LMFDB - Embedded newform 29.16.a.a.1.7

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			1.7
Root			$62.3494$ 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)

$f(q)$	$=$	$q-70.3494 q^{2} -4845.56 q^{3} -27819.0 q^{4} +4719.52 q^{5} +340882. q^{6} -2.30433e6 q^{7} +4.26226e6 q^{8} +9.13052e6 q^{9} +O(q^{10})$	\(q-70.3494 q^{2} -4845.56 q^{3} -27819.0 q^{4} +4719.52 q^{5} +340882. q^{6} -2.30433e6 q^{7} +4.26226e6 q^{8} +9.13052e6 q^{9} -332016. q^{10} -1.37602e7 q^{11} +1.34798e8 q^{12} +7.31720e7 q^{13} +1.62108e8 q^{14} -2.28687e7 q^{15} +6.11724e8 q^{16} +2.82447e9 q^{17} -6.42326e8 q^{18} +2.96680e9 q^{19} -1.31292e8 q^{20} +1.11657e10 q^{21} +9.68023e8 q^{22} -7.26683e9 q^{23} -2.06530e10 q^{24} -3.04953e10 q^{25} -5.14761e9 q^{26} +2.52860e10 q^{27} +6.41040e10 q^{28} +1.72499e10 q^{29} +1.60880e9 q^{30} +2.84569e10 q^{31} -1.82700e11 q^{32} +6.66759e10 q^{33} -1.98700e11 q^{34} -1.08753e10 q^{35} -2.54001e11 q^{36} -2.22819e10 q^{37} -2.08713e11 q^{38} -3.54559e11 q^{39} +2.01158e10 q^{40} +5.74546e11 q^{41} -7.85504e11 q^{42} +3.24258e11 q^{43} +3.82795e11 q^{44} +4.30917e10 q^{45} +5.11218e11 q^{46} -4.37350e12 q^{47} -2.96414e12 q^{48} +5.62361e11 q^{49} +2.14533e12 q^{50} -1.36861e13 q^{51} -2.03557e12 q^{52} -7.41433e11 q^{53} -1.77886e12 q^{54} -6.49417e10 q^{55} -9.82163e12 q^{56} -1.43758e13 q^{57} -1.21352e12 q^{58} -6.92378e12 q^{59} +6.36184e11 q^{60} +5.42668e12 q^{61} -2.00193e12 q^{62} -2.10397e13 q^{63} -7.19213e12 q^{64} +3.45337e11 q^{65} -4.69061e12 q^{66} +1.83301e13 q^{67} -7.85739e13 q^{68} +3.52119e13 q^{69} +7.65073e11 q^{70} -7.53451e13 q^{71} +3.89166e13 q^{72} +1.51654e14 q^{73} +1.56752e12 q^{74} +1.47767e14 q^{75} -8.25334e13 q^{76} +3.17080e13 q^{77} +2.49430e13 q^{78} +2.72297e14 q^{79} +2.88705e12 q^{80} -2.53538e14 q^{81} -4.04190e13 q^{82} -1.54552e14 q^{83} -3.10619e14 q^{84} +1.33302e13 q^{85} -2.28114e13 q^{86} -8.35853e13 q^{87} -5.86496e13 q^{88} +4.51001e14 q^{89} -3.03148e12 q^{90} -1.68612e14 q^{91} +2.02156e14 q^{92} -1.37890e14 q^{93} +3.07673e14 q^{94} +1.40019e13 q^{95} +8.85284e14 q^{96} +7.04240e14 q^{97} -3.95618e13 q^{98} -1.25638e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−70.3494	−0.388629	−0.194315	−	0.980939i	$-0.562248\pi$
$2$	−70.3494	−0.388629	−0.194315	+	0.980939i	$0.562248\pi$
$3$	−4845.56	−1.27919	−0.639594	−	0.768713i	$-0.720897\pi$
$3$	−4845.56	−1.27919	−0.639594	+	0.768713i	$0.720897\pi$
$4$	−27819.0	−0.848967
$5$	4719.52	0.0270161	0.0135081	−	0.999909i	$-0.495700\pi$
$5$	4719.52	0.0270161	0.0135081	+	0.999909i	$0.495700\pi$
$6$	340882.	0.497130
$7$	−2.30433e6	−1.05757	−0.528785	−	0.848756i	$-0.677352\pi$
$7$	−2.30433e6	−1.05757	−0.528785	+	0.848756i	$0.677352\pi$
$8$	4.26226e6	0.718563
$9$	9.13052e6	0.636321
$10$	−332016.	−0.0104993
$11$	−1.37602e7	−0.212902	−0.106451	−	0.994318i	$-0.533949\pi$
$11$	−1.37602e7	−0.212902	−0.106451	+	0.994318i	$0.533949\pi$
$12$	1.34798e8	1.08599
$13$	7.31720e7	0.323422	0.161711	−	0.986838i	$-0.448299\pi$
$13$	7.31720e7	0.323422	0.161711	+	0.986838i	$0.448299\pi$
$14$	1.62108e8	0.411002
$15$	−2.28687e7	−0.0345587
$16$	6.11724e8	0.569713
$17$	2.82447e9	1.66944	0.834719	−	0.550676i	$-0.185630\pi$
$17$	2.82447e9	1.66944	0.834719	+	0.550676i	$0.185630\pi$
$18$	−6.42326e8	−0.247293
$19$	2.96680e9	0.761442	0.380721	−	0.924690i	$-0.375676\pi$
$19$	2.96680e9	0.761442	0.380721	+	0.924690i	$0.375676\pi$
$20$	−1.31292e8	−0.0229358
$21$	1.11657e10	1.35283
$22$	9.68023e8	0.0827400
$23$	−7.26683e9	−0.445027	−0.222514	−	0.974930i	$-0.571426\pi$
$23$	−7.26683e9	−0.445027	−0.222514	+	0.974930i	$0.571426\pi$
$24$	−2.06530e10	−0.919177
$25$	−3.04953e10	−0.999270
$26$	−5.14761e9	−0.125691
$27$	2.52860e10	0.465213
$28$	6.41040e10	0.897842
$29$	1.72499e10	0.185695
$29$	1.72499e10	0.185695
$30$	1.60880e9	0.0134305
$31$	2.84569e10	0.185770	0.0928850	−	0.995677i	$-0.470391\pi$
$31$	2.84569e10	0.185770	0.0928850	+	0.995677i	$0.470391\pi$
$32$	−1.82700e11	−0.939970
$33$	6.66759e10	0.272342
$34$	−1.98700e11	−0.648793
$35$	−1.08753e10	−0.0285714
$36$	−2.54001e11	−0.540216
$37$	−2.22819e10	−0.0385869	−0.0192935	−	0.999814i	$-0.506142\pi$
$37$	−2.22819e10	−0.0385869	−0.0192935	+	0.999814i	$0.506142\pi$
$38$	−2.08713e11	−0.295919
$39$	−3.54559e11	−0.413718
$40$	2.01158e10	0.0194128
$41$	5.74546e11	0.460729	0.230365	−	0.973104i	$-0.426008\pi$
$41$	5.74546e11	0.460729	0.230365	+	0.973104i	$0.426008\pi$
$42$	−7.85504e11	−0.525749
$43$	3.24258e11	0.181919	0.0909593	−	0.995855i	$-0.471007\pi$
$43$	3.24258e11	0.181919	0.0909593	+	0.995855i	$0.471007\pi$
$44$	3.82795e11	0.180747
$45$	4.30917e10	0.0171909
$46$	5.11218e11	0.172951
$47$	−4.37350e12	−1.25920	−0.629601	−	0.776918i	$-0.716782\pi$
$47$	−4.37350e12	−1.25920	−0.629601	+	0.776918i	$0.716782\pi$
$48$	−2.96414e12	−0.728769
$49$	5.62361e11	0.118453
$50$	2.14533e12	0.388346
$51$	−1.36861e13	−2.13553
$52$	−2.03557e12	−0.274575
$53$	−7.41433e11	−0.0866967	−0.0433484	−	0.999060i	$-0.513803\pi$
$53$	−7.41433e11	−0.0866967	−0.0433484	+	0.999060i	$0.513803\pi$
$54$	−1.77886e12	−0.180796
$55$	−6.49417e10	−0.00575179
$56$	−9.82163e12	−0.759930
$57$	−1.43758e13	−0.974027
$58$	−1.21352e12	−0.0721667
$59$	−6.92378e12	−0.362204	−0.181102	−	0.983464i	$-0.557966\pi$
$59$	−6.92378e12	−0.362204	−0.181102	+	0.983464i	$0.557966\pi$
$60$	6.36184e11	0.0293392
$61$	5.42668e12	0.221085	0.110543	−	0.993871i	$-0.464741\pi$
$61$	5.42668e12	0.221085	0.110543	+	0.993871i	$0.464741\pi$
$62$	−2.00193e12	−0.0721957
$63$	−2.10397e13	−0.672954
$64$	−7.19213e12	−0.204413
$65$	3.45337e11	0.00873762
$66$	−4.69061e12	−0.105840
$67$	1.83301e13	0.369491	0.184745	−	0.982786i	$-0.440854\pi$
$67$	1.83301e13	0.369491	0.184745	+	0.982786i	$0.440854\pi$
$68$	−7.85739e13	−1.41730
$69$	3.52119e13	0.569273
$70$	7.65073e11	0.0111037
$71$	−7.53451e13	−0.983144	−0.491572	−	0.870837i	$-0.663578\pi$
$71$	−7.53451e13	−0.983144	−0.491572	+	0.870837i	$0.663578\pi$
$72$	3.89166e13	0.457237
$73$	1.51654e14	1.60670	0.803348	−	0.595510i	$-0.203050\pi$
$73$	1.51654e14	1.60670	0.803348	+	0.595510i	$0.203050\pi$
