LMFDB - Embedded newform 29.16.a.a.1.2

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			1.2
Root			$302.732$ 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)

$f(q)$	$=$	$q-310.732 q^{2} -3409.71 q^{3} +63786.1 q^{4} -228689. q^{5} +1.05951e6 q^{6} -499515. q^{7} -9.63832e6 q^{8} -2.72276e6 q^{9} +O(q^{10})$	\(q-310.732 q^{2} -3409.71 q^{3} +63786.1 q^{4} -228689. q^{5} +1.05951e6 q^{6} -499515. q^{7} -9.63832e6 q^{8} -2.72276e6 q^{9} +7.10609e7 q^{10} -2.17244e7 q^{11} -2.17492e8 q^{12} -4.18821e8 q^{13} +1.55215e8 q^{14} +7.79764e8 q^{15} +9.04786e8 q^{16} +1.37837e9 q^{17} +8.46048e8 q^{18} +4.88556e9 q^{19} -1.45872e10 q^{20} +1.70320e9 q^{21} +6.75045e9 q^{22} +2.70022e10 q^{23} +3.28639e10 q^{24} +2.17811e10 q^{25} +1.30141e11 q^{26} +5.82095e10 q^{27} -3.18621e10 q^{28} +1.72499e10 q^{29} -2.42297e11 q^{30} -1.32776e11 q^{31} +3.46828e10 q^{32} +7.40739e10 q^{33} -4.28304e11 q^{34} +1.14234e11 q^{35} -1.73674e11 q^{36} +1.33278e10 q^{37} -1.51810e12 q^{38} +1.42806e12 q^{39} +2.20418e12 q^{40} -5.86664e11 q^{41} -5.29239e11 q^{42} +1.11986e12 q^{43} -1.38571e12 q^{44} +6.22666e11 q^{45} -8.39043e12 q^{46} +4.68896e12 q^{47} -3.08506e12 q^{48} -4.49805e12 q^{49} -6.76807e12 q^{50} -4.69986e12 q^{51} -2.67150e13 q^{52} +9.23472e11 q^{53} -1.80875e13 q^{54} +4.96812e12 q^{55} +4.81449e12 q^{56} -1.66584e13 q^{57} -5.36008e12 q^{58} +1.94049e13 q^{59} +4.97381e13 q^{60} -1.75558e13 q^{61} +4.12578e13 q^{62} +1.36006e12 q^{63} -4.04251e13 q^{64} +9.57798e13 q^{65} -2.30171e13 q^{66} +1.55256e13 q^{67} +8.79211e13 q^{68} -9.20697e13 q^{69} -3.54960e13 q^{70} -1.02644e14 q^{71} +2.62428e13 q^{72} -6.43021e13 q^{73} -4.14136e12 q^{74} -7.42672e13 q^{75} +3.11631e14 q^{76} +1.08517e13 q^{77} -4.43744e14 q^{78} +1.93423e14 q^{79} -2.06915e14 q^{80} -1.59409e14 q^{81} +1.82295e14 q^{82} +3.27831e14 q^{83} +1.08641e14 q^{84} -3.15219e14 q^{85} -3.47975e14 q^{86} -5.88171e13 q^{87} +2.09386e14 q^{88} +2.02028e14 q^{89} -1.93482e14 q^{90} +2.09208e14 q^{91} +1.72236e15 q^{92} +4.52729e14 q^{93} -1.45701e15 q^{94} -1.11727e15 q^{95} -1.18258e14 q^{96} -4.89990e13 q^{97} +1.39769e15 q^{98} +5.91503e13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−310.732	−1.71657	−0.858283	−	0.513177i	$-0.828469\pi$
$2$	−310.732	−1.71657	−0.858283	+	0.513177i	$0.828469\pi$
$3$	−3409.71	−0.900137	−0.450068	−	0.892994i	$-0.648600\pi$
$3$	−3409.71	−0.900137	−0.450068	+	0.892994i	$0.648600\pi$
$4$	63786.1	1.94660
$5$	−228689.	−1.30909	−0.654546	−	0.756022i	$-0.727140\pi$
$5$	−228689.	−1.30909	−0.654546	+	0.756022i	$0.727140\pi$
$6$	1.05951e6	1.54514
$7$	−499515.	−0.229252	−0.114626	−	0.993409i	$-0.536567\pi$
$7$	−499515.	−0.229252	−0.114626	+	0.993409i	$0.536567\pi$
$8$	−9.63832e6	−1.62490
$9$	−2.72276e6	−0.189754
$10$	7.10609e7	2.24714
$11$	−2.17244e7	−0.336126	−0.168063	−	0.985776i	$-0.553751\pi$
$11$	−2.17244e7	−0.336126	−0.168063	+	0.985776i	$0.553751\pi$
$12$	−2.17492e8	−1.75220
$13$	−4.18821e8	−1.85120	−0.925601	−	0.378501i	$-0.876440\pi$
$13$	−4.18821e8	−1.85120	−0.925601	+	0.378501i	$0.876440\pi$
$14$	1.55215e8	0.393526
$15$	7.79764e8	1.17836
$16$	9.04786e8	0.842648
$17$	1.37837e9	0.814704	0.407352	−	0.913271i	$-0.366452\pi$
$17$	1.37837e9	0.814704	0.407352	+	0.913271i	$0.366452\pi$
$18$	8.46048e8	0.325725
$19$	4.88556e9	1.25390	0.626949	−	0.779060i	$-0.284303\pi$
$19$	4.88556e9	1.25390	0.626949	+	0.779060i	$0.284303\pi$
$20$	−1.45872e10	−2.54828
$21$	1.70320e9	0.206358
$22$	6.75045e9	0.576982
$23$	2.70022e10	1.65364	0.826818	−	0.562469i	$-0.190149\pi$
$23$	2.70022e10	1.65364	0.826818	+	0.562469i	$0.190149\pi$
$24$	3.28639e10	1.46263
$25$	2.17811e10	0.713722
$26$	1.30141e11	3.17771
$27$	5.82095e10	1.07094
$28$	−3.18621e10	−0.446262
$29$	1.72499e10	0.185695
$29$	1.72499e10	0.185695
$30$	−2.42297e11	−2.02274
$31$	−1.32776e11	−0.866777	−0.433389	−	0.901207i	$-0.642682\pi$
$31$	−1.32776e11	−0.866777	−0.433389	+	0.901207i	$0.642682\pi$
$32$	3.46828e10	0.178439
$33$	7.40739e10	0.302559
$34$	−4.28304e11	−1.39849
$35$	1.14234e11	0.300112
$36$	−1.73674e11	−0.369375
$37$	1.33278e10	0.0230805	0.0115402	−	0.999933i	$-0.496327\pi$
$37$	1.33278e10	0.0230805	0.0115402	+	0.999933i	$0.496327\pi$
$38$	−1.51810e12	−2.15240
$39$	1.42806e12	1.66633
$40$	2.20418e12	2.12714
$41$	−5.86664e11	−0.470447	−0.235223	−	0.971941i	$-0.575582\pi$
$41$	−5.86664e11	−0.470447	−0.235223	+	0.971941i	$0.575582\pi$
$42$	−5.29239e11	−0.354227
$43$	1.11986e12	0.628274	0.314137	−	0.949378i	$-0.398285\pi$
$43$	1.11986e12	0.628274	0.314137	+	0.949378i	$0.398285\pi$
$44$	−1.38571e12	−0.654302
$45$	6.22666e11	0.248405
$46$	−8.39043e12	−2.83858
$47$	4.68896e12	1.35003	0.675014	−	0.737805i	$-0.264138\pi$
$47$	4.68896e12	1.35003	0.675014	+	0.737805i	$0.264138\pi$
$48$	−3.08506e12	−0.758498
$49$	−4.49805e12	−0.947443
$50$	−6.76807e12	−1.22515
$51$	−4.69986e12	−0.733345
$52$	−2.67150e13	−3.60355
$53$	9.23472e11	0.107983	0.0539914	−	0.998541i	$-0.482806\pi$
$53$	9.23472e11	0.107983	0.0539914	+	0.998541i	$0.482806\pi$
$54$	−1.80875e13	−1.83834
$55$	4.96812e12	0.440020
$56$	4.81449e12	0.372511
$57$	−1.66584e13	−1.12868
$58$	−5.36008e12	−0.318758
$59$	1.94049e13	1.01513	0.507564	−	0.861614i	$-0.330546\pi$
$59$	1.94049e13	1.01513	0.507564	+	0.861614i	$0.330546\pi$
$60$	4.97381e13	2.29380
$61$	−1.75558e13	−0.715230	−0.357615	−	0.933869i	$-0.616410\pi$
$61$	−1.75558e13	−0.715230	−0.357615	+	0.933869i	$0.616410\pi$
$62$	4.12578e13	1.48788
$63$	1.36006e12	0.0435015
$64$	−4.04251e13	−1.14895
$65$	9.57798e13	2.42339
$66$	−2.30171e13	−0.519363
$67$	1.55256e13	0.312958	0.156479	−	0.987681i	$-0.449986\pi$
$67$	1.55256e13	0.312958	0.156479	+	0.987681i	$0.449986\pi$
$68$	8.79211e13	1.58590
$69$	−9.20697e13	−1.48850
$70$	−3.54960e13	−0.515162
$71$	−1.02644e14	−1.33936	−0.669680	−	0.742650i	$-0.733569\pi$
$71$	−1.02644e14	−1.33936	−0.669680	+	0.742650i	$0.733569\pi$
$72$	2.62428e13	0.308331
$73$	−6.43021e13	−0.681246	−0.340623	−	0.940200i	$-0.610638\pi$
$73$	−6.43021e13	−0.681246	−0.340623	+	0.940200i	$0.610638\pi$
$74$	−4.14136e12	−0.0396191
$75$	−7.42672e13	−0.642447
$76$	3.11631e14	2.44084
$77$	1.08517e13	0.0770576
$78$	−4.43744e14	−2.86037
$79$	1.93423e14	1.13320	0.566598	−	0.823994i	$-0.308259\pi$
$79$	1.93423e14	1.13320	0.566598	+	0.823994i	$0.308259\pi$
$80$	−2.06915e14	−1.10310
$81$	−1.59409e14	−0.774239
$82$	1.82295e14	0.807553
$83$	3.27831e14	1.32607	0.663033	−	0.748591i	$-0.269269\pi$
$83$	3.27831e14	1.32607	0.663033	+	0.748591i	$0.269269\pi$
$84$	1.08641e14	0.401697
$85$	−3.15219e14	−1.06652
