LMFDB - Embedded newform 1920.2.bh.f.703.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(703,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 0, 3]))

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

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

chi := DirichletCharacter("1920.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.bh (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			703.2
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1920.703
Dual form			1920.2.bh.f.1087.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{3} +(2.12132 - 0.707107i) q^{5} +(1.00000 + 1.00000i) q^{7} +1.00000i q^{9} -1.41421 q^{11} +(-1.41421 + 1.41421i) q^{13} +(2.00000 + 1.00000i) q^{15} +(-2.00000 + 2.00000i) q^{17} +5.65685i q^{19} +1.41421i q^{21} +(-2.00000 + 2.00000i) q^{23} +(4.00000 - 3.00000i) q^{25} +(-0.707107 + 0.707107i) q^{27} +1.41421 q^{29} +10.0000i q^{31} +(-1.00000 - 1.00000i) q^{33} +(2.82843 + 1.41421i) q^{35} +(4.24264 + 4.24264i) q^{37} -2.00000 q^{39} -2.00000 q^{41} +(-2.82843 - 2.82843i) q^{43} +(0.707107 + 2.12132i) q^{45} +(8.00000 + 8.00000i) q^{47} -5.00000i q^{49} -2.82843 q^{51} +(4.24264 - 4.24264i) q^{53} +(-3.00000 + 1.00000i) q^{55} +(-4.00000 + 4.00000i) q^{57} -4.24264i q^{59} -2.82843i q^{61} +(-1.00000 + 1.00000i) q^{63} +(-2.00000 + 4.00000i) q^{65} +(8.48528 - 8.48528i) q^{67} -2.82843 q^{69} +8.00000i q^{71} +(3.00000 + 3.00000i) q^{73} +(4.94975 + 0.707107i) q^{75} +(-1.41421 - 1.41421i) q^{77} +10.0000 q^{79} -1.00000 q^{81} +(-7.07107 - 7.07107i) q^{83} +(-2.82843 + 5.65685i) q^{85} +(1.00000 + 1.00000i) q^{87} -10.0000i q^{89} -2.82843 q^{91} +(-7.07107 + 7.07107i) q^{93} +(4.00000 + 12.0000i) q^{95} +(3.00000 - 3.00000i) q^{97} -1.41421i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{7} + 8 q^{15} - 8 q^{17} - 8 q^{23} + 16 q^{25} - 4 q^{33} - 8 q^{39} - 8 q^{41} + 32 q^{47} - 12 q^{55} - 16 q^{57} - 4 q^{63} - 8 q^{65} + 12 q^{73} + 40 q^{79} - 4 q^{81} + 4 q^{87} + 16 q^{95}+ \cdots + 12 q^{97}+O(q^{100}) $ 4 * q + 4 * q^7 + 8 * q^15 - 8 * q^17 - 8 * q^23 + 16 * q^25 - 4 * q^33 - 8 * q^39 - 8 * q^41 + 32 * q^47 - 12 * q^55 - 16 * q^57 - 4 * q^63 - 8 * q^65 + 12 * q^73 + 40 * q^79 - 4 * q^81 + 4 * q^87 + 16 * q^95 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		0			0
$5$	2.12132	−	0.707107i	0.948683	−	0.316228i
$5$	2.12132	−	0.707107i	0.948683	−	0.316228i
$6$		0			0
$7$	1.00000	+	1.00000i	0.377964	+	0.377964i	0.870367	−	0.492403i	$-0.163881\pi$
$7$	1.00000	+	1.00000i	0.377964	+	0.377964i	−0.492403	+	0.870367i	$0.663881\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−1.41421			−0.426401			−0.213201	−	0.977008i	$-0.568389\pi$
$11$	−1.41421			−0.426401			−0.213201	+	0.977008i	$0.568389\pi$
$12$		0			0
$13$	−1.41421	+	1.41421i	−0.392232	+	0.392232i	−0.875482	−	0.483250i	$-0.839456\pi$
$13$	−1.41421	+	1.41421i	−0.392232	+	0.392232i	0.483250	+	0.875482i	$0.339456\pi$
$14$		0			0
$15$	2.00000	+	1.00000i	0.516398	+	0.258199i
$16$		0			0
$17$	−2.00000	+	2.00000i	−0.485071	+	0.485071i	−0.906747	−	0.421676i	$-0.861442\pi$
$17$	−2.00000	+	2.00000i	−0.485071	+	0.485071i	0.421676	+	0.906747i	$0.361442\pi$
$18$		0			0
$19$			5.65685i			1.29777i	0.760886	+	0.648886i	$0.224765\pi$
$19$			5.65685i			1.29777i	−0.760886	+	0.648886i	$0.775235\pi$
$20$		0			0
$21$			1.41421i			0.308607i
$22$		0			0
$23$	−2.00000	+	2.00000i	−0.417029	+	0.417029i	−0.884178	−	0.467150i	$-0.845281\pi$
$23$	−2.00000	+	2.00000i	−0.417029	+	0.417029i	0.467150	+	0.884178i	$0.345281\pi$
$24$		0			0
$25$	4.00000	−	3.00000i	0.800000	−	0.600000i
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$	1.41421			0.262613			0.131306	−	0.991342i	$-0.458083\pi$
$29$	1.41421			0.262613			0.131306	+	0.991342i	$0.458083\pi$
$30$		0			0
$31$			10.0000i			1.79605i	0.439941	+	0.898027i	$0.354999\pi$
$31$			10.0000i			1.79605i	−0.439941	+	0.898027i	$0.645001\pi$
$32$		0			0
$33$	−1.00000	−	1.00000i	−0.174078	−	0.174078i
$34$		0			0
$35$	2.82843	+	1.41421i	0.478091	+	0.239046i
$36$		0			0
$37$	4.24264	+	4.24264i	0.697486	+	0.697486i	0.963868	−	0.266382i	$-0.0858282\pi$
$37$	4.24264	+	4.24264i	0.697486	+	0.697486i	−0.266382	+	0.963868i	$0.585828\pi$
$38$		0			0
$39$	−2.00000			−0.320256
$40$		0			0
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		0			0
$43$	−2.82843	−	2.82843i	−0.431331	−	0.431331i	0.457750	−	0.889081i	$-0.348656\pi$
$43$	−2.82843	−	2.82843i	−0.431331	−	0.431331i	−0.889081	+	0.457750i	$0.848656\pi$
$44$		0			0
$45$	0.707107	+	2.12132i	0.105409	+	0.316228i
$46$		0			0
$47$	8.00000	+	8.00000i	1.16692	+	1.16692i	0.982928	+	0.183992i	$0.0589021\pi$
$47$	8.00000	+	8.00000i	1.16692	+	1.16692i	0.183992	+	0.982928i	$0.441098\pi$
$48$		0			0
$49$		−	5.00000i		−	0.714286i
$50$		0			0
$51$	−2.82843			−0.396059
$52$		0			0
$53$	4.24264	−	4.24264i	0.582772	−	0.582772i	−0.352892	−	0.935664i	$-0.614802\pi$
$53$	4.24264	−	4.24264i	0.582772	−	0.582772i	0.935664	+	0.352892i	$0.114802\pi$
$54$		0			0
$55$	−3.00000	+	1.00000i	−0.404520	+	0.134840i
$56$		0			0
$57$	−4.00000	+	4.00000i	−0.529813	+	0.529813i
$58$		0			0
$59$		−	4.24264i		−	0.552345i	−0.961108	−	0.276172i	$-0.910934\pi$
$59$		−	4.24264i		−	0.552345i	0.961108	−	0.276172i	$-0.0890661\pi$
$60$		0			0
$61$		−	2.82843i		−	0.362143i	−0.983470	−	0.181071i	$-0.942043\pi$
$61$		−	2.82843i		−	0.362143i	0.983470	−	0.181071i	$-0.0579565\pi$
$62$		0			0
$63$	−1.00000	+	1.00000i	−0.125988	+	0.125988i
$64$		0			0
$65$	−2.00000	+	4.00000i	−0.248069	+	0.496139i
$66$		0			0
$67$	8.48528	−	8.48528i	1.03664	−	1.03664i	0.0373395	−	0.999303i	$-0.488112\pi$
$67$	8.48528	−	8.48528i	1.03664	−	1.03664i	0.999303	−	0.0373395i	$-0.0118883\pi$
$68$		0			0
$69$	−2.82843			−0.340503
$70$		0			0
$71$			8.00000i			0.949425i	0.880141	+	0.474713i	$0.157448\pi$
$71$			8.00000i			0.949425i	−0.880141	+	0.474713i	$0.842552\pi$
$72$		0			0
$73$	3.00000	+	3.00000i	0.351123	+	0.351123i	0.860527	−	0.509404i	$-0.170134\pi$
$73$	3.00000	+	3.00000i	0.351123	+	0.351123i	−0.509404	+	0.860527i	$0.670134\pi$
$74$		0			0
$75$	4.94975	+	0.707107i	0.571548	+	0.0816497i
$76$		0			0