$74$	1.56752e12	0.0149960
$75$	1.47767e14	1.27825
$76$	−8.25334e13	−0.646439
$77$	3.17080e13	0.225159
$78$	2.49430e13	0.160783
$79$	2.72297e14	1.59529	0.797646	−	0.603126i	$-0.206078\pi$
$79$	2.72297e14	1.59529	0.797646	+	0.603126i	$0.206078\pi$
$80$	2.88705e12	0.0153914
$81$	−2.53538e14	−1.23142
$82$	−4.04190e13	−0.179053
$83$	−1.54552e14	−0.625157	−0.312579	−	0.949892i	$-0.601193\pi$
$83$	−1.54552e14	−0.625157	−0.312579	+	0.949892i	$0.601193\pi$
$84$	−3.10619e14	−1.14851
$85$	1.33302e13	0.0451018
$86$	−2.28114e13	−0.0706989
$87$	−8.35853e13	−0.237539
$88$	−5.86496e13	−0.152984
$89$	4.51001e14	1.08082	0.540409	−	0.841403i	$-0.318270\pi$
$89$	4.51001e14	1.08082	0.540409	+	0.841403i	$0.318270\pi$
$90$	−3.03148e12	−0.00668090
$91$	−1.68612e14	−0.342042
$92$	2.02156e14	0.377813
$93$	−1.37890e14	−0.237635
$94$	3.07673e14	0.489363
$95$	1.40019e13	0.0205712
$96$	8.85284e14	1.20240
$97$	7.04240e14	0.884978	0.442489	−	0.896774i	$-0.354096\pi$
$97$	7.04240e14	0.884978	0.442489	+	0.896774i	$0.354096\pi$
$98$	−3.95618e13	−0.0460342
$99$	−1.25638e14	−0.135474
$100$	8.48348e14	0.848348
$101$	1.92443e15	1.78604	0.893020	−	0.450017i	$-0.148582\pi$
$101$	1.92443e15	1.78604	0.893020	+	0.450017i	$0.148582\pi$
$102$	9.62812e14	0.829928
$103$	−1.85229e14	−0.148398	−0.0741992	−	0.997243i	$-0.523640\pi$
$103$	−1.85229e14	−0.148398	−0.0741992	+	0.997243i	$0.523640\pi$
$104$	3.11878e14	0.232399
$105$	5.26970e13	0.0365482
$106$	5.21594e13	0.0336929
$107$	−4.43039e14	−0.266725	−0.133363	−	0.991067i	$-0.542577\pi$
$107$	−4.43039e14	−0.266725	−0.133363	+	0.991067i	$0.542577\pi$
$108$	−7.03431e14	−0.394951
$109$	3.90790e14	0.204760	0.102380	−	0.994745i	$-0.467354\pi$
$109$	3.90790e14	0.204760	0.102380	+	0.994745i	$0.467354\pi$
$110$	4.56861e12	0.00223532
$111$	1.07968e14	0.0493599
$112$	−1.40961e15	−0.602511
$113$	−2.82834e15	−1.13095	−0.565475	−	0.824765i	$-0.691307\pi$
$113$	−2.82834e15	−1.13095	−0.565475	+	0.824765i	$0.691307\pi$
$114$	1.01133e15	0.378536
$115$	−3.42960e13	−0.0120229
$116$	−4.79874e14	−0.157649
$117$	6.68098e14	0.205801
$118$	4.87084e14	0.140763
$119$	−6.50851e15	−1.76555
$120$	−9.74724e13	−0.0248326
$121$	−3.98790e15	−0.954673
$122$	−3.81763e14	−0.0859203
$123$	−2.78400e15	−0.589359
$124$	−7.91643e14	−0.157713
$125$	−2.87952e14	−0.0540125
$126$	1.48013e15	0.261530
$127$	−8.41181e15	−1.40075	−0.700377	−	0.713773i	$-0.746985\pi$
$127$	−8.41181e15	−1.40075	−0.700377	+	0.713773i	$0.746985\pi$
$128$	6.49268e15	1.01941
$129$	−1.57121e15	−0.232708
$130$	−2.42943e13	−0.00339570
$131$	−5.58272e15	−0.736735	−0.368367	−	0.929680i	$-0.620083\pi$
$131$	−5.58272e15	−0.736735	−0.368367	+	0.929680i	$0.620083\pi$
$132$	−1.85485e15	−0.231209
$133$	−6.83649e15	−0.805278
$134$	−1.28951e15	−0.143595
$135$	1.19338e14	0.0125683
$136$	1.20386e16	1.19960
$137$	−2.63778e15	−0.248791	−0.124396	−	0.992233i	$-0.539699\pi$
$137$	−2.63778e15	−0.248791	−0.124396	+	0.992233i	$0.539699\pi$
$138$	−2.47713e15	−0.221236
$139$	7.89492e15	0.667939	0.333969	−	0.942584i	$-0.391612\pi$
$139$	7.89492e15	0.667939	0.333969	+	0.942584i	$0.391612\pi$
$140$	3.02540e14	0.0242562
$141$	2.11921e16	1.61076
$142$	5.30048e15	0.382079
$143$	−1.00686e15	−0.0688573
$144$	5.58536e15	0.362520
$145$	8.14112e13	0.00501677
$146$	−1.06688e16	−0.624409
$147$	−2.72495e15	−0.151523
$148$	6.19860e14	0.0327590
$149$	−3.47170e16	−1.74440	−0.872199	−	0.489151i	$-0.837307\pi$
$149$	−3.47170e16	−1.74440	−0.872199	+	0.489151i	$0.837307\pi$
$150$	−1.03953e16	−0.496767
$151$	−2.59439e16	−1.17953	−0.589764	−	0.807575i	$-0.700779\pi$
$151$	−2.59439e16	−1.17953	−0.589764	+	0.807575i	$0.700779\pi$
$152$	1.26453e16	0.547144
$153$	2.57889e16	1.06230
$154$	−2.23064e15	−0.0875033
$155$	1.34303e14	0.00501879
$156$	9.86347e15	0.351233
$157$	1.56168e16	0.530083	0.265041	−	0.964237i	$-0.414614\pi$
$157$	1.56168e16	0.530083	0.265041	+	0.964237i	$0.414614\pi$
$158$	−1.91560e16	−0.619977
$159$	3.59265e15	0.110901
$160$	−8.62258e14	−0.0253944
$161$	1.67452e16	0.470647
$162$	1.78362e16	0.478565
$163$	4.60070e16	1.17874	0.589368	−	0.807865i	$-0.299377\pi$
$163$	4.60070e16	1.17874	0.589368	+	0.807865i	$0.299377\pi$
$164$	−1.59833e16	−0.391144
$165$	3.14679e14	0.00735762
$166$	1.08727e16	0.242954
$167$	−8.49790e15	−0.181526	−0.0907628	−	0.995873i	$-0.528931\pi$
$167$	−8.49790e15	−0.181526	−0.0907628	+	0.995873i	$0.528931\pi$
$168$	4.75913e16	0.972093
$169$	−4.58317e16	−0.895398
$170$	−9.37769e14	−0.0175279
$171$	2.70885e16	0.484522
$172$	−9.02051e15	−0.154443
$173$	9.14612e16	1.49931	0.749654	−	0.661830i	$-0.230220\pi$
$173$	9.14612e16	1.49931	0.749654	+	0.661830i	$0.230220\pi$
$174$	5.88017e15	0.0923147
$175$	7.02712e16	1.05680
$176$	−8.41746e15	−0.121293
$177$	3.35496e16	0.463327
$178$	−3.17276e16	−0.420037
$179$	−3.89485e16	−0.494416	−0.247208	−	0.968962i	$-0.579513\pi$
$179$	−3.89485e16	−0.494416	−0.247208	+	0.968962i	$0.579513\pi$
$180$	−1.19877e15	−0.0145945
$181$	3.33493e16	0.389491	0.194746	−	0.980854i	$-0.437612\pi$
$181$	3.33493e16	0.389491	0.194746	+	0.980854i	$0.437612\pi$
$182$	1.18618e16	0.132927
$183$	−2.62953e16	−0.282810
$184$	−3.09731e16	−0.319780
$185$	−1.05160e14	−0.00104247
$186$	9.70046e15	0.0923518
$187$	−3.88653e16	−0.355427
$188$	1.21666e17	1.06902
$189$	−5.82672e16	−0.491995
$190$	−9.85026e14	−0.00799458
$191$	9.57842e16	0.747384	0.373692	−	0.927553i	$-0.378092\pi$
$191$	9.57842e16	0.747384	0.373692	+	0.927553i	$0.378092\pi$
$192$	3.48499e16	0.261482
$193$	−2.72739e17	−1.96819	−0.984096	−	0.177638i	$-0.943154\pi$
$193$	−2.72739e17	−1.96819	−0.984096	+	0.177638i	$0.943154\pi$
$194$	−4.95429e16	−0.343928
$195$	−1.67335e15	−0.0111771
$196$	−1.56443e16	−0.100562
$197$	−8.09927e16	−0.501128	−0.250564	−	0.968100i	$-0.580616\pi$
$197$	−8.09927e16	−0.501128	−0.250564	+	0.968100i	$0.580616\pi$
$198$	8.83855e15	0.0526492
$199$	−1.44654e17	−0.829719	−0.414859	−	0.909886i	$-0.636169\pi$
$199$	−1.44654e17	−0.829719	−0.414859	+	0.909886i	$0.636169\pi$
$200$	−1.29979e17	−0.718038
$201$	−8.88195e16	−0.472648
$202$	−1.35382e17	−0.694108
$203$	−3.97494e16	−0.196386
$204$	3.80734e17	1.81299
