LMFDB - Embedded newform 177.12.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,12,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, 12, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
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:	$135.996742959$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-67.3482 q^{2} +243.000 q^{3} +2487.78 q^{4} +9961.02 q^{5} -16365.6 q^{6} -37608.5 q^{7} -29618.6 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-67.3482 q^{2} +243.000 q^{3} +2487.78 q^{4} +9961.02 q^{5} -16365.6 q^{6} -37608.5 q^{7} -29618.6 q^{8} +59049.0 q^{9} -670857. q^{10} +181051. q^{11} +604531. q^{12} -10898.1 q^{13} +2.53287e6 q^{14} +2.42053e6 q^{15} -3.10022e6 q^{16} -8.94272e6 q^{17} -3.97684e6 q^{18} -483641. q^{19} +2.47809e7 q^{20} -9.13887e6 q^{21} -1.21934e7 q^{22} -5.76947e7 q^{23} -7.19731e6 q^{24} +5.03939e7 q^{25} +733965. q^{26} +1.43489e7 q^{27} -9.35619e7 q^{28} -7.44117e7 q^{29} -1.63018e8 q^{30} -3.78363e6 q^{31} +2.69453e8 q^{32} +4.39953e7 q^{33} +6.02276e8 q^{34} -3.74620e8 q^{35} +1.46901e8 q^{36} +2.66928e8 q^{37} +3.25723e7 q^{38} -2.64823e6 q^{39} -2.95031e8 q^{40} +9.21400e8 q^{41} +6.15487e8 q^{42} +1.72347e9 q^{43} +4.50414e8 q^{44} +5.88188e8 q^{45} +3.88563e9 q^{46} +5.56453e8 q^{47} -7.53354e8 q^{48} -5.62925e8 q^{49} -3.39394e9 q^{50} -2.17308e9 q^{51} -2.71120e7 q^{52} -5.10556e8 q^{53} -9.66373e8 q^{54} +1.80345e9 q^{55} +1.11391e9 q^{56} -1.17525e8 q^{57} +5.01149e9 q^{58} +7.14924e8 q^{59} +6.02175e9 q^{60} +4.70006e9 q^{61} +2.54821e8 q^{62} -2.22075e9 q^{63} -1.17979e10 q^{64} -1.08556e8 q^{65} -2.96300e9 q^{66} +6.76322e8 q^{67} -2.22475e10 q^{68} -1.40198e10 q^{69} +2.52300e10 q^{70} +2.31176e10 q^{71} -1.74895e9 q^{72} +1.24600e10 q^{73} -1.79771e10 q^{74} +1.22457e10 q^{75} -1.20319e9 q^{76} -6.80905e9 q^{77} +1.78353e8 q^{78} -1.81125e10 q^{79} -3.08814e10 q^{80} +3.48678e9 q^{81} -6.20547e10 q^{82} +2.88119e10 q^{83} -2.27355e10 q^{84} -8.90786e10 q^{85} -1.16073e11 q^{86} -1.80820e10 q^{87} -5.36246e9 q^{88} +1.17986e10 q^{89} -3.96134e10 q^{90} +4.09860e8 q^{91} -1.43532e11 q^{92} -9.19423e8 q^{93} -3.74761e10 q^{94} -4.81756e9 q^{95} +6.54771e10 q^{96} -6.35855e9 q^{97} +3.79120e10 q^{98} +1.06909e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) $ 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9} + 616281 q^{10} + 1082362 q^{11} + 7099002 q^{12} + 503712 q^{13} + 1321669 q^{14} + 6454566 q^{15} + 34870338 q^{16} + 13513579 q^{17} + 5668704 q^{18} + 35971687 q^{19} + 96105997 q^{20} + 34586919 q^{21} - 47598882 q^{22} + 61380539 q^{23} + 80756433 q^{24} + 294744746 q^{25} + 62820734 q^{26} + 401769396 q^{27} + 148068294 q^{28} + 322339307 q^{29} + 149756283 q^{30} + 151247077 q^{31} + 466383494 q^{32} + 263013966 q^{33} + 684479860 q^{34} + 960297361 q^{35} + 1725057486 q^{36} + 863508437 q^{37} + 992640509 q^{38} + 122402016 q^{39} + 3067680252 q^{40} + 3081170377 q^{41} + 321165567 q^{42} + 2554238300 q^{43} + 4350123570 q^{44} + 1568459538 q^{45} - 1987059155 q^{46} + 6203398333 q^{47} + 8473492134 q^{48} + 10327857997 q^{49} + 17577682253 q^{50} + 3283799697 q^{51} + 32137181618 q^{52} + 14571770754 q^{53} + 1377495072 q^{54} + 18251419334 q^{55} + 33498842836 q^{56} + 8741119941 q^{57} + 11860778276 q^{58} + 20017880372 q^{59} + 23353757271 q^{60} + 2761613771 q^{61} + 13785829526 q^{62} + 8404621317 q^{63} + 86547545293 q^{64} + 32034985256 q^{65} - 11566528326 q^{66} + 39381333296 q^{67} + 38995496621 q^{68} + 14915470977 q^{69} + 8551800364 q^{70} + 26130020296 q^{71} + 19623813219 q^{72} + 41382402799 q^{73} + 23815315058 q^{74} + 71622973278 q^{75} + 10611720128 q^{76} - 8426124313 q^{77} + 15265438362 q^{78} + 59825111206 q^{79} + 4009687655 q^{80} + 97629963228 q^{81} - 39592715115 q^{82} + 35433122727 q^{83} + 35980595442 q^{84} - 8950496085 q^{85} - 182032360688 q^{86} + 78328451601 q^{87} - 220003602335 q^{88} + 102303043039 q^{89} + 36390776769 q^{90} - 111146323655 q^{91} - 163000203526 q^{92} + 36753039711 q^{93} - 81314346008 q^{94} + 208102168887 q^{95} + 113331189042 q^{96} - 171891031490 q^{97} + 72304707792 q^{98} + 63912393738 q^{99}+O(q^{100}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9 + 616281 * q^10 + 1082362 * q^11 + 7099002 * q^12 + 503712 * q^13 + 1321669 * q^14 + 6454566 * q^15 + 34870338 * q^16 + 13513579 * q^17 + 5668704 * q^18 + 35971687 * q^19 + 96105997 * q^20 + 34586919 * q^21 - 47598882 * q^22 + 61380539 * q^23 + 80756433 * q^24 + 294744746 * q^25 + 62820734 * q^26 + 401769396 * q^27 + 148068294 * q^28 + 322339307 * q^29 + 149756283 * q^30 + 151247077 * q^31 + 466383494 * q^32 + 263013966 * q^33 + 684479860 * q^34 + 960297361 * q^35 + 1725057486 * q^36 + 863508437 * q^37 + 992640509 * q^38 + 122402016 * q^39 + 3067680252 * q^40 + 3081170377 * q^41 + 321165567 * q^42 + 2554238300 * q^43 + 4350123570 * q^44 + 1568459538 * q^45 - 1987059155 * q^46 + 6203398333 * q^47 + 8473492134 * q^48 + 10327857997 * q^49 + 17577682253 * q^50 + 3283799697 * q^51 + 32137181618 * q^52 + 14571770754 * q^53 + 1377495072 * q^54 + 18251419334 * q^55 + 33498842836 * q^56 + 8741119941 * q^57 + 11860778276 * q^58 + 20017880372 * q^59 + 23353757271 * q^60 + 2761613771 * q^61 + 13785829526 * q^62 + 8404621317 * q^63 + 86547545293 * q^64 + 32034985256 * q^65 - 11566528326 * q^66 + 39381333296 * q^67 + 38995496621 * q^68 + 14915470977 * q^69 + 8551800364 * q^70 + 26130020296 * q^71 + 19623813219 * q^72 + 41382402799 * q^73 + 23815315058 * q^74 + 71622973278 * q^75 + 10611720128 * q^76 - 8426124313 * q^77 + 15265438362 * q^78 + 59825111206 * q^79 + 4009687655 * q^80 + 97629963228 * q^81 - 39592715115 * q^82 + 35433122727 * q^83 + 35980595442 * q^84 - 8950496085 * q^85 - 182032360688 * q^86 + 78328451601 * q^87 - 220003602335 * q^88 + 102303043039 * q^89 + 36390776769 * q^90 - 111146323655 * q^91 - 163000203526 * q^92 + 36753039711 * q^93 - 81314346008 * q^94 + 208102168887 * q^95 + 113331189042 * q^96 - 171891031490 * q^97 + 72304707792 * q^98 + 63912393738 * 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 $

$2$	−67.3482	−1.48820	−0.744100	−	0.668069i	$-0.767121\pi$
$2$	−67.3482	−1.48820	−0.744100	+	0.668069i	$0.767121\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	2487.78	1.21474
$5$	9961.02	1.42551	0.712753	−	0.701415i	$-0.247448\pi$
$5$	9961.02	1.42551	0.712753	+	0.701415i	$0.247448\pi$
$6$	−16365.6	−0.859212
$7$	−37608.5	−0.845760	−0.422880	−	0.906186i	$-0.638981\pi$
$7$	−37608.5	−0.845760	−0.422880	+	0.906186i	$0.638981\pi$
$8$	−29618.6	−0.319572
$9$	59049.0	0.333333
$10$	−670857.	−2.12144
$11$	181051.	0.338954	0.169477	−	0.985534i	$-0.445792\pi$
$11$	181051.	0.338954	0.169477	+	0.985534i	$0.445792\pi$
$12$	604531.	0.701329
$13$	−10898.1	−0.00814068	−0.00407034	−	0.999992i	$-0.501296\pi$
$13$	−10898.1	−0.00814068	−0.00407034	+	0.999992i	$0.501296\pi$
$14$	2.53287e6	1.25866
$15$	2.42053e6	0.823016
$16$	−3.10022e6	−0.739150
