LMFDB - Embedded newform 1734.2.f.a.1483.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1734,2,Mod(829,1734)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1734, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1734.829");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1734 = 2 \cdot 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1734.f (of order $4$, degree $2$, not 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:	$13.8460597105$
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			1483.2
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1734.1483
Dual form			1734.2.f.a.829.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(2.82843 + 2.82843i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(0.707107 + 0.707107i) q^{10} +(2.12132 + 2.12132i) q^{11} +(-0.707107 + 0.707107i) q^{12} -6.00000 q^{13} +(2.82843 - 2.82843i) q^{14} +1.00000i q^{15} +1.00000 q^{16} -1.00000 q^{18} +4.00000i q^{19} +(0.707107 - 0.707107i) q^{20} +4.00000 q^{21} +(2.12132 - 2.12132i) q^{22} +(-4.24264 - 4.24264i) q^{23} +(0.707107 + 0.707107i) q^{24} +4.00000i q^{25} +6.00000i q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.82843 - 2.82843i) q^{28} +(-4.94975 + 4.94975i) q^{29} +1.00000 q^{30} +(2.12132 - 2.12132i) q^{31} -1.00000i q^{32} +3.00000 q^{33} -4.00000 q^{35} +1.00000i q^{36} +(-5.65685 + 5.65685i) q^{37} +4.00000 q^{38} +(-4.24264 + 4.24264i) q^{39} +(-0.707107 - 0.707107i) q^{40} +(1.41421 + 1.41421i) q^{41} -4.00000i q^{42} +4.00000i q^{43} +(-2.12132 - 2.12132i) q^{44} +(0.707107 + 0.707107i) q^{45} +(-4.24264 + 4.24264i) q^{46} +2.00000 q^{47} +(0.707107 - 0.707107i) q^{48} +9.00000i q^{49} +4.00000 q^{50} +6.00000 q^{52} +13.0000i q^{53} +(-0.707107 + 0.707107i) q^{54} -3.00000 q^{55} +(-2.82843 + 2.82843i) q^{56} +(2.82843 + 2.82843i) q^{57} +(4.94975 + 4.94975i) q^{58} -9.00000i q^{59} -1.00000i q^{60} +(-7.07107 - 7.07107i) q^{61} +(-2.12132 - 2.12132i) q^{62} +(2.82843 - 2.82843i) q^{63} -1.00000 q^{64} +(4.24264 - 4.24264i) q^{65} -3.00000i q^{66} -6.00000 q^{67} -6.00000 q^{69} +4.00000i q^{70} +(8.48528 - 8.48528i) q^{71} +1.00000 q^{72} +(-4.94975 + 4.94975i) q^{73} +(5.65685 + 5.65685i) q^{74} +(2.82843 + 2.82843i) q^{75} -4.00000i q^{76} +12.0000i q^{77} +(4.24264 + 4.24264i) q^{78} +(3.53553 + 3.53553i) q^{79} +(-0.707107 + 0.707107i) q^{80} -1.00000 q^{81} +(1.41421 - 1.41421i) q^{82} +12.0000i q^{83} -4.00000 q^{84} +4.00000 q^{86} +7.00000i q^{87} +(-2.12132 + 2.12132i) q^{88} -4.00000 q^{89} +(0.707107 - 0.707107i) q^{90} +(-16.9706 - 16.9706i) q^{91} +(4.24264 + 4.24264i) q^{92} -3.00000i q^{93} -2.00000i q^{94} +(-2.82843 - 2.82843i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(2.12132 - 2.12132i) q^{97} +9.00000 q^{98} +(2.12132 - 2.12132i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 24 q^{13} + 4 q^{16} - 4 q^{18} + 16 q^{21} + 4 q^{30} + 12 q^{33} - 16 q^{35} + 16 q^{38} + 8 q^{47} + 16 q^{50} + 24 q^{52} - 12 q^{55} - 4 q^{64} - 24 q^{67} - 24 q^{69} + 4 q^{72} - 4 q^{81}+ \cdots + 36 q^{98}+O(q^{100}) $ 4 * q - 4 * q^4 - 24 * q^13 + 4 * q^16 - 4 * q^18 + 16 * q^21 + 4 * q^30 + 12 * q^33 - 16 * q^35 + 16 * q^38 + 8 * q^47 + 16 * q^50 + 24 * q^52 - 12 * q^55 - 4 * q^64 - 24 * q^67 - 24 * q^69 + 4 * q^72 - 4 * q^81 - 16 * q^84 + 16 * q^86 - 16 * q^89 + 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1734\mathbb{Z}\right)^\times$.

$n$	$1157$	$1159$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i	−0.847316	−	0.531089i	$-0.821783\pi$
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i	0.531089	+	0.847316i	$0.321783\pi$
$6$	−0.707107	−	0.707107i	−0.288675	−	0.288675i
$7$	2.82843	+	2.82843i	1.06904	+	1.06904i	0.997433	+	0.0716124i	$0.0228145\pi$
$7$	2.82843	+	2.82843i	1.06904	+	1.06904i	0.0716124	+	0.997433i	$0.477186\pi$
$8$			1.00000i			0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	0.707107	+	0.707107i	0.223607	+	0.223607i
$11$	2.12132	+	2.12132i	0.639602	+	0.639602i	0.950457	−	0.310855i	$-0.100615\pi$
$11$	2.12132	+	2.12132i	0.639602	+	0.639602i	−0.310855	+	0.950457i	$0.600615\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−6.00000			−1.66410			−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000			−1.66410			−0.832050	+	0.554700i	$0.812833\pi$
$14$	2.82843	−	2.82843i	0.755929	−	0.755929i
$15$			1.00000i			0.258199i
$16$	1.00000			0.250000
$17$		0			0
$17$		0			0
$18$	−1.00000			−0.235702
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$	0.707107	−	0.707107i	0.158114	−	0.158114i
$21$	4.00000			0.872872
$22$	2.12132	−	2.12132i	0.452267	−	0.452267i
$23$	−4.24264	−	4.24264i	−0.884652	−	0.884652i	0.109351	−	0.994003i	$-0.465123\pi$
$23$	−4.24264	−	4.24264i	−0.884652	−	0.884652i	−0.994003	+	0.109351i	$0.965123\pi$
$24$	0.707107	+	0.707107i	0.144338	+	0.144338i
$25$			4.00000i			0.800000i
$26$			6.00000i			1.17670i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−2.82843	−	2.82843i	−0.534522	−	0.534522i
$29$	−4.94975	+	4.94975i	−0.919145	+	0.919145i	−0.996967	−	0.0778222i	$-0.975203\pi$
$29$	−4.94975	+	4.94975i	−0.919145	+	0.919145i	0.0778222	+	0.996967i	$0.475203\pi$
$30$	1.00000			0.182574
$31$	2.12132	−	2.12132i	0.381000	−	0.381000i	−0.490462	−	0.871463i	$-0.663172\pi$
$31$	2.12132	−	2.12132i	0.381000	−	0.381000i	0.871463	+	0.490462i	$0.163172\pi$
$32$		−	1.00000i		−	0.176777i
$33$	3.00000			0.522233
$34$		0			0
$35$	−4.00000			−0.676123
$36$			1.00000i			0.166667i
$37$	−5.65685	+	5.65685i	−0.929981	+	0.929981i	−0.997704	−	0.0677230i	$-0.978427\pi$
$37$	−5.65685	+	5.65685i	−0.929981	+	0.929981i	0.0677230	+	0.997704i	$0.478427\pi$
$38$	4.00000			0.648886
$39$	−4.24264	+	4.24264i	−0.679366	+	0.679366i
$40$	−0.707107	−	0.707107i	−0.111803	−	0.111803i
$41$	1.41421	+	1.41421i	0.220863	+	0.220863i	0.808862	−	0.587999i	$-0.200084\pi$
$41$	1.41421	+	1.41421i	0.220863	+	0.220863i	−0.587999	+	0.808862i	$0.700084\pi$
$42$		−	4.00000i		−	0.617213i
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$	−2.12132	−	2.12132i	−0.319801	−	0.319801i
$45$	0.707107	+	0.707107i	0.105409	+	0.105409i
$46$	−4.24264	+	4.24264i	−0.625543	+	0.625543i
$47$	2.00000			0.291730			0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000			0.291730			0.145865	+	0.989305i	$0.453403\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$			9.00000i			1.28571i
$50$	4.00000			0.565685
$51$		0			0
$52$	6.00000			0.832050
$53$			13.0000i			1.78569i	0.450367	+	0.892844i	$0.351293\pi$
$53$			13.0000i			1.78569i	−0.450367	+	0.892844i	$0.648707\pi$
$54$	−0.707107	+	0.707107i	−0.0962250	+	0.0962250i
$55$	−3.00000			−0.404520
$56$	−2.82843	+	2.82843i	−0.377964	+	0.377964i
$57$	2.82843	+	2.82843i	0.374634	+	0.374634i
$58$	4.94975	+	4.94975i	0.649934	+	0.649934i
$59$		−	9.00000i		−	1.17170i	−0.810419	−	0.585850i	$-0.800761\pi$
$59$		−	9.00000i		−	1.17170i	0.810419	−	0.585850i	$-0.199239\pi$
$60$		−	1.00000i		−	0.129099i
$61$	−7.07107	−	7.07107i	−0.905357	−	0.905357i	0.0905357	−	0.995893i	$-0.471142\pi$
$61$	−7.07107	−	7.07107i	−0.905357	−	0.905357i	−0.995893	+	0.0905357i	$0.971142\pi$
$62$	−2.12132	−	2.12132i	−0.269408	−	0.269408i
$63$	2.82843	−	2.82843i	0.356348	−	0.356348i
$64$	−1.00000			−0.125000
$65$	4.24264	−	4.24264i	0.526235	−	0.526235i
$66$		−	3.00000i		−	0.369274i
$67$	−6.00000			−0.733017			−0.366508	−	0.930415i	$-0.619447\pi$
$67$	−6.00000			−0.733017			−0.366508	+	0.930415i	$0.619447\pi$
$68$		0			0
$69$	−6.00000			−0.722315
$70$			4.00000i			0.478091i
$71$	8.48528	−	8.48528i	1.00702	−	1.00702i	0.00704243	−	0.999975i	$-0.497758\pi$
$71$	8.48528	−	8.48528i	1.00702	−	1.00702i	0.999975	−	0.00704243i	$-0.00224169\pi$
$72$	1.00000			0.117851
