LMFDB - Embedded newform 11.18.a.b.1.6

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			1.6
Root			$-299.068$ 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)

$f(q)$	$=$	$q+331.068 q^{2} -15871.6 q^{3} -21465.7 q^{4} -1.31288e6 q^{5} -5.25459e6 q^{6} +1.35437e7 q^{7} -5.05004e7 q^{8} +1.22768e8 q^{9} +O(q^{10})$	\(q+331.068 q^{2} -15871.6 q^{3} -21465.7 q^{4} -1.31288e6 q^{5} -5.25459e6 q^{6} +1.35437e7 q^{7} -5.05004e7 q^{8} +1.22768e8 q^{9} -4.34652e8 q^{10} +2.14359e8 q^{11} +3.40696e8 q^{12} +4.32535e9 q^{13} +4.48390e9 q^{14} +2.08374e10 q^{15} -1.39055e10 q^{16} -2.94565e10 q^{17} +4.06445e10 q^{18} -1.62096e10 q^{19} +2.81818e10 q^{20} -2.14960e11 q^{21} +7.09674e10 q^{22} +9.94013e10 q^{23} +8.01523e11 q^{24} +9.60703e11 q^{25} +1.43199e12 q^{26} +1.01141e11 q^{27} -2.90726e11 q^{28} -3.70169e12 q^{29} +6.89862e12 q^{30} +7.70078e12 q^{31} +2.01551e12 q^{32} -3.40222e12 q^{33} -9.75211e12 q^{34} -1.77812e13 q^{35} -2.63530e12 q^{36} +3.70177e13 q^{37} -5.36647e12 q^{38} -6.86502e13 q^{39} +6.63008e13 q^{40} -3.34371e13 q^{41} -7.11666e13 q^{42} -4.08364e13 q^{43} -4.60137e12 q^{44} -1.61179e14 q^{45} +3.29086e13 q^{46} -6.10617e13 q^{47} +2.20703e14 q^{48} -4.91984e13 q^{49} +3.18059e14 q^{50} +4.67522e14 q^{51} -9.28468e13 q^{52} -1.74230e14 q^{53} +3.34846e13 q^{54} -2.81427e14 q^{55} -6.83963e14 q^{56} +2.57272e14 q^{57} -1.22551e15 q^{58} +1.20308e15 q^{59} -4.47291e14 q^{60} +1.88737e15 q^{61} +2.54949e15 q^{62} +1.66273e15 q^{63} +2.48990e15 q^{64} -5.67864e15 q^{65} -1.12637e15 q^{66} +5.98763e15 q^{67} +6.32305e14 q^{68} -1.57766e15 q^{69} -5.88680e15 q^{70} -1.34322e15 q^{71} -6.19982e15 q^{72} -5.79439e15 q^{73} +1.22554e16 q^{74} -1.52479e16 q^{75} +3.47950e14 q^{76} +2.90322e15 q^{77} -2.27279e16 q^{78} -9.67629e15 q^{79} +1.82562e16 q^{80} -1.74595e16 q^{81} -1.10700e16 q^{82} +3.68267e16 q^{83} +4.61428e15 q^{84} +3.86727e16 q^{85} -1.35197e16 q^{86} +5.87518e16 q^{87} -1.08252e16 q^{88} +6.03377e16 q^{89} -5.33612e16 q^{90} +5.85813e16 q^{91} -2.13372e15 q^{92} -1.22224e17 q^{93} -2.02156e16 q^{94} +2.12811e16 q^{95} -3.19893e16 q^{96} +8.77334e16 q^{97} -1.62880e16 q^{98} +2.63164e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	331.068	0.914456	0.457228	−	0.889350i	$-0.348842\pi$
$2$	331.068	0.914456	0.457228	+	0.889350i	$0.348842\pi$
$3$	−15871.6	−1.39666	−0.698329	−	0.715777i	$-0.746073\pi$
$3$	−15871.6	−1.39666	−0.698329	+	0.715777i	$0.746073\pi$
$4$	−21465.7	−0.163771
$5$	−1.31288e6	−1.50307	−0.751534	−	0.659694i	$-0.770686\pi$
$5$	−1.31288e6	−1.50307	−0.751534	+	0.659694i	$0.770686\pi$
$6$	−5.25459e6	−1.27718
$7$	1.35437e7	0.887982	0.443991	−	0.896031i	$-0.353562\pi$
$7$	1.35437e7	0.887982	0.443991	+	0.896031i	$0.353562\pi$
$8$	−5.05004e7	−1.06422
$9$	1.22768e8	0.950655
$10$	−4.34652e8	−1.37449
$11$	2.14359e8	0.301511
$11$	2.14359e8	0.301511
$12$	3.40696e8	0.228732
$13$	4.32535e9	1.47063	0.735313	−	0.677727i	$-0.237035\pi$
$13$	4.32535e9	1.47063	0.735313	+	0.677727i	$0.237035\pi$
$14$	4.48390e9	0.812021
$15$	2.08374e10	2.09927
$16$	−1.39055e10	−0.809409
$17$	−2.94565e10	−1.02415	−0.512077	−	0.858940i	$-0.671124\pi$
$17$	−2.94565e10	−1.02415	−0.512077	+	0.858940i	$0.671124\pi$
$18$	4.06445e10	0.869332
$19$	−1.62096e10	−0.218960	−0.109480	−	0.993989i	$-0.534919\pi$
$19$	−1.62096e10	−0.218960	−0.109480	+	0.993989i	$0.534919\pi$
$20$	2.81818e10	0.246158
$21$	−2.14960e11	−1.24021
$22$	7.09674e10	0.275719
$23$	9.94013e10	0.264670	0.132335	−	0.991205i	$-0.457752\pi$
$23$	9.94013e10	0.264670	0.132335	+	0.991205i	$0.457752\pi$
$24$	8.01523e11	1.48635
$25$	9.60703e11	1.25921
$26$	1.43199e12	1.34482
$27$	1.01141e11	0.0689184
$28$	−2.90726e11	−0.145425
$29$	−3.70169e12	−1.37410	−0.687049	−	0.726611i	$-0.741094\pi$
$29$	−3.70169e12	−1.37410	−0.687049	+	0.726611i	$0.741094\pi$
$30$	6.89862e12	1.91969
$31$	7.70078e12	1.62166	0.810831	−	0.585280i	$-0.199015\pi$
$31$	7.70078e12	1.62166	0.810831	+	0.585280i	$0.199015\pi$
$32$	2.01551e12	0.324048
$33$	−3.40222e12	−0.421108
$34$	−9.75211e12	−0.936543
$35$	−1.77812e13	−1.33470
$36$	−2.63530e12	−0.155689
$37$	3.70177e13	1.73258	0.866292	−	0.499537i	$-0.166497\pi$
$37$	3.70177e13	1.73258	0.866292	+	0.499537i	$0.166497\pi$
$38$	−5.36647e12	−0.200230
$39$	−6.86502e13	−2.05396
$40$	6.63008e13	1.59959
$41$	−3.34371e13	−0.653982	−0.326991	−	0.945028i	$-0.606035\pi$
$41$	−3.34371e13	−0.653982	−0.326991	+	0.945028i	$0.606035\pi$
$42$	−7.11666e13	−1.13412
$43$	−4.08364e13	−0.532802	−0.266401	−	0.963862i	$-0.585835\pi$
$43$	−4.08364e13	−0.532802	−0.266401	+	0.963862i	$0.585835\pi$
$44$	−4.60137e12	−0.0493787
$45$	−1.61179e14	−1.42890
$46$	3.29086e13	0.242029
$47$	−6.10617e13	−0.374057	−0.187028	−	0.982355i	$-0.559886\pi$
$47$	−6.10617e13	−0.374057	−0.187028	+	0.982355i	$0.559886\pi$
$48$	2.20703e14	1.13047
$49$	−4.91984e13	−0.211487
$50$	3.18059e14	1.15149
$51$	4.67522e14	1.43039
$52$	−9.28468e13	−0.240845
$53$	−1.74230e14	−0.384395	−0.192198	−	0.981356i	$-0.561561\pi$
$53$	−1.74230e14	−0.384395	−0.192198	+	0.981356i	$0.561561\pi$
$54$	3.34846e13	0.0630228
$55$	−2.81427e14	−0.453192
$56$	−6.83963e14	−0.945006
$57$	2.57272e14	0.305813
$58$	−1.22551e15	−1.25655
$59$	1.20308e15	1.06673	0.533364	−	0.845886i	$-0.320927\pi$
$59$	1.20308e15	1.06673	0.533364	+	0.845886i	$0.320927\pi$
$60$	−4.47291e14	−0.343799
$61$	1.88737e15	1.26053	0.630266	−	0.776380i	$-0.282946\pi$
$61$	1.88737e15	1.26053	0.630266	+	0.776380i	$0.282946\pi$
$62$	2.54949e15	1.48294
$63$	1.66273e15	0.844165
$64$	2.48990e15	1.10574
$65$	−5.67864e15	−2.21045
$66$	−1.12637e15	−0.385085
$67$	5.98763e15	1.80144	0.900719	−	0.434403i	$-0.143041\pi$
$67$	5.98763e15	1.80144	0.900719	+	0.434403i	$0.143041\pi$
$68$	6.32305e14	0.167726
$69$	−1.57766e15	−0.369654
$70$	−5.88680e15	−1.22052
$71$	−1.34322e15	−0.246861	−0.123431	−	0.992353i	$-0.539390\pi$
$71$	−1.34322e15	−0.246861	−0.123431	+	0.992353i	$0.539390\pi$
$72$	−6.19982e15	−1.01170
$73$	−5.79439e15	−0.840936	−0.420468	−	0.907307i	$-0.638134\pi$
$73$	−5.79439e15	−0.840936	−0.420468	+	0.907307i	$0.638134\pi$
