LMFDB - Embedded newform 30.3.f.a.7.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [30,3,Mod(7,30)] 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("30.7"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	30.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.817440793081$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.1
Root			$-1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	30.7
Dual form			30.3.f.a.13.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.89898 - 1.00000i) q^{5} -2.44949 q^{6} +(-8.89898 - 8.89898i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(5.89898 + 3.89898i) q^{10} +5.79796 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-6.79796 + 6.79796i) q^{13} -17.7980i q^{14} +(-4.77526 + 7.22474i) q^{15} -4.00000 q^{16} +(6.10102 + 6.10102i) q^{17} +(3.00000 - 3.00000i) q^{18} +6.20204i q^{19} +(2.00000 + 9.79796i) q^{20} +21.7980 q^{21} +(5.79796 + 5.79796i) q^{22} +(-18.6969 + 18.6969i) q^{23} -4.89898i q^{24} +(23.0000 - 9.79796i) q^{25} -13.5959 q^{26} +(3.67423 + 3.67423i) q^{27} +(17.7980 - 17.7980i) q^{28} -6.20204i q^{29} +(-12.0000 + 2.44949i) q^{30} -0.404082 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-7.10102 + 7.10102i) q^{33} +12.2020i q^{34} +(-52.4949 - 34.6969i) q^{35} +6.00000 q^{36} +(-27.0000 - 27.0000i) q^{37} +(-6.20204 + 6.20204i) q^{38} -16.6515i q^{39} +(-7.79796 + 11.7980i) q^{40} -1.79796 q^{41} +(21.7980 + 21.7980i) q^{42} +(36.4949 - 36.4949i) q^{43} +11.5959i q^{44} +(-3.00000 - 14.6969i) q^{45} -37.3939 q^{46} +(38.6969 + 38.6969i) q^{47} +(4.89898 - 4.89898i) q^{48} +109.384i q^{49} +(32.7980 + 13.2020i) q^{50} -14.9444 q^{51} +(-13.5959 - 13.5959i) q^{52} +(69.0908 - 69.0908i) q^{53} +7.34847i q^{54} +(28.4041 - 5.79796i) q^{55} +35.5959 q^{56} +(-7.59592 - 7.59592i) q^{57} +(6.20204 - 6.20204i) q^{58} +20.0000i q^{59} +(-14.4495 - 9.55051i) q^{60} -63.1918 q^{61} +(-0.404082 - 0.404082i) q^{62} +(-26.6969 + 26.6969i) q^{63} -8.00000i q^{64} +(-26.5051 + 40.1010i) q^{65} -14.2020 q^{66} +(40.0908 + 40.0908i) q^{67} +(-12.2020 + 12.2020i) q^{68} -45.7980i q^{69} +(-17.7980 - 87.1918i) q^{70} +25.7980 q^{71} +(6.00000 + 6.00000i) q^{72} +(-56.7980 + 56.7980i) q^{73} -54.0000i q^{74} +(-16.1691 + 40.1691i) q^{75} -12.4041 q^{76} +(-51.5959 - 51.5959i) q^{77} +(16.6515 - 16.6515i) q^{78} -139.373i q^{79} +(-19.5959 + 4.00000i) q^{80} -9.00000 q^{81} +(-1.79796 - 1.79796i) q^{82} +(13.7071 - 13.7071i) q^{83} +43.5959i q^{84} +(35.9898 + 23.7878i) q^{85} +72.9898 q^{86} +(7.59592 + 7.59592i) q^{87} +(-11.5959 + 11.5959i) q^{88} +58.6061i q^{89} +(11.6969 - 17.6969i) q^{90} +120.990 q^{91} +(-37.3939 - 37.3939i) q^{92} +(0.494897 - 0.494897i) q^{93} +77.3939i q^{94} +(6.20204 + 30.3837i) q^{95} +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} + 4 q^{10} - 16 q^{11} + 12 q^{13} - 24 q^{15} - 16 q^{16} + 44 q^{17} + 12 q^{18} + 8 q^{20} + 48 q^{21} - 16 q^{22} - 16 q^{23} + 92 q^{25} + 24 q^{26} + 32 q^{28} - 48 q^{30}+ \cdots - 124 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 16 * q^7 - 8 * q^8 + 4 * q^10 - 16 * q^11 + 12 * q^13 - 24 * q^15 - 16 * q^16 + 44 * q^17 + 12 * q^18 + 8 * q^20 + 48 * q^21 - 16 * q^22 - 16 * q^23 + 92 * q^25 + 24 * q^26 + 32 * q^28 - 48 * q^30 - 80 * q^31 - 16 * q^32 - 48 * q^33 - 112 * q^35 + 24 * q^36 - 108 * q^37 - 64 * q^38 + 8 * q^40 + 32 * q^41 + 48 * q^42 + 48 * q^43 - 12 * q^45 - 32 * q^46 + 96 * q^47 + 92 * q^50 + 48 * q^51 + 24 * q^52 + 100 * q^53 + 192 * q^55 + 64 * q^56 + 48 * q^57 + 64 * q^58 - 48 * q^60 - 96 * q^61 - 80 * q^62 - 48 * q^63 - 204 * q^65 - 96 * q^66 - 16 * q^67 - 88 * q^68 - 32 * q^70 + 64 * q^71 + 24 * q^72 - 188 * q^73 + 48 * q^75 - 128 * q^76 - 128 * q^77 + 96 * q^78 - 36 * q^81 + 32 * q^82 + 192 * q^83 - 52 * q^85 + 96 * q^86 - 48 * q^87 + 32 * q^88 - 12 * q^90 + 288 * q^91 - 32 * q^92 - 96 * q^93 + 64 * q^95 + 132 * q^97 - 124 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	1.00000	+	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
$5$	4.89898	−	1.00000i	0.979796	−	0.200000i
$5$	4.89898	−	1.00000i	0.979796	−	0.200000i
$6$	−2.44949			−0.408248
$7$	−8.89898	−	8.89898i	−1.27128	−	1.27128i	−0.945416	−	0.325867i	$-0.894344\pi$
$7$	−8.89898	−	8.89898i	−1.27128	−	1.27128i	−0.325867	−	0.945416i	$-0.605656\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	5.89898	+	3.89898i	0.589898	+	0.389898i
$11$	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	$-0.870560\pi$
$13$	−6.79796	+	6.79796i	−0.522920	+	0.522920i	0.395532	+	0.918452i	$0.370560\pi$
$14$		−	17.7980i		−	1.27128i
$15$	−4.77526	+	7.22474i	−0.318350	+	0.481650i
$16$	−4.00000			−0.250000
$17$	6.10102	+	6.10102i	0.358884	+	0.358884i	0.863401	−	0.504518i	$-0.168330\pi$
$17$	6.10102	+	6.10102i	0.358884	+	0.358884i	−0.504518	+	0.863401i	$0.668330\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$			6.20204i			0.326423i	0.986591	+	0.163212i	$0.0521853\pi$
$19$			6.20204i			0.326423i	−0.986591	+	0.163212i	$0.947815\pi$
$20$	2.00000	+	9.79796i	0.100000	+	0.489898i
$21$	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	$-0.944926\pi$
$23$	−18.6969	+	18.6969i	−0.812910	+	0.812910i	0.172159	+	0.985069i	$0.444926\pi$
$24$		−	4.89898i		−	0.204124i
$25$	23.0000	−	9.79796i	0.920000	−	0.391918i
$26$	−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	$-0.965897\pi$
$29$		−	6.20204i		−	0.213863i	0.994266	−	0.106932i	$-0.0341026\pi$
$30$	−12.0000	+	2.44949i	−0.400000	+	0.0816497i
$31$	−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
$35$	−52.4949	−	34.6969i	−1.49985	−	0.991341i
$36$	6.00000			0.166667
$37$	−27.0000	−	27.0000i	−0.729730	−	0.729730i	0.240836	−	0.970566i	$-0.422578\pi$
$37$	−27.0000	−	27.0000i	−0.729730	−	0.729730i	−0.970566	+	0.240836i	$0.922578\pi$
$38$	−6.20204	+	6.20204i	−0.163212	+	0.163212i
$39$		−	16.6515i		−	0.426962i
$40$	−7.79796	+	11.7980i	−0.194949	+	0.294949i
$41$	−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	$-0.545114\pi$
$43$	36.4949	−	36.4949i	0.848719	−	0.848719i	0.989973	+	0.141255i	$0.0451137\pi$
$44$			11.5959i			0.263544i
$45$	−3.00000	−	14.6969i	−0.0666667	−	0.326599i
$46$	−37.3939			−0.812910
