0.207380
$362$	−1.81671e8	−0.201282
$363$	−1.73436e9	−1.90312
$364$	3.63983e9	3.95573
$365$	6.29785e8	0.677903
$366$	8.70485e8	0.928063
$367$	−1.07850e9	−1.13890	−0.569452	−	0.822024i	$-0.692845\pi$
$367$	−1.07850e9	−1.13890	−0.569452	+	0.822024i	$0.692845\pi$
$368$	−2.05925e8	−0.215398
$369$	4.30320e8	0.445861
$370$	1.00840e9	1.03497
$371$	−6.50222e8	−0.661079
$372$	1.61238e9	1.62393
$373$	4.29210e8	0.428242	0.214121	−	0.976807i	$-0.431311\pi$
$373$	4.29210e8	0.428242	0.214121	+	0.976807i	$0.431311\pi$
$374$	5.87949e9	5.81152
$375$	−8.03749e8	−0.787065
$376$	2.93790e8	0.285023
$377$	3.71565e8	0.357141
$378$	2.39765e9	2.28331
$379$	4.96839e8	0.468790	0.234395	−	0.972141i	$-0.424689\pi$
$379$	4.96839e8	0.468790	0.234395	+	0.972141i	$0.424689\pi$
$380$	1.11310e9	1.04062
$381$	7.01103e7	0.0649448
$382$	−2.11991e9	−1.94579
$383$	−8.74354e7	−0.0795228	−0.0397614	−	0.999209i	$-0.512660\pi$
$383$	−8.74354e7	−0.0795228	−0.0397614	+	0.999209i	$0.512660\pi$
$384$	−1.59062e9	−1.43353
$385$	−1.60962e9	−1.43751
$386$	1.65233e9	1.46232
$387$	6.74364e7	0.0591434
$388$	−3.72997e9	−3.24186
$389$	−1.92667e9	−1.65953	−0.829763	−	0.558116i	$-0.811524\pi$
$389$	−1.92667e9	−1.65953	−0.829763	+	0.558116i	$0.811524\pi$
$390$	1.65425e9	1.41213
$391$	−7.52485e8	−0.636619
$392$	−9.50280e8	−0.796802
$393$	7.57914e8	0.629863
$394$	2.19419e9	1.80733
$395$	5.49284e8	0.448443
$396$	1.66027e9	1.34352
$397$	1.16563e9	0.934961	0.467481	−	0.884003i	$-0.345162\pi$
$397$	1.16563e9	0.934961	0.467481	+	0.884003i	$0.345162\pi$
$398$	7.55310e8	0.600530
$399$	−1.09707e9	−0.864631
$400$	−4.88569e8	−0.381694
$401$	7.50534e8	0.581253	0.290626	−	0.956837i	$-0.406136\pi$
$401$	7.50534e8	0.581253	0.290626	+	0.956837i	$0.406136\pi$
$402$	−8.72607e8	−0.669927
$403$	2.48568e9	1.89181
$404$	−2.19937e9	−1.65945
$405$	3.85888e8	0.288648
$406$	−5.94178e8	−0.440631
$407$	−2.46276e9	−1.81068
$408$	2.92878e9	2.13489
$409$	8.51195e8	0.615174	0.307587	−	0.951520i	$-0.400479\pi$
$409$	8.51195e8	0.615174	0.307587	+	0.951520i	$0.400479\pi$
$410$	−1.69897e9	−1.21742
$411$	1.15915e9	0.823558
$412$	−3.79516e9	−2.67356
$413$	−1.91908e9	−1.34050
$414$	−3.26129e8	−0.225885
$415$	−6.06369e7	−0.0416456
$416$	−1.03168e9	−0.702619
$417$	1.79545e9	1.21254
$418$	−4.17231e9	−2.79421
$419$	−1.60505e9	−1.06596	−0.532978	−	0.846129i	$-0.678927\pi$
$419$	−1.60505e9	−1.06596	−0.532978	+	0.846129i	$0.678927\pi$
$420$	−1.72358e9	−1.13516
$421$	−8.58777e8	−0.560910	−0.280455	−	0.959867i	$-0.590485\pi$
$421$	−8.58777e8	−0.560910	−0.280455	+	0.959867i	$0.590485\pi$
$422$	2.67743e9	1.73430
$423$	1.16771e8	0.0750140
$424$	−1.23182e9	−0.784817
$425$	−1.78532e9	−1.12812
$426$	−2.17905e9	−1.36563
$427$	−1.39820e9	−0.869107
$428$	−1.99497e8	−0.122994
$429$	−4.04008e9	−2.47053
$430$	−2.66249e8	−0.161491
$431$	9.60074e8	0.577610	0.288805	−	0.957388i	$-0.406742\pi$
$431$	9.60074e8	0.577610	0.288805	+	0.957388i	$0.406742\pi$
$432$	1.13996e9	0.680293
$433$	−4.31741e8	−0.255574	−0.127787	−	0.991802i	$-0.540787\pi$
$433$	−4.31741e8	−0.255574	−0.127787	+	0.991802i	$0.540787\pi$
$434$	−3.97492e9	−2.33407
$435$	−1.75948e8	−0.102488
$436$	1.75808e9	1.01586
$437$	5.33992e8	0.306090
$438$	−2.52779e9	−1.43741
$439$	−1.43295e9	−0.808363	−0.404182	−	0.914679i	$-0.632444\pi$
$439$	−1.43295e9	−0.808363	−0.404182	+	0.914679i	$0.632444\pi$
$440$	−3.04938e9	−1.70658
$441$	−3.77701e8	−0.209707
$442$	9.70569e9	5.34624
$443$	1.62330e9	0.887127	0.443564	−	0.896243i	$-0.353714\pi$
$443$	1.62330e9	0.887127	0.443564	+	0.896243i	$0.353714\pi$
$444$	−2.63712e9	−1.42985
$445$	8.03819e8	0.432413
$446$	2.31768e9	1.23704
$447$	−2.94496e8	−0.155956
$448$	3.12978e9	1.64453
$449$	−7.89867e8	−0.411805	−0.205903	−	0.978573i	$-0.566013\pi$
$449$	−7.89867e8	−0.411805	−0.205903	+	0.978573i	$0.566013\pi$
$450$	−7.73760e8	−0.400279
$451$	4.14930e9	2.12989
$452$	7.37839e8	0.375818
$453$	3.45986e8	0.174870
$454$	2.21608e9	1.11145
$455$	−2.65712e9	−1.32242
$456$	−2.07837e9	−1.02647
