LMFDB - Embedded newform 450.3.i.b.401.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,3,Mod(101,450)]

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([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("450.101");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	450.i (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.2616118962$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			401.2
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	450.401
Dual form			450.3.i.b.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(-2.44949 - 1.73205i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-4.22474 - 0.389270i) q^{6} +(3.17423 + 5.49794i) q^{7} -2.82843i q^{8} +(3.00000 + 8.48528i) q^{9} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(-2.44949 - 1.73205i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-4.22474 - 0.389270i) q^{6} +(3.17423 + 5.49794i) q^{7} -2.82843i q^{8} +(3.00000 + 8.48528i) q^{9} +(8.17423 - 4.71940i) q^{11} +(-5.44949 + 2.51059i) q^{12} +(9.84847 - 17.0580i) q^{13} +(7.77526 + 4.48905i) q^{14} +(-2.00000 - 3.46410i) q^{16} -1.90702i q^{17} +(9.67423 + 8.27098i) q^{18} +4.69694 q^{19} +(1.74745 - 18.9651i) q^{21} +(6.67423 - 11.5601i) q^{22} +(-8.17423 - 4.71940i) q^{23} +(-4.89898 + 6.92820i) q^{24} -27.8557i q^{26} +(7.34847 - 25.9808i) q^{27} +12.6969 q^{28} +(-2.84847 + 1.64456i) q^{29} +(20.5227 - 35.5464i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-28.1969 - 2.59808i) q^{33} +(-1.34847 - 2.33562i) q^{34} +(17.6969 + 3.28913i) q^{36} -17.3031 q^{37} +(5.75255 - 3.32124i) q^{38} +(-53.6691 + 24.7255i) q^{39} +(-53.5454 - 30.9145i) q^{41} +(-11.2702 - 24.4630i) q^{42} +(0.477296 + 0.826701i) q^{43} -18.8776i q^{44} -13.3485 q^{46} +(12.2196 - 7.05501i) q^{47} +(-1.10102 + 11.9494i) q^{48} +(4.34847 - 7.53177i) q^{49} +(-3.30306 + 4.67123i) q^{51} +(-19.6969 - 34.1161i) q^{52} -9.53512i q^{53} +(-9.37117 - 37.0160i) q^{54} +(15.5505 - 8.97809i) q^{56} +(-11.5051 - 8.13534i) q^{57} +(-2.32577 + 4.02834i) q^{58} +(79.2650 + 45.7637i) q^{59} +(37.5454 + 65.0306i) q^{61} -58.0470i q^{62} +(-37.1288 + 43.4281i) q^{63} -8.00000 q^{64} +(-36.3712 + 16.7563i) q^{66} +(15.4773 - 26.8075i) q^{67} +(-3.30306 - 1.90702i) q^{68} +(11.8485 + 25.7183i) q^{69} -85.9026i q^{71} +(24.0000 - 8.48528i) q^{72} +96.0908 q^{73} +(-21.1918 + 12.2351i) q^{74} +(4.69694 - 8.13534i) q^{76} +(51.8939 + 29.9609i) q^{77} +(-48.2474 + 68.2322i) q^{78} +(-14.8712 - 25.7576i) q^{79} +(-63.0000 + 50.9117i) q^{81} -87.4393 q^{82} +(76.1288 - 43.9530i) q^{83} +(-31.1010 - 21.9917i) q^{84} +(1.16913 + 0.674999i) q^{86} +(9.82577 + 0.905350i) q^{87} +(-13.3485 - 23.1202i) q^{88} +41.3766i q^{89} +125.045 q^{91} +(-16.3485 + 9.43879i) q^{92} +(-111.838 + 51.5241i) q^{93} +(9.97730 - 17.2812i) q^{94} +(7.10102 + 15.4135i) q^{96} +(47.9393 + 83.0333i) q^{97} -12.2993i q^{98} +(64.5681 + 55.2025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4} - 12 q^{6} - 2 q^{7} + 12 q^{9}+O(q^{10}) $ 4 * q + 4 * q^4 - 12 * q^6 - 2 * q^7 + 12 * q^9	$ 4 q + 4 q^{4} - 12 q^{6} - 2 q^{7} + 12 q^{9} + 18 q^{11} - 12 q^{12} + 10 q^{13} + 36 q^{14} - 8 q^{16} + 24 q^{18} - 40 q^{19} - 42 q^{21} + 12 q^{22} - 18 q^{23} - 8 q^{28} + 18 q^{29} + 38 q^{31} - 54 q^{33} + 24 q^{34} + 12 q^{36} - 128 q^{37} + 72 q^{38} - 102 q^{39} - 126 q^{41} + 48 q^{42} + 46 q^{43} - 24 q^{46} - 54 q^{47} - 24 q^{48} - 12 q^{49} - 72 q^{51} - 20 q^{52} + 36 q^{54} + 72 q^{56} - 144 q^{57} - 24 q^{58} + 126 q^{59} + 62 q^{61} - 222 q^{63} - 32 q^{64} - 72 q^{66} + 106 q^{67} - 72 q^{68} + 18 q^{69} + 96 q^{72} + 208 q^{73} + 72 q^{74} - 40 q^{76} + 90 q^{77} - 144 q^{78} + 14 q^{79} - 252 q^{81} - 144 q^{82} + 378 q^{83} - 144 q^{84} - 108 q^{86} + 54 q^{87} - 24 q^{88} + 412 q^{91} - 36 q^{92} - 222 q^{93} + 84 q^{94} + 48 q^{96} - 14 q^{97} + 126 q^{99}+O(q^{100}) $ 4 * q + 4 * q^4 - 12 * q^6 - 2 * q^7 + 12 * q^9 + 18 * q^11 - 12 * q^12 + 10 * q^13 + 36 * q^14 - 8 * q^16 + 24 * q^18 - 40 * q^19 - 42 * q^21 + 12 * q^22 - 18 * q^23 - 8 * q^28 + 18 * q^29 + 38 * q^31 - 54 * q^33 + 24 * q^34 + 12 * q^36 - 128 * q^37 + 72 * q^38 - 102 * q^39 - 126 * q^41 + 48 * q^42 + 46 * q^43 - 24 * q^46 - 54 * q^47 - 24 * q^48 - 12 * q^49 - 72 * q^51 - 20 * q^52 + 36 * q^54 + 72 * q^56 - 144 * q^57 - 24 * q^58 + 126 * q^59 + 62 * q^61 - 222 * q^63 - 32 * q^64 - 72 * q^66 + 106 * q^67 - 72 * q^68 + 18 * q^69 + 96 * q^72 + 208 * q^73 + 72 * q^74 - 40 * q^76 + 90 * q^77 - 144 * q^78 + 14 * q^79 - 252 * q^81 - 144 * q^82 + 378 * q^83 - 144 * q^84 - 108 * q^86 + 54 * q^87 - 24 * q^88 + 412 * q^91 - 36 * q^92 - 222 * q^93 + 84 * q^94 + 48 * q^96 - 14 * q^97 + 126 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$	−2.44949	−	1.73205i	−0.816497	−	0.577350i
$3$	−2.44949	−	1.73205i	−0.816497	−	0.577350i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−4.22474	−	0.389270i	−0.704124	−	0.0648783i
$7$	3.17423	+	5.49794i	0.453462	+	0.785419i	0.998598	−	0.0529281i	$-0.0168554\pi$
$7$	3.17423	+	5.49794i	0.453462	+	0.785419i	−0.545136	+	0.838347i	$0.683522\pi$
$8$		−	2.82843i		−	0.353553i
$9$	3.00000	+	8.48528i	0.333333	+	0.942809i
$10$		0			0
$11$	8.17423	−	4.71940i	0.743112	−	0.429036i	−0.0800876	−	0.996788i	$-0.525520\pi$
$11$	8.17423	−	4.71940i	0.743112	−	0.429036i	0.823200	+	0.567752i	$0.192187\pi$
$12$	−5.44949	+	2.51059i	−0.454124	+	0.209216i
$13$	9.84847	−	17.0580i	0.757575	−	1.31216i	−0.186510	−	0.982453i	$-0.559718\pi$
$13$	9.84847	−	17.0580i	0.757575	−	1.31216i	0.944084	−	0.329704i	$-0.106949\pi$
$14$	7.77526	+	4.48905i	0.555375	+	0.320646i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$		−	1.90702i		−	0.112178i	−0.998426	−	0.0560889i	$-0.982137\pi$
$17$		−	1.90702i		−	0.112178i	0.998426	−	0.0560889i	$-0.0178630\pi$
$18$	9.67423	+	8.27098i	0.537457	+	0.459499i
$19$	4.69694			0.247207			0.123604	−	0.992332i	$-0.460555\pi$
$19$	4.69694			0.247207			0.123604	+	0.992332i	$0.460555\pi$
$20$		0			0
$21$	1.74745	−	18.9651i	0.0832118	−	0.903099i
$22$	6.67423	−	11.5601i	0.303374	−	0.525460i
$23$	−8.17423	−	4.71940i	−0.355402	−	0.205191i	0.311660	−	0.950194i	$-0.399115\pi$
$23$	−8.17423	−	4.71940i	−0.355402	−	0.205191i	−0.667062	+	0.745002i	$0.732448\pi$
$24$	−4.89898	+	6.92820i	−0.204124	+	0.288675i
$25$		0			0
$26$		−	27.8557i		−	1.07137i
$27$	7.34847	−	25.9808i	0.272166	−	0.962250i
$28$	12.6969			0.453462
$29$	−2.84847	+	1.64456i	−0.0982231	+	0.0567091i	−0.548307	−	0.836277i	$-0.684727\pi$
$29$	−2.84847	+	1.64456i	−0.0982231	+	0.0567091i	0.450084	+	0.892986i	$0.351394\pi$
$30$		0			0
$31$	20.5227	−	35.5464i	0.662023	−	1.14666i	−0.318061	−	0.948070i	$-0.603032\pi$
$31$	20.5227	−	35.5464i	0.662023	−	1.14666i	0.980083	−	0.198587i	$-0.0636351\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$	−28.1969	−	2.59808i	−0.854453	−	0.0787296i
$34$	−1.34847	−	2.33562i	−0.0396609	−	0.0686946i
$35$		0			0
$36$	17.6969	+	3.28913i	0.491582	+	0.0913647i
$37$	−17.3031			−0.467650			−0.233825	−	0.972279i	$-0.575124\pi$
$37$	−17.3031			−0.467650			−0.233825	+	0.972279i	$0.575124\pi$
$38$	5.75255	−	3.32124i	0.151383	−	0.0874010i
$39$	−53.6691	+	24.7255i	−1.37613	+	0.633986i
$40$		0			0
$41$	−53.5454	−	30.9145i	−1.30599	−	0.754011i	−0.324562	−	0.945864i	$-0.605217\pi$
$41$	−53.5454	−	30.9145i	−1.30599	−	0.754011i	−0.981424	+	0.191853i	$0.938550\pi$
$42$	−11.2702	−	24.4630i	−0.268337	−	0.582453i
$43$	0.477296	+	0.826701i	0.0110999	+	0.0192256i	0.871522	−	0.490356i	$-0.163133\pi$
$43$	0.477296	+	0.826701i	0.0110999	+	0.0192256i	−0.860422	+	0.509582i	$0.829800\pi$
$44$		−	18.8776i		−	0.429036i
$45$		0			0
$46$	−13.3485			−0.290184
$47$	12.2196	−	7.05501i	0.259992	−	0.150107i	−0.364339	−	0.931267i	$-0.618705\pi$
$47$	12.2196	−	7.05501i	0.259992	−	0.150107i	0.624331	+	0.781160i	$0.285372\pi$
$48$	−1.10102	+	11.9494i	−0.0229379	+	0.248945i
$49$	4.34847	−	7.53177i	0.0887443	−	0.153710i
$50$		0			0
$51$	−3.30306	+	4.67123i	−0.0647659	+	0.0915928i
$52$	−19.6969	−	34.1161i	−0.378787	−	0.656079i
$53$		−	9.53512i		−	0.179908i	−0.995946	−	0.0899539i	$-0.971328\pi$
$53$		−	9.53512i		−	0.179908i	0.995946	−	0.0899539i	$-0.0286720\pi$
$54$	−9.37117	−	37.0160i	−0.173540	−	0.685481i
$55$		0			0
$56$	15.5505	−	8.97809i	0.277688	−	0.160323i
$57$	−11.5051	−	8.13534i	−0.201844	−	0.142725i
$58$	−2.32577	+	4.02834i	−0.0400994	+	0.0694542i
$59$	79.2650	+	45.7637i	1.34348	+	0.775656i	0.987316	−	0.158769i	$-0.0507526\pi$
