LMFDB - Embedded newform 11.18.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,18,Mod(1,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("11.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	11.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:	$20.1544296079$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 715858 x^{6} - 57426812 x^{5} + 132277346400 x^{4} + 17831801296448 x^{3} + \cdots + 70\!\cdots\!00 $ x^8 - 715858x^6 - 57426812x^5 + 132277346400x^4 + 17831801296448x^3 - 5237791784459264x^2 - 427120471274668032x + 70348376081176985600
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{11}\cdot 3^{5}\cdot 11 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$142.296$ of defining polynomial
Character	$\chi$	$=$	11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-110.296 q^{2} +17080.3 q^{3} -118907. q^{4} -1.10266e6 q^{5} -1.88389e6 q^{6} +1.13516e7 q^{7} +2.75717e7 q^{8} +1.62598e8 q^{9} +O(q^{10})$	\(q-110.296 q^{2} +17080.3 q^{3} -118907. q^{4} -1.10266e6 q^{5} -1.88389e6 q^{6} +1.13516e7 q^{7} +2.75717e7 q^{8} +1.62598e8 q^{9} +1.21619e8 q^{10} +2.14359e8 q^{11} -2.03097e9 q^{12} +9.04312e8 q^{13} -1.25204e9 q^{14} -1.88338e10 q^{15} +1.25443e10 q^{16} +2.89990e10 q^{17} -1.79339e10 q^{18} +8.96979e10 q^{19} +1.31114e11 q^{20} +1.93890e11 q^{21} -2.36429e10 q^{22} -3.73973e11 q^{23} +4.70933e11 q^{24} +4.52920e11 q^{25} -9.97419e10 q^{26} +5.71468e11 q^{27} -1.34979e12 q^{28} +5.34389e12 q^{29} +2.07729e12 q^{30} +7.08525e12 q^{31} -4.99746e12 q^{32} +3.66132e12 q^{33} -3.19848e12 q^{34} -1.25170e13 q^{35} -1.93340e13 q^{36} +1.67255e13 q^{37} -9.89332e12 q^{38} +1.54459e13 q^{39} -3.04022e13 q^{40} +8.69335e12 q^{41} -2.13853e13 q^{42} +1.07218e13 q^{43} -2.54887e13 q^{44} -1.79290e14 q^{45} +4.12478e13 q^{46} -1.97115e14 q^{47} +2.14261e14 q^{48} -1.03771e14 q^{49} -4.99552e13 q^{50} +4.95313e14 q^{51} -1.07529e14 q^{52} -1.87563e14 q^{53} -6.30306e13 q^{54} -2.36365e14 q^{55} +3.12984e14 q^{56} +1.53207e15 q^{57} -5.89410e14 q^{58} +6.36161e14 q^{59} +2.23947e15 q^{60} +4.99140e14 q^{61} -7.81475e14 q^{62} +1.84575e15 q^{63} -1.09301e15 q^{64} -9.97148e14 q^{65} -4.03829e14 q^{66} -5.80850e15 q^{67} -3.44818e15 q^{68} -6.38759e15 q^{69} +1.38058e15 q^{70} +9.89860e15 q^{71} +4.48309e15 q^{72} -7.18447e15 q^{73} -1.84476e15 q^{74} +7.73602e15 q^{75} -1.06657e16 q^{76} +2.43333e15 q^{77} -1.70363e15 q^{78} +2.52277e16 q^{79} -1.38321e16 q^{80} -1.12370e16 q^{81} -9.58842e14 q^{82} -2.43269e16 q^{83} -2.30548e16 q^{84} -3.19761e16 q^{85} -1.18258e15 q^{86} +9.12754e16 q^{87} +5.91023e15 q^{88} +4.37620e14 q^{89} +1.97750e16 q^{90} +1.02654e16 q^{91} +4.44680e16 q^{92} +1.21018e17 q^{93} +2.17410e16 q^{94} -9.89063e16 q^{95} -8.53583e16 q^{96} +5.16443e16 q^{97} +1.14455e16 q^{98} +3.48543e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 256 q^{2} + 3058 q^{3} + 391332 q^{4} + 1795234 q^{5} + 13170682 q^{6} - 896364 q^{7} - 101682420 q^{8} + 413432462 q^{9}+O(q^{10}) $ 8 * q + 256 * q^2 + 3058 * q^3 + 391332 * q^4 + 1795234 * q^5 + 13170682 * q^6 - 896364 * q^7 - 101682420 * q^8 + 413432462 * q^9	\( 8 q + 256 q^{2} + 3058 q^{3} + 391332 q^{4} + 1795234 q^{5} + 13170682 q^{6} - 896364 q^{7} - 101682420 q^{8} + 413432462 q^{9} - 717567014 q^{10} + 1714871048 q^{11} - 3285295504 q^{12} + 1804014468 q^{13} + 17794023508 q^{14} + 8875276234 q^{15} + 53793011976 q^{16} - 27416338904 q^{17} + 28258692878 q^{18} + 58429836440 q^{19} + 650385049400 q^{20} + 562668763708 q^{21} + 54875873536 q^{22} + 1231860549578 q^{23} + 3528111117084 q^{24} + 3225446670918 q^{25} + 3698352129748 q^{26} + 5544189136510 q^{27} + 553346903392 q^{28} + 4016405848668 q^{29} + 28329117219490 q^{30} + 21044142033258 q^{31} - 7034951233624 q^{32} + 655509458098 q^{33} + 10491977089288 q^{34} - 37564178328188 q^{35} + 18688387613044 q^{36} - 38179864040434 q^{37} - 32101053490680 q^{38} - 133370005047128 q^{39} - 229151934325836 q^{40} - 84601913468108 q^{41} - 374381853665348 q^{42} - 79795156805452 q^{43} + 83885489619492 q^{44} + 85333967988848 q^{45} - 63876340102558 q^{46} - 333992064138544 q^{47} - 921917930639032 q^{48} + 16663435022976 q^{49} - 203190218406730 q^{50} + 445337187172876 q^{51} + 383080290241336 q^{52} + 351380494472328 q^{53} + 21\!\cdots\!38 q^{54}+ \cdots + 88\!\cdots\!22 q^{99}+O(q^{100}) \) 8 * q + 256 * q^2 + 3058 * q^3 + 391332 * q^4 + 1795234 * q^5 + 13170682 * q^6 - 896364 * q^7 - 101682420 * q^8 + 413432462 * q^9 - 717567014 * q^10 + 1714871048 * q^11 - 3285295504 * q^12 + 1804014468 * q^13 + 17794023508 * q^14 + 8875276234 * q^15 + 53793011976 * q^16 - 27416338904 * q^17 + 28258692878 * q^18 + 58429836440 * q^19 + 650385049400 * q^20 + 562668763708 * q^21 + 54875873536 * q^22 + 1231860549578 * q^23 + 3528111117084 * q^24 + 3225446670918 * q^25 + 3698352129748 * q^26 + 5544189136510 * q^27 + 553346903392 * q^28 + 4016405848668 * q^29 + 28329117219490 * q^30 + 21044142033258 * q^31 - 7034951233624 * q^32 + 655509458098 * q^33 + 10491977089288 * q^34 - 37564178328188 * q^35 + 18688387613044 * q^36 - 38179864040434 * q^37 - 32101053490680 * q^38 - 133370005047128 * q^39 - 229151934325836 * q^40 - 84601913468108 * q^41 - 374381853665348 * q^42 - 79795156805452 * q^43 + 83885489619492 * q^44 + 85333967988848 * q^45 - 63876340102558 * q^46 - 333992064138544 * q^47 - 921917930639032 * q^48 + 16663435022976 * q^49 - 203190218406730 * q^50 + 445337187172876 * q^51 + 383080290241336 * q^52 + 351380494472328 * q^53 + 2142853805961238 * q^54 + 384824351373154 * q^55 + 4437023751861816 * q^56 + 3266305594995600 * q^57 + 4039861017699420 * q^58 + 1023638486071814 * q^59 - 3214396297711936 * q^60 + 3794216197393316 * q^61 + 425349364206562 * q^62 - 2372860203801592 * q^63 + 6201620853304640 * q^64 - 2999195217446768 * q^65 + 2823252655526842 * q^66 + 5095474549488046 * q^67 - 16863568290550648 * q^68 + 2954340406561046 * q^69 - 1215862479252572 * q^70 - 1512701018213922 * q^71 - 47801016625093920 * q^72 + 1243757422569468 * q^73 - 32612646811059594 * q^74 - 12043436835518416 * q^75 - 57190847748178480 * q^76 - 192143584008684 * q^77 - 39902196048908264 * q^78 + 11583193006100356 * q^79 + 11760711968111960 * q^80 + 34892948392364408 * q^81 - 36998674460297948 * q^82 + 28335131925089508 * q^83 + 99838504514799680 * q^84 - 13434364728244100 * q^85 - 50273004015301116 * q^86 + 149533775100988560 * q^87 - 21796529768572020 * q^88 + 188410727637478542 * q^89 + 27756107460171104 * q^90 + 136202135129762480 * q^91 + 55575922205377216 * q^92 + 150258196291800646 * q^93 + 9488865070270352 * q^94 + 95643103186605600 * q^95 + 143914463501217272 * q^96 + 209457880210246906 * q^97 - 306362245050391368 * q^98 + 88622919923395022 * 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 $

$2$	−110.296	−0.304653	−0.152326	−	0.988330i	$-0.548676\pi$
$2$	−110.296	−0.304653	−0.152326	+	0.988330i	$0.548676\pi$
$3$	17080.3	1.50302	0.751512	−	0.659720i	$-0.229325\pi$
$3$	17080.3	1.50302	0.751512	+	0.659720i	$0.229325\pi$
$4$	−118907.	−0.907187
$5$	−1.10266e6	−1.26240	−0.631199	−	0.775621i	$-0.717437\pi$
