LMFDB - Embedded newform 29.16.a.a.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,16,Mod(1,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	29.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:	$41.3811164790$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 381613 x^{14} - 3733354 x^{13} + 57580338072 x^{12} + 1053633121552 x^{11} + \cdots + 56\!\cdots\!24 $ x^16 - 381613x^14 - 3733354x^13 + 57580338072x^12 + 1053633121552x^11 - 4368708806733008x^10 - 112027323561555872x^9 + 175073374072500887552x^8 + 5628322450139411218432x^7 - 3559766404200168515698688x^6 - 136592485261791822734163968x^5 + 31960388770880055093699280896x^4 + 1389289310261686682407697121280x^3 - 81097743966968601971743751405568x^2 - 3651876483524920831899376851877888x + 5681589407398948985967076414849024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{33}\cdot 3^{7}\cdot 5^{4}\cdot 7^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-132.963$ of defining polynomial
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+124.963 q^{2} +7403.83 q^{3} -17152.2 q^{4} -74071.9 q^{5} +925205. q^{6} -3.34724e6 q^{7} -6.23818e6 q^{8} +4.04678e7 q^{9} +O(q^{10})$	\(q+124.963 q^{2} +7403.83 q^{3} -17152.2 q^{4} -74071.9 q^{5} +925205. q^{6} -3.34724e6 q^{7} -6.23818e6 q^{8} +4.04678e7 q^{9} -9.25625e6 q^{10} -4.48201e7 q^{11} -1.26992e8 q^{12} +1.62410e8 q^{13} -4.18281e8 q^{14} -5.48416e8 q^{15} -2.17498e8 q^{16} -1.69240e9 q^{17} +5.05698e9 q^{18} -4.63612e9 q^{19} +1.27050e9 q^{20} -2.47824e10 q^{21} -5.60086e9 q^{22} -1.79627e10 q^{23} -4.61865e10 q^{24} -2.50309e10 q^{25} +2.02952e10 q^{26} +1.93380e11 q^{27} +5.74127e10 q^{28} +1.72499e10 q^{29} -6.85317e10 q^{30} +5.62799e9 q^{31} +1.77234e11 q^{32} -3.31840e11 q^{33} -2.11488e11 q^{34} +2.47937e11 q^{35} -6.94113e11 q^{36} -3.63259e11 q^{37} -5.79343e11 q^{38} +1.20246e12 q^{39} +4.62074e11 q^{40} +1.63101e12 q^{41} -3.09688e12 q^{42} -2.04520e12 q^{43} +7.68765e11 q^{44} -2.99753e12 q^{45} -2.24468e12 q^{46} -1.24908e11 q^{47} -1.61032e12 q^{48} +6.45646e12 q^{49} -3.12794e12 q^{50} -1.25303e13 q^{51} -2.78569e12 q^{52} -2.63411e12 q^{53} +2.41653e13 q^{54} +3.31991e12 q^{55} +2.08807e13 q^{56} -3.43250e13 q^{57} +2.15560e12 q^{58} -2.33309e13 q^{59} +9.40656e12 q^{60} +4.13138e13 q^{61} +7.03291e11 q^{62} -1.35455e14 q^{63} +2.92746e13 q^{64} -1.20300e13 q^{65} -4.14678e13 q^{66} -2.05179e13 q^{67} +2.90285e13 q^{68} -1.32993e14 q^{69} +3.09829e13 q^{70} +7.64088e13 q^{71} -2.52446e14 q^{72} +8.78192e13 q^{73} -4.53939e13 q^{74} -1.85325e14 q^{75} +7.95198e13 q^{76} +1.50024e14 q^{77} +1.50262e14 q^{78} -1.76744e14 q^{79} +1.61105e13 q^{80} +8.51083e14 q^{81} +2.03816e14 q^{82} +1.96866e14 q^{83} +4.25074e14 q^{84} +1.25360e14 q^{85} -2.55574e14 q^{86} +1.27715e14 q^{87} +2.79596e14 q^{88} -6.69665e14 q^{89} -3.74580e14 q^{90} -5.43625e14 q^{91} +3.08101e14 q^{92} +4.16687e13 q^{93} -1.56089e13 q^{94} +3.43406e14 q^{95} +1.31221e15 q^{96} +4.02136e14 q^{97} +8.06819e14 q^{98} -1.81377e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 128 q^{2} - 3214 q^{3} + 239962 q^{4} - 82010 q^{5} - 112778 q^{6} - 3706320 q^{7} - 21137070 q^{8} + 73272578 q^{9}+O(q^{10}) $ 16 * q - 128 * q^2 - 3214 * q^3 + 239962 * q^4 - 82010 * q^5 - 112778 * q^6 - 3706320 * q^7 - 21137070 * q^8 + 73272578 * q^9	\( 16 q - 128 q^{2} - 3214 q^{3} + 239962 q^{4} - 82010 q^{5} - 112778 q^{6} - 3706320 q^{7} - 21137070 q^{8} + 73272578 q^{9} + 27111646 q^{10} - 128305158 q^{11} - 566454670 q^{12} - 500341634 q^{13} - 2456995576 q^{14} - 1005836398 q^{15} + 3638194738 q^{16} - 1889649440 q^{17} + 7114827706 q^{18} - 11903789760 q^{19} + 21125268698 q^{20} + 1845797984 q^{21} + 14207940510 q^{22} - 6296706268 q^{23} + 19916867274 q^{24} + 57929280374 q^{25} + 46861268662 q^{26} - 66882170482 q^{27} - 50278055968 q^{28} + 275998020944 q^{29} - 288715178542 q^{30} - 791595409290 q^{31} - 846144416938 q^{32} - 1192946764766 q^{33} - 1500307227904 q^{34} - 731093348200 q^{35} - 766217409340 q^{36} - 22311934700 q^{37} + 1194772372172 q^{38} - 1484120611454 q^{39} - 5651885433026 q^{40} + 871755491316 q^{41} - 5429421460912 q^{42} - 4296897329422 q^{43} - 10539797438606 q^{44} - 4399313787580 q^{45} - 20780033587764 q^{46} - 7817561912774 q^{47} - 36311476834866 q^{48} - 18565097654464 q^{49} - 33573686907474 q^{50} - 27333906159300 q^{51} - 48854284368422 q^{52} - 41630222638006 q^{53} - 88633328654882 q^{54} - 68569446879302 q^{55} - 66690562169864 q^{56} - 80322439188772 q^{57} - 2207984167552 q^{58} - 60146094578732 q^{59} - 170149488214170 q^{60} - 71628304977160 q^{61} - 95316700851110 q^{62} - 99862426093816 q^{63} - 20954801982074 q^{64} - 53095801190146 q^{65} - 84071816219318 q^{66} - 44591877980312 q^{67} + 24848392371308 q^{68} + 33786235351468 q^{69} - 254302493648008 q^{70} - 2238339487076 q^{71} - 335696824658688 q^{72} + 60304297937180 q^{73} - 4683993400652 q^{74} - 408007582551580 q^{75} - 511662725684676 q^{76} + 2082869459792 q^{77} + 134746909641474 q^{78} - 9999680374282 q^{79} + 10\!\cdots\!46 q^{80}+ \cdots + 531562034651476 q^{99}+O(q^{100}) \) 16 * q - 128 * q^2 - 3214 * q^3 + 239962 * q^4 - 82010 * q^5 - 112778 * q^6 - 3706320 * q^7 - 21137070 * q^8 + 73272578 * q^9 + 27111646 * q^10 - 128305158 * q^11 - 566454670 * q^12 - 500341634 * q^13 - 2456995576 * q^14 - 1005836398 * q^15 + 3638194738 * q^16 - 1889649440 * q^17 + 7114827706 * q^18 - 11903789760 * q^19 + 21125268698 * q^20 + 1845797984 * q^21 + 14207940510 * q^22 - 6296706268 * q^23 + 19916867274 * q^24 + 57929280374 * q^25 + 46861268662 * q^26 - 66882170482 * q^27 - 50278055968 * q^28 + 275998020944 * q^29 - 288715178542 * q^30 - 791595409290 * q^31 - 846144416938 * q^32 - 1192946764766 * q^33 - 1500307227904 * q^34 - 731093348200 * q^35 - 766217409340 * q^36 - 22311934700 * q^37 + 1194772372172 * q^38 - 1484120611454 * q^39 - 5651885433026 * q^40 + 871755491316 * q^41 - 5429421460912 * q^42 - 4296897329422 * q^43 - 10539797438606 * q^44 - 4399313787580 * q^45 - 20780033587764 * q^46 - 7817561912774 * q^47 - 36311476834866 * q^48 - 18565097654464 * q^49 - 33573686907474 * q^50 - 27333906159300 * q^51 - 48854284368422 * q^52 - 41630222638006 * q^53 - 88633328654882 * q^54 - 68569446879302 * q^55 - 66690562169864 * q^56 - 80322439188772 * q^57 - 2207984167552 * q^58 - 60146094578732 * q^59 - 170149488214170 * q^60 - 71628304977160 * q^61 - 95316700851110 * q^62 - 99862426093816 * q^63 - 20954801982074 * q^64 - 53095801190146 * q^65 - 84071816219318 * q^66 - 44591877980312 * q^67 + 24848392371308 * q^68 + 33786235351468 * q^69 - 254302493648008 * q^70 - 2238339487076 * q^71 - 335696824658688 * q^72 + 60304297937180 * q^73 - 4683993400652 * q^74 - 408007582551580 * q^75 - 511662725684676 * q^76 + 2082869459792 * q^77 + 134746909641474 * q^78 - 9999680374282 * q^79 + 1065964290115846 * q^80 + 1227860473120604 * q^81 - 482856386515020 * q^82 + 1449900899821108 * q^83 + 2256322335776952 * q^84 + 1364385639985788 * q^85 + 1206993542651814 * q^86 - 55441102457126 * q^87 + 2648043460385618 * q^88 - 162544796147532 * q^89 + 1885912570259156 * q^90 + 858443116817000 * q^91 + 2263858121857900 * q^92 + 3752667465062574 * q^93 + 3639931425958406 * q^94 - 73522560256708 * q^95 + 6634505750804190 * q^96 + 463840517939252 * q^97 + 2013726729859888 * q^98 + 531562034651476 * 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 $

