LMFDB - Embedded newform 150.3.f.b.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,3,Mod(7,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("150.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	150.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.08720396540$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.2
Root			$1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	150.43
Dual form			150.3.f.b.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(8.89898 - 8.89898i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(8.89898 - 8.89898i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +5.79796 q^{11} +(2.44949 - 2.44949i) q^{12} +(6.79796 + 6.79796i) q^{13} +17.7980i q^{14} -4.00000 q^{16} +(-6.10102 + 6.10102i) q^{17} +(-3.00000 - 3.00000i) q^{18} -6.20204i q^{19} +21.7980 q^{21} +(-5.79796 + 5.79796i) q^{22} +(18.6969 + 18.6969i) q^{23} +4.89898i q^{24} -13.5959 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-17.7980 - 17.7980i) q^{28} +6.20204i q^{29} -0.404082 q^{31} +(4.00000 - 4.00000i) q^{32} +(7.10102 + 7.10102i) q^{33} -12.2020i q^{34} +6.00000 q^{36} +(27.0000 - 27.0000i) q^{37} +(6.20204 + 6.20204i) q^{38} +16.6515i q^{39} -1.79796 q^{41} +(-21.7980 + 21.7980i) q^{42} +(-36.4949 - 36.4949i) q^{43} -11.5959i q^{44} -37.3939 q^{46} +(-38.6969 + 38.6969i) q^{47} +(-4.89898 - 4.89898i) q^{48} -109.384i q^{49} -14.9444 q^{51} +(13.5959 - 13.5959i) q^{52} +(-69.0908 - 69.0908i) q^{53} -7.34847i q^{54} +35.5959 q^{56} +(7.59592 - 7.59592i) q^{57} +(-6.20204 - 6.20204i) q^{58} -20.0000i q^{59} -63.1918 q^{61} +(0.404082 - 0.404082i) q^{62} +(26.6969 + 26.6969i) q^{63} +8.00000i q^{64} -14.2020 q^{66} +(-40.0908 + 40.0908i) q^{67} +(12.2020 + 12.2020i) q^{68} +45.7980i q^{69} +25.7980 q^{71} +(-6.00000 + 6.00000i) q^{72} +(56.7980 + 56.7980i) q^{73} +54.0000i q^{74} -12.4041 q^{76} +(51.5959 - 51.5959i) q^{77} +(-16.6515 - 16.6515i) q^{78} +139.373i q^{79} -9.00000 q^{81} +(1.79796 - 1.79796i) q^{82} +(-13.7071 - 13.7071i) q^{83} -43.5959i q^{84} +72.9898 q^{86} +(-7.59592 + 7.59592i) q^{87} +(11.5959 + 11.5959i) q^{88} -58.6061i q^{89} +120.990 q^{91} +(37.3939 - 37.3939i) q^{92} +(-0.494897 - 0.494897i) q^{93} -77.3939i q^{94} +9.79796 q^{96} +(15.9898 - 15.9898i) q^{97} +(109.384 + 109.384i) q^{98} +17.3939i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 16 q^{7} + 8 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 + 16 * q^7 + 8 * q^8	$ 4 q - 4 q^{2} + 16 q^{7} + 8 q^{8} - 16 q^{11} - 12 q^{13} - 16 q^{16} - 44 q^{17} - 12 q^{18} + 48 q^{21} + 16 q^{22} + 16 q^{23} + 24 q^{26} - 32 q^{28} - 80 q^{31} + 16 q^{32} + 48 q^{33} + 24 q^{36} + 108 q^{37} + 64 q^{38} + 32 q^{41} - 48 q^{42} - 48 q^{43} - 32 q^{46} - 96 q^{47} + 48 q^{51} - 24 q^{52} - 100 q^{53} + 64 q^{56} - 48 q^{57} - 64 q^{58} - 96 q^{61} + 80 q^{62} + 48 q^{63} - 96 q^{66} + 16 q^{67} + 88 q^{68} + 64 q^{71} - 24 q^{72} + 188 q^{73} - 128 q^{76} + 128 q^{77} - 96 q^{78} - 36 q^{81} - 32 q^{82} - 192 q^{83} + 96 q^{86} + 48 q^{87} - 32 q^{88} + 288 q^{91} + 32 q^{92} + 96 q^{93} - 132 q^{97} + 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 - 12 * q^18 + 48 * q^21 + 16 * q^22 + 16 * q^23 + 24 * q^26 - 32 * q^28 - 80 * q^31 + 16 * q^32 + 48 * q^33 + 24 * q^36 + 108 * q^37 + 64 * q^38 + 32 * q^41 - 48 * q^42 - 48 * q^43 - 32 * q^46 - 96 * q^47 + 48 * q^51 - 24 * q^52 - 100 * q^53 + 64 * q^56 - 48 * q^57 - 64 * q^58 - 96 * q^61 + 80 * q^62 + 48 * q^63 - 96 * q^66 + 16 * q^67 + 88 * q^68 + 64 * q^71 - 24 * q^72 + 188 * q^73 - 128 * q^76 + 128 * q^77 - 96 * q^78 - 36 * q^81 - 32 * q^82 - 192 * q^83 + 96 * q^86 + 48 * q^87 - 32 * q^88 + 288 * q^91 + 32 * q^92 + 96 * q^93 - 132 * q^97 + 124 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

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

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
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$		−	2.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	−2.44949			−0.408248
$7$	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
$9$			3.00000i			0.333333i
$10$		0			0
$11$	5.79796			0.527087			0.263544	−	0.964647i	$-0.415109\pi$
$11$	5.79796			0.527087			0.263544	+	0.964647i	$0.415109\pi$
$12$	2.44949	−	2.44949i	0.204124	−	0.204124i
$13$	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	−0.863401	−	0.504518i	$-0.831670\pi$
$17$	−6.10102	+	6.10102i	−0.358884	+	0.358884i	0.504518	+	0.863401i	$0.331670\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$		−	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
$21$	21.7980			1.03800
$22$	−5.79796	+	5.79796i	−0.263544	+	0.263544i
$23$	18.6969	+	18.6969i	0.812910	+	0.812910i	0.985069	−	0.172159i	$-0.0550742\pi$
$23$	18.6969	+	18.6969i	0.812910	+	0.812910i	−0.172159	+	0.985069i	$0.555074\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$	−13.5959			−0.522920
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	−17.7980	−	17.7980i	−0.635641	−	0.635641i
$29$			6.20204i			0.213863i	0.994266	+	0.106932i	$0.0341026\pi$
$29$			6.20204i			0.213863i	−0.994266	+	0.106932i	$0.965897\pi$
$30$		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
$33$	7.10102	+	7.10102i	0.215182	+	0.215182i
$34$		−	12.2020i		−	0.358884i
$35$		0			0
$36$	6.00000			0.166667
$37$	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
$39$			16.6515i			0.426962i
$40$		0			0
$41$	−1.79796			−0.0438527			−0.0219263	−	0.999760i	$-0.506980\pi$
$41$	−1.79796			−0.0438527			−0.0219263	+	0.999760i	$0.506980\pi$
$42$	−21.7980	+	21.7980i	−0.518999	+	0.518999i
$43$	−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	−0.986585	−	0.163246i	$-0.947803\pi$