$86$	−3.47975e14	−1.07847
$87$	−5.88171e13	−0.167151
$88$	2.09386e14	0.546171
$89$	2.02028e14	0.484157	0.242078	−	0.970257i	$-0.422171\pi$
$89$	2.02028e14	0.484157	0.242078	+	0.970257i	$0.422171\pi$
$90$	−1.93482e14	−0.426404
$91$	2.09208e14	0.424392
$92$	1.72236e15	3.21897
$93$	4.52729e14	0.780218
$94$	−1.45701e15	−2.31741
$95$	−1.11727e15	−1.64147
$96$	−1.18258e14	−0.160619
$97$	−4.89990e13	−0.0615742	−0.0307871	−	0.999526i	$-0.509801\pi$
$97$	−4.89990e13	−0.0615742	−0.0307871	+	0.999526i	$0.509801\pi$
$98$	1.39769e15	1.62635
$99$	5.91503e13	0.0637812
$100$	1.38933e15	1.38933
$101$	3.48230e13	0.0323188	0.0161594	−	0.999869i	$-0.494856\pi$
$101$	3.48230e13	0.0323188	0.0161594	+	0.999869i	$0.494856\pi$
$102$	1.46039e15	1.25884
$103$	−6.55430e13	−0.0525106	−0.0262553	−	0.999655i	$-0.508358\pi$
$103$	−6.55430e13	−0.0525106	−0.0262553	+	0.999655i	$0.508358\pi$
$104$	4.03673e15	3.00802
$105$	−3.89504e14	−0.270142
$106$	−2.86952e14	−0.185360
$107$	−1.91269e15	−1.15150	−0.575752	−	0.817625i	$-0.695290\pi$
$107$	−1.91269e15	−1.15150	−0.575752	+	0.817625i	$0.695290\pi$
$108$	3.71296e15	2.08469
$109$	−1.66680e15	−0.873340	−0.436670	−	0.899622i	$-0.643842\pi$
$109$	−1.66680e15	−0.873340	−0.436670	+	0.899622i	$0.643842\pi$
$110$	−1.54375e15	−0.755323
$111$	−4.54439e13	−0.0207756
$112$	−4.51954e14	−0.193179
$113$	2.58753e13	0.0103466	0.00517328	−	0.999987i	$-0.498353\pi$
$113$	2.58753e13	0.0103466	0.00517328	+	0.999987i	$0.498353\pi$
$114$	5.17628e15	1.93745
$115$	−6.17510e15	−2.16476
$116$	1.10030e15	0.361474
$117$	1.14035e15	0.351273
$118$	−6.02971e15	−1.74253
$119$	−6.88518e14	−0.186773
$120$	−7.51561e15	−1.91472
$121$	−3.70530e15	−0.887019
$122$	5.45513e15	1.22774
$123$	2.00036e15	0.423466
$124$	−8.46928e15	−1.68727
$125$	1.99794e15	0.374764
$126$	−4.22614e14	−0.0746732
$127$	9.95466e15	1.65767	0.828835	−	0.559492i	$-0.189004\pi$
$127$	9.95466e15	1.65767	0.828835	+	0.559492i	$0.189004\pi$
$128$	1.14249e16	1.79381
$129$	−3.81839e15	−0.565532
$130$	−2.97618e16	−4.15991
$131$	−1.01004e16	−1.33292	−0.666460	−	0.745541i	$-0.732191\pi$
$131$	−1.01004e16	−1.33292	−0.666460	+	0.745541i	$0.732191\pi$
$132$	4.72489e15	0.588962
$133$	−2.44041e15	−0.287459
$134$	−4.82429e15	−0.537214
$135$	−1.33119e16	−1.40196
$136$	−1.32852e16	−1.32381
$137$	−1.92780e16	−1.81827	−0.909134	−	0.416504i	$-0.863255\pi$
$137$	−1.92780e16	−1.81827	−0.909134	+	0.416504i	$0.863255\pi$
$138$	2.86090e16	2.55511
$139$	−9.37047e15	−0.792776	−0.396388	−	0.918083i	$-0.629736\pi$
$139$	−9.37047e15	−0.792776	−0.396388	+	0.918083i	$0.629736\pi$
$140$	7.28652e15	0.584198
$141$	−1.59880e16	−1.21521
$142$	3.18948e16	2.29910
$143$	9.09863e15	0.622237
$144$	−2.46352e15	−0.159896
$145$	−3.94486e15	−0.243092
$146$	1.99807e16	1.16940
$147$	1.53370e16	0.852829
$148$	8.50127e14	0.0449284
$149$	3.15422e16	1.58488	0.792438	−	0.609953i	$-0.208811\pi$
$149$	3.15422e16	1.58488	0.792438	+	0.609953i	$0.208811\pi$
$150$	2.30772e16	1.10280
$151$	2.85386e16	1.29749	0.648747	−	0.761004i	$-0.275293\pi$
$151$	2.85386e16	1.29749	0.648747	+	0.761004i	$0.275293\pi$
$152$	−4.70886e16	−2.03746
$153$	−3.75298e15	−0.154593
$154$	−3.37195e15	−0.132274
$155$	3.03645e16	1.13469
$156$	9.10905e16	3.24368
$157$	−3.07224e16	−1.04282	−0.521408	−	0.853307i	$-0.674593\pi$
$157$	−3.07224e16	−1.04282	−0.521408	+	0.853307i	$0.674593\pi$
$158$	−6.01026e16	−1.94521
$159$	−3.14877e15	−0.0971993
$160$	−7.93158e15	−0.233593
$161$	−1.34880e16	−0.379100
$162$	4.95334e16	1.32903
$163$	9.81195e15	0.251390	0.125695	−	0.992069i	$-0.459884\pi$
$163$	9.81195e15	0.251390	0.125695	+	0.992069i	$0.459884\pi$
$164$	−3.74210e16	−0.915771
$165$	−1.69399e16	−0.396078
$166$	−1.01868e17	−2.27628
$167$	1.06511e16	0.227520	0.113760	−	0.993508i	$-0.463710\pi$
$167$	1.06511e16	0.227520	0.113760	+	0.993508i	$0.463710\pi$
$168$	−1.64160e16	−0.335311
$169$	1.24225e17	2.42695
$170$	9.79485e16	1.83076
$171$	−1.33022e16	−0.237932
$172$	7.14313e16	1.22300
$173$	−7.00413e16	−1.14818	−0.574088	−	0.818794i	$-0.694643\pi$
$173$	−7.00413e16	−1.14818	−0.574088	+	0.818794i	$0.694643\pi$
$174$	1.82763e16	0.286926
$175$	−1.08800e16	−0.163622
$176$	−1.96559e16	−0.283236
$177$	−6.61650e16	−0.913754
$178$	−6.27764e16	−0.831087
$179$	1.00365e17	1.27404	0.637021	−	0.770846i	$-0.280166\pi$
$179$	1.00365e17	1.27404	0.637021	+	0.770846i	$0.280166\pi$
$180$	3.97174e16	0.483546
$181$	−6.02265e16	−0.703393	−0.351696	−	0.936114i	$-0.614395\pi$
$181$	−6.02265e16	−0.703393	−0.351696	+	0.936114i	$0.614395\pi$
$182$	−6.50074e16	−0.728497
$183$	5.98601e16	0.643805
$184$	−2.60256e17	−2.68699
$185$	−3.04791e15	−0.0302144
$186$	−1.40677e17	−1.33930
$187$	−2.99443e16	−0.273843
$188$	2.99091e17	2.62796
$189$	−2.90765e16	−0.245516
$190$	3.47172e17	2.81769
$191$	−1.59756e16	−0.124655	−0.0623273	−	0.998056i	$-0.519852\pi$
$191$	−1.59756e16	−0.124655	−0.0623273	+	0.998056i	$0.519852\pi$
$192$	1.37838e17	1.03421
$193$	2.04630e17	1.47669	0.738344	−	0.674424i	$-0.235608\pi$
$193$	2.04630e17	1.47669	0.738344	+	0.674424i	$0.235608\pi$
$194$	1.52255e16	0.105696
$195$	−3.26582e17	−2.18139
$196$	−2.86913e17	−1.84429
$197$	3.47795e16	0.215192	0.107596	−	0.994195i	$-0.465685\pi$
$197$	3.47795e16	0.215192	0.107596	+	0.994195i	$0.465685\pi$
$198$	−1.83799e16	−0.109485
$199$	2.72140e17	1.56097	0.780485	−	0.625175i	$-0.214972\pi$
$199$	2.72140e17	1.56097	0.780485	+	0.625175i	$0.214972\pi$
$200$	−2.09933e17	−1.15973
$201$	−5.29377e16	−0.281705
$202$	−1.08206e16	−0.0554774
$203$	−8.61657e15	−0.0425710
$204$	−2.99786e17	−1.42753
$205$	1.34164e17	0.615858
$206$	2.03663e16	0.0901379
$207$	−7.35205e16	−0.313784
$208$	−3.78944e17	−1.55991
$209$	−1.06136e17	−0.421468
$210$	1.21031e17	0.463716
$211$	−3.94970e17	−1.46031	−0.730156	−	0.683281i	$-0.760552\pi$
$211$	−3.94970e17	−1.46031	−0.730156	+	0.683281i	$0.760552\pi$
$212$	5.89047e16	0.210199
$213$	3.49988e17	1.20561
$214$	5.94332e17	1.97663
$215$	−2.56099e17	−0.822468
$216$	−5.61042e17	−1.74017
$217$	6.63237e16	0.198711
$218$	5.17926e17	1.49915
$219$	2.19252e17	0.613214
$220$	3.16897e17	0.856542
$221$	−5.77292e17	−1.50818
$222$	1.41208e16	0.0356626
$223$	7.04006e17	1.71906	0.859528	−	0.511089i	$-0.170758\pi$
$223$	7.04006e17	1.71906	0.859528	+	0.511089i	$0.170758\pi$
$224$	−1.73246e16	−0.0409075
$225$	−5.93047e16	−0.135432
$226$	−8.04026e15	−0.0177606
$227$	−8.51504e16	−0.181967	−0.0909835	−	0.995852i	$-0.529001\pi$
$227$	−8.51504e16	−0.181967	−0.0909835	+	0.995852i	$0.529001\pi$
$228$	−1.06257e18	−2.19709
$229$	−8.61224e17	−1.72326	−0.861629	−	0.507539i	$-0.830555\pi$