$73$	−4.94975	+	4.94975i	−0.579324	+	0.579324i	−0.934717	−	0.355393i	$-0.884347\pi$
$73$	−4.94975	+	4.94975i	−0.579324	+	0.579324i	0.355393	+	0.934717i	$0.384347\pi$
$74$	5.65685	+	5.65685i	0.657596	+	0.657596i
$75$	2.82843	+	2.82843i	0.326599	+	0.326599i
$76$		−	4.00000i		−	0.458831i
$77$			12.0000i			1.36753i
$78$	4.24264	+	4.24264i	0.480384	+	0.480384i
$79$	3.53553	+	3.53553i	0.397779	+	0.397779i	0.877449	−	0.479670i	$-0.159244\pi$
$79$	3.53553	+	3.53553i	0.397779	+	0.397779i	−0.479670	+	0.877449i	$0.659244\pi$
$80$	−0.707107	+	0.707107i	−0.0790569	+	0.0790569i
$81$	−1.00000			−0.111111
$82$	1.41421	−	1.41421i	0.156174	−	0.156174i
$83$			12.0000i			1.31717i	0.752506	+	0.658586i	$0.228845\pi$
$83$			12.0000i			1.31717i	−0.752506	+	0.658586i	$0.771155\pi$
$84$	−4.00000			−0.436436
$85$		0			0
$86$	4.00000			0.431331
$87$			7.00000i			0.750479i
$88$	−2.12132	+	2.12132i	−0.226134	+	0.226134i
$89$	−4.00000			−0.423999			−0.212000	−	0.977270i	$-0.567998\pi$
$89$	−4.00000			−0.423999			−0.212000	+	0.977270i	$0.567998\pi$
$90$	0.707107	−	0.707107i	0.0745356	−	0.0745356i
$91$	−16.9706	−	16.9706i	−1.77900	−	1.77900i
$92$	4.24264	+	4.24264i	0.442326	+	0.442326i
$93$		−	3.00000i		−	0.311086i
$94$		−	2.00000i		−	0.206284i
$95$	−2.82843	−	2.82843i	−0.290191	−	0.290191i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	2.12132	−	2.12132i	0.215387	−	0.215387i	−0.591164	−	0.806551i	$-0.701331\pi$
$97$	2.12132	−	2.12132i	0.215387	−	0.215387i	0.806551	+	0.591164i	$0.201331\pi$
$98$	9.00000			0.909137
$99$	2.12132	−	2.12132i	0.213201	−	0.213201i
$100$		−	4.00000i		−	0.400000i
$101$	17.0000			1.69156			0.845782	−	0.533529i	$-0.179135\pi$
$101$	17.0000			1.69156			0.845782	+	0.533529i	$0.179135\pi$
$102$		0			0
$103$	13.0000			1.28093			0.640464	−	0.767988i	$-0.278742\pi$
$103$	13.0000			1.28093			0.640464	+	0.767988i	$0.278742\pi$
$104$		−	6.00000i		−	0.588348i
$105$	−2.82843	+	2.82843i	−0.276026	+	0.276026i
$106$	13.0000			1.26267
$107$	10.6066	−	10.6066i	1.02538	−	1.02538i	0.0257094	−	0.999669i	$-0.491816\pi$
$107$	10.6066	−	10.6066i	1.02538	−	1.02538i	0.999669	−	0.0257094i	$-0.00818447\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$	7.07107	+	7.07107i	0.677285	+	0.677285i	0.959385	−	0.282100i	$-0.0910309\pi$
$109$	7.07107	+	7.07107i	0.677285	+	0.677285i	−0.282100	+	0.959385i	$0.591031\pi$
$110$			3.00000i			0.286039i
$111$			8.00000i			0.759326i
$112$	2.82843	+	2.82843i	0.267261	+	0.267261i
$113$	7.07107	+	7.07107i	0.665190	+	0.665190i	0.956599	−	0.291409i	$-0.0941239\pi$
$113$	7.07107	+	7.07107i	0.665190	+	0.665190i	−0.291409	+	0.956599i	$0.594124\pi$
$114$	2.82843	−	2.82843i	0.264906	−	0.264906i
$115$	6.00000			0.559503
$116$	4.94975	−	4.94975i	0.459573	−	0.459573i
$117$			6.00000i			0.554700i
$118$	−9.00000			−0.828517
$119$		0			0
$120$	−1.00000			−0.0912871
$121$		−	2.00000i		−	0.181818i
$122$	−7.07107	+	7.07107i	−0.640184	+	0.640184i
$123$	2.00000			0.180334
$124$	−2.12132	+	2.12132i	−0.190500	+	0.190500i
$125$	−6.36396	−	6.36396i	−0.569210	−	0.569210i
$126$	−2.82843	−	2.82843i	−0.251976	−	0.251976i
$127$			16.0000i			1.41977i	0.704317	+	0.709885i	$0.251253\pi$
$127$			16.0000i			1.41977i	−0.704317	+	0.709885i	$0.748747\pi$
$128$			1.00000i			0.0883883i
$129$	2.82843	+	2.82843i	0.249029	+	0.249029i
$130$	−4.24264	−	4.24264i	−0.372104	−	0.372104i
$131$	14.1421	−	14.1421i	1.23560	−	1.23560i	0.273824	−	0.961780i	$-0.411711\pi$
$131$	14.1421	−	14.1421i	1.23560	−	1.23560i	0.961780	−	0.273824i	$-0.0882887\pi$
$132$	−3.00000			−0.261116
$133$	−11.3137	+	11.3137i	−0.981023	+	0.981023i
$134$			6.00000i			0.518321i
$135$	1.00000			0.0860663
$136$		0			0
$137$	12.0000			1.02523			0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000			1.02523			0.512615	+	0.858619i	$0.328677\pi$
$138$			6.00000i			0.510754i
$139$	−5.65685	+	5.65685i	−0.479808	+	0.479808i	−0.905070	−	0.425262i	$-0.860182\pi$
$139$	−5.65685	+	5.65685i	−0.479808	+	0.479808i	0.425262	+	0.905070i	$0.360182\pi$
$140$	4.00000			0.338062
$141$	1.41421	−	1.41421i	0.119098	−	0.119098i
$142$	−8.48528	−	8.48528i	−0.712069	−	0.712069i
$143$	−12.7279	−	12.7279i	−1.06436	−	1.06436i
$144$		−	1.00000i		−	0.0833333i
$145$		−	7.00000i		−	0.581318i
$146$	4.94975	+	4.94975i	0.409644	+	0.409644i
$147$	6.36396	+	6.36396i	0.524891	+	0.524891i
$148$	5.65685	−	5.65685i	0.464991	−	0.464991i
$149$	−15.0000			−1.22885			−0.614424	−	0.788976i	$-0.710612\pi$
$149$	−15.0000			−1.22885			−0.614424	+	0.788976i	$0.710612\pi$
$150$	2.82843	−	2.82843i	0.230940	−	0.230940i
$151$		−	9.00000i		−	0.732410i	−0.930534	−	0.366205i	$-0.880657\pi$
$151$		−	9.00000i		−	0.732410i	0.930534	−	0.366205i	$-0.119343\pi$
$152$	−4.00000			−0.324443
$153$		0			0
$154$	12.0000			0.966988
$155$			3.00000i			0.240966i
$156$	4.24264	−	4.24264i	0.339683	−	0.339683i
$157$	−12.0000			−0.957704			−0.478852	−	0.877896i	$-0.658947\pi$
$157$	−12.0000			−0.957704			−0.478852	+	0.877896i	$0.658947\pi$
$158$	3.53553	−	3.53553i	0.281272	−	0.281272i
$159$	9.19239	+	9.19239i	0.729004	+	0.729004i
$160$	0.707107	+	0.707107i	0.0559017	+	0.0559017i
$161$		−	24.0000i		−	1.89146i
$162$			1.00000i			0.0785674i
$163$	4.24264	+	4.24264i	0.332309	+	0.332309i	0.853463	−	0.521154i	$-0.174498\pi$
$163$	4.24264	+	4.24264i	0.332309	+	0.332309i	−0.521154	+	0.853463i	$0.674498\pi$
$164$	−1.41421	−	1.41421i	−0.110432	−	0.110432i
$165$	−2.12132	+	2.12132i	−0.165145	+	0.165145i
$166$	12.0000			0.931381
$167$	5.65685	−	5.65685i	0.437741	−	0.437741i	−0.453510	−	0.891251i	$-0.649829\pi$
$167$	5.65685	−	5.65685i	0.437741	−	0.437741i	0.891251	+	0.453510i	$0.149829\pi$
$168$			4.00000i			0.308607i
$169$	23.0000			1.76923
$170$		0			0
$171$	4.00000			0.305888
$172$		−	4.00000i		−	0.304997i
$173$	9.19239	−	9.19239i	0.698884	−	0.698884i	−0.265286	−	0.964170i	$-0.585466\pi$
$173$	9.19239	−	9.19239i	0.698884	−	0.698884i	0.964170	+	0.265286i	$0.0854662\pi$
$174$	7.00000			0.530669
$175$	−11.3137	+	11.3137i	−0.855236	+	0.855236i
$176$	2.12132	+	2.12132i	0.159901	+	0.159901i
$177$	−6.36396	−	6.36396i	−0.478345	−	0.478345i
$178$			4.00000i			0.299813i
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$	−0.707107	−	0.707107i	−0.0527046	−	0.0527046i
$181$	−7.07107	−	7.07107i	−0.525588	−	0.525588i	0.393665	−	0.919254i	$-0.371207\pi$
$181$	−7.07107	−	7.07107i	−0.525588	−	0.525588i	−0.919254	+	0.393665i	$0.871207\pi$
$182$	−16.9706	+	16.9706i	−1.25794	+	1.25794i
$183$	−10.0000			−0.739221
$184$	4.24264	−	4.24264i	0.312772	−	0.312772i
$185$		−	8.00000i		−	0.588172i
$186$	−3.00000			−0.219971
$187$		0			0
$188$	−2.00000			−0.145865
$189$		−	4.00000i		−	0.290957i
$190$	−2.82843	+	2.82843i	−0.205196	+	0.205196i
$191$	−14.0000			−1.01300			−0.506502	−	0.862239i	$-0.669062\pi$
$191$	−14.0000			−1.01300			−0.506502	+	0.862239i	$0.669062\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	−6.36396	−	6.36396i	−0.458088	−	0.458088i	0.439939	−	0.898027i	$-0.355000\pi$
$193$	−6.36396	−	6.36396i	−0.458088	−	0.458088i	−0.898027	+	0.439939i	$0.855000\pi$
$194$	−2.12132	−	2.12132i	−0.152302	−	0.152302i
$195$		−	6.00000i		−	0.429669i
$196$		−	9.00000i		−	0.642857i
$197$	−7.07107	−	7.07107i	−0.503793	−	0.503793i	0.408822	−	0.912614i	$-0.365940\pi$
$197$	−7.07107	−	7.07107i	−0.503793	−	0.503793i	−0.912614	+	0.408822i	$0.865940\pi$
$198$	−2.12132	−	2.12132i	−0.150756	−	0.150756i
$199$	−0.707107	+	0.707107i	−0.0501255	+	0.0501255i	−0.731725	−	0.681600i	$-0.761285\pi$
$199$	−0.707107	+	0.707107i	−0.0501255	+	0.0501255i	0.681600	+	0.731725i	$0.261285\pi$
$200$	−4.00000			−0.282843
$201$	−4.24264	+	4.24264i	−0.299253	+	0.299253i
$202$		−	17.0000i		−	1.19612i
$203$	−28.0000			−1.96521
