LMFDB - Embedded newform 177.12.a.d.1.8

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			1.8
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)

$f(q)$	$=$	$q-40.3996 q^{2} +243.000 q^{3} -415.876 q^{4} +13699.0 q^{5} -9817.09 q^{6} +81088.1 q^{7} +99539.5 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-40.3996 q^{2} +243.000 q^{3} -415.876 q^{4} +13699.0 q^{5} -9817.09 q^{6} +81088.1 q^{7} +99539.5 q^{8} +59049.0 q^{9} -553432. q^{10} +243519. q^{11} -101058. q^{12} -2.52179e6 q^{13} -3.27592e6 q^{14} +3.32885e6 q^{15} -3.16964e6 q^{16} -6.01606e6 q^{17} -2.38555e6 q^{18} +1.38791e7 q^{19} -5.69706e6 q^{20} +1.97044e7 q^{21} -9.83808e6 q^{22} +3.48489e7 q^{23} +2.41881e7 q^{24} +1.38833e8 q^{25} +1.01879e8 q^{26} +1.43489e7 q^{27} -3.37226e7 q^{28} +6.14157e7 q^{29} -1.34484e8 q^{30} -3.78178e7 q^{31} -7.58049e7 q^{32} +5.91752e7 q^{33} +2.43046e8 q^{34} +1.11082e9 q^{35} -2.45570e7 q^{36} -1.90765e7 q^{37} -5.60708e8 q^{38} -6.12796e8 q^{39} +1.36359e9 q^{40} +6.76940e8 q^{41} -7.96049e8 q^{42} -2.86835e8 q^{43} -1.01274e8 q^{44} +8.08910e8 q^{45} -1.40788e9 q^{46} -2.03944e9 q^{47} -7.70222e8 q^{48} +4.59795e9 q^{49} -5.60881e9 q^{50} -1.46190e9 q^{51} +1.04875e9 q^{52} -1.43758e9 q^{53} -5.79690e8 q^{54} +3.33596e9 q^{55} +8.07146e9 q^{56} +3.37261e9 q^{57} -2.48117e9 q^{58} +7.14924e8 q^{59} -1.38439e9 q^{60} -5.11606e9 q^{61} +1.52782e9 q^{62} +4.78817e9 q^{63} +9.55390e9 q^{64} -3.45460e10 q^{65} -2.39065e9 q^{66} +1.62352e10 q^{67} +2.50193e9 q^{68} +8.46828e9 q^{69} -4.48767e10 q^{70} -1.34058e10 q^{71} +5.87771e9 q^{72} +1.98131e10 q^{73} +7.70681e8 q^{74} +3.37365e10 q^{75} -5.77196e9 q^{76} +1.97465e10 q^{77} +2.47567e10 q^{78} +3.88114e10 q^{79} -4.34207e10 q^{80} +3.48678e9 q^{81} -2.73481e10 q^{82} +8.01748e9 q^{83} -8.19458e9 q^{84} -8.24138e10 q^{85} +1.15880e10 q^{86} +1.49240e10 q^{87} +2.42398e10 q^{88} -5.58096e10 q^{89} -3.26796e10 q^{90} -2.04487e11 q^{91} -1.44928e10 q^{92} -9.18972e9 q^{93} +8.23925e10 q^{94} +1.90129e11 q^{95} -1.84206e10 q^{96} +6.19919e10 q^{97} -1.85755e11 q^{98} +1.43796e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−40.3996	−0.892713	−0.446356	−	0.894855i	$-0.647279\pi$
$2$	−40.3996	−0.892713	−0.446356	+	0.894855i	$0.647279\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	−415.876	−0.203064
$5$	13699.0	1.96044	0.980218	−	0.197922i	$-0.0634193\pi$
$5$	13699.0	1.96044	0.980218	+	0.197922i	$0.0634193\pi$
$6$	−9817.09	−0.515408
$7$	81088.1	1.82355	0.911775	−	0.410690i	$-0.134712\pi$
$7$	81088.1	1.82355	0.911775	+	0.410690i	$0.134712\pi$
$8$	99539.5	1.07399
$9$	59049.0	0.333333
$10$	−553432.	−1.75011
$11$	243519.	0.455904	0.227952	−	0.973672i	$-0.426797\pi$
$11$	243519.	0.455904	0.227952	+	0.973672i	$0.426797\pi$
$12$	−101058.	−0.117239
$13$	−2.52179e6	−1.88374	−0.941870	−	0.335976i	$-0.890934\pi$
$13$	−2.52179e6	−1.88374	−0.941870	+	0.335976i	$0.890934\pi$
$14$	−3.27592e6	−1.62791
$15$	3.32885e6	1.13186
$16$	−3.16964e6	−0.755701
$17$	−6.01606e6	−1.02765	−0.513823	−	0.857896i	$-0.671771\pi$
$17$	−6.01606e6	−1.02765	−0.513823	+	0.857896i	$0.671771\pi$
$18$	−2.38555e6	−0.297571
$19$	1.38791e7	1.28592	0.642962	−	0.765898i	$-0.277705\pi$
$19$	1.38791e7	1.28592	0.642962	+	0.765898i	$0.277705\pi$
$20$	−5.69706e6	−0.398094
$21$	1.97044e7	1.05283
$22$	−9.83808e6	−0.406992
$23$	3.48489e7	1.12898	0.564490	−	0.825440i	$-0.309073\pi$
$23$	3.48489e7	1.12898	0.564490	+	0.825440i	$0.309073\pi$
$24$	2.41881e7	0.620069
$25$	1.38833e8	2.84331
$26$	1.01879e8	1.68164
$27$	1.43489e7	0.192450
$28$	−3.37226e7	−0.370298
$29$	6.14157e7	0.556020	0.278010	−	0.960578i	$-0.410325\pi$
$29$	6.14157e7	0.556020	0.278010	+	0.960578i	$0.410325\pi$
$30$	−1.34484e8	−1.01042
$31$	−3.78178e7	−0.237250	−0.118625	−	0.992939i	$-0.537849\pi$
$31$	−3.78178e7	−0.237250	−0.118625	+	0.992939i	$0.537849\pi$
$32$	−7.58049e7	−0.399367
$33$	5.91752e7	0.263217
$34$	2.43046e8	0.917392
$35$	1.11082e9	3.57495
$36$	−2.45570e7	−0.0676881
$37$	−1.90765e7	−0.0452260	−0.0226130	−	0.999744i	$-0.507199\pi$
$37$	−1.90765e7	−0.0452260	−0.0226130	+	0.999744i	$0.507199\pi$
$38$	−5.60708e8	−1.14796
$39$	−6.12796e8	−1.08758
$40$	1.36359e9	2.10549
$41$	6.76940e8	0.912513	0.456257	−	0.889848i	$-0.349190\pi$
$41$	6.76940e8	0.912513	0.456257	+	0.889848i	$0.349190\pi$
$42$	−7.96049e8	−0.939872
$43$	−2.86835e8	−0.297547	−0.148774	−	0.988871i	$-0.547533\pi$
$43$	−2.86835e8	−0.297547	−0.148774	+	0.988871i	$0.547533\pi$
$44$	−1.01274e8	−0.0925779
$45$	8.08910e8	0.653478
$46$	−1.40788e9	−1.00785
$47$	−2.03944e9	−1.29710	−0.648549	−	0.761173i	$-0.724624\pi$
$47$	−2.03944e9	−1.29710	−0.648549	+	0.761173i	$0.724624\pi$
$48$	−7.70222e8	−0.436304
$49$	4.59795e9	2.32533
$50$	−5.60881e9	−2.53826
$51$	−1.46190e9	−0.593311
$52$	1.04875e9	0.382520
$53$	−1.43758e9	−0.472186	−0.236093	−	0.971730i	$-0.575867\pi$
$53$	−1.43758e9	−0.472186	−0.236093	+	0.971730i	$0.575867\pi$
$54$	−5.79690e8	−0.171803
$55$	3.33596e9	0.893771
$56$	8.07146e9	1.95848
$57$	3.37261e9	0.742429
$58$	−2.48117e9	−0.496366
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	−1.38439e9	−0.229840
$61$	−5.11606e9	−0.775571	−0.387785	−	0.921750i	$-0.626760\pi$
$61$	−5.11606e9	−0.775571	−0.387785	+	0.921750i	$0.626760\pi$
$62$	1.52782e9	0.211796
$63$	4.78817e9	0.607850
$64$	9.55390e9	1.11222
$65$	−3.45460e10	−3.69295
$66$	−2.39065e9	−0.234977
$67$	1.62352e10	1.46909	0.734543	−	0.678562i	$-0.237397\pi$
$67$	1.62352e10	1.46909	0.734543	+	0.678562i	$0.237397\pi$
$68$	2.50193e9	0.208678
$69$	8.46828e9	0.651817
$70$	−4.48767e10	−3.19140
$71$	−1.34058e10	−0.881801	−0.440901	−	0.897556i	$-0.645341\pi$
$71$	−1.34058e10	−0.881801	−0.440901	+	0.897556i	$0.645341\pi$
$72$	5.87771e9	0.357997
$73$	1.98131e10	1.11860	0.559302	−	0.828964i	$-0.311069\pi$
$73$	1.98131e10	1.11860	0.559302	+	0.828964i	$0.311069\pi$
$74$	7.70681e8	0.0403738
$75$	3.37365e10	1.64158
$76$	−5.77196e9	−0.261125
$77$	1.97465e10	0.831365
$78$	2.47567e10	0.970895
$79$	3.88114e10	1.41909	0.709546	−	0.704659i	$-0.248900\pi$