$229$	−8.61224e17	−1.72326	−0.861629	+	0.507539i	$0.830555\pi$
$230$	1.91880e18	3.71596
$231$	−3.70010e16	−0.0693624
$232$	−1.66260e17	−0.301736
$233$	−9.32271e17	−1.63822	−0.819111	−	0.573635i	$-0.805533\pi$
$233$	−9.32271e17	−1.63822	−0.819111	+	0.573635i	$0.805533\pi$
$234$	−3.54343e17	−0.602983
$235$	−1.07231e18	−1.76731
$236$	1.23776e18	1.97605
$237$	−6.59517e17	−1.02003
$238$	2.13944e17	0.320608
$239$	1.57885e17	0.229275	0.114638	−	0.993407i	$-0.463429\pi$
$239$	1.57885e17	0.229275	0.114638	+	0.993407i	$0.463429\pi$
$240$	7.05519e17	0.992944
$241$	5.75552e17	0.785157	0.392579	−	0.919718i	$-0.371583\pi$
$241$	5.75552e17	0.785157	0.392579	+	0.919718i	$0.371583\pi$
$242$	1.15135e18	1.52263
$243$	−2.91704e17	−0.374020
$244$	−1.11981e18	−1.39227
$245$	1.02865e18	1.24029
$246$	−6.21574e17	−0.726908
$247$	−2.04618e18	−2.32122
$248$	1.27974e18	1.40843
$249$	−1.11781e18	−1.19364
$250$	−6.20824e17	−0.643307
$251$	2.42474e16	0.0243844	0.0121922	−	0.999926i	$-0.496119\pi$
$251$	2.42474e16	0.0243844	0.0121922	+	0.999926i	$0.496119\pi$
$252$	8.67530e16	0.0846799
$253$	−5.86605e17	−0.555830
$254$	−3.09323e18	−2.84550
$255$	1.07481e18	0.960016
$256$	−2.22542e18	−1.93024
$257$	1.79536e18	1.51235	0.756175	−	0.654370i	$-0.227066\pi$
$257$	1.79536e18	1.51235	0.756175	+	0.654370i	$0.227066\pi$
$258$	1.18649e18	0.970773
$259$	−6.65742e15	−0.00529124
$260$	6.10943e18	4.71737
$261$	−4.69673e16	−0.0352364
$262$	3.13851e18	2.28804
$263$	1.97024e17	0.139589	0.0697946	−	0.997561i	$-0.477766\pi$
$263$	1.97024e17	0.139589	0.0697946	+	0.997561i	$0.477766\pi$
$264$	−7.13948e17	−0.491628
$265$	−2.11188e17	−0.141359
$266$	7.58313e17	0.493442
$267$	−6.88857e17	−0.435807
$268$	9.90316e17	0.609204
$269$	−8.86390e17	−0.530253	−0.265126	−	0.964214i	$-0.585414\pi$
$269$	−8.86390e17	−0.530253	−0.265126	+	0.964214i	$0.585414\pi$
$270$	4.13642e18	2.40656
$271$	−3.49628e17	−0.197850	−0.0989251	−	0.995095i	$-0.531540\pi$
$271$	−3.49628e17	−0.197850	−0.0989251	+	0.995095i	$0.531540\pi$
$272$	1.24713e18	0.686509
$273$	−7.13338e17	−0.382011
$274$	5.99029e18	3.12118
$275$	−4.73180e17	−0.239901
$276$	−5.87277e18	−2.89751
$277$	1.32292e18	0.635239	0.317619	−	0.948218i	$-0.397117\pi$
$277$	1.32292e18	0.635239	0.317619	+	0.948218i	$0.397117\pi$
$278$	2.91170e18	1.36085
$279$	3.61518e17	0.164474
$280$	−1.10102e18	−0.487652
$281$	2.65037e18	1.14290	0.571452	−	0.820635i	$-0.306380\pi$
$281$	2.65037e18	1.14290	0.571452	+	0.820635i	$0.306380\pi$
$282$	4.96798e18	2.08599
$283$	−4.22853e18	−1.72898	−0.864492	−	0.502646i	$-0.832360\pi$
$283$	−4.22853e18	−1.72898	−0.864492	+	0.502646i	$0.832360\pi$
$284$	−6.54728e18	−2.60720
$285$	3.80958e18	1.47755
$286$	−2.82723e18	−1.06811
$287$	2.93047e17	0.107851
$288$	−9.44331e16	−0.0338595
$289$	−9.62509e17	−0.336257
$290$	1.22579e18	0.417284
$291$	1.67072e17	0.0554252
$292$	−4.10158e18	−1.32611
$293$	2.05139e18	0.646459	0.323230	−	0.946321i	$-0.395231\pi$
$293$	2.05139e18	0.646459	0.323230	+	0.946321i	$0.395231\pi$
$294$	−4.76571e18	−1.46394
$295$	−4.43768e18	−1.32890
$296$	−1.28457e17	−0.0375034
$297$	−1.26456e18	−0.359971
$298$	−9.80117e18	−2.72054
$299$	−1.13091e19	−3.06121
$300$	−4.73722e18	−1.25059
$301$	−5.59385e17	−0.144033
$302$	−8.86785e18	−2.22723
$303$	−1.18736e17	−0.0290913
$304$	4.42039e18	1.05659
$305$	4.01481e18	0.936302
$306$	1.16617e18	0.265370
$307$	−2.27592e18	−0.505382	−0.252691	−	0.967547i	$-0.581316\pi$
$307$	−2.27592e18	−0.505382	−0.252691	+	0.967547i	$0.581316\pi$
$308$	6.92185e17	0.150000
$309$	2.23483e17	0.0472667
$310$	−9.43520e18	−1.94777
$311$	6.00218e18	1.20950	0.604751	−	0.796415i	$-0.293273\pi$
$311$	6.00218e18	1.20950	0.604751	+	0.796415i	$0.293273\pi$
$312$	−1.37641e19	−2.70762
$313$	6.81852e18	1.30951	0.654754	−	0.755842i	$-0.272772\pi$
$313$	6.81852e18	1.30951	0.654754	+	0.755842i	$0.272772\pi$
$314$	9.54643e18	1.79006
$315$	−3.11031e17	−0.0569475
$316$	1.23377e19	2.20588
$317$	7.64189e18	1.33431	0.667155	−	0.744919i	$-0.267512\pi$
$317$	7.64189e18	1.33431	0.667155	+	0.744919i	$0.267512\pi$
$318$	9.78424e17	0.166849
$319$	−3.74743e17	−0.0624170
$320$	9.24477e18	1.50408
$321$	6.52171e18	1.03651
$322$	4.19115e18	0.650750
$323$	6.73413e18	1.02156
$324$	−1.01681e19	−1.50713
$325$	−9.12238e18	−1.32124
$326$	−3.04888e18	−0.431528
$327$	5.68329e18	0.786126
$328$	5.65445e18	0.764428
$329$	−2.34221e18	−0.309497
$330$	5.26376e18	0.679894
$331$	−7.44930e18	−0.940601	−0.470300	−	0.882506i	$-0.655854\pi$
$331$	−7.44930e18	−0.940601	−0.470300	+	0.882506i	$0.655854\pi$
$332$	2.09111e19	2.58132
$333$	−3.62883e16	−0.00437961
$334$	−3.30963e18	−0.390554
$335$	−3.55053e18	−0.409691
$336$	1.54103e18	0.173887
$337$	1.26728e19	1.39845	0.699227	−	0.714900i	$-0.253528\pi$
$337$	1.26728e19	1.39845	0.699227	+	0.714900i	$0.253528\pi$
$338$	−3.86008e19	−4.16601
$339$	−8.82272e16	−0.00931332
$340$	−2.01066e19	−2.07609
$341$	2.88448e18	0.291346
$342$	4.13342e18	0.408426
$343$	4.61832e18	0.446455
$344$	−1.07935e19	−1.02088
$345$	2.10553e19	1.94858
$346$	2.17641e19	1.97092
$347$	1.40478e19	1.24491	0.622454	−	0.782657i	$-0.286136\pi$
$347$	1.40478e19	1.24491	0.622454	+	0.782657i	$0.286136\pi$
$348$	−3.75172e18	−0.325376
$349$	3.39969e18	0.288569	0.144284	−	0.989536i	$-0.453912\pi$
$349$	3.39969e18	0.288569	0.144284	+	0.989536i	$0.453912\pi$
$350$	3.38075e18	0.280868
$351$	−2.43794e19	−1.98253
$352$	−7.53462e17	−0.0599780
$353$	−2.19132e19	−1.70764	−0.853819	−	0.520569i	$-0.825720\pi$
$353$	−2.19132e19	−1.70764	−0.853819	+	0.520569i	$0.825720\pi$
$354$	2.05596e19	1.56852
$355$	2.34736e19	1.75334
$356$	1.28866e19	0.942459
$357$	2.34765e18	0.168121
$358$	−3.11865e19	−2.18698
$359$	6.65900e18	0.457300	0.228650	−	0.973509i	$-0.426569\pi$
$359$	6.65900e18	0.457300	0.228650	+	0.973509i	$0.426569\pi$
$360$	−6.00145e18	−0.403634
$361$	8.68757e18	0.572261
$362$	1.87143e19	1.20742
$363$	1.26340e19	0.798439
$364$	1.33445e19	0.826121
$365$	1.47052e19	0.891813
$366$	−1.86004e19	−1.10513
$367$	7.06670e18	0.411359	0.205680	−	0.978619i	$-0.434060\pi$
$367$	7.06670e18	0.411359	0.205680	+	0.978619i	$0.434060\pi$
$368$	2.44312e19	1.39343
$369$	1.59735e18	0.0892691
$370$	9.47083e17	0.0518651
$371$	−4.61288e17	−0.0247553
$372$	2.88778e19	1.51877
$373$	−3.46645e19	−1.78677	−0.893386	−	0.449290i	$-0.851677\pi$
$373$	−3.46645e19	−1.78677	−0.893386	+	0.449290i	$0.851677\pi$
$374$	9.30464e18	0.470070
$375$	−6.81241e18	−0.337339
$376$	−4.51937e19	−2.19366
$377$	−7.22462e18	−0.343759
$378$	9.03500e18	0.421444
$379$	−2.44600e19	−1.11857	−0.559284	−	0.828976i	$-0.688924\pi$
