LMFDB - Embedded newform 177.14.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,14,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	177.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:	$189.798744245$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-138.949 q^{2} +729.000 q^{3} +11114.9 q^{4} -41433.2 q^{5} -101294. q^{6} -70948.7 q^{7} -406128. q^{8} +531441. q^{9} +O(q^{10})$	\(q-138.949 q^{2} +729.000 q^{3} +11114.9 q^{4} -41433.2 q^{5} -101294. q^{6} -70948.7 q^{7} -406128. q^{8} +531441. q^{9} +5.75710e6 q^{10} -5.18939e6 q^{11} +8.10273e6 q^{12} +2.69393e7 q^{13} +9.85826e6 q^{14} -3.02048e7 q^{15} -3.46218e7 q^{16} +1.85474e8 q^{17} -7.38433e7 q^{18} +3.25790e8 q^{19} -4.60523e8 q^{20} -5.17216e7 q^{21} +7.21062e8 q^{22} +1.17438e9 q^{23} -2.96067e8 q^{24} +4.96003e8 q^{25} -3.74319e9 q^{26} +3.87420e8 q^{27} -7.88584e8 q^{28} +2.93323e9 q^{29} +4.19693e9 q^{30} -1.23680e9 q^{31} +8.13766e9 q^{32} -3.78307e9 q^{33} -2.57715e10 q^{34} +2.93963e9 q^{35} +5.90689e9 q^{36} -1.79980e10 q^{37} -4.52682e10 q^{38} +1.96388e10 q^{39} +1.68272e10 q^{40} +5.41462e10 q^{41} +7.18667e9 q^{42} -4.68366e10 q^{43} -5.76794e10 q^{44} -2.20193e10 q^{45} -1.63179e11 q^{46} +2.60361e10 q^{47} -2.52393e10 q^{48} -9.18553e10 q^{49} -6.89192e10 q^{50} +1.35211e11 q^{51} +2.99426e11 q^{52} +1.43333e11 q^{53} -5.38317e10 q^{54} +2.15013e11 q^{55} +2.88142e10 q^{56} +2.37501e11 q^{57} -4.07569e11 q^{58} -4.21805e10 q^{59} -3.35722e11 q^{60} +5.85159e11 q^{61} +1.71852e11 q^{62} -3.77050e10 q^{63} -8.47100e11 q^{64} -1.11618e12 q^{65} +5.25654e11 q^{66} -1.43954e11 q^{67} +2.06152e12 q^{68} +8.56122e11 q^{69} -4.08459e11 q^{70} +9.28219e11 q^{71} -2.15833e11 q^{72} +1.49894e12 q^{73} +2.50081e12 q^{74} +3.61586e11 q^{75} +3.62111e12 q^{76} +3.68181e11 q^{77} -2.72879e12 q^{78} -2.13123e12 q^{79} +1.43449e12 q^{80} +2.82430e11 q^{81} -7.52357e12 q^{82} +5.02222e11 q^{83} -5.74878e11 q^{84} -7.68478e12 q^{85} +6.50790e12 q^{86} +2.13832e12 q^{87} +2.10756e12 q^{88} +2.89567e12 q^{89} +3.05956e12 q^{90} -1.91131e12 q^{91} +1.30530e13 q^{92} -9.01626e11 q^{93} -3.61770e12 q^{94} -1.34985e13 q^{95} +5.93236e12 q^{96} +1.54484e12 q^{97} +1.27632e13 q^{98} -2.75786e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9}+O(q^{10}) $ 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9} + 4647481 q^{10} + 17937316 q^{11} + 92499894 q^{12} + 40664720 q^{13} + 139193613 q^{14} + 59054832 q^{15} + 370110498 q^{16} + 213442823 q^{17} + 164746710 q^{18} - 62592329 q^{19} + 1637085153 q^{20} + 731143989 q^{21} + 4142028314 q^{22} + 1873486387 q^{23} + 3377255067 q^{24} + 8307272395 q^{25} - 534777728 q^{26} + 12010035159 q^{27} + 766416778 q^{28} + 13765513563 q^{29} + 3388013649 q^{30} + 14274077235 q^{31} + 30574460156 q^{32} + 13076303364 q^{33} - 677551028 q^{34} + 36023610185 q^{35} + 67432422726 q^{36} - 18278838391 q^{37} - 23650502933 q^{38} + 29644580880 q^{39} + 10045447572 q^{40} + 34748006725 q^{41} + 101472143877 q^{42} + 40350158146 q^{43} + 163101196592 q^{44} + 43050972528 q^{45} + 296118466353 q^{46} + 233954631099 q^{47} + 269810553042 q^{48} + 324065402790 q^{49} - 102960745787 q^{50} + 155599817967 q^{51} + 668297695096 q^{52} + 500927963876 q^{53} + 120100351590 q^{54} + 884972340924 q^{55} + 1392234478810 q^{56} - 45629807841 q^{57} + 689262776200 q^{58} - 1307596542871 q^{59} + 1193435076537 q^{60} + 1716832157925 q^{61} + 1816094290366 q^{62} + 533003967981 q^{63} + 4381780009133 q^{64} + 1457007885906 q^{65} + 3019538640906 q^{66} + 1212131702006 q^{67} + 6552992665503 q^{68} + 1365771576123 q^{69} + 8806714081634 q^{70} + 6074000239936 q^{71} + 2462018943843 q^{72} + 3756145185973 q^{73} + 8066450143602 q^{74} + 6056001575955 q^{75} + 7913230001992 q^{76} + 6031241575915 q^{77} - 389852963712 q^{78} + 11377744190862 q^{79} + 16473302366969 q^{80} + 8755315630911 q^{81} + 10413363680159 q^{82} + 19915461517429 q^{83} + 558717831162 q^{84} + 15280981141573 q^{85} + 7573325358452 q^{86} + 10035059387427 q^{87} + 19271409121081 q^{88} + 14115863121241 q^{89} + 2469861950121 q^{90} + 18296287784699 q^{91} + 15158951168774 q^{92} + 10405802304315 q^{93} - 18637923572412 q^{94} - 2294034679397 q^{95} + 22288781453724 q^{96} + 38558536599054 q^{97} - 1998410212380 q^{98} + 9532625152356 q^{99}+O(q^{100}) \) 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9 + 4647481 * q^10 + 17937316 * q^11 + 92499894 * q^12 + 40664720 * q^13 + 139193613 * q^14 + 59054832 * q^15 + 370110498 * q^16 + 213442823 * q^17 + 164746710 * q^18 - 62592329 * q^19 + 1637085153 * q^20 + 731143989 * q^21 + 4142028314 * q^22 + 1873486387 * q^23 + 3377255067 * q^24 + 8307272395 * q^25 - 534777728 * q^26 + 12010035159 * q^27 + 766416778 * q^28 + 13765513563 * q^29 + 3388013649 * q^30 + 14274077235 * q^31 + 30574460156 * q^32 + 13076303364 * q^33 - 677551028 * q^34 + 36023610185 * q^35 + 67432422726 * q^36 - 18278838391 * q^37 - 23650502933 * q^38 + 29644580880 * q^39 + 10045447572 * q^40 + 34748006725 * q^41 + 101472143877 * q^42 + 40350158146 * q^43 + 163101196592 * q^44 + 43050972528 * q^45 + 296118466353 * q^46 + 233954631099 * q^47 + 269810553042 * q^48 + 324065402790 * q^49 - 102960745787 * q^50 + 155599817967 * q^51 + 668297695096 * q^52 + 500927963876 * q^53 + 120100351590 * q^54 + 884972340924 * q^55 + 1392234478810 * q^56 - 45629807841 * q^57 + 689262776200 * q^58 - 1307596542871 * q^59 + 1193435076537 * q^60 + 1716832157925 * q^61 + 1816094290366 * q^62 + 533003967981 * q^63 + 4381780009133 * q^64 + 1457007885906 * q^65 + 3019538640906 * q^66 + 1212131702006 * q^67 + 6552992665503 * q^68 + 1365771576123 * q^69 + 8806714081634 * q^70 + 6074000239936 * q^71 + 2462018943843 * q^72 + 3756145185973 * q^73 + 8066450143602 * q^74 + 6056001575955 * q^75 + 7913230001992 * q^76 + 6031241575915 * q^77 - 389852963712 * q^78 + 11377744190862 * q^79 + 16473302366969 * q^80 + 8755315630911 * q^81 + 10413363680159 * q^82 + 19915461517429 * q^83 + 558717831162 * q^84 + 15280981141573 * q^85 + 7573325358452 * q^86 + 10035059387427 * q^87 + 19271409121081 * q^88 + 14115863121241 * q^89 + 2469861950121 * q^90 + 18296287784699 * q^91 + 15158951168774 * q^92 + 10405802304315 * q^93 - 18637923572412 * q^94 - 2294034679397 * q^95 + 22288781453724 * q^96 + 38558536599054 * q^97 - 1998410212380 * q^98 + 9532625152356 * 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 $

$2$	−138.949	−1.53519	−0.767593	−	0.640938i	$-0.778546\pi$
$2$	−138.949	−1.53519	−0.767593	+	0.640938i	$0.778546\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	11114.9	1.35679
$5$	−41433.2	−1.18589	−0.592943	−	0.805244i	$-0.702034\pi$
$5$	−41433.2	−1.18589	−0.592943	+	0.805244i	$0.702034\pi$
$6$	−101294.	−0.886340
$7$	−70948.7	−0.227933	−0.113966	−	0.993485i	$-0.536356\pi$
$7$	−70948.7	−0.227933	−0.113966	+	0.993485i	$0.536356\pi$
$8$	−406128.	−0.547745
$9$	531441.	0.333333
$10$	5.75710e6	1.82055
$11$	−5.18939e6	−0.883211	−0.441605	−	0.897209i	$-0.645591\pi$
