LMFDB - Embedded newform 825.2.ce.c.659.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(164,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 3, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("825.164");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.ce (of order $10$, degree $4$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$448$
Relative dimension:	$112$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			659.14
Character	$\chi$	$=$	825.659
Dual form			825.2.ce.c.164.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41506 + 1.94767i) q^{2} +(1.71742 - 0.224677i) q^{3} +(-1.17297 - 3.61003i) q^{4} +(1.40120 - 1.74259i) q^{5} +(-1.99266 + 3.66289i) q^{6} +4.95869 q^{7} +(4.11171 + 1.33598i) q^{8} +(2.89904 - 0.771727i) q^{9} +O(q^{10})$	\(q+(-1.41506 + 1.94767i) q^{2} +(1.71742 - 0.224677i) q^{3} +(-1.17297 - 3.61003i) q^{4} +(1.40120 - 1.74259i) q^{5} +(-1.99266 + 3.66289i) q^{6} +4.95869 q^{7} +(4.11171 + 1.33598i) q^{8} +(2.89904 - 0.771727i) q^{9} +(1.41121 + 5.19495i) q^{10} +(-2.88168 - 1.64192i) q^{11} +(-2.82556 - 5.93638i) q^{12} +(-1.23817 + 0.899583i) q^{13} +(-7.01686 + 9.65788i) q^{14} +(2.01493 - 3.30758i) q^{15} +(-2.27863 + 1.65552i) q^{16} +(6.05362 + 1.96694i) q^{17} +(-2.59926 + 6.73841i) q^{18} +(-5.88718 - 1.91286i) q^{19} +(-7.93438 - 3.01436i) q^{20} +(8.51614 - 1.11410i) q^{21} +(7.27568 - 3.28913i) q^{22} +(-2.56531 - 1.86381i) q^{23} +(7.36169 + 1.37062i) q^{24} +(-1.07327 - 4.88345i) q^{25} -3.68451i q^{26} +(4.80547 - 1.97672i) q^{27} +(-5.81639 - 17.9010i) q^{28} +(-1.69561 - 5.21855i) q^{29} +(3.59082 + 8.60483i) q^{30} +(-1.69882 + 5.22843i) q^{31} +1.86596i q^{32} +(-5.31795 - 2.17242i) q^{33} +(-12.3972 + 9.00708i) q^{34} +(6.94812 - 8.64099i) q^{35} +(-6.18644 - 9.56040i) q^{36} +(2.35949 + 3.24756i) q^{37} +(12.0563 - 8.75944i) q^{38} +(-1.92434 + 1.82315i) q^{39} +(8.08940 - 5.29308i) q^{40} +(5.61093 - 4.07658i) q^{41} +(-9.88098 + 18.1631i) q^{42} -5.17232 q^{43} +(-2.54726 + 12.3289i) q^{44} +(2.71733 - 6.13320i) q^{45} +(7.26015 - 2.35897i) q^{46} +(-0.454147 - 1.39772i) q^{47} +(-3.54139 + 3.35517i) q^{48} +17.5886 q^{49} +(11.0301 + 4.82001i) q^{50} +(10.8385 + 2.01795i) q^{51} +(4.69986 + 3.41465i) q^{52} +(-0.0394584 - 0.121441i) q^{53} +(-2.95005 + 12.1566i) q^{54} +(-6.89902 + 2.72094i) q^{55} +(20.3887 + 6.62470i) q^{56} +(-10.5405 - 1.96247i) q^{57} +(12.5634 + 4.08209i) q^{58} +(5.93388 + 8.16728i) q^{59} +(-14.3039 - 3.39425i) q^{60} +(-4.74234 + 6.52728i) q^{61} +(-7.77929 - 10.7073i) q^{62} +(14.3755 - 3.82676i) q^{63} +(-8.19152 - 5.95149i) q^{64} +(-0.167315 + 3.41813i) q^{65} +(11.7564 - 7.28348i) q^{66} +(-2.20602 - 0.716780i) q^{67} -24.1609i q^{68} +(-4.82446 - 2.62457i) q^{69} +(6.99774 + 25.7602i) q^{70} +(0.895057 - 0.290822i) q^{71} +(12.9510 + 0.699932i) q^{72} +(0.580929 + 0.422069i) q^{73} -9.66400 q^{74} +(-2.94046 - 8.14578i) q^{75} +23.4966i q^{76} +(-14.2894 - 8.14179i) q^{77} +(-0.827823 - 6.32784i) q^{78} +(-6.95785 + 2.26074i) q^{79} +(-0.307913 + 6.29043i) q^{80} +(7.80888 - 4.47453i) q^{81} +16.6968i q^{82} +(-5.58872 - 1.81588i) q^{83} +(-14.0111 - 29.4367i) q^{84} +(11.9099 - 7.79292i) q^{85} +(7.31916 - 10.0740i) q^{86} +(-4.08456 - 8.58147i) q^{87} +(-9.65508 - 10.6010i) q^{88} +(-7.28816 + 10.0313i) q^{89} +(8.10023 + 13.9713i) q^{90} +(-6.13971 + 4.46076i) q^{91} +(-3.71937 + 11.4470i) q^{92} +(-1.74287 + 9.36107i) q^{93} +(3.36494 + 1.09333i) q^{94} +(-11.5825 + 7.57867i) q^{95} +(0.419237 + 3.20463i) q^{96} +(-0.273258 + 0.0887869i) q^{97} +(-24.8890 + 34.2568i) q^{98} +(-9.62123 - 2.53613i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 448 q - 10 q^{3} + 108 q^{4} - 14 q^{9}+O(q^{10}) $ 448 * q - 10 * q^3 + 108 * q^4 - 14 * q^9	$ 448 q - 10 q^{3} + 108 q^{4} - 14 q^{9} - 40 q^{12} - 10 q^{15} - 140 q^{16} + 10 q^{22} - 36 q^{25} - 10 q^{27} - 32 q^{31} + 20 q^{33} - 28 q^{34} - 6 q^{36} - 20 q^{37} - 70 q^{42} + 82 q^{45} - 60 q^{48} + 440 q^{49} + 6 q^{55} + 40 q^{58} + 88 q^{60} + 188 q^{64} - 30 q^{66} - 140 q^{67} + 34 q^{69} - 76 q^{70} + 70 q^{75} + 60 q^{78} + 50 q^{81} - 80 q^{88} - 80 q^{91} + 120 q^{97} - 40 q^{99}+O(q^{100}) $ 448 * q - 10 * q^3 + 108 * q^4 - 14 * q^9 - 40 * q^12 - 10 * q^15 - 140 * q^16 + 10 * q^22 - 36 * q^25 - 10 * q^27 - 32 * q^31 + 20 * q^33 - 28 * q^34 - 6 * q^36 - 20 * q^37 - 70 * q^42 + 82 * q^45 - 60 * q^48 + 440 * q^49 + 6 * q^55 + 40 * q^58 + 88 * q^60 + 188 * q^64 - 30 * q^66 - 140 * q^67 + 34 * q^69 - 76 * q^70 + 70 * q^75 + 60 * q^78 + 50 * q^81 - 80 * q^88 - 80 * q^91 + 120 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−1.41506	+	1.94767i	−1.00060	+	1.37721i	−0.0756440	+	0.997135i	$0.524101\pi$
$2$	−1.41506	+	1.94767i	−1.00060	+	1.37721i	−0.924956	+	0.380073i	$0.875899\pi$
$3$	1.71742	−	0.224677i	0.991551	−	0.129717i
$3$	1.71742	−	0.224677i	0.991551	−	0.129717i
$4$	−1.17297	−	3.61003i	−0.586484	−	1.80501i
$5$	1.40120	−	1.74259i	0.626636	−	0.779312i
$5$	1.40120	−	1.74259i	0.626636	−	0.779312i
$6$	−1.99266	+	3.66289i	−0.813499	+	1.49537i
$7$	4.95869			1.87421			0.937105	−	0.349048i	$-0.113495\pi$
$7$	4.95869			1.87421			0.937105	+	0.349048i	$0.113495\pi$
$8$	4.11171	+	1.33598i	1.45371	+	0.472339i
$9$	2.89904	−	0.771727i	0.966347	−	0.257242i
$10$	1.41121	+	5.19495i	0.446263	+	1.64279i
$11$	−2.88168	−	1.64192i	−0.868860	−	0.495058i
$11$	−2.88168	−	1.64192i	−0.868860	−	0.495058i
$12$	−2.82556	−	5.93638i	−0.815670	−	1.71369i
$13$	−1.23817	+	0.899583i	−0.343407	+	0.249500i	−0.746098	−	0.665836i	$-0.768075\pi$
$13$	−1.23817	+	0.899583i	−0.343407	+	0.249500i	0.402691	+	0.915336i	$0.368075\pi$
$14$	−7.01686	+	9.65788i	−1.87534	+	2.58118i
$15$	2.01493	−	3.30758i	0.520251	−	0.854013i
$16$	−2.27863	+	1.65552i	−0.569656	+	0.413880i
$17$	6.05362	+	1.96694i	1.46822	+	0.477053i	0.930569	−	0.366116i	$-0.119313\pi$
$17$	6.05362	+	1.96694i	1.46822	+	0.477053i	0.537648	+	0.843169i	$0.319313\pi$
$18$	−2.59926	+	6.73841i	−0.612651	+	1.58826i
$19$	−5.88718	−	1.91286i	−1.35061	−	0.438840i	−0.457713	−	0.889100i	$-0.651331\pi$
$19$	−5.88718	−	1.91286i	−1.35061	−	0.438840i	−0.892898	+	0.450260i	$0.851331\pi$
$20$	−7.93438	−	3.01436i	−1.77418	−	0.674032i
$21$	8.51614	−	1.11410i	1.85837	−	0.243117i
$22$	7.27568	−	3.28913i	1.55118	−	0.701245i
$23$	−2.56531	−	1.86381i	−0.534904	−	0.388631i	0.287285	−	0.957845i	$-0.407247\pi$
$23$	−2.56531	−	1.86381i	−0.534904	−	0.388631i	−0.822189	+	0.569214i	$0.807247\pi$
$24$	7.36169	+	1.37062i	1.50270	+	0.279777i
$25$	−1.07327	−	4.88345i	−0.214655	−	0.976690i
$26$		−	3.68451i		−	0.722592i
$27$	4.80547	−	1.97672i	0.924814	−	0.380420i
$28$	−5.81639	−	17.9010i	−1.09919	−	3.38297i
$29$	−1.69561	−	5.21855i	−0.314867	−	0.969061i	−0.975809	−	0.218624i	$-0.929843\pi$
$29$	−1.69561	−	5.21855i	−0.314867	−	0.969061i	0.660942	−	0.750437i	$-0.270157\pi$
$30$	3.59082	+	8.60483i	0.655590	+	1.57102i
$31$	−1.69882	+	5.22843i	−0.305117	+	0.939053i	0.674517	+	0.738259i	$0.264352\pi$
$31$	−1.69882	+	5.22843i	−0.305117	+	0.939053i	−0.979634	+	0.200793i	$0.935648\pi$
$32$			1.86596i			0.329858i
$33$	−5.31795	−	2.17242i	−0.925736	−	0.378170i
$34$	−12.3972	+	9.00708i	−2.12610	+	1.54470i
$35$	6.94812	−	8.64099i	1.17445	−	1.46059i
$36$	−6.18644	−	9.56040i	−1.03107	−	1.59340i
$37$	2.35949	+	3.24756i	0.387898	+	0.533896i	0.957655	−	0.287917i	$-0.0929627\pi$
$37$	2.35949	+	3.24756i	0.387898	+	0.533896i	−0.569757	+	0.821813i	$0.692963\pi$
$38$	12.0563	−	8.75944i	1.95580	−	1.42097i
$39$	−1.92434	+	1.82315i	−0.308141	+	0.291937i
$40$	8.08940	−	5.29308i	1.27905	−	0.836910i
$41$	5.61093	−	4.07658i	0.876281	−	0.636655i	−0.0559842	−	0.998432i	$-0.517830\pi$
$41$	5.61093	−	4.07658i	0.876281	−	0.636655i	0.932265	+	0.361777i	$0.117830\pi$
$42$	−9.88098	+	18.1631i	−1.52467	+	2.80263i
$43$	−5.17232			−0.788772			−0.394386	−	0.918945i	$-0.629043\pi$
$43$	−5.17232			−0.788772			−0.394386	+	0.918945i	$0.629043\pi$
$44$	−2.54726	+	12.3289i	−0.384014	+	1.85865i
$45$	2.71733	−	6.13320i	0.405076	−	0.914283i
$46$	7.26015	−	2.35897i	1.07045	−	0.347811i
$47$	−0.454147	−	1.39772i	−0.0662441	−	0.203878i	0.912456	−	0.409176i	$-0.134184\pi$
$47$	−0.454147	−	1.39772i	−0.0662441	−	0.203878i	−0.978700	+	0.205298i	$0.934184\pi$
$48$	−3.54139	+	3.35517i	−0.511156	+	0.484277i
$49$	17.5886			2.51266
$50$	11.0301	+	4.82001i	1.55989	+	0.681652i
$51$	10.8385	+	2.01795i	1.51769	+	0.282569i
$52$	4.69986	+	3.41465i	0.651753	+	0.473526i
$53$	−0.0394584	−	0.121441i	−0.00542003	−	0.0166811i	0.948310	−	0.317346i	$-0.102792\pi$
$53$	−0.0394584	−	0.121441i	−0.00542003	−	0.0166811i	−0.953730	+	0.300665i	$0.902792\pi$
$54$	−2.95005	+	12.1566i	−0.401451	+	1.65431i
$55$	−6.89902	+	2.72094i	−0.930264	+	0.366892i
$56$	20.3887	+	6.62470i	2.72456	+	0.885263i
$57$	−10.5405	−	1.96247i	−1.39612	−	0.259935i
$58$	12.5634	+	4.08209i	1.64965	+	0.536005i
$59$	5.93388	+	8.16728i	0.772525	+	1.06329i	0.996068	+	0.0885951i	$0.0282377\pi$
$59$	5.93388	+	8.16728i	0.772525	+	1.06329i	−0.223543	+	0.974694i	$0.571762\pi$
$60$	−14.3039	−	3.39425i	−1.84662	−	0.438195i
$61$	−4.74234	+	6.52728i	−0.607195	+	0.835732i	−0.996343	−	0.0854432i	$-0.972769\pi$
$61$	−4.74234	+	6.52728i	−0.607195	+	0.835732i	0.389148	+	0.921175i	$0.372769\pi$
$62$	−7.77929	−	10.7073i	−0.987971	−	1.35983i
$63$	14.3755	−	3.82676i	1.81114	−	0.482126i
$64$	−8.19152	−	5.95149i	−1.02394	−	0.743936i
