LMFDB - Embedded newform 29.16.a.a.1.14

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			1.14
Root			$-271.654$ 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)

$f(q)$	$=$	$q+263.654 q^{2} -7375.70 q^{3} +36745.2 q^{4} +191009. q^{5} -1.94463e6 q^{6} -906747. q^{7} +1.04862e6 q^{8} +4.00521e7 q^{9} +O(q^{10})$	\(q+263.654 q^{2} -7375.70 q^{3} +36745.2 q^{4} +191009. q^{5} -1.94463e6 q^{6} -906747. q^{7} +1.04862e6 q^{8} +4.00521e7 q^{9} +5.03603e7 q^{10} -3.10129e7 q^{11} -2.71022e8 q^{12} +2.22349e8 q^{13} -2.39067e8 q^{14} -1.40883e9 q^{15} -9.27597e8 q^{16} -5.52176e8 q^{17} +1.05599e10 q^{18} +3.42927e9 q^{19} +7.01868e9 q^{20} +6.68790e9 q^{21} -8.17668e9 q^{22} -2.92619e10 q^{23} -7.73428e9 q^{24} +5.96696e9 q^{25} +5.86232e10 q^{26} -1.89579e11 q^{27} -3.33186e10 q^{28} +1.72499e10 q^{29} -3.71443e11 q^{30} -2.60761e11 q^{31} -2.78925e11 q^{32} +2.28742e11 q^{33} -1.45583e11 q^{34} -1.73197e11 q^{35} +1.47172e12 q^{36} -7.43239e11 q^{37} +9.04139e11 q^{38} -1.63998e12 q^{39} +2.00295e11 q^{40} -4.05516e11 q^{41} +1.76329e12 q^{42} +1.92456e11 q^{43} -1.13958e12 q^{44} +7.65032e12 q^{45} -7.71502e12 q^{46} -1.47831e11 q^{47} +6.84168e12 q^{48} -3.92537e12 q^{49} +1.57321e12 q^{50} +4.07269e12 q^{51} +8.17028e12 q^{52} +7.47422e12 q^{53} -4.99833e13 q^{54} -5.92376e12 q^{55} -9.50828e11 q^{56} -2.52933e13 q^{57} +4.54799e12 q^{58} +2.62892e12 q^{59} -5.17677e13 q^{60} +3.24935e12 q^{61} -6.87505e13 q^{62} -3.63171e13 q^{63} -4.31442e13 q^{64} +4.24708e13 q^{65} +6.03088e13 q^{66} +6.15302e13 q^{67} -2.02899e13 q^{68} +2.15827e14 q^{69} -4.56640e13 q^{70} -7.16612e13 q^{71} +4.19993e13 q^{72} +1.02373e14 q^{73} -1.95958e14 q^{74} -4.40105e13 q^{75} +1.26009e14 q^{76} +2.81209e13 q^{77} -4.32387e14 q^{78} -2.23998e14 q^{79} -1.77180e14 q^{80} +8.23577e14 q^{81} -1.06916e14 q^{82} +2.57846e14 q^{83} +2.45748e14 q^{84} -1.05471e14 q^{85} +5.07418e13 q^{86} -1.27230e14 q^{87} -3.25207e13 q^{88} -5.73775e14 q^{89} +2.01704e15 q^{90} -2.01615e14 q^{91} -1.07524e15 q^{92} +1.92329e15 q^{93} -3.89761e13 q^{94} +6.55022e14 q^{95} +2.05727e15 q^{96} -1.10292e15 q^{97} -1.03494e15 q^{98} -1.24213e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	263.654	1.45649	0.728247	−	0.685315i	$-0.240335\pi$
$2$	263.654	1.45649	0.728247	+	0.685315i	$0.240335\pi$
$3$	−7375.70	−1.94713	−0.973563	−	0.228418i	$-0.926645\pi$
$3$	−7375.70	−1.94713	−0.973563	+	0.228418i	$0.926645\pi$
$4$	36745.2	1.12138
$5$	191009.	1.09340	0.546700	−	0.837328i	$-0.315884\pi$
$5$	191009.	1.09340	0.546700	+	0.837328i	$0.315884\pi$
$6$	−1.94463e6	−2.83598
$7$	−906747.	−0.416151	−0.208075	−	0.978113i	$-0.566720\pi$
$7$	−906747.	−0.416151	−0.208075	+	0.978113i	$0.566720\pi$
$8$	1.04862e6	0.176783
$9$	4.00521e7	2.79130
$10$	5.03603e7	1.59253
$11$	−3.10129e7	−0.479842	−0.239921	−	0.970792i	$-0.577121\pi$
$11$	−3.10129e7	−0.479842	−0.239921	+	0.970792i	$0.577121\pi$
$12$	−2.71022e8	−2.18346
$13$	2.22349e8	0.982790	0.491395	−	0.870937i	$-0.336487\pi$
$13$	2.22349e8	0.982790	0.491395	+	0.870937i	$0.336487\pi$
$14$	−2.39067e8	−0.606121
$15$	−1.40883e9	−2.12899
$16$	−9.27597e8	−0.863892
$17$	−5.52176e8	−0.326371	−0.163185	−	0.986595i	$-0.552177\pi$
$17$	−5.52176e8	−0.326371	−0.163185	+	0.986595i	$0.552177\pi$
$18$	1.05599e10	4.06551
$19$	3.42927e9	0.880135	0.440068	−	0.897965i	$-0.354954\pi$
$19$	3.42927e9	0.880135	0.440068	+	0.897965i	$0.354954\pi$
$20$	7.01868e9	1.22611
$21$	6.68790e9	0.810298
$22$	−8.17668e9	−0.698887
$23$	−2.92619e10	−1.79203	−0.896013	−	0.444028i	$-0.853549\pi$
$23$	−2.92619e10	−1.79203	−0.896013	+	0.444028i	$0.853549\pi$
$24$	−7.73428e9	−0.344219
$25$	5.96696e9	0.195525
$26$	5.86232e10	1.43143
$27$	−1.89579e11	−3.48789
$28$	−3.33186e10	−0.466661
$29$	1.72499e10	0.185695
$29$	1.72499e10	0.185695
$30$	−3.71443e11	−3.10086
$31$	−2.60761e11	−1.70227	−0.851137	−	0.524944i	$-0.824086\pi$
$31$	−2.60761e11	−1.70227	−0.851137	+	0.524944i	$0.824086\pi$
$32$	−2.78925e11	−1.43504
$33$	2.28742e11	0.934312
$34$	−1.45583e11	−0.475357
$35$	−1.73197e11	−0.455020
$36$	1.47172e12	3.13010
$37$	−7.43239e11	−1.28711	−0.643555	−	0.765400i	$-0.722541\pi$
$37$	−7.43239e11	−1.28711	−0.643555	+	0.765400i	$0.722541\pi$
$38$	9.04139e11	1.28191
$39$	−1.63998e12	−1.91362
$40$	2.00295e11	0.193295
$41$	−4.05516e11	−0.325184	−0.162592	−	0.986693i	$-0.551985\pi$
$41$	−4.05516e11	−0.325184	−0.162592	+	0.986693i	$0.551985\pi$
$42$	1.76329e12	1.18019
$43$	1.92456e11	0.107974	0.0539869	−	0.998542i	$-0.482807\pi$
$43$	1.92456e11	0.107974	0.0539869	+	0.998542i	$0.482807\pi$
$44$	−1.13958e12	−0.538083
$45$	7.65032e12	3.05201
$46$	−7.71502e12	−2.61008
$47$	−1.47831e11	−0.0425629	−0.0212814	−	0.999774i	$-0.506775\pi$
$47$	−1.47831e11	−0.0425629	−0.0212814	+	0.999774i	$0.506775\pi$
$48$	6.84168e12	1.68211
$49$	−3.92537e12	−0.826819
$50$	1.57321e12	0.284781
$51$	4.07269e12	0.635485
$52$	8.17028e12	1.10208
$53$	7.47422e12	0.873971	0.436985	−	0.899469i	$-0.356046\pi$
$53$	7.47422e12	0.873971	0.436985	+	0.899469i	$0.356046\pi$
$54$	−4.99833e13	−5.08009
$55$	−5.92376e12	−0.524659
$56$	−9.50828e11	−0.0735685
$57$	−2.52933e13	−1.71373
$58$	4.54799e12	0.270464
$59$	2.62892e12	0.137527	0.0687634	−	0.997633i	$-0.478095\pi$
$59$	2.62892e12	0.137527	0.0687634	+	0.997633i	$0.478095\pi$
$60$	−5.17677e13	−2.38740
$61$	3.24935e12	0.132380	0.0661900	−	0.997807i	$-0.478916\pi$
$61$	3.24935e12	0.132380	0.0661900	+	0.997807i	$0.478916\pi$
$62$	−6.87505e13	−2.47935
$63$	−3.63171e13	−1.16160
$64$	−4.31442e13	−1.22623
$65$	4.24708e13	1.07458
$66$	6.03088e13	1.36082
$67$	6.15302e13	1.24030	0.620151	−	0.784482i	$-0.287071\pi$
$67$	6.15302e13	1.24030	0.620151	+	0.784482i	$0.287071\pi$
$68$	−2.02899e13	−0.365984
$69$	2.15827e14	3.48930
$70$	−4.56640e13	−0.662733
$71$	−7.16612e13	−0.935074	−0.467537	−	0.883973i	$-0.654859\pi$
$71$	−7.16612e13	−0.935074	−0.467537	+	0.883973i	$0.654859\pi$
$72$	4.19993e13	0.493455
$73$	1.02373e14	1.08459	0.542294	−	0.840189i	$-0.317556\pi$
$73$	1.02373e14	1.08459	0.542294	+	0.840189i	$0.317556\pi$