$17$	−8.94272e6	−1.52757	−0.763784	−	0.645472i	$-0.776661\pi$
$17$	−8.94272e6	−1.52757	−0.763784	+	0.645472i	$0.776661\pi$
$18$	−3.97684e6	−0.496066
$19$	−483641.	−0.0448103	−0.0224052	−	0.999749i	$-0.507132\pi$
$19$	−483641.	−0.0448103	−0.0224052	+	0.999749i	$0.507132\pi$
$20$	2.47809e7	1.73162
$21$	−9.13887e6	−0.488300
$22$	−1.21934e7	−0.504430
$23$	−5.76947e7	−1.86910	−0.934550	−	0.355831i	$-0.884198\pi$
$23$	−5.76947e7	−1.86910	−0.934550	+	0.355831i	$0.884198\pi$
$24$	−7.19731e6	−0.184505
$25$	5.03939e7	1.03207
$26$	733965.	0.0121150
$27$	1.43489e7	0.192450
$28$	−9.35619e7	−1.02738
$29$	−7.44117e7	−0.673678	−0.336839	−	0.941562i	$-0.609358\pi$
$29$	−7.44117e7	−0.673678	−0.336839	+	0.941562i	$0.609358\pi$
$30$	−1.63018e8	−1.22481
$31$	−3.78363e6	−0.0237367	−0.0118683	−	0.999930i	$-0.503778\pi$
$31$	−3.78363e6	−0.0237367	−0.0118683	+	0.999930i	$0.503778\pi$
$32$	2.69453e8	1.41958
$33$	4.39953e7	0.195695
$34$	6.02276e8	2.27332
$35$	−3.74620e8	−1.20564
$36$	1.46901e8	0.404912
$37$	2.66928e8	0.632827	0.316413	−	0.948621i	$-0.397521\pi$
$37$	2.66928e8	0.632827	0.316413	+	0.948621i	$0.397521\pi$
$38$	3.25723e7	0.0666867
$39$	−2.64823e6	−0.00470002
$40$	−2.95031e8	−0.455552
$41$	9.21400e8	1.24204	0.621022	−	0.783793i	$-0.286718\pi$
$41$	9.21400e8	1.24204	0.621022	+	0.783793i	$0.286718\pi$
$42$	6.15487e8	0.726688
$43$	1.72347e9	1.78784	0.893919	−	0.448229i	$-0.147945\pi$
$43$	1.72347e9	1.78784	0.893919	+	0.448229i	$0.147945\pi$
$44$	4.50414e8	0.411740
$45$	5.88188e8	0.475169
$46$	3.88563e9	2.78159
$47$	5.56453e8	0.353908	0.176954	−	0.984219i	$-0.443376\pi$
$47$	5.56453e8	0.353908	0.176954	+	0.984219i	$0.443376\pi$
$48$	−7.53354e8	−0.426749
$49$	−5.62925e8	−0.284690
$50$	−3.39394e9	−1.53592
$51$	−2.17308e9	−0.881941
$52$	−2.71120e7	−0.00988879
$53$	−5.10556e8	−0.167697	−0.0838487	−	0.996478i	$-0.526721\pi$
$53$	−5.10556e8	−0.167697	−0.0838487	+	0.996478i	$0.526721\pi$
$54$	−9.66373e8	−0.286404
$55$	1.80345e9	0.483180
$56$	1.11391e9	0.270281
$57$	−1.17525e8	−0.0258713
$58$	5.01149e9	1.00257
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	6.02175e9	0.999748
$61$	4.70006e9	0.712507	0.356253	−	0.934389i	$-0.384054\pi$
$61$	4.70006e9	0.712507	0.356253	+	0.934389i	$0.384054\pi$
$62$	2.54821e8	0.0353249
$63$	−2.22075e9	−0.281920
$64$	−1.17979e10	−1.37346
$65$	−1.08556e8	−0.0116046
$66$	−2.96300e9	−0.291233
$67$	6.76322e8	0.0611987	0.0305994	−	0.999532i	$-0.490258\pi$
$67$	6.76322e8	0.0611987	0.0305994	+	0.999532i	$0.490258\pi$
$68$	−2.22475e10	−1.85559
$69$	−1.40198e10	−1.07913
$70$	2.52300e10	1.79423
$71$	2.31176e10	1.52063	0.760313	−	0.649556i	$-0.225045\pi$
$71$	2.31176e10	1.52063	0.760313	+	0.649556i	$0.225045\pi$
$72$	−1.74895e9	−0.106524
$73$	1.24600e10	0.703467	0.351733	−	0.936100i	$-0.385592\pi$
$73$	1.24600e10	0.703467	0.351733	+	0.936100i	$0.385592\pi$
$74$	−1.79771e10	−0.941772
$75$	1.22457e10	0.595864
$76$	−1.20319e9	−0.0544328
$77$	−6.80905e9	−0.286673
$78$	1.78353e8	0.00699457
$79$	−1.81125e10	−0.662262	−0.331131	−	0.943585i	$-0.607430\pi$
$79$	−1.81125e10	−0.662262	−0.331131	+	0.943585i	$0.607430\pi$
$80$	−3.08814e10	−1.05366
$81$	3.48678e9	0.111111
$82$	−6.20547e10	−1.84841
$83$	2.88119e10	0.802864	0.401432	−	0.915889i	$-0.368513\pi$
$83$	2.88119e10	0.802864	0.401432	+	0.915889i	$0.368513\pi$
$84$	−2.27355e10	−0.593156
$85$	−8.90786e10	−2.17756
$86$	−1.16073e11	−2.66066
$87$	−1.80820e10	−0.388948
$88$	−5.36246e9	−0.108320
$89$	1.17986e10	0.223967	0.111984	−	0.993710i	$-0.464280\pi$
$89$	1.17986e10	0.223967	0.111984	+	0.993710i	$0.464280\pi$
$90$	−3.96134e10	−0.707146
$91$	4.09860e8	0.00688506
$92$	−1.43532e11	−2.27047
$93$	−9.19423e8	−0.0137044
$94$	−3.74761e10	−0.526686
$95$	−4.81756e9	−0.0638774
$96$	6.54771e10	0.819592
$97$	−6.35855e9	−0.0751819	−0.0375909	−	0.999293i	$-0.511968\pi$
$97$	−6.35855e9	−0.0751819	−0.0375909	+	0.999293i	$0.511968\pi$
$98$	3.79120e10	0.423675
$99$	1.06909e10	0.112985
$100$	1.25369e11	1.25369
$101$	8.42346e10	0.797486	0.398743	−	0.917063i	$-0.369447\pi$
$101$	8.42346e10	0.797486	0.398743	+	0.917063i	$0.369447\pi$
$102$	1.46353e11	1.31250
$103$	−1.34168e9	−0.0114036	−0.00570181	−	0.999984i	$-0.501815\pi$
$103$	−1.34168e9	−0.0114036	−0.00570181	+	0.999984i	$0.501815\pi$
$104$	3.22785e8	0.00260153
$105$	−9.10325e10	−0.696074
$106$	3.43851e10	0.249567
$107$	3.85074e10	0.265420	0.132710	−	0.991155i	$-0.457632\pi$
$107$	3.85074e10	0.265420	0.132710	+	0.991155i	$0.457632\pi$
$108$	3.56970e10	0.233776
$109$	−9.99136e10	−0.621983	−0.310992	−	0.950413i	$-0.600661\pi$
$109$	−9.99136e10	−0.621983	−0.310992	+	0.950413i	$0.600661\pi$
$110$	−1.21459e11	−0.719068
$111$	6.48635e10	0.365363
$112$	1.16595e11	0.625144
$113$	1.27390e11	0.650437	0.325219	−	0.945639i	$-0.394562\pi$
$113$	1.27390e11	0.650437	0.325219	+	0.945639i	$0.394562\pi$
$114$	7.91508e9	0.0385016
$115$	−5.74698e11	−2.66441
$116$	−1.85120e11	−0.818341
$117$	−6.43519e8	−0.00271356
$118$	−4.81489e10	−0.193747
$119$	3.36322e11	1.29196
$120$	−7.16926e10	−0.263013
$121$	−2.52532e11	−0.885110
$122$	−3.16540e11	−1.06035
$123$	2.23900e11	0.717095
$124$	−9.41285e9	−0.0288338
$125$	1.55964e10	0.0457108
$126$	1.49563e11	0.419553
$127$	3.52951e11	0.947968	0.473984	−	0.880533i	$-0.342815\pi$
$127$	3.52951e11	0.947968	0.473984	+	0.880533i	$0.342815\pi$
$128$	2.42730e11	0.624408
$129$	4.18804e11	1.03221
$130$	7.31104e9	0.0172699
$131$	−3.81317e11	−0.863563	−0.431782	−	0.901978i	$-0.642115\pi$
$131$	−3.81317e11	−0.863563	−0.431782	+	0.901978i	$0.642115\pi$
$132$	1.09451e11	0.237718
$133$	1.81890e10	0.0378988
$134$	−4.55491e10	−0.0910759
$135$	1.42930e11	0.274339
$136$	2.64870e11	0.488168
$137$	6.74048e11	1.19324	0.596620	−	0.802524i	$-0.296510\pi$
$137$	6.74048e11	1.19324	0.596620	+	0.802524i	$0.296510\pi$
$138$	9.44209e11	1.60595
$139$	7.18276e11	1.17411	0.587057	−	0.809546i	$-0.300287\pi$
$139$	7.18276e11	1.17411	0.587057	+	0.809546i	$0.300287\pi$
$140$	−9.31972e11	−1.46453
$141$	1.35218e11	0.204329
$142$	−1.55693e12	−2.26300
$143$	−1.97310e9	−0.00275931
$144$	−1.83065e11	−0.246383
$145$	−7.41216e11	−0.960331
$146$	−8.39161e11	−1.04690
$147$	−1.36791e11	−0.164366
$148$	6.64059e11	0.768718
$149$	−1.16882e12	−1.30384	−0.651920	−	0.758287i	$-0.726036\pi$
$149$	−1.16882e12	−1.30384	−0.651920	+	0.758287i	$0.726036\pi$
$150$	−8.24727e11	−0.886764
$151$	1.56463e11	0.162196	0.0810979	−	0.996706i	$-0.474157\pi$
$151$	1.56463e11	0.162196	0.0810979	+	0.996706i	$0.474157\pi$
$152$	1.43247e10	0.0143201
$153$	−5.28058e11	−0.509189
$154$	4.58577e11	0.426627
$155$	−3.76889e10	−0.0338367
$156$	−6.58821e9	−0.00570929
$157$	2.01386e12	1.68492	0.842462	−	0.538756i	$-0.181106\pi$
$157$	2.01386e12	1.68492	0.842462	+	0.538756i	$0.181106\pi$
$158$	1.21985e12	0.985578
$159$	−1.24065e11	−0.0968202
$160$	2.68403e12	2.02361
$161$	2.16981e12	1.58081
$162$	−2.34829e11	−0.165355
$163$	−2.10323e12	−1.43171	−0.715855	−	0.698249i	$-0.753963\pi$
$163$	−2.10323e12	−1.43171	−0.715855	+	0.698249i	$0.753963\pi$
$164$	2.29224e12	1.50876