$79$	3.88114e10	1.41909	0.709546	+	0.704659i	$0.248900\pi$
$80$	−4.34207e10	−1.48150
$81$	3.48678e9	0.111111
$82$	−2.73481e10	−0.814612
$83$	8.01748e9	0.223413	0.111706	−	0.993741i	$-0.464368\pi$
$83$	8.01748e9	0.223413	0.111706	+	0.993741i	$0.464368\pi$
$84$	−8.19458e9	−0.213792
$85$	−8.24138e10	−2.01463
$86$	1.15880e10	0.265624
$87$	1.49240e10	0.321018
$88$	2.42398e10	0.489637
$89$	−5.58096e10	−1.05941	−0.529705	−	0.848182i	$-0.677697\pi$
$89$	−5.58096e10	−1.05941	−0.529705	+	0.848182i	$0.677697\pi$
$90$	−3.26796e10	−0.583368
$91$	−2.04487e11	−3.43510
$92$	−1.44928e10	−0.229255
$93$	−9.18972e9	−0.136976
$94$	8.23925e10	1.15794
$95$	1.90129e11	2.52097
$96$	−1.84206e10	−0.230575
$97$	6.19919e10	0.732978	0.366489	−	0.930422i	$-0.380560\pi$
$97$	6.19919e10	0.732978	0.366489	+	0.930422i	$0.380560\pi$
$98$	−1.85755e11	−2.07586
$99$	1.43796e10	0.151968
$100$	−5.77374e10	−0.577374
$101$	9.69644e10	0.918004	0.459002	−	0.888435i	$-0.348207\pi$
$101$	9.69644e10	0.918004	0.459002	+	0.888435i	$0.348207\pi$
$102$	5.90602e10	0.529656
$103$	−5.00427e10	−0.425340	−0.212670	−	0.977124i	$-0.568216\pi$
$103$	−5.00427e10	−0.425340	−0.212670	+	0.977124i	$0.568216\pi$
$104$	−2.51018e11	−2.02312
$105$	2.69930e11	2.06400
$106$	5.80774e10	0.421527
$107$	2.73516e10	0.188526	0.0942630	−	0.995547i	$-0.469951\pi$
$107$	2.73516e10	0.188526	0.0942630	+	0.995547i	$0.469951\pi$
$108$	−5.96736e9	−0.0390797
$109$	−1.07991e11	−0.672270	−0.336135	−	0.941814i	$-0.609120\pi$
$109$	−1.07991e11	−0.672270	−0.336135	+	0.941814i	$0.609120\pi$
$110$	−1.34771e11	−0.797881
$111$	−4.63558e9	−0.0261113
$112$	−2.57020e11	−1.37806
$113$	2.16520e11	1.10552	0.552759	−	0.833341i	$-0.313575\pi$
$113$	2.16520e11	1.10552	0.552759	+	0.833341i	$0.313575\pi$
$114$	−1.36252e11	−0.662775
$115$	4.77394e11	2.21329
$116$	−2.55413e10	−0.112908
$117$	−1.48909e11	−0.627914
$118$	−2.88826e10	−0.116221
$119$	−4.87831e11	−1.87396
$120$	3.31352e11	1.21560
$121$	−2.26010e11	−0.792151
$122$	2.06687e11	0.692362
$123$	1.64496e11	0.526840
$124$	1.57275e10	0.0481770
$125$	1.23298e12	3.61369
$126$	−1.93440e11	−0.542635
$127$	−4.06073e10	−0.109065	−0.0545323	−	0.998512i	$-0.517367\pi$
$127$	−4.06073e10	−0.109065	−0.0545323	+	0.998512i	$0.517367\pi$
$128$	−2.30725e11	−0.593526
$129$	−6.97009e10	−0.171789
$130$	1.39564e12	3.29674
$131$	−5.09433e11	−1.15371	−0.576853	−	0.816848i	$-0.695719\pi$
$131$	−5.09433e11	−1.15371	−0.576853	+	0.816848i	$0.695719\pi$
$132$	−2.46095e10	−0.0534499
$133$	1.12543e12	2.34495
$134$	−6.55896e11	−1.31147
$135$	1.96565e11	0.377286
$136$	−5.98836e11	−1.10368
$137$	−5.93432e11	−1.05053	−0.525264	−	0.850939i	$-0.676034\pi$
$137$	−5.93432e11	−1.05053	−0.525264	+	0.850939i	$0.676034\pi$
$138$	−3.42115e11	−0.581885
$139$	−6.07937e11	−0.993751	−0.496875	−	0.867822i	$-0.665519\pi$
$139$	−6.07937e11	−0.993751	−0.496875	+	0.867822i	$0.665519\pi$
$140$	−4.61964e11	−0.725945
$141$	−4.95584e11	−0.748880
$142$	5.41587e11	0.787195
$143$	−6.14106e11	−0.858806
$144$	−1.87164e11	−0.251900
$145$	8.41331e11	1.09004
$146$	−8.00440e11	−0.998592
$147$	1.11730e12	1.34253
$148$	7.93344e9	0.00918379
$149$	−3.40159e9	−0.00379452	−0.00189726	−	0.999998i	$-0.500604\pi$
$149$	−3.40159e9	−0.00379452	−0.00189726	+	0.999998i	$0.500604\pi$
$150$	−1.36294e12	−1.46546
$151$	−1.30730e10	−0.0135520	−0.00677598	−	0.999977i	$-0.502157\pi$
$151$	−1.30730e10	−0.0135520	−0.00677598	+	0.999977i	$0.502157\pi$
$152$	1.38151e12	1.38107
$153$	−3.55242e11	−0.342548
$154$	−7.97751e11	−0.742170
$155$	−5.18064e11	−0.465114
$156$	2.54847e11	0.220848
$157$	−2.11552e12	−1.76999	−0.884993	−	0.465605i	$-0.845837\pi$
$157$	−2.11552e12	−1.76999	−0.884993	+	0.465605i	$0.845837\pi$
$158$	−1.56797e12	−1.26684
$159$	−3.49331e11	−0.272617
$160$	−1.03845e12	−0.782934
$161$	2.82583e12	2.05875
$162$	−1.40865e11	−0.0991903
$163$	1.09655e12	0.746443	0.373222	−	0.927742i	$-0.378253\pi$
$163$	1.09655e12	0.746443	0.373222	+	0.927742i	$0.378253\pi$
$164$	−2.81523e11	−0.185299
$165$	8.10639e11	0.516019
$166$	−3.23903e11	−0.199444
$167$	5.82427e11	0.346977	0.173488	−	0.984836i	$-0.444496\pi$
$167$	5.82427e11	0.346977	0.173488	+	0.984836i	$0.444496\pi$
$168$	1.96137e12	1.13073
$169$	4.56728e12	2.54848
$170$	3.32948e12	1.79849
$171$	8.19545e11	0.428641
$172$	1.19288e11	0.0604212
$173$	−1.73135e12	−0.849438	−0.424719	−	0.905325i	$-0.639627\pi$
$173$	−1.73135e12	−0.849438	−0.424719	+	0.905325i	$0.639627\pi$
$174$	−6.02923e11	−0.286577
$175$	1.12577e13	5.18491
$176$	−7.71868e11	−0.344527
$177$	1.73727e11	0.0751646
$178$	2.25468e12	0.945749
$179$	1.76913e12	0.719563	0.359781	−	0.933037i	$-0.382851\pi$
$179$	1.76913e12	0.719563	0.359781	+	0.933037i	$0.382851\pi$
$180$	−3.36406e11	−0.132698
$181$	4.22975e12	1.61839	0.809194	−	0.587541i	$-0.199904\pi$
$181$	4.22975e12	1.61839	0.809194	+	0.587541i	$0.199904\pi$
$182$	8.26120e12	3.06655
$183$	−1.24320e12	−0.447776
$184$	3.46884e12	1.21251
$185$	−2.61328e11	−0.0886627
$186$	3.71260e11	0.122281
$187$	−1.46503e12	−0.468508
$188$	8.48154e11	0.263394
$189$	1.16352e12	0.350942
$190$	−7.68112e12	−2.25050
$191$	1.64378e12	0.467906	0.233953	−	0.972248i	$-0.424834\pi$
$191$	1.64378e12	0.467906	0.233953	+	0.972248i	$0.424834\pi$
$192$	2.32160e12	0.642141
$193$	−9.12185e11	−0.245198	−0.122599	−	0.992456i	$-0.539123\pi$
$193$	−9.12185e11	−0.245198	−0.122599	+	0.992456i	$0.539123\pi$
$194$	−2.50445e12	−0.654338
$195$	−8.39467e12	−2.13213
$196$	−1.91217e12	−0.472192
$197$	5.60318e12	1.34546	0.672729	−	0.739889i	$-0.265122\pi$
$197$	5.60318e12	1.34546	0.672729	+	0.739889i	$0.265122\pi$
$198$	−5.80929e11	−0.135664
$199$	−6.58348e12	−1.49542	−0.747710	−	0.664025i	$-0.768847\pi$
$199$	−6.58348e12	−1.49542	−0.747710	+	0.664025i	$0.768847\pi$
$200$	1.38194e13	3.05369
$201$	3.94516e12	0.848177
$202$	−3.91732e12	−0.819514
$203$	4.98008e12	1.01393
$204$	6.07970e11	0.120480
$205$	9.27338e12	1.78892
$206$	2.02170e12	0.379706
$207$	2.05779e12	0.376326
$208$	7.99317e12	1.42354
$209$	3.37982e12	0.586259