$59$	79.2650	+	45.7637i	1.34348	+	0.775656i	0.356160	+	0.934425i	$0.384086\pi$
$60$		0			0
$61$	37.5454	+	65.0306i	0.615498	+	1.06607i	0.990297	+	0.138968i	$0.0443786\pi$
$61$	37.5454	+	65.0306i	0.615498	+	1.06607i	−0.374798	+	0.927106i	$0.622288\pi$
$62$		−	58.0470i		−	0.936241i
$63$	−37.1288	+	43.4281i	−0.589346	+	0.689335i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	−36.3712	+	16.7563i	−0.551078	+	0.253883i
$67$	15.4773	−	26.8075i	0.231004	−	0.400111i	−0.727100	−	0.686532i	$-0.759132\pi$
$67$	15.4773	−	26.8075i	0.231004	−	0.400111i	0.958104	+	0.286421i	$0.0924655\pi$
$68$	−3.30306	−	1.90702i	−0.0485744	−	0.0280445i
$69$	11.8485	+	25.7183i	0.171717	+	0.372729i
$70$		0			0
$71$		−	85.9026i		−	1.20990i	−0.796265	−	0.604948i	$-0.793194\pi$
$71$		−	85.9026i		−	1.20990i	0.796265	−	0.604948i	$-0.206806\pi$
$72$	24.0000	−	8.48528i	0.333333	−	0.117851i
$73$	96.0908			1.31631			0.658156	−	0.752881i	$-0.271337\pi$
$73$	96.0908			1.31631			0.658156	+	0.752881i	$0.271337\pi$
$74$	−21.1918	+	12.2351i	−0.286376	+	0.165339i
$75$		0			0
$76$	4.69694	−	8.13534i	0.0618018	−	0.107044i
$77$	51.8939	+	29.9609i	0.673946	+	0.389103i
$78$	−48.2474	+	68.2322i	−0.618557	+	0.874772i
$79$	−14.8712	−	25.7576i	−0.188243	−	0.326046i	0.756422	−	0.654084i	$-0.226946\pi$
$79$	−14.8712	−	25.7576i	−0.188243	−	0.326046i	−0.944664	+	0.328038i	$0.893612\pi$
$80$		0			0
$81$	−63.0000	+	50.9117i	−0.777778	+	0.628539i
$82$	−87.4393			−1.06633
$83$	76.1288	−	43.9530i	0.917215	−	0.529554i	0.0344693	−	0.999406i	$-0.489026\pi$
$83$	76.1288	−	43.9530i	0.917215	−	0.529554i	0.882745	+	0.469852i	$0.155693\pi$
$84$	−31.1010	−	21.9917i	−0.370250	−	0.261806i
$85$		0			0
$86$	1.16913	+	0.674999i	0.0135946	+	0.00784882i
$87$	9.82577	+	0.905350i	0.112940	+	0.0104063i
$88$	−13.3485	−	23.1202i	−0.151687	−	0.262730i
$89$			41.3766i			0.464905i	0.972608	+	0.232453i	$0.0746751\pi$
$89$			41.3766i			0.464905i	−0.972608	+	0.232453i	$0.925325\pi$
$90$		0			0
$91$	125.045			1.37413
$92$	−16.3485	+	9.43879i	−0.177701	+	0.102596i
$93$	−111.838	+	51.5241i	−1.20256	+	0.554023i
$94$	9.97730	−	17.2812i	0.106141	−	0.183842i
$95$		0			0
$96$	7.10102	+	15.4135i	0.0739690	+	0.160557i
$97$	47.9393	+	83.0333i	0.494219	+	0.856013i	0.999978	−	0.00666202i	$-0.00212060\pi$
$97$	47.9393	+	83.0333i	0.494219	+	0.856013i	−0.505758	+	0.862675i	$0.668787\pi$
$98$		−	12.2993i		−	0.125503i
$99$	64.5681	+	55.2025i	0.652203	+	0.557601i
$100$		0			0
$101$	−136.772	+	78.9656i	−1.35418	+	0.781838i	−0.988832	−	0.149032i	$-0.952384\pi$
$101$	−136.772	+	78.9656i	−1.35418	+	0.781838i	−0.365350	+	0.930870i	$0.619051\pi$
$102$	−0.742346	+	8.05669i	−0.00727790	+	0.0789871i
$103$	14.5681	−	25.2327i	0.141438	−	0.244978i	−0.786600	−	0.617462i	$-0.788161\pi$
$103$	14.5681	−	25.2327i	0.141438	−	0.244978i	0.928038	+	0.372485i	$0.121494\pi$
$104$	−48.2474	−	27.8557i	−0.463918	−	0.267843i
$105$		0			0
$106$	−6.74235	−	11.6781i	−0.0636070	−	0.110171i
$107$			171.805i			1.60566i	0.596210	+	0.802829i	$0.296673\pi$
$107$			171.805i			1.60566i	−0.596210	+	0.802829i	$0.703327\pi$
$108$	−37.6515	−	38.7087i	−0.348625	−	0.358414i
$109$	116.272			1.06672			0.533360	−	0.845888i	$-0.320929\pi$
$109$	116.272			1.06672			0.533360	+	0.845888i	$0.320929\pi$
$110$		0			0
$111$	42.3837	+	29.9698i	0.381835	+	0.269998i
$112$	12.6969	−	21.9917i	0.113366	−	0.196355i
$113$	−175.166	−	101.132i	−1.55014	−	0.894976i	−0.998129	−	0.0611424i	$-0.980526\pi$
$113$	−175.166	−	101.132i	−1.55014	−	0.894976i	−0.552015	−	0.833834i	$-0.686141\pi$
$114$	−19.8434	−	1.82838i	−0.174065	−	0.0160384i
$115$		0			0
$116$			6.57826i			0.0567091i
$117$	174.288	+	32.3929i	1.48964	+	0.276862i
$118$	129.439			1.09694
$119$	10.4847	−	6.05334i	0.0881067	−	0.0508684i
$120$		0			0
$121$	−15.9546	+	27.6342i	−0.131856	+	0.228382i
$122$	91.9671	+	53.0972i	0.753829	+	0.435223i
$123$	77.6135	+	168.468i	0.631004	+	1.36966i
$124$	−41.0454	−	71.0927i	−0.331011	−	0.573328i
$125$		0			0
$126$	−14.7650	+	79.4424i	−0.117183	+	0.630495i
$127$	−10.0908			−0.0794552			−0.0397276	−	0.999211i	$-0.512649\pi$
$127$	−10.0908			−0.0794552			−0.0397276	+	0.999211i	$0.512649\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$	0.262756	−	2.85170i	0.00203687	−	0.0221062i
$130$		0			0
$131$	4.29567	+	2.48010i	0.0327913	+	0.0189321i	0.516306	−	0.856404i	$-0.327307\pi$
$131$	4.29567	+	2.48010i	0.0327913	+	0.0189321i	−0.483515	+	0.875336i	$0.660640\pi$
$132$	−32.6969	+	46.2405i	−0.247704	+	0.350306i
$133$	14.9092	+	25.8235i	0.112099	+	0.194161i
$134$		−	43.7764i		−	0.326690i
$135$		0			0
$136$	−5.39388			−0.0396609
$137$	−203.242	+	117.342i	−1.48352	+	0.856511i	−0.999825	−	0.0187249i	$-0.994039\pi$
$137$	−203.242	+	117.342i	−1.48352	+	0.856511i	−0.483696	+	0.875236i	$0.660706\pi$
$138$	32.6969	+	23.1202i	0.236934	+	0.167538i
$139$	−53.2650	+	92.2578i	−0.383202	+	0.663725i	−0.991518	−	0.129970i	$-0.958512\pi$
$139$	−53.2650	+	92.2578i	−0.383202	+	0.663725i	0.608316	+	0.793695i	$0.291845\pi$
$140$		0			0
$141$	−42.1515	−	3.88386i	−0.298947	−	0.0275451i
$142$	−60.7423	−	105.209i	−0.427763	−	0.740907i
$143$		−	185.915i		−	1.30011i
$144$	23.3939	−	27.3629i	0.162457	−	0.190020i
$145$		0			0
$146$	117.687	−	67.9465i	0.806074	−	0.465387i
$147$	−23.6969	+	10.9172i	−0.161204	+	0.0742668i
$148$	−17.3031	+	29.9698i	−0.116913	+	0.202499i
$149$	−91.0301	−	52.5563i	−0.610940	−	0.352727i	0.162393	−	0.986726i	$-0.448079\pi$
$149$	−91.0301	−	52.5563i	−0.610940	−	0.352727i	−0.773333	+	0.634000i	$0.781412\pi$
$150$		0			0
$151$	142.614	+	247.014i	0.944460	+	1.63585i	0.756828	+	0.653614i	$0.226748\pi$
$151$	142.614	+	247.014i	0.944460	+	1.63585i	0.187632	+	0.982239i	$0.439919\pi$
$152$		−	13.2849i		−	0.0874010i
$153$	16.1816	−	5.72107i	0.105762	−	0.0373926i
$154$	84.7423			0.550275
$155$		0			0
$156$	−10.8434	+	117.683i	−0.0695088	+	0.754379i
$157$	−98.5908	+	170.764i	−0.627967	+	1.08767i	0.359992	+	0.932955i	$0.382779\pi$
$157$	−98.5908	+	170.764i	−0.627967	+	1.08767i	−0.987959	+	0.154715i	$0.950554\pi$
$158$	−36.4268	−	21.0310i	−0.230549	−	0.133108i
$159$	−16.5153	+	23.3562i	−0.103870	+	0.146894i
$160$		0			0
$161$		−	59.9219i		−	0.372186i
$162$	−41.1589	+	106.902i	−0.254067	+	0.659886i
$163$	249.060			1.52798			0.763988	−	0.645230i	$-0.223238\pi$
$163$	249.060			1.52798			0.763988	+	0.645230i	$0.223238\pi$
$164$	−107.091	+	61.8289i	−0.652993	+	0.377006i
$165$		0			0
$166$	62.1589	−	107.662i	0.374451	−	0.648569i
$167$	41.9472	+	24.2182i	0.251181	+	0.145019i	0.620305	−	0.784361i	$-0.287009\pi$
$167$	41.9472	+	24.2182i	0.251181	+	0.145019i	−0.369124	+	0.929380i	$0.620342\pi$
$168$	−53.6413	−	4.94253i	−0.319294	−	0.0294198i
$169$	−109.485	−	189.633i	−0.647838	−	1.12209i
$170$		0			0
$171$	14.0908	+	39.8548i	0.0824024	+	0.233069i
$172$	1.90918			0.0110999
$173$	−86.9847	+	50.2206i	−0.502802	+	0.290293i	−0.729870	−	0.683586i	$-0.760419\pi$
$173$	−86.9847	+	50.2206i	−0.502802	+	0.290293i	0.227068	+	0.973879i	$0.427086\pi$
$174$	12.6742	−	5.83904i	0.0728404	−	0.0335577i
$175$		0			0
$176$	−32.6969	−	18.8776i	−0.185778	−	0.107259i
$177$	−114.894	−	249.389i	−0.649118	−	1.40898i
$178$	29.2577	+	50.6757i	0.164369	+	0.284695i
$179$		−	285.071i		−	1.59257i	−0.604919	−	0.796287i	$-0.706794\pi$
$179$		−	285.071i		−	1.59257i	0.604919	−	0.796287i	$-0.293206\pi$
$180$		0			0
$181$	37.1214			0.205091			0.102545	−	0.994728i	$-0.467301\pi$
$181$	37.1214			0.205091			0.102545	+	0.994728i	$0.467301\pi$
$182$	153.149	−	88.4205i	0.841476	−	0.485827i
$183$	20.6691	−	224.322i	0.112946	−	1.22580i
$184$	−13.3485	+	23.1202i	−0.0725460	+	0.125653i
$185$		0			0
$186$	−100.540	+	142.185i	−0.540539	+	0.764438i
$187$	−9.00000	−	15.5885i	−0.0481283	−	0.0833607i
$188$		−	28.2201i		−	0.150107i
$189$	166.166	−	42.0676i	0.879187	−	0.222580i
$190$		0			0
$191$	−15.5227	+	8.96204i	−0.0812707	+	0.0469217i	−0.540085	−	0.841611i	$-0.681608\pi$
$191$	−15.5227	+	8.96204i	−0.0812707	+	0.0469217i	0.458814	+	0.888532i	$0.348274\pi$
$192$	19.5959	+	13.8564i	0.102062	+	0.0721688i
$193$	−47.7270	+	82.6657i	−0.247290	+	0.428319i	−0.962773	−	0.270311i	$-0.912873\pi$
$193$	−47.7270	+	82.6657i	−0.247290	+	0.428319i	0.715483	+	0.698630i	$0.246207\pi$
$194$	117.427	+	67.7964i	0.605293	+	0.349466i
$195$		0			0
$196$	−8.69694	−	15.0635i	−0.0443721	−	0.0768548i
$197$		−	160.363i		−	0.814026i	−0.913422	−	0.407013i	$-0.866570\pi$
$197$		−	160.363i		−	0.814026i	0.913422	−	0.407013i	$-0.133430\pi$
$198$	118.114	+	21.9524i	0.596533	+	0.110871i
$199$	6.51531			0.0327402			0.0163701	−	0.999866i	$-0.494789\pi$
