LMFDB - Embedded newform 450.2.e.n.301.1

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			301.1
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	450.301
Dual form			450.2.e.n.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.72474 - 0.158919i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.724745 - 1.57313i) q^{6} +(0.224745 + 0.389270i) q^{7} -1.00000 q^{8} +(2.94949 + 0.548188i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.72474 - 0.158919i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.724745 - 1.57313i) q^{6} +(0.224745 + 0.389270i) q^{7} -1.00000 q^{8} +(2.94949 + 0.548188i) q^{9} +(1.72474 + 2.98735i) q^{11} +(1.00000 - 1.41421i) q^{12} +(-1.22474 + 2.12132i) q^{13} +(-0.224745 + 0.389270i) q^{14} +(-0.500000 - 0.866025i) q^{16} -5.89898 q^{17} +(1.00000 + 2.82843i) q^{18} -5.44949 q^{19} +(-0.325765 - 0.707107i) q^{21} +(-1.72474 + 2.98735i) q^{22} +(-3.44949 + 5.97469i) q^{23} +(1.72474 + 0.158919i) q^{24} -2.44949 q^{26} +(-5.00000 - 1.41421i) q^{27} -0.449490 q^{28} +(3.00000 + 5.19615i) q^{29} +(-0.775255 + 1.34278i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.50000 - 5.42650i) q^{33} +(-2.94949 - 5.10867i) q^{34} +(-1.94949 + 2.28024i) q^{36} +8.00000 q^{37} +(-2.72474 - 4.71940i) q^{38} +(2.44949 - 3.46410i) q^{39} +(0.500000 - 0.866025i) q^{41} +(0.449490 - 0.635674i) q^{42} +(-1.27526 - 2.20881i) q^{43} -3.44949 q^{44} -6.89898 q^{46} +(2.22474 + 3.85337i) q^{47} +(0.724745 + 1.57313i) q^{48} +(3.39898 - 5.88721i) q^{49} +(10.1742 + 0.937458i) q^{51} +(-1.22474 - 2.12132i) q^{52} +3.55051 q^{53} +(-1.27526 - 5.03723i) q^{54} +(-0.224745 - 0.389270i) q^{56} +(9.39898 + 0.866025i) q^{57} +(-3.00000 + 5.19615i) q^{58} +(-6.62372 + 11.4726i) q^{59} +(-2.22474 - 3.85337i) q^{61} -1.55051 q^{62} +(0.449490 + 1.27135i) q^{63} +1.00000 q^{64} +(3.44949 - 4.87832i) q^{66} +(-2.27526 + 3.94086i) q^{67} +(2.94949 - 5.10867i) q^{68} +(6.89898 - 9.75663i) q^{69} -2.44949 q^{71} +(-2.94949 - 0.548188i) q^{72} +14.7980 q^{73} +(4.00000 + 6.92820i) q^{74} +(2.72474 - 4.71940i) q^{76} +(-0.775255 + 1.34278i) q^{77} +(4.22474 + 0.389270i) q^{78} +(-3.67423 - 6.36396i) q^{79} +(8.39898 + 3.23375i) q^{81} +1.00000 q^{82} +(2.00000 + 3.46410i) q^{83} +(0.775255 + 0.0714323i) q^{84} +(1.27526 - 2.20881i) q^{86} +(-4.34847 - 9.43879i) q^{87} +(-1.72474 - 2.98735i) q^{88} +3.10102 q^{89} -1.10102 q^{91} +(-3.44949 - 5.97469i) q^{92} +(1.55051 - 2.19275i) q^{93} +(-2.22474 + 3.85337i) q^{94} +(-1.00000 + 1.41421i) q^{96} +(-6.50000 - 11.2583i) q^{97} +6.79796 q^{98} +(3.44949 + 9.75663i) 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
$3$	−1.72474	−	0.158919i	−0.995782	−	0.0917517i
$3$	−1.72474	−	0.158919i	−0.995782	−	0.0917517i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.724745	−	1.57313i	−0.295876	−	0.642229i
$7$	0.224745	+	0.389270i	0.0849456	+	0.147130i	0.905368	−	0.424628i	$-0.139595\pi$
$7$	0.224745	+	0.389270i	0.0849456	+	0.147130i	−0.820422	+	0.571758i	$0.806262\pi$
$8$	−1.00000			−0.353553
$9$	2.94949	+	0.548188i	0.983163	+	0.182729i
$10$		0			0
$11$	1.72474	+	2.98735i	0.520030	+	0.900719i	0.999729	+	0.0232854i	$0.00741263\pi$
$11$	1.72474	+	2.98735i	0.520030	+	0.900719i	−0.479699	+	0.877433i	$0.659254\pi$
$12$	1.00000	−	1.41421i	0.288675	−	0.408248i
$13$	−1.22474	+	2.12132i	−0.339683	+	0.588348i	−0.984373	−	0.176096i	$-0.943653\pi$
$13$	−1.22474	+	2.12132i	−0.339683	+	0.588348i	0.644690	+	0.764444i	$0.276986\pi$
$14$	−0.224745	+	0.389270i	−0.0600656	+	0.104037i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.89898			−1.43071			−0.715356	−	0.698760i	$-0.753736\pi$
$17$	−5.89898			−1.43071			−0.715356	+	0.698760i	$0.753736\pi$
$18$	1.00000	+	2.82843i	0.235702	+	0.666667i
$19$	−5.44949			−1.25020			−0.625099	−	0.780545i	$-0.714942\pi$
$19$	−5.44949			−1.25020			−0.625099	+	0.780545i	$0.714942\pi$
$20$		0			0
$21$	−0.325765	−	0.707107i	−0.0710878	−	0.154303i
$22$	−1.72474	+	2.98735i	−0.367717	+	0.636904i
$23$	−3.44949	+	5.97469i	−0.719268	+	1.24581i	0.242022	+	0.970271i	$0.422189\pi$
$23$	−3.44949	+	5.97469i	−0.719268	+	1.24581i	−0.961290	+	0.275538i	$0.911144\pi$
$24$	1.72474	+	0.158919i	0.352062	+	0.0324391i
$25$		0			0
$26$	−2.44949			−0.480384
$27$	−5.00000	−	1.41421i	−0.962250	−	0.272166i
$28$	−0.449490			−0.0849456
$29$	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
$31$	−0.775255	+	1.34278i	−0.139240	+	0.241171i	−0.927209	−	0.374544i	$-0.877799\pi$
$31$	−0.775255	+	1.34278i	−0.139240	+	0.241171i	0.787969	+	0.615715i	$0.211133\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−2.50000	−	5.42650i	−0.435194	−	0.944633i
$34$	−2.94949	−	5.10867i	−0.505833	−	0.876129i
$35$		0			0
$36$	−1.94949	+	2.28024i	−0.324915	+	0.380040i
$37$	8.00000			1.31519			0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000			1.31519			0.657596	+	0.753371i	$0.271573\pi$
$38$	−2.72474	−	4.71940i	−0.442012	−	0.765587i
$39$	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	$0.141786\pi$
$42$	0.449490	−	0.635674i	0.0693578	−	0.0980867i
$43$	−1.27526	−	2.20881i	−0.194475	−	0.336840i	0.752254	−	0.658874i	$-0.228967\pi$
$43$	−1.27526	−	2.20881i	−0.194475	−	0.336840i	−0.946728	+	0.322034i	$0.895634\pi$
$44$	−3.44949			−0.520030
$45$		0			0
$46$	−6.89898			−1.01720
$47$	2.22474	+	3.85337i	0.324512	+	0.562072i	0.981414	−	0.191905i	$-0.0614665\pi$
$47$	2.22474	+	3.85337i	0.324512	+	0.562072i	−0.656901	+	0.753977i	$0.728133\pi$
$48$	0.724745	+	1.57313i	0.104608	+	0.227062i
$49$	3.39898	−	5.88721i	0.485568	−	0.841029i
$50$		0			0
$51$	10.1742	+	0.937458i	1.42468	+	0.131270i
$52$	−1.22474	−	2.12132i	−0.169842	−	0.294174i
$53$	3.55051			0.487700			0.243850	−	0.969813i	$-0.421590\pi$
$53$	3.55051			0.487700			0.243850	+	0.969813i	$0.421590\pi$
$54$	−1.27526	−	5.03723i	−0.173540	−	0.685481i
$55$		0			0
$56$	−0.224745	−	0.389270i	−0.0300328	−	0.0520183i
$57$	9.39898	+	0.866025i	1.24493	+	0.114708i
$58$	−3.00000	+	5.19615i	−0.393919	+	0.682288i
$59$	−6.62372	+	11.4726i	−0.862335	+	1.49361i	0.00733331	+	0.999973i	$0.497666\pi$
$59$	−6.62372	+	11.4726i	−0.862335	+	1.49361i	−0.869669	+	0.493636i	$0.835668\pi$
$60$		0			0
$61$	−2.22474	−	3.85337i	−0.284849	−	0.493374i	0.687723	−	0.725973i	$-0.258610\pi$
$61$	−2.22474	−	3.85337i	−0.284849	−	0.493374i	−0.972573	+	0.232599i	$0.925277\pi$
$62$	−1.55051			−0.196915
$63$	0.449490	+	1.27135i	0.0566304	+	0.160175i
$64$	1.00000			0.125000
$65$		0			0
$66$	3.44949	−	4.87832i	0.424603	−	0.600479i
$67$	−2.27526	+	3.94086i	−0.277967	+	0.481452i	−0.970879	−	0.239569i	$-0.922994\pi$
$67$	−2.27526	+	3.94086i	−0.277967	+	0.481452i	0.692913	+	0.721022i	$0.256327\pi$
$68$	2.94949	−	5.10867i	0.357678	−	0.619517i
$69$	6.89898	−	9.75663i	0.830540	−	1.17456i
$70$		0			0
$71$	−2.44949			−0.290701			−0.145350	−	0.989380i	$-0.546431\pi$
$71$	−2.44949			−0.290701			−0.145350	+	0.989380i	$0.546431\pi$
$72$	−2.94949	−	0.548188i	−0.347601	−	0.0646046i
$73$	14.7980			1.73197			0.865985	−	0.500070i	$-0.166692\pi$
$73$	14.7980			1.73197			0.865985	+	0.500070i	$0.166692\pi$
$74$	4.00000	+	6.92820i	0.464991	+	0.805387i
$75$		0			0
$76$	2.72474	−	4.71940i	0.312550	−	0.541352i
$77$	−0.775255	+	1.34278i	−0.0883485	+	0.153024i
$78$	4.22474	+	0.389270i	0.478358	+	0.0440761i
$79$	−3.67423	−	6.36396i	−0.413384	−	0.716002i	0.581874	−	0.813279i	$-0.302320\pi$
$79$	−3.67423	−	6.36396i	−0.413384	−	0.716002i	−0.995257	+	0.0972777i	$0.968987\pi$
$80$		0			0
$81$	8.39898	+	3.23375i	0.933220	+	0.359306i
$82$	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	$0.762881\pi$
$84$	0.775255	+	0.0714323i	0.0845873	+	0.00779390i
$85$		0			0
$86$	1.27526	−	2.20881i	0.137514	−	0.238182i
