LMFDB - Embedded newform 225.2.e.c.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(76,225)]

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, 0]))

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

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

chi := DirichletCharacter("225.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.e (of order $3$, degree $2$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1223810289.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 8x^{6} - 2x^{5} + 23x^{4} - 8x^{3} + 37x^{2} + 15x + 9 $ x^8 - 2x^7 + 8x^6 - 2x^5 + 23x^4 - 8x^3 + 37x^2 + 15*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Root			$1.31686 - 2.28087i$ of defining polynomial
Character	$\chi$	$=$	225.151
Dual form			225.2.e.c.76.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31686 + 2.28087i) q^{2} +(-1.71558 - 0.238330i) q^{3} +(-2.46825 - 4.27513i) q^{4} +(2.80278 - 3.59916i) q^{6} +(0.898714 - 1.55662i) q^{7} +7.73393 q^{8} +(2.88640 + 0.817746i) q^{9} +O(q^{10})$	\(q+(-1.31686 + 2.28087i) q^{2} +(-1.71558 - 0.238330i) q^{3} +(-2.46825 - 4.27513i) q^{4} +(2.80278 - 3.59916i) q^{6} +(0.898714 - 1.55662i) q^{7} +7.73393 q^{8} +(2.88640 + 0.817746i) q^{9} +(-0.904062 + 1.56588i) q^{11} +(3.21558 + 7.92257i) q^{12} +(-0.985914 - 1.70765i) q^{13} +(2.36696 + 4.09970i) q^{14} +(-5.24801 + 9.08982i) q^{16} +4.80812 q^{17} +(-5.66616 + 5.50664i) q^{18} +2.96467 q^{19} +(-1.91280 + 2.45630i) q^{21} +(-2.38105 - 4.12410i) q^{22} +(0.866963 + 1.50162i) q^{23} +(-13.2681 - 1.84323i) q^{24} +5.19325 q^{26} +(-4.75694 - 2.09082i) q^{27} -8.87300 q^{28} +(3.68382 - 6.38057i) q^{29} +(1.31151 + 2.27161i) q^{31} +(-6.08789 - 10.5445i) q^{32} +(1.92418 - 2.47092i) q^{33} +(-6.33163 + 10.9667i) q^{34} +(-3.62838 - 14.3581i) q^{36} +11.6351 q^{37} +(-3.90406 + 6.76203i) q^{38} +(1.28442 + 3.16458i) q^{39} +(1.23324 + 2.13603i) q^{41} +(-3.08362 - 7.59746i) q^{42} +(3.63907 - 6.30306i) q^{43} +8.92580 q^{44} -4.56668 q^{46} +(-3.14604 + 5.44910i) q^{47} +(11.1697 - 14.3435i) q^{48} +(1.88463 + 3.26427i) q^{49} +(-8.24870 - 1.14592i) q^{51} +(-4.86696 + 8.42983i) q^{52} +1.72540 q^{53} +(11.0331 - 8.09664i) q^{54} +(6.95059 - 12.0388i) q^{56} +(-5.08612 - 0.706570i) q^{57} +(9.70218 + 16.8047i) q^{58} +(-5.51300 - 9.54880i) q^{59} +(6.33521 - 10.9729i) q^{61} -6.90833 q^{62} +(3.86696 - 3.75810i) q^{63} +11.0756 q^{64} +(3.10197 + 7.64268i) q^{66} +(-4.55187 - 7.88407i) q^{67} +(-11.8676 - 20.5554i) q^{68} +(-1.12946 - 2.78277i) q^{69} +1.27460 q^{71} +(22.3232 + 6.32439i) q^{72} -3.58770 q^{73} +(-15.3218 + 26.5382i) q^{74} +(-7.31755 - 12.6744i) q^{76} +(1.62499 + 2.81456i) q^{77} +(-8.90941 - 1.23771i) q^{78} +(-1.05545 + 1.82809i) q^{79} +(7.66258 + 4.72068i) q^{81} -6.49602 q^{82} +(-0.549415 + 0.951614i) q^{83} +(15.2223 + 2.11470i) q^{84} +(9.58431 + 16.6005i) q^{86} +(-7.84056 + 10.0684i) q^{87} +(-6.99195 + 12.1104i) q^{88} -13.2935 q^{89} -3.54422 q^{91} +(4.27976 - 7.41277i) q^{92} +(-1.70861 - 4.20969i) q^{93} +(-8.28580 - 14.3514i) q^{94} +(7.93115 + 19.5409i) q^{96} +(1.91638 - 3.31926i) q^{97} -9.92718 q^{98} +(-3.88998 + 3.78046i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + q^{3} - 4 q^{4} + 8 q^{6} + q^{7} + 18 q^{8} + 5 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + q^3 - 4 * q^4 + 8 * q^6 + q^7 + 18 * q^8 + 5 * q^9	$ 8 q - 2 q^{2} + q^{3} - 4 q^{4} + 8 q^{6} + q^{7} + 18 q^{8} + 5 q^{9} + q^{11} + 11 q^{12} - 2 q^{13} - 3 q^{14} - 4 q^{16} + 22 q^{17} - 5 q^{18} + 4 q^{19} - 15 q^{21} - 3 q^{22} - 15 q^{23} - 33 q^{24} - 20 q^{26} - 2 q^{27} - 8 q^{28} - q^{29} + 4 q^{31} - 10 q^{32} - 28 q^{33} - 9 q^{34} - 14 q^{36} - 2 q^{37} - 23 q^{38} + 25 q^{39} + 5 q^{41} - 21 q^{42} + 10 q^{43} + 44 q^{44} - 20 q^{47} + 53 q^{48} + 3 q^{49} + 11 q^{51} - 17 q^{52} + 40 q^{53} + 26 q^{54} + 30 q^{56} - 8 q^{57} + 18 q^{58} - 17 q^{59} + 13 q^{61} - 12 q^{62} + 9 q^{63} + 38 q^{64} - 8 q^{66} - 17 q^{67} - 34 q^{68} - 27 q^{69} - 16 q^{71} + 18 q^{72} + 4 q^{73} - 40 q^{74} - 11 q^{76} - 12 q^{77} - 61 q^{78} + 7 q^{79} + 17 q^{81} + 24 q^{82} - 30 q^{83} + 27 q^{84} + 34 q^{86} - 23 q^{87} - 9 q^{88} - 18 q^{89} - 34 q^{91} + 12 q^{92} + 15 q^{93} - 3 q^{94} + 34 q^{96} + 19 q^{97} + 26 q^{98} - 17 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 + q^3 - 4 * q^4 + 8 * q^6 + q^7 + 18 * q^8 + 5 * q^9 + q^11 + 11 * q^12 - 2 * q^13 - 3 * q^14 - 4 * q^16 + 22 * q^17 - 5 * q^18 + 4 * q^19 - 15 * q^21 - 3 * q^22 - 15 * q^23 - 33 * q^24 - 20 * q^26 - 2 * q^27 - 8 * q^28 - q^29 + 4 * q^31 - 10 * q^32 - 28 * q^33 - 9 * q^34 - 14 * q^36 - 2 * q^37 - 23 * q^38 + 25 * q^39 + 5 * q^41 - 21 * q^42 + 10 * q^43 + 44 * q^44 - 20 * q^47 + 53 * q^48 + 3 * q^49 + 11 * q^51 - 17 * q^52 + 40 * q^53 + 26 * q^54 + 30 * q^56 - 8 * q^57 + 18 * q^58 - 17 * q^59 + 13 * q^61 - 12 * q^62 + 9 * q^63 + 38 * q^64 - 8 * q^66 - 17 * q^67 - 34 * q^68 - 27 * q^69 - 16 * q^71 + 18 * q^72 + 4 * q^73 - 40 * q^74 - 11 * q^76 - 12 * q^77 - 61 * q^78 + 7 * q^79 + 17 * q^81 + 24 * q^82 - 30 * q^83 + 27 * q^84 + 34 * q^86 - 23 * q^87 - 9 * q^88 - 18 * q^89 - 34 * q^91 + 12 * q^92 + 15 * q^93 - 3 * q^94 + 34 * q^96 + 19 * q^97 + 26 * q^98 - 17 * 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 $

$2$	−1.31686	+	2.28087i	−0.931162	+	1.61282i	−0.149823	+	0.988713i	$0.547870\pi$
$2$	−1.31686	+	2.28087i	−0.931162	+	1.61282i	−0.781339	+	0.624107i	$0.785463\pi$
$3$	−1.71558	−	0.238330i	−0.990488	−	0.137600i
$3$	−1.71558	−	0.238330i	−0.990488	−	0.137600i
$4$	−2.46825	−	4.27513i	−1.23412	−	2.13757i
$5$		0			0
$5$		0			0
$6$	2.80278	−	3.59916i	1.14423	−	1.46935i
$7$	0.898714	−	1.55662i	0.339682	−	0.588346i	−0.644691	−	0.764443i	$-0.723014\pi$
$7$	0.898714	−	1.55662i	0.339682	−	0.588346i	0.984373	+	0.176097i	$0.0563473\pi$
$8$	7.73393			2.73436
$9$	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	$0.254545\pi$
$12$	3.21558	+	7.92257i	0.928257	+	2.28705i
$13$	−0.985914	−	1.70765i	−0.273443	−	0.473618i	0.696298	−	0.717753i	$-0.254829\pi$
$13$	−0.985914	−	1.70765i	−0.273443	−	0.473618i	−0.969741	+	0.244135i	$0.921496\pi$
$14$	2.36696	+	4.09970i	0.632598	+	1.09569i
$15$		0			0
$16$	−5.24801	+	9.08982i	−1.31200	+	2.27246i
$17$	4.80812			1.16614			0.583071	−	0.812421i	$-0.301851\pi$
$17$	4.80812			1.16614			0.583071	+	0.812421i	$0.301851\pi$
$18$	−5.66616	+	5.50664i	−1.33553	+	1.29793i
$19$	2.96467			0.680142			0.340071	−	0.940400i	$-0.389549\pi$
$19$	2.96467			0.680142			0.340071	+	0.940400i	$0.389549\pi$
$20$		0			0
$21$	−1.91280	+	2.45630i	−0.417407	+	0.536010i
$22$	−2.38105	−	4.12410i	−0.507641	−	0.879261i
$23$	0.866963	+	1.50162i	0.180774	+	0.313110i	0.942144	−	0.335207i	$-0.108806\pi$
$23$	0.866963	+	1.50162i	0.180774	+	0.313110i	−0.761370	+	0.648317i	$0.775473\pi$
$24$	−13.2681	−	1.84323i	−2.70835	−	0.376247i
$25$		0			0
$26$	5.19325			1.01848
$27$	−4.75694	−	2.09082i	−0.915473	−	0.402379i
$28$	−8.87300			−1.67684
$29$	3.68382	−	6.38057i	0.684069	−	1.18484i	−0.289659	−	0.957130i	$-0.593542\pi$
$29$	3.68382	−	6.38057i	0.684069	−	1.18484i	0.973728	−	0.227713i	$-0.0731247\pi$
$30$		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	$0.757643\pi$
$32$	−6.08789	−	10.5445i	−1.07620	−	1.86403i
$33$	1.92418	−	2.47092i	0.334957	−	0.430132i
$34$	−6.33163	+	10.9667i	−1.08587	+	1.88078i
$35$		0			0
$36$	−3.62838	−	14.3581i	−0.604729	−	2.39302i
$37$	11.6351			1.91280			0.956399	−	0.292063i	$-0.0943417\pi$
$37$	11.6351			1.91280			0.956399	+	0.292063i	$0.0943417\pi$
$38$	−3.90406	+	6.76203i	−0.633322	+	1.09695i
$39$	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	$0.771641\pi$
$42$	−3.08362	−	7.59746i	−0.475813	−	1.17231i