$74$	1.22554e16	1.58437
$75$	−1.52479e16	−1.75869
$76$	3.47950e14	0.0358593
$77$	2.90322e15	0.267737
$78$	−2.27279e16	−1.87826
$79$	−9.67629e15	−0.717593	−0.358797	−	0.933416i	$-0.616813\pi$
$79$	−9.67629e15	−0.717593	−0.358797	+	0.933416i	$0.616813\pi$
$80$	1.82562e16	1.21660
$81$	−1.74595e16	−1.04691
$82$	−1.10700e16	−0.598037
$83$	3.68267e16	1.79473	0.897365	−	0.441289i	$-0.145479\pi$
$83$	3.68267e16	1.79473	0.897365	+	0.441289i	$0.145479\pi$
$84$	4.61428e15	0.203110
$85$	3.86727e16	1.53937
$86$	−1.35197e16	−0.487224
$87$	5.87518e16	1.91914
$88$	−1.08252e16	−0.320873
$89$	6.03377e16	1.62470	0.812351	−	0.583169i	$-0.198187\pi$
$89$	6.03377e16	1.62470	0.812351	+	0.583169i	$0.198187\pi$
$90$	−5.33612e16	−1.30666
$91$	5.85813e16	1.30589
$92$	−2.13372e15	−0.0433452
$93$	−1.22224e17	−2.26491
$94$	−2.02156e16	−0.342058
$95$	2.12811e16	0.329112
$96$	−3.19893e16	−0.452585
$97$	8.77334e16	1.13659	0.568297	−	0.822824i	$-0.307603\pi$
$97$	8.77334e16	1.13659	0.568297	+	0.822824i	$0.307603\pi$
$98$	−1.62880e16	−0.193396
$99$	2.63164e16	0.286633
$100$	−2.06222e16	−0.206222
$101$	−1.98699e16	−0.182585	−0.0912923	−	0.995824i	$-0.529100\pi$
$101$	−1.98699e16	−0.182585	−0.0912923	+	0.995824i	$0.529100\pi$
$102$	1.54782e17	1.30803
$103$	−8.67554e16	−0.674808	−0.337404	−	0.941360i	$-0.609549\pi$
$103$	−8.67554e16	−0.674808	−0.337404	+	0.941360i	$0.609549\pi$
$104$	−2.18432e17	−1.56507
$105$	2.82216e17	1.86412
$106$	−5.76820e16	−0.351512
$107$	1.95520e16	0.110009	0.0550047	−	0.998486i	$-0.482483\pi$
$107$	1.95520e16	0.110009	0.0550047	+	0.998486i	$0.482483\pi$
$108$	−2.17107e15	−0.0112868
$109$	−1.19234e17	−0.573160	−0.286580	−	0.958056i	$-0.592518\pi$
$109$	−1.19234e17	−0.573160	−0.286580	+	0.958056i	$0.592518\pi$
$110$	−9.31714e16	−0.414424
$111$	−5.87530e17	−2.41983
$112$	−1.88333e17	−0.718741
$113$	3.26899e17	1.15677	0.578385	−	0.815764i	$-0.303683\pi$
$113$	3.26899e17	1.15677	0.578385	+	0.815764i	$0.303683\pi$
$114$	8.51745e16	0.279652
$115$	−1.30502e17	−0.397818
$116$	7.94596e16	0.225037
$117$	5.31013e17	1.39806
$118$	3.98303e17	0.975476
$119$	−3.98950e17	−0.909430
$120$	−1.05230e18	−2.23408
$121$	4.59497e16	0.0909091
$122$	6.24849e17	1.15270
$123$	5.30700e17	0.913389
$124$	−1.65303e17	−0.265581
$125$	−2.59640e17	−0.389615
$126$	5.50478e17	0.771951
$127$	−1.45996e17	−0.191429	−0.0957146	−	0.995409i	$-0.530514\pi$
$127$	−1.45996e17	−0.191429	−0.0957146	+	0.995409i	$0.530514\pi$
$128$	5.60150e17	0.687099
$129$	6.48140e17	0.744143
$130$	−1.88002e18	−2.02136
$131$	7.39090e17	0.744546	0.372273	−	0.928123i	$-0.378579\pi$
$131$	7.39090e17	0.744546	0.372273	+	0.928123i	$0.378579\pi$
$132$	7.30311e16	0.0689651
$133$	−2.19538e17	−0.194433
$134$	1.98232e18	1.64733
$135$	−1.32786e17	−0.103589
$136$	1.48756e18	1.08992
$137$	−8.41889e17	−0.579602	−0.289801	−	0.957087i	$-0.593589\pi$
$137$	−8.41889e17	−0.579602	−0.289801	+	0.957087i	$0.593589\pi$
$138$	−5.22313e17	−0.338032
$139$	−1.95516e18	−1.19003	−0.595014	−	0.803716i	$-0.702853\pi$
$139$	−1.95516e18	−1.19003	−0.595014	+	0.803716i	$0.702853\pi$
$140$	3.81687e17	0.218584
$141$	9.69148e17	0.522429
$142$	−4.44699e17	−0.225744
$143$	9.27177e17	0.443411
$144$	−1.70715e18	−0.769468
$145$	4.85986e18	2.06536
$146$	−1.91834e18	−0.768999
$147$	7.80857e17	0.295375
$148$	−7.94611e17	−0.283746
$149$	3.06189e18	1.03254	0.516270	−	0.856426i	$-0.327320\pi$
$149$	3.06189e18	1.03254	0.516270	+	0.856426i	$0.327320\pi$
$150$	−5.04810e18	−1.60825
$151$	−4.13321e18	−1.24447	−0.622234	−	0.782832i	$-0.713775\pi$
$151$	−4.13321e18	−1.24447	−0.622234	+	0.782832i	$0.713775\pi$
$152$	8.18589e17	0.233021
$153$	−3.61630e18	−0.973616
$154$	9.61163e17	0.244833
$155$	−1.01102e19	−2.43747
$156$	1.47363e18	0.336379
$157$	4.82465e18	1.04308	0.521541	−	0.853226i	$-0.325357\pi$
$157$	4.82465e18	1.04308	0.521541	+	0.853226i	$0.325357\pi$
$158$	−3.20351e18	−0.656208
$159$	2.76531e18	0.536869
$160$	−2.64611e18	−0.487067
$161$	1.34626e18	0.235023
$162$	−5.78029e18	−0.957353
$163$	−5.35822e18	−0.842221	−0.421110	−	0.907009i	$-0.638359\pi$
$163$	−5.35822e18	−0.842221	−0.421110	+	0.907009i	$0.638359\pi$
$164$	7.17751e17	0.107103
$165$	4.46669e18	0.632954
$166$	1.21922e19	1.64120
$167$	−8.45034e18	−1.08090	−0.540448	−	0.841377i	$-0.681745\pi$
$167$	−8.45034e18	−1.08090	−0.540448	+	0.841377i	$0.681745\pi$
$168$	1.08556e19	1.31985
$169$	1.00582e19	1.16274
$170$	1.28033e19	1.40769
$171$	−1.99001e18	−0.208156
$172$	8.76584e17	0.0872573
$173$	−1.14890e19	−1.08866	−0.544329	−	0.838872i	$-0.683216\pi$
$173$	−1.14890e19	−1.08866	−0.544329	+	0.838872i	$0.683216\pi$
$174$	1.94509e19	1.75497
$175$	1.30115e19	1.11816
$176$	−2.98077e18	−0.244046
$177$	−1.90949e19	−1.48986
$178$	1.99759e19	1.48572
$179$	3.59786e18	0.255149	0.127574	−	0.991829i	$-0.459281\pi$
$179$	3.59786e18	0.255149	0.127574	+	0.991829i	$0.459281\pi$
$180$	3.45982e18	0.234012
$181$	5.57740e18	0.359885	0.179943	−	0.983677i	$-0.442409\pi$
$181$	5.57740e18	0.359885	0.179943	+	0.983677i	$0.442409\pi$
$182$	1.93944e19	1.19418
$183$	−2.99556e19	−1.76053
$184$	−5.01981e18	−0.281667
$185$	−4.85996e19	−2.60419
$186$	−4.04644e19	−2.07116
$187$	−6.31426e18	−0.308794
$188$	1.31073e18	0.0612594
$189$	1.36982e18	0.0611983
$190$	7.04551e18	0.300959
$191$	1.10179e19	0.450105	0.225053	−	0.974347i	$-0.427745\pi$
$191$	1.10179e19	0.450105	0.225053	+	0.974347i	$0.427745\pi$
$192$	−3.95187e19	−1.54434
$193$	3.56324e18	0.133232	0.0666159	−	0.997779i	$-0.478780\pi$
$193$	3.56324e18	0.133232	0.0666159	+	0.997779i	$0.478780\pi$
$194$	2.90458e19	1.03936
$195$	9.01292e19	3.08725
$196$	1.05608e18	0.0346354
$197$	1.72833e19	0.542829	0.271414	−	0.962463i	$-0.412509\pi$
$197$	1.72833e19	0.542829	0.271414	+	0.962463i	$0.412509\pi$
$198$	8.71251e18	0.262113
$199$	4.62972e19	1.33445	0.667226	−	0.744855i	$-0.267481\pi$
$199$	4.62972e19	1.33445	0.667226	+	0.744855i	$0.267481\pi$
$200$	−4.85159e19	−1.34008
$201$	−9.50333e19	−2.51599
$202$	−6.57830e18	−0.166965
$203$	−5.01347e19	−1.22017
$204$	−1.00357e19	−0.234256
$205$	4.38987e19	0.982979
