LMFDB - Embedded newform 1710.2.n.e.647.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(647,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("1710.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.n (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:	$13.6544187456$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.1
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1710.647
Dual form			1710.2.n.e.1673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-2.12132 + 0.707107i) q^{5} +(3.00000 + 3.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.00000 - 2.00000i) q^{10} +1.41421i q^{11} +(4.00000 - 4.00000i) q^{13} -4.24264 q^{14} -1.00000 q^{16} +(2.82843 - 2.82843i) q^{17} -1.00000i q^{19} +(0.707107 + 2.12132i) q^{20} +(-1.00000 - 1.00000i) q^{22} +(4.00000 - 3.00000i) q^{25} +5.65685i q^{26} +(3.00000 - 3.00000i) q^{28} +2.82843 q^{29} -4.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +4.00000i q^{34} +(-8.48528 - 4.24264i) q^{35} +(6.00000 + 6.00000i) q^{37} +(0.707107 + 0.707107i) q^{38} +(-2.00000 - 1.00000i) q^{40} -8.48528i q^{41} +(3.00000 - 3.00000i) q^{43} +1.41421 q^{44} +(-5.65685 + 5.65685i) q^{47} +11.0000i q^{49} +(-0.707107 + 4.94975i) q^{50} +(-4.00000 - 4.00000i) q^{52} +(-1.41421 - 1.41421i) q^{53} +(-1.00000 - 3.00000i) q^{55} +4.24264i q^{56} +(-2.00000 + 2.00000i) q^{58} +5.65685 q^{59} +10.0000 q^{61} +(2.82843 - 2.82843i) q^{62} +1.00000i q^{64} +(-5.65685 + 11.3137i) q^{65} +(-10.0000 - 10.0000i) q^{67} +(-2.82843 - 2.82843i) q^{68} +(9.00000 - 3.00000i) q^{70} +5.65685i q^{71} +(-3.00000 + 3.00000i) q^{73} -8.48528 q^{74} -1.00000 q^{76} +(-4.24264 + 4.24264i) q^{77} +4.00000i q^{79} +(2.12132 - 0.707107i) q^{80} +(6.00000 + 6.00000i) q^{82} +(4.24264 + 4.24264i) q^{83} +(-4.00000 + 8.00000i) q^{85} +4.24264i q^{86} +(-1.00000 + 1.00000i) q^{88} +14.1421 q^{89} +24.0000 q^{91} -8.00000i q^{94} +(0.707107 + 2.12132i) q^{95} +(12.0000 + 12.0000i) q^{97} +(-7.77817 - 7.77817i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 12 q^{7} + 4 q^{10} + 16 q^{13} - 4 q^{16} - 4 q^{22} + 16 q^{25} + 12 q^{28} - 16 q^{31} + 24 q^{37} - 8 q^{40} + 12 q^{43} - 16 q^{52} - 4 q^{55} - 8 q^{58} + 40 q^{61} - 40 q^{67} + 36 q^{70} - 12 q^{73}+ \cdots + 48 q^{97}+O(q^{100}) $ 4 * q + 12 * q^7 + 4 * q^10 + 16 * q^13 - 4 * q^16 - 4 * q^22 + 16 * q^25 + 12 * q^28 - 16 * q^31 + 24 * q^37 - 8 * q^40 + 12 * q^43 - 16 * q^52 - 4 * q^55 - 8 * q^58 + 40 * q^61 - 40 * q^67 + 36 * q^70 - 12 * q^73 - 4 * q^76 + 24 * q^82 - 16 * q^85 - 4 * q^88 + 96 * q^91 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−2.12132	+	0.707107i	−0.948683	+	0.316228i
$5$	−2.12132	+	0.707107i	−0.948683	+	0.316228i
$6$		0			0
$7$	3.00000	+	3.00000i	1.13389	+	1.13389i	0.989524	+	0.144370i	$0.0461154\pi$
$7$	3.00000	+	3.00000i	1.13389	+	1.13389i	0.144370	+	0.989524i	$0.453885\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	1.00000	−	2.00000i	0.316228	−	0.632456i
$11$			1.41421i			0.426401i	0.977008	+	0.213201i	$0.0683888\pi$
$11$			1.41421i			0.426401i	−0.977008	+	0.213201i	$0.931611\pi$
$12$		0			0
$13$	4.00000	−	4.00000i	1.10940	−	1.10940i	0.116171	−	0.993229i	$-0.462938\pi$
$13$	4.00000	−	4.00000i	1.10940	−	1.10940i	0.993229	−	0.116171i	$-0.0370621\pi$
$14$	−4.24264			−1.13389
$15$		0			0
$16$	−1.00000			−0.250000
$17$	2.82843	−	2.82843i	0.685994	−	0.685994i	−0.275350	−	0.961344i	$-0.588794\pi$
$17$	2.82843	−	2.82843i	0.685994	−	0.685994i	0.961344	+	0.275350i	$0.0887937\pi$
$18$		0			0
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	0.707107	+	2.12132i	0.158114	+	0.474342i
$21$		0			0
$22$	−1.00000	−	1.00000i	−0.213201	−	0.213201i
$23$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$23$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$24$		0			0
$25$	4.00000	−	3.00000i	0.800000	−	0.600000i
$26$			5.65685i			1.10940i
$27$		0			0
$28$	3.00000	−	3.00000i	0.566947	−	0.566947i
$29$	2.82843			0.525226			0.262613	−	0.964901i	$-0.415416\pi$
$29$	2.82843			0.525226			0.262613	+	0.964901i	$0.415416\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$			4.00000i			0.685994i
$35$	−8.48528	−	4.24264i	−1.43427	−	0.717137i
$36$		0			0
$37$	6.00000	+	6.00000i	0.986394	+	0.986394i	0.999909	−	0.0135147i	$-0.00430201\pi$
$37$	6.00000	+	6.00000i	0.986394	+	0.986394i	−0.0135147	+	0.999909i	$0.504302\pi$
$38$	0.707107	+	0.707107i	0.114708	+	0.114708i
$39$		0			0
$40$	−2.00000	−	1.00000i	−0.316228	−	0.158114i
$41$		−	8.48528i		−	1.32518i	−0.748983	−	0.662589i	$-0.769458\pi$
$41$		−	8.48528i		−	1.32518i	0.748983	−	0.662589i	$-0.230542\pi$
$42$		0			0
$43$	3.00000	−	3.00000i	0.457496	−	0.457496i	−0.440337	−	0.897833i	$-0.645141\pi$
$43$	3.00000	−	3.00000i	0.457496	−	0.457496i	0.897833	+	0.440337i	$0.145141\pi$
$44$	1.41421			0.213201
$45$		0			0
$46$		0			0
$47$	−5.65685	+	5.65685i	−0.825137	+	0.825137i	−0.986840	−	0.161703i	$-0.948301\pi$
$47$	−5.65685	+	5.65685i	−0.825137	+	0.825137i	0.161703	+	0.986840i	$0.448301\pi$
$48$		0			0
$49$			11.0000i			1.57143i
$50$	−0.707107	+	4.94975i	−0.100000	+	0.700000i
$51$		0			0
$52$	−4.00000	−	4.00000i	−0.554700	−	0.554700i
$53$	−1.41421	−	1.41421i	−0.194257	−	0.194257i	0.603276	−	0.797533i	$-0.293862\pi$
$53$	−1.41421	−	1.41421i	−0.194257	−	0.194257i	−0.797533	+	0.603276i	$0.793862\pi$
$54$		0			0
$55$	−1.00000	−	3.00000i	−0.134840	−	0.404520i
$56$			4.24264i			0.566947i
$57$		0			0
$58$	−2.00000	+	2.00000i	−0.262613	+	0.262613i
$59$	5.65685			0.736460			0.368230	−	0.929735i	$-0.379964\pi$
$59$	5.65685			0.736460			0.368230	+	0.929735i	$0.379964\pi$
$60$		0			0
$61$	10.0000			1.28037			0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000			1.28037			0.640184	+	0.768221i	$0.278858\pi$
$62$	2.82843	−	2.82843i	0.359211	−	0.359211i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−5.65685	+	11.3137i	−0.701646	+	1.40329i
$66$		0			0
$67$	−10.0000	−	10.0000i	−1.22169	−	1.22169i	−0.967029	−	0.254665i	$-0.918035\pi$
$67$	−10.0000	−	10.0000i	−1.22169	−	1.22169i	−0.254665	−	0.967029i	$-0.581965\pi$
$68$	−2.82843	−	2.82843i	−0.342997	−	0.342997i
$69$		0			0
$70$	9.00000	−	3.00000i	1.07571	−	0.358569i
$71$			5.65685i			0.671345i	0.941979	+	0.335673i	$0.108964\pi$
$71$			5.65685i			0.671345i	−0.941979	+	0.335673i	$0.891036\pi$
$72$		0			0
$73$	−3.00000	+	3.00000i	−0.351123	+	0.351123i	−0.860527	−	0.509404i	$-0.829866\pi$
$73$	−3.00000	+	3.00000i	−0.351123	+	0.351123i	0.509404	+	0.860527i	$0.329866\pi$
$74$	−8.48528			−0.986394
$75$		0			0
$76$	−1.00000			−0.114708
$77$	−4.24264	+	4.24264i	−0.483494	+	0.483494i
$78$		0			0