$77$	−1.41421	−	1.41421i	−0.161165	−	0.161165i
$78$		0			0
$79$	10.0000			1.12509			0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000			1.12509			0.562544	+	0.826767i	$0.309823\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−7.07107	−	7.07107i	−0.776151	−	0.776151i	0.203023	−	0.979174i	$-0.434923\pi$
$83$	−7.07107	−	7.07107i	−0.776151	−	0.776151i	−0.979174	+	0.203023i	$0.934923\pi$
$84$		0			0
$85$	−2.82843	+	5.65685i	−0.306786	+	0.613572i
$86$		0			0
$87$	1.00000	+	1.00000i	0.107211	+	0.107211i
$88$		0			0
$89$		−	10.0000i		−	1.06000i	−0.847998	−	0.529999i	$-0.822192\pi$
$89$		−	10.0000i		−	1.06000i	0.847998	−	0.529999i	$-0.177808\pi$
$90$		0			0
$91$	−2.82843			−0.296500
$92$		0			0
$93$	−7.07107	+	7.07107i	−0.733236	+	0.733236i
$94$		0			0
$95$	4.00000	+	12.0000i	0.410391	+	1.23117i
$96$		0			0
$97$	3.00000	−	3.00000i	0.304604	−	0.304604i	−0.538208	−	0.842812i	$-0.680899\pi$
$97$	3.00000	−	3.00000i	0.304604	−	0.304604i	0.842812	+	0.538208i	$0.180899\pi$
$98$		0			0
$99$		−	1.41421i		−	0.142134i
$100$		0			0
$101$		−	18.3848i		−	1.82935i	−0.404186	−	0.914677i	$-0.632445\pi$
$101$		−	18.3848i		−	1.82935i	0.404186	−	0.914677i	$-0.367555\pi$
$102$		0			0
$103$	−9.00000	+	9.00000i	−0.886796	+	0.886796i	−0.994214	−	0.107418i	$-0.965742\pi$
$103$	−9.00000	+	9.00000i	−0.886796	+	0.886796i	0.107418	+	0.994214i	$0.465742\pi$
$104$		0			0
$105$	1.00000	+	3.00000i	0.0975900	+	0.292770i
$106$		0			0
$107$	4.24264	−	4.24264i	0.410152	−	0.410152i	−0.471640	−	0.881791i	$-0.656338\pi$
$107$	4.24264	−	4.24264i	0.410152	−	0.410152i	0.881791	+	0.471640i	$0.156338\pi$
$108$		0			0
$109$	−8.48528			−0.812743			−0.406371	−	0.913708i	$-0.633206\pi$
$109$	−8.48528			−0.812743			−0.406371	+	0.913708i	$0.633206\pi$
$110$		0			0
$111$			6.00000i			0.569495i
$112$		0			0
$113$	8.00000	+	8.00000i	0.752577	+	0.752577i	0.974959	−	0.222383i	$-0.0713835\pi$
$113$	8.00000	+	8.00000i	0.752577	+	0.752577i	−0.222383	+	0.974959i	$0.571383\pi$
$114$		0			0
$115$	−2.82843	+	5.65685i	−0.263752	+	0.527504i
$116$		0			0
$117$	−1.41421	−	1.41421i	−0.130744	−	0.130744i
$118$		0			0
$119$	−4.00000			−0.366679
$120$		0			0
$121$	−9.00000			−0.818182
$122$		0			0
$123$	−1.41421	−	1.41421i	−0.127515	−	0.127515i
$124$		0			0
$125$	6.36396	−	9.19239i	0.569210	−	0.822192i
$126$		0			0
$127$	13.0000	+	13.0000i	1.15356	+	1.15356i	0.985833	+	0.167731i	$0.0536439\pi$
$127$	13.0000	+	13.0000i	1.15356	+	1.15356i	0.167731	+	0.985833i	$0.446356\pi$
$128$		0			0
$129$		−	4.00000i		−	0.352180i
$130$		0			0
$131$	−1.41421			−0.123560			−0.0617802	−	0.998090i	$-0.519678\pi$
$131$	−1.41421			−0.123560			−0.0617802	+	0.998090i	$0.519678\pi$
$132$		0			0
$133$	−5.65685	+	5.65685i	−0.490511	+	0.490511i
$134$		0			0
$135$	−1.00000	+	2.00000i	−0.0860663	+	0.172133i
$136$		0			0
$137$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$137$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$138$		0			0
$139$			2.82843i			0.239904i	0.992780	+	0.119952i	$0.0382741\pi$
$139$			2.82843i			0.239904i	−0.992780	+	0.119952i	$0.961726\pi$
$140$		0			0
$141$			11.3137i			0.952786i
$142$		0			0
$143$	2.00000	−	2.00000i	0.167248	−	0.167248i
$144$		0			0
$145$	3.00000	−	1.00000i	0.249136	−	0.0830455i
$146$		0			0
$147$	3.53553	−	3.53553i	0.291606	−	0.291606i
$148$		0			0
$149$	9.89949			0.810998			0.405499	−	0.914095i	$-0.367098\pi$
$149$	9.89949			0.810998			0.405499	+	0.914095i	$0.367098\pi$
$150$		0			0
$151$		−	8.00000i		−	0.651031i	−0.945537	−	0.325515i	$-0.894462\pi$
$151$		−	8.00000i		−	0.651031i	0.945537	−	0.325515i	$-0.105538\pi$
$152$		0			0
$153$	−2.00000	−	2.00000i	−0.161690	−	0.161690i
$154$		0			0
$155$	7.07107	+	21.2132i	0.567962	+	1.70389i
$156$		0			0
$157$	−7.07107	−	7.07107i	−0.564333	−	0.564333i	0.366203	−	0.930535i	$-0.380658\pi$
$157$	−7.07107	−	7.07107i	−0.564333	−	0.564333i	−0.930535	+	0.366203i	$0.880658\pi$
$158$		0			0
$159$	6.00000			0.475831
$160$		0			0
$161$	−4.00000			−0.315244
$162$		0			0
$163$	−5.65685	−	5.65685i	−0.443079	−	0.443079i	0.449966	−	0.893045i	$-0.351436\pi$
$163$	−5.65685	−	5.65685i	−0.443079	−	0.443079i	−0.893045	+	0.449966i	$0.851436\pi$
$164$		0			0
$165$	−2.82843	−	1.41421i	−0.220193	−	0.110096i
$166$		0			0
$167$	−10.0000	−	10.0000i	−0.773823	−	0.773823i	0.204949	−	0.978773i	$-0.434297\pi$
$167$	−10.0000	−	10.0000i	−0.773823	−	0.773823i	−0.978773	+	0.204949i	$0.934297\pi$
$168$		0			0
$169$			9.00000i			0.692308i
$170$		0			0
$171$	−5.65685			−0.432590
$172$		0			0
$173$	11.3137	−	11.3137i	0.860165	−	0.860165i	−0.131192	−	0.991357i	$-0.541880\pi$
$173$	11.3137	−	11.3137i	0.860165	−	0.860165i	0.991357	+	0.131192i	$0.0418803\pi$
$174$		0			0
$175$	7.00000	+	1.00000i	0.529150	+	0.0755929i
$176$		0			0
$177$	3.00000	−	3.00000i	0.225494	−	0.225494i
$178$		0			0
$179$			18.3848i			1.37414i	0.726590	+	0.687071i	$0.241104\pi$
$179$			18.3848i			1.37414i	−0.726590	+	0.687071i	$0.758896\pi$
$180$		0			0
$181$			19.7990i			1.47165i	0.677173	+	0.735824i	$0.263205\pi$
$181$			19.7990i			1.47165i	−0.677173	+	0.735824i	$0.736795\pi$
$182$		0			0
$183$	2.00000	−	2.00000i	0.147844	−	0.147844i
$184$		0			0
$185$	12.0000	+	6.00000i	0.882258	+	0.441129i
$186$		0			0
$187$	2.82843	−	2.82843i	0.206835	−	0.206835i
$188$		0			0
$189$	−1.41421			−0.102869
$190$		0			0
$191$			12.0000i			0.868290i	0.900843	+	0.434145i	$0.142949\pi$
$191$			12.0000i			0.868290i	−0.900843	+	0.434145i	$0.857051\pi$
$192$		0			0
$193$	5.00000	+	5.00000i	0.359908	+	0.359908i	0.863779	−	0.503871i	$-0.168091\pi$
$193$	5.00000	+	5.00000i	0.359908	+	0.359908i	−0.503871	+	0.863779i	$0.668091\pi$
$194$		0			0
$195$	−4.24264	+	1.41421i	−0.303822	+	0.101274i
$196$		0			0
$197$	−9.89949	−	9.89949i	−0.705310	−	0.705310i	0.260235	−	0.965545i	$-0.416200\pi$
$197$	−9.89949	−	9.89949i	−0.705310	−	0.705310i	−0.965545	+	0.260235i	$0.916200\pi$
$198$		0			0
$199$	−8.00000			−0.567105			−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000			−0.567105			−0.283552	+	0.958957i	$0.591513\pi$
$200$		0			0
$201$	12.0000			0.846415
$202$		0			0
$203$	1.41421	+	1.41421i	0.0992583	+	0.0992583i
$204$		0			0
