LMFDB - Embedded newform 450.2.e.n.301.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(151,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("450.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			301.2
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	450.301
Dual form			450.2.e.n.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.724745 - 1.57313i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.72474 - 0.158919i) q^{6} +(-2.22474 - 3.85337i) q^{7} -1.00000 q^{8} +(-1.94949 - 2.28024i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.724745 - 1.57313i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.72474 - 0.158919i) q^{6} +(-2.22474 - 3.85337i) q^{7} -1.00000 q^{8} +(-1.94949 - 2.28024i) q^{9} +(-0.724745 - 1.25529i) q^{11} +(1.00000 + 1.41421i) q^{12} +(1.22474 - 2.12132i) q^{13} +(2.22474 - 3.85337i) q^{14} +(-0.500000 - 0.866025i) q^{16} +3.89898 q^{17} +(1.00000 - 2.82843i) q^{18} -0.550510 q^{19} +(-7.67423 + 0.707107i) q^{21} +(0.724745 - 1.25529i) q^{22} +(1.44949 - 2.51059i) q^{23} +(-0.724745 + 1.57313i) q^{24} +2.44949 q^{26} +(-5.00000 + 1.41421i) q^{27} +4.44949 q^{28} +(3.00000 + 5.19615i) q^{29} +(-3.22474 + 5.58542i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.50000 + 0.230351i) q^{33} +(1.94949 + 3.37662i) q^{34} +(2.94949 - 0.548188i) q^{36} +8.00000 q^{37} +(-0.275255 - 0.476756i) q^{38} +(-2.44949 - 3.46410i) q^{39} +(0.500000 - 0.866025i) q^{41} +(-4.44949 - 6.29253i) q^{42} +(-3.72474 - 6.45145i) q^{43} +1.44949 q^{44} +2.89898 q^{46} +(-0.224745 - 0.389270i) q^{47} +(-1.72474 + 0.158919i) q^{48} +(-6.39898 + 11.0834i) q^{49} +(2.82577 - 6.13361i) q^{51} +(1.22474 + 2.12132i) q^{52} +8.44949 q^{53} +(-3.72474 - 3.62302i) q^{54} +(2.22474 + 3.85337i) q^{56} +(-0.398979 + 0.866025i) q^{57} +(-3.00000 + 5.19615i) q^{58} +(5.62372 - 9.74058i) q^{59} +(0.224745 + 0.389270i) q^{61} -6.44949 q^{62} +(-4.44949 + 12.5851i) q^{63} +1.00000 q^{64} +(-1.44949 - 2.04989i) q^{66} +(-4.72474 + 8.18350i) q^{67} +(-1.94949 + 3.37662i) q^{68} +(-2.89898 - 4.09978i) q^{69} +2.44949 q^{71} +(1.94949 + 2.28024i) q^{72} -4.79796 q^{73} +(4.00000 + 6.92820i) q^{74} +(0.275255 - 0.476756i) q^{76} +(-3.22474 + 5.58542i) q^{77} +(1.77526 - 3.85337i) q^{78} +(3.67423 + 6.36396i) q^{79} +(-1.39898 + 8.89060i) q^{81} +1.00000 q^{82} +(2.00000 + 3.46410i) q^{83} +(3.22474 - 6.99964i) q^{84} +(3.72474 - 6.45145i) q^{86} +(10.3485 - 0.953512i) q^{87} +(0.724745 + 1.25529i) q^{88} +12.8990 q^{89} -10.8990 q^{91} +(1.44949 + 2.51059i) q^{92} +(6.44949 + 9.12096i) q^{93} +(0.224745 - 0.389270i) q^{94} +(-1.00000 - 1.41421i) q^{96} +(-6.50000 - 11.2583i) q^{97} -12.7980 q^{98} +(-1.44949 + 4.09978i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 2 * q^9	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 2 q^{9} + 2 q^{11} + 4 q^{12} + 4 q^{14} - 2 q^{16} - 4 q^{17} + 4 q^{18} - 12 q^{19} - 16 q^{21} - 2 q^{22} - 4 q^{23} + 2 q^{24} - 20 q^{27} + 8 q^{28} + 12 q^{29} - 8 q^{31} + 2 q^{32} - 10 q^{33} - 2 q^{34} + 2 q^{36} + 32 q^{37} - 6 q^{38} + 2 q^{41} - 8 q^{42} - 10 q^{43} - 4 q^{44} - 8 q^{46} + 4 q^{47} - 2 q^{48} - 6 q^{49} + 26 q^{51} + 24 q^{53} - 10 q^{54} + 4 q^{56} + 18 q^{57} - 12 q^{58} - 2 q^{59} - 4 q^{61} - 16 q^{62} - 8 q^{63} + 4 q^{64} + 4 q^{66} - 14 q^{67} + 2 q^{68} + 8 q^{69} - 2 q^{72} + 20 q^{73} + 16 q^{74} + 6 q^{76} - 8 q^{77} + 12 q^{78} + 14 q^{81} + 4 q^{82} + 8 q^{83} + 8 q^{84} + 10 q^{86} + 12 q^{87} - 2 q^{88} + 32 q^{89} - 24 q^{91} - 4 q^{92} + 16 q^{93} - 4 q^{94} - 4 q^{96} - 26 q^{97} - 12 q^{98} + 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 2 * q^9 + 2 * q^11 + 4 * q^12 + 4 * q^14 - 2 * q^16 - 4 * q^17 + 4 * q^18 - 12 * q^19 - 16 * q^21 - 2 * q^22 - 4 * q^23 + 2 * q^24 - 20 * q^27 + 8 * q^28 + 12 * q^29 - 8 * q^31 + 2 * q^32 - 10 * q^33 - 2 * q^34 + 2 * q^36 + 32 * q^37 - 6 * q^38 + 2 * q^41 - 8 * q^42 - 10 * q^43 - 4 * q^44 - 8 * q^46 + 4 * q^47 - 2 * q^48 - 6 * q^49 + 26 * q^51 + 24 * q^53 - 10 * q^54 + 4 * q^56 + 18 * q^57 - 12 * q^58 - 2 * q^59 - 4 * q^61 - 16 * q^62 - 8 * q^63 + 4 * q^64 + 4 * q^66 - 14 * q^67 + 2 * q^68 + 8 * q^69 - 2 * q^72 + 20 * q^73 + 16 * q^74 + 6 * q^76 - 8 * q^77 + 12 * q^78 + 14 * q^81 + 4 * q^82 + 8 * q^83 + 8 * q^84 + 10 * q^86 + 12 * q^87 - 2 * q^88 + 32 * q^89 - 24 * q^91 - 4 * q^92 + 16 * q^93 - 4 * q^94 - 4 * q^96 - 26 * q^97 - 12 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.724745	−	1.57313i	0.418432	−	0.908248i
$3$	0.724745	−	1.57313i	0.418432	−	0.908248i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.72474	−	0.158919i	0.704124	−	0.0648783i
$7$	−2.22474	−	3.85337i	−0.840875	−	1.45644i	−0.889156	−	0.457604i	$-0.848708\pi$
$7$	−2.22474	−	3.85337i	−0.840875	−	1.45644i	0.0482818	−	0.998834i	$-0.484625\pi$
$8$	−1.00000			−0.353553
$9$	−1.94949	−	2.28024i	−0.649830	−	0.760080i
$10$		0			0
$11$	−0.724745	−	1.25529i	−0.218519	−	0.378486i	0.735837	−	0.677159i	$-0.236789\pi$
$11$	−0.724745	−	1.25529i	−0.218519	−	0.378486i	−0.954355	+	0.298674i	$0.903456\pi$
$12$	1.00000	+	1.41421i	0.288675	+	0.408248i
$13$	1.22474	−	2.12132i	0.339683	−	0.588348i	−0.644690	−	0.764444i	$-0.723014\pi$
$13$	1.22474	−	2.12132i	0.339683	−	0.588348i	0.984373	+	0.176096i	$0.0563468\pi$
$14$	2.22474	−	3.85337i	0.594588	−	1.02986i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.89898			0.945641			0.472821	−	0.881159i	$-0.343236\pi$
$17$	3.89898			0.945641			0.472821	+	0.881159i	$0.343236\pi$
$18$	1.00000	−	2.82843i	0.235702	−	0.666667i
$19$	−0.550510			−0.126296			−0.0631479	−	0.998004i	$-0.520114\pi$
$19$	−0.550510			−0.126296			−0.0631479	+	0.998004i	$0.520114\pi$
$20$		0			0
$21$	−7.67423	+	0.707107i	−1.67466	+	0.154303i
$22$	0.724745	−	1.25529i	0.154516	−	0.267630i
$23$	1.44949	−	2.51059i	0.302240	−	0.523494i	−0.674403	−	0.738363i	$-0.735599\pi$
$23$	1.44949	−	2.51059i	0.302240	−	0.523494i	0.976643	+	0.214869i	$0.0689324\pi$
$24$	−0.724745	+	1.57313i	−0.147938	+	0.321114i
$25$		0			0
$26$	2.44949			0.480384
$27$	−5.00000	+	1.41421i	−0.962250	+	0.272166i
$28$	4.44949			0.840875
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	0.997738	+	0.0672232i	$0.0214140\pi$
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	−0.440652	+	0.897678i	$0.645253\pi$
$30$		0			0
$31$	−3.22474	+	5.58542i	−0.579181	+	1.00317i	0.416392	+	0.909185i	$0.363294\pi$
$31$	−3.22474	+	5.58542i	−0.579181	+	1.00317i	−0.995573	+	0.0939863i	$0.970039\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−2.50000	+	0.230351i	−0.435194	+	0.0400989i
$34$	1.94949	+	3.37662i	0.334335	+	0.579085i
$35$		0			0
$36$	2.94949	−	0.548188i	0.491582	−	0.0913647i
$37$	8.00000			1.31519			0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000			1.31519			0.657596	+	0.753371i	$0.271573\pi$
$38$	−0.275255	−	0.476756i	−0.0446523	−	0.0773400i
$39$	−2.44949	−	3.46410i	−0.392232	−	0.554700i
$40$		0			0
$41$	0.500000	−	0.866025i	0.0780869	−	0.135250i	−0.824338	−	0.566099i	$-0.808452\pi$
$41$	0.500000	−	0.866025i	0.0780869	−	0.135250i	0.902424	+	0.430848i	$0.141786\pi$
$42$	−4.44949	−	6.29253i	−0.686571	−	0.970958i
$43$	−3.72474	−	6.45145i	−0.568018	−	0.983836i	−0.996762	−	0.0804103i	$-0.974377\pi$
$43$	−3.72474	−	6.45145i	−0.568018	−	0.983836i	0.428744	−	0.903426i	$-0.358956\pi$
$44$	1.44949			0.218519
$45$		0			0
$46$	2.89898			0.427431
$47$	−0.224745	−	0.389270i	−0.0327824	−	0.0567808i	0.849169	−	0.528122i	$-0.177104\pi$
$47$	−0.224745	−	0.389270i	−0.0327824	−	0.0567808i	−0.881951	+	0.471341i	$0.843770\pi$
$48$	−1.72474	+	0.158919i	−0.248945	+	0.0229379i
$49$	−6.39898	+	11.0834i	−0.914140	+	1.58334i
$50$		0			0
$51$	2.82577	−	6.13361i	0.395686	−	0.858877i
$52$	1.22474	+	2.12132i	0.169842	+	0.294174i
$53$	8.44949			1.16063			0.580313	−	0.814393i	$-0.302930\pi$
$53$	8.44949			1.16063			0.580313	+	0.814393i	$0.302930\pi$
$54$	−3.72474	−	3.62302i	−0.506874	−	0.493031i
$55$		0			0
$56$	2.22474	+	3.85337i	0.297294	+	0.514928i
$57$	−0.398979	+	0.866025i	−0.0528461	+	0.114708i
$58$	−3.00000	+	5.19615i	−0.393919	+	0.682288i
$59$	5.62372	−	9.74058i	0.732147	−	1.26812i	−0.223817	−	0.974631i	$-0.571852\pi$
$59$	5.62372	−	9.74058i	0.732147	−	1.26812i	0.955964	−	0.293484i	$-0.0948147\pi$
$60$		0			0
$61$	0.224745	+	0.389270i	0.0287756	+	0.0498409i	0.880055	−	0.474873i	$-0.157506\pi$