$79$			4.00000i			0.450035i	0.974355	+	0.225018i	$0.0722440\pi$
$79$			4.00000i			0.450035i	−0.974355	+	0.225018i	$0.927756\pi$
$80$	2.12132	−	0.707107i	0.237171	−	0.0790569i
$81$		0			0
$82$	6.00000	+	6.00000i	0.662589	+	0.662589i
$83$	4.24264	+	4.24264i	0.465690	+	0.465690i	0.900515	−	0.434825i	$-0.143190\pi$
$83$	4.24264	+	4.24264i	0.465690	+	0.465690i	−0.434825	+	0.900515i	$0.643190\pi$
$84$		0			0
$85$	−4.00000	+	8.00000i	−0.433861	+	0.867722i
$86$			4.24264i			0.457496i
$87$		0			0
$88$	−1.00000	+	1.00000i	−0.106600	+	0.106600i
$89$	14.1421			1.49906			0.749532	−	0.661968i	$-0.230279\pi$
$89$	14.1421			1.49906			0.749532	+	0.661968i	$0.230279\pi$
$90$		0			0
$91$	24.0000			2.51588
$92$		0			0
$93$		0			0
$94$		−	8.00000i		−	0.825137i
$95$	0.707107	+	2.12132i	0.0725476	+	0.217643i
$96$		0			0
$97$	12.0000	+	12.0000i	1.21842	+	1.21842i	0.968187	+	0.250229i	$0.0805058\pi$
$97$	12.0000	+	12.0000i	1.21842	+	1.21842i	0.250229	+	0.968187i	$0.419494\pi$
$98$	−7.77817	−	7.77817i	−0.785714	−	0.785714i
$99$		0			0
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$			15.5563i			1.54791i	0.633238	+	0.773957i	$0.281726\pi$
$101$			15.5563i			1.54791i	−0.633238	+	0.773957i	$0.718274\pi$
$102$		0			0
$103$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$103$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$104$	5.65685			0.554700
$105$		0			0
$106$	2.00000			0.194257
$107$	8.48528	−	8.48528i	0.820303	−	0.820303i	−0.165848	−	0.986151i	$-0.553036\pi$
$107$	8.48528	−	8.48528i	0.820303	−	0.820303i	0.986151	+	0.165848i	$0.0530362\pi$
$108$		0			0
$109$			2.00000i			0.191565i	0.995402	+	0.0957826i	$0.0305354\pi$
$109$			2.00000i			0.191565i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$	2.82843	+	1.41421i	0.269680	+	0.134840i
$111$		0			0
$112$	−3.00000	−	3.00000i	−0.283473	−	0.283473i
$113$	1.41421	+	1.41421i	0.133038	+	0.133038i	0.770490	−	0.637452i	$-0.220012\pi$
$113$	1.41421	+	1.41421i	0.133038	+	0.133038i	−0.637452	+	0.770490i	$0.720012\pi$
$114$		0			0
$115$		0			0
$116$		−	2.82843i		−	0.262613i
$117$		0			0
$118$	−4.00000	+	4.00000i	−0.368230	+	0.368230i
$119$	16.9706			1.55569
$120$		0			0
$121$	9.00000			0.818182
$122$	−7.07107	+	7.07107i	−0.640184	+	0.640184i
$123$		0			0
$124$			4.00000i			0.359211i
$125$	−6.36396	+	9.19239i	−0.569210	+	0.822192i
$126$		0			0
$127$	−10.0000	−	10.0000i	−0.887357	−	0.887357i	0.106912	−	0.994268i	$-0.465904\pi$
$127$	−10.0000	−	10.0000i	−0.887357	−	0.887357i	−0.994268	+	0.106912i	$0.965904\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−4.00000	−	12.0000i	−0.350823	−	1.05247i
$131$			12.7279i			1.11204i	0.831168	+	0.556022i	$0.187673\pi$
$131$			12.7279i			1.11204i	−0.831168	+	0.556022i	$0.812327\pi$
$132$		0			0
$133$	3.00000	−	3.00000i	0.260133	−	0.260133i
$134$	14.1421			1.22169
$135$		0			0
$136$	4.00000			0.342997
$137$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$137$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$138$		0			0
$139$			14.0000i			1.18746i	0.804663	+	0.593732i	$0.202346\pi$
$139$			14.0000i			1.18746i	−0.804663	+	0.593732i	$0.797654\pi$
$140$	−4.24264	+	8.48528i	−0.358569	+	0.717137i
$141$		0			0
$142$	−4.00000	−	4.00000i	−0.335673	−	0.335673i
$143$	5.65685	+	5.65685i	0.473050	+	0.473050i
$144$		0			0
$145$	−6.00000	+	2.00000i	−0.498273	+	0.166091i
$146$		−	4.24264i		−	0.351123i
$147$		0			0
$148$	6.00000	−	6.00000i	0.493197	−	0.493197i
$149$	18.3848			1.50614			0.753070	−	0.657941i	$-0.228572\pi$
$149$	18.3848			1.50614			0.753070	+	0.657941i	$0.228572\pi$
$150$		0			0
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$	0.707107	−	0.707107i	0.0573539	−	0.0573539i
$153$		0			0
$154$		−	6.00000i		−	0.483494i
$155$	8.48528	−	2.82843i	0.681554	−	0.227185i
$156$		0			0
$157$	−7.00000	−	7.00000i	−0.558661	−	0.558661i	0.370265	−	0.928926i	$-0.379267\pi$
$157$	−7.00000	−	7.00000i	−0.558661	−	0.558661i	−0.928926	+	0.370265i	$0.879267\pi$
$158$	−2.82843	−	2.82843i	−0.225018	−	0.225018i
$159$		0			0
$160$	−1.00000	+	2.00000i	−0.0790569	+	0.158114i
$161$		0			0
$162$		0			0
$163$	−1.00000	+	1.00000i	−0.0783260	+	0.0783260i	−0.745184	−	0.666858i	$-0.767639\pi$
$163$	−1.00000	+	1.00000i	−0.0783260	+	0.0783260i	0.666858	+	0.745184i	$0.267639\pi$
$164$	−8.48528			−0.662589
$165$		0			0
$166$	−6.00000			−0.465690
$167$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$167$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$168$		0			0
$169$		−	19.0000i		−	1.46154i
$170$	−2.82843	−	8.48528i	−0.216930	−	0.650791i
$171$		0			0
$172$	−3.00000	−	3.00000i	−0.228748	−	0.228748i
$173$	−4.24264	−	4.24264i	−0.322562	−	0.322562i	0.527187	−	0.849749i	$-0.323247\pi$
$173$	−4.24264	−	4.24264i	−0.322562	−	0.322562i	−0.849749	+	0.527187i	$0.823247\pi$
$174$		0			0
$175$	21.0000	+	3.00000i	1.58745	+	0.226779i
$176$		−	1.41421i		−	0.106600i
$177$		0			0
$178$	−10.0000	+	10.0000i	−0.749532	+	0.749532i
$179$	−11.3137			−0.845626			−0.422813	−	0.906217i	$-0.638957\pi$
$179$	−11.3137			−0.845626			−0.422813	+	0.906217i	$0.638957\pi$
$180$		0			0
$181$	18.0000			1.33793			0.668965	−	0.743294i	$-0.266738\pi$
$181$	18.0000			1.33793			0.668965	+	0.743294i	$0.266738\pi$
$182$	−16.9706	+	16.9706i	−1.25794	+	1.25794i
$183$		0			0
$184$		0			0
$185$	−16.9706	−	8.48528i	−1.24770	−	0.623850i
$186$		0			0
$187$	4.00000	+	4.00000i	0.292509	+	0.292509i
$188$	5.65685	+	5.65685i	0.412568	+	0.412568i
$189$		0			0
$190$	−2.00000	−	1.00000i	−0.145095	−	0.0725476i
$191$		−	24.0416i		−	1.73959i	−0.493412	−	0.869796i	$-0.664251\pi$
$191$		−	24.0416i		−	1.73959i	0.493412	−	0.869796i	$-0.335749\pi$
$192$		0			0
$193$	−18.0000	+	18.0000i	−1.29567	+	1.29567i	−0.364442	+	0.931226i	$0.618740\pi$
$193$	−18.0000	+	18.0000i	−1.29567	+	1.29567i	−0.931226	+	0.364442i	$0.881260\pi$
$194$	−16.9706			−1.21842
$195$		0			0
$196$	11.0000			0.785714
$197$	−15.5563	+	15.5563i	−1.10834	+	1.10834i	−0.114976	+	0.993368i	$0.536679\pi$
$197$	−15.5563	+	15.5563i	−1.10834	+	1.10834i	−0.993368	+	0.114976i	$0.963321\pi$
$198$		0			0
$199$			2.00000i			0.141776i	0.997484	+	0.0708881i	$0.0225833\pi$
$199$			2.00000i			0.141776i	−0.997484	+	0.0708881i	$0.977417\pi$
$200$	4.94975	+	0.707107i	0.350000	+	0.0500000i
$201$		0			0
$202$	−11.0000	−	11.0000i	−0.773957	−	0.773957i
$203$	8.48528	+	8.48528i	0.595550	+	0.595550i
$204$		0			0
$205$	6.00000	+	18.0000i	0.419058	+	1.25717i
$206$		0			0
$207$		0			0
$208$	−4.00000	+	4.00000i	−0.277350	+	0.277350i
$209$	1.41421			0.0978232
$210$		0			0
$211$	16.0000			1.10149			0.550743	−	0.834675i	$-0.314345\pi$
$211$	16.0000			1.10149			0.550743	+	0.834675i	$0.314345\pi$