$205$	2.71158e15	0.0124471
$206$	1.30307e16	0.0576720
$207$	−6.63499e16	−0.283180
$208$	4.47611e16	0.184258
$209$	−4.08239e16	−0.162113
$210$	−3.70720e15	−0.0142037
$211$	−3.93895e17	−1.45634	−0.728168	−	0.685399i	$-0.759628\pi$
$211$	−3.93895e17	−1.45634	−0.728168	+	0.685399i	$0.759628\pi$
$212$	2.06259e16	0.0736027
$213$	3.65089e17	1.25763
$214$	3.11676e16	0.103657
$215$	1.53034e15	0.00491474
$216$	1.07776e17	0.334285
$217$	−6.55741e16	−0.196465
$218$	−2.74919e16	−0.0795757
$219$	−7.34850e17	−2.05527
$220$	1.80661e15	0.00488308
$221$	2.06672e17	0.539934
$222$	−7.59551e15	−0.0191827
$223$	3.95369e16	0.0965420	0.0482710	−	0.998834i	$-0.484629\pi$
$223$	3.95369e16	0.0965420	0.0482710	+	0.998834i	$0.484629\pi$
$224$	4.21001e17	0.994083
$225$	−2.78438e17	−0.635857
$226$	1.98972e17	0.439520
$227$	−2.27650e17	−0.486489	−0.243245	−	0.969965i	$-0.578212\pi$
$227$	−2.27650e17	−0.486489	−0.243245	+	0.969965i	$0.578212\pi$
$228$	3.99920e17	0.826917
$229$	−5.10573e17	−1.02163	−0.510813	−	0.859692i	$-0.670656\pi$
$229$	−5.10573e17	−1.02163	−0.510813	+	0.859692i	$0.670656\pi$
$230$	2.41270e15	0.00467246
$231$	−1.53643e17	−0.288020
$232$	7.35234e16	0.133434
$233$	6.56879e17	1.15429	0.577147	−	0.816641i	$-0.304166\pi$
$233$	6.56879e17	1.15429	0.577147	+	0.816641i	$0.304166\pi$
$234$	−4.70003e16	−0.0799801
$235$	−2.06409e16	−0.0340188
$236$	1.92612e17	0.307499
$237$	−1.31943e18	−2.04068
$238$	4.57870e17	0.686143
$239$	−2.87357e17	−0.417290	−0.208645	−	0.977991i	$-0.566905\pi$
$239$	−2.87357e17	−0.417290	−0.208645	+	0.977991i	$0.566905\pi$
$240$	−1.39894e16	−0.0196885
$241$	−1.72750e17	−0.235662	−0.117831	−	0.993034i	$-0.537594\pi$
$241$	−1.72750e17	−0.235662	−0.117831	+	0.993034i	$0.537594\pi$
$242$	2.80547e17	0.371014
$243$	8.65705e17	1.11000
$244$	−1.50964e17	−0.187694
$245$	2.65408e15	0.00320013
$246$	1.95852e17	0.229042
$247$	2.17087e17	0.246267
$248$	1.21291e17	0.133487
$249$	7.48891e17	0.799693
$250$	2.02572e16	0.0209909
$251$	−1.20684e18	−1.21366	−0.606828	−	0.794833i	$-0.707558\pi$
$251$	−1.20684e18	−1.21366	−0.606828	+	0.794833i	$0.707558\pi$
$252$	5.85302e17	0.571316
$253$	9.99932e16	0.0947472
$254$	5.91766e17	0.544374
$255$	−6.45921e16	−0.0576936
$256$	−2.21084e17	−0.191760
$257$	9.55584e17	0.804953	0.402476	−	0.915430i	$-0.368150\pi$
$257$	9.55584e17	0.804953	0.402476	+	0.915430i	$0.368150\pi$
$258$	1.10534e17	0.0904372
$259$	5.13449e16	0.0408083
$260$	−9.60692e15	−0.00741795
$261$	1.57500e17	0.118162
$262$	3.92741e17	0.286317
$263$	−3.68713e16	−0.0261228	−0.0130614	−	0.999915i	$-0.504158\pi$
$263$	−3.68713e16	−0.0261228	−0.0130614	+	0.999915i	$0.504158\pi$
$264$	2.84190e17	0.195695
$265$	−3.49921e15	−0.00234221
$266$	4.80943e17	0.312955
$267$	−2.18535e18	−1.38257
$268$	−5.09924e17	−0.313685
$269$	7.56814e17	0.452738	0.226369	−	0.974042i	$-0.427314\pi$
$269$	7.56814e17	0.452738	0.226369	+	0.974042i	$0.427314\pi$
$270$	−8.39536e15	−0.00488440
$271$	2.72626e18	1.54276	0.771378	−	0.636378i	$-0.219568\pi$
$271$	2.72626e18	1.54276	0.771378	+	0.636378i	$0.219568\pi$
$272$	1.72780e18	0.951100
$273$	8.17021e17	0.437535
$274$	1.85567e17	0.0966876
$275$	4.19622e17	0.212747
$276$	−9.79557e17	−0.483294
$277$	2.68856e18	1.29099	0.645493	−	0.763766i	$-0.276652\pi$
$277$	2.68856e18	1.29099	0.645493	+	0.763766i	$0.276652\pi$
$278$	−5.55403e17	−0.259581
$279$	2.59827e17	0.118209
$280$	−4.63534e16	−0.0205304
$281$	−2.37967e18	−1.02617	−0.513086	−	0.858337i	$-0.671498\pi$
$281$	−2.37967e18	−1.02617	−0.513086	+	0.858337i	$0.671498\pi$
$282$	−1.49085e18	−0.625987
$283$	−2.00988e18	−0.821812	−0.410906	−	0.911678i	$-0.634788\pi$
$283$	−2.00988e18	−0.821812	−0.410906	+	0.911678i	$0.634788\pi$
$284$	2.09602e18	0.834657
$285$	−6.78470e16	−0.0263145
$286$	7.08322e16	0.0267600
$287$	−1.32394e18	−0.487253
$288$	−1.66815e18	−0.598123
$289$	5.11522e18	1.78702
$290$	−5.72723e15	−0.00194966
$291$	−3.41243e18	−1.13205
$292$	−4.21887e18	−1.36403
$293$	1.59267e18	0.501902	0.250951	−	0.968000i	$-0.419257\pi$
$293$	1.59267e18	0.501902	0.250951	+	0.968000i	$0.419257\pi$
$294$	1.91699e17	0.0588863
$295$	−3.26769e16	−0.00978534
$296$	−9.49714e16	−0.0277271
$297$	−3.47941e17	−0.0990449
$298$	2.44232e18	0.677924
$299$	−5.31729e17	−0.143932
$300$	−4.11072e18	−1.08520
$301$	−7.47196e17	−0.192391
$302$	1.82514e18	0.458399
$303$	−9.32492e18	−2.28468
$304$	1.81487e18	0.433803
$305$	2.56113e16	0.00597287
$306$	−1.81423e18	−0.412841
$307$	−4.55639e18	−1.01177	−0.505886	−	0.862600i	$-0.668835\pi$
$307$	−4.55639e18	−1.01177	−0.505886	+	0.862600i	$0.668835\pi$
$308$	−8.82085e17	−0.191152
$309$	8.97537e17	0.189829
$310$	−9.44816e15	−0.00195045
$311$	−4.82102e18	−0.971485	−0.485743	−	0.874102i	$-0.661451\pi$
$311$	−4.82102e18	−0.971485	−0.485743	+	0.874102i	$0.661451\pi$
$312$	−1.51122e18	−0.297282
$313$	−5.24434e18	−1.00718	−0.503592	−	0.863942i	$-0.667988\pi$
$313$	−5.24434e18	−1.00718	−0.503592	+	0.863942i	$0.667988\pi$
$314$	−1.09863e18	−0.206006
$315$	−9.92973e16	−0.0181806
$316$	−7.57503e18	−1.35435
$317$	6.12555e18	1.06955	0.534775	−	0.844995i	$-0.320396\pi$
$317$	6.12555e18	1.06955	0.534775	+	0.844995i	$0.320396\pi$
$318$	−2.52741e17	−0.0430995
$319$	−2.37362e17	−0.0395349
$320$	−3.39434e16	−0.00552244
$321$	2.14677e18	0.341192
$322$	−1.17801e18	−0.182907
$323$	8.37966e18	1.27118
$324$	7.05316e18	1.04543
$325$	−2.23140e18	−0.323186
$326$	−3.23656e18	−0.458092
$327$	−1.89360e18	−0.261926
$328$	2.44886e18	0.331063
$329$	1.00780e19	1.33169
$330$	−2.21375e16	−0.00285939
$331$	4.55976e18	0.575748	0.287874	−	0.957668i	$-0.407052\pi$
$331$	4.55976e18	0.575748	0.287874	+	0.957668i	$0.407052\pi$
$332$	4.29948e18	0.530738
$333$	−2.03446e17	−0.0245537
$334$	5.97822e17	0.0705462
$335$	8.65093e16	0.00998221
$336$	6.83036e18	0.770724
$337$	−1.00829e17	−0.0111265	−0.00556326	−	0.999985i	$-0.501771\pi$
$337$	−1.00829e17	−0.0111265	−0.00556326	+	0.999985i	$0.501771\pi$
$338$	3.22424e18	0.347978
$339$	1.37049e19	1.44670
$340$	−3.70831e17	−0.0382899
$341$	−3.91574e17	−0.0395508
$342$	−1.90566e18	−0.188299
$343$	9.64407e18	0.932297
$344$	1.38207e18	0.130720
$345$	1.66183e17	0.0153796
