LMFDB - Embedded newform 23.10.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,10,Mod(1,23)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("23.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	23.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:	$11.8458242318$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 640x^{5} - 1455x^{4} + 114552x^{3} + 321544x^{2} - 5741296x - 13379024 $ x^7 - 640x^5 - 1455x^4 + 114552x^3 + 321544x^2 - 5741296*x - 13379024
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{7}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-10.3773$ of defining polynomial
Character	$\chi$	$=$	23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-20.7546 q^{2} +245.319 q^{3} -81.2472 q^{4} -680.714 q^{5} -5091.50 q^{6} -8213.17 q^{7} +12312.6 q^{8} +40498.5 q^{9} +O(q^{10})$	\(q-20.7546 q^{2} +245.319 q^{3} -81.2472 q^{4} -680.714 q^{5} -5091.50 q^{6} -8213.17 q^{7} +12312.6 q^{8} +40498.5 q^{9} +14127.9 q^{10} -64490.0 q^{11} -19931.5 q^{12} +23617.4 q^{13} +170461. q^{14} -166992. q^{15} -213944. q^{16} -654861. q^{17} -840530. q^{18} +5927.44 q^{19} +55306.1 q^{20} -2.01485e6 q^{21} +1.33846e6 q^{22} -279841. q^{23} +3.02052e6 q^{24} -1.48975e6 q^{25} -490170. q^{26} +5.10645e6 q^{27} +667297. q^{28} -907081. q^{29} +3.46585e6 q^{30} +368517. q^{31} -1.86373e6 q^{32} -1.58206e7 q^{33} +1.35914e7 q^{34} +5.59082e6 q^{35} -3.29039e6 q^{36} -6.33005e6 q^{37} -123022. q^{38} +5.79381e6 q^{39} -8.38136e6 q^{40} +2.53987e7 q^{41} +4.18174e7 q^{42} -3.13783e7 q^{43} +5.23963e6 q^{44} -2.75679e7 q^{45} +5.80798e6 q^{46} +6.11683e7 q^{47} -5.24847e7 q^{48} +2.71026e7 q^{49} +3.09192e7 q^{50} -1.60650e8 q^{51} -1.91885e6 q^{52} +7.51263e7 q^{53} -1.05982e8 q^{54} +4.38992e7 q^{55} -1.01126e8 q^{56} +1.45412e6 q^{57} +1.88261e7 q^{58} +3.86273e7 q^{59} +1.35677e7 q^{60} +7.48746e6 q^{61} -7.64843e6 q^{62} -3.32622e8 q^{63} +1.48220e8 q^{64} -1.60767e7 q^{65} +3.28351e8 q^{66} +1.12424e8 q^{67} +5.32056e7 q^{68} -6.86504e7 q^{69} -1.16035e8 q^{70} -3.63690e8 q^{71} +4.98642e8 q^{72} -1.03141e8 q^{73} +1.31378e8 q^{74} -3.65465e8 q^{75} -481588. q^{76} +5.29668e8 q^{77} -1.20248e8 q^{78} -1.27219e8 q^{79} +1.45635e8 q^{80} +4.55578e8 q^{81} -5.27140e8 q^{82} +6.71853e8 q^{83} +1.63701e8 q^{84} +4.45773e8 q^{85} +6.51243e8 q^{86} -2.22524e8 q^{87} -7.94039e8 q^{88} -1.29959e8 q^{89} +5.72161e8 q^{90} -1.93974e8 q^{91} +2.27363e7 q^{92} +9.04044e7 q^{93} -1.26952e9 q^{94} -4.03489e6 q^{95} -4.57208e8 q^{96} -1.21481e9 q^{97} -5.62504e8 q^{98} -2.61175e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 89 q^{3} + 1536 q^{4} - 2388 q^{5} - 12518 q^{6} - 9896 q^{7} + 34920 q^{8} + 33064 q^{9}+O(q^{10}) $ 7 * q - 89 * q^3 + 1536 * q^4 - 2388 * q^5 - 12518 * q^6 - 9896 * q^7 + 34920 * q^8 + 33064 * q^9	\( 7 q - 89 q^{3} + 1536 q^{4} - 2388 q^{5} - 12518 q^{6} - 9896 q^{7} + 34920 q^{8} + 33064 q^{9} - 60820 q^{10} - 78484 q^{11} - 343492 q^{12} - 296769 q^{13} - 711120 q^{14} - 237870 q^{15} - 253440 q^{16} - 1128820 q^{17} - 499874 q^{18} - 1301252 q^{19} - 3482704 q^{20} - 108908 q^{21} - 1562088 q^{22} - 1958887 q^{23} - 4606464 q^{24} - 1320899 q^{25} + 692230 q^{26} + 2977921 q^{27} - 8371144 q^{28} + 2813849 q^{29} + 25535196 q^{30} + 7334751 q^{31} + 26028800 q^{32} + 646330 q^{33} + 14981564 q^{34} + 23410104 q^{35} + 40211900 q^{36} - 13324320 q^{37} + 37578632 q^{38} + 6304533 q^{39} - 45307920 q^{40} - 15691573 q^{41} + 124523248 q^{42} - 46474818 q^{43} + 43428040 q^{44} - 72736710 q^{45} + 8232227 q^{47} - 163054384 q^{48} + 29219031 q^{49} + 50366304 q^{50} - 136344764 q^{51} - 100922292 q^{52} - 53545400 q^{53} - 26171642 q^{54} - 181608484 q^{55} - 420111696 q^{56} - 218913370 q^{57} - 39304854 q^{58} - 341275144 q^{59} + 420822384 q^{60} - 277157656 q^{61} + 464777594 q^{62} - 574619276 q^{63} + 340566208 q^{64} + 106659278 q^{65} + 258025876 q^{66} + 89654580 q^{67} + 62700400 q^{68} + 24905849 q^{69} + 1187910040 q^{70} - 286098961 q^{71} + 1446323640 q^{72} - 637495039 q^{73} + 189880036 q^{74} - 160733159 q^{75} + 228563936 q^{76} + 511682536 q^{77} + 1199383686 q^{78} + 274469546 q^{79} - 345318560 q^{80} - 237775217 q^{81} - 570256066 q^{82} + 1164579762 q^{83} + 3447171416 q^{84} - 18639492 q^{85} + 415245796 q^{86} - 595368433 q^{87} + 103329440 q^{88} - 504153000 q^{89} - 1414126968 q^{90} - 1692320156 q^{91} - 429835776 q^{92} - 2753858687 q^{93} - 2214048622 q^{94} + 162962164 q^{95} - 3332565856 q^{96} - 3519929016 q^{97} + 2474592568 q^{98} - 1883749262 q^{99}+O(q^{100}) \) 7 * q - 89 * q^3 + 1536 * q^4 - 2388 * q^5 - 12518 * q^6 - 9896 * q^7 + 34920 * q^8 + 33064 * q^9 - 60820 * q^10 - 78484 * q^11 - 343492 * q^12 - 296769 * q^13 - 711120 * q^14 - 237870 * q^15 - 253440 * q^16 - 1128820 * q^17 - 499874 * q^18 - 1301252 * q^19 - 3482704 * q^20 - 108908 * q^21 - 1562088 * q^22 - 1958887 * q^23 - 4606464 * q^24 - 1320899 * q^25 + 692230 * q^26 + 2977921 * q^27 - 8371144 * q^28 + 2813849 * q^29 + 25535196 * q^30 + 7334751 * q^31 + 26028800 * q^32 + 646330 * q^33 + 14981564 * q^34 + 23410104 * q^35 + 40211900 * q^36 - 13324320 * q^37 + 37578632 * q^38 + 6304533 * q^39 - 45307920 * q^40 - 15691573 * q^41 + 124523248 * q^42 - 46474818 * q^43 + 43428040 * q^44 - 72736710 * q^45 + 8232227 * q^47 - 163054384 * q^48 + 29219031 * q^49 + 50366304 * q^50 - 136344764 * q^51 - 100922292 * q^52 - 53545400 * q^53 - 26171642 * q^54 - 181608484 * q^55 - 420111696 * q^56 - 218913370 * q^57 - 39304854 * q^58 - 341275144 * q^59 + 420822384 * q^60 - 277157656 * q^61 + 464777594 * q^62 - 574619276 * q^63 + 340566208 * q^64 + 106659278 * q^65 + 258025876 * q^66 + 89654580 * q^67 + 62700400 * q^68 + 24905849 * q^69 + 1187910040 * q^70 - 286098961 * q^71 + 1446323640 * q^72 - 637495039 * q^73 + 189880036 * q^74 - 160733159 * q^75 + 228563936 * q^76 + 511682536 * q^77 + 1199383686 * q^78 + 274469546 * q^79 - 345318560 * q^80 - 237775217 * q^81 - 570256066 * q^82 + 1164579762 * q^83 + 3447171416 * q^84 - 18639492 * q^85 + 415245796 * q^86 - 595368433 * q^87 + 103329440 * q^88 - 504153000 * q^89 - 1414126968 * q^90 - 1692320156 * q^91 - 429835776 * q^92 - 2753858687 * q^93 - 2214048622 * q^94 + 162962164 * q^95 - 3332565856 * q^96 - 3519929016 * q^97 + 2474592568 * q^98 - 1883749262 * 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 $

$2$	−20.7546	−0.917232	−0.458616	−	0.888635i	$-0.651655\pi$
$2$	−20.7546	−0.917232	−0.458616	+	0.888635i	$0.651655\pi$
$3$	245.319	1.74858	0.874291	−	0.485402i	$-0.161327\pi$
$3$	245.319	1.74858	0.874291	+	0.485402i	$0.161327\pi$
$4$	−81.2472	−0.158686
$5$	−680.714	−0.487079	−0.243540	−	0.969891i	$-0.578309\pi$
$5$	−680.714	−0.487079	−0.243540	+	0.969891i	$0.578309\pi$
$6$	−5091.50	−1.60385
$7$	−8213.17	−1.29291	−0.646457	−	0.762950i	$-0.723750\pi$
$7$	−8213.17	−1.29291	−0.646457	+	0.762950i	$0.723750\pi$
$8$	12312.6	1.06278
$9$	40498.5	2.05754
$10$	14127.9	0.446765
$11$	−64490.0	−1.32808	−0.664042	−	0.747696i	$-0.731160\pi$