$212$	−1.41421	+	1.41421i	−0.0971286	+	0.0971286i
$213$		0			0
$214$			12.0000i			0.820303i
$215$	−4.24264	+	8.48528i	−0.289346	+	0.578691i
$216$		0			0
$217$	−12.0000	−	12.0000i	−0.814613	−	0.814613i
$218$	−1.41421	−	1.41421i	−0.0957826	−	0.0957826i
$219$		0			0
$220$	−3.00000	+	1.00000i	−0.202260	+	0.0674200i
$221$		−	22.6274i		−	1.52208i
$222$		0			0
$223$	−12.0000	+	12.0000i	−0.803579	+	0.803579i	−0.983653	−	0.180074i	$-0.942366\pi$
$223$	−12.0000	+	12.0000i	−0.803579	+	0.803579i	0.180074	+	0.983653i	$0.442366\pi$
$224$	4.24264			0.283473
$225$		0			0
$226$	−2.00000			−0.133038
$227$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$227$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$228$		0			0
$229$		−	8.00000i		−	0.528655i	−0.964433	−	0.264327i	$-0.914850\pi$
$229$		−	8.00000i		−	0.528655i	0.964433	−	0.264327i	$-0.0851500\pi$
$230$		0			0
$231$		0			0
$232$	2.00000	+	2.00000i	0.131306	+	0.131306i
$233$	−7.07107	−	7.07107i	−0.463241	−	0.463241i	0.436475	−	0.899716i	$-0.356227\pi$
$233$	−7.07107	−	7.07107i	−0.463241	−	0.463241i	−0.899716	+	0.436475i	$0.856227\pi$
$234$		0			0
$235$	8.00000	−	16.0000i	0.521862	−	1.04372i
$236$		−	5.65685i		−	0.368230i
$237$		0			0
$238$	−12.0000	+	12.0000i	−0.777844	+	0.777844i
$239$	−18.3848			−1.18921			−0.594606	−	0.804017i	$-0.702692\pi$
$239$	−18.3848			−1.18921			−0.594606	+	0.804017i	$0.702692\pi$
$240$		0			0
$241$	−10.0000			−0.644157			−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000			−0.644157			−0.322078	+	0.946713i	$0.604381\pi$
$242$	−6.36396	+	6.36396i	−0.409091	+	0.409091i
$243$		0			0
$244$		−	10.0000i		−	0.640184i
$245$	−7.77817	−	23.3345i	−0.496929	−	1.49079i
$246$		0			0
$247$	−4.00000	−	4.00000i	−0.254514	−	0.254514i
$248$	−2.82843	−	2.82843i	−0.179605	−	0.179605i
$249$		0			0
$250$	−2.00000	−	11.0000i	−0.126491	−	0.695701i
$251$		−	18.3848i		−	1.16044i	−0.814461	−	0.580218i	$-0.802967\pi$
$251$		−	18.3848i		−	1.16044i	0.814461	−	0.580218i	$-0.197033\pi$
$252$		0			0
$253$		0			0
$254$	14.1421			0.887357
$255$		0			0
$256$	1.00000			0.0625000
$257$	15.5563	−	15.5563i	0.970378	−	0.970378i	−0.0291953	−	0.999574i	$-0.509294\pi$
$257$	15.5563	−	15.5563i	0.970378	−	0.970378i	0.999574	+	0.0291953i	$0.00929448\pi$
$258$		0			0
$259$			36.0000i			2.23693i
$260$	11.3137	+	5.65685i	0.701646	+	0.350823i
$261$		0			0
$262$	−9.00000	−	9.00000i	−0.556022	−	0.556022i
$263$	7.07107	+	7.07107i	0.436021	+	0.436021i	0.890670	−	0.454650i	$-0.150236\pi$
$263$	7.07107	+	7.07107i	0.436021	+	0.436021i	−0.454650	+	0.890670i	$0.650236\pi$
$264$		0			0
$265$	4.00000	+	2.00000i	0.245718	+	0.122859i
$266$			4.24264i			0.260133i
$267$		0			0
$268$	−10.0000	+	10.0000i	−0.610847	+	0.610847i
$269$	2.82843			0.172452			0.0862261	−	0.996276i	$-0.472519\pi$
$269$	2.82843			0.172452			0.0862261	+	0.996276i	$0.472519\pi$
$270$		0			0
$271$	−14.0000			−0.850439			−0.425220	−	0.905090i	$-0.639803\pi$
$271$	−14.0000			−0.850439			−0.425220	+	0.905090i	$0.639803\pi$
$272$	−2.82843	+	2.82843i	−0.171499	+	0.171499i
$273$		0			0
$274$		0			0
$275$	4.24264	+	5.65685i	0.255841	+	0.341121i
$276$		0			0
$277$	15.0000	+	15.0000i	0.901263	+	0.901263i	0.995545	−	0.0942828i	$-0.0300558\pi$
$277$	15.0000	+	15.0000i	0.901263	+	0.901263i	−0.0942828	+	0.995545i	$0.530056\pi$
$278$	−9.89949	−	9.89949i	−0.593732	−	0.593732i
$279$		0			0
$280$	−3.00000	−	9.00000i	−0.179284	−	0.537853i
$281$		−	22.6274i		−	1.34984i	−0.737892	−	0.674919i	$-0.764178\pi$
$281$		−	22.6274i		−	1.34984i	0.737892	−	0.674919i	$-0.235822\pi$
$282$		0			0
$283$	−19.0000	+	19.0000i	−1.12943	+	1.12943i	−0.139163	+	0.990269i	$0.544441\pi$
$283$	−19.0000	+	19.0000i	−1.12943	+	1.12943i	−0.990269	+	0.139163i	$0.955559\pi$
$284$	5.65685			0.335673
$285$		0			0
$286$	−8.00000			−0.473050
$287$	25.4558	−	25.4558i	1.50261	−	1.50261i
$288$		0			0
$289$			1.00000i			0.0588235i
$290$	2.82843	−	5.65685i	0.166091	−	0.332182i
$291$		0			0
$292$	3.00000	+	3.00000i	0.175562	+	0.175562i
$293$	12.7279	+	12.7279i	0.743573	+	0.743573i	0.973264	−	0.229691i	$-0.0737714\pi$
$293$	12.7279	+	12.7279i	0.743573	+	0.743573i	−0.229691	+	0.973264i	$0.573771\pi$
$294$		0			0
$295$	−12.0000	+	4.00000i	−0.698667	+	0.232889i
$296$			8.48528i			0.493197i
$297$		0			0
$298$	−13.0000	+	13.0000i	−0.753070	+	0.753070i
$299$		0			0
$300$		0			0
$301$	18.0000			1.03750
$302$	11.3137	−	11.3137i	0.651031	−	0.651031i
$303$		0			0
$304$			1.00000i			0.0573539i
$305$	−21.2132	+	7.07107i	−1.21466	+	0.404888i
$306$		0			0
$307$	−10.0000	−	10.0000i	−0.570730	−	0.570730i	0.361602	−	0.932332i	$-0.382230\pi$
$307$	−10.0000	−	10.0000i	−0.570730	−	0.570730i	−0.932332	+	0.361602i	$0.882230\pi$
$308$	4.24264	+	4.24264i	0.241747	+	0.241747i
$309$		0			0
$310$	−4.00000	+	8.00000i	−0.227185	+	0.454369i
$311$			21.2132i			1.20289i	0.798914	+	0.601445i	$0.205408\pi$
$311$			21.2132i			1.20289i	−0.798914	+	0.601445i	$0.794592\pi$
$312$		0			0
$313$	−7.00000	+	7.00000i	−0.395663	+	0.395663i	−0.876700	−	0.481037i	$-0.840260\pi$
$313$	−7.00000	+	7.00000i	−0.395663	+	0.395663i	0.481037	+	0.876700i	$0.340260\pi$
$314$	9.89949			0.558661
$315$		0			0
$316$	4.00000			0.225018
$317$	4.24264	−	4.24264i	0.238290	−	0.238290i	−0.577851	−	0.816142i	$-0.696109\pi$
$317$	4.24264	−	4.24264i	0.238290	−	0.238290i	0.816142	+	0.577851i	$0.196109\pi$
$318$		0			0
$319$			4.00000i			0.223957i
$320$	−0.707107	−	2.12132i	−0.0395285	−	0.118585i
$321$		0			0
$322$		0			0
$323$	−2.82843	−	2.82843i	−0.157378	−	0.157378i
$324$		0			0
$325$	4.00000	−	28.0000i	0.221880	−	1.55316i
$326$		−	1.41421i		−	0.0783260i
$327$		0			0
$328$	6.00000	−	6.00000i	0.331295	−	0.331295i
$329$	−33.9411			−1.87123
$330$		0			0
$331$	12.0000			0.659580			0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000			0.659580			0.329790	+	0.944054i	$0.393022\pi$
$332$	4.24264	−	4.24264i	0.232845	−	0.232845i
$333$		0			0
$334$		0			0
$335$	28.2843	+	14.1421i	1.54533	+	0.772667i
$336$		0			0
$337$	−12.0000	−	12.0000i	−0.653682	−	0.653682i	0.300196	−	0.953878i	$-0.402948\pi$
$337$	−12.0000	−	12.0000i	−0.653682	−	0.653682i	−0.953878	+	0.300196i	$0.902948\pi$
$338$	13.4350	+	13.4350i	0.730769	+	0.730769i
$339$		0			0
$340$	8.00000	+	4.00000i	0.433861	+	0.216930i
$341$		−	5.65685i		−	0.306336i
$342$		0			0
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$	4.24264			0.228748
$345$		0			0
$346$	6.00000			0.322562
$347$	21.2132	−	21.2132i	1.13878	−	1.13878i	0.150116	−	0.988668i	$-0.452035\pi$
$347$	21.2132	−	21.2132i	1.13878	−	1.13878i	0.988668	−	0.150116i	$-0.0479647\pi$
$348$		0			0