$74$	−1.95958e14	−1.87467
$75$	−4.40105e13	−0.380712
$76$	1.26009e14	0.986962
$77$	2.81209e13	0.199686
$78$	−4.32387e14	−2.78717
$79$	−2.23998e14	−1.31232	−0.656162	−	0.754620i	$-0.727821\pi$
$79$	−2.23998e14	−1.31232	−0.656162	+	0.754620i	$0.727821\pi$
$80$	−1.77180e14	−0.944580
$81$	8.23577e14	4.00006
$82$	−1.06916e14	−0.473629
$83$	2.57846e14	1.04298	0.521488	−	0.853259i	$-0.325377\pi$
$83$	2.57846e14	1.04298	0.521488	+	0.853259i	$0.325377\pi$
$84$	2.45748e14	0.908649
$85$	−1.05471e14	−0.356854
$86$	5.07418e13	0.157263
$87$	−1.27230e14	−0.361572
$88$	−3.25207e13	−0.0848280
$89$	−5.73775e14	−1.37504	−0.687522	−	0.726164i	$-0.741301\pi$
$89$	−5.73775e14	−1.37504	−0.687522	+	0.726164i	$0.741301\pi$
$90$	2.01704e15	4.44524
$91$	−2.01615e14	−0.408989
$92$	−1.07524e15	−2.00953
$93$	1.92329e15	3.31454
$94$	−3.89761e13	−0.0619926
$95$	6.55022e14	0.962340
$96$	2.05727e15	2.79420
$97$	−1.10292e15	−1.38597	−0.692986	−	0.720951i	$-0.743705\pi$
$97$	−1.10292e15	−1.38597	−0.692986	+	0.720951i	$0.743705\pi$
$98$	−1.03494e15	−1.20426
$99$	−1.24213e15	−1.33938
$100$	2.19257e14	0.219257
$101$	−1.01083e15	−0.938138	−0.469069	−	0.883162i	$-0.655410\pi$
$101$	−1.01083e15	−0.938138	−0.469069	+	0.883162i	$0.655410\pi$
$102$	1.07378e15	0.925580
$103$	−1.47734e15	−1.18359	−0.591794	−	0.806090i	$-0.701580\pi$
$103$	−1.47734e15	−1.18359	−0.591794	+	0.806090i	$0.701580\pi$
$104$	2.33159e14	0.173741
$105$	1.27745e15	0.885980
$106$	1.97061e15	1.27293
$107$	2.75315e14	0.165749	0.0828745	−	0.996560i	$-0.473590\pi$
$107$	2.75315e14	0.165749	0.0828745	+	0.996560i	$0.473590\pi$
$108$	−6.96614e15	−3.91123
$109$	−1.44984e15	−0.759666	−0.379833	−	0.925055i	$-0.624019\pi$
$109$	−1.44984e15	−0.759666	−0.379833	+	0.925055i	$0.624019\pi$
$110$	−1.56182e15	−0.764163
$111$	5.48191e15	2.50617
$112$	8.41095e14	0.359509
$113$	4.74433e15	1.89708	0.948542	−	0.316650i	$-0.102558\pi$
$113$	4.74433e15	1.89708	0.948542	+	0.316650i	$0.102558\pi$
$114$	−6.66866e15	−2.49604
$115$	−5.58930e15	−1.95940
$116$	6.33851e14	0.208234
$117$	8.90556e15	2.74326
$118$	6.93124e14	0.200307
$119$	5.00684e14	0.135819
$120$	−1.47732e15	−0.376370
$121$	−3.21545e15	−0.769752
$122$	8.56703e14	0.192811
$123$	2.99097e15	0.633175
$124$	−9.58171e15	−1.90889
$125$	−4.68940e15	−0.879613
$126$	−9.57514e15	−1.69187
$127$	8.36593e15	1.39311	0.696556	−	0.717502i	$-0.254715\pi$
$127$	8.36593e15	1.39311	0.696556	+	0.717502i	$0.254715\pi$
$128$	−2.23530e15	−0.350962
$129$	−1.41950e15	−0.210239
$130$	1.11976e16	1.56512
$131$	−1.40551e16	−1.85481	−0.927407	−	0.374053i	$-0.877968\pi$
$131$	−1.40551e16	−1.85481	−0.927407	+	0.374053i	$0.877968\pi$
$132$	8.40519e15	1.04772
$133$	−3.10948e15	−0.366269
$134$	1.62227e16	1.80649
$135$	−3.62114e16	−3.81366
$136$	−5.79021e14	−0.0576969
$137$	7.13028e15	0.672516	0.336258	−	0.941770i	$-0.390839\pi$
$137$	7.13028e15	0.672516	0.336258	+	0.941770i	$0.390839\pi$
$138$	5.69037e16	5.08215
$139$	6.45527e15	0.546139	0.273069	−	0.961994i	$-0.411961\pi$
$139$	6.45527e15	0.546139	0.273069	+	0.961994i	$0.411961\pi$
$140$	−6.36417e15	−0.510248
$141$	1.09036e15	0.0828753
$142$	−1.88937e16	−1.36193
$143$	−6.89571e15	−0.471583
$144$	−3.71522e16	−2.41138
$145$	3.29489e15	0.203039
$146$	2.69911e16	1.57970
$147$	2.89524e16	1.60992
$148$	−2.73105e16	−1.44333
$149$	1.47182e16	0.739535	0.369768	−	0.929124i	$-0.379437\pi$
$149$	1.47182e16	0.739535	0.369768	+	0.929124i	$0.379437\pi$
$150$	−1.16035e16	−0.554505
$151$	9.63676e15	0.438131	0.219066	−	0.975710i	$-0.429699\pi$
$151$	9.63676e15	0.438131	0.219066	+	0.975710i	$0.429699\pi$
$152$	3.59598e15	0.155593
$153$	−2.21158e16	−0.910998
$154$	7.41417e15	0.290842
$155$	−4.98077e16	−1.86127
$156$	−6.02616e16	−2.14588
$157$	−8.41250e15	−0.285547	−0.142773	−	0.989755i	$-0.545602\pi$
$157$	−8.41250e15	−0.285547	−0.142773	+	0.989755i	$0.545602\pi$
$158$	−5.90579e16	−1.91139
$159$	−5.51277e16	−1.70173
$160$	−5.32773e16	−1.56907
$161$	2.65332e16	0.745753
$162$	2.17139e17	5.82606
$163$	3.50050e15	0.0896857	0.0448429	−	0.998994i	$-0.485721\pi$
$163$	3.50050e15	0.0896857	0.0448429	+	0.998994i	$0.485721\pi$
$164$	−1.49008e16	−0.364654
$165$	4.36919e16	1.02158
$166$	6.79819e16	1.51909
$167$	5.06379e16	1.08169	0.540845	−	0.841122i	$-0.318105\pi$
$167$	5.06379e16	1.08169	0.540845	+	0.841122i	$0.318105\pi$
$168$	7.01303e15	0.143247
$169$	−1.74667e15	−0.0341241
$170$	−2.78078e16	−0.519756
$171$	1.37349e17	2.45672
$172$	7.07185e15	0.121079
$173$	−8.63546e16	−1.41560	−0.707799	−	0.706414i	$-0.750312\pi$
$173$	−8.63546e16	−1.41560	−0.707799	+	0.706414i	$0.750312\pi$
$174$	−3.35447e16	−0.526628
$175$	−5.41052e15	−0.0813680
$176$	2.87675e16	0.414531
$177$	−1.93901e16	−0.267782
$178$	−1.51278e17	−2.00274
$179$	3.27351e16	0.415543	0.207771	−	0.978177i	$-0.433379\pi$
$179$	3.27351e16	0.415543	0.207771	+	0.978177i	$0.433379\pi$
$180$	2.81113e17	3.42245
$181$	6.30074e16	0.735872	0.367936	−	0.929851i	$-0.380065\pi$
$181$	6.30074e16	0.735872	0.367936	+	0.929851i	$0.380065\pi$
$182$	−5.31564e16	−0.595690
$183$	−2.39662e16	−0.257761
$184$	−3.06845e16	−0.316800
$185$	−1.41966e17	−1.40733
$186$	5.07083e17	4.82761
$187$	1.71246e16	0.156606
$188$	−5.43208e15	−0.0477290
$189$	1.71900e17	1.45149
$190$	1.72699e17	1.40164
$191$	−1.01255e17	−0.790074	−0.395037	−	0.918665i	$-0.629268\pi$
$191$	−1.01255e17	−0.790074	−0.395037	+	0.918665i	$0.629268\pi$
$192$	3.18219e17	2.38763
$193$	−1.17808e17	−0.850152	−0.425076	−	0.905158i	$-0.639753\pi$
$193$	−1.17808e17	−0.850152	−0.425076	+	0.905158i	$0.639753\pi$
$194$	−2.90788e17	−2.01866
$195$	−3.13252e17	−2.09235
$196$	−1.44239e17	−0.927174
$197$	9.11768e16	0.564141	0.282070	−	0.959394i	$-0.408979\pi$
$197$	9.11768e16	0.564141	0.282070	+	0.959394i	$0.408979\pi$
$198$	−3.27493e17	−1.95080
$199$	−4.76046e16	−0.273055	−0.136528	−	0.990636i	$-0.543594\pi$
$199$	−4.76046e16	−0.273055	−0.136528	+	0.990636i	$0.543594\pi$
$200$	6.25704e15	0.0345656
$201$	−4.53829e17	−2.41503
$202$	−2.66508e17	−1.36639
$203$	−1.56413e16	−0.0772773
$204$	1.49652e17	0.712617
$205$	−7.74574e16	−0.355557