$206$	−2.87220e19	−0.617082
$207$	1.22033e19	0.251610
$208$	−6.01463e19	−1.19034
$209$	−3.47466e18	−0.0660190
$210$	9.34329e19	1.70465
$211$	−6.25999e19	−1.09691	−0.548457	−	0.836179i	$-0.684785\pi$
$211$	−6.25999e19	−1.09691	−0.548457	+	0.836179i	$0.684785\pi$
$212$	3.73997e18	0.0629526
$213$	2.13191e19	0.344781
$214$	6.47306e18	0.100599
$215$	5.36132e19	0.800838
$216$	−5.10766e18	−0.0733441
$217$	1.04297e20	1.44001
$218$	−3.94747e19	−0.524129
$219$	9.19662e19	1.17450
$220$	6.04103e18	0.0742195
$221$	−1.27409e20	−1.50615
$222$	−1.94513e20	−2.21283
$223$	−1.24676e19	−0.136518	−0.0682592	−	0.997668i	$-0.521744\pi$
$223$	−1.24676e19	−0.136518	−0.0682592	+	0.997668i	$0.521744\pi$
$224$	2.72975e19	0.287749
$225$	1.17943e20	1.19708
$226$	1.08226e20	1.05782
$227$	4.14994e19	0.390680	0.195340	−	0.980736i	$-0.437419\pi$
$227$	4.14994e19	0.390680	0.195340	+	0.980736i	$0.437419\pi$
$228$	−5.52252e18	−0.0500831
$229$	1.31836e20	1.15194	0.575972	−	0.817469i	$-0.304624\pi$
$229$	1.31836e20	1.15194	0.575972	+	0.817469i	$0.304624\pi$
$230$	−4.32049e19	−0.363787
$231$	−4.60787e19	−0.373937
$232$	1.86937e20	1.46234
$233$	−1.38444e20	−1.04412	−0.522059	−	0.852909i	$-0.674836\pi$
$233$	−1.38444e20	−1.04412	−0.522059	+	0.852909i	$0.674836\pi$
$234$	1.75802e20	1.27846
$235$	8.01665e19	0.562232
$236$	−2.58251e19	−0.174699
$237$	1.53578e20	1.00223
$238$	−1.32080e20	−0.831634
$239$	−2.54179e20	−1.54439	−0.772197	−	0.635383i	$-0.780842\pi$
$239$	−2.54179e20	−1.54439	−0.772197	+	0.635383i	$0.780842\pi$
$240$	−2.89756e20	−1.69917
$241$	3.21599e19	0.182041	0.0910206	−	0.995849i	$-0.470987\pi$
$241$	3.21599e19	0.182041	0.0910206	+	0.995849i	$0.470987\pi$
$242$	1.52125e19	0.0831323
$243$	2.64049e20	1.39326
$244$	−4.05138e19	−0.206438
$245$	6.45913e19	0.317879
$246$	1.75698e20	0.835254
$247$	−7.01120e19	−0.322009
$248$	−3.88893e20	−1.72580
$249$	−5.84499e20	−2.50662
$250$	−8.59585e19	−0.356286
$251$	2.28737e20	0.916451	0.458226	−	0.888836i	$-0.348485\pi$
$251$	2.28737e20	0.916451	0.458226	+	0.888836i	$0.348485\pi$
$252$	−3.56917e19	−0.138249
$253$	2.13076e19	0.0798012
$254$	−4.83345e19	−0.175054
$255$	−6.13798e20	−2.14998
$256$	−1.40908e20	−0.477415
$257$	4.98005e20	1.63231	0.816153	−	0.577835i	$-0.196102\pi$
$257$	4.98005e20	1.63231	0.816153	+	0.577835i	$0.196102\pi$
$258$	2.14579e20	0.680485
$259$	5.01357e20	1.53850
$260$	1.21896e20	0.362007
$261$	−4.54448e20	−1.30629
$262$	2.44689e20	0.680854
$263$	5.89913e19	0.158915	0.0794573	−	0.996838i	$-0.474681\pi$
$263$	5.89913e19	0.158915	0.0794573	+	0.996838i	$0.474681\pi$
$264$	1.71814e20	0.448151
$265$	2.28742e20	0.577772
$266$	−7.26819e19	−0.177800
$267$	−9.57656e20	−2.26915
$268$	−1.28529e20	−0.295022
$269$	8.32964e20	1.85239	0.926194	−	0.377049i	$-0.123061\pi$
$269$	8.32964e20	1.85239	0.926194	+	0.377049i	$0.123061\pi$
$270$	−4.39611e19	−0.0947276
$271$	−3.25010e20	−0.678668	−0.339334	−	0.940666i	$-0.610202\pi$
$271$	−3.25010e20	−0.678668	−0.339334	+	0.940666i	$0.610202\pi$
$272$	4.09608e20	0.828958
$273$	−9.29779e20	−1.82388
$274$	−2.78723e20	−0.530021
$275$	2.05935e20	0.379667
$276$	3.38656e19	0.0605385
$277$	6.07679e20	1.05341	0.526703	−	0.850049i	$-0.323428\pi$
$277$	6.07679e20	1.05341	0.526703	+	0.850049i	$0.323428\pi$
$278$	−6.47292e20	−1.08823
$279$	9.45407e20	1.54164
$280$	8.97959e20	1.42041
$281$	7.38259e20	1.13294	0.566468	−	0.824084i	$-0.308310\pi$
$281$	7.38259e20	1.13294	0.566468	+	0.824084i	$0.308310\pi$
$282$	3.20854e20	0.477738
$283$	8.82684e20	1.27532	0.637662	−	0.770316i	$-0.279902\pi$
$283$	8.82684e20	1.27532	0.637662	+	0.770316i	$0.279902\pi$
$284$	2.88333e19	0.0404286
$285$	−3.37766e20	−0.459657
$286$	3.06959e20	0.405479
$287$	−4.52862e20	−0.580724
$288$	2.47439e20	0.308058
$289$	4.04435e19	0.0488896
$290$	1.60895e21	1.88868
$291$	−1.39247e21	−1.58743
$292$	1.24381e20	0.137721
$293$	−9.70212e20	−1.04350	−0.521749	−	0.853099i	$-0.674720\pi$
$293$	−9.70212e20	−1.04350	−0.521749	+	0.853099i	$0.674720\pi$
$294$	2.58517e20	0.270108
$295$	−1.57950e21	−1.60337
$296$	−1.86941e21	−1.84385
$297$	2.16805e19	0.0207797
$298$	1.01370e21	0.944212
$299$	4.29945e20	0.389232
$300$	3.27307e20	0.288022
$301$	−5.53077e20	−0.473119
$302$	−1.36838e21	−1.13801
$303$	3.15367e20	0.255008
$304$	2.25403e20	0.177228
$305$	−2.47788e21	−1.89466
$306$	−1.19724e21	−0.890329
$307$	−1.52113e21	−1.10025	−0.550123	−	0.835084i	$-0.685419\pi$
$307$	−1.52113e21	−1.10025	−0.550123	+	0.835084i	$0.685419\pi$
$308$	−6.23196e19	−0.0438474
$309$	1.37695e21	0.942476
$310$	−3.34716e21	−2.22896
$311$	2.32618e21	1.50723	0.753615	−	0.657317i	$-0.228309\pi$
$311$	2.32618e21	1.50723	0.753615	+	0.657317i	$0.228309\pi$
$312$	3.46686e21	2.18586
$313$	2.41499e21	1.48179	0.740897	−	0.671619i	$-0.234401\pi$
$313$	2.41499e21	1.48179	0.740897	+	0.671619i	$0.234401\pi$
$314$	1.59729e21	0.953852
$315$	−2.18296e21	−1.26884
$316$	2.07709e20	0.117521
$317$	−5.14256e20	−0.283254	−0.141627	−	0.989920i	$-0.545233\pi$
$317$	−5.14256e20	−0.283254	−0.141627	+	0.989920i	$0.545233\pi$
$318$	9.15506e20	0.490943
$319$	−7.93491e20	−0.414306
$320$	−3.26893e21	−1.66200
$321$	−3.10322e20	−0.153645
$322$	4.45705e20	0.214918
$323$	4.77476e20	0.224249
$324$	3.74781e20	0.171453
$325$	4.15538e21	1.85183
$326$	−1.77394e21	−0.770173
$327$	1.89244e21	0.800509
$328$	1.68859e21	0.695978
$329$	−8.27002e20	−0.332156
$330$	1.47878e21	0.578809
$331$	−2.69870e20	−0.102948	−0.0514738	−	0.998674i	$-0.516392\pi$
$331$	−2.69870e20	−0.102948	−0.0514738	+	0.998674i	$0.516392\pi$
$332$	−7.90512e20	−0.293924
$333$	4.54458e21	1.64709
$334$	−2.79764e21	−0.988432
$335$	−7.86102e21	−2.70768
$336$	2.98914e21	1.00384
$337$	3.70694e21	1.21384	0.606920	−	0.794763i	$-0.292405\pi$
$337$	3.70694e21	1.21384	0.606920	+	0.794763i	$0.292405\pi$
$338$	3.32996e21	1.06328
$339$	−5.18842e21	−1.61561
$340$	−8.30138e20	−0.252104
$341$	1.65073e21	0.488950
$342$	−6.58829e20	−0.190349
$343$	−3.81701e21	−1.07578
$344$	2.06226e21	0.567017
$345$	2.07127e21	0.555615
$346$	−3.80365e21	−0.995529
$347$	1.64081e21	0.419043	0.209522	−	0.977804i	$-0.432809\pi$