$457$	3.17411e9	1.55566	0.777831	−	0.628474i	$-0.216320\pi$
$457$	3.17411e9	1.55566	0.777831	+	0.628474i	$0.216320\pi$
$458$	2.66862e9	1.29795
$459$	4.16561e9	2.01064
$460$	8.38938e8	0.401863
$461$	−1.10733e9	−0.526408	−0.263204	−	0.964740i	$-0.584779\pi$
$461$	−1.10733e9	−0.526408	−0.263204	+	0.964740i	$0.584779\pi$
$462$	6.46059e9	3.04807
$463$	−1.45587e9	−0.681693	−0.340847	−	0.940119i	$-0.610714\pi$
$463$	−1.45587e9	−0.681693	−0.340847	+	0.940119i	$0.610714\pi$
$464$	−2.82501e8	−0.131283
$465$	−1.17705e9	−0.542889
$466$	7.02046e8	0.321377
$467$	−2.23002e9	−1.01321	−0.506606	−	0.862178i	$-0.669100\pi$
$467$	−2.23002e9	−1.01321	−0.506606	+	0.862178i	$0.669100\pi$
$468$	2.74072e9	1.23596
$469$	1.40161e9	0.627369
$470$	−4.61028e8	−0.204826
$471$	−2.01500e9	−0.888591
$472$	−3.63563e9	−1.59141
$473$	6.50245e8	0.282529
$474$	−2.20468e9	−0.950871
$475$	1.26693e9	0.542406
$476$	−1.01125e10	−4.29766
$477$	−4.89605e8	−0.206553
$478$	7.11908e8	0.298144
$479$	9.33167e8	0.387958	0.193979	−	0.981006i	$-0.437861\pi$
$479$	9.33167e8	0.387958	0.193979	+	0.981006i	$0.437861\pi$
$480$	4.88536e8	0.201629
$481$	−4.06545e9	−1.66572
$482$	−7.60461e8	−0.309323
$483$	−8.26857e8	−0.333899
$484$	1.13448e10	4.54818
$485$	2.72292e9	1.08377
$486$	3.10625e9	1.22747
$487$	−1.72559e9	−0.676994	−0.338497	−	0.940967i	$-0.609919\pi$
$487$	−1.72559e9	−0.676994	−0.338497	+	0.940967i	$0.609919\pi$
$488$	−2.64885e9	−1.03178
$489$	−1.30399e9	−0.504305
$490$	1.49122e9	0.572606
$491$	−6.20324e8	−0.236501	−0.118251	−	0.992984i	$-0.537729\pi$
$491$	−6.20324e8	−0.236501	−0.118251	+	0.992984i	$0.537729\pi$
$492$	4.44305e9	1.68191
$493$	−1.03231e9	−0.388012
$494$	−6.88752e9	−2.57051
$495$	−1.21202e9	−0.449148
$496$	−1.88987e9	−0.695418
$497$	3.50007e9	1.27888
$498$	2.43380e8	0.0883045
$499$	3.98852e9	1.43701	0.718506	−	0.695521i	$-0.244826\pi$
$499$	3.98852e9	1.43701	0.718506	+	0.695521i	$0.244826\pi$
$500$	5.25748e9	1.88097
$501$	1.81734e9	0.645662
$502$	−1.16603e9	−0.411385
$503$	1.29341e9	0.453157	0.226579	−	0.973993i	$-0.427246\pi$
$503$	1.29341e9	0.453157	0.226579	+	0.973993i	$0.427246\pi$
$504$	−2.03886e9	−0.709381
$505$	1.60556e9	0.554763
$506$	−3.14464e9	−1.07906
$507$	−4.37328e9	−1.49032
$508$	−4.58605e8	−0.155209
$509$	2.09129e9	0.702913	0.351456	−	0.936204i	$-0.385687\pi$
$509$	2.09129e9	0.702913	0.351456	+	0.936204i	$0.385687\pi$
$510$	−4.59596e9	−1.53420
$511$	4.06023e9	1.34610
$512$	3.58818e9	1.18149
$513$	−2.95608e9	−0.966729
$514$	−1.90101e9	−0.617466
$515$	2.77051e9	0.893787
$516$	6.96280e8	0.223105
$517$	1.12594e9	0.358343
$518$	6.50116e9	2.05512
$519$	−2.18547e9	−0.686215
$520$	−5.03382e9	−1.56995
$521$	4.31681e9	1.33731	0.668653	−	0.743575i	$-0.266871\pi$
$521$	4.31681e9	1.33731	0.668653	+	0.743575i	$0.266871\pi$
$522$	−4.47405e8	−0.137675
$523$	5.49978e9	1.68108	0.840542	−	0.541746i	$-0.182237\pi$
$523$	5.49978e9	1.68108	0.840542	+	0.541746i	$0.182237\pi$
$524$	−4.95767e9	−1.50528
$525$	−1.96177e9	−0.591685
$526$	5.24273e9	1.57075
$527$	−6.90592e9	−2.05534
$528$	3.07168e9	0.908150
$529$	−3.00236e9	−0.881795
$530$	1.93303e9	0.563993
$531$	−1.44503e9	−0.418838
$532$	7.17618e9	2.06634
$533$	6.84953e9	1.95937
$534$	−3.22631e9	−0.916880
$535$	1.45635e8	0.0411176
$536$	2.65531e9	0.744797
$537$	1.90105e8	0.0529765
$538$	−5.28357e9	−1.46281
$539$	−3.64193e9	−1.00178
$540$	−4.64420e9	−1.26921
$541$	−5.48712e9	−1.48989	−0.744945	−	0.667126i	$-0.767524\pi$
$541$	−5.48712e9	−1.48989	−0.744945	+	0.667126i	$0.767524\pi$
$542$	−9.11641e9	−2.45938
$543$	−3.46825e8	−0.0929633
$544$	2.86630e9	0.763354
$545$	−1.28342e9	−0.339610
$546$	1.06650e10	2.80404
$547$	−5.58182e9	−1.45821	−0.729105	−	0.684402i	$-0.760063\pi$
$547$	−5.58182e9	−1.45821	−0.729105	+	0.684402i	$0.760063\pi$
$548$	−7.58225e9	−1.96819
$549$	−1.05282e9	−0.271551
$550$	−7.46085e9	−1.91214
$551$	7.32566e8	0.186559
$552$	−1.56645e9	−0.396397
$553$	3.54124e9	0.890466
$554$	−4.57823e9	−1.14397
$555$	1.92512e9	0.478006
$556$	−1.17444e10	−2.89780
$557$	−1.55205e9	−0.380551	−0.190276	−	0.981731i	$-0.560938\pi$