$2$	124.963	0.690330	0.345165	−	0.938542i	$-0.387823\pi$
$2$	124.963	0.690330	0.345165	+	0.938542i	$0.387823\pi$
$3$	7403.83	1.95455	0.977276	−	0.211973i	$-0.0679888\pi$
$3$	7403.83	1.95455	0.977276	+	0.211973i	$0.0679888\pi$
$4$	−17152.2	−0.523445
$5$	−74071.9	−0.424012	−0.212006	−	0.977268i	$-0.568000\pi$
$5$	−74071.9	−0.424012	−0.212006	+	0.977268i	$0.568000\pi$
$6$	925205.	1.34928
$7$	−3.34724e6	−1.53621	−0.768107	−	0.640322i	$-0.778801\pi$
$7$	−3.34724e6	−1.53621	−0.768107	+	0.640322i	$0.778801\pi$
$8$	−6.23818e6	−1.05168
$9$	4.04678e7	2.82027
$10$	−9.25625e6	−0.292708
$11$	−4.48201e7	−0.693470	−0.346735	−	0.937963i	$-0.612710\pi$
$11$	−4.48201e7	−0.693470	−0.346735	+	0.937963i	$0.612710\pi$
$12$	−1.26992e8	−1.02310
$13$	1.62410e8	0.717856	0.358928	−	0.933365i	$-0.383142\pi$
$13$	1.62410e8	0.717856	0.358928	+	0.933365i	$0.383142\pi$
$14$	−4.18281e8	−1.06049
$15$	−5.48416e8	−0.828754
$16$	−2.17498e8	−0.202561
$17$	−1.69240e9	−1.00032	−0.500158	−	0.865934i	$-0.666725\pi$
$17$	−1.69240e9	−1.00032	−0.500158	+	0.865934i	$0.666725\pi$
$18$	5.05698e9	1.94692
$19$	−4.63612e9	−1.18988	−0.594939	−	0.803771i	$-0.702824\pi$
$19$	−4.63612e9	−1.18988	−0.594939	+	0.803771i	$0.702824\pi$
$20$	1.27050e9	0.221947
$21$	−2.47824e10	−3.00261
$22$	−5.60086e9	−0.478723
$23$	−1.79627e10	−1.10005	−0.550027	−	0.835147i	$-0.685383\pi$
$23$	−1.79627e10	−1.10005	−0.550027	+	0.835147i	$0.685383\pi$
$24$	−4.61865e10	−2.05556
$25$	−2.50309e10	−0.820214
$26$	2.02952e10	0.495557
$27$	1.93380e11	3.55781
$28$	5.74127e10	0.804123
$29$	1.72499e10	0.185695
$29$	1.72499e10	0.185695
$30$	−6.85317e10	−0.572113
$31$	5.62799e9	0.0367401	0.0183701	−	0.999831i	$-0.494152\pi$
$31$	5.62799e9	0.0367401	0.0183701	+	0.999831i	$0.494152\pi$
$32$	1.77234e11	0.911846
$33$	−3.31840e11	−1.35542
$34$	−2.11488e11	−0.690547
$35$	2.47937e11	0.651374
$36$	−6.94113e11	−1.47626
$37$	−3.63259e11	−0.629077	−0.314538	−	0.949245i	$-0.601850\pi$
$37$	−3.63259e11	−0.629077	−0.314538	+	0.949245i	$0.601850\pi$
$38$	−5.79343e11	−0.821408
$39$	1.20246e12	1.40309
$40$	4.62074e11	0.445925
$41$	1.63101e12	1.30791	0.653954	−	0.756534i	$-0.273109\pi$
$41$	1.63101e12	1.30791	0.653954	+	0.756534i	$0.273109\pi$
$42$	−3.09688e12	−2.07279
$43$	−2.04520e12	−1.14742	−0.573710	−	0.819058i	$-0.694496\pi$
$43$	−2.04520e12	−1.14742	−0.573710	+	0.819058i	$0.694496\pi$
$44$	7.68765e11	0.362993
$45$	−2.99753e12	−1.19583
$46$	−2.24468e12	−0.759400
$47$	−1.24908e11	−0.0359630	−0.0179815	−	0.999838i	$-0.505724\pi$
$47$	−1.24908e11	−0.0359630	−0.0179815	+	0.999838i	$0.505724\pi$
$48$	−1.61032e12	−0.395915
$49$	6.45646e12	1.35995
$50$	−3.12794e12	−0.566218
$51$	−1.25303e13	−1.95517
$52$	−2.78569e12	−0.375758
$53$	−2.63411e12	−0.308010	−0.154005	−	0.988070i	$-0.549217\pi$
$53$	−2.63411e12	−0.308010	−0.154005	+	0.988070i	$0.549217\pi$
$54$	2.41653e13	2.45606
$55$	3.31991e12	0.294040
$56$	2.08807e13	1.61560
$57$	−3.43250e13	−2.32568
$58$	2.15560e12	0.128191
$59$	−2.33309e13	−1.22051	−0.610255	−	0.792205i	$-0.708933\pi$
$59$	−2.33309e13	−1.22051	−0.610255	+	0.792205i	$0.708933\pi$
$60$	9.40656e12	0.433807
$61$	4.13138e13	1.68314	0.841572	−	0.540145i	$-0.181631\pi$
$61$	4.13138e13	1.68314	0.841572	+	0.540145i	$0.181631\pi$
$62$	7.03291e11	0.0253628
$63$	−1.35455e14	−4.33254
$64$	2.92746e13	0.832035
$65$	−1.20300e13	−0.304380
$66$	−4.14678e13	−0.935688
$67$	−2.05179e13	−0.413592	−0.206796	−	0.978384i	$-0.566304\pi$
$67$	−2.05179e13	−0.413592	−0.206796	+	0.978384i	$0.566304\pi$
$68$	2.90285e13	0.523610
$69$	−1.32993e14	−2.15011
$70$	3.09829e13	0.449663
$71$	7.64088e13	0.997025	0.498512	−	0.866883i	$-0.333880\pi$
$71$	7.64088e13	0.997025	0.498512	+	0.866883i	$0.333880\pi$
$72$	−2.52446e14	−2.96602
$73$	8.78192e13	0.930397	0.465198	−	0.885207i	$-0.345983\pi$
$73$	8.78192e13	0.930397	0.465198	+	0.885207i	$0.345983\pi$
$74$	−4.53939e13	−0.434270
$75$	−1.85325e14	−1.60315
$76$	7.95198e13	0.622836
$77$	1.50024e14	1.06532
$78$	1.50262e14	0.968592
$79$	−1.76744e14	−1.03548	−0.517739	−	0.855539i	$-0.673226\pi$
$79$	−1.76744e14	−1.03548	−0.517739	+	0.855539i	$0.673226\pi$
$80$	1.61105e13	0.0858882
$81$	8.51083e14	4.13365
$82$	2.03816e14	0.902888
$83$	1.96866e14	0.796315	0.398158	−	0.917317i	$-0.369650\pi$
$83$	1.96866e14	0.796315	0.398158	+	0.917317i	$0.369650\pi$
$84$	4.25074e14	1.57170
$85$	1.25360e14	0.424146
$86$	−2.55574e14	−0.792098
$87$	1.27715e14	0.362951
$88$	2.79596e14	0.729308
$89$	−6.69665e14	−1.60484	−0.802421	−	0.596758i	$-0.796455\pi$
$89$	−6.69665e14	−1.60484	−0.802421	+	0.596758i	$0.796455\pi$
$90$	−3.74580e14	−0.825517
$91$	−5.43625e14	−1.10278
$92$	3.08101e14	0.575817
$93$	4.16687e13	0.0718105
$94$	−1.56089e13	−0.0248263
$95$	3.43406e14	0.504523
$96$	1.31221e15	1.78225
$97$	4.02136e14	0.505342	0.252671	−	0.967552i	$-0.418691\pi$
$97$	4.02136e14	0.505342	0.252671	+	0.967552i	$0.418691\pi$
$98$	8.06819e14	0.938816
$99$	−1.81377e15	−1.95577
$100$	4.29337e14	0.429337
$101$	1.44285e15	1.33909	0.669546	−	0.742770i	$-0.266489\pi$
$101$	1.44285e15	1.33909	0.669546	+	0.742770i	$0.266489\pi$
$102$	−1.56582e15	−1.34971
$103$	1.82630e14	0.146316	0.0731581	−	0.997320i	$-0.476692\pi$
$103$	1.82630e14	0.146316	0.0731581	+	0.997320i	$0.476692\pi$
$104$	−1.01314e15	−0.754954
$105$	1.83568e15	1.27314
$106$	−3.29166e14	−0.212628
$107$	−2.08327e15	−1.25420	−0.627101	−	0.778938i	$-0.715759\pi$
$107$	−2.08327e15	−1.25420	−0.627101	+	0.778938i	$0.715759\pi$
$108$	−3.31690e15	−1.86232
$109$	2.60827e15	1.36664	0.683320	−	0.730119i	$-0.260536\pi$
$109$	2.60827e15	1.36664	0.683320	+	0.730119i	$0.260536\pi$
$110$	4.14866e14	0.202984
$111$	−2.68951e15	−1.22956
$112$	7.28017e14	0.311176
$113$	−1.87179e15	−0.748460	−0.374230	−	0.927336i	$-0.622093\pi$
$113$	−1.87179e15	−0.748460	−0.374230	+	0.927336i	$0.622093\pi$
$114$	−4.28936e15	−1.60548
$115$	1.33053e15	0.466436
$116$	−2.95874e14	−0.0972013
$117$	6.57237e15	2.02455
$118$	−2.91550e15	−0.842555
$119$	5.66488e15	1.53670
$120$	3.42112e15	0.871583
$121$	−2.16841e15	−0.519099
$122$	5.16270e15	1.16192
$123$	1.20757e16	2.55637
$124$	−9.65327e13	−0.0192314
$125$	4.11458e15	0.771793
$126$	−1.69269e16	−2.99088
$127$	−7.49757e15	−1.24851	−0.624256	−	0.781220i	$-0.714598\pi$
$127$	−7.49757e15	−1.24851	−0.624256	+	0.781220i	$0.714598\pi$
$128$	−2.14935e15	−0.337467
$129$	−1.51423e16	−2.24269
$130$	−1.50331e15	−0.210122
$131$	−5.86676e15	−0.774219	−0.387110	−	0.922034i	$-0.626526\pi$
$131$	−5.86676e15	−0.774219	−0.387110	+	0.922034i	$0.626526\pi$
$132$	5.69181e15	0.709489
$133$	1.55182e16	1.82791
$134$	−2.56398e15	−0.285515
$135$	−1.43240e16	−1.50856
$136$	1.05575e16	1.05201
$137$	1.79060e15	0.168886	0.0844430	−	0.996428i	$-0.473089\pi$
$137$	1.79060e15	0.168886	0.0844430	+	0.996428i	$0.473089\pi$
$138$	−1.66192e16	−1.48429
$139$	−2.08457e16	−1.76362	−0.881810	−	0.471606i	$-0.843675\pi$
$139$	−2.08457e16	−1.76362	−0.881810	+	0.471606i	$0.843675\pi$
$140$	−4.25267e15	−0.340958
$141$	−9.24796e14	−0.0702914
$142$	9.54828e15	0.688276
