LMFDB - Embedded newform 225.2.k.c.124.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(49,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("225.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.k (of order $6$, degree $2$, not 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:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 102x^{12} - 406x^{10} + 1167x^{8} - 1842x^{6} + 2023x^{4} - 441x^{2} + 81 $ x^16 - 12x^14 + 102x^12 - 406x^10 + 1167x^8 - 1842x^6 + 2023x^4 - 441*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			124.1
Root			$-2.28087 - 1.31686i$ of defining polynomial
Character	$\chi$	$=$	225.124
Dual form			225.2.k.c.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.28087 - 1.31686i) q^{2} +(-0.238330 + 1.71558i) q^{3} +(2.46825 + 4.27513i) q^{4} +(2.80278 - 3.59916i) q^{6} +(1.55662 + 0.898714i) q^{7} -7.73393i q^{8} +(-2.88640 - 0.817746i) q^{9} +O(q^{10})$	\(q+(-2.28087 - 1.31686i) q^{2} +(-0.238330 + 1.71558i) q^{3} +(2.46825 + 4.27513i) q^{4} +(2.80278 - 3.59916i) q^{6} +(1.55662 + 0.898714i) q^{7} -7.73393i q^{8} +(-2.88640 - 0.817746i) q^{9} +(-0.904062 + 1.56588i) q^{11} +(-7.92257 + 3.21558i) q^{12} +(-1.70765 + 0.985914i) q^{13} +(-2.36696 - 4.09970i) q^{14} +(-5.24801 + 9.08982i) q^{16} +4.80812i q^{17} +(5.50664 + 5.66616i) q^{18} -2.96467 q^{19} +(-1.91280 + 2.45630i) q^{21} +(4.12410 - 2.38105i) q^{22} +(1.50162 - 0.866963i) q^{23} +(13.2681 + 1.84323i) q^{24} +5.19325 q^{26} +(2.09082 - 4.75694i) q^{27} +8.87300i q^{28} +(-3.68382 + 6.38057i) q^{29} +(1.31151 + 2.27161i) q^{31} +(10.5445 - 6.08789i) q^{32} +(-2.47092 - 1.92418i) q^{33} +(6.33163 - 10.9667i) q^{34} +(-3.62838 - 14.3581i) q^{36} +11.6351i q^{37} +(6.76203 + 3.90406i) q^{38} +(-1.28442 - 3.16458i) q^{39} +(1.23324 + 2.13603i) q^{41} +(7.59746 - 3.08362i) q^{42} +(-6.30306 - 3.63907i) q^{43} -8.92580 q^{44} -4.56668 q^{46} +(-5.44910 - 3.14604i) q^{47} +(-14.3435 - 11.1697i) q^{48} +(-1.88463 - 3.26427i) q^{49} +(-8.24870 - 1.14592i) q^{51} +(-8.42983 - 4.86696i) q^{52} -1.72540i q^{53} +(-11.0331 + 8.09664i) q^{54} +(6.95059 - 12.0388i) q^{56} +(0.706570 - 5.08612i) q^{57} +(16.8047 - 9.70218i) q^{58} +(5.51300 + 9.54880i) q^{59} +(6.33521 - 10.9729i) q^{61} -6.90833i q^{62} +(-3.75810 - 3.86696i) q^{63} -11.0756 q^{64} +(3.10197 + 7.64268i) q^{66} +(7.88407 - 4.55187i) q^{67} +(-20.5554 + 11.8676i) q^{68} +(1.12946 + 2.78277i) q^{69} +1.27460 q^{71} +(-6.32439 + 22.3232i) q^{72} +3.58770i q^{73} +(15.3218 - 26.5382i) q^{74} +(-7.31755 - 12.6744i) q^{76} +(-2.81456 + 1.62499i) q^{77} +(-1.23771 + 8.90941i) q^{78} +(1.05545 - 1.82809i) q^{79} +(7.66258 + 4.72068i) q^{81} -6.49602i q^{82} +(0.951614 + 0.549415i) q^{83} +(-15.2223 - 2.11470i) q^{84} +(9.58431 + 16.6005i) q^{86} +(-10.0684 - 7.84056i) q^{87} +(12.1104 + 6.99195i) q^{88} +13.2935 q^{89} -3.54422 q^{91} +(7.41277 + 4.27976i) q^{92} +(-4.20969 + 1.70861i) q^{93} +(8.28580 + 14.3514i) q^{94} +(7.93115 + 19.5409i) q^{96} +(3.31926 + 1.91638i) q^{97} +9.92718i q^{98} +(3.88998 - 3.78046i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 16 q^{6} - 10 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 16 * q^6 - 10 * q^9	$ 16 q + 8 q^{4} + 16 q^{6} - 10 q^{9} + 2 q^{11} + 6 q^{14} - 8 q^{16} - 8 q^{19} - 30 q^{21} + 66 q^{24} - 40 q^{26} + 2 q^{29} + 8 q^{31} + 18 q^{34} - 28 q^{36} - 50 q^{39} + 10 q^{41} - 88 q^{44} - 6 q^{49} + 22 q^{51} - 52 q^{54} + 60 q^{56} + 34 q^{59} + 26 q^{61} - 76 q^{64} - 16 q^{66} + 54 q^{69} - 32 q^{71} + 80 q^{74} - 22 q^{76} - 14 q^{79} + 34 q^{81} - 54 q^{84} + 68 q^{86} + 36 q^{89} - 68 q^{91} + 6 q^{94} + 68 q^{96} + 34 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 16 * q^6 - 10 * q^9 + 2 * q^11 + 6 * q^14 - 8 * q^16 - 8 * q^19 - 30 * q^21 + 66 * q^24 - 40 * q^26 + 2 * q^29 + 8 * q^31 + 18 * q^34 - 28 * q^36 - 50 * q^39 + 10 * q^41 - 88 * q^44 - 6 * q^49 + 22 * q^51 - 52 * q^54 + 60 * q^56 + 34 * q^59 + 26 * q^61 - 76 * q^64 - 16 * q^66 + 54 * q^69 - 32 * q^71 + 80 * q^74 - 22 * q^76 - 14 * q^79 + 34 * q^81 - 54 * q^84 + 68 * q^86 + 36 * q^89 - 68 * q^91 + 6 * q^94 + 68 * q^96 + 34 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.28087	−	1.31686i	−1.61282	−	0.931162i	−0.988713	−	0.149823i	$-0.952130\pi$
$2$	−2.28087	−	1.31686i	−1.61282	−	0.931162i	−0.624107	−	0.781339i	$-0.714537\pi$
$3$	−0.238330	+	1.71558i	−0.137600	+	0.990488i
$3$	−0.238330	+	1.71558i	−0.137600	+	0.990488i
$4$	2.46825	+	4.27513i	1.23412	+	2.13757i
$5$		0			0
$5$		0			0
$6$	2.80278	−	3.59916i	1.14423	−	1.46935i
$7$	1.55662	+	0.898714i	0.588346	+	0.339682i	0.764443	−	0.644691i	$-0.223014\pi$
$7$	1.55662	+	0.898714i	0.588346	+	0.339682i	−0.176097	+	0.984373i	$0.556347\pi$
$8$		−	7.73393i		−	2.73436i
$9$	−2.88640	−	0.817746i	−0.962133	−	0.272582i
$10$		0			0
$11$	−0.904062	+	1.56588i	−0.272585	+	0.472131i	−0.969523	−	0.245000i	$-0.921212\pi$
$11$	−0.904062	+	1.56588i	−0.272585	+	0.472131i	0.696938	+	0.717131i	$0.254545\pi$
$12$	−7.92257	+	3.21558i	−2.28705	+	0.928257i
$13$	−1.70765	+	0.985914i	−0.473618	+	0.273443i	−0.717753	−	0.696298i	$-0.754829\pi$
$13$	−1.70765	+	0.985914i	−0.473618	+	0.273443i	0.244135	+	0.969741i	$0.421496\pi$
$14$	−2.36696	−	4.09970i	−0.632598	−	1.09569i
$15$		0			0
$16$	−5.24801	+	9.08982i	−1.31200	+	2.27246i
$17$			4.80812i			1.16614i	0.812421	+	0.583071i	$0.198149\pi$
$17$			4.80812i			1.16614i	−0.812421	+	0.583071i	$0.801851\pi$
$18$	5.50664	+	5.66616i	1.29793	+	1.33553i
$19$	−2.96467			−0.680142			−0.340071	−	0.940400i	$-0.610451\pi$
$19$	−2.96467			−0.680142			−0.340071	+	0.940400i	$0.610451\pi$
$20$		0			0
$21$	−1.91280	+	2.45630i	−0.417407	+	0.536010i
$22$	4.12410	−	2.38105i	0.879261	−	0.507641i
$23$	1.50162	−	0.866963i	0.313110	−	0.180774i	−0.335207	−	0.942144i	$-0.608806\pi$
$23$	1.50162	−	0.866963i	0.313110	−	0.180774i	0.648317	+	0.761370i	$0.275473\pi$
$24$	13.2681	+	1.84323i	2.70835	+	0.376247i
$25$		0			0
$26$	5.19325			1.01848
$27$	2.09082	−	4.75694i	0.402379	−	0.915473i
$28$			8.87300i			1.67684i
$29$	−3.68382	+	6.38057i	−0.684069	+	1.18484i	0.289659	+	0.957130i	$0.406458\pi$
$29$	−3.68382	+	6.38057i	−0.684069	+	1.18484i	−0.973728	+	0.227713i	$0.926875\pi$
$30$		0			0
$31$	1.31151	+	2.27161i	0.235555	+	0.407993i	0.959434	−	0.281934i	$-0.0909760\pi$
$31$	1.31151	+	2.27161i	0.235555	+	0.407993i	−0.723879	+	0.689927i	$0.757643\pi$
$32$	10.5445	−	6.08789i	1.86403	−	1.07620i
$33$	−2.47092	−	1.92418i	−0.430132	−	0.334957i
$34$	6.33163	−	10.9667i	1.08587	−	1.88078i
$35$		0			0
$36$	−3.62838	−	14.3581i	−0.604729	−	2.39302i
$37$			11.6351i			1.91280i	0.292063	+	0.956399i	$0.405658\pi$
$37$			11.6351i			1.91280i	−0.292063	+	0.956399i	$0.594342\pi$
$38$	6.76203	+	3.90406i	1.09695	+	0.633322i
$39$	−1.28442	−	3.16458i	−0.205673	−	0.506738i
$40$		0			0
$41$	1.23324	+	2.13603i	0.192600	+	0.333592i	0.946111	−	0.323842i	$-0.104975\pi$
$41$	1.23324	+	2.13603i	0.192600	+	0.333592i	−0.753511	+	0.657435i	$0.771641\pi$
$42$	7.59746	−	3.08362i	1.17231	−	0.475813i
$43$	−6.30306	−	3.63907i	−0.961207	−	0.554953i	−0.0646628	−	0.997907i	$-0.520597\pi$
$43$	−6.30306	−	3.63907i	−0.961207	−	0.554953i	−0.896544	+	0.442954i	$0.853931\pi$
$44$	−8.92580			−1.34562
$45$		0			0
$46$	−4.56668			−0.673321
$47$	−5.44910	−	3.14604i	−0.794833	−	0.458897i	0.0468283	−	0.998903i	$-0.485089\pi$
$47$	−5.44910	−	3.14604i	−0.794833	−	0.458897i	−0.841661	+	0.540006i	$0.818422\pi$
$48$	−14.3435	−	11.1697i	−2.07031	−	1.61221i
$49$	−1.88463	−	3.26427i	−0.269233	−	0.466324i
$50$		0			0
$51$	−8.24870	−	1.14592i	−1.15505	−	0.160461i
$52$	−8.42983	−	4.86696i	−1.16901	−	0.674926i
$53$		−	1.72540i		−	0.237001i	−0.992954	−	0.118501i	$-0.962191\pi$
$53$		−	1.72540i		−	0.237001i	0.992954	−	0.118501i	$-0.0378088\pi$
$54$	−11.0331	+	8.09664i	−1.50142	+	1.10181i
$55$		0			0
$56$	6.95059	−	12.0388i	0.928811	−	1.60875i
$57$	0.706570	−	5.08612i	0.0935875	−	0.673673i
$58$	16.8047	−	9.70218i	2.20656	−	1.27396i
$59$	5.51300	+	9.54880i	0.717732	+	1.24315i	0.961896	+	0.273414i	$0.0881529\pi$
$59$	5.51300	+	9.54880i	0.717732	+	1.24315i	−0.244165	+	0.969734i	$0.578514\pi$
$60$		0			0
$61$	6.33521	−	10.9729i	0.811141	−	1.40494i	−0.100925	−	0.994894i	$-0.532180\pi$