$61$	0.224745	+	0.389270i	0.0287756	+	0.0498409i	−0.851279	+	0.524713i	$0.824173\pi$
$62$	−6.44949			−0.819086
$63$	−4.44949	+	12.5851i	−0.560583	+	1.58557i
$64$	1.00000			0.125000
$65$		0			0
$66$	−1.44949	−	2.04989i	−0.178420	−	0.252324i
$67$	−4.72474	+	8.18350i	−0.577219	+	0.999773i	0.418577	+	0.908181i	$0.362529\pi$
$67$	−4.72474	+	8.18350i	−0.577219	+	0.999773i	−0.995797	+	0.0915922i	$0.970804\pi$
$68$	−1.94949	+	3.37662i	−0.236410	+	0.409475i
$69$	−2.89898	−	4.09978i	−0.348996	−	0.493555i
$70$		0			0
$71$	2.44949			0.290701			0.145350	−	0.989380i	$-0.453569\pi$
$71$	2.44949			0.290701			0.145350	+	0.989380i	$0.453569\pi$
$72$	1.94949	+	2.28024i	0.229750	+	0.268729i
$73$	−4.79796			−0.561559			−0.280779	−	0.959772i	$-0.590593\pi$
$73$	−4.79796			−0.561559			−0.280779	+	0.959772i	$0.590593\pi$
$74$	4.00000	+	6.92820i	0.464991	+	0.805387i
$75$		0			0
$76$	0.275255	−	0.476756i	0.0315739	−	0.0546876i
$77$	−3.22474	+	5.58542i	−0.367494	+	0.636518i
$78$	1.77526	−	3.85337i	0.201008	−	0.436308i
$79$	3.67423	+	6.36396i	0.413384	+	0.716002i	0.995257	−	0.0972777i	$-0.0310135\pi$
$79$	3.67423	+	6.36396i	0.413384	+	0.716002i	−0.581874	+	0.813279i	$0.697680\pi$
$80$		0			0
$81$	−1.39898	+	8.89060i	−0.155442	+	0.987845i
$82$	1.00000			0.110432
$83$	2.00000	+	3.46410i	0.219529	+	0.380235i	0.954664	−	0.297686i	$-0.0962148\pi$
$83$	2.00000	+	3.46410i	0.219529	+	0.380235i	−0.735135	+	0.677920i	$0.762881\pi$
$84$	3.22474	−	6.99964i	0.351849	−	0.763723i
$85$		0			0
$86$	3.72474	−	6.45145i	0.401650	−	0.695677i
$87$	10.3485	−	0.953512i	1.10947	−	0.102227i
$88$	0.724745	+	1.25529i	0.0772581	+	0.133815i
$89$	12.8990			1.36729			0.683645	−	0.729815i	$-0.260394\pi$
$89$	12.8990			1.36729			0.683645	+	0.729815i	$0.260394\pi$
$90$		0			0
$91$	−10.8990			−1.14252
$92$	1.44949	+	2.51059i	0.151120	+	0.261747i
$93$	6.44949	+	9.12096i	0.668781	+	0.945799i
$94$	0.224745	−	0.389270i	0.0231807	−	0.0401501i
$95$		0			0
$96$	−1.00000	−	1.41421i	−0.102062	−	0.144338i
$97$	−6.50000	−	11.2583i	−0.659975	−	1.14311i	−0.980622	−	0.195911i	$-0.937234\pi$
$97$	−6.50000	−	11.2583i	−0.659975	−	1.14311i	0.320647	−	0.947199i	$-0.396100\pi$
$98$	−12.7980			−1.29279
$99$	−1.44949	+	4.09978i	−0.145679	+	0.412043i
$100$		0			0
$101$	4.00000	+	6.92820i	0.398015	+	0.689382i	0.993481	−	0.113998i	$-0.0363659\pi$
$101$	4.00000	+	6.92820i	0.398015	+	0.689382i	−0.595466	+	0.803380i	$0.703033\pi$
$102$	6.72474	−	0.619620i	0.665849	−	0.0613516i
$103$	−5.12372	+	8.87455i	−0.504856	+	0.874435i	0.495129	+	0.868820i	$0.335121\pi$
$103$	−5.12372	+	8.87455i	−0.504856	+	0.874435i	−0.999984	+	0.00561582i	$0.998212\pi$
$104$	−1.22474	+	2.12132i	−0.120096	+	0.208013i
$105$		0			0
$106$	4.22474	+	7.31747i	0.410343	+	0.710736i
$107$	1.65153			0.159660			0.0798298	−	0.996809i	$-0.474562\pi$
$107$	1.65153			0.159660			0.0798298	+	0.996809i	$0.474562\pi$
$108$	1.27526	−	5.03723i	0.122711	−	0.484708i
$109$	−8.00000			−0.766261			−0.383131	−	0.923694i	$-0.625154\pi$
$109$	−8.00000			−0.766261			−0.383131	+	0.923694i	$0.625154\pi$
$110$		0			0
$111$	5.79796	−	12.5851i	0.550318	−	1.19452i
$112$	−2.22474	+	3.85337i	−0.210219	+	0.364109i
$113$	−2.44949	+	4.24264i	−0.230429	+	0.399114i	−0.957934	−	0.286988i	$-0.907346\pi$
$113$	−2.44949	+	4.24264i	−0.230429	+	0.399114i	0.727506	+	0.686102i	$0.240679\pi$
$114$	−0.949490	+	0.0874863i	−0.0889279	+	0.00819385i
$115$		0			0
$116$	−6.00000			−0.557086
$117$	−7.22474	+	1.34278i	−0.667928	+	0.124140i
$118$	11.2474			1.03541
$119$	−8.67423	−	15.0242i	−0.795166	−	1.37727i
$120$		0			0
$121$	4.44949	−	7.70674i	0.404499	−	0.700613i
$122$	−0.224745	+	0.389270i	−0.0203474	+	0.0352428i
$123$	−1.00000	−	1.41421i	−0.0901670	−	0.127515i
$124$	−3.22474	−	5.58542i	−0.289591	−	0.501586i
$125$		0			0
$126$	−13.1237	+	2.43916i	−1.16915	+	0.217297i
$127$	−2.89898			−0.257243			−0.128621	−	0.991694i	$-0.541055\pi$
$127$	−2.89898			−0.257243			−0.128621	+	0.991694i	$0.541055\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−12.8485	+	1.18386i	−1.13124	+	0.104233i
$130$		0			0
$131$	2.44949	−	4.24264i	0.214013	−	0.370681i	−0.738954	−	0.673756i	$-0.764680\pi$
$131$	2.44949	−	4.24264i	0.214013	−	0.370681i	0.952967	+	0.303075i	$0.0980132\pi$
$132$	1.05051	−	2.28024i	0.0914352	−	0.198469i
$133$	1.22474	+	2.12132i	0.106199	+	0.183942i
$134$	−9.44949			−0.816312
$135$		0			0
$136$	−3.89898			−0.334335
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	0.794808	−	0.606861i	$-0.207572\pi$
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	−0.922961	+	0.384893i	$0.874238\pi$
$138$	2.10102	−	4.56048i	0.178851	−	0.388214i
$139$	5.62372	−	9.74058i	0.476998	−	0.826185i	−0.522654	−	0.852545i	$-0.675058\pi$
$139$	5.62372	−	9.74058i	0.476998	−	0.826185i	0.999653	+	0.0263597i	$0.00839153\pi$
$140$		0			0
$141$	−0.775255	+	0.0714323i	−0.0652883	+	0.00601568i
$142$	1.22474	+	2.12132i	0.102778	+	0.178017i
$143$	−3.55051			−0.296909
$144$	−1.00000	+	2.82843i	−0.0833333	+	0.235702i
$145$		0			0
$146$	−2.39898	−	4.15515i	−0.198541	−	0.343883i
$147$	12.7980	+	18.0990i	1.05556	+	1.49278i
$148$	−4.00000	+	6.92820i	−0.328798	+	0.569495i
$149$	−8.12372	+	14.0707i	−0.665521	+	1.15272i	0.313622	+	0.949548i	$0.398457\pi$
$149$	−8.12372	+	14.0707i	−0.665521	+	1.15272i	−0.979144	+	0.203169i	$0.934876\pi$
$150$		0			0
$151$	3.44949	+	5.97469i	0.280715	+	0.486213i	0.971561	−	0.236789i	$-0.0760949\pi$
$151$	3.44949	+	5.97469i	0.280715	+	0.486213i	−0.690846	+	0.723002i	$0.742762\pi$
$152$	0.550510			0.0446523
$153$	−7.60102	−	8.89060i	−0.614506	−	0.718763i
$154$	−6.44949			−0.519715
$155$		0			0
$156$	4.22474	−	0.389270i	0.338250	−	0.0311665i
$157$	−8.00000	+	13.8564i	−0.638470	+	1.10586i	0.347299	+	0.937754i	$0.387099\pi$
$157$	−8.00000	+	13.8564i	−0.638470	+	1.10586i	−0.985769	+	0.168107i	$0.946235\pi$
$158$	−3.67423	+	6.36396i	−0.292306	+	0.506290i
$159$	6.12372	−	13.2922i	0.485643	−	1.05414i
$160$		0			0
$161$	−12.8990			−1.01658
$162$	−8.39898	+	3.23375i	−0.659886	+	0.254067i
$163$	−0.898979			−0.0704135			−0.0352068	−	0.999380i	$-0.511209\pi$
$163$	−0.898979			−0.0704135			−0.0352068	+	0.999380i	$0.511209\pi$
$164$	0.500000	+	0.866025i	0.0390434	+	0.0676252i
$165$		0			0
$166$	−2.00000	+	3.46410i	−0.155230	+	0.268866i
$167$	12.1237	−	20.9989i	0.938162	−	1.62494i	0.169266	−	0.985570i	$-0.445860\pi$
$167$	12.1237	−	20.9989i	0.938162	−	1.62494i	0.768896	−	0.639374i	$-0.220806\pi$
$168$	7.67423	−	0.707107i	0.592080	−	0.0545545i
$169$	3.50000	+	6.06218i	0.269231	+	0.466321i
$170$		0			0
$171$	1.07321	+	1.25529i	0.0820707	+	0.0959948i
$172$	7.44949			0.568018
$173$	−3.89898	−	6.75323i	−0.296434	−	0.513439i	0.678884	−	0.734246i	$-0.262464\pi$
$173$	−3.89898	−	6.75323i	−0.296434	−	0.513439i	−0.975317	+	0.220807i	$0.929131\pi$
$174$	6.00000	+	8.48528i	0.454859	+	0.643268i
$175$		0			0
$176$	−0.724745	+	1.25529i	−0.0546297	+	0.0946214i
$177$	−11.2474	−	15.9063i	−0.845410	−	1.19559i
$178$	6.44949	+	11.1708i	0.483410	+	0.837290i
$179$	8.89898			0.665141			0.332570	−	0.943078i	$-0.392084\pi$
$179$	8.89898			0.665141			0.332570	+	0.943078i	$0.392084\pi$
$180$		0			0
$181$	10.4495			0.776704			0.388352	−	0.921511i	$-0.373044\pi$
$181$	10.4495			0.776704			0.388352	+	0.921511i	$0.373044\pi$
$182$	−5.44949	−	9.43879i	−0.403943	−	0.699650i
$183$	0.775255	−	0.0714323i	0.0573085	−	0.00528043i
$184$	−1.44949	+	2.51059i	−0.106858	+	0.185083i
$185$		0			0
$186$	−4.67423	+	10.1459i	−0.342732	+	0.743933i
$187$	−2.82577	−	4.89437i	−0.206640	−	0.357912i
$188$	0.449490			0.0327824
$189$	16.5732	+	16.1206i	1.20552	+	1.17260i
$190$		0			0
$191$	3.12372	+	5.41045i	0.226025	+	0.391486i	0.956626	−	0.291318i	$-0.0940936\pi$
$191$	3.12372	+	5.41045i	0.226025	+	0.391486i	−0.730602	+	0.682804i	$0.760760\pi$
$192$	0.724745	−	1.57313i	0.0523040	−	0.113531i
$193$	7.84847	−	13.5939i	0.564945	−	0.978514i	−0.432110	−	0.901821i	$-0.642231\pi$
$193$	7.84847	−	13.5939i	0.564945	−	0.978514i	0.997055	−	0.0766927i	$-0.0244360\pi$
$194$	6.50000	−	11.2583i	0.466673	−	0.808301i
$195$		0			0
$196$	−6.39898	−	11.0834i	−0.457070	−	0.791668i
$197$	−8.00000			−0.569976			−0.284988	−	0.958531i	$-0.591990\pi$
$197$	−8.00000			−0.569976			−0.284988	+	0.958531i	$0.591990\pi$
$198$	−4.27526	+	0.794593i	−0.303829	+	0.0564693i
$199$	20.4495			1.44963			0.724813	−	0.688946i	$-0.241926\pi$
$199$	20.4495			1.44963			0.724813	+	0.688946i	$0.241926\pi$
