LMFDB - Embedded newform 525.2.t.h.26.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(26,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("525.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.t (of order $6$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 8 x^{18} - 15 x^{17} + 18 x^{16} - 45 x^{15} + 59 x^{14} - 147 x^{13} + 271 x^{12} + \cdots + 59049 $ x^20 - 3x^19 + 8x^18 - 15x^17 + 18x^16 - 45x^15 + 59x^14 - 147x^13 + 271x^12 - 330x^11 + 879x^10 - 990x^9 + 2439x^8 - 3969x^7 + 4779x^6 - 10935x^5 + 13122x^4 - 32805x^3 + 52488x^2 - 59049*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.5
Root			$-1.39625 - 1.02493i$ of defining polynomial
Character	$\chi$	$=$	525.26
Dual form			525.2.t.h.101.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766266 - 0.442404i) q^{2} +(1.39625 + 1.02493i) q^{3} +(-0.608557 - 1.05405i) q^{4} +(-0.616465 - 1.40308i) q^{6} +(-2.63771 - 0.206062i) q^{7} +2.84653i q^{8} +(0.899028 + 2.86212i) q^{9} +O(q^{10})$	\(q+(-0.766266 - 0.442404i) q^{2} +(1.39625 + 1.02493i) q^{3} +(-0.608557 - 1.05405i) q^{4} +(-0.616465 - 1.40308i) q^{6} +(-2.63771 - 0.206062i) q^{7} +2.84653i q^{8} +(0.899028 + 2.86212i) q^{9} +(-1.25362 + 0.723775i) q^{11} +(0.230634 - 2.09545i) q^{12} +4.04326i q^{13} +(1.93003 + 1.32483i) q^{14} +(0.0422021 - 0.0730962i) q^{16} +(2.87862 + 4.98592i) q^{17} +(0.577320 - 2.59088i) q^{18} +(-0.356910 - 0.206062i) q^{19} +(-3.47171 - 2.99119i) q^{21} +1.28081 q^{22} +(6.33444 + 3.65719i) q^{23} +(-2.91750 + 3.97447i) q^{24} +(1.78875 - 3.09821i) q^{26} +(-1.67821 + 4.91768i) q^{27} +(1.38800 + 2.90569i) q^{28} -1.82121i q^{29} +(2.30936 - 1.33331i) q^{31} +(4.86566 - 2.80919i) q^{32} +(-2.49218 - 0.274300i) q^{33} -5.09406i q^{34} +(2.46972 - 2.68939i) q^{36} +(2.92387 - 5.06429i) q^{37} +(0.182325 + 0.315797i) q^{38} +(-4.14406 + 5.64540i) q^{39} -6.46287 q^{41} +(1.33694 + 3.82795i) q^{42} -10.3583 q^{43} +(1.52579 + 0.880917i) q^{44} +(-3.23592 - 5.60477i) q^{46} +(-5.43364 + 9.41134i) q^{47} +(0.133843 - 0.0588063i) q^{48} +(6.91508 + 1.08706i) q^{49} +(-1.09095 + 9.91198i) q^{51} +(4.26180 - 2.46055i) q^{52} +(-1.20893 + 0.697977i) q^{53} +(3.46156 - 3.02581i) q^{54} +(0.586561 - 7.50833i) q^{56} +(-0.287136 - 0.653522i) q^{57} +(-0.805713 + 1.39554i) q^{58} +(0.583941 + 1.01142i) q^{59} +(3.58903 + 2.07213i) q^{61} -2.35944 q^{62} +(-1.78160 - 7.73472i) q^{63} -5.14000 q^{64} +(1.78832 + 1.31274i) q^{66} +(-3.46011 - 5.99309i) q^{67} +(3.50361 - 6.06843i) q^{68} +(5.09609 + 11.5987i) q^{69} +13.3217i q^{71} +(-8.14712 + 2.55911i) q^{72} +(2.72344 - 1.57238i) q^{73} +(-4.48093 + 2.58707i) q^{74} +0.501602i q^{76} +(3.45582 - 1.65079i) q^{77} +(5.67300 - 2.49253i) q^{78} +(6.42216 - 11.1235i) q^{79} +(-7.38350 + 5.14626i) q^{81} +(4.95228 + 2.85920i) q^{82} -11.5010 q^{83} +(-1.04014 + 5.47967i) q^{84} +(7.93724 + 4.58257i) q^{86} +(1.86662 - 2.54287i) q^{87} +(-2.06025 - 3.56845i) q^{88} +(3.90111 - 6.75692i) q^{89} +(0.833161 - 10.6650i) q^{91} -8.90244i q^{92} +(4.59099 + 0.505303i) q^{93} +(8.32723 - 4.80773i) q^{94} +(9.67290 + 1.06464i) q^{96} +3.86099i q^{97} +(-4.81787 - 3.89224i) q^{98} +(-3.19857 - 2.93731i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{3} + 14 q^{4} - 7 q^{9}+O(q^{10}) $ 20 * q - 3 * q^3 + 14 * q^4 - 7 * q^9	$ 20 q - 3 q^{3} + 14 q^{4} - 7 q^{9} + 21 q^{12} - 18 q^{16} - 14 q^{18} - 9 q^{21} - 20 q^{22} + 18 q^{24} + 10 q^{28} + 42 q^{31} - 12 q^{33} - 36 q^{36} - 24 q^{37} - 33 q^{42} - 36 q^{43} - 8 q^{46} - 4 q^{49} + 21 q^{51} + 84 q^{52} - 75 q^{54} - 6 q^{57} + 4 q^{58} - 90 q^{61} + 5 q^{63} - 120 q^{64} + 6 q^{66} - 20 q^{67} + 35 q^{72} + 48 q^{73} + 108 q^{78} + 46 q^{79} + 29 q^{81} - 36 q^{82} + 75 q^{84} - 69 q^{87} - 4 q^{88} - 30 q^{91} + 30 q^{93} + 6 q^{94} + 135 q^{96} + 94 q^{99}+O(q^{100}) $ 20 * q - 3 * q^3 + 14 * q^4 - 7 * q^9 + 21 * q^12 - 18 * q^16 - 14 * q^18 - 9 * q^21 - 20 * q^22 + 18 * q^24 + 10 * q^28 + 42 * q^31 - 12 * q^33 - 36 * q^36 - 24 * q^37 - 33 * q^42 - 36 * q^43 - 8 * q^46 - 4 * q^49 + 21 * q^51 + 84 * q^52 - 75 * q^54 - 6 * q^57 + 4 * q^58 - 90 * q^61 + 5 * q^63 - 120 * q^64 + 6 * q^66 - 20 * q^67 + 35 * q^72 + 48 * q^73 + 108 * q^78 + 46 * q^79 + 29 * q^81 - 36 * q^82 + 75 * q^84 - 69 * q^87 - 4 * q^88 - 30 * q^91 + 30 * q^93 + 6 * q^94 + 135 * q^96 + 94 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.766266	−	0.442404i	−0.541832	−	0.312827i	0.203989	−	0.978973i	$-0.434609\pi$
$2$	−0.766266	−	0.442404i	−0.541832	−	0.312827i	−0.745821	+	0.666146i	$0.767943\pi$
$3$	1.39625	+	1.02493i	0.806125	+	0.591745i
$3$	1.39625	+	1.02493i	0.806125	+	0.591745i
$4$	−0.608557	−	1.05405i	−0.304279	−	0.527026i
$5$		0			0
$5$		0			0
$6$	−0.616465	−	1.40308i	−0.251671	−	0.572804i
$7$	−2.63771	−	0.206062i	−0.996962	−	0.0778841i
$7$	−2.63771	−	0.206062i	−0.996962	−	0.0778841i
$8$			2.84653i			1.00640i
$9$	0.899028	+	2.86212i	0.299676	+	0.954041i
$10$		0			0
$11$	−1.25362	+	0.723775i	−0.377979	+	0.218227i	−0.676939	−	0.736039i	$-0.736694\pi$
$11$	−1.25362	+	0.723775i	−0.377979	+	0.218227i	0.298959	+	0.954266i	$0.403360\pi$
$12$	0.230634	−	2.09545i	0.0665783	−	0.604904i
$13$			4.04326i			1.12140i	0.828020	+	0.560699i	$0.189467\pi$
$13$			4.04326i			1.12140i	−0.828020	+	0.560699i	$0.810533\pi$
$14$	1.93003	+	1.32483i	0.515822	+	0.354077i
$15$		0			0
$16$	0.0422021	−	0.0730962i	0.0105505	−	0.0182741i
$17$	2.87862	+	4.98592i	0.698168	+	1.20926i	0.969101	+	0.246665i	$0.0793346\pi$
$17$	2.87862	+	4.98592i	0.698168	+	1.20926i	−0.270933	+	0.962598i	$0.587332\pi$
$18$	0.577320	−	2.59088i	0.136076	−	0.610677i
$19$	−0.356910	−	0.206062i	−0.0818807	−	0.0472738i	0.458501	−	0.888694i	$-0.348387\pi$
$19$	−0.356910	−	0.206062i	−0.0818807	−	0.0472738i	−0.540381	+	0.841420i	$0.681720\pi$
$20$		0			0
$21$	−3.47171	−	2.99119i	−0.757589	−	0.652732i
$22$	1.28081			0.273069
$23$	6.33444	+	3.65719i	1.32082	+	0.762578i	0.983860	−	0.178940i	$-0.0572669\pi$
$23$	6.33444	+	3.65719i	1.32082	+	0.762578i	0.336963	+	0.941518i	$0.390600\pi$
$24$	−2.91750	+	3.97447i	−0.595532	+	0.811285i
$25$		0			0
$26$	1.78875	−	3.09821i	0.350803	−	0.607609i
$27$	−1.67821	+	4.91768i	−0.322973	+	0.946408i
$28$	1.38800	+	2.90569i	0.262307	+	0.549124i
$29$		−	1.82121i		−	0.338191i	−0.985600	−	0.169095i	$-0.945915\pi$
$29$		−	1.82121i		−	0.338191i	0.985600	−	0.169095i	$-0.0540846\pi$
$30$		0			0
$31$	2.30936	−	1.33331i	0.414772	−	0.239469i	−0.278066	−	0.960562i	$-0.589693\pi$
$31$	2.30936	−	1.33331i	0.414772	−	0.239469i	0.692838	+	0.721093i	$0.256360\pi$
$32$	4.86566	−	2.80919i	0.860135	−	0.496599i
$33$	−2.49218	−	0.274300i	−0.433833	−	0.0477495i
$34$		−	5.09406i		−	0.873623i
$35$		0			0
$36$	2.46972	−	2.68939i	0.411619	−	0.448231i
$37$	2.92387	−	5.06429i	0.480682	−	0.832565i	−0.519073	−	0.854730i	$-0.673723\pi$
$37$	2.92387	−	5.06429i	0.480682	−	0.832565i	0.999754	+	0.0221652i	$0.00705597\pi$
$38$	0.182325	+	0.315797i	0.0295771	+	0.0512290i
$39$	−4.14406	+	5.64540i	−0.663581	+	0.903987i
$40$		0			0
$41$	−6.46287			−1.00933			−0.504665	−	0.863315i	$-0.668384\pi$
$41$	−6.46287			−1.00933			−0.504665	+	0.863315i	$0.668384\pi$
$42$	1.33694	+	3.82795i	0.206294	+	0.590665i
$43$	−10.3583			−1.57963			−0.789815	−	0.613345i	$-0.789823\pi$
$43$	−10.3583			−1.57963			−0.789815	+	0.613345i	$0.789823\pi$
$44$	1.52579	+	0.880917i	0.230022	+	0.132803i
$45$		0			0
$46$	−3.23592	−	5.60477i	−0.477110	−	0.826378i
$47$	−5.43364	+	9.41134i	−0.792578	+	1.37279i	0.131788	+	0.991278i	$0.457928\pi$
$47$	−5.43364	+	9.41134i	−0.792578	+	1.37279i	−0.924366	+	0.381507i	$0.875405\pi$
$48$	0.133843	−	0.0588063i	0.0193186	−	0.00848796i
$49$	6.91508	+	1.08706i	0.987868	+	0.155295i
$50$		0			0
$51$	−1.09095	+	9.91198i	−0.152764	+	1.38795i
$52$	4.26180	−	2.46055i	0.591005	−	0.341217i
$53$	−1.20893	+	0.697977i	−0.166059	+	0.0958745i	−0.580726	−	0.814099i	$-0.697231\pi$
$53$	−1.20893	+	0.697977i	−0.166059	+	0.0958745i	0.414667	+	0.909973i	$0.363898\pi$
$54$	3.46156	−	3.02581i	0.471059	−	0.411760i
$55$		0			0
$56$	0.586561	−	7.50833i	0.0783825	−	1.00334i
$57$	−0.287136	−	0.653522i	−0.0380320	−	0.0865611i
$58$	−0.805713	+	1.39554i	−0.105795	+	0.183243i
$59$	0.583941	+	1.01142i	0.0760227	+	0.131675i	0.901531	−	0.432715i	$-0.142445\pi$
$59$	0.583941	+	1.01142i	0.0760227	+	0.131675i	−0.825508	+	0.564391i	$0.809111\pi$