$11$	−64490.0	−1.32808	−0.664042	+	0.747696i	$0.731160\pi$
$12$	−19931.5	−0.277475
$13$	23617.4	0.229344	0.114672	−	0.993403i	$-0.463418\pi$
$13$	23617.4	0.229344	0.114672	+	0.993403i	$0.463418\pi$
$14$	170461.	1.18590
$15$	−166992.	−0.851698
$16$	−213944.	−0.816133
$17$	−654861.	−1.90164	−0.950821	−	0.309740i	$-0.899758\pi$
$17$	−654861.	−1.90164	−0.950821	+	0.309740i	$0.899758\pi$
$18$	−840530.	−1.88724
$19$	5927.44	0.0104346	0.00521731	−	0.999986i	$-0.498339\pi$
$19$	5927.44	0.0104346	0.00521731	+	0.999986i	$0.498339\pi$
$20$	55306.1	0.0772926
$21$	−2.01485e6	−2.26077
$22$	1.33846e6	1.21816
$23$	−279841.	−0.208514
$23$	−279841.	−0.208514
$24$	3.02052e6	1.85836
$25$	−1.48975e6	−0.762754
$26$	−490170.	−0.210362
$27$	5.10645e6	1.84919
$28$	667297.	0.205167
$29$	−907081.	−0.238152	−0.119076	−	0.992885i	$-0.537993\pi$
$29$	−907081.	−0.238152	−0.119076	+	0.992885i	$0.537993\pi$
$30$	3.46585e6	0.781204
$31$	368517.	0.0716689	0.0358344	−	0.999358i	$-0.488591\pi$
$31$	368517.	0.0716689	0.0358344	+	0.999358i	$0.488591\pi$
$32$	−1.86373e6	−0.314201
$33$	−1.58206e7	−2.32226
$34$	1.35914e7	1.74425
$35$	5.59082e6	0.629752
$36$	−3.29039e6	−0.326502
$37$	−6.33005e6	−0.555264	−0.277632	−	0.960687i	$-0.589550\pi$
$37$	−6.33005e6	−0.555264	−0.277632	+	0.960687i	$0.589550\pi$
$38$	−123022.	−0.00957096
$39$	5.79381e6	0.401027
$40$	−8.38136e6	−0.517660
$41$	2.53987e7	1.40373	0.701867	−	0.712308i	$-0.252350\pi$
$41$	2.53987e7	1.40373	0.701867	+	0.712308i	$0.252350\pi$
$42$	4.18174e7	2.07365
$43$	−3.13783e7	−1.39966	−0.699828	−	0.714312i	$-0.746740\pi$
$43$	−3.13783e7	−1.39966	−0.699828	+	0.714312i	$0.746740\pi$
$44$	5.23963e6	0.210748
$45$	−2.75679e7	−1.00218
$46$	5.80798e6	0.191256
$47$	6.11683e7	1.82846	0.914231	−	0.405194i	$-0.132796\pi$
$47$	6.11683e7	1.82846	0.914231	+	0.405194i	$0.132796\pi$
$48$	−5.24847e7	−1.42708
$49$	2.71026e7	0.671629
$50$	3.09192e7	0.699622
$51$	−1.60650e8	−3.32518
$52$	−1.91885e6	−0.0363937
$53$	7.51263e7	1.30783	0.653914	−	0.756569i	$-0.273126\pi$
$53$	7.51263e7	1.30783	0.653914	+	0.756569i	$0.273126\pi$
$54$	−1.05982e8	−1.69614
$55$	4.38992e7	0.646882
$56$	−1.01126e8	−1.37409
$57$	1.45412e6	0.0182458
$58$	1.88261e7	0.218441
$59$	3.86273e7	0.415012	0.207506	−	0.978234i	$-0.433465\pi$
$59$	3.86273e7	0.415012	0.207506	+	0.978234i	$0.433465\pi$
$60$	1.35677e7	0.135152
$61$	7.48746e6	0.0692389	0.0346194	−	0.999401i	$-0.488978\pi$
$61$	7.48746e6	0.0692389	0.0346194	+	0.999401i	$0.488978\pi$
$62$	−7.64843e6	−0.0657369
$63$	−3.32622e8	−2.66022
$64$	1.48220e8	1.10433
$65$	−1.60767e7	−0.111709
$66$	3.28351e8	2.13005
$67$	1.12424e8	0.681591	0.340795	−	0.940138i	$-0.389304\pi$
$67$	1.12424e8	0.681591	0.340795	+	0.940138i	$0.389304\pi$
$68$	5.32056e7	0.301764
$69$	−6.86504e7	−0.364605
$70$	−1.16035e8	−0.577628
$71$	−3.63690e8	−1.69851	−0.849257	−	0.527980i	$-0.822950\pi$
$71$	−3.63690e8	−1.69851	−0.849257	+	0.527980i	$0.822950\pi$
$72$	4.98642e8	2.18672
$73$	−1.03141e8	−0.425088	−0.212544	−	0.977151i	$-0.568175\pi$
$73$	−1.03141e8	−0.425088	−0.212544	+	0.977151i	$0.568175\pi$
$74$	1.31378e8	0.509306
$75$	−3.65465e8	−1.33374
$76$	−481588.	−0.00165583
$77$	5.29668e8	1.71710
$78$	−1.20248e8	−0.367835
$79$	−1.27219e8	−0.367476	−0.183738	−	0.982975i	$-0.558820\pi$
$79$	−1.27219e8	−0.367476	−0.183738	+	0.982975i	$0.558820\pi$
$80$	1.45635e8	0.397521
$81$	4.55578e8	1.17593
$82$	−5.27140e8	−1.28755
$83$	6.71853e8	1.55390	0.776949	−	0.629563i	$-0.216766\pi$
$83$	6.71853e8	1.55390	0.776949	+	0.629563i	$0.216766\pi$
$84$	1.63701e8	0.358752
$85$	4.45773e8	0.926251
$86$	6.51243e8	1.28381
$87$	−2.22524e8	−0.416429
$88$	−7.94039e8	−1.41146
$89$	−1.29959e8	−0.219559	−0.109779	−	0.993956i	$-0.535014\pi$
$89$	−1.29959e8	−0.219559	−0.109779	+	0.993956i	$0.535014\pi$
$90$	5.72161e8	0.919235
$91$	−1.93974e8	−0.296523
$92$	2.27363e7	0.0330883
$93$	9.04044e7	0.125319
$94$	−1.26952e9	−1.67712
$95$	−4.03489e6	−0.00508248
$96$	−4.57208e8	−0.549405
$97$	−1.21481e9	−1.39327	−0.696634	−	0.717427i	$-0.745320\pi$
$97$	−1.21481e9	−1.39327	−0.696634	+	0.717427i	$0.745320\pi$
$98$	−5.62504e8	−0.616039
$99$	−2.61175e9	−2.73258
$100$	1.21038e8	0.121038
$101$	−1.00269e9	−0.958783	−0.479392	−	0.877601i	$-0.659143\pi$
$101$	−1.00269e9	−0.958783	−0.479392	+	0.877601i	$0.659143\pi$
$102$	3.33422e9	3.04996
$103$	4.57781e8	0.400766	0.200383	−	0.979718i	$-0.435781\pi$
$103$	4.57781e8	0.400766	0.200383	+	0.979718i	$0.435781\pi$
$104$	2.90792e8	0.243743
$105$	1.37154e9	1.10117
$106$	−1.55922e9	−1.19958
$107$	−2.32120e8	−0.171193	−0.0855966	−	0.996330i	$-0.527280\pi$
$107$	−2.32120e8	−0.171193	−0.0855966	+	0.996330i	$0.527280\pi$
$108$	−4.14885e8	−0.293441
$109$	−2.90456e8	−0.197088	−0.0985442	−	0.995133i	$-0.531419\pi$
$109$	−2.90456e8	−0.197088	−0.0985442	+	0.995133i	$0.531419\pi$
$110$	−9.11110e8	−0.593340
$111$	−1.55288e9	−0.970925
$112$	1.75716e9	1.05519
$113$	7.63750e8	0.440654	0.220327	−	0.975426i	$-0.429288\pi$
$113$	7.63750e8	0.440654	0.220327	+	0.975426i	$0.429288\pi$
$114$	−3.01796e7	−0.0167356
$115$	1.90492e8	0.101563
$116$	7.36978e7	0.0377914
$117$	9.56472e8	0.471885
$118$	−8.01693e8	−0.380662
$119$	5.37849e9	2.45866
$120$	−2.05611e9	−0.905171
$121$	1.80101e9	0.763805
$122$	−1.55399e8	−0.0635081
$123$	6.23080e9	2.45454
$124$	−2.99410e7	−0.0113728
$125$	2.34362e9	0.858601
$126$	6.90342e9	2.44004
$127$	−4.02680e9	−1.37355	−0.686774	−	0.726871i	$-0.740974\pi$
$127$	−4.02680e9	−1.37355	−0.686774	+	0.726871i	$0.740974\pi$
$128$	−2.12202e9	−0.698724
$129$	−7.69770e9	−2.44741
$130$	3.33666e8	0.102463
$131$	−6.10641e9	−1.81161	−0.905806	−	0.423694i	$-0.860733\pi$
$131$	−6.10641e9	−1.81161	−0.905806	+	0.423694i	$0.860733\pi$
$132$	1.28538e9	0.368510
$133$	−4.86831e7	−0.0134911
$134$	−2.33332e9	−0.625177
$135$	−3.47603e9	−0.900704
$136$	−8.06304e9	−2.02103
$137$	1.16005e9	0.281341	0.140671	−	0.990056i	$-0.455074\pi$
$137$	1.16005e9	0.281341	0.140671	+	0.990056i	$0.455074\pi$
$138$	1.42481e9	0.334427
$139$	−2.32826e8	−0.0529011	−0.0264506	−	0.999650i	$-0.508420\pi$
$139$	−2.32826e8	−0.0529011	−0.0264506	+	0.999650i	$0.508420\pi$
$140$	−4.54239e8	−0.0999328
$141$	1.50058e10	3.19722
$142$	7.54824e9	1.55793
$143$	−1.52309e9	−0.304588
$144$	−8.66443e9	−1.67922
$145$	6.17463e8	0.115999
$146$	2.14065e9	0.389904
$147$	6.64880e9	1.17440
$148$	5.14299e8	0.0881126
$149$	4.78089e9	0.794641	0.397320	−	0.917680i	$-0.369940\pi$
$149$	4.78089e9	0.794641	0.397320	+	0.917680i	$0.369940\pi$
$150$	7.58508e9	1.22335
$151$	7.80865e9	1.22231	0.611153	−	0.791513i	$-0.290706\pi$
$151$	7.80865e9	1.22231	0.611153	+	0.791513i	$0.290706\pi$
$152$	7.29823e7	0.0110897
$153$	−2.65209e10	−3.91270
$154$	−1.09930e10	−1.57498
$155$	−2.50855e8	−0.0349084
$156$	−4.70731e8	−0.0636374
$157$	−4.41626e9	−0.580104	−0.290052	−	0.957011i	$-0.593673\pi$
$157$	−4.41626e9	−0.580104	−0.290052	+	0.957011i	$0.593673\pi$
$158$	2.64037e9	0.337061
$159$	1.84299e10	2.28684
$160$	1.26866e9	0.153041
$161$	2.29838e9	0.269591
$162$	−9.45534e9	−1.07860