$11$	−5.18939e6	−0.883211	−0.441605	+	0.897209i	$0.645591\pi$
$12$	8.10273e6	0.783345
$13$	2.69393e7	1.54794	0.773971	−	0.633221i	$-0.218268\pi$
$13$	2.69393e7	1.54794	0.773971	+	0.633221i	$0.218268\pi$
$14$	9.85826e6	0.349919
$15$	−3.02048e7	−0.684672
$16$	−3.46218e7	−0.515904
$17$	1.85474e8	1.86366	0.931828	−	0.362901i	$-0.118214\pi$
$17$	1.85474e8	1.86366	0.931828	+	0.362901i	$0.118214\pi$
$18$	−7.38433e7	−0.511728
$19$	3.25790e8	1.58869	0.794345	−	0.607466i	$-0.207814\pi$
$19$	3.25790e8	1.58869	0.794345	+	0.607466i	$0.207814\pi$
$20$	−4.60523e8	−1.60900
$21$	−5.17216e7	−0.131597
$22$	7.21062e8	1.35589
$23$	1.17438e9	1.65416	0.827079	−	0.562086i	$-0.190001\pi$
$23$	1.17438e9	1.65416	0.827079	+	0.562086i	$0.190001\pi$
$24$	−2.96067e8	−0.316240
$25$	4.96003e8	0.406326
$26$	−3.74319e9	−2.37638
$27$	3.87420e8	0.192450
$28$	−7.88584e8	−0.309258
$29$	2.93323e9	0.915711	0.457856	−	0.889027i	$-0.348618\pi$
$29$	2.93323e9	0.915711	0.457856	+	0.889027i	$0.348618\pi$
$30$	4.19693e9	1.05110
$31$	−1.23680e9	−0.250292	−0.125146	−	0.992138i	$-0.539940\pi$
$31$	−1.23680e9	−0.250292	−0.125146	+	0.992138i	$0.539940\pi$
$32$	8.13766e9	1.33975
$33$	−3.78307e9	−0.509922
$34$	−2.57715e10	−2.86106
$35$	2.93963e9	0.270302
$36$	5.90689e9	0.452265
$37$	−1.79980e10	−1.15322	−0.576611	−	0.817019i	$-0.695625\pi$
$37$	−1.79980e10	−1.15322	−0.576611	+	0.817019i	$0.695625\pi$
$38$	−4.52682e10	−2.43893
$39$	1.96388e10	0.893705
$40$	1.68272e10	0.649563
$41$	5.41462e10	1.78022	0.890109	−	0.455748i	$-0.150628\pi$
$41$	5.41462e10	1.78022	0.890109	+	0.455748i	$0.150628\pi$
$42$	7.18667e9	0.202026
$43$	−4.68366e10	−1.12990	−0.564950	−	0.825125i	$-0.691105\pi$
$43$	−4.68366e10	−1.12990	−0.564950	+	0.825125i	$0.691105\pi$
$44$	−5.76794e10	−1.19833
$45$	−2.20193e10	−0.395295
$46$	−1.63179e11	−2.53944
$47$	2.60361e10	0.352322	0.176161	−	0.984361i	$-0.443632\pi$
$47$	2.60361e10	0.352322	0.176161	+	0.984361i	$0.443632\pi$
$48$	−2.52393e10	−0.297858
$49$	−9.18553e10	−0.948047
$50$	−6.89192e10	−0.623785
$51$	1.35211e11	1.07598
$52$	2.99426e11	2.10024
$53$	1.43333e11	0.888288	0.444144	−	0.895955i	$-0.353508\pi$
$53$	1.43333e11	0.888288	0.444144	+	0.895955i	$0.353508\pi$
$54$	−5.38317e10	−0.295447
$55$	2.15013e11	1.04739
$56$	2.88142e10	0.124849
$57$	2.37501e11	0.917231
$58$	−4.07569e11	−1.40579
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	−3.35722e11	−0.928958
$61$	5.85159e11	1.45422	0.727110	−	0.686521i	$-0.240863\pi$
$61$	5.85159e11	1.45422	0.727110	+	0.686521i	$0.240863\pi$
$62$	1.71852e11	0.384245
$63$	−3.77050e10	−0.0759776
$64$	−8.47100e11	−1.54087
$65$	−1.11618e12	−1.83568
$66$	5.25654e11	0.782824
$67$	−1.43954e11	−0.194419	−0.0972096	−	0.995264i	$-0.530992\pi$
$67$	−1.43954e11	−0.194419	−0.0972096	+	0.995264i	$0.530992\pi$
$68$	2.06152e12	2.52860
$69$	8.56122e11	0.955029
$70$	−4.08459e11	−0.414964
$71$	9.28219e11	0.859946	0.429973	−	0.902842i	$-0.358523\pi$
$71$	9.28219e11	0.859946	0.429973	+	0.902842i	$0.358523\pi$
$72$	−2.15833e11	−0.182582
$73$	1.49894e12	1.15927	0.579635	−	0.814876i	$-0.303195\pi$
$73$	1.49894e12	1.15927	0.579635	+	0.814876i	$0.303195\pi$
$74$	2.50081e12	1.77041
$75$	3.61586e11	0.234592
$76$	3.62111e12	2.15553
$77$	3.68181e11	0.201313
$78$	−2.72879e12	−1.37200
$79$	−2.13123e12	−0.986401	−0.493200	−	0.869916i	$-0.664173\pi$
$79$	−2.13123e12	−0.986401	−0.493200	+	0.869916i	$0.664173\pi$
$80$	1.43449e12	0.611804
$81$	2.82430e11	0.111111
$82$	−7.52357e12	−2.73296
$83$	5.02222e11	0.168612	0.0843060	−	0.996440i	$-0.473133\pi$
$83$	5.02222e11	0.168612	0.0843060	+	0.996440i	$0.473133\pi$
$84$	−5.74878e11	−0.178550
$85$	−7.68478e12	−2.21008
$86$	6.50790e12	1.73461
$87$	2.13832e12	0.528686
$88$	2.10756e12	0.483774
$89$	2.89567e12	0.617609	0.308804	−	0.951126i	$-0.400071\pi$
$89$	2.89567e12	0.617609	0.308804	+	0.951126i	$0.400071\pi$
$90$	3.05956e12	0.606852
$91$	−1.91131e12	−0.352827
$92$	1.30530e13	2.24435
$93$	−9.01626e11	−0.144506
$94$	−3.61770e12	−0.540880
$95$	−1.34985e13	−1.88401
$96$	5.93236e12	0.773507
$97$	1.54484e12	0.188308	0.0941539	−	0.995558i	$-0.469985\pi$
$97$	1.54484e12	0.188308	0.0941539	+	0.995558i	$0.469985\pi$
$98$	1.27632e13	1.45543
$99$	−2.75786e12	−0.294404
$100$	5.51300e12	0.551300
$101$	−1.77667e13	−1.66540	−0.832701	−	0.553723i	$-0.813206\pi$
$101$	−1.77667e13	−1.66540	−0.832701	+	0.553723i	$0.813206\pi$
$102$	−1.87874e13	−1.65183
$103$	1.44864e13	1.19541	0.597706	−	0.801716i	$-0.296079\pi$
$103$	1.44864e13	1.19541	0.597706	+	0.801716i	$0.296079\pi$
$104$	−1.09408e13	−0.847877
$105$	2.14299e12	0.156059
$106$	−1.99160e13	−1.36369
$107$	−1.12737e13	−0.726227	−0.363113	−	0.931745i	$-0.618286\pi$
$107$	−1.12737e13	−0.726227	−0.363113	+	0.931745i	$0.618286\pi$
$108$	4.30612e12	0.261115
$109$	−3.38427e12	−0.193283	−0.0966414	−	0.995319i	$-0.530810\pi$
$109$	−3.38427e12	−0.193283	−0.0966414	+	0.995319i	$0.530810\pi$
$110$	−2.98759e13	−1.60793
$111$	−1.31205e13	−0.665813
$112$	2.45637e12	0.117592
$113$	−8.65959e12	−0.391280	−0.195640	−	0.980676i	$-0.562678\pi$
$113$	−8.65959e12	−0.391280	−0.195640	+	0.980676i	$0.562678\pi$
$114$	−3.30005e13	−1.40812
$115$	−4.86582e13	−1.96164
$116$	3.26024e13	1.24243
$117$	1.43167e13	0.515981
$118$	5.86095e12	0.199864
$119$	−1.31592e13	−0.424788
$120$	1.22670e13	0.375025
$121$	−7.59290e12	−0.219939
$122$	−8.13073e13	−2.23250
$123$	3.94726e13	1.02781
$124$	−1.37468e13	−0.339595
$125$	3.00266e13	0.704030
$126$	5.23908e12	0.116640
$127$	−7.84144e13	−1.65833	−0.829166	−	0.559003i	$-0.811184\pi$
$127$	−7.84144e13	−1.65833	−0.829166	+	0.559003i	$0.811184\pi$
$128$	5.10400e13	1.02576
$129$	−3.41439e13	−0.652348
$130$	1.55092e14	2.81811
$131$	7.97712e12	0.137906	0.0689529	−	0.997620i	$-0.478034\pi$
$131$	7.97712e12	0.137906	0.0689529	+	0.997620i	$0.478034\pi$
$132$	−4.20483e13	−0.691859
$133$	−2.31144e13	−0.362115
$134$	2.00023e13	0.298469
$135$	−1.60521e13	−0.228224
$136$	−7.53263e13	−1.02081
$137$	−1.43376e14	−1.85264	−0.926321	−	0.376735i	$-0.877047\pi$
$137$	−1.43376e14	−1.85264	−0.926321	+	0.376735i	$0.877047\pi$
$138$	−1.18957e14	−1.46615
$139$	2.41401e13	0.283885	0.141943	−	0.989875i	$-0.454665\pi$
$139$	2.41401e13	0.283885	0.141943	+	0.989875i	$0.454665\pi$
$140$	3.26735e13	0.366745
$141$	1.89803e13	0.203413
$142$	−1.28975e14	−1.32018
$143$	−1.39799e14	−1.36716
$144$	−1.83994e13	−0.171968
$145$	−1.21533e14	−1.08593
$146$	−2.08276e14	−1.77969
$147$	−6.69625e13	−0.547355
$148$	−2.00045e14	−1.56468
$149$	1.01737e14	0.761671	0.380836	−	0.924643i	$-0.375636\pi$
$149$	1.01737e14	0.761671	0.380836	+	0.924643i	$0.375636\pi$
$150$	−5.02421e13	−0.360142
$151$	1.83739e14	1.26139	0.630696	−	0.776030i	$-0.282769\pi$
$151$	1.83739e14	1.26139	0.630696	+	0.776030i	$0.282769\pi$
$152$	−1.32312e14	−0.870197
$153$	9.85686e13	0.621218
$154$	−5.11584e13	−0.309052
$155$	5.12444e13	0.296818
$156$	2.18282e14	1.21257
$157$	1.16751e13	0.0622173	0.0311087	−	0.999516i	$-0.490096\pi$
$157$	1.16751e13	0.0622173	0.0311087	+	0.999516i	$0.490096\pi$
$158$	2.96132e14	1.51431
$159$	1.04490e14	0.512853
$160$	−3.37169e14	−1.58879
$161$	−8.33206e13	−0.377037