$379$	−2.44600e19	−1.11857	−0.559284	+	0.828976i	$0.688924\pi$
$380$	−7.12666e19	−3.19528
$381$	−3.39425e19	−1.49213
$382$	4.96414e18	0.213978
$383$	2.22068e19	0.938630	0.469315	−	0.883031i	$-0.344501\pi$
$383$	2.22068e19	0.938630	0.469315	+	0.883031i	$0.344501\pi$
$384$	−3.89555e19	−1.61467
$385$	−2.48165e18	−0.100875
$386$	−6.35849e19	−2.53483
$387$	−3.04910e18	−0.119217
$388$	−3.12545e18	−0.119860
$389$	−3.49736e18	−0.131558	−0.0657792	−	0.997834i	$-0.520953\pi$
$389$	−3.49736e18	−0.131558	−0.0657792	+	0.997834i	$0.520953\pi$
$390$	1.01479e20	3.74449
$391$	3.72191e19	1.34722
$392$	4.33536e19	1.53950
$393$	3.44395e19	1.19981
$394$	−1.08071e19	−0.369391
$395$	−4.42337e19	−1.48346
$396$	3.77297e18	0.124156
$397$	3.32785e19	1.07457	0.537286	−	0.843400i	$-0.319450\pi$
$397$	3.32785e19	1.07457	0.537286	+	0.843400i	$0.319450\pi$
$398$	−8.45625e19	−2.67951
$399$	8.32110e18	0.258752
$400$	1.97072e19	0.601416
$401$	−3.90898e19	−1.17079	−0.585397	−	0.810747i	$-0.699061\pi$
$401$	−3.90898e19	−1.17079	−0.585397	+	0.810747i	$0.699061\pi$
$402$	1.64494e19	0.483566
$403$	5.56095e19	1.60458
$404$	2.22122e18	0.0629117
$405$	3.64551e19	1.01355
$406$	2.67744e18	0.0730760
$407$	−2.89537e17	−0.00775794
$408$	4.52987e19	1.19161
$409$	−7.48433e19	−1.93298	−0.966492	−	0.256697i	$-0.917366\pi$
$409$	−7.48433e19	−1.93298	−0.966492	+	0.256697i	$0.917366\pi$
$410$	−4.16889e19	−1.05716
$411$	6.57325e19	1.63669
$412$	−4.18073e18	−0.102217
$413$	−9.69303e18	−0.232720
$414$	2.28451e19	0.538631
$415$	−7.49714e19	−1.73594
$416$	−1.45259e19	−0.330326
$417$	3.19506e19	0.713607
$418$	3.29797e19	0.723477
$419$	−6.18899e19	−1.33357	−0.666783	−	0.745252i	$-0.732329\pi$
$419$	−6.18899e19	−1.33357	−0.666783	+	0.745252i	$0.732329\pi$
$420$	−2.48449e19	−0.525858
$421$	3.63986e19	0.756778	0.378389	−	0.925647i	$-0.376478\pi$
$421$	3.63986e19	0.756778	0.378389	+	0.925647i	$0.376478\pi$
$422$	1.22730e20	2.50672
$423$	−1.27669e19	−0.256173
$424$	−8.90072e18	−0.175461
$425$	3.00225e19	0.581472
$426$	−1.08752e20	−2.06950
$427$	8.76936e18	0.163968
$428$	−1.22003e20	−2.24151
$429$	−3.10237e19	−0.560098
$430$	7.95780e19	1.41182
$431$	4.68212e19	0.816324	0.408162	−	0.912909i	$-0.366170\pi$
$431$	4.68212e19	0.816324	0.408162	+	0.912909i	$0.366170\pi$
$432$	5.26671e19	0.902426
$433$	−6.09647e19	−1.02664	−0.513321	−	0.858197i	$-0.671585\pi$
$433$	−6.09647e19	−1.02664	−0.513321	+	0.858197i	$0.671585\pi$
$434$	−2.06089e19	−0.341100
$435$	1.34508e19	0.218816
$436$	−1.06318e20	−1.70004
$437$	1.31921e20	2.07349
$438$	−6.81285e19	−1.05262
$439$	−2.38716e19	−0.362574	−0.181287	−	0.983430i	$-0.558026\pi$
$439$	−2.38716e19	−0.362574	−0.181287	+	0.983430i	$0.558026\pi$
$440$	−4.78844e19	−0.714988
$441$	1.22471e19	0.179781
$442$	1.79383e20	2.58889
$443$	3.23614e19	0.459198	0.229599	−	0.973285i	$-0.426259\pi$
$443$	3.23614e19	0.459198	0.229599	+	0.973285i	$0.426259\pi$
$444$	−2.89869e18	−0.0404417
$445$	−4.62015e19	−0.633806
$446$	−2.18757e20	−2.95087
$447$	−1.07550e20	−1.42660
$448$	2.01929e19	0.263399
$449$	−8.76740e19	−1.12467	−0.562333	−	0.826911i	$-0.690096\pi$
$449$	−8.76740e19	−1.12467	−0.562333	+	0.826911i	$0.690096\pi$
$450$	1.84278e19	0.232477
$451$	1.27449e19	0.158129
$452$	1.65048e18	0.0201406
$453$	−9.73084e19	−1.16792
$454$	2.64589e19	0.312358
$455$	−4.78435e19	−0.555568
$456$	1.60559e20	1.83399
$457$	−1.65878e20	−1.86387	−0.931936	−	0.362622i	$-0.881881\pi$
$457$	−1.65878e20	−1.86387	−0.931936	+	0.362622i	$0.881881\pi$
$458$	2.67610e20	2.95809
$459$	8.02344e19	0.872500
$460$	−3.93886e20	−4.21392
$461$	1.48871e20	1.56695	0.783473	−	0.621425i	$-0.213446\pi$
$461$	1.48871e20	1.56695	0.783473	+	0.621425i	$0.213446\pi$
$462$	1.14974e19	0.119065
$463$	9.55302e19	0.973381	0.486691	−	0.873574i	$-0.338204\pi$
$463$	9.55302e19	0.973381	0.486691	+	0.873574i	$0.338204\pi$
$464$	1.56074e19	0.156476
$465$	−1.03534e20	−1.02138
$466$	2.89686e20	2.81212
$467$	2.99880e19	0.286465	0.143232	−	0.989689i	$-0.454250\pi$
$467$	2.99880e19	0.286465	0.143232	+	0.989689i	$0.454250\pi$
$468$	7.27386e19	0.683787
$469$	−7.75526e18	−0.0717463
$470$	3.33202e20	3.03371
$471$	1.04755e20	0.938678
$472$	−1.87030e20	−1.64948
$473$	−2.43282e19	−0.211179
$474$	2.04933e20	1.75095
$475$	1.06413e20	0.894935
$476$	−4.39179e19	−0.363571
$477$	−2.51439e18	−0.0204902
$478$	−4.90599e19	−0.393566
$479$	−1.79568e20	−1.41812	−0.709060	−	0.705148i	$-0.750881\pi$
$479$	−1.79568e20	−1.41812	−0.709060	+	0.705148i	$0.750881\pi$
$480$	2.70444e19	0.210266
$481$	−5.58195e18	−0.0427266
$482$	−1.78842e20	−1.34777
$483$	4.59902e19	0.341241
$484$	−2.36347e20	−1.72667
$485$	1.12055e19	0.0806063
$486$	9.06415e19	0.642030
$487$	3.68629e19	0.257112	0.128556	−	0.991702i	$-0.458966\pi$
$487$	3.68629e19	0.257112	0.128556	+	0.991702i	$0.458966\pi$
$488$	1.69208e20	1.16218
$489$	−3.34559e19	−0.226285
$490$	−3.19635e20	−2.12904
$491$	−2.55986e20	−1.67921	−0.839604	−	0.543199i	$-0.817213\pi$
$491$	−2.55986e20	−1.67921	−0.839604	+	0.543199i	$0.817213\pi$
$492$	1.27595e20	0.824319
$493$	2.37768e19	0.151287
$494$	6.35812e20	3.98452
$495$	−1.35270e19	−0.0834955
$496$	−1.20134e20	−0.730388
$497$	5.12724e19	0.307051
$498$	3.47339e20	2.04896
$499$	1.38625e20	0.805543	0.402771	−	0.915301i	$-0.368047\pi$
$499$	1.38625e20	0.805543	0.402771	+	0.915301i	$0.368047\pi$
$500$	1.27441e20	0.729515
$501$	−3.63171e19	−0.204799
$502$	−7.53443e18	−0.0418575
$503$	−3.39728e19	−0.185940	−0.0929698	−	0.995669i	$-0.529636\pi$
$503$	−3.39728e19	−0.185940	−0.0929698	+	0.995669i	$0.529636\pi$
$504$	−1.31087e19	−0.0706855
$505$	−7.96362e18	−0.0423083
$506$	1.82277e20	0.954119
$507$	−4.23573e20	−2.18458
$508$	6.34969e20	3.22682
$509$	−3.15500e19	−0.157985	−0.0789925	−	0.996875i	$-0.525170\pi$
$509$	−3.15500e19	−0.157985	−0.0789925	+	0.996875i	$0.525170\pi$
$510$	−3.33976e20	−1.64793
$511$	3.21199e19	0.156177
$512$	3.17138e20	1.51958
$513$	2.84386e20	1.34285
$514$	−5.57874e20	−2.59605
$515$	1.49890e19	0.0687412
$516$	−2.43560e20	−1.10086
$517$	−1.01865e20	−0.453780
$518$	2.06867e18	0.00908277
$519$	2.38821e20	1.03352
$520$	−9.23156e20	−3.93777
$521$	2.50243e19	0.105215	0.0526076	−	0.998615i	$-0.483247\pi$
$521$	2.50243e19	0.105215	0.0526076	+	0.998615i	$0.483247\pi$
$522$	1.45942e19	0.0604856
$523$	−3.75210e20	−1.53289	−0.766445	−	0.642310i	$-0.777976\pi$
$523$	−3.75210e20	−1.53289	−0.766445	+	0.642310i	$0.777976\pi$
$524$	−6.44266e20	−2.59466
$525$	3.70976e19	0.147282
$526$	−6.12217e19	−0.239614
$527$	−1.83015e20	−0.706167
$528$	6.70210e19	0.254951
$529$	4.62482e20	1.73451
$530$	6.56227e19	0.242653
$531$	−5.28348e19	−0.192625