$200$		0			0
$201$	9.44949	+	13.3636i	0.666516	+	0.942595i
$202$	−4.00000	+	6.92820i	−0.281439	+	0.487467i
$203$	13.3485	−	23.1202i	0.936879	−	1.62272i
$204$	3.89898	+	5.51399i	0.272983	+	0.386056i
$205$		0			0
$206$	−10.2474			−0.713974
$207$	−8.55051	+	1.58919i	−0.594302	+	0.110456i
$208$	−2.44949			−0.169842
$209$	0.398979	+	0.691053i	0.0275980	+	0.0478011i
$210$		0			0
$211$	7.89898	−	13.6814i	0.543788	−	0.941869i	−0.454894	−	0.890546i	$-0.650323\pi$
$211$	7.89898	−	13.6814i	0.543788	−	0.941869i	0.998682	−	0.0513231i	$-0.0163438\pi$
$212$	−4.22474	+	7.31747i	−0.290157	+	0.502566i
$213$	1.77526	−	3.85337i	0.121638	−	0.264029i
$214$	0.825765	+	1.43027i	0.0564482	+	0.0977711i
$215$		0			0
$216$	5.00000	−	1.41421i	0.340207	−	0.0962250i
$217$	28.6969			1.94808
$218$	−4.00000	−	6.92820i	−0.270914	−	0.469237i
$219$	−3.47730	+	7.54782i	−0.234974	+	0.510035i
$220$		0			0
$221$	4.77526	−	8.27098i	0.321218	−	0.556367i
$222$	13.7980	−	1.27135i	0.926058	−	0.0853274i
$223$	−9.44949	−	16.3670i	−0.632785	−	1.09602i	−0.986980	−	0.160844i	$-0.948579\pi$
$223$	−9.44949	−	16.3670i	−0.632785	−	1.09602i	0.354195	−	0.935171i	$-0.384755\pi$
$224$	−4.44949			−0.297294
$225$		0			0
$226$	−4.89898			−0.325875
$227$	−0.724745	−	1.25529i	−0.0481030	−	0.0833169i	0.840971	−	0.541080i	$-0.181984\pi$
$227$	−0.724745	−	1.25529i	−0.0481030	−	0.0833169i	−0.889074	+	0.457763i	$0.848651\pi$
$228$	−0.550510	−	0.778539i	−0.0364584	−	0.0515600i
$229$	6.77526	−	11.7351i	0.447721	−	0.775476i	−0.550516	−	0.834825i	$-0.685569\pi$
$229$	6.77526	−	11.7351i	0.447721	−	0.775476i	0.998237	+	0.0593484i	$0.0189023\pi$
$230$		0			0
$231$	6.44949	+	9.12096i	0.424345	+	0.600115i
$232$	−3.00000	−	5.19615i	−0.196960	−	0.341144i
$233$	15.6969			1.02834			0.514170	−	0.857688i	$-0.328100\pi$
$233$	15.6969			1.02834			0.514170	+	0.857688i	$0.328100\pi$
$234$	−4.77526	−	5.58542i	−0.312168	−	0.365130i
$235$		0			0
$236$	5.62372	+	9.74058i	0.366073	+	0.634058i
$237$	12.6742	−	1.16781i	0.823280	−	0.0758573i
$238$	8.67423	−	15.0242i	0.562267	−	0.973875i
$239$	−14.3485	+	24.8523i	−0.928125	+	1.60756i	−0.141669	+	0.989914i	$0.545247\pi$
$239$	−14.3485	+	24.8523i	−0.928125	+	1.60756i	−0.786456	+	0.617646i	$0.788086\pi$
$240$		0			0
$241$	−0.500000	−	0.866025i	−0.0322078	−	0.0557856i	0.849472	−	0.527633i	$-0.176921\pi$
$241$	−0.500000	−	0.866025i	−0.0322078	−	0.0557856i	−0.881680	+	0.471848i	$0.843587\pi$
$242$	8.89898			0.572048
$243$	12.9722	+	8.64420i	0.832167	+	0.554526i
$244$	−0.449490			−0.0287756
$245$		0			0
$246$	0.724745	−	1.57313i	0.0462080	−	0.100299i
$247$	−0.674235	+	1.16781i	−0.0429005	+	0.0743059i
$248$	3.22474	−	5.58542i	0.204772	−	0.354675i
$249$	6.89898	−	0.635674i	0.437205	−	0.0402842i
$250$		0			0
$251$	11.4495			0.722685			0.361343	−	0.932433i	$-0.382318\pi$
$251$	11.4495			0.722685			0.361343	+	0.932433i	$0.382318\pi$
$252$	−8.67423	−	10.1459i	−0.546425	−	0.639132i
$253$	−4.20204			−0.264180
$254$	−1.44949	−	2.51059i	−0.0909491	−	0.157528i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.94949	+	17.2330i	−0.620632	+	1.07497i	0.368736	+	0.929534i	$0.379791\pi$
$257$	−9.94949	+	17.2330i	−0.620632	+	1.07497i	−0.989368	+	0.145432i	$0.953543\pi$
$258$	−7.44949	−	10.5352i	−0.463785	−	0.655891i
$259$	−17.7980	−	30.8270i	−1.10591	−	1.91549i
$260$		0			0
$261$	6.00000	−	16.9706i	0.371391	−	1.05045i
$262$	4.89898			0.302660
$263$	3.77526	+	6.53893i	0.232792	+	0.403208i	0.958629	−	0.284659i	$-0.0918805\pi$
$263$	3.77526	+	6.53893i	0.232792	+	0.403208i	−0.725837	+	0.687867i	$0.758547\pi$
$264$	2.50000	−	0.230351i	0.153864	−	0.0141771i
$265$		0			0
$266$	−1.22474	+	2.12132i	−0.0750939	+	0.130066i
$267$	9.34847	−	20.2918i	0.572117	−	1.24184i
$268$	−4.72474	−	8.18350i	−0.288610	−	0.499887i
$269$	−28.0454			−1.70996			−0.854979	−	0.518662i	$-0.826430\pi$
$269$	−28.0454			−1.70996			−0.854979	+	0.518662i	$0.826430\pi$
$270$		0			0
$271$	23.5959			1.43335			0.716675	−	0.697407i	$-0.245663\pi$
$271$	23.5959			1.43335			0.716675	+	0.697407i	$0.245663\pi$
$272$	−1.94949	−	3.37662i	−0.118205	−	0.204737i
$273$	−7.89898	+	17.1455i	−0.478068	+	1.03770i
$274$	1.50000	−	2.59808i	0.0906183	−	0.156956i
$275$		0			0
$276$	5.00000	−	0.460702i	0.300965	−	0.0277310i
$277$	−4.79796	−	8.31031i	−0.288281	−	0.499318i	0.685118	−	0.728432i	$-0.259751\pi$
$277$	−4.79796	−	8.31031i	−0.288281	−	0.499318i	−0.973400	+	0.229114i	$0.926417\pi$
$278$	11.2474			0.674577
$279$	19.0227	−	3.53553i	1.13886	−	0.211667i
$280$		0			0
$281$	−6.00000	−	10.3923i	−0.357930	−	0.619953i	0.629685	−	0.776851i	$-0.283184\pi$
$281$	−6.00000	−	10.3923i	−0.357930	−	0.619953i	−0.987615	+	0.156898i	$0.949851\pi$
$282$	−0.449490	−	0.635674i	−0.0267667	−	0.0378539i
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	−0.919327	−	0.393494i	$-0.871266\pi$
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	0.800439	+	0.599414i	$0.204600\pi$
$284$	−1.22474	+	2.12132i	−0.0726752	+	0.125877i
$285$		0			0
$286$	−1.77526	−	3.07483i	−0.104973	−	0.181819i
$287$	−4.44949			−0.262645
$288$	−2.94949	+	0.548188i	−0.173800	+	0.0323023i
$289$	−1.79796			−0.105762
$290$		0			0
$291$	−22.4217	+	2.06594i	−1.31438	+	0.121108i
$292$	2.39898	−	4.15515i	0.140390	−	0.243162i
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	0.473763	+	0.880652i	$0.342895\pi$
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	−0.999549	+	0.0300351i	$0.990438\pi$
$294$	−9.27526	+	20.1329i	−0.540944	+	1.17417i
$295$		0			0
$296$	−8.00000			−0.464991
$297$	5.39898	+	5.25153i	0.313281	+	0.304725i
$298$	−16.2474			−0.941189
$299$	−3.55051	−	6.14966i	−0.205331	−	0.355644i
$300$		0			0
$301$	−16.5732	+	28.7056i	−0.955264	+	1.65457i
$302$	−3.44949	+	5.97469i	−0.198496	+	0.343805i
$303$	13.7980	−	1.27135i	0.792672	−	0.0730371i
$304$	0.275255	+	0.476756i	0.0157870	+	0.0273438i
$305$		0			0
$306$	3.89898	−	11.0280i	0.222890	−	0.630428i
$307$	−23.9444			−1.36658			−0.683289	−	0.730148i	$-0.739451\pi$
$307$	−23.9444			−1.36658			−0.683289	+	0.730148i	$0.739451\pi$
$308$	−3.22474	−	5.58542i	−0.183747	−	0.318259i
$309$	10.2474	+	14.4921i	0.582957	+	0.824426i
$310$		0			0
$311$	−11.4495	+	19.8311i	−0.649241	+	1.12452i	0.334063	+	0.942551i	$0.391580\pi$
$311$	−11.4495	+	19.8311i	−0.649241	+	1.12452i	−0.983304	+	0.181968i	$0.941753\pi$
$312$	2.44949	+	3.46410i	0.138675	+	0.196116i
$313$	−3.84847	−	6.66574i	−0.217528	−	0.376770i	0.736523	−	0.676412i	$-0.236466\pi$
$313$	−3.84847	−	6.66574i	−0.217528	−	0.376770i	−0.954052	+	0.299642i	$0.903133\pi$
$314$	−16.0000			−0.902932
$315$		0			0
$316$	−7.34847			−0.413384
$317$	15.4722	+	26.7986i	0.869005	+	1.50516i	0.863015	+	0.505179i	$0.168573\pi$
$317$	15.4722	+	26.7986i	0.869005	+	1.50516i	0.00599020	+	0.999982i	$0.498093\pi$
$318$	14.5732	−	1.34278i	0.817225	−	0.0752994i
$319$	4.34847	−	7.53177i	0.243468	−	0.421698i
$320$		0			0
$321$	1.19694	−	2.59808i	0.0668066	−	0.145010i
$322$	−6.44949	−	11.1708i	−0.359416	−	0.622527i
$323$	−2.14643			−0.119430
$324$	−7.00000	−	5.65685i	−0.388889	−	0.314270i
$325$		0			0
$326$	−0.449490	−	0.778539i	−0.0248949	−	0.0431193i
$327$	−5.79796	+	12.5851i	−0.320628	+	0.695955i
$328$	−0.500000	+	0.866025i	−0.0276079	+	0.0478183i
$329$	−1.00000	+	1.73205i	−0.0551318	+	0.0954911i
$330$		0			0
$331$	−16.6969	−	28.9199i	−0.917747	−	1.58958i	−0.802829	−	0.596209i	$-0.796673\pi$
$331$	−16.6969	−	28.9199i	−0.917747	−	1.58958i	−0.114917	−	0.993375i	$-0.536660\pi$
$332$	−4.00000			−0.219529
$333$	−15.5959	−	18.2419i	−0.854651	−	0.999651i
$334$	24.2474			1.32676
$335$		0			0
$336$	4.44949	+	6.29253i	0.242740	+	0.343286i
$337$	10.2980	−	17.8366i	0.560966	−	0.971621i	−0.436447	−	0.899730i	$-0.643763\pi$
$337$	10.2980	−	17.8366i	0.560966	−	0.971621i	0.997413	−	0.0718909i	$-0.0229033\pi$
$338$	−3.50000	+	6.06218i	−0.190375	+	0.329739i
$339$	4.89898	+	6.92820i	0.266076	+	0.376288i
$340$		0			0
$341$	9.34847			0.506248
$342$	−0.550510	+	1.55708i	−0.0297682	+	0.0841971i
$343$	25.7980			1.39296
$344$	3.72474	+	6.45145i	0.200825	+	0.347839i
$345$		0			0
$346$	3.89898	−	6.75323i	0.209610	−	0.363056i
$347$	7.62372	−	13.2047i	0.409263	−	0.708864i	−0.585544	−	0.810640i	$-0.699119\pi$
$347$	7.62372	−	13.2047i	0.409263	−	0.708864i	0.994807	+	0.101776i	$0.0324525\pi$
$348$	−4.34847	+	9.43879i	−0.233102	+	0.505972i
