LMFDB - Embedded newform 5.20.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,20,Mod(1,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("5.1");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	5.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:	$11.4408348278$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 323561x^{2} - 26738538x + 10870990650 $ x^4 - 2x^3 - 323561x^2 - 26738538*x + 10870990650
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$150.720$ of defining polynomial
Character	$\chi$	$=$	5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-602.379 q^{2} -7268.55 q^{3} -161427. q^{4} -1.95312e6 q^{5} +4.37842e6 q^{6} -1.76809e8 q^{7} +4.13061e8 q^{8} -1.10943e9 q^{9} +O(q^{10})$	\(q-602.379 q^{2} -7268.55 q^{3} -161427. q^{4} -1.95312e6 q^{5} +4.37842e6 q^{6} -1.76809e8 q^{7} +4.13061e8 q^{8} -1.10943e9 q^{9} +1.17652e9 q^{10} +1.39586e10 q^{11} +1.17334e9 q^{12} +1.93474e10 q^{13} +1.06506e11 q^{14} +1.41964e10 q^{15} -1.64185e11 q^{16} +4.63866e11 q^{17} +6.68297e11 q^{18} -4.52545e11 q^{19} +3.15288e11 q^{20} +1.28515e12 q^{21} -8.40838e12 q^{22} -1.05040e13 q^{23} -3.00235e12 q^{24} +3.81470e12 q^{25} -1.16545e13 q^{26} +1.65119e13 q^{27} +2.85418e13 q^{28} +3.98365e13 q^{29} -8.55160e12 q^{30} +2.74723e14 q^{31} -1.17661e14 q^{32} -1.01459e14 q^{33} -2.79423e14 q^{34} +3.45331e14 q^{35} +1.79092e14 q^{36} -9.95533e14 q^{37} +2.72604e14 q^{38} -1.40628e14 q^{39} -8.06759e14 q^{40} +1.83489e14 q^{41} -7.74145e14 q^{42} -2.67686e14 q^{43} -2.25330e15 q^{44} +2.16685e15 q^{45} +6.32739e15 q^{46} -1.98742e15 q^{47} +1.19338e15 q^{48} +1.98626e16 q^{49} -2.29789e15 q^{50} -3.37163e15 q^{51} -3.12320e15 q^{52} +9.08292e15 q^{53} -9.94642e15 q^{54} -2.72629e16 q^{55} -7.30329e16 q^{56} +3.28935e15 q^{57} -2.39967e16 q^{58} +6.50053e16 q^{59} -2.29168e15 q^{60} +4.68466e16 q^{61} -1.65487e17 q^{62} +1.96157e17 q^{63} +1.56957e17 q^{64} -3.77879e16 q^{65} +6.11167e16 q^{66} +8.23716e15 q^{67} -7.48807e16 q^{68} +7.63488e16 q^{69} -2.08020e17 q^{70} +1.76105e17 q^{71} -4.58262e17 q^{72} +2.64213e17 q^{73} +5.99689e17 q^{74} -2.77273e16 q^{75} +7.30531e16 q^{76} -2.46801e18 q^{77} +8.47112e16 q^{78} +3.99397e17 q^{79} +3.20673e17 q^{80} +1.16943e18 q^{81} -1.10530e17 q^{82} -9.57676e17 q^{83} -2.07458e17 q^{84} -9.05989e17 q^{85} +1.61249e17 q^{86} -2.89553e17 q^{87} +5.76575e18 q^{88} +4.73978e18 q^{89} -1.30527e18 q^{90} -3.42080e18 q^{91} +1.69563e18 q^{92} -1.99683e18 q^{93} +1.19718e18 q^{94} +8.83877e17 q^{95} +8.55226e17 q^{96} +1.13670e18 q^{97} -1.19648e19 q^{98} -1.54861e19 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 420 q^{2} + 3080 q^{3} + 2084992 q^{4} - 7812500 q^{5} - 58071752 q^{6} + 214021400 q^{7} + 81737760 q^{8} + 154064548 q^{9}+O(q^{10}) $ 4 * q - 420 * q^2 + 3080 * q^3 + 2084992 * q^4 - 7812500 * q^5 - 58071752 * q^6 + 214021400 * q^7 + 81737760 * q^8 + 154064548 * q^9	$ 4 q - 420 q^{2} + 3080 q^{3} + 2084992 q^{4} - 7812500 q^{5} - 58071752 q^{6} + 214021400 q^{7} + 81737760 q^{8} + 154064548 q^{9} + 820312500 q^{10} + 11585712768 q^{11} + 105629359360 q^{12} + 14812333160 q^{13} + 185174155944 q^{14} - 6015625000 q^{15} + 1785780098944 q^{16} + 849033742440 q^{17} - 2113778999620 q^{18} + 1978167708560 q^{19} - 4072250000000 q^{20} - 1487020185552 q^{21} - 7953348762240 q^{22} - 26569906952760 q^{23} - 39774243472320 q^{24} + 15258789062500 q^{25} - 48695658207912 q^{26} - 7557605929360 q^{27} + 236612033519360 q^{28} + 116267174339640 q^{29} + 113421390625000 q^{30} + 251049672388688 q^{31} - 142495342974720 q^{32} + 359905680636160 q^{33} + 411849015040344 q^{34} - 418010546875000 q^{35} - 168308645735296 q^{36} + 53471657716520 q^{37} - 52\!\cdots\!60 q^{38}+ \cdots - 25\!\cdots\!84 q^{99}+O(q^{100}) $ 4 * q - 420 * q^2 + 3080 * q^3 + 2084992 * q^4 - 7812500 * q^5 - 58071752 * q^6 + 214021400 * q^7 + 81737760 * q^8 + 154064548 * q^9 + 820312500 * q^10 + 11585712768 * q^11 + 105629359360 * q^12 + 14812333160 * q^13 + 185174155944 * q^14 - 6015625000 * q^15 + 1785780098944 * q^16 + 849033742440 * q^17 - 2113778999620 * q^18 + 1978167708560 * q^19 - 4072250000000 * q^20 - 1487020185552 * q^21 - 7953348762240 * q^22 - 26569906952760 * q^23 - 39774243472320 * q^24 + 15258789062500 * q^25 - 48695658207912 * q^26 - 7557605929360 * q^27 + 236612033519360 * q^28 + 116267174339640 * q^29 + 113421390625000 * q^30 + 251049672388688 * q^31 - 142495342974720 * q^32 + 359905680636160 * q^33 + 411849015040344 * q^34 - 418010546875000 * q^35 - 168308645735296 * q^36 + 53471657716520 * q^37 - 5247417886886160 * q^38 - 3407032515417904 * q^39 - 159644062500000 * q^40 + 5606221897948248 * q^41 - 6858180778710960 * q^42 + 3924193112762600 * q^43 + 7741056858814464 * q^44 - 300907320312500 * q^45 - 13726548710068872 * q^46 + 9972444326989560 * q^47 + 45169928589418240 * q^48 + 40183155980030772 * q^49 - 1602172851562500 * q^50 + 21906201621258448 * q^51 - 98153899497030400 * q^52 - 7462276270800120 * q^53 - 40810202919142640 * q^54 - 22628345250000000 * q^55 - 85257126419530560 * q^56 + 24746009355310880 * q^57 - 168144043315298040 * q^58 + 186154941962838480 * q^59 - 206307342500000000 * q^60 + 248517593110644968 * q^61 - 622575860488793040 * q^62 + 375323610989436120 * q^63 + 797725889363156992 * q^64 - 28930338203125000 * q^65 + 66770019182287616 * q^66 - 83976946080676360 * q^67 + 1012065979784551680 * q^68 + 721386544222156176 * q^69 - 361668273328125000 * q^70 - 326854508200029072 * q^71 - 3247857120459936480 * q^72 + 706071038062266440 * q^73 + 1007811588432673944 * q^74 + 11749267578125000 * q^75 + 453476009937236480 * q^76 - 3188023247458540800 * q^77 - 422235733076613200 * q^78 + 1300235890504742240 * q^79 - 3487851755750000000 * q^80 - 565640020943583596 * q^81 - 3526321594330914840 * q^82 - 894716269324765080 * q^83 + 11741177868239906304 * q^84 - 1658269028203125000 * q^85 + 10889898572595403608 * q^86 - 3243563654475579280 * q^87 + 8680694316508369920 * q^88 - 4392730519471649880 * q^89 + 4128474608632812500 * q^90 - 1164625388848487312 * q^91 + 1015783757806275840 * q^92 + 589775737588352160 * q^93 + 6912955459089075144 * q^94 - 3863608805781250000 * q^95 - 34035929850443648512 * q^96 + 1437870497951780360 * q^97 + 1735173204679501740 * q^98 - 25265427652281702784 * 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 $

$2$	−602.379	−0.831927	−0.415963	−	0.909381i	$-0.636556\pi$
$2$	−602.379	−0.831927	−0.415963	+	0.909381i	$0.636556\pi$
$3$	−7268.55	−0.213204	−0.106602	−	0.994302i	$-0.533997\pi$
$3$	−7268.55	−0.213204	−0.106602	+	0.994302i	$0.533997\pi$
$4$	−161427.	−0.307898
$5$	−1.95312e6	−0.447214
$5$	−1.95312e6	−0.447214
$6$	4.37842e6	0.177370
$7$	−1.76809e8	−1.65605	−0.828025	−	0.560691i	$-0.810536\pi$
$7$	−1.76809e8	−1.65605	−0.828025	+	0.560691i	$0.810536\pi$
$8$	4.13061e8	1.08808
$9$	−1.10943e9	−0.954544
$10$	1.17652e9	0.372049
$11$	1.39586e10	1.78489	0.892445	−	0.451155i	$-0.148988\pi$
$11$	1.39586e10	1.78489	0.892445	+	0.451155i	$0.148988\pi$
$12$	1.17334e9	0.0656451