$532$	−1.55664e20	−0.559567
$533$	2.45707e20	0.870892
$534$	2.14050e20	0.748092
$535$	4.37410e20	1.50742
$536$	−1.49640e20	−0.508526
$537$	−3.42215e20	−1.14681
$538$	2.75430e20	0.910214
$539$	9.77172e19	0.318460
$540$	−8.49113e20	−2.72905
$541$	−3.74860e20	−1.18820	−0.594100	−	0.804391i	$-0.702492\pi$
$541$	−3.74860e20	−1.18820	−0.594100	+	0.804391i	$0.702492\pi$
$542$	1.08640e20	0.339623
$543$	2.05355e20	0.633150
$544$	4.78059e19	0.145375
$545$	3.81178e20	1.14328
$546$	2.21657e20	0.655746
$547$	1.93162e20	0.563659	0.281829	−	0.959465i	$-0.409059\pi$
$547$	1.93162e20	0.563659	0.281829	+	0.959465i	$0.409059\pi$
$548$	−1.22967e21	−3.53944
$549$	4.78001e19	0.135718
$550$	1.47032e20	0.411805
$551$	8.42753e19	0.232843
$552$	8.87397e20	2.41866
$553$	−9.66177e19	−0.259788
$554$	−4.11075e20	−1.09043
$555$	1.03925e19	0.0271971
$556$	−5.97706e20	−1.54322
$557$	−3.93510e20	−1.00240	−0.501201	−	0.865331i	$-0.667108\pi$
$557$	−3.93510e20	−1.00240	−0.501201	+	0.865331i	$0.667108\pi$
$558$	−1.12335e20	−0.282331
$559$	−4.69020e20	−1.16306
$560$	1.03357e20	0.252889
$561$	1.02101e20	0.246496
$562$	−8.23555e20	−1.96187
$563$	1.41521e20	0.332665	0.166333	−	0.986070i	$-0.446807\pi$
$563$	1.41521e20	0.332665	0.166333	+	0.986070i	$0.446807\pi$
$564$	−1.01981e21	−2.36553
$565$	−5.91738e18	−0.0135446
$566$	1.31394e21	2.96792
$567$	7.96272e19	0.177496
$568$	9.89318e20	2.17632
$569$	8.12013e20	1.76287	0.881436	−	0.472303i	$-0.156577\pi$
$569$	8.12013e20	1.76287	0.881436	+	0.472303i	$0.156577\pi$
$570$	−1.18376e21	−2.53630
$571$	1.00090e20	0.211652	0.105826	−	0.994385i	$-0.466251\pi$
$571$	1.00090e20	0.211652	0.105826	+	0.994385i	$0.466251\pi$
$572$	5.80367e20	1.21125
$573$	5.44724e19	0.112206
$574$	−9.10591e19	−0.185133
$575$	5.88136e20	1.18024
$576$	1.10068e20	0.218018
$577$	6.80416e19	0.133032	0.0665160	−	0.997785i	$-0.478812\pi$
$577$	6.80416e19	0.133032	0.0665160	+	0.997785i	$0.478812\pi$
$578$	2.99082e20	0.577207
$579$	−6.97729e20	−1.32922
$580$	−2.51627e20	−0.473203
$581$	−1.63757e20	−0.304003
$582$	−5.19147e19	−0.0951410
$583$	−2.00618e19	−0.0362958
$584$	6.19764e20	1.10696
$585$	−2.60786e20	−0.459848
$586$	−6.37432e20	−1.10969
$587$	−8.46141e20	−1.45431	−0.727155	−	0.686473i	$-0.759158\pi$
$587$	−8.46141e20	−1.45431	−0.727155	+	0.686473i	$0.759158\pi$
$588$	9.78291e20	1.66012
$589$	−6.48686e20	−1.08685
$590$	1.37893e21	2.28114
$591$	−1.18588e20	−0.193702
$592$	1.20588e19	0.0194487
$593$	−5.90219e20	−0.939947	−0.469973	−	0.882681i	$-0.655737\pi$
$593$	−5.90219e20	−0.939947	−0.469973	+	0.882681i	$0.655737\pi$
$594$	3.92940e20	0.617914
$595$	1.57457e20	0.244503
$596$	2.01196e21	3.08512
$597$	−9.27920e20	−1.40509
$598$	3.51409e21	5.25478
$599$	1.08967e20	0.160914	0.0804571	−	0.996758i	$-0.474362\pi$
$599$	1.08967e20	0.160914	0.0804571	+	0.996758i	$0.474362\pi$
$600$	7.15811e20	1.04391
$601$	−3.79839e20	−0.547068	−0.273534	−	0.961862i	$-0.588193\pi$
$601$	−3.79839e20	−0.547068	−0.273534	+	0.961862i	$0.588193\pi$
$602$	1.73819e20	0.247242
$603$	−4.22724e19	−0.0593851
$604$	1.82037e21	2.52570
$605$	8.47361e20	1.16119
$606$	3.68951e19	0.0499372
$607$	−4.29069e20	−0.573604	−0.286802	−	0.957990i	$-0.592592\pi$
$607$	−4.29069e20	−0.573604	−0.286802	+	0.957990i	$0.592592\pi$
$608$	1.69445e20	0.223744
$609$	2.93800e19	0.0383198
$610$	−1.24753e21	−1.60722
$611$	−1.96384e21	−2.49917
$612$	−2.39388e20	−0.300931
$613$	−2.92492e20	−0.363213	−0.181606	−	0.983371i	$-0.558130\pi$
$613$	−2.92492e20	−0.363213	−0.181606	+	0.983371i	$0.558130\pi$
$614$	7.07201e20	0.867521
$615$	−4.57459e20	−0.554356
$616$	−1.04592e20	−0.125211
$617$	1.39345e21	1.64799	0.823994	−	0.566599i	$-0.191741\pi$
$617$	1.39345e21	1.64799	0.823994	+	0.566599i	$0.191741\pi$
$618$	−6.94431e19	−0.0811364
$619$	−5.80022e19	−0.0669522	−0.0334761	−	0.999440i	$-0.510658\pi$
$619$	−5.80022e19	−0.0669522	−0.0334761	+	0.999440i	$0.510658\pi$
$620$	1.93683e21	2.20879
$621$	1.57178e21	1.77095
$622$	−1.86507e21	−2.07619
$623$	−1.00916e20	−0.110994
$624$	1.29209e21	1.40413
$625$	−1.12161e21	−1.20432
$626$	−2.11873e21	−2.24786
$627$	3.61892e20	0.379379
$628$	−1.95966e21	−2.02995
$629$	1.83706e19	0.0188038
$630$	9.66471e19	0.0977541
$631$	1.66067e20	0.165983	0.0829913	−	0.996550i	$-0.473553\pi$
$631$	1.66067e20	0.165983	0.0829913	+	0.996550i	$0.473553\pi$
$632$	−1.86427e21	−1.84133
$633$	1.34673e21	1.31448
$634$	−2.37458e21	−2.29043
$635$	−2.27652e21	−2.17004
$636$	−2.00848e20	−0.189208
$637$	1.88388e21	1.75391
$638$	1.16444e20	0.107143
$639$	2.79476e20	0.254149
$640$	−2.61274e21	−2.34826
$641$	−2.54217e20	−0.225824	−0.112912	−	0.993605i	$-0.536018\pi$
$641$	−2.54217e20	−0.225824	−0.112912	+	0.993605i	$0.536018\pi$
$642$	−2.02650e21	−1.77924
$643$	1.27233e20	0.110413	0.0552063	−	0.998475i	$-0.482418\pi$
$643$	1.27233e20	0.110413	0.0552063	+	0.998475i	$0.482418\pi$
$644$	−8.60347e20	−0.737955
$645$	8.73223e20	0.740334
$646$	−2.09251e21	−1.75357
$647$	−1.37675e21	−1.14044	−0.570219	−	0.821493i	$-0.693142\pi$
$647$	−1.37675e21	−1.14044	−0.570219	+	0.821493i	$0.693142\pi$
$648$	1.53644e21	1.25806
$649$	−4.21559e20	−0.341211
$650$	2.83461e21	2.26800
$651$	−2.26145e20	−0.178867
$652$	6.25866e20	0.489356
$653$	−7.44379e20	−0.575367	−0.287684	−	0.957725i	$-0.592885\pi$
$653$	−7.44379e20	−0.575367	−0.287684	+	0.957725i	$0.592885\pi$
$654$	−1.76598e21	−1.34944
$655$	2.30985e21	1.74491
$656$	−5.30805e20	−0.396421
$657$	1.75079e20	0.129269
$658$	7.27798e20	0.531272
$659$	−3.26467e20	−0.235612	−0.117806	−	0.993037i	$-0.537586\pi$
$659$	−3.26467e20	−0.235612	−0.117806	+	0.993037i	$0.537586\pi$
$660$	−1.08053e21	−0.771005
$661$	−5.01527e20	−0.353821	−0.176910	−	0.984227i	$-0.556610\pi$
$661$	−5.01527e20	−0.353821	−0.176910	+	0.984227i	$0.556610\pi$
$662$	2.31473e21	1.61460
$663$	1.96840e21	1.35757
$664$	−3.15974e21	−2.15472
$665$	5.58095e20	0.376310
$666$	1.12759e19	0.00751789
$667$	4.65784e20	0.307073
$668$	6.79391e20	0.442891
$669$	−2.40046e21	−1.54738
$670$	1.10326e21	0.703262
$671$	3.81388e20	0.240407
$672$	5.90719e19	0.0368223
$673$	1.09616e21	0.675711	0.337856	−	0.941198i	$-0.390298\pi$
$673$	1.09616e21	0.675711	0.337856	+	0.941198i	$0.390298\pi$
$674$	−3.93784e21	−2.40054
$675$	1.26787e21	0.764354
$676$	7.92386e21	4.72429
$677$	−9.44685e20	−0.557021	−0.278511	−	0.960433i	$-0.589841\pi$
$677$	−9.44685e20	−0.557021	−0.278511	+	0.960433i	$0.589841\pi$
$678$	2.74150e19	0.0159869
$679$	2.44757e19	0.0141160
$680$	3.03818e21	1.73299
$681$	2.90338e20	0.163795
$682$	−8.96299e20	−0.500115
$683$	8.41410e20	0.464358	0.232179	−	0.972673i	$-0.425415\pi$
