LMFDB - Embedded newform 960.3.bg.e.577.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [960,3,Mod(193,960)] 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("960.193"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(960, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 0, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	960.bg (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$26.1581053786$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			577.2
Root			$-1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	960.577
Dual form			960.3.bg.e.193.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22474 - 1.22474i) q^{3} +(-4.89898 + 1.00000i) q^{5} +(-8.89898 - 8.89898i) q^{7} -3.00000i q^{9} -5.79796 q^{11} +(6.79796 - 6.79796i) q^{13} +(-4.77526 + 7.22474i) q^{15} +(6.10102 + 6.10102i) q^{17} -6.20204i q^{19} -21.7980 q^{21} +(-18.6969 + 18.6969i) q^{23} +(23.0000 - 9.79796i) q^{25} +(-3.67423 - 3.67423i) q^{27} +6.20204i q^{29} -0.404082 q^{31} +(-7.10102 + 7.10102i) q^{33} +(52.4949 + 34.6969i) q^{35} +(27.0000 + 27.0000i) q^{37} -16.6515i q^{39} -1.79796 q^{41} +(-36.4949 + 36.4949i) q^{43} +(3.00000 + 14.6969i) q^{45} +(38.6969 + 38.6969i) q^{47} +109.384i q^{49} +14.9444 q^{51} +(-69.0908 + 69.0908i) q^{53} +(28.4041 - 5.79796i) q^{55} +(-7.59592 - 7.59592i) q^{57} -20.0000i q^{59} +63.1918 q^{61} +(-26.6969 + 26.6969i) q^{63} +(-26.5051 + 40.1010i) q^{65} +(-40.0908 - 40.0908i) q^{67} +45.7980i q^{69} +25.7980 q^{71} +(-56.7980 + 56.7980i) q^{73} +(16.1691 - 40.1691i) q^{75} +(51.5959 + 51.5959i) q^{77} -139.373i q^{79} -9.00000 q^{81} +(-13.7071 + 13.7071i) q^{83} +(-35.9898 - 23.7878i) q^{85} +(7.59592 + 7.59592i) q^{87} +58.6061i q^{89} -120.990 q^{91} +(-0.494897 + 0.494897i) q^{93} +(6.20204 + 30.3837i) q^{95} +(-15.9898 - 15.9898i) q^{97} +17.3939i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{7} + 16 q^{11} - 12 q^{13} - 24 q^{15} + 44 q^{17} - 48 q^{21} - 16 q^{23} + 92 q^{25} - 80 q^{31} - 48 q^{33} + 112 q^{35} + 108 q^{37} + 32 q^{41} - 48 q^{43} + 12 q^{45} + 96 q^{47} - 48 q^{51}+ \cdots + 132 q^{97}+O(q^{100}) $ 4 * q - 16 * q^7 + 16 * q^11 - 12 * q^13 - 24 * q^15 + 44 * q^17 - 48 * q^21 - 16 * q^23 + 92 * q^25 - 80 * q^31 - 48 * q^33 + 112 * q^35 + 108 * q^37 + 32 * q^41 - 48 * q^43 + 12 * q^45 + 96 * q^47 - 48 * q^51 - 100 * q^53 + 192 * q^55 + 48 * q^57 + 96 * q^61 - 48 * q^63 - 204 * q^65 + 16 * q^67 + 64 * q^71 - 188 * q^73 - 48 * q^75 + 128 * q^77 - 36 * q^81 - 192 * q^83 + 52 * q^85 - 48 * q^87 - 288 * q^91 + 96 * q^93 + 64 * q^95 + 132 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$4$		0			0
$5$	−4.89898	+	1.00000i	−0.979796	+	0.200000i
$5$	−4.89898	+	1.00000i	−0.979796	+	0.200000i
$6$		0			0
$7$	−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	$-0.605656\pi$
$8$		0			0
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	−5.79796			−0.527087			−0.263544	−	0.964647i	$-0.584891\pi$
$11$	−5.79796			−0.527087			−0.263544	+	0.964647i	$0.584891\pi$
$12$		0			0
$13$	6.79796	−	6.79796i	0.522920	−	0.522920i	−0.395532	−	0.918452i	$-0.629440\pi$
$13$	6.79796	−	6.79796i	0.522920	−	0.522920i	0.918452	+	0.395532i	$0.129440\pi$
$14$		0			0
$15$	−4.77526	+	7.22474i	−0.318350	+	0.481650i
$16$		0			0
$17$	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	$0.668330\pi$
$18$		0			0
$19$		−	6.20204i		−	0.326423i	−0.986591	−	0.163212i	$-0.947815\pi$
$19$		−	6.20204i		−	0.326423i	0.986591	−	0.163212i	$-0.0521853\pi$
$20$		0			0
$21$	−21.7980			−1.03800
$22$		0			0
$23$	−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	$0.444926\pi$
$24$		0			0
$25$	23.0000	−	9.79796i	0.920000	−	0.391918i
$26$		0			0
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$		0			0
$29$			6.20204i			0.213863i	0.994266	+	0.106932i	$0.0341026\pi$
$29$			6.20204i			0.213863i	−0.994266	+	0.106932i	$0.965897\pi$
$30$		0			0
$31$	−0.404082			−0.0130349			−0.00651745	−	0.999979i	$-0.502075\pi$
$31$	−0.404082			−0.0130349			−0.00651745	+	0.999979i	$0.502075\pi$
$32$		0			0
$33$	−7.10102	+	7.10102i	−0.215182	+	0.215182i
$34$		0			0
$35$	52.4949	+	34.6969i	1.49985	+	0.991341i
$36$		0			0
$37$	27.0000	+	27.0000i	0.729730	+	0.729730i	0.970566	−	0.240836i	$-0.0774216\pi$
$37$	27.0000	+	27.0000i	0.729730	+	0.729730i	−0.240836	+	0.970566i	$0.577422\pi$
$38$		0			0
$39$		−	16.6515i		−	0.426962i
$40$		0			0
$41$	−1.79796			−0.0438527			−0.0219263	−	0.999760i	$-0.506980\pi$
$41$	−1.79796			−0.0438527			−0.0219263	+	0.999760i	$0.506980\pi$
$42$		0			0
$43$	−36.4949	+	36.4949i	−0.848719	+	0.848719i	−0.989973	−	0.141255i	$-0.954886\pi$
$43$	−36.4949	+	36.4949i	−0.848719	+	0.848719i	0.141255	+	0.989973i	$0.454886\pi$
$44$		0			0
$45$	3.00000	+	14.6969i	0.0666667	+	0.326599i
$46$		0			0
$47$	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	$0.552197\pi$
$48$		0			0
$49$			109.384i			2.23232i
$50$		0			0
$51$	14.9444			0.293027
$52$		0			0
$53$	−69.0908	+	69.0908i	−1.30360	+	1.30360i	−0.377653	+	0.925947i	$0.623269\pi$
$53$	−69.0908	+	69.0908i	−1.30360	+	1.30360i	−0.925947	+	0.377653i	$0.876731\pi$
$54$		0			0
$55$	28.4041	−	5.79796i	0.516438	−	0.105417i
$56$		0			0
$57$	−7.59592	−	7.59592i	−0.133262	−	0.133262i
$58$		0			0
$59$		−	20.0000i		−	0.338983i	−0.985532	−	0.169492i	$-0.945787\pi$
$59$		−	20.0000i		−	0.338983i	0.985532	−	0.169492i	$-0.0542125\pi$
$60$		0			0
$61$	63.1918			1.03593			0.517966	−	0.855401i	$-0.326689\pi$
$61$	63.1918			1.03593			0.517966	+	0.855401i	$0.326689\pi$
$62$		0			0
$63$	−26.6969	+	26.6969i	−0.423761	+	0.423761i
$64$		0			0
$65$	−26.5051	+	40.1010i	−0.407771	+	0.616939i
$66$		0			0
$67$	−40.0908	−	40.0908i	−0.598370	−	0.598370i	0.341508	−	0.939879i	$-0.389062\pi$
$67$	−40.0908	−	40.0908i	−0.598370	−	0.598370i	−0.939879	+	0.341508i	$0.889062\pi$
$68$		0			0
$69$			45.7980i			0.663739i
$70$		0			0
$71$	25.7980			0.363352			0.181676	−	0.983358i	$-0.441848\pi$