$204$		0			0
$205$	−2.00000			−0.139686
$206$		−	13.0000i		−	0.905753i
$207$	−4.24264	+	4.24264i	−0.294884	+	0.294884i
$208$	−6.00000			−0.416025
$209$	−8.48528	+	8.48528i	−0.586939	+	0.586939i
$210$	2.82843	+	2.82843i	0.195180	+	0.195180i
$211$	5.65685	+	5.65685i	0.389434	+	0.389434i	0.874486	−	0.485052i	$-0.161199\pi$
$211$	5.65685	+	5.65685i	0.389434	+	0.389434i	−0.485052	+	0.874486i	$0.661199\pi$
$212$		−	13.0000i		−	0.892844i
$213$		−	12.0000i		−	0.822226i
$214$	−10.6066	−	10.6066i	−0.725052	−	0.725052i
$215$	−2.82843	−	2.82843i	−0.192897	−	0.192897i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	12.0000			0.814613
$218$	7.07107	−	7.07107i	0.478913	−	0.478913i
$219$			7.00000i			0.473016i
$220$	3.00000			0.202260
$221$		0			0
$222$	8.00000			0.536925
$223$			17.0000i			1.13840i	0.822198	+	0.569202i	$0.192748\pi$
$223$			17.0000i			1.13840i	−0.822198	+	0.569202i	$0.807252\pi$
$224$	2.82843	−	2.82843i	0.188982	−	0.188982i
$225$	4.00000			0.266667
$226$	7.07107	−	7.07107i	0.470360	−	0.470360i
$227$	14.1421	+	14.1421i	0.938647	+	0.938647i	0.998224	−	0.0595772i	$-0.0189752\pi$
$227$	14.1421	+	14.1421i	0.938647	+	0.938647i	−0.0595772	+	0.998224i	$0.518975\pi$
$228$	−2.82843	−	2.82843i	−0.187317	−	0.187317i
$229$			14.0000i			0.925146i	0.886581	+	0.462573i	$0.153074\pi$
$229$			14.0000i			0.925146i	−0.886581	+	0.462573i	$0.846926\pi$
$230$		−	6.00000i		−	0.395628i
$231$	8.48528	+	8.48528i	0.558291	+	0.558291i
$232$	−4.94975	−	4.94975i	−0.324967	−	0.324967i
$233$	16.9706	−	16.9706i	1.11178	−	1.11178i	0.118869	−	0.992910i	$-0.462073\pi$
$233$	16.9706	−	16.9706i	1.11178	−	1.11178i	0.992910	−	0.118869i	$-0.0379267\pi$
$234$	6.00000			0.392232
$235$	−1.41421	+	1.41421i	−0.0922531	+	0.0922531i
$236$			9.00000i			0.585850i
$237$	5.00000			0.324785
$238$		0			0
$239$	−26.0000			−1.68180			−0.840900	−	0.541190i	$-0.817974\pi$
$239$	−26.0000			−1.68180			−0.840900	+	0.541190i	$0.817974\pi$
$240$			1.00000i			0.0645497i
$241$	−10.6066	+	10.6066i	−0.683231	+	0.683231i	−0.960727	−	0.277496i	$-0.910496\pi$
$241$	−10.6066	+	10.6066i	−0.683231	+	0.683231i	0.277496	+	0.960727i	$0.410496\pi$
$242$	−2.00000			−0.128565
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	7.07107	+	7.07107i	0.452679	+	0.452679i
$245$	−6.36396	−	6.36396i	−0.406579	−	0.406579i
$246$		−	2.00000i		−	0.127515i
$247$		−	24.0000i		−	1.52708i
$248$	2.12132	+	2.12132i	0.134704	+	0.134704i
$249$	8.48528	+	8.48528i	0.537733	+	0.537733i
$250$	−6.36396	+	6.36396i	−0.402492	+	0.402492i
$251$	15.0000			0.946792			0.473396	−	0.880850i	$-0.343028\pi$
$251$	15.0000			0.946792			0.473396	+	0.880850i	$0.343028\pi$
$252$	−2.82843	+	2.82843i	−0.178174	+	0.178174i
$253$		−	18.0000i		−	1.13165i
$254$	16.0000			1.00393
$255$		0			0
$256$	1.00000			0.0625000
$257$		0			0		1.00000			$0$
$257$		0			0		−1.00000			$\pi$
$258$	2.82843	−	2.82843i	0.176090	−	0.176090i
$259$	−32.0000			−1.98838
$260$	−4.24264	+	4.24264i	−0.263117	+	0.263117i
$261$	4.94975	+	4.94975i	0.306382	+	0.306382i
$262$	−14.1421	−	14.1421i	−0.873704	−	0.873704i
$263$			18.0000i			1.10993i	0.831875	+	0.554964i	$0.187268\pi$
$263$			18.0000i			1.10993i	−0.831875	+	0.554964i	$0.812732\pi$
$264$			3.00000i			0.184637i
$265$	−9.19239	−	9.19239i	−0.564684	−	0.564684i
$266$	11.3137	+	11.3137i	0.693688	+	0.693688i
$267$	−2.82843	+	2.82843i	−0.173097	+	0.173097i
$268$	6.00000			0.366508
$269$	−6.36396	+	6.36396i	−0.388018	+	0.388018i	−0.873980	−	0.485962i	$-0.838469\pi$
$269$	−6.36396	+	6.36396i	−0.388018	+	0.388018i	0.485962	+	0.873980i	$0.338469\pi$
$270$		−	1.00000i		−	0.0608581i
$271$	5.00000			0.303728			0.151864	−	0.988401i	$-0.451472\pi$
$271$	5.00000			0.303728			0.151864	+	0.988401i	$0.451472\pi$
$272$		0			0
$273$	−24.0000			−1.45255
$274$		−	12.0000i		−	0.724947i
$275$	−8.48528	+	8.48528i	−0.511682	+	0.511682i
$276$	6.00000			0.361158
$277$	15.5563	−	15.5563i	0.934690	−	0.934690i	−0.0633039	−	0.997994i	$-0.520164\pi$
$277$	15.5563	−	15.5563i	0.934690	−	0.934690i	0.997994	+	0.0633039i	$0.0201637\pi$
$278$	5.65685	+	5.65685i	0.339276	+	0.339276i
$279$	−2.12132	−	2.12132i	−0.127000	−	0.127000i
$280$		−	4.00000i		−	0.239046i
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	−1.41421	−	1.41421i	−0.0842152	−	0.0842152i
$283$	2.82843	+	2.82843i	0.168133	+	0.168133i	0.786158	−	0.618026i	$-0.212067\pi$
$283$	2.82843	+	2.82843i	0.168133	+	0.168133i	−0.618026	+	0.786158i	$0.712067\pi$
$284$	−8.48528	+	8.48528i	−0.503509	+	0.503509i
$285$	−4.00000			−0.236940
$286$	−12.7279	+	12.7279i	−0.752618	+	0.752618i
$287$			8.00000i			0.472225i
$288$	−1.00000			−0.0589256
$289$		0			0
$290$	−7.00000			−0.411054
$291$		−	3.00000i		−	0.175863i
$292$	4.94975	−	4.94975i	0.289662	−	0.289662i
$293$	19.0000			1.10999			0.554996	−	0.831853i	$-0.312720\pi$
$293$	19.0000			1.10999			0.554996	+	0.831853i	$0.312720\pi$
$294$	6.36396	−	6.36396i	0.371154	−	0.371154i
$295$	6.36396	+	6.36396i	0.370524	+	0.370524i
$296$	−5.65685	−	5.65685i	−0.328798	−	0.328798i
$297$		−	3.00000i		−	0.174078i
$298$			15.0000i			0.868927i
$299$	25.4558	+	25.4558i	1.47215	+	1.47215i
$300$	−2.82843	−	2.82843i	−0.163299	−	0.163299i
$301$	−11.3137	+	11.3137i	−0.652111	+	0.652111i
$302$	−9.00000			−0.517892
$303$	12.0208	−	12.0208i	0.690578	−	0.690578i
$304$			4.00000i			0.229416i
$305$	10.0000			0.572598
$306$		0			0
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$		−	12.0000i		−	0.683763i
$309$	9.19239	−	9.19239i	0.522937	−	0.522937i
$310$	3.00000			0.170389
$311$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$311$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$312$	−4.24264	−	4.24264i	−0.240192	−	0.240192i
$313$	−9.89949	−	9.89949i	−0.559553	−	0.559553i	0.369627	−	0.929180i	$-0.379485\pi$
$313$	−9.89949	−	9.89949i	−0.559553	−	0.559553i	−0.929180	+	0.369627i	$0.879485\pi$
$314$			12.0000i			0.677199i
$315$			4.00000i			0.225374i
$316$	−3.53553	−	3.53553i	−0.198889	−	0.198889i
$317$	−1.41421	−	1.41421i	−0.0794301	−	0.0794301i	0.666276	−	0.745706i	$-0.267887\pi$
$317$	−1.41421	−	1.41421i	−0.0794301	−	0.0794301i	−0.745706	+	0.666276i	$0.767887\pi$
$318$	9.19239	−	9.19239i	0.515484	−	0.515484i
$319$	−21.0000			−1.17577
$320$	0.707107	−	0.707107i	0.0395285	−	0.0395285i
$321$		−	15.0000i		−	0.837218i
$322$	−24.0000			−1.33747
$323$		0			0
$324$	1.00000			0.0555556
$325$		−	24.0000i		−	1.33128i
$326$	4.24264	−	4.24264i	0.234978	−	0.234978i
$327$	10.0000			0.553001
$328$	−1.41421	+	1.41421i	−0.0780869	+	0.0780869i
$329$	5.65685	+	5.65685i	0.311872	+	0.311872i
$330$	2.12132	+	2.12132i	0.116775	+	0.116775i
$331$			22.0000i			1.20923i	0.796518	+	0.604615i	$0.206673\pi$
$331$			22.0000i			1.20923i	−0.796518	+	0.604615i	$0.793327\pi$
$332$		−	12.0000i		−	0.658586i
$333$	5.65685	+	5.65685i	0.309994	+	0.309994i
$334$	−5.65685	−	5.65685i	−0.309529	−	0.309529i
$335$	4.24264	−	4.24264i	0.231800	−	0.231800i
$336$	4.00000			0.218218
$337$	−21.2132	+	21.2132i	−1.15556	+	1.15556i	−0.170136	+	0.985421i	$0.554421\pi$
$337$	−21.2132	+	21.2132i	−1.15556	+	1.15556i	−0.985421	+	0.170136i	$0.945579\pi$
$338$		−	23.0000i		−	1.25104i
$339$	10.0000			0.543125
$340$		0			0
$341$	9.00000			0.487377
$342$		−	4.00000i		−	0.216295i
$343$	−5.65685	+	5.65685i	−0.305441	+	0.305441i
$344$	−4.00000			−0.215666
$345$	4.24264	−	4.24264i	0.228416	−	0.228416i
$346$	−9.19239	−	9.19239i	−0.494186	−	0.494186i
$347$	12.0208	+	12.0208i	0.645311	+	0.645311i	0.951856	−	0.306545i	$-0.0991730\pi$
$347$	12.0208	+	12.0208i	0.645311	+	0.645311i	−0.306545	+	0.951856i	$0.599173\pi$
$348$		−	7.00000i		−	0.375239i
$349$		−	12.0000i		−	0.642345i	−0.947021	−	0.321173i	$-0.895923\pi$