$683$	8.41410e20	0.464358	0.232179	+	0.972673i	$0.425415\pi$
$684$	−8.48497e20	−0.463158
$685$	4.40867e21	2.38028
$686$	−1.43506e21	−0.766370
$687$	2.93653e21	1.55117
$688$	1.01323e21	0.529413
$689$	−3.86770e20	−0.199898
$690$	−6.54255e21	−3.34487
$691$	−2.95392e21	−1.49387	−0.746936	−	0.664896i	$-0.768476\pi$
$691$	−2.95392e21	−1.49387	−0.746936	+	0.664896i	$0.768476\pi$
$692$	−4.46767e21	−2.23504
$693$	−2.95465e19	−0.0146220
$694$	−4.36509e21	−2.13697
$695$	2.14292e21	1.03782
$696$	5.66898e20	0.271604
$697$	−8.08642e20	−0.383275
$698$	−1.05639e21	−0.495347
$699$	3.17878e21	1.47462
$700$	−6.93992e20	−0.318507
$701$	1.08164e21	0.491129	0.245565	−	0.969380i	$-0.421027\pi$
$701$	1.08164e21	0.491129	0.245565	+	0.969380i	$0.421027\pi$
$702$	7.57544e21	3.40314
$703$	6.51136e19	0.0289406
$704$	8.78209e20	0.386192
$705$	3.65628e21	1.59082
$706$	6.80913e21	2.93127
$707$	−1.73946e19	−0.00740915
$708$	−4.22041e21	−1.77871
$709$	−3.45399e20	−0.144037	−0.0720186	−	0.997403i	$-0.522944\pi$
$709$	−3.45399e20	−0.144037	−0.0720186	+	0.997403i	$0.522944\pi$
$710$	−7.29399e21	−3.00973
$711$	−5.26645e20	−0.215028
$712$	−1.94721e21	−0.786706
$713$	−3.58525e21	−1.43333
$714$	−7.29489e20	−0.288591
$715$	−2.08076e21	−0.814565
$716$	6.40188e21	2.48005
$717$	−5.38343e20	−0.206379
$718$	−2.06916e21	−0.784985
$719$	−1.75390e21	−0.658474	−0.329237	−	0.944247i	$-0.606792\pi$
$719$	−1.75390e21	−0.658474	−0.329237	+	0.944247i	$0.606792\pi$
$720$	5.63379e20	0.209318
$721$	3.27397e19	0.0120382
$722$	−2.69950e21	−0.982324
$723$	−1.96247e21	−0.706749
$724$	−3.84161e21	−1.36922
$725$	3.75721e20	0.132535
$726$	−3.92579e21	−1.37057
$727$	9.29294e20	0.321103	0.160552	−	0.987027i	$-0.448673\pi$
$727$	9.29294e20	0.321103	0.160552	+	0.987027i	$0.448673\pi$
$728$	−2.01641e21	−0.689594
$729$	3.28197e21	1.11091
$730$	−4.56937e21	−1.53086
$731$	1.54358e21	0.511857
$732$	3.81824e21	1.25323
$733$	4.81993e21	1.56589	0.782944	−	0.622092i	$-0.213717\pi$
$733$	4.81993e21	1.56589	0.782944	+	0.622092i	$0.213717\pi$
$734$	−2.19585e21	−0.706125
$735$	−3.50741e21	−1.11643
$736$	9.36512e20	0.295073
$737$	−3.37283e20	−0.105193
$738$	−4.96346e20	−0.153236
$739$	−3.54227e21	−1.08255	−0.541276	−	0.840845i	$-0.682058\pi$
$739$	−3.54227e21	−1.08255	−0.541276	+	0.840845i	$0.682058\pi$
$740$	−1.94415e20	−0.0588154
$741$	6.97688e21	2.08941
$742$	1.43337e20	0.0424941
$743$	7.35452e20	0.215843	0.107922	−	0.994159i	$-0.465580\pi$
$743$	7.35452e20	0.215843	0.107922	+	0.994159i	$0.465580\pi$
$744$	−4.36354e21	−1.26778
$745$	−7.21336e21	−2.07475
$746$	1.07714e22	3.06711
$747$	−8.92607e20	−0.251626
$748$	−1.91003e21	−0.533063
$749$	9.55415e20	0.263985
$750$	2.11683e21	0.579065
$751$	1.84150e21	0.498739	0.249369	−	0.968408i	$-0.419777\pi$
$751$	1.84150e21	0.498739	0.249369	+	0.968408i	$0.419777\pi$
$752$	4.24251e21	1.13760
$753$	−8.26767e19	−0.0219493
$754$	2.24492e21	0.590086
$755$	−6.52646e21	−1.69854
$756$	−1.85468e21	−0.477920
$757$	5.14916e21	1.31376	0.656882	−	0.753994i	$-0.271875\pi$
$757$	5.14916e21	1.31376	0.656882	+	0.753994i	$0.271875\pi$
$758$	7.60049e21	1.92009
$759$	2.00016e21	0.500323
$760$	1.07686e22	2.66722
$761$	7.18759e21	1.76278	0.881390	−	0.472389i	$-0.156608\pi$
$761$	7.18759e21	1.76278	0.881390	+	0.472389i	$0.156608\pi$
$762$	1.05470e22	2.56134
$763$	8.32589e20	0.200215
$764$	−1.01902e21	−0.242652
$765$	8.58266e20	0.202377
$766$	−6.90035e21	−1.61122
$767$	−8.12717e21	−1.87921
$768$	7.58803e21	1.73748
$769$	2.12437e21	0.481707	0.240854	−	0.970561i	$-0.422573\pi$
$769$	2.12437e21	0.481707	0.240854	+	0.970561i	$0.422573\pi$
$770$	7.71128e20	0.173159
$771$	−6.12165e21	−1.36132
$772$	1.30525e22	2.87452
$773$	−1.52650e21	−0.332928	−0.166464	−	0.986048i	$-0.553235\pi$
$773$	−1.52650e21	−0.332928	−0.166464	+	0.986048i	$0.553235\pi$
$774$	9.47452e20	0.204645
$775$	−2.89201e21	−0.618638
$776$	4.72268e20	0.100052
$777$	2.26999e19	0.00476284
$778$	1.08674e21	0.225829
$779$	−2.86618e21	−0.589892
$780$	−2.08314e22	−4.24628
$781$	2.22988e21	0.450194
$782$	−1.15651e22	−2.31260
$783$	1.00411e21	0.198869
$784$	−4.06977e21	−0.798361
$785$	7.02588e21	1.36514
$786$	−1.07014e22	−2.05955
$787$	−1.00394e22	−1.91380	−0.956899	−	0.290421i	$-0.906205\pi$
$787$	−1.00394e22	−1.91380	−0.956899	+	0.290421i	$0.906205\pi$
$788$	2.21845e21	0.418893
$789$	−6.71797e20	−0.125649
$790$	1.37448e22	2.54645
$791$	−1.29251e19	−0.00237197
$792$	−5.70109e20	−0.103638
$793$	7.35272e21	1.32403
$794$	−1.03407e22	−1.84457
$795$	7.20090e20	0.127243
$796$	1.73588e22	3.03858
$797$	−6.49543e21	−1.12634	−0.563171	−	0.826340i	$-0.690419\pi$
$797$	−6.49543e21	−1.12634	−0.563171	+	0.826340i	$0.690419\pi$
$798$	−2.58563e21	−0.444165
$799$	6.46314e21	1.09987
$800$	7.55429e20	0.127356
$801$	−5.50074e20	−0.0918707
$802$	1.21464e22	2.00974
$803$	1.39692e21	0.228984
$804$	−3.37669e21	−0.548367
$805$	3.08456e21	0.496276
$806$	−1.72796e22	−2.75437
$807$	3.02234e21	0.477300
$808$	−3.35635e20	−0.0525148
$809$	−1.06010e22	−1.64335	−0.821677	−	0.569953i	$-0.806961\pi$
$809$	−1.06010e22	−1.64335	−0.821677	+	0.569953i	$0.806961\pi$
$810$	−1.13277e22	−1.73983
$811$	5.57652e21	0.848607	0.424304	−	0.905520i	$-0.360519\pi$
$811$	5.57652e21	0.848607	0.424304	+	0.905520i	$0.360519\pi$
$812$	−5.49618e20	−0.0828687
$813$	1.19213e21	0.178092
$814$	8.99684e19	0.0133170
$815$	−2.24388e21	−0.329093
$816$	−4.25237e21	−0.617952
$817$	5.47112e21	0.787791
$818$	2.32562e22	3.31809
$819$	−5.69622e20	−0.0805300
$820$	8.55778e21	1.19883
$821$	−9.62173e21	−1.33561	−0.667805	−	0.744336i	$-0.732766\pi$
$821$	−9.62173e21	−1.33561	−0.667805	+	0.744336i	$0.732766\pi$
$822$	−2.04252e22	−2.80949
$823$	−3.17080e21	−0.432185	−0.216092	−	0.976373i	$-0.569331\pi$
$823$	−3.17080e21	−0.432185	−0.216092	+	0.976373i	$0.569331\pi$
$824$	6.31724e20	0.0853244
$825$	1.61341e21	0.215943
$826$	3.01193e21	0.399479
$827$	−6.33099e21	−0.832110	−0.416055	−	0.909340i	$-0.636588\pi$
$827$	−6.33099e21	−0.832110	−0.416055	+	0.909340i	$0.636588\pi$
$828$	−4.68959e21	−0.610812
$829$	−3.08238e21	−0.397857	−0.198929	−	0.980014i	$-0.563746\pi$
$829$	−3.08238e21	−0.397857	−0.198929	+	0.980014i	$0.563746\pi$
$830$	2.32960e22	2.97986
$831$	−4.51079e21	−0.571802
$832$	1.69309e22	2.12694
$833$	−6.19999e21	−0.771886
$834$	−9.92807e21	−1.22495
$835$	−2.43579e21	−0.297845
$836$	−6.76999e21	−0.820429
$837$	−7.72884e21	−0.928268
$838$	1.92312e22	2.28915
$839$	−9.00857e21	−1.06277	−0.531387	−	0.847129i	$-0.678329\pi$
$839$	−9.00857e21	−1.06277	−0.531387	+	0.847129i	$0.678329\pi$
$840$	3.75416e21	0.438953