$205$	−4.24264	+	1.41421i	−0.296319	+	0.0987730i
$206$		0			0
$207$	−2.00000	−	2.00000i	−0.139010	−	0.139010i
$208$		0			0
$209$		−	8.00000i		−	0.553372i
$210$		0			0
$211$	−14.1421			−0.973585			−0.486792	−	0.873518i	$-0.661833\pi$
$211$	−14.1421			−0.973585			−0.486792	+	0.873518i	$0.661833\pi$
$212$		0			0
$213$	−5.65685	+	5.65685i	−0.387601	+	0.387601i
$214$		0			0
$215$	−8.00000	−	4.00000i	−0.545595	−	0.272798i
$216$		0			0
$217$	−10.0000	+	10.0000i	−0.678844	+	0.678844i
$218$		0			0
$219$			4.24264i			0.286691i
$220$		0			0
$221$		−	5.65685i		−	0.380521i
$222$		0			0
$223$	−7.00000	+	7.00000i	−0.468755	+	0.468755i	−0.901511	−	0.432756i	$-0.857541\pi$
$223$	−7.00000	+	7.00000i	−0.468755	+	0.468755i	0.432756	+	0.901511i	$0.357541\pi$
$224$		0			0
$225$	3.00000	+	4.00000i	0.200000	+	0.266667i
$226$		0			0
$227$	14.1421	−	14.1421i	0.938647	−	0.938647i	−0.0595772	−	0.998224i	$-0.518975\pi$
$227$	14.1421	−	14.1421i	0.938647	−	0.938647i	0.998224	+	0.0595772i	$0.0189752\pi$
$228$		0			0
$229$	−11.3137			−0.747631			−0.373815	−	0.927503i	$-0.621951\pi$
$229$	−11.3137			−0.747631			−0.373815	+	0.927503i	$0.621951\pi$
$230$		0			0
$231$		−	2.00000i		−	0.131590i
$232$		0			0
$233$	−18.0000	−	18.0000i	−1.17922	−	1.17922i	−0.979943	−	0.199276i	$-0.936141\pi$
$233$	−18.0000	−	18.0000i	−1.17922	−	1.17922i	−0.199276	−	0.979943i	$-0.563859\pi$
$234$		0			0
$235$	22.6274	+	11.3137i	1.47605	+	0.738025i
$236$		0			0
$237$	7.07107	+	7.07107i	0.459315	+	0.459315i
$238$		0			0
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$		0			0
$241$	−28.0000			−1.80364			−0.901819	−	0.432113i	$-0.857768\pi$
$241$	−28.0000			−1.80364			−0.901819	+	0.432113i	$0.857768\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	−3.53553	−	10.6066i	−0.225877	−	0.677631i
$246$		0			0
$247$	−8.00000	−	8.00000i	−0.509028	−	0.509028i
$248$		0			0
$249$		−	10.0000i		−	0.633724i
$250$		0			0
$251$	−24.0416			−1.51749			−0.758747	−	0.651385i	$-0.774188\pi$
$251$	−24.0416			−1.51749			−0.758747	+	0.651385i	$0.774188\pi$
$252$		0			0
$253$	2.82843	−	2.82843i	0.177822	−	0.177822i
$254$		0			0
$255$	−6.00000	+	2.00000i	−0.375735	+	0.125245i
$256$		0			0
$257$	−4.00000	+	4.00000i	−0.249513	+	0.249513i	−0.820771	−	0.571258i	$-0.806456\pi$
$257$	−4.00000	+	4.00000i	−0.249513	+	0.249513i	0.571258	+	0.820771i	$0.306456\pi$
$258$		0			0
$259$			8.48528i			0.527250i
$260$		0			0
$261$			1.41421i			0.0875376i
$262$		0			0
$263$	6.00000	−	6.00000i	0.369976	−	0.369976i	−0.497492	−	0.867468i	$-0.665746\pi$
$263$	6.00000	−	6.00000i	0.369976	−	0.369976i	0.867468	+	0.497492i	$0.165746\pi$
$264$		0			0
$265$	6.00000	−	12.0000i	0.368577	−	0.737154i
$266$		0			0
$267$	7.07107	−	7.07107i	0.432742	−	0.432742i
$268$		0			0
$269$	18.3848			1.12094			0.560470	−	0.828175i	$-0.310621\pi$
$269$	18.3848			1.12094			0.560470	+	0.828175i	$0.310621\pi$
$270$		0			0
$271$		−	16.0000i		−	0.971931i	−0.873978	−	0.485965i	$-0.838468\pi$
$271$		−	16.0000i		−	0.971931i	0.873978	−	0.485965i	$-0.161532\pi$
$272$		0			0
$273$	−2.00000	−	2.00000i	−0.121046	−	0.121046i
$274$		0			0
$275$	−5.65685	+	4.24264i	−0.341121	+	0.255841i
$276$		0			0
$277$	18.3848	+	18.3848i	1.10463	+	1.10463i	0.993844	+	0.110790i	$0.0353382\pi$
$277$	18.3848	+	18.3848i	1.10463	+	1.10463i	0.110790	+	0.993844i	$0.464662\pi$
$278$		0			0
$279$	−10.0000			−0.598684
$280$		0			0
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$		0			0
$283$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$283$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$284$		0			0
$285$	−5.65685	+	11.3137i	−0.335083	+	0.670166i
$286$		0			0
$287$	−2.00000	−	2.00000i	−0.118056	−	0.118056i
$288$		0			0
$289$			9.00000i			0.529412i
$290$		0			0
$291$	4.24264			0.248708
$292$		0			0
$293$	21.2132	−	21.2132i	1.23929	−	1.23929i	0.278996	−	0.960292i	$-0.409998\pi$
$293$	21.2132	−	21.2132i	1.23929	−	1.23929i	0.960292	−	0.278996i	$-0.0900018\pi$
$294$		0			0
$295$	−3.00000	−	9.00000i	−0.174667	−	0.524000i
$296$		0			0
$297$	1.00000	−	1.00000i	0.0580259	−	0.0580259i
$298$		0			0
$299$		−	5.65685i		−	0.327144i
$300$		0			0
$301$		−	5.65685i		−	0.326056i
$302$		0			0
$303$	13.0000	−	13.0000i	0.746830	−	0.746830i
$304$		0			0
$305$	−2.00000	−	6.00000i	−0.114520	−	0.343559i
$306$		0			0
$307$	19.7990	−	19.7990i	1.12999	−	1.12999i	0.139810	−	0.990178i	$-0.455351\pi$
$307$	19.7990	−	19.7990i	1.12999	−	1.12999i	0.990178	−	0.139810i	$-0.0446491\pi$
$308$		0			0
$309$	−12.7279			−0.724066
$310$		0			0
$311$		−	20.0000i		−	1.13410i	−0.823685	−	0.567048i	$-0.808085\pi$
$311$		−	20.0000i		−	1.13410i	0.823685	−	0.567048i	$-0.191915\pi$
$312$		0			0
$313$	5.00000	+	5.00000i	0.282617	+	0.282617i	0.834152	−	0.551535i	$-0.185958\pi$
$313$	5.00000	+	5.00000i	0.282617	+	0.282617i	−0.551535	+	0.834152i	$0.685958\pi$
$314$		0			0
$315$	−1.41421	+	2.82843i	−0.0796819	+	0.159364i
$316$		0			0
$317$	8.48528	+	8.48528i	0.476581	+	0.476581i	0.904036	−	0.427456i	$-0.140590\pi$
$317$	8.48528	+	8.48528i	0.476581	+	0.476581i	−0.427456	+	0.904036i	$0.640590\pi$
$318$		0			0
$319$	−2.00000			−0.111979
$320$		0			0
$321$	6.00000			0.334887
$322$		0			0
$323$	−11.3137	−	11.3137i	−0.629512	−	0.629512i
$324$		0			0
$325$	−1.41421	+	9.89949i	−0.0784465	+	0.549125i
$326$		0			0
$327$	−6.00000	−	6.00000i	−0.331801	−	0.331801i
$328$		0			0
$329$			16.0000i			0.882109i
$330$		0			0
$331$	−33.9411			−1.86557			−0.932786	−	0.360429i	$-0.882630\pi$
$331$	−33.9411			−1.86557			−0.932786	+	0.360429i	$0.882630\pi$
$332$		0			0
$333$	−4.24264	+	4.24264i	−0.232495	+	0.232495i
$334$		0			0
$335$	12.0000	−	24.0000i	0.655630	−	1.31126i
$336$		0			0
$337$	3.00000	−	3.00000i	0.163420	−	0.163420i	−0.620660	−	0.784080i	$-0.713135\pi$
$337$	3.00000	−	3.00000i	0.163420	−	0.163420i	0.784080	+	0.620660i	$0.213135\pi$
$338$		0			0
$339$			11.3137i			0.614476i
$340$		0			0
$341$		−	14.1421i		−	0.765840i
$342$		0			0
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$		0			0
$345$	−6.00000	+	2.00000i	−0.323029	+	0.107676i
$346$		0			0
$347$	14.1421	−	14.1421i	0.759190	−	0.759190i	−0.216985	−	0.976175i	$-0.569622\pi$