$61$	6.33521	−	10.9729i	0.811141	−	1.40494i	0.912066	−	0.410043i	$-0.134486\pi$
$62$		−	6.90833i		−	0.877358i
$63$	−3.75810	−	3.86696i	−0.473476	−	0.487192i
$64$	−11.0756			−1.38445
$65$		0			0
$66$	3.10197	+	7.64268i	0.381826	+	0.940748i
$67$	7.88407	−	4.55187i	0.963193	−	0.556100i	0.0660386	−	0.997817i	$-0.478964\pi$
$67$	7.88407	−	4.55187i	0.963193	−	0.556100i	0.897154	+	0.441717i	$0.145631\pi$
$68$	−20.5554	+	11.8676i	−2.49271	+	1.43916i
$69$	1.12946	+	2.78277i	0.135971	+	0.335006i
$70$		0			0
$71$	1.27460			0.151268			0.0756338	−	0.997136i	$-0.475902\pi$
$71$	1.27460			0.151268			0.0756338	+	0.997136i	$0.475902\pi$
$72$	−6.32439	+	22.3232i	−0.745336	+	2.63081i
$73$			3.58770i			0.419908i	0.977711	+	0.209954i	$0.0673315\pi$
$73$			3.58770i			0.419908i	−0.977711	+	0.209954i	$0.932669\pi$
$74$	15.3218	−	26.5382i	1.78112	−	3.08500i
$75$		0			0
$76$	−7.31755	−	12.6744i	−0.839380	−	1.45385i
$77$	−2.81456	+	1.62499i	−0.320749	+	0.185184i
$78$	−1.23771	+	8.90941i	−0.140143	+	1.00879i
$79$	1.05545	−	1.82809i	0.118747	−	0.205676i	−0.800524	−	0.599300i	$-0.795445\pi$
$79$	1.05545	−	1.82809i	0.118747	−	0.205676i	0.919272	+	0.393624i	$0.128779\pi$
$80$		0			0
$81$	7.66258	+	4.72068i	0.851398	+	0.524520i
$82$		−	6.49602i		−	0.717366i
$83$	0.951614	+	0.549415i	0.104453	+	0.0603061i	0.551317	−	0.834296i	$-0.314126\pi$
$83$	0.951614	+	0.549415i	0.104453	+	0.0603061i	−0.446863	+	0.894602i	$0.647459\pi$
$84$	−15.2223	−	2.11470i	−1.66089	−	0.230733i
$85$		0			0
$86$	9.58431	+	16.6005i	1.03350	+	1.79008i
$87$	−10.0684	−	7.84056i	−1.07944	−	0.840596i
$88$	12.1104	+	6.99195i	1.29097	+	0.745344i
$89$	13.2935			1.40910			0.704552	−	0.709653i	$-0.251148\pi$
$89$	13.2935			1.40910			0.704552	+	0.709653i	$0.251148\pi$
$90$		0			0
$91$	−3.54422			−0.371535
$92$	7.41277	+	4.27976i	0.772834	+	0.446196i
$93$	−4.20969	+	1.70861i	−0.436524	+	0.177174i
$94$	8.28580	+	14.3514i	0.854615	+	1.48024i
$95$		0			0
$96$	7.93115	+	19.5409i	0.809470	+	1.99438i
$97$	3.31926	+	1.91638i	0.337020	+	0.194579i	0.658954	−	0.752184i	$-0.270999\pi$
$97$	3.31926	+	1.91638i	0.337020	+	0.194579i	−0.321933	+	0.946762i	$0.604333\pi$
$98$			9.92718i			1.00280i
$99$	3.88998	−	3.78046i	0.390957	−	0.379951i
$100$		0			0
$101$	−3.27618	+	5.67452i	−0.325993	+	0.564636i	−0.981713	−	0.190368i	$-0.939032\pi$
$101$	−3.27618	+	5.67452i	−0.325993	+	0.564636i	0.655720	+	0.755004i	$0.272365\pi$
$102$	17.3052	+	13.4761i	1.71347	+	1.33433i
$103$	6.99365	−	4.03779i	0.689105	−	0.397855i	−0.114172	−	0.993461i	$-0.536421\pi$
$103$	6.99365	−	4.03779i	0.689105	−	0.397855i	0.803277	+	0.595606i	$0.203088\pi$
$104$	7.62499	+	13.2069i	0.747691	+	1.29504i
$105$		0			0
$106$	−2.27211	+	3.93541i	−0.220687	+	0.382241i
$107$		−	8.97674i		−	0.867814i	−0.900958	−	0.433907i	$-0.857135\pi$
$107$		−	8.97674i		−	0.867814i	0.900958	−	0.433907i	$-0.142865\pi$
$108$	25.4972	−	2.80278i	2.45347	−	0.269697i
$109$	6.34164			0.607419			0.303710	−	0.952765i	$-0.401775\pi$
$109$	6.34164			0.607419			0.303710	+	0.952765i	$0.401775\pi$
$110$		0			0
$111$	−19.9609	−	2.77299i	−1.89460	−	0.263201i
$112$	−16.3383	+	9.43292i	−1.54382	+	0.891327i
$113$	12.9060	−	7.45127i	1.21409	−	0.700957i	0.250444	−	0.968131i	$-0.419423\pi$
$113$	12.9060	−	7.45127i	1.21409	−	0.700957i	0.963648	+	0.267174i	$0.0860899\pi$
$114$	−8.30931	+	10.6703i	−0.778238	+	0.999367i
$115$		0			0
$116$	−36.3704			−3.37691
$117$	5.73519	−	1.44931i	0.530219	−	0.133989i
$118$		−	29.0394i		−	2.67330i
$119$	−4.32113	+	7.48441i	−0.396117	+	0.686095i
$120$		0			0
$121$	3.86534	+	6.69497i	0.351395	+	0.608634i
$122$	−28.8996	+	16.6852i	−2.61645	+	1.51061i
$123$	−3.95845	+	1.60663i	−0.356921	+	0.144865i
$124$	−6.47428	+	11.2138i	−0.581408	+	1.00703i
$125$		0			0
$126$	3.47948	+	13.7689i	0.309977	+	1.22663i
$127$			3.62303i			0.321492i	0.986996	+	0.160746i	$0.0513899\pi$
$127$			3.62303i			0.321492i	−0.986996	+	0.160746i	$0.948610\pi$
$128$	4.17289	+	2.40922i	0.368835	+	0.212947i
$129$	7.74531	−	9.94607i	0.681936	−	0.875703i
$130$		0			0
$131$	−3.64673	−	6.31631i	−0.318616	−	0.551859i	0.661584	−	0.749871i	$-0.269885\pi$
$131$	−3.64673	−	6.31631i	−0.318616	−	0.551859i	−0.980200	+	0.198012i	$0.936551\pi$
$132$	2.12729	−	15.3129i	0.185157	−	1.33282i
$133$	−4.61486	−	2.66439i	−0.400159	−	0.231032i
$134$	−23.9767			−2.07127
$135$		0			0
$136$	37.1857			3.18865
$137$	6.17148	+	3.56310i	0.527265	+	0.304417i	0.739902	−	0.672715i	$-0.234872\pi$
$137$	6.17148	+	3.56310i	0.527265	+	0.304417i	−0.212637	+	0.977131i	$0.568205\pi$
$138$	1.08838	−	7.83449i	0.0926488	−	0.666916i
$139$	−7.35533	−	12.7398i	−0.623871	−	1.08058i	−0.988758	−	0.149525i	$-0.952226\pi$
$139$	−7.35533	−	12.7398i	−0.623871	−	1.08058i	0.364887	−	0.931052i	$-0.381108\pi$
$140$		0			0
$141$	6.69595	−	8.59855i	0.563901	−	0.724128i
$142$	−2.90721	−	1.67848i	−0.243967	−	0.140855i
$143$		−	3.56531i		−	0.298146i
$144$	22.5810	−	21.9453i	1.88175	−	1.82878i
$145$		0			0
$146$	4.72450	−	8.18308i	0.391003	−	0.677236i
$147$	6.04927	−	2.45525i	0.498935	−	0.202505i
$148$	−49.7416	+	28.7183i	−4.08873	+	2.36063i
$149$	−0.282655	−	0.489572i	−0.0231560	−	0.0401073i	0.854215	−	0.519920i	$-0.174038\pi$
$149$	−0.282655	−	0.489572i	−0.0231560	−	0.0401073i	−0.877371	+	0.479812i	$0.840705\pi$
$150$		0			0
$151$	−0.0766925	+	0.132835i	−0.00624115	+	0.0108100i	−0.869129	−	0.494585i	$-0.835320\pi$
$151$	−0.0766925	+	0.132835i	−0.00624115	+	0.0108100i	0.862888	+	0.505395i	$0.168653\pi$
$152$			22.9285i			1.85975i
$153$	3.93183	−	13.8782i	0.317869	−	1.12198i
$154$	8.55953			0.689746
$155$		0			0
$156$	10.3587	−	13.3021i	0.829362	−	1.06502i
$157$	−9.92525	+	5.73035i	−0.792121	+	0.457332i	−0.840709	−	0.541487i	$-0.817861\pi$
$157$	−9.92525	+	5.73035i	−0.792121	+	0.457332i	0.0485874	+	0.998819i	$0.484528\pi$
$158$	−4.81469	+	2.77976i	−0.383036	+	0.221146i
$159$	2.96005	+	0.411214i	0.234747	+	0.0326114i
$160$		0			0
$161$	3.11661			0.245623
$162$	−11.2609	−	20.8578i	−0.884738	−	1.63875i
$163$			22.0595i			1.72783i	0.503637	+	0.863915i	$0.331995\pi$
$163$			22.0595i			1.72783i	−0.503637	+	0.863915i	$0.668005\pi$
$164$	−6.08789	+	10.5445i	−0.475384	+	0.823389i
$165$		0			0
$166$	−1.44701	−	2.50629i	−0.112310	−	0.194526i
$167$	14.7817	−	8.53421i	1.14384	−	0.660397i	0.196462	−	0.980511i	$-0.437055\pi$
$167$	14.7817	−	8.53421i	1.14384	−	0.660397i	0.947379	+	0.320115i	$0.103721\pi$
$168$	18.9969	+	14.7935i	1.46564	+	1.14134i
$169$	−4.55595	+	7.89113i	−0.350457	+	0.607010i
$170$		0			0
$171$	8.55722	+	2.42435i	0.654387	+	0.185395i
$172$		−	35.9285i		−	2.73953i
$173$	10.3444	+	5.97233i	0.786468	+	0.454067i	0.838718	−	0.544567i	$-0.183306\pi$
$173$	10.3444	+	5.97233i	0.786468	+	0.454067i	−0.0522497	+	0.998634i	$0.516639\pi$
$174$	12.6398	+	31.1420i	0.958218	+	2.36087i
$175$		0			0
$176$	−9.48906	−	16.4355i	−0.715265	−	1.23887i
$177$	−17.6956	+	7.18221i	−1.33008	+	0.539848i
$178$	−30.3207	−	17.5056i	−2.27263	−	1.31210i
$179$	−8.54921			−0.638998			−0.319499	−	0.947587i	$-0.603515\pi$
$179$	−8.54921			−0.638998			−0.319499	+	0.947587i	$0.603515\pi$
$180$		0			0
$181$	−10.5524			−0.784351			−0.392176	−	0.919890i	$-0.628277\pi$
$181$	−10.5524			−0.784351			−0.392176	+	0.919890i	$0.628277\pi$
$182$	8.08390	+	4.66724i	0.599219	+	0.345959i
$183$	17.3150	+	13.4837i	1.27996	+	0.996744i
$184$	−6.70503	−	11.6135i	−0.494301	−	0.856155i
$185$		0			0
$186$	11.8518	+	1.64646i	0.869013	+	0.120724i
$187$	−7.52895	−	4.34684i	−0.550571	−	0.317873i
$188$		−	31.0608i		−	2.26534i
$189$	7.52973	−	5.52569i	0.547708	−	0.401935i
$190$		0			0
$191$	8.66862	−	15.0145i	0.627239	−	1.08641i	−0.360864	−	0.932618i	$-0.617518\pi$
$191$	8.66862	−	15.0145i	0.627239	−	1.08641i	0.988103	−	0.153792i	$-0.0491485\pi$
$192$	2.63964	−	19.0010i	0.190500	−	1.37128i
$193$	−1.35059	+	0.779763i	−0.0972175	+	0.0561286i	−0.547821	−	0.836596i	$-0.684542\pi$
$193$	−1.35059	+	0.779763i	−0.0972175	+	0.0561286i	0.450603	+	0.892724i	$0.351209\pi$
$194$	−5.04721	−	8.74202i	−0.362369	−	0.627641i
$195$		0			0
$196$	9.30346	−	16.1141i	0.664533	−	1.15100i
$197$			17.9767i			1.28079i	0.768046	+	0.640395i	$0.221229\pi$
$197$			17.9767i			1.28079i	−0.768046	+	0.640395i	$0.778771\pi$
$198$	−13.8509	+	3.50019i	−0.984339	+	0.248748i