$71$	25.7980			0.363352			0.181676	+	0.983358i	$0.441848\pi$
$72$		0			0
$73$	−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	$0.435436\pi$
$74$		0			0
$75$	16.1691	−	40.1691i	0.215588	−	0.535588i
$76$		0			0
$77$	51.5959	+	51.5959i	0.670077	+	0.670077i
$78$		0			0
$79$		−	139.373i		−	1.76422i	−0.471042	−	0.882111i	$-0.656122\pi$
$79$		−	139.373i		−	1.76422i	0.471042	−	0.882111i	$-0.343878\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$		0			0
$83$	−13.7071	+	13.7071i	−0.165146	+	0.165146i	−0.784842	−	0.619696i	$-0.787256\pi$
$83$	−13.7071	+	13.7071i	−0.165146	+	0.165146i	0.619696	+	0.784842i	$0.287256\pi$
$84$		0			0
$85$	−35.9898	−	23.7878i	−0.423409	−	0.279856i
$86$		0			0
$87$	7.59592	+	7.59592i	0.0873094	+	0.0873094i
$88$		0			0
$89$			58.6061i			0.658496i	0.944244	+	0.329248i	$0.106795\pi$
$89$			58.6061i			0.658496i	−0.944244	+	0.329248i	$0.893205\pi$
$90$		0			0
$91$	−120.990			−1.32956
$92$		0			0
$93$	−0.494897	+	0.494897i	−0.00532148	+	0.00532148i
$94$		0			0
$95$	6.20204	+	30.3837i	0.0652846	+	0.319828i
$96$		0			0
$97$	−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	$0.787187\pi$
$98$		0			0
$99$			17.3939i			0.175696i
$100$		0			0
$101$	128.384			1.27113			0.635563	−	0.772049i	$-0.280768\pi$
$101$	128.384			1.27113			0.635563	+	0.772049i	$0.280768\pi$
$102$		0			0
$103$	−32.4949	+	32.4949i	−0.315484	+	0.315484i	−0.847030	−	0.531545i	$-0.821612\pi$
$103$	−32.4949	+	32.4949i	−0.315484	+	0.315484i	0.531545	+	0.847030i	$0.321612\pi$
$104$		0			0
$105$	106.788	−	21.7980i	1.01703	−	0.207600i
$106$		0			0
$107$	−24.8990	−	24.8990i	−0.232701	−	0.232701i	0.581118	−	0.813819i	$-0.302615\pi$
$107$	−24.8990	−	24.8990i	−0.232701	−	0.232701i	−0.813819	+	0.581118i	$0.802615\pi$
$108$		0			0
$109$			130.000i			1.19266i	0.802739	+	0.596330i	$0.203375\pi$
$109$			130.000i			1.19266i	−0.802739	+	0.596330i	$0.796625\pi$
$110$		0			0
$111$	66.1362			0.595822
$112$		0			0
$113$	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	$0.232648\pi$
$114$		0			0
$115$	72.8990	−	110.293i	0.633904	−	0.959068i
$116$		0			0
$117$	−20.3939	−	20.3939i	−0.174307	−	0.174307i
$118$		0			0
$119$		−	108.586i		−	0.912485i
$120$		0			0
$121$	−87.3837			−0.722179
$122$		0			0
$123$	−2.20204	+	2.20204i	−0.0179028	+	0.0179028i
$124$		0			0
$125$	−102.879	+	71.0000i	−0.823029	+	0.568000i
$126$		0			0
$127$	−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	$0.840341\pi$
$128$		0			0
$129$			89.3939i			0.692976i
$130$		0			0
$131$	114.202			0.871771			0.435886	−	0.900002i	$-0.356435\pi$
$131$	114.202			0.871771			0.435886	+	0.900002i	$0.356435\pi$
$132$		0			0
$133$	−55.1918	+	55.1918i	−0.414976	+	0.414976i
$134$		0			0
$135$	21.6742	+	14.3258i	0.160550	+	0.106117i
$136$		0			0
$137$	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	$0.723517\pi$
$138$		0			0
$139$			73.7980i			0.530921i	0.964122	+	0.265460i	$0.0855239\pi$
$139$			73.7980i			0.530921i	−0.964122	+	0.265460i	$0.914476\pi$
$140$		0			0
$141$	94.7878			0.672254
$142$		0			0
$143$	−39.4143	+	39.4143i	−0.275624	+	0.275624i
$144$		0			0
$145$	−6.20204	−	30.3837i	−0.0427727	−	0.209543i
$146$		0			0
$147$	133.967	+	133.967i	0.911341	+	0.911341i
$148$		0			0
$149$		−	270.767i		−	1.81723i	−0.417634	−	0.908615i	$-0.637141\pi$
$149$		−	270.767i		−	1.81723i	0.417634	−	0.908615i	$-0.362859\pi$
$150$		0			0
$151$	21.6163			0.143154			0.0715772	−	0.997435i	$-0.477197\pi$
$151$	21.6163			0.143154			0.0715772	+	0.997435i	$0.477197\pi$
$152$		0			0
$153$	18.3031	−	18.3031i	0.119628	−	0.119628i
$154$		0			0
$155$	1.97959	−	0.404082i	0.0127715	−	0.00260698i
$156$		0			0
$157$	−123.000	−	123.000i	−0.783439	−	0.783439i	0.196970	−	0.980410i	$-0.436890\pi$
$157$	−123.000	−	123.000i	−0.783439	−	0.783439i	−0.980410	+	0.196970i	$0.936890\pi$
$158$		0			0
$159$			169.237i			1.06439i
$160$		0			0
$161$	332.767			2.06688
$162$		0			0
$163$	112.495	−	112.495i	0.690153	−	0.690153i	−0.272113	−	0.962265i	$-0.587722\pi$
$163$	112.495	−	112.495i	0.690153	−	0.690153i	0.962265	+	0.272113i	$0.0877223\pi$
$164$		0			0
$165$	27.6867	−	41.8888i	0.167798	−	0.253871i
$166$		0			0
$167$	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	$0.480976\pi$
$168$		0			0
$169$			76.5755i			0.453110i
$170$		0			0
$171$	−18.6061			−0.108808
$172$		0			0
$173$	−142.889	+	142.889i	−0.825947	+	0.825947i	−0.986953	−	0.161007i	$-0.948526\pi$
$173$	−142.889	+	142.889i	−0.825947	+	0.825947i	0.161007	+	0.986953i	$0.448526\pi$
$174$		0			0
$175$	−291.868	−	117.485i	−1.66782	−	0.671341i
$176$		0			0
$177$	−24.4949	−	24.4949i	−0.138389	−	0.138389i
$178$		0			0
$179$			133.171i			0.743974i	0.928238	+	0.371987i	$0.121323\pi$
$179$			133.171i			0.743974i	−0.928238	+	0.371987i	$0.878677\pi$
$180$		0			0
$181$	−137.192			−0.757966			−0.378983	−	0.925404i	$-0.623726\pi$
$181$	−137.192			−0.757966			−0.378983	+	0.925404i	$0.623726\pi$
$182$		0			0
$183$	77.3939	−	77.3939i	0.422917	−	0.422917i
$184$		0			0
$185$	−159.272	−	105.272i	−0.860932	−	0.569040i
$186$		0			0
$187$	−35.3735	−	35.3735i	−0.189163	−	0.189163i
$188$		0			0
$189$			65.3939i			0.345999i
$190$		0			0
$191$	−266.606			−1.39584			−0.697922	−	0.716174i	$-0.745892\pi$
$191$	−266.606			−1.39584			−0.697922	+	0.716174i	$0.745892\pi$
$192$		0			0
$193$	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	$0.108490\pi$
$194$		0			0
$195$	16.6515	+	81.5755i	0.0853925	+	0.418336i
$196$		0			0
$197$	246.687	+	246.687i	1.25222	+	1.25222i	0.954724	+	0.297493i	$0.0961505\pi$
$197$	246.687	+	246.687i	1.25222	+	1.25222i	0.297493	+	0.954724i	$0.403850\pi$
$198$		0			0
$199$			154.565i			0.776710i	0.921510	+	0.388355i	$0.126957\pi$
$199$			154.565i			0.776710i	−0.921510	+	0.388355i	$0.873043\pi$
$200$		0			0
$201$	−98.2020			−0.488567
$202$		0			0
$203$	55.1918	−	55.1918i	0.271881	−	0.271881i
$204$		0			0
$205$	8.80816	−	1.79796i	0.0429667	−	0.00877053i
$206$		0			0
$207$	56.0908	+	56.0908i	0.270970	+	0.270970i
$208$		0			0