$143$	−7.27923e15	−0.497812
$144$	−8.80165e15	−0.571275
$145$	−1.27773e15	−0.0787371
$146$	1.09742e16	0.642280
$147$	4.78025e16	2.65810
$148$	6.23071e15	0.329287
$149$	−1.21065e16	−0.608307	−0.304153	−	0.952623i	$-0.598373\pi$
$149$	−1.21065e16	−0.608307	−0.304153	+	0.952623i	$0.598373\pi$
$150$	−2.31587e16	−1.10670
$151$	1.16230e16	0.528433	0.264216	−	0.964463i	$-0.414887\pi$
$151$	1.16230e16	0.528433	0.264216	+	0.964463i	$0.414887\pi$
$152$	2.89210e16	1.25137
$153$	−6.84878e16	−2.82116
$154$	1.87474e16	0.735421
$155$	−4.16876e14	−0.0155783
$156$	−2.06248e16	−0.734439
$157$	1.06337e16	0.360940	0.180470	−	0.983580i	$-0.442238\pi$
$157$	1.06337e16	0.360940	0.180470	+	0.983580i	$0.442238\pi$
$158$	−2.20864e16	−0.714821
$159$	−1.95025e16	−0.602021
$160$	−1.31280e16	−0.386634
$161$	6.01256e16	1.68992
$162$	1.06354e17	2.85358
$163$	5.03592e16	1.29024	0.645122	−	0.764080i	$-0.276807\pi$
$163$	5.03592e16	1.29024	0.645122	+	0.764080i	$0.276807\pi$
$164$	−2.79755e16	−0.684618
$165$	2.45801e16	0.574716
$166$	2.46010e16	0.549720
$167$	5.38497e16	1.15030	0.575148	−	0.818049i	$-0.304944\pi$
$167$	5.38497e16	1.15030	0.575148	+	0.818049i	$0.304944\pi$
$168$	1.54597e17	3.15778
$169$	−2.48089e16	−0.484682
$170$	1.56653e16	0.292801
$171$	−1.87613e17	−3.35578
$172$	3.50798e16	0.600611
$173$	−7.23889e16	−1.18666	−0.593330	−	0.804959i	$-0.702187\pi$
$173$	−7.23889e16	−1.18666	−0.593330	+	0.804959i	$0.702187\pi$
$174$	1.59597e16	0.250556
$175$	8.37845e16	1.26002
$176$	9.74827e15	0.140470
$177$	−1.72738e17	−2.38555
$178$	−8.36833e16	−1.10787
$179$	−1.13362e17	−1.43903	−0.719513	−	0.694479i	$-0.755635\pi$
$179$	−1.13362e17	−1.43903	−0.719513	+	0.694479i	$0.755635\pi$
$180$	5.14143e16	0.625951
$181$	1.82181e16	0.212772	0.106386	−	0.994325i	$-0.466072\pi$
$181$	1.82181e16	0.212772	0.106386	+	0.994325i	$0.466072\pi$
$182$	−6.79330e16	−0.761282
$183$	3.05880e17	3.28979
$184$	1.12055e17	1.15690
$185$	2.69073e16	0.266736
$186$	5.20705e15	0.0495729
$187$	7.58537e16	0.693689
$188$	2.14245e15	0.0188246
$189$	−6.47289e17	−5.46556
$190$	4.29131e16	0.348287
$191$	8.74105e16	0.682046	0.341023	−	0.940055i	$-0.389227\pi$
$191$	8.74105e16	0.682046	0.341023	+	0.940055i	$0.389227\pi$
$192$	2.16744e17	1.62625
$193$	1.81936e17	1.31292	0.656462	−	0.754359i	$-0.272052\pi$
$193$	1.81936e17	1.31292	0.656462	+	0.754359i	$0.272052\pi$
$194$	5.02522e16	0.348853
$195$	−8.90682e16	−0.594926
$196$	−1.10743e17	−0.711860
$197$	1.47983e16	0.0915620	0.0457810	−	0.998952i	$-0.485422\pi$
$197$	1.47983e16	0.0915620	0.0457810	+	0.998952i	$0.485422\pi$
$198$	−2.26654e17	−1.35013
$199$	9.16868e16	0.525907	0.262953	−	0.964809i	$-0.415303\pi$
$199$	9.16868e16	0.525907	0.262953	+	0.964809i	$0.415303\pi$
$200$	1.56148e17	0.862602
$201$	−1.51911e17	−0.808386
$202$	1.80303e17	0.924415
$203$	−5.77395e16	−0.285268
$204$	2.14922e17	1.02342
$205$	−1.20812e17	−0.554569
$206$	2.28220e16	0.101006
$207$	−7.26913e17	−3.10245
$208$	−3.53238e16	−0.145409
$209$	2.07791e17	0.825145
$210$	2.29392e17	0.878888
$211$	−2.63010e17	−0.972419	−0.486209	−	0.873842i	$-0.661621\pi$
$211$	−2.63010e17	−0.972419	−0.486209	+	0.873842i	$0.661621\pi$
$212$	4.51808e16	0.161226
$213$	5.65718e17	1.94874
$214$	−2.60332e17	−0.865813
$215$	1.51492e17	0.486520
$216$	−1.20634e18	−3.74168
$217$	−1.88382e16	−0.0564407
$218$	3.25937e17	0.943432
$219$	6.50199e17	1.81851
$220$	−5.69439e16	−0.153914
$221$	−2.74863e17	−0.718083
$222$	−3.36089e17	−0.848803
$223$	−4.48964e17	−1.09629	−0.548144	−	0.836384i	$-0.684666\pi$
$223$	−4.48964e17	−1.09629	−0.548144	+	0.836384i	$0.684666\pi$
$224$	−5.93244e17	−1.40079
$225$	−1.01295e18	−2.31322
$226$	−2.33904e17	−0.516684
$227$	−1.33489e17	−0.285267	−0.142633	−	0.989776i	$-0.545557\pi$
$227$	−1.33489e17	−0.285267	−0.142633	+	0.989776i	$0.545557\pi$
$228$	5.88751e17	1.21736
$229$	−2.36539e17	−0.473301	−0.236651	−	0.971595i	$-0.576050\pi$
$229$	−2.36539e17	−0.473301	−0.236651	+	0.971595i	$0.576050\pi$
$230$	1.66268e17	0.321995
$231$	1.11075e18	2.08222
$232$	−1.07608e17	−0.195292
$233$	9.96690e16	0.175142	0.0875711	−	0.996158i	$-0.472089\pi$
$233$	9.96690e16	0.175142	0.0875711	+	0.996158i	$0.472089\pi$
$234$	8.21303e17	1.39761
$235$	9.25216e15	0.0152487
$236$	4.00177e17	0.638870
$237$	−1.30858e18	−2.02390
$238$	7.07901e17	1.06083
$239$	−6.19151e17	−0.899109	−0.449555	−	0.893253i	$-0.648417\pi$
$239$	−6.19151e17	−0.899109	−0.449555	+	0.893253i	$0.648417\pi$
$240$	1.19279e17	0.167873
$241$	3.85592e17	0.526017	0.263009	−	0.964793i	$-0.415285\pi$
$241$	3.85592e17	0.526017	0.263009	+	0.964793i	$0.415285\pi$
$242$	−2.70971e17	−0.358350
$243$	3.52648e18	4.52163
$244$	−7.08624e17	−0.881033
$245$	−4.78242e17	−0.576637
$246$	1.50902e18	1.76474
$247$	−7.52952e17	−0.854161
$248$	−3.51085e16	−0.0386388
$249$	1.45756e18	1.55644
$250$	5.14171e17	0.532792
$251$	−1.20264e18	−1.20944	−0.604719	−	0.796439i	$-0.706715\pi$
$251$	−1.20264e18	−1.20944	−0.604719	+	0.796439i	$0.706715\pi$
$252$	2.32336e18	2.26784
$253$	8.05092e17	0.762854
$254$	−9.36920e17	−0.861885
$255$	9.28141e17	0.829015
$256$	−1.22786e18	−1.06500
$257$	6.57725e17	0.554046	0.277023	−	0.960863i	$-0.410652\pi$
$257$	6.57725e17	0.554046	0.277023	+	0.960863i	$0.410652\pi$
$258$	−1.89223e18	−1.54820
$259$	1.21592e18	0.966396
$260$	2.06342e17	0.159326
$261$	6.98064e17	0.523711
$262$	−7.33129e17	−0.534466
$263$	−1.15286e18	−0.816787	−0.408394	−	0.912806i	$-0.633911\pi$
$263$	−1.15286e18	−0.816787	−0.408394	+	0.912806i	$0.633911\pi$
$264$	2.07008e18	1.42547
$265$	1.95113e17	0.130600
$266$	1.93920e18	1.26186
$267$	−4.95808e18	−3.13675
$268$	3.51928e17	0.216492
$269$	−1.70824e18	−1.02189	−0.510947	−	0.859612i	$-0.670705\pi$
$269$	−1.70824e18	−1.02189	−0.510947	+	0.859612i	$0.670705\pi$
$270$	−1.78997e18	−1.04140
$271$	1.69089e18	0.956857	0.478428	−	0.878127i	$-0.341207\pi$
$271$	1.69089e18	0.956857	0.478428	+	0.878127i	$0.341207\pi$
$272$	3.68094e17	0.202624
$273$	−4.02491e18	−2.15544
$274$	2.23758e17	0.116587
$275$	1.12189e18	0.568793
$276$	2.28113e18	1.12546
$277$	−2.74409e18	−1.31765	−0.658825	−	0.752296i	$-0.728946\pi$
$277$	−2.74409e18	−1.31765	−0.658825	+	0.752296i	$0.728946\pi$
$278$	−2.60494e18	−1.21748
$279$	2.27752e17	0.103617
$280$	−1.54667e18	−0.685036
$281$	−4.78863e17	−0.206497	−0.103249	−	0.994656i	$-0.532924\pi$
$281$	−4.78863e17	−0.206497	−0.103249	+	0.994656i	$0.532924\pi$
$282$	−1.15565e17	−0.0485243
$283$	3.71975e18	1.52095	0.760477	−	0.649365i	$-0.224965\pi$
$283$	3.71975e18	1.52095	0.760477	+	0.649365i	$0.224965\pi$
$284$	−1.31058e18	−0.521887
$285$	2.54252e18	0.986116
$286$	−9.09635e17	−0.343654
$287$	−5.45938e18	−2.00923
$288$	7.17226e18	2.57165
$289$	1.80500e15	0.000630586 0
$290$	−1.59669e17	−0.0543546
$291$	2.97735e18	0.987717
$292$	−1.50630e18	−0.487011
$293$	−4.42671e18	−1.39500	−0.697500	−	0.716585i	$-0.745704\pi$
$293$	−4.42671e18	−1.39500	−0.697500	+	0.716585i	$0.745704\pi$
$294$	5.97355e18	1.83496
$295$	1.72817e18	0.517512
$296$	2.26608e18	0.661587
$297$	−8.66730e18	−2.46724
$298$	−1.51287e18	−0.419932
$299$	−2.91733e18	−0.789680
$300$	3.17874e18	0.839160
$301$	6.84578e18	1.76268
$302$	1.45244e18	0.364793
$303$	1.06826e19	2.61732
$304$	1.00834e18	0.241022
$305$	−3.06019e18	−0.713674