$163$	−1.22785e10	−1.36239	−0.681197	−	0.732100i	$-0.738540\pi$
$163$	−1.22785e10	−1.36239	−0.681197	+	0.732100i	$0.738540\pi$
$164$	−2.06358e9	−0.222753
$165$	1.07693e10	1.13113
$166$	−1.39440e10	−1.42529
$167$	4.17356e9	0.415224	0.207612	−	0.978211i	$-0.433431\pi$
$167$	4.17356e9	0.415224	0.207612	+	0.978211i	$0.433431\pi$
$168$	−2.48080e10	−2.40271
$169$	−1.00467e10	−0.947401
$170$	−9.25183e9	−0.849586
$171$	2.40053e8	0.0214696
$172$	2.54940e9	0.222106
$173$	4.42172e9	0.375304	0.187652	−	0.982236i	$-0.439912\pi$
$173$	4.42172e9	0.375304	0.187652	+	0.982236i	$0.439912\pi$
$174$	4.61840e9	0.381962
$175$	1.22356e10	0.986176
$176$	1.37973e10	1.08389
$177$	9.47602e9	0.725682
$178$	2.69724e9	0.201386
$179$	−1.55504e10	−1.13214	−0.566072	−	0.824356i	$-0.691538\pi$
$179$	−1.55504e10	−1.13214	−0.566072	+	0.824356i	$0.691538\pi$
$180$	2.23982e9	0.159033
$181$	7.23254e9	0.500884	0.250442	−	0.968132i	$-0.419424\pi$
$181$	7.23254e9	0.500884	0.250442	+	0.968132i	$0.419424\pi$
$182$	4.02585e9	0.271980
$183$	1.83682e9	0.121070
$184$	−3.44557e9	−0.221606
$185$	4.30896e9	0.270458
$186$	−1.87631e9	−0.114946
$187$	4.22320e10	2.52554
$188$	−4.96975e9	−0.290151
$189$	−4.19402e10	−2.39085
$190$	8.37426e7	0.00466181
$191$	3.21598e10	1.74849	0.874244	−	0.485487i	$-0.161358\pi$
$191$	3.21598e10	1.74849	0.874244	+	0.485487i	$0.161358\pi$
$192$	3.63613e10	1.93101
$193$	−3.01398e10	−1.56363	−0.781813	−	0.623512i	$-0.785705\pi$
$193$	−3.01398e10	−1.56363	−0.781813	+	0.623512i	$0.785705\pi$
$194$	2.52128e10	1.27795
$195$	−3.94393e9	−0.195332
$196$	−2.20201e9	−0.106578
$197$	−1.31062e10	−0.619982	−0.309991	−	0.950740i	$-0.600326\pi$
$197$	−1.31062e10	−0.619982	−0.309991	+	0.950740i	$0.600326\pi$
$198$	5.42058e10	2.50641
$199$	−2.50354e10	−1.13166	−0.565830	−	0.824522i	$-0.691444\pi$
$199$	−2.50354e10	−1.13166	−0.565830	+	0.824522i	$0.691444\pi$
$200$	−1.83427e10	−0.810642
$201$	2.75798e10	1.19182
$202$	2.08104e10	0.879427
$203$	7.45001e9	0.307911
$204$	1.30524e10	0.527659
$205$	−1.72893e10	−0.683730
$206$	−9.50106e9	−0.367595
$207$	−1.13332e10	−0.429026
$208$	−5.05282e9	−0.187175
$209$	−3.82261e8	−0.0138580
$210$	−2.84657e10	−1.01003
$211$	−5.64597e10	−1.96096	−0.980478	−	0.196630i	$-0.937000\pi$
$211$	−5.64597e10	−1.96096	−0.980478	+	0.196630i	$0.937000\pi$
$212$	−6.10380e9	−0.207534
$213$	−8.92202e10	−2.96999
$214$	4.81756e9	0.157024
$215$	2.13596e10	0.681743
$216$	6.28737e10	1.96529
$217$	−3.02670e9	−0.0926617
$218$	6.02829e9	0.180776
$219$	−2.53025e10	−0.743302
$220$	−3.56669e9	−0.102651
$221$	−1.54661e10	−0.436131
$222$	3.22295e10	0.890563
$223$	4.11617e10	1.11461	0.557303	−	0.830309i	$-0.311836\pi$
$223$	4.11617e10	1.11461	0.557303	+	0.830309i	$0.311836\pi$
$224$	1.53071e10	0.406235
$225$	−6.03328e10	−1.56940
$226$	−1.58513e10	−0.404182
$227$	−4.27354e10	−1.06825	−0.534124	−	0.845406i	$-0.679358\pi$
$227$	−4.27354e10	−1.06825	−0.534124	+	0.845406i	$0.679358\pi$
$228$	−1.18143e8	−0.00289535
$229$	3.59495e10	0.863839	0.431920	−	0.901912i	$-0.357836\pi$
$229$	3.59495e10	0.863839	0.431920	+	0.901912i	$0.357836\pi$
$230$	−3.95358e9	−0.0931568
$231$	1.29938e11	3.00249
$232$	−1.11685e10	−0.253105
$233$	−1.07006e10	−0.237851	−0.118925	−	0.992903i	$-0.537945\pi$
$233$	−1.07006e10	−0.237851	−0.118925	+	0.992903i	$0.537945\pi$
$234$	−1.98512e10	−0.432828
$235$	−4.16381e10	−0.890606
$236$	−3.13836e9	−0.0658565
$237$	−3.12092e10	−0.642562
$238$	−1.11628e11	−2.25516
$239$	1.19776e10	0.237453	0.118727	−	0.992927i	$-0.462119\pi$
$239$	1.19776e10	0.237453	0.118727	+	0.992927i	$0.462119\pi$
$240$	3.57270e10	0.695099
$241$	−1.50320e10	−0.287039	−0.143520	−	0.989647i	$-0.545842\pi$
$241$	−1.50320e10	−0.287039	−0.143520	+	0.989647i	$0.545842\pi$
$242$	−3.73792e10	−0.700586
$243$	1.12518e10	0.207012
$244$	−6.08335e8	−0.0109872
$245$	−1.84491e10	−0.327136
$246$	−1.29318e11	−2.25139
$247$	1.39991e8	0.00239312
$248$	4.53741e9	0.0761685
$249$	1.64818e11	2.71712
$250$	−4.86408e10	−0.787536
$251$	5.60716e10	0.891684	0.445842	−	0.895112i	$-0.352904\pi$
$251$	5.60716e10	0.891684	0.445842	+	0.895112i	$0.352904\pi$
$252$	2.70246e10	0.422140
$253$	1.80469e10	0.276924
$254$	8.35747e10	1.25986
$255$	1.09357e11	1.61963
$256$	−3.18471e10	−0.463436
$257$	−3.85420e10	−0.551106	−0.275553	−	0.961286i	$-0.588861\pi$
$257$	−3.85420e10	−0.551106	−0.275553	+	0.961286i	$0.588861\pi$
$258$	1.59763e11	2.24484
$259$	5.19898e10	0.717909
$260$	1.30619e9	0.0177266
$261$	−3.67355e10	−0.490008
$262$	1.26736e11	1.66167
$263$	−6.28459e10	−0.809984	−0.404992	−	0.914320i	$-0.632726\pi$
$263$	−6.28459e10	−0.809984	−0.404992	+	0.914320i	$0.632726\pi$
$264$	−1.94793e11	−2.46806
$265$	−5.11395e10	−0.637016
$266$	1.01040e9	0.0123744
$267$	−3.18814e10	−0.383916
$268$	−9.13416e9	−0.108159
$269$	6.79246e9	0.0790937	0.0395468	−	0.999218i	$-0.487409\pi$
$269$	6.79246e9	0.0790937	0.0395468	+	0.999218i	$0.487409\pi$
$270$	7.21436e10	0.826154
$271$	1.08042e11	1.21684	0.608418	−	0.793617i	$-0.291804\pi$
$271$	1.08042e11	1.21684	0.608418	+	0.793617i	$0.291804\pi$
$272$	1.40104e11	1.55199
$273$	−4.75856e10	−0.518494
$274$	−2.40763e10	−0.258055
$275$	9.60742e10	1.01300
$276$	5.57765e9	0.0578576
$277$	−8.78460e10	−0.896526	−0.448263	−	0.893902i	$-0.647957\pi$
$277$	−8.78460e10	−0.896526	−0.448263	+	0.893902i	$0.647957\pi$
$278$	4.83221e9	0.0485226
$279$	1.49244e10	0.147461
$280$	6.88376e10	0.669290
$281$	3.34748e10	0.320287	0.160144	−	0.987094i	$-0.448804\pi$
$281$	3.34748e10	0.320287	0.160144	+	0.987094i	$0.448804\pi$
$282$	−3.11438e11	−2.93259
$283$	9.57118e10	0.887006	0.443503	−	0.896273i	$-0.353736\pi$
$283$	9.57118e10	0.887006	0.443503	+	0.896273i	$0.353736\pi$
$284$	2.95488e10	0.269530
$285$	−9.89837e8	−0.00888714
$286$	3.16111e10	0.279378
$287$	−2.08604e11	−1.81491
$288$	−7.54781e10	−0.646480
$289$	3.10255e11	2.61624
$290$	−1.28152e10	−0.106398
$291$	−2.98016e11	−2.43624
$292$	8.37993e9	0.0674555
$293$	1.42970e11	1.13329	0.566645	−	0.823962i	$-0.308241\pi$
$293$	1.42970e11	1.13329	0.566645	+	0.823962i	$0.308241\pi$
$294$	−1.37993e11	−1.07719
$295$	−2.62941e10	−0.202144
$296$	−7.79394e10	−0.590126
$297$	−3.29315e11	−2.45588
$298$	−9.92255e10	−0.728870
$299$	−6.60913e9	−0.0478216
$300$	2.96930e10	0.211645
$301$	2.57715e11	1.80964
$302$	−1.62065e11	−1.12114
$303$	−2.45979e11	−1.67651
$304$	−1.26814e9	−0.00851603
$305$	−5.09682e9	−0.0337248
$306$	5.50430e11	3.58886
$307$	−1.27647e11	−0.820138	−0.410069	−	0.912054i	$-0.634495\pi$
$307$	−1.27647e11	−0.820138	−0.410069	+	0.912054i	$0.634495\pi$
$308$	−4.30340e10	−0.272479
$309$	1.12303e11	0.700772
$310$	5.20639e9	0.0320191
$311$	2.40766e11	1.45939	0.729697	−	0.683771i	$-0.239661\pi$
$311$	2.40766e11	1.45939	0.729697	+	0.683771i	$0.239661\pi$
$312$	7.13369e10	0.426205
$313$	8.72981e10	0.514109	0.257055	−	0.966397i	$-0.417248\pi$
$313$	8.72981e10	0.514109	0.257055	+	0.966397i	$0.417248\pi$
$314$	9.16576e10	0.532090
$315$	2.26420e11	1.29574
$316$	1.03362e10	0.0583133
$317$	−1.34485e11	−0.748011	−0.374006	−	0.927426i	$-0.622016\pi$