$165$	4.38238e11	0.278964
$166$	−1.94043e12	−1.19482
$167$	1.48637e12	0.885494	0.442747	−	0.896647i	$-0.354004\pi$
$167$	1.48637e12	0.885494	0.442747	+	0.896647i	$0.354004\pi$
$168$	2.70680e11	0.156047
$169$	−1.79204e12	−0.999934
$170$	5.99929e12	3.24064
$171$	−2.85585e10	−0.0149368
$172$	4.28763e12	2.17175
$173$	3.24076e12	1.58999	0.794994	−	0.606618i	$-0.207474\pi$
$173$	3.24076e12	1.58999	0.794994	+	0.606618i	$0.207474\pi$
$174$	1.21779e12	0.578832
$175$	−1.89524e12	−0.872881
$176$	−5.61297e11	−0.250538
$177$	1.73727e11	0.0751646
$178$	−7.94613e11	−0.333308
$179$	4.64086e12	1.88759	0.943793	−	0.330536i	$-0.107230\pi$
$179$	4.64086e12	1.88759	0.943793	+	0.330536i	$0.107230\pi$
$180$	1.46328e12	0.577205
$181$	9.82599e11	0.375962	0.187981	−	0.982173i	$-0.439806\pi$
$181$	9.82599e11	0.375962	0.187981	+	0.982173i	$0.439806\pi$
$182$	−2.76033e10	−0.0102463
$183$	1.14211e12	0.411366
$184$	1.70883e12	0.597312
$185$	2.65888e12	0.902098
$186$	6.19215e10	0.0203948
$187$	−1.61908e12	−0.517774
$188$	1.38433e12	0.429905
$189$	−5.39641e11	−0.162767
$190$	3.24454e11	0.0950623
$191$	−2.35067e12	−0.669126	−0.334563	−	0.942373i	$-0.608589\pi$
$191$	−2.35067e12	−0.669126	−0.334563	+	0.942373i	$0.608589\pi$
$192$	−2.86690e12	−0.792968
$193$	5.53479e12	1.48777	0.743886	−	0.668307i	$-0.232981\pi$
$193$	5.53479e12	1.48777	0.743886	+	0.668307i	$0.232981\pi$
$194$	4.28237e11	0.111886
$195$	−2.63791e10	−0.00669991
$196$	−1.40043e12	−0.345823
$197$	2.76354e12	0.663594	0.331797	−	0.943351i	$-0.392345\pi$
$197$	2.76354e12	0.663594	0.331797	+	0.943351i	$0.392345\pi$
$198$	−7.20010e11	−0.168143
$199$	7.05978e12	1.60361	0.801806	−	0.597584i	$-0.203872\pi$
$199$	7.05978e12	1.60361	0.801806	+	0.597584i	$0.203872\pi$
$200$	−1.49259e12	−0.329820
$201$	1.64346e11	0.0353331
$202$	−5.67305e12	−1.18682
$203$	2.79851e12	0.569770
$204$	−5.40615e12	−1.07133
$205$	9.17809e12	1.77054
$206$	9.03594e10	0.0169709
$207$	−3.40681e12	−0.623033
$208$	3.37864e10	0.00601719
$209$	−8.75634e10	−0.0151886
$210$	6.13088e12	1.03590
$211$	−7.30005e12	−1.20163	−0.600817	−	0.799386i	$-0.705158\pi$
$211$	−7.30005e12	−1.20163	−0.600817	+	0.799386i	$0.705158\pi$
$212$	−1.27015e12	−0.203708
$213$	5.61759e12	0.877934
$214$	−2.59341e12	−0.394998
$215$	1.71676e13	2.54857
$216$	−4.24994e11	−0.0615017
$217$	1.42297e11	0.0200755
$218$	6.72900e12	0.925635
$219$	3.02779e12	0.406147
$220$	4.48659e12	0.586937
$221$	9.74582e10	0.0124354
$222$	−4.36844e12	−0.543733
$223$	−5.75506e12	−0.698832	−0.349416	−	0.936968i	$-0.613620\pi$
$223$	−5.75506e12	−0.698832	−0.349416	+	0.936968i	$0.613620\pi$
$224$	−1.01337e13	−1.20062
$225$	2.97571e12	0.344022
$226$	−8.57952e12	−0.967980
$227$	−5.66844e12	−0.624196	−0.312098	−	0.950050i	$-0.601032\pi$
$227$	−5.66844e12	−0.624196	−0.312098	+	0.950050i	$0.601032\pi$
$228$	−2.92376e11	−0.0314268
$229$	1.33296e12	0.139869	0.0699345	−	0.997552i	$-0.477721\pi$
$229$	1.33296e12	0.139869	0.0699345	+	0.997552i	$0.477721\pi$
$230$	3.87049e13	3.96518
$231$	−1.65460e12	−0.165511
$232$	2.20397e12	0.215289
$233$	1.11677e13	1.06538	0.532692	−	0.846309i	$-0.321181\pi$
$233$	1.11677e13	1.06538	0.532692	+	0.846309i	$0.321181\pi$
$234$	4.33399e10	0.00403832
$235$	5.54284e12	0.504498
$236$	1.77858e12	0.158145
$237$	−4.40134e12	−0.382357
$238$	−2.26507e13	−1.92269
$239$	−7.64841e12	−0.634429	−0.317214	−	0.948354i	$-0.602747\pi$
$239$	−7.64841e12	−0.634429	−0.317214	+	0.948354i	$0.602747\pi$
$240$	−7.50417e12	−0.608333
$241$	−9.77672e12	−0.774639	−0.387319	−	0.921946i	$-0.626599\pi$
$241$	−9.77672e12	−0.774639	−0.387319	+	0.921946i	$0.626599\pi$
$242$	1.70076e13	1.31722
$243$	8.47289e11	0.0641500
$244$	1.16927e13	0.865508
$245$	−5.60730e12	−0.405827
$246$	−1.50793e13	−1.06718
$247$	5.27074e9	0.000364786 0
$248$	1.12066e11	0.00758558
$249$	7.00128e12	0.463534
$250$	−1.05039e12	−0.0680267
$251$	8.03236e12	0.508906	0.254453	−	0.967085i	$-0.418105\pi$
$251$	8.03236e12	0.508906	0.254453	+	0.967085i	$0.418105\pi$
$252$	−5.52473e12	−0.342459
$253$	−1.04457e13	−0.633538
$254$	−2.37706e13	−1.41077
$255$	−2.16461e13	−1.25721
$256$	7.81474e12	0.444217
$257$	−6.58689e11	−0.0366478	−0.0183239	−	0.999832i	$-0.505833\pi$
$257$	−6.58689e11	−0.0366478	−0.0183239	+	0.999832i	$0.505833\pi$
$258$	−2.82057e13	−1.53613
$259$	−1.00388e13	−0.535220
$260$	−2.70063e11	−0.0140965
$261$	−4.39394e12	−0.224559
$262$	2.56810e13	1.28515
$263$	1.51824e13	0.744017	0.372008	−	0.928229i	$-0.378669\pi$
$263$	1.51824e13	0.744017	0.372008	+	0.928229i	$0.378669\pi$
$264$	−1.30308e12	−0.0625387
$265$	−5.08566e12	−0.239054
$266$	−1.22500e12	−0.0564010
$267$	2.86705e12	0.129308
$268$	1.68254e12	0.0743404
$269$	−2.72108e13	−1.17789	−0.588943	−	0.808175i	$-0.700456\pi$
$269$	−2.72108e13	−1.17789	−0.588943	+	0.808175i	$0.700456\pi$
$270$	−9.62607e12	−0.408271
$271$	−7.63387e12	−0.317259	−0.158629	−	0.987338i	$-0.550707\pi$
$271$	−7.63387e12	−0.317259	−0.158629	+	0.987338i	$0.550707\pi$
$272$	2.77244e13	1.12910
$273$	9.95960e10	0.00397509
$274$	−4.53959e13	−1.77578
$275$	9.12384e12	0.349823
$276$	−3.48782e13	−1.31085
$277$	4.00591e13	1.47592	0.737959	−	0.674845i	$-0.235790\pi$
$277$	4.00591e13	1.47592	0.737959	+	0.674845i	$0.235790\pi$
$278$	−4.83746e13	−1.74731
$279$	−2.23420e11	−0.00791222
$280$	1.10957e13	0.385288
$281$	−2.49514e13	−0.849593	−0.424797	−	0.905289i	$-0.639654\pi$
$281$	−2.49514e13	−0.849593	−0.424797	+	0.905289i	$0.639654\pi$
$282$	−9.10670e12	−0.304082
$283$	−3.60074e13	−1.17914	−0.589572	−	0.807716i	$-0.700704\pi$
$283$	−3.60074e13	−1.17914	−0.589572	+	0.807716i	$0.700704\pi$
$284$	5.75117e13	1.84716
$285$	−1.17067e12	−0.0368796
$286$	1.32885e11	0.00410641
$287$	−3.46525e13	−1.05047
$288$	1.59109e13	0.473192
$289$	4.57003e13	1.33346
$290$	4.99196e13	1.42916
$291$	−1.54513e12	−0.0434063
$292$	3.09979e13	0.854527
$293$	−5.02048e13	−1.35823	−0.679115	−	0.734032i	$-0.737636\pi$
$293$	−5.02048e13	−1.35823	−0.679115	+	0.734032i	$0.737636\pi$
$294$	9.21261e12	0.244609
$295$	7.12138e12	0.185585
$296$	−7.90603e12	−0.202234
$297$	2.59788e12	0.0652316
$298$	7.87182e13	1.94037
$299$	6.28760e11	0.0152157
$300$	3.04647e13	0.723818
$301$	−6.48173e13	−1.51208
$302$	−1.05375e13	−0.241380
$303$	2.04690e13	0.460429
$304$	1.49939e12	0.0331216
$305$	4.68174e13	1.01568
$306$	3.55638e13	0.757775
$307$	1.79977e13	0.376666	0.188333	−	0.982105i	$-0.439692\pi$
$307$	1.79977e13	0.376666	0.188333	+	0.982105i	$0.439692\pi$
$308$	−1.69394e13	−0.348233
$309$	−3.26027e11	−0.00658388
$310$	2.53828e12	0.0503558
$311$	3.13168e13	0.610374	0.305187	−	0.952293i	$-0.401281\pi$
$311$	3.13168e13	0.610374	0.305187	+	0.952293i	$0.401281\pi$
$312$	7.84367e10	0.00150200
$313$	−3.78048e13	−0.711301	−0.355650	−	0.934619i	$-0.615741\pi$
$313$	−3.78048e13	−0.711301	−0.355650	+	0.934619i	$0.615741\pi$
$314$	−1.35630e14	−2.50750
$315$	−2.21209e13	−0.401879
$316$	−4.50600e13	−0.804475
$317$	2.71569e13	0.476491	0.238246	−	0.971205i	$-0.423428\pi$
$317$	2.71569e13	0.476491	0.238246	+	0.971205i	$0.423428\pi$
