LMFDB - Embedded newform 825.2.ce.c.659.13

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			659.13
Character	$\chi$	$=$	825.659
Dual form			825.2.ce.c.164.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41506 + 1.94767i) q^{2} +(1.52148 - 0.827705i) q^{3} +(-1.17297 - 3.61003i) q^{4} +(-1.40120 + 1.74259i) q^{5} +(-0.540897 + 4.13459i) q^{6} -4.95869 q^{7} +(4.11171 + 1.33598i) q^{8} +(1.62981 - 2.51868i) q^{9} +O(q^{10})$	\(q+(-1.41506 + 1.94767i) q^{2} +(1.52148 - 0.827705i) q^{3} +(-1.17297 - 3.61003i) q^{4} +(-1.40120 + 1.74259i) q^{5} +(-0.540897 + 4.13459i) q^{6} -4.95869 q^{7} +(4.11171 + 1.33598i) q^{8} +(1.62981 - 2.51868i) q^{9} +(-1.41121 - 5.19495i) q^{10} +(-2.45205 - 2.23326i) q^{11} +(-4.77269 - 4.52171i) q^{12} +(1.23817 - 0.899583i) q^{13} +(7.01686 - 9.65788i) q^{14} +(-0.689545 + 3.81111i) 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} +(-7.54456 + 4.10434i) q^{21} +(7.81945 - 1.61557i) q^{22} +(2.56531 + 1.86381i) q^{23} +(7.36169 - 1.37062i) q^{24} +(-1.07327 - 4.88345i) q^{25} +3.68451i q^{26} +(0.395002 - 5.18112i) q^{27} +(5.81639 + 17.9010i) q^{28} +(-1.69561 - 5.21855i) q^{29} +(-6.44701 - 6.73596i) q^{30} +(-1.69882 + 5.22843i) q^{31} +1.86596i q^{32} +(-5.57923 - 1.36829i) q^{33} +(-12.3972 + 9.00708i) q^{34} +(6.94812 - 8.64099i) q^{35} +(-11.0042 - 2.92933i) q^{36} +(2.35949 + 3.24756i) q^{37} +(-12.0563 + 8.75944i) q^{38} +(1.13926 - 2.39354i) q^{39} +(-8.08940 + 5.29308i) q^{40} +(5.61093 - 4.07658i) q^{41} +(2.68214 - 20.5022i) q^{42} +5.17232 q^{43} +(-5.18595 + 11.4715i) q^{44} +(2.10534 + 6.36926i) q^{45} +(-7.26015 + 2.35897i) q^{46} +(0.454147 + 1.39772i) q^{47} +(-2.09660 + 4.40487i) 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} +(9.53213 + 8.10094i) q^{54} +(7.32748 - 1.14368i) 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} +(14.5670 - 1.98103i) q^{60} +(4.74234 - 6.52728i) q^{61} +(-7.77929 - 10.7073i) q^{62} +(-8.08172 + 12.4893i) q^{63} +(-8.19152 - 5.95149i) q^{64} +(-0.167315 + 3.41813i) q^{65} +(10.5599 - 8.93026i) q^{66} +(-2.20602 - 0.716780i) q^{67} -24.1609i q^{68} +(5.44576 + 0.712427i) q^{69} +(6.99774 + 25.7602i) q^{70} +(-0.895057 + 0.290822i) q^{71} +(10.0662 - 8.17869i) q^{72} +(-0.580929 - 0.422069i) q^{73} -9.66400 q^{74} +(-5.67502 - 6.54172i) q^{75} -23.4966i q^{76} +(12.1590 + 11.0741i) q^{77} +(3.04969 + 5.60591i) q^{78} +(6.95785 - 2.26074i) q^{79} +(0.307913 - 6.29043i) q^{80} +(-3.68745 - 8.20992i) q^{81} +16.6968i q^{82} +(-5.58872 - 1.81588i) q^{83} +(23.6663 + 22.4218i) q^{84} +(-11.9099 + 7.79292i) q^{85} +(-7.31916 + 10.0740i) q^{86} +(-6.89926 - 6.53646i) q^{87} +(-7.09854 - 12.4584i) q^{88} +(7.28816 - 10.0313i) q^{89} +(-15.3844 - 4.91240i) 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} +(1.54446 + 2.83902i) 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	$0.875899\pi$
$3$	1.52148	−	0.827705i	0.878427	−	0.477876i
$3$	1.52148	−	0.827705i	0.878427	−	0.477876i
$4$	−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
$6$	−0.540897	+	4.13459i	−0.220820	+	1.68794i
$7$	−4.95869			−1.87421			−0.937105	−	0.349048i	$-0.886505\pi$
$7$	−4.95869			−1.87421			−0.937105	+	0.349048i	$0.886505\pi$
$8$	4.11171	+	1.33598i	1.45371	+	0.472339i
$9$	1.62981	−	2.51868i	0.543270	−	0.839558i
$10$	−1.41121	−	5.19495i	−0.446263	−	1.64279i
$11$	−2.45205	−	2.23326i	−0.739321	−	0.673353i
$11$	−2.45205	−	2.23326i	−0.739321	−	0.673353i
$12$	−4.77269	−	4.52171i	−1.37776	−	1.30531i
$13$	1.23817	−	0.899583i	0.343407	−	0.249500i	−0.402691	−	0.915336i	$-0.631925\pi$
$13$	1.23817	−	0.899583i	0.343407	−	0.249500i	0.746098	+	0.665836i	$0.231925\pi$
$14$	7.01686	−	9.65788i	1.87534	−	2.58118i
$15$	−0.689545	+	3.81111i	−0.178040	+	0.984023i
$16$	−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	0.892898	−	0.450260i	$-0.148669\pi$
$19$	5.88718	+	1.91286i	1.35061	+	0.438840i	0.457713	+	0.889100i	$0.348669\pi$
$20$	7.93438	+	3.01436i	1.77418	+	0.674032i
$21$	−7.54456	+	4.10434i	−1.64636	+	0.895639i
$22$	7.81945	−	1.61557i	1.66711	−	0.344441i
$23$	2.56531	+	1.86381i	0.534904	+	0.388631i	0.822189	−	0.569214i	$-0.192753\pi$
$23$	2.56531	+	1.86381i	0.534904	+	0.388631i	−0.287285	+	0.957845i	$0.592753\pi$
$24$	7.36169	−	1.37062i	1.50270	−	0.279777i
$25$	−1.07327	−	4.88345i	−0.214655	−	0.976690i
$26$			3.68451i			0.722592i
$27$	0.395002	−	5.18112i	0.0760183	−	0.997106i
$28$	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	$-0.270157\pi$
$30$	−6.44701	−	6.73596i	−1.17706	−	1.22981i
$31$	−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
$33$	−5.57923	−	1.36829i	−0.971219	−	0.238189i
$34$	−12.3972	+	9.00708i	−2.12610	+	1.54470i
$35$	6.94812	−	8.64099i	1.17445	−	1.46059i
$36$	−11.0042	−	2.92933i	−1.83403	−	0.488221i
$37$	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
$39$	1.13926	−	2.39354i	0.182428	−	0.383273i
$40$	−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	$0.117830\pi$
$42$	2.68214	−	20.5022i	0.413864	−	3.16355i
$43$	5.17232			0.788772			0.394386	−	0.918945i	$-0.370957\pi$
$43$	5.17232			0.788772			0.394386	+	0.918945i	$0.370957\pi$
$44$	−5.18595	+	11.4715i	−0.781812	+	1.72940i
$45$	2.10534	+	6.36926i	0.313846	+	0.949474i
$46$	−7.26015	+	2.35897i	−1.07045	+	0.347811i
$47$	0.454147	+	1.39772i	0.0662441	+	0.203878i	0.978700	−	0.205298i	$-0.0658162\pi$
$47$	0.454147	+	1.39772i	0.0662441	+	0.203878i	−0.912456	+	0.409176i	$0.865816\pi$
$48$	−2.09660	+	4.40487i	−0.302619	+	0.635788i
$49$	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	0.953730	−	0.300665i	$-0.0972085\pi$
$53$	0.0394584	+	0.121441i	0.00542003	+	0.0166811i	−0.948310	+	0.317346i	$0.897208\pi$
$54$	9.53213	+	8.10094i	1.29716	+	1.10240i
$55$	7.32748	−	1.14368i	0.988037	−	0.154214i
$56$	−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	$-0.971762\pi$
$59$	−5.93388	−	8.16728i	−0.772525	−	1.06329i	0.223543	−	0.974694i	$-0.428238\pi$
$60$	14.5670	−	1.98103i	1.88059	−	0.255750i
$61$	4.74234	−	6.52728i	0.607195	−	0.835732i	−0.389148	−	0.921175i	$-0.627231\pi$
$61$	4.74234	−	6.52728i	0.607195	−	0.835732i	0.996343	+	0.0854432i	$0.0272306\pi$
$62$	−7.77929	−	10.7073i	−0.987971	−	1.35983i
$63$	−8.08172	+	12.4893i	−1.01820	+	1.57351i
$64$	−8.19152	−	5.95149i	−1.02394	−	0.743936i
$65$	−0.167315	+	3.41813i	−0.0207529	+	0.423966i
$66$	10.5599	−	8.93026i	1.29984	−	1.09924i
$67$	−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
$69$	5.44576	+	0.712427i	0.655592	+	0.0857661i
$70$	6.99774	+	25.7602i	0.836390	+	3.07893i
$71$	−0.895057	+	0.290822i	−0.106224	+	0.0345142i	−0.361647	−	0.932315i	$-0.617785\pi$
$71$	−0.895057	+	0.290822i	−0.106224	+	0.0345142i	0.255423	+	0.966829i	$0.417785\pi$
$72$	10.0662	−	8.17869i	1.18631	−	0.963867i
$73$	−0.580929	−	0.422069i	−0.0679925	−	0.0493995i	0.553270	−	0.833002i	$-0.313380\pi$