$47$	38.6969	+	38.6969i	0.823339	+	0.823339i	0.986585	−	0.163246i	$-0.0521965\pi$
$47$	38.6969	+	38.6969i	0.823339	+	0.823339i	−0.163246	+	0.986585i	$0.552197\pi$
$48$	4.89898	−	4.89898i	0.102062	−	0.102062i
$49$			109.384i			2.23232i
$50$	32.7980	+	13.2020i	0.655959	+	0.264041i
$51$	−14.9444			−0.293027
$52$	−13.5959	−	13.5959i	−0.261460	−	0.261460i
$53$	69.0908	−	69.0908i	1.30360	−	1.30360i	0.377653	−	0.925947i	$-0.376731\pi$
$53$	69.0908	−	69.0908i	1.30360	−	1.30360i	0.925947	−	0.377653i	$-0.123269\pi$
$54$			7.34847i			0.136083i
$55$	28.4041	−	5.79796i	0.516438	−	0.105417i
$56$	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	$0.0542125\pi$
$59$			20.0000i			0.338983i	−0.985532	+	0.169492i	$0.945787\pi$
$60$	−14.4495	−	9.55051i	−0.240825	−	0.159175i
$61$	−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
$65$	−26.5051	+	40.1010i	−0.407771	+	0.616939i
$66$	−14.2020			−0.215182
$67$	40.0908	+	40.0908i	0.598370	+	0.598370i	0.939879	−	0.341508i	$-0.110938\pi$
$67$	40.0908	+	40.0908i	0.598370	+	0.598370i	−0.341508	+	0.939879i	$0.610938\pi$
$68$	−12.2020	+	12.2020i	−0.179442	+	0.179442i
$69$		−	45.7980i		−	0.663739i
$70$	−17.7980	−	87.1918i	−0.254257	−	1.24560i
$71$	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	$-0.935436\pi$
$73$	−56.7980	+	56.7980i	−0.778054	+	0.778054i	0.201445	+	0.979500i	$0.435436\pi$
$74$		−	54.0000i		−	0.729730i
$75$	−16.1691	+	40.1691i	−0.215588	+	0.535588i
$76$	−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	$-0.656122\pi$
$79$		−	139.373i		−	1.76422i	0.471042	−	0.882111i	$-0.343878\pi$
$80$	−19.5959	+	4.00000i	−0.244949	+	0.0500000i
$81$	−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	$-0.712744\pi$
$83$	13.7071	−	13.7071i	0.165146	−	0.165146i	0.784842	+	0.619696i	$0.212744\pi$
$84$			43.5959i			0.518999i
$85$	35.9898	+	23.7878i	0.423409	+	0.279856i
$86$	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	$0.106795\pi$
$89$			58.6061i			0.658496i	−0.944244	+	0.329248i	$0.893205\pi$
$90$	11.6969	−	17.6969i	0.129966	−	0.196633i
$91$	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
$95$	6.20204	+	30.3837i	0.0652846	+	0.319828i
$96$	9.79796			0.102062
$97$	−15.9898	−	15.9898i	−0.164843	−	0.164843i	0.619865	−	0.784708i	$-0.287187\pi$
$97$	−15.9898	−	15.9898i	−0.164843	−	0.164843i	−0.784708	+	0.619865i	$0.787187\pi$
$98$	−109.384	+	109.384i	−1.11616	+	1.11616i
$99$		−	17.3939i		−	0.175696i
$100$	19.5959	+	46.0000i	0.195959	+	0.460000i
$101$	−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	$-0.821612\pi$
$103$	−32.4949	+	32.4949i	−0.315484	+	0.315484i	0.531545	+	0.847030i	$0.321612\pi$
$104$		−	27.1918i		−	0.261460i
$105$	106.788	−	21.7980i	1.01703	−	0.207600i
$106$	138.182			1.30360
$107$	24.8990	+	24.8990i	0.232701	+	0.232701i	0.813819	−	0.581118i	$-0.197385\pi$
$107$	24.8990	+	24.8990i	0.232701	+	0.232701i	−0.581118	+	0.813819i	$0.697385\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$		−	130.000i		−	1.19266i	−0.802739	−	0.596330i	$-0.796625\pi$
$109$		−	130.000i		−	1.19266i	0.802739	−	0.596330i	$-0.203375\pi$
$110$	34.2020	+	22.6061i	0.310928	+	0.205510i
$111$	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	$-0.732648\pi$
$113$	8.70714	−	8.70714i	0.0770544	−	0.0770544i	0.744584	+	0.667529i	$0.232648\pi$
$114$		−	15.1918i		−	0.133262i
$115$	−72.8990	+	110.293i	−0.633904	+	0.959068i
$116$	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
$120$	−4.89898	−	24.0000i	−0.0408248	−	0.200000i
$121$	−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
$125$	102.879	−	71.0000i	0.823029	−	0.568000i
$126$	−53.3939			−0.423761
$127$	−50.2929	−	50.2929i	−0.396007	−	0.396007i	0.480815	−	0.876822i	$-0.340341\pi$
$127$	−50.2929	−	50.2929i	−0.396007	−	0.396007i	−0.876822	+	0.480815i	$0.840341\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$			89.3939i			0.692976i
$130$	−66.6061	+	13.5959i	−0.512355	+	0.104584i
$131$	−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
$135$	21.6742	+	14.3258i	0.160550	+	0.106117i
$136$	−24.4041			−0.179442
$137$	16.1010	+	16.1010i	0.117526	+	0.117526i	0.763424	−	0.645898i	$-0.223517\pi$
$137$	16.1010	+	16.1010i	0.117526	+	0.117526i	−0.645898	+	0.763424i	$0.723517\pi$
$138$	45.7980	−	45.7980i	0.331869	−	0.331869i
$139$		−	73.7980i		−	0.530921i	−0.964122	−	0.265460i	$-0.914476\pi$
$139$		−	73.7980i		−	0.530921i	0.964122	−	0.265460i	$-0.0855239\pi$
$140$	69.3939	−	104.990i	0.495671	−	0.749927i
$141$	−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
$145$	−6.20204	−	30.3837i	−0.0427727	−	0.209543i
$146$	−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	$0.362859\pi$
$149$			270.767i			1.81723i	−0.417634	+	0.908615i	$0.637141\pi$
$150$	−56.3383	+	24.0000i	−0.375588	+	0.160000i
$151$	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
$155$	−1.97959	+	0.404082i	−0.0127715	+	0.00260698i
$156$	33.3031			0.213481
$157$	123.000	+	123.000i	0.783439	+	0.783439i	0.980410	−	0.196970i	$-0.0631102\pi$
$157$	123.000	+	123.000i	0.783439	+	0.783439i	−0.196970	+	0.980410i	$0.563110\pi$
$158$	139.373	−	139.373i	0.882111	−	0.882111i
$159$			169.237i			1.06439i
$160$	−23.5959	−	15.5959i	−0.147474	−	0.0974745i
$161$	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	$-0.912278\pi$
$163$	−112.495	+	112.495i	−0.690153	+	0.690153i	0.272113	+	0.962265i	$0.412278\pi$
$164$		−	3.59592i		−	0.0219263i
$165$	−27.6867	+	41.8888i	−0.167798	+	0.253871i
$166$	27.4143			0.165146
$167$	176.677	+	176.677i	1.05794	+	1.05794i	0.998215	+	0.0597286i	$0.0190235\pi$
$167$	176.677	+	176.677i	1.05794	+	1.05794i	0.0597286	+	0.998215i	$0.480976\pi$
$168$	−43.5959	+	43.5959i	−0.259500	+	0.259500i
$169$			76.5755i			0.453110i
$170$	12.2020	+	59.7775i	0.0717767	+	0.351633i
$171$	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	$-0.551474\pi$
$173$	142.889	−	142.889i	0.825947	−	0.825947i	0.986953	+	0.161007i	$0.0514741\pi$
$174$			15.1918i			0.0873094i
$175$	−291.868	−	117.485i	−1.66782	−	0.671341i
$176$	−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	$-0.878677\pi$
$179$		−	133.171i		−	0.743974i	0.928238	−	0.371987i	$-0.121323\pi$
$180$	29.3939	−	6.00000i	0.163299	−	0.0333333i
$181$	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