$347$	14.1421	−	14.1421i	0.759190	−	0.759190i	0.976175	+	0.216985i	$0.0696224\pi$
$348$		0			0
$349$	19.7990			1.05982			0.529908	−	0.848055i	$-0.322227\pi$
$349$	19.7990			1.05982			0.529908	+	0.848055i	$0.322227\pi$
$350$		0			0
$351$		−	2.00000i		−	0.106752i
$352$		0			0
$353$	−2.00000	−	2.00000i	−0.106449	−	0.106449i	0.651876	−	0.758325i	$-0.273982\pi$
$353$	−2.00000	−	2.00000i	−0.106449	−	0.106449i	−0.758325	+	0.651876i	$0.773982\pi$
$354$		0			0
$355$	5.65685	+	16.9706i	0.300235	+	0.900704i
$356$		0			0
$357$	−2.82843	−	2.82843i	−0.149696	−	0.149696i
$358$		0			0
$359$	−16.0000			−0.844448			−0.422224	−	0.906492i	$-0.638750\pi$
$359$	−16.0000			−0.844448			−0.422224	+	0.906492i	$0.638750\pi$
$360$		0			0
$361$	−13.0000			−0.684211
$362$		0			0
$363$	−6.36396	−	6.36396i	−0.334021	−	0.334021i
$364$		0			0
$365$	8.48528	+	4.24264i	0.444140	+	0.222070i
$366$		0			0
$367$	−9.00000	−	9.00000i	−0.469796	−	0.469796i	0.432052	−	0.901849i	$-0.357790\pi$
$367$	−9.00000	−	9.00000i	−0.469796	−	0.469796i	−0.901849	+	0.432052i	$0.857790\pi$
$368$		0			0
$369$		−	2.00000i		−	0.104116i
$370$		0			0
$371$	8.48528			0.440534
$372$		0			0
$373$	−18.3848	+	18.3848i	−0.951928	+	0.951928i	−0.998896	−	0.0469687i	$-0.985044\pi$
$373$	−18.3848	+	18.3848i	−0.951928	+	0.951928i	0.0469687	+	0.998896i	$0.485044\pi$
$374$		0			0
$375$	11.0000	−	2.00000i	0.568038	−	0.103280i
$376$		0			0
$377$	−2.00000	+	2.00000i	−0.103005	+	0.103005i
$378$		0			0
$379$		−	25.4558i		−	1.30758i	−0.756677	−	0.653789i	$-0.773178\pi$
$379$		−	25.4558i		−	1.30758i	0.756677	−	0.653789i	$-0.226822\pi$
$380$		0			0
$381$			18.3848i			0.941881i
$382$		0			0
$383$	−8.00000	+	8.00000i	−0.408781	+	0.408781i	−0.881313	−	0.472532i	$-0.843340\pi$
$383$	−8.00000	+	8.00000i	−0.408781	+	0.408781i	0.472532	+	0.881313i	$0.343340\pi$
$384$		0			0
$385$	−4.00000	−	2.00000i	−0.203859	−	0.101929i
$386$		0			0
$387$	2.82843	−	2.82843i	0.143777	−	0.143777i
$388$		0			0
$389$	9.89949			0.501924			0.250962	−	0.967997i	$-0.419253\pi$
$389$	9.89949			0.501924			0.250962	+	0.967997i	$0.419253\pi$
$390$		0			0
$391$		−	8.00000i		−	0.404577i
$392$		0			0
$393$	−1.00000	−	1.00000i	−0.0504433	−	0.0504433i
$394$		0			0
$395$	21.2132	−	7.07107i	1.06735	−	0.355784i
$396$		0			0
$397$	−15.5563	−	15.5563i	−0.780751	−	0.780751i	0.199207	−	0.979957i	$-0.436163\pi$
$397$	−15.5563	−	15.5563i	−0.780751	−	0.780751i	−0.979957	+	0.199207i	$0.936163\pi$
$398$		0			0
$399$	−8.00000			−0.400501
$400$		0			0
$401$	30.0000			1.49813			0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000			1.49813			0.749064	+	0.662497i	$0.230503\pi$
$402$		0			0
$403$	−14.1421	−	14.1421i	−0.704470	−	0.704470i
$404$		0			0
$405$	−2.12132	+	0.707107i	−0.105409	+	0.0351364i
$406$		0			0
$407$	−6.00000	−	6.00000i	−0.297409	−	0.297409i
$408$		0			0
$409$			8.00000i			0.395575i	0.980245	+	0.197787i	$0.0633755\pi$
$409$			8.00000i			0.395575i	−0.980245	+	0.197787i	$0.936624\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	4.24264	−	4.24264i	0.208767	−	0.208767i
$414$		0			0
$415$	−20.0000	−	10.0000i	−0.981761	−	0.490881i
$416$		0			0
$417$	−2.00000	+	2.00000i	−0.0979404	+	0.0979404i
$418$		0			0
$419$			24.0416i			1.17451i	0.809402	+	0.587255i	$0.199792\pi$
$419$			24.0416i			1.17451i	−0.809402	+	0.587255i	$0.800208\pi$
$420$		0			0
$421$			39.5980i			1.92989i	0.262457	+	0.964944i	$0.415467\pi$
$421$			39.5980i			1.92989i	−0.262457	+	0.964944i	$0.584533\pi$
$422$		0			0
$423$	−8.00000	+	8.00000i	−0.388973	+	0.388973i
$424$		0			0
$425$	−2.00000	+	14.0000i	−0.0970143	+	0.679100i
$426$		0			0
$427$	2.82843	−	2.82843i	0.136877	−	0.136877i
$428$		0			0
$429$	2.82843			0.136558
$430$		0			0
$431$		−	36.0000i		−	1.73406i	−0.498257	−	0.867029i	$-0.666026\pi$
$431$		−	36.0000i		−	1.73406i	0.498257	−	0.867029i	$-0.333974\pi$
$432$		0			0
$433$	21.0000	+	21.0000i	1.00920	+	1.00920i	0.999957	+	0.00923827i	$0.00294067\pi$
$433$	21.0000	+	21.0000i	1.00920	+	1.00920i	0.00923827	+	0.999957i	$0.497059\pi$
$434$		0			0
$435$	2.82843	+	1.41421i	0.135613	+	0.0678064i
$436$		0			0
$437$	−11.3137	−	11.3137i	−0.541208	−	0.541208i
$438$		0			0
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		0			0
$441$	5.00000			0.238095
$442$		0			0
$443$	−19.7990	−	19.7990i	−0.940678	−	0.940678i	0.0576580	−	0.998336i	$-0.481637\pi$
$443$	−19.7990	−	19.7990i	−0.940678	−	0.940678i	−0.998336	+	0.0576580i	$0.981637\pi$
$444$		0			0
$445$	−7.07107	−	21.2132i	−0.335201	−	1.00560i
$446$		0			0
$447$	7.00000	+	7.00000i	0.331089	+	0.331089i
$448$		0			0
$449$		−	34.0000i		−	1.60456i	−0.596948	−	0.802280i	$-0.703620\pi$
$449$		−	34.0000i		−	1.60456i	0.596948	−	0.802280i	$-0.296380\pi$
$450$		0			0
$451$	2.82843			0.133185
$452$		0			0
$453$	5.65685	−	5.65685i	0.265782	−	0.265782i
$454$		0			0
$455$	−6.00000	+	2.00000i	−0.281284	+	0.0937614i
$456$		0			0
$457$	21.0000	−	21.0000i	0.982339	−	0.982339i	−0.0175082	−	0.999847i	$-0.505573\pi$
$457$	21.0000	−	21.0000i	0.982339	−	0.982339i	0.999847	+	0.0175082i	$0.00557330\pi$
$458$		0			0
$459$		−	2.82843i		−	0.132020i
$460$		0			0
$461$		−	4.24264i		−	0.197599i	−0.995107	−	0.0987997i	$-0.968500\pi$
$461$		−	4.24264i		−	0.197599i	0.995107	−	0.0987997i	$-0.0315003\pi$
$462$		0			0
$463$	27.0000	−	27.0000i	1.25480	−	1.25480i	0.301252	−	0.953545i	$-0.402596\pi$
$463$	27.0000	−	27.0000i	1.25480	−	1.25480i	0.953545	−	0.301252i	$-0.0974045\pi$
$464$		0			0
$465$	−10.0000	+	20.0000i	−0.463739	+	0.927478i
$466$		0			0
$467$	26.8701	−	26.8701i	1.24340	−	1.24340i	0.284816	−	0.958582i	$-0.408068\pi$
$467$	26.8701	−	26.8701i	1.24340	−	1.24340i	0.958582	−	0.284816i	$-0.0919324\pi$
$468$		0			0
$469$	16.9706			0.783628
$470$		0			0
$471$		−	10.0000i		−	0.460776i
$472$		0			0
$473$	4.00000	+	4.00000i	0.183920	+	0.183920i
$474$		0			0
$475$	16.9706	+	22.6274i	0.778663	+	1.03822i
$476$		0			0
$477$	4.24264	+	4.24264i	0.194257	+	0.194257i
$478$		0			0
$479$	−32.0000			−1.46212			−0.731059	−	0.682315i	$-0.760973\pi$
$479$	−32.0000			−1.46212			−0.731059	+	0.682315i	$0.760973\pi$
$480$		0			0
$481$	−12.0000			−0.547153
$482$		0			0
$483$	−2.82843	−	2.82843i	−0.128698	−	0.128698i
