LMFDB - Embedded newform 930.2.s.d.439.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(439,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("930.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.4
Character	$\chi$	$=$	930.439
Dual form			930.2.s.d.769.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-0.347530 + 2.20890i) q^{5} +(0.500000 - 0.866025i) q^{6} +(3.10811 + 1.79447i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-0.347530 + 2.20890i) q^{5} +(0.500000 - 0.866025i) q^{6} +(3.10811 + 1.79447i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(2.20890 + 0.347530i) q^{10} +(0.121003 + 0.209583i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(0.613486 - 0.354196i) q^{13} +(1.79447 - 3.10811i) q^{14} +(-1.40542 + 1.73920i) q^{15} +1.00000 q^{16} +(-3.14725 - 1.81706i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-4.13634 + 7.16434i) q^{19} +(0.347530 - 2.20890i) q^{20} +(1.79447 + 3.10811i) q^{21} +(0.209583 - 0.121003i) q^{22} -1.53169i q^{23} +(-0.500000 + 0.866025i) q^{24} +(-4.75845 - 1.53531i) q^{25} +(-0.354196 - 0.613486i) q^{26} +1.00000i q^{27} +(-3.10811 - 1.79447i) q^{28} -0.496947 q^{29} +(1.73920 + 1.40542i) q^{30} +(2.15968 + 5.13184i) q^{31} -1.00000i q^{32} +0.242005i q^{33} +(-1.81706 + 3.14725i) q^{34} +(-5.04396 + 6.24187i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.31254 + 0.757798i) q^{37} +(7.16434 + 4.13634i) q^{38} +0.708393 q^{39} +(-2.20890 - 0.347530i) q^{40} +(3.25548 + 5.63866i) q^{41} +(3.10811 - 1.79447i) q^{42} +(2.87415 + 1.65939i) q^{43} +(-0.121003 - 0.209583i) q^{44} +(-2.08673 + 0.803479i) q^{45} -1.53169 q^{46} -6.95389i q^{47} +(0.866025 + 0.500000i) q^{48} +(2.94024 + 5.09265i) q^{49} +(-1.53531 + 4.75845i) q^{50} +(-1.81706 - 3.14725i) q^{51} +(-0.613486 + 0.354196i) q^{52} +(3.26471 - 1.88488i) q^{53} +1.00000 q^{54} +(-0.504999 + 0.194446i) q^{55} +(-1.79447 + 3.10811i) q^{56} +(-7.16434 + 4.13634i) q^{57} +0.496947i q^{58} +(-2.36422 + 4.09495i) q^{59} +(1.40542 - 1.73920i) q^{60} +12.8443 q^{61} +(5.13184 - 2.15968i) q^{62} +3.58894i q^{63} -1.00000 q^{64} +(0.569178 + 1.47822i) q^{65} +0.242005 q^{66} +(7.72991 - 4.46287i) q^{67} +(3.14725 + 1.81706i) q^{68} +(0.765843 - 1.32648i) q^{69} +(6.24187 + 5.04396i) q^{70} +(-3.20667 - 5.55412i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(4.51674 - 2.60774i) q^{73} +(0.757798 - 1.31254i) q^{74} +(-3.35328 - 3.70884i) q^{75} +(4.13634 - 7.16434i) q^{76} +0.868543i q^{77} -0.708393i q^{78} +(-2.44051 + 4.22709i) q^{79} +(-0.347530 + 2.20890i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.63866 - 3.25548i) q^{82} +(4.82737 - 2.78708i) q^{83} +(-1.79447 - 3.10811i) q^{84} +(5.10747 - 6.32046i) q^{85} +(1.65939 - 2.87415i) q^{86} +(-0.430369 - 0.248474i) q^{87} +(-0.209583 + 0.121003i) q^{88} -13.1965 q^{89} +(0.803479 + 2.08673i) q^{90} +2.54238 q^{91} +1.53169i q^{92} +(-0.695578 + 5.52414i) q^{93} -6.95389 q^{94} +(-14.3878 - 11.6266i) q^{95} +(0.500000 - 0.866025i) q^{96} +0.598433i q^{97} +(5.09265 - 2.94024i) q^{98} +(-0.121003 + 0.209583i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9}+O(q^{10}) $ 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9	$ 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9} + 4 q^{10} + 2 q^{11} - 8 q^{14} - 8 q^{15} + 28 q^{16} + 4 q^{19} - 2 q^{20} - 8 q^{21} - 14 q^{24} - 14 q^{25} - 12 q^{26} + 24 q^{29} + 4 q^{30} + 10 q^{34} + 8 q^{35} - 14 q^{36} + 24 q^{39} - 4 q^{40} + 20 q^{41} - 2 q^{44} - 2 q^{45} + 12 q^{46} + 2 q^{49} - 8 q^{50} + 10 q^{51} + 28 q^{54} + 6 q^{55} + 8 q^{56} - 20 q^{59} + 8 q^{60} + 32 q^{61} - 28 q^{64} - 12 q^{65} + 4 q^{66} - 6 q^{69} - 16 q^{70} - 16 q^{71} - 6 q^{74} - 8 q^{75} - 4 q^{76} + 10 q^{79} + 2 q^{80} - 14 q^{81} + 8 q^{84} + 72 q^{85} + 18 q^{86} - 80 q^{89} - 4 q^{90} + 32 q^{91} - 12 q^{94} - 32 q^{95} + 14 q^{96} - 2 q^{99}+O(q^{100}) $ 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9 + 4 * q^10 + 2 * q^11 - 8 * q^14 - 8 * q^15 + 28 * q^16 + 4 * q^19 - 2 * q^20 - 8 * q^21 - 14 * q^24 - 14 * q^25 - 12 * q^26 + 24 * q^29 + 4 * q^30 + 10 * q^34 + 8 * q^35 - 14 * q^36 + 24 * q^39 - 4 * q^40 + 20 * q^41 - 2 * q^44 - 2 * q^45 + 12 * q^46 + 2 * q^49 - 8 * q^50 + 10 * q^51 + 28 * q^54 + 6 * q^55 + 8 * q^56 - 20 * q^59 + 8 * q^60 + 32 * q^61 - 28 * q^64 - 12 * q^65 + 4 * q^66 - 6 * q^69 - 16 * q^70 - 16 * q^71 - 6 * q^74 - 8 * q^75 - 4 * q^76 + 10 * q^79 + 2 * q^80 - 14 * q^81 + 8 * q^84 + 72 * q^85 + 18 * q^86 - 80 * q^89 - 4 * q^90 + 32 * q^91 - 12 * q^94 - 32 * q^95 + 14 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−1.00000			−0.500000
$5$	−0.347530	+	2.20890i	−0.155420	+	0.987848i
$5$	−0.347530	+	2.20890i	−0.155420	+	0.987848i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	3.10811	+	1.79447i	1.17476	+	0.678246i	0.954796	−	0.297263i	$-0.0960738\pi$
$7$	3.10811	+	1.79447i	1.17476	+	0.678246i	0.219961	+	0.975509i	$0.429407\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	2.20890	+	0.347530i	0.698514	+	0.109899i
$11$	0.121003	+	0.209583i	0.0364837	+	0.0631916i	0.883691	−	0.468071i	$-0.155051\pi$
$11$	0.121003	+	0.209583i	0.0364837	+	0.0631916i	−0.847207	+	0.531263i	$0.821718\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	0.613486	−	0.354196i	0.170150	−	0.0982364i	−0.412506	−	0.910955i	$-0.635347\pi$
$13$	0.613486	−	0.354196i	0.170150	−	0.0982364i	0.582657	+	0.812718i	$0.302013\pi$
$14$	1.79447	−	3.10811i	0.479592	−	0.830678i
$15$	−1.40542	+	1.73920i	−0.362877	+	0.449058i
$16$	1.00000			0.250000
$17$	−3.14725	−	1.81706i	−0.763320	−	0.440703i	0.0671666	−	0.997742i	$-0.478604\pi$
$17$	−3.14725	−	1.81706i	−0.763320	−	0.440703i	−0.830486	+	0.557039i	$0.811937\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−4.13634	+	7.16434i	−0.948940	+	1.64361i	−0.201278	+	0.979534i	$0.564509\pi$
$19$	−4.13634	+	7.16434i	−0.948940	+	1.64361i	−0.747663	+	0.664079i	$0.768824\pi$
$20$	0.347530	−	2.20890i	0.0777100	−	0.493924i
$21$	1.79447	+	3.10811i	0.391585	+	0.678246i
$22$	0.209583	−	0.121003i	0.0446832	−	0.0257979i
$23$		−	1.53169i		−	0.319379i	−0.987167	−	0.159689i	$-0.948951\pi$
$23$		−	1.53169i		−	0.319379i	0.987167	−	0.159689i	$-0.0510492\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−4.75845	−	1.53531i	−0.951689	−	0.307063i
$26$	−0.354196	−	0.613486i	−0.0694636	−	0.120314i
$27$			1.00000i			0.192450i
$28$	−3.10811	−	1.79447i	−0.587378	−	0.339123i
$29$	−0.496947			−0.0922808			−0.0461404	−	0.998935i	$-0.514692\pi$
$29$	−0.496947			−0.0922808			−0.0461404	+	0.998935i	$0.514692\pi$
$30$	1.73920	+	1.40542i	0.317532	+	0.256593i
$31$	2.15968	+	5.13184i	0.387891	+	0.921705i
$31$	2.15968	+	5.13184i	0.387891	+	0.921705i
$32$		−	1.00000i		−	0.176777i
$33$			0.242005i			0.0421277i
$34$	−1.81706	+	3.14725i	−0.311624	+	0.539749i
$35$	−5.04396	+	6.24187i	−0.852585	+	1.05507i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	1.31254	+	0.757798i	0.215781	+	0.124581i	0.603995	−	0.796988i	$-0.293575\pi$
$37$	1.31254	+	0.757798i	0.215781	+	0.124581i	−0.388214	+	0.921569i	$0.626908\pi$
$38$	7.16434	+	4.13634i	1.16221	+	0.671002i
$39$	0.708393			0.113434
$40$	−2.20890	−	0.347530i	−0.349257	−	0.0549493i
$41$	3.25548	+	5.63866i	0.508420	+	0.880610i	0.999952	+	0.00975054i	$0.00310374\pi$
$41$	3.25548	+	5.63866i	0.508420	+	0.880610i	−0.491532	+	0.870860i	$0.663563\pi$
$42$	3.10811	−	1.79447i	0.479592	−	0.276893i
$43$	2.87415	+	1.65939i	0.438303	+	0.253055i	0.702878	−	0.711311i	$-0.251898\pi$
$43$	2.87415	+	1.65939i	0.438303	+	0.253055i	−0.264574	+	0.964365i	$0.585231\pi$
$44$	−0.121003	−	0.209583i	−0.0182418	−	0.0315958i
$45$	−2.08673	+	0.803479i	−0.311071	+	0.119776i
$46$	−1.53169			−0.225835
$47$		−	6.95389i		−	1.01433i	−0.861849	−	0.507165i	$-0.830694\pi$
$47$		−	6.95389i		−	1.01433i	0.861849	−	0.507165i	$-0.169306\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	2.94024	+	5.09265i	0.420035	+	0.727522i
$50$	−1.53531	+	4.75845i	−0.217126	+	0.672946i
$51$	−1.81706	−	3.14725i	−0.254440	−	0.440703i
$52$	−0.613486	+	0.354196i	−0.0850752	+	0.0491182i
$53$	3.26471	−	1.88488i	0.448442	−	0.258908i	−0.258730	−	0.965950i	$-0.583304\pi$
$53$	3.26471	−	1.88488i	0.448442	−	0.258908i	0.707172	+	0.707042i	$0.249971\pi$
$54$	1.00000			0.136083
$55$	−0.504999	+	0.194446i	−0.0680940	+	0.0262191i
$56$	−1.79447	+	3.10811i	−0.239796	+	0.415339i
$57$	−7.16434	+	4.13634i	−0.948940	+	0.547871i
$58$			0.496947i			0.0652524i
$59$	−2.36422	+	4.09495i	−0.307795	+	0.533117i	−0.977880	−	0.209168i	$-0.932925\pi$
$59$	−2.36422	+	4.09495i	−0.307795	+	0.533117i	0.670084	+	0.742285i	$0.266258\pi$
$60$	1.40542	−	1.73920i	0.181439	−	0.224529i
$61$	12.8443			1.64454			0.822270	−	0.569098i	$-0.192708\pi$
$61$	12.8443			1.64454			0.822270	+	0.569098i	$0.192708\pi$
$62$	5.13184	−	2.15968i	0.651744	−	0.274280i
$63$			3.58894i			0.452164i
$64$	−1.00000			−0.125000
$65$	0.569178	+	1.47822i	0.0705979	+	0.183351i
$66$	0.242005			0.0297888