$209$			35.9592i			0.172053i
$210$		0			0
$211$	−190.747			−0.904014			−0.452007	−	0.892014i	$-0.649292\pi$
$211$	−190.747			−0.904014			−0.452007	+	0.892014i	$0.649292\pi$
$212$		0			0
$213$	31.5959	−	31.5959i	0.148338	−	0.148338i
$214$		0			0
$215$	142.293	−	215.283i	0.661827	−	1.00131i
$216$		0			0
$217$	3.59592	+	3.59592i	0.0165711	+	0.0165711i
$218$		0			0
$219$			139.126i			0.635279i
$220$		0			0
$221$	82.9490			0.375335
$222$		0			0
$223$	−16.6765	+	16.6765i	−0.0747826	+	0.0747826i	−0.743509	−	0.668726i	$-0.766840\pi$
$223$	−16.6765	+	16.6765i	−0.0747826	+	0.0747826i	0.668726	+	0.743509i	$0.266840\pi$
$224$		0			0
$225$	−29.3939	−	69.0000i	−0.130639	−	0.306667i
$226$		0			0
$227$	42.0704	+	42.0704i	0.185332	+	0.185332i	0.793675	−	0.608342i	$-0.208165\pi$
$227$	42.0704	+	42.0704i	0.185332	+	0.185332i	−0.608342	+	0.793675i	$0.708165\pi$
$228$		0			0
$229$			173.939i			0.759558i	0.925077	+	0.379779i	$0.124000\pi$
$229$			173.939i			0.759558i	−0.925077	+	0.379779i	$0.876000\pi$
$230$		0			0
$231$	126.384			0.547115
$232$		0			0
$233$	−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	$0.889748\pi$
$234$		0			0
$235$	−228.272	−	150.879i	−0.971372	−	0.642036i
$236$		0			0
$237$	−170.697	−	170.697i	−0.720240	−	0.720240i
$238$		0			0
$239$		−	37.2122i		−	0.155700i	−0.996965	−	0.0778499i	$-0.975195\pi$
$239$		−	37.2122i		−	0.155700i	0.996965	−	0.0778499i	$-0.0248055\pi$
$240$		0			0
$241$	165.939			0.688543			0.344271	−	0.938870i	$-0.388126\pi$
$241$	165.939			0.688543			0.344271	+	0.938870i	$0.388126\pi$
$242$		0			0
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	−109.384	−	535.868i	−0.446464	−	2.18722i
$246$		0			0
$247$	−42.1612	−	42.1612i	−0.170693	−	0.170693i
$248$		0			0
$249$			33.5755i			0.134841i
$250$		0			0
$251$	−255.414			−1.01759			−0.508793	−	0.860889i	$-0.669908\pi$
$251$	−255.414			−1.01759			−0.508793	+	0.860889i	$0.669908\pi$
$252$		0			0
$253$	108.404	−	108.404i	0.428475	−	0.428475i
$254$		0			0
$255$	−73.2122	+	14.9444i	−0.287107	+	0.0586054i
$256$		0			0
$257$	−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	$-0.517173\pi$
$258$		0			0
$259$		−	480.545i		−	1.85539i
$260$		0			0
$261$	18.6061			0.0712878
$262$		0			0
$263$	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	$0.248885\pi$
$264$		0			0
$265$	269.384	−	407.565i	1.01654	−	1.53798i
$266$		0			0
$267$	71.7775	+	71.7775i	0.268830	+	0.268830i
$268$		0			0
$269$			41.1510i			0.152978i	0.997070	+	0.0764889i	$0.0243710\pi$
$269$			41.1510i			0.152978i	−0.997070	+	0.0764889i	$0.975629\pi$
$270$		0			0
$271$	−484.727			−1.78866			−0.894329	−	0.447409i	$-0.852347\pi$
$271$	−484.727			−1.78866			−0.894329	+	0.447409i	$0.852347\pi$
$272$		0			0
$273$	−148.182	+	148.182i	−0.542790	+	0.542790i
$274$		0			0
$275$	−133.353	+	56.8082i	−0.484920	+	0.206575i
$276$		0			0
$277$	−51.9898	−	51.9898i	−0.187689	−	0.187689i	0.607007	−	0.794696i	$-0.292370\pi$
$277$	−51.9898	−	51.9898i	−0.187689	−	0.187689i	−0.794696	+	0.607007i	$0.792370\pi$
$278$		0			0
$279$			1.21225i			0.00434497i
$280$		0			0
$281$	242.524			0.863076			0.431538	−	0.902095i	$-0.357971\pi$
$281$	242.524			0.863076			0.431538	+	0.902095i	$0.357971\pi$
$282$		0			0
$283$	−104.717	+	104.717i	−0.370026	+	0.370026i	−0.867487	−	0.497461i	$-0.834266\pi$
$283$	−104.717	+	104.717i	−0.370026	+	0.370026i	0.497461	+	0.867487i	$0.334266\pi$
$284$		0			0
$285$	44.8082	+	29.6163i	0.157222	+	0.103917i
$286$		0			0
$287$	16.0000	+	16.0000i	0.0557491	+	0.0557491i
$288$		0			0
$289$		−	214.555i		−	0.742405i
$290$		0			0
$291$	−39.1668			−0.134594
$292$		0			0
$293$	60.9092	−	60.9092i	0.207881	−	0.207881i	−0.595485	−	0.803366i	$-0.703040\pi$
$293$	60.9092	−	60.9092i	0.207881	−	0.207881i	0.803366	+	0.595485i	$0.203040\pi$
$294$		0			0
$295$	20.0000	+	97.9796i	0.0677966	+	0.332134i
$296$		0			0
$297$	21.3031	+	21.3031i	0.0717275	+	0.0717275i
$298$		0			0
$299$			254.202i			0.850174i
$300$		0			0
$301$	649.535			2.15792
$302$		0			0
$303$	157.237	−	157.237i	0.518935	−	0.518935i
$304$		0			0
$305$	−309.576	+	63.1918i	−1.01500	+	0.207186i
$306$		0			0
$307$	201.303	+	201.303i	0.655710	+	0.655710i	0.954362	−	0.298652i	$-0.0965369\pi$
$307$	201.303	+	201.303i	0.655710	+	0.655710i	−0.298652	+	0.954362i	$0.596537\pi$
$308$		0			0
$309$			79.5959i			0.257592i
$310$		0			0
$311$	559.737			1.79980			0.899898	−	0.436100i	$-0.143641\pi$
$311$	559.737			1.79980			0.899898	+	0.436100i	$0.143641\pi$
$312$		0			0
$313$	−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	$0.317943\pi$
$314$		0			0
$315$	104.091	−	157.485i	0.330447	−	0.499951i
$316$		0			0
$317$	−362.828	−	362.828i	−1.14457	−	1.14457i	−0.987605	−	0.156962i	$-0.949830\pi$
$317$	−362.828	−	362.828i	−1.14457	−	1.14457i	−0.156962	−	0.987605i	$-0.550170\pi$
$318$		0			0
$319$		−	35.9592i		−	0.112725i
$320$		0			0
$321$	−60.9898			−0.189999
$322$		0			0
$323$	37.8388	−	37.8388i	0.117148	−	0.117148i
$324$		0			0
$325$	89.7469	−	222.959i	0.276144	−	0.686028i
$326$		0			0
$327$	159.217	+	159.217i	0.486902	+	0.486902i
$328$		0			0
$329$		−	688.727i		−	2.09339i
$330$		0			0
$331$	−14.0204			−0.0423577			−0.0211789	−	0.999776i	$-0.506742\pi$
$331$	−14.0204			−0.0423577			−0.0211789	+	0.999776i	$0.506742\pi$
$332$		0			0
$333$	81.0000	−	81.0000i	0.243243	−	0.243243i
$334$		0			0
$335$	236.495	+	156.313i	0.705955	+	0.466607i
$336$		0			0
$337$	−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	$0.863510\pi$
$338$		0			0
$339$		−	21.3281i		−	0.0629146i
$340$		0			0
$341$	2.34285			0.00687053
$342$		0			0
$343$	537.353	−	537.353i	1.56663	−	1.56663i
$344$		0			0
$345$	−45.7980	−	224.363i	−0.132748	−	0.650328i
$346$		0			0
$347$	−163.505	−	163.505i	−0.471196	−	0.471196i	0.431105	−	0.902302i	$-0.358124\pi$
$347$	−163.505	−	163.505i	−0.471196	−	0.471196i	−0.902302	+	0.431105i	$0.858124\pi$
$348$		0			0
$349$		−	280.000i		−	0.802292i	−0.916014	−	0.401146i	$-0.868612\pi$
