LMFDB - Embedded newform 225.2.h.e.136.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(46,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	16.0.1130304400000000000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5x^{14} + 5x^{12} - 10x^{10} + 205x^{8} - 700x^{6} + 1250x^{4} - 1250x^{2} + 625 $ x^16 - 5x^14 + 5x^12 - 10x^10 + 205x^8 - 700x^6 + 1250x^4 - 1250*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			136.4
Root			$1.13937 + 0.289499i$ of defining polynomial
Character	$\chi$	$=$	225.136
Dual form			225.2.h.e.91.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.64259 - 1.19341i) q^{2} +(0.655837 - 2.01846i) q^{4} +(2.23130 - 0.145994i) q^{5} -0.504300 q^{7} +(-0.0767537 - 0.236224i) q^{8} +O(q^{10})$	\(q+(1.64259 - 1.19341i) q^{2} +(0.655837 - 2.01846i) q^{4} +(2.23130 - 0.145994i) q^{5} -0.504300 q^{7} +(-0.0767537 - 0.236224i) q^{8} +(3.49087 - 2.90266i) q^{10} +(-2.78196 + 2.02121i) q^{11} +(-3.99517 - 2.90266i) q^{13} +(-0.828357 + 0.601837i) q^{14} +(3.02602 + 2.19853i) q^{16} +(0.363841 + 1.11979i) q^{17} +(-1.83504 - 5.64767i) q^{19} +(1.16868 - 4.59953i) q^{20} +(-2.15748 + 6.64004i) q^{22} +(-2.40939 + 1.75052i) q^{23} +(4.95737 - 0.651513i) q^{25} -10.0265 q^{26} +(-0.330738 + 1.01791i) q^{28} +(-1.55064 + 4.77239i) q^{29} +(1.10061 + 3.38734i) q^{31} +8.09103 q^{32} +(1.93401 + 1.40514i) q^{34} +(-1.12524 + 0.0736248i) q^{35} +(1.21435 + 0.882274i) q^{37} +(-9.75420 - 7.08684i) q^{38} +(-0.205748 - 0.515879i) q^{40} +(7.10690 + 5.16346i) q^{41} -10.2500 q^{43} +(2.25522 + 6.94085i) q^{44} +(-1.86854 + 5.75078i) q^{46} +(-0.881597 + 2.71328i) q^{47} -6.74568 q^{49} +(7.36541 - 6.98635i) q^{50} +(-8.47909 + 6.16042i) q^{52} +(4.09875 - 12.6147i) q^{53} +(-5.91229 + 4.91607i) q^{55} +(0.0387069 + 0.119127i) q^{56} +(3.14835 + 9.68964i) q^{58} +(7.68621 + 5.58436i) q^{59} +(6.86106 - 4.98485i) q^{61} +(5.85034 + 4.25052i) q^{62} +(7.23820 - 5.25886i) q^{64} +(-9.33819 - 5.89343i) q^{65} +(-2.99836 - 9.22800i) q^{67} +2.49886 q^{68} +(-1.76045 + 1.46381i) q^{70} +(4.23839 - 13.0444i) q^{71} +(10.0633 - 7.31141i) q^{73} +3.04759 q^{74} -12.6031 q^{76} +(1.40294 - 1.01930i) q^{77} +(-4.54026 + 13.9735i) q^{79} +(7.07292 + 4.46380i) q^{80} +17.8359 q^{82} +(0.110065 + 0.338746i) q^{83} +(0.975319 + 2.44546i) q^{85} +(-16.8365 + 12.2324i) q^{86} +(0.690983 + 0.502029i) q^{88} +(-5.26703 + 3.82672i) q^{89} +(2.01476 + 1.46381i) q^{91} +(1.95319 + 6.01131i) q^{92} +(1.78995 + 5.50891i) q^{94} +(-4.91904 - 12.3337i) q^{95} +(3.39322 - 10.4433i) q^{97} +(-11.0804 + 8.05038i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{4}+O(q^{10}) $ 16 * q - 2 * q^4	$ 16 q - 2 q^{4} + 14 q^{16} + 14 q^{19} - 30 q^{22} + 10 q^{25} + 30 q^{28} + 18 q^{31} - 20 q^{34} + 10 q^{37} - 10 q^{40} - 80 q^{43} - 32 q^{49} - 40 q^{52} - 70 q^{55} - 10 q^{58} + 32 q^{61} - 8 q^{64} - 40 q^{67} + 50 q^{70} + 60 q^{73} - 88 q^{76} + 36 q^{79} + 120 q^{82} + 20 q^{88} + 30 q^{91} + 30 q^{94} + 40 q^{97}+O(q^{100}) $ 16 * q - 2 * q^4 + 14 * q^16 + 14 * q^19 - 30 * q^22 + 10 * q^25 + 30 * q^28 + 18 * q^31 - 20 * q^34 + 10 * q^37 - 10 * q^40 - 80 * q^43 - 32 * q^49 - 40 * q^52 - 70 * q^55 - 10 * q^58 + 32 * q^61 - 8 * q^64 - 40 * q^67 + 50 * q^70 + 60 * q^73 - 88 * q^76 + 36 * q^79 + 120 * q^82 + 20 * q^88 + 30 * q^91 + 30 * q^94 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	1.64259	−	1.19341i	1.16149	−	0.843869i	0.171521	−	0.985180i	$-0.445132\pi$
$2$	1.64259	−	1.19341i	1.16149	−	0.843869i	0.989965	+	0.141311i	$0.0451317\pi$
$3$		0			0
$3$		0			0
$4$	0.655837	−	2.01846i	0.327919	−	1.00923i
$5$	2.23130	−	0.145994i	0.997866	−	0.0652906i
$5$	2.23130	−	0.145994i	0.997866	−	0.0652906i
$6$		0			0
$7$	−0.504300			−0.190607			−0.0953037	−	0.995448i	$-0.530382\pi$
$7$	−0.504300			−0.190607			−0.0953037	+	0.995448i	$0.530382\pi$
$8$	−0.0767537	−	0.236224i	−0.0271365	−	0.0835177i
$9$		0			0
$10$	3.49087	−	2.90266i	1.10391	−	0.917903i
$11$	−2.78196	+	2.02121i	−0.838792	+	0.609418i	−0.922033	−	0.387112i	$-0.873473\pi$
$11$	−2.78196	+	2.02121i	−0.838792	+	0.609418i	0.0832413	+	0.996529i	$0.473473\pi$
$12$		0			0
$13$	−3.99517	−	2.90266i	−1.10806	−	0.805054i	−0.125705	−	0.992068i	$-0.540119\pi$
$13$	−3.99517	−	2.90266i	−1.10806	−	0.805054i	−0.982357	+	0.187014i	$0.940119\pi$
$14$	−0.828357	+	0.601837i	−0.221388	+	0.160848i
$15$		0			0
$16$	3.02602	+	2.19853i	0.756505	+	0.549633i
$17$	0.363841	+	1.11979i	0.0882443	+	0.271588i	0.985434	−	0.170057i	$-0.0543951\pi$
$17$	0.363841	+	1.11979i	0.0882443	+	0.271588i	−0.897190	+	0.441645i	$0.854395\pi$
$18$		0			0
$19$	−1.83504	−	5.64767i	−0.420987	−	1.29566i	−0.906785	−	0.421593i	$-0.861471\pi$
$19$	−1.83504	−	5.64767i	−0.420987	−	1.29566i	0.485799	−	0.874071i	$-0.338529\pi$
$20$	1.16868	−	4.59953i	0.261326	−	1.02849i
$21$		0			0
$22$	−2.15748	+	6.64004i	−0.459976	+	1.41566i
$23$	−2.40939	+	1.75052i	−0.502392	+	0.365009i	−0.809930	−	0.586527i	$-0.800495\pi$
$23$	−2.40939	+	1.75052i	−0.502392	+	0.365009i	0.307538	+	0.951536i	$0.400495\pi$
$24$		0			0
$25$	4.95737	−	0.651513i	0.991474	−	0.130303i
$26$	−10.0265			−1.96636
$27$		0			0
$28$	−0.330738	+	1.01791i	−0.0625037	+	0.192367i
$29$	−1.55064	+	4.77239i	−0.287947	+	0.886211i	0.697552	+	0.716534i	$0.254272\pi$
$29$	−1.55064	+	4.77239i	−0.287947	+	0.886211i	−0.985500	+	0.169677i	$0.945728\pi$
$30$		0			0
$31$	1.10061	+	3.38734i	0.197676	+	0.608383i	0.999935	+	0.0114076i	$0.00363122\pi$
$31$	1.10061	+	3.38734i	0.197676	+	0.608383i	−0.802259	+	0.596976i	$0.796369\pi$
$32$	8.09103			1.43031
$33$		0			0
$34$	1.93401	+	1.40514i	0.331680	+	0.240979i
$35$	−1.12524	+	0.0736248i	−0.190201	+	0.0124449i
$36$		0			0
$37$	1.21435	+	0.882274i	0.199637	+	0.145045i	0.683113	−	0.730313i	$-0.260626\pi$
$37$	1.21435	+	0.882274i	0.199637	+	0.145045i	−0.483475	+	0.875358i	$0.660626\pi$
$38$	−9.75420	−	7.08684i	−1.58234	−	1.14964i
$39$		0			0
$40$	−0.205748	−	0.515879i	−0.0325316	−	0.0815677i
$41$	7.10690	+	5.16346i	1.10991	+	0.806397i	0.982650	−	0.185472i	$-0.0593814\pi$
$41$	7.10690	+	5.16346i	1.10991	+	0.806397i	0.127261	+	0.991869i	$0.459381\pi$
$42$		0			0
$43$	−10.2500			−1.56311			−0.781554	−	0.623838i	$-0.785573\pi$
$43$	−10.2500			−1.56311			−0.781554	+	0.623838i	$0.785573\pi$
$44$	2.25522	+	6.94085i	0.339987	+	1.04637i
$45$		0			0
$46$	−1.86854	+	5.75078i	−0.275501	+	0.847906i
$47$	−0.881597	+	2.71328i	−0.128594	+	0.395772i	−0.994539	−	0.104368i	$-0.966718\pi$
$47$	−0.881597	+	2.71328i	−0.128594	+	0.395772i	0.865945	+	0.500140i	$0.166718\pi$
$48$		0			0
$49$	−6.74568			−0.963669
$50$	7.36541	−	6.98635i	1.04163	−	0.988020i
$51$		0			0
$52$	−8.47909	+	6.16042i	−1.17584	+	0.854297i
$53$	4.09875	−	12.6147i	0.563007	−	1.73276i	−0.110793	−	0.993844i	$-0.535339\pi$
$53$	4.09875	−	12.6147i	0.563007	−	1.73276i	0.673800	−	0.738914i	$-0.264661\pi$
$54$		0			0
$55$	−5.91229	+	4.91607i	−0.797213	+	0.662883i
$56$	0.0387069	+	0.119127i	0.00517242	+	0.0159191i
$57$		0			0
$58$	3.14835	+	9.68964i	0.413399	+	1.27231i
$59$	7.68621	+	5.58436i	1.00066	+	0.727022i	0.962230	−	0.272239i	$-0.0877643\pi$
$59$	7.68621	+	5.58436i	1.00066	+	0.727022i	0.0384302	+	0.999261i	$0.487764\pi$
$60$		0			0
$61$	6.86106	−	4.98485i	0.878469	−	0.638245i	−0.0543773	−	0.998520i	$-0.517317\pi$
$61$	6.86106	−	4.98485i	0.878469	−	0.638245i	0.932846	+	0.360276i	$0.117317\pi$
$62$	5.85034	+	4.25052i	0.742994	+	0.539817i
$63$		0			0
$64$	7.23820	−	5.25886i	0.904775	−	0.657357i
$65$	−9.33819	−	5.89343i	−1.15826	−	0.730990i
$66$		0			0