$67$	7.72991	−	4.46287i	0.944359	−	0.545226i	0.0530352	−	0.998593i	$-0.483110\pi$
$67$	7.72991	−	4.46287i	0.944359	−	0.545226i	0.891324	+	0.453367i	$0.149777\pi$
$68$	3.14725	+	1.81706i	0.381660	+	0.220351i
$69$	0.765843	−	1.32648i	0.0921967	−	0.159689i
$70$	6.24187	+	5.04396i	0.746046	+	0.602868i
$71$	−3.20667	−	5.55412i	−0.380562	−	0.659153i	0.610581	−	0.791954i	$-0.290936\pi$
$71$	−3.20667	−	5.55412i	−0.380562	−	0.659153i	−0.991143	+	0.132801i	$0.957603\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	4.51674	−	2.60774i	0.528644	−	0.305213i	−0.211820	−	0.977309i	$-0.567939\pi$
$73$	4.51674	−	2.60774i	0.528644	−	0.305213i	0.740464	+	0.672096i	$0.234606\pi$
$74$	0.757798	−	1.31254i	0.0880922	−	0.152580i
$75$	−3.35328	−	3.70884i	−0.387203	−	0.428260i
$76$	4.13634	−	7.16434i	0.474470	−	0.821806i
$77$			0.868543i			0.0989797i
$78$		−	0.708393i		−	0.0802097i
$79$	−2.44051	+	4.22709i	−0.274579	+	0.475585i	−0.970029	−	0.242990i	$-0.921872\pi$
$79$	−2.44051	+	4.22709i	−0.274579	+	0.475585i	0.695450	+	0.718575i	$0.255205\pi$
$80$	−0.347530	+	2.20890i	−0.0388550	+	0.246962i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.63866	−	3.25548i	0.622685	−	0.359508i
$83$	4.82737	−	2.78708i	0.529873	−	0.305922i	−0.211092	−	0.977466i	$-0.567702\pi$
$83$	4.82737	−	2.78708i	0.529873	−	0.305922i	0.740965	+	0.671544i	$0.234369\pi$
$84$	−1.79447	−	3.10811i	−0.195793	−	0.339123i
$85$	5.10747	−	6.32046i	0.553983	−	0.685550i
$86$	1.65939	−	2.87415i	0.178937	−	0.309927i
$87$	−0.430369	−	0.248474i	−0.0461404	−	0.0266392i
$88$	−0.209583	+	0.121003i	−0.0223416	+	0.0128989i
$89$	−13.1965			−1.39882			−0.699411	−	0.714719i	$-0.746554\pi$
$89$	−13.1965			−1.39882			−0.699411	+	0.714719i	$0.746554\pi$
$90$	0.803479	+	2.08673i	0.0846941	+	0.219960i
$91$	2.54238			0.266514
$92$			1.53169i			0.159689i
$93$	−0.695578	+	5.52414i	−0.0721280	+	0.572827i
$94$	−6.95389			−0.717239
$95$	−14.3878	−	11.6266i	−1.47616	−	1.19286i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$			0.598433i			0.0607617i	0.999538	+	0.0303809i	$0.00967202\pi$
$97$			0.598433i			0.0607617i	−0.999538	+	0.0303809i	$0.990328\pi$
$98$	5.09265	−	2.94024i	0.514435	−	0.297009i
$99$	−0.121003	+	0.209583i	−0.0121612	+	0.0210639i
$100$	4.75845	+	1.53531i	0.475845	+	0.153531i
$101$	3.03628			0.302122			0.151061	−	0.988524i	$-0.451731\pi$
$101$	3.03628			0.302122			0.151061	+	0.988524i	$0.451731\pi$
$102$	−3.14725	+	1.81706i	−0.311624	+	0.179916i
$103$	−7.56574	+	4.36808i	−0.745475	+	0.430400i	−0.824056	−	0.566508i	$-0.808294\pi$
$103$	−7.56574	+	4.36808i	−0.745475	+	0.430400i	0.0785817	+	0.996908i	$0.474961\pi$
$104$	0.354196	+	0.613486i	0.0347318	+	0.0601572i
$105$	−7.48913	+	2.88364i	−0.730864	+	0.281414i
$106$	−1.88488	−	3.26471i	−0.183076	−	0.317096i
$107$	−0.212138	−	0.122478i	−0.0205082	−	0.0118404i	0.489711	−	0.871885i	$-0.337102\pi$
$107$	−0.212138	−	0.122478i	−0.0205082	−	0.0118404i	−0.510219	+	0.860044i	$0.670436\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	−2.76333			−0.264679			−0.132339	−	0.991204i	$-0.542249\pi$
$109$	−2.76333			−0.264679			−0.132339	+	0.991204i	$0.542249\pi$
$110$	0.194446	+	0.504999i	0.0185397	+	0.0481498i
$111$	0.757798	+	1.31254i	0.0719270	+	0.124581i
$112$	3.10811	+	1.79447i	0.293689	+	0.169561i
$113$	−1.95146	+	1.12668i	−0.183578	+	0.105989i	−0.588973	−	0.808153i	$-0.700467\pi$
$113$	−1.95146	+	1.12668i	−0.183578	+	0.105989i	0.405395	+	0.914142i	$0.367134\pi$
$114$	4.13634	+	7.16434i	0.387403	+	0.671002i
$115$	3.38334	+	0.532306i	0.315498	+	0.0496378i
$116$	0.496947			0.0461404
$117$	0.613486	+	0.354196i	0.0567168	+	0.0327455i
$118$	4.09495	+	2.36422i	0.376971	+	0.217644i
$119$	−6.52133	−	11.2953i	−0.597810	−	1.03544i
$120$	−1.73920	−	1.40542i	−0.158766	−	0.128296i
$121$	5.47072	−	9.47556i	0.497338	−	0.861414i
$122$		−	12.8443i		−	1.16286i
$123$			6.51096i			0.587073i
$124$	−2.15968	−	5.13184i	−0.193945	−	0.460853i
$125$	5.04505	−	9.97735i	0.451243	−	0.892401i
$126$	3.58894			0.319728
$127$	−5.05887	−	2.92074i	−0.448902	−	0.259174i	0.258464	−	0.966021i	$-0.416784\pi$
$127$	−5.05887	−	2.92074i	−0.448902	−	0.259174i	−0.707366	+	0.706847i	$0.750117\pi$
$128$			1.00000i			0.0883883i
$129$	1.65939	+	2.87415i	0.146101	+	0.253055i
$130$	1.47822	−	0.569178i	0.129649	−	0.0499202i
$131$	2.30983	−	4.00075i	0.201811	−	0.349547i	−0.747301	−	0.664486i	$-0.768651\pi$
$131$	2.30983	−	4.00075i	0.201811	−	0.349547i	0.949112	+	0.314939i	$0.101984\pi$
$132$		−	0.242005i		−	0.0210639i
$133$	−25.7124	+	14.8451i	−2.22955	+	1.28723i
$134$	−4.46287	−	7.72991i	−0.385533	−	0.667763i
$135$	−2.20890	−	0.347530i	−0.190112	−	0.0299106i
$136$	1.81706	−	3.14725i	0.155812	−	0.269874i
$137$	8.83590	−	5.10141i	0.754902	−	0.435843i	−0.0725604	−	0.997364i	$-0.523117\pi$
$137$	8.83590	−	5.10141i	0.754902	−	0.435843i	0.827462	+	0.561521i	$0.189784\pi$
$138$	−1.32648	−	0.765843i	−0.112917	−	0.0651929i
$139$	17.0843			1.44907			0.724537	−	0.689236i	$-0.242054\pi$
$139$	17.0843			1.44907			0.724537	+	0.689236i	$0.242054\pi$
$140$	5.04396	−	6.24187i	0.426292	−	0.527534i
$141$	3.47695	−	6.02225i	0.292812	−	0.507165i
$142$	−5.55412	+	3.20667i	−0.466091	+	0.269098i
$143$	0.148467	+	0.0857174i	0.0124154	+	0.00716805i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	0.172704	−	1.09771i	0.0143423	−	0.0911595i
$146$	−2.60774	−	4.51674i	−0.215818	−	0.373808i
$147$			5.88049i			0.485014i
$148$	−1.31254	−	0.757798i	−0.107890	−	0.0622906i
$149$	−0.127232	+	0.220372i	−0.0104232	+	0.0180536i	−0.871190	−	0.490946i	$-0.836651\pi$
$149$	−0.127232	+	0.220372i	−0.0104232	+	0.0180536i	0.860767	+	0.509000i	$0.169985\pi$
$150$	−3.70884	+	3.35328i	−0.302826	+	0.273794i
$151$	18.4193			1.49894			0.749470	−	0.662038i	$-0.230308\pi$
$151$	18.4193			1.49894			0.749470	+	0.662038i	$0.230308\pi$
$152$	−7.16434	−	4.13634i	−0.581105	−	0.335501i
$153$		−	3.63413i		−	0.293802i
$154$	0.868543			0.0699892
$155$	−12.0863	+	2.98705i	−0.970791	+	0.239926i
$156$	−0.708393			−0.0567168
$157$		−	10.8271i		−	0.864098i	−0.901850	−	0.432049i	$-0.857791\pi$
$157$		−	10.8271i		−	0.864098i	0.901850	−	0.432049i	$-0.142209\pi$
$158$	4.22709	+	2.44051i	0.336289	+	0.194157i
$159$	3.76976			0.298961
$160$	2.20890	+	0.347530i	0.174629	+	0.0274746i
$161$	2.74856	−	4.76065i	0.216617	−	0.375192i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$			11.3711i			0.890653i	0.895368	+	0.445326i	$0.146912\pi$
$163$			11.3711i			0.890653i	−0.895368	+	0.445326i	$0.853088\pi$
$164$	−3.25548	−	5.63866i	−0.254210	−	0.440305i
$165$	−0.534565	−	0.0841041i	−0.0416158	−	0.00654749i
$166$	−2.78708	−	4.82737i	−0.216320	−	0.374677i
$167$	15.2639	+	8.81263i	1.18116	+	0.681942i	0.956282	−	0.292445i	$-0.0944689\pi$
$167$	15.2639	+	8.81263i	1.18116	+	0.681942i	0.224876	+	0.974387i	$0.427802\pi$
$168$	−3.10811	+	1.79447i	−0.239796	+	0.138446i
$169$	−6.24909	+	10.8237i	−0.480699	+	0.832595i
$170$	−6.32046	−	5.10747i	−0.484757	−	0.391725i
$171$	−8.27267			−0.632627
$172$	−2.87415	−	1.65939i	−0.219152	−	0.126527i
$173$	−13.1278	+	7.57936i	−0.998091	+	0.576248i	−0.907683	−	0.419657i	$-0.862150\pi$
$173$	−13.1278	+	7.57936i	−0.998091	+	0.576248i	−0.0904080	+	0.995905i	$0.528817\pi$
$174$	−0.248474	+	0.430369i	−0.0188367	+	0.0326262i
$175$	−12.0347	−	13.3108i	−0.909739	−	1.00620i
$176$	0.121003	+	0.209583i	0.00912092	+	0.0157979i
$177$	−4.09495	+	2.36422i	−0.307795	+	0.177706i
$178$			13.1965i			0.989117i
$179$	10.6796	−	18.4977i	0.798234	−	1.38258i	−0.122532	−	0.992465i	$-0.539101\pi$
$179$	10.6796	−	18.4977i	0.798234	−	1.38258i	0.920765	−	0.390117i	$-0.127565\pi$
$180$	2.08673	−	0.803479i	0.155535	−	0.0598878i
$181$	−1.29325	−	2.23997i	−0.0961265	−	0.166496i	0.813952	−	0.580933i	$-0.197312\pi$
$181$	−1.29325	−	2.23997i	−0.0961265	−	0.166496i	−0.910078	+	0.414437i	$0.863979\pi$
$182$		−	2.54238i		−	0.188454i
$183$	11.1235	+	6.42213i	0.822270	+	0.474738i
$184$	1.53169			0.112917
$185$	−2.13004	+	2.63592i	−0.156604	+	0.193796i
$186$	5.52414	+	0.695578i	0.405050	+	0.0510022i
$187$		−	0.879479i		−	0.0643139i
$188$			6.95389i			0.507165i
$189$	−1.79447	+	3.10811i	−0.130528	+	0.226082i
$190$	−11.6266	+	14.3878i	−0.843479	+	1.04380i
$191$	−9.15916	−	15.8641i	−0.662733	−	1.14789i	−0.979895	−	0.199516i	$-0.936063\pi$
$191$	−9.15916	−	15.8641i	−0.662733	−	1.14789i	0.317161	−	0.948372i	$-0.397270\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	6.87375	+	3.96856i	0.494784	+	0.285663i	0.726557	−	0.687106i	$-0.241119\pi$
$193$	6.87375	+	3.96856i	0.494784	+	0.285663i	−0.231773	+	0.972770i	$0.574453\pi$
$194$	0.598433			0.0429650
$195$	−0.246187	+	1.56477i	−0.0176298	+	0.112055i
$196$	−2.94024	−	5.09265i	−0.210017	−	0.363761i
$197$	−14.7115	+	8.49372i	−1.04815	+	0.605152i	−0.922132	−	0.386875i	$-0.873554\pi$
$197$	−14.7115	+	8.49372i	−1.04815	+	0.605152i	−0.126022	+	0.992027i	$0.540221\pi$
$198$	0.209583	+	0.121003i	0.0148944	+	0.00859929i
$199$	4.48651	+	7.77086i	0.318040	+	0.550862i	0.980079	−	0.198608i	$-0.0636420\pi$