$347$	1.64081e21	0.419043	0.209522	+	0.977804i	$0.432809\pi$
$348$	−1.26115e21	−0.314299
$349$	−3.00267e21	−0.730285	−0.365142	−	0.930952i	$-0.618980\pi$
$349$	−3.00267e21	−0.730285	−0.365142	+	0.930952i	$0.618980\pi$
$350$	4.30769e21	1.02251
$351$	4.37470e20	0.101353
$352$	4.32042e20	0.0977042
$353$	5.10573e21	1.12713	0.563564	−	0.826073i	$-0.309430\pi$
$353$	5.10573e21	1.12713	0.563564	+	0.826073i	$0.309430\pi$
$354$	−6.32171e21	−1.36241
$355$	1.76349e21	0.371049
$356$	−1.29519e21	−0.266078
$357$	6.33198e21	1.27016
$358$	1.19114e21	0.233322
$359$	3.67090e21	0.702215	0.351108	−	0.936335i	$-0.385805\pi$
$359$	3.67090e21	0.702215	0.351108	+	0.936335i	$0.385805\pi$
$360$	8.13960e21	1.52066
$361$	−5.21764e21	−0.952056
$362$	1.84650e21	0.329099
$363$	−7.29296e20	−0.126969
$364$	−1.25749e21	−0.213866
$365$	7.60731e21	1.26398
$366$	−9.91735e21	−1.60993
$367$	3.15864e21	0.501001	0.250501	−	0.968116i	$-0.419405\pi$
$367$	3.15864e21	0.501001	0.250501	+	0.968116i	$0.419405\pi$
$368$	−1.38223e21	−0.214227
$369$	−4.10499e21	−0.621711
$370$	−1.60898e22	−2.38142
$371$	−2.35972e21	−0.341336
$372$	2.62362e21	0.370925
$373$	−1.67347e21	−0.231256	−0.115628	−	0.993293i	$-0.536888\pi$
$373$	−1.67347e21	−0.231256	−0.115628	+	0.993293i	$0.536888\pi$
$374$	−2.09045e21	−0.282378
$375$	4.12090e21	0.544159
$376$	3.08364e21	0.398077
$377$	−1.60111e22	−2.02078
$378$	4.53506e20	0.0559632
$379$	−6.03565e21	−0.728267	−0.364133	−	0.931347i	$-0.618635\pi$
$379$	−6.03565e21	−0.728267	−0.364133	+	0.931347i	$0.618635\pi$
$380$	−4.56815e20	−0.0538989
$381$	2.31718e21	0.267361
$382$	3.64767e21	0.411601
$383$	−1.21749e22	−1.34362	−0.671808	−	0.740725i	$-0.734482\pi$
$383$	−1.21749e22	−1.34362	−0.671808	+	0.740725i	$0.734482\pi$
$384$	−8.89047e21	−0.959642
$385$	−3.81156e21	−0.402427
$386$	1.17968e21	0.121835
$387$	−5.01340e21	−0.506511
$388$	−1.88326e21	−0.186141
$389$	1.21184e22	1.17185	0.585927	−	0.810364i	$-0.300731\pi$
$389$	1.21184e22	1.17185	0.585927	+	0.810364i	$0.300731\pi$
$390$	2.98389e22	2.82315
$391$	−2.92801e21	−0.271063
$392$	2.48454e21	0.225068
$393$	−1.17306e22	−1.03988
$394$	5.72194e21	0.496393
$395$	1.27038e22	1.07859
$396$	−5.64900e20	−0.0469421
$397$	1.25310e22	1.01921	0.509607	−	0.860408i	$-0.329791\pi$
$397$	1.25310e22	1.01921	0.509607	+	0.860408i	$0.329791\pi$
$398$	1.53275e22	1.22030
$399$	3.48441e21	0.271556
$400$	−1.33591e22	−1.01922
$401$	1.12245e22	0.838379	0.419190	−	0.907899i	$-0.362314\pi$
$401$	1.12245e22	0.838379	0.419190	+	0.907899i	$0.362314\pi$
$402$	−3.14625e22	−2.30076
$403$	3.33086e22	2.38486
$404$	4.26522e20	0.0299020
$405$	2.29222e22	1.57358
$406$	−1.65980e22	−1.11580
$407$	7.93507e21	0.522394
$408$	−2.36100e22	−1.52225
$409$	−8.02597e21	−0.506815	−0.253407	−	0.967360i	$-0.581551\pi$
$409$	−8.02597e21	−0.506815	−0.253407	+	0.967360i	$0.581551\pi$
$410$	1.45335e22	0.898891
$411$	1.33621e22	0.809506
$412$	1.86227e21	0.110514
$413$	1.62942e22	0.947236
$414$	4.04012e21	0.230086
$415$	−4.83489e22	−2.69760
$416$	8.71777e21	0.476554
$417$	3.10316e22	1.66206
$418$	−1.15035e21	−0.0603715
$419$	−2.04119e21	−0.104970	−0.0524849	−	0.998622i	$-0.516714\pi$
$419$	−2.04119e21	−0.104970	−0.0524849	+	0.998622i	$0.516714\pi$
$420$	−6.05798e21	−0.305287
$421$	−2.06312e22	−1.01889	−0.509444	−	0.860504i	$-0.670149\pi$
$421$	−2.06312e22	−1.01889	−0.509444	+	0.860504i	$0.670149\pi$
$422$	−2.07248e22	−1.00308
$423$	−7.49641e21	−0.355599
$424$	8.79868e21	0.409080
$425$	−2.82989e22	−1.28963
$426$	7.05809e21	0.315287
$427$	2.55620e22	1.11933
$428$	−4.19698e20	−0.0180163
$429$	−1.47158e22	−0.619293
$430$	1.77496e22	0.732331
$431$	1.85817e22	0.751673	0.375837	−	0.926686i	$-0.377355\pi$
$431$	1.85817e22	0.751673	0.375837	+	0.926686i	$0.377355\pi$
$432$	−1.40642e21	−0.0557831
$433$	−3.10294e22	−1.20677	−0.603387	−	0.797449i	$-0.706182\pi$
$433$	−3.10294e22	−1.20677	−0.603387	+	0.797449i	$0.706182\pi$
$434$	3.45295e22	1.31682
$435$	−7.71338e22	−2.88460
$436$	2.55945e21	0.0938667
$437$	−1.61125e21	−0.0579523
$438$	3.04471e22	1.07403
$439$	4.80358e22	1.66195	0.830973	−	0.556313i	$-0.187784\pi$
$439$	4.80358e22	1.66195	0.830973	+	0.556313i	$0.187784\pi$
$440$	1.42122e22	0.482295
$441$	−6.03997e21	−0.201051
$442$	−4.21812e22	−1.37731
$443$	−4.05552e22	−1.29902	−0.649508	−	0.760354i	$-0.725025\pi$
$443$	−4.05552e22	−1.29902	−0.649508	+	0.760354i	$0.725025\pi$
$444$	1.26118e22	0.396297
$445$	−7.92159e22	−2.44204
$446$	−4.12763e21	−0.124840
$447$	−4.85971e22	−1.44210
$448$	3.37225e22	0.981875
$449$	−1.93309e22	−0.552277	−0.276139	−	0.961118i	$-0.589055\pi$
$449$	−1.93309e22	−0.552277	−0.276139	+	0.961118i	$0.589055\pi$
$450$	3.90473e22	1.09467
$451$	−7.16754e21	−0.197183
$452$	−7.01713e21	−0.189445
$453$	6.56007e22	1.73810
$454$	1.37391e22	0.357260
$455$	−7.69099e22	−1.96284
$456$	−1.29923e22	−0.325451
$457$	3.00561e22	0.739001	0.369501	−	0.929231i	$-0.379529\pi$
$457$	3.00561e22	0.739001	0.369501	+	0.929231i	$0.379529\pi$
$458$	4.36467e22	1.05340
$459$	−2.97926e21	−0.0705830
$460$	2.80131e21	0.0651508
$461$	−2.97559e19	−0.000679384 0	−0.000339692	−	1.00000i	$-0.500108\pi$
$461$	−2.97559e19	−0.000679384 0	−0.000339692		1.00000i	$0.500108\pi$
$462$	−1.52552e22	−0.341949
$463$	−1.98211e21	−0.0436204	−0.0218102	−	0.999762i	$-0.506943\pi$
$463$	−1.98211e21	−0.0436204	−0.0218102	+	0.999762i	$0.506943\pi$
$464$	5.14740e22	1.11221
$465$	1.60465e23	3.40431
$466$	−4.58345e22	−0.954799
$467$	2.90652e20	0.00594538	0.00297269	−	0.999996i	$-0.499054\pi$
$467$	2.90652e20	0.00594538	0.00297269	+	0.999996i	$0.499054\pi$
$468$	−1.13986e22	−0.228961
$469$	8.10948e22	1.59964
$470$	2.65406e22	0.514137
$471$	−7.65749e22	−1.45683
$472$	−6.07563e22	−1.13523
$473$	−8.75365e21	−0.160646
$474$	5.08449e22	0.916498
$475$	−1.55726e22	−0.275718
$476$	8.56375e21	0.148938
$477$	−2.13898e22	−0.365427
$478$	−8.41507e22	−1.41228
$479$	−4.81956e22	−0.794613	−0.397306	−	0.917686i	$-0.630055\pi$
$479$	−4.81956e22	−0.794613	−0.397306	+	0.917686i	$0.630055\pi$
$480$	4.19980e22	0.680266
$481$	1.60114e23	2.54799
