LMFDB - Embedded newform 450.3.g.j.343.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [450,3,Mod(307,450)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("450.307"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(450, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	450.g (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,4,0,0,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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 $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			343.2
Root			$1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	450.343
Dual form			450.3.g.j.307.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(8.89898 - 8.89898i) q^{7} +(-2.00000 - 2.00000i) q^{8} -5.79796 q^{11} +(6.79796 + 6.79796i) q^{13} -17.7980i q^{14} -4.00000 q^{16} +(6.10102 - 6.10102i) q^{17} -6.20204i q^{19} +(-5.79796 + 5.79796i) q^{22} +(-18.6969 - 18.6969i) q^{23} +13.5959 q^{26} +(-17.7980 - 17.7980i) q^{28} -6.20204i q^{29} -0.404082 q^{31} +(-4.00000 + 4.00000i) q^{32} -12.2020i q^{34} +(27.0000 - 27.0000i) q^{37} +(-6.20204 - 6.20204i) q^{38} +1.79796 q^{41} +(-36.4949 - 36.4949i) q^{43} +11.5959i q^{44} -37.3939 q^{46} +(38.6969 - 38.6969i) q^{47} -109.384i q^{49} +(13.5959 - 13.5959i) q^{52} +(69.0908 + 69.0908i) q^{53} -35.5959 q^{56} +(-6.20204 - 6.20204i) q^{58} +20.0000i q^{59} -63.1918 q^{61} +(-0.404082 + 0.404082i) q^{62} +8.00000i q^{64} +(-40.0908 + 40.0908i) q^{67} +(-12.2020 - 12.2020i) q^{68} -25.7980 q^{71} +(56.7980 + 56.7980i) q^{73} -54.0000i q^{74} -12.4041 q^{76} +(-51.5959 + 51.5959i) q^{77} +139.373i q^{79} +(1.79796 - 1.79796i) q^{82} +(13.7071 + 13.7071i) q^{83} -72.9898 q^{86} +(11.5959 + 11.5959i) q^{88} +58.6061i q^{89} +120.990 q^{91} +(-37.3939 + 37.3939i) q^{92} -77.3939i q^{94} +(15.9898 - 15.9898i) q^{97} +(-109.384 - 109.384i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 16 q^{7} - 8 q^{8} + 16 q^{11} - 12 q^{13} - 16 q^{16} + 44 q^{17} + 16 q^{22} - 16 q^{23} - 24 q^{26} - 32 q^{28} - 80 q^{31} - 16 q^{32} + 108 q^{37} - 64 q^{38} - 32 q^{41} - 48 q^{43}+ \cdots - 124 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 16 * q^7 - 8 * q^8 + 16 * q^11 - 12 * q^13 - 16 * q^16 + 44 * q^17 + 16 * q^22 - 16 * q^23 - 24 * q^26 - 32 * q^28 - 80 * q^31 - 16 * q^32 + 108 * q^37 - 64 * q^38 - 32 * q^41 - 48 * q^43 - 32 * q^46 + 96 * q^47 - 24 * q^52 + 100 * q^53 - 64 * q^56 - 64 * q^58 - 96 * q^61 - 80 * q^62 + 16 * q^67 - 88 * q^68 - 64 * q^71 + 188 * q^73 - 128 * q^76 - 128 * q^77 - 32 * q^82 + 192 * q^83 - 96 * q^86 - 32 * q^88 + 288 * q^91 - 32 * q^92 - 132 * q^97 - 124 * q^98

Character values

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

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	2.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	8.89898	−	8.89898i	1.27128	−	1.27128i	0.325867	−	0.945416i	$-0.394344\pi$
$7$	8.89898	−	8.89898i	1.27128	−	1.27128i	0.945416	−	0.325867i	$-0.105656\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$	−5.79796			−0.527087			−0.263544	−	0.964647i	$-0.584891\pi$
$11$	−5.79796			−0.527087			−0.263544	+	0.964647i	$0.584891\pi$
$12$		0			0
$13$	6.79796	+	6.79796i	0.522920	+	0.522920i	0.918452	−	0.395532i	$-0.129440\pi$
$13$	6.79796	+	6.79796i	0.522920	+	0.522920i	−0.395532	+	0.918452i	$0.629440\pi$
$14$		−	17.7980i		−	1.27128i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	6.10102	−	6.10102i	0.358884	−	0.358884i	−0.504518	−	0.863401i	$-0.668330\pi$
$17$	6.10102	−	6.10102i	0.358884	−	0.358884i	0.863401	+	0.504518i	$0.168330\pi$
$18$		0			0
$19$		−	6.20204i		−	0.326423i	−0.986591	−	0.163212i	$-0.947815\pi$
$19$		−	6.20204i		−	0.326423i	0.986591	−	0.163212i	$-0.0521853\pi$
$20$		0			0
$21$		0			0
$22$	−5.79796	+	5.79796i	−0.263544	+	0.263544i
$23$	−18.6969	−	18.6969i	−0.812910	−	0.812910i	0.172159	−	0.985069i	$-0.444926\pi$
$23$	−18.6969	−	18.6969i	−0.812910	−	0.812910i	−0.985069	+	0.172159i	$0.944926\pi$
$24$		0			0
$25$		0			0
$26$	13.5959			0.522920
$27$		0			0
$28$	−17.7980	−	17.7980i	−0.635641	−	0.635641i
$29$		−	6.20204i		−	0.213863i	−0.994266	−	0.106932i	$-0.965897\pi$
$29$		−	6.20204i		−	0.213863i	0.994266	−	0.106932i	$-0.0341026\pi$
$30$		0			0
$31$	−0.404082			−0.0130349			−0.00651745	−	0.999979i	$-0.502075\pi$
$31$	−0.404082			−0.0130349			−0.00651745	+	0.999979i	$0.502075\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	12.2020i		−	0.358884i
$35$		0			0
$36$		0			0
$37$	27.0000	−	27.0000i	0.729730	−	0.729730i	−0.240836	−	0.970566i	$-0.577422\pi$
$37$	27.0000	−	27.0000i	0.729730	−	0.729730i	0.970566	+	0.240836i	$0.0774216\pi$
$38$	−6.20204	−	6.20204i	−0.163212	−	0.163212i
$39$		0			0
$40$		0			0
$41$	1.79796			0.0438527			0.0219263	−	0.999760i	$-0.493020\pi$
$41$	1.79796			0.0438527			0.0219263	+	0.999760i	$0.493020\pi$
$42$		0			0
$43$	−36.4949	−	36.4949i	−0.848719	−	0.848719i	0.141255	−	0.989973i	$-0.454886\pi$
$43$	−36.4949	−	36.4949i	−0.848719	−	0.848719i	−0.989973	+	0.141255i	$0.954886\pi$
$44$			11.5959i			0.263544i
$45$		0			0
$46$	−37.3939			−0.812910
$47$	38.6969	−	38.6969i	0.823339	−	0.823339i	−0.163246	−	0.986585i	$-0.552197\pi$
$47$	38.6969	−	38.6969i	0.823339	−	0.823339i	0.986585	+	0.163246i	$0.0521965\pi$
$48$		0			0
$49$		−	109.384i		−	2.23232i
$50$		0			0
$51$		0			0
$52$	13.5959	−	13.5959i	0.261460	−	0.261460i
$53$	69.0908	+	69.0908i	1.30360	+	1.30360i	0.925947	+	0.377653i	$0.123269\pi$
$53$	69.0908	+	69.0908i	1.30360	+	1.30360i	0.377653	+	0.925947i	$0.376731\pi$
$54$		0			0
$55$		0			0
$56$	−35.5959			−0.635641
$57$		0			0
$58$	−6.20204	−	6.20204i	−0.106932	−	0.106932i
$59$			20.0000i			0.338983i	0.985532	+	0.169492i	$0.0542125\pi$
$59$			20.0000i			0.338983i	−0.985532	+	0.169492i	$0.945787\pi$
$60$		0			0
$61$	−63.1918			−1.03593			−0.517966	−	0.855401i	$-0.673311\pi$
$61$	−63.1918			−1.03593			−0.517966	+	0.855401i	$0.673311\pi$
$62$	−0.404082	+	0.404082i	−0.00651745	+	0.00651745i
$63$		0			0
$64$			8.00000i			0.125000i
$65$		0			0
$66$		0			0
$67$	−40.0908	+	40.0908i	−0.598370	+	0.598370i	−0.939879	−	0.341508i	$-0.889062\pi$
$67$	−40.0908	+	40.0908i	−0.598370	+	0.598370i	0.341508	+	0.939879i	$0.389062\pi$
$68$	−12.2020	−	12.2020i	−0.179442	−	0.179442i
$69$		0			0
$70$		0			0
$71$	−25.7980			−0.363352			−0.181676	−	0.983358i	$-0.558152\pi$
$71$	−25.7980			−0.363352			−0.181676	+	0.983358i	$0.558152\pi$