$185$	−159.272	−	105.272i	−0.860932	−	0.569040i
$186$	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
$190$	−24.1816	+	36.5857i	−0.127272	+	0.192556i
$191$	−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	$-0.608490\pi$
$193$	117.384	−	117.384i	0.608206	−	0.608206i	0.942477	+	0.334271i	$0.108490\pi$
$194$		−	31.9796i		−	0.164843i
$195$	−16.6515	−	81.5755i	−0.0853925	−	0.418336i
$196$	−218.767			−1.11616
$197$	−246.687	−	246.687i	−1.25222	−	1.25222i	−0.954724	−	0.297493i	$-0.903850\pi$
$197$	−246.687	−	246.687i	−1.25222	−	1.25222i	−0.297493	−	0.954724i	$-0.596150\pi$
$198$	17.3939	−	17.3939i	0.0878479	−	0.0878479i
$199$			154.565i			0.776710i	0.921510	+	0.388355i	$0.126957\pi$
$199$			154.565i			0.776710i	−0.921510	+	0.388355i	$0.873043\pi$
$200$	−26.4041	+	65.5959i	−0.132020	+	0.327980i
$201$	−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
$205$	−8.80816	+	1.79796i	−0.0429667	+	0.00877053i
$206$	−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
$210$	128.586	+	84.9898i	0.612313	+	0.404713i
$211$	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
$215$	142.293	−	215.283i	0.661827	−	1.00131i
$216$	−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
$220$	11.5959	+	56.8082i	0.0527087	+	0.258219i
$221$	−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	$-0.766840\pi$
$223$	−16.6765	+	16.6765i	−0.0747826	+	0.0747826i	0.668726	+	0.743509i	$0.266840\pi$
$224$			71.1918i			0.317821i
$225$	−29.3939	−	69.0000i	−0.130639	−	0.306667i
$226$	17.4143			0.0770544
$227$	−42.0704	−	42.0704i	−0.185332	−	0.185332i	0.608342	−	0.793675i	$-0.291835\pi$
$227$	−42.0704	−	42.0704i	−0.185332	−	0.185332i	−0.793675	+	0.608342i	$0.791835\pi$
$228$	15.1918	−	15.1918i	0.0666309	−	0.0666309i
$229$		−	173.939i		−	0.759558i	−0.925077	−	0.379779i	$-0.876000\pi$
$229$		−	173.939i		−	0.759558i	0.925077	−	0.379779i	$-0.124000\pi$
$230$	−183.192	+	37.3939i	−0.796486	+	0.162582i
$231$	126.384			0.547115
$232$	12.4041	+	12.4041i	0.0534659	+	0.0534659i
$233$	−298.262	+	298.262i	−1.28010	+	1.28010i	−0.339483	+	0.940612i	$0.610252\pi$
$233$	−298.262	+	298.262i	−1.28010	+	1.28010i	−0.940612	+	0.339483i	$0.889748\pi$
$234$			40.7878i			0.174307i
$235$	228.272	+	150.879i	0.971372	+	0.642036i
$236$	−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	$-0.975195\pi$
$239$		−	37.2122i		−	0.155700i	0.996965	−	0.0778499i	$-0.0248055\pi$
$240$	19.1010	−	28.8990i	0.0795876	−	0.120412i
$241$	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
$245$	109.384	+	535.868i	0.446464	+	2.18722i
$246$	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
$250$	173.879	+	31.8786i	0.695514	+	0.127514i
$251$	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
$255$	−73.2122	+	14.9444i	−0.287107	+	0.0586054i
$256$	16.0000			0.0625000
$257$	−270.485	−	270.485i	−1.05247	−	1.05247i	−0.998545	−	0.0539246i	$-0.982827\pi$
$257$	−270.485	−	270.485i	−1.05247	−	1.05247i	−0.0539246	−	0.998545i	$-0.517173\pi$
$258$	−89.3939	+	89.3939i	−0.346488	+	0.346488i
$259$			480.545i			1.85539i
$260$	−80.2020	−	53.0102i	−0.308469	−	0.203885i
$261$	−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	$-0.748885\pi$
$263$	1.30306	−	1.30306i	0.00495461	−	0.00495461i	0.709580	+	0.704625i	$0.248885\pi$
$264$		−	28.4041i		−	0.107591i
$265$	269.384	−	407.565i	1.01654	−	1.53798i
$266$	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	$-0.975629\pi$
$269$		−	41.1510i		−	0.152978i	0.997070	−	0.0764889i	$-0.0243710\pi$
$270$	7.34847	+	36.0000i	0.0272166	+	0.133333i
$271$	−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
$275$	133.353	−	56.8082i	0.484920	−	0.206575i
$276$	91.5959			0.331869
$277$	51.9898	+	51.9898i	0.187689	+	0.187689i	0.794696	−	0.607007i	$-0.207630\pi$
$277$	51.9898	+	51.9898i	0.187689	+	0.187689i	−0.607007	+	0.794696i	$0.707630\pi$
$278$	73.7980	−	73.7980i	0.265460	−	0.265460i
$279$			1.21225i			0.00434497i
$280$	174.384	−	35.5959i	0.622799	−	0.127128i
$281$	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	$-0.665734\pi$
$283$	104.717	−	104.717i	0.370026	−	0.370026i	0.867487	+	0.497461i	$0.165734\pi$
$284$			51.5959i			0.181676i
$285$	−44.8082	−	29.6163i	−0.157222	−	0.103917i
$286$	−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
$290$	24.1816	−	36.5857i	0.0833849	−	0.126158i
$291$	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	$-0.796960\pi$
$293$	−60.9092	+	60.9092i	−0.207881	+	0.207881i	0.595485	+	0.803366i	$0.296960\pi$
$294$		−	267.934i		−	0.911341i
$295$	20.0000	+	97.9796i	0.0677966	+	0.332134i
$296$	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
$300$	−80.3383	−	32.3383i	−0.267794	−	0.107794i
$301$	−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
$305$	−309.576	+	63.1918i	−1.01500	+	0.207186i
$306$	36.6061			0.119628
$307$	−201.303	−	201.303i	−0.655710	−	0.655710i	0.298652	−	0.954362i	$-0.403463\pi$
$307$	−201.303	−	201.303i	−0.655710	−	0.655710i	−0.954362	+	0.298652i	$0.903463\pi$
$308$	103.192	−	103.192i	0.335038	−	0.335038i
$309$		−	79.5959i		−	0.257592i
$310$	−2.38367	−	1.57551i	−0.00768926	−	0.00508228i
$311$	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	$-0.817943\pi$
$313$	−93.7673	+	93.7673i	−0.299576	+	0.299576i	0.541272	+	0.840848i	$0.317943\pi$
$314$			246.000i			0.783439i
$315$	−104.091	+	157.485i	−0.330447	+	0.499951i
$316$	278.747			0.882111
$317$	362.828	+	362.828i	1.14457	+	1.14457i	0.987605	+	0.156962i	$0.0501699\pi$
$317$	362.828	+	362.828i	1.14457	+	1.14457i	0.156962	+	0.987605i	$0.449830\pi$
$318$	−169.237	+	169.237i	−0.532193	+	0.532193i
$319$		−	35.9592i		−	0.112725i
$320$	−8.00000	−	39.1918i	−0.0250000	−	0.122474i
$321$	−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
$325$	−89.7469	+	222.959i	−0.276144	+	0.686028i
$326$	−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
$330$	−69.5755	+	14.2020i	−0.210835	+	0.0430365i
$331$	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
$335$	236.495	+	156.313i	0.705955	+	0.466607i
$336$	−87.1918			−0.259500
$337$	−166.373	−	166.373i	−0.493690	−	0.493690i	0.415777	−	0.909467i	$-0.363510\pi$
$337$	−166.373	−	166.373i	−0.493690	−	0.493690i	−0.909467	+	0.415777i	$0.863510\pi$
$338$	−76.5755	+	76.5755i	−0.226555	+	0.226555i
$339$			21.3281i			0.0629146i