$557$	−1.55205e9	−0.380551	−0.190276	+	0.981731i	$0.560938\pi$
$558$	−2.99304e9	−0.729277
$559$	1.07340e9	0.259909
$560$	2.02021e9	0.486114
$561$	1.12245e10	2.68408
$562$	1.06348e10	2.52727
$563$	−2.49961e9	−0.590328	−0.295164	−	0.955447i	$-0.595374\pi$
$563$	−2.49961e9	−0.590328	−0.295164	+	0.955447i	$0.595374\pi$
$564$	1.20566e9	0.282974
$565$	−5.38631e8	−0.125638
$566$	3.90954e8	0.0906293
$567$	2.48782e9	0.573163
$568$	6.63076e9	1.51825
$569$	6.84845e9	1.55847	0.779236	−	0.626730i	$-0.215607\pi$
$569$	6.84845e9	1.55847	0.779236	+	0.626730i	$0.215607\pi$
$570$	3.26147e9	0.737651
$571$	−4.81071e7	−0.0108139	−0.00540696	−	0.999985i	$-0.501721\pi$
$571$	−4.81071e7	−0.0108139	−0.00540696	+	0.999985i	$0.501721\pi$
$572$	2.64270e10	5.90420
$573$	−4.04709e9	−0.898673
$574$	−1.09532e10	−2.41742
$575$	9.54875e8	0.209464
$576$	2.35667e9	0.513830
$577$	−6.83896e9	−1.48209	−0.741045	−	0.671455i	$-0.765669\pi$
$577$	−6.83896e9	−1.48209	−0.741045	+	0.671455i	$0.765669\pi$
$578$	−1.91005e10	−4.11431
$579$	3.15444e9	0.675379
$580$	1.15091e9	0.244931
$581$	−3.90926e8	−0.0826948
$582$	−1.09291e10	−2.29801
$583$	−4.72094e9	−0.986707
$584$	7.69196e9	1.59806
$585$	−2.00076e9	−0.413189
$586$	−4.48697e9	−0.921111
$587$	1.56312e9	0.318976	0.159488	−	0.987200i	$-0.449016\pi$
$587$	1.56312e9	0.318976	0.159488	+	0.987200i	$0.449016\pi$
$588$	−3.89976e9	−0.791075
$589$	4.90070e9	0.988222
$590$	5.70519e9	1.14364
$591$	4.18890e9	0.834725
$592$	3.09097e9	0.612306
$593$	−3.33176e9	−0.656118	−0.328059	−	0.944657i	$-0.606395\pi$
$593$	−3.33176e9	−0.656118	−0.328059	+	0.944657i	$0.606395\pi$
$594$	1.74081e10	3.40800
$595$	7.38220e9	1.43673
$596$	1.92636e9	0.372713
$597$	1.44195e9	0.277358
$598$	−5.19108e9	−0.992667
$599$	2.00026e9	0.380271	0.190136	−	0.981758i	$-0.439107\pi$
$599$	2.00026e9	0.380271	0.190136	+	0.981758i	$0.439107\pi$
$600$	−3.71651e9	−0.702434
$601$	−8.58111e9	−1.61244	−0.806218	−	0.591618i	$-0.798489\pi$
$601$	−8.58111e9	−1.61244	−0.806218	+	0.591618i	$0.798489\pi$
$602$	−1.71651e9	−0.320670
$603$	1.05539e9	0.196020
$604$	−2.26316e9	−0.417914
$605$	−8.28183e9	−1.52049
$606$	−6.44430e9	−1.17631
$607$	2.24609e9	0.407631	0.203815	−	0.979009i	$-0.434666\pi$
$607$	2.24609e9	0.407631	0.203815	+	0.979009i	$0.434666\pi$
$608$	−2.03404e9	−0.367026
$609$	−1.13434e9	−0.203508
$610$	4.15669e9	0.741470
$611$	1.85867e9	0.329654
$612$	−7.61449e9	−1.34280
$613$	−7.36697e9	−1.29175	−0.645873	−	0.763445i	$-0.723507\pi$
$613$	−7.36697e9	−1.29175	−0.645873	+	0.763445i	$0.723507\pi$
$614$	−6.57351e9	−1.14606
$615$	−3.24348e9	−0.562274
$616$	−1.96593e10	−3.38872
$617$	8.07677e9	1.38433	0.692165	−	0.721739i	$-0.256657\pi$
$617$	8.07677e9	1.38433	0.692165	+	0.721739i	$0.256657\pi$
$618$	−1.11201e10	−1.89517
$619$	4.11289e9	0.696995	0.348498	−	0.937310i	$-0.386692\pi$
$619$	4.11289e9	0.696995	0.348498	+	0.937310i	$0.386692\pi$
$620$	7.69934e9	1.29743
$621$	−2.22797e9	−0.373327
$622$	1.38876e10	2.31399
$623$	5.18222e9	0.858634
$624$	5.07064e9	0.835442
$625$	−1.19481e8	−0.0195757
$626$	−5.56094e9	−0.906020
$627$	−7.96531e9	−1.29052
$628$	1.31805e10	2.12360
$629$	1.12949e10	1.80970
$630$	3.19946e9	0.509782
$631$	−1.93829e9	−0.307126	−0.153563	−	0.988139i	$-0.549075\pi$
$631$	−1.93829e9	−0.307126	−0.153563	+	0.988139i	$0.549075\pi$
$632$	6.70876e9	1.05714
$633$	5.11145e9	0.800997
$634$	−1.32383e10	−2.06309
$635$	3.34787e8	0.0518872
$636$	−5.05517e9	−0.779176
$637$	−6.01198e9	−0.921572
$638$	−4.31403e9	−0.657674
$639$	2.63548e9	0.399583
$640$	−7.59545e9	−1.14531
$641$	−4.63296e9	−0.694793	−0.347397	−	0.937718i	$-0.612934\pi$
$641$	−4.63296e9	−0.694793	−0.347397	+	0.937718i	$0.612934\pi$
$642$	−5.84541e8	−0.0871851
$643$	4.81785e9	0.714685	0.357342	−	0.933973i	$-0.383683\pi$
$643$	4.81785e9	0.714685	0.357342	+	0.933973i	$0.383683\pi$
$644$	5.40864e9	0.797971
$645$	−5.08292e8	−0.0745855
$646$	1.91354e10	2.79270
$647$	−4.86975e9	−0.706873	−0.353437	−	0.935458i	$-0.614987\pi$