$318$	8.35557e12	0.144088
$319$	−1.34723e13	−0.228345
$320$	−1.17520e14	−1.95788
$321$	9.35730e12	0.153240
$322$	−1.46133e14	−2.35256
$323$	4.32506e12	0.0684508
$324$	8.67436e12	0.134971
$325$	−5.49195e11	−0.00840172
$326$	1.41649e14	2.13067
$327$	−2.42790e13	−0.359102
$328$	−2.72905e13	−0.396923
$329$	−2.09274e13	−0.299321
$330$	−2.95146e13	−0.415154
$331$	5.48421e13	0.758683	0.379341	−	0.925257i	$-0.376151\pi$
$331$	5.48421e13	0.758683	0.379341	+	0.925257i	$0.376151\pi$
$332$	7.16776e13	0.975269
$333$	1.57618e13	0.210942
$334$	−1.00104e14	−1.31779
$335$	6.73686e12	0.0872391
$336$	2.83325e13	0.360927
$337$	−2.15246e12	−0.0269756	−0.0134878	−	0.999909i	$-0.504293\pi$
$337$	−2.15246e12	−0.0269756	−0.0134878	+	0.999909i	$0.504293\pi$
$338$	1.20691e14	1.48810
$339$	3.09559e13	0.375530
$340$	−2.21608e14	−2.64516
$341$	−6.85029e11	−0.00804563
$342$	1.92336e12	0.0222289
$343$	9.55351e13	1.08654
$344$	−5.10468e13	−0.571343
$345$	−1.39652e14	−1.53830
$346$	−2.18260e14	−2.36622
$347$	1.26013e14	1.34463	0.672317	−	0.740264i	$-0.265299\pi$
$347$	1.26013e14	1.34463	0.672317	+	0.740264i	$0.265299\pi$
$348$	−4.49842e13	−0.472470
$349$	2.68537e13	0.277629	0.138814	−	0.990318i	$-0.455671\pi$
$349$	2.68537e13	0.277629	0.138814	+	0.990318i	$0.455671\pi$
$350$	1.27641e14	1.29902
$351$	−1.56375e11	−0.00156667
$352$	4.87847e13	0.481170
$353$	4.36781e13	0.424134	0.212067	−	0.977255i	$-0.431980\pi$
$353$	4.36781e13	0.424134	0.212067	+	0.977255i	$0.431980\pi$
$354$	−1.17002e13	−0.111860
$355$	2.30275e14	2.16766
$356$	2.93523e13	0.272061
$357$	8.17264e13	0.745911
$358$	−3.12554e14	−2.80911
$359$	1.69035e14	1.49609	0.748046	−	0.663647i	$-0.230992\pi$
$359$	1.69035e14	1.49609	0.748046	+	0.663647i	$0.230992\pi$
$360$	−1.74213e13	−0.151851
$361$	−1.16256e14	−0.997992
$362$	−6.61763e13	−0.559507
$363$	−6.13654e13	−0.511019
$364$	1.01964e12	0.00836354
$365$	1.24115e14	1.00280
$366$	−7.69193e13	−0.612194
$367$	5.93070e13	0.464989	0.232494	−	0.972598i	$-0.425311\pi$
$367$	5.93070e13	0.464989	0.232494	+	0.972598i	$0.425311\pi$
$368$	1.78866e14	1.38155
$369$	5.44078e13	0.414015
$370$	−1.79071e14	−1.34250
$371$	1.92013e13	0.141832
$372$	−2.28732e12	−0.0166472
$373$	5.12519e13	0.367546	0.183773	−	0.982969i	$-0.441169\pi$
$373$	5.12519e13	0.367546	0.183773	+	0.982969i	$0.441169\pi$
$374$	1.09042e14	0.770552
$375$	3.78992e12	0.0263911
$376$	−1.64813e13	−0.113099
$377$	8.10943e11	0.00548419
$378$	3.63439e13	0.242229
$379$	1.27387e14	0.836775	0.418388	−	0.908269i	$-0.362595\pi$
$379$	1.27387e14	0.836775	0.418388	+	0.908269i	$0.362595\pi$
$380$	−1.19850e13	−0.0775942
$381$	8.57670e13	0.547310
$382$	1.58313e14	0.995792
$383$	1.87412e14	1.16199	0.580996	−	0.813906i	$-0.302663\pi$
$383$	1.87412e14	1.16199	0.580996	+	0.813906i	$0.302663\pi$
$384$	5.89834e13	0.360502
$385$	−6.78251e13	−0.408655
$386$	−3.72758e14	−2.21410
$387$	1.01769e14	0.595946
$388$	−1.58187e13	−0.0913263
$389$	1.98704e14	1.13106	0.565529	−	0.824729i	$-0.308672\pi$
$389$	1.98704e14	1.13106	0.565529	+	0.824729i	$0.308672\pi$
$390$	1.77658e12	0.00997080
$391$	5.15947e14	2.85518
$392$	1.66730e13	0.0909789
$393$	−9.26600e13	−0.498578
$394$	−1.86120e14	−0.987559
$395$	−1.80419e14	−0.944059
$396$	2.65965e13	0.137247
$397$	−1.60357e14	−0.816092	−0.408046	−	0.912961i	$-0.633790\pi$
$397$	−1.60357e14	−0.816092	−0.408046	+	0.912961i	$0.633790\pi$
$398$	−4.75464e14	−2.38650
$399$	4.41993e12	0.0218809
$400$	−1.56232e14	−0.762852
$401$	−2.18004e14	−1.04995	−0.524977	−	0.851116i	$-0.675926\pi$
$401$	−2.18004e14	−1.04995	−0.524977	+	0.851116i	$0.675926\pi$
$402$	−1.10684e13	−0.0525827
$403$	4.12342e10	0.000193233 0
$404$	2.09557e14	0.968736
$405$	3.47319e13	0.158390
$406$	−1.88475e14	−0.847931
$407$	4.83275e13	0.214499
$408$	6.43635e13	0.281844
$409$	−1.26493e13	−0.0546498	−0.0273249	−	0.999627i	$-0.508699\pi$
$409$	−1.26493e13	−0.0546498	−0.0273249	+	0.999627i	$0.508699\pi$
$410$	−6.18128e14	−2.63492
$411$	1.63794e14	0.688917
$412$	−3.33780e12	−0.0138524
$413$	−2.68873e13	−0.110109
$414$	2.29443e14	0.927198
$415$	2.86996e14	1.14449
$416$	−2.93652e12	−0.0115563
$417$	1.74541e14	0.677875
$418$	5.89724e12	0.0226037
$419$	3.16015e14	1.19545	0.597725	−	0.801702i	$-0.296072\pi$
$419$	3.16015e14	1.19545	0.597725	+	0.801702i	$0.296072\pi$
$420$	−2.26469e14	−0.845547
$421$	−4.96360e14	−1.82913	−0.914567	−	0.404435i	$-0.867468\pi$
$421$	−4.96360e14	−1.82913	−0.914567	+	0.404435i	$0.867468\pi$
$422$	4.91645e14	1.78827
$423$	3.28580e13	0.117969
$424$	1.51219e13	0.0535914
$425$	−4.50658e14	−1.57655
$426$	−3.78334e14	−1.30654
$427$	−1.76762e14	−0.602610
$428$	9.57981e13	0.322416
$429$	−4.79463e11	−0.00159309
$430$	−1.15620e15	−3.79278
$431$	3.66809e14	1.18800	0.593998	−	0.804467i	$-0.297549\pi$
$431$	3.66809e14	1.18800	0.593998	+	0.804467i	$0.297549\pi$
$432$	−4.44848e13	−0.142250
$433$	−6.77200e13	−0.213813	−0.106906	−	0.994269i	$-0.534095\pi$
$433$	−6.77200e13	−0.213813	−0.106906	+	0.994269i	$0.534095\pi$
$434$	−9.58344e12	−0.0298764
$435$	−1.80116e14	−0.554447
$436$	−2.48563e14	−0.755546
$437$	2.79035e13	0.0837550
$438$	−2.03916e14	−0.604427
$439$	−7.84505e13	−0.229636	−0.114818	−	0.993387i	$-0.536629\pi$
$439$	−7.84505e13	−0.229636	−0.114818	+	0.993387i	$0.536629\pi$
$440$	−5.34156e13	−0.154411
$441$	−3.32401e13	−0.0948966
$442$	−6.56364e12	−0.0185064
$443$	−6.76883e14	−1.88492	−0.942461	−	0.334317i	$-0.891495\pi$
$443$	−6.76883e14	−1.88492	−0.942461	+	0.334317i	$0.891495\pi$
$444$	1.61366e14	0.443820
$445$	1.17526e14	0.319267
$446$	3.87593e14	1.04000
$447$	−2.84024e14	−0.752773
$448$	4.43703e14	1.16162
$449$	2.48132e14	0.641694	0.320847	−	0.947131i	$-0.396032\pi$
$449$	2.48132e14	0.641694	0.320847	+	0.947131i	$0.396032\pi$
$450$	−2.00409e14	−0.511974
$451$	1.66820e14	0.420995
$452$	3.16920e14	0.790111
$453$	3.80206e13	0.0936438
$454$	3.81759e14	0.928928
$455$	4.08262e12	0.00981469
$456$	3.48091e12	0.00826773
$457$	7.18385e13	0.168585	0.0842924	−	0.996441i	$-0.473137\pi$
$457$	7.18385e13	0.168585	0.0842924	+	0.996441i	$0.473137\pi$
$458$	−8.97724e13	−0.208153
$459$	−1.28318e14	−0.293980
$460$	−1.42972e15	−3.23656
$461$	1.29741e14	0.290217	0.145108	−	0.989416i	$-0.453647\pi$
$461$	1.29741e14	0.290217	0.145108	+	0.989416i	$0.453647\pi$
$462$	1.11434e14	0.246313
$463$	5.56814e14	1.21623	0.608114	−	0.793850i	$-0.291926\pi$
$463$	5.56814e14	1.21623	0.608114	+	0.793850i	$0.291926\pi$
$464$	2.30693e14	0.497949
$465$	−9.15839e12	−0.0195357
$466$	−7.52124e14	−1.58550
$467$	−7.28759e14	−1.51824	−0.759121	−	0.650950i	$-0.774371\pi$
$467$	−7.28759e14	−1.51824	−0.759121	+	0.650950i	$0.774371\pi$
$468$	−1.60094e12	−0.00329626
$469$	−2.54355e13	−0.0517594
$470$	−3.73301e14	−0.750794
$471$	4.89367e14	0.972791
$472$	−2.11750e13	−0.0416048
$473$	3.12036e14	0.605994
$474$	2.96423e14	0.569024
$475$	−2.43725e13	−0.0462472
$476$	8.36697e14	1.56939
$477$	−3.01478e13	−0.0558992
$478$	5.15107e14	0.944157
$479$	−8.15098e14	−1.47695	−0.738473	−	0.674283i	$-0.764453\pi$