$199$	4.48651	+	7.77086i	0.318040	+	0.550862i	−0.662039	+	0.749469i	$0.730309\pi$
$200$	1.53531	−	4.75845i	0.108563	−	0.336473i
$201$	8.92574			0.629573
$202$		−	3.03628i		−	0.213632i
$203$	−1.54457	−	0.891757i	−0.108407	−	0.0625891i
$204$	1.81706	+	3.14725i	0.127220	+	0.220351i
$205$	−13.5866	+	5.23142i	−0.948928	+	0.365378i
$206$	4.36808	+	7.56574i	0.304339	+	0.527130i
$207$	1.32648	−	0.765843i	0.0921967	−	0.0532298i
$208$	0.613486	−	0.354196i	0.0425376	−	0.0245591i
$209$	−2.00203			−0.138483
$210$	2.88364	+	7.48913i	0.198990	+	0.516799i
$211$	6.21432	−	10.7635i	0.427811	−	0.740991i	−0.568867	−	0.822429i	$-0.692618\pi$
$211$	6.21432	−	10.7635i	0.427811	−	0.740991i	0.996678	+	0.0814387i	$0.0259515\pi$
$212$	−3.26471	+	1.88488i	−0.224221	+	0.129454i
$213$		−	6.41335i		−	0.439435i
$214$	−0.122478	+	0.212138i	−0.00837243	+	0.0145015i
$215$	−4.66427	+	5.77201i	−0.318101	+	0.393648i
$216$	−1.00000			−0.0680414
$217$	−2.49639	+	19.8258i	−0.169466	+	1.34586i
$218$			2.76333i			0.187156i
$219$	5.21548			0.352429
$220$	0.504999	−	0.194446i	0.0340470	−	0.0131096i
$221$	−2.57439			−0.173172
$222$	1.31254	−	0.757798i	0.0880922	−	0.0508600i
$223$	−18.3534	−	10.5963i	−1.22903	−	0.709583i	−0.262207	−	0.965012i	$-0.584450\pi$
$223$	−18.3534	−	10.5963i	−1.22903	−	0.709583i	−0.966828	+	0.255428i	$0.917784\pi$
$224$	1.79447	−	3.10811i	0.119898	−	0.207670i
$225$	−1.04960	−	4.88859i	−0.0699735	−	0.325906i
$226$	1.12668	+	1.95146i	0.0749453	+	0.129809i
$227$	−0.293045	+	0.169189i	−0.0194501	+	0.0112295i	−0.509694	−	0.860356i	$-0.670241\pi$
$227$	−0.293045	+	0.169189i	−0.0194501	+	0.0112295i	0.490243	+	0.871586i	$0.336908\pi$
$228$	7.16434	−	4.13634i	0.474470	−	0.273935i
$229$	3.80734	−	6.59451i	0.251596	−	0.435777i	−0.712369	−	0.701805i	$-0.752378\pi$
$229$	3.80734	−	6.59451i	0.251596	−	0.435777i	0.963965	+	0.266027i	$0.0857112\pi$
$230$	0.532306	−	3.38334i	0.0350992	−	0.223091i
$231$	−0.434272	+	0.752180i	−0.0285730	+	0.0494898i
$232$		−	0.496947i		−	0.0326262i
$233$		−	21.5368i		−	1.41092i	−0.708747	−	0.705462i	$-0.750739\pi$
$233$		−	21.5368i		−	1.41092i	0.708747	−	0.705462i	$-0.249261\pi$
$234$	0.354196	−	0.613486i	0.0231545	−	0.0401048i
$235$	15.3604	+	2.41668i	1.00200	+	0.157647i
$236$	2.36422	−	4.09495i	0.153898	−	0.266559i
$237$	−4.22709	+	2.44051i	−0.274579	+	0.158528i
$238$	−11.2953	+	6.52133i	−0.732164	+	0.422715i
$239$	7.86144	+	13.6164i	0.508514	+	0.880773i	0.999951	+	0.00985954i	$0.00313844\pi$
$239$	7.86144	+	13.6164i	0.508514	+	0.880773i	−0.491437	+	0.870913i	$0.663528\pi$
$240$	−1.40542	+	1.73920i	−0.0907193	+	0.112265i
$241$	−6.59807	+	11.4282i	−0.425019	+	0.736155i	−0.996422	−	0.0845147i	$-0.973066\pi$
$241$	−6.59807	+	11.4282i	−0.425019	+	0.736155i	0.571403	+	0.820670i	$0.306399\pi$
$242$	−9.47556	−	5.47072i	−0.609112	−	0.351671i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−12.8443			−0.822270
$245$	−12.2710	+	4.72485i	−0.783963	+	0.301859i
$246$	6.51096			0.415124
$247$			5.86030i			0.372882i
$248$	−5.13184	+	2.15968i	−0.325872	+	0.137140i
$249$	5.57417			0.353248
$250$	−9.97735	−	5.04505i	−0.631023	−	0.319077i
$251$	14.1796	−	24.5597i	0.895007	−	1.55020i	0.0612100	−	0.998125i	$-0.480504\pi$
$251$	14.1796	−	24.5597i	0.895007	−	1.55020i	0.833797	−	0.552072i	$-0.186163\pi$
$252$		−	3.58894i		−	0.226082i
$253$	0.321015	−	0.185338i	0.0201821	−	0.0116521i
$254$	−2.92074	+	5.05887i	−0.183263	+	0.317422i
$255$	7.58343	−	2.91994i	0.474893	−	0.182854i
$256$	1.00000			0.0625000
$257$	−14.8651	+	8.58234i	−0.927256	+	0.535352i	−0.885943	−	0.463794i	$-0.846488\pi$
$257$	−14.8651	+	8.58234i	−0.927256	+	0.535352i	−0.0413136	+	0.999146i	$0.513154\pi$
$258$	2.87415	−	1.65939i	0.178937	−	0.103309i
$259$	2.71969	+	4.71064i	0.168993	+	0.292705i
$260$	−0.569178	−	1.47822i	−0.0352989	−	0.0916753i
$261$	−0.248474	−	0.430369i	−0.0153801	−	0.0266392i
$262$	−4.00075	−	2.30983i	−0.247167	−	0.142702i
$263$		−	26.5382i		−	1.63641i	−0.574925	−	0.818206i	$-0.694969\pi$
$263$		−	26.5382i		−	1.63641i	0.574925	−	0.818206i	$-0.305031\pi$
$264$	−0.242005			−0.0148944
$265$	3.02892	+	7.86645i	0.186065	+	0.483232i
$266$	14.8451	+	25.7124i	0.910209	+	1.57653i
$267$	−11.4285	−	6.59823i	−0.699411	−	0.403805i
$268$	−7.72991	+	4.46287i	−0.472180	+	0.272613i
$269$	−7.79873	−	13.5078i	−0.475497	−	0.823585i	0.524109	−	0.851651i	$-0.324398\pi$
$269$	−7.79873	−	13.5078i	−0.475497	−	0.823585i	−0.999606	+	0.0280662i	$0.991065\pi$
$270$	−0.347530	+	2.20890i	−0.0211500	+	0.134429i
$271$	−8.17223			−0.496428			−0.248214	−	0.968705i	$-0.579844\pi$
$271$	−8.17223			−0.496428			−0.248214	+	0.968705i	$0.579844\pi$
$272$	−3.14725	−	1.81706i	−0.190830	−	0.110176i
$273$	2.20176	+	1.27119i	0.133257	+	0.0769359i
$274$	−5.10141	−	8.83590i	−0.308187	−	0.533796i
$275$	−0.254009	−	1.18307i	−0.0153173	−	0.0713416i
$276$	−0.765843	+	1.32648i	−0.0460983	+	0.0798447i
$277$		−	17.9774i		−	1.08016i	−0.841615	−	0.540078i	$-0.818395\pi$
$277$		−	17.9774i		−	1.08016i	0.841615	−	0.540078i	$-0.181605\pi$
$278$		−	17.0843i		−	1.02465i
$279$	−3.36446	+	4.43626i	−0.201425	+	0.265592i
$280$	−6.24187	−	5.04396i	−0.373023	−	0.301434i
$281$	−31.2439			−1.86385			−0.931927	−	0.362646i	$-0.881874\pi$
$281$	−31.2439			−1.86385			−0.931927	+	0.362646i	$0.881874\pi$
$282$	−6.02225	−	3.47695i	−0.358620	−	0.207049i
$283$		−	30.6594i		−	1.82251i	−0.411838	−	0.911257i	$-0.635113\pi$
$283$		−	30.6594i		−	1.82251i	0.411838	−	0.911257i	$-0.364887\pi$
$284$	3.20667	+	5.55412i	0.190281	+	0.329576i
$285$	−6.64691	−	17.2628i	−0.393729	−	1.02256i
$286$	0.0857174	−	0.148467i	0.00506858	−	0.00877904i
$287$			23.3674i			1.37934i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−1.89655	−	3.28493i	−0.111562	−	0.193231i
$290$	−1.09771	−	0.172704i	−0.0644595	−	0.0101415i
$291$	−0.299217	+	0.518259i	−0.0175404	+	0.0303809i
$292$	−4.51674	+	2.60774i	−0.264322	+	0.152606i
$293$	19.6599	+	11.3506i	1.14854	+	0.663112i	0.948532	−	0.316682i	$-0.102569\pi$
$293$	19.6599	+	11.3506i	1.14854	+	0.663112i	0.200012	+	0.979794i	$0.435902\pi$
$294$	5.88049			0.342957
$295$	−8.22368	−	6.64544i	−0.478801	−	0.386912i
$296$	−0.757798	+	1.31254i	−0.0440461	+	0.0762901i
$297$	−0.209583	+	0.121003i	−0.0121612	+	0.00702129i
$298$	0.220372	+	0.127232i	0.0127658	+	0.00737034i
$299$	−0.542517	−	0.939668i	−0.0313746	−	0.0543424i
$300$	3.35328	+	3.70884i	0.193602	+	0.214130i
$301$	5.95545	+	10.3151i	0.343266	+	0.594555i
$302$		−	18.4193i		−	1.05991i
$303$	2.62950	+	1.51814i	0.151061	+	0.0872150i
$304$	−4.13634	+	7.16434i	−0.237235	+	0.410903i
$305$	−4.46376	+	28.3716i	−0.255594	+	1.62456i
$306$	−3.63413			−0.207749
$307$	22.4497	+	12.9614i	1.28127	+	0.739744i	0.977081	−	0.212867i	$-0.0682801\pi$
$307$	22.4497	+	12.9614i	1.28127	+	0.739744i	0.304193	+	0.952611i	$0.401613\pi$
$308$		−	0.868543i		−	0.0494898i
$309$	−8.73617			−0.496983
$310$	2.98705	+	12.0863i	0.169653	+	0.686453i
$311$	26.0921			1.47955			0.739774	−	0.672856i	$-0.234933\pi$
$311$	26.0921			1.47955			0.739774	+	0.672856i	$0.234933\pi$
$312$			0.708393i			0.0401048i
$313$	−17.9774	−	10.3792i	−1.01614	−	0.586669i	−0.103157	−	0.994665i	$-0.532895\pi$
$313$	−17.9774	−	10.3792i	−1.01614	−	0.586669i	−0.912984	+	0.407996i	$0.866228\pi$
$314$	−10.8271			−0.611009
$315$	−7.92760	−	1.24726i	−0.446669	−	0.0702753i
$316$	2.44051	−	4.22709i	0.137290	−	0.237793i
$317$	11.1766	+	6.45280i	0.627739	+	0.362425i	0.779876	−	0.625934i	$-0.215282\pi$
$317$	11.1766	+	6.45280i	0.627739	+	0.362425i	−0.152137	+	0.988359i	$0.548615\pi$
$318$		−	3.76976i		−	0.211397i
$319$	−0.0601320	−	0.104152i	−0.00336675	−	0.00583137i
$320$	0.347530	−	2.20890i	0.0194275	−	0.123481i
$321$	−0.122478	−	0.212138i	−0.00683606	−	0.0118404i
$322$	−4.76065	−	2.74856i	−0.265301	−	0.153171i
$323$	26.0361	−	15.0320i	1.44869	−	0.836401i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−3.46304	+	0.743530i	−0.192095	+	0.0412436i
$326$	11.3711			0.629787
$327$	−2.39311	−	1.38166i	−0.132339	−	0.0764061i
$328$	−5.63866	+	3.25548i	−0.311343	+	0.179754i
$329$	12.4785	−	21.6135i	0.687965	−	1.19159i
$330$	−0.0841041	+	0.534565i	−0.00462978	+	0.0294268i
$331$	−2.46229	−	4.26481i	−0.135340	−	0.234415i	0.790387	−	0.612607i	$-0.209879\pi$
$331$	−2.46229	−	4.26481i	−0.135340	−	0.234415i	−0.925727	+	0.378192i	$0.876546\pi$
$332$	−4.82737	+	2.78708i	−0.264936	+	0.152961i
$333$			1.51560i			0.0830541i
$334$	8.81263	−	15.2639i	0.482206	−	0.835205i
$335$	7.17164	+	18.6256i	0.391828	+	1.01762i
$336$	1.79447	+	3.10811i	0.0978964	+	0.169561i
$337$			1.14989i			0.0626386i	0.999509	+	0.0313193i	$0.00997088\pi$
$337$			1.14989i			0.0626386i	−0.999509	+	0.0313193i	$0.990029\pi$
$338$	10.8237	+	6.24909i	0.588734	+	0.339906i
$339$	−2.25335			−0.122385
$340$	−5.10747	+	6.32046i	−0.276991	+	0.342775i
$341$	−0.814218	+	1.07360i	−0.0440924	+	0.0581387i
$342$			8.27267i			0.447335i
$343$		−	4.01787i		−	0.216944i
$344$	−1.65939	+	2.87415i	−0.0894683	+	0.154964i