$47$	−38.6969	+	38.6969i	−0.823339	+	0.823339i	0.163246	+	0.986585i	$0.447803\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$		−	109.384i		−	2.23232i
$50$		0			0
$51$	−14.9444			−0.293027
$52$	13.5959	−	13.5959i	0.261460	−	0.261460i
$53$	−69.0908	−	69.0908i	−1.30360	−	1.30360i	−0.925947	−	0.377653i	$-0.876731\pi$
$53$	−69.0908	−	69.0908i	−1.30360	−	1.30360i	−0.377653	−	0.925947i	$-0.623269\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	35.5959			0.635641
$57$	7.59592	−	7.59592i	0.133262	−	0.133262i
$58$	−6.20204	−	6.20204i	−0.106932	−	0.106932i
$59$		−	20.0000i		−	0.338983i	−0.985532	−	0.169492i	$-0.945787\pi$
$59$		−	20.0000i		−	0.338983i	0.985532	−	0.169492i	$-0.0542125\pi$
$60$		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
$63$	26.6969	+	26.6969i	0.423761	+	0.423761i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	−14.2020			−0.215182
$67$	−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
$69$			45.7980i			0.663739i
$70$		0			0
$71$	25.7980			0.363352			0.181676	−	0.983358i	$-0.441848\pi$
$71$	25.7980			0.363352			0.181676	+	0.983358i	$0.441848\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	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
$78$	−16.6515	−	16.6515i	−0.213481	−	0.213481i
$79$			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
$81$	−9.00000			−0.111111
$82$	1.79796	−	1.79796i	0.0219263	−	0.0219263i
$83$	−13.7071	−	13.7071i	−0.165146	−	0.165146i	0.619696	−	0.784842i	$-0.287256\pi$
$83$	−13.7071	−	13.7071i	−0.165146	−	0.165146i	−0.784842	+	0.619696i	$0.787256\pi$
$84$		−	43.5959i		−	0.518999i
$85$		0			0
$86$	72.9898			0.848719
$87$	−7.59592	+	7.59592i	−0.0873094	+	0.0873094i
$88$	11.5959	+	11.5959i	0.131772	+	0.131772i
$89$		−	58.6061i		−	0.658496i	−0.944244	−	0.329248i	$-0.893205\pi$
$89$		−	58.6061i		−	0.658496i	0.944244	−	0.329248i	$-0.106795\pi$
$90$		0			0
$91$	120.990			1.32956
$92$	37.3939	−	37.3939i	0.406455	−	0.406455i
$93$	−0.494897	−	0.494897i	−0.00532148	−	0.00532148i
$94$		−	77.3939i		−	0.823339i
$95$		0			0
$96$	9.79796			0.102062
$97$	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
$99$			17.3939i			0.175696i
$100$		0			0
$101$	−128.384			−1.27113			−0.635563	−	0.772049i	$-0.719232\pi$
$101$	−128.384			−1.27113			−0.635563	+	0.772049i	$0.719232\pi$
$102$	14.9444	−	14.9444i	0.146514	−	0.146514i
$103$	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	−0.813819	−	0.581118i	$-0.802615\pi$
$107$	−24.8990	+	24.8990i	−0.232701	+	0.232701i	0.581118	+	0.813819i	$0.302615\pi$
$108$	7.34847	+	7.34847i	0.0680414	+	0.0680414i
$109$			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
$111$	66.1362			0.595822
$112$	−35.5959	+	35.5959i	−0.317821	+	0.317821i
$113$	−8.70714	−	8.70714i	−0.0770544	−	0.0770544i	0.667529	−	0.744584i	$-0.267352\pi$
$113$	−8.70714	−	8.70714i	−0.0770544	−	0.0770544i	−0.744584	+	0.667529i	$0.767352\pi$
$114$			15.1918i			0.133262i
$115$		0			0
$116$	12.4041			0.106932
$117$	−20.3939	+	20.3939i	−0.174307	+	0.174307i
$118$	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
$123$	−2.20204	−	2.20204i	−0.0179028	−	0.0179028i
$124$			0.808164i			0.00651745i
$125$		0			0
$126$	−53.3939			−0.423761
$127$	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
$129$		−	89.3939i		−	0.692976i
$130$		0			0
$131$	−114.202			−0.871771			−0.435886	−	0.900002i	$-0.643565\pi$
$131$	−114.202			−0.871771			−0.435886	+	0.900002i	$0.643565\pi$
$132$	14.2020	−	14.2020i	0.107591	−	0.107591i
$133$	−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	−0.763424	−	0.645898i	$-0.776483\pi$
$137$	−16.1010	+	16.1010i	−0.117526	+	0.117526i	0.645898	+	0.763424i	$0.276483\pi$
$138$	−45.7980	−	45.7980i	−0.331869	−	0.331869i
$139$			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
$141$	−94.7878			−0.672254
$142$	−25.7980	+	25.7980i	−0.181676	+	0.181676i
$143$	39.4143	+	39.4143i	0.275624	+	0.275624i
$144$		−	12.0000i		−	0.0833333i
$145$		0			0
$146$	−113.596			−0.778054
$147$	133.967	−	133.967i	0.911341	−	0.911341i
$148$	−54.0000	−	54.0000i	−0.364865	−	0.364865i
$149$		−	270.767i		−	1.81723i	−0.417634	−	0.908615i	$-0.637141\pi$
$149$		−	270.767i		−	1.81723i	0.417634	−	0.908615i	$-0.362859\pi$
$150$		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
$153$	−18.3031	−	18.3031i	−0.119628	−	0.119628i
$154$			103.192i			0.670077i
$155$		0			0
$156$	33.3031			0.213481
$157$	−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
$159$		−	169.237i		−	1.06439i
$160$		0			0
$161$	332.767			2.06688
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	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	$0.519024\pi$
$167$	−176.677	+	176.677i	−1.05794	+	1.05794i	−0.998215	+	0.0597286i	$0.980976\pi$
$168$	43.5959	+	43.5959i	0.259500	+	0.259500i
$169$		−	76.5755i		−	0.453110i
$170$		0			0
$171$	18.6061			0.108808
$172$	−72.9898	+	72.9898i	−0.424359	+	0.424359i
$173$	−142.889	−	142.889i	−0.825947	−	0.825947i	0.161007	−	0.986953i	$-0.448526\pi$
$173$	−142.889	−	142.889i	−0.825947	−	0.825947i	−0.986953	+	0.161007i	$0.948526\pi$
$174$		−	15.1918i		−	0.0873094i
$175$		0			0
$176$	−23.1918			−0.131772
$177$	24.4949	−	24.4949i	0.138389	−	0.138389i
$178$	58.6061	+	58.6061i	0.329248	+	0.329248i
$179$			133.171i			0.743974i	0.928238	+	0.371987i	$0.121323\pi$
$179$			133.171i			0.743974i	−0.928238	+	0.371987i	$0.878677\pi$
$180$		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
$183$	−77.3939	−	77.3939i	−0.422917	−	0.422917i
$184$			74.7878i			0.406455i
$185$		0			0
$186$	0.989795			0.00532148
$187$	−35.3735	+	35.3735i	−0.189163	+	0.189163i