$67$	−2.99836	−	9.22800i	−0.366308	−	1.12738i	−0.949158	−	0.314800i	$-0.898063\pi$
$67$	−2.99836	−	9.22800i	−0.366308	−	1.12738i	0.582850	−	0.812579i	$-0.301937\pi$
$68$	2.49886			0.303032
$69$		0			0
$70$	−1.76045	+	1.46381i	−0.210414	+	0.174959i
$71$	4.23839	−	13.0444i	0.503004	−	1.54809i	−0.301096	−	0.953594i	$-0.597353\pi$
$71$	4.23839	−	13.0444i	0.503004	−	1.54809i	0.804100	−	0.594494i	$-0.202647\pi$
$72$		0			0
$73$	10.0633	−	7.31141i	1.17782	−	0.855736i	0.185896	−	0.982569i	$-0.440481\pi$
$73$	10.0633	−	7.31141i	1.17782	−	0.855736i	0.991924	+	0.126833i	$0.0404813\pi$
$74$	3.04759			0.354275
$75$		0			0
$76$	−12.6031			−1.44567
$77$	1.40294	−	1.01930i	0.159880	−	0.116159i
$78$		0			0
$79$	−4.54026	+	13.9735i	−0.510819	+	1.57214i	0.279943	+	0.960016i	$0.409684\pi$
$79$	−4.54026	+	13.9735i	−0.510819	+	1.57214i	−0.790763	+	0.612123i	$0.790316\pi$
$80$	7.07292	+	4.46380i	0.790777	+	0.499068i
$81$		0			0
$82$	17.8359			1.96964
$83$	0.110065	+	0.338746i	0.0120812	+	0.0371823i	0.956915	−	0.290367i	$-0.0937773\pi$
$83$	0.110065	+	0.338746i	0.0120812	+	0.0371823i	−0.944834	+	0.327549i	$0.893777\pi$
$84$		0			0
$85$	0.975319	+	2.44546i	0.105788	+	0.265247i
$86$	−16.8365	+	12.2324i	−1.81553	+	1.31906i
$87$		0			0
$88$	0.690983	+	0.502029i	0.0736590	+	0.0535164i
$89$	−5.26703	+	3.82672i	−0.558304	+	0.405632i	−0.830838	−	0.556515i	$-0.812138\pi$
$89$	−5.26703	+	3.82672i	−0.558304	+	0.405632i	0.272534	+	0.962146i	$0.412138\pi$
$90$		0			0
$91$	2.01476	+	1.46381i	0.211205	+	0.153449i
$92$	1.95319	+	6.01131i	0.203634	+	0.626722i
$93$		0			0
$94$	1.78995	+	5.50891i	0.184620	+	0.568201i
$95$	−4.91904	−	12.3337i	−0.504683	−	1.26541i
$96$		0			0
$97$	3.39322	−	10.4433i	0.344530	−	1.06035i	−0.617306	−	0.786723i	$-0.711776\pi$
$97$	3.39322	−	10.4433i	0.344530	−	1.06035i	0.961835	−	0.273629i	$-0.0882242\pi$
$98$	−11.0804	+	8.05038i	−1.11929	+	0.813211i
$99$		0			0
$100$	1.93618	−	10.4335i	0.193618	−	1.04335i
$101$	−8.10395			−0.806373			−0.403187	−	0.915118i	$-0.632097\pi$
$101$	−8.10395			−0.806373			−0.403187	+	0.915118i	$0.632097\pi$
$102$		0			0
$103$	1.66863	−	5.13553i	0.164415	−	0.506019i	−0.834577	−	0.550891i	$-0.814288\pi$
$103$	1.66863	−	5.13553i	0.164415	−	0.506019i	0.998993	+	0.0448722i	$0.0142881\pi$
$104$	−0.379033	+	1.16654i	−0.0371673	+	0.114389i
$105$		0			0
$106$	−8.32192	−	25.6122i	−0.808296	−	2.48768i
$107$	−10.6007			−1.02481			−0.512403	−	0.858745i	$-0.671245\pi$
$107$	−10.6007			−1.02481			−0.512403	+	0.858745i	$0.671245\pi$
$108$		0			0
$109$	2.26426	+	1.64508i	0.216876	+	0.157570i	0.690920	−	0.722932i	$-0.257206\pi$
$109$	2.26426	+	1.64508i	0.216876	+	0.157570i	−0.474043	+	0.880502i	$0.657206\pi$
$110$	−3.84457	+	15.1309i	−0.366565	+	1.44267i
$111$		0			0
$112$	−1.52602	−	1.10872i	−0.144195	−	0.104764i
$113$	−5.77531	−	4.19601i	−0.543296	−	0.394728i	0.282012	−	0.959411i	$-0.408998\pi$
$113$	−5.77531	−	4.19601i	−0.543296	−	0.394728i	−0.825308	+	0.564683i	$0.808998\pi$
$114$		0			0
$115$	−5.12049	+	4.25769i	−0.477488	+	0.397032i
$116$	8.61591	+	6.25982i	0.799967	+	0.581210i
$117$		0			0
$118$	19.2897			1.77576
$119$	−0.183485	−	0.564708i	−0.0168200	−	0.0517667i
$120$		0			0
$121$	0.254807	−	0.784215i	0.0231643	−	0.0712923i
$122$	5.32093	−	16.3761i	0.481734	−	1.48263i
$123$		0			0
$124$	7.55902			0.678820
$125$	10.9663	−	2.17747i	0.980851	−	0.194759i
$126$		0			0
$127$	3.66227	−	2.66079i	0.324974	−	0.236107i	−0.413321	−	0.910585i	$-0.635631\pi$
$127$	3.66227	−	2.66079i	0.324974	−	0.236107i	0.738295	+	0.674478i	$0.235631\pi$
$128$	0.612881	−	1.88625i	0.0541715	−	0.166723i
$129$		0			0
$130$	−22.3721	+	1.46381i	−1.96216	+	0.128385i
$131$	2.99410	+	9.21489i	0.261596	+	0.805109i	0.992458	+	0.122584i	$0.0391180\pi$
$131$	2.99410	+	9.21489i	0.261596	+	0.805109i	−0.730863	+	0.682525i	$0.760882\pi$
$132$		0			0
$133$	0.925409	+	2.84812i	0.0802431	+	0.246963i
$134$	−15.9379	−	11.5795i	−1.37682	−	1.00032i
$135$		0			0
$136$	0.236594	−	0.171896i	0.0202878	−	0.0147399i
$137$	3.22362	+	2.34210i	0.275412	+	0.200099i	0.716914	−	0.697162i	$-0.245554\pi$
$137$	3.22362	+	2.34210i	0.275412	+	0.200099i	−0.441502	+	0.897260i	$0.645554\pi$
$138$		0			0
$139$	−4.01391	+	2.91628i	−0.340456	+	0.247356i	−0.744854	−	0.667227i	$-0.767481\pi$
$139$	−4.01391	+	2.91628i	−0.340456	+	0.247356i	0.404398	+	0.914583i	$0.367481\pi$
$140$	−0.589367	+	2.31954i	−0.0498106	+	0.196037i
$141$		0			0
$142$	−8.60542	−	26.4848i	−0.722151	−	2.22255i
$143$	16.9813			1.42005
$144$		0			0
$145$	−2.76321	+	10.8750i	−0.229472	+	0.903120i
$146$	7.80435	−	24.0193i	0.645892	−	1.98785i
$147$		0			0
$148$	2.57725	−	1.87248i	0.211849	−	0.153917i
$149$	−5.62123			−0.460509			−0.230254	−	0.973130i	$-0.573956\pi$
$149$	−5.62123			−0.460509			−0.230254	+	0.973130i	$0.573956\pi$
$150$		0			0
$151$	−2.35414			−0.191577			−0.0957886	−	0.995402i	$-0.530537\pi$
$151$	−2.35414			−0.191577			−0.0957886	+	0.995402i	$0.530537\pi$
$152$	−1.19327	+	0.866959i	−0.0967867	+	0.0703196i
$153$		0			0
$154$	1.08802	−	3.34857i	0.0876748	−	0.269835i
$155$	2.95032	+	7.39747i	0.236976	+	0.594179i
$156$		0			0
$157$	20.7688			1.65753			0.828767	−	0.559594i	$-0.189043\pi$
$157$	20.7688			1.65753			0.828767	+	0.559594i	$0.189043\pi$
$158$	9.21833	+	28.3711i	0.733371	+	2.25708i
$159$		0			0
$160$	18.0535	−	1.18124i	1.42725	−	0.0933855i
$161$	1.21505	−	0.882787i	0.0957595	−	0.0695734i
$162$		0			0
$163$	5.65797	+	4.11075i	0.443166	+	0.321979i	0.786892	−	0.617091i	$-0.211689\pi$
$163$	5.65797	+	4.11075i	0.443166	+	0.321979i	−0.343725	+	0.939070i	$0.611689\pi$
$164$	15.0832	−	10.9586i	1.17780	−	0.855722i
$165$		0			0
$166$	0.585056	+	0.425068i	0.0454092	+	0.0329917i
$167$	−4.59910	−	14.1546i	−0.355889	−	1.09531i	−0.955492	−	0.295016i	$-0.904675\pi$
$167$	−4.59910	−	14.1546i	−0.355889	−	1.09531i	0.599603	−	0.800297i	$-0.295325\pi$
$168$		0			0
$169$	3.51874	+	10.8296i	0.270672	+	0.833043i
$170$	4.52049	+	2.85293i	0.346706	+	0.218810i
$171$		0			0
$172$	−6.72232	+	20.6892i	−0.512572	+	1.57753i
$173$	−1.26528	+	0.919283i	−0.0961978	+	0.0698918i	−0.634844	−	0.772640i	$-0.718936\pi$
$173$	−1.26528	+	0.919283i	−0.0961978	+	0.0698918i	0.538647	+	0.842532i	$0.318936\pi$
$174$		0			0
$175$	−2.50000	+	0.328558i	−0.188982	+	0.0248366i
$176$	−12.8620			−0.969506
$177$		0			0
$178$	−4.08472	+	12.5715i	−0.306162	+	0.942271i
$179$	3.69979	−	11.3868i	0.276535	−	0.851089i	−0.712274	−	0.701902i	$-0.752334\pi$
$179$	3.69979	−	11.3868i	0.276535	−	0.851089i	0.988809	−	0.149187i	$-0.0476655\pi$
$180$		0			0
$181$	−0.257789	−	0.793394i	−0.0191613	−	0.0589725i	0.941019	−	0.338355i	$-0.109870\pi$
$181$	−0.257789	−	0.793394i	−0.0191613	−	0.0589725i	−0.960180	+	0.279382i	$0.909870\pi$
$182$	5.05636			0.374803
$183$		0			0
$184$	0.598444	+	0.434795i	0.0441179	+	0.0320535i
$185$	2.83837	+	1.79133i	0.208681	+	0.131701i
$186$		0			0
$187$	−3.27551	−	2.37980i	−0.239529	−	0.174028i
$188$	4.89845	+	3.55893i	0.357256	+	0.259562i
$189$		0			0
$190$	−22.7992	−	14.3888i	−1.65403	−	1.04387i
$191$	21.4128	+	15.5573i	1.54938	+	1.12569i	0.944092	+	0.329683i	$0.106942\pi$
$191$	21.4128	+	15.5573i	1.54938	+	1.12569i	0.605287	+	0.796007i	$0.293058\pi$
$192$		0			0
$193$	−3.97684			−0.286259			−0.143130	−	0.989704i	$-0.545717\pi$
$193$	−3.97684			−0.286259			−0.143130	+	0.989704i	$0.545717\pi$
$194$	−6.88944	−	21.2035i	−0.494633	−	1.52232i
$195$		0			0
$196$	−4.42407	+	13.6159i	−0.316005	+	0.972563i
$197$	−7.21923	+	22.2185i	−0.514349	+	1.58300i	0.270115	+	0.962828i	$0.412938\pi$
$197$	−7.21923	+	22.2185i	−0.514349	+	1.58300i	−0.784464	+	0.620174i	$0.787062\pi$
$198$		0			0