$162$	−3.92433e13	−0.170576
$163$	1.62999e14	0.680714	0.340357	−	0.940296i	$-0.389452\pi$
$163$	1.62999e14	0.680714	0.340357	+	0.940296i	$0.389452\pi$
$164$	6.01827e14	2.41539
$165$	1.56744e14	0.604709
$166$	−6.97834e13	−0.258851
$167$	1.69086e14	0.603185	0.301593	−	0.953437i	$-0.402482\pi$
$167$	1.69086e14	0.603185	0.301593	+	0.953437i	$0.402482\pi$
$168$	2.10056e13	0.0720816
$169$	4.22851e14	1.39612
$170$	1.06779e15	3.39289
$171$	1.73138e14	0.529564
$172$	−5.20582e14	−1.53304
$173$	3.60649e14	1.02279	0.511394	−	0.859346i	$-0.329129\pi$
$173$	3.60649e14	1.02279	0.511394	+	0.859346i	$0.329129\pi$
$174$	−2.97118e14	−0.811631
$175$	−3.51908e13	−0.0926150
$176$	1.79666e14	0.455652
$177$	−3.07496e13	−0.0751646
$178$	−4.02350e14	−0.948144
$179$	1.24489e14	0.282869	0.141434	−	0.989948i	$-0.454829\pi$
$179$	1.24489e14	0.282869	0.141434	+	0.989948i	$0.454829\pi$
$180$	−2.44741e14	−0.536334
$181$	−8.33659e14	−1.76229	−0.881146	−	0.472844i	$-0.843227\pi$
$181$	−8.33659e14	−1.76229	−0.881146	+	0.472844i	$0.843227\pi$
$182$	2.65575e14	0.541655
$183$	4.26581e14	0.839594
$184$	−4.76948e14	−0.906056
$185$	7.45714e14	1.36759
$186$	1.25280e14	0.221844
$187$	−9.62499e14	−1.64600
$188$	2.89388e14	0.478029
$189$	−2.74870e13	−0.0438657
$190$	1.87561e15	2.89230
$191$	−1.36584e14	−0.203555	−0.101778	−	0.994807i	$-0.532453\pi$
$191$	−1.36584e14	−0.203555	−0.101778	+	0.994807i	$0.532453\pi$
$192$	−6.17536e14	−0.889619
$193$	9.83407e14	1.36965	0.684827	−	0.728706i	$-0.259878\pi$
$193$	9.83407e14	1.36965	0.684827	+	0.728706i	$0.259878\pi$
$194$	−2.14655e14	−0.289087
$195$	−8.13695e14	−1.05983
$196$	−1.02096e15	−1.28630
$197$	−4.96889e14	−0.605660	−0.302830	−	0.953045i	$-0.597931\pi$
$197$	−4.96889e14	−0.605660	−0.302830	+	0.953045i	$0.597931\pi$
$198$	3.83202e14	0.451964
$199$	−5.60855e12	−0.00640185	−0.00320093	−	0.999995i	$-0.501019\pi$
$199$	−5.60855e12	−0.00640185	−0.00320093	+	0.999995i	$0.501019\pi$
$200$	−2.01441e14	−0.222563
$201$	−1.04943e14	−0.112248
$202$	2.46867e15	2.55670
$203$	−2.08109e14	−0.208721
$204$	1.50285e15	1.45989
$205$	−2.24345e15	−2.11113
$206$	−2.01287e15	−1.83518
$207$	6.24113e14	0.551386
$208$	−9.32686e14	−0.798590
$209$	−1.69065e15	−1.40315
$210$	−2.97766e14	−0.239580
$211$	3.99701e14	0.311816	0.155908	−	0.987772i	$-0.450170\pi$
$211$	3.99701e14	0.311816	0.155908	+	0.987772i	$0.450170\pi$
$212$	1.59313e15	1.20522
$213$	6.76671e14	0.496490
$214$	1.56647e15	1.11489
$215$	1.94059e15	1.33993
$216$	−1.57342e14	−0.105413
$217$	8.77492e13	0.0570499
$218$	4.70242e14	0.296725
$219$	1.09272e15	0.669305
$220$	2.38984e15	1.42109
$221$	4.99655e15	2.88483
$222$	1.82309e15	1.02215
$223$	−2.93097e15	−1.59599	−0.797994	−	0.602665i	$-0.794105\pi$
$223$	−2.93097e15	−1.59599	−0.797994	+	0.602665i	$0.794105\pi$
$224$	−5.77356e14	−0.305374
$225$	2.63596e14	0.135442
$226$	1.20324e15	0.600687
$227$	−1.07733e15	−0.522612	−0.261306	−	0.965256i	$-0.584153\pi$
$227$	−1.07733e15	−0.522612	−0.261306	+	0.965256i	$0.584153\pi$
$228$	2.63979e15	1.24449
$229$	−2.49956e15	−1.14534	−0.572669	−	0.819787i	$-0.694092\pi$
$229$	−2.49956e15	−1.14534	−0.572669	+	0.819787i	$0.694092\pi$
$230$	6.76101e15	3.01149
$231$	2.68404e14	0.116228
$232$	−1.19127e15	−0.501576
$233$	−2.90153e15	−1.18799	−0.593996	−	0.804468i	$-0.702451\pi$
$233$	−2.90153e15	−1.18799	−0.593996	+	0.804468i	$0.702451\pi$
$234$	−1.98929e15	−0.792126
$235$	−1.07876e15	−0.417814
$236$	−4.68831e14	−0.176640
$237$	−1.55366e15	−0.569499
$238$	1.82845e15	0.652129
$239$	4.58142e15	1.59006	0.795031	−	0.606569i	$-0.207455\pi$
$239$	4.58142e15	1.59006	0.795031	+	0.606569i	$0.207455\pi$
$240$	1.04574e15	0.353225
$241$	4.26214e15	1.40125	0.700627	−	0.713528i	$-0.252904\pi$
$241$	4.26214e15	1.40125	0.700627	+	0.713528i	$0.252904\pi$
$242$	1.05503e15	0.337647
$243$	2.05891e14	0.0641500
$244$	6.50396e15	1.97308
$245$	3.80585e15	1.12428
$246$	−5.48468e15	−1.57788
$247$	8.77656e15	2.45920
$248$	5.02298e14	0.137096
$249$	3.66120e14	0.0973482
$250$	−4.17217e15	−1.08082
$251$	6.52652e15	1.64741	0.823707	−	0.567016i	$-0.191902\pi$
$251$	6.52652e15	1.64741	0.823707	+	0.567016i	$0.191902\pi$
$252$	−4.19086e14	−0.103086
$253$	−6.09431e15	−1.46097
$254$	1.08956e16	2.54585
$255$	−5.60221e15	−1.27599
$256$	−1.52522e14	−0.0338667
$257$	3.00150e15	0.649789	0.324895	−	0.945750i	$-0.394671\pi$
$257$	3.00150e15	0.649789	0.324895	+	0.945750i	$0.394671\pi$
$258$	4.74426e15	1.00148
$259$	1.27693e15	0.262857
$260$	−1.24062e16	−2.49064
$261$	1.55884e15	0.305237
$262$	−1.10841e15	−0.211711
$263$	3.71597e15	0.692404	0.346202	−	0.938160i	$-0.387471\pi$
$263$	3.71597e15	0.692404	0.346202	+	0.938160i	$0.387471\pi$
$264$	1.53641e15	0.279307
$265$	−5.93875e15	−1.05341
$266$	3.21172e15	0.555914
$267$	2.11094e15	0.356577
$268$	−1.60003e15	−0.263787
$269$	4.47192e15	0.719621	0.359811	−	0.933025i	$-0.382841\pi$
$269$	4.47192e15	0.719621	0.359811	+	0.933025i	$0.382841\pi$
$270$	2.23042e15	0.350366
$271$	−4.48733e15	−0.688158	−0.344079	−	0.938941i	$-0.611809\pi$
$271$	−4.48733e15	−0.688158	−0.344079	+	0.938941i	$0.611809\pi$
$272$	−6.42144e15	−0.961468
$273$	−1.39334e15	−0.203705
$274$	1.99219e16	2.84415
$275$	−2.57395e15	−0.358871
$276$	9.51567e15	1.29578
$277$	−1.04846e16	−1.39454	−0.697271	−	0.716807i	$-0.745603\pi$
$277$	−1.04846e16	−1.39454	−0.697271	+	0.716807i	$0.745603\pi$
$278$	−3.35424e15	−0.435816
$279$	−6.57285e14	−0.0834308
$280$	−1.19387e15	−0.148057
$281$	−1.08002e16	−1.30870	−0.654352	−	0.756190i	$-0.727058\pi$
$281$	−1.08002e16	−1.30870	−0.654352	+	0.756190i	$0.727058\pi$
$282$	−2.63730e15	−0.312277
$283$	5.90391e15	0.683169	0.341584	−	0.939851i	$-0.389037\pi$
$283$	5.90391e15	0.683169	0.341584	+	0.939851i	$0.389037\pi$
$284$	1.03170e16	1.16677
$285$	−9.84041e15	−1.08773
$286$	1.94249e16	2.09884
$287$	−3.84160e15	−0.405770
$288$	4.32469e15	0.446584
$289$	2.44961e16	2.47321
$290$	1.68869e16	1.66710
$291$	1.12619e15	0.108720
$292$	1.66605e16	1.57289
$293$	−1.88698e16	−1.74232	−0.871158	−	0.491003i	$-0.836630\pi$
$293$	−1.88698e16	−1.74232	−0.871158	+	0.491003i	$0.836630\pi$
$294$	9.30438e15	0.840291
$295$	1.74767e15	0.154389
$296$	7.30949e15	0.631671
$297$	−2.01048e15	−0.169974
$298$	−1.41362e16	−1.16931
$299$	3.16369e16	2.56054
$300$	4.01898e15	0.318293
$301$	3.32299e15	0.257542
$302$	−2.55303e16	−1.93647
$303$	−1.29520e16	−0.961520
$304$	−1.12794e16	−0.819613
$305$	−2.42450e16	−1.72454
$306$	−1.36960e16	−0.953685
$307$	1.00079e16	0.682247	0.341123	−	0.940019i	$-0.389193\pi$
$307$	1.00079e16	0.682247	0.341123	+	0.940019i	$0.389193\pi$
$308$	4.09228e15	0.273140
$309$	1.05606e16	0.690171
$310$	−7.12037e15	−0.455671
$311$	−1.68400e16	−1.05536	−0.527679	−	0.849444i	$-0.676938\pi$
$311$	−1.68400e16	−1.05536	−0.527679	+	0.849444i	$0.676938\pi$
$312$	−7.97585e15	−0.489522
$313$	−6.43117e15	−0.386591	−0.193296	−	0.981141i	$-0.561918\pi$
$313$	−6.43117e15	−0.386591	−0.193296	+	0.981141i	$0.561918\pi$
$314$	−1.62224e15	−0.0955151
$315$	1.56224e15	0.0901008
$316$	−2.36883e16	−1.33834
$317$	−1.76534e16	−0.977111	−0.488556	−	0.872533i	$-0.662476\pi$