$340$	−47.5755	+	71.9796i	−0.139928	+	0.211705i
$341$	−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
$345$	−45.7980	−	224.363i	−0.132748	−	0.650328i
$346$	285.778			0.825947
$347$	163.505	+	163.505i	0.471196	+	0.471196i	0.902302	−	0.431105i	$-0.141876\pi$
$347$	163.505	+	163.505i	0.471196	+	0.471196i	−0.431105	+	0.902302i	$0.641876\pi$
$348$	−15.1918	+	15.1918i	−0.0436547	+	0.0436547i
$349$			280.000i			0.802292i	0.916014	+	0.401146i	$0.131388\pi$
$349$			280.000i			0.802292i	−0.916014	+	0.401146i	$0.868612\pi$
$350$	−174.384	−	409.353i	−0.498239	−	1.16958i
$351$	−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	$-0.574510\pi$
$353$	261.495	−	261.495i	0.740779	−	0.740779i	0.972728	+	0.231949i	$0.0745103\pi$
$354$		−	48.9898i		−	0.138389i
$355$	126.384	−	25.7980i	0.356010	−	0.0726703i
$356$	−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	$0.201680\pi$
$359$			425.090i			1.18409i	−0.805903	+	0.592047i	$0.798320\pi$
$360$	35.3939	+	23.3939i	0.0983163	+	0.0649830i
$361$	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
$365$	−221.454	+	335.050i	−0.606723	+	0.917945i
$366$	154.788			0.422917
$367$	−316.495	−	316.495i	−0.862384	−	0.862384i	0.129231	−	0.991615i	$-0.458749\pi$
$367$	−316.495	−	316.495i	−0.862384	−	0.862384i	−0.991615	+	0.129231i	$0.958749\pi$
$368$	74.7878	−	74.7878i	0.203228	−	0.203228i
$369$			5.39388i			0.0146176i
$370$	−54.0000	−	264.545i	−0.145946	−	0.714986i
$371$	−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	$-0.619051\pi$
$373$	210.939	−	210.939i	0.565519	−	0.565519i	0.930870	+	0.365351i	$0.119051\pi$
$374$			70.7469i			0.189163i
$375$	−39.0431	+	212.957i	−0.104115	+	0.567885i
$376$	−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	$0.150027\pi$
$379$			344.182i			0.908131i	−0.890968	+	0.454065i	$0.849973\pi$
$380$	−60.7673	+	12.4041i	−0.159914	+	0.0326423i
$381$	123.192			0.323338
$382$	−266.606	−	266.606i	−0.697922	−	0.697922i
$383$	−409.707	+	409.707i	−1.06973	+	1.06973i	−0.0723523	+	0.997379i	$0.523051\pi$
$383$	−409.707	+	409.707i	−1.06973	+	1.06973i	−0.997379	+	0.0723523i	$0.976949\pi$
$384$			19.5959i			0.0510310i
$385$	−304.363	−	201.171i	−0.790554	−	0.522523i
$386$	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	$-0.873482\pi$
$389$		−	301.151i		−	0.774167i	0.922045	−	0.387084i	$-0.126518\pi$
$390$	64.9240	−	98.2270i	0.166472	−	0.251864i
$391$	−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
$395$	−139.373	−	682.788i	−0.352844	−	1.72858i
$396$	34.7878			0.0878479
$397$	479.343	+	479.343i	1.20741	+	1.20741i	0.971862	+	0.235551i	$0.0756894\pi$
$397$	479.343	+	479.343i	1.20741	+	1.20741i	0.235551	+	0.971862i	$0.424311\pi$
$398$	−154.565	+	154.565i	−0.388355	+	0.388355i
$399$			135.192i			0.338827i
$400$	−92.0000	+	39.1918i	−0.230000	+	0.0979796i
$401$	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
$405$	−44.0908	+	9.00000i	−0.108866	+	0.0222222i
$406$	−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	$0.101775\pi$
$409$			257.110i			0.628631i	−0.949319	+	0.314316i	$0.898225\pi$
$410$	−10.6061	−	7.01021i	−0.0258686	−	0.0170981i
$411$	−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
$415$	53.4439	−	80.8582i	0.128780	−	0.194839i
$416$	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	$0.148091\pi$
$419$			375.959i			0.897277i	−0.893713	+	0.448639i	$0.851909\pi$
$420$	43.5959	+	213.576i	0.103800	+	0.508513i
$421$	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
$425$	200.101	+	80.5459i	0.470826	+	0.189520i
$426$	−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
$430$	357.576	−	72.9898i	0.831571	−	0.169744i
$431$	−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	$-0.886671\pi$
$433$	−254.918	+	254.918i	−0.588726	+	0.588726i	0.348560	+	0.937286i	$0.386671\pi$
$434$			7.19184i			0.0165711i
$435$	44.8082	+	29.6163i	0.103007	+	0.0680835i
$436$	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	$-0.889244\pi$
$439$		−	299.373i		−	0.681944i	0.940073	−	0.340972i	$-0.110756\pi$
$440$	−45.2122	+	68.4041i	−0.102755	+	0.155464i
$441$	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	$-0.675802\pi$
$443$	144.717	−	144.717i	0.326676	−	0.326676i	0.851321	+	0.524645i	$0.175802\pi$
$444$			132.272i			0.297911i
$445$	58.6061	+	287.110i	0.131699	+	0.645191i
$446$	−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	$0.391916\pi$
$449$			846.727i			1.88581i	−0.333069	+	0.942903i	$0.608084\pi$
$450$	39.6061	−	98.3939i	0.0880136	−	0.218653i
$451$	−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
$455$	592.727	−	120.990i	1.30270	−	0.265912i
$456$	30.3837			0.0666309
$457$	−38.3939	−	38.3939i	−0.0840129	−	0.0840129i	0.663852	−	0.747864i	$-0.268921\pi$
$457$	−38.3939	−	38.3939i	−0.0840129	−	0.0840129i	−0.747864	+	0.663852i	$0.768921\pi$
$458$	173.939	−	173.939i	0.379779	−	0.379779i
$459$			44.8332i			0.0976757i
$460$	−220.586	−	145.798i	−0.479534	−	0.316952i
$461$	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	$-0.998960\pi$
$463$	−461.485	+	461.485i	−0.996727	+	0.996727i	0.00326746	+	0.999995i	$0.498960\pi$
$464$			24.8082i			0.0534659i
$465$	1.92959	−	2.91939i	0.00414967	−	0.00627826i
$466$	−596.524			−1.28010
$467$	17.3031	+	17.3031i	0.0370515	+	0.0370515i	0.725390	−	0.688338i	$-0.241660\pi$
$467$	17.3031	+	17.3031i	0.0370515	+	0.0370515i	−0.688338	+	0.725390i	$0.741660\pi$
$468$	−40.7878	+	40.7878i	−0.0871533	+	0.0871533i
$469$		−	713.535i		−	1.52140i
$470$	77.3939	+	379.151i	0.164668	+	0.806704i
$471$	−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
$475$	60.7673	+	142.647i	0.127931	+	0.300309i
$476$	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	$-0.699044\pi$
$479$		−	776.727i		−	1.62156i	0.585352	−	0.810779i	$-0.300956\pi$
$480$	48.0000	−	9.79796i	0.100000	−	0.0204124i
$481$	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
$485$	−94.3235	−	62.3439i	−0.194481	−	0.128544i
$486$	22.0454			0.0453609
$487$	−439.423	−	439.423i	−0.902307	−	0.902307i	0.0933285	−	0.995635i	$-0.470249\pi$
$487$	−439.423	−	439.423i	−0.902307	−	0.902307i	−0.995635	+	0.0933285i	$0.970249\pi$
$488$	126.384	−	126.384i	0.258983	−	0.258983i
$489$		−	275.555i		−	0.563507i
$490$	−426.485	+	645.252i	−0.870377	+	1.31684i