$206$	−3.89505e17	−1.72389
$207$	−1.17200e18	−5.00208
$208$	−2.06251e17	−0.849024
$209$	−1.06352e17	−0.422325
$210$	3.36804e17	1.29043
$211$	3.51011e17	1.29778	0.648891	−	0.760881i	$-0.275233\pi$
$211$	3.51011e17	1.29778	0.648891	+	0.760881i	$0.275233\pi$
$212$	2.74642e17	0.980050
$213$	5.28552e17	1.82071
$214$	7.25877e16	0.241413
$215$	3.67609e16	0.118059
$216$	−1.98796e17	−0.616601
$217$	2.36444e17	0.708402
$218$	−3.82257e17	−1.10645
$219$	−7.55074e17	−2.11183
$220$	−2.17670e17	−0.588340
$221$	−1.22776e17	−0.320754
$222$	1.44533e18	3.65022
$223$	3.91999e17	0.957191	0.478595	−	0.878036i	$-0.341146\pi$
$223$	3.91999e17	0.957191	0.478595	+	0.878036i	$0.341146\pi$
$224$	2.52915e17	0.597192
$225$	2.38989e17	0.545770
$226$	1.25086e18	2.76309
$227$	−3.35738e17	−0.717475	−0.358738	−	0.933438i	$-0.616793\pi$
$227$	−3.35738e17	−0.717475	−0.358738	+	0.933438i	$0.616793\pi$
$228$	−9.29407e17	−1.92174
$229$	9.03509e17	1.80787	0.903933	−	0.427674i	$-0.140667\pi$
$229$	9.03509e17	1.80787	0.903933	+	0.427674i	$0.140667\pi$
$230$	−1.47364e18	−2.85386
$231$	−2.07411e17	−0.388815
$232$	1.80885e16	0.0328278
$233$	−3.00066e17	−0.527287	−0.263644	−	0.964620i	$-0.584924\pi$
$233$	−3.00066e17	−0.527287	−0.263644	+	0.964620i	$0.584924\pi$
$234$	2.34798e18	3.99555
$235$	−2.82370e16	−0.0465383
$236$	9.66003e16	0.154219
$237$	1.65214e18	2.55526
$238$	1.32007e17	0.197820
$239$	−4.12988e17	−0.599727	−0.299863	−	0.953982i	$-0.596941\pi$
$239$	−4.12988e17	−0.599727	−0.299863	+	0.953982i	$0.596941\pi$
$240$	1.30682e18	1.83922
$241$	5.23398e17	0.714009	0.357005	−	0.934103i	$-0.383798\pi$
$241$	5.23398e17	0.714009	0.357005	+	0.934103i	$0.383798\pi$
$242$	−8.47764e17	−1.12114
$243$	−3.35420e18	−4.30073
$244$	1.19398e17	0.148448
$245$	−7.49782e17	−0.904044
$246$	7.88580e17	0.922215
$247$	7.62495e17	0.864988
$248$	−2.73438e17	−0.300934
$249$	−1.90179e18	−2.03081
$250$	−1.23638e18	−1.28115
$251$	−1.46985e18	−1.47815	−0.739075	−	0.673623i	$-0.764737\pi$
$251$	−1.46985e18	−1.47815	−0.739075	+	0.673623i	$0.764737\pi$
$252$	−1.33448e18	−1.30259
$253$	9.07499e17	0.859889
$254$	2.20571e18	2.02906
$255$	7.77922e17	0.694839
$256$	8.24405e17	0.715057
$257$	5.90158e17	0.497130	0.248565	−	0.968615i	$-0.420041\pi$
$257$	5.90158e17	0.497130	0.248565	+	0.968615i	$0.420041\pi$
$258$	−3.74257e17	−0.306212
$259$	6.73930e17	0.535632
$260$	1.56060e18	1.20501
$261$	6.90894e17	0.518332
$262$	−3.70569e18	−2.70153
$263$	2.68567e18	1.90276	0.951381	−	0.308016i	$-0.0996650\pi$
$263$	2.68567e18	1.90276	0.951381	+	0.308016i	$0.0996650\pi$
$264$	2.39863e17	0.165171
$265$	1.42765e18	0.955600
$266$	−8.19825e17	−0.533469
$267$	4.23199e18	2.67738
$268$	2.26094e18	1.39085
$269$	8.25365e17	0.493746	0.246873	−	0.969048i	$-0.420597\pi$
$269$	8.25365e17	0.493746	0.246873	+	0.969048i	$0.420597\pi$
$270$	−9.54727e18	−5.55458
$271$	3.60918e17	0.204239	0.102120	−	0.994772i	$-0.467438\pi$
$271$	3.60918e17	0.204239	0.102120	+	0.994772i	$0.467438\pi$
$272$	5.12197e17	0.281949
$273$	1.48705e18	0.796353
$274$	1.87992e18	0.979515
$275$	−1.85053e17	−0.0938211
$276$	7.93063e18	3.91282
$277$	−2.47700e18	−1.18940	−0.594700	−	0.803948i	$-0.702729\pi$
$277$	−2.47700e18	−1.18940	−0.594700	+	0.803948i	$0.702729\pi$
$278$	1.70195e18	0.795448
$279$	−1.04440e19	−4.75156
$280$	−1.81617e17	−0.0804399
$281$	1.98617e18	0.856485	0.428242	−	0.903664i	$-0.359133\pi$
$281$	1.98617e18	0.856485	0.428242	+	0.903664i	$0.359133\pi$
$282$	2.87476e17	0.120707
$283$	1.88474e18	0.770641	0.385320	−	0.922783i	$-0.374091\pi$
$283$	1.88474e18	0.770641	0.385320	+	0.922783i	$0.374091\pi$
$284$	−2.63321e18	−1.04857
$285$	−4.83125e18	−1.87380
$286$	−1.81808e18	−0.686859
$287$	3.67701e17	0.135326
$288$	−1.11716e19	−4.00562
$289$	−2.55752e18	−0.893482
$290$	8.68709e17	0.295726
$291$	8.13478e18	2.69866
$292$	3.76173e18	1.21623
$293$	−2.15036e18	−0.677649	−0.338824	−	0.940850i	$-0.610029\pi$
$293$	−2.15036e18	−0.677649	−0.338824	+	0.940850i	$0.610029\pi$
$294$	7.63340e18	2.34484
$295$	5.02148e17	0.150372
$296$	−7.79372e17	−0.227540
$297$	5.87941e18	1.67363
$298$	3.88052e18	1.07713
$299$	−6.50637e18	−1.76118
$300$	−1.61718e18	−0.426922
$301$	−1.74509e17	−0.0449334
$302$	2.54077e18	0.638135
$303$	7.45556e18	1.82667
$304$	−3.18098e18	−0.760342
$305$	6.20656e17	0.144744
$306$	−5.83092e18	−1.32686
$307$	−5.17909e18	−1.15005	−0.575023	−	0.818137i	$-0.695007\pi$
$307$	−5.17909e18	−1.15005	−0.575023	+	0.818137i	$0.695007\pi$
$308$	1.03331e18	0.223924
$309$	1.08964e19	2.30459
$310$	−1.31320e19	−2.71093
$311$	−3.53172e18	−0.711678	−0.355839	−	0.934547i	$-0.615805\pi$
$311$	−3.53172e18	−0.711678	−0.355839	+	0.934547i	$0.615805\pi$
$312$	−1.71971e18	−0.338295
$313$	2.50044e18	0.480214	0.240107	−	0.970746i	$-0.422818\pi$
$313$	2.50044e18	0.480214	0.240107	+	0.970746i	$0.422818\pi$
$314$	−2.21799e18	−0.415898
$315$	−6.93691e18	−1.27010
$316$	−8.23086e18	−1.47161
$317$	2.13767e18	0.373247	0.186624	−	0.982431i	$-0.440246\pi$
$317$	2.13767e18	0.373247	0.186624	+	0.982431i	$0.440246\pi$
$318$	−1.45346e19	−2.47856
$319$	−5.34970e17	−0.0891044
$320$	−8.24094e18	−1.34076
$321$	−2.03064e18	−0.322734
$322$	6.99556e18	1.08618
$323$	−1.89356e18	−0.287250
$324$	3.02625e19	4.48557
$325$	1.32675e18	0.192160
$326$	9.22920e17	0.130627
$327$	1.06936e19	1.47917
$328$	−4.25231e17	−0.0574872
$329$	1.34045e17	0.0177126
$330$	1.15195e19	1.48792
$331$	−5.02904e18	−0.635001	−0.317501	−	0.948258i	$-0.602844\pi$
$331$	−5.02904e18	−0.635001	−0.317501	+	0.948258i	$0.602844\pi$
$332$	9.47460e18	1.16957
$333$	−2.97683e19	−3.59271
$334$	1.33509e19	1.57547
$335$	1.17528e19	1.35615
$336$	−6.20367e18	−0.700010
$337$	−2.41565e18	−0.266569	−0.133285	−	0.991078i	$-0.542552\pi$
$337$	−2.41565e18	−0.266569	−0.133285	+	0.991078i	$0.542552\pi$
$338$	−4.60516e17	−0.0497015
$339$	−3.49928e19	−3.69386
$340$	−3.87555e18	−0.400167
$341$	8.08696e18	0.816822
$342$	3.62127e19	3.57820
$343$	7.86415e18	0.760232
$344$	2.01813e17	0.0190880
$345$	4.12250e19	3.81520
$346$	−2.27677e19	−2.06181
$347$	−2.09317e18	−0.185496	−0.0927479	−	0.995690i	$-0.529565\pi$