$349$		−	280.000i		−	0.802292i	0.916014	−	0.401146i	$-0.131388\pi$
$350$		0			0
$351$	−49.9546			−0.142321
$352$		0			0
$353$	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	$0.0745103\pi$
$354$		0			0
$355$	−126.384	+	25.7980i	−0.356010	+	0.0726703i
$356$		0			0
$357$	−132.990	−	132.990i	−0.372520	−	0.372520i
$358$		0			0
$359$			425.090i			1.18409i	0.805903	+	0.592047i	$0.201680\pi$
$359$			425.090i			1.18409i	−0.805903	+	0.592047i	$0.798320\pi$
$360$		0			0
$361$	322.535			0.893448
$362$		0			0
$363$	−107.023	+	107.023i	−0.294828	+	0.294828i
$364$		0			0
$365$	221.454	−	335.050i	0.606723	−	0.917945i
$366$		0			0
$367$	−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	$0.958749\pi$
$368$		0			0
$369$			5.39388i			0.0146176i
$370$		0			0
$371$	1229.68			3.31449
$372$		0			0
$373$	−210.939	+	210.939i	−0.565519	+	0.565519i	−0.930870	−	0.365351i	$-0.880949\pi$
$373$	−210.939	+	210.939i	−0.565519	+	0.565519i	0.365351	+	0.930870i	$0.380949\pi$
$374$		0			0
$375$	−39.0431	+	212.957i	−0.104115	+	0.567885i
$376$		0			0
$377$	42.1612	+	42.1612i	0.111833	+	0.111833i
$378$		0			0
$379$		−	344.182i		−	0.908131i	−0.890968	−	0.454065i	$-0.849973\pi$
$379$		−	344.182i		−	0.908131i	0.890968	−	0.454065i	$-0.150027\pi$
$380$		0			0
$381$	−123.192			−0.323338
$382$		0			0
$383$	−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	$0.976949\pi$
$384$		0			0
$385$	−304.363	−	201.171i	−0.790554	−	0.522523i
$386$		0			0
$387$	109.485	+	109.485i	0.282906	+	0.282906i
$388$		0			0
$389$			301.151i			0.774167i	0.922045	+	0.387084i	$0.126518\pi$
$389$			301.151i			0.774167i	−0.922045	+	0.387084i	$0.873482\pi$
$390$		0			0
$391$	−228.141			−0.583480
$392$		0			0
$393$	139.868	−	139.868i	0.355899	−	0.355899i
$394$		0			0
$395$	139.373	+	682.788i	0.352844	+	1.72858i
$396$		0			0
$397$	−479.343	−	479.343i	−1.20741	−	1.20741i	−0.971862	−	0.235551i	$-0.924311\pi$
$397$	−479.343	−	479.343i	−1.20741	−	1.20741i	−0.235551	−	0.971862i	$-0.575689\pi$
$398$		0			0
$399$			135.192i			0.338827i
$400$		0			0
$401$	101.233			0.252451			0.126225	−	0.992002i	$-0.459714\pi$
$401$	101.233			0.252451			0.126225	+	0.992002i	$0.459714\pi$
$402$		0			0
$403$	−2.74693	+	2.74693i	−0.00681621	+	0.00681621i
$404$		0			0
$405$	44.0908	−	9.00000i	0.108866	−	0.0222222i
$406$		0			0
$407$	−156.545	−	156.545i	−0.384631	−	0.384631i
$408$		0			0
$409$			257.110i			0.628631i	0.949319	+	0.314316i	$0.101775\pi$
$409$			257.110i			0.628631i	−0.949319	+	0.314316i	$0.898225\pi$
$410$		0			0
$411$	39.4393			0.0959593
$412$		0			0
$413$	−177.980	+	177.980i	−0.430943	+	0.430943i
$414$		0			0
$415$	53.4439	−	80.8582i	0.128780	−	0.194839i
$416$		0			0
$417$	90.3837	+	90.3837i	0.216747	+	0.216747i
$418$		0			0
$419$		−	375.959i		−	0.897277i	−0.893713	−	0.448639i	$-0.851909\pi$
$419$		−	375.959i		−	0.897277i	0.893713	−	0.448639i	$-0.148091\pi$
$420$		0			0
$421$	−158.829			−0.377265			−0.188633	−	0.982048i	$-0.560405\pi$
$421$	−158.829			−0.377265			−0.188633	+	0.982048i	$0.560405\pi$
$422$		0			0
$423$	116.091	−	116.091i	0.274446	−	0.274446i
$424$		0			0
$425$	200.101	+	80.5459i	0.470826	+	0.189520i
$426$		0			0
$427$	−562.343	−	562.343i	−1.31696	−	1.31696i
$428$		0			0
$429$			96.5449i			0.225046i
$430$		0			0
$431$	−152.182			−0.353090			−0.176545	−	0.984293i	$-0.556492\pi$
$431$	−152.182			−0.353090			−0.176545	+	0.984293i	$0.556492\pi$
$432$		0			0
$433$	−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	$0.386671\pi$
$434$		0			0
$435$	−44.8082	−	29.6163i	−0.103007	−	0.0680835i
$436$		0			0
$437$	115.959	+	115.959i	0.265353	+	0.265353i
$438$		0			0
$439$		−	299.373i		−	0.681944i	−0.940073	−	0.340972i	$-0.889244\pi$
$439$		−	299.373i		−	0.681944i	0.940073	−	0.340972i	$-0.110756\pi$
$440$		0			0
$441$	328.151			0.744107
$442$		0			0
$443$	−144.717	+	144.717i	−0.326676	+	0.326676i	−0.851321	−	0.524645i	$-0.824198\pi$
$443$	−144.717	+	144.717i	−0.326676	+	0.326676i	0.524645	+	0.851321i	$0.324198\pi$
$444$		0			0
$445$	−58.6061	−	287.110i	−0.131699	−	0.645191i
$446$		0			0
$447$	−331.621	−	331.621i	−0.741881	−	0.741881i
$448$		0			0
$449$			846.727i			1.88581i	0.333069	+	0.942903i	$0.391916\pi$
$449$			846.727i			1.88581i	−0.333069	+	0.942903i	$0.608084\pi$
$450$		0			0
$451$	10.4245			0.0231142
$452$		0			0
$453$	26.4745	−	26.4745i	0.0584426	−	0.0584426i
$454$		0			0
$455$	592.727	−	120.990i	1.30270	−	0.265912i
$456$		0			0
$457$	−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	$0.768921\pi$
$458$		0			0
$459$		−	44.8332i		−	0.0976757i
$460$		0			0
$461$	−78.7265			−0.170773			−0.0853867	−	0.996348i	$-0.527213\pi$
$461$	−78.7265			−0.170773			−0.0853867	+	0.996348i	$0.527213\pi$
$462$		0			0
$463$	−461.485	+	461.485i	−0.996727	+	0.996727i	−0.999995	−	0.00326746i	$-0.998960\pi$
$463$	−461.485	+	461.485i	−0.996727	+	0.996727i	0.00326746	+	0.999995i	$0.498960\pi$
$464$		0			0
$465$	1.92959	−	2.91939i	0.00414967	−	0.00627826i
$466$		0			0
$467$	−17.3031	−	17.3031i	−0.0370515	−	0.0370515i	0.688338	−	0.725390i	$-0.258340\pi$
$467$	−17.3031	−	17.3031i	−0.0370515	−	0.0370515i	−0.725390	+	0.688338i	$0.758340\pi$
$468$		0			0
$469$			713.535i			1.52140i
$470$		0			0
$471$	−301.287			−0.639676
$472$		0			0
$473$	211.596	−	211.596i	0.447349	−	0.447349i
$474$		0			0
$475$	−60.7673	−	142.647i	−0.127931	−	0.300309i
$476$		0			0
$477$	207.272	+	207.272i	0.434533	+	0.434533i
$478$		0			0
$479$		−	776.727i		−	1.62156i	−0.585352	−	0.810779i	$-0.699044\pi$
$479$		−	776.727i		−	1.62156i	0.585352	−	0.810779i	$-0.300956\pi$
$480$		0			0
$481$	367.090			0.763180
$482$		0			0
$483$	407.555	−	407.555i	0.843799	−	0.843799i
$484$		0			0
$485$	94.3235	+	62.3439i	0.194481	+	0.128544i
$486$		0			0
$487$	−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	$0.970249\pi$
$488$		0			0
$489$		−	275.555i		−	0.563507i
$490$		0			0
$491$	−246.080			−0.501180			−0.250590	−	0.968093i	$-0.580625\pi$
$491$	−246.080			−0.501180			−0.250590	+	0.968093i	$0.580625\pi$