$306$	−8.55844e18	−1.94753
$307$	−5.04904e18	−1.12117	−0.560584	−	0.828097i	$-0.689423\pi$
$307$	−5.04904e18	−1.12117	−0.560584	+	0.828097i	$0.689423\pi$
$308$	−2.57324e18	−0.557635
$309$	1.35216e18	0.285983
$310$	−5.20941e16	−0.0107541
$311$	−3.07714e18	−0.620074	−0.310037	−	0.950724i	$-0.600341\pi$
$311$	−3.07714e18	−0.620074	−0.310037	+	0.950724i	$0.600341\pi$
$312$	−7.50114e18	−1.47560
$313$	−6.66073e18	−1.27920	−0.639601	−	0.768707i	$-0.720900\pi$
$313$	−6.66073e18	−1.27920	−0.639601	+	0.768707i	$0.720900\pi$
$314$	1.32881e18	0.249168
$315$	1.00334e19	1.83705
$316$	3.03155e18	0.542016
$317$	7.51479e18	1.31212	0.656058	−	0.754710i	$-0.272223\pi$
$317$	7.51479e18	1.31212	0.656058	+	0.754710i	$0.272223\pi$
$318$	−2.43709e18	−0.415593
$319$	−7.73141e17	−0.128774
$320$	−2.16843e18	−0.352793
$321$	−1.54242e19	−2.45140
$322$	7.51348e18	1.16660
$323$	7.84618e18	1.19025
$324$	−1.45980e19	−2.16374
$325$	−4.06527e18	−0.588795
$326$	6.29304e18	0.890693
$327$	1.93112e19	2.67117
$328$	−1.01745e19	−1.37550
$329$	4.18096e17	0.0552468
$330$	3.07160e18	0.396743
$331$	−8.46742e18	−1.06916	−0.534578	−	0.845119i	$-0.679529\pi$
$331$	−8.46742e18	−1.06916	−0.534578	+	0.845119i	$0.679529\pi$
$332$	−3.37669e18	−0.416827
$333$	−1.47003e19	−1.77417
$334$	6.72922e18	0.794084
$335$	1.51980e18	0.175368
$336$	5.39012e18	0.608210
$337$	−4.23618e17	−0.0467466	−0.0233733	−	0.999727i	$-0.507441\pi$
$337$	−4.23618e17	−0.0467466	−0.0233733	+	0.999727i	$0.507441\pi$
$338$	−3.10020e18	−0.334591
$339$	−1.38584e19	−1.46290
$340$	−2.15020e18	−0.222017
$341$	−2.52247e17	−0.0254782
$342$	−2.34447e19	−2.31659
$343$	−5.72009e18	−0.552964
$344$	1.27583e19	1.20672
$345$	9.85105e18	0.911674
$346$	−9.04594e18	−0.819187
$347$	9.28709e18	0.823017	0.411508	−	0.911406i	$-0.365002\pi$
$347$	9.28709e18	0.823017	0.411508	+	0.911406i	$0.365002\pi$
$348$	−2.19060e18	−0.189985
$349$	1.08945e19	0.924738	0.462369	−	0.886688i	$-0.347000\pi$
$349$	1.08945e19	0.924738	0.462369	+	0.886688i	$0.347000\pi$
$350$	1.04700e19	0.869831
$351$	3.14068e19	2.55400
$352$	−7.94363e18	−0.632338
$353$	1.58025e19	1.23145	0.615723	−	0.787963i	$-0.288864\pi$
$353$	1.58025e19	1.23145	0.615723	+	0.787963i	$0.288864\pi$
$354$	−2.15859e19	−1.64682
$355$	−5.65975e18	−0.422751
$356$	1.14863e19	0.840047
$357$	4.19418e19	3.00355
$358$	−1.41660e19	−0.993403
$359$	−9.77113e18	−0.671022	−0.335511	−	0.942036i	$-0.608909\pi$
$359$	−9.77113e18	−0.671022	−0.335511	+	0.942036i	$0.608909\pi$
$360$	1.86991e19	1.25763
$361$	6.31246e18	0.415810
$362$	2.27659e18	0.146883
$363$	−1.60545e19	−1.01461
$364$	9.32439e18	0.577245
$365$	−6.50494e18	−0.394500
$366$	3.82237e19	2.27104
$367$	1.27585e19	0.742683	0.371342	−	0.928496i	$-0.378898\pi$
$367$	1.27585e19	0.742683	0.371342	+	0.928496i	$0.378898\pi$
$368$	3.90685e18	0.222827
$369$	6.60033e19	3.68866
$370$	3.36242e18	0.184136
$371$	8.81699e18	0.473169
$372$	−7.14712e17	−0.0375888
$373$	−2.90831e19	−1.49908	−0.749540	−	0.661959i	$-0.769725\pi$
$373$	−2.90831e19	−1.49908	−0.749540	+	0.661959i	$0.769725\pi$
$374$	9.47890e18	0.478874
$375$	3.04637e19	1.50851
$376$	7.79198e17	0.0378215
$377$	2.80155e18	0.133303
$378$	−8.08872e19	−3.77304
$379$	−2.80652e19	−1.28343	−0.641717	−	0.766942i	$-0.721778\pi$
$379$	−2.80652e19	−1.28343	−0.641717	+	0.766942i	$0.721778\pi$
$380$	−5.89019e18	−0.264090
$381$	−5.55108e19	−2.44028
$382$	1.09231e19	0.470836
$383$	1.35319e19	0.571964	0.285982	−	0.958235i	$-0.407680\pi$
$383$	1.35319e19	0.571964	0.285982	+	0.958235i	$0.407680\pi$
$384$	−1.59134e19	−0.659597
$385$	−1.11125e19	−0.451708
$386$	2.27353e19	0.906350
$387$	−8.27648e19	−3.23604
$388$	−6.89754e18	−0.264519
$389$	−1.64341e19	−0.618191	−0.309096	−	0.951031i	$-0.600026\pi$
$389$	−1.64341e19	−0.618191	−0.309096	+	0.951031i	$0.600026\pi$
$390$	−1.11302e19	−0.410695
$391$	3.04002e19	1.10040
$392$	−4.02766e19	−1.43023
$393$	−4.34365e19	−1.51325
$394$	1.84924e18	0.0632079
$395$	1.30918e19	0.439056
$396$	3.11102e19	1.02374
$397$	5.50369e19	1.77715	0.888577	−	0.458728i	$-0.151695\pi$
$397$	5.50369e19	1.77715	0.888577	+	0.458728i	$0.151695\pi$
$398$	1.14575e19	0.363049
$399$	1.14894e20	3.57274
$400$	5.44417e18	0.166143
$401$	−2.99573e19	−0.897263	−0.448632	−	0.893717i	$-0.648088\pi$
$401$	−2.99573e19	−0.897263	−0.448632	+	0.893717i	$0.648088\pi$
$402$	−1.89833e19	−0.558053
$403$	9.14042e17	0.0263741
$404$	−2.47481e19	−0.700941
$405$	−6.30413e19	−1.75272
$406$	−7.21530e18	−0.196929
$407$	1.62813e19	0.436246
$408$	7.81661e19	2.05621
$409$	−2.98111e19	−0.769934	−0.384967	−	0.922930i	$-0.625787\pi$
$409$	−2.98111e19	−0.769934	−0.384967	+	0.922930i	$0.625787\pi$
$410$	−1.50970e19	−0.382836
$411$	1.32573e19	0.330096
$412$	−3.13251e18	−0.0765885
$413$	7.80942e19	1.87497
$414$	−9.08372e19	−2.14171
$415$	−1.45822e19	−0.337648
$416$	2.87845e19	0.654574
$417$	−1.54338e20	−3.44708
$418$	2.59662e19	0.569622
$419$	−1.64681e19	−0.354846	−0.177423	−	0.984135i	$-0.556776\pi$
$419$	−1.64681e19	−0.354846	−0.177423	+	0.984135i	$0.556776\pi$
$420$	−3.14860e19	−0.666420
$421$	−5.10346e19	−1.06108	−0.530541	−	0.847659i	$-0.678011\pi$
$421$	−5.10346e19	−1.06108	−0.530541	+	0.847659i	$0.678011\pi$
$422$	−3.28665e19	−0.671290
$423$	−5.05474e18	−0.101425
$424$	1.64320e19	0.323927
$425$	4.23624e19	0.820472
$426$	7.06938e19	1.34527
$427$	−1.38287e20	−2.58567
$428$	3.57328e19	0.656506
$429$	−5.38942e19	−0.972999
$430$	1.89309e19	0.335859
$431$	8.47274e19	1.47722	0.738609	−	0.674134i	$-0.235483\pi$
$431$	8.47274e19	1.47722	0.738609	+	0.674134i	$0.235483\pi$
$432$	−4.20597e19	−0.720672
$433$	1.71569e19	0.288922	0.144461	−	0.989511i	$-0.453855\pi$
$433$	1.71569e19	0.288922	0.144461	+	0.989511i	$0.453855\pi$
$434$	−2.35408e18	−0.0389627
$435$	−9.46011e18	−0.153896
$436$	−4.47377e19	−0.715360
$437$	8.32774e19	1.30893
$438$	8.12508e19	1.25537
$439$	−1.80827e19	−0.274650	−0.137325	−	0.990526i	$-0.543850\pi$
$439$	−1.80827e19	−0.274650	−0.137325	+	0.990526i	$0.543850\pi$
$440$	−2.07102e19	−0.309236
$441$	2.61279e20	3.83543
$442$	−3.43477e19	−0.495714
$443$	5.69884e19	0.808646	0.404323	−	0.914616i	$-0.367507\pi$
$443$	5.69884e19	0.808646	0.404323	+	0.914616i	$0.367507\pi$
$444$	4.61311e19	0.643608
$445$	4.96034e19	0.680473
$446$	−5.61039e19	−0.756800
$447$	−8.96346e19	−1.18897
$448$	−9.79892e19	−1.27818
$449$	2.53342e19	0.324982	0.162491	−	0.986710i	$-0.448047\pi$
$449$	2.53342e19	0.324982	0.162491	+	0.986710i	$0.448047\pi$
$450$	−1.26581e20	−1.59689
$451$	−7.31020e19	−0.906996
$452$	3.21054e19	0.391777
$453$	8.60544e19	1.03285
$454$	−1.66812e19	−0.196928
$455$	4.02674e19	0.467593
$456$	2.14126e20	2.44587
$457$	−1.96917e19	−0.221264	−0.110632	−	0.993861i	$-0.535288\pi$
$457$	−1.96917e19	−0.221264	−0.110632	+	0.993861i	$0.535288\pi$
$458$	−2.95587e19	−0.326734
$459$	−3.27277e20	−3.55893
$460$	−2.28217e19	−0.244154
$461$	1.30634e20	1.37499	0.687496	−	0.726189i	$-0.258710\pi$
$461$	1.30634e20	1.37499	0.687496	+	0.726189i	$0.258710\pi$
$462$	1.38803e20	1.43742
$463$	−1.37237e20	−1.39835	−0.699174	−	0.714952i	$-0.746449\pi$
$463$	−1.37237e20	−1.39835	−0.699174	+	0.714952i	$0.746449\pi$
$464$	−3.75181e18	−0.0376145
$465$	−3.08648e18	−0.0304485
$466$	1.24549e19	0.120906
$467$	9.46017e19	0.903696	0.451848	−	0.892095i	$-0.350765\pi$