$199$	−11.0225			−0.781362			−0.390681	−	0.920526i	$-0.627760\pi$
$199$	−11.0225			−0.781362			−0.390681	+	0.920526i	$0.627760\pi$
$200$		0			0
$201$	5.93007	+	14.6106i	0.418275	+	1.03055i
$202$	14.9451	−	8.62856i	1.05153	−	0.607104i
$203$	−11.4686	+	6.62141i	−0.804939	+	0.464732i
$204$	−15.4609	−	38.0927i	−1.08248	−	2.66702i
$205$		0			0
$206$	−21.2688			−1.48187
$207$	−5.04324	+	1.27445i	−0.350529	+	0.0885806i
$208$		−	20.6964i		−	1.43503i
$209$	2.68025	−	4.64232i	0.185397	−	0.321116i
$210$		0			0
$211$	11.9643	+	20.7227i	0.823655	+	1.42661i	0.902943	+	0.429760i	$0.141402\pi$
$211$	11.9643	+	20.7227i	0.823655	+	1.42661i	−0.0792886	+	0.996852i	$0.525265\pi$
$212$	7.37630	−	4.25871i	0.506606	−	0.292489i
$213$	−0.303776	+	2.18668i	−0.0208144	+	0.149829i
$214$	−11.8211	+	20.4748i	−0.808076	+	1.39963i
$215$		0			0
$216$	−36.7898	−	16.1703i	−2.50323	−	1.10025i
$217$			4.71470i			0.320055i
$218$	−14.4645	−	8.35107i	−0.979658	−	0.565606i
$219$	−6.15497	−	0.855056i	−0.415914	−	0.0577793i
$220$		0			0
$221$	−4.74040	−	8.21061i	−0.318874	−	0.552305i
$222$	41.8766	+	32.6106i	2.81057	+	2.18868i
$223$	18.8020	+	10.8553i	1.25907	+	0.726927i	0.972895	−	0.231249i	$-0.0742812\pi$
$223$	18.8020	+	10.8553i	1.25907	+	0.726927i	0.286180	+	0.958176i	$0.407615\pi$
$224$	21.8851			1.46226
$225$		0			0
$226$	−39.2492			−2.61082
$227$	−12.2111	−	7.05010i	−0.810481	−	0.467932i	0.0366416	−	0.999328i	$-0.488334\pi$
$227$	−12.2111	−	7.05010i	−0.810481	−	0.467932i	−0.847123	+	0.531397i	$0.821667\pi$
$228$	23.4878	−	9.53312i	1.55552	−	0.631347i
$229$	1.83879	+	3.18488i	0.121511	+	0.210463i	0.920364	−	0.391064i	$-0.127893\pi$
$229$	1.83879	+	3.18488i	0.121511	+	0.210463i	−0.798853	+	0.601526i	$0.794559\pi$
$230$		0			0
$231$	−2.11699	−	5.21587i	−0.139288	−	0.343179i
$232$	49.3469	+	28.4904i	3.23978	+	1.87049i
$233$			5.34164i			0.349943i	0.984574	+	0.174971i	$0.0559833\pi$
$233$			5.34164i			0.349943i	−0.984574	+	0.174971i	$0.944017\pi$
$234$	−14.9898	−	4.24676i	−0.979913	−	0.277619i
$235$		0			0
$236$	−27.2149	+	47.1376i	−1.77154	+	3.06840i
$237$	2.88469	+	2.24639i	0.187380	+	0.145919i
$238$	19.7119	−	11.3807i	1.27773	−	0.737698i
$239$	−11.0167	−	19.0815i	−0.712613	−	1.23428i	−0.963873	−	0.266362i	$-0.914178\pi$
$239$	−11.0167	−	19.0815i	−0.712613	−	1.23428i	0.251260	−	0.967920i	$-0.419155\pi$
$240$		0			0
$241$	9.32358	−	16.1489i	0.600585	−	1.04024i	−0.392148	−	0.919902i	$-0.628268\pi$
$241$	9.32358	−	16.1489i	0.600585	−	1.04024i	0.992733	−	0.120341i	$-0.0383988\pi$
$242$		−	20.3605i		−	1.30882i
$243$	−9.92491	+	12.0207i	−0.636683	+	0.771126i
$244$	62.5475			4.00420
$245$		0			0
$246$	11.1444	+	1.54820i	0.710542	+	0.0987095i
$247$	5.06263	−	2.92291i	0.322127	−	0.185980i
$248$	17.5684	−	10.1431i	1.11560	−	0.644091i
$249$	−1.16936	+	1.50162i	−0.0741052	+	0.0951616i
$250$		0			0
$251$	14.6929			0.927407			0.463704	−	0.885990i	$-0.346520\pi$
$251$	14.6929			0.927407			0.463704	+	0.885990i	$0.346520\pi$
$252$	7.25586	−	25.6110i	0.457076	−	1.61334i
$253$			3.13515i			0.197105i
$254$	4.77103	−	8.26366i	0.299361	−	0.518508i
$255$		0			0
$256$	4.73035	+	8.19320i	0.295647	+	0.512075i
$257$	19.2335	−	11.1045i	1.19975	−	0.692678i	0.239253	−	0.970957i	$-0.423098\pi$
$257$	19.2335	−	11.1045i	1.19975	−	0.692678i	0.960500	+	0.278280i	$0.0897642\pi$
$258$	−30.7637	+	12.4862i	−1.91526	+	0.777357i
$259$	−10.4566	+	18.1114i	−0.649743	+	1.12539i
$260$		0			0
$261$	15.8507	−	15.4044i	0.981132	−	0.953510i
$262$			19.2089i			1.18673i
$263$	4.97100	+	2.87001i	0.306525	+	0.176972i	0.645370	−	0.763870i	$-0.276703\pi$
$263$	4.97100	+	2.87001i	0.306525	+	0.176972i	−0.338846	+	0.940842i	$0.610036\pi$
$264$	−14.8815	+	19.1099i	−0.915892	+	1.17613i
$265$		0			0
$266$	7.01727	+	12.1543i	0.430256	+	0.745226i
$267$	−3.16823	+	22.8059i	−0.193892	+	1.39570i
$268$	38.9197	+	22.4703i	2.37740	+	1.37259i
$269$	15.6162			0.952139			0.476070	−	0.879408i	$-0.342061\pi$
$269$	15.6162			0.952139			0.476070	+	0.879408i	$0.342061\pi$
$270$		0			0
$271$	−6.75315			−0.410225			−0.205112	−	0.978738i	$-0.565756\pi$
$271$	−6.75315			−0.410225			−0.205112	+	0.978738i	$0.565756\pi$
$272$	−43.7050	−	25.2331i	−2.65000	−	1.52998i
$273$	0.844693	−	6.08037i	0.0511232	−	0.368001i
$274$	−9.38423	−	16.2540i	−0.566922	−	0.981938i
$275$		0			0
$276$	−9.10894	+	11.6972i	−0.548294	+	0.704087i
$277$	−26.2376	−	15.1483i	−1.57646	−	0.910172i	−0.995347	−	0.0963529i	$-0.969282\pi$
$277$	−26.2376	−	15.1483i	−1.57646	−	0.910172i	−0.581118	−	0.813820i	$-0.697384\pi$
$278$			38.7438i			2.32370i
$279$	−1.92795	−	7.62925i	−0.115423	−	0.456751i
$280$		0			0
$281$	−9.31755	+	16.1385i	−0.555838	+	0.962740i	0.441999	+	0.897015i	$0.354269\pi$
$281$	−9.31755	+	16.1385i	−0.555838	+	0.962740i	−0.997838	+	0.0657249i	$0.979064\pi$
$282$	−26.5957	+	10.7945i	−1.58375	+	0.642805i
$283$	4.91354	−	2.83683i	0.292079	−	0.168632i	−0.346800	−	0.937939i	$-0.612732\pi$
$283$	4.91354	−	2.83683i	0.292079	−	0.168632i	0.638879	+	0.769307i	$0.279398\pi$
$284$	3.14604	+	5.44910i	0.186683	+	0.323345i
$285$		0			0
$286$	−4.69502	+	8.13201i	−0.277622	+	0.480856i
$287$			4.43332i			0.261690i
$288$	−35.4141	+	8.94931i	−2.08679	+	0.527343i
$289$	−6.11806			−0.359886
$290$		0			0
$291$	−4.07877	+	5.23772i	−0.239102	+	0.307040i
$292$	−15.3379	+	8.85533i	−0.897582	+	0.518219i
$293$	−15.8286	+	9.13867i	−0.924720	+	0.533887i	−0.885138	−	0.465329i	$-0.845936\pi$
$293$	−15.8286	+	9.13867i	−0.924720	+	0.533887i	−0.0395819	+	0.999216i	$0.512603\pi$
$294$	−17.0308	−	2.36594i	−0.993257	−	0.137985i
$295$		0			0
$296$	89.9850			5.23027
$297$	5.55857	+	7.57454i	0.322541	+	0.439520i
$298$			1.48887i			0.0862478i
$299$	−1.70950	+	2.96094i	−0.0988631	+	0.171236i
$300$		0			0
$301$	−6.54097	−	11.3293i	−0.377015	−	0.653009i
$302$	0.349852	−	0.201987i	0.0201317	−	0.0116230i
$303$	−8.95425	−	6.97295i	−0.514408	−	0.400585i
$304$	15.5586	−	26.9483i	0.892349	−	1.54559i
$305$		0			0
$306$	−27.2436	+	26.4766i	−1.55741	+	1.51357i
$307$		−	15.5050i		−	0.884915i	−0.896789	−	0.442458i	$-0.854107\pi$
$307$		−	15.5050i		−	0.884915i	0.896789	−	0.442458i	$-0.145893\pi$
$308$	−13.8941	−	8.02174i	−0.791688	−	0.457081i
$309$	5.26033	+	12.9605i	0.299250	+	0.737295i
$310$		0			0
$311$	−15.2232	−	26.3673i	−0.863228	−	1.49515i	−0.868796	−	0.495170i	$-0.835106\pi$
$311$	−15.2232	−	26.3673i	−0.863228	−	1.49515i	0.00556798	−	0.999984i	$-0.498228\pi$
$312$	−24.4746	+	9.93365i	−1.38560	+	0.562382i
$313$	−6.01832	−	3.47468i	−0.340176	−	0.196401i	0.320174	−	0.947359i	$-0.396259\pi$
$313$	−6.01832	−	3.47468i	−0.340176	−	0.196401i	−0.660350	+	0.750958i	$0.729592\pi$
$314$	30.1843			1.70340
$315$		0			0
$316$	10.4205			0.586196
$317$	13.9820	+	8.07253i	0.785309	+	0.453398i	0.838308	−	0.545196i	$-0.183545\pi$
$317$	13.9820	+	8.07253i	0.785309	+	0.453398i	−0.0529995	+	0.998595i	$0.516878\pi$
$318$	−6.20998	−	4.83590i	−0.348238	−	0.271184i
$319$	−6.66081	−	11.5369i	−0.372934	−	0.645940i
$320$		0			0
$321$	15.4003	+	2.13943i	0.859560	+	0.119411i
$322$	−7.10858	−	4.10414i	−0.396146	−	0.228715i
$323$		−	14.2545i		−	0.793142i
$324$	−1.26838	+	44.4104i	−0.0704655	+	2.46724i
$325$		0			0
$326$	29.0493	−	50.3148i	1.60889	−	2.78668i
$327$	−1.51140	+	10.8796i	−0.0835808	+	0.601642i
$328$	16.5199	−	9.53779i	0.912160	−	0.526636i
$329$	−5.65478	−	9.79436i	−0.311758	−	0.539981i
$330$		0			0
$331$	−6.31112	+	10.9312i	−0.346890	+	0.600832i	−0.985695	−	0.168537i	$-0.946096\pi$
$331$	−6.31112	+	10.9312i	−0.346890	+	0.600832i	0.638805	+	0.769369i	$0.279429\pi$
$332$			5.42437i			0.297701i
$333$	9.51456	−	33.5835i	0.521394	−	1.84037i
$334$	−44.9535			−2.45975
$335$		0			0
$336$	−12.2890	−	30.2777i	−0.670419	−	1.65179i
$337$	−5.99324	+	3.46020i	−0.326473	+	0.188489i	−0.654274	−	0.756258i	$-0.727026\pi$
$337$	−5.99324	+	3.46020i	−0.326473	+	0.188489i	0.327801	+	0.944747i	$0.393692\pi$
$338$	20.7831	−	11.9991i	1.13045	−	0.652665i
$339$	9.70734	+	23.9170i	0.527230	+	1.29900i
$340$		0			0
$341$	−4.74276			−0.256835
$342$	−16.3254	−	16.7983i	−0.882776	−	0.908348i
$343$		−	19.3570i		−	1.04518i
$344$	−28.1443	+	48.7474i	−1.51744	+	2.62828i
$345$		0			0
$346$	−15.7295	−	27.2442i	−0.845621	−	1.46466i