$5$	−1.10266e6	−1.26240	−0.631199	+	0.775621i	$0.717437\pi$
$6$	−1.88389e6	−0.457900
$7$	1.13516e7	0.744261	0.372131	−	0.928180i	$-0.378627\pi$
$7$	1.13516e7	0.744261	0.372131	+	0.928180i	$0.378627\pi$
$8$	2.75717e7	0.581029
$9$	1.62598e8	1.25908
$10$	1.21619e8	0.384593
$11$	2.14359e8	0.301511
$11$	2.14359e8	0.301511
$12$	−2.03097e9	−1.36352
$13$	9.04312e8	0.307468	0.153734	−	0.988112i	$-0.450870\pi$
$13$	9.04312e8	0.307468	0.153734	+	0.988112i	$0.450870\pi$
$14$	−1.25204e9	−0.226741
$15$	−1.88338e10	−1.89742
$16$	1.25443e10	0.730175
$17$	2.89990e10	1.00825	0.504124	−	0.863631i	$-0.331815\pi$
$17$	2.89990e10	1.00825	0.504124	+	0.863631i	$0.331815\pi$
$18$	−1.79339e10	−0.383582
$19$	8.96979e10	1.21165	0.605824	−	0.795599i	$-0.292844\pi$
$19$	8.96979e10	1.21165	0.605824	+	0.795599i	$0.292844\pi$
$20$	1.31114e11	1.14523
$21$	1.93890e11	1.11864
$22$	−2.36429e10	−0.0918562
$23$	−3.73973e11	−0.995758	−0.497879	−	0.867246i	$-0.665888\pi$
$23$	−3.73973e11	−0.995758	−0.497879	+	0.867246i	$0.665888\pi$
$24$	4.70933e11	0.873301
$25$	4.52920e11	0.593651
$26$	−9.97419e10	−0.0936708
$27$	5.71468e11	0.389403
$28$	−1.34979e12	−0.675184
$29$	5.34389e12	1.98369	0.991846	−	0.127439i	$-0.0406757\pi$
$29$	5.34389e12	1.98369	0.991846	+	0.127439i	$0.0406757\pi$
$30$	2.07729e12	0.578052
$31$	7.08525e12	1.49204	0.746021	−	0.665923i	$-0.231962\pi$
$31$	7.08525e12	1.49204	0.746021	+	0.665923i	$0.231962\pi$
$32$	−4.99746e12	−0.803479
$33$	3.66132e12	0.453179
$34$	−3.19848e12	−0.307165
$35$	−1.25170e13	−0.939554
$36$	−1.93340e13	−1.14222
$37$	1.67255e13	0.782825	0.391413	−	0.920215i	$-0.371987\pi$
$37$	1.67255e13	0.782825	0.391413	+	0.920215i	$0.371987\pi$
$38$	−9.89332e12	−0.369132
$39$	1.54459e13	0.462131
$40$	−3.04022e13	−0.733491
$41$	8.69335e12	0.170030	0.0850148	−	0.996380i	$-0.472906\pi$
$41$	8.69335e12	0.170030	0.0850148	+	0.996380i	$0.472906\pi$
$42$	−2.13853e13	−0.340797
$43$	1.07218e13	0.139890	0.0699451	−	0.997551i	$-0.477718\pi$
$43$	1.07218e13	0.139890	0.0699451	+	0.997551i	$0.477718\pi$
$44$	−2.54887e13	−0.273527
$45$	−1.79290e14	−1.58946
$46$	4.12478e13	0.303360
$47$	−1.97115e14	−1.20750	−0.603750	−	0.797173i	$-0.706328\pi$
$47$	−1.97115e14	−1.20750	−0.603750	+	0.797173i	$0.706328\pi$
$48$	2.14261e14	1.09747
$49$	−1.03771e14	−0.446075
$50$	−4.99552e13	−0.180857
$51$	4.95313e14	1.51542
$52$	−1.07529e14	−0.278931
$53$	−1.87563e14	−0.413810	−0.206905	−	0.978361i	$-0.566339\pi$
$53$	−1.87563e14	−0.413810	−0.206905	+	0.978361i	$0.566339\pi$
$54$	−6.30306e13	−0.118633
$55$	−2.36365e14	−0.380628
$56$	3.12984e14	0.432438
$57$	1.53207e15	1.82114
$58$	−5.89410e14	−0.604337
$59$	6.36161e14	0.564059	0.282030	−	0.959406i	$-0.408992\pi$
$59$	6.36161e14	0.564059	0.282030	+	0.959406i	$0.408992\pi$
$60$	2.23947e15	1.72131
$61$	4.99140e14	0.333364	0.166682	−	0.986011i	$-0.446695\pi$
$61$	4.99140e14	0.333364	0.166682	+	0.986011i	$0.446695\pi$
$62$	−7.81475e14	−0.454554
$63$	1.84575e15	0.937084
$64$	−1.09301e15	−0.485393
$65$	−9.97148e14	−0.388147
$66$	−4.03829e14	−0.138062
$67$	−5.80850e15	−1.74754	−0.873772	−	0.486336i	$-0.838333\pi$
$67$	−5.80850e15	−1.74754	−0.873772	+	0.486336i	$0.838333\pi$
$68$	−3.44818e15	−0.914670
$69$	−6.38759e15	−1.49665
$70$	1.38058e15	0.286238
$71$	9.89860e15	1.81919	0.909594	−	0.415498i	$-0.136393\pi$
$71$	9.89860e15	1.81919	0.909594	+	0.415498i	$0.136393\pi$
$72$	4.48309e15	0.731562
$73$	−7.18447e15	−1.04268	−0.521339	−	0.853349i	$-0.674567\pi$
$73$	−7.18447e15	−1.04268	−0.521339	+	0.853349i	$0.674567\pi$
$74$	−1.84476e15	−0.238490
$75$	7.73602e15	0.892271
$76$	−1.06657e16	−1.09919
$77$	2.43333e15	0.224403
$78$	−1.70363e15	−0.140789
$79$	2.52277e16	1.87088	0.935442	−	0.353480i	$-0.115002\pi$
$79$	2.52277e16	1.87088	0.935442	+	0.353480i	$0.115002\pi$
$80$	−1.38321e16	−0.921772
$81$	−1.12370e16	−0.673797
$82$	−9.58842e14	−0.0517999
$83$	−2.43269e16	−1.18556	−0.592780	−	0.805364i	$-0.701970\pi$
$83$	−2.43269e16	−1.18556	−0.592780	+	0.805364i	$0.701970\pi$
$84$	−2.30548e16	−1.01482
$85$	−3.19761e16	−1.27281
$86$	−1.18258e15	−0.0426179
$87$	9.12754e16	2.98154
$88$	5.91023e15	0.175187
$89$	4.37620e14	0.0117837	0.00589186	−	0.999983i	$-0.498125\pi$
$89$	4.37620e14	0.0117837	0.00589186	+	0.999983i	$0.498125\pi$
$90$	1.97750e16	0.484233
$91$	1.02654e16	0.228836
$92$	4.44680e16	0.903339
$93$	1.21018e17	2.24257
$94$	2.17410e16	0.367868
$95$	−9.89063e16	−1.52958
$96$	−8.53583e16	−1.20765
$97$	5.16443e16	0.669057	0.334528	−	0.942386i	$-0.391423\pi$
$97$	5.16443e16	0.669057	0.334528	+	0.942386i	$0.391423\pi$
$98$	1.14455e16	0.135898
$99$	3.48543e16	0.379627
$100$	−5.38552e16	−0.538552
$101$	−1.47503e15	−0.0135541	−0.00677704	−	0.999977i	$-0.502157\pi$
$101$	−1.47503e15	−0.0135541	−0.00677704	+	0.999977i	$0.502157\pi$
$102$	−5.46311e16	−0.461677
$103$	1.24430e17	0.967854	0.483927	−	0.875108i	$-0.339210\pi$
$103$	1.24430e17	0.967854	0.483927	+	0.875108i	$0.339210\pi$
$104$	2.49334e16	0.178648
$105$	−2.13795e17	−1.41217
$106$	2.06874e16	0.126068
$107$	−2.74994e17	−1.54725	−0.773625	−	0.633643i	$-0.781559\pi$
$107$	−2.74994e17	−1.54725	−0.773625	+	0.633643i	$0.781559\pi$
$108$	−6.79514e16	−0.353262
$109$	−2.19286e17	−1.05411	−0.527054	−	0.849832i	$-0.676703\pi$
$109$	−2.19286e17	−1.05411	−0.527054	+	0.849832i	$0.676703\pi$
$110$	2.60701e16	0.115959
$111$	2.85677e17	1.17660
$112$	1.42398e17	0.543441
$113$	6.81219e16	0.241057	0.120529	−	0.992710i	$-0.461541\pi$
$113$	6.81219e16	0.241057	0.120529	+	0.992710i	$0.461541\pi$
$114$	−1.68981e17	−0.554814
$115$	4.12365e17	1.25704
$116$	−6.35425e17	−1.79958
$117$	1.47039e17	0.387127
$118$	−7.01660e16	−0.171842
$119$	3.29186e17	0.750400
$120$	−5.19279e17	−1.10245
$121$	4.59497e16	0.0909091
$122$	−5.50531e16	−0.101560
$123$	1.48485e17	0.255558
$124$	−8.42484e17	−1.35356
$125$	3.41846e17	0.512975
$126$	−2.03579e17	−0.285485
$127$	9.46735e17	1.24136	0.620679	−	0.784065i	$-0.286857\pi$
$127$	9.46735e17	1.24136	0.620679	+	0.784065i	$0.286857\pi$
$128$	7.75581e17	0.951355
$129$	1.83132e17	0.210258
$130$	1.09981e17	0.118250
$131$	9.88374e17	0.995670	0.497835	−	0.867272i	$-0.334128\pi$
$131$	9.88374e17	0.995670	0.497835	+	0.867272i	$0.334128\pi$
$132$	−4.35356e17	−0.411118
$133$	1.01822e18	0.901783
$134$	6.40654e17	0.532394
$135$	−6.30135e17	−0.491582
$136$	7.99551e17	0.585822
$137$	−8.45299e17	−0.581950	−0.290975	−	0.956731i	$-0.593980\pi$
$137$	−8.45299e17	−0.581950	−0.290975	+	0.956731i	$0.593980\pi$
$138$	7.04526e17	0.455958
$139$	5.01017e17	0.304949	0.152474	−	0.988307i	$-0.451276\pi$
$139$	5.01017e17	0.304949	0.152474	+	0.988307i	$0.451276\pi$
$140$	1.48836e18	0.852351
$141$	−3.36679e18	−1.81490
$142$	−1.09178e18	−0.554220
$143$	1.93847e17	0.0927050
$144$	2.03968e18	0.919348
$145$	−5.89249e18	−2.50421
$146$	7.92419e17	0.317655
$147$	−1.77244e18	−0.670462
$148$	−1.98878e18	−0.710169
$149$	−1.70567e18	−0.575192	−0.287596	−	0.957752i	$-0.592856\pi$
$149$	−1.70567e18	−0.575192	−0.287596	+	0.957752i	$0.592856\pi$
$150$	−8.53252e17	−0.271833
$151$	3.70714e18	1.11618	0.558090	−	0.829780i	$-0.311534\pi$
$151$	3.70714e18	1.11618	0.558090	+	0.829780i	$0.311534\pi$
$152$	2.47312e18	0.704003