$199$	−4.43506			−0.314393			−0.157197	−	0.987567i	$-0.550246\pi$
$199$	−4.43506			−0.314393			−0.157197	+	0.987567i	$0.550246\pi$
$200$	−0.534399	−	1.12104i	−0.0377877	−	0.0792697i
$201$		0			0
$202$	−13.3115	+	9.67135i	−0.936592	+	0.680474i
$203$	0.781989	−	2.40671i	0.0548849	−	0.168918i
$204$		0			0
$205$	16.6114	+	10.4837i	1.16019	+	0.732210i
$206$	−3.38792	−	10.4269i	−0.236047	−	0.726479i
$207$		0			0
$208$	−5.70788	−	17.5670i	−0.395770	−	1.21806i
$209$	16.5201	+	12.0026i	1.14272	+	0.830235i
$210$		0			0
$211$	5.09234	−	3.69980i	0.350571	−	0.254705i	−0.398538	−	0.917152i	$-0.630482\pi$
$211$	5.09234	−	3.69980i	0.350571	−	0.254705i	0.749109	+	0.662447i	$0.230482\pi$
$212$	−22.7741	−	16.5463i	−1.56413	−	1.13641i
$213$		0			0
$214$	−17.4126	+	12.6510i	−1.19030	+	0.864803i
$215$	−22.8708	+	1.49644i	−1.55977	+	0.102056i
$216$		0			0
$217$	−0.555038	−	1.70823i	−0.0376784	−	0.115962i
$218$	5.68250			0.384868
$219$		0			0
$220$	6.04539	+	15.1578i	0.407580	+	1.02194i
$221$	1.79676	−	5.52985i	0.120863	−	0.371978i
$222$		0			0
$223$	−19.7640	+	14.3594i	−1.32350	+	0.961577i	−0.323615	+	0.946189i	$0.604898\pi$
$223$	−19.7640	+	14.3594i	−1.32350	+	0.961577i	−0.999882	+	0.0153877i	$0.995102\pi$
$224$	−4.08030			−0.272627
$225$		0			0
$226$	−14.4940			−0.964129
$227$	−10.8784	+	7.90360i	−0.722023	+	0.524581i	−0.887030	−	0.461712i	$-0.847235\pi$
$227$	−10.8784	+	7.90360i	−0.722023	+	0.524581i	0.165007	+	0.986292i	$0.447235\pi$
$228$		0			0
$229$	4.68153	−	14.4083i	0.309364	−	0.952126i	−0.668648	−	0.743579i	$-0.733127\pi$
$229$	4.68153	−	14.4083i	0.309364	−	0.952126i	0.978012	−	0.208547i	$-0.0668733\pi$
$230$	−3.32969	+	13.1045i	−0.219553	+	0.864085i
$231$		0			0
$232$	1.24637			0.0818281
$233$	−0.986111	−	3.03494i	−0.0646023	−	0.198825i	0.913545	−	0.406737i	$-0.133333\pi$
$233$	−0.986111	−	3.03494i	−0.0646023	−	0.198825i	−0.978148	+	0.207911i	$0.933333\pi$
$234$		0			0
$235$	−1.57098	+	6.18283i	−0.102480	+	0.403324i
$236$	16.3127	−	11.8519i	1.06187	−	0.771491i
$237$		0			0
$238$	−0.975319	−	0.708611i	−0.0632206	−	0.0459324i
$239$	−18.2944	+	13.2917i	−1.18337	+	0.859767i	−0.992548	−	0.121858i	$-0.961115\pi$
$239$	−18.2944	+	13.2917i	−1.18337	+	0.859767i	−0.190820	+	0.981625i	$0.561115\pi$
$240$		0			0
$241$	15.5019	+	11.2628i	0.998567	+	0.725501i	0.961780	−	0.273822i	$-0.0882878\pi$
$241$	15.5019	+	11.2628i	0.998567	+	0.725501i	0.0367866	+	0.999323i	$0.488288\pi$
$242$	−0.517348	−	1.59223i	−0.0332564	−	0.102353i
$243$		0			0
$244$	−5.56198	−	17.1180i	−0.356069	−	1.09587i
$245$	−15.0516	+	0.984831i	−0.961613	+	0.0629185i
$246$		0			0
$247$	−9.06198	+	27.8899i	−0.576600	+	1.77459i
$248$	0.715693	−	0.519981i	0.0454465	−	0.0330188i
$249$		0			0
$250$	15.4144	−	16.6639i	0.974895	−	1.05392i
$251$	21.1160			1.33283			0.666414	−	0.745582i	$-0.267828\pi$
$251$	21.1160			1.33283			0.666414	+	0.745582i	$0.267828\pi$
$252$		0			0
$253$	3.16464	−	9.73975i	0.198959	−	0.612333i
$254$	2.84018	−	8.74119i	0.178209	−	0.548471i
$255$		0			0
$256$	4.28513	+	13.1883i	0.267820	+	0.824267i
$257$	−18.4143			−1.14865			−0.574325	−	0.818627i	$-0.694735\pi$
$257$	−18.4143			−1.14865			−0.574325	+	0.818627i	$0.694735\pi$
$258$		0			0
$259$	−0.612394	−	0.444931i	−0.0380523	−	0.0276466i
$260$	−18.0200	+	14.9836i	−1.11755	+	0.929245i
$261$		0			0
$262$	15.9152	+	11.5631i	0.983246	+	0.714370i
$263$	0.481568	+	0.349879i	0.0296947	+	0.0215745i	0.602534	−	0.798093i	$-0.294158\pi$
$263$	0.481568	+	0.349879i	0.0296947	+	0.0215745i	−0.572839	+	0.819668i	$0.694158\pi$
$264$		0			0
$265$	7.30387	−	28.7455i	0.448673	−	1.76582i
$266$	4.91904	+	3.57389i	0.301606	+	0.219129i
$267$		0			0
$268$	−20.5928			−1.25790
$269$	2.41478	+	7.43193i	0.147232	+	0.453133i	0.997291	−	0.0735538i	$-0.0234341\pi$
$269$	2.41478	+	7.43193i	0.147232	+	0.453133i	−0.850059	+	0.526687i	$0.823434\pi$
$270$		0			0
$271$	−6.51138	+	20.0400i	−0.395538	+	1.21734i	0.533003	+	0.846113i	$0.321063\pi$
$271$	−6.51138	+	20.0400i	−0.395538	+	1.21734i	−0.928542	+	0.371228i	$0.878937\pi$
$272$	−1.36090	+	4.18841i	−0.0825166	+	0.253960i
$273$		0			0
$274$	8.09017			0.488745
$275$	−12.4743	+	11.8324i	−0.752232	+	0.713519i
$276$		0			0
$277$	−16.1304	+	11.7194i	−0.969184	+	0.704153i	−0.955265	−	0.295750i	$-0.904430\pi$
$277$	−16.1304	+	11.7194i	−0.969184	+	0.704153i	−0.0139182	+	0.999903i	$0.504430\pi$
$278$	−3.11289	+	9.58050i	−0.186699	+	0.574600i
$279$		0			0
$280$	0.103758	+	0.260158i	0.00620075	+	0.0155474i
$281$	−3.17758	−	9.77960i	−0.189559	−	0.583402i	0.810438	−	0.585824i	$-0.199229\pi$
$281$	−3.17758	−	9.77960i	−0.189559	−	0.583402i	−0.999997	+	0.00242215i	$0.999229\pi$
$282$		0			0
$283$	−2.98891	−	9.19891i	−0.177672	−	0.546819i	0.822073	−	0.569382i	$-0.192817\pi$
$283$	−2.98891	−	9.19891i	−0.177672	−	0.546819i	−0.999745	+	0.0225631i	$0.992817\pi$
$284$	−23.5499	−	17.1100i	−1.39743	−	1.01529i
$285$		0			0
$286$	27.8933	−	20.2657i	1.64937	−	1.19833i
$287$	−3.58400	−	2.60393i	−0.211557	−	0.153705i
$288$		0			0
$289$	12.6317	−	9.17750i	0.743044	−	0.539853i
$290$	8.43954	+	21.1608i	0.495587	+	1.24261i
$291$		0			0
$292$	−8.15791	−	25.1075i	−0.477405	−	1.46930i
$293$	11.0903			0.647900			0.323950	−	0.946074i	$-0.394989\pi$
$293$	11.0903			0.647900			0.323950	+	0.946074i	$0.394989\pi$
$294$		0			0
$295$	17.9655	+	11.3382i	1.04599	+	0.660137i
$296$	0.115208	−	0.354575i	0.00669636	−	0.0206093i
$297$		0			0
$298$	−9.23337	+	6.70844i	−0.534875	+	0.388609i
$299$	14.7071			0.850533
$300$		0			0
$301$	5.16906			0.297940
$302$	−3.86689	+	2.80946i	−0.222514	+	0.161666i
$303$		0			0
$304$	6.86372	−	21.1243i	0.393661	−	1.21156i
$305$	14.5813	−	12.1244i	0.834923	−	0.694239i
$306$		0			0
$307$	2.14760			0.122570			0.0612850	−	0.998120i	$-0.480480\pi$
$307$	2.14760			0.122570			0.0612850	+	0.998120i	$0.480480\pi$
$308$	−1.13731	−	3.50027i	−0.0648040	−	0.199446i
$309$		0			0
$310$	13.6744	+	8.63006i	0.776654	+	0.490154i
$311$	8.93231	−	6.48970i	0.506505	−	0.367997i	−0.304991	−	0.952355i	$-0.598654\pi$
$311$	8.93231	−	6.48970i	0.506505	−	0.367997i	0.811496	+	0.584358i	$0.198654\pi$
$312$		0			0
$313$	9.40884	+	6.83592i	0.531819	+	0.386389i	0.821038	−	0.570874i	$-0.193396\pi$
$313$	9.40884	+	6.83592i	0.531819	+	0.386389i	−0.289219	+	0.957263i	$0.593396\pi$
$314$	34.1147	−	24.7858i	1.92520	−	1.39874i
$315$		0			0
$316$	25.2272	+	18.3287i	1.41914	+	1.03107i
$317$	3.25520	+	10.0185i	0.182830	+	0.562694i	0.999904	−	0.0138389i	$-0.00440520\pi$
$317$	3.25520	+	10.0185i	0.182830	+	0.562694i	−0.817074	+	0.576533i	$0.804405\pi$
$318$		0			0
$319$	−5.33218	−	16.4108i	−0.298545	−	0.918826i
$320$	15.3828	−	12.7908i	0.859925	−	0.715028i
$321$		0			0
$322$	0.942305	−	2.90012i	0.0525126	−	0.161617i
$323$	5.65652	−	4.10970i	0.314737	−	0.228670i
$324$		0			0
$325$	−21.6967	−	11.7867i	−1.20352	−	0.653807i
$326$	14.1995			0.786440
$327$		0			0
$328$	0.674251	−	2.07513i	0.0372293	−	0.114580i
$329$	0.444589	−	1.36830i	0.0245110	−	0.0754370i
$330$		0			0
$331$	−7.22593	−	22.2391i	−0.397173	−	1.22237i	−0.927256	−	0.374427i	$-0.877839\pi$
$331$	−7.22593	−	22.2391i	−0.397173	−	1.22237i	0.530083	−	0.847945i	$-0.322161\pi$
$332$	0.755931			0.0414871
$333$		0			0
$334$	−24.4467	−	17.7615i	−1.33766	−	0.971868i
$335$	−8.03746	−	20.1527i	−0.439133	−	1.10106i
$336$		0			0
$337$	−3.37793	−	2.45421i	−0.184008	−	0.133689i	0.491968	−	0.870613i	$-0.336278\pi$
$337$	−3.37793	−	2.45421i	−0.184008	−	0.133689i	−0.675976	+	0.736924i	$0.736278\pi$
$338$	18.7040	+	13.5892i	1.01736	+	0.739157i
$339$		0			0
$340$	5.57571	−	0.364820i	0.302385	−	0.0197851i