$60$		0			0
$61$	3.58903	+	2.07213i	0.459529	+	0.265309i	0.711846	−	0.702335i	$-0.247859\pi$
$61$	3.58903	+	2.07213i	0.459529	+	0.265309i	−0.252317	+	0.967645i	$0.581193\pi$
$62$	−2.35944			−0.299649
$63$	−1.78160	−	7.73472i	−0.224461	−	0.974483i
$64$	−5.14000			−0.642499
$65$		0			0
$66$	1.78832	+	1.31274i	0.220127	+	0.161587i
$67$	−3.46011	−	5.99309i	−0.422720	−	0.732173i	0.573484	−	0.819217i	$-0.305591\pi$
$67$	−3.46011	−	5.99309i	−0.422720	−	0.732173i	−0.996205	+	0.0870436i	$0.972258\pi$
$68$	3.50361	−	6.06843i	0.424875	−	0.735906i
$69$	5.09609	+	11.5987i	0.613497	+	1.39632i
$70$		0			0
$71$			13.3217i			1.58100i	0.612463	+	0.790499i	$0.290179\pi$
$71$			13.3217i			1.58100i	−0.612463	+	0.790499i	$0.709821\pi$
$72$	−8.14712	+	2.55911i	−0.960147	+	0.301594i
$73$	2.72344	−	1.57238i	0.318755	−	0.184033i	−0.332082	−	0.943250i	$-0.607751\pi$
$73$	2.72344	−	1.57238i	0.318755	−	0.184033i	0.650838	+	0.759217i	$0.274418\pi$
$74$	−4.48093	+	2.58707i	−0.520898	+	0.300740i
$75$		0			0
$76$			0.501602i			0.0575377i
$77$	3.45582	−	1.65079i	0.393828	−	0.188125i
$78$	5.67300	−	2.49253i	0.642341	−	0.282223i
$79$	6.42216	−	11.1235i	0.722550	−	1.25149i	−0.237425	−	0.971406i	$-0.576303\pi$
$79$	6.42216	−	11.1235i	0.722550	−	1.25149i	0.959975	−	0.280087i	$-0.0903633\pi$
$80$		0			0
$81$	−7.38350	+	5.14626i	−0.820389	+	0.571806i
$82$	4.95228	+	2.85920i	0.546888	+	0.315746i
$83$	−11.5010			−1.26240			−0.631200	−	0.775620i	$-0.717437\pi$
$83$	−11.5010			−1.26240			−0.631200	+	0.775620i	$0.717437\pi$
$84$	−1.04014	+	5.47967i	−0.113488	+	0.597881i
$85$		0			0
$86$	7.93724	+	4.58257i	0.855894	+	0.494151i
$87$	1.86662	−	2.54287i	0.200123	−	0.272624i
$88$	−2.06025	−	3.56845i	−0.219623	−	0.380399i
$89$	3.90111	−	6.75692i	0.413517	−	0.716232i	−0.581755	−	0.813364i	$-0.697634\pi$
$89$	3.90111	−	6.75692i	0.413517	−	0.716232i	0.995271	+	0.0971324i	$0.0309670\pi$
$90$		0			0
$91$	0.833161	−	10.6650i	0.0873390	−	1.11799i
$92$		−	8.90244i		−	0.928144i
$93$	4.59099	+	0.505303i	0.476063	+	0.0523975i
$94$	8.32723	−	4.80773i	0.858889	−	0.495880i
$95$		0			0
$96$	9.67290	+	1.06464i	0.987236	+	0.108659i
$97$			3.86099i			0.392024i	0.980601	+	0.196012i	$0.0627992\pi$
$97$			3.86099i			0.392024i	−0.980601	+	0.196012i	$0.937201\pi$
$98$	−4.81787	−	3.89224i	−0.486678	−	0.393176i
$99$	−3.19857	−	2.93731i	−0.321468	−	0.295211i
$100$		0			0
$101$	6.61336	+	11.4547i	0.658054	+	1.13978i	0.981119	+	0.193406i	$0.0619535\pi$
$101$	6.61336	+	11.4547i	0.658054	+	1.13978i	−0.323065	+	0.946377i	$0.604713\pi$
$102$	5.22106	−	7.11258i	0.516962	−	0.704250i
$103$	14.7144	+	8.49538i	1.44986	+	0.837075i	0.998472	−	0.0552547i	$-0.0175971\pi$
$103$	14.7144	+	8.49538i	1.44986	+	0.837075i	0.451384	+	0.892330i	$0.350930\pi$
$104$	−11.5092			−1.12857
$105$		0			0
$106$	1.23515			0.119968
$107$	−11.2134	−	6.47403i	−1.08404	−	0.625868i	−0.152054	−	0.988372i	$-0.548589\pi$
$107$	−11.2134	−	6.47403i	−1.08404	−	0.625868i	−0.931982	+	0.362504i	$0.881922\pi$
$108$	6.20478	−	1.22376i	0.597055	−	0.117757i
$109$	−3.63427	−	6.29474i	−0.348100	−	0.602927i	0.637812	−	0.770192i	$-0.279840\pi$
$109$	−3.63427	−	6.29474i	−0.348100	−	0.602927i	−0.985912	+	0.167265i	$0.946506\pi$
$110$		0			0
$111$	9.27301	−	4.07425i	0.880156	−	0.386711i
$112$	−0.126380	+	0.184111i	−0.0119417	+	0.0173968i
$113$		−	4.78517i		−	0.450151i	−0.974341	−	0.225075i	$-0.927737\pi$
$113$		−	4.78517i		−	0.450151i	0.974341	−	0.225075i	$-0.0722628\pi$
$114$	−0.0690985	+	0.627802i	−0.00647167	+	0.0587990i
$115$		0			0
$116$	−1.91965	+	1.10831i	−0.178235	+	0.102904i
$117$	−11.5723	+	3.63500i	−1.06986	+	0.336056i
$118$		−	1.03335i		−	0.0951278i
$119$	−6.56557	−	13.7446i	−0.601865	−	1.25997i
$120$		0			0
$121$	−4.45230	+	7.71161i	−0.404754	+	0.701055i
$122$	−1.83344	−	3.17561i	−0.165992	−	0.287506i
$123$	−9.02378	−	6.62400i	−0.813647	−	0.597266i
$124$	−2.81075	−	1.62279i	−0.252413	−	0.145731i
$125$		0			0
$126$	−2.05669	+	6.71505i	−0.183224	+	0.598224i
$127$	−9.16192			−0.812989			−0.406495	−	0.913653i	$-0.633249\pi$
$127$	−9.16192			−0.812989			−0.406495	+	0.913653i	$0.633249\pi$
$128$	−5.79271	−	3.34442i	−0.512008	−	0.295608i
$129$	−14.4628	−	10.6166i	−1.27338	−	0.934738i
$130$		0			0
$131$	10.4220	−	18.0514i	0.910574	−	1.57716i	0.0973191	−	0.995253i	$-0.468973\pi$
$131$	10.4220	−	18.0514i	0.910574	−	1.57716i	0.813255	−	0.581907i	$-0.197693\pi$
$132$	1.22751	+	2.79382i	0.106841	+	0.243170i
$133$	0.898964	+	0.617078i	0.0779501	+	0.0535074i
$134$			6.12308i			0.528953i
$135$		0			0
$136$	−14.1926	+	8.19408i	−1.21700	+	0.702637i
$137$	8.20795	−	4.73886i	0.701253	−	0.404868i	−0.106561	−	0.994306i	$-0.533984\pi$
$137$	8.20795	−	4.73886i	0.701253	−	0.404868i	0.807814	+	0.589438i	$0.200651\pi$
$138$	1.22636	−	11.1423i	0.104395	−	0.948492i
$139$		−	5.75447i		−	0.488088i	−0.969764	−	0.244044i	$-0.921526\pi$
$139$		−	5.75447i		−	0.488088i	0.969764	−	0.244044i	$-0.0784741\pi$
$140$		0			0
$141$	−17.2327	+	7.57147i	−1.45126	+	0.637633i
$142$	5.89359	−	10.2080i	0.494579	−	0.856636i
$143$	−2.92641	−	5.06869i	−0.244719	−	0.423865i
$144$	0.247151	+	0.0550721i	0.0205959	+	0.00458935i
$145$		0			0
$146$	−2.78251			−0.230282
$147$	8.54101	+	8.60530i	0.704450	+	0.709753i
$148$	−7.11737			−0.585044
$149$	5.57080	+	3.21630i	0.456378	+	0.263490i	0.710520	−	0.703677i	$-0.248460\pi$
$149$	5.57080	+	3.21630i	0.456378	+	0.263490i	−0.254142	+	0.967167i	$0.581793\pi$
$150$		0			0
$151$	−2.06002	−	3.56807i	−0.167642	−	0.290365i	0.769948	−	0.638107i	$-0.220282\pi$
$151$	−2.06002	−	3.56807i	−0.167642	−	0.290365i	−0.937591	+	0.347741i	$0.886949\pi$
$152$	0.586561	−	1.01595i	0.0475764	−	0.0824047i
$153$	−11.6824	+	12.7214i	−0.944462	+	1.02847i
$154$	−3.37840	−	0.263925i	−0.272239	−	0.0212677i
$155$		0			0
$156$	8.47244	+	0.932512i	0.678338	+	0.0746607i
$157$	1.07366	−	0.619880i	0.0856877	−	0.0494718i	−0.456544	−	0.889701i	$-0.650913\pi$
$157$	1.07366	−	0.619880i	0.0856877	−	0.0494718i	0.542232	+	0.840229i	$0.317580\pi$
$158$	−9.84218	+	5.68238i	−0.783001	+	0.452066i
$159$	−2.40335	−	0.264523i	−0.190598	−	0.0209780i
$160$		0			0
$161$	−15.9548	−	10.9519i	−1.25742	−	0.863132i
$162$	7.93445	−	0.676913i	0.623389	−	0.0531833i
$163$	3.72151	−	6.44585i	0.291491	−	0.504878i	−0.682671	−	0.730726i	$-0.739182\pi$
$163$	3.72151	−	6.44585i	0.291491	−	0.504878i	0.974163	+	0.225848i	$0.0725152\pi$
$164$	3.93302	+	6.81220i	0.307118	+	0.531943i
$165$		0			0
$166$	8.81284	+	5.08809i	0.684009	+	0.394913i
$167$	2.50723			0.194015			0.0970077	−	0.995284i	$-0.469073\pi$
$167$	2.50723			0.194015			0.0970077	+	0.995284i	$0.469073\pi$
$168$	8.51452	−	9.88232i	0.656909	−	0.762438i
$169$	−3.34791			−0.257532
$170$		0			0
$171$	0.268903	−	1.20677i	0.0205635	−	0.0922844i
$172$	6.30363	+	10.9182i	0.480647	+	0.832506i
$173$	8.52481	−	14.7654i	0.648130	−	1.12259i	−0.335440	−	0.942062i	$-0.608885\pi$
$173$	8.52481	−	14.7654i	0.648130	−	1.12259i	0.983569	−	0.180532i	$-0.0577818\pi$
$174$	−2.55531	+	1.12272i	−0.193717	+	0.0851128i
$175$		0			0
$176$			0.122179i			0.00920962i
$177$	−0.221305	+	2.01069i	−0.0166343	+	0.151133i
$178$	−5.97858	+	3.45173i	−0.448113	+	0.258718i
$179$	10.1751	−	5.87462i	0.760525	−	0.439090i	−0.0689590	−	0.997619i	$-0.521968\pi$
$179$	10.1751	−	5.87462i	0.760525	−	0.439090i	0.829484	+	0.558530i	$0.188634\pi$
$180$		0			0
$181$		−	2.41221i		−	0.179298i	−0.995973	−	0.0896490i	$-0.971425\pi$
$181$		−	2.41221i		−	0.179298i	0.995973	−	0.0896490i	$-0.0285745\pi$
$182$	−5.35664	+	7.80360i	−0.397061	+	0.578442i
$183$	2.88740	+	6.57173i	0.213442	+	0.485796i
$184$	−10.4103	+	18.0312i	−0.767458	+	1.32928i
$185$		0			0
$186$	−3.29437	−	2.41827i	−0.241555	−	0.177316i
$187$	−7.21737	−	4.16695i	−0.527786	−	0.304718i
$188$	13.2267			0.964658
$189$	5.44000	−	12.6256i	0.395702	−	0.918379i
$190$		0			0
$191$	11.9159	+	6.87963i	0.862202	+	0.497793i	0.864749	−	0.502204i	$-0.167477\pi$
$191$	11.9159	+	6.87963i	0.862202	+	0.497793i	−0.00254675	+	0.999997i	$0.500811\pi$
$192$	−7.17672	−	5.26815i	−0.517935	−	0.380196i
$193$	4.60685	+	7.97929i	0.331608	+	0.574362i	0.982827	−	0.184528i	$-0.0590755\pi$
$193$	4.60685	+	7.97929i	0.331608	+	0.574362i	−0.651219	+	0.758890i	$0.725742\pi$
$194$	1.70812	−	2.95855i	0.122636	−	0.212411i
$195$		0			0
$196$	−3.06240	−	7.95039i	−0.218743	−	0.567885i