$210$	−1.09050e13	−1.84256
$211$	−5.28623e12	−0.870146	−0.435073	−	0.900395i	$-0.643277\pi$
$211$	−5.28623e12	−0.870146	−0.435073	+	0.900395i	$0.643277\pi$
$212$	5.97853e11	0.0958842
$213$	−3.25760e12	−0.509108
$214$	−1.10499e12	−0.168300
$215$	−3.92934e12	−0.583322
$216$	1.42828e12	0.206690
$217$	−3.06657e12	−0.432637
$218$	4.36281e12	0.600144
$219$	4.81458e12	0.645826
$220$	−1.38735e12	−0.181493
$221$	1.51713e13	1.93582
$222$	1.87275e11	0.0233098
$223$	−1.45141e11	−0.0176244	−0.00881219	−	0.999961i	$-0.502805\pi$
$223$	−1.45141e11	−0.0176244	−0.00881219	+	0.999961i	$0.502805\pi$
$224$	−6.14687e12	−0.728266
$225$	8.19797e12	0.947769
$226$	−8.74729e12	−0.986909
$227$	−6.12191e11	−0.0674131	−0.0337066	−	0.999432i	$-0.510731\pi$
$227$	−6.12191e11	−0.0674131	−0.0337066	+	0.999432i	$0.510731\pi$
$228$	−1.40259e12	−0.150761
$229$	−1.04956e13	−1.10131	−0.550656	−	0.834732i	$-0.685622\pi$
$229$	−1.04956e13	−1.10131	−0.550656	+	0.834732i	$0.685622\pi$
$230$	−1.92865e13	−1.97583
$231$	4.79840e12	0.479989
$232$	6.11329e12	0.597160
$233$	1.51599e13	1.44624	0.723120	−	0.690723i	$-0.242707\pi$
$233$	1.51599e13	1.44624	0.723120	+	0.690723i	$0.242707\pi$
$234$	6.01587e12	0.560546
$235$	−2.79382e13	−2.54288
$236$	−2.97320e11	−0.0264367
$237$	9.43118e12	0.819314
$238$	1.97081e13	1.67291
$239$	−1.63433e13	−1.35567	−0.677833	−	0.735216i	$-0.737081\pi$
$239$	−1.63433e13	−1.35567	−0.677833	+	0.735216i	$0.737081\pi$
$240$	−1.05512e13	−0.855346
$241$	−1.46376e13	−1.15978	−0.579892	−	0.814694i	$-0.696905\pi$
$241$	−1.46376e13	−1.15978	−0.579892	+	0.814694i	$0.696905\pi$
$242$	9.13070e12	0.707163
$243$	8.47289e11	0.0641500
$244$	2.12764e12	0.157491
$245$	6.29871e13	4.55867
$246$	−6.64558e12	−0.470316
$247$	−3.50001e13	−2.42235
$248$	−3.76436e12	−0.254804
$249$	1.94825e12	0.128988
$250$	−4.98118e13	−3.22598
$251$	−1.96061e13	−1.24218	−0.621091	−	0.783739i	$-0.713310\pi$
$251$	−1.96061e13	−1.24218	−0.621091	+	0.783739i	$0.713310\pi$
$252$	−1.99128e12	−0.123433
$253$	8.48639e12	0.514707
$254$	1.64052e12	0.0973633
$255$	−2.00265e13	−1.16315
$256$	−1.02452e13	−0.582372
$257$	−5.08443e12	−0.282885	−0.141443	−	0.989946i	$-0.545174\pi$
$257$	−5.08443e12	−0.282885	−0.141443	+	0.989946i	$0.545174\pi$
$258$	2.81589e12	0.153358
$259$	−1.54687e12	−0.0824719
$260$	1.43668e13	0.749907
$261$	3.62653e12	0.185340
$262$	2.05809e13	1.02993
$263$	−3.25812e13	−1.59665	−0.798326	−	0.602226i	$-0.794281\pi$
$263$	−3.25812e13	−1.59665	−0.798326	+	0.602226i	$0.794281\pi$
$264$	5.89027e12	0.282692
$265$	−1.96933e13	−0.925691
$266$	−4.54667e13	−2.09336
$267$	−1.35617e13	−0.611651
$268$	−6.75184e12	−0.298319
$269$	1.22091e13	0.528503	0.264251	−	0.964454i	$-0.414875\pi$
$269$	1.22091e13	0.528503	0.264251	+	0.964454i	$0.414875\pi$
$270$	−7.94114e12	−0.336808
$271$	4.35296e13	1.80906	0.904531	−	0.426407i	$-0.140221\pi$
$271$	4.35296e13	1.80906	0.904531	+	0.426407i	$0.140221\pi$
$272$	1.90687e13	0.776592
$273$	−4.96904e13	−1.98325
$274$	2.39744e13	0.937820
$275$	3.38086e13	1.29628
$276$	−3.52175e12	−0.132361
$277$	8.69092e12	0.320204	0.160102	−	0.987100i	$-0.448818\pi$
$277$	8.69092e12	0.320204	0.160102	+	0.987100i	$0.448818\pi$
$278$	2.45604e13	0.887134
$279$	−2.23310e12	−0.0790834
$280$	1.10571e14	3.83946
$281$	1.49019e13	0.507407	0.253704	−	0.967282i	$-0.418351\pi$
$281$	1.49019e13	0.507407	0.253704	+	0.967282i	$0.418351\pi$
$282$	2.00214e13	0.668535
$283$	−1.55611e13	−0.509584	−0.254792	−	0.966996i	$-0.582007\pi$
$283$	−1.55611e13	−0.509584	−0.254792	+	0.966996i	$0.582007\pi$
$284$	5.57513e12	0.179062
$285$	4.62013e13	1.45548
$286$	2.48096e13	0.766667
$287$	5.48918e13	1.66401
$288$	−4.47620e12	−0.133122
$289$	1.92110e12	0.0560548
$290$	−3.39894e13	−0.973093
$291$	1.50640e13	0.423185
$292$	−8.23978e12	−0.227149
$293$	3.73651e13	1.01087	0.505434	−	0.862865i	$-0.331333\pi$
$293$	3.73651e13	1.01087	0.505434	+	0.862865i	$0.331333\pi$
$294$	−4.51385e13	−1.19850
$295$	9.79372e12	0.255227
$296$	−1.89886e12	−0.0485723
$297$	3.49424e12	0.0877389
$298$	1.37423e11	0.00338742
$299$	−8.78817e13	−2.12670
$300$	−1.40302e13	−0.333347
$301$	−2.32589e13	−0.542592
$302$	5.28144e11	0.0120980
$303$	2.35623e13	0.530010
$304$	−4.39916e13	−0.971774
$305$	−7.00847e13	−1.52046
$306$	1.43516e13	0.305797
$307$	5.48864e13	1.14869	0.574346	−	0.818613i	$-0.305256\pi$
$307$	5.48864e13	1.14869	0.574346	+	0.818613i	$0.305256\pi$
$308$	−8.21210e12	−0.168820
$309$	−1.21604e13	−0.245570
$310$	2.09296e13	0.415213
$311$	−2.07281e13	−0.403997	−0.201998	−	0.979386i	$-0.564744\pi$
$311$	−2.07281e13	−0.403997	−0.201998	+	0.979386i	$0.564744\pi$
$312$	−6.09974e13	−1.16805
$313$	−1.47776e13	−0.278042	−0.139021	−	0.990289i	$-0.544396\pi$
$313$	−1.47776e13	−0.278042	−0.139021	+	0.990289i	$0.544396\pi$
$314$	8.54662e13	1.58009
$315$	6.55929e13	1.19165
$316$	−1.61407e13	−0.288167
$317$	6.52417e13	1.14472	0.572360	−	0.820002i	$-0.306028\pi$
$317$	6.52417e13	1.14472	0.572360	+	0.820002i	$0.306028\pi$
$318$	1.41128e13	0.243369
$319$	1.49559e13	0.253492
$320$	1.30879e14	2.18044
$321$	6.64643e12	0.108846
$322$	−1.14162e14	−1.83787
$323$	−8.34973e13	−1.32147
$324$	−1.45007e12	−0.0225627
$325$	−3.50109e14	−5.35605
$326$	−4.43002e13	−0.666359
$327$	−2.62419e13	−0.388135
$328$	6.73823e13	0.980030
$329$	−1.65374e14	−2.36532
$330$	−3.27495e13	−0.460657
$331$	3.77281e13	0.521928	0.260964	−	0.965348i	$-0.415960\pi$
$331$	3.77281e13	0.521928	0.260964	+	0.965348i	$0.415960\pi$
$332$	−3.33428e12	−0.0453672
$333$	−1.12645e12	−0.0150753
$334$	−2.35298e13	−0.309751
$335$	2.22406e14	2.88005
$336$	−6.24558e13	−0.795622
$337$	−1.04357e14	−1.30784	−0.653922	−	0.756562i	$-0.726877\pi$
$337$	−1.04357e14	−1.30784	−0.653922	+	0.756562i	$0.726877\pi$
$338$	−1.84516e14	−2.27506
$339$	5.26142e13	0.638271
$340$	3.42739e13	0.409100
$341$	−9.20936e12	−0.108163
$342$	−3.31092e13	−0.382654
$343$	2.12501e14	2.41681
$344$	−2.85514e13	−0.319563
$345$	1.16007e14	1.27784
$346$	6.99458e13	0.758304
$347$	−4.74108e13	−0.505901	−0.252950	−	0.967479i	$-0.581401\pi$