$347$	11.9566	−	6.90317i	0.641866	−	0.370581i	−0.143467	−	0.989655i	$-0.545825\pi$
$347$	11.9566	−	6.90317i	0.641866	−	0.370581i	0.785333	+	0.619074i	$0.212492\pi$
$348$	8.66816	−	62.3962i	0.464662	−	3.34479i
$349$	3.28384	−	5.68778i	0.175780	−	0.304460i	−0.764651	−	0.644445i	$-0.777089\pi$
$349$	3.28384	−	5.68778i	0.175780	−	0.304460i	0.940431	+	0.339985i	$0.110422\pi$
$350$		0			0
$351$	1.11954	+	10.1846i	0.0597564	+	0.543612i
$352$			22.0153i			1.17342i
$353$	−3.05273	−	1.76250i	−0.162481	−	0.0938082i	0.416555	−	0.909111i	$-0.363237\pi$
$353$	−3.05273	−	1.76250i	−0.162481	−	0.0938082i	−0.579035	+	0.815302i	$0.696571\pi$
$354$	49.8194	+	6.92097i	2.64787	+	0.367846i
$355$		0			0
$356$	32.8116	+	56.8313i	1.73901	+	3.01205i
$357$	−11.8102	−	9.19698i	−0.625063	−	0.486756i
$358$	19.4996	+	11.2581i	1.03059	+	0.595010i
$359$	−22.9285			−1.21012			−0.605061	−	0.796179i	$-0.706851\pi$
$359$	−22.9285			−1.21012			−0.605061	+	0.796179i	$0.706851\pi$
$360$		0			0
$361$	−10.2107			−0.537407
$362$	24.0686	+	13.8960i	1.26502	+	0.730358i
$363$	−12.4070	+	5.03568i	−0.651196	+	0.264304i
$364$	−8.74801	−	15.1520i	−0.458520	−	0.794181i
$365$		0			0
$366$	−21.7371	−	53.5560i	−1.13621	−	2.79942i
$367$	−3.61939	−	2.08966i	−0.188931	−	0.109079i	0.402551	−	0.915397i	$-0.368124\pi$
$367$	−3.61939	−	2.08966i	−0.188931	−	0.109079i	−0.591482	+	0.806318i	$0.701457\pi$
$368$			18.1993i			0.948706i
$369$	−1.81289	−	7.17392i	−0.0943751	−	0.373459i
$370$		0			0
$371$	1.55064	−	2.68578i	0.0805051	−	0.139439i
$372$	−17.6951	−	13.7797i	−0.917447	−	0.714444i
$373$	−5.92440	+	3.42045i	−0.306754	+	0.177104i	−0.645473	−	0.763783i	$-0.723340\pi$
$373$	−5.92440	+	3.42045i	−0.306754	+	0.177104i	0.338719	+	0.940888i	$0.390006\pi$
$374$	11.4484	+	19.8292i	0.591982	+	1.02534i
$375$		0			0
$376$	−24.3312	+	42.1429i	−1.25479	+	2.17336i
$377$		−	14.5277i		−	0.748217i
$378$	−24.4509	+	2.68776i	−1.25762	+	0.138244i
$379$	12.7764			0.656280			0.328140	−	0.944629i	$-0.393578\pi$
$379$	12.7764			0.656280			0.328140	+	0.944629i	$0.393578\pi$
$380$		0			0
$381$	−6.21558	−	0.863476i	−0.318434	−	0.0442372i
$382$	−39.5440	+	22.8307i	−2.02325	+	1.16812i
$383$	−6.52515	+	3.76730i	−0.333420	+	0.192500i	−0.657358	−	0.753578i	$-0.728326\pi$
$383$	−6.52515	+	3.76730i	−0.333420	+	0.192500i	0.323939	+	0.946078i	$0.394993\pi$
$384$	−5.12773	+	6.58472i	−0.261673	+	0.336025i
$385$		0			0
$386$	4.10736			0.209059
$387$	15.2173	+	15.6581i	0.773538	+	0.795946i
$388$			18.9204i			0.960538i
$389$	2.72588	−	4.72135i	0.138207	−	0.239382i	−0.788611	−	0.614893i	$-0.789199\pi$
$389$	2.72588	−	4.72135i	0.138207	−	0.239382i	0.926818	+	0.375511i	$0.122533\pi$
$390$		0			0
$391$	4.16847	+	7.22000i	0.210808	+	0.365131i
$392$	−25.2456	+	14.5756i	−1.27510	+	0.736177i
$393$	11.7052	−	4.75087i	0.590451	−	0.239649i
$394$	23.6729	−	41.0026i	1.19262	−	2.06568i
$395$		0			0
$396$	25.7634	+	7.29904i	1.29466	+	0.366791i
$397$		−	5.64549i		−	0.283339i	−0.989914	−	0.141670i	$-0.954753\pi$
$397$		−	5.64549i		−	0.283339i	0.989914	−	0.141670i	$-0.0452470\pi$
$398$	25.1408	+	14.5151i	1.26020	+	0.727574i
$399$	5.67082	−	7.28214i	0.283896	−	0.364563i
$400$		0			0
$401$	2.75209	+	4.76676i	0.137433	+	0.238040i	0.926524	−	0.376235i	$-0.122782\pi$
$401$	2.75209	+	4.76676i	0.137433	+	0.238040i	−0.789091	+	0.614276i	$0.789448\pi$
$402$	5.71438	−	41.1339i	0.285007	−	2.05157i
$403$	−4.47922	−	2.58608i	−0.223126	−	0.128822i
$404$	−32.3458			−1.60926
$405$		0			0
$406$	34.8779			1.73096
$407$	−18.2192	−	10.5188i	−0.903091	−	0.521400i
$408$	−8.86246	+	63.7948i	−0.438757	+	3.15831i
$409$	16.4265	+	28.4515i	0.812238	+	1.40684i	0.911295	+	0.411755i	$0.135084\pi$
$409$	16.4265	+	28.4515i	0.812238	+	1.40684i	−0.0990570	+	0.995082i	$0.531583\pi$
$410$		0			0
$411$	−7.58362	+	9.73844i	−0.374072	+	0.480362i
$412$	34.5241	+	19.9325i	1.70088	+	0.982005i
$413$			19.8184i			0.975202i
$414$	13.1813	+	3.73439i	0.647824	+	0.183535i
$415$		0			0
$416$	−12.0043	+	20.7920i	−0.588558	+	1.01941i
$417$	23.6091	−	9.58235i	1.15614	−	0.469250i
$418$	−12.2266	+	7.05903i	−0.598022	+	0.345268i
$419$	11.4295	+	19.7965i	0.558369	+	0.967124i	0.997633	+	0.0687656i	$0.0219060\pi$
$419$	11.4295	+	19.7965i	0.558369	+	0.967124i	−0.439264	+	0.898358i	$0.644761\pi$
$420$		0			0
$421$	−8.97071	+	15.5377i	−0.437205	+	0.757262i	−0.997473	−	0.0710498i	$-0.977365\pi$
$421$	−8.97071	+	15.5377i	−0.437205	+	0.757262i	0.560267	+	0.828312i	$0.310698\pi$
$422$		−	63.0212i		−	3.06782i
$423$	13.1556	+	13.5367i	0.639648	+	0.658177i
$424$	−13.3441			−0.648046
$425$		0			0
$426$	3.57243	−	4.58750i	0.173085	−	0.222265i
$427$	19.7230	−	11.3871i	0.954463	−	0.551060i
$428$	38.3768	−	22.1568i	1.85501	−	1.07099i
$429$	6.11656	+	0.849720i	0.295310	+	0.0410249i
$430$		0			0
$431$	−6.18871			−0.298100			−0.149050	−	0.988830i	$-0.547622\pi$
$431$	−6.18871			−0.298100			−0.149050	+	0.988830i	$0.547622\pi$
$432$	32.2671	+	43.9697i	1.55245	+	2.11549i
$433$			3.11806i			0.149844i	0.997189	+	0.0749221i	$0.0238708\pi$
$433$			3.11806i			0.149844i	−0.997189	+	0.0749221i	$0.976129\pi$
$434$	6.20861	−	10.7536i	0.298023	−	0.516190i
$435$		0			0
$436$	15.6528	+	27.1114i	0.749631	+	1.29840i
$437$	−4.45182	+	2.57026i	−0.212960	+	0.122952i
$438$	12.9127	+	10.0555i	0.616992	+	0.480471i
$439$	6.75494	−	11.6999i	0.322396	−	0.558406i	−0.658586	−	0.752505i	$-0.728845\pi$
$439$	6.75494	−	11.6999i	0.322396	−	0.558406i	0.980982	+	0.194100i	$0.0621785\pi$
$440$		0			0
$441$	2.77044	+	10.9631i	0.131926	+	0.522054i
$442$			24.9698i			1.18769i
$443$	−21.0248	−	12.1387i	−0.998918	−	0.576726i	−0.0909904	−	0.995852i	$-0.529003\pi$
$443$	−21.0248	−	12.1387i	−0.998918	−	0.576726i	−0.907928	+	0.419126i	$0.862337\pi$
$444$	−37.4135	−	92.1799i	−1.77557	−	4.37466i
$445$		0			0
$446$	−28.5899	−	49.5192i	−1.35377	−	2.34480i
$447$	0.907263	−	0.368236i	0.0429121	−	0.0174169i
$448$	−17.2404	−	9.95377i	−0.814534	−	0.470271i
$449$	24.1437			1.13941			0.569705	−	0.821849i	$-0.307057\pi$
$449$	24.1437			1.13941			0.569705	+	0.821849i	$0.307057\pi$
$450$		0			0
$451$	−4.45970			−0.209999
$452$	63.7104	+	36.7832i	2.99668	+	1.73014i
$453$	−0.209611	−	0.163230i	−0.00984838	−	0.00766924i
$454$	18.5680	+	32.1607i	0.871440	+	1.50938i
$455$		0			0
$456$	−39.3357	−	5.46456i	−1.84206	−	0.255902i
$457$	2.44355	+	1.41078i	0.114304	+	0.0659937i	0.556062	−	0.831141i	$-0.312312\pi$
$457$	2.44355	+	1.41078i	0.114304	+	0.0659937i	−0.441758	+	0.897134i	$0.645645\pi$
$458$		−	9.68573i		−	0.452585i
$459$	22.8720	+	10.0529i	1.06757	+	0.469230i
$460$		0			0
$461$	−10.7286	+	18.5825i	−0.499681	+	0.865474i	−1.00000		0.000367761i	$-0.999883\pi$
$461$	−10.7286	+	18.5825i	−0.499681	+	0.865474i	0.500318	+	0.865841i	$0.333216\pi$
$462$	−2.03999	+	14.6845i	−0.0949090	+	0.683185i
$463$	17.1502	−	9.90167i	0.797037	−	0.460170i	−0.0453970	−	0.998969i	$-0.514455\pi$
$463$	17.1502	−	9.90167i	0.797037	−	0.460170i	0.842434	+	0.538799i	$0.181122\pi$
$464$	−38.6655	−	66.9706i	−1.79500	−	3.10903i
$465$		0			0
$466$	7.03421	−	12.1836i	0.325853	−	0.564395i
$467$			22.7210i			1.05140i	0.850669	+	0.525701i	$0.176197\pi$
$467$			22.7210i			1.05140i	−0.850669	+	0.525701i	$0.823803\pi$
$468$	20.3519	+	20.9415i	0.940767	+	0.968019i
$469$	16.3633			0.755588
$470$		0			0
$471$	−7.46536	−	18.3932i	−0.343986	−	0.847516i
$472$	73.8497	−	42.6372i	3.39921	−	1.96253i
$473$	11.3967	−	6.57989i	0.524021	−	0.302544i
$474$	−3.62141	−	8.92247i	−0.166337	−	0.409822i
$475$		0			0
$476$	−42.6625			−1.95543
$477$	−1.41094	+	4.98018i	−0.0646023	+	0.228027i
$478$			58.0300i			2.65423i
$479$	10.6440	−	18.4359i	0.486336	−	0.842359i	−0.513541	−	0.858065i	$-0.671666\pi$
$479$	10.6440	−	18.4359i	0.486336	−	0.842359i	0.999877	+	0.0157065i	$0.00499974\pi$
$480$		0			0
$481$	−11.4712	−	19.8687i	−0.523042	−	0.905935i
$482$	−42.5318	+	24.5557i	−1.93727	+	1.11848i
$483$	−0.742781	+	5.34677i	−0.0337977	+	0.243287i
$484$	−19.0813	+	33.0497i	−0.867330	+	1.50226i
$485$		0			0
$486$	38.4670	−	14.3478i	1.74490	−	0.650831i
$487$		−	9.58690i		−	0.434424i	−0.976124	−	0.217212i	$-0.930304\pi$
$487$		−	9.58690i		−	0.434424i	0.976124	−	0.217212i	$-0.0696963\pi$
$488$	−84.8637	−	48.9961i	−3.84160	−	2.21795i
$489$	−37.8447	−	5.25743i	−1.71140	−	0.237749i