$153$	4.71518e18	1.26947
$154$	−2.68386e17	−0.0683650
$155$	−7.81262e18	−1.88355
$156$	−1.83663e18	−0.419239
$157$	4.48513e18	0.969678	0.484839	−	0.874603i	$-0.338878\pi$
$157$	4.48513e18	0.969678	0.484839	+	0.874603i	$0.338878\pi$
$158$	−2.78251e18	−0.569970
$159$	−3.20363e18	−0.621967
$160$	5.51050e18	1.01431
$161$	−4.24521e18	−0.741104
$162$	1.23940e18	0.205274
$163$	1.16340e19	1.82867	0.914335	−	0.404959i	$-0.132714\pi$
$163$	1.16340e19	1.82867	0.914335	+	0.404959i	$0.132714\pi$
$164$	−1.03370e18	−0.154249
$165$	−4.03719e18	−0.572092
$166$	2.68316e18	0.361184
$167$	−1.28862e19	−1.64829	−0.824147	−	0.566377i	$-0.808345\pi$
$167$	−1.28862e19	−1.64829	−0.824147	+	0.566377i	$0.808345\pi$
$168$	5.34587e18	0.649964
$169$	−7.83264e18	−0.905464
$170$	3.52683e18	0.387765
$171$	1.45847e19	1.52556
$172$	−1.27490e18	−0.126906
$173$	3.11262e18	0.294941	0.147470	−	0.989066i	$-0.452887\pi$
$173$	3.11262e18	0.294941	0.147470	+	0.989066i	$0.452887\pi$
$174$	−1.00673e19	−0.908333
$175$	5.14138e18	0.441831
$176$	2.68898e18	0.220156
$177$	1.08658e19	0.847794
$178$	−4.82677e16	−0.00358994
$179$	−6.32020e18	−0.448209	−0.224104	−	0.974565i	$-0.571946\pi$
$179$	−6.32020e18	−0.448209	−0.224104	+	0.974565i	$0.571946\pi$
$180$	2.13188e19	1.44194
$181$	1.04913e18	0.0676958	0.0338479	−	0.999427i	$-0.489224\pi$
$181$	1.04913e18	0.0676958	0.0338479	+	0.999427i	$0.489224\pi$
$182$	−1.13223e18	−0.0697156
$183$	8.52548e18	0.501054
$184$	−1.03111e19	−0.578565
$185$	−1.84426e19	−0.988238
$186$	−1.33479e19	−0.683206
$187$	6.21620e18	0.303998
$188$	2.34383e19	1.09543
$189$	6.48710e18	0.289818
$190$	1.09090e19	0.465991
$191$	8.15134e18	0.333001	0.166501	−	0.986041i	$-0.446753\pi$
$191$	8.15134e18	0.333001	0.166501	+	0.986041i	$0.446753\pi$
$192$	−1.86689e19	−0.729557
$193$	−2.30916e18	−0.0863411	−0.0431705	−	0.999068i	$-0.513746\pi$
$193$	−2.30916e18	−0.0863411	−0.0431705	+	0.999068i	$0.513746\pi$
$194$	−5.69616e18	−0.203830
$195$	−1.70316e19	−0.583394
$196$	1.23390e19	0.404674
$197$	−2.42591e19	−0.761926	−0.380963	−	0.924590i	$-0.624407\pi$
$197$	−2.42591e19	−0.761926	−0.380963	+	0.924590i	$0.624407\pi$
$198$	−3.84429e18	−0.115654
$199$	−3.97015e19	−1.14434	−0.572170	−	0.820135i	$-0.693898\pi$
$199$	−3.97015e19	−1.14434	−0.572170	+	0.820135i	$0.693898\pi$
$200$	1.24877e19	0.344929
$201$	−9.92111e19	−2.62660
$202$	1.62690e17	0.00412928
$203$	6.06619e19	1.47639
$204$	−5.88961e19	−1.37477
$205$	−9.58581e18	−0.214645
$206$	−1.37242e19	−0.294859
$207$	−6.08072e19	−1.25374
$208$	1.13440e19	0.224505
$209$	1.92275e19	0.365326
$210$	2.35807e19	0.430222
$211$	5.34372e19	0.936360	0.468180	−	0.883633i	$-0.344910\pi$
$211$	5.34372e19	0.936360	0.468180	+	0.883633i	$0.344910\pi$
$212$	2.23025e19	0.375403
$213$	1.69071e20	2.73428
$214$	3.03307e19	0.471374
$215$	−1.18225e19	−0.176597
$216$	1.57563e19	0.226255
$217$	8.04292e19	1.11047
$218$	2.41863e19	0.321137
$219$	−1.22713e20	−1.56717
$220$	2.81054e19	0.345300
$221$	2.62241e19	0.310004
$222$	−3.15091e19	−0.358456
$223$	5.34269e19	0.585018	0.292509	−	0.956263i	$-0.405510\pi$
$223$	5.34269e19	0.585018	0.292509	+	0.956263i	$0.405510\pi$
$224$	−5.67294e19	−0.597998
$225$	7.36437e19	0.747454
$226$	−7.51358e18	−0.0734387
$227$	−1.61389e20	−1.51933	−0.759667	−	0.650313i	$-0.774638\pi$
$227$	−1.61389e20	−1.51933	−0.759667	+	0.650313i	$0.774638\pi$
$228$	−1.82174e20	−1.65211
$229$	5.63049e19	0.491977	0.245989	−	0.969273i	$-0.420887\pi$
$229$	5.63049e19	0.491977	0.245989	+	0.969273i	$0.420887\pi$
$230$	−4.54823e19	−0.382962
$231$	4.15620e19	0.337283
$232$	1.47340e20	1.15258
$233$	−6.78255e19	−0.511526	−0.255763	−	0.966739i	$-0.582327\pi$
$233$	−6.78255e19	−0.511526	−0.255763	+	0.966739i	$0.582327\pi$
$234$	−1.62178e19	−0.117939
$235$	2.17351e20	1.52435
$236$	−7.56438e19	−0.511707
$237$	4.30897e20	2.81198
$238$	−3.63080e19	−0.228611
$239$	−1.60002e20	−0.972169	−0.486085	−	0.873912i	$-0.661575\pi$
$239$	−1.60002e20	−0.972169	−0.486085	+	0.873912i	$0.661575\pi$
$240$	−2.36257e20	−1.38544
$241$	2.63348e20	1.49068	0.745340	−	0.666684i	$-0.232287\pi$
$241$	2.63348e20	1.49068	0.745340	+	0.666684i	$0.232287\pi$
$242$	−5.06807e18	−0.0276957
$243$	−2.65732e20	−1.40214
$244$	−5.93511e19	−0.302423
$245$	1.14424e20	0.563125
$246$	−1.63773e19	−0.0778565
$247$	8.11148e19	0.372543
$248$	1.95352e20	0.866920
$249$	−4.15512e20	−1.78193
$250$	−3.77043e19	−0.156279
$251$	−1.11123e20	−0.445221	−0.222610	−	0.974907i	$-0.571458\pi$
$251$	−1.11123e20	−0.445221	−0.222610	+	0.974907i	$0.571458\pi$
$252$	−2.19472e20	−0.850111
$253$	−8.01645e19	−0.300232
$254$	−1.04421e20	−0.378183
$255$	−5.46162e20	−1.91307
$256$	5.77192e19	0.195560
$257$	−2.96890e20	−0.973114	−0.486557	−	0.873649i	$-0.661747\pi$
$257$	−2.96890e20	−0.973114	−0.486557	+	0.873649i	$0.661747\pi$
$258$	−2.01988e19	−0.0640557
$259$	1.89862e20	0.582627
$260$	1.18568e20	0.352122
$261$	8.68905e20	2.49763
$262$	−1.09014e20	−0.303333
$263$	−1.54826e20	−0.417082	−0.208541	−	0.978014i	$-0.566871\pi$
$263$	−1.54826e20	−0.417082	−0.208541	+	0.978014i	$0.566871\pi$
$264$	1.00949e20	0.263310
$265$	2.06818e20	0.522394
$266$	−1.12305e20	−0.274730
$267$	7.47470e18	0.0177112
$268$	6.90670e20	1.58535
$269$	−6.91485e20	−1.53776	−0.768880	−	0.639393i	$-0.779186\pi$
$269$	−6.91485e20	−1.53776	−0.768880	+	0.639393i	$0.779186\pi$
$270$	6.95013e19	0.149762
$271$	−4.66789e19	−0.0974725	−0.0487362	−	0.998812i	$-0.515519\pi$
$271$	−4.66789e19	−0.0974725	−0.0487362	+	0.998812i	$0.515519\pi$
$272$	3.63773e20	0.736197
$273$	1.75337e20	0.343946
$274$	9.32331e19	0.177293
$275$	9.70873e19	0.178992
$276$	7.59528e20	1.35774
$277$	−1.01071e21	−1.75206	−0.876031	−	0.482255i	$-0.839818\pi$
$277$	−1.01071e21	−1.75206	−0.876031	+	0.482255i	$0.839818\pi$
$278$	−5.52602e19	−0.0929034
$279$	1.15205e21	1.87860
$280$	−3.45115e20	−0.545909
$281$	9.68948e20	1.48695	0.743475	−	0.668763i	$-0.233176\pi$
$281$	9.68948e20	1.48695	0.743475	+	0.668763i	$0.233176\pi$
$282$	3.71343e20	0.552915
$283$	4.42978e20	0.640026	0.320013	−	0.947413i	$-0.396313\pi$
$283$	4.42978e20	0.640026	0.320013	+	0.947413i	$0.396313\pi$
$284$	−1.17701e21	−1.65034
$285$	−1.68935e21	−2.29900
$286$	−2.13806e19	−0.0282428
$287$	9.86838e19	0.126546
$288$	−8.12576e20	−1.01164
$289$	1.37028e19	0.0165645
$290$	6.49918e20	0.762914
$291$	8.82103e20	1.00561
$292$	8.54282e20	0.945904
$293$	−5.89335e20	−0.633852	−0.316926	−	0.948450i	$-0.602651\pi$
$293$	−5.89335e20	−0.633852	−0.316926	+	0.948450i	$0.602651\pi$
$294$	1.95493e20	0.204258
$295$	−7.01469e20	−0.712068
$296$	4.61150e20	0.454844
$297$	1.22499e20	0.117410
$298$	1.88129e20	0.175234
$299$	−3.38188e20	−0.306164
$300$	−9.19865e20	−0.809457
$301$	1.21710e20	0.104115
$302$	−4.08882e20	−0.340047
$303$	−2.51941e19	−0.0203721
$304$	1.12520e21	0.884715
$305$	−5.50382e20	−0.420838
$306$	−5.20065e20	−0.386746
$307$	−1.12216e21	−0.811667	−0.405833	−	0.913947i	$-0.633019\pi$
$307$	−1.12216e21	−0.811667	−0.405833	+	0.913947i	$0.633019\pi$
$308$	−2.89339e20	−0.203576
$309$	2.12531e21	1.45471
$310$	8.61701e20	0.573829
$311$	−1.03440e21	−0.670234	−0.335117	−	0.942177i	$-0.608776\pi$
$311$	−1.03440e21	−0.670234	−0.335117	+	0.942177i	$0.608776\pi$