$347$	−2.09317e18	−0.185496	−0.0927479	+	0.995690i	$0.529565\pi$
$348$	−4.67510e18	−0.405458
$349$	5.57134e18	0.472900	0.236450	−	0.971644i	$-0.424016\pi$
$349$	5.57134e18	0.472900	0.236450	+	0.971644i	$0.424016\pi$
$350$	−1.42650e18	−0.118512
$351$	−4.21528e19	−3.42786
$352$	8.65030e18	0.688591
$353$	−2.01158e19	−1.56757	−0.783784	−	0.621034i	$-0.786713\pi$
$353$	−2.01158e19	−1.56757	−0.783784	+	0.621034i	$0.786713\pi$
$354$	−5.11228e18	−0.390023
$355$	−1.36879e19	−1.02241
$356$	−2.10835e19	−1.54194
$357$	−3.69290e18	−0.264457
$358$	8.63072e18	0.605236
$359$	−9.09302e18	−0.624453	−0.312227	−	0.950008i	$-0.601075\pi$
$359$	−9.09302e18	−0.624453	−0.312227	+	0.950008i	$0.601075\pi$
$360$	8.02225e18	0.539545
$361$	−3.42125e18	−0.225362
$362$	1.66121e19	1.07179
$363$	2.37162e19	1.49880
$364$	−7.40837e18	−0.458630
$365$	1.95542e19	1.18589
$366$	−6.31879e18	−0.375427
$367$	1.02954e19	0.599307	0.299654	−	0.954048i	$-0.403129\pi$
$367$	1.02954e19	0.599307	0.299654	+	0.954048i	$0.403129\pi$
$368$	2.71433e19	1.54812
$369$	−1.62418e19	−0.907687
$370$	−3.74297e19	−2.04976
$371$	−6.77723e18	−0.363704
$372$	7.06719e19	3.71685
$373$	3.16111e19	1.62938	0.814692	−	0.579894i	$-0.196906\pi$
$373$	3.16111e19	1.62938	0.814692	+	0.579894i	$0.196906\pi$
$374$	4.51497e18	0.228096
$375$	3.45876e19	1.71272
$376$	−1.55018e17	−0.00752441
$377$	3.83550e18	0.182499
$378$	4.53222e19	2.11408
$379$	1.37193e19	0.627391	0.313695	−	0.949524i	$-0.398433\pi$
$379$	1.37193e19	0.627391	0.313695	+	0.949524i	$0.398433\pi$
$380$	2.40689e19	1.07915
$381$	−6.17046e19	−2.71257
$382$	−2.66964e19	−1.15074
$383$	1.04096e19	0.439991	0.219995	−	0.975501i	$-0.429396\pi$
$383$	1.04096e19	0.439991	0.219995	+	0.975501i	$0.429396\pi$
$384$	1.64869e19	0.683368
$385$	5.37135e18	0.218337
$386$	−3.10606e19	−1.23824
$387$	7.70828e18	0.301388
$388$	−4.05269e19	−1.55420
$389$	3.89296e19	1.46439	0.732196	−	0.681094i	$-0.238495\pi$
$389$	3.89296e19	1.46439	0.732196	+	0.681094i	$0.238495\pi$
$390$	−8.25900e19	−3.04749
$391$	1.61578e19	0.584864
$392$	−4.11621e18	−0.146168
$393$	1.03667e20	3.61156
$394$	2.40391e19	0.821668
$395$	−4.27857e19	−1.43490
$396$	−4.56425e19	−1.50195
$397$	2.69248e19	0.869408	0.434704	−	0.900573i	$-0.356853\pi$
$397$	2.69248e19	0.869408	0.434704	+	0.900573i	$0.356853\pi$
$398$	−1.25511e19	−0.397704
$399$	2.29346e19	0.713172
$400$	−5.53493e18	−0.168913
$401$	3.93215e19	1.17773	0.588867	−	0.808230i	$-0.299574\pi$
$401$	3.93215e19	1.17773	0.588867	+	0.808230i	$0.299574\pi$
$402$	−1.19654e20	−3.51747
$403$	−5.79800e19	−1.67298
$404$	−3.71431e19	−1.05201
$405$	1.57311e20	4.37367
$406$	−4.12388e18	−0.112554
$407$	2.30500e19	0.617609
$408$	4.27069e18	0.112343
$409$	−5.37492e19	−1.38819	−0.694093	−	0.719885i	$-0.744194\pi$
$409$	−5.37492e19	−1.38819	−0.694093	+	0.719885i	$0.744194\pi$
$410$	−2.04219e19	−0.517866
$411$	−5.25909e19	−1.30947
$412$	−5.42851e19	−1.32725
$413$	−2.38376e18	−0.0572319
$414$	−3.09003e20	−7.28551
$415$	4.92509e19	1.14039
$416$	−6.20189e19	−1.41034
$417$	−4.76121e19	−1.06340
$418$	−2.80400e19	−0.615115
$419$	−4.26366e18	−0.0918709	−0.0459354	−	0.998944i	$-0.514627\pi$
$419$	−4.26366e18	−0.0918709	−0.0459354	+	0.998944i	$0.514627\pi$
$420$	4.69402e19	0.993517
$421$	−8.09529e19	−1.68313	−0.841563	−	0.540159i	$-0.818364\pi$
$421$	−8.09529e19	−1.68313	−0.841563	+	0.540159i	$0.818364\pi$
$422$	9.25453e19	1.89021
$423$	−5.92094e18	−0.118806
$424$	7.83758e18	0.154503
$425$	−3.29481e18	−0.0638137
$426$	1.39355e20	2.65185
$427$	−2.94634e18	−0.0550901
$428$	1.01165e19	0.185867
$429$	5.08607e19	0.918233
$430$	9.69216e18	0.171952
$431$	9.64776e19	1.68208	0.841040	−	0.540973i	$-0.181944\pi$
$431$	9.64776e19	1.68208	0.841040	+	0.540973i	$0.181944\pi$
$432$	1.75853e20	3.01316
$433$	1.43136e17	0.00241040	0.00120520	−	0.999999i	$-0.499616\pi$
$433$	1.43136e17	0.00241040	0.00120520	+	0.999999i	$0.499616\pi$
$434$	6.23393e19	1.03178
$435$	−2.43021e19	−0.395343
$436$	−5.32749e19	−0.851871
$437$	−1.00347e20	−1.57722
$438$	−1.99078e20	−3.07587
$439$	1.03640e20	1.57415	0.787074	−	0.616859i	$-0.211595\pi$
$439$	1.03640e20	1.57415	0.787074	+	0.616859i	$0.211595\pi$
$440$	−6.21175e18	−0.0927510
$441$	−1.57219e20	−2.30790
$442$	−3.23704e19	−0.467176
$443$	8.86215e19	1.25751	0.628754	−	0.777604i	$-0.283565\pi$
$443$	8.86215e19	1.25751	0.628754	+	0.777604i	$0.283565\pi$
$444$	2.01434e20	2.81035
$445$	−1.09596e20	−1.50347
$446$	1.03352e20	1.39414
$447$	−1.08557e20	−1.43997
$448$	3.91208e19	0.510297
$449$	4.84646e19	0.621694	0.310847	−	0.950460i	$-0.399387\pi$
$449$	4.84646e19	0.621694	0.310847	+	0.950460i	$0.399387\pi$
$450$	6.30104e19	0.794911
$451$	1.25763e19	0.156037
$452$	1.74332e20	2.12735
$453$	−7.10779e19	−0.853096
$454$	−8.85186e19	−1.04500
$455$	−3.85102e19	−0.447189
$456$	−2.65229e19	−0.302960
$457$	−1.38327e20	−1.55431	−0.777154	−	0.629311i	$-0.783337\pi$
$457$	−1.38327e20	−1.55431	−0.777154	+	0.629311i	$0.783337\pi$
$458$	2.38213e20	2.63315
$459$	1.04681e20	1.13834
$460$	−2.05380e20	−2.19723
$461$	−9.88131e19	−1.04006	−0.520029	−	0.854149i	$-0.674079\pi$
$461$	−9.88131e19	−1.04006	−0.520029	+	0.854149i	$0.674079\pi$
$462$	−5.46848e19	−0.566306
$463$	1.01135e19	0.103049	0.0515246	−	0.998672i	$-0.483592\pi$
$463$	1.01135e19	0.103049	0.0515246	+	0.998672i	$0.483592\pi$
$464$	−1.60009e19	−0.160421
$465$	3.67367e20	3.62412
$466$	−7.91135e19	−0.767991
$467$	5.96190e19	0.569519	0.284760	−	0.958599i	$-0.408086\pi$
$467$	5.96190e19	0.569519	0.284760	+	0.958599i	$0.408086\pi$
$468$	3.27237e20	3.07623
$469$	−5.57923e19	−0.516153
$470$	−7.44480e18	−0.0677827
$471$	6.20481e19	0.555996
$472$	2.75673e18	0.0243124
$473$	−5.96864e18	−0.0518104
$474$	4.35594e20	3.72172
$475$	2.04623e19	0.172089
$476$	1.83978e19	0.152305
$477$	2.99358e20	2.43952
$478$	−1.08886e20	−0.873498
$479$	−7.67244e19	−0.605923	−0.302961	−	0.953003i	$-0.597975\pi$
$479$	−7.67244e19	−0.605923	−0.302961	+	0.953003i	$0.597975\pi$
$480$	3.92958e20	3.05518
$481$	−1.65259e20	−1.26496
$482$	1.37996e20	1.03995
$483$	−1.95701e20	−1.45208