$13$	1.93474e10	0.506013	0.253006	−	0.967465i	$-0.418581\pi$
$13$	1.93474e10	0.506013	0.253006	+	0.967465i	$0.418581\pi$
$14$	1.06506e11	1.37771
$15$	1.41964e10	0.0953478
$16$	−1.64185e11	−0.597301
$17$	4.63866e11	0.948698	0.474349	−	0.880337i	$-0.342683\pi$
$17$	4.63866e11	0.948698	0.474349	+	0.880337i	$0.342683\pi$
$18$	6.68297e11	0.794111
$19$	−4.52545e11	−0.321738	−0.160869	−	0.986976i	$-0.551430\pi$
$19$	−4.52545e11	−0.321738	−0.160869	+	0.986976i	$0.551430\pi$
$20$	3.15288e11	0.137696
$21$	1.28515e12	0.353077
$22$	−8.40838e12	−1.48490
$23$	−1.05040e13	−1.21602	−0.608009	−	0.793930i	$-0.708032\pi$
$23$	−1.05040e13	−1.21602	−0.608009	+	0.793930i	$0.708032\pi$
$24$	−3.00235e12	−0.231982
$25$	3.81470e12	0.200000
$26$	−1.16545e13	−0.420965
$27$	1.65119e13	0.416717
$28$	2.85418e13	0.509895
$29$	3.98365e13	0.509918	0.254959	−	0.966952i	$-0.417938\pi$
$29$	3.98365e13	0.509918	0.254959	+	0.966952i	$0.417938\pi$
$30$	−8.55160e12	−0.0793224
$31$	2.74723e14	1.86620	0.933100	−	0.359616i	$-0.117092\pi$
$31$	2.74723e14	1.86620	0.933100	+	0.359616i	$0.117092\pi$
$32$	−1.17661e14	−0.591165
$33$	−1.01459e14	−0.380546
$34$	−2.79423e14	−0.789247
$35$	3.45331e14	0.740608
$36$	1.79092e14	0.293902
$37$	−9.95533e14	−1.25933	−0.629665	−	0.776867i	$-0.716808\pi$
$37$	−9.95533e14	−1.25933	−0.629665	+	0.776867i	$0.716808\pi$
$38$	2.72604e14	0.267663
$39$	−1.40628e14	−0.107884
$40$	−8.06759e14	−0.486602
$41$	1.83489e14	0.0875311	0.0437656	−	0.999042i	$-0.486065\pi$
$41$	1.83489e14	0.0875311	0.0437656	+	0.999042i	$0.486065\pi$
$42$	−7.74145e14	−0.293734
$43$	−2.67686e14	−0.0812223	−0.0406112	−	0.999175i	$-0.512930\pi$
$43$	−2.67686e14	−0.0812223	−0.0406112	+	0.999175i	$0.512930\pi$
$44$	−2.25330e15	−0.549564
$45$	2.16685e15	0.426885
$46$	6.32739e15	1.01164
$47$	−1.98742e15	−0.259036	−0.129518	−	0.991577i	$-0.541343\pi$
$47$	−1.98742e15	−0.259036	−0.129518	+	0.991577i	$0.541343\pi$
$48$	1.19338e15	0.127347
$49$	1.98626e16	1.74250
$50$	−2.29789e15	−0.166385
$51$	−3.37163e15	−0.202266
$52$	−3.12320e15	−0.155800
$53$	9.08292e15	0.378098	0.189049	−	0.981968i	$-0.439459\pi$
$53$	9.08292e15	0.378098	0.189049	+	0.981968i	$0.439459\pi$
$54$	−9.94642e15	−0.346678
$55$	−2.72629e16	−0.798227
$56$	−7.30329e16	−1.80191
$57$	3.28935e15	0.0685959
$58$	−2.39967e16	−0.424214
$59$	6.50053e16	0.976910	0.488455	−	0.872589i	$-0.337561\pi$
$59$	6.50053e16	0.976910	0.488455	+	0.872589i	$0.337561\pi$
$60$	−2.29168e15	−0.0293574
$61$	4.68466e16	0.512914	0.256457	−	0.966556i	$-0.417445\pi$
$61$	4.68466e16	0.512914	0.256457	+	0.966556i	$0.417445\pi$
$62$	−1.65487e17	−1.55254
$63$	1.96157e17	1.58077
$64$	1.56957e17	1.08911
$65$	−3.77879e16	−0.226296
$66$	6.11167e16	0.316586
$67$	8.23716e15	0.0369885	0.0184943	−	0.999829i	$-0.494113\pi$
$67$	8.23716e15	0.0369885	0.0184943	+	0.999829i	$0.494113\pi$
$68$	−7.48807e16	−0.292102
$69$	7.63488e16	0.259260
$70$	−2.08020e17	−0.616132
$71$	1.76105e17	0.455846	0.227923	−	0.973679i	$-0.426807\pi$
$71$	1.76105e17	0.455846	0.227923	+	0.973679i	$0.426807\pi$
$72$	−4.58262e17	−1.03862
$73$	2.64213e17	0.525276	0.262638	−	0.964894i	$-0.415408\pi$
$73$	2.64213e17	0.525276	0.262638	+	0.964894i	$0.415408\pi$
$74$	5.99689e17	1.04767
$75$	−2.77273e16	−0.0426408
$76$	7.30531e16	0.0990626
$77$	−2.46801e18	−2.95587
$78$	8.47112e16	0.0897515
$79$	3.99397e17	0.374927	0.187464	−	0.982272i	$-0.439973\pi$
$79$	3.99397e17	0.374927	0.187464	+	0.982272i	$0.439973\pi$
$80$	3.20673e17	0.267121
$81$	1.16943e18	0.865698
$82$	−1.10530e17	−0.0728195
$83$	−9.57676e17	−0.562311	−0.281156	−	0.959662i	$-0.590718\pi$
$83$	−9.57676e17	−0.562311	−0.281156	+	0.959662i	$0.590718\pi$
$84$	−2.07458e17	−0.108712
$85$	−9.05989e17	−0.424271
$86$	1.61249e17	0.0675710
$87$	−2.89553e17	−0.108717
$88$	5.76575e18	1.94210
$89$	4.73978e18	1.43401	0.717006	−	0.697067i	$-0.245512\pi$
$89$	4.73978e18	1.43401	0.717006	+	0.697067i	$0.245512\pi$
$90$	−1.30527e18	−0.355137
$91$	−3.42080e18	−0.837982
$92$	1.69563e18	0.374410
$93$	−1.99683e18	−0.397882
$94$	1.19718e18	0.215499
$95$	8.83877e17	0.143886
$96$	8.55226e17	0.126039
$97$	1.13670e18	0.151815	0.0759077	−	0.997115i	$-0.475815\pi$
$97$	1.13670e18	0.151815	0.0759077	+	0.997115i	$0.475815\pi$
$98$	−1.19648e19	−1.44964
$99$	−1.54861e19	−1.70376
$100$	−6.15796e17	−0.0615796
$101$	−6.26392e18	−0.569893	−0.284946	−	0.958543i	$-0.591976\pi$
$101$	−6.26392e18	−0.569893	−0.284946	+	0.958543i	$0.591976\pi$
$102$	2.03100e18	0.168271
$103$	1.15445e19	0.871808	0.435904	−	0.899993i	$-0.356429\pi$
$103$	1.15445e19	0.871808	0.435904	+	0.899993i	$0.356429\pi$
$104$	7.99166e18	0.550580
$105$	−2.51005e18	−0.157901
$106$	−5.47136e18	−0.314550
$107$	2.67312e19	1.40563	0.702816	−	0.711371i	$-0.251926\pi$
$107$	2.67312e19	1.40563	0.702816	+	0.711371i	$0.251926\pi$
$108$	−2.66547e18	−0.128306
$109$	−1.27992e19	−0.564459	−0.282229	−	0.959347i	$-0.591074\pi$
$109$	−1.27992e19	−0.564459	−0.282229	+	0.959347i	$0.591074\pi$
$110$	1.64226e19	0.664067
$111$	7.23608e18	0.268494
$112$	2.90294e19	0.989160
$113$	−9.74394e18	−0.305133	−0.152567	−	0.988293i	$-0.548754\pi$
$113$	−9.74394e18	−0.305133	−0.152567	+	0.988293i	$0.548754\pi$
$114$	−1.98143e18	−0.0570668
$115$	2.05156e19	0.543820
$116$	−6.43070e18	−0.157003
$117$	−2.14646e19	−0.483011
$118$	−3.91578e19	−0.812717
$119$	−8.20159e19	−1.57109
$120$	5.86396e18	0.103746
$121$	1.33684e20	2.18583
$122$	−2.82194e19	−0.426707
$123$	−1.33370e18	−0.0186620
$124$	−4.43477e19	−0.574600
$125$	−7.45058e18	−0.0894427
$126$	−1.18161e20	−1.31509
$127$	1.26795e20	1.30908	0.654540	−	0.756027i	$-0.272862\pi$
$127$	1.26795e20	1.30908	0.654540	+	0.756027i	$0.272862\pi$
$128$	−3.28591e19	−0.314892
$129$	1.94569e18	0.0173169
$130$	2.27627e19	0.188261
$131$	−1.50856e20	−1.16007	−0.580036	−	0.814591i	$-0.696961\pi$
$131$	−1.50856e20	−1.16007	−0.580036	+	0.814591i	$0.696961\pi$
$132$	1.63782e19	0.117169
$133$	8.00142e19	0.532815
$134$	−4.96189e18	−0.0307717
$135$	−3.22498e19	−0.186361
$136$	1.91605e20	1.03225
$137$	−3.57080e19	−0.179441	−0.0897203	−	0.995967i	$-0.528597\pi$
$137$	−3.57080e19	−0.179441	−0.0897203	+	0.995967i	$0.528597\pi$
$138$	−4.59909e19	−0.215685
$139$	3.60820e20	1.57998	0.789988	−	0.613123i	$-0.210087\pi$
$139$	3.60820e20	1.57998	0.789988	+	0.613123i	$0.210087\pi$
$140$	−5.57458e19	−0.228032
$141$	1.44456e19	0.0552275
$142$	−1.06082e20	−0.379230
$143$	2.70063e20	0.903177
$144$	1.82151e20	0.570150
$145$	−7.78057e19	−0.228042
$146$	−1.59157e20	−0.436991
$147$	−1.44372e20	−0.371509
$148$	1.60706e20	0.387745
$149$	−6.43116e20	−1.45553	−0.727763	−	0.685829i	$-0.759440\pi$
$149$	−6.43116e20	−1.45553	−0.727763	+	0.685829i	$0.759440\pi$
$150$	1.67024e19	0.0354740
$151$	−5.78979e20	−1.15447	−0.577234	−	0.816579i	$-0.695868\pi$
$151$	−5.78979e20	−1.15447	−0.577234	+	0.816579i	$0.695868\pi$
$152$	−1.86929e20	−0.350076
$153$	−5.14627e20	−0.905574
$154$	1.48668e21	2.45907
$155$	−5.36568e20	−0.834590
$156$	2.27011e19	0.0332173
$157$	−8.94796e20	−1.23219	−0.616095	−	0.787672i	$-0.711286\pi$
$157$	−8.94796e20	−1.23219	−0.616095	+	0.787672i	$0.711286\pi$
$158$	−2.40588e20	−0.311912
$159$	−6.60196e19	−0.0806121