$346$	−6.43424e18	−0.582675
$347$	−1.16850e19	−1.03552	−0.517759	−	0.855527i	$-0.673233\pi$
$347$	−1.16850e19	−1.03552	−0.517759	+	0.855527i	$0.673233\pi$
$348$	2.32525e18	0.201663
$349$	−9.62643e18	−0.817099	−0.408549	−	0.912736i	$-0.633965\pi$
$349$	−9.62643e18	−0.817099	−0.408549	+	0.912736i	$0.633965\pi$
$350$	−4.94353e18	−0.410702
$351$	1.85023e18	0.150460
$352$	2.51399e18	0.200122
$353$	2.27535e18	0.177312	0.0886558	−	0.996062i	$-0.471743\pi$
$353$	2.27535e18	0.177312	0.0886558	+	0.996062i	$0.471743\pi$
$354$	−2.36019e18	−0.180062
$355$	−3.55593e17	−0.0265608
$356$	−1.25464e19	−0.917579
$357$	3.15373e19	2.25847
$358$	2.74000e18	0.192145
$359$	−1.22882e19	−0.843880	−0.421940	−	0.906624i	$-0.638651\pi$
$359$	−1.22882e19	−0.843880	−0.421940	+	0.906624i	$0.638651\pi$
$360$	1.83668e17	0.0123528
$361$	−6.37920e18	−0.420206
$362$	−2.34611e18	−0.151368
$363$	1.93236e19	1.22121
$364$	4.69062e18	0.290382
$365$	7.15737e17	0.0434067
$366$	1.84986e18	0.109908
$367$	2.29903e18	0.133829	0.0669144	−	0.997759i	$-0.478685\pi$
$367$	2.29903e18	0.133829	0.0669144	+	0.997759i	$0.478685\pi$
$368$	−4.44530e18	−0.253538
$369$	5.24590e18	0.293172
$370$	7.39796e15	0.000405134 0
$371$	1.70850e18	0.0916878
$372$	3.83595e18	0.201744
$373$	−3.03375e19	−1.56373	−0.781867	−	0.623445i	$-0.785733\pi$
$373$	−3.03375e19	−1.56373	−0.781867	+	0.623445i	$0.785733\pi$
$374$	2.73415e18	0.138129
$375$	1.39529e18	0.0690922
$376$	−1.86410e19	−0.904816
$377$	1.26221e18	0.0600580
$378$	4.09907e18	0.191204
$379$	−1.65644e19	−0.757497	−0.378748	−	0.925500i	$-0.623645\pi$
$379$	−1.65644e19	−0.757497	−0.378748	+	0.925500i	$0.623645\pi$
$380$	−3.89518e17	−0.0174643
$381$	4.07599e19	1.79183
$382$	−6.73836e18	−0.290455
$383$	6.60678e18	0.279254	0.139627	−	0.990204i	$-0.455410\pi$
$383$	6.60678e18	0.279254	0.139627	+	0.990204i	$0.455410\pi$
$384$	−3.14606e19	−1.30402
$385$	1.49647e17	0.00608292
$386$	1.91870e19	0.764897
$387$	2.96064e18	0.115759
$388$	−1.95912e19	−0.751317
$389$	3.75563e19	1.41274	0.706368	−	0.707845i	$-0.250332\pi$
$389$	3.75563e19	1.41274	0.706368	+	0.707845i	$0.250332\pi$
$390$	1.17719e17	0.00434373
$391$	−2.05250e19	−0.742945
$392$	2.39693e18	0.0851156
$393$	2.70514e19	0.942422
$394$	5.69779e18	0.194753
$395$	1.28511e18	0.0430986
$396$	3.49511e18	0.115013
$397$	−1.77388e19	−0.572789	−0.286394	−	0.958112i	$-0.592457\pi$
$397$	−1.77388e19	−0.572789	−0.286394	+	0.958112i	$0.592457\pi$
$398$	1.01763e19	0.322453
$399$	3.31266e19	1.03010
$400$	−1.86547e19	−0.569297
$401$	4.59486e18	0.137623	0.0688113	−	0.997630i	$-0.478079\pi$
$401$	4.59486e18	0.137623	0.0688113	+	0.997630i	$0.478079\pi$
$402$	6.24840e18	0.183685
$403$	2.08225e18	0.0600822
$404$	−5.35356e19	−1.51629
$405$	−1.19658e18	−0.0332681
$406$	2.79634e18	0.0763212
$407$	3.06604e17	0.00821524
$408$	−5.83339e19	−1.53451
$409$	3.85955e19	0.996809	0.498405	−	0.866945i	$-0.333919\pi$
$409$	3.85955e19	0.996809	0.498405	+	0.866945i	$0.333919\pi$
$410$	−1.90758e17	−0.00483732
$411$	1.27815e19	0.318251
$412$	5.15287e18	0.125985
$413$	1.59546e19	0.383056
$414$	4.66768e18	0.110052
$415$	−7.29412e17	−0.0168893
$416$	−1.33685e19	−0.304007
$417$	−3.82553e19	−0.854419
$418$	2.87194e18	0.0630017
$419$	−4.38264e19	−0.944345	−0.472173	−	0.881506i	$-0.656530\pi$
$419$	−4.38264e19	−0.944345	−0.472173	+	0.881506i	$0.656530\pi$
$420$	−1.46598e18	−0.0310282
$421$	−6.19169e19	−1.28734	−0.643671	−	0.765302i	$-0.722589\pi$
$421$	−6.19169e19	−1.28734	−0.643671	+	0.765302i	$0.722589\pi$
$422$	2.77103e19	0.565975
$423$	−3.99323e19	−0.801257
$424$	−3.16018e18	−0.0622970
$425$	−8.61331e19	−1.66822
$426$	−2.56838e19	−0.488750
$427$	−1.25048e19	−0.233813
$428$	1.23249e19	0.226441
$429$	4.87881e18	0.0880814
$430$	−1.07659e17	−0.00191001
$431$	−4.55377e19	−0.793947	−0.396974	−	0.917830i	$-0.629940\pi$
$431$	−4.55377e19	−0.793947	−0.396974	+	0.917830i	$0.629940\pi$
$432$	1.54681e19	0.265038
$433$	−1.14804e20	−1.93329	−0.966647	−	0.256111i	$-0.917559\pi$
$433$	−1.14804e20	−1.93329	−0.966647	+	0.256111i	$0.917559\pi$
$434$	4.61310e18	0.0763519
$435$	−3.94483e17	−0.00641739
$436$	−1.08714e19	−0.173834
$437$	−2.15593e19	−0.338862
$438$	5.16963e19	0.798736
$439$	9.71317e19	1.47529	0.737644	−	0.675189i	$-0.235938\pi$
$439$	9.71317e19	1.47529	0.737644	+	0.675189i	$0.235938\pi$
$440$	−2.76798e17	−0.00413303
$441$	5.13465e18	0.0753739
$442$	−1.45393e19	−0.209834
$443$	7.08935e19	1.00596	0.502978	−	0.864299i	$-0.332238\pi$
$443$	7.08935e19	1.00596	0.502978	+	0.864299i	$0.332238\pi$
$444$	−3.00357e18	−0.0419049
$445$	2.12851e18	0.0291995
$446$	−2.78140e18	−0.0375191
$447$	1.68223e20	2.23141
$448$	1.65730e19	0.216181
$449$	5.83517e19	0.748525	0.374262	−	0.927323i	$-0.377896\pi$
$449$	5.83517e19	0.748525	0.374262	+	0.927323i	$0.377896\pi$
$450$	1.95879e19	0.247113
$451$	−7.90588e18	−0.0980903
$452$	7.86815e19	0.960140
$453$	1.25713e20	1.50884
$454$	1.60150e19	0.189064
$455$	−7.95770e17	−0.00924064
$456$	−6.12734e19	−0.699900
$457$	−9.42044e19	−1.05852	−0.529261	−	0.848459i	$-0.677531\pi$
$457$	−9.42044e19	−1.05852	−0.529261	+	0.848459i	$0.677531\pi$
$458$	3.59185e19	0.397034
$459$	7.14196e19	0.776645
$460$	9.54079e17	0.0102071
$461$	2.97006e19	0.312614	0.156307	−	0.987709i	$-0.450041\pi$
$461$	2.97006e19	0.312614	0.156307	+	0.987709i	$0.450041\pi$
$462$	1.08087e19	0.111933
$463$	−8.39832e18	−0.0855726	−0.0427863	−	0.999084i	$-0.513623\pi$
$463$	−8.39832e18	−0.0855726	−0.0427863	+	0.999084i	$0.513623\pi$
$464$	1.05522e19	0.105793
$465$	−6.50774e17	−0.00641997
$466$	−4.62111e19	−0.448592
$467$	−1.12160e20	−1.07142	−0.535712	−	0.844401i	$-0.679957\pi$
$467$	−1.12160e20	−1.07142	−0.535712	+	0.844401i	$0.679957\pi$
$468$	−1.85858e19	−0.174718
$469$	−4.22385e19	−0.390762
$470$	1.45207e18	0.0132207
$471$	−7.56720e19	−0.678076
$472$	−2.95109e19	−0.260266
$473$	−4.46186e18	−0.0387309
$474$	9.28213e19	0.793068
$475$	−9.04736e19	−0.760886
$476$	1.81060e20	1.49889
$477$	−6.76966e18	−0.0551670
$478$	2.02154e19	0.162171
$479$	1.66577e20	1.31552	0.657762	−	0.753226i	$-0.271503\pi$
$479$	1.66577e20	1.31552	0.657762	+	0.753226i	$0.271503\pi$