$345$	2.66390	+	2.15266i	0.143420	+	0.115895i
$346$	7.57936	+	13.1278i	0.407469	+	0.705757i
$347$	−0.185974	−	0.107372i	−0.00998361	−	0.00576404i	0.495000	−	0.868893i	$-0.335168\pi$
$347$	−0.185974	−	0.107372i	−0.00998361	−	0.00576404i	−0.504983	+	0.863129i	$0.668501\pi$
$348$	0.430369	+	0.248474i	0.0230702	+	0.0133196i
$349$	−35.8927			−1.92129			−0.960646	−	0.277774i	$-0.910403\pi$
$349$	−35.8927			−1.92129			−0.960646	+	0.277774i	$0.910403\pi$
$350$	−13.3108	+	12.0347i	−0.711493	+	0.643282i
$351$	0.354196	+	0.613486i	0.0189056	+	0.0327455i
$352$	0.209583	−	0.121003i	0.0111708	−	0.00644947i
$353$	18.3744	+	10.6085i	0.977972	+	0.564632i	0.901657	−	0.432452i	$-0.142351\pi$
$353$	18.3744	+	10.6085i	0.977972	+	0.564632i	0.0763144	+	0.997084i	$0.475685\pi$
$354$	2.36422	+	4.09495i	0.125657	+	0.217644i
$355$	13.3829	−	5.15299i	0.710290	−	0.273492i
$356$	13.1965			0.699411
$357$		−	13.0427i		−	0.690291i
$358$	−18.4977	−	10.6796i	−0.977633	−	0.564436i
$359$	−0.983349	−	1.70321i	−0.0518992	−	0.0898920i	0.838909	−	0.544272i	$-0.183194\pi$
$359$	−0.983349	−	1.70321i	−0.0518992	−	0.0898920i	−0.890808	+	0.454380i	$0.849861\pi$
$360$	−0.803479	−	2.08673i	−0.0423470	−	0.109980i
$361$	−24.7185	−	42.8138i	−1.30098	−	2.25336i
$362$	−2.23997	+	1.29325i	−0.117730	+	0.0679717i
$363$	9.47556	−	5.47072i	0.497338	−	0.287138i
$364$	−2.54238			−0.133257
$365$	4.19052	+	10.8833i	0.219342	+	0.569656i
$366$	6.42213	−	11.1235i	0.335690	−	0.581432i
$367$	−11.4332	+	6.60094i	−0.596807	+	0.344566i	−0.767784	−	0.640708i	$-0.778641\pi$
$367$	−11.4332	+	6.60094i	−0.596807	+	0.344566i	0.170978	+	0.985275i	$0.445307\pi$
$368$		−	1.53169i		−	0.0798447i
$369$	−3.25548	+	5.63866i	−0.169473	+	0.293537i
$370$	2.63592	+	2.13004i	0.137035	+	0.110736i
$371$	13.5294			0.702413
$372$	0.695578	−	5.52414i	0.0360640	−	0.286414i
$373$		−	12.8821i		−	0.667010i	−0.942748	−	0.333505i	$-0.891769\pi$
$373$		−	12.8821i		−	0.667010i	0.942748	−	0.333505i	$-0.108231\pi$
$374$	−0.879479			−0.0454768
$375$	9.35782	−	6.11811i	0.483236	−	0.315938i
$376$	6.95389			0.358620
$377$	−0.304870	+	0.176017i	−0.0157016	+	0.00906533i
$378$	3.10811	+	1.79447i	0.159864	+	0.0922976i
$379$	14.5298	−	25.1663i	0.746345	−	1.29271i	−0.203219	−	0.979133i	$-0.565140\pi$
$379$	14.5298	−	25.1663i	0.746345	−	1.29271i	0.949564	−	0.313574i	$-0.101526\pi$
$380$	14.3878	+	11.6266i	0.738078	+	0.596430i
$381$	−2.92074	−	5.05887i	−0.149634	−	0.259174i
$382$	−15.8641	+	9.15916i	−0.811679	+	0.468623i
$383$	−17.4567	+	10.0786i	−0.891996	+	0.514994i	−0.874595	−	0.484855i	$-0.838873\pi$
$383$	−17.4567	+	10.0786i	−0.891996	+	0.514994i	−0.0174011	+	0.999849i	$0.505539\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	−1.91852	−	0.301845i	−0.0977769	−	0.0153834i
$386$	3.96856	−	6.87375i	0.201995	−	0.349865i
$387$			3.31878i			0.168703i
$388$		−	0.598433i		−	0.0303809i
$389$	−15.4967	+	26.8411i	−0.785714	+	1.36090i	0.142857	+	0.989743i	$0.454371\pi$
$389$	−15.4967	+	26.8411i	−0.785714	+	1.36090i	−0.928571	+	0.371154i	$0.878962\pi$
$390$	1.56477	+	0.246187i	0.0792350	+	0.0124662i
$391$	−2.78317	+	4.82060i	−0.140751	+	0.243788i
$392$	−5.09265	+	2.94024i	−0.257218	+	0.148505i
$393$	4.00075	−	2.30983i	0.201811	−	0.116516i
$394$	8.49372	+	14.7115i	0.427907	+	0.741157i
$395$	−8.48906	−	6.85988i	−0.427131	−	0.345158i
$396$	0.121003	−	0.209583i	0.00608062	−	0.0105319i
$397$	32.7058	+	18.8827i	1.64146	+	0.947697i	0.980315	+	0.197438i	$0.0632620\pi$
$397$	32.7058	+	18.8827i	1.64146	+	0.947697i	0.661144	+	0.750259i	$0.270071\pi$
$398$	7.77086	−	4.48651i	0.389518	−	0.224888i
$399$	−29.6901			−1.48636
$400$	−4.75845	−	1.53531i	−0.237922	−	0.0767657i
$401$	25.8779			1.29228			0.646141	−	0.763218i	$-0.276382\pi$
$401$	25.8779			1.29228			0.646141	+	0.763218i	$0.276382\pi$
$402$		−	8.92574i		−	0.445175i
$403$	3.14261	+	2.38336i	0.156545	+	0.118724i
$404$	−3.03628			−0.151061
$405$	−1.73920	−	1.40542i	−0.0864213	−	0.0698358i
$406$	−0.891757	+	1.54457i	−0.0442572	+	0.0766556i
$407$			0.366782i			0.0181807i
$408$	3.14725	−	1.81706i	0.155812	−	0.0899581i
$409$	3.45724	−	5.98811i	0.170949	−	0.296093i	−0.767803	−	0.640686i	$-0.778650\pi$
$409$	3.45724	−	5.98811i	0.170949	−	0.296093i	0.938752	+	0.344593i	$0.111983\pi$
$410$	5.23142	+	13.5866i	0.258361	+	0.670993i
$411$	10.2028			0.503268
$412$	7.56574	−	4.36808i	0.372737	−	0.215200i
$413$	−14.6965	+	8.48505i	−0.723169	+	0.417522i
$414$	−0.765843	−	1.32648i	−0.0376391	−	0.0651929i
$415$	4.47872	+	11.6318i	0.219852	+	0.570980i
$416$	−0.354196	−	0.613486i	−0.0173659	−	0.0300786i
$417$	14.7955	+	8.54217i	0.724537	+	0.418312i
$418$			2.00203i			0.0979226i
$419$	−15.6618			−0.765127			−0.382563	−	0.923929i	$-0.624959\pi$
$419$	−15.6618			−0.765127			−0.382563	+	0.923929i	$0.624959\pi$
$420$	7.48913	−	2.88364i	0.365432	−	0.140707i
$421$	16.0093	+	27.7290i	0.780247	+	1.35143i	0.931798	+	0.362978i	$0.118240\pi$
$421$	16.0093	+	27.7290i	0.780247	+	1.35143i	−0.151551	+	0.988449i	$0.548427\pi$
$422$	−10.7635	−	6.21432i	−0.523960	−	0.302508i
$423$	6.02225	−	3.47695i	0.292812	−	0.169055i
$424$	1.88488	+	3.26471i	0.0915378	+	0.158548i
$425$	12.1862	+	13.4784i	0.591120	+	0.653799i
$426$	−6.41335			−0.310728
$427$	39.9214	+	23.0486i	1.93193	+	1.11540i
$428$	0.212138	+	0.122478i	0.0102541	+	0.00592020i
$429$	0.0857174	+	0.148467i	0.00413848	+	0.00716805i
$430$	5.77201	+	4.66427i	0.278351	+	0.224931i
$431$	−5.99616	+	10.3856i	−0.288825	+	0.500259i	−0.973529	−	0.228561i	$-0.926598\pi$
$431$	−5.99616	+	10.3856i	−0.288825	+	0.500259i	0.684705	+	0.728821i	$0.259931\pi$
$432$			1.00000i			0.0481125i
$433$			15.4387i			0.741936i	0.928646	+	0.370968i	$0.120974\pi$
$433$			15.4387i			0.741936i	−0.928646	+	0.370968i	$0.879026\pi$
$434$	19.8258	+	2.49639i	0.951670	+	0.119830i
$435$	0.698419	−	0.864289i	0.0334866	−	0.0414395i
$436$	2.76333			0.132339
$437$	10.9735	+	6.33557i	0.524935	+	0.303071i
$438$		−	5.21548i		−	0.249205i
$439$	2.91680	+	5.05205i	0.139211	+	0.241121i	0.927198	−	0.374571i	$-0.122210\pi$
$439$	2.91680	+	5.05205i	0.139211	+	0.241121i	−0.787987	+	0.615692i	$0.788877\pi$
$440$	−0.194446	−	0.504999i	−0.00926986	−	0.0240749i
$441$	−2.94024	+	5.09265i	−0.140012	+	0.242507i
$442$			2.57439i			0.122451i
$443$	−2.33058	+	1.34556i	−0.110729	+	0.0639296i	−0.554342	−	0.832289i	$-0.687030\pi$
$443$	−2.33058	+	1.34556i	−0.110729	+	0.0639296i	0.443613	+	0.896219i	$0.353697\pi$
$444$	−0.757798	−	1.31254i	−0.0359635	−	0.0622906i
$445$	4.58616	−	29.1496i	0.217405	−	1.38182i
$446$	−10.5963	+	18.3534i	−0.501751	+	0.869059i
$447$	−0.220372	+	0.127232i	−0.0104232	+	0.00601785i
$448$	−3.10811	−	1.79447i	−0.146845	−	0.0847807i
$449$	22.2668			1.05084			0.525418	−	0.850844i	$-0.323909\pi$
$449$	22.2668			1.05084			0.525418	+	0.850844i	$0.323909\pi$
$450$	−4.88859	+	1.04960i	−0.230450	+	0.0494787i
$451$	−0.787844	+	1.36459i	−0.0370981	+	0.0642558i
$452$	1.95146	−	1.12668i	0.0917889	−	0.0529943i
$453$	15.9516	+	9.20964i	0.749470	+	0.432707i
$454$	0.169189	+	0.293045i	0.00794046	+	0.0137533i
$455$	−0.883552	+	5.61585i	−0.0414216	+	0.263275i
$456$	−4.13634	−	7.16434i	−0.193702	−	0.335501i
$457$			20.0496i			0.937880i	0.883230	+	0.468940i	$0.155364\pi$
$457$			20.0496i			0.937880i	−0.883230	+	0.468940i	$0.844636\pi$
$458$	−6.59451	−	3.80734i	−0.308141	−	0.177905i
$459$	1.81706	−	3.14725i	0.0848133	−	0.146901i
$460$	−3.38334	−	0.532306i	−0.157749	−	0.0248189i
$461$	−26.9454			−1.25497			−0.627486	−	0.778628i	$-0.715916\pi$
$461$	−26.9454			−1.25497			−0.627486	+	0.778628i	$0.715916\pi$
$462$	0.752180	+	0.434272i	0.0349946	+	0.0202041i
$463$		−	17.4636i		−	0.811602i	−0.913962	−	0.405801i	$-0.866993\pi$
$463$		−	17.4636i		−	0.811602i	0.913962	−	0.405801i	$-0.133007\pi$
$464$	−0.496947			−0.0230702
$465$	−11.9605	−	3.45626i	−0.554656	−	0.160280i
$466$	−21.5368			−0.997674
$467$			34.2917i			1.58683i	0.608680	+	0.793416i	$0.291699\pi$
$467$			34.2917i			1.58683i	−0.608680	+	0.793416i	$0.708301\pi$
$468$	−0.613486	−	0.354196i	−0.0283584	−	0.0163727i
$469$	32.0339			1.47919
$470$	2.41668	−	15.3604i	0.111473	−	0.708524i
$471$	5.41356	−	9.37656i	0.249444	−	0.432049i
$472$	−4.09495	−	2.36422i	−0.188485	−	0.108822i
$473$			0.803163i			0.0369295i
$474$	2.44051	+	4.22709i	0.112096	+	0.194157i
$475$	30.6820	−	27.7406i	1.40779	−	1.27282i
$476$	6.52133	+	11.2953i	0.298905	+	0.517718i
$477$	3.26471	+	1.88488i	0.149481	+	0.0863027i
$478$	13.6164	−	7.86144i	0.622800	−	0.359574i
$479$	4.31599	−	7.47552i	0.197203	−	0.341565i	−0.750418	−	0.660964i	$-0.770148\pi$
$479$	4.31599	−	7.47552i	0.197203	−	0.341565i	0.947620	+	0.319399i	$0.103481\pi$
$480$	1.73920	+	1.40542i	0.0793831	+	0.0641482i
$481$	1.07364			0.0489536
$482$	11.4282	+	6.59807i	0.520540	+	0.300534i
$483$	4.76065	−	2.74856i	0.216617	−	0.125064i
$484$	−5.47072	+	9.47556i	−0.248669	+	0.430707i
$485$	−1.32188	−	0.207973i	−0.0600234	−	0.00944359i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	2.40243	−	1.38704i	0.108865	−	0.0628530i	−0.444579	−	0.895740i	$-0.646647\pi$