$199$	6.51531			0.0327402			0.0163701	+	0.999866i	$0.494789\pi$
$200$		0			0
$201$	−84.3434	+	38.8571i	−0.419619	+	0.193319i
$202$	−111.674	+	193.425i	−0.552843	+	0.957552i
$203$	−18.0834	−	10.4405i	−0.0890809	−	0.0514309i
$204$	4.78775	+	10.3923i	0.0234694	+	0.0509427i
$205$		0			0
$206$		−	41.2048i		−	0.200024i
$207$	15.5227	−	83.5189i	0.0749889	−	0.403473i
$208$	−78.7878			−0.378787
$209$	38.3939	−	22.1667i	0.183703	−	0.106061i
$210$		0			0
$211$	77.2196	−	133.748i	0.365970	−	0.633878i	−0.622961	−	0.782253i	$-0.714071\pi$
$211$	77.2196	−	133.748i	0.365970	−	0.633878i	0.988931	+	0.148374i	$0.0474040\pi$
$212$	−16.5153	−	9.53512i	−0.0779024	−	0.0449770i
$213$	−148.788	+	210.418i	−0.698534	+	0.987876i
$214$	121.485	+	210.418i	0.567685	+	0.983260i
$215$		0			0
$216$	−73.4847	−	20.7846i	−0.340207	−	0.0962250i
$217$	260.576			1.20081
$218$	142.404	−	82.2170i	0.653230	−	0.377142i
$219$	−235.373	−	166.434i	−1.07476	−	0.759973i
$220$		0			0
$221$	−32.5301	−	18.7813i	−0.147195	−	0.0849831i
$222$	73.1010	+	6.73555i	0.329284	+	0.0303403i
$223$	46.3865	+	80.3437i	0.208011	+	0.360286i	0.951088	−	0.308920i	$-0.0999676\pi$
$223$	46.3865	+	80.3437i	0.208011	+	0.360286i	−0.743077	+	0.669206i	$0.766634\pi$
$224$		−	35.9124i		−	0.160323i
$225$		0			0
$226$	−286.045			−1.26569
$227$	−147.053	+	84.9010i	−0.647810	+	0.374013i	−0.787617	−	0.616166i	$-0.788685\pi$
$227$	−147.053	+	84.9010i	−0.647810	+	0.374013i	0.139807	+	0.990179i	$0.455352\pi$
$228$	−25.5959	+	11.7921i	−0.112263	+	0.0517197i
$229$	−203.772	+	352.944i	−0.889836	+	1.54124i	−0.0497675	+	0.998761i	$0.515848\pi$
$229$	−203.772	+	352.944i	−0.889836	+	1.54124i	−0.840068	+	0.542480i	$0.817485\pi$
$230$		0			0
$231$	−75.2196	−	163.272i	−0.325626	−	0.706805i
$232$	4.65153	+	8.05669i	0.0200497	+	0.0347271i
$233$		−	15.2562i		−	0.0654772i	−0.999464	−	0.0327386i	$-0.989577\pi$
$233$		−	15.2562i		−	0.0654772i	0.999464	−	0.0327386i	$-0.0104229\pi$
$234$	236.363	−	83.5670i	1.01010	−	0.357124i
$235$		0			0
$236$	158.530	−	91.5274i	0.671738	−	0.387828i
$237$	−8.18673	+	88.8507i	−0.0345432	+	0.374897i
$238$	8.56072	−	14.8276i	0.0359694	−	0.0623008i
$239$	48.9620	+	28.2682i	0.204862	+	0.118277i	0.598921	−	0.800808i	$-0.295596\pi$
$239$	48.9620	+	28.2682i	0.204862	+	0.118277i	−0.394059	+	0.919085i	$0.628930\pi$
$240$		0			0
$241$	−42.1061	−	72.9299i	−0.174714	−	0.302614i	0.765348	−	0.643617i	$-0.222567\pi$
$241$	−42.1061	−	72.9299i	−0.174714	−	0.302614i	−0.940062	+	0.341003i	$0.889233\pi$
$242$			45.1264i			0.186473i
$243$	242.499	−	15.5885i	0.997940	−	0.0641500i
$244$	150.182			0.615498
$245$		0			0
$246$	214.182	+	151.449i	0.870657	+	0.615647i
$247$	46.2577	−	80.1206i	0.187278	−	0.324375i
$248$	−100.540	−	58.0470i	−0.405404	−	0.234060i
$249$	−262.606	−	24.1966i	−1.05464	−	0.0971750i
$250$		0			0
$251$			218.903i			0.872123i	0.899917	+	0.436062i	$0.143627\pi$
$251$			218.903i			0.872123i	−0.899917	+	0.436062i	$0.856373\pi$
$252$	38.0908	+	107.737i	0.151154	+	0.427528i
$253$	−89.0908			−0.352138
$254$	−12.3587	+	7.13528i	−0.0486562	+	0.0280917i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	11.1061	+	6.41212i	0.0432145	+	0.0249499i	0.521452	−	0.853281i	$-0.325391\pi$
$257$	11.1061	+	6.41212i	0.0432145	+	0.0249499i	−0.478237	+	0.878231i	$0.658724\pi$
$258$	−1.69464	−	3.67840i	−0.00656839	−	0.0142574i
$259$	−54.9240	−	95.1311i	−0.212062	−	0.367302i
$260$		0			0
$261$	−22.5000	−	19.2364i	−0.0862069	−	0.0737026i
$262$	7.01479			0.0267740
$263$	−291.386	+	168.232i	−1.10793	+	0.639666i	−0.938293	−	0.345840i	$-0.887594\pi$
$263$	−291.386	+	168.232i	−1.10793	+	0.639666i	−0.169640	+	0.985506i	$0.554261\pi$
$264$	−7.34847	+	79.7530i	−0.0278351	+	0.302095i
$265$		0			0
$266$	36.5199	+	21.0848i	0.137293	+	0.0792661i
$267$	71.6663	−	101.351i	0.268413	−	0.379594i
$268$	−30.9546	−	53.6149i	−0.115502	−	0.200056i
$269$			60.4468i			0.224709i	0.993668	+	0.112355i	$0.0358393\pi$
$269$			60.4468i			0.224709i	−0.993668	+	0.112355i	$0.964161\pi$
$270$		0			0
$271$	274.636			1.01342			0.506708	−	0.862118i	$-0.330862\pi$
$271$	274.636			1.01342			0.506708	+	0.862118i	$0.330862\pi$
$272$	−6.60612	+	3.81405i	−0.0242872	+	0.0140222i
$273$	−306.297	−	216.585i	−1.12197	−	0.793352i
$274$	−165.947	+	287.428i	−0.605645	+	1.04901i
$275$		0			0
$276$	56.3939	+	5.19615i	0.204326	+	0.0188266i
$277$	−24.5000	−	42.4352i	−0.0884477	−	0.153196i	0.818407	−	0.574638i	$-0.194857\pi$
$277$	−24.5000	−	42.4352i	−0.0884477	−	0.153196i	−0.906855	+	0.421442i	$0.861524\pi$
$278$			150.656i			0.541929i
$279$	363.189	+	67.5018i	1.30175	+	0.241942i
$280$		0			0
$281$	−297.121	+	171.543i	−1.05737	+	0.610473i	−0.924704	−	0.380688i	$-0.875687\pi$
$281$	−297.121	+	171.543i	−1.05737	+	0.610473i	−0.132666	+	0.991161i	$0.542354\pi$
$282$	−54.3712	+	25.0489i	−0.192806	+	0.0888259i
$283$	−171.704	+	297.401i	−0.606729	+	1.05089i	0.385047	+	0.922897i	$0.374185\pi$
$283$	−171.704	+	297.401i	−0.606729	+	1.05089i	−0.991776	+	0.127988i	$0.959148\pi$
$284$	−148.788	−	85.9026i	−0.523901	−	0.302474i
$285$		0			0
$286$	−131.462	−	227.699i	−0.459657	−	0.796150i
$287$		−	392.519i		−	1.36766i
$288$	9.30306	−	50.0545i	0.0323023	−	0.173800i
$289$	285.363			0.987416
$290$		0			0
$291$	26.3911	−	286.422i	0.0906910	−	0.984270i
$292$	96.0908	−	166.434i	0.329078	−	0.569980i
$293$	248.076	+	143.226i	0.846674	+	0.488828i	0.859527	−	0.511090i	$-0.170758\pi$
$293$	248.076	+	143.226i	0.846674	+	0.488828i	−0.0128532	+	0.999917i	$0.504091\pi$
$294$	−21.3031	+	30.1271i	−0.0724594	+	0.102473i
$295$		0			0
$296$			48.9404i			0.165339i
$297$	−62.5454	−	247.053i	−0.210591	−	0.831829i
$298$	−148.652			−0.498831
$299$	−161.007	+	92.9577i	−0.538486	+	0.310895i
$300$		0			0
$301$	−3.03010	+	5.24829i	−0.0100668	+	0.0174362i
$302$	349.330	+	201.686i	1.15672	+	0.667834i
$303$	471.795	+	43.4714i	1.55708	+	0.143470i
$304$	−9.39388	−	16.2707i	−0.0309009	−	0.0535219i
$305$		0			0
$306$	15.7730	−	18.4490i	0.0515456	−	0.0602908i
$307$	−154.091			−0.501924			−0.250962	−	0.967997i	$-0.580747\pi$
$307$	−154.091			−0.501924			−0.250962	+	0.967997i	$0.580747\pi$
$308$	103.788	−	59.9219i	0.336973	−	0.194552i
$309$	−79.3888	+	36.5746i	−0.256922	+	0.118364i
$310$		0			0
$311$	−62.3411	−	35.9926i	−0.200454	−	0.115732i	0.396413	−	0.918072i	$-0.370255\pi$
$311$	−62.3411	−	35.9926i	−0.200454	−	0.115732i	−0.596867	+	0.802340i	$0.703588\pi$
$312$	69.9342	+	151.799i	0.224148	+	0.486536i
$313$	−183.803	−	318.356i	−0.587230	−	1.01711i	−0.994593	−	0.103846i	$-0.966885\pi$
$313$	−183.803	−	318.356i	−0.587230	−	1.01711i	0.407363	−	0.913266i	$-0.366448\pi$
$314$			278.857i			0.888079i
$315$		0			0
$316$	−59.4847			−0.188243
$317$	93.1821	−	53.7987i	0.293950	−	0.169712i	−0.345772	−	0.938319i	$-0.612383\pi$
$317$	93.1821	−	53.7987i	0.293950	−	0.169712i	0.639722	+	0.768607i	$0.279050\pi$
$318$	−3.71173	+	40.2834i	−0.0116721	+	0.126677i
$319$	−15.5227	+	26.8861i	−0.0486605	+	0.0842825i
$320$		0			0
$321$	297.576	−	420.835i	0.927027	−	1.31101i
$322$	−42.3712	−	73.3890i	−0.131587	−	0.227916i
$323$		−	8.95717i		−	0.0277312i
$324$	25.1816	+	160.031i	0.0777211	+	0.493922i
$325$		0			0
$326$	305.035	−	176.112i	0.935691	−	0.540221i
$327$	−284.808	−	201.390i	−0.870973	−	0.615871i
$328$	−87.4393	+	151.449i	−0.266583	+	0.461736i
$329$	77.5760	+	44.7885i	0.235793	+	0.136135i
$330$		0			0
$331$	−8.59873	−	14.8934i	−0.0259780	−	0.0449953i	0.852744	−	0.522329i	$-0.174937\pi$
$331$	−8.59873	−	14.8934i	−0.0259780	−	0.0449953i	−0.878722	+	0.477334i	$0.841603\pi$
$332$		−	175.812i		−	0.529554i
$333$	−51.9092	−	146.821i	−0.155883	−	0.440905i
$334$	68.4995			0.205088
$335$		0			0
$336$	−69.1918	+	31.8768i	−0.205928	+	0.0948714i
$337$	182.197	−	315.574i	0.540644	−	0.936422i	−0.458223	−	0.888837i	$-0.651514\pi$
$337$	182.197	−	315.574i	0.540644	−	0.936422i	0.998867	−	0.0475854i	$-0.0151526\pi$
$338$	−268.182	−	154.835i	−0.793437	−	0.458091i
$339$	253.902	+	551.120i	0.748973	+	1.62572i
$340$		0			0
$341$		−	387.419i		−	1.13613i
$342$	45.4393	+	38.8483i	0.132863	+	0.113592i
$343$	366.287			1.06789
$344$	2.33826	−	1.35000i	0.00679728	−	0.00392441i
$345$		0			0
$346$	−71.0227	+	123.015i	−0.205268	+	0.355534i
$347$	−505.234	−	291.697i	−1.45601	−	0.840626i	−0.457196	−	0.889366i	$-0.651146\pi$
$347$	−505.234	−	291.697i	−1.45601	−	0.840626i	−0.998811	+	0.0487402i	$0.984479\pi$
$348$	11.3939	−	16.1134i	0.0327410	−	0.0463028i
$349$	−156.379	−	270.856i	−0.448076	−	0.776091i	0.550185	−	0.835043i	$-0.314557\pi$