$312$	4.25870e20	0.268512
$313$	−3.51193e20	−0.215486	−0.107743	−	0.994179i	$-0.534362\pi$
$313$	−3.51193e20	−0.215486	−0.107743	+	0.994179i	$0.534362\pi$
$314$	−4.94692e20	−0.295415
$315$	−2.03524e21	−1.18297
$316$	−2.99974e21	−1.69724
$317$	2.36338e20	0.130176	0.0650879	−	0.997880i	$-0.479267\pi$
$317$	2.36338e20	0.130176	0.0650879	+	0.997880i	$0.479267\pi$
$318$	3.53348e20	0.189484
$319$	1.14551e21	0.598106
$320$	1.20522e21	0.612759
$321$	−4.69699e21	−2.32555
$322$	4.68230e20	0.225779
$323$	2.60115e21	1.22164
$324$	1.33616e21	0.611260
$325$	4.09580e20	0.182528
$326$	−1.28319e21	−0.557109
$327$	−3.74548e21	−1.58435
$328$	2.39690e20	0.0987922
$329$	−2.23758e21	−0.898696
$330$	4.45286e20	0.174289
$331$	5.79289e20	0.220982	0.110491	−	0.993877i	$-0.464758\pi$
$331$	5.79289e20	0.220982	0.110491	+	0.993877i	$0.464758\pi$
$332$	2.89264e21	1.07552
$333$	2.71953e21	0.985640
$334$	1.42130e21	0.502157
$335$	6.40480e21	2.20610
$336$	2.43221e21	0.816804
$337$	−1.64541e21	−0.538791	−0.269395	−	0.963030i	$-0.586824\pi$
$337$	−1.64541e21	−0.538791	−0.269395	+	0.963030i	$0.586824\pi$
$338$	8.63909e20	0.275852
$339$	1.16355e21	0.362315
$340$	3.80217e21	1.15468
$341$	1.51879e21	0.449867
$342$	−1.60863e21	−0.464766
$343$	−3.81871e21	−1.07626
$344$	2.95619e20	0.0812803
$345$	7.04334e21	1.88937
$346$	−3.43310e20	−0.0898544
$347$	−1.70142e21	−0.434522	−0.217261	−	0.976114i	$-0.569712\pi$
$347$	−1.70142e21	−0.434522	−0.217261	+	0.976114i	$0.569712\pi$
$348$	−1.08533e22	−2.70481
$349$	8.05802e21	1.95980	0.979902	−	0.199482i	$-0.0639258\pi$
$349$	8.05802e21	1.95980	0.979902	+	0.199482i	$0.0639258\pi$
$350$	−5.67074e20	−0.134605
$351$	5.16785e20	0.119729
$352$	−1.07125e21	−0.242258
$353$	−3.42348e21	−0.755758	−0.377879	−	0.925855i	$-0.623346\pi$
$353$	−3.42348e21	−0.755758	−0.377879	+	0.925855i	$0.623346\pi$
$354$	−1.19846e21	−0.258283
$355$	−1.09148e22	−2.29654
$356$	−5.20360e19	−0.0106900
$357$	5.62262e21	1.12787
$358$	6.97093e20	0.136548
$359$	1.73506e21	0.331904	0.165952	−	0.986134i	$-0.446930\pi$
$359$	1.73506e21	0.331904	0.165952	+	0.986134i	$0.446930\pi$
$360$	−4.94333e21	−0.923524
$361$	2.56532e21	0.468091
$362$	−1.15715e20	−0.0206237
$363$	7.84837e20	0.136639
$364$	−1.22063e21	−0.207597
$365$	7.92203e21	1.31628
$366$	−9.40326e20	−0.152647
$367$	−6.74117e21	−1.06924	−0.534618	−	0.845094i	$-0.679545\pi$
$367$	−6.74117e21	−1.06924	−0.534618	+	0.845094i	$0.679545\pi$
$368$	−4.69124e21	−0.727078
$369$	1.41352e21	0.214081
$370$	2.03414e21	0.301069
$371$	−2.12914e21	−0.307983
$372$	−1.43899e22	−2.03443
$373$	−5.47174e21	−0.756136	−0.378068	−	0.925778i	$-0.623412\pi$
$373$	−5.47174e21	−0.756136	−0.378068	+	0.925778i	$0.623412\pi$
$374$	−6.85622e20	−0.0926139
$375$	5.83885e21	0.771013
$376$	−5.43478e21	−0.701593
$377$	4.83254e21	0.609922
$378$	−7.15501e20	−0.0882937
$379$	−1.21548e22	−1.46661	−0.733305	−	0.679900i	$-0.762023\pi$
$379$	−1.21548e22	−1.46661	−0.733305	+	0.679900i	$0.762023\pi$
$380$	1.17606e22	1.38762
$381$	1.61706e22	1.86579
$382$	−8.99061e20	−0.101450
$383$	5.97297e20	0.0659175	0.0329587	−	0.999457i	$-0.489507\pi$
$383$	5.97297e20	0.0659175	0.0329587	+	0.999457i	$0.489507\pi$
$384$	1.32472e22	1.42991
$385$	−2.68313e21	−0.283286
$386$	2.54691e20	0.0263040
$387$	1.74335e21	0.176133
$388$	−6.14086e21	−0.606960
$389$	−5.14037e20	−0.0497076	−0.0248538	−	0.999691i	$-0.507912\pi$
$389$	−5.14037e20	−0.0497076	−0.0248538	+	0.999691i	$0.507912\pi$
$390$	1.87852e21	0.177732
$391$	−1.08449e22	−1.00397
$392$	−2.86113e21	−0.259183
$393$	1.68818e22	1.49652
$394$	2.67569e21	0.232123
$395$	−2.78175e22	−2.36180
$396$	−4.14441e21	−0.344393
$397$	−1.05235e22	−0.855936	−0.427968	−	0.903794i	$-0.640770\pi$
$397$	−1.05235e22	−0.855936	−0.427968	+	0.903794i	$0.640770\pi$
$398$	4.37891e21	0.348626
$399$	1.73915e22	1.35540
$400$	5.68156e21	0.433469
$401$	2.42679e21	0.181261	0.0906305	−	0.995885i	$-0.471112\pi$
$401$	2.42679e21	0.181261	0.0906305	+	0.995885i	$0.471112\pi$
$402$	1.09426e22	0.800200
$403$	6.40727e21	0.458755
$404$	1.75391e20	0.0122961
$405$	1.23906e22	0.850601
$406$	−6.69077e21	−0.449785
$407$	3.58526e21	0.236031
$408$	1.36566e22	0.880504
$409$	−1.97910e22	−1.24974	−0.624869	−	0.780730i	$-0.714847\pi$
$409$	−1.97910e22	−1.24974	−0.624869	+	0.780730i	$0.714847\pi$
$410$	1.05728e21	0.0653922
$411$	−1.44380e22	−0.874684
$412$	−1.47956e22	−0.878024
$413$	7.22147e21	0.419807
$414$	6.70680e21	0.381955
$415$	2.68243e22	1.49665
$416$	−4.51926e21	−0.247044
$417$	8.55754e21	0.458345
$418$	−2.12072e21	−0.111297
$419$	−9.15210e21	−0.470654	−0.235327	−	0.971916i	$-0.575616\pi$
$419$	−9.15210e21	−0.470654	−0.235327	+	0.971916i	$0.575616\pi$
$420$	2.54216e22	1.28110
$421$	3.11825e22	1.53997	0.769986	−	0.638061i	$-0.220263\pi$
$421$	3.11825e22	1.53997	0.769986	+	0.638061i	$0.220263\pi$
$422$	−5.89391e21	−0.285264
$423$	−3.20504e22	−1.52034
$424$	−5.17141e21	−0.240436
$425$	1.31342e22	0.598547
$426$	−1.86479e22	−0.833006
$427$	5.66606e21	0.248110
$428$	3.26986e22	1.40365
$429$	3.31098e21	0.139338
$430$	1.30398e21	0.0538008
$431$	−1.00655e22	−0.407173	−0.203587	−	0.979057i	$-0.565260\pi$
$431$	−1.00655e22	−0.407173	−0.203587	+	0.979057i	$0.565260\pi$
$432$	7.16867e21	0.284333
$433$	−3.58707e22	−1.39506	−0.697529	−	0.716557i	$-0.745717\pi$
$433$	−3.58707e22	−1.39506	−0.697529	+	0.716557i	$0.745717\pi$
$434$	−8.87102e21	−0.338307
$435$	−1.00646e23	−3.76389
$436$	2.60746e22	0.956273
$437$	−3.35446e22	−1.20651
$438$	1.35348e22	0.477443
$439$	1.31693e22	0.455632	0.227816	−	0.973704i	$-0.426841\pi$
$439$	1.31693e22	0.455632	0.227816	+	0.973704i	$0.426841\pi$
$440$	−6.51697e21	−0.221156
$441$	−1.68729e22	−0.561644
$442$	−2.89242e21	−0.0944435
$443$	1.62980e22	0.522038	0.261019	−	0.965334i	$-0.415941\pi$
$443$	1.62980e22	0.522038	0.261019	+	0.965334i	$0.415941\pi$
$444$	−3.39690e22	−1.06740
$445$	−4.82546e20	−0.0148757
$446$	−5.89278e21	−0.178227
$447$	−2.91335e22	−0.864527
$448$	−1.24074e22	−0.361259
$449$	2.82419e22	0.806863	0.403432	−	0.915010i	$-0.367817\pi$
$449$	2.82419e22	0.806863	0.403432	+	0.915010i	$0.367817\pi$
$450$	−8.12261e21	−0.227714
$451$	1.86350e21	0.0512658
$452$	−8.10016e21	−0.218684
$453$	6.33191e22	1.67765
$454$	1.78005e22	0.462869
$455$	−1.13193e22	−0.288883
$456$	4.22417e22	1.05813
$457$	6.43988e22	1.58340	0.791699	−	0.610911i	$-0.209197\pi$
$457$	6.43988e22	1.58340	0.791699	+	0.610911i	$0.209197\pi$
$458$	−6.21021e21	−0.149882
$459$	1.65720e22	0.392615
$460$	−4.90330e22	−1.14037
$461$	8.03127e22	1.83369	0.916846	−	0.399240i	$-0.130726\pi$
$461$	8.03127e22	1.83369	0.916846	+	0.399240i	$0.130726\pi$
$462$	−4.58413e21	−0.102754
$463$	2.45490e21	0.0540251	0.0270126	−	0.999635i	$-0.491401\pi$
$463$	2.45490e21	0.0540251	0.0270126	+	0.999635i	$0.491401\pi$
$464$	6.70354e22	1.44844
$465$	−1.33442e23	−2.83102
$466$	7.48088e21	0.155838
$467$	1.94745e22	0.398357	0.199178	−	0.979963i	$-0.436173\pi$
$467$	1.94745e22	0.398357	0.199178	+	0.979963i	$0.436173\pi$
$468$	−1.74839e22	−0.351196
$469$	−6.59360e22	−1.30063
$470$	−2.39729e22	−0.464396
$471$	7.66075e22	1.45745
$472$	1.75400e22	0.327735
$473$	2.29832e21	0.0421785