$341$	−9.90837	−	7.19885i	−0.536568	−	0.389840i
$342$		0			0
$343$	6.93194			0.374290
$344$	0.786724	+	2.42129i	0.0424173	+	0.130547i
$345$		0			0
$346$	−0.981261	+	3.02001i	−0.0527529	+	0.162357i
$347$	2.58175	−	7.94582i	0.138596	−	0.426554i	−0.857536	−	0.514424i	$-0.828006\pi$
$347$	2.58175	−	7.94582i	0.138596	−	0.426554i	0.996132	+	0.0878696i	$0.0280059\pi$
$348$		0			0
$349$	8.84117			0.473257			0.236628	−	0.971600i	$-0.423958\pi$
$349$	8.84117			0.473257			0.236628	+	0.971600i	$0.423958\pi$
$350$	−3.71437	+	3.52321i	−0.198541	+	0.188324i
$351$		0			0
$352$	−22.5089	+	16.3537i	−1.19973	+	0.871653i
$353$	2.87823	−	8.85828i	0.153193	−	0.471479i	−0.844781	−	0.535113i	$-0.820269\pi$
$353$	2.87823	−	8.85828i	0.153193	−	0.471479i	0.997973	+	0.0636341i	$0.0202691\pi$
$354$		0			0
$355$	7.55269	−	29.7247i	0.400855	−	1.57763i
$356$	4.26977	+	13.1410i	0.226297	+	0.696471i
$357$		0			0
$358$	−7.51188	−	23.1192i	−0.397015	−	1.22189i
$359$	5.70869	+	4.14761i	0.301293	+	0.218902i	0.728152	−	0.685416i	$-0.240380\pi$
$359$	5.70869	+	4.14761i	0.301293	+	0.218902i	−0.426858	+	0.904319i	$0.640380\pi$
$360$		0			0
$361$	−13.1574	+	9.55944i	−0.692497	+	0.503128i
$362$	−1.37029	−	0.995572i	−0.0720207	−	0.0523261i
$363$		0			0
$364$	4.27600	−	3.10670i	0.224123	−	0.162835i
$365$	21.3868	−	17.7831i	1.11944	−	0.930811i
$366$		0			0
$367$	1.03134	+	3.17412i	0.0538353	+	0.165688i	0.974359	−	0.224998i	$-0.0722377\pi$
$367$	1.03134	+	3.17412i	0.0538353	+	0.165688i	−0.920524	+	0.390686i	$0.872238\pi$
$368$	−11.1394			−0.580683
$369$		0			0
$370$	6.80008	−	0.444931i	0.353519	−	0.0231308i
$371$	−2.06700	+	6.36157i	−0.107313	+	0.330276i
$372$		0			0
$373$	−13.6425	+	9.91184i	−0.706381	+	0.513216i	−0.882004	−	0.471242i	$-0.843806\pi$
$373$	−13.6425	+	9.91184i	−0.706381	+	0.513216i	0.175623	+	0.984457i	$0.443806\pi$
$374$	−8.22041			−0.425067
$375$		0			0
$376$	0.708606			0.0365436
$377$	20.0477	−	14.5655i	1.03251	−	0.750163i
$378$		0			0
$379$	−0.605237	+	1.86273i	−0.0310889	+	0.0956819i	−0.965397	−	0.260785i	$-0.916019\pi$
$379$	−0.605237	+	1.86273i	−0.0310889	+	0.0956819i	0.934308	+	0.356467i	$0.116019\pi$
$380$	−28.1212	+	1.83998i	−1.44259	+	0.0943887i
$381$		0			0
$382$	53.7388			2.74952
$383$	4.58432	+	14.1091i	0.234248	+	0.720940i	0.997220	+	0.0745092i	$0.0237390\pi$
$383$	4.58432	+	14.1091i	0.234248	+	0.720940i	−0.762973	+	0.646431i	$0.776261\pi$
$384$		0			0
$385$	2.98156	−	2.47917i	0.151955	−	0.126350i
$386$	−6.53231	+	4.74600i	−0.332486	+	0.241565i
$387$		0			0
$388$	−18.8539	−	13.6982i	−0.957162	−	0.695419i
$389$	−24.1901	+	17.5751i	−1.22649	+	0.891094i	−0.996622	−	0.0821294i	$-0.973828\pi$
$389$	−24.1901	+	17.5751i	−1.22649	+	0.891094i	−0.229863	+	0.973223i	$0.573828\pi$
$390$		0			0
$391$	−2.83684	−	2.06109i	−0.143465	−	0.104234i
$392$	0.517756	+	1.59349i	0.0261506	+	0.0804834i
$393$		0			0
$394$	14.6576	+	45.1114i	0.738438	+	2.27268i
$395$	−8.09062	+	31.8418i	−0.407083	+	1.60214i
$396$		0			0
$397$	0.858602	−	2.64251i	0.0430920	−	0.132624i	−0.927196	−	0.374577i	$-0.877788\pi$
$397$	0.858602	−	2.64251i	0.0430920	−	0.132624i	0.970288	+	0.241953i	$0.0777880\pi$
$398$	−7.28499	+	5.29285i	−0.365163	+	0.265307i
$399$		0			0
$400$	16.4335	+	8.92745i	0.821674	+	0.446373i
$401$	−8.54941			−0.426937			−0.213469	−	0.976950i	$-0.568476\pi$
$401$	−8.54941			−0.426937			−0.213469	+	0.976950i	$0.568476\pi$
$402$		0			0
$403$	5.43516	−	16.7277i	0.270745	−	0.833266i
$404$	−5.31487	+	16.3575i	−0.264425	+	0.813816i
$405$		0			0
$406$	−1.58771	−	4.88648i	−0.0787969	−	0.242512i
$407$	−5.16152			−0.255847
$408$		0			0
$409$	−5.03563	−	3.65860i	−0.248996	−	0.180906i	0.456286	−	0.889833i	$-0.349180\pi$
$409$	−5.03563	−	3.65860i	−0.248996	−	0.180906i	−0.705282	+	0.708927i	$0.749180\pi$
$410$	39.7971	−	2.60393i	1.96544	−	0.128599i
$411$		0			0
$412$	−9.27150	−	6.73614i	−0.456774	−	0.331866i
$413$	−3.87615	−	2.81619i	−0.190733	−	0.138576i
$414$		0			0
$415$	0.295044	+	0.739775i	0.0144831	+	0.0363141i
$416$	−32.3251	−	23.4855i	−1.58487	−	1.15147i
$417$		0			0
$418$	41.4598			2.02786
$419$	−11.5879	−	35.6639i	−0.566106	−	1.74229i	−0.664644	−	0.747160i	$-0.731417\pi$
$419$	−11.5879	−	35.6639i	−0.566106	−	1.74229i	0.0985382	−	0.995133i	$-0.468583\pi$
$420$		0			0
$421$	2.92653	−	9.00692i	0.142630	−	0.438970i	−0.854069	−	0.520161i	$-0.825872\pi$
$421$	2.92653	−	9.00692i	0.142630	−	0.438970i	0.996699	+	0.0811902i	$0.0258721\pi$
$422$	3.94924	−	12.1545i	0.192246	−	0.591672i
$423$		0			0
$424$	−3.29448			−0.159994
$425$	2.53325	+	5.31415i	0.122881	+	0.257774i
$426$		0			0
$427$	−3.46003	+	2.51386i	−0.167443	+	0.121654i
$428$	−6.95232	+	21.3970i	−0.336053	+	1.03427i
$429$		0			0
$430$	−35.7814	+	29.7523i	−1.72553	+	1.43478i
$431$	3.05401	+	9.39927i	0.147106	+	0.452747i	0.997276	−	0.0737623i	$-0.0235006\pi$
$431$	3.05401	+	9.39927i	0.147106	+	0.452747i	−0.850170	+	0.526509i	$0.823501\pi$
$432$		0			0
$433$	7.50377	+	23.0942i	0.360608	+	1.10984i	0.952686	+	0.303957i	$0.0983080\pi$
$433$	7.50377	+	23.0942i	0.360608	+	1.10984i	−0.592077	+	0.805881i	$0.701692\pi$
$434$	−2.95032	−	2.14354i	−0.141620	−	0.102893i
$435$		0			0
$436$	4.80551	−	3.49141i	0.230142	−	0.167208i
$437$	14.3077	+	10.3951i	0.684429	+	0.497267i
$438$		0			0
$439$	1.42111	−	1.03250i	0.0678258	−	0.0492784i	−0.553356	−	0.832945i	$-0.686653\pi$
$439$	1.42111	−	1.03250i	0.0678258	−	0.0492784i	0.621182	+	0.783667i	$0.286653\pi$
$440$	1.61508	+	1.01930i	0.0769960	+	0.0485930i
$441$		0			0
$442$	−3.64805	−	11.2276i	−0.173520	−	0.534040i
$443$	−37.3529			−1.77469			−0.887346	−	0.461105i	$-0.847453\pi$
$443$	−37.3529			−1.77469			−0.887346	+	0.461105i	$0.847453\pi$
$444$		0			0
$445$	−11.1936	+	9.30751i	−0.530629	+	0.441218i
$446$	−15.3275	+	47.1732i	−0.725779	+	2.23372i
$447$		0			0
$448$	−3.65022	+	2.65204i	−0.172457	+	0.125297i
$449$	−12.9452			−0.610923			−0.305461	−	0.952204i	$-0.598811\pi$
$449$	−12.9452			−0.610923			−0.305461	+	0.952204i	$0.598811\pi$
$450$		0			0
$451$	−30.2075			−1.42242
$452$	−12.2571	+	8.90534i	−0.576528	+	0.418872i
$453$		0			0
$454$	−8.43646	+	25.9648i	−0.395943	+	1.21859i
$455$	4.70925	+	2.97206i	0.220773	+	0.139332i
$456$		0			0
$457$	−22.2891			−1.04264			−0.521320	−	0.853361i	$-0.674560\pi$
$457$	−22.2891			−1.04264			−0.521320	+	0.853361i	$0.674560\pi$
$458$	−9.50516	−	29.2539i	−0.444147	−	1.36694i
$459$		0			0
$460$	5.23577	+	13.1279i	0.244119	+	0.612089i
$461$	−0.434539	+	0.315711i	−0.0202385	+	0.0147041i	−0.597859	−	0.801602i	$-0.703982\pi$
$461$	−0.434539	+	0.315711i	−0.0202385	+	0.0147041i	0.577620	+	0.816306i	$0.303982\pi$
$462$		0			0
$463$	18.0822	+	13.1375i	0.840349	+	0.610550i	0.922468	−	0.386073i	$-0.126169\pi$
$463$	18.0822	+	13.1375i	0.840349	+	0.610550i	−0.0821189	+	0.996623i	$0.526169\pi$
$464$	−15.1845	+	11.0322i	−0.704925	+	0.512158i
$465$		0			0
$466$	−5.24171	−	3.80832i	−0.242817	−	0.176417i
$467$	−11.5807	−	35.6417i	−0.535890	−	1.64930i	−0.741717	−	0.670712i	$-0.765988\pi$
$467$	−11.5807	−	35.6417i	−0.535890	−	1.64930i	0.205827	−	0.978588i	$-0.434012\pi$
$468$		0			0
$469$	1.51207	+	4.65367i	0.0698209	+	0.214887i
$470$	4.79819	+	12.0307i	0.221324	+	0.554934i
$471$		0			0
$472$	0.729213	−	2.24429i	0.0335647	−	0.103302i
$473$	28.5150	−	20.7174i	1.31112	−	0.952585i
$474$		0			0
$475$	−12.7765	−	26.8020i	−0.586226	−	1.22976i
$476$	−1.26018			−0.0577601
$477$		0			0
$478$	−14.1878	+	43.6656i	−0.648935	+	1.99722i
$479$	5.75361	−	17.7078i	0.262889	−	0.809089i	−0.729283	−	0.684212i	$-0.760146\pi$
$479$	5.75361	−	17.7078i	0.262889	−	0.809089i	0.992172	−	0.124877i	$-0.0398538\pi$