$487$	2.40243	−	1.38704i	0.108865	−	0.0628530i	0.553444	+	0.832887i	$0.313313\pi$
$488$			12.8443i			0.581432i
$489$	−5.68555	+	9.84766i	−0.257109	+	0.445326i
$490$	4.72485	+	12.2710i	0.213447	+	0.554345i
$491$	5.44013	+	9.42258i	0.245510	+	0.425235i	0.962275	−	0.272079i	$-0.0877114\pi$
$491$	5.44013	+	9.42258i	0.245510	+	0.425235i	−0.716765	+	0.697315i	$0.754378\pi$
$492$		−	6.51096i		−	0.293537i
$493$	1.56402	+	0.902985i	0.0704398	+	0.0406684i
$494$	5.86030			0.263667
$495$	−0.420895	−	0.340119i	−0.0189178	−	0.0152872i
$496$	2.15968	+	5.13184i	0.0969727	+	0.230426i
$497$		−	23.0171i		−	1.03246i
$498$		−	5.57417i		−	0.249784i
$499$	−9.45048	+	16.3687i	−0.423061	+	0.732764i	−0.996237	−	0.0866685i	$-0.972378\pi$
$499$	−9.45048	+	16.3687i	−0.423061	+	0.732764i	0.573176	+	0.819432i	$0.305711\pi$
$500$	−5.04505	+	9.97735i	−0.225622	+	0.446201i
$501$	8.81263	+	15.2639i	0.393719	+	0.681942i
$502$	−24.5597	−	14.1796i	−1.09615	−	0.632865i
$503$	25.9889	+	15.0047i	1.15879	+	0.669027i	0.951013	−	0.309150i	$-0.100044\pi$
$503$	25.9889	+	15.0047i	1.15879	+	0.669027i	0.207775	+	0.978177i	$0.433378\pi$
$504$	−3.58894			−0.159864
$505$	−1.05520	+	6.70684i	−0.0469557	+	0.298450i
$506$	−0.185338	−	0.321015i	−0.00823929	−	0.0142709i
$507$	−10.8237	+	6.24909i	−0.480699	+	0.277532i
$508$	5.05887	+	2.92074i	0.224451	+	0.129587i
$509$	13.4691	+	23.3291i	0.597006	+	1.03404i	0.993260	+	0.115904i	$0.0369764\pi$
$509$	13.4691	+	23.3291i	0.597006	+	1.03404i	−0.396255	+	0.918141i	$0.629690\pi$
$510$	−2.91994	−	7.58343i	−0.129297	−	0.335800i
$511$	18.7180			0.828037
$512$		−	1.00000i		−	0.0441942i
$513$	−7.16434	−	4.13634i	−0.316313	−	0.182624i
$514$	8.58234	+	14.8651i	0.378551	+	0.655669i
$515$	−7.01932	−	18.2300i	−0.309308	−	0.803309i
$516$	−1.65939	−	2.87415i	−0.0730506	−	0.126527i
$517$	1.45742	−	0.841440i	0.0640971	−	0.0370065i
$518$	4.71064	−	2.71969i	0.206974	−	0.119496i
$519$	−15.1587			−0.665394
$520$	−1.47822	+	0.569178i	−0.0648243	+	0.0249601i
$521$	3.21978	−	5.57681i	0.141061	−	0.244325i	−0.786835	−	0.617163i	$-0.788282\pi$
$521$	3.21978	−	5.57681i	0.141061	−	0.244325i	0.927896	+	0.372838i	$0.121615\pi$
$522$	−0.430369	+	0.248474i	−0.0188367	+	0.0108754i
$523$		−	45.0061i		−	1.96798i	−0.178230	−	0.983989i	$-0.557037\pi$
$523$		−	45.0061i		−	1.96798i	0.178230	−	0.983989i	$-0.442963\pi$
$524$	−2.30983	+	4.00075i	−0.100905	+	0.174773i
$525$	−3.76696	−	17.5449i	−0.164404	−	0.765721i
$526$	−26.5382			−1.15712
$527$	2.52782	−	20.0755i	0.110114	−	0.874500i
$528$			0.242005i			0.0105319i
$529$	20.6539			0.897997
$530$	7.86645	−	3.02892i	0.341697	−	0.131568i
$531$	−4.72844			−0.205197
$532$	25.7124	−	14.8451i	1.11477	−	0.643615i
$533$	3.99438	+	2.30616i	0.173016	+	0.0998908i
$534$	−6.59823	+	11.4285i	−0.285533	+	0.494558i
$535$	0.344266	−	0.426027i	0.0148839	−	0.0184187i
$536$	4.46287	+	7.72991i	0.192767	+	0.333881i
$537$	18.4977	−	10.6796i	0.798234	−	0.460860i
$538$	−13.5078	+	7.79873i	−0.582363	+	0.336227i
$539$	−0.711555	+	1.23245i	−0.0306488	+	0.0530854i
$540$	2.20890	+	0.347530i	0.0950558	+	0.0149553i
$541$	2.88336	−	4.99413i	0.123965	−	0.214714i	−0.797363	−	0.603500i	$-0.793772\pi$
$541$	2.88336	−	4.99413i	0.123965	−	0.214714i	0.921328	+	0.388786i	$0.127105\pi$
$542$			8.17223i			0.351028i
$543$		−	2.58650i		−	0.110997i
$544$	−1.81706	+	3.14725i	−0.0779060	+	0.134937i
$545$	0.960338	−	6.10390i	0.0411363	−	0.261462i
$546$	1.27119	−	2.20176i	0.0544019	−	0.0942268i
$547$	21.4533	−	12.3861i	0.917277	−	0.529590i	0.0345118	−	0.999404i	$-0.489012\pi$
$547$	21.4533	−	12.3861i	0.917277	−	0.529590i	0.882765	+	0.469814i	$0.155679\pi$
$548$	−8.83590	+	5.10141i	−0.377451	+	0.217921i
$549$	6.42213	+	11.1235i	0.274090	+	0.474738i
$550$	−1.18307	+	0.254009i	−0.0504461	+	0.0108310i
$551$	2.05554	−	3.56030i	0.0875690	−	0.151674i
$552$	1.32648	+	0.765843i	0.0564587	+	0.0325964i
$553$	−15.1708	+	8.75885i	−0.645127	+	0.372464i
$554$	−17.9774			−0.763786
$555$	−3.16263	+	1.21775i	−0.134246	+	0.0516905i
$556$	−17.0843			−0.724537
$557$		−	24.6349i		−	1.04382i	−0.853002	−	0.521908i	$-0.825220\pi$
$557$		−	24.6349i		−	1.04382i	0.853002	−	0.521908i	$-0.174780\pi$
$558$	4.43626	+	3.36446i	0.187802	+	0.142429i
$559$	2.35100			0.0994366
$560$	−5.04396	+	6.24187i	−0.213146	+	0.263767i
$561$	0.439740	−	0.761651i	0.0185658	−	0.0321569i
$562$			31.2439i			1.31794i
$563$	3.22224	−	1.86036i	0.135801	−	0.0784048i	−0.430560	−	0.902562i	$-0.641684\pi$
$563$	3.22224	−	1.86036i	0.135801	−	0.0784048i	0.566361	+	0.824157i	$0.308351\pi$
$564$	−3.47695	+	6.02225i	−0.146406	+	0.253582i
$565$	−1.81052	−	4.70212i	−0.0761691	−	0.197820i
$566$	−30.6594			−1.28871
$567$	−3.10811	+	1.79447i	−0.130528	+	0.0753606i
$568$	5.55412	−	3.20667i	0.233046	−	0.134549i
$569$	18.8640	+	32.6734i	0.790820	+	1.36974i	0.925460	+	0.378846i	$0.123679\pi$
$569$	18.8640	+	32.6734i	0.790820	+	1.36974i	−0.134639	+	0.990895i	$0.542988\pi$
$570$	−17.2628	+	6.64691i	−0.723059	+	0.278409i
$571$	1.56822	+	2.71624i	0.0656280	+	0.113671i	0.896972	−	0.442087i	$-0.145762\pi$
$571$	1.56822	+	2.71624i	0.0656280	+	0.113671i	−0.831344	+	0.555758i	$0.812428\pi$
$572$	−0.148467	−	0.0857174i	−0.00620772	−	0.00358403i
$573$		−	18.3183i		−	0.765258i
$574$	23.3674			0.975338
$575$	−2.35162	+	7.28845i	−0.0980693	+	0.303949i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−18.7289	−	10.8131i	−0.779692	−	0.450156i	0.0566288	−	0.998395i	$-0.481965\pi$
$577$	−18.7289	−	10.8131i	−0.779692	−	0.450156i	−0.836321	+	0.548240i	$0.815298\pi$
$578$	−3.28493	+	1.89655i	−0.136635	+	0.0788862i
$579$	3.96856	+	6.87375i	0.164928	+	0.285663i
$580$	−0.172704	+	1.09771i	−0.00717114	+	0.0455797i
$581$	20.0053			0.829962
$582$	0.518259	+	0.299217i	0.0214825	+	0.0124029i
$583$	0.790077	+	0.456151i	0.0327216	+	0.0188918i
$584$	2.60774	+	4.51674i	0.107909	+	0.186904i
$585$	−0.995587	+	1.23203i	−0.0411625	+	0.0509383i
$586$	11.3506	−	19.6599i	0.468891	−	0.812143i
$587$			31.7414i			1.31011i	0.755582	+	0.655054i	$0.227354\pi$
$587$			31.7414i			1.31011i	−0.755582	+	0.655054i	$0.772646\pi$
$588$		−	5.88049i		−	0.242507i
$589$	−45.6994	−	5.75428i	−1.88301	−	0.237101i
$590$	−6.64544	+	8.22368i	−0.273588	+	0.338564i
$591$	−16.9874			−0.698770
$592$	1.31254	+	0.757798i	0.0539452	+	0.0311453i
$593$		−	18.1581i		−	0.745663i	−0.927899	−	0.372831i	$-0.878387\pi$
$593$		−	18.1581i		−	0.745663i	0.927899	−	0.372831i	$-0.121613\pi$
$594$	0.121003	+	0.209583i	0.00496480	+	0.00859929i
$595$	27.2165	−	10.4795i	1.11577	−	0.429618i
$596$	0.127232	−	0.220372i	0.00521162	−	0.00902678i
$597$			8.97302i			0.367241i
$598$	−0.939668	+	0.542517i	−0.0384259	+	0.0221852i
$599$	−19.5410	−	33.8460i	−0.798423	−	1.38291i	−0.920643	−	0.390406i	$-0.872335\pi$
$599$	−19.5410	−	33.8460i	−0.798423	−	1.38291i	0.122220	−	0.992503i	$-0.460999\pi$
$600$	3.70884	−	3.35328i	0.151413	−	0.136897i
$601$	−8.60588	+	14.9058i	−0.351041	+	0.608021i	−0.986432	−	0.164169i	$-0.947506\pi$
$601$	−8.60588	+	14.9058i	−0.351041	+	0.608021i	0.635391	+	0.772191i	$0.280839\pi$
$602$	10.3151	−	5.95545i	0.420414	−	0.242726i
$603$	7.72991	+	4.46287i	0.314786	+	0.181742i
$604$	−18.4193			−0.749470
$605$	19.0293	+	15.3773i	0.773651	+	0.625176i
$606$	1.51814	−	2.62950i	0.0616703	−	0.106816i
$607$	42.3387	−	24.4442i	1.71847	−	0.992161i	0.796753	−	0.604305i	$-0.206549\pi$
$607$	42.3387	−	24.4442i	1.71847	−	0.992161i	0.921720	−	0.387856i	$-0.126784\pi$
$608$	7.16434	+	4.13634i	0.290552	+	0.167751i
$609$	−0.891757	−	1.54457i	−0.0361358	−	0.0625891i
$610$	28.3716	+	4.46376i	1.14873	+	0.180732i
$611$	−2.46304	−	4.26611i	−0.0996440	−	0.172589i
$612$			3.63413i			0.146901i
$613$	−36.1531	−	20.8730i	−1.46021	−	0.843052i	−0.461188	−	0.887303i	$-0.652576\pi$
$613$	−36.1531	−	20.8730i	−1.46021	−	0.843052i	−0.999020	+	0.0442511i	$0.985910\pi$
$614$	12.9614	−	22.4497i	0.523078	−	0.905997i
$615$	−14.3820	−	2.26275i	−0.579940	−	0.0912429i
$616$	−0.868543			−0.0349946
$617$	−29.7484	−	17.1753i	−1.19763	−	0.691450i	−0.237601	−	0.971363i	$-0.576361\pi$
$617$	−29.7484	−	17.1753i	−1.19763	−	0.691450i	−0.960025	+	0.279913i	$0.909694\pi$
$618$			8.73617i			0.351420i
$619$	43.0207			1.72915			0.864575	−	0.502504i	$-0.167588\pi$
$619$	43.0207			1.72915			0.864575	+	0.502504i	$0.167588\pi$
$620$	12.0863	−	2.98705i	0.485396	−	0.119963i
$621$	1.53169			0.0614644
$622$		−	26.0921i		−	1.04620i
$623$	−41.0161	−	23.6807i	−1.64328	−	0.948746i
$624$	0.708393			0.0283584
$625$	20.2856	+	14.6114i	0.811425	+	0.584457i
$626$	−10.3792	+	17.9774i	−0.414838	+	0.718520i
$627$	−1.73381	−	1.00102i	−0.0692417	−	0.0399767i
$628$			10.8271i			0.432049i
$629$	−2.75393	−	4.76995i	−0.109807	−	0.190191i
$630$	−1.24726	+	7.92760i	−0.0496922	+	0.315843i
$631$	12.4633	+	21.5871i	0.496156	+	0.859368i	0.999990	−	0.00443272i	$-0.00141098\pi$
$631$	12.4633	+	21.5871i	0.496156	+	0.859368i	−0.503834	+	0.863801i	$0.668078\pi$
$632$	−4.22709	−	2.44051i	−0.168145	−	0.0970784i