$43$	3.63907	−	6.30306i	0.554953	−	0.961207i	−0.442954	−	0.896544i	$-0.646069\pi$
$43$	3.63907	−	6.30306i	0.554953	−	0.961207i	0.997907	−	0.0646628i	$-0.0205972\pi$
$44$	8.92580			1.34562
$45$		0			0
$46$	−4.56668			−0.673321
$47$	−3.14604	+	5.44910i	−0.458897	+	0.794833i	−0.998903	−	0.0468283i	$-0.985089\pi$
$47$	−3.14604	+	5.44910i	−0.458897	+	0.794833i	0.540006	+	0.841661i	$0.318422\pi$
$48$	11.1697	−	14.3435i	1.61221	−	2.07031i
$49$	1.88463	+	3.26427i	0.269233	+	0.466324i
$50$		0			0
$51$	−8.24870	−	1.14592i	−1.15505	−	0.160461i
$52$	−4.86696	+	8.42983i	−0.674926	+	1.16901i
$53$	1.72540			0.237001			0.118501	−	0.992954i	$-0.462191\pi$
$53$	1.72540			0.237001			0.118501	+	0.992954i	$0.462191\pi$
$54$	11.0331	−	8.09664i	1.50142	−	1.10181i
$55$		0			0
$56$	6.95059	−	12.0388i	0.928811	−	1.60875i
$57$	−5.08612	−	0.706570i	−0.673673	−	0.0935875i
$58$	9.70218	+	16.8047i	1.27396	+	2.20656i
$59$	−5.51300	−	9.54880i	−0.717732	−	1.24315i	−0.961896	−	0.273414i	$-0.911847\pi$
$59$	−5.51300	−	9.54880i	−0.717732	−	1.24315i	0.244165	−	0.969734i	$-0.421486\pi$
$60$		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	$-0.134486\pi$
$62$	−6.90833			−0.877358
$63$	3.86696	−	3.75810i	0.487192	−	0.473476i
$64$	11.0756			1.38445
$65$		0			0
$66$	3.10197	+	7.64268i	0.381826	+	0.940748i
$67$	−4.55187	−	7.88407i	−0.556100	−	0.963193i	−0.997817	−	0.0660386i	$-0.978964\pi$
$67$	−4.55187	−	7.88407i	−0.556100	−	0.963193i	0.441717	−	0.897154i	$-0.354369\pi$
$68$	−11.8676	−	20.5554i	−1.43916	−	2.49271i
$69$	−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	$0.475902\pi$
$72$	22.3232	+	6.32439i	2.63081	+	0.745336i
$73$	−3.58770			−0.419908			−0.209954	−	0.977711i	$-0.567331\pi$
$73$	−3.58770			−0.419908			−0.209954	+	0.977711i	$0.567331\pi$
$74$	−15.3218	+	26.5382i	−1.78112	+	3.08500i
$75$		0			0
$76$	−7.31755	−	12.6744i	−0.839380	−	1.45385i
$77$	1.62499	+	2.81456i	0.185184	+	0.320749i
$78$	−8.90941	−	1.23771i	−1.00879	−	0.140143i
$79$	−1.05545	+	1.82809i	−0.118747	+	0.205676i	−0.919272	−	0.393624i	$-0.871221\pi$
$79$	−1.05545	+	1.82809i	−0.118747	+	0.205676i	0.800524	+	0.599300i	$0.204555\pi$
$80$		0			0
$81$	7.66258	+	4.72068i	0.851398	+	0.524520i
$82$	−6.49602			−0.717366
$83$	−0.549415	+	0.951614i	−0.0603061	+	0.104453i	−0.894602	−	0.446863i	$-0.852541\pi$
$83$	−0.549415	+	0.951614i	−0.0603061	+	0.104453i	0.834296	+	0.551317i	$0.185874\pi$
$84$	15.2223	+	2.11470i	1.66089	+	0.230733i
$85$		0			0
$86$	9.58431	+	16.6005i	1.03350	+	1.79008i
$87$	−7.84056	+	10.0684i	−0.840596	+	1.07944i
$88$	−6.99195	+	12.1104i	−0.745344	+	1.29097i
$89$	−13.2935			−1.40910			−0.704552	−	0.709653i	$-0.748852\pi$
$89$	−13.2935			−1.40910			−0.704552	+	0.709653i	$0.748852\pi$
$90$		0			0
$91$	−3.54422			−0.371535
$92$	4.27976	−	7.41277i	0.446196	−	0.772834i
$93$	−1.70861	−	4.20969i	−0.177174	−	0.436524i
$94$	−8.28580	−	14.3514i	−0.854615	−	1.48024i
$95$		0			0
$96$	7.93115	+	19.5409i	0.809470	+	1.99438i
$97$	1.91638	−	3.31926i	0.194579	−	0.337020i	−0.752184	−	0.658954i	$-0.770999\pi$
$97$	1.91638	−	3.31926i	0.194579	−	0.337020i	0.946762	+	0.321933i	$0.104333\pi$
$98$	−9.92718			−1.00280
$99$	−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	$0.272365\pi$
$102$	13.4761	−	17.3052i	1.33433	−	1.71347i
$103$	4.03779	+	6.99365i	0.397855	+	0.689105i	0.993461	−	0.114172i	$-0.0364214\pi$
$103$	4.03779	+	6.99365i	0.397855	+	0.689105i	−0.595606	+	0.803277i	$0.703088\pi$
$104$	−7.62499	−	13.2069i	−0.747691	−	1.29504i
$105$		0			0
$106$	−2.27211	+	3.93541i	−0.220687	+	0.382241i
$107$	−8.97674			−0.867814			−0.433907	−	0.900958i	$-0.642865\pi$
$107$	−8.97674			−0.867814			−0.433907	+	0.900958i	$0.642865\pi$
$108$	2.80278	+	25.4972i	0.269697	+	2.45347i
$109$	−6.34164			−0.607419			−0.303710	−	0.952765i	$-0.598225\pi$
$109$	−6.34164			−0.607419			−0.303710	+	0.952765i	$0.598225\pi$
$110$		0			0
$111$	−19.9609	−	2.77299i	−1.89460	−	0.263201i
$112$	9.43292	+	16.3383i	0.891327	+	1.54382i
$113$	7.45127	+	12.9060i	0.700957	+	1.21409i	0.968131	+	0.250444i	$0.0805767\pi$
$113$	7.45127	+	12.9060i	0.700957	+	1.21409i	−0.267174	+	0.963648i	$0.586090\pi$
$114$	8.30931	−	10.6703i	0.778238	−	0.999367i
$115$		0			0
$116$	−36.3704			−3.37691
$117$	−1.44931	−	5.73519i	−0.133989	−	0.530219i
$118$	29.0394			2.67330
$119$	4.32113	−	7.48441i	0.396117	−	0.686095i
$120$		0			0
$121$	3.86534	+	6.69497i	0.351395	+	0.608634i
$122$	16.6852	+	28.8996i	1.51061	+	2.61645i
$123$	−1.60663	−	3.95845i	−0.144865	−	0.356921i
$124$	6.47428	−	11.2138i	0.581408	−	1.00703i
$125$		0			0
$126$	3.47948	+	13.7689i	0.309977	+	1.22663i
$127$	3.62303			0.321492			0.160746	−	0.986996i	$-0.448610\pi$
$127$	3.62303			0.321492			0.160746	+	0.986996i	$0.448610\pi$
$128$	−2.40922	+	4.17289i	−0.212947	+	0.368835i
$129$	−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	$0.936551\pi$
$132$	−15.3129	−	2.12729i	−1.33282	−	0.185157i
$133$	2.66439	−	4.61486i	0.231032	−	0.400159i
$134$	23.9767			2.07127
$135$		0			0
$136$	37.1857			3.18865
$137$	3.56310	−	6.17148i	0.304417	−	0.527265i	−0.672715	−	0.739902i	$-0.734872\pi$
$137$	3.56310	−	6.17148i	0.304417	−	0.527265i	0.977131	+	0.212637i	$0.0682052\pi$
$138$	7.83449	+	1.08838i	0.666916	+	0.0926488i
$139$	7.35533	+	12.7398i	0.623871	+	1.08058i	0.988758	+	0.149525i	$0.0477744\pi$
$139$	7.35533	+	12.7398i	0.623871	+	1.08058i	−0.364887	+	0.931052i	$0.618892\pi$
$140$		0			0
$141$	6.69595	−	8.59855i	0.563901	−	0.724128i
$142$	−1.67848	+	2.90721i	−0.140855	+	0.243967i
$143$	3.56531			0.298146
$144$	−22.5810	+	21.9453i	−1.88175	+	1.82878i
$145$		0			0
$146$	4.72450	−	8.18308i	0.391003	−	0.677236i
$147$	−2.45525	−	6.04927i	−0.202505	−	0.498935i
$148$	−28.7183	−	49.7416i	−2.36063	−	4.08873i
$149$	0.282655	+	0.489572i	0.0231560	+	0.0401073i	0.877371	−	0.479812i	$-0.159295\pi$
$149$	0.282655	+	0.489572i	0.0231560	+	0.0401073i	−0.854215	+	0.519920i	$0.825962\pi$
$150$		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	$0.168653\pi$
$152$	22.9285			1.85975
$153$	13.8782	+	3.93183i	1.12198	+	0.317869i
$154$	−8.55953			−0.689746
$155$		0			0
$156$	10.3587	−	13.3021i	0.829362	−	1.06502i
$157$	5.73035	+	9.92525i	0.457332	+	0.792121i	0.998819	−	0.0485874i	$-0.0154719\pi$
$157$	5.73035	+	9.92525i	0.457332	+	0.792121i	−0.541487	+	0.840709i	$0.682139\pi$
$158$	−2.77976	−	4.81469i	−0.221146	−	0.383036i
$159$	−2.96005	−	0.411214i	−0.234747	−	0.0326114i
$160$		0			0
$161$	3.11661			0.245623
$162$	−20.8578	+	11.2609i	−1.63875	+	0.884738i
$163$	−22.0595			−1.72783			−0.863915	−	0.503637i	$-0.831995\pi$
$163$	−22.0595			−1.72783			−0.863915	+	0.503637i	$0.831995\pi$
$164$	6.08789	−	10.5445i	0.475384	−	0.823389i
$165$		0			0
$166$	−1.44701	−	2.50629i	−0.112310	−	0.194526i
$167$	−8.53421	−	14.7817i	−0.660397	−	1.14384i	−0.980511	−	0.196462i	$-0.937055\pi$
$167$	−8.53421	−	14.7817i	−0.660397	−	1.14384i	0.320115	−	0.947379i	$-0.396279\pi$
$168$	−14.7935	+	18.9969i	−1.14134	+	1.46564i
$169$	4.55595	−	7.89113i	0.350457	−	0.607010i
$170$		0			0
$171$	8.55722	+	2.42435i	0.654387	+	0.185395i
$172$	−35.9285			−2.73953
$173$	−5.97233	+	10.3444i	−0.454067	+	0.786468i	−0.998634	−	0.0522497i	$-0.983361\pi$
$173$	−5.97233	+	10.3444i	−0.454067	+	0.786468i	0.544567	+	0.838718i	$0.316694\pi$
$174$	−12.6398	−	31.1420i	−0.958218	−	2.36087i
$175$		0			0
$176$	−9.48906	−	16.4355i	−0.715265	−	1.23887i
$177$	7.18221	+	17.6956i	0.539848	+	1.33008i
$178$	17.5056	−	30.3207i	1.31210	−	2.27263i
$179$	8.54921			0.638998			0.319499	−	0.947587i	$-0.396485\pi$
$179$	8.54921			0.638998			0.319499	+	0.947587i	$0.396485\pi$
$180$		0			0
$181$	−10.5524			−0.784351			−0.392176	−	0.919890i	$-0.628277\pi$
$181$	−10.5524			−0.784351			−0.392176	+	0.919890i	$0.628277\pi$