$72$		0			0
$73$	56.7980	+	56.7980i	0.778054	+	0.778054i	0.979500	−	0.201445i	$-0.0645639\pi$
$73$	56.7980	+	56.7980i	0.778054	+	0.778054i	−0.201445	+	0.979500i	$0.564564\pi$
$74$		−	54.0000i		−	0.729730i
$75$		0			0
$76$	−12.4041			−0.163212
$77$	−51.5959	+	51.5959i	−0.670077	+	0.670077i
$78$		0			0
$79$			139.373i			1.76422i	0.471042	+	0.882111i	$0.343878\pi$
$79$			139.373i			1.76422i	−0.471042	+	0.882111i	$0.656122\pi$
$80$		0			0
$81$		0			0
$82$	1.79796	−	1.79796i	0.0219263	−	0.0219263i
$83$	13.7071	+	13.7071i	0.165146	+	0.165146i	0.784842	−	0.619696i	$-0.212744\pi$
$83$	13.7071	+	13.7071i	0.165146	+	0.165146i	−0.619696	+	0.784842i	$0.712744\pi$
$84$		0			0
$85$		0			0
$86$	−72.9898			−0.848719
$87$		0			0
$88$	11.5959	+	11.5959i	0.131772	+	0.131772i
$89$			58.6061i			0.658496i	0.944244	+	0.329248i	$0.106795\pi$
$89$			58.6061i			0.658496i	−0.944244	+	0.329248i	$0.893205\pi$
$90$		0			0
$91$	120.990			1.32956
$92$	−37.3939	+	37.3939i	−0.406455	+	0.406455i
$93$		0			0
$94$		−	77.3939i		−	0.823339i
$95$		0			0
$96$		0			0
$97$	15.9898	−	15.9898i	0.164843	−	0.164843i	−0.619865	−	0.784708i	$-0.712813\pi$
$97$	15.9898	−	15.9898i	0.164843	−	0.164843i	0.784708	+	0.619865i	$0.212813\pi$
$98$	−109.384	−	109.384i	−1.11616	−	1.11616i
$99$		0			0
$100$		0			0
$101$	128.384			1.27113			0.635563	−	0.772049i	$-0.280768\pi$
$101$	128.384			1.27113			0.635563	+	0.772049i	$0.280768\pi$
$102$		0			0
$103$	32.4949	+	32.4949i	0.315484	+	0.315484i	0.847030	−	0.531545i	$-0.178388\pi$
$103$	32.4949	+	32.4949i	0.315484	+	0.315484i	−0.531545	+	0.847030i	$0.678388\pi$
$104$		−	27.1918i		−	0.261460i
$105$		0			0
$106$	138.182			1.30360
$107$	24.8990	−	24.8990i	0.232701	−	0.232701i	−0.581118	−	0.813819i	$-0.697385\pi$
$107$	24.8990	−	24.8990i	0.232701	−	0.232701i	0.813819	+	0.581118i	$0.197385\pi$
$108$		0			0
$109$			130.000i			1.19266i	0.802739	+	0.596330i	$0.203375\pi$
$109$			130.000i			1.19266i	−0.802739	+	0.596330i	$0.796625\pi$
$110$		0			0
$111$		0			0
$112$	−35.5959	+	35.5959i	−0.317821	+	0.317821i
$113$	8.70714	+	8.70714i	0.0770544	+	0.0770544i	0.744584	−	0.667529i	$-0.232648\pi$
$113$	8.70714	+	8.70714i	0.0770544	+	0.0770544i	−0.667529	+	0.744584i	$0.732648\pi$
$114$		0			0
$115$		0			0
$116$	−12.4041			−0.106932
$117$		0			0
$118$	20.0000	+	20.0000i	0.169492	+	0.169492i
$119$		−	108.586i		−	0.912485i
$120$		0			0
$121$	−87.3837			−0.722179
$122$	−63.1918	+	63.1918i	−0.517966	+	0.517966i
$123$		0			0
$124$			0.808164i			0.00651745i
$125$		0			0
$126$		0			0
$127$	50.2929	−	50.2929i	0.396007	−	0.396007i	−0.480815	−	0.876822i	$-0.659659\pi$
$127$	50.2929	−	50.2929i	0.396007	−	0.396007i	0.876822	+	0.480815i	$0.159659\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		0			0
$130$		0			0
$131$	114.202			0.871771			0.435886	−	0.900002i	$-0.356435\pi$
$131$	114.202			0.871771			0.435886	+	0.900002i	$0.356435\pi$
$132$		0			0
$133$	−55.1918	−	55.1918i	−0.414976	−	0.414976i
$134$			80.1816i			0.598370i
$135$		0			0
$136$	−24.4041			−0.179442
$137$	16.1010	−	16.1010i	0.117526	−	0.117526i	−0.645898	−	0.763424i	$-0.723517\pi$
$137$	16.1010	−	16.1010i	0.117526	−	0.117526i	0.763424	+	0.645898i	$0.223517\pi$
$138$		0			0
$139$			73.7980i			0.530921i	0.964122	+	0.265460i	$0.0855239\pi$
$139$			73.7980i			0.530921i	−0.964122	+	0.265460i	$0.914476\pi$
$140$		0			0
$141$		0			0
$142$	−25.7980	+	25.7980i	−0.181676	+	0.181676i
$143$	−39.4143	−	39.4143i	−0.275624	−	0.275624i
$144$		0			0
$145$		0			0
$146$	113.596			0.778054
$147$		0			0
$148$	−54.0000	−	54.0000i	−0.364865	−	0.364865i
$149$			270.767i			1.81723i	0.417634	+	0.908615i	$0.362859\pi$
$149$			270.767i			1.81723i	−0.417634	+	0.908615i	$0.637141\pi$
$150$		0			0
$151$	21.6163			0.143154			0.0715772	−	0.997435i	$-0.477197\pi$
$151$	21.6163			0.143154			0.0715772	+	0.997435i	$0.477197\pi$
$152$	−12.4041	+	12.4041i	−0.0816058	+	0.0816058i
$153$		0			0
$154$			103.192i			0.670077i
$155$		0			0
$156$		0			0
$157$	−123.000	+	123.000i	−0.783439	+	0.783439i	−0.980410	−	0.196970i	$-0.936890\pi$
$157$	−123.000	+	123.000i	−0.783439	+	0.783439i	0.196970	+	0.980410i	$0.436890\pi$
$158$	139.373	+	139.373i	0.882111	+	0.882111i
$159$		0			0
$160$		0			0
$161$	−332.767			−2.06688
$162$		0			0
$163$	112.495	+	112.495i	0.690153	+	0.690153i	0.962265	−	0.272113i	$-0.0877223\pi$
$163$	112.495	+	112.495i	0.690153	+	0.690153i	−0.272113	+	0.962265i	$0.587722\pi$
$164$		−	3.59592i		−	0.0219263i
$165$		0			0
$166$	27.4143			0.165146
$167$	176.677	−	176.677i	1.05794	−	1.05794i	0.0597286	−	0.998215i	$-0.480976\pi$
$167$	176.677	−	176.677i	1.05794	−	1.05794i	0.998215	−	0.0597286i	$-0.0190235\pi$
$168$		0			0
$169$		−	76.5755i		−	0.453110i
$170$		0			0
$171$		0			0
$172$	−72.9898	+	72.9898i	−0.424359	+	0.424359i
$173$	142.889	+	142.889i	0.825947	+	0.825947i	0.986953	−	0.161007i	$-0.0514741\pi$
$173$	142.889	+	142.889i	0.825947	+	0.825947i	−0.161007	+	0.986953i	$0.551474\pi$
$174$		0			0
$175$		0			0
$176$	23.1918			0.131772
$177$		0			0
$178$	58.6061	+	58.6061i	0.329248	+	0.329248i
$179$		−	133.171i		−	0.743974i	−0.928238	−	0.371987i	$-0.878677\pi$
$179$		−	133.171i		−	0.743974i	0.928238	−	0.371987i	$-0.121323\pi$
$180$		0			0
$181$	137.192			0.757966			0.378983	−	0.925404i	$-0.376274\pi$
$181$	137.192			0.757966			0.378983	+	0.925404i	$0.376274\pi$
$182$	120.990	−	120.990i	0.664779	−	0.664779i
$183$		0			0
$184$			74.7878i			0.406455i
$185$		0			0
$186$		0			0
$187$	−35.3735	+	35.3735i	−0.189163	+	0.189163i
$188$	−77.3939	−	77.3939i	−0.411670	−	0.411670i
$189$		0			0
$190$		0			0
$191$	266.606			1.39584			0.697922	−	0.716174i	$-0.254108\pi$
$191$	266.606			1.39584			0.697922	+	0.716174i	$0.254108\pi$
$192$		0			0
$193$	−117.384	−	117.384i	−0.608206	−	0.608206i	0.334271	−	0.942477i	$-0.391510\pi$
$193$	−117.384	−	117.384i	−0.608206	−	0.608206i	−0.942477	+	0.334271i	$0.891510\pi$
$194$		−	31.9796i		−	0.164843i
$195$		0			0
$196$	−218.767			−1.11616
$197$	−246.687	+	246.687i	−1.25222	+	1.25222i	−0.297493	+	0.954724i	$0.596150\pi$
$197$	−246.687	+	246.687i	−1.25222	+	1.25222i	−0.954724	+	0.297493i	$0.903850\pi$
$198$		0			0
$199$		−	154.565i		−	0.776710i	−0.921510	−	0.388355i	$-0.873043\pi$
$199$		−	154.565i		−	0.776710i	0.921510	−	0.388355i	$-0.126957\pi$
$200$		0			0
$201$		0			0
$202$	128.384	−	128.384i	0.635563	−	0.635563i
$203$	−55.1918	−	55.1918i	−0.271881	−	0.271881i