$87$	−4.34847	−	9.43879i	−0.466205	−	1.01194i
$88$	−1.72474	−	2.98735i	−0.183858	−	0.318452i
$89$	3.10102			0.328708			0.164354	−	0.986401i	$-0.447446\pi$
$89$	3.10102			0.328708			0.164354	+	0.986401i	$0.447446\pi$
$90$		0			0
$91$	−1.10102			−0.115418
$92$	−3.44949	−	5.97469i	−0.359634	−	0.622905i
$93$	1.55051	−	2.19275i	0.160780	−	0.227378i
$94$	−2.22474	+	3.85337i	−0.229465	+	0.397445i
$95$		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	$-0.396100\pi$
$98$	6.79796			0.686698
$99$	3.44949	+	9.75663i	0.346687	+	0.980578i
$100$		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	$0.703033\pi$
$102$	4.27526	+	9.27987i	0.423313	+	0.918844i
$103$	7.12372	−	12.3387i	0.701921	−	1.21576i	−0.265870	−	0.964009i	$-0.585659\pi$
$103$	7.12372	−	12.3387i	0.701921	−	1.21576i	0.967791	−	0.251755i	$-0.0810076\pi$
$104$	1.22474	−	2.12132i	0.120096	−	0.208013i
$105$		0			0
$106$	1.77526	+	3.07483i	0.172428	+	0.298654i
$107$	16.3485			1.58047			0.790233	−	0.612806i	$-0.209959\pi$
$107$	16.3485			1.58047			0.790233	+	0.612806i	$0.209959\pi$
$108$	3.72474	−	3.62302i	0.358414	−	0.348625i
$109$	−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
$111$	−13.7980	−	1.27135i	−1.30964	−	0.120671i
$112$	0.224745	−	0.389270i	0.0212364	−	0.0367825i
$113$	2.44949	−	4.24264i	0.230429	−	0.399114i	−0.727506	−	0.686102i	$-0.759321\pi$
$113$	2.44949	−	4.24264i	0.230429	−	0.399114i	0.957934	+	0.286988i	$0.0926538\pi$
$114$	3.94949	+	8.57277i	0.369904	+	0.802913i
$115$		0			0
$116$	−6.00000			−0.557086
$117$	−4.77526	+	5.58542i	−0.441472	+	0.516372i
$118$	−13.2474			−1.21953
$119$	−1.32577	−	2.29629i	−0.121533	−	0.210501i
$120$		0			0
$121$	−0.449490	+	0.778539i	−0.0408627	+	0.0707763i
$122$	2.22474	−	3.85337i	0.201419	−	0.348868i
$123$	−1.00000	+	1.41421i	−0.0901670	+	0.127515i
$124$	−0.775255	−	1.34278i	−0.0696200	−	0.120585i
$125$		0			0
$126$	−0.876276	+	1.02494i	−0.0780648	+	0.0913093i
$127$	6.89898			0.612185			0.306093	−	0.952002i	$-0.400978\pi$
$127$	6.89898			0.612185			0.306093	+	0.952002i	$0.400978\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	1.84847	+	4.01229i	0.162749	+	0.353262i
$130$		0			0
$131$	−2.44949	+	4.24264i	−0.214013	+	0.370681i	−0.952967	−	0.303075i	$-0.901987\pi$
$131$	−2.44949	+	4.24264i	−0.214013	+	0.370681i	0.738954	+	0.673756i	$0.235320\pi$
$132$	5.94949	+	0.548188i	0.517837	+	0.0477137i
$133$	−1.22474	−	2.12132i	−0.106199	−	0.183942i
$134$	−4.55051			−0.393104
$135$		0			0
$136$	5.89898			0.505833
$137$	−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	$0.874238\pi$
$138$	11.8990	+	1.09638i	1.01291	+	0.0933298i
$139$	−6.62372	+	11.4726i	−0.561817	+	0.973096i	0.435521	+	0.900179i	$0.356564\pi$
$139$	−6.62372	+	11.4726i	−0.561817	+	0.973096i	−0.997338	+	0.0729170i	$0.976769\pi$
$140$		0			0
$141$	−3.22474	−	6.99964i	−0.271573	−	0.589476i
$142$	−1.22474	−	2.12132i	−0.102778	−	0.178017i
$143$	−8.44949			−0.706582
$144$	−1.00000	−	2.82843i	−0.0833333	−	0.235702i
$145$		0			0
$146$	7.39898	+	12.8154i	0.612344	+	1.06061i
$147$	−6.79796	+	9.61377i	−0.560686	+	0.792930i
$148$	−4.00000	+	6.92820i	−0.328798	+	0.569495i
$149$	4.12372	−	7.14250i	0.337829	−	0.585136i	−0.646195	−	0.763172i	$-0.723641\pi$
$149$	4.12372	−	7.14250i	0.337829	−	0.585136i	0.984024	+	0.178036i	$0.0569742\pi$
$150$		0			0
$151$	−1.44949	−	2.51059i	−0.117958	−	0.204309i	0.801000	−	0.598664i	$-0.204301\pi$
$151$	−1.44949	−	2.51059i	−0.117958	−	0.204309i	−0.918958	+	0.394355i	$0.870968\pi$
$152$	5.44949			0.442012
$153$	−17.3990	−	3.23375i	−1.40662	−	0.261433i
$154$	−1.55051			−0.124944
$155$		0			0
$156$	1.77526	+	3.85337i	0.142134	+	0.308517i
$157$	−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	−	0.564242i	−0.485643	−	0.0447473i
$160$		0			0
$161$	−3.10102			−0.244395
$162$	1.39898	+	8.89060i	0.109914	+	0.698512i
$163$	8.89898			0.697022			0.348511	−	0.937305i	$-0.386687\pi$
$163$	8.89898			0.697022			0.348511	+	0.937305i	$0.386687\pi$
$164$	0.500000	+	0.866025i	0.0390434	+	0.0676252i
$165$		0			0
$166$	−2.00000	+	3.46410i	−0.155230	+	0.268866i
$167$	−0.123724	+	0.214297i	−0.00957408	+	0.0165828i	−0.870773	−	0.491686i	$-0.836381\pi$
$167$	−0.123724	+	0.214297i	−0.00957408	+	0.0165828i	0.861199	+	0.508268i	$0.169714\pi$
$168$	0.325765	+	0.707107i	0.0251333	+	0.0545545i
$169$	3.50000	+	6.06218i	0.269231	+	0.466321i
$170$		0			0
$171$	−16.0732	−	2.98735i	−1.22915	−	0.228448i
$172$	2.55051			0.194475
$173$	5.89898	+	10.2173i	0.448491	+	0.776809i	0.998288	−	0.0584890i	$-0.0186282\pi$
$173$	5.89898	+	10.2173i	0.448491	+	0.776809i	−0.549797	+	0.835298i	$0.685295\pi$
$174$	6.00000	−	8.48528i	0.454859	−	0.643268i
$175$		0			0
$176$	1.72474	−	2.98735i	0.130008	−	0.225180i
$177$	13.2474	−	18.7347i	0.995739	−	1.40819i
$178$	1.55051	+	2.68556i	0.116216	+	0.201291i
$179$	−0.898979			−0.0671929			−0.0335964	−	0.999435i	$-0.510696\pi$
$179$	−0.898979			−0.0671929			−0.0335964	+	0.999435i	$0.510696\pi$
$180$		0			0
$181$	5.55051			0.412566			0.206283	−	0.978492i	$-0.433863\pi$
$181$	5.55051			0.412566			0.206283	+	0.978492i	$0.433863\pi$
$182$	−0.550510	−	0.953512i	−0.0408065	−	0.0706790i
$183$	3.22474	+	6.99964i	0.238380	+	0.517428i
$184$	3.44949	−	5.97469i	0.254300	−	0.440460i
$185$		0			0
$186$	2.67423	+	0.246405i	0.196084	+	0.0180673i
$187$	−10.1742	−	17.6223i	−0.744014	−	1.28867i
$188$	−4.44949			−0.324512
$189$	−0.573214	−	2.26418i	−0.0416952	−	0.164695i
$190$		0			0
$191$	−9.12372	−	15.8028i	−0.660170	−	1.14345i	−0.980571	−	0.196165i	$-0.937151\pi$
$191$	−9.12372	−	15.8028i	−0.660170	−	1.14345i	0.320401	−	0.947282i	$-0.396182\pi$
$192$	−1.72474	−	0.158919i	−0.124473	−	0.0114690i
$193$	−6.84847	+	11.8619i	−0.492964	+	0.853838i	−0.999967	−	0.00810596i	$-0.997420\pi$
$193$	−6.84847	+	11.8619i	−0.492964	+	0.853838i	0.507004	+	0.861944i	$0.330753\pi$
$194$	6.50000	−	11.2583i	0.466673	−	0.808301i
$195$		0			0
$196$	3.39898	+	5.88721i	0.242784	+	0.420515i
$197$	−8.00000			−0.569976			−0.284988	−	0.958531i	$-0.591990\pi$
$197$	−8.00000			−0.569976			−0.284988	+	0.958531i	$0.591990\pi$
$198$	−6.72474	+	7.86566i	−0.477907	+	0.558988i
$199$	15.5505			1.10235			0.551173	−	0.834391i	$-0.314180\pi$
$199$	15.5505			1.10235			0.551173	+	0.834391i	$0.314180\pi$
$200$		0			0
$201$	4.55051	−	6.43539i	0.320968	−	0.453918i
$202$	−4.00000	+	6.92820i	−0.281439	+	0.487467i
$203$	−1.34847	+	2.33562i	−0.0946440	+	0.163928i
$204$	−5.89898	+	8.34242i	−0.413011	+	0.584086i
$205$		0			0
$206$	14.2474			0.992667
$207$	−13.4495	+	15.7313i	−0.934804	+	1.09340i
$208$	2.44949			0.169842
$209$	−9.39898	−	16.2795i	−0.650141	−	1.12608i
$210$		0			0
$211$	−1.89898	+	3.28913i	−0.130731	+	0.226433i	−0.923959	−	0.382492i	$-0.875066\pi$
$211$	−1.89898	+	3.28913i	−0.130731	+	0.226433i	0.793227	+	0.608925i	$0.208399\pi$
$212$	−1.77526	+	3.07483i	−0.121925	+	0.211180i
$213$	4.22474	+	0.389270i	0.289475	+	0.0266723i
$214$	8.17423	+	14.1582i	0.558779	+	0.967834i
$215$		0			0
$216$	5.00000	+	1.41421i	0.340207	+	0.0962250i
$217$	−0.696938			−0.0473113
$218$	−4.00000	−	6.92820i	−0.270914	−	0.469237i
$219$	−25.5227	−	2.35167i	−1.72466	−	0.158911i
$220$		0			0
$221$	7.22474	−	12.5136i	0.485989	−	0.841758i
$222$	−5.79796	−	12.5851i	−0.389134	−	0.844654i
$223$	−4.55051	−	7.88171i	−0.304725	−	0.527799i	0.672475	−	0.740120i	$-0.265231\pi$
$223$	−4.55051	−	7.88171i	−0.304725	−	0.527799i	−0.977200	+	0.212321i	$0.931898\pi$
$224$	0.449490			0.0300328
$225$		0			0
$226$	4.89898			0.325875
$227$	1.72474	+	2.98735i	0.114475	+	0.198277i	0.917570	−	0.397574i	$-0.130148\pi$
$227$	1.72474	+	2.98735i	0.114475	+	0.198277i	−0.803095	+	0.595852i	$0.796815\pi$
$228$	−5.44949	+	7.70674i	−0.360901	+	0.510391i