$482$	1.06471e22	0.166469
$483$	−2.13674e22	−0.328247
$484$	−9.86345e20	−0.0148882
$485$	−1.15183e23	−1.70838
$486$	8.74183e22	1.27407
$487$	8.63726e21	0.123703	0.0618514	−	0.998085i	$-0.480300\pi$
$487$	8.63726e21	0.123703	0.0618514	+	0.998085i	$0.480300\pi$
$488$	−9.53130e22	−1.34148
$489$	8.50435e22	1.17629
$490$	2.13841e22	0.290687
$491$	5.12313e22	0.684451	0.342226	−	0.939618i	$-0.388819\pi$
$491$	5.12313e22	0.684451	0.342226	+	0.939618i	$0.388819\pi$
$492$	−1.13919e22	−0.149586
$493$	1.09039e23	1.40729
$494$	−2.32119e22	−0.294463
$495$	−3.45501e22	−0.430829
$496$	−1.07084e23	−1.31259
$497$	−1.81923e22	−0.219208
$498$	−1.93509e23	−2.29220
$499$	1.11675e23	1.30047	0.650234	−	0.759734i	$-0.274671\pi$
$499$	1.11675e23	1.30047	0.650234	+	0.759734i	$0.274671\pi$
$500$	5.57335e21	0.0638075
$501$	1.34120e23	1.50964
$502$	7.57275e22	0.838054
$503$	−1.42926e23	−1.55519	−0.777597	−	0.628763i	$-0.783562\pi$
$503$	−1.42926e23	−1.55519	−0.777597	+	0.628763i	$0.783562\pi$
$504$	−8.39686e22	−0.898374
$505$	2.60867e22	0.274437
$506$	7.05426e21	0.0729746
$507$	−1.59640e23	−1.62396
$508$	3.13390e21	0.0313505
$509$	−2.53584e22	−0.249471	−0.124736	−	0.992190i	$-0.539808\pi$
$509$	−2.53584e22	−0.249471	−0.124736	+	0.992190i	$0.539808\pi$
$510$	−2.03209e23	−1.96606
$511$	−7.84775e22	−0.746737
$512$	−1.20070e23	−1.12367
$513$	−1.63945e21	−0.0150904
$514$	1.64874e23	1.49267
$515$	1.13899e23	1.01428
$516$	−1.39128e22	−0.121869
$517$	−1.30891e22	−0.112782
$518$	1.65983e23	1.40689
$519$	1.82349e23	1.52048
$520$	2.86774e23	2.35240
$521$	2.13998e23	1.72699	0.863495	−	0.504357i	$-0.168271\pi$
$521$	2.13998e23	1.72699	0.863495	+	0.504357i	$0.168271\pi$
$522$	−1.50454e23	−1.19455
$523$	5.25084e22	0.410171	0.205085	−	0.978744i	$-0.434253\pi$
$523$	5.25084e22	0.410171	0.205085	+	0.978744i	$0.434253\pi$
$524$	−1.58651e22	−0.121935
$525$	−2.06513e23	−1.56169
$526$	1.95301e22	0.145320
$527$	−2.26838e23	−1.66083
$528$	4.73097e22	0.340849
$529$	−1.31169e23	−0.929950
$530$	7.57293e22	0.528347
$531$	1.47700e23	1.01409
$532$	4.71253e21	0.0318424
$533$	−1.44627e23	−0.961763
$534$	−3.17050e23	−2.07504
$535$	−2.56694e22	−0.165352
$536$	−3.02378e23	−1.91712
$537$	−5.71038e22	−0.356356
$538$	2.75768e23	1.69393
$539$	−1.05461e22	−0.0637658
$540$	2.85034e21	0.0169648
$541$	4.04655e22	0.237087	0.118544	−	0.992949i	$-0.462177\pi$
$541$	4.04655e22	0.237087	0.118544	+	0.992949i	$0.462177\pi$
$542$	−1.07601e23	−0.620612
$543$	−8.85223e22	−0.502637
$544$	−5.93698e22	−0.331875
$545$	1.56540e23	0.861498
$546$	−3.07820e23	−1.66786
$547$	8.88223e22	0.473838	0.236919	−	0.971529i	$-0.423862\pi$
$547$	8.88223e22	0.473838	0.236919	+	0.971529i	$0.423862\pi$
$548$	1.80718e22	0.0949218
$549$	2.31708e23	1.19833
$550$	6.81787e22	0.347189
$551$	6.00028e22	0.300873
$552$	7.96724e22	0.393392
$553$	−1.31053e23	−0.637210
$554$	2.01183e23	0.963294
$555$	7.71354e23	3.63717
$556$	4.19690e22	0.194891
$557$	−1.16631e23	−0.533389	−0.266695	−	0.963781i	$-0.585932\pi$
$557$	−1.16631e23	−0.533389	−0.266695	+	0.963781i	$0.585932\pi$
$558$	3.12995e23	1.40976
$559$	−1.76632e23	−0.783553
$560$	2.47257e23	1.08032
$561$	1.00217e23	0.431279
$562$	2.44414e23	1.03602
$563$	4.37968e22	0.182861	0.0914305	−	0.995811i	$-0.470856\pi$
$563$	4.37968e22	0.182861	0.0914305	+	0.995811i	$0.470856\pi$
$564$	−2.08035e22	−0.0855585
$565$	−4.29178e23	−1.73870
$566$	2.92229e23	1.16623
$567$	−2.36467e23	−0.929638
$568$	6.78334e22	0.262714
$569$	−1.22199e23	−0.466242	−0.233121	−	0.972448i	$-0.574894\pi$
$569$	−1.22199e23	−0.466242	−0.233121	+	0.972448i	$0.574894\pi$
$570$	−1.11824e23	−0.420336
$571$	−9.07549e22	−0.336096	−0.168048	−	0.985779i	$-0.553746\pi$
$571$	−9.07549e22	−0.336096	−0.168048	+	0.985779i	$0.553746\pi$
$572$	−1.99025e22	−0.0726176
$573$	−1.74871e23	−0.628643
$574$	−1.49928e23	−0.531047
$575$	9.54952e22	0.333277
$576$	3.05679e23	1.05117
$577$	3.64755e22	0.123597	0.0617984	−	0.998089i	$-0.480316\pi$
$577$	3.64755e22	0.123597	0.0617984	+	0.998089i	$0.480316\pi$
$578$	1.33895e22	0.0447074
$579$	−5.65543e22	−0.186079
$580$	−1.04321e23	−0.338245
$581$	4.98770e23	1.59369
$582$	−4.61003e23	−1.45164
$583$	−3.73477e22	−0.115899
$584$	2.92619e23	0.894939
$585$	−6.97154e23	−2.10138
$586$	−3.21206e23	−0.954233
$587$	−6.55037e21	−0.0191797	−0.00958985	−	0.999954i	$-0.503053\pi$
$587$	−6.55037e21	−0.0191797	−0.00958985	+	0.999954i	$0.503053\pi$
$588$	−1.67617e22	−0.0483738
$589$	−1.24826e23	−0.355080
$590$	−5.22923e23	−1.46621
$591$	−2.74313e23	−0.758146
$592$	−5.14751e23	−1.40237
$593$	−3.78329e23	−1.01602	−0.508012	−	0.861350i	$-0.669620\pi$
$593$	−3.78329e23	−1.01602	−0.508012	+	0.861350i	$0.669620\pi$
$594$	7.17772e21	0.0190021
$595$	5.23772e23	1.36694
$596$	−6.57258e22	−0.169100
$597$	−7.34810e23	−1.86377
$598$	1.42341e23	0.355935
$599$	−2.79608e22	−0.0689320	−0.0344660	−	0.999406i	$-0.510973\pi$
$599$	−2.79608e22	−0.0689320	−0.0344660	+	0.999406i	$0.510973\pi$
$600$	7.70026e23	1.87163
$601$	4.89303e23	1.17259	0.586293	−	0.810099i	$-0.300587\pi$
$601$	4.89303e23	1.17259	0.586293	+	0.810099i	$0.300587\pi$
$602$	−1.83106e23	−0.432646
$603$	7.35088e23	1.71255
$604$	8.87224e22	0.203807
$605$	−6.03263e22	−0.136643
$606$	1.04408e23	0.233194
$607$	−4.26073e23	−0.938383	−0.469191	−	0.883096i	$-0.655455\pi$
$607$	−4.26073e23	−0.938383	−0.469191	+	0.883096i	$0.655455\pi$
$608$	−3.26705e22	−0.0709537
$609$	7.95718e23	1.70417
$610$	−8.20349e23	−1.73259
$611$	−2.64113e23	−0.550098
$612$	7.76266e22	0.159450
$613$	2.22150e23	0.450021	0.225010	−	0.974356i	$-0.427758\pi$
$613$	2.22150e23	0.450021	0.225010	+	0.974356i	$0.427758\pi$
$614$	−5.03597e23	−1.00613
$615$	−6.96743e23	−1.37289
$616$	−1.46614e23	−0.284930
$617$	−2.67314e23	−0.512386	−0.256193	−	0.966626i	$-0.582468\pi$
$617$	−2.67314e23	−0.512386	−0.256193	+	0.966626i	$0.582468\pi$
$618$	4.55864e23	0.861853
$619$	7.21329e23	1.34513	0.672563	−	0.740040i	$-0.265193\pi$
$619$	7.21329e23	1.34513	0.672563	+	0.740040i	$0.265193\pi$
$620$	2.17022e23	0.399186
$621$	1.00535e22	0.0182407
$622$	7.70123e23	1.37829