$484$	−1.18152e20	−0.863181
$485$	−2.10667e20	−1.51542
$486$	−8.84348e20	−6.26399
$487$	1.59773e20	1.11439	0.557195	−	0.830382i	$-0.311878\pi$
$487$	1.59773e20	1.11439	0.557195	+	0.830382i	$0.311878\pi$
$488$	3.40732e18	0.0234026
$489$	−2.58187e19	−0.174629
$490$	−1.97683e20	−1.31674
$491$	1.38174e19	0.0906391	0.0453196	−	0.998973i	$-0.485569\pi$
$491$	1.38174e19	0.0906391	0.0453196	+	0.998973i	$0.485569\pi$
$492$	1.09904e20	0.710027
$493$	−9.52498e18	−0.0606055
$494$	2.01035e20	1.25985
$495$	−2.37259e20	−1.46448
$496$	2.41881e20	1.47058
$497$	6.49785e19	0.389132
$498$	−5.01415e20	−2.95786
$499$	−1.27660e19	−0.0741825	−0.0370913	−	0.999312i	$-0.511809\pi$
$499$	−1.27660e19	−0.0741825	−0.0370913	+	0.999312i	$0.511809\pi$
$500$	−1.72313e20	−0.986377
$501$	−3.73491e20	−2.10619
$502$	−3.87530e20	−2.15292
$503$	1.77970e20	0.974063	0.487032	−	0.873384i	$-0.338080\pi$
$503$	1.77970e20	0.974063	0.487032	+	0.873384i	$0.338080\pi$
$504$	−3.80827e19	−0.205352
$505$	−1.93077e20	−1.02576
$506$	2.39265e20	1.25242
$507$	1.28829e19	0.0664439
$508$	3.07408e20	1.56220
$509$	9.32745e19	0.467067	0.233534	−	0.972349i	$-0.424971\pi$
$509$	9.32745e19	0.467067	0.233534	+	0.972349i	$0.424971\pi$
$510$	2.05102e20	1.01203
$511$	−9.28265e19	−0.451352
$512$	2.90603e20	1.39244
$513$	−6.50118e20	−3.06981
$514$	1.55597e20	0.724067
$515$	−2.82185e20	−1.29413
$516$	−5.21599e19	−0.235757
$517$	4.58467e18	0.0204234
$518$	1.77684e20	0.780145
$519$	6.36926e20	2.75635
$520$	4.45355e19	0.189968
$521$	−2.71126e20	−1.13996	−0.569979	−	0.821659i	$-0.693049\pi$
$521$	−2.71126e20	−1.13996	−0.569979	+	0.821659i	$0.693049\pi$
$522$	1.82157e20	0.754947
$523$	−3.53297e20	−1.44337	−0.721684	−	0.692223i	$-0.756632\pi$
$523$	−3.53297e20	−1.44337	−0.721684	+	0.692223i	$0.756632\pi$
$524$	−5.16460e20	−2.07994
$525$	3.99064e19	0.158434
$526$	7.08087e20	2.77136
$527$	1.43986e20	0.555572
$528$	−2.12181e20	−0.807145
$529$	5.89626e20	2.21136
$530$	3.76404e20	1.39183
$531$	1.05294e20	0.383879
$532$	−1.14258e20	−0.410725
$533$	−9.01663e19	−0.319588
$534$	1.11578e21	3.89959
$535$	5.25877e19	0.181230
$536$	6.45216e19	0.219265
$537$	−2.41444e20	−0.809114
$538$	2.17610e20	0.719139
$539$	1.21737e20	0.396742
$540$	−1.33060e21	−4.27655
$541$	−1.88494e20	−0.597474	−0.298737	−	0.954335i	$-0.596565\pi$
$541$	−1.88494e20	−0.597474	−0.298737	+	0.954335i	$0.596565\pi$
$542$	9.51574e19	0.297473
$543$	−4.64724e20	−1.43284
$544$	1.54016e20	0.468354
$545$	−2.76934e20	−0.830619
$546$	3.92066e20	1.15988
$547$	−3.46208e20	−1.01026	−0.505129	−	0.863044i	$-0.668555\pi$
$547$	−3.46208e20	−1.01026	−0.505129	+	0.863044i	$0.668555\pi$
$548$	2.62004e20	0.754143
$549$	1.30143e20	0.369513
$550$	−4.87899e19	−0.136650
$551$	5.91544e19	0.163437
$552$	2.26320e20	0.616850
$553$	2.03110e20	0.546125
$554$	−6.53070e20	−1.73235
$555$	1.04710e21	2.74024
$556$	2.37200e20	0.612427
$557$	−1.29177e20	−0.329058	−0.164529	−	0.986372i	$-0.552610\pi$
$557$	−1.29177e20	−0.329058	−0.164529	+	0.986372i	$0.552610\pi$
$558$	−2.75360e21	−6.92062
$559$	4.27925e19	0.106116
$560$	1.60657e20	0.393088
$561$	−1.26306e20	−0.304932
$562$	5.23662e20	1.24747
$563$	−4.46668e20	−1.04996	−0.524978	−	0.851116i	$-0.675927\pi$
$563$	−4.46668e20	−1.04996	−0.524978	+	0.851116i	$0.675927\pi$
$564$	4.00654e19	0.0929343
$565$	9.06211e20	2.07427
$566$	4.96917e20	1.12243
$567$	−7.46776e20	−1.66463
$568$	−7.51450e19	−0.165306
$569$	8.63405e19	0.187444	0.0937222	−	0.995598i	$-0.470123\pi$
$569$	8.63405e19	0.187444	0.0937222	+	0.995598i	$0.470123\pi$
$570$	−1.27378e21	−2.72918
$571$	−4.64427e20	−0.982080	−0.491040	−	0.871137i	$-0.663383\pi$
$571$	−4.64427e20	−0.982080	−0.491040	+	0.871137i	$0.663383\pi$
$572$	−2.53384e20	−0.528822
$573$	7.46830e20	1.53837
$574$	9.69456e19	0.197101
$575$	−1.74605e20	−0.350386
$576$	−1.72802e21	−3.42278
$577$	−3.11965e20	−0.609940	−0.304970	−	0.952362i	$-0.598646\pi$
$577$	−3.11965e20	−0.609940	−0.304970	+	0.952362i	$0.598646\pi$
$578$	−6.74301e20	−1.30135
$579$	8.68920e20	1.65535
$580$	1.21071e20	0.227684
$581$	−2.33801e20	−0.434035
$582$	2.14477e21	3.93059
$583$	−2.31798e20	−0.419368
$584$	1.07350e20	0.191737
$585$	1.70104e21	2.99948
$586$	−5.66951e20	−0.986992
$587$	4.47386e20	0.768947	0.384474	−	0.923136i	$-0.374383\pi$
$587$	4.47386e20	0.768947	0.384474	+	0.923136i	$0.374383\pi$
$588$	1.06386e21	1.80533
$589$	−8.94218e20	−1.49823
$590$	1.32393e20	0.219016
$591$	−6.72493e20	−1.09845
$592$	6.89426e20	1.11192
$593$	−4.78058e20	−0.761326	−0.380663	−	0.924714i	$-0.624304\pi$
$593$	−4.78058e20	−0.761326	−0.380663	+	0.924714i	$0.624304\pi$
$594$	1.55013e21	2.43764
$595$	9.56353e19	0.148505
$596$	5.40826e20	0.829297
$597$	3.51117e20	0.531673
$598$	−1.71543e21	−2.56516
$599$	−8.87462e20	−1.31054	−0.655268	−	0.755397i	$-0.727444\pi$
$599$	−8.87462e20	−1.31054	−0.655268	+	0.755397i	$0.727444\pi$
$600$	−4.61501e19	−0.0673036
$601$	−7.46995e20	−1.07587	−0.537934	−	0.842987i	$-0.680795\pi$
$601$	−7.46995e20	−1.07587	−0.537934	+	0.842987i	$0.680795\pi$
$602$	−4.60100e19	−0.0654453
$603$	2.46442e21	3.46206
$604$	3.54105e20	0.491310
$605$	−6.14180e20	−0.841647
$606$	1.96569e21	2.66054
$607$	−8.47902e20	−1.13352	−0.566762	−	0.823882i	$-0.691804\pi$
$607$	−8.47902e20	−1.13352	−0.566762	+	0.823882i	$0.691804\pi$
$608$	−9.56510e20	−1.26303
$609$	1.15365e20	0.150469
$610$	1.63638e20	0.210819
$611$	−3.28701e19	−0.0418304
$612$	−8.12652e20	−1.02157
$613$	7.80117e20	0.968738	0.484369	−	0.874864i	$-0.339049\pi$
$613$	7.80117e20	0.968738	0.484369	+	0.874864i	$0.339049\pi$
$614$	−1.36549e21	−1.67504
$615$	5.71303e20	0.692314
$616$	2.94880e19	0.0353012
$617$	−6.57205e20	−0.777253	−0.388626	−	0.921395i	$-0.627050\pi$
$617$	−6.57205e20	−0.777253	−0.388626	+	0.921395i	$0.627050\pi$
$618$	2.87287e21	3.35663
$619$	5.82164e20	0.671994	0.335997	−	0.941863i	$-0.390927\pi$
$619$	5.82164e20	0.671994	0.335997	+	0.941863i	$0.390927\pi$
$620$	−1.83020e21	−2.08718
$621$	5.54746e21	6.25039
$622$	−9.31151e20	−1.03655
$623$	5.20268e20	0.572225
$624$	1.52124e21	1.65316
$625$	−1.07782e21	−1.15730