$480$		0			0
$481$	−2.29058	−	7.04968i	−0.104441	−	0.321438i
$482$	38.9045			1.77205
$483$		0			0
$484$	−1.41579	−	1.02864i	−0.0643543	−	0.0467561i
$485$	6.04663	−	23.7974i	0.274563	−	1.08058i
$486$		0			0
$487$	1.44904	+	1.05279i	0.0656622	+	0.0477064i	0.620132	−	0.784497i	$-0.287079\pi$
$487$	1.44904	+	1.05279i	0.0656622	+	0.0477064i	−0.554470	+	0.832204i	$0.687079\pi$
$488$	−1.70415	−	1.23814i	−0.0771433	−	0.0560479i
$489$		0			0
$490$	−23.5483	+	19.5804i	−1.06381	+	0.884555i
$491$	−22.0663	−	16.0321i	−0.995839	−	0.723519i	−0.0346469	−	0.999400i	$-0.511031\pi$
$491$	−22.0663	−	16.0321i	−0.995839	−	0.723519i	−0.961192	+	0.275880i	$0.911031\pi$
$492$		0			0
$493$	−5.90825			−0.266094
$494$	18.3990	+	56.6264i	0.827811	+	2.54774i
$495$		0			0
$496$	−4.11669	+	12.6699i	−0.184845	+	0.568894i
$497$	−2.13742	+	6.57829i	−0.0958763	+	0.295077i
$498$		0			0
$499$	10.5722			0.473275			0.236637	−	0.971598i	$-0.423955\pi$
$499$	10.5722			0.473275			0.236637	+	0.971598i	$0.423955\pi$
$500$	2.79695	−	23.5630i	0.125083	−	1.05377i
$501$		0			0
$502$	34.6849	−	25.2000i	1.54806	−	1.12473i
$503$	−8.37251	+	25.7679i	−0.373312	+	1.14894i	0.571299	+	0.820742i	$0.306440\pi$
$503$	−8.37251	+	25.7679i	−0.373312	+	1.14894i	−0.944610	+	0.328194i	$0.893560\pi$
$504$		0			0
$505$	−18.0823	+	1.18313i	−0.804653	+	0.0526486i
$506$	−6.42533	−	19.7751i	−0.285641	−	0.879112i
$507$		0			0
$508$	−2.96885	−	9.13719i	−0.131721	−	0.405397i
$509$	22.7355	+	16.5183i	1.00773	+	0.732161i	0.963732	−	0.266871i	$-0.0859897\pi$
$509$	22.7355	+	16.5183i	1.00773	+	0.732161i	0.0440004	+	0.999032i	$0.485990\pi$
$510$		0			0
$511$	−5.07492	+	3.68714i	−0.224501	+	0.163110i
$512$	25.9868	+	18.8805i	1.14847	+	0.834410i
$513$		0			0
$514$	−30.2471	+	21.9758i	−1.33414	+	0.969311i
$515$	2.97346	−	11.7025i	0.131026	−	0.515674i
$516$		0			0
$517$	−3.03154	−	9.33011i	−0.133327	−	0.410338i
$518$	−1.53690			−0.0675274
$519$		0			0
$520$	−0.675427	+	2.65824i	−0.0296194	+	0.116572i
$521$	−10.2133	+	31.4332i	−0.447452	+	1.37711i	0.432321	+	0.901720i	$0.357695\pi$
$521$	−10.2133	+	31.4332i	−0.447452	+	1.37711i	−0.879772	+	0.475395i	$0.842305\pi$
$522$		0			0
$523$	32.9601	−	23.9469i	1.44125	−	1.04713i	0.453465	−	0.891274i	$-0.350188\pi$
$523$	32.9601	−	23.9469i	1.44125	−	1.04713i	0.987780	−	0.155852i	$-0.0498122\pi$
$524$	20.5635			0.898321
$525$		0			0
$526$	1.20857			0.0526961
$527$	−3.39265	+	2.46490i	−0.147786	+	0.107373i
$528$		0			0
$529$	−4.36657	+	13.4389i	−0.189851	+	0.584301i
$530$	−22.3079	−	55.9335i	−0.968993	−	2.42960i
$531$		0			0
$532$	6.35572			0.275555
$533$	−13.4055	−	41.2579i	−0.580656	−	1.78708i
$534$		0			0
$535$	−23.6533	+	1.54764i	−1.02262	+	0.0669102i
$536$	−1.94974	+	1.41657i	−0.0842158	+	0.0611863i
$537$		0			0
$538$	12.8359	+	9.32579i	0.553393	+	0.402063i
$539$	18.7662	−	13.6344i	0.808317	−	0.587277i
$540$		0			0
$541$	−36.5725	−	26.5715i	−1.57238	−	1.14240i	−0.924837	−	0.380364i	$-0.875799\pi$
$541$	−36.5725	−	26.5715i	−1.57238	−	1.14240i	−0.647538	−	0.762033i	$-0.724201\pi$
$542$	13.2204	+	40.6882i	0.567865	+	1.74771i
$543$		0			0
$544$	2.94385	+	9.06022i	0.126216	+	0.388454i
$545$	5.29240	+	3.34009i	0.226702	+	0.143074i
$546$		0			0
$547$	0.753668	−	2.31955i	0.0322245	−	0.0991768i	−0.933651	−	0.358185i	$-0.883396\pi$
$547$	0.753668	−	2.31955i	0.0322245	−	0.0991768i	0.965875	+	0.259008i	$0.0833957\pi$
$548$	6.84159	−	4.97071i	0.292258	−	0.212338i
$549$		0			0
$550$	−6.36936	+	34.3228i	−0.271590	+	1.46353i
$551$	29.7984			1.26945
$552$		0			0
$553$	2.28965	−	7.04682i	0.0973659	−	0.299661i
$554$	−12.5096	+	38.5005i	−0.531480	+	1.63573i
$555$		0			0
$556$	3.25392	+	10.0145i	0.137997	+	0.424710i
$557$	−7.91914			−0.335545			−0.167772	−	0.985826i	$-0.553657\pi$
$557$	−7.91914			−0.335545			−0.167772	+	0.985826i	$0.553657\pi$
$558$		0			0
$559$	40.9505	+	29.7523i	1.73202	+	1.25839i
$560$	−3.56687	−	2.25109i	−0.150728	−	0.0951260i
$561$		0			0
$562$	−16.8906	−	12.2717i	−0.712485	−	0.517651i
$563$	19.4577	+	14.1369i	0.820045	+	0.595797i	0.916725	−	0.399518i	$-0.130822\pi$
$563$	19.4577	+	14.1369i	0.820045	+	0.595797i	−0.0966805	+	0.995315i	$0.530822\pi$
$564$		0			0
$565$	−13.4990	−	8.51939i	−0.567909	−	0.358413i
$566$	−15.8876	−	11.5430i	−0.667807	−	0.485190i
$567$		0			0
$568$	−3.40671			−0.142942
$569$	4.52263	+	13.9192i	0.189598	+	0.583524i	0.999997	−	0.00235460i	$-0.000749494\pi$
$569$	4.52263	+	13.9192i	0.189598	+	0.583524i	−0.810399	+	0.585879i	$0.800749\pi$
$570$		0			0
$571$	6.53259	−	20.1052i	0.273380	−	0.841378i	−0.716263	−	0.697830i	$-0.754149\pi$
$571$	6.53259	−	20.1052i	0.273380	−	0.841378i	0.989643	−	0.143548i	$-0.0458511\pi$
$572$	11.1370	−	34.2761i	0.465660	−	1.43315i
$573$		0			0
$574$	−8.99461			−0.375428
$575$	−10.8037	+	10.2477i	−0.450547	+	0.427360i
$576$		0			0
$577$	3.19476	−	2.32113i	0.132999	−	0.0966298i	−0.519296	−	0.854594i	$-0.673806\pi$
$577$	3.19476	−	2.32113i	0.132999	−	0.0966298i	0.652296	+	0.757964i	$0.273806\pi$
$578$	9.79625	−	30.1497i	0.407470	−	1.25406i
$579$		0			0
$580$	20.1385	+	12.7096i	0.836207	+	0.527739i
$581$	−0.0555059	−	0.170830i	−0.00230277	−	0.00708721i
$582$		0			0
$583$	14.0943	+	43.3779i	0.583728	+	1.79653i
$584$	−2.49952	−	1.81601i	−0.103431	−	0.0751471i
$585$		0			0
$586$	18.2168	−	13.2353i	0.752528	−	0.546743i
$587$	16.4014	+	11.9164i	0.676960	+	0.491840i	0.872348	−	0.488886i	$-0.162596\pi$
$587$	16.4014	+	11.9164i	0.676960	+	0.491840i	−0.195388	+	0.980726i	$0.562596\pi$
$588$		0			0
$589$	17.1109	−	12.4318i	0.705041	−	0.512243i
$590$	43.0411	−	2.81619i	1.77198	−	0.115941i
$591$		0			0
$592$	1.73493	+	5.33956i	0.0713051	+	0.219455i
$593$	−30.2561			−1.24247			−0.621234	−	0.783625i	$-0.713368\pi$
$593$	−30.2561			−1.24247			−0.621234	+	0.783625i	$0.713368\pi$
$594$		0			0
$595$	−0.491853	−	1.23324i	−0.0201640	−	0.0505580i
$596$	−3.68661	+	11.3462i	−0.151009	+	0.464759i
$597$		0			0
$598$	24.1577	−	17.5516i	0.987883	−	0.717739i
$599$	1.02686			0.0419563			0.0209781	−	0.999780i	$-0.493322\pi$
$599$	1.02686			0.0419563			0.0209781	+	0.999780i	$0.493322\pi$
$600$		0			0
$601$	−16.9840			−0.692791			−0.346396	−	0.938089i	$-0.612594\pi$
$601$	−16.9840			−0.692791			−0.346396	+	0.938089i	$0.612594\pi$
$602$	8.49065	−	6.16882i	0.346053	−	0.251422i
$603$		0			0
$604$	−1.54393	+	4.75173i	−0.0628217	+	0.193345i
$605$	0.454059	−	1.78702i	0.0184601	−	0.0726526i
$606$		0			0
$607$	10.7660			0.436977			0.218488	−	0.975840i	$-0.429887\pi$
$607$	10.7660			0.436977			0.218488	+	0.975840i	$0.429887\pi$
$608$	−14.8473	−	45.6954i	−0.602139	−	1.85319i
$609$		0			0
$610$	9.48175	−	37.3168i	0.383905	−	1.51091i
$611$	11.3979	−	8.28103i	0.461108	−	0.335015i
$612$		0			0
$613$	4.08204	+	2.96577i	0.164872	+	0.119786i	0.667162	−	0.744913i	$-0.267509\pi$
$613$	4.08204	+	2.96577i	0.164872	+	0.119786i	−0.502290	+	0.864699i	$0.667509\pi$
$614$	3.52763	−	2.56297i	0.142363	−	0.103433i
$615$		0			0
$616$	−0.348462	−	0.253173i	−0.0140400	−	0.0102006i
$617$	9.60737	+	29.5684i	0.386778	+	1.19038i	0.935182	+	0.354167i	$0.115236\pi$
$617$	9.60737	+	29.5684i	0.386778	+	1.19038i	−0.548404	+	0.836213i	$0.684764\pi$
$618$		0			0
$619$	−10.7533	−	33.0951i	−0.432210	−	1.33021i	−0.895919	−	0.444218i	$-0.853481\pi$
$619$	−10.7533	−	33.0951i	−0.432210	−	1.33021i	0.463708	−	0.885988i	$-0.346519\pi$
$620$	16.8664	−	1.10357i	0.677372	−	0.0443206i
$621$		0			0
$622$	6.92724	−	21.3198i	0.277757	−	0.854848i
$623$	2.65616	−	1.92981i	0.106417	−	0.0773163i
$624$		0			0
$625$	24.1511	−	6.45958i	0.966042	−	0.258383i