$349$		−	12.0000i		−	0.642345i	0.947021	−	0.321173i	$-0.104077\pi$
$350$	11.3137	+	11.3137i	0.604743	+	0.604743i
$351$	4.24264	+	4.24264i	0.226455	+	0.226455i
$352$	2.12132	−	2.12132i	0.113067	−	0.113067i
$353$	4.00000			0.212899			0.106449	−	0.994318i	$-0.466052\pi$
$353$	4.00000			0.212899			0.106449	+	0.994318i	$0.466052\pi$
$354$	−6.36396	+	6.36396i	−0.338241	+	0.338241i
$355$			12.0000i			0.636894i
$356$	4.00000			0.212000
$357$		0			0
$358$		0			0
$359$		−	30.0000i		−	1.58334i	−0.610949	−	0.791670i	$-0.709212\pi$
$359$		−	30.0000i		−	1.58334i	0.610949	−	0.791670i	$-0.290788\pi$
$360$	−0.707107	+	0.707107i	−0.0372678	+	0.0372678i
$361$	3.00000			0.157895
$362$	−7.07107	+	7.07107i	−0.371647	+	0.371647i
$363$	−1.41421	−	1.41421i	−0.0742270	−	0.0742270i
$364$	16.9706	+	16.9706i	0.889499	+	0.889499i
$365$		−	7.00000i		−	0.366397i
$366$			10.0000i			0.522708i
$367$	−12.0208	−	12.0208i	−0.627481	−	0.627481i	0.319952	−	0.947434i	$-0.396333\pi$
$367$	−12.0208	−	12.0208i	−0.627481	−	0.627481i	−0.947434	+	0.319952i	$0.896333\pi$
$368$	−4.24264	−	4.24264i	−0.221163	−	0.221163i
$369$	1.41421	−	1.41421i	0.0736210	−	0.0736210i
$370$	−8.00000			−0.415900
$371$	−36.7696	+	36.7696i	−1.90898	+	1.90898i
$372$			3.00000i			0.155543i
$373$	−32.0000			−1.65690			−0.828449	−	0.560065i	$-0.810776\pi$
$373$	−32.0000			−1.65690			−0.828449	+	0.560065i	$0.810776\pi$
$374$		0			0
$375$	−9.00000			−0.464758
$376$			2.00000i			0.103142i
$377$	29.6985	−	29.6985i	1.52955	−	1.52955i
$378$	−4.00000			−0.205738
$379$	−7.07107	+	7.07107i	−0.363216	+	0.363216i	−0.864996	−	0.501779i	$-0.832679\pi$
$379$	−7.07107	+	7.07107i	−0.363216	+	0.363216i	0.501779	+	0.864996i	$0.332679\pi$
$380$	2.82843	+	2.82843i	0.145095	+	0.145095i
$381$	11.3137	+	11.3137i	0.579619	+	0.579619i
$382$			14.0000i			0.716302i
$383$			2.00000i			0.102195i	0.998694	+	0.0510976i	$0.0162720\pi$
$383$			2.00000i			0.102195i	−0.998694	+	0.0510976i	$0.983728\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	−8.48528	−	8.48528i	−0.432450	−	0.432450i
$386$	−6.36396	+	6.36396i	−0.323917	+	0.323917i
$387$	4.00000			0.203331
$388$	−2.12132	+	2.12132i	−0.107694	+	0.107694i
$389$		−	5.00000i		−	0.253510i	−0.991934	−	0.126755i	$-0.959544\pi$
$389$		−	5.00000i		−	0.253510i	0.991934	−	0.126755i	$-0.0404562\pi$
$390$	−6.00000			−0.303822
$391$		0			0
$392$	−9.00000			−0.454569
$393$		−	20.0000i		−	1.00887i
$394$	−7.07107	+	7.07107i	−0.356235	+	0.356235i
$395$	−5.00000			−0.251577
$396$	−2.12132	+	2.12132i	−0.106600	+	0.106600i
$397$	15.5563	+	15.5563i	0.780751	+	0.780751i	0.979957	−	0.199207i	$-0.0638365\pi$
$397$	15.5563	+	15.5563i	0.780751	+	0.780751i	−0.199207	+	0.979957i	$0.563837\pi$
$398$	0.707107	+	0.707107i	0.0354441	+	0.0354441i
$399$			16.0000i			0.801002i
$400$			4.00000i			0.200000i
$401$	−8.48528	−	8.48528i	−0.423735	−	0.423735i	0.462753	−	0.886487i	$-0.346862\pi$
$401$	−8.48528	−	8.48528i	−0.423735	−	0.423735i	−0.886487	+	0.462753i	$0.846862\pi$
$402$	4.24264	+	4.24264i	0.211604	+	0.211604i
$403$	−12.7279	+	12.7279i	−0.634023	+	0.634023i
$404$	−17.0000			−0.845782
$405$	0.707107	−	0.707107i	0.0351364	−	0.0351364i
$406$			28.0000i			1.38962i
$407$	−24.0000			−1.18964
$408$		0			0
$409$	19.0000			0.939490			0.469745	−	0.882802i	$-0.344346\pi$
$409$	19.0000			0.939490			0.469745	+	0.882802i	$0.344346\pi$
$410$			2.00000i			0.0987730i
$411$	8.48528	−	8.48528i	0.418548	−	0.418548i
$412$	−13.0000			−0.640464
$413$	25.4558	−	25.4558i	1.25260	−	1.25260i
$414$	4.24264	+	4.24264i	0.208514	+	0.208514i
$415$	−8.48528	−	8.48528i	−0.416526	−	0.416526i
$416$			6.00000i			0.294174i
$417$			8.00000i			0.391762i
$418$	8.48528	+	8.48528i	0.415029	+	0.415029i
$419$	2.12132	+	2.12132i	0.103633	+	0.103633i	0.757022	−	0.653389i	$-0.226653\pi$
$419$	2.12132	+	2.12132i	0.103633	+	0.103633i	−0.653389	+	0.757022i	$0.726653\pi$
$420$	2.82843	−	2.82843i	0.138013	−	0.138013i
$421$	−22.0000			−1.07221			−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000			−1.07221			−0.536107	+	0.844150i	$0.680106\pi$
$422$	5.65685	−	5.65685i	0.275371	−	0.275371i
$423$		−	2.00000i		−	0.0972433i
$424$	−13.0000			−0.631336
$425$		0			0
$426$	−12.0000			−0.581402
$427$		−	40.0000i		−	1.93574i
$428$	−10.6066	+	10.6066i	−0.512689	+	0.512689i
$429$	−18.0000			−0.869048
$430$	−2.82843	+	2.82843i	−0.136399	+	0.136399i
$431$	7.07107	+	7.07107i	0.340601	+	0.340601i	0.856593	−	0.515992i	$-0.172577\pi$
$431$	7.07107	+	7.07107i	0.340601	+	0.340601i	−0.515992	+	0.856593i	$0.672577\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$			3.00000i			0.144171i	0.997398	+	0.0720854i	$0.0229654\pi$
$433$			3.00000i			0.144171i	−0.997398	+	0.0720854i	$0.977035\pi$
$434$		−	12.0000i		−	0.576018i
$435$	−4.94975	−	4.94975i	−0.237322	−	0.237322i
$436$	−7.07107	−	7.07107i	−0.338643	−	0.338643i
$437$	16.9706	−	16.9706i	0.811812	−	0.811812i
$438$	7.00000			0.334473
$439$	19.7990	−	19.7990i	0.944954	−	0.944954i	−0.0536078	−	0.998562i	$-0.517072\pi$
$439$	19.7990	−	19.7990i	0.944954	−	0.944954i	0.998562	+	0.0536078i	$0.0170721\pi$
$440$		−	3.00000i		−	0.143019i
$441$	9.00000			0.428571
$442$		0			0
$443$	−12.0000			−0.570137			−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000			−0.570137			−0.285069	+	0.958507i	$0.592016\pi$
$444$		−	8.00000i		−	0.379663i
$445$	2.82843	−	2.82843i	0.134080	−	0.134080i
$446$	17.0000			0.804973
$447$	−10.6066	+	10.6066i	−0.501675	+	0.501675i
$448$	−2.82843	−	2.82843i	−0.133631	−	0.133631i
$449$	2.82843	+	2.82843i	0.133482	+	0.133482i	0.770691	−	0.637209i	$-0.219911\pi$
$449$	2.82843	+	2.82843i	0.133482	+	0.133482i	−0.637209	+	0.770691i	$0.719911\pi$
$450$		−	4.00000i		−	0.188562i
$451$			6.00000i			0.282529i
$452$	−7.07107	−	7.07107i	−0.332595	−	0.332595i
$453$	−6.36396	−	6.36396i	−0.299005	−	0.299005i
$454$	14.1421	−	14.1421i	0.663723	−	0.663723i
$455$	24.0000			1.12514
$456$	−2.82843	+	2.82843i	−0.132453	+	0.132453i
$457$		−	17.0000i		−	0.795226i	−0.917553	−	0.397613i	$-0.869839\pi$
$457$		−	17.0000i		−	0.795226i	0.917553	−	0.397613i	$-0.130161\pi$
$458$	14.0000			0.654177
$459$		0			0
$460$	−6.00000			−0.279751
$461$			35.0000i			1.63011i	0.579382	+	0.815056i	$0.303294\pi$
$461$			35.0000i			1.63011i	−0.579382	+	0.815056i	$0.696706\pi$
$462$	8.48528	−	8.48528i	0.394771	−	0.394771i
$463$	−5.00000			−0.232370			−0.116185	−	0.993228i	$-0.537067\pi$
$463$	−5.00000			−0.232370			−0.116185	+	0.993228i	$0.537067\pi$
$464$	−4.94975	+	4.94975i	−0.229786	+	0.229786i
$465$	2.12132	+	2.12132i	0.0983739	+	0.0983739i
$466$	−16.9706	−	16.9706i	−0.786146	−	0.786146i
$467$			3.00000i			0.138823i	0.997588	+	0.0694117i	$0.0221122\pi$
$467$			3.00000i			0.138823i	−0.997588	+	0.0694117i	$0.977888\pi$
$468$		−	6.00000i		−	0.277350i
$469$	−16.9706	−	16.9706i	−0.783628	−	0.783628i
$470$	1.41421	+	1.41421i	0.0652328	+	0.0652328i
$471$	−8.48528	+	8.48528i	−0.390981	+	0.390981i
$472$	9.00000			0.414259
$473$	−8.48528	+	8.48528i	−0.390154	+	0.390154i
$474$		−	5.00000i		−	0.229658i
$475$	−16.0000			−0.734130
$476$		0			0
$477$	13.0000			0.595229
$478$			26.0000i			1.18921i
$479$	9.89949	−	9.89949i	0.452319	−	0.452319i	−0.443804	−	0.896124i	$-0.646371\pi$
$479$	9.89949	−	9.89949i	0.452319	−	0.452319i	0.896124	+	0.443804i	$0.146371\pi$
$480$	1.00000			0.0456435
$481$	33.9411	−	33.9411i	1.54758	−	1.54758i
$482$	10.6066	+	10.6066i	0.483117	+	0.483117i
$483$	−16.9706	−	16.9706i	−0.772187	−	0.772187i
$484$			2.00000i			0.0909091i
$485$			3.00000i			0.136223i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	−17.6777	−	17.6777i	−0.801052	−	0.801052i	0.182208	−	0.983260i	$-0.441675\pi$
$487$	−17.6777	−	17.6777i	−0.801052	−	0.801052i	−0.983260	+	0.182208i	$0.941675\pi$