$317$	−1.34485e11	−0.748011	−0.374006	+	0.927426i	$0.622016\pi$
$318$	−3.82506e11	−2.09757
$319$	5.84976e10	0.316286
$320$	−1.00896e11	−0.537895
$321$	−5.69436e10	−0.299345
$322$	−4.77020e10	−0.247278
$323$	−3.88165e9	−0.0198429
$324$	−3.70145e10	−0.186603
$325$	−3.51842e10	−0.174933
$326$	2.54836e11	1.24963
$327$	−7.12544e10	−0.344625
$328$	3.12724e11	1.49187
$329$	−5.02386e11	−2.36405
$330$	−2.23513e11	−1.03750
$331$	2.95477e11	1.35300	0.676501	−	0.736442i	$-0.263496\pi$
$331$	2.95477e11	1.35300	0.676501	+	0.736442i	$0.263496\pi$
$332$	−5.45862e10	−0.246582
$333$	−2.56358e11	−1.14248
$334$	−8.66205e10	−0.380857
$335$	−7.65288e10	−0.331989
$336$	4.31066e11	1.84509
$337$	−1.56063e10	−0.0659119	−0.0329560	−	0.999457i	$-0.510492\pi$
$337$	−1.56063e10	−0.0659119	−0.0329560	+	0.999457i	$0.510492\pi$
$338$	2.08515e11	0.868986
$339$	1.87362e11	0.770520
$340$	−3.62178e10	−0.146983
$341$	−2.37657e10	−0.0951822
$342$	−4.98220e9	−0.0196926
$343$	1.08833e11	0.424556
$344$	−3.86348e11	−1.48753
$345$	4.67313e10	0.177591
$346$	−9.17709e10	−0.344241
$347$	−3.04593e11	−1.12781	−0.563907	−	0.825838i	$-0.690702\pi$
$347$	−3.04593e11	−1.12781	−0.563907	+	0.825838i	$0.690702\pi$
$348$	1.80795e10	0.0660814
$349$	−3.66230e11	−1.32142	−0.660708	−	0.750643i	$-0.729744\pi$
$349$	−3.66230e11	−1.32142	−0.660708	+	0.750643i	$0.729744\pi$
$350$	−2.53945e11	−0.904552
$351$	1.20601e11	0.424102
$352$	1.20192e11	0.417284
$353$	−3.47852e10	−0.119236	−0.0596181	−	0.998221i	$-0.518988\pi$
$353$	−3.47852e10	−0.119236	−0.0596181	+	0.998221i	$0.518988\pi$
$354$	−1.96671e11	−0.665618
$355$	2.47569e11	0.827311
$356$	1.05588e10	0.0348409
$357$	1.31945e12	4.29917
$358$	3.22741e11	1.03844
$359$	4.09271e11	1.30043	0.650213	−	0.759752i	$-0.274679\pi$
$359$	4.09271e11	1.30043	0.650213	+	0.759752i	$0.274679\pi$
$360$	−3.39433e11	−1.06511
$361$	−3.22653e11	−0.999891
$362$	−1.50108e11	−0.459427
$363$	4.41823e11	1.33558
$364$	1.57599e10	0.0470540
$365$	7.02096e10	0.207052
$366$	−3.81224e10	−0.111049
$367$	1.24952e11	0.359538	0.179769	−	0.983709i	$-0.442465\pi$
$367$	1.24952e11	0.359538	0.179769	+	0.983709i	$0.442465\pi$
$368$	5.98704e10	0.170175
$369$	1.02861e12	2.88824
$370$	−8.94306e10	−0.248072
$371$	−6.17026e11	−1.69091
$372$	−7.34511e9	−0.0198863
$373$	−1.29182e11	−0.345552	−0.172776	−	0.984961i	$-0.555274\pi$
$373$	−1.29182e11	−0.345552	−0.172776	+	0.984961i	$0.555274\pi$
$374$	−8.76507e11	−2.31650
$375$	5.74934e11	1.50133
$376$	7.53140e11	1.94326
$377$	−2.14229e10	−0.0546189
$378$	8.70451e11	2.19296
$379$	1.99319e11	0.496218	0.248109	−	0.968732i	$-0.420191\pi$
$379$	1.99319e11	0.496218	0.248109	+	0.968732i	$0.420191\pi$
$380$	3.27824e8	0.000806519 0
$381$	−9.87853e11	−2.40176
$382$	−6.67462e11	−1.60377
$383$	2.04535e11	0.485705	0.242852	−	0.970063i	$-0.421917\pi$
$383$	2.04535e11	0.485705	0.242852	+	0.970063i	$0.421917\pi$
$384$	−5.20573e11	−1.22178
$385$	−3.60552e11	−0.836363
$386$	6.25540e11	1.43421
$387$	−1.27077e12	−2.87985
$388$	9.86997e10	0.221092
$389$	−3.56696e11	−0.789814	−0.394907	−	0.918721i	$-0.629223\pi$
$389$	−3.56696e11	−0.789814	−0.394907	+	0.918721i	$0.629223\pi$
$390$	8.18546e10	0.179165
$391$	1.83257e11	0.396520
$392$	3.33704e11	0.713796
$393$	−1.49802e12	−3.16775
$394$	2.72014e11	0.568667
$395$	8.65996e10	0.178990
$396$	2.12197e11	0.433622
$397$	−3.64936e11	−0.737326	−0.368663	−	0.929563i	$-0.620184\pi$
$397$	−3.64936e11	−0.737326	−0.368663	+	0.929563i	$0.620184\pi$
$398$	5.19600e11	1.03800
$399$	−1.19429e10	−0.0235902
$400$	3.18724e11	0.622508
$401$	−3.13646e11	−0.605746	−0.302873	−	0.953031i	$-0.597946\pi$
$401$	−3.13646e11	−0.605746	−0.302873	+	0.953031i	$0.597946\pi$
$402$	−5.72408e11	−1.09317
$403$	8.70344e9	0.0164368
$404$	8.14658e10	0.152145
$405$	−3.10118e11	−0.572770
$406$	−1.54622e11	−0.282426
$407$	4.08225e11	0.737437
$408$	−1.97802e12	−3.53394
$409$	−2.47598e10	−0.0437514	−0.0218757	−	0.999761i	$-0.506964\pi$
$409$	−2.47598e10	−0.0437514	−0.0218757	+	0.999761i	$0.506964\pi$
$410$	3.58832e11	0.627139
$411$	2.84582e11	0.491948
$412$	−3.71935e10	−0.0635959
$413$	−3.17253e11	−0.536575
$414$	2.35215e11	0.393517
$415$	−4.57340e11	−0.756872
$416$	−4.40164e10	−0.0720601
$417$	−5.71167e10	−0.0925019
$418$	7.93367e9	0.0127110
$419$	−8.17546e11	−1.29583	−0.647916	−	0.761712i	$-0.724359\pi$
$419$	−8.17546e11	−1.29583	−0.647916	+	0.761712i	$0.724359\pi$
$420$	−1.11433e11	−0.174741
$421$	−7.27406e11	−1.12852	−0.564258	−	0.825599i	$-0.690838\pi$
$421$	−7.27406e11	−1.12852	−0.564258	+	0.825599i	$0.690838\pi$
$422$	1.17180e12	1.79865
$423$	2.47723e12	3.76213
$424$	9.25000e11	1.38994
$425$	9.75581e11	1.45049
$426$	1.85173e12	2.72417
$427$	−6.14958e10	−0.0895200
$428$	1.88591e10	0.0271659
$429$	−3.73643e11	−0.532597
$430$	−4.43310e11	−0.625317
$431$	−5.04732e11	−0.704552	−0.352276	−	0.935896i	$-0.614592\pi$
$431$	−5.04732e11	−0.704552	−0.352276	+	0.935896i	$0.614592\pi$
$432$	−1.09250e12	−1.50919
$433$	−1.20647e12	−1.64939	−0.824693	−	0.565581i	$-0.808652\pi$
$433$	−1.20647e12	−1.64939	−0.824693	+	0.565581i	$0.808652\pi$
$434$	6.28179e10	0.0849923
$435$	1.51475e11	0.202834
$436$	2.35987e10	0.0312752
$437$	−1.65874e9	−0.00217577
$438$	5.25143e11	0.681780
$439$	1.04789e12	1.34656	0.673282	−	0.739386i	$-0.264884\pi$
$439$	1.04789e12	1.34656	0.673282	+	0.739386i	$0.264884\pi$
$440$	5.40514e11	0.687495
$441$	1.09762e12	1.38190
$442$	3.20993e11	0.400033
$443$	6.25979e11	0.772223	0.386112	−	0.922452i	$-0.373818\pi$
$443$	6.25979e11	0.772223	0.386112	+	0.922452i	$0.373818\pi$
$444$	1.26167e11	0.154072
$445$	8.84648e10	0.106943
$446$	−8.54295e11	−1.02235
$447$	1.17285e12	1.38949
$448$	−1.21736e12	−1.42780
$449$	1.27198e11	0.147697	0.0738487	−	0.997269i	$-0.476472\pi$
$449$	1.27198e11	0.147697	0.0738487	+	0.997269i	$0.476472\pi$
$450$	1.25218e12	1.43950
$451$	−1.63796e12	−1.86428
$452$	−6.20525e10	−0.0699256
$453$	1.91561e12	2.13730
$454$	8.86956e11	0.979830
$455$	1.32041e11	0.144430
$456$	1.79040e10	0.0193913
$457$	−1.02786e12	−1.10233	−0.551163	−	0.834398i	$-0.685816\pi$
$457$	−1.02786e12	−1.10233	−0.551163	+	0.834398i	$0.685816\pi$
$458$	−7.46117e11	−0.792341
$459$	−3.34402e12	−3.51650
$460$	−1.54769e10	−0.0161166
$461$	1.03720e12	1.06957	0.534783	−	0.844989i	$-0.320393\pi$
$461$	1.03720e12	1.06957	0.534783	+	0.844989i	$0.320393\pi$
$462$	−2.69680e12	−2.75398
$463$	−3.76913e11	−0.381177	−0.190589	−	0.981670i	$-0.561040\pi$
$463$	−3.76913e11	−0.381177	−0.190589	+	0.981670i	$0.561040\pi$
$464$	1.94065e11	0.194364
$465$	−6.15396e10	−0.0610402
$466$	2.22086e11	0.218164
$467$	4.08760e11	0.397688	0.198844	−	0.980031i	$-0.436281\pi$
$467$	4.08760e11	0.397688	0.198844	+	0.980031i	$0.436281\pi$
$468$	−7.77107e10	−0.0748815
$469$	−9.23361e11	−0.881239
$470$	8.64181e11	0.816892
$471$	−1.08339e12	−1.01436
$472$	4.75602e11	0.441067
$473$	2.02359e12	1.85886
$474$	6.47734e11	0.589379
$475$	−8.83043e9	−0.00795904
$476$	−4.36987e11	−0.390155
$477$	3.04251e12	2.69091
$478$	−2.48590e11	−0.217800
$479$	−2.12928e12	−1.84809	−0.924046	−	0.382282i	$-0.875138\pi$