$480$	4.17812e18	0.0324841
$481$	−1.63041e18	−0.0124799
$482$	1.21528e19	0.0915851
$483$	−8.11396e19	−0.602046
$484$	1.10939e20	0.810486
$485$	3.32368e18	0.0239087
$486$	−6.09018e19	−0.431378
$487$	1.55355e20	1.08357	0.541787	−	0.840516i	$-0.317748\pi$
$487$	1.55355e20	1.08357	0.541787	+	0.840516i	$0.317748\pi$
$488$	2.31299e19	0.158864
$489$	−2.22929e20	−1.50783
$490$	−1.86713e17	−0.00124366
$491$	−2.39091e20	−1.56839	−0.784193	−	0.620517i	$-0.786923\pi$
$491$	−2.39091e20	−1.56839	−0.784193	+	0.620517i	$0.786923\pi$
$492$	7.74479e19	0.500347
$493$	4.87218e19	0.310007
$494$	−1.52720e19	−0.0957067
$495$	−5.92951e17	−0.00365999
$496$	1.74078e19	0.105836
$497$	1.73620e20	1.03974
$498$	−5.26841e19	−0.310784
$499$	−2.87042e20	−1.66798	−0.833992	−	0.551777i	$-0.813950\pi$
$499$	−2.87042e20	−1.66798	−0.833992	+	0.551777i	$0.813950\pi$
$500$	8.01052e18	0.0458549
$501$	4.11770e19	0.232205
$502$	8.49003e19	0.471662
$503$	3.12385e20	1.70974	0.854872	−	0.518839i	$-0.173636\pi$
$503$	3.12385e20	1.70974	0.854872	+	0.518839i	$0.173636\pi$
$504$	−8.96766e19	−0.483560
$505$	9.08238e18	0.0482519
$506$	−7.03446e18	−0.0368216
$507$	2.22080e20	1.14538
$508$	2.34008e20	1.18919
$509$	1.00304e20	0.502268	0.251134	−	0.967952i	$-0.419197\pi$
$509$	1.00304e20	0.502268	0.251134	+	0.967952i	$0.419197\pi$
$510$	4.54402e18	0.0224214
$511$	−3.49461e20	−1.69919
$512$	−1.97199e20	−0.944887
$513$	7.50187e19	0.354233
$514$	−6.72248e19	−0.312828
$515$	−8.74192e17	−0.00400915
$516$	4.37094e19	0.197561
$517$	6.01804e19	0.268087
$518$	−3.61208e18	−0.0158593
$519$	−4.43180e20	−1.91790
$520$	1.47192e18	0.00627853
$521$	−2.20803e20	−0.928373	−0.464187	−	0.885737i	$-0.653653\pi$
$521$	−2.20803e20	−0.928373	−0.464187	+	0.885737i	$0.653653\pi$
$522$	−1.10801e19	−0.0459212
$523$	2.87371e20	1.17403	0.587016	−	0.809576i	$-0.300303\pi$
$523$	2.87371e20	1.17403	0.587016	+	0.809576i	$0.300303\pi$
$524$	1.55305e20	0.625464
$525$	−3.40503e20	−1.35184
$526$	2.59387e18	0.0101521
$527$	8.03758e19	0.310132
$528$	4.07873e19	0.155157
$529$	−2.13828e20	−0.801951
$530$	2.46167e17	0.000910252 0
$531$	−6.32176e19	−0.230478
$532$	1.90184e20	0.683654
$533$	4.20407e19	0.149010
$534$	1.53738e20	0.537307
$535$	−2.09094e18	−0.00720588
$536$	7.81275e19	0.265502
$537$	1.88727e20	0.632451
$538$	−5.32414e19	−0.175947
$539$	−7.73821e18	−0.0252188
$540$	−3.31986e18	−0.0106700
$541$	−3.85435e20	−1.22172	−0.610860	−	0.791739i	$-0.709176\pi$
$541$	−3.85435e20	−1.22172	−0.610860	+	0.791739i	$0.709176\pi$
$542$	−1.91791e20	−0.599560
$543$	−1.61596e20	−0.498232
$544$	−5.16031e20	−1.56922
$545$	1.84434e18	0.00553182
$546$	−5.74769e19	−0.170039
$547$	−2.36845e20	−0.691130	−0.345565	−	0.938395i	$-0.612313\pi$
$547$	−2.36845e20	−0.691130	−0.345565	+	0.938395i	$0.612313\pi$
$548$	7.33804e19	0.211216
$549$	4.95483e19	0.140681
$550$	−2.95202e19	−0.0826796
$551$	5.11770e19	0.141396
$552$	1.50082e20	0.409059
$553$	−6.27462e20	−1.68713
$554$	−1.89139e20	−0.501715
$555$	5.09559e17	0.00133351
$556$	−2.19628e20	−0.567058
$557$	5.74848e20	1.46433	0.732165	−	0.681127i	$-0.238510\pi$
$557$	5.74848e20	1.46433	0.732165	+	0.681127i	$0.238510\pi$
$558$	−1.82786e19	−0.0459396
$559$	2.37266e19	0.0588365
$560$	−6.65270e18	−0.0162775
$561$	1.88324e20	0.454658
$562$	1.67409e20	0.398800
$563$	2.42997e20	0.571199	0.285600	−	0.958349i	$-0.407807\pi$
$563$	2.42997e20	0.571199	0.285600	+	0.958349i	$0.407807\pi$
$564$	−5.89541e20	−1.36748
$565$	−1.33484e19	−0.0305539
$566$	1.41394e20	0.319380
$567$	5.84234e20	1.30231
$568$	−3.21140e20	−0.706451
$569$	−4.02347e20	−0.873493	−0.436746	−	0.899585i	$-0.643869\pi$
$569$	−4.02347e20	−0.873493	−0.436746	+	0.899585i	$0.643869\pi$
$570$	4.77300e18	0.0102266
$571$	−8.50696e20	−1.79889	−0.899443	−	0.437038i	$-0.856028\pi$
$571$	−8.50696e20	−1.79889	−0.899443	+	0.437038i	$0.856028\pi$
$572$	2.80099e19	0.0584576
$573$	−4.64128e20	−0.956044
$574$	9.31386e19	0.189361
$575$	2.21604e20	0.444702
$576$	−6.56679e19	−0.130072
$577$	1.73837e20	0.339878	0.169939	−	0.985455i	$-0.445643\pi$
$577$	1.73837e20	0.339878	0.169939	+	0.985455i	$0.445643\pi$
$578$	−3.59853e20	−0.694490
$579$	1.32157e21	2.51769
$580$	−2.26478e18	−0.00425907
$581$	3.56139e20	0.661147
$582$	2.40063e20	0.439949
$583$	1.02023e19	0.0184579
$584$	6.46390e20	1.15451
$585$	3.15311e18	0.00555993
$586$	−1.12043e20	−0.195054
$587$	4.81747e20	0.828006	0.414003	−	0.910276i	$-0.364130\pi$
$587$	4.81747e20	0.828006	0.414003	+	0.910276i	$0.364130\pi$
$588$	7.58053e19	0.128638
$589$	8.44262e19	0.141453
$590$	2.29880e18	0.00380287
$591$	3.92455e20	0.641037
$592$	−1.36304e19	−0.0219835
$593$	7.44116e20	1.18503	0.592516	−	0.805558i	$-0.298135\pi$
$593$	7.44116e20	1.18503	0.592516	+	0.805558i	$0.298135\pi$
$594$	2.44775e19	0.0384918
$595$	−3.07171e19	−0.0476982
$596$	9.65792e20	1.48094
$597$	7.00927e20	1.06137
$598$	3.74068e19	0.0559361
$599$	−4.77516e20	−0.705159	−0.352580	−	0.935782i	$-0.614695\pi$
$599$	−4.77516e20	−0.705159	−0.352580	+	0.935782i	$0.614695\pi$
$600$	6.29820e20	0.918506
$601$	−1.07172e21	−1.54356	−0.771780	−	0.635890i	$-0.780633\pi$
$601$	−1.07172e21	−1.54356	−0.771780	+	0.635890i	$0.780633\pi$
$602$	5.25648e19	0.0747690
$603$	1.67363e20	0.235115
$604$	7.21733e20	1.00138
$605$	−1.88210e19	−0.0257916
$606$	6.56003e20	0.887894
$607$	−1.08004e21	−1.44386	−0.721928	−	0.691969i	$-0.756744\pi$
$607$	−1.08004e21	−1.44386	−0.721928	+	0.691969i	$0.756744\pi$
$608$	−5.42035e20	−0.715733
$609$	1.92608e20	0.251214
$610$	−1.80174e18	−0.00232123
$611$	−3.20018e20	−0.407254
$612$	−7.17420e20	−0.901857
$613$	7.86443e20	0.976593	0.488297	−	0.872678i	$-0.337618\pi$
$613$	7.86443e20	0.976593	0.488297	+	0.872678i	$0.337618\pi$
$614$	3.20539e20	0.393205
$615$	−1.31391e19	−0.0159222
$616$	1.35148e20	0.161791
$617$	−1.09601e21	−1.29621	−0.648107	−	0.761549i	$-0.724439\pi$
$617$	−1.09601e21	−1.29621	−0.648107	+	0.761549i	$0.724439\pi$
$618$	−6.31412e19	−0.0737733
$619$	3.34319e20	0.385906	0.192953	−	0.981208i	$-0.438193\pi$
$619$	3.34319e20	0.385906	0.192953	+	0.981208i	$0.438193\pi$
$620$	−3.73618e18	−0.00426079