$229$	9.22474	−	15.9777i	0.609588	−	1.05584i	−0.381720	−	0.924278i	$-0.624668\pi$
$229$	9.22474	−	15.9777i	0.609588	−	1.05584i	0.991308	−	0.131560i	$-0.0419986\pi$
$230$		0			0
$231$	1.55051	−	2.19275i	0.102016	−	0.144273i
$232$	−3.00000	−	5.19615i	−0.196960	−	0.341144i
$233$	−13.6969			−0.897316			−0.448658	−	0.893703i	$-0.648098\pi$
$233$	−13.6969			−0.897316			−0.448658	+	0.893703i	$0.648098\pi$
$234$	−7.22474	−	1.34278i	−0.472296	−	0.0877804i
$235$		0			0
$236$	−6.62372	−	11.4726i	−0.431168	−	0.746804i
$237$	5.32577	+	11.5601i	0.345946	+	0.750910i
$238$	1.32577	−	2.29629i	0.0859366	−	0.148847i
$239$	0.348469	−	0.603566i	0.0225406	−	0.0390415i	−0.854535	−	0.519394i	$-0.826158\pi$
$239$	0.348469	−	0.603566i	0.0225406	−	0.0390415i	0.877076	+	0.480352i	$0.159491\pi$
$240$		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	$0.843587\pi$
$242$	−0.898979			−0.0577886
$243$	−13.9722	−	6.91215i	−0.896317	−	0.443415i
$244$	4.44949			0.284849
$245$		0			0
$246$	−1.72474	−	0.158919i	−0.109966	−	0.0101323i
$247$	6.67423	−	11.5601i	0.424671	−	0.735552i
$248$	0.775255	−	1.34278i	0.0492287	−	0.0852667i
$249$	−2.89898	−	6.29253i	−0.183715	−	0.398773i
$250$		0			0
$251$	6.55051			0.413465			0.206732	−	0.978398i	$-0.433717\pi$
$251$	6.55051			0.413465			0.206732	+	0.978398i	$0.433717\pi$
$252$	−1.32577	−	0.246405i	−0.0835154	−	0.0155221i
$253$	−23.7980			−1.49616
$254$	3.44949	+	5.97469i	0.216440	+	0.374885i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.05051	+	8.74774i	−0.315042	+	0.545669i	−0.979446	−	0.201704i	$-0.935352\pi$
$257$	−5.05051	+	8.74774i	−0.315042	+	0.545669i	0.664404	+	0.747373i	$0.268685\pi$
$258$	−2.55051	+	3.60697i	−0.158788	+	0.224560i
$259$	1.79796	+	3.11416i	0.111720	+	0.193504i
$260$		0			0
$261$	6.00000	+	16.9706i	0.371391	+	1.05045i
$262$	−4.89898			−0.302660
$263$	6.22474	+	10.7816i	0.383834	+	0.664820i	0.991607	−	0.129291i	$-0.0412701\pi$
$263$	6.22474	+	10.7816i	0.383834	+	0.664820i	−0.607773	+	0.794111i	$0.707937\pi$
$264$	2.50000	+	5.42650i	0.153864	+	0.333978i
$265$		0			0
$266$	1.22474	−	2.12132i	0.0750939	−	0.130066i
$267$	−5.34847	−	0.492810i	−0.327321	−	0.0301595i
$268$	−2.27526	−	3.94086i	−0.138983	−	0.240726i
$269$	16.0454			0.978306			0.489153	−	0.872198i	$-0.337306\pi$
$269$	16.0454			0.978306			0.489153	+	0.872198i	$0.337306\pi$
$270$		0			0
$271$	−15.5959			−0.947385			−0.473692	−	0.880690i	$-0.657079\pi$
$271$	−15.5959			−0.947385			−0.473692	+	0.880690i	$0.657079\pi$
$272$	2.94949	+	5.10867i	0.178839	+	0.309758i
$273$	1.89898	+	0.174973i	0.114931	+	0.0105898i
$274$	1.50000	−	2.59808i	0.0906183	−	0.156956i
$275$		0			0
$276$	5.00000	+	10.8530i	0.300965	+	0.653274i
$277$	14.7980	+	25.6308i	0.889123	+	1.54001i	0.840914	+	0.541169i	$0.182018\pi$
$277$	14.7980	+	25.6308i	0.889123	+	1.54001i	0.0482095	+	0.998837i	$0.484648\pi$
$278$	−13.2474			−0.794529
$279$	−3.02270	+	3.53553i	−0.180965	+	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	$0.949851\pi$
$282$	4.44949	−	6.29253i	0.264963	−	0.374715i
$283$	−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
$286$	−4.22474	−	7.31747i	−0.249814	−	0.432691i
$287$	0.449490			0.0265325
$288$	1.94949	−	2.28024i	0.114875	−	0.134364i
$289$	17.7980			1.04694
$290$		0			0
$291$	9.42168	+	20.4507i	0.552309	+	1.19884i
$292$	−7.39898	+	12.8154i	−0.432993	+	0.749965i
$293$	−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	$0.990438\pi$
$294$	−11.7247	−	1.08032i	−0.683801	−	0.0630057i
$295$		0			0
$296$	−8.00000			−0.464991
$297$	−4.39898	−	17.3759i	−0.255255	−	1.00825i
$298$	8.24745			0.477762
$299$	−8.44949	−	14.6349i	−0.488647	−	0.846361i
$300$		0			0
$301$	0.573214	−	0.992836i	0.0330395	−	0.0572261i
$302$	1.44949	−	2.51059i	0.0834088	−	0.144468i
$303$	−5.79796	−	12.5851i	−0.333084	−	0.722993i
$304$	2.72474	+	4.71940i	0.156275	+	0.270676i
$305$		0			0
$306$	−5.89898	−	16.6848i	−0.337222	−	0.953808i
$307$	29.9444			1.70902			0.854508	−	0.519438i	$-0.173859\pi$
$307$	29.9444			1.70902			0.854508	+	0.519438i	$0.173859\pi$
$308$	−0.775255	−	1.34278i	−0.0441743	−	0.0765121i
$309$	−14.2474	+	20.1489i	−0.810509	+	1.14623i
$310$		0			0
$311$	−6.55051	+	11.3458i	−0.371445	+	0.643362i	−0.989788	−	0.142546i	$-0.954471\pi$
$311$	−6.55051	+	11.3458i	−0.371445	+	0.643362i	0.618343	+	0.785909i	$0.287804\pi$
$312$	−2.44949	+	3.46410i	−0.138675	+	0.196116i
$313$	10.8485	+	18.7901i	0.613192	+	1.06208i	0.990699	+	0.136073i	$0.0434480\pi$
$313$	10.8485	+	18.7901i	0.613192	+	1.06208i	−0.377507	+	0.926007i	$0.623219\pi$
$314$	−16.0000			−0.902932
$315$		0			0
$316$	7.34847			0.413384
$317$	−11.4722	−	19.8704i	−0.644343	−	1.11603i	−0.984453	−	0.175649i	$-0.943798\pi$
$317$	−11.4722	−	19.8704i	−0.644343	−	1.11603i	0.340110	−	0.940386i	$-0.389536\pi$
$318$	−2.57321	−	5.58542i	−0.144299	−	0.313215i
$319$	−10.3485	+	17.9241i	−0.579403	+	1.00356i
$320$		0			0
$321$	−28.1969	−	2.59808i	−1.57380	−	0.145010i
$322$	−1.55051	−	2.68556i	−0.0864066	−	0.149661i
$323$	32.1464			1.78868
$324$	−7.00000	+	5.65685i	−0.388889	+	0.314270i
$325$		0			0
$326$	4.44949	+	7.70674i	0.246434	+	0.426837i
$327$	13.7980	+	1.27135i	0.763029	+	0.0703058i
$328$	−0.500000	+	0.866025i	−0.0276079	+	0.0478183i
$329$	−1.00000	+	1.73205i	−0.0551318	+	0.0954911i
$330$		0			0
$331$	12.6969	+	21.9917i	0.697887	+	1.20878i	0.969198	+	0.246284i	$0.0792095\pi$
$331$	12.6969	+	21.9917i	0.697887	+	1.20878i	−0.271311	+	0.962492i	$0.587457\pi$
$332$	−4.00000			−0.219529
$333$	23.5959	+	4.38551i	1.29305	+	0.240324i
$334$	−0.247449			−0.0135398
$335$		0			0
$336$	−0.449490	+	0.635674i	−0.0245217	+	0.0346789i
$337$	−9.29796	+	16.1045i	−0.506492	+	0.877270i	0.493480	+	0.869757i	$0.335725\pi$
$337$	−9.29796	+	16.1045i	−0.506492	+	0.877270i	−0.999972	+	0.00751272i	$0.997609\pi$
$338$	−3.50000	+	6.06218i	−0.190375	+	0.329739i
$339$	−4.89898	+	6.92820i	−0.266076	+	0.376288i
$340$		0			0
$341$	−5.34847			−0.289636
$342$	−5.44949	−	15.4135i	−0.294675	−	0.833466i
$343$	6.20204			0.334879
$344$	1.27526	+	2.20881i	0.0687571	+	0.119091i
$345$		0			0
$346$	−5.89898	+	10.2173i	−0.317131	+	0.549287i
$347$	−4.62372	+	8.00853i	−0.248215	+	0.429920i	−0.963030	−	0.269392i	$-0.913177\pi$
$347$	−4.62372	+	8.00853i	−0.248215	+	0.429920i	0.714816	+	0.699313i	$0.246510\pi$
$348$	10.3485	+	0.953512i	0.554736	+	0.0511136i
$349$	13.7980	+	23.8988i	0.738588	+	1.27927i	0.953131	+	0.302557i	$0.0978403\pi$
$349$	13.7980	+	23.8988i	0.738588	+	1.27927i	−0.214543	+	0.976714i	$0.568826\pi$
$350$		0			0
$351$	9.12372	−	8.87455i	0.486988	−	0.473688i
$352$	3.44949			0.183858
$353$	−16.2980	−	28.2289i	−0.867453	−	1.50247i	−0.864591	−	0.502476i	$-0.832422\pi$
$353$	−16.2980	−	28.2289i	−0.867453	−	1.50247i	−0.00286194	−	0.999996i	$-0.500911\pi$
$354$	22.8485	+	2.10527i	1.21438	+	0.111894i
$355$		0			0
$356$	−1.55051	+	2.68556i	−0.0821769	+	0.142335i
$357$	1.92168	+	4.17121i	0.101706	+	0.220764i
$358$	−0.449490	−	0.778539i	−0.0237563	−	0.0411471i
$359$	3.55051			0.187389			0.0936944	−	0.995601i	$-0.470132\pi$
$359$	3.55051			0.187389			0.0936944	+	0.995601i	$0.470132\pi$
$360$		0			0
$361$	10.6969			0.562997
$362$	2.77526	+	4.80688i	0.145864	+	0.252644i
$363$	0.898979	−	1.27135i	0.0471842	−	0.0667285i
$364$	0.550510	−	0.953512i	0.0288546	−	0.0499776i
$365$		0			0
$366$	−4.44949	+	6.29253i	−0.232579	+	0.328916i
$367$	−13.7980	−	23.8988i	−0.720248	−	1.24751i	−0.960900	−	0.276894i	$-0.910695\pi$
$367$	−13.7980	−	23.8988i	−0.720248	−	1.24751i	0.240653	−	0.970611i	$-0.422638\pi$
$368$	6.89898			0.359634
$369$	1.94949	−	2.28024i	0.101486	−	0.118704i
$370$		0			0
$371$	0.797959	+	1.38211i	0.0414280	+	0.0717553i
$372$	1.12372	+	2.43916i	0.0582624	+	0.126464i