$204$		0			0
$205$		0			0
$206$	64.9898			0.315484
$207$		0			0
$208$	−27.1918	−	27.1918i	−0.130730	−	0.130730i
$209$			35.9592i			0.172053i
$210$		0			0
$211$	190.747			0.904014			0.452007	−	0.892014i	$-0.350708\pi$
$211$	190.747			0.904014			0.452007	+	0.892014i	$0.350708\pi$
$212$	138.182	−	138.182i	0.651800	−	0.651800i
$213$		0			0
$214$		−	49.7980i		−	0.232701i
$215$		0			0
$216$		0			0
$217$	−3.59592	+	3.59592i	−0.0165711	+	0.0165711i
$218$	130.000	+	130.000i	0.596330	+	0.596330i
$219$		0			0
$220$		0			0
$221$	82.9490			0.375335
$222$		0			0
$223$	16.6765	+	16.6765i	0.0747826	+	0.0747826i	0.743509	−	0.668726i	$-0.233160\pi$
$223$	16.6765	+	16.6765i	0.0747826	+	0.0747826i	−0.668726	+	0.743509i	$0.733160\pi$
$224$			71.1918i			0.317821i
$225$		0			0
$226$	17.4143			0.0770544
$227$	−42.0704	+	42.0704i	−0.185332	+	0.185332i	−0.793675	−	0.608342i	$-0.791835\pi$
$227$	−42.0704	+	42.0704i	−0.185332	+	0.185332i	0.608342	+	0.793675i	$0.291835\pi$
$228$		0			0
$229$			173.939i			0.759558i	0.925077	+	0.379779i	$0.124000\pi$
$229$			173.939i			0.759558i	−0.925077	+	0.379779i	$0.876000\pi$
$230$		0			0
$231$		0			0
$232$	−12.4041	+	12.4041i	−0.0534659	+	0.0534659i
$233$	−298.262	−	298.262i	−1.28010	−	1.28010i	−0.940612	−	0.339483i	$-0.889748\pi$
$233$	−298.262	−	298.262i	−1.28010	−	1.28010i	−0.339483	−	0.940612i	$-0.610252\pi$
$234$		0			0
$235$		0			0
$236$	40.0000			0.169492
$237$		0			0
$238$	−108.586	−	108.586i	−0.456242	−	0.456242i
$239$		−	37.2122i		−	0.155700i	−0.996965	−	0.0778499i	$-0.975195\pi$
$239$		−	37.2122i		−	0.155700i	0.996965	−	0.0778499i	$-0.0248055\pi$
$240$		0			0
$241$	165.939			0.688543			0.344271	−	0.938870i	$-0.388126\pi$
$241$	165.939			0.688543			0.344271	+	0.938870i	$0.388126\pi$
$242$	−87.3837	+	87.3837i	−0.361090	+	0.361090i
$243$		0			0
$244$			126.384i			0.517966i
$245$		0			0
$246$		0			0
$247$	42.1612	−	42.1612i	0.170693	−	0.170693i
$248$	0.808164	+	0.808164i	0.00325873	+	0.00325873i
$249$		0			0
$250$		0			0
$251$	−255.414			−1.01759			−0.508793	−	0.860889i	$-0.669908\pi$
$251$	−255.414			−1.01759			−0.508793	+	0.860889i	$0.669908\pi$
$252$		0			0
$253$	108.404	+	108.404i	0.428475	+	0.428475i
$254$		−	100.586i		−	0.396007i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−270.485	+	270.485i	−1.05247	+	1.05247i	−0.0539246	+	0.998545i	$0.517173\pi$
$257$	−270.485	+	270.485i	−1.05247	+	1.05247i	−0.998545	+	0.0539246i	$0.982827\pi$
$258$		0			0
$259$		−	480.545i		−	1.85539i
$260$		0			0
$261$		0			0
$262$	114.202	−	114.202i	0.435886	−	0.435886i
$263$	1.30306	+	1.30306i	0.00495461	+	0.00495461i	0.709580	−	0.704625i	$-0.248885\pi$
$263$	1.30306	+	1.30306i	0.00495461	+	0.00495461i	−0.704625	+	0.709580i	$0.748885\pi$
$264$		0			0
$265$		0			0
$266$	−110.384			−0.414976
$267$		0			0
$268$	80.1816	+	80.1816i	0.299185	+	0.299185i
$269$		−	41.1510i		−	0.152978i	−0.997070	−	0.0764889i	$-0.975629\pi$
$269$		−	41.1510i		−	0.152978i	0.997070	−	0.0764889i	$-0.0243710\pi$
$270$		0			0
$271$	−484.727			−1.78866			−0.894329	−	0.447409i	$-0.852347\pi$
$271$	−484.727			−1.78866			−0.894329	+	0.447409i	$0.852347\pi$
$272$	−24.4041	+	24.4041i	−0.0897209	+	0.0897209i
$273$		0			0
$274$		−	32.2020i		−	0.117526i
$275$		0			0
$276$		0			0
$277$	−51.9898	+	51.9898i	−0.187689	+	0.187689i	−0.794696	−	0.607007i	$-0.792370\pi$
$277$	−51.9898	+	51.9898i	−0.187689	+	0.187689i	0.607007	+	0.794696i	$0.292370\pi$
$278$	73.7980	+	73.7980i	0.265460	+	0.265460i
$279$		0			0
$280$		0			0
$281$	−242.524			−0.863076			−0.431538	−	0.902095i	$-0.642029\pi$
$281$	−242.524			−0.863076			−0.431538	+	0.902095i	$0.642029\pi$
$282$		0			0
$283$	−104.717	−	104.717i	−0.370026	−	0.370026i	0.497461	−	0.867487i	$-0.334266\pi$
$283$	−104.717	−	104.717i	−0.370026	−	0.370026i	−0.867487	+	0.497461i	$0.834266\pi$
$284$			51.5959i			0.181676i
$285$		0			0
$286$	−78.8286			−0.275624
$287$	16.0000	−	16.0000i	0.0557491	−	0.0557491i
$288$		0			0
$289$			214.555i			0.742405i
$290$		0			0
$291$		0			0
$292$	113.596	−	113.596i	0.389027	−	0.389027i
$293$	−60.9092	−	60.9092i	−0.207881	−	0.207881i	0.595485	−	0.803366i	$-0.296960\pi$
$293$	−60.9092	−	60.9092i	−0.207881	−	0.207881i	−0.803366	+	0.595485i	$0.796960\pi$
$294$		0			0
$295$		0			0
$296$	−108.000			−0.364865
$297$		0			0
$298$	270.767	+	270.767i	0.908615	+	0.908615i
$299$		−	254.202i		−	0.850174i
$300$		0			0
$301$	−649.535			−2.15792
$302$	21.6163	−	21.6163i	0.0715772	−	0.0715772i
$303$		0			0
$304$			24.8082i			0.0816058i
$305$		0			0
$306$		0			0
$307$	201.303	−	201.303i	0.655710	−	0.655710i	−0.298652	−	0.954362i	$-0.596537\pi$
$307$	201.303	−	201.303i	0.655710	−	0.655710i	0.954362	+	0.298652i	$0.0965369\pi$
$308$	103.192	+	103.192i	0.335038	+	0.335038i
$309$		0			0
$310$		0			0
$311$	−559.737			−1.79980			−0.899898	−	0.436100i	$-0.856359\pi$
$311$	−559.737			−1.79980			−0.899898	+	0.436100i	$0.856359\pi$
$312$		0			0
$313$	93.7673	+	93.7673i	0.299576	+	0.299576i	0.840848	−	0.541272i	$-0.182057\pi$
$313$	93.7673	+	93.7673i	0.299576	+	0.299576i	−0.541272	+	0.840848i	$0.682057\pi$
$314$			246.000i			0.783439i
$315$		0			0
$316$	278.747			0.882111
$317$	362.828	−	362.828i	1.14457	−	1.14457i	0.156962	−	0.987605i	$-0.449830\pi$
$317$	362.828	−	362.828i	1.14457	−	1.14457i	0.987605	−	0.156962i	$-0.0501699\pi$
$318$		0			0
$319$			35.9592i			0.112725i
$320$		0			0
$321$		0			0
$322$	−332.767	+	332.767i	−1.03344	+	1.03344i
$323$	−37.8388	−	37.8388i	−0.117148	−	0.117148i
$324$		0			0
$325$		0			0
$326$	224.990			0.690153
$327$		0			0
$328$	−3.59592	−	3.59592i	−0.0109632	−	0.0109632i
$329$		−	688.727i		−	2.09339i
$330$		0			0
$331$	14.0204			0.0423577			0.0211789	−	0.999776i	$-0.493258\pi$
$331$	14.0204			0.0423577			0.0211789	+	0.999776i	$0.493258\pi$
$332$	27.4143	−	27.4143i	0.0825732	−	0.0825732i
$333$		0			0
$334$		−	353.353i		−	1.05794i
$335$		0			0
$336$		0			0
$337$	166.373	−	166.373i	0.493690	−	0.493690i	−0.415777	−	0.909467i	$-0.636490\pi$
$337$	166.373	−	166.373i	0.493690	−	0.493690i	0.909467	+	0.415777i	$0.136490\pi$
$338$	−76.5755	−	76.5755i	−0.226555	−	0.226555i
$339$		0			0
$340$		0			0
$341$	2.34285			0.00687053
$342$		0			0
$343$	−537.353	−	537.353i	−1.56663	−	1.56663i
$344$			145.980i			0.424359i
$345$		0			0
$346$	285.778			0.825947
$347$	163.505	−	163.505i	0.471196	−	0.471196i	−0.431105	−	0.902302i	$-0.641876\pi$