$197$			4.11728i			0.293344i	0.989185	+	0.146672i	$0.0468562\pi$
$197$			4.11728i			0.293344i	−0.989185	+	0.146672i	$0.953144\pi$
$198$	1.15148	+	3.66582i	0.0818321	+	0.260519i
$199$	0.0694265	−	0.0400834i	0.00492151	−	0.00284144i	−0.497537	−	0.867443i	$-0.665762\pi$
$199$	0.0694265	−	0.0400834i	0.00492151	−	0.00284144i	0.502459	+	0.864601i	$0.332429\pi$
$200$		0			0
$201$	1.31133	−	11.9142i	0.0924941	−	0.840366i
$202$		−	11.7031i		−	0.823428i
$203$	−0.375283	+	4.80384i	−0.0263397	+	0.337164i
$204$	11.1116	−	4.88208i	0.777971	−	0.341814i
$205$		0			0
$206$	−7.51679	−	13.0195i	−0.523719	−	0.907108i
$207$	−4.77250	+	21.4179i	−0.331711	+	1.48865i
$208$	0.295547	+	0.170634i	0.0204925	+	0.0118313i
$209$	0.596570			0.0412656
$210$		0			0
$211$	17.5804			1.21028			0.605141	−	0.796118i	$-0.293117\pi$
$211$	17.5804			1.21028			0.605141	+	0.796118i	$0.293117\pi$
$212$	1.47141	+	0.849517i	0.101057	+	0.0583451i
$213$	−13.6539	+	18.6005i	−0.935548	+	1.27448i
$214$	5.72828	+	9.92167i	0.391577	+	0.678231i
$215$		0			0
$216$	−13.9983	−	4.77709i	−0.952465	−	0.325040i
$217$	−6.36616	+	3.04101i	−0.432163	+	0.206437i
$218$			6.43127i			0.435580i
$219$	5.41419	+	0.595909i	0.365857	+	0.0402678i
$220$		0			0
$221$	−20.1593	+	11.6390i	−1.35606	+	0.782924i
$222$	−8.90807	−	0.980459i	−0.597870	−	0.0658041i
$223$		−	27.4965i		−	1.84130i	−0.390387	−	0.920651i	$-0.627659\pi$
$223$		−	27.4965i		−	1.84130i	0.390387	−	0.920651i	$-0.372341\pi$
$224$	−13.4131	+	6.40721i	−0.896199	+	0.428100i
$225$		0			0
$226$	−2.11698	+	3.66671i	−0.140819	+	0.243906i
$227$	−6.20253	−	10.7431i	−0.411676	−	0.713044i	0.583397	−	0.812187i	$-0.301723\pi$
$227$	−6.20253	−	10.7431i	−0.411676	−	0.713044i	−0.995073	+	0.0991431i	$0.968390\pi$
$228$	−0.514108	+	0.700361i	−0.0340476	+	0.0463826i
$229$	23.5513	+	13.5973i	1.55631	+	0.898538i	0.997605	+	0.0691740i	$0.0220364\pi$
$229$	23.5513	+	13.5973i	1.55631	+	0.898538i	0.558709	+	0.829364i	$0.311297\pi$
$230$		0			0
$231$	6.51714	+	1.23707i	0.428796	+	0.0813931i
$232$	5.18414			0.340355
$233$	25.0585	+	14.4675i	1.64163	+	0.947798i	0.980253	+	0.197749i	$0.0633632\pi$
$233$	25.0585	+	14.4675i	1.64163	+	0.947798i	0.661382	+	0.750049i	$0.269970\pi$
$234$	10.4756	+	2.33425i	0.684811	+	0.152595i
$235$		0			0
$236$	0.710723	−	1.23101i	0.0462641	−	0.0801318i
$237$	20.3678	−	8.94892i	1.32303	−	0.581295i
$238$	−1.04969	+	13.4367i	−0.0680413	+	0.870970i
$239$			19.2419i			1.24465i	0.782757	+	0.622327i	$0.213813\pi$
$239$			19.2419i			1.24465i	−0.782757	+	0.622327i	$0.786187\pi$
$240$		0			0
$241$	4.90603	−	2.83250i	0.316025	−	0.182457i	−0.333594	−	0.942717i	$-0.608262\pi$
$241$	4.90603	−	2.83250i	0.316025	−	0.182457i	0.649619	+	0.760260i	$0.274928\pi$
$242$	6.82329	−	3.93943i	0.438618	−	0.253236i
$243$	−15.5838	−	0.382125i	−0.999700	−	0.0245133i
$244$		−	5.04404i		−	0.322911i
$245$		0			0
$246$	3.98413	+	9.06791i	0.254019	+	0.578149i
$247$	0.833161	−	1.44308i	0.0530127	−	0.0918208i
$248$	3.79530	+	6.57365i	0.241002	+	0.417427i
$249$	−16.0583	−	11.7878i	−1.01765	−	0.747018i
$250$		0			0
$251$	6.55844			0.413965			0.206983	−	0.978345i	$-0.433636\pi$
$251$	6.55844			0.413965			0.206983	+	0.978345i	$0.433636\pi$
$252$	−7.06859	+	6.58492i	−0.445279	+	0.414811i
$253$	−10.5879			−0.665659
$254$	7.02047	+	4.05327i	0.440504	+	0.254325i
$255$		0			0
$256$	8.09917	+	14.0282i	0.506198	+	0.876761i
$257$	−4.36647	+	7.56295i	−0.272373	+	0.471764i	−0.969469	−	0.245214i	$-0.921142\pi$
$257$	−4.36647	+	7.56295i	−0.272373	+	0.471764i	0.697096	+	0.716978i	$0.254475\pi$
$258$	6.38555	+	14.5335i	0.397547	+	0.904818i
$259$	−8.75590	+	12.7557i	−0.544065	+	0.792598i
$260$		0			0
$261$	5.21254	−	1.63732i	0.322648	−	0.101348i
$262$	−15.9721	+	9.22147i	−0.986757	+	0.569704i
$263$	−19.5217	+	11.2709i	−1.20376	+	0.694992i	−0.961389	−	0.275192i	$-0.911259\pi$
$263$	−19.5217	+	11.2709i	−1.20376	+	0.694992i	−0.242372	+	0.970183i	$0.577925\pi$
$264$	0.780803	−	7.09407i	0.0480551	−	0.436610i
$265$		0			0
$266$	−0.415848	−	0.870551i	−0.0254973	−	0.0533769i
$267$	12.3723	−	5.43597i	0.757173	−	0.332676i
$268$	−4.21135	+	7.29428i	−0.257249	+	0.445569i
$269$	7.09460	+	12.2882i	0.432565	+	0.749225i	0.997093	−	0.0761890i	$-0.0242752\pi$
$269$	7.09460	+	12.2882i	0.432565	+	0.749225i	−0.564528	+	0.825414i	$0.690942\pi$
$270$		0			0
$271$	−11.0247	−	6.36513i	−0.669705	−	0.386654i	0.126260	−	0.991997i	$-0.459703\pi$
$271$	−11.0247	−	6.36513i	−0.669705	−	0.386654i	−0.795965	+	0.605343i	$0.793036\pi$
$272$	0.485936			0.0294642
$273$	12.0942	−	14.0370i	0.731972	−	0.849558i
$274$	−8.38597			−0.506615
$275$		0			0
$276$	9.12440	−	12.4300i	0.549224	−	0.748200i
$277$	14.4086	+	24.9564i	0.865727	+	1.49948i	0.866323	+	0.499484i	$0.166477\pi$
$277$	14.4086	+	24.9564i	0.865727	+	1.49948i	−0.000595725		1.00000i	$0.500190\pi$
$278$	−2.54580	+	4.40946i	−0.152687	+	0.264462i
$279$	5.89226	+	5.41098i	0.352761	+	0.323947i
$280$		0			0
$281$		−	13.4500i		−	0.802357i	−0.916000	−	0.401179i	$-0.868601\pi$
$281$		−	13.4500i		−	0.802357i	0.916000	−	0.401179i	$-0.131399\pi$
$282$	16.5545	+	1.82206i	0.985806	+	0.108502i
$283$	12.1908	−	7.03838i	0.724670	−	0.418388i	−0.0917992	−	0.995778i	$-0.529262\pi$
$283$	12.1908	−	7.03838i	0.724670	−	0.418388i	0.816469	+	0.577389i	$0.195928\pi$
$284$	14.0418	−	8.10703i	0.833227	−	0.481064i
$285$		0			0
$286$			5.17862i			0.306218i
$287$	17.0472	+	1.33175i	1.00626	+	0.0786107i
$288$	12.4146	+	11.4006i	0.731538	+	0.671785i
$289$	−8.07292	+	13.9827i	−0.474878	+	0.822512i
$290$		0			0
$291$	−3.95726	+	5.39091i	−0.231978	+	0.316021i
$292$	−3.31474	−	1.91377i	−0.193981	−	0.111995i
$293$	16.7139			0.976436			0.488218	−	0.872722i	$-0.337647\pi$
$293$	16.7139			0.976436			0.488218	+	0.872722i	$0.337647\pi$
$294$	−2.73767	−	10.3725i	−0.159664	−	0.604938i
$295$		0			0
$296$	14.4157	+	8.32289i	0.837893	+	0.483758i
$297$	−1.45546	−	7.37953i	−0.0844544	−	0.428204i
$298$	−2.84581	−	4.92909i	−0.164853	−	0.285534i
$299$	−14.7870	+	25.6118i	−0.855152	+	1.48117i
$300$		0			0
$301$	27.3223	+	2.13446i	1.57483	+	0.123028i
$302$			3.64545i			0.209772i
$303$	−2.50636	+	22.7718i	−0.143987	+	1.30821i
$304$	−0.0301247	+	0.0173925i	−0.00172777	+	0.000997528i
$305$		0			0
$306$	14.5798	−	4.57970i	0.833473	−	0.261804i
$307$			9.72258i			0.554897i	0.960741	+	0.277449i	$0.0894888\pi$
$307$			9.72258i			0.554897i	−0.960741	+	0.277449i	$0.910511\pi$
$308$	−3.84309	−	2.63802i	−0.218980	−	0.150315i
$309$	11.8378	+	26.9430i	0.673431	+	1.53273i
$310$		0			0
$311$	−2.50723	−	4.34265i	−0.142172	−	0.246249i	0.786142	−	0.618046i	$-0.212075\pi$
$311$	−2.50723	−	4.34265i	−0.142172	−	0.246249i	−0.928314	+	0.371796i	$0.878742\pi$
$312$	−16.0698	−	11.7962i	−0.909772	−	0.667828i
$313$	15.3536	+	8.86441i	0.867837	+	0.501046i	0.866629	−	0.498953i	$-0.166282\pi$
$313$	15.3536	+	8.86441i	0.867837	+	0.501046i	0.00120811	+	0.999999i	$0.499615\pi$
$314$	−1.09695			−0.0619045
$315$		0			0
$316$	−15.6330			−0.879426
$317$	−3.63917	−	2.10107i	−0.204396	−	0.118008i	0.394308	−	0.918978i	$-0.370984\pi$
$317$	−3.63917	−	2.10107i	−0.204396	−	0.118008i	−0.598704	+	0.800970i	$0.704318\pi$
$318$	1.72458	+	1.26595i	0.0967096	+	0.0709907i
$319$	1.31815	+	2.28310i	0.0738022	+	0.127829i
$320$		0			0
$321$	−9.02120	−	20.5323i	−0.503514	−	1.14600i
$322$	7.38049	+	15.4506i	0.411299	+	0.861027i
$323$		−	2.37270i		−	0.132020i
$324$	9.91770	+	4.65080i	0.550983	+	0.258378i
$325$		0			0
$326$	−5.70334	+	3.29282i	−0.315879	+	0.182373i
$327$	1.37733	−	12.5139i	0.0761667	−	0.692021i
$328$		−	18.3967i		−	1.01579i
$329$	16.2717	−	23.7048i	0.897089	−	1.30689i
$330$		0			0
$331$	0.680140	−	1.17804i	0.0373839	−	0.0647508i	−0.846728	−	0.532026i	$-0.821431\pi$
$331$	0.680140	−	1.17804i	0.0373839	−	0.0647508i	0.884112	+	0.467275i	$0.154764\pi$
$332$	6.99902	+	12.1227i	0.384121	+	0.665317i
$333$	17.1233	+	3.81554i	0.938350	+	0.209090i
$334$	−1.92121	−	1.10921i	−0.105124	−	0.0606933i
$335$		0			0
$336$	−0.365158	+	0.127534i	−0.0199210	+	0.00695756i
$337$	−26.2620			−1.43058			−0.715292	−	0.698826i	$-0.753706\pi$
$337$	−26.2620			−1.43058			−0.715292	+	0.698826i	$0.753706\pi$
$338$	2.56539	+	1.48113i	0.139539	+	0.0805629i
$339$	4.90447	−	6.68129i	0.266374	−	0.362878i
$340$		0			0
$341$	−1.93003	+	3.34291i	−0.104517	+	0.181029i
$342$	−0.739933	+	0.805747i	−0.0400110	+	0.0435698i