$373$	6.79796	−	11.7744i	0.351985	−	0.609656i	−0.634612	−	0.772831i	$-0.718840\pi$
$373$	6.79796	−	11.7744i	0.351985	−	0.609656i	0.986597	+	0.163175i	$0.0521735\pi$
$374$	10.1742	−	17.6223i	0.526097	−	0.911227i
$375$		0			0
$376$	−2.22474	−	3.85337i	−0.114732	−	0.198722i
$377$	−14.6969			−0.756931
$378$	1.67423	−	1.62851i	0.0861133	−	0.0837615i
$379$	4.14643			0.212988			0.106494	−	0.994313i	$-0.466038\pi$
$379$	4.14643			0.212988			0.106494	+	0.994313i	$0.466038\pi$
$380$		0			0
$381$	−11.8990	−	1.09638i	−0.609603	−	0.0561691i
$382$	9.12372	−	15.8028i	0.466810	−	0.808539i
$383$	8.89898	−	15.4135i	0.454717	−	0.787592i	−0.543955	−	0.839114i	$-0.683074\pi$
$383$	8.89898	−	15.4135i	0.454717	−	0.787592i	0.998672	+	0.0515220i	$0.0164072\pi$
$384$	−0.724745	−	1.57313i	−0.0369845	−	0.0802786i
$385$		0			0
$386$	−13.6969			−0.697156
$387$	−2.55051	−	7.21393i	−0.129650	−	0.366705i
$388$	13.0000			0.659975
$389$	−8.77526	−	15.1992i	−0.444923	−	0.770629i	0.553124	−	0.833099i	$-0.313436\pi$
$389$	−8.77526	−	15.1992i	−0.444923	−	0.770629i	−0.998047	+	0.0624697i	$0.980102\pi$
$390$		0			0
$391$	20.3485	−	35.2446i	1.02907	−	1.78240i
$392$	−3.39898	+	5.88721i	−0.171674	+	0.297349i
$393$	4.89898	−	6.92820i	0.247121	−	0.349482i
$394$	−4.00000	−	6.92820i	−0.201517	−	0.349038i
$395$		0			0
$396$	−10.1742	−	1.89097i	−0.511275	−	0.0950248i
$397$	−1.79796			−0.0902370			−0.0451185	−	0.998982i	$-0.514367\pi$
$397$	−1.79796			−0.0902370			−0.0451185	+	0.998982i	$0.514367\pi$
$398$	7.77526	+	13.4671i	0.389738	+	0.675047i
$399$	1.77526	+	3.85337i	0.0888739	+	0.192910i
$400$		0			0
$401$	−4.60102	+	7.96920i	−0.229764	+	0.397963i	−0.957738	−	0.287642i	$-0.907129\pi$
$401$	−4.60102	+	7.96920i	−0.229764	+	0.397963i	0.727974	+	0.685605i	$0.240462\pi$
$402$	7.84847	+	0.723161i	0.391446	+	0.0360680i
$403$	−1.89898	−	3.28913i	−0.0945949	−	0.163843i
$404$	−8.00000			−0.398015
$405$		0			0
$406$	−2.69694			−0.133847
$407$	13.7980	+	23.8988i	0.683939	+	1.18462i
$408$	−10.1742	−	0.937458i	−0.503700	−	0.0464111i
$409$	−7.94949	+	13.7689i	−0.393077	+	0.680829i	−0.992854	−	0.119338i	$-0.961923\pi$
$409$	−7.94949	+	13.7689i	−0.393077	+	0.680829i	0.599777	+	0.800167i	$0.295256\pi$
$410$		0			0
$411$	2.17423	+	4.71940i	0.107247	+	0.232791i
$412$	7.12372	+	12.3387i	0.350961	+	0.607882i
$413$	−5.95459			−0.293006
$414$	−20.3485	−	3.78194i	−1.00007	−	0.185872i
$415$		0			0
$416$	1.22474	+	2.12132i	0.0600481	+	0.104006i
$417$	13.2474	−	18.7347i	0.648730	−	0.917443i
$418$	9.39898	−	16.2795i	0.459719	−	0.796257i
$419$	4.44949	−	7.70674i	0.217372	−	0.376499i	−0.736632	−	0.676294i	$-0.763585\pi$
$419$	4.44949	−	7.70674i	0.217372	−	0.376499i	0.954004	+	0.299795i	$0.0969183\pi$
$420$		0			0
$421$	5.77526	+	10.0030i	0.281469	+	0.487518i	0.971747	−	0.236026i	$-0.0758451\pi$
$421$	5.77526	+	10.0030i	0.281469	+	0.487518i	−0.690278	+	0.723544i	$0.742512\pi$
$422$	−3.79796			−0.184882
$423$	4.44949	+	12.5851i	0.216342	+	0.611906i
$424$	−3.55051			−0.172428
$425$		0			0
$426$	1.77526	+	3.85337i	0.0860114	+	0.186696i
$427$	1.00000	−	1.73205i	0.0483934	−	0.0838198i
$428$	−8.17423	+	14.1582i	−0.395117	+	0.684362i
$429$	14.5732	+	1.34278i	0.703601	+	0.0648301i
$430$		0			0
$431$	38.2474			1.84231			0.921157	−	0.389190i	$-0.127245\pi$
$431$	38.2474			1.84231			0.921157	+	0.389190i	$0.127245\pi$
$432$	1.27526	+	5.03723i	0.0613557	+	0.242354i
$433$	23.0000			1.10531			0.552655	−	0.833410i	$-0.313615\pi$
$433$	23.0000			1.10531			0.552655	+	0.833410i	$0.313615\pi$
$434$	−0.348469	−	0.603566i	−0.0167271	−	0.0289721i
$435$		0			0
$436$	4.00000	−	6.92820i	0.191565	−	0.331801i
$437$	18.7980	−	32.5590i	0.899228	−	1.55751i
$438$	−10.7247	−	23.2791i	−0.512448	−	1.11232i
$439$	−11.0227	−	19.0919i	−0.526085	−	0.911206i	−0.999538	−	0.0303869i	$-0.990326\pi$
$439$	−11.0227	−	19.0919i	−0.526085	−	0.911206i	0.473453	−	0.880819i	$-0.343007\pi$
$440$		0			0
$441$	13.2526	−	15.5010i	0.631074	−	0.738141i
$442$	14.4495			0.687292
$443$	−10.6237	−	18.4008i	−0.504748	−	0.874250i	−0.999985	−	0.00549166i	$-0.998252\pi$
$443$	−10.6237	−	18.4008i	−0.504748	−	0.874250i	0.495237	−	0.868758i	$-0.335081\pi$
$444$	8.00000	−	11.3137i	0.379663	−	0.536925i
$445$		0			0
$446$	4.55051	−	7.88171i	0.215473	−	0.373210i
$447$	−8.24745	+	11.6637i	−0.390091	+	0.551672i
$448$	0.224745	+	0.389270i	0.0106182	+	0.0183913i
$449$	18.7980			0.887131			0.443565	−	0.896242i	$-0.353713\pi$
$449$	18.7980			0.887131			0.443565	+	0.896242i	$0.353713\pi$
$450$		0			0
$451$	3.44949			0.162430
$452$	2.44949	+	4.24264i	0.115214	+	0.199557i
$453$	2.10102	+	4.56048i	0.0987146	+	0.214270i
$454$	−1.72474	+	2.98735i	−0.0809463	+	0.140203i
$455$		0			0
$456$	−9.39898	−	0.866025i	−0.440148	−	0.0405554i
$457$	8.94949	+	15.5010i	0.418639	+	0.725105i	0.995803	−	0.0915238i	$-0.0291738\pi$
$457$	8.94949	+	15.5010i	0.418639	+	0.725105i	−0.577163	+	0.816629i	$0.695840\pi$
$458$	18.4495			0.862088
$459$	29.4949	+	8.34242i	1.37670	+	0.389391i
$460$		0			0
$461$	1.22474	+	2.12132i	0.0570421	+	0.0987997i	0.893136	−	0.449786i	$-0.148500\pi$
$461$	1.22474	+	2.12132i	0.0570421	+	0.0987997i	−0.836094	+	0.548586i	$0.815166\pi$
$462$	2.67423	+	0.246405i	0.124417	+	0.0114638i
$463$	−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
$466$	−6.84847	−	11.8619i	−0.317249	−	0.549492i
$467$	−10.3485			−0.478870			−0.239435	−	0.970912i	$-0.576962\pi$
$467$	−10.3485			−0.478870			−0.239435	+	0.970912i	$0.576962\pi$
$468$	−2.44949	−	6.92820i	−0.113228	−	0.320256i
$469$	−2.04541			−0.0944482
$470$		0			0
$471$	16.0000	−	22.6274i	0.737241	−	1.04262i
$472$	6.62372	−	11.4726i	0.304882	−	0.528070i
$473$	4.39898	−	7.61926i	0.202265	−	0.350334i
$474$	−7.34847	+	10.3923i	−0.337526	+	0.477334i
$475$		0			0
$476$	2.65153			0.121533
$477$	10.4722	+	1.94635i	0.479489	+	0.0891171i
$478$	0.696938			0.0318772
$479$	−8.34847	−	14.4600i	−0.381451	−	0.660693i	0.609819	−	0.792541i	$-0.291242\pi$
$479$	−8.34847	−	14.4600i	−0.381451	−	0.660693i	−0.991270	+	0.131848i	$0.957909\pi$
$480$		0			0
$481$	−9.79796	+	16.9706i	−0.446748	+	0.773791i
$482$	0.500000	−	0.866025i	0.0227744	−	0.0394464i
$483$	5.34847	+	0.492810i	0.243364	+	0.0224236i
$484$	−0.449490	−	0.778539i	−0.0204314	−	0.0353881i
$485$		0			0
$486$	−1.00000	−	15.5563i	−0.0453609	−	0.705650i
$487$	−25.1010			−1.13744			−0.568718	−	0.822533i	$-0.692560\pi$
$487$	−25.1010			−1.13744			−0.568718	+	0.822533i	$0.692560\pi$
$488$	2.22474	+	3.85337i	0.100709	+	0.174434i
$489$	−15.3485	−	1.41421i	−0.694082	−	0.0639529i
$490$		0			0
$491$	−9.27526	+	16.0652i	−0.418586	+	0.725013i	−0.995798	−	0.0915820i	$-0.970808\pi$
$491$	−9.27526	+	16.0652i	−0.418586	+	0.725013i	0.577211	+	0.816595i	$0.304141\pi$
$492$	−0.724745	−	1.57313i	−0.0326740	−	0.0709223i
$493$	−17.6969	−	30.6520i	−0.797030	−	1.38050i
$494$	13.3485			0.600576
$495$		0			0
$496$	1.55051			0.0696200
$497$	−0.550510	−	0.953512i	−0.0246938	−	0.0427708i
$498$	4.00000	−	5.65685i	0.179244	−	0.253490i
$499$	10.6237	−	18.4008i	0.475583	−	0.823734i	−0.524026	−	0.851703i	$-0.675570\pi$
$499$	10.6237	−	18.4008i	0.475583	−	0.823734i	0.999609	+	0.0279682i	$0.00890372\pi$
$500$		0			0
$501$	0.247449	−	0.349945i	0.0110552	−	0.0156344i
$502$	3.27526	+	5.67291i	0.146182	+	0.253194i
$503$	14.4495			0.644271			0.322135	−	0.946694i	$-0.395599\pi$
$503$	14.4495			0.644271			0.322135	+	0.946694i	$0.395599\pi$
$504$	−0.449490	−	1.27135i	−0.0200219	−	0.0566304i
$505$		0			0
$506$	−11.8990	−	20.6096i	−0.528974	−	0.916210i
$507$	−5.07321	−	11.0119i	−0.225309	−	0.489057i
$508$	−3.44949	+	5.97469i	−0.153046	+	0.265084i
$509$	−15.7980	+	27.3629i	−0.700232	+	1.21284i	0.268153	+	0.963376i	$0.413587\pi$
$509$	−15.7980	+	27.3629i	−0.700232	+	1.21284i	−0.968385	+	0.249461i	$0.919746\pi$