$347$	163.505	−	163.505i	0.471196	−	0.471196i	0.902302	+	0.431105i	$0.141876\pi$
$348$		0			0
$349$		−	280.000i		−	0.802292i	−0.916014	−	0.401146i	$-0.868612\pi$
$349$		−	280.000i		−	0.802292i	0.916014	−	0.401146i	$-0.131388\pi$
$350$		0			0
$351$		0			0
$352$	23.1918	−	23.1918i	0.0658859	−	0.0658859i
$353$	261.495	+	261.495i	0.740779	+	0.740779i	0.972728	−	0.231949i	$-0.0745103\pi$
$353$	261.495	+	261.495i	0.740779	+	0.740779i	−0.231949	+	0.972728i	$0.574510\pi$
$354$		0			0
$355$		0			0
$356$	117.212			0.329248
$357$		0			0
$358$	−133.171	−	133.171i	−0.371987	−	0.371987i
$359$			425.090i			1.18409i	0.805903	+	0.592047i	$0.201680\pi$
$359$			425.090i			1.18409i	−0.805903	+	0.592047i	$0.798320\pi$
$360$		0			0
$361$	322.535			0.893448
$362$	137.192	−	137.192i	0.378983	−	0.378983i
$363$		0			0
$364$		−	241.980i		−	0.664779i
$365$		0			0
$366$		0			0
$367$	316.495	−	316.495i	0.862384	−	0.862384i	−0.129231	−	0.991615i	$-0.541251\pi$
$367$	316.495	−	316.495i	0.862384	−	0.862384i	0.991615	+	0.129231i	$0.0412508\pi$
$368$	74.7878	+	74.7878i	0.203228	+	0.203228i
$369$		0			0
$370$		0			0
$371$	1229.68			3.31449
$372$		0			0
$373$	−210.939	−	210.939i	−0.565519	−	0.565519i	0.365351	−	0.930870i	$-0.380949\pi$
$373$	−210.939	−	210.939i	−0.565519	−	0.565519i	−0.930870	+	0.365351i	$0.880949\pi$
$374$			70.7469i			0.189163i
$375$		0			0
$376$	−154.788			−0.411670
$377$	42.1612	−	42.1612i	0.111833	−	0.111833i
$378$		0			0
$379$		−	344.182i		−	0.908131i	−0.890968	−	0.454065i	$-0.849973\pi$
$379$		−	344.182i		−	0.908131i	0.890968	−	0.454065i	$-0.150027\pi$
$380$		0			0
$381$		0			0
$382$	266.606	−	266.606i	0.697922	−	0.697922i
$383$	−409.707	−	409.707i	−1.06973	−	1.06973i	−0.997379	−	0.0723523i	$-0.976949\pi$
$383$	−409.707	−	409.707i	−1.06973	−	1.06973i	−0.0723523	−	0.997379i	$-0.523051\pi$
$384$		0			0
$385$		0			0
$386$	−234.767			−0.608206
$387$		0			0
$388$	−31.9796	−	31.9796i	−0.0824216	−	0.0824216i
$389$		−	301.151i		−	0.774167i	−0.922045	−	0.387084i	$-0.873482\pi$
$389$		−	301.151i		−	0.774167i	0.922045	−	0.387084i	$-0.126518\pi$
$390$		0			0
$391$	−228.141			−0.583480
$392$	−218.767	+	218.767i	−0.558080	+	0.558080i
$393$		0			0
$394$			493.373i			1.25222i
$395$		0			0
$396$		0			0
$397$	−479.343	+	479.343i	−1.20741	+	1.20741i	−0.235551	+	0.971862i	$0.575689\pi$
$397$	−479.343	+	479.343i	−1.20741	+	1.20741i	−0.971862	+	0.235551i	$0.924311\pi$
$398$	−154.565	−	154.565i	−0.388355	−	0.388355i
$399$		0			0
$400$		0			0
$401$	−101.233			−0.252451			−0.126225	−	0.992002i	$-0.540286\pi$
$401$	−101.233			−0.252451			−0.126225	+	0.992002i	$0.540286\pi$
$402$		0			0
$403$	−2.74693	−	2.74693i	−0.00681621	−	0.00681621i
$404$		−	256.767i		−	0.635563i
$405$		0			0
$406$	−110.384			−0.271881
$407$	−156.545	+	156.545i	−0.384631	+	0.384631i
$408$		0			0
$409$		−	257.110i		−	0.628631i	−0.949319	−	0.314316i	$-0.898225\pi$
$409$		−	257.110i		−	0.628631i	0.949319	−	0.314316i	$-0.101775\pi$
$410$		0			0
$411$		0			0
$412$	64.9898	−	64.9898i	0.157742	−	0.157742i
$413$	177.980	+	177.980i	0.430943	+	0.430943i
$414$		0			0
$415$		0			0
$416$	−54.3837			−0.130730
$417$		0			0
$418$	35.9592	+	35.9592i	0.0860267	+	0.0860267i
$419$			375.959i			0.897277i	0.893713	+	0.448639i	$0.148091\pi$
$419$			375.959i			0.897277i	−0.893713	+	0.448639i	$0.851909\pi$
$420$		0			0
$421$	158.829			0.377265			0.188633	−	0.982048i	$-0.439595\pi$
$421$	158.829			0.377265			0.188633	+	0.982048i	$0.439595\pi$
$422$	190.747	−	190.747i	0.452007	−	0.452007i
$423$		0			0
$424$		−	276.363i		−	0.651800i
$425$		0			0
$426$		0			0
$427$	−562.343	+	562.343i	−1.31696	+	1.31696i
$428$	−49.7980	−	49.7980i	−0.116350	−	0.116350i
$429$		0			0
$430$		0			0
$431$	152.182			0.353090			0.176545	−	0.984293i	$-0.443508\pi$
$431$	152.182			0.353090			0.176545	+	0.984293i	$0.443508\pi$
$432$		0			0
$433$	254.918	+	254.918i	0.588726	+	0.588726i	0.937286	−	0.348560i	$-0.113329\pi$
$433$	254.918	+	254.918i	0.588726	+	0.588726i	−0.348560	+	0.937286i	$0.613329\pi$
$434$			7.19184i			0.0165711i
$435$		0			0
$436$	260.000			0.596330
$437$	−115.959	+	115.959i	−0.265353	+	0.265353i
$438$		0			0
$439$			299.373i			0.681944i	0.940073	+	0.340972i	$0.110756\pi$
$439$			299.373i			0.681944i	−0.940073	+	0.340972i	$0.889244\pi$
$440$		0			0
$441$		0			0
$442$	82.9490	−	82.9490i	0.187667	−	0.187667i
$443$	144.717	+	144.717i	0.326676	+	0.326676i	0.851321	−	0.524645i	$-0.175802\pi$
$443$	144.717	+	144.717i	0.326676	+	0.326676i	−0.524645	+	0.851321i	$0.675802\pi$
$444$		0			0
$445$		0			0
$446$	33.3531			0.0747826
$447$		0			0
$448$	71.1918	+	71.1918i	0.158910	+	0.158910i
$449$			846.727i			1.88581i	0.333069	+	0.942903i	$0.391916\pi$
$449$			846.727i			1.88581i	−0.333069	+	0.942903i	$0.608084\pi$
$450$		0			0
$451$	−10.4245			−0.0231142
$452$	17.4143	−	17.4143i	0.0385272	−	0.0385272i
$453$		0			0
$454$			84.1408i			0.185332i
$455$		0			0
$456$		0			0
$457$	38.3939	−	38.3939i	0.0840129	−	0.0840129i	−0.663852	−	0.747864i	$-0.731079\pi$
$457$	38.3939	−	38.3939i	0.0840129	−	0.0840129i	0.747864	+	0.663852i	$0.231079\pi$
$458$	173.939	+	173.939i	0.379779	+	0.379779i
$459$		0			0
$460$		0			0
$461$	−78.7265			−0.170773			−0.0853867	−	0.996348i	$-0.527213\pi$
$461$	−78.7265			−0.170773			−0.0853867	+	0.996348i	$0.527213\pi$
$462$		0			0
$463$	461.485	+	461.485i	0.996727	+	0.996727i	0.999995	−	0.00326746i	$-0.00104007\pi$
$463$	461.485	+	461.485i	0.996727	+	0.996727i	−0.00326746	+	0.999995i	$0.501040\pi$
$464$			24.8082i			0.0534659i
$465$		0			0
$466$	−596.524			−1.28010
$467$	17.3031	−	17.3031i	0.0370515	−	0.0370515i	−0.688338	−	0.725390i	$-0.741660\pi$
$467$	17.3031	−	17.3031i	0.0370515	−	0.0370515i	0.725390	+	0.688338i	$0.241660\pi$
$468$		0			0
$469$			713.535i			1.52140i
$470$		0			0
$471$		0			0
$472$	40.0000	−	40.0000i	0.0847458	−	0.0847458i
$473$	211.596	+	211.596i	0.447349	+	0.447349i
$474$		0			0
$475$		0			0
$476$	−217.171			−0.456242
$477$		0			0
$478$	−37.2122	−	37.2122i	−0.0778499	−	0.0778499i
$479$		−	776.727i		−	1.62156i	−0.585352	−	0.810779i	$-0.699044\pi$
$479$		−	776.727i		−	1.62156i	0.585352	−	0.810779i	$-0.300956\pi$
$480$		0			0
$481$	367.090			0.763180
$482$	165.939	−	165.939i	0.344271	−	0.344271i
$483$		0			0
$484$			174.767i			0.361090i
$485$		0			0
$486$		0			0
$487$	439.423	−	439.423i	0.902307	−	0.902307i	−0.0933285	−	0.995635i	$-0.529751\pi$
$487$	439.423	−	439.423i	0.902307	−	0.902307i	0.995635	+	0.0933285i	$0.0297507\pi$
