LMFDB - Embedded newform 57.4.d.c.56.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,4,Mod(56,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("57.56");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	57.d (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$3.36310887033$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 23x^{10} + 1659x^{8} + 14266x^{6} + 685507x^{4} - 16582767x^{2} + 113486409 $ x^12 - 23x^10 + 1659x^8 + 14266x^6 + 685507x^4 - 16582767*x^2 + 113486409
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			56.4
Root			$3.00654 + 0.806605i$ of defining polynomial
Character	$\chi$	$=$	57.56
Dual form			57.4.d.c.56.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.12662 q^{2} +(5.13317 + 0.806605i) q^{3} -3.47747 q^{4} -17.1306i q^{5} +(-10.9163 - 1.71535i) q^{6} -6.31010 q^{7} +24.4083 q^{8} +(25.6988 + 8.28087i) q^{9} +O(q^{10})$	\(q-2.12662 q^{2} +(5.13317 + 0.806605i) q^{3} -3.47747 q^{4} -17.1306i q^{5} +(-10.9163 - 1.71535i) q^{6} -6.31010 q^{7} +24.4083 q^{8} +(25.6988 + 8.28087i) q^{9} +36.4304i q^{10} -55.5716i q^{11} +(-17.8504 - 2.80494i) q^{12} -49.2191i q^{13} +13.4192 q^{14} +(13.8176 - 87.9342i) q^{15} -24.0875 q^{16} +44.7335i q^{17} +(-54.6516 - 17.6103i) q^{18} +(37.3525 + 73.9175i) q^{19} +59.5712i q^{20} +(-32.3908 - 5.08976i) q^{21} +118.180i q^{22} -27.6029i q^{23} +(125.292 + 19.6878i) q^{24} -168.458 q^{25} +104.670i q^{26} +(125.237 + 63.2358i) q^{27} +21.9432 q^{28} -132.644 q^{29} +(-29.3849 + 187.003i) q^{30} +253.085i q^{31} -144.041 q^{32} +(44.8243 - 285.258i) q^{33} -95.1314i q^{34} +108.096i q^{35} +(-89.3667 - 28.7965i) q^{36} +59.8298i q^{37} +(-79.4347 - 157.195i) q^{38} +(39.7003 - 252.650i) q^{39} -418.128i q^{40} +294.516 q^{41} +(68.8830 + 10.8240i) q^{42} +393.748 q^{43} +193.249i q^{44} +(141.856 - 440.236i) q^{45} +58.7010i q^{46} -237.604i q^{47} +(-123.645 - 19.4291i) q^{48} -303.183 q^{49} +358.246 q^{50} +(-36.0823 + 229.625i) q^{51} +171.158i q^{52} -92.2667 q^{53} +(-266.331 - 134.479i) q^{54} -951.975 q^{55} -154.019 q^{56} +(132.114 + 409.559i) q^{57} +282.083 q^{58} +628.710 q^{59} +(-48.0504 + 305.789i) q^{60} +475.307 q^{61} -538.217i q^{62} +(-162.162 - 52.2531i) q^{63} +499.021 q^{64} -843.152 q^{65} +(-95.3245 + 606.637i) q^{66} +46.7464i q^{67} -155.559i q^{68} +(22.2646 - 141.690i) q^{69} -229.879i q^{70} +52.5694 q^{71} +(627.263 + 202.122i) q^{72} +397.956 q^{73} -127.236i q^{74} +(-864.721 - 135.879i) q^{75} +(-129.892 - 257.046i) q^{76} +350.662i q^{77} +(-84.4277 + 537.291i) q^{78} -1066.08i q^{79} +412.633i q^{80} +(591.854 + 425.617i) q^{81} -626.326 q^{82} +877.475i q^{83} +(112.638 + 17.6995i) q^{84} +766.312 q^{85} -837.355 q^{86} +(-680.882 - 106.991i) q^{87} -1356.41i q^{88} -444.652 q^{89} +(-301.675 + 936.216i) q^{90} +310.577i q^{91} +95.9883i q^{92} +(-204.140 + 1299.13i) q^{93} +505.295i q^{94} +(1266.25 - 639.871i) q^{95} +(-739.387 - 116.184i) q^{96} +1448.46i q^{97} +644.756 q^{98} +(460.181 - 1428.12i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 28 q^{4} - 66 q^{6} + 124 q^{7} + 54 q^{9}+O(q^{10}) $ 12 * q + 28 * q^4 - 66 * q^6 + 124 * q^7 + 54 * q^9	$ 12 q + 28 q^{4} - 66 q^{6} + 124 q^{7} + 54 q^{9} + 20 q^{16} - 200 q^{19} - 198 q^{24} - 156 q^{25} + 92 q^{28} - 672 q^{30} - 1146 q^{36} + 414 q^{39} + 654 q^{42} + 3376 q^{43} - 276 q^{45} - 360 q^{49} + 900 q^{54} - 1912 q^{55} + 1506 q^{57} - 2332 q^{58} + 696 q^{61} - 1002 q^{63} + 836 q^{64} + 4320 q^{66} + 404 q^{73} - 4904 q^{76} - 2106 q^{81} - 3704 q^{82} + 736 q^{85} - 4230 q^{87} - 4452 q^{93} + 426 q^{96} + 1044 q^{99}+O(q^{100}) $ 12 * q + 28 * q^4 - 66 * q^6 + 124 * q^7 + 54 * q^9 + 20 * q^16 - 200 * q^19 - 198 * q^24 - 156 * q^25 + 92 * q^28 - 672 * q^30 - 1146 * q^36 + 414 * q^39 + 654 * q^42 + 3376 * q^43 - 276 * q^45 - 360 * q^49 + 900 * q^54 - 1912 * q^55 + 1506 * q^57 - 2332 * q^58 + 696 * q^61 - 1002 * q^63 + 836 * q^64 + 4320 * q^66 + 404 * q^73 - 4904 * q^76 - 2106 * q^81 - 3704 * q^82 + 736 * q^85 - 4230 * q^87 - 4452 * q^93 + 426 * q^96 + 1044 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−2.12662			−0.751875			−0.375938	−	0.926645i	$-0.622679\pi$
$2$	−2.12662			−0.751875			−0.375938	+	0.926645i	$0.622679\pi$
$3$	5.13317	+	0.806605i	0.987878	+	0.155231i
$3$	5.13317	+	0.806605i	0.987878	+	0.155231i
$4$	−3.47747			−0.434684
$5$		−	17.1306i		−	1.53221i	−0.642717	−	0.766104i	$-0.722193\pi$
$5$		−	17.1306i		−	1.53221i	0.642717	−	0.766104i	$-0.277807\pi$
$6$	−10.9163	−	1.71535i	−0.742761	−	0.116714i
$7$	−6.31010			−0.340713			−0.170357	−	0.985382i	$-0.554492\pi$
$7$	−6.31010			−0.340713			−0.170357	+	0.985382i	$0.554492\pi$
$8$	24.4083			1.07870
$9$	25.6988	+	8.28087i	0.951807	+	0.306699i
$10$			36.4304i			1.15203i
$11$		−	55.5716i		−	1.52322i	−0.648033	−	0.761612i	$-0.724408\pi$
$11$		−	55.5716i		−	1.52322i	0.648033	−	0.761612i	$-0.275592\pi$
$12$	−17.8504	−	2.80494i	−0.429414	−	0.0674764i
$13$		−	49.2191i		−	1.05007i	−0.851081	−	0.525035i	$-0.824052\pi$
$13$		−	49.2191i		−	1.05007i	0.851081	−	0.525035i	$-0.175948\pi$
$14$	13.4192			0.256174
$15$	13.8176	−	87.9342i	0.237846	−	1.51363i
$16$	−24.0875			−0.376367
$17$			44.7335i			0.638204i	0.947720	+	0.319102i	$0.103381\pi$
$17$			44.7335i			0.638204i	−0.947720	+	0.319102i	$0.896619\pi$
$18$	−54.6516	−	17.6103i	−0.715640	−	0.230599i
$19$	37.3525	+	73.9175i	0.451013	+	0.892517i
$19$	37.3525	+	73.9175i	0.451013	+	0.892517i
$20$			59.5712i			0.666026i
$21$	−32.3908	−	5.08976i	−0.336583	−	0.0528893i
$22$			118.180i			1.14527i
$23$		−	27.6029i		−	0.250244i	−0.992141	−	0.125122i	$-0.960068\pi$
$23$		−	27.6029i		−	0.250244i	0.992141	−	0.125122i	$-0.0399322\pi$
$24$	125.292	+	19.6878i	1.06563	+	0.167448i
$25$	−168.458			−1.34766
$26$			104.670i			0.789522i
$27$	125.237	+	63.2358i	0.892660	+	0.450731i
$28$	21.9432			0.148102
$29$	−132.644			−0.849356			−0.424678	−	0.905344i	$-0.639613\pi$
$29$	−132.644			−0.849356			−0.424678	+	0.905344i	$0.639613\pi$
$30$	−29.3849	+	187.003i	−0.178831	+	1.13806i
$31$			253.085i			1.46630i	0.680065	+	0.733152i	$0.261952\pi$
$31$			253.085i			1.46630i	−0.680065	+	0.733152i	$0.738048\pi$
$32$	−144.041			−0.795722
$33$	44.8243	−	285.258i	0.236452	−	1.50476i
$34$		−	95.1314i		−	0.479850i
$35$			108.096i			0.522044i
$36$	−89.3667	−	28.7965i	−0.413735	−	0.133317i
$37$			59.8298i			0.265837i	0.991127	+	0.132918i	$0.0424348\pi$
$37$			59.8298i			0.265837i	−0.991127	+	0.132918i	$0.957565\pi$
$38$	−79.4347	−	157.195i	−0.339106	−	0.671062i
$39$	39.7003	−	252.650i	0.163004	−	1.03734i
$40$		−	418.128i		−	1.65280i
$41$	294.516			1.12185			0.560924	−	0.827868i	$-0.310446\pi$
$41$	294.516			1.12185			0.560924	+	0.827868i	$0.310446\pi$
$42$	68.8830	+	10.8240i	0.253069	+	0.0397662i
$43$	393.748			1.39642			0.698210	−	0.715893i	$-0.253980\pi$
$43$	393.748			1.39642			0.698210	+	0.715893i	$0.253980\pi$
$44$			193.249i			0.662121i
$45$	141.856	−	440.236i	0.469927	−	1.45837i
$46$			58.7010i			0.188152i
$47$		−	237.604i		−	0.737407i	−0.929547	−	0.368703i	$-0.879802\pi$
$47$		−	237.604i		−	0.737407i	0.929547	−	0.368703i	$-0.120198\pi$
$48$	−123.645	−	19.4291i	−0.371804	−	0.0584238i
$49$	−303.183			−0.883914
$50$	358.246			1.01327
$51$	−36.0823	+	229.625i	−0.0990692	+	0.630468i
$52$			171.158i			0.456448i
$53$	−92.2667			−0.239128			−0.119564	−	0.992826i	$-0.538150\pi$
$53$	−92.2667			−0.239128			−0.119564	+	0.992826i	$0.538150\pi$
$54$	−266.331	−	134.479i	−0.671169	−	0.338894i
$55$	−951.975			−2.33390
$56$	−154.019			−0.367528
$57$	132.114	+	409.559i	0.307000	+	0.951710i