$349$	−156.379	−	270.856i	−0.448076	−	0.776091i	−0.998261	+	0.0589524i	$0.981224\pi$
$350$		0			0
$351$	−370.810	−	381.221i	−1.05644	−	1.08610i
$352$	−53.3939			−0.151687
$353$	32.5760	−	18.8078i	0.0922834	−	0.0532798i	−0.453148	−	0.891435i	$-0.649699\pi$
$353$	32.5760	−	18.8078i	0.0922834	−	0.0532798i	0.545431	+	0.838155i	$0.316366\pi$
$354$	−317.060	−	224.195i	−0.895650	−	0.633320i
$355$		0			0
$356$	71.6663	+	41.3766i	0.201310	+	0.116226i
$357$	−36.1668	−	3.33243i	−0.101308	−	0.00933453i
$358$	−201.576	−	349.139i	−0.563060	−	0.975249i
$359$		−	294.028i		−	0.819019i	−0.912306	−	0.409510i	$-0.865700\pi$
$359$		−	294.028i		−	0.819019i	0.912306	−	0.409510i	$-0.134300\pi$
$360$		0			0
$361$	−338.939			−0.938889
$362$	45.4643	−	26.2488i	0.125592	−	0.0725105i
$363$	86.9444	−	40.0554i	0.239516	−	0.110346i
$364$	125.045	−	216.585i	0.343531	−	0.595014i
$365$		0			0
$366$	−133.305	−	289.353i	−0.364222	−	0.790581i
$367$	−16.6135	−	28.7755i	−0.0452684	−	0.0784072i	0.842503	−	0.538691i	$-0.181081\pi$
$367$	−16.6135	−	28.7755i	−0.0452684	−	0.0784072i	−0.887772	+	0.460284i	$0.847748\pi$
$368$			37.7552i			0.102596i
$369$	101.682	−	547.091i	0.275560	−	1.48263i
$370$		0			0
$371$	52.4235	−	30.2667i	0.141303	−	0.0815814i
$372$	−22.5959	+	245.234i	−0.0607417	+	0.659230i
$373$	−112.515	+	194.881i	−0.301648	+	0.522470i	−0.976509	−	0.215475i	$-0.930870\pi$
$373$	−112.515	+	194.881i	−0.301648	+	0.522470i	0.674861	+	0.737945i	$0.264203\pi$
$374$	−22.0454	−	12.7279i	−0.0589449	−	0.0340319i
$375$		0			0
$376$	−19.9546	−	34.5624i	−0.0530707	−	0.0919212i
$377$			64.7858i			0.171846i
$378$	173.765	−	169.019i	0.459696	−	0.447141i
$379$	−166.334			−0.438875			−0.219438	−	0.975627i	$-0.570422\pi$
$379$	−166.334			−0.438875			−0.219438	+	0.975627i	$0.570422\pi$
$380$		0			0
$381$	24.7173	+	17.4778i	0.0648749	+	0.0458735i
$382$	−12.6742	+	21.9524i	−0.0331786	+	0.0574671i
$383$	638.249	+	368.493i	1.66645	+	0.962124i	0.969530	+	0.244972i	$0.0787787\pi$
$383$	638.249	+	368.493i	1.66645	+	0.962124i	0.696917	+	0.717152i	$0.254555\pi$
$384$	33.7980	+	3.11416i	0.0880155	+	0.00810978i
$385$		0			0
$386$			134.992i			0.349721i
$387$	−5.58290	+	6.53010i	−0.0144261	+	0.0168736i
$388$	191.757			0.494219
$389$	−146.682	+	84.6867i	−0.377074	+	0.217704i	−0.676544	−	0.736402i	$-0.736523\pi$
$389$	−146.682	+	84.6867i	−0.377074	+	0.217704i	0.299471	+	0.954106i	$0.403190\pi$
$390$		0			0
$391$	−9.00000	+	15.5885i	−0.0230179	+	0.0398682i
$392$	−21.3031	−	12.2993i	−0.0543445	−	0.0313758i
$393$	−6.22652	−	13.5153i	−0.0158436	−	0.0343901i
$394$	−113.394	−	196.404i	−0.287802	−	0.498487i
$395$		0			0
$396$	160.182	−	56.6328i	0.404499	−	0.143012i
$397$	256.272			0.645523			0.322761	−	0.946480i	$-0.395389\pi$
$397$	256.272			0.645523			0.322761	+	0.946480i	$0.395389\pi$
$398$	7.97959	−	4.60702i	0.0200492	−	0.0115754i
$399$	8.20766	−	89.0778i	0.0205706	−	0.223253i
$400$		0			0
$401$	226.364	+	130.691i	0.564498	+	0.325913i	0.754949	−	0.655784i	$-0.227662\pi$
$401$	226.364	+	130.691i	0.564498	+	0.325913i	−0.190451	+	0.981697i	$0.560995\pi$
$402$	−75.8230	+	107.230i	−0.188614	+	0.266741i
$403$	−404.234	−	700.155i	−1.00306	−	1.73736i
$404$			315.862i			0.781838i
$405$		0			0
$406$	−29.5301			−0.0727342
$407$	−141.439	+	81.6600i	−0.347517	+	0.200639i
$408$	13.2122	+	9.34247i	0.0323830	+	0.0228982i
$409$	221.894	−	384.331i	0.542528	−	0.939686i	−0.456230	−	0.889862i	$-0.650801\pi$
$409$	221.894	−	384.331i	0.542528	−	0.939686i	0.998758	−	0.0498240i	$-0.0158660\pi$
$410$		0			0
$411$	701.082	+	64.5980i	1.70580	+	0.157173i
$412$	−29.1362	−	50.4654i	−0.0707190	−	0.122489i
$413$			581.059i			1.40692i
$414$	−40.0454	−	113.266i	−0.0967280	−	0.273588i
$415$		0			0
$416$	−96.4949	+	55.7114i	−0.231959	+	0.133922i
$417$	290.267	−	133.727i	0.696085	−	0.320688i
$418$	31.3485	−	54.2971i	0.0749963	−	0.129897i
$419$	9.32525	+	5.38394i	0.0222560	+	0.0128495i	0.511087	−	0.859529i	$-0.329243\pi$
$419$	9.32525	+	5.38394i	0.0222560	+	0.0128495i	−0.488831	+	0.872379i	$0.662576\pi$
$420$		0			0
$421$	−127.152	−	220.233i	−0.302023	−	0.523119i	0.674571	−	0.738210i	$-0.264328\pi$
$421$	−127.152	−	220.233i	−0.302023	−	0.523119i	−0.976594	+	0.215091i	$0.930995\pi$
$422$		−	218.410i		−	0.517560i
$423$	96.5227	+	82.5221i	0.228186	+	0.195088i
$424$	−26.9694			−0.0636070
$425$		0			0
$426$	−33.4393	+	362.917i	−0.0784960	+	0.851917i
$427$	−238.356	+	412.844i	−0.558210	+	0.966849i
$428$	297.576	+	171.805i	0.695270	+	0.401414i
$429$	−322.015	+	455.398i	−0.750617	+	1.06153i
$430$		0			0
$431$			698.663i			1.62103i	0.585719	+	0.810514i	$0.300812\pi$
$431$			698.663i			1.62103i	−0.585719	+	0.810514i	$0.699188\pi$
$432$	−104.697	+	26.5057i	−0.242354	+	0.0613557i
$433$	−211.728			−0.488978			−0.244489	−	0.969652i	$-0.578620\pi$
$433$	−211.728			−0.488978			−0.244489	+	0.969652i	$0.578620\pi$
$434$	319.139	−	184.255i	0.735342	−	0.424550i
$435$		0			0
$436$	116.272	−	201.390i	0.266680	−	0.461903i
$437$	−38.3939	−	22.1667i	−0.0878578	−	0.0507247i
$438$	−405.959	−	37.4052i	−0.926847	−	0.0854001i
$439$	−139.931	−	242.368i	−0.318750	−	0.552092i	0.661477	−	0.749965i	$-0.269930\pi$
$439$	−139.931	−	242.368i	−0.318750	−	0.552092i	−0.980228	+	0.197874i	$0.936596\pi$
$440$		0			0
$441$	76.9546	+	14.3027i	0.174500	+	0.0324324i
$442$	−53.1214			−0.120184
$443$	477.400	−	275.627i	1.07765	−	0.622183i	0.147391	−	0.989078i	$-0.452913\pi$
$443$	477.400	−	275.627i	1.07765	−	0.622183i	0.930262	+	0.366895i	$0.119579\pi$
$444$	94.2929	−	43.4409i	0.212371	−	0.0978398i
$445$		0			0
$446$	113.623	+	65.6004i	0.254761	+	0.147086i
$447$	131.947	+	286.405i	0.295184	+	0.640727i
$448$	−25.3939	−	43.9835i	−0.0566828	−	0.0981774i
$449$			542.865i			1.20905i	0.796585	+	0.604527i	$0.206638\pi$
$449$			542.865i			1.20905i	−0.796585	+	0.604527i	$0.793362\pi$
$450$		0			0
$451$	−583.590			−1.29399
$452$	−350.333	+	202.265i	−0.775072	+	0.447488i
$453$	78.5102	−	852.072i	0.173312	−	1.88095i
$454$	−120.068	+	207.964i	−0.264467	+	0.458071i
$455$		0			0
$456$	−23.0102	+	32.5413i	−0.0504610	+	0.0713626i
$457$	46.1821	+	79.9898i	0.101055	+	0.175032i	0.912120	−	0.409924i	$-0.134445\pi$
$457$	46.1821	+	79.9898i	0.101055	+	0.175032i	−0.811065	+	0.584957i	$0.801112\pi$
$458$			576.356i			1.25842i
$459$	−49.5459	−	14.0137i	−0.107943	−	0.0305309i
$460$		0			0
$461$	−199.030	+	114.910i	−0.431736	+	0.249263i	−0.700086	−	0.714059i	$-0.746855\pi$
$461$	−199.030	+	114.910i	−0.431736	+	0.249263i	0.268350	+	0.963321i	$0.413522\pi$
$462$	−207.576	−	146.778i	−0.449298	−	0.317701i
$463$	−255.401	+	442.368i	−0.551623	+	0.955438i	0.446535	+	0.894766i	$0.352658\pi$
$463$	−255.401	+	442.368i	−0.551623	+	0.955438i	−0.998158	+	0.0606723i	$0.980676\pi$
$464$	11.3939	+	6.57826i	0.0245558	+	0.0141773i
$465$		0			0
$466$	−10.7878	−	18.6849i	−0.0231497	−	0.0400964i
$467$			833.657i			1.78513i	0.450915	+	0.892567i	$0.351098\pi$
$467$			833.657i			1.78513i	−0.450915	+	0.892567i	$0.648902\pi$
$468$	230.394	−	269.482i	0.492295	−	0.575817i
$469$	196.514			0.419007
$470$		0			0
$471$	537.270	−	247.521i	1.14070	−	0.525523i
$472$	129.439	−	224.195i	0.274236	−	0.474990i
$473$	7.80306	+	4.50510i	0.0164970	+	0.00952452i
$474$	52.8003	+	114.608i	0.111393	+	0.241790i
$475$		0			0
$476$		−	24.2134i		−	0.0508684i
$477$	80.9082	−	28.6054i	0.169619	−	0.0599693i
$478$	79.9546			0.167269
$479$	569.144	−	328.595i	1.18819	−	0.686003i	0.230296	−	0.973121i	$-0.426031\pi$
$479$	569.144	−	328.595i	1.18819	−	0.686003i	0.957895	+	0.287118i	$0.0926972\pi$
$480$		0			0
$481$	−170.409	+	295.156i	−0.354280	+	0.613631i
$482$	−103.139	−	59.5471i	−0.213980	−	0.123542i
$483$	−103.788	+	146.778i	−0.214881	+	0.303888i
$484$	31.9092	+	55.2683i	0.0659281	+	0.114191i
$485$		0			0
$486$	285.977	−	190.565i	0.588431	−	0.392109i
$487$	351.666			0.722107			0.361054	−	0.932545i	$-0.382417\pi$
$487$	351.666			0.722107			0.361054	+	0.932545i	$0.382417\pi$
$488$	183.934	−	106.194i	0.376914	−	0.217612i
$489$	−610.070	−	431.385i	−1.24759	−	0.882178i
$490$		0			0
$491$	212.539	+	122.709i	0.432869	+	0.249917i	0.700568	−	0.713586i	$-0.252930\pi$
$491$	212.539	+	122.709i	0.432869	+	0.249917i	−0.267699	+	0.963503i	$0.586263\pi$
$492$	369.409	+	34.0374i	0.750831	+	0.0691818i
$493$	3.13622	+	5.43210i	0.00636151	+	0.0110185i
$494$		−	130.836i		−	0.264851i
$495$		0			0
$496$	−164.182			−0.331011
$497$	472.287	−	272.675i	0.950276	−	0.548642i
$498$	−338.734	+	156.056i	−0.680190	+	0.313365i