$484$		0			0
$485$	4.24264	−	8.48528i	0.192648	−	0.385297i
$486$		0			0
$487$	−9.00000	−	9.00000i	−0.407829	−	0.407829i	0.473152	−	0.880981i	$-0.343116\pi$
$487$	−9.00000	−	9.00000i	−0.407829	−	0.407829i	−0.880981	+	0.473152i	$0.843116\pi$
$488$		0			0
$489$		−	8.00000i		−	0.361773i
$490$		0			0
$491$	−29.6985			−1.34027			−0.670137	−	0.742237i	$-0.733765\pi$
$491$	−29.6985			−1.34027			−0.670137	+	0.742237i	$0.733765\pi$
$492$		0			0
$493$	−2.82843	+	2.82843i	−0.127386	+	0.127386i
$494$		0			0
$495$	−1.00000	−	3.00000i	−0.0449467	−	0.134840i
$496$		0			0
$497$	−8.00000	+	8.00000i	−0.358849	+	0.358849i
$498$		0			0
$499$			33.9411i			1.51941i	0.650266	+	0.759707i	$0.274658\pi$
$499$			33.9411i			1.51941i	−0.650266	+	0.759707i	$0.725342\pi$
$500$		0			0
$501$		−	14.1421i		−	0.631824i
$502$		0			0
$503$	16.0000	−	16.0000i	0.713405	−	0.713405i	−0.253841	−	0.967246i	$-0.581694\pi$
$503$	16.0000	−	16.0000i	0.713405	−	0.713405i	0.967246	+	0.253841i	$0.0816941\pi$
$504$		0			0
$505$	−13.0000	−	39.0000i	−0.578492	−	1.73548i
$506$		0			0
$507$	−6.36396	+	6.36396i	−0.282633	+	0.282633i
$508$		0			0
$509$	−18.3848			−0.814891			−0.407445	−	0.913230i	$-0.633580\pi$
$509$	−18.3848			−0.814891			−0.407445	+	0.913230i	$0.633580\pi$
$510$		0			0
$511$			6.00000i			0.265424i
$512$		0			0
$513$	−4.00000	−	4.00000i	−0.176604	−	0.176604i
$514$		0			0
$515$	−12.7279	+	25.4558i	−0.560859	+	1.12172i
$516$		0			0
$517$	−11.3137	−	11.3137i	−0.497576	−	0.497576i
$518$		0			0
$519$	16.0000			0.702322
$520$		0			0
$521$	−22.0000			−0.963837			−0.481919	−	0.876216i	$-0.660060\pi$
$521$	−22.0000			−0.963837			−0.481919	+	0.876216i	$0.660060\pi$
$522$		0			0
$523$	5.65685	+	5.65685i	0.247357	+	0.247357i	0.819885	−	0.572528i	$-0.194037\pi$
$523$	5.65685	+	5.65685i	0.247357	+	0.247357i	−0.572528	+	0.819885i	$0.694037\pi$
$524$		0			0
$525$	4.24264	+	5.65685i	0.185164	+	0.246885i
$526$		0			0
$527$	−20.0000	−	20.0000i	−0.871214	−	0.871214i
$528$		0			0
$529$			15.0000i			0.652174i
$530$		0			0
$531$	4.24264			0.184115
$532$		0			0
$533$	2.82843	−	2.82843i	0.122513	−	0.122513i
$534$		0			0
$535$	6.00000	−	12.0000i	0.259403	−	0.518805i
$536$		0			0
$537$	−13.0000	+	13.0000i	−0.560991	+	0.560991i
$538$		0			0
$539$			7.07107i			0.304572i
$540$		0			0
$541$		−	25.4558i		−	1.09443i	−0.836991	−	0.547216i	$-0.815688\pi$
$541$		−	25.4558i		−	1.09443i	0.836991	−	0.547216i	$-0.184312\pi$
$542$		0			0
$543$	−14.0000	+	14.0000i	−0.600798	+	0.600798i
$544$		0			0
$545$	−18.0000	+	6.00000i	−0.771035	+	0.257012i
$546$		0			0
$547$	5.65685	−	5.65685i	0.241870	−	0.241870i	−0.575754	−	0.817623i	$-0.695291\pi$
$547$	5.65685	−	5.65685i	0.241870	−	0.241870i	0.817623	+	0.575754i	$0.195291\pi$
$548$		0			0
$549$	2.82843			0.120714
$550$		0			0
$551$			8.00000i			0.340811i
$552$		0			0
$553$	10.0000	+	10.0000i	0.425243	+	0.425243i
$554$		0			0
$555$	4.24264	+	12.7279i	0.180090	+	0.540270i
$556$		0			0
$557$	9.89949	+	9.89949i	0.419455	+	0.419455i	0.885016	−	0.465561i	$-0.154147\pi$
$557$	9.89949	+	9.89949i	0.419455	+	0.419455i	−0.465561	+	0.885016i	$0.654147\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$		0			0
$561$	4.00000			0.168880
$562$		0			0
$563$	−2.82843	−	2.82843i	−0.119204	−	0.119204i	0.644988	−	0.764192i	$-0.276862\pi$
$563$	−2.82843	−	2.82843i	−0.119204	−	0.119204i	−0.764192	+	0.644988i	$0.776862\pi$
$564$		0			0
$565$	22.6274	+	11.3137i	0.951943	+	0.475971i
$566$		0			0
$567$	−1.00000	−	1.00000i	−0.0419961	−	0.0419961i
$568$		0			0
$569$			30.0000i			1.25767i	0.777541	+	0.628833i	$0.216467\pi$
$569$			30.0000i			1.25767i	−0.777541	+	0.628833i	$0.783533\pi$
$570$		0			0
$571$	5.65685			0.236732			0.118366	−	0.992970i	$-0.462234\pi$
$571$	5.65685			0.236732			0.118366	+	0.992970i	$0.462234\pi$
$572$		0			0
$573$	−8.48528	+	8.48528i	−0.354478	+	0.354478i
$574$		0			0
$575$	−2.00000	+	14.0000i	−0.0834058	+	0.583840i
$576$		0			0
$577$	27.0000	−	27.0000i	1.12402	−	1.12402i	0.132895	−	0.991130i	$-0.457573\pi$
$577$	27.0000	−	27.0000i	1.12402	−	1.12402i	0.991130	−	0.132895i	$-0.0424272\pi$
$578$		0			0
$579$			7.07107i			0.293864i
$580$		0			0
$581$		−	14.1421i		−	0.586715i
$582$		0			0
$583$	−6.00000	+	6.00000i	−0.248495	+	0.248495i
$584$		0			0
$585$	−4.00000	−	2.00000i	−0.165380	−	0.0826898i
$586$		0			0
$587$	−15.5563	+	15.5563i	−0.642079	+	0.642079i	−0.951066	−	0.308987i	$-0.900010\pi$
$587$	−15.5563	+	15.5563i	−0.642079	+	0.642079i	0.308987	+	0.951066i	$0.400010\pi$
$588$		0			0
$589$	−56.5685			−2.33087
$590$		0			0
$591$		−	14.0000i		−	0.575883i
$592$		0			0
$593$	−16.0000	−	16.0000i	−0.657041	−	0.657041i	0.297638	−	0.954679i	$-0.403801\pi$
$593$	−16.0000	−	16.0000i	−0.657041	−	0.657041i	−0.954679	+	0.297638i	$0.903801\pi$
$594$		0			0
$595$	−8.48528	+	2.82843i	−0.347863	+	0.115954i
$596$		0			0
$597$	−5.65685	−	5.65685i	−0.231520	−	0.231520i
$598$		0			0
$599$	36.0000			1.47092			0.735460	−	0.677568i	$-0.236966\pi$
$599$	36.0000			1.47092			0.735460	+	0.677568i	$0.236966\pi$
$600$		0			0
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$		0			0
$603$	8.48528	+	8.48528i	0.345547	+	0.345547i
$604$		0			0
$605$	−19.0919	+	6.36396i	−0.776195	+	0.258732i
$606$		0			0
$607$	−21.0000	−	21.0000i	−0.852364	−	0.852364i	0.138060	−	0.990424i	$-0.455913\pi$
$607$	−21.0000	−	21.0000i	−0.852364	−	0.852364i	−0.990424	+	0.138060i	$0.955913\pi$
$608$		0			0
$609$			2.00000i			0.0810441i
$610$		0			0
$611$	−22.6274			−0.915407
$612$		0			0
$613$	−7.07107	+	7.07107i	−0.285598	+	0.285598i	−0.835337	−	0.549739i	$-0.814727\pi$
$613$	−7.07107	+	7.07107i	−0.285598	+	0.285598i	0.549739	+	0.835337i	$0.314727\pi$
$614$		0			0
$615$	−4.00000	−	2.00000i	−0.161296	−	0.0806478i
$616$		0			0
$617$	2.00000	−	2.00000i	0.0805170	−	0.0805170i	−0.665701	−	0.746218i	$-0.731868\pi$
$617$	2.00000	−	2.00000i	0.0805170	−	0.0805170i	0.746218	+	0.665701i	$0.231868\pi$
$618$		0			0
$619$			8.48528i			0.341052i	0.985353	+	0.170526i	$0.0545467\pi$
$619$			8.48528i			0.341052i	−0.985353	+	0.170526i	$0.945453\pi$
$620$		0			0
$621$		−	2.82843i		−	0.113501i
$622$		0			0
$623$	10.0000	−	10.0000i	0.400642	−	0.400642i