$492$		0			0
$493$	−37.8388	+	37.8388i	−0.0767521	+	0.0767521i
$494$		0			0
$495$	−17.3939	−	85.2122i	−0.0351391	−	0.172146i
$496$		0			0
$497$	−229.576	−	229.576i	−0.461923	−	0.461923i
$498$		0			0
$499$			597.839i			1.19807i	0.800721	+	0.599037i	$0.204450\pi$
$499$			597.839i			1.19807i	−0.800721	+	0.599037i	$0.795550\pi$
$500$		0			0
$501$	432.767			0.863807
$502$		0			0
$503$	−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	$0.991131\pi$
$504$		0			0
$505$	−628.949	+	128.384i	−1.24544	+	0.254225i
$506$		0			0
$507$	93.7855	+	93.7855i	0.184981	+	0.184981i
$508$		0			0
$509$			452.059i			0.888132i	0.895994	+	0.444066i	$0.146464\pi$
$509$			452.059i			0.888132i	−0.895994	+	0.444066i	$0.853536\pi$
$510$		0			0
$511$	1010.89			1.97825
$512$		0			0
$513$	−22.7878	+	22.7878i	−0.0444206	+	0.0444206i
$514$		0			0
$515$	126.697	−	191.687i	0.246013	−	0.372207i
$516$		0			0
$517$	−224.363	−	224.363i	−0.433971	−	0.433971i
$518$		0			0
$519$			350.005i			0.674383i
$520$		0			0
$521$	779.494			1.49615			0.748075	−	0.663614i	$-0.230978\pi$
$521$	779.494			1.49615			0.748075	+	0.663614i	$0.230978\pi$
$522$		0			0
$523$	−179.283	+	179.283i	−0.342797	+	0.342797i	−0.857418	−	0.514621i	$-0.827933\pi$
$523$	−179.283	+	179.283i	−0.342797	+	0.342797i	0.514621	+	0.857418i	$0.327933\pi$
$524$		0			0
$525$	−501.353	+	213.576i	−0.954958	+	0.406810i
$526$		0			0
$527$	−2.46531	−	2.46531i	−0.00467801	−	0.00467801i
$528$		0			0
$529$		−	170.151i		−	0.321647i
$530$		0			0
$531$	−60.0000			−0.112994
$532$		0			0
$533$	−12.2225	+	12.2225i	−0.0229314	+	0.0229314i
$534$		0			0
$535$	146.879	+	97.0806i	0.274539	+	0.181459i
$536$		0			0
$537$	163.101	+	163.101i	0.303726	+	0.303726i
$538$		0			0
$539$		−	634.202i		−	1.17663i
$540$		0			0
$541$	385.110			0.711849			0.355924	−	0.934515i	$-0.384166\pi$
$541$	385.110			0.711849			0.355924	+	0.934515i	$0.384166\pi$
$542$		0			0
$543$	−168.025	+	168.025i	−0.309438	+	0.309438i
$544$		0			0
$545$	−130.000	−	636.867i	−0.238532	−	1.16856i
$546$		0			0
$547$	504.372	+	504.372i	0.922070	+	0.922070i	0.997176	−	0.0751053i	$-0.0239293\pi$
$547$	504.372	+	504.372i	0.922070	+	0.922070i	−0.0751053	+	0.997176i	$0.523929\pi$
$548$		0			0
$549$		−	189.576i		−	0.345311i
$550$		0			0
$551$	38.4653			0.0698100
$552$		0			0
$553$	−1240.28	+	1240.28i	−2.24282	+	2.24282i
$554$		0			0
$555$	−324.000	+	66.1362i	−0.583784	+	0.119164i
$556$		0			0
$557$	130.101	+	130.101i	0.233575	+	0.233575i	0.814183	−	0.580608i	$-0.197185\pi$
$557$	130.101	+	130.101i	0.233575	+	0.233575i	−0.580608	+	0.814183i	$0.697185\pi$
$558$		0			0
$559$			496.182i			0.887624i
$560$		0			0
$561$	−86.6469			−0.154451
$562$		0			0
$563$	−666.879	+	666.879i	−1.18451	+	1.18451i	−0.205946	+	0.978563i	$0.566027\pi$
$563$	−666.879	+	666.879i	−1.18451	+	1.18451i	−0.978563	+	0.205946i	$0.933973\pi$
$564$		0			0
$565$	−33.9490	+	51.3633i	−0.0600867	+	0.0909084i
$566$		0			0
$567$	80.0908	+	80.0908i	0.141254	+	0.141254i
$568$		0			0
$569$			987.494i			1.73549i	0.497010	+	0.867745i	$0.334431\pi$
$569$			987.494i			1.73549i	−0.497010	+	0.867745i	$0.665569\pi$
$570$		0			0
$571$	−452.767			−0.792938			−0.396469	−	0.918048i	$-0.629764\pi$
$571$	−452.767			−0.792938			−0.396469	+	0.918048i	$0.629764\pi$
$572$		0			0
$573$	−326.524	+	326.524i	−0.569851	+	0.569851i
$574$		0			0
$575$	−246.838	+	613.221i	−0.429283	+	1.06647i
$576$		0			0
$577$	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	$0.557949\pi$
$578$		0			0
$579$		−	287.530i		−	0.496598i
$580$		0			0
$581$	243.959			0.419895
$582$		0			0
$583$	400.586	−	400.586i	0.687111	−	0.687111i
$584$		0			0
$585$	120.303	+	79.5153i	0.205646	+	0.135924i
$586$		0			0
$587$	−375.909	−	375.909i	−0.640390	−	0.640390i	0.310261	−	0.950651i	$-0.399584\pi$
$587$	−375.909	−	375.909i	−0.640390	−	0.640390i	−0.950651	+	0.310261i	$0.899584\pi$
$588$		0			0
$589$			2.50613i			0.00425490i
$590$		0			0
$591$	604.257			1.02243
$592$		0			0
$593$	−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	$0.407680\pi$
$594$		0			0
$595$	108.586	+	531.959i	0.182497	+	0.894049i
$596$		0			0
$597$	189.303	+	189.303i	0.317091	+	0.317091i
$598$		0			0
$599$			509.131i			0.849968i	0.905201	+	0.424984i	$0.139720\pi$
$599$			509.131i			0.849968i	−0.905201	+	0.424984i	$0.860280\pi$
$600$		0			0
$601$	−390.302			−0.649421			−0.324711	−	0.945813i	$-0.605267\pi$
$601$	−390.302			−0.649421			−0.324711	+	0.945813i	$0.605267\pi$
$602$		0			0
$603$	−120.272	+	120.272i	−0.199457	+	0.199457i
$604$		0			0
$605$	428.091	−	87.3837i	0.707588	−	0.144436i
$606$		0			0
$607$	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	$0.554805\pi$
$608$		0			0
$609$		−	135.192i		−	0.221990i
$610$		0			0
$611$	526.120			0.861081
$612$		0			0
$613$	−74.1102	+	74.1102i	−0.120898	+	0.120898i	−0.764967	−	0.644069i	$-0.777245\pi$
$613$	−74.1102	+	74.1102i	−0.120898	+	0.120898i	0.644069	+	0.764967i	$0.277245\pi$
$614$		0			0
$615$	8.58571	−	12.9898i	0.0139605	−	0.0211216i
$616$		0			0
$617$	−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	$0.900853\pi$
$618$		0			0
$619$			838.120i			1.35399i	0.735987	+	0.676995i	$0.236718\pi$
$619$			838.120i			1.35399i	−0.735987	+	0.676995i	$0.763282\pi$
$620$		0			0
$621$	137.394			0.221246
$622$		0			0
$623$	521.535	−	521.535i	0.837134	−	0.837134i
$624$		0			0
$625$	433.000	−	450.706i	0.692800	−	0.721130i
$626$		0			0
$627$	44.0408	+	44.0408i	0.0702405	+	0.0702405i
$628$		0			0
$629$			329.455i			0.523776i
$630$		0			0
$631$	149.980			0.237686			0.118843	−	0.992913i	$-0.462082\pi$
$631$	149.980			0.237686			0.118843	+	0.992913i	$0.462082\pi$
$632$		0			0
$633$	−233.616	+	233.616i	−0.369062	+	0.369062i
$634$		0			0
$635$	296.677	+	196.091i	0.467207	+	0.308804i
$636$		0			0
$637$	743.586	+	743.586i	1.16732	+	1.16732i
$638$		0			0
$639$		−	77.3939i		−	0.121117i
$640$		0			0
$641$	−378.243			−0.590082			−0.295041	−	0.955485i	$-0.595333\pi$