$626$	6.59251e20	0.699429
$627$	7.84419e20	0.822321
$628$	−3.09119e20	−0.320206
$629$	4.10399e20	0.420075
$630$	−1.82894e21	−1.84989
$631$	−1.17161e21	−1.17102	−0.585510	−	0.810665i	$-0.699106\pi$
$631$	−1.17161e21	−1.17102	−0.585510	+	0.810665i	$0.699106\pi$
$632$	−2.34888e20	−0.231997
$633$	−2.58895e21	−2.52695
$634$	5.63605e20	0.543632
$635$	1.59797e21	1.52323
$636$	−2.02568e21	−1.90828
$637$	−8.72804e20	−0.812589
$638$	−1.41047e20	−0.129780
$639$	−2.87018e21	−2.61007
$640$	−4.26962e20	−0.383742
$641$	1.88158e20	0.167143	0.0835714	−	0.996502i	$-0.473367\pi$
$641$	1.88158e20	0.167143	0.0835714	+	0.996502i	$0.473367\pi$
$642$	−5.35386e20	−0.470061
$643$	1.01358e21	0.879582	0.439791	−	0.898100i	$-0.355052\pi$
$643$	1.01358e21	0.879582	0.439791	+	0.898100i	$0.355052\pi$
$644$	9.74968e20	0.836269
$645$	−2.71138e20	−0.229875
$646$	−4.99244e20	−0.418378
$647$	5.01153e20	0.415134	0.207567	−	0.978221i	$-0.433446\pi$
$647$	5.01153e20	0.415134	0.207567	+	0.978221i	$0.433446\pi$
$648$	8.63615e20	0.707144
$649$	−8.15306e19	−0.0659911
$650$	3.49802e20	0.279880
$651$	−1.74394e21	−1.37935
$652$	1.28627e20	0.100571
$653$	−6.10073e20	−0.471556	−0.235778	−	0.971807i	$-0.575764\pi$
$653$	−6.10073e20	−0.471556	−0.235778	+	0.971807i	$0.575764\pi$
$654$	2.81941e21	2.15440
$655$	−2.68466e21	−2.02806
$656$	3.76156e20	0.280924
$657$	4.10026e21	3.02741
$658$	3.53415e19	0.0257983
$659$	−5.33183e19	−0.0384800	−0.0192400	−	0.999815i	$-0.506125\pi$
$659$	−5.33183e19	−0.0384800	−0.0192400	+	0.999815i	$0.506125\pi$
$660$	1.60547e21	1.14557
$661$	−1.53579e21	−1.08348	−0.541738	−	0.840547i	$-0.682234\pi$
$661$	−1.53579e21	−1.08348	−0.541738	+	0.840547i	$0.682234\pi$
$662$	−1.32592e21	−0.924876
$663$	9.05560e20	0.624548
$664$	2.70381e20	0.184381
$665$	−5.93939e20	−0.400479
$666$	−7.84852e21	−5.23276
$667$	−5.04765e20	−0.332771
$668$	1.86070e21	1.21298
$669$	−2.89127e21	−1.86377
$670$	3.09868e21	1.97522
$671$	−1.00772e20	−0.0635215
$672$	−1.86542e21	−1.16281
$673$	3.01684e21	1.85969	0.929844	−	0.367955i	$-0.119942\pi$
$673$	3.01684e21	1.85969	0.929844	+	0.367955i	$0.119942\pi$
$674$	−6.36895e20	−0.388257
$675$	−1.13121e21	−0.681970
$676$	−6.41819e19	−0.0382659
$677$	9.23034e20	0.544255	0.272128	−	0.962261i	$-0.412273\pi$
$677$	9.23034e20	0.544255	0.272128	+	0.962261i	$0.412273\pi$
$678$	−9.22598e21	−5.38009
$679$	1.00007e21	0.576773
$680$	−1.10598e20	−0.0630858
$681$	2.47631e21	1.39702
$682$	2.13216e21	1.18970
$683$	−2.87384e20	−0.158602	−0.0793008	−	0.996851i	$-0.525269\pi$
$683$	−2.87384e20	−0.158602	−0.0793008	+	0.996851i	$0.525269\pi$
$684$	5.04694e21	2.75491
$685$	1.36195e21	0.735329
$686$	2.07341e21	1.10727
$687$	−6.66402e21	−3.52014
$688$	−1.78522e20	−0.0932778
$689$	1.66189e21	0.858930
$690$	1.08691e22	5.55682
$691$	−1.08407e21	−0.548242	−0.274121	−	0.961695i	$-0.588387\pi$
$691$	−1.08407e21	−0.548242	−0.274121	+	0.961695i	$0.588387\pi$
$692$	−3.17312e21	−1.58742
$693$	1.12630e21	0.557385
$694$	−5.51873e20	−0.270173
$695$	1.23302e21	0.597149
$696$	−1.33415e20	−0.0639200
$697$	2.23917e20	0.106131
$698$	1.46891e21	0.688776
$699$	2.21320e21	1.02669
$700$	−1.98811e20	−0.0912441
$701$	−7.52083e17	−0.000341492 0	−0.000170746	−	1.00000i	$-0.500054\pi$
$701$	−7.52083e17	−0.000341492 0	−0.000170746		1.00000i	$0.500054\pi$
$702$	−1.11137e22	−4.99266
$703$	−2.54877e21	−1.13283
$704$	1.33803e21	0.588397
$705$	2.08268e20	0.0906159
$706$	−5.30359e21	−2.28315
$707$	9.16564e20	0.390407
$708$	−7.12495e20	−0.300284
$709$	3.14101e20	0.130985	0.0654926	−	0.997853i	$-0.479138\pi$
$709$	3.14101e20	0.130985	0.0654926	+	0.997853i	$0.479138\pi$
$710$	−3.60888e21	−1.48914
$711$	−8.97160e21	−3.66309
$712$	−6.01669e20	−0.243085
$713$	7.63036e21	3.05052
$714$	−9.73646e20	−0.385181
$715$	−1.31714e21	−0.515630
$716$	1.20286e21	0.465980
$717$	3.04608e21	1.16774
$718$	−2.39741e21	−0.909512
$719$	−1.02992e21	−0.386669	−0.193334	−	0.981133i	$-0.561930\pi$
$719$	−1.02992e21	−0.386669	−0.193334	+	0.981133i	$0.561930\pi$
$720$	−7.09642e21	−2.63661
$721$	1.33957e21	0.492551
$722$	−9.02026e20	−0.328239
$723$	−3.86043e21	−1.39027
$724$	2.31522e21	0.825189
$725$	1.02929e20	0.0363081
$726$	6.25286e21	2.18300
$727$	−1.09791e21	−0.379365	−0.189682	−	0.981845i	$-0.560746\pi$
$727$	−1.09791e21	−0.379365	−0.189682	+	0.981845i	$0.560746\pi$
$728$	−2.11416e20	−0.0723024
$729$	1.29222e22	4.37401
$730$	5.15554e21	1.72724
$731$	−1.06270e20	−0.0352395
$732$	−8.80645e20	−0.289047
$733$	9.37043e20	0.304425	0.152212	−	0.988348i	$-0.451360\pi$
$733$	9.37043e20	0.304425	0.152212	+	0.988348i	$0.451360\pi$
$734$	2.71443e21	0.872888
$735$	5.53017e21	1.76029
$736$	8.16190e21	2.57162
$737$	−1.90823e21	−0.595149
$738$	−4.28221e21	−1.32204
$739$	−8.88638e20	−0.271576	−0.135788	−	0.990738i	$-0.543357\pi$
$739$	−8.88638e20	−0.271576	−0.135788	+	0.990738i	$0.543357\pi$
$740$	−5.21656e21	−1.57814
$741$	−5.62394e21	−1.68424
$742$	−1.78684e21	−0.529732
$743$	−2.98620e21	−0.876401	−0.438201	−	0.898877i	$-0.644384\pi$
$743$	−2.98620e21	−0.876401	−0.438201	+	0.898877i	$0.644384\pi$
$744$	2.01680e21	0.585956
$745$	2.81132e21	0.808609
$746$	8.33438e21	2.37319
$747$	1.03273e22	2.91126
$748$	6.29248e20	0.175614
$749$	−2.49641e20	−0.0689766
$750$	9.11915e21	2.49456
$751$	1.10482e21	0.299221	0.149610	−	0.988745i	$-0.452198\pi$
$751$	1.10482e21	0.299221	0.149610	+	0.988745i	$0.452198\pi$
$752$	1.37127e20	0.0367697
$753$	1.08411e22	2.87815
$754$	1.01124e21	0.265809
$755$	1.84071e21	0.479053
$756$	6.31652e21	1.62766
$757$	−3.16956e21	−0.808685	−0.404342	−	0.914608i	$-0.632500\pi$
$757$	−3.16956e21	−0.808685	−0.404342	+	0.914608i	$0.632500\pi$
$758$	3.61715e21	0.913791
$759$	−6.69344e21	−1.67431
$760$	6.86866e20	0.170126
$761$	4.94825e21	1.21357	0.606787	−	0.794864i	$-0.292458\pi$
$761$	4.94825e21	1.21357	0.606787	+	0.794864i	$0.292458\pi$
$762$	−1.62686e22	−3.95084
$763$	1.31464e21	0.316136
$764$	−3.72066e21	−0.885970
$765$	−4.22433e21	−0.996086
$766$	2.74453e21	0.640844
$767$	5.84539e20	0.135160
$768$	−6.08056e21	−1.39231