$474$	−4.75262e22	−0.856678
$475$	4.06259e22	0.719296
$476$	−3.91425e22	−0.680753
$477$	−3.04973e22	−0.521020
$478$	1.76475e22	0.296174
$479$	−2.77709e22	−0.457866	−0.228933	−	0.973442i	$-0.573524\pi$
$479$	−2.77709e22	−0.457866	−0.228933	+	0.973442i	$0.573524\pi$
$480$	9.41212e22	1.52453
$481$	1.51251e22	0.240694
$482$	−2.90462e22	−0.454139
$483$	−7.25096e22	−1.11390
$484$	−5.46373e21	−0.0824715
$485$	−5.69462e22	−0.844617
$486$	2.93092e22	0.427165
$487$	3.03055e22	0.434035	0.217018	−	0.976168i	$-0.430367\pi$
$487$	3.03055e22	0.434035	0.217018	+	0.976168i	$0.430367\pi$
$488$	1.37621e22	0.193694
$489$	1.98713e23	2.74853
$490$	−1.26205e22	−0.171557
$491$	3.08833e22	0.412602	0.206301	−	0.978489i	$-0.433857\pi$
$491$	3.08833e22	0.412602	0.206301	+	0.978489i	$0.433857\pi$
$492$	−1.76559e22	−0.231839
$493$	1.54968e23	2.00005
$494$	−8.94664e21	−0.113496
$495$	−3.84324e22	−0.479241
$496$	8.88796e22	1.08945
$497$	1.12365e23	1.35395
$498$	4.58294e22	0.542868
$499$	−1.01842e23	−1.18597	−0.592984	−	0.805214i	$-0.702050\pi$
$499$	−1.01842e23	−1.18597	−0.592984	+	0.805214i	$0.702050\pi$
$500$	−4.06479e22	−0.465364
$501$	−2.20100e23	−2.47742
$502$	1.22564e22	0.135638
$503$	−5.43006e22	−0.590849	−0.295425	−	0.955366i	$-0.595461\pi$
$503$	−5.43006e22	−0.590849	−0.295425	+	0.955366i	$0.595461\pi$
$504$	5.08905e22	0.544474
$505$	1.62646e21	0.0171106
$506$	8.84182e21	0.0914666
$507$	−1.33784e23	−1.36093
$508$	−1.12573e23	−1.12614
$509$	−1.02058e23	−1.00403	−0.502016	−	0.864858i	$-0.667408\pi$
$509$	−1.02058e23	−1.00403	−0.502016	+	0.864858i	$0.667408\pi$
$510$	6.02395e22	0.582820
$511$	−8.15556e22	−0.776025
$512$	−1.08023e23	−1.01093
$513$	5.12594e22	0.471820
$514$	3.27458e22	0.296462
$515$	−1.37204e23	−1.22182
$516$	−2.17757e22	−0.190743
$517$	−4.22533e22	−0.364075
$518$	−2.09410e22	−0.177499
$519$	5.31647e22	0.443303
$520$	−2.74930e22	−0.225525
$521$	−4.45997e22	−0.359924	−0.179962	−	0.983674i	$-0.557598\pi$
$521$	−4.45997e22	−0.359924	−0.179962	+	0.983674i	$0.557598\pi$
$522$	−9.58367e22	−0.760909
$523$	1.53515e23	1.19918	0.599592	−	0.800306i	$-0.295330\pi$
$523$	1.53515e23	1.19918	0.599592	+	0.800306i	$0.295330\pi$
$524$	−1.17524e23	−0.903259
$525$	8.78165e22	0.664083
$526$	1.70767e22	0.127065
$527$	2.05465e23	1.50435
$528$	4.59287e22	0.330900
$529$	−1.19400e21	−0.00846510
$530$	−2.28112e22	−0.159149
$531$	1.03438e23	0.710196
$532$	−1.21073e23	−0.818085
$533$	7.86150e21	0.0522786
$534$	−8.24429e20	−0.00539576
$535$	3.03225e23	1.95325
$536$	−1.60150e23	−1.01537
$537$	−1.07951e23	−0.673668
$538$	7.62680e22	0.468482
$539$	−2.22442e22	−0.134497
$540$	7.49273e22	0.445957
$541$	−7.98219e22	−0.467676	−0.233838	−	0.972276i	$-0.575129\pi$
$541$	−7.98219e22	−0.467676	−0.233838	+	0.972276i	$0.575129\pi$
$542$	5.14850e21	0.0296952
$543$	1.79195e22	0.101748
$544$	−1.44921e23	−0.810106
$545$	2.41798e23	1.33071
$546$	−1.93390e22	−0.104784
$547$	1.87949e23	1.00265	0.501324	−	0.865259i	$-0.332846\pi$
$547$	1.87949e23	1.00265	0.501324	+	0.865259i	$0.332846\pi$
$548$	1.00512e23	0.527937
$549$	8.11591e22	0.419732
$550$	−1.07083e22	−0.0545305
$551$	4.79335e23	2.40354
$552$	−1.76116e23	−0.869597
$553$	2.86375e23	1.39243
$554$	1.11477e23	0.533770
$555$	−3.15005e23	−1.48534
$556$	−5.95743e22	−0.276645
$557$	−3.05381e23	−1.39660	−0.698301	−	0.715804i	$-0.746060\pi$
$557$	−3.05381e23	−1.39660	−0.698301	+	0.715804i	$0.746060\pi$
$558$	−1.27066e23	−0.572320
$559$	9.69587e21	0.0430117
$560$	−1.57017e23	−0.686039
$561$	1.06175e23	0.456917
$562$	−1.06871e23	−0.453003
$563$	−2.16218e23	−0.902758	−0.451379	−	0.892332i	$-0.649068\pi$
$563$	−2.16218e23	−0.902758	−0.451379	+	0.892332i	$0.649068\pi$
$564$	4.00334e23	1.64646
$565$	−7.51153e22	−0.304310
$566$	−4.88587e22	−0.194985
$567$	−1.27559e23	−0.501481
$568$	2.72921e23	1.05700
$569$	5.24116e22	0.199974	0.0999870	−	0.994989i	$-0.468120\pi$
$569$	5.24116e22	0.199974	0.0999870	+	0.994989i	$0.468120\pi$
$570$	1.86329e23	0.700396
$571$	−3.18560e23	−1.17974	−0.589868	−	0.807500i	$-0.700820\pi$
$571$	−3.18560e23	−1.17974	−0.589868	+	0.807500i	$0.700820\pi$
$572$	−2.30497e22	−0.0841008
$573$	1.39228e23	0.500508
$574$	−1.08844e22	−0.0385527
$575$	−1.69380e23	−0.591133
$576$	−1.77721e23	−0.611148
$577$	−1.89278e23	−0.641365	−0.320682	−	0.947187i	$-0.603912\pi$
$577$	−1.89278e23	−0.641365	−0.320682	+	0.947187i	$0.603912\pi$
$578$	−1.51136e21	−0.00504641
$579$	−3.94413e22	−0.129773
$580$	7.00657e23	2.27179
$581$	−2.76151e23	−0.882367
$582$	−9.72924e22	−0.306361
$583$	−4.02057e22	−0.124769
$584$	−1.98088e23	−0.605827
$585$	−1.62134e23	−0.488708
$586$	6.50013e22	0.193105
$587$	−1.37281e23	−0.401965	−0.200982	−	0.979595i	$-0.564413\pi$
$587$	−1.37281e23	−0.401965	−0.200982	+	0.979595i	$0.564413\pi$
$588$	2.10755e23	0.608234
$589$	6.35532e23	1.80783
$590$	7.73692e22	0.216933
$591$	−4.14354e23	−1.14519
$592$	2.09810e23	0.571599
$593$	1.24789e23	0.335130	0.167565	−	0.985861i	$-0.446410\pi$
$593$	1.24789e23	0.335130	0.167565	+	0.985861i	$0.446410\pi$
$594$	−1.35112e22	−0.0357691
$595$	−3.62981e23	−0.947304
$596$	2.02816e23	0.521806
$597$	−6.78114e23	−1.71997
$598$	3.73008e22	0.0932735
$599$	7.11937e23	1.75515	0.877574	−	0.479441i	$-0.159161\pi$
$599$	7.11937e23	1.75515	0.877574	+	0.479441i	$0.159161\pi$
$600$	2.13295e23	0.518436
$601$	−4.35761e23	−1.04428	−0.522138	−	0.852861i	$-0.674865\pi$
$601$	−4.35761e23	−1.04428	−0.522138	+	0.852861i	$0.674865\pi$
$602$	−1.34242e22	−0.0317188
$603$	−9.44449e23	−2.20030
$604$	−4.40804e23	−1.01258
$605$	−5.06669e22	−0.114764
$606$	2.77880e21	0.00620641
$607$	−7.04147e22	−0.155081	−0.0775406	−	0.996989i	$-0.524707\pi$
$607$	−7.04147e22	−0.155081	−0.0775406	+	0.996989i	$0.524707\pi$
$608$	−4.48262e23	−0.973534
$609$	1.03613e24	2.21904
$610$	6.07049e22	0.128209
$611$	−1.78253e23	−0.371268
$612$	−5.60667e23	−1.15164
$613$	1.31977e23	0.267353	0.133677	−	0.991025i	$-0.457322\pi$
$613$	1.31977e23	0.267353	0.133677	+	0.991025i	$0.457322\pi$
$614$	1.23770e23	0.247276
$615$	−1.63729e23	−0.322617
$616$	6.70908e22	0.130385
$617$	−2.21141e23	−0.423882	−0.211941	−	0.977283i	$-0.567978\pi$
$617$	−2.21141e23	−0.423882	−0.211941	+	0.977283i	$0.567978\pi$
$618$	−2.34413e23	−0.443180
$619$	3.80163e23	0.708924	0.354462	−	0.935070i	$-0.384664\pi$
$619$	3.80163e23	0.708924	0.354462	+	0.935070i	$0.384664\pi$
$620$	9.28974e23	1.70873
$621$	−2.13714e23	−0.387752
$622$	1.14090e23	0.204188
$623$	4.96771e21	0.00877016
$624$	1.93759e23	0.337437
$625$	−7.22491e23	−1.24123
$626$	3.87352e22	0.0656484
$627$	3.28413e23	0.549093
$628$	−5.33312e23	−0.879679
$629$	4.85024e23	0.789282
$630$	2.24479e23	0.360396
$631$	1.04546e24	1.65599	0.827996	−	0.560735i	$-0.189481\pi$
$631$	1.04546e24	1.65599	0.827996	+	0.560735i	$0.189481\pi$
$632$	6.95569e23	1.08704
$633$	9.12725e23	1.40737
$634$	−2.60672e22	−0.0396584
$635$	−1.04393e24	−1.56709
$636$	3.80934e23	0.564240
$637$	−9.38411e22	−0.137154
$638$	−1.26345e23	−0.182214
$639$	1.60949e24	2.29050
$640$	−8.55203e23	−1.20099
$641$	−5.16774e23	−0.716156	−0.358078	−	0.933692i	$-0.616568\pi$
$641$	−5.16774e23	−0.716156	−0.358078	+	0.933692i	$0.616568\pi$
$642$	5.18059e23	0.708486