$343$	−18.0160	−	4.29230i	−0.972772	−	0.231762i
$344$		−	29.4853i		−	1.58974i
$345$		0			0
$346$	−13.0646	+	7.54283i	−0.702355	+	0.405505i
$347$	−5.43714	+	3.13913i	−0.291881	+	0.168517i	−0.638790	−	0.769381i	$-0.720565\pi$
$347$	−5.43714	+	3.13913i	−0.291881	+	0.168517i	0.346909	+	0.937899i	$0.387231\pi$
$348$	−3.81626	−	0.420034i	−0.204573	−	0.0225162i
$349$			4.99426i			0.267336i	0.991026	+	0.133668i	$0.0426756\pi$
$349$			4.99426i			0.267336i	−0.991026	+	0.133668i	$0.957324\pi$
$350$		0			0
$351$	−19.8834	−	6.78545i	−1.06130	−	0.362181i
$352$	−4.06644	+	7.04329i	−0.216742	+	0.375408i
$353$	0.393860	+	0.682186i	0.0209631	+	0.0363091i	0.876317	−	0.481736i	$-0.159993\pi$
$353$	0.393860	+	0.682186i	0.0209631	+	0.0363091i	−0.855354	+	0.518045i	$0.826660\pi$
$354$	1.05912	−	1.44282i	0.0562914	−	0.0766849i
$355$		0			0
$356$	−9.49619			−0.503297
$357$	4.92011	−	25.9202i	0.260400	−	1.37184i
$358$	−10.3958			−0.549436
$359$	−21.9487	−	12.6721i	−1.15841	−	0.668808i	−0.207487	−	0.978238i	$-0.566528\pi$
$359$	−21.9487	−	12.6721i	−1.15841	−	0.668808i	−0.950922	+	0.309430i	$0.899862\pi$
$360$		0			0
$361$	−9.41508	−	16.3074i	−0.495530	−	0.858284i
$362$	−1.06717	+	1.84840i	−0.0560893	+	0.0971495i
$363$	−14.1204	+	6.20403i	−0.741129	+	0.325627i
$364$	−11.7484	+	5.61204i	−0.615786	+	0.294151i
$365$		0			0
$366$	0.694845	−	6.31309i	0.0363201	−	0.329991i
$367$	1.58130	−	0.912964i	0.0825432	−	0.0476563i	−0.458160	−	0.888870i	$-0.651491\pi$
$367$	1.58130	−	0.912964i	0.0825432	−	0.0476563i	0.540703	+	0.841213i	$0.318158\pi$
$368$	0.534654	−	0.308683i	0.0278708	−	0.0160912i
$369$	−5.81030	−	18.4975i	−0.302472	−	0.962942i
$370$		0			0
$371$	3.33264	−	1.59195i	0.173022	−	0.0826499i
$372$	−2.26126	−	5.14664i	−0.117241	−	0.266841i
$373$	−1.05009	+	1.81882i	−0.0543718	+	0.0941748i	−0.891930	−	0.452173i	$-0.850649\pi$
$373$	−1.05009	+	1.81882i	−0.0543718	+	0.0941748i	0.837558	+	0.546348i	$0.183982\pi$
$374$	3.68695	+	6.38599i	0.190648	+	0.330212i
$375$		0			0
$376$	−26.7897	−	15.4670i	−1.38157	−	0.797651i
$377$	7.36363			0.379246
$378$	−9.75412	+	7.26792i	−0.501698	+	0.373821i
$379$	−19.2106			−0.986782			−0.493391	−	0.869808i	$-0.664243\pi$
$379$	−19.2106			−0.986782			−0.493391	+	0.869808i	$0.664243\pi$
$380$		0			0
$381$	−12.7923	−	9.39035i	−0.655371	−	0.481082i
$382$	−6.08716	−	10.5433i	−0.311446	−	0.539440i
$383$	1.58032	−	2.73720i	0.0807506	−	0.139864i	−0.822822	−	0.568299i	$-0.807602\pi$
$383$	1.58032	−	2.73720i	0.0807506	−	0.139864i	0.903573	+	0.428435i	$0.140935\pi$
$384$	−4.66026	−	10.6068i	−0.237818	−	0.541275i
$385$		0			0
$386$		−	8.15235i		−	0.414944i
$387$	−9.31242	−	29.6468i	−0.473377	−	1.50703i
$388$	4.06969	−	2.34963i	0.206607	−	0.119285i
$389$	−9.77019	+	5.64082i	−0.495368	+	0.286001i	−0.726799	−	0.686850i	$-0.758993\pi$
$389$	−9.77019	+	5.64082i	−0.495368	+	0.286001i	0.231430	+	0.972851i	$0.425659\pi$
$390$		0			0
$391$			42.1107i			2.12963i
$392$	−3.09436	+	19.6840i	−0.156289	+	0.994191i
$393$	33.0532	−	14.5225i	1.66731	−	0.732561i
$394$	1.82150	−	3.15493i	0.0917659	−	0.158943i
$395$		0			0
$396$	−1.14956	+	5.15898i	−0.0577677	+	0.259248i
$397$	26.5154	+	15.3087i	1.33077	+	0.768319i	0.985417	−	0.170154i	$-0.0544266\pi$
$397$	26.5154	+	15.3087i	1.33077	+	0.768319i	0.345351	+	0.938474i	$0.387760\pi$
$398$	−0.0709323			−0.00355551
$399$	0.622716	+	1.78297i	0.0311748	+	0.0892603i
$400$		0			0
$401$	−20.4532	−	11.8087i	−1.02139	−	0.589697i	−0.106881	−	0.994272i	$-0.534086\pi$
$401$	−20.4532	−	11.8087i	−1.02139	−	0.589697i	−0.914505	+	0.404574i	$0.867420\pi$
$402$	−6.27574	+	8.54934i	−0.313005	+	0.426403i
$403$	5.39090	+	9.33731i	0.268540	+	0.465125i
$404$	8.04922	−	13.9417i	0.400464	−	0.693623i
$405$		0			0
$406$	2.41281	−	3.51500i	0.119746	−	0.174446i
$407$			8.46491i			0.419590i
$408$	−28.2147	−	3.10543i	−1.39684	−	0.153742i
$409$	−11.1411	+	6.43231i	−0.550891	+	0.318057i	−0.749481	−	0.662025i	$-0.769697\pi$
$409$	−11.1411	+	6.43231i	−0.550891	+	0.318057i	0.198590	+	0.980083i	$0.436364\pi$
$410$		0			0
$411$	16.3174	+	1.79596i	0.804876	+	0.0885880i
$412$		−	20.6797i		−	1.01882i
$413$	−1.33186	−	2.78815i	−0.0655364	−	0.137196i
$414$	13.1324	−	14.3004i	0.645420	−	0.702828i
$415$		0			0
$416$	11.3583	+	19.6731i	0.556885	+	0.964553i
$417$	5.89794	−	8.03468i	0.288823	−	0.393460i
$418$	−0.457132	−	0.263925i	−0.0223590	−	0.0129090i
$419$	3.78089			0.184708			0.0923542	−	0.995726i	$-0.470561\pi$
$419$	3.78089			0.184708			0.0923542	+	0.995726i	$0.470561\pi$
$420$		0			0
$421$	−2.43659			−0.118752			−0.0593759	−	0.998236i	$-0.518911\pi$
$421$	−2.43659			−0.118752			−0.0593759	+	0.998236i	$0.518911\pi$
$422$	−13.4712	−	7.77763i	−0.655770	−	0.378609i
$423$	−31.8214	−	7.09069i	−1.54721	−	0.344761i
$424$	−1.98681	−	3.44126i	−0.0964881	−	0.167122i
$425$		0			0
$426$	18.6914	−	8.21238i	0.905603	−	0.397891i
$427$	−9.03986	−	6.20525i	−0.437470	−	0.300293i
$428$			15.7593i			0.761753i
$429$	1.10906	−	10.0765i	0.0535461	−	0.486499i
$430$		0			0
$431$	26.4558	−	15.2743i	1.27433	−	0.735737i	0.298533	−	0.954399i	$-0.403503\pi$
$431$	26.4558	−	15.2743i	1.27433	−	0.735737i	0.975800	+	0.218663i	$0.0701695\pi$
$432$	0.288640	+	0.330208i	0.0138872	+	0.0158871i
$433$		−	37.7749i		−	1.81534i	−0.419680	−	0.907672i	$-0.637858\pi$
$433$		−	37.7749i		−	1.81534i	0.419680	−	0.907672i	$-0.362142\pi$
$434$	6.22353	+	0.486191i	0.298739	+	0.0233379i
$435$		0			0
$436$	−4.42332	+	7.66142i	−0.211839	+	0.366916i
$437$	−1.50722	−	2.61057i	−0.0720999	−	0.124881i
$438$	−3.88508	−	2.85189i	−0.185636	−	0.136268i
$439$	−3.55267	−	2.05113i	−0.169560	−	0.0978953i	0.412819	−	0.910813i	$-0.364544\pi$
$439$	−3.55267	−	2.05113i	−0.169560	−	0.0978953i	−0.582378	+	0.812918i	$0.697878\pi$
$440$		0			0
$441$	3.10553	+	20.7691i	0.147883	+	0.989005i
$442$	20.5966			0.979679
$443$	−22.7315	−	13.1240i	−1.08001	−	0.623541i	−0.149107	−	0.988821i	$-0.547640\pi$
$443$	−22.7315	−	13.1240i	−1.08001	−	0.623541i	−0.930898	+	0.365280i	$0.880973\pi$
$444$	−9.93763	−	7.29482i	−0.471619	−	0.346197i
$445$		0			0
$446$	−12.1646	+	21.0696i	−0.576009	+	0.997677i
$447$	4.48174	+	10.2005i	0.211979	+	0.482465i
$448$	13.5578	+	1.05916i	0.640548	+	0.0500405i
$449$			14.6382i			0.690821i	0.938452	+	0.345411i	$0.112260\pi$
$449$			14.6382i			0.690821i	−0.938452	+	0.345411i	$0.887740\pi$
$450$		0			0
$451$	8.10195	−	4.67766i	0.381506	−	0.220263i
$452$	−5.04381	+	2.91205i	−0.237241	+	0.136971i
$453$	0.780718	−	7.09330i	0.0366813	−	0.333272i
$454$			10.9761i			0.515134i
$455$		0			0
$456$	1.86027	−	0.817340i	0.0871151	−	0.0382754i
$457$	−14.5940	+	25.2776i	−0.682679	+	1.18244i	0.291481	+	0.956577i	$0.405852\pi$
$457$	−14.5940	+	25.2776i	−0.682679	+	1.18244i	−0.974160	+	0.225858i	$0.927481\pi$
$458$	−12.0310	−	20.8384i	−0.562174	−	0.973714i
$459$	−29.3501	+	5.78870i	−1.36995	+	0.270193i
$460$		0			0
$461$	15.8295			0.737255			0.368627	−	0.929577i	$-0.379828\pi$
$461$	15.8295			0.737255			0.368627	+	0.929577i	$0.379828\pi$
$462$	−4.44658	−	3.83113i	−0.206874	−	0.178241i
$463$	19.1466			0.889816			0.444908	−	0.895576i	$-0.353236\pi$
$463$	19.1466			0.889816			0.444908	+	0.895576i	$0.353236\pi$
$464$	−0.133124	−	0.0768591i	−0.00618012	−	0.00356809i
$465$		0			0
$466$	−12.8010	−	22.1719i	−0.592994	−	1.02710i
$467$	7.45251	−	12.9081i	0.344861	−	0.597317i	−0.640468	−	0.767985i	$-0.721259\pi$
$467$	7.45251	−	12.9081i	0.344861	−	0.597317i	0.985328	+	0.170669i	$0.0545928\pi$
$468$	10.8739	+	9.98570i	0.502645	+	0.461589i
$469$	7.89185	+	16.5211i	0.364412	+	0.762872i
$470$		0			0
$471$	2.13444	+	0.234925i	0.0983497	+	0.0108248i
$472$	−2.87903	+	1.66221i	−0.132518	+	0.0765092i
$473$	12.9854	−	7.49710i	0.597067	−	0.344717i
$474$	−19.5662	−	2.15354i	−0.898705	−	0.0989152i
$475$		0			0
$476$	−10.4920	+	15.2848i	−0.480900	+	0.700579i
$477$	−3.08456	−	2.83261i	−0.141232	−	0.129696i
$478$	8.51269	−	14.7444i	0.389362	−	0.674394i
$479$	−10.9530	−	18.9712i	−0.500456	−	0.866815i	−1.00000		0.000526656i	$-0.999832\pi$
$479$	−10.9530	−	18.9712i	−0.500456	−	0.866815i	0.499544	−	0.866289i	$-0.333501\pi$
$480$		0			0
$481$	20.4762	+	11.8220i	0.933636	+	0.539035i
$482$	−5.01243			−0.228310
$483$	−11.0520	−	31.6443i	−0.502883	−	1.43986i
$484$	10.8379			0.492632
$485$		0			0
$486$	11.7723	+	7.18714i	0.534001	+	0.326015i
$487$	−6.21983	−	10.7731i	−0.281848	−	0.488174i	0.689992	−	0.723817i	$-0.257614\pi$