$491$	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
$495$	−17.3939	−	85.2122i	−0.0351391	−	0.172146i
$496$	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	$-0.795550\pi$
$499$		−	597.839i		−	1.19807i	0.800721	−	0.599037i	$-0.204450\pi$
$500$	142.000	+	205.757i	0.284000	+	0.411514i
$501$	−432.767			−0.863807
$502$	255.414	+	255.414i	0.508793	+	0.508793i
$503$	−516.817	+	516.817i	−1.02747	+	1.02747i	−0.0278580	+	0.999612i	$0.508869\pi$
$503$	−516.817	+	516.817i	−1.02747	+	1.02747i	−0.999612	+	0.0278580i	$0.991131\pi$
$504$		−	106.788i		−	0.211880i
$505$	−628.949	+	128.384i	−1.24544	+	0.254225i
$506$	−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	$-0.853536\pi$
$509$		−	452.059i		−	0.888132i	0.895994	−	0.444066i	$-0.146464\pi$
$510$	−88.1566	−	58.2679i	−0.172856	−	0.114251i
$511$	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
$515$	−126.697	+	191.687i	−0.246013	+	0.372207i
$516$	−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
$520$	−27.1918	−	133.212i	−0.0522920	−	0.256177i
$521$	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	$-0.672067\pi$
$523$	179.283	−	179.283i	0.342797	−	0.342797i	0.857418	+	0.514621i	$0.172067\pi$
$524$		−	228.404i		−	0.435886i
$525$	501.353	−	213.576i	0.954958	−	0.406810i
$526$	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
$530$	676.949	−	138.182i	1.27726	−	0.260720i
$531$	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
$535$	146.879	+	97.0806i	0.274539	+	0.181459i
$536$	−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
$540$	−28.6515	+	43.3485i	−0.0530584	+	0.0802749i
$541$	−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
$545$	−130.000	−	636.867i	−0.238532	−	1.16856i
$546$	−296.363			−0.542790
$547$	−504.372	−	504.372i	−0.922070	−	0.922070i	0.0751053	−	0.997176i	$-0.476071\pi$
$547$	−504.372	−	504.372i	−0.922070	−	0.922070i	−0.997176	+	0.0751053i	$0.976071\pi$
$548$	−32.2020	+	32.2020i	−0.0587628	+	0.0587628i
$549$			189.576i			0.345311i
$550$	190.161	+	76.5449i	0.345748	+	0.139173i
$551$	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
$555$	324.000	−	66.1362i	0.583784	−	0.119164i
$556$	147.596			0.265460
$557$	−130.101	−	130.101i	−0.233575	−	0.233575i	0.580608	−	0.814183i	$-0.302815\pi$
$557$	−130.101	−	130.101i	−0.233575	−	0.233575i	−0.814183	+	0.580608i	$0.802815\pi$
$558$	−1.21225	+	1.21225i	−0.00217248	+	0.00217248i
$559$			496.182i			0.887624i
$560$	209.980	+	138.788i	0.374964	+	0.247835i
$561$	−86.6469			−0.154451
$562$	242.524	+	242.524i	0.431538	+	0.431538i
$563$	666.879	−	666.879i	1.18451	−	1.18451i	0.205946	−	0.978563i	$-0.433973\pi$
$563$	666.879	−	666.879i	1.18451	−	1.18451i	0.978563	−	0.205946i	$-0.0660270\pi$
$564$		−	189.576i		−	0.336127i
$565$	33.9490	−	51.3633i	0.0600867	−	0.0909084i
$566$	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	$0.334431\pi$
$569$			987.494i			1.73549i	−0.497010	+	0.867745i	$0.665569\pi$
$570$	−15.1918	−	74.4245i	−0.0266523	−	0.130569i
$571$	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
$575$	−246.838	+	613.221i	−0.429283	+	1.06647i
$576$	−24.0000			−0.0416667
$577$	463.000	+	463.000i	0.802426	+	0.802426i	0.983474	−	0.181048i	$-0.0579489\pi$
$577$	463.000	+	463.000i	0.802426	+	0.802426i	−0.181048	+	0.983474i	$0.557949\pi$
$578$	214.555	−	214.555i	0.371203	−	0.371203i
$579$			287.530i			0.496598i
$580$	60.7673	−	12.4041i	0.104771	−	0.0213863i
$581$	−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
$585$	120.303	+	79.5153i	0.205646	+	0.135924i
$586$	−121.818			−0.207881
$587$	375.909	+	375.909i	0.640390	+	0.640390i	0.950651	−	0.310261i	$-0.100416\pi$
$587$	375.909	+	375.909i	0.640390	+	0.640390i	−0.310261	+	0.950651i	$0.600416\pi$
$588$	267.934	−	267.934i	0.455670	−	0.455670i
$589$		−	2.50613i		−	0.00425490i
$590$	−77.9796	+	117.980i	−0.132169	+	0.199965i
$591$	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	$-0.907680\pi$
$593$	−398.646	+	398.646i	−0.672253	+	0.672253i	0.285982	+	0.958235i	$0.407680\pi$
$594$			42.6061i			0.0717275i
$595$	−108.586	−	531.959i	−0.182497	−	0.894049i
$596$	−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	$0.139720\pi$
$599$			509.131i			0.849968i	−0.905201	+	0.424984i	$0.860280\pi$
$600$	−48.0000	−	112.677i	−0.0800000	−	0.187794i
$601$	−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
$605$	−428.091	+	87.3837i	−0.707588	+	0.144436i
$606$	314.474			0.518935
$607$	494.030	+	494.030i	0.813887	+	0.813887i	0.985214	−	0.171327i	$-0.0548054\pi$
$607$	494.030	+	494.030i	0.813887	+	0.813887i	−0.171327	+	0.985214i	$0.554805\pi$
$608$	24.8082	−	24.8082i	0.0408029	−	0.0408029i
$609$		−	135.192i		−	0.221990i
$610$	−372.767	−	246.384i	−0.611094	−	0.403908i
$611$	−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	$-0.722755\pi$
$613$	74.1102	−	74.1102i	0.120898	−	0.120898i	0.764967	+	0.644069i	$0.222755\pi$
$614$		−	402.606i		−	0.655710i
$615$	8.58571	−	12.9898i	0.0139605	−	0.0211216i
$616$	206.384			0.335038
$617$	−398.221	−	398.221i	−0.645416	−	0.645416i	0.306466	−	0.951882i	$-0.400853\pi$
$617$	−398.221	−	398.221i	−0.645416	−	0.645416i	−0.951882	+	0.306466i	$0.900853\pi$
$618$	79.5959	−	79.5959i	0.128796	−	0.128796i
$619$		−	838.120i		−	1.35399i	−0.735987	−	0.676995i	$-0.763282\pi$
$619$		−	838.120i		−	1.35399i	0.735987	−	0.676995i	$-0.236718\pi$
$620$	−0.808164	−	3.95918i	−0.00130349	−	0.00638577i
$621$	−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
$625$	433.000	−	450.706i	0.692800	−	0.721130i
$626$	−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
$630$	−261.576	+	53.3939i	−0.415199	+	0.0847522i
$631$	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
$635$	−296.677	−	196.091i	−0.467207	−	0.308804i
$636$	−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
$640$	31.1918	−	47.1918i	0.0487372	−	0.0737372i
$641$	−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	$-0.851667\pi$
$643$	−285.526	+	285.526i	−0.444052	+	0.444052i	0.449319	+	0.893371i	$0.351667\pi$
$644$			665.535i			1.03344i
$645$	89.3939	+	437.939i	0.138595	+	0.678975i
$646$	−75.6776			−0.117148
$647$	−360.677	−	360.677i	−0.557460	−	0.557460i	0.371124	−	0.928583i	$-0.378973\pi$