$160$	2.29807e20	0.264377
$161$	1.85720e21	2.01379
$162$	−7.04440e20	−0.720197
$163$	1.43994e21	1.38855	0.694277	−	0.719708i	$-0.255724\pi$
$163$	1.43994e21	1.38855	0.694277	+	0.719708i	$0.255724\pi$
$164$	−2.96201e19	−0.0269507
$165$	1.98162e20	0.170185
$166$	5.76884e20	0.467802
$167$	−1.44331e20	−0.110548	−0.0552742	−	0.998471i	$-0.517603\pi$
$167$	−1.44331e20	−0.110548	−0.0552742	+	0.998471i	$0.517603\pi$
$168$	5.30843e20	0.384174
$169$	−1.08760e21	−0.743951
$170$	5.45749e20	0.352962
$171$	5.02067e20	0.307113
$172$	4.32118e19	0.0250082
$173$	2.09222e19	0.0114596	0.00572979	−	0.999984i	$-0.498176\pi$
$173$	2.09222e19	0.0114596	0.00572979	+	0.999984i	$0.498176\pi$
$174$	1.74421e20	0.0904442
$175$	−6.74474e20	−0.331210
$176$	−2.29179e21	−1.06612
$177$	−4.72494e20	−0.208281
$178$	−2.85514e21	−1.19299
$179$	2.30052e21	0.911426	0.455713	−	0.890127i	$-0.349384\pi$
$179$	2.30052e21	0.911426	0.455713	+	0.890127i	$0.349384\pi$
$180$	−3.49789e20	−0.131437
$181$	−2.28886e21	−0.815967	−0.407983	−	0.912989i	$-0.633768\pi$
$181$	−2.28886e21	−0.815967	−0.407983	+	0.912989i	$0.633768\pi$
$182$	2.06062e21	0.697140
$183$	−3.40507e20	−0.109355
$184$	−4.33879e21	−1.32312
$185$	1.94440e21	0.563189
$186$	1.20285e21	0.331008
$187$	6.47493e21	1.69332
$188$	3.20823e20	0.0797566
$189$	−2.91946e21	−0.690104
$190$	−5.32429e20	−0.119702
$191$	8.70600e20	0.186210	0.0931048	−	0.995656i	$-0.470321\pi$
$191$	8.70600e20	0.186210	0.0931048	+	0.995656i	$0.470321\pi$
$192$	−1.14085e21	−0.232202
$193$	−4.54209e21	−0.879957	−0.439978	−	0.898008i	$-0.645014\pi$
$193$	−4.54209e21	−0.879957	−0.439978	+	0.898008i	$0.645014\pi$
$194$	−6.84727e20	−0.126299
$195$	2.74663e20	0.0482472
$196$	−3.20637e21	−0.536514
$197$	6.60053e21	1.05233	0.526163	−	0.850384i	$-0.323630\pi$
$197$	6.60053e21	1.05233	0.526163	+	0.850384i	$0.323630\pi$
$198$	9.32850e21	1.41740
$199$	2.34627e21	0.339840	0.169920	−	0.985458i	$-0.445649\pi$
$199$	2.34627e21	0.339840	0.169920	+	0.985458i	$0.445649\pi$
$200$	1.57570e21	0.217615
$201$	−5.98722e19	−0.00788610
$202$	3.77325e21	0.474109
$203$	−7.04346e21	−0.844450
$204$	5.44273e20	0.0622774
$205$	−3.58376e20	−0.0391451
$206$	−6.95416e21	−0.725281
$207$	1.16534e22	1.16074
$208$	−3.17655e21	−0.302242
$209$	−6.31690e21	−0.574268
$210$	1.51200e21	0.131362
$211$	6.77827e21	0.562905	0.281453	−	0.959575i	$-0.409184\pi$
$211$	6.77827e21	0.562905	0.281453	+	0.959575i	$0.409184\pi$
$212$	−1.46623e21	−0.116416
$213$	−1.28003e21	−0.0971882
$214$	−1.61023e22	−1.16938
$215$	5.22824e20	0.0363237
$216$	6.82041e21	0.453419
$217$	−4.85735e22	−3.09052
$218$	7.70999e21	0.469588
$219$	−1.92045e21	−0.111991
$220$	4.40098e21	0.245773
$221$	8.97462e21	0.480053
$222$	−4.35886e21	−0.223367
$223$	−6.59692e19	−0.00323925	−0.00161963	−	0.999999i	$-0.500516\pi$
$223$	−6.59692e19	−0.00323925	−0.00161963	+	0.999999i	$0.500516\pi$
$224$	2.08036e22	0.978999
$225$	−4.23214e21	−0.190909
$226$	5.86955e21	0.253848
$227$	8.57187e21	0.355492	0.177746	−	0.984076i	$-0.443119\pi$
$227$	8.57187e21	0.355492	0.177746	+	0.984076i	$0.443119\pi$
$228$	−5.30990e20	−0.0211206
$229$	3.56492e22	1.36023	0.680116	−	0.733105i	$-0.261929\pi$
$229$	3.56492e22	1.36023	0.680116	+	0.733105i	$0.261929\pi$
$230$	−1.23582e22	−0.452418
$231$	1.79389e22	0.630204
$232$	1.64549e22	0.554829
$233$	−1.15795e22	−0.374806	−0.187403	−	0.982283i	$-0.560007\pi$
$233$	−1.15795e22	−0.374806	−0.187403	+	0.982283i	$0.560007\pi$
$234$	1.29298e22	0.401830
$235$	3.88168e21	0.115844
$236$	−1.04936e22	−0.300789
$237$	−2.90303e21	−0.0799361
$238$	4.94046e22	1.30703
$239$	1.75682e22	0.446630	0.223315	−	0.974746i	$-0.428312\pi$
$239$	1.75682e22	0.446630	0.223315	+	0.974746i	$0.428312\pi$
$240$	−2.33083e21	−0.0569513
$241$	−6.46238e22	−1.51786	−0.758928	−	0.651175i	$-0.774277\pi$
$241$	−6.46238e22	−1.51786	−0.758928	+	0.651175i	$0.774277\pi$
$242$	−8.05283e22	−1.81845
$243$	−2.76912e22	−0.601287
$244$	−7.56232e21	−0.157925
$245$	−3.87942e22	−0.779271
$246$	8.03390e20	0.0155254
$247$	−8.75558e21	−0.162804
$248$	1.13477e23	2.03057
$249$	6.96091e21	0.119887
$250$	4.48808e21	0.0744098
$251$	6.55426e22	1.04622	0.523111	−	0.852265i	$-0.324771\pi$
$251$	6.55426e22	1.04622	0.523111	+	0.852265i	$0.324771\pi$
$252$	−3.16652e22	−0.486717
$253$	−1.46621e23	−2.17046
$254$	−7.63786e22	−1.08906
$255$	6.58522e21	0.0904563
$256$	−6.24969e22	−0.827140
$257$	9.77816e22	1.24707	0.623537	−	0.781794i	$-0.285695\pi$
$257$	9.77816e22	1.24707	0.623537	+	0.781794i	$0.285695\pi$
$258$	−1.17204e21	−0.0144064
$259$	1.76019e23	2.08551
$260$	6.10000e21	0.0696760
$261$	−4.41958e22	−0.486739
$262$	9.08724e22	0.965094
$263$	8.55330e22	0.876100	0.438050	−	0.898950i	$-0.355669\pi$
$263$	8.55330e22	0.876100	0.438050	+	0.898950i	$0.355669\pi$
$264$	−4.19086e22	−0.414063
$265$	−1.77401e22	−0.169091
$266$	−4.81989e22	−0.443263
$267$	−3.44513e22	−0.305737
$268$	−1.32970e21	−0.0113887
$269$	−1.22658e23	−1.01403	−0.507013	−	0.861938i	$-0.669250\pi$
$269$	−1.22658e23	−1.01403	−0.507013	+	0.861938i	$0.669250\pi$
$270$	1.94266e22	0.155039
$271$	2.44438e23	1.88347	0.941737	−	0.336349i	$-0.109192\pi$
$271$	2.44438e23	1.88347	0.941737	+	0.336349i	$0.109192\pi$
$272$	−7.61598e22	−0.566658
$273$	2.48643e22	0.178661
$274$	2.15098e22	0.149281
$275$	5.32479e22	0.356978
$276$	−1.23248e22	−0.0798257
$277$	1.93773e23	1.21265	0.606325	−	0.795217i	$-0.292643\pi$
$277$	1.93773e23	1.21265	0.606325	+	0.795217i	$0.292643\pi$
$278$	−2.17351e23	−1.31442
$279$	−3.04785e23	−1.78137
$280$	1.42642e23	0.805838
$281$	1.36795e23	0.747068	0.373534	−	0.927617i	$-0.378146\pi$
$281$	1.36795e23	0.747068	0.373534	+	0.927617i	$0.378146\pi$
$282$	−8.70175e21	−0.0459452
$283$	−1.05694e23	−0.539608	−0.269804	−	0.962915i	$-0.586959\pi$
$283$	−1.05694e23	−0.539608	−0.269804	+	0.962915i	$0.586959\pi$
$284$	−2.84282e22	−0.140354
$285$	−6.42450e21	−0.0306770
$286$	−1.62680e23	−0.751377
$287$	−3.24425e22	−0.144956
$288$	1.30537e23	0.564293
$289$	−2.39005e22	−0.0999719
$290$	4.68685e22	0.189714
$291$	−8.26219e21	−0.0323677
$292$	−4.26512e22	−0.161731
$293$	−3.41313e23	−1.25288	−0.626442	−	0.779468i	$-0.715490\pi$
$293$	−3.41313e23	−1.25288	−0.626442	+	0.779468i	$0.715490\pi$
$294$	8.69669e22	0.309068
$295$	−1.26963e23	−0.436887
$296$	−4.11216e23	−1.37025
$297$	2.30483e23	0.743794
$298$	3.87400e23	1.21089
$299$	−2.03225e23	−0.615320
$300$	4.47594e21	0.0131290
$301$	4.73294e22	0.134508
$302$	3.48765e23	0.960432
$303$	4.55296e22	0.121503
$304$	7.43010e22	0.192175
$305$	−9.14973e22	−0.229382
$306$	3.10001e23	0.753371
$307$	2.62324e23	0.618051	0.309025	−	0.951054i	$-0.399997\pi$
$307$	2.62324e23	0.618051	0.309025	+	0.951054i	$0.399997\pi$
$308$	3.98404e23	0.910106
$309$	−8.39116e22	−0.185873
$310$	3.23217e23	0.694318
$311$	1.92851e23	0.401789	0.200895	−	0.979613i	$-0.435615\pi$
$311$	1.92851e23	0.401789	0.200895	+	0.979613i	$0.435615\pi$
$312$	−5.80877e22	−0.117386
$313$	−5.14311e23	−1.00822	−0.504109	−	0.863640i	$-0.668179\pi$
$313$	−5.14311e23	−1.00822	−0.504109	+	0.863640i	$0.668179\pi$
$314$	5.39007e23	1.02509
$315$	−3.83120e23	−0.706943