$624$		0			0
$625$	7.00000	−	24.0000i	0.280000	−	0.960000i
$626$		0			0
$627$	5.65685	−	5.65685i	0.225913	−	0.225913i
$628$		0			0
$629$	−16.9706			−0.676661
$630$		0			0
$631$			6.00000i			0.238856i	0.992843	+	0.119428i	$0.0381061\pi$
$631$			6.00000i			0.238856i	−0.992843	+	0.119428i	$0.961894\pi$
$632$		0			0
$633$	−10.0000	−	10.0000i	−0.397464	−	0.397464i
$634$		0			0
$635$	36.7696	+	18.3848i	1.45916	+	0.729578i
$636$		0			0
$637$	7.07107	+	7.07107i	0.280166	+	0.280166i
$638$		0			0
$639$	−8.00000			−0.316475
$640$		0			0
$641$	22.0000			0.868948			0.434474	−	0.900684i	$-0.356934\pi$
$641$	22.0000			0.868948			0.434474	+	0.900684i	$0.356934\pi$
$642$		0			0
$643$	−31.1127	−	31.1127i	−1.22697	−	1.22697i	−0.965106	−	0.261859i	$-0.915665\pi$
$643$	−31.1127	−	31.1127i	−1.22697	−	1.22697i	−0.261859	−	0.965106i	$-0.584335\pi$
$644$		0			0
$645$	−2.82843	−	8.48528i	−0.111369	−	0.334108i
$646$		0			0
$647$	24.0000	+	24.0000i	0.943537	+	0.943537i	0.998489	−	0.0549517i	$-0.0175005\pi$
$647$	24.0000	+	24.0000i	0.943537	+	0.943537i	−0.0549517	+	0.998489i	$0.517500\pi$
$648$		0			0
$649$			6.00000i			0.235521i
$650$		0			0
$651$	−14.1421			−0.554274
$652$		0			0
$653$	−2.82843	+	2.82843i	−0.110685	+	0.110685i	−0.760280	−	0.649595i	$-0.774938\pi$
$653$	−2.82843	+	2.82843i	−0.110685	+	0.110685i	0.649595	+	0.760280i	$0.274938\pi$
$654$		0			0
$655$	−3.00000	+	1.00000i	−0.117220	+	0.0390732i
$656$		0			0
$657$	−3.00000	+	3.00000i	−0.117041	+	0.117041i
$658$		0			0
$659$			4.24264i			0.165270i	0.996580	+	0.0826349i	$0.0263335\pi$
$659$			4.24264i			0.165270i	−0.996580	+	0.0826349i	$0.973666\pi$
$660$		0			0
$661$		−	14.1421i		−	0.550065i	−0.961435	−	0.275033i	$-0.911311\pi$
$661$		−	14.1421i		−	0.550065i	0.961435	−	0.275033i	$-0.0886887\pi$
$662$		0			0
$663$	4.00000	−	4.00000i	0.155347	−	0.155347i
$664$		0			0
$665$	−8.00000	+	16.0000i	−0.310227	+	0.620453i
$666$		0			0
$667$	−2.82843	+	2.82843i	−0.109517	+	0.109517i
$668$		0			0
$669$	−9.89949			−0.382737
$670$		0			0
$671$			4.00000i			0.154418i
$672$		0			0
$673$	−5.00000	−	5.00000i	−0.192736	−	0.192736i	0.604141	−	0.796877i	$-0.293516\pi$
$673$	−5.00000	−	5.00000i	−0.192736	−	0.192736i	−0.796877	+	0.604141i	$0.793516\pi$
$674$		0			0
$675$	−0.707107	+	4.94975i	−0.0272166	+	0.190516i
$676$		0			0
$677$	8.48528	+	8.48528i	0.326116	+	0.326116i	0.851107	−	0.524992i	$-0.175932\pi$
$677$	8.48528	+	8.48528i	0.326116	+	0.326116i	−0.524992	+	0.851107i	$0.675932\pi$
$678$		0			0
$679$	6.00000			0.230259
$680$		0			0
$681$	20.0000			0.766402
$682$		0			0
$683$	21.2132	+	21.2132i	0.811701	+	0.811701i	0.984889	−	0.173188i	$-0.0554069\pi$
$683$	21.2132	+	21.2132i	0.811701	+	0.811701i	−0.173188	+	0.984889i	$0.555407\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−8.00000	−	8.00000i	−0.305219	−	0.305219i
$688$		0			0
$689$			12.0000i			0.457164i
$690$		0			0
$691$	16.9706			0.645591			0.322795	−	0.946469i	$-0.395377\pi$
$691$	16.9706			0.645591			0.322795	+	0.946469i	$0.395377\pi$
$692$		0			0
$693$	1.41421	−	1.41421i	0.0537215	−	0.0537215i
$694$		0			0
$695$	2.00000	+	6.00000i	0.0758643	+	0.227593i
$696$		0			0
$697$	4.00000	−	4.00000i	0.151511	−	0.151511i
$698$		0			0
$699$		−	25.4558i		−	0.962828i
$700$		0			0
$701$			9.89949i			0.373899i	0.982370	+	0.186949i	$0.0598600\pi$
$701$			9.89949i			0.373899i	−0.982370	+	0.186949i	$0.940140\pi$
$702$		0			0
$703$	−24.0000	+	24.0000i	−0.905177	+	0.905177i
$704$		0			0
$705$	8.00000	+	24.0000i	0.301297	+	0.903892i
$706$		0			0
$707$	18.3848	−	18.3848i	0.691431	−	0.691431i
$708$		0			0
$709$	16.9706			0.637343			0.318671	−	0.947865i	$-0.396763\pi$
$709$	16.9706			0.637343			0.318671	+	0.947865i	$0.396763\pi$
$710$		0			0
$711$			10.0000i			0.375029i
$712$		0			0
$713$	−20.0000	−	20.0000i	−0.749006	−	0.749006i
$714$		0			0
$715$	2.82843	−	5.65685i	0.105777	−	0.211554i
$716$		0			0
$717$	11.3137	+	11.3137i	0.422518	+	0.422518i
$718$		0			0
$719$	−8.00000			−0.298350			−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000			−0.298350			−0.149175	+	0.988811i	$0.547662\pi$
$720$		0			0
$721$	−18.0000			−0.670355
$722$		0			0
$723$	−19.7990	−	19.7990i	−0.736332	−	0.736332i
$724$		0			0
$725$	5.65685	−	4.24264i	0.210090	−	0.157568i
$726$		0			0
$727$	27.0000	+	27.0000i	1.00137	+	1.00137i	0.999999	+	0.00137552i	$0.000437841\pi$
$727$	27.0000	+	27.0000i	1.00137	+	1.00137i	0.00137552	+	0.999999i	$0.499562\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	11.3137			0.418453
$732$		0			0
$733$	21.2132	−	21.2132i	0.783528	−	0.783528i	−0.196897	−	0.980424i	$-0.563086\pi$
$733$	21.2132	−	21.2132i	0.783528	−	0.783528i	0.980424	+	0.196897i	$0.0630864\pi$
$734$		0			0
$735$	5.00000	−	10.0000i	0.184428	−	0.368856i
$736$		0			0
$737$	−12.0000	+	12.0000i	−0.442026	+	0.442026i
$738$		0			0
$739$			28.2843i			1.04045i	0.854028	+	0.520227i	$0.174153\pi$
$739$			28.2843i			1.04045i	−0.854028	+	0.520227i	$0.825847\pi$
$740$		0			0
$741$		−	11.3137i		−	0.415619i
$742$		0			0
$743$	−16.0000	+	16.0000i	−0.586983	+	0.586983i	−0.936813	−	0.349830i	$-0.886239\pi$
$743$	−16.0000	+	16.0000i	−0.586983	+	0.586983i	0.349830	+	0.936813i	$0.386239\pi$
$744$		0			0
$745$	21.0000	−	7.00000i	0.769380	−	0.256460i
$746$		0			0
$747$	7.07107	−	7.07107i	0.258717	−	0.258717i
$748$		0			0
$749$	8.48528			0.310045
$750$		0			0
$751$		−	10.0000i		−	0.364905i	−0.983215	−	0.182453i	$-0.941596\pi$
$751$		−	10.0000i		−	0.364905i	0.983215	−	0.182453i	$-0.0584036\pi$
$752$		0			0
$753$	−17.0000	−	17.0000i	−0.619514	−	0.619514i
$754$		0			0
$755$	−5.65685	−	16.9706i	−0.205874	−	0.617622i
$756$		0			0
$757$	15.5563	+	15.5563i	0.565405	+	0.565405i	0.930838	−	0.365433i	$-0.119079\pi$
$757$	15.5563	+	15.5563i	0.565405	+	0.565405i	−0.365433	+	0.930838i	$0.619079\pi$
$758$		0			0
$759$	4.00000			0.145191
$760$		0			0
$761$	14.0000			0.507500			0.253750	−	0.967270i	$-0.418336\pi$
$761$	14.0000			0.507500			0.253750	+	0.967270i	$0.418336\pi$
$762$		0			0
$763$	−8.48528	−	8.48528i	−0.307188	−	0.307188i
$764$		0			0
$765$	−5.65685	−	2.82843i	−0.204524	−	0.102262i
$766$		0			0