$490$		0			0
$491$	18.9222	+	32.7742i	0.853945	+	1.47908i	0.877620	+	0.479357i	$0.159130\pi$
$491$	18.9222	+	32.7742i	0.853945	+	1.47908i	−0.0236745	+	0.999720i	$0.507537\pi$
$492$	−16.6390	−	12.9573i	−0.750144	−	0.584160i
$493$	−30.6786	−	17.7123i	−1.38169	−	0.797721i
$494$	−15.3963			−0.692711
$495$		0			0
$496$	−27.5314			−1.23619
$497$	1.98407	+	1.14550i	0.0889977	+	0.0513829i
$498$	4.64459	−	1.88513i	0.208129	−	0.0844745i
$499$	8.46266	+	14.6577i	0.378840	+	0.656171i	0.990894	−	0.134646i	$-0.0429896\pi$
$499$	8.46266	+	14.6577i	0.378840	+	0.656171i	−0.612053	+	0.790816i	$0.709656\pi$
$500$		0			0
$501$	11.1182	+	27.3930i	0.496723	+	1.22383i
$502$	−33.5126	−	19.3485i	−1.49574	−	0.863566i
$503$		−	40.4168i		−	1.80210i	−0.433719	−	0.901048i	$-0.642799\pi$
$503$		−	40.4168i		−	1.80210i	0.433719	−	0.901048i	$-0.357201\pi$
$504$	−29.9068	+	29.0649i	−1.33216	+	1.29465i
$505$		0			0
$506$	4.12856	−	7.15088i	0.183537	−	0.317896i
$507$	−12.4520	−	9.69676i	−0.553013	−	0.430648i
$508$	−15.4889	+	8.94253i	−0.687210	+	0.396761i
$509$	−20.7034	−	35.8593i	−0.917660	−	1.58943i	−0.802959	−	0.596034i	$-0.796742\pi$
$509$	−20.7034	−	35.8593i	−0.917660	−	1.58943i	−0.114701	−	0.993400i	$-0.536591\pi$
$510$		0			0
$511$	−3.22431	+	5.58467i	−0.142635	+	0.247051i
$512$		−	34.5537i		−	1.52707i
$513$	−6.19860	+	14.1028i	−0.273675	+	0.622652i
$514$	−58.4922			−2.57998
$515$		0			0
$516$	61.6381	+	8.56285i	2.71347	+	0.376959i
$517$	9.85265	−	5.68843i	0.433319	−	0.250177i
$518$	47.7004	−	27.5398i	2.09584	−	1.21003i
$519$	−12.7113	+	16.3232i	−0.557966	+	0.716507i
$520$		0			0
$521$	−17.0301			−0.746103			−0.373052	−	0.927811i	$-0.621689\pi$
$521$	−17.0301			−0.746103			−0.373052	+	0.927811i	$0.621689\pi$
$522$	−56.4389	+	14.2624i	−2.47026	+	0.624248i
$523$		−	9.57651i		−	0.418751i	−0.977835	−	0.209376i	$-0.932857\pi$
$523$		−	9.57651i		−	0.418751i	0.977835	−	0.209376i	$-0.0671432\pi$
$524$	18.0021	−	31.1805i	0.786424	−	1.36213i
$525$		0			0
$526$	−7.55880	−	13.0922i	−0.329579	−	0.570848i
$527$	−10.9222	+	6.30592i	−0.475777	+	0.274690i
$528$	30.4579	−	12.3621i	1.32551	−	0.537992i
$529$	−9.99675	+	17.3149i	−0.434641	+	0.752821i
$530$		0			0
$531$	−8.10422	−	32.0699i	−0.351693	−	1.39171i
$532$		−	26.3055i		−	1.14049i
$533$	−4.21189	−	2.43174i	−0.182437	−	0.105330i
$534$	37.2586	−	47.8452i	1.61234	−	2.07047i
$535$		0			0
$536$	−35.2038	−	60.9748i	−1.52057	−	2.63371i
$537$	2.03753	−	14.6668i	0.0879260	−	0.632920i
$538$	−35.6187	−	20.5644i	−1.53563	−	0.886596i
$539$	6.81528			0.293555
$540$		0			0
$541$	−0.833751			−0.0358458			−0.0179229	−	0.999839i	$-0.505705\pi$
$541$	−0.833751			−0.0358458			−0.0179229	+	0.999839i	$0.505705\pi$
$542$	15.4031	+	8.89297i	0.661619	+	0.381986i
$543$	2.51495	−	18.1034i	0.107927	−	0.776891i
$544$	29.2713	+	50.6994i	1.25500	+	2.17372i
$545$		0			0
$546$	−9.93365	+	12.7562i	−0.425121	+	0.545915i
$547$	24.5319	+	14.1635i	1.04891	+	0.605587i	0.922343	−	0.386371i	$-0.126272\pi$
$547$	24.5319	+	14.1635i	1.04891	+	0.605587i	0.126565	+	0.991958i	$0.459605\pi$
$548$			35.1785i			1.50275i
$549$	−27.2590	+	26.4916i	−1.16339	+	1.13063i
$550$		0			0
$551$	10.9213	−	18.9163i	0.465264	−	0.805861i
$552$	21.5218	−	8.73515i	0.916027	−	0.371793i
$553$	3.28586	−	1.89709i	0.139729	−	0.0806727i
$554$	39.8964	+	69.1026i	1.69504	+	2.93589i
$555$		0			0
$556$	36.3096	−	62.8901i	1.53987	−	2.66713i
$557$			11.5042i			0.487448i	0.969845	+	0.243724i	$0.0783690\pi$
$557$			11.5042i			0.487448i	−0.969845	+	0.243724i	$0.921631\pi$
$558$	−5.64926	+	19.9402i	−0.239152	+	0.844135i
$559$	14.3512			0.606993
$560$		0			0
$561$	9.25171	−	11.8805i	0.390608	−	0.501595i
$562$	42.5043	−	24.5398i	1.79293	−	1.03515i
$563$	−28.5840	+	16.5030i	−1.20467	+	0.695517i	−0.961590	−	0.274490i	$-0.911491\pi$
$563$	−28.5840	+	16.5030i	−1.20467	+	0.695517i	−0.243080	+	0.970006i	$0.578158\pi$
$564$	53.2872	+	7.40273i	2.24380	+	0.311711i
$565$		0			0
$566$	−14.9429			−0.628095
$567$	7.68517	+	14.2348i	0.322747	+	0.597804i
$568$		−	9.85769i		−	0.413619i
$569$	−13.5044	+	23.3903i	−0.566135	+	0.980574i	0.430809	+	0.902443i	$0.358228\pi$
$569$	−13.5044	+	23.3903i	−0.566135	+	0.980574i	−0.996943	+	0.0781305i	$0.975105\pi$
$570$		0			0
$571$	12.2122	+	21.1521i	0.511064	+	0.885189i	0.999918	+	0.0128232i	$0.00408185\pi$
$571$	12.2122	+	21.1521i	0.511064	+	0.885189i	−0.488854	+	0.872366i	$0.662585\pi$
$572$	15.2422	−	8.80007i	0.637307	−	0.367950i
$573$	23.6925	+	18.4501i	0.989768	+	0.770763i
$574$	5.83807	−	10.1118i	0.243676	−	0.422060i
$575$		0			0
$576$	31.9685	+	9.05701i	1.33202	+	0.377375i
$577$			14.7976i			0.616033i	0.951381	+	0.308017i	$0.0996653\pi$
$577$			14.7976i			0.616033i	−0.951381	+	0.308017i	$0.900335\pi$
$578$	13.9545	+	8.05663i	0.580431	+	0.335112i
$579$	−1.01586	−	2.50288i	−0.0422175	−	0.104016i
$580$		0			0
$581$	0.987533	+	1.71046i	0.0409698	+	0.0709617i
$582$	16.2005	−	6.57538i	0.671532	−	0.272558i
$583$	2.70177	+	1.55987i	0.111896	+	0.0646030i
$584$	27.7470			1.14818
$585$		0			0
$586$	48.1375			1.98854
$587$	−26.4813	−	15.2890i	−1.09300	−	0.631044i	−0.158626	−	0.987339i	$-0.550706\pi$
$587$	−26.4813	−	15.2890i	−1.09300	−	0.631044i	−0.934374	+	0.356295i	$0.884040\pi$
$588$	25.4276	+	19.8013i	1.04862	+	0.816590i
$589$	−3.88821	−	6.73457i	−0.160211	−	0.277493i
$590$		0			0
$591$	−30.8405	−	4.28440i	−1.26861	−	0.176237i
$592$	−105.761	−	61.0611i	−4.34675	−	2.50960i
$593$			5.09990i			0.209428i	0.994502	+	0.104714i	$0.0333927\pi$
$593$			5.09990i			0.209428i	−0.994502	+	0.104714i	$0.966607\pi$
$594$	−2.70376	−	24.5964i	−0.110936	−	1.00920i
$595$		0			0
$596$	1.39532	−	2.41677i	0.0571547	−	0.0989949i
$597$	2.62698	−	18.9099i	0.107515	−	0.773929i
$598$	7.79831	−	4.50236i	0.318897	−	0.184115i
$599$	−0.282655	−	0.489572i	−0.0115490	−	0.0200034i	0.860193	−	0.509968i	$-0.170343\pi$
$599$	−0.282655	−	0.489572i	−0.0115490	−	0.0200034i	−0.871742	+	0.489965i	$0.837010\pi$
$600$		0			0
$601$	5.50480	−	9.53459i	0.224546	−	0.388924i	−0.731637	−	0.681694i	$-0.761244\pi$
$601$	5.50480	−	9.53459i	0.224546	−	0.388924i	0.956183	+	0.292770i	$0.0945769\pi$
$602$			34.4542i			1.40425i
$603$	−26.4788	+	6.69134i	−1.07830	+	0.272492i
$604$	−0.757185			−0.0308094
$605$		0			0
$606$	11.2411	+	27.6959i	0.456638	+	1.12507i
$607$	−16.5396	+	9.54913i	−0.671321	+	0.387587i	−0.796577	−	0.604537i	$-0.793358\pi$
$607$	−16.5396	+	9.54913i	−0.671321	+	0.387587i	0.125256	+	0.992124i	$0.460025\pi$
$608$	−31.2611	+	18.0486i	−1.26780	+	0.731967i
$609$	−8.62621	−	21.2534i	−0.349552	−	0.861229i
$610$		0			0
$611$	12.4069			0.501929
$612$	69.0357	−	17.4457i	2.79060	−	0.705200i
$613$		−	9.33918i		−	0.377206i	−0.982053	−	0.188603i	$-0.939604\pi$
$613$		−	9.33918i		−	0.377206i	0.982053	−	0.188603i	$-0.0603959\pi$
$614$	−20.4179	+	35.3648i	−0.823999	+	1.42721i
$615$		0			0
$616$	12.5675	+	21.7676i	0.506360	+	0.877041i
$617$	−21.1444	+	12.2077i	−0.851241	+	0.491464i	−0.861069	−	0.508488i	$-0.830205\pi$
$617$	−21.1444	+	12.2077i	−0.851241	+	0.491464i	0.00982861	+	0.999952i	$0.496871\pi$
$618$	5.06900	−	36.4883i	0.203905	−	1.46777i
$619$	19.7431	−	34.1961i	0.793544	−	1.37446i	−0.130216	−	0.991486i	$-0.541567\pi$
$619$	19.7431	−	34.1961i	0.793544	−	1.37446i	0.923760	−	0.382973i	$-0.125100\pi$
$620$		0			0
$621$	−0.984464	−	8.95580i	−0.0395052	−	0.359384i
$622$			80.1874i			3.21522i
$623$	20.6928	+	11.9470i	0.829040	+	0.478647i
$624$	35.5062	+	4.93256i	1.42138	+	0.197461i
$625$		0			0
$626$	9.15135	+	15.8506i	0.365761	+	0.633517i
$627$	7.32547	+	5.70457i	0.292551	+	0.227819i
$628$	−48.9960	−	28.2879i	−1.95515	−	1.12881i
$629$	−55.9430			−2.23059
$630$		0			0
$631$	42.1634			1.67850			0.839249	−	0.543747i	$-0.182995\pi$
$631$	42.1634			1.67850			0.839249	+	0.543747i	$0.182995\pi$
$632$	−14.1383	−	8.16277i	−0.562393	−	0.324698i
$633$	−38.4029	+	15.5868i	−1.52638	+	0.619518i
$634$	−21.2608	−	36.8248i	−0.844375	−	1.46250i
$635$		0			0
$636$	5.54814	+	13.6696i	0.219998	+	0.542034i
$637$	6.43658	+	3.71616i	0.255027	+	0.147240i
$638$			35.0855i			1.38905i
$639$	−3.67901	−	1.04230i	−0.145539	−	0.0412328i
$640$		0			0
$641$	−17.6577	+	30.5841i	−0.697438	+	1.20800i	0.271913	+	0.962322i	$0.412344\pi$