$349$	−5.79796	−	10.0424i	−0.310358	−	0.537555i	0.668082	−	0.744088i	$-0.267115\pi$
$349$	−5.79796	−	10.0424i	−0.310358	−	0.537555i	−0.978440	+	0.206532i	$0.933782\pi$
$350$		0			0
$351$	−3.12372	+	12.3387i	−0.166732	+	0.658589i
$352$	−1.44949			−0.0772581
$353$	3.29796	+	5.71223i	0.175533	+	0.304031i	0.940345	−	0.340221i	$-0.110502\pi$
$353$	3.29796	+	5.71223i	0.175533	+	0.304031i	−0.764813	+	0.644253i	$0.777169\pi$
$354$	8.15153	−	17.6937i	0.433249	−	0.940411i
$355$		0			0
$356$	−6.44949	+	11.1708i	−0.341822	+	0.592054i
$357$	−29.9217	+	2.75699i	−1.58362	+	0.145916i
$358$	4.44949	+	7.70674i	0.235163	+	0.407314i
$359$	8.44949			0.445947			0.222974	−	0.974825i	$-0.428424\pi$
$359$	8.44949			0.445947			0.222974	+	0.974825i	$0.428424\pi$
$360$		0			0
$361$	−18.6969			−0.984049
$362$	5.22474	+	9.04952i	0.274606	+	0.475632i
$363$	−8.89898	−	12.5851i	−0.467075	−	0.660544i
$364$	5.44949	−	9.43879i	0.285631	−	0.494727i
$365$		0			0
$366$	0.449490	+	0.635674i	0.0234952	+	0.0332272i
$367$	5.79796	+	10.0424i	0.302651	+	0.524207i	0.976736	−	0.214447i	$-0.0687950\pi$
$367$	5.79796	+	10.0424i	0.302651	+	0.524207i	−0.674085	+	0.738654i	$0.735462\pi$
$368$	−2.89898			−0.151120
$369$	−2.94949	+	0.548188i	−0.153544	+	0.0285375i
$370$		0			0
$371$	−18.7980	−	32.5590i	−0.975941	−	1.69038i
$372$	−11.1237	+	1.02494i	−0.576738	+	0.0531409i
$373$	−12.7980	+	22.1667i	−0.662653	+	1.14775i	0.317263	+	0.948338i	$0.397236\pi$
$373$	−12.7980	+	22.1667i	−0.662653	+	1.14775i	−0.979916	+	0.199411i	$0.936097\pi$
$374$	2.82577	−	4.89437i	0.146117	−	0.253082i
$375$		0			0
$376$	0.224745	+	0.389270i	0.0115903	+	0.0200750i
$377$	14.6969			0.756931
$378$	−5.67423	+	22.4131i	−0.291851	+	1.15281i
$379$	−30.1464			−1.54852			−0.774259	−	0.632869i	$-0.781877\pi$
$379$	−30.1464			−1.54852			−0.774259	+	0.632869i	$0.781877\pi$
$380$		0			0
$381$	−2.10102	+	4.56048i	−0.107639	+	0.233640i
$382$	−3.12372	+	5.41045i	−0.159824	+	0.276823i
$383$	−0.898979	+	1.55708i	−0.0459357	+	0.0795630i	−0.888079	−	0.459691i	$-0.847960\pi$
$383$	−0.898979	+	1.55708i	−0.0459357	+	0.0795630i	0.842143	+	0.539254i	$0.181294\pi$
$384$	1.72474	−	0.158919i	0.0880155	−	0.00810978i
$385$		0			0
$386$	15.6969			0.798953
$387$	−7.44949	+	21.0703i	−0.378679	+	1.07107i
$388$	13.0000			0.659975
$389$	−11.2247	−	19.4418i	−0.569117	−	0.985740i	−0.996654	−	0.0817417i	$-0.973952\pi$
$389$	−11.2247	−	19.4418i	−0.569117	−	0.985740i	0.427536	−	0.903998i	$-0.359382\pi$
$390$		0			0
$391$	5.65153	−	9.78874i	0.285810	−	0.495038i
$392$	6.39898	−	11.0834i	0.323197	−	0.559794i
$393$	−4.89898	−	6.92820i	−0.247121	−	0.349482i
$394$	−4.00000	−	6.92820i	−0.201517	−	0.349038i
$395$		0			0
$396$	−2.82577	−	3.30518i	−0.142000	−	0.166092i
$397$	17.7980			0.893254			0.446627	−	0.894720i	$-0.352625\pi$
$397$	17.7980			0.893254			0.446627	+	0.894720i	$0.352625\pi$
$398$	10.2247	+	17.7098i	0.512520	+	0.887711i
$399$	4.22474	−	0.389270i	0.211502	−	0.0194879i
$400$		0			0
$401$	−14.3990	+	24.9398i	−0.719051	+	1.24543i	0.242326	+	0.970195i	$0.422090\pi$
$401$	−14.3990	+	24.9398i	−0.719051	+	1.24543i	−0.961376	+	0.275237i	$0.911244\pi$
$402$	−6.84847	+	14.8653i	−0.341571	+	0.741414i
$403$	7.89898	+	13.6814i	0.393476	+	0.681521i
$404$	−8.00000			−0.398015
$405$		0			0
$406$	26.6969			1.32495
$407$	−5.79796	−	10.0424i	−0.287394	−	0.497781i
$408$	−2.82577	+	6.13361i	−0.139896	+	0.303659i
$409$	−3.05051	+	5.28364i	−0.150838	+	0.261259i	−0.931536	−	0.363650i	$-0.881531\pi$
$409$	−3.05051	+	5.28364i	−0.150838	+	0.261259i	0.780698	+	0.624909i	$0.214864\pi$
$410$		0			0
$411$	−5.17423	+	0.476756i	−0.255226	+	0.0235166i
$412$	−5.12372	−	8.87455i	−0.252428	−	0.437218i
$413$	−50.0454			−2.46257
$414$	−5.65153	−	6.61037i	−0.277758	−	0.324882i
$415$		0			0
$416$	−1.22474	−	2.12132i	−0.0600481	−	0.104006i
$417$	−11.2474	−	15.9063i	−0.550790	−	0.778935i
$418$	−0.398979	+	0.691053i	−0.0195147	+	0.0338005i
$419$	−0.449490	+	0.778539i	−0.0219590	+	0.0380341i	−0.876796	−	0.480862i	$-0.840324\pi$
$419$	−0.449490	+	0.778539i	−0.0219590	+	0.0380341i	0.854837	+	0.518896i	$0.173657\pi$
$420$		0			0
$421$	8.22474	+	14.2457i	0.400850	+	0.694292i	0.993829	−	0.110926i	$-0.0353817\pi$
$421$	8.22474	+	14.2457i	0.400850	+	0.694292i	−0.592979	+	0.805218i	$0.702048\pi$
$422$	15.7980			0.769033
$423$	−0.449490	+	1.27135i	−0.0218549	+	0.0618151i
$424$	−8.44949			−0.410343
$425$		0			0
$426$	4.22474	−	0.389270i	0.204690	−	0.0188602i
$427$	1.00000	−	1.73205i	0.0483934	−	0.0838198i
$428$	−0.825765	+	1.43027i	−0.0399149	+	0.0691346i
$429$	−2.57321	+	5.58542i	−0.124236	+	0.269667i
$430$		0			0
$431$	13.7526			0.662437			0.331219	−	0.943554i	$-0.392540\pi$
$431$	13.7526			0.662437			0.331219	+	0.943554i	$0.392540\pi$
$432$	3.72474	+	3.62302i	0.179207	+	0.174313i
$433$	23.0000			1.10531			0.552655	−	0.833410i	$-0.313615\pi$
$433$	23.0000			1.10531			0.552655	+	0.833410i	$0.313615\pi$
$434$	14.3485	+	24.8523i	0.688749	+	1.19295i
$435$		0			0
$436$	4.00000	−	6.92820i	0.191565	−	0.331801i
$437$	−0.797959	+	1.38211i	−0.0381716	+	0.0661151i
$438$	−8.27526	+	0.762485i	−0.395407	+	0.0364329i
$439$	11.0227	+	19.0919i	0.526085	+	0.911206i	0.999538	+	0.0303869i	$0.00967395\pi$
$439$	11.0227	+	19.0919i	0.526085	+	0.911206i	−0.473453	+	0.880819i	$0.656993\pi$
$440$		0			0
$441$	37.7474	−	7.01569i	1.79750	−	0.334080i
$442$	9.55051			0.454271
$443$	1.62372	+	2.81237i	0.0771455	+	0.133620i	0.902017	−	0.431700i	$-0.142086\pi$
$443$	1.62372	+	2.81237i	0.0771455	+	0.133620i	−0.824872	+	0.565320i	$0.808753\pi$
$444$	8.00000	+	11.3137i	0.379663	+	0.536925i
$445$		0			0
$446$	9.44949	−	16.3670i	0.447446	−	0.775000i
$447$	16.2474	+	22.9774i	0.768478	+	1.08679i
$448$	−2.22474	−	3.85337i	−0.105109	−	0.182055i
$449$	−0.797959			−0.0376580			−0.0188290	−	0.999823i	$-0.505994\pi$
$449$	−0.797959			−0.0376580			−0.0188290	+	0.999823i	$0.505994\pi$
$450$		0			0
$451$	−1.44949			−0.0682538
$452$	−2.44949	−	4.24264i	−0.115214	−	0.199557i
$453$	11.8990	−	1.09638i	0.559063	−	0.0515123i
$454$	0.724745	−	1.25529i	0.0340140	−	0.0589139i
$455$		0			0
$456$	0.398979	−	0.866025i	0.0186839	−	0.0405554i
$457$	4.05051	+	7.01569i	0.189475	+	0.328180i	0.945075	−	0.326853i	$-0.105988\pi$
$457$	4.05051	+	7.01569i	0.189475	+	0.328180i	−0.755600	+	0.655033i	$0.772655\pi$
$458$	13.5505			0.633174
$459$	−19.4949	+	5.51399i	−0.909944	+	0.257371i
$460$		0			0
$461$	−1.22474	−	2.12132i	−0.0570421	−	0.0987997i	0.836094	−	0.548586i	$-0.184834\pi$
$461$	−1.22474	−	2.12132i	−0.0570421	−	0.0987997i	−0.893136	+	0.449786i	$0.851500\pi$
$462$	−4.67423	+	10.1459i	−0.217465	+	0.472030i
$463$	−12.0000	+	20.7846i	−0.557687	+	0.965943i	0.440002	+	0.897997i	$0.354978\pi$
$463$	−12.0000	+	20.7846i	−0.557687	+	0.965943i	−0.997689	+	0.0679458i	$0.978356\pi$
$464$	3.00000	−	5.19615i	0.139272	−	0.241225i
$465$		0			0
$466$	7.84847	+	13.5939i	0.363573	+	0.629727i
$467$	4.34847			0.201223			0.100612	−	0.994926i	$-0.467920\pi$
$467$	4.34847			0.201223			0.100612	+	0.994926i	$0.467920\pi$
$468$	2.44949	−	6.92820i	0.113228	−	0.320256i
$469$	42.0454			1.94148
$470$		0			0
$471$	16.0000	+	22.6274i	0.737241	+	1.04262i
$472$	−5.62372	+	9.74058i	−0.258853	+	0.448346i
$473$	−5.39898	+	9.35131i	−0.248245	+	0.429974i
$474$	7.34847	+	10.3923i	0.337526	+	0.477334i
$475$		0			0
$476$	17.3485			0.795166
$477$	−16.4722	−	19.2669i	−0.754210	−	0.882169i
$478$	−28.6969			−1.31257
$479$	6.34847	+	10.9959i	0.290069	+	0.502414i	0.973826	−	0.227296i	$-0.0729884\pi$
$479$	6.34847	+	10.9959i	0.290069	+	0.502414i	−0.683757	+	0.729710i	$0.739655\pi$
$480$		0			0
$481$	9.79796	−	16.9706i	0.446748	−	0.773791i
$482$	0.500000	−	0.866025i	0.0227744	−	0.0394464i
$483$	−9.34847	+	20.2918i	−0.425370	+	0.923309i
$484$	4.44949	+	7.70674i	0.202250	+	0.350306i
$485$		0			0
$486$	−1.00000	+	15.5563i	−0.0453609	+	0.705650i
$487$	−34.8990			−1.58142			−0.790712	−	0.612188i	$-0.790289\pi$
$487$	−34.8990			−1.58142			−0.790712	+	0.612188i	$0.790289\pi$
$488$	−0.224745	−	0.389270i	−0.0101737	−	0.0176214i
$489$	−0.651531	+	1.41421i	−0.0294632	+	0.0639529i
$490$		0			0
$491$	−11.7247	+	20.3079i	−0.529130	+	0.916481i	0.470293	+	0.882511i	$0.344148\pi$
$491$	−11.7247	+	20.3079i	−0.529130	+	0.916481i	−0.999423	+	0.0339700i	$0.989185\pi$
$492$	1.72474	−	0.158919i	0.0777575	−	0.00716460i
$493$	11.6969	+	20.2597i	0.526804	+	0.912451i
$494$	−1.34847			−0.0606705
$495$		0			0