$347$	−4.74108e13	−0.505901	−0.252950	+	0.967479i	$0.581401\pi$
$348$	−6.20653e12	−0.0651873
$349$	1.29110e14	1.33481	0.667406	−	0.744694i	$-0.267405\pi$
$349$	1.29110e14	1.33481	0.667406	+	0.744694i	$0.267405\pi$
$350$	−4.54807e14	−4.62864
$351$	−3.61850e13	−0.362526
$352$	−1.84600e13	−0.182073
$353$	1.30632e14	1.26849	0.634246	−	0.773132i	$-0.281311\pi$
$353$	1.30632e14	1.26849	0.634246	+	0.773132i	$0.281311\pi$
$354$	−7.01848e12	−0.0671004
$355$	−1.83645e14	−1.72871
$356$	2.32099e13	0.215128
$357$	−1.18543e14	−1.08193
$358$	−7.14722e13	−0.642363
$359$	8.73656e13	0.773252	0.386626	−	0.922237i	$-0.373640\pi$
$359$	8.73656e13	0.773252	0.386626	+	0.922237i	$0.373640\pi$
$360$	8.05185e13	0.701830
$361$	7.61381e13	0.653601
$362$	−1.70880e14	−1.44476
$363$	−5.49204e13	−0.457349
$364$	8.50413e13	0.697545
$365$	2.71419e14	2.19295
$366$	5.02248e13	0.399735
$367$	−7.59876e13	−0.595771	−0.297886	−	0.954602i	$-0.596281\pi$
$367$	−7.59876e13	−0.595771	−0.297886	+	0.954602i	$0.596281\pi$
$368$	−1.10458e14	−0.853170
$369$	3.99726e13	0.304171
$370$	1.05575e13	0.0791503
$371$	−1.16570e14	−0.861056
$372$	3.82178e12	0.0278150
$373$	1.89148e14	1.35645	0.678225	−	0.734854i	$-0.262749\pi$
$373$	1.89148e14	1.35645	0.678225	+	0.734854i	$0.262749\pi$
$374$	5.91865e13	0.418243
$375$	2.99614e14	2.08636
$376$	−2.03005e14	−1.39307
$377$	−1.54878e14	−1.04740
$378$	−4.70059e13	−0.313291
$379$	−2.08609e14	−1.37031	−0.685153	−	0.728399i	$-0.740265\pi$
$379$	−2.08609e14	−1.37031	−0.685153	+	0.728399i	$0.740265\pi$
$380$	−7.90699e13	−0.511919
$381$	−9.86757e12	−0.0629684
$382$	−6.64078e13	−0.417706
$383$	9.82899e13	0.609418	0.304709	−	0.952445i	$-0.401441\pi$
$383$	9.82899e13	0.609418	0.304709	+	0.952445i	$0.401441\pi$
$384$	−5.60662e13	−0.342672
$385$	2.70507e14	1.62984
$386$	3.68519e13	0.218892
$387$	−1.69373e13	−0.0991823
$388$	−2.57809e13	−0.148842
$389$	2.48814e14	1.41629	0.708145	−	0.706067i	$-0.249532\pi$
$389$	2.48814e14	1.41629	0.708145	+	0.706067i	$0.249532\pi$
$390$	3.39141e14	1.90338
$391$	−2.09653e14	−1.16019
$392$	4.57677e14	2.49739
$393$	−1.23792e14	−0.666092
$394$	−2.26366e14	−1.20111
$395$	5.31676e14	2.78204
$396$	−5.98012e12	−0.0308593
$397$	−2.14738e14	−1.09285	−0.546424	−	0.837508i	$-0.684011\pi$
$397$	−2.14738e14	−1.09285	−0.546424	+	0.837508i	$0.684011\pi$
$398$	2.65969e14	1.33498
$399$	2.73479e14	1.35386
$400$	−4.40052e14	−2.14869
$401$	3.08242e14	1.48456	0.742280	−	0.670090i	$-0.233745\pi$
$401$	3.08242e14	1.48456	0.742280	+	0.670090i	$0.233745\pi$
$402$	−1.59383e14	−0.757178
$403$	9.53686e13	0.446918
$404$	−4.03251e13	−0.186414
$405$	4.77653e13	0.217826
$406$	−2.01193e14	−0.905148
$407$	−4.64549e12	−0.0206187
$408$	−1.45517e14	−0.637211
$409$	1.12336e14	0.485335	0.242668	−	0.970110i	$-0.421978\pi$
$409$	1.12336e14	0.485335	0.242668	+	0.970110i	$0.421978\pi$
$410$	−3.74640e14	−1.59699
$411$	−1.44204e14	−0.606523
$412$	2.08116e13	0.0863714
$413$	5.79718e13	0.237406
$414$	−8.31339e13	−0.335951
$415$	1.09831e14	0.437987
$416$	1.91164e14	0.752304
$417$	−1.47729e14	−0.573742
$418$	−1.36543e14	−0.523360
$419$	−2.45661e14	−0.929307	−0.464653	−	0.885493i	$-0.653821\pi$
$419$	−2.45661e14	−0.929307	−0.464653	+	0.885493i	$0.653821\pi$
$420$	−1.12257e14	−0.419125
$421$	−1.51149e14	−0.556998	−0.278499	−	0.960437i	$-0.589837\pi$
$421$	−1.51149e14	−0.556998	−0.278499	+	0.960437i	$0.589837\pi$
$422$	2.13561e14	0.776790
$423$	−1.20427e14	−0.432366
$424$	−1.43096e14	−0.507124
$425$	−8.35230e14	−2.92191
$426$	1.31606e14	0.454487
$427$	−4.14851e14	−1.41429
$428$	−1.13749e13	−0.0382829
$429$	−1.49228e14	−0.495832
$430$	1.58744e14	0.520739
$431$	2.50477e14	0.811227	0.405614	−	0.914045i	$-0.367058\pi$
$431$	2.50477e14	0.811227	0.405614	+	0.914045i	$0.367058\pi$
$432$	−4.54808e13	−0.145435
$433$	−2.39225e14	−0.755306	−0.377653	−	0.925947i	$-0.623269\pi$
$433$	−2.39225e14	−0.755306	−0.377653	+	0.925947i	$0.623269\pi$
$434$	1.23888e14	0.386221
$435$	2.04443e14	0.629336
$436$	4.49110e13	0.136514
$437$	4.83670e14	1.45178
$438$	−1.94507e14	−0.576537
$439$	1.61931e14	0.473997	0.236999	−	0.971510i	$-0.423836\pi$
$439$	1.61931e14	0.473997	0.236999	+	0.971510i	$0.423836\pi$
$440$	3.32060e14	0.959902
$441$	2.71504e14	0.775112
$442$	−6.12912e14	−1.72813
$443$	4.08945e14	1.13879	0.569396	−	0.822063i	$-0.307177\pi$
$443$	4.08945e14	1.13879	0.569396	+	0.822063i	$0.307177\pi$
$444$	1.92783e12	0.00530226
$445$	−7.64534e14	−2.07691
$446$	5.86364e12	0.0157335
$447$	−8.26585e11	−0.00219077
$448$	7.74707e14	2.02819
$449$	−3.70093e13	−0.0957098	−0.0478549	−	0.998854i	$-0.515239\pi$
$449$	−3.70093e13	−0.0957098	−0.0478549	+	0.998854i	$0.515239\pi$
$450$	−3.31194e14	−0.846085
$451$	1.64848e14	0.416019
$452$	−9.00452e13	−0.224491
$453$	−3.17674e12	−0.00782423
$454$	2.47322e13	0.0601805
$455$	−2.80126e15	−6.73428
$456$	3.35708e14	0.797361
$457$	−4.04975e14	−0.950362	−0.475181	−	0.879888i	$-0.657617\pi$
$457$	−4.04975e14	−0.950362	−0.475181	+	0.879888i	$0.657617\pi$
$458$	4.24016e14	0.983155
$459$	−8.63239e13	−0.197770
$460$	−1.98536e14	−0.449440
$461$	4.27921e14	0.957212	0.478606	−	0.878030i	$-0.341142\pi$
$461$	4.27921e14	0.957212	0.478606	+	0.878030i	$0.341142\pi$
$462$	−1.93853e14	−0.428492
$463$	−3.91795e14	−0.855783	−0.427892	−	0.903830i	$-0.640743\pi$
$463$	−3.91795e14	−0.855783	−0.427892	+	0.903830i	$0.640743\pi$
$464$	−1.94665e14	−0.420185
$465$	−1.25890e14	−0.268533
$466$	−6.12455e14	−1.29108
$467$	1.59037e14	0.331326	0.165663	−	0.986182i	$-0.447024\pi$
$467$	1.59037e14	0.331326	0.165663	+	0.986182i	$0.447024\pi$
$468$	6.19278e13	0.127507
$469$	1.31648e15	2.67895
$470$	1.12869e15	2.27006
$471$	−5.14072e14	−1.02190
$472$	7.11632e13	0.139822
$473$	−6.98499e13	−0.135653
$474$	−3.81016e14	−0.731411
$475$	1.92688e15	3.65628
$476$	2.02877e14	0.380535
$477$	−8.48874e13	−0.157395
$478$	6.60264e14	1.21022
$479$	−2.13649e14	−0.387128	−0.193564	−	0.981088i	$-0.562005\pi$
$479$	−2.13649e14	−0.387128	−0.193564	+	0.981088i	$0.562005\pi$
$480$	−2.52343e14	−0.452027