$487$	−6.21983	−	10.7731i	−0.281848	−	0.488174i	−0.971840	+	0.235642i	$0.924281\pi$
$488$	−5.89838	+	10.2163i	−0.267007	+	0.462470i
$489$	11.8027	−	5.18572i	0.533737	−	0.234506i
$490$		0			0
$491$			23.2765i			1.05045i	0.850962	+	0.525227i	$0.176020\pi$
$491$			23.2765i			1.05045i	−0.850962	+	0.525227i	$0.823980\pi$
$492$	−1.49056	+	13.5426i	−0.0671995	+	0.610548i
$493$	9.08043	−	5.24259i	0.408962	−	0.236114i
$494$	−1.27685	+	0.737187i	−0.0574480	+	0.0331676i
$495$		0			0
$496$		−	0.225074i		−	0.0101061i
$497$	2.74510	−	35.1389i	0.123135	−	1.57620i
$498$	7.08997	+	16.1368i	0.317709	+	0.723108i
$499$	13.2171	−	22.8927i	0.591680	−	1.02482i	−0.402327	−	0.915496i	$-0.631798\pi$
$499$	13.2171	−	22.8927i	0.591680	−	1.02482i	0.994006	−	0.109323i	$-0.0348683\pi$
$500$		0			0
$501$	3.50072	+	2.56974i	0.156401	+	0.114808i
$502$	−5.02551	−	2.90148i	−0.224300	−	0.129499i
$503$	−17.4645			−0.778702			−0.389351	−	0.921090i	$-0.627301\pi$
$503$	−17.4645			−0.778702			−0.389351	+	0.921090i	$0.627301\pi$
$504$	22.0171	−	5.07139i	0.980720	−	0.225898i
$505$		0			0
$506$	8.11319	+	4.68415i	0.360675	+	0.208236i
$507$	−4.67453	−	3.43139i	−0.207603	−	0.152393i
$508$	5.57555	+	9.65714i	0.247375	+	0.428466i
$509$	1.20504	−	2.08719i	0.0534124	−	0.0925129i	−0.838083	−	0.545543i	$-0.816324\pi$
$509$	1.20504	−	2.08719i	0.0534124	−	0.0925129i	0.891495	+	0.453030i	$0.149657\pi$
$510$		0			0
$511$	−7.50768	+	3.58630i	−0.332120	+	0.158648i
$512$		−	0.954733i		−	0.0421937i
$513$	1.61232	−	1.40935i	0.0711856	−	0.0622244i
$514$	6.69176	−	3.86349i	0.295161	−	0.170411i
$515$		0			0
$516$	−2.38898	+	21.7053i	−0.105169	+	0.955525i
$517$		−	15.7309i		−	0.691846i
$518$	12.3525	−	5.90059i	0.542738	−	0.259257i
$519$	27.0363	−	11.8788i	1.18676	−	0.521424i
$520$		0			0
$521$	15.7340	+	27.2520i	0.689317	+	1.19393i	0.972059	+	0.234736i	$0.0754226\pi$
$521$	15.7340	+	27.2520i	0.689317	+	1.19393i	−0.282742	+	0.959196i	$0.591244\pi$
$522$	−4.71855	−	1.05142i	−0.206525	−	0.0460196i
$523$	14.8061	+	8.54828i	0.647424	+	0.373790i	0.787469	−	0.616355i	$-0.211391\pi$
$523$	14.8061	+	8.54828i	0.647424	+	0.373790i	−0.140045	+	0.990145i	$0.544725\pi$
$524$	−25.3695			−1.10827
$525$		0			0
$526$	19.9451			0.869649
$527$	13.2955	+	7.67617i	0.579162	+	0.334379i
$528$	−0.125226	+	0.170593i	−0.00544975	+	0.00742411i
$529$	15.2501	+	26.4140i	0.663049	+	1.14843i
$530$		0			0
$531$	−2.36982	+	2.58060i	−0.102841	+	0.111989i
$532$	0.103361	−	1.32308i	0.00448127	−	0.0573629i
$533$		−	26.1310i		−	1.13186i
$534$	−11.8854	−	1.30815i	−0.514331	−	0.0566094i
$535$		0			0
$536$	17.0595	−	9.84932i	0.736859	−	0.425426i
$537$	20.2281	+	2.22639i	0.872908	+	0.0960759i
$538$		−	12.5547i		−	0.541272i
$539$	−9.45564	+	3.64220i	−0.407283	+	0.156881i
$540$		0			0
$541$	10.8422	−	18.7792i	0.466142	−	0.807382i	−0.533110	−	0.846046i	$-0.678977\pi$
$541$	10.8422	−	18.7792i	0.466142	−	0.807382i	0.999252	+	0.0386641i	$0.0123102\pi$
$542$	5.63192	+	9.75478i	0.241912	+	0.419004i
$543$	2.47235	−	3.36805i	0.106099	−	0.144537i
$544$	28.0128	+	16.1732i	1.20104	+	0.693419i
$545$		0			0
$546$	−15.4774	+	5.40558i	−0.662371	+	0.231338i
$547$	9.42694			0.403067			0.201533	−	0.979482i	$-0.435408\pi$
$547$	9.42694			0.403067			0.201533	+	0.979482i	$0.435408\pi$
$548$	−9.99001	−	5.76774i	−0.426752	−	0.246386i
$549$	−2.70405	+	12.1352i	−0.115406	+	0.517916i
$550$		0			0
$551$	−0.375283	+	0.650009i	−0.0159876	+	0.0276913i
$552$	−33.0161	+	14.5062i	−1.40526	+	0.617424i
$553$	−19.2320	+	28.0173i	−0.817826	+	1.19142i
$554$		−	25.4977i		−	1.08329i
$555$		0			0
$556$	−6.06551	+	3.50192i	−0.257235	+	0.148515i
$557$	−4.89952	+	2.82874i	−0.207599	+	0.119858i	−0.600195	−	0.799854i	$-0.704910\pi$
$557$	−4.89952	+	2.82874i	−0.207599	+	0.119858i	0.392596	+	0.919711i	$0.371577\pi$
$558$	−2.12120	−	6.75301i	−0.0897977	−	0.285878i
$559$		−	41.8814i		−	1.77139i
$560$		0			0
$561$	−5.80641	−	13.2154i	−0.245147	−	0.557956i
$562$	−5.95032	+	10.3063i	−0.250999	+	0.434743i
$563$	−3.65140	−	6.32441i	−0.153888	−	0.266542i	0.778765	−	0.627315i	$-0.215846\pi$
$563$	−3.65140	−	6.32441i	−0.153888	−	0.266542i	−0.932654	+	0.360773i	$0.882513\pi$
$564$	18.4678	+	13.5565i	0.777635	+	0.570831i
$565$		0			0
$566$	−12.4552			−0.523533
$567$	20.5360	−	12.0529i	0.862431	−	0.506174i
$568$	−37.9207			−1.59112
$569$	−12.6704	−	7.31525i	−0.531170	−	0.306671i	0.210323	−	0.977632i	$-0.432549\pi$
$569$	−12.6704	−	7.31525i	−0.531170	−	0.306671i	−0.741493	+	0.670961i	$0.765882\pi$
$570$		0			0
$571$	15.0693	+	26.1009i	0.630632	+	1.09229i	0.987423	+	0.158103i	$0.0505377\pi$
$571$	15.0693	+	26.1009i	0.630632	+	1.09229i	−0.356790	+	0.934184i	$0.616129\pi$
$572$	−3.56177	+	6.16917i	−0.148925	+	0.257946i
$573$	9.58638	+	21.8187i	0.400477	+	0.911487i
$574$	−12.4735	−	8.56223i	−0.520635	−	0.357380i
$575$		0			0
$576$	−4.62100	−	14.7113i	−0.192542	−	0.612971i
$577$	39.2538	−	22.6632i	1.63416	−	0.943482i	0.651367	−	0.758762i	$-0.274196\pi$
$577$	39.2538	−	22.6632i	1.63416	−	0.943482i	0.982791	−	0.184720i	$-0.0591377\pi$
$578$	12.3720	−	7.14299i	0.514608	−	0.297109i
$579$	−1.74593	+	15.8628i	−0.0725582	+	0.659235i
$580$		0			0
$581$	30.3364	+	2.36992i	1.25856	+	0.0983208i
$582$	5.41727	−	2.38017i	0.224553	−	0.0986611i
$583$	1.01036	−	1.74999i	0.0418447	−	0.0724771i
$584$	4.47583	+	7.75237i	0.185211	+	0.320795i
$585$		0			0
$586$	−12.8073	−	7.39430i	−0.529065	−	0.305456i
$587$	−27.9328			−1.15291			−0.576455	−	0.817129i	$-0.695564\pi$
$587$	−27.9328			−1.15291			−0.576455	+	0.817129i	$0.695564\pi$
$588$	3.87274	−	14.2395i	0.159709	−	0.587226i
$589$	−1.09897			−0.0452825
$590$		0			0
$591$	−4.21993	+	5.74875i	−0.173585	+	0.236472i
$592$	−0.246787	−	0.427448i	−0.0101429	−	0.0175680i
$593$	−14.7273	+	25.5085i	−0.604779	+	1.04751i	0.387307	+	0.921951i	$0.373405\pi$
$593$	−14.7273	+	25.5085i	−0.604779	+	1.04751i	−0.992086	+	0.125558i	$0.959928\pi$
$594$	−2.14947	+	6.29859i	−0.0881937	+	0.258434i
$595$		0			0
$596$		−	7.82921i		−	0.320697i
$597$	0.138020	+	0.0151910i	0.00564876	+	0.000621726i
$598$	22.6615	−	13.0836i	0.926698	−	0.535029i
$599$	−13.1940	+	7.61757i	−0.539093	+	0.311245i	−0.744711	−	0.667387i	$-0.767413\pi$
$599$	−13.1940	+	7.61757i	−0.539093	+	0.311245i	0.205618	+	0.978632i	$0.434079\pi$
$600$		0			0
$601$			18.6064i			0.758970i	0.925198	+	0.379485i	$0.123899\pi$
$601$			18.6064i			0.758970i	−0.925198	+	0.379485i	$0.876101\pi$
$602$	−19.9919	−	13.7231i	−0.814808	−	0.559310i
$603$	14.0422	−	15.2912i	0.571844	−	0.622707i
$604$	−2.50729	+	4.34275i	−0.102020	+	0.176704i
$605$		0			0
$606$	11.9949	−	16.3405i	0.487259	−	0.663786i
$607$	−16.5452	−	9.55240i	−0.671550	−	0.387720i	0.125113	−	0.992142i	$-0.460071\pi$
$607$	−16.5452	−	9.55240i	−0.671550	−	0.387720i	−0.796664	+	0.604423i	$0.793404\pi$
$608$	−2.31547			−0.0939046
$609$	−5.44760	+	6.32273i	−0.220748	+	0.256210i
$610$		0			0
$611$	−38.0525	−	21.9696i	−1.53944	−	0.888795i
$612$	20.5184	+	4.57208i	0.829409	+	0.184815i
$613$	−6.23054	−	10.7916i	−0.251649	−	0.435869i	0.712331	−	0.701844i	$-0.247640\pi$
$613$	−6.23054	−	10.7916i	−0.251649	−	0.435869i	−0.963980	+	0.265975i	$0.914306\pi$
$614$	4.30131	−	7.45009i	0.173587	−	0.300661i
$615$		0			0
$616$	4.69902	+	9.83710i	0.189329	+	0.396348i
$617$		−	19.4451i		−	0.782829i	−0.920214	−	0.391414i	$-0.871986\pi$
$617$		−	19.4451i		−	0.782829i	0.920214	−	0.391414i	$-0.128014\pi$
$618$	2.84875	−	25.8826i	0.114593	−	1.04115i
$619$	−9.61812	+	5.55302i	−0.386585	+	0.223195i	−0.680679	−	0.732582i	$-0.738315\pi$
$619$	−9.61812	+	5.55302i	−0.386585	+	0.223195i	0.294095	+	0.955776i	$0.404982\pi$
$620$		0			0
$621$	−28.6155	+	25.0132i	−1.14830	+	1.00375i
$622$			4.43684i			0.177901i
$623$	−11.6824	+	17.0189i	−0.468044	+	0.681850i
$624$	0.237769	+	0.541163i	0.00951837	+	0.0216639i
$625$		0			0
$626$	−7.84330	−	13.5850i	−0.313481	−	0.542966i
$627$	0.832961	+	0.611444i	0.0332653	+	0.0244187i
$628$	−1.30677	−	0.754465i	−0.0521459	−	0.0301064i
$629$	33.6669			1.34239
$630$		0			0
$631$	9.89504			0.393915			0.196958	−	0.980412i	$-0.436894\pi$
$631$	9.89504			0.393915			0.196958	+	0.980412i	$0.436894\pi$
$632$	31.6634	+	18.2809i	1.25950	+	0.727174i
$633$	24.5466	+	18.0187i	0.975639	+	0.716178i
$634$	1.85905	+	3.21996i	0.0738322	+	0.127881i
$635$		0			0