$73$	−0.580929	−	0.422069i	−0.0679925	−	0.0493995i	−0.621262	+	0.783603i	$0.713380\pi$
$74$	−9.66400			−1.12342
$75$	−5.67502	−	6.54172i	−0.655295	−	0.755373i
$76$		−	23.4966i		−	2.69524i
$77$	12.1590	+	11.0741i	1.38564	+	1.26201i
$78$	3.04969	+	5.60591i	0.345309	+	0.634744i
$79$	6.95785	−	2.26074i	0.782819	−	0.254353i	0.109776	−	0.993956i	$-0.464987\pi$
$79$	6.95785	−	2.26074i	0.782819	−	0.254353i	0.673043	+	0.739603i	$0.264987\pi$
$80$	0.307913	−	6.29043i	0.0344258	−	0.703292i
$81$	−3.68745	−	8.20992i	−0.409716	−	0.912213i
$82$			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	$0.704525\pi$
$84$	23.6663	+	22.4218i	2.58220	+	2.44642i
$85$	−11.9099	+	7.79292i	−1.29181	+	0.845261i
$86$	−7.31916	+	10.0740i	−0.789245	+	1.08630i
$87$	−6.89926	−	6.53646i	−0.739679	−	0.700782i
$88$	−7.09854	−	12.4584i	−0.756707	−	1.32807i
$89$	7.28816	−	10.0313i	0.772543	−	1.06331i	−0.223522	−	0.974699i	$-0.571756\pi$
$89$	7.28816	−	10.0313i	0.772543	−	1.06331i	0.996066	−	0.0886160i	$-0.0282444\pi$
$90$	−15.3844	−	4.91240i	−1.62166	−	0.517813i
$91$	−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
$96$	1.54446	+	2.83902i	0.157631	+	0.289756i
$97$	−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	$0.468537\pi$
$102$	−11.4069	+	23.9653i	−1.12945	+	2.37292i
$103$	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
$105$	3.41924	−	18.8981i	0.333684	−	1.84427i
$106$	−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	$0.896598\pi$
$108$	−19.1673	+	4.65132i	−1.84437	+	0.447573i
$109$	−11.0040	−	15.1458i	−1.05400	−	1.45070i	−0.885292	−	0.465035i	$-0.846042\pi$
$109$	−11.0040	−	15.1458i	−1.05400	−	1.45070i	−0.168704	−	0.985667i	$-0.553958\pi$
$110$	−8.14133	+	15.8899i	−0.776245	+	1.51504i
$111$	6.27795	+	2.98814i	0.595876	+	0.283622i
$112$	11.2990	−	8.20921i	1.06766	−	0.775697i
$113$	7.30886	−	5.31020i	0.687560	−	0.499542i	−0.188297	−	0.982112i	$-0.560297\pi$
$113$	7.30886	−	5.31020i	0.687560	−	0.499542i	0.875857	+	0.482570i	$0.160297\pi$
$114$	−11.0933	+	23.3064i	−1.03898	+	2.18285i
$115$	−6.84238	+	1.85873i	−0.638055	+	0.173327i
$116$	−16.8502	+	12.2424i	−1.56450	+	1.13668i
$117$	−0.247778	−	4.58470i	−0.0229071	−	0.423855i
$118$	24.3039			2.23736
$119$	−30.0180	−	9.75345i	−2.75175	−	0.894097i
$120$	−7.92676	+	14.7490i	−0.723611	+	1.34639i
$121$	1.02510	+	10.9521i	0.0931906	+	0.995648i
$122$	6.00224	+	18.4730i	0.543418	+	1.67247i
$123$	5.16272	−	10.8466i	0.465507	−	0.978009i
$124$	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	0.464227	−	0.885716i	$-0.346332\pi$
$127$	−2.64477	−	1.92154i	−0.234686	−	0.170509i	−0.698912	+	0.715207i	$0.746332\pi$
$128$	19.6338	−	6.37939i	1.73540	−	0.563864i
$129$	7.86959	−	4.28116i	0.692879	−	0.376935i
$130$	−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
$135$	8.47511	+	7.94811i	0.729421	+	0.684065i
$136$	22.2630	+	16.1750i	1.90903	+	1.38699i
$137$	11.3535	−	8.24883i	0.969999	−	0.704745i	0.0145476	−	0.999894i	$-0.495369\pi$
$137$	11.3535	−	8.24883i	0.969999	−	0.704745i	0.955451	+	0.295149i	$0.0953692\pi$
$138$	−9.09365	+	9.59839i	−0.774103	+	0.817069i
$139$	−6.98918	+	9.61978i	−0.592814	+	0.815939i	−0.995027	−	0.0996074i	$-0.968241\pi$
$139$	−6.98918	+	9.61978i	−0.592814	+	0.815939i	0.402212	+	0.915546i	$0.368241\pi$
$140$	−39.3442	−	14.9473i	−3.32519	−	1.26328i
$141$	1.84787	+	1.75070i	0.155619	+	0.147436i
$142$	0.700138	−	2.15480i	0.0587543	−	0.180827i
$143$	−5.04506	−	0.559333i	−0.421889	−	0.0467738i
$144$	0.455989	+	8.43729i	0.0379991	+	0.703108i
$145$	11.4697	+	4.35748i	0.952508	+	0.361869i
$146$	1.64410	−	0.534201i	0.136067	−	0.0442108i
$147$	26.7608	−	14.5582i	2.20719	−	1.20074i
$148$	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	$0.373563\pi$
$150$	20.7716	−	1.79611i	1.69599	−	0.146651i
$151$			11.4106i			0.928583i	0.885682	+	0.464292i	$0.153691\pi$
$151$			11.4106i			0.928583i	−0.885682	+	0.464292i	$0.846309\pi$
$152$	21.6509	+	15.7303i	1.75612	+	1.27589i
$153$	14.8203	−	12.0414i	1.19815	−	0.973486i
$154$	−38.7743	+	8.01113i	−3.12452	+	0.645555i
$155$	−6.73064	−	10.2864i	−0.540618	−	0.826225i
$156$	−9.97706	−	1.30522i	−0.798804	−	0.104501i
$157$			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
$159$	0.160552	+	0.152109i	0.0127326	+	0.0120631i
$160$	−3.25161	−	2.61458i	−0.257062	−	0.206701i
$161$	−12.7206	−	9.24205i	−1.00252	−	0.728376i
$162$	21.2081	+	4.43563i	1.66627	+	0.348496i
$163$	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
$165$	10.2020	−	7.80509i	0.794224	−	0.607625i
$166$	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
$171$	14.4128	−	11.7103i	1.10218	−	0.895508i
$172$	−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
$177$	−15.7884	−	7.51486i	−1.18673	−	0.564851i
$178$	9.22441	+	28.3898i	0.691399	+	2.12791i
$179$	−0.918859	+	0.298555i	−0.0686787	+	0.0223151i	−0.343155	−	0.939279i	$-0.611496\pi$
$179$	−0.918859	+	0.298555i	−0.0686787	+	0.0223151i	0.274476	+	0.961594i	$0.411496\pi$
$180$	20.5237	−	15.0713i	1.52975	−	1.12335i
$181$	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
$183$	1.81273	−	13.8564i	0.134001	−	1.02429i
$184$	8.05782	+	11.0906i	0.594031	+	0.817613i
$185$	−8.96531	−	0.438847i	−0.659143	−	0.0322647i
$186$	−20.6985	−	9.85196i	−1.51769	−	0.722381i
$187$	−10.4511	−	18.3423i	−0.764259	−	1.34132i
$188$	4.51310	−	3.27896i	0.329152	−	0.239143i
$189$	−1.95870	+	25.6916i	−0.142474	+	1.86879i
$190$	1.62919	−	33.2830i	0.118194	−	2.41461i
$191$	3.76250	+	5.17864i	0.272245	+	0.374713i	0.923146	−	0.384449i	$-0.125609\pi$
$191$	3.76250	+	5.17864i	0.272245	+	0.374713i	−0.650901	+	0.759163i	$0.725609\pi$
$192$	−17.3893	−	2.27491i	−1.25497	−	0.164178i
$193$	1.25848			0.0905872			0.0452936	−	0.998974i	$-0.485578\pi$
$193$	1.25848			0.0905872			0.0452936	+	0.998974i	$0.485578\pi$
$194$	0.213750	−	0.657855i	0.0153464	−	0.0472312i
$195$	2.57463	+	5.33910i	0.184373	+	0.382341i
$196$	−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	$0.342587\pi$
$198$	8.67510	−	22.3277i	0.616513	−	1.58676i
$199$	−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
$204$	−19.9981	−	36.7603i	−1.40015	−	2.57374i
$205$	−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
$209$	−10.1637	−	17.8380i	−0.703041	−	1.23388i
$210$	31.9688	+	33.4015i	2.20605	+	2.30493i
$211$	8.47470	−	11.6644i	0.583422	−	0.803012i	−0.410643	−	0.911796i	$-0.634696\pi$
$211$	8.47470	−	11.6644i	0.583422	−	0.803012i	0.994065	+	0.108784i	$0.0346957\pi$
$212$	0.392120	−	0.284892i	0.0269309	−	0.0195665i
$213$	−1.12110	+	1.18332i	−0.0768163	+	0.0810799i
$214$	−12.8602	−	9.34350i	−0.879107	−	0.638708i
$215$	−7.24746	+	9.01326i	−0.494273	+	0.614699i
$216$	8.54599	−	20.7756i	0.581481	−	1.41360i
$217$	8.42392	−	25.9262i	0.571853	−	1.75998i
$218$	45.0703			3.05255