$481$	4.81069e13	0.0851941
$482$	5.91354e14	1.03535
$483$	6.86677e14	1.18862
$484$	9.39920e13	0.160858
$485$	8.49225e14	1.43696
$486$	−3.42301e13	−0.0572675
$487$	2.97727e14	0.492504	0.246252	−	0.969206i	$-0.420801\pi$
$487$	2.97727e14	0.492504	0.246252	+	0.969206i	$0.420801\pi$
$488$	−5.09250e14	−0.832956
$489$	2.66462e14	0.430959
$490$	−2.54465e15	−4.06958
$491$	−7.38058e14	−1.16719	−0.583596	−	0.812044i	$-0.698355\pi$
$491$	−7.38058e14	−1.16719	−0.583596	+	0.812044i	$0.698355\pi$
$492$	−6.84101e13	−0.106982
$493$	−3.69481e14	−0.571391
$494$	1.41399e15	2.16246
$495$	1.96985e14	0.297924
$496$	1.19869e14	0.179290
$497$	−1.08705e15	−1.60801
$498$	−7.87084e13	−0.115149
$499$	−6.14412e14	−0.889010	−0.444505	−	0.895776i	$-0.646620\pi$
$499$	−6.14412e14	−0.889010	−0.444505	+	0.895776i	$0.646620\pi$
$500$	−5.12766e14	−0.733810
$501$	1.41530e14	0.200327
$502$	7.92076e14	1.10891
$503$	6.02635e14	0.834508	0.417254	−	0.908790i	$-0.362993\pi$
$503$	6.02635e14	0.834508	0.417254	+	0.908790i	$0.362993\pi$
$504$	4.76612e14	0.652825
$505$	1.32831e15	1.79969
$506$	−3.42846e14	−0.459485
$507$	1.10985e15	1.47137
$508$	1.68876e13	0.0221471
$509$	2.20861e14	0.286531	0.143266	−	0.989684i	$-0.454240\pi$
$509$	2.20861e14	0.286531	0.143266	+	0.989684i	$0.454240\pi$
$510$	8.09064e14	1.03836
$511$	1.60660e15	2.03983
$512$	8.86427e14	1.11342
$513$	1.99149e14	0.247476
$514$	2.05409e14	0.252535
$515$	−6.85533e14	−0.833852
$516$	2.89869e13	0.0348842
$517$	−4.96644e14	−0.591353
$518$	6.24930e13	0.0736237
$519$	−4.20718e14	−0.490423
$520$	−3.43869e15	−3.96620
$521$	−1.64552e15	−1.87800	−0.939000	−	0.343916i	$-0.888247\pi$
$521$	−1.64552e15	−1.87800	−0.939000	+	0.343916i	$0.888247\pi$
$522$	−1.46510e14	−0.165455
$523$	−8.38560e14	−0.937077	−0.468538	−	0.883443i	$-0.655219\pi$
$523$	−8.38560e14	−0.937077	−0.468538	+	0.883443i	$0.655219\pi$
$524$	2.11861e14	0.234276
$525$	2.73563e15	2.99351
$526$	1.31626e15	1.42535
$527$	2.27514e14	0.243809
$528$	−1.87564e14	−0.198913
$529$	2.61636e14	0.274594
$530$	7.95600e14	0.826376
$531$	4.22156e13	0.0433963
$532$	−4.68037e14	−0.476175
$533$	−1.70710e15	−1.71894
$534$	5.47888e14	0.546028
$535$	3.74688e14	0.369593
$536$	1.61605e15	1.57778
$537$	4.29899e14	0.415440
$538$	−4.93243e14	−0.471801
$539$	1.11969e15	1.06013
$540$	−8.17466e13	−0.0766133
$541$	−3.43251e14	−0.318439	−0.159220	−	0.987243i	$-0.550898\pi$
$541$	−3.43251e14	−0.318439	−0.159220	+	0.987243i	$0.550898\pi$
$542$	−1.75858e15	−1.61497
$543$	1.02783e15	0.934377
$544$	4.56047e14	0.410408
$545$	−1.47937e15	−1.31794
$546$	2.00747e15	1.77048
$547$	7.83013e14	0.683657	0.341829	−	0.939762i	$-0.388954\pi$
$547$	7.83013e14	0.683657	0.341829	+	0.939762i	$0.388954\pi$
$548$	2.46794e14	0.213325
$549$	−3.02098e14	−0.258524
$550$	−1.36585e15	−1.15720
$551$	8.52392e14	0.714999
$552$	8.42929e14	0.700045
$553$	3.14714e15	2.58779
$554$	−3.51109e14	−0.285850
$555$	−6.35026e13	−0.0511894
$556$	2.52826e14	0.201795
$557$	−1.49786e15	−1.18377	−0.591886	−	0.806022i	$-0.701616\pi$
$557$	−1.49786e15	−1.18377	−0.591886	+	0.806022i	$0.701616\pi$
$558$	9.02163e13	0.0705987
$559$	7.23339e14	0.560501
$560$	−3.52090e15	−2.70159
$561$	−3.56002e14	−0.270493
$562$	−6.02030e14	−0.452969
$563$	1.62851e15	1.21337	0.606686	−	0.794941i	$-0.292498\pi$
$563$	1.62851e15	1.21337	0.606686	+	0.794941i	$0.292498\pi$
$564$	2.06101e14	0.152071
$565$	2.96609e15	2.16730
$566$	6.28663e14	0.454912
$567$	2.82737e14	0.202617
$568$	−1.33440e15	−0.947046
$569$	1.83836e15	1.29215	0.646075	−	0.763274i	$-0.276410\pi$
$569$	1.83836e15	1.29215	0.646075	+	0.763274i	$0.276410\pi$
$570$	−1.86651e15	−1.29933
$571$	−3.60398e14	−0.248476	−0.124238	−	0.992252i	$-0.539649\pi$
$571$	−3.60398e14	−0.248476	−0.124238	+	0.992252i	$0.539649\pi$
$572$	2.55392e14	0.174393
$573$	3.99437e14	0.270146
$574$	−2.21760e15	−1.48549
$575$	4.83819e15	3.21004
$576$	5.64148e14	0.370740
$577$	2.10156e15	1.36797	0.683983	−	0.729498i	$-0.260246\pi$
$577$	2.10156e15	1.36797	0.683983	+	0.729498i	$0.260246\pi$
$578$	−7.76117e13	−0.0500408
$579$	−2.21661e14	−0.141565
$580$	−3.49889e14	−0.221348
$581$	6.50122e14	0.407405
$582$	−6.08581e14	−0.377782
$583$	−3.50078e14	−0.215272
$584$	1.97218e15	1.20137
$585$	−2.03990e15	−1.23098
$586$	−1.50953e15	−0.902414
$587$	−1.67311e15	−0.990868	−0.495434	−	0.868646i	$-0.664991\pi$
$587$	−1.67311e15	−0.990868	−0.495434	+	0.868646i	$0.664991\pi$
$588$	−4.64658e14	−0.272620
$589$	−5.24875e14	−0.305086
$590$	−3.95662e14	−0.227844
$591$	1.36157e15	0.776801
$592$	6.04655e13	0.0341773
$593$	−1.24514e15	−0.697297	−0.348648	−	0.937254i	$-0.613359\pi$
$593$	−1.24514e15	−0.697297	−0.348648	+	0.937254i	$0.613359\pi$
$594$	−1.41166e14	−0.0783256
$595$	−6.68277e15	−3.67378
$596$	1.41464e12	0.000770532 0
$597$	−1.59978e15	−0.863381
$598$	3.55038e15	1.89854
$599$	−1.49657e15	−0.792958	−0.396479	−	0.918044i	$-0.629768\pi$
$599$	−1.49657e15	−0.792958	−0.396479	+	0.918044i	$0.629768\pi$
$600$	3.35811e15	1.76305
$601$	−1.44646e14	−0.0752484	−0.0376242	−	0.999292i	$-0.511979\pi$
$601$	−1.44646e14	−0.0752484	−0.0376242	+	0.999292i	$0.511979\pi$
$602$	9.39649e14	0.484379
$603$	9.58674e14	0.489695
$604$	5.43674e12	0.00275192
$605$	−3.09610e15	−1.55296
$606$	−9.51908e14	−0.473147
$607$	2.85266e15	1.40512	0.702558	−	0.711626i	$-0.252041\pi$
$607$	2.85266e15	1.40512	0.702558	+	0.711626i	$0.252041\pi$
$608$	−1.05210e15	−0.513556
$609$	1.21016e15	0.585393
$610$	2.83139e15	1.35733
$611$	5.14305e15	2.44340
$612$	1.47737e14	0.0695594
$613$	−4.25071e15	−1.98348	−0.991742	−	0.128247i	$-0.959065\pi$
$613$	−4.25071e15	−1.98348	−0.991742	+	0.128247i	$0.959065\pi$
$614$	−2.21739e15	−1.02545
$615$	2.25343e15	1.03284
$616$	1.96556e15	0.892878
$617$	−2.26950e15	−1.02179	−0.510895	−	0.859643i	$-0.670686\pi$
$617$	−2.26950e15	−1.02179	−0.510895	+	0.859643i	$0.670686\pi$
$618$	4.91274e14	0.219224
$619$	−3.23002e15	−1.42859	−0.714293	−	0.699847i	$-0.753251\pi$
$619$	−3.23002e15	−1.42859	−0.714293	+	0.699847i	$0.753251\pi$