$188$	77.3939	+	77.3939i	0.411670	+	0.411670i
$189$			65.3939i			0.345999i
$190$		0			0
$191$	−266.606			−1.39584			−0.697922	−	0.716174i	$-0.745892\pi$
$191$	−266.606			−1.39584			−0.697922	+	0.716174i	$0.745892\pi$
$192$	−9.79796	+	9.79796i	−0.0510310	+	0.0510310i
$193$	−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	$-0.403850\pi$
$197$	246.687	−	246.687i	1.25222	−	1.25222i	0.954724	−	0.297493i	$-0.0961505\pi$
$198$	−17.3939	−	17.3939i	−0.0878479	−	0.0878479i
$199$		−	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
$201$	−98.2020			−0.488567
$202$	128.384	−	128.384i	0.635563	−	0.635563i
$203$	55.1918	+	55.1918i	0.271881	+	0.271881i
$204$			29.8888i			0.146514i
$205$		0			0
$206$	−64.9898			−0.315484
$207$	−56.0908	+	56.0908i	−0.270970	+	0.270970i
$208$	−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
$213$	31.5959	+	31.5959i	0.148338	+	0.148338i
$214$		−	49.7980i		−	0.232701i
$215$		0			0
$216$	−14.6969			−0.0680414
$217$	−3.59592	+	3.59592i	−0.0165711	+	0.0165711i
$218$	−130.000	−	130.000i	−0.596330	−	0.596330i
$219$			139.126i			0.635279i
$220$		0			0
$221$	−82.9490			−0.375335
$222$	−66.1362	+	66.1362i	−0.297911	+	0.297911i
$223$	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	−0.608342	−	0.793675i	$-0.708165\pi$
$227$	42.0704	−	42.0704i	0.185332	−	0.185332i	0.793675	+	0.608342i	$0.208165\pi$
$228$	−15.1918	−	15.1918i	−0.0666309	−	0.0666309i
$229$			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
$231$	126.384			0.547115
$232$	−12.4041	+	12.4041i	−0.0534659	+	0.0534659i
$233$	298.262	+	298.262i	1.28010	+	1.28010i	0.940612	+	0.339483i	$0.110252\pi$
$233$	298.262	+	298.262i	1.28010	+	1.28010i	0.339483	+	0.940612i	$0.389748\pi$
$234$		−	40.7878i		−	0.174307i
$235$		0			0
$236$	−40.0000			−0.169492
$237$	−170.697	+	170.697i	−0.720240	+	0.720240i
$238$	−108.586	−	108.586i	−0.456242	−	0.456242i
$239$			37.2122i			0.155700i	0.996965	+	0.0778499i	$0.0248055\pi$
$239$			37.2122i			0.155700i	−0.996965	+	0.0778499i	$0.975195\pi$
$240$		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
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$			126.384i			0.517966i
$245$		0			0
$246$	4.40408			0.0179028
$247$	42.1612	−	42.1612i	0.170693	−	0.170693i
$248$	−0.808164	−	0.808164i	−0.00325873	−	0.00325873i
$249$		−	33.5755i		−	0.134841i
$250$		0			0
$251$	255.414			1.01759			0.508793	−	0.860889i	$-0.330092\pi$
$251$	255.414			1.01759			0.508793	+	0.860889i	$0.330092\pi$
$252$	53.3939	−	53.3939i	0.211880	−	0.211880i
$253$	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	$-0.482827\pi$
$257$	270.485	−	270.485i	1.05247	−	1.05247i	0.998545	−	0.0539246i	$-0.0171731\pi$
$258$	89.3939	+	89.3939i	0.346488	+	0.346488i
$259$		−	480.545i		−	1.85539i
$260$		0			0
$261$	−18.6061			−0.0712878
$262$	114.202	−	114.202i	0.435886	−	0.435886i
$263$	−1.30306	−	1.30306i	−0.00495461	−	0.00495461i	0.704625	−	0.709580i	$-0.251115\pi$
$263$	−1.30306	−	1.30306i	−0.00495461	−	0.00495461i	−0.709580	+	0.704625i	$0.751115\pi$
$264$			28.4041i			0.107591i
$265$		0			0
$266$	110.384			0.414976
$267$	71.7775	−	71.7775i	0.268830	−	0.268830i
$268$	80.1816	+	80.1816i	0.299185	+	0.299185i
$269$			41.1510i			0.152978i	0.997070	+	0.0764889i	$0.0243710\pi$
$269$			41.1510i			0.152978i	−0.997070	+	0.0764889i	$0.975629\pi$
$270$		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
$273$	148.182	+	148.182i	0.542790	+	0.542790i
$274$		−	32.2020i		−	0.117526i
$275$		0			0
$276$	91.5959			0.331869
$277$	−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
$279$		−	1.21225i		−	0.00434497i
$280$		0			0
$281$	242.524			0.863076			0.431538	−	0.902095i	$-0.357971\pi$
$281$	242.524			0.863076			0.431538	+	0.902095i	$0.357971\pi$
$282$	94.7878	−	94.7878i	0.336127	−	0.336127i
$283$	−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
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$			214.555i			0.742405i
$290$		0			0
$291$	39.1668			0.134594
$292$	113.596	−	113.596i	0.389027	−	0.389027i
$293$	60.9092	+	60.9092i	0.207881	+	0.207881i	0.803366	−	0.595485i	$-0.203040\pi$
$293$	60.9092	+	60.9092i	0.207881	+	0.207881i	−0.595485	+	0.803366i	$0.703040\pi$
$294$			267.934i			0.911341i
$295$		0			0
$296$	108.000			0.364865
$297$	−21.3031	+	21.3031i	−0.0717275	+	0.0717275i
$298$	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
$303$	−157.237	−	157.237i	−0.518935	−	0.518935i
$304$			24.8082i			0.0816058i
$305$		0			0
$306$	36.6061			0.119628
$307$	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
$309$			79.5959i			0.257592i
$310$		0			0
$311$	559.737			1.79980			0.899898	−	0.436100i	$-0.143641\pi$
$311$	559.737			1.79980			0.899898	+	0.436100i	$0.143641\pi$
$312$	−33.3031	+	33.3031i	−0.106741	+	0.106741i
$313$	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	$0.550170\pi$
$317$	−362.828	+	362.828i	−1.14457	+	1.14457i	−0.987605	+	0.156962i	$0.949830\pi$
$318$	169.237	+	169.237i	0.532193	+	0.532193i
$319$			35.9592i			0.112725i
$320$		0			0
$321$	−60.9898			−0.189999
$322$	−332.767	+	332.767i	−1.03344	+	1.03344i
$323$	37.8388	+	37.8388i	0.117148	+	0.117148i
$324$			18.0000i			0.0555556i
$325$		0			0
$326$	−224.990			−0.690153
$327$	−159.217	+	159.217i	−0.486902	+	0.486902i
$328$	−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
$333$	81.0000	+	81.0000i	0.243243	+	0.243243i
$334$		−	353.353i		−	1.05794i
$335$		0			0
$336$	−87.1918			−0.259500
$337$	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
$339$		−	21.3281i		−	0.0629146i
$340$		0			0
$341$	−2.34285			−0.00687053
$342$	−18.6061	+	18.6061i	−0.0544039	+	0.0544039i