$647$	−4.86975e9	−0.706873	−0.353437	+	0.935458i	$0.614987\pi$
$648$	4.71309e9	0.680445
$649$	−1.39335e10	−2.00080
$650$	−1.23161e10	−1.75905
$651$	−7.58846e9	−1.07800
$652$	8.52966e9	1.20522
$653$	−4.32144e9	−0.607340	−0.303670	−	0.952777i	$-0.598212\pi$
$653$	−4.32144e9	−0.607340	−0.303670	+	0.952777i	$0.598212\pi$
$654$	5.15129e9	0.720102
$655$	3.61915e9	0.503225
$656$	−5.20771e9	−0.720250
$657$	3.05727e9	0.420587
$658$	−2.97225e9	−0.406719
$659$	−1.84953e9	−0.251746	−0.125873	−	0.992046i	$-0.540173\pi$
$659$	−1.84953e9	−0.251746	−0.125873	+	0.992046i	$0.540173\pi$
$660$	−1.25140e10	−1.69431
$661$	1.67946e9	0.226186	0.113093	−	0.993584i	$-0.463924\pi$
$661$	1.67946e9	0.226186	0.113093	+	0.993584i	$0.463924\pi$
$662$	2.48229e10	3.32544
$663$	1.85290e10	2.46919
$664$	−7.40597e8	−0.0981733
$665$	−5.23869e9	−0.690791
$666$	4.89525e9	0.642118
$667$	5.52130e8	0.0720445
$668$	−1.18876e10	−1.54304
$669$	4.42466e9	0.571332
$670$	−4.16682e9	−0.535234
$671$	−1.01517e10	−1.29720
$672$	3.14960e9	0.400371
$673$	−3.83952e9	−0.485540	−0.242770	−	0.970084i	$-0.578056\pi$
$673$	−3.83952e9	−0.485540	−0.242770	+	0.970084i	$0.578056\pi$
$674$	8.61153e9	1.08335
$675$	−5.28600e9	−0.661552
$676$	2.86065e10	3.56165
$677$	1.14031e10	1.41241	0.706206	−	0.708006i	$-0.250405\pi$
$677$	1.14031e10	1.41241	0.706206	+	0.708006i	$0.250405\pi$
$678$	2.16192e9	0.266401
$679$	1.75547e10	2.15203
$680$	1.39853e10	1.70566
$681$	4.23069e9	0.513329
$682$	−2.88599e10	−3.48377
$683$	2.62449e9	0.315190	0.157595	−	0.987504i	$-0.449626\pi$
$683$	2.62449e9	0.315190	0.157595	+	0.987504i	$0.449626\pi$
$684$	5.40353e9	0.645626
$685$	5.53512e9	0.657977
$686$	−8.16588e9	−0.965759
$687$	5.09463e9	0.599466
$688$	−8.16111e8	−0.0955410
$689$	−7.79318e9	−0.907711
$690$	2.45815e9	0.284863
$691$	1.64230e9	0.189356	0.0946778	−	0.995508i	$-0.469818\pi$
$691$	1.64230e9	0.189356	0.0946778	+	0.995508i	$0.469818\pi$
$692$	1.42956e10	1.63995
$693$	−7.81386e9	−0.891866
$694$	−1.18635e9	−0.134727
$695$	8.57353e9	0.968752
$696$	−2.14896e9	−0.241600
$697$	−1.90299e10	−2.12873
$698$	−1.41883e10	−1.57919
$699$	1.34027e9	0.148430
$700$	1.28323e10	1.41404
$701$	−5.25977e9	−0.576705	−0.288352	−	0.957524i	$-0.593107\pi$
$701$	−5.25977e9	−0.576705	−0.288352	+	0.957524i	$0.593107\pi$
$702$	2.87368e10	3.13515
$703$	−8.01532e9	−0.870116
$704$	2.27238e10	2.45457
$705$	−8.80142e8	−0.0945999
$706$	−2.94610e10	−3.15088
$707$	1.03511e10	1.10158
$708$	−1.49199e10	−1.57997
$709$	−9.05667e9	−0.954348	−0.477174	−	0.878809i	$-0.658339\pi$
$709$	−9.05667e9	−0.954348	−0.477174	+	0.878809i	$0.658339\pi$
$710$	−1.04053e10	−1.09106
$711$	2.66648e9	0.278225
$712$	9.81755e9	1.01935
$713$	3.69362e9	0.381627
$714$	−2.96302e10	−3.04643
$715$	−1.92920e10	−1.97381
$716$	−1.24351e9	−0.126606
$717$	1.35909e9	0.137700
$718$	2.19907e10	2.21719
$719$	1.23375e10	1.23787	0.618935	−	0.785443i	$-0.287565\pi$
$719$	1.23375e10	1.23787	0.618935	+	0.785443i	$0.287565\pi$
$720$	1.52118e9	0.151886
$721$	1.78615e10	1.77478
$722$	3.55285e9	0.351315
$723$	−1.45179e9	−0.142863
$724$	2.26865e9	0.222169
$725$	1.30996e9	0.127666
$726$	3.32410e10	3.22401
$727$	8.00292e8	0.0772464	0.0386232	−	0.999254i	$-0.487703\pi$
$727$	8.00292e8	0.0772464	0.0386232	+	0.999254i	$0.487703\pi$
$728$	−3.24530e10	−3.11742
$729$	1.07603e10	1.02867
$730$	−1.20706e10	−1.14841
$731$	−2.98221e9	−0.282376
$732$	−1.08704e10	−1.02437
$733$	−8.12305e9	−0.761825	−0.380912	−	0.924611i	$-0.624390\pi$
$733$	−8.12305e9	−0.761825	−0.380912	+	0.924611i	$0.624390\pi$
$734$	2.06706e10	1.92938
$735$	2.84687e9	0.264461
$736$	−1.53304e9	−0.141736
$737$	1.01764e10	0.936393
$738$	−8.24759e9	−0.755318
$739$	−1.58853e10	−1.44791	−0.723954	−	0.689848i	$-0.757677\pi$
$739$	−1.58853e10	−1.44791	−0.723954	+	0.689848i	$0.757677\pi$
$740$	−1.25926e10	−1.14237
$741$	−1.31489e10	−1.18720
$742$	1.24623e10	1.11991
$743$	1.84265e10	1.64810	0.824048	−	0.566521i	$-0.191711\pi$
$743$	1.84265e10	1.64810	0.824048	+	0.566521i	$0.191711\pi$
$744$	−1.43761e10	−1.27978