$488$	126.384	+	126.384i	0.258983	+	0.258983i
$489$		0			0
$490$		0			0
$491$	−246.080			−0.501180			−0.250590	−	0.968093i	$-0.580625\pi$
$491$	−246.080			−0.501180			−0.250590	+	0.968093i	$0.580625\pi$
$492$		0			0
$493$	−37.8388	−	37.8388i	−0.0767521	−	0.0767521i
$494$		−	84.3224i		−	0.170693i
$495$		0			0
$496$	1.61633			0.00325873
$497$	−229.576	+	229.576i	−0.461923	+	0.461923i
$498$		0			0
$499$			597.839i			1.19807i	0.800721	+	0.599037i	$0.204450\pi$
$499$			597.839i			1.19807i	−0.800721	+	0.599037i	$0.795550\pi$
$500$		0			0
$501$		0			0
$502$	−255.414	+	255.414i	−0.508793	+	0.508793i
$503$	−516.817	−	516.817i	−1.02747	−	1.02747i	−0.999612	−	0.0278580i	$-0.991131\pi$
$503$	−516.817	−	516.817i	−1.02747	−	1.02747i	−0.0278580	−	0.999612i	$-0.508869\pi$
$504$		0			0
$505$		0			0
$506$	216.808			0.428475
$507$		0			0
$508$	−100.586	−	100.586i	−0.198003	−	0.198003i
$509$		−	452.059i		−	0.888132i	−0.895994	−	0.444066i	$-0.853536\pi$
$509$		−	452.059i		−	0.888132i	0.895994	−	0.444066i	$-0.146464\pi$
$510$		0			0
$511$	1010.89			1.97825
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$		0			0
$514$			540.969i			1.05247i
$515$		0			0
$516$		0			0
$517$	−224.363	+	224.363i	−0.433971	+	0.433971i
$518$	−480.545	−	480.545i	−0.927693	−	0.927693i
$519$		0			0
$520$		0			0
$521$	−779.494			−1.49615			−0.748075	−	0.663614i	$-0.769022\pi$
$521$	−779.494			−1.49615			−0.748075	+	0.663614i	$0.769022\pi$
$522$		0			0
$523$	−179.283	−	179.283i	−0.342797	−	0.342797i	0.514621	−	0.857418i	$-0.327933\pi$
$523$	−179.283	−	179.283i	−0.342797	−	0.342797i	−0.857418	+	0.514621i	$0.827933\pi$
$524$		−	228.404i		−	0.435886i
$525$		0			0
$526$	2.60612			0.00495461
$527$	−2.46531	+	2.46531i	−0.00467801	+	0.00467801i
$528$		0			0
$529$			170.151i			0.321647i
$530$		0			0
$531$		0			0
$532$	−110.384	+	110.384i	−0.207488	+	0.207488i
$533$	12.2225	+	12.2225i	0.0229314	+	0.0229314i
$534$		0			0
$535$		0			0
$536$	160.363			0.299185
$537$		0			0
$538$	−41.1510	−	41.1510i	−0.0764889	−	0.0764889i
$539$			634.202i			1.17663i
$540$		0			0
$541$	−385.110			−0.711849			−0.355924	−	0.934515i	$-0.615834\pi$
$541$	−385.110			−0.711849			−0.355924	+	0.934515i	$0.615834\pi$
$542$	−484.727	+	484.727i	−0.894329	+	0.894329i
$543$		0			0
$544$			48.8082i			0.0897209i
$545$		0			0
$546$		0			0
$547$	504.372	−	504.372i	0.922070	−	0.922070i	−0.0751053	−	0.997176i	$-0.523929\pi$
$547$	504.372	−	504.372i	0.922070	−	0.922070i	0.997176	+	0.0751053i	$0.0239293\pi$
$548$	−32.2020	−	32.2020i	−0.0587628	−	0.0587628i
$549$		0			0
$550$		0			0
$551$	−38.4653			−0.0698100
$552$		0			0
$553$	1240.28	+	1240.28i	2.24282	+	2.24282i
$554$			103.980i			0.187689i
$555$		0			0
$556$	147.596			0.265460
$557$	−130.101	+	130.101i	−0.233575	+	0.233575i	−0.814183	−	0.580608i	$-0.802815\pi$
$557$	−130.101	+	130.101i	−0.233575	+	0.233575i	0.580608	+	0.814183i	$0.302815\pi$
$558$		0			0
$559$		−	496.182i		−	0.887624i
$560$		0			0
$561$		0			0
$562$	−242.524	+	242.524i	−0.431538	+	0.431538i
$563$	666.879	+	666.879i	1.18451	+	1.18451i	0.978563	+	0.205946i	$0.0660270\pi$
$563$	666.879	+	666.879i	1.18451	+	1.18451i	0.205946	+	0.978563i	$0.433973\pi$
$564$		0			0
$565$		0			0
$566$	−209.435			−0.370026
$567$		0			0
$568$	51.5959	+	51.5959i	0.0908379	+	0.0908379i
$569$			987.494i			1.73549i	0.497010	+	0.867745i	$0.334431\pi$
$569$			987.494i			1.73549i	−0.497010	+	0.867745i	$0.665569\pi$
$570$		0			0
$571$	452.767			0.792938			0.396469	−	0.918048i	$-0.370236\pi$
$571$	452.767			0.792938			0.396469	+	0.918048i	$0.370236\pi$
$572$	−78.8286	+	78.8286i	−0.137812	+	0.137812i
$573$		0			0
$574$		−	32.0000i		−	0.0557491i
$575$		0			0
$576$		0			0
$577$	−463.000	+	463.000i	−0.802426	+	0.802426i	−0.983474	−	0.181048i	$-0.942051\pi$
$577$	−463.000	+	463.000i	−0.802426	+	0.802426i	0.181048	+	0.983474i	$0.442051\pi$
$578$	214.555	+	214.555i	0.371203	+	0.371203i
$579$		0			0
$580$		0			0
$581$	243.959			0.419895
$582$		0			0
$583$	−400.586	−	400.586i	−0.687111	−	0.687111i
$584$		−	227.192i		−	0.389027i
$585$		0			0
$586$	−121.818			−0.207881
$587$	375.909	−	375.909i	0.640390	−	0.640390i	−0.310261	−	0.950651i	$-0.600416\pi$
$587$	375.909	−	375.909i	0.640390	−	0.640390i	0.950651	+	0.310261i	$0.100416\pi$
$588$		0			0
$589$			2.50613i			0.00425490i
$590$		0			0
$591$		0			0
$592$	−108.000	+	108.000i	−0.182432	+	0.182432i
$593$	−398.646	−	398.646i	−0.672253	−	0.672253i	0.285982	−	0.958235i	$-0.407680\pi$
$593$	−398.646	−	398.646i	−0.672253	−	0.672253i	−0.958235	+	0.285982i	$0.907680\pi$
$594$		0			0
$595$		0			0
$596$	541.535			0.908615
$597$		0			0
$598$	−254.202	−	254.202i	−0.425087	−	0.425087i
$599$			509.131i			0.849968i	0.905201	+	0.424984i	$0.139720\pi$
$599$			509.131i			0.849968i	−0.905201	+	0.424984i	$0.860280\pi$
$600$		0			0
$601$	−390.302			−0.649421			−0.324711	−	0.945813i	$-0.605267\pi$
$601$	−390.302			−0.649421			−0.324711	+	0.945813i	$0.605267\pi$
$602$	−649.535	+	649.535i	−1.07896	+	1.07896i
$603$		0			0
$604$		−	43.2327i		−	0.0715772i
$605$		0			0
$606$		0			0
$607$	−494.030	+	494.030i	−0.813887	+	0.813887i	−0.985214	−	0.171327i	$-0.945195\pi$
$607$	−494.030	+	494.030i	−0.813887	+	0.813887i	0.171327	+	0.985214i	$0.445195\pi$
$608$	24.8082	+	24.8082i	0.0408029	+	0.0408029i
$609$		0			0
$610$		0			0
$611$	526.120			0.861081
$612$		0			0
$613$	−74.1102	−	74.1102i	−0.120898	−	0.120898i	0.644069	−	0.764967i	$-0.277245\pi$
$613$	−74.1102	−	74.1102i	−0.120898	−	0.120898i	−0.764967	+	0.644069i	$0.777245\pi$
$614$		−	402.606i		−	0.655710i
$615$		0			0
$616$	206.384			0.335038
$617$	−398.221	+	398.221i	−0.645416	+	0.645416i	−0.951882	−	0.306466i	$-0.900853\pi$
$617$	−398.221	+	398.221i	−0.645416	+	0.645416i	0.306466	+	0.951882i	$0.400853\pi$
$618$		0			0
$619$			838.120i			1.35399i	0.735987	+	0.676995i	$0.236718\pi$
$619$			838.120i			1.35399i	−0.735987	+	0.676995i	$0.763282\pi$
$620$		0			0
$621$		0			0
$622$	−559.737	+	559.737i	−0.899898	+	0.899898i
$623$	521.535	+	521.535i	0.837134	+	0.837134i
$624$		0			0
$625$		0			0
$626$	187.535			0.299576
$627$		0			0
$628$	246.000	+	246.000i	0.391720	+	0.391720i
$629$		−	329.455i		−	0.523776i
$630$		0			0
$631$	149.980			0.237686			0.118843	−	0.992913i	$-0.462082\pi$
$631$	149.980			0.237686			0.118843	+	0.992913i	$0.462082\pi$
$632$	278.747	−	278.747i	0.441055	−	0.441055i