$479$	−2.12928e12	−1.84809	−0.924046	+	0.382282i	$0.875138\pi$
$480$	3.11228e11	0.267604
$481$	−1.49500e11	−0.127347
$482$	3.11984e11	0.263281
$483$	5.63838e11	0.471403
$484$	−1.46327e11	−0.121205
$485$	8.26936e11	0.678632
$486$	−2.33527e11	−0.189878
$487$	1.15510e12	0.930550	0.465275	−	0.885166i	$-0.345955\pi$
$487$	1.15510e12	0.930550	0.465275	+	0.885166i	$0.345955\pi$
$488$	9.21901e10	0.0735860
$489$	−3.01216e12	−2.38226
$490$	3.82904e11	0.300060
$491$	−6.40303e11	−0.497186	−0.248593	−	0.968608i	$-0.579968\pi$
$491$	−6.40303e11	−0.497186	−0.248593	+	0.968608i	$0.579968\pi$
$492$	−5.06235e11	−0.389502
$493$	5.94012e11	0.452881
$494$	−2.90546e9	−0.00219504
$495$	1.77785e12	1.33098
$496$	−7.88422e10	−0.0584913
$497$	2.98705e12	2.19603
$498$	−3.42074e12	−2.49223
$499$	−2.20283e11	−0.159048	−0.0795239	−	0.996833i	$-0.525340\pi$
$499$	−2.20283e11	−0.159048	−0.0795239	+	0.996833i	$0.525340\pi$
$500$	−1.90412e11	−0.136248
$501$	1.02385e12	0.726053
$502$	−1.16374e12	−0.817881
$503$	−1.15567e12	−0.804969	−0.402485	−	0.915427i	$-0.631853\pi$
$503$	−1.15567e12	−0.804969	−0.402485	+	0.915427i	$0.631853\pi$
$504$	−4.09544e12	−2.82724
$505$	6.82545e11	0.467003
$506$	−3.74557e11	−0.254004
$507$	−2.46465e12	−1.65661
$508$	3.27167e11	0.217963
$509$	−3.65043e11	−0.241054	−0.120527	−	0.992710i	$-0.538458\pi$
$509$	−3.65043e11	−0.241054	−0.120527	+	0.992710i	$0.538458\pi$
$510$	−2.26965e12	−1.48557
$511$	8.47116e11	0.549603
$512$	1.74745e12	1.12380
$513$	3.02682e10	0.0192956
$514$	7.99923e11	0.505492
$515$	−3.11618e11	−0.195205
$516$	6.25416e11	0.388370
$517$	−3.94474e12	−2.42835
$518$	−1.07903e12	−0.658489
$519$	1.08473e12	0.656250
$520$	−1.97946e11	−0.118722
$521$	1.45700e12	0.866342	0.433171	−	0.901312i	$-0.357395\pi$
$521$	1.45700e12	0.866342	0.433171	+	0.901312i	$0.357395\pi$
$522$	7.62429e11	0.449451
$523$	−1.08494e12	−0.634088	−0.317044	−	0.948411i	$-0.602690\pi$
$523$	−1.08494e12	−0.634088	−0.317044	+	0.948411i	$0.602690\pi$
$524$	4.96129e11	0.287477
$525$	3.00163e12	1.72441
$526$	1.30434e12	0.742943
$527$	−2.41328e11	−0.136289
$528$	3.38474e12	1.89527
$529$	7.83110e10	0.0434783
$530$	1.06138e12	0.584291
$531$	1.56435e12	0.853902
$532$	3.95537e9	0.00214084
$533$	5.99853e11	0.321938
$534$	6.61685e11	0.352140
$535$	1.58008e11	0.0833846
$536$	1.38424e12	0.724383
$537$	−3.81480e12	−1.97965
$538$	−1.40975e11	−0.0725472
$539$	−1.74785e12	−0.891979
$540$	2.82418e11	0.142929
$541$	−4.66724e10	−0.0234246	−0.0117123	−	0.999931i	$-0.503728\pi$
$541$	−4.66724e10	−0.0234246	−0.0117123	+	0.999931i	$0.503728\pi$
$542$	−2.24237e12	−1.11612
$543$	1.77428e12	0.875837
$544$	1.22048e12	0.597497
$545$	1.97717e11	0.0959977
$546$	9.87619e11	0.475579
$547$	−3.49836e11	−0.167079	−0.0835394	−	0.996504i	$-0.526622\pi$
$547$	−3.49836e11	−0.167079	−0.0835394	+	0.996504i	$0.526622\pi$
$548$	−9.42506e10	−0.0446449
$549$	3.03231e11	0.142462
$550$	−1.99398e12	−0.929156
$551$	−5.37667e9	−0.00248503
$552$	−8.45265e11	−0.387496
$553$	1.04487e12	0.475115
$554$	1.82321e12	0.822322
$555$	1.05707e12	0.472917
$556$	1.89165e10	0.00839466
$557$	−4.32976e12	−1.90597	−0.952984	−	0.303021i	$-0.902005\pi$
$557$	−4.32976e12	−1.90597	−0.952984	+	0.303021i	$0.902005\pi$
$558$	−3.09750e11	−0.135256
$559$	−7.41075e11	−0.321003
$560$	−1.19612e12	−0.513961
$561$	1.03603e13	4.41611
$562$	−6.94755e11	−0.293777
$563$	1.50296e12	0.630464	0.315232	−	0.949015i	$-0.397918\pi$
$563$	1.50296e12	0.630464	0.315232	+	0.949015i	$0.397918\pi$
$564$	−1.21918e12	−0.507353
$565$	−5.19895e11	−0.214634
$566$	−1.98646e12	−0.813590
$567$	−3.74174e12	−1.52037
$568$	−4.47797e12	−1.80515
$569$	2.24523e12	0.897956	0.448978	−	0.893543i	$-0.351788\pi$
$569$	2.24523e12	0.897956	0.448978	+	0.893543i	$0.351788\pi$
$570$	2.05437e10	0.00815157
$571$	1.80947e12	0.712342	0.356171	−	0.934421i	$-0.384082\pi$
$571$	1.80947e12	0.712342	0.356171	+	0.934421i	$0.384082\pi$
$572$	1.23747e11	0.0483339
$573$	7.88941e12	3.05737
$574$	4.32950e12	1.66469
$575$	4.16894e11	0.159045
$576$	6.00271e12	2.27220
$577$	3.23916e12	1.21658	0.608291	−	0.793714i	$-0.291855\pi$
$577$	3.23916e12	1.21658	0.608291	+	0.793714i	$0.291855\pi$
$578$	−6.43921e12	−2.39970
$579$	−7.39388e12	−2.73413
$580$	−5.01671e10	−0.0184074
$581$	−5.51805e12	−2.00906
$582$	6.18519e12	2.23460
$583$	−4.84490e12	−1.73690
$584$	−1.26994e12	−0.451777
$585$	−6.51084e11	−0.229845
$586$	−2.96729e12	−1.03949
$587$	1.24450e12	0.432636	0.216318	−	0.976323i	$-0.430595\pi$
$587$	1.24450e12	0.432636	0.216318	+	0.976323i	$0.430595\pi$
$588$	−5.40196e11	−0.186360
$589$	2.18437e9	0.000747837 0
$590$	5.45724e11	0.185412
$591$	−3.21520e12	−1.08409
$592$	1.35428e12	0.453169
$593$	−2.76317e11	−0.0917617	−0.0458808	−	0.998947i	$-0.514609\pi$
$593$	−2.76317e11	−0.0917617	−0.0458808	+	0.998947i	$0.514609\pi$
$594$	6.83480e12	2.25261
$595$	−3.66121e12	−1.19756
$596$	−3.88434e11	−0.126098
$597$	−6.14167e12	−1.97880
$598$	1.37170e11	0.0438635
$599$	3.76778e12	1.19582	0.597909	−	0.801564i	$-0.295998\pi$
$599$	3.76778e12	1.19582	0.597909	+	0.801564i	$0.295998\pi$
$600$	−4.49983e12	−1.41747
$601$	1.86107e12	0.581871	0.290936	−	0.956743i	$-0.406033\pi$
$601$	1.86107e12	0.581871	0.290936	+	0.956743i	$0.406033\pi$
$602$	−5.34878e12	−1.65986
$603$	4.55302e12	1.40240
$604$	−6.34431e11	−0.193963
$605$	−1.22597e12	−0.372033
$606$	5.10520e12	1.53775
$607$	−1.13772e12	−0.340161	−0.170081	−	0.985430i	$-0.554403\pi$
$607$	−1.13772e12	−0.340161	−0.170081	+	0.985430i	$0.554403\pi$
$608$	−1.10471e10	−0.00327856
$609$	1.82763e12	0.538407
$610$	1.05782e11	0.0309335
$611$	1.44464e12	0.419347
$612$	2.15475e12	0.620891
$613$	8.27017e11	0.236560	0.118280	−	0.992980i	$-0.462262\pi$
$613$	8.27017e11	0.236560	0.118280	+	0.992980i	$0.462262\pi$
$614$	2.64926e12	0.752257
$615$	−4.24139e12	−1.19556
$616$	6.52158e12	1.82490
$617$	4.80795e12	1.33560	0.667800	−	0.744341i	$-0.267236\pi$
$617$	4.80795e12	1.33560	0.667800	+	0.744341i	$0.267236\pi$
$618$	−2.33079e12	−0.642770
$619$	1.86334e12	0.510133	0.255067	−	0.966924i	$-0.417903\pi$
$619$	1.86334e12	0.510133	0.255067	+	0.966924i	$0.417903\pi$
$620$	2.03813e10	0.00553947
$621$	−1.42899e12	−0.385583
$622$	−4.99699e12	−1.33860
$623$	1.06737e12	0.283871
$624$	−1.23955e12	−0.327291
$625$	1.31434e12	0.344547
$626$	−1.81184e12	−0.471557
$627$	−9.37760e10	−0.0242319
$628$	3.58809e11	0.0920544
$629$	4.14530e12	1.05591
$630$	−4.69926e12	−1.18849
$631$	−4.46874e12	−1.12216	−0.561078	−	0.827763i	$-0.689613\pi$
$631$	−4.46874e12	−1.12216	−0.561078	+	0.827763i	$0.689613\pi$
$632$	−1.56639e12	−0.390548
$633$	−1.38507e13	−3.42889
$634$	2.79119e12	0.686100
$635$	2.74110e12	0.669027
$636$	−1.49738e12	−0.362890
$637$	6.40095e11	0.154034
$638$	−1.21409e12	−0.290108
$639$	−1.47289e13	−3.49476
$640$	1.44449e12	0.340334
$641$	−4.77947e12	−1.11820	−0.559098	−	0.829101i	$-0.688853\pi$
$641$	−4.77947e12	−1.11820	−0.559098	+	0.829101i	$0.688853\pi$
$642$	1.18184e12	0.274569
$643$	9.00889e11	0.207836	0.103918	−	0.994586i	$-0.466862\pi$