$623$	8.17196e23	1.44271
$624$	9.54618e23	1.66250
$625$	−3.92084e23	−0.673595
$626$	7.99525e23	1.35503
$627$	5.51485e22	0.0922060
$628$	−1.03565e23	−0.170826
$629$	−1.09041e24	−1.77443
$630$	−7.22709e23	−1.16030
$631$	9.05273e23	1.43394	0.716968	−	0.697106i	$-0.245529\pi$
$631$	9.05273e23	1.43394	0.716968	+	0.697106i	$0.245529\pi$
$632$	4.88657e23	0.763675
$633$	9.93560e23	1.53201
$634$	−1.70254e23	−0.259023
$635$	1.91674e23	0.287731
$636$	−5.93594e22	−0.0879233
$637$	−2.12800e23	−0.311019
$638$	−2.62700e23	−0.378864
$639$	−1.64905e23	−0.234680
$640$	−7.35407e23	−1.03276
$641$	−6.49451e23	−0.900022	−0.450011	−	0.893023i	$-0.648580\pi$
$641$	−6.49451e23	−0.900022	−0.450011	+	0.893023i	$0.648580\pi$
$642$	−1.02738e23	−0.140502
$643$	−7.75336e23	−1.04640	−0.523198	−	0.852211i	$-0.675261\pi$
$643$	−7.75336e23	−1.04640	−0.523198	+	0.852211i	$0.675261\pi$
$644$	−2.88985e22	−0.0384898
$645$	−8.50927e23	−1.11850
$646$	1.58077e23	0.205066
$647$	−3.82852e23	−0.490168	−0.245084	−	0.969502i	$-0.578816\pi$
$647$	−3.82852e23	−0.490168	−0.245084	+	0.969502i	$0.578816\pi$
$648$	8.81713e23	1.11414
$649$	2.57892e23	0.321631
$650$	1.37571e24	1.69342
$651$	−1.65536e24	−2.01120
$652$	1.15018e23	0.137931
$653$	1.35232e24	1.60073	0.800365	−	0.599514i	$-0.204639\pi$
$653$	1.35232e24	1.60073	0.800365	+	0.599514i	$0.204639\pi$
$654$	6.26527e23	0.732030
$655$	−9.70334e23	−1.11910
$656$	4.64961e23	0.529338
$657$	−7.11364e23	−0.799440
$658$	−2.73794e23	−0.303742
$659$	7.41653e23	0.812222	0.406111	−	0.913824i	$-0.366885\pi$
$659$	7.41653e23	0.812222	0.406111	+	0.913824i	$0.366885\pi$
$660$	−9.58808e22	−0.103659
$661$	4.30889e23	0.459889	0.229945	−	0.973204i	$-0.426146\pi$
$661$	4.30889e23	0.459889	0.229945	+	0.973204i	$0.426146\pi$
$662$	−8.93453e22	−0.0941410
$663$	2.02219e24	2.10357
$664$	−1.85976e24	−1.90998
$665$	2.88226e23	0.292246
$666$	1.50457e24	1.50619
$667$	−3.67953e23	−0.363683
$668$	1.81393e23	0.177019
$669$	1.97881e23	0.190670
$670$	−2.60253e24	−2.47606
$671$	4.04575e23	0.380065
$672$	−4.33255e23	−0.401887
$673$	−9.18433e23	−0.841239	−0.420620	−	0.907237i	$-0.638187\pi$
$673$	−9.18433e23	−0.841239	−0.420620	+	0.907237i	$0.638187\pi$
$674$	1.22725e24	1.11000
$675$	9.71665e22	0.0867830
$676$	−2.15907e23	−0.190423
$677$	−1.17467e24	−1.02309	−0.511543	−	0.859258i	$-0.670926\pi$
$677$	−1.17467e24	−1.02309	−0.511543	+	0.859258i	$0.670926\pi$
$678$	−1.71772e24	−1.47741
$679$	1.18824e24	1.00928
$680$	−1.95299e24	−1.63823
$681$	−6.58662e23	−0.545647
$682$	5.46505e23	0.447123
$683$	2.46895e23	0.199497	0.0997483	−	0.995013i	$-0.468196\pi$
$683$	2.46895e23	0.199497	0.0997483	+	0.995013i	$0.468196\pi$
$684$	4.27170e22	0.0340898
$685$	1.10530e24	0.871182
$686$	−1.26369e24	−0.983753
$687$	−2.09245e24	−1.60887
$688$	5.67852e23	0.431255
$689$	−7.53605e23	−0.565302
$690$	6.85732e23	0.508086
$691$	1.11168e24	0.813607	0.406803	−	0.913516i	$-0.366643\pi$
$691$	1.11168e24	0.813607	0.406803	+	0.913516i	$0.366643\pi$
$692$	2.46620e23	0.178290
$693$	3.56421e23	0.254525
$694$	5.43222e23	0.383197
$695$	2.56688e24	1.78869
$696$	−2.96699e24	−2.04239
$697$	9.84938e23	0.669777
$698$	−9.94091e23	−0.667813
$699$	2.19733e24	1.45828
$700$	−2.79301e23	−0.183122
$701$	−1.10372e24	−0.714914	−0.357457	−	0.933930i	$-0.616356\pi$
$701$	−1.10372e24	−0.714914	−0.357457	+	0.933930i	$0.616356\pi$
$702$	1.44832e23	0.0926831
$703$	−6.00040e23	−0.379367
$704$	5.33732e23	0.333392
$705$	−1.27237e24	−0.785247
$706$	1.69035e24	1.03071
$707$	−2.69112e23	−0.162132
$708$	4.09886e23	0.243994
$709$	3.08981e24	1.81735	0.908676	−	0.417503i	$-0.137095\pi$
$709$	3.08981e24	1.81735	0.908676	+	0.417503i	$0.137095\pi$
$710$	5.83835e23	0.339308
$711$	−1.18794e24	−0.682184
$712$	−3.04708e24	−1.72903
$713$	7.65468e23	0.429206
$714$	2.09632e24	1.16151
$715$	−1.21727e24	−0.666476
$716$	−7.72307e22	−0.0417858
$717$	4.03423e24	2.15699
$718$	1.21532e24	0.642145
$719$	8.89853e23	0.464646	0.232323	−	0.972639i	$-0.425367\pi$
$719$	8.89853e23	0.464646	0.232323	+	0.972639i	$0.425367\pi$
$720$	2.24128e24	1.15656
$721$	−1.17499e24	−0.599218
$722$	−1.72739e24	−0.870613
$723$	−5.10429e23	−0.254249
$724$	−1.19723e23	−0.0589386
$725$	−3.55623e24	−1.73028
$726$	−2.41447e23	−0.116107
$727$	−1.92606e24	−0.915436	−0.457718	−	0.889097i	$-0.651333\pi$
$727$	−1.92606e24	−0.915436	−0.457718	+	0.889097i	$0.651333\pi$
$728$	−2.95838e24	−1.38975
$729$	−1.93616e24	−0.898995
$730$	2.51854e24	1.15586
$731$	1.20290e24	0.545671
$732$	6.43019e23	0.288323
$733$	2.41530e24	1.07050	0.535252	−	0.844693i	$-0.320217\pi$
$733$	2.41530e24	1.07050	0.535252	+	0.844693i	$0.320217\pi$
$734$	1.04573e24	0.458143
$735$	−1.02517e24	−0.443969
$736$	2.00344e23	0.0857660
$737$	1.28350e24	0.543154
$738$	−1.35903e24	−0.568527
$739$	2.20380e24	0.911370	0.455685	−	0.890141i	$-0.349394\pi$
$739$	2.20380e24	0.911370	0.455685	+	0.890141i	$0.349394\pi$
$740$	1.04323e24	0.426490
$741$	1.11279e24	0.449737
$742$	−7.81229e23	−0.312137
$743$	−3.00973e24	−1.18884	−0.594419	−	0.804155i	$-0.702618\pi$
$743$	−3.00973e24	−1.18884	−0.594419	+	0.804155i	$0.702618\pi$
$744$	6.17235e24	2.41035
$745$	−4.01988e24	−1.55198
$746$	−5.54034e23	−0.211474
$747$	4.52113e24	1.70617
$748$	1.35540e23	0.0505713
$749$	2.64807e23	0.0976864
$750$	1.36430e24	0.497610
$751$	−3.45959e23	−0.124763	−0.0623815	−	0.998052i	$-0.519870\pi$
$751$	−3.45959e23	−0.124763	−0.0623815	+	0.998052i	$0.519870\pi$
$752$	8.49096e23	0.302765
$753$	−3.63042e24	−1.27997
$754$	−5.30077e24	−1.84792
$755$	5.42639e24	1.87052
$756$	−2.94043e22	−0.0100225
$757$	−3.19461e24	−1.07672	−0.538361	−	0.842715i	$-0.680956\pi$
$757$	−3.19461e24	−1.07672	−0.538361	+	0.842715i	$0.680956\pi$
$758$	−1.99821e24	−0.665968
$759$	−3.38185e23	−0.111455
$760$	−1.07471e24	−0.350247
$761$	1.94913e24	0.628162	0.314081	−	0.949396i	$-0.398304\pi$
$761$	1.94913e24	0.628162	0.314081	+	0.949396i	$0.398304\pi$
$762$	7.67147e23	0.244490
$763$	−1.61487e24	−0.508956
$764$	−2.36507e23	−0.0737140
$765$	4.74776e24	1.46341
$766$	−4.03072e24	−1.22868
$767$	5.20376e24	1.56876