$58$	282.083			0.638610
$59$	628.710			1.38731			0.693654	−	0.720309i	$-0.256000\pi$
$59$	628.710			1.38731			0.693654	+	0.720309i	$0.256000\pi$
$60$	−48.0504	+	305.789i	−0.103388	+	0.657952i
$61$	475.307			0.997652			0.498826	−	0.866702i	$-0.333765\pi$
$61$	475.307			0.997652			0.498826	+	0.866702i	$0.333765\pi$
$62$		−	538.217i		−	1.10248i
$63$	−162.162	−	52.2531i	−0.324293	−	0.104496i
$64$	499.021			0.974650
$65$	−843.152			−1.60893
$66$	−95.3245	+	606.637i	−0.177782	+	1.13139i
$67$			46.7464i			0.0852386i	0.999091	+	0.0426193i	$0.0135703\pi$
$67$			46.7464i			0.0852386i	−0.999091	+	0.0426193i	$0.986430\pi$
$68$		−	155.559i		−	0.277417i
$69$	22.2646	−	141.690i	0.0388456	−	0.247210i
$70$		−	229.879i		−	0.392512i
$71$	52.5694			0.0878710			0.0439355	−	0.999034i	$-0.486010\pi$
$71$	52.5694			0.0878710			0.0439355	+	0.999034i	$0.486010\pi$
$72$	627.263	+	202.122i	1.02672	+	0.330837i
$73$	397.956			0.638045			0.319022	−	0.947747i	$-0.396646\pi$
$73$	397.956			0.638045			0.319022	+	0.947747i	$0.396646\pi$
$74$		−	127.236i		−	0.199876i
$75$	−864.721	−	135.879i	−1.33133	−	0.209199i
$76$	−129.892	−	257.046i	−0.196048	−	0.387963i
$77$			350.662i			0.518983i
$78$	−84.4277	+	537.291i	−0.122558	+	0.779951i
$79$		−	1066.08i		−	1.51826i	−0.650937	−	0.759132i	$-0.725624\pi$
$79$		−	1066.08i		−	1.51826i	0.650937	−	0.759132i	$-0.274376\pi$
$80$			412.633i			0.576672i
$81$	591.854	+	425.617i	0.811871	+	0.583836i
$82$	−626.326			−0.843489
$83$			877.475i			1.16043i	0.814465	+	0.580213i	$0.197031\pi$
$83$			877.475i			1.16043i	−0.814465	+	0.580213i	$0.802969\pi$
$84$	112.638	+	17.6995i	0.146307	+	0.0229901i
$85$	766.312			0.977862
$86$	−837.355			−1.04993
$87$	−680.882	−	106.991i	−0.839060	−	0.131847i
$88$		−	1356.41i		−	1.64311i
$89$	−444.652			−0.529584			−0.264792	−	0.964306i	$-0.585303\pi$
$89$	−444.652			−0.529584			−0.264792	+	0.964306i	$0.585303\pi$
$90$	−301.675	+	936.216i	−0.353326	+	1.09651i
$91$			310.577i			0.357773i
$92$			95.9883i			0.108777i
$93$	−204.140	+	1299.13i	−0.227616	+	1.44853i
$94$			505.295i			0.554438i
$95$	1266.25	−	639.871i	1.36752	−	0.691046i
$96$	−739.387	−	116.184i	−0.786077	−	0.123521i
$97$			1448.46i			1.51617i	0.652154	+	0.758086i	$0.273865\pi$
$97$			1448.46i			1.51617i	−0.652154	+	0.758086i	$0.726135\pi$
$98$	644.756			0.664593
$99$	460.181	−	1428.12i	0.467171	−	1.44982i
$100$	585.806			0.585806
$101$			779.974i			0.768419i	0.923246	+	0.384209i	$0.125526\pi$
$101$			779.974i			0.768419i	−0.923246	+	0.384209i	$0.874474\pi$
$102$	76.7334	−	488.325i	0.0744877	−	0.474033i
$103$		−	561.012i		−	0.536681i	−0.963324	−	0.268340i	$-0.913525\pi$
$103$		−	561.012i		−	0.536681i	0.963324	−	0.268340i	$-0.0864752\pi$
$104$		−	1201.35i		−	1.13271i
$105$	−87.1906	+	554.874i	−0.0810374	+	0.515716i
$106$	196.217			0.179795
$107$	−319.902			−0.289029			−0.144514	−	0.989503i	$-0.546162\pi$
$107$	−319.902			−0.289029			−0.144514	+	0.989503i	$0.546162\pi$
$108$	−435.507	−	219.901i	−0.388025	−	0.195926i
$109$			58.8543i			0.0517176i	0.999666	+	0.0258588i	$0.00823203\pi$
$109$			58.8543i			0.0517176i	−0.999666	+	0.0258588i	$0.991768\pi$
$110$	2024.49			1.75480
$111$	−48.2590	+	307.116i	−0.0412662	+	0.262614i
$112$	151.994			0.128233
$113$	−1753.11			−1.45946			−0.729729	−	0.683736i	$-0.760354\pi$
$113$	−1753.11			−1.45946			−0.729729	+	0.683736i	$0.760354\pi$
$114$	−280.958	−	870.979i	−0.230825	−	0.715567i
$115$	−472.855			−0.383425
$116$	461.265			0.369201
$117$	407.577	−	1264.87i	0.322055	−	0.999464i
$118$	−1337.03			−1.04308
$119$		−	282.273i		−	0.217445i
$120$	337.264	−	2146.32i	0.256566	−	1.63276i
$121$	−1757.20			−1.32021
$122$	−1010.80			−0.750110
$123$	1511.80	+	237.558i	1.10825	+	0.174146i
$124$		−	880.095i		−	0.637378i
$125$			744.457i			0.532690i
$126$	344.857	+	111.123i	0.243828	+	0.0785683i
$127$			1907.79i			1.33298i	0.745514	+	0.666491i	$0.232204\pi$
$127$			1907.79i			1.33298i	−0.745514	+	0.666491i	$0.767796\pi$
$128$	91.0989			0.0629069
$129$	2021.18	+	317.599i	1.37949	+	0.216768i
$130$	1793.07			1.20971
$131$		−	2388.86i		−	1.59325i	−0.604475	−	0.796624i	$-0.706617\pi$
$131$		−	2388.86i		−	1.59325i	0.604475	−	0.796624i	$-0.293383\pi$
$132$	−155.875	+	991.977i	−0.102782	+	0.654095i
$133$	−235.698	−	466.426i	−0.153666	−	0.304093i
$134$		−	99.4121i		−	0.0640888i
$135$	1083.27	−	2145.38i	0.690614	−	1.36774i
$136$			1091.87i			0.688433i
$137$			1833.67i			1.14351i	0.820424	+	0.571756i	$0.193737\pi$
$137$			1833.67i			1.14351i	−0.820424	+	0.571756i	$0.806263\pi$
$138$	−47.3485	+	301.322i	−0.0292071	+	0.185871i
$139$	649.396			0.396266			0.198133	−	0.980175i	$-0.436512\pi$
$139$	649.396			0.396266			0.198133	+	0.980175i	$0.436512\pi$
$140$		−	375.900i		−	0.226924i
$141$	191.653	−	1219.66i	0.114469	−	0.728468i
$142$	−111.795			−0.0660680
$143$	−2735.18			−1.59949
$144$	−619.018	−	199.465i	−0.358228	−	0.115431i
$145$			2272.27i			1.30139i
$146$	−846.303			−0.479730
$147$	−1556.29	−	244.549i	−0.873200	−	0.137211i
$148$		−	208.056i		−	0.115555i
$149$		−	1498.18i		−	0.823731i	−0.911245	−	0.411865i	$-0.864877\pi$
$149$		−	1498.18i		−	0.823731i	0.911245	−	0.411865i	$-0.135123\pi$
$150$	1838.94	+	288.963i	1.00099	+	0.157292i
$151$		−	1096.47i		−	0.590921i	−0.955355	−	0.295461i	$-0.904527\pi$
$151$		−	1096.47i		−	0.590921i	0.955355	−	0.295461i	$-0.0954731\pi$
$152$	911.710	+	1804.20i	0.486509	+	0.962761i
$153$	−370.433	+	1149.60i	−0.195737	+	0.607447i
$154$		−	745.727i		−	0.390210i
$155$	4335.50			2.24668
$156$	−138.057	+	878.581i	−0.0708550	+	0.450915i
$157$	−2722.72			−1.38405			−0.692027	−	0.721871i	$-0.743282\pi$
$157$	−2722.72			−1.38405			−0.692027	+	0.721871i	$0.743282\pi$
$158$			2267.14i			1.14154i
$159$	−473.620	−	74.4228i	−0.236230	−	0.0371202i
$160$			2467.51i			1.21921i
$161$			174.177i			0.0852613i
$162$	−1258.65	−	905.127i	−0.610426	−	0.438972i
$163$	1330.44			0.639312			0.319656	−	0.947534i	$-0.396433\pi$
$163$	1330.44			0.639312			0.319656	+	0.947534i	$0.396433\pi$
$164$	−1024.17			−0.487649
$165$	−4886.65	−	767.868i	−2.30561	−	0.362294i
$166$		−	1866.06i		−	0.872496i
$167$	990.318			0.458881			0.229441	−	0.973323i	$-0.426310\pi$
$167$	990.318			0.458881			0.229441	+	0.973323i	$0.426310\pi$
$168$	−790.603	−	124.232i	−0.363073	−	0.0570519i
$169$	−225.516			−0.102647
$170$	−1629.66			−0.735230
$171$	347.812	+	2208.90i	0.155543	+	0.987829i
$172$	−1369.25			−0.607001
$173$	327.692			0.144011			0.0720056	−	0.997404i	$-0.477060\pi$
$173$	327.692			0.144011			0.0720056	+	0.997404i	$0.477060\pi$
$174$	1447.98	+	227.530i	0.630869	+	0.0991321i
$175$	1062.98			0.459166
$176$			1338.58i			0.573291i
$177$	3227.27	+	507.121i	1.37049	+	0.215353i
$178$	945.607			0.398181
$179$	−936.951			−0.391235			−0.195617	−	0.980680i	$-0.562671\pi$
$179$	−936.951			−0.391235			−0.195617	+	0.980680i	$0.562671\pi$
$180$	−493.301	+	1530.91i	−0.204269	+	0.633928i
$181$			3849.62i			1.58088i	0.612538	+	0.790441i	$0.290149\pi$
$181$			3849.62i			1.58088i	−0.612538	+	0.790441i	$0.709851\pi$
$182$		−	660.481i		−	0.269001i
$183$	2439.83	+	383.385i	0.985559	+	0.154867i
$184$		−	673.739i		−	0.269939i
$185$	1024.92			0.407317
$186$	434.128	−	2762.76i	0.171139	−	1.08911i
$187$	2485.91			0.972128
$188$			826.261i			0.320539i
$189$	−790.256	−	399.024i	−0.304141	−	0.153570i
$190$	−2692.84	+	1360.76i	−1.02821	+	0.519580i
$191$		−	1662.11i		−	0.629664i	−0.949147	−	0.314832i	$-0.898052\pi$
$191$		−	1662.11i		−	0.629664i	0.949147	−	0.314832i	$-0.101948\pi$
$192$	2561.56	+	402.513i	0.962836	+	0.151296i
$193$			1625.86i			0.606383i	0.952930	+	0.303192i	$0.0980523\pi$