$182$	4.66724	−	8.08390i	0.345959	−	0.599219i
$183$	−13.4837	+	17.3150i	−0.996744	+	1.27996i
$184$	6.70503	+	11.6135i	0.494301	+	0.856155i
$185$		0			0
$186$	11.8518	+	1.64646i	0.869013	+	0.120724i
$187$	−4.34684	+	7.52895i	−0.317873	+	0.550571i
$188$	31.0608			2.26534
$189$	−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	$-0.0491485\pi$
$192$	−19.0010	−	2.63964i	−1.37128	−	0.190500i
$193$	−0.779763	−	1.35059i	−0.0561286	−	0.0972175i	0.836596	−	0.547821i	$-0.184542\pi$
$193$	−0.779763	−	1.35059i	−0.0561286	−	0.0972175i	−0.892724	+	0.450603i	$0.851209\pi$
$194$	5.04721	+	8.74202i	0.362369	+	0.627641i
$195$		0			0
$196$	9.30346	−	16.1141i	0.664533	−	1.15100i
$197$	17.9767			1.28079			0.640395	−	0.768046i	$-0.278771\pi$
$197$	17.9767			1.28079			0.640395	+	0.768046i	$0.278771\pi$
$198$	−3.50019	−	13.8509i	−0.248748	−	0.984339i
$199$	11.0225			0.781362			0.390681	−	0.920526i	$-0.372240\pi$
$199$	11.0225			0.781362			0.390681	+	0.920526i	$0.372240\pi$
$200$		0			0
$201$	5.93007	+	14.6106i	0.418275	+	1.03055i
$202$	−8.62856	−	14.9451i	−0.607104	−	1.05153i
$203$	−6.62141	−	11.4686i	−0.464732	−	0.804939i
$204$	15.4609	+	38.0927i	1.08248	+	2.66702i
$205$		0			0
$206$	−21.2688			−1.48187
$207$	1.27445	+	5.04324i	0.0885806	+	0.350529i
$208$	20.6964			1.43503
$209$	−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	$0.525265\pi$
$212$	−4.25871	−	7.37630i	−0.292489	−	0.506606i
$213$	−2.18668	−	0.303776i	−0.149829	−	0.0208144i
$214$	11.8211	−	20.4748i	0.808076	−	1.39963i
$215$		0			0
$216$	−36.7898	−	16.1703i	−2.50323	−	1.10025i
$217$	4.71470			0.320055
$218$	8.35107	−	14.4645i	0.565606	−	0.979658i
$219$	6.15497	+	0.855056i	0.415914	+	0.0577793i
$220$		0			0
$221$	−4.74040	−	8.21061i	−0.318874	−	0.552305i
$222$	32.6106	−	41.8766i	2.18868	−	2.81057i
$223$	−10.8553	+	18.8020i	−0.726927	+	1.25907i	0.231249	+	0.972895i	$0.425719\pi$
$223$	−10.8553	+	18.8020i	−0.726927	+	1.25907i	−0.958176	+	0.286180i	$0.907615\pi$
$224$	−21.8851			−1.46226
$225$		0			0
$226$	−39.2492			−2.61082
$227$	−7.05010	+	12.2111i	−0.467932	+	0.810481i	−0.999328	−	0.0366416i	$-0.988334\pi$
$227$	−7.05010	+	12.2111i	−0.467932	+	0.810481i	0.531397	+	0.847123i	$0.321667\pi$
$228$	9.53312	+	23.4878i	0.631347	+	1.55552i
$229$	−1.83879	−	3.18488i	−0.121511	−	0.210463i	0.798853	−	0.601526i	$-0.205441\pi$
$229$	−1.83879	−	3.18488i	−0.121511	−	0.210463i	−0.920364	+	0.391064i	$0.872107\pi$
$230$		0			0
$231$	−2.11699	−	5.21587i	−0.139288	−	0.343179i
$232$	28.4904	−	49.3469i	1.87049	−	3.23978i
$233$	−5.34164			−0.349943			−0.174971	−	0.984574i	$-0.555983\pi$
$233$	−5.34164			−0.349943			−0.174971	+	0.984574i	$0.555983\pi$
$234$	14.9898	+	4.24676i	0.979913	+	0.277619i
$235$		0			0
$236$	−27.2149	+	47.1376i	−1.77154	+	3.06840i
$237$	2.24639	−	2.88469i	0.145919	−	0.187380i
$238$	11.3807	+	19.7119i	0.737698	+	1.27773i
$239$	11.0167	+	19.0815i	0.712613	+	1.23428i	0.963873	+	0.266362i	$0.0858218\pi$
$239$	11.0167	+	19.0815i	0.712613	+	1.23428i	−0.251260	+	0.967920i	$0.580845\pi$
$240$		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	$-0.0383988\pi$
$242$	−20.3605			−1.30882
$243$	−12.0207	−	9.92491i	−0.771126	−	0.636683i
$244$	−62.5475			−4.00420
$245$		0			0
$246$	11.1444	+	1.54820i	0.710542	+	0.0987095i
$247$	−2.92291	−	5.06263i	−0.185980	−	0.322127i
$248$	10.1431	+	17.5684i	0.644091	+	1.11560i
$249$	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	$0.346520\pi$
$252$	−25.6110	−	7.25586i	−1.61334	−	0.457076i
$253$	−3.13515			−0.197105
$254$	−4.77103	+	8.26366i	−0.299361	+	0.518508i
$255$		0			0
$256$	4.73035	+	8.19320i	0.295647	+	0.512075i
$257$	−11.1045	−	19.2335i	−0.692678	−	1.19975i	−0.970957	−	0.239253i	$-0.923098\pi$
$257$	−11.1045	−	19.2335i	−0.692678	−	1.19975i	0.278280	−	0.960500i	$-0.410236\pi$
$258$	−12.4862	−	30.7637i	−0.777357	−	1.91526i
$259$	10.4566	−	18.1114i	0.649743	−	1.12539i
$260$		0			0
$261$	15.8507	−	15.4044i	0.981132	−	0.953510i
$262$	19.2089			1.18673
$263$	−2.87001	+	4.97100i	−0.176972	+	0.306525i	−0.940842	−	0.338846i	$-0.889964\pi$
$263$	−2.87001	+	4.97100i	−0.176972	+	0.306525i	0.763870	+	0.645370i	$0.223297\pi$
$264$	14.8815	−	19.1099i	0.915892	−	1.17613i
$265$		0			0
$266$	7.01727	+	12.1543i	0.430256	+	0.745226i
$267$	22.8059	+	3.16823i	1.39570	+	0.193892i
$268$	−22.4703	+	38.9197i	−1.37259	+	2.37740i
$269$	−15.6162			−0.952139			−0.476070	−	0.879408i	$-0.657939\pi$
$269$	−15.6162			−0.952139			−0.476070	+	0.879408i	$0.657939\pi$
$270$		0			0
$271$	−6.75315			−0.410225			−0.205112	−	0.978738i	$-0.565756\pi$
$271$	−6.75315			−0.410225			−0.205112	+	0.978738i	$0.565756\pi$
$272$	−25.2331	+	43.7050i	−1.52998	+	2.65000i
$273$	6.08037	+	0.844693i	0.368001	+	0.0511232i
$274$	9.38423	+	16.2540i	0.566922	+	0.981938i
$275$		0			0
$276$	−9.10894	+	11.6972i	−0.548294	+	0.704087i
$277$	−15.1483	+	26.2376i	−0.910172	+	1.57646i	−0.0963529	+	0.995347i	$0.530718\pi$
$277$	−15.1483	+	26.2376i	−0.910172	+	1.57646i	−0.813820	+	0.581118i	$0.802616\pi$
$278$	−38.7438			−2.32370
$279$	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	$0.979064\pi$
$282$	10.7945	+	26.5957i	0.642805	+	1.58375i
$283$	2.83683	+	4.91354i	0.168632	+	0.292079i	0.937939	−	0.346800i	$-0.112732\pi$
$283$	2.83683	+	4.91354i	0.168632	+	0.292079i	−0.769307	+	0.638879i	$0.779398\pi$
$284$	−3.14604	−	5.44910i	−0.186683	−	0.323345i
$285$		0			0
$286$	−4.69502	+	8.13201i	−0.277622	+	0.480856i
$287$	4.43332			0.261690
$288$	−8.94931	−	35.4141i	−0.527343	−	2.08679i
$289$	6.11806			0.359886
$290$		0			0
$291$	−4.07877	+	5.23772i	−0.239102	+	0.307040i
$292$	8.85533	+	15.3379i	0.518219	+	0.897582i
$293$	−9.13867	−	15.8286i	−0.533887	−	0.924720i	−0.999216	−	0.0395819i	$-0.987397\pi$
$293$	−9.13867	−	15.8286i	−0.533887	−	0.924720i	0.465329	−	0.885138i	$-0.345936\pi$
$294$	17.0308	+	2.36594i	0.993257	+	0.137985i
$295$		0			0
$296$	89.9850			5.23027
$297$	7.57454	−	5.55857i	0.439520	−	0.322541i
$298$	−1.48887			−0.0862478
$299$	1.70950	−	2.96094i	0.0988631	−	0.171236i
$300$		0			0
$301$	−6.54097	−	11.3293i	−0.377015	−	0.653009i
$302$	−0.201987	−	0.349852i	−0.0116230	−	0.0201317i
$303$	6.97295	−	8.95425i	0.400585	−	0.514408i
$304$	−15.5586	+	26.9483i	−0.892349	+	1.54559i
$305$		0			0
$306$	−27.2436	+	26.4766i	−1.55741	+	1.51357i
$307$	−15.5050			−0.884915			−0.442458	−	0.896789i	$-0.645893\pi$
$307$	−15.5050			−0.884915			−0.442458	+	0.896789i	$0.645893\pi$
$308$	8.02174	−	13.8941i	0.457081	−	0.791688i
$309$	−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	$-0.498228\pi$
$312$	9.93365	+	24.4746i	0.562382	+	1.38560i
$313$	3.47468	−	6.01832i	0.196401	−	0.340176i	−0.750958	−	0.660350i	$-0.770408\pi$
$313$	3.47468	−	6.01832i	0.196401	−	0.340176i	0.947359	+	0.320174i	$0.103741\pi$
$314$	−30.1843			−1.70340
$315$		0			0
$316$	10.4205			0.586196
$317$	8.07253	−	13.9820i	0.453398	−	0.785309i	−0.545196	−	0.838308i	$-0.683545\pi$
$317$	8.07253	−	13.9820i	0.453398	−	0.785309i	0.998595	+	0.0529995i	$0.0168782\pi$
$318$	4.83590	−	6.20998i	0.271184	−	0.348238i
$319$	6.66081	+	11.5369i	0.372934	+	0.645940i
$320$		0			0
$321$	15.4003	+	2.13943i	0.859560	+	0.119411i
$322$	−4.10414	+	7.10858i	−0.228715	+	0.396146i
$323$	14.2545			0.793142
$324$	1.26838	−	44.4104i	0.0704655	−	2.46724i
$325$		0			0
$326$	29.0493	−	50.3148i	1.60889	−	2.78668i
$327$	10.8796	+	1.51140i	0.601642	+	0.0835808i
$328$	9.53779	+	16.5199i	0.526636	+	0.912160i
$329$	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	$0.279429\pi$
$332$	5.42437			0.297701
$333$	33.5835	+	9.51456i	1.84037	+	0.521394i
$334$	44.9535			2.45975
$335$		0			0
$336$	−12.2890	−	30.2777i	−0.670419	−	1.65179i
$337$	3.46020	+	5.99324i	0.188489	+	0.326473i	0.944747	−	0.327801i	$-0.106308\pi$