$317$	−1.76534e16	−0.977111	−0.488556	+	0.872533i	$0.662476\pi$
$318$	−1.45188e16	−0.787325
$319$	−1.52217e16	−0.808766
$320$	3.50980e16	1.82729
$321$	−8.21853e15	−0.419287
$322$	1.15773e16	0.578822
$323$	6.04256e16	2.96077
$324$	3.13916e15	0.150755
$325$	1.33620e16	0.628968
$326$	−2.26485e16	−1.04502
$327$	−2.46714e15	−0.111592
$328$	−2.19903e16	−0.975104
$329$	−1.84723e15	−0.0803059
$330$	−2.17795e16	−0.928341
$331$	3.65153e16	1.52613	0.763067	−	0.646319i	$-0.223693\pi$
$331$	3.65153e16	1.52613	0.763067	+	0.646319i	$0.223693\pi$
$332$	5.58213e15	0.228772
$333$	−9.56487e15	−0.384407
$334$	−2.34944e16	−0.926001
$335$	5.96449e15	0.230559
$336$	1.79069e15	0.0678915
$337$	−1.46271e16	−0.543956	−0.271978	−	0.962303i	$-0.587678\pi$
$337$	−1.46271e16	−0.543956	−0.271978	+	0.962303i	$0.587678\pi$
$338$	−5.87548e16	−2.14331
$339$	−6.31284e15	−0.225906
$340$	−8.54152e16	−2.99863
$341$	6.41823e15	0.221061
$342$	−2.40574e16	−0.812978
$343$	1.33912e16	0.444024
$344$	1.90216e16	0.618897
$345$	−3.54718e16	−1.13256
$346$	−5.01119e16	−1.57017
$347$	4.07037e15	0.125168	0.0625839	−	0.998040i	$-0.480066\pi$
$347$	4.07037e15	0.125168	0.0625839	+	0.998040i	$0.480066\pi$
$348$	2.37671e16	0.717318
$349$	3.81341e16	1.12966	0.564831	−	0.825207i	$-0.308941\pi$
$349$	3.81341e16	1.12966	0.564831	+	0.825207i	$0.308941\pi$
$350$	4.88972e15	0.142181
$351$	1.04368e16	0.297902
$352$	−4.22295e16	−1.18328
$353$	7.20818e15	0.198285	0.0991426	−	0.995073i	$-0.468390\pi$
$353$	7.20818e15	0.198285	0.0991426	+	0.995073i	$0.468390\pi$
$354$	4.27263e15	0.115392
$355$	−3.84590e16	−1.01980
$356$	3.21849e16	0.837968
$357$	−9.59302e15	−0.245252
$358$	−1.72976e16	−0.434256
$359$	6.56684e16	1.61898	0.809492	−	0.587131i	$-0.199743\pi$
$359$	6.56684e16	1.61898	0.809492	+	0.587131i	$0.199743\pi$
$360$	8.94265e15	0.216521
$361$	6.40862e16	1.52394
$362$	1.15836e17	2.70544
$363$	−5.53522e15	−0.126982
$364$	−2.12439e16	−0.478713
$365$	−6.21057e16	−1.37476
$366$	−5.92730e16	−1.28893
$367$	3.21659e16	0.687174	0.343587	−	0.939121i	$-0.388358\pi$
$367$	3.21659e16	0.687174	0.343587	+	0.939121i	$0.388358\pi$
$368$	−4.06590e16	−0.853387
$369$	2.87755e16	0.593406
$370$	−1.03616e17	−2.09950
$371$	−1.01693e16	−0.202470
$372$	−1.00214e16	−0.196065
$373$	1.36046e16	0.261565	0.130782	−	0.991411i	$-0.458251\pi$
$373$	1.36046e16	0.261565	0.130782	+	0.991411i	$0.458251\pi$
$374$	1.33738e17	2.52691
$375$	2.18894e16	0.406472
$376$	−1.05740e16	−0.192983
$377$	7.90191e16	1.41747
$378$	3.81929e15	0.0673420
$379$	2.41382e16	0.418360	0.209180	−	0.977877i	$-0.432921\pi$
$379$	2.41382e16	0.418360	0.209180	+	0.977877i	$0.432921\pi$
$380$	−1.50034e17	−2.55621
$381$	−5.71641e16	−0.957438
$382$	1.89782e16	0.312495
$383$	9.00843e16	1.45833	0.729167	−	0.684335i	$-0.239908\pi$
$383$	9.00843e16	1.45833	0.729167	+	0.684335i	$0.239908\pi$
$384$	3.72082e16	0.592223
$385$	−1.52549e16	−0.238734
$386$	−1.36644e17	−2.10267
$387$	−2.48909e16	−0.376633
$388$	1.71707e16	0.255495
$389$	−2.97279e16	−0.435002	−0.217501	−	0.976060i	$-0.569791\pi$
$389$	−2.97279e16	−0.435002	−0.217501	+	0.976060i	$0.569791\pi$
$390$	1.13062e17	1.62704
$391$	2.17817e17	3.08278
$392$	3.73050e16	0.519287
$393$	5.81532e15	0.0796199
$394$	6.90423e16	0.929800
$395$	8.83034e16	1.16976
$396$	−3.06532e16	−0.399445
$397$	−1.34288e17	−1.72147	−0.860736	−	0.509051i	$-0.829996\pi$
$397$	−1.34288e17	−1.72147	−0.860736	+	0.509051i	$0.829996\pi$
$398$	7.79303e14	0.00982803
$399$	−1.68504e16	−0.209067
$400$	−1.71725e16	−0.209625
$401$	−2.15972e16	−0.259393	−0.129697	−	0.991554i	$-0.541400\pi$
$401$	−2.15972e16	−0.259393	−0.129697	+	0.991554i	$0.541400\pi$
$402$	1.45817e16	0.172321
$403$	−3.33185e16	−0.387438
$404$	−1.97475e17	−2.25961
$405$	−1.17019e16	−0.131765
$406$	2.89165e16	0.320425
$407$	9.33987e16	1.01854
$408$	−5.49129e16	−0.589363
$409$	3.86915e16	0.408708	0.204354	−	0.978897i	$-0.434491\pi$
$409$	3.86915e16	0.408708	0.204354	+	0.978897i	$0.434491\pi$
$410$	3.11725e17	3.24098
$411$	−1.04521e17	−1.06962
$412$	1.61014e17	1.62193
$413$	2.99265e15	0.0296743
$414$	−8.67199e16	−0.846480
$415$	−2.08087e16	−0.199955
$416$	2.19223e17	2.07386
$417$	1.75981e16	0.163901
$418$	2.34915e17	2.15409
$419$	9.01511e16	0.813917	0.406958	−	0.913447i	$-0.366589\pi$
$419$	9.01511e16	0.813917	0.406958	+	0.913447i	$0.366589\pi$
$420$	2.38190e16	0.211740
$421$	−1.54430e16	−0.135176	−0.0675878	−	0.997713i	$-0.521530\pi$
$421$	−1.54430e16	−0.135176	−0.0675878	+	0.997713i	$0.521530\pi$
$422$	−5.55381e16	−0.478696
$423$	1.38367e16	0.117441
$424$	−5.82117e16	−0.486555
$425$	9.19957e16	0.757251
$426$	−9.40229e16	−0.762204
$427$	−4.15163e16	−0.331465
$428$	−1.25306e17	−0.985340
$429$	−1.01913e17	−0.789329
$430$	−2.69643e17	−2.05705
$431$	−1.21401e17	−0.912266	−0.456133	−	0.889912i	$-0.650766\pi$
$431$	−1.21401e17	−0.912266	−0.456133	+	0.889912i	$0.650766\pi$
$432$	−1.34132e16	−0.0992858
$433$	−5.65871e16	−0.412616	−0.206308	−	0.978487i	$-0.566145\pi$
$433$	−5.65871e16	−0.412616	−0.206308	+	0.978487i	$0.566145\pi$
$434$	−1.21927e16	−0.0875822
$435$	−8.85974e16	−0.626962
$436$	−3.76157e16	−0.262245
$437$	3.82601e17	2.62795
$438$	−1.51833e17	−1.02751
$439$	2.21807e16	0.147895	0.0739477	−	0.997262i	$-0.476440\pi$
$439$	2.21807e16	0.147895	0.0739477	+	0.997262i	$0.476440\pi$
$440$	−8.73228e16	−0.573701
$441$	−4.88157e16	−0.316016
$442$	−6.94266e17	−4.42875
$443$	7.82941e15	0.0492158	0.0246079	−	0.999697i	$-0.492166\pi$
$443$	7.82941e15	0.0492158	0.0246079	+	0.999697i	$0.492166\pi$
$444$	−1.45833e17	−0.903371
$445$	−1.19977e17	−0.732414
$446$	4.07256e17	2.45014
$447$	7.41662e16	0.439751
$448$	6.01006e16	0.351214
$449$	2.55848e17	1.47361	0.736803	−	0.676107i	$-0.236334\pi$
$449$	2.55848e17	1.47361	0.736803	+	0.676107i	$0.236334\pi$
$450$	−3.66265e16	−0.207928
$451$	−2.80986e17	−1.57231
$452$	−9.62501e16	−0.530886
$453$	1.33945e17	0.728265
$454$	1.49693e17	0.802306
$455$	7.91915e16	0.418412
$456$	−9.64558e16	−0.502408
$457$	−9.76623e16	−0.501501	−0.250751	−	0.968052i	$-0.580677\pi$
$457$	−9.76623e16	−0.501501	−0.250751	+	0.968052i	$0.580677\pi$
$458$	3.47312e17	1.75831
$459$	7.18565e16	0.358661
$460$	−5.40829e17	−2.66155
$461$	9.01704e16	0.437530	0.218765	−	0.975778i	$-0.429797\pi$
$461$	9.01704e16	0.437530	0.218765	+	0.975778i	$0.429797\pi$
$462$	−3.72945e16	−0.178431
$463$	4.03703e17	1.90452	0.952260	−	0.305288i	$-0.0987528\pi$
$463$	4.03703e17	1.90452	0.952260	+	0.305288i	$0.0987528\pi$
$464$	−1.01553e17	−0.472420
$465$	3.73572e16	0.171368
$466$	4.03165e17	1.82379
$467$	−4.66211e16	−0.207980	−0.103990	−	0.994578i	$-0.533161\pi$
$467$	−4.66211e16	−0.207980	−0.103990	+	0.994578i	$0.533161\pi$
$468$	1.59127e17	0.700079
$469$	1.02134e16	0.0443145
$470$	1.49893e17	0.641422
$471$	8.51112e15	0.0359212
$472$	1.71307e16	0.0713103
$473$	2.43053e17	0.997940
$474$	2.15880e17	0.874286
$475$	1.61593e17	0.645526
$476$	−1.46262e17	−0.576350
$477$	7.61732e16	0.296096
$478$	−6.36585e17	−2.44104
$479$	−3.28090e17	−1.24111	−0.620557	−	0.784161i	$-0.713093\pi$