$316$	−6.44735e22	−0.115439
$317$	−4.64488e23	−0.807070	−0.403535	−	0.914964i	$-0.632219\pi$
$317$	−4.64488e23	−0.807070	−0.403535	+	0.914964i	$0.632219\pi$
$318$	3.97689e22	0.0670634
$319$	5.56062e23	0.910148
$320$	−3.06556e23	−0.487063
$321$	−1.94297e23	−0.299687
$322$	−1.11874e24	−1.67532
$323$	−2.09920e23	−0.305233
$324$	−1.88778e23	−0.266547
$325$	7.38046e22	0.101203
$326$	−8.67391e23	−1.15517
$327$	9.30318e22	0.120345
$328$	7.57919e22	0.0952404
$329$	3.51394e23	0.428976
$330$	−1.19368e23	−0.141582
$331$	−4.24264e23	−0.488957	−0.244478	−	0.969655i	$-0.578617\pi$
$331$	−4.24264e23	−0.488957	−0.244478	+	0.969655i	$0.578617\pi$
$332$	1.54595e23	0.173134
$333$	1.10447e24	1.20209
$334$	8.69418e22	0.0919681
$335$	−1.60882e22	−0.0165418
$336$	−2.11001e23	−0.210893
$337$	−1.26198e24	−1.22622	−0.613112	−	0.789996i	$-0.710082\pi$
$337$	−1.26198e24	−1.22622	−0.613112	+	0.789996i	$0.710082\pi$
$338$	6.55146e23	0.618913
$339$	7.08243e22	0.0650557
$340$	1.46251e23	0.130632
$341$	3.83475e24	3.33096
$342$	−3.02435e23	−0.255496
$343$	−1.49646e24	−1.22962
$344$	−1.10571e23	−0.0883760
$345$	−1.49119e23	−0.115945
$346$	−1.26031e22	−0.00953353
$347$	−3.03592e23	−0.223440	−0.111720	−	0.993740i	$-0.535636\pi$
$347$	−3.03592e23	−0.223440	−0.111720	+	0.993740i	$0.535636\pi$
$348$	4.67418e22	0.0334736
$349$	1.52003e24	1.05928	0.529640	−	0.848223i	$-0.322327\pi$
$349$	1.52003e24	1.05928	0.529640	+	0.848223i	$0.322327\pi$
$350$	4.06289e23	0.275543
$351$	3.19463e23	0.210864
$352$	−1.64239e24	−1.05516
$353$	1.86593e24	1.16690	0.583452	−	0.812147i	$-0.301701\pi$
$353$	1.86593e24	1.16690	0.583452	+	0.812147i	$0.301701\pi$
$354$	2.84620e23	0.173275
$355$	−3.43956e23	−0.203860
$356$	−7.65129e23	−0.441530
$357$	5.96136e23	0.334963
$358$	−1.38578e24	−0.758240
$359$	−2.84818e24	−1.51765	−0.758823	−	0.651297i	$-0.774225\pi$
$359$	−2.84818e24	−1.51765	−0.758823	+	0.651297i	$0.774225\pi$
$360$	8.95042e23	0.464483
$361$	−1.77362e24	−0.896484
$362$	1.37876e24	0.678824
$363$	−9.71686e23	−0.466029
$364$	5.52211e23	0.258013
$365$	−5.16041e23	−0.234910
$366$	2.05114e23	0.0909757
$367$	3.75183e24	1.62150	0.810748	−	0.585395i	$-0.199061\pi$
$367$	3.75183e24	1.62150	0.810748	+	0.585395i	$0.199061\pi$
$368$	1.72460e24	0.726328
$369$	−2.03568e23	−0.0835523
$370$	−1.17127e24	−0.468532
$371$	−1.60594e24	−0.626150
$372$	3.22343e23	0.122507
$373$	−3.34549e24	−1.23944	−0.619720	−	0.784823i	$-0.712754\pi$
$373$	−3.34549e24	−1.23944	−0.619720	+	0.784823i	$0.712754\pi$
$374$	−3.90036e24	−1.40872
$375$	5.41549e22	0.0190696
$376$	−8.20924e23	−0.281850
$377$	7.70734e23	0.258025
$378$	1.75862e24	0.574116
$379$	1.87499e24	0.596936	0.298468	−	0.954420i	$-0.403524\pi$
$379$	1.87499e24	0.596936	0.298468	+	0.954420i	$0.403524\pi$
$380$	−1.42682e23	−0.0443021
$381$	−9.21614e23	−0.279101
$382$	−5.24432e23	−0.154913
$383$	−2.09774e24	−0.604453	−0.302227	−	0.953236i	$-0.597730\pi$
$383$	−2.09774e24	−0.604453	−0.302227	+	0.953236i	$0.597730\pi$
$384$	2.38838e23	0.0671363
$385$	4.82033e24	1.32191
$386$	2.73606e24	0.732059
$387$	2.96979e23	0.0775303
$388$	−1.83495e23	−0.0467437
$389$	6.88159e23	0.171068	0.0855338	−	0.996335i	$-0.472740\pi$
$389$	6.88159e23	0.171068	0.0855338	+	0.996335i	$0.472740\pi$
$390$	−1.65451e23	−0.0401381
$391$	−4.87245e24	−1.15363
$392$	8.20447e24	1.89598
$393$	1.09650e24	0.247332
$394$	−3.97602e24	−0.875457
$395$	−7.80072e23	−0.167673
$396$	2.49988e24	0.524583
$397$	6.02887e24	1.23517	0.617584	−	0.786505i	$-0.288112\pi$
$397$	6.02887e24	1.23517	0.617584	+	0.786505i	$0.288112\pi$
$398$	−1.41335e24	−0.282722
$399$	−5.81587e23	−0.113598
$400$	−6.26315e23	−0.119460
$401$	−6.72812e23	−0.125321	−0.0626603	−	0.998035i	$-0.519958\pi$
$401$	−6.72812e23	−0.125321	−0.0626603	+	0.998035i	$0.519958\pi$
$402$	3.60658e22	0.00656066
$403$	5.31518e24	0.944321
$404$	1.01117e24	0.175469
$405$	−2.28404e24	−0.387152
$406$	4.24284e24	0.702520
$407$	−1.38963e25	−2.24777
$408$	−1.39269e24	−0.220081
$409$	2.81211e24	0.434171	0.217086	−	0.976153i	$-0.430345\pi$
$409$	2.81211e24	0.434171	0.217086	+	0.976153i	$0.430345\pi$
$410$	2.15878e23	0.0325659
$411$	2.59545e23	0.0382575
$412$	−1.86359e24	−0.268428
$413$	−1.14935e25	−1.61781
$414$	−7.01979e24	−0.965653
$415$	1.87046e24	0.251473
$416$	−2.27644e24	−0.299137
$417$	−2.62264e24	−0.336857
$418$	3.80517e24	0.477749
$419$	−3.47790e24	−0.426858	−0.213429	−	0.976959i	$-0.568463\pi$
$419$	−3.47790e24	−0.426858	−0.213429	+	0.976959i	$0.568463\pi$
$420$	4.05191e23	0.0486173
$421$	7.98673e24	0.936891	0.468446	−	0.883492i	$-0.344814\pi$
$421$	7.98673e24	0.936891	0.468446	+	0.883492i	$0.344814\pi$
$422$	−4.08309e24	−0.468296
$423$	2.20490e24	0.247261
$424$	3.75180e24	0.411399
$425$	1.76951e24	0.189740
$426$	7.71063e23	0.0808535
$427$	−8.28292e24	−0.849412
$428$	−4.31514e24	−0.432792
$429$	−1.96297e24	−0.192561
$430$	−3.14939e23	−0.0302187
$431$	6.63420e24	0.622665	0.311332	−	0.950301i	$-0.399225\pi$
$431$	6.63420e24	0.622665	0.311332	+	0.950301i	$0.399225\pi$
$432$	−2.71100e24	−0.248905
$433$	2.19607e25	1.97247	0.986236	−	0.165345i	$-0.0528738\pi$
$433$	2.19607e25	1.97247	0.986236	+	0.165345i	$0.0528738\pi$
$434$	2.92597e25	2.57109
$435$	5.65534e23	0.0486195
$436$	2.06615e24	0.173796
$437$	4.75353e24	0.391240
$438$	1.15684e24	0.0931682
$439$	3.60776e24	0.284331	0.142166	−	0.989843i	$-0.454593\pi$
$439$	3.60776e24	0.284331	0.142166	+	0.989843i	$0.454593\pi$
$440$	−1.12612e25	−0.868531
$441$	−2.20362e25	−1.66330
$442$	−5.40612e24	−0.399369
$443$	1.63931e25	1.18529	0.592646	−	0.805463i	$-0.298084\pi$
$443$	1.63931e25	1.18529	0.592646	+	0.805463i	$0.298084\pi$
$444$	−1.16810e24	−0.0826688
$445$	−9.25738e24	−0.641310
$446$	3.97384e22	0.00269482
$447$	4.67452e24	0.310324
$448$	−2.77514e25	−1.80362
$449$	5.63016e24	0.358245	0.179123	−	0.983827i	$-0.442674\pi$
$449$	5.63016e24	0.358245	0.179123	+	0.983827i	$0.442674\pi$
$450$	2.54935e24	0.158822
$451$	2.56125e24	0.156233
$452$	1.57294e24	0.0939499
$453$	4.20833e24	0.246137
$454$	−5.16351e24	−0.295743
$455$	6.68126e24	0.374757
$456$	1.35870e24	0.0746375
$457$	−7.63075e24	−0.410547	−0.205274	−	0.978705i	$-0.565808\pi$
$457$	−7.63075e24	−0.410547	−0.205274	+	0.978705i	$0.565808\pi$
$458$	−2.14743e25	−1.13161
$459$	7.65931e24	0.395338
$460$	−3.31178e24	−0.167441
$461$	−2.09159e25	−1.03590	−0.517949	−	0.855411i	$-0.673304\pi$
$461$	−2.09159e25	−1.03590	−0.517949	+	0.855411i	$0.673304\pi$
$462$	−1.08060e25	−0.524283
$463$	2.39688e25	1.13927	0.569636	−	0.821897i	$-0.307084\pi$
$463$	2.39688e25	1.13927	0.569636	+	0.821897i	$0.307084\pi$
$464$	−6.54055e24	−0.304574
$465$	3.90007e24	0.177938
$466$	6.97522e24	0.311811
$467$	−7.18154e24	−0.314563	−0.157281	−	0.987554i	$-0.550273\pi$
$467$	−7.18154e24	−0.314563	−0.157281	+	0.987554i	$0.550273\pi$
$468$	3.46497e24	0.148718
$469$	−1.45641e24	−0.0612549
$470$	−2.33824e24	−0.0963739
$471$	6.50387e24	0.262708
$472$	2.68511e25	1.06295
$473$	−3.73653e24	−0.144973
$474$	1.74873e24	0.0665010
$475$	−1.72632e24	−0.0643477
$476$	1.32396e25	0.483736
$477$	−1.00769e25	−0.360912
$478$	−1.05827e25	−0.371564
$479$	−2.29371e25	−0.789497	−0.394748	−	0.918789i	$-0.629168\pi$