$745$	−1.40626e9	−0.124600
$746$	−8.22631e9	−0.725469
$747$	−2.94360e8	−0.0258379
$748$	−7.34215e10	−6.41457
$749$	9.38910e8	0.0816465
$750$	1.54048e10	1.33334
$751$	4.18559e9	0.360592	0.180296	−	0.983612i	$-0.442294\pi$
$751$	4.18559e9	0.360592	0.180296	+	0.983612i	$0.442294\pi$
$752$	−1.41315e9	−0.121179
$753$	−2.22606e9	−0.190000
$754$	−7.12147e9	−0.605020
$755$	1.65213e9	0.139711
$756$	−2.99412e10	−2.52024
$757$	1.67312e10	1.40182	0.700908	−	0.713252i	$-0.252778\pi$
$757$	1.67312e10	1.40182	0.700908	+	0.713252i	$0.252778\pi$
$758$	−9.52250e9	−0.794161
$759$	−6.00340e9	−0.498369
$760$	−9.92452e9	−0.820091
$761$	−1.16945e10	−0.961911	−0.480955	−	0.876745i	$-0.659710\pi$
$761$	−1.16945e10	−0.961911	−0.480955	+	0.876745i	$0.659710\pi$
$762$	−1.34374e9	−0.110021
$763$	−8.27419e9	−0.674356
$764$	2.64728e10	2.14770
$765$	5.55866e9	0.448905
$766$	1.67580e9	0.134717
$767$	−2.30009e10	−1.84061
$768$	1.74730e10	1.39189
$769$	−1.70901e10	−1.35519	−0.677597	−	0.735433i	$-0.736979\pi$
$769$	−1.70901e10	−1.35519	−0.677597	+	0.735433i	$0.736979\pi$
$770$	3.08503e10	2.43524
$771$	−3.62919e9	−0.285180
$772$	−2.06338e10	−1.61406
$773$	−1.12070e9	−0.0872690	−0.0436345	−	0.999048i	$-0.513894\pi$
$773$	−1.12070e9	−0.0872690	−0.0436345	+	0.999048i	$0.513894\pi$
$774$	−1.29250e9	−0.100193
$775$	8.76334e9	0.676260
$776$	3.32567e10	2.55484
$777$	1.24113e10	0.949168
$778$	3.69269e10	2.81134
$779$	1.35043e10	1.02351
$780$	−2.06578e10	−1.55867
$781$	2.54122e10	1.90882
$782$	1.44223e10	1.07847
$783$	−3.05648e9	−0.227539
$784$	4.57092e9	0.338764
$785$	−9.62192e9	−0.709934
$786$	−1.45263e10	−1.06703
$787$	3.19989e9	0.234004	0.117002	−	0.993132i	$-0.462672\pi$
$787$	3.19989e9	0.234004	0.117002	+	0.993132i	$0.462672\pi$
$788$	−2.74004e10	−1.99487
$789$	1.00088e10	0.725461
$790$	−1.05277e10	−0.759692
$791$	−3.47255e9	−0.249477
$792$	−1.48031e10	−1.05880
$793$	−1.67580e10	−1.19335
$794$	−2.23406e10	−1.58388
$795$	3.69033e9	0.260483
$796$	−9.43209e9	−0.662846
$797$	1.93896e10	1.35664	0.678322	−	0.734765i	$-0.262708\pi$
$797$	1.93896e10	1.35664	0.678322	+	0.734765i	$0.262708\pi$
$798$	2.10267e10	1.46474
$799$	−5.16390e9	−0.358150
$800$	−3.63723e9	−0.251163
$801$	3.90212e9	0.268279
$802$	−1.43849e10	−0.984680
$803$	2.94793e10	2.00915
$804$	1.08969e10	0.739444
$805$	−3.94836e9	−0.266767
$806$	−4.76410e10	−3.20485
$807$	−1.00868e10	−0.675609
$808$	1.96098e10	1.30777
$809$	−2.20959e10	−1.46721	−0.733604	−	0.679577i	$-0.762163\pi$
$809$	−2.20959e10	−1.46721	−0.733604	+	0.679577i	$0.762163\pi$
$810$	−7.39598e9	−0.488988
$811$	1.03080e10	0.678583	0.339292	−	0.940681i	$-0.389813\pi$
$811$	1.03080e10	0.678583	0.339292	+	0.940681i	$0.389813\pi$
$812$	7.41993e9	0.486355
$813$	−1.74040e10	−1.13588
$814$	4.72017e10	3.06741
$815$	−6.22675e9	−0.402911
$816$	−1.40876e10	−0.907658
$817$	2.11629e9	0.135768
$818$	−1.63141e10	−1.04214
$819$	−1.28989e10	−0.820462
$820$	2.12162e10	1.34375
$821$	−1.08963e10	−0.687192	−0.343596	−	0.939117i	$-0.611645\pi$
$821$	−1.08963e10	−0.687192	−0.343596	+	0.939117i	$0.611645\pi$
$822$	−2.22165e10	−1.39516
$823$	1.58099e10	0.988622	0.494311	−	0.869285i	$-0.335420\pi$
$823$	1.58099e10	0.988622	0.494311	+	0.869285i	$0.335420\pi$
$824$	3.38379e10	2.10697
$825$	−1.42434e10	−0.883132
$826$	3.67813e10	2.27090
$827$	6.58783e9	0.405017	0.202508	−	0.979281i	$-0.435091\pi$
$827$	6.58783e9	0.405017	0.202508	+	0.979281i	$0.435091\pi$
$828$	4.07260e9	0.249325
$829$	1.31751e10	0.803180	0.401590	−	0.915819i	$-0.368458\pi$
$829$	1.31751e10	0.803180	0.401590	+	0.915819i	$0.368458\pi$
$830$	1.16218e9	0.0705503
$831$	−8.74024e9	−0.528347
$832$	3.75117e10	2.25806
$833$	1.67029e10	1.00123
$834$	−3.44118e10	−2.05412
$835$	8.67808e9	0.515847
$836$	5.21026e10	3.08417
$837$	−2.04472e10	−1.20530
$838$	3.07626e10	1.80580
$839$	1.44377e10	0.843981	0.421990	−	0.906600i	$-0.361332\pi$
$839$	1.44377e10	0.843981	0.421990	+	0.906600i	$0.361332\pi$
$840$	1.53676e10	0.894598
$841$	−1.64924e10	−0.956090
$842$	1.64595e10	0.950218