$337$	3.46020	+	5.99324i	0.188489	+	0.326473i	−0.756258	+	0.654274i	$0.772974\pi$
$338$	11.9991	+	20.7831i	0.652665	+	1.13045i
$339$	−9.70734	−	23.9170i	−0.527230	−	1.29900i
$340$		0			0
$341$	−4.74276			−0.256835
$342$	−16.7983	+	16.3254i	−0.908348	+	0.882776i
$343$	19.3570			1.04518
$344$	28.1443	−	48.7474i	1.51744	−	2.62828i
$345$		0			0
$346$	−15.7295	−	27.2442i	−0.845621	−	1.46466i
$347$	−6.90317	−	11.9566i	−0.370581	−	0.641866i	0.619074	−	0.785333i	$-0.287508\pi$
$347$	−6.90317	−	11.9566i	−0.370581	−	0.641866i	−0.989655	+	0.143467i	$0.954175\pi$
$348$	62.3962	+	8.66816i	3.34479	+	0.464662i
$349$	−3.28384	+	5.68778i	−0.175780	+	0.304460i	−0.940431	−	0.339985i	$-0.889578\pi$
$349$	−3.28384	+	5.68778i	−0.175780	+	0.304460i	0.764651	+	0.644445i	$0.222911\pi$
$350$		0			0
$351$	1.11954	+	10.1846i	0.0597564	+	0.543612i
$352$	22.0153			1.17342
$353$	1.76250	−	3.05273i	0.0938082	−	0.162481i	−0.815302	−	0.579035i	$-0.803429\pi$
$353$	1.76250	−	3.05273i	0.0938082	−	0.162481i	0.909111	+	0.416555i	$0.136763\pi$
$354$	−49.8194	−	6.92097i	−2.64787	−	0.367846i
$355$		0			0
$356$	32.8116	+	56.8313i	1.73901	+	3.01205i
$357$	−9.19698	+	11.8102i	−0.486756	+	0.625063i
$358$	−11.2581	+	19.4996i	−0.595010	+	1.03059i
$359$	22.9285			1.21012			0.605061	−	0.796179i	$-0.293149\pi$
$359$	22.9285			1.21012			0.605061	+	0.796179i	$0.293149\pi$
$360$		0			0
$361$	−10.2107			−0.537407
$362$	13.8960	−	24.0686i	0.730358	−	1.26502i
$363$	−5.03568	−	12.4070i	−0.264304	−	0.651196i
$364$	8.74801	+	15.1520i	0.458520	+	0.794181i
$365$		0			0
$366$	−21.7371	−	53.5560i	−1.13621	−	2.79942i
$367$	−2.08966	+	3.61939i	−0.109079	+	0.188931i	−0.915397	−	0.402551i	$-0.868124\pi$
$367$	−2.08966	+	3.61939i	−0.109079	+	0.188931i	0.806318	+	0.591482i	$0.201457\pi$
$368$	−18.1993			−0.948706
$369$	1.81289	+	7.17392i	0.0943751	+	0.373459i
$370$		0			0
$371$	1.55064	−	2.68578i	0.0805051	−	0.139439i
$372$	−13.7797	+	17.6951i	−0.714444	+	0.917447i
$373$	−3.42045	−	5.92440i	−0.177104	−	0.306754i	0.763783	−	0.645473i	$-0.223340\pi$
$373$	−3.42045	−	5.92440i	−0.177104	−	0.306754i	−0.940888	+	0.338719i	$0.890006\pi$
$374$	−11.4484	−	19.8292i	−0.591982	−	1.02534i
$375$		0			0
$376$	−24.3312	+	42.1429i	−1.25479	+	2.17336i
$377$	−14.5277			−0.748217
$378$	−2.68776	−	24.4509i	−0.138244	−	1.25762i
$379$	−12.7764			−0.656280			−0.328140	−	0.944629i	$-0.606422\pi$
$379$	−12.7764			−0.656280			−0.328140	+	0.944629i	$0.606422\pi$
$380$		0			0
$381$	−6.21558	−	0.863476i	−0.318434	−	0.0442372i
$382$	22.8307	+	39.5440i	1.16812	+	2.02325i
$383$	−3.76730	−	6.52515i	−0.192500	−	0.333420i	0.753578	−	0.657358i	$-0.228326\pi$
$383$	−3.76730	−	6.52515i	−0.192500	−	0.333420i	−0.946078	+	0.323939i	$0.894993\pi$
$384$	5.12773	−	6.58472i	0.261673	−	0.336025i
$385$		0			0
$386$	4.10736			0.209059
$387$	15.6581	−	15.2173i	0.795946	−	0.773538i
$388$	−18.9204			−0.960538
$389$	−2.72588	+	4.72135i	−0.138207	+	0.239382i	−0.926818	−	0.375511i	$-0.877467\pi$
$389$	−2.72588	+	4.72135i	−0.138207	+	0.239382i	0.788611	+	0.614893i	$0.210801\pi$
$390$		0			0
$391$	4.16847	+	7.22000i	0.210808	+	0.365131i
$392$	14.5756	+	25.2456i	0.736177	+	1.27510i
$393$	4.75087	+	11.7052i	0.239649	+	0.590451i
$394$	−23.6729	+	41.0026i	−1.19262	+	2.06568i
$395$		0			0
$396$	25.7634	+	7.29904i	1.29466	+	0.366791i
$397$	−5.64549			−0.283339			−0.141670	−	0.989914i	$-0.545247\pi$
$397$	−5.64549			−0.283339			−0.141670	+	0.989914i	$0.545247\pi$
$398$	−14.5151	+	25.1408i	−0.727574	+	1.26020i
$399$	−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	$0.789448\pi$
$402$	−41.1339	−	5.71438i	−2.05157	−	0.285007i
$403$	2.58608	−	4.47922i	0.128822	−	0.223126i
$404$	32.3458			1.60926
$405$		0			0
$406$	34.8779			1.73096
$407$	−10.5188	+	18.2192i	−0.521400	+	0.903091i
$408$	−63.7948	−	8.86246i	−3.15831	−	0.438757i
$409$	−16.4265	−	28.4515i	−0.812238	−	1.40684i	−0.911295	−	0.411755i	$-0.864916\pi$
$409$	−16.4265	−	28.4515i	−0.812238	−	1.40684i	0.0990570	−	0.995082i	$-0.468417\pi$
$410$		0			0
$411$	−7.58362	+	9.73844i	−0.374072	+	0.480362i
$412$	19.9325	−	34.5241i	0.982005	−	1.70088i
$413$	−19.8184			−0.975202
$414$	−13.1813	−	3.73439i	−0.647824	−	0.183535i
$415$		0			0
$416$	−12.0043	+	20.7920i	−0.588558	+	1.01941i
$417$	−9.58235	−	23.6091i	−0.469250	−	1.15614i
$418$	−7.05903	−	12.2266i	−0.345268	−	0.598022i
$419$	−11.4295	−	19.7965i	−0.558369	−	0.967124i	−0.997633	−	0.0687656i	$-0.978094\pi$
$419$	−11.4295	−	19.7965i	−0.558369	−	0.967124i	0.439264	−	0.898358i	$-0.355239\pi$
$420$		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	$0.310698\pi$
$422$	−63.0212			−3.06782
$423$	−13.5367	+	13.1556i	−0.658177	+	0.639648i
$424$	13.3441			0.648046
$425$		0			0
$426$	3.57243	−	4.58750i	0.173085	−	0.222265i
$427$	−11.3871	−	19.7230i	−0.551060	−	0.954463i
$428$	22.1568	+	38.3768i	1.07099	+	1.85501i
$429$	−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	$0.547622\pi$
$432$	43.9697	−	32.2671i	2.11549	−	1.55245i
$433$	−3.11806			−0.149844			−0.0749221	−	0.997189i	$-0.523871\pi$
$433$	−3.11806			−0.149844			−0.0749221	+	0.997189i	$0.523871\pi$
$434$	−6.20861	+	10.7536i	−0.298023	+	0.516190i
$435$		0			0
$436$	15.6528	+	27.1114i	0.749631	+	1.29840i
$437$	2.57026	+	4.45182i	0.122952	+	0.212960i
$438$	−10.0555	+	12.9127i	−0.480471	+	0.616992i
$439$	−6.75494	+	11.6999i	−0.322396	+	0.558406i	−0.980982	−	0.194100i	$-0.937822\pi$
$439$	−6.75494	+	11.6999i	−0.322396	+	0.558406i	0.658586	+	0.752505i	$0.271155\pi$
$440$		0			0
$441$	2.77044	+	10.9631i	0.131926	+	0.522054i
$442$	24.9698			1.18769
$443$	12.1387	−	21.0248i	0.576726	−	0.998918i	−0.419126	−	0.907928i	$-0.637663\pi$
$443$	12.1387	−	21.0248i	0.576726	−	0.998918i	0.995852	−	0.0909904i	$-0.0290032\pi$
$444$	37.4135	+	92.1799i	1.77557	+	4.37466i
$445$		0			0
$446$	−28.5899	−	49.5192i	−1.35377	−	2.34480i
$447$	−0.368236	−	0.907263i	−0.0174169	−	0.0429121i
$448$	9.95377	−	17.2404i	0.470271	−	0.814534i
$449$	−24.1437			−1.13941			−0.569705	−	0.821849i	$-0.692943\pi$
$449$	−24.1437			−1.13941			−0.569705	+	0.821849i	$0.692943\pi$
$450$		0			0
$451$	−4.45970			−0.209999
$452$	36.7832	−	63.7104i	1.73014	−	2.99668i
$453$	0.163230	−	0.209611i	0.00766924	−	0.00984838i
$454$	−18.5680	−	32.1607i	−0.871440	−	1.50938i
$455$		0			0
$456$	−39.3357	−	5.46456i	−1.84206	−	0.255902i
$457$	1.41078	−	2.44355i	0.0659937	−	0.114304i	−0.831141	−	0.556062i	$-0.812312\pi$
$457$	1.41078	−	2.44355i	0.0659937	−	0.114304i	0.897134	+	0.441758i	$0.145645\pi$
$458$	9.68573			0.452585
$459$	−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	$0.333216\pi$
$462$	14.6845	+	2.03999i	0.683185	+	0.0949090i
$463$	9.90167	+	17.1502i	0.460170	+	0.797037i	0.998969	−	0.0453970i	$-0.0144553\pi$
$463$	9.90167	+	17.1502i	0.460170	+	0.797037i	−0.538799	+	0.842434i	$0.681122\pi$
$464$	38.6655	+	66.9706i	1.79500	+	3.10903i
$465$		0			0
$466$	7.03421	−	12.1836i	0.325853	−	0.564395i
$467$	22.7210			1.05140			0.525701	−	0.850669i	$-0.323803\pi$
$467$	22.7210			1.05140			0.525701	+	0.850669i	$0.323803\pi$
$468$	−20.9415	+	20.3519i	−0.968019	+	0.940767i
$469$	−16.3633			−0.755588
$470$		0			0
$471$	−7.46536	−	18.3932i	−0.343986	−	0.847516i
$472$	−42.6372	−	73.8497i	−1.96253	−	3.39921i
$473$	6.57989	+	11.3967i	0.302544	+	0.524021i
$474$	3.62141	+	8.92247i	0.166337	+	0.409822i
$475$		0			0
$476$	−42.6625			−1.95543
$477$	4.98018	+	1.41094i	0.228027	+	0.0646023i
$478$	−58.0300			−2.65423
$479$	−10.6440	+	18.4359i	−0.486336	+	0.842359i	−0.999877	−	0.0157065i	$-0.995000\pi$
$479$	−10.6440	+	18.4359i	−0.486336	+	0.842359i	0.513541	+	0.858065i	$0.328334\pi$
$480$		0			0
$481$	−11.4712	−	19.8687i	−0.523042	−	0.905935i
$482$	24.5557	+	42.5318i	1.11848	+	1.93727i