$65$	−0.167315	+	3.41813i	−0.0207529	+	0.423966i
$66$	11.7564	−	7.28348i	1.44711	−	0.896535i
$67$	−2.20602	−	0.716780i	−0.269508	−	0.0875686i	0.171145	−	0.985246i	$-0.445253\pi$
$67$	−2.20602	−	0.716780i	−0.269508	−	0.0875686i	−0.440654	+	0.897677i	$0.645253\pi$
$68$		−	24.1609i		−	2.92994i
$69$	−4.82446	−	2.62457i	−0.580797	−	0.315961i
$70$	6.99774	+	25.7602i	0.836390	+	3.07893i
$71$	0.895057	−	0.290822i	0.106224	−	0.0345142i	−0.255423	−	0.966829i	$-0.582215\pi$
$71$	0.895057	−	0.290822i	0.106224	−	0.0345142i	0.361647	+	0.932315i	$0.382215\pi$
$72$	12.9510	+	0.699932i	1.52629	+	0.0824878i
$73$	0.580929	+	0.422069i	0.0679925	+	0.0493995i	0.621262	−	0.783603i	$-0.286620\pi$
$73$	0.580929	+	0.422069i	0.0679925	+	0.0493995i	−0.553270	+	0.833002i	$0.686620\pi$
$74$	−9.66400			−1.12342
$75$	−2.94046	−	8.14578i	−0.339535	−	0.940594i
$76$			23.4966i			2.69524i
$77$	−14.2894	−	8.14179i	−1.62843	−	0.927843i
$78$	−0.827823	−	6.32784i	−0.0937325	−	0.716487i
$79$	−6.95785	+	2.26074i	−0.782819	+	0.254353i	−0.673043	−	0.739603i	$-0.735013\pi$
$79$	−6.95785	+	2.26074i	−0.782819	+	0.254353i	−0.109776	+	0.993956i	$0.535013\pi$
$80$	−0.307913	+	6.29043i	−0.0344258	+	0.703292i
$81$	7.80888	−	4.47453i	0.867653	−	0.497170i
$82$			16.6968i			1.84386i
$83$	−5.58872	−	1.81588i	−0.613441	−	0.199319i	−0.0142151	−	0.999899i	$-0.504525\pi$
$83$	−5.58872	−	1.81588i	−0.613441	−	0.199319i	−0.599226	+	0.800580i	$0.704525\pi$
$84$	−14.0111	−	29.4367i	−1.52874	−	3.21181i
$85$	11.9099	−	7.79292i	1.29181	−	0.845261i
$86$	7.31916	−	10.0740i	0.789245	−	1.08630i
$87$	−4.08456	−	8.58147i	−0.437910	−	0.920030i
$88$	−9.65508	−	10.6010i	−1.02924	−	1.13007i
$89$	−7.28816	+	10.0313i	−0.772543	+	1.06331i	0.223522	+	0.974699i	$0.428244\pi$
$89$	−7.28816	+	10.0313i	−0.772543	+	1.06331i	−0.996066	+	0.0886160i	$0.971756\pi$
$90$	8.10023	+	13.9713i	0.853839	+	1.47271i
$91$	−6.13971	+	4.46076i	−0.643616	+	0.467615i
$92$	−3.71937	+	11.4470i	−0.387771	+	1.19344i
$93$	−1.74287	+	9.36107i	−0.180728	+	0.970698i
$94$	3.36494	+	1.09333i	0.347067	+	0.112769i
$95$	−11.5825	+	7.57867i	−1.18833	+	0.777555i
$96$	0.419237	+	3.20463i	0.0427882	+	0.327071i
$97$	−0.273258	+	0.0887869i	−0.0277452	+	0.00901495i	−0.322857	−	0.946448i	$-0.604643\pi$
$97$	−0.273258	+	0.0887869i	−0.0277452	+	0.00901495i	0.295112	+	0.955463i	$0.404643\pi$
$98$	−24.8890	+	34.2568i	−2.51417	+	3.46046i
$99$	−9.62123	−	2.53613i	−0.966970	−	0.254891i
$100$	−16.3705	+	9.60268i	−1.63705	+	0.960268i
$101$	1.98348			0.197364			0.0986820	−	0.995119i	$-0.468537\pi$
$101$	1.98348			0.197364			0.0986820	+	0.995119i	$0.468537\pi$
$102$	−19.2675	+	18.2543i	−1.90776	+	1.80744i
$103$	8.93362	−	2.90271i	0.880256	−	0.286012i	0.166192	−	0.986093i	$-0.446853\pi$
$103$	8.93362	−	2.90271i	0.880256	−	0.286012i	0.714063	+	0.700081i	$0.246853\pi$
$104$	−6.29283	+	2.04466i	−0.617062	+	0.200496i
$105$	9.99140	−	16.4013i	0.975060	−	1.60060i
$106$	0.292362	+	0.0949941i	0.0283967	+	0.00922664i
$107$			6.60289i			0.638325i	0.947700	+	0.319163i	$0.103402\pi$
$107$			6.60289i			0.638325i	−0.947700	+	0.319163i	$0.896598\pi$
$108$	−12.7727	−	15.0293i	−1.22905	−	1.44619i
$109$	11.0040	+	15.1458i	1.05400	+	1.45070i	0.885292	+	0.465035i	$0.153958\pi$
$109$	11.0040	+	15.1458i	1.05400	+	1.45070i	0.168704	+	0.985667i	$0.446042\pi$
$110$	4.46306	−	17.2873i	0.425536	−	1.64828i
$111$	4.78188	+	5.04730i	0.453876	+	0.479068i
$112$	−11.2990	+	8.20921i	−1.06766	+	0.775697i
$113$	−7.30886	+	5.31020i	−0.687560	+	0.499542i	−0.875857	−	0.482570i	$-0.839703\pi$
$113$	−7.30886	+	5.31020i	−0.687560	+	0.499542i	0.188297	+	0.982112i	$0.439703\pi$
$114$	18.7377	−	17.7524i	1.75495	−	1.66266i
$115$	−6.84238	+	1.85873i	−0.638055	+	0.173327i
$116$	−16.8502	+	12.2424i	−1.56450	+	1.13668i
$117$	−2.89527	+	3.56346i	−0.267668	+	0.329442i
$118$	−24.3039			−2.23736
$119$	30.0180	+	9.75345i	2.75175	+	0.894097i
$120$	12.7036	−	10.9079i	1.15968	−	0.995753i
$121$	5.60818	+	9.46300i	0.509835	+	0.860272i
$122$	−6.00224	−	18.4730i	−0.543418	−	1.67247i
$123$	8.72040	−	8.26184i	0.786292	−	0.744945i
$124$	20.8674			1.87395
$125$	−10.0137	−	4.97241i	−0.895657	−	0.444746i
$126$	−12.8889	+	33.4137i	−1.14824	+	2.97673i
$127$	2.64477	+	1.92154i	0.234686	+	0.170509i	0.698912	−	0.715207i	$-0.253668\pi$
$127$	2.64477	+	1.92154i	0.234686	+	0.170509i	−0.464227	+	0.885716i	$0.653668\pi$
$128$	19.6338	−	6.37939i	1.73540	−	0.563864i
$129$	−8.88303	+	1.16210i	−0.782107	+	0.102317i
$130$	−6.42061	−	5.16274i	−0.563125	−	0.452802i
$131$	−0.610305	+	1.87833i	−0.0533226	+	0.164110i	−0.974171	−	0.225810i	$-0.927497\pi$
$131$	−0.610305	+	1.87833i	−0.0533226	+	0.164110i	0.920849	+	0.389920i	$0.127497\pi$
$132$	−1.60470	+	21.7461i	−0.139671	+	1.89276i
$133$	−29.1927	−	9.48529i	−2.53133	−	0.822479i
$134$	4.51771	−	3.28231i	0.390270	−	0.283548i
$135$	3.28880	−	11.1438i	0.283055	−	0.959104i
$136$	22.2630	+	16.1750i	1.90903	+	1.38699i
$137$	−11.3535	+	8.24883i	−0.969999	+	0.704745i	−0.955451	−	0.295149i	$-0.904631\pi$
$137$	−11.3535	+	8.24883i	−0.969999	+	0.704745i	−0.0145476	+	0.999894i	$0.504631\pi$
$138$	11.9387	−	5.68251i	1.01629	−	0.483728i
$139$	6.98918	−	9.61978i	0.592814	−	0.815939i	−0.402212	−	0.915546i	$-0.631759\pi$
$139$	6.98918	−	9.61978i	0.592814	−	0.815939i	0.995027	+	0.0996074i	$0.0317587\pi$
$140$	−39.3442	−	14.9473i	−3.32519	−	1.26328i
$141$	−1.09399	−	2.29843i	−0.0921309	−	0.193563i
$142$	−0.700138	+	2.15480i	−0.0587543	+	0.180827i
$143$	5.04506	−	0.559333i	0.421889	−	0.0467738i
$144$	−5.32822	+	6.55789i	−0.444018	+	0.546491i
$145$	−11.4697	−	4.35748i	−0.952508	−	0.361869i
$146$	−1.64410	+	0.534201i	−0.136067	+	0.0442108i
$147$	30.2070	−	3.95176i	2.49143	−	0.325935i
$148$	8.95618	−	12.3271i	0.736193	−	1.01328i
$149$	9.44426			0.773704			0.386852	−	0.922142i	$-0.373563\pi$
$149$	9.44426			0.773704			0.386852	+	0.922142i	$0.373563\pi$
$150$	20.0262	+	5.79976i	1.63513	+	0.473548i
$151$		−	11.4106i		−	0.928583i	−0.885682	−	0.464292i	$-0.846309\pi$
$151$		−	11.4106i		−	0.928583i	0.885682	−	0.464292i	$-0.153691\pi$
$152$	−21.6509	−	15.7303i	−1.75612	−	1.27589i
$153$	19.0676	+	1.03050i	1.54153	+	0.0833110i
$154$	36.0779	−	16.3098i	2.90724	−	1.31428i
$155$	6.73064	+	10.2864i	0.540618	+	0.826225i
$156$	8.83880	+	4.80842i	0.707671	+	0.384982i
$157$			11.7814i			0.940254i	0.882599	+	0.470127i	$0.155792\pi$
$157$			11.7814i			0.940254i	−0.882599	+	0.470127i	$0.844208\pi$
$158$	5.44262	−	16.7507i	0.432991	−	1.33261i
$159$	−0.0950514	−	0.199699i	−0.00753807	−	0.0158371i
$160$	3.25161	+	2.61458i	0.257062	+	0.206701i
$161$	−12.7206	−	9.24205i	−1.00252	−	0.728376i
$162$	−2.33515	+	21.5408i	−0.183467	+	1.69241i
$163$	5.84606	+	8.04642i	0.457899	+	0.630244i	0.974071	−	0.226241i	$-0.0726436\pi$
$163$	5.84606	+	8.04642i	0.457899	+	0.630244i	−0.516172	+	0.856485i	$0.672644\pi$
$164$	−21.2980	−	15.4739i	−1.66310	−	1.20831i
$165$	−11.2372	+	6.22304i	−0.874812	+	0.484463i
$166$	11.4451	−	8.31537i	0.888313	−	0.645398i
$167$	6.72985	+	2.18666i	0.520772	+	0.169209i	0.557596	−	0.830113i	$-0.311724\pi$
$167$	6.72985	+	2.18666i	0.520772	+	0.169209i	−0.0368238	+	0.999322i	$0.511724\pi$
$168$	36.5044	+	6.79650i	2.81637	+	0.524361i
$169$	−3.29341	+	10.1361i	−0.253339	+	0.779697i
$170$	−1.67525	+	34.2240i	−0.128486	+	2.62486i
$171$	−18.5434	−	1.00217i	−1.41805	−	0.0766377i
$172$	6.06697	+	18.6722i	0.462602	+	1.42374i
$173$	−2.93809	+	4.04393i	−0.223378	+	0.307454i	−0.905967	−	0.423349i	$-0.860854\pi$
$173$	−2.93809	+	4.04393i	−0.223378	+	0.307454i	0.682588	+	0.730803i	$0.260854\pi$
$174$	22.4937	+	4.18796i	1.70525	+	0.317488i
$175$	−5.32204	−	24.2155i	−0.402308	−	1.83052i
$176$	9.28451	−	1.02935i	0.699846	−	0.0775902i
$177$	12.0259	+	12.6934i	0.903925	+	0.954096i
$178$	−9.22441	−	28.3898i	−0.691399	−	2.12791i
$179$	0.918859	−	0.298555i	0.0686787	−	0.0223151i	−0.274476	−	0.961594i	$-0.588504\pi$
$179$	0.918859	−	0.298555i	0.0686787	−	0.0223151i	0.343155	+	0.939279i	$0.388504\pi$
$180$	−25.3284	−	2.61559i	−1.88786	−	0.194954i
$181$	2.96477	−	9.12462i	0.220369	−	0.678227i	−0.778359	−	0.627819i	$-0.783948\pi$
$181$	2.96477	−	9.12462i	0.220369	−	0.678227i	0.998729	−	0.0504082i	$-0.0160522\pi$
$182$		−	18.2704i		−	1.35429i
$183$	−6.67805	+	12.2755i	−0.493656	+	0.907434i
$184$	−8.05782	−	11.0906i	−0.594031	−	0.817613i
$185$	8.96531	+	0.438847i	0.659143	+	0.0322647i
$186$	−15.7660	−	16.6410i	−1.15602	−	1.22018i
$187$	−14.2150	−	15.6077i	−1.03951	−	1.14135i
$188$	−4.51310	+	3.27896i	−0.329152	+	0.239143i
$189$	23.8289	−	9.80196i	1.73329	−	0.712988i
$190$	1.62919	−	33.2830i	0.118194	−	2.41461i
$191$	−3.76250	−	5.17864i	−0.272245	−	0.374713i	0.650901	−	0.759163i	$-0.274391\pi$
$191$	−3.76250	−	5.17864i	−0.272245	−	0.374713i	−0.923146	+	0.384449i	$0.874391\pi$
$192$	−15.4054	−	8.38074i	−1.11179	−	0.604828i
$193$	−1.25848			−0.0905872			−0.0452936	−	0.998974i	$-0.514422\pi$
$193$	−1.25848			−0.0905872			−0.0452936	+	0.998974i	$0.514422\pi$
$194$	0.213750	−	0.657855i	0.0153464	−	0.0472312i
$195$	0.480623	+	5.90794i	0.0344181	+	0.423076i
$196$	−20.6309	−	63.4955i	−1.47364	−	4.53539i
$197$	4.78931	−	1.55614i	0.341225	−	0.110871i	−0.133392	−	0.991063i	$-0.542587\pi$
$197$	4.78931	−	1.55614i	0.341225	−	0.110871i	0.474616	+	0.880193i	$0.342587\pi$
$198$	18.5542	−	15.1502i	1.31859	−	1.07668i
$199$	−7.84120			−0.555848			−0.277924	−	0.960603i	$-0.589646\pi$