$633$		0			0
$634$		−	725.655i		−	1.14457i
$635$		0			0
$636$		0			0
$637$	743.586	−	743.586i	1.16732	−	1.16732i
$638$	35.9592	+	35.9592i	0.0563624	+	0.0563624i
$639$		0			0
$640$		0			0
$641$	378.243			0.590082			0.295041	−	0.955485i	$-0.404667\pi$
$641$	378.243			0.590082			0.295041	+	0.955485i	$0.404667\pi$
$642$		0			0
$643$	285.526	+	285.526i	0.444052	+	0.444052i	0.893371	−	0.449319i	$-0.148333\pi$
$643$	285.526	+	285.526i	0.444052	+	0.444052i	−0.449319	+	0.893371i	$0.648333\pi$
$644$			665.535i			1.03344i
$645$		0			0
$646$	−75.6776			−0.117148
$647$	−360.677	+	360.677i	−0.557460	+	0.557460i	−0.928583	−	0.371124i	$-0.878973\pi$
$647$	−360.677	+	360.677i	−0.557460	+	0.557460i	0.371124	+	0.928583i	$0.378973\pi$
$648$		0			0
$649$		−	115.959i		−	0.178674i
$650$		0			0
$651$		0			0
$652$	224.990	−	224.990i	0.345076	−	0.345076i
$653$	547.838	+	547.838i	0.838955	+	0.838955i	0.988721	−	0.149766i	$-0.0478521\pi$
$653$	547.838	+	547.838i	0.838955	+	0.838955i	−0.149766	+	0.988721i	$0.547852\pi$
$654$		0			0
$655$		0			0
$656$	−7.19184			−0.0109632
$657$		0			0
$658$	−688.727	−	688.727i	−1.04670	−	1.04670i
$659$			25.5755i			0.0388096i	0.999812	+	0.0194048i	$0.00617712\pi$
$659$			25.5755i			0.0388096i	−0.999812	+	0.0194048i	$0.993823\pi$
$660$		0			0
$661$	−824.727			−1.24770			−0.623848	−	0.781546i	$-0.714431\pi$
$661$	−824.727			−1.24770			−0.623848	+	0.781546i	$0.714431\pi$
$662$	14.0204	−	14.0204i	0.0211789	−	0.0211789i
$663$		0			0
$664$		−	54.8286i		−	0.0825732i
$665$		0			0
$666$		0			0
$667$	−115.959	+	115.959i	−0.173852	+	0.173852i
$668$	−353.353	−	353.353i	−0.528972	−	0.528972i
$669$		0			0
$670$		0			0
$671$	366.384			0.546026
$672$		0			0
$673$	−902.857	−	902.857i	−1.34154	−	1.34154i	−0.894527	−	0.447014i	$-0.852487\pi$
$673$	−902.857	−	902.857i	−1.34154	−	1.34154i	−0.447014	−	0.894527i	$-0.647513\pi$
$674$		−	332.747i		−	0.493690i
$675$		0			0
$676$	−153.151			−0.226555
$677$	688.160	−	688.160i	1.01648	−	1.01648i	0.0166229	−	0.999862i	$-0.494709\pi$
$677$	688.160	−	688.160i	1.01648	−	1.01648i	0.999862	−	0.0166229i	$-0.00529149\pi$
$678$		0			0
$679$		−	284.586i		−	0.419125i
$680$		0			0
$681$		0			0
$682$	2.34285	−	2.34285i	0.00343527	−	0.00343527i
$683$	1.92959	+	1.92959i	0.00282518	+	0.00282518i	0.708518	−	0.705693i	$-0.249364\pi$
$683$	1.92959	+	1.92959i	0.00282518	+	0.00282518i	−0.705693	+	0.708518i	$0.749364\pi$
$684$		0			0
$685$		0			0
$686$	−1074.71			−1.56663
$687$		0			0
$688$	145.980	+	145.980i	0.212180	+	0.212180i
$689$			939.353i			1.36336i
$690$		0			0
$691$	−162.706			−0.235465			−0.117732	−	0.993045i	$-0.537562\pi$
$691$	−162.706			−0.235465			−0.117732	+	0.993045i	$0.537562\pi$
$692$	285.778	−	285.778i	0.412973	−	0.412973i
$693$		0			0
$694$		−	327.010i		−	0.471196i
$695$		0			0
$696$		0			0
$697$	10.9694	−	10.9694i	0.0157380	−	0.0157380i
$698$	−280.000	−	280.000i	−0.401146	−	0.401146i
$699$		0			0
$700$		0			0
$701$	−260.222			−0.371216			−0.185608	−	0.982624i	$-0.559425\pi$
$701$	−260.222			−0.371216			−0.185608	+	0.982624i	$0.559425\pi$
$702$		0			0
$703$	−167.455	−	167.455i	−0.238201	−	0.238201i
$704$		−	46.3837i		−	0.0658859i
$705$		0			0
$706$	522.990			0.740779
$707$	1142.48	−	1142.48i	1.61596	−	1.61596i
$708$		0			0
$709$		−	151.637i		−	0.213874i	−0.994266	−	0.106937i	$-0.965896\pi$
$709$		−	151.637i		−	0.213874i	0.994266	−	0.106937i	$-0.0341043\pi$
$710$		0			0
$711$		0			0
$712$	117.212	−	117.212i	0.164624	−	0.164624i
$713$	7.55510	+	7.55510i	0.0105962	+	0.0105962i
$714$		0			0
$715$		0			0
$716$	−266.343			−0.371987
$717$		0			0
$718$	425.090	+	425.090i	0.592047	+	0.592047i
$719$		−	1281.82i		−	1.78278i	−0.453241	−	0.891388i	$-0.649732\pi$
$719$		−	1281.82i		−	1.78278i	0.453241	−	0.891388i	$-0.350268\pi$
$720$		0			0
$721$	578.343			0.802140
$722$	322.535	−	322.535i	0.446724	−	0.446724i
$723$		0			0
$724$		−	274.384i		−	0.378983i
$725$		0			0
$726$		0			0
$727$	−638.352	+	638.352i	−0.878063	+	0.878063i	−0.993334	−	0.115271i	$-0.963226\pi$
$727$	−638.352	+	638.352i	−0.878063	+	0.878063i	0.115271	+	0.993334i	$0.463226\pi$
$728$	−241.980	−	241.980i	−0.332390	−	0.332390i
$729$		0			0
$730$		0			0
$731$	−445.312			−0.609182
$732$		0			0
$733$	−400.414	−	400.414i	−0.546268	−	0.546268i	0.379091	−	0.925359i	$-0.376237\pi$
$733$	−400.414	−	400.414i	−0.546268	−	0.546268i	−0.925359	+	0.379091i	$0.876237\pi$
$734$		−	632.990i		−	0.862384i
$735$		0			0
$736$	149.576			0.203228
$737$	232.445	−	232.445i	0.315393	−	0.315393i
$738$		0			0
$739$		−	382.647i		−	0.517790i	−0.965905	−	0.258895i	$-0.916642\pi$
$739$		−	382.647i		−	0.517790i	0.965905	−	0.258895i	$-0.0833584\pi$
$740$		0			0
$741$		0			0
$742$	1229.68	−	1229.68i	1.65724	−	1.65724i
$743$	135.383	+	135.383i	0.182211	+	0.182211i	0.792319	−	0.610108i	$-0.208874\pi$
$743$	135.383	+	135.383i	0.182211	+	0.182211i	−0.610108	+	0.792319i	$0.708874\pi$
$744$		0			0
$745$		0			0
$746$	−421.878			−0.565519
$747$		0			0
$748$	70.7469	+	70.7469i	0.0945815	+	0.0945815i
$749$		−	443.151i		−	0.591657i
$750$		0			0
$751$	−571.273			−0.760684			−0.380342	−	0.924846i	$-0.624194\pi$
$751$	−571.273			−0.760684			−0.380342	+	0.924846i	$0.624194\pi$
$752$	−154.788	+	154.788i	−0.205835	+	0.205835i
$753$		0			0
$754$		−	84.3224i		−	0.111833i
$755$		0			0
$756$		0			0
$757$	917.908	−	917.908i	1.21256	−	1.21256i	0.242379	−	0.970182i	$-0.422072\pi$
$757$	917.908	−	917.908i	1.21256	−	1.21256i	0.970182	−	0.242379i	$-0.0779276\pi$
$758$	−344.182	−	344.182i	−0.454065	−	0.454065i
$759$		0			0
$760$		0			0
$761$	616.261			0.809804			0.404902	−	0.914360i	$-0.367306\pi$
$761$	616.261			0.809804			0.404902	+	0.914360i	$0.367306\pi$
$762$		0			0
$763$	1156.87	+	1156.87i	1.51621	+	1.51621i
$764$		−	533.212i		−	0.697922i
$765$		0			0
$766$	−819.414			−1.06973
$767$	−135.959	+	135.959i	−0.177261	+	0.177261i
$768$		0			0
$769$		−	154.424i		−	0.200812i	−0.994947	−	0.100406i	$-0.967986\pi$
$769$		−	154.424i		−	0.200812i	0.994947	−	0.100406i	$-0.0320142\pi$
$770$		0			0
$771$		0			0
$772$	−234.767	+	234.767i	−0.304103	+	0.304103i
$773$	−184.323	−	184.323i	−0.238452	−	0.238452i	0.577757	−	0.816209i	$-0.303928\pi$
$773$	−184.323	−	184.323i	−0.238452	−	0.238452i	−0.816209	+	0.577757i	$0.803928\pi$
$774$		0			0
$775$		0			0
$776$	−63.9592			−0.0824216
$777$		0			0
$778$	−301.151	−	301.151i	−0.387084	−	0.387084i
$779$		−	11.1510i		−	0.0143145i