$499$	−315.113	+	545.792i	−0.631489	+	1.09377i	0.355758	+	0.934578i	$0.384223\pi$
$499$	−315.113	+	545.792i	−0.631489	+	1.09377i	−0.987247	+	0.159193i	$0.949111\pi$
$500$		0			0
$501$	−60.8020	−	131.977i	−0.121361	−	0.263427i
$502$	154.788	+	268.100i	0.308342	+	0.534064i
$503$		−	286.891i		−	0.570360i	−0.958474	−	0.285180i	$-0.907947\pi$
$503$		−	286.891i		−	0.570360i	0.958474	−	0.285180i	$-0.0920534\pi$
$504$	122.833	+	105.016i	0.243717	+	0.208365i
$505$		0			0
$506$	−109.114	+	62.9967i	−0.215639	+	0.124499i
$507$	−60.2724	+	654.137i	−0.118881	+	1.29021i
$508$	−10.0908	+	17.4778i	−0.0198638	+	0.0344051i
$509$	755.454	+	436.161i	1.48419	+	0.856898i	0.999838	−	0.0179741i	$-0.00572163\pi$
$509$	755.454	+	436.161i	1.48419	+	0.856898i	0.484353	+	0.874873i	$0.339055\pi$
$510$		0			0
$511$	305.015	+	528.301i	0.596898	+	1.03386i
$512$			22.6274i			0.0441942i
$513$	34.5153	−	122.030i	0.0672813	−	0.237875i
$514$	18.1362			0.0352845
$515$		0			0
$516$	−4.67653	−	3.30680i	−0.00906304	−	0.00640854i
$517$	66.5908	−	115.339i	0.128802	−	0.223092i
$518$	−134.536	−	77.6742i	−0.259721	−	0.149950i
$519$	300.053	+	27.6470i	0.578136	+	0.0532697i
$520$		0			0
$521$			206.132i			0.395646i	0.980238	+	0.197823i	$0.0633872\pi$
$521$			206.132i			0.395646i	−0.980238	+	0.197823i	$0.936613\pi$
$522$	−41.1589	−	7.64974i	−0.0788485	−	0.0146547i
$523$	−884.817			−1.69181			−0.845906	−	0.533333i	$-0.820939\pi$
$523$	−884.817			−1.69181			−0.845906	+	0.533333i	$0.820939\pi$
$524$	8.59133	−	4.96021i	0.0163957	−	0.00946604i
$525$		0			0
$526$	−237.916	+	412.083i	−0.452312	+	0.783427i
$527$	−67.7878	−	39.1373i	−0.128630	−	0.0742643i
$528$	47.3939	+	102.873i	0.0897611	+	0.194836i
$529$	−219.955	−	380.973i	−0.415793	−	0.720175i
$530$		0			0
$531$	−150.523	+	809.877i	−0.283470	+	1.52519i
$532$	59.6367			0.112099
$533$	−1054.68	+	608.920i	−1.97876	+	1.14244i
$534$	16.1066	−	174.805i	0.0301622	−	0.327351i
$535$		0			0
$536$	−75.8230	−	43.7764i	−0.141461	−	0.0816724i
$537$	−493.757	+	698.278i	−0.919473	+	1.30033i
$538$	42.7423	+	74.0319i	0.0794467	+	0.137606i
$539$		−	82.0886i		−	0.152298i
$540$		0			0
$541$	−509.151			−0.941129			−0.470565	−	0.882365i	$-0.655950\pi$
$541$	−509.151			−0.941129			−0.470565	+	0.882365i	$0.655950\pi$
$542$	336.359	−	194.197i	0.620588	−	0.358297i
$543$	−90.9286	−	64.2962i	−0.167456	−	0.118409i
$544$	−5.39388	+	9.34247i	−0.00991521	+	0.0171737i
$545$		0			0
$546$	−528.285	−	48.6764i	−0.967555	−	0.0891509i
$547$	274.022	+	474.620i	0.500955	+	0.867679i	0.999999	+	0.00110267i	$0.000350992\pi$
$547$	274.022	+	474.620i	0.500955	+	0.867679i	−0.499045	+	0.866576i	$0.666316\pi$
$548$			469.368i			0.856511i
$549$	−439.166	+	513.675i	−0.799939	+	0.935656i
$550$		0			0
$551$	−13.3791	+	7.72442i	−0.0242815	+	0.0140189i
$552$	72.7423	−	33.5125i	0.131780	−	0.0607111i
$553$	94.4092	−	163.522i	0.170722	−	0.295699i
$554$	−60.0125	−	34.6482i	−0.108326	−	0.0625419i
$555$		0			0
$556$	106.530	+	184.516i	0.191601	+	0.331862i
$557$			406.542i			0.729879i	0.931031	+	0.364939i	$0.118910\pi$
$557$			406.542i			0.729879i	−0.931031	+	0.364939i	$0.881090\pi$
$558$	492.545	−	174.141i	0.882697	−	0.312080i
$559$	18.8025			0.0336360
$560$		0			0
$561$	−4.95459	+	53.7722i	−0.00883172	+	0.0958507i
$562$	−242.598	+	420.192i	−0.431669	+	0.747673i
$563$	525.220	+	303.236i	0.932895	+	0.538607i	0.887726	−	0.460372i	$-0.152284\pi$
$563$	525.220	+	303.236i	0.932895	+	0.538607i	0.0451687	+	0.998979i	$0.485617\pi$
$564$	−48.8786	+	69.1247i	−0.0866641	+	0.122562i
$565$		0			0
$566$			485.653i			0.858045i
$567$	−479.886	−	184.764i	−0.846360	−	0.325863i
$568$	−242.969			−0.427763
$569$	−224.954	+	129.877i	−0.395350	+	0.228255i	−0.684476	−	0.729036i	$-0.739969\pi$
$569$	−224.954	+	129.877i	−0.395350	+	0.228255i	0.289126	+	0.957291i	$0.406635\pi$
$570$		0			0
$571$	43.9166	−	76.0657i	0.0769117	−	0.133215i	−0.825004	−	0.565126i	$-0.808827\pi$
$571$	43.9166	−	76.0657i	0.0769117	−	0.133215i	0.901916	+	0.431911i	$0.142161\pi$
$572$	−322.015	−	185.915i	−0.562963	−	0.325027i
$573$	53.5454	+	4.93369i	0.0934475	+	0.00861029i
$574$	−277.553	−	480.736i	−0.483541	−	0.837518i
$575$		0			0
$576$	−24.0000	−	67.8823i	−0.0416667	−	0.117851i
$577$	132.091			0.228927			0.114463	−	0.993427i	$-0.463485\pi$
$577$	132.091			0.228927			0.114463	+	0.993427i	$0.463485\pi$
$578$	349.497	−	201.782i	0.604666	−	0.349104i
$579$	260.088	−	119.823i	0.449202	−	0.206948i
$580$		0			0
$581$	483.302	+	279.034i	0.831844	+	0.480266i
$582$	−170.209	−	369.456i	−0.292455	−	0.634804i
$583$	−45.0000	−	77.9423i	−0.0771870	−	0.133692i
$584$		−	271.786i		−	0.465387i
$585$		0			0
$586$	405.106			0.691306
$587$	491.614	−	283.833i	0.837502	−	0.483532i	−0.0189125	−	0.999821i	$-0.506020\pi$
$587$	491.614	−	283.833i	0.837502	−	0.483532i	0.856414	+	0.516289i	$0.172687\pi$
$588$	−4.78775	+	51.9615i	−0.00814244	+	0.0883699i
$589$	96.3939	−	166.959i	0.163657	−	0.283462i
$590$		0			0
$591$	−277.757	+	392.808i	−0.469978	+	0.664650i
$592$	34.6061	+	59.9396i	0.0584563	+	0.101249i
$593$			77.0321i			0.129902i	0.997888	+	0.0649512i	$0.0206892\pi$
$593$			77.0321i			0.129902i	−0.997888	+	0.0649512i	$0.979311\pi$
$594$	−251.295	−	258.351i	−0.423056	−	0.434934i
$595$		0			0
$596$	−182.060	+	105.113i	−0.305470	+	0.176363i
$597$	−15.9592	−	11.2848i	−0.0267323	−	0.0189026i
$598$	−131.462	+	227.699i	−0.219836	+	0.380767i
$599$	−764.917	−	441.625i	−1.27699	−	0.737270i	−0.300696	−	0.953720i	$-0.597219\pi$
$599$	−764.917	−	441.625i	−1.27699	−	0.737270i	−0.976294	+	0.216450i	$0.930552\pi$
$600$		0			0
$601$	397.545	+	688.569i	0.661473	+	1.14571i	0.980229	+	0.197868i	$0.0634018\pi$
$601$	397.545	+	688.569i	0.661473	+	1.14571i	−0.318755	+	0.947837i	$0.603265\pi$
$602$			8.57042i			0.0142366i
$603$	273.901	+	50.9068i	0.454230	+	0.0844226i
$604$	570.454			0.944460
$605$		0			0
$606$	608.568	−	280.368i	1.00424	−	0.462654i
$607$	−148.372	+	256.987i	−0.244434	+	0.423373i	−0.961972	−	0.273147i	$-0.911936\pi$
$607$	−148.372	+	256.987i	−0.244434	+	0.423373i	0.717538	+	0.696519i	$0.245269\pi$
$608$	−23.0102	−	13.2849i	−0.0378457	−	0.0218502i
$609$	26.2117	+	56.8952i	0.0430406	+	0.0934240i
$610$		0			0
$611$		−	277.924i		−	0.454868i
$612$	6.27245	−	33.7485i	0.0102491	−	0.0551446i
$613$	517.181			0.843688			0.421844	−	0.906668i	$-0.361383\pi$
$613$	517.181			0.843688			0.421844	+	0.906668i	$0.361383\pi$
$614$	−188.722	+	108.959i	−0.307365	+	0.177457i
$615$		0			0
$616$	84.7423	−	146.778i	0.137569	−	0.238276i
$617$	229.909	+	132.738i	0.372623	+	0.215134i	0.674604	−	0.738180i	$-0.264314\pi$
$617$	229.909	+	132.738i	0.372623	+	0.215134i	−0.301981	+	0.953314i	$0.597648\pi$
$618$	−71.3689	+	100.931i	−0.115484	+	0.163319i
$619$	98.5227	+	170.646i	0.159164	+	0.275681i	0.934568	−	0.355786i	$-0.115787\pi$
$619$	98.5227	+	170.646i	0.159164	+	0.275681i	−0.775403	+	0.631466i	$0.782453\pi$
$620$		0			0
$621$	−182.682	+	177.693i	−0.294173	+	0.286139i
$622$	−101.803			−0.163670
$623$	−227.486	+	131.339i	−0.365146	+	0.210817i
$624$	192.990	+	136.464i	0.309279	+	0.218693i
$625$		0			0
$626$	−450.224	−	259.937i	−0.719207	−	0.415234i
$627$	−132.439	−	12.2030i	−0.211227	−	0.0194625i
$628$	197.182	+	341.529i	0.313983	+	0.543835i
$629$			32.9973i			0.0524600i
$630$		0			0
$631$	−160.879			−0.254958			−0.127479	−	0.991841i	$-0.540689\pi$
$631$	−160.879			−0.254958			−0.127479	+	0.991841i	$0.540689\pi$
$632$	−72.8536	+	42.0620i	−0.115275	+	0.0665538i
$633$	−420.808	+	193.867i	−0.664783	+	0.306267i
$634$	76.0829	−	131.779i	0.120005	−	0.207854i
$635$		0			0
$636$	23.9388	+	51.9615i	0.0376396	+	0.0817005i
$637$	−85.6515	−	148.353i	−0.134461	−	0.232893i
$638$			43.9048i			0.0688164i
$639$	728.908	−	257.708i	1.14070	−	0.403299i
$640$		0			0
$641$	−267.894	+	154.669i	−0.417931	+	0.241293i	−0.694192	−	0.719790i	$-0.744238\pi$
$641$	−267.894	+	154.669i	−0.417931	+	0.241293i	0.276261	+	0.961083i	$0.410905\pi$
$642$	66.8786	−	725.834i	0.104172	−	1.13058i
$643$	197.296	−	341.726i	0.306836	−	0.531456i	−0.670832	−	0.741609i	$-0.734063\pi$
$643$	197.296	−	341.726i	0.306836	−	0.531456i	0.977668	+	0.210153i	$0.0673963\pi$
$644$	−103.788	−	59.9219i	−0.161161	−	0.0930464i
$645$		0			0
$646$	−6.33368	−	10.9703i	−0.00980445	−	0.0169818i
$647$		−	418.736i		−	0.647196i	−0.946195	−	0.323598i	$-0.895108\pi$
$647$		−	418.736i		−	0.647196i	0.946195	−	0.323598i	$-0.104892\pi$
$648$	144.000	+	178.191i	0.222222	+	0.274986i
$649$	863.908			1.33114
$650$		0			0
$651$	−638.277	−	451.330i	−0.980456	−	0.693287i