$643$	9.00889e11	0.207836	0.103918	+	0.994586i	$0.466862\pi$
$644$	−1.86737e11	−0.0427804
$645$	5.23993e12	1.19208
$646$	8.05621e10	0.0182005
$647$	−1.96121e12	−0.440003	−0.220002	−	0.975500i	$-0.570606\pi$
$647$	−1.96121e12	−0.440003	−0.220002	+	0.975500i	$0.570606\pi$
$648$	5.60935e12	1.24976
$649$	−2.49107e12	−0.551170
$650$	7.30233e11	0.160454
$651$	−7.42507e11	−0.162027
$652$	9.97597e11	0.216193
$653$	−6.72784e12	−1.44799	−0.723996	−	0.689804i	$-0.757697\pi$
$653$	−6.72784e12	−1.44799	−0.723996	+	0.689804i	$0.757697\pi$
$654$	1.47886e12	0.316101
$655$	4.15672e12	0.882398
$656$	−5.43392e12	−1.14563
$657$	−4.17707e12	−0.874636
$658$	1.04268e13	2.16838
$659$	8.62492e12	1.78144	0.890719	−	0.454554i	$-0.150201\pi$
$659$	8.62492e12	1.78144	0.890719	+	0.454554i	$0.150201\pi$
$660$	−8.74978e11	−0.179494
$661$	6.49372e12	1.32308	0.661542	−	0.749908i	$-0.269902\pi$
$661$	6.49372e12	1.32308	0.661542	+	0.749908i	$0.269902\pi$
$662$	−6.13251e12	−1.24102
$663$	−3.79414e12	−0.762610
$664$	8.27226e12	1.65146
$665$	3.31393e10	0.00657122
$666$	5.32060e12	1.04792
$667$	2.53838e11	0.0496582
$668$	−3.39090e11	−0.0658902
$669$	1.00978e13	1.94898
$670$	1.58832e12	0.304511
$671$	−4.82866e11	−0.0919550
$672$	3.75513e12	0.710334
$673$	−3.92264e12	−0.737074	−0.368537	−	0.929613i	$-0.620141\pi$
$673$	−3.92264e12	−0.737074	−0.368537	+	0.929613i	$0.620141\pi$
$674$	3.23901e11	0.0604565
$675$	−7.60735e12	−1.41048
$676$	8.16268e11	0.150339
$677$	3.39555e12	0.621243	0.310622	−	0.950534i	$-0.399463\pi$
$677$	3.39555e12	0.621243	0.310622	+	0.950534i	$0.399463\pi$
$678$	−3.88863e12	−0.706746
$679$	9.97743e12	1.80138
$680$	5.48862e12	0.984404
$681$	−1.04838e13	−1.86792
$682$	4.93247e11	0.0873041
$683$	8.37410e12	1.47247	0.736233	−	0.676729i	$-0.236603\pi$
$683$	8.37410e12	1.47247	0.736233	+	0.676729i	$0.236603\pi$
$684$	−1.95036e10	−0.00340693
$685$	−7.89661e11	−0.137035
$686$	−2.25877e12	−0.389416
$687$	8.81910e12	1.51049
$688$	6.71321e12	1.14230
$689$	1.77429e12	0.299943
$690$	−9.69888e11	−0.162892
$691$	3.93005e11	0.0655763	0.0327882	−	0.999462i	$-0.489561\pi$
$691$	3.93005e11	0.0655763	0.0327882	+	0.999462i	$0.489561\pi$
$692$	−3.59252e11	−0.0595555
$693$	2.14508e13	3.53300
$694$	6.32171e12	1.03447
$695$	1.58488e11	0.0257670
$696$	−2.73985e12	−0.442574
$697$	−1.66326e13	−2.66940
$698$	7.60095e12	1.21204
$699$	−2.62505e12	−0.415902
$700$	−9.94109e11	−0.156492
$701$	8.36745e11	0.130877	0.0654383	−	0.997857i	$-0.479155\pi$
$701$	8.36745e11	0.130877	0.0654383	+	0.997857i	$0.479155\pi$
$702$	−2.50303e12	−0.389000
$703$	−3.75210e10	−0.00579397
$704$	−9.55873e12	−1.46664
$705$	−1.02146e13	−1.55730
$706$	7.21952e11	0.109367
$707$	8.23527e12	1.23963
$708$	−7.69900e11	−0.115155
$709$	−5.52840e12	−0.821659	−0.410829	−	0.911712i	$-0.634761\pi$
$709$	−5.52840e12	−0.821659	−0.410829	+	0.911712i	$0.634761\pi$
$710$	−5.13819e12	−0.758836
$711$	−5.15217e12	−0.756097
$712$	−1.60013e12	−0.233343
$713$	−1.03126e11	−0.0149440
$714$	−2.73846e13	−3.94334
$715$	1.03679e12	0.148359
$716$	1.26342e12	0.179655
$717$	2.93833e12	0.415207
$718$	−8.49425e12	−1.19279
$719$	8.42349e12	1.17547	0.587736	−	0.809053i	$-0.300019\pi$
$719$	8.42349e12	1.17547	0.587736	+	0.809053i	$0.300019\pi$
$720$	5.89800e12	0.817916
$721$	−3.75984e12	−0.518156
$722$	6.69652e12	0.917132
$723$	−3.68765e12	−0.501911
$724$	−5.87624e11	−0.0794833
$725$	1.35133e12	0.181652
$726$	−9.16985e12	−1.22503
$727$	7.29215e12	0.968168	0.484084	−	0.875021i	$-0.339153\pi$
$727$	7.29215e12	0.968168	0.484084	+	0.875021i	$0.339153\pi$
$728$	−2.38833e12	−0.315139
$729$	−6.20686e12	−0.813950
$730$	−1.45717e12	−0.189914
$731$	2.05484e13	2.66164
$732$	−1.49236e11	−0.0192121
$733$	−4.39943e12	−0.562896	−0.281448	−	0.959576i	$-0.590815\pi$
$733$	−4.39943e12	−0.562896	−0.281448	+	0.959576i	$0.590815\pi$
$734$	−2.59332e12	−0.329780
$735$	−4.52593e12	−0.572025
$736$	5.21547e11	0.0655154
$737$	−7.25024e12	−0.905209
$738$	−2.13484e13	−2.64918
$739$	−8.10335e12	−0.999459	−0.499729	−	0.866182i	$-0.666567\pi$
$739$	−8.10335e12	−0.999459	−0.499729	+	0.866182i	$0.666567\pi$
$740$	−3.50091e11	−0.0429178
$741$	3.43425e10	0.00418456
$742$	1.28061e13	1.55096
$743$	−1.21851e13	−1.46683	−0.733416	−	0.679780i	$-0.762075\pi$
$743$	−1.21851e13	−1.46683	−0.733416	+	0.679780i	$0.762075\pi$
$744$	1.11311e12	0.133187
$745$	−3.25442e12	−0.387053
$746$	2.68112e12	0.316951
$747$	2.72091e13	3.19721
$748$	−3.43123e12	−0.400768
$749$	1.90645e12	0.221338
$750$	−1.19325e13	−1.37707
$751$	−1.49726e12	−0.171758	−0.0858790	−	0.996306i	$-0.527370\pi$
$751$	−1.49726e12	−0.171758	−0.0858790	+	0.996306i	$0.527370\pi$
$752$	−1.30866e13	−1.49227
$753$	1.37554e13	1.55918
$754$	4.44624e11	0.0500982
$755$	−5.31546e12	−0.595359
$756$	3.40752e12	0.379394
$757$	−7.16512e12	−0.793035	−0.396517	−	0.918027i	$-0.629781\pi$
$757$	−7.16512e12	−0.793035	−0.396517	+	0.918027i	$0.629781\pi$
$758$	−4.13678e12	−0.455147
$759$	4.42726e12	0.484225
$760$	−4.96800e10	−0.00540158
$761$	9.35065e11	0.101067	0.0505337	−	0.998722i	$-0.483908\pi$
$761$	9.35065e11	0.101067	0.0505337	+	0.998722i	$0.483908\pi$
$762$	2.05025e13	2.20297
$763$	2.38557e12	0.254818
$764$	−2.61289e12	−0.277460
$765$	1.80532e13	1.90580
$766$	−4.24503e12	−0.445504
$767$	9.12278e11	0.0951805
$768$	−7.81270e12	−0.810356
$769$	9.18034e12	0.946651	0.473326	−	0.880888i	$-0.343053\pi$
$769$	9.18034e12	0.946651	0.473326	+	0.880888i	$0.343053\pi$
$770$	7.48311e12	0.767139
$771$	−9.45509e12	−0.963654
$772$	2.44878e12	0.248126
$773$	−1.54555e13	−1.55695	−0.778474	−	0.627677i	$-0.784006\pi$
$773$	−1.54555e13	−1.55695	−0.778474	+	0.627677i	$0.784006\pi$
$774$	2.63744e13	2.64149
$775$	−5.49000e11	−0.0546657
$776$	−1.49574e13	−1.48074
$777$	1.27541e13	1.25532
$778$	7.40308e12	0.724443
$779$	1.50550e11	0.0146474
$780$	3.20433e11	0.0309964
$781$	2.34544e13	2.25577
$782$	−3.80342e12	−0.363701
$783$	−4.63197e12	−0.440390
$784$	−5.79846e12	−0.548138
$785$	3.00621e12	0.282557
$786$	3.10908e13	2.90556
$787$	6.70423e12	0.622963	0.311482	−	0.950252i	$-0.399175\pi$
$787$	6.70423e12	0.622963	0.311482	+	0.950252i	$0.399175\pi$
$788$	1.06484e12	0.0983824
$789$	−1.54173e13	−1.41632
$790$	−1.79734e12	−0.164175
$791$	−6.27281e12	−0.569728
$792$	−3.21574e13	−2.90414
$793$	1.76835e11	0.0158795
$794$	7.57409e12	0.676299
$795$	−1.25455e13	−1.11387
$796$	2.03406e12	0.179579
$797$	−8.78602e12	−0.771312	−0.385656	−	0.922643i	$-0.626025\pi$
$797$	−8.78602e12	−0.771312	−0.385656	+	0.922643i	$0.626025\pi$
$798$	2.47870e11	0.0216377
$799$	−4.00567e13	−3.47708
$800$	2.77649e12	0.239658
$801$	−5.26314e12	−0.451751
$802$	6.50960e12	0.555610
$803$	6.65157e12	0.564553
$804$	−2.24079e12	−0.189125
$805$	−1.56454e12	−0.131312
$806$	−1.80636e11	−0.0150764
$807$	1.66632e12	0.138302
$808$	−1.23457e13	−1.01898
$809$	1.51728e12	0.124537	0.0622685	−	0.998059i	$-0.480167\pi$
$809$	1.51728e12	0.124537	0.0622685	+	0.998059i	$0.480167\pi$
$810$	6.43638e12	0.525362
$811$	−7.32275e11	−0.0594402	−0.0297201	−	0.999558i	$-0.509462\pi$