$641$	−378.243			−0.590082			−0.295041	+	0.955485i	$0.595333\pi$
$642$		0			0
$643$	285.526	−	285.526i	0.444052	−	0.444052i	−0.449319	−	0.893371i	$-0.648333\pi$
$643$	285.526	−	285.526i	0.444052	−	0.444052i	0.893371	+	0.449319i	$0.148333\pi$
$644$		0			0
$645$	−89.3939	−	437.939i	−0.138595	−	0.678975i
$646$		0			0
$647$	−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	$0.878973\pi$
$648$		0			0
$649$			115.959i			0.178674i
$650$		0			0
$651$	8.80816			0.0135302
$652$		0			0
$653$	−547.838	+	547.838i	−0.838955	+	0.838955i	−0.988721	−	0.149766i	$-0.952148\pi$
$653$	−547.838	+	547.838i	−0.838955	+	0.838955i	0.149766	+	0.988721i	$0.452148\pi$
$654$		0			0
$655$	−559.473	+	114.202i	−0.854158	+	0.174354i
$656$		0			0
$657$	170.394	+	170.394i	0.259351	+	0.259351i
$658$		0			0
$659$		−	25.5755i		−	0.0388096i	−0.999812	−	0.0194048i	$-0.993823\pi$
$659$		−	25.5755i		−	0.0388096i	0.999812	−	0.0194048i	$-0.00617712\pi$
$660$		0			0
$661$	824.727			1.24770			0.623848	−	0.781546i	$-0.285569\pi$
$661$	824.727			1.24770			0.623848	+	0.781546i	$0.285569\pi$
$662$		0			0
$663$	101.591	−	101.591i	0.153230	−	0.153230i
$664$		0			0
$665$	215.192	−	325.576i	0.323597	−	0.489587i
$666$		0			0
$667$	−115.959	−	115.959i	−0.173852	−	0.173852i
$668$		0			0
$669$			40.8490i			0.0610598i
$670$		0			0
$671$	−366.384			−0.546026
$672$		0			0
$673$	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	$-0.147513\pi$
$674$		0			0
$675$	−120.507	−	48.5074i	−0.178529	−	0.0718628i
$676$		0			0
$677$	−688.160	−	688.160i	−1.01648	−	1.01648i	−0.999862	−	0.0166229i	$-0.994709\pi$
$677$	−688.160	−	688.160i	−1.01648	−	1.01648i	−0.0166229	−	0.999862i	$-0.505291\pi$
$678$		0			0
$679$			284.586i			0.419125i
$680$		0			0
$681$	103.051			0.151323
$682$		0			0
$683$	−1.92959	+	1.92959i	−0.00282518	+	0.00282518i	−0.708518	−	0.705693i	$-0.750636\pi$
$683$	−1.92959	+	1.92959i	−0.00282518	+	0.00282518i	0.705693	+	0.708518i	$0.250636\pi$
$684$		0			0
$685$	−94.9796	−	62.7775i	−0.138656	−	0.0916461i
$686$		0			0
$687$	213.031	+	213.031i	0.310088	+	0.310088i
$688$		0			0
$689$			939.353i			1.36336i
$690$		0			0
$691$	162.706			0.235465			0.117732	−	0.993045i	$-0.462438\pi$
$691$	162.706			0.235465			0.117732	+	0.993045i	$0.462438\pi$
$692$		0			0
$693$	154.788	−	154.788i	0.223359	−	0.223359i
$694$		0			0
$695$	−73.7980	−	361.535i	−0.106184	−	0.520194i
$696$		0			0
$697$	−10.9694	−	10.9694i	−0.0157380	−	0.0157380i
$698$		0			0
$699$			730.590i			1.04519i
$700$		0			0
$701$	−260.222			−0.371216			−0.185608	−	0.982624i	$-0.559425\pi$
$701$	−260.222			−0.371216			−0.185608	+	0.982624i	$0.559425\pi$
$702$		0			0
$703$	167.455	−	167.455i	0.238201	−	0.238201i
$704$		0			0
$705$	−464.363	+	94.7878i	−0.658671	+	0.134451i
$706$		0			0
$707$	−1142.48	−	1142.48i	−1.61596	−	1.61596i
$708$		0			0
$709$		−	151.637i		−	0.213874i	−0.994266	−	0.106937i	$-0.965896\pi$
$709$		−	151.637i		−	0.213874i	0.994266	−	0.106937i	$-0.0341043\pi$
$710$		0			0
$711$	−418.120			−0.588074
$712$		0			0
$713$	7.55510	−	7.55510i	0.0105962	−	0.0105962i
$714$		0			0
$715$	153.675	−	232.504i	0.214931	−	0.325181i
$716$		0			0
$717$	−45.5755	−	45.5755i	−0.0635642	−	0.0635642i
$718$		0			0
$719$		−	1281.82i		−	1.78278i	−0.453241	−	0.891388i	$-0.649732\pi$
$719$		−	1281.82i		−	1.78278i	0.453241	−	0.891388i	$-0.350268\pi$
$720$		0			0
$721$	578.343			0.802140
$722$		0			0
$723$	203.233	−	203.233i	0.281096	−	0.281096i
$724$		0			0
$725$	60.7673	+	142.647i	0.0838170	+	0.196754i
$726$		0			0
$727$	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	$0.536774\pi$
$728$		0			0
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	−445.312			−0.609182
$732$		0			0
$733$	−400.414	+	400.414i	−0.546268	+	0.546268i	−0.925359	−	0.379091i	$-0.876237\pi$
$733$	−400.414	+	400.414i	−0.546268	+	0.546268i	0.379091	+	0.925359i	$0.376237\pi$
$734$		0			0
$735$	−790.269	−	522.335i	−1.07520	−	0.710660i
$736$		0			0
$737$	232.445	+	232.445i	0.315393	+	0.315393i
$738$		0			0
$739$		−	382.647i		−	0.517790i	−0.965905	−	0.258895i	$-0.916642\pi$
$739$		−	382.647i		−	0.517790i	0.965905	−	0.258895i	$-0.0833584\pi$
$740$		0			0
$741$	−103.273			−0.139370
$742$		0			0
$743$	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	$0.208874\pi$
$744$		0			0
$745$	270.767	+	1326.48i	0.363446	+	1.78051i
$746$		0			0
$747$	41.1214	+	41.1214i	0.0550488	+	0.0550488i
$748$		0			0
$749$			443.151i			0.591657i
$750$		0			0
$751$	−571.273			−0.760684			−0.380342	−	0.924846i	$-0.624194\pi$
$751$	−571.273			−0.760684			−0.380342	+	0.924846i	$0.624194\pi$
$752$		0			0
$753$	−312.817	+	312.817i	−0.415428	+	0.415428i
$754$		0			0
$755$	−105.898	+	21.6163i	−0.140262	+	0.0286309i
$756$		0			0
$757$	917.908	+	917.908i	1.21256	+	1.21256i	0.970182	+	0.242379i	$0.0779276\pi$
$757$	917.908	+	917.908i	1.21256	+	1.21256i	0.242379	+	0.970182i	$0.422072\pi$
$758$		0			0
$759$		−	265.535i		−	0.349848i
$760$		0			0
$761$	−616.261			−0.809804			−0.404902	−	0.914360i	$-0.632694\pi$
$761$	−616.261			−0.809804			−0.404902	+	0.914360i	$0.632694\pi$
$762$		0			0
$763$	1156.87	−	1156.87i	1.51621	−	1.51621i
$764$		0			0
$765$	−71.3633	+	107.969i	−0.0932853	+	0.141136i
$766$		0			0
$767$	−135.959	−	135.959i	−0.177261	−	0.177261i
$768$		0			0
$769$			154.424i			0.200812i	0.994947	+	0.100406i	$0.0320142\pi$
$769$			154.424i			0.200812i	−0.994947	+	0.100406i	$0.967986\pi$
$770$		0			0
$771$	−662.549			−0.859338
$772$		0			0
$773$	184.323	−	184.323i	0.238452	−	0.238452i	−0.577757	−	0.816209i	$-0.696072\pi$
$773$	184.323	−	184.323i	0.238452	−	0.238452i	0.816209	+	0.577757i	$0.196072\pi$
$774$		0			0
$775$	−9.29389	+	3.95918i	−0.0119921	+	0.00510862i
$776$		0			0
$777$	−588.545	−	588.545i	−0.757458	−	0.757458i
$778$		0			0
$779$			11.1510i			0.0143145i
$780$		0			0
$781$	−149.576			−0.191518
$782$		0			0
$783$	22.7878	−	22.7878i	0.0291031	−	0.0291031i
$784$		0			0
$785$	725.574	+	479.574i	0.924299	+	0.610923i