$767$	6.00000	+	6.00000i	0.216647	+	0.216647i
$768$		0			0
$769$			50.0000i			1.80305i	0.432731	+	0.901523i	$0.357550\pi$
$769$			50.0000i			1.80305i	−0.432731	+	0.901523i	$0.642450\pi$
$770$		0			0
$771$	−5.65685			−0.203727
$772$		0			0
$773$	−25.4558	+	25.4558i	−0.915583	+	0.915583i	−0.996704	−	0.0811212i	$-0.974150\pi$
$773$	−25.4558	+	25.4558i	−0.915583	+	0.915583i	0.0811212	+	0.996704i	$0.474150\pi$
$774$		0			0
$775$	30.0000	+	40.0000i	1.07763	+	1.43684i
$776$		0			0
$777$	−6.00000	+	6.00000i	−0.215249	+	0.215249i
$778$		0			0
$779$		−	11.3137i		−	0.405356i
$780$		0			0
$781$		−	11.3137i		−	0.404836i
$782$		0			0
$783$	−1.00000	+	1.00000i	−0.0357371	+	0.0357371i
$784$		0			0
$785$	−20.0000	−	10.0000i	−0.713831	−	0.356915i
$786$		0			0
$787$	36.7696	−	36.7696i	1.31069	−	1.31069i	0.389789	−	0.920904i	$-0.372548\pi$
$787$	36.7696	−	36.7696i	1.31069	−	1.31069i	0.920904	−	0.389789i	$-0.127452\pi$
$788$		0			0
$789$	8.48528			0.302084
$790$		0			0
$791$			16.0000i			0.568895i
$792$		0			0
$793$	4.00000	+	4.00000i	0.142044	+	0.142044i
$794$		0			0
$795$	12.7279	−	4.24264i	0.451413	−	0.150471i
$796$		0			0
$797$	−5.65685	−	5.65685i	−0.200376	−	0.200376i	0.599785	−	0.800161i	$-0.295253\pi$
$797$	−5.65685	−	5.65685i	−0.200376	−	0.200376i	−0.800161	+	0.599785i	$0.795253\pi$
$798$		0			0
$799$	−32.0000			−1.13208
$800$		0			0
$801$	10.0000			0.353333
$802$		0			0
$803$	−4.24264	−	4.24264i	−0.149720	−	0.149720i
$804$		0			0
$805$	−8.48528	+	2.82843i	−0.299067	+	0.0996890i
$806$		0			0
$807$	13.0000	+	13.0000i	0.457622	+	0.457622i
$808$		0			0
$809$		−	18.0000i		−	0.632846i	−0.948618	−	0.316423i	$-0.897518\pi$
$809$		−	18.0000i		−	0.632846i	0.948618	−	0.316423i	$-0.102482\pi$
$810$		0			0
$811$	−42.4264			−1.48979			−0.744896	−	0.667180i	$-0.767501\pi$
$811$	−42.4264			−1.48979			−0.744896	+	0.667180i	$0.767501\pi$
$812$		0			0
$813$	11.3137	−	11.3137i	0.396789	−	0.396789i
$814$		0			0
$815$	−16.0000	−	8.00000i	−0.560456	−	0.280228i
$816$		0			0
$817$	16.0000	−	16.0000i	0.559769	−	0.559769i
$818$		0			0
$819$		−	2.82843i		−	0.0988332i
$820$		0			0
$821$			12.7279i			0.444208i	0.975023	+	0.222104i	$0.0712924\pi$
$821$			12.7279i			0.444208i	−0.975023	+	0.222104i	$0.928708\pi$
$822$		0			0
$823$	3.00000	−	3.00000i	0.104573	−	0.104573i	−0.652884	−	0.757458i	$-0.726441\pi$
$823$	3.00000	−	3.00000i	0.104573	−	0.104573i	0.757458	+	0.652884i	$0.226441\pi$
$824$		0			0
$825$	−7.00000	−	1.00000i	−0.243709	−	0.0348155i
$826$		0			0
$827$	−8.48528	+	8.48528i	−0.295062	+	0.295062i	−0.839076	−	0.544014i	$-0.816904\pi$
$827$	−8.48528	+	8.48528i	−0.295062	+	0.295062i	0.544014	+	0.839076i	$0.316904\pi$
$828$		0			0
$829$	25.4558			0.884118			0.442059	−	0.896986i	$-0.354248\pi$
$829$	25.4558			0.884118			0.442059	+	0.896986i	$0.354248\pi$
$830$		0			0
$831$			26.0000i			0.901930i
$832$		0			0
$833$	10.0000	+	10.0000i	0.346479	+	0.346479i
$834$		0			0
$835$	−28.2843	−	14.1421i	−0.978818	−	0.489409i
$836$		0			0
$837$	−7.07107	−	7.07107i	−0.244412	−	0.244412i
$838$		0			0
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$		0			0
$841$	−27.0000			−0.931034
$842$		0			0
$843$	12.7279	+	12.7279i	0.438373	+	0.438373i
$844$		0			0
$845$	6.36396	+	19.0919i	0.218927	+	0.656781i
$846$		0			0
$847$	−9.00000	−	9.00000i	−0.309244	−	0.309244i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−16.9706			−0.581743
$852$		0			0
$853$	18.3848	−	18.3848i	0.629483	−	0.629483i	−0.318455	−	0.947938i	$-0.603164\pi$
$853$	18.3848	−	18.3848i	0.629483	−	0.629483i	0.947938	+	0.318455i	$0.103164\pi$
$854$		0			0
$855$	−12.0000	+	4.00000i	−0.410391	+	0.136797i
$856$		0			0
$857$	30.0000	−	30.0000i	1.02478	−	1.02478i	0.0250954	−	0.999685i	$-0.492011\pi$
$857$	30.0000	−	30.0000i	1.02478	−	1.02478i	0.999685	−	0.0250954i	$-0.00798896\pi$
$858$		0			0
$859$		−	25.4558i		−	0.868542i	−0.900782	−	0.434271i	$-0.857006\pi$
$859$		−	25.4558i		−	0.868542i	0.900782	−	0.434271i	$-0.142994\pi$
$860$		0			0
$861$		−	2.82843i		−	0.0963925i
$862$		0			0
$863$	−22.0000	+	22.0000i	−0.748889	+	0.748889i	−0.974271	−	0.225382i	$-0.927637\pi$
$863$	−22.0000	+	22.0000i	−0.748889	+	0.748889i	0.225382	+	0.974271i	$0.427637\pi$
$864$		0			0
$865$	16.0000	−	32.0000i	0.544016	−	1.08803i
$866$		0			0
$867$	−6.36396	+	6.36396i	−0.216131	+	0.216131i
$868$		0			0
$869$	−14.1421			−0.479739
$870$		0			0
$871$			24.0000i			0.813209i
$872$		0			0
$873$	3.00000	+	3.00000i	0.101535	+	0.101535i
$874$		0			0
$875$	15.5563	−	2.82843i	0.525901	−	0.0956183i
$876$		0			0
$877$	−35.3553	−	35.3553i	−1.19386	−	1.19386i	−0.975973	−	0.217892i	$-0.930082\pi$
$877$	−35.3553	−	35.3553i	−1.19386	−	1.19386i	−0.217892	−	0.975973i	$-0.569918\pi$
$878$		0			0
$879$	30.0000			1.01187
$880$		0			0
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$		0			0
$883$	11.3137	+	11.3137i	0.380737	+	0.380737i	0.871368	−	0.490631i	$-0.163234\pi$
$883$	11.3137	+	11.3137i	0.380737	+	0.380737i	−0.490631	+	0.871368i	$0.663234\pi$
$884$		0			0
$885$	4.24264	−	8.48528i	0.142615	−	0.285230i
$886$		0			0
$887$	10.0000	+	10.0000i	0.335767	+	0.335767i	0.854772	−	0.519004i	$-0.173697\pi$
$887$	10.0000	+	10.0000i	0.335767	+	0.335767i	−0.519004	+	0.854772i	$0.673697\pi$
$888$		0			0
$889$			26.0000i			0.872012i
$890$		0			0
$891$	1.41421			0.0473779
$892$		0			0
$893$	−45.2548	+	45.2548i	−1.51440	+	1.51440i
$894$		0			0
$895$	13.0000	+	39.0000i	0.434542	+	1.30363i
$896$		0			0
$897$	4.00000	−	4.00000i	0.133556	−	0.133556i
$898$		0			0
$899$			14.1421i			0.471667i
$900$		0			0
$901$			16.9706i			0.565371i
$902$		0			0
$903$	4.00000	−	4.00000i	0.133112	−	0.133112i
$904$		0			0
$905$	14.0000	+	42.0000i	0.465376	+	1.39613i
$906$		0			0
$907$	22.6274	−	22.6274i	0.751331	−	0.751331i	−0.223397	−	0.974728i	$-0.571714\pi$
$907$	22.6274	−	22.6274i	0.751331	−	0.751331i	0.974728	+	0.223397i	$0.0717145\pi$
$908$		0			0
$909$	18.3848			0.609785
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$	10.0000	+	10.0000i	0.330952	+	0.330952i
$914$		0			0
$915$	2.82843	−	5.65685i	0.0935049	−	0.187010i
$916$		0			0
$917$	−1.41421	−	1.41421i	−0.0467014	−	0.0467014i
$918$		0			0