$479$	−8.15098e14	−1.47695	−0.738473	+	0.674283i	$0.764453\pi$
$480$	6.52219e14	1.16833
$481$	−2.90900e12	−0.00515164
$482$	6.58444e14	1.15282
$483$	5.27264e14	0.912681
$484$	−6.28246e14	−1.07518
$485$	−6.33376e13	−0.107172
$486$	−5.70634e13	−0.0954680
$487$	−7.69461e14	−1.27285	−0.636425	−	0.771338i	$-0.719588\pi$
$487$	−7.69461e14	−1.27285	−0.636425	+	0.771338i	$0.719588\pi$
$488$	−1.39209e14	−0.227697
$489$	−5.11085e14	−0.826598
$490$	3.77642e14	0.603951
$491$	4.61449e14	0.729753	0.364877	−	0.931056i	$-0.381111\pi$
$491$	4.61449e14	0.729753	0.364877	+	0.931056i	$0.381111\pi$
$492$	5.57015e14	0.871082
$493$	6.65443e14	1.02909
$494$	−3.54975e11	−0.000542875 0
$495$	1.06492e14	0.161060
$496$	1.17301e13	0.0175450
$497$	−8.69421e14	−1.28609
$498$	−4.71524e14	−0.689830
$499$	8.66882e13	0.125432	0.0627158	−	0.998031i	$-0.480024\pi$
$499$	8.66882e13	0.125432	0.0627158	+	0.998031i	$0.480024\pi$
$500$	3.88004e13	0.0555266
$501$	3.61187e14	0.511240
$502$	−5.40965e14	−0.757354
$503$	9.55447e14	1.32307	0.661535	−	0.749914i	$-0.269905\pi$
$503$	9.55447e14	1.32307	0.661535	+	0.749914i	$0.269905\pi$
$504$	6.57753e13	0.0900938
$505$	8.39063e14	1.13682
$506$	7.03496e14	0.942831
$507$	−4.35466e14	−0.577312
$508$	8.78065e14	1.15153
$509$	1.23788e14	0.160595	0.0802973	−	0.996771i	$-0.474413\pi$
$509$	1.23788e14	0.160595	0.0802973	+	0.996771i	$0.474413\pi$
$510$	1.45783e15	1.87098
$511$	−4.68604e14	−0.594964
$512$	−1.02342e15	−1.28549
$513$	−6.93972e12	−0.00862375
$514$	4.43615e13	0.0545393
$515$	−1.33645e13	−0.0162559
$516$	1.04189e15	1.25386
$517$	1.00746e14	0.119958
$518$	6.76094e14	0.796514
$519$	7.87505e14	0.917980
$520$	3.21527e12	0.00370850
$521$	−8.29006e14	−0.946128	−0.473064	−	0.881028i	$-0.656852\pi$
$521$	−8.29006e14	−0.946128	−0.473064	+	0.881028i	$0.656852\pi$
$522$	2.95924e14	0.334189
$523$	−6.50445e14	−0.726860	−0.363430	−	0.931621i	$-0.618394\pi$
$523$	−6.50445e14	−0.726860	−0.363430	+	0.931621i	$0.618394\pi$
$524$	−9.48634e14	−1.04900
$525$	−4.60543e14	−0.503958
$526$	−1.02250e15	−1.10725
$527$	3.38359e13	0.0362593
$528$	−1.36395e14	−0.144648
$529$	2.37587e15	2.49354
$530$	3.42510e14	0.355760
$531$	4.22156e13	0.0433963
$532$	4.52503e13	0.0460371
$533$	−1.00415e13	−0.0101111
$534$	−1.93091e14	−0.192435
$535$	3.83573e14	0.378358
$536$	−2.00317e13	−0.0195574
$537$	1.12773e15	1.08980
$538$	1.83260e15	1.75293
$539$	−1.01918e14	−0.0964966
$540$	3.55578e14	0.333249
$541$	−1.05175e15	−0.975725	−0.487862	−	0.872921i	$-0.662223\pi$
$541$	−1.05175e15	−0.975725	−0.487862	+	0.872921i	$0.662223\pi$
$542$	5.14127e14	0.472144
$543$	2.38772e14	0.217062
$544$	−2.40964e15	−2.16850
$545$	−9.95241e14	−0.886641
$546$	−6.70761e12	−0.00591573
$547$	1.20682e15	1.05369	0.526846	−	0.849961i	$-0.323375\pi$
$547$	1.20682e15	1.05369	0.526846	+	0.849961i	$0.323375\pi$
$548$	1.67688e15	1.44947
$549$	2.77534e14	0.237502
$550$	−6.14474e14	−0.520606
$551$	3.59885e13	0.0301877
$552$	4.15246e14	0.344859
$553$	6.81186e14	0.560115
$554$	−2.69791e15	−2.19646
$555$	6.46107e14	0.520827
$556$	1.78691e15	1.42624
$557$	4.93551e14	0.390057	0.195028	−	0.980798i	$-0.437520\pi$
$557$	4.93551e14	0.390057	0.195028	+	0.980798i	$0.437520\pi$
$558$	1.50469e13	0.0117750
$559$	−1.87825e13	−0.0145542
$560$	1.16140e15	0.891146
$561$	−3.93437e14	−0.298937
$562$	1.68044e15	1.26436
$563$	−1.00373e14	−0.0747857	−0.0373929	−	0.999301i	$-0.511905\pi$
$563$	−1.00373e14	−0.0747857	−0.0373929	+	0.999301i	$0.511905\pi$
$564$	3.36393e14	0.248206
$565$	1.26894e15	0.927202
$566$	2.42504e15	1.75480
$567$	−1.31133e14	−0.0939734
$568$	−6.84711e14	−0.485950
$569$	1.45512e15	1.02278	0.511388	−	0.859350i	$-0.329132\pi$
$569$	1.45512e15	1.02278	0.511388	+	0.859350i	$0.329132\pi$
$570$	7.88423e13	0.0548842
$571$	1.64681e15	1.13539	0.567694	−	0.823240i	$-0.307836\pi$
$571$	1.64681e15	1.13539	0.567694	+	0.823240i	$0.307836\pi$
$572$	−4.90864e12	−0.00335184
$573$	−5.71212e14	−0.386320
$574$	2.33379e15	1.56331
$575$	−2.90746e15	−1.92904
$576$	−6.96656e14	−0.457820
$577$	−2.39991e15	−1.56217	−0.781084	−	0.624426i	$-0.785333\pi$
$577$	−2.39991e15	−1.56217	−0.781084	+	0.624426i	$0.785333\pi$
$578$	−3.07783e15	−1.98446
$579$	1.34495e15	0.858965
$580$	−1.84399e15	−1.16655
$581$	−1.08357e15	−0.679030
$582$	1.04062e14	0.0645972
$583$	−9.24365e13	−0.0568416
$584$	−3.69048e14	−0.224808
$585$	−6.41011e12	−0.00386819
$586$	3.38120e15	2.02132
$587$	−1.14328e15	−0.677085	−0.338543	−	0.940951i	$-0.609934\pi$
$587$	−1.14328e15	−0.677085	−0.338543	+	0.940951i	$0.609934\pi$
$588$	−3.40305e14	−0.199661
$589$	1.82992e12	0.00106365
$590$	−4.79612e14	−0.276188
$591$	6.71541e14	0.383126
$592$	−8.27536e14	−0.467754
$593$	−1.90189e14	−0.106508	−0.0532542	−	0.998581i	$-0.516959\pi$
$593$	−1.90189e14	−0.106508	−0.0532542	+	0.998581i	$0.516959\pi$
$594$	−1.74962e14	−0.0970777
$595$	3.35012e15	1.84169
$596$	−2.90778e15	−1.58382
$597$	1.71553e15	0.925846
$598$	−4.23459e13	−0.0226441
$599$	−1.12882e15	−0.598104	−0.299052	−	0.954237i	$-0.596670\pi$
$599$	−1.12882e15	−0.598104	−0.299052	+	0.954237i	$0.596670\pi$
$600$	−3.62700e14	−0.190421
$601$	−3.10749e15	−1.61659	−0.808295	−	0.588778i	$-0.799609\pi$
$601$	−3.10749e15	−1.61659	−0.808295	+	0.588778i	$0.799609\pi$
$602$	4.36533e15	2.25028
$603$	3.99362e13	0.0203996
$604$	3.89247e14	0.197025
$605$	−2.51548e15	−1.26173
$606$	−1.37855e15	−0.685210
$607$	1.59490e15	0.785587	0.392794	−	0.919627i	$-0.371509\pi$
$607$	1.59490e15	0.785587	0.392794	+	0.919627i	$0.371509\pi$
$608$	−1.30319e14	−0.0636116
$609$	6.80039e14	0.328957
$610$	−3.15307e15	−1.51154
$611$	−6.06426e12	−0.00288105
$612$	−1.31369e15	−0.618531
$613$	−2.80189e15	−1.30743	−0.653716	−	0.756740i	$-0.726791\pi$
$613$	−2.80189e15	−1.30743	−0.653716	+	0.756740i	$0.726791\pi$
$614$	−1.21211e15	−0.560554
$615$	2.23028e15	1.02222
$616$	2.01674e14	0.0916129
$617$	1.29479e15	0.582949	0.291474	−	0.956579i	$-0.405854\pi$
$617$	1.29479e15	0.582949	0.291474	+	0.956579i	$0.405854\pi$
$618$	2.19573e13	0.00979813
$619$	2.21313e15	0.978831	0.489415	−	0.872051i	$-0.337210\pi$
$619$	2.21313e15	0.978831	0.489415	+	0.872051i	$0.337210\pi$
$620$	−9.37617e13	−0.0411028
$621$	−8.27855e14	−0.359709
$622$	−2.10913e15	−0.908358
$623$	−4.43727e14	−0.189423
$624$	8.21009e12	0.00347402
$625$	−2.30528e15	−0.966905
$626$	2.54609e15	1.05856
$627$	−2.12779e13	−0.00876915
$628$	5.01003e15	2.04674
$629$	−2.38706e15	−0.966686
$630$	1.48980e15	0.598076
$631$	1.83838e14	0.0731600	0.0365800	−	0.999331i	$-0.488354\pi$
$631$	1.83838e14	0.0731600	0.0365800	+	0.999331i	$0.488354\pi$
$632$	5.36467e14	0.211641
$633$	−1.77391e15	−0.693764
$634$	−1.82897e15	−0.709114
$635$	3.51575e15	1.35133
$636$	−3.08647e14	−0.117611
$637$	6.13478e12	0.00231757
$638$	9.07334e14	0.339824
$639$	1.36507e15	0.506876
$640$	2.41784e15	0.890097
$641$	−1.34809e15	−0.492040	−0.246020	−	0.969265i	$-0.579123\pi$
$641$	−1.34809e15	−0.492040	−0.246020	+	0.969265i	$0.579123\pi$
$642$	−6.30198e14	−0.228052
$643$	−4.86516e15	−1.74557	−0.872784	−	0.488106i	$-0.837688\pi$