$643$	3.00281e23	0.405261	0.202631	−	0.979255i	$-0.435051\pi$
$643$	3.00281e23	0.405261	0.202631	+	0.979255i	$0.435051\pi$
$644$	5.04784e23	0.672320
$645$	−2.01933e23	−0.265430
$646$	−2.86896e23	−0.372176
$647$	−2.63485e23	−0.337341	−0.168670	−	0.985673i	$-0.553947\pi$
$647$	−2.63485e23	−0.337341	−0.168670	+	0.985673i	$0.553947\pi$
$648$	−3.09824e23	−0.391496
$649$	1.36367e23	0.170070
$650$	−4.51751e22	−0.0556078
$651$	1.37376e24	1.66906
$652$	−1.38336e24	−1.65895
$653$	−4.96457e23	−0.587652	−0.293826	−	0.955859i	$-0.594929\pi$
$653$	−4.96457e23	−0.587652	−0.293826	+	0.955859i	$0.594929\pi$
$654$	4.13111e23	0.482676
$655$	−1.08984e24	−1.25693
$656$	1.09052e23	0.124151
$657$	−1.16818e24	−1.31282
$658$	2.46796e23	0.273790
$659$	1.72673e24	1.89103	0.945515	−	0.325578i	$-0.105559\pi$
$659$	1.72673e24	1.89103	0.945515	+	0.325578i	$0.105559\pi$
$660$	4.80050e23	0.518995
$661$	−1.48358e23	−0.158343	−0.0791714	−	0.996861i	$-0.525227\pi$
$661$	−1.48358e23	−0.158343	−0.0791714	+	0.996861i	$0.525227\pi$
$662$	−6.38932e22	−0.0673228
$663$	4.47917e23	0.465943
$664$	−6.70734e23	−0.688845
$665$	−1.12275e24	−1.13841
$666$	−2.99954e23	−0.300278
$667$	−1.99847e24	−1.97528
$668$	1.53226e24	1.49531
$669$	9.12550e23	0.879295
$670$	−7.06424e23	−0.672093
$671$	1.06995e23	0.100513
$672$	−9.68957e23	−0.898805
$673$	−1.59146e24	−1.45769	−0.728847	−	0.684676i	$-0.759944\pi$
$673$	−1.59146e24	−1.45769	−0.728847	+	0.684676i	$0.759944\pi$
$674$	1.81482e23	0.164144
$675$	2.58829e23	0.231170
$676$	9.31354e23	0.821425
$677$	8.22538e23	0.716394	0.358197	−	0.933646i	$-0.383392\pi$
$677$	8.22538e23	0.716394	0.358197	+	0.933646i	$0.383392\pi$
$678$	−1.28334e23	−0.110380
$679$	5.86248e23	0.497953
$680$	−8.81633e23	−0.739541
$681$	−2.75657e24	−2.28359
$682$	−1.67516e23	−0.137053
$683$	1.34657e24	1.08806	0.544031	−	0.839065i	$-0.316898\pi$
$683$	1.34657e24	1.08806	0.544031	+	0.839065i	$0.316898\pi$
$684$	−1.73422e24	−1.38397
$685$	9.32077e23	0.734653
$686$	4.21188e23	0.327885
$687$	9.61708e23	0.739453
$688$	1.34498e23	0.102144
$689$	−1.69615e23	−0.127233
$690$	−7.76852e23	−0.575601
$691$	1.15261e23	0.0843563	0.0421782	−	0.999110i	$-0.486570\pi$
$691$	1.15261e23	0.0843563	0.0421782	+	0.999110i	$0.486570\pi$
$692$	−3.70112e23	−0.267566
$693$	3.95653e23	0.282542
$694$	1.87660e23	0.132378
$695$	−5.52451e23	−0.384967
$696$	2.51662e24	1.73236
$697$	2.52099e23	0.171432
$698$	−8.88768e23	−0.597059
$699$	−1.15848e24	−0.768836
$700$	−6.11345e23	−0.400823
$701$	−1.86262e24	−1.20649	−0.603243	−	0.797558i	$-0.706125\pi$
$701$	−1.86262e24	−1.20649	−0.603243	+	0.797558i	$0.706125\pi$
$702$	−5.69993e22	−0.0364757
$703$	1.50024e24	0.948509
$704$	−2.34296e23	−0.146351
$705$	3.71242e24	2.29113
$706$	3.77596e23	0.230243
$707$	−1.67440e22	−0.0100878
$708$	−1.29202e24	−0.769108
$709$	−1.61230e24	−0.948316	−0.474158	−	0.880440i	$-0.657248\pi$
$709$	−1.61230e24	−0.948316	−0.474158	+	0.880440i	$0.657248\pi$
$710$	1.20386e24	0.699647
$711$	4.10196e24	2.35559
$712$	1.20659e22	0.00684668
$713$	−2.64969e24	−1.48571
$714$	−6.20152e23	−0.343608
$715$	−2.13748e23	−0.117031
$716$	7.51515e23	0.406609
$717$	−2.73288e24	−1.46119
$718$	−1.91371e23	−0.101116
$719$	1.59840e24	0.834623	0.417312	−	0.908763i	$-0.362972\pi$
$719$	1.59840e24	0.834623	0.417312	+	0.908763i	$0.362972\pi$
$720$	−2.24907e24	−1.16058
$721$	1.41249e24	0.720336
$722$	−2.82945e23	−0.142605
$723$	4.49807e24	2.24053
$724$	−1.24749e23	−0.0614128
$725$	2.42035e24	1.17762
$726$	−8.65644e22	−0.0416273
$727$	−1.69515e24	−0.805687	−0.402843	−	0.915269i	$-0.631978\pi$
$727$	−1.69515e24	−0.805687	−0.402843	+	0.915269i	$0.631978\pi$
$728$	2.83035e23	0.132961
$729$	−3.08764e24	−1.43365
$730$	−8.73768e23	−0.401007
$731$	3.10923e23	0.141044
$732$	−1.01374e24	−0.454550
$733$	1.31324e24	0.582050	0.291025	−	0.956715i	$-0.406004\pi$
$733$	1.31324e24	0.582050	0.291025	+	0.956715i	$0.406004\pi$
$734$	7.43524e23	0.325746
$735$	1.95440e24	0.846390
$736$	1.86892e24	0.800071
$737$	−1.24510e24	−0.526904
$738$	−1.55906e23	−0.0652203
$739$	3.51619e24	1.45410	0.727051	−	0.686583i	$-0.240890\pi$
$739$	3.51619e24	1.45410	0.727051	+	0.686583i	$0.240890\pi$
$740$	2.19295e24	0.896516
$741$	1.38547e24	0.559941
$742$	2.34836e23	0.0938278
$743$	2.95965e24	1.16906	0.584529	−	0.811373i	$-0.301279\pi$
$743$	2.95965e24	1.16906	0.584529	+	0.811373i	$0.301279\pi$
$744$	3.33668e24	1.30300
$745$	1.88078e24	0.726121
$746$	6.03511e23	0.230359
$747$	−3.95551e24	−1.49272
$748$	−7.39148e23	−0.275783
$749$	−3.12163e24	−1.15156
$750$	−6.44002e23	−0.234891
$751$	−2.97467e24	−1.07275	−0.536375	−	0.843979i	$-0.680207\pi$
$751$	−2.97467e24	−1.07275	−0.536375	+	0.843979i	$0.680207\pi$
$752$	−2.47267e24	−0.881687
$753$	−1.89801e24	−0.669178
$754$	−5.33010e23	−0.185814
$755$	−4.08771e24	−1.40907
$756$	−7.71360e23	−0.262919
$757$	1.53899e24	0.518707	0.259353	−	0.965783i	$-0.416491\pi$
$757$	1.53899e24	0.518707	0.259353	+	0.965783i	$0.416491\pi$
$758$	1.34063e24	0.446807
$759$	−1.36924e24	−0.451256
$760$	−2.72701e24	−0.888733
$761$	−8.58671e23	−0.276731	−0.138365	−	0.990381i	$-0.544185\pi$
$761$	−8.58671e23	−0.276731	−0.138365	+	0.990381i	$0.544185\pi$
$762$	−1.78355e24	−0.568418
$763$	−2.48925e24	−0.784532
$764$	−9.69250e23	−0.302094
$765$	−5.19924e24	−1.60257
$766$	−6.58794e22	−0.0200819
$767$	5.75287e23	0.173430
$768$	9.85863e23	0.293931
$769$	3.42361e23	0.100951	0.0504755	−	0.998725i	$-0.483926\pi$
$769$	3.42361e23	0.100951	0.0504755	+	0.998725i	$0.483926\pi$
$770$	2.95939e23	0.0863039
$771$	−5.07098e24	−1.46261
$772$	2.74575e23	0.0783275
$773$	1.91502e24	0.540317	0.270158	−	0.962816i	$-0.412924\pi$
$773$	1.91502e24	0.540317	0.270158	+	0.962816i	$0.412924\pi$
$774$	−1.92284e23	−0.0536593
$775$	3.20905e24	0.885751
$776$	1.42392e24	0.388742
$777$	3.24291e24	0.875701
$778$	5.66962e22	0.0151436
$779$	7.79775e23	0.206016
$780$	2.02518e24	0.529247
$781$	2.12185e24	0.548506
$782$	1.19614e24	0.305863
$783$	3.05386e24	0.772457
$784$	−1.30173e24	−0.325713
$785$	−4.94557e24	−1.22412
$786$	−1.86199e24	−0.455917
$787$	−2.34707e24	−0.568513	−0.284256	−	0.958748i	$-0.591747\pi$
$787$	−2.34707e24	−0.568513	−0.284256	+	0.958748i	$0.591747\pi$
$788$	2.88458e24	0.691209
$789$	−2.64449e24	−0.626884
$790$	3.06816e24	0.719529
$791$	7.73296e23	0.179410
$792$	9.60991e23	0.220574
$793$	4.51378e23	0.102499
$794$	1.16070e24	0.260763
$795$	3.53252e24	0.785170
$796$	4.72077e24	1.03813
$797$	7.61953e24	1.65780	0.828901	−	0.559395i	$-0.188967\pi$
$797$	7.61953e24	1.65780	0.828901	+	0.559395i	$0.188967\pi$
$798$	−1.91821e24	−0.412926
$799$	−5.71614e24	−1.21746
$800$	−2.26345e24	−0.476986
$801$	7.11560e22	0.0148366
$802$	−2.67665e23	−0.0552216
$803$	−1.54006e24	−0.314379
$804$	1.17969e25	2.38282
$805$	4.68102e24	0.935569
$806$	−7.06697e23	−0.139761
$807$	−1.18108e25	−2.31129
$808$	−4.06691e22	−0.00787531
$809$	−4.39926e23	−0.0842979	−0.0421489	−	0.999111i	$-0.513420\pi$
$809$	−4.39926e23	−0.0842979	−0.0421489	+	0.999111i	$0.513420\pi$
$810$	−1.36664e24	−0.259138
$811$	−3.34251e24	−0.627185	−0.313593	−	0.949558i	$-0.601533\pi$
$811$	−3.34251e24	−0.627185	−0.313593	+	0.949558i	$0.601533\pi$
$812$	−7.21311e24	−1.33936