$193$			1625.86i			0.606383i	−0.952930	+	0.303192i	$0.901948\pi$
$194$		−	3080.33i		−	1.13997i
$195$	−4328.04	−	680.091i	−1.58942	−	0.249755i
$196$	1054.31			0.384223
$197$			1181.90i			0.427447i	0.976894	+	0.213723i	$0.0685591\pi$
$197$			1181.90i			0.427447i	−0.976894	+	0.213723i	$0.931441\pi$
$198$	−978.633	+	3037.08i	−0.351255	+	1.09008i
$199$	−3641.24			−1.29709			−0.648544	−	0.761177i	$-0.724622\pi$
$199$	−3641.24			−1.29709			−0.648544	+	0.761177i	$0.724622\pi$
$200$	−4111.76			−1.45373
$201$	−37.7059	+	239.957i	−0.0132317	+	0.0842053i
$202$		−	1658.71i		−	0.577755i
$203$	836.995			0.289387
$204$	125.475	−	798.512i	0.0430638	−	0.274054i
$205$		−	5045.25i		−	1.71890i
$206$			1193.06i			0.403517i
$207$	228.576	−	709.361i	0.0767495	−	0.238184i
$208$			1185.56i			0.395211i
$209$	4107.71	−	2075.74i	1.35950	−	0.686994i
$210$	185.422	−	1180.01i	0.0609300	−	0.387754i
$211$		−	3720.98i		−	1.21404i	−0.794686	−	0.607021i	$-0.792364\pi$
$211$		−	3720.98i		−	1.21404i	0.794686	−	0.607021i	$-0.207636\pi$
$212$	320.855			0.103945
$213$	269.847	+	42.4027i	0.0868058	+	0.0136403i
$214$	680.311			0.217314
$215$		−	6745.15i		−	2.13961i
$216$	3056.81	+	1543.48i	0.962915	+	0.486205i
$217$		−	1596.99i		−	0.499589i
$218$		−	125.161i		−	0.0388852i
$219$	2042.78	+	320.993i	0.630310	+	0.0990444i
$220$	3310.46			1.01451
$221$	2201.74			0.670159
$222$	102.629	−	653.121i	0.0310270	−	0.197453i
$223$			1159.80i			0.348277i	0.984721	+	0.174138i	$0.0557140\pi$
$223$			1159.80i			0.348277i	−0.984721	+	0.174138i	$0.944286\pi$
$224$	908.914			0.271113
$225$	−4329.16	−	1394.98i	−1.28271	−	0.413326i
$226$	3728.21			1.09733
$227$	−5359.63			−1.56710			−0.783548	−	0.621331i	$-0.786592\pi$
$227$	−5359.63			−1.56710			−0.783548	+	0.621331i	$0.786592\pi$
$228$	−459.424	−	1424.23i	−0.133448	−	0.413693i
$229$	4649.78			1.34177			0.670887	−	0.741559i	$-0.265913\pi$
$229$	4649.78			1.34177			0.670887	+	0.741559i	$0.265913\pi$
$230$	1005.58			0.288288
$231$	−282.846	+	1800.01i	−0.0805623	+	0.512692i
$232$	−3237.60			−0.916203
$233$			1652.74i			0.464698i	0.972632	+	0.232349i	$0.0746412\pi$
$233$			1652.74i			0.464698i	−0.972632	+	0.232349i	$0.925359\pi$
$234$	−866.763	+	2689.90i	−0.242146	+	0.751472i
$235$	−4070.30			−1.12986
$236$	−2186.32			−0.603040
$237$	859.901	−	5472.34i	0.235682	−	1.49986i
$238$			600.288i			0.163491i
$239$		−	1292.50i		−	0.349810i	−0.984585	−	0.174905i	$-0.944038\pi$
$239$		−	1292.50i		−	0.349810i	0.984585	−	0.174905i	$-0.0559619\pi$
$240$	−332.832	+	2118.11i	−0.0895174	+	0.569681i
$241$		−	3281.17i		−	0.877007i	−0.898730	−	0.438503i	$-0.855509\pi$
$241$		−	3281.17i		−	0.877007i	0.898730	−	0.438503i	$-0.144491\pi$
$242$	3736.91			0.992635
$243$	2694.78	+	2662.15i	0.711401	+	0.702787i
$244$	−1652.86			−0.433663
$245$			5193.70i			1.35434i
$246$	−3215.03	−	505.197i	−0.833265	−	0.130936i
$247$	3638.15	−	1838.45i	0.937206	−	0.473595i
$248$			6177.37i			1.58171i
$249$	−707.776	+	4504.22i	−0.180134	+	1.14636i
$250$		−	1583.18i		−	0.400516i
$251$		−	343.392i		−	0.0863535i	−0.999067	−	0.0431767i	$-0.986252\pi$
$251$		−	343.392i		−	0.0863535i	0.999067	−	0.0431767i	$-0.0137479\pi$
$252$	563.913	+	181.709i	0.140965	+	0.0454229i
$253$	−1533.94			−0.381177
$254$		−	4057.14i		−	1.00224i
$255$	3933.61	+	618.111i	0.966008	+	0.151795i
$256$	−4185.90			−1.02195
$257$	−3100.69			−0.752591			−0.376296	−	0.926500i	$-0.622802\pi$
$257$	−3100.69			−0.752591			−0.376296	+	0.926500i	$0.622802\pi$
$258$	−4298.28	−	675.415i	−1.03721	−	0.162982i
$259$		−	377.532i		−	0.0905742i
$260$	2932.04			0.699374
$261$	−3408.78	−	1098.41i	−0.808423	−	0.260497i
$262$			5080.20i			1.19792i
$263$			4314.96i			1.01168i	0.862627	+	0.505840i	$0.168817\pi$
$263$			4314.96i			1.01168i	−0.862627	+	0.505840i	$0.831183\pi$
$264$	1094.08	−	6962.66i	0.255061	−	1.62319i
$265$			1580.58i			0.366395i
$266$	501.241	+	991.914i	0.115538	+	0.228640i
$267$	−2282.47	−	358.658i	−0.523165	−	0.0822080i
$268$		−	162.559i		−	0.0370518i
$269$	1190.47			0.269830			0.134915	−	0.990857i	$-0.456924\pi$
$269$	1190.47			0.269830			0.134915	+	0.990857i	$0.456924\pi$
$270$	−2303.70	+	4562.42i	−0.519256	+	1.02837i
$271$	821.667			0.184180			0.0920898	−	0.995751i	$-0.470645\pi$
$271$	821.667			0.184180			0.0920898	+	0.995751i	$0.470645\pi$
$272$		−	1077.52i		−	0.240199i
$273$	−250.513	+	1594.24i	−0.0555375	+	0.353436i
$274$		−	3899.53i		−	0.859778i
$275$			9361.46i			2.05279i
$276$	−77.4246	+	492.724i	−0.0168856	+	0.107458i
$277$	7379.74			1.60074			0.800371	−	0.599504i	$-0.204636\pi$
$277$	7379.74			1.60074			0.800371	+	0.599504i	$0.204636\pi$
$278$	−1381.02			−0.297943
$279$	−2095.77	+	6503.98i	−0.449714	+	1.39564i
$280$			2638.43i			0.563130i
$281$	−3839.84			−0.815179			−0.407590	−	0.913165i	$-0.633631\pi$
$281$	−3839.84			−0.815179			−0.407590	+	0.913165i	$0.633631\pi$
$282$	−407.573	+	2593.76i	−0.0860660	+	0.547717i
$283$	0.826925			0.000173695			8.68473e−5	−	1.00000i	$-0.499972\pi$
$283$	0.826925			0.000173695			8.68473e−5		1.00000i	$0.499972\pi$
$284$	−182.808			−0.0381961
$285$	7016.00	−	2263.20i	1.45822	−	0.470387i
$286$	5816.71			1.20262
$287$	−1858.43			−0.382228
$288$	−3701.68	−	1192.79i	−0.757374	−	0.244047i
$289$	2911.91			0.592695
$290$		−	4832.26i		−	0.978483i
$291$	−1168.33	+	7435.18i	−0.235357	+	1.49779i
$292$	−1383.88			−0.277348
$293$	−3879.13			−0.773452			−0.386726	−	0.922195i	$-0.626394\pi$
$293$	−3879.13			−0.773452			−0.386726	+	0.922195i	$0.626394\pi$
$294$	3309.64	+	520.063i	0.656537	+	0.103166i
$295$		−	10770.2i		−	2.12564i
$296$			1460.34i			0.286759i
$297$	3514.12	−	6959.60i	0.686565	−	1.35972i
$298$			3186.07i			0.619343i
$299$	−1358.59			−0.262773
$300$	3007.04	+	472.514i	0.578705	+	0.0909354i
$301$	−2484.59			−0.475779
$302$			2331.77i			0.444299i
$303$	−629.131	+	4003.73i	−0.119283	+	0.759104i
$304$	−899.727	−	1780.48i	−0.169746	−	0.335914i
$305$		−	8142.29i		−	1.52861i
$306$	787.771	−	2444.76i	0.147169	−	0.456724i
$307$		−	7164.11i		−	1.33185i	−0.746019	−	0.665924i	$-0.768037\pi$
$307$		−	7164.11i		−	1.33185i	0.746019	−	0.665924i	$-0.231963\pi$
$308$		−	1219.42i		−	0.225593i
$309$	452.515	−	2879.77i	0.0833096	−	0.530175i
$310$	−9219.98			−1.68922
$311$		−	2711.15i		−	0.494325i	−0.968974	−	0.247163i	$-0.920502\pi$
$311$		−	2711.15i		−	0.494325i	0.968974	−	0.247163i	$-0.0794982\pi$
$312$	969.016	−	6166.74i	0.175833	−	1.11898i
$313$	−5403.92			−0.975872			−0.487936	−	0.872879i	$-0.662250\pi$
$313$	−5403.92			−0.975872			−0.487936	+	0.872879i	$0.662250\pi$
$314$	5790.20			1.04064
$315$	−895.128	+	2777.93i	−0.160110	+	0.496885i
$316$			3707.24i			0.659964i
$317$	622.217			0.110243			0.0551217	−	0.998480i	$-0.482445\pi$
$317$	622.217			0.110243			0.0551217	+	0.998480i	$0.482445\pi$
$318$	1007.21	+	158.269i	0.177615	+	0.0279097i
$319$			7371.23i			1.29376i
$320$		−	8548.53i		−	1.49337i
$321$	−1642.11	−	258.034i	−0.285525	−	0.0448663i
$322$		−	370.409i		−	0.0641059i
$323$	−3306.59	+	1670.91i	−0.569608	+	0.287838i
$324$	−2058.16	−	1480.07i	−0.352907	−	0.253784i
$325$			8291.33i			1.41514i
$326$	−2829.34			−0.480683
$327$	−47.4721	+	302.109i	−0.00802818	+	0.0510907i
$328$	7188.64			1.21014
$329$			1499.31i			0.251244i
$330$	10392.1	+	1632.97i	1.73353	+	0.272400i
$331$			6202.24i			1.02993i	0.857212	+	0.514964i	$0.172195\pi$
$331$			6202.24i			1.02993i	−0.857212	+	0.514964i	$0.827805\pi$
$332$		−	3051.39i		−	0.504418i
$333$	−495.443	+	1537.55i	−0.0815319	+	0.253025i
$334$	−2106.04			−0.345021
$335$	800.795			0.130603
$336$	780.211	+	122.599i	0.126679	+	0.0199058i
$337$			3796.54i			0.613682i	0.951761	+	0.306841i	$0.0992720\pi$