$467$	9.46017e19	0.903696	0.451848	+	0.892095i	$0.350765\pi$
$468$	−1.12731e20	−1.05974
$469$	6.86783e19	0.635365
$470$	1.15618e18	0.0105267
$471$	7.87297e19	0.705476
$472$	1.45543e20	1.28359
$473$	9.16661e19	0.795702
$474$	−1.63524e20	−1.39716
$475$	1.16046e20	0.975954
$476$	−9.71654e19	−0.804377
$477$	−1.06596e20	−0.868670
$478$	−7.73710e19	−0.620682
$479$	1.16853e20	0.922837	0.461419	−	0.887182i	$-0.347341\pi$
$479$	1.16853e20	0.922837	0.461419	+	0.887182i	$0.347341\pi$
$480$	−9.71978e19	−0.755696
$481$	−5.89969e19	−0.451586
$482$	4.81847e19	0.363125
$483$	4.45160e20	3.30303
$484$	3.71930e19	0.271720
$485$	−2.97870e19	−0.214271
$486$	4.40680e20	3.12141
$487$	−1.55447e20	−1.08421	−0.542106	−	0.840310i	$-0.682373\pi$
$487$	−1.55447e20	−1.08421	−0.542106	+	0.840310i	$0.682373\pi$
$488$	−2.57723e20	−1.77013
$489$	3.72851e20	2.52185
$490$	−5.97626e19	−0.398070
$491$	−1.68541e20	−1.10559	−0.552796	−	0.833317i	$-0.686439\pi$
$491$	−1.68541e20	−1.10559	−0.552796	+	0.833317i	$0.686439\pi$
$492$	−2.07126e20	−1.33812
$493$	−2.91937e19	−0.185754
$494$	−9.40911e19	−0.589653
$495$	1.34349e20	0.829272
$496$	−1.22408e18	−0.00744210
$497$	−2.55759e20	−1.53164
$498$	1.82141e20	1.07446
$499$	−2.23472e20	−1.29858	−0.649292	−	0.760539i	$-0.724935\pi$
$499$	−2.23472e20	−1.29858	−0.649292	+	0.760539i	$0.724935\pi$
$500$	−7.05743e19	−0.403991
$501$	3.98694e20	2.24831
$502$	−1.50286e20	−0.834912
$503$	−6.74562e18	−0.0369200	−0.0184600	−	0.999830i	$-0.505876\pi$
$503$	−6.74562e18	−0.0369200	−0.0184600	+	0.999830i	$0.505876\pi$
$504$	8.44996e20	4.55644
$505$	−1.06875e20	−0.567792
$506$	1.00607e20	0.526621
$507$	−1.83681e20	−0.947337
$508$	1.28600e20	0.653528
$509$	−1.42487e20	−0.713494	−0.356747	−	0.934201i	$-0.616114\pi$
$509$	−1.42487e20	−0.713494	−0.356747	+	0.934201i	$0.616114\pi$
$510$	1.15983e20	0.572294
$511$	−2.93952e20	−1.42929
$512$	−8.30072e19	−0.397733
$513$	−8.96532e20	−4.23336
$514$	8.21913e19	0.382475
$515$	−1.35277e19	−0.0620399
$516$	2.59725e20	1.17393
$517$	5.59838e18	0.0249392
$518$	1.51944e20	0.667132
$519$	−5.35955e20	−2.31939
$520$	7.50455e19	0.320110
$521$	4.67374e19	0.196509	0.0982543	−	0.995161i	$-0.468674\pi$
$521$	4.67374e19	0.196509	0.0982543	+	0.995161i	$0.468674\pi$
$522$	8.72322e19	0.361533
$523$	−4.03766e20	−1.64955	−0.824777	−	0.565457i	$-0.808700\pi$
$523$	−4.03766e20	−1.64955	−0.824777	+	0.565457i	$0.808700\pi$
$524$	1.00628e20	0.405261
$525$	6.20327e20	2.46278
$526$	−1.44065e20	−0.563852
$527$	−9.52483e18	−0.0367517
$528$	7.21745e19	0.274555
$529$	5.60249e19	0.210118
$530$	2.43819e19	0.0901570
$531$	−9.44151e20	−3.44217
$532$	−2.66172e20	−0.956809
$533$	2.64892e20	0.938890
$534$	−6.19577e20	−2.16539
$535$	1.54312e20	0.531797
$536$	1.27994e20	0.434966
$537$	−8.39311e20	−2.81265
$538$	−2.13466e20	−0.705444
$539$	−2.89379e20	−0.943087
$540$	2.45689e20	0.789646
$541$	−8.71183e19	−0.276141	−0.138070	−	0.990422i	$-0.544090\pi$
$541$	−8.71183e19	−0.276141	−0.138070	+	0.990422i	$0.544090\pi$
$542$	2.11299e20	0.660547
$543$	1.34884e20	0.415874
$544$	−2.99951e20	−0.912133
$545$	−1.93200e20	−0.579472
$546$	−5.02965e20	−1.48796
$547$	5.02732e20	1.46701	0.733503	−	0.679686i	$-0.237884\pi$
$547$	5.02732e20	1.46701	0.733503	+	0.679686i	$0.237884\pi$
$548$	−3.07128e19	−0.0884025
$549$	1.67188e21	4.74692
$550$	1.40195e20	0.392655
$551$	−7.99725e19	−0.220955
$552$	8.29635e20	2.26123
$553$	5.91604e20	1.59072
$554$	−3.42910e20	−0.909613
$555$	1.99217e20	0.521350
$556$	3.57550e20	0.923157
$557$	−7.48375e19	−0.190636	−0.0953181	−	0.995447i	$-0.530387\pi$
$557$	−7.48375e19	−0.190636	−0.0953181	+	0.995447i	$0.530387\pi$
$558$	2.84606e19	0.0715300
$559$	−3.32161e20	−0.823683
$560$	−5.39256e19	−0.131943
$561$	5.61608e20	1.35585
$562$	−5.98402e19	−0.142551
$563$	3.72489e20	0.875589	0.437795	−	0.899075i	$-0.355760\pi$
$563$	3.72489e20	0.875589	0.437795	+	0.899075i	$0.355760\pi$
$564$	1.58623e19	0.0367937
$565$	1.38647e20	0.317356
$566$	4.64832e20	1.04996
$567$	−2.84878e21	−6.35018
$568$	−4.76652e20	−1.04855
$569$	−2.72339e20	−0.591246	−0.295623	−	0.955305i	$-0.595527\pi$
$569$	−2.72339e20	−0.591246	−0.295623	+	0.955305i	$0.595527\pi$
$570$	3.17721e20	0.680745
$571$	1.79049e20	0.378618	0.189309	−	0.981918i	$-0.439375\pi$
$571$	1.79049e20	0.378618	0.189309	+	0.981918i	$0.439375\pi$
$572$	1.24855e20	0.260577
$573$	6.47173e20	1.33309
$574$	−6.82221e20	−1.38703
$575$	4.49624e20	0.902279
$576$	1.18468e21	2.34656
$577$	−7.41937e20	−1.45060	−0.725301	−	0.688432i	$-0.758299\pi$
$577$	−7.41937e20	−1.45060	−0.725301	+	0.688432i	$0.758299\pi$
$578$	2.25559e17	0.000435312 0
$579$	1.34702e21	2.56618
$580$	2.19160e19	0.0412145
$581$	−6.58958e20	−1.22331
$582$	3.72059e20	0.681850
$583$	1.18061e20	0.213595
$584$	−5.47832e20	−0.978479
$585$	−4.86828e20	−0.858434
$586$	−5.53176e20	−0.963010
$587$	2.74742e20	0.472214	0.236107	−	0.971727i	$-0.424128\pi$
$587$	2.74742e20	0.472214	0.236107	+	0.971727i	$0.424128\pi$
$588$	−8.19921e20	−1.39137
$589$	−2.60920e19	−0.0437163
$590$	2.15957e20	0.357254
$591$	1.09564e20	0.178963
$592$	7.90080e19	0.127426
$593$	2.60336e20	0.414596	0.207298	−	0.978278i	$-0.433533\pi$
$593$	2.60336e20	0.414596	0.207298	+	0.978278i	$0.433533\pi$
$594$	−1.08309e21	−1.70321
$595$	−4.19609e20	−0.651579
$596$	2.07654e20	0.318415
$597$	6.78834e20	1.02791
$598$	−3.64558e20	−0.545140
$599$	1.51892e20	0.224303	0.112152	−	0.993691i	$-0.464226\pi$
$599$	1.51892e20	0.224303	0.112152	+	0.993691i	$0.464226\pi$
$600$	1.15609e21	1.68600
$601$	1.45498e20	0.209555	0.104778	−	0.994496i	$-0.466587\pi$
$601$	1.45498e20	0.209555	0.104778	+	0.994496i	$0.466587\pi$
$602$	8.55469e20	1.21683
$603$	−8.30314e20	−1.16644
$604$	−1.99360e20	−0.276605
$605$	1.60618e20	0.220105
$606$	1.33493e21	1.80682
$607$	1.37589e21	1.83936	0.919681	−	0.392666i	$-0.128447\pi$
$607$	1.37589e21	1.83936	0.919681	+	0.392666i	$0.128447\pi$
$608$	−8.21676e20	−1.08499
$609$	−4.27493e20	−0.557570
$610$	−3.82411e20	−0.492670
$611$	−2.02863e19	−0.0258162
$612$	1.17472e21	1.47672
$613$	−5.35872e20	−0.665438	−0.332719	−	0.943026i	$-0.607966\pi$
$613$	−5.35872e20	−0.665438	−0.332719	+	0.943026i	$0.607966\pi$
$614$	−6.30943e20	−0.773976
$615$	−8.94471e20	−1.08393
$616$	−9.35875e20	−1.12037
$617$	8.80815e20	1.04171	0.520854	−	0.853646i	$-0.325614\pi$
$617$	8.80815e20	1.04171	0.520854	+	0.853646i	$0.325614\pi$
$618$	1.68970e20	0.197422
$619$	−2.22539e19	−0.0256877	−0.0128439	−	0.999918i	$-0.504088\pi$
$619$	−2.22539e19	−0.0256877	−0.0128439	+	0.999918i	$0.504088\pi$
$620$	7.15036e18	0.00815437
$621$	−3.47363e21	−3.91378
$622$	−3.84528e20	−0.428056
$623$	2.24153e21	2.46538
$624$	−2.61531e20	−0.284210
$625$	4.59108e20	0.492964
$626$	−8.32344e20	−0.883071
$627$	1.53845e21	1.61279
$628$	−1.82391e20	−0.188932
$629$	6.14781e20	0.629275
$630$	1.25381e21	1.26817
$631$	2.87276e20	0.287130	0.143565	−	0.989641i	$-0.454143\pi$
$631$	2.87276e20	0.287130	0.143565	+	0.989641i	$0.454143\pi$
$632$	1.10256e21	1.08899
$633$	−1.94728e21	−1.90064
$634$	9.39071e20	0.905793
$635$	5.55360e20	0.529385
$636$	3.34511e20	0.315125
$637$	1.04859e21	0.976251
$638$	−9.66141e19	−0.0888966
$639$	3.09210e21	2.81188
$640$	1.59206e20	0.143090