$479$	−3.28090e17	−1.24111	−0.620557	+	0.784161i	$0.713093\pi$
$480$	−2.45796e17	−0.917291
$481$	−4.84853e17	−1.78512
$482$	−5.92221e17	−2.15118
$483$	−6.07407e16	−0.217682
$484$	−8.43939e16	−0.298412
$485$	−6.40078e16	−0.223312
$486$	−2.86084e16	−0.0984822
$487$	−1.00806e17	−0.342410	−0.171205	−	0.985235i	$-0.554766\pi$
$487$	−1.00806e17	−0.342410	−0.171205	+	0.985235i	$0.554766\pi$
$488$	−2.37650e17	−0.796541
$489$	1.18826e17	0.393010
$490$	−5.28820e17	−1.72597
$491$	−4.60172e17	−1.48214	−0.741072	−	0.671426i	$-0.765682\pi$
$491$	−4.60172e17	−1.48214	−0.741072	+	0.671426i	$0.765682\pi$
$492$	4.38732e17	1.39452
$493$	5.44038e17	1.70657
$494$	−1.21949e18	−3.77533
$495$	1.14267e17	0.349129
$496$	4.28201e16	0.129127
$497$	−6.58559e16	−0.196010
$498$	−5.08721e16	−0.149448
$499$	−2.88208e17	−0.835704	−0.417852	−	0.908515i	$-0.637217\pi$
$499$	−2.88208e17	−0.835704	−0.417852	+	0.908515i	$0.637217\pi$
$500$	3.33741e17	0.955224
$501$	1.23264e17	0.348249
$502$	−9.06854e17	−2.52908
$503$	9.44084e16	0.259907	0.129954	−	0.991520i	$-0.458517\pi$
$503$	9.44084e16	0.259907	0.129954	+	0.991520i	$0.458517\pi$
$504$	1.53131e16	0.0416163
$505$	7.36132e17	1.97498
$506$	8.46799e17	2.24286
$507$	3.08258e17	0.806052
$508$	−8.71564e17	−2.25001
$509$	−3.43197e16	−0.0874737	−0.0437369	−	0.999043i	$-0.513926\pi$
$509$	−3.43197e16	−0.0874737	−0.0437369	+	0.999043i	$0.513926\pi$
$510$	7.78421e17	1.95888
$511$	−1.06348e17	−0.264236
$512$	−3.96927e17	−0.973769
$513$	1.26218e17	0.305744
$514$	−4.17055e17	−0.997547
$515$	−6.00216e17	−1.41762
$516$	−3.79504e17	−0.885102
$517$	−1.35112e17	−0.311175
$518$	−1.77429e17	−0.403535
$519$	2.62913e17	0.590507
$520$	4.53312e17	1.00549
$521$	−3.51007e17	−0.768900	−0.384450	−	0.923146i	$-0.625609\pi$
$521$	−3.51007e17	−0.768900	−0.384450	+	0.923146i	$0.625609\pi$
$522$	−2.16599e17	−0.468596
$523$	−8.27856e17	−1.76886	−0.884431	−	0.466671i	$-0.845453\pi$
$523$	−8.27856e17	−1.76886	−0.884431	+	0.466671i	$0.845453\pi$
$524$	8.86645e16	0.187110
$525$	−2.56541e16	−0.0534713
$526$	−5.16330e17	−1.06297
$527$	−2.29394e17	−0.466459
$528$	1.30976e17	0.263071
$529$	8.75128e17	1.73624
$530$	8.25184e17	1.61718
$531$	−2.24165e16	−0.0433963
$532$	−2.56913e17	−0.491315
$533$	1.45866e18	2.75567
$534$	−2.93313e17	−0.547411
$535$	4.67105e17	0.861222
$536$	5.84640e16	0.106492
$537$	9.07523e16	0.163314
$538$	−6.21369e17	−1.10475
$539$	4.76673e17	0.837325
$540$	−1.78416e17	−0.309653
$541$	−3.57711e17	−0.613409	−0.306704	−	0.951805i	$-0.599226\pi$
$541$	−3.57711e17	−0.613409	−0.306704	+	0.951805i	$0.599226\pi$
$542$	6.23511e17	1.05645
$543$	−6.07738e17	−1.01746
$544$	1.50933e18	2.49684
$545$	1.40221e17	0.229211
$546$	1.93604e17	0.312724
$547$	−1.74264e17	−0.278157	−0.139079	−	0.990281i	$-0.544414\pi$
$547$	−1.74264e17	−0.278157	−0.139079	+	0.990281i	$0.544414\pi$
$548$	−1.59360e18	−2.51365
$549$	3.10978e17	0.484740
$550$	3.57649e17	0.550934
$551$	9.55616e17	1.45478
$552$	−3.47695e17	−0.523112
$553$	1.51208e17	0.224833
$554$	1.45682e18	2.14088
$555$	5.43625e17	0.789578
$556$	2.68314e17	0.385173
$557$	6.12253e16	0.0868704	0.0434352	−	0.999056i	$-0.486170\pi$
$557$	6.12253e16	0.0868704	0.0434352	+	0.999056i	$0.486170\pi$
$558$	9.13292e16	0.128082
$559$	−1.26174e18	−1.74902
$560$	−1.01775e17	−0.139450
$561$	−7.01662e17	−0.950318
$562$	1.50068e18	2.00910
$563$	−4.31503e16	−0.0571057	−0.0285528	−	0.999592i	$-0.509090\pi$
$563$	−4.31503e16	−0.0571057	−0.0285528	+	0.999592i	$0.509090\pi$
$564$	2.10964e17	0.275990
$565$	3.58794e17	0.464013
$566$	−8.20343e17	−1.04879
$567$	−2.00380e16	−0.0253259
$568$	−3.76976e17	−0.471031
$569$	1.29788e17	0.160326	0.0801632	−	0.996782i	$-0.474456\pi$
$569$	1.29788e17	0.160326	0.0801632	+	0.996782i	$0.474456\pi$
$570$	1.36732e18	1.66987
$571$	−9.58576e17	−1.15742	−0.578711	−	0.815533i	$-0.696444\pi$
$571$	−9.58576e17	−1.15742	−0.578711	+	0.815533i	$0.696444\pi$
$572$	−1.55384e18	−1.85495
$573$	−9.95695e16	−0.117523
$574$	5.33787e17	0.622932
$575$	5.82495e17	0.672127
$576$	−4.50183e17	−0.513622
$577$	1.44548e18	1.63068	0.815339	−	0.578984i	$-0.196551\pi$
$577$	1.44548e18	1.63068	0.815339	+	0.578984i	$0.196551\pi$
$578$	−3.40371e18	−3.79684
$579$	7.16904e17	0.790770
$580$	−1.35082e18	−1.47338
$581$	−3.56320e16	−0.0384322
$582$	−1.56483e17	−0.166905
$583$	−7.43813e17	−0.784545
$584$	−6.08760e17	−0.634984
$585$	−5.93184e17	−0.611894
$586$	2.62194e18	2.67478
$587$	−4.85405e17	−0.489730	−0.244865	−	0.969557i	$-0.578744\pi$
$587$	−4.85405e17	−0.489730	−0.244865	+	0.969557i	$0.578744\pi$
$588$	−7.44279e17	−0.742648
$589$	−4.02937e17	−0.397637
$590$	−2.42838e17	−0.237016
$591$	−3.62232e17	−0.349678
$592$	6.23122e17	0.594952
$593$	−1.12161e17	−0.105922	−0.0529612	−	0.998597i	$-0.516866\pi$
$593$	−1.12161e17	−0.105922	−0.0529612	+	0.998597i	$0.516866\pi$
$594$	2.79354e17	0.260941
$595$	5.45225e17	0.503751
$596$	1.13079e18	1.03343
$597$	−4.08863e15	−0.00369611
$598$	−4.39592e18	−3.93090
$599$	9.43281e17	0.834386	0.417193	−	0.908818i	$-0.363014\pi$
$599$	9.43281e17	0.834386	0.417193	+	0.908818i	$0.363014\pi$
$600$	−1.46850e17	−0.128497
$601$	−2.15525e18	−1.86558	−0.932789	−	0.360422i	$-0.882633\pi$
$601$	−2.15525e18	−1.86558	−0.932789	+	0.360422i	$0.882633\pi$
$602$	−4.61727e17	−0.395374
$603$	−7.65033e16	−0.0648064
$604$	2.04223e18	1.71145
$605$	3.14598e17	0.260823
$606$	1.79966e18	1.47611
$607$	−1.05989e18	−0.860068	−0.430034	−	0.902813i	$-0.641498\pi$
$607$	−1.05989e18	−0.860068	−0.430034	+	0.902813i	$0.641498\pi$
$608$	2.65117e18	2.12845
$609$	−1.51711e17	−0.120505
$610$	3.36882e18	2.64749
$611$	7.01395e17	0.545374
$612$	1.09558e18	0.842865
$613$	−1.04123e18	−0.792601	−0.396300	−	0.918121i	$-0.629706\pi$
$613$	−1.04123e18	−0.792601	−0.396300	+	0.918121i	$0.629706\pi$
$614$	−1.39058e18	−1.04738
$615$	−1.63547e18	−1.21886
$616$	−1.49529e17	−0.110268
$617$	−1.32142e18	−0.964245	−0.482123	−	0.876104i	$-0.660134\pi$
$617$	−1.32142e18	−0.964245	−0.482123	+	0.876104i	$0.660134\pi$
$618$	−1.46738e18	−1.05954
$619$	1.24518e18	0.889701	0.444850	−	0.895605i	$-0.353257\pi$
$619$	1.24518e18	0.889701	0.444850	+	0.895605i	$0.353257\pi$
$620$	5.69575e17	0.402721
$621$	4.54978e17	0.318343
$622$	2.33990e18	1.62017
$623$	−2.05444e17	−0.140773
$624$	−6.79928e17	−0.461066
$625$	−1.84957e18	−1.24123
$626$	8.93606e17	0.593489
$627$	−1.23249e18	−0.810108
$628$	1.29767e17	0.0844161
$629$	−3.33816e18	−2.14921
$630$	−2.17072e17	−0.138321
$631$	2.50990e18	1.58295	0.791473	−	0.611204i	$-0.209314\pi$
$631$	2.50990e18	1.58295	0.791473	+	0.611204i	$0.209314\pi$
$632$	8.65551e17	0.540296
$633$	2.91382e17	0.180027
$634$	2.45293e18	1.50005
$635$	3.24895e18	1.96659
$636$	1.16139e18	0.695836
$637$	−2.47452e18	−1.46752
$638$	2.11504e18	1.24161
$639$	4.93293e17	0.286649
$640$	−2.11475e18	−1.21643
$641$	7.47974e17	0.425902	0.212951	−	0.977063i	$-0.431693\pi$
$641$	7.47974e17	0.425902	0.212951	+	0.977063i	$0.431693\pi$
$642$	1.14196e18	0.643683
$643$	4.39565e17	0.245274	0.122637	−	0.992452i	$-0.460865\pi$
$643$	4.39565e17	0.245274	0.122637	+	0.992452i	$0.460865\pi$
$644$	−9.26096e17	−0.511562