$647$	−360.677	−	360.677i	−0.557460	−	0.557460i	−0.928583	+	0.371124i	$0.878973\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$			115.959i			0.178674i
$650$	−312.706	+	133.212i	−0.481086	+	0.204942i
$651$	−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	$-0.547852\pi$
$653$	547.838	−	547.838i	0.838955	−	0.838955i	0.988721	+	0.149766i	$0.0478521\pi$
$654$			318.434i			0.486902i
$655$	−559.473	+	114.202i	−0.854158	+	0.174354i
$656$	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	$0.00617712\pi$
$659$			25.5755i			0.0388096i	−0.999812	+	0.0194048i	$0.993823\pi$
$660$	−83.7775	−	55.3735i	−0.126936	−	0.0838992i
$661$	−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
$665$	215.192	−	325.576i	0.323597	−	0.489587i
$666$	−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
$670$	80.1816	+	392.808i	0.119674	+	0.586281i
$671$	−366.384			−0.546026
$672$	−87.1918	−	87.1918i	−0.129750	−	0.129750i
$673$	902.857	−	902.857i	1.34154	−	1.34154i	0.447014	−	0.894527i	$-0.352487\pi$
$673$	902.857	−	902.857i	1.34154	−	1.34154i	0.894527	−	0.447014i	$-0.147513\pi$
$674$		−	332.747i		−	0.493690i
$675$	120.507	+	48.5074i	0.178529	+	0.0718628i
$676$	−153.151			−0.226555
$677$	688.160	+	688.160i	1.01648	+	1.01648i	0.999862	+	0.0166229i	$0.00529149\pi$
$677$	688.160	+	688.160i	1.01648	+	1.01648i	0.0166229	+	0.999862i	$0.494709\pi$
$678$	−21.3281	+	21.3281i	−0.0314573	+	0.0314573i
$679$			284.586i			0.419125i
$680$	−119.555	+	24.4041i	−0.175816	+	0.0358884i
$681$	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	$-0.749364\pi$
$683$	1.92959	−	1.92959i	0.00282518	−	0.00282518i	0.708518	+	0.705693i	$0.249364\pi$
$684$			37.2122i			0.0544039i
$685$	94.9796	+	62.7775i	0.138656	+	0.0916461i
$686$	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
$690$	178.565	−	270.161i	0.258790	−	0.391538i
$691$	−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
$695$	−73.7980	−	361.535i	−0.106184	−	0.520194i
$696$	−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
$700$	234.969	−	583.737i	0.335671	−	0.833910i
$701$	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
$705$	−464.363	+	94.7878i	−0.658671	+	0.134451i
$706$	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	$0.0341043\pi$
$709$			151.637i			0.213874i	−0.994266	+	0.106937i	$0.965896\pi$
$710$	152.182	+	100.586i	0.214340	+	0.141670i
$711$	−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
$715$	−153.675	+	232.504i	−0.214931	+	0.325181i
$716$	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	$-0.649732\pi$
$719$		−	1281.82i		−	1.78278i	0.453241	−	0.891388i	$-0.350268\pi$
$720$	12.0000	+	58.7878i	0.0166667	+	0.0816497i
$721$	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
$725$	−60.7673	−	142.647i	−0.0838170	−	0.196754i
$726$	214.045			0.294828
$727$	638.352	+	638.352i	0.878063	+	0.878063i	0.993334	−	0.115271i	$-0.0367736\pi$
$727$	638.352	+	638.352i	0.878063	+	0.878063i	−0.115271	+	0.993334i	$0.536774\pi$
$728$	−241.980	+	241.980i	−0.332390	+	0.332390i
$729$			27.0000i			0.0370370i
$730$	−556.504	+	113.596i	−0.762334	+	0.155611i
$731$	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	$-0.623763\pi$
$733$	400.414	−	400.414i	0.546268	−	0.546268i	0.925359	+	0.379091i	$0.123763\pi$
$734$		−	632.990i		−	0.862384i
$735$	−790.269	−	522.335i	−1.07520	−	0.710660i
$736$	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	$0.0833584\pi$
$739$			382.647i			0.517790i	−0.965905	+	0.258895i	$0.916642\pi$
$740$	210.545	−	318.545i	0.284520	−	0.430466i
$741$	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	$-0.708874\pi$
$743$	135.383	−	135.383i	0.182211	−	0.182211i	0.792319	+	0.610108i	$0.208874\pi$
$744$			1.97959i			0.00266074i
$745$	270.767	+	1326.48i	0.363446	+	1.78051i
$746$	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
$750$	−252.000	+	173.914i	−0.336000	+	0.231885i
$751$	−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
$755$	105.898	−	21.6163i	0.140262	−	0.0286309i
$756$	130.788			0.173000
$757$	−917.908	−	917.908i	−1.21256	−	1.21256i	−0.970182	−	0.242379i	$-0.922072\pi$
$757$	−917.908	−	917.908i	−1.21256	−	1.21256i	−0.242379	−	0.970182i	$-0.577928\pi$
$758$	−344.182	+	344.182i	−0.454065	+	0.454065i
$759$		−	265.535i		−	0.349848i
$760$	−73.1714	−	48.3633i	−0.0962782	−	0.0636359i
$761$	−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
$765$	71.3633	−	107.969i	0.0932853	−	0.141136i
$766$	−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	$0.0320142\pi$
$769$			154.424i			0.200812i	−0.994947	+	0.100406i	$0.967986\pi$
$770$	−103.192	−	505.535i	−0.134015	−	0.656539i
$771$	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	$-0.803928\pi$
$773$	−184.323	+	184.323i	−0.238452	+	0.238452i	0.577757	+	0.816209i	$0.303928\pi$
$774$		−	218.969i		−	0.282906i
$775$	−9.29389	+	3.95918i	−0.0119921	+	0.00510862i
$776$	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
$780$	163.151	−	33.3031i	0.209168	−	0.0426962i
$781$	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
$785$	725.574	+	479.574i	0.924299	+	0.610923i
$786$	279.737			0.355899
$787$	−784.858	−	784.858i	−0.997278	−	0.997278i	0.00271783	−	0.999996i	$-0.499135\pi$
$787$	−784.858	−	784.858i	−0.997278	−	0.997278i	−0.999996	+	0.00271783i	$0.999135\pi$
$788$	493.373	−	493.373i	0.626108	−	0.626108i
$789$			3.19184i			0.00404542i
$790$	543.414	−	822.161i	0.687866	−	1.04071i
$791$	−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
$795$	169.237	+	829.090i	0.212877	+	1.04288i
$796$	−309.131			−0.388355
$797$	−485.191	−	485.191i	−0.608771	−	0.608771i	0.333854	−	0.942625i	$-0.391651\pi$
$797$	−485.191	−	485.191i	−0.608771	−	0.608771i	−0.942625	+	0.333854i	$0.891651\pi$
$798$	−135.192	+	135.192i	−0.169413	+	0.169413i
$799$			472.182i			0.590966i
$800$	−131.192	−	52.8082i	−0.163990	−	0.0660102i
$801$	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
$805$	1630.22	−	332.767i	2.02512	−	0.413376i
$806$	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	$-0.920922\pi$
$809$		−	397.839i		−	0.491766i	0.969300	−	0.245883i	$-0.0790779\pi$
$810$	−53.0908	−	35.0908i	−0.0655442	−	0.0433220i
$811$	−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
$815$	−438.615	+	663.605i	−0.538178	+	0.814239i