$652$	249.060	−	431.385i	0.381994	−	0.661633i
$653$	459.621	+	265.363i	0.703861	+	0.406375i	0.808784	−	0.588106i	$-0.200126\pi$
$653$	459.621	+	265.363i	0.703861	+	0.406375i	−0.104923	+	0.994480i	$0.533460\pi$
$654$	−491.221	−	45.2613i	−0.751103	−	0.0692069i
$655$		0			0
$656$			247.316i			0.377006i
$657$	288.272	+	815.358i	0.438771	+	1.24103i
$658$	126.681			0.192524
$659$	310.204	−	179.096i	0.470719	−	0.271770i	−0.245822	−	0.969315i	$-0.579058\pi$
$659$	310.204	−	179.096i	0.470719	−	0.271770i	0.716541	+	0.697545i	$0.245724\pi$
$660$		0			0
$661$	111.136	−	192.493i	0.168133	−	0.291214i	−0.769631	−	0.638489i	$-0.779560\pi$
$661$	111.136	−	192.493i	0.168133	−	0.291214i	0.937763	+	0.347275i	$0.112893\pi$
$662$	−21.0625	−	12.1604i	−0.0318165	−	0.0183692i
$663$	47.1520	+	102.348i	0.0711192	+	0.154371i
$664$	−124.318	−	215.325i	−0.187226	−	0.324284i
$665$		0			0
$666$	−167.394	−	143.113i	−0.251342	−	0.214885i
$667$	31.0454			0.0465448
$668$	83.8944	−	48.4365i	0.125590	−	0.0725097i
$669$	25.5362	−	277.145i	0.0381708	−	0.414267i
$670$		0			0
$671$	613.810	+	354.383i	0.914769	+	0.528142i
$672$	−62.2020	+	87.9670i	−0.0925626	+	0.130903i
$673$	−144.606	−	250.464i	−0.214867	−	0.372161i	0.738364	−	0.674402i	$-0.235599\pi$
$673$	−144.606	−	250.464i	−0.214867	−	0.372161i	−0.953231	+	0.302241i	$0.902265\pi$
$674$		−	515.331i		−	0.764586i
$675$		0			0
$676$	−437.939			−0.647838
$677$	−402.227	+	232.226i	−0.594131	+	0.343022i	−0.766729	−	0.641971i	$-0.778117\pi$
$677$	−402.227	+	232.226i	−0.594131	+	0.343022i	0.172598	+	0.984992i	$0.444784\pi$
$678$	700.665	+	495.445i	1.03343	+	0.730745i
$679$	−304.341	+	527.134i	−0.448220	+	0.776339i
$680$		0			0
$681$	507.257	+	46.7389i	0.744871	+	0.0686327i
$682$	−273.947	−	474.490i	−0.401681	−	0.695733i
$683$		−	1126.36i		−	1.64913i	−0.565767	−	0.824565i	$-0.691420\pi$
$683$		−	1126.36i		−	1.64913i	0.565767	−	0.824565i	$-0.308580\pi$
$684$	83.1214	+	15.4488i	0.121523	+	0.0225860i
$685$		0			0
$686$	448.608	−	259.004i	0.653948	−	0.377557i
$687$	1110.46	−	511.589i	1.61638	−	0.744671i
$688$	1.90918	−	3.30680i	0.00277498	−	0.00480640i
$689$	−162.650	−	93.9063i	−0.236067	−	0.136294i
$690$		0			0
$691$	−518.841	−	898.658i	−0.750855	−	1.30052i	−0.947409	−	0.320025i	$-0.896309\pi$
$691$	−518.841	−	898.658i	−0.750855	−	1.30052i	0.196554	−	0.980493i	$-0.437025\pi$
$692$			200.883i			0.290293i
$693$	−98.5454	+	530.217i	−0.142201	+	0.765104i
$694$	−825.044			−1.18882
$695$		0			0
$696$	2.56072	−	27.7915i	0.00367919	−	0.0399303i
$697$	−58.9546	+	102.112i	−0.0845833	+	0.146503i
$698$	−383.048	−	221.153i	−0.548779	−	0.316838i
$699$	−26.4245	+	37.3699i	−0.0378033	+	0.0534619i
$700$		0			0
$701$		−	778.180i		−	1.11010i	−0.831817	−	0.555050i	$-0.812699\pi$
$701$		−	778.180i		−	1.11010i	0.831817	−	0.555050i	$-0.187301\pi$
$702$	−723.712	−	204.697i	−1.03093	−	0.291591i
$703$	−81.2714			−0.115607
$704$	−65.3939	+	37.7552i	−0.0928890	+	0.0536295i
$705$		0			0
$706$	26.5982	−	46.0695i	0.0376745	−	0.0652542i
$707$	−868.296	−	501.311i	−1.22814	−	0.709068i
$708$	−546.848	−	50.3868i	−0.772384	−	0.0711678i
$709$	586.014	+	1015.01i	0.826536	+	1.43160i	0.900739	+	0.434360i	$0.143025\pi$
$709$	586.014	+	1015.01i	0.826536	+	1.43160i	−0.0742031	+	0.997243i	$0.523641\pi$
$710$		0			0
$711$	173.947	−	203.459i	0.244651	−	0.286159i
$712$	117.031			0.164369
$713$	−335.515	+	193.710i	−0.470568	+	0.271682i
$714$	−46.6515	+	21.4924i	−0.0653383	+	0.0301015i
$715$		0			0
$716$	−493.757	−	285.071i	−0.689605	−	0.398144i
$717$	−70.9699	−	154.047i	−0.0989817	−	0.214850i
$718$	−207.909	−	360.109i	−0.289567	−	0.501545i
$719$			515.416i			0.716851i	0.933558	+	0.358426i	$0.116686\pi$
$719$			515.416i			0.716851i	−0.933558	+	0.358426i	$0.883314\pi$
$720$		0			0
$721$	184.970			0.256547
$722$	−415.114	+	239.666i	−0.574949	+	0.331947i
$723$	−23.1799	+	251.571i	−0.0320607	+	0.347954i
$724$	37.1214	−	64.2962i	0.0512727	−	0.0888069i
$725$		0			0
$726$	78.1612	−	110.537i	0.107660	−	0.152254i
$727$	−420.704	−	728.681i	−0.578685	−	1.00231i	−0.995630	−	0.0933809i	$-0.970233\pi$
$727$	−420.704	−	728.681i	−0.578685	−	1.00231i	0.416945	−	0.908932i	$-0.363101\pi$
$728$		−	353.682i		−	0.485827i
$729$	−621.000	−	381.838i	−0.851852	−	0.523783i
$730$		0			0
$731$	1.57654	−	0.910215i	0.00215669	−	0.00124516i
$732$	−367.868	−	260.122i	−0.502552	−	0.355358i
$733$	303.181	−	525.125i	0.413617	−	0.716405i	−0.581665	−	0.813428i	$-0.697599\pi$
$733$	303.181	−	525.125i	0.413617	−	0.716405i	0.995282	+	0.0970229i	$0.0309320\pi$
$734$	−40.6946	−	23.4951i	−0.0554423	−	0.0320096i
$735$		0			0
$736$	26.6969	+	46.2405i	0.0362730	+	0.0628267i
$737$		−	292.174i		−	0.396437i
$738$	−262.318	−	741.947i	−0.355444	−	1.00535i
$739$	−389.362			−0.526877			−0.263439	−	0.964676i	$-0.584857\pi$
$739$	−389.362			−0.526877			−0.263439	+	0.964676i	$0.584857\pi$
$740$		0			0
$741$	−252.081	+	116.134i	−0.340190	+	0.156726i
$742$	42.8036	−	74.1380i	0.0576868	−	0.0999164i
$743$	−904.779	−	522.375i	−1.21774	−	0.703061i	−0.253304	−	0.967387i	$-0.581517\pi$
$743$	−904.779	−	522.375i	−1.21774	−	0.703061i	−0.964434	+	0.264325i	$0.914851\pi$
$744$	145.732	+	316.326i	0.195877	+	0.425170i
$745$		0			0
$746$			318.240i			0.426595i
$747$	601.340	+	514.116i	0.805007	+	0.688240i
$748$	−36.0000			−0.0481283
$749$	−944.574	+	545.350i	−1.26111	+	0.728105i
$750$		0			0
$751$	645.916	−	1118.76i	0.860074	−	1.48969i	−0.0117826	−	0.999931i	$-0.503751\pi$
$751$	645.916	−	1118.76i	0.860074	−	1.48969i	0.871857	−	0.489761i	$-0.162916\pi$
$752$	−48.8786	−	28.2201i	−0.0649981	−	0.0375267i
$753$	379.151	−	536.201i	0.503521	−	0.712086i
$754$	45.8105	+	79.3460i	0.0607566	+	0.105233i
$755$		0			0
$756$	93.3031	−	329.876i	0.123417	−	0.436344i
$757$	−1042.36			−1.37697			−0.688483	−	0.725252i	$-0.741723\pi$
$757$	−1042.36			−1.37697			−0.688483	+	0.725252i	$0.741723\pi$
$758$	−203.716	+	117.616i	−0.268755	+	0.155166i
$759$	218.227	+	154.310i	0.287519	+	0.203307i
$760$		0			0
$761$	−281.607	−	162.586i	−0.370048	−	0.213647i	0.303431	−	0.952853i	$-0.401868\pi$
$761$	−281.607	−	162.586i	−0.370048	−	0.213647i	−0.673479	+	0.739206i	$0.735201\pi$
$762$	42.6311	+	3.92805i	0.0559464	+	0.00515492i
$763$	369.076	+	639.258i	0.483717	+	0.837822i
$764$			35.8481i			0.0469217i
$765$		0			0
$766$	1042.26			1.36065
$767$	1561.28	−	901.405i	2.03557	−	1.17523i
$768$	43.5959	−	20.0847i	0.0567655	−	0.0261520i
$769$	−171.348	+	296.783i	−0.222819	+	0.385934i	−0.955663	−	0.294463i	$-0.904859\pi$
$769$	−171.348	+	296.783i	−0.222819	+	0.385934i	0.732844	+	0.680397i	$0.238193\pi$
$770$		0			0
$771$	−16.0982	−	34.9428i	−0.0208797	−	0.0453214i
$772$	95.4541	+	165.331i	0.123645	+	0.214160i
$773$		−	532.579i		−	0.688977i	−0.938791	−	0.344488i	$-0.888052\pi$
$773$		−	532.579i		−	0.688977i	0.938791	−	0.344488i	$-0.111948\pi$
$774$	−2.22016	+	11.9454i	−0.00286842	+	0.0154333i
$775$		0			0
$776$	234.854	−	135.593i	0.302646	−	0.174733i
$777$	−30.2362	+	328.154i	−0.0389140	+	0.422334i
$778$	−119.765	+	207.439i	−0.153940	+	0.266631i
$779$	−251.499	−	145.203i	−0.322849	−	0.186397i
$780$		0			0
$781$	−405.409	−	702.188i	−0.519089	−	0.899089i
$782$			25.4558i			0.0325522i
$783$	21.7951	+	86.0904i	0.0278354	+	0.109949i
$784$	−34.7878			−0.0443721
$785$		0			0
$786$	−17.1827	−	12.1500i	−0.0218609	−	0.0154580i
$787$	−51.9768	+	90.0264i	−0.0660442	+	0.114392i	−0.897157	−	0.441712i	$-0.854371\pi$
$787$	−51.9768	+	90.0264i	−0.0660442	+	0.114392i	0.831113	+	0.556104i	$0.187704\pi$
$788$	−277.757	−	160.363i	−0.352484	−	0.203507i
$789$	1005.13	+	92.6135i	1.27393	+	0.117381i
$790$		0			0
$791$		−	1284.07i		−	1.62335i
$792$	156.136	−	182.626i	0.197142	−	0.230589i
$793$	1479.06			1.86514
$794$	313.868	−	181.212i	0.395300	−	0.228227i
$795$		0			0
$796$	6.51531	−	11.2848i	0.00818506	−	0.0141769i
$797$	956.331	+	552.138i	1.19991	+	0.692770i	0.960536	−	0.278156i	$-0.0897233\pi$
$797$	956.331	+	552.138i	1.19991	+	0.692770i	0.239378	+	0.970927i	$0.423057\pi$
$798$	−52.9352	−	114.901i	−0.0663349	−	0.143987i
$799$	−13.4541	−	23.3031i	−0.0168386	−	0.0291654i
$800$		0			0
$801$	−351.092	+	124.130i	−0.438317	+	0.154968i
$802$	369.650			0.460911
$803$	785.469	−	453.491i	0.978168	−	0.564746i
$804$	−17.0408	+	184.944i	−0.0211951	+	0.230030i
$805$		0			0
$806$	−990.168	−	571.674i	−1.22850	−	0.709273i
$807$	104.697	−	148.064i	0.129736	−	0.183474i
$808$	223.348	+	386.851i	0.276421	+	0.478776i
$809$			256.465i			0.317015i	0.987358	+	0.158508i	$0.0506683\pi$