$621$	−1.83749e20	−0.207033
$622$	3.39156e20	0.377548
$623$	−1.03925e21	−1.14304
$624$	−2.16893e20	−0.235700
$625$	9.29284e20	0.997811
$626$	3.68936e20	0.391421
$627$	1.97814e20	0.207373
$628$	−4.34442e20	−0.450023
$629$	−6.29347e19	−0.0644185
$630$	6.98551e18	0.00706552
$631$	−1.30980e21	−1.30913	−0.654566	−	0.756005i	$-0.727149\pi$
$631$	−1.30980e21	−1.30913	−0.654566	+	0.756005i	$0.727149\pi$
$632$	1.16060e21	1.14632
$633$	1.90864e21	1.86293
$634$	−4.30929e20	−0.415658
$635$	−3.96998e19	−0.0378429
$636$	−9.99439e19	−0.0941516
$637$	4.11491e19	0.0383102
$638$	1.66983e19	0.0153644
$639$	−6.87939e20	−0.625596
$640$	3.06424e19	0.0275405
$641$	−5.80472e19	−0.0515640	−0.0257820	−	0.999668i	$-0.508208\pi$
$641$	−5.80472e19	−0.0515640	−0.0257820	+	0.999668i	$0.508208\pi$
$642$	−1.51024e20	−0.132597
$643$	−4.47432e20	−0.388280	−0.194140	−	0.980974i	$-0.562192\pi$
$643$	−4.47432e20	−0.388280	−0.194140	+	0.980974i	$0.562192\pi$
$644$	−4.65833e20	−0.399564
$645$	−7.41536e18	−0.00628687
$646$	−5.89504e20	−0.494018
$647$	−1.06901e21	−0.885523	−0.442761	−	0.896639i	$-0.646001\pi$
$647$	−1.06901e21	−0.885523	−0.442761	+	0.896639i	$0.646001\pi$
$648$	−1.08064e21	−0.884850
$649$	9.52727e19	0.0771140
$650$	1.56978e20	0.125600
$651$	3.17743e20	0.251315
$652$	−1.27987e21	−1.00071
$653$	2.42180e20	0.187193	0.0935966	−	0.995610i	$-0.470164\pi$
$653$	2.42180e20	0.187193	0.0935966	+	0.995610i	$0.470164\pi$
$654$	1.33213e20	0.101792
$655$	−2.63478e19	−0.0199037
$656$	3.51464e20	0.262483
$657$	1.38468e21	1.02237
$658$	−7.08980e20	−0.517535
$659$	−1.05698e20	−0.0762825	−0.0381413	−	0.999272i	$-0.512144\pi$
$659$	−1.05698e20	−0.0762825	−0.0381413	+	0.999272i	$0.512144\pi$
$660$	−8.75403e18	−0.00624638
$661$	2.38704e20	0.168402	0.0842012	−	0.996449i	$-0.473166\pi$
$661$	2.38704e20	0.168402	0.0842012	+	0.996449i	$0.473166\pi$
$662$	−3.20777e20	−0.223752
$663$	−1.00144e21	−0.690677
$664$	−6.58741e20	−0.449215
$665$	−3.22650e19	−0.0217555
$666$	1.43123e19	0.00954228
$667$	−1.25352e20	−0.0826395
$668$	2.36403e20	0.154109
$669$	−1.91578e20	−0.123495
$670$	−6.08588e18	−0.00387938
$671$	−7.46722e19	−0.0470696
$672$	−2.03998e21	−1.27162
$673$	1.67961e21	1.03537	0.517685	−	0.855571i	$-0.326794\pi$
$673$	1.67961e21	1.03537	0.517685	+	0.855571i	$0.326794\pi$
$674$	7.09323e18	0.00432409
$675$	−7.71105e20	−0.464874
$676$	1.27499e21	0.760164
$677$	−3.98066e20	−0.234714	−0.117357	−	0.993090i	$-0.537442\pi$
$677$	−3.98066e20	−0.234714	−0.117357	+	0.993090i	$0.537442\pi$
$678$	−9.64131e20	−0.562229
$679$	−1.62280e21	−0.935925
$680$	5.68166e19	0.0324085
$681$	1.10309e21	0.622311
$682$	2.75470e19	0.0153706
$683$	1.12921e21	0.623188	0.311594	−	0.950215i	$-0.399137\pi$
$683$	1.12921e21	0.623188	0.311594	+	0.950215i	$0.399137\pi$
$684$	−7.53572e20	−0.411343
$685$	−1.24491e19	−0.00672138
$686$	−6.78455e20	−0.362318
$687$	2.47401e21	1.30685
$688$	1.98356e20	0.103641
$689$	−5.42521e19	−0.0280397
$690$	−1.16909e19	−0.00597695
$691$	3.00798e21	1.52121	0.760605	−	0.649215i	$-0.224902\pi$
$691$	3.00798e21	1.52121	0.760605	+	0.649215i	$0.224902\pi$
$692$	−2.54435e21	−1.27286
$693$	2.89511e20	0.143273
$694$	8.22032e20	0.402432
$695$	3.72602e19	0.0180451
$696$	−3.56262e20	−0.170687
$697$	1.62279e21	0.769159
$698$	6.77214e20	0.317549
$699$	−3.18295e21	−1.47656
$700$	−1.95487e21	−0.897186
$701$	2.43285e21	1.10466	0.552331	−	0.833625i	$-0.313738\pi$
$701$	2.43285e21	1.10466	0.552331	+	0.833625i	$0.313738\pi$
$702$	−1.30163e20	−0.0584733
$703$	−6.61061e19	−0.0293817
$704$	9.89653e19	0.0435199
$705$	1.00016e20	0.0435164
$706$	−1.60069e20	−0.0689085
$707$	−4.43451e21	−1.88886
$708$	−9.33314e20	−0.393349
$709$	2.02815e21	0.845770	0.422885	−	0.906183i	$-0.361017\pi$
$709$	2.02815e21	0.845770	0.422885	+	0.906183i	$0.361017\pi$
$710$	2.50158e19	0.0103223
$711$	2.48622e21	1.01512
$712$	1.92228e21	0.776635
$713$	−2.06792e20	−0.0826727
$714$	−2.21863e21	−0.877706
$715$	−4.75191e18	−0.00186026
$716$	1.08351e21	0.419743
$717$	1.39241e21	0.533792
$718$	8.64469e20	0.327956
$719$	−4.13044e21	−1.55071	−0.775353	−	0.631528i	$-0.782428\pi$
$719$	−4.13044e21	−1.55071	−0.775353	+	0.631528i	$0.782428\pi$
$720$	2.63602e19	0.00979390
$721$	4.26828e20	0.156942
$722$	4.48773e20	0.163304
$723$	8.37069e20	0.301456
$724$	−9.27743e20	−0.330665
$725$	−5.26040e20	−0.185560
$726$	−1.35941e21	−0.474596
$727$	−2.57115e21	−0.888420	−0.444210	−	0.895923i	$-0.646516\pi$
$727$	−2.57115e21	−0.888420	−0.444210	+	0.895923i	$0.646516\pi$
$728$	−7.18669e20	−0.245778
$729$	−5.56833e20	−0.188481
$730$	−5.03517e19	−0.0168691
$731$	9.15857e20	0.303702
$732$	7.31507e20	0.240096
$733$	5.14387e21	1.67113	0.835564	−	0.549393i	$-0.185141\pi$
$733$	5.14387e21	1.67113	0.835564	+	0.549393i	$0.185141\pi$
$734$	−1.61736e20	−0.0520098
$735$	−1.28605e19	−0.00409357
$736$	1.32765e21	0.418312
$737$	−2.52226e20	−0.0786654
$738$	−3.69046e20	−0.113935
$739$	1.01869e21	0.311322	0.155661	−	0.987811i	$-0.450249\pi$
$739$	1.01869e21	0.311322	0.155661	+	0.987811i	$0.450249\pi$
$740$	2.92545e18	0.000885022 0
$741$	−1.05191e21	−0.315022
$742$	−1.20192e20	−0.0356326
$743$	−1.55461e21	−0.456252	−0.228126	−	0.973632i	$-0.573260\pi$
$743$	−1.55461e21	−0.456252	−0.228126	+	0.973632i	$0.573260\pi$
$744$	−5.87722e20	−0.170755
$745$	−1.63848e20	−0.0471269
$746$	2.13422e21	0.607713
$747$	−1.41114e21	−0.397801
$748$	1.08119e21	0.301746
$749$	1.02091e21	0.282080
$750$	−9.81576e19	−0.0268513
$751$	3.57784e21	0.968995	0.484497	−	0.874793i	$-0.339003\pi$
$751$	3.57784e21	0.968995	0.484497	+	0.874793i	$0.339003\pi$
$752$	−2.67538e21	−0.717384
$753$	5.84780e21	1.55249
$754$	−8.87957e19	−0.0233403
$755$	−1.22443e20	−0.0318663
$756$	1.62093e21	0.417688
$757$	6.72875e20	0.171678	0.0858391	−	0.996309i	$-0.472643\pi$
$757$	6.72875e20	0.171678	0.0858391	+	0.996309i	$0.472643\pi$
$758$	1.16529e21	0.294385
$759$	−4.84523e20	−0.121200
$760$	5.96797e19	0.0147817
$761$	4.06558e21	0.997097	0.498548	−	0.866862i	$-0.333867\pi$
$761$	4.06558e21	0.997097	0.498548	+	0.866862i	$0.333867\pi$
$762$	−2.86744e21	−0.696357
$763$	−9.00508e20	−0.216548
$764$	−2.66462e21	−0.634504