$496$	6.44949			0.289591
$497$	−5.44949	−	9.43879i	−0.244443	−	0.423388i
$498$	4.00000	+	5.65685i	0.179244	+	0.253490i
$499$	−1.62372	+	2.81237i	−0.0726879	+	0.125899i	−0.900078	−	0.435728i	$-0.856491\pi$
$499$	−1.62372	+	2.81237i	−0.0726879	+	0.125899i	0.827391	+	0.561627i	$0.189824\pi$
$500$		0			0
$501$	−24.2474	−	34.2911i	−1.08330	−	1.53201i
$502$	5.72474	+	9.91555i	0.255508	+	0.442553i
$503$	9.55051			0.425836			0.212918	−	0.977070i	$-0.431703\pi$
$503$	9.55051			0.425836			0.212918	+	0.977070i	$0.431703\pi$
$504$	4.44949	−	12.5851i	0.198196	−	0.560583i
$505$		0			0
$506$	−2.10102	−	3.63907i	−0.0934018	−	0.161777i
$507$	12.0732	−	1.11243i	0.536190	−	0.0494048i
$508$	1.44949	−	2.51059i	0.0643107	−	0.111389i
$509$	3.79796	−	6.57826i	0.168342	−	0.291576i	−0.769495	−	0.638652i	$-0.779492\pi$
$509$	3.79796	−	6.57826i	0.168342	−	0.291576i	0.937837	+	0.347076i	$0.112826\pi$
$510$		0			0
$511$	10.6742	+	18.4883i	0.472200	+	0.817875i
$512$	−1.00000			−0.0441942
$513$	2.75255	−	0.778539i	0.121528	−	0.0343733i
$514$	−19.8990			−0.877706
$515$		0			0
$516$	5.39898	−	11.7190i	0.237677	−	0.515902i
$517$	−0.325765	+	0.564242i	−0.0143271	+	0.0248153i
$518$	17.7980	−	30.8270i	0.781997	−	1.35446i
$519$	−13.4495	+	1.23924i	−0.590367	+	0.0543966i
$520$		0			0
$521$	−7.69694			−0.337209			−0.168604	−	0.985684i	$-0.553926\pi$
$521$	−7.69694			−0.337209			−0.168604	+	0.985684i	$0.553926\pi$
$522$	17.6969	−	3.28913i	0.774574	−	0.143961i
$523$	−29.7980			−1.30297			−0.651487	−	0.758660i	$-0.725854\pi$
$523$	−29.7980			−1.30297			−0.651487	+	0.758660i	$0.725854\pi$
$524$	2.44949	+	4.24264i	0.107006	+	0.185341i
$525$		0			0
$526$	−3.77526	+	6.53893i	−0.164609	+	0.285111i
$527$	−12.5732	+	21.7774i	−0.547698	+	0.948640i
$528$	1.44949	+	2.04989i	0.0630809	+	0.0892099i
$529$	7.29796	+	12.6404i	0.317303	+	0.549584i
$530$		0			0
$531$	−33.1742	+	6.16572i	−1.43964	+	0.267569i
$532$	−2.44949			−0.106199
$533$	−1.22474	−	2.12132i	−0.0530496	−	0.0918846i
$534$	22.2474	−	2.04989i	0.962741	−	0.0887073i
$535$		0			0
$536$	4.72474	−	8.18350i	0.204078	−	0.353473i
$537$	6.44949	−	13.9993i	0.278316	−	0.604113i
$538$	−14.0227	−	24.2880i	−0.604562	−	1.04713i
$539$	18.5505			0.799027
$540$		0			0
$541$	−39.5959			−1.70236			−0.851181	−	0.524873i	$-0.824113\pi$
$541$	−39.5959			−1.70236			−0.851181	+	0.524873i	$0.824113\pi$
$542$	11.7980	+	20.4347i	0.506766	+	0.877744i
$543$	7.57321	−	16.4384i	0.324998	−	0.705440i
$544$	1.94949	−	3.37662i	0.0835837	−	0.144771i
$545$		0			0
$546$	−18.7980	+	1.73205i	−0.804478	+	0.0741249i
$547$	3.62372	+	6.27647i	0.154939	+	0.268363i	0.933037	−	0.359781i	$-0.117148\pi$
$547$	3.62372	+	6.27647i	0.154939	+	0.268363i	−0.778098	+	0.628143i	$0.783815\pi$
$548$	3.00000			0.128154
$549$	0.449490	−	1.27135i	0.0191838	−	0.0542599i
$550$		0			0
$551$	−1.65153	−	2.86054i	−0.0703576	−	0.121863i
$552$	2.89898	+	4.09978i	0.123389	+	0.174498i
$553$	16.3485	−	28.3164i	0.695208	−	1.20413i
$554$	4.79796	−	8.31031i	0.203846	−	0.353071i
$555$		0			0
$556$	5.62372	+	9.74058i	0.238499	+	0.413092i
$557$	−38.9444			−1.65013			−0.825063	−	0.565040i	$-0.808861\pi$
$557$	−38.9444			−1.65013			−0.825063	+	0.565040i	$0.808861\pi$
$558$	12.5732	+	14.7064i	0.532267	+	0.622571i
$559$	−18.2474			−0.771785
$560$		0			0
$561$	−9.74745	+	0.898133i	−0.411538	+	0.0379192i
$562$	6.00000	−	10.3923i	0.253095	−	0.438373i
$563$	−18.0732	+	31.3037i	−0.761695	+	1.31929i	0.180281	+	0.983615i	$0.442299\pi$
$563$	−18.0732	+	31.3037i	−0.761695	+	1.31929i	−0.941976	+	0.335680i	$0.891034\pi$
$564$	0.325765	−	0.707107i	0.0137172	−	0.0297746i
$565$		0			0
$566$	−4.00000			−0.168133
$567$	37.3712	−	14.3885i	1.56944	−	0.604262i
$568$	−2.44949			−0.102778
$569$	−8.74745	−	15.1510i	−0.366712	−	0.635164i	0.622337	−	0.782749i	$-0.286183\pi$
$569$	−8.74745	−	15.1510i	−0.366712	−	0.635164i	−0.989049	+	0.147585i	$0.952850\pi$
$570$		0			0
$571$	−6.37628	+	11.0440i	−0.266839	+	0.462178i	−0.968044	−	0.250781i	$-0.919312\pi$
$571$	−6.37628	+	11.0440i	−0.266839	+	0.462178i	0.701205	+	0.712960i	$0.252646\pi$
$572$	1.77526	−	3.07483i	0.0742271	−	0.128565i
$573$	10.7753	−	0.992836i	0.450143	−	0.0414763i
$574$	−2.22474	−	3.85337i	−0.0928591	−	0.160837i
$575$		0			0
$576$	−1.94949	−	2.28024i	−0.0812287	−	0.0950100i
$577$	13.6969			0.570211			0.285106	−	0.958496i	$-0.407971\pi$
$577$	13.6969			0.570211			0.285106	+	0.958496i	$0.407971\pi$
$578$	−0.898979	−	1.55708i	−0.0373926	−	0.0647659i
$579$	−15.6969	−	22.1988i	−0.652343	−	0.922552i
$580$		0			0
$581$	8.89898	−	15.4135i	0.369192	−	0.639459i
$582$	−13.0000	−	18.3848i	−0.538867	−	0.762073i
$583$	−6.12372	−	10.6066i	−0.253619	−	0.439281i
$584$	4.79796			0.198541
$585$		0			0
$586$	−18.0000			−0.743573
$587$	−14.9722	−	25.9326i	−0.617969	−	1.07035i	−0.989856	−	0.142075i	$-0.954623\pi$
$587$	−14.9722	−	25.9326i	−0.617969	−	1.07035i	0.371887	−	0.928278i	$-0.378711\pi$
$588$	−22.0732	+	2.03383i	−0.910284	+	0.0838739i
$589$	1.77526	−	3.07483i	0.0731481	−	0.126696i
$590$		0			0
$591$	−5.79796	+	12.5851i	−0.238496	+	0.517680i
$592$	−4.00000	−	6.92820i	−0.164399	−	0.284747i
$593$	41.3939			1.69984			0.849921	−	0.526910i	$-0.176649\pi$
$593$	41.3939			1.69984			0.849921	+	0.526910i	$0.176649\pi$
$594$	−1.84847	+	7.30142i	−0.0758436	+	0.299581i
$595$		0			0
$596$	−8.12372	−	14.0707i	−0.332761	−	0.576358i
$597$	14.8207	−	32.1698i	0.606569	−	1.31662i
$598$	3.55051	−	6.14966i	0.145191	−	0.251478i
$599$	−7.10102	+	12.2993i	−0.290140	+	0.502537i	−0.973843	−	0.227224i	$-0.927035\pi$
$599$	−7.10102	+	12.2993i	−0.290140	+	0.502537i	0.683703	+	0.729761i	$0.260368\pi$
$600$		0			0
$601$	−9.60102	−	16.6295i	−0.391634	−	0.678330i	0.601031	−	0.799225i	$-0.294757\pi$
$601$	−9.60102	−	16.6295i	−0.391634	−	0.678330i	−0.992665	+	0.120896i	$0.961423\pi$
$602$	−33.1464			−1.35095
$603$	27.8712	−	5.18010i	1.13500	−	0.210950i
$604$	−6.89898			−0.280715
$605$		0			0
$606$	8.00000	+	11.3137i	0.324978	+	0.459588i
$607$	−5.79796	+	10.0424i	−0.235332	+	0.407607i	−0.959369	−	0.282154i	$-0.908951\pi$
$607$	−5.79796	+	10.0424i	−0.235332	+	0.407607i	0.724037	+	0.689761i	$0.242284\pi$
$608$	−0.275255	+	0.476756i	−0.0111631	+	0.0193350i
$609$	−26.6969	−	37.7552i	−1.08181	−	1.52992i
$610$		0			0
$611$	−1.10102			−0.0445425
$612$	11.5000	−	2.13737i	0.464860	−	0.0863982i
$613$	16.9444			0.684377			0.342189	−	0.939631i	$-0.388832\pi$
$613$	16.9444			0.684377			0.342189	+	0.939631i	$0.388832\pi$
$614$	−11.9722	−	20.7364i	−0.483158	−	0.836855i
$615$		0			0
$616$	3.22474	−	5.58542i	0.129929	−	0.225043i
$617$	−18.8485	+	32.6465i	−0.758811	+	1.31430i	0.184647	+	0.982805i	$0.440886\pi$
$617$	−18.8485	+	32.6465i	−0.758811	+	1.31430i	−0.943457	+	0.331494i	$0.892447\pi$
$618$	−7.42679	+	16.1206i	−0.298749	+	0.648465i
$619$	16.7247	+	28.9681i	0.672224	+	1.16433i	0.977272	+	0.211989i	$0.0679943\pi$
$619$	16.7247	+	28.9681i	0.672224	+	1.16433i	−0.305048	+	0.952337i	$0.598672\pi$
$620$		0			0
$621$	−3.69694	+	14.6028i	−0.148353	+	0.585992i
$622$	−22.8990			−0.918165
$623$	−28.6969	−	49.7046i	−1.14972	−	1.99137i
$624$	−1.77526	+	3.85337i	−0.0710671	+	0.154258i
$625$		0			0
$626$	3.84847	−	6.66574i	0.153816	−	0.266417i
$627$	1.37628	−	0.126811i	0.0549632	−	0.00506433i
$628$	−8.00000	−	13.8564i	−0.319235	−	0.552931i
$629$	31.1918			1.24370
$630$		0			0
$631$	3.34847			0.133300			0.0666502	−	0.997776i	$-0.478769\pi$
$631$	3.34847			0.133300			0.0666502	+	0.997776i	$0.478769\pi$
$632$	−3.67423	−	6.36396i	−0.146153	−	0.253145i
$633$	−15.7980	−	22.3417i	−0.627912	−	0.888002i
$634$	−15.4722	+	26.7986i	−0.614479	+	1.06431i
$635$		0			0
$636$	8.44949	+	11.9494i	0.335044	+	0.473824i
$637$	15.6742	+	27.1486i	0.621036	+	1.07567i
$638$	8.69694			0.344315
$639$	−4.77526	−	5.58542i	−0.188906	−	0.220956i
$640$		0			0
$641$	18.5000	+	32.0429i	0.730706	+	1.26562i	0.956582	+	0.291464i	$0.0941423\pi$
$641$	18.5000	+	32.0429i	0.730706	+	1.26562i	−0.225876	+	0.974156i	$0.572524\pi$
$642$	2.84847	−	0.262459i	0.112420	−	0.0103584i
$643$	4.62372	−	8.00853i	0.182342	−	0.315825i	−0.760336	−	0.649530i	$-0.774966\pi$
$643$	4.62372	−	8.00853i	0.182342	−	0.315825i	0.942678	+	0.333705i	$0.108299\pi$
$644$	6.44949	−	11.1708i	0.254145	−	0.440193i
$645$		0			0
$646$	−1.07321	−	1.85886i	−0.0422250	−	0.0731359i
$647$	25.1010			0.986823			0.493411	−	0.869796i	$-0.335750\pi$