$769$	−2.90685e21	−0.659137	−0.329569	−	0.944132i	$-0.606903\pi$
$769$	−2.90685e21	−0.659137	−0.329569	+	0.944132i	$0.606903\pi$
$770$	1.41618e21	0.318007
$771$	−4.35283e21	−0.967974
$772$	−4.32890e21	−0.953340
$773$	−6.08091e21	−1.32624	−0.663120	−	0.748513i	$-0.730768\pi$
$773$	−6.08091e21	−1.32624	−0.663120	+	0.748513i	$0.730768\pi$
$774$	2.03232e21	0.438969
$775$	−1.55595e21	−0.332837
$776$	−1.15653e21	−0.245017
$777$	−4.97071e21	−1.04294
$778$	1.02639e22	2.13288
$779$	−1.39062e21	−0.286206
$780$	−1.15105e22	−2.34631
$781$	2.22242e21	0.448688
$782$	4.26005e21	0.851852
$783$	−3.27022e21	−0.647685
$784$	3.64116e21	0.714282
$785$	−1.60686e21	−0.312217
$786$	2.73321e22	5.26021
$787$	1.71185e21	0.326328	0.163164	−	0.986599i	$-0.447830\pi$
$787$	1.71185e21	0.326328	0.163164	+	0.986599i	$0.447830\pi$
$788$	3.35031e21	0.632614
$789$	−1.98087e22	−3.70492
$790$	−1.12806e22	−2.08992
$791$	−4.30191e21	−0.789473
$792$	−1.30252e21	−0.236780
$793$	7.22490e20	0.130102
$794$	7.09882e21	1.26629
$795$	−1.05299e22	−1.86067
$796$	−1.74924e21	−0.306198
$797$	6.26582e21	1.08653	0.543263	−	0.839562i	$-0.317188\pi$
$797$	6.26582e21	1.08653	0.543263	+	0.839562i	$0.317188\pi$
$798$	6.04679e21	1.03873
$799$	8.16287e19	0.0138913
$800$	−1.66434e21	−0.280586
$801$	−2.29809e22	−3.83816
$802$	1.03673e22	1.71536
$803$	−3.17489e21	−0.520430
$804$	−1.66761e22	−2.70815
$805$	5.06808e21	0.815407
$806$	−1.52866e22	−2.43668
$807$	−6.08765e21	−0.961387
$808$	−1.05997e21	−0.165847
$809$	1.10397e22	1.71137	0.855683	−	0.517500i	$-0.173137\pi$
$809$	1.10397e22	1.71137	0.855683	+	0.517500i	$0.173137\pi$
$810$	4.14756e22	6.37022
$811$	−4.46445e20	−0.0679378	−0.0339689	−	0.999423i	$-0.510815\pi$
$811$	−4.46445e20	−0.0679378	−0.0339689	+	0.999423i	$0.510815\pi$
$812$	−5.74742e20	−0.0866568
$813$	−2.66203e21	−0.397679
$814$	6.07723e21	0.899544
$815$	6.68628e20	0.0980624
$816$	−3.77782e21	−0.548990
$817$	6.59984e20	0.0950316
$818$	−1.41712e22	−2.02188
$819$	−8.07509e21	−1.14161
$820$	−2.84619e21	−0.398713
$821$	−5.60175e21	−0.777590	−0.388795	−	0.921324i	$-0.627108\pi$
$821$	−5.60175e21	−0.777590	−0.388795	+	0.921324i	$0.627108\pi$
$822$	−1.38658e22	−1.90724
$823$	9.35824e21	1.27554	0.637772	−	0.770225i	$-0.279856\pi$
$823$	9.35824e21	1.27554	0.637772	+	0.770225i	$0.279856\pi$
$824$	−1.54916e21	−0.209238
$825$	1.36490e21	0.182682
$826$	−6.28488e20	−0.0833579
$827$	2.85055e21	0.374660	0.187330	−	0.982297i	$-0.440017\pi$
$827$	2.85055e21	0.374660	0.187330	+	0.982297i	$0.440017\pi$
$828$	−4.30655e22	−5.60922
$829$	−1.90635e21	−0.246062	−0.123031	−	0.992403i	$-0.539261\pi$
$829$	−1.90635e21	−0.246062	−0.123031	+	0.992403i	$0.539261\pi$
$830$	1.29852e22	1.66097
$831$	1.82696e22	2.31591
$832$	−9.59308e21	−1.20513
$833$	2.16750e21	0.269849
$834$	−1.25531e22	−1.54884
$835$	9.67232e21	1.18272
$836$	−3.90792e21	−0.473586
$837$	4.94348e22	5.93734
$838$	−1.12413e21	−0.133809
$839$	3.73048e21	0.440099	0.220049	−	0.975489i	$-0.429378\pi$
$839$	3.73048e21	0.440099	0.220049	+	0.975489i	$0.429378\pi$
$840$	1.33955e21	0.156627
$841$	2.97558e20	0.0344828
$842$	−2.13435e22	−2.45146
$843$	−1.46494e22	−1.66768
$844$	1.28980e22	1.45530
$845$	−3.33631e20	−0.0373113
$846$	−1.56108e21	−0.173040
$847$	2.91559e21	0.320333
$848$	−6.93307e21	−0.755016
$849$	−1.39012e22	−1.50054
$850$	−8.68689e20	−0.0929443
$851$	2.17486e22	2.30653
$852$	1.94218e22	2.04170
$853$	−1.49267e22	−1.55541	−0.777705	−	0.628629i	$-0.783616\pi$
$853$	−1.49267e22	−1.55541	−0.777705	+	0.628629i	$0.783616\pi$
$854$	−7.76812e20	−0.0802384
$855$	2.62350e22	2.68618
$856$	2.88699e20	0.0293017
$857$	−5.95504e19	−0.00599140	−0.00299570	−	0.999996i	$-0.500954\pi$
$857$	−5.95504e19	−0.00599140	−0.00299570	+	0.999996i	$0.500954\pi$
$858$	1.34096e22	1.33740
$859$	−1.02478e22	−1.01317	−0.506584	−	0.862190i	$-0.669092\pi$
$859$	−1.02478e22	−1.01317	−0.506584	+	0.862190i	$0.669092\pi$
$860$	1.35079e21	0.132388
$861$	−2.71205e21	−0.263496
$862$	2.54367e22	2.44994
$863$	−1.77899e22	−1.69861	−0.849303	−	0.527905i	$-0.822978\pi$
$863$	−1.77899e22	−1.69861	−0.849303	+	0.527905i	$0.822978\pi$
$864$	5.28785e22	5.00525
$865$	−1.64945e22	−1.54781
$866$	3.77383e19	0.00351074
$867$	1.88635e22	1.73972
$868$	8.68819e21	0.794385
$869$	6.94684e21	0.629708
$870$	−6.40734e21	−0.575815
$871$	1.36812e22	1.21896
$872$	−1.52033e21	−0.134296
$873$	−4.41741e22	−3.86866
$874$	−2.64569e22	−2.29722
$875$	4.25209e21	0.366052
$876$	−2.77454e22	−2.36815
$877$	−8.97590e20	−0.0759593	−0.0379796	−	0.999279i	$-0.512092\pi$
$877$	−8.97590e20	−0.0759593	−0.0379796	+	0.999279i	$0.512092\pi$
$878$	2.73252e22	2.29274
$879$	1.58604e22	1.31947
$880$	5.49486e21	0.453249
$881$	1.14265e22	0.934535	0.467268	−	0.884116i	$-0.345238\pi$
$881$	1.14265e22	0.934535	0.467268	+	0.884116i	$0.345238\pi$
$882$	−4.14515e22	−3.36144
$883$	−1.31437e22	−1.05685	−0.528425	−	0.848980i	$-0.677217\pi$
$883$	−1.31437e22	−1.05685	−0.528425	+	0.848980i	$0.677217\pi$
$884$	−4.51144e21	−0.359685
$885$	−3.70370e21	−0.292793
$886$	2.33654e22	1.83155
$887$	−2.54021e22	−1.97443	−0.987217	−	0.159380i	$-0.949051\pi$
$887$	−2.54021e22	−1.97443	−0.987217	+	0.159380i	$0.949051\pi$
$888$	5.74842e21	0.443048
$889$	−7.58578e21	−0.579745
$890$	−2.88955e22	−2.18980
$891$	−2.55415e22	−1.91940
$892$	1.44041e22	1.07337
$893$	−5.06951e20	−0.0374611
$894$	−2.86216e22	−2.09731
$895$	6.25270e21	0.454355
$896$	2.02685e21	0.146053
$897$	4.79891e22	3.42925
$898$	1.27779e22	0.905494
$899$	−4.49809e21	−0.316104
$900$	8.78172e21	0.612013
$901$	−4.12709e21	−0.285238
$902$	3.31578e21	0.227267
$903$	1.28713e21	0.0874910
$904$	4.97498e21	0.335373
$905$	1.20350e22	0.804603
$906$	−1.87399e22	−1.24253
$907$	3.72959e20	0.0245248	0.0122624	−	0.999925i	$-0.496097\pi$
$907$	3.72959e20	0.0245248	0.0122624	+	0.999925i	$0.496097\pi$
$908$	−1.23368e22	−0.804560
$909$	−4.04858e22	−2.61862
$910$	−1.01534e22	−0.651328
$911$	8.66704e21	0.551421	0.275710	−	0.961241i	$-0.411087\pi$
$911$	8.66704e21	0.551421	0.275710	+	0.961241i	$0.411087\pi$
$912$	2.34620e22	1.48048
$913$	−7.99655e21	−0.500463
$914$	−3.64705e22	−2.26384