$479$	−2.29371e25	−0.789497	−0.394748	+	0.918789i	$0.629168\pi$
$480$	−1.67036e24	−0.0563663
$481$	−1.92610e25	−0.637237
$482$	3.89280e25	1.26274
$483$	−1.34992e25	−0.429348
$484$	−2.15802e25	−0.673014
$485$	−2.22013e24	−0.0678939
$486$	1.66806e25	0.500227
$487$	4.44702e25	1.30781	0.653904	−	0.756578i	$-0.273130\pi$
$487$	4.44702e25	1.30781	0.653904	+	0.756578i	$0.273130\pi$
$488$	1.93505e25	0.558089
$489$	−1.04663e25	−0.296045
$490$	2.33688e25	0.648297
$491$	3.67924e25	1.00112	0.500558	−	0.865703i	$-0.333128\pi$
$491$	3.67924e25	1.00112	0.500558	+	0.865703i	$0.333128\pi$
$492$	2.15295e23	0.00574599
$493$	1.84788e25	0.483758
$494$	5.27418e24	0.135441
$495$	3.02463e25	0.761943
$496$	−4.51053e25	−1.11468
$497$	−3.11370e25	−0.754904
$498$	−4.19311e24	−0.0997372
$499$	−4.77794e25	−1.11503	−0.557513	−	0.830168i	$-0.688244\pi$
$499$	−4.77794e25	−1.11503	−0.557513	+	0.830168i	$0.688244\pi$
$500$	1.20273e24	0.0275392
$501$	1.04907e24	0.0235694
$502$	−3.94815e25	−0.870379
$503$	−5.05128e25	−1.09271	−0.546356	−	0.837553i	$-0.683985\pi$
$503$	−5.05128e25	−1.09271	−0.546356	+	0.837553i	$0.683985\pi$
$504$	8.10249e25	1.72000
$505$	1.22342e25	0.254864
$506$	8.83215e25	1.80566
$507$	7.90525e24	0.158613
$508$	−2.04681e25	−0.403063
$509$	−8.38037e25	−1.61974	−0.809868	−	0.586613i	$-0.800461\pi$
$509$	−8.38037e25	−1.61974	−0.809868	+	0.586613i	$0.800461\pi$
$510$	−3.96680e24	−0.0752530
$511$	−4.67153e25	−0.869883
$512$	5.48745e25	1.00301
$513$	−7.47238e24	−0.134074
$514$	−5.89016e25	−1.03747
$515$	−2.25478e25	−0.389885
$516$	−3.14087e23	−0.00533185
$517$	−2.77416e25	−0.462350
$518$	−1.06030e26	−1.73499
$519$	−1.52074e23	−0.00244323
$520$	−1.56087e25	−0.246227
$521$	−3.89398e25	−0.603164	−0.301582	−	0.953440i	$-0.597515\pi$
$521$	−3.89398e25	−0.603164	−0.301582	+	0.953440i	$0.597515\pi$
$522$	2.66226e25	0.404931
$523$	1.30312e26	1.94634	0.973172	−	0.230079i	$-0.0738984\pi$
$523$	1.30312e26	1.94634	0.973172	+	0.230079i	$0.0738984\pi$
$524$	2.43522e25	0.357184
$525$	4.90244e24	0.0706154
$526$	−5.15233e25	−0.728851
$527$	1.27435e26	1.77046
$528$	1.66580e25	0.227300
$529$	3.57184e25	0.478700
$530$	1.06863e25	0.140671
$531$	−7.21188e25	−0.932503
$532$	−1.29165e25	−0.164053
$533$	3.55003e24	0.0442918
$534$	2.07527e25	0.254351
$535$	−5.22093e25	−0.628618
$536$	3.40245e24	0.0402463
$537$	−1.67214e25	−0.194320
$538$	7.38867e25	0.843596
$539$	2.77255e26	3.11018
$540$	5.20599e24	0.0573803
$541$	1.65622e26	1.79368	0.896840	−	0.442356i	$-0.145857\pi$
$541$	1.65622e26	1.79368	0.896840	+	0.442356i	$0.145857\pi$
$542$	−1.47244e26	−1.56691
$543$	1.66367e25	0.173967
$544$	−5.45791e25	−0.560837
$545$	2.49985e25	0.252434
$546$	−1.49777e25	−0.148633
$547$	−1.15104e26	−1.12257	−0.561283	−	0.827624i	$-0.689692\pi$
$547$	−1.15104e26	−1.12257	−0.561283	+	0.827624i	$0.689692\pi$
$548$	5.76425e24	0.0552494
$549$	−5.19730e25	−0.489599
$550$	−3.20754e25	−0.296980
$551$	−1.80278e25	−0.164060
$552$	3.15367e25	0.282094
$553$	−7.06171e25	−0.620899
$554$	−1.16725e26	−1.00884
$555$	−1.41330e25	−0.120074
$556$	−5.82462e25	−0.486471
$557$	5.90917e25	0.485179	0.242589	−	0.970129i	$-0.422003\pi$
$557$	5.90917e25	0.485179	0.242589	+	0.970129i	$0.422003\pi$
$558$	1.83596e26	1.48197
$559$	−5.17904e24	−0.0410995
$560$	−5.66980e25	−0.442366
$561$	−4.70633e25	−0.361023
$562$	−8.24024e25	−0.621505
$563$	−2.27592e26	−1.68783	−0.843913	−	0.536479i	$-0.819754\pi$
$563$	−2.27592e26	−1.68783	−0.843913	+	0.536479i	$0.819754\pi$
$564$	−2.33192e24	−0.0170044
$565$	1.90311e25	0.136460
$566$	6.36677e25	0.448914
$567$	−2.06766e26	−1.43364
$568$	7.27422e25	0.495995
$569$	2.27931e26	1.52840	0.764201	−	0.644979i	$-0.223134\pi$
$569$	2.27931e26	1.52840	0.764201	+	0.644979i	$0.223134\pi$
$570$	3.86999e24	0.0255210
$571$	1.08514e26	0.703793	0.351896	−	0.936039i	$-0.385537\pi$
$571$	1.08514e26	0.703793	0.351896	+	0.936039i	$0.385537\pi$
$572$	−4.35955e25	−0.278086
$573$	−6.32800e24	−0.0397006
$574$	1.95427e25	0.120593
$575$	−4.00696e25	−0.243204
$576$	−1.74133e26	−1.03960
$577$	−8.81902e24	−0.0517905	−0.0258952	−	0.999665i	$-0.508244\pi$
$577$	−8.81902e24	−0.0517905	−0.0258952	+	0.999665i	$0.508244\pi$
$578$	1.43972e25	0.0831693
$579$	3.30144e25	0.187610
$580$	1.25600e25	0.0702137
$581$	1.69326e26	0.931216
$582$	4.97697e24	0.0269275
$583$	1.26785e26	0.674864
$584$	1.09136e26	0.571539
$585$	4.19231e25	0.216009
$586$	2.05600e26	1.04231
$587$	−5.42583e25	−0.270648	−0.135324	−	0.990801i	$-0.543207\pi$
$587$	−5.42583e25	−0.270648	−0.135324	+	0.990801i	$0.543207\pi$
$588$	2.33056e25	0.114387
$589$	−1.24324e26	−0.600428
$590$	7.64801e25	0.363458
$591$	−4.79763e25	−0.224360
$592$	1.63451e26	0.752198
$593$	−3.64055e26	−1.64872	−0.824362	−	0.566063i	$-0.808466\pi$
$593$	−3.64055e26	−1.64872	−0.824362	+	0.566063i	$0.808466\pi$
$594$	−1.38838e26	−0.618782
$595$	1.60187e26	0.702614
$596$	1.03817e26	0.448154
$597$	−1.70540e25	−0.0724552
$598$	1.22419e26	0.511901
$599$	−2.77124e26	−1.14056	−0.570281	−	0.821450i	$-0.693166\pi$
$599$	−2.77124e26	−1.14056	−0.570281	+	0.821450i	$0.693166\pi$
$600$	−1.14531e25	−0.0463964
$601$	6.13522e25	0.244637	0.122319	−	0.992491i	$-0.460967\pi$
$601$	6.13522e25	0.244637	0.122319	+	0.992491i	$0.460967\pi$
$602$	−2.85102e25	−0.111901
$603$	−9.13855e24	−0.0353072
$604$	9.34629e25	0.355458
$605$	−2.61101e26	−0.977535
$606$	−2.74261e25	−0.101082
$607$	3.18411e26	1.15530	0.577650	−	0.816284i	$-0.303970\pi$
$607$	3.18411e26	1.15530	0.577650	+	0.816284i	$0.303970\pi$
$608$	5.32470e25	0.190200
$609$	5.11957e25	0.180040
$610$	5.51161e25	0.190829
$611$	−3.84514e25	−0.131075
$612$	8.30748e25	0.278824
$613$	3.26862e26	1.08016	0.540082	−	0.841612i	$-0.318393\pi$
$613$	3.26862e26	1.08016	0.540082	+	0.841612i	$0.318393\pi$
$614$	−1.58019e26	−0.514173
$615$	2.60487e24	0.00834590
$616$	−1.01944e27	−3.21621
$617$	5.63998e26	1.75214	0.876069	−	0.482185i	$-0.160157\pi$
$617$	5.63998e26	1.75214	0.876069	+	0.482185i	$0.160157\pi$
$618$	5.05466e25	0.154633
$619$	−1.10545e26	−0.333026	−0.166513	−	0.986039i	$-0.553251\pi$
$619$	−1.10545e26	−0.333026	−0.166513	+	0.986039i	$0.553251\pi$
$620$	8.66166e25	0.256969
$621$	−1.73441e26	−0.506735
$622$	−1.16169e26	−0.334259
$623$	−8.38036e26	−2.37480
$624$	2.30889e25	0.0644392
$625$	1.45519e25	0.0400000
$626$	3.09810e26	0.838763
$627$	4.59147e25	0.122436
$628$	1.44444e26	0.379389
$629$	−4.61794e26	−1.19472
$630$	2.30784e26	0.588125
$631$	−1.19564e26	−0.300139	−0.150070	−	0.988675i	$-0.547950\pi$
$631$	−1.19564e26	−0.300139	−0.150070	+	0.988675i	$0.547950\pi$
$632$	1.64975e26	0.407949
$633$	−4.92682e25	−0.120014
$634$	2.79798e26	0.671423
$635$	−2.47646e26	−0.585439
$636$	1.06574e25	0.0248203
$637$	3.84291e26	0.881729
$638$	−3.34960e26	−0.757176
$639$	−1.95376e26	−0.435125
$640$	6.41780e25	0.140824
$641$	7.84345e26	1.69573	0.847863	−	0.530215i	$-0.177889\pi$
$641$	7.84345e26	1.69573	0.847863	+	0.530215i	$0.177889\pi$
$642$	1.17040e26	0.249317
$643$	−5.20443e25	−0.109237	−0.0546184	−	0.998507i	$-0.517394\pi$
$643$	−5.20443e25	−0.109237	−0.0546184	+	0.998507i	$0.517394\pi$