$349$		−	12.0000i		−	0.642345i	−0.947021	−	0.321173i	$-0.895923\pi$
$349$		−	12.0000i		−	0.642345i	0.947021	−	0.321173i	$-0.104077\pi$
$350$	−16.9706	+	12.7279i	−0.907115	+	0.680336i
$351$		0			0
$352$	1.00000	+	1.00000i	0.0533002	+	0.0533002i
$353$	−12.7279	−	12.7279i	−0.677439	−	0.677439i	0.281981	−	0.959420i	$-0.409008\pi$
$353$	−12.7279	−	12.7279i	−0.677439	−	0.677439i	−0.959420	+	0.281981i	$0.909008\pi$
$354$		0			0
$355$	−4.00000	−	12.0000i	−0.212298	−	0.636894i
$356$		−	14.1421i		−	0.749532i
$357$		0			0
$358$	8.00000	−	8.00000i	0.422813	−	0.422813i
$359$	12.7279			0.671754			0.335877	−	0.941906i	$-0.390967\pi$
$359$	12.7279			0.671754			0.335877	+	0.941906i	$0.390967\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	−12.7279	+	12.7279i	−0.668965	+	0.668965i
$363$		0			0
$364$		−	24.0000i		−	1.25794i
$365$	4.24264	−	8.48528i	0.222070	−	0.444140i
$366$		0			0
$367$	−15.0000	−	15.0000i	−0.782994	−	0.782994i	0.197341	−	0.980335i	$-0.436769\pi$
$367$	−15.0000	−	15.0000i	−0.782994	−	0.782994i	−0.980335	+	0.197341i	$0.936769\pi$
$368$		0			0
$369$		0			0
$370$	18.0000	−	6.00000i	0.935775	−	0.311925i
$371$		−	8.48528i		−	0.440534i
$372$		0			0
$373$	24.0000	−	24.0000i	1.24267	−	1.24267i	0.283785	−	0.958888i	$-0.408410\pi$
$373$	24.0000	−	24.0000i	1.24267	−	1.24267i	0.958888	−	0.283785i	$-0.0915902\pi$
$374$	−5.65685			−0.292509
$375$		0			0
$376$	−8.00000			−0.412568
$377$	11.3137	−	11.3137i	0.582686	−	0.582686i
$378$		0			0
$379$			8.00000i			0.410932i	0.978664	+	0.205466i	$0.0658711\pi$
$379$			8.00000i			0.410932i	−0.978664	+	0.205466i	$0.934129\pi$
$380$	2.12132	−	0.707107i	0.108821	−	0.0362738i
$381$		0			0
$382$	17.0000	+	17.0000i	0.869796	+	0.869796i
$383$	19.7990	+	19.7990i	1.01168	+	1.01168i	0.999931	+	0.0117502i	$0.00374028\pi$
$383$	19.7990	+	19.7990i	1.01168	+	1.01168i	0.0117502	+	0.999931i	$0.496260\pi$
$384$		0			0
$385$	6.00000	−	12.0000i	0.305788	−	0.611577i
$386$		−	25.4558i		−	1.29567i
$387$		0			0
$388$	12.0000	−	12.0000i	0.609208	−	0.609208i
$389$	1.41421			0.0717035			0.0358517	−	0.999357i	$-0.488586\pi$
$389$	1.41421			0.0717035			0.0358517	+	0.999357i	$0.488586\pi$
$390$		0			0
$391$		0			0
$392$	−7.77817	+	7.77817i	−0.392857	+	0.392857i
$393$		0			0
$394$		−	22.0000i		−	1.10834i
$395$	−2.82843	−	8.48528i	−0.142314	−	0.426941i
$396$		0			0
$397$	−15.0000	−	15.0000i	−0.752828	−	0.752828i	0.222178	−	0.975006i	$-0.428683\pi$
$397$	−15.0000	−	15.0000i	−0.752828	−	0.752828i	−0.975006	+	0.222178i	$0.928683\pi$
$398$	−1.41421	−	1.41421i	−0.0708881	−	0.0708881i
$399$		0			0
$400$	−4.00000	+	3.00000i	−0.200000	+	0.150000i
$401$			11.3137i			0.564980i	0.959270	+	0.282490i	$0.0911603\pi$
$401$			11.3137i			0.564980i	−0.959270	+	0.282490i	$0.908840\pi$
$402$		0			0
$403$	−16.0000	+	16.0000i	−0.797017	+	0.797017i
$404$	15.5563			0.773957
$405$		0			0
$406$	−12.0000			−0.595550
$407$	−8.48528	+	8.48528i	−0.420600	+	0.420600i
$408$		0			0
$409$			14.0000i			0.692255i	0.938187	+	0.346128i	$0.112504\pi$
$409$			14.0000i			0.692255i	−0.938187	+	0.346128i	$0.887496\pi$
$410$	−16.9706	−	8.48528i	−0.838116	−	0.419058i
$411$		0			0
$412$		0			0
$413$	16.9706	+	16.9706i	0.835067	+	0.835067i
$414$		0			0
$415$	−12.0000	−	6.00000i	−0.589057	−	0.294528i
$416$		−	5.65685i		−	0.277350i
$417$		0			0
$418$	−1.00000	+	1.00000i	−0.0489116	+	0.0489116i
$419$	−26.8701			−1.31269			−0.656344	−	0.754462i	$-0.727898\pi$
$419$	−26.8701			−1.31269			−0.656344	+	0.754462i	$0.727898\pi$
$420$		0			0
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$	−11.3137	+	11.3137i	−0.550743	+	0.550743i
$423$		0			0
$424$		−	2.00000i		−	0.0971286i
$425$	2.82843	−	19.7990i	0.137199	−	0.960392i
$426$		0			0
$427$	30.0000	+	30.0000i	1.45180	+	1.45180i
$428$	−8.48528	−	8.48528i	−0.410152	−	0.410152i
$429$		0			0
$430$	−3.00000	−	9.00000i	−0.144673	−	0.434019i
$431$		−	19.7990i		−	0.953684i	−0.878989	−	0.476842i	$-0.841781\pi$
$431$		−	19.7990i		−	0.953684i	0.878989	−	0.476842i	$-0.158219\pi$
$432$		0			0
$433$	−6.00000	+	6.00000i	−0.288342	+	0.288342i	−0.836424	−	0.548083i	$-0.815358\pi$
$433$	−6.00000	+	6.00000i	−0.288342	+	0.288342i	0.548083	+	0.836424i	$0.315358\pi$
$434$	16.9706			0.814613
$435$		0			0
$436$	2.00000			0.0957826
$437$		0			0
$438$		0			0
$439$			16.0000i			0.763638i	0.924237	+	0.381819i	$0.124702\pi$
$439$			16.0000i			0.763638i	−0.924237	+	0.381819i	$0.875298\pi$
$440$	1.41421	−	2.82843i	0.0674200	−	0.134840i
$441$		0			0
$442$	16.0000	+	16.0000i	0.761042	+	0.761042i
$443$	−25.4558	−	25.4558i	−1.20944	−	1.20944i	−0.971207	−	0.238236i	$-0.923431\pi$
$443$	−25.4558	−	25.4558i	−1.20944	−	1.20944i	−0.238236	−	0.971207i	$-0.576569\pi$
$444$		0			0
$445$	−30.0000	+	10.0000i	−1.42214	+	0.474045i
$446$		−	16.9706i		−	0.803579i
$447$		0			0
$448$	−3.00000	+	3.00000i	−0.141737	+	0.141737i
$449$	36.7696			1.73526			0.867631	−	0.497208i	$-0.165642\pi$
$449$	36.7696			1.73526			0.867631	+	0.497208i	$0.165642\pi$
$450$		0			0
$451$	12.0000			0.565058
$452$	1.41421	−	1.41421i	0.0665190	−	0.0665190i
$453$		0			0
$454$		0			0
$455$	−50.9117	+	16.9706i	−2.38678	+	0.795592i
$456$		0			0
$457$	−17.0000	−	17.0000i	−0.795226	−	0.795226i	0.187112	−	0.982339i	$-0.440087\pi$
$457$	−17.0000	−	17.0000i	−0.795226	−	0.795226i	−0.982339	+	0.187112i	$0.940087\pi$
$458$	5.65685	+	5.65685i	0.264327	+	0.264327i
$459$		0			0
$460$		0			0
$461$		−	24.0416i		−	1.11973i	−0.828584	−	0.559865i	$-0.810853\pi$
$461$		−	24.0416i		−	1.11973i	0.828584	−	0.559865i	$-0.189147\pi$
$462$		0			0
$463$	−15.0000	+	15.0000i	−0.697109	+	0.697109i	−0.963786	−	0.266677i	$-0.914074\pi$
$463$	−15.0000	+	15.0000i	−0.697109	+	0.697109i	0.266677	+	0.963786i	$0.414074\pi$
$464$	−2.82843			−0.131306
$465$		0			0
$466$	10.0000			0.463241
$467$	25.4558	−	25.4558i	1.17796	−	1.17796i	0.197692	−	0.980264i	$-0.436655\pi$
$467$	25.4558	−	25.4558i	1.17796	−	1.17796i	0.980264	−	0.197692i	$-0.0633445\pi$
$468$		0			0
$469$		−	60.0000i		−	2.77054i
$470$	5.65685	+	16.9706i	0.260931	+	0.782794i
$471$		0			0
$472$	4.00000	+	4.00000i	0.184115	+	0.184115i
$473$	4.24264	+	4.24264i	0.195077	+	0.195077i
$474$		0			0
$475$	−3.00000	−	4.00000i	−0.137649	−	0.183533i
$476$		−	16.9706i		−	0.777844i
$477$		0			0
$478$	13.0000	−	13.0000i	0.594606	−	0.594606i
$479$	−1.41421			−0.0646171			−0.0323085	−	0.999478i	$-0.510286\pi$
$479$	−1.41421			−0.0646171			−0.0323085	+	0.999478i	$0.510286\pi$
$480$		0			0
$481$	48.0000			2.18861
$482$	7.07107	−	7.07107i	0.322078	−	0.322078i
$483$		0			0
$484$		−	9.00000i		−	0.409091i
$485$	−33.9411	−	16.9706i	−1.54119	−	0.770594i
$486$		0			0