$768$	2.23644e24	0.666786
$769$	−2.77980e24	−0.819671	−0.409836	−	0.912159i	$-0.634414\pi$
$769$	−2.77980e24	−0.819671	−0.409836	+	0.912159i	$0.634414\pi$
$770$	−1.26189e24	−0.368001
$771$	−7.90413e24	−2.27977
$772$	−7.64875e22	−0.0218194
$773$	−2.07712e24	−0.586052	−0.293026	−	0.956105i	$-0.594662\pi$
$773$	−2.07712e24	−0.586052	−0.293026	+	0.956105i	$0.594662\pi$
$774$	−1.65978e24	−0.463182
$775$	7.39817e24	2.04202
$776$	−4.43057e24	−1.20958
$777$	−7.95734e24	−2.14877
$778$	4.01202e24	1.07161
$779$	5.42000e23	0.143196
$780$	−1.93469e24	−0.505600
$781$	−2.87932e23	−0.0744314
$782$	−9.69372e23	−0.247875
$783$	−3.74393e23	−0.0947006
$784$	6.84129e23	0.171179
$785$	−6.33416e24	−1.56782
$786$	−3.88361e24	−0.950921
$787$	−3.50106e24	−0.848035	−0.424018	−	0.905654i	$-0.639381\pi$
$787$	−3.50106e24	−0.848035	−0.424018	+	0.905654i	$0.639381\pi$
$788$	−3.70998e23	−0.0888994
$789$	−9.36286e23	−0.221949
$790$	4.20581e24	0.986325
$791$	4.42743e24	1.02719
$792$	−1.32899e24	−0.305040
$793$	8.16353e24	1.85377
$794$	4.14860e24	0.932026
$795$	−3.63051e24	−0.806950
$796$	−9.93802e23	−0.218544
$797$	−7.93711e24	−1.72690	−0.863448	−	0.504437i	$-0.831700\pi$
$797$	−7.93711e24	−1.72690	−0.863448	+	0.504437i	$0.831700\pi$
$798$	1.15358e24	0.248326
$799$	1.79866e24	0.383091
$800$	1.93631e24	0.408046
$801$	7.40752e24	1.54453
$802$	3.71608e24	0.766661
$803$	−1.24208e24	−0.253552
$804$	2.03996e24	0.412045
$805$	−1.76748e24	−0.353255
$806$	1.10274e25	2.18085
$807$	−1.32205e25	−2.58715
$808$	1.00344e24	0.194310
$809$	8.27578e24	1.58579	0.792897	−	0.609356i	$-0.208572\pi$
$809$	8.27578e24	1.58579	0.792897	+	0.609356i	$0.208572\pi$
$810$	7.58881e24	1.43897
$811$	−7.47549e24	−1.40269	−0.701346	−	0.712821i	$-0.747417\pi$
$811$	−7.47549e24	−1.40269	−0.701346	+	0.712821i	$0.747417\pi$
$812$	1.07618e24	0.199829
$813$	5.15843e24	0.947868
$814$	2.62705e24	0.477706
$815$	7.03468e24	1.26591
$816$	−6.50114e24	−1.15777
$817$	6.61940e23	0.116663
$818$	−2.65714e24	−0.463460
$819$	7.19189e24	1.24145
$820$	−9.42318e23	−0.160983
$821$	−1.35838e23	−0.0229671	−0.0114835	−	0.999934i	$-0.503655\pi$
$821$	−1.35838e23	−0.0229671	−0.0114835	+	0.999934i	$0.503655\pi$
$822$	4.42378e24	0.740258
$823$	6.08697e23	0.100810	0.0504049	−	0.998729i	$-0.483949\pi$
$823$	6.08697e23	0.100810	0.0504049	+	0.998729i	$0.483949\pi$
$824$	4.38119e24	0.718142
$825$	−3.26852e24	−0.530265
$826$	5.39450e24	0.866206
$827$	2.26277e23	0.0359620	0.0179810	−	0.999838i	$-0.494276\pi$
$827$	2.26277e23	0.0359620	0.0179810	+	0.999838i	$0.494276\pi$
$828$	−2.61952e23	−0.0412063
$829$	−1.68005e24	−0.261583	−0.130791	−	0.991410i	$-0.541752\pi$
$829$	−1.68005e24	−0.261583	−0.130791	+	0.991410i	$0.541752\pi$
$830$	−1.60068e25	−2.46684
$831$	−9.64484e24	−1.47125
$832$	1.07697e25	1.62613
$833$	1.44921e24	0.216595
$834$	1.02736e25	1.51988
$835$	1.10942e25	1.62466
$836$	7.45862e22	0.0108120
$837$	7.78865e23	0.111762
$838$	−6.75773e23	−0.0959902
$839$	−1.56894e24	−0.220612	−0.110306	−	0.993898i	$-0.535183\pi$
$839$	−1.56894e24	−0.220612	−0.110306	+	0.993898i	$0.535183\pi$
$840$	−1.42520e25	−1.98382
$841$	6.44539e24	0.888143
$842$	−6.83033e24	−0.931727
$843$	−1.17174e25	−1.58232
$844$	1.34375e24	0.179642
$845$	−1.32052e25	−1.74768
$846$	−2.48182e24	−0.325179
$847$	6.22330e23	0.0807257
$848$	2.42276e24	0.311133
$849$	−1.40096e25	−1.78119
$850$	−9.36888e24	−1.17931
$851$	3.67961e24	0.458564
$852$	−4.57631e23	−0.0564649
$853$	2.36058e24	0.288371	0.144186	−	0.989551i	$-0.453944\pi$
$853$	2.36058e24	0.288371	0.144186	+	0.989551i	$0.453944\pi$
$854$	8.46277e24	1.02358
$855$	2.61264e24	0.312872
$856$	−9.87385e23	−0.117074
$857$	−5.54312e24	−0.650755	−0.325378	−	0.945584i	$-0.605491\pi$
$857$	−5.54312e24	−0.650755	−0.325378	+	0.945584i	$0.605491\pi$
$858$	−4.87193e24	−0.566316
$859$	−1.09955e25	−1.26553	−0.632765	−	0.774344i	$-0.718080\pi$
$859$	−1.09955e25	−1.26553	−0.632765	+	0.774344i	$0.718080\pi$
$860$	−1.15085e24	−0.131154
$861$	7.18765e24	0.811073
$862$	6.15182e24	0.687372
$863$	−9.50696e24	−1.05184	−0.525920	−	0.850534i	$-0.676279\pi$
$863$	−9.50696e24	−1.05184	−0.525920	+	0.850534i	$0.676279\pi$
$864$	2.03850e23	0.0223329
$865$	1.50837e25	1.63633
$866$	−1.02728e25	−1.10354
$867$	−6.41903e23	−0.0682821
$868$	−2.23882e24	−0.235831
$869$	−2.07420e24	−0.216363
$870$	−2.55366e25	−2.63784
$871$	2.58986e25	2.64924
$872$	6.02138e24	0.609966
$873$	1.07708e25	1.08051
$874$	−5.33434e23	−0.0529949
$875$	−3.51648e24	−0.345971
$876$	−1.97412e24	−0.192349
$877$	−2.42949e24	−0.234433	−0.117216	−	0.993106i	$-0.537397\pi$
$877$	−2.42949e24	−0.234433	−0.117216	+	0.993106i	$0.537397\pi$
$878$	1.59031e25	1.51978
$879$	1.53988e25	1.45741
$880$	3.91339e24	0.366818
$881$	2.31361e24	0.214781	0.107390	−	0.994217i	$-0.465751\pi$
$881$	2.31361e24	0.214781	0.107390	+	0.994217i	$0.465751\pi$
$882$	−1.99964e24	−0.183852
$883$	−5.09990e24	−0.464404	−0.232202	−	0.972668i	$-0.574593\pi$
$883$	−5.09990e24	−0.464404	−0.232202	+	0.972668i	$0.574593\pi$
$884$	2.73494e24	0.246663
$885$	2.50692e25	2.23935
$886$	−1.34265e25	−1.18789
$887$	−4.90313e24	−0.429658	−0.214829	−	0.976652i	$-0.568919\pi$
$887$	−4.90313e24	−0.429658	−0.214829	+	0.976652i	$0.568919\pi$
$888$	2.96705e25	2.57522
$889$	−1.97732e24	−0.169986
$890$	−2.62259e25	−2.23314
$891$	−3.74260e24	−0.315655
$892$	2.67626e23	0.0223577
$893$	9.89783e23	0.0819035
$894$	−1.60890e25	−1.31874
$895$	−4.72354e24	−0.383506
$896$	7.58650e24	0.610132
$897$	−6.82392e24	−0.543624
$898$	−6.39984e24	−0.505033
$899$	−2.85059e25	−2.22832
$900$	−2.53174e24	−0.196046
$901$	5.13220e24	0.393679
$902$	−2.37294e24	−0.180315
$903$	8.77822e24	0.660786
$904$	−1.65086e25	−1.23105
$905$	−7.32244e24	−0.540932
$906$	2.17183e25	1.58941
$907$	−8.16713e23	−0.0592117	−0.0296059	−	0.999562i	$-0.509425\pi$
$907$	−8.16713e23	−0.0592117	−0.0296059	+	0.999562i	$0.509425\pi$
$908$	−8.90814e23	−0.0639819
$909$	−2.43938e24	−0.173575
$910$	−2.54624e25	−1.79493
$911$	1.86772e25	1.30439	0.652194	−	0.758052i	$-0.273849\pi$
$911$	1.86772e25	1.30439	0.652194	+	0.758052i	$0.273849\pi$