$645$	1.41469e18	0.773611
$646$	−8.39609e18	−4.54533
$647$	1.42137e18	0.761780	0.380890	−	0.924620i	$-0.375618\pi$
$647$	1.42137e18	0.761780	0.380890	+	0.924620i	$0.375618\pi$
$648$	−1.14703e17	−0.0608605
$649$	2.18891e17	0.114984
$650$	−1.85663e18	−0.965583
$651$	6.39692e16	0.0329378
$652$	1.81171e18	0.923588
$653$	−8.42454e17	−0.425217	−0.212609	−	0.977137i	$-0.568196\pi$
$653$	−8.42454e17	−0.425217	−0.212609	+	0.977137i	$0.568196\pi$
$654$	3.42806e17	0.171314
$655$	−3.30517e17	−0.163541
$656$	−1.87464e18	−0.918422
$657$	7.96596e17	0.386423
$658$	2.56671e17	0.123284
$659$	2.67379e18	1.27166	0.635831	−	0.771829i	$-0.280658\pi$
$659$	2.67379e18	1.27166	0.635831	+	0.771829i	$0.280658\pi$
$660$	1.74219e18	0.820466
$661$	2.15043e18	1.00280	0.501401	−	0.865215i	$-0.332818\pi$
$661$	2.15043e18	1.00280	0.501401	+	0.865215i	$0.332818\pi$
$662$	−5.07377e18	−2.34290
$663$	3.64248e18	1.66556
$664$	−2.03967e17	−0.0923563
$665$	9.57701e17	0.429427
$666$	1.32903e18	0.590136
$667$	3.44472e18	1.51473
$668$	1.87937e18	0.818398
$669$	−2.13668e18	−0.921444
$670$	−8.28760e17	−0.353951
$671$	−3.03662e18	−1.28438
$672$	−4.20893e17	−0.176308
$673$	3.45008e18	1.43130	0.715652	−	0.698457i	$-0.246130\pi$
$673$	3.45008e18	1.43130	0.715652	+	0.698457i	$0.246130\pi$
$674$	2.03242e18	0.835074
$675$	1.92162e17	0.0781974
$676$	4.69993e18	1.89425
$677$	2.80155e18	1.11834	0.559168	−	0.829054i	$-0.311121\pi$
$677$	2.80155e18	1.11834	0.559168	+	0.829054i	$0.311121\pi$
$678$	8.77164e17	0.346807
$679$	−1.09605e17	−0.0429216
$680$	3.12101e18	1.21056
$681$	−7.85371e17	−0.301730
$682$	−8.91808e17	−0.339370
$683$	3.34878e18	1.26227	0.631135	−	0.775673i	$-0.282589\pi$
$683$	3.34878e18	1.26227	0.631135	+	0.775673i	$0.282589\pi$
$684$	1.92441e18	0.718509
$685$	5.94050e18	2.19702
$686$	−1.86069e18	−0.681659
$687$	−1.82218e18	−0.661261
$688$	1.62156e18	0.582921
$689$	3.86130e18	1.37502
$690$	4.92878e18	1.73868
$691$	−4.63969e18	−1.62137	−0.810684	−	0.585484i	$-0.800905\pi$
$691$	−4.63969e18	−1.62137	−0.810684	+	0.585484i	$0.800905\pi$
$692$	4.00857e18	1.38771
$693$	1.95666e17	0.0671043
$694$	−5.65575e17	−0.192156
$695$	−1.00020e18	−0.336655
$696$	−8.68433e17	−0.289585
$697$	1.00427e19	3.31771
$698$	−5.29870e18	−1.73424
$699$	−2.11522e18	−0.685888
$700$	−3.91140e17	−0.125659
$701$	1.36370e18	0.434062	0.217031	−	0.976165i	$-0.430363\pi$
$701$	1.36370e18	0.434062	0.217031	+	0.976165i	$0.430363\pi$
$702$	−1.45019e18	−0.457334
$703$	−5.86357e18	−1.83211
$704$	4.39593e18	1.36091
$705$	−7.86415e17	−0.241225
$706$	−1.00157e18	−0.304404
$707$	1.26053e18	0.379600
$708$	−3.41777e17	−0.101983
$709$	−2.65012e18	−0.783548	−0.391774	−	0.920061i	$-0.628138\pi$
$709$	−2.65012e18	−0.783548	−0.391774	+	0.920061i	$0.628138\pi$
$710$	5.34385e18	1.56558
$711$	−1.13262e18	−0.328800
$712$	−1.17601e18	−0.338292
$713$	−1.45247e18	−0.414023
$714$	1.33294e18	0.376507
$715$	5.79230e18	1.62129
$716$	1.38367e18	0.383795
$717$	3.33986e18	0.918023
$718$	−9.12456e18	−2.48544
$719$	−5.97402e18	−1.61261	−0.806305	−	0.591500i	$-0.798536\pi$
$719$	−5.97402e18	−1.61261	−0.806305	+	0.591500i	$0.798536\pi$
$720$	7.62346e17	0.203935
$721$	−1.02779e18	−0.272474
$722$	−8.90472e18	−2.33953
$723$	3.10710e18	0.809014
$724$	−9.26600e18	−2.39107
$725$	1.45489e18	0.372077
$726$	7.69114e17	0.194941
$727$	−1.37966e17	−0.0346576	−0.0173288	−	0.999850i	$-0.505516\pi$
$727$	−1.37966e17	−0.0346576	−0.0173288	+	0.999850i	$0.505516\pi$
$728$	7.76236e17	0.193259
$729$	1.50095e17	0.0370370
$730$	8.62953e18	2.11051
$731$	−8.68698e18	−2.10574
$732$	4.74139e18	1.13916
$733$	6.64805e18	1.58314	0.791568	−	0.611081i	$-0.209265\pi$
$733$	6.64805e18	1.58314	0.791568	+	0.611081i	$0.209265\pi$
$734$	−4.46943e18	−1.05494
$735$	2.77447e18	0.649101
$736$	9.55669e18	2.21616
$737$	7.47037e17	0.171713
$738$	−3.99833e18	−0.910988
$739$	−1.06037e18	−0.239480	−0.119740	−	0.992805i	$-0.538206\pi$
$739$	−1.06037e18	−0.239480	−0.119740	+	0.992805i	$0.538206\pi$
$740$	8.28850e18	1.85554
$741$	6.39811e18	1.41982
$742$	1.41302e18	0.310829
$743$	7.25562e18	1.58215	0.791074	−	0.611721i	$-0.209522\pi$
$743$	7.25562e18	1.58215	0.791074	+	0.611721i	$0.209522\pi$
$744$	3.66176e17	0.0791526
$745$	−4.21528e18	−0.903255
$746$	−1.89035e18	−0.401550
$747$	2.66902e17	0.0562040
$748$	−1.06980e19	−2.23328
$749$	7.99855e17	0.165531
$750$	−3.04151e18	−0.624010
$751$	8.39096e18	1.70668	0.853340	−	0.521356i	$-0.174573\pi$
$751$	8.39096e18	1.70668	0.853340	+	0.521356i	$0.174573\pi$
$752$	−9.01416e17	−0.181765
$753$	4.75783e18	0.951134
$754$	−1.09796e19	−2.17608
$755$	−7.61287e18	−1.49587
$756$	−3.05514e17	−0.0595167
$757$	−7.30335e17	−0.141058	−0.0705292	−	0.997510i	$-0.522469\pi$
$757$	−7.30335e17	−0.141058	−0.0705292	+	0.997510i	$0.522469\pi$
$758$	−3.35398e18	−0.642259
$759$	−4.44275e18	−0.843491
$760$	5.48212e18	1.03195
$761$	−1.96604e18	−0.366937	−0.183469	−	0.983026i	$-0.558733\pi$
$761$	−1.96604e18	−0.366937	−0.183469	+	0.983026i	$0.558733\pi$
$762$	7.94290e18	1.46985
$763$	2.40110e17	0.0440555
$764$	−1.51811e18	−0.276182
$765$	−4.08401e18	−0.736694
$766$	−1.25171e19	−2.23881
$767$	−1.13631e18	−0.201525
$768$	−1.11189e17	−0.0195530
$769$	−3.49818e18	−0.609988	−0.304994	−	0.952354i	$-0.598654\pi$
$769$	−3.49818e18	−0.609988	−0.304994	+	0.952354i	$0.598654\pi$
$770$	2.11965e18	0.366501
$771$	2.18809e18	0.375156
$772$	1.09304e19	1.85834
$773$	1.14812e19	1.93562	0.967809	−	0.251687i	$-0.0809854\pi$
$773$	1.14812e19	1.93562	0.967809	+	0.251687i	$0.0809854\pi$
$774$	3.45857e18	0.578202
$775$	−6.13455e17	−0.101700
$776$	−6.27405e17	−0.103145
$777$	9.30885e17	0.151761
$778$	4.13066e18	0.667809
$779$	1.76403e19	2.82821
$780$	−9.04411e18	−1.43797
$781$	−4.81689e18	−0.759513
$782$	−3.02655e19	−4.73264
$783$	1.13639e18	0.176229
$784$	3.18019e18	0.489101
$785$	−4.83734e17	−0.0737826
$786$	−8.08033e17	−0.122231
$787$	−9.59380e18	−1.43931	−0.719656	−	0.694331i	$-0.755700\pi$
$787$	−9.59380e18	−1.43931	−0.719656	+	0.694331i	$0.755700\pi$
$788$	−5.52285e18	−0.821756
$789$	2.70894e18	0.399759
$790$	−1.22697e19	−1.79580
$791$	6.14387e17	0.0891856
$792$	1.12004e18	0.161258
$793$	1.57638e19	2.25105
$794$	1.86592e19	2.64278
$795$	−4.32935e18	−0.608186
$796$	−6.23382e16	−0.00868599
$797$	−6.90283e18	−0.953999	−0.476999	−	0.878904i	$-0.658276\pi$
$797$	−6.90283e18	−0.953999	−0.476999	+	0.878904i	$0.658276\pi$
$798$	2.34135e18	0.320957
$799$	4.82903e18	0.656607
$800$	4.03630e18	0.544376
$801$	1.53888e18	0.205870
$802$	3.00091e18	0.398217
$803$	−7.77857e18	−1.02388
$804$	−1.16642e18	−0.152297
$805$	3.45223e18	0.447123
$806$	4.62957e18	0.594789
$807$	3.26003e18	0.415474
$808$	7.21557e18	0.912215
$809$	−1.20433e19	−1.51035	−0.755176	−	0.655522i	$-0.772449\pi$
$809$	−1.20433e19	−1.51035	−0.755176	+	0.655522i	$0.772449\pi$
$810$	1.62597e18	0.202284
$811$	−4.40733e18	−0.543927	−0.271963	−	0.962308i	$-0.587673\pi$
$811$	−4.40733e18	−0.543927	−0.271963	+	0.962308i	$0.587673\pi$
$812$	−2.31310e18	−0.283191
$813$	−3.27127e18	−0.397308
$814$	−1.29777e19	−1.56364
$815$	−6.75355e18	−0.807249