$488$	7.07107	−	7.07107i	0.320092	−	0.320092i
$489$	6.00000			0.271329
$490$	−6.36396	+	6.36396i	−0.287494	+	0.287494i
$491$		−	23.0000i		−	1.03798i	−0.854782	−	0.518988i	$-0.826309\pi$
$491$		−	23.0000i		−	1.03798i	0.854782	−	0.518988i	$-0.173691\pi$
$492$	−2.00000			−0.0901670
$493$		0			0
$494$	−24.0000			−1.07981
$495$			3.00000i			0.134840i
$496$	2.12132	−	2.12132i	0.0952501	−	0.0952501i
$497$	48.0000			2.15309
$498$	8.48528	−	8.48528i	0.380235	−	0.380235i
$499$	−5.65685	−	5.65685i	−0.253236	−	0.253236i	0.569060	−	0.822296i	$-0.307307\pi$
$499$	−5.65685	−	5.65685i	−0.253236	−	0.253236i	−0.822296	+	0.569060i	$0.807307\pi$
$500$	6.36396	+	6.36396i	0.284605	+	0.284605i
$501$		−	8.00000i		−	0.357414i
$502$		−	15.0000i		−	0.669483i
$503$	−1.41421	−	1.41421i	−0.0630567	−	0.0630567i	0.674875	−	0.737932i	$-0.264197\pi$
$503$	−1.41421	−	1.41421i	−0.0630567	−	0.0630567i	−0.737932	+	0.674875i	$0.764197\pi$
$504$	2.82843	+	2.82843i	0.125988	+	0.125988i
$505$	−12.0208	+	12.0208i	−0.534919	+	0.534919i
$506$	−18.0000			−0.800198
$507$	16.2635	−	16.2635i	0.722285	−	0.722285i
$508$		−	16.0000i		−	0.709885i
$509$	−31.0000			−1.37405			−0.687025	−	0.726633i	$-0.741084\pi$
$509$	−31.0000			−1.37405			−0.687025	+	0.726633i	$0.741084\pi$
$510$		0			0
$511$	−28.0000			−1.23865
$512$		−	1.00000i		−	0.0441942i
$513$	2.82843	−	2.82843i	0.124878	−	0.124878i
$514$		0			0
$515$	−9.19239	+	9.19239i	−0.405065	+	0.405065i
$516$	−2.82843	−	2.82843i	−0.124515	−	0.124515i
$517$	4.24264	+	4.24264i	0.186591	+	0.186591i
$518$			32.0000i			1.40600i
$519$		−	13.0000i		−	0.570637i
$520$	4.24264	+	4.24264i	0.186052	+	0.186052i
$521$	−14.1421	−	14.1421i	−0.619578	−	0.619578i	0.325845	−	0.945423i	$-0.394351\pi$
$521$	−14.1421	−	14.1421i	−0.619578	−	0.619578i	−0.945423	+	0.325845i	$0.894351\pi$
$522$	4.94975	−	4.94975i	0.216645	−	0.216645i
$523$	26.0000			1.13690			0.568450	−	0.822718i	$-0.307543\pi$
$523$	26.0000			1.13690			0.568450	+	0.822718i	$0.307543\pi$
$524$	−14.1421	+	14.1421i	−0.617802	+	0.617802i
$525$			16.0000i			0.698297i
$526$	18.0000			0.784837
$527$		0			0
$528$	3.00000			0.130558
$529$			13.0000i			0.565217i
$530$	−9.19239	+	9.19239i	−0.399292	+	0.399292i
$531$	−9.00000			−0.390567
$532$	11.3137	−	11.3137i	0.490511	−	0.490511i
$533$	−8.48528	−	8.48528i	−0.367538	−	0.367538i
$534$	2.82843	+	2.82843i	0.122398	+	0.122398i
$535$			15.0000i			0.648507i
$536$		−	6.00000i		−	0.259161i
$537$		0			0
$538$	6.36396	+	6.36396i	0.274370	+	0.274370i
$539$	−19.0919	+	19.0919i	−0.822346	+	0.822346i
$540$	−1.00000			−0.0430331
$541$	−12.7279	+	12.7279i	−0.547216	+	0.547216i	−0.925635	−	0.378419i	$-0.876468\pi$
$541$	−12.7279	+	12.7279i	−0.547216	+	0.547216i	0.378419	+	0.925635i	$0.376468\pi$
$542$		−	5.00000i		−	0.214768i
$543$	−10.0000			−0.429141
$544$		0			0
$545$	−10.0000			−0.428353
$546$			24.0000i			1.02711i
$547$	18.3848	−	18.3848i	0.786076	−	0.786076i	−0.194772	−	0.980848i	$-0.562397\pi$
$547$	18.3848	−	18.3848i	0.786076	−	0.786076i	0.980848	+	0.194772i	$0.0623968\pi$
$548$	−12.0000			−0.512615
$549$	−7.07107	+	7.07107i	−0.301786	+	0.301786i
$550$	8.48528	+	8.48528i	0.361814	+	0.361814i
$551$	−19.7990	−	19.7990i	−0.843465	−	0.843465i
$552$		−	6.00000i		−	0.255377i
$553$			20.0000i			0.850487i
$554$	−15.5563	−	15.5563i	−0.660926	−	0.660926i
$555$	−5.65685	−	5.65685i	−0.240120	−	0.240120i
$556$	5.65685	−	5.65685i	0.239904	−	0.239904i
$557$	−14.0000			−0.593199			−0.296600	−	0.955002i	$-0.595853\pi$
$557$	−14.0000			−0.593199			−0.296600	+	0.955002i	$0.595853\pi$
$558$	−2.12132	+	2.12132i	−0.0898027	+	0.0898027i
$559$		−	24.0000i		−	1.01509i
$560$	−4.00000			−0.169031
$561$		0			0
$562$		0			0
$563$			23.0000i			0.969334i	0.874699	+	0.484667i	$0.161059\pi$
$563$			23.0000i			0.969334i	−0.874699	+	0.484667i	$0.838941\pi$
$564$	−1.41421	+	1.41421i	−0.0595491	+	0.0595491i
$565$	−10.0000			−0.420703
$566$	2.82843	−	2.82843i	0.118888	−	0.118888i
$567$	−2.82843	−	2.82843i	−0.118783	−	0.118783i
$568$	8.48528	+	8.48528i	0.356034	+	0.356034i
$569$		−	18.0000i		−	0.754599i	−0.926091	−	0.377300i	$-0.876853\pi$
$569$		−	18.0000i		−	0.754599i	0.926091	−	0.377300i	$-0.123147\pi$
$570$			4.00000i			0.167542i
$571$	14.1421	+	14.1421i	0.591830	+	0.591830i	0.938125	−	0.346296i	$-0.112561\pi$
$571$	14.1421	+	14.1421i	0.591830	+	0.591830i	−0.346296	+	0.938125i	$0.612561\pi$
$572$	12.7279	+	12.7279i	0.532181	+	0.532181i
$573$	−9.89949	+	9.89949i	−0.413557	+	0.413557i
$574$	8.00000			0.333914
$575$	16.9706	−	16.9706i	0.707721	−	0.707721i
$576$			1.00000i			0.0416667i
$577$	30.0000			1.24892			0.624458	−	0.781058i	$-0.285320\pi$
$577$	30.0000			1.24892			0.624458	+	0.781058i	$0.285320\pi$
$578$		0			0
$579$	−9.00000			−0.374027
$580$			7.00000i			0.290659i
$581$	−33.9411	+	33.9411i	−1.40812	+	1.40812i
$582$	−3.00000			−0.124354
$583$	−27.5772	+	27.5772i	−1.14213	+	1.14213i
$584$	−4.94975	−	4.94975i	−0.204822	−	0.204822i
$585$	−4.24264	−	4.24264i	−0.175412	−	0.175412i
$586$		−	19.0000i		−	0.784883i
$587$			3.00000i			0.123823i	0.998082	+	0.0619116i	$0.0197197\pi$
$587$			3.00000i			0.123823i	−0.998082	+	0.0619116i	$0.980280\pi$
$588$	−6.36396	−	6.36396i	−0.262445	−	0.262445i
$589$	8.48528	+	8.48528i	0.349630	+	0.349630i
$590$	6.36396	−	6.36396i	0.262000	−	0.262000i
$591$	−10.0000			−0.411345
$592$	−5.65685	+	5.65685i	−0.232495	+	0.232495i
$593$			6.00000i			0.246390i	0.992382	+	0.123195i	$0.0393141\pi$
$593$			6.00000i			0.246390i	−0.992382	+	0.123195i	$0.960686\pi$
$594$	−3.00000			−0.123091
$595$		0			0
$596$	15.0000			0.614424
$597$			1.00000i			0.0409273i
$598$	25.4558	−	25.4558i	1.04097	−	1.04097i
$599$	4.00000			0.163436			0.0817178	−	0.996656i	$-0.473959\pi$
$599$	4.00000			0.163436			0.0817178	+	0.996656i	$0.473959\pi$
$600$	−2.82843	+	2.82843i	−0.115470	+	0.115470i
$601$	3.53553	+	3.53553i	0.144217	+	0.144217i	0.775529	−	0.631312i	$-0.217483\pi$
$601$	3.53553	+	3.53553i	0.144217	+	0.144217i	−0.631312	+	0.775529i	$0.717483\pi$
$602$	11.3137	+	11.3137i	0.461112	+	0.461112i
$603$			6.00000i			0.244339i
$604$			9.00000i			0.366205i
$605$	1.41421	+	1.41421i	0.0574960	+	0.0574960i
$606$	−12.0208	−	12.0208i	−0.488312	−	0.488312i
$607$	9.19239	−	9.19239i	0.373108	−	0.373108i	−0.495500	−	0.868608i	$-0.665015\pi$
$607$	9.19239	−	9.19239i	0.373108	−	0.373108i	0.868608	+	0.495500i	$0.165015\pi$
$608$	4.00000			0.162221
$609$	−19.7990	+	19.7990i	−0.802296	+	0.802296i
$610$		−	10.0000i		−	0.404888i
$611$	−12.0000			−0.485468
$612$		0			0
$613$	24.0000			0.969351			0.484675	−	0.874694i	$-0.338938\pi$
$613$	24.0000			0.969351			0.484675	+	0.874694i	$0.338938\pi$
$614$			12.0000i			0.484281i
$615$	−1.41421	+	1.41421i	−0.0570266	+	0.0570266i
$616$	−12.0000			−0.483494
$617$	−8.48528	+	8.48528i	−0.341605	+	0.341605i	−0.856970	−	0.515366i	$-0.827656\pi$
$617$	−8.48528	+	8.48528i	−0.341605	+	0.341605i	0.515366	+	0.856970i	$0.327656\pi$
$618$	−9.19239	−	9.19239i	−0.369772	−	0.369772i
$619$	7.07107	+	7.07107i	0.284210	+	0.284210i	0.834786	−	0.550575i	$-0.185592\pi$
$619$	7.07107	+	7.07107i	0.284210	+	0.284210i	−0.550575	+	0.834786i	$0.685592\pi$
$620$		−	3.00000i		−	0.120483i
$621$			6.00000i			0.240772i
$622$		0			0
$623$	−11.3137	−	11.3137i	−0.453274	−	0.453274i
$624$	−4.24264	+	4.24264i	−0.169842	+	0.169842i
$625$	−11.0000			−0.440000
$626$	−9.89949	+	9.89949i	−0.395663	+	0.395663i
$627$			12.0000i			0.479234i
$628$	12.0000			0.478852
$629$		0			0
$630$	4.00000			0.159364
$631$		−	25.0000i		−	0.995234i	−0.867397	−	0.497617i	$-0.834208\pi$
$631$		−	25.0000i		−	0.995234i	0.867397	−	0.497617i	$-0.165792\pi$
$632$	−3.53553	+	3.53553i	−0.140636	+	0.140636i