$641$	−3.94279e20	−0.350243	−0.175121	−	0.984547i	$-0.556032\pi$
$641$	−3.94279e20	−0.350243	−0.175121	+	0.984547i	$0.556032\pi$
$642$	−1.92745e21	−1.69228
$643$	2.03022e21	1.76182	0.880909	−	0.473286i	$-0.156932\pi$
$643$	2.03022e21	1.76182	0.880909	+	0.473286i	$0.156932\pi$
$644$	−1.03129e21	−0.884579
$645$	1.12162e21	0.950929
$646$	9.80482e20	0.821667
$647$	2.11411e21	1.75124	0.875618	−	0.483005i	$-0.160455\pi$
$647$	2.11411e21	1.75124	0.875618	+	0.483005i	$0.160455\pi$
$648$	−5.30921e21	−4.34728
$649$	1.04569e21	0.846388
$650$	−5.08009e20	−0.406463
$651$	−1.39475e20	−0.110316
$652$	−8.63773e20	−0.675371
$653$	−1.25862e21	−0.972853	−0.486427	−	0.873721i	$-0.661700\pi$
$653$	−1.25862e21	−0.972853	−0.486427	+	0.873721i	$0.661700\pi$
$654$	2.41318e21	1.84399
$655$	4.34562e20	0.328278
$656$	−3.54741e20	−0.264931
$657$	3.55385e21	2.62397
$658$	5.22466e19	0.0381385
$659$	1.81186e21	1.30762	0.653812	−	0.756657i	$-0.273169\pi$
$659$	1.81186e21	1.30762	0.653812	+	0.756657i	$0.273169\pi$
$660$	−4.21603e20	−0.300832
$661$	1.62492e21	1.14636	0.573179	−	0.819430i	$-0.305710\pi$
$661$	1.62492e21	1.14636	0.573179	+	0.819430i	$0.305710\pi$
$662$	−1.05811e21	−0.738070
$663$	−2.03504e21	−1.40353
$664$	−1.22809e21	−0.837468
$665$	−1.14946e21	−0.775055
$666$	−1.83699e21	−1.22476
$667$	−3.09855e20	−0.204275
$668$	−9.23643e20	−0.602117
$669$	−3.32405e21	−2.14275
$670$	1.89919e20	0.121062
$671$	−1.85169e21	−1.16721
$672$	−4.39228e21	−2.73792
$673$	−1.22179e21	−0.753153	−0.376576	−	0.926386i	$-0.622899\pi$
$673$	−1.22179e21	−0.753153	−0.376576	+	0.926386i	$0.622899\pi$
$674$	−5.29366e19	−0.0322706
$675$	−4.84048e21	−2.91816
$676$	4.25528e20	0.253705
$677$	1.15831e20	0.0682983	0.0341491	−	0.999417i	$-0.489128\pi$
$677$	1.15831e20	0.0682983	0.0341491	+	0.999417i	$0.489128\pi$
$678$	−1.73179e21	−1.00989
$679$	−1.34605e21	−0.776313
$680$	−7.82016e20	−0.446066
$681$	−9.88329e20	−0.557568
$682$	−3.15216e19	−0.0175883
$683$	−7.30613e20	−0.403211	−0.201605	−	0.979467i	$-0.564616\pi$
$683$	−7.30613e20	−0.403211	−0.201605	+	0.979467i	$0.564616\pi$
$684$	3.21799e21	1.75656
$685$	−1.32633e20	−0.0716097
$686$	−7.14800e20	−0.381728
$687$	−1.75130e21	−0.925091
$688$	4.44826e20	0.232422
$689$	−4.27805e20	−0.221107
$690$	1.23102e21	0.629355
$691$	−2.26491e19	−0.0114542	−0.00572712	−	0.999984i	$-0.501823\pi$
$691$	−2.26491e19	−0.0114542	−0.00572712	+	0.999984i	$0.501823\pi$
$692$	1.24163e21	0.621151
$693$	6.07113e21	3.00449
$694$	1.16054e21	0.568153
$695$	1.54408e21	0.747796
$696$	−7.96711e20	−0.381708
$697$	−2.76032e21	−1.30832
$698$	1.36142e21	0.638374
$699$	7.37933e20	0.342324
$700$	−1.43709e21	−0.659553
$701$	1.15262e21	0.523360	0.261680	−	0.965155i	$-0.415724\pi$
$701$	1.15262e21	0.523360	0.261680	+	0.965155i	$0.415724\pi$
$702$	3.92469e21	1.76310
$703$	1.68411e21	0.748524
$704$	−1.31209e21	−0.576991
$705$	6.85014e19	0.0298044
$706$	1.97473e21	0.850104
$707$	−4.82956e21	−2.05713
$708$	2.96285e21	1.24870
$709$	−7.52853e20	−0.313952	−0.156976	−	0.987602i	$-0.550175\pi$
$709$	−7.52853e20	−0.313952	−0.156976	+	0.987602i	$0.550175\pi$
$710$	−7.07259e20	−0.291837
$711$	−7.15243e21	−2.92033
$712$	4.17749e21	1.68778
$713$	−1.01094e20	−0.0404161
$714$	5.24118e21	2.07344
$715$	5.39186e20	0.211078
$716$	1.94441e21	0.753251
$717$	−4.58409e21	−1.75736
$718$	−1.22103e21	−0.463226
$719$	−2.33917e21	−0.878203	−0.439101	−	0.898438i	$-0.644703\pi$
$719$	−2.33917e21	−0.878203	−0.439101	+	0.898438i	$0.644703\pi$
$720$	6.51955e20	0.242228
$721$	−6.11306e20	−0.224773
$722$	7.88824e20	0.287046
$723$	2.85486e21	1.02813
$724$	−3.12482e20	−0.111374
$725$	−4.31780e20	−0.152310
$726$	−2.00622e21	−0.700413
$727$	4.21845e20	0.145762	0.0728810	−	0.997341i	$-0.476781\pi$
$727$	4.21845e20	0.145762	0.0728810	+	0.997341i	$0.476781\pi$
$728$	3.39123e21	1.15977
$729$	1.38974e22	4.70410
$730$	−8.12877e20	−0.272335
$731$	3.46130e21	1.14778
$732$	−5.24653e21	−1.72202
$733$	2.03644e21	0.661594	0.330797	−	0.943702i	$-0.392682\pi$
$733$	2.03644e21	0.661594	0.330797	+	0.943702i	$0.392682\pi$
$734$	1.59434e21	0.512696
$735$	−3.54082e21	−1.12707
$736$	−3.18360e21	−1.00308
$737$	9.19614e20	0.286813
$738$	8.24798e21	2.54639
$739$	3.82485e21	1.16891	0.584455	−	0.811426i	$-0.301309\pi$
$739$	3.82485e21	1.16891	0.584455	+	0.811426i	$0.301309\pi$
$740$	−4.61520e20	−0.139622
$741$	−5.57473e21	−1.66950
$742$	1.10180e21	0.326642
$743$	−4.40823e21	−1.29374	−0.646871	−	0.762599i	$-0.723923\pi$
$743$	−4.40823e21	−1.29374	−0.646871	+	0.762599i	$0.723923\pi$
$744$	−2.59937e20	−0.0755216
$745$	8.96753e20	0.257929
$746$	−3.63431e21	−1.03486
$747$	7.96673e21	2.24582
$748$	−1.30106e21	−0.363108
$749$	6.97321e21	1.92672
$750$	3.80683e21	1.04137
$751$	1.94565e20	0.0526946	0.0263473	−	0.999653i	$-0.491612\pi$
$751$	1.94565e20	0.0526946	0.0263473	+	0.999653i	$0.491612\pi$
$752$	2.71671e19	0.00728468
$753$	−8.90417e21	−2.36391
$754$	3.50090e20	0.0920227
$755$	−8.60935e20	−0.224062
$756$	1.11025e22	2.86092
$757$	−4.64533e21	−1.18522	−0.592608	−	0.805491i	$-0.701902\pi$
$757$	−4.64533e21	−1.18522	−0.592608	+	0.805491i	$0.701902\pi$
$758$	−3.50711e21	−0.885993
$759$	5.96076e21	1.49104
$760$	−2.14223e21	−0.530596
$761$	6.60748e20	0.162051	0.0810253	−	0.996712i	$-0.474181\pi$
$761$	6.60748e20	0.162051	0.0810253	+	0.996712i	$0.474181\pi$
$762$	−6.93679e21	−1.68460
$763$	−8.73051e21	−2.09945
$764$	−1.49929e21	−0.357013
$765$	5.07302e21	1.19621
$766$	1.69099e21	0.394844
$767$	−3.78917e21	−0.876151
$768$	−9.09086e21	−2.08159
$769$	−1.13671e21	−0.257751	−0.128876	−	0.991661i	$-0.541137\pi$
$769$	−1.13671e21	−0.257751	−0.128876	+	0.991661i	$0.541137\pi$
$770$	−1.38866e21	−0.311828
$771$	4.86969e21	1.08291
$772$	−3.12061e21	−0.687243
$773$	5.84555e21	1.27491	0.637454	−	0.770488i	$-0.279987\pi$
$773$	5.84555e21	1.27491	0.637454	+	0.770488i	$0.279987\pi$
$774$	−1.03425e22	−2.23393
$775$	−1.40874e20	−0.0301348
$776$	−2.50860e21	−0.531458
$777$	9.00243e21	1.88887
$778$	−2.05365e21	−0.426756
$779$	−7.56155e21	−1.55625
$780$	1.52772e21	0.311411
$781$	−3.42465e21	−0.691407
$782$	3.79890e21	0.759639
$783$	3.33578e21	0.660669
$784$	−1.40427e21	−0.275473
$785$	−7.87655e20	−0.153043
$786$	−5.42796e21	−1.04464
$787$	8.42312e21	1.60569	0.802846	−	0.596186i	$-0.203318\pi$
$787$	8.42312e21	1.60569	0.802846	+	0.596186i	$0.203318\pi$
$788$	−2.53824e20	−0.0479276
$789$	−8.53559e21	−1.59645
$790$	1.63598e21	0.303093
$791$	6.26533e21	1.14979
$792$	1.13146e22	2.05685
$793$	6.70977e21	1.20826
$794$	6.87758e21	1.22682
$795$	1.44459e21	0.255264
$796$	−1.57263e21	−0.275283
$797$	9.00221e21	1.56103	0.780516	−	0.625136i	$-0.214957\pi$
$797$	9.00221e21	1.56103	0.780516	+	0.625136i	$0.214957\pi$
$798$	1.43575e22	2.46637
$799$	2.11394e20	0.0359743
$800$	−4.43632e21	−0.747908
$801$	−2.70999e22	−4.52609
$802$	−3.74356e21	−0.619408
$803$	−3.93607e21	−0.645202
$804$	2.60561e21	0.423145
$805$	−4.45362e21	−0.716546
$806$	1.14221e20	0.0182069
$807$	−1.26475e22	−1.99734
$808$	−9.00076e21	−1.40830
$809$	6.75565e21	1.04726	0.523628	−	0.851947i	$-0.324578\pi$
$809$	6.75565e21	1.04726	0.523628	+	0.851947i	$0.324578\pi$
$810$	−7.87783e21	−1.20995
$811$	7.14018e21	1.08656	0.543279	−	0.839552i	$-0.317183\pi$
$811$	7.14018e21	1.08656	0.543279	+	0.839552i	$0.317183\pi$