$843$	2.03028e10	1.16724
$844$	−3.34350e10	−1.91427
$845$	−2.08831e10	−1.19068
$846$	−2.23805e9	−0.127079
$847$	−5.33930e10	−3.01920
$848$	5.92517e9	0.333668
$849$	7.46366e8	0.0418577
$850$	3.42177e10	1.91110
$851$	−6.04109e9	−0.336018
$852$	2.72114e10	1.50734
$853$	−1.27917e10	−0.705679	−0.352840	−	0.935684i	$-0.614784\pi$
$853$	−1.27917e10	−0.705679	−0.352840	+	0.935684i	$0.614784\pi$
$854$	2.67982e10	1.47232
$855$	−3.94463e9	−0.215837
$856$	1.77873e9	0.0969288
$857$	−2.68071e10	−1.45485	−0.727423	−	0.686189i	$-0.759282\pi$
$857$	−2.68071e10	−1.45485	−0.727423	+	0.686189i	$0.759282\pi$
$858$	7.74329e10	4.18523
$859$	7.43216e9	0.400073	0.200036	−	0.979788i	$-0.435894\pi$
$859$	7.43216e9	0.400073	0.200036	+	0.979788i	$0.435894\pi$
$860$	3.32484e9	0.178249
$861$	−2.09107e10	−1.11650
$862$	−1.84009e10	−0.978508
$863$	2.49200e10	1.31980	0.659902	−	0.751352i	$-0.270598\pi$
$863$	2.49200e10	1.31980	0.659902	+	0.751352i	$0.270598\pi$
$864$	8.48661e9	0.447648
$865$	−1.04360e10	−0.548247
$866$	8.27482e9	0.432958
$867$	−3.64645e10	−1.90022
$868$	4.96376e10	2.57627
$869$	2.57111e10	1.32908
$870$	3.37225e9	0.173621
$871$	1.67989e10	0.861424
$872$	−1.56752e10	−0.800580
$873$	1.32183e10	0.672399
$874$	−1.02346e10	−0.518537
$875$	−2.47437e10	−1.24864
$876$	3.15663e10	1.58657
$877$	−3.16610e10	−1.58499	−0.792493	−	0.609881i	$-0.791217\pi$
$877$	−3.16610e10	−1.58499	−0.792493	+	0.609881i	$0.791217\pi$
$878$	2.74642e10	1.36942
$879$	−8.56602e9	−0.425420
$880$	1.46677e10	0.725560
$881$	9.18139e9	0.452369	0.226185	−	0.974084i	$-0.427375\pi$
$881$	9.18139e9	0.452369	0.226185	+	0.974084i	$0.427375\pi$
$882$	7.23908e9	0.355258
$883$	−2.18382e10	−1.06746	−0.533732	−	0.845653i	$-0.679211\pi$
$883$	−2.18382e10	−1.06746	−0.533732	+	0.845653i	$0.679211\pi$
$884$	−1.21202e11	−5.90101
$885$	1.08917e10	0.528195
$886$	−3.11124e10	−1.50285
$887$	−3.51106e10	−1.68929	−0.844647	−	0.535324i	$-0.820189\pi$
$887$	−3.51106e10	−1.68929	−0.844647	+	0.535324i	$0.820189\pi$
$888$	2.35128e10	1.12683
$889$	2.15837e9	0.103031
$890$	−1.54061e10	−0.732535
$891$	1.80628e10	0.855486
$892$	−2.89426e10	−1.36540
$893$	3.66450e9	0.172201
$894$	5.64436e9	0.264200
$895$	9.07778e8	0.0423252
$896$	−4.89679e10	−2.27422
$897$	−9.91022e9	−0.458469
$898$	1.51387e10	0.697624
$899$	5.06716e9	0.232598
$900$	9.66249e9	0.441815
$901$	2.16516e10	0.986174
$902$	−7.95261e10	−3.60817
$903$	−3.27696e9	−0.148103
$904$	−6.57863e9	−0.296174
$905$	−1.65614e9	−0.0742724
$906$	−6.63122e9	−0.296241
$907$	1.81270e10	0.806676	0.403338	−	0.915051i	$-0.367850\pi$
$907$	1.81270e10	0.806676	0.403338	+	0.915051i	$0.367850\pi$
$908$	−2.76738e10	−1.22678
$909$	7.79416e9	0.344188
$910$	5.09267e10	2.24027
$911$	4.43842e10	1.94498	0.972488	−	0.232952i	$-0.0748386\pi$
$911$	4.43842e10	1.94498	0.972488	+	0.232952i	$0.0748386\pi$
$912$	9.99712e9	0.436408
$913$	−2.83832e9	−0.123428
$914$	−6.08354e10	−2.63539
$915$	7.93549e9	0.342452
$916$	−3.33250e10	−1.43264
$917$	2.33327e10	0.999245
$918$	−7.98388e10	−3.40616
$919$	−3.80235e10	−1.61602	−0.808012	−	0.589166i	$-0.799456\pi$
$919$	−3.80235e10	−1.61602	−0.808012	+	0.589166i	$0.799456\pi$
$920$	−7.48004e9	−0.316699
$921$	−1.25494e10	−0.529315
$922$	2.12232e10	0.891769
$923$	4.19497e10	1.75600
$924$	−8.06781e10	−3.36437
$925$	−1.43329e10	−0.595438
$926$	2.79034e10	1.15483
$927$	1.34493e10	0.554526
$928$	−2.10313e9	−0.0863868
$929$	−3.00377e10	−1.22917	−0.614585	−	0.788851i	$-0.710677\pi$
$929$	−3.00377e10	−1.22917	−0.614585	+	0.788851i	$0.710677\pi$
$930$	2.25596e10	0.919688
$931$	−1.18530e10	−0.481400
$932$	−8.76696e9	−0.354726
$933$	2.65127e10	1.06873
$934$	4.27409e10	1.71645
$935$	5.35985e10	2.14443
$936$	−2.44365e10	−0.974033
$937$	−4.22202e10	−1.67661	−0.838303	−	0.545204i	$-0.816452\pi$
$937$	−4.22202e10	−1.67661	−0.838303	+	0.545204i	$0.816452\pi$
$938$	−2.68635e10	−1.06280
$939$	−1.06163e10	−0.418451
$940$	5.75718e9	0.226080
$941$	3.37621e10	1.32089	0.660444	−	0.750875i	$-0.270368\pi$