$643$	−4.86516e15	−1.74557	−0.872784	+	0.488106i	$0.837688\pi$
$644$	5.39802e15	1.92027
$645$	4.17172e15	1.47142
$646$	−2.91285e14	−0.101868
$647$	3.74698e15	1.29929	0.649647	−	0.760236i	$-0.274917\pi$
$647$	3.74698e15	1.29929	0.649647	+	0.760236i	$0.274917\pi$
$648$	−1.03274e14	−0.0355080
$649$	1.29437e14	0.0441280
$650$	3.69873e13	0.0125034
$651$	3.45781e13	0.0115906
$652$	−5.23238e15	−1.73915
$653$	1.46018e15	0.481264	0.240632	−	0.970616i	$-0.422645\pi$
$653$	1.46018e15	0.481264	0.240632	+	0.970616i	$0.422645\pi$
$654$	1.63515e15	0.534416
$655$	−3.79831e15	−1.23101
$656$	−2.85654e15	−0.918057
$657$	7.35753e14	0.234489
$658$	1.40942e15	0.445450
$659$	−4.59347e14	−0.143970	−0.0719849	−	0.997406i	$-0.522933\pi$
$659$	−4.59347e14	−0.143970	−0.0719849	+	0.997406i	$0.522933\pi$
$660$	1.09024e15	0.338868
$661$	3.53993e15	1.09115	0.545577	−	0.838061i	$-0.316310\pi$
$661$	3.53993e15	1.09115	0.545577	+	0.838061i	$0.316310\pi$
$662$	−3.69352e15	−1.12907
$663$	2.36823e13	0.00717960
$664$	−8.53366e14	−0.256573
$665$	1.81181e14	0.0540249
$666$	−1.06153e15	−0.313924
$667$	4.29316e15	1.25917
$668$	3.69776e15	1.07564
$669$	−1.39848e15	−0.403471
$670$	−4.53716e14	−0.129829
$671$	8.50948e14	0.241507
$672$	−2.46250e15	−0.693178
$673$	−4.34346e15	−1.21270	−0.606349	−	0.795198i	$-0.707367\pi$
$673$	−4.34346e15	−1.21270	−0.606349	+	0.795198i	$0.707367\pi$
$674$	1.44964e14	0.0401451
$675$	7.23097e14	0.198621
$676$	−4.45821e15	−1.21466
$677$	6.18104e15	1.67041	0.835207	−	0.549936i	$-0.185348\pi$
$677$	6.18104e15	1.67041	0.835207	+	0.549936i	$0.185348\pi$
$678$	−2.08482e15	−0.558864
$679$	2.39136e14	0.0635858
$680$	2.63838e15	0.695886
$681$	−1.37743e15	−0.360380
$682$	4.61355e13	0.0119735
$683$	7.29907e15	1.87912	0.939558	−	0.342391i	$-0.111237\pi$
$683$	7.29907e15	1.87912	0.939558	+	0.342391i	$0.111237\pi$
$684$	−7.10473e13	−0.0181443
$685$	6.71421e15	1.70097
$686$	−6.43412e15	−1.61699
$687$	3.23909e14	0.0807535
$688$	−5.34315e15	−1.32148
$689$	5.56407e12	0.00136517
$690$	9.40529e15	2.28930
$691$	−1.15596e15	−0.279135	−0.139567	−	0.990213i	$-0.544571\pi$
$691$	−1.15596e15	−0.279135	−0.139567	+	0.990213i	$0.544571\pi$
$692$	8.06231e15	1.93142
$693$	−4.02067e14	−0.0955578
$694$	−8.48676e15	−2.00108
$695$	7.15476e15	1.67371
$696$	5.35564e14	0.124297
$697$	−8.23982e15	−1.89731
$698$	−1.80855e15	−0.413167
$699$	2.71375e15	0.615099
$700$	−4.71494e15	−1.06032
$701$	−2.84226e15	−0.634183	−0.317092	−	0.948395i	$-0.602706\pi$
$701$	−2.84226e15	−0.634183	−0.317092	+	0.948395i	$0.602706\pi$
$702$	1.05316e13	0.00233152
$703$	−1.29097e14	−0.0283572
$704$	−2.13602e15	−0.465539
$705$	1.34691e15	0.291272
$706$	−2.94164e15	−0.631196
$707$	−3.16794e15	−0.674482
$708$	4.32194e14	0.0913053
$709$	−4.22203e15	−0.885049	−0.442524	−	0.896756i	$-0.645917\pi$
$709$	−4.22203e15	−0.885049	−0.442524	+	0.896756i	$0.645917\pi$
$710$	−1.55086e16	−3.22591
$711$	−1.06953e15	−0.220754
$712$	−3.49457e14	−0.0715737
$713$	2.18295e14	0.0443662
$714$	−5.50413e15	−1.11006
$715$	−1.96541e13	−0.00393341
$716$	1.15455e16	2.29292
$717$	−1.85856e15	−0.366288
$718$	−1.13842e16	−2.22648
$719$	6.37112e15	1.23654	0.618268	−	0.785968i	$-0.287835\pi$
$719$	6.37112e15	1.23654	0.618268	+	0.785968i	$0.287835\pi$
$720$	−1.82351e15	−0.351221
$721$	5.04584e13	0.00964472
$722$	7.82966e15	1.48521
$723$	−2.37574e15	−0.447238
$724$	2.44449e15	0.456695
$725$	−3.74989e15	−0.695280
$726$	4.13285e15	0.760498
$727$	−4.81292e15	−0.878961	−0.439481	−	0.898252i	$-0.644837\pi$
$727$	−4.81292e15	−0.878961	−0.439481	+	0.898252i	$0.644837\pi$
$728$	−1.21395e13	−0.00220027
$729$	2.05891e14	0.0370370
$730$	−8.35890e15	−1.49236
$731$	−1.54125e16	−2.73104
$732$	2.84133e15	0.499702
$733$	−8.66668e15	−1.51280	−0.756399	−	0.654110i	$-0.773043\pi$
$733$	−8.66668e15	−1.51280	−0.756399	+	0.654110i	$0.773043\pi$
$734$	−3.99422e15	−0.691996
$735$	−1.36258e15	−0.234304
$736$	−1.55460e16	−2.65333
$737$	1.22449e14	0.0207435
$738$	−3.66427e15	−0.616137
$739$	−6.34588e15	−1.05913	−0.529563	−	0.848271i	$-0.677644\pi$
$739$	−6.34588e15	−1.05913	−0.529563	+	0.848271i	$0.677644\pi$
$740$	6.61471e15	1.09581
$741$	1.28079e12	0.000210610 0
$742$	−1.29317e15	−0.211074
$743$	−1.45746e15	−0.236134	−0.118067	−	0.993006i	$-0.537670\pi$
$743$	−1.45746e15	−0.236134	−0.118067	+	0.993006i	$0.537670\pi$
$744$	2.72320e13	0.00437953
$745$	−1.16427e16	−1.85863
$746$	−3.45172e15	−0.546981
$747$	1.70131e15	0.267621
$748$	−4.02793e15	−0.628960
$749$	−1.44821e15	−0.224482
$750$	−2.55244e14	−0.0392752
$751$	−1.26410e16	−1.93092	−0.965458	−	0.260558i	$-0.916093\pi$
$751$	−1.26410e16	−1.93092	−0.965458	+	0.260558i	$0.916093\pi$
$752$	−1.72513e15	−0.261591
$753$	1.95186e15	0.293817
$754$	−5.46155e13	−0.00816157
$755$	1.55854e15	0.231211
$756$	−1.34251e15	−0.197719
$757$	5.70005e15	0.833396	0.416698	−	0.909045i	$-0.363187\pi$
$757$	5.70005e15	0.833396	0.416698	+	0.909045i	$0.363187\pi$
$758$	−8.57927e15	−1.24529
$759$	−2.53829e15	−0.365773
$760$	1.42689e14	0.0204134
$761$	1.12577e16	1.59895	0.799476	−	0.600698i	$-0.205111\pi$
$761$	1.12577e16	1.59895	0.799476	+	0.600698i	$0.205111\pi$
$762$	−5.77626e15	−0.814506
$763$	3.75760e15	0.526049
$764$	−5.84795e15	−0.812812
$765$	−5.26000e15	−0.725852
$766$	−1.26218e16	−1.72928
$767$	−7.79129e12	−0.00105983
$768$	1.89898e15	0.256469
$769$	8.29147e15	1.11183	0.555913	−	0.831241i	$-0.312369\pi$
$769$	8.29147e15	1.11183	0.555913	+	0.831241i	$0.312369\pi$
$770$	4.56790e15	0.608160
$771$	−1.60061e14	−0.0211586
$772$	1.37694e16	1.80725
$773$	2.75697e15	0.359289	0.179645	−	0.983732i	$-0.442505\pi$
$773$	2.75697e15	0.359289	0.179645	+	0.983732i	$0.442505\pi$
$774$	−6.85399e15	−0.886886
$775$	−1.90672e14	−0.0244978
$776$	1.88331e14	0.0240260
$777$	−2.43942e15	−0.309009
$778$	−1.33824e16	−1.68324
$779$	−4.45627e14	−0.0556564
$780$	−6.56254e13	−0.00813863
$781$	4.18546e15	0.515422
$782$	−3.47481e16	−4.24907
$783$	−1.06773e15	−0.129649
$784$	1.74519e15	0.210428
$785$	2.00601e16	2.40187
$786$	6.24049e15	0.741984
$787$	6.89600e15	0.814210	0.407105	−	0.913381i	$-0.366538\pi$
$787$	6.89600e15	0.814210	0.407105	+	0.913381i	$0.366538\pi$
$788$	6.87510e15	0.806092
$789$	3.68931e15	0.429558
$790$	1.21509e16	1.40495
$791$	−4.79097e15	−0.550114
$792$	−3.16648e14	−0.0361067
$793$	−5.12215e13	−0.00580029
$794$	1.07997e16	1.21451
$795$	−1.23582e15	−0.138018
$796$	1.75632e16	1.94797
$797$	9.13323e15	1.00601	0.503007	−	0.864283i	$-0.332227\pi$
$797$	9.13323e15	1.00601	0.503007	+	0.864283i	$0.332227\pi$
$798$	−2.97675e14	−0.0325631
$799$	−4.97620e15	−0.540618
$800$	1.35788e16	1.46510
$801$	6.96694e14	0.0746558
$802$	1.46822e16	1.56254
$803$	2.25590e15	0.238443
$804$	4.08858e14	0.0429204
$805$	2.16136e16	2.25345
$806$	−2.77705e12	−0.000287569 0
$807$	−6.61222e15	−0.680053
$808$	−2.49491e15	−0.254854
$809$	1.06543e16	1.08096	0.540479	−	0.841357i	$-0.318243\pi$
$809$	1.06543e16	1.08096	0.540479	+	0.841357i	$0.318243\pi$
$810$	−2.33913e15	−0.235715