$199$	−7.84120			−0.555848			−0.277924	+	0.960603i	$0.589646\pi$
$200$	2.11118	−	21.5132i	0.149283	−	1.52121i
$201$	−3.94970	−	0.735368i	−0.278590	−	0.0518689i
$202$	−2.80675	+	3.86317i	−0.197483	+	0.271811i
$203$	−8.40801	−	25.8772i	−0.590127	−	1.81622i
$204$	−5.42838	−	41.4943i	−0.380063	−	2.90518i
$205$	0.758212	−	15.4897i	0.0529558	−	1.08185i
$206$	−6.98812	+	21.5072i	−0.486885	+	1.49848i
$207$	−8.87529	−	3.42354i	−0.616875	−	0.237952i
$208$	1.33205	−	4.09963i	0.0923610	−	0.284258i
$209$	13.8242	+	15.1785i	0.956240	+	1.04992i
$210$	17.8058	+	42.6687i	1.22871	+	2.94442i
$211$	−8.47470	+	11.6644i	−0.583422	+	0.803012i	−0.994065	−	0.108784i	$-0.965304\pi$
$211$	−8.47470	+	11.6644i	−0.583422	+	0.803012i	0.410643	+	0.911796i	$0.365304\pi$
$212$	−0.392120	+	0.284892i	−0.0269309	+	0.0195665i
$213$	1.47185	−	0.700560i	0.100849	−	0.0480016i
$214$	−12.8602	−	9.34350i	−0.879107	−	0.638708i
$215$	−7.24746	+	9.01326i	−0.494273	+	0.614699i
$216$	22.3996	−	1.70772i	1.52410	−	0.116196i
$217$	−8.42392	+	25.9262i	−0.571853	+	1.75998i
$218$	−45.0703			−3.05255
$219$	1.09253	+	0.594348i	0.0738260	+	0.0401623i
$220$	17.9150	+	21.7141i	1.20783	+	1.46396i
$221$	−9.26483	+	3.01033i	−0.623220	+	0.202496i
$222$	−16.5971	+	2.17127i	−1.11393	+	0.145726i
$223$	−3.27703	+	4.51045i	−0.219446	+	0.302042i	−0.904519	−	0.426432i	$-0.859770\pi$
$223$	−3.27703	+	4.51045i	−0.219446	+	0.302042i	0.685073	+	0.728474i	$0.259770\pi$
$224$			9.25272i			0.618223i
$225$	−6.88015	−	13.3290i	−0.458677	−	0.888603i
$226$		−	21.7495i		−	1.44676i
$227$	11.2573	−	15.4943i	0.747172	−	1.02839i	−0.251001	−	0.967987i	$-0.580760\pi$
$227$	11.2573	−	15.4943i	0.747172	−	1.02839i	0.998174	−	0.0604078i	$-0.0192401\pi$
$228$	5.27913	+	40.3534i	0.349619	+	2.67247i
$229$	−8.27459	−	25.4666i	−0.546800	−	1.68288i	−0.716670	−	0.697412i	$-0.754335\pi$
$229$	−8.27459	−	25.4666i	−0.546800	−	1.68288i	0.169870	−	0.985467i	$-0.445665\pi$
$230$	6.06221	−	15.9569i	0.399730	−	1.05217i
$231$	−26.3701	−	10.7724i	−1.73502	−	0.708769i
$232$		−	23.7225i		−	1.55746i
$233$	−1.23181	−	0.400239i	−0.0806985	−	0.0262205i	0.268390	−	0.963310i	$-0.413509\pi$
$233$	−1.23181	−	0.400239i	−0.0806985	−	0.0262205i	−0.349088	+	0.937090i	$0.613509\pi$
$234$	−2.84343	−	10.6815i	−0.185881	−	0.698274i
$235$	−3.07201	−	1.16709i	−0.200396	−	0.0761327i
$236$	22.5238	−	31.0014i	1.46618	−	2.01802i
$237$	−11.4416	+	5.44590i	−0.743211	+	0.353749i
$238$	−61.4738	+	44.6634i	−3.98476	+	2.89510i
$239$	10.9767	+	7.97500i	0.710021	+	0.515860i	0.883180	−	0.469034i	$-0.155398\pi$
$239$	10.9767	+	7.97500i	0.710021	+	0.515860i	−0.173160	+	0.984894i	$0.555398\pi$
$240$	0.884498	+	10.8725i	0.0570941	+	0.701815i
$241$	9.94988	+	13.6948i	0.640928	+	0.882162i	0.998665	−	0.0516604i	$-0.0164513\pi$
$241$	9.94988	+	13.6948i	0.640928	+	0.882162i	−0.357736	+	0.933823i	$0.616451\pi$
$242$	−26.3667	−	2.46787i	−1.69491	−	0.158641i
$243$	12.4058	−	9.43911i	0.795831	−	0.605519i
$244$	29.1263	+	9.46370i	1.86462	+	0.605851i
$245$	24.6452	−	30.6499i	1.57452	−	1.95815i
$246$	3.75139	+	28.6754i	0.239180	+	1.82828i
$247$	9.01011	−	2.92756i	0.573299	−	0.186276i
$248$	−13.9701	+	19.2282i	−0.887103	+	1.22099i
$249$	−10.0061	−	1.86298i	−0.634113	−	0.118061i
$250$	23.8547	−	12.4672i	1.50870	−	0.788493i
$251$		−	15.0793i		−	0.951797i	−0.879500	−	0.475898i	$-0.842123\pi$
$251$		−	15.0793i		−	0.951797i	0.879500	−	0.475898i	$-0.157877\pi$
$252$	−30.6767	−	47.4071i	−1.93245	−	2.98637i
$253$	4.33218	+	9.58294i	0.272362	+	0.602474i
$254$	−7.48504	+	2.43204i	−0.469653	+	0.152600i
$255$	18.7034	−	16.0596i	1.17125	−	1.00569i
$256$	−9.10030	+	28.0078i	−0.568769	+	1.75049i
$257$	19.6754			1.22732			0.613658	−	0.789572i	$-0.289697\pi$
$257$	19.6754			1.22732			0.613658	+	0.789572i	$0.289697\pi$
$258$	10.3067	−	18.9456i	0.641665	−	1.17950i
$259$	11.7000	+	16.1037i	0.727003	+	1.00063i
$260$	12.5358	−	3.40534i	0.777436	−	0.211190i
$261$	−8.94294	−	13.8203i	−0.553554	−	0.855452i
$262$	−2.79473	−	3.84662i	−0.172659	−	0.237645i
$263$	−4.13239	−	5.68775i	−0.254814	−	0.350722i	0.662376	−	0.749172i	$-0.269548\pi$
$263$	−4.13239	−	5.68775i	−0.254814	−	0.350722i	−0.917190	+	0.398450i	$0.869548\pi$
$264$	−18.9636	−	16.0370i	−1.16713	−	0.987011i
$265$	−0.266911	−	0.101402i	−0.0163962	−	0.00622910i
$266$	59.7837	−	43.4354i	3.66557	−	2.66319i
$267$	−10.2630	+	18.8654i	−0.628086	+	1.15454i
$268$			8.80456i			0.537824i
$269$	−23.3047	−	7.57216i	−1.42091	−	0.461682i	−0.505021	−	0.863107i	$-0.668515\pi$
$269$	−23.3047	−	7.57216i	−1.42091	−	0.461682i	−0.915892	+	0.401425i	$0.868515\pi$
$270$	17.0505	+	22.1746i	1.03766	+	1.34951i
$271$	−9.19673	+	2.98820i	−0.558662	+	0.181520i	−0.574719	−	0.818351i	$-0.694889\pi$
$271$	−9.19673	+	2.98820i	−0.558662	+	0.181520i	0.0160572	+	0.999871i	$0.494889\pi$
$272$	−17.0502	+	5.53995i	−1.03382	+	0.335909i
$273$	−9.54221	+	9.04043i	−0.577521	+	0.547152i
$274$		−	33.7855i		−	2.04106i
$275$	−4.92541	+	15.8348i	−0.297014	+	0.954873i
$276$	−3.81582	+	20.4950i	−0.229685	+	1.23365i
$277$	−10.4346	−	7.58116i	−0.626953	−	0.455508i	0.228390	−	0.973570i	$-0.426654\pi$
$277$	−10.4346	−	7.58116i	−0.626953	−	0.455508i	−0.855343	+	0.518062i	$0.826654\pi$
$278$	8.84600	+	27.2252i	0.530548	+	1.63286i
$279$	−0.890029	+	16.4684i	−0.0532846	+	0.985940i
$280$	40.1129	−	26.2468i	2.39720	−	1.56854i
$281$	−2.90611	+	8.94409i	−0.173364	+	0.533560i	−0.999555	−	0.0298305i	$-0.990503\pi$
$281$	−2.90611	+	8.94409i	−0.173364	+	0.533560i	0.826191	+	0.563390i	$0.190503\pi$
$282$	6.02465	+	1.12169i	0.358762	+	0.0667956i
$283$	7.68677	−	23.6575i	0.456931	−	1.40629i	−0.411922	−	0.911219i	$-0.635142\pi$
$283$	7.68677	−	23.6575i	0.456931	−	1.40629i	0.868853	−	0.495070i	$-0.164858\pi$
$284$	−2.09975	−	2.89006i	−0.124597	−	0.171493i
$285$	−18.1892	+	15.6180i	−1.07743	+	0.925132i
$286$	−6.04968	+	10.6176i	−0.357725	+	0.627831i
$287$	27.8229	−	20.2145i	1.64233	−	1.19323i
$288$	1.44001	+	5.40949i	0.0848534	+	0.318757i
$289$	19.0241	+	13.8218i	1.11907	+	0.813049i
$290$	24.7173	−	16.1731i	1.45145	−	0.949716i
$291$	−0.449350	+	0.213879i	−0.0263413	+	0.0125378i
$292$	0.842270	−	2.59224i	0.0492901	−	0.151699i
$293$		−	27.3130i		−	1.59564i	−0.602893	−	0.797822i	$-0.705986\pi$
$293$		−	27.3130i		−	1.59564i	0.602893	−	0.797822i	$-0.294014\pi$
$294$	−35.0481	+	64.4252i	−2.04405	+	3.75735i
$295$	22.5468	+	1.10365i	1.31273	+	0.0642572i
$296$	5.36289	+	16.5053i	0.311712	+	0.959350i
$297$	−17.0935	−	2.19393i	−0.991864	−	0.127305i
$298$	−13.3642	+	18.3943i	−0.774168	+	1.06555i
$299$	4.85294			0.280653
$300$	−25.9574	+	20.1699i	−1.49865	+	1.16451i
$301$	−25.6480			−1.47832
$302$	22.2241	+	16.1467i	1.27885	+	0.929141i
$303$	3.40647	−	0.445642i	0.195697	−	0.0256015i
$304$	16.5814	−	5.38764i	0.951011	−	0.309002i
$305$	4.72942	+	17.4100i	0.270806	+	0.996894i
$306$	−28.9889	+	35.6791i	−1.65719	+	2.03964i
$307$	−29.4353			−1.67996			−0.839981	−	0.542616i	$-0.817434\pi$
$307$	−29.4353			−1.67996			−0.839981	+	0.542616i	$0.817434\pi$
$308$	−12.6311	+	61.1351i	−0.719723	+	3.48350i
$309$	14.6906	−	6.99234i	0.835718	−	0.397780i
$310$	−29.5588	−	1.44689i	−1.67883	−	0.0821777i
$311$	−15.8581	+	21.8268i	−0.899231	+	1.23769i	0.0714811	+	0.997442i	$0.477227\pi$
$311$	−15.8581	+	21.8268i	−0.899231	+	1.23769i	−0.970713	+	0.240244i	$0.922773\pi$
$312$	−10.3480	+	4.92539i	−0.585841	+	0.278845i
$313$	−1.01869	−	1.40210i	−0.0575795	−	0.0792514i	0.779256	−	0.626705i	$-0.215597\pi$
$313$	−1.01869	−	1.40210i	−0.0575795	−	0.0792514i	−0.836836	+	0.547454i	$0.815597\pi$
$314$	−22.9461	−	16.6713i	−1.29493	−	0.940819i
$315$	13.4744	−	30.4126i	0.759197	−	1.71356i
$316$	16.3227	+	22.4662i	0.918222	+	1.26382i
$317$	−1.29720	+	3.99236i	−0.0728578	+	0.224233i	−0.980854	−	0.194746i	$-0.937612\pi$
$317$	−1.29720	+	3.99236i	−0.0728578	+	0.224233i	0.907996	+	0.418979i	$0.137612\pi$
$318$	0.523450	+	0.0974576i	0.0293536	+	0.00546515i
$319$	−3.68225	+	17.8223i	−0.206166	+	0.997856i
$320$	−21.8490	+	5.93527i	−1.22140	+	0.331792i
$321$	1.48351	+	11.3399i	0.0828017	+	0.632932i
$322$	36.0009	−	11.6974i	2.00625	−	0.651870i
$323$	−31.8762	−	23.1594i	−1.77364	−	1.28863i
$324$	−25.3128	−	22.9418i	−1.40626	−	1.27454i
$325$	5.72197	+	5.08104i	0.317398	+	0.281846i
$326$	−23.9443			−1.32615
$327$	22.3014	+	23.5392i	1.23327	+	1.30172i
$328$	28.5168	−	9.26566i	1.57458	−	0.511611i
$329$	−2.25197	−	6.93086i	−0.124155	−	0.382111i
$330$	3.78088	−	30.6922i	0.208131	−	1.68955i
$331$	−7.40537	+	22.7914i	−0.407036	+	1.25273i	0.512147	+	0.858898i	$0.328850\pi$
$331$	−7.40537	+	22.7914i	−0.407036	+	1.25273i	−0.919183	+	0.393830i	$0.871150\pi$
$332$			22.3054i			1.22417i
$333$	9.34650	+	7.59393i	0.512185	+	0.416145i
$334$	−13.7821	+	10.0132i	−0.754120	+	0.547901i
$335$	−4.34014	+	2.83985i	−0.237127	+	0.155158i
$336$	−17.5607	+	16.6373i	−0.958014	+	0.907637i
$337$	18.4483	−	13.4034i	1.00494	−	0.730132i	0.0417984	−	0.999126i	$-0.486691\pi$
$337$	18.4483	−	13.4034i	1.00494	−	0.730132i	0.963142	+	0.268994i	$0.0866913\pi$
$338$	−15.0813	−	20.7576i	−0.820314	−	1.12907i
$339$	−11.3593	+	10.7620i	−0.616952	+	0.584509i
$340$	−42.1026	−	33.8542i	−2.28333	−	1.83600i
$341$	13.4801	−	12.2773i	0.729990	−	0.664855i
$342$	28.1919	−	34.6982i	1.52444	−	1.87626i
$343$	52.5058			2.83505
$344$	−21.2671	−	6.91010i	−1.14665	−	0.372568i
$345$	−11.3336	+	4.72954i	−0.610181	+	0.254630i