$483$	−5.34677	−	0.742781i	−0.243287	−	0.0337977i
$484$	19.0813	−	33.0497i	0.867330	−	1.50226i
$485$		0			0
$486$	38.4670	−	14.3478i	1.74490	−	0.650831i
$487$	−9.58690			−0.434424			−0.217212	−	0.976124i	$-0.569696\pi$
$487$	−9.58690			−0.434424			−0.217212	+	0.976124i	$0.569696\pi$
$488$	48.9961	−	84.8637i	2.21795	−	3.84160i
$489$	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	$0.507537\pi$
$492$	−12.9573	+	16.6390i	−0.584160	+	0.750144i
$493$	17.7123	−	30.6786i	0.797721	−	1.38169i
$494$	15.3963			0.692711
$495$		0			0
$496$	−27.5314			−1.23619
$497$	1.14550	−	1.98407i	0.0513829	−	0.0889977i
$498$	1.88513	+	4.64459i	0.0844745	+	0.208129i
$499$	−8.46266	−	14.6577i	−0.378840	−	0.656171i	0.612053	−	0.790816i	$-0.290344\pi$
$499$	−8.46266	−	14.6577i	−0.378840	−	0.656171i	−0.990894	+	0.134646i	$0.957010\pi$
$500$		0			0
$501$	11.1182	+	27.3930i	0.496723	+	1.22383i
$502$	−19.3485	+	33.5126i	−0.863566	+	1.49574i
$503$	40.4168			1.80210			0.901048	−	0.433719i	$-0.142799\pi$
$503$	40.4168			1.80210			0.901048	+	0.433719i	$0.142799\pi$
$504$	29.9068	−	29.0649i	1.33216	−	1.29465i
$505$		0			0
$506$	4.12856	−	7.15088i	0.183537	−	0.317896i
$507$	−9.69676	+	12.4520i	−0.430648	+	0.553013i
$508$	−8.94253	−	15.4889i	−0.396761	−	0.687210i
$509$	20.7034	+	35.8593i	0.917660	+	1.58943i	0.802959	+	0.596034i	$0.203258\pi$
$509$	20.7034	+	35.8593i	0.917660	+	1.58943i	0.114701	+	0.993400i	$0.463409\pi$
$510$		0			0
$511$	−3.22431	+	5.58467i	−0.142635	+	0.247051i
$512$	−34.5537			−1.52707
$513$	−14.1028	−	6.19860i	−0.622652	−	0.273675i
$514$	58.4922			2.57998
$515$		0			0
$516$	61.6381	+	8.56285i	2.71347	+	0.376959i
$517$	−5.68843	−	9.85265i	−0.250177	−	0.433319i
$518$	27.5398	+	47.7004i	1.21003	+	2.09584i
$519$	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	$0.621689\pi$
$522$	14.2624	+	56.4389i	0.624248	+	2.47026i
$523$	9.57651			0.418751			0.209376	−	0.977835i	$-0.432857\pi$
$523$	9.57651			0.418751			0.209376	+	0.977835i	$0.432857\pi$
$524$	−18.0021	+	31.1805i	−0.786424	+	1.36213i
$525$		0			0
$526$	−7.55880	−	13.0922i	−0.329579	−	0.570848i
$527$	6.30592	+	10.9222i	0.274690	+	0.475777i
$528$	12.3621	+	30.4579i	0.537992	+	1.32551i
$529$	9.99675	−	17.3149i	0.434641	−	0.752821i
$530$		0			0
$531$	−8.10422	−	32.0699i	−0.351693	−	1.39171i
$532$	−26.3055			−1.14049
$533$	2.43174	−	4.21189i	0.105330	−	0.182437i
$534$	−37.2586	+	47.8452i	−1.61234	+	2.07047i
$535$		0			0
$536$	−35.2038	−	60.9748i	−1.52057	−	2.63371i
$537$	−14.6668	−	2.03753i	−0.632920	−	0.0879260i
$538$	20.5644	−	35.6187i	0.886596	−	1.53563i
$539$	−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	$0.505705\pi$
$542$	8.89297	−	15.4031i	0.381986	−	0.661619i
$543$	18.1034	+	2.51495i	0.776891	+	0.107927i
$544$	−29.2713	−	50.6994i	−1.25500	−	2.17372i
$545$		0			0
$546$	−9.93365	+	12.7562i	−0.425121	+	0.545915i
$547$	14.1635	−	24.5319i	0.605587	−	1.04891i	−0.386371	−	0.922343i	$-0.626272\pi$
$547$	14.1635	−	24.5319i	0.605587	−	1.04891i	0.991958	−	0.126565i	$-0.0403951\pi$
$548$	−35.1785			−1.50275
$549$	27.2590	−	26.4916i	1.16339	−	1.13063i
$550$		0			0
$551$	10.9213	−	18.9163i	0.465264	−	0.805861i
$552$	−8.73515	−	21.5218i	−0.371793	−	0.916027i
$553$	1.89709	+	3.28586i	0.0806727	+	0.139729i
$554$	−39.8964	−	69.1026i	−1.69504	−	2.93589i
$555$		0			0
$556$	36.3096	−	62.8901i	1.53987	−	2.66713i
$557$	11.5042			0.487448			0.243724	−	0.969845i	$-0.421631\pi$
$557$	11.5042			0.487448			0.243724	+	0.969845i	$0.421631\pi$
$558$	−19.9402	−	5.64926i	−0.844135	−	0.239152i
$559$	−14.3512			−0.606993
$560$		0			0
$561$	9.25171	−	11.8805i	0.390608	−	0.501595i
$562$	−24.5398	−	42.5043i	−1.03515	−	1.79293i
$563$	−16.5030	−	28.5840i	−0.695517	−	1.20467i	−0.970006	−	0.243080i	$-0.921842\pi$
$563$	−16.5030	−	28.5840i	−0.695517	−	1.20467i	0.274490	−	0.961590i	$-0.411491\pi$
$564$	−53.2872	−	7.40273i	−2.24380	−	0.311711i
$565$		0			0
$566$	−14.9429			−0.628095
$567$	14.2348	−	7.68517i	0.597804	−	0.322747i
$568$	9.85769			0.413619
$569$	13.5044	−	23.3903i	0.566135	−	0.980574i	−0.430809	−	0.902443i	$-0.641772\pi$
$569$	13.5044	−	23.3903i	0.566135	−	0.980574i	0.996943	−	0.0781305i	$-0.0248951\pi$
$570$		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	$0.662585\pi$
$572$	−8.80007	−	15.2422i	−0.367950	−	0.637307i
$573$	−18.4501	+	23.6925i	−0.770763	+	0.989768i
$574$	−5.83807	+	10.1118i	−0.243676	+	0.422060i
$575$		0			0
$576$	31.9685	+	9.05701i	1.33202	+	0.377375i
$577$	14.7976			0.616033			0.308017	−	0.951381i	$-0.400335\pi$
$577$	14.7976			0.616033			0.308017	+	0.951381i	$0.400335\pi$
$578$	−8.05663	+	13.9545i	−0.335112	+	0.580431i
$579$	1.01586	+	2.50288i	0.0422175	+	0.104016i
$580$		0			0
$581$	0.987533	+	1.71046i	0.0409698	+	0.0709617i
$582$	−6.57538	−	16.2005i	−0.272558	−	0.671532i
$583$	−1.55987	+	2.70177i	−0.0646030	+	0.111896i
$584$	−27.7470			−1.14818
$585$		0			0
$586$	48.1375			1.98854
$587$	−15.2890	+	26.4813i	−0.631044	+	1.09300i	0.356295	+	0.934374i	$0.384040\pi$
$587$	−15.2890	+	26.4813i	−0.631044	+	1.09300i	−0.987339	+	0.158626i	$0.949294\pi$
$588$	−19.8013	+	25.4276i	−0.816590	+	1.04862i
$589$	3.88821	+	6.73457i	0.160211	+	0.277493i
$590$		0			0
$591$	−30.8405	−	4.28440i	−1.26861	−	0.176237i
$592$	−61.0611	+	105.761i	−2.50960	+	4.34675i
$593$	−5.09990			−0.209428			−0.104714	−	0.994502i	$-0.533393\pi$
$593$	−5.09990			−0.209428			−0.104714	+	0.994502i	$0.533393\pi$
$594$	2.70376	+	24.5964i	0.110936	+	1.00920i
$595$		0			0
$596$	1.39532	−	2.41677i	0.0571547	−	0.0989949i
$597$	−18.9099	−	2.62698i	−0.773929	−	0.107515i
$598$	4.50236	+	7.79831i	0.184115	+	0.318897i
$599$	0.282655	+	0.489572i	0.0115490	+	0.0200034i	0.871742	−	0.489965i	$-0.162990\pi$
$599$	0.282655	+	0.489572i	0.0115490	+	0.0200034i	−0.860193	+	0.509968i	$0.829657\pi$
$600$		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	$0.0945769\pi$
$602$	34.4542			1.40425
$603$	−6.69134	−	26.4788i	−0.272492	−	1.07830i
$604$	0.757185			0.0308094
$605$		0			0
$606$	11.2411	+	27.6959i	0.456638	+	1.12507i
$607$	9.54913	+	16.5396i	0.387587	+	0.671321i	0.992124	−	0.125256i	$-0.0399753\pi$
$607$	9.54913	+	16.5396i	0.387587	+	0.671321i	−0.604537	+	0.796577i	$0.706642\pi$
$608$	−18.0486	−	31.2611i	−0.731967	−	1.26780i
$609$	8.62621	+	21.2534i	0.349552	+	0.861229i
$610$		0			0
$611$	12.4069			0.501929
$612$	−17.4457	−	69.0357i	−0.705200	−	2.79060i
$613$	9.33918			0.377206			0.188603	−	0.982053i	$-0.439604\pi$
$613$	9.33918			0.377206			0.188603	+	0.982053i	$0.439604\pi$
$614$	20.4179	−	35.3648i	0.823999	−	1.42721i
$615$		0			0
$616$	12.5675	+	21.7676i	0.506360	+	0.877041i
$617$	12.2077	+	21.1444i	0.491464	+	0.851241i	0.999952	−	0.00982861i	$-0.00312859\pi$
$617$	12.2077	+	21.1444i	0.491464	+	0.851241i	−0.508488	+	0.861069i	$0.669795\pi$
$618$	36.4883	+	5.06900i	1.46777	+	0.203905i
$619$	−19.7431	+	34.1961i	−0.793544	+	1.37446i	0.130216	+	0.991486i	$0.458433\pi$
$619$	−19.7431	+	34.1961i	−0.793544	+	1.37446i	−0.923760	+	0.382973i	$0.874900\pi$
$620$		0			0
$621$	−0.984464	−	8.95580i	−0.0395052	−	0.359384i
$622$	80.1874			3.21522
$623$	−11.9470	+	20.6928i	−0.478647	+	0.829040i
$624$	−35.5062	−	4.93256i	−1.42138	−	0.197461i
$625$		0			0
$626$	9.15135	+	15.8506i	0.365761	+	0.633517i
$627$	5.70457	−	7.32547i	0.227819	−	0.292551i
$628$	28.2879	−	48.9960i	1.12881	−	1.95515i
$629$	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	$0.182995\pi$
$632$	−8.16277	+	14.1383i	−0.324698	+	0.562393i
$633$	−15.5868	−	38.4029i	−0.619518	−	1.52638i
$634$	21.2608	+	36.8248i	0.844375	+	1.46250i
$635$		0			0
$636$	5.54814	+	13.6696i	0.219998	+	0.542034i
$637$	3.71616	−	6.43658i	0.147240	−	0.255027i
$638$	−35.0855			−1.38905
$639$	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	$0.920990\pi$