$337$			3796.54i			0.613682i	−0.951761	+	0.306841i	$0.900728\pi$
$338$	479.589			0.0771780
$339$	−8999.01	−	1414.07i	−1.44177	−	0.226553i
$340$	−2664.83			−0.425060
$341$	14064.3			2.23351
$342$	−739.666	−	4697.50i	−0.116949	−	0.742724i
$343$	4077.48			0.641875
$344$	9610.72			1.50632
$345$	−2427.24	−	381.407i	−0.378778	−	0.0595196i
$346$	−696.877			−0.108278
$347$			9300.26i			1.43880i	0.694595	+	0.719401i	$0.255584\pi$
$347$			9300.26i			1.43880i	−0.694595	+	0.719401i	$0.744416\pi$
$348$	2367.75	+	372.058i	0.364726	+	0.0573115i
$349$	−6933.92			−1.06351			−0.531754	−	0.846899i	$-0.678467\pi$
$349$	−6933.92			−1.06351			−0.531754	+	0.846899i	$0.678467\pi$
$350$	−2260.57			−0.345236
$351$	3112.41	−	6164.03i	0.473299	−	0.937355i
$352$			8004.60i			1.21206i
$353$		−	1917.45i		−	0.289110i	−0.989497	−	0.144555i	$-0.953825\pi$
$353$		−	1917.45i		−	0.289110i	0.989497	−	0.144555i	$-0.0461750\pi$
$354$	−6863.20	−	1078.46i	−1.03044	−	0.161919i
$355$		−	900.546i		−	0.134637i
$356$	1546.26			0.230202
$357$	227.683	−	1448.95i	0.0337542	−	0.214809i
$358$	1992.54			0.294160
$359$		−	2421.08i		−	0.355933i	−0.984037	−	0.177966i	$-0.943048\pi$
$359$		−	2421.08i		−	0.355933i	0.984037	−	0.177966i	$-0.0569518\pi$
$360$	3462.47	−	10745.4i	0.506911	−	1.57314i
$361$	−4068.58	+	5522.00i	−0.593174	+	0.805074i
$362$		−	8186.69i		−	1.18863i
$363$	−9020.01	−	1417.37i	−1.30421	−	0.204938i
$364$		−	1080.02i		−	0.155518i
$365$		−	6817.23i		−	0.977617i
$366$	−5188.60	−	815.315i	−0.741017	−	0.116440i
$367$	−419.571			−0.0596769			−0.0298384	−	0.999555i	$-0.509499\pi$
$367$	−419.571			−0.0596769			−0.0298384	+	0.999555i	$0.509499\pi$
$368$			664.884i			0.0941833i
$369$	7568.71	+	2438.85i	1.06778	+	0.344069i
$370$	−2179.62			−0.306252
$371$	582.212			0.0814742
$372$	709.889	−	4517.68i	0.0989410	−	0.629652i
$373$		−	11631.7i		−	1.61466i	−0.590100	−	0.807330i	$-0.700912\pi$
$373$		−	11631.7i		−	1.61466i	0.590100	−	0.807330i	$-0.299088\pi$
$374$	−5286.60			−0.730919
$375$	−600.482	+	3821.42i	−0.0826901	+	0.526233i
$376$		−	5799.50i		−	0.795443i
$377$			6528.60i			0.891883i
$378$	1680.58	+	848.575i	0.228676	+	0.115466i
$379$		−	583.690i		−	0.0791085i	−0.999217	−	0.0395543i	$-0.987406\pi$
$379$		−	583.690i		−	0.0791085i	0.999217	−	0.0395543i	$-0.0125938\pi$
$380$	−4403.35	+	2225.13i	−0.594440	+	0.300386i
$381$	−1538.83	+	9792.98i	−0.206920	+	1.31682i
$382$			3534.68i			0.473429i
$383$	10035.3			1.33885			0.669427	−	0.742878i	$-0.266540\pi$
$383$	10035.3			1.33885			0.669427	+	0.742878i	$0.266540\pi$
$384$	467.626	+	73.4808i	0.0621443	+	0.00976511i
$385$	6007.06			0.795190
$386$		−	3457.59i		−	0.455925i
$387$	10118.9	+	3260.58i	1.32912	+	0.428281i
$388$		−	5036.97i		−	0.659055i
$389$			2158.16i			0.281294i	0.990060	+	0.140647i	$0.0449182\pi$
$389$			2158.16i			0.281294i	−0.990060	+	0.140647i	$0.955082\pi$
$390$	9204.12	+	1446.30i	1.19505	+	0.187785i
$391$	1234.78			0.159707
$392$	−7400.16			−0.953481
$393$	1926.86	−	12262.4i	0.247322	−	1.57393i
$394$		−	2513.46i		−	0.321387i
$395$	−18262.5			−2.32630
$396$	−1600.27	+	4966.25i	−0.203072	+	0.630211i
$397$	−14921.9			−1.88642			−0.943211	−	0.332194i	$-0.892211\pi$
$397$	−14921.9			−1.88642			−0.943211	+	0.332194i	$0.892211\pi$
$398$	7743.54			0.975248
$399$	−833.655	−	2584.36i	−0.104599	−	0.324260i
$400$	4057.72			0.507215
$401$	−11383.1			−1.41757			−0.708787	−	0.705423i	$-0.750757\pi$
$401$	−11383.1			−1.41757			−0.708787	+	0.705423i	$0.750757\pi$
$402$	80.1863	−	510.299i	0.00994858	−	0.0633119i
$403$	12456.6			1.53972
$404$		−	2712.33i		−	0.334019i
$405$	7291.07	−	10138.8i	0.894559	−	1.24396i
$406$	−1779.97			−0.217583
$407$	3324.84			0.404929
$408$	−880.706	+	5604.74i	−0.106866	+	0.680088i
$409$			1237.38i			0.149596i	0.997199	+	0.0747978i	$0.0238311\pi$
$409$			1237.38i			0.149596i	−0.997199	+	0.0747978i	$0.976169\pi$
$410$			10729.3i			1.29240i
$411$	−1479.05	+	9412.53i	−0.177509	+	1.12965i
$412$			1950.90i			0.233286i
$413$	−3967.22			−0.472674
$414$	−486.096	+	1508.54i	−0.0577060	+	0.179084i
$415$	15031.7			1.77801
$416$			7089.57i			0.835564i
$417$	3333.45	+	523.806i	0.391463	+	0.0615129i
$418$	−8735.56	+	4414.31i	−1.02218	+	0.516534i
$419$			13831.7i			1.61270i	0.591437	+	0.806351i	$0.298561\pi$
$419$			13831.7i			1.61270i	−0.591437	+	0.806351i	$0.701439\pi$
$420$	303.203	−	1929.56i	0.0352257	−	0.224173i
$421$			15524.0i			1.79714i	0.438833	+	0.898569i	$0.355392\pi$
$421$			15524.0i			1.79714i	−0.438833	+	0.898569i	$0.644608\pi$
$422$			7913.12i			0.912808i
$423$	1967.57	−	6106.13i	0.226162	−	0.701869i
$424$	−2252.07			−0.257949
$425$		−	7535.70i		−	0.860083i
$426$	−573.864	−	90.1747i	−0.0652672	−	0.0102558i
$427$	−2999.23			−0.339913
$428$	1112.45			0.125636
$429$	−14040.1	−	2206.21i	−1.58010	−	0.248291i
$430$			14344.4i			1.60872i
$431$	13216.9			1.47711			0.738557	−	0.674191i	$-0.235507\pi$
$431$	13216.9			1.47711			0.738557	+	0.674191i	$0.235507\pi$
$432$	−3016.63	−	1523.19i	−0.335967	−	0.169640i
$433$		−	5963.99i		−	0.661920i	−0.943645	−	0.330960i	$-0.892628\pi$
$433$		−	5963.99i		−	0.661920i	0.943645	−	0.330960i	$-0.107372\pi$
$434$			3396.20i			0.375629i
$435$	−1832.82	+	11663.9i	−0.202016	+	1.28562i
$436$		−	204.664i		−	0.0224808i
$437$	2040.34	−	1031.04i	0.223347	−	0.112863i
$438$	−4344.22	−	682.632i	−0.473915	−	0.0744690i
$439$		−	12001.6i		−	1.30479i	−0.757877	−	0.652397i	$-0.773763\pi$
$439$		−	12001.6i		−	1.30479i	0.757877	−	0.652397i	$-0.226237\pi$
$440$	−23236.1			−2.51758
$441$	−7791.42	−	2510.62i	−0.841316	−	0.271096i
$442$	−4682.28			−0.503876
$443$			11806.1i			1.26619i	0.774073	+	0.633096i	$0.218216\pi$
$443$			11806.1i			1.26619i	−0.774073	+	0.633096i	$0.781784\pi$
$444$	167.819	−	1067.99i	0.0179377	−	0.114154i
$445$			7617.16i			0.811433i
$446$		−	2466.45i		−	0.261861i
$447$	1208.44	−	7690.42i	0.127869	−	0.813746i
$448$	−3148.87			−0.332076
$449$	−756.626			−0.0795264			−0.0397632	−	0.999209i	$-0.512660\pi$
$449$	−756.626			−0.0795264			−0.0397632	+	0.999209i	$0.512660\pi$
$450$	9206.49	+	2966.59i	0.964440	+	0.310770i
$451$		−	16366.8i		−	1.70883i
$452$	6096.39			0.634403
$453$	884.414	−	5628.34i	0.0917294	−	0.583758i
$454$	11397.9			1.17826
$455$	5320.37			0.548182
$456$	3224.68	+	9996.63i	0.331161	+	1.02661i
$457$	−6815.24			−0.697600			−0.348800	−	0.937197i	$-0.613411\pi$
$457$	−6815.24			−0.697600			−0.348800	+	0.937197i	$0.613411\pi$
$458$	−9888.35			−1.00885
$459$	−2828.76	+	5602.28i	−0.287659	+	0.569699i
$460$	1644.34			0.166669
$461$		−	5864.07i		−	0.592445i	−0.955119	−	0.296222i	$-0.904273\pi$
$461$		−	5864.07i		−	0.592445i	0.955119	−	0.296222i	$-0.0957270\pi$
$462$	601.507	−	3827.94i	0.0605728	−	0.385480i
$463$	−10261.0			−1.02995			−0.514977	−	0.857204i	$-0.672199\pi$
$463$	−10261.0			−1.02995			−0.514977	+	0.857204i	$0.672199\pi$
$464$	3195.05			0.319669
$465$	22254.8	+	3497.04i	2.21945	+	0.348755i
$466$		−	3514.76i		−	0.349395i
$467$		−	9744.19i		−	0.965540i	−0.875747	−	0.482770i	$-0.839631\pi$
$467$		−	9744.19i		−	0.965540i	0.875747	−	0.482770i	$-0.160369\pi$
$468$	−1417.34	+	4398.55i	−0.139992	+	0.434451i
$469$		−	294.975i		−	0.0290419i
$470$	8656.00			0.849514
$471$	−13976.2	−	2196.16i	−1.36728	−	0.214848i
$472$	15345.7			1.49649
$473$		−	21881.2i		−	2.12706i
$474$	−1828.69	+	11637.6i	−0.177203	+	1.12771i
$475$	−6292.32	−	12452.0i	−0.607813	−	1.20281i
$476$			981.595i			0.0945196i
$477$	−2371.14	−	764.049i	−0.227604	−	0.0733404i
$478$			2748.65i			0.263014i
$479$			5090.79i			0.485603i	0.970076	+	0.242802i	$0.0780664\pi$