$346$	−3.71865	−	11.4448i	−0.199916	−	0.615277i
$347$	−22.5741	+	7.33477i	−1.21184	+	0.393751i	−0.844104	−	0.536179i	$-0.819867\pi$
$347$	−22.5741	+	7.33477i	−1.21184	+	0.393751i	−0.367737	+	0.929930i	$0.619867\pi$
$348$	−26.1883	+	24.8112i	−1.40384	+	1.33002i
$349$		−	7.84341i		−	0.419848i	−0.977718	−	0.209924i	$-0.932678\pi$
$349$		−	7.84341i		−	0.419848i	0.977718	−	0.209924i	$-0.0673217\pi$
$350$	54.6948	+	23.9009i	2.92356	+	1.27756i
$351$	−4.17177	+	6.77044i	−0.222672	+	0.361380i
$352$	3.06376	−	5.37710i	0.163299	−	0.286600i
$353$	−0.603074	−	1.85607i	−0.0320984	−	0.0987886i	0.933724	−	0.357994i	$-0.116539\pi$
$353$	−0.603074	−	1.85607i	−0.0320984	−	0.0987886i	−0.965822	+	0.259206i	$0.916539\pi$
$354$	−41.7400	+	5.46053i	−2.21846	+	0.290224i
$355$	0.747370	−	1.96722i	0.0396663	−	0.104409i
$356$	44.7620	+	14.5441i	2.37238	+	0.770834i
$357$	53.7448	+	10.0064i	2.84448	+	0.529594i
$358$	−0.718756	+	2.21211i	−0.0379875	+	0.116913i
$359$	−16.5773	+	12.0441i	−0.874919	+	0.635666i	−0.931902	−	0.362709i	$-0.881852\pi$
$359$	−16.5773	+	12.0441i	−0.874919	+	0.635666i	0.0569835	+	0.998375i	$0.481852\pi$
$360$	19.3667	−	21.5877i	1.02071	−	1.13777i
$361$	15.6285	+	11.3548i	0.822553	+	0.597620i
$362$	13.5764	+	18.6863i	0.713559	+	0.982129i
$363$	11.7577	+	14.9919i	0.617119	+	0.786870i
$364$	23.3051	+	16.9322i	1.22152	+	0.887487i
$365$	1.54949	−	0.420919i	0.0811042	−	0.0220319i
$366$	−14.4588	−	30.3773i	−0.755774	−	1.58785i
$367$	−35.3523	−	11.4867i	−1.84538	−	0.599599i	−0.997600	−	0.0692443i	$-0.977941\pi$
$367$	−35.3523	−	11.4867i	−1.84538	−	0.599599i	−0.847776	−	0.530355i	$-0.822059\pi$
$368$	8.93095			0.465558
$369$	13.1203	−	16.1483i	0.683017	−	0.840646i
$370$	−13.5412	+	16.8404i	−0.703973	+	0.875493i
$371$	−0.195662	−	0.602186i	−0.0101583	−	0.0312640i
$372$	35.8380	−	4.68842i	1.85812	−	0.243083i
$373$	16.5811	+	12.0469i	0.858536	+	0.623763i	0.927486	−	0.373857i	$-0.121965\pi$
$373$	16.5811	+	12.0469i	0.858536	+	0.623763i	−0.0689505	+	0.997620i	$0.521965\pi$
$374$	50.5137	−	5.60033i	2.61200	−	0.289586i
$375$	−18.3150	−	6.28985i	−0.945781	−	0.324806i
$376$		−	6.35375i		−	0.327670i
$377$	6.79398	+	4.93611i	0.349908	+	0.254223i
$378$	−14.6284	+	60.2811i	−0.752403	+	3.10052i
$379$	−5.28323	−	16.2601i	−0.271381	−	0.835225i	−0.990154	−	0.139981i	$-0.955296\pi$
$379$	−5.28323	−	16.2601i	−0.271381	−	0.835225i	0.718773	−	0.695245i	$-0.244704\pi$
$380$	40.9450	+	32.9234i	2.10044	+	1.68894i
$381$	4.97390	+	2.70587i	0.254821	+	0.138626i
$382$	15.4104			0.788467
$383$	−8.49699	+	26.1510i	−0.434176	+	1.33626i	0.459753	+	0.888047i	$0.347938\pi$
$383$	−8.49699	+	26.1510i	−0.434176	+	1.33626i	−0.893929	+	0.448209i	$0.852062\pi$
$384$	32.2860	−	15.3673i	1.64759	−	0.784210i
$385$	−34.2101	+	13.4923i	−1.74351	+	0.687632i
$386$	1.78083	−	2.45110i	0.0906416	−	0.124757i
$387$	−14.9948	+	3.99162i	−0.762227	+	0.202905i
$388$	0.641046	+	0.882325i	0.0325442	+	0.0447932i
$389$	5.55431	−	7.64485i	0.281615	−	0.387609i	−0.644653	−	0.764475i	$-0.722998\pi$
$389$	5.55431	−	7.64485i	0.281615	−	0.387609i	0.926268	+	0.376866i	$0.122998\pi$
$390$	−12.1868	−	7.42401i	−0.617103	−	0.375929i
$391$	−11.8634	−	16.3286i	−0.599959	−	0.825772i
$392$	72.3195	+	23.4980i	3.65268	+	1.18683i
$393$	−0.626132	+	3.36299i	−0.0315842	+	0.169640i
$394$	−3.74633	+	11.5300i	−0.188738	+	0.580874i
$395$	−5.80978	+	15.2925i	−0.292322	+	0.769447i
$396$	2.12990	+	37.7077i	0.107032	+	1.89488i
$397$	−13.6241	+	4.42673i	−0.683773	+	0.222171i	−0.630246	−	0.776395i	$-0.717046\pi$
$397$	−13.6241	+	4.42673i	−0.683773	+	0.222171i	−0.0535265	+	0.998566i	$0.517046\pi$
$398$	11.0958	−	15.2720i	0.556181	−	0.765518i
$399$	−52.2672	−	9.73127i	−2.61663	−	0.487173i
$400$	10.5302	+	9.35073i	0.526512	+	0.467536i
$401$			26.8471i			1.34068i	0.742054	+	0.670341i	$0.233852\pi$
$401$			26.8471i			1.34068i	−0.742054	+	0.670341i	$0.766148\pi$
$402$	7.02133	−	6.65211i	0.350192	−	0.331777i
$403$	−2.59998	−	8.00191i	−0.129514	−	0.398604i
$404$	−2.32656	−	7.16043i	−0.115751	−	0.356245i
$405$	3.14450	−	19.8774i	0.156251	−	0.987717i
$406$	62.2980	+	20.2419i	3.09180	+	1.00459i
$407$	−1.46706	−	13.2325i	−0.0727195	−	0.655913i
$408$	41.8689	+	22.7772i	2.07282	+	1.12764i
$409$	−14.2965	−	19.6775i	−0.706917	−	0.972988i	−0.999858	−	0.0168572i	$-0.994634\pi$
$409$	−14.2965	−	19.6775i	−0.706917	−	0.972988i	0.292941	−	0.956131i	$-0.405366\pi$
$410$	29.0958	+	23.3956i	1.43694	+	1.15543i
$411$	−17.6455	+	16.7176i	−0.870386	+	0.824617i
$412$	−20.9577	−	28.8458i	−1.03251	−	1.42113i
$413$	29.4243	+	40.4990i	1.44787	+	1.99283i
$414$	19.2270	−	12.4416i	0.944955	−	0.611471i
$415$	−10.9953	+	7.19445i	−0.539736	+	0.353162i
$416$	−1.67859	−	2.31038i	−0.0822995	−	0.113275i
$417$	9.84199	−	18.0915i	0.481964	−	0.885943i
$418$	−49.1249	+	5.44635i	−2.40278	+	0.266390i
$419$	−17.1907	−	5.58560i	−0.839821	−	0.272874i	−0.142645	−	0.989774i	$-0.545561\pi$
$419$	−17.1907	−	5.58560i	−0.839821	−	0.272874i	−0.697176	+	0.716900i	$0.745561\pi$
$420$	−70.9286	−	16.8310i	−3.46096	−	0.821270i
$421$	−6.52221	−	20.0733i	−0.317873	−	0.978313i	−0.974556	−	0.224146i	$-0.928041\pi$
$421$	−6.52221	−	20.0733i	−0.317873	−	0.978313i	0.656682	−	0.754167i	$-0.271959\pi$
$422$	−10.7262	−	33.0118i	−0.522142	−	1.60699i
$423$	−2.39525	−	3.70157i	−0.116461	−	0.179976i
$424$		−	0.552044i		−	0.0268096i
$425$	3.10826	−	31.6736i	0.150773	−	1.53639i
$426$	−0.718295	+	3.85800i	−0.0348015	+	0.186921i
$427$	−23.5158	+	32.3668i	−1.13801	+	1.56634i
$428$	23.8366	−	7.74498i	1.15219	−	0.374368i
$429$	8.53880	−	2.09412i	0.412257	−	0.101105i
$430$	−7.29922	−	26.8700i	−0.352000	−	1.29578i
$431$	−6.08457	+	18.7264i	−0.293084	+	0.902019i	0.690775	+	0.723070i	$0.257270\pi$
$431$	−6.08457	+	18.7264i	−0.293084	+	0.902019i	−0.983858	+	0.178949i	$0.942730\pi$
$432$	−7.67737	+	12.4598i	−0.369378	+	0.599470i
$433$	8.87876	+	2.88489i	0.426686	+	0.138639i	0.514485	−	0.857500i	$-0.327983\pi$
$433$	8.87876	+	2.88489i	0.426686	+	0.138639i	−0.0877986	+	0.996138i	$0.527983\pi$
$434$	−38.5751	−	53.0941i	−1.85167	−	2.54860i
$435$	−20.6773	−	4.90663i	−0.991401	−	0.235255i
$436$	41.7692	−	57.4904i	2.00038	−	2.75329i
$437$	11.5372	+	15.8796i	0.551901	+	0.759627i
$438$	−2.70358	+	1.28684i	−0.129182	+	0.0614874i
$439$	1.00757	−	1.38680i	0.0480887	−	0.0661884i	−0.784295	−	0.620387i	$-0.786975\pi$
$439$	1.00757	−	1.38680i	0.0480887	−	0.0661884i	0.832384	+	0.554199i	$0.186975\pi$
$440$	−32.0019	+	1.97080i	−1.52563	+	0.0939543i
$441$	50.9902	−	13.5736i	2.42810	−	0.646363i
$442$	7.24721	−	22.3046i	0.344714	−	1.06092i
$443$	7.75578			0.368488			0.184244	−	0.982881i	$-0.441016\pi$
$443$	7.75578			0.368488			0.184244	+	0.982881i	$0.441016\pi$
$444$	12.6119	−	23.1830i	0.598533	−	1.10022i
$445$	7.26830	+	26.7562i	0.344551	+	1.26836i
$446$	−4.14764	−	12.7651i	−0.196397	−	0.604447i
$447$	16.2197	−	2.12190i	0.767167	−	0.100363i
$448$	−40.6192	−	29.5116i	−1.91908	−	1.39429i
$449$		−	4.99437i		−	0.235699i	−0.993031	−	0.117849i	$-0.962400\pi$
$449$		−	4.99437i		−	0.235699i	0.993031	−	0.117849i	$-0.0376000\pi$
$450$	35.6964	+	5.46119i	1.68274	+	0.257443i
$451$	−22.8624	+	2.53469i	−1.07655	+	0.119354i
$452$	27.7430	+	20.1565i	1.30492	+	0.948082i
$453$	−2.56370	−	19.5968i	−0.120453	−	0.920738i
$454$	14.2480	+	43.8509i	0.668692	+	2.05802i
$455$	−0.829666	+	16.9494i	−0.0388953	+	0.794602i
$456$	−40.7178	−	22.1510i	−1.90678	−	1.03731i
$457$	−24.2334			−1.13359			−0.566794	−	0.823859i	$-0.691817\pi$
$457$	−24.2334			−1.13359			−0.566794	+	0.823859i	$0.691817\pi$
$458$	61.3095	+	19.9207i	2.86480	+	0.930831i
$459$	32.9786	−	2.51425i	1.53931	−	0.117355i
$460$	14.7360	+	22.5209i	0.687068	+	1.05004i
$461$	1.88114	+	1.36673i	0.0876135	+	0.0636549i	0.630730	−	0.776003i	$-0.282756\pi$
$461$	1.88114	+	1.36673i	0.0876135	+	0.0636549i	−0.543116	+	0.839658i	$0.682756\pi$
$462$	58.2963	−	36.1166i	2.71219	−	1.68029i
$463$	14.0123	+	19.2863i	0.651206	+	0.896308i	0.999151	−	0.0412070i	$-0.0131203\pi$
$463$	14.0123	+	19.2863i	0.651206	+	0.896308i	−0.347945	+	0.937515i	$0.613120\pi$
$464$	12.5031	+	9.08401i	0.580441	+	0.421715i
$465$	13.8704	+	16.1539i	0.643226	+	0.749117i
$466$	2.52262	−	1.83279i	0.116858	−	0.0849024i
$467$	7.07167	−	21.7644i	0.327238	−	1.00713i	−0.643182	−	0.765713i	$-0.722386\pi$
$467$	7.07167	−	21.7644i	0.327238	−	1.00713i	0.970420	−	0.241422i	$-0.0776137\pi$
$468$	16.2602	+	6.27219i	0.751630	+	0.289932i
$469$	−10.9390	−	3.55429i	−0.505115	−	0.164122i
$470$	6.62019	−	4.33174i	0.305367	−	0.199808i
$471$	2.64699	+	20.2335i	0.121967	+	0.932310i
$472$	13.4871	+	41.5090i	0.620794	+	1.91061i
$473$	14.9050	+	8.49255i	0.685332	+	0.390488i
$474$	5.58376	−	29.9907i	0.256471	−	1.37752i
$475$	−3.02280	+	30.8028i	−0.138696	+	1.41333i
$476$		−	119.806i		−	5.49132i
$477$	−0.208110	−	0.321610i	−0.00952872	−	0.0147255i
$478$	−31.0653	+	10.0937i	−1.42089	+	0.461676i
$479$	6.03377	+	18.5700i	0.275690	+	0.848487i	0.989036	+	0.147675i	$0.0471788\pi$
$479$	6.03377	+	18.5700i	0.275690	+	0.848487i	−0.713346	+	0.700812i	$0.752821\pi$
$480$	6.17181	+	3.75977i	0.281703	+	0.171609i
$481$	−5.84291	−	1.89848i	−0.266414	−	0.0865630i
$482$	−40.7527			−1.85623
$483$	−23.9230	−	13.0144i	−1.08854	−	0.592177i
$484$	27.5835	−	31.3455i	1.25379	−	1.42479i
$485$	−0.228170	+	0.600586i	−0.0103607	+	0.0272712i
$486$	0.829298	+	37.5192i	0.0376177	+	1.70191i