$912$	−3.57750e24	−0.247528
$913$	7.89413e24	0.541131
$914$	9.95063e24	0.675784
$915$	3.93280e25	2.64620
$916$	−2.82995e24	−0.188655
$917$	1.00100e25	0.661144
$918$	−9.86338e23	−0.0645450
$919$	−1.69935e25	−1.10179	−0.550897	−	0.834573i	$-0.685714\pi$
$919$	−1.69935e25	−1.10179	−0.550897	+	0.834573i	$0.685714\pi$
$920$	6.59038e24	0.423364
$921$	2.41427e25	1.53667
$922$	−9.85124e21	−0.000621267 0
$923$	−5.80991e24	−0.363041
$924$	9.89113e23	0.0612398
$925$	3.55630e25	2.18169
$926$	−6.56215e23	−0.0398890
$927$	−1.06508e25	−0.641510
$928$	−7.46079e24	−0.445274
$929$	−6.96988e24	−0.412184	−0.206092	−	0.978533i	$-0.566075\pi$
$929$	−6.96988e24	−0.412184	−0.206092	+	0.978533i	$0.566075\pi$
$930$	5.31248e25	3.11309
$931$	7.97483e23	0.0463073
$932$	2.97181e24	0.170996
$933$	−3.69201e25	−2.10508
$934$	9.62257e22	0.00543679
$935$	8.28983e24	0.464138
$936$	−2.68164e25	−1.48784
$937$	2.89507e25	1.59174	0.795870	−	0.605468i	$-0.207014\pi$
$937$	2.89507e25	1.59174	0.795870	+	0.605468i	$0.207014\pi$
$938$	2.68479e25	1.46280
$939$	−3.83297e25	−2.06956
$940$	−1.72083e24	−0.0920771
$941$	9.07747e24	0.481341	0.240671	−	0.970607i	$-0.422633\pi$
$941$	9.07747e24	0.481341	0.240671	+	0.970607i	$0.422633\pi$
$942$	−2.53515e25	−1.33221
$943$	−3.32369e24	−0.173090
$944$	−1.67295e25	−0.863420
$945$	−1.79841e24	−0.0919852
$946$	−2.89806e24	−0.146904
$947$	−1.79812e25	−0.903324	−0.451662	−	0.892189i	$-0.649169\pi$
$947$	−1.79812e25	−0.903324	−0.451662	+	0.892189i	$0.649169\pi$
$948$	−3.29667e24	−0.164136
$949$	−2.50627e25	−1.23670
$950$	−5.15559e24	−0.252132
$951$	8.16206e24	0.395608
$952$	2.01471e25	0.967831
$953$	−1.72497e25	−0.821280	−0.410640	−	0.911798i	$-0.634695\pi$
$953$	−1.72497e25	−0.821280	−0.410640	+	0.911798i	$0.634695\pi$
$954$	−7.08149e24	−0.334167
$955$	−1.44651e25	−0.676539
$956$	5.45614e24	0.252926
$957$	1.25940e25	0.578644
$958$	−1.59560e25	−0.726638
$959$	−1.14023e25	−0.514677
$960$	5.18831e25	2.32124
$961$	3.67519e25	1.62979
$962$	5.30088e25	2.33002
$963$	2.40036e24	0.104581
$964$	−6.90336e23	−0.0298130
$965$	−4.67809e24	−0.200256
$966$	−7.07405e24	−0.300167
$967$	−2.85617e25	−1.20132	−0.600659	−	0.799505i	$-0.705095\pi$
$967$	−2.85617e25	−1.20132	−0.600659	+	0.799505i	$0.705095\pi$
$968$	−2.32048e24	−0.0967470
$969$	−7.57832e24	−0.313199
$970$	−3.81335e25	−1.56224
$971$	−2.77330e24	−0.112625	−0.0563123	−	0.998413i	$-0.517934\pi$
$971$	−2.77330e24	−0.112625	−0.0563123	+	0.998413i	$0.517934\pi$
$972$	−5.66801e24	−0.228175
$973$	−2.64801e25	−1.05672
$974$	2.85952e24	0.113121
$975$	−6.59525e25	−2.58638
$976$	−2.62449e25	−1.02029
$977$	8.86239e24	0.341545	0.170772	−	0.985311i	$-0.445374\pi$
$977$	8.86239e24	0.341545	0.170772	+	0.985311i	$0.445374\pi$
$978$	2.81552e25	1.07567
$979$	1.29339e25	0.489866
$980$	−1.38650e24	−0.0520593
$981$	−1.46381e25	−0.544877
$982$	1.69611e25	0.625900
$983$	7.27580e24	0.266180	0.133090	−	0.991104i	$-0.457510\pi$
$983$	7.27580e24	0.266180	0.133090	+	0.991104i	$0.457510\pi$
$984$	−2.68006e25	−0.972044
$985$	−2.26908e25	−0.815909
$986$	3.60993e25	1.28690
$987$	1.31259e25	0.463908
$988$	1.50500e24	0.0527356
$989$	−4.05919e24	−0.141017
$990$	−1.14384e25	−0.393974
$991$	3.89039e23	0.0132852	0.00664258	−	0.999978i	$-0.497886\pi$
$991$	3.89039e23	0.0132852	0.00664258	+	0.999978i	$0.497886\pi$
$992$	1.55210e25	0.525497
$993$	4.28327e24	0.143783
$994$	−6.02288e24	−0.200456
$995$	−6.07824e25	−2.00577
$996$	1.25467e25	0.410511
$997$	1.18479e24	0.0384354	0.0192177	−	0.999815i	$-0.493882\pi$
$997$	1.18479e24	0.0384354	0.0192177	+	0.999815i	$0.493882\pi$
$998$	3.69719e25	1.18922
$999$	3.74400e24	0.119407

Twists

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

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

\(f(q)\)	\(=\)	\(q+331.068 q^{2} -15871.6 q^{3} -21465.7 q^{4} -1.31288e6 q^{5} -5.25459e6 q^{6} +1.35437e7 q^{7} -5.05004e7 q^{8} +1.22768e8 q^{9} +O(q^{10})\)	\(q+331.068 q^{2} -15871.6 q^{3} -21465.7 q^{4} -1.31288e6 q^{5} -5.25459e6 q^{6} +1.35437e7 q^{7} -5.05004e7 q^{8} +1.22768e8 q^{9} -4.34652e8 q^{10} +2.14359e8 q^{11} +3.40696e8 q^{12} +4.32535e9 q^{13} +4.48390e9 q^{14} +2.08374e10 q^{15} -1.39055e10 q^{16} -2.94565e10 q^{17} +4.06445e10 q^{18} -1.62096e10 q^{19} +2.81818e10 q^{20} -2.14960e11 q^{21} +7.09674e10 q^{22} +9.94013e10 q^{23} +8.01523e11 q^{24} +9.60703e11 q^{25} +1.43199e12 q^{26} +1.01141e11 q^{27} -2.90726e11 q^{28} -3.70169e12 q^{29} +6.89862e12 q^{30} +7.70078e12 q^{31} +2.01551e12 q^{32} -3.40222e12 q^{33} -9.75211e12 q^{34} -1.77812e13 q^{35} -2.63530e12 q^{36} +3.70177e13 q^{37} -5.36647e12 q^{38} -6.86502e13 q^{39} +6.63008e13 q^{40} -3.34371e13 q^{41} -7.11666e13 q^{42} -4.08364e13 q^{43} -4.60137e12 q^{44} -1.61179e14 q^{45} +3.29086e13 q^{46} -6.10617e13 q^{47} +2.20703e14 q^{48} -4.91984e13 q^{49} +3.18059e14 q^{50} +4.67522e14 q^{51} -9.28468e13 q^{52} -1.74230e14 q^{53} +3.34846e13 q^{54} -2.81427e14 q^{55} -6.83963e14 q^{56} +2.57272e14 q^{57} -1.22551e15 q^{58} +1.20308e15 q^{59} -4.47291e14 q^{60} +1.88737e15 q^{61} +2.54949e15 q^{62} +1.66273e15 q^{63} +2.48990e15 q^{64} -5.67864e15 q^{65} -1.12637e15 q^{66} +5.98763e15 q^{67} +6.32305e14 q^{68} -1.57766e15 q^{69} -5.88680e15 q^{70} -1.34322e15 q^{71} -6.19982e15 q^{72} -5.79439e15 q^{73} +1.22554e16 q^{74} -1.52479e16 q^{75} +3.47950e14 q^{76} +2.90322e15 q^{77} -2.27279e16 q^{78} -9.67629e15 q^{79} +1.82562e16 q^{80} -1.74595e16 q^{81} -1.10700e16 q^{82} +3.68267e16 q^{83} +4.61428e15 q^{84} +3.86727e16 q^{85} -1.35197e16 q^{86} +5.87518e16 q^{87} -1.08252e16 q^{88} +6.03377e16 q^{89} -5.33612e16 q^{90} +5.85813e16 q^{91} -2.13372e15 q^{92} -1.22224e17 q^{93} -2.02156e16 q^{94} +2.12811e16 q^{95} -3.19893e16 q^{96} +8.77334e16 q^{97} -1.62880e16 q^{98} +2.63164e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 256 q^{2} + 3058 q^{3} + 391332 q^{4} + 1795234 q^{5} + 13170682 q^{6} - 896364 q^{7} - 101682420 q^{8} + 413432462 q^{9}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

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