$219$	−1.23322	−	0.161333i	−0.0833333	−	0.0109019i
$220$	−12.7236	−	25.1109i	−0.857828	−	1.69298i
$221$	9.26483	−	3.01033i	0.623220	−	0.202496i
$222$	−14.7036	+	7.99894i	−0.986840	+	0.536854i
$223$	−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
$225$	−14.0491	−	5.25586i	−0.936604	−	0.350391i
$226$			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	$-0.0192401\pi$
$228$	−19.4483	−	35.7496i	−1.28799	−	2.36758i
$229$	−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
$231$	27.6657	+	6.78492i	1.82027	+	0.446415i
$232$		−	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	$0.613509\pi$
$234$	9.28008	+	6.00505i	0.606658	+	0.392562i
$235$	−3.07201	−	1.16709i	−0.200396	−	0.0761327i
$236$	−22.5238	+	31.0014i	−1.46618	+	2.01802i
$237$	8.71500	−	9.19872i	0.566100	−	0.597521i
$238$	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	$0.555398\pi$
$240$	−4.73814	−	9.82564i	−0.305846	−	0.634242i
$241$	−9.94988	−	13.6948i	−0.640928	−	0.882162i	0.357736	−	0.933823i	$-0.383549\pi$
$241$	−9.94988	−	13.6948i	−0.640928	−	0.882162i	−0.998665	+	0.0516604i	$0.983549\pi$
$242$	−22.7817	−	13.5014i	−1.46446	−	0.867903i
$243$	−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
$246$	13.8201	+	25.4039i	0.881135	+	1.61970i
$247$	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	$0.157877\pi$
$251$			15.0793i			0.951797i	−0.879500	+	0.475898i	$0.842123\pi$
$252$	54.5664	+	14.5256i	3.43736	+	0.915028i
$253$	−2.12790	−	10.2992i	−0.133780	−	0.647502i
$254$	7.48504	−	2.43204i	0.469653	−	0.152600i
$255$	−11.6705	+	21.7147i	−0.730832	+	1.35983i
$256$	−9.10030	+	28.0078i	−0.568769	+	1.75049i
$257$	−19.6754			−1.22732			−0.613658	−	0.789572i	$-0.710303\pi$
$257$	−19.6754			−1.22732			−0.613658	+	0.789572i	$0.710303\pi$
$258$	−2.79769	+	21.3854i	−0.174177	+	1.33140i
$259$	−11.7000	−	16.1037i	−0.727003	−	1.00063i
$260$	12.5358	−	3.40534i	0.777436	−	0.211190i
$261$	−15.9074	−	4.23455i	−0.984641	−	0.262112i
$262$	−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	$0.869548\pi$
$264$	−21.1122	−	13.0797i	−1.29937	−	0.805002i
$265$	−0.266911	−	0.101402i	−0.0163962	−	0.00622910i
$266$	59.7837	−	43.4354i	3.66557	−	2.66319i
$267$	2.78585	−	21.2949i	0.170491	−	1.30322i
$268$			8.80456i			0.537824i
$269$	23.3047	+	7.57216i	1.42091	+	0.461682i	0.915892	−	0.401425i	$-0.131485\pi$
$269$	23.3047	+	7.57216i	1.42091	+	0.461682i	0.505021	+	0.863107i	$0.331485\pi$
$270$	−27.4731	+	5.25961i	−1.67196	+	0.320090i
$271$	9.19673	−	2.98820i	0.558662	−	0.181520i	−0.0160572	−	0.999871i	$-0.505111\pi$
$271$	9.19673	−	2.98820i	0.558662	−	0.181520i	0.574719	+	0.818351i	$0.305111\pi$
$272$	−17.0502	+	5.53995i	−1.03382	+	0.335909i
$273$	−5.64926	+	11.8688i	−0.341908	+	0.718334i
$274$			33.7855i			2.04106i
$275$	−8.27429	+	14.3714i	−0.498959	+	0.866626i
$276$	−3.81582	−	20.4950i	−0.229685	−	1.23365i
$277$	10.4346	+	7.58116i	0.626953	+	0.455508i	0.855343	−	0.518062i	$-0.173346\pi$
$277$	10.4346	+	7.58116i	0.626953	+	0.455508i	−0.228390	+	0.973570i	$0.573346\pi$
$278$	−8.84600	−	27.2252i	−0.530548	−	1.63286i
$279$	10.4000	+	12.8001i	0.622629	+	0.766322i
$280$	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	$0.364858\pi$
$283$	−7.68677	+	23.6575i	−0.456931	+	1.40629i	−0.868853	+	0.495070i	$0.835142\pi$
$284$	2.09975	+	2.89006i	0.124597	+	0.171493i
$285$	−11.3496	+	21.1177i	−0.672291	+	1.25090i
$286$	8.22847	−	9.03460i	0.486560	−	0.534227i
$287$	−27.8229	+	20.2145i	−1.64233	+	1.19323i
$288$	4.69975	+	3.04116i	0.276935	+	0.179202i
$289$	19.0241	+	13.8218i	1.11907	+	0.813049i
$290$	−24.7173	+	16.1731i	−1.45145	+	0.949716i
$291$	−0.342268	+	0.361265i	−0.0200641	+	0.0211777i
$292$	−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	$-0.294014\pi$
$294$	−9.51365	+	72.7218i	−0.554847	+	4.24122i
$295$	22.5468	+	1.10365i	1.31273	+	0.0642572i
$296$	5.36289	+	16.5053i	0.311712	+	0.959350i
$297$	−12.5393	+	11.8222i	−0.727607	+	0.685994i
$298$	−13.3642	+	18.3943i	−0.774168	+	1.06555i
$299$	4.85294			0.280653
$300$	−16.9592	+	28.1602i	−0.979138	+	1.62583i
$301$	−25.6480			−1.47832
$302$	−22.2241	−	16.1467i	−1.27885	−	0.929141i
$303$	3.01783	−	1.64174i	0.173370	−	0.0943155i
$304$	−16.5814	+	5.38764i	−0.951011	+	0.309002i
$305$	4.72942	+	17.4100i	0.270806	+	0.996894i
$306$	2.48088	+	45.9043i	0.141822	+	2.62417i
$307$	29.4353			1.67996			0.839981	−	0.542616i	$-0.182566\pi$
$307$	29.4353			1.67996			0.839981	+	0.542616i	$0.182566\pi$
$308$	25.7155	−	56.8837i	1.46528	−	3.24125i
$309$	11.1897	−	11.8108i	0.636562	−	0.671894i
$310$	29.5588	+	1.44689i	1.67883	+	0.0821777i
$311$	15.8581	−	21.8268i	0.899231	−	1.23769i	−0.0714811	−	0.997442i	$-0.522773\pi$
$311$	15.8581	−	21.8268i	0.899231	−	1.23769i	0.970713	−	0.240244i	$-0.0772275\pi$
$312$	7.88204	−	8.31952i	0.446232	−	0.471000i
$313$	−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
$315$	−10.4397	−	31.5832i	−0.588213	−	1.77951i
$316$	−16.3227	−	22.4662i	−0.918222	−	1.26382i
$317$	1.29720	−	3.99236i	0.0728578	−	0.224233i	−0.907996	−	0.418979i	$-0.862388\pi$
$317$	1.29720	−	3.99236i	0.0728578	−	0.224233i	0.980854	+	0.194746i	$0.0623881\pi$
$318$	−0.523450	+	0.0974576i	−0.0293536	+	0.00546515i
$319$	−7.49667	+	16.5829i	−0.419733	+	0.928464i
$320$	21.8490	−	5.93527i	1.22140	−	0.331792i
$321$	5.46524	+	10.0462i	0.305040	+	0.560722i
$322$	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
$327$	−29.2787	−	13.9359i	−1.61911	−	0.770657i
$328$	28.5168	−	9.26566i	1.57458	−	0.511611i
$329$	−2.25197	−	6.93086i	−0.124155	−	0.382111i
$330$	0.765253	+	30.9148i	0.0421258	+	1.70180i
$331$	−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
$333$	12.0251	−	0.649889i	0.658970	−	0.0356137i
$334$	−13.7821	+	10.0132i	−0.754120	+	0.547901i
$335$	4.34014	−	2.83985i	0.237127	−	0.155158i
$336$	10.3964	−	21.8424i	0.567171	−	1.19160i
$337$	−18.4483	+	13.4034i	−1.00494	+	0.730132i	−0.963142	−	0.268994i	$-0.913309\pi$
$337$	−18.4483	+	13.4034i	−1.00494	+	0.730132i	−0.0417984	+	0.999126i	$0.513309\pi$
$338$	−15.0813	−	20.7576i	−0.820314	−	1.12907i
$339$	6.72502	−	14.1290i	0.365253	−	0.767379i
$340$	42.1026	+	33.8542i	2.28333	+	1.83600i
$341$	15.8420	−	9.02646i	0.857894	−	0.488810i
$342$	2.41267	+	44.6422i	0.130462	+	2.41397i
$343$	−52.5058			−2.83505
$344$	21.2671	+	6.91010i	1.14665	+	0.372568i
$345$	−8.87207	+	8.49149i	−0.477656	+	0.457167i
$346$	−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	$0.619867\pi$
$348$	−15.5042	+	32.5736i	−0.831112	+	1.74613i
$349$			7.84341i			0.419848i	0.977718	+	0.209924i	$0.0673217\pi$
$349$			7.84341i			0.419848i	−0.977718	+	0.209924i	$0.932678\pi$
$350$	−54.6948	−	23.9009i	−2.92356	−	1.27756i
$351$	−4.17177	−	6.77044i	−0.222672	−	0.361380i
$352$	4.16717	−	4.57543i	0.222111	−	0.243871i