$633$	10.7635	−	6.21432i	0.427811	−	0.246997i
$634$	6.45280	−	11.1766i	0.256273	−	0.443879i
$635$	8.20971	−	10.1595i	0.325793	−	0.403166i
$636$	−3.76976			−0.149481
$637$	3.60760	+	2.08285i	0.142938	+	0.0825254i
$638$	−0.104152	+	0.0601320i	−0.00412340	+	0.00238065i
$639$	3.20667	−	5.55412i	0.126854	−	0.219718i
$640$	−2.20890	−	0.347530i	−0.0873143	−	0.0137373i
$641$	−2.64555	−	4.58222i	−0.104493	−	0.180987i	0.809038	−	0.587756i	$-0.199989\pi$
$641$	−2.64555	−	4.58222i	−0.104493	−	0.180987i	−0.913531	+	0.406769i	$0.866655\pi$
$642$	−0.212138	+	0.122478i	−0.00837243	+	0.00483383i
$643$			38.3672i			1.51305i	0.653963	+	0.756526i	$0.273105\pi$
$643$			38.3672i			1.51305i	−0.653963	+	0.756526i	$0.726895\pi$
$644$	−2.74856	+	4.76065i	−0.108309	+	0.187596i
$645$	−6.92538	+	2.66657i	−0.272687	+	0.104996i
$646$	−15.0320	−	26.0361i	−0.591425	−	1.02438i
$647$			46.9826i			1.84708i	0.383506	+	0.923538i	$0.374716\pi$
$647$			46.9826i			1.84708i	−0.383506	+	0.923538i	$0.625284\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−1.14431			−0.0449181
$650$	0.743530	+	3.46304i	0.0291637	+	0.135832i
$651$	−12.0748	+	15.9215i	−0.473250	+	0.624012i
$652$		−	11.3711i		−	0.445326i
$653$			50.0183i			1.95737i	0.205373	+	0.978684i	$0.434159\pi$
$653$			50.0183i			1.95737i	−0.205373	+	0.978684i	$0.565841\pi$
$654$	−1.38166	+	2.39311i	−0.0540273	+	0.0935780i
$655$	8.03450	+	6.49256i	0.313934	+	0.253685i
$656$	3.25548	+	5.63866i	0.127105	+	0.220153i
$657$	4.51674	+	2.60774i	0.176215	+	0.101738i
$658$	−21.6135	−	12.4785i	−0.842581	−	0.486464i
$659$	−29.7346			−1.15829			−0.579147	−	0.815223i	$-0.696614\pi$
$659$	−29.7346			−1.15829			−0.579147	+	0.815223i	$0.696614\pi$
$660$	0.534565	+	0.0841041i	0.0208079	+	0.00327375i
$661$	4.62367	+	8.00844i	0.179840	+	0.311492i	0.941826	−	0.336102i	$-0.109109\pi$
$661$	4.62367	+	8.00844i	0.179840	+	0.311492i	−0.761986	+	0.647594i	$0.775775\pi$
$662$	−4.26481	+	2.46229i	−0.165757	+	0.0956997i
$663$	−2.22949	−	1.28719i	−0.0865861	−	0.0499905i
$664$	2.78708	+	4.82737i	0.108160	+	0.187338i
$665$	−23.8554	−	61.9551i	−0.925072	−	2.40252i
$666$	1.51560			0.0587281
$667$			0.761167i			0.0294725i
$668$	−15.2639	−	8.81263i	−0.590579	−	0.340971i
$669$	−10.5963	−	18.3534i	−0.409678	−	0.709583i
$670$	18.6256	−	7.17164i	0.719568	−	0.277065i
$671$	1.55419	+	2.69194i	0.0599989	+	0.103921i
$672$	3.10811	−	1.79447i	0.119898	−	0.0692232i
$673$	−28.3301	+	16.3564i	−1.09204	+	0.630492i	−0.934120	−	0.356959i	$-0.883813\pi$
$673$	−28.3301	+	16.3564i	−1.09204	+	0.630492i	−0.157924	+	0.987451i	$0.550480\pi$
$674$	1.14989			0.0442922
$675$	1.53531	−	4.75845i	0.0590943	−	0.183153i
$676$	6.24909	−	10.8237i	0.240350	−	0.416298i
$677$	−9.87119	+	5.69913i	−0.379381	+	0.219036i	−0.677549	−	0.735478i	$-0.736958\pi$
$677$	−9.87119	+	5.69913i	−0.379381	+	0.219036i	0.298168	+	0.954513i	$0.403624\pi$
$678$			2.25335i			0.0865394i
$679$	−1.07387	+	1.86000i	−0.0412114	+	0.0713802i
$680$	6.32046	+	5.10747i	0.242379	+	0.195863i
$681$	−0.338379			−0.0129667
$682$	1.07360	+	0.814218i	0.0411102	+	0.0311780i
$683$			5.83163i			0.223141i	0.993757	+	0.111571i	$0.0355881\pi$
$683$			5.83163i			0.223141i	−0.993757	+	0.111571i	$0.964412\pi$
$684$	8.27267			0.316313
$685$	8.19775	+	21.2905i	0.313220	+	0.813467i
$686$	−4.01787			−0.153403
$687$	6.59451	−	3.80734i	0.251596	−	0.145259i
$688$	2.87415	+	1.65939i	0.109576	+	0.0632636i
$689$	1.33523	−	2.31269i	0.0508684	−	0.0881066i
$690$	2.15266	−	2.66390i	0.0819503	−	0.101413i
$691$	14.5617	+	25.2216i	0.553953	+	0.959474i	0.997984	+	0.0634629i	$0.0202144\pi$
$691$	14.5617	+	25.2216i	0.553953	+	0.959474i	−0.444032	+	0.896011i	$0.646452\pi$
$692$	13.1278	−	7.57936i	0.499045	−	0.288124i
$693$	−0.752180	+	0.434272i	−0.0285730	+	0.0164966i
$694$	−0.107372	+	0.185974i	−0.00407579	+	0.00705948i
$695$	−5.93731	+	37.7375i	−0.225215	+	1.43147i
$696$	0.248474	−	0.430369i	0.00941837	−	0.0163131i
$697$		−	23.6617i		−	0.896249i
$698$			35.8927i			1.35856i
$699$	10.7684	−	18.6514i	0.407299	−	0.705462i
$700$	12.0347	+	13.3108i	0.454869	+	0.503102i
$701$	5.36748	−	9.29674i	0.202727	−	0.351133i	−0.746679	−	0.665184i	$-0.768353\pi$
$701$	5.36748	−	9.29674i	0.202727	−	0.351133i	0.949406	+	0.314051i	$0.101686\pi$
$702$	0.613486	−	0.354196i	0.0231545	−	0.0133683i
$703$	−10.8582	+	6.26901i	−0.409526	+	0.236440i
$704$	−0.121003	−	0.209583i	−0.00456046	−	0.00789895i
$705$	12.0942	+	9.77312i	0.455493	+	0.368077i
$706$	10.6085	−	18.3744i	0.399255	−	0.691530i
$707$	9.43712	+	5.44852i	0.354919	+	0.204913i
$708$	4.09495	−	2.36422i	0.153898	−	0.0888529i
$709$	−27.2406			−1.02304			−0.511521	−	0.859271i	$-0.670918\pi$
$709$	−27.2406			−1.02304			−0.511521	+	0.859271i	$0.670918\pi$
$710$	−5.15299	−	13.3829i	−0.193388	−	0.502251i
$711$	−4.88103			−0.183053
$712$		−	13.1965i		−	0.494558i
$713$	7.86036	−	3.30796i	0.294373	−	0.123884i
$714$	−13.0427			−0.488110
$715$	−0.240938	+	0.298159i	−0.00901056	+	0.0111505i
$716$	−10.6796	+	18.4977i	−0.399117	+	0.691291i
$717$			15.7229i			0.587182i
$718$	−1.70321	+	0.983349i	−0.0635633	+	0.0366983i
$719$	2.90703	−	5.03512i	0.108414	−	0.187778i	−0.806714	−	0.590942i	$-0.798756\pi$
$719$	2.90703	−	5.03512i	0.108414	−	0.187778i	0.915128	+	0.403164i	$0.132090\pi$
$720$	−2.08673	+	0.803479i	−0.0777677	+	0.0299439i
$721$	−31.3536			−1.16767
$722$	−42.8138	+	24.7185i	−1.59336	+	0.919929i
$723$	−11.4282	+	6.59807i	−0.425019	+	0.245385i
$724$	1.29325	+	2.23997i	0.0480632	+	0.0832480i
$725$	2.36470	+	0.762970i	0.0878227	+	0.0283360i
$726$	−5.47072	−	9.47556i	−0.203037	−	0.351671i
$727$	−37.3020	−	21.5363i	−1.38345	−	0.798738i	−0.390888	−	0.920438i	$-0.627832\pi$
$727$	−37.3020	−	21.5363i	−1.38345	−	0.798738i	−0.992567	+	0.121700i	$0.961165\pi$
$728$			2.54238i			0.0942268i
$729$	−1.00000			−0.0370370
$730$	10.8833	−	4.19052i	0.402808	−	0.155098i
$731$	−6.03044	−	10.4450i	−0.223044	−	0.386323i
$732$	−11.1235	−	6.42213i	−0.411135	−	0.237369i
$733$	−15.6886	+	9.05783i	−0.579473	+	0.334559i	−0.760924	−	0.648841i	$-0.775254\pi$
$733$	−15.6886	+	9.05783i	−0.579473	+	0.334559i	0.181451	+	0.983400i	$0.441921\pi$
$734$	6.60094	+	11.4332i	0.243645	+	0.422006i
$735$	−12.9894	−	2.04364i	−0.479121	−	0.0753809i
$736$	−1.53169			−0.0564587
$737$	1.87068	+	1.08004i	0.0689074	+	0.0397837i
$738$	5.63866	+	3.25548i	0.207562	+	0.119836i
$739$	−26.5666	−	46.0147i	−0.977268	−	1.69268i	−0.672237	−	0.740336i	$-0.734667\pi$
$739$	−26.5666	−	46.0147i	−0.977268	−	1.69268i	−0.305031	−	0.952342i	$-0.598667\pi$
$740$	2.13004	−	2.63592i	0.0783020	−	0.0968982i
$741$	−2.93015	+	5.07517i	−0.107642	+	0.186441i
$742$		−	13.5294i		−	0.496681i
$743$		−	27.0870i		−	0.993727i	−0.867829	−	0.496863i	$-0.834485\pi$
$743$		−	27.0870i		−	0.993727i	0.867829	−	0.496863i	$-0.165515\pi$
$744$	−5.52414	−	0.695578i	−0.202525	−	0.0255011i
$745$	−0.442562	−	0.357627i	−0.0162142	−	0.0131025i
$746$	−12.8821			−0.471647
$747$	4.82737	+	2.78708i	0.176624	+	0.101974i
$748$			0.879479i			0.0321569i
$749$	−0.439567	−	0.761352i	−0.0160614	−	0.0278192i
$750$	−6.11811	−	9.35782i	−0.223402	−	0.341699i
$751$	−14.7864	+	25.6107i	−0.539562	+	0.934549i	0.459366	+	0.888247i	$0.348077\pi$
$751$	−14.7864	+	25.6107i	−0.539562	+	0.934549i	−0.998928	+	0.0463013i	$0.985257\pi$
$752$		−	6.95389i		−	0.253582i
$753$	24.5597	−	14.1796i	0.895007	−	0.516732i
$754$	0.176017	+	0.304870i	0.00641016	+	0.0111027i
$755$	−6.40125	+	40.6863i	−0.232965	+	1.48073i
$756$	1.79447	−	3.10811i	0.0652642	−	0.113041i
$757$	−38.0398	+	21.9623i	−1.38258	+	0.798234i	−0.992465	−	0.122532i	$-0.960899\pi$
$757$	−38.0398	+	21.9623i	−1.38258	+	0.798234i	−0.390117	+	0.920765i	$0.627565\pi$
$758$	−25.1663	−	14.5298i	−0.914082	−	0.527745i
$759$	0.370676			0.0134547
$760$	11.6266	−	14.3878i	0.421740	−	0.521900i
$761$	−0.204263	+	0.353795i	−0.00740455	+	0.0128250i	−0.869704	−	0.493574i	$-0.835690\pi$
$761$	−0.204263	+	0.353795i	−0.00740455	+	0.0128250i	0.862299	+	0.506399i	$0.169024\pi$
$762$	−5.05887	+	2.92074i	−0.183263	+	0.105807i
$763$	−8.58873	−	4.95870i	−0.310933	−	0.179517i
$764$	9.15916	+	15.8641i	0.331367	+	0.573944i
$765$	8.02741	+	1.26297i	0.290232	+	0.0456627i
$766$	10.0786	+	17.4567i	0.364156	+	0.630736i
$767$			3.34959i			0.120947i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	−6.97418	+	12.0796i	−0.251495	+	0.435603i	−0.963938	−	0.266128i	$-0.914256\pi$
$769$	−6.97418	+	12.0796i	−0.251495	+	0.435603i	0.712442	+	0.701731i	$0.247589\pi$
$770$	−0.301845	+	1.91852i	−0.0108777	+	0.0691387i
$771$	−17.1647			−0.618171
$772$	−6.87375	−	3.96856i	−0.247392	−	0.142832i
$773$			24.6110i			0.885194i	0.896721	+	0.442597i	$0.145943\pi$
$773$			24.6110i			0.885194i	−0.896721	+	0.442597i	$0.854057\pi$
$774$	3.31878			0.119291
$775$	−2.39776	−	27.7354i	−0.0861300	−	0.996284i
$776$	−0.598433			−0.0214825
$777$			5.43938i			0.195137i
$778$	26.8411	+	15.4967i	0.962300	+	0.555584i
$779$	−53.8630			−1.92984
$780$	0.246187	−	1.56477i	0.00881492	−	0.0560276i