$626$	23.6129			0.943763
$627$		0			0
$628$	13.6210	−	41.9211i	0.543536	−	1.67283i
$629$	−0.546130	+	1.68082i	−0.0217756	+	0.0670186i
$630$		0			0
$631$	−2.86250	−	8.80987i	−0.113954	−	0.350715i	0.877773	−	0.479076i	$-0.159028\pi$
$631$	−2.86250	−	8.80987i	−0.113954	−	0.350715i	−0.991727	+	0.128361i	$0.959028\pi$
$632$	3.64935			0.145163
$633$		0			0
$634$	17.3031	+	12.5715i	0.687195	+	0.499277i
$635$	7.78315	−	6.47169i	0.308865	−	0.256821i
$636$		0			0
$637$	26.9502	+	19.5804i	1.06780	+	0.775806i
$638$	−28.3434	−	20.5927i	−1.12213	−	0.815272i
$639$		0			0
$640$	1.09214	−	4.29827i	0.0431705	−	0.169904i
$641$	−35.3179	−	25.6600i	−1.39497	−	1.01351i	−0.995299	−	0.0968498i	$-0.969123\pi$
$641$	−35.3179	−	25.6600i	−1.39497	−	1.01351i	−0.399674	−	0.916657i	$-0.630877\pi$
$642$		0			0
$643$	−35.4133			−1.39656			−0.698281	−	0.715824i	$-0.746051\pi$
$643$	−35.4133			−1.39656			−0.698281	+	0.715824i	$0.746051\pi$
$644$	−0.984994	−	3.03150i	−0.0388142	−	0.119458i
$645$		0			0
$646$	4.38678	−	13.5011i	0.172595	−	0.531194i
$647$	−10.2984	+	31.6951i	−0.404870	+	1.24606i	0.516134	+	0.856508i	$0.327371\pi$
$647$	−10.2984	+	31.6951i	−0.404870	+	1.24606i	−0.921004	+	0.389554i	$0.872629\pi$
$648$		0			0
$649$	−32.6699			−1.28240
$650$	−49.7051	+	6.53240i	−1.94960	+	0.256222i
$651$		0			0
$652$	12.0081	−	8.72439i	0.470273	−	0.341674i
$653$	−5.78030	+	17.7899i	−0.226201	+	0.696174i	0.771967	+	0.635663i	$0.219273\pi$
$653$	−5.78030	+	17.7899i	−0.226201	+	0.696174i	−0.998168	+	0.0605113i	$0.980727\pi$
$654$		0			0
$655$	8.02604	+	20.1240i	0.313603	+	0.786311i
$656$	10.1536	+	31.2495i	0.396430	+	1.22009i
$657$		0			0
$658$	−0.902672	−	2.77814i	−0.0351898	−	0.108303i
$659$	20.9712	+	15.2365i	0.816921	+	0.593528i	0.915829	−	0.401569i	$-0.131535\pi$
$659$	20.9712	+	15.2365i	0.816921	+	0.593528i	−0.0989077	+	0.995097i	$0.531535\pi$
$660$		0			0
$661$	−18.6395	+	13.5424i	−0.724992	+	0.526738i	−0.887975	−	0.459891i	$-0.847888\pi$
$661$	−18.6395	+	13.5424i	−0.724992	+	0.526738i	0.162983	+	0.986629i	$0.447888\pi$
$662$	−38.4097	−	27.9063i	−1.49283	−	1.08461i
$663$		0			0
$664$	0.0715720	−	0.0520001i	0.00277753	−	0.00201800i
$665$	2.48067	+	6.21989i	0.0961963	+	0.241197i
$666$		0			0
$667$	−4.61807	−	14.2130i	−0.178813	−	0.550328i
$668$	−31.5867			−1.22213
$669$		0			0
$670$	−37.2527	−	23.5106i	−1.43920	−	0.908292i
$671$	−9.01174	+	27.7353i	−0.347894	+	1.07071i
$672$		0			0
$673$	4.97293	−	3.61304i	0.191692	−	0.139273i	−0.487800	−	0.872956i	$-0.662200\pi$
$673$	4.97293	−	3.61304i	0.191692	−	0.139273i	0.679492	+	0.733683i	$0.262200\pi$
$674$	−8.47744			−0.326539
$675$		0			0
$676$	24.1668			0.929491
$677$	28.7547	−	20.8915i	1.10513	−	0.802925i	0.123241	−	0.992377i	$-0.460671\pi$
$677$	28.7547	−	20.8915i	1.10513	−	0.802925i	0.981890	+	0.189452i	$0.0606711\pi$
$678$		0			0
$679$	−1.71120	+	5.26653i	−0.0656698	+	0.202111i
$680$	0.502816	−	0.418091i	0.0192821	−	0.0160331i
$681$		0			0
$682$	−24.8666			−0.952191
$683$	5.23883	+	16.1235i	0.200458	+	0.616947i	0.999869	+	0.0161627i	$0.00514496\pi$
$683$	5.23883	+	16.1235i	0.200458	+	0.616947i	−0.799411	+	0.600784i	$0.794855\pi$
$684$		0			0
$685$	7.53478	+	4.75528i	0.287889	+	0.181690i
$686$	11.3863	−	8.27266i	0.434732	−	0.315852i
$687$		0			0
$688$	−31.0167	−	22.5349i	−1.18250	−	0.859136i
$689$	−52.9914	+	38.5005i	−2.01881	+	1.46675i
$690$		0			0
$691$	12.9241	+	9.38990i	0.491656	+	0.357209i	0.805821	−	0.592160i	$-0.201725\pi$
$691$	12.9241	+	9.38990i	0.491656	+	0.357209i	−0.314165	+	0.949368i	$0.601725\pi$
$692$	1.02571	+	3.15683i	0.0389918	+	0.120004i
$693$		0			0
$694$	−5.24187	−	16.1328i	−0.198979	−	0.612394i
$695$	−8.53047	+	7.09309i	−0.323579	+	0.269056i
$696$		0			0
$697$	−3.19620	+	9.83689i	−0.121065	+	0.372599i
$698$	14.5224	−	10.5512i	0.549681	−	0.399367i
$699$		0			0
$700$	−0.976413	+	5.26163i	−0.0369049	+	0.198871i
$701$	−19.5403			−0.738026			−0.369013	−	0.929424i	$-0.620304\pi$
$701$	−19.5403			−0.738026			−0.369013	+	0.929424i	$0.620304\pi$
$702$		0			0
$703$	2.75442	−	8.47723i	0.103885	−	0.319725i
$704$	−9.50710	+	29.2598i	−0.358312	+	1.10277i
$705$		0			0
$706$	−5.84382	−	17.9854i	−0.219935	−	0.676891i
$707$	4.08682			0.153701
$708$		0			0
$709$	10.6571	+	7.74285i	0.400236	+	0.290789i	0.769637	−	0.638481i	$-0.220437\pi$
$709$	10.6571	+	7.74285i	0.400236	+	0.290789i	−0.369401	+	0.929270i	$0.620437\pi$
$710$	−23.0679	−	57.8390i	−0.865722	−	2.17066i
$711$		0			0
$712$	1.30823	+	0.950482i	0.0490278	+	0.0356208i
$713$	−8.58141	−	6.23476i	−0.321376	−	0.233493i
$714$		0			0
$715$	37.8903	−	2.47917i	1.41702	−	0.0927157i
$716$	−20.5573	−	14.9358i	−0.768263	−	0.558175i
$717$		0			0
$718$	14.3268			0.534673
$719$	2.58348	+	7.95114i	0.0963476	+	0.296527i	0.987603	−	0.156975i	$-0.0501743\pi$
$719$	2.58348	+	7.95114i	0.0963476	+	0.296527i	−0.891255	+	0.453503i	$0.850174\pi$
$720$		0			0
$721$	−0.841492	+	2.58984i	−0.0313388	+	0.0964509i
$722$	−10.2039	+	31.4045i	−0.379751	+	1.16875i
$723$		0			0
$724$	−1.77050			−0.0658002
$725$	−4.57784	+	24.6688i	−0.170017	+	0.916175i
$726$		0			0
$727$	0.213756	−	0.155303i	0.00792778	−	0.00575987i	−0.583814	−	0.811887i	$-0.698440\pi$
$727$	0.213756	−	0.155303i	0.00792778	−	0.00575987i	0.591742	+	0.806127i	$0.298440\pi$
$728$	0.191146	−	0.588288i	0.00708436	−	0.0218034i
$729$		0			0
$730$	13.9071	−	54.7336i	0.514726	−	2.02578i
$731$	−3.72936	−	11.4778i	−0.137935	−	0.424522i
$732$		0			0
$733$	5.55648	+	17.1011i	0.205233	+	0.631643i	0.999704	+	0.0243402i	$0.00774850\pi$
$733$	5.55648	+	17.1011i	0.205233	+	0.631643i	−0.794470	+	0.607303i	$0.792251\pi$
$734$	5.48210	+	3.98298i	0.202348	+	0.147014i
$735$		0			0
$736$	−19.4944	+	14.1635i	−0.718574	+	0.522074i
$737$	26.9930	+	19.6116i	0.994301	+	0.722402i
$738$		0			0
$739$	30.3496	−	22.0502i	1.11643	−	0.811132i	0.132763	−	0.991148i	$-0.457615\pi$
$739$	30.3496	−	22.0502i	1.11643	−	0.811132i	0.983664	+	0.180016i	$0.0576150\pi$
$740$	5.47724	−	4.55432i	0.201347	−	0.167420i
$741$		0			0
$742$	4.19674	+	12.9162i	0.154067	+	0.474170i
$743$	18.6523			0.684285			0.342142	−	0.939648i	$-0.388847\pi$
$743$	18.6523			0.684285			0.342142	+	0.939648i	$0.388847\pi$
$744$		0			0
$745$	−12.5426	+	0.820667i	−0.459526	+	0.0300669i
$746$	−10.5801	+	32.5622i	−0.387365	+	1.19219i
$747$		0			0
$748$	−6.95173	+	5.05073i	−0.254180	+	0.184673i
$749$	5.34592			0.195336
$750$		0			0
$751$	51.3728			1.87462			0.937310	−	0.348496i	$-0.113307\pi$
$751$	51.3728			1.87462			0.937310	+	0.348496i	$0.113307\pi$
$752$	−8.63296	+	6.27221i	−0.314812	+	0.228724i
$753$		0			0
$754$	15.5475	−	47.8504i	0.566208	−	1.74261i
$755$	−5.25278	+	0.343691i	−0.191168	+	0.0125082i
$756$		0			0
$757$	−33.8427			−1.23003			−0.615016	−	0.788514i	$-0.710851\pi$
$757$	−33.8427			−1.23003			−0.615016	+	0.788514i	$0.710851\pi$
$758$	1.22884	+	3.78199i	0.0446336	+	0.137368i
$759$		0			0
$760$	−2.53596	+	2.10865i	−0.0919889	+	0.0764888i
$761$	−8.76122	+	6.36540i	−0.317594	+	0.230746i	−0.735148	−	0.677906i	$-0.762887\pi$
$761$	−8.76122	+	6.36540i	−0.317594	+	0.230746i	0.417554	+	0.908652i	$0.362887\pi$
$762$		0			0
$763$	−1.14186	−	0.829613i	−0.0413382	−	0.0300340i
$764$	45.4452	−	33.0179i	1.64415	−	1.19454i
$765$		0			0
$766$	24.3681	+	17.7044i	0.880455	+	0.639688i
$767$	−14.4982	−	44.6210i	−0.523501	−	1.61117i
$768$		0			0
$769$	−10.2290	−	31.4815i	−0.368866	−	1.13525i	−0.947524	−	0.319683i	$-0.896423\pi$
$769$	−10.2290	−	31.4815i	−0.368866	−	1.13525i	0.578658	−	0.815570i	$-0.303577\pi$
$770$	1.93881	−	7.63049i	0.0698700	−	0.274984i
$771$		0			0