$812$	9.90362e20	0.149322
$813$	1.25191e22	1.87023
$814$	2.03456e21	0.301153
$815$	−3.73020e21	−0.547079
$816$	2.72530e21	0.396040
$817$	9.48179e21	1.36529
$818$	−3.72529e21	−0.531508
$819$	−2.19993e22	−3.11014
$820$	2.07220e21	0.290287
$821$	2.62911e20	0.0364952	0.0182476	−	0.999833i	$-0.494191\pi$
$821$	2.62911e20	0.0364952	0.0182476	+	0.999833i	$0.494191\pi$
$822$	1.65667e21	0.227875
$823$	2.32414e21	0.316784	0.158392	−	0.987376i	$-0.449369\pi$
$823$	2.32414e21	0.316784	0.158392	+	0.987376i	$0.449369\pi$
$824$	−1.13928e21	−0.153878
$825$	8.30627e21	1.11174
$826$	9.75889e21	1.29434
$827$	7.56471e21	0.994263	0.497131	−	0.867675i	$-0.334387\pi$
$827$	7.56471e21	0.994263	0.497131	+	0.867675i	$0.334387\pi$
$828$	1.24682e22	1.62396
$829$	−3.26830e21	−0.421854	−0.210927	−	0.977502i	$-0.567648\pi$
$829$	−3.26830e21	−0.421854	−0.210927	+	0.977502i	$0.567648\pi$
$830$	−1.82224e21	−0.233088
$831$	−2.03168e22	−2.57541
$832$	4.75449e21	0.597281
$833$	−1.09269e22	−1.36038
$834$	−1.92865e22	−2.37962
$835$	−3.98875e21	−0.487740
$836$	−3.56409e21	−0.431918
$837$	1.08834e21	0.130714
$838$	−2.05791e21	−0.244960
$839$	3.53277e21	0.416774	0.208387	−	0.978047i	$-0.433179\pi$
$839$	3.53277e21	0.416774	0.208387	+	0.978047i	$0.433179\pi$
$840$	−1.14513e22	−1.33894
$841$	2.97558e20	0.0344828
$842$	−6.37743e21	−0.732496
$843$	−3.54542e21	−0.403609
$844$	4.51121e21	0.509008
$845$	1.83764e21	0.205511
$846$	−6.31656e20	−0.0700169
$847$	7.25818e21	0.797448
$848$	5.72912e20	0.0623906
$849$	2.75404e22	2.97278
$850$	5.29374e21	0.566396
$851$	6.52513e21	0.692018
$852$	−9.70333e21	−1.02006
$853$	1.25334e22	1.30602	0.653009	−	0.757350i	$-0.273506\pi$
$853$	1.25334e22	1.30602	0.653009	+	0.757350i	$0.273506\pi$
$854$	−1.72808e22	−1.78496
$855$	1.38969e22	1.42289
$856$	1.29958e22	1.31902
$857$	−1.32650e22	−1.33460	−0.667301	−	0.744788i	$-0.732550\pi$
$857$	−1.32650e22	−1.33460	−0.667301	+	0.744788i	$0.732550\pi$
$858$	−6.73478e21	−0.671690
$859$	−1.84238e22	−1.82151	−0.910754	−	0.412949i	$-0.864499\pi$
$859$	−1.84238e22	−1.82151	−0.910754	+	0.412949i	$0.864499\pi$
$860$	−2.59843e21	−0.254667
$861$	−4.04203e22	−3.92714
$862$	1.05878e22	1.01977
$863$	−4.79838e21	−0.458157	−0.229078	−	0.973408i	$-0.573571\pi$
$863$	−4.79838e21	−0.458157	−0.229078	+	0.973408i	$0.573571\pi$
$864$	3.42734e22	3.24417
$865$	5.36199e21	0.503159
$866$	2.14398e21	0.199451
$867$	1.33639e19	0.00123251
$868$	3.23118e20	0.0295436
$869$	7.92168e21	0.718073
$870$	−1.18216e21	−0.106239
$871$	−3.33231e21	−0.296899
$872$	−1.62709e22	−1.43727
$873$	1.62736e22	1.42520
$874$	1.04066e22	0.903593
$875$	−1.37725e22	−1.18564
$876$	−1.11524e22	−0.951889
$877$	−6.04658e21	−0.511697	−0.255848	−	0.966717i	$-0.582355\pi$
$877$	−6.04658e21	−0.511697	−0.255848	+	0.966717i	$0.582355\pi$
$878$	−2.25967e21	−0.189599
$879$	−3.27746e22	−2.72660
$880$	−7.22073e20	−0.0595609
$881$	−1.41511e22	−1.15737	−0.578684	−	0.815552i	$-0.696434\pi$
$881$	−1.41511e22	−1.15737	−0.578684	+	0.815552i	$0.696434\pi$
$882$	3.26502e22	2.64771
$883$	−1.29031e22	−1.03750	−0.518752	−	0.854925i	$-0.673603\pi$
$883$	−1.29031e22	−1.03750	−0.518752	+	0.854925i	$0.673603\pi$
$884$	4.71452e21	0.375877
$885$	1.27950e22	1.01150
$886$	7.12144e21	0.558232
$887$	1.62231e22	1.26098	0.630488	−	0.776199i	$-0.282855\pi$
$887$	1.62231e22	1.26098	0.630488	+	0.776199i	$0.282855\pi$
$888$	1.67776e22	1.29311
$889$	2.50962e22	1.91798
$890$	6.19859e21	0.469751
$891$	−3.81456e22	−2.86656
$892$	7.70074e21	0.573847
$893$	5.79087e20	0.0427915
$894$	−1.12010e22	−0.820779
$895$	8.39692e21	0.610165
$896$	7.19438e21	0.518422
$897$	−2.15994e22	−1.54347
$898$	3.16583e21	0.224344
$899$	9.70822e19	0.00682247
$900$	1.73743e22	1.21085
$901$	4.45797e21	0.308107
$902$	−9.13505e21	−0.626126
$903$	5.06850e22	3.44525
$904$	1.16766e22	0.787140
$905$	−1.34945e21	−0.0902180
$906$	1.07536e22	0.713006
$907$	−1.62118e22	−1.06605	−0.533025	−	0.846100i	$-0.678945\pi$
$907$	−1.62118e22	−1.06605	−0.533025	+	0.846100i	$0.678945\pi$
$908$	2.28963e21	0.149321
$909$	5.83889e22	3.77660
$910$	5.03193e21	0.322793
$911$	1.21096e21	0.0770443	0.0385222	−	0.999258i	$-0.487735\pi$
$911$	1.21096e21	0.0770443	0.0385222	+	0.999258i	$0.487735\pi$
$912$	7.46561e21	0.471090
$913$	−8.82356e21	−0.552221
$914$	−2.46073e21	−0.152745
$915$	−2.26571e22	−1.39491
$916$	4.05718e21	0.247747
$917$	1.96375e22	1.18937
$918$	−4.08975e22	−2.45684
$919$	2.40106e22	1.43066	0.715330	−	0.698787i	$-0.246277\pi$
$919$	2.40106e22	1.43066	0.715330	+	0.698787i	$0.246277\pi$
$920$	−8.30012e21	−0.490541
$921$	−3.73822e22	−2.19138
$922$	1.63244e22	0.949197
$923$	1.24096e22	0.715720
$924$	−1.90519e22	−1.08993
$925$	9.09271e21	0.515977
$926$	−1.71496e22	−0.965321
$927$	7.39063e21	0.412651
$928$	3.05726e21	0.169326
$929$	1.12497e22	0.618047	0.309024	−	0.951054i	$-0.399998\pi$
$929$	1.12497e22	0.618047	0.309024	+	0.951054i	$0.399998\pi$
$930$	−3.85696e20	−0.0210195
$931$	−2.99329e22	−1.61818
$932$	−1.70955e21	−0.0916773
$933$	−2.27826e22	−1.21197
$934$	1.18217e22	0.623848
$935$	−5.61863e21	−0.294133
$936$	−4.09997e22	−2.12918
$937$	1.00644e22	0.518491	0.259245	−	0.965812i	$-0.416526\pi$
$937$	1.00644e22	0.518491	0.259245	+	0.965812i	$0.416526\pi$
$938$	8.58225e21	0.438611
$939$	−4.93149e22	−2.50026
$940$	−1.58695e20	−0.00798188
$941$	2.61107e22	1.30286	0.651428	−	0.758710i	$-0.274170\pi$
$941$	2.61107e22	1.30286	0.651428	+	0.758710i	$0.274170\pi$
$942$	9.83831e21	0.487011
$943$	−2.92974e22	−1.43877
$944$	5.07442e21	0.247227
$945$	4.79459e22	2.31746
$946$	1.14549e22	0.549296
$947$	−2.93691e22	−1.39722	−0.698611	−	0.715501i	$-0.746198\pi$
$947$	−2.93691e22	−1.39722	−0.698611	+	0.715501i	$0.746198\pi$
$948$	2.24451e22	1.05940
$949$	1.42627e22	0.667891
$950$	1.45015e22	0.673730
$951$	5.56382e22	2.56460
$952$	−3.53386e22	−1.61611
$953$	−5.59594e21	−0.253908	−0.126954	−	0.991909i	$-0.540520\pi$
$953$	−5.59594e21	−0.253908	−0.126954	+	0.991909i	$0.540520\pi$
$954$	−1.33206e22	−0.599669
$955$	−6.47466e21	−0.289196
$956$	1.06198e22	0.470634
$957$	−5.72421e21	−0.251696
$958$	1.46024e22	0.637062
$959$	−5.99356e21	−0.259445
$960$	−1.60547e22	−0.689552
$961$	−2.34336e22	−0.998650
$962$	−7.37243e21	−0.311744
$963$	−8.43054e22	−3.53719
$964$	−6.61377e21	−0.275341
$965$	−1.34764e22	−0.556696
$966$	5.56285e22	2.28018
$967$	−4.02743e22	−1.63806	−0.819029	−	0.573752i	$-0.805488\pi$
$967$	−4.02743e22	−1.63806	−0.819029	+	0.573752i	$0.805488\pi$
$968$	1.35269e22	0.545926
$969$	5.80918e22	2.32641
$970$	−3.72227e21	−0.147918
$971$	1.43089e22	0.564239	0.282120	−	0.959379i	$-0.408963\pi$
$971$	1.43089e22	0.564239	0.282120	+	0.959379i	$0.408963\pi$
$972$	−6.04871e22	−2.36682
$973$	6.97755e22	2.70930
$974$	−1.94251e22	−0.748464
$975$	−3.00986e22	−1.15083
$976$	−8.98565e21	−0.340938
$977$	−2.12035e22	−0.798359	−0.399180	−	0.916873i	$-0.630705\pi$
$977$	−2.12035e22	−0.798359	−0.399180	+	0.916873i	$0.630705\pi$
$978$	4.65926e22	1.74091
$979$	3.00144e22	1.11291
$980$	8.20293e21	0.301838
$981$	1.05551e23	3.85429
$982$	−2.10614e22	−0.763223
$983$	−1.07221e22	−0.385594	−0.192797	−	0.981239i	$-0.561756\pi$
$983$	−1.07221e22	−0.385594	−0.192797	+	0.981239i	$0.561756\pi$
$984$	−7.53305e22	−2.68849
$985$	−1.09614e21	−0.0388234