$353$	0.603074	+	1.85607i	0.0320984	+	0.0987886i	0.965822	−	0.259206i	$-0.0834607\pi$
$353$	0.603074	+	1.85607i	0.0320984	+	0.0987886i	−0.933724	+	0.357994i	$0.883461\pi$
$354$	36.9780	−	20.1165i	1.96536	−	1.06918i
$355$	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	$0.481852\pi$
$360$	0.147373	+	29.0013i	0.00776724	+	1.52850i
$361$	15.6285	+	11.3548i	0.822553	+	0.597620i
$362$	13.5764	+	18.6863i	0.713559	+	0.982129i
$363$	10.6248	+	15.8150i	0.557657	+	0.830071i
$364$	23.3051	+	16.9322i	1.22152	+	0.887487i
$365$	1.54949	−	0.420919i	0.0811042	−	0.0220319i
$366$	24.4225	+	23.1382i	1.27658	+	1.20946i
$367$	−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
$369$	−1.12284	−	20.7762i	−0.0584526	−	1.08156i
$370$	13.5412	−	16.8404i	0.703973	−	0.875493i
$371$	−0.195662	−	0.602186i	−0.0101583	−	0.0312640i
$372$	31.7494	−	17.2721i	1.64613	−	0.895515i
$373$	−16.5811	−	12.0469i	−0.858536	−	0.623763i	0.0689505	−	0.997620i	$-0.478035\pi$
$373$	−16.5811	−	12.0469i	−0.858536	−	0.623763i	−0.927486	+	0.373857i	$0.878035\pi$
$374$	50.5137	+	5.60033i	2.61200	+	0.289586i
$375$	19.3514	−	0.723003i	0.999303	−	0.0373357i
$376$			6.35375i			0.327670i
$377$	−6.79398	−	4.93611i	−0.349908	−	0.254223i
$378$	−47.2669	−	40.1701i	−2.43115	−	2.06613i
$379$	−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
$381$	−5.61444	−	0.734495i	−0.287637	−	0.0376293i
$382$	−15.4104			−0.788467
$383$	8.49699	−	26.1510i	0.434176	−	1.33626i	−0.459753	−	0.888047i	$-0.652062\pi$
$383$	8.49699	−	26.1510i	0.434176	−	1.33626i	0.893929	−	0.448209i	$-0.147938\pi$
$384$	24.5921	−	25.9571i	1.25496	−	1.32462i
$385$	−36.3347	+	5.67118i	−1.85179	+	0.289030i
$386$	−1.78083	+	2.45110i	−0.0906416	+	0.124757i
$387$	8.42989	−	13.0274i	0.428516	−	0.662220i
$388$	0.641046	+	0.882325i	0.0325442	+	0.0447932i
$389$	−5.55431	+	7.64485i	−0.281615	+	0.387609i	−0.926268	−	0.376866i	$-0.877002\pi$
$389$	−5.55431	+	7.64485i	−0.281615	+	0.387609i	0.644653	+	0.764475i	$0.277002\pi$
$390$	−14.0421	−	2.54064i	−0.711047	−	0.128650i
$391$	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
$396$	20.4409	+	31.7581i	1.02719	+	1.59590i
$397$	−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	$-0.766148\pi$
$401$		−	26.8471i		−	1.34068i	0.742054	−	0.670341i	$-0.233852\pi$
$402$	4.15682	−	8.73329i	0.207323	−	0.435577i
$403$	2.59998	+	8.00191i	0.129514	+	0.398604i
$404$	−2.32656	−	7.16043i	−0.115751	−	0.356245i
$405$	19.4734	+	5.07801i	0.967642	+	0.252328i
$406$	−62.2980	−	20.2419i	−3.09180	−	1.00459i
$407$	1.46706	−	13.2325i	0.0727195	−	0.655913i
$408$	47.2608	+	6.18277i	2.33976	+	0.306093i
$409$	14.2965	+	19.6775i	0.706917	+	0.972988i	0.999858	+	0.0168572i	$0.00536606\pi$
$409$	14.2965	+	19.6775i	0.706917	+	0.972988i	−0.292941	+	0.956131i	$0.594634\pi$
$410$	−29.0958	−	23.3956i	−1.43694	−	1.15543i
$411$	10.4466	−	21.9478i	0.515293	−	1.08261i
$412$	−20.9577	−	28.8458i	−1.03251	−	1.42113i
$413$	29.4243	+	40.4990i	1.44787	+	1.99283i
$414$	−5.89119	+	22.1306i	−0.289536	+	1.08766i
$415$	10.9953	−	7.19445i	0.539736	−	0.353162i
$416$	1.67859	+	2.31038i	0.0822995	+	0.113275i
$417$	−2.67156	+	20.4213i	−0.130827	+	1.00003i
$418$	49.1249	+	5.44635i	2.40278	+	0.266390i
$419$	17.1907	+	5.58560i	0.839821	+	0.272874i	0.697176	−	0.716900i	$-0.254439\pi$
$419$	17.1907	+	5.58560i	0.839821	+	0.272874i	0.142645	+	0.989774i	$0.454439\pi$
$420$	−72.2333	+	9.82333i	−3.52463	+	0.479329i
$421$	−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
$423$	4.26057	+	1.13417i	0.207156	+	0.0551451i
$424$			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
$429$	−8.13892	+	3.32481i	−0.392951	+	0.160523i
$430$	−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
$435$	21.0577	−	2.86372i	1.00964	−	0.137305i
$436$	−41.7692	+	57.4904i	−2.00038	+	2.75329i
$437$	11.5372	+	15.8796i	0.551901	+	0.759627i
$438$	2.05931	−	2.17361i	0.0983975	−	0.103859i
$439$	−1.00757	+	1.38680i	−0.0480887	+	0.0661884i	−0.832384	−	0.554199i	$-0.813025\pi$
$439$	−1.00757	+	1.38680i	−0.0480887	+	0.0661884i	0.784295	+	0.620387i	$0.213025\pi$
$440$	31.6564	+	5.08684i	1.50916	+	0.242506i
$441$	28.6661	−	44.3001i	1.36505	−	2.10953i
$442$	−7.24721	+	22.3046i	−0.344714	+	1.06092i
$443$	−7.75578			−0.368488			−0.184244	−	0.982881i	$-0.558984\pi$
$443$	−7.75578			−0.368488			−0.184244	+	0.982881i	$0.558984\pi$
$444$	3.42343	−	26.1686i	0.162469	−	1.24190i
$445$	7.26830	+	26.7562i	0.344551	+	1.26836i
$446$	−4.14764	−	12.7651i	−0.196397	−	0.604447i
$447$	14.3693	−	7.81706i	0.679642	−	0.369734i
$448$	40.6192	+	29.5116i	1.91908	+	1.39429i
$449$			4.99437i			0.235699i	0.993031	+	0.117849i	$0.0376000\pi$
$449$			4.99437i			0.235699i	−0.993031	+	0.117849i	$0.962400\pi$
$450$	30.1170	−	19.9255i	1.41973	−	0.939297i
$451$	−22.8624	−	2.53469i	−1.07655	−	0.119354i
$452$	−27.7430	−	20.1565i	−1.30492	−	0.948082i
$453$	9.44463	+	17.3610i	0.443747	+	0.815693i
$454$	14.2480	+	43.8509i	0.668692	+	2.05802i
$455$	0.829666	−	16.9494i	0.0388953	−	0.794602i
$456$	45.9614	+	6.01278i	2.15234	+	0.281574i
$457$	24.2334			1.13359			0.566794	−	0.823859i	$-0.308183\pi$
$457$	24.2334			1.13359			0.566794	+	0.823859i	$0.308183\pi$
$458$	61.3095	+	19.9207i	2.86480	+	0.930831i
$459$	12.5821	−	30.5875i	0.587284	−	1.42770i
$460$	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	$0.682756\pi$
$462$	−52.3634	+	44.2824i	−2.43617	+	2.06021i
$463$	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
$465$	−18.7547	−	10.0796i	−0.869727	−	0.467431i
$466$	2.52262	−	1.83279i	0.116858	−	0.0849024i
$467$	−7.07167	+	21.7644i	−0.327238	+	1.00713i	0.643182	+	0.765713i	$0.277614\pi$
$467$	−7.07167	+	21.7644i	−0.327238	+	1.00713i	−0.970420	+	0.241422i	$0.922386\pi$
$468$	−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
$471$	9.75148	+	17.9251i	0.449325	+	0.825945i
$472$	−13.4871	−	41.5090i	−0.620794	−	1.91061i
$473$	−12.6828	−	11.5511i	−0.583155	−	0.531122i
$474$	5.58376	+	29.9907i	0.256471	+	1.37752i
$475$	3.02280	−	30.8028i	0.138696	−	1.41333i
$476$			119.806i			5.49132i
$477$	0.370179	+	0.0985419i	0.0169493	+	0.00451192i
$478$	−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	$0.752821\pi$
$480$	−7.11137	−	1.28666i	−0.324588	−	0.0587279i
$481$	5.84291	+	1.89848i	0.266414	+	0.0865630i
$482$	40.7527			1.85623
$483$	−27.0038	−	3.53271i	−1.22872	−	0.160744i
$484$	38.3351	−	16.5471i	1.74250	−	0.752143i
$485$	0.228170	−	0.600586i	0.0103607	−	0.0272712i
$486$	35.9392	−	10.8054i	1.63023	−	0.490142i
$487$	−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
$489$	15.5547	+	7.40365i	0.703409	+	0.334805i
$490$	−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	$0.339110\pi$
$492$	−45.2124	−	5.91479i	−2.03833	−	0.266659i
$493$		−	34.9263i		−	1.57300i
$494$	−7.04795	+	21.6914i	−0.317102	+	0.975941i
$495$	9.06182	−	20.3195i	0.407299	−	0.913295i