$343$	−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	−0.902302	−	0.431105i	$-0.858124\pi$
$347$	−163.505	+	163.505i	−0.471196	+	0.471196i	0.431105	+	0.902302i	$0.358124\pi$
$348$	15.1918	+	15.1918i	0.0436547	+	0.0436547i
$349$		−	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
$351$	−49.9546			−0.142321
$352$	23.1918	−	23.1918i	0.0658859	−	0.0658859i
$353$	−261.495	−	261.495i	−0.740779	−	0.740779i	0.231949	−	0.972728i	$-0.425490\pi$
$353$	−261.495	−	261.495i	−0.740779	−	0.740779i	−0.972728	+	0.231949i	$0.925490\pi$
$354$			48.9898i			0.138389i
$355$		0			0
$356$	−117.212			−0.329248
$357$	−132.990	+	132.990i	−0.372520	+	0.372520i
$358$	−133.171	−	133.171i	−0.371987	−	0.371987i
$359$		−	425.090i		−	1.18409i	−0.805903	−	0.592047i	$-0.798320\pi$
$359$		−	425.090i		−	1.18409i	0.805903	−	0.592047i	$-0.201680\pi$
$360$		0			0
$361$	322.535			0.893448
$362$	−137.192	+	137.192i	−0.378983	+	0.378983i
$363$	−107.023	−	107.023i	−0.294828	−	0.294828i
$364$		−	241.980i		−	0.664779i
$365$		0			0
$366$	154.788			0.422917
$367$	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
$369$		−	5.39388i		−	0.0146176i
$370$		0			0
$371$	−1229.68			−3.31449
$372$	−0.989795	+	0.989795i	−0.00266074	+	0.00266074i
$373$	−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
$378$	−65.3939	−	65.3939i	−0.173000	−	0.173000i
$379$		−	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
$381$	123.192			0.323338
$382$	266.606	−	266.606i	0.697922	−	0.697922i
$383$	409.707	+	409.707i	1.06973	+	1.06973i	0.997379	+	0.0723523i	$0.0230506\pi$
$383$	409.707	+	409.707i	1.06973	+	1.06973i	0.0723523	+	0.997379i	$0.476949\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	234.767			0.608206
$387$	109.485	−	109.485i	0.282906	−	0.282906i
$388$	−31.9796	−	31.9796i	−0.0824216	−	0.0824216i
$389$			301.151i			0.774167i	0.922045	+	0.387084i	$0.126518\pi$
$389$			301.151i			0.774167i	−0.922045	+	0.387084i	$0.873482\pi$
$390$		0			0
$391$	−228.141			−0.583480
$392$	218.767	−	218.767i	0.558080	−	0.558080i
$393$	−139.868	−	139.868i	−0.355899	−	0.355899i
$394$			493.373i			1.25222i
$395$		0			0
$396$	34.7878			0.0878479
$397$	−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
$399$		−	135.192i		−	0.338827i
$400$		0			0
$401$	101.233			0.252451			0.126225	−	0.992002i	$-0.459714\pi$
$401$	101.233			0.252451			0.126225	+	0.992002i	$0.459714\pi$
$402$	98.2020	−	98.2020i	0.244284	−	0.244284i
$403$	−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
$408$	−29.8888	−	29.8888i	−0.0732568	−	0.0732568i
$409$		−	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
$411$	−39.4393			−0.0959593
$412$	64.9898	−	64.9898i	0.157742	−	0.157742i
$413$	−177.980	−	177.980i	−0.430943	−	0.430943i
$414$		−	112.182i		−	0.270970i
$415$		0			0
$416$	54.3837			0.130730
$417$	−90.3837	+	90.3837i	−0.216747	+	0.216747i
$418$	35.9592	+	35.9592i	0.0860267	+	0.0860267i
$419$		−	375.959i		−	0.897277i	−0.893713	−	0.448639i	$-0.851909\pi$
$419$		−	375.959i		−	0.897277i	0.893713	−	0.448639i	$-0.148091\pi$
$420$		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
$423$	−116.091	−	116.091i	−0.274446	−	0.274446i
$424$		−	276.363i		−	0.651800i
$425$		0			0
$426$	−63.1918			−0.148338
$427$	−562.343	+	562.343i	−1.31696	+	1.31696i
$428$	49.7980	+	49.7980i	0.116350	+	0.116350i
$429$			96.5449i			0.225046i
$430$		0			0
$431$	−152.182			−0.353090			−0.176545	−	0.984293i	$-0.556492\pi$
$431$	−152.182			−0.353090			−0.176545	+	0.984293i	$0.556492\pi$
$432$	14.6969	−	14.6969i	0.0340207	−	0.0340207i
$433$	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
$438$	−139.126	−	139.126i	−0.317639	−	0.317639i
$439$			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
$441$	328.151			0.744107
$442$	82.9490	−	82.9490i	0.187667	−	0.187667i
$443$	−144.717	−	144.717i	−0.326676	−	0.326676i	0.524645	−	0.851321i	$-0.324198\pi$
$443$	−144.717	−	144.717i	−0.326676	−	0.326676i	−0.851321	+	0.524645i	$0.824198\pi$
$444$		−	132.272i		−	0.297911i
$445$		0			0
$446$	−33.3531			−0.0747826
$447$	331.621	−	331.621i	0.741881	−	0.741881i
$448$	71.1918	+	71.1918i	0.158910	+	0.158910i
$449$		−	846.727i		−	1.88581i	−0.333069	−	0.942903i	$-0.608084\pi$
$449$		−	846.727i		−	1.88581i	0.333069	−	0.942903i	$-0.391916\pi$
$450$		0			0
$451$	−10.4245			−0.0231142
$452$	−17.4143	+	17.4143i	−0.0385272	+	0.0385272i
$453$	26.4745	+	26.4745i	0.0584426	+	0.0584426i
$454$			84.1408i			0.185332i
$455$		0			0
$456$	30.3837			0.0666309
$457$	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
$459$		−	44.8332i		−	0.0976757i
$460$		0			0
$461$	78.7265			0.170773			0.0853867	−	0.996348i	$-0.472787\pi$
$461$	78.7265			0.170773			0.0853867	+	0.996348i	$0.472787\pi$
$462$	−126.384	+	126.384i	−0.273558	+	0.273558i
$463$	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	−0.725390	−	0.688338i	$-0.758340\pi$
$467$	−17.3031	+	17.3031i	−0.0370515	+	0.0370515i	0.688338	+	0.725390i	$0.258340\pi$
$468$	40.7878	+	40.7878i	0.0871533	+	0.0871533i
$469$			713.535i			1.52140i
$470$		0			0
$471$	−301.287			−0.639676
$472$	40.0000	−	40.0000i	0.0847458	−	0.0847458i
$473$	−211.596	−	211.596i	−0.447349	−	0.447349i
$474$		−	341.394i		−	0.720240i
$475$		0			0
$476$	217.171			0.456242
$477$	207.272	−	207.272i	0.434533	−	0.434533i
$478$	−37.2122	−	37.2122i	−0.0778499	−	0.0778499i
$479$			776.727i			1.62156i	0.585352	+	0.810779i	$0.300956\pi$
$479$			776.727i			1.62156i	−0.585352	+	0.810779i	$0.699044\pi$
$480$		0			0
$481$	367.090			0.763180
$482$	−165.939	+	165.939i	−0.344271	+	0.344271i
$483$	407.555	+	407.555i	0.843799	+	0.843799i
$484$			174.767i			0.361090i
$485$		0			0
$486$	22.0454			0.0453609