$765$	1.21711e20	0.0286992
$766$	−4.64783e20	−0.108526
$767$	−5.06627e20	−0.117145
$768$	1.07128e21	0.245297
$769$	7.34284e21	1.66501	0.832504	−	0.554019i	$-0.186906\pi$
$769$	7.34284e21	1.66501	0.832504	+	0.554019i	$0.186906\pi$
$770$	−1.05276e19	−0.00236400
$771$	−4.63034e21	−1.02969
$772$	7.58731e21	1.67093
$773$	2.41732e21	0.527215	0.263608	−	0.964630i	$-0.415088\pi$
$773$	2.41732e21	0.527215	0.263608	+	0.964630i	$0.415088\pi$
$774$	−2.08279e20	−0.0449872
$775$	−8.67803e20	−0.185634
$776$	3.00165e21	0.635912
$777$	−2.48794e20	−0.0522015
$778$	−2.64207e21	−0.549031
$779$	1.70457e21	0.350819
$780$	4.65509e19	0.00948896
$781$	1.03676e21	0.209314
$782$	1.44392e21	0.288730
$783$	4.36181e20	0.0863879
$784$	3.44010e20	0.0674839
$785$	7.37037e19	0.0143208
$786$	−1.90305e21	−0.366253
$787$	−6.95028e21	−1.32493	−0.662463	−	0.749094i	$-0.730489\pi$
$787$	−6.95028e21	−1.32493	−0.662463	+	0.749094i	$0.730489\pi$
$788$	2.25313e21	0.425442
$789$	1.78662e20	0.0334160
$790$	−9.04070e19	−0.0167494
$791$	6.51742e21	1.19606
$792$	−5.35501e20	−0.0973467
$793$	3.97081e20	0.0715040
$794$	1.24791e21	0.222603
$795$	1.69556e19	0.00299613
$796$	4.02411e21	0.704404
$797$	−9.57087e21	−1.65964	−0.829820	−	0.558031i	$-0.811557\pi$
$797$	−9.57087e21	−1.65964	−0.829820	+	0.558031i	$0.811557\pi$
$798$	−2.33044e21	−0.400328
$799$	−1.23528e22	−2.10216
$800$	5.57150e21	0.939284
$801$	4.11787e21	0.687747
$802$	−3.23246e20	−0.0534841
$803$	−2.08680e21	−0.342069
$804$	2.47087e21	0.401263
$805$	7.90292e19	0.0127151
$806$	−1.46485e20	−0.0233497
$807$	−3.66718e21	−0.579137
$808$	8.20240e21	1.28338
$809$	−6.02926e21	−0.934652	−0.467326	−	0.884085i	$-0.654783\pi$
$809$	−6.02926e21	−0.934652	−0.467326	+	0.884085i	$0.654783\pi$
$810$	8.41785e19	0.0129290
$811$	−7.05285e21	−1.07327	−0.536634	−	0.843815i	$-0.680304\pi$
$811$	−7.05285e21	−1.07327	−0.536634	+	0.843815i	$0.680304\pi$
$812$	1.10579e21	0.166725
$813$	−1.32102e22	−1.97347
$814$	−2.15694e19	−0.00319268
$815$	2.17131e20	0.0318449
$816$	−8.37214e21	−1.21664
$817$	9.62009e20	0.138520
$818$	−2.71517e21	−0.387389
$819$	−1.53952e21	−0.217648
$820$	−7.54334e19	−0.0105672
$821$	−1.26709e22	−1.75887	−0.879434	−	0.476022i	$-0.842078\pi$
$821$	−1.26709e22	−1.75887	−0.879434	+	0.476022i	$0.842078\pi$
$822$	−8.99174e20	−0.123682
$823$	1.34418e22	1.83214	0.916070	−	0.401019i	$-0.131344\pi$
$823$	1.34418e22	1.83214	0.916070	+	0.401019i	$0.131344\pi$
$824$	−7.89493e20	−0.106634
$825$	−2.03330e21	−0.272143
$826$	−1.12240e21	−0.148867
$827$	−1.48506e22	−1.95188	−0.975939	−	0.218045i	$-0.930032\pi$
$827$	−1.48506e22	−1.95188	−0.975939	+	0.218045i	$0.930032\pi$
$828$	1.84579e21	0.240411
$829$	−1.16206e22	−1.49992	−0.749962	−	0.661481i	$-0.769928\pi$
$829$	−1.16206e22	−1.49992	−0.749962	+	0.661481i	$0.769928\pi$
$830$	5.13137e19	0.00656369
$831$	−1.30276e22	−1.65141
$832$	−5.26263e20	−0.0661116
$833$	1.58837e21	0.197749
$834$	2.69124e21	0.332052
$835$	−4.01060e19	−0.00490412
$836$	1.13568e21	0.137628
$837$	7.19563e20	0.0864227
$838$	3.08316e21	0.367000
$839$	6.60402e21	0.779101	0.389551	−	0.921005i	$-0.372630\pi$
$839$	6.60402e21	0.779101	0.389551	+	0.921005i	$0.372630\pi$
$840$	2.24608e20	0.0262622
$841$	2.97558e20	0.0344828
$842$	4.35582e21	0.500299
$843$	1.15308e22	1.31267
$844$	1.09577e22	1.23638
$845$	−2.16304e20	−0.0241902
$846$	2.80922e21	0.311392
$847$	9.18944e21	1.00963
$848$	−4.53552e20	−0.0493922
$849$	9.73901e21	1.05125
$850$	6.05942e21	0.648319
$851$	1.61919e20	0.0171722
$852$	−1.01564e22	−1.06768
$853$	−8.77090e21	−0.913958	−0.456979	−	0.889478i	$-0.651069\pi$
$853$	−8.77090e21	−0.913958	−0.456979	+	0.889478i	$0.651069\pi$
$854$	8.79708e20	0.0908666
$855$	1.27845e20	0.0130899
$856$	−1.88835e21	−0.191659
$857$	−1.61039e22	−1.62022	−0.810112	−	0.586275i	$-0.800594\pi$
$857$	−1.61039e22	−1.62022	−0.810112	+	0.586275i	$0.800594\pi$
$858$	−3.43222e20	−0.0342310
$859$	6.16956e21	0.609966	0.304983	−	0.952358i	$-0.401349\pi$
$859$	6.16956e21	0.609966	0.304983	+	0.952358i	$0.401349\pi$
$860$	−4.25725e19	−0.00417245
$861$	6.41524e21	0.623288
$862$	3.20355e21	0.308551
$863$	5.72322e21	0.546462	0.273231	−	0.961948i	$-0.411908\pi$
$863$	5.72322e21	0.546462	0.273231	+	0.961948i	$0.411908\pi$
$864$	−4.61976e21	−0.437287
$865$	4.31653e20	0.0405055
$866$	8.07640e21	0.751335
$867$	−2.47861e22	−2.28594
$868$	1.82420e21	0.166792
$869$	−3.74687e21	−0.339641
$870$	2.77516e19	0.00249399
$871$	1.34125e21	0.119502
$872$	1.66565e21	0.147133
$873$	6.43007e21	0.563130
$874$	1.51668e21	0.131692
$875$	6.63535e20	0.0571220
$876$	2.04428e22	1.74485
$877$	8.10775e21	0.686126	0.343063	−	0.939312i	$-0.388536\pi$
$877$	8.10775e21	0.686126	0.343063	+	0.939312i	$0.388536\pi$
$878$	−6.83316e21	−0.573341
$879$	−7.71738e21	−0.642027
$880$	−3.97264e19	−0.00327687
$881$	1.24644e22	1.01942	0.509708	−	0.860347i	$-0.329753\pi$
$881$	1.24644e22	1.01942	0.509708	+	0.860347i	$0.329753\pi$
$882$	−3.61219e20	−0.0292925
$883$	−1.91390e21	−0.153892	−0.0769458	−	0.997035i	$-0.524517\pi$
$883$	−1.91390e21	−0.153892	−0.0769458	+	0.997035i	$0.524517\pi$
$884$	−5.74941e21	−0.458386
$885$	1.58338e20	0.0125173
$886$	−4.98732e21	−0.390944
$887$	1.22545e22	0.952509	0.476255	−	0.879307i	$-0.341994\pi$
$887$	1.22545e22	0.952509	0.476255	+	0.879307i	$0.341994\pi$
$888$	4.60189e20	0.0354682
$889$	1.93836e22	1.48139
$890$	−1.49739e20	−0.0113478
$891$	3.48873e21	0.262171
$892$	−1.09988e21	−0.0819610
$893$	−1.29753e22	−0.958810
$894$	−1.18344e22	−0.867193
$895$	−1.83818e20	−0.0133572
$896$	−1.49613e22	−1.07810
$897$	2.57652e21	0.184116
$898$	−4.10501e21	−0.290899
$899$	4.90879e20	0.0344966
$900$	7.74585e21	0.539822
$901$	−2.09416e21	−0.144735
$902$	5.56174e20	0.0381208
$903$	3.62058e21	0.246105
$904$	−1.20551e22	−0.812659
$905$	1.57393e20	0.0105225
$906$	−8.84382e21	−0.586379
$907$	2.62749e22	1.72777	0.863884	−	0.503690i	$-0.168025\pi$
$907$	2.62749e22	1.72777	0.863884	+	0.503690i	$0.168025\pi$
$908$	6.33298e21	0.413013
$909$	1.75710e22	1.13650
$910$	5.59820e19	0.00359118
$911$	−1.93554e22	−1.23144	−0.615722	−	0.787963i	$-0.711136\pi$