$786$		0			0
$787$	784.858	+	784.858i	0.997278	+	0.997278i	0.999996	−	0.00271783i	$-0.000865114\pi$
$787$	784.858	+	784.858i	0.997278	+	0.997278i	−0.00271783	+	0.999996i	$0.500865\pi$
$788$		0			0
$789$		−	3.19184i		−	0.00404542i
$790$		0			0
$791$	−154.969			−0.195916
$792$		0			0
$793$	429.576	−	429.576i	0.541709	−	0.541709i
$794$		0			0
$795$	−169.237	−	829.090i	−0.212877	−	1.04288i
$796$		0			0
$797$	485.191	+	485.191i	0.608771	+	0.608771i	0.942625	−	0.333854i	$-0.108349\pi$
$797$	485.191	+	485.191i	0.608771	+	0.608771i	−0.333854	+	0.942625i	$0.608349\pi$
$798$		0			0
$799$			472.182i			0.590966i
$800$		0			0
$801$	175.818			0.219499
$802$		0			0
$803$	329.312	−	329.312i	0.410102	−	0.410102i
$804$		0			0
$805$	−1630.22	+	332.767i	−2.02512	+	0.413376i
$806$		0			0
$807$	50.3995	+	50.3995i	0.0624529	+	0.0624529i
$808$		0			0
$809$		−	397.839i		−	0.491766i	−0.969300	−	0.245883i	$-0.920922\pi$
$809$		−	397.839i		−	0.491766i	0.969300	−	0.245883i	$-0.0790779\pi$
$810$		0			0
$811$	1005.49			1.23982			0.619910	−	0.784673i	$-0.287169\pi$
$811$	1005.49			1.23982			0.619910	+	0.784673i	$0.287169\pi$
$812$		0			0
$813$	−593.666	+	593.666i	−0.730217	+	0.730217i
$814$		0			0
$815$	−438.615	+	663.605i	−0.538178	+	0.814239i
$816$		0			0
$817$	226.343	+	226.343i	0.277041	+	0.277041i
$818$		0			0
$819$			362.969i			0.443186i
$820$		0			0
$821$	101.312			0.123401			0.0617005	−	0.998095i	$-0.480348\pi$
$821$	101.312			0.123401			0.0617005	+	0.998095i	$0.480348\pi$
$822$		0			0
$823$	68.2724	−	68.2724i	0.0829556	−	0.0829556i	−0.664411	−	0.747367i	$-0.731318\pi$
$823$	68.2724	−	68.2724i	0.0829556	−	0.0829556i	0.747367	+	0.664411i	$0.231318\pi$
$824$		0			0
$825$	−93.7480	+	232.899i	−0.113634	+	0.282302i
$826$		0			0
$827$	363.464	+	363.464i	0.439497	+	0.439497i	0.891843	−	0.452345i	$-0.149413\pi$
$827$	363.464	+	363.464i	0.439497	+	0.439497i	−0.452345	+	0.891843i	$0.649413\pi$
$828$		0			0
$829$		−	891.535i		−	1.07543i	−0.843125	−	0.537717i	$-0.819287\pi$
$829$		−	891.535i		−	1.07543i	0.843125	−	0.537717i	$-0.180713\pi$
$830$		0			0
$831$	−127.348			−0.153247
$832$		0			0
$833$	−667.352	+	667.352i	−0.801143	+	0.801143i
$834$		0			0
$835$	−1042.21	−	688.858i	−1.24816	−	0.824980i
$836$		0			0
$837$	1.48469	+	1.48469i	0.00177383	+	0.00177383i
$838$		0			0
$839$		−	705.090i		−	0.840393i	−0.907433	−	0.420197i	$-0.861961\pi$
$839$		−	705.090i		−	0.840393i	0.907433	−	0.420197i	$-0.138039\pi$
$840$		0			0
$841$	802.535			0.954262
$842$		0			0
$843$	297.031	−	297.031i	0.352349	−	0.352349i
$844$		0			0
$845$	−76.5755	−	375.142i	−0.0906219	−	0.443955i
$846$		0			0
$847$	777.626	+	777.626i	0.918094	+	0.918094i
$848$		0			0
$849$			256.504i			0.302125i
$850$		0			0
$851$	−1009.63			−1.18641
$852$		0			0
$853$	−450.555	+	450.555i	−0.528201	+	0.528201i	−0.920036	−	0.391835i	$-0.871840\pi$
$853$	−450.555	+	450.555i	−0.528201	+	0.528201i	0.391835	+	0.920036i	$0.371840\pi$
$854$		0			0
$855$	91.1510	−	18.6061i	0.106609	−	0.0217615i
$856$		0			0
$857$	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	$0.733300\pi$
$858$		0			0
$859$			1467.53i			1.70842i	0.519928	+	0.854210i	$0.325959\pi$
$859$			1467.53i			1.70842i	−0.519928	+	0.854210i	$0.674041\pi$
$860$		0			0
$861$	39.1918			0.0455190
$862$		0			0
$863$	−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	$0.327654\pi$
$864$		0			0
$865$	557.120	−	842.898i	0.644070	−	0.974448i
$866$		0			0
$867$	−262.775	−	262.775i	−0.303086	−	0.303086i
$868$		0			0
$869$			808.082i			0.929898i
$870$		0			0
$871$	−545.071			−0.625800
$872$		0			0
$873$	−47.9694	+	47.9694i	−0.0549477	+	0.0549477i
$874$		0			0
$875$	1547.34	+	283.687i	1.76839	+	0.324213i
$876$		0			0
$877$	−113.102	−	113.102i	−0.128965	−	0.128965i	0.639678	−	0.768643i	$-0.279068\pi$
$877$	−113.102	−	113.102i	−0.128965	−	0.128965i	−0.768643	+	0.639678i	$0.779068\pi$
$878$		0			0
$879$		−	149.196i		−	0.169734i
$880$		0			0
$881$	−1370.44			−1.55555			−0.777777	−	0.628540i	$-0.783653\pi$
$881$	−1370.44			−1.55555			−0.777777	+	0.628540i	$0.783653\pi$
$882$		0			0
$883$	−175.587	+	175.587i	−0.198852	+	0.198852i	−0.799508	−	0.600655i	$-0.794906\pi$
$883$	−175.587	+	175.587i	−0.198852	+	0.198852i	0.600655	+	0.799508i	$0.294906\pi$
$884$		0			0
$885$	144.495	+	95.5051i	0.163271	+	0.107915i
$886$		0			0
$887$	−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	$0.883917\pi$
$888$		0			0
$889$			895.110i			1.00687i
$890$		0			0
$891$	52.1816			0.0585652
$892$		0			0
$893$	240.000	−	240.000i	0.268757	−	0.268757i
$894$		0			0
$895$	−133.171	−	652.404i	−0.148795	−	0.728943i
$896$		0			0
$897$	311.333	+	311.333i	0.347082	+	0.347082i
$898$		0			0
$899$		−	2.50613i		−	0.00278769i
$900$		0			0
$901$	−843.049			−0.935681
$902$		0			0
$903$	795.514	−	795.514i	0.880968	−	0.880968i
$904$		0			0
$905$	672.100	−	137.192i	0.742652	−	0.151593i
$906$		0			0
$907$	922.697	+	922.697i	1.01731	+	1.01731i	0.999848	+	0.0174589i	$0.00555761\pi$
$907$	922.697	+	922.697i	1.01731	+	1.01731i	0.0174589	+	0.999848i	$0.494442\pi$
$908$		0			0
$909$		−	385.151i		−	0.423708i
$910$		0			0
$911$	1338.97			1.46978			0.734890	−	0.678186i	$-0.237234\pi$
$911$	1338.97			1.46978			0.734890	+	0.678186i	$0.237234\pi$
$912$		0			0
$913$	79.4735	−	79.4735i	0.0870465	−	0.0870465i
$914$		0			0
$915$	−301.757	+	456.545i	−0.329789	+	0.498956i
$916$		0			0
$917$	−1016.28	−	1016.28i	−1.10827	−	1.10827i
$918$		0			0
$919$			1371.57i			1.49246i	0.665687	+	0.746231i	$0.268139\pi$
$919$			1371.57i			1.49246i	−0.665687	+	0.746231i	$0.731861\pi$
$920$		0			0
$921$	493.090			0.535385
$922$		0			0
$923$	175.373	−	175.373i	0.190004	−	0.190004i
$924$		0			0
$925$	885.545	+	356.455i	0.957346	+	0.385357i
$926$		0			0
$927$	97.4847	+	97.4847i	0.105161	+	0.105161i
$928$		0			0
$929$			218.645i			0.235355i	0.993052	+	0.117678i	$0.0375449\pi$
$929$			218.645i			0.235355i	−0.993052	+	0.117678i	$0.962455\pi$
$930$		0			0