$986$	−3.64814e21	−0.128231
$987$	3.09551e21	0.107983
$988$	1.29148e22	0.447106
$989$	3.67374e22	1.26222
$990$	1.67887e22	0.572471
$991$	−9.69936e21	−0.328239	−0.164120	−	0.986440i	$-0.552478\pi$
$991$	−9.69936e21	−0.328239	−0.164120	+	0.986440i	$0.552478\pi$
$992$	9.97470e20	0.0335013
$993$	−6.26913e22	−2.08972
$994$	−3.19604e22	−1.05734
$995$	−6.79142e21	−0.222991
$996$	−2.50005e22	−0.814710
$997$	3.80096e22	1.22936	0.614680	−	0.788776i	$-0.289285\pi$
$997$	3.80096e22	1.22936	0.614680	+	0.788776i	$0.289285\pi$
$998$	−2.79258e22	−0.896451
$999$	−7.02470e22	−2.23814

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.16.a.a.1.11	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.16.a.a.1.11	✓	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q+124.963 q^{2} +7403.83 q^{3} -17152.2 q^{4} -74071.9 q^{5} +925205. q^{6} -3.34724e6 q^{7} -6.23818e6 q^{8} +4.04678e7 q^{9} +O(q^{10})\)	\(q+124.963 q^{2} +7403.83 q^{3} -17152.2 q^{4} -74071.9 q^{5} +925205. q^{6} -3.34724e6 q^{7} -6.23818e6 q^{8} +4.04678e7 q^{9} -9.25625e6 q^{10} -4.48201e7 q^{11} -1.26992e8 q^{12} +1.62410e8 q^{13} -4.18281e8 q^{14} -5.48416e8 q^{15} -2.17498e8 q^{16} -1.69240e9 q^{17} +5.05698e9 q^{18} -4.63612e9 q^{19} +1.27050e9 q^{20} -2.47824e10 q^{21} -5.60086e9 q^{22} -1.79627e10 q^{23} -4.61865e10 q^{24} -2.50309e10 q^{25} +2.02952e10 q^{26} +1.93380e11 q^{27} +5.74127e10 q^{28} +1.72499e10 q^{29} -6.85317e10 q^{30} +5.62799e9 q^{31} +1.77234e11 q^{32} -3.31840e11 q^{33} -2.11488e11 q^{34} +2.47937e11 q^{35} -6.94113e11 q^{36} -3.63259e11 q^{37} -5.79343e11 q^{38} +1.20246e12 q^{39} +4.62074e11 q^{40} +1.63101e12 q^{41} -3.09688e12 q^{42} -2.04520e12 q^{43} +7.68765e11 q^{44} -2.99753e12 q^{45} -2.24468e12 q^{46} -1.24908e11 q^{47} -1.61032e12 q^{48} +6.45646e12 q^{49} -3.12794e12 q^{50} -1.25303e13 q^{51} -2.78569e12 q^{52} -2.63411e12 q^{53} +2.41653e13 q^{54} +3.31991e12 q^{55} +2.08807e13 q^{56} -3.43250e13 q^{57} +2.15560e12 q^{58} -2.33309e13 q^{59} +9.40656e12 q^{60} +4.13138e13 q^{61} +7.03291e11 q^{62} -1.35455e14 q^{63} +2.92746e13 q^{64} -1.20300e13 q^{65} -4.14678e13 q^{66} -2.05179e13 q^{67} +2.90285e13 q^{68} -1.32993e14 q^{69} +3.09829e13 q^{70} +7.64088e13 q^{71} -2.52446e14 q^{72} +8.78192e13 q^{73} -4.53939e13 q^{74} -1.85325e14 q^{75} +7.95198e13 q^{76} +1.50024e14 q^{77} +1.50262e14 q^{78} -1.76744e14 q^{79} +1.61105e13 q^{80} +8.51083e14 q^{81} +2.03816e14 q^{82} +1.96866e14 q^{83} +4.25074e14 q^{84} +1.25360e14 q^{85} -2.55574e14 q^{86} +1.27715e14 q^{87} +2.79596e14 q^{88} -6.69665e14 q^{89} -3.74580e14 q^{90} -5.43625e14 q^{91} +3.08101e14 q^{92} +4.16687e13 q^{93} -1.56089e13 q^{94} +3.43406e14 q^{95} +1.31221e15 q^{96} +4.02136e14 q^{97} +8.06819e14 q^{98} -1.81377e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 128 q^{2} - 3214 q^{3} + 239962 q^{4} - 82010 q^{5} - 112778 q^{6} - 3706320 q^{7} - 21137070 q^{8} + 73272578 q^{9}+O(q^{10}) \) 16 * q - 128 * q^2 - 3214 * q^3 + 239962 * q^4 - 82010 * q^5 - 112778 * q^6 - 3706320 * q^7 - 21137070 * q^8 + 73272578 * q^9	\( 16 q - 128 q^{2} - 3214 q^{3} + 239962 q^{4} - 82010 q^{5} - 112778 q^{6} - 3706320 q^{7} - 21137070 q^{8} + 73272578 q^{9} + 27111646 q^{10} - 128305158 q^{11} - 566454670 q^{12} - 500341634 q^{13} - 2456995576 q^{14} - 1005836398 q^{15} + 3638194738 q^{16} - 1889649440 q^{17} + 7114827706 q^{18} - 11903789760 q^{19} + 21125268698 q^{20} + 1845797984 q^{21} + 14207940510 q^{22} - 6296706268 q^{23} + 19916867274 q^{24} + 57929280374 q^{25} + 46861268662 q^{26} - 66882170482 q^{27} - 50278055968 q^{28} + 275998020944 q^{29} - 288715178542 q^{30} - 791595409290 q^{31} - 846144416938 q^{32} - 1192946764766 q^{33} - 1500307227904 q^{34} - 731093348200 q^{35} - 766217409340 q^{36} - 22311934700 q^{37} + 1194772372172 q^{38} - 1484120611454 q^{39} - 5651885433026 q^{40} + 871755491316 q^{41} - 5429421460912 q^{42} - 4296897329422 q^{43} - 10539797438606 q^{44} - 4399313787580 q^{45} - 20780033587764 q^{46} - 7817561912774 q^{47} - 36311476834866 q^{48} - 18565097654464 q^{49} - 33573686907474 q^{50} - 27333906159300 q^{51} - 48854284368422 q^{52} - 41630222638006 q^{53} - 88633328654882 q^{54} - 68569446879302 q^{55} - 66690562169864 q^{56} - 80322439188772 q^{57} - 2207984167552 q^{58} - 60146094578732 q^{59} - 170149488214170 q^{60} - 71628304977160 q^{61} - 95316700851110 q^{62} - 99862426093816 q^{63} - 20954801982074 q^{64} - 53095801190146 q^{65} - 84071816219318 q^{66} - 44591877980312 q^{67} + 24848392371308 q^{68} + 33786235351468 q^{69} - 254302493648008 q^{70} - 2238339487076 q^{71} - 335696824658688 q^{72} + 60304297937180 q^{73} - 4683993400652 q^{74} - 408007582551580 q^{75} - 511662725684676 q^{76} + 2082869459792 q^{77} + 134746909641474 q^{78} - 9999680374282 q^{79} + 10\!\cdots\!46 q^{80}+ \cdots + 531562034651476 q^{99}+O(q^{100}) \) 16 * q - 128 * q^2 - 3214 * q^3 + 239962 * q^4 - 82010 * q^5 - 112778 * q^6 - 3706320 * q^7 - 21137070 * q^8 + 73272578 * q^9 + 27111646 * q^10 - 128305158 * q^11 - 566454670 * q^12 - 500341634 * q^13 - 2456995576 * q^14 - 1005836398 * q^15 + 3638194738 * q^16 - 1889649440 * q^17 + 7114827706 * q^18 - 11903789760 * q^19 + 21125268698 * q^20 + 1845797984 * q^21 + 14207940510 * q^22 - 6296706268 * q^23 + 19916867274 * q^24 + 57929280374 * q^25 + 46861268662 * q^26 - 66882170482 * q^27 - 50278055968 * q^28 + 275998020944 * q^29 - 288715178542 * q^30 - 791595409290 * q^31 - 846144416938 * q^32 - 1192946764766 * q^33 - 1500307227904 * q^34 - 731093348200 * q^35 - 766217409340 * q^36 - 22311934700 * q^37 + 1194772372172 * q^38 - 1484120611454 * q^39 - 5651885433026 * q^40 + 871755491316 * q^41 - 5429421460912 * q^42 - 4296897329422 * q^43 - 10539797438606 * q^44 - 4399313787580 * q^45 - 20780033587764 * q^46 - 7817561912774 * q^47 - 36311476834866 * q^48 - 18565097654464 * q^49 - 33573686907474 * q^50 - 27333906159300 * q^51 - 48854284368422 * q^52 - 41630222638006 * q^53 - 88633328654882 * q^54 - 68569446879302 * q^55 - 66690562169864 * q^56 - 80322439188772 * q^57 - 2207984167552 * q^58 - 60146094578732 * q^59 - 170149488214170 * q^60 - 71628304977160 * q^61 - 95316700851110 * q^62 - 99862426093816 * q^63 - 20954801982074 * q^64 - 53095801190146 * q^65 - 84071816219318 * q^66 - 44591877980312 * q^67 + 24848392371308 * q^68 + 33786235351468 * q^69 - 254302493648008 * q^70 - 2238339487076 * q^71 - 335696824658688 * q^72 + 60304297937180 * q^73 - 4683993400652 * q^74 - 408007582551580 * q^75 - 511662725684676 * q^76 + 2082869459792 * q^77 + 134746909641474 * q^78 - 9999680374282 * q^79 + 1065964290115846 * q^80 + 1227860473120604 * q^81 - 482856386515020 * q^82 + 1449900899821108 * q^83 + 2256322335776952 * q^84 + 1364385639985788 * q^85 + 1206993542651814 * q^86 - 55441102457126 * q^87 + 2648043460385618 * q^88 - 162544796147532 * q^89 + 1885912570259156 * q^90 + 858443116817000 * q^91 + 2263858121857900 * q^92 + 3752667465062574 * q^93 + 3639931425958406 * q^94 - 73522560256708 * q^95 + 6634505750804190 * q^96 + 463840517939252 * q^97 + 2013726729859888 * q^98 + 531562034651476 * q^99

Introduction

L-functions

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