$941$	3.37621e10	1.32089	0.660444	+	0.750875i	$0.270368\pi$
$942$	3.86198e10	1.50533
$943$	1.01781e10	0.395254
$944$	1.74876e10	0.676596
$945$	2.18574e10	0.842532
$946$	−1.24627e10	−0.478622
$947$	−2.01458e10	−0.770832	−0.385416	−	0.922743i	$-0.625942\pi$
$947$	−2.01458e10	−0.770832	−0.385416	+	0.922743i	$0.625942\pi$
$948$	2.75314e10	1.04954
$949$	4.86635e10	1.84830
$950$	−2.42821e10	−0.918871
$951$	−2.52730e10	−0.952851
$952$	9.01635e10	3.38689
$953$	−2.24395e10	−0.839825	−0.419913	−	0.907565i	$-0.637939\pi$
$953$	−2.24395e10	−0.839825	−0.419913	+	0.907565i	$0.637939\pi$
$954$	9.38385e9	0.349914
$955$	−1.93254e10	−0.717989
$956$	−8.89011e9	−0.329082
$957$	−8.23586e9	−0.303750
$958$	−1.78852e10	−0.657226
$959$	3.56850e10	1.30653
$960$	−1.77630e10	−0.647989
$961$	6.38552e9	0.232094
$962$	7.79191e10	2.82183
$963$	7.06982e8	0.0255103
$964$	9.49642e9	0.341421
$965$	1.50629e10	0.539589
$966$	1.58477e10	0.565647
$967$	−3.16478e10	−1.12551	−0.562757	−	0.826622i	$-0.690259\pi$
$967$	−3.16478e10	−1.12551	−0.562757	+	0.826622i	$0.690259\pi$
$968$	−1.01151e11	−3.58432
$969$	3.65312e10	1.28983
$970$	−5.21879e10	−1.83598
$971$	−2.82843e10	−0.991468	−0.495734	−	0.868474i	$-0.665101\pi$
$971$	−2.82843e10	−0.991468	−0.495734	+	0.868474i	$0.665101\pi$
$972$	−3.87900e10	−1.35484
$973$	5.52736e10	1.92363
$974$	3.30728e10	1.14687
$975$	−2.35126e10	−0.812427
$976$	1.27412e10	0.438667
$977$	2.65176e10	0.909709	0.454855	−	0.890566i	$-0.349691\pi$
$977$	2.65176e10	0.909709	0.454855	+	0.890566i	$0.349691\pi$
$978$	2.49925e10	0.854326
$979$	3.76255e10	1.28157
$980$	−1.86219e10	−0.632024
$981$	−6.23031e9	−0.210702
$982$	1.18892e10	0.400648
$983$	4.89517e10	1.64373	0.821866	−	0.569681i	$-0.192933\pi$
$983$	4.89517e10	1.64373	0.821866	+	0.569681i	$0.192933\pi$
$984$	−3.96146e10	−1.32548
$985$	2.00026e10	0.666898
$986$	1.97854e10	0.657318
$987$	−5.67428e9	−0.187845
$988$	8.60094e10	2.83724
$989$	1.59503e9	0.0524304
$990$	2.32297e10	0.760886
$991$	−1.75057e10	−0.571374	−0.285687	−	0.958323i	$-0.592222\pi$
$991$	−1.75057e10	−0.571374	−0.285687	+	0.958323i	$0.592222\pi$
$992$	−1.40694e10	−0.457600
$993$	4.73891e10	1.53588
$994$	−6.70829e10	−2.16650
$995$	6.88553e9	0.221593
$996$	−3.03926e9	−0.0974677
$997$	−1.49917e10	−0.479090	−0.239545	−	0.970885i	$-0.576998\pi$
$997$	−1.49917e10	−0.479090	−0.239545	+	0.970885i	$0.576998\pi$
$998$	−7.64447e10	−2.43439
$999$	3.34423e10	1.06125

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.a.b.1.2	✓	13
3.2	odd	2		387.8.a.d.1.12		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.b.1.2	✓	13	1.1	even	1	trivial
387.8.a.d.1.12		13	3.2	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	43.a (trivial)

\(f(q)\)	\(=\)	\(q-19.1662 q^{2} -36.5899 q^{3} +239.342 q^{4} -174.722 q^{5} +701.287 q^{6} -1126.43 q^{7} -2133.99 q^{8} -848.182 q^{9} +O(q^{10})\)	\(q-19.1662 q^{2} -36.5899 q^{3} +239.342 q^{4} -174.722 q^{5} +701.287 q^{6} -1126.43 q^{7} -2133.99 q^{8} -848.182 q^{9} +3348.75 q^{10} -8178.46 q^{11} -8757.47 q^{12} -13500.8 q^{13} +21589.4 q^{14} +6393.05 q^{15} +10264.6 q^{16} +37508.8 q^{17} +16256.4 q^{18} -26617.7 q^{19} -41818.2 q^{20} +41216.0 q^{21} +156750. q^{22} -20061.6 q^{23} +78082.3 q^{24} -47597.3 q^{25} +258757. q^{26} +111057. q^{27} -269602. q^{28} -27521.8 q^{29} -122530. q^{30} -184114. q^{31} +76416.8 q^{32} +299249. q^{33} -718900. q^{34} +196812. q^{35} -203005. q^{36} +301128. q^{37} +510158. q^{38} +493991. q^{39} +372855. q^{40} -507344. q^{41} -789952. q^{42} -79507.0 q^{43} -1.95745e6 q^{44} +148196. q^{45} +384503. q^{46} -137672. q^{47} -375582. q^{48} +445307. q^{49} +912256. q^{50} -1.37244e6 q^{51} -3.23129e6 q^{52} +577240. q^{53} -2.12853e6 q^{54} +1.42896e6 q^{55} +2.40379e6 q^{56} +973937. q^{57} +527487. q^{58} +1.70368e6 q^{59} +1.53012e6 q^{60} +1.24127e6 q^{61} +3.52877e6 q^{62} +955420. q^{63} -2.77849e6 q^{64} +2.35888e6 q^{65} -5.73545e6 q^{66} -1.24429e6 q^{67} +8.97742e6 q^{68} +734050. q^{69} -3.77214e6 q^{70} -3.10722e6 q^{71} +1.81001e6 