$641$	−17.6577	+	30.5841i	−0.697438	+	1.20800i	−0.969352	+	0.245677i	$0.920990\pi$
$642$	−32.3087	−	25.1598i	−1.27512	−	0.992978i
$643$	−12.2936	+	7.09771i	−0.484812	+	0.279906i	−0.722420	−	0.691455i	$-0.756970\pi$
$643$	−12.2936	+	7.09771i	−0.484812	+	0.279906i	0.237608	+	0.971361i	$0.423637\pi$
$644$	7.69256	+	13.3239i	0.303129	+	0.525036i
$645$		0			0
$646$	−18.7712	+	32.5127i	−0.738544	+	1.27919i
$647$			17.4897i			0.687593i	0.939044	+	0.343796i	$0.111713\pi$
$647$			17.4897i			0.687593i	−0.939044	+	0.343796i	$0.888287\pi$
$648$	36.5094	−	59.2618i	1.43422	−	2.32803i
$649$	−19.9364			−0.782572
$650$		0			0
$651$	−8.08842	−	1.12365i	−0.317010	−	0.0440395i
$652$	−94.3072	+	54.4483i	−3.69335	+	2.13236i
$653$	9.50650	−	5.48858i	0.372018	−	0.214785i	−0.302322	−	0.953206i	$-0.597762\pi$
$653$	9.50650	−	5.48858i	0.372018	−	0.214785i	0.674340	+	0.738421i	$0.264428\pi$
$654$	17.7742	−	22.8246i	0.695026	−	0.892512i
$655$		0			0
$656$	−25.8882			−1.01077
$657$	2.93383	−	10.3555i	0.114459	−	0.404007i
$658$			29.7862i			1.16119i
$659$	−7.89381	+	13.6725i	−0.307499	+	0.532604i	−0.977815	−	0.209472i	$-0.932825\pi$
$659$	−7.89381	+	13.6725i	−0.307499	+	0.532604i	0.670316	+	0.742076i	$0.266159\pi$
$660$		0			0
$661$	−24.9466	−	43.2088i	−0.970311	−	1.68063i	−0.694614	−	0.719383i	$-0.744425\pi$
$661$	−24.9466	−	43.2088i	−0.970311	−	1.68063i	−0.275697	−	0.961245i	$-0.588909\pi$
$662$	28.7897	−	16.6217i	1.11894	−	0.646022i
$663$	15.2157	−	6.17567i	0.590929	−	0.239843i
$664$	4.24913	−	7.35972i	0.164898	−	0.285612i
$665$		0			0
$666$	−65.9263	+	64.0703i	−2.55459	+	2.48267i
$667$			12.7750i			0.494649i
$668$	72.9698	+	42.1291i	2.82328	+	1.63002i
$669$	−23.1042	+	29.6691i	−0.893261	+	1.14707i
$670$		0			0
$671$	11.4549	+	19.8404i	0.442210	+	0.765929i
$672$	−5.21587	+	37.5455i	−0.201207	+	1.44835i
$673$	24.9757	+	14.4197i	0.962743	+	0.555840i	0.897016	−	0.441998i	$-0.145730\pi$
$673$	24.9757	+	14.4197i	0.962743	+	0.555840i	0.0657266	+	0.997838i	$0.479063\pi$
$674$	18.2264			0.702055
$675$		0			0
$676$	−44.9809			−1.73003
$677$	−9.06176	−	5.23181i	−0.348272	−	0.201075i	0.315652	−	0.948875i	$-0.397777\pi$
$677$	−9.06176	−	5.23181i	−0.348272	−	0.201075i	−0.663924	+	0.747800i	$0.731110\pi$
$678$	9.35426	−	67.3349i	0.359248	−	2.58598i
$679$	3.44455	+	5.96614i	0.132190	+	0.228959i
$680$		0			0
$681$	15.0053	−	19.2689i	0.575003	−	0.738385i
$682$	10.8176	+	6.24556i	0.414228	+	0.239155i
$683$			16.1875i			0.619396i	0.950835	+	0.309698i	$0.100228\pi$
$683$			16.1875i			0.619396i	−0.950835	+	0.309698i	$0.899772\pi$
$684$	10.7569	+	42.5672i	0.411302	+	1.62760i
$685$		0			0
$686$	−25.4904	+	44.1507i	−0.973229	+	1.68568i
$687$	−5.90214	+	2.39553i	−0.225181	+	0.0913953i
$688$	66.1570	−	38.1958i	2.52221	−	1.45620i
$689$	1.70109	+	2.94638i	0.0648065	+	0.112248i
$690$		0			0
$691$	−4.94181	+	8.55946i	−0.187995	+	0.325617i	−0.944582	−	0.328276i	$-0.893532\pi$
$691$	−4.94181	+	8.55946i	−0.187995	+	0.325617i	0.756586	+	0.653894i	$0.226866\pi$
$692$			58.9648i			2.24150i
$693$	9.45276	−	2.38876i	0.359081	−	0.0907415i
$694$	−36.3621			−1.38029
$695$		0			0
$696$	−60.6383	+	77.8682i	−2.29849	+	2.95158i
$697$	−10.2703	+	5.92957i	−0.389016	+	0.224598i
$698$	−14.9800	+	8.64872i	−0.567002	+	0.327359i
$699$	−9.16399	−	1.27307i	−0.346614	−	0.0481521i
$700$		0			0
$701$	43.9692			1.66069			0.830346	−	0.557248i	$-0.188143\pi$
$701$	43.9692			1.66069			0.830346	+	0.557248i	$0.188143\pi$
$702$	10.8582	−	24.7040i	0.409815	−	0.932391i
$703$		−	34.4942i		−	1.30097i
$704$	10.0130	−	17.3430i	0.377379	−	0.653640i
$705$		0			0
$706$	4.64193	+	8.04005i	0.174701	+	0.302591i
$707$	−10.1995	+	5.88870i	−0.383593	+	0.221467i
$708$	−74.3820	−	57.9236i	−2.79545	−	2.17690i
$709$	12.6130	−	21.8464i	0.473692	−	0.820458i	−0.525855	−	0.850574i	$-0.676254\pi$
$709$	12.6130	−	21.8464i	0.473692	−	0.820458i	0.999546	+	0.0301162i	$0.00958774\pi$
$710$		0			0
$711$	−4.54136	+	4.41351i	−0.170314	+	0.165520i
$712$		−	102.811i		−	3.85299i
$713$	3.93880	+	2.27407i	0.147509	+	0.0851645i
$714$	14.8264	+	36.5295i	0.554865	+	1.36708i
$715$		0			0
$716$	−21.1016	−	36.5490i	−0.788603	−	1.36590i
$717$	35.3614	−	14.3523i	1.32060	−	0.535998i
$718$	52.2971	+	30.1937i	1.95171	+	1.12682i
$719$	36.8600			1.37465			0.687323	−	0.726352i	$-0.258786\pi$
$719$	36.8600			1.37465			0.687323	+	0.726352i	$0.258786\pi$
$720$		0			0
$721$	14.5153			0.540576
$722$	23.2893	+	13.4461i	0.866740	+	0.500412i
$723$	25.4826	+	19.8441i	0.947708	+	0.738009i
$724$	−26.0459	−	45.1128i	−0.967988	−	1.67660i
$725$		0			0
$726$	34.9300	+	4.85252i	1.29637	+	0.180094i
$727$	33.1213	+	19.1226i	1.22840	+	0.709217i	0.966695	−	0.255931i	$-0.0823820\pi$
$727$	33.1213	+	19.1226i	1.22840	+	0.709217i	0.261705	+	0.965148i	$0.415715\pi$
$728$			27.4107i			1.01591i
$729$	−18.2569	−	19.8918i	−0.676183	−	0.736734i
$730$		0			0
$731$	17.4971	−	30.3059i	0.647154	−	1.12090i
$732$	−14.9070	+	107.305i	−0.550977	+	3.96611i
$733$	−34.2801	+	19.7916i	−1.26616	+	0.731020i	−0.974260	−	0.225428i	$-0.927622\pi$
$733$	−34.2801	+	19.7916i	−1.26616	+	0.731020i	−0.291903	+	0.956448i	$0.594289\pi$
$734$	5.50358	+	9.53248i	0.203141	+	0.351850i
$735$		0			0
$736$	10.5559	−	18.2834i	0.389097	−	0.673936i
$737$			16.4607i			0.606338i
$738$	−5.31210	+	18.7501i	−0.195541	+	0.690201i
$739$	8.24773			0.303398			0.151699	−	0.988427i	$-0.451526\pi$
$739$	8.24773			0.303398			0.151699	+	0.988427i	$0.451526\pi$
$740$		0			0
$741$	3.80790	+	9.38194i	0.139887	+	0.344654i
$742$	−7.07361	+	4.08395i	−0.259680	+	0.149927i
$743$	−1.13292	+	0.654091i	−0.0415627	+	0.0239963i	−0.520637	−	0.853778i	$-0.674306\pi$
$743$	−1.13292	+	0.654091i	−0.0415627	+	0.0239963i	0.479075	+	0.877774i	$0.340972\pi$
$744$	13.2142	+	32.5574i	0.484458	+	1.19361i
$745$		0			0
$746$	18.0171			0.659651
$747$	−2.29746	−	2.36401i	−0.0840595	−	0.0864946i
$748$		−	42.9164i		−	1.56918i
$749$	8.06752	−	13.9734i	0.294781	−	0.510575i
$750$		0			0
$751$	−14.2234	−	24.6357i	−0.519020	−	0.898969i	−0.999756	−	0.0221034i	$-0.992964\pi$
$751$	−14.2234	−	24.6357i	−0.519020	−	0.898969i	0.480736	−	0.876866i	$-0.340370\pi$
$752$	57.1939	−	33.0209i	2.08565	−	1.20415i
$753$	−3.50176	+	25.2068i	−0.127611	+	0.918585i
$754$	−19.1310	+	33.1359i	−0.696711	+	1.20674i
$755$		0			0
$756$	42.2083	+	18.5518i	1.53510	+	0.674724i
$757$		−	38.2012i		−	1.38845i	−0.719760	−	0.694223i	$-0.755748\pi$
$757$		−	38.2012i		−	1.38845i	0.719760	−	0.694223i	$-0.244252\pi$
$758$	−29.1414	−	16.8248i	−1.05846	−	0.611103i
$759$	−5.37859	−	0.747201i	−0.195231	−	0.0271217i
$760$		0			0
$761$	−11.0952	−	19.2174i	−0.402200	−	0.696632i	0.591791	−	0.806092i	$-0.298421\pi$
$761$	−11.0952	−	19.2174i	−0.402200	−	0.696632i	−0.993991	+	0.109460i	$0.965088\pi$
$762$	13.0398	+	10.1545i	0.472384	+	0.367860i
$763$	9.87152	+	5.69932i	0.357373	+	0.206329i
$764$	85.5852			3.09637
$765$		0			0
$766$	19.8440			0.716994
$767$	−18.8286	−	10.8707i	−0.679861	−	0.392518i
$768$	−15.1834	+	6.16258i	−0.547885	+	0.222373i
$769$	−8.45652	−	14.6471i	−0.304950	−	0.528189i	0.672300	−	0.740279i	$-0.265306\pi$
$769$	−8.45652	−	14.6471i	−0.304950	−	0.528189i	−0.977250	+	0.212090i	$0.931973\pi$
$770$		0			0
$771$	14.4666	+	35.6431i	0.521003	+	1.28365i
$772$	−6.66718	−	3.84930i	−0.239957	−	0.138539i
$773$			38.6464i			1.39001i	0.719003	+	0.695007i	$0.244599\pi$
$773$			38.6464i			1.39001i	−0.719003	+	0.695007i	$0.755401\pi$
$774$	−14.0891	−	55.7532i	−0.506423	−	2.00401i
$775$		0			0
$776$	14.8211	−	25.6709i	0.532047	−	0.921533i
$777$	−28.5793	−	22.2556i	−1.02528	−	0.798416i
$778$	−12.4347	+	7.17920i	−0.445807	+	0.257387i
$779$	−3.65615	−	6.33264i	−0.130995	−	0.226890i
$780$		0			0
$781$	−1.15232	+	1.99588i	−0.0412333	+	0.0714181i
$782$		−	21.9572i		−	0.785187i
$783$	22.6498	+	30.8644i	0.809437	+	1.10300i
$784$	39.5622			1.41294
$785$		0			0
$786$	−32.9544	−	4.57807i	−1.17544	−	0.163294i
$787$	9.45240	−	5.45734i	0.336942	−	0.194533i	−0.321977	−	0.946747i	$-0.604347\pi$
$787$	9.45240	−	5.45734i	0.336942	−	0.194533i	0.658919	+	0.752214i	$0.271014\pi$
$788$	−76.8530	+	44.3711i	−2.73777	+	1.58065i
$789$	−6.10845	+	7.84411i	−0.217467	+	0.279258i
$790$		0			0
$791$	26.7862			0.952409
$792$	−29.2378	−	30.0848i	−1.03892	−	1.06902i