$813$	−7.97292e23	−0.146503
$814$	−3.95440e23	−0.0719074
$815$	−1.28284e25	−2.30851
$816$	6.21336e24	1.10652
$817$	9.61725e23	0.169498
$818$	2.18286e24	0.380736
$819$	1.66913e24	0.288123
$820$	1.13982e24	0.194723
$821$	−6.48399e24	−1.09629	−0.548145	−	0.836383i	$-0.684666\pi$
$821$	−6.48399e24	−1.09629	−0.548145	+	0.836383i	$0.684666\pi$
$822$	1.59245e24	0.266475
$823$	1.04364e25	1.72842	0.864212	−	0.503128i	$-0.167818\pi$
$823$	1.04364e25	1.72842	0.864212	+	0.503128i	$0.167818\pi$
$824$	3.43075e24	0.562351
$825$	1.65828e24	0.269030
$826$	−7.96499e23	−0.127895
$827$	1.09277e25	1.73673	0.868367	−	0.495923i	$-0.165170\pi$
$827$	1.09277e25	1.73673	0.868367	+	0.495923i	$0.165170\pi$
$828$	7.23039e24	1.13738
$829$	1.19885e24	0.186660	0.0933301	−	0.995635i	$-0.470249\pi$
$829$	1.19885e24	0.186660	0.0933301	+	0.995635i	$0.470249\pi$
$830$	−2.95862e24	−0.455958
$831$	−1.72633e25	−2.63339
$832$	−9.88419e23	−0.149243
$833$	−3.00925e24	−0.449755
$834$	−9.43862e23	−0.139636
$835$	1.42091e25	2.08080
$836$	−2.28628e24	−0.331419
$837$	4.04899e24	0.581006
$838$	1.00944e24	0.143386
$839$	−1.31653e24	−0.185120	−0.0925599	−	0.995707i	$-0.529505\pi$
$839$	−1.31653e24	−0.185120	−0.0925599	+	0.995707i	$0.529505\pi$
$840$	−5.89467e24	−0.820514
$841$	2.13000e25	2.93504
$842$	−3.43930e24	−0.469156
$843$	1.65500e25	2.23492
$844$	−6.35404e24	−0.849453
$845$	8.63674e24	1.14306
$846$	3.53503e24	0.463175
$847$	5.21605e23	0.0676601
$848$	−2.35284e24	−0.302154
$849$	7.56621e24	0.961974
$850$	−1.44865e24	−0.182349
$851$	−6.25490e24	−0.779505
$852$	−2.01037e25	−2.48051
$853$	−1.23681e24	−0.151090	−0.0755449	−	0.997142i	$-0.524070\pi$
$853$	−1.23681e24	−0.151090	−0.0755449	+	0.997142i	$0.524070\pi$
$854$	−6.24944e23	−0.0755873
$855$	−1.60819e25	−1.92587
$856$	−7.58203e24	−0.898998
$857$	−9.90634e24	−1.16299	−0.581495	−	0.813550i	$-0.697532\pi$
$857$	−9.90634e24	−1.16299	−0.581495	+	0.813550i	$0.697532\pi$
$858$	−3.65187e23	−0.0424496
$859$	−8.36619e24	−0.962911	−0.481455	−	0.876471i	$-0.659892\pi$
$859$	−8.36619e24	−0.962911	−0.481455	+	0.876471i	$0.659892\pi$
$860$	1.40578e24	0.160207
$861$	1.68555e24	0.190202
$862$	1.11019e24	0.124046
$863$	−1.68426e25	−1.86345	−0.931726	−	0.363162i	$-0.881697\pi$
$863$	−1.68426e25	−1.86345	−0.931726	+	0.363162i	$0.881697\pi$
$864$	−2.85589e24	−0.312877
$865$	−3.43217e24	−0.372333
$866$	3.95639e24	0.425008
$867$	2.34049e23	0.0248968
$868$	−9.56358e24	−1.00740
$869$	5.40778e24	0.564093
$870$	1.11008e25	1.14668
$871$	−5.25269e24	−0.537313
$872$	−6.04607e24	−0.612468
$873$	8.39726e24	0.842396
$874$	3.69984e24	0.367566
$875$	3.88052e24	0.381787
$876$	1.45914e25	1.42172
$877$	9.55975e24	0.922466	0.461233	−	0.887279i	$-0.347407\pi$
$877$	9.55975e24	0.922466	0.461233	+	0.887279i	$0.347407\pi$
$878$	−1.45252e24	−0.138810
$879$	−1.00660e25	−0.952694
$880$	−2.96503e24	−0.277925
$881$	−6.59071e24	−0.611839	−0.305919	−	0.952057i	$-0.598964\pi$
$881$	−6.59071e24	−0.611839	−0.305919	+	0.952057i	$0.598964\pi$
$882$	1.86101e24	0.171106
$883$	−5.53781e24	−0.504280	−0.252140	−	0.967691i	$-0.581134\pi$
$883$	−5.53781e24	−0.504280	−0.252140	+	0.967691i	$0.581134\pi$
$884$	−3.11823e24	−0.281231
$885$	−1.19813e25	−1.07025
$886$	−1.79760e24	−0.159040
$887$	6.83929e24	0.599322	0.299661	−	0.954046i	$-0.403126\pi$
$887$	6.83929e24	0.599322	0.299661	+	0.954046i	$0.403126\pi$
$888$	7.87660e24	0.683642
$889$	1.07470e25	0.923894
$890$	5.32229e22	0.00453193
$891$	−2.40876e24	−0.203158
$892$	−6.35282e24	−0.530720
$893$	−1.76808e25	−1.46307
$894$	3.21331e24	0.263380
$895$	6.96903e24	0.565818
$896$	8.80412e24	0.708057
$897$	−5.77637e24	−0.460171
$898$	−3.11497e24	−0.245813
$899$	3.78628e25	2.95975
$900$	−8.75674e24	−0.678080
$901$	−5.43913e24	−0.417224
$902$	−2.05536e23	−0.0156183
$903$	2.07885e24	0.156487
$904$	1.87823e24	0.140061
$905$	−1.15683e24	−0.0854591
$906$	−6.98385e24	−0.511099
$907$	1.79044e25	1.29807	0.649035	−	0.760759i	$-0.275173\pi$
$907$	1.79044e25	1.29807	0.649035	+	0.760759i	$0.275173\pi$
$908$	1.91902e25	1.37832
$909$	−2.39837e23	−0.0170657
$910$	1.24847e24	0.0880088
$911$	6.60589e24	0.461344	0.230672	−	0.973032i	$-0.425908\pi$
$911$	6.60589e24	0.461344	0.230672	+	0.973032i	$0.425908\pi$
$912$	1.92188e25	1.32975
$913$	−5.21470e24	−0.357460
$914$	−7.10293e24	−0.482386
$915$	−9.40071e24	−0.632530
$916$	−6.69504e24	−0.446315
$917$	1.12197e25	0.741039
$918$	−1.82783e24	−0.119611
$919$	1.47703e25	0.957651	0.478826	−	0.877910i	$-0.341063\pi$
$919$	1.47703e25	0.957651	0.478826	+	0.877910i	$0.341063\pi$
$920$	1.13696e25	0.730380
$921$	−1.91668e25	−1.21995
$922$	−8.85817e24	−0.558639
$923$	8.95141e24	0.559342
$924$	−4.94201e24	−0.305979
$925$	7.57531e24	0.464725
$926$	−2.70766e23	−0.0164589
$927$	2.02321e25	1.21861
$928$	−2.67059e25	−1.59386
$929$	−7.44933e24	−0.440538	−0.220269	−	0.975439i	$-0.570694\pi$
$929$	−7.44933e24	−0.440538	−0.220269	+	0.975439i	$0.570694\pi$
$930$	1.47181e25	0.862478
$931$	−9.30801e24	−0.540486
$932$	8.06492e24	0.464050
$933$	−1.76679e25	−1.00738
$934$	−2.14796e24	−0.121360
$935$	−6.85435e24	−0.383767
$936$	4.05411e24	0.224932
$937$	2.27009e25	1.24812	0.624059	−	0.781377i	$-0.285482\pi$
$937$	2.27009e25	1.24812	0.624059	+	0.781377i	$0.285482\pi$
$938$	7.27248e24	0.396240
$939$	−5.99850e24	−0.323881
$940$	−2.58445e25	−1.38287
$941$	1.68629e25	0.894170	0.447085	−	0.894491i	$-0.352462\pi$
$941$	1.68629e25	0.894170	0.447085	+	0.894491i	$0.352462\pi$
$942$	−8.44950e24	−0.444016
$943$	−3.25108e24	−0.169308
$944$	7.98019e24	0.411862
$945$	−7.15306e24	−0.365866
$946$	−2.53495e23	−0.0128498
$947$	1.02947e25	0.517178	0.258589	−	0.965987i	$-0.416742\pi$
$947$	1.02947e25	0.517178	0.258589	+	0.965987i	$0.416742\pi$
$948$	−5.12366e25	−2.55099
$949$	−6.49700e24	−0.320590
$950$	−4.48088e24	−0.219135
$951$	4.03674e24	0.195657
$952$	9.07622e24	0.436004
$953$	−2.14207e25	−1.01987	−0.509935	−	0.860213i	$-0.670331\pi$
$953$	−2.14207e25	−1.01987	−0.509935	+	0.860213i	$0.670331\pi$
$954$	3.36373e24	0.158730
$955$	−8.98816e24	−0.420380
$956$	1.90253e25	0.881939
$957$	1.95657e25	0.898967
$958$	3.06302e24	0.139490
$959$	−9.59553e24	−0.433123
$960$	2.05855e25	0.920992
$961$	2.76507e25	1.22619
$962$	−1.66824e24	−0.0733279
$963$	−4.47134e25	−1.94811
$964$	−3.13138e25	−1.35233
$965$	2.54622e24	0.108997
$966$	7.99752e24	0.339352
$967$	−9.24396e24	−0.388806	−0.194403	−	0.980922i	$-0.562277\pi$
$967$	−9.24396e24	−0.388806	−0.194403	+	0.980922i	$0.562277\pi$
$968$	1.26691e24	0.0528208
$969$	4.44285e25	1.83616
$970$	6.28093e24	0.257315
$971$	−3.51550e25	−1.42766	−0.713828	−	0.700321i	$-0.753040\pi$
$971$	−3.51550e25	−1.42766	−0.713828	+	0.700321i	$0.753040\pi$
$972$	3.15973e25	1.27200
$973$	5.68736e24	0.226961
$974$	−3.34257e24	−0.132230
$975$	6.99577e24	0.274345
$976$	6.26137e24	0.243414
$977$	−3.92970e24	−0.151445	−0.0757226	−	0.997129i	$-0.524126\pi$
$977$	−3.92970e24	−0.151445	−0.0757226	+	0.997129i	$0.524126\pi$
$978$	−2.19173e25	−0.837348
$979$	9.38077e22	0.00355292
$980$	−1.36058e25	−0.510859
$981$	−3.56554e25	−1.32721
$982$	−3.40631e24	−0.125700
$983$	−1.91293e25	−0.699834	−0.349917	−	0.936781i	$-0.613790\pi$