$479$			5090.79i			0.485603i	−0.970076	+	0.242802i	$0.921934\pi$
$480$	−1990.31	+	12666.1i	−0.189260	+	1.20443i
$481$	2944.77			0.279147
$482$			6977.81i			0.659400i
$483$	−140.492	+	894.080i	−0.0132352	+	0.0842278i
$484$	6110.62			0.573875
$485$	24813.0			2.32309
$486$	−5730.79	−	5661.40i	−0.534884	−	0.528408i
$487$			4882.29i			0.454286i	0.973861	+	0.227143i	$0.0729386\pi$
$487$			4882.29i			0.454286i	−0.973861	+	0.227143i	$0.927061\pi$
$488$	11601.4			1.07617
$489$	6829.35	+	1073.14i	0.631562	+	0.0992411i
$490$		−	11045.1i		−	1.01830i
$491$		−	14332.2i		−	1.31732i	−0.752441	−	0.658659i	$-0.771124\pi$
$491$		−	14332.2i		−	1.31732i	0.752441	−	0.658659i	$-0.228876\pi$
$492$	−5257.24	−	826.102i	−0.481737	−	0.0756983i
$493$		−	5933.62i		−	0.542063i
$494$	−7736.97	+	3909.70i	−0.704662	+	0.356085i
$495$	−24464.6	−	7883.19i	−2.22142	−	0.715804i
$496$		−	6096.18i		−	0.551868i
$497$	−331.718			−0.0299388
$498$	1505.17	−	9578.79i	0.135439	−	0.861920i
$499$	10297.5			0.923809			0.461904	−	0.886930i	$-0.347166\pi$
$499$	10297.5			0.923809			0.461904	+	0.886930i	$0.347166\pi$
$500$		−	2588.83i		−	0.231552i
$501$	5083.47	+	798.796i	0.453319	+	0.0712326i
$502$			730.266i			0.0649270i
$503$		−	15803.0i		−	1.40083i	−0.713734	−	0.700417i	$-0.752997\pi$
$503$		−	15803.0i		−	1.40083i	0.713734	−	0.700417i	$-0.247003\pi$
$504$	−3958.09	−	1275.41i	−0.349816	−	0.112721i
$505$	13361.4			1.17738
$506$	3262.11			0.286598
$507$	−1157.61	−	181.903i	−0.101403	−	0.0159341i
$508$		−	6634.27i		−	0.579425i
$509$	−16564.8			−1.44248			−0.721238	−	0.692688i	$-0.756426\pi$
$509$	−16564.8			−1.44248			−0.721238	+	0.692688i	$0.756426\pi$
$510$	−8365.31	−	1314.49i	−0.726318	−	0.114131i
$511$	−2511.14			−0.217390
$512$	8173.05			0.705471
$513$	3.66930	+	11619.2i	0.000315797	+	1.00000i
$514$	6594.01			0.565855
$515$	−9610.47			−0.822307
$516$	−7028.58	−	1104.44i	−0.599643	−	0.0942255i
$517$	−13204.0			−1.12324
$518$			802.869i			0.0681005i
$519$	1682.10	+	264.318i	0.142266	+	0.0223550i
$520$	−20579.9			−1.73555
$521$	16754.8			1.40890			0.704452	−	0.709751i	$-0.251193\pi$
$521$	16754.8			1.40890			0.704452	+	0.709751i	$0.251193\pi$
$522$	7249.20	+	2335.90i	0.607833	+	0.195861i
$523$			1927.55i			0.161158i	0.996748	+	0.0805792i	$0.0256770\pi$
$523$			1927.55i			0.161158i	−0.996748	+	0.0805792i	$0.974323\pi$
$524$			8307.18i			0.692559i
$525$	5456.48	+	857.409i	0.453600	+	0.0712769i
$526$		−	9176.30i		−	0.760658i
$527$	−11321.4			−0.935801
$528$	−1079.70	+	6871.15i	−0.0889926	+	0.566341i
$529$	11405.1			0.937378
$530$		−	3361.31i		−	0.275483i
$531$	16157.1	+	5206.27i	1.32045	+	0.425486i
$532$	819.632	+	1621.98i	0.0667962	+	0.132184i
$533$		−	14495.8i		−	1.17802i
$534$	4853.96	+	762.731i	0.393355	+	0.0618101i
$535$			5480.11i			0.442852i
$536$			1141.00i			0.0919471i
$537$	−4809.53	−	755.750i	−0.386492	−	0.0607318i
$538$	−2531.68			−0.202878
$539$			16848.3i			1.34640i
$540$	−3767.03	+	7460.49i	−0.300199	+	0.594534i
$541$	4128.95			0.328128			0.164064	−	0.986450i	$-0.447540\pi$
$541$	4128.95			0.328128			0.164064	+	0.986450i	$0.447540\pi$
$542$	−1747.38			−0.138480
$543$	−3105.12	+	19760.7i	−0.245402	+	1.56172i
$544$		−	6443.47i		−	0.507833i
$545$	1008.21			0.0792421
$546$	532.747	−	3390.36i	0.0417573	−	0.265740i
$547$			22929.5i			1.79231i	0.443741	+	0.896155i	$0.353651\pi$
$547$			22929.5i			1.79231i	−0.443741	+	0.896155i	$0.646349\pi$
$548$		−	6376.53i		−	0.497066i
$549$	12214.8	+	3935.95i	0.949572	+	0.305979i
$550$		−	19908.3i		−	1.54344i
$551$	−4954.57	−	9804.69i	−0.383071	−	0.758065i
$552$	543.441	−	3458.41i	0.0419029	−	0.266666i
$553$			6727.04i			0.517293i
$554$	−15693.9			−1.20356
$555$	5261.09	+	826.707i	0.402380	+	0.0632284i
$556$	−2258.25			−0.172250
$557$			385.234i			0.0293050i	0.999893	+	0.0146525i	$0.00466420\pi$
$557$			385.234i			0.0293050i	−0.999893	+	0.0146525i	$0.995336\pi$
$558$	4456.90	−	13831.5i	0.338129	−	1.04935i
$559$		−	19379.9i		−	1.46634i
$560$		−	2603.75i		−	0.196480i
$561$	12760.6	+	2005.15i	0.960344	+	0.150905i
$562$	8165.89			0.612913
$563$	8424.09			0.630609			0.315305	−	0.948991i	$-0.397893\pi$
$563$	8424.09			0.630609			0.315305	+	0.948991i	$0.397893\pi$
$564$	−666.466	+	4241.33i	−0.0497576	+	0.316653i
$565$			30031.8i			2.23619i
$566$	−1.75856			−0.000130597
$567$	−3734.66	−	2685.68i	−0.276615	−	0.198921i
$568$	1283.13			0.0947867
$569$	−17404.6			−1.28232			−0.641159	−	0.767408i	$-0.721546\pi$
$569$	−17404.6			−1.28232			−0.641159	+	0.767408i	$0.721546\pi$
$570$	−14920.4	+	4812.97i	−1.09640	+	0.353672i
$571$	−12600.5			−0.923491			−0.461746	−	0.887012i	$-0.652777\pi$
$571$	−12600.5			−0.923491			−0.461746	+	0.887012i	$0.652777\pi$
$572$	9511.51			0.695273
$573$	1340.66	−	8531.87i	0.0977434	−	0.622031i
$574$	3952.18			0.287388
$575$			4649.92i			0.337244i
$576$	12824.2	+	4132.33i	0.927679	+	0.298924i
$577$	1251.71			0.0903111			0.0451556	−	0.998980i	$-0.485622\pi$
$577$	1251.71			0.0903111			0.0451556	+	0.998980i	$0.485622\pi$
$578$	−6192.54			−0.445633
$579$	−1311.43	+	8345.81i	−0.0941296	+	0.599033i
$580$		−	7901.74i		−	0.565693i
$581$		−	5536.95i		−	0.395373i
$582$	2484.61	−	15811.8i	0.176959	−	1.12615i
$583$			5127.41i			0.364246i
$584$	9713.42			0.688261
$585$	−21668.0	−	6982.04i	−1.53139	−	0.493456i
$586$	8249.46			0.581539
$587$			12024.2i			0.845469i	0.906254	+	0.422734i	$0.138930\pi$
$587$			12024.2i			0.845469i	−0.906254	+	0.422734i	$0.861070\pi$
$588$	5411.94	+	850.410i	0.379566	+	0.0596434i
$589$	−18707.4	+	9453.36i	−1.30870	+	0.661322i
$590$			22904.1i			1.59822i
$591$	−953.328	+	6066.90i	−0.0663531	+	0.422265i
$592$		−	1441.15i		−	0.100052i
$593$			14645.2i			1.01418i	0.861894	+	0.507089i	$0.169279\pi$
$593$			14645.2i			1.01418i	−0.861894	+	0.507089i	$0.830721\pi$
$594$	−7473.21	+	14800.5i	−0.516211	+	1.02234i
$595$	−4835.51			−0.333170
$596$			5209.88i			0.358062i
$597$	−18691.1	−	2937.04i	−1.28136	−	0.201348i
$598$	2889.21			0.197573
$599$	13003.2			0.886972			0.443486	−	0.896281i	$-0.353742\pi$
$599$	13003.2			0.886972			0.443486	+	0.896281i	$0.353742\pi$
$600$	−21106.3	−	3316.57i	−1.43610	−	0.225664i
$601$		−	22343.8i		−	1.51651i	−0.651957	−	0.758256i	$-0.726052\pi$
$601$		−	22343.8i		−	1.51651i	0.651957	−	0.758256i	$-0.273948\pi$
$602$	5283.79			0.357726
$603$	−387.101	+	1201.33i	−0.0261426	+	0.0811307i
$604$			3812.92i			0.256864i
$605$			30102.0i			2.02284i
$606$	1337.92	−	8514.44i	0.0896856	−	0.570752i
$607$			16091.9i			1.07603i	0.842935	+	0.538016i	$0.180826\pi$
$607$			16091.9i			1.07603i	−0.842935	+	0.538016i	$0.819174\pi$
$608$	−5380.30	−	10647.2i	−0.358881	−	0.710196i
$609$	4296.43	+	675.124i	0.285879	+	0.0449219i
$610$			17315.6i			1.14932i
$611$	−11694.7			−0.774329
$612$	1288.17	−	3997.69i	0.0850835	−	0.264047i
$613$	1405.63			0.0926147			0.0463073	−	0.998927i	$-0.485255\pi$
$613$	1405.63			0.0926147			0.0463073	+	0.998927i	$0.485255\pi$
$614$			15235.4i			1.00138i
$615$	4069.52	−	25898.1i	0.266827	−	1.69807i
$616$			8559.06i			0.559828i
$617$			855.316i			0.0558083i	0.999611	+	0.0279041i	$0.00888332\pi$
$617$			855.316i			0.0558083i	−0.999611	+	0.0279041i	$0.991117\pi$
$618$	−962.329	+	6124.18i	−0.0626384	+	0.398626i
$619$	3622.54			0.235222			0.117611	−	0.993060i	$-0.462476\pi$
$619$	3622.54			0.235222			0.117611	+	0.993060i	$0.462476\pi$
$620$	−15076.6			−0.976596
$621$	1745.49	−	3456.90i	0.112793	−	0.223382i
$622$			5765.59i			0.371671i
$623$	2805.80			0.180436
$624$	−956.280	+	6085.69i	−0.0613491	+	0.390421i
$625$	−8304.22			−0.531470
$626$	11492.1			0.733734
$627$	22759.9	−	7341.81i	1.44967	−	0.467629i
$628$	9468.17			0.601626