$793$			24.9839i			0.887204i
$794$	−7.43433	+	12.8766i	−0.263835	+	0.456975i
$795$		0			0
$796$	−27.2062	−	47.1225i	−0.964298	−	1.67021i
$797$	−2.53356	+	1.46275i	−0.0897432	+	0.0518133i	−0.544200	−	0.838956i	$-0.683167\pi$
$797$	−2.53356	+	1.46275i	−0.0897432	+	0.0518133i	0.454457	+	0.890769i	$0.349833\pi$
$798$	−22.5240	+	9.14193i	−0.797340	+	0.323621i
$799$	15.1265	−	26.1999i	0.535139	−	0.926888i
$800$		0			0
$801$	−38.3702	−	10.8707i	−1.35574	−	0.384096i
$802$		−	14.4965i		−	0.511888i
$803$	−5.61791	−	3.24350i	−0.198252	−	0.114461i
$804$	−47.8252	+	61.4144i	−1.68667	+	2.16592i
$805$		0			0
$806$	6.81102	+	11.7970i	0.239908	+	0.415532i
$807$	−3.72182	+	26.7909i	−0.131014	+	0.943083i
$808$	43.8863	+	25.3378i	1.54391	+	0.891380i
$809$	37.9241			1.33334			0.666671	−	0.745352i	$-0.267719\pi$
$809$	37.9241			1.33334			0.666671	+	0.745352i	$0.267719\pi$
$810$		0			0
$811$	19.5050			0.684912			0.342456	−	0.939534i	$-0.388741\pi$
$811$	19.5050			0.684912			0.342456	+	0.939534i	$0.388741\pi$
$812$	−56.6148	−	32.6866i	−1.98679	−	1.14707i
$813$	1.60948	−	11.5855i	0.0564469	−	0.406323i
$814$	27.7037	+	47.9843i	0.971016	+	1.68185i
$815$		0			0
$816$	53.7055	−	68.9654i	1.88007	−	2.41427i
$817$	18.6865	+	10.7887i	0.653758	+	0.377447i
$818$		−	86.5257i		−	3.02530i
$819$	10.2300	+	2.89827i	0.357466	+	0.101274i
$820$		0			0
$821$	−22.3762	+	38.7567i	−0.780934	+	1.35262i	0.150464	+	0.988615i	$0.451923\pi$
$821$	−22.3762	+	38.7567i	−0.780934	+	1.35262i	−0.931398	+	0.364002i	$0.881410\pi$
$822$	30.1214	−	12.2255i	1.05061	−	0.426415i
$823$	31.0898	−	17.9497i	1.08372	−	0.625687i	0.151824	−	0.988408i	$-0.451485\pi$
$823$	31.0898	−	17.9497i	1.08372	−	0.625687i	0.931898	+	0.362721i	$0.118152\pi$
$824$	−31.2279	−	54.0884i	−1.08788	−	1.88426i
$825$		0			0
$826$	26.0981	−	45.2033i	0.908071	−	1.57282i
$827$		−	16.2717i		−	0.565822i	−0.959146	−	0.282911i	$-0.908700\pi$
$827$		−	16.2717i		−	0.565822i	0.959146	−	0.282911i	$-0.0913001\pi$
$828$	−17.8964	−	18.4149i	−0.621944	−	0.639961i
$829$	20.6592			0.717525			0.358762	−	0.933429i	$-0.383199\pi$
$829$	20.6592			0.717525			0.358762	+	0.933429i	$0.383199\pi$
$830$		0			0
$831$	32.2412	−	41.4023i	1.11844	−	1.43623i
$832$	18.9132	−	10.9196i	0.655698	−	0.378568i
$833$	15.6950	−	9.06152i	0.543800	−	0.313963i
$834$	−66.4680	−	9.23382i	−2.30160	−	0.319741i
$835$		0			0
$836$	26.4621			0.915210
$837$	13.5480	−	1.48927i	0.468289	−	0.0514765i
$838$		−	60.2044i		−	2.07973i
$839$	−6.11836	+	10.5973i	−0.211229	+	0.365860i	−0.952100	−	0.305788i	$-0.901080\pi$
$839$	−6.11836	+	10.5973i	−0.211229	+	0.365860i	0.740870	+	0.671648i	$0.234413\pi$
$840$		0			0
$841$	−12.6411	−	21.8951i	−0.435901	−	0.755003i
$842$	40.9221	−	23.6264i	1.41027	−	0.814218i
$843$	−25.4661	−	19.8312i	−0.877099	−	0.683024i
$844$	−59.0616	+	102.298i	−2.03299	+	3.52123i
$845$		0			0
$846$	−12.1803	−	48.1996i	−0.418767	−	1.65714i
$847$			13.8953i			0.477450i
$848$	15.6836	+	9.05490i	0.538575	+	0.310947i
$849$	3.69576	+	9.10565i	0.126838	+	0.312505i
$850$		0			0
$851$	10.0872	+	17.4715i	0.345785	+	0.598917i
$852$	−10.0981	+	4.09858i	−0.345956	+	0.140415i
$853$	14.2282	+	8.21464i	0.487164	+	0.281264i	0.723397	−	0.690432i	$-0.242580\pi$
$853$	14.2282	+	8.21464i	0.487164	+	0.281264i	−0.236233	+	0.971696i	$0.575913\pi$
$854$	−59.9809			−2.05250
$855$		0			0
$856$	−69.4255			−2.37291
$857$	−42.5129	−	24.5449i	−1.45221	−	0.838436i	−0.453607	−	0.891202i	$-0.649863\pi$
$857$	−42.5129	−	24.5449i	−1.45221	−	0.838436i	−0.998607	+	0.0527655i	$0.983196\pi$
$858$	−12.8321	−	9.99276i	−0.438081	−	0.341147i
$859$	20.5454	+	35.5856i	0.700999	+	1.21417i	0.968116	+	0.250502i	$0.0805958\pi$
$859$	20.5454	+	35.5856i	0.700999	+	1.21417i	−0.267117	+	0.963664i	$0.586071\pi$
$860$		0			0
$861$	−7.60569	−	1.05659i	−0.259201	−	0.0360086i
$862$	14.1157	+	8.14968i	0.480781	+	0.277579i
$863$		−	47.8366i		−	1.62838i	−0.580601	−	0.814188i	$-0.697183\pi$
$863$		−	47.8366i		−	1.62838i	0.580601	−	0.814188i	$-0.302817\pi$
$864$	−6.91299	−	62.8884i	−0.235185	−	2.13951i
$865$		0			0
$866$	4.10605	−	7.11189i	0.139529	−	0.241672i
$867$	1.45812	−	10.4960i	0.0495202	−	0.356462i
$868$	−20.1560	+	11.6371i	−0.684138	+	0.394987i
$869$	1.90838	+	3.30542i	0.0647375	+	0.112129i
$870$		0			0
$871$	−8.97551	+	15.5460i	−0.304123	+	0.526757i
$872$		−	49.0458i		−	1.66090i
$873$	−8.01361	−	8.24574i	−0.271219	−	0.279076i
$874$	13.5387			0.457954
$875$		0			0
$876$	−11.5365	−	28.4238i	−0.389783	−	0.960351i
$877$	−9.85292	+	5.68859i	−0.332710	+	0.192090i	−0.657043	−	0.753853i	$-0.728193\pi$
$877$	−9.85292	+	5.68859i	−0.332710	+	0.192090i	0.324334	+	0.945943i	$0.394860\pi$
$878$	−30.8143	+	17.7906i	−1.03993	+	0.600405i
$879$	−11.9056	−	29.3333i	−0.401567	−	0.989386i
$880$		0			0
$881$	−43.9924			−1.48214			−0.741071	−	0.671426i	$-0.765682\pi$
$881$	−43.9924			−1.48214			−0.741071	+	0.671426i	$0.765682\pi$
$882$	8.11791	−	28.6538i	0.273344	−	0.964823i
$883$		−	37.6820i		−	1.26810i	−0.773291	−	0.634051i	$-0.781391\pi$
$883$		−	37.6820i		−	1.26810i	0.773291	−	0.634051i	$-0.218609\pi$
$884$	23.4010	−	40.5317i	0.787060	−	1.36323i
$885$		0			0
$886$	31.9699	+	55.3735i	1.07405	+	1.86031i
$887$	−28.8241	+	16.6416i	−0.967820	+	0.558771i	−0.898571	−	0.438828i	$-0.855394\pi$
$887$	−28.8241	+	16.6416i	−0.967820	+	0.558771i	−0.0692492	+	0.997599i	$0.522060\pi$
$888$	−21.4461	+	154.376i	−0.719685	+	5.18052i
$889$	−3.25606	+	5.63967i	−0.109205	+	0.189148i
$890$		0			0
$891$	−14.3195	+	7.73091i	−0.479721	+	0.258995i
$892$			107.175i			3.58847i
$893$	16.1548	+	9.32697i	0.540599	+	0.312115i
$894$	−2.55427	−	0.354842i	−0.0854274	−	0.0118677i
$895$		0			0
$896$	4.33040	+	7.50047i	0.144669	+	0.250573i
$897$	−4.67230	−	3.63846i	−0.156003	−	0.121485i
$898$	−55.0686	−	31.7939i	−1.83766	−	1.06098i
$899$	−19.3255			−0.644543
$900$		0			0
$901$	8.29592			0.276377
$902$	10.1720	+	5.87281i	0.338691	+	0.195543i
$903$	20.9952	−	8.52141i	0.698675	−	0.283575i
$904$	−57.6276	−	99.8139i	−1.91667	−	3.31976i
$905$		0			0
$906$	0.263144	+	0.648336i	0.00874236	+	0.0215395i
$907$	12.1922	+	7.03918i	0.404836	+	0.233732i	0.688568	−	0.725171i	$-0.258239\pi$
$907$	12.1922	+	7.03918i	0.404836	+	0.233732i	−0.283733	+	0.958903i	$0.591573\pi$
$908$		−	69.6056i		−	2.30994i
$909$	14.0967	−	13.6998i	0.467558	−	0.454395i
$910$		0			0
$911$	−3.65761	+	6.33517i	−0.121182	+	0.209894i	−0.920234	−	0.391368i	$-0.872002\pi$
$911$	−3.65761	+	6.33517i	−0.121182	+	0.209894i	0.799052	+	0.601262i	$0.205335\pi$
$912$	42.5238	+	33.1146i	1.40810	+	1.09653i
$913$	−1.72064	+	0.993410i	−0.0569448	+	0.0328771i
$914$	−3.71561	−	6.43563i	−0.122902	−	0.212872i
$915$		0			0
$916$	−9.07719	+	15.7222i	−0.299919	+	0.519475i
$917$		−	13.1094i		−	0.432912i
$918$	−38.9297	−	53.0486i	−1.28487	−	1.75087i
$919$	−4.44684			−0.146688			−0.0733438	−	0.997307i	$-0.523367\pi$
$919$	−4.44684			−0.146688			−0.0733438	+	0.997307i	$0.523367\pi$
$920$		0			0
$921$	26.5999	+	3.69530i	0.876498	+	0.121764i
$922$	48.9412	−	28.2562i	1.61179	−	0.930569i
$923$	−2.17658	+	1.25665i	−0.0716430	+	0.0413631i
$924$	17.0733	−	21.9245i	0.561669	−	0.721263i
$925$		0			0
$926$	−52.1565			−1.71397
$927$	−23.4883	+	5.93562i	−0.771458	+	0.194951i
$928$			89.7068i			2.94477i
$929$	6.55663	−	11.3564i	0.215116	−	0.372592i	−0.738192	−	0.674590i	$-0.764320\pi$
$929$	6.55663	−	11.3564i	0.215116	−	0.372592i	0.953309	+	0.301998i	$0.0976536\pi$
$930$		0			0
$931$	5.58730	+	9.67749i	0.183116	+	0.317167i
$932$	−22.8362	+	13.1845i	−0.748026	+	0.431873i
$933$	48.8633	−	19.8324i	1.59971	−	0.649284i
$934$	29.9204	−	51.8236i	0.979025	−	1.69572i
$935$		0			0
$936$	−11.2089	−	44.3556i	−0.366374	−	1.44981i
$937$		−	33.5187i		−	1.09501i	−0.836803	−	0.547504i	$-0.815578\pi$
$937$		−	33.5187i		−	1.09501i	0.836803	−	0.547504i	$-0.184422\pi$
$938$	−37.3226	−	21.5482i	−1.21863	−	0.703574i
$939$	7.39543	−	9.49677i	0.241341	−	0.309915i
$940$		0			0
$941$	−0.895381	−	1.55085i	−0.0291886	−	0.0505561i	0.851062	−	0.525065i	$-0.175959\pi$
$941$	−0.895381	−	1.55085i	−0.0291886	−	0.0505561i	−0.880251	+	0.474509i	$0.842626\pi$
$942$	−7.19383	+	51.7834i	−0.234388	+	1.68720i
$943$	3.70373	+	2.13835i	0.120610	+	0.0696342i
$944$	−115.729			−3.76667
$945$		0			0