$644$	−2.99803e26	−0.620041
$645$	−3.80017e24	−0.00774437
$646$	1.26452e26	0.253931
$647$	−3.27477e26	−0.648022	−0.324011	−	0.946053i	$-0.605031\pi$
$647$	−3.27477e26	−0.648022	−0.324011	+	0.946053i	$0.605031\pi$
$648$	4.83045e26	0.941945
$649$	9.07383e26	1.74368
$650$	−4.44583e25	−0.0841931
$651$	3.53059e26	0.658912
$652$	−2.32446e26	−0.427533
$653$	8.02573e26	1.45482	0.727410	−	0.686203i	$-0.240724\pi$
$653$	8.02573e26	1.45482	0.727410	+	0.686203i	$0.240724\pi$
$654$	−5.60404e25	−0.100118
$655$	2.94640e26	0.518800
$656$	−3.01260e25	−0.0522824
$657$	−2.93126e26	−0.501399
$658$	−2.11672e26	−0.356877
$659$	1.05697e25	0.0175651	0.00878253	−	0.999961i	$-0.497204\pi$
$659$	1.05697e25	0.0175651	0.00878253	+	0.999961i	$0.497204\pi$
$660$	−3.19887e25	−0.0523997
$661$	−7.11467e26	−1.14879	−0.574395	−	0.818578i	$-0.694763\pi$
$661$	−7.11467e26	−1.14879	−0.574395	+	0.818578i	$0.694763\pi$
$662$	2.55568e26	0.406776
$663$	−6.52324e25	−0.102349
$664$	−3.95578e26	−0.611837
$665$	−1.56278e26	−0.238282
$666$	−6.65312e26	−1.00005
$667$	−4.18442e26	−0.620069
$668$	2.32989e25	0.0340376
$669$	4.79500e23	0.000690622 0
$670$	9.69120e24	0.0137615
$671$	6.53914e26	0.915496
$672$	−1.51212e26	−0.208727
$673$	−1.29229e27	−1.75880	−0.879398	−	0.476087i	$-0.842055\pi$
$673$	−1.29229e27	−1.75880	−0.879398	+	0.476087i	$0.842055\pi$
$674$	7.60193e26	1.02013
$675$	6.29879e25	0.0833434
$676$	1.75568e26	0.229061
$677$	−1.30752e26	−0.168212	−0.0841061	−	0.996457i	$-0.526803\pi$
$677$	−1.30752e26	−0.168212	−0.0841061	+	0.996457i	$0.526803\pi$
$678$	−4.26631e25	−0.0541215
$679$	−2.00980e26	−0.251414
$680$	−3.74228e26	−0.461638
$681$	−6.23050e25	−0.0757923
$682$	−2.30997e27	−2.77112
$683$	5.44217e26	0.643837	0.321918	−	0.946767i	$-0.395672\pi$
$683$	5.44217e26	0.643837	0.321918	+	0.946767i	$0.395672\pi$
$684$	−8.10473e25	−0.0945596
$685$	6.97423e25	0.0802482
$686$	9.01439e26	1.02296
$687$	−2.59118e26	−0.290007
$688$	4.39500e25	0.0485142
$689$	1.75731e26	0.191323
$690$	8.98260e25	0.0964574
$691$	6.89644e26	0.730438	0.365219	−	0.930922i	$-0.380994\pi$
$691$	6.89644e26	0.730438	0.365219	+	0.930922i	$0.380994\pi$
$692$	−3.37741e24	−0.00352838
$693$	2.73809e27	2.82151
$694$	1.82878e26	0.185886
$695$	−7.04727e26	−0.706586
$696$	−1.19603e26	−0.118292
$697$	8.51142e25	0.0830406
$698$	−9.15635e26	−0.881243
$699$	8.41658e25	0.0799103
$700$	1.08878e26	0.101979
$701$	1.40735e26	0.130041	0.0650206	−	0.997884i	$-0.479289\pi$
$701$	1.40735e26	0.130041	0.0650206	+	0.997884i	$0.479289\pi$
$702$	−1.92438e26	−0.175423
$703$	4.50524e26	0.405175
$704$	2.19090e27	1.94394
$705$	−2.82141e25	−0.0246985
$706$	−1.12400e27	−0.970779
$707$	1.10752e27	0.943771
$708$	7.62734e25	0.0641294
$709$	−6.90974e26	−0.573221	−0.286611	−	0.958047i	$-0.592529\pi$
$709$	−6.90974e26	−0.573221	−0.286611	+	0.958047i	$0.592529\pi$
$710$	2.07192e26	0.169597
$711$	−4.43103e26	−0.357885
$712$	1.95782e27	1.56031
$713$	−2.88569e27	−2.26933
$714$	−3.59100e26	−0.278665
$715$	−5.27467e26	−0.403913
$716$	−3.71366e26	−0.280626
$717$	−1.27696e26	−0.0952234
$718$	1.71569e27	1.26257
$719$	1.46959e27	1.06726	0.533631	−	0.845718i	$-0.320827\pi$
$719$	1.46959e27	1.06726	0.533631	+	0.845718i	$0.320827\pi$
$720$	−3.55765e26	−0.254979
$721$	−2.04117e27	−1.44376
$722$	1.06839e27	0.745809
$723$	4.69721e26	0.323613
$724$	3.69484e26	0.251234
$725$	1.51964e26	0.101984
$726$	5.85323e26	0.387702
$727$	−2.73609e27	−1.78877	−0.894384	−	0.447299i	$-0.852386\pi$
$727$	−2.73609e27	−1.78877	−0.894384	+	0.447299i	$0.852386\pi$
$728$	−1.41300e27	−0.911788
$729$	−1.15791e27	−0.737501
$730$	3.10853e26	0.195428
$731$	−1.24171e26	−0.0770555
$732$	5.49671e25	0.0336703
$733$	4.74553e26	0.286944	0.143472	−	0.989654i	$-0.454173\pi$
$733$	4.74553e26	0.286944	0.143472	+	0.989654i	$0.454173\pi$
$734$	−2.26003e27	−1.34897
$735$	2.81977e26	0.166144
$736$	1.23591e27	0.718867
$737$	1.14979e26	0.0660205
$738$	1.22625e26	0.0695094
$739$	1.52077e27	0.851021	0.425511	−	0.904953i	$-0.360095\pi$
$739$	1.52077e27	0.851021	0.425511	+	0.904953i	$0.360095\pi$
$740$	−3.13879e26	−0.173405
$741$	6.36404e25	0.0347104
$742$	9.67388e26	0.520911
$743$	−1.10141e25	−0.00585541	−0.00292770	−	0.999996i	$-0.500932\pi$
$743$	−1.10141e25	−0.00585541	−0.00292770	+	0.999996i	$0.500932\pi$
$744$	−8.24814e26	−0.432925
$745$	1.25609e27	0.650931
$746$	2.01525e27	1.03112
$747$	1.06247e27	0.536751
$748$	−1.04523e27	−0.521371
$749$	−4.72632e27	−2.32780
$750$	−3.26218e25	−0.0158645
$751$	−3.52240e27	−1.69145	−0.845725	−	0.533619i	$-0.820832\pi$
$751$	−3.52240e27	−1.69145	−0.845725	+	0.533619i	$0.820832\pi$
$752$	3.26304e26	0.154722
$753$	−4.76400e26	−0.223059
$754$	−4.64274e26	−0.214658
$755$	1.13082e27	0.516293
$756$	4.71280e26	0.212482
$757$	9.19972e26	0.409604	0.204802	−	0.978803i	$-0.434345\pi$
$757$	9.19972e26	0.409604	0.204802	+	0.978803i	$0.434345\pi$
$758$	−1.12946e27	−0.496607
$759$	1.06572e27	0.462751
$760$	3.65095e26	0.156559
$761$	2.05800e27	0.871547	0.435773	−	0.900056i	$-0.356475\pi$
$761$	2.05800e27	0.871547	0.435773	+	0.900056i	$0.356475\pi$
$762$	5.55161e26	0.232192
$763$	2.26302e27	0.934772
$764$	−1.40539e26	−0.0573335
$765$	1.00513e27	0.404985
$766$	1.26363e27	0.502861
$767$	1.25768e27	0.494329
$768$	4.54262e26	0.176350
$769$	2.38843e27	0.915825	0.457912	−	0.888997i	$-0.348597\pi$
$769$	2.38843e27	0.915825	0.457912	+	0.888997i	$0.348597\pi$
$770$	−2.90367e27	−1.09973
$771$	−7.10730e26	−0.265881
$772$	7.33217e26	0.270937
$773$	−2.73487e27	−0.998233	−0.499117	−	0.866535i	$-0.666342\pi$
$773$	−2.73487e27	−0.998233	−0.499117	+	0.866535i	$0.666342\pi$
$774$	−1.78894e26	−0.0644995
$775$	1.04798e27	0.373240
$776$	4.69528e26	0.165187
$777$	−1.27941e27	−0.444640
$778$	−4.14533e26	−0.142316
$779$	−8.30369e25	−0.0281621
$780$	−4.43381e25	−0.0148552
$781$	2.45818e27	0.813635
$782$	2.93506e27	0.959739
$783$	6.57776e26	0.212491
$784$	−3.26114e27	−1.04080
$785$	1.74765e27	0.551052
$786$	−6.60510e26	−0.205762
$787$	3.73459e27	1.14943	0.574716	−	0.818353i	$-0.305113\pi$
$787$	3.73459e27	1.14943	0.574716	+	0.818353i	$0.305113\pi$
$788$	−1.06551e27	−0.324009
$789$	−6.21700e26	−0.186788
$790$	4.69899e26	0.139491
$791$	1.72282e27	0.505316
$792$	−6.39670e27	−1.85382
$793$	9.06361e26	0.259541
$794$	−3.63167e27	−1.02757
$795$	1.28945e26	0.0360508
$796$	−3.78752e26	−0.104636
$797$	−5.95253e27	−1.62498	−0.812489	−	0.582976i	$-0.801888\pi$
$797$	−5.95253e27	−1.62498	−0.812489	+	0.582976i	$0.801888\pi$
$798$	3.50336e26	0.0945055
$799$	−9.21896e26	−0.245747
$800$	−4.48842e26	−0.118233
$801$	−5.25845e27	−1.36883
$802$	4.05288e26	0.104257
$803$	3.68805e27	0.937560
$804$	9.66500e24	0.00242812
$805$	−3.62735e27	−0.900593
$806$	−3.20175e27	−0.785606
$807$	8.91545e26	0.216195
$808$	−2.58738e27	−0.620086
$809$	6.81289e27	1.61369	0.806846	−	0.590762i	$-0.201173\pi$
$809$	6.81289e27	1.61369	0.806846	+	0.590762i	$0.201173\pi$
$810$	1.37586e27	0.322082
$811$	−3.53406e27	−0.817665	−0.408832	−	0.912609i	$-0.634064\pi$
$811$	−3.53406e27	−0.817665	−0.408832	+	0.912609i	$0.634064\pi$
$812$	1.13701e27	0.260004
$813$	−1.77671e27	−0.401565
$814$	8.37082e27	1.86998