$487$	−7.79227	−	10.7251i	−0.353101	−	0.486002i	0.595109	−	0.803645i	$-0.297109\pi$
$487$	−7.79227	−	10.7251i	−0.353101	−	0.486002i	−0.948211	+	0.317643i	$0.897109\pi$
$488$	−28.2194	+	20.5026i	−1.27743	+	0.928110i
$489$	11.8480	+	12.5056i	0.535784	+	0.565522i
$490$	24.8212	+	91.3721i	1.12131	+	4.12777i
$491$	−4.39411	+	3.19251i	−0.198303	+	0.144076i	−0.682506	−	0.730880i	$-0.739110\pi$
$491$	−4.39411	+	3.19251i	−0.198303	+	0.144076i	0.484203	+	0.874956i	$0.339110\pi$
$492$	−40.0542	−	21.7900i	−1.80578	−	0.982369i
$493$		−	34.9263i		−	1.57300i
$494$	−7.04795	+	21.6914i	−0.317102	+	0.975941i
$495$	−17.9007	+	13.2123i	−0.804577	+	0.593848i
$496$	−4.78478	−	14.7260i	−0.214843	−	0.661219i
$497$	4.43831	−	1.44210i	0.199086	−	0.0646868i
$498$	17.7878	−	16.8524i	0.797089	−	0.755174i
$499$	−6.90081			−0.308923			−0.154461	−	0.987999i	$-0.549364\pi$
$499$	−6.90081			−0.308923			−0.154461	+	0.987999i	$0.549364\pi$
$500$	−6.20472	+	41.9824i	−0.277484	+	1.87751i
$501$	12.0493	+	2.24337i	0.538321	+	0.100226i
$502$	29.3694	+	21.3381i	1.31082	+	0.952368i
$503$	2.16417	−	0.703182i	0.0964956	−	0.0313533i	−0.260371	−	0.965509i	$-0.583845\pi$
$503$	2.16417	−	0.703182i	0.0964956	−	0.0313533i	0.356867	+	0.934155i	$0.383845\pi$
$504$	64.2202	+	3.47075i	2.86060	+	0.154599i
$505$	2.77926	−	3.45641i	0.123675	−	0.153808i
$506$	−24.7947	−	5.12282i	−1.10226	−	0.227737i
$507$	−3.37881	+	18.1478i	−0.150058	+	0.805972i
$508$	3.83458	−	11.8016i	0.170132	−	0.523612i
$509$	18.0666	+	24.8665i	0.800786	+	1.10219i	0.992680	+	0.120772i	$0.0385368\pi$
$509$	18.0666	+	24.8665i	0.800786	+	1.10219i	−0.191895	+	0.981416i	$0.561463\pi$
$510$	4.81224	+	59.1533i	0.213089	+	2.61935i
$511$	2.88065	+	2.09291i	0.127432	+	0.0925850i
$512$	−17.4038	−	23.9542i	−0.769145	−	1.05864i
$513$	−32.0719	+	2.44512i	−1.41601	+	0.107955i
$514$	−27.8419	+	38.3211i	−1.22805	+	1.69027i
$515$	7.45955	−	19.6350i	0.328707	−	0.865220i
$516$	14.6147	+	30.7049i	0.643378	+	1.35171i
$517$	−0.986241	+	4.77346i	−0.0433748	+	0.209936i
$518$	−47.9208			−2.10552
$519$	−4.13734	+	7.60523i	−0.181609	+	0.333832i
$520$	−5.25449	+	13.8308i	−0.230425	+	0.606522i
$521$	−31.0233	+	10.0801i	−1.35916	+	0.441617i	−0.895762	−	0.444535i	$-0.853369\pi$
$521$	−31.0233	+	10.0801i	−1.35916	+	0.441617i	−0.463395	+	0.886152i	$0.653369\pi$
$522$	39.5721	+	2.13865i	1.73202	+	0.0936063i
$523$	−6.86794	−	4.98985i	−0.300314	−	0.218191i	0.427415	−	0.904055i	$-0.359424\pi$
$523$	−6.86794	−	4.98985i	−0.300314	−	0.218191i	−0.727729	+	0.685865i	$0.759424\pi$
$524$	7.49667			0.327494
$525$	−14.5808	−	40.3924i	−0.636359	−	1.76287i
$526$	16.9254			0.737984
$527$	−20.5680	+	28.3094i	−0.895956	+	1.23318i
$528$	15.7141	−	3.85383i	0.683868	−	0.167717i
$529$	−4.00035	−	12.3118i	−0.173928	−	0.535296i
$530$	0.575194	−	0.376362i	0.0249848	−	0.0163481i
$531$	23.5055	+	19.0979i	1.02005	+	0.828780i
$532$			116.512i			5.05145i
$533$	−3.28007	+	10.0950i	−0.142075	+	0.437263i
$534$	−22.2207	−	46.6846i	−0.961583	−	2.02024i
$535$	11.5062	+	9.25197i	0.497455	+	0.399997i
$536$	−8.11293	−	5.89439i	−0.350425	−	0.254599i
$537$	1.51099	−	0.719190i	0.0652038	−	0.0310353i
$538$	47.7256	−	34.6747i	2.05760	−	1.49493i
$539$	−50.6849	−	28.8792i	−2.18315	−	1.24391i
$540$	−44.0870	+	1.19863i	−1.89720	+	0.0515810i
$541$	−3.21826	−	4.42956i	−0.138364	−	0.190442i	0.734212	−	0.678920i	$-0.237552\pi$
$541$	−3.21826	−	4.42956i	−0.138364	−	0.190442i	−0.872576	+	0.488479i	$0.837552\pi$
$542$	7.19394	−	22.1407i	0.309006	−	0.951023i
$543$	3.04165	−	16.3369i	0.130530	−	0.701083i
$544$	−3.67023	+	11.2958i	−0.157360	+	0.484303i
$545$	41.8118	+	2.04667i	1.79102	+	0.0876695i
$546$	−4.10492	−	31.3778i	−0.175674	−	1.34285i
$547$	5.54428	+	17.0636i	0.237056	+	0.729585i	0.996842	+	0.0794110i	$0.0253039\pi$
$547$	5.54428	+	17.0636i	0.237056	+	0.729585i	−0.759785	+	0.650174i	$0.774696\pi$
$548$	43.0959	+	31.3110i	1.84096	+	1.33754i
$549$	−8.71097	+	22.5826i	−0.371775	+	0.963803i
$550$	−23.8711	−	32.0003i	−1.01787	−	1.36450i
$551$			33.9660i			1.44700i
$552$	−16.3304	−	17.2368i	−0.695070	−	0.733649i
$553$	−34.5018	+	11.2103i	−1.46717	+	0.476711i
$554$	29.5312	−	9.59525i	1.25466	−	0.407663i
$555$	15.4958	−	1.26061i	0.657759	−	0.0535100i
$556$	−42.9257	−	13.9474i	−1.82046	−	0.591502i
$557$			26.0202i			1.10251i	0.834336	+	0.551256i	$0.185851\pi$
$557$			26.0202i			1.10251i	−0.834336	+	0.551256i	$0.814149\pi$
$558$	−30.8156	−	25.0374i	−1.30453	−	1.05992i
$559$	6.40422	−	4.65293i	0.270869	−	0.196798i
$560$	−1.52685	+	31.1923i	−0.0645211	+	1.31812i
$561$	−27.9198	−	23.6111i	−1.17878	−	0.996860i
$562$	−13.3078	−	18.3166i	−0.561355	−	0.772639i
$563$	−18.1784	−	25.0204i	−0.766129	−	1.05449i	−0.996679	−	0.0814256i	$-0.974053\pi$
$563$	−18.1784	−	25.0204i	−0.766129	−	1.05449i	0.230551	−	0.973060i	$-0.425947\pi$
$564$	−7.01418	+	6.64533i	−0.295350	+	0.279819i
$565$	−0.987655	+	20.1770i	−0.0415510	+	0.848855i
$566$	35.1996	+	48.4481i	1.47955	+	2.03642i
$567$	38.7218	−	22.1878i	1.62616	−	0.931802i
$568$	4.06875			0.170721
$569$	−1.93148	+	5.94448i	−0.0809718	+	0.249206i	−0.983345	−	0.181751i	$-0.941824\pi$
$569$	−1.93148	+	5.94448i	−0.0809718	+	0.249206i	0.902373	+	0.430956i	$0.141824\pi$
$570$	−4.67993	−	57.5269i	−0.196021	−	2.40954i
$571$	−17.0538	+	5.54112i	−0.713680	+	0.231889i	−0.643281	−	0.765630i	$-0.722427\pi$
$571$	−17.0538	+	5.54112i	−0.713680	+	0.231889i	−0.0703989	+	0.997519i	$0.522427\pi$
$572$	−7.93691	−	17.5567i	−0.331859	−	0.734083i
$573$	−7.62531	−	8.04854i	−0.318552	−	0.336233i
$574$			82.7945i			3.45578i
$575$	−6.34853	+	14.5279i	−0.264752	+	0.605857i
$576$	−28.3405	−	10.9320i	−1.18085	−	0.455500i
$577$	27.7922	−	38.2527i	1.15700	−	1.59248i	0.435285	−	0.900293i	$-0.356648\pi$
$577$	27.7922	−	38.2527i	1.15700	−	1.59248i	0.721719	−	0.692186i	$-0.243352\pi$
$578$	−53.8406	+	17.4939i	−2.23948	+	0.727650i
$579$	−2.16133	+	0.282751i	−0.0898219	+	0.0117507i
$580$	−2.27699	+	46.5172i	−0.0945469	+	1.93152i
$581$	−27.7127	−	9.00441i	−1.14972	−	0.373566i
$582$	0.219293	−	1.17784i	0.00908999	−	0.0488228i
$583$	−0.0856893	+	0.414741i	−0.00354889	+	0.0171768i
$584$	1.82474	+	2.51154i	0.0755082	+	0.103928i
$585$	2.15280	+	10.0384i	0.0890075	+	0.415037i
$586$	53.1967	+	38.6496i	2.19753	+	1.59660i
$587$	11.2287	−	8.15816i	0.463460	−	0.336723i	−0.331427	−	0.943481i	$-0.607530\pi$
$587$	11.2287	−	8.15816i	0.463460	−	0.336723i	0.794887	+	0.606757i	$0.207530\pi$
$588$	−49.6978	−	104.413i	−2.04950	−	4.30591i
$589$	20.0025	−	27.5311i	0.824188	−	1.13440i
$590$	−34.0547	+	42.3519i	−1.40201	+	1.74360i
$591$	7.87562	−	3.74859i	0.323960	−	0.154196i
$592$	−10.7528	−	3.49380i	−0.441937	−	0.143594i
$593$		−	2.33414i		−	0.0958516i	−0.998851	−	0.0479258i	$-0.984739\pi$
$593$		−	2.33414i		−	0.0958516i	0.998851	−	0.0479258i	$-0.0152611\pi$
$594$	28.4614	−	30.1878i	1.16778	−	1.23862i
$595$	59.0576	−	38.6427i	2.42112	−	1.58420i
$596$	−11.0778	−	34.0940i	−0.453765	−	1.39655i
$597$	−13.4666	+	1.76173i	−0.551151	+	0.0721029i
$598$	−6.86722	+	9.45191i	−0.280821	+	0.386518i
$599$			11.8708i			0.485028i	0.970148	+	0.242514i	$0.0779721\pi$
$599$			11.8708i			0.485028i	−0.970148	+	0.242514i	$0.922028\pi$
$600$	−1.20774	−	37.4215i	−0.0493058	−	1.52773i
$601$		−	24.5582i		−	1.00175i	−0.865519	−	0.500876i	$-0.833011\pi$
$601$		−	24.5582i		−	1.00175i	0.865519	−	0.500876i	$-0.166989\pi$
$602$	36.2935	−	49.9537i	1.47921	−	2.03596i
$603$	−6.94850	−	0.375528i	−0.282965	−	0.0152927i
$604$	−41.1926	+	13.3843i	−1.67610	+	0.544600i
$605$	24.3484	+	3.48677i	0.989901	+	0.141757i
$606$	−3.95240	+	7.26528i	−0.160555	+	0.295132i
$607$	40.0055			1.62377			0.811886	−	0.583816i	$-0.198441\pi$
$607$	40.0055			1.62377			0.811886	+	0.583816i	$0.198441\pi$
$608$	3.56932	−	10.9852i	0.144755	−	0.445510i
$609$	−20.2541	−	42.5529i	−0.820736	−	1.72433i
$610$	−40.6013	−	15.4249i	−1.64390	−	0.624536i
$611$	1.81968	+	1.32207i	0.0736162	+	0.0534853i
$612$	−18.6456	−	70.0434i	−0.753703	−	2.83133i
$613$	13.0232	−	9.46188i	0.526001	−	0.382162i	−0.292859	−	0.956156i	$-0.594607\pi$
$613$	13.0232	−	9.46188i	0.526001	−	0.382162i	0.818860	+	0.573994i	$0.194607\pi$
$614$	41.6528	−	57.3302i	1.68097	−	2.31366i
$615$	−2.17801	−	26.7726i	−0.0878256	−	1.07958i
$616$	−47.8766	−	52.5670i	−1.92900	−	2.11798i
$617$	7.31781	−	22.5219i	0.294604	−	0.906698i	−0.688750	−	0.724999i	$-0.741840\pi$
$617$	7.31781	−	22.5219i	0.294604	−	0.906698i	0.983354	−	0.181699i	$-0.0581596\pi$
$618$	−7.16935	+	38.5069i	−0.288393	+	1.54898i
$619$	5.99643	−	18.4551i	0.241017	−	0.741774i	−0.755249	−	0.655438i	$-0.772484\pi$
$619$	5.99643	−	18.4551i	0.241017	−	0.741774i	0.996266	−	0.0863361i	$-0.0275159\pi$
$620$	29.2394	−	36.3635i	1.17428	−	1.46039i
$621$	−16.0118	−	3.88557i	−0.642530	−	0.155922i
$622$	−20.0712	−	61.7727i	−0.804780	−	2.47686i
$623$	−36.1397	+	49.7421i	−1.44791	+	1.99288i
$624$	1.36659	−	7.34005i	0.0547076	−	0.293837i
$625$	−22.6962	+	10.4826i	−0.907847	+	0.419302i
$626$	4.17233			0.166760
$627$	27.1522	+	22.9619i	1.08435	+	0.917010i
$628$	42.5310	−	13.8192i	1.69717	−	0.551444i
$629$	7.89570	+	24.3005i	0.314822	+	0.968923i
$630$	40.1666	+	69.2795i	1.60027	+	2.76016i
$631$	10.0104	−	30.8090i	0.398509	−	1.22649i	−0.527685	−	0.849440i	$-0.676940\pi$
$631$	10.0104	−	30.8090i	0.398509	−	1.22649i	0.926195	−	0.377046i	$-0.123060\pi$
$632$	−31.6290			−1.25813
$633$	−11.9339	+	21.9367i	−0.474329	+	0.871907i