$620$	2.15450e14	0.0944480
$621$	5.00044e14	0.217272
$622$	8.37407e14	0.360653
$623$	−4.52549e15	−1.93189
$624$	1.94234e15	0.821884
$625$	1.01115e16	4.24109
$626$	5.97010e14	0.248212
$627$	8.21297e14	0.338477
$628$	8.79794e14	0.359421
$629$	1.14765e14	0.0464763
$630$	−2.64993e15	−1.06380
$631$	−3.18248e15	−1.26650	−0.633248	−	0.773949i	$-0.718279\pi$
$631$	−3.18248e15	−1.26650	−0.633248	+	0.773949i	$0.718279\pi$
$632$	3.86327e15	1.52409
$633$	−1.28455e15	−0.502379
$634$	−2.63574e15	−1.02191
$635$	−5.56278e14	−0.213814
$636$	1.45278e14	0.0553588
$637$	−1.15951e16	−4.38033
$638$	−6.04212e14	−0.226295
$639$	−7.91597e14	−0.293934
$640$	−3.16069e15	−1.16357
$641$	−1.47472e15	−0.538257	−0.269129	−	0.963104i	$-0.586736\pi$
$641$	−1.47472e15	−0.538257	−0.269129	+	0.963104i	$0.586736\pi$
$642$	−2.68513e14	−0.0971678
$643$	−3.97386e15	−1.42578	−0.712889	−	0.701277i	$-0.752614\pi$
$643$	−3.97386e15	−1.42578	−0.712889	+	0.701277i	$0.752614\pi$
$644$	−1.17519e15	−0.418059
$645$	−9.54830e14	−0.336781
$646$	3.37325e15	1.17970
$647$	2.37355e15	0.823048	0.411524	−	0.911399i	$-0.364997\pi$
$647$	2.37355e15	0.823048	0.411524	+	0.911399i	$0.364997\pi$
$648$	3.47073e14	0.119332
$649$	1.74098e14	0.0593537
$650$	1.41443e16	4.78142
$651$	−7.45176e14	−0.249783
$652$	−4.56029e14	−0.151576
$653$	−1.53417e15	−0.505652	−0.252826	−	0.967512i	$-0.581360\pi$
$653$	−1.53417e15	−0.505652	−0.252826	+	0.967512i	$0.581360\pi$
$654$	1.06016e15	0.346493
$655$	−6.97870e15	−2.26176
$656$	−2.14566e15	−0.689587
$657$	1.16994e15	0.372868
$658$	6.68105e15	2.11155
$659$	1.56688e15	0.491097	0.245548	−	0.969384i	$-0.421032\pi$
$659$	1.56688e15	0.491097	0.245548	+	0.969384i	$0.421032\pi$
$660$	−3.37125e14	−0.104785
$661$	1.01475e15	0.312789	0.156394	−	0.987695i	$-0.450013\pi$
$661$	1.01475e15	0.312789	0.156394	+	0.987695i	$0.450013\pi$
$662$	−1.52420e15	−0.465932
$663$	3.68662e15	1.11764
$664$	7.98056e14	0.239943
$665$	1.54172e16	4.59712
$666$	4.55079e13	0.0134579
$667$	2.14027e15	0.627735
$668$	−2.42217e14	−0.0704586
$669$	−3.52693e13	−0.0101754
$670$	−8.98510e15	−2.57105
$671$	−1.24586e15	−0.353586
$672$	−1.49369e15	−0.420465
$673$	1.80573e15	0.504161	0.252081	−	0.967706i	$-0.418885\pi$
$673$	1.80573e15	0.504161	0.252081	+	0.967706i	$0.418885\pi$
$674$	4.21596e15	1.16753
$675$	1.99211e15	0.547195
$676$	−1.89942e15	−0.517505
$677$	4.58025e15	1.23780	0.618901	−	0.785469i	$-0.287578\pi$
$677$	4.58025e15	1.23780	0.618901	+	0.785469i	$0.287578\pi$
$678$	−2.12559e15	−0.569792
$679$	5.02681e15	1.33662
$680$	−8.20343e15	−2.16370
$681$	−1.48762e14	−0.0389210
$682$	3.72054e14	0.0965588
$683$	−2.47746e15	−0.637811	−0.318906	−	0.947786i	$-0.603315\pi$
$683$	−2.47746e15	−0.637811	−0.318906	+	0.947786i	$0.603315\pi$
$684$	−3.40829e14	−0.0870418
$685$	−8.12940e15	−2.05949
$686$	−8.58494e15	−2.15752
$687$	−2.55042e15	−0.635843
$688$	9.09163e14	0.224856
$689$	3.62527e15	0.889477
$690$	−4.68662e15	−1.14075
$691$	2.68415e15	0.648153	0.324077	−	0.946031i	$-0.394946\pi$
$691$	2.68415e15	0.648153	0.324077	+	0.946031i	$0.394946\pi$
$692$	7.20027e14	0.172491
$693$	1.16601e15	0.277122
$694$	1.91538e15	0.451624
$695$	−8.32811e15	−1.94818
$696$	1.48553e15	0.344771
$697$	−4.07251e15	−0.937740
$698$	−5.21599e15	−1.19160
$699$	3.68387e15	0.834987
$700$	−4.68182e15	−1.05287
$701$	−7.26486e15	−1.62098	−0.810491	−	0.585751i	$-0.800800\pi$
$701$	−7.26486e15	−1.62098	−0.810491	+	0.585751i	$0.800800\pi$
$702$	1.46186e15	0.323632
$703$	−2.64763e14	−0.0581572
$704$	2.32656e15	0.507066
$705$	−6.78899e15	−1.46813
$706$	−5.27746e15	−1.13240
$707$	7.86265e15	1.67403
$708$	−7.22487e13	−0.0152632
$709$	3.38334e15	0.709237	0.354618	−	0.935011i	$-0.384611\pi$
$709$	3.38334e15	0.709237	0.354618	+	0.935011i	$0.384611\pi$
$710$	7.41918e15	1.54324
$711$	2.29178e15	0.473031
$712$	−5.55526e15	−1.13780
$713$	−1.31791e15	−0.267851
$714$	4.78908e15	0.965855
$715$	−8.41261e15	−1.68363
$716$	−7.35739e14	−0.146118
$717$	−3.97143e15	−0.782694
$718$	−3.52953e15	−0.690291
$719$	6.46634e15	1.25502	0.627509	−	0.778610i	$-0.284075\pi$
$719$	6.46634e15	1.25502	0.627509	+	0.778610i	$0.284075\pi$
$720$	−2.56395e15	−0.493834
$721$	−4.05787e15	−0.775629
$722$	−3.07595e15	−0.583478
$723$	−3.55694e15	−0.669601
$724$	−1.75905e15	−0.328637
$725$	8.52655e15	1.58094
$726$	2.21876e15	0.408281
$727$	−2.69385e15	−0.491965	−0.245983	−	0.969274i	$-0.579111\pi$
$727$	−2.69385e15	−0.491965	−0.245983	+	0.969274i	$0.579111\pi$
$728$	−2.03546e16	−3.68926
$729$	2.05891e14	0.0370370
$730$	−1.09652e16	−1.95767
$731$	1.72562e15	0.305773
$732$	5.17018e14	0.0909273
$733$	−4.65478e15	−0.812508	−0.406254	−	0.913760i	$-0.633165\pi$
$733$	−4.65478e15	−0.812508	−0.406254	+	0.913760i	$0.633165\pi$
$734$	3.06987e15	0.531852
$735$	1.53059e16	2.63195
$736$	−2.64172e15	−0.450877
$737$	3.95360e15	0.669763
$738$	−1.61488e15	−0.271537
$739$	6.77408e15	1.13059	0.565296	−	0.824888i	$-0.308762\pi$
$739$	6.77408e15	1.13059	0.565296	+	0.824888i	$0.308762\pi$
$740$	1.08680e14	0.0180042
$741$	−8.50503e15	−1.39854
$742$	4.70939e15	0.768675
$743$	−2.48045e15	−0.401876	−0.200938	−	0.979604i	$-0.564399\pi$
$743$	−2.48045e15	−0.401876	−0.200938	+	0.979604i	$0.564399\pi$
$744$	−9.14740e14	−0.147111
$745$	−4.65982e13	−0.00743891
$746$	−7.64151e15	−1.21092
$747$	4.73424e14	0.0744710
$748$	6.09270e14	0.0951373
$749$	2.21789e15	0.343787
$750$	−1.21043e16	−1.86252
$751$	3.82204e15	0.583815	0.291908	−	0.956447i	$-0.405710\pi$
$751$	3.82204e15	0.583815	0.291908	+	0.956447i	$0.405710\pi$
$752$	6.46429e15	0.980218
$753$	−4.76427e15	−0.717174
$754$	6.25699e15	0.935025
$755$	−1.79087e14	−0.0265677
$756$	−4.83882e14	−0.0712639
$757$	−3.65438e14	−0.0534301	−0.0267150	−	0.999643i	$-0.508505\pi$
$757$	−3.65438e14	−0.0534301	−0.0267150	+	0.999643i	$0.508505\pi$
$758$	8.42772e15	1.22329
$759$	2.06219e15	0.297166
$760$	1.89253e16	2.70750
$761$	3.79818e15	0.539461	0.269730	−	0.962936i	$-0.413065\pi$
$761$	3.79818e15	0.539461	0.269730	+	0.962936i	$0.413065\pi$
$762$	3.98646e14	0.0562127