$647$	25.1010			0.986823			0.493411	+	0.869796i	$0.335750\pi$
$648$	1.39898	−	8.89060i	0.0549571	−	0.349256i
$649$	−16.3031			−0.639951
$650$		0			0
$651$	20.7980	−	45.1441i	0.815136	−	1.76934i
$652$	0.449490	−	0.778539i	0.0176034	−	0.0304899i
$653$	17.0000	−	29.4449i	0.665261	−	1.15227i	−0.313953	−	0.949439i	$-0.601653\pi$
$653$	17.0000	−	29.4449i	0.665261	−	1.15227i	0.979214	−	0.202828i	$-0.0650132\pi$
$654$	−13.7980	+	1.27135i	−0.539543	+	0.0497137i
$655$		0			0
$656$	−1.00000			−0.0390434
$657$	9.35357	+	10.9405i	0.364918	+	0.426829i
$658$	−2.00000			−0.0779681
$659$	8.10102	+	14.0314i	0.315571	+	0.546585i	0.979559	−	0.201159i	$-0.0644706\pi$
$659$	8.10102	+	14.0314i	0.315571	+	0.546585i	−0.663988	+	0.747743i	$0.731137\pi$
$660$		0			0
$661$	6.89898	−	11.9494i	0.268339	−	0.464777i	−0.700094	−	0.714051i	$-0.746859\pi$
$661$	6.89898	−	11.9494i	0.268339	−	0.464777i	0.968433	+	0.249274i	$0.0801919\pi$
$662$	16.6969	−	28.9199i	0.648945	−	1.12401i
$663$	−9.55051	−	13.5065i	−0.370911	−	0.524547i
$664$	−2.00000	−	3.46410i	−0.0776151	−	0.134433i
$665$		0			0
$666$	8.00000	−	22.6274i	0.309994	−	0.876795i
$667$	17.3939			0.673494
$668$	12.1237	+	20.9989i	0.469081	+	0.812472i
$669$	−32.5959	+	3.00340i	−1.26023	+	0.116118i
$670$		0			0
$671$	0.325765	−	0.564242i	0.0125760	−	0.0217823i
$672$	−3.22474	+	6.99964i	−0.124397	+	0.270017i
$673$	9.55051	+	16.5420i	0.368145	+	0.637646i	0.989276	−	0.146061i	$-0.0466596\pi$
$673$	9.55051	+	16.5420i	0.368145	+	0.637646i	−0.621130	+	0.783707i	$0.713326\pi$
$674$	20.5959			0.793325
$675$		0			0
$676$	−7.00000			−0.269231
$677$	−0.202041	−	0.349945i	−0.00776507	−	0.0134495i	0.862117	−	0.506710i	$-0.169138\pi$
$677$	−0.202041	−	0.349945i	−0.00776507	−	0.0134495i	−0.869882	+	0.493260i	$0.835805\pi$
$678$	−3.55051	+	7.70674i	−0.136357	+	0.295976i
$679$	−28.9217	+	50.0938i	−1.10991	+	1.92242i
$680$		0			0
$681$	−2.50000	+	0.230351i	−0.0958002	+	0.00882707i
$682$	4.67423	+	8.09601i	0.178986	+	0.310012i
$683$	−40.5505			−1.55162			−0.775811	−	0.630965i	$-0.782659\pi$
$683$	−40.5505			−1.55162			−0.775811	+	0.630965i	$0.782659\pi$
$684$	−1.62372	+	0.301783i	−0.0620847	+	0.0115390i
$685$		0			0
$686$	12.8990	+	22.3417i	0.492485	+	0.853010i
$687$	−13.5505	−	19.1633i	−0.516984	−	0.731126i
$688$	−3.72474	+	6.45145i	−0.142005	+	0.245959i
$689$	10.3485	−	17.9241i	0.394245	−	0.682853i
$690$		0			0
$691$	10.7980	+	18.7026i	0.410774	+	0.711481i	0.994975	−	0.100128i	$-0.0319253\pi$
$691$	10.7980	+	18.7026i	0.410774	+	0.711481i	−0.584201	+	0.811609i	$0.698592\pi$
$692$	7.79796			0.296434
$693$	19.0227	−	3.53553i	0.722613	−	0.134304i
$694$	15.2474			0.578785
$695$		0			0
$696$	−10.3485	+	0.953512i	−0.392258	+	0.0361428i
$697$	1.94949	−	3.37662i	0.0738422	−	0.127898i
$698$	5.79796	−	10.0424i	0.219456	−	0.380109i
$699$	11.3763	−	24.6934i	0.430290	−	0.933989i
$700$		0			0
$701$	19.3939			0.732497			0.366248	−	0.930517i	$-0.380642\pi$
$701$	19.3939			0.732497			0.366248	+	0.930517i	$0.380642\pi$
$702$	−12.2474	+	3.46410i	−0.462250	+	0.130744i
$703$	−4.40408			−0.166103
$704$	−0.724745	−	1.25529i	−0.0273149	−	0.0473107i
$705$		0			0
$706$	−3.29796	+	5.71223i	−0.124120	+	0.214983i
$707$	17.7980	−	30.8270i	0.669361	−	1.15937i
$708$	19.3990	−	1.78743i	0.729058	−	0.0671757i
$709$	−11.3258	−	19.6168i	−0.425348	−	0.736724i	0.571105	−	0.820877i	$-0.306515\pi$
$709$	−11.3258	−	19.6168i	−0.425348	−	0.736724i	−0.996453	+	0.0841527i	$0.973182\pi$
$710$		0			0
$711$	7.34847	−	20.7846i	0.275589	−	0.779484i
$712$	−12.8990			−0.483410
$713$	9.34847	+	16.1920i	0.350103	+	0.606396i
$714$	−17.3485	−	24.5344i	−0.649250	−	0.918178i
$715$		0			0
$716$	−4.44949	+	7.70674i	−0.166285	+	0.288014i
$717$	28.6969	+	40.5836i	1.07171	+	1.51562i
$718$	4.22474	+	7.31747i	0.157666	+	0.273086i
$719$	22.2020			0.827996			0.413998	−	0.910278i	$-0.364132\pi$
$719$	22.2020			0.827996			0.413998	+	0.910278i	$0.364132\pi$
$720$		0			0
$721$	45.5959			1.69808
$722$	−9.34847	−	16.1920i	−0.347914	−	0.602605i
$723$	−1.72474	+	0.158919i	−0.0641440	+	0.00591025i
$724$	−5.22474	+	9.04952i	−0.194176	+	0.336323i
$725$		0			0
$726$	6.44949	−	13.9993i	0.239363	−	0.519562i
$727$	5.32577	+	9.22450i	0.197522	+	0.342118i	0.947724	−	0.319090i	$-0.103377\pi$
$727$	5.32577	+	9.22450i	0.197522	+	0.342118i	−0.750203	+	0.661208i	$0.770044\pi$
$728$	10.8990			0.403943
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$		0			0
$731$	−14.5227	−	25.1541i	−0.537142	−	0.930357i
$732$	−0.325765	+	0.707107i	−0.0120406	+	0.0261354i
$733$	6.57321	−	11.3851i	0.242787	−	0.420520i	−0.718720	−	0.695300i	$-0.755272\pi$
$733$	6.57321	−	11.3851i	0.242787	−	0.420520i	0.961507	+	0.274780i	$0.0886050\pi$
$734$	−5.79796	+	10.0424i	−0.214007	+	0.370670i
$735$		0			0
$736$	−1.44949	−	2.51059i	−0.0534289	−	0.0925416i
$737$	13.6969			0.504533
$738$	−1.94949	−	2.28024i	−0.0717617	−	0.0839368i
$739$	7.24745			0.266602			0.133301	−	0.991076i	$-0.457442\pi$
$739$	7.24745			0.266602			0.133301	+	0.991076i	$0.457442\pi$
$740$		0			0
$741$	1.34847	+	1.90702i	0.0495373	+	0.0700563i
$742$	18.7980	−	32.5590i	0.690095	−	1.19528i
$743$	6.55051	−	11.3458i	0.240315	−	0.416238i	−0.720489	−	0.693466i	$-0.756083\pi$
$743$	6.55051	−	11.3458i	0.240315	−	0.416238i	0.960804	+	0.277229i	$0.0894160\pi$
$744$	−6.44949	−	9.12096i	−0.236450	−	0.334390i
$745$		0			0
$746$	−25.5959			−0.937133
$747$	4.00000	−	11.3137i	0.146352	−	0.413947i
$748$	5.65153			0.206640
$749$	−3.67423	−	6.36396i	−0.134254	−	0.232534i
$750$		0			0
$751$	−22.4949	+	38.9623i	−0.820850	+	1.42175i	0.0841993	+	0.996449i	$0.473167\pi$
$751$	−22.4949	+	38.9623i	−0.820850	+	1.42175i	−0.905050	+	0.425306i	$0.860167\pi$
$752$	−0.224745	+	0.389270i	−0.00819560	+	0.0141952i
$753$	8.29796	−	18.0116i	0.302394	−	0.656378i
$754$	7.34847	+	12.7279i	0.267615	+	0.463524i
$755$		0			0
$756$	−22.2474	+	6.29253i	−0.809132	+	0.228857i
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$	−15.0732	−	26.1076i	−0.547484	−	0.948270i
$759$	−3.04541	+	6.61037i	−0.110541	+	0.239941i
$760$		0			0
$761$	24.2474	−	41.9978i	0.878969	−	1.52242i	0.0264959	−	0.999649i	$-0.491565\pi$
$761$	24.2474	−	41.9978i	0.878969	−	1.52242i	0.852473	−	0.522771i	$-0.175102\pi$
$762$	−5.00000	+	0.460702i	−0.181131	+	0.0166895i
$763$	17.7980	+	30.8270i	0.644329	+	1.11601i
$764$	−6.24745			−0.226025
$765$		0			0
$766$	−1.79796			−0.0649629
$767$	−13.7753	−	23.8594i	−0.497396	−	0.861515i
$768$	1.00000	+	1.41421i	0.0360844	+	0.0510310i
$769$	12.2474	−	21.2132i	0.441654	−	0.764968i	−0.556158	−	0.831076i	$-0.687725\pi$
$769$	12.2474	−	21.2132i	0.441654	−	0.764968i	0.997812	+	0.0661088i	$0.0210584\pi$
$770$		0			0
$771$	19.8990	+	28.1414i	0.716644	+	1.01349i
$772$	7.84847	+	13.5939i	0.282473	+	0.489257i
$773$	−23.3939			−0.841419			−0.420710	−	0.907195i	$-0.638219\pi$
$773$	−23.3939			−0.841419			−0.420710	+	0.907195i	$0.638219\pi$
$774$	−21.9722	+	4.08372i	−0.789774	+	0.146786i
$775$		0			0
$776$	6.50000	+	11.2583i	0.233336	+	0.404151i
$777$	−61.3939	+	5.65685i	−2.20249	+	0.202939i
$778$	11.2247	−	19.4418i	0.402427	−	0.697023i
$779$	−0.275255	+	0.476756i	−0.00986204	+	0.0170816i
$780$		0			0
$781$	−1.77526	−	3.07483i	−0.0635236	−	0.110026i
$782$	11.3031			0.404197
$783$	−22.3485	−	21.7381i	−0.798669	−	0.776857i
$784$	12.7980			0.457070
$785$		0			0
$786$	3.55051	−	7.70674i	0.126643	−	0.274890i
$787$	−3.69694	+	6.40329i	−0.131782	+	0.228252i	−0.924363	−	0.381513i	$-0.875403\pi$
$787$	−3.69694	+	6.40329i	−0.131782	+	0.228252i	0.792582	+	0.609766i	$0.208736\pi$
$788$	4.00000	−	6.92820i	0.142494	−	0.246807i
$789$	13.0227	−	1.19992i	0.463621	−	0.0427182i
$790$		0			0
$791$	21.7980			0.775046
$792$	1.44949	−	4.09978i	0.0515054	−	0.145679i
$793$	1.10102			0.0390984
$794$	8.89898	+	15.4135i	0.315813	+	0.547004i
$795$		0			0
$796$	−10.2247	+	17.7098i	−0.362406	+	0.627706i
$797$	17.7980	−	30.8270i	0.630436	−	1.09195i	−0.357027	−	0.934094i	$-0.616209\pi$
$797$	17.7980	−	30.8270i	0.630436	−	1.09195i	0.987463	−	0.157853i	$-0.0504572\pi$
$798$	2.44949	+	3.46410i	0.0867110	+	0.122628i
$799$	−0.876276	−	1.51775i	−0.0310004	−	0.0536943i
$800$		0			0
$801$	−25.1464	−	29.4128i	−0.888505	−	1.03925i
$802$	−28.7980			−1.01689
$803$	3.47730	+	6.02285i	0.122711	+	0.212542i
$804$	−16.2980	+	1.50170i	−0.574785	+	0.0529609i
$805$		0			0
$806$	−7.89898	+	13.6814i	−0.278230	+	0.481908i