$642$	−25.1598	+	32.3087i	−0.992978	+	1.27512i
$643$	−7.09771	−	12.2936i	−0.279906	−	0.484812i	0.691455	−	0.722420i	$-0.256970\pi$
$643$	−7.09771	−	12.2936i	−0.279906	−	0.484812i	−0.971361	+	0.237608i	$0.923637\pi$
$644$	−7.69256	−	13.3239i	−0.303129	−	0.525036i
$645$		0			0
$646$	−18.7712	+	32.5127i	−0.738544	+	1.27919i
$647$	17.4897			0.687593			0.343796	−	0.939044i	$-0.388287\pi$
$647$	17.4897			0.687593			0.343796	+	0.939044i	$0.388287\pi$
$648$	59.2618	+	36.5094i	2.32803	+	1.43422i
$649$	19.9364			0.782572
$650$		0			0
$651$	−8.08842	−	1.12365i	−0.317010	−	0.0440395i
$652$	54.4483	+	94.3072i	2.13236	+	3.69335i
$653$	5.48858	+	9.50650i	0.214785	+	0.372018i	0.953206	−	0.302322i	$-0.0977617\pi$
$653$	5.48858	+	9.50650i	0.214785	+	0.372018i	−0.738421	+	0.674340i	$0.764428\pi$
$654$	−17.7742	+	22.8246i	−0.695026	+	0.892512i
$655$		0			0
$656$	−25.8882			−1.01077
$657$	−10.3555	−	2.93383i	−0.404007	−	0.114459i
$658$	−29.7862			−1.16119
$659$	7.89381	−	13.6725i	0.307499	−	0.532604i	−0.670316	−	0.742076i	$-0.733841\pi$
$659$	7.89381	−	13.6725i	0.307499	−	0.532604i	0.977815	+	0.209472i	$0.0671746\pi$
$660$		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	$-0.588909\pi$
$662$	−16.6217	−	28.7897i	−0.646022	−	1.11894i
$663$	6.17567	+	15.2157i	0.239843	+	0.590929i
$664$	−4.24913	+	7.35972i	−0.164898	+	0.285612i
$665$		0			0
$666$	−65.9263	+	64.0703i	−2.55459	+	2.48267i
$667$	12.7750			0.494649
$668$	−42.1291	+	72.9698i	−1.63002	+	2.82328i
$669$	23.1042	−	29.6691i	0.893261	−	1.14707i
$670$		0			0
$671$	11.4549	+	19.8404i	0.442210	+	0.765929i
$672$	37.5455	+	5.21587i	1.44835	+	0.201207i
$673$	−14.4197	+	24.9757i	−0.555840	+	0.962743i	0.441998	+	0.897016i	$0.354270\pi$
$673$	−14.4197	+	24.9757i	−0.555840	+	0.962743i	−0.997838	+	0.0657266i	$0.979063\pi$
$674$	−18.2264			−0.702055
$675$		0			0
$676$	−44.9809			−1.73003
$677$	−5.23181	+	9.06176i	−0.201075	+	0.348272i	−0.948875	−	0.315652i	$-0.897777\pi$
$677$	−5.23181	+	9.06176i	−0.201075	+	0.348272i	0.747800	+	0.663924i	$0.231110\pi$
$678$	67.3349	+	9.35426i	2.58598	+	0.359248i
$679$	−3.44455	−	5.96614i	−0.132190	−	0.228959i
$680$		0			0
$681$	15.0053	−	19.2689i	0.575003	−	0.738385i
$682$	6.24556	−	10.8176i	0.239155	−	0.414228i
$683$	−16.1875			−0.619396			−0.309698	−	0.950835i	$-0.600228\pi$
$683$	−16.1875			−0.619396			−0.309698	+	0.950835i	$0.600228\pi$
$684$	−10.7569	−	42.5672i	−0.411302	−	1.62760i
$685$		0			0
$686$	−25.4904	+	44.1507i	−0.973229	+	1.68568i
$687$	2.39553	+	5.90214i	0.0913953	+	0.225181i
$688$	38.1958	+	66.1570i	1.45620	+	2.52221i
$689$	−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	$0.226866\pi$
$692$	58.9648			2.24150
$693$	2.38876	+	9.45276i	0.0907415	+	0.359081i
$694$	36.3621			1.38029
$695$		0			0
$696$	−60.6383	+	77.8682i	−2.29849	+	2.95158i
$697$	5.92957	+	10.2703i	0.224598	+	0.389016i
$698$	−8.64872	−	14.9800i	−0.327359	−	0.567002i
$699$	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	$0.188143\pi$
$702$	−24.7040	−	10.8582i	−0.932391	−	0.409815i
$703$	34.4942			1.30097
$704$	−10.0130	+	17.3430i	−0.377379	+	0.653640i
$705$		0			0
$706$	4.64193	+	8.04005i	0.174701	+	0.302591i
$707$	5.88870	+	10.1995i	0.221467	+	0.383593i
$708$	57.9236	−	74.3820i	2.17690	−	2.79545i
$709$	−12.6130	+	21.8464i	−0.473692	+	0.820458i	−0.999546	−	0.0301162i	$-0.990412\pi$
$709$	−12.6130	+	21.8464i	−0.473692	+	0.820458i	0.525855	+	0.850574i	$0.323746\pi$
$710$		0			0
$711$	−4.54136	+	4.41351i	−0.170314	+	0.165520i
$712$	−102.811			−3.85299
$713$	−2.27407	+	3.93880i	−0.0851645	+	0.147509i
$714$	−14.8264	−	36.5295i	−0.554865	−	1.36708i
$715$		0			0
$716$	−21.1016	−	36.5490i	−0.788603	−	1.36590i
$717$	−14.3523	−	35.3614i	−0.535998	−	1.32060i
$718$	−30.1937	+	52.2971i	−1.12682	+	1.95171i
$719$	−36.8600			−1.37465			−0.687323	−	0.726352i	$-0.741214\pi$
$719$	−36.8600			−1.37465			−0.687323	+	0.726352i	$0.741214\pi$
$720$		0			0
$721$	14.5153			0.540576
$722$	13.4461	−	23.2893i	0.500412	−	0.866740i
$723$	−19.8441	+	25.4826i	−0.738009	+	0.947708i
$724$	26.0459	+	45.1128i	0.967988	+	1.67660i
$725$		0			0
$726$	34.9300	+	4.85252i	1.29637	+	0.180094i
$727$	19.1226	−	33.1213i	0.709217	−	1.22840i	−0.255931	−	0.966695i	$-0.582382\pi$
$727$	19.1226	−	33.1213i	0.709217	−	1.22840i	0.965148	−	0.261705i	$-0.0842847\pi$
$728$	−27.4107			−1.01591
$729$	18.2569	+	19.8918i	0.676183	+	0.736734i
$730$		0			0
$731$	17.4971	−	30.3059i	0.647154	−	1.12090i
$732$	107.305	+	14.9070i	3.96611	+	0.550977i
$733$	−19.7916	−	34.2801i	−0.731020	−	1.26616i	−0.956448	−	0.291903i	$-0.905711\pi$
$733$	−19.7916	−	34.2801i	−0.731020	−	1.26616i	0.225428	−	0.974260i	$-0.427622\pi$
$734$	−5.50358	−	9.53248i	−0.203141	−	0.351850i
$735$		0			0
$736$	10.5559	−	18.2834i	0.389097	−	0.673936i
$737$	16.4607			0.606338
$738$	−18.7501	−	5.31210i	−0.690201	−	0.195541i
$739$	−8.24773			−0.303398			−0.151699	−	0.988427i	$-0.548474\pi$
$739$	−8.24773			−0.303398			−0.151699	+	0.988427i	$0.548474\pi$
$740$		0			0
$741$	3.80790	+	9.38194i	0.139887	+	0.344654i
$742$	4.08395	+	7.07361i	0.149927	+	0.259680i
$743$	−0.654091	−	1.13292i	−0.0239963	−	0.0415627i	0.853778	−	0.520637i	$-0.174306\pi$
$743$	−0.654091	−	1.13292i	−0.0239963	−	0.0415627i	−0.877774	+	0.479075i	$0.840972\pi$
$744$	−13.2142	−	32.5574i	−0.484458	−	1.19361i
$745$		0			0
$746$	18.0171			0.659651
$747$	−2.36401	+	2.29746i	−0.0864946	+	0.0840595i
$748$	42.9164			1.56918
$749$	−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	$-0.340370\pi$
$752$	−33.0209	−	57.1939i	−1.20415	−	2.08565i
$753$	−25.2068	−	3.50176i	−0.918585	−	0.127611i
$754$	19.1310	−	33.1359i	0.696711	−	1.20674i
$755$		0			0
$756$	42.2083	+	18.5518i	1.53510	+	0.674724i
$757$	−38.2012			−1.38845			−0.694223	−	0.719760i	$-0.744252\pi$
$757$	−38.2012			−1.38845			−0.694223	+	0.719760i	$0.744252\pi$
$758$	16.8248	−	29.1414i	0.611103	−	1.05846i
$759$	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	$0.965088\pi$
$762$	10.1545	−	13.0398i	0.367860	−	0.472384i
$763$	−5.69932	+	9.87152i	−0.206329	+	0.357373i
$764$	−85.5852			−3.09637
$765$		0			0
$766$	19.8440			0.716994
$767$	−10.8707	+	18.8286i	−0.392518	+	0.679861i
$768$	−6.16258	−	15.1834i	−0.222373	−	0.547885i
$769$	8.45652	+	14.6471i	0.304950	+	0.528189i	0.977250	−	0.212090i	$-0.0680270\pi$
$769$	8.45652	+	14.6471i	0.304950	+	0.528189i	−0.672300	+	0.740279i	$0.734694\pi$
$770$		0			0
$771$	14.4666	+	35.6431i	0.521003	+	1.28365i
$772$	−3.84930	+	6.66718i	−0.138539	+	0.239957i
$773$	−38.6464			−1.39001			−0.695007	−	0.719003i	$-0.744599\pi$
$773$	−38.6464			−1.39001			−0.695007	+	0.719003i	$0.744599\pi$
$774$	14.0891	+	55.7532i	0.506423	+	2.00401i
$775$		0			0
$776$	14.8211	−	25.6709i	0.532047	−	0.921533i
$777$	−22.2556	+	28.5793i	−0.798416	+	1.02528i
$778$	−7.17920	−	12.4347i	−0.257387	−	0.445807i
$779$	3.65615	+	6.33264i	0.130995	+	0.226890i
$780$		0			0
$781$	−1.15232	+	1.99588i	−0.0412333	+	0.0714181i
$782$	−21.9572			−0.785187
$783$	−30.8644	+	22.6498i	−1.10300	+	0.809437i
$784$	−39.5622			−1.41294
$785$		0			0
$786$	−32.9544	−	4.57807i	−1.17544	−	0.163294i
$787$	−5.45734	−	9.45240i	−0.194533	−	0.336942i	0.752214	−	0.658919i	$-0.228986\pi$
$787$	−5.45734	−	9.45240i	−0.194533	−	0.336942i	−0.946747	+	0.321977i	$0.895653\pi$
$788$	−44.3711	−	76.8530i	−1.58065	−	2.73777i
$789$	6.10845	−	7.84411i	0.217467	−	0.279258i
$790$		0			0
$791$	26.7862			0.952409
$792$	−30.0848	+	29.2378i	−1.06902	+	1.03892i
$793$	−24.9839			−0.887204
$794$	7.43433	−	12.8766i	0.263835	−	0.456975i
$795$		0			0
$796$	−27.2062	−	47.1225i	−0.964298	−	1.67021i
$797$	1.46275	+	2.53356i	0.0518133	+	0.0897432i	0.890769	−	0.454457i	$-0.150167\pi$