$510$		0			0
$511$	3.32577	+	5.76039i	0.147123	+	0.254825i
$512$	−1.00000			−0.0441942
$513$	27.2474	+	7.70674i	1.20300	+	0.340261i
$514$	−10.1010			−0.445537
$515$		0			0
$516$	−4.39898	−	0.405324i	−0.193654	−	0.0178434i
$517$	−7.67423	+	13.2922i	−0.337512	+	0.584589i
$518$	−1.79796	+	3.11416i	−0.0789978	+	0.136828i
$519$	−8.55051	−	18.5597i	−0.375326	−	0.814683i
$520$		0			0
$521$	21.6969			0.950560			0.475280	−	0.879835i	$-0.342347\pi$
$521$	21.6969			0.950560			0.475280	+	0.879835i	$0.342347\pi$
$522$	−11.6969	+	13.6814i	−0.511961	+	0.598820i
$523$	−10.2020			−0.446104			−0.223052	−	0.974807i	$-0.571602\pi$
$523$	−10.2020			−0.446104			−0.223052	+	0.974807i	$0.571602\pi$
$524$	−2.44949	−	4.24264i	−0.107006	−	0.185341i
$525$		0			0
$526$	−6.22474	+	10.7816i	−0.271412	+	0.470099i
$527$	4.57321	−	7.92104i	0.199212	−	0.345046i
$528$	−3.44949	+	4.87832i	−0.150120	+	0.212301i
$529$	−12.2980	−	21.3007i	−0.534694	−	0.926117i
$530$		0			0
$531$	−25.8258	+	30.2073i	−1.12074	+	1.31089i
$532$	2.44949			0.106199
$533$	1.22474	+	2.12132i	0.0530496	+	0.0918846i
$534$	−2.24745	−	4.87832i	−0.0972566	−	0.211105i
$535$		0			0
$536$	2.27526	−	3.94086i	0.0982761	−	0.170219i
$537$	1.55051	+	0.142865i	0.0669095	+	0.00616506i
$538$	8.02270	+	13.8957i	0.345883	+	0.599087i
$539$	23.4495			1.01004
$540$		0			0
$541$	−0.404082			−0.0173728			−0.00868642	−	0.999962i	$-0.502765\pi$
$541$	−0.404082			−0.0173728			−0.00868642	+	0.999962i	$0.502765\pi$
$542$	−7.79796	−	13.5065i	−0.334951	−	0.580152i
$543$	−9.57321	−	0.882079i	−0.410826	−	0.0378537i
$544$	−2.94949	+	5.10867i	−0.126458	+	0.219032i
$545$		0			0
$546$	0.797959	+	1.73205i	0.0341495	+	0.0741249i
$547$	−8.62372	−	14.9367i	−0.368724	−	0.638648i	0.620642	−	0.784094i	$-0.286872\pi$
$547$	−8.62372	−	14.9367i	−0.368724	−	0.638648i	−0.989366	+	0.145445i	$0.953539\pi$
$548$	3.00000			0.128154
$549$	−4.44949	−	12.5851i	−0.189900	−	0.537117i
$550$		0			0
$551$	−16.3485	−	28.3164i	−0.696468	−	1.20632i
$552$	−6.89898	+	9.75663i	−0.293640	+	0.415270i
$553$	1.65153	−	2.86054i	0.0702302	−	0.121642i
$554$	−14.7980	+	25.6308i	−0.628705	+	1.08895i
$555$		0			0
$556$	−6.62372	−	11.4726i	−0.280908	−	0.486548i
$557$	14.9444			0.633214			0.316607	−	0.948557i	$-0.397456\pi$
$557$	14.9444			0.633214			0.316607	+	0.948557i	$0.397456\pi$
$558$	−4.57321	−	0.849971i	−0.193600	−	0.0359822i
$559$	6.24745			0.264239
$560$		0			0
$561$	14.7474	+	32.0108i	0.622638	+	1.35150i
$562$	6.00000	−	10.3923i	0.253095	−	0.438373i
$563$	−0.926786	+	1.60524i	−0.0390594	+	0.0676528i	−0.884894	−	0.465792i	$-0.845769\pi$
$563$	−0.926786	+	1.60524i	−0.0390594	+	0.0676528i	0.845835	+	0.533445i	$0.179103\pi$
$564$	7.67423	+	0.707107i	0.323144	+	0.0297746i
$565$		0			0
$566$	−4.00000			−0.168133
$567$	0.628827	+	3.99624i	0.0264082	+	0.167826i
$568$	2.44949			0.102778
$569$	15.7474	+	27.2754i	0.660167	+	1.14344i	0.980571	+	0.196162i	$0.0628480\pi$
$569$	15.7474	+	27.2754i	0.660167	+	1.14344i	−0.320404	+	0.947281i	$0.603819\pi$
$570$		0			0
$571$	−18.6237	+	32.2572i	−0.779379	+	1.34992i	0.152922	+	0.988238i	$0.451132\pi$
$571$	−18.6237	+	32.2572i	−0.779379	+	1.34992i	−0.932300	+	0.361685i	$0.882202\pi$
$572$	4.22474	−	7.31747i	0.176645	−	0.305959i
$573$	13.2247	+	28.7056i	0.552472	+	1.19920i
$574$	0.224745	+	0.389270i	0.00938067	+	0.0162478i
$575$		0			0
$576$	2.94949	+	0.548188i	0.122895	+	0.0228412i
$577$	−15.6969			−0.653472			−0.326736	−	0.945116i	$-0.605949\pi$
$577$	−15.6969			−0.653472			−0.326736	+	0.945116i	$0.605949\pi$
$578$	8.89898	+	15.4135i	0.370149	+	0.641116i
$579$	13.6969	−	19.3704i	0.569225	−	0.805006i
$580$		0			0
$581$	−0.898979	+	1.55708i	−0.0372960	+	0.0645985i
$582$	−13.0000	+	18.3848i	−0.538867	+	0.762073i
$583$	6.12372	+	10.6066i	0.253619	+	0.439281i
$584$	−14.7980			−0.612344
$585$		0			0
$586$	−18.0000			−0.743573
$587$	11.9722	+	20.7364i	0.494145	+	0.855885i	0.999977	−	0.00674727i	$-0.00214774\pi$
$587$	11.9722	+	20.7364i	0.494145	+	0.855885i	−0.505832	+	0.862632i	$0.668814\pi$
$588$	−4.92679	−	10.6941i	−0.203177	−	0.441017i
$589$	4.22474	−	7.31747i	0.174078	−	0.301511i
$590$		0			0
$591$	13.7980	+	1.27135i	0.567572	+	0.0522963i
$592$	−4.00000	−	6.92820i	−0.164399	−	0.284747i
$593$	−17.3939			−0.714281			−0.357140	−	0.934051i	$-0.616248\pi$
$593$	−17.3939			−0.714281			−0.357140	+	0.934051i	$0.616248\pi$
$594$	12.8485	−	12.4976i	0.527179	−	0.512782i
$595$		0			0
$596$	4.12372	+	7.14250i	0.168914	+	0.292568i
$597$	−26.8207	−	2.47127i	−1.09770	−	0.101142i
$598$	8.44949	−	14.6349i	0.345525	−	0.598467i
$599$	−16.8990	+	29.2699i	−0.690474	+	1.19594i	0.281209	+	0.959646i	$0.409264\pi$
$599$	−16.8990	+	29.2699i	−0.690474	+	1.19594i	−0.971683	+	0.236289i	$0.924069\pi$
$600$		0			0
$601$	−19.3990	−	33.6000i	−0.791301	−	1.37057i	−0.925162	−	0.379573i	$-0.876071\pi$
$601$	−19.3990	−	33.6000i	−0.791301	−	1.37057i	0.133861	−	0.991000i	$-0.457262\pi$
$602$	1.14643			0.0467249
$603$	−8.87117	+	10.3763i	−0.361262	+	0.422554i
$604$	2.89898			0.117958
$605$		0			0
$606$	8.00000	−	11.3137i	0.324978	−	0.459588i
$607$	13.7980	−	23.8988i	0.560042	−	0.970021i	−0.437450	−	0.899243i	$-0.644118\pi$
$607$	13.7980	−	23.8988i	0.560042	−	0.970021i	0.997492	−	0.0707783i	$-0.0225483\pi$
$608$	−2.72474	+	4.71940i	−0.110503	+	0.191397i
$609$	2.69694	−	3.81405i	0.109285	−	0.154553i
$610$		0			0
$611$	−10.8990			−0.440926
$612$	11.5000	−	13.4511i	0.464860	−	0.543728i
$613$	−36.9444			−1.49217			−0.746085	−	0.665851i	$-0.768069\pi$
$613$	−36.9444			−1.49217			−0.746085	+	0.665851i	$0.768069\pi$
$614$	14.9722	+	25.9326i	0.604229	+	1.04655i
$615$		0			0
$616$	0.775255	−	1.34278i	0.0312359	−	0.0541022i
$617$	−4.15153	+	7.19066i	−0.167134	+	0.289485i	−0.937411	−	0.348224i	$-0.886785\pi$
$617$	−4.15153	+	7.19066i	−0.167134	+	0.289485i	0.770277	+	0.637710i	$0.220118\pi$
$618$	−24.5732	−	2.26418i	−0.988480	−	0.0910789i
$619$	14.2753	+	24.7255i	0.573771	+	0.993800i	0.996174	+	0.0873923i	$0.0278534\pi$
$619$	14.2753	+	24.7255i	0.573771	+	0.993800i	−0.422403	+	0.906408i	$0.638813\pi$
$620$		0			0
$621$	25.6969	−	24.9951i	1.03118	−	1.00302i
$622$	−13.1010			−0.525303
$623$	0.696938	+	1.20713i	0.0279222	+	0.0483628i
$624$	−4.22474	−	0.389270i	−0.169125	−	0.0155833i
$625$		0			0
$626$	−10.8485	+	18.7901i	−0.433592	+	0.751003i
$627$	13.6237	+	29.5717i	0.544079	+	1.18098i
$628$	−8.00000	−	13.8564i	−0.319235	−	0.552931i
$629$	−47.1918			−1.88166
$630$		0			0
$631$	−11.3485			−0.451775			−0.225888	−	0.974153i	$-0.572528\pi$
$631$	−11.3485			−0.451775			−0.225888	+	0.974153i	$0.572528\pi$
$632$	3.67423	+	6.36396i	0.146153	+	0.253145i
$633$	3.79796	−	5.37113i	0.150955	−	0.213483i
$634$	11.4722	−	19.8704i	0.455619	−	0.789155i
$635$		0			0
$636$	3.55051	−	5.02118i	0.140787	−	0.199103i
$637$	8.32577	+	14.4206i	0.329879	+	0.571367i
$638$	−20.6969			−0.819400
$639$	−7.22474	−	1.34278i	−0.285806	−	0.0531196i
$640$		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	$0.572524\pi$
$642$	−11.8485	−	25.7183i	−0.467622	−	1.01502i
$643$	−7.62372	+	13.2047i	−0.300650	+	0.520742i	−0.976283	−	0.216496i	$-0.930537\pi$
$643$	−7.62372	+	13.2047i	−0.300650	+	0.520742i	0.675633	+	0.737238i	$0.263870\pi$
$644$	1.55051	−	2.68556i	0.0610987	−	0.105826i
$645$		0			0
$646$	16.0732	+	27.8396i	0.632392	+	1.09534i
$647$	34.8990			1.37202			0.686010	−	0.727592i	$-0.259361\pi$
$647$	34.8990			1.37202			0.686010	+	0.727592i	$0.259361\pi$
$648$	−8.39898	−	3.23375i	−0.329943	−	0.127034i
$649$	−45.6969			−1.79376
$650$		0			0
$651$	1.20204	+	0.110756i	0.0471117	+	0.00434089i
$652$	−4.44949	+	7.70674i	−0.174255	+	0.301819i
$653$	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	$-0.0650132\pi$