$841$	2.97558e20	0.0344828
$842$	−1.13102e22	−1.29906
$843$	−9.03702e21	−1.02877
$844$	−2.51936e22	−2.84264
$845$	−2.84090e22	−3.17710
$846$	3.96709e21	0.439738
$847$	1.85085e21	0.203351
$848$	8.35544e20	0.0909915
$849$	1.44181e22	1.55632
$850$	−9.32893e21	−0.998136
$851$	3.59879e20	0.0381667
$852$	2.23244e22	2.34683
$853$	−6.34840e21	−0.661525	−0.330763	−	0.943714i	$-0.607306\pi$
$853$	−6.34840e21	−0.661525	−0.330763	+	0.943714i	$0.607306\pi$
$854$	−2.72492e21	−0.281462
$855$	3.04207e21	0.311475
$856$	1.84351e22	1.87108
$857$	−3.48565e21	−0.350693	−0.175347	−	0.984507i	$-0.556105\pi$
$857$	−3.48565e21	−0.350693	−0.175347	+	0.984507i	$0.556105\pi$
$858$	9.64005e21	0.961446
$859$	−1.08865e22	−1.07632	−0.538160	−	0.842843i	$-0.680880\pi$
$859$	−1.08865e22	−1.07632	−0.538160	+	0.842843i	$0.680880\pi$
$860$	−1.63356e22	−1.60102
$861$	−9.99208e20	−0.0970805
$862$	−1.45488e22	−1.40127
$863$	−8.34332e21	−0.796632	−0.398316	−	0.917248i	$-0.630405\pi$
$863$	−8.34332e21	−0.796632	−0.398316	+	0.917248i	$0.630405\pi$
$864$	2.01887e21	0.191098
$865$	1.60177e22	1.50307
$866$	1.89437e22	1.76230
$867$	3.28188e21	0.302677
$868$	4.23053e21	0.386810
$869$	−4.20199e21	−0.380897
$870$	−4.17960e21	−0.375613
$871$	−6.50244e21	−0.579349
$872$	1.60651e22	1.41909
$873$	1.33413e20	0.0116840
$874$	−4.09920e22	−3.55929
$875$	−9.98003e20	−0.0859155
$876$	1.39852e22	1.19368
$877$	−1.56624e22	−1.32544	−0.662722	−	0.748866i	$-0.730599\pi$
$877$	−1.56624e22	−1.32544	−0.662722	+	0.748866i	$0.730599\pi$
$878$	7.41765e21	0.622383
$879$	−6.99466e21	−0.581902
$880$	4.49509e21	0.370782
$881$	5.34262e21	0.436953	0.218477	−	0.975842i	$-0.429891\pi$
$881$	5.34262e21	0.436953	0.218477	+	0.975842i	$0.429891\pi$
$882$	−3.80556e21	−0.308606
$883$	1.26085e22	1.01381	0.506905	−	0.862002i	$-0.330790\pi$
$883$	1.26085e22	1.01381	0.506905	+	0.862002i	$0.330790\pi$
$884$	−3.68233e22	−2.93582
$885$	1.51312e22	1.19619
$886$	−1.00557e22	−0.788243
$887$	3.23374e20	0.0251349	0.0125675	−	0.999921i	$-0.496000\pi$
$887$	3.23374e20	0.0251349	0.0125675	+	0.999921i	$0.496000\pi$
$888$	4.38002e20	0.0337582
$889$	−4.97250e21	−0.380025
$890$	1.43563e22	1.08797
$891$	3.46306e21	0.260242
$892$	4.49058e22	3.34631
$893$	2.29082e22	1.69280
$894$	3.34192e22	2.44886
$895$	−2.29523e22	−1.66784
$896$	−5.70689e21	−0.411234
$897$	3.85608e22	2.75551
$898$	2.72431e22	1.93056
$899$	−2.29037e21	−0.160957
$900$	−3.78282e21	−0.263631
$901$	1.27289e21	0.0879741
$902$	−3.96024e21	−0.271439
$903$	1.90734e21	0.129649
$904$	−2.49394e20	−0.0168121
$905$	1.37731e22	0.920806
$906$	3.02368e22	2.00482
$907$	1.32392e22	0.870574	0.435287	−	0.900292i	$-0.356647\pi$
$907$	1.32392e22	0.870574	0.435287	+	0.900292i	$0.356647\pi$
$908$	−5.43141e21	−0.354217
$909$	−9.48146e19	−0.00613262
$910$	1.48665e22	0.953669
$911$	7.02262e21	0.446798	0.223399	−	0.974727i	$-0.428285\pi$
$911$	7.02262e21	0.446798	0.223399	+	0.974727i	$0.428285\pi$
$912$	−1.50722e22	−0.951079
$913$	−7.12193e21	−0.445725
$914$	5.15434e22	3.19946
$915$	−1.36893e22	−0.842800
$916$	−5.49342e22	−3.35449
$917$	5.04530e21	0.305575
$918$	−2.49314e22	−1.49770
$919$	1.98361e22	1.18193	0.590964	−	0.806698i	$-0.298748\pi$
$919$	1.98361e22	1.18193	0.590964	+	0.806698i	$0.298748\pi$
$920$	5.95176e22	3.51752
$921$	7.76024e21	0.454912
$922$	−4.62590e22	−2.68977
$923$	4.29896e22	2.47942
$924$	−2.36015e21	−0.135021
$925$	2.90293e20	0.0164730
$926$	−2.96842e22	−1.67087
$927$	1.78458e20	0.00996409
$928$	5.98274e20	0.0331353
$929$	3.35301e22	1.84212	0.921058	−	0.389426i	$-0.127327\pi$
$929$	3.35301e22	1.84212	0.921058	+	0.389426i	$0.127327\pi$
$930$	3.21713e22	1.75326
$931$	−2.19755e22	−1.18800
$932$	−5.94660e22	−3.18896
$933$	−2.04657e22	−1.08872
$934$	−9.31823e21	−0.491736
$935$	6.84793e21	0.358486
$936$	−1.09911e22	−0.570783
$937$	−2.34413e22	−1.20763	−0.603817	−	0.797123i	$-0.706354\pi$
$937$	−2.34413e22	−1.20763	−0.603817	+	0.797123i	$0.706354\pi$
$938$	2.40980e21	0.123157
$939$	−2.32492e22	−1.17874
$940$	−6.83988e22	−3.44025
$941$	1.89652e22	0.946316	0.473158	−	0.880978i	$-0.343114\pi$
$941$	1.89652e22	0.946316	0.473158	+	0.880978i	$0.343114\pi$
$942$	−3.25506e22	−1.61130
$943$	−1.58412e22	−0.777948
$944$	1.75573e22	0.855395
$945$	6.64948e21	0.321402
$946$	7.55953e21	0.362503
$947$	2.13706e22	1.01670	0.508349	−	0.861151i	$-0.330256\pi$
$947$	2.13706e22	1.01670	0.508349	+	0.861151i	$0.330256\pi$
$948$	−4.20680e22	−1.98559
$949$	2.69311e22	1.26112
$950$	−3.30658e22	−1.53621
$951$	−2.60567e22	−1.20106
$952$	6.63616e21	0.303487
$953$	−6.93517e21	−0.314674	−0.157337	−	0.987545i	$-0.550291\pi$
$953$	−6.93517e21	−0.314674	−0.157337	+	0.987545i	$0.550291\pi$
$954$	7.81302e20	0.0351727
$955$	3.65345e21	0.163184
$956$	1.00709e22	0.446307
$957$	1.27777e21	0.0561839
$958$	5.57975e22	2.43430
$959$	9.62966e21	0.416842
$960$	−3.15220e22	−1.35388
$961$	−5.83574e21	−0.248697
$962$	1.73449e21	0.0733430
$963$	5.20779e21	0.218502
$964$	3.67122e22	1.52839
$965$	−4.67966e22	−1.93312
$966$	−1.42906e22	−0.585763
$967$	1.92855e22	0.784391	0.392196	−	0.919882i	$-0.371716\pi$
$967$	1.92855e22	0.784391	0.392196	+	0.919882i	$0.371716\pi$
$968$	3.57129e22	1.44132
$969$	−2.29614e22	−0.919540
$970$	−3.48191e21	−0.138366
$971$	9.40475e21	0.370854	0.185427	−	0.982658i	$-0.440633\pi$
$971$	9.40475e21	0.370854	0.185427	+	0.982658i	$0.440633\pi$
$972$	−1.86066e22	−0.728066
$973$	4.68069e21	0.181746
$974$	−1.14545e22	−0.441350
$975$	3.11047e22	1.18930
$976$	−1.58842e22	−0.602687
$977$	−6.13569e21	−0.231022	−0.115511	−	0.993306i	$-0.536851\pi$
$977$	−6.13569e21	−0.231022	−0.115511	+	0.993306i	$0.536851\pi$
$978$	1.03958e22	0.388434
$979$	−4.38893e21	−0.162738
$980$	6.56138e22	2.41435
$981$	4.53829e21	0.165720
$982$	7.95428e22	2.88247
$983$	−1.13772e22	−0.409151	−0.204575	−	0.978851i	$-0.565581\pi$
$983$	−1.13772e22	−0.409151	−0.204575	+	0.978851i	$0.565581\pi$
$984$	−1.92801e22	−0.688090
$985$	−7.95368e21	−0.281706
$986$	−7.38820e21	−0.259694
$987$	7.98626e21	0.278589
$988$	−1.30518e23	−4.51848
$989$	3.02386e22	1.03894
$990$	4.20327e21	0.143326
$991$	−9.69130e21	−0.327966	−0.163983	−	0.986463i	$-0.552434\pi$
$991$	−9.69130e21	−0.327966	−0.163983	+	0.986463i	$0.552434\pi$
$992$	−4.60505e21	−0.154667
$993$	2.54000e22	0.846669
$994$	−1.59319e22	−0.527073
$995$	−6.22355e22	−2.04345
$996$	−7.13009e22	−2.32354
$997$	2.72230e21	0.0880485	0.0440243	−	0.999030i	$-0.485982\pi$
$997$	2.72230e21	0.0880485	0.0440243	+	0.999030i	$0.485982\pi$
$998$	−4.30753e22	−1.38277
$999$	7.75803e20	0.0247178