$983$	−1.91293e25	−0.699834	−0.349917	+	0.936781i	$0.613790\pi$
$984$	4.09399e24	0.148487
$985$	2.67496e25	0.961854
$986$	−1.70923e25	−0.609322
$987$	−3.82186e25	−1.35076
$988$	−9.64510e24	−0.337966
$989$	−4.00968e24	−0.139297
$990$	4.23894e24	0.146002
$991$	−4.22310e25	−1.44213	−0.721066	−	0.692866i	$-0.756348\pi$
$991$	−4.22310e25	−1.44213	−0.721066	+	0.692866i	$0.756348\pi$
$992$	−3.54083e25	−1.19882
$993$	9.89445e24	0.332141
$994$	−1.23934e25	−0.412485
$995$	4.37772e25	1.44461
$996$	4.94072e25	1.61654
$997$	−1.18915e25	−0.385770	−0.192885	−	0.981221i	$-0.561784\pi$
$997$	−1.18915e25	−0.385770	−0.192885	+	0.981221i	$0.561784\pi$
$998$	1.12328e25	0.361308
$999$	9.55809e24	0.304835

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.18.a.b.1.3	✓	8
3.2	odd	2		99.18.a.e.1.6		8
11.10	odd	2		121.18.a.d.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.18.a.b.1.3	✓	8	1.1	even	1	trivial
99.18.a.e.1.6		8	3.2	odd	2
121.18.a.d.1.6		8	11.10	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:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	11.a (trivial)

\(f(q)\)	\(=\)	\(q-110.296 q^{2} +17080.3 q^{3} -118907. q^{4} -1.10266e6 q^{5} -1.88389e6 q^{6} +1.13516e7 q^{7} +2.75717e7 q^{8} +1.62598e8 q^{9} +O(q^{10})\)	\(q-110.296 q^{2} +17080.3 q^{3} -118907. q^{4} -1.10266e6 q^{5} -1.88389e6 q^{6} +1.13516e7 q^{7} +2.75717e7 q^{8} +1.62598e8 q^{9} +1.21619e8 q^{10} +2.14359e8 q^{11} -2.03097e9 q^{12} +9.04312e8 q^{13} -1.25204e9 q^{14} -1.88338e10 q^{15} +1.25443e10 q^{16} +2.89990e10 q^{17} -1.79339e10 q^{18} +8.96979e10 q^{19} +1.31114e11 q^{20} +1.93890e11 q^{21} -2.36429e10 q^{22} -3.73973e11 q^{23} +4.70933e11 q^{24} +4.52920e11 q^{25} -9.97419e10 q^{26} +5.71468e11 q^{27} -1.34979e12 q^{28} +5.34389e12 q^{29} +2.07729e12 q^{30} +7.08525e12 q^{31} -4.99746e12 q^{32} +3.66132e12 q^{33} -3.19848e12 q^{34} -1.25170e13 q^{35} -1.93340e13 q^{36} +1.67255e13 q^{37} -9.89332e12 q^{38} +1.54459e13 q^{39} -3.04022e13 q^{40} +8.69335e12 q^{41} -2.13853e13 q^{42} +1.07218e13 q^{43} -2.54887e13 q^{44} -1.79290e14 q^{45} +4.12478e13 q^{46} -1.97115e14 q^{47} +2.14261e14 q^{48} -1.03771e14 q^{49} -4.99552e13 q^{50} +4.95313e14 q^{51} -1.07529e14 q^{52} -1.87563e14 q^{53} -6.30306e13 q^{54} -2.36365e14 q^{55} +3.12984e14 q^{56} +1.53207e15 q^{57} -5.89410e14 q^{58} +6.36161e14 q^{59} +2.23947e15 q^{60} +4.99140e14 q^{61} -7.81475e14 q^{62} +1.84575e15 q^{63} -1.09301e15 q^{64} -9.97148e14 q^{65} -4.03829e14 q^{66} -5.80850e15 q^{67} -3.44818e15 q^{68} -6.38759e15 q^{69} +1.38058e15 q^{70} +9.89860e15 q^{71} +4.48309e15 q^{72} -7.18447e15 q^{73} -1.84476e15 q^{74} +7.73602e15 q^{75} -1.06657e16 q^{76} +2.43333e15 q^{77} -1.70363e15 q^{78} +2.52277e16 q^{79} -1.38321e16 q^{80} -1.12370e16 q^{81} -9.58842e14 q^{82} -2.43269e16 q^{83} -2.30548e16 q^{84} -3.19761e16 q^{85} -1.18258e15 q^{86} +9.12754e16 q^{87} +5.91023e15 q^{88} +4.37620e14 q^{89} +1.97750e16 q^{90} +1.02654e16 q^{91} +4.44680e16 q^{92} +1.21018e17 q^{93} +2.17410e16 q^{94} -9.89063e16 q^{95} -8.53583e16 q^{96} +5.16443e16 q^{97} +1.14455e16 q^{98} +3.48543e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 256 q^{2} + 3058 q^{3} + 391332 q^{4} + 1795234 q^{5} + 13170682 q^{6} - 896364 q^{7} - 101682420 q^{8} + 413432462 q^{9}+O(q^{10}) \) 8 * q + 256 * q^2 + 3058 * q^3 + 391332 * q^4 + 1795234 * q^5 + 13170682 * q^6 - 896364 * q^7 - 101682420 * q^8 + 413432462 * q^9	\( 8 q + 256 q^{2} + 3058 q^{3} + 391332 q^{4} + 1795234 q^{5} + 13170682 q^{6} - 896364 q^{7} - 101682420 q^{8} + 413432462 q^{9} - 717567014 q^{10} + 1714871048 q^{11} - 3285295504 q^{12} + 1804014468 q^{13} + 17794023508 q^{14} + 8875276234 q^{15} + 53793011976 q^{16} - 27416338904 q^{17} + 28258692878 q^{18} + 58429836440 q^{19} + 650385049400 q^{20} + 562668763708 q^{21} + 54875873536 q^{22} + 1231860549578 q^{23} + 3528111117084 q^{24} + 3225446670918 q^{25} + 3698352129748 q^{26} + 5544189136510 q^{27} + 553346903392 q^{28} + 4016405848668 q^{29} + 28329117219490 q^{30} + 21044142033258 q^{31} - 7034951233624 q^{32} + 655509458098 q^{33} + 10491977089288 q^{34} - 37564178328188 q^{35} + 18688387613044 q^{36} - 38179864040434 q^{37} - 32101053490680 q^{38} - 133370005047128 q^{39} - 229151934325836 q^{40} - 84601913468108 q^{41} - 374381853665348 q^{42} - 79795156805452 q^{43} + 83885489619492 q^{44} + 85333967988848 q^{45} - 63876340102558 q^{46} - 333992064138544 q^{47} - 921917930639032 q^{48} + 16663435022976 q^{49} - 203190218406730 q^{50} + 445337187172876 q^{51} + 383080290241336 q^{52} + 351380494472328 q^{53} + 21\!\cdots\!38 q^{54}+ \cdots + 88\!\cdots\!22 q^{99}+O(q^{100}) \) 8 * q + 256 * q^2 + 3058 * q^3 + 391332 * q^4 + 1795234 * q^5 + 13170682 * q^6 - 896364 * q^7 - 101682420 * q^8 + 413432462 * q^9 - 717567014 * q^10 + 1714871048 * q^11 - 3285295504 * q^12 + 1804014468 * q^13 + 17794023508 * q^14 + 8875276234 * q^15 + 53793011976 * q^16 - 27416338904 * q^17 + 28258692878 * q^18 + 58429836440 * q^19 + 650385049400 * q^20 + 562668763708 * q^21 + 54875873536 * q^22 + 1231860549578 * q^23 + 3528111117084 * q^24 + 3225446670918 * q^25 + 3698352129748 * q^26 + 5544189136510 * q^27 + 553346903392 * q^28 + 4016405848668 * q^29 + 28329117219490 * q^30 + 21044142033258 * q^31 - 7034951233624 * q^32 + 655509458098 * q^33 + 10491977089288 * q^34 - 37564178328188 * q^35 + 18688387613044 * q^36 - 38179864040434 * q^37 - 32101053490680 * q^38 - 133370005047128 * q^39 - 229151934325836 * q^40 - 84601913468108 * q^41 - 374381853665348 * q^42 - 79795156805452 * q^43 + 83885489619492 * q^44 + 85333967988848 * q^45 - 63876340102558 * q^46 - 333992064138544 * q^47 - 921917930639032 * q^48 + 16663435022976 * q^49 - 203190218406730 * q^50 + 445337187172876 * q^51 + 383080290241336 * q^52 + 351380494472328 * q^53 + 2142853805961238 * q^54 + 384824351373154 * q^55 + 4437023751861816 * q^56 + 3266305594995600 * q^57 + 4039861017699420 * q^58 + 1023638486071814 * q^59 - 3214396297711936 * q^60 + 3794216197393316 * q^61 + 425349364206562 * q^62 - 2372860203801592 * q^63 + 6201620853304640 * q^64 - 2999195217446768 * q^65 + 2823252655526842 * q^66 + 5095474549488046 * q^67 - 16863568290550648 * q^68 + 2954340406561046 * q^69 - 1215862479252572 * q^70 - 1512701018213922 * q^71 - 47801016625093920 * q^72 + 1243757422569468 * q^73 - 32612646811059594 * q^74 - 12043436835518416 * q^75 - 57190847748178480 * q^76 - 192143584008684 * q^77 - 39902196048908264 * q^78 + 11583193006100356 * q^79 + 11760711968111960 * q^80 + 34892948392364408 * q^81 - 36998674460297948 * q^82 + 28335131925089508 * q^83 + 99838504514799680 * q^84 - 13434364728244100 * q^85 - 50273004015301116 * q^86 + 149533775100988560 * q^87 - 21796529768572020 * q^88 + 188410727637478542 * q^89 + 27756107460171104 * q^90 + 136202135129762480 * q^91 + 55575922205377216 * q^92 + 150258196291800646 * q^93 + 9488865070270352 * q^94 + 95643103186605600 * q^95 + 143914463501217272 * q^96 + 209457880210246906 * q^97 - 306362245050391368 * q^98 + 88622919923395022 * q^99

Introduction

L-functions

Modular forms

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