$636$	1.18375	+	2.69423i	0.0469389	+	0.106833i
$637$	−4.39528	+	27.9594i	−0.174147	+	1.10779i
$638$		−	2.33262i		−	0.0923493i
$639$	−38.1284	+	11.9766i	−1.50834	+	0.473787i
$640$		0			0
$641$	2.40816	−	1.39035i	0.0951166	−	0.0549156i	−0.451687	−	0.892176i	$-0.649178\pi$
$641$	2.40816	−	1.39035i	0.0951166	−	0.0549156i	0.546804	+	0.837261i	$0.315844\pi$
$642$	−2.17093	+	19.7242i	−0.0856798	+	0.778453i
$643$			37.8005i			1.49071i	0.666669	+	0.745354i	$0.267719\pi$
$643$			37.8005i			1.49071i	−0.666669	+	0.745354i	$0.732281\pi$
$644$	−1.83445	+	23.4821i	−0.0722876	+	0.925325i
$645$		0			0
$646$	−1.04969	+	1.81812i	−0.0412995	+	0.0715329i
$647$	10.1708	+	17.6163i	0.399855	+	0.692569i	0.993708	−	0.112005i	$-0.0357271\pi$
$647$	10.1708	+	17.6163i	0.399855	+	0.692569i	−0.593853	+	0.804574i	$0.702394\pi$
$648$	−14.6490	−	21.0173i	−0.575466	−	0.825639i
$649$	−1.46408	−	0.845285i	−0.0574700	−	0.0331803i
$650$		0			0
$651$	−12.0056	−	2.27887i	−0.470536	−	0.0893161i
$652$	−9.05901			−0.354778
$653$	−21.5592	−	12.4472i	−0.843677	−	0.487097i	0.0148355	−	0.999890i	$-0.495278\pi$
$653$	−21.5592	−	12.4472i	−0.843677	−	0.487097i	−0.858512	+	0.512793i	$0.828611\pi$
$654$	−6.59161	+	8.97966i	−0.257753	+	0.351132i
$655$		0			0
$656$	−0.272747	+	0.472411i	−0.0106490	+	0.0184446i
$657$	6.94880	+	6.38122i	0.271099	+	0.248955i
$658$	−22.9556	+	10.9655i	−0.894901	+	0.427480i
$659$			29.3981i			1.14519i	0.819840	+	0.572593i	$0.194062\pi$
$659$			29.3981i			1.14519i	−0.819840	+	0.572593i	$0.805938\pi$
$660$		0			0
$661$	17.1948	−	9.92744i	0.668801	−	0.386133i	−0.126821	−	0.991926i	$-0.540477\pi$
$661$	17.1948	−	9.92744i	0.668801	−	0.386133i	0.795622	+	0.605793i	$0.207144\pi$
$662$	−1.04234	+	0.601794i	−0.0405116	+	0.0233894i
$663$	−40.0767	−	4.41100i	−1.55645	−	0.171309i
$664$		−	32.7380i		−	1.27048i
$665$		0			0
$666$	−11.4330	−	10.4991i	−0.443019	−	0.406833i
$667$	6.66053	−	11.5364i	0.257897	−	0.446690i
$668$	−1.52579	−	2.64275i	−0.0590347	−	0.102251i
$669$	28.1821	−	38.3920i	1.08958	−	1.48432i
$670$		0			0
$671$	−5.99903			−0.231590
$672$	−25.2950	−	4.80143i	−0.975775	−	0.185219i
$673$	−17.4983			−0.674509			−0.337255	−	0.941414i	$-0.609498\pi$
$673$	−17.4983			−0.674509			−0.337255	+	0.941414i	$0.609498\pi$
$674$	20.1237	+	11.6184i	0.775136	+	0.447525i
$675$		0			0
$676$	2.03740	+	3.52888i	0.0783614	+	0.135726i
$677$	2.18727	−	3.78846i	0.0840635	−	0.145602i	−0.820928	−	0.571031i	$-0.806543\pi$
$677$	2.18727	−	3.78846i	0.0840635	−	0.145602i	0.904992	+	0.425429i	$0.139877\pi$
$678$	−6.71396	+	2.94989i	−0.257848	+	0.113290i
$679$	0.795603	−	10.1842i	0.0305324	−	0.390834i
$680$		0			0
$681$	2.35066	−	21.3572i	0.0900776	−	0.818410i
$682$	2.95783	−	1.70771i	0.113261	−	0.0653915i
$683$	25.4692	−	14.7046i	0.974550	−	0.562657i	0.0739300	−	0.997263i	$-0.476446\pi$
$683$	25.4692	−	14.7046i	0.974550	−	0.562657i	0.900620	+	0.434606i	$0.143113\pi$
$684$	−1.43565	+	0.450954i	−0.0548933	+	0.0172426i
$685$		0			0
$686$	11.9061	+	11.2594i	0.454578	+	0.429886i
$687$	18.9471	+	43.1238i	0.722878	+	1.64527i
$688$	−0.437143	+	0.757154i	−0.0166659	+	0.0288662i
$689$	−2.82210	−	4.88802i	−0.107513	−	0.186219i
$690$		0			0
$691$	−43.6753	−	25.2160i	−1.66149	−	0.959260i	−0.972006	−	0.234956i	$-0.924505\pi$
$691$	−43.6753	−	25.2160i	−1.66149	−	0.959260i	−0.689481	−	0.724304i	$-0.742161\pi$
$692$	−20.7513			−0.788848
$693$	7.83165	+	8.40689i	0.297500	+	0.319351i
$694$	5.55506			0.210867
$695$		0			0
$696$	7.23835	+	5.31339i	0.274369	+	0.201404i
$697$	−18.6041	−	32.2233i	−0.704682	−	1.22055i
$698$	2.20948	−	3.82693i	0.0836301	−	0.144852i
$699$	20.1597	+	45.8835i	0.762509	+	1.73547i
$700$		0			0
$701$		−	19.8266i		−	0.748842i	−0.927259	−	0.374421i	$-0.877841\pi$
$701$		−	19.8266i		−	0.748842i	0.927259	−	0.374421i	$-0.122159\pi$
$702$	12.2341	+	13.9960i	0.461747	+	0.528244i
$703$	−2.08712	+	1.20500i	−0.0787171	+	0.0454473i
$704$	6.44358	−	3.72020i	0.242852	−	0.140210i
$705$		0			0
$706$		−	0.696982i		−	0.0262313i
$707$	−15.0838	−	31.5769i	−0.567284	−	1.18757i
$708$	2.25405	−	0.990353i	0.0847123	−	0.0372197i
$709$	13.2605	−	22.9678i	0.498008	−	0.862575i	−0.501990	−	0.864874i	$-0.667398\pi$
$709$	13.2605	−	22.9678i	0.498008	−	0.862575i	0.999997	+	0.00229888i	$0.000731757\pi$
$710$		0			0
$711$	37.6106	+	8.38067i	1.41051	+	0.314300i
$712$	19.2338	+	11.1046i	0.720816	+	0.416163i
$713$	19.5046			0.730455
$714$	−15.2373	+	17.6851i	−0.570242	+	0.661848i
$715$		0			0
$716$	−12.3843	−	7.15008i	−0.462823	−	0.267211i
$717$	−19.7216	+	26.8665i	−0.736518	+	1.00335i
$718$	11.2124	+	19.4204i	0.418442	+	0.724763i
$719$	−1.12519	+	1.94889i	−0.0419627	+	0.0726815i	−0.886244	−	0.463219i	$-0.846694\pi$
$719$	−1.12519	+	1.94889i	−0.0419627	+	0.0726815i	0.844281	+	0.535900i	$0.180028\pi$
$720$		0			0
$721$	−37.0619	−	25.4405i	−1.38026	−	0.947453i
$722$			16.6611i			0.620061i
$723$	9.75315	+	1.07347i	0.362724	+	0.0399229i
$724$	−2.54259	+	1.46797i	−0.0944947	+	0.0545566i
$725$		0			0
$726$	13.5647	+	1.49298i	0.503432	+	0.0554098i
$727$			6.85964i			0.254410i	0.991876	+	0.127205i	$0.0406006\pi$
$727$			6.85964i			0.254410i	−0.991876	+	0.127205i	$0.959399\pi$
$728$	30.3581	+	2.37162i	1.12515	+	0.0878980i
$729$	−21.3672	−	16.5059i	−0.791377	−	0.611328i
$730$		0			0
$731$	−29.8177	−	51.6458i	−1.10285	−	1.91019i
$732$	5.16980	−	7.04274i	0.191081	−	0.260307i
$733$	4.77925	+	2.75930i	0.176526	+	0.101917i	0.585659	−	0.810557i	$-0.300836\pi$
$733$	4.77925	+	2.75930i	0.176526	+	0.101917i	−0.409134	+	0.912474i	$0.634169\pi$
$734$	−1.61560			−0.0596327
$735$		0			0
$736$	41.0950			1.51478
$737$	8.67531	+	5.00869i	0.319559	+	0.184498i
$738$	−3.73114	+	16.7445i	−0.137345	+	0.616375i
$739$	−5.01222	−	8.68142i	−0.184378	−	0.319351i	0.758989	−	0.651103i	$-0.225694\pi$
$739$	−5.01222	−	8.68142i	−0.184378	−	0.319351i	−0.943367	+	0.331752i	$0.892360\pi$
$740$		0			0
$741$	2.64236	−	1.16096i	0.0970694	−	0.0426490i
$742$	−3.25798	−	0.254518i	−0.119604	−	0.00934363i
$743$			26.2588i			0.963342i	0.876352	+	0.481671i	$0.159970\pi$
$743$			26.2588i			0.963342i	−0.876352	+	0.481671i	$0.840030\pi$
$744$	−1.43836	+	13.0684i	−0.0527328	+	0.479110i
$745$		0			0
$746$	1.60930	−	0.929132i	0.0589208	−	0.0340180i
$747$	−10.3397	−	32.9173i	−0.378311	−	1.20438i
$748$			10.1433i			0.370876i
$749$	28.2436	+	19.3873i	1.03200	+	0.708396i
$750$		0			0
$751$	−5.68833	+	9.85247i	−0.207570	+	0.359522i	−0.950949	−	0.309349i	$-0.899889\pi$
$751$	−5.68833	+	9.85247i	−0.207570	+	0.359522i	0.743378	+	0.668871i	$0.233222\pi$
$752$	0.458622	+	0.794357i	0.0167242	+	0.0289672i
$753$	9.15722	+	6.72196i	0.333708	+	0.244962i
$754$	−5.64251	−	3.25770i	−0.205488	−	0.118639i
$755$		0			0
$756$	−16.6186	+	1.94937i	−0.604413	+	0.0708980i
$757$	−20.1866			−0.733693			−0.366847	−	0.930281i	$-0.619563\pi$
$757$	−20.1866			−0.733693			−0.366847	+	0.930281i	$0.619563\pi$
$758$	14.7204	+	8.49884i	0.534670	+	0.308692i
$759$	−14.7834	−	10.8519i	−0.536604	−	0.393900i
$760$		0			0
$761$	−2.04697	+	3.54546i	−0.0742026	+	0.128523i	−0.900739	−	0.434360i	$-0.856974\pi$
$761$	−2.04697	+	3.54546i	−0.0742026	+	0.128523i	0.826537	+	0.562883i	$0.190308\pi$
$762$	5.64801	+	12.8549i	0.204606	+	0.465684i
$763$	8.28907	+	17.3526i	0.300084	+	0.628207i
$764$		−	16.7466i		−	0.605871i
$765$		0			0
$766$	−2.42189	+	1.39828i	−0.0875066	+	0.0505219i
$767$	−4.08941	+	2.36102i	−0.147660	+	0.0852516i
$768$	−3.06946	+	27.8879i	−0.110760	+	1.00632i
$769$			8.66796i			0.312575i	0.987712	+	0.156287i	$0.0499526\pi$
$769$			8.66796i			0.312575i	−0.987712	+	0.156287i	$0.950047\pi$
$770$		0			0
$771$	−13.8482	+	6.08443i	−0.498730	+	0.219125i
$772$	5.60706	−	9.71171i	0.201803	−	0.349532i
$773$	22.1640	+	38.3891i	0.797183	+	1.38076i	0.921444	+	0.388512i	$0.127011\pi$
$773$	22.1640	+	38.3891i	0.797183	+	1.38076i	−0.124261	+	0.992250i	$0.539656\pi$
$774$	−5.98007	+	26.8372i	−0.214949	+	0.964643i
$775$		0			0
$776$	−10.9904			−0.394533
$777$	−25.2991	+	8.83590i	−0.907601	+	0.316986i
$778$	9.98209			0.357875
$779$	2.30666	+	1.33175i	0.0826446	+	0.0477149i
$780$		0			0
$781$	−9.64194	−	16.7003i	−0.345016	−	0.597585i
$782$	18.6299	−	32.2680i	0.666206	−	1.15390i
$783$	8.95615	+	3.05639i	0.320067	+	0.109226i
$784$	0.371291	−	0.459590i	0.0132604	−	0.0164139i
$785$		0			0
$786$	−31.7524	−	3.49480i	−1.13257	−	0.124655i