$816$	−4.68123e18	−0.555104
$817$	−1.52589e19	−1.79506
$818$	−5.37614e18	−0.627443
$819$	−1.01575e18	−0.117609
$820$	−2.49356e19	−2.86437
$821$	1.01852e19	1.16075	0.580373	−	0.814351i	$-0.302907\pi$
$821$	1.01852e19	1.16075	0.580373	+	0.814351i	$0.302907\pi$
$822$	1.45231e19	1.64207
$823$	−1.33841e19	−1.50137	−0.750687	−	0.660658i	$-0.770277\pi$
$823$	−1.33841e19	−1.50137	−0.750687	+	0.660658i	$0.770277\pi$
$824$	−5.88332e18	−0.654780
$825$	−1.87641e18	−0.207194
$826$	−4.15826e17	−0.0455556
$827$	−4.64686e18	−0.505096	−0.252548	−	0.967584i	$-0.581269\pi$
$827$	−4.64686e18	−0.505096	−0.252548	+	0.967584i	$0.581269\pi$
$828$	6.93692e18	0.748117
$829$	−1.17913e19	−1.26170	−0.630850	−	0.775905i	$-0.717294\pi$
$829$	−1.17913e19	−1.26170	−0.630850	+	0.775905i	$0.717294\pi$
$830$	2.89134e18	0.306967
$831$	−7.64325e18	−0.805140
$832$	−2.28203e19	−2.38517
$833$	−1.70368e19	−1.76683
$834$	−2.44524e18	−0.251619
$835$	−7.00577e18	−0.715309
$836$	−1.87914e19	−1.90378
$837$	−4.79161e17	−0.0481688
$838$	−1.25264e19	−1.24951
$839$	1.84904e19	1.83018	0.915090	−	0.403250i	$-0.132120\pi$
$839$	1.84904e19	1.83018	0.915090	+	0.403250i	$0.132120\pi$
$840$	−8.70328e17	−0.0854806
$841$	−1.65681e18	−0.161473
$842$	2.14579e18	0.207519
$843$	−7.87335e18	−0.755580
$844$	4.44262e18	0.423071
$845$	−1.75201e19	−1.65564
$846$	−1.92259e18	−0.180293
$847$	5.38706e17	0.0501314
$848$	−4.96245e18	−0.458272
$849$	4.30395e18	0.394428
$850$	−1.27827e19	−1.16252
$851$	−2.11365e19	−1.90761
$852$	7.52110e18	0.673634
$853$	1.44059e19	1.28047	0.640237	−	0.768177i	$-0.278836\pi$
$853$	1.44059e19	1.28047	0.640237	+	0.768177i	$0.278836\pi$
$854$	5.76865e18	0.508859
$855$	−7.17366e18	−0.628002
$856$	4.57857e18	0.397787
$857$	−2.08680e19	−1.79931	−0.899656	−	0.436600i	$-0.856182\pi$
$857$	−2.08680e19	−1.79931	−0.899656	+	0.436600i	$0.856182\pi$
$858$	1.41608e19	1.21177
$859$	1.98253e18	0.168370	0.0841849	−	0.996450i	$-0.473171\pi$
$859$	1.98253e18	0.168370	0.0841849	+	0.996450i	$0.473171\pi$
$860$	2.15693e19	1.81801
$861$	−2.80053e18	−0.234271
$862$	1.68686e19	1.40050
$863$	1.29868e19	1.07012	0.535060	−	0.844814i	$-0.320289\pi$
$863$	1.29868e19	1.07012	0.535060	+	0.844814i	$0.320289\pi$
$864$	3.15270e18	0.257836
$865$	−1.49428e19	−1.21291
$866$	7.86273e18	0.633442
$867$	1.78577e19	1.42791
$868$	9.75320e17	0.0774050
$869$	1.10598e19	0.871199
$870$	1.23105e19	0.962502
$871$	−3.87803e18	−0.300949
$872$	1.37445e18	0.105870
$873$	8.20994e17	0.0627693
$874$	−5.31620e19	−4.03438
$875$	−2.13035e18	−0.160472
$876$	1.21455e19	0.908109
$877$	1.98747e18	0.147504	0.0737519	−	0.997277i	$-0.476503\pi$
$877$	1.98747e18	0.147504	0.0737519	+	0.997277i	$0.476503\pi$
$878$	−3.08198e18	−0.227047
$879$	−1.37561e19	−1.00593
$880$	−7.44413e18	−0.540352
$881$	1.97321e19	1.42177	0.710887	−	0.703306i	$-0.248294\pi$
$881$	1.97321e19	1.42177	0.710887	+	0.703306i	$0.248294\pi$
$882$	6.78289e18	0.485142
$883$	8.30718e18	0.589806	0.294903	−	0.955527i	$-0.404713\pi$
$883$	8.30718e18	0.589806	0.294903	+	0.955527i	$0.404713\pi$
$884$	5.55359e19	3.91412
$885$	1.27405e18	0.0891366
$886$	−1.08789e18	−0.0755554
$887$	−1.77383e19	−1.22295	−0.611475	−	0.791264i	$-0.709424\pi$
$887$	−1.77383e19	−1.22295	−0.611475	+	0.791264i	$0.709424\pi$
$888$	5.32862e18	0.364695
$889$	5.56340e18	0.377988
$890$	1.66706e19	1.12439
$891$	−1.46564e18	−0.0981345
$892$	−3.25773e19	−2.16543
$893$	8.48231e18	0.559731
$894$	−1.03053e19	−0.675099
$895$	−5.15796e18	−0.335450
$896$	−3.62122e18	−0.233805
$897$	2.30633e19	1.47833
$898$	−3.55499e19	−2.26226
$899$	−3.62781e18	−0.229196
$900$	2.92983e18	0.183767
$901$	2.65846e19	1.65546
$902$	3.90428e19	2.41378
$903$	2.42246e18	0.148692
$904$	3.51690e18	0.214321
$905$	3.45411e19	2.08988
$906$	−1.86116e19	−1.11802
$907$	−1.26981e19	−0.757344	−0.378672	−	0.925531i	$-0.623619\pi$
$907$	−1.26981e19	−0.757344	−0.378672	+	0.925531i	$0.623619\pi$
$908$	−1.19743e19	−0.709076
$909$	−9.44198e18	−0.555134
$910$	−1.10036e19	−0.642341
$911$	−7.29103e18	−0.422590	−0.211295	−	0.977422i	$-0.567768\pi$
$911$	−7.29103e18	−0.422590	−0.211295	+	0.977422i	$0.567768\pi$
$912$	−8.22270e18	−0.473204
$913$	−2.60623e18	−0.148920
$914$	1.35701e19	0.769897
$915$	−1.76746e19	−0.995663
$916$	−2.77823e19	−1.55399
$917$	−5.65966e17	−0.0314333
$918$	−9.98440e18	−0.550610
$919$	−2.66229e19	−1.45782	−0.728911	−	0.684608i	$-0.759973\pi$
$919$	−2.66229e19	−1.45782	−0.728911	+	0.684608i	$0.759973\pi$
$920$	1.97615e19	1.07448
$921$	7.29573e18	0.393895
$922$	−1.25291e19	−0.671689
$923$	2.50056e19	1.33115
$924$	2.98327e18	0.157697
$925$	−8.92706e18	−0.468584
$926$	−5.60942e19	−2.92379
$927$	7.69865e18	0.398471
$928$	2.38696e19	1.22683
$929$	−3.20490e19	−1.63573	−0.817866	−	0.575409i	$-0.804843\pi$
$929$	−3.20490e19	−1.63573	−0.817866	+	0.575409i	$0.804843\pi$
$930$	−5.19075e18	−0.263082
$931$	−2.99255e19	−1.50615
$932$	−3.22501e19	−1.61186
$933$	−1.22764e19	−0.609311
$934$	6.47796e18	0.319288
$935$	3.98794e19	1.95197
$936$	−5.81439e18	−0.282626
$937$	2.05096e19	0.990032	0.495016	−	0.868884i	$-0.335162\pi$
$937$	2.05096e19	0.990032	0.495016	+	0.868884i	$0.335162\pi$
$938$	−1.41914e18	−0.0680310
$939$	−4.68833e18	−0.223199
$940$	−1.19902e19	−0.566888
$941$	2.23551e19	1.04965	0.524824	−	0.851211i	$-0.324131\pi$
$941$	2.23551e19	1.04965	0.524824	+	0.851211i	$0.324131\pi$
$942$	−1.18261e18	−0.0551457
$943$	6.35881e19	2.94476
$944$	1.46036e18	0.0671650
$945$	1.13887e18	0.0520197
$946$	−3.37721e19	−1.53202
$947$	−7.36937e18	−0.332013	−0.166007	−	0.986125i	$-0.553087\pi$
$947$	−7.36937e18	−0.332013	−0.166007	+	0.986125i	$0.553087\pi$
$948$	−1.72687e19	−0.772692
$949$	4.03803e19	1.79448
$950$	−2.24532e19	−0.991002
$951$	−1.28694e19	−0.564136
$952$	5.34430e18	0.232676
$953$	−2.53079e19	−1.09434	−0.547170	−	0.837022i	$-0.684295\pi$
$953$	−2.53079e19	−1.09434	−0.547170	+	0.837022i	$0.684295\pi$
$954$	−1.05842e19	−0.454562
$955$	5.65909e18	0.241393
$956$	5.09218e19	2.15739
$957$	−1.10966e19	−0.466941
$958$	4.55878e19	1.90534
$959$	1.01723e19	0.422278
$960$	2.55864e19	1.05499
$961$	−2.28879e19	−0.937354
$962$	6.73700e19	2.74049
$963$	−5.99131e18	−0.242076
$964$	4.73731e19	1.90121
$965$	−4.07457e19	−1.62425
$966$	8.43987e18	0.334183
$967$	−1.05027e19	−0.413075	−0.206538	−	0.978439i	$-0.566220\pi$
$967$	−1.05027e19	−0.413075	−0.206538	+	0.978439i	$0.566220\pi$
$968$	3.08369e18	0.120470
$969$	4.40503e19	1.70940
$970$	8.89382e18	0.342825
$971$	−2.74594e19	−1.05140	−0.525698	−	0.850671i	$-0.676196\pi$
$971$	−2.74594e19	−1.05140	−0.525698	+	0.850671i	$0.676196\pi$
$972$	2.28845e18	0.0870384
$973$	−1.71271e18	−0.0647068
$974$	1.40068e19	0.525663
$975$	9.74088e18	0.363135
$976$	−2.02592e19	−0.750238
$977$	1.41607e19	0.520918	0.260459	−	0.965485i	$-0.416126\pi$
$977$	1.41607e19	0.520918	0.260459	+	0.965485i	$0.416126\pi$
$978$	−1.65108e19	−0.603343
$979$	−1.50268e19	−0.545479
$980$	4.23015e19	1.52541
$981$	−1.79854e18	−0.0644276
$982$	6.39405e19	2.27537
$983$	2.85506e19	1.00929	0.504647	−	0.863326i	$-0.331623\pi$
$983$	2.85506e19	1.00929	0.504647	+	0.863326i	$0.331623\pi$