$487$	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
$489$			275.555i			0.563507i
$490$		0			0
$491$	246.080			0.501180			0.250590	−	0.968093i	$-0.419375\pi$
$491$	246.080			0.501180			0.250590	+	0.968093i	$0.419375\pi$
$492$	−4.40408	+	4.40408i	−0.00895139	+	0.00895139i
$493$	−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
$498$	33.5755	+	33.5755i	0.0674207	+	0.0674207i
$499$			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
$501$	−432.767			−0.863807
$502$	−255.414	+	255.414i	−0.508793	+	0.508793i
$503$	516.817	+	516.817i	1.02747	+	1.02747i	0.999612	+	0.0278580i	$0.00886861\pi$
$503$	516.817	+	516.817i	1.02747	+	1.02747i	0.0278580	+	0.999612i	$0.491131\pi$
$504$			106.788i			0.211880i
$505$		0			0
$506$	−216.808			−0.428475
$507$	93.7855	−	93.7855i	0.184981	−	0.184981i
$508$	−100.586	−	100.586i	−0.198003	−	0.198003i
$509$			452.059i			0.888132i	0.895994	+	0.444066i	$0.146464\pi$
$509$			452.059i			0.888132i	−0.895994	+	0.444066i	$0.853536\pi$
$510$		0			0
$511$	1010.89			1.97825
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	22.7878	+	22.7878i	0.0444206	+	0.0444206i
$514$			540.969i			1.05247i
$515$		0			0
$516$	−178.788			−0.346488
$517$	−224.363	+	224.363i	−0.433971	+	0.433971i
$518$	480.545	+	480.545i	0.927693	+	0.927693i
$519$		−	350.005i		−	0.674383i
$520$		0			0
$521$	779.494			1.49615			0.748075	−	0.663614i	$-0.230978\pi$
$521$	779.494			1.49615			0.748075	+	0.663614i	$0.230978\pi$
$522$	18.6061	−	18.6061i	0.0356439	−	0.0356439i
$523$	−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
$528$	−28.4041	−	28.4041i	−0.0537956	−	0.0537956i
$529$			170.151i			0.321647i
$530$		0			0
$531$	60.0000			0.112994
$532$	−110.384	+	110.384i	−0.207488	+	0.207488i
$533$	−12.2225	−	12.2225i	−0.0229314	−	0.0229314i
$534$			143.555i			0.268830i
$535$		0			0
$536$	−160.363			−0.299185
$537$	−163.101	+	163.101i	−0.303726	+	0.303726i
$538$	−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
$543$	168.025	+	168.025i	0.309438	+	0.309438i
$544$			48.8082i			0.0897209i
$545$		0			0
$546$	−296.363			−0.542790
$547$	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
$549$		−	189.576i		−	0.345311i
$550$		0			0
$551$	38.4653			0.0698100
$552$	−91.5959	+	91.5959i	−0.165935	+	0.165935i
$553$	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	−0.580608	−	0.814183i	$-0.697185\pi$
$557$	130.101	−	130.101i	0.233575	−	0.233575i	0.814183	+	0.580608i	$0.197185\pi$
$558$	1.21225	+	1.21225i	0.00217248	+	0.00217248i
$559$		−	496.182i		−	0.887624i
$560$		0			0
$561$	−86.6469			−0.154451
$562$	−242.524	+	242.524i	−0.431538	+	0.431538i
$563$	−666.879	−	666.879i	−1.18451	−	1.18451i	−0.978563	−	0.205946i	$-0.933973\pi$
$563$	−666.879	−	666.879i	−1.18451	−	1.18451i	−0.205946	−	0.978563i	$-0.566027\pi$
$564$			189.576i			0.336127i
$565$		0			0
$566$	209.435			0.370026
$567$	−80.0908	+	80.0908i	−0.141254	+	0.141254i
$568$	51.5959	+	51.5959i	0.0908379	+	0.0908379i
$569$		−	987.494i		−	1.73549i	−0.497010	−	0.867745i	$-0.665569\pi$
$569$		−	987.494i		−	1.73549i	0.497010	−	0.867745i	$-0.334431\pi$
$570$		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
$573$	−326.524	−	326.524i	−0.569851	−	0.569851i
$574$		−	32.0000i		−	0.0557491i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	−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
$579$		−	287.530i		−	0.496598i
$580$		0			0
$581$	−243.959			−0.419895
$582$	−39.1668	+	39.1668i	−0.0672970	+	0.0672970i
$583$	−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	−0.950651	−	0.310261i	$-0.899584\pi$
$587$	−375.909	+	375.909i	−0.640390	+	0.640390i	0.310261	+	0.950651i	$0.399584\pi$
$588$	−267.934	−	267.934i	−0.455670	−	0.455670i
$589$			2.50613i			0.00425490i
$590$		0			0
$591$	604.257			1.02243
$592$	−108.000	+	108.000i	−0.182432	+	0.182432i
$593$	398.646	+	398.646i	0.672253	+	0.672253i	0.958235	−	0.285982i	$-0.0923198\pi$
$593$	398.646	+	398.646i	0.672253	+	0.672253i	−0.285982	+	0.958235i	$0.592320\pi$
$594$		−	42.6061i		−	0.0717275i
$595$		0			0
$596$	−541.535			−0.908615
$597$	189.303	−	189.303i	0.317091	−	0.317091i
$598$	−254.202	−	254.202i	−0.425087	−	0.425087i
$599$		−	509.131i		−	0.849968i	−0.905201	−	0.424984i	$-0.860280\pi$
$599$		−	509.131i		−	0.849968i	0.905201	−	0.424984i	$-0.139720\pi$
$600$		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
$603$	−120.272	−	120.272i	−0.199457	−	0.199457i
$604$		−	43.2327i		−	0.0715772i
$605$		0			0
$606$	314.474			0.518935
$607$	−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
$609$			135.192i			0.221990i
$610$		0			0
$611$	−526.120			−0.861081
$612$	−36.6061	+	36.6061i	−0.0598139	+	0.0598139i
$613$	−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	−0.306466	−	0.951882i	$-0.599147\pi$
$617$	398.221	−	398.221i	0.645416	−	0.645416i	0.951882	+	0.306466i	$0.0991466\pi$
$618$	−79.5959	−	79.5959i	−0.128796	−	0.128796i
$619$			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
$621$	−137.394			−0.221246
$622$	−559.737	+	559.737i	−0.899898	+	0.899898i
$623$	−521.535	−	521.535i	−0.837134	−	0.837134i
$624$		−	66.6061i		−	0.106741i
$625$		0			0
$626$	−187.535			−0.299576
$627$	44.0408	−	44.0408i	0.0702405	−	0.0702405i
$628$	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
$633$	233.616	+	233.616i	0.369062	+	0.369062i
$634$		−	725.655i		−	1.14457i
$635$		0			0
$636$	−338.474			−0.532193
$637$	743.586	−	743.586i	1.16732	−	1.16732i
$638$	−35.9592	−	35.9592i	−0.0563624	−	0.0563624i
$639$			77.3939i			0.121117i
$640$		0			0
$641$	−378.243			−0.590082			−0.295041	−	0.955485i	$-0.595333\pi$
$641$	−378.243			−0.590082			−0.295041	+	0.955485i	$0.595333\pi$