$629$	−2676.40			−0.169658
$630$	1903.60	−	5907.61i	0.120383	−	0.373595i
$631$	6154.97			0.388313			0.194156	−	0.980971i	$-0.437803\pi$
$631$	6154.97			0.388313			0.194156	+	0.980971i	$0.437803\pi$
$632$		−	26021.0i		−	1.63776i
$633$	3001.36	−	19100.4i	0.188457	−	1.19933i
$634$	−1323.22			−0.0828893
$635$	32681.5			2.04240
$636$	1647.00	+	258.803i	0.102685	+	0.0161355i
$637$			14922.4i			0.928172i
$638$		−	15675.8i		−	0.972746i
$639$	1350.97	+	435.321i	0.0836362	+	0.0269499i
$640$		−	1560.58i		−	0.0963864i
$641$	−14638.8			−0.902023			−0.451012	−	0.892518i	$-0.648937\pi$
$641$	−14638.8			−0.902023			−0.451012	+	0.892518i	$0.648937\pi$
$642$	3492.15	+	548.742i	0.214679	+	0.0337338i
$643$	7403.66			0.454078			0.227039	−	0.973886i	$-0.427096\pi$
$643$	7403.66			0.454078			0.227039	+	0.973886i	$0.427096\pi$
$644$		−	605.695i		−	0.0370617i
$645$	5440.67	−	34624.0i	0.332134	−	2.11367i
$646$	7031.87	−	3553.39i	0.428274	−	0.216419i
$647$			25405.3i			1.54372i	0.635792	+	0.771860i	$0.280674\pi$
$647$			25405.3i			1.54372i	−0.635792	+	0.771860i	$0.719326\pi$
$648$	14446.1	+	10388.6i	0.875768	+	0.629786i
$649$		−	34938.4i		−	2.11318i
$650$		−	17632.5i		−	1.06401i
$651$	1288.14	−	8197.62i	0.0775518	−	0.493533i
$652$	−4626.55			−0.277898
$653$			14063.5i			0.842797i	0.906876	+	0.421398i	$0.138461\pi$
$653$			14063.5i			0.842797i	−0.906876	+	0.421398i	$0.861539\pi$
$654$	100.955	−	642.472i	0.00603619	−	0.0384138i
$655$	−40922.6			−2.44119
$656$	−7094.15			−0.422226
$657$	10227.0	+	3295.42i	0.607295	+	0.195688i
$658$		−	3188.46i		−	0.188904i
$659$	−25324.1			−1.49695			−0.748473	−	0.663165i	$-0.769213\pi$
$659$	−25324.1			−1.49695			−0.748473	+	0.663165i	$0.769213\pi$
$660$	16993.2	+	2670.24i	1.00221	+	0.157483i
$661$			13688.1i			0.805453i	0.915320	+	0.402726i	$0.131937\pi$
$661$			13688.1i			0.805453i	−0.915320	+	0.402726i	$0.868063\pi$
$662$		−	13189.8i		−	0.774377i
$663$	11301.9	+	1775.94i	0.662036	+	0.104030i
$664$			21417.6i			1.25176i
$665$	−7990.17	+	4037.65i	−0.465933	+	0.235449i
$666$	1053.62	−	3269.80i	0.0613018	−	0.190243i
$667$			3661.35i			0.212546i
$668$	−3443.80			−0.199468
$669$	−935.497	+	5953.42i	−0.0540634	+	0.344055i
$670$	−1702.99			−0.0981974
$671$		−	26413.6i		−	1.51965i
$672$	4665.61	+	733.134i	0.267827	+	0.0420852i
$673$		−	6903.14i		−	0.395388i	−0.980264	−	0.197694i	$-0.936655\pi$
$673$		−	6903.14i		−	0.395388i	0.980264	−	0.197694i	$-0.0633453\pi$
$674$		−	8073.82i		−	0.461412i
$675$	−21097.1	−	10652.6i	−1.20300	−	0.607433i
$676$	784.226			0.0446191
$677$	−1320.39			−0.0749583			−0.0374791	−	0.999297i	$-0.511933\pi$
$677$	−1320.39			−0.0749583			−0.0374791	+	0.999297i	$0.511933\pi$
$678$	19137.5	+	3007.19i	1.08403	+	0.170340i
$679$		−	9139.92i		−	0.516580i
$680$	18704.4			1.05482
$681$	−27511.8	−	4323.10i	−1.54810	−	0.243262i
$682$	−29909.6			−1.67932
$683$	6966.44			0.390283			0.195141	−	0.980775i	$-0.437483\pi$
$683$	6966.44			0.390283			0.195141	+	0.980775i	$0.437483\pi$
$684$	−1209.51	−	7681.38i	−0.0676121	−	0.429393i
$685$	31411.9			1.75210
$686$	−8671.26			−0.482610
$687$	23868.1	+	3750.54i	1.32551	+	0.208285i
$688$	−9484.40			−0.525566
$689$			4541.28i			0.251102i
$690$	5161.83	+	811.109i	0.284793	+	0.0447513i
$691$	18006.4			0.991313			0.495656	−	0.868519i	$-0.334928\pi$
$691$	18006.4			0.991313			0.495656	+	0.868519i	$0.334928\pi$
$692$	−1139.54			−0.0625993
$693$	−2903.79	+	9011.59i	−0.159171	+	0.493971i
$694$		−	19778.2i		−	1.08180i
$695$		−	11124.5i		−	0.607162i
$696$	−16619.2	−	2611.47i	−0.905097	−	0.142223i
$697$			13174.8i			0.715968i
$698$	14745.8			0.799625
$699$	−1333.11	+	8483.79i	−0.0721356	+	0.459065i
$700$	−3696.50			−0.199592
$701$			2566.42i			0.138277i	0.997607	+	0.0691385i	$0.0220251\pi$
$701$			2566.42i			0.138277i	−0.997607	+	0.0691385i	$0.977975\pi$
$702$	−6618.92	+	13108.6i	−0.355862	+	0.704774i
$703$	−4422.47	+	2234.79i	−0.237264	+	0.119896i
$704$		−	27731.4i		−	1.48461i
$705$	−20893.5	−	3283.13i	−1.11616	−	0.175390i
$706$			4077.70i			0.217375i
$707$		−	4921.71i		−	0.261810i
$708$	−11222.7	−	1763.50i	−0.595730	−	0.0936106i
$709$	386.464			0.0204711			0.0102355	−	0.999948i	$-0.496742\pi$
$709$	386.464			0.0204711			0.0102355	+	0.999948i	$0.496742\pi$
$710$			1915.12i			0.101230i
$711$	8828.03	−	27396.8i	0.465650	−	1.44509i
$712$	−10853.2			−0.571264
$713$	6985.88			0.366933
$714$	−484.195	+	3081.38i	−0.0253789	+	0.161509i
$715$			46855.3i			2.45076i
$716$	3258.22			0.170063
$717$	1042.53	−	6634.60i	0.0543015	−	0.345570i
$718$			5148.73i			0.267617i
$719$		−	11571.3i		−	0.600189i	−0.953910	−	0.300094i	$-0.902982\pi$
$719$		−	11571.3i		−	0.600189i	0.953910	−	0.300094i	$-0.0970182\pi$
$720$	−3416.96	+	10604.2i	−0.176865	+	0.548880i
$721$			3540.04i			0.182854i
$722$	8652.35	−	11743.2i	0.445993	−	0.605315i
$723$	2646.61	−	16842.8i	0.136139	−	0.866376i
$724$		−	13386.9i		−	0.687184i
$725$	22344.9			1.14464
$726$	19182.2	+	3014.21i	0.980603	+	0.154088i
$727$	814.501			0.0415518			0.0207759	−	0.999784i	$-0.493386\pi$
$727$	814.501			0.0415518			0.0207759	+	0.999784i	$0.493386\pi$
$728$			7580.65i			0.385931i
$729$	11685.5	+	15838.9i	0.593683	+	0.804699i
$730$			14497.7i			0.735046i
$731$			17613.8i			0.891201i
$732$	−8484.43	−	1333.21i	−0.428406	−	0.0673180i
$733$	14533.7			0.732350			0.366175	−	0.930546i	$-0.380667\pi$
$733$	14533.7			0.732350			0.366175	+	0.930546i	$0.380667\pi$
$734$	892.270			0.0448696
$735$	−4189.27	+	26660.1i	−0.210236	+	1.33792i
$736$			3975.95i			0.199124i
$737$	2597.77			0.129838
$738$	−16095.8	−	5186.52i	−0.802839	−	0.258697i
$739$	32354.9			1.61055			0.805273	−	0.592905i	$-0.202019\pi$
$739$	32354.9			1.61055			0.805273	+	0.592905i	$0.202019\pi$
$740$	−3564.13			−0.177054
$741$	20158.1	−	6502.54i	0.999362	−	0.322371i
$742$	−1238.15			−0.0612585
$743$	−8037.10			−0.396841			−0.198420	−	0.980117i	$-0.563581\pi$
$743$	−8037.10			−0.396841			−0.198420	+	0.980117i	$0.563581\pi$
$744$	−4982.69	+	31709.4i	−0.245530	+	1.56253i
$745$	−25664.8			−1.26213
$746$			24736.3i			1.21402i
$747$	−7266.26	+	22550.0i	−0.355902	+	1.10450i
$748$	−8644.69			−0.422568
$749$	2018.61			0.0984759
$750$	1277.00	−	8126.72i	0.0621726	−	0.395661i
$751$		−	6767.43i		−	0.328824i	−0.986392	−	0.164412i	$-0.947427\pi$
$751$		−	6767.43i		−	0.328824i	0.986392	−	0.164412i	$-0.0525727\pi$
$752$			5723.28i			0.277535i
$753$	276.982	−	1762.69i	0.0134048	−	0.0853067i
$754$		−	13883.9i		−	0.670585i
$755$	−18783.1			−0.905414
$756$	2748.09	+	1387.60i	0.132205	+	0.0667544i
$757$	−26475.7			−1.27117			−0.635585	−	0.772031i	$-0.719241\pi$
$757$	−26475.7			−1.27117			−0.635585	+	0.772031i	$0.719241\pi$
$758$			1241.29i			0.0594797i
$759$	−7873.96	−	1237.28i	−0.376557	−	0.0591706i
$760$	30907.0	−	15618.1i	1.47515	−	0.745433i
$761$		−	18016.3i		−	0.858200i	−0.903257	−	0.429100i	$-0.858831\pi$
$761$		−	18016.3i		−	0.858200i	0.903257	−	0.429100i	$-0.141169\pi$
$762$	3272.51	−	20826.0i	0.155578	−	0.990087i
$763$		−	371.376i		−	0.0176209i
$764$			5779.92i			0.273705i
$765$	19693.3	+	6345.73i	0.930735	+	0.299909i
$766$	−21341.4			−1.00665
$767$		−	30944.5i		−	1.45677i
$768$	−21486.9	−	3376.37i	−1.00956	−	0.158638i
$769$	−12848.5			−0.602507			−0.301254	−	0.953544i	$-0.597405\pi$
$769$	−12848.5			−0.602507			−0.301254	+	0.953544i	$0.597405\pi$
$770$	−12774.8			−0.597883
$771$	−15916.4	−	2501.04i	−0.743469	−	0.116826i
$772$		−	5653.88i		−	0.263585i
$773$	−8557.58			−0.398182			−0.199091	−	0.979981i	$-0.563799\pi$
$773$	−8557.58			−0.398182			−0.199091	+	0.979981i	$0.563799\pi$
$774$	−21519.0	−	6934.03i	−0.999334	−	0.322014i