$780$		0			0
$781$	149.576			0.191518
$782$	−228.141	+	228.141i	−0.291740	+	0.291740i
$783$		0			0
$784$			437.535i			0.558080i
$785$		0			0
$786$		0			0
$787$	784.858	−	784.858i	0.997278	−	0.997278i	−0.00271783	−	0.999996i	$-0.500865\pi$
$787$	784.858	−	784.858i	0.997278	−	0.997278i	0.999996	+	0.00271783i	$0.000865114\pi$
$788$	493.373	+	493.373i	0.626108	+	0.626108i
$789$		0			0
$790$		0			0
$791$	154.969			0.195916
$792$		0			0
$793$	−429.576	−	429.576i	−0.541709	−	0.541709i
$794$			958.686i			1.20741i
$795$		0			0
$796$	−309.131			−0.388355
$797$	−485.191	+	485.191i	−0.608771	+	0.608771i	−0.942625	−	0.333854i	$-0.891651\pi$
$797$	−485.191	+	485.191i	−0.608771	+	0.608771i	0.333854	+	0.942625i	$0.391651\pi$
$798$		0			0
$799$		−	472.182i		−	0.590966i
$800$		0			0
$801$		0			0
$802$	−101.233	+	101.233i	−0.126225	+	0.126225i
$803$	−329.312	−	329.312i	−0.410102	−	0.410102i
$804$		0			0
$805$		0			0
$806$	−5.49387			−0.00681621
$807$		0			0
$808$	−256.767	−	256.767i	−0.317781	−	0.317781i
$809$		−	397.839i		−	0.491766i	−0.969300	−	0.245883i	$-0.920922\pi$
$809$		−	397.839i		−	0.491766i	0.969300	−	0.245883i	$-0.0790779\pi$
$810$		0			0
$811$	−1005.49			−1.23982			−0.619910	−	0.784673i	$-0.712831\pi$
$811$	−1005.49			−1.23982			−0.619910	+	0.784673i	$0.712831\pi$
$812$	−110.384	+	110.384i	−0.135940	+	0.135940i
$813$		0			0
$814$			313.090i			0.384631i
$815$		0			0
$816$		0			0
$817$	−226.343	+	226.343i	−0.277041	+	0.277041i
$818$	−257.110	−	257.110i	−0.314316	−	0.314316i
$819$		0			0
$820$		0			0
$821$	101.312			0.123401			0.0617005	−	0.998095i	$-0.480348\pi$
$821$	101.312			0.123401			0.0617005	+	0.998095i	$0.480348\pi$
$822$		0			0
$823$	−68.2724	−	68.2724i	−0.0829556	−	0.0829556i	0.664411	−	0.747367i	$-0.268682\pi$
$823$	−68.2724	−	68.2724i	−0.0829556	−	0.0829556i	−0.747367	+	0.664411i	$0.768682\pi$
$824$		−	129.980i		−	0.157742i
$825$		0			0
$826$	355.959			0.430943
$827$	−363.464	+	363.464i	−0.439497	+	0.439497i	−0.891843	−	0.452345i	$-0.850587\pi$
$827$	−363.464	+	363.464i	−0.439497	+	0.439497i	0.452345	+	0.891843i	$0.350587\pi$
$828$		0			0
$829$		−	891.535i		−	1.07543i	−0.843125	−	0.537717i	$-0.819287\pi$
$829$		−	891.535i		−	1.07543i	0.843125	−	0.537717i	$-0.180713\pi$
$830$		0			0
$831$		0			0
$832$	−54.3837	+	54.3837i	−0.0653650	+	0.0653650i
$833$	−667.352	−	667.352i	−0.801143	−	0.801143i
$834$		0			0
$835$		0			0
$836$	71.9184			0.0860267
$837$		0			0
$838$	375.959	+	375.959i	0.448639	+	0.448639i
$839$		−	705.090i		−	0.840393i	−0.907433	−	0.420197i	$-0.861961\pi$
$839$		−	705.090i		−	0.840393i	0.907433	−	0.420197i	$-0.138039\pi$
$840$		0			0
$841$	802.535			0.954262
$842$	158.829	−	158.829i	0.188633	−	0.188633i
$843$		0			0
$844$		−	381.494i		−	0.452007i
$845$		0			0
$846$		0			0
$847$	−777.626	+	777.626i	−0.918094	+	0.918094i
$848$	−276.363	−	276.363i	−0.325900	−	0.325900i
$849$		0			0
$850$		0			0
$851$	−1009.63			−1.18641
$852$		0			0
$853$	−450.555	−	450.555i	−0.528201	−	0.528201i	0.391835	−	0.920036i	$-0.371840\pi$
$853$	−450.555	−	450.555i	−0.528201	−	0.528201i	−0.920036	+	0.391835i	$0.871840\pi$
$854$			1124.69i			1.31696i
$855$		0			0
$856$	−99.5959			−0.116350
$857$	63.5561	−	63.5561i	0.0741612	−	0.0741612i	−0.669053	−	0.743214i	$-0.733300\pi$
$857$	63.5561	−	63.5561i	0.0741612	−	0.0741612i	0.743214	+	0.669053i	$0.233300\pi$
$858$		0			0
$859$			1467.53i			1.70842i	0.519928	+	0.854210i	$0.325959\pi$
$859$			1467.53i			1.70842i	−0.519928	+	0.854210i	$0.674041\pi$
$860$		0			0
$861$		0			0
$862$	152.182	−	152.182i	0.176545	−	0.176545i
$863$	−294.797	−	294.797i	−0.341596	−	0.341596i	0.515371	−	0.856967i	$-0.327654\pi$
$863$	−294.797	−	294.797i	−0.341596	−	0.341596i	−0.856967	+	0.515371i	$0.827654\pi$
$864$		0			0
$865$		0			0
$866$	509.837			0.588726
$867$		0			0
$868$	7.19184	+	7.19184i	0.00828553	+	0.00828553i
$869$		−	808.082i		−	0.929898i
$870$		0			0
$871$	−545.071			−0.625800
$872$	260.000	−	260.000i	0.298165	−	0.298165i
$873$		0			0
$874$			231.918i			0.265353i
$875$		0			0
$876$		0			0
$877$	−113.102	+	113.102i	−0.128965	+	0.128965i	−0.768643	−	0.639678i	$-0.779068\pi$
$877$	−113.102	+	113.102i	−0.128965	+	0.128965i	0.639678	+	0.768643i	$0.279068\pi$
$878$	299.373	+	299.373i	0.340972	+	0.340972i
$879$		0			0
$880$		0			0
$881$	1370.44			1.55555			0.777777	−	0.628540i	$-0.216347\pi$
$881$	1370.44			1.55555			0.777777	+	0.628540i	$0.216347\pi$
$882$		0			0
$883$	−175.587	−	175.587i	−0.198852	−	0.198852i	0.600655	−	0.799508i	$-0.294906\pi$
$883$	−175.587	−	175.587i	−0.198852	−	0.198852i	−0.799508	+	0.600655i	$0.794906\pi$
$884$		−	165.898i		−	0.187667i
$885$		0			0
$886$	289.435			0.326676
$887$	−512.313	+	512.313i	−0.577580	+	0.577580i	−0.934236	−	0.356656i	$-0.883917\pi$
$887$	−512.313	+	512.313i	−0.577580	+	0.577580i	0.356656	+	0.934236i	$0.383917\pi$
$888$		0			0
$889$		−	895.110i		−	1.00687i
$890$		0			0
$891$		0			0
$892$	33.3531	−	33.3531i	0.0373913	−	0.0373913i
$893$	−240.000	−	240.000i	−0.268757	−	0.268757i
$894$		0			0
$895$		0			0
$896$	142.384			0.158910
$897$		0			0
$898$	846.727	+	846.727i	0.942903	+	0.942903i
$899$			2.50613i			0.00278769i
$900$		0			0
$901$	843.049			0.935681
$902$	−10.4245	+	10.4245i	−0.0115571	+	0.0115571i
$903$		0			0
$904$		−	34.8286i		−	0.0385272i
$905$		0			0
$906$		0			0
$907$	922.697	−	922.697i	1.01731	−	1.01731i	0.0174589	−	0.999848i	$-0.494442\pi$
$907$	922.697	−	922.697i	1.01731	−	1.01731i	0.999848	−	0.0174589i	$-0.00555761\pi$
$908$	84.1408	+	84.1408i	0.0926661	+	0.0926661i
$909$		0			0
$910$		0			0
$911$	−1338.97			−1.46978			−0.734890	−	0.678186i	$-0.762766\pi$
$911$	−1338.97			−1.46978			−0.734890	+	0.678186i	$0.762766\pi$
$912$		0			0
$913$	−79.4735	−	79.4735i	−0.0870465	−	0.0870465i
$914$		−	76.7878i		−	0.0840129i
$915$		0			0
$916$	347.878			0.379779
$917$	1016.28	−	1016.28i	1.10827	−	1.10827i
$918$		0			0
$919$		−	1371.57i		−	1.49246i	−0.665687	−	0.746231i	$-0.731861\pi$
$919$		−	1371.57i		−	1.49246i	0.665687	−	0.746231i	$-0.268139\pi$
$920$		0			0
$921$		0			0
$922$	−78.7265	+	78.7265i	−0.0853867	+	0.0853867i
$923$	−175.373	−	175.373i	−0.190004	−	0.190004i
$924$		0			0
$925$		0			0
$926$	922.969			0.996727
$927$		0			0
$928$	24.8082	+	24.8082i	0.0267329	+	0.0267329i
$929$			218.645i			0.235355i	0.993052	+	0.117678i	$0.0375449\pi$
$929$			218.645i			0.235355i	−0.993052	+	0.117678i	$0.962455\pi$
$930$		0			0