$797$	1.46275	+	2.53356i	0.0518133	+	0.0897432i	−0.838956	+	0.544200i	$0.816833\pi$
$798$	−9.14193	−	22.5240i	−0.323621	−	0.797340i
$799$	−15.1265	+	26.1999i	−0.535139	+	0.926888i
$800$		0			0
$801$	−38.3702	−	10.8707i	−1.35574	−	0.384096i
$802$	−14.4965			−0.511888
$803$	3.24350	−	5.61791i	0.114461	−	0.198252i
$804$	47.8252	−	61.4144i	1.68667	−	2.16592i
$805$		0			0
$806$	6.81102	+	11.7970i	0.239908	+	0.415532i
$807$	26.7909	+	3.72182i	0.943083	+	0.131014i
$808$	−25.3378	+	43.8863i	−0.891380	+	1.54391i
$809$	−37.9241			−1.33334			−0.666671	−	0.745352i	$-0.732281\pi$
$809$	−37.9241			−1.33334			−0.666671	+	0.745352i	$0.732281\pi$
$810$		0			0
$811$	19.5050			0.684912			0.342456	−	0.939534i	$-0.388741\pi$
$811$	19.5050			0.684912			0.342456	+	0.939534i	$0.388741\pi$
$812$	−32.6866	+	56.6148i	−1.14707	+	1.98679i
$813$	11.5855	+	1.60948i	0.406323	+	0.0564469i
$814$	−27.7037	−	47.9843i	−0.971016	−	1.68185i
$815$		0			0
$816$	53.7055	−	68.9654i	1.88007	−	2.41427i
$817$	10.7887	−	18.6865i	0.377447	−	0.653758i
$818$	86.5257			3.02530
$819$	−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	$0.881410\pi$
$822$	−12.2255	−	30.1214i	−0.426415	−	1.05061i
$823$	17.9497	+	31.0898i	0.625687	+	1.08372i	0.988408	+	0.151824i	$0.0485146\pi$
$823$	17.9497	+	31.0898i	0.625687	+	1.08372i	−0.362721	+	0.931898i	$0.618152\pi$
$824$	31.2279	+	54.0884i	1.08788	+	1.88426i
$825$		0			0
$826$	26.0981	−	45.2033i	0.908071	−	1.57282i
$827$	−16.2717			−0.565822			−0.282911	−	0.959146i	$-0.591300\pi$
$827$	−16.2717			−0.565822			−0.282911	+	0.959146i	$0.591300\pi$
$828$	18.4149	−	17.8964i	0.639961	−	0.621944i
$829$	−20.6592			−0.717525			−0.358762	−	0.933429i	$-0.616801\pi$
$829$	−20.6592			−0.717525			−0.358762	+	0.933429i	$0.616801\pi$
$830$		0			0
$831$	32.2412	−	41.4023i	1.11844	−	1.43623i
$832$	−10.9196	−	18.9132i	−0.378568	−	0.655698i
$833$	9.06152	+	15.6950i	0.313963	+	0.543800i
$834$	66.4680	+	9.23382i	2.30160	+	0.319741i
$835$		0			0
$836$	26.4621			0.915210
$837$	−1.48927	−	13.5480i	−0.0514765	−	0.468289i
$838$	60.2044			2.07973
$839$	6.11836	−	10.5973i	0.211229	−	0.365860i	−0.740870	−	0.671648i	$-0.765587\pi$
$839$	6.11836	−	10.5973i	0.211229	−	0.365860i	0.952100	+	0.305788i	$0.0989200\pi$
$840$		0			0
$841$	−12.6411	−	21.8951i	−0.435901	−	0.755003i
$842$	−23.6264	−	40.9221i	−0.814218	−	1.41027i
$843$	19.8312	−	25.4661i	0.683024	−	0.877099i
$844$	59.0616	−	102.298i	2.03299	−	3.52123i
$845$		0			0
$846$	−12.1803	−	48.1996i	−0.418767	−	1.65714i
$847$	13.8953			0.477450
$848$	−9.05490	+	15.6836i	−0.310947	+	0.538575i
$849$	−3.69576	−	9.10565i	−0.126838	−	0.312505i
$850$		0			0
$851$	10.0872	+	17.4715i	0.345785	+	0.598917i
$852$	4.09858	+	10.0981i	0.140415	+	0.345956i
$853$	−8.21464	+	14.2282i	−0.281264	+	0.487164i	−0.971696	−	0.236233i	$-0.924087\pi$
$853$	−8.21464	+	14.2282i	−0.281264	+	0.487164i	0.690432	+	0.723397i	$0.257420\pi$
$854$	59.9809			2.05250
$855$		0			0
$856$	−69.4255			−2.37291
$857$	−24.5449	+	42.5129i	−0.838436	+	1.45221i	0.0527655	+	0.998607i	$0.483196\pi$
$857$	−24.5449	+	42.5129i	−0.838436	+	1.45221i	−0.891202	+	0.453607i	$0.850137\pi$
$858$	9.99276	−	12.8321i	0.341147	−	0.438081i
$859$	−20.5454	−	35.5856i	−0.700999	−	1.21417i	−0.968116	−	0.250502i	$-0.919404\pi$
$859$	−20.5454	−	35.5856i	−0.700999	−	1.21417i	0.267117	−	0.963664i	$-0.413929\pi$
$860$		0			0
$861$	−7.60569	−	1.05659i	−0.259201	−	0.0360086i
$862$	8.14968	−	14.1157i	0.277579	−	0.480781i
$863$	47.8366			1.62838			0.814188	−	0.580601i	$-0.197183\pi$
$863$	47.8366			1.62838			0.814188	+	0.580601i	$0.197183\pi$
$864$	6.91299	+	62.8884i	0.235185	+	2.13951i
$865$		0			0
$866$	4.10605	−	7.11189i	0.139529	−	0.241672i
$867$	−10.4960	−	1.45812i	−0.356462	−	0.0495202i
$868$	−11.6371	−	20.1560i	−0.394987	−	0.684138i
$869$	−1.90838	−	3.30542i	−0.0647375	−	0.112129i
$870$		0			0
$871$	−8.97551	+	15.5460i	−0.304123	+	0.526757i
$872$	−49.0458			−1.66090
$873$	8.24574	−	8.01361i	0.279076	−	0.271219i
$874$	−13.5387			−0.457954
$875$		0			0
$876$	−11.5365	−	28.4238i	−0.389783	−	0.960351i
$877$	5.68859	+	9.85292i	0.192090	+	0.332710i	0.945943	−	0.324334i	$-0.105140\pi$
$877$	5.68859	+	9.85292i	0.192090	+	0.332710i	−0.753853	+	0.657043i	$0.771807\pi$
$878$	−17.7906	−	30.8143i	−0.600405	−	1.03993i
$879$	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	$0.765682\pi$
$882$	−28.6538	−	8.11791i	−0.964823	−	0.273344i
$883$	37.6820			1.26810			0.634051	−	0.773291i	$-0.281391\pi$
$883$	37.6820			1.26810			0.634051	+	0.773291i	$0.281391\pi$
$884$	−23.4010	+	40.5317i	−0.787060	+	1.36323i
$885$		0			0
$886$	31.9699	+	55.3735i	1.07405	+	1.86031i
$887$	16.6416	+	28.8241i	0.558771	+	0.967820i	0.997599	+	0.0692492i	$0.0220603\pi$
$887$	16.6416	+	28.8241i	0.558771	+	0.967820i	−0.438828	+	0.898571i	$0.644606\pi$
$888$	−154.376	−	21.4461i	−5.18052	−	0.719685i
$889$	3.25606	−	5.63967i	0.109205	−	0.189148i
$890$		0			0
$891$	−14.3195	+	7.73091i	−0.479721	+	0.258995i
$892$	107.175			3.58847
$893$	−9.32697	+	16.1548i	−0.312115	+	0.540599i
$894$	2.55427	+	0.354842i	0.0854274	+	0.0118677i
$895$		0			0
$896$	4.33040	+	7.50047i	0.144669	+	0.250573i
$897$	−3.63846	+	4.67230i	−0.121485	+	0.156003i
$898$	31.7939	−	55.0686i	1.06098	−	1.83766i
$899$	19.3255			0.644543
$900$		0			0
$901$	8.29592			0.276377
$902$	5.87281	−	10.1720i	0.195543	−	0.338691i
$903$	8.52141	+	20.9952i	0.283575	+	0.698675i
$904$	57.6276	+	99.8139i	1.91667	+	3.31976i
$905$		0			0
$906$	0.263144	+	0.648336i	0.00874236	+	0.0215395i
$907$	7.03918	−	12.1922i	0.233732	−	0.404836i	−0.725171	−	0.688568i	$-0.758239\pi$
$907$	7.03918	−	12.1922i	0.233732	−	0.404836i	0.958903	+	0.283733i	$0.0915728\pi$
$908$	69.6056			2.30994
$909$	−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	$0.205335\pi$
$912$	33.1146	−	42.5238i	1.09653	−	1.40810i
$913$	−0.993410	−	1.72064i	−0.0328771	−	0.0569448i
$914$	3.71561	+	6.43563i	0.122902	+	0.212872i
$915$		0			0
$916$	−9.07719	+	15.7222i	−0.299919	+	0.519475i
$917$	−13.1094			−0.432912
$918$	53.0486	−	38.9297i	1.75087	−	1.28487i
$919$	4.44684			0.146688			0.0733438	−	0.997307i	$-0.476633\pi$
$919$	4.44684			0.146688			0.0733438	+	0.997307i	$0.476633\pi$
$920$		0			0
$921$	26.5999	+	3.69530i	0.876498	+	0.121764i
$922$	−28.2562	−	48.9412i	−0.930569	−	1.61179i
$923$	−1.25665	−	2.17658i	−0.0413631	−	0.0716430i
$924$	−17.0733	+	21.9245i	−0.561669	+	0.721263i
$925$		0			0
$926$	−52.1565			−1.71397
$927$	5.93562	+	23.4883i	0.194951	+	0.771458i
$928$	−89.7068			−2.94477
$929$	−6.55663	+	11.3564i	−0.215116	+	0.372592i	−0.953309	−	0.301998i	$-0.902346\pi$
$929$	−6.55663	+	11.3564i	−0.215116	+	0.372592i	0.738192	+	0.674590i	$0.235680\pi$
$930$		0			0
$931$	5.58730	+	9.67749i	0.183116	+	0.317167i
$932$	13.1845	+	22.8362i	0.431873	+	0.748026i
$933$	19.8324	+	48.8633i	0.649284	+	1.59971i
$934$	−29.9204	+	51.8236i	−0.979025	+	1.69572i
$935$		0			0
$936$	−11.2089	−	44.3556i	−0.366374	−	1.44981i
$937$	−33.5187			−1.09501			−0.547504	−	0.836803i	$-0.684422\pi$
$937$	−33.5187			−1.09501			−0.547504	+	0.836803i	$0.684422\pi$
$938$	21.5482	−	37.3226i	0.703574	−	1.21863i
$939$	−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	$0.842626\pi$
$942$	51.7834	+	7.19383i	1.68720	+	0.234388i
$943$	−2.13835	+	3.70373i	−0.0696342	+	0.120610i
$944$	115.729			3.76667
$945$		0			0
$946$	−34.6592			−1.12687
$947$	26.3175	−	45.5832i	0.855204	−	1.48126i	−0.0212525	−	0.999774i	$-0.506765\pi$
$947$	26.3175	−	45.5832i	0.855204	−	1.48126i	0.876456	−	0.481482i	$-0.159901\pi$
$948$	−17.8771	−	2.48351i	−0.580620	−	0.0806606i
$949$	3.53716	+	6.12654i	0.114821	+	0.198876i
$950$		0			0
$951$	−17.1814	+	22.0633i	−0.557144	+	0.715451i
$952$	33.4193	−	57.8839i	1.08312	−	1.87603i