$634$	−5.94017	−	8.17594i	−0.235914	−	0.324708i
$635$	7.05433	−	1.91631i	0.279942	−	0.0760463i
$636$	−0.609425	+	0.577378i	−0.0241653	+	0.0228945i
$637$	−21.7777	+	15.8224i	−0.862865	+	0.626908i
$638$	−29.5012	−	32.3914i	−1.16796	−	1.28239i
$639$	2.37037	−	1.53384i	0.0937705	−	0.0606779i
$640$	16.3941	−	43.1525i	0.648035	−	1.70575i
$641$	−20.9750	−	28.8696i	−0.828462	−	1.14028i	−0.988207	−	0.153122i	$-0.951067\pi$
$641$	−20.9750	−	28.8696i	−0.828462	−	1.14028i	0.159745	−	0.987158i	$-0.448933\pi$
$642$	−24.1856	−	13.1573i	−0.954531	−	0.519277i
$643$		−	19.5401i		−	0.770587i	−0.922794	−	0.385293i	$-0.874100\pi$
$643$		−	19.5401i		−	0.770587i	0.922794	−	0.385293i	$-0.125900\pi$
$644$	−18.4432	+	56.7623i	−0.726764	+	2.23675i
$645$	−10.4218	+	17.1079i	−0.410360	+	0.673621i
$646$	90.2137	−	29.3122i	3.54941	−	1.15327i
$647$	−4.81679	−	14.8246i	−0.189368	−	0.582814i	0.810629	−	0.585561i	$-0.199126\pi$
$647$	−4.81679	−	14.8246i	−0.189368	−	0.582814i	−0.999996	+	0.00274697i	$0.999126\pi$
$648$	38.0857	−	7.96553i	1.49615	−	0.312915i
$649$	−3.68950	−	33.2785i	−0.144826	−	1.30629i
$650$	−17.9931	+	3.95449i	−0.705748	+	0.155108i
$651$	−8.64238	+	46.4187i	−0.338722	+	1.81929i
$652$	22.1905	−	30.5426i	0.869048	−	1.19614i
$653$	−12.4383	−	38.2810i	−0.486747	−	1.49805i	−0.829435	−	0.558603i	$-0.811337\pi$
$653$	−12.4383	−	38.2810i	−0.486747	−	1.49805i	0.342688	−	0.939449i	$-0.388663\pi$
$654$	−77.4045	+	10.1262i	−3.02676	+	0.395968i
$655$	2.41800	+	3.69543i	0.0944791	+	0.144392i
$656$	−6.03636	+	18.5780i	−0.235680	+	0.725349i
$657$	2.00986	+	0.775278i	0.0784120	+	0.0302465i
$658$	16.6857	+	5.42151i	0.650476	+	0.211352i
$659$	1.97854	−	1.43749i	0.0770729	−	0.0559968i	−0.548582	−	0.836097i	$-0.684832\pi$
$659$	1.97854	−	1.43749i	0.0770729	−	0.0559968i	0.625655	+	0.780100i	$0.284832\pi$
$660$	35.6462	+	33.2670i	1.38753	+	1.29492i
$661$	23.8636	+	17.3379i	0.928187	+	0.674367i	0.945548	−	0.325482i	$-0.105526\pi$
$661$	23.8636	+	17.3379i	0.928187	+	0.674367i	−0.0173611	+	0.999849i	$0.505526\pi$
$662$	−33.9110	−	46.6744i	−1.31799	−	1.81405i
$663$	−15.2352	+	7.25158i	−0.591687	+	0.281628i
$664$	−20.5532	−	14.9328i	−0.797620	−	0.579505i
$665$	−57.4338	+	37.5803i	−2.22719	+	1.45730i
$666$	−28.0163	+	7.45797i	−1.08561	+	0.288990i
$667$	−5.37661	+	16.5475i	−0.208183	+	0.640722i
$668$		−	26.8598i		−	1.03924i
$669$	−4.61464	+	8.48259i	−0.178412	+	0.327956i
$670$	0.610483	−	12.4717i	0.0235850	−	0.481824i
$671$	24.3832	−	11.0230i	0.941303	−	0.425537i
$672$	2.07887	+	15.8908i	0.0801941	+	0.613000i
$673$	15.5957	+	11.3309i	0.601170	+	0.436775i	0.846294	−	0.532716i	$-0.178829\pi$
$673$	15.5957	+	11.3309i	0.601170	+	0.436775i	−0.245124	+	0.969492i	$0.578829\pi$
$674$			54.8977i			2.11458i
$675$	−14.8108	−	21.3457i	−0.570069	−	0.821597i
$676$	40.4545			1.55594
$677$	−7.95613	+	10.9507i	−0.305779	+	0.420869i	−0.934059	−	0.357118i	$-0.883759\pi$
$677$	−7.95613	+	10.9507i	−0.305779	+	0.420869i	0.628280	+	0.777987i	$0.283759\pi$
$678$	−4.88660	−	37.3530i	−0.187669	−	1.43453i
$679$	−1.35500	+	0.440267i	−0.0520002	+	0.0168959i
$680$	59.3813	−	16.1309i	2.27717	−	0.618592i
$681$	15.8522	−	29.1395i	0.607459	−	1.11663i
$682$	4.83693	+	43.6280i	0.185215	+	1.67060i
$683$	14.6470	−	45.0789i	0.560453	−	1.72490i	−0.120635	−	0.992697i	$-0.538493\pi$
$683$	14.6470	−	45.0789i	0.560453	−	1.72490i	0.681089	−	0.732201i	$-0.261507\pi$
$684$	18.1329	+	68.1176i	0.693331	+	2.60454i
$685$	−1.53422	+	31.3429i	−0.0586195	+	1.19755i
$686$	−74.2990	+	102.264i	−2.83675	+	3.90445i
$687$	−19.9327	−	41.8776i	−0.760479	−	1.59773i
$688$	11.7858	−	8.56287i	0.449329	−	0.326456i
$689$	0.158102	+	0.114868i	0.00602321	+	0.00437612i
$690$	6.82619	−	28.7667i	0.259869	−	1.09513i
$691$	8.67115	−	6.29996i	0.329866	−	0.239662i	−0.410508	−	0.911857i	$-0.634648\pi$
$691$	8.67115	−	6.29996i	0.329866	−	0.239662i	0.740374	+	0.672195i	$0.234648\pi$
$692$	18.0450	+	5.86317i	0.685967	+	0.222884i
$693$	−47.7087	−	12.5759i	−1.81230	−	0.477719i
$694$	17.6581	−	54.3460i	0.670291	−	2.06294i
$695$	−6.97014	−	25.6585i	−0.264392	−	0.973284i
$696$	−5.32989	−	40.7414i	−0.202029	−	1.54430i
$697$	41.9848	−	13.6417i	1.59029	−	0.516716i
$698$	15.2764	+	11.0989i	0.578219	+	0.420100i
$699$	−2.20545	−	0.410619i	−0.0834179	−	0.0155310i
$700$	−81.1761	+	47.6168i	−3.06817	+	1.79974i
$701$	49.0201			1.85146			0.925731	−	0.378183i	$-0.123451\pi$
$701$	49.0201			1.85146			0.925731	+	0.378183i	$0.123451\pi$
$702$	−7.28325	−	17.7058i	−0.274889	−	0.668263i
$703$	−7.67862	−	23.6324i	−0.289605	−	0.891311i
$704$	13.8335	+	30.6001i	0.521368	+	1.15329i
$705$	−5.53814	−	1.31417i	−0.208578	−	0.0494947i
$706$	4.46839	+	1.45187i	0.168170	+	0.0546418i
$707$	9.83549			0.369902
$708$	31.7175	−	58.3029i	1.19202	−	2.19116i
$709$	−17.8783	+	12.9893i	−0.671434	+	0.487825i	−0.870505	−	0.492160i	$-0.836208\pi$
$709$	−17.8783	+	12.9893i	−0.671434	+	0.487825i	0.199071	+	0.979985i	$0.436208\pi$
$710$	2.77392	+	4.23937i	0.104103	+	0.159101i
$711$	−18.4264	+	11.9235i	−0.691044	+	0.447168i
$712$	−43.3684	+	31.5090i	−1.62530	+	1.18085i
$713$	14.1028	−	10.2463i	0.528153	−	0.383726i
$714$	−95.5414	+	90.5173i	−3.57555	+	3.38753i
$715$	6.09445	−	9.57523i	0.227919	−	0.358093i
$716$	−2.15559	−	2.96691i	−0.0805580	−	0.110879i
$717$	20.6433	+	11.2302i	0.770938	+	0.419400i
$718$		−	49.3304i		−	1.84099i
$719$	14.1223	+	4.58861i	0.526672	+	0.171126i	0.560271	−	0.828309i	$-0.310697\pi$
$719$	14.1223	+	4.58861i	0.526672	+	0.171126i	−0.0335990	+	0.999435i	$0.510697\pi$
$720$	3.96184	+	18.4739i	0.147649	+	0.688480i
$721$	44.2991	−	14.3936i	1.64978	−	0.536047i
$722$	−44.2306	+	14.3714i	−1.64609	+	0.534848i
$723$	20.1650	+	21.2842i	0.749945	+	0.791570i
$724$	−36.4177			−1.35345
$725$	−23.6647	+	13.8814i	−0.878884	+	0.515541i
$726$	−45.8371	+	1.68562i	−1.70117	+	0.0625592i
$727$	−17.1976	+	23.6705i	−0.637825	+	0.877891i	−0.998497	−	0.0548013i	$-0.982547\pi$
$727$	−17.1976	+	23.6705i	−0.637825	+	0.877891i	0.360672	+	0.932693i	$0.382547\pi$
$728$	−31.2042	+	10.1389i	−1.15650	+	0.375771i
$729$	19.1851	−	18.9982i	0.710560	−	0.703636i
$730$	−1.37282	+	3.61352i	−0.0508103	+	0.133742i
$731$	−31.3112	−	10.1736i	−1.15809	−	0.376286i
$732$	52.1482	+	9.70912i	1.92745	+	0.358859i
$733$	−5.37603	+	16.5457i	−0.198568	+	0.611130i	0.801348	+	0.598198i	$0.204116\pi$
$733$	−5.37603	+	16.5457i	−0.198568	+	0.611130i	−0.999916	+	0.0129319i	$0.995884\pi$
$734$	72.3979	−	52.6002i	2.67226	−	1.94151i
$735$	35.4398	−	58.1758i	1.30722	−	2.14585i
$736$	3.47779	−	4.78677i	0.128193	−	0.176443i
$737$	5.18015	+	5.68765i	0.190813	+	0.209507i
$738$	12.8854	+	48.4048i	0.474318	+	1.78181i
$739$	−18.8005	+	25.8766i	−0.691587	+	0.951887i	0.308413	+	0.951253i	$0.400202\pi$
$739$	−18.8005	+	25.8766i	−0.691587	+	0.951887i	−1.00000		0.000634867i	$0.999798\pi$
$740$	−8.93178	−	32.8798i	−0.328339	−	1.20868i
$741$	14.8164	−	7.05220i	0.544292	−	0.259069i
$742$	1.44973	+	0.471047i	0.0532213	+	0.0172927i
$743$		−	21.8957i		−	0.803274i	−0.915799	−	0.401637i	$-0.868441\pi$
$743$		−	21.8957i		−	0.803274i	0.915799	−	0.401637i	$-0.131559\pi$
$744$	−19.6724	+	36.1616i	−0.721224	+	1.32575i
$745$	13.2333	−	16.4575i	0.484830	−	0.602957i
$746$	−46.9265	+	15.2474i	−1.71810	+	0.558245i
$747$	−17.6033	−	0.951361i	−0.644070	−	0.0348085i
$748$	−39.6703	+	69.6239i	−1.45049	+	2.54570i
$749$			32.7417i			1.19636i
$750$	38.1673	−	26.7709i	1.39367	−	0.977536i
$751$	32.1837			1.17440			0.587201	−	0.809441i	$-0.300230\pi$
$751$	32.1837			1.17440			0.587201	+	0.809441i	$0.300230\pi$
$752$	3.34878	+	2.43303i	0.122117	+	0.0887235i
$753$	−3.38796	−	25.8974i	−0.123464	−	0.943755i
$754$	−19.2278	+	6.24749i	−0.700236	+	0.227520i
$755$	−19.8841	−	15.9886i	−0.723656	−	0.581884i
$756$	−63.3359	−	74.5254i	−2.30350	−	2.71046i
$757$			6.12488i			0.222613i	0.993786	+	0.111306i	$0.0355035\pi$
$757$			6.12488i			0.222613i	−0.993786	+	0.111306i	$0.964497\pi$
$758$	39.1454	+	12.7191i	1.42182	+	0.461978i
$759$	9.59323	+	15.4846i	0.348212	+	0.562054i
$760$	−57.7487	+	15.6874i	−2.09476	+	0.569042i
$761$	7.06306	+	5.13161i	0.256036	+	0.186021i	0.708397	−	0.705814i	$-0.249418\pi$
$761$	7.06306	+	5.13161i	0.256036	+	0.186021i	−0.452362	+	0.891834i	$0.649418\pi$
$762$	−12.3085	+	5.85854i	−0.445890	+	0.212232i
$763$	54.5657	+	75.1032i	1.97541	+	2.71892i
$764$	−14.2817	+	19.6571i	−0.516695	+	0.711170i
$765$	28.5133	−	31.7832i	1.03090	−	1.14912i
$766$	−38.9097	−	53.5547i	−1.40587	−	1.93501i
$767$	−14.6943	−	4.77447i	−0.530580	−	0.172396i
$768$	−9.33630	+	50.1457i	−0.336895	+	1.80948i
$769$	7.74735	+	2.51727i	0.279377	+	0.0907750i	0.445354	−	0.895355i	$-0.353078\pi$
$769$	7.74735	+	2.51727i	0.279377	+	0.0907750i	−0.165977	+	0.986130i	$0.553078\pi$
$770$	22.1309	−	85.7224i	0.797544	−	3.08922i
$771$	33.7908	−	4.42060i	1.21695	−	0.159204i
$772$	1.47616	+	4.54314i	0.0531280	+	0.163511i
$773$	−6.40773	−	4.65549i	−0.230470	−	0.167446i	0.466557	−	0.884491i	$-0.345494\pi$
$773$	−6.40773	−	4.65549i	−0.230470	−	0.167446i	−0.697027	+	0.717045i	$0.745494\pi$
$774$	13.4442	−	34.8532i	0.483242	−	1.25277i
$775$	27.3560	+	2.68456i	0.982658	+	0.0964322i
$776$	−1.24218			−0.0445915
$777$	23.7119	+	25.0280i	0.850659	+	0.897874i
$778$	7.02993	+	21.6359i	0.252035	+	0.775684i
$779$	−40.8305	+	13.2666i	−1.46290	+	0.475326i
$780$	20.7641	−	8.66489i	0.743473	−	0.310253i
$781$	−3.05678	−	0.631559i	−0.109380	−	0.0225990i