$931$	−678.402			−0.728681
$932$	−596.524	+	596.524i	−0.640048	+	0.640048i
$933$		0			0
$934$		−	34.6061i		−	0.0370515i
$935$		0			0
$936$		0			0
$937$	1127.38	−	1127.38i	1.20318	−	1.20318i	0.229992	−	0.973193i	$-0.426130\pi$
$937$	1127.38	−	1127.38i	1.20318	−	1.20318i	0.973193	−	0.229992i	$-0.0738699\pi$
$938$	713.535	+	713.535i	0.760698	+	0.760698i
$939$		0			0
$940$		0			0
$941$	588.384			0.625275			0.312637	−	0.949873i	$-0.398788\pi$
$941$	588.384			0.625275			0.312637	+	0.949873i	$0.398788\pi$
$942$		0			0
$943$	−33.6163	−	33.6163i	−0.0356483	−	0.0356483i
$944$		−	80.0000i		−	0.0847458i
$945$		0			0
$946$	423.192			0.447349
$947$	−926.879	+	926.879i	−0.978752	+	0.978752i	−0.999779	−	0.0210265i	$-0.993307\pi$
$947$	−926.879	+	926.879i	−0.978752	+	0.978752i	0.0210265	+	0.999779i	$0.493307\pi$
$948$		0			0
$949$			772.220i			0.813720i
$950$		0			0
$951$		0			0
$952$	−217.171	+	217.171i	−0.228121	+	0.228121i
$953$	1271.29	+	1271.29i	1.33399	+	1.33399i	0.901768	+	0.432220i	$0.142270\pi$
$953$	1271.29	+	1271.29i	1.33399	+	1.33399i	0.432220	+	0.901768i	$0.357730\pi$
$954$		0			0
$955$		0			0
$956$	−74.4245			−0.0778499
$957$		0			0
$958$	−776.727	−	776.727i	−0.810779	−	0.810779i
$959$		−	286.565i		−	0.298817i
$960$		0			0
$961$	−960.837			−0.999830
$962$	367.090	−	367.090i	0.381590	−	0.381590i
$963$		0			0
$964$		−	331.878i		−	0.344271i
$965$		0			0
$966$		0			0
$967$	−753.121	+	753.121i	−0.778823	+	0.778823i	−0.979631	−	0.200808i	$-0.935643\pi$
$967$	−753.121	+	753.121i	−0.778823	+	0.778823i	0.200808	+	0.979631i	$0.435643\pi$
$968$	174.767	+	174.767i	0.180545	+	0.180545i
$969$		0			0
$970$		0			0
$971$	−1803.86			−1.85773			−0.928865	−	0.370419i	$-0.879214\pi$
$971$	−1803.86			−1.85773			−0.928865	+	0.370419i	$0.879214\pi$
$972$		0			0
$973$	656.727	+	656.727i	0.674950	+	0.674950i
$974$		−	878.847i		−	0.902307i
$975$		0			0
$976$	252.767			0.258983
$977$	223.838	−	223.838i	0.229107	−	0.229107i	−0.583212	−	0.812320i	$-0.698204\pi$
$977$	223.838	−	223.838i	0.229107	−	0.229107i	0.812320	+	0.583212i	$0.198204\pi$
$978$		0			0
$979$		−	339.796i		−	0.347085i
$980$		0			0
$981$		0			0
$982$	−246.080	+	246.080i	−0.250590	+	0.250590i
$983$	−976.536	−	976.536i	−0.993424	−	0.993424i	0.00655459	−	0.999979i	$-0.497914\pi$
$983$	−976.536	−	976.536i	−0.993424	−	0.993424i	−0.999979	+	0.00655459i	$0.997914\pi$
$984$		0			0
$985$		0			0
$986$	−75.6776			−0.0767521
$987$		0			0
$988$	−84.3224	−	84.3224i	−0.0853466	−	0.0853466i
$989$			1364.69i			1.37986i
$990$		0			0
$991$	1331.03			1.34312			0.671558	−	0.740952i	$-0.265625\pi$
$991$	1331.03			1.34312			0.671558	+	0.740952i	$0.265625\pi$
$992$	1.61633	−	1.61633i	0.00162936	−	0.00162936i
$993$		0			0
$994$			459.151i			0.461923i
$995$		0			0
$996$		0			0
$997$	−852.616	+	852.616i	−0.855182	+	0.855182i	−0.990766	−	0.135584i	$-0.956709\pi$
$997$	−852.616	+	852.616i	−0.855182	+	0.855182i	0.135584	+	0.990766i	$0.456709\pi$
$998$	597.839	+	597.839i	0.599037	+	0.599037i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.3.g.j.343.2		4
3.2	odd	2		150.3.f.b.43.2		4
5.2	odd	4	inner	450.3.g.j.307.2		4
5.3	odd	4		90.3.g.d.37.1		4
5.4	even	2		90.3.g.d.73.1		4
12.11	even	2		1200.3.bg.d.193.1		4
15.2	even	4		150.3.f.b.7.2		4
15.8	even	4		30.3.f.a.7.1	✓	4
15.14	odd	2		30.3.f.a.13.1	yes	4
20.3	even	4		720.3.bh.i.577.1		4
20.19	odd	2		720.3.bh.i.433.1		4
60.23	odd	4		240.3.bg.b.97.2		4
60.47	odd	4		1200.3.bg.d.1057.1		4
60.59	even	2		240.3.bg.b.193.2		4
120.29	odd	2		960.3.bg.e.193.2		4
120.53	even	4		960.3.bg.e.577.2		4
120.59	even	2		960.3.bg.g.193.1		4
120.83	odd	4		960.3.bg.g.577.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.f.a.7.1	✓	4	15.8	even	4
30.3.f.a.13.1	yes	4	15.14	odd	2
90.3.g.d.37.1		4	5.3	odd	4
90.3.g.d.73.1		4	5.4	even	2
150.3.f.b.7.2		4	15.2	even	4
150.3.f.b.43.2		4	3.2	odd	2
240.3.bg.b.97.2		4	60.23	odd	4
240.3.bg.b.193.2		4	60.59	even	2
450.3.g.j.307.2		4	5.2	odd	4	inner
450.3.g.j.343.2		4	1.1	even	1	trivial
720.3.bh.i.433.1		4	20.19	odd	2
720.3.bh.i.577.1		4	20.3	even	4
960.3.bg.e.193.2		4	120.29	odd	2
960.3.bg.e.577.2		4	120.53	even	4
960.3.bg.g.193.1		4	120.59	even	2
960.3.bg.g.577.1		4	120.83	odd	4
1200.3.bg.d.193.1		4	12.11	even	2
1200.3.bg.d.1057.1		4	60.47	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	450.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(8.89898 - 8.89898i) q^{7} +(-2.00000 - 2.00000i) q^{8} -5.79796 q^{11} +(6.79796 + 6.79796i) q^{13} -17.7980i q^{14} -4.00000 q^{16} +(6.10102 - 6.10102i) q^{17} -6.20204i q^{19} +(-5.79796 + 5.79796i) q^{22} +(-18.6969 - 18.6969i) q^{23} +13.5959 q^{26} +(-17.7980 - 17.7980i) q^{28} -6.20204i q^{29} -0.404082 q^{31} +(-4.00000 + 4.00000i) q^{32} -12.2020i q^{34} +(27.0000 - 27.0000i) q^{37} +(-6.20204 - 6.20204i) q^{38} +1.79796 q^{41} +(-36.4949 - 36.4949i) q^{43} +11.5959i q^{44} -37.3939 q^{46} +(38.6969 - 38.6969i) q^{47} -109.384i q^{49} +(13.5959 - 13.5959i) q^{52} +(69.0908 + 69.0908i) q^{53} -35.5959 q^{56} +(-6.20204 - 6.20204i) q^{58} +20.0000i q^{59} -63.1918 q^{61} +(-0.404082 + 0.404082i) q^{62} +8.00000i q^{64} +(-40.0908 + 40.0908i) q^{67} +(-12.2020 - 12.2020i) q^{68} -25.7980 q^{71} +(56.7980 + 56.7980i) q^{73} -54.0000i q^{74} -12.4041 q^{76} +(-51.5959 + 51.5959i) q^{77} +139.373i q^{79} +(1.79796 - 1.79796i) q^{82} +(13.7071 + 13.7071i) q^{83} -72.9898 q^{86} +(11.5959 + 11.5959i) q^{88} +58.6061i q^{89} +120.990 q^{91} +(-37.3939 + 37.3939i) q^{92} -77.3939i q^{94} +(15.9898 - 15.9898i) q^{97} +(-109.384 - 109.384i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 16 q^{7} - 8 q^{8} + 16 q^{11} - 12 q^{13} - 16 q^{16} + 44 q^{17} + 16 q^{22} - 16 q^{23} - 24 q^{26} - 32 q^{28} - 80 q^{31} - 16 q^{32} + 108 q^{37} - 64 q^{38} - 32 q^{41} - 48 q^{43}+ \cdots - 124 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 16 * q^7 - 8 * q^8 + 16 * q^11 - 12 * q^13 - 16 * q^16 + 44 * q^17 + 16 * q^22 - 16 * q^23 - 24 * q^26 - 32 * q^28 - 80 * q^31 - 16 * q^32 + 108 * q^37 - 64 * q^38 - 32 * q^41 - 48 * q^43 - 32 * q^46 + 96 * q^47 - 24 * q^52 + 100 * q^53 - 64 * q^56 - 64 * q^58 - 96 * q^61 - 80 * q^62 + 16 * q^67 - 88 * q^68 - 64 * q^71 + 188 * q^73 - 128 * q^76 - 128 * q^77 - 32 * q^82 + 192 * q^83 - 96 * q^86 - 32 * q^88 + 288 * q^91 - 32 * q^92 - 132 * q^97 - 124 * q^98

Introduction

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