$787$	21.8059	−	12.5896i	0.777296	−	0.448772i	−0.0581753	−	0.998306i	$-0.518528\pi$
$787$	21.8059	−	12.5896i	0.777296	−	0.448772i	0.835471	+	0.549535i	$0.185195\pi$
$788$	4.33982	−	2.50560i	0.154600	−	0.0892583i
$789$	−38.8091	−	4.27149i	−1.38164	−	0.152069i
$790$		0			0
$791$	−0.986040	+	12.6219i	−0.0350596	+	0.448783i
$792$	8.36114	−	9.10482i	0.297100	−	0.323526i
$793$	−8.37815	+	14.5114i	−0.297517	+	0.515314i
$794$	−13.5452	−	23.4610i	−0.480702	−	0.832600i
$795$		0			0
$796$	−0.0845000	−	0.0487861i	−0.00299502	−	0.00172918i
$797$	48.5237			1.71880			0.859400	−	0.511305i	$-0.170838\pi$
$797$	48.5237			1.71880			0.859400	+	0.511305i	$0.170838\pi$
$798$	0.311628	−	1.64172i	0.0110315	−	0.0581164i
$799$	−62.5656			−2.21341
$800$		0			0
$801$	22.8463	+	5.09080i	0.807235	+	0.179874i
$802$	10.4484	+	18.0972i	0.368947	+	0.639034i
$803$	−2.27610	+	3.94232i	−0.0803219	+	0.139122i
$804$	−13.3562	+	5.86829i	−0.471039	+	0.206958i
$805$		0			0
$806$		−	9.53983i		−	0.336026i
$807$	−2.68874	+	24.4289i	−0.0946483	+	0.859937i
$808$	−32.6061	+	18.8251i	−1.14708	+	0.662266i
$809$	−0.751275	+	0.433749i	−0.0264134	+	0.0152498i	−0.513149	−	0.858300i	$-0.671521\pi$
$809$	−0.751275	+	0.433749i	−0.0264134	+	0.0152498i	0.486735	+	0.873550i	$0.338188\pi$
$810$		0			0
$811$		−	19.2304i		−	0.675271i	−0.941277	−	0.337636i	$-0.890373\pi$
$811$		−	19.2304i		−	0.675271i	0.941277	−	0.337636i	$-0.109627\pi$
$812$	5.29188	−	2.52785i	0.185709	−	0.0887100i
$813$	−8.86946	−	20.1869i	−0.311065	−	0.707986i
$814$	3.74491	−	6.48637i	0.131259	−	0.227347i
$815$		0			0
$816$	0.678488	+	0.498051i	0.0237518	+	0.0174353i
$817$	3.69699	+	2.13446i	0.129341	+	0.0746751i
$818$	11.3827			0.397987
$819$	31.2734	−	7.20348i	1.09278	−	0.251710i
$820$		0			0
$821$	−32.0917	−	18.5281i	−1.12001	−	0.646636i	−0.178604	−	0.983921i	$-0.557158\pi$
$821$	−32.0917	−	18.5281i	−1.12001	−	0.646636i	−0.941403	+	0.337285i	$0.890491\pi$
$822$	−11.7089	−	8.59505i	−0.408395	−	0.299787i
$823$	12.2789	+	21.2677i	0.428016	+	0.741345i	0.996697	−	0.0812133i	$-0.0258795\pi$
$823$	12.2789	+	21.2677i	0.428016	+	0.741345i	−0.568681	+	0.822558i	$0.692546\pi$
$824$	−24.1824	+	41.8851i	−0.842432	+	1.45914i
$825$		0			0
$826$	−0.212934	+	2.72569i	−0.00740894	+	0.0948388i
$827$			28.2836i			0.983518i	0.870731	+	0.491759i	$0.163646\pi$
$827$			28.2836i			0.983518i	−0.870731	+	0.491759i	$0.836354\pi$
$828$	25.4799	−	8.00354i	0.885487	−	0.278142i
$829$	41.6000	−	24.0178i	1.44483	−	0.834171i	0.446660	−	0.894704i	$-0.352613\pi$
$829$	41.6000	−	24.0178i	1.44483	−	0.834171i	0.998166	+	0.0605325i	$0.0192799\pi$
$830$		0			0
$831$	−5.46063	+	49.6132i	−0.189427	+	1.72106i
$832$		−	20.7823i		−	0.720497i
$833$	14.4859	+	37.6073i	0.501906	+	1.30301i
$834$	−8.07397	+	3.54743i	−0.279579	+	0.122837i
$835$		0			0
$836$	−0.363047	−	0.628816i	−0.0125562	−	0.0217480i
$837$	2.68118	+	13.5943i	0.0926753	+	0.469886i
$838$	−2.89717	−	1.67268i	−0.100081	−	0.0577818i
$839$	26.6446			0.919874			0.459937	−	0.887952i	$-0.347872\pi$
$839$	26.6446			0.919874			0.459937	+	0.887952i	$0.347872\pi$
$840$		0			0
$841$	25.6832			0.885627
$842$	1.86707	+	1.07796i	0.0643436	+	0.0371488i
$843$	13.7853	−	18.7795i	0.474791	−	0.646801i
$844$	−10.6987	−	18.5306i	−0.368263	−	0.637850i
$845$		0			0
$846$	21.2467	+	19.5113i	0.730478	+	0.670812i
$847$	13.3330	−	19.4236i	0.458126	−	0.667402i
$848$			0.117824i			0.00404611i
$849$	24.2353	+	2.66744i	0.831754	+	0.0915463i
$850$		0			0
$851$	37.0422	−	21.3863i	1.26979	−	0.733114i
$852$	27.9150	+	3.07244i	0.956353	+	0.105260i
$853$		−	35.4466i		−	1.21367i	−0.794829	−	0.606834i	$-0.792439\pi$
$853$		−	35.4466i		−	1.21367i	0.794829	−	0.606834i	$-0.207561\pi$
$854$	4.18171	+	8.75415i	0.143095	+	0.299561i
$855$		0			0
$856$	18.4285	−	31.9191i	0.629874	−	1.09097i
$857$	−5.70072	−	9.87394i	−0.194733	−	0.337287i	0.752080	−	0.659072i	$-0.229051\pi$
$857$	−5.70072	−	9.87394i	−0.194733	−	0.337287i	−0.946813	+	0.321785i	$0.895717\pi$
$858$	−5.30774	+	7.23065i	−0.181203	+	0.246850i
$859$	−18.3838	−	10.6139i	−0.627248	−	0.362142i	0.152438	−	0.988313i	$-0.451288\pi$
$859$	−18.3838	−	10.6139i	−0.627248	−	0.362142i	−0.779686	+	0.626171i	$0.784621\pi$
$860$		0			0
$861$	22.4372	+	19.3317i	0.764658	+	0.658822i
$862$	−27.0296			−0.920633
$863$	−1.21717	−	0.702733i	−0.0414329	−	0.0239213i	0.479140	−	0.877738i	$-0.340948\pi$
$863$	−1.21717	−	0.702733i	−0.0414329	−	0.0239213i	−0.520573	+	0.853817i	$0.674282\pi$
$864$	5.64908	+	28.6422i	0.192186	+	0.974427i
$865$		0			0
$866$	−16.7118	+	28.9456i	−0.567889	+	0.983612i
$867$	−25.6031	+	11.2492i	−0.869528	+	0.382042i
$868$	7.07956	+	4.85964i	0.240296	+	0.164947i
$869$			18.5928i			0.630718i
$870$		0			0
$871$	24.2316	−	13.9901i	0.821057	−	0.474037i
$872$	17.9182	−	10.3451i	0.606786	−	0.350328i
$873$	−11.0506	+	3.47114i	−0.374007	+	0.117480i
$874$			2.66719i			0.0902192i
$875$		0			0
$876$	−2.66673	−	6.06949i	−0.0901004	−	0.205069i
$877$	1.05597	−	1.82900i	0.0356577	−	0.0617610i	−0.847646	−	0.530563i	$-0.821981\pi$
$877$	1.05597	−	1.82900i	0.0356577	−	0.0617610i	0.883304	+	0.468802i	$0.155314\pi$
$878$	1.81486	+	3.14343i	0.0612486	+	0.106086i
$879$	23.3368	+	17.1306i	0.787130	+	0.577801i
$880$		0			0
$881$	35.9949			1.21270			0.606349	−	0.795199i	$-0.292634\pi$
$881$	35.9949			1.21270			0.606349	+	0.795199i	$0.292634\pi$
$882$	6.80867	−	17.2886i	0.229260	−	0.582136i
$883$	−17.2298			−0.579828			−0.289914	−	0.957053i	$-0.593627\pi$
$883$	−17.2298			−0.579828			−0.289914	+	0.957053i	$0.593627\pi$
$884$	24.5362	+	14.1660i	0.825242	+	0.476454i
$885$		0			0
$886$	11.6122	+	20.1130i	0.390121	+	0.675709i
$887$	3.12159	−	5.40675i	0.104813	−	0.181541i	−0.808849	−	0.588016i	$-0.799909\pi$
$887$	3.12159	−	5.40675i	0.104813	−	0.181541i	0.913662	+	0.406476i	$0.133242\pi$
$888$	11.5975	+	26.3959i	0.389186	+	0.885789i
$889$	24.1665	+	1.88792i	0.810520	+	0.0633189i
$890$		0			0
$891$	5.53134	−	11.7954i	0.185307	−	0.395162i
$892$	−28.9827	+	16.7332i	−0.970414	+	0.560269i
$893$	3.87864	−	2.23933i	0.129794	−	0.0749364i
$894$	1.07852	−	9.79900i	0.0360711	−	0.327728i
$895$		0			0
$896$	14.5904	+	10.0153i	0.487430	+	0.334587i
$897$	−46.8966	+	20.6048i	−1.56583	+	0.687974i
$898$	6.47602	−	11.2168i	0.216108	−	0.374309i
$899$	−2.42824	−	4.20583i	−0.0809863	−	0.140272i
$900$		0			0
$901$	−6.96011	−	4.01842i	−0.231875	−	0.133873i
$902$	−8.27767			−0.275616
$903$	35.9611	+	30.9837i	1.19671	+	1.03107i
$904$	13.6211			0.453032
$905$		0			0
$906$	−3.73634	+	5.08996i	−0.124132	+	0.169103i
$907$	−19.7880	−	34.2738i	−0.657049	−	1.13804i	−0.981376	−	0.192097i	$-0.938471\pi$
$907$	−19.7880	−	34.2738i	−0.657049	−	1.13804i	0.324327	−	0.945945i	$-0.394862\pi$
$908$	−7.54918	+	13.0756i	−0.250528	+	0.433928i
$909$	−26.8391	+	29.2263i	−0.890197	+	0.969376i
$910$		0			0
$911$			24.4007i			0.808431i	0.914664	+	0.404215i	$0.132455\pi$
$911$			24.4007i			0.808431i	−0.914664	+	0.404215i	$0.867545\pi$
$912$	−0.0598877	−	0.00659149i	−0.00198308	−	0.000218266i
$913$	14.4178	−	8.32415i	0.477161	−	0.275489i
$914$	22.3658	−	12.9129i	0.739795	−	0.427121i
$915$		0			0
$916$		−	33.0990i		−	1.09362i
$917$	−31.2100	+	45.4669i	−1.03064	+	1.50145i
$918$	25.0509	+	8.54892i	0.826804	+	0.282156i
$919$	10.5155	−	18.2133i	0.346873	−	0.600802i	−0.638819	−	0.769357i	$-0.720577\pi$
$919$	10.5155	−	18.2133i	0.346873	−	0.600802i	0.985692	+	0.168555i	$0.0539100\pi$
$920$		0			0
$921$	−9.96499	+	13.5752i	−0.328357	+	0.447317i
$922$	−12.1296	−	7.00305i	−0.399468	−	0.230633i
$923$	−53.8632			−1.77293
$924$	−2.66212	−	7.62223i	−0.0875773	−	0.250753i
$925$		0			0
$926$	−14.6714	−	8.47052i	−0.482131	−	0.278358i
$927$	−11.0861	+	49.7521i	−0.364117	+	1.63407i
$928$	−5.11613	−	8.86140i	−0.167945	−	0.290890i
$929$	6.50741	−	11.2712i	0.213501	−	0.369795i	−0.739307	−	0.673369i	$-0.764847\pi$
$929$	6.50741	−	11.2712i	0.213501	−	0.369795i	0.952808	+	0.303574i	$0.0981799\pi$
$930$		0			0
$931$	−2.24405	−	1.81292i	−0.0735459	−	0.0594160i
$932$		−	35.2172i		−	1.15358i
$933$	0.950203	−	8.63317i	0.0311082	−	0.282637i
$934$	−11.4212	+	6.59404i	−0.373713	+	0.215764i
$935$		0			0
$936$	−10.3471	−	32.9409i	−0.338207	−	1.07671i
$937$			29.9338i			0.977896i	0.872313	+	0.488948i	$0.162619\pi$
$937$			29.9338i			0.977896i	−0.872313	+	0.488948i	$0.837381\pi$
$938$	1.26173	−	16.1509i	0.0411970	−	0.527346i