$782$	48.5901			1.73758
$783$	−18.4638	−	21.7259i	−0.659844	−	0.776419i
$784$	−40.0779	+	29.1183i	−1.43135	+	1.03994i
$785$	20.5301	+	16.5080i	0.732752	+	0.589197i
$786$	−5.66396	−	5.97834i	−0.202027	−	0.213240i
$787$	23.3785	−	16.9854i	0.833352	−	0.605466i	−0.0871536	−	0.996195i	$-0.527777\pi$
$787$	23.3785	−	16.9854i	0.833352	−	0.605466i	0.920506	+	0.390729i	$0.127777\pi$
$788$	−11.2354	−	15.4642i	−0.400246	−	0.550891i
$789$	−8.37495	−	8.83979i	−0.298156	−	0.314705i
$790$	−21.5634	−	32.9553i	−0.767192	−	1.17250i
$791$	−36.2424	+	26.3317i	−1.28863	+	0.936246i
$792$	−36.1715	−	23.2816i	−1.28530	−	0.827275i
$793$		−	12.3480i		−	0.438491i
$794$	10.6571	−	32.7993i	0.378207	−	1.16400i
$795$	−0.481180	−	0.114182i	−0.0170657	−	0.00404961i
$796$	9.19748	+	28.3069i	0.325996	+	1.00331i
$797$	−1.47270	−	4.53250i	−0.0521657	−	0.160550i	0.921580	−	0.388189i	$-0.126899\pi$
$797$	−1.47270	−	4.53250i	−0.0521657	−	0.160550i	−0.973745	+	0.227639i	$0.926899\pi$
$798$	92.9146	−	88.0287i	3.28914	−	3.11618i
$799$		−	9.35453i		−	0.330940i
$800$	9.11232	−	2.00269i	0.322169	−	0.0708057i
$801$	−13.3873	+	34.7056i	−0.473016	+	1.22626i
$802$	−52.2892	−	37.9904i	−1.84640	−	1.34149i
$803$	−0.981046	−	2.17011i	−0.0346204	−	0.0765815i
$804$	1.97818	+	15.1211i	0.0697649	+	0.533280i
$805$	−33.9292	+	9.21687i	−1.19585	+	0.324852i
$806$	19.2642	+	6.25931i	0.678552	+	0.220475i
$807$	−41.7252	−	7.76853i	−1.46880	−	0.273465i
$808$	8.15552	+	2.64989i	0.286910	+	0.0932228i
$809$	−10.5403	+	7.65798i	−0.370577	+	0.269240i	−0.757450	−	0.652893i	$-0.773555\pi$
$809$	−10.5403	+	7.65798i	−0.370577	+	0.269240i	0.386873	+	0.922133i	$0.373555\pi$
$810$	34.2649	+	34.2522i	1.20395	+	1.20350i
$811$	−7.70056	+	10.5989i	−0.270403	+	0.372178i	−0.922526	−	0.385935i	$-0.873879\pi$
$811$	−7.70056	+	10.5989i	−0.270403	+	0.372178i	0.652122	+	0.758114i	$0.273879\pi$
$812$	−83.5551	+	60.7063i	−2.93221	+	2.13037i
$813$	−15.1232	+	7.19827i	−0.530395	+	0.252454i
$814$	27.8486	+	15.8675i	0.976092	+	0.556157i
$815$	22.2132	+	1.08732i	0.778093	+	0.0380872i
$816$	−28.0376	+	13.3452i	−0.981514	+	0.467175i
$817$	30.4504	+	9.89393i	1.06532	+	0.346145i
$818$	58.5556			2.04735
$819$	−14.3568	+	17.6701i	−0.501666	+	0.617443i
$820$	−56.8076	+	15.4318i	−1.98381	+	0.538900i
$821$	14.5397	+	44.7485i	0.507437	+	1.56173i	0.796634	+	0.604462i	$0.206612\pi$
$821$	14.5397	+	44.7485i	0.507437	+	1.56173i	−0.289197	+	0.957270i	$0.593388\pi$
$822$	−7.59082	−	58.0239i	−0.264760	−	2.02381i
$823$	1.29899	−	1.78791i	0.0452800	−	0.0623226i	−0.785777	−	0.618510i	$-0.787736\pi$
$823$	1.29899	−	1.78791i	0.0452800	−	0.0623226i	0.831057	+	0.556188i	$0.187736\pi$
$824$	40.6104			1.41473
$825$	−4.90128	+	28.3015i	−0.170641	+	0.985333i
$826$	−120.516			−4.19328
$827$	2.33377	−	3.21216i	0.0811530	−	0.111698i	−0.766510	−	0.642232i	$-0.778009\pi$
$827$	2.33377	−	3.21216i	0.0811530	−	0.111698i	0.847664	+	0.530534i	$0.178009\pi$
$828$	−1.94861	+	36.0557i	−0.0677190	+	1.25302i
$829$	10.8712	+	33.4582i	0.377573	+	1.16205i	0.941726	+	0.336380i	$0.109203\pi$
$829$	10.8712	+	33.4582i	0.377573	+	1.16205i	−0.564153	+	0.825670i	$0.690797\pi$
$830$	1.54659	−	31.5957i	0.0536830	−	1.09670i
$831$	−19.6238	−	10.6756i	−0.680743	−	0.370333i
$832$	15.4964			0.537239
$833$	106.475	+	34.5958i	3.68914	+	1.19867i
$834$	21.3091	+	44.7695i	0.737875	+	1.55024i
$835$	13.2403	−	8.66346i	0.458201	−	0.299811i
$836$	38.5796	−	67.7097i	1.33430	−	2.34179i
$837$	2.17152	+	28.4831i	0.0750588	+	0.984522i
$838$	35.2048	−	25.5778i	1.21613	−	0.883570i
$839$	−12.4401	+	17.1223i	−0.429479	+	0.591127i	−0.967834	−	0.251591i	$-0.919046\pi$
$839$	−12.4401	+	17.1223i	−0.429479	+	0.591127i	0.538355	+	0.842718i	$0.319046\pi$
$840$	62.9935	−	54.0891i	2.17348	−	1.86625i
$841$	−0.896709	+	0.651497i	−0.0309210	+	0.0224654i
$842$	48.3255	+	15.7019i	1.66541	+	0.541123i
$843$	−2.98148	+	16.0137i	−0.102688	+	0.551540i
$844$	52.0494	+	16.9119i	1.79162	+	0.582131i
$845$	13.0483	+	19.9417i	0.448876	+	0.686016i
$846$	10.5988	+	0.572809i	0.364396	+	0.0196936i
$847$	27.8092	+	46.9241i	0.955537	+	1.61233i
$848$	0.290958	+	0.211393i	0.00999154	+	0.00725928i
$849$	7.88612	−	42.3568i	0.270651	−	1.45368i
$850$	57.2912	+	50.8740i	1.96507	+	1.74496i
$851$		−	12.7286i		−	0.436332i
$852$	−4.25547	−	4.49166i	−0.145790	−	0.153882i
$853$	13.0791	+	40.2535i	0.447821	+	1.37825i	0.879360	+	0.476158i	$0.157971\pi$
$853$	13.0791	+	40.2535i	0.447821	+	1.37825i	−0.431539	+	0.902094i	$0.642029\pi$
$854$	−29.7633	−	91.6020i	−1.01848	−	3.13456i
$855$	−27.7294	+	30.9094i	−0.948324	+	1.05708i
$856$	−8.82130	+	27.1492i	−0.301506	+	0.927940i
$857$		−	35.4565i		−	1.21117i	−0.795780	−	0.605586i	$-0.792939\pi$
$857$		−	35.4565i		−	1.21117i	0.795780	−	0.605586i	$-0.207061\pi$
$858$	−8.00430	+	19.5940i	−0.273262	+	0.668930i
$859$	25.0513	−	18.2009i	0.854740	−	0.621005i	−0.0717086	−	0.997426i	$-0.522845\pi$
$859$	25.0513	−	18.2009i	0.854740	−	0.621005i	0.926449	+	0.376420i	$0.122845\pi$
$860$	41.0392	+	15.5912i	1.39942	+	0.531657i
$861$	43.2418	−	40.9679i	1.47368	−	1.39618i
$862$	−27.8627	−	38.3497i	−0.949008	−	1.30620i
$863$	38.4427	−	27.9303i	1.30861	−	0.950758i	0.308606	−	0.951190i	$-0.400138\pi$
$863$	38.4427	−	27.9303i	1.30861	−	0.950758i	1.00000		0.000432303i	$0.000137606\pi$
$864$	3.68848	+	8.96682i	0.125485	+	0.305057i
$865$	2.93008	+	10.7862i	0.0996257	+	0.366743i
$866$	−18.1828	+	13.2106i	−0.617877	+	0.448914i
$867$	35.7778	+	19.4636i	1.21508	+	0.661018i
$868$	103.475			3.51217
$869$	23.7623	+	4.90951i	0.806080	+	0.166544i
$870$	38.8162	−	33.3293i	1.31599	−	1.12997i
$871$	3.37623	−	1.09700i	0.114399	−	0.0371706i
$872$	25.0111	+	76.9762i	0.846982	+	2.60674i
$873$	−0.723667	+	0.468277i	−0.0244924	+	0.0158488i
$874$	−47.2542			−1.59840
$875$	−49.6551	−	24.6567i	−1.67865	−	0.833547i
$876$	0.864113	−	4.64120i	0.0291957	−	0.156812i
$877$	−16.0137	−	11.6347i	−0.540746	−	0.392875i	0.283616	−	0.958938i	$-0.408466\pi$
$877$	−16.0137	−	11.6347i	−0.540746	−	0.392875i	−0.824362	+	0.566063i	$0.808466\pi$
$878$	1.27525	+	3.92482i	0.0430376	+	0.132456i
$879$	−6.13660	−	46.9078i	−0.206982	−	1.58216i
$880$	11.2157	−	17.6215i	0.378082	−	0.594019i
$881$	19.5852	+	6.36360i	0.659841	+	0.214395i	0.619748	−	0.784801i	$-0.287235\pi$
$881$	19.5852	+	6.36360i	0.659841	+	0.214395i	0.0400925	+	0.999196i	$0.487235\pi$
$882$	−45.7174	+	118.519i	−1.53939	+	3.99076i
$883$	−40.5617	−	13.1793i	−1.36501	−	0.443518i	−0.467296	−	0.884101i	$-0.654772\pi$
$883$	−40.5617	−	13.1793i	−1.36501	−	0.443518i	−0.897712	+	0.440582i	$0.854772\pi$
$884$	21.7347	+	29.9153i	0.731018	+	1.00616i
$885$	38.9702	−	3.17031i	1.30997	−	0.106569i
$886$	−10.9749	+	15.1057i	−0.368709	+	0.507485i
$887$	−9.23778	−	12.7147i	−0.310174	−	0.426918i	0.625261	−	0.780415i	$-0.284992\pi$
$887$	−9.23778	−	12.7147i	−0.310174	−	0.426918i	−0.935436	+	0.353497i	$0.884992\pi$
$888$	12.9187	+	27.1415i	0.433522	+	0.910810i
$889$	13.1146	+	9.52833i	0.439850	+	0.319570i
$890$	−62.3972	−	23.7054i	−2.09156	−	0.794607i
$891$	−29.8495	+	0.0726135i	−0.999997	+	0.00243264i
$892$	20.1267	+	6.53956i	0.673892	+	0.218961i
$893$			9.09734i			0.304431i
$894$	−18.8192	+	34.5932i	−0.629407	+	1.15697i
$895$	0.767244	−	2.01953i	0.0256462	−	0.0675056i
$896$	97.3578	−	31.6335i	3.25249	−	1.05680i
$897$	8.33453	−	1.09034i	0.278282	−	0.0364055i
$898$	9.72736	+	7.06734i	0.324606	+	0.235840i
$899$	30.1653			1.00607
$900$	−40.0480	+	40.4721i	−1.33493	+	1.34907i
$901$		−	0.812766i		−	0.0270772i
$902$	27.4149	−	48.1150i	0.912817	−	1.60205i
$903$	−44.0482	+	5.76249i	−1.46583	+	0.191764i
$904$	−37.1463	+	12.0696i	−1.23547	+	0.401427i
$905$	−11.7463	−	17.9518i	−0.390459	−	0.596738i
$906$	41.7958	+	22.7375i	1.38857	+	0.755401i
$907$			5.74334i			0.190705i	0.995444	+	0.0953523i	$0.0303978\pi$
$907$			5.74334i			0.190705i	−0.995444	+	0.0953523i	$0.969602\pi$
$908$	−69.1394	−	22.4647i	−2.29447	−	0.745519i
$909$	5.75020	−	1.53071i	0.190722	−	0.0507704i
$910$	−31.8378	−	25.6004i	−1.05541	−	0.848646i
$911$	11.0306	−	15.1823i	0.365460	−	0.503012i	−0.586200	−	0.810166i	$-0.699377\pi$
$911$	11.0306	−	15.1823i	0.365460	−	0.503012i	0.951660	+	0.307154i	$0.0993767\pi$
$912$	27.2668	−	12.9783i	0.902893	−	0.429754i
$913$	13.1234	+	14.4090i	0.434320	+	0.476870i
$914$	34.2917	−	47.1985i	1.13427	−	1.56119i
$915$	12.0340	+	28.8376i	0.397832	+	0.953343i
$916$	−82.2292	+	59.7430i	−2.71693	+	1.97396i
$917$	−3.02632	+	9.31404i	−0.0999377	+	0.307577i
$918$	−41.7698	+	67.7891i	−1.37861	+	2.23737i
$919$	−4.34001	−	1.41015i	−0.143164	−	0.0465167i	0.236559	−	0.971617i	$-0.423980\pi$
$919$	−4.34001	−	1.41015i	−0.143164	−	0.0465167i	−0.379722	+	0.925101i	$0.623980\pi$
$920$	−30.6171	−	1.49869i	−1.00942	−	0.0494104i
$921$	−50.5527	+	6.61342i	−1.66577	+	0.217920i
$922$	−5.32386	+	1.72983i	−0.175332	+	0.0569689i
$923$	−0.846615	+	1.16527i	−0.0278667	+	0.0383552i
$924$	−7.95722	+	107.832i	−0.261773	+	3.54742i
$925$	13.3269	−	15.0080i	0.438187	−	0.493460i
$926$	−57.3914			−1.88600
$927$	23.6588	−	15.3094i	0.777058	−	0.502826i
$928$	9.73761	−	3.16394i	0.319653	−	0.103861i
$929$	47.0291	−	15.2807i	1.54298	−	0.501343i	0.590780	−	0.806833i	$-0.298820\pi$
$929$	47.0291	−	15.2807i	1.54298	−	0.501343i	0.952195	+	0.305490i	$0.0988202\pi$
$930$	−51.0899	+	4.15626i	−1.67530	+	0.136289i
$931$	−103.547	−	33.6446i	−3.39363	−	1.10266i