q^{72} -3.60450e6 q^{73} -5.77146e6 q^{74} +1.74158e6 q^{75} -6.37071e6 q^{76} +9.21248e6 q^{77} -9.46790e6 q^{78} -3.14376e6 q^{79} -1.79346e6 q^{80} -2.20858e6 q^{81} +9.72384e6 q^{82} +347048. q^{83} +9.86470e6 q^{84} -6.55361e6 q^{85} +1.52384e6 q^{86} +1.00702e6 q^{87} +1.74527e7 q^{88} -4.60056e6 q^{89} -2.84035e6 q^{90} +1.52077e7 q^{91} -4.80156e6 q^{92} +6.73672e6 q^{93} +2.63864e6 q^{94} +4.65069e6 q^{95} -2.79608e6 q^{96} -1.55843e7 q^{97} -8.53482e6 q^{98} +6.93682e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9}+O(q^{10}) \) 13 * q + 16 * q^2 + 94 * q^3 + 922 * q^4 + 998 * q^5 + 183 * q^6 + 1360 * q^7 + 3870 * q^8 + 10011 * q^9	\( 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9} + 4667 q^{10} + 1620 q^{11} - 19681 q^{12} + 13550 q^{13} + 44160 q^{14} + 31412 q^{15} + 114026 q^{16} + 110880 q^{17} + 159267 q^{18} + 105058 q^{19} + 167251 q^{20} + 129840 q^{21} + 201504 q^{22} + 160184 q^{23} + 161289 q^{24} + 270149 q^{25} + 272104 q^{26} + 252544 q^{27} + 208172 q^{28} + 285546 q^{29} + 107580 q^{30} - 99616 q^{31} + 200126 q^{32} + 531468 q^{33} - 80941 q^{34} - 187104 q^{35} - 608975 q^{36} + 176038 q^{37} + 652165 q^{38} - 794680 q^{39} - 895387 q^{40} - 410260 q^{41} - 3413218 q^{42} - 1033591 q^{43} - 2177076 q^{44} - 1051178 q^{45} - 3975765 q^{46} - 424556 q^{47} - 2360477 q^{48} - 1561359 q^{49} - 4063801 q^{50} - 2375738 q^{51} - 4172312 q^{52} + 3992458 q^{53} - 10438626 q^{54} + 406960 q^{55} + 1559556 q^{56} - 3116152 q^{57} - 4052005 q^{58} + 2248836 q^{59} - 2911436 q^{60} + 6210394 q^{61} + 885317 q^{62} + 11622368 q^{63} - 3096318 q^{64} + 5600420 q^{65} - 2174604 q^{66} - 1993648 q^{67} + 9327135 q^{68} + 13366240 q^{69} - 1105098 q^{70} + 4978064 q^{71} + 11370663 q^{72} + 8224814 q^{73} - 3613563 q^{74} + 27115592 q^{75} + 10687121 q^{76} + 17261892 q^{77} - 15226630 q^{78} + 6945708 q^{79} + 15822799 q^{80} + 35113185 q^{81} - 508449 q^{82} + 22937328 q^{83} - 14010106 q^{84} - 575532 q^{85} - 1272112 q^{86} + 9081380 q^{87} + 11202656 q^{88} + 9291302 q^{89} + 2841402 q^{90} + 25581108 q^{91} - 14388137 q^{92} + 25930480 q^{93} - 24645805 q^{94} + 30750464 q^{95} - 22461255 q^{96} + 10001852 q^{97} - 32304856 q^{98} + 5055452 q^{99}+O(q^{100}) \) 13 * q + 16 * q^2 + 94 * q^3 + 922 * q^4 + 998 * q^5 + 183 * q^6 + 1360 * q^7 + 3870 * q^8 + 10011 * q^9 + 4667 * q^10 + 1620 * q^11 - 19681 * q^12 + 13550 * q^13 + 44160 * q^14 + 31412 * q^15 + 114026 * q^16 + 110880 * q^17 + 159267 * q^18 + 105058 * q^19 + 167251 * q^20 + 129840 * q^21 + 201504 * q^22 + 160184 * q^23 + 161289 * q^24 + 270149 * q^25 + 272104 * q^26 + 252544 * q^27 + 208172 * q^28 + 285546 * q^29 + 107580 * q^30 - 99616 * q^31 + 200126 * q^32 + 531468 * q^33 - 80941 * q^34 - 187104 * q^35 - 608975 * q^36 + 176038 * q^37 + 652165 * q^38 - 794680 * q^39 - 895387 * q^40 - 410260 * q^41 - 3413218 * q^42 - 1033591 * q^43 - 2177076 * q^44 - 1051178 * q^45 - 3975765 * q^46 - 424556 * q^47 - 2360477 * q^48 - 1561359 * q^49 - 4063801 * q^50 - 2375738 * q^51 - 4172312 * q^52 + 3992458 * q^53 - 10438626 * q^54 + 406960 * q^55 + 1559556 * q^56 - 3116152 * q^57 - 4052005 * q^58 + 2248836 * q^59 - 2911436 * q^60 + 6210394 * q^61 + 885317 * q^62 + 11622368 * q^63 - 3096318 * q^64 + 5600420 * q^65 - 2174604 * q^66 - 1993648 * q^67 + 9327135 * q^68 + 13366240 * q^69 - 1105098 * q^70 + 4978064 * q^71 + 11370663 * q^72 + 8224814 * q^73 - 3613563 * q^74 + 27115592 * q^75 + 10687121 * q^76 + 17261892 * q^77 - 15226630 * q^78 + 6945708 * q^79 + 15822799 * q^80 + 35113185 * q^81 - 508449 * q^82 + 22937328 * q^83 - 14010106 * q^84 - 575532 * q^85 - 1272112 * q^86 + 9081380 * q^87 + 11202656 * q^88 + 9291302 * q^89 + 2841402 * q^90 + 25581108 * q^91 - 14388137 * q^92 + 25930480 * q^93 - 24645805 * q^94 + 30750464 * q^95 - 22461255 * q^96 + 10001852 * q^97 - 32304856 * q^98 + 5055452 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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