$496$	−4.78478	−	14.7260i	−0.214843	−	0.661219i
$497$	4.43831	−	1.44210i	0.199086	−	0.0646868i
$498$	10.5309	−	22.1249i	0.471899	−	0.991438i
$499$	−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	$0.383845\pi$
$504$	−49.9152	+	40.5556i	−2.22340	+	1.80649i
$505$	−2.77926	+	3.45641i	−0.123675	+	0.153808i
$506$	23.0704	+	10.4295i	1.02561	+	0.463648i
$507$	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	$-0.961463\pi$
$509$	−18.0666	−	24.8665i	−0.800786	−	1.10219i	0.191895	−	0.981416i	$-0.438537\pi$
$510$	−25.7785	−	53.4578i	−1.14149	−	2.36715i
$511$	2.88065	+	2.09291i	0.127432	+	0.0925850i
$512$	−17.4038	−	23.9542i	−0.769145	−	1.05864i
$513$	12.2362	−	29.7466i	0.540241	−	1.31334i
$514$	27.8419	−	38.3211i	1.22805	−	1.69027i
$515$	−7.45955	+	19.6350i	−0.328707	+	0.865220i
$516$	−24.6859	−	23.3878i	−1.08673	−	1.02959i
$517$	2.00788	−	4.44150i	0.0883065	−	0.195337i
$518$	47.9208			2.10552
$519$	−1.12306	+	8.58463i	−0.0492969	+	0.376823i
$520$	−5.25449	+	13.8308i	−0.230425	+	0.606522i
$521$	31.0233	−	10.0801i	1.35916	−	0.441617i	0.463395	−	0.886152i	$-0.346631\pi$
$521$	31.0233	−	10.0801i	1.35916	−	0.441617i	0.895762	+	0.444535i	$0.146631\pi$
$522$	30.7574	−	24.9901i	1.34621	−	1.09379i
$523$	6.86794	+	4.98985i	0.300314	+	0.218191i	0.727729	−	0.685865i	$-0.240576\pi$
$523$	6.86794	+	4.98985i	0.300314	+	0.218191i	−0.427415	+	0.904055i	$0.640576\pi$
$524$	7.49667			0.327494
$525$	28.1407	+	32.4384i	1.22816	+	1.41573i
$526$	16.9254			0.737984
$527$	−20.5680	+	28.3094i	−0.895956	+	1.23318i
$528$	14.9782	−	6.11870i	0.651842	−	0.266282i
$529$	−4.00035	−	12.3118i	−0.173928	−	0.535296i
$530$	0.575194	−	0.376362i	0.0249848	−	0.0163481i
$531$	−30.2418	+	1.63440i	−1.31238	+	0.0709271i
$532$			116.512i			5.05145i
$533$	3.28007	−	10.0950i	0.142075	−	0.437263i
$534$	37.5332	+	35.5595i	1.62422	+	1.53881i
$535$	−11.5062	−	9.25197i	−0.497455	−	0.399997i
$536$	−8.11293	−	5.89439i	−0.350425	−	0.254599i
$537$	−1.15091	+	1.21479i	−0.0496655	+	0.0524221i
$538$	−47.7256	+	34.6747i	−2.05760	+	1.49493i
$539$	−43.1282	−	39.2800i	−1.85766	−	1.69191i
$540$	18.7519	−	39.9183i	0.806952	−	1.71781i
$541$	3.21826	+	4.42956i	0.138364	+	0.190442i	0.872576	−	0.488479i	$-0.162448\pi$
$541$	3.21826	+	4.42956i	0.138364	+	0.190442i	−0.734212	+	0.678920i	$0.762448\pi$
$542$	−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
$546$	−15.1225	−	27.7980i	−0.647182	−	1.18964i
$547$	−5.54428	−	17.0636i	−0.237056	−	0.729585i	−0.996842	−	0.0794110i	$-0.974696\pi$
$547$	−5.54428	−	17.0636i	−0.237056	−	0.729585i	0.759785	−	0.650174i	$-0.225304\pi$
$548$	−43.0959	−	31.3110i	−1.84096	−	1.33754i
$549$	−8.71097	−	22.5826i	−0.371775	−	0.963803i
$550$	−16.2820	−	36.4519i	−0.694266	−	1.55432i
$551$		−	33.9660i		−	1.44700i
$552$	21.4396	+	10.2047i	0.912530	+	0.434341i
$553$	−34.5018	+	11.2103i	−1.46717	+	0.476711i
$554$	−29.5312	+	9.59525i	−1.25466	+	0.407663i
$555$	−14.0038	+	6.75293i	−0.594427	+	0.286646i
$556$	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	$0.814149\pi$
$558$	−39.6469	+	2.14270i	−1.67839	+	0.0907076i
$559$	6.40422	−	4.65293i	0.270869	−	0.196798i
$560$	−1.52685	+	31.1923i	−0.0645211	+	1.31812i
$561$	−31.0832	−	19.2571i	−1.31233	−	0.813035i
$562$	−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	$-0.425947\pi$
$564$	4.15259	−	8.72440i	0.174856	−	0.367363i
$565$	−0.987655	+	20.1770i	−0.0415510	+	0.848855i
$566$	−35.1996	−	48.4481i	−1.47955	−	2.03642i
$567$	18.2849	+	40.7105i	0.767895	+	1.70968i
$568$	−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	$0.141824\pi$
$570$	−25.0698	−	51.9880i	−1.05006	−	2.17754i
$571$	17.0538	−	5.54112i	0.713680	−	0.231889i	0.0703989	−	0.997519i	$-0.477573\pi$
$571$	17.0538	−	5.54112i	0.713680	−	0.231889i	0.643281	+	0.765630i	$0.277573\pi$
$572$	3.89849	+	18.8689i	0.163004	+	0.788948i
$573$	10.0110	+	4.76496i	0.418214	+	0.199059i
$574$		−	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
$579$	1.91475	−	1.04165i	0.0795743	−	0.0432894i
$580$	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
$583$	0.174454	−	0.385899i	0.00722516	−	0.0159823i
$584$	−1.82474	−	2.51154i	−0.0755082	−	0.103928i
$585$	8.33646	+	5.99230i	0.344670	+	0.247751i
$586$	53.1967	+	38.6496i	2.19753	+	1.59660i
$587$	−11.2287	+	8.15816i	−0.463460	+	0.336723i	−0.794887	−	0.606757i	$-0.792470\pi$
$587$	−11.2287	+	8.15816i	−0.463460	+	0.336723i	0.331427	+	0.943481i	$0.392470\pi$
$588$	−83.9451	−	79.5308i	−3.46184	−	3.27980i
$589$	−20.0025	+	27.5311i	−0.824188	+	1.13440i
$590$	−34.0547	+	42.3519i	−1.40201	+	1.74360i
$591$	5.99882	−	6.33178i	0.246759	−	0.260455i
$592$	−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	$-0.0152611\pi$
$594$	−5.28177	−	41.1516i	−0.216714	−	1.68847i
$595$	59.0576	−	38.6427i	2.42112	−	1.58420i
$596$	−11.0778	−	34.0940i	−0.453765	−	1.39655i
$597$	−11.9302	+	6.49020i	−0.488272	+	0.265626i
$598$	−6.86722	+	9.45191i	−0.280821	+	0.386518i
$599$		−	11.8708i		−	0.485028i	−0.970148	−	0.242514i	$-0.922028\pi$
$599$		−	11.8708i		−	0.485028i	0.970148	−	0.242514i	$-0.0779721\pi$
$600$	−14.5945	−	34.4794i	−0.595817	−	1.40762i
$601$			24.5582i			1.00175i	0.865519	+	0.500876i	$0.166989\pi$
$601$			24.5582i			1.00175i	−0.865519	+	0.500876i	$0.833011\pi$
$602$	36.2935	−	49.9537i	1.47921	−	2.03596i
$603$	−5.40073	+	4.38804i	−0.219935	+	0.178695i
$604$	41.1926	−	13.3843i	1.67610	−	0.544600i
$605$	−20.5215	−	13.5598i	−0.834317	−	0.551284i
$606$	−1.07286	+	8.20090i	−0.0435820	+	0.333139i
$607$	−40.0055			−1.62377			−0.811886	−	0.583816i	$-0.801559\pi$
$607$	−40.0055			−1.62377			−0.811886	+	0.583816i	$0.801559\pi$
$608$	−3.56932	+	10.9852i	−0.144755	+	0.445510i
$609$	34.2113	+	32.4123i	1.38631	+	1.31341i
$610$	−40.6013	−	15.4249i	−1.64390	−	0.624536i
$611$	1.81968	+	1.32207i	0.0736162	+	0.0534853i
$612$	−60.8534	−	39.3776i	−2.45985	−	1.59174i
$613$	−13.0232	+	9.46188i	−0.526001	+	0.382162i	−0.818860	−	0.573994i	$-0.805393\pi$
$613$	−13.0232	+	9.46188i	−0.526001	+	0.382162i	0.292859	+	0.956156i	$0.405393\pi$
$614$	−41.6528	+	57.3302i	−1.68097	+	2.31366i
$615$	11.6673	+	24.1948i	0.470471	+	0.975630i
$616$	35.1995	+	61.7774i	1.41823	+	2.48908i
$617$	−7.31781	+	22.5219i	−0.294604	+	0.906698i	0.688750	+	0.724999i	$0.258160\pi$
$617$	−7.31781	+	22.5219i	−0.294604	+	0.906698i	−0.983354	+	0.181699i	$0.941840\pi$
$618$	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
$621$	10.6699	−	12.5550i	0.428169	−	0.503814i
$622$	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
$627$	−30.2286	−	18.7276i	−1.20721	−	0.747910i
$628$	42.5310	−	13.8192i	1.69717	−	0.551444i
$629$	7.89570	+	24.3005i	0.314822	+	0.968923i
$630$	76.2865	+	24.3591i	3.03933	+	0.970490i
$631$	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
$633$	3.23939	−	24.7618i	0.128754	−	0.984191i