$939$	12.3521	+	28.1133i	0.403094	+	0.917444i
$940$		0			0
$941$	−3.58035	−	6.20135i	−0.116716	−	0.202158i	0.801748	−	0.597662i	$-0.203903\pi$
$941$	−3.58035	−	6.20135i	−0.116716	−	0.202158i	−0.918464	+	0.395504i	$0.870570\pi$
$942$	−1.53162	−	1.12430i	−0.0499028	−	0.0366317i
$943$	−40.9387	−	23.6360i	−1.33315	−	0.769693i
$944$	0.0985743			0.00320832
$945$		0			0
$946$	−13.2670			−0.431347
$947$	−20.0088	−	11.5521i	−0.650200	−	0.375393i	0.138333	−	0.990386i	$-0.455826\pi$
$947$	−20.0088	−	11.5521i	−0.650200	−	0.375393i	−0.788533	+	0.614993i	$0.789159\pi$
$948$	−21.8276	−	16.0228i	−0.708927	−	0.520396i
$949$	6.35754	+	11.0116i	0.206374	+	0.357451i
$950$		0			0
$951$	−2.92773	−	6.66352i	−0.0949380	−	0.216079i
$952$	39.1244	−	18.6891i	1.26803	−	0.605717i
$953$		−	42.4806i		−	1.37608i	−0.725672	−	0.688040i	$-0.758471\pi$
$953$		−	42.4806i		−	1.37608i	0.725672	−	0.688040i	$-0.241529\pi$
$954$	1.11044	+	3.53515i	0.0359517	+	0.114455i
$955$		0			0
$956$	20.2820	−	11.7098i	0.655965	−	0.378722i
$957$	−0.499559	+	4.53880i	−0.0161484	+	0.146718i
$958$			19.3826i			0.626225i
$959$	−22.6267	+	10.8084i	−0.730655	+	0.349022i
$960$		0			0
$961$	−11.9446	+	20.6886i	−0.385309	+	0.667375i
$962$	−10.4602	−	18.1175i	−0.337249	−	0.584133i
$963$	8.44836	−	37.9143i	0.272245	−	1.22177i
$964$	−5.97119	−	3.44747i	−0.192319	−	0.111036i
$965$		0			0
$966$	−5.53079	+	29.1374i	−0.177950	+	0.937480i
$967$	2.04795			0.0658575			0.0329288	−	0.999458i	$-0.489517\pi$
$967$	2.04795			0.0658575			0.0329288	+	0.999458i	$0.489517\pi$
$968$	−21.9513	−	12.6736i	−0.705542	−	0.407345i
$969$	2.43185	−	3.31288i	0.0781224	−	0.106425i
$970$		0			0
$971$	−29.0027	+	50.2341i	−0.930740	+	1.61209i	−0.148679	+	0.988885i	$0.547502\pi$
$971$	−29.0027	+	50.2341i	−0.930740	+	1.61209i	−0.782060	+	0.623203i	$0.785831\pi$
$972$	9.08084	+	16.6587i	0.291268	+	0.534326i
$973$	−1.18578	+	15.1786i	−0.0380142	+	0.486605i
$974$			11.0067i			0.352678i
$975$		0			0
$976$	0.302930	−	0.174897i	0.00969655	−	0.00559830i
$977$	−43.0694	+	24.8661i	−1.37791	+	0.795538i	−0.991908	−	0.126960i	$-0.959478\pi$
$977$	−43.0694	+	24.8661i	−1.37791	+	0.795538i	−0.386004	+	0.922497i	$0.626145\pi$
$978$	−11.3382	−	1.24793i	−0.362556	−	0.0399044i
$979$			11.2941i			0.360961i
$980$		0			0
$981$	14.7490	−	16.0609i	0.470900	−	0.512785i
$982$	10.2976	−	17.8360i	0.328610	−	0.569170i
$983$	6.95123	+	12.0399i	0.221710	+	0.384013i	0.955327	−	0.295550i	$-0.0955029\pi$
$983$	6.95123	+	12.0399i	0.221710	+	0.384013i	−0.733617	+	0.679563i	$0.762170\pi$
$984$	18.8554	−	25.6864i	0.601089	−	0.818854i
$985$		0			0
$986$	−9.27737			−0.295452
$987$	47.0152	−	16.4204i	1.49651	−	0.522666i
$988$	−2.02810			−0.0645226
$989$	−65.6142	−	37.8824i	−2.08641	−	1.20459i
$990$		0			0
$991$	−4.79414	−	8.30370i	−0.152291	−	0.263776i	0.779778	−	0.626056i	$-0.215332\pi$
$991$	−4.79414	−	8.30370i	−0.152291	−	0.263776i	−0.932069	+	0.362280i	$0.881998\pi$
$992$	7.49102	−	12.9748i	0.237840	−	0.411951i
$993$	2.15705	−	0.947737i	0.0684521	−	0.0300755i
$994$	−17.6491	+	25.7113i	−0.559795	+	0.815514i
$995$		0			0
$996$	−2.65252	+	24.0998i	−0.0840484	+	0.763631i
$997$	20.5651	−	11.8733i	0.651303	−	0.376030i	−0.137652	−	0.990481i	$-0.543956\pi$
$997$	20.5651	−	11.8733i	0.651303	−	0.376030i	0.788955	+	0.614451i	$0.210622\pi$
$998$	−20.2557	+	11.6946i	−0.641182	+	0.370187i
$999$	19.9977	+	22.8776i	0.632699	+	0.723817i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.t.h.26.5	✓	20
3.2	odd	2	inner	525.2.t.h.26.6	yes	20
5.2	odd	4		525.2.q.g.299.11		40
5.3	odd	4		525.2.q.g.299.10		40
5.4	even	2		525.2.t.i.26.6	yes	20
7.3	odd	6	inner	525.2.t.h.101.6	yes	20
15.2	even	4		525.2.q.g.299.9		40
15.8	even	4		525.2.q.g.299.12		40
15.14	odd	2		525.2.t.i.26.5	yes	20
21.17	even	6	inner	525.2.t.h.101.5	yes	20
35.3	even	12		525.2.q.g.374.9		40
35.17	even	12		525.2.q.g.374.12		40
35.24	odd	6		525.2.t.i.101.5	yes	20
105.17	odd	12		525.2.q.g.374.10		40
105.38	odd	12		525.2.q.g.374.11		40
105.59	even	6		525.2.t.i.101.6	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.q.g.299.9		40	15.2	even	4
525.2.q.g.299.10		40	5.3	odd	4
525.2.q.g.299.11		40	5.2	odd	4
525.2.q.g.299.12		40	15.8	even	4
525.2.q.g.374.9		40	35.3	even	12
525.2.q.g.374.10		40	105.17	odd	12
525.2.q.g.374.11		40	105.38	odd	12
525.2.q.g.374.12		40	35.17	even	12
525.2.t.h.26.5	✓	20	1.1	even	1	trivial
525.2.t.h.26.6	yes	20	3.2	odd	2	inner
525.2.t.h.101.5	yes	20	21.17	even	6	inner
525.2.t.h.101.6	yes	20	7.3	odd	6	inner
525.2.t.i.26.5	yes	20	15.14	odd	2
525.2.t.i.26.6	yes	20	5.4	even	2
525.2.t.i.101.5	yes	20	35.24	odd	6
525.2.t.i.101.6	yes	20	105.59	even	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766266 - 0.442404i) q^{2} +(1.39625 + 1.02493i) q^{3} +(-0.608557 - 1.05405i) q^{4} +(-0.616465 - 1.40308i) q^{6} +(-2.63771 - 0.206062i) q^{7} +2.84653i q^{8} +(0.899028 + 2.86212i) q^{9} +O(q^{10})\)	\(q+(-0.766266 - 0.442404i) q^{2} +(1.39625 + 1.02493i) q^{3} +(-0.608557 - 1.05405i) q^{4} +(-0.616465 - 1.40308i) q^{6} +(-2.63771 - 0.206062i) q^{7} +2.84653i q^{8} +(0.899028 + 2.86212i) q^{9} +(-1.25362 + 0.723775i) q^{11} +(0.230634 - 2.09545i) q^{12} +4.04326i q^{13} +(1.93003 + 1.32483i) q^{14} +(0.0422021 - 0.0730962i) q^{16} +(2.87862 + 4.98592i) q^{17} +(0.577320 - 2.59088i) q^{18} +(-0.356910 - 0.206062i) q^{19} +(-3.47171 - 2.99119i) q^{21} +1.28081 q^{22} +(6.33444 + 3.65719i) q^{23} +(-2.91750 + 3.97447i) q^{24} +(1.78875 - 3.09821i) q^{26} +(-1.67821 + 4.91768i) q^{27} +(1.38800 + 2.90569i) q^{28} -1.82121i q^{29} +(2.30936 - 1.33331i) q^{31} +(4.86566 - 2.80919i) q^{32} +(-2.49218 - 0.274300i) q^{33} -5.09406i q^{34} +(2.46972 - 2.68939i) q^{36} +(2.92387 - 5.06429i) q^{37} +(0.182325 + 0.315797i) q^{38} +(-4.14406 + 5.64540i) q^{39} -6.46287 q^{41} +(1.33694 + 3.82795i) q^{42} -10.3583 q^{43} +(1.52579 + 0.880917i) q^{44} +(-3.23592 - 5.60477i) q^{46} +(-5.43364 + 9.41134i) q^{47} +(0.133843 - 0.0588063i) q^{48} +(6.91508 + 1.08706i) q^{49} +(-1.09095 + 9.91198i) q^{51} +(4.26180 - 2.46055i) q^{52} +(-1.20893 + 0.697977i) q^{53} +(3.46156 - 3.02581i) q^{54} +(0.586561 - 7.50833i) q^{56} +(-0.287136 - 0.653522i) q^{57} +(-0.805713 + 1.39554i) q^{58} +(0.583941 + 1.01142i) q^{59} +(3.58903 + 2.07213i) q^{61} -2.35944 q^{62} +(-1.78160 - 7.73472i) q^{63} -5.14000 q^{64} +(1.78832 + 1.31274i) q^{66} +(-3.46011 - 5.99309i) q^{67} +(3.50361 - 6.06843i) q^{68} +(5.09609 + 11.5987i) q^{69} +13.3217i q^{71} +(-8.14712 + 2.55911i) q^{72} +(2.72344 - 1.57238i) q^{73} +(-4.48093 + 2.58707i) q^{74} +0.501602i q^{76} +(3.45582 - 1.65079i) q^{77} +(5.67300 - 2.49253i) q^{78} +(6.42216 - 11.1235i) q^{79} +(-7.38350 + 5.14626i) q^{81} +(4.95228 + 2.85920i) q^{82} -11.5010 q^{83} +(-1.04014 + 5.47967i) q^{84} +(7.93724 + 4.58257i) q^{86} +(1.86662 - 2.54287i) q^{87} +(-2.06025 - 3.56845i) q^{88} +(3.90111 - 6.75692i) q^{89} +(0.833161 - 10.6650i) q^{91} -8.90244i q^{92} +(4.59099 + 0.505303i) q^{93} +(8.32723 - 4.80773i) q^{94} +(9.67290 + 1.06464i) q^{96} +3.86099i q^{97} +(-4.81787 - 3.89224i) q^{98} +(-3.19857 - 2.93731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{3} + 14 q^{4} - 7 q^{9}+O(q^{10}) \) 20 * q - 3 * q^3 + 14 * q^4 - 7 * q^9	\( 20 q - 3 q^{3} + 14 q^{4} - 7 q^{9} + 21 q^{12} - 18 q^{16} - 14 q^{18} - 9 q^{21} - 20 q^{22} + 18 q^{24} + 10 q^{28} + 42 q^{31} - 12 q^{33} - 36 q^{36} - 24 q^{37} - 33 q^{42} - 36 q^{43} - 8 q^{46} - 4 q^{49} + 21 q^{51} + 84 q^{52} - 75 q^{54} - 6 q^{57} + 4 q^{58} - 90 q^{61} + 5 q^{63} - 120 q^{64} + 6 q^{66} - 20 q^{67} + 35 q^{72} + 48 q^{73} + 108 q^{78} + 46 q^{79} + 29 q^{81} - 36 q^{82} + 75 q^{84} - 69 q^{87} - 4 q^{88} - 30 q^{91} + 30 q^{93} + 6 q^{94} + 135 q^{96} + 94 q^{99}+O(q^{100}) \) 20 * q - 3 * q^3 + 14 * q^4 - 7 * q^9 + 21 * q^12 - 18 * q^16 - 14 * q^18 - 9 * q^21 - 20 * q^22 + 18 * q^24 + 10 * q^28 + 42 * q^31 - 12 * q^33 - 36 * q^36 - 24 * q^37 - 33 * q^42 - 36 * q^43 - 8 * q^46 - 4 * q^49 + 21 * q^51 + 84 * q^52 - 75 * q^54 - 6 * q^57 + 4 * q^58 - 90 * q^61 + 5 * q^63 - 120 * q^64 + 6 * q^66 - 20 * q^67 + 35 * q^72 + 48 * q^73 + 108 * q^78 + 46 * q^79 + 29 * q^81 - 36 * q^82 + 75 * q^84 - 69 * q^87 - 4 * q^88 - 30 * q^91 + 30 * q^93 + 6 * q^94 + 135 * q^96 + 94 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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