$763$	−8.75682e15	−1.22592
$764$	−6.83606e14	−0.0950151
$765$	−4.86645e15	−0.671544
$766$	−3.97087e15	−0.544035
$767$	−1.80289e15	−0.245242
$768$	−2.48958e15	−0.336233
$769$	4.53653e15	0.608316	0.304158	−	0.952622i	$-0.401625\pi$
$769$	4.53653e15	0.608316	0.304158	+	0.952622i	$0.401625\pi$
$770$	−1.09284e16	−1.45498
$771$	−1.23552e15	−0.163324
$772$	3.79355e14	0.0497910
$773$	−1.07123e16	−1.39604	−0.698018	−	0.716080i	$-0.745934\pi$
$773$	−1.07123e16	−1.39604	−0.698018	+	0.716080i	$0.745934\pi$
$774$	6.84260e14	0.0885413
$775$	−5.25037e15	−0.674575
$776$	6.17065e15	0.787211
$777$	−3.75890e14	−0.0476152
$778$	−1.00520e16	−1.26434
$779$	9.39530e15	1.17342
$780$	3.49114e15	0.432959
$781$	−3.26456e15	−0.402017
$782$	8.46989e15	1.03572
$783$	8.81248e14	0.107006
$784$	−1.45738e16	−1.75726
$785$	−2.89805e16	−3.46994
$786$	5.00115e15	0.594629
$787$	2.44806e15	0.289042	0.144521	−	0.989502i	$-0.453836\pi$
$787$	2.44806e15	0.289042	0.144521	+	0.989502i	$0.453836\pi$
$788$	−2.33023e15	−0.273215
$789$	−7.91722e15	−0.921827
$790$	−2.14795e16	−2.48356
$791$	1.75571e16	2.01597
$792$	1.43134e15	0.163212
$793$	1.29016e16	1.46097
$794$	8.67530e15	0.975600
$795$	−4.78547e15	−0.534448
$796$	2.73791e15	0.303666
$797$	6.35980e15	0.700523	0.350262	−	0.936652i	$-0.386093\pi$
$797$	6.35980e15	0.700523	0.350262	+	0.936652i	$0.386093\pi$
$798$	−1.10484e16	−1.20860
$799$	1.22694e16	1.33296
$800$	−1.05242e16	−1.13552
$801$	−3.29550e15	−0.353137
$802$	−1.24528e16	−1.32528
$803$	4.82487e15	0.509977
$804$	−1.64070e15	−0.172234
$805$	3.87109e16	4.03605
$806$	−3.85285e15	−0.398969
$807$	2.96682e15	0.305131
$808$	9.65178e15	0.985928
$809$	−1.83448e16	−1.86122	−0.930609	−	0.366016i	$-0.880722\pi$
$809$	−1.83448e16	−1.86122	−0.930609	+	0.366016i	$0.880722\pi$
$810$	−1.92970e15	−0.194456
$811$	1.63616e16	1.63761	0.818806	−	0.574070i	$-0.194636\pi$
$811$	1.63616e16	1.63761	0.818806	+	0.574070i	$0.194636\pi$
$812$	−2.07109e15	−0.205893
$813$	1.05777e16	1.04446
$814$	1.87676e14	0.0184066
$815$	1.50216e16	1.46335
$816$	4.63370e15	0.448366
$817$	−3.98100e15	−0.382623
$818$	−4.53833e15	−0.433265
$819$	−1.20748e16	−1.14503
$820$	−3.85657e15	−0.363266
$821$	−1.29000e16	−1.20699	−0.603493	−	0.797368i	$-0.706225\pi$
$821$	−1.29000e16	−1.20699	−0.603493	+	0.797368i	$0.706225\pi$
$822$	5.82578e15	0.541451
$823$	1.23403e16	1.13927	0.569635	−	0.821898i	$-0.307085\pi$
$823$	1.23403e16	1.13927	0.569635	+	0.821898i	$0.307085\pi$
$824$	−4.98123e15	−0.456811
$825$	8.21550e15	0.748406
$826$	−2.34204e15	−0.211935
$827$	−1.93782e16	−1.74194	−0.870969	−	0.491339i	$-0.836508\pi$
$827$	−1.93782e16	−1.74194	−0.870969	+	0.491339i	$0.836508\pi$
$828$	−8.55786e14	−0.0764185
$829$	7.37677e15	0.654359	0.327180	−	0.944962i	$-0.393902\pi$
$829$	7.37677e15	0.654359	0.327180	+	0.944962i	$0.393902\pi$
$830$	−4.43713e15	−0.390996
$831$	2.11189e15	0.184870
$832$	−2.40930e16	−2.09514
$833$	−2.76615e16	−2.38962
$834$	5.96818e15	0.512187
$835$	7.97864e15	0.680226
$836$	−1.40559e15	−0.119048
$837$	−5.42644e14	−0.0456588
$838$	9.92460e15	0.829604
$839$	−6.24517e15	−0.518625	−0.259312	−	0.965793i	$-0.583496\pi$
$839$	−6.24517e15	−0.518625	−0.259312	+	0.965793i	$0.583496\pi$
$840$	2.68687e16	2.21672
$841$	−8.42862e15	−0.690842
$842$	6.10635e15	0.497239
$843$	3.62116e15	0.292952
$844$	2.19841e15	0.176696
$845$	6.25670e16	4.99613
$846$	4.86520e15	0.385979
$847$	−1.83267e16	−1.44453
$848$	4.55660e15	0.356832
$849$	−3.78135e15	−0.294208
$850$	3.37429e16	2.60843
$851$	−6.64794e14	−0.0510592
$852$	1.35476e15	0.103382
$853$	1.86753e16	1.41595	0.707974	−	0.706239i	$-0.249609\pi$
$853$	1.86753e16	1.41595	0.707974	+	0.706239i	$0.249609\pi$
$854$	1.67598e16	1.26256
$855$	1.12269e16	0.840324
$856$	2.72256e15	0.202475
$857$	−1.10225e16	−0.814487	−0.407243	−	0.913320i	$-0.633510\pi$
$857$	−1.10225e16	−0.814487	−0.407243	+	0.913320i	$0.633510\pi$
$858$	6.02873e15	0.442635
$859$	−2.69302e16	−1.96462	−0.982308	−	0.187274i	$-0.940035\pi$
$859$	−2.69302e16	−1.96462	−0.982308	+	0.187274i	$0.940035\pi$
$860$	1.63412e15	0.118452
$861$	1.33387e16	0.960718
$862$	−1.01192e16	−0.724193
$863$	−6.34538e15	−0.451230	−0.225615	−	0.974217i	$-0.572439\pi$
$863$	−6.34538e15	−0.451230	−0.225615	+	0.974217i	$0.572439\pi$
$864$	−1.08772e15	−0.0768583
$865$	−2.37177e16	−1.66527
$866$	9.66458e15	0.674271
$867$	4.66828e14	0.0323632
$868$	1.27531e15	0.0878532
$869$	9.45134e15	0.646971
$870$	−8.25942e15	−0.561816
$871$	−4.09419e16	−2.76738
$872$	−1.07494e16	−0.722012
$873$	3.66056e15	0.244326
$874$	−1.95401e16	−1.29602
$875$	9.99798e16	6.58974
$876$	−2.00227e15	−0.131144
$877$	−9.50822e15	−0.618873	−0.309437	−	0.950920i	$-0.600140\pi$
$877$	−9.50822e15	−0.618873	−0.309437	+	0.950920i	$0.600140\pi$
$878$	−6.54195e15	−0.423143
$879$	9.07972e15	0.583624
$880$	−1.05738e16	−0.675424
$881$	1.54562e16	0.981151	0.490575	−	0.871399i	$-0.336787\pi$
$881$	1.54562e16	0.981151	0.490575	+	0.871399i	$0.336787\pi$
$882$	−1.09686e16	−0.691952
$883$	5.14415e15	0.322500	0.161250	−	0.986914i	$-0.448447\pi$
$883$	5.14415e15	0.322500	0.161250	+	0.986914i	$0.448447\pi$
$884$	−6.30936e15	−0.393095
$885$	2.37987e15	0.147355
$886$	−1.65212e16	−1.01661
$887$	3.16092e14	0.0193301	0.00966504	−	0.999953i	$-0.496923\pi$
$887$	3.16092e14	0.0193301	0.00966504	+	0.999953i	$0.496923\pi$
$888$	−4.61423e14	−0.0280432
$889$	−3.29277e15	−0.198885
$890$	3.08868e16	1.85408
$891$	8.49100e14	0.0506561
$892$	6.03607e13	0.00357888
$893$	−2.83055e16	−1.66797
$894$	3.33937e13	0.00195573
$895$	2.42353e16	1.41066
$896$	−1.87090e16	−1.08232
$897$	−2.13553e16	−1.22785
$898$	1.49516e15	0.0854413
$899$	−2.32260e15	−0.131916
$900$	−3.40934e15	−0.192458
$901$	8.64855e15	0.485240
$902$	−6.65979e15	−0.371385
$903$	−5.65191e15	−0.313266
$904$	2.15522e16	1.18732
$905$	5.79432e16	3.17275
$906$	1.28339e14	0.00698479
$907$	−8.28539e15	−0.448201	−0.224101	−	0.974566i	$-0.571944\pi$
$907$	−8.28539e15	−0.448201	−0.224101	+	0.974566i	$0.571944\pi$
$908$	2.54595e14	0.0136892
$909$	5.72565e15	0.306001