$634$	5.94017	+	8.17594i	0.235914	+	0.324708i
$635$	7.05433	−	1.91631i	0.279942	−	0.0760463i
$636$	0.360797	−	0.758017i	0.0143065	−	0.0300573i
$637$	21.7777	−	15.8224i	0.862865	−	0.626908i
$638$	−21.6897	−	38.0668i	−0.858703	−	1.50708i
$639$	−0.726286	+	2.72834i	−0.0287314	+	0.107932i
$640$	−16.3941	+	43.1525i	−0.648035	+	1.70575i
$641$	20.9750	+	28.8696i	0.828462	+	1.14028i	0.988207	+	0.153122i	$0.0489328\pi$
$641$	20.9750	+	28.8696i	0.828462	+	1.14028i	−0.159745	+	0.987158i	$0.551067\pi$
$642$	−27.3002	−	3.57148i	−1.07745	−	0.140955i
$643$		−	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
$645$	−3.56655	+	19.7123i	−0.140433	+	0.776170i
$646$	−90.2137	+	29.3122i	−3.54941	+	1.15327i
$647$	4.81679	+	14.8246i	0.189368	+	0.582814i	0.999996	−	0.00274697i	$-0.000874390\pi$
$647$	4.81679	+	14.8246i	0.189368	+	0.582814i	−0.810629	+	0.585561i	$0.800874\pi$
$648$	−4.19347	−	38.6832i	−0.164735	−	1.51962i
$649$	−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	$0.188663\pi$
$653$	12.4383	+	38.2810i	0.486747	+	1.49805i	−0.342688	+	0.939449i	$0.611337\pi$
$654$	68.5736	−	37.3049i	2.68144	−	1.45874i
$655$	−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	$0.284832\pi$
$660$	−40.1432	−	27.6743i	−1.56257	−	1.07722i
$661$	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
$663$	11.6046	−	12.2487i	0.450685	−	0.475700i
$664$	−20.5532	−	14.9328i	−0.797620	−	0.579505i
$665$	57.4338	−	37.5803i	2.22719	−	1.45730i
$666$	−15.7505	+	24.3405i	−0.610318	+	0.943174i
$667$	5.37661	−	16.5475i	0.208183	−	0.640722i
$668$		−	26.8598i		−	1.03924i
$669$	−1.25262	+	9.57498i	−0.0484291	+	0.370190i
$670$	−0.610483	+	12.4717i	−0.0235850	+	0.481824i
$671$	−26.2056	+	5.41432i	−1.01165	+	0.209017i
$672$	−7.65852	−	14.0778i	−0.295434	−	0.543064i
$673$	−15.5957	−	11.3309i	−0.601170	−	0.436775i	0.245124	−	0.969492i	$-0.421171\pi$
$673$	−15.5957	−	11.3309i	−0.601170	−	0.436775i	−0.846294	+	0.532716i	$0.821171\pi$
$674$		−	54.8977i		−	2.11458i
$675$	−25.7257	+	3.63178i	−0.990182	+	0.139787i
$676$	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	$0.283759\pi$
$678$	18.0022	+	33.0914i	0.691369	+	1.27087i
$679$	1.35500	−	0.440267i	0.0520002	−	0.0168959i
$680$	−59.3813	+	16.1309i	−2.27717	+	0.618592i
$681$	4.30301	−	32.8920i	0.164892	−	1.26043i
$682$	−4.83693	+	43.6280i	−0.185215	+	1.67060i
$683$	−14.6470	+	45.0789i	−0.560453	+	1.72490i	0.120635	+	0.992697i	$0.461507\pi$
$683$	−14.6470	+	45.0789i	−0.560453	+	1.72490i	−0.681089	+	0.732201i	$0.738493\pi$
$684$	−59.1803	−	38.2950i	−2.26281	−	1.46424i
$685$	−1.53422	+	31.3429i	−0.0586195	+	1.19755i
$686$	74.2990	−	102.264i	2.83675	−	3.90445i
$687$	−33.6685	−	31.8980i	−1.28453	−	1.21698i
$688$	−11.7858	+	8.56287i	−0.449329	+	0.326456i
$689$	0.158102	+	0.114868i	0.00602321	+	0.00437612i
$690$	−3.98407	−	29.2958i	−0.151671	−	1.11527i
$691$	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
$696$	−19.6352	−	36.0933i	−0.744271	−	1.36811i
$697$	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	$0.123451\pi$
$702$	19.0899	+	1.45539i	0.720501	+	0.0549302i
$703$	7.67862	+	23.6324i	0.289605	+	0.891311i
$704$	6.79479	+	32.8871i	0.256088	+	1.23948i
$705$	−5.64001	+	0.767010i	−0.212415	+	0.0288873i
$706$	−4.46839	−	1.45187i	−0.168170	−	0.0546418i
$707$	−9.83549			−0.369902
$708$	−8.60957	+	65.8112i	−0.323568	+	2.47333i
$709$	−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
$711$	5.64588	−	21.2091i	0.211737	−	0.795405i
$712$	43.3684	−	31.5090i	1.62530	−	1.18085i
$713$	−14.1028	+	10.2463i	−0.528153	+	0.383726i
$714$	56.5632	−	118.837i	2.11682	−	4.44735i
$715$	8.04383	−	8.00776i	0.300822	−	0.299473i
$716$	2.15559	+	2.96691i	0.0805580	+	0.110879i
$717$	23.3017	+	3.04839i	0.870219	+	0.113844i
$718$		−	49.3304i		−	1.84099i
$719$	−14.1223	−	4.58861i	−0.526672	−	0.171126i	0.0335990	−	0.999435i	$-0.489303\pi$
$719$	−14.1223	−	4.58861i	−0.526672	−	0.171126i	−0.560271	+	0.828309i	$0.689303\pi$
$720$	−15.3417	−	11.0277i	−0.571752	−	0.410979i
$721$	−44.2991	+	14.3936i	−1.64978	+	0.536047i
$722$	−44.2306	+	14.3714i	−1.64609	+	0.534848i
$723$	−26.4739	−	12.6009i	−0.984573	−	0.468631i
$724$	−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
$729$	−26.6879	−	4.09311i	−0.988442	−	0.151597i
$730$	−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	$-0.795884\pi$
$733$	5.37603	−	16.5457i	0.198568	−	0.611130i	0.999916	−	0.0129319i	$-0.00411646\pi$
$734$	72.3979	−	52.6002i	2.67226	−	1.94151i
$735$	−12.1282	+	67.0322i	−0.447354	+	2.47252i
$736$	−3.47779	+	4.78677i	−0.128193	+	0.176443i
$737$	3.80852	+	6.68420i	0.140289	+	0.246216i
$738$	42.0539	+	27.2127i	1.54803	+	1.00171i
$739$	18.8005	−	25.8766i	0.691587	−	0.951887i	−0.308413	−	0.951253i	$-0.599798\pi$
$739$	18.8005	−	25.8766i	0.691587	−	0.951887i	1.00000		0.000634867i	$-0.000202084\pi$
$740$	8.93178	+	32.8798i	0.328339	+	1.20868i
$741$	11.2855	−	11.9119i	0.414585	−	0.437596i
$742$	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	$-0.131559\pi$
$744$	−5.33997	+	40.8185i	−0.195773	+	1.49648i
$745$	−13.2333	+	16.4575i	−0.484830	+	0.602957i
$746$	46.9265	−	15.2474i	1.71810	−	0.558245i
$747$	−13.6822	+	11.1166i	−0.500604	+	0.406736i
$748$	−53.9575	+	59.2437i	−1.97288	+	2.16616i
$749$		−	32.7417i		−	1.19636i
$750$	−25.9753	+	38.7132i	−0.948484	+	1.41361i
$751$	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
$753$	12.4812	+	22.9429i	0.454841	+	0.836084i
$754$	19.2278	−	6.24749i	0.700236	−	0.227520i
$755$	−19.8841	−	15.9886i	−0.723656	−	0.581884i
$756$	95.0447	−	23.0645i	3.45674	−	0.838847i
$757$			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
$759$	−11.7622	−	13.9087i	−0.426942	−	0.504854i
$760$	−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	$0.649418\pi$
$762$	9.37534	−	9.89571i	0.339633	−	0.358484i
$763$	54.5657	+	75.1032i	1.97541	+	2.71892i
$764$	14.2817	−	19.6571i	0.516695	−	0.711170i
$765$	0.216975	+	42.6982i	0.00784475	+	1.54376i
$766$	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	0.165977	−	0.986130i	$-0.446922\pi$
$769$	−7.74735	−	2.51727i	−0.279377	−	0.0907750i	−0.445354	+	0.895355i	$0.646922\pi$
$770$	40.3704	−	78.7930i	1.45485	−	2.83950i
$771$	−29.9357	+	16.2854i	−1.07811	+	0.586505i
$772$	−1.47616	−	4.54314i	−0.0531280	−	0.163511i
$773$	6.40773	+	4.65549i	0.230470	+	0.167446i	0.697027	−	0.717045i	$-0.254506\pi$
$773$	6.40773	+	4.65549i	0.230470	+	0.167446i	−0.466557	+	0.884491i	$0.654506\pi$
$774$	13.4442	+	34.8532i	0.483242	+	1.25277i
$775$	27.3560	+	2.68456i	0.982658	+	0.0964322i
$776$	−1.24218			−0.0445915
$777$	−31.1304	−	14.8173i	−1.11680	−	0.531567i
$778$	−7.02993	−	21.6359i	−0.252035	−	0.775684i
$779$	40.8305	−	13.2666i	1.46290	−	0.475326i
$780$	16.2543	−	15.5571i	0.581999	−	0.557033i
$781$	2.84420	+	1.28579i	0.101774	+	0.0460090i