$654$	5.79796	+	12.5851i	0.226718	+	0.492115i
$655$		0			0
$656$	−1.00000			−0.0390434
$657$	43.6464	+	8.11207i	1.70281	+	0.316482i
$658$	−2.00000			−0.0779681
$659$	17.8990	+	31.0019i	0.697245	+	1.20766i	0.969418	+	0.245416i	$0.0789245\pi$
$659$	17.8990	+	31.0019i	0.697245	+	1.20766i	−0.272173	+	0.962248i	$0.587742\pi$
$660$		0			0
$661$	−2.89898	+	5.02118i	−0.112757	+	0.195301i	−0.916881	−	0.399161i	$-0.869302\pi$
$661$	−2.89898	+	5.02118i	−0.112757	+	0.195301i	0.804124	+	0.594462i	$0.202635\pi$
$662$	−12.6969	+	21.9917i	−0.493481	+	0.854733i
$663$	−14.4495	+	20.4347i	−0.561172	+	0.793617i
$664$	−2.00000	−	3.46410i	−0.0776151	−	0.134433i
$665$		0			0
$666$	8.00000	+	22.6274i	0.309994	+	0.876795i
$667$	−41.3939			−1.60278
$668$	−0.123724	−	0.214297i	−0.00478704	−	0.00829139i
$669$	6.59592	+	14.3171i	0.255013	+	0.553531i
$670$		0			0
$671$	7.67423	−	13.2922i	0.296261	−	0.513138i
$672$	−0.775255	−	0.0714323i	−0.0299061	−	0.00275556i
$673$	14.4495	+	25.0273i	0.556987	+	0.964730i	0.997746	+	0.0671042i	$0.0213760\pi$
$673$	14.4495	+	25.0273i	0.556987	+	0.964730i	−0.440759	+	0.897625i	$0.645291\pi$
$674$	−18.5959			−0.716288
$675$		0			0
$676$	−7.00000			−0.269231
$677$	−19.7980	−	34.2911i	−0.760897	−	1.31791i	−0.942389	−	0.334520i	$-0.891426\pi$
$677$	−19.7980	−	34.2911i	−0.760897	−	1.31791i	0.181491	−	0.983393i	$-0.441908\pi$
$678$	−8.44949	−	0.778539i	−0.324501	−	0.0298996i
$679$	2.92168	−	5.06050i	0.112124	−	0.194204i
$680$		0			0
$681$	−2.50000	−	5.42650i	−0.0958002	−	0.207944i
$682$	−2.67423	−	4.63191i	−0.102402	−	0.177365i
$683$	−45.4495			−1.73908			−0.869538	−	0.493866i	$-0.835583\pi$
$683$	−45.4495			−1.73908			−0.869538	+	0.493866i	$0.835583\pi$
$684$	10.6237	−	12.4261i	0.406208	−	0.475125i
$685$		0			0
$686$	3.10102	+	5.37113i	0.118398	+	0.205071i
$687$	−18.4495	+	26.0915i	−0.703892	+	0.995454i
$688$	−1.27526	+	2.20881i	−0.0486186	+	0.0842100i
$689$	−4.34847	+	7.53177i	−0.165663	+	0.286938i
$690$		0			0
$691$	−8.79796	−	15.2385i	−0.334690	−	0.579700i	0.648735	−	0.761014i	$-0.275298\pi$
$691$	−8.79796	−	15.2385i	−0.334690	−	0.579700i	−0.983425	+	0.181314i	$0.941965\pi$
$692$	−11.7980			−0.448491
$693$	−3.02270	+	3.53553i	−0.114823	+	0.134304i
$694$	−9.24745			−0.351028
$695$		0			0
$696$	4.34847	+	9.43879i	0.164828	+	0.357777i
$697$	−2.94949	+	5.10867i	−0.111720	+	0.193505i
$698$	−13.7980	+	23.8988i	−0.522260	+	0.904582i
$699$	23.6237	+	2.17670i	0.893531	+	0.0823303i
$700$		0			0
$701$	−39.3939			−1.48789			−0.743943	−	0.668243i	$-0.767047\pi$
$701$	−39.3939			−1.48789			−0.743943	+	0.668243i	$0.767047\pi$
$702$	12.2474	+	3.46410i	0.462250	+	0.130744i
$703$	−43.5959			−1.64425
$704$	1.72474	+	2.98735i	0.0650038	+	0.112590i
$705$		0			0
$706$	16.2980	−	28.2289i	0.613382	−	1.06241i
$707$	−1.79796	+	3.11416i	−0.0676192	+	0.117120i
$708$	9.60102	+	20.8400i	0.360828	+	0.783215i
$709$	−18.6742	−	32.3447i	−0.701326	−	1.21473i	−0.968001	−	0.250945i	$-0.919259\pi$
$709$	−18.6742	−	32.3447i	−0.701326	−	1.21473i	0.266676	−	0.963786i	$-0.414075\pi$
$710$		0			0
$711$	−7.34847	−	20.7846i	−0.275589	−	0.779484i
$712$	−3.10102			−0.116216
$713$	−5.34847	−	9.26382i	−0.200302	−	0.346933i
$714$	−2.65153	+	3.74983i	−0.0992310	+	0.140334i
$715$		0			0
$716$	0.449490	−	0.778539i	0.0167982	−	0.0290954i
$717$	−0.696938	+	0.985620i	−0.0260276	+	0.0368086i
$718$	1.77526	+	3.07483i	0.0662519	+	0.114752i
$719$	41.7980			1.55880			0.779400	−	0.626526i	$-0.215524\pi$
$719$	41.7980			1.55880			0.779400	+	0.626526i	$0.215524\pi$
$720$		0			0
$721$	6.40408			0.238500
$722$	5.34847	+	9.26382i	0.199049	+	0.344764i
$723$	0.724745	+	1.57313i	0.0269536	+	0.0585054i
$724$	−2.77526	+	4.80688i	−0.103142	+	0.178646i
$725$		0			0
$726$	1.55051	+	0.142865i	0.0575448	+	0.00530220i
$727$	12.6742	+	21.9524i	0.470061	+	0.814170i	0.999414	−	0.0342318i	$-0.0108985\pi$
$727$	12.6742	+	21.9524i	0.470061	+	0.814170i	−0.529353	+	0.848402i	$0.677565\pi$
$728$	1.10102			0.0408065
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$		0			0
$731$	7.52270	+	13.0297i	0.278237	+	0.481921i
$732$	−7.67423	−	0.707107i	−0.283648	−	0.0261354i
$733$	−10.5732	+	18.3133i	−0.390531	+	0.676419i	−0.992520	−	0.122086i	$-0.961042\pi$
$733$	−10.5732	+	18.3133i	−0.390531	+	0.676419i	0.601989	+	0.798504i	$0.294375\pi$
$734$	13.7980	−	23.8988i	0.509292	−	0.882120i
$735$		0			0
$736$	3.44949	+	5.97469i	0.127150	+	0.220230i
$737$	−15.6969			−0.578204
$738$	2.94949	+	0.548188i	0.108572	+	0.0201791i
$739$	−17.2474			−0.634458			−0.317229	−	0.948349i	$-0.602752\pi$
$739$	−17.2474			−0.634458			−0.317229	+	0.948349i	$0.602752\pi$
$740$		0			0
$741$	−13.3485	+	18.8776i	−0.490368	+	0.693485i
$742$	−0.797959	+	1.38211i	−0.0292940	+	0.0507387i
$743$	11.4495	−	19.8311i	0.420041	−	0.727532i	−0.575902	−	0.817519i	$-0.695349\pi$
$743$	11.4495	−	19.8311i	0.420041	−	0.727532i	0.995943	+	0.0899863i	$0.0286823\pi$
$744$	−1.55051	+	2.19275i	−0.0568445	+	0.0803902i
$745$		0			0
$746$	13.5959			0.497782
$747$	4.00000	+	11.3137i	0.146352	+	0.413947i
$748$	20.3485			0.744014
$749$	3.67423	+	6.36396i	0.134254	+	0.232534i
$750$		0			0
$751$	26.4949	−	45.8905i	0.966813	−	1.67457i	0.262148	−	0.965028i	$-0.415569\pi$
$751$	26.4949	−	45.8905i	0.966813	−	1.67457i	0.704664	−	0.709541i	$-0.251098\pi$
$752$	2.22474	−	3.85337i	0.0811281	−	0.140518i
$753$	−11.2980	−	1.04100i	−0.411721	−	0.0379361i
$754$	−7.34847	−	12.7279i	−0.267615	−	0.463524i
$755$		0			0
$756$	2.24745	+	0.635674i	0.0817389	+	0.0231193i
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$	2.07321	+	3.59091i	0.0753025	+	0.130428i
$759$	41.0454	+	3.78194i	1.48985	+	0.137276i
$760$		0			0
$761$	−0.247449	+	0.428594i	−0.00897001	+	0.0155365i	−0.870476	−	0.492212i	$-0.836189\pi$
$761$	−0.247449	+	0.428594i	−0.00897001	+	0.0155365i	0.861506	+	0.507748i	$0.169522\pi$
$762$	−5.00000	−	10.8530i	−0.181131	−	0.393163i
$763$	−1.79796	−	3.11416i	−0.0650905	−	0.112740i
$764$	18.2474			0.660170
$765$		0			0
$766$	17.7980			0.643066
$767$	−16.2247	−	28.1021i	−0.585842	−	1.01471i
$768$	1.00000	−	1.41421i	0.0360844	−	0.0510310i
$769$	−12.2474	+	21.2132i	−0.441654	+	0.764968i	−0.997812	−	0.0661088i	$-0.978942\pi$
$769$	−12.2474	+	21.2132i	−0.441654	+	0.764968i	0.556158	+	0.831076i	$0.312275\pi$
$770$		0			0
$771$	10.1010	−	14.2850i	0.363779	−	0.514462i
$772$	−6.84847	−	11.8619i	−0.246482	−	0.426919i
$773$	35.3939			1.27303			0.636515	−	0.771265i	$-0.280375\pi$
$773$	35.3939			1.27303			0.636515	+	0.771265i	$0.280375\pi$
$774$	4.97219	−	5.81577i	0.178722	−	0.209044i
$775$		0			0
$776$	6.50000	+	11.2583i	0.233336	+	0.404151i
$777$	−2.60612	−	5.65685i	−0.0934941	−	0.202939i
$778$	8.77526	−	15.1992i	0.314608	−	0.544917i
$779$	−2.72474	+	4.71940i	−0.0976241	+	0.169090i
$780$		0			0
$781$	−4.22474	−	7.31747i	−0.151173	−	0.261840i
$782$	40.6969			1.45532
$783$	−7.65153	−	30.2234i	−0.273443	−	1.08010i
$784$	−6.79796			−0.242784
$785$		0			0
$786$	8.44949	+	0.778539i	0.301383	+	0.0277696i
$787$	25.6969	−	44.5084i	0.915997	−	1.58655i	0.110562	−	0.993869i	$-0.464735\pi$
$787$	25.6969	−	44.5084i	0.915997	−	1.58655i	0.805435	−	0.592684i	$-0.201932\pi$
$788$	4.00000	−	6.92820i	0.142494	−	0.246807i
$789$	−9.02270	−	19.5847i	−0.321217	−	0.697234i
$790$		0			0
$791$	2.20204			0.0782956
$792$	−3.44949	−	9.75663i	−0.122572	−	0.346687i
$793$	10.8990			0.387034
$794$	−0.898979	−	1.55708i	−0.0319036	−	0.0552586i
$795$		0			0
$796$	−7.77526	+	13.4671i	−0.275587	+	0.477330i
$797$	−1.79796	+	3.11416i	−0.0636870	+	0.110309i	−0.896111	−	0.443830i	$-0.853619\pi$
$797$	−1.79796	+	3.11416i	−0.0636870	+	0.110309i	0.832424	+	0.554139i	$0.186953\pi$
$798$	−2.44949	+	3.46410i	−0.0867110	+	0.122628i