$807$	−20.3258	+	44.1191i	−0.715501	+	1.55307i
$808$	−4.00000	−	6.92820i	−0.140720	−	0.243733i
$809$	47.0908			1.65562			0.827812	−	0.561005i	$-0.189585\pi$
$809$	47.0908			1.65562			0.827812	+	0.561005i	$0.189585\pi$
$810$		0			0
$811$	−17.2474			−0.605640			−0.302820	−	0.953048i	$-0.597928\pi$
$811$	−17.2474			−0.605640			−0.302820	+	0.953048i	$0.597928\pi$
$812$	13.3485	+	23.1202i	0.468439	+	0.811361i
$813$	17.1010	−	37.1195i	0.599759	−	1.30184i
$814$	5.79796	−	10.0424i	0.203218	−	0.351985i
$815$		0			0
$816$	−6.72474	+	0.619620i	−0.235413	+	0.0216911i
$817$	2.05051	+	3.55159i	0.0717383	+	0.124254i
$818$	−6.10102			−0.213317
$819$	21.2474	+	24.8523i	0.742446	+	0.868409i
$820$		0			0
$821$	21.0227	+	36.4124i	0.733697	+	1.27080i	0.955292	+	0.295662i	$0.0955404\pi$
$821$	21.0227	+	36.4124i	0.733697	+	1.27080i	−0.221595	+	0.975139i	$0.571126\pi$
$822$	−3.00000	−	4.24264i	−0.104637	−	0.147979i
$823$	−3.79796	+	6.57826i	−0.132389	+	0.229304i	−0.924597	−	0.380947i	$-0.875598\pi$
$823$	−3.79796	+	6.57826i	−0.132389	+	0.229304i	0.792208	+	0.610251i	$0.208931\pi$
$824$	5.12372	−	8.87455i	0.178493	−	0.309160i
$825$		0			0
$826$	−25.0227	−	43.3406i	−0.870651	−	1.50801i
$827$	−13.7980			−0.479802			−0.239901	−	0.970797i	$-0.577115\pi$
$827$	−13.7980			−0.479802			−0.239901	+	0.970797i	$0.577115\pi$
$828$	2.89898	−	8.19955i	0.100747	−	0.284954i
$829$	−21.5505			−0.748480			−0.374240	−	0.927332i	$-0.622096\pi$
$829$	−21.5505			−0.748480			−0.374240	+	0.927332i	$0.622096\pi$
$830$		0			0
$831$	−16.5505	+	1.52497i	−0.574131	+	0.0529006i
$832$	1.22474	−	2.12132i	0.0424604	−	0.0735436i
$833$	−24.9495	+	43.2138i	−0.864449	+	1.49727i
$834$	8.15153	−	17.6937i	0.282264	−	0.612684i
$835$		0			0
$836$	−0.797959			−0.0275980
$837$	8.22474	−	32.4876i	0.284289	−	1.12294i
$838$	−0.898979			−0.0310547
$839$	−7.87628	−	13.6421i	−0.271919	−	0.470978i	0.697434	−	0.716649i	$-0.254325\pi$
$839$	−7.87628	−	13.6421i	−0.271919	−	0.470978i	−0.969353	+	0.245671i	$0.920992\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	−8.22474	+	14.2457i	−0.283443	+	0.490938i
$843$	−20.6969	+	1.90702i	−0.712840	+	0.0656814i
$844$	7.89898	+	13.6814i	0.271894	+	0.470934i
$845$		0			0
$846$	−1.32577	+	0.246405i	−0.0455808	+	0.00847158i
$847$	−39.5959			−1.36053
$848$	−4.22474	−	7.31747i	−0.145078	−	0.251283i
$849$	4.00000	+	5.65685i	0.137280	+	0.194143i
$850$		0			0
$851$	11.5959	−	20.0847i	0.397503	−	0.688495i
$852$	2.44949	+	3.46410i	0.0839181	+	0.118678i
$853$	12.5732	+	21.7774i	0.430499	+	0.745646i	0.996916	−	0.0784728i	$-0.0250044\pi$
$853$	12.5732	+	21.7774i	0.430499	+	0.745646i	−0.566418	+	0.824118i	$0.691671\pi$
$854$	2.00000			0.0684386
$855$		0			0
$856$	−1.65153			−0.0564482
$857$	26.6969	+	46.2405i	0.911950	+	1.57954i	0.811306	+	0.584621i	$0.198757\pi$
$857$	26.6969	+	46.2405i	0.911950	+	1.57954i	0.100644	+	0.994923i	$0.467910\pi$
$858$	−6.12372	+	0.564242i	−0.209061	+	0.0192629i
$859$	−17.8712	+	30.9538i	−0.609757	+	1.05613i	0.381524	+	0.924359i	$0.375399\pi$
$859$	−17.8712	+	30.9538i	−0.609757	+	1.05613i	−0.991280	+	0.131770i	$0.957934\pi$
$860$		0			0
$861$	−3.22474	+	6.99964i	−0.109899	+	0.238547i
$862$	6.87628	+	11.9101i	0.234207	+	0.405658i
$863$	21.5505			0.733588			0.366794	−	0.930302i	$-0.380455\pi$
$863$	21.5505			0.733588			0.366794	+	0.930302i	$0.380455\pi$
$864$	−1.27526	+	5.03723i	−0.0433851	+	0.171370i
$865$		0			0
$866$	11.5000	+	19.9186i	0.390786	+	0.676861i
$867$	−1.30306	+	2.82843i	−0.0442543	+	0.0960584i
$868$	−14.3485	+	24.8523i	−0.487019	+	0.843541i
$869$	5.32577	−	9.22450i	0.180664	−	0.312920i
$870$		0			0
$871$	11.5732	+	20.0454i	0.392143	+	0.679212i
$872$	8.00000			0.270914
$873$	−13.0000	+	36.7696i	−0.439983	+	1.24446i
$874$	−1.59592			−0.0539827
$875$		0			0
$876$	−4.79796	−	6.78534i	−0.162108	−	0.229255i
$877$	27.5732	−	47.7582i	0.931081	−	1.61268i	0.149604	−	0.988746i	$-0.452200\pi$
$877$	27.5732	−	47.7582i	0.931081	−	1.61268i	0.781477	−	0.623934i	$-0.214467\pi$
$878$	−11.0227	+	19.0919i	−0.371998	+	0.644320i
$879$	18.0000	+	25.4558i	0.607125	+	0.858604i
$880$		0			0
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$	24.9495	+	29.1824i	0.840093	+	0.982623i
$883$	−11.4495			−0.385306			−0.192653	−	0.981267i	$-0.561709\pi$
$883$	−11.4495			−0.385306			−0.192653	+	0.981267i	$0.561709\pi$
$884$	4.77526	+	8.27098i	0.160609	+	0.278183i
$885$		0			0
$886$	−1.62372	+	2.81237i	−0.0545501	+	0.0944835i
$887$	−2.32577	+	4.02834i	−0.0780916	+	0.135259i	−0.902427	−	0.430844i	$-0.858216\pi$
$887$	−2.32577	+	4.02834i	−0.0780916	+	0.135259i	0.824335	+	0.566102i	$0.191549\pi$
$888$	−5.79796	+	12.5851i	−0.194567	+	0.422327i
$889$	6.44949	+	11.1708i	0.216309	+	0.374658i
$890$		0			0
$891$	12.1742	−	4.68729i	0.407852	−	0.157030i
$892$	18.8990			0.632785
$893$	0.123724	+	0.214297i	0.00414028	+	0.00717117i
$894$	−11.7753	+	25.5594i	−0.393823	+	0.854834i
$895$		0			0
$896$	2.22474	−	3.85337i	0.0743235	−	0.128732i
$897$	−12.2474	+	1.12848i	−0.408930	+	0.0376790i
$898$	−0.398979	−	0.691053i	−0.0133141	−	0.0230607i
$899$	−38.6969			−1.29062
$900$		0			0
$901$	32.9444			1.09754
$902$	−0.724745	−	1.25529i	−0.0241314	−	0.0417967i
$903$	33.1464	+	46.8761i	1.10304	+	1.55994i
$904$	2.44949	−	4.24264i	0.0814688	−	0.141108i
$905$		0			0
$906$	6.89898	+	9.75663i	0.229203	+	0.324142i
$907$	−16.8712	−	29.2217i	−0.560198	−	0.970292i	−0.997479	−	0.0709665i	$-0.977392\pi$
$907$	−16.8712	−	29.2217i	−0.560198	−	0.970292i	0.437281	−	0.899325i	$-0.355942\pi$
$908$	1.44949			0.0481030
$909$	8.00000	−	22.6274i	0.265343	−	0.750504i
$910$		0			0
$911$	0.123724	+	0.214297i	0.00409917	+	0.00709997i	0.868068	−	0.496446i	$-0.165362\pi$
$911$	0.123724	+	0.214297i	0.00409917	+	0.00709997i	−0.863969	+	0.503546i	$0.832029\pi$
$912$	0.949490	−	0.0874863i	0.0314407	−	0.00289696i
$913$	2.89898	−	5.02118i	0.0959422	−	0.166177i
$914$	−4.05051	+	7.01569i	−0.133979	+	0.232058i
$915$		0			0
$916$	6.77526	+	11.7351i	0.223861	+	0.387738i
$917$	−21.7980			−0.719832
$918$	−14.5227	−	14.1261i	−0.479321	−	0.466230i
$919$	10.8990			0.359524			0.179762	−	0.983710i	$-0.442467\pi$
$919$	10.8990			0.359524			0.179762	+	0.983710i	$0.442467\pi$
$920$		0			0
$921$	−17.3536	+	37.6677i	−0.571820	+	1.24119i
$922$	1.22474	−	2.12132i	0.0403348	−	0.0698620i
$923$	3.00000	−	5.19615i	0.0987462	−	0.171033i
$924$	−11.1237	+	1.02494i	−0.365944	+	0.0337182i
$925$		0			0
$926$	−24.0000			−0.788689
$927$	30.2247	−	5.61753i	0.992711	−	0.184504i
$928$	6.00000			0.196960
$929$	27.7980	+	48.1475i	0.912021	+	1.57967i	0.811205	+	0.584762i	$0.198812\pi$
$929$	27.7980	+	48.1475i	0.912021	+	1.57967i	0.100817	+	0.994905i	$0.467854\pi$
$930$		0			0
$931$	3.52270	−	6.10150i	0.115452	−	0.199969i
$932$	−7.84847	+	13.5939i	−0.257085	+	0.445285i
$933$	22.8990	+	32.3840i	0.749679	+	1.06021i
$934$	2.17423	+	3.76588i	0.0711431	+	0.123224i
$935$		0			0
$936$	7.22474	−	1.34278i	0.236148	−	0.0438902i
$937$	−39.5959			−1.29354			−0.646771	−	0.762684i	$-0.723881\pi$
$937$	−39.5959			−1.29354			−0.646771	+	0.762684i	$0.723881\pi$
$938$	21.0227	+	36.4124i	0.686416	+	1.18891i
$939$	−13.2753	+	1.22319i	−0.433222	+	0.0399172i
$940$		0			0
$941$	24.8990	−	43.1263i	0.811684	−	1.40588i	−0.100001	−	0.994987i	$-0.531885\pi$
$941$	24.8990	−	43.1263i	0.811684	−	1.40588i	0.911685	−	0.410890i	$-0.134782\pi$
$942$	−11.5959	+	25.1701i	−0.377815	+	0.820087i
$943$	−1.44949	−	2.51059i	−0.0472019	−	0.0817561i
$944$	−11.2474			−0.366073
$945$		0			0
$946$	−10.7980			−0.351072
$947$	10.6237	+	18.4008i	0.345225	+	0.597947i	0.985395	−	0.170287i	$-0.0544694\pi$
$947$	10.6237	+	18.4008i	0.345225	+	0.597947i	−0.640170	+	0.768233i	$0.721136\pi$
$948$	−5.32577	+	11.5601i	−0.172973	+	0.375455i
$949$	−5.87628	+	10.1780i	−0.190752	+	0.330392i
$950$		0			0
$951$	53.3712	−	4.91764i	1.73068	−	0.159465i
$952$	8.67423	+	15.0242i	0.281134	+	0.486938i
$953$	−50.7980			−1.64551			−0.822754	−	0.568398i	$-0.807563\pi$
$953$	−50.7980			−1.64551			−0.822754	+	0.568398i	$0.807563\pi$
$954$	8.44949	−	23.8988i	0.273562	−	0.773751i
$955$		0			0
$956$	−14.3485	−	24.8523i	−0.464063	−	0.803780i
$957$	−8.69694	−	12.2993i	−0.281132	−	0.397581i
$958$	−6.34847	+	10.9959i	−0.205110	+	0.355260i
$959$	−6.67423	+	11.5601i	−0.215522	+	0.373296i
$960$		0			0
$961$	−5.29796	−	9.17633i	−0.170902	−	0.296011i
$962$	19.5959			0.631798