$811$	9.11486e15	0.912295	0.456147	−	0.889904i	$-0.349229\pi$
$811$	9.11486e15	0.912295	0.456147	+	0.889904i	$0.349229\pi$
$812$	6.96210e15	0.692121
$813$	−1.85503e15	−0.183169
$814$	−3.25477e15	−0.319217
$815$	−2.09503e16	−2.04091
$816$	6.73703e15	0.651887
$817$	−8.33542e14	−0.0801136
$818$	8.51908e14	0.0813298
$819$	2.42018e13	0.00229502
$820$	2.28331e16	2.15074
$821$	−2.30932e15	−0.216071	−0.108035	−	0.994147i	$-0.534456\pi$
$821$	−2.30932e15	−0.216071	−0.108035	+	0.994147i	$0.534456\pi$
$822$	−1.10312e16	−1.02525
$823$	−2.26195e15	−0.208825	−0.104413	−	0.994534i	$-0.533296\pi$
$823$	−2.26195e15	−0.208825	−0.104413	+	0.994534i	$0.533296\pi$
$824$	3.97385e13	0.00364428
$825$	2.21709e15	0.201970
$826$	1.81081e15	0.163864
$827$	6.19451e15	0.556835	0.278418	−	0.960460i	$-0.410190\pi$
$827$	6.19451e15	0.556835	0.278418	+	0.960460i	$0.410190\pi$
$828$	−8.47541e15	−0.756822
$829$	−5.84390e15	−0.518385	−0.259193	−	0.965826i	$-0.583456\pi$
$829$	−5.84390e15	−0.518385	−0.259193	+	0.965826i	$0.583456\pi$
$830$	−1.93286e16	−1.70322
$831$	9.73436e15	0.852122
$832$	1.28575e14	0.0111809
$833$	5.03407e15	0.434883
$834$	−1.17550e16	−1.00881
$835$	1.48057e16	1.26228
$836$	−2.17839e14	−0.0184502
$837$	−5.42910e13	−0.00456812
$838$	−2.12831e16	−1.77907
$839$	4.69763e15	0.390111	0.195056	−	0.980792i	$-0.437511\pi$
$839$	4.69763e15	0.390111	0.195056	+	0.980792i	$0.437511\pi$
$840$	2.69625e15	0.222446
$841$	−6.66341e15	−0.546158
$842$	3.34290e16	2.72212
$843$	−6.06320e15	−0.490513
$844$	−1.81609e16	−1.45967
$845$	−1.78506e16	−1.42541
$846$	−2.21293e15	−0.175562
$847$	9.49737e15	0.748591
$848$	1.58284e15	0.123954
$849$	−8.74981e15	−0.680779
$850$	3.03510e16	2.34622
$851$	−1.54003e16	−1.18282
$852$	1.39753e16	1.06646
$853$	−5.10348e15	−0.386943	−0.193471	−	0.981106i	$-0.561975\pi$
$853$	−5.10348e15	−0.386943	−0.193471	+	0.981106i	$0.561975\pi$
$854$	1.19046e16	0.896803
$855$	−2.84472e14	−0.0212925
$856$	−1.14053e15	−0.0848208
$857$	9.17857e15	0.678235	0.339118	−	0.940744i	$-0.389872\pi$
$857$	9.17857e15	0.678235	0.339118	+	0.940744i	$0.389872\pi$
$858$	3.22910e13	0.00237083
$859$	2.19842e16	1.60379	0.801896	−	0.597464i	$-0.203825\pi$
$859$	2.19842e16	1.60379	0.801896	+	0.597464i	$0.203825\pi$
$860$	4.27092e16	3.09585
$861$	−8.42056e15	−0.606490
$862$	−2.47039e16	−1.76797
$863$	1.88282e16	1.33891	0.669454	−	0.742854i	$-0.266528\pi$
$863$	1.88282e16	1.33891	0.669454	+	0.742854i	$0.266528\pi$
$864$	3.86636e15	0.273197
$865$	3.22813e16	2.26654
$866$	4.56082e15	0.318196
$867$	1.11052e16	0.769875
$868$	3.54004e14	0.0243865
$869$	−3.27928e15	−0.224476
$870$	1.21305e16	0.825128
$871$	−7.37060e12	−0.000498199 0
$872$	2.95930e15	0.198769
$873$	−3.75466e14	−0.0250606
$874$	−1.87925e15	−0.124644
$875$	−5.86557e14	−0.0386603
$876$	7.53248e15	0.493362
$877$	7.00820e15	0.456151	0.228075	−	0.973643i	$-0.426757\pi$
$877$	7.00820e15	0.456151	0.228075	+	0.973643i	$0.426757\pi$
$878$	5.28350e15	0.341745
$879$	−1.21998e16	−0.784174
$880$	−5.59109e15	−0.357143
$881$	−2.67563e16	−1.69847	−0.849237	−	0.528011i	$-0.822938\pi$
$881$	−2.67563e16	−1.69847	−0.849237	+	0.528011i	$0.822938\pi$
$882$	2.23866e15	0.141225
$883$	−7.83053e15	−0.490916	−0.245458	−	0.969407i	$-0.578938\pi$
$883$	−7.83053e15	−0.490916	−0.245458	+	0.969407i	$0.578938\pi$
$884$	2.42455e14	0.0151058
$885$	1.73049e15	0.107148
$886$	4.55869e16	2.80514
$887$	4.92294e15	0.301054	0.150527	−	0.988606i	$-0.451903\pi$
$887$	4.92294e15	0.301054	0.150527	+	0.988606i	$0.451903\pi$
$888$	−1.92116e15	−0.116760
$889$	−1.32740e16	−0.801754
$890$	−7.91516e15	−0.475132
$891$	6.31284e14	0.0376615
$892$	−1.43173e16	−0.848898
$893$	−2.69124e14	−0.0158587
$894$	1.91285e16	1.12028
$895$	4.62277e16	2.69077
$896$	−9.12872e15	−0.528100
$897$	1.52789e14	0.00878481
$898$	−1.67113e16	−0.954969
$899$	2.81546e14	0.0159909
$900$	7.40291e15	0.417897
$901$	4.56576e15	0.256169
$902$	−1.12350e16	−0.626525
$903$	−1.57506e16	−0.873001
$904$	−3.77312e15	−0.207862
$905$	9.78769e15	0.535936
$906$	−2.56062e15	−0.139361
$907$	−3.37947e14	−0.0182814	−0.00914069	−	0.999958i	$-0.502910\pi$
$907$	−3.37947e14	−0.0182814	−0.00914069	+	0.999958i	$0.502910\pi$
$908$	−1.41018e16	−0.758234
$909$	4.97397e15	0.265829
$910$	−2.74958e14	−0.0146062
$911$	−3.12034e16	−1.64760	−0.823799	−	0.566882i	$-0.808150\pi$
$911$	−3.12034e16	−1.64760	−0.823799	+	0.566882i	$0.808150\pi$
$912$	3.64353e14	0.0191227
$913$	5.21640e15	0.272133
$914$	−4.83820e15	−0.250888
$915$	1.13766e16	0.586404
$916$	3.31611e15	0.169904
$917$	1.43408e16	0.730367
$918$	8.64200e15	0.437502
$919$	1.51270e16	0.761232	0.380616	−	0.924733i	$-0.375712\pi$
$919$	1.51270e16	0.761232	0.380616	+	0.924733i	$0.375712\pi$
$920$	1.70217e16	0.851472
$921$	4.37345e15	0.217468
$922$	−8.73783e15	−0.431900
$923$	−2.51937e14	−0.0123789
$924$	−4.11628e15	−0.201052
$925$	1.34515e16	0.653119
$926$	−3.75004e16	−1.80999
$927$	−7.92246e13	−0.00380121
$928$	−2.00505e16	−0.956336
$929$	−4.80904e15	−0.228020	−0.114010	−	0.993480i	$-0.536370\pi$
$929$	−4.80904e15	−0.228020	−0.114010	+	0.993480i	$0.536370\pi$
$930$	6.16801e14	0.0290729
$931$	2.72253e14	0.0127570
$932$	2.77828e16	1.29416
$933$	7.60999e15	0.352399
$934$	4.90806e16	2.25945
$935$	−1.61277e16	−0.738090
$936$	1.90601e13	0.000867178 0
$937$	2.84930e16	1.28876	0.644378	−	0.764708i	$-0.277117\pi$
$937$	2.84930e16	1.28876	0.644378	+	0.764708i	$0.277117\pi$
$938$	1.71304e15	0.0770284
$939$	−9.18657e15	−0.410670
$940$	1.37894e16	0.612833
$941$	2.63741e16	1.16529	0.582646	−	0.812726i	$-0.302017\pi$
$941$	2.63741e16	1.16529	0.582646	+	0.812726i	$0.302017\pi$
$942$	−3.29580e16	−1.44771
$943$	−5.31599e16	−2.32151
$944$	−2.21642e15	−0.0962292
$945$	−5.37538e15	−0.232025
$946$	−2.10151e16	−0.901840
$947$	2.20792e16	0.942018	0.471009	−	0.882128i	$-0.343890\pi$
$947$	2.20792e16	0.942018	0.471009	+	0.882128i	$0.343890\pi$
$948$	−1.09496e16	−0.464464
$949$	−1.35790e14	−0.00572670
$950$	1.64145e15	0.0688251
$951$	6.59913e15	0.275102
$952$	−9.96139e15	−0.412873
$953$	1.76709e15	0.0728196	0.0364098	−	0.999337i	$-0.488408\pi$
$953$	1.76709e15	0.0728196	0.0364098	+	0.999337i	$0.488408\pi$
$954$	2.03040e15	0.0831891
$955$	−2.34151e16	−0.953842
$956$	−1.90276e16	−0.770665
$957$	−3.27376e15	−0.131835
$958$	5.48954e16	2.19799
$959$	−2.53500e16	−1.00919
$960$	−2.85572e16	−1.13038
$961$	−2.53942e16	−0.999437
$962$	1.95916e14	0.00766667
$963$	2.27382e15	0.0884733
$964$	−2.43223e16	−0.940983
$965$	5.51322e16	2.12083
$966$	−3.55103e16	−1.35825
$967$	2.32514e16	0.884307	0.442153	−	0.896939i	$-0.354215\pi$
$967$	2.32514e16	0.884307	0.442153	+	0.896939i	$0.354215\pi$
$968$	7.47964e15	0.282857
$969$	1.05099e15	0.0395201
$970$	4.26568e15	0.159494
$971$	−2.77595e16	−1.03206	−0.516032	−	0.856569i	$-0.672591\pi$
$971$	−2.77595e16	−1.03206	−0.516032	+	0.856569i	$0.672591\pi$
$972$	2.10787e15	0.0779254
$973$	−2.70133e16	−0.993018
$974$	5.18218e16	1.89426
$975$	−1.33454e14	−0.00485074
$976$	−1.45712e16	−0.526649
$977$	−3.62673e16	−1.30345	−0.651727	−	0.758454i	$-0.725955\pi$