$799$	−13.1237	−	22.7310i	−0.464284	−	0.804163i
$800$		0			0
$801$	9.14643	+	1.69994i	0.323173	+	0.0600645i
$802$	−9.20204			−0.324935
$803$	25.5227	+	44.2066i	0.900677	+	1.56002i
$804$	3.29796	+	7.15855i	0.116310	+	0.252463i
$805$		0			0
$806$	1.89898	−	3.28913i	0.0668887	−	0.115855i
$807$	−27.6742	−	2.54991i	−0.974179	−	0.0897612i
$808$	−4.00000	−	6.92820i	−0.140720	−	0.243733i
$809$	−41.0908			−1.44468			−0.722338	−	0.691540i	$-0.756933\pi$
$809$	−41.0908			−1.44468			−0.722338	+	0.691540i	$0.756933\pi$
$810$		0			0
$811$	7.24745			0.254492			0.127246	−	0.991871i	$-0.459386\pi$
$811$	7.24745			0.254492			0.127246	+	0.991871i	$0.459386\pi$
$812$	−1.34847	−	2.33562i	−0.0473220	−	0.0819641i
$813$	26.8990	+	2.47848i	0.943388	+	0.0869242i
$814$	−13.7980	+	23.8988i	−0.483618	+	0.837651i
$815$		0			0
$816$	−4.27526	−	9.27987i	−0.149664	−	0.324861i
$817$	6.94949	+	12.0369i	0.243132	+	0.421117i
$818$	−15.8990			−0.555895
$819$	−3.24745	−	0.603566i	−0.113475	−	0.0210903i
$820$		0			0
$821$	−1.02270	−	1.77138i	−0.0356926	−	0.0618214i	0.847627	−	0.530592i	$-0.178030\pi$
$821$	−1.02270	−	1.77138i	−0.0356926	−	0.0618214i	−0.883320	+	0.468771i	$0.844697\pi$
$822$	−3.00000	+	4.24264i	−0.104637	+	0.147979i
$823$	15.7980	−	27.3629i	0.550682	−	0.953810i	−0.447543	−	0.894262i	$-0.647701\pi$
$823$	15.7980	−	27.3629i	0.550682	−	0.953810i	0.998225	−	0.0595473i	$-0.0189657\pi$
$824$	−7.12372	+	12.3387i	−0.248167	+	0.429837i
$825$		0			0
$826$	−2.97730	−	5.15683i	−0.103593	−	0.179429i
$827$	5.79796			0.201615			0.100807	−	0.994906i	$-0.467857\pi$
$827$	5.79796			0.201615			0.100807	+	0.994906i	$0.467857\pi$
$828$	−6.89898	−	19.5133i	−0.239756	−	0.678133i
$829$	−26.4495			−0.918629			−0.459314	−	0.888274i	$-0.651905\pi$
$829$	−26.4495			−0.918629			−0.459314	+	0.888274i	$0.651905\pi$
$830$		0			0
$831$	−21.4495	−	46.5583i	−0.744075	−	1.61509i
$832$	−1.22474	+	2.12132i	−0.0424604	+	0.0735436i
$833$	−20.0505	+	34.7285i	−0.694709	+	1.20327i
$834$	22.8485	+	2.10527i	0.791178	+	0.0728994i
$835$		0			0
$836$	18.7980			0.650141
$837$	5.77526	−	5.61753i	0.199622	−	0.194170i
$838$	8.89898			0.307410
$839$	−20.1237	−	34.8553i	−0.694748	−	1.20334i	−0.970266	−	0.242043i	$-0.922183\pi$
$839$	−20.1237	−	34.8553i	−0.694748	−	1.20334i	0.275517	−	0.961296i	$-0.411151\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	−5.77526	+	10.0030i	−0.199028	+	0.344727i
$843$	8.69694	+	18.8776i	0.299538	+	0.650179i
$844$	−1.89898	−	3.28913i	−0.0653656	−	0.113216i
$845$		0			0
$846$	−8.67423	+	10.1459i	−0.298226	+	0.348823i
$847$	−0.404082			−0.0138844
$848$	−1.77526	−	3.07483i	−0.0609625	−	0.105590i
$849$	4.00000	−	5.65685i	0.137280	−	0.194143i
$850$		0			0
$851$	−27.5959	+	47.7975i	−0.945976	+	1.63848i
$852$	−2.44949	+	3.46410i	−0.0839181	+	0.118678i
$853$	−4.57321	−	7.92104i	−0.156584	−	0.271211i	0.777051	−	0.629438i	$-0.216715\pi$
$853$	−4.57321	−	7.92104i	−0.156584	−	0.271211i	−0.933635	+	0.358227i	$0.883381\pi$
$854$	2.00000			0.0684386
$855$		0			0
$856$	−16.3485			−0.558779
$857$	−2.69694	−	4.67123i	−0.0921257	−	0.159566i	0.816280	−	0.577657i	$-0.196033\pi$
$857$	−2.69694	−	4.67123i	−0.0921257	−	0.159566i	−0.908405	+	0.418091i	$0.862699\pi$
$858$	6.12372	+	13.2922i	0.209061	+	0.453787i
$859$	18.8712	−	32.6858i	0.643876	−	1.11523i	−0.340684	−	0.940178i	$-0.610659\pi$
$859$	18.8712	−	32.6858i	0.643876	−	1.11523i	0.984560	−	0.175048i	$-0.0560081\pi$
$860$		0			0
$861$	−0.775255	−	0.0714323i	−0.0264206	−	0.00243441i
$862$	19.1237	+	33.1233i	0.651357	+	1.12818i
$863$	26.4495			0.900351			0.450176	−	0.892940i	$-0.351361\pi$
$863$	26.4495			0.900351			0.450176	+	0.892940i	$0.351361\pi$
$864$	−3.72474	+	3.62302i	−0.126718	+	0.123258i
$865$		0			0
$866$	11.5000	+	19.9186i	0.390786	+	0.676861i
$867$	−30.6969	−	2.82843i	−1.04252	−	0.0960584i
$868$	0.348469	−	0.603566i	0.0118278	−	0.0204864i
$869$	12.6742	−	21.9524i	0.429944	−	0.744685i
$870$		0			0
$871$	−5.57321	−	9.65309i	−0.188841	−	0.327082i
$872$	8.00000			0.270914
$873$	−13.0000	−	36.7696i	−0.439983	−	1.24446i
$874$	37.5959			1.27170
$875$		0			0
$876$	14.7980	−	20.9275i	0.499977	−	0.707074i
$877$	10.4268	−	18.0597i	0.352088	−	0.609834i	−0.634527	−	0.772900i	$-0.718805\pi$
$877$	10.4268	−	18.0597i	0.352088	−	0.609834i	0.986615	+	0.163067i	$0.0521386\pi$
$878$	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	$0.668641\pi$
$882$	20.0505	+	3.72656i	0.675136	+	0.125480i
$883$	−6.55051			−0.220442			−0.110221	−	0.993907i	$-0.535156\pi$
$883$	−6.55051			−0.220442			−0.110221	+	0.993907i	$0.535156\pi$
$884$	7.22474	+	12.5136i	0.242994	+	0.420879i
$885$		0			0
$886$	10.6237	−	18.4008i	0.356911	−	0.618188i
$887$	−9.67423	+	16.7563i	−0.324829	+	0.562620i	−0.981478	−	0.191576i	$-0.938640\pi$
$887$	−9.67423	+	16.7563i	−0.324829	+	0.562620i	0.656649	+	0.754197i	$0.271973\pi$
$888$	13.7980	+	1.27135i	0.463029	+	0.0426637i
$889$	1.55051	+	2.68556i	0.0520024	+	0.0900709i
$890$		0			0
$891$	4.82577	+	30.6681i	0.161669	+	1.02742i
$892$	9.10102			0.304725
$893$	−12.1237	−	20.9989i	−0.405705	−	0.702702i
$894$	−14.2247	−	1.31067i	−0.475747	−	0.0438355i
$895$		0			0
$896$	−0.224745	+	0.389270i	−0.00750820	+	0.0130046i
$897$	12.2474	+	26.5843i	0.408930	+	0.887625i
$898$	9.39898	+	16.2795i	0.313648	+	0.543254i
$899$	−9.30306			−0.310274
$900$		0			0
$901$	−20.9444			−0.697759
$902$	1.72474	+	2.98735i	0.0574277	+	0.0994677i
$903$	−1.14643	+	1.62129i	−0.0381507	+	0.0539533i
$904$	−2.44949	+	4.24264i	−0.0814688	+	0.141108i
$905$		0			0
$906$	−2.89898	+	4.09978i	−0.0963121	+	0.136206i
$907$	19.8712	+	34.4179i	0.659811	+	1.14283i	0.980664	+	0.195698i	$0.0626972\pi$
$907$	19.8712	+	34.4179i	0.659811	+	1.14283i	−0.320853	+	0.947129i	$0.603969\pi$
$908$	−3.44949			−0.114475
$909$	8.00000	+	22.6274i	0.265343	+	0.750504i
$910$		0			0
$911$	−12.1237	−	20.9989i	−0.401677	−	0.695725i	0.592252	−	0.805753i	$-0.298239\pi$
$911$	−12.1237	−	20.9989i	−0.401677	−	0.695725i	−0.993928	+	0.110028i	$0.964906\pi$
$912$	−3.94949	−	8.57277i	−0.130781	−	0.283873i
$913$	−6.89898	+	11.9494i	−0.228323	+	0.395467i
$914$	−8.94949	+	15.5010i	−0.296023	+	0.512727i
$915$		0			0
$916$	9.22474	+	15.9777i	0.304794	+	0.527919i
$917$	−2.20204			−0.0727178
$918$	7.52270	+	29.7145i	0.248286	+	0.980726i
$919$	1.10102			0.0363193			0.0181597	−	0.999835i	$-0.494219\pi$
$919$	1.10102			0.0363193			0.0181597	+	0.999835i	$0.494219\pi$
$920$		0			0
$921$	−51.6464	−	4.75872i	−1.70181	−	0.156805i
$922$	−1.22474	+	2.12132i	−0.0403348	+	0.0698620i
$923$	3.00000	−	5.19615i	0.0987462	−	0.171033i
$924$	1.12372	+	2.43916i	0.0369678	+	0.0802424i
$925$		0			0
$926$	−24.0000			−0.788689
$927$	27.7753	−	32.4876i	0.912259	−	1.06703i
$928$	6.00000			0.196960
$929$	8.20204	+	14.2064i	0.269100	+	0.466095i	0.968630	−	0.248508i	$-0.0799404\pi$
$929$	8.20204	+	14.2064i	0.269100	+	0.466095i	−0.699529	+	0.714604i	$0.746607\pi$
$930$		0			0
$931$	−18.5227	+	32.0823i	−0.607057	+	1.05145i
$932$	6.84847	−	11.8619i	0.224329	−	0.388549i
$933$	13.1010	−	18.5276i	0.428908	−	0.606568i
$934$	−5.17423	−	8.96204i	−0.169306	−	0.293247i
$935$		0			0
$936$	4.77526	−	5.58542i	0.156084	−	0.182565i
$937$	−0.404082			−0.0132008			−0.00660039	−	0.999978i	$-0.502101\pi$
$937$	−0.404082			−0.0132008			−0.00660039	+	0.999978i	$0.502101\pi$
$938$	−1.02270	−	1.77138i	−0.0333925	−	0.0578374i
$939$	−15.7247	−	34.1322i	−0.513158	−	1.11386i
$940$		0			0
$941$	15.1010	−	26.1557i	0.492279	−	0.852653i	−0.507681	−	0.861545i	$-0.669497\pi$
$941$	15.1010	−	26.1557i	0.492279	−	0.852653i	0.999960	+	0.00889239i	$0.00283057\pi$
$942$	27.5959	+	2.54270i	0.899124	+	0.0828456i
$943$	3.44949	+	5.97469i	0.112331	+	0.194563i
$944$	13.2474			0.431168
$945$		0			0