$642$	60.9898	−	60.9898i	0.0949997	−	0.0949997i
$643$	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	−0.371124	−	0.928583i	$-0.621027\pi$
$647$	360.677	−	360.677i	0.557460	−	0.557460i	0.928583	+	0.371124i	$0.121027\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$		−	115.959i		−	0.178674i
$650$		0			0
$651$	−8.80816			−0.0135302
$652$	224.990	−	224.990i	0.345076	−	0.345076i
$653$	−547.838	−	547.838i	−0.838955	−	0.838955i	0.149766	−	0.988721i	$-0.452148\pi$
$653$	−547.838	−	547.838i	−0.838955	−	0.838955i	−0.988721	+	0.149766i	$0.952148\pi$
$654$		−	318.434i		−	0.486902i
$655$		0			0
$656$	7.19184			0.0109632
$657$	−170.394	+	170.394i	−0.259351	+	0.259351i
$658$	−688.727	−	688.727i	−1.04670	−	1.04670i
$659$		−	25.5755i		−	0.0388096i	−0.999812	−	0.0194048i	$-0.993823\pi$
$659$		−	25.5755i		−	0.0388096i	0.999812	−	0.0194048i	$-0.00617712\pi$
$660$		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
$663$	−101.591	−	101.591i	−0.153230	−	0.153230i
$664$		−	54.8286i		−	0.0825732i
$665$		0			0
$666$	−162.000			−0.243243
$667$	−115.959	+	115.959i	−0.173852	+	0.173852i
$668$	353.353	+	353.353i	0.528972	+	0.528972i
$669$			40.8490i			0.0610598i
$670$		0			0
$671$	−366.384			−0.546026
$672$	87.1918	−	87.1918i	0.129750	−	0.129750i
$673$	−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	$0.505291\pi$
$677$	−688.160	+	688.160i	−1.01648	+	1.01648i	−0.999862	+	0.0166229i	$0.994709\pi$
$678$	21.3281	+	21.3281i	0.0314573	+	0.0314573i
$679$		−	284.586i		−	0.419125i
$680$		0			0
$681$	103.051			0.151323
$682$	2.34285	−	2.34285i	0.00343527	−	0.00343527i
$683$	−1.92959	−	1.92959i	−0.00282518	−	0.00282518i	0.705693	−	0.708518i	$-0.250636\pi$
$683$	−1.92959	−	1.92959i	−0.00282518	−	0.00282518i	−0.708518	+	0.705693i	$0.750636\pi$
$684$		−	37.2122i		−	0.0544039i
$685$		0			0
$686$	1074.71			1.56663
$687$	−213.031	+	213.031i	−0.310088	+	0.310088i
$688$	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
$693$	154.788	+	154.788i	0.223359	+	0.223359i
$694$		−	327.010i		−	0.471196i
$695$		0			0
$696$	−30.3837			−0.0436547
$697$	10.9694	−	10.9694i	0.0157380	−	0.0157380i
$698$	280.000	+	280.000i	0.401146	+	0.401146i
$699$			730.590i			1.04519i
$700$		0			0
$701$	260.222			0.371216			0.185608	−	0.982624i	$-0.440575\pi$
$701$	260.222			0.371216			0.185608	+	0.982624i	$0.440575\pi$
$702$	49.9546	−	49.9546i	0.0711604	−	0.0711604i
$703$	−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
$708$	−48.9898	−	48.9898i	−0.0691946	−	0.0691946i
$709$		−	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
$711$	−418.120			−0.588074
$712$	117.212	−	117.212i	0.164624	−	0.164624i
$713$	−7.55510	−	7.55510i	−0.0105962	−	0.0105962i
$714$		−	265.980i		−	0.372520i
$715$		0			0
$716$	266.343			0.371987
$717$	−45.5755	+	45.5755i	−0.0635642	+	0.0635642i
$718$	425.090	+	425.090i	0.592047	+	0.592047i
$719$			1281.82i			1.78278i	0.453241	+	0.891388i	$0.350268\pi$
$719$			1281.82i			1.78278i	−0.453241	+	0.891388i	$0.649732\pi$
$720$		0			0
$721$	578.343			0.802140
$722$	−322.535	+	322.535i	−0.446724	+	0.446724i
$723$	203.233	+	203.233i	0.281096	+	0.281096i
$724$		−	274.384i		−	0.378983i
$725$		0			0
$726$	214.045			0.294828
$727$	−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
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	445.312			0.609182
$732$	−154.788	+	154.788i	−0.211459	+	0.211459i
$733$	−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
$738$	5.39388	+	5.39388i	0.00730878	+	0.00730878i
$739$		−	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
$741$	103.273			0.139370
$742$	1229.68	−	1229.68i	1.65724	−	1.65724i
$743$	−135.383	−	135.383i	−0.182211	−	0.182211i	0.610108	−	0.792319i	$-0.291126\pi$
$743$	−135.383	−	135.383i	−0.182211	−	0.182211i	−0.792319	+	0.610108i	$0.791126\pi$
$744$		−	1.97959i		−	0.00266074i
$745$		0			0
$746$	421.878			0.565519
$747$	41.1214	−	41.1214i	0.0550488	−	0.0550488i
$748$	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
$753$	312.817	+	312.817i	0.415428	+	0.415428i
$754$		−	84.3224i		−	0.111833i
$755$		0			0
$756$	130.788			0.173000
$757$	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
$759$			265.535i			0.349848i
$760$		0			0
$761$	−616.261			−0.809804			−0.404902	−	0.914360i	$-0.632694\pi$
$761$	−616.261			−0.809804			−0.404902	+	0.914360i	$0.632694\pi$
$762$	−123.192	+	123.192i	−0.161669	+	0.161669i
$763$	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
$768$	19.5959	+	19.5959i	0.0255155	+	0.0255155i
$769$		−	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
$771$	662.549			0.859338
$772$	−234.767	+	234.767i	−0.304103	+	0.304103i
$773$	184.323	+	184.323i	0.238452	+	0.238452i	0.816209	−	0.577757i	$-0.196072\pi$
$773$	184.323	+	184.323i	0.238452	+	0.238452i	−0.577757	+	0.816209i	$0.696072\pi$
$774$			218.969i			0.282906i
$775$		0			0
$776$	63.9592			0.0824216
$777$	588.545	−	588.545i	0.757458	−	0.757458i
$778$	−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
$783$	−22.7878	−	22.7878i	−0.0291031	−	0.0291031i
$784$			437.535i			0.558080i
$785$		0			0
$786$	279.737			0.355899
$787$	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
$789$		−	3.19184i		−	0.00404542i
$790$		0			0
$791$	−154.969			−0.195916
$792$	−34.7878	+	34.7878i	−0.0439239	+	0.0439239i
$793$	−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	−0.333854	−	0.942625i	$-0.608349\pi$
$797$	485.191	−	485.191i	0.608771	−	0.608771i	0.942625	+	0.333854i	$0.108349\pi$
$798$	135.192	+	135.192i	0.169413	+	0.169413i
$799$		−	472.182i		−	0.590966i
$800$		0			0
$801$	175.818			0.219499
$802$	−101.233	+	101.233i	−0.126225	+	0.126225i
$803$	329.312	+	329.312i	0.410102	+	0.410102i