$932$			4.91633i			0.161040i
$933$	−22.3310	+	41.0487i	−0.731085	+	1.34387i
$934$	32.3829	+	44.5712i	1.05960	+	1.45841i
$935$	−47.1159	+	2.90158i	−1.54086	+	0.0948919i
$936$	−16.6652	+	10.7839i	−0.544720	+	0.352483i
$937$	−34.1075	+	24.7805i	−1.11424	+	0.809545i	−0.983327	−	0.181849i	$-0.941792\pi$
$937$	−34.1075	+	24.7805i	−1.11424	+	0.809545i	−0.130916	+	0.991393i	$0.541792\pi$
$938$	22.4019	−	16.2759i	0.731449	−	0.531429i
$939$	−2.06453	−	2.17912i	−0.0673733	−	0.0711128i
$940$	−0.609861	+	12.4590i	−0.0198915	+	0.406368i
$941$	−24.1952	+	17.5788i	−0.788740	+	0.573053i	−0.907589	−	0.419859i	$-0.862079\pi$
$941$	−24.1952	+	17.5788i	−0.788740	+	0.573053i	0.118849	+	0.992912i	$0.462079\pi$
$942$	−43.1538	−	23.4762i	−1.40603	−	0.764896i
$943$	−21.9918			−0.716150
$944$	−27.0422	−	8.78653i	−0.880147	−	0.285977i
$945$	16.3082	−	55.2586i	0.530505	−	1.79756i
$946$	−37.6321	+	17.0124i	−1.22353	+	0.553122i
$947$	13.9935	+	43.0675i	0.454727	+	1.39951i	0.871455	+	0.490475i	$0.163177\pi$
$947$	13.9935	+	43.0675i	0.454727	+	1.39951i	−0.416729	+	0.909031i	$0.636823\pi$
$948$	33.0805	+	34.9166i	1.07440	+	1.13404i
$949$	−1.09898			−0.0356742
$950$	−55.7161	−	49.4752i	−1.80767	−	1.60519i
$951$	−1.33084	+	7.14799i	−0.0431553	+	0.231790i
$952$	110.395	+	80.2068i	3.57793	+	2.59952i
$953$	0.663543	−	0.215598i	0.0214943	−	0.00698391i	−0.298250	−	0.954488i	$-0.596403\pi$
$953$	0.663543	−	0.215598i	0.0214943	−	0.00698391i	0.319744	+	0.947504i	$0.396403\pi$
$954$	0.920878	+	0.0497684i	0.0298145	+	0.00161131i
$955$	−14.2963	−	0.699796i	−0.462617	−	0.0226449i
$956$	15.9147	−	48.9804i	0.514718	−	1.58414i
$957$	−2.31971	+	31.4356i	−0.0749856	+	1.01617i
$958$	−44.7064	−	14.5260i	−1.44440	−	0.469313i
$959$	−56.2988	+	40.9034i	−1.81798	+	1.32084i
$960$	−36.1903	+	15.1023i	−1.16804	+	0.487424i
$961$	0.629082	+	0.457055i	0.0202930	+	0.0147437i
$962$	11.9657	−	8.69357i	0.385789	−	0.280292i
$963$	5.09562	+	19.1420i	0.164204	+	0.616844i
$964$	37.7678	−	51.9830i	1.21642	−	1.67426i
$965$	−1.76338	+	2.19302i	−0.0567652	+	0.0705957i
$966$	59.2004	−	28.1778i	1.90474	−	0.906607i
$967$	−14.8366	+	45.6624i	−0.477114	+	1.46840i	0.365972	+	0.930626i	$0.380737\pi$
$967$	−14.8366	+	45.6624i	−0.477114	+	1.46840i	−0.843086	+	0.537779i	$0.819263\pi$
$968$	10.4169	+	46.4015i	0.334811	+	1.49140i
$969$	−59.9482	−	32.6126i	−1.92581	−	1.04767i
$970$	−0.846868	−	1.29427i	−0.0271913	−	0.0415564i
$971$	−40.8869	+	13.2850i	−1.31212	+	0.426335i	−0.879783	−	0.475376i	$-0.842312\pi$
$971$	−40.8869	+	13.2850i	−1.31212	+	0.426335i	−0.432340	+	0.901710i	$0.642312\pi$
$972$	−48.6270	−	33.7134i	−1.55971	−	1.08136i
$973$	34.6572	−	47.7015i	1.11106	−	1.52924i
$974$	31.9155			1.02264
$975$	10.9686	+	7.44068i	0.351276	+	0.238292i
$976$		−	22.7243i		−	0.727386i
$977$	−0.633566	−	0.460313i	−0.0202696	−	0.0147267i	0.577604	−	0.816317i	$-0.303988\pi$
$977$	−0.633566	−	0.460313i	−0.0202696	−	0.0147267i	−0.597874	+	0.801590i	$0.703988\pi$
$978$	−41.1223	+	5.37972i	−1.31495	+	0.172024i
$979$	37.4728	−	16.9404i	1.19763	−	0.541417i
$980$	−139.555	−	53.0185i	−4.45792	−	1.69361i
$981$	43.5896	+	35.4161i	1.39171	+	1.13075i
$982$		−	13.0758i		−	0.417267i
$983$	−10.2129	+	31.4321i	−0.325741	+	1.00253i	0.645364	+	0.763876i	$0.276706\pi$
$983$	−10.2129	+	31.4321i	−0.325741	+	1.00253i	−0.971105	+	0.238653i	$0.923294\pi$
$984$	46.8934	−	22.3201i	1.49491	−	0.711537i
$985$	3.99906	−	10.5263i	0.127421	−	0.335396i
$986$	68.0247	+	49.4229i	2.16635	+	1.57394i
$987$	−5.42478	−	11.3972i	−0.172673	−	0.362777i
$988$	−21.1371	−	29.0928i	−0.672462	−	0.925565i
$989$	13.2686	+	9.64021i	0.421917	+	0.306541i
$990$	−0.402475	−	53.5608i	−0.0127915	−	1.70227i
$991$	28.0926	−	20.4104i	0.892390	−	0.648359i	−0.0441102	−	0.999027i	$-0.514045\pi$
$991$	28.0926	−	20.4104i	0.892390	−	0.648359i	0.936500	+	0.350667i	$0.114045\pi$
$992$	−9.75603	−	3.16993i	−0.309754	−	0.100645i
$993$	−7.59742	+	40.8061i	−0.241097	+	1.29494i
$994$	−3.47177	+	10.6850i	−0.110118	+	0.338908i
$995$	−10.9871	+	13.6640i	−0.348314	+	0.433179i
$996$	5.01150	+	38.3077i	0.158795	+	1.21382i
$997$	15.7401	+	48.4431i	0.498495	+	1.53421i	0.811438	+	0.584438i	$0.198685\pi$
$997$	15.7401	+	48.4431i	0.498495	+	1.53421i	−0.312944	+	0.949772i	$0.601315\pi$
$998$	9.76508	−	13.4405i	0.309108	−	0.425451i
$999$	17.7580	+	10.9420i	0.561839	+	0.346190i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.ce.c.659.14	yes	448
3.2	odd	2	inner	825.2.ce.c.659.99	yes	448
11.10	odd	2	inner	825.2.ce.c.659.100	yes	448
25.14	even	10	inner	825.2.ce.c.164.13	✓	448
33.32	even	2	inner	825.2.ce.c.659.13	yes	448
75.14	odd	10	inner	825.2.ce.c.164.100	yes	448
275.164	odd	10	inner	825.2.ce.c.164.99	yes	448
825.164	even	10	inner	825.2.ce.c.164.14	yes	448

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.ce.c.164.13	✓	448	25.14	even	10	inner
825.2.ce.c.164.14	yes	448	825.164	even	10	inner
825.2.ce.c.164.99	yes	448	275.164	odd	10	inner
825.2.ce.c.164.100	yes	448	75.14	odd	10	inner
825.2.ce.c.659.13	yes	448	33.32	even	2	inner
825.2.ce.c.659.14	yes	448	1.1	even	1	trivial
825.2.ce.c.659.99	yes	448	3.2	odd	2	inner
825.2.ce.c.659.100	yes	448	11.10	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.ce (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41506 + 1.94767i) q^{2} +(1.71742 - 0.224677i) q^{3} +(-1.17297 - 3.61003i) q^{4} +(1.40120 - 1.74259i) q^{5} +(-1.99266 + 3.66289i) q^{6} +4.95869 q^{7} +(4.11171 + 1.33598i) q^{8} +(2.89904 - 0.771727i) q^{9} +O(q^{10})\)	\(q+(-1.41506 + 1.94767i) q^{2} +(1.71742 - 0.224677i) q^{3} +(-1.17297 - 3.61003i) q^{4} +(1.40120 - 1.74259i) q^{5} +(-1.99266 + 3.66289i) q^{6} +4.95869 q^{7} +(4.11171 + 1.33598i) q^{8} +(2.89904 - 0.771727i) q^{9} +(1.41121 + 5.19495i) q^{10} +(-2.88168 - 1.64192i) q^{11} +(-2.82556 - 5.93638i) q^{12} +(-1.23817 + 0.899583i) q^{13} +(-7.01686 + 9.65788i) q^{14} +(2.01493 - 3.30758i) q^{15} +(-2.27863 + 1.65552i) q^{16} +(6.05362 + 1.96694i) q^{17} +(-2.59926 + 6.73841i) q^{18} +(-5.88718 - 1.91286i) q^{19} +(-7.93438 - 3.01436i) q^{20} +(8.51614 - 1.11410i) q^{21} +(7.27568 - 3.28913i) q^{22} +(-2.56531 - 1.86381i) q^{23} +(7.36169 + 1.37062i) q^{24} +(-1.07327 - 4.88345i) q^{25} -3.68451i q^{26} +(4.80547 - 1.97672i) q^{27} +(-5.81639 - 17.9010i) q^{28} +(-1.69561 - 5.21855i) q^{29} +(3.59082 + 8.60483i) q^{30} +(-1.69882 + 5.22843i) q^{31} +1.86596i q^{32} +(-5.31795 - 2.17242i) q^{33} +(-12.3972 + 9.00708i) q^{34} +(6.94812 - 8.64099i) q^{35} +(-6.18644 - 9.56040i) q^{36} +(2.35949 + 3.24756i) q^{37} +(12.0563 - 8.75944i) q^{38} +(-1.92434 + 1.82315i) q^{39} +(8.08940 - 5.29308i) q^{40} +(5.61093 - 4.07658i) q^{41} +(-9.88098 + 18.1631i) q^{42} -5.17232 q^{43} +(-2.54726 + 12.3289i) q^{44} +(2.71733 - 6.13320i) q^{45} +(7.26015 - 2.35897i) q^{46} +(-0.454147 - 1.39772i) q^{47} +(-3.54139 + 3.35517i) q^{48} +17.5886 q^{49} +(11.0301 + 4.82001i) q^{50} +(10.8385 + 2.01795i) q^{51} +(4.69986 + 3.41465i) q^{52} +(-0.0394584 - 0.121441i) q^{53} +(-2.95005 + 12.1566i) q^{54} +(-6.89902 + 2.72094i) q^{55} +(20.3887 + 6.62470i) q^{56} +(-10.5405 - 1.96247i) q^{57} +(12.5634 + 4.08209i) q^{58} +(5.93388 + 8.16728i) q^{59} +(-14.3039 - 3.39425i) q^{60} +(-4.74234 + 6.52728i) q^{61} +(-7.77929 - 10.7073i) q^{62} +(14.3755 - 3.82676i) q^{63} +(-8.19152 - 5.95149i) q^{64} +(-0.167315 + 3.41813i) q^{65} +(11.7564 - 7.28348i) q^{66} +(-2.20602 - 0.716780i) q^{67} -24.1609i q^{68} +(-4.82446 - 2.62457i) q^{69} +(6.99774 + 25.7602i) q^{70} +(0.895057 - 0.290822i) q^{71} +(12.9510 + 0.699932i) q^{72} +(0.580929 + 0.422069i) q^{73} -9.66400 q^{74} +(-2.94046 - 8.14578i) q^{75} +23.4966i q^{76} +(-14.2894 - 8.14179i) q^{77} +(-0.827823 - 6.32784i) q^{78} +(-6.95785 + 2.26074i) q^{79} +(-0.307913 + 6.29043i) q^{80} +(7.80888 - 4.47453i) q^{81} +16.6968i q^{82} +(-5.58872 - 1.81588i) q^{83} +(-14.0111 - 29.4367i) q^{84} +(11.9099 - 7.79292i) q^{85} +(7.31916 - 10.0740i) q^{86} +(-4.08456 - 8.58147i) q^{87} +(-9.65508 - 10.6010i) q^{88} +(-7.28816 + 10.0313i) q^{89} +(8.10023 + 13.9713i) q^{90} +(-6.13971 + 4.46076i) q^{91} +(-3.71937 + 11.4470i) q^{92} +(-1.74287 + 9.36107i) q^{93} +(3.36494 + 1.09333i) q^{94} +(-11.5825 + 7.57867i) q^{95} +(0.419237 + 3.20463i) q^{96} +(-0.273258 + 0.0887869i) q^{97} +(-24.8890 + 34.2568i) q^{98} +(-9.62123 - 2.53613i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 448 q - 10 q^{3} + 108 q^{4} - 14 q^{9}+O(q^{10}) \) 448 * q - 10 * q^3 + 108 * q^4 - 14 * q^9	\( 448 q - 10 q^{3} + 108 q^{4} - 14 q^{9} - 40 q^{12} - 10 q^{15} - 140 q^{16} + 10 q^{22} - 36 q^{25} - 10 q^{27} - 32 q^{31} + 20 q^{33} - 28 q^{34} - 6 q^{36} - 20 q^{37} - 70 q^{42} + 82 q^{45} - 60 q^{48} + 440 q^{49} + 6 q^{55} + 40 q^{58} + 88 q^{60} + 188 q^{64} - 30 q^{66} - 140 q^{67} + 34 q^{69} - 76 q^{70} + 70 q^{75} + 60 q^{78} + 50 q^{81} - 80 q^{88} - 80 q^{91} + 120 q^{97} - 40 q^{99}+O(q^{100}) \) 448 * q - 10 * q^3 + 108 * q^4 - 14 * q^9 - 40 * q^12 - 10 * q^15 - 140 * q^16 + 10 * q^22 - 36 * q^25 - 10 * q^27 - 32 * q^31 + 20 * q^33 - 28 * q^34 - 6 * q^36 - 20 * q^37 - 70 * q^42 + 82 * q^45 - 60 * q^48 + 440 * q^49 + 6 * q^55 + 40 * q^58 + 88 * q^60 + 188 * q^64 - 30 * q^66 - 140 * q^67 + 34 * q^69 - 76 * q^70 + 70 * q^75 + 60 * q^78 + 50 * q^81 - 80 * q^88 - 80 * q^91 + 120 * q^97 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more