$811$	−7.32275e11	−0.0594402	−0.0297201	+	0.999558i	$0.509462\pi$
$812$	−6.05293e11	−0.0488611
$813$	2.65049e13	2.12774
$814$	−8.47254e12	−0.676400
$815$	8.35817e12	0.663594
$816$	3.43702e13	2.71379
$817$	−1.85993e11	−0.0146049
$818$	5.13879e11	0.0401301
$819$	−7.85567e12	−0.610107
$820$	1.40471e12	0.108498
$821$	−5.97477e12	−0.458962	−0.229481	−	0.973313i	$-0.573703\pi$
$821$	−5.97477e12	−0.458962	−0.229481	+	0.973313i	$0.573703\pi$
$822$	−5.90638e12	−0.451230
$823$	1.05927e13	0.804833	0.402417	−	0.915457i	$-0.368170\pi$
$823$	1.05927e13	0.804833	0.402417	+	0.915457i	$0.368170\pi$
$824$	5.63648e12	0.425927
$825$	2.35688e13	1.77131
$826$	6.58445e12	0.492163
$827$	1.53469e12	0.114089	0.0570446	−	0.998372i	$-0.481832\pi$
$827$	1.53469e12	0.114089	0.0570446	+	0.998372i	$0.481832\pi$
$828$	9.20787e11	0.0680805
$829$	5.20240e12	0.382568	0.191284	−	0.981535i	$-0.438735\pi$
$829$	5.20240e12	0.382568	0.191284	+	0.981535i	$0.438735\pi$
$830$	9.49189e12	0.694227
$831$	−2.15503e13	−1.56765
$832$	3.50059e12	0.253271
$833$	−1.77485e13	−1.27720
$834$	1.18543e12	0.0848457
$835$	−2.84100e12	−0.202247
$836$	3.10576e10	0.00219907
$837$	1.88182e12	0.132530
$838$	1.69678e13	1.18858
$839$	−1.05169e13	−0.732757	−0.366379	−	0.930466i	$-0.619403\pi$
$839$	−1.05169e13	−0.732757	−0.366379	+	0.930466i	$0.619403\pi$
$840$	1.68872e13	1.17031
$841$	−1.36844e13	−0.943283
$842$	1.50970e13	1.03511
$843$	8.21201e12	0.560048
$844$	4.58719e12	0.311176
$845$	6.83894e12	0.461459
$846$	−5.14138e13	−3.45075
$847$	−1.47920e13	−0.987534
$848$	−1.60729e13	−1.06736
$849$	2.34800e13	1.55100
$850$	−2.02478e13	−1.33043
$851$	1.77141e12	0.115781
$852$	7.24889e12	0.471296
$853$	−3.36609e12	−0.217699	−0.108849	−	0.994058i	$-0.534717\pi$
$853$	−3.36609e12	−0.217699	−0.108849	+	0.994058i	$0.534717\pi$
$854$	1.27632e12	0.0821106
$855$	−1.63407e11	−0.0104574
$856$	−2.85801e12	−0.181941
$857$	−3.27810e12	−0.207591	−0.103796	−	0.994599i	$-0.533099\pi$
$857$	−3.27810e12	−0.207591	−0.103796	+	0.994599i	$0.533099\pi$
$858$	7.75480e12	0.488515
$859$	1.61044e13	1.00919	0.504597	−	0.863355i	$-0.331641\pi$
$859$	1.61044e13	1.00919	0.504597	+	0.863355i	$0.331641\pi$
$860$	−1.73541e12	−0.108183
$861$	−5.11746e13	−3.17352
$862$	1.04755e13	0.646238
$863$	−2.10506e12	−0.129186	−0.0645931	−	0.997912i	$-0.520575\pi$
$863$	−2.10506e12	−0.129186	−0.0645931	+	0.997912i	$0.520575\pi$
$864$	−9.51702e12	−0.581018
$865$	−3.00992e12	−0.182803
$866$	2.50398e13	1.51287
$867$	7.61115e13	4.57472
$868$	2.45911e11	0.0147041
$869$	8.20434e12	0.488039
$870$	−3.14381e12	−0.186046
$871$	2.65517e12	0.156319
$872$	−3.57627e12	−0.209462
$873$	−4.91979e13	−2.86670
$874$	3.44265e10	0.00199568
$875$	−1.92485e13	−1.11010
$876$	2.05576e12	0.117952
$877$	1.07060e13	0.611124	0.305562	−	0.952172i	$-0.401156\pi$
$877$	1.07060e13	0.611124	0.305562	+	0.952172i	$0.401156\pi$
$878$	−2.17486e13	−1.23511
$879$	3.50734e13	1.98165
$880$	−9.39199e12	−0.527941
$881$	9.28368e12	0.519193	0.259596	−	0.965717i	$-0.416410\pi$
$881$	9.28368e12	0.519193	0.259596	+	0.965717i	$0.416410\pi$
$882$	−2.27806e13	−1.26752
$883$	−1.54697e13	−0.856366	−0.428183	−	0.903692i	$-0.640846\pi$
$883$	−1.54697e13	−0.856366	−0.428183	+	0.903692i	$0.640846\pi$
$884$	1.25658e12	0.0692078
$885$	−6.45046e12	−0.353465
$886$	−1.29919e13	−0.708308
$887$	−3.51893e13	−1.90877	−0.954386	−	0.298575i	$-0.903489\pi$
$887$	−3.51893e13	−1.90877	−0.954386	+	0.298575i	$0.903489\pi$
$888$	−1.91200e13	−1.03188
$889$	3.30729e13	1.77588
$890$	−1.83605e12	−0.0980911
$891$	−2.93802e13	−1.56173
$892$	−3.34427e12	−0.176872
$893$	3.62572e11	0.0190793
$894$	−2.43419e13	−1.27449
$895$	1.05853e13	0.551444
$896$	1.74286e13	0.903390
$897$	−1.62135e12	−0.0836199
$898$	−2.63995e12	−0.135473
$899$	−3.34275e11	−0.0170681
$900$	4.90187e12	0.249041
$901$	−4.91973e13	−2.48702
$902$	3.39953e13	1.70997
$903$	6.32225e13	3.16430
$904$	9.40374e12	0.468320
$905$	−4.92329e12	−0.243970
$906$	−3.97577e13	−1.96040
$907$	3.40034e12	0.166836	0.0834181	−	0.996515i	$-0.473416\pi$
$907$	3.40034e12	0.166836	0.0834181	+	0.996515i	$0.473416\pi$
$908$	3.47213e12	0.169516
$909$	−4.06075e13	−1.97273
$910$	−2.74045e12	−0.132476
$911$	2.44389e13	1.17557	0.587786	−	0.809016i	$-0.300000\pi$
$911$	2.44389e13	1.17557	0.587786	+	0.809016i	$0.300000\pi$
$912$	−3.11100e11	−0.0148910
$913$	−4.33278e13	−2.06371
$914$	2.13328e13	1.01109
$915$	−1.25035e12	−0.0589706
$916$	−2.92080e12	−0.137079
$917$	5.01530e13	2.34226
$918$	6.94036e13	3.22545
$919$	1.29528e13	0.599024	0.299512	−	0.954093i	$-0.403176\pi$
$919$	1.29528e13	0.599024	0.299512	+	0.954093i	$0.403176\pi$
$920$	2.34545e12	0.107940
$921$	−3.13142e13	−1.43408
$922$	−2.15266e13	−0.981040
$923$	−8.58944e12	−0.389544
$924$	−1.05571e13	−0.476452
$925$	9.43022e12	0.423530
$926$	7.82268e12	0.349628
$927$	1.85395e13	0.824591
$928$	1.69055e12	0.0748276
$929$	−1.26100e13	−0.555448	−0.277724	−	0.960661i	$-0.589580\pi$
$929$	−1.26100e13	−0.555448	−0.277724	+	0.960661i	$0.589580\pi$
$930$	1.27723e12	0.0559880
$931$	1.60649e11	0.00700818
$932$	8.69390e11	0.0377436
$933$	5.90644e13	2.55187
$934$	−8.48364e12	−0.364772
$935$	−2.87479e13	−1.23014
$936$	1.17767e13	0.501511
$937$	2.95339e12	0.125168	0.0625838	−	0.998040i	$-0.480066\pi$
$937$	2.95339e12	0.125168	0.0625838	+	0.998040i	$0.480066\pi$
$938$	1.91640e13	0.808300
$939$	2.14159e13	0.898962
$940$	3.38298e12	0.141327
$941$	−2.61120e13	−1.08564	−0.542822	−	0.839848i	$-0.682644\pi$
$941$	−2.61120e13	−1.08564	−0.542822	+	0.839848i	$0.682644\pi$
$942$	2.24854e13	0.930403
$943$	−7.10761e12	−0.292699
$944$	−8.26409e12	−0.338705
$945$	2.85493e13	1.16453
$946$	−4.19987e13	−1.70500
$947$	2.08887e13	0.843989	0.421995	−	0.906598i	$-0.361330\pi$
$947$	2.08887e13	0.843989	0.421995	+	0.906598i	$0.361330\pi$
$948$	2.53566e12	0.101966
$949$	−2.43593e12	−0.0974915
$950$	1.83272e11	0.00730028
$951$	−3.29918e13	−1.30796
$952$	6.62232e13	2.61303
$953$	−3.40604e13	−1.33761	−0.668807	−	0.743436i	$-0.733195\pi$
$953$	−3.40604e13	−1.33761	−0.668807	+	0.743436i	$0.733195\pi$
$954$	−6.31459e13	−2.46819
$955$	−2.18916e13	−0.851652
$956$	−9.73144e11	−0.0376805
$957$	1.43506e13	0.553052
$958$	4.41924e13	1.69513
$959$	−9.52768e12	−0.363750
$960$	−2.47516e13	−0.940554
$961$	−2.63038e13	−0.994864
$962$	3.10280e12	0.116806
$963$	−9.40054e12	−0.352236
$964$	1.22131e12	0.0455491
$965$	2.05166e13	0.761610
$966$	−1.17022e13	−0.432385
$967$	4.35137e13	1.60032	0.800160	−	0.599786i	$-0.204748\pi$
$967$	4.35137e13	1.60032	0.800160	+	0.599786i	$0.204748\pi$
$968$	2.21751e13	0.811759
$969$	−9.52244e11	−0.0346969
$970$	−1.71627e13	−0.622463
$971$	5.30012e13	1.91337	0.956686	−	0.291123i	$-0.0940289\pi$
$971$	5.30012e13	1.91337	0.956686	+	0.291123i	$0.0940289\pi$
$972$	−9.14179e11	−0.0328498
$973$	1.91224e12	0.0683966
$974$	−2.39737e13	−0.853530
$975$	−8.63135e12	−0.305885
$976$	−1.60190e12	−0.0565081
$977$	−2.35108e13	−0.825547	−0.412774	−	0.910834i	$-0.635440\pi$
$977$	−2.35108e13	−0.825547	−0.412774	+	0.910834i	$0.635440\pi$