$984$	−1.60309e19	−0.562977
$985$	2.05877e19	0.718244
$986$	−7.55936e19	−2.61990
$987$	−1.34663e18	−0.0463646
$988$	9.75502e19	3.33663
$989$	−5.50039e19	−1.86903
$990$	−1.58773e19	−0.535978
$991$	−9.64838e18	−0.323576	−0.161788	−	0.986826i	$-0.551726\pi$
$991$	−9.64838e18	−0.323576	−0.161788	+	0.986826i	$0.551726\pi$
$992$	−1.00646e19	−0.335330
$993$	2.66196e19	0.881114
$994$	9.15062e18	0.300912
$995$	2.32380e17	0.00759187
$996$	4.06937e18	0.132081
$997$	−1.29828e19	−0.418650	−0.209325	−	0.977846i	$-0.567127\pi$
$997$	−1.29828e19	−0.418650	−0.209325	+	0.977846i	$0.567127\pi$
$998$	4.00462e19	1.28296
$999$	−6.97279e18	−0.221938

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.c.1.3	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.c.1.3	✓	31	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-138.949 q^{2} +729.000 q^{3} +11114.9 q^{4} -41433.2 q^{5} -101294. q^{6} -70948.7 q^{7} -406128. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-138.949 q^{2} +729.000 q^{3} +11114.9 q^{4} -41433.2 q^{5} -101294. q^{6} -70948.7 q^{7} -406128. q^{8} +531441. q^{9} +5.75710e6 q^{10} -5.18939e6 q^{11} +8.10273e6 q^{12} +2.69393e7 q^{13} +9.85826e6 q^{14} -3.02048e7 q^{15} -3.46218e7 q^{16} +1.85474e8 q^{17} -7.38433e7 q^{18} +3.25790e8 q^{19} -4.60523e8 q^{20} -5.17216e7 q^{21} +7.21062e8 q^{22} +1.17438e9 q^{23} -2.96067e8 q^{24} +4.96003e8 q^{25} -3.74319e9 q^{26} +3.87420e8 q^{27} -7.88584e8 q^{28} +2.93323e9 q^{29} +4.19693e9 q^{30} -1.23680e9 q^{31} +8.13766e9 q^{32} -3.78307e9 q^{33} -2.57715e10 q^{34} +2.93963e9 q^{35} +5.90689e9 q^{36} -1.79980e10 q^{37} -4.52682e10 q^{38} +1.96388e10 q^{39} +1.68272e10 q^{40} +5.41462e10 q^{41} +7.18667e9 q^{42} -4.68366e10 q^{43} -5.76794e10 q^{44} -2.20193e10 q^{45} -1.63179e11 q^{46} +2.60361e10 q^{47} -2.52393e10 q^{48} -9.18553e10 q^{49} -6.89192e10 q^{50} +1.35211e11 q^{51} +2.99426e11 q^{52} +1.43333e11 q^{53} -5.38317e10 q^{54} +2.15013e11 q^{55} +2.88142e10 q^{56} +2.37501e11 q^{57} -4.07569e11 q^{58} -4.21805e10 q^{59} -3.35722e11 q^{60} +5.85159e11 q^{61} +1.71852e11 q^{62} -3.77050e10 q^{63} -8.47100e11 q^{64} -1.11618e12 q^{65} +5.25654e11 q^{66} -1.43954e11 q^{67} +2.06152e12 q^{68} +8.56122e11 q^{69} -4.08459e11 q^{70} +9.28219e11 q^{71} -2.15833e11 q^{72} +1.49894e12 q^{73} +2.50081e12 q^{74} +3.61586e11 q^{75} +3.62111e12 q^{76} +3.68181e11 q^{77} -2.72879e12 q^{78} -2.13123e12 q^{79} +1.43449e12 q^{80} +2.82430e11 q^{81} -7.52357e12 q^{82} +5.02222e11 q^{83} -5.74878e11 q^{84} -7.68478e12 q^{85} +6.50790e12 q^{86} +2.13832e12 q^{87} +2.10756e12 q^{88} +2.89567e12 q^{89} +3.05956e12 q^{90} -1.91131e12 q^{91} +1.30530e13 q^{92} -9.01626e11 q^{93} -3.61770e12 q^{94} -1.34985e13 q^{95} +5.93236e12 q^{96} +1.54484e12 q^{97} +1.27632e13 q^{98} -2.75786e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9}+O(q^{10}) \) 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9} + 4647481 q^{10} + 17937316 q^{11} + 92499894 q^{12} + 40664720 q^{13} + 139193613 q^{14} + 59054832 q^{15} + 370110498 q^{16} + 213442823 q^{17} + 164746710 q^{18} - 62592329 q^{19} + 1637085153 q^{20} + 731143989 q^{21} + 4142028314 q^{22} + 1873486387 q^{23} + 3377255067 q^{24} + 8307272395 q^{25} - 534777728 q^{26} + 12010035159 q^{27} + 766416778 q^{28} + 13765513563 q^{29} + 3388013649 q^{30} + 14274077235 q^{31} + 30574460156 q^{32} + 13076303364 q^{33} - 677551028 q^{34} + 36023610185 q^{35} + 67432422726 q^{36} - 18278838391 q^{37} - 23650502933 q^{38} + 29644580880 q^{39} + 10045447572 q^{40} + 34748006725 q^{41} + 101472143877 q^{42} + 40350158146 q^{43} + 163101196592 q^{44} + 43050972528 q^{45} + 296118466353 q^{46} + 233954631099 q^{47} + 269810553042 q^{48} + 324065402790 q^{49} - 102960745787 q^{50} + 155599817967 q^{51} + 668297695096 q^{52} + 500927963876 q^{53} + 120100351590 q^{54} + 884972340924 q^{55} + 1392234478810 q^{56} - 45629807841 q^{57} + 689262776200 q^{58} - 1307596542871 q^{59} + 1193435076537 q^{60} + 1716832157925 q^{61} + 1816094290366 q^{62} + 533003967981 q^{63} + 4381780009133 q^{64} + 1457007885906 q^{65} + 3019538640906 q^{66} + 1212131702006 q^{67} + 6552992665503 q^{68} + 1365771576123 q^{69} + 8806714081634 q^{70} + 6074000239936 q^{71} + 2462018943843 q^{72} + 3756145185973 q^{73} + 8066450143602 q^{74} + 6056001575955 q^{75} + 7913230001992 q^{76} + 6031241575915 q^{77} - 389852963712 q^{78} + 11377744190862 q^{79} + 16473302366969 q^{80} + 8755315630911 q^{81} + 10413363680159 q^{82} + 19915461517429 q^{83} + 558717831162 q^{84} + 15280981141573 q^{85} + 7573325358452 q^{86} + 10035059387427 q^{87} + 19271409121081 q^{88} + 14115863121241 q^{89} + 2469861950121 q^{90} + 18296287784699 q^{91} + 15158951168774 q^{92} + 10405802304315 q^{93} - 18637923572412 q^{94} - 2294034679397 q^{95} + 22288781453724 q^{96} + 38558536599054 q^{97} - 1998410212380 q^{98} + 9532625152356 q^{99}+O(q^{100}) \) 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9 + 4647481 * q^10 + 17937316 * q^11 + 92499894 * q^12 + 40664720 * q^13 + 139193613 * q^14 + 59054832 * q^15 + 370110498 * q^16 + 213442823 * q^17 + 164746710 * q^18 - 62592329 * q^19 + 1637085153 * q^20 + 731143989 * q^21 + 4142028314 * q^22 + 1873486387 * q^23 + 3377255067 * q^24 + 8307272395 * q^25 - 534777728 * q^26 + 12010035159 * q^27 + 766416778 * q^28 + 13765513563 * q^29 + 3388013649 * q^30 + 14274077235 * q^31 + 30574460156 * q^32 + 13076303364 * q^33 - 677551028 * q^34 + 36023610185 * q^35 + 67432422726 * q^36 - 18278838391 * q^37 - 23650502933 * q^38 + 29644580880 * q^39 + 10045447572 * q^40 + 34748006725 * q^41 + 101472143877 * q^42 + 40350158146 * q^43 + 163101196592 * q^44 + 43050972528 * q^45 + 296118466353 * q^46 + 233954631099 * q^47 + 269810553042 * q^48 + 324065402790 * q^49 - 102960745787 * q^50 + 155599817967 * q^51 + 668297695096 * q^52 + 500927963876 * q^53 + 120100351590 * q^54 + 884972340924 * q^55 + 1392234478810 * q^56 - 45629807841 * q^57 + 689262776200 * q^58 - 1307596542871 * q^59 + 1193435076537 * q^60 + 1716832157925 * q^61 + 1816094290366 * q^62 + 533003967981 * q^63 + 4381780009133 * q^64 + 1457007885906 * q^65 + 3019538640906 * q^66 + 1212131702006 * q^67 + 6552992665503 * q^68 + 1365771576123 * q^69 + 8806714081634 * q^70 + 6074000239936 * q^71 + 2462018943843 * q^72 + 3756145185973 * q^73 + 8066450143602 * q^74 + 6056001575955 * q^75 + 7913230001992 * q^76 + 6031241575915 * q^77 - 389852963712 * q^78 + 11377744190862 * q^79 + 16473302366969 * q^80 + 8755315630911 * q^81 + 10413363680159 * q^82 + 19915461517429 * q^83 + 558717831162 * q^84 + 15280981141573 * q^85 + 7573325358452 * q^86 + 10035059387427 * q^87 + 19271409121081 * q^88 + 14115863121241 * q^89 + 2469861950121 * q^90 + 18296287784699 * q^91 + 15158951168774 * q^92 + 10405802304315 * q^93 - 18637923572412 * q^94 - 2294034679397 * q^95 + 22288781453724 * q^96 + 38558536599054 * q^97 - 1998410212380 * q^98 + 9532625152356 * q^99

Introduction

L-functions

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