$781$	0.776032	−	1.34413i	0.0277686	−	0.0480967i
$782$	4.82060	+	2.78317i	0.172384	+	0.0995260i
$783$		−	0.496947i		−	0.0177595i
$784$	2.94024	+	5.09265i	0.105009	+	0.181880i
$785$	23.9160	+	3.76274i	0.853598	+	0.134298i
$786$	−2.30983	−	4.00075i	−0.0823890	−	0.142702i
$787$	−16.1515	−	9.32508i	−0.575739	−	0.332403i	0.183699	−	0.982983i	$-0.441193\pi$
$787$	−16.1515	−	9.32508i	−0.575739	−	0.332403i	−0.759438	+	0.650579i	$0.774526\pi$
$788$	14.7115	−	8.49372i	0.524077	−	0.302576i
$789$	13.2691	−	22.9827i	0.472392	−	0.818206i
$790$	−6.85988	+	8.48906i	−0.244064	+	0.302027i
$791$	−8.08714			−0.287545
$792$	−0.209583	−	0.121003i	−0.00744720	−	0.00429965i
$793$	7.87977	−	4.54939i	0.279819	−	0.161554i
$794$	18.8827	−	32.7058i	0.670123	−	1.16069i
$795$	−1.31010	+	8.32700i	−0.0464646	+	0.295328i
$796$	−4.48651	−	7.77086i	−0.159020	−	0.275431i
$797$	4.66931	−	2.69583i	0.165395	−	0.0954910i	−0.415017	−	0.909813i	$-0.636225\pi$
$797$	4.66931	−	2.69583i	0.165395	−	0.0954910i	0.580413	+	0.814322i	$0.302891\pi$
$798$			29.6901i			1.05102i
$799$	−12.6357	+	21.8856i	−0.447018	+	0.774258i
$800$	−1.53531	+	4.75845i	−0.0542816	+	0.168236i
$801$	−6.59823	−	11.4285i	−0.233137	−	0.403805i
$802$		−	25.8779i		−	0.913782i
$803$	1.09307	+	0.631087i	0.0385738	+	0.0222706i
$804$	−8.92574			−0.314786
$805$	9.56058	+	7.72576i	0.336966	+	0.272297i
$806$	2.38336	−	3.14261i	0.0839502	−	0.110694i
$807$		−	15.5975i		−	0.549057i
$808$			3.03628i			0.106816i
$809$	−15.9054	+	27.5489i	−0.559203	+	0.968568i	0.438360	+	0.898799i	$0.355559\pi$
$809$	−15.9054	+	27.5489i	−0.559203	+	0.968568i	−0.997563	+	0.0697685i	$0.977774\pi$
$810$	−1.40542	+	1.73920i	−0.0493813	+	0.0611091i
$811$	−13.7661	−	23.8436i	−0.483394	−	0.837263i	0.516424	−	0.856333i	$-0.327263\pi$
$811$	−13.7661	−	23.8436i	−0.483394	−	0.837263i	−0.999818	+	0.0190701i	$0.993929\pi$
$812$	1.54457	+	0.891757i	0.0542037	+	0.0312945i
$813$	−7.07736	−	4.08612i	−0.248214	−	0.143306i
$814$	0.366782			0.0128557
$815$	−25.1176	−	3.95179i	−0.879830	−	0.138425i
$816$	−1.81706	−	3.14725i	−0.0636100	−	0.110176i
$817$	−23.7769	+	13.7276i	−0.831847	+	0.480267i
$818$	−5.98811	−	3.45724i	−0.209369	−	0.120879i
$819$	1.27119	+	2.20176i	0.0444189	+	0.0769359i
$820$	13.5866	−	5.23142i	0.474464	−	0.182689i
$821$	10.3712			0.361958			0.180979	−	0.983487i	$-0.442073\pi$
$821$	10.3712			0.361958			0.180979	+	0.983487i	$0.442073\pi$
$822$		−	10.2028i		−	0.355864i
$823$	−31.4893	−	18.1804i	−1.09765	−	0.633727i	−0.162046	−	0.986783i	$-0.551809\pi$
$823$	−31.4893	−	18.1804i	−1.09765	−	0.633727i	−0.935602	+	0.353056i	$0.885143\pi$
$824$	−4.36808	−	7.56574i	−0.152169	−	0.263565i
$825$	0.371554	−	1.15157i	0.0129359	−	0.0400925i
$826$	8.48505	+	14.6965i	0.295233	+	0.511358i
$827$	10.5171	−	6.07206i	0.365716	−	0.211146i	−0.305869	−	0.952074i	$-0.598947\pi$
$827$	10.5171	−	6.07206i	0.365716	−	0.211146i	0.671585	+	0.740927i	$0.265614\pi$
$828$	−1.32648	+	0.765843i	−0.0460983	+	0.0266149i
$829$	35.1522			1.22089			0.610443	−	0.792060i	$-0.290992\pi$
$829$	35.1522			1.22089			0.610443	+	0.792060i	$0.290992\pi$
$830$	11.6318	−	4.47872i	0.403744	−	0.155459i
$831$	8.98869	−	15.5689i	0.311814	−	0.540078i
$832$	−0.613486	+	0.354196i	−0.0212688	+	0.0122795i
$833$		−	21.3704i		−	0.740442i
$834$	8.54217	−	14.7955i	0.295791	−	0.512325i
$835$	−24.7709	+	30.6538i	−0.857231	+	1.06082i
$836$	2.00203			0.0692417
$837$	−5.13184	+	2.15968i	−0.177382	+	0.0746496i
$838$			15.6618i			0.541026i
$839$	26.3914			0.911134			0.455567	−	0.890202i	$-0.349437\pi$
$839$	26.3914			0.911134			0.455567	+	0.890202i	$0.349437\pi$
$840$	−2.88364	−	7.48913i	−0.0994949	−	0.258400i
$841$	−28.7530			−0.991484
$842$	27.7290	−	16.0093i	0.955603	−	0.551718i
$843$	−27.0580	−	15.6219i	−0.931927	−	0.538048i
$844$	−6.21432	+	10.7635i	−0.213906	+	0.370495i
$845$	−21.7368	−	17.5652i	−0.747768	−	0.604260i
$846$	−3.47695	−	6.02225i	−0.119540	−	0.207049i
$847$	34.0072	−	19.6341i	1.16850	−	0.674635i
$848$	3.26471	−	1.88488i	0.112110	−	0.0647270i
$849$	15.3297	−	26.5518i	0.526114	−	0.911257i
$850$	13.4784	−	12.1862i	0.462306	−	0.417985i
$851$	1.16071	−	2.01041i	0.0397886	−	0.0689158i
$852$			6.41335i			0.219718i
$853$			11.1103i			0.380410i	0.981744	+	0.190205i	$0.0609153\pi$
$853$			11.1103i			0.380410i	−0.981744	+	0.190205i	$0.939085\pi$
$854$	23.0486	−	39.9214i	0.788708	−	1.36608i
$855$	2.87500	−	18.2735i	0.0983229	−	0.624940i
$856$	0.122478	−	0.212138i	0.00418622	−	0.00725074i
$857$	8.87235	−	5.12245i	0.303074	−	0.174980i	−0.340749	−	0.940154i	$-0.610681\pi$
$857$	8.87235	−	5.12245i	0.303074	−	0.174980i	0.643823	+	0.765175i	$0.277347\pi$
$858$	0.148467	−	0.0857174i	0.00506858	−	0.00292635i
$859$	−2.35433	−	4.07782i	−0.0803287	−	0.139133i	0.823062	−	0.567951i	$-0.192264\pi$
$859$	−2.35433	−	4.07782i	−0.0803287	−	0.139133i	−0.903391	+	0.428818i	$0.858930\pi$
$860$	4.66427	−	5.77201i	0.159050	−	0.196824i
$861$	−11.6837	+	20.2368i	−0.398180	+	0.689668i
$862$	10.3856	+	5.99616i	0.353737	+	0.204230i
$863$	−25.3890	+	14.6584i	−0.864253	+	0.498977i	−0.865434	−	0.501023i	$-0.832957\pi$
$863$	−25.3890	+	14.6584i	−0.864253	+	0.498977i	0.00118133	+	0.999999i	$0.499624\pi$
$864$	1.00000			0.0340207
$865$	−12.1797	−	31.6321i	−0.414122	−	1.07552i
$866$	15.4387			0.524628
$867$		−	3.79311i		−	0.128821i
$868$	2.49639	−	19.8258i	0.0847329	−	0.672932i
$869$	−1.18123			−0.0400706
$870$	−0.864289	−	0.698419i	−0.0293021	−	0.0236786i
$871$	3.16146	−	5.47581i	0.107122	−	0.185541i
$872$		−	2.76333i		−	0.0935780i
$873$	−0.518259	+	0.299217i	−0.0175404	+	0.0101270i
$874$	6.33557	−	10.9735i	0.214304	−	0.371185i
$875$	33.5846	−	21.9575i	1.13537	−	0.742300i
$876$	−5.21548			−0.176215
$877$	−6.69972	+	3.86809i	−0.226234	+	0.130616i	−0.608833	−	0.793298i	$-0.708362\pi$
$877$	−6.69972	+	3.86809i	−0.226234	+	0.130616i	0.382600	+	0.923914i	$0.375029\pi$
$878$	5.05205	−	2.91680i	0.170498	−	0.0984372i
$879$	11.3506	+	19.6599i	0.382848	+	0.663112i
$880$	−0.504999	+	0.194446i	−0.0170235	+	0.00655478i
$881$	−18.6650	−	32.3288i	−0.628841	−	1.08919i	−0.987785	−	0.155826i	$-0.950196\pi$
$881$	−18.6650	−	32.3288i	−0.628841	−	1.08919i	0.358943	−	0.933359i	$-0.383137\pi$
$882$	5.09265	+	2.94024i	0.171478	+	0.0990031i
$883$		−	44.8104i		−	1.50799i	−0.656879	−	0.753996i	$-0.728124\pi$
$883$		−	44.8104i		−	1.50799i	0.656879	−	0.753996i	$-0.271876\pi$
$884$	2.57439			0.0865861
$885$	−3.79920	−	9.86696i	−0.127709	−	0.331674i
$886$	1.34556	+	2.33058i	0.0452051	+	0.0782975i
$887$	−32.8911	−	18.9897i	−1.10438	−	0.637611i	−0.167009	−	0.985955i	$-0.553411\pi$
$887$	−32.8911	−	18.9897i	−1.10438	−	0.637611i	−0.937367	+	0.348344i	$0.886744\pi$
$888$	−1.31254	+	0.757798i	−0.0440461	+	0.0254300i
$889$	−10.4824	−	18.1560i	−0.351567	−	0.608932i
$890$	−29.1496	−	4.58616i	−0.977098	−	0.153729i
$891$	−0.242005			−0.00810749
$892$	18.3534	+	10.5963i	0.614517	+	0.354792i
$893$	49.8201	+	28.7636i	1.66716	+	0.962538i
$894$	0.127232	+	0.220372i	0.00425527	+	0.00737034i
$895$	37.1480	+	30.0187i	1.24172	+	1.00341i
$896$	−1.79447	+	3.10811i	−0.0599490	+	0.103835i
$897$		−	1.08503i		−	0.0362283i
$898$		−	22.2668i		−	0.743054i
$899$	−1.07325	−	2.55025i	−0.0357949	−	0.0850557i
$900$	1.04960	+	4.88859i	0.0349867	+	0.162953i
$901$	−13.6998			−0.456406
$902$	1.36459	+	0.787844i	0.0454357	+	0.0262323i
$903$			11.9109i			0.396370i
$904$	−1.12668	−	1.95146i	−0.0374727	−	0.0649045i
$905$	5.39731	−	2.07820i	0.179413	−	0.0690816i
$906$	9.20964	−	15.9516i	0.305970	−	0.529955i
$907$		−	8.29606i		−	0.275466i	−0.990469	−	0.137733i	$-0.956018\pi$
$907$		−	8.29606i		−	0.275466i	0.990469	−	0.137733i	$-0.0439816\pi$
$908$	0.293045	−	0.169189i	0.00972503	−	0.00561475i
$909$	1.51814	+	2.62950i	0.0503536	+	0.0872150i
$910$	5.61585	+	0.883552i	0.186164	+	0.0292895i
$911$	−21.6983	+	37.5826i	−0.718897	+	1.24517i	0.242540	+	0.970141i	$0.422019\pi$
$911$	−21.6983	+	37.5826i	−0.718897	+	1.24517i	−0.961437	+	0.275025i	$0.911314\pi$
$912$	−7.16434	+	4.13634i	−0.237235	+	0.136968i
$913$	1.16825	+	0.674489i	0.0386634	+	0.0223223i
$914$	20.0496			0.663181
$915$	−18.0516	+	22.3387i	−0.596766	+	0.738494i
$916$	−3.80734	+	6.59451i	−0.125798	+	0.217889i
$917$	14.3584	−	8.28985i	0.474157	−	0.273755i
$918$	−3.14725	−	1.81706i	−0.103875	−	0.0599721i
$919$	−0.684237	−	1.18513i	−0.0225709	−	0.0390940i	0.854519	−	0.519420i	$-0.173852\pi$
$919$	−0.684237	−	1.18513i	−0.0225709	−	0.0390940i	−0.877090	+	0.480326i	$0.840518\pi$
$920$	−0.532306	+	3.38334i	−0.0175496	+	0.111545i
$921$	12.9614	+	22.4497i	0.427091	+	0.739744i
$922$			26.9454i			0.887399i
$923$	−3.93450	−	2.27158i	−0.129506	−	0.0747701i
$924$	0.434272	−	0.752180i	0.0142865	−	0.0247449i
$925$	−5.08221	−	5.62111i	−0.167102	−	0.184821i
$926$	−17.4636			−0.573889
$927$	−7.56574	−	4.36808i	−0.248492	−	0.143467i
$928$			0.496947i			0.0163131i
$929$	58.2051			1.90965			0.954823	−	0.297174i	$-0.0960441\pi$
$929$	58.2051			1.90965			0.954823	+	0.297174i	$0.0960441\pi$