$815$	−2.81239e27	−0.620980
$816$	5.53571e26	0.120814
$817$	1.21140e26	0.0261323
$818$	−1.69396e27	−0.361199
$819$	3.79514e27	0.799891
$820$	5.78517e25	0.0120527
$821$	−3.47371e26	−0.0715374	−0.0357687	−	0.999360i	$-0.511388\pi$
$821$	−3.47371e26	−0.0715374	−0.0357687	+	0.999360i	$0.511388\pi$
$822$	−1.56345e26	−0.0318274
$823$	5.03398e27	1.01301	0.506504	−	0.862238i	$-0.330938\pi$
$823$	5.03398e27	1.01301	0.506504	+	0.862238i	$0.330938\pi$
$824$	4.76857e27	0.948593
$825$	−3.87035e26	−0.0761092
$826$	6.92346e27	1.34590
$827$	2.44393e26	0.0469663	0.0234832	−	0.999724i	$-0.492524\pi$
$827$	2.44393e26	0.0469663	0.0234832	+	0.999724i	$0.492524\pi$
$828$	−1.88118e27	−0.357390
$829$	−4.46885e27	−0.839320	−0.419660	−	0.907681i	$-0.637851\pi$
$829$	−4.46885e27	−0.839320	−0.419660	+	0.907681i	$0.637851\pi$
$830$	−1.12673e27	−0.209207
$831$	−1.40845e27	−0.258542
$832$	3.03671e27	0.551102
$833$	9.21360e27	1.65311
$834$	1.57982e27	0.280241
$835$	2.81896e26	0.0494387
$836$	1.01972e27	0.176816
$837$	4.53619e27	0.777677
$838$	2.09501e27	0.355115
$839$	−4.50449e27	−0.754930	−0.377465	−	0.926024i	$-0.623204\pi$
$839$	−4.50449e27	−0.754930	−0.377465	+	0.926024i	$0.623204\pi$
$840$	−1.03680e27	−0.171808
$841$	−4.51631e27	−0.739984
$842$	−4.81104e27	−0.779425
$843$	−9.94300e26	−0.159278
$844$	−1.09420e27	−0.173317
$845$	2.12421e27	0.332705
$846$	−1.32819e27	−0.205703
$847$	−2.36365e28	−3.61985
$848$	−1.49128e27	−0.225838
$849$	7.68240e26	0.115047
$850$	−1.06592e27	−0.157849
$851$	1.04571e28	1.53137
$852$	2.06632e26	0.0299241
$853$	−1.64693e27	−0.235862	−0.117931	−	0.993022i	$-0.537626\pi$
$853$	−1.64693e27	−0.235862	−0.117931	+	0.993022i	$0.537626\pi$
$854$	4.98946e27	0.706649
$855$	−9.80600e26	−0.137345
$856$	1.10416e28	1.52943
$857$	4.71231e27	0.645529	0.322765	−	0.946479i	$-0.395388\pi$
$857$	4.71231e27	0.645529	0.322765	+	0.946479i	$0.395388\pi$
$858$	1.18245e27	0.160197
$859$	−5.14098e27	−0.688829	−0.344414	−	0.938818i	$-0.611922\pi$
$859$	−5.14098e27	−0.688829	−0.344414	+	0.938818i	$0.611922\pi$
$860$	−8.43981e25	−0.0111840
$861$	2.35810e26	0.0309052
$862$	−3.99630e27	−0.518012
$863$	−1.54630e28	−1.98240	−0.991201	−	0.132367i	$-0.957742\pi$
$863$	−1.54630e28	−1.98240	−0.991201	+	0.132367i	$0.957742\pi$
$864$	−1.94281e27	−0.246348
$865$	−4.08636e25	−0.00512488
$866$	−1.32287e28	−1.64095
$867$	1.73722e26	0.0213144
$868$	7.84109e27	0.951566
$869$	5.57502e27	0.669205
$870$	−3.40666e26	−0.0404479
$871$	1.59368e26	0.0187167
$872$	−5.28686e27	−0.614174
$873$	−1.26109e27	−0.144915
$874$	−2.86343e27	−0.325483
$875$	1.31733e27	0.148122
$876$	3.10012e26	0.0344818
$877$	1.37805e28	1.51625	0.758123	−	0.652111i	$-0.226116\pi$
$877$	1.37805e28	1.51625	0.758123	+	0.652111i	$0.226116\pi$
$878$	−2.17324e27	−0.236543
$879$	2.48085e27	0.267120
$880$	4.47615e27	0.476782
$881$	−3.30415e27	−0.348168	−0.174084	−	0.984731i	$-0.555696\pi$
$881$	−3.30415e27	−0.348168	−0.174084	+	0.984731i	$0.555696\pi$
$882$	1.32741e28	1.38374
$883$	6.38124e27	0.658080	0.329040	−	0.944316i	$-0.393275\pi$
$883$	6.38124e27	0.658080	0.329040	+	0.944316i	$0.393275\pi$
$884$	−1.44875e27	−0.147807
$885$	9.22839e26	0.0931462
$886$	−9.87485e27	−0.986075
$887$	−4.02881e27	−0.398018	−0.199009	−	0.979998i	$-0.563772\pi$
$887$	−4.02881e27	−0.398018	−0.199009	+	0.979998i	$0.563772\pi$
$888$	2.98894e27	0.292142
$889$	−2.24185e28	−2.16790
$890$	5.57645e27	0.533523
$891$	1.63236e28	1.54518
$892$	1.06492e25	0.000997359 0
$893$	8.99397e26	0.0833417
$894$	−2.81583e27	−0.258167
$895$	−4.49320e27	−0.407602
$896$	5.80980e27	0.521477
$897$	1.47715e27	0.131189
$898$	−3.39149e27	−0.298034
$899$	1.09440e28	0.951609
$900$	6.83182e26	0.0587804
$901$	4.21326e27	0.358701
$902$	−1.54284e27	−0.129975
$903$	−3.44016e26	−0.0286777
$904$	−4.02484e27	−0.332008
$905$	4.47043e27	0.364911
$906$	−2.53501e27	−0.204768
$907$	1.05115e28	0.840228	0.420114	−	0.907471i	$-0.361990\pi$
$907$	1.05115e28	0.840228	0.420114	+	0.907471i	$0.361990\pi$
$908$	−1.38373e27	−0.109455
$909$	6.94938e27	0.543988
$910$	−4.02465e27	−0.311770
$911$	−7.38563e27	−0.566191	−0.283096	−	0.959092i	$-0.591361\pi$
$911$	−7.38563e27	−0.566191	−0.283096	+	0.959092i	$0.591361\pi$
$912$	−5.40060e26	−0.0409724
$913$	−1.33678e28	−1.00366
$914$	4.59661e27	0.341545
$915$	6.65052e26	0.0489052
$916$	−5.75475e27	−0.418813
$917$	2.66727e28	1.92114
$918$	−4.61381e27	−0.328893
$919$	−1.23956e28	−0.874522	−0.437261	−	0.899335i	$-0.644051\pi$
$919$	−1.23956e28	−0.874522	−0.437261	+	0.899335i	$0.644051\pi$
$920$	8.47419e27	0.591717
$921$	−1.90672e27	−0.131771
$922$	1.25993e28	0.861792
$923$	3.40718e27	0.230664
$924$	−2.89582e27	−0.194038
$925$	−3.79766e27	−0.251866
$926$	−1.44383e28	−0.947790
$927$	−1.28078e28	−0.832179
$928$	−4.68721e27	−0.301445
$929$	−1.36438e28	−0.868530	−0.434265	−	0.900785i	$-0.642992\pi$
$929$	−1.36438e28	−0.868530	−0.434265	+	0.900785i	$0.642992\pi$
$930$	−2.34932e27	−0.148031
$931$	−8.98873e27	−0.560630
$932$	1.86924e27	0.115402
$933$	−1.40175e27	−0.0856631
$934$	4.32601e27	0.261693
$935$	−1.26463e28	−0.757277
$936$	−8.86618e27	−0.525553
$937$	2.61541e28	1.53466	0.767332	−	0.641250i	$-0.221584\pi$
$937$	2.61541e28	1.53466	0.767332	+	0.641250i	$0.221584\pi$
$938$	8.77309e26	0.0509595
$939$	3.73829e27	0.214956
$940$	−6.26608e26	−0.0356682
$941$	−4.09338e26	−0.0230664	−0.0115332	−	0.999933i	$-0.503671\pi$
$941$	−4.09338e26	−0.0230664	−0.0115332	+	0.999933i	$0.503671\pi$
$942$	−3.91779e27	−0.218554
$943$	−1.92736e27	−0.106439
$944$	−1.06729e28	−0.583509
$945$	5.70206e27	0.308624
$946$	2.25081e27	0.120607
$947$	−2.64380e28	−1.40250	−0.701251	−	0.712914i	$-0.747375\pi$
$947$	−2.64380e28	−1.40250	−0.701251	+	0.712914i	$0.747375\pi$
$948$	4.68629e26	0.0246122
$949$	5.11184e27	0.265796
$950$	1.03990e27	0.0535325
$951$	3.37615e27	0.172071
$952$	−3.38775e28	−1.70947
$953$	3.14992e28	1.57368	0.786840	−	0.617157i	$-0.211716\pi$
$953$	3.14992e28	1.57368	0.786840	+	0.617157i	$0.211716\pi$
$954$	6.07009e27	0.300252
$955$	−1.70039e27	−0.0832754
$956$	−2.83599e27	−0.137517
$957$	−4.04176e27	−0.194047
$958$	1.38168e28	0.656803
$959$	6.31351e27	0.297163
$960$	2.22822e27	0.103844
$961$	5.38019e28	2.48271
$962$	1.16024e28	0.530134
$963$	−2.96563e28	−1.34174
$964$	1.04320e28	0.467345
$965$	8.87127e27	0.393529
$966$	8.13162e27	0.357186
$967$	8.24399e27	0.358580	0.179290	−	0.983796i	$-0.442620\pi$
$967$	8.24399e27	0.358580	0.179290	+	0.983796i	$0.442620\pi$
$968$	5.52195e28	2.37835
$969$	1.52582e27	0.0650768
$970$	1.33736e27	0.0564828
$971$	1.13772e28	0.475831	0.237916	−	0.971286i	$-0.423536\pi$
$971$	1.13772e28	0.475831	0.237916	+	0.971286i	$0.423536\pi$
$972$	4.47011e27	0.185135
$973$	−6.37964e28	−2.61652
$974$	−2.67879e28	−1.08800
$975$	−5.36452e26	−0.0215768
$976$	−7.69150e27	−0.306364
$977$	−2.92316e28	−1.15306	−0.576532	−	0.817074i	$-0.695594\pi$
$977$	−2.92316e28	−1.15306	−0.576532	+	0.817074i	$0.695594\pi$
$978$	6.30467e27	0.246288
$979$	6.61607e28	2.55955
$980$	6.26244e27	0.239936
$981$	1.41999e28	0.538801
$982$	−2.21630e28	−0.832854
$983$	−1.31441e27	−0.0489184	−0.0244592	−	0.999701i	$-0.507786\pi$