$782$	−48.5901			−1.73758
$783$	−27.7077	+	6.72382i	−0.990193	+	0.240290i
$784$	−40.0779	+	29.1183i	−1.43135	+	1.03994i
$785$	−20.5301	−	16.5080i	−0.732752	−	0.589197i
$786$	−7.43600	−	3.53934i	−0.265233	−	0.126244i
$787$	−23.3785	+	16.9854i	−0.833352	+	0.605466i	−0.920506	−	0.390729i	$-0.872223\pi$
$787$	−23.3785	+	16.9854i	−0.833352	+	0.605466i	0.0871536	+	0.996195i	$0.472223\pi$
$788$	−11.2354	−	15.4642i	−0.400246	−	0.550891i
$789$	−10.9951	−	5.23340i	−0.391437	−	0.186314i
$790$	−21.5634	−	32.9553i	−0.767192	−	1.17250i
$791$	−36.2424	+	26.3317i	−1.28863	+	0.936246i
$792$	−42.9480	−	2.42590i	−1.52609	−	0.0862005i
$793$		−	12.3480i		−	0.438491i
$794$	10.6571	−	32.7993i	0.378207	−	1.16400i
$795$	−0.490031	+	0.0666415i	−0.0173796	+	0.00236353i
$796$	9.19748	+	28.3069i	0.325996	+	1.00331i
$797$	1.47270	+	4.53250i	0.0521657	+	0.160550i	0.973745	−	0.227639i	$-0.0731008\pi$
$797$	1.47270	+	4.53250i	0.0521657	+	0.160550i	−0.921580	+	0.388189i	$0.873101\pi$
$798$	55.0080	−	115.569i	1.94726	−	4.09111i
$799$			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
$803$	0.481875	+	2.33230i	0.0170050	+	0.0823051i
$804$	7.28758	+	13.3960i	0.257013	+	0.472439i
$805$	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	$0.373555\pi$
$810$	−37.4464	+	30.7420i	−1.31573	+	1.08016i
$811$	7.70056	−	10.5989i	0.270403	−	0.372178i	−0.652122	−	0.758114i	$-0.726121\pi$
$811$	7.70056	−	10.5989i	0.270403	−	0.372178i	0.922526	+	0.385935i	$0.126121\pi$
$812$	83.5551	−	60.7063i	2.93221	−	2.13037i
$813$	11.5193	−	12.1587i	0.404000	−	0.426423i
$814$	23.6966	+	21.5822i	0.830566	+	0.756457i
$815$	−22.2132	−	1.08732i	−0.778093	−	0.0380872i
$816$	−21.3561	+	22.5415i	−0.747615	+	0.789110i
$817$	30.4504	+	9.89393i	1.06532	+	0.346145i
$818$	−58.5556			−2.04735
$819$	1.22865	+	22.7341i	0.0429326	+	0.794394i
$820$	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	$0.593388\pi$
$822$	27.9645	+	51.4041i	0.975373	+	1.79292i
$823$	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
$825$	−0.693928	+	28.7144i	−0.0241595	+	0.999708i
$826$	−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	$0.178009\pi$
$828$	−22.7695	−	28.0243i	−0.791295	−	0.973913i
$829$	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
$831$	22.1510	+	2.89784i	0.768409	+	0.100525i
$832$	−15.4964			−0.537239
$833$	106.475	+	34.5958i	3.68914	+	1.19867i
$834$	−35.9934	−	34.1007i	−1.24635	−	1.18081i
$835$	−13.2403	+	8.66346i	−0.458201	+	0.299811i
$836$	−52.4740	+	57.6148i	−1.81485	+	1.99265i
$837$	26.4180	+	10.8670i	0.913141	+	0.375619i
$838$	−35.2048	+	25.5778i	−1.21613	+	0.883570i
$839$	12.4401	−	17.1223i	0.429479	−	0.591127i	−0.538355	−	0.842718i	$-0.680954\pi$
$839$	12.4401	−	17.1223i	0.429479	−	0.591127i	0.967834	+	0.251591i	$0.0809539\pi$
$840$	39.3064	−	73.1356i	1.35620	−	2.52342i
$841$	−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
$846$	−8.23796	+	6.69326i	−0.283227	+	0.230119i
$847$	−5.08314	−	54.3083i	−0.174659	−	1.86605i
$848$	−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
$852$	5.58684	+	2.65919i	0.191402	+	0.0911024i
$853$	−13.0791	−	40.2535i	−0.447821	−	1.37825i	−0.879360	−	0.476158i	$-0.842029\pi$
$853$	−13.0791	−	40.2535i	−0.447821	−	1.37825i	0.431539	−	0.902094i	$-0.357971\pi$
$854$	−29.7633	−	91.6020i	−1.01848	−	3.13456i
$855$	0.211010	+	41.5242i	0.00721638	+	1.42010i
$856$	−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	$-0.207061\pi$
$858$	5.04147	−	20.5567i	0.172113	−	0.701795i
$859$	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
$861$	−25.6004	+	53.7852i	−0.872458	+	1.83299i
$862$	−27.8627	−	38.3497i	−0.949008	−	1.30620i
$863$	−38.4427	+	27.9303i	−1.30861	+	0.950758i	−1.00000		0.000432303i	$-0.999862\pi$
$863$	−38.4427	+	27.9303i	−1.30861	+	0.950758i	−0.308606	+	0.951190i	$0.599862\pi$
$864$	9.66775	+	0.737059i	0.328904	+	0.0250752i
$865$	−2.93008	−	10.7862i	−0.0996257	−	0.366743i
$866$	−18.1828	+	13.2106i	−0.617877	+	0.448914i
$867$	40.3852	+	5.28329i	1.37155	+	0.179430i
$868$	−103.475			−3.51217
$869$	−22.1098	−	9.99523i	−0.750024	−	0.339065i
$870$	−24.2203	+	45.0656i	−0.821146	+	1.52787i
$871$	−3.37623	+	1.09700i	−0.114399	+	0.0371706i
$872$	−25.0111	−	76.9762i	−0.846982	−	2.60674i
$873$	−0.221733	+	0.832954i	−0.00750452	+	0.0281912i
$874$	−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	0.824362	−	0.566063i	$-0.191534\pi$
$877$	16.0137	+	11.6347i	0.540746	+	0.392875i	−0.283616	+	0.958938i	$0.591534\pi$
$878$	−1.27525	−	3.92482i	−0.0430376	−	0.132456i
$879$	−22.6071	−	41.5562i	−0.762519	−	1.40166i
$880$	−14.8032	+	14.7368i	−0.499016	+	0.496778i
$881$	−19.5852	−	6.36360i	−0.659841	−	0.214395i	−0.0400925	−	0.999196i	$-0.512765\pi$
$881$	−19.5852	−	6.36360i	−0.659841	−	0.214395i	−0.619748	+	0.784801i	$0.712765\pi$
$882$	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
$885$	35.2180	−	16.9829i	1.18384	−	0.570875i
$886$	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	$0.884992\pi$
$888$	21.8210	+	20.6736i	0.732266	+	0.693760i
$889$	13.1146	+	9.52833i	0.439850	+	0.319570i
$890$	−62.3972	−	23.7054i	−2.09156	−	0.794607i
$891$	−9.29307	+	28.3662i	−0.311330	+	0.950302i
$892$	20.1267	+	6.53956i	0.673892	+	0.218961i
$893$			9.09734i			0.304431i
$894$	−5.10837	+	39.0481i	−0.170849	+	1.30597i
$895$	0.767244	−	2.01953i	0.0256462	−	0.0675056i
$896$	−97.3578	+	31.6335i	−3.25249	+	1.05680i
$897$	7.38366	−	4.01681i	0.246533	−	0.134117i
$898$	−9.72736	−	7.06734i	−0.324606	−	0.235840i
$899$	30.1653			1.00607
$900$	−2.49469	+	56.8824i	−0.0831563	+	1.89608i
$901$			0.812766i			0.0270772i
$902$	37.2884	−	40.9415i	1.24157	−	1.36320i
$903$	−39.0229	+	21.2289i	−1.29860	+	0.706455i
$904$	37.1463	−	12.0696i	1.23547	−	0.401427i
$905$	11.7463	+	17.9518i	0.390459	+	0.596738i
$906$	−47.1783	−	6.17197i	−1.56739	−	0.205050i
$907$			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
$909$	3.23270	−	4.99575i	0.107222	−	0.165699i
$910$	31.8378	+	25.6004i	1.05541	+	0.848646i
$911$	−11.0306	+	15.1823i	−0.365460	+	0.503012i	−0.951660	−	0.307154i	$-0.900623\pi$
$911$	−11.0306	+	15.1823i	−0.365460	+	0.503012i	0.586200	+	0.810166i	$0.300623\pi$
$912$	−20.7690	+	21.9217i	−0.687730	+	0.725901i
$913$	9.64847	+	16.9337i	0.319318	+	0.560424i
$914$	−34.2917	+	47.1985i	−1.13427	+	1.56119i
$915$	21.6061	+	22.5744i	0.714275	+	0.746287i
$916$	−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	0.379722	−	0.925101i	$-0.376020\pi$
$919$	4.34001	+	1.41015i	0.143164	+	0.0465167i	−0.236559	+	0.971617i	$0.576020\pi$
$920$	−30.6171	−	1.49869i	−1.00942	−	0.0494104i
$921$	44.7852	−	24.3637i	1.47572	−	0.802813i
$922$	−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
$927$	7.24911	−	27.2317i	0.238092	−	0.894408i
$928$	9.73761	−	3.16394i	0.319653	−	0.103861i