$919$	10.0000			0.329870			0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000			0.329870			0.164935	+	0.986304i	$0.447259\pi$
$920$		0			0
$921$	28.0000			0.922631
$922$		0			0
$923$	−11.3137	−	11.3137i	−0.372395	−	0.372395i
$924$		0			0
$925$	29.6985	+	4.24264i	0.976480	+	0.139497i
$926$		0			0
$927$	−9.00000	−	9.00000i	−0.295599	−	0.295599i
$928$		0			0
$929$		−	2.00000i		−	0.0656179i	−0.999462	−	0.0328089i	$-0.989555\pi$
$929$		−	2.00000i		−	0.0656179i	0.999462	−	0.0328089i	$-0.0104453\pi$
$930$		0			0
$931$	28.2843			0.926980
$932$		0			0
$933$	14.1421	−	14.1421i	0.462993	−	0.462993i
$934$		0			0
$935$	4.00000	−	8.00000i	0.130814	−	0.261628i
$936$		0			0
$937$	−17.0000	+	17.0000i	−0.555366	+	0.555366i	−0.927985	−	0.372619i	$-0.878460\pi$
$937$	−17.0000	+	17.0000i	−0.555366	+	0.555366i	0.372619	+	0.927985i	$0.378460\pi$
$938$		0			0
$939$			7.07107i			0.230756i
$940$		0			0
$941$			41.0122i			1.33696i	0.743730	+	0.668480i	$0.233055\pi$
$941$			41.0122i			1.33696i	−0.743730	+	0.668480i	$0.766945\pi$
$942$		0			0
$943$	4.00000	−	4.00000i	0.130258	−	0.130258i
$944$		0			0
$945$	−3.00000	+	1.00000i	−0.0975900	+	0.0325300i
$946$		0			0
$947$	2.82843	−	2.82843i	0.0919115	−	0.0919115i	−0.659656	−	0.751568i	$-0.729298\pi$
$947$	2.82843	−	2.82843i	0.0919115	−	0.0919115i	0.751568	+	0.659656i	$0.229298\pi$
$948$		0			0
$949$	−8.48528			−0.275444
$950$		0			0
$951$			12.0000i			0.389127i
$952$		0			0
$953$	−4.00000	−	4.00000i	−0.129573	−	0.129573i	0.639346	−	0.768919i	$-0.279205\pi$
$953$	−4.00000	−	4.00000i	−0.129573	−	0.129573i	−0.768919	+	0.639346i	$0.779205\pi$
$954$		0			0
$955$	8.48528	+	25.4558i	0.274577	+	0.823732i
$956$		0			0
$957$	−1.41421	−	1.41421i	−0.0457150	−	0.0457150i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−69.0000			−2.22581
$962$		0			0
$963$	4.24264	+	4.24264i	0.136717	+	0.136717i
$964$		0			0
$965$	14.1421	+	7.07107i	0.455251	+	0.227626i
$966$		0			0
$967$	39.0000	+	39.0000i	1.25416	+	1.25416i	0.953840	+	0.300316i	$0.0970920\pi$
$967$	39.0000	+	39.0000i	1.25416	+	1.25416i	0.300316	+	0.953840i	$0.402908\pi$
$968$		0			0
$969$		−	16.0000i		−	0.513994i
$970$		0			0
$971$	−26.8701			−0.862301			−0.431151	−	0.902280i	$-0.641892\pi$
$971$	−26.8701			−0.862301			−0.431151	+	0.902280i	$0.641892\pi$
$972$		0			0
$973$	−2.82843	+	2.82843i	−0.0906752	+	0.0906752i
$974$		0			0
$975$	−8.00000	+	6.00000i	−0.256205	+	0.192154i
$976$		0			0
$977$	−14.0000	+	14.0000i	−0.447900	+	0.447900i	−0.894656	−	0.446756i	$-0.852579\pi$
$977$	−14.0000	+	14.0000i	−0.447900	+	0.447900i	0.446756	+	0.894656i	$0.352579\pi$
$978$		0			0
$979$			14.1421i			0.451985i
$980$		0			0
$981$		−	8.48528i		−	0.270914i
$982$		0			0
$983$	−20.0000	+	20.0000i	−0.637901	+	0.637901i	−0.950037	−	0.312136i	$-0.898955\pi$
$983$	−20.0000	+	20.0000i	−0.637901	+	0.637901i	0.312136	+	0.950037i	$0.398955\pi$
$984$		0			0
$985$	−28.0000	−	14.0000i	−0.892154	−	0.446077i
$986$		0			0
$987$	−11.3137	+	11.3137i	−0.360119	+	0.360119i
$988$		0			0
$989$	11.3137			0.359755
$990$		0			0
$991$			32.0000i			1.01651i	0.861206	+	0.508257i	$0.169710\pi$
$991$			32.0000i			1.01651i	−0.861206	+	0.508257i	$0.830290\pi$
$992$		0			0
$993$	−24.0000	−	24.0000i	−0.761617	−	0.761617i
$994$		0			0
$995$	−16.9706	+	5.65685i	−0.538003	+	0.179334i
$996$		0			0
$997$	26.8701	+	26.8701i	0.850983	+	0.850983i	0.990254	−	0.139271i	$-0.0444759\pi$
$997$	26.8701	+	26.8701i	0.850983	+	0.850983i	−0.139271	+	0.990254i	$0.544476\pi$
$998$		0			0
$999$	−6.00000			−0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.bh.f.703.2	yes	4
4.3	odd	2		1920.2.bh.c.703.1	✓	4
5.2	odd	4		1920.2.bh.c.1087.2	yes	4
8.3	odd	2		1920.2.bh.c.703.2	yes	4
8.5	even	2	inner	1920.2.bh.f.703.1	yes	4
20.7	even	4	inner	1920.2.bh.f.1087.1	yes	4
40.27	even	4	inner	1920.2.bh.f.1087.2	yes	4
40.37	odd	4		1920.2.bh.c.1087.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1920.2.bh.c.703.1	✓	4	4.3	odd	2
1920.2.bh.c.703.2	yes	4	8.3	odd	2
1920.2.bh.c.1087.1	yes	4	40.37	odd	4
1920.2.bh.c.1087.2	yes	4	5.2	odd	4
1920.2.bh.f.703.1	yes	4	8.5	even	2	inner
1920.2.bh.f.703.2	yes	4	1.1	even	1	trivial
1920.2.bh.f.1087.1	yes	4	20.7	even	4	inner
1920.2.bh.f.1087.2	yes	4	40.27	even	4	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:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.bh (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(2.12132 - 0.707107i) q^{5} +(1.00000 + 1.00000i) q^{7} +1.00000i q^{9} -1.41421 q^{11} +(-1.41421 + 1.41421i) q^{13} +(2.00000 + 1.00000i) q^{15} +(-2.00000 + 2.00000i) q^{17} +5.65685i q^{19} +1.41421i q^{21} +(-2.00000 + 2.00000i) q^{23} +(4.00000 - 3.00000i) q^{25} +(-0.707107 + 0.707107i) q^{27} +1.41421 q^{29} +10.0000i q^{31} +(-1.00000 - 1.00000i) q^{33} +(2.82843 + 1.41421i) q^{35} +(4.24264 + 4.24264i) q^{37} -2.00000 q^{39} -2.00000 q^{41} +(-2.82843 - 2.82843i) q^{43} +(0.707107 + 2.12132i) q^{45} +(8.00000 + 8.00000i) q^{47} -5.00000i q^{49} -2.82843 q^{51} +(4.24264 - 4.24264i) q^{53} +(-3.00000 + 1.00000i) q^{55} +(-4.00000 + 4.00000i) q^{57} -4.24264i q^{59} -2.82843i q^{61} +(-1.00000 + 1.00000i) q^{63} +(-2.00000 + 4.00000i) q^{65} +(8.48528 - 8.48528i) q^{67} -2.82843 q^{69} +8.00000i q^{71} +(3.00000 + 3.00000i) q^{73} +(4.94975 + 0.707107i) q^{75} +(-1.41421 - 1.41421i) q^{77} +10.0000 q^{79} -1.00000 q^{81} +(-7.07107 - 7.07107i) q^{83} +(-2.82843 + 5.65685i) q^{85} +(1.00000 + 1.00000i) q^{87} -10.0000i q^{89} -2.82843 q^{91} +(-7.07107 + 7.07107i) q^{93} +(4.00000 + 12.0000i) q^{95} +(3.00000 - 3.00000i) q^{97} -1.41421i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{7} + 8 q^{15} - 8 q^{17} - 8 q^{23} + 16 q^{25} - 4 q^{33} - 8 q^{39} - 8 q^{41} + 32 q^{47} - 12 q^{55} - 16 q^{57} - 4 q^{63} - 8 q^{65} + 12 q^{73} + 40 q^{79} - 4 q^{81} + 4 q^{87} + 16 q^{95}+ \cdots + 12 q^{97}+O(q^{100}) \) 4 * q + 4 * q^7 + 8 * q^15 - 8 * q^17 - 8 * q^23 + 16 * q^25 - 4 * q^33 - 8 * q^39 - 8 * q^41 + 32 * q^47 - 12 * q^55 - 16 * q^57 - 4 * q^63 - 8 * q^65 + 12 * q^73 + 40 * q^79 - 4 * q^81 + 4 * q^87 + 16 * q^95 + 12 * q^97

Introduction

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