$930$	−3.45626	+	11.9605i	−0.113335	+	0.392201i
$931$	−48.6473			−1.59435
$932$			21.5368i			0.705462i
$933$	22.5964	+	13.0461i	0.739774	+	0.427109i
$934$	34.2917			1.12206
$935$	1.94268	+	0.305645i	0.0635324	+	0.00999566i
$936$	−0.354196	+	0.613486i	−0.0115773	+	0.0200524i
$937$	12.8168	+	7.39979i	0.418707	+	0.241741i	0.694524	−	0.719469i	$-0.255615\pi$
$937$	12.8168	+	7.39979i	0.418707	+	0.241741i	−0.275817	+	0.961210i	$0.588948\pi$
$938$		−	32.0339i		−	1.04594i
$939$	−10.3792	−	17.9774i	−0.338714	−	0.586669i
$940$	−15.3604	−	2.41668i	−0.501002	−	0.0788235i
$941$	10.5680	+	18.3043i	0.344507	+	0.596704i	0.985264	−	0.171040i	$-0.0547126\pi$
$941$	10.5680	+	18.3043i	0.344507	+	0.596704i	−0.640757	+	0.767744i	$0.721379\pi$
$942$	−9.37656	−	5.41356i	−0.305505	−	0.176383i
$943$	8.63665	−	4.98637i	0.281248	−	0.162379i
$944$	−2.36422	+	4.09495i	−0.0769488	+	0.133279i
$945$	−6.24187	−	5.04396i	−0.203048	−	0.164080i
$946$	0.803163			0.0261131
$947$	21.3840	+	12.3461i	0.694888	+	0.401194i	0.805440	−	0.592677i	$-0.201929\pi$
$947$	21.3840	+	12.3461i	0.694888	+	0.401194i	−0.110553	+	0.993870i	$0.535262\pi$
$948$	4.22709	−	2.44051i	0.137290	−	0.0792642i
$949$	1.84730	−	3.19962i	0.0599660	−	0.103864i
$950$	−27.7406	−	30.6820i	−0.900023	−	0.995457i
$951$	6.45280	+	11.1766i	0.209246	+	0.362425i
$952$	11.2953	−	6.52133i	0.366082	−	0.211358i
$953$			32.7202i			1.05991i	0.848025	+	0.529956i	$0.177792\pi$
$953$			32.7202i			1.05991i	−0.848025	+	0.529956i	$0.822208\pi$
$954$	1.88488	−	3.26471i	0.0610252	−	0.105699i
$955$	38.2253	−	14.7184i	1.23694	−	0.476275i
$956$	−7.86144	−	13.6164i	−0.254257	−	0.440386i
$957$		−	0.120264i		−	0.00388758i
$958$	−7.47552	−	4.31599i	−0.241523	−	0.139443i
$959$	36.6173			1.18243
$960$	1.40542	−	1.73920i	0.0453597	−	0.0561323i
$961$	−21.6715	+	22.1663i	−0.699082	+	0.715042i
$962$		−	1.07364i		−	0.0346154i
$963$		−	0.244956i		−	0.00789361i
$964$	6.59807	−	11.4282i	0.212510	−	0.368077i
$965$	−11.1550	+	13.8042i	−0.359091	+	0.444373i
$966$	−2.74856	−	4.76065i	−0.0884336	−	0.153171i
$967$	−37.3297	−	21.5523i	−1.20044	−	0.693075i	−0.239788	−	0.970825i	$-0.577078\pi$
$967$	−37.3297	−	21.5523i	−1.20044	−	0.693075i	−0.960653	+	0.277750i	$0.910411\pi$
$968$	9.47556	+	5.47072i	0.304556	+	0.175835i
$969$	30.0640			0.965793
$970$	−0.207973	+	1.32188i	−0.00667762	+	0.0424429i
$971$	10.0021	+	17.3241i	0.320981	+	0.555956i	0.980691	−	0.195565i	$-0.0626541\pi$
$971$	10.0021	+	17.3241i	0.320981	+	0.555956i	−0.659710	+	0.751521i	$0.729321\pi$
$972$	0.866025	−	0.500000i	0.0277778	−	0.0160375i
$973$	53.1000	+	30.6573i	1.70231	+	0.982828i
$974$	−1.38704	−	2.40243i	−0.0444438	−	0.0769789i
$975$	−3.37085	−	1.08761i	−0.107954	−	0.0348312i
$976$	12.8443			0.411135
$977$			4.18433i			0.133869i	0.997757	+	0.0669343i	$0.0213218\pi$
$977$			4.18433i			0.133869i	−0.997757	+	0.0669343i	$0.978678\pi$
$978$	9.84766	+	5.68555i	0.314893	+	0.181804i
$979$	−1.59681	−	2.76575i	−0.0510342	−	0.0883939i
$980$	12.2710	−	4.72485i	0.391981	−	0.150930i
$981$	−1.38166	−	2.39311i	−0.0441131	−	0.0764061i
$982$	9.42258	−	5.44013i	0.300687	−	0.173602i
$983$	4.58388	−	2.64650i	0.146203	−	0.0844103i	−0.425114	−	0.905140i	$-0.639766\pi$
$983$	4.58388	−	2.64650i	0.146203	−	0.0844103i	0.571317	+	0.820729i	$0.306433\pi$
$984$	−6.51096			−0.207562
$985$	−13.6490	−	35.4481i	−0.434895	−	1.12947i
$986$	0.902985	−	1.56402i	0.0287569	−	0.0498084i
$987$	21.6135	−	12.4785i	0.687965	−	0.397197i
$988$		−	5.86030i		−	0.186441i
$989$	2.54166	−	4.40229i	0.0808202	−	0.139985i
$990$	−0.340119	+	0.420895i	−0.0108097	+	0.0133769i
$991$	25.5055			0.810210			0.405105	−	0.914270i	$-0.367235\pi$
$991$	25.5055			0.810210			0.405105	+	0.914270i	$0.367235\pi$
$992$	5.13184	−	2.15968i	0.162936	−	0.0685700i
$993$		−	4.92458i		−	0.156277i
$994$	−23.0171			−0.730058
$995$	−18.7242	+	7.20963i	−0.593598	+	0.228561i
$996$	−5.57417			−0.176624
$997$	−32.5961	+	18.8193i	−1.03233	+	0.596015i	−0.917651	−	0.397388i	$-0.869917\pi$
$997$	−32.5961	+	18.8193i	−1.03233	+	0.596015i	−0.114677	+	0.993403i	$0.536583\pi$
$998$	16.3687	+	9.45048i	0.518142	+	0.299150i
$999$	−0.757798	+	1.31254i	−0.0239757	+	0.0415271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.s.d.439.4	✓	28
5.4	even	2	inner	930.2.s.d.439.14	yes	28
31.25	even	3	inner	930.2.s.d.769.7	yes	28
155.149	even	6	inner	930.2.s.d.769.11	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.s.d.439.4	✓	28	1.1	even	1	trivial
930.2.s.d.439.14	yes	28	5.4	even	2	inner
930.2.s.d.769.7	yes	28	31.25	even	3	inner
930.2.s.d.769.11	yes	28	155.149	even	6	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-0.347530 + 2.20890i) q^{5} +(0.500000 - 0.866025i) q^{6} +(3.10811 + 1.79447i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-0.347530 + 2.20890i) q^{5} +(0.500000 - 0.866025i) q^{6} +(3.10811 + 1.79447i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(2.20890 + 0.347530i) q^{10} +(0.121003 + 0.209583i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(0.613486 - 0.354196i) q^{13} +(1.79447 - 3.10811i) q^{14} +(-1.40542 + 1.73920i) q^{15} +1.00000 q^{16} +(-3.14725 - 1.81706i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-4.13634 + 7.16434i) q^{19} +(0.347530 - 2.20890i) q^{20} +(1.79447 + 3.10811i) q^{21} +(0.209583 - 0.121003i) q^{22} -1.53169i q^{23} +(-0.500000 + 0.866025i) q^{24} +(-4.75845 - 1.53531i) q^{25} +(-0.354196 - 0.613486i) q^{26} +1.00000i q^{27} +(-3.10811 - 1.79447i) q^{28} -0.496947 q^{29} +(1.73920 + 1.40542i) q^{30} +(2.15968 + 5.13184i) q^{31} -1.00000i q^{32} +0.242005i q^{33} +(-1.81706 + 3.14725i) q^{34} +(-5.04396 + 6.24187i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.31254 + 0.757798i) q^{37} +(7.16434 + 4.13634i) q^{38} +0.708393 q^{39} +(-2.20890 - 0.347530i) q^{40} +(3.25548 + 5.63866i) q^{41} +(3.10811 - 1.79447i) q^{42} +(2.87415 + 1.65939i) q^{43} +(-0.121003 - 0.209583i) q^{44} +(-2.08673 + 0.803479i) q^{45} -1.53169 q^{46} -6.95389i q^{47} +(0.866025 + 0.500000i) q^{48} +(2.94024 + 5.09265i) q^{49} +(-1.53531 + 4.75845i) q^{50} +(-1.81706 - 3.14725i) q^{51} +(-0.613486 + 0.354196i) q^{52} +(3.26471 - 1.88488i) q^{53} +1.00000 q^{54} +(-0.504999 + 0.194446i) q^{55} +(-1.79447 + 3.10811i) q^{56} +(-7.16434 + 4.13634i) q^{57} +0.496947i q^{58} +(-2.36422 + 4.09495i) q^{59} +(1.40542 - 1.73920i) q^{60} +12.8443 q^{61} +(5.13184 - 2.15968i) q^{62} +3.58894i q^{63} -1.00000 q^{64} +(0.569178 + 1.47822i) q^{65} +0.242005 q^{66} +(7.72991 - 4.46287i) q^{67} +(3.14725 + 1.81706i) q^{68} +(0.765843 - 1.32648i) q^{69} +(6.24187 + 5.04396i) q^{70} +(-3.20667 - 5.55412i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(4.51674 - 2.60774i) q^{73} +(0.757798 - 1.31254i) q^{74} +(-3.35328 - 3.70884i) q^{75} +(4.13634 - 7.16434i) q^{76} +0.868543i q^{77} -0.708393i q^{78} +(-2.44051 + 4.22709i) q^{79} +(-0.347530 + 2.20890i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.63866 - 3.25548i) q^{82} +(4.82737 - 2.78708i) q^{83} +(-1.79447 - 3.10811i) q^{84} +(5.10747 - 6.32046i) q^{85} +(1.65939 - 2.87415i) q^{86} +(-0.430369 - 0.248474i) q^{87} +(-0.209583 + 0.121003i) q^{88} -13.1965 q^{89} +(0.803479 + 2.08673i) q^{90} +2.54238 q^{91} +1.53169i q^{92} +(-0.695578 + 5.52414i) q^{93} -6.95389 q^{94} +(-14.3878 - 11.6266i) q^{95} +(0.500000 - 0.866025i) q^{96} +0.598433i q^{97} +(5.09265 - 2.94024i) q^{98} +(-0.121003 + 0.209583i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9}+O(q^{10}) \) 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9	\( 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9} + 4 q^{10} + 2 q^{11} - 8 q^{14} - 8 q^{15} + 28 q^{16} + 4 q^{19} - 2 q^{20} - 8 q^{21} - 14 q^{24} - 14 q^{25} - 12 q^{26} + 24 q^{29} + 4 q^{30} + 10 q^{34} + 8 q^{35} - 14 q^{36} + 24 q^{39} - 4 q^{40} + 20 q^{41} - 2 q^{44} - 2 q^{45} + 12 q^{46} + 2 q^{49} - 8 q^{50} + 10 q^{51} + 28 q^{54} + 6 q^{55} + 8 q^{56} - 20 q^{59} + 8 q^{60} + 32 q^{61} - 28 q^{64} - 12 q^{65} + 4 q^{66} - 6 q^{69} - 16 q^{70} - 16 q^{71} - 6 q^{74} - 8 q^{75} - 4 q^{76} + 10 q^{79} + 2 q^{80} - 14 q^{81} + 8 q^{84} + 72 q^{85} + 18 q^{86} - 80 q^{89} - 4 q^{90} + 32 q^{91} - 12 q^{94} - 32 q^{95} + 14 q^{96} - 2 q^{99}+O(q^{100}) \) 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9 + 4 * q^10 + 2 * q^11 - 8 * q^14 - 8 * q^15 + 28 * q^16 + 4 * q^19 - 2 * q^20 - 8 * q^21 - 14 * q^24 - 14 * q^25 - 12 * q^26 + 24 * q^29 + 4 * q^30 + 10 * q^34 + 8 * q^35 - 14 * q^36 + 24 * q^39 - 4 * q^40 + 20 * q^41 - 2 * q^44 - 2 * q^45 + 12 * q^46 + 2 * q^49 - 8 * q^50 + 10 * q^51 + 28 * q^54 + 6 * q^55 + 8 * q^56 - 20 * q^59 + 8 * q^60 + 32 * q^61 - 28 * q^64 - 12 * q^65 + 4 * q^66 - 6 * q^69 - 16 * q^70 - 16 * q^71 - 6 * q^74 - 8 * q^75 - 4 * q^76 + 10 * q^79 + 2 * q^80 - 14 * q^81 + 8 * q^84 + 72 * q^85 + 18 * q^86 - 80 * q^89 - 4 * q^90 + 32 * q^91 - 12 * q^94 - 32 * q^95 + 14 * q^96 - 2 * q^99

Introduction

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