$775$		−	42634.1i		−	1.97608i
$776$			35354.4i			1.63550i
$777$	304.519	−	1937.94i	0.0140599	−	0.0894762i
$778$		−	4589.60i		−	0.211498i
$779$	11000.9	+	21769.9i	0.505968	+	1.00127i
$780$	15050.6	+	2364.99i	0.690896	+	0.108565i
$781$		−	2921.37i		−	0.133847i
$782$	−2625.90			−0.120079
$783$	−16611.9	−	8387.84i	−0.758186	−	0.382831i
$784$	7302.90			0.332676
$785$			46641.8i			2.12066i
$786$	−4097.72	+	26077.5i	−0.185955	+	1.18340i
$787$			1832.29i			0.0829914i	0.999139	+	0.0414957i	$0.0132123\pi$
$787$			1832.29i			0.0829914i	−0.999139	+	0.0414957i	$0.986788\pi$
$788$		−	4110.03i		−	0.185804i
$789$	−3480.47	+	22149.4i	−0.157044	+	0.999417i
$790$	38837.5			1.74908
$791$	11062.3			0.497257
$792$	11232.2	−	34858.0i	0.503939	−	1.56392i
$793$		−	23394.2i		−	1.04760i
$794$	31733.3			1.41835
$795$	−1274.91	+	8113.40i	−0.0568759	+	0.361953i
$796$	12662.3			0.563823
$797$	−39316.6			−1.74739			−0.873693	−	0.486478i	$-0.838281\pi$
$797$	−39316.6			−1.74739			−0.873693	+	0.486478i	$0.838281\pi$
$798$	1772.87	+	5495.96i	0.0786453	+	0.243803i
$799$	10628.9			0.470616
$800$	24264.8			1.07236
$801$	−11427.0	−	3682.10i	−0.504062	−	0.162423i
$802$	24207.7			1.06584
$803$		−	22115.1i		−	0.971885i
$804$	131.121	−	834.444i	0.00575160	−	0.0366027i
$805$	2983.76			0.130638
$806$	−26490.5			−1.15768
$807$	6110.87	+	960.238i	0.266559	+	0.0418860i
$808$			19037.8i			0.828896i
$809$			31759.6i			1.38023i	0.723699	+	0.690115i	$0.242440\pi$
$809$			31759.6i			1.38023i	−0.723699	+	0.690115i	$0.757560\pi$
$810$	−15505.4	+	21561.5i	−0.672596	+	0.935300i
$811$		−	10094.1i		−	0.437054i	−0.975831	−	0.218527i	$-0.929875\pi$
$811$		−	10094.1i		−	0.437054i	0.975831	−	0.218527i	$-0.0701252\pi$
$812$	−2910.62			−0.125792
$813$	4217.75	+	662.760i	0.181947	+	0.0285904i
$814$	−7070.69			−0.304456
$815$		−	22791.2i		−	0.979558i
$816$	869.130	−	5531.07i	0.0372863	−	0.237287i
$817$	14707.5	+	29104.9i	0.629804	+	1.24633i
$818$		−	2631.45i		−	0.112477i
$819$	−2571.85	+	7981.45i	−0.109729	+	0.340531i
$820$			17544.7i			0.747179i
$821$			558.619i			0.0237466i	0.999930	+	0.0118733i	$0.00377947\pi$
$821$			558.619i			0.0237466i	−0.999930	+	0.0118733i	$0.996221\pi$
$822$	3145.38	−	20016.9i	0.133464	−	0.849356i
$823$	−33614.5			−1.42373			−0.711864	−	0.702317i	$-0.752149\pi$
$823$	−33614.5			−1.42373			−0.711864	+	0.702317i	$0.752149\pi$
$824$		−	13693.3i		−	0.578919i
$825$	−7551.00	+	48053.9i	−0.318657	+	2.02791i
$826$	8436.80			0.355392
$827$	−874.477			−0.0367697			−0.0183848	−	0.999831i	$-0.505852\pi$
$827$	−874.477			−0.0367697			−0.0183848	+	0.999831i	$0.505852\pi$
$828$	−794.866	+	2466.78i	−0.0333617	+	0.103534i
$829$		−	6157.91i		−	0.257989i	−0.991645	−	0.128995i	$-0.958825\pi$
$829$		−	6157.91i		−	0.257989i	0.991645	−	0.128995i	$-0.0411750\pi$
$830$	−31966.7			−1.33685
$831$	37881.4	+	5952.54i	1.58134	+	0.248485i
$832$		−	24561.3i		−	1.02345i
$833$		−	13562.4i		−	0.564118i
$834$	−7089.01	−	1113.94i	−0.294331	−	0.0462500i
$835$		−	16964.8i		−	0.703101i
$836$	−14284.4	+	7218.31i	−0.590954	+	0.298625i
$837$	−16004.0	+	31695.5i	−0.660909	+	1.30891i
$838$		−	29414.8i		−	1.21255i
$839$	32680.7			1.34477			0.672387	−	0.740200i	$-0.265269\pi$
$839$	32680.7			1.34477			0.672387	+	0.740200i	$0.265269\pi$
$840$	−2128.17	+	13543.5i	−0.0874153	+	0.556304i
$841$	−6794.64			−0.278594
$842$		−	33013.8i		−	1.35122i
$843$	−19710.5	−	3097.23i	−0.805298	−	0.126541i
$844$			12939.6i			0.527724i
$845$			3863.23i			0.157277i
$846$	−4184.28	+	12985.5i	−0.170046	+	0.527718i
$847$	11088.1			0.449814
$848$	2222.47			0.0899999
$849$	4.24474	+	0.667002i	0.000171589	+	2.69628e-5i
$850$			16025.6i			0.646675i
$851$	1651.48			0.0665240
$852$	−938.386	−	147.454i	−0.0377331	−	0.00592922i
$853$	4047.05			0.162448			0.0812241	−	0.996696i	$-0.474117\pi$
$853$	4047.05			0.162448			0.0812241	+	0.996696i	$0.474117\pi$
$854$	6378.24			0.255572
$855$	37839.8	−	5958.24i	1.51356	−	0.238324i
$856$	−7808.25			−0.311776
$857$	42125.8			1.67910			0.839551	−	0.543280i	$-0.182818\pi$
$857$	42125.8			1.67910			0.839551	+	0.543280i	$0.182818\pi$
$858$	29858.1	+	4691.78i	1.18804	+	0.186684i
$859$	1086.17			0.0431426			0.0215713	−	0.999767i	$-0.493133\pi$
$859$	1086.17			0.0431426			0.0215713	+	0.999767i	$0.493133\pi$
$860$			23456.1i			0.930052i
$861$	−9539.62	−	1499.02i	−0.377595	−	0.0593337i
$862$	−28107.4			−1.11061
$863$	−13093.8			−0.516474			−0.258237	−	0.966082i	$-0.583142\pi$
$863$	−13093.8			−0.516474			−0.258237	+	0.966082i	$0.583142\pi$
$864$	−18039.2	−	9108.56i	−0.710309	−	0.358657i
$865$		−	5613.56i		−	0.220655i
$866$			12683.2i			0.497681i
$867$	14947.3	+	2348.76i	0.585511	+	0.0920048i
$868$			5553.49i			0.217163i
$869$	−59243.5			−2.31266
$870$	3897.72	−	24804.8i	0.151891	−	0.966622i
$871$	2300.82			0.0895065
$872$			1436.53i			0.0557879i
$873$	−11994.5	+	37223.6i	−0.465008	+	1.44310i
$874$	−4339.03	+	2192.63i	−0.167929	+	0.0848590i
$875$		−	4697.60i		−	0.181495i
$876$	−7103.69	−	1116.24i	−0.273986	−	0.0430530i
$877$			12668.3i			0.487773i	0.969804	+	0.243887i	$0.0784225\pi$
$877$			12668.3i			0.487773i	−0.969804	+	0.243887i	$0.921578\pi$
$878$			25522.9i			0.981043i
$879$	−19912.2	−	3128.93i	−0.764076	−	0.120064i
$880$	22930.7			0.878401
$881$		−	39697.0i		−	1.51808i	−0.651046	−	0.759038i	$-0.725670\pi$
$881$		−	39697.0i		−	1.51808i	0.651046	−	0.759038i	$-0.274330\pi$
$882$	16569.4	+	5339.14i	0.632564	+	0.203830i
$883$	−12200.0			−0.464964			−0.232482	−	0.972601i	$-0.574685\pi$
$883$	−12200.0			−0.464964			−0.232482	+	0.972601i	$0.574685\pi$
$884$	−7656.49			−0.291307
$885$	8687.29	−	55285.2i	0.329966	−	2.09988i
$886$		−	25107.1i		−	0.952018i
$887$	−37757.5			−1.42928			−0.714640	−	0.699492i	$-0.753409\pi$
$887$	−37757.5			−1.42928			−0.714640	+	0.699492i	$0.753409\pi$
$888$	−1177.92	+	7496.18i	−0.0445139	+	0.283283i
$889$		−	12038.3i		−	0.454164i
$890$		−	16198.8i		−	0.610097i
$891$	23652.2	−	32890.3i	0.889314	−	1.23666i
$892$		−	4033.15i		−	0.151390i
$893$	17563.1	−	8875.10i	0.658148	−	0.332580i
$894$	−2569.90	+	16354.6i	−0.0961413	+	0.611835i
$895$			16050.5i			0.599453i
$896$	−574.843			−0.0214332
$897$	−6973.86	−	1095.84i	−0.259588	−	0.0407906i
$898$	1609.06			0.0597940
$899$		−	33570.2i		−	1.24541i
$900$	15054.5	+	4850.99i	0.557574	+	0.179666i
$901$		−	4127.41i		−	0.152613i
$902$			34805.9i			1.28482i
$903$	−12753.8	−	2004.08i	−0.470012	−	0.0738557i
$904$	−42790.4			−1.57432
$905$	65946.3			2.42224
$906$	−1880.82	+	11969.4i	−0.0689690	+	0.438913i
$907$		−	37198.9i		−	1.36182i	−0.732368	−	0.680909i	$-0.761585\pi$
$907$		−	37198.9i		−	1.36182i	0.732368	−	0.680909i	$-0.238415\pi$
$908$	18637.9			0.681191
$909$	−6458.86	+	20044.4i	−0.235673	+	0.731386i
$910$	−11314.4			−0.412165
$911$	5121.34			0.186254			0.0931271	−	0.995654i	$-0.470314\pi$
$911$	5121.34			0.186254			0.0931271	+	0.995654i	$0.470314\pi$
$912$	−3182.30	−	9865.24i	−0.115544	−	0.358192i
$913$	48762.7			1.76759
$914$	14493.4			0.524508
$915$	6567.61	−	41795.7i	0.237288	−	1.51008i
$916$	−16169.5			−0.583248
$917$			15073.9i			0.542841i
$918$	6015.71	−	11913.9i	0.216283	−	0.428343i
$919$	38423.0			1.37917			0.689586	−	0.724204i	$-0.257793\pi$
$919$	38423.0			1.37917			0.689586	+	0.724204i	$0.257793\pi$
$920$	−11541.6			−0.413602
$921$	5778.61	−	36774.6i	0.206744	−	1.31570i
$922$			12470.7i			0.445445i
$923$		−	2587.42i		−	0.0922707i
$924$	983.588	−	6259.47i	0.0350191	−	0.222859i
$925$		−	10078.8i		−	0.358258i
$926$	21821.3			0.774396
$927$	4645.67	−	14417.3i	0.164599	−	0.510816i
$928$	19106.2			0.675852