$487$	−28.0000	−	28.0000i	−1.26880	−	1.26880i	−0.946708	−	0.322093i	$-0.895614\pi$
$487$	−28.0000	−	28.0000i	−1.26880	−	1.26880i	−0.322093	−	0.946708i	$-0.604386\pi$
$488$	7.07107	+	7.07107i	0.320092	+	0.320092i
$489$		0			0
$490$	22.0000	+	11.0000i	0.993859	+	0.496929i
$491$			7.07107i			0.319113i	0.987189	+	0.159556i	$0.0510064\pi$
$491$			7.07107i			0.319113i	−0.987189	+	0.159556i	$0.948994\pi$
$492$		0			0
$493$	8.00000	−	8.00000i	0.360302	−	0.360302i
$494$	5.65685			0.254514
$495$		0			0
$496$	4.00000			0.179605
$497$	−16.9706	+	16.9706i	−0.761234	+	0.761234i
$498$		0			0
$499$			30.0000i			1.34298i	0.741012	+	0.671492i	$0.234346\pi$
$499$			30.0000i			1.34298i	−0.741012	+	0.671492i	$0.765654\pi$
$500$	9.19239	+	6.36396i	0.411096	+	0.284605i
$501$		0			0
$502$	13.0000	+	13.0000i	0.580218	+	0.580218i
$503$	−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	$0.764197\pi$
$504$		0			0
$505$	−11.0000	−	33.0000i	−0.489494	−	1.46848i
$506$		0			0
$507$		0			0
$508$	−10.0000	+	10.0000i	−0.443678	+	0.443678i
$509$	16.9706			0.752207			0.376103	−	0.926578i	$-0.377264\pi$
$509$	16.9706			0.752207			0.376103	+	0.926578i	$0.377264\pi$
$510$		0			0
$511$	−18.0000			−0.796273
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			22.0000i			0.970378i
$515$		0			0
$516$		0			0
$517$	−8.00000	−	8.00000i	−0.351840	−	0.351840i
$518$	−25.4558	−	25.4558i	−1.11847	−	1.11847i
$519$		0			0
$520$	−12.0000	+	4.00000i	−0.526235	+	0.175412i
$521$			5.65685i			0.247831i	0.992293	+	0.123916i	$0.0395452\pi$
$521$			5.65685i			0.247831i	−0.992293	+	0.123916i	$0.960455\pi$
$522$		0			0
$523$	8.00000	−	8.00000i	0.349816	−	0.349816i	−0.510225	−	0.860041i	$-0.670438\pi$
$523$	8.00000	−	8.00000i	0.349816	−	0.349816i	0.860041	+	0.510225i	$0.170438\pi$
$524$	12.7279			0.556022
$525$		0			0
$526$	−10.0000			−0.436021
$527$	−11.3137	+	11.3137i	−0.492833	+	0.492833i
$528$		0			0
$529$		−	23.0000i		−	1.00000i
$530$	−4.24264	+	1.41421i	−0.184289	+	0.0614295i
$531$		0			0
$532$	−3.00000	−	3.00000i	−0.130066	−	0.130066i
$533$	−33.9411	−	33.9411i	−1.47015	−	1.47015i
$534$		0			0
$535$	−12.0000	+	24.0000i	−0.518805	+	1.03761i
$536$		−	14.1421i		−	0.610847i
$537$		0			0
$538$	−2.00000	+	2.00000i	−0.0862261	+	0.0862261i
$539$	−15.5563			−0.670059
$540$		0			0
$541$	8.00000			0.343947			0.171973	−	0.985102i	$-0.444986\pi$
$541$	8.00000			0.343947			0.171973	+	0.985102i	$0.444986\pi$
$542$	9.89949	−	9.89949i	0.425220	−	0.425220i
$543$		0			0
$544$		−	4.00000i		−	0.171499i
$545$	−1.41421	−	4.24264i	−0.0605783	−	0.181735i
$546$		0			0
$547$	−18.0000	−	18.0000i	−0.769624	−	0.769624i	0.208416	−	0.978040i	$-0.433169\pi$
$547$	−18.0000	−	18.0000i	−0.769624	−	0.769624i	−0.978040	+	0.208416i	$0.933169\pi$
$548$		0			0
$549$		0			0
$550$	−7.00000	−	1.00000i	−0.298481	−	0.0426401i
$551$		−	2.82843i		−	0.120495i
$552$		0			0
$553$	−12.0000	+	12.0000i	−0.510292	+	0.510292i
$554$	−21.2132			−0.901263
$555$		0			0
$556$	14.0000			0.593732
$557$	12.7279	−	12.7279i	0.539299	−	0.539299i	−0.384024	−	0.923323i	$-0.625462\pi$
$557$	12.7279	−	12.7279i	0.539299	−	0.539299i	0.923323	+	0.384024i	$0.125462\pi$
$558$		0			0
$559$		−	24.0000i		−	1.01509i
$560$	8.48528	+	4.24264i	0.358569	+	0.179284i
$561$		0			0
$562$	16.0000	+	16.0000i	0.674919	+	0.674919i
$563$	11.3137	+	11.3137i	0.476816	+	0.476816i	0.904112	−	0.427296i	$-0.140534\pi$
$563$	11.3137	+	11.3137i	0.476816	+	0.476816i	−0.427296	+	0.904112i	$0.640534\pi$
$564$		0			0
$565$	−4.00000	−	2.00000i	−0.168281	−	0.0841406i
$566$		−	26.8701i		−	1.12943i
$567$		0			0
$568$	−4.00000	+	4.00000i	−0.167836	+	0.167836i
$569$	−31.1127			−1.30431			−0.652156	−	0.758085i	$-0.726135\pi$
$569$	−31.1127			−1.30431			−0.652156	+	0.758085i	$0.726135\pi$
$570$		0			0
$571$	−26.0000			−1.08807			−0.544033	−	0.839064i	$-0.683103\pi$
$571$	−26.0000			−1.08807			−0.544033	+	0.839064i	$0.683103\pi$
$572$	5.65685	−	5.65685i	0.236525	−	0.236525i
$573$		0			0
$574$			36.0000i			1.50261i
$575$		0			0
$576$		0			0
$577$	−15.0000	−	15.0000i	−0.624458	−	0.624458i	0.322210	−	0.946668i	$-0.395574\pi$
$577$	−15.0000	−	15.0000i	−0.624458	−	0.624458i	−0.946668	+	0.322210i	$0.895574\pi$
$578$	−0.707107	−	0.707107i	−0.0294118	−	0.0294118i
$579$		0			0
$580$	2.00000	+	6.00000i	0.0830455	+	0.249136i
$581$			25.4558i			1.05609i
$582$		0			0
$583$	2.00000	−	2.00000i	0.0828315	−	0.0828315i
$584$	−4.24264			−0.175562
$585$		0			0
$586$	−18.0000			−0.743573
$587$	−8.48528	+	8.48528i	−0.350225	+	0.350225i	−0.860193	−	0.509968i	$-0.829657\pi$
$587$	−8.48528	+	8.48528i	−0.350225	+	0.350225i	0.509968	+	0.860193i	$0.329657\pi$
$588$		0			0
$589$			4.00000i			0.164817i
$590$	5.65685	−	11.3137i	0.232889	−	0.465778i
$591$		0			0
$592$	−6.00000	−	6.00000i	−0.246598	−	0.246598i
$593$	−25.4558	−	25.4558i	−1.04535	−	1.04535i	−0.998922	−	0.0464244i	$-0.985217\pi$
$593$	−25.4558	−	25.4558i	−1.04535	−	1.04535i	−0.0464244	−	0.998922i	$-0.514783\pi$
$594$		0			0
$595$	−36.0000	+	12.0000i	−1.47586	+	0.491952i
$596$		−	18.3848i		−	0.753070i
$597$		0			0
$598$		0			0
$599$	−25.4558			−1.04010			−0.520049	−	0.854137i	$-0.674086\pi$
$599$	−25.4558			−1.04010			−0.520049	+	0.854137i	$0.674086\pi$
$600$		0			0
$601$	38.0000			1.55005			0.775026	−	0.631929i	$-0.217737\pi$
$601$	38.0000			1.55005			0.775026	+	0.631929i	$0.217737\pi$
$602$	−12.7279	+	12.7279i	−0.518751	+	0.518751i
$603$		0			0
$604$			16.0000i			0.651031i
$605$	−19.0919	+	6.36396i	−0.776195	+	0.258732i
$606$		0			0
$607$	8.00000	+	8.00000i	0.324710	+	0.324710i	0.850571	−	0.525861i	$-0.176257\pi$
$607$	8.00000	+	8.00000i	0.324710	+	0.324710i	−0.525861	+	0.850571i	$0.676257\pi$
$608$	−0.707107	−	0.707107i	−0.0286770	−	0.0286770i
$609$		0			0
$610$	10.0000	−	20.0000i	0.404888	−	0.809776i
$611$			45.2548i			1.83081i
$612$		0			0
$613$	29.0000	−	29.0000i	1.17130	−	1.17130i	0.189399	−	0.981900i	$-0.439346\pi$
$613$	29.0000	−	29.0000i	1.17130	−	1.17130i	0.981900	−	0.189399i	$-0.0606539\pi$
$614$	14.1421			0.570730
$615$		0			0
$616$	−6.00000			−0.241747
$617$	8.48528	−	8.48528i	0.341605	−	0.341605i	−0.515366	−	0.856970i	$-0.672344\pi$
$617$	8.48528	−	8.48528i	0.341605	−	0.341605i	0.856970	+	0.515366i	$0.172344\pi$
$618$		0			0
$619$			30.0000i			1.20580i	0.797816	+	0.602901i	$0.205989\pi$
$619$			30.0000i			1.20580i	−0.797816	+	0.602901i	$0.794011\pi$
$620$	−2.82843	−	8.48528i	−0.113592	−	0.340777i
$621$		0			0
$622$	−15.0000	−	15.0000i	−0.601445	−	0.601445i
$623$	42.4264	+	42.4264i	1.69978	+	1.69978i
$624$		0			0
$625$	7.00000	−	24.0000i	0.280000	−	0.960000i
$626$		−	9.89949i		−	0.395663i
$627$		0			0