$929$	−47.0291	+	15.2807i	−1.54298	+	0.501343i	−0.952195	−	0.305490i	$-0.901180\pi$
$929$	−47.0291	+	15.2807i	−1.54298	+	0.501343i	−0.590780	+	0.806833i	$0.701180\pi$
$930$	46.1708	−	22.2646i	1.51400	−	0.730084i
$931$	103.547	+	33.6446i	3.39363	+	1.10266i
$932$			4.91633i			0.161040i
$933$	6.06165	−	46.3350i	0.198449	−	1.51694i
$934$	−32.3829	−	44.5712i	−1.05960	−	1.45841i
$935$	46.6073	+	7.48928i	1.52422	+	0.244926i
$936$	5.10626	−	19.1820i	0.166903	−	0.626983i
$937$	34.1075	−	24.7805i	1.11424	−	0.809545i	0.130916	−	0.991393i	$-0.458208\pi$
$937$	34.1075	−	24.7805i	1.11424	−	0.809545i	0.983327	+	0.181849i	$0.0582081\pi$
$938$	−22.4019	+	16.2759i	−0.731449	+	0.531429i
$939$	−2.71044	−	1.29010i	−0.0884518	−	0.0421008i
$940$	−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	$0.462079\pi$
$942$	−48.7111	−	6.37250i	−1.58709	−	0.207627i
$943$	21.9918			0.716150
$944$	27.0422	+	8.78653i	0.880147	+	0.285977i
$945$	−42.0255	−	39.4123i	−1.36709	−	1.28208i
$946$	40.4447	−	8.35626i	1.31497	−	0.271685i
$947$	−13.9935	−	43.0675i	−0.454727	−	1.39951i	−0.871455	−	0.490475i	$-0.836823\pi$
$947$	−13.9935	−	43.0675i	−0.454727	−	1.39951i	0.416729	−	0.909031i	$-0.363177\pi$
$948$	−43.4301	−	20.6716i	−1.41054	−	0.671382i
$949$	−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	$0.396403\pi$
$954$	−0.715753	+	0.581542i	−0.0231734	+	0.0188281i
$955$	−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
$960$	28.3302	−	27.1149i	0.914352	−	0.875130i
$961$	0.629082	+	0.457055i	0.0202930	+	0.0147437i
$962$	−11.9657	+	8.69357i	−0.385789	+	0.280292i
$963$	16.6305	+	10.7614i	0.535911	+	0.346783i
$964$	−37.7678	+	51.9830i	−1.21642	+	1.67426i
$965$	−1.76338	+	2.19302i	−0.0567652	+	0.0705957i
$966$	45.0926	−	47.5955i	1.45083	−	1.53136i
$967$	14.8366	−	45.6624i	0.477114	−	1.46840i	−0.365972	−	0.930626i	$-0.619263\pi$
$967$	14.8366	−	45.6624i	0.477114	−	1.46840i	0.843086	−	0.537779i	$-0.180737\pi$
$968$	−10.4169	+	46.4015i	−0.334811	+	1.49140i
$969$	67.6683	+	8.85252i	2.17382	+	0.284384i
$970$	0.846868	+	1.29427i	0.0271913	+	0.0415564i
$971$	40.8869	−	13.2850i	1.31212	−	0.426335i	0.432340	−	0.901710i	$-0.357688\pi$
$971$	40.8869	−	13.2850i	1.31212	−	0.426335i	0.879783	+	0.475376i	$0.157688\pi$
$972$	−19.5239	+	55.8570i	−0.626228	+	1.79161i
$973$	34.6572	−	47.7015i	1.11106	−	1.52924i
$974$	31.9155			1.02264
$975$	−12.9115	−	2.99461i	−0.413498	−	0.0959042i
$976$			22.7243i			0.727386i
$977$	0.633566	+	0.460313i	0.0202696	+	0.0147267i	0.597874	−	0.801590i	$-0.296012\pi$
$977$	0.633566	+	0.460313i	0.0202696	+	0.0147267i	−0.577604	+	0.816317i	$0.696012\pi$
$978$	−36.4308	+	19.8188i	−1.16493	+	0.633736i
$979$	−40.2734	+	8.32087i	−1.28714	+	0.265936i
$980$	139.555	+	53.0185i	4.45792	+	1.69361i
$981$	−56.0818	+	3.03091i	−1.79055	+	0.0967695i
$982$		−	13.0758i		−	0.417267i
$983$	10.2129	−	31.4321i	0.325741	−	1.00253i	−0.645364	−	0.763876i	$-0.723294\pi$
$983$	10.2129	−	31.4321i	0.325741	−	1.00253i	0.971105	−	0.238653i	$-0.0767059\pi$
$984$	35.7185	−	37.7010i	1.13866	−	1.20186i
$985$	−3.99906	+	10.5263i	−0.127421	+	0.335396i
$986$	68.0247	+	49.4229i	2.16635	+	1.57394i
$987$	−9.16304	−	8.68120i	−0.291663	−	0.276326i
$988$	−21.1371	−	29.0928i	−0.672462	−	0.925565i
$989$	13.2686	+	9.64021i	0.421917	+	0.306541i
$990$	26.7526	+	46.4028i	0.850254	+	1.47478i
$991$	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
$996$	18.4623	+	33.9372i	0.585000	+	1.07534i
$997$	−15.7401	−	48.4431i	−0.498495	−	1.53421i	−0.811438	−	0.584438i	$-0.801315\pi$
$997$	−15.7401	−	48.4431i	−0.498495	−	1.53421i	0.312944	−	0.949772i	$-0.398685\pi$
$998$	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.659.13	yes	448
3.2	odd	2	inner	825.2.ce.c.659.100	yes	448
11.10	odd	2	inner	825.2.ce.c.659.99	yes	448
25.14	even	10	inner	825.2.ce.c.164.14	yes	448
33.32	even	2	inner	825.2.ce.c.659.14	yes	448
75.14	odd	10	inner	825.2.ce.c.164.99	yes	448
275.164	odd	10	inner	825.2.ce.c.164.100	yes	448
825.164	even	10	inner	825.2.ce.c.164.13	✓	448

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

\(f(q)\)	\(=\)	\(q+(-1.41506 + 1.94767i) q^{2} +(1.52148 - 0.827705i) q^{3} +(-1.17297 - 3.61003i) q^{4} +(-1.40120 + 1.74259i) q^{5} +(-0.540897 + 4.13459i) q^{6} -4.95869 q^{7} +(4.11171 + 1.33598i) q^{8} +(1.62981 - 2.51868i) q^{9} +O(q^{10})\)	\(q+(-1.41506 + 1.94767i) q^{2} +(1.52148 - 0.827705i) q^{3} +(-1.17297 - 3.61003i) q^{4} +(-1.40120 + 1.74259i) q^{5} +(-0.540897 + 4.13459i) q^{6} -4.95869 q^{7} +(4.11171 + 1.33598i) q^{8} +(1.62981 - 2.51868i) q^{9} +(-1.41121 - 5.19495i) q^{10} +(-2.45205 - 2.23326i) q^{11} +(-4.77269 - 4.52171i) q^{12} +(1.23817 - 0.899583i) q^{13} +(7.01686 - 9.65788i) q^{14} +(-0.689545 + 3.81111i) 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} +(-7.54456 + 4.10434i) q^{21} +(7.81945 - 1.61557i) q^{22} +(2.56531 + 1.86381i) q^{23} +(7.36169 - 1.37062i) q^{24} +(-1.07327 - 4.88345i) q^{25} +3.68451i q^{26} +(0.395002 - 5.18112i) q^{27} +(5.81639 + 17.9010i) q^{28} +(-1.69561 - 5.21855i) q^{29} +(-6.44701 - 6.73596i) q^{30} +(-1.69882 + 5.22843i) q^{31} +1.86596i q^{32} +(-5.57923 - 1.36829i) q^{33} +(-12.3972 + 9.00708i) q^{34} +(6.94812 - 8.64099i) q^{35} +(-11.0042 - 2.92933i) q^{36} +(2.35949 + 3.24756i) q^{37} +(-12.0563 + 8.75944i) q^{38} +(1.13926 - 2.39354i) q^{39} +(-8.08940 + 5.29308i) q^{40} +(5.61093 - 4.07658i) q^{41} +(2.68214 - 20.5022i) q^{42} +5.17232 q^{43} +(-5.18595 + 11.4715i) q^{44} +(2.10534 + 6.36926i) q^{45} +(-7.26015 + 2.35897i) q^{46} +(0.454147 + 1.39772i) q^{47} +(-2.09660 + 4.40487i) 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} +(9.53213 + 8.10094i) q^{54} +(7.32748 - 1.14368i) 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} +(14.5670 - 1.98103i) q^{60} +(4.74234 - 6.52728i) q^{61} +(-7.77929 - 10.7073i) q^{62} +(-8.08172 + 12.4893i) q^{63} +(-8.19152 - 5.95149i) q^{64} +(-0.167315 + 3.41813i) q^{65} +(10.5599 - 8.93026i) q^{66} +(-2.20602 - 0.716780i) q^{67} -24.1609i q^{68} +(5.44576 + 0.712427i) q^{69} +(6.99774 + 25.7602i) q^{70} +(-0.895057 + 0.290822i) q^{71} +(10.0662 - 8.17869i) q^{72} +(-0.580929 - 0.422069i) q^{73} -9.66400 q^{74} +(-5.67502 - 6.54172i) q^{75} -23.4966i q^{76} +(12.1590 + 11.0741i) q^{77} +(3.04969 + 5.60591i) q^{78} +(6.95785 - 2.26074i) q^{79} +(0.307913 - 6.29043i) q^{80} +(-3.68745 - 8.20992i) q^{81} +16.6968i q^{82} +(-5.58872 - 1.81588i) q^{83} +(23.6663 + 22.4218i) q^{84} +(-11.9099 + 7.79292i) q^{85} +(-7.31916 + 10.0740i) q^{86} +(-6.89926 - 6.53646i) q^{87} +(-7.09854 - 12.4584i) q^{88} +(7.28816 - 10.0313i) q^{89} +(-15.3844 - 4.91240i) 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} +(1.54446 + 2.83902i) 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

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