$804$			196.404i			0.244284i
$805$		0			0
$806$	5.49387			0.00681621
$807$	−50.3995	+	50.3995i	−0.0624529	+	0.0624529i
$808$	−256.767	−	256.767i	−0.317781	−	0.317781i
$809$			397.839i			0.491766i	0.969300	+	0.245883i	$0.0790779\pi$
$809$			397.839i			0.491766i	−0.969300	+	0.245883i	$0.920922\pi$
$810$		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
$813$	−593.666	−	593.666i	−0.730217	−	0.730217i
$814$			313.090i			0.384631i
$815$		0			0
$816$	59.7775			0.0732568
$817$	−226.343	+	226.343i	−0.277041	+	0.277041i
$818$	257.110	+	257.110i	0.314316	+	0.314316i
$819$			362.969i			0.443186i
$820$		0			0
$821$	−101.312			−0.123401			−0.0617005	−	0.998095i	$-0.519652\pi$
$821$	−101.312			−0.123401			−0.0617005	+	0.998095i	$0.519652\pi$
$822$	39.4393	−	39.4393i	0.0479797	−	0.0479797i
$823$	−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	−0.452345	−	0.891843i	$-0.649413\pi$
$827$	363.464	−	363.464i	0.439497	−	0.439497i	0.891843	+	0.452345i	$0.149413\pi$
$828$	112.182	+	112.182i	0.135485	+	0.135485i
$829$		−	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
$831$	−127.348			−0.153247
$832$	−54.3837	+	54.3837i	−0.0653650	+	0.0653650i
$833$	667.352	+	667.352i	0.801143	+	0.801143i
$834$		−	180.767i		−	0.216747i
$835$		0			0
$836$	−71.9184			−0.0860267
$837$	1.48469	−	1.48469i	0.00177383	−	0.00177383i
$838$	375.959	+	375.959i	0.448639	+	0.448639i
$839$			705.090i			0.840393i	0.907433	+	0.420197i	$0.138039\pi$
$839$			705.090i			0.840393i	−0.907433	+	0.420197i	$0.861961\pi$
$840$		0			0
$841$	802.535			0.954262
$842$	−158.829	+	158.829i	−0.188633	+	0.188633i
$843$	297.031	+	297.031i	0.352349	+	0.352349i
$844$		−	381.494i		−	0.452007i
$845$		0			0
$846$	232.182			0.274446
$847$	−777.626	+	777.626i	−0.918094	+	0.918094i
$848$	276.363	+	276.363i	0.325900	+	0.325900i
$849$		−	256.504i		−	0.302125i
$850$		0			0
$851$	1009.63			1.18641
$852$	63.1918	−	63.1918i	0.0741688	−	0.0741688i
$853$	−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	−0.743214	−	0.669053i	$-0.766700\pi$
$857$	−63.5561	+	63.5561i	−0.0741612	+	0.0741612i	0.669053	+	0.743214i	$0.266700\pi$
$858$	−96.5449	−	96.5449i	−0.112523	−	0.112523i
$859$			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
$861$	−39.1918			−0.0455190
$862$	152.182	−	152.182i	0.176545	−	0.176545i
$863$	294.797	+	294.797i	0.341596	+	0.341596i	0.856967	−	0.515371i	$-0.172346\pi$
$863$	294.797	+	294.797i	0.341596	+	0.341596i	−0.515371	+	0.856967i	$0.672346\pi$
$864$			29.3939i			0.0340207i
$865$		0			0
$866$	−509.837			−0.588726
$867$	−262.775	+	262.775i	−0.303086	+	0.303086i
$868$	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
$873$	47.9694	+	47.9694i	0.0549477	+	0.0549477i
$874$			231.918i			0.265353i
$875$		0			0
$876$	278.252			0.317639
$877$	−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
$879$			149.196i			0.169734i
$880$		0			0
$881$	−1370.44			−1.55555			−0.777777	−	0.628540i	$-0.783653\pi$
$881$	−1370.44			−1.55555			−0.777777	+	0.628540i	$0.783653\pi$
$882$	−328.151	+	328.151i	−0.372053	+	0.372053i
$883$	−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	−0.356656	−	0.934236i	$-0.616083\pi$
$887$	512.313	−	512.313i	0.577580	−	0.577580i	0.934236	+	0.356656i	$0.116083\pi$
$888$	132.272	+	132.272i	0.148955	+	0.148955i
$889$		−	895.110i		−	1.00687i
$890$		0			0
$891$	−52.1816			−0.0585652
$892$	33.3531	−	33.3531i	0.0373913	−	0.0373913i
$893$	240.000	+	240.000i	0.268757	+	0.268757i
$894$			663.242i			0.741881i
$895$		0			0
$896$	−142.384			−0.158910
$897$	−311.333	+	311.333i	−0.347082	+	0.347082i
$898$	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
$903$	−795.514	−	795.514i	−0.880968	−	0.880968i
$904$		−	34.8286i		−	0.0385272i
$905$		0			0
$906$	−52.9490			−0.0584426
$907$	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
$909$		−	385.151i		−	0.423708i
$910$		0			0
$911$	1338.97			1.46978			0.734890	−	0.678186i	$-0.237234\pi$
$911$	1338.97			1.46978			0.734890	+	0.678186i	$0.237234\pi$
$912$	−30.3837	+	30.3837i	−0.0333154	+	0.0333154i
$913$	−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
$918$	44.8332	+	44.8332i	0.0488379	+	0.0488379i
$919$		−	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
$921$	493.090			0.535385
$922$	−78.7265	+	78.7265i	−0.0853867	+	0.0853867i
$923$	175.373	+	175.373i	0.190004	+	0.190004i
$924$		−	252.767i		−	0.273558i
$925$		0			0
$926$	−922.969			−0.996727
$927$	−97.4847	+	97.4847i	−0.105161	+	0.105161i
$928$	24.8082	+	24.8082i	0.0267329	+	0.0267329i
$929$		−	218.645i		−	0.235355i	−0.993052	−	0.117678i	$-0.962455\pi$
$929$		−	218.645i		−	0.235355i	0.993052	−	0.117678i	$-0.0375449\pi$
$930$		0			0
$931$	−678.402			−0.728681
$932$	596.524	−	596.524i	0.640048	−	0.640048i
$933$	685.535	+	685.535i	0.734764	+	0.734764i
$934$		−	34.6061i		−	0.0370515i
$935$		0			0
$936$	−81.5755			−0.0871533
$937$	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
$939$			229.682i			0.244603i
$940$		0			0
$941$	−588.384			−0.625275			−0.312637	−	0.949873i	$-0.601212\pi$
$941$	−588.384			−0.625275			−0.312637	+	0.949873i	$0.601212\pi$
$942$	301.287	−	301.287i	0.319838	−	0.319838i
$943$	−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	−0.0210265	−	0.999779i	$-0.506693\pi$
$947$	926.879	−	926.879i	0.978752	−	0.978752i	0.999779	+	0.0210265i	$0.00669343\pi$
$948$	341.394	+	341.394i	0.360120	+	0.360120i
$949$			772.220i			0.813720i
$950$		0			0
$951$	−888.742			−0.934535
$952$	−217.171	+	217.171i	−0.228121	+	0.228121i
$953$	−1271.29	−	1271.29i	−1.33399	−	1.33399i	−0.901768	−	0.432220i	$-0.857730\pi$
$953$	−1271.29	−	1271.29i	−1.33399	−	1.33399i	−0.432220	−	0.901768i	$-0.642270\pi$