$628$	−7.00000	+	7.00000i	−0.279330	+	0.279330i
$629$	33.9411			1.35332
$630$		0			0
$631$	40.0000			1.59237			0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000			1.59237			0.796187	+	0.605050i	$0.206847\pi$
$632$	−2.82843	+	2.82843i	−0.112509	+	0.112509i
$633$		0			0
$634$			6.00000i			0.238290i
$635$	28.2843	+	14.1421i	1.12243	+	0.561214i
$636$		0			0
$637$	44.0000	+	44.0000i	1.74334	+	1.74334i
$638$	−2.82843	−	2.82843i	−0.111979	−	0.111979i
$639$		0			0
$640$	2.00000	+	1.00000i	0.0790569	+	0.0395285i
$641$			2.82843i			0.111716i	0.998439	+	0.0558581i	$0.0177894\pi$
$641$			2.82843i			0.111716i	−0.998439	+	0.0558581i	$0.982211\pi$
$642$		0			0
$643$	19.0000	−	19.0000i	0.749287	−	0.749287i	−0.225058	−	0.974345i	$-0.572257\pi$
$643$	19.0000	−	19.0000i	0.749287	−	0.749287i	0.974345	+	0.225058i	$0.0722573\pi$
$644$		0			0
$645$		0			0
$646$	4.00000			0.157378
$647$	−32.5269	+	32.5269i	−1.27876	+	1.27876i	−0.337405	+	0.941359i	$0.609549\pi$
$647$	−32.5269	+	32.5269i	−1.27876	+	1.27876i	−0.941359	+	0.337405i	$0.890451\pi$
$648$		0			0
$649$			8.00000i			0.314027i
$650$	16.9706	+	22.6274i	0.665640	+	0.887520i
$651$		0			0
$652$	1.00000	+	1.00000i	0.0391630	+	0.0391630i
$653$	−25.4558	−	25.4558i	−0.996164	−	0.996164i	0.00382851	−	0.999993i	$-0.498781\pi$
$653$	−25.4558	−	25.4558i	−0.996164	−	0.996164i	−0.999993	+	0.00382851i	$0.998781\pi$
$654$		0			0
$655$	−9.00000	−	27.0000i	−0.351659	−	1.05498i
$656$			8.48528i			0.331295i
$657$		0			0
$658$	24.0000	−	24.0000i	0.935617	−	0.935617i
$659$	25.4558			0.991619			0.495809	−	0.868431i	$-0.334871\pi$
$659$	25.4558			0.991619			0.495809	+	0.868431i	$0.334871\pi$
$660$		0			0
$661$	34.0000			1.32245			0.661223	−	0.750189i	$-0.270038\pi$
$661$	34.0000			1.32245			0.661223	+	0.750189i	$0.270038\pi$
$662$	−8.48528	+	8.48528i	−0.329790	+	0.329790i
$663$		0			0
$664$			6.00000i			0.232845i
$665$	−4.24264	+	8.48528i	−0.164523	+	0.329045i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$	−30.0000	+	10.0000i	−1.15900	+	0.386334i
$671$			14.1421i			0.545951i
$672$		0			0
$673$	12.0000	−	12.0000i	0.462566	−	0.462566i	−0.436930	−	0.899496i	$-0.643934\pi$
$673$	12.0000	−	12.0000i	0.462566	−	0.462566i	0.899496	+	0.436930i	$0.143934\pi$
$674$	16.9706			0.653682
$675$		0			0
$676$	−19.0000			−0.730769
$677$	−4.24264	+	4.24264i	−0.163058	+	0.163058i	−0.783920	−	0.620862i	$-0.786783\pi$
$677$	−4.24264	+	4.24264i	−0.163058	+	0.163058i	0.620862	+	0.783920i	$0.286783\pi$
$678$		0			0
$679$			72.0000i			2.76311i
$680$	−8.48528	+	2.82843i	−0.325396	+	0.108465i
$681$		0			0
$682$	4.00000	+	4.00000i	0.153168	+	0.153168i
$683$	28.2843	+	28.2843i	1.08227	+	1.08227i	0.996298	+	0.0859698i	$0.0273989\pi$
$683$	28.2843	+	28.2843i	1.08227	+	1.08227i	0.0859698	+	0.996298i	$0.472601\pi$
$684$		0			0
$685$		0			0
$686$		−	16.9706i		−	0.647939i
$687$		0			0
$688$	−3.00000	+	3.00000i	−0.114374	+	0.114374i
$689$	−11.3137			−0.431018
$690$		0			0
$691$	10.0000			0.380418			0.190209	−	0.981744i	$-0.439083\pi$
$691$	10.0000			0.380418			0.190209	+	0.981744i	$0.439083\pi$
$692$	−4.24264	+	4.24264i	−0.161281	+	0.161281i
$693$		0			0
$694$			30.0000i			1.13878i
$695$	−9.89949	−	29.6985i	−0.375509	−	1.12653i
$696$		0			0
$697$	−24.0000	−	24.0000i	−0.909065	−	0.909065i
$698$	8.48528	+	8.48528i	0.321173	+	0.321173i
$699$		0			0
$700$	3.00000	−	21.0000i	0.113389	−	0.793725i
$701$			38.1838i			1.44218i	0.692841	+	0.721090i	$0.256359\pi$
$701$			38.1838i			1.44218i	−0.692841	+	0.721090i	$0.743641\pi$
$702$		0			0
$703$	6.00000	−	6.00000i	0.226294	−	0.226294i
$704$	−1.41421			−0.0533002
$705$		0			0
$706$	18.0000			0.677439
$707$	−46.6690	+	46.6690i	−1.75517	+	1.75517i
$708$		0			0
$709$			32.0000i			1.20179i	0.799330	+	0.600893i	$0.205188\pi$
$709$			32.0000i			1.20179i	−0.799330	+	0.600893i	$0.794812\pi$
$710$	11.3137	+	5.65685i	0.424596	+	0.212298i
$711$		0			0
$712$	10.0000	+	10.0000i	0.374766	+	0.374766i
$713$		0			0
$714$		0			0
$715$	−16.0000	−	8.00000i	−0.598366	−	0.299183i
$716$			11.3137i			0.422813i
$717$		0			0
$718$	−9.00000	+	9.00000i	−0.335877	+	0.335877i
$719$	−9.89949			−0.369189			−0.184594	−	0.982815i	$-0.559097\pi$
$719$	−9.89949			−0.369189			−0.184594	+	0.982815i	$0.559097\pi$
$720$		0			0
$721$		0			0
$722$	0.707107	−	0.707107i	0.0263158	−	0.0263158i
$723$		0			0
$724$		−	18.0000i		−	0.668965i
$725$	11.3137	−	8.48528i	0.420181	−	0.315135i
$726$		0			0
$727$	11.0000	+	11.0000i	0.407967	+	0.407967i	0.881029	−	0.473062i	$-0.156851\pi$
$727$	11.0000	+	11.0000i	0.407967	+	0.407967i	−0.473062	+	0.881029i	$0.656851\pi$
$728$	16.9706	+	16.9706i	0.628971	+	0.628971i
$729$		0			0
$730$	3.00000	+	9.00000i	0.111035	+	0.333105i
$731$		−	16.9706i		−	0.627679i
$732$		0			0
$733$	−21.0000	+	21.0000i	−0.775653	+	0.775653i	−0.979088	−	0.203436i	$-0.934789\pi$
$733$	−21.0000	+	21.0000i	−0.775653	+	0.775653i	0.203436	+	0.979088i	$0.434789\pi$
$734$	21.2132			0.782994
$735$		0			0
$736$		0			0
$737$	14.1421	−	14.1421i	0.520932	−	0.520932i
$738$		0			0
$739$		−	20.0000i		−	0.735712i	−0.929883	−	0.367856i	$-0.880092\pi$
$739$		−	20.0000i		−	0.735712i	0.929883	−	0.367856i	$-0.119908\pi$
$740$	−8.48528	+	16.9706i	−0.311925	+	0.623850i
$741$		0			0
$742$	6.00000	+	6.00000i	0.220267	+	0.220267i
$743$	33.9411	+	33.9411i	1.24518	+	1.24518i	0.957824	+	0.287355i	$0.0927759\pi$
$743$	33.9411	+	33.9411i	1.24518	+	1.24518i	0.287355	+	0.957824i	$0.407224\pi$
$744$		0			0
$745$	−39.0000	+	13.0000i	−1.42885	+	0.476283i
$746$			33.9411i			1.24267i
$747$		0			0
$748$	4.00000	−	4.00000i	0.146254	−	0.146254i
$749$	50.9117			1.86027
$750$		0			0
$751$	−16.0000			−0.583848			−0.291924	−	0.956441i	$-0.594295\pi$
$751$	−16.0000			−0.583848			−0.291924	+	0.956441i	$0.594295\pi$
$752$	5.65685	−	5.65685i	0.206284	−	0.206284i
$753$		0			0
$754$			16.0000i			0.582686i
$755$	33.9411	−	11.3137i	1.23524	−	0.411748i
$756$		0			0
$757$	19.0000	+	19.0000i	0.690567	+	0.690567i	0.962357	−	0.271790i	$-0.0876156\pi$
$757$	19.0000	+	19.0000i	0.690567	+	0.690567i	−0.271790	+	0.962357i	$0.587616\pi$
$758$	−5.65685	−	5.65685i	−0.205466	−	0.205466i
$759$		0			0
$760$	−1.00000	+	2.00000i	−0.0362738	+	0.0725476i
$761$			21.2132i			0.768978i	0.923130	+	0.384489i	$0.125622\pi$
$761$			21.2132i			0.768978i	−0.923130	+	0.384489i	$0.874378\pi$
$762$		0			0
$763$	−6.00000	+	6.00000i	−0.217215	+	0.217215i
$764$	−24.0416			−0.869796
$765$		0			0
$766$	−28.0000			−1.01168
$767$	22.6274	−	22.6274i	0.817029	−	0.817029i
$768$		0			0
$769$			16.0000i			0.576975i	0.957484	+	0.288487i	$0.0931523\pi$
$769$			16.0000i			0.576975i	−0.957484	+	0.288487i	$0.906848\pi$