$931$	678.402			0.728681
$932$		0			0
$933$	685.535	−	685.535i	0.734764	−	0.734764i
$934$		0			0
$935$	208.667	+	137.920i	0.223174	+	0.147508i
$936$		0			0
$937$	−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	$-0.573870\pi$
$938$		0			0
$939$			229.682i			0.244603i
$940$		0			0
$941$	588.384			0.625275			0.312637	−	0.949873i	$-0.398788\pi$
$941$	588.384			0.625275			0.312637	+	0.949873i	$0.398788\pi$
$942$		0			0
$943$	33.6163	−	33.6163i	0.0356483	−	0.0356483i
$944$		0			0
$945$	−65.3939	−	320.363i	−0.0691999	−	0.339009i
$946$		0			0
$947$	926.879	+	926.879i	0.978752	+	0.978752i	0.999779	−	0.0210265i	$-0.00669343\pi$
$947$	926.879	+	926.879i	0.978752	+	0.978752i	−0.0210265	+	0.999779i	$0.506693\pi$
$948$		0			0
$949$			772.220i			0.813720i
$950$		0			0
$951$	−888.742			−0.934535
$952$		0			0
$953$	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	$-0.142270\pi$
$954$		0			0
$955$	1306.10	−	266.606i	1.36764	−	0.279169i
$956$		0			0
$957$	−44.0408	−	44.0408i	−0.0460197	−	0.0460197i
$958$		0			0
$959$		−	286.565i		−	0.298817i
$960$		0			0
$961$	−960.837			−0.999830
$962$		0			0
$963$	−74.6969	+	74.6969i	−0.0775669	+	0.0775669i
$964$		0			0
$965$	−457.677	+	692.444i	−0.474276	+	0.717558i
$966$		0			0
$967$	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	$0.564357\pi$
$968$		0			0
$969$		−	92.6857i		−	0.0956509i
$970$		0			0
$971$	−1803.86			−1.85773			−0.928865	−	0.370419i	$-0.879214\pi$
$971$	−1803.86			−1.85773			−0.928865	+	0.370419i	$0.879214\pi$
$972$		0			0
$973$	656.727	−	656.727i	0.674950	−	0.674950i
$974$		0			0
$975$	−163.151	−	382.985i	−0.167334	−	0.392805i
$976$		0			0
$977$	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	$0.698204\pi$
$978$		0			0
$979$		−	339.796i		−	0.347085i
$980$		0			0
$981$	390.000			0.397554
$982$		0			0
$983$	−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	$0.497914\pi$
$984$		0			0
$985$	−1455.20	−	961.827i	−1.47736	−	0.976474i
$986$		0			0
$987$	−843.514	−	843.514i	−0.854624	−	0.854624i
$988$		0			0
$989$		−	1364.69i		−	1.37986i
$990$		0			0
$991$	1331.03			1.34312			0.671558	−	0.740952i	$-0.265625\pi$
$991$	1331.03			1.34312			0.671558	+	0.740952i	$0.265625\pi$
$992$		0			0
$993$	−17.1714	+	17.1714i	−0.0172925	+	0.0172925i
$994$		0			0
$995$	−154.565	−	757.212i	−0.155342	−	0.761017i
$996$		0			0
$997$	−852.616	−	852.616i	−0.855182	−	0.855182i	0.135584	−	0.990766i	$-0.456709\pi$
$997$	−852.616	−	852.616i	−0.855182	−	0.855182i	−0.990766	+	0.135584i	$0.956709\pi$
$998$		0			0
$999$		−	198.409i		−	0.198607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.3.bg.e.577.2		4
4.3	odd	2		960.3.bg.g.577.1		4
5.3	odd	4	inner	960.3.bg.e.193.2		4
8.3	odd	2		240.3.bg.b.97.2		4
8.5	even	2		30.3.f.a.7.1	✓	4
20.3	even	4		960.3.bg.g.193.1		4
24.5	odd	2		90.3.g.d.37.1		4
24.11	even	2		720.3.bh.i.577.1		4
40.3	even	4		240.3.bg.b.193.2		4
40.13	odd	4		30.3.f.a.13.1	yes	4
40.19	odd	2		1200.3.bg.d.1057.1		4
40.27	even	4		1200.3.bg.d.193.1		4
40.29	even	2		150.3.f.b.7.2		4
40.37	odd	4		150.3.f.b.43.2		4
120.29	odd	2		450.3.g.j.307.2		4
120.53	even	4		90.3.g.d.73.1		4
120.77	even	4		450.3.g.j.343.2		4
120.83	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	8.5	even	2
30.3.f.a.13.1	yes	4	40.13	odd	4
90.3.g.d.37.1		4	24.5	odd	2
90.3.g.d.73.1		4	120.53	even	4
150.3.f.b.7.2		4	40.29	even	2
150.3.f.b.43.2		4	40.37	odd	4
240.3.bg.b.97.2		4	8.3	odd	2
240.3.bg.b.193.2		4	40.3	even	4
450.3.g.j.307.2		4	120.29	odd	2
450.3.g.j.343.2		4	120.77	even	4
720.3.bh.i.433.1		4	120.83	odd	4
720.3.bh.i.577.1		4	24.11	even	2
960.3.bg.e.193.2		4	5.3	odd	4	inner
960.3.bg.e.577.2		4	1.1	even	1	trivial
960.3.bg.g.193.1		4	20.3	even	4
960.3.bg.g.577.1		4	4.3	odd	2
1200.3.bg.d.193.1		4	40.27	even	4
1200.3.bg.d.1057.1		4	40.19	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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	960.bg (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 1.22474i) q^{3} +(-4.89898 + 1.00000i) q^{5} +(-8.89898 - 8.89898i) q^{7} -3.00000i q^{9} -5.79796 q^{11} +(6.79796 - 6.79796i) q^{13} +(-4.77526 + 7.22474i) q^{15} +(6.10102 + 6.10102i) q^{17} -6.20204i q^{19} -21.7980 q^{21} +(-18.6969 + 18.6969i) q^{23} +(23.0000 - 9.79796i) q^{25} +(-3.67423 - 3.67423i) q^{27} +6.20204i q^{29} -0.404082 q^{31} +(-7.10102 + 7.10102i) q^{33} +(52.4949 + 34.6969i) q^{35} +(27.0000 + 27.0000i) q^{37} -16.6515i q^{39} -1.79796 q^{41} +(-36.4949 + 36.4949i) q^{43} +(3.00000 + 14.6969i) q^{45} +(38.6969 + 38.6969i) q^{47} +109.384i q^{49} +14.9444 q^{51} +(-69.0908 + 69.0908i) q^{53} +(28.4041 - 5.79796i) q^{55} +(-7.59592 - 7.59592i) q^{57} -20.0000i q^{59} +63.1918 q^{61} +(-26.6969 + 26.6969i) q^{63} +(-26.5051 + 40.1010i) q^{65} +(-40.0908 - 40.0908i) q^{67} +45.7980i q^{69} +25.7980 q^{71} +(-56.7980 + 56.7980i) q^{73} +(16.1691 - 40.1691i) q^{75} +(51.5959 + 51.5959i) q^{77} -139.373i q^{79} -9.00000 q^{81} +(-13.7071 + 13.7071i) q^{83} +(-35.9898 - 23.7878i) q^{85} +(7.59592 + 7.59592i) q^{87} +58.6061i q^{89} -120.990 q^{91} +(-0.494897 + 0.494897i) q^{93} +(6.20204 + 30.3837i) q^{95} +(-15.9898 - 15.9898i) q^{97} +17.3939i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{7} + 16 q^{11} - 12 q^{13} - 24 q^{15} + 44 q^{17} - 48 q^{21} - 16 q^{23} + 92 q^{25} - 80 q^{31} - 48 q^{33} + 112 q^{35} + 108 q^{37} + 32 q^{41} - 48 q^{43} + 12 q^{45} + 96 q^{47} - 48 q^{51}+ \cdots + 132 q^{97}+O(q^{100}) \) 4 * q - 16 * q^7 + 16 * q^11 - 12 * q^13 - 24 * q^15 + 44 * q^17 - 48 * q^21 - 16 * q^23 + 92 * q^25 - 80 * q^31 - 48 * q^33 + 112 * q^35 + 108 * q^37 + 32 * q^41 - 48 * q^43 + 12 * q^45 + 96 * q^47 - 48 * q^51 - 100 * q^53 + 192 * q^55 + 48 * q^57 + 96 * q^61 - 48 * q^63 - 204 * q^65 + 16 * q^67 + 64 * q^71 - 188 * q^73 - 48 * q^75 + 128 * q^77 - 36 * q^81 - 192 * q^83 + 52 * q^85 - 48 * q^87 - 288 * q^91 + 96 * q^93 + 64 * q^95 + 132 * q^97

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