$809$			256.465i			0.317015i	−0.987358	+	0.158508i	$0.949332\pi$
$810$		0			0
$811$	735.362			0.906735			0.453368	−	0.891324i	$-0.350222\pi$
$811$	735.362			0.906735			0.453368	+	0.891324i	$0.350222\pi$
$812$	−36.1668	+	20.8809i	−0.0445404	+	0.0257154i
$813$	−672.717	−	475.683i	−0.827451	−	0.585096i
$814$	−115.485	+	200.025i	−0.141873	+	0.245731i
$815$		0			0
$816$	22.7878	+	2.09967i	0.0279262	+	0.00257313i
$817$	2.24183	+	3.88296i	0.00274398	+	0.00475271i
$818$		−	627.611i		−	0.767250i
$819$	375.136	+	1061.05i	0.458042	+	1.29554i
$820$		0			0
$821$	1078.45	−	622.645i	1.31358	−	0.758398i	0.330896	−	0.943667i	$-0.392649\pi$
$821$	1078.45	−	622.645i	1.31358	−	0.758398i	0.982688	+	0.185269i	$0.0593157\pi$
$822$	904.325	−	416.624i	1.10015	−	0.506842i
$823$	−771.129	+	1335.63i	−0.936973	+	1.62288i	−0.165896	+	0.986143i	$0.553052\pi$
$823$	−771.129	+	1335.63i	−0.936973	+	1.62288i	−0.771077	+	0.636742i	$0.780282\pi$
$824$	−71.3689	−	41.2048i	−0.0866127	−	0.0500059i
$825$		0			0
$826$	410.871	+	711.649i	0.497422	+	0.861560i
$827$			955.707i			1.15563i	0.816167	+	0.577815i	$0.196095\pi$
$827$			955.707i			1.15563i	−0.816167	+	0.577815i	$0.803905\pi$
$828$	−129.136	−	110.405i	−0.155962	−	0.133339i
$829$	1082.88			1.30625			0.653123	−	0.757252i	$-0.273458\pi$
$829$	1082.88			1.30625			0.653123	+	0.757252i	$0.273458\pi$
$830$		0			0
$831$	−13.4875	+	146.380i	−0.0162304	+	0.176149i
$832$	−78.7878	+	136.464i	−0.0946968	+	0.164020i
$833$	−14.3633	−	8.29263i	−0.0172428	−	0.00995514i
$834$	260.944	−	369.031i	0.312883	−	0.442483i
$835$		0			0
$836$		−	88.6669i		−	0.106061i
$837$	−772.711	−	794.407i	−0.923191	−	0.949112i
$838$	15.2281			0.0181719
$839$	903.778	−	521.797i	1.07721	−	0.621927i	0.147067	−	0.989127i	$-0.453017\pi$
$839$	903.778	−	521.797i	1.07721	−	0.621927i	0.930142	+	0.367200i	$0.119683\pi$
$840$		0			0
$841$	−415.091	+	718.958i	−0.493568	+	0.854885i
$842$	−311.456	−	179.819i	−0.369901	−	0.213562i
$843$	1024.92	+	94.4361i	1.21580	+	0.112024i
$844$	−154.439	−	267.497i	−0.182985	−	0.316939i
$845$		0			0
$846$	176.568	+	32.8166i	0.208709	+	0.0387903i
$847$	−202.574			−0.239167
$848$	−33.0306	+	19.0702i	−0.0389512	+	0.0224885i
$849$	935.701	−	431.079i	1.10212	−	0.507749i
$850$		0			0
$851$	141.439	+	81.6600i	0.166204	+	0.0959577i
$852$	215.666	+	468.126i	0.253129	+	0.549443i
$853$	236.909	+	410.338i	0.277736	+	0.481053i	0.970822	−	0.239802i	$-0.0770827\pi$
$853$	236.909	+	410.338i	0.277736	+	0.481053i	−0.693086	+	0.720855i	$0.743749\pi$
$854$			674.172i			0.789429i
$855$		0			0
$856$	485.939			0.567685
$857$	−793.939	+	458.381i	−0.926417	+	0.534867i	−0.885677	−	0.464303i	$-0.846305\pi$
$857$	−793.939	+	458.381i	−0.926417	+	0.534867i	−0.0407403	+	0.999170i	$0.512972\pi$
$858$	−72.3712	+	785.445i	−0.0843487	+	0.915437i
$859$	−478.901	+	829.480i	−0.557510	+	0.965635i	0.440194	+	0.897903i	$0.354910\pi$
$859$	−478.901	+	829.480i	−0.557510	+	0.965635i	−0.997704	+	0.0677322i	$0.978424\pi$
$860$		0			0
$861$	−679.863	+	961.471i	−0.789620	+	1.11669i
$862$	494.030	+	855.684i	0.573120	+	0.992673i
$863$		−	524.200i		−	0.607416i	−0.952765	−	0.303708i	$-0.901775\pi$
$863$		−	524.200i		−	0.607416i	0.952765	−	0.303708i	$-0.0982247\pi$
$864$	−109.485	+	106.495i	−0.126718	+	0.123258i
$865$		0			0
$866$	−259.312	+	149.714i	−0.299437	+	0.172880i
$867$	−698.994	−	494.264i	−0.806222	−	0.570085i
$868$	260.576	−	451.330i	0.300202	−	0.519965i
$869$	−243.121	−	140.366i	−0.279771	−	0.161526i
$870$		0			0
$871$	−304.855	−	528.025i	−0.350006	−	0.606228i
$872$		−	328.868i		−	0.377142i
$873$	−560.743	+	655.878i	−0.642317	+	0.751292i
$874$	−62.6969			−0.0717356
$875$		0			0
$876$	−523.646	+	241.245i	−0.597769	+	0.275393i
$877$	503.878	−	872.742i	0.574547	−	0.995145i	−0.421543	−	0.906808i	$-0.638511\pi$
$877$	503.878	−	872.742i	0.574547	−	0.995145i	0.996091	−	0.0883370i	$-0.0281552\pi$
$878$	−342.760	−	197.893i	−0.390388	−	0.225390i
$879$	−359.583	−	780.511i	−0.409082	−	0.887954i
$880$		0			0
$881$		−	1536.71i		−	1.74428i	−0.489254	−	0.872141i	$-0.662731\pi$
$881$		−	1536.71i		−	1.74428i	0.489254	−	0.872141i	$-0.337269\pi$
$882$	104.363	−	36.8980i	0.118326	−	0.0418345i
$883$	294.213			0.333197			0.166599	−	0.986025i	$-0.446722\pi$
$883$	294.213			0.333197			0.166599	+	0.986025i	$0.446722\pi$
$884$	−65.0602	+	37.5625i	−0.0735975	+	0.0424915i
$885$		0			0
$886$	389.796	−	675.146i	0.439950	−	0.762016i
$887$	497.794	+	287.402i	0.561211	+	0.324015i	0.753631	−	0.657297i	$-0.228300\pi$
$887$	497.794	+	287.402i	0.561211	+	0.324015i	−0.192420	+	0.981313i	$0.561634\pi$
$888$	84.7673	−	119.879i	0.0954587	−	0.134999i
$889$	−32.0306	−	55.4787i	−0.0360299	−	0.0624057i
$890$		0			0
$891$	−274.704	+	713.486i	−0.308310	+	0.800770i
$892$	185.546			0.208011
$893$	57.3949	−	33.1370i	0.0642720	−	0.0371075i
$894$	364.120	+	257.472i	0.407294	+	0.288000i
$895$		0			0
$896$	−62.2020	−	35.9124i	−0.0694219	−	0.0400808i
$897$	555.393	+	51.1741i	0.619168	+	0.0570503i
$898$	383.864	+	664.872i	0.427465	+	0.740391i
$899$			135.004i			0.150171i
$900$		0			0
$901$	−18.1837			−0.0201817
$902$	−714.749	+	412.661i	−0.792405	+	0.457495i
$903$	16.5125	−	7.60734i	0.0182863	−	0.00842452i
$904$	−286.045	+	495.445i	−0.316422	+	0.548059i
$905$		0			0
$906$	−506.351	−	1099.09i	−0.558886	−	1.21312i
$907$	−255.037	−	441.737i	−0.281187	−	0.487031i	0.690490	−	0.723342i	$-0.257395\pi$
$907$	−255.037	−	441.737i	−0.281187	−	0.487031i	−0.971677	+	0.236311i	$0.924062\pi$
$908$			339.604i			0.374013i
$909$	−1080.36	−	923.656i	−1.18852	−	1.01612i
$910$		0			0
$911$	−803.127	+	463.685i	−0.881588	+	0.508985i	−0.871182	−	0.490961i	$-0.836646\pi$
$911$	−803.127	+	463.685i	−0.881588	+	0.508985i	−0.0104064	+	0.999946i	$0.503313\pi$
$912$	−5.17143	+	56.1255i	−0.00567042	+	0.0615411i
$913$	414.863	−	718.564i	0.454396	−	0.787036i
$914$	113.123	+	65.3114i	0.123767	+	0.0714567i
$915$		0			0
$916$	407.545	+	705.888i	0.444918	+	0.770621i
$917$			31.4897i			0.0343399i
$918$	−70.5903	+	17.8710i	−0.0768958	+	0.0194674i
$919$	−1240.63			−1.34998			−0.674991	−	0.737826i	$-0.735853\pi$
$919$	−1240.63			−1.34998			−0.674991	+	0.737826i	$0.735853\pi$
$920$		0			0
$921$	377.444	+	266.893i	0.409820	+	0.289786i
$922$	−162.507	+	281.471i	−0.176255	+	0.305283i
$923$	−1465.33	−	846.010i	−1.58757	−	0.916587i
$924$	−358.015	−	32.9876i	−0.387462	−	0.0357009i
$925$		0			0
$926$			722.384i			0.780112i
$927$	257.811	+	47.9164i	0.278113	+	0.0516897i
$928$	18.6061			0.0200497
$929$	293.576	−	169.496i	0.316013	−	0.182450i	−0.333601	−	0.942714i	$-0.608264\pi$
$929$	293.576	−	169.496i	0.316013	−	0.182450i	0.649614	+	0.760264i	$0.274931\pi$
$930$		0			0
$931$	20.4245	−	35.3763i	0.0219382	−	0.0379981i
$932$	−26.4245	−	15.2562i	−0.0283525	−	0.0163693i
$933$	90.3627	+	196.141i	0.0968518	+	0.210227i
$934$	589.485	+	1021.02i	0.631140	+	1.09317i
$935$		0			0
$936$	91.6209	−	492.960i	0.0978856	−	0.526667i
$937$	−1322.21			−1.41111			−0.705556	−	0.708655i	$-0.749302\pi$
$937$	−1322.21			−1.41111			−0.705556	+	0.708655i	$0.749302\pi$
$938$	240.680	−	138.957i	0.256588	−	0.148141i
$939$	−101.185	+	1098.17i	−0.107759	+	1.16951i
$940$		0			0
$941$	−310.984	−	179.547i	−0.330482	−	0.190804i	0.325573	−	0.945517i	$-0.394443\pi$
$941$	−310.984	−	179.547i	−0.330482	−	0.190804i	−0.656055	+	0.754713i	$0.727776\pi$
$942$	482.994	−	683.057i	0.512733	−	0.725114i
$943$	291.795	+	505.404i	0.309433	+	0.535953i
$944$		−	366.110i		−	0.387828i
$945$		0			0
$946$	12.7423			0.0134697
$947$	671.855	−	387.896i	0.709457	−	0.409605i	−0.101403	−	0.994845i	$-0.532333\pi$
$947$	671.855	−	387.896i	0.709457	−	0.409605i	0.810860	+	0.585240i	$0.199000\pi$
$948$	145.707	+	103.031i	0.153700	+	0.108682i
$949$	946.347	−	1639.12i	0.997205	−	1.72721i
$950$		0			0
$951$	−321.431	−	29.6168i	−0.337992	−	0.0311428i
$952$	−17.1214	−	29.6552i	−0.0179847	−	0.0311504i
$953$		−	465.082i		−	0.488019i	−0.969773	−	0.244010i	$-0.921537\pi$
$953$		−	465.082i		−	0.488019i	0.969773	−	0.244010i	$-0.0784628\pi$
$954$	78.8648	−	92.2450i	0.0826675	−	0.0966928i
$955$		0			0
$956$	97.9240	−	56.5364i	0.102431	−	0.0591385i
$957$	84.5908	−	38.9711i	0.0883917	−	0.0407222i
$958$	464.704	−	804.891i	0.485077	−	0.840178i
$959$	−1290.28	−	744.942i	−1.34544	−	0.776791i
$960$		0			0
$961$	−361.863	−	626.765i	−0.376548	−	0.652200i
$962$			481.989i			0.501028i
$963$	−1457.82	+	515.416i	−1.51383	+	0.535219i
$964$	−168.424			−0.174714
$965$		0			0
$966$	−23.3258	+	253.155i	−0.0241468	+	0.262065i