$770$	4.24264	+	12.7279i	0.152894	+	0.458682i
$771$		0			0
$772$	18.0000	+	18.0000i	0.647834	+	0.647834i
$773$	18.3848	+	18.3848i	0.661254	+	0.661254i	0.955676	−	0.294421i	$-0.0951269\pi$
$773$	18.3848	+	18.3848i	0.661254	+	0.661254i	−0.294421	+	0.955676i	$0.595127\pi$
$774$		0			0
$775$	−16.0000	+	12.0000i	−0.574737	+	0.431053i
$776$			16.9706i			0.609208i
$777$		0			0
$778$	−1.00000	+	1.00000i	−0.0358517	+	0.0358517i
$779$	−8.48528			−0.304017
$780$		0			0
$781$	−8.00000			−0.286263
$782$		0			0
$783$		0			0
$784$		−	11.0000i		−	0.392857i
$785$	19.7990	+	9.89949i	0.706656	+	0.353328i
$786$		0			0
$787$	−28.0000	−	28.0000i	−0.998092	−	0.998092i	0.00190598	−	0.999998i	$-0.499393\pi$
$787$	−28.0000	−	28.0000i	−0.998092	−	0.998092i	−0.999998	+	0.00190598i	$0.999393\pi$
$788$	15.5563	+	15.5563i	0.554172	+	0.554172i
$789$		0			0
$790$	8.00000	+	4.00000i	0.284627	+	0.142314i
$791$			8.48528i			0.301702i
$792$		0			0
$793$	40.0000	−	40.0000i	1.42044	−	1.42044i
$794$	21.2132			0.752828
$795$		0			0
$796$	2.00000			0.0708881
$797$	15.5563	−	15.5563i	0.551034	−	0.551034i	−0.375705	−	0.926739i	$-0.622599\pi$
$797$	15.5563	−	15.5563i	0.551034	−	0.551034i	0.926739	+	0.375705i	$0.122599\pi$
$798$		0			0
$799$			32.0000i			1.13208i
$800$	0.707107	−	4.94975i	0.0250000	−	0.175000i
$801$		0			0
$802$	−8.00000	−	8.00000i	−0.282490	−	0.282490i
$803$	−4.24264	−	4.24264i	−0.149720	−	0.149720i
$804$		0			0
$805$		0			0
$806$		−	22.6274i		−	0.797017i
$807$		0			0
$808$	−11.0000	+	11.0000i	−0.386979	+	0.386979i
$809$	−26.8701			−0.944701			−0.472350	−	0.881411i	$-0.656594\pi$
$809$	−26.8701			−0.944701			−0.472350	+	0.881411i	$0.656594\pi$
$810$		0			0
$811$	16.0000			0.561836			0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000			0.561836			0.280918	+	0.959732i	$0.409361\pi$
$812$	8.48528	−	8.48528i	0.297775	−	0.297775i
$813$		0			0
$814$		−	12.0000i		−	0.420600i
$815$	1.41421	−	2.82843i	0.0495377	−	0.0990755i
$816$		0			0
$817$	−3.00000	−	3.00000i	−0.104957	−	0.104957i
$818$	−9.89949	−	9.89949i	−0.346128	−	0.346128i
$819$		0			0
$820$	18.0000	−	6.00000i	0.628587	−	0.209529i
$821$			26.8701i			0.937771i	0.883259	+	0.468886i	$0.155344\pi$
$821$			26.8701i			0.937771i	−0.883259	+	0.468886i	$0.844656\pi$
$822$		0			0
$823$	25.0000	−	25.0000i	0.871445	−	0.871445i	−0.121185	−	0.992630i	$-0.538669\pi$
$823$	25.0000	−	25.0000i	0.871445	−	0.871445i	0.992630	+	0.121185i	$0.0386693\pi$
$824$		0			0
$825$		0			0
$826$	−24.0000			−0.835067
$827$	−14.1421	+	14.1421i	−0.491770	+	0.491770i	−0.908864	−	0.417093i	$-0.863049\pi$
$827$	−14.1421	+	14.1421i	−0.491770	+	0.491770i	0.417093	+	0.908864i	$0.363049\pi$
$828$		0			0
$829$			6.00000i			0.208389i	0.994557	+	0.104194i	$0.0332264\pi$
$829$			6.00000i			0.208389i	−0.994557	+	0.104194i	$0.966774\pi$
$830$	12.7279	−	4.24264i	0.441793	−	0.147264i
$831$		0			0
$832$	4.00000	+	4.00000i	0.138675	+	0.138675i
$833$	31.1127	+	31.1127i	1.07799	+	1.07799i
$834$		0			0
$835$		0			0
$836$		−	1.41421i		−	0.0489116i
$837$		0			0
$838$	19.0000	−	19.0000i	0.656344	−	0.656344i
$839$	−33.9411			−1.17178			−0.585889	−	0.810391i	$-0.699255\pi$
$839$	−33.9411			−1.17178			−0.585889	+	0.810391i	$0.699255\pi$
$840$		0			0
$841$	−21.0000			−0.724138
$842$	−1.41421	+	1.41421i	−0.0487370	+	0.0487370i
$843$		0			0
$844$		−	16.0000i		−	0.550743i
$845$	13.4350	+	40.3051i	0.462179	+	1.38654i
$846$		0			0
$847$	27.0000	+	27.0000i	0.927731	+	0.927731i
$848$	1.41421	+	1.41421i	0.0485643	+	0.0485643i
$849$		0			0
$850$	12.0000	+	16.0000i	0.411597	+	0.548795i
$851$		0			0
$852$		0			0
$853$	−23.0000	+	23.0000i	−0.787505	+	0.787505i	−0.981085	−	0.193580i	$-0.937990\pi$
$853$	−23.0000	+	23.0000i	−0.787505	+	0.787505i	0.193580	+	0.981085i	$0.437990\pi$
$854$	−42.4264			−1.45180
$855$		0			0
$856$	12.0000			0.410152
$857$	−12.7279	+	12.7279i	−0.434778	+	0.434778i	−0.890250	−	0.455472i	$-0.849470\pi$
$857$	−12.7279	+	12.7279i	−0.434778	+	0.434778i	0.455472	+	0.890250i	$0.349470\pi$
$858$		0			0
$859$		−	28.0000i		−	0.955348i	−0.878537	−	0.477674i	$-0.841480\pi$
$859$		−	28.0000i		−	0.955348i	0.878537	−	0.477674i	$-0.158520\pi$
$860$	8.48528	+	4.24264i	0.289346	+	0.144673i
$861$		0			0
$862$	14.0000	+	14.0000i	0.476842	+	0.476842i
$863$	−2.82843	−	2.82843i	−0.0962808	−	0.0962808i	0.657326	−	0.753607i	$-0.271688\pi$
$863$	−2.82843	−	2.82843i	−0.0962808	−	0.0962808i	−0.753607	+	0.657326i	$0.771688\pi$
$864$		0			0
$865$	12.0000	+	6.00000i	0.408012	+	0.204006i
$866$		−	8.48528i		−	0.288342i
$867$		0			0
$868$	−12.0000	+	12.0000i	−0.407307	+	0.407307i
$869$	−5.65685			−0.191896
$870$		0			0
$871$	−80.0000			−2.71070
$872$	−1.41421	+	1.41421i	−0.0478913	+	0.0478913i
$873$		0			0
$874$		0			0
$875$	−46.6690	+	8.48528i	−1.57770	+	0.286855i
$876$		0			0
$877$	36.0000	+	36.0000i	1.21563	+	1.21563i	0.969146	+	0.246488i	$0.0792765\pi$
$877$	36.0000	+	36.0000i	1.21563	+	1.21563i	0.246488	+	0.969146i	$0.420724\pi$
$878$	−11.3137	−	11.3137i	−0.381819	−	0.381819i
$879$		0			0
$880$	1.00000	+	3.00000i	0.0337100	+	0.101130i
$881$		−	32.5269i		−	1.09586i	−0.836524	−	0.547930i	$-0.815416\pi$
$881$		−	32.5269i		−	1.09586i	0.836524	−	0.547930i	$-0.184584\pi$
$882$		0			0
$883$	21.0000	−	21.0000i	0.706706	−	0.706706i	−0.259135	−	0.965841i	$-0.583437\pi$
$883$	21.0000	−	21.0000i	0.706706	−	0.706706i	0.965841	+	0.259135i	$0.0834374\pi$
$884$	−22.6274			−0.761042
$885$		0			0
$886$	36.0000			1.20944
$887$	8.48528	−	8.48528i	0.284908	−	0.284908i	−0.550155	−	0.835063i	$-0.685431\pi$
$887$	8.48528	−	8.48528i	0.284908	−	0.284908i	0.835063	+	0.550155i	$0.185431\pi$
$888$		0			0
$889$		−	60.0000i		−	2.01234i
$890$	14.1421	−	28.2843i	0.474045	−	0.948091i
$891$		0			0
$892$	12.0000	+	12.0000i	0.401790	+	0.401790i
$893$	5.65685	+	5.65685i	0.189299	+	0.189299i
$894$		0			0
$895$	24.0000	−	8.00000i	0.802232	−	0.267411i
$896$		−	4.24264i		−	0.141737i
$897$		0			0
$898$	−26.0000	+	26.0000i	−0.867631	+	0.867631i
$899$	−11.3137			−0.377333
$900$		0			0
$901$	−8.00000			−0.266519
$902$	−8.48528	+	8.48528i	−0.282529	+	0.282529i
$903$		0			0
$904$			2.00000i			0.0665190i
$905$	−38.1838	+	12.7279i	−1.26927	+	0.423090i
$906$		0			0
$907$	−36.0000	−	36.0000i	−1.19536	−	1.19536i	−0.975540	−	0.219820i	$-0.929453\pi$
$907$	−36.0000	−	36.0000i	−1.19536	−	1.19536i	−0.219820	−	0.975540i	$-0.570547\pi$
$908$		0			0
$909$		0			0
$910$	24.0000	−	48.0000i	0.795592	−	1.59118i
$911$			5.65685i			0.187420i	0.995600	+	0.0937100i	$0.0298726\pi$
$911$			5.65685i			0.187420i	−0.995600	+	0.0937100i	$0.970127\pi$
$912$		0			0
$913$	−6.00000	+	6.00000i	−0.198571	+	0.198571i