$910$	1.13170e17	6.01178
$911$	1.57578e16	0.832041	0.416021	−	0.909355i	$-0.363424\pi$
$911$	1.57578e16	0.832041	0.416021	+	0.909355i	$0.363424\pi$
$912$	−1.06900e16	−0.561054
$913$	1.95241e15	0.101855
$914$	1.63608e16	0.848400
$915$	−1.70306e16	−0.877836
$916$	4.36485e15	0.223637
$917$	−4.13089e16	−2.10384
$918$	3.48745e15	0.176552
$919$	−2.20165e16	−1.10793	−0.553966	−	0.832539i	$-0.686886\pi$
$919$	−2.20165e16	−1.10793	−0.553966	+	0.832539i	$0.686886\pi$
$920$	4.75195e16	2.37705
$921$	1.33374e16	0.663198
$922$	−1.72878e16	−0.854516
$923$	3.38066e16	1.66108
$924$	−1.99554e15	−0.0974685
$925$	−2.64845e15	−0.128591
$926$	1.58284e16	0.763968
$927$	−2.95497e15	−0.141780
$928$	−4.65561e15	−0.222056
$929$	2.69393e16	1.27732	0.638660	−	0.769489i	$-0.279489\pi$
$929$	2.69393e16	1.27732	0.638660	+	0.769489i	$0.279489\pi$
$930$	5.08588e15	0.239723
$931$	6.38152e16	2.99020
$932$	−6.30465e15	−0.293680
$933$	−5.03693e15	−0.233248
$934$	−6.42503e15	−0.295779
$935$	−2.00694e16	−0.918480
$936$	−1.48224e16	−0.674373
$937$	9.92259e15	0.448804	0.224402	−	0.974497i	$-0.427957\pi$
$937$	9.92259e15	0.448804	0.224402	+	0.974497i	$0.427957\pi$
$938$	−5.31854e16	−2.39153
$939$	−3.59097e15	−0.160528
$940$	1.16188e16	0.516368
$941$	−3.58941e16	−1.58591	−0.792957	−	0.609277i	$-0.791460\pi$
$941$	−3.58941e16	−1.58591	−0.792957	+	0.609277i	$0.791460\pi$
$942$	2.07683e16	0.912264
$943$	2.35906e16	1.03021
$944$	−2.26605e15	−0.0983838
$945$	1.59391e16	0.688000
$946$	2.82190e15	0.121099
$947$	−2.97714e16	−1.27021	−0.635103	−	0.772427i	$-0.719042\pi$
$947$	−2.97714e16	−1.27021	−0.635103	+	0.772427i	$0.719042\pi$
$948$	−3.92220e15	−0.166373
$949$	−4.99645e16	−2.10716
$950$	−7.78450e16	−3.26400
$951$	1.58537e16	0.660905
$952$	−4.85584e16	−2.01262
$953$	−2.67158e16	−1.10093	−0.550463	−	0.834860i	$-0.685549\pi$
$953$	−2.67158e16	−1.10093	−0.550463	+	0.834860i	$0.685549\pi$
$954$	3.42941e15	0.140509
$955$	2.25180e16	0.917300
$956$	6.79680e15	0.275287
$957$	3.63429e15	0.146354
$958$	8.63131e15	0.345594
$959$	−4.81203e16	−1.91569
$960$	3.18035e16	1.25888
$961$	−2.39783e16	−0.943712
$962$	−1.94350e15	−0.0760538
$963$	1.61508e15	0.0628420
$964$	6.08743e15	0.235511
$965$	−1.24960e16	−0.480696
$966$	−2.77414e16	−1.06110
$967$	1.42091e16	0.540407	0.270204	−	0.962803i	$-0.412909\pi$
$967$	1.42091e16	0.540407	0.270204	+	0.962803i	$0.412909\pi$
$968$	−2.24969e16	−0.850763
$969$	−2.02898e16	−0.762953
$970$	−3.43083e16	−1.28279
$971$	3.06573e16	1.13980	0.569899	−	0.821715i	$-0.306982\pi$
$971$	3.06573e16	1.13980	0.569899	+	0.821715i	$0.306982\pi$
$972$	−3.52367e14	−0.0130266
$973$	−4.92965e16	−1.81215
$974$	−1.20281e16	−0.439664
$975$	−8.50765e16	−3.09232
$976$	1.62161e16	0.586099
$977$	1.34379e16	0.482959	0.241480	−	0.970406i	$-0.422367\pi$
$977$	1.34379e16	0.482959	0.241480	+	0.970406i	$0.422367\pi$
$978$	−1.07649e16	−0.384723
$979$	−1.35907e16	−0.482990
$980$	−2.61948e16	−0.925703
$981$	−6.37679e15	−0.224090
$982$	2.98172e16	1.04197
$983$	2.54085e16	0.882946	0.441473	−	0.897275i	$-0.354456\pi$
$983$	2.54085e16	0.882946	0.441473	+	0.897275i	$0.354456\pi$
$984$	1.63739e16	0.565821
$985$	7.67577e16	2.63768
$986$	1.49269e16	0.510088
$987$	−4.01860e16	−1.36562
$988$	1.45557e16	0.491892
$989$	−9.99588e15	−0.335924
$990$	−7.95812e15	−0.265960
$991$	−4.18641e16	−1.39135	−0.695675	−	0.718356i	$-0.744895\pi$
$991$	−4.18641e16	−1.39135	−0.695675	+	0.718356i	$0.744895\pi$
$992$	2.86677e15	0.0947499
$993$	9.16793e15	0.301336
$994$	4.39162e16	1.43549
$995$	−9.01868e16	−2.93168
$996$	−8.10229e14	−0.0261928
$997$	4.12186e16	1.32516	0.662582	−	0.748989i	$-0.269460\pi$
$997$	4.12186e16	1.32516	0.662582	+	0.748989i	$0.269460\pi$
$998$	2.48220e16	0.793631
$999$	−2.73726e14	−0.00870375

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.d.1.8	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.d.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-40.3996 q^{2} +243.000 q^{3} -415.876 q^{4} +13699.0 q^{5} -9817.09 q^{6} +81088.1 q^{7} +99539.5 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-40.3996 q^{2} +243.000 q^{3} -415.876 q^{4} +13699.0 q^{5} -9817.09 q^{6} +81088.1 q^{7} +99539.5 q^{8} +59049.0 q^{9} -553432. q^{10} +243519. q^{11} -101058. q^{12} -2.52179e6 q^{13} -3.27592e6 q^{14} +3.32885e6 q^{15} -3.16964e6 q^{16} -6.01606e6 q^{17} -2.38555e6 q^{18} +1.38791e7 q^{19} -5.69706e6 q^{20} +1.97044e7 q^{21} -9.83808e6 q^{22} +3.48489e7 q^{23} +2.41881e7 q^{24} +1.38833e8 q^{25} +1.01879e8 q^{26} +1.43489e7 q^{27} -3.37226e7 q^{28} +6.14157e7 q^{29} -1.34484e8 q^{30} -3.78178e7 q^{31} -7.58049e7 q^{32} +5.91752e7 q^{33} +2.43046e8 q^{34} +1.11082e9 q^{35} -2.45570e7 q^{36} -1.90765e7 q^{37} -5.60708e8 q^{38} -6.12796e8 q^{39} +1.36359e9 q^{40} +6.76940e8 q^{41} -7.96049e8 q^{42} -2.86835e8 q^{43} -1.01274e8 q^{44} +8.08910e8 q^{45} -1.40788e9 q^{46} -2.03944e9 q^{47} -7.70222e8 q^{48} +4.59795e9 q^{49} -5.60881e9 q^{50} -1.46190e9 q^{51} +1.04875e9 q^{52} -1.43758e9 q^{53} -5.79690e8 q^{54} +3.33596e9 q^{55} +8.07146e9 q^{56} +3.37261e9 q^{57} -2.48117e9 q^{58} +7.14924e8 q^{59} -1.38439e9 q^{60} -5.11606e9 q^{61} +1.52782e9 q^{62} +4.78817e9 q^{63} +9.55390e9 q^{64} -3.45460e10 q^{65} -2.39065e9 q^{66} +1.62352e10 q^{67} +2.50193e9 q^{68} +8.46828e9 q^{69} -4.48767e10 q^{70} -1.34058e10 q^{71} +5.87771e9 q^{72} +1.98131e10 q^{73} +7.70681e8 q^{74} +3.37365e10 q^{75} -5.77196e9 q^{76} +1.97465e10 q^{77} +2.47567e10 q^{78} +3.88114e10 q^{79} -4.34207e10 q^{80} +3.48678e9 q^{81} -2.73481e10 q^{82} +8.01748e9 q^{83} -8.19458e9 q^{84} -8.24138e10 q^{85} +1.15880e10 q^{86} +1.49240e10 q^{87} +2.42398e10 q^{88} -5.58096e10 q^{89} -3.26796e10 q^{90} -2.04487e11 q^{91} -1.44928e10 q^{92} -9.18972e9 q^{93} +8.23925e10 q^{94} +1.90129e11 q^{95} -1.84206e10 q^{96} +6.19919e10 q^{97} -1.85755e11 q^{98} +1.43796e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) \) 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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