$963$	−3.21964	−	3.76588i	−0.103752	−	0.121354i
$964$	1.00000			0.0322078
$965$		0			0
$966$	−22.2474	+	2.04989i	−0.715800	+	0.0659541i
$967$	14.3485	−	24.8523i	0.461416	−	0.799195i	−0.537616	−	0.843190i	$-0.680675\pi$
$967$	14.3485	−	24.8523i	0.461416	−	0.799195i	0.999032	+	0.0439944i	$0.0140084\pi$
$968$	−4.44949	+	7.70674i	−0.143012	+	0.247704i
$969$	−1.55561	+	3.37662i	−0.0499735	+	0.108473i
$970$		0			0
$971$	−23.3939			−0.750745			−0.375373	−	0.926874i	$-0.622485\pi$
$971$	−23.3939			−0.750745			−0.375373	+	0.926874i	$0.622485\pi$
$972$	−13.9722	+	6.91215i	−0.448158	+	0.221707i
$973$	−50.0454			−1.60438
$974$	−17.4495	−	30.2234i	−0.559118	−	0.968420i
$975$		0			0
$976$	0.224745	−	0.389270i	0.00719391	−	0.0124602i
$977$	−18.9495	+	32.8215i	−0.606248	+	1.05005i	0.385605	+	0.922664i	$0.373993\pi$
$977$	−18.9495	+	32.8215i	−0.606248	+	1.05005i	−0.991853	+	0.127388i	$0.959341\pi$
$978$	−1.55051	+	0.142865i	−0.0495799	+	0.00456831i
$979$	−9.34847	−	16.1920i	−0.298778	−	0.517499i
$980$		0			0
$981$	15.5959	+	18.2419i	0.497939	+	0.582419i
$982$	−23.4495			−0.748303
$983$	18.6969	+	32.3840i	0.596340	+	1.03289i	0.993356	+	0.115079i	$0.0367122\pi$
$983$	18.6969	+	32.3840i	0.596340	+	1.03289i	−0.397017	+	0.917811i	$0.629954\pi$
$984$	1.00000	+	1.41421i	0.0318788	+	0.0450835i
$985$		0			0
$986$	−11.6969	+	20.2597i	−0.372506	+	0.645200i
$987$	2.00000	+	2.82843i	0.0636607	+	0.0900298i
$988$	−0.674235	−	1.16781i	−0.0214503	−	0.0371529i
$989$	−21.5959			−0.686710
$990$		0			0
$991$	4.00000			0.127064			0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000			0.127064			0.0635321	+	0.997980i	$0.479763\pi$
$992$	3.22474	+	5.58542i	0.102386	+	0.177337i
$993$	−57.5959	+	5.30691i	−1.82775	+	0.168410i
$994$	5.44949	−	9.43879i	0.172847	−	0.299380i
$995$		0			0
$996$	−2.89898	+	6.29253i	−0.0918577	+	0.199386i
$997$	16.4722	+	28.5307i	0.521680	+	0.903576i	0.999682	+	0.0252170i	$0.00802769\pi$
$997$	16.4722	+	28.5307i	0.521680	+	0.903576i	−0.478002	+	0.878359i	$0.658639\pi$
$998$	−3.24745			−0.102796
$999$	−40.0000	+	11.3137i	−1.26554	+	0.357950i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.e.n.301.2		4
3.2	odd	2		1350.2.e.j.901.1		4
5.2	odd	4		90.2.i.b.49.1	✓	8
5.3	odd	4		90.2.i.b.49.4	yes	8
5.4	even	2		450.2.e.k.301.1		4
9.2	odd	6		1350.2.e.j.451.1		4
9.4	even	3		4050.2.a.bq.1.2		2
9.5	odd	6		4050.2.a.bz.1.2		2
9.7	even	3	inner	450.2.e.n.151.2		4
15.2	even	4		270.2.i.b.199.3		8
15.8	even	4		270.2.i.b.199.2		8
15.14	odd	2		1350.2.e.m.901.2		4
20.3	even	4		720.2.by.c.49.1		8
20.7	even	4		720.2.by.c.49.4		8
45.2	even	12		270.2.i.b.19.2		8
45.4	even	6		4050.2.a.bs.1.1		2
45.7	odd	12		90.2.i.b.79.4	yes	8
45.13	odd	12		810.2.c.f.649.3		4
45.14	odd	6		4050.2.a.bm.1.1		2
45.22	odd	12		810.2.c.f.649.1		4
45.23	even	12		810.2.c.e.649.2		4
45.29	odd	6		1350.2.e.m.451.2		4
45.32	even	12		810.2.c.e.649.4		4
45.34	even	6		450.2.e.k.151.1		4
45.38	even	12		270.2.i.b.19.3		8
45.43	odd	12		90.2.i.b.79.1	yes	8
60.23	odd	4		2160.2.by.d.1009.4		8
60.47	odd	4		2160.2.by.d.1009.1		8
180.7	even	12		720.2.by.c.529.1		8
180.43	even	12		720.2.by.c.529.4		8
180.47	odd	12		2160.2.by.d.289.4		8
180.83	odd	12		2160.2.by.d.289.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.i.b.49.1	✓	8	5.2	odd	4
90.2.i.b.49.4	yes	8	5.3	odd	4
90.2.i.b.79.1	yes	8	45.43	odd	12
90.2.i.b.79.4	yes	8	45.7	odd	12
270.2.i.b.19.2		8	45.2	even	12
270.2.i.b.19.3		8	45.38	even	12
270.2.i.b.199.2		8	15.8	even	4
270.2.i.b.199.3		8	15.2	even	4
450.2.e.k.151.1		4	45.34	even	6
450.2.e.k.301.1		4	5.4	even	2
450.2.e.n.151.2		4	9.7	even	3	inner
450.2.e.n.301.2		4	1.1	even	1	trivial
720.2.by.c.49.1		8	20.3	even	4
720.2.by.c.49.4		8	20.7	even	4
720.2.by.c.529.1		8	180.7	even	12
720.2.by.c.529.4		8	180.43	even	12
810.2.c.e.649.2		4	45.23	even	12
810.2.c.e.649.4		4	45.32	even	12
810.2.c.f.649.1		4	45.22	odd	12
810.2.c.f.649.3		4	45.13	odd	12
1350.2.e.j.451.1		4	9.2	odd	6
1350.2.e.j.901.1		4	3.2	odd	2
1350.2.e.m.451.2		4	45.29	odd	6
1350.2.e.m.901.2		4	15.14	odd	2
2160.2.by.d.289.1		8	180.83	odd	12
2160.2.by.d.289.4		8	180.47	odd	12
2160.2.by.d.1009.1		8	60.47	odd	4
2160.2.by.d.1009.4		8	60.23	odd	4
4050.2.a.bm.1.1		2	45.14	odd	6
4050.2.a.bq.1.2		2	9.4	even	3
4050.2.a.bs.1.1		2	45.4	even	6
4050.2.a.bz.1.2		2	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.724745 - 1.57313i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.72474 - 0.158919i) q^{6} +(-2.22474 - 3.85337i) q^{7} -1.00000 q^{8} +(-1.94949 - 2.28024i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.724745 - 1.57313i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.72474 - 0.158919i) q^{6} +(-2.22474 - 3.85337i) q^{7} -1.00000 q^{8} +(-1.94949 - 2.28024i) q^{9} +(-0.724745 - 1.25529i) q^{11} +(1.00000 + 1.41421i) q^{12} +(1.22474 - 2.12132i) q^{13} +(2.22474 - 3.85337i) q^{14} +(-0.500000 - 0.866025i) q^{16} +3.89898 q^{17} +(1.00000 - 2.82843i) q^{18} -0.550510 q^{19} +(-7.67423 + 0.707107i) q^{21} +(0.724745 - 1.25529i) q^{22} +(1.44949 - 2.51059i) q^{23} +(-0.724745 + 1.57313i) q^{24} +2.44949 q^{26} +(-5.00000 + 1.41421i) q^{27} +4.44949 q^{28} +(3.00000 + 5.19615i) q^{29} +(-3.22474 + 5.58542i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.50000 + 0.230351i) q^{33} +(1.94949 + 3.37662i) q^{34} +(2.94949 - 0.548188i) q^{36} +8.00000 q^{37} +(-0.275255 - 0.476756i) q^{38} +(-2.44949 - 3.46410i) q^{39} +(0.500000 - 0.866025i) q^{41} +(-4.44949 - 6.29253i) q^{42} +(-3.72474 - 6.45145i) q^{43} +1.44949 q^{44} +2.89898 q^{46} +(-0.224745 - 0.389270i) q^{47} +(-1.72474 + 0.158919i) q^{48} +(-6.39898 + 11.0834i) q^{49} +(2.82577 - 6.13361i) q^{51} +(1.22474 + 2.12132i) q^{52} +8.44949 q^{53} +(-3.72474 - 3.62302i) q^{54} +(2.22474 + 3.85337i) q^{56} +(-0.398979 + 0.866025i) q^{57} +(-3.00000 + 5.19615i) q^{58} +(5.62372 - 9.74058i) q^{59} +(0.224745 + 0.389270i) q^{61} -6.44949 q^{62} +(-4.44949 + 12.5851i) q^{63} +1.00000 q^{64} +(-1.44949 - 2.04989i) q^{66} +(-4.72474 + 8.18350i) q^{67} +(-1.94949 + 3.37662i) q^{68} +(-2.89898 - 4.09978i) q^{69} +2.44949 q^{71} +(1.94949 + 2.28024i) q^{72} -4.79796 q^{73} +(4.00000 + 6.92820i) q^{74} +(0.275255 - 0.476756i) q^{76} +(-3.22474 + 5.58542i) q^{77} +(1.77526 - 3.85337i) q^{78} +(3.67423 + 6.36396i) q^{79} +(-1.39898 + 8.89060i) q^{81} +1.00000 q^{82} +(2.00000 + 3.46410i) q^{83} +(3.22474 - 6.99964i) q^{84} +(3.72474 - 6.45145i) q^{86} +(10.3485 - 0.953512i) q^{87} +(0.724745 + 1.25529i) q^{88} +12.8990 q^{89} -10.8990 q^{91} +(1.44949 + 2.51059i) q^{92} +(6.44949 + 9.12096i) q^{93} +(0.224745 - 0.389270i) q^{94} +(-1.00000 - 1.41421i) q^{96} +(-6.50000 - 11.2583i) q^{97} -12.7980 q^{98} +(-1.44949 + 4.09978i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 2 q^{9} + 2 q^{11} + 4 q^{12} + 4 q^{14} - 2 q^{16} - 4 q^{17} + 4 q^{18} - 12 q^{19} - 16 q^{21} - 2 q^{22} - 4 q^{23} + 2 q^{24} - 20 q^{27} + 8 q^{28} + 12 q^{29} - 8 q^{31} + 2 q^{32} - 10 q^{33} - 2 q^{34} + 2 q^{36} + 32 q^{37} - 6 q^{38} + 2 q^{41} - 8 q^{42} - 10 q^{43} - 4 q^{44} - 8 q^{46} + 4 q^{47} - 2 q^{48} - 6 q^{49} + 26 q^{51} + 24 q^{53} - 10 q^{54} + 4 q^{56} + 18 q^{57} - 12 q^{58} - 2 q^{59} - 4 q^{61} - 16 q^{62} - 8 q^{63} + 4 q^{64} + 4 q^{66} - 14 q^{67} + 2 q^{68} + 8 q^{69} - 2 q^{72} + 20 q^{73} + 16 q^{74} + 6 q^{76} - 8 q^{77} + 12 q^{78} + 14 q^{81} + 4 q^{82} + 8 q^{83} + 8 q^{84} + 10 q^{86} + 12 q^{87} - 2 q^{88} + 32 q^{89} - 24 q^{91} - 4 q^{92} + 16 q^{93} - 4 q^{94} - 4 q^{96} - 26 q^{97} - 12 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 2 * q^9 + 2 * q^11 + 4 * q^12 + 4 * q^14 - 2 * q^16 - 4 * q^17 + 4 * q^18 - 12 * q^19 - 16 * q^21 - 2 * q^22 - 4 * q^23 + 2 * q^24 - 20 * q^27 + 8 * q^28 + 12 * q^29 - 8 * q^31 + 2 * q^32 - 10 * q^33 - 2 * q^34 + 2 * q^36 + 32 * q^37 - 6 * q^38 + 2 * q^41 - 8 * q^42 - 10 * q^43 - 4 * q^44 - 8 * q^46 + 4 * q^47 - 2 * q^48 - 6 * q^49 + 26 * q^51 + 24 * q^53 - 10 * q^54 + 4 * q^56 + 18 * q^57 - 12 * q^58 - 2 * q^59 - 4 * q^61 - 16 * q^62 - 8 * q^63 + 4 * q^64 + 4 * q^66 - 14 * q^67 + 2 * q^68 + 8 * q^69 - 2 * q^72 + 20 * q^73 + 16 * q^74 + 6 * q^76 - 8 * q^77 + 12 * q^78 + 14 * q^81 + 4 * q^82 + 8 * q^83 + 8 * q^84 + 10 * q^86 + 12 * q^87 - 2 * q^88 + 32 * q^89 - 24 * q^91 - 4 * q^92 + 16 * q^93 - 4 * q^94 - 4 * q^96 - 26 * q^97 - 12 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more