$915$	−4.57777e21	−0.281836
$916$	3.31997e22	2.02730
$917$	1.27445e22	0.771882
$918$	2.75996e22	1.65799
$919$	1.01477e22	0.604648	0.302324	−	0.953205i	$-0.402237\pi$
$919$	1.01477e22	0.604648	0.302324	+	0.953205i	$0.402237\pi$
$920$	−5.86103e21	−0.346390
$921$	3.81994e22	2.23929
$922$	−2.60524e22	−1.51484
$923$	−1.59338e22	−0.918982
$924$	−7.62138e21	−0.436007
$925$	−4.43488e21	−0.251663
$926$	2.66646e21	0.150091
$927$	−5.91704e22	−3.30375
$928$	−4.81143e21	−0.266480
$929$	−3.30586e21	−0.181621	−0.0908105	−	0.995868i	$-0.528946\pi$
$929$	−3.30586e21	−0.181621	−0.0908105	+	0.995868i	$0.528946\pi$
$930$	9.68576e22	5.27851
$931$	−1.34612e22	−0.727712
$932$	−1.10260e22	−0.591287
$933$	2.60489e22	1.38573
$934$	1.57188e22	0.829502
$935$	3.27096e21	0.171233
$936$	9.33851e21	0.484963
$937$	−7.31835e21	−0.377022	−0.188511	−	0.982071i	$-0.560366\pi$
$937$	−7.31835e21	−0.377022	−0.188511	+	0.982071i	$0.560366\pi$
$938$	−1.47099e22	−0.751774
$939$	−1.84425e22	−0.935037
$940$	−1.03758e21	−0.0521869
$941$	3.88944e21	0.194073	0.0970366	−	0.995281i	$-0.469064\pi$
$941$	3.88944e21	0.194073	0.0970366	+	0.995281i	$0.469064\pi$
$942$	1.63592e22	0.809805
$943$	1.18662e22	0.582739
$944$	−2.43858e21	−0.118808
$945$	3.28346e22	1.58706
$946$	−1.57365e21	−0.0754615
$947$	1.77275e22	0.843380	0.421690	−	0.906740i	$-0.361437\pi$
$947$	1.77275e22	0.843380	0.421690	+	0.906740i	$0.361437\pi$
$948$	6.07084e22	2.86541
$949$	2.27626e22	1.06592
$950$	5.39496e21	0.250646
$951$	−1.57668e22	−0.726759
$952$	5.25025e20	0.0240106
$953$	−1.24731e22	−0.565948	−0.282974	−	0.959128i	$-0.591321\pi$
$953$	−1.24731e22	−0.565948	−0.282974	+	0.959128i	$0.591321\pi$
$954$	7.89269e22	3.55314
$955$	−1.93407e22	−0.863868
$956$	−1.51753e22	−0.672519
$957$	3.94578e21	0.173497
$958$	−2.02287e22	−0.882523
$959$	−6.46536e21	−0.279868
$960$	6.07827e22	2.61063
$961$	4.45309e22	1.89774
$962$	−4.35711e22	−1.84241
$963$	1.10269e22	0.462656
$964$	1.92324e22	0.800673
$965$	−2.25025e22	−0.929557
$966$	−5.15972e22	−2.11494
$967$	−3.76222e22	−1.53019	−0.765095	−	0.643917i	$-0.777308\pi$
$967$	−3.76222e22	−1.53019	−0.765095	+	0.643917i	$0.777308\pi$
$968$	−3.37177e21	−0.136079
$969$	1.39663e22	0.559312
$970$	−5.55432e22	−2.20720
$971$	−9.55067e21	−0.376608	−0.188304	−	0.982111i	$-0.560299\pi$
$971$	−9.55067e21	−0.376608	−0.188304	+	0.982111i	$0.560299\pi$
$972$	−1.23251e23	−4.82274
$973$	−5.85329e21	−0.227276
$974$	4.21248e22	1.62310
$975$	−9.78571e21	−0.374160
$976$	−3.01409e21	−0.114362
$977$	−1.23664e22	−0.465624	−0.232812	−	0.972522i	$-0.574793\pi$
$977$	−1.23664e22	−0.465624	−0.232812	+	0.972522i	$0.574793\pi$
$978$	−6.80719e21	−0.254347
$979$	1.77945e22	0.659803
$980$	−2.75509e22	−1.01377
$981$	−5.80693e22	−2.12046
$982$	3.64301e21	0.132015
$983$	6.99457e21	0.251542	0.125771	−	0.992059i	$-0.459860\pi$
$983$	6.99457e21	0.251542	0.125771	+	0.992059i	$0.459860\pi$
$984$	3.13638e21	0.111935
$985$	1.74156e22	0.616832
$986$	−2.51129e21	−0.0882716
$987$	−9.88677e20	−0.0344886
$988$	2.80181e22	0.969977
$989$	−5.63164e21	−0.193492
$990$	−6.25542e22	−2.13301
$991$	−2.31198e22	−0.782406	−0.391203	−	0.920304i	$-0.627941\pi$
$991$	−2.31198e22	−0.782406	−0.391203	+	0.920304i	$0.627941\pi$
$992$	7.27328e22	2.44283
$993$	3.70927e22	1.23643
$994$	1.71318e22	0.566768
$995$	−9.09292e21	−0.298559
$996$	−6.98819e22	−2.27730
$997$	−2.57759e22	−0.833682	−0.416841	−	0.908979i	$-0.636863\pi$
$997$	−2.57759e22	−0.833682	−0.416841	+	0.908979i	$0.636863\pi$
$998$	−3.36581e21	−0.108046
$999$	1.40903e23	4.48930

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.16.a.a.1.14	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.16.a.a.1.14	✓	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)

\(f(q)\)	\(=\)	\(q+263.654 q^{2} -7375.70 q^{3} +36745.2 q^{4} +191009. q^{5} -1.94463e6 q^{6} -906747. q^{7} +1.04862e6 q^{8} +4.00521e7 q^{9} +O(q^{10})\)	\(q+263.654 q^{2} -7375.70 q^{3} +36745.2 q^{4} +191009. q^{5} -1.94463e6 q^{6} -906747. q^{7} +1.04862e6 q^{8} +4.00521e7 q^{9} +5.03603e7 q^{10} -3.10129e7 q^{11} -2.71022e8 q^{12} +2.22349e8 q^{13} -2.39067e8 q^{14} -1.40883e9 q^{15} -9.27597e8 q^{16} -5.52176e8 q^{17} +1.05599e10 q^{18} +3.42927e9 q^{19} +7.01868e9 q^{20} +6.68790e9 q^{21} -8.17668e9 q^{22} -2.92619e10 q^{23} -7.73428e9 q^{24} +5.96696e9 q^{25} +5.86232e10 q^{26} -1.89579e11 q^{27} -3.33186e10 q^{28} +1.72499e10 q^{29} -3.71443e11 q^{30} -2.60761e11 q^{31} -2.78925e11 q^{32} +2.28742e11 q^{33} -1.45583e11 q^{34} -1.73197e11 q^{35} +1.47172e12 q^{36} -7.43239e11 q^{37} +9.04139e11 q^{38} -1.63998e12 q^{39} +2.00295e11 q^{40} -4.05516e11 q^{41} +1.76329e12 q^{42} +1.92456e11 q^{43} -1.13958e12 q^{44} +7.65032e12 q^{45} -7.71502e12 q^{46} -1.47831e11 q^{47} +6.84168e12 q^{48} -3.92537e12 q^{49} +1.57321e12 q^{50} +4.07269e12 q^{51} +8.17028e12 q^{52} +7.47422e12 q^{53} -4.99833e13 q^{54} -5.92376e12 q^{55} -9.50828e11 q^{56} -2.52933e13 q^{57} +4.54799e12 q^{58} +2.62892e12 q^{59} -5.17677e13 q^{60} +3.24935e12 q^{61} -6.87505e13 q^{62} -3.63171e13 q^{63} -4.31442e13 q^{64} +4.24708e13 q^{65} +6.03088e13 q^{66} +6.15302e13 q^{67} -2.02899e13 q^{68} +2.15827e14 q^{69} -4.56640e13 q^{70} -7.16612e13 q^{71} +4.19993e13 q^{72} +1.02373e14 q^{73} -1.95958e14 q^{74} -4.40105e13 q^{75} +1.26009e14 q^{76} +2.81209e13 q^{77} -4.32387e14 q^{78} -2.23998e14 q^{79} -1.77180e14 q^{80} +8.23577e14 q^{81} -1.06916e14 q^{82} +2.57846e14 q^{83} +2.45748e14 q^{84} -1.05471e14 q^{85} +5.07418e13 q^{86} -1.27230e14 q^{87} -3.25207e13 q^{88} -5.73775e14 q^{89} +2.01704e15 q^{90} -2.01615e14 q^{91} -1.07524e15 q^{92} +1.92329e15 q^{93} -3.89761e13 q^{94} +6.55022e14 q^{95} +2.05727e15 q^{96} -1.10292e15 q^{97} -1.03494e15 q^{98} -1.24213e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 128 q^{2} - 3214 q^{3} + 239962 q^{4} - 82010 q^{5} - 112778 q^{6} - 3706320 q^{7} - 21137070 q^{8} + 73272578 q^{9}+O(q^{10}) \) 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

Modular forms

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