$983$	−1.31441e27	−0.0489184	−0.0244592	+	0.999701i	$0.507786\pi$
$984$	−5.50897e26	−0.0203057
$985$	−1.28917e28	−0.470614
$986$	−1.11312e28	−0.402451
$987$	−2.55412e27	−0.0914595
$988$	1.41339e27	0.0501269
$989$	2.81177e27	0.0987678
$990$	−1.82197e28	−0.633881
$991$	−3.06268e28	−1.05536	−0.527682	−	0.849442i	$-0.676939\pi$
$991$	−3.06268e28	−1.05536	−0.527682	+	0.849442i	$0.676939\pi$
$992$	−3.23242e28	−1.10323
$993$	3.08378e27	0.104248
$994$	1.87563e28	0.628025
$995$	−4.58256e27	−0.151981
$996$	−1.12368e27	−0.0369130
$997$	−3.41995e28	−1.11280	−0.556399	−	0.830916i	$-0.687817\pi$
$997$	−3.41995e28	−1.11280	−0.556399	+	0.830916i	$0.687817\pi$
$998$	2.87813e28	0.927621
$999$	−1.64381e28	−0.524784

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.20.a.b.1.2	✓	4
3.2	odd	2		45.20.a.f.1.3		4
4.3	odd	2		80.20.a.g.1.3		4
5.2	odd	4		25.20.b.c.24.3		8
5.3	odd	4		25.20.b.c.24.6		8
5.4	even	2		25.20.a.c.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.20.a.b.1.2	✓	4	1.1	even	1	trivial
25.20.a.c.1.3		4	5.4	even	2
25.20.b.c.24.3		8	5.2	odd	4
25.20.b.c.24.6		8	5.3	odd	4
45.20.a.f.1.3		4	3.2	odd	2
80.20.a.g.1.3		4	4.3	odd	2

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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)

\(f(q)\)	\(=\)	\(q-602.379 q^{2} -7268.55 q^{3} -161427. q^{4} -1.95312e6 q^{5} +4.37842e6 q^{6} -1.76809e8 q^{7} +4.13061e8 q^{8} -1.10943e9 q^{9} +O(q^{10})\)	\(q-602.379 q^{2} -7268.55 q^{3} -161427. q^{4} -1.95312e6 q^{5} +4.37842e6 q^{6} -1.76809e8 q^{7} +4.13061e8 q^{8} -1.10943e9 q^{9} +1.17652e9 q^{10} +1.39586e10 q^{11} +1.17334e9 q^{12} +1.93474e10 q^{13} +1.06506e11 q^{14} +1.41964e10 q^{15} -1.64185e11 q^{16} +4.63866e11 q^{17} +6.68297e11 q^{18} -4.52545e11 q^{19} +3.15288e11 q^{20} +1.28515e12 q^{21} -8.40838e12 q^{22} -1.05040e13 q^{23} -3.00235e12 q^{24} +3.81470e12 q^{25} -1.16545e13 q^{26} +1.65119e13 q^{27} +2.85418e13 q^{28} +3.98365e13 q^{29} -8.55160e12 q^{30} +2.74723e14 q^{31} -1.17661e14 q^{32} -1.01459e14 q^{33} -2.79423e14 q^{34} +3.45331e14 q^{35} +1.79092e14 q^{36} -9.95533e14 q^{37} +2.72604e14 q^{38} -1.40628e14 q^{39} -8.06759e14 q^{40} +1.83489e14 q^{41} -7.74145e14 q^{42} -2.67686e14 q^{43} -2.25330e15 q^{44} +2.16685e15 q^{45} +6.32739e15 q^{46} -1.98742e15 q^{47} +1.19338e15 q^{48} +1.98626e16 q^{49} -2.29789e15 q^{50} -3.37163e15 q^{51} -3.12320e15 q^{52} +9.08292e15 q^{53} -9.94642e15 q^{54} -2.72629e16 q^{55} -7.30329e16 q^{56} +3.28935e15 q^{57} -2.39967e16 q^{58} +6.50053e16 q^{59} -2.29168e15 q^{60} +4.68466e16 q^{61} -1.65487e17 q^{62} +1.96157e17 q^{63} +1.56957e17 q^{64} -3.77879e16 q^{65} +6.11167e16 q^{66} +8.23716e15 q^{67} -7.48807e16 q^{68} +7.63488e16 q^{69} -2.08020e17 q^{70} +1.76105e17 q^{71} -4.58262e17 q^{72} +2.64213e17 q^{73} +5.99689e17 q^{74} -2.77273e16 q^{75} +7.30531e16 q^{76} -2.46801e18 q^{77} +8.47112e16 q^{78} +3.99397e17 q^{79} +3.20673e17 q^{80} +1.16943e18 q^{81} -1.10530e17 q^{82} -9.57676e17 q^{83} -2.07458e17 q^{84} -9.05989e17 q^{85} +1.61249e17 q^{86} -2.89553e17 q^{87} +5.76575e18 q^{88} +4.73978e18 q^{89} -1.30527e18 q^{90} -3.42080e18 q^{91} +1.69563e18 q^{92} -1.99683e18 q^{93} +1.19718e18 q^{94} +8.83877e17 q^{95} +8.55226e17 q^{96} +1.13670e18 q^{97} -1.19648e19 q^{98} -1.54861e19 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 420 q^{2} + 3080 q^{3} + 2084992 q^{4} - 7812500 q^{5} - 58071752 q^{6} + 214021400 q^{7} + 81737760 q^{8} + 154064548 q^{9}+O(q^{10}) \) 4 * q - 420 * q^2 + 3080 * q^3 + 2084992 * q^4 - 7812500 * q^5 - 58071752 * q^6 + 214021400 * q^7 + 81737760 * q^8 + 154064548 * q^9	\( 4 q - 420 q^{2} + 3080 q^{3} + 2084992 q^{4} - 7812500 q^{5} - 58071752 q^{6} + 214021400 q^{7} + 81737760 q^{8} + 154064548 q^{9} + 820312500 q^{10} + 11585712768 q^{11} + 105629359360 q^{12} + 14812333160 q^{13} + 185174155944 q^{14} - 6015625000 q^{15} + 1785780098944 q^{16} + 849033742440 q^{17} - 2113778999620 q^{18} + 1978167708560 q^{19} - 4072250000000 q^{20} - 1487020185552 q^{21} - 7953348762240 q^{22} - 26569906952760 q^{23} - 39774243472320 q^{24} + 15258789062500 q^{25} - 48695658207912 q^{26} - 7557605929360 q^{27} + 236612033519360 q^{28} + 116267174339640 q^{29} + 113421390625000 q^{30} + 251049672388688 q^{31} - 142495342974720 q^{32} + 359905680636160 q^{33} + 411849015040344 q^{34} - 418010546875000 q^{35} - 168308645735296 q^{36} + 53471657716520 q^{37} - 52\!\cdots\!60 q^{38}+ \cdots - 25\!\cdots\!84 q^{99}+O(q^{100}) \) 4 * q - 420 * q^2 + 3080 * q^3 + 2084992 * q^4 - 7812500 * q^5 - 58071752 * q^6 + 214021400 * q^7 + 81737760 * q^8 + 154064548 * q^9 + 820312500 * q^10 + 11585712768 * q^11 + 105629359360 * q^12 + 14812333160 * q^13 + 185174155944 * q^14 - 6015625000 * q^15 + 1785780098944 * q^16 + 849033742440 * q^17 - 2113778999620 * q^18 + 1978167708560 * q^19 - 4072250000000 * q^20 - 1487020185552 * q^21 - 7953348762240 * q^22 - 26569906952760 * q^23 - 39774243472320 * q^24 + 15258789062500 * q^25 - 48695658207912 * q^26 - 7557605929360 * q^27 + 236612033519360 * q^28 + 116267174339640 * q^29 + 113421390625000 * q^30 + 251049672388688 * q^31 - 142495342974720 * q^32 + 359905680636160 * q^33 + 411849015040344 * q^34 - 418010546875000 * q^35 - 168308645735296 * q^36 + 53471657716520 * q^37 - 5247417886886160 * q^38 - 3407032515417904 * q^39 - 159644062500000 * q^40 + 5606221897948248 * q^41 - 6858180778710960 * q^42 + 3924193112762600 * q^43 + 7741056858814464 * q^44 - 300907320312500 * q^45 - 13726548710068872 * q^46 + 9972444326989560 * q^47 + 45169928589418240 * q^48 + 40183155980030772 * q^49 - 1602172851562500 * q^50 + 21906201621258448 * q^51 - 98153899497030400 * q^52 - 7462276270800120 * q^53 - 40810202919142640 * q^54 - 22628345250000000 * q^55 - 85257126419530560 * q^56 + 24746009355310880 * q^57 - 168144043315298040 * q^58 + 186154941962838480 * q^59 - 206307342500000000 * q^60 + 248517593110644968 * q^61 - 622575860488793040 * q^62 + 375323610989436120 * q^63 + 797725889363156992 * q^64 - 28930338203125000 * q^65 + 66770019182287616 * q^66 - 83976946080676360 * q^67 + 1012065979784551680 * q^68 + 721386544222156176 * q^69 - 361668273328125000 * q^70 - 326854508200029072 * q^71 - 3247857120459936480 * q^72 + 706071038062266440 * q^73 + 1007811588432673944 * q^74 + 11749267578125000 * q^75 + 453476009937236480 * q^76 - 3188023247458540800 * q^77 - 422235733076613200 * q^78 + 1300235890504742240 * q^79 - 3487851755750000000 * q^80 - 565640020943583596 * q^81 - 3526321594330914840 * q^82 - 894716269324765080 * q^83 + 11741177868239906304 * q^84 - 1658269028203125000 * q^85 + 10889898572595403608 * q^86 - 3243563654475579280 * q^87 + 8680694316508369920 * q^88 - 4392730519471649880 * q^89 + 4128474608632812500 * q^90 - 1164625388848487312 * q^91 + 1015783757806275840 * q^92 + 589775737588352160 * q^93 + 6912955459089075144 * q^94 - 3863608805781250000 * q^95 - 34035929850443648512 * q^96 + 1437870497951780360 * q^97 + 1735173204679501740 * q^98 - 25265427652281702784 * q^99

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