$929$			40357.5i			1.42528i	0.701530	+	0.712640i	$0.252501\pi$
$929$			40357.5i			1.42528i	−0.701530	+	0.712640i	$0.747499\pi$
$930$	−47327.7	−	7436.88i	−1.66875	−	0.262220i
$931$	−11324.6	−	22410.5i	−0.398657	−	0.788909i
$932$		−	5747.36i		−	0.201997i
$933$	2186.83	−	13916.8i	0.0767347	−	0.488333i
$934$			20722.2i			0.725966i
$935$		−	42585.2i		−	1.48950i
$936$	9948.24	−	30873.3i	0.347402	−	1.07812i
$937$	43127.4			1.50364			0.751821	−	0.659368i	$-0.229176\pi$
$937$	43127.4			1.50364			0.751821	+	0.659368i	$0.229176\pi$
$938$			627.300i			0.0218359i
$939$	−27739.2	−	4358.83i	−0.964042	−	0.151486i
$940$	14154.3			0.491132
$941$	−13450.8			−0.465975			−0.232987	−	0.972480i	$-0.574850\pi$
$941$	−13450.8			−0.465975			−0.232987	+	0.972480i	$0.574850\pi$
$942$	29722.0	+	4670.40i	1.02802	+	0.161539i
$943$		−	8129.51i		−	0.280735i
$944$	−15144.0			−0.522136
$945$	−6835.53	+	13537.6i	−0.235301	+	0.466007i
$946$			46533.2i			1.59929i
$947$		−	4211.93i		−	0.144529i	−0.997385	−	0.0722646i	$-0.976977\pi$
$947$		−	4211.93i		−	0.144529i	0.997385	−	0.0722646i	$-0.0230226\pi$
$948$	−2990.28	+	19029.9i	−0.102447	+	0.651964i
$949$		−	19587.0i		−	0.669992i
$950$	13381.4	+	26480.7i	0.457000	+	0.904364i
$951$	3193.94	+	501.883i	0.108907	+	0.0171132i
$952$		−	6889.79i		−	0.234558i
$953$	11117.4			0.377890			0.188945	−	0.981988i	$-0.439493\pi$
$953$	11117.4			0.377890			0.188945	+	0.981988i	$0.439493\pi$
$954$	5042.53	+	1624.84i	0.171130	+	0.0551429i
$955$	−28472.9			−0.964776
$956$			4494.62i			0.152057i
$957$	−5945.67	+	37837.7i	−0.200832	+	1.27808i
$958$		−	10826.2i		−	0.365113i
$959$		−	11570.6i		−	0.389609i
$960$	6895.29	−	43881.0i	0.231817	−	1.47527i
$961$	−34261.0			−1.15005
$962$	−6262.42			−0.209884
$963$	−8221.09	−	2649.07i	−0.275100	−	0.0886448i
$964$			11410.2i			0.381220i
$965$	27852.0			0.929106
$966$	298.774	−	1901.37i	0.00995123	−	0.0633288i
$967$	−18719.4			−0.622517			−0.311259	−	0.950325i	$-0.600751\pi$
$967$	−18719.4			−0.622517			−0.311259	+	0.950325i	$0.600751\pi$
$968$	−42890.3			−1.42412
$969$	−18321.0	+	5909.94i	−0.607385	+	0.195928i
$970$	−52767.9			−1.74667
$971$	−6734.08			−0.222561			−0.111281	−	0.993789i	$-0.535495\pi$
$971$	−6734.08			−0.222561			−0.111281	+	0.993789i	$0.535495\pi$
$972$	−9371.02	−	9257.55i	−0.309234	−	0.305490i
$973$	−4097.75			−0.135013
$974$		−	10382.8i		−	0.341567i
$975$	−6687.83	+	42560.8i	−0.219674	+	1.39799i
$976$	−11448.9			−0.375483
$977$	−9763.99			−0.319731			−0.159866	−	0.987139i	$-0.551106\pi$
$977$	−9763.99			−0.319731			−0.159866	+	0.987139i	$0.551106\pi$
$978$	−14523.5	−	2282.16i	−0.474856	−	0.0746169i
$979$			24710.0i			0.806676i
$980$		−	18060.9i		−	0.588710i
$981$	−487.365	+	1512.48i	−0.0158617	+	0.0492251i
$982$			30479.2i			0.990459i
$983$	19242.8			0.624363			0.312182	−	0.950022i	$-0.398940\pi$
$983$	19242.8			0.624363			0.312182	+	0.950022i	$0.398940\pi$
$984$	36900.5	+	5798.39i	1.19547	+	0.187851i
$985$	20246.7			0.654938
$986$			12618.6i			0.407563i
$987$	−1209.35	+	7696.18i	−0.0390009	+	0.248199i
$988$	−12651.5	+	6393.17i	−0.407388	+	0.205864i
$989$		−	10868.6i		−	0.349445i
$990$	52027.0	+	16764.6i	1.67023	+	0.538195i
$991$			8606.01i			0.275862i	0.990442	+	0.137931i	$0.0440452\pi$
$991$			8606.01i			0.275862i	−0.990442	+	0.137931i	$0.955955\pi$
$992$		−	36454.7i		−	1.16677i
$993$	−5002.76	+	31837.1i	−0.159877	+	1.01744i
$994$	705.440			0.0225103
$995$			62376.6i			1.98741i
$996$	2461.27	−	15663.3i	0.0783015	−	0.498304i
$997$	26416.9			0.839150			0.419575	−	0.907721i	$-0.362179\pi$
$997$	26416.9			0.839150			0.419575	+	0.907721i	$0.362179\pi$
$998$	−21899.0			−0.694589
$999$	−3783.39	+	7492.89i	−0.119821	+	0.237302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.4.d.c.56.4	yes	12
3.2	odd	2	inner	57.4.d.c.56.10	yes	12
19.18	odd	2	inner	57.4.d.c.56.9	yes	12
57.56	even	2	inner	57.4.d.c.56.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.4.d.c.56.3	✓	12	57.56	even	2	inner
57.4.d.c.56.4	yes	12	1.1	even	1	trivial
57.4.d.c.56.9	yes	12	19.18	odd	2	inner
57.4.d.c.56.10	yes	12	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	57.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.12662 q^{2} +(5.13317 + 0.806605i) q^{3} -3.47747 q^{4} -17.1306i q^{5} +(-10.9163 - 1.71535i) q^{6} -6.31010 q^{7} +24.4083 q^{8} +(25.6988 + 8.28087i) q^{9} +O(q^{10})\)	\(q-2.12662 q^{2} +(5.13317 + 0.806605i) q^{3} -3.47747 q^{4} -17.1306i q^{5} +(-10.9163 - 1.71535i) q^{6} -6.31010 q^{7} +24.4083 q^{8} +(25.6988 + 8.28087i) q^{9} +36.4304i q^{10} -55.5716i q^{11} +(-17.8504 - 2.80494i) q^{12} -49.2191i q^{13} +13.4192 q^{14} +(13.8176 - 87.9342i) q^{15} -24.0875 q^{16} +44.7335i q^{17} +(-54.6516 - 17.6103i) q^{18} +(37.3525 + 73.9175i) q^{19} +59.5712i q^{20} +(-32.3908 - 5.08976i) q^{21} +118.180i q^{22} -27.6029i q^{23} +(125.292 + 19.6878i) q^{24} -168.458 q^{25} +104.670i q^{26} +(125.237 + 63.2358i) q^{27} +21.9432 q^{28} -132.644 q^{29} +(-29.3849 + 187.003i) q^{30} +253.085i q^{31} -144.041 q^{32} +(44.8243 - 285.258i) q^{33} -95.1314i q^{34} +108.096i q^{35} +(-89.3667 - 28.7965i) q^{36} +59.8298i q^{37} +(-79.4347 - 157.195i) q^{38} +(39.7003 - 252.650i) q^{39} -418.128i q^{40} +294.516 q^{41} +(68.8830 + 10.8240i) q^{42} +393.748 q^{43} +193.249i q^{44} +(141.856 - 440.236i) q^{45} +58.7010i q^{46} -237.604i q^{47} +(-123.645 - 19.4291i) q^{48} -303.183 q^{49} +358.246 q^{50} +(-36.0823 + 229.625i) q^{51} +171.158i q^{52} -92.2667 q^{53} +(-266.331 - 134.479i) q^{54} -951.975 q^{55} -154.019 q^{56} +(132.114 + 409.559i) q^{57} +282.083 q^{58} +628.710 q^{59} +(-48.0504 + 305.789i) q^{60} +475.307 q^{61} -538.217i q^{62} +(-162.162 - 52.2531i) q^{63} +499.021 q^{64} -843.152 q^{65} +(-95.3245 + 606.637i) q^{66} +46.7464i q^{67} -155.559i q^{68} +(22.2646 - 141.690i) q^{69} -229.879i q^{70} +52.5694 q^{71} +(627.263 + 202.122i) q^{72} +397.956 q^{73} -127.236i q^{74} +(-864.721 - 135.879i) q^{75} +(-129.892 - 257.046i) q^{76} +350.662i q^{77} +(-84.4277 + 537.291i) q^{78} -1066.08i q^{79} +412.633i q^{80} +(591.854 + 425.617i) q^{81} -626.326 q^{82} +877.475i q^{83} +(112.638 + 17.6995i) q^{84} +766.312 q^{85} -837.355 q^{86} +(-680.882 - 106.991i) q^{87} -1356.41i q^{88} -444.652 q^{89} +(-301.675 + 936.216i) q^{90} +310.577i q^{91} +95.9883i q^{92} +(-204.140 + 1299.13i) q^{93} +505.295i q^{94} +(1266.25 - 639.871i) q^{95} +(-739.387 - 116.184i) q^{96} +1448.46i q^{97} +644.756 q^{98} +(460.181 - 1428.12i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 28 q^{4} - 66 q^{6} + 124 q^{7} + 54 q^{9}+O(q^{10}) \) 12 * q + 28 * q^4 - 66 * q^6 + 124 * q^7 + 54 * q^9	\( 12 q + 28 q^{4} - 66 q^{6} + 124 q^{7} + 54 q^{9} + 20 q^{16} - 200 q^{19} - 198 q^{24} - 156 q^{25} + 92 q^{28} - 672 q^{30} - 1146 q^{36} + 414 q^{39} + 654 q^{42} + 3376 q^{43} - 276 q^{45} - 360 q^{49} + 900 q^{54} - 1912 q^{55} + 1506 q^{57} - 2332 q^{58} + 696 q^{61} - 1002 q^{63} + 836 q^{64} + 4320 q^{66} + 404 q^{73} - 4904 q^{76} - 2106 q^{81} - 3704 q^{82} + 736 q^{85} - 4230 q^{87} - 4452 q^{93} + 426 q^{96} + 1044 q^{99}+O(q^{100}) \) 12 * q + 28 * q^4 - 66 * q^6 + 124 * q^7 + 54 * q^9 + 20 * q^16 - 200 * q^19 - 198 * q^24 - 156 * q^25 + 92 * q^28 - 672 * q^30 - 1146 * q^36 + 414 * q^39 + 654 * q^42 + 3376 * q^43 - 276 * q^45 - 360 * q^49 + 900 * q^54 - 1912 * q^55 + 1506 * q^57 - 2332 * q^58 + 696 * q^61 - 1002 * q^63 + 836 * q^64 + 4320 * q^66 + 404 * q^73 - 4904 * q^76 - 2106 * q^81 - 3704 * q^82 + 736 * q^85 - 4230 * q^87 - 4452 * q^93 + 426 * q^96 + 1044 * q^99

Introduction

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