$953$	−18.4072			−0.596268			−0.298134	−	0.954524i	$-0.596364\pi$
$953$	−18.4072			−0.596268			−0.298134	+	0.954524i	$0.596364\pi$
$954$	−9.77637	+	9.50114i	−0.316522	+	0.307611i
$955$		0			0
$956$	54.3841	−	94.1960i	1.75891	−	3.04652i
$957$	−8.67754	−	21.3798i	−0.280505	−	0.691112i
$958$	−28.0333	−	48.5551i	−0.905715	−	1.56874i
$959$	−6.40442	−	11.0928i	−0.206810	−	0.358205i
$960$		0			0
$961$	12.0599	−	20.8883i	0.389028	−	0.673816i
$962$	60.4240			1.94815
$963$	−25.9104	−	7.34070i	−0.834952	−	0.236551i
$964$	−92.0517			−2.96479
$965$		0			0
$966$	8.73515	−	11.2172i	0.281049	−	0.360906i
$967$	3.04790	+	5.27911i	0.0980137	+	0.169765i	0.910862	−	0.412710i	$-0.135418\pi$
$967$	3.04790	+	5.27911i	0.0980137	+	0.169765i	−0.812849	+	0.582475i	$0.802084\pi$
$968$	29.8943	+	51.7784i	0.960839	+	1.66422i
$969$	−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	$0.684338\pi$
$972$	−12.7603	+	75.8871i	−0.409288	+	2.43408i
$973$	26.4414			0.847671
$974$	12.6246	−	21.8665i	0.404519	−	0.700648i
$975$		0			0
$976$	66.4945	+	115.172i	2.12844	+	3.68656i
$977$	−24.3957	−	42.2546i	−0.780488	−	1.35184i	−0.931658	−	0.363337i	$-0.881637\pi$
$977$	−24.3957	−	42.2546i	−0.780488	−	1.35184i	0.151170	−	0.988508i	$-0.451696\pi$
$978$	−61.8277	+	79.3955i	−1.97703	+	2.53879i
$979$	12.0181	−	20.8160i	0.384100	−	0.665281i
$980$		0			0
$981$	−18.3045	−	5.18586i	−0.584418	−	0.165572i
$982$	−99.6715			−3.18065
$983$	−16.7086	+	28.9402i	−0.532922	+	0.923048i	0.466339	+	0.884606i	$0.345573\pi$
$983$	−16.7086	+	28.9402i	−0.532922	+	0.923048i	−0.999261	+	0.0384416i	$0.987761\pi$
$984$	−12.4256	−	30.6143i	−0.396113	−	0.975949i
$985$		0			0
$986$	46.6493	+	80.7989i	1.48562	+	2.57316i
$987$	−7.36691	−	18.1507i	−0.234491	−	0.577742i
$988$	−14.4289	+	24.9917i	−0.459046	+	0.795091i
$989$	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	$0.599444\pi$
$992$	15.9687	−	27.6586i	0.507006	−	0.878161i
$993$	13.4324	−	17.2491i	0.426265	−	0.547384i
$994$	3.01694	+	5.22549i	0.0956915	+	0.165743i
$995$		0			0
$996$	−9.30592	−	1.29279i	−0.294869	−	0.0409636i
$997$	−19.7721	+	34.2463i	−0.626189	+	1.08459i	0.362121	+	0.932131i	$0.382053\pi$
$997$	−19.7721	+	34.2463i	−0.626189	+	1.08459i	−0.988310	+	0.152460i	$0.951281\pi$
$998$	44.5766			1.41105
$999$	−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.e.c.151.1	yes	8
3.2	odd	2		675.2.e.e.451.4		8
5.2	odd	4		225.2.k.c.124.1		16
5.3	odd	4		225.2.k.c.124.8		16
5.4	even	2		225.2.e.e.151.4	yes	8
9.2	odd	6		2025.2.a.p.1.1		4
9.4	even	3	inner	225.2.e.c.76.1	✓	8
9.5	odd	6		675.2.e.e.226.4		8
9.7	even	3		2025.2.a.y.1.4		4
15.2	even	4		675.2.k.c.424.8		16
15.8	even	4		675.2.k.c.424.1		16
15.14	odd	2		675.2.e.c.451.1		8
45.2	even	12		2025.2.b.o.649.1		8
45.4	even	6		225.2.e.e.76.4	yes	8
45.7	odd	12		2025.2.b.n.649.8		8
45.13	odd	12		225.2.k.c.49.1		16
45.14	odd	6		675.2.e.c.226.1		8
45.22	odd	12		225.2.k.c.49.8		16
45.23	even	12		675.2.k.c.199.8		16
45.29	odd	6		2025.2.a.z.1.4		4
45.32	even	12		675.2.k.c.199.1		16
45.34	even	6		2025.2.a.q.1.1		4
45.38	even	12		2025.2.b.o.649.8		8
45.43	odd	12		2025.2.b.n.649.1		8

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

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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31686 + 2.28087i) q^{2} +(-1.71558 - 0.238330i) q^{3} +(-2.46825 - 4.27513i) q^{4} +(2.80278 - 3.59916i) q^{6} +(0.898714 - 1.55662i) q^{7} +7.73393 q^{8} +(2.88640 + 0.817746i) q^{9} +O(q^{10})\)	\(q+(-1.31686 + 2.28087i) q^{2} +(-1.71558 - 0.238330i) q^{3} +(-2.46825 - 4.27513i) q^{4} +(2.80278 - 3.59916i) q^{6} +(0.898714 - 1.55662i) q^{7} +7.73393 q^{8} +(2.88640 + 0.817746i) q^{9} +(-0.904062 + 1.56588i) q^{11} +(3.21558 + 7.92257i) q^{12} +(-0.985914 - 1.70765i) q^{13} +(2.36696 + 4.09970i) q^{14} +(-5.24801 + 9.08982i) q^{16} +4.80812 q^{17} +(-5.66616 + 5.50664i) q^{18} +2.96467 q^{19} +(-1.91280 + 2.45630i) q^{21} +(-2.38105 - 4.12410i) q^{22} +(0.866963 + 1.50162i) q^{23} +(-13.2681 - 1.84323i) q^{24} +5.19325 q^{26} +(-4.75694 - 2.09082i) q^{27} -8.87300 q^{28} +(3.68382 - 6.38057i) q^{29} +(1.31151 + 2.27161i) q^{31} +(-6.08789 - 10.5445i) q^{32} +(1.92418 - 2.47092i) q^{33} +(-6.33163 + 10.9667i) q^{34} +(-3.62838 - 14.3581i) q^{36} +11.6351 q^{37} +(-3.90406 + 6.76203i) q^{38} +(1.28442 + 3.16458i) q^{39} +(1.23324 + 2.13603i) q^{41} +(-3.08362 - 7.59746i) q^{42} +(3.63907 - 6.30306i) q^{43} +8.92580 q^{44} -4.56668 q^{46} +(-3.14604 + 5.44910i) q^{47} +(11.1697 - 14.3435i) q^{48} +(1.88463 + 3.26427i) q^{49} +(-8.24870 - 1.14592i) q^{51} +(-4.86696 + 8.42983i) q^{52} +1.72540 q^{53} +(11.0331 - 8.09664i) q^{54} +(6.95059 - 12.0388i) q^{56} +(-5.08612 - 0.706570i) q^{57} +(9.70218 + 16.8047i) q^{58} +(-5.51300 - 9.54880i) q^{59} +(6.33521 - 10.9729i) q^{61} -6.90833 q^{62} +(3.86696 - 3.75810i) q^{63} +11.0756 q^{64} +(3.10197 + 7.64268i) q^{66} +(-4.55187 - 7.88407i) q^{67} +(-11.8676 - 20.5554i) q^{68} +(-1.12946 - 2.78277i) q^{69} +1.27460 q^{71} +(22.3232 + 6.32439i) q^{72} -3.58770 q^{73} +(-15.3218 + 26.5382i) q^{74} +(-7.31755 - 12.6744i) q^{76} +(1.62499 + 2.81456i) q^{77} +(-8.90941 - 1.23771i) q^{78} +(-1.05545 + 1.82809i) q^{79} +(7.66258 + 4.72068i) q^{81} -6.49602 q^{82} +(-0.549415 + 0.951614i) q^{83} +(15.2223 + 2.11470i) q^{84} +(9.58431 + 16.6005i) q^{86} +(-7.84056 + 10.0684i) q^{87} +(-6.99195 + 12.1104i) q^{88} -13.2935 q^{89} -3.54422 q^{91} +(4.27976 - 7.41277i) q^{92} +(-1.70861 - 4.20969i) q^{93} +(-8.28580 - 14.3514i) q^{94} +(7.93115 + 19.5409i) q^{96} +(1.91638 - 3.31926i) q^{97} -9.92718 q^{98} +(-3.88998 + 3.78046i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + q^{3} - 4 q^{4} + 8 q^{6} + q^{7} + 18 q^{8} + 5 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + q^3 - 4 * q^4 + 8 * q^6 + q^7 + 18 * q^8 + 5 * q^9	\( 8 q - 2 q^{2} + q^{3} - 4 q^{4} + 8 q^{6} + q^{7} + 18 q^{8} + 5 q^{9} + q^{11} + 11 q^{12} - 2 q^{13} - 3 q^{14} - 4 q^{16} + 22 q^{17} - 5 q^{18} + 4 q^{19} - 15 q^{21} - 3 q^{22} - 15 q^{23} - 33 q^{24} - 20 q^{26} - 2 q^{27} - 8 q^{28} - q^{29} + 4 q^{31} - 10 q^{32} - 28 q^{33} - 9 q^{34} - 14 q^{36} - 2 q^{37} - 23 q^{38} + 25 q^{39} + 5 q^{41} - 21 q^{42} + 10 q^{43} + 44 q^{44} - 20 q^{47} + 53 q^{48} + 3 q^{49} + 11 q^{51} - 17 q^{52} + 40 q^{53} + 26 q^{54} + 30 q^{56} - 8 q^{57} + 18 q^{58} - 17 q^{59} + 13 q^{61} - 12 q^{62} + 9 q^{63} + 38 q^{64} - 8 q^{66} - 17 q^{67} - 34 q^{68} - 27 q^{69} - 16 q^{71} + 18 q^{72} + 4 q^{73} - 40 q^{74} - 11 q^{76} - 12 q^{77} - 61 q^{78} + 7 q^{79} + 17 q^{81} + 24 q^{82} - 30 q^{83} + 27 q^{84} + 34 q^{86} - 23 q^{87} - 9 q^{88} - 18 q^{89} - 34 q^{91} + 12 q^{92} + 15 q^{93} - 3 q^{94} + 34 q^{96} + 19 q^{97} + 26 q^{98} - 17 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + q^3 - 4 * q^4 + 8 * q^6 + q^7 + 18 * q^8 + 5 * q^9 + q^11 + 11 * q^12 - 2 * q^13 - 3 * q^14 - 4 * q^16 + 22 * q^17 - 5 * q^18 + 4 * q^19 - 15 * q^21 - 3 * q^22 - 15 * q^23 - 33 * q^24 - 20 * q^26 - 2 * q^27 - 8 * q^28 - q^29 + 4 * q^31 - 10 * q^32 - 28 * q^33 - 9 * q^34 - 14 * q^36 - 2 * q^37 - 23 * q^38 + 25 * q^39 + 5 * q^41 - 21 * q^42 + 10 * q^43 + 44 * q^44 - 20 * q^47 + 53 * q^48 + 3 * q^49 + 11 * q^51 - 17 * q^52 + 40 * q^53 + 26 * q^54 + 30 * q^56 - 8 * q^57 + 18 * q^58 - 17 * q^59 + 13 * q^61 - 12 * q^62 + 9 * q^63 + 38 * q^64 - 8 * q^66 - 17 * q^67 - 34 * q^68 - 27 * q^69 - 16 * q^71 + 18 * q^72 + 4 * q^73 - 40 * q^74 - 11 * q^76 - 12 * q^77 - 61 * q^78 + 7 * q^79 + 17 * q^81 + 24 * q^82 - 30 * q^83 + 27 * q^84 + 34 * q^86 - 23 * q^87 - 9 * q^88 - 18 * q^89 - 34 * q^91 + 12 * q^92 + 15 * q^93 - 3 * q^94 + 34 * q^96 + 19 * q^97 + 26 * q^98 - 17 * q^99

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