$954$			414.545i			0.434533i
$955$		0			0
$956$	74.4245			0.0778499
$957$	−44.0408	+	44.0408i	−0.0460197	+	0.0460197i
$958$	−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
$963$	−74.6969	−	74.6969i	−0.0775669	−	0.0775669i
$964$		−	331.878i		−	0.344271i
$965$		0			0
$966$	−815.110			−0.843799
$967$	−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
$969$			92.6857i			0.0956509i
$970$		0			0
$971$	1803.86			1.85773			0.928865	−	0.370419i	$-0.120786\pi$
$971$	1803.86			1.85773			0.928865	+	0.370419i	$0.120786\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	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	−0.812320	−	0.583212i	$-0.801796\pi$
$977$	−223.838	+	223.838i	−0.229107	+	0.229107i	0.583212	+	0.812320i	$0.301796\pi$
$978$	−275.555	−	275.555i	−0.281754	−	0.281754i
$979$		−	339.796i		−	0.347085i
$980$		0			0
$981$	−390.000			−0.397554
$982$	−246.080	+	246.080i	−0.250590	+	0.250590i
$983$	976.536	+	976.536i	0.993424	+	0.993424i	0.999979	−	0.00655459i	$-0.00208641\pi$
$983$	976.536	+	976.536i	0.993424	+	0.993424i	−0.00655459	+	0.999979i	$0.502086\pi$
$984$		−	8.80816i		−	0.00895139i
$985$		0			0
$986$	75.6776			0.0767521
$987$	−843.514	+	843.514i	−0.854624	+	0.854624i
$988$	−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
$993$	17.1714	+	17.1714i	0.0172925	+	0.0172925i
$994$			459.151i			0.461923i
$995$		0			0
$996$	−67.1510			−0.0674207
$997$	−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
$999$			198.409i			0.198607i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.f.a.7.1	✓	4	5.3	odd	4
30.3.f.a.13.1	yes	4	5.4	even	2
90.3.g.d.37.1		4	15.8	even	4
90.3.g.d.73.1		4	15.14	odd	2
150.3.f.b.7.2		4	5.2	odd	4	inner
150.3.f.b.43.2		4	1.1	even	1	trivial
240.3.bg.b.97.2		4	20.3	even	4
240.3.bg.b.193.2		4	20.19	odd	2
450.3.g.j.307.2		4	15.2	even	4
450.3.g.j.343.2		4	3.2	odd	2
720.3.bh.i.433.1		4	60.59	even	2
720.3.bh.i.577.1		4	60.23	odd	4
960.3.bg.e.193.2		4	40.29	even	2
960.3.bg.e.577.2		4	40.13	odd	4
960.3.bg.g.193.1		4	40.19	odd	2
960.3.bg.g.577.1		4	40.3	even	4
1200.3.bg.d.193.1		4	4.3	odd	2
1200.3.bg.d.1057.1		4	20.7	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	150.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(8.89898 - 8.89898i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(8.89898 - 8.89898i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +5.79796 q^{11} +(2.44949 - 2.44949i) q^{12} +(6.79796 + 6.79796i) q^{13} +17.7980i q^{14} -4.00000 q^{16} +(-6.10102 + 6.10102i) q^{17} +(-3.00000 - 3.00000i) q^{18} -6.20204i q^{19} +21.7980 q^{21} +(-5.79796 + 5.79796i) q^{22} +(18.6969 + 18.6969i) q^{23} +4.89898i q^{24} -13.5959 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-17.7980 - 17.7980i) q^{28} +6.20204i q^{29} -0.404082 q^{31} +(4.00000 - 4.00000i) q^{32} +(7.10102 + 7.10102i) q^{33} -12.2020i q^{34} +6.00000 q^{36} +(27.0000 - 27.0000i) q^{37} +(6.20204 + 6.20204i) q^{38} +16.6515i q^{39} -1.79796 q^{41} +(-21.7980 + 21.7980i) q^{42} +(-36.4949 - 36.4949i) q^{43} -11.5959i q^{44} -37.3939 q^{46} +(-38.6969 + 38.6969i) q^{47} +(-4.89898 - 4.89898i) q^{48} -109.384i q^{49} -14.9444 q^{51} +(13.5959 - 13.5959i) q^{52} +(-69.0908 - 69.0908i) q^{53} -7.34847i q^{54} +35.5959 q^{56} +(7.59592 - 7.59592i) q^{57} +(-6.20204 - 6.20204i) q^{58} -20.0000i q^{59} -63.1918 q^{61} +(0.404082 - 0.404082i) q^{62} +(26.6969 + 26.6969i) q^{63} +8.00000i q^{64} -14.2020 q^{66} +(-40.0908 + 40.0908i) q^{67} +(12.2020 + 12.2020i) q^{68} +45.7980i q^{69} +25.7980 q^{71} +(-6.00000 + 6.00000i) q^{72} +(56.7980 + 56.7980i) q^{73} +54.0000i q^{74} -12.4041 q^{76} +(51.5959 - 51.5959i) q^{77} +(-16.6515 - 16.6515i) q^{78} +139.373i q^{79} -9.00000 q^{81} +(1.79796 - 1.79796i) q^{82} +(-13.7071 - 13.7071i) q^{83} -43.5959i q^{84} +72.9898 q^{86} +(-7.59592 + 7.59592i) q^{87} +(11.5959 + 11.5959i) q^{88} -58.6061i q^{89} +120.990 q^{91} +(37.3939 - 37.3939i) q^{92} +(-0.494897 - 0.494897i) q^{93} -77.3939i q^{94} +9.79796 q^{96} +(15.9898 - 15.9898i) q^{97} +(109.384 + 109.384i) q^{98} +17.3939i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 16 q^{7} + 8 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 + 16 * q^7 + 8 * q^8	\( 4 q - 4 q^{2} + 16 q^{7} + 8 q^{8} - 16 q^{11} - 12 q^{13} - 16 q^{16} - 44 q^{17} - 12 q^{18} + 48 q^{21} + 16 q^{22} + 16 q^{23} + 24 q^{26} - 32 q^{28} - 80 q^{31} + 16 q^{32} + 48 q^{33} + 24 q^{36} + 108 q^{37} + 64 q^{38} + 32 q^{41} - 48 q^{42} - 48 q^{43} - 32 q^{46} - 96 q^{47} + 48 q^{51} - 24 q^{52} - 100 q^{53} + 64 q^{56} - 48 q^{57} - 64 q^{58} - 96 q^{61} + 80 q^{62} + 48 q^{63} - 96 q^{66} + 16 q^{67} + 88 q^{68} + 64 q^{71} - 24 q^{72} + 188 q^{73} - 128 q^{76} + 128 q^{77} - 96 q^{78} - 36 q^{81} - 32 q^{82} - 192 q^{83} + 96 q^{86} + 48 q^{87} - 32 q^{88} + 288 q^{91} + 32 q^{92} + 96 q^{93} - 132 q^{97} + 124 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + 16 * q^7 + 8 * q^8 - 16 * q^11 - 12 * q^13 - 16 * q^16 - 44 * q^17 - 12 * q^18 + 48 * q^21 + 16 * q^22 + 16 * q^23 + 24 * q^26 - 32 * q^28 - 80 * q^31 + 16 * q^32 + 48 * q^33 + 24 * q^36 + 108 * q^37 + 64 * q^38 + 32 * q^41 - 48 * q^42 - 48 * q^43 - 32 * q^46 - 96 * q^47 + 48 * q^51 - 24 * q^52 - 100 * q^53 + 64 * q^56 - 48 * q^57 - 64 * q^58 - 96 * q^61 + 80 * q^62 + 48 * q^63 - 96 * q^66 + 16 * q^67 + 88 * q^68 + 64 * q^71 - 24 * q^72 + 188 * q^73 - 128 * q^76 + 128 * q^77 - 96 * q^78 - 36 * q^81 - 32 * q^82 - 192 * q^83 + 96 * q^86 + 48 * q^87 - 32 * q^88 + 288 * q^91 + 32 * q^92 + 96 * q^93 - 132 * q^97 + 124 * q^98

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