$978$	6.25162e13	2.18508
$979$	8.38104e12	0.291592
$980$	1.49894e12	0.0519119
$981$	−1.17630e13	−0.405517
$982$	1.32892e13	0.456035
$983$	2.69175e13	0.919484	0.459742	−	0.888052i	$-0.347942\pi$
$983$	2.69175e13	0.919484	0.459742	+	0.888052i	$0.347942\pi$
$984$	7.67173e13	2.60865
$985$	8.92158e12	0.301980
$986$	−1.23285e13	−0.415397
$987$	−1.23245e14	−4.13373
$988$	−1.13739e10	−0.000379754 0
$989$	8.78093e12	0.291848
$990$	−3.68986e13	−1.22082
$991$	3.41023e13	1.12319	0.561594	−	0.827413i	$-0.310188\pi$
$991$	3.41023e13	1.12319	0.561594	+	0.827413i	$0.310188\pi$
$992$	−6.86815e11	−0.0225184
$993$	7.24863e13	2.36583
$994$	−6.19950e13	−2.01427
$995$	1.70420e13	0.551209
$996$	−1.33910e13	−0.431169
$997$	−2.35965e13	−0.756343	−0.378172	−	0.925736i	$-0.623447\pi$
$997$	−2.35965e13	−0.756343	−0.378172	+	0.925736i	$0.623447\pi$
$998$	4.57187e12	0.145884
$999$	−3.23241e13	−1.02679

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.10.a.a.1.3	✓	7
3.2	odd	2		207.10.a.b.1.5		7
4.3	odd	2		368.10.a.f.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.10.a.a.1.3	✓	7	1.1	even	1	trivial
207.10.a.b.1.5		7	3.2	odd	2
368.10.a.f.1.1		7	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:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	23.a (trivial)

\(f(q)\)	\(=\)	\(q-20.7546 q^{2} +245.319 q^{3} -81.2472 q^{4} -680.714 q^{5} -5091.50 q^{6} -8213.17 q^{7} +12312.6 q^{8} +40498.5 q^{9} +O(q^{10})\)	\(q-20.7546 q^{2} +245.319 q^{3} -81.2472 q^{4} -680.714 q^{5} -5091.50 q^{6} -8213.17 q^{7} +12312.6 q^{8} +40498.5 q^{9} +14127.9 q^{10} -64490.0 q^{11} -19931.5 q^{12} +23617.4 q^{13} +170461. q^{14} -166992. q^{15} -213944. q^{16} -654861. q^{17} -840530. q^{18} +5927.44 q^{19} +55306.1 q^{20} -2.01485e6 q^{21} +1.33846e6 q^{22} -279841. q^{23} +3.02052e6 q^{24} -1.48975e6 q^{25} -490170. q^{26} +5.10645e6 q^{27} +667297. q^{28} -907081. q^{29} +3.46585e6 q^{30} +368517. q^{31} -1.86373e6 q^{32} -1.58206e7 q^{33} +1.35914e7 q^{34} +5.59082e6 q^{35} -3.29039e6 q^{36} -6.33005e6 q^{37} -123022. q^{38} +5.79381e6 q^{39} -8.38136e6 q^{40} +2.53987e7 q^{41} +4.18174e7 q^{42} -3.13783e7 q^{43} +5.23963e6 q^{44} -2.75679e7 q^{45} +5.80798e6 q^{46} +6.11683e7 q^{47} -5.24847e7 q^{48} +2.71026e7 q^{49} +3.09192e7 q^{50} -1.60650e8 q^{51} -1.91885e6 q^{52} +7.51263e7 q^{53} -1.05982e8 q^{54} +4.38992e7 q^{55} -1.01126e8 q^{56} +1.45412e6 q^{57} +1.88261e7 q^{58} +3.86273e7 q^{59} +1.35677e7 q^{60} +7.48746e6 q^{61} -7.64843e6 q^{62} -3.32622e8 q^{63} +1.48220e8 q^{64} -1.60767e7 q^{65} +3.28351e8 q^{66} +1.12424e8 q^{67} +5.32056e7 q^{68} -6.86504e7 q^{69} -1.16035e8 q^{70} -3.63690e8 q^{71} +4.98642e8 q^{72} -1.03141e8 q^{73} +1.31378e8 q^{74} -3.65465e8 q^{75} -481588. q^{76} +5.29668e8 q^{77} -1.20248e8 q^{78} -1.27219e8 q^{79} +1.45635e8 q^{80} +4.55578e8 q^{81} -5.27140e8 q^{82} +6.71853e8 q^{83} +1.63701e8 q^{84} +4.45773e8 q^{85} +6.51243e8 q^{86} -2.22524e8 q^{87} -7.94039e8 q^{88} -1.29959e8 q^{89} +5.72161e8 q^{90} -1.93974e8 q^{91} +2.27363e7 q^{92} +9.04044e7 q^{93} -1.26952e9 q^{94} -4.03489e6 q^{95} -4.57208e8 q^{96} -1.21481e9 q^{97} -5.62504e8 q^{98} -2.61175e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 89 q^{3} + 1536 q^{4} - 2388 q^{5} - 12518 q^{6} - 9896 q^{7} + 34920 q^{8} + 33064 q^{9}+O(q^{10}) \) 7 * q - 89 * q^3 + 1536 * q^4 - 2388 * q^5 - 12518 * q^6 - 9896 * q^7 + 34920 * q^8 + 33064 * q^9	\( 7 q - 89 q^{3} + 1536 q^{4} - 2388 q^{5} - 12518 q^{6} - 9896 q^{7} + 34920 q^{8} + 33064 q^{9} - 60820 q^{10} - 78484 q^{11} - 343492 q^{12} - 296769 q^{13} - 711120 q^{14} - 237870 q^{15} - 253440 q^{16} - 1128820 q^{17} - 499874 q^{18} - 1301252 q^{19} - 3482704 q^{20} - 108908 q^{21} - 1562088 q^{22} - 1958887 q^{23} - 4606464 q^{24} - 1320899 q^{25} + 692230 q^{26} + 2977921 q^{27} - 8371144 q^{28} + 2813849 q^{29} + 25535196 q^{30} + 7334751 q^{31} + 26028800 q^{32} + 646330 q^{33} + 14981564 q^{34} + 23410104 q^{35} + 40211900 q^{36} - 13324320 q^{37} + 37578632 q^{38} + 6304533 q^{39} - 45307920 q^{40} - 15691573 q^{41} + 124523248 q^{42} - 46474818 q^{43} + 43428040 q^{44} - 72736710 q^{45} + 8232227 q^{47} - 163054384 q^{48} + 29219031 q^{49} + 50366304 q^{50} - 136344764 q^{51} - 100922292 q^{52} - 53545400 q^{53} - 26171642 q^{54} - 181608484 q^{55} - 420111696 q^{56} - 218913370 q^{57} - 39304854 q^{58} - 341275144 q^{59} + 420822384 q^{60} - 277157656 q^{61} + 464777594 q^{62} - 574619276 q^{63} + 340566208 q^{64} + 106659278 q^{65} + 258025876 q^{66} + 89654580 q^{67} + 62700400 q^{68} + 24905849 q^{69} + 1187910040 q^{70} - 286098961 q^{71} + 1446323640 q^{72} - 637495039 q^{73} + 189880036 q^{74} - 160733159 q^{75} + 228563936 q^{76} + 511682536 q^{77} + 1199383686 q^{78} + 274469546 q^{79} - 345318560 q^{80} - 237775217 q^{81} - 570256066 q^{82} + 1164579762 q^{83} + 3447171416 q^{84} - 18639492 q^{85} + 415245796 q^{86} - 595368433 q^{87} + 103329440 q^{88} - 504153000 q^{89} - 1414126968 q^{90} - 1692320156 q^{91} - 429835776 q^{92} - 2753858687 q^{93} - 2214048622 q^{94} + 162962164 q^{95} - 3332565856 q^{96} - 3519929016 q^{97} + 2474592568 q^{98} - 1883749262 q^{99}+O(q^{100}) \) 7 * q - 89 * q^3 + 1536 * q^4 - 2388 * q^5 - 12518 * q^6 - 9896 * q^7 + 34920 * q^8 + 33064 * q^9 - 60820 * q^10 - 78484 * q^11 - 343492 * q^12 - 296769 * q^13 - 711120 * q^14 - 237870 * q^15 - 253440 * q^16 - 1128820 * q^17 - 499874 * q^18 - 1301252 * q^19 - 3482704 * q^20 - 108908 * q^21 - 1562088 * q^22 - 1958887 * q^23 - 4606464 * q^24 - 1320899 * q^25 + 692230 * q^26 + 2977921 * q^27 - 8371144 * q^28 + 2813849 * q^29 + 25535196 * q^30 + 7334751 * q^31 + 26028800 * q^32 + 646330 * q^33 + 14981564 * q^34 + 23410104 * q^35 + 40211900 * q^36 - 13324320 * q^37 + 37578632 * q^38 + 6304533 * q^39 - 45307920 * q^40 - 15691573 * q^41 + 124523248 * q^42 - 46474818 * q^43 + 43428040 * q^44 - 72736710 * q^45 + 8232227 * q^47 - 163054384 * q^48 + 29219031 * q^49 + 50366304 * q^50 - 136344764 * q^51 - 100922292 * q^52 - 53545400 * q^53 - 26171642 * q^54 - 181608484 * q^55 - 420111696 * q^56 - 218913370 * q^57 - 39304854 * q^58 - 341275144 * q^59 + 420822384 * q^60 - 277157656 * q^61 + 464777594 * q^62 - 574619276 * q^63 + 340566208 * q^64 + 106659278 * q^65 + 258025876 * q^66 + 89654580 * q^67 + 62700400 * q^68 + 24905849 * q^69 + 1187910040 * q^70 - 286098961 * q^71 + 1446323640 * q^72 - 637495039 * q^73 + 189880036 * q^74 - 160733159 * q^75 + 228563936 * q^76 + 511682536 * q^77 + 1199383686 * q^78 + 274469546 * q^79 - 345318560 * q^80 - 237775217 * q^81 - 570256066 * q^82 + 1164579762 * q^83 + 3447171416 * q^84 - 18639492 * q^85 + 415245796 * q^86 - 595368433 * q^87 + 103329440 * q^88 - 504153000 * q^89 - 1414126968 * q^90 - 1692320156 * q^91 - 429835776 * q^92 - 2753858687 * q^93 - 2214048622 * q^94 + 162962164 * q^95 - 3332565856 * q^96 - 3519929016 * q^97 + 2474592568 * q^98 - 1883749262 * q^99

Introduction

L-functions

Modular forms

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