$816$	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
$820$	−3.59592	−	17.6163i	−0.00438527	−	0.0214833i
$821$	−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	$-0.731318\pi$
$823$	68.2724	−	68.2724i	0.0829556	−	0.0829556i	0.747367	+	0.664411i	$0.231318\pi$
$824$		−	129.980i		−	0.157742i
$825$	−93.7480	+	232.899i	−0.113634	+	0.282302i
$826$	355.959			0.430943
$827$	−363.464	−	363.464i	−0.439497	−	0.439497i	0.452345	−	0.891843i	$-0.350587\pi$
$827$	−363.464	−	363.464i	−0.439497	−	0.439497i	−0.891843	+	0.452345i	$0.850587\pi$
$828$	−112.182	+	112.182i	−0.135485	+	0.135485i
$829$			891.535i			1.07543i	0.843125	+	0.537717i	$0.180713\pi$
$829$			891.535i			1.07543i	−0.843125	+	0.537717i	$0.819287\pi$
$830$	134.302	−	27.4143i	0.161810	−	0.0330293i
$831$	−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
$835$	1042.21	+	688.858i	1.24816	+	0.824980i
$836$	−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	$-0.861961\pi$
$839$		−	705.090i		−	0.840393i	0.907433	−	0.420197i	$-0.138039\pi$
$840$	−169.980	+	257.171i	−0.202357	+	0.306156i
$841$	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
$845$	76.5755	+	375.142i	0.0906219	+	0.443955i
$846$	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
$850$	119.555	+	280.647i	0.140653	+	0.330173i
$851$	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	$-0.628160\pi$
$853$	450.555	−	450.555i	0.528201	−	0.528201i	0.920036	+	0.391835i	$0.128160\pi$
$854$			1124.69i			1.31696i
$855$	91.1510	−	18.6061i	0.106609	−	0.0217615i
$856$	−99.5959			−0.116350
$857$	63.5561	+	63.5561i	0.0741612	+	0.0741612i	0.743214	−	0.669053i	$-0.233300\pi$
$857$	63.5561	+	63.5561i	0.0741612	+	0.0741612i	−0.669053	+	0.743214i	$0.733300\pi$
$858$	96.5449	−	96.5449i	0.112523	−	0.112523i
$859$		−	1467.53i		−	1.70842i	−0.519928	−	0.854210i	$-0.674041\pi$
$859$		−	1467.53i		−	1.70842i	0.519928	−	0.854210i	$-0.325959\pi$
$860$	430.565	+	284.586i	0.500657	+	0.330914i
$861$	−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	$-0.827654\pi$
$863$	−294.797	+	294.797i	−0.341596	+	0.341596i	0.515371	+	0.856967i	$0.327654\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	557.120	−	842.898i	0.644070	−	0.974448i
$866$	−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
$870$	15.1918	+	74.4245i	0.0174619	+	0.0855454i
$871$	−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
$875$	−1547.34	−	283.687i	−1.76839	−	0.324213i
$876$	278.252			0.317639
$877$	113.102	+	113.102i	0.128965	+	0.128965i	0.768643	−	0.639678i	$-0.220932\pi$
$877$	113.102	+	113.102i	0.128965	+	0.128965i	−0.639678	+	0.768643i	$0.720932\pi$
$878$	299.373	−	299.373i	0.340972	−	0.340972i
$879$		−	149.196i		−	0.169734i
$880$	−113.616	+	23.1918i	−0.129109	+	0.0263544i
$881$	−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	$-0.705094\pi$
$883$	175.587	−	175.587i	0.198852	−	0.198852i	0.799508	+	0.600655i	$0.205094\pi$
$884$		−	165.898i		−	0.187667i
$885$	−144.495	−	95.5051i	−0.163271	−	0.107915i
$886$	289.435			0.326676
$887$	−512.313	−	512.313i	−0.577580	−	0.577580i	0.356656	−	0.934236i	$-0.383917\pi$
$887$	−512.313	−	512.313i	−0.577580	−	0.577580i	−0.934236	+	0.356656i	$0.883917\pi$
$888$	−132.272	+	132.272i	−0.148955	+	0.148955i
$889$			895.110i			1.00687i
$890$	−228.504	+	345.716i	−0.256746	+	0.388445i
$891$	−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
$895$	−133.171	−	652.404i	−0.148795	−	0.728943i
$896$	−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
$900$	138.000	−	58.7878i	0.153333	−	0.0653197i
$901$	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
$905$	672.100	−	137.192i	0.742652	−	0.151593i
$906$	−52.9490			−0.0584426
$907$	−922.697	−	922.697i	−1.01731	−	1.01731i	−0.999848	−	0.0174589i	$-0.994442\pi$
$907$	−922.697	−	922.697i	−1.01731	−	1.01731i	−0.0174589	−	0.999848i	$-0.505558\pi$
$908$	84.1408	−	84.1408i	0.0926661	−	0.0926661i
$909$			385.151i			0.423708i
$910$	713.716	+	471.737i	0.784304	+	0.518392i
$911$	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
$915$	301.757	−	456.545i	0.329789	−	0.498956i
$916$	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	$0.268139\pi$
$919$			1371.57i			1.49246i	−0.665687	+	0.746231i	$0.731861\pi$
$920$	−74.7878	−	366.384i	−0.0812910	−	0.398243i
$921$	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
$925$	−885.545	−	356.455i	−0.957346	−	0.385357i
$926$	−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	$0.0375449\pi$
$929$			218.645i			0.235355i	−0.993052	+	0.117678i	$0.962455\pi$
$930$	4.84898	−	0.989795i	0.00521396	−	0.00106430i
$931$	−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
$935$	208.667	+	137.920i	0.223174	+	0.147508i
$936$	−81.5755			−0.0871533
$937$	−1127.38	−	1127.38i	−1.20318	−	1.20318i	−0.973193	−	0.229992i	$-0.926130\pi$
$937$	−1127.38	−	1127.38i	−1.20318	−	1.20318i	−0.229992	−	0.973193i	$-0.573870\pi$
$938$	713.535	−	713.535i	0.760698	−	0.760698i
$939$		−	229.682i		−	0.244603i
$940$	−301.757	+	456.545i	−0.321018	+	0.485686i
$941$	−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
$945$	−65.3939	−	320.363i	−0.0691999	−	0.339009i
$946$	423.192			0.447349
$947$	−926.879	−	926.879i	−0.978752	−	0.978752i	0.0210265	−	0.999779i	$-0.493307\pi$
$947$	−926.879	−	926.879i	−0.978752	−	0.978752i	−0.999779	+	0.0210265i	$0.993307\pi$
$948$	−341.394	+	341.394i	−0.360120	+	0.360120i
$949$		−	772.220i		−	0.813720i
$950$	−81.8796	+	203.414i	−0.0861891	+	0.214120i
$951$	−888.742			−0.934535
$952$	217.171	+	217.171i	0.228121	+	0.228121i
$953$	1271.29	−	1271.29i	1.33399	−	1.33399i	0.432220	−	0.901768i	$-0.357730\pi$
$953$	1271.29	−	1271.29i	1.33399	−	1.33399i	0.901768	−	0.432220i	$-0.142270\pi$
$954$		−	414.545i		−	0.434533i
$955$	−1306.10	+	266.606i	−1.36764	+	0.279169i
$956$	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
$960$	57.7980	+	38.2020i	0.0602062	+	0.0397938i
$961$	−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
$965$	457.677	−	692.444i	0.474276	−	0.717558i
$966$	−815.110			−0.843799
$967$	753.121	+	753.121i	0.778823	+	0.778823i	0.979631	−	0.200808i	$-0.0643567\pi$
$967$	753.121	+	753.121i	0.778823	+	0.778823i	−0.200808	+	0.979631i	$0.564357\pi$
$968$	174.767	−	174.767i	0.180545	−	0.180545i