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.16.a.a.1.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.16.a.a.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-310.732 q^{2} -3409.71 q^{3} +63786.1 q^{4} -228689. q^{5} +1.05951e6 q^{6} -499515. q^{7} -9.63832e6 q^{8} -2.72276e6 q^{9} +O(q^{10})\)	\(q-310.732 q^{2} -3409.71 q^{3} +63786.1 q^{4} -228689. q^{5} +1.05951e6 q^{6} -499515. q^{7} -9.63832e6 q^{8} -2.72276e6 q^{9} +7.10609e7 q^{10} -2.17244e7 q^{11} -2.17492e8 q^{12} -4.18821e8 q^{13} +1.55215e8 q^{14} +7.79764e8 q^{15} +9.04786e8 q^{16} +1.37837e9 q^{17} +8.46048e8 q^{18} +4.88556e9 q^{19} -1.45872e10 q^{20} +1.70320e9 q^{21} +6.75045e9 q^{22} +2.70022e10 q^{23} +3.28639e10 q^{24} +2.17811e10 q^{25} +1.30141e11 q^{26} +5.82095e10 q^{27} -3.18621e10 q^{28} +1.72499e10 q^{29} -2.42297e11 q^{30} -1.32776e11 q^{31} +3.46828e10 q^{32} +7.40739e10 q^{33} -4.28304e11 q^{34} +1.14234e11 q^{35} -1.73674e11 q^{36} +1.33278e10 q^{37} -1.51810e12 q^{38} +1.42806e12 q^{39} +2.20418e12 q^{40} -5.86664e11 q^{41} -5.29239e11 q^{42} +1.11986e12 q^{43} -1.38571e12 q^{44} +6.22666e11 q^{45} -8.39043e12 q^{46} +4.68896e12 q^{47} -3.08506e12 q^{48} -4.49805e12 q^{49} -6.76807e12 q^{50} -4.69986e12 q^{51} -2.67150e13 q^{52} +9.23472e11 q^{53} -1.80875e13 q^{54} +4.96812e12 q^{55} +4.81449e12 q^{56} -1.66584e13 q^{57} -5.36008e12 q^{58} +1.94049e13 q^{59} +4.97381e13 q^{60} -1.75558e13 q^{61} +4.12578e13 q^{62} +1.36006e12 q^{63} -4.04251e13 q^{64} +9.57798e13 q^{65} -2.30171e13 q^{66} +1.55256e13 q^{67} +8.79211e13 q^{68} -9.20697e13 q^{69} -3.54960e13 q^{70} -1.02644e14 q^{71} +2.62428e13 q^{72} -6.43021e13 q^{73} -4.14136e12 q^{74} -7.42672e13 q^{75} +3.11631e14 q^{76} +1.08517e13 q^{77} -4.43744e14 q^{78} +1.93423e14 q^{79} -2.06915e14 q^{80} -1.59409e14 q^{81} +1.82295e14 q^{82} +3.27831e14 q^{83} +1.08641e14 q^{84} -3.15219e14 q^{85} -3.47975e14 q^{86} -5.88171e13 q^{87} +2.09386e14 q^{88} +2.02028e14 q^{89} -1.93482e14 q^{90} +2.09208e14 q^{91} +1.72236e15 q^{92} +4.52729e14 q^{93} -1.45701e15 q^{94} -1.11727e15 q^{95} -1.18258e14 q^{96} -4.89990e13 q^{97} +1.39769e15 q^{98} +5.91503e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 128 q^{2} - 3214 q^{3} + 239962 q^{4} - 82010 q^{5} - 112778 q^{6} - 3706320 q^{7} - 21137070 q^{8} + 73272578 q^{9}+O(q^{10}) \) 16 * q - 128 * q^2 - 3214 * q^3 + 239962 * q^4 - 82010 * q^5 - 112778 * q^6 - 3706320 * q^7 - 21137070 * q^8 + 73272578 * q^9	\( 16 q - 128 q^{2} - 3214 q^{3} + 239962 q^{4} - 82010 q^{5} - 112778 q^{6} - 3706320 q^{7} - 21137070 q^{8} + 73272578 q^{9} + 27111646 q^{10} - 128305158 q^{11} - 566454670 q^{12} - 500341634 q^{13} - 2456995576 q^{14} - 1005836398 q^{15} + 3638194738 q^{16} - 1889649440 q^{17} + 7114827706 q^{18} - 11903789760 q^{19} + 21125268698 q^{20} + 1845797984 q^{21} + 14207940510 q^{22} - 6296706268 q^{23} + 19916867274 q^{24} + 57929280374 q^{25} + 46861268662 q^{26} - 66882170482 q^{27} - 50278055968 q^{28} + 275998020944 q^{29} - 288715178542 q^{30} - 791595409290 q^{31} - 846144416938 q^{32} - 1192946764766 q^{33} - 1500307227904 q^{34} - 731093348200 q^{35} - 766217409340 q^{36} - 22311934700 q^{37} + 1194772372172 q^{38} - 1484120611454 q^{39} - 5651885433026 q^{40} + 871755491316 q^{41} - 5429421460912 q^{42} - 4296897329422 q^{43} - 10539797438606 q^{44} - 4399313787580 q^{45} - 20780033587764 q^{46} - 7817561912774 q^{47} - 36311476834866 q^{48} - 18565097654464 q^{49} - 33573686907474 q^{50} - 27333906159300 q^{51} - 48854284368422 q^{52} - 41630222638006 q^{53} - 88633328654882 q^{54} - 68569446879302 q^{55} - 66690562169864 q^{56} - 80322439188772 q^{57} - 2207984167552 q^{58} - 60146094578732 q^{59} - 170149488214170 q^{60} - 71628304977160 q^{61} - 95316700851110 q^{62} - 99862426093816 q^{63} - 20954801982074 q^{64} - 53095801190146 q^{65} - 84071816219318 q^{66} - 44591877980312 q^{67} + 24848392371308 q^{68} + 33786235351468 q^{69} - 254302493648008 q^{70} - 2238339487076 q^{71} - 335696824658688 q^{72} + 60304297937180 q^{73} - 4683993400652 q^{74} - 408007582551580 q^{75} - 511662725684676 q^{76} + 2082869459792 q^{77} + 134746909641474 q^{78} - 9999680374282 q^{79} + 10\!\cdots\!46 q^{80}+ \cdots + 531562034651476 q^{99}+O(q^{100}) \) 16 * q - 128 * q^2 - 3214 * q^3 + 239962 * q^4 - 82010 * q^5 - 112778 * q^6 - 3706320 * q^7 - 21137070 * q^8 + 73272578 * q^9 + 27111646 * q^10 - 128305158 * q^11 - 566454670 * q^12 - 500341634 * q^13 - 2456995576 * q^14 - 1005836398 * q^15 + 3638194738 * q^16 - 1889649440 * q^17 + 7114827706 * q^18 - 11903789760 * q^19 + 21125268698 * q^20 + 1845797984 * q^21 + 14207940510 * q^22 - 6296706268 * q^23 + 19916867274 * q^24 + 57929280374 * q^25 + 46861268662 * q^26 - 66882170482 * q^27 - 50278055968 * q^28 + 275998020944 * q^29 - 288715178542 * q^30 - 791595409290 * q^31 - 846144416938 * q^32 - 1192946764766 * q^33 - 1500307227904 * q^34 - 731093348200 * q^35 - 766217409340 * q^36 - 22311934700 * q^37 + 1194772372172 * q^38 - 1484120611454 * q^39 - 5651885433026 * q^40 + 871755491316 * q^41 - 5429421460912 * q^42 - 4296897329422 * q^43 - 10539797438606 * q^44 - 4399313787580 * q^45 - 20780033587764 * q^46 - 7817561912774 * q^47 - 36311476834866 * q^48 - 18565097654464 * q^49 - 33573686907474 * q^50 - 27333906159300 * q^51 - 48854284368422 * q^52 - 41630222638006 * q^53 - 88633328654882 * q^54 - 68569446879302 * q^55 - 66690562169864 * q^56 - 80322439188772 * q^57 - 2207984167552 * q^58 - 60146094578732 * q^59 - 170149488214170 * q^60 - 71628304977160 * q^61 - 95316700851110 * q^62 - 99862426093816 * q^63 - 20954801982074 * q^64 - 53095801190146 * q^65 - 84071816219318 * q^66 - 44591877980312 * q^67 + 24848392371308 * q^68 + 33786235351468 * q^69 - 254302493648008 * q^70 - 2238339487076 * q^71 - 335696824658688 * q^72 + 60304297937180 * q^73 - 4683993400652 * q^74 - 408007582551580 * q^75 - 511662725684676 * q^76 + 2082869459792 * q^77 + 134746909641474 * q^78 - 9999680374282 * q^79 + 1065964290115846 * q^80 + 1227860473120604 * q^81 - 482856386515020 * q^82 + 1449900899821108 * q^83 + 2256322335776952 * q^84 + 1364385639985788 * q^85 + 1206993542651814 * q^86 - 55441102457126 * q^87 + 2648043460385618 * q^88 - 162544796147532 * q^89 + 1885912570259156 * q^90 + 858443116817000 * q^91 + 2263858121857900 * q^92 + 3752667465062574 * q^93 + 3639931425958406 * q^94 - 73522560256708 * q^95 + 6634505750804190 * q^96 + 463840517939252 * q^97 + 2013726729859888 * q^98 + 531562034651476 * q^99

Introduction

L-functions

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