$967$	612.113	−	1060.21i	0.633002	−	1.09639i	−0.353933	−	0.935271i	$-0.615156\pi$
$967$	612.113	−	1060.21i	0.633002	−	1.09639i	0.986935	−	0.161121i	$-0.0515109\pi$
$968$	78.1612	+	45.1264i	0.0807451	+	0.0466182i
$969$	−15.5143	+	21.9405i	−0.0160106	+	0.0226424i
$970$		0			0
$971$			658.702i			0.678375i	0.940719	+	0.339188i	$0.110152\pi$
$971$			658.702i			0.678375i	−0.940719	+	0.339188i	$0.889848\pi$
$972$	215.499	−	435.610i	0.221707	−	0.448158i
$973$	−676.303			−0.695070
$974$	430.702	−	248.666i	0.442199	−	0.255304i
$975$		0			0
$976$	150.182	−	260.122i	0.153875	−	0.266519i
$977$	−1314.92	−	759.170i	−1.34588	−	0.777042i	−0.358214	−	0.933639i	$-0.616614\pi$
$977$	−1314.92	−	759.170i	−1.34588	−	0.777042i	−0.987663	+	0.156597i	$0.949948\pi$
$978$	−1052.22	−	96.9515i	−1.07589	−	0.0991325i
$979$	195.272	+	338.222i	0.199461	+	0.345477i
$980$		0			0
$981$	348.817	+	986.604i	0.355573	+	1.00571i
$982$	347.074			0.353436
$983$	−716.930	+	413.920i	−0.729329	+	0.421078i	−0.818177	−	0.574967i	$-0.805015\pi$
$983$	−716.930	+	413.920i	−0.729329	+	0.421078i	0.0888477	+	0.996045i	$0.471682\pi$
$984$	476.499	−	219.524i	0.484247	−	0.223094i
$985$		0			0
$986$	7.68215	+	4.43529i	0.00779122	+	0.00449826i
$987$	−112.446	−	244.075i	−0.113927	−	0.247289i
$988$	−92.5153	−	160.241i	−0.0936390	−	0.162187i
$989$		−	9.01020i		−	0.00911041i
$990$		0			0
$991$	429.546			0.433447			0.216723	−	0.976233i	$-0.430463\pi$
$991$	429.546			0.433447			0.216723	+	0.976233i	$0.430463\pi$
$992$	−201.081	+	116.094i	−0.202702	+	0.117030i
$993$	−4.73369	+	51.3747i	−0.00476706	+	0.0517369i
$994$	385.621	−	667.915i	0.387949	−	0.671947i
$995$		0			0
$996$	−304.515	+	430.650i	−0.305738	+	0.432379i
$997$	−347.499	−	601.886i	−0.348545	−	0.603697i	0.637447	−	0.770495i	$-0.279991\pi$
$997$	−347.499	−	601.886i	−0.348545	−	0.603697i	−0.985991	+	0.166798i	$0.946657\pi$
$998$			891.274i			0.893060i
$999$	−127.151	+	449.547i	−0.127278	+	0.449997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.3.i.b.401.2		4
3.2	odd	2		1350.3.i.b.1151.1		4
5.2	odd	4		450.3.k.a.149.3		8
5.3	odd	4		450.3.k.a.149.2		8
5.4	even	2		18.3.d.a.5.1	✓	4
9.2	odd	6	inner	450.3.i.b.101.2		4
9.7	even	3		1350.3.i.b.251.1		4
15.2	even	4		1350.3.k.a.449.2		8
15.8	even	4		1350.3.k.a.449.3		8
15.14	odd	2		54.3.d.a.17.2		4
20.19	odd	2		144.3.q.c.113.1		4
40.19	odd	2		576.3.q.e.257.2		4
40.29	even	2		576.3.q.f.257.1		4
45.2	even	12		450.3.k.a.299.2		8
45.4	even	6		162.3.b.a.161.2		4
45.7	odd	12		1350.3.k.a.899.3		8
45.14	odd	6		162.3.b.a.161.3		4
45.29	odd	6		18.3.d.a.11.1	yes	4
45.34	even	6		54.3.d.a.35.2		4
45.38	even	12		450.3.k.a.299.3		8
45.43	odd	12		1350.3.k.a.899.2		8
60.59	even	2		432.3.q.d.17.2		4
120.29	odd	2		1728.3.q.d.449.1		4
120.59	even	2		1728.3.q.c.449.2		4
180.59	even	6		1296.3.e.g.161.1		4
180.79	odd	6		432.3.q.d.305.2		4
180.119	even	6		144.3.q.c.65.1		4
180.139	odd	6		1296.3.e.g.161.3		4
360.29	odd	6		576.3.q.f.65.1		4
360.259	odd	6		1728.3.q.c.1601.2		4
360.299	even	6		576.3.q.e.65.2		4
360.349	even	6		1728.3.q.d.1601.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.3.d.a.5.1	✓	4	5.4	even	2
18.3.d.a.11.1	yes	4	45.29	odd	6
54.3.d.a.17.2		4	15.14	odd	2
54.3.d.a.35.2		4	45.34	even	6
144.3.q.c.65.1		4	180.119	even	6
144.3.q.c.113.1		4	20.19	odd	2
162.3.b.a.161.2		4	45.4	even	6
162.3.b.a.161.3		4	45.14	odd	6
432.3.q.d.17.2		4	60.59	even	2
432.3.q.d.305.2		4	180.79	odd	6
450.3.i.b.101.2		4	9.2	odd	6	inner
450.3.i.b.401.2		4	1.1	even	1	trivial
450.3.k.a.149.2		8	5.3	odd	4
450.3.k.a.149.3		8	5.2	odd	4
450.3.k.a.299.2		8	45.2	even	12
450.3.k.a.299.3		8	45.38	even	12
576.3.q.e.65.2		4	360.299	even	6
576.3.q.e.257.2		4	40.19	odd	2
576.3.q.f.65.1		4	360.29	odd	6
576.3.q.f.257.1		4	40.29	even	2
1296.3.e.g.161.1		4	180.59	even	6
1296.3.e.g.161.3		4	180.139	odd	6
1350.3.i.b.251.1		4	9.7	even	3
1350.3.i.b.1151.1		4	3.2	odd	2
1350.3.k.a.449.2		8	15.2	even	4
1350.3.k.a.449.3		8	15.8	even	4
1350.3.k.a.899.2		8	45.43	odd	12
1350.3.k.a.899.3		8	45.7	odd	12
1728.3.q.c.449.2		4	120.59	even	2
1728.3.q.c.1601.2		4	360.259	odd	6
1728.3.q.d.449.1		4	120.29	odd	2
1728.3.q.d.1601.1		4	360.349	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	450.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(-2.44949 - 1.73205i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-4.22474 - 0.389270i) q^{6} +(3.17423 + 5.49794i) q^{7} -2.82843i q^{8} +(3.00000 + 8.48528i) q^{9} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(-2.44949 - 1.73205i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-4.22474 - 0.389270i) q^{6} +(3.17423 + 5.49794i) q^{7} -2.82843i q^{8} +(3.00000 + 8.48528i) q^{9} +(8.17423 - 4.71940i) q^{11} +(-5.44949 + 2.51059i) q^{12} +(9.84847 - 17.0580i) q^{13} +(7.77526 + 4.48905i) q^{14} +(-2.00000 - 3.46410i) q^{16} -1.90702i q^{17} +(9.67423 + 8.27098i) q^{18} +4.69694 q^{19} +(1.74745 - 18.9651i) q^{21} +(6.67423 - 11.5601i) q^{22} +(-8.17423 - 4.71940i) q^{23} +(-4.89898 + 6.92820i) q^{24} -27.8557i q^{26} +(7.34847 - 25.9808i) q^{27} +12.6969 q^{28} +(-2.84847 + 1.64456i) q^{29} +(20.5227 - 35.5464i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-28.1969 - 2.59808i) q^{33} +(-1.34847 - 2.33562i) q^{34} +(17.6969 + 3.28913i) q^{36} -17.3031 q^{37} +(5.75255 - 3.32124i) q^{38} +(-53.6691 + 24.7255i) q^{39} +(-53.5454 - 30.9145i) q^{41} +(-11.2702 - 24.4630i) q^{42} +(0.477296 + 0.826701i) q^{43} -18.8776i q^{44} -13.3485 q^{46} +(12.2196 - 7.05501i) q^{47} +(-1.10102 + 11.9494i) q^{48} +(4.34847 - 7.53177i) q^{49} +(-3.30306 + 4.67123i) q^{51} +(-19.6969 - 34.1161i) q^{52} -9.53512i q^{53} +(-9.37117 - 37.0160i) q^{54} +(15.5505 - 8.97809i) q^{56} +(-11.5051 - 8.13534i) q^{57} +(-2.32577 + 4.02834i) q^{58} +(79.2650 + 45.7637i) q^{59} +(37.5454 + 65.0306i) q^{61} -58.0470i q^{62} +(-37.1288 + 43.4281i) q^{63} -8.00000 q^{64} +(-36.3712 + 16.7563i) q^{66} +(15.4773 - 26.8075i) q^{67} +(-3.30306 - 1.90702i) q^{68} +(11.8485 + 25.7183i) q^{69} -85.9026i q^{71} +(24.0000 - 8.48528i) q^{72} +96.0908 q^{73} +(-21.1918 + 12.2351i) q^{74} +(4.69694 - 8.13534i) q^{76} +(51.8939 + 29.9609i) q^{77} +(-48.2474 + 68.2322i) q^{78} +(-14.8712 - 25.7576i) q^{79} +(-63.0000 + 50.9117i) q^{81} -87.4393 q^{82} +(76.1288 - 43.9530i) q^{83} +(-31.1010 - 21.9917i) q^{84} +(1.16913 + 0.674999i) q^{86} +(9.82577 + 0.905350i) q^{87} +(-13.3485 - 23.1202i) q^{88} +41.3766i q^{89} +125.045 q^{91} +(-16.3485 + 9.43879i) q^{92} +(-111.838 + 51.5241i) q^{93} +(9.97730 - 17.2812i) q^{94} +(7.10102 + 15.4135i) q^{96} +(47.9393 + 83.0333i) q^{97} -12.2993i q^{98} +(64.5681 + 55.2025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4} - 12 q^{6} - 2 q^{7} + 12 q^{9}+O(q^{10}) \) 4 * q + 4 * q^4 - 12 * q^6 - 2 * q^7 + 12 * q^9	\( 4 q + 4 q^{4} - 12 q^{6} - 2 q^{7} + 12 q^{9} + 18 q^{11} - 12 q^{12} + 10 q^{13} + 36 q^{14} - 8 q^{16} + 24 q^{18} - 40 q^{19} - 42 q^{21} + 12 q^{22} - 18 q^{23} - 8 q^{28} + 18 q^{29} + 38 q^{31} - 54 q^{33} + 24 q^{34} + 12 q^{36} - 128 q^{37} + 72 q^{38} - 102 q^{39} - 126 q^{41} + 48 q^{42} + 46 q^{43} - 24 q^{46} - 54 q^{47} - 24 q^{48} - 12 q^{49} - 72 q^{51} - 20 q^{52} + 36 q^{54} + 72 q^{56} - 144 q^{57} - 24 q^{58} + 126 q^{59} + 62 q^{61} - 222 q^{63} - 32 q^{64} - 72 q^{66} + 106 q^{67} - 72 q^{68} + 18 q^{69} + 96 q^{72} + 208 q^{73} + 72 q^{74} - 40 q^{76} + 90 q^{77} - 144 q^{78} + 14 q^{79} - 252 q^{81} - 144 q^{82} + 378 q^{83} - 144 q^{84} - 108 q^{86} + 54 q^{87} - 24 q^{88} + 412 q^{91} - 36 q^{92} - 222 q^{93} + 84 q^{94} + 48 q^{96} - 14 q^{97} + 126 q^{99}+O(q^{100}) \) 4 * q + 4 * q^4 - 12 * q^6 - 2 * q^7 + 12 * q^9 + 18 * q^11 - 12 * q^12 + 10 * q^13 + 36 * q^14 - 8 * q^16 + 24 * q^18 - 40 * q^19 - 42 * q^21 + 12 * q^22 - 18 * q^23 - 8 * q^28 + 18 * q^29 + 38 * q^31 - 54 * q^33 + 24 * q^34 + 12 * q^36 - 128 * q^37 + 72 * q^38 - 102 * q^39 - 126 * q^41 + 48 * q^42 + 46 * q^43 - 24 * q^46 - 54 * q^47 - 24 * q^48 - 12 * q^49 - 72 * q^51 - 20 * q^52 + 36 * q^54 + 72 * q^56 - 144 * q^57 - 24 * q^58 + 126 * q^59 + 62 * q^61 - 222 * q^63 - 32 * q^64 - 72 * q^66 + 106 * q^67 - 72 * q^68 + 18 * q^69 + 96 * q^72 + 208 * q^73 + 72 * q^74 - 40 * q^76 + 90 * q^77 - 144 * q^78 + 14 * q^79 - 252 * q^81 - 144 * q^82 + 378 * q^83 - 144 * q^84 - 108 * q^86 + 54 * q^87 - 24 * q^88 + 412 * q^91 - 36 * q^92 - 222 * q^93 + 84 * q^94 + 48 * q^96 - 14 * q^97 + 126 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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