$633$	8.00000			0.317971
$634$	−1.41421	+	1.41421i	−0.0561656	+	0.0561656i
$635$	−11.3137	−	11.3137i	−0.448971	−	0.448971i
$636$	−9.19239	−	9.19239i	−0.364502	−	0.364502i
$637$		−	54.0000i		−	2.13956i
$638$			21.0000i			0.831398i
$639$	−8.48528	−	8.48528i	−0.335673	−	0.335673i
$640$	−0.707107	−	0.707107i	−0.0279508	−	0.0279508i
$641$	11.3137	−	11.3137i	0.446865	−	0.446865i	−0.447446	−	0.894311i	$-0.647666\pi$
$641$	11.3137	−	11.3137i	0.446865	−	0.446865i	0.894311	+	0.447446i	$0.147666\pi$
$642$	−15.0000			−0.592003
$643$	26.8701	−	26.8701i	1.05965	−	1.05965i	0.0615475	−	0.998104i	$-0.480396\pi$
$643$	26.8701	−	26.8701i	1.05965	−	1.05965i	0.998104	−	0.0615475i	$-0.0196036\pi$
$644$			24.0000i			0.945732i
$645$	−4.00000			−0.157500
$646$		0			0
$647$	4.00000			0.157256			0.0786281	−	0.996904i	$-0.474946\pi$
$647$	4.00000			0.157256			0.0786281	+	0.996904i	$0.474946\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	19.0919	−	19.0919i	0.749422	−	0.749422i
$650$	−24.0000			−0.941357
$651$	8.48528	−	8.48528i	0.332564	−	0.332564i
$652$	−4.24264	−	4.24264i	−0.166155	−	0.166155i
$653$	−15.5563	−	15.5563i	−0.608767	−	0.608767i	0.333857	−	0.942624i	$-0.391650\pi$
$653$	−15.5563	−	15.5563i	−0.608767	−	0.608767i	−0.942624	+	0.333857i	$0.891650\pi$
$654$		−	10.0000i		−	0.391031i
$655$			20.0000i			0.781465i
$656$	1.41421	+	1.41421i	0.0552158	+	0.0552158i
$657$	4.94975	+	4.94975i	0.193108	+	0.193108i
$658$	5.65685	−	5.65685i	0.220527	−	0.220527i
$659$	3.00000			0.116863			0.0584317	−	0.998291i	$-0.481390\pi$
$659$	3.00000			0.116863			0.0584317	+	0.998291i	$0.481390\pi$
$660$	2.12132	−	2.12132i	0.0825723	−	0.0825723i
$661$			22.0000i			0.855701i	0.903850	+	0.427850i	$0.140729\pi$
$661$			22.0000i			0.855701i	−0.903850	+	0.427850i	$0.859271\pi$
$662$	22.0000			0.855054
$663$		0			0
$664$	−12.0000			−0.465690
$665$		−	16.0000i		−	0.620453i
$666$	5.65685	−	5.65685i	0.219199	−	0.219199i
$667$	42.0000			1.62625
$668$	−5.65685	+	5.65685i	−0.218870	+	0.218870i
$669$	12.0208	+	12.0208i	0.464752	+	0.464752i
$670$	−4.24264	−	4.24264i	−0.163908	−	0.163908i
$671$		−	30.0000i		−	1.15814i
$672$		−	4.00000i		−	0.154303i
$673$	24.0416	+	24.0416i	0.926737	+	0.926737i	0.997494	−	0.0707568i	$-0.0225414\pi$
$673$	24.0416	+	24.0416i	0.926737	+	0.926737i	−0.0707568	+	0.997494i	$0.522541\pi$
$674$	21.2132	+	21.2132i	0.817102	+	0.817102i
$675$	2.82843	−	2.82843i	0.108866	−	0.108866i
$676$	−23.0000			−0.884615
$677$	15.5563	−	15.5563i	0.597879	−	0.597879i	−0.341869	−	0.939748i	$-0.611060\pi$
$677$	15.5563	−	15.5563i	0.597879	−	0.597879i	0.939748	+	0.341869i	$0.111060\pi$
$678$		−	10.0000i		−	0.384048i
$679$	12.0000			0.460518
$680$		0			0
$681$	20.0000			0.766402
$682$		−	9.00000i		−	0.344628i
$683$	−19.0919	+	19.0919i	−0.730531	+	0.730531i	−0.970725	−	0.240194i	$-0.922789\pi$
$683$	−19.0919	+	19.0919i	−0.730531	+	0.730531i	0.240194	+	0.970725i	$0.422789\pi$
$684$	−4.00000			−0.152944
$685$	−8.48528	+	8.48528i	−0.324206	+	0.324206i
$686$	5.65685	+	5.65685i	0.215980	+	0.215980i
$687$	9.89949	+	9.89949i	0.377689	+	0.377689i
$688$			4.00000i			0.152499i
$689$		−	78.0000i		−	2.97156i
$690$	−4.24264	−	4.24264i	−0.161515	−	0.161515i
$691$	5.65685	+	5.65685i	0.215197	+	0.215197i	0.806471	−	0.591274i	$-0.201375\pi$
$691$	5.65685	+	5.65685i	0.215197	+	0.215197i	−0.591274	+	0.806471i	$0.701375\pi$
$692$	−9.19239	+	9.19239i	−0.349442	+	0.349442i
$693$	12.0000			0.455842
$694$	12.0208	−	12.0208i	0.456304	−	0.456304i
$695$		−	8.00000i		−	0.303457i
$696$	−7.00000			−0.265334
$697$		0			0
$698$	−12.0000			−0.454207
$699$		−	24.0000i		−	0.907763i
$700$	11.3137	−	11.3137i	0.427618	−	0.427618i
$701$	15.0000			0.566542			0.283271	−	0.959040i	$-0.408580\pi$
$701$	15.0000			0.566542			0.283271	+	0.959040i	$0.408580\pi$
$702$	4.24264	−	4.24264i	0.160128	−	0.160128i
$703$	−22.6274	−	22.6274i	−0.853409	−	0.853409i
$704$	−2.12132	−	2.12132i	−0.0799503	−	0.0799503i
$705$			2.00000i			0.0753244i
$706$		−	4.00000i		−	0.150542i
$707$	48.0833	+	48.0833i	1.80836	+	1.80836i
$708$	6.36396	+	6.36396i	0.239172	+	0.239172i
$709$	5.65685	−	5.65685i	0.212448	−	0.212448i	−0.592859	−	0.805306i	$-0.702001\pi$
$709$	5.65685	−	5.65685i	0.212448	−	0.212448i	0.805306	+	0.592859i	$0.202001\pi$
$710$	12.0000			0.450352
$711$	3.53553	−	3.53553i	0.132593	−	0.132593i
$712$		−	4.00000i		−	0.149906i
$713$	−18.0000			−0.674105
$714$		0			0
$715$	18.0000			0.673162
$716$		0			0
$717$	−18.3848	+	18.3848i	−0.686592	+	0.686592i
$718$	−30.0000			−1.11959
$719$	8.48528	−	8.48528i	0.316448	−	0.316448i	−0.530953	−	0.847401i	$-0.678166\pi$
$719$	8.48528	−	8.48528i	0.316448	−	0.316448i	0.847401	+	0.530953i	$0.178166\pi$
$720$	0.707107	+	0.707107i	0.0263523	+	0.0263523i
$721$	36.7696	+	36.7696i	1.36937	+	1.36937i
$722$		−	3.00000i		−	0.111648i
$723$			15.0000i			0.557856i
$724$	7.07107	+	7.07107i	0.262794	+	0.262794i
$725$	−19.7990	−	19.7990i	−0.735316	−	0.735316i
$726$	−1.41421	+	1.41421i	−0.0524864	+	0.0524864i
$727$	41.0000			1.52061			0.760303	−	0.649569i	$-0.225051\pi$
$727$	41.0000			1.52061			0.760303	+	0.649569i	$0.225051\pi$
$728$	16.9706	−	16.9706i	0.628971	−	0.628971i
$729$			1.00000i			0.0370370i
$730$	−7.00000			−0.259082
$731$		0			0
$732$	10.0000			0.369611
$733$		−	12.0000i		−	0.443230i	−0.975134	−	0.221615i	$-0.928867\pi$
$733$		−	12.0000i		−	0.443230i	0.975134	−	0.221615i	$-0.0711328\pi$
$734$	−12.0208	+	12.0208i	−0.443696	+	0.443696i
$735$	−9.00000			−0.331970
$736$	−4.24264	+	4.24264i	−0.156386	+	0.156386i
$737$	−12.7279	−	12.7279i	−0.468839	−	0.468839i
$738$	−1.41421	−	1.41421i	−0.0520579	−	0.0520579i
$739$		−	6.00000i		−	0.220714i	−0.993892	−	0.110357i	$-0.964801\pi$
$739$		−	6.00000i		−	0.220714i	0.993892	−	0.110357i	$-0.0351994\pi$
$740$			8.00000i			0.294086i
$741$	−16.9706	−	16.9706i	−0.623429	−	0.623429i
$742$	36.7696	+	36.7696i	1.34985	+	1.34985i
$743$	−7.07107	+	7.07107i	−0.259412	+	0.259412i	−0.824815	−	0.565403i	$-0.808721\pi$
$743$	−7.07107	+	7.07107i	−0.259412	+	0.259412i	0.565403	+	0.824815i	$0.308721\pi$
$744$	3.00000			0.109985
$745$	10.6066	−	10.6066i	0.388596	−	0.388596i
$746$			32.0000i			1.17160i
$747$	12.0000			0.439057
$748$		0			0
$749$	60.0000			2.19235
$750$			9.00000i			0.328634i
$751$	−24.7487	+	24.7487i	−0.903094	+	0.903094i	−0.995703	−	0.0926084i	$-0.970480\pi$
$751$	−24.7487	+	24.7487i	−0.903094	+	0.903094i	0.0926084	+	0.995703i	$0.470480\pi$
$752$	2.00000			0.0729325
$753$	10.6066	−	10.6066i	0.386526	−	0.386526i
$754$	−29.6985	−	29.6985i	−1.08156	−	1.08156i
$755$	6.36396	+	6.36396i	0.231608	+	0.231608i
$756$			4.00000i			0.145479i
$757$		−	38.0000i		−	1.38113i	−0.723269	−	0.690567i	$-0.757361\pi$
$757$		−	38.0000i		−	1.38113i	0.723269	−	0.690567i	$-0.242639\pi$
$758$	7.07107	+	7.07107i	0.256833	+	0.256833i
$759$	−12.7279	−	12.7279i	−0.461994	−	0.461994i
$760$	2.82843	−	2.82843i	0.102598	−	0.102598i
$761$	−34.0000			−1.23250			−0.616250	−	0.787551i	$-0.711349\pi$
$761$	−34.0000			−1.23250			−0.616250	+	0.787551i	$0.711349\pi$
$762$	11.3137	−	11.3137i	0.409852	−	0.409852i
$763$			40.0000i			1.44810i
$764$	14.0000			0.506502
$765$		0			0
$766$	2.00000			0.0722629
$767$			54.0000i			1.94983i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	55.0000			1.98335			0.991675	−	0.128763i	$-0.0411007\pi$
$769$	55.0000			1.98335			0.991675	+	0.128763i	$0.0411007\pi$
$770$	−8.48528	+	8.48528i	−0.305788	+	0.305788i
$771$		0			0
$772$	6.36396	+	6.36396i	0.229044	+	0.229044i
$773$			51.0000i			1.83434i	0.398493	+	0.917171i	$0.369533\pi$
$773$			51.0000i			1.83434i	−0.398493	+	0.917171i	$0.630467\pi$
$774$		−	4.00000i		−	0.143777i
$775$	8.48528	+	8.48528i	0.304800	+	0.304800i