$946$	8.79796			0.286046
$947$	−1.62372	−	2.81237i	−0.0527640	−	0.0913898i	0.838437	−	0.544998i	$-0.183470\pi$
$947$	−1.62372	−	2.81237i	−0.0527640	−	0.0913898i	−0.891201	+	0.453609i	$0.850136\pi$
$948$	−12.6742	−	1.16781i	−0.411640	−	0.0379287i
$949$	−18.1237	+	31.3912i	−0.588321	+	1.01900i
$950$		0			0
$951$	16.6288	+	36.0946i	0.539227	+	1.17045i
$952$	1.32577	+	2.29629i	0.0429683	+	0.0744233i
$953$	−31.2020			−1.01073			−0.505367	−	0.862905i	$-0.668643\pi$
$953$	−31.2020			−1.01073			−0.505367	+	0.862905i	$0.668643\pi$
$954$	3.55051	+	10.0424i	0.114952	+	0.325133i
$955$		0			0
$956$	0.348469	+	0.603566i	0.0112703	+	0.0195207i
$957$	20.6969	−	29.2699i	0.669037	−	0.946161i
$958$	8.34847	−	14.4600i	0.269727	−	0.467181i
$959$	0.674235	−	1.16781i	0.0217722	−	0.0377105i
$960$		0			0
$961$	14.2980	+	24.7648i	0.461224	+	0.798864i
$962$	−19.5959			−0.631798
$963$	48.2196	+	8.96204i	1.55386	+	0.288798i
$964$	1.00000			0.0322078
$965$		0			0
$966$	2.24745	+	4.87832i	0.0723105	+	0.156957i
$967$	−0.348469	+	0.603566i	−0.0112060	+	0.0194094i	−0.871574	−	0.490264i	$-0.836900\pi$
$967$	−0.348469	+	0.603566i	−0.0112060	+	0.0194094i	0.860368	+	0.509673i	$0.170234\pi$
$968$	0.449490	−	0.778539i	0.0144471	−	0.0250232i
$969$	−55.4444	−	5.10867i	−1.78113	−	0.164114i
$970$		0			0
$971$	35.3939			1.13584			0.567922	−	0.823083i	$-0.307748\pi$
$971$	35.3939			1.13584			0.567922	+	0.823083i	$0.307748\pi$
$972$	12.9722	−	8.64420i	0.416083	−	0.277263i
$973$	−5.95459			−0.190895
$974$	−12.5505	−	21.7381i	−0.402144	−	0.696534i
$975$		0			0
$976$	−2.22474	+	3.85337i	−0.0712123	+	0.123343i
$977$	−14.0505	+	24.3362i	−0.449516	+	0.778584i	−0.998354	−	0.0573443i	$-0.981737\pi$
$977$	−14.0505	+	24.3362i	−0.449516	+	0.778584i	0.548839	+	0.835928i	$0.315070\pi$
$978$	−6.44949	−	13.9993i	−0.206232	−	0.447647i
$979$	5.34847	+	9.26382i	0.170938	+	0.296073i
$980$		0			0
$981$	−23.5959	−	4.38551i	−0.753360	−	0.140018i
$982$	−18.5505			−0.591971
$983$	−10.6969	−	18.5276i	−0.341179	−	0.590940i	0.643473	−	0.765469i	$-0.277493\pi$
$983$	−10.6969	−	18.5276i	−0.341179	−	0.590940i	−0.984652	+	0.174529i	$0.944160\pi$
$984$	1.00000	−	1.41421i	0.0318788	−	0.0450835i
$985$		0			0
$986$	17.6969	−	30.6520i	0.563585	−	0.976158i
$987$	2.00000	−	2.82843i	0.0636607	−	0.0900298i
$988$	6.67423	+	11.5601i	0.212336	+	0.367776i
$989$	17.5959			0.559518
$990$		0			0
$991$	4.00000			0.127064			0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000			0.127064			0.0635321	+	0.997980i	$0.479763\pi$
$992$	0.775255	+	1.34278i	0.0246144	+	0.0426333i
$993$	−18.4041	−	39.9479i	−0.584036	−	1.26771i
$994$	0.550510	−	0.953512i	0.0174611	−	0.0302436i
$995$		0			0
$996$	6.89898	+	0.635674i	0.218603	+	0.0201421i
$997$	−10.4722	−	18.1384i	−0.331658	−	0.574448i	0.651179	−	0.758924i	$-0.274275\pi$
$997$	−10.4722	−	18.1384i	−0.331658	−	0.574448i	−0.982837	+	0.184476i	$0.940941\pi$
$998$	21.2474			0.672576
$999$	−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.301.1		4
3.2	odd	2		1350.2.e.j.901.2		4
5.2	odd	4		90.2.i.b.49.2	✓	8
5.3	odd	4		90.2.i.b.49.3	yes	8
5.4	even	2		450.2.e.k.301.2		4
9.2	odd	6		1350.2.e.j.451.2		4
9.4	even	3		4050.2.a.bq.1.1		2
9.5	odd	6		4050.2.a.bz.1.1		2
9.7	even	3	inner	450.2.e.n.151.1		4
15.2	even	4		270.2.i.b.199.4		8
15.8	even	4		270.2.i.b.199.1		8
15.14	odd	2		1350.2.e.m.901.1		4
20.3	even	4		720.2.by.c.49.2		8
20.7	even	4		720.2.by.c.49.3		8
45.2	even	12		270.2.i.b.19.1		8
45.4	even	6		4050.2.a.bs.1.2		2
45.7	odd	12		90.2.i.b.79.3	yes	8
45.13	odd	12		810.2.c.f.649.4		4
45.14	odd	6		4050.2.a.bm.1.2		2
45.22	odd	12		810.2.c.f.649.2		4
45.23	even	12		810.2.c.e.649.1		4
45.29	odd	6		1350.2.e.m.451.1		4
45.32	even	12		810.2.c.e.649.3		4
45.34	even	6		450.2.e.k.151.2		4
45.38	even	12		270.2.i.b.19.4		8
45.43	odd	12		90.2.i.b.79.2	yes	8
60.23	odd	4		2160.2.by.d.1009.2		8
60.47	odd	4		2160.2.by.d.1009.3		8
180.7	even	12		720.2.by.c.529.2		8
180.43	even	12		720.2.by.c.529.3		8
180.47	odd	12		2160.2.by.d.289.2		8
180.83	odd	12		2160.2.by.d.289.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.i.b.49.2	✓	8	5.2	odd	4
90.2.i.b.49.3	yes	8	5.3	odd	4
90.2.i.b.79.2	yes	8	45.43	odd	12
90.2.i.b.79.3	yes	8	45.7	odd	12
270.2.i.b.19.1		8	45.2	even	12
270.2.i.b.19.4		8	45.38	even	12
270.2.i.b.199.1		8	15.8	even	4
270.2.i.b.199.4		8	15.2	even	4
450.2.e.k.151.2		4	45.34	even	6
450.2.e.k.301.2		4	5.4	even	2
450.2.e.n.151.1		4	9.7	even	3	inner
450.2.e.n.301.1		4	1.1	even	1	trivial
720.2.by.c.49.2		8	20.3	even	4
720.2.by.c.49.3		8	20.7	even	4
720.2.by.c.529.2		8	180.7	even	12
720.2.by.c.529.3		8	180.43	even	12
810.2.c.e.649.1		4	45.23	even	12
810.2.c.e.649.3		4	45.32	even	12
810.2.c.f.649.2		4	45.22	odd	12
810.2.c.f.649.4		4	45.13	odd	12
1350.2.e.j.451.2		4	9.2	odd	6
1350.2.e.j.901.2		4	3.2	odd	2
1350.2.e.m.451.1		4	45.29	odd	6
1350.2.e.m.901.1		4	15.14	odd	2
2160.2.by.d.289.2		8	180.47	odd	12
2160.2.by.d.289.3		8	180.83	odd	12
2160.2.by.d.1009.2		8	60.23	odd	4
2160.2.by.d.1009.3		8	60.47	odd	4
4050.2.a.bm.1.2		2	45.14	odd	6
4050.2.a.bq.1.1		2	9.4	even	3
4050.2.a.bs.1.2		2	45.4	even	6
4050.2.a.bz.1.1		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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.72474 - 0.158919i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.724745 - 1.57313i) q^{6} +(0.224745 + 0.389270i) q^{7} -1.00000 q^{8} +(2.94949 + 0.548188i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.72474 - 0.158919i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.724745 - 1.57313i) q^{6} +(0.224745 + 0.389270i) q^{7} -1.00000 q^{8} +(2.94949 + 0.548188i) q^{9} +(1.72474 + 2.98735i) q^{11} +(1.00000 - 1.41421i) q^{12} +(-1.22474 + 2.12132i) q^{13} +(-0.224745 + 0.389270i) q^{14} +(-0.500000 - 0.866025i) q^{16} -5.89898 q^{17} +(1.00000 + 2.82843i) q^{18} -5.44949 q^{19} +(-0.325765 - 0.707107i) q^{21} +(-1.72474 + 2.98735i) q^{22} +(-3.44949 + 5.97469i) q^{23} +(1.72474 + 0.158919i) q^{24} -2.44949 q^{26} +(-5.00000 - 1.41421i) q^{27} -0.449490 q^{28} +(3.00000 + 5.19615i) q^{29} +(-0.775255 + 1.34278i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.50000 - 5.42650i) q^{33} +(-2.94949 - 5.10867i) q^{34} +(-1.94949 + 2.28024i) q^{36} +8.00000 q^{37} +(-2.72474 - 4.71940i) q^{38} +(2.44949 - 3.46410i) q^{39} +(0.500000 - 0.866025i) q^{41} +(0.449490 - 0.635674i) q^{42} +(-1.27526 - 2.20881i) q^{43} -3.44949 q^{44} -6.89898 q^{46} +(2.22474 + 3.85337i) q^{47} +(0.724745 + 1.57313i) q^{48} +(3.39898 - 5.88721i) q^{49} +(10.1742 + 0.937458i) q^{51} +(-1.22474 - 2.12132i) q^{52} +3.55051 q^{53} +(-1.27526 - 5.03723i) q^{54} +(-0.224745 - 0.389270i) q^{56} +(9.39898 + 0.866025i) q^{57} +(-3.00000 + 5.19615i) q^{58} +(-6.62372 + 11.4726i) q^{59} +(-2.22474 - 3.85337i) q^{61} -1.55051 q^{62} +(0.449490 + 1.27135i) q^{63} +1.00000 q^{64} +(3.44949 - 4.87832i) q^{66} +(-2.27526 + 3.94086i) q^{67} +(2.94949 - 5.10867i) q^{68} +(6.89898 - 9.75663i) q^{69} -2.44949 q^{71} +(-2.94949 - 0.548188i) q^{72} +14.7980 q^{73} +(4.00000 + 6.92820i) q^{74} +(2.72474 - 4.71940i) q^{76} +(-0.775255 + 1.34278i) q^{77} +(4.22474 + 0.389270i) q^{78} +(-3.67423 - 6.36396i) q^{79} +(8.39898 + 3.23375i) q^{81} +1.00000 q^{82} +(2.00000 + 3.46410i) q^{83} +(0.775255 + 0.0714323i) q^{84} +(1.27526 - 2.20881i) q^{86} +(-4.34847 - 9.43879i) q^{87} +(-1.72474 - 2.98735i) q^{88} +3.10102 q^{89} -1.10102 q^{91} +(-3.44949 - 5.97469i) q^{92} +(1.55051 - 2.19275i) q^{93} +(-2.22474 + 3.85337i) q^{94} +(-1.00000 + 1.41421i) q^{96} +(-6.50000 - 11.2583i) q^{97} +6.79796 q^{98} +(3.44949 + 9.75663i) 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

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