$969$		−	92.6857i		−	0.0956509i
$970$	−31.9796	−	156.667i	−0.0329686	−	0.161513i
$971$	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
$975$	−163.151	−	382.985i	−0.167334	−	0.392805i
$976$	252.767			0.258983
$977$	223.838	+	223.838i	0.229107	+	0.229107i	0.812320	−	0.583212i	$-0.198204\pi$
$977$	223.838	+	223.838i	0.229107	+	0.229107i	−0.583212	+	0.812320i	$0.698204\pi$
$978$	275.555	−	275.555i	0.281754	−	0.281754i
$979$			339.796i			0.347085i
$980$	−1071.74	+	218.767i	−1.09361	+	0.223232i
$981$	−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	$-0.997914\pi$
$983$	−976.536	+	976.536i	−0.993424	+	0.993424i	0.00655459	+	0.999979i	$0.497914\pi$
$984$			8.80816i			0.00895139i
$985$	−1455.20	−	961.827i	−1.47736	−	0.976474i
$986$	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
$990$	67.8184	−	102.606i	0.0685034	−	0.103643i
$991$	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
$995$	154.565	+	757.212i	0.155342	+	0.761017i
$996$	−67.1510			−0.0674207
$997$	852.616	+	852.616i	0.855182	+	0.855182i	0.990766	−	0.135584i	$-0.0432911\pi$
$997$	852.616	+	852.616i	0.855182	+	0.855182i	−0.135584	+	0.990766i	$0.543291\pi$
$998$	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	30.3.f.a.7.1	✓	4
3.2	odd	2		90.3.g.d.37.1		4
4.3	odd	2		240.3.bg.b.97.2		4
5.2	odd	4		150.3.f.b.43.2		4
5.3	odd	4	inner	30.3.f.a.13.1	yes	4
5.4	even	2		150.3.f.b.7.2		4
8.3	odd	2		960.3.bg.g.577.1		4
8.5	even	2		960.3.bg.e.577.2		4
12.11	even	2		720.3.bh.i.577.1		4
15.2	even	4		450.3.g.j.343.2		4
15.8	even	4		90.3.g.d.73.1		4
15.14	odd	2		450.3.g.j.307.2		4
20.3	even	4		240.3.bg.b.193.2		4
20.7	even	4		1200.3.bg.d.193.1		4
20.19	odd	2		1200.3.bg.d.1057.1		4
40.3	even	4		960.3.bg.g.193.1		4
40.13	odd	4		960.3.bg.e.193.2		4
60.23	odd	4		720.3.bh.i.433.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.f.a.7.1	✓	4	1.1	even	1	trivial
30.3.f.a.13.1	yes	4	5.3	odd	4	inner
90.3.g.d.37.1		4	3.2	odd	2
90.3.g.d.73.1		4	15.8	even	4
150.3.f.b.7.2		4	5.4	even	2
150.3.f.b.43.2		4	5.2	odd	4
240.3.bg.b.97.2		4	4.3	odd	2
240.3.bg.b.193.2		4	20.3	even	4
450.3.g.j.307.2		4	15.14	odd	2
450.3.g.j.343.2		4	15.2	even	4
720.3.bh.i.433.1		4	60.23	odd	4
720.3.bh.i.577.1		4	12.11	even	2
960.3.bg.e.193.2		4	40.13	odd	4
960.3.bg.e.577.2		4	8.5	even	2
960.3.bg.g.193.1		4	40.3	even	4
960.3.bg.g.577.1		4	8.3	odd	2
1200.3.bg.d.193.1		4	20.7	even	4
1200.3.bg.d.1057.1		4	20.19	odd	2

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:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	30.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} +(4.89898 - 1.00000i) q^{5} -2.44949 q^{6} +(-8.89898 - 8.89898i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(5.89898 + 3.89898i) q^{10} +5.79796 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-6.79796 + 6.79796i) q^{13} -17.7980i q^{14} +(-4.77526 + 7.22474i) q^{15} -4.00000 q^{16} +(6.10102 + 6.10102i) q^{17} +(3.00000 - 3.00000i) q^{18} +6.20204i q^{19} +(2.00000 + 9.79796i) q^{20} +21.7980 q^{21} +(5.79796 + 5.79796i) q^{22} +(-18.6969 + 18.6969i) q^{23} -4.89898i q^{24} +(23.0000 - 9.79796i) q^{25} -13.5959 q^{26} +(3.67423 + 3.67423i) q^{27} +(17.7980 - 17.7980i) q^{28} -6.20204i q^{29} +(-12.0000 + 2.44949i) q^{30} -0.404082 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-7.10102 + 7.10102i) q^{33} +12.2020i q^{34} +(-52.4949 - 34.6969i) q^{35} +6.00000 q^{36} +(-27.0000 - 27.0000i) q^{37} +(-6.20204 + 6.20204i) q^{38} -16.6515i q^{39} +(-7.79796 + 11.7980i) q^{40} -1.79796 q^{41} +(21.7980 + 21.7980i) q^{42} +(36.4949 - 36.4949i) q^{43} +11.5959i q^{44} +(-3.00000 - 14.6969i) q^{45} -37.3939 q^{46} +(38.6969 + 38.6969i) q^{47} +(4.89898 - 4.89898i) q^{48} +109.384i q^{49} +(32.7980 + 13.2020i) q^{50} -14.9444 q^{51} +(-13.5959 - 13.5959i) q^{52} +(69.0908 - 69.0908i) q^{53} +7.34847i q^{54} +(28.4041 - 5.79796i) q^{55} +35.5959 q^{56} +(-7.59592 - 7.59592i) q^{57} +(6.20204 - 6.20204i) q^{58} +20.0000i q^{59} +(-14.4495 - 9.55051i) q^{60} -63.1918 q^{61} +(-0.404082 - 0.404082i) q^{62} +(-26.6969 + 26.6969i) q^{63} -8.00000i q^{64} +(-26.5051 + 40.1010i) q^{65} -14.2020 q^{66} +(40.0908 + 40.0908i) q^{67} +(-12.2020 + 12.2020i) q^{68} -45.7980i q^{69} +(-17.7980 - 87.1918i) q^{70} +25.7980 q^{71} +(6.00000 + 6.00000i) q^{72} +(-56.7980 + 56.7980i) q^{73} -54.0000i q^{74} +(-16.1691 + 40.1691i) q^{75} -12.4041 q^{76} +(-51.5959 - 51.5959i) q^{77} +(16.6515 - 16.6515i) q^{78} -139.373i q^{79} +(-19.5959 + 4.00000i) q^{80} -9.00000 q^{81} +(-1.79796 - 1.79796i) q^{82} +(13.7071 - 13.7071i) q^{83} +43.5959i q^{84} +(35.9898 + 23.7878i) q^{85} +72.9898 q^{86} +(7.59592 + 7.59592i) q^{87} +(-11.5959 + 11.5959i) q^{88} +58.6061i q^{89} +(11.6969 - 17.6969i) q^{90} +120.990 q^{91} +(-37.3939 - 37.3939i) q^{92} +(0.494897 - 0.494897i) q^{93} +77.3939i q^{94} +(6.20204 + 30.3837i) q^{95} +9.79796 q^{96} +(-15.9898 - 15.9898i) q^{97} +(-109.384 + 109.384i) q^{98} -17.3939i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 16 q^{7} - 8 q^{8} + 4 q^{10} - 16 q^{11} + 12 q^{13} - 24 q^{15} - 16 q^{16} + 44 q^{17} + 12 q^{18} + 8 q^{20} + 48 q^{21} - 16 q^{22} - 16 q^{23} + 92 q^{25} + 24 q^{26} + 32 q^{28} - 48 q^{30}+ \cdots - 124 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 16 * q^7 - 8 * q^8 + 4 * q^10 - 16 * q^11 + 12 * q^13 - 24 * q^15 - 16 * q^16 + 44 * q^17 + 12 * q^18 + 8 * q^20 + 48 * q^21 - 16 * q^22 - 16 * q^23 + 92 * q^25 + 24 * q^26 + 32 * q^28 - 48 * q^30 - 80 * q^31 - 16 * q^32 - 48 * q^33 - 112 * q^35 + 24 * q^36 - 108 * q^37 - 64 * q^38 + 8 * q^40 + 32 * q^41 + 48 * q^42 + 48 * q^43 - 12 * q^45 - 32 * q^46 + 96 * q^47 + 92 * q^50 + 48 * q^51 + 24 * q^52 + 100 * q^53 + 192 * q^55 + 64 * q^56 + 48 * q^57 + 64 * q^58 - 48 * q^60 - 96 * q^61 - 80 * q^62 - 48 * q^63 - 204 * q^65 - 96 * q^66 - 16 * q^67 - 88 * q^68 - 32 * q^70 + 64 * q^71 + 24 * q^72 - 188 * q^73 + 48 * q^75 - 128 * q^76 - 128 * q^77 + 96 * q^78 - 36 * q^81 + 32 * q^82 + 192 * q^83 - 52 * q^85 + 96 * q^86 - 48 * q^87 + 32 * q^88 - 12 * q^90 + 288 * q^91 - 32 * q^92 - 96 * q^93 + 64 * q^95 + 132 * q^97 - 124 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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