$776$	2.12132	+	2.12132i	0.0761510	+	0.0761510i
$777$	−22.6274	+	22.6274i	−0.811754	+	0.811754i
$778$	−5.00000			−0.179259
$779$	−5.65685	+	5.65685i	−0.202678	+	0.202678i
$780$			6.00000i			0.214834i
$781$	36.0000			1.28818
$782$		0			0
$783$	7.00000			0.250160
$784$			9.00000i			0.321429i
$785$	8.48528	−	8.48528i	0.302853	−	0.302853i
$786$	−20.0000			−0.713376
$787$	16.9706	−	16.9706i	0.604935	−	0.604935i	−0.336683	−	0.941618i	$-0.609305\pi$
$787$	16.9706	−	16.9706i	0.604935	−	0.604935i	0.941618	+	0.336683i	$0.109305\pi$
$788$	7.07107	+	7.07107i	0.251896	+	0.251896i
$789$	12.7279	+	12.7279i	0.453126	+	0.453126i
$790$			5.00000i			0.177892i
$791$			40.0000i			1.42224i
$792$	2.12132	+	2.12132i	0.0753778	+	0.0753778i
$793$	42.4264	+	42.4264i	1.50661	+	1.50661i
$794$	15.5563	−	15.5563i	0.552074	−	0.552074i
$795$	−13.0000			−0.461062
$796$	0.707107	−	0.707107i	0.0250627	−	0.0250627i
$797$		−	14.0000i		−	0.495905i	−0.968772	−	0.247953i	$-0.920242\pi$
$797$		−	14.0000i		−	0.495905i	0.968772	−	0.247953i	$-0.0797578\pi$
$798$	16.0000			0.566394
$799$		0			0
$800$	4.00000			0.141421
$801$			4.00000i			0.141333i
$802$	−8.48528	+	8.48528i	−0.299626	+	0.299626i
$803$	−21.0000			−0.741074
$804$	4.24264	−	4.24264i	0.149626	−	0.149626i
$805$	16.9706	+	16.9706i	0.598134	+	0.598134i
$806$	12.7279	+	12.7279i	0.448322	+	0.448322i
$807$			9.00000i			0.316815i
$808$			17.0000i			0.598058i
$809$	−31.1127	−	31.1127i	−1.09386	−	1.09386i	−0.995112	−	0.0987522i	$-0.968515\pi$
$809$	−31.1127	−	31.1127i	−1.09386	−	1.09386i	−0.0987522	−	0.995112i	$-0.531485\pi$
$810$	−0.707107	−	0.707107i	−0.0248452	−	0.0248452i
$811$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$811$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$812$	28.0000			0.982607
$813$	3.53553	−	3.53553i	0.123997	−	0.123997i
$814$			24.0000i			0.841200i
$815$	−6.00000			−0.210171
$816$		0			0
$817$	−16.0000			−0.559769
$818$		−	19.0000i		−	0.664319i
$819$	−16.9706	+	16.9706i	−0.592999	+	0.592999i
$820$	2.00000			0.0698430
$821$	21.2132	−	21.2132i	0.740346	−	0.740346i	−0.232299	−	0.972645i	$-0.574625\pi$
$821$	21.2132	−	21.2132i	0.740346	−	0.740346i	0.972645	+	0.232299i	$0.0746247\pi$
$822$	−8.48528	−	8.48528i	−0.295958	−	0.295958i
$823$	−27.5772	−	27.5772i	−0.961280	−	0.961280i	0.0379983	−	0.999278i	$-0.487902\pi$
$823$	−27.5772	−	27.5772i	−0.961280	−	0.961280i	−0.999278	+	0.0379983i	$0.987902\pi$
$824$			13.0000i			0.452876i
$825$			12.0000i			0.417786i
$826$	−25.4558	−	25.4558i	−0.885722	−	0.885722i
$827$	3.53553	+	3.53553i	0.122943	+	0.122943i	0.765901	−	0.642958i	$-0.222293\pi$
$827$	3.53553	+	3.53553i	0.122943	+	0.122943i	−0.642958	+	0.765901i	$0.722293\pi$
$828$	4.24264	−	4.24264i	0.147442	−	0.147442i
$829$	12.0000			0.416777			0.208389	−	0.978046i	$-0.433178\pi$
$829$	12.0000			0.416777			0.208389	+	0.978046i	$0.433178\pi$
$830$	−8.48528	+	8.48528i	−0.294528	+	0.294528i
$831$		−	22.0000i		−	0.763172i
$832$	6.00000			0.208013
$833$		0			0
$834$	8.00000			0.277017
$835$			8.00000i			0.276851i
$836$	8.48528	−	8.48528i	0.293470	−	0.293470i
$837$	−3.00000			−0.103695
$838$	2.12132	−	2.12132i	0.0732798	−	0.0732798i
$839$	−21.2132	−	21.2132i	−0.732361	−	0.732361i	0.238726	−	0.971087i	$-0.423270\pi$
$839$	−21.2132	−	21.2132i	−0.732361	−	0.732361i	−0.971087	+	0.238726i	$0.923270\pi$
$840$	−2.82843	−	2.82843i	−0.0975900	−	0.0975900i
$841$		−	20.0000i		−	0.689655i
$842$			22.0000i			0.758170i
$843$		0			0
$844$	−5.65685	−	5.65685i	−0.194717	−	0.194717i
$845$	−16.2635	+	16.2635i	−0.559480	+	0.559480i
$846$	−2.00000			−0.0687614
$847$	5.65685	−	5.65685i	0.194372	−	0.194372i
$848$			13.0000i			0.446422i
$849$	4.00000			0.137280
$850$		0			0
$851$	48.0000			1.64542
$852$			12.0000i			0.411113i
$853$	−22.6274	+	22.6274i	−0.774748	+	0.774748i	−0.978932	−	0.204184i	$-0.934546\pi$
$853$	−22.6274	+	22.6274i	−0.774748	+	0.774748i	0.204184	+	0.978932i	$0.434546\pi$
$854$	−40.0000			−1.36877
$855$	−2.82843	+	2.82843i	−0.0967302	+	0.0967302i
$856$	10.6066	+	10.6066i	0.362526	+	0.362526i
$857$	35.3553	+	35.3553i	1.20772	+	1.20772i	0.971765	+	0.235950i	$0.0758202\pi$
$857$	35.3553	+	35.3553i	1.20772	+	1.20772i	0.235950	+	0.971765i	$0.424180\pi$
$858$			18.0000i			0.614510i
$859$			40.0000i			1.36478i	0.730987	+	0.682391i	$0.239060\pi$
$859$			40.0000i			1.36478i	−0.730987	+	0.682391i	$0.760940\pi$
$860$	2.82843	+	2.82843i	0.0964486	+	0.0964486i
$861$	5.65685	+	5.65685i	0.192785	+	0.192785i
$862$	7.07107	−	7.07107i	0.240842	−	0.240842i
$863$	30.0000			1.02121			0.510606	−	0.859815i	$-0.329421\pi$
$863$	30.0000			1.02121			0.510606	+	0.859815i	$0.329421\pi$
$864$	−0.707107	+	0.707107i	−0.0240563	+	0.0240563i
$865$			13.0000i			0.442013i
$866$	3.00000			0.101944
$867$		0			0
$868$	−12.0000			−0.407307
$869$			15.0000i			0.508840i
$870$	−4.94975	+	4.94975i	−0.167812	+	0.167812i
$871$	36.0000			1.21981
$872$	−7.07107	+	7.07107i	−0.239457	+	0.239457i
$873$	−2.12132	−	2.12132i	−0.0717958	−	0.0717958i
$874$	−16.9706	−	16.9706i	−0.574038	−	0.574038i
$875$		−	36.0000i		−	1.21702i
$876$		−	7.00000i		−	0.236508i
$877$	12.7279	+	12.7279i	0.429791	+	0.429791i	0.888557	−	0.458766i	$-0.151708\pi$
$877$	12.7279	+	12.7279i	0.429791	+	0.429791i	−0.458766	+	0.888557i	$0.651708\pi$
$878$	−19.7990	−	19.7990i	−0.668184	−	0.668184i
$879$	13.4350	−	13.4350i	0.453152	−	0.453152i
$880$	−3.00000			−0.101130
$881$	32.5269	−	32.5269i	1.09586	−	1.09586i	0.100970	−	0.994889i	$-0.467805\pi$
$881$	32.5269	−	32.5269i	1.09586	−	1.09586i	0.994889	−	0.100970i	$-0.0321946\pi$
$882$		−	9.00000i		−	0.303046i
$883$	2.00000			0.0673054			0.0336527	−	0.999434i	$-0.489286\pi$
$883$	2.00000			0.0673054			0.0336527	+	0.999434i	$0.489286\pi$
$884$		0			0
$885$	9.00000			0.302532
$886$			12.0000i			0.403148i
$887$	−25.4558	+	25.4558i	−0.854724	+	0.854724i	−0.990711	−	0.135987i	$-0.956579\pi$
$887$	−25.4558	+	25.4558i	−0.854724	+	0.854724i	0.135987	+	0.990711i	$0.456579\pi$
$888$	−8.00000			−0.268462
$889$	−45.2548	+	45.2548i	−1.51780	+	1.51780i
$890$	−2.82843	−	2.82843i	−0.0948091	−	0.0948091i
$891$	−2.12132	−	2.12132i	−0.0710669	−	0.0710669i
$892$		−	17.0000i		−	0.569202i
$893$			8.00000i			0.267710i
$894$	10.6066	+	10.6066i	0.354738	+	0.354738i
$895$		0			0
$896$	−2.82843	+	2.82843i	−0.0944911	+	0.0944911i
$897$	36.0000			1.20201
$898$	2.82843	−	2.82843i	0.0943858	−	0.0943858i
$899$			21.0000i			0.700389i
$900$	−4.00000			−0.133333
$901$		0			0
$902$	6.00000			0.199778
$903$			16.0000i			0.532447i
$904$	−7.07107	+	7.07107i	−0.235180	+	0.235180i
$905$	10.0000			0.332411
$906$	−6.36396	+	6.36396i	−0.211428	+	0.211428i
$907$	38.1838	+	38.1838i	1.26787	+	1.26787i	0.947186	+	0.320685i	$0.103913\pi$
$907$	38.1838	+	38.1838i	1.26787	+	1.26787i	0.320685	+	0.947186i	$0.396087\pi$
$908$	−14.1421	−	14.1421i	−0.469323	−	0.469323i
$909$		−	17.0000i		−	0.563854i
$910$		−	24.0000i		−	0.795592i
$911$	−15.5563	−	15.5563i	−0.515405	−	0.515405i	0.400773	−	0.916178i	$-0.368742\pi$
$911$	−15.5563	−	15.5563i	−0.515405	−	0.515405i	−0.916178	+	0.400773i	$0.868742\pi$
$912$	2.82843	+	2.82843i	0.0936586	+	0.0936586i
$913$	−25.4558	+	25.4558i	−0.842465	+	0.842465i
$914$	−17.0000			−0.562310
$915$	7.07107	−	7.07107i	0.233762	−	0.233762i
$916$		−	14.0000i		−	0.462573i
$917$	80.0000			2.64183
$918$		0			0
$919$	16.0000			0.527791			0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000			0.527791			0.263896	+	0.964551i	$0.414993\pi$
$920$			6.00000i			0.197814i
$921$	−8.48528	+	8.48528i	−0.279600	+	0.279600i
$922$	35.0000			1.15266
$923$	−50.9117	+	50.9117i	−1.67578	+	1.67578i
$924$	−8.48528	−	8.48528i	−0.279145	−	0.279145i