$772$	−2.60816	+	8.02708i	−0.0938696	+	0.288901i
$773$	−8.15139	+	5.92233i	−0.293185	+	0.213011i	−0.724648	−	0.689119i	$-0.757998\pi$
$773$	−8.15139	+	5.92233i	−0.293185	+	0.213011i	0.431463	+	0.902131i	$0.357998\pi$
$774$		0			0
$775$	7.66304	+	16.0752i	0.275264	+	0.577439i
$776$	−2.72739			−0.0979075
$777$		0			0
$778$	−18.7600	+	57.7374i	−0.672579	+	2.06999i
$779$	16.1201	−	49.6125i	0.577562	−	1.77755i
$780$		0			0
$781$	14.5745	+	44.8557i	0.521516	+	1.60506i
$782$	−7.11950			−0.254593
$783$		0			0
$784$	−20.4126	−	14.8306i	−0.729021	−	0.529664i
$785$	46.3415	−	3.03213i	1.65400	−	0.108221i
$786$		0			0
$787$	−5.26393	−	3.82447i	−0.187639	−	0.136328i	0.490000	−	0.871722i	$-0.336997\pi$
$787$	−5.26393	−	3.82447i	−0.187639	−	0.136328i	−0.677639	+	0.735395i	$0.736997\pi$
$788$	40.1125	+	29.1434i	1.42895	+	1.03819i
$789$		0			0
$790$	24.7108	+	61.9585i	0.879172	+	2.20439i
$791$	2.91249	+	2.11605i	0.103556	+	0.0752380i
$792$		0			0
$793$	−41.8805			−1.48722
$794$	−1.74327	−	5.36522i	−0.0618662	−	0.190405i
$795$		0			0
$796$	−2.90868	+	8.95199i	−0.103095	+	0.317295i
$797$	5.20336	−	16.0143i	0.184312	−	0.567255i	−0.815623	−	0.578583i	$-0.803606\pi$
$797$	5.20336	−	16.0143i	0.184312	−	0.567255i	0.999936	+	0.0113279i	$0.00360587\pi$
$798$		0			0
$799$	−3.35905			−0.118835
$800$	40.1102	−	5.27141i	1.41811	−	0.186372i
$801$		0			0
$802$	−14.0432	+	10.2030i	−0.495882	+	0.360279i
$803$	−13.2178	+	40.6801i	−0.466445	+	1.43557i
$804$		0			0
$805$	2.58226	−	2.14715i	0.0910127	−	0.0756771i
$806$	−11.0353	−	33.9631i	−0.388702	−	1.19630i
$807$		0			0
$808$	0.622008	+	1.91435i	0.0218822	+	0.0673464i
$809$	−33.7304	−	24.5065i	−1.18590	−	0.861604i	−0.193072	−	0.981185i	$-0.561845\pi$
$809$	−33.7304	−	24.5065i	−1.18590	−	0.861604i	−0.992824	+	0.119581i	$0.961845\pi$
$810$		0			0
$811$	28.0451	−	20.3760i	0.984797	−	0.715497i	0.0260215	−	0.999661i	$-0.491716\pi$
$811$	28.0451	−	20.3760i	0.984797	−	0.715497i	0.958776	+	0.284164i	$0.0917162\pi$
$812$	−4.34500	−	3.15683i	−0.152480	−	0.110783i
$813$		0			0
$814$	−8.47826	+	6.15982i	−0.297163	+	0.215902i
$815$	13.2248	+	8.34628i	0.463243	+	0.292358i
$816$		0			0
$817$	18.8091	+	57.8885i	0.658047	+	2.02526i
$818$	−12.6377			−0.441867
$819$		0			0
$820$	32.0552	−	26.6539i	1.11942	−	0.930795i
$821$	−8.05430	+	24.7886i	−0.281097	+	0.865128i	0.706444	+	0.707769i	$0.250298\pi$
$821$	−8.05430	+	24.7886i	−0.281097	+	0.865128i	−0.987541	+	0.157359i	$0.949702\pi$
$822$		0			0
$823$	10.0510	−	7.30244i	0.350354	−	0.254547i	−0.398663	−	0.917097i	$-0.630526\pi$
$823$	10.0510	−	7.30244i	0.350354	−	0.254547i	0.749018	+	0.662550i	$0.230526\pi$
$824$	−1.34121			−0.0467232
$825$		0			0
$826$	−9.72781			−0.338474
$827$	25.5860	−	18.5893i	0.889713	−	0.646414i	−0.0460905	−	0.998937i	$-0.514676\pi$
$827$	25.5860	−	18.5893i	0.889713	−	0.646414i	0.935803	+	0.352523i	$0.114676\pi$
$828$		0			0
$829$	−12.1998	+	37.5471i	−0.423716	+	1.30406i	0.480502	+	0.876993i	$0.340454\pi$
$829$	−12.1998	+	37.5471i	−0.423716	+	1.30406i	−0.904218	+	0.427070i	$0.859546\pi$
$830$	1.36749	+	0.863039i	0.0474663	+	0.0299565i
$831$		0			0
$832$	−44.1826			−1.53176
$833$	−2.45435	−	7.55373i	−0.0850383	−	0.261721i
$834$		0			0
$835$	−12.3284	−	30.9116i	−0.426643	−	1.06974i
$836$	35.0612	−	25.4734i	1.21262	−	0.881018i
$837$		0			0
$838$	−61.5958	−	44.7520i	−2.12779	−	1.54593i
$839$	15.3954	−	11.1854i	0.531509	−	0.386164i	−0.289413	−	0.957204i	$-0.593460\pi$
$839$	15.3954	−	11.1854i	0.531509	−	0.386164i	0.820922	+	0.571041i	$0.193460\pi$
$840$		0			0
$841$	3.09027	+	2.24522i	0.106561	+	0.0774212i
$842$	−5.94188	−	18.2872i	−0.204771	−	0.630219i
$843$		0			0
$844$	−4.12815	−	12.7051i	−0.142097	−	0.437329i
$845$	9.43241	+	23.6503i	0.324485	+	0.813594i
$846$		0			0
$847$	−0.128499	+	0.395479i	−0.00441528	+	0.0135888i
$848$	40.1367	−	29.1610i	1.37830	−	1.00139i
$849$		0			0
$850$	10.5031	+	5.70576i	0.360252	+	0.195706i
$851$	−4.47027			−0.153239
$852$		0			0
$853$	8.92882	−	27.4801i	0.305717	−	0.940900i	−0.673692	−	0.739012i	$-0.735292\pi$
$853$	8.92882	−	27.4801i	0.305717	−	0.940900i	0.979409	−	0.201887i	$-0.0647075\pi$
$854$	−2.68334	+	8.25848i	−0.0918221	+	0.282599i
$855$		0			0
$856$	0.813642	+	2.50413i	0.0278097	+	0.0855894i
$857$	54.7084			1.86880			0.934401	−	0.356222i	$-0.115935\pi$
$857$	54.7084			1.86880			0.934401	+	0.356222i	$0.115935\pi$
$858$		0			0
$859$	−14.0341	−	10.1963i	−0.478836	−	0.347895i	0.322039	−	0.946726i	$-0.395632\pi$
$859$	−14.0341	−	10.1963i	−0.478836	−	0.347895i	−0.800875	+	0.598832i	$0.795632\pi$
$860$	−11.9790	+	47.1451i	−0.408480	+	1.60763i
$861$		0			0
$862$	16.2337	+	11.7945i	0.552921	+	0.401721i
$863$	25.6542	+	18.6388i	0.873278	+	0.634473i	0.931464	−	0.363832i	$-0.118532\pi$
$863$	25.6542	+	18.6388i	0.873278	+	0.634473i	−0.0581867	+	0.998306i	$0.518532\pi$
$864$		0			0
$865$	−2.68902	+	2.23592i	−0.0914293	+	0.0760235i
$866$	39.8866	+	28.9793i	1.35540	+	0.984756i
$867$		0			0
$868$	−3.81201			−0.129388
$869$	−15.6125	−	48.0504i	−0.529619	−	1.63000i
$870$		0			0
$871$	−14.8068	+	45.5707i	−0.501710	+	1.54410i
$872$	0.214816	−	0.661137i	0.00727460	−	0.0223889i
$873$		0			0
$874$	35.9073			1.21458
$875$	−5.53027	+	1.09810i	−0.186957	+	0.0371224i
$876$		0			0
$877$	−26.0784	+	18.9470i	−0.880603	+	0.639796i	−0.933411	−	0.358809i	$-0.883183\pi$
$877$	−26.0784	+	18.9470i	−0.880603	+	0.639796i	0.0528077	+	0.998605i	$0.483183\pi$
$878$	1.10211	−	3.39194i	0.0371943	−	0.114472i
$879$		0			0
$880$	−28.6988	+	1.87777i	−0.967438	+	0.0632997i
$881$	−11.5043	−	35.4065i	−0.387589	−	1.19288i	−0.934585	−	0.355740i	$-0.884229\pi$
$881$	−11.5043	−	35.4065i	−0.387589	−	1.19288i	0.546996	−	0.837135i	$-0.315771\pi$
$882$		0			0
$883$	1.68169	+	5.17572i	0.0565935	+	0.174177i	0.975358	−	0.220630i	$-0.0708114\pi$
$883$	1.68169	+	5.17572i	0.0565935	+	0.174177i	−0.918764	+	0.394807i	$0.870811\pi$
$884$	−9.98340	−	7.25336i	−0.335778	−	0.243957i
$885$		0			0
$886$	−61.3556	+	44.5774i	−2.06128	+	1.49761i
$887$	−38.4937	−	27.9673i	−1.29249	−	0.939052i	−0.292641	−	0.956222i	$-0.594534\pi$
$887$	−38.4937	−	27.9673i	−1.29249	−	0.939052i	−0.999853	+	0.0171708i	$0.994534\pi$
$888$		0			0
$889$	−1.84688	+	1.34184i	−0.0619424	+	0.0450038i
$890$	−7.27886	+	28.6470i	−0.243988	+	0.960250i
$891$		0			0
$892$	16.0219	+	49.3103i	0.536452	+	1.65103i
$893$	16.9414			0.566924
$894$		0			0
$895$	6.59293	−	25.9475i	0.220377	−	0.867328i
$896$	−0.309076	+	0.951237i	−0.0103255	+	0.0317786i
$897$		0			0
$898$	−21.2637	+	15.4490i	−0.709579	+	0.515539i
$899$	−17.8723			−0.596076
$900$		0			0
$901$	15.6170			0.520279
$902$	−49.6186	+	36.0500i	−1.65212	+	1.20033i
$903$		0			0
$904$	−0.547920	+	1.68633i	−0.0182236	+	0.0560863i
$905$	−0.691035	−	1.73266i	−0.0229708	−	0.0575956i
$906$		0			0
$907$	21.0436			0.698742			0.349371	−	0.936985i	$-0.386395\pi$
$907$	21.0436			0.698742			0.349371	+	0.936985i	$0.386395\pi$
$908$	8.81866	+	27.1410i	0.292657	+	0.900707i
$909$		0			0
$910$	11.2822	−	0.738200i	0.374003	−	0.0244711i
$911$	3.57453	−	2.59705i	0.118430	−	0.0860441i	−0.526994	−	0.849869i	$-0.676681\pi$
$911$	3.57453	−	2.59705i	0.118430	−	0.0860441i	0.645423	+	0.763825i	$0.276681\pi$
$912$		0			0
$913$	−0.990875	−	0.719913i	−0.0327932	−	0.0238256i
$914$	−36.6118	+	26.6001i	−1.21101	+	0.879852i
$915$		0			0
$916$	−26.0122	−	18.8990i	−0.859467	−	0.624439i
$917$	−1.50992	−	4.64706i	−0.0498620	−	0.153460i
$918$		0			0
$919$	13.5305	+	41.6425i	0.446329	+	1.37366i	0.881019	+	0.473081i	$0.156858\pi$
$919$	13.5305	+	41.6425i	0.446329	+	1.37366i	−0.434690	+	0.900580i	$0.643142\pi$