$911$	−1.93554e22	−1.23144	−0.615722	+	0.787963i	$0.711136\pi$
$912$	−8.79404e21	−0.554916
$913$	2.12667e21	0.133097
$914$	6.62723e21	0.411373
$915$	−1.24101e20	−0.00764043
$916$	1.42036e22	0.867327
$917$	1.28644e22	0.779148
$918$	−5.02433e21	−0.301827
$919$	−2.24978e22	−1.34052	−0.670261	−	0.742126i	$-0.733818\pi$
$919$	−2.24978e22	−1.34052	−0.670261	+	0.742126i	$0.733818\pi$
$920$	−1.46178e20	−0.00863922
$921$	2.20782e22	1.29425
$922$	−2.08942e21	−0.121491
$923$	−5.51315e21	−0.317971
$924$	4.27419e21	0.244520
$925$	6.79494e20	0.0385587
$926$	5.90817e20	0.0332560
$927$	−1.69123e21	−0.0944291
$928$	−3.15155e21	−0.174548
$929$	−1.91921e21	−0.105440	−0.0527198	−	0.998609i	$-0.516789\pi$
$929$	−1.91921e21	−0.105440	−0.0527198	+	0.998609i	$0.516789\pi$
$930$	4.57816e19	0.00249499
$931$	1.66842e21	0.0901948
$932$	−1.82737e22	−0.979957
$933$	2.33605e22	1.24271
$934$	7.89039e21	0.416387
$935$	−1.83426e20	−0.00960227
$936$	2.84761e21	0.147881
$937$	3.84974e22	1.98328	0.991641	−	0.129026i	$-0.0411849\pi$
$937$	3.84974e22	1.98328	0.991641	+	0.129026i	$0.0411849\pi$
$938$	2.97145e21	0.151862
$939$	2.54118e22	1.28838
$940$	5.74207e20	0.0288808
$941$	−3.32685e22	−1.66001	−0.830006	−	0.557755i	$-0.811663\pi$
$941$	−3.32685e22	−1.66001	−0.830006	+	0.557755i	$0.811663\pi$
$942$	5.32348e21	0.263520
$943$	−4.17513e21	−0.205037
$944$	−4.23544e21	−0.206352
$945$	−2.74994e20	−0.0132918
$946$	3.13889e20	0.0150519
$947$	−3.00773e21	−0.143092	−0.0715458	−	0.997437i	$-0.522793\pi$
$947$	−3.00773e21	−0.143092	−0.0715458	+	0.997437i	$0.522793\pi$
$948$	3.67052e22	1.73247
$949$	1.10969e22	0.519641
$950$	6.36477e21	0.295703
$951$	−2.96817e22	−1.36815
$952$	−2.77409e22	−1.26866
$953$	2.50185e22	1.13518	0.567590	−	0.823312i	$-0.307876\pi$
$953$	2.50185e22	1.13518	0.567590	+	0.823312i	$0.307876\pi$
$954$	4.76242e20	0.0214395
$955$	4.52056e20	0.0201914
$956$	7.99398e21	0.354266
$957$	1.15015e21	0.0505726
$958$	−1.17186e22	−0.511251
$959$	6.07832e21	0.263114
$960$	1.64475e20	0.00706424
$961$	−2.26555e22	−0.965490
$962$	1.14699e20	0.00485004
$963$	−4.04518e21	−0.169723
$964$	4.80572e21	0.200069
$965$	−1.28720e21	−0.0531729
$966$	5.70813e21	0.233973
$967$	−9.97642e21	−0.405767	−0.202883	−	0.979203i	$-0.565031\pi$
$967$	−9.97642e21	−0.405767	−0.202883	+	0.979203i	$0.565031\pi$
$968$	−1.69975e22	−0.685992
$969$	−4.06041e22	−1.62608
$970$	−2.33819e20	−0.00929162
$971$	−1.38580e22	−0.546458	−0.273229	−	0.961949i	$-0.588092\pi$
$971$	−1.38580e22	−0.546458	−0.273229	+	0.961949i	$0.588092\pi$
$972$	−2.40830e22	−0.942353
$973$	−1.81925e22	−0.706391
$974$	−1.09292e22	−0.421109
$975$	1.08124e22	0.413416
$976$	3.31963e21	0.125955
$977$	4.38121e22	1.64962	0.824812	−	0.565407i	$-0.191281\pi$
$977$	4.38121e22	1.64962	0.824812	+	0.565407i	$0.191281\pi$
$978$	1.56830e22	0.585985
$979$	−6.20587e21	−0.230108
$980$	−7.38336e19	−0.00271681
$981$	3.56812e21	0.130293
$982$	1.68199e22	0.609521
$983$	−3.56018e22	−1.28032	−0.640162	−	0.768240i	$-0.721133\pi$
$983$	−3.56018e22	−1.28032	−0.640162	+	0.768240i	$0.721133\pi$
$984$	−1.18661e22	−0.423492
$985$	−3.82247e20	−0.0135386
$986$	−3.42755e21	−0.120478
$987$	−4.88334e22	−1.70349
$988$	−6.03914e21	−0.209073
$989$	−2.35633e21	−0.0809587
$990$	4.17138e19	0.00142238
$991$	−5.55874e21	−0.188115	−0.0940576	−	0.995567i	$-0.529984\pi$
$991$	−5.55874e21	−0.188115	−0.0940576	+	0.995567i	$0.529984\pi$
$992$	−5.19909e21	−0.174618
$993$	−2.20946e22	−0.736490
$994$	−1.22140e22	−0.404075
$995$	−6.82696e20	−0.0224158
$996$	−2.08334e22	−0.678914
$997$	−2.99117e22	−0.967448	−0.483724	−	0.875221i	$-0.660716\pi$
$997$	−2.99117e22	−0.967448	−0.483724	+	0.875221i	$0.660716\pi$
$998$	2.01933e22	0.648227
$999$	−5.63421e20	−0.0179511

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.16.a.a.1.7	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.16.a.a.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-70.3494 q^{2} -4845.56 q^{3} -27819.0 q^{4} +4719.52 q^{5} +340882. q^{6} -2.30433e6 q^{7} +4.26226e6 q^{8} +9.13052e6 q^{9} +O(q^{10})\)	\(q-70.3494 q^{2} -4845.56 q^{3} -27819.0 q^{4} +4719.52 q^{5} +340882. q^{6} -2.30433e6 q^{7} +4.26226e6 q^{8} +9.13052e6 q^{9} -332016. q^{10} -1.37602e7 q^{11} +1.34798e8 q^{12} +7.31720e7 q^{13} +1.62108e8 q^{14} -2.28687e7 q^{15} +6.11724e8 q^{16} +2.82447e9 q^{17} -6.42326e8 q^{18} +2.96680e9 q^{19} -1.31292e8 q^{20} +1.11657e10 q^{21} +9.68023e8 q^{22} -7.26683e9 q^{23} -2.06530e10 q^{24} -3.04953e10 q^{25} -5.14761e9 q^{26} +2.52860e10 q^{27} +6.41040e10 q^{28} +1.72499e10 q^{29} +1.60880e9 q^{30} +2.84569e10 q^{31} -1.82700e11 q^{32} +6.66759e10 q^{33} -1.98700e11 q^{34} -1.08753e10 q^{35} -2.54001e11 q^{36} -2.22819e10 q^{37} -2.08713e11 q^{38} -3.54559e11 q^{39} +2.01158e10 q^{40} +5.74546e11 q^{41} -7.85504e11 q^{42} +3.24258e11 q^{43} +3.82795e11 q^{44} +4.30917e10 q^{45} +5.11218e11 q^{46} -4.37350e12 q^{47} -2.96414e12 q^{48} +5.62361e11 q^{49} +2.14533e12 q^{50} -1.36861e13 q^{51} -2.03557e12 q^{52} -7.41433e11 q^{53} -1.77886e12 q^{54} -6.49417e10 q^{55} -9.82163e12 q^{56} -1.43758e13 q^{57} -1.21352e12 q^{58} -6.92378e12 q^{59} +6.36184e11 q^{60} +5.42668e12 q^{61} -2.00193e12 q^{62} -2.10397e13 q^{63} -7.19213e12 q^{64} +3.45337e11 q^{65} -4.69061e12 q^{66} +1.83301e13 q^{67} -7.85739e13 q^{68} +3.52119e13 q^{69} +7.65073e11 q^{70} -7.53451e13 q^{71} +3.89166e13 q^{72} +1.51654e14 q^{73} +1.56752e12 q^{74} +1.47767e14 q^{75} -8.25334e13 q^{76} +3.17080e13 q^{77} +2.49430e13 q^{78} +2.72297e14 q^{79} +2.88705e12 q^{80} -2.53538e14 q^{81} -4.04190e13 q^{82} -1.54552e14 q^{83} -3.10619e14 q^{84} +1.33302e13 q^{85} -2.28114e13 q^{86} -8.35853e13 q^{87} -5.86496e13 q^{88} +4.51001e14 q^{89} -3.03148e12 q^{90} -1.68612e14 q^{91} +2.02156e14 q^{92} -1.37890e14 q^{93} +3.07673e14 q^{94} +1.40019e13 q^{95} +8.85284e14 q^{96} +7.04240e14 q^{97} -3.95618e13 q^{98} -1.25638e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 128 q^{2} - 3214 q^{3} + 239962 q^{4} - 82010 q^{5} - 112778 q^{6} - 3706320 q^{7} - 21137070 q^{8} + 73272578 q^{9}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more