$946$	−34.6592			−1.12687
$947$	45.5832	+	26.3175i	1.48126	+	0.855204i	0.999774	−	0.0212525i	$-0.00676539\pi$
$947$	45.5832	+	26.3175i	1.48126	+	0.855204i	0.481482	+	0.876456i	$0.340099\pi$
$948$	−2.48351	+	17.8771i	−0.0806606	+	0.580620i
$949$	−3.53716	−	6.12654i	−0.114821	−	0.198876i
$950$		0			0
$951$	−17.1814	+	22.0633i	−0.557144	+	0.715451i
$952$	57.8839	+	33.4193i	1.87603	+	1.08312i
$953$			18.4072i			0.596268i	0.954524	+	0.298134i	$0.0963642\pi$
$953$			18.4072i			0.596268i	−0.954524	+	0.298134i	$0.903636\pi$
$954$	9.77637	−	9.50114i	0.316522	−	0.307611i
$955$		0			0
$956$	54.3841	−	94.1960i	1.75891	−	3.04652i
$957$	21.3798	−	8.67754i	0.691112	−	0.280505i
$958$	−48.5551	+	28.0333i	−1.56874	+	0.905715i
$959$	6.40442	+	11.0928i	0.206810	+	0.358205i
$960$		0			0
$961$	12.0599	−	20.8883i	0.389028	−	0.673816i
$962$			60.4240i			1.94815i
$963$	−7.34070	+	25.9104i	−0.236551	+	0.834952i
$964$	92.0517			2.96479
$965$		0			0
$966$	8.73515	−	11.2172i	0.281049	−	0.360906i
$967$	−5.27911	+	3.04790i	−0.169765	+	0.0980137i	−0.582475	−	0.812849i	$-0.697916\pi$
$967$	−5.27911	+	3.04790i	−0.169765	+	0.0980137i	0.412710	+	0.910862i	$0.364582\pi$
$968$	51.7784	−	29.8943i	1.66422	−	0.960839i
$969$	24.4547	+	3.39728i	0.785598	+	0.109136i
$970$		0			0
$971$	−34.1077			−1.09457			−0.547283	−	0.836947i	$-0.684338\pi$
$971$	−34.1077			−1.09457			−0.547283	+	0.836947i	$0.684338\pi$
$972$	−75.8871	−	12.7603i	−2.43408	−	0.409288i
$973$		−	26.4414i		−	0.847671i
$974$	−12.6246	+	21.8665i	−0.404519	+	0.700648i
$975$		0			0
$976$	66.4945	+	115.172i	2.12844	+	3.68656i
$977$	42.2546	−	24.3957i	1.35184	−	0.780488i	0.363337	−	0.931658i	$-0.381637\pi$
$977$	42.2546	−	24.3957i	1.35184	−	0.780488i	0.988508	+	0.151170i	$0.0483040\pi$
$978$	79.3955	+	61.8277i	2.53879	+	1.97703i
$979$	−12.0181	+	20.8160i	−0.384100	+	0.665281i
$980$		0			0
$981$	−18.3045	−	5.18586i	−0.584418	−	0.165572i
$982$		−	99.6715i		−	3.18065i
$983$	28.9402	+	16.7086i	0.923048	+	0.532922i	0.884606	−	0.466339i	$-0.154427\pi$
$983$	28.9402	+	16.7086i	0.923048	+	0.532922i	0.0384416	+	0.999261i	$0.487761\pi$
$984$	12.4256	+	30.6143i	0.396113	+	0.975949i
$985$		0			0
$986$	46.6493	+	80.7989i	1.48562	+	2.57316i
$987$	18.1507	−	7.36691i	0.577742	−	0.234491i
$988$	24.9917	+	14.4289i	0.795091	+	0.459046i
$989$	−12.6198			−0.401285
$990$		0			0
$991$	−19.3512			−0.614713			−0.307356	−	0.951595i	$-0.599444\pi$
$991$	−19.3512			−0.614713			−0.307356	+	0.951595i	$0.599444\pi$
$992$	27.6586	+	15.9687i	0.878161	+	0.507006i
$993$	−17.2491	−	13.4324i	−0.547384	−	0.426265i
$994$	−3.01694	−	5.22549i	−0.0956915	−	0.165743i
$995$		0			0
$996$	−9.30592	−	1.29279i	−0.294869	−	0.0409636i
$997$	−34.2463	−	19.7721i	−1.08459	−	0.626189i	−0.152460	−	0.988310i	$-0.548719\pi$
$997$	−34.2463	−	19.7721i	−1.08459	−	0.626189i	−0.932131	+	0.362121i	$0.882053\pi$
$998$		−	44.5766i		−	1.41105i
$999$	55.3474	+	24.3269i	1.75112	+	0.769669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.k.c.124.1		16
3.2	odd	2		675.2.k.c.424.8		16
5.2	odd	4		225.2.e.e.151.4	yes	8
5.3	odd	4		225.2.e.c.151.1	yes	8
5.4	even	2	inner	225.2.k.c.124.8		16
9.2	odd	6		2025.2.b.o.649.1		8
9.4	even	3	inner	225.2.k.c.49.8		16
9.5	odd	6		675.2.k.c.199.1		16
9.7	even	3		2025.2.b.n.649.8		8
15.2	even	4		675.2.e.c.451.1		8
15.8	even	4		675.2.e.e.451.4		8
15.14	odd	2		675.2.k.c.424.1		16
45.2	even	12		2025.2.a.z.1.4		4
45.4	even	6	inner	225.2.k.c.49.1		16
45.7	odd	12		2025.2.a.q.1.1		4
45.13	odd	12		225.2.e.c.76.1	✓	8
45.14	odd	6		675.2.k.c.199.8		16
45.22	odd	12		225.2.e.e.76.4	yes	8
45.23	even	12		675.2.e.e.226.4		8
45.29	odd	6		2025.2.b.o.649.8		8
45.32	even	12		675.2.e.c.226.1		8
45.34	even	6		2025.2.b.n.649.1		8
45.38	even	12		2025.2.a.p.1.1		4
45.43	odd	12		2025.2.a.y.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.e.c.76.1	✓	8	45.13	odd	12
225.2.e.c.151.1	yes	8	5.3	odd	4
225.2.e.e.76.4	yes	8	45.22	odd	12
225.2.e.e.151.4	yes	8	5.2	odd	4
225.2.k.c.49.1		16	45.4	even	6	inner
225.2.k.c.49.8		16	9.4	even	3	inner
225.2.k.c.124.1		16	1.1	even	1	trivial
225.2.k.c.124.8		16	5.4	even	2	inner
675.2.e.c.226.1		8	45.32	even	12
675.2.e.c.451.1		8	15.2	even	4
675.2.e.e.226.4		8	45.23	even	12
675.2.e.e.451.4		8	15.8	even	4
675.2.k.c.199.1		16	9.5	odd	6
675.2.k.c.199.8		16	45.14	odd	6
675.2.k.c.424.1		16	15.14	odd	2
675.2.k.c.424.8		16	3.2	odd	2
2025.2.a.p.1.1		4	45.38	even	12
2025.2.a.q.1.1		4	45.7	odd	12
2025.2.a.y.1.4		4	45.43	odd	12
2025.2.a.z.1.4		4	45.2	even	12
2025.2.b.n.649.1		8	45.34	even	6
2025.2.b.n.649.8		8	9.7	even	3
2025.2.b.o.649.1		8	9.2	odd	6
2025.2.b.o.649.8		8	45.29	odd	6

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.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.28087 - 1.31686i) q^{2} +(-0.238330 + 1.71558i) q^{3} +(2.46825 + 4.27513i) q^{4} +(2.80278 - 3.59916i) q^{6} +(1.55662 + 0.898714i) q^{7} -7.73393i q^{8} +(-2.88640 - 0.817746i) q^{9} +O(q^{10})\)	\(q+(-2.28087 - 1.31686i) q^{2} +(-0.238330 + 1.71558i) q^{3} +(2.46825 + 4.27513i) q^{4} +(2.80278 - 3.59916i) q^{6} +(1.55662 + 0.898714i) q^{7} -7.73393i q^{8} +(-2.88640 - 0.817746i) q^{9} +(-0.904062 + 1.56588i) q^{11} +(-7.92257 + 3.21558i) q^{12} +(-1.70765 + 0.985914i) q^{13} +(-2.36696 - 4.09970i) q^{14} +(-5.24801 + 9.08982i) q^{16} +4.80812i q^{17} +(5.50664 + 5.66616i) q^{18} -2.96467 q^{19} +(-1.91280 + 2.45630i) q^{21} +(4.12410 - 2.38105i) q^{22} +(1.50162 - 0.866963i) q^{23} +(13.2681 + 1.84323i) q^{24} +5.19325 q^{26} +(2.09082 - 4.75694i) q^{27} +8.87300i q^{28} +(-3.68382 + 6.38057i) q^{29} +(1.31151 + 2.27161i) q^{31} +(10.5445 - 6.08789i) q^{32} +(-2.47092 - 1.92418i) q^{33} +(6.33163 - 10.9667i) q^{34} +(-3.62838 - 14.3581i) q^{36} +11.6351i q^{37} +(6.76203 + 3.90406i) q^{38} +(-1.28442 - 3.16458i) q^{39} +(1.23324 + 2.13603i) q^{41} +(7.59746 - 3.08362i) q^{42} +(-6.30306 - 3.63907i) q^{43} -8.92580 q^{44} -4.56668 q^{46} +(-5.44910 - 3.14604i) q^{47} +(-14.3435 - 11.1697i) q^{48} +(-1.88463 - 3.26427i) q^{49} +(-8.24870 - 1.14592i) q^{51} +(-8.42983 - 4.86696i) q^{52} -1.72540i q^{53} +(-11.0331 + 8.09664i) q^{54} +(6.95059 - 12.0388i) q^{56} +(0.706570 - 5.08612i) q^{57} +(16.8047 - 9.70218i) q^{58} +(5.51300 + 9.54880i) q^{59} +(6.33521 - 10.9729i) q^{61} -6.90833i q^{62} +(-3.75810 - 3.86696i) q^{63} -11.0756 q^{64} +(3.10197 + 7.64268i) q^{66} +(7.88407 - 4.55187i) q^{67} +(-20.5554 + 11.8676i) q^{68} +(1.12946 + 2.78277i) q^{69} +1.27460 q^{71} +(-6.32439 + 22.3232i) q^{72} +3.58770i q^{73} +(15.3218 - 26.5382i) q^{74} +(-7.31755 - 12.6744i) q^{76} +(-2.81456 + 1.62499i) q^{77} +(-1.23771 + 8.90941i) q^{78} +(1.05545 - 1.82809i) q^{79} +(7.66258 + 4.72068i) q^{81} -6.49602i q^{82} +(0.951614 + 0.549415i) q^{83} +(-15.2223 - 2.11470i) q^{84} +(9.58431 + 16.6005i) q^{86} +(-10.0684 - 7.84056i) q^{87} +(12.1104 + 6.99195i) q^{88} +13.2935 q^{89} -3.54422 q^{91} +(7.41277 + 4.27976i) q^{92} +(-4.20969 + 1.70861i) q^{93} +(8.28580 + 14.3514i) q^{94} +(7.93115 + 19.5409i) q^{96} +(3.31926 + 1.91638i) q^{97} +9.92718i q^{98} +(3.88998 - 3.78046i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 16 q^{6} - 10 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 16 * q^6 - 10 * q^9	\( 16 q + 8 q^{4} + 16 q^{6} - 10 q^{9} + 2 q^{11} + 6 q^{14} - 8 q^{16} - 8 q^{19} - 30 q^{21} + 66 q^{24} - 40 q^{26} + 2 q^{29} + 8 q^{31} + 18 q^{34} - 28 q^{36} - 50 q^{39} + 10 q^{41} - 88 q^{44} - 6 q^{49} + 22 q^{51} - 52 q^{54} + 60 q^{56} + 34 q^{59} + 26 q^{61} - 76 q^{64} - 16 q^{66} + 54 q^{69} - 32 q^{71} + 80 q^{74} - 22 q^{76} - 14 q^{79} + 34 q^{81} - 54 q^{84} + 68 q^{86} + 36 q^{89} - 68 q^{91} + 6 q^{94} + 68 q^{96} + 34 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 16 * q^6 - 10 * q^9 + 2 * q^11 + 6 * q^14 - 8 * q^16 - 8 * q^19 - 30 * q^21 + 66 * q^24 - 40 * q^26 + 2 * q^29 + 8 * q^31 + 18 * q^34 - 28 * q^36 - 50 * q^39 + 10 * q^41 - 88 * q^44 - 6 * q^49 + 22 * q^51 - 52 * q^54 + 60 * q^56 + 34 * q^59 + 26 * q^61 - 76 * q^64 - 16 * q^66 + 54 * q^69 - 32 * q^71 + 80 * q^74 - 22 * q^76 - 14 * q^79 + 34 * q^81 - 54 * q^84 + 68 * q^86 + 36 * q^89 - 68 * q^91 + 6 * q^94 + 68 * q^96 + 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more