$914$	24.0416			0.795226
$915$		0			0
$916$	−8.00000			−0.264327
$917$	−38.1838	+	38.1838i	−1.26094	+	1.26094i
$918$		0			0
$919$		−	48.0000i		−	1.58337i	−0.610927	−	0.791687i	$-0.709203\pi$
$919$		−	48.0000i		−	1.58337i	0.610927	−	0.791687i	$-0.290797\pi$
$920$		0			0
$921$		0			0
$922$	17.0000	+	17.0000i	0.559865	+	0.559865i
$923$	22.6274	+	22.6274i	0.744791	+	0.744791i
$924$		0			0
$925$	42.0000	+	6.00000i	1.38095	+	0.197279i
$926$		−	21.2132i		−	0.697109i
$927$		0			0
$928$	2.00000	−	2.00000i	0.0656532	−	0.0656532i
$929$	−41.0122			−1.34557			−0.672783	−	0.739840i	$-0.734901\pi$
$929$	−41.0122			−1.34557			−0.672783	+	0.739840i	$0.734901\pi$
$930$		0			0
$931$	11.0000			0.360510
$932$	−7.07107	+	7.07107i	−0.231621	+	0.231621i
$933$		0			0
$934$			36.0000i			1.17796i
$935$	−11.3137	−	5.65685i	−0.369998	−	0.184999i
$936$		0			0
$937$	−35.0000	−	35.0000i	−1.14340	−	1.14340i	−0.987824	−	0.155576i	$-0.950277\pi$
$937$	−35.0000	−	35.0000i	−1.14340	−	1.14340i	−0.155576	−	0.987824i	$-0.549723\pi$
$938$	42.4264	+	42.4264i	1.38527	+	1.38527i
$939$		0			0
$940$	−16.0000	−	8.00000i	−0.521862	−	0.260931i
$941$			19.7990i			0.645429i	0.946496	+	0.322714i	$0.104595\pi$
$941$			19.7990i			0.645429i	−0.946496	+	0.322714i	$0.895405\pi$
$942$		0			0
$943$		0			0
$944$	−5.65685			−0.184115
$945$		0			0
$946$	−6.00000			−0.195077
$947$	9.89949	−	9.89949i	0.321690	−	0.321690i	−0.527725	−	0.849415i	$-0.676955\pi$
$947$	9.89949	−	9.89949i	0.321690	−	0.321690i	0.849415	+	0.527725i	$0.176955\pi$
$948$		0			0
$949$			24.0000i			0.779073i
$950$	4.94975	+	0.707107i	0.160591	+	0.0229416i
$951$		0			0
$952$	12.0000	+	12.0000i	0.388922	+	0.388922i
$953$	4.24264	+	4.24264i	0.137433	+	0.137433i	0.772476	−	0.635044i	$-0.219018\pi$
$953$	4.24264	+	4.24264i	0.137433	+	0.137433i	−0.635044	+	0.772476i	$0.719018\pi$
$954$		0			0
$955$	17.0000	+	51.0000i	0.550107	+	1.65032i
$956$			18.3848i			0.594606i
$957$		0			0
$958$	1.00000	−	1.00000i	0.0323085	−	0.0323085i
$959$		0			0
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−33.9411	+	33.9411i	−1.09431	+	1.09431i
$963$		0			0
$964$			10.0000i			0.322078i
$965$	25.4558	−	50.9117i	0.819453	−	1.63891i
$966$		0			0
$967$	9.00000	+	9.00000i	0.289420	+	0.289420i	0.836851	−	0.547431i	$-0.184394\pi$
$967$	9.00000	+	9.00000i	0.289420	+	0.289420i	−0.547431	+	0.836851i	$0.684394\pi$
$968$	6.36396	+	6.36396i	0.204545	+	0.204545i
$969$		0			0
$970$	36.0000	−	12.0000i	1.15589	−	0.385297i
$971$		−	8.48528i		−	0.272306i	−0.990688	−	0.136153i	$-0.956526\pi$
$971$		−	8.48528i		−	0.272306i	0.990688	−	0.136153i	$-0.0434738\pi$
$972$		0			0
$973$	−42.0000	+	42.0000i	−1.34646	+	1.34646i
$974$	39.5980			1.26880
$975$		0			0
$976$	−10.0000			−0.320092
$977$	4.24264	−	4.24264i	0.135734	−	0.135734i	−0.635975	−	0.771709i	$-0.719402\pi$
$977$	4.24264	−	4.24264i	0.135734	−	0.135734i	0.771709	+	0.635975i	$0.219402\pi$
$978$		0			0
$979$			20.0000i			0.639203i
$980$	−23.3345	+	7.77817i	−0.745394	+	0.248465i
$981$		0			0
$982$	−5.00000	−	5.00000i	−0.159556	−	0.159556i
$983$	−42.4264	−	42.4264i	−1.35319	−	1.35319i	−0.882066	−	0.471127i	$-0.843847\pi$
$983$	−42.4264	−	42.4264i	−1.35319	−	1.35319i	−0.471127	−	0.882066i	$-0.656153\pi$
$984$		0			0
$985$	22.0000	−	44.0000i	0.700978	−	1.40196i
$986$			11.3137i			0.360302i
$987$		0			0
$988$	−4.00000	+	4.00000i	−0.127257	+	0.127257i
$989$		0			0
$990$		0			0
$991$	48.0000			1.52477			0.762385	−	0.647124i	$-0.224028\pi$
$991$	48.0000			1.52477			0.762385	+	0.647124i	$0.224028\pi$
$992$	−2.82843	+	2.82843i	−0.0898027	+	0.0898027i
$993$		0			0
$994$		−	24.0000i		−	0.761234i
$995$	−1.41421	−	4.24264i	−0.0448336	−	0.134501i
$996$		0			0
$997$	−1.00000	−	1.00000i	−0.0316703	−	0.0316703i	0.691094	−	0.722765i	$-0.257129\pi$
$997$	−1.00000	−	1.00000i	−0.0316703	−	0.0316703i	−0.722765	+	0.691094i	$0.757129\pi$
$998$	−21.2132	−	21.2132i	−0.671492	−	0.671492i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.n.e.647.1	✓	4
3.2	odd	2	inner	1710.2.n.e.647.2	yes	4
5.3	odd	4	inner	1710.2.n.e.1673.2	yes	4
15.8	even	4	inner	1710.2.n.e.1673.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1710.2.n.e.647.1	✓	4	1.1	even	1	trivial
1710.2.n.e.647.2	yes	4	3.2	odd	2	inner
1710.2.n.e.1673.1	yes	4	15.8	even	4	inner
1710.2.n.e.1673.2	yes	4	5.3	odd	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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-2.12132 + 0.707107i) q^{5} +(3.00000 + 3.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.00000 - 2.00000i) q^{10} +1.41421i q^{11} +(4.00000 - 4.00000i) q^{13} -4.24264 q^{14} -1.00000 q^{16} +(2.82843 - 2.82843i) q^{17} -1.00000i q^{19} +(0.707107 + 2.12132i) q^{20} +(-1.00000 - 1.00000i) q^{22} +(4.00000 - 3.00000i) q^{25} +5.65685i q^{26} +(3.00000 - 3.00000i) q^{28} +2.82843 q^{29} -4.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +4.00000i q^{34} +(-8.48528 - 4.24264i) q^{35} +(6.00000 + 6.00000i) q^{37} +(0.707107 + 0.707107i) q^{38} +(-2.00000 - 1.00000i) q^{40} -8.48528i q^{41} +(3.00000 - 3.00000i) q^{43} +1.41421 q^{44} +(-5.65685 + 5.65685i) q^{47} +11.0000i q^{49} +(-0.707107 + 4.94975i) q^{50} +(-4.00000 - 4.00000i) q^{52} +(-1.41421 - 1.41421i) q^{53} +(-1.00000 - 3.00000i) q^{55} +4.24264i q^{56} +(-2.00000 + 2.00000i) q^{58} +5.65685 q^{59} +10.0000 q^{61} +(2.82843 - 2.82843i) q^{62} +1.00000i q^{64} +(-5.65685 + 11.3137i) q^{65} +(-10.0000 - 10.0000i) q^{67} +(-2.82843 - 2.82843i) q^{68} +(9.00000 - 3.00000i) q^{70} +5.65685i q^{71} +(-3.00000 + 3.00000i) q^{73} -8.48528 q^{74} -1.00000 q^{76} +(-4.24264 + 4.24264i) q^{77} +4.00000i q^{79} +(2.12132 - 0.707107i) q^{80} +(6.00000 + 6.00000i) q^{82} +(4.24264 + 4.24264i) q^{83} +(-4.00000 + 8.00000i) q^{85} +4.24264i q^{86} +(-1.00000 + 1.00000i) q^{88} +14.1421 q^{89} +24.0000 q^{91} -8.00000i q^{94} +(0.707107 + 2.12132i) q^{95} +(12.0000 + 12.0000i) q^{97} +(-7.77817 - 7.77817i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 12 q^{7} + 4 q^{10} + 16 q^{13} - 4 q^{16} - 4 q^{22} + 16 q^{25} + 12 q^{28} - 16 q^{31} + 24 q^{37} - 8 q^{40} + 12 q^{43} - 16 q^{52} - 4 q^{55} - 8 q^{58} + 40 q^{61} - 40 q^{67} + 36 q^{70} - 12 q^{73}+ \cdots + 48 q^{97}+O(q^{100}) \) 4 * q + 12 * q^7 + 4 * q^10 + 16 * q^13 - 4 * q^16 - 4 * q^22 + 16 * q^25 + 12 * q^28 - 16 * q^31 + 24 * q^37 - 8 * q^40 + 12 * q^43 - 16 * q^52 - 4 * q^55 - 8 * q^58 + 40 * q^61 - 40 * q^67 + 36 * q^70 - 12 * q^73 - 4 * q^76 + 24 * q^82 - 16 * q^85 - 4 * q^88 + 96 * q^91 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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