$920$	1.39878	+	0.882787i	0.0461165	+	0.0291046i
$921$		0			0
$922$	−0.336996	+	1.03717i	−0.0110984	+	0.0341573i
$923$	−54.7967	+	39.8121i	−1.80365	+	1.31043i
$924$		0			0
$925$	6.59478	+	3.58260i	0.216835	+	0.117795i
$926$	45.3800			1.49128
$927$		0			0
$928$	−12.5463	+	38.6135i	−0.411853	+	1.26755i
$929$	0.921674	−	2.83662i	0.0302391	−	0.0930665i	−0.934798	−	0.355180i	$-0.884420\pi$
$929$	0.921674	−	2.83662i	0.0302391	−	0.0930665i	0.965037	+	0.262114i	$0.0844195\pi$
$930$		0			0
$931$	12.3786	+	38.0974i	0.405692	+	1.24859i
$932$	−6.77263			−0.221845
$933$		0			0
$934$	−61.5575	−	44.7242i	−2.01422	−	1.46342i
$935$	−7.65608	−	4.83183i	−0.250381	−	0.158018i
$936$		0			0
$937$	−20.5941	−	14.9625i	−0.672780	−	0.488803i	0.198175	−	0.980167i	$-0.436499\pi$
$937$	−20.5941	−	14.9625i	−0.672780	−	0.488803i	−0.870955	+	0.491363i	$0.836499\pi$
$938$	8.03746	+	5.83956i	0.262432	+	0.190668i
$939$		0			0
$940$	11.4495	+	7.22589i	0.373441	+	0.235683i
$941$	−14.1636	−	10.2904i	−0.461719	−	0.335458i	0.332486	−	0.943108i	$-0.392112\pi$
$941$	−14.1636	−	10.2904i	−0.461719	−	0.335458i	−0.794205	+	0.607650i	$0.792112\pi$
$942$		0			0
$943$	−26.1620			−0.851952
$944$	10.9812	+	33.7968i	0.357409	+	1.09999i
$945$		0			0
$946$	22.1141	−	68.0603i	0.718992	−	2.21283i
$947$	8.48958	−	26.1282i	0.275874	−	0.849054i	−0.713112	−	0.701050i	$-0.752715\pi$
$947$	8.48958	−	26.1282i	0.275874	−	0.849054i	0.988987	−	0.148004i	$-0.0472849\pi$
$948$		0			0
$949$	−61.4272			−1.99401
$950$	−52.9724	−	28.7771i	−1.71865	−	0.933653i
$951$		0			0
$952$	−0.119314	+	0.0866869i	−0.00386700	+	0.00280954i
$953$	8.11556	−	24.9771i	0.262889	−	0.809088i	−0.729284	−	0.684212i	$-0.760146\pi$
$953$	8.11556	−	24.9771i	0.262889	−	0.809088i	0.992172	−	0.124877i	$-0.0398535\pi$
$954$		0			0
$955$	50.0497	+	31.5869i	1.61957	+	1.02213i
$956$	14.8305	+	45.6437i	0.479654	+	1.47622i
$957$		0			0
$958$	−11.6819	−	35.9531i	−0.377424	−	1.16159i
$959$	−1.62567	−	1.18112i	−0.0524956	−	0.0381403i
$960$		0			0
$961$	14.8168	−	10.7651i	0.477962	−	0.347260i
$962$	−12.1757	−	8.84613i	−0.392559	−	0.285211i
$963$		0			0
$964$	32.9003	−	23.9034i	1.05965	−	0.769878i
$965$	−8.87350	+	0.580595i	−0.285648	+	0.0186900i
$966$		0			0
$967$	4.99684	+	15.3787i	0.160688	+	0.494545i	0.998693	−	0.0511170i	$-0.0162781\pi$
$967$	4.99684	+	15.3787i	0.160688	+	0.494545i	−0.838005	+	0.545662i	$0.816278\pi$
$968$	−0.204808			−0.00658276
$969$		0			0
$970$	−18.4680	−	46.3055i	−0.592971	−	1.48678i
$971$	13.8119	−	42.5085i	0.443244	−	1.36416i	−0.441155	−	0.897431i	$-0.645431\pi$
$971$	13.8119	−	42.5085i	0.443244	−	1.36416i	0.884398	−	0.466733i	$-0.154569\pi$
$972$		0			0
$973$	2.02421	−	1.47068i	0.0648933	−	0.0471478i
$974$	3.63658			0.116524
$975$		0			0
$976$	31.7211			1.01537
$977$	−18.0949	+	13.1467i	−0.578907	+	0.420600i	−0.838330	−	0.545164i	$-0.816468\pi$
$977$	−18.0949	+	13.1467i	−0.578907	+	0.420600i	0.259423	+	0.965764i	$0.416468\pi$
$978$		0			0
$979$	6.91804	−	21.2915i	0.221102	−	0.680481i
$980$	−7.88357	+	31.0270i	−0.251831	+	0.991120i
$981$		0			0
$982$	−55.3788			−1.76721
$983$	1.51247	+	4.65491i	0.0482404	+	0.148469i	0.972275	−	0.233840i	$-0.0751292\pi$
$983$	1.51247	+	4.65491i	0.0482404	+	0.148469i	−0.924035	+	0.382308i	$0.875129\pi$
$984$		0			0
$985$	−12.8645	+	50.6300i	−0.409896	+	1.61321i
$986$	−9.70483	+	7.05097i	−0.309065	+	0.224549i
$987$		0			0
$988$	50.3515	+	36.5825i	1.60189	+	1.16384i
$989$	24.6962	−	17.9428i	0.785292	−	0.570548i
$990$		0			0
$991$	10.8113	+	7.85485i	0.343431	+	0.249518i	0.746108	−	0.665825i	$-0.231920\pi$
$991$	10.8113	+	7.85485i	0.343431	+	0.249518i	−0.402677	+	0.915342i	$0.631920\pi$
$992$	8.90508	+	27.4070i	0.282737	+	0.870174i
$993$		0			0
$994$	4.33971	+	13.3563i	0.137647	+	0.423635i
$995$	−9.89593	+	0.647493i	−0.313722	+	0.0205269i
$996$		0			0
$997$	13.4967	−	41.5386i	0.427445	−	1.31554i	−0.473188	−	0.880961i	$-0.656897\pi$
$997$	13.4967	−	41.5386i	0.427445	−	1.31554i	0.900633	−	0.434580i	$-0.143103\pi$
$998$	17.3657	−	12.6169i	0.549702	−	0.399382i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.h.e.136.4	yes	16
3.2	odd	2	inner	225.2.h.e.136.1	yes	16
25.4	even	10		5625.2.a.v.1.7		8
25.16	even	5	inner	225.2.h.e.91.4	yes	16
25.21	even	5		5625.2.a.w.1.2		8
75.29	odd	10		5625.2.a.v.1.2		8
75.41	odd	10	inner	225.2.h.e.91.1	✓	16
75.71	odd	10		5625.2.a.w.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.h.e.91.1	✓	16	75.41	odd	10	inner
225.2.h.e.91.4	yes	16	25.16	even	5	inner
225.2.h.e.136.1	yes	16	3.2	odd	2	inner
225.2.h.e.136.4	yes	16	1.1	even	1	trivial
5625.2.a.v.1.2		8	75.29	odd	10
5625.2.a.v.1.7		8	25.4	even	10
5625.2.a.w.1.2		8	25.21	even	5
5625.2.a.w.1.7		8	75.71	odd	10

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.64259 - 1.19341i) q^{2} +(0.655837 - 2.01846i) q^{4} +(2.23130 - 0.145994i) q^{5} -0.504300 q^{7} +(-0.0767537 - 0.236224i) q^{8} +O(q^{10})\)	\(q+(1.64259 - 1.19341i) q^{2} +(0.655837 - 2.01846i) q^{4} +(2.23130 - 0.145994i) q^{5} -0.504300 q^{7} +(-0.0767537 - 0.236224i) q^{8} +(3.49087 - 2.90266i) q^{10} +(-2.78196 + 2.02121i) q^{11} +(-3.99517 - 2.90266i) q^{13} +(-0.828357 + 0.601837i) q^{14} +(3.02602 + 2.19853i) q^{16} +(0.363841 + 1.11979i) q^{17} +(-1.83504 - 5.64767i) q^{19} +(1.16868 - 4.59953i) q^{20} +(-2.15748 + 6.64004i) q^{22} +(-2.40939 + 1.75052i) q^{23} +(4.95737 - 0.651513i) q^{25} -10.0265 q^{26} +(-0.330738 + 1.01791i) q^{28} +(-1.55064 + 4.77239i) q^{29} +(1.10061 + 3.38734i) q^{31} +8.09103 q^{32} +(1.93401 + 1.40514i) q^{34} +(-1.12524 + 0.0736248i) q^{35} +(1.21435 + 0.882274i) q^{37} +(-9.75420 - 7.08684i) q^{38} +(-0.205748 - 0.515879i) q^{40} +(7.10690 + 5.16346i) q^{41} -10.2500 q^{43} +(2.25522 + 6.94085i) q^{44} +(-1.86854 + 5.75078i) q^{46} +(-0.881597 + 2.71328i) q^{47} -6.74568 q^{49} +(7.36541 - 6.98635i) q^{50} +(-8.47909 + 6.16042i) q^{52} +(4.09875 - 12.6147i) q^{53} +(-5.91229 + 4.91607i) q^{55} +(0.0387069 + 0.119127i) q^{56} +(3.14835 + 9.68964i) q^{58} +(7.68621 + 5.58436i) q^{59} +(6.86106 - 4.98485i) q^{61} +(5.85034 + 4.25052i) q^{62} +(7.23820 - 5.25886i) q^{64} +(-9.33819 - 5.89343i) q^{65} +(-2.99836 - 9.22800i) q^{67} +2.49886 q^{68} +(-1.76045 + 1.46381i) q^{70} +(4.23839 - 13.0444i) q^{71} +(10.0633 - 7.31141i) q^{73} +3.04759 q^{74} -12.6031 q^{76} +(1.40294 - 1.01930i) q^{77} +(-4.54026 + 13.9735i) q^{79} +(7.07292 + 4.46380i) q^{80} +17.8359 q^{82} +(0.110065 + 0.338746i) q^{83} +(0.975319 + 2.44546i) q^{85} +(-16.8365 + 12.2324i) q^{86} +(0.690983 + 0.502029i) q^{88} +(-5.26703 + 3.82672i) q^{89} +(2.01476 + 1.46381i) q^{91} +(1.95319 + 6.01131i) q^{92} +(1.78995 + 5.50891i) q^{94} +(-4.91904 - 12.3337i) q^{95} +(3.39322 - 10.4433i) q^{97} +(-11.0804 + 8.05038i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{4}+O(q^{10}) \) 16 * q - 2 * q^4	\( 16 q - 2 q^{4} + 14 q^{16} + 14 q^{19} - 30 q^{22} + 10 q^{25} + 30 q^{28} + 18 q^{31} - 20 q^{34} + 10 q^{37} - 10 q^{40} - 80 q^{43} - 32 q^{49} - 40 q^{52} - 70 q^{55} - 10 q^{58} + 32 q^{61} - 8 q^{64} - 40 q^{67} + 50 q^{70} + 60 q^{73} - 88 q^{76} + 36 q^{79} + 120 q^{82} + 20 q^{88} + 30 q^{91} + 30 q^{94} + 40 q^{97}+O(q^{100}) \) 16 * q - 2 * q^4 + 14 * q^16 + 14 * q^19 - 30 * q^22 + 10 * q^25 + 30 * q^28 + 18 * q^31 - 20 * q^34 + 10 * q^37 - 10 * q^40 - 80 * q^43 - 32 * q^49 - 40 * q^52 - 70 * q^55 - 10 * q^58 + 32 * q^61 - 8 * q^64 - 40 * q^67 + 50 * q^70 + 60 * q^73 - 88 * q^76 + 36 * q^79 + 120 * q^82 + 20 * q^88 + 30 * q^91 + 30 * q^94 + 40 * q^97

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