$977$	−3.62673e16	−1.30345	−0.651727	+	0.758454i	$0.725955\pi$
$978$	3.44206e16	1.23014
$979$	2.13614e15	0.0759145
$980$	−1.39498e16	−0.492973
$981$	−5.89980e15	−0.207328
$982$	−3.10778e16	−1.08602
$983$	−2.32610e16	−0.808321	−0.404160	−	0.914688i	$-0.632436\pi$
$983$	−2.32610e16	−0.808321	−0.404160	+	0.914688i	$0.632436\pi$
$984$	−6.63160e15	−0.229163
$985$	2.75277e16	0.945956
$986$	−4.48164e16	−1.53149
$987$	−5.08536e15	−0.172813
$988$	1.31125e13	0.000443120 0
$989$	−9.94352e16	−3.34165
$990$	−7.17204e15	−0.239689
$991$	−5.06166e16	−1.68224	−0.841120	−	0.540849i	$-0.818103\pi$
$991$	−5.06166e16	−1.68224	−0.841120	+	0.540849i	$0.818103\pi$
$992$	−1.01951e15	−0.0336960
$993$	1.33266e16	0.438026
$994$	5.85539e16	1.91395
$995$	7.03227e16	2.28596
$996$	1.74177e16	0.563072
$997$	−3.16497e16	−1.01753	−0.508764	−	0.860906i	$-0.669897\pi$
$997$	−3.16497e16	−1.01753	−0.508764	+	0.860906i	$0.669897\pi$
$998$	−5.83830e15	−0.186667
$999$	3.83013e15	0.121788

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.d.1.5	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.d.1.5	✓	28	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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-67.3482 q^{2} +243.000 q^{3} +2487.78 q^{4} +9961.02 q^{5} -16365.6 q^{6} -37608.5 q^{7} -29618.6 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-67.3482 q^{2} +243.000 q^{3} +2487.78 q^{4} +9961.02 q^{5} -16365.6 q^{6} -37608.5 q^{7} -29618.6 q^{8} +59049.0 q^{9} -670857. q^{10} +181051. q^{11} +604531. q^{12} -10898.1 q^{13} +2.53287e6 q^{14} +2.42053e6 q^{15} -3.10022e6 q^{16} -8.94272e6 q^{17} -3.97684e6 q^{18} -483641. q^{19} +2.47809e7 q^{20} -9.13887e6 q^{21} -1.21934e7 q^{22} -5.76947e7 q^{23} -7.19731e6 q^{24} +5.03939e7 q^{25} +733965. q^{26} +1.43489e7 q^{27} -9.35619e7 q^{28} -7.44117e7 q^{29} -1.63018e8 q^{30} -3.78363e6 q^{31} +2.69453e8 q^{32} +4.39953e7 q^{33} +6.02276e8 q^{34} -3.74620e8 q^{35} +1.46901e8 q^{36} +2.66928e8 q^{37} +3.25723e7 q^{38} -2.64823e6 q^{39} -2.95031e8 q^{40} +9.21400e8 q^{41} +6.15487e8 q^{42} +1.72347e9 q^{43} +4.50414e8 q^{44} +5.88188e8 q^{45} +3.88563e9 q^{46} +5.56453e8 q^{47} -7.53354e8 q^{48} -5.62925e8 q^{49} -3.39394e9 q^{50} -2.17308e9 q^{51} -2.71120e7 q^{52} -5.10556e8 q^{53} -9.66373e8 q^{54} +1.80345e9 q^{55} +1.11391e9 q^{56} -1.17525e8 q^{57} +5.01149e9 q^{58} +7.14924e8 q^{59} +6.02175e9 q^{60} +4.70006e9 q^{61} +2.54821e8 q^{62} -2.22075e9 q^{63} -1.17979e10 q^{64} -1.08556e8 q^{65} -2.96300e9 q^{66} +6.76322e8 q^{67} -2.22475e10 q^{68} -1.40198e10 q^{69} +2.52300e10 q^{70} +2.31176e10 q^{71} -1.74895e9 q^{72} +1.24600e10 q^{73} -1.79771e10 q^{74} +1.22457e10 q^{75} -1.20319e9 q^{76} -6.80905e9 q^{77} +1.78353e8 q^{78} -1.81125e10 q^{79} -3.08814e10 q^{80} +3.48678e9 q^{81} -6.20547e10 q^{82} +2.88119e10 q^{83} -2.27355e10 q^{84} -8.90786e10 q^{85} -1.16073e11 q^{86} -1.80820e10 q^{87} -5.36246e9 q^{88} +1.17986e10 q^{89} -3.96134e10 q^{90} +4.09860e8 q^{91} -1.43532e11 q^{92} -9.19423e8 q^{93} -3.74761e10 q^{94} -4.81756e9 q^{95} +6.54771e10 q^{96} -6.35855e9 q^{97} +3.79120e10 q^{98} +1.06909e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9} + 616281 q^{10} + 1082362 q^{11} + 7099002 q^{12} + 503712 q^{13} + 1321669 q^{14} + 6454566 q^{15} + 34870338 q^{16} + 13513579 q^{17} + 5668704 q^{18} + 35971687 q^{19} + 96105997 q^{20} + 34586919 q^{21} - 47598882 q^{22} + 61380539 q^{23} + 80756433 q^{24} + 294744746 q^{25} + 62820734 q^{26} + 401769396 q^{27} + 148068294 q^{28} + 322339307 q^{29} + 149756283 q^{30} + 151247077 q^{31} + 466383494 q^{32} + 263013966 q^{33} + 684479860 q^{34} + 960297361 q^{35} + 1725057486 q^{36} + 863508437 q^{37} + 992640509 q^{38} + 122402016 q^{39} + 3067680252 q^{40} + 3081170377 q^{41} + 321165567 q^{42} + 2554238300 q^{43} + 4350123570 q^{44} + 1568459538 q^{45} - 1987059155 q^{46} + 6203398333 q^{47} + 8473492134 q^{48} + 10327857997 q^{49} + 17577682253 q^{50} + 3283799697 q^{51} + 32137181618 q^{52} + 14571770754 q^{53} + 1377495072 q^{54} + 18251419334 q^{55} + 33498842836 q^{56} + 8741119941 q^{57} + 11860778276 q^{58} + 20017880372 q^{59} + 23353757271 q^{60} + 2761613771 q^{61} + 13785829526 q^{62} + 8404621317 q^{63} + 86547545293 q^{64} + 32034985256 q^{65} - 11566528326 q^{66} + 39381333296 q^{67} + 38995496621 q^{68} + 14915470977 q^{69} + 8551800364 q^{70} + 26130020296 q^{71} + 19623813219 q^{72} + 41382402799 q^{73} + 23815315058 q^{74} + 71622973278 q^{75} + 10611720128 q^{76} - 8426124313 q^{77} + 15265438362 q^{78} + 59825111206 q^{79} + 4009687655 q^{80} + 97629963228 q^{81} - 39592715115 q^{82} + 35433122727 q^{83} + 35980595442 q^{84} - 8950496085 q^{85} - 182032360688 q^{86} + 78328451601 q^{87} - 220003602335 q^{88} + 102303043039 q^{89} + 36390776769 q^{90} - 111146323655 q^{91} - 163000203526 q^{92} + 36753039711 q^{93} - 81314346008 q^{94} + 208102168887 q^{95} + 113331189042 q^{96} - 171891031490 q^{97} + 72304707792 q^{98} + 63912393738 q^{99}+O(q^{100}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9 + 616281 * q^10 + 1082362 * q^11 + 7099002 * q^12 + 503712 * q^13 + 1321669 * q^14 + 6454566 * q^15 + 34870338 * q^16 + 13513579 * q^17 + 5668704 * q^18 + 35971687 * q^19 + 96105997 * q^20 + 34586919 * q^21 - 47598882 * q^22 + 61380539 * q^23 + 80756433 * q^24 + 294744746 * q^25 + 62820734 * q^26 + 401769396 * q^27 + 148068294 * q^28 + 322339307 * q^29 + 149756283 * q^30 + 151247077 * q^31 + 466383494 * q^32 + 263013966 * q^33 + 684479860 * q^34 + 960297361 * q^35 + 1725057486 * q^36 + 863508437 * q^37 + 992640509 * q^38 + 122402016 * q^39 + 3067680252 * q^40 + 3081170377 * q^41 + 321165567 * q^42 + 2554238300 * q^43 + 4350123570 * q^44 + 1568459538 * q^45 - 1987059155 * q^46 + 6203398333 * q^47 + 8473492134 * q^48 + 10327857997 * q^49 + 17577682253 * q^50 + 3283799697 * q^51 + 32137181618 * q^52 + 14571770754 * q^53 + 1377495072 * q^54 + 18251419334 * q^55 + 33498842836 * q^56 + 8741119941 * q^57 + 11860778276 * q^58 + 20017880372 * q^59 + 23353757271 * q^60 + 2761613771 * q^61 + 13785829526 * q^62 + 8404621317 * q^63 + 86547545293 * q^64 + 32034985256 * q^65 - 11566528326 * q^66 + 39381333296 * q^67 + 38995496621 * q^68 + 14915470977 * q^69 + 8551800364 * q^70 + 26130020296 * q^71 + 19623813219 * q^72 + 41382402799 * q^73 + 23815315058 * q^74 + 71622973278 * q^75 + 10611720128 * q^76 - 8426124313 * q^77 + 15265438362 * q^78 + 59825111206 * q^79 + 4009687655 * q^80 + 97629963228 * q^81 - 39592715115 * q^82 + 35433122727 * q^83 + 35980595442 * q^84 - 8950496085 * q^85 - 182032360688 * q^86 + 78328451601 * q^87 - 220003602335 * q^88 + 102303043039 * q^89 + 36390776769 * q^90 - 111146323655 * q^91 - 163000203526 * q^92 + 36753039711 * q^93 - 81314346008 * q^94 + 208102168887 * q^95 + 113331189042 * q^96 - 171891031490 * q^97 + 72304707792 * q^98 + 63912393738 * q^99

Introduction

L-functions

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