$925$	−22.6274	−	22.6274i	−0.743985	−	0.743985i
$926$			5.00000i			0.164310i
$927$		−	13.0000i		−	0.426976i
$928$	4.94975	+	4.94975i	0.162483	+	0.162483i
$929$	−5.65685	−	5.65685i	−0.185595	−	0.185595i	0.608193	−	0.793789i	$-0.291894\pi$
$929$	−5.65685	−	5.65685i	−0.185595	−	0.185595i	−0.793789	+	0.608193i	$0.791894\pi$
$930$	2.12132	−	2.12132i	0.0695608	−	0.0695608i
$931$	−36.0000			−1.17985
$932$	−16.9706	+	16.9706i	−0.555889	+	0.555889i
$933$		0			0
$934$	3.00000			0.0981630
$935$		0			0
$936$	−6.00000			−0.196116
$937$			19.0000i			0.620703i	0.950622	+	0.310351i	$0.100447\pi$
$937$			19.0000i			0.620703i	−0.950622	+	0.310351i	$0.899553\pi$
$938$	−16.9706	+	16.9706i	−0.554109	+	0.554109i
$939$	−14.0000			−0.456873
$940$	1.41421	−	1.41421i	0.0461266	−	0.0461266i
$941$	21.2132	+	21.2132i	0.691531	+	0.691531i	0.962569	−	0.271038i	$-0.0873669\pi$
$941$	21.2132	+	21.2132i	0.691531	+	0.691531i	−0.271038	+	0.962569i	$0.587367\pi$
$942$	8.48528	+	8.48528i	0.276465	+	0.276465i
$943$		−	12.0000i		−	0.390774i
$944$		−	9.00000i		−	0.292925i
$945$	2.82843	+	2.82843i	0.0920087	+	0.0920087i
$946$	8.48528	+	8.48528i	0.275880	+	0.275880i
$947$	−2.12132	+	2.12132i	−0.0689336	+	0.0689336i	−0.740733	−	0.671799i	$-0.765522\pi$
$947$	−2.12132	+	2.12132i	−0.0689336	+	0.0689336i	0.671799	+	0.740733i	$0.265522\pi$
$948$	−5.00000			−0.162392
$949$	29.6985	−	29.6985i	0.964054	−	0.964054i
$950$			16.0000i			0.519109i
$951$	−2.00000			−0.0648544
$952$		0			0
$953$	4.00000			0.129573			0.0647864	−	0.997899i	$-0.479363\pi$
$953$	4.00000			0.129573			0.0647864	+	0.997899i	$0.479363\pi$
$954$		−	13.0000i		−	0.420891i
$955$	9.89949	−	9.89949i	0.320340	−	0.320340i
$956$	26.0000			0.840900
$957$	−14.8492	+	14.8492i	−0.480008	+	0.480008i
$958$	−9.89949	−	9.89949i	−0.319838	−	0.319838i
$959$	33.9411	+	33.9411i	1.09602	+	1.09602i
$960$		−	1.00000i		−	0.0322749i
$961$			22.0000i			0.709677i
$962$	−33.9411	−	33.9411i	−1.09431	−	1.09431i
$963$	−10.6066	−	10.6066i	−0.341793	−	0.341793i
$964$	10.6066	−	10.6066i	0.341616	−	0.341616i
$965$	9.00000			0.289720
$966$	−16.9706	+	16.9706i	−0.546019	+	0.546019i
$967$			13.0000i			0.418052i	0.977910	+	0.209026i	$0.0670293\pi$
$967$			13.0000i			0.418052i	−0.977910	+	0.209026i	$0.932971\pi$
$968$	2.00000			0.0642824
$969$		0			0
$970$	3.00000			0.0963242
$971$		−	19.0000i		−	0.609739i	−0.952394	−	0.304870i	$-0.901387\pi$
$971$		−	19.0000i		−	0.609739i	0.952394	−	0.304870i	$-0.0986129\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	−32.0000			−1.02587
$974$	−17.6777	+	17.6777i	−0.566429	+	0.566429i
$975$	−16.9706	−	16.9706i	−0.543493	−	0.543493i
$976$	−7.07107	−	7.07107i	−0.226339	−	0.226339i
$977$			16.0000i			0.511885i	0.966692	+	0.255943i	$0.0823858\pi$
$977$			16.0000i			0.511885i	−0.966692	+	0.255943i	$0.917614\pi$
$978$		−	6.00000i		−	0.191859i
$979$	−8.48528	−	8.48528i	−0.271191	−	0.271191i
$980$	6.36396	+	6.36396i	0.203289	+	0.203289i
$981$	7.07107	−	7.07107i	0.225762	−	0.225762i
$982$	−23.0000			−0.733959
$983$	9.89949	−	9.89949i	0.315745	−	0.315745i	−0.531385	−	0.847130i	$-0.678328\pi$
$983$	9.89949	−	9.89949i	0.315745	−	0.315745i	0.847130	+	0.531385i	$0.178328\pi$
$984$			2.00000i			0.0637577i
$985$	10.0000			0.318626
$986$		0			0
$987$	8.00000			0.254643
$988$			24.0000i			0.763542i
$989$	16.9706	−	16.9706i	0.539633	−	0.539633i
$990$	3.00000			0.0953463
$991$	−2.82843	+	2.82843i	−0.0898479	+	0.0898479i	−0.750602	−	0.660754i	$-0.770237\pi$
$991$	−2.82843	+	2.82843i	−0.0898479	+	0.0898479i	0.660754	+	0.750602i	$0.270237\pi$
$992$	−2.12132	−	2.12132i	−0.0673520	−	0.0673520i
$993$	15.5563	+	15.5563i	0.493666	+	0.493666i
$994$		−	48.0000i		−	1.52247i
$995$		−	1.00000i		−	0.0317021i
$996$	−8.48528	−	8.48528i	−0.268866	−	0.268866i
$997$	−15.5563	−	15.5563i	−0.492675	−	0.492675i	0.416473	−	0.909148i	$-0.363266\pi$
$997$	−15.5563	−	15.5563i	−0.492675	−	0.492675i	−0.909148	+	0.416473i	$0.863266\pi$
$998$	−5.65685	+	5.65685i	−0.179065	+	0.179065i
$999$	8.00000			0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1734.2.f.a.1483.2		4
17.2	even	8		1734.2.b.g.577.1		2
17.4	even	4	inner	1734.2.f.a.829.1		4
17.8	even	8		1734.2.a.a.1.1	✓	1
17.9	even	8		1734.2.a.g.1.1	yes	1
17.13	even	4	inner	1734.2.f.a.829.2		4
17.15	even	8		1734.2.b.g.577.2		2
17.16	even	2	inner	1734.2.f.a.1483.1		4
51.8	odd	8		5202.2.a.m.1.1		1
51.26	odd	8		5202.2.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1734.2.a.a.1.1	✓	1	17.8	even	8
1734.2.a.g.1.1	yes	1	17.9	even	8
1734.2.b.g.577.1		2	17.2	even	8
1734.2.b.g.577.2		2	17.15	even	8
1734.2.f.a.829.1		4	17.4	even	4	inner
1734.2.f.a.829.2		4	17.13	even	4	inner
1734.2.f.a.1483.1		4	17.16	even	2	inner
1734.2.f.a.1483.2		4	1.1	even	1	trivial
5202.2.a.i.1.1		1	51.26	odd	8
5202.2.a.m.1.1		1	51.8	odd	8

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:	\( N \)	\(=\)	\( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1734.f (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(2.82843 + 2.82843i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(0.707107 + 0.707107i) q^{10} +(2.12132 + 2.12132i) q^{11} +(-0.707107 + 0.707107i) q^{12} -6.00000 q^{13} +(2.82843 - 2.82843i) q^{14} +1.00000i q^{15} +1.00000 q^{16} -1.00000 q^{18} +4.00000i q^{19} +(0.707107 - 0.707107i) q^{20} +4.00000 q^{21} +(2.12132 - 2.12132i) q^{22} +(-4.24264 - 4.24264i) q^{23} +(0.707107 + 0.707107i) q^{24} +4.00000i q^{25} +6.00000i q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.82843 - 2.82843i) q^{28} +(-4.94975 + 4.94975i) q^{29} +1.00000 q^{30} +(2.12132 - 2.12132i) q^{31} -1.00000i q^{32} +3.00000 q^{33} -4.00000 q^{35} +1.00000i q^{36} +(-5.65685 + 5.65685i) q^{37} +4.00000 q^{38} +(-4.24264 + 4.24264i) q^{39} +(-0.707107 - 0.707107i) q^{40} +(1.41421 + 1.41421i) q^{41} -4.00000i q^{42} +4.00000i q^{43} +(-2.12132 - 2.12132i) q^{44} +(0.707107 + 0.707107i) q^{45} +(-4.24264 + 4.24264i) q^{46} +2.00000 q^{47} +(0.707107 - 0.707107i) q^{48} +9.00000i q^{49} +4.00000 q^{50} +6.00000 q^{52} +13.0000i q^{53} +(-0.707107 + 0.707107i) q^{54} -3.00000 q^{55} +(-2.82843 + 2.82843i) q^{56} +(2.82843 + 2.82843i) q^{57} +(4.94975 + 4.94975i) q^{58} -9.00000i q^{59} -1.00000i q^{60} +(-7.07107 - 7.07107i) q^{61} +(-2.12132 - 2.12132i) q^{62} +(2.82843 - 2.82843i) q^{63} -1.00000 q^{64} +(4.24264 - 4.24264i) q^{65} -3.00000i q^{66} -6.00000 q^{67} -6.00000 q^{69} +4.00000i q^{70} +(8.48528 - 8.48528i) q^{71} +1.00000 q^{72} +(-4.94975 + 4.94975i) q^{73} +(5.65685 + 5.65685i) q^{74} +(2.82843 + 2.82843i) q^{75} -4.00000i q^{76} +12.0000i q^{77} +(4.24264 + 4.24264i) q^{78} +(3.53553 + 3.53553i) q^{79} +(-0.707107 + 0.707107i) q^{80} -1.00000 q^{81} +(1.41421 - 1.41421i) q^{82} +12.0000i q^{83} -4.00000 q^{84} +4.00000 q^{86} +7.00000i q^{87} +(-2.12132 + 2.12132i) q^{88} -4.00000 q^{89} +(0.707107 - 0.707107i) q^{90} +(-16.9706 - 16.9706i) q^{91} +(4.24264 + 4.24264i) q^{92} -3.00000i q^{93} -2.00000i q^{94} +(-2.82843 - 2.82843i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(2.12132 - 2.12132i) q^{97} +9.00000 q^{98} +(2.12132 - 2.12132i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 24 q^{13} + 4 q^{16} - 4 q^{18} + 16 q^{21} + 4 q^{30} + 12 q^{33} - 16 q^{35} + 16 q^{38} + 8 q^{47} + 16 q^{50} + 24 q^{52} - 12 q^{55} - 4 q^{64} - 24 q^{67} - 24 q^{69} + 4 q^{72} - 4 q^{81}+ \cdots + 36 q^{98}+O(q^{100}) \) 4 * q - 4 * q^4 - 24 * q^13 + 4 * q^16 - 4 * q^18 + 16 * q^21 + 4 * q^30 + 12 * q^33 - 16 * q^35 + 16 * q^38 + 8 * q^47 + 16 * q^50 + 24 * q^52 - 12 * q^55 - 4 * q^64 - 24 * q^67 - 24 * q^69 + 4 * q^72 - 4 * q^81 - 16 * q^84 + 16 * q^86 - 16 * q^89 + 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more