LMFDB - Embedded newform 1710.2.p.b.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(37,1710)]

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([0, 1, 2]))

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

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

chi := DirichletCharacter("1710.37");

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.p (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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24x^{14} + 212x^{12} + 880x^{10} + 1858x^{8} + 1960x^{6} + 892x^{4} + 96x^{2} + 1 $ x^16 + 24x^14 + 212x^12 + 880x^10 + 1858x^8 + 1960x^6 + 892x^4 + 96*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.4
Root			$1.66380i$ of defining polynomial
Character	$\chi$	$=$	1710.37
Dual form			1710.2.p.b.1063.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(1.96854 + 1.06059i) q^{5} +(1.65823 + 1.65823i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(1.96854 + 1.06059i) q^{5} +(1.65823 + 1.65823i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.14192 + 0.642014i) q^{10} +0.804733 q^{11} +(-3.05219 - 3.05219i) q^{13} -2.34509 q^{14} -1.00000 q^{16} +(4.37090 + 4.37090i) q^{17} +(3.48315 - 2.62062i) q^{19} +(1.06059 - 1.96854i) q^{20} +(-0.569032 + 0.569032i) q^{22} +(-6.20477 + 6.20477i) q^{23} +(2.75028 + 4.17564i) q^{25} +4.31645 q^{26} +(1.65823 - 1.65823i) q^{28} +5.64487 q^{29} +3.13000i q^{31} +(0.707107 - 0.707107i) q^{32} -6.18139 q^{34} +(1.50558 + 5.02299i) q^{35} +(0.524538 - 0.524538i) q^{37} +(-0.609901 + 4.31602i) q^{38} +(0.642014 + 2.14192i) q^{40} +1.45541i q^{41} +(1.90794 - 1.90794i) q^{43} -0.804733i q^{44} -8.77487i q^{46} +(-0.499434 - 0.499434i) q^{47} -1.50057i q^{49} +(-4.89736 - 1.00788i) q^{50} +(-3.05219 + 3.05219i) q^{52} +(-3.40535 - 3.40535i) q^{53} +(1.58415 + 0.853494i) q^{55} +2.34509i q^{56} +(-3.99153 + 3.99153i) q^{58} -2.77684 q^{59} +6.17945 q^{61} +(-2.21324 - 2.21324i) q^{62} +1.00000i q^{64} +(-2.77122 - 9.24550i) q^{65} +(0.345265 - 0.345265i) q^{67} +(4.37090 - 4.37090i) q^{68} +(-4.61639 - 2.48718i) q^{70} +6.68211i q^{71} +(1.05445 - 1.05445i) q^{73} +0.741809i q^{74} +(-2.62062 - 3.48315i) q^{76} +(1.33443 + 1.33443i) q^{77} +7.16924 q^{79} +(-1.96854 - 1.06059i) q^{80} +(-1.02913 - 1.02913i) q^{82} +(4.12119 - 4.12119i) q^{83} +(3.96854 + 13.2400i) q^{85} +2.69824i q^{86} +(0.569032 + 0.569032i) q^{88} -16.7356 q^{89} -10.1225i q^{91} +(6.20477 + 6.20477i) q^{92} +0.706307 q^{94} +(9.63613 - 1.46458i) q^{95} +(-8.25033 + 8.25033i) q^{97} +(1.06106 + 1.06106i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} - 16 q^{16} + 32 q^{17} - 8 q^{20} + 8 q^{23} + 32 q^{25} + 32 q^{26} + 8 q^{28} + 24 q^{35} - 8 q^{38} + 24 q^{43} - 32 q^{47} - 56 q^{55} - 64 q^{61} + 8 q^{62} + 32 q^{68} + 16 q^{73} - 16 q^{76} - 72 q^{77} + 40 q^{82} + 16 q^{83} + 32 q^{85} - 8 q^{92} - 24 q^{95}+O(q^{100}) $ 16 * q + 8 * q^7 - 16 * q^16 + 32 * q^17 - 8 * q^20 + 8 * q^23 + 32 * q^25 + 32 * q^26 + 8 * q^28 + 24 * q^35 - 8 * q^38 + 24 * q^43 - 32 * q^47 - 56 * q^55 - 64 * q^61 + 8 * q^62 + 32 * q^68 + 16 * q^73 - 16 * q^76 - 72 * q^77 + 40 * q^82 + 16 * q^83 + 32 * q^85 - 8 * q^92 - 24 * q^95

Display 100 coefficients 10 coefficients

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
$5$	1.96854	+	1.06059i	0.880357	+	0.474312i
$5$	1.96854	+	1.06059i	0.880357	+	0.474312i
$6$		0			0
$7$	1.65823	+	1.65823i	0.626751	+	0.626751i	0.947249	−	0.320498i	$-0.103850\pi$
$7$	1.65823	+	1.65823i	0.626751	+	0.626751i	−0.320498	+	0.947249i	$0.603850\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	−2.14192	+	0.642014i	−0.677334	+	0.203023i
$11$	0.804733			0.242636			0.121318	−	0.992614i	$-0.461288\pi$
$11$	0.804733			0.242636			0.121318	+	0.992614i	$0.461288\pi$
$12$		0			0
$13$	−3.05219	−	3.05219i	−0.846526	−	0.846526i	0.143172	−	0.989698i	$-0.454270\pi$
$13$	−3.05219	−	3.05219i	−0.846526	−	0.846526i	−0.989698	+	0.143172i	$0.954270\pi$
$14$	−2.34509			−0.626751
$15$		0			0
$16$	−1.00000			−0.250000
$17$	4.37090	+	4.37090i	1.06010	+	1.06010i	0.998075	+	0.0620254i	$0.0197560\pi$
$17$	4.37090	+	4.37090i	1.06010	+	1.06010i	0.0620254	+	0.998075i	$0.480244\pi$
$18$		0			0
$19$	3.48315	−	2.62062i	0.799090	−	0.601212i
$19$	3.48315	−	2.62062i	0.799090	−	0.601212i
$20$	1.06059	−	1.96854i	0.237156	−	0.440178i
$21$		0			0
$22$	−0.569032	+	0.569032i	−0.121318	+	0.121318i
$23$	−6.20477	+	6.20477i	−1.29378	+	1.29378i	−0.361356	+	0.932428i	$0.617686\pi$
$23$	−6.20477	+	6.20477i	−1.29378	+	1.29378i	−0.932428	+	0.361356i	$0.882314\pi$
$24$		0			0
$25$	2.75028	+	4.17564i	0.550057	+	0.835127i
$26$	4.31645			0.846526
$27$		0			0
$28$	1.65823	−	1.65823i	0.313375	−	0.313375i
$29$	5.64487			1.04823			0.524113	−	0.851649i	$-0.324397\pi$
$29$	5.64487			1.04823			0.524113	+	0.851649i	$0.324397\pi$
$30$		0			0
$31$			3.13000i			0.562164i	0.959684	+	0.281082i	$0.0906933\pi$
$31$			3.13000i			0.562164i	−0.959684	+	0.281082i	$0.909307\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	−6.18139			−1.06010
$35$	1.50558	+	5.02299i	0.254489	+	0.849040i
$36$		0			0
$37$	0.524538	−	0.524538i	0.0862335	−	0.0862335i	−0.662674	−	0.748908i	$-0.730579\pi$
$37$	0.524538	−	0.524538i	0.0862335	−	0.0862335i	0.748908	+	0.662674i	$0.230579\pi$
$38$	−0.609901	+	4.31602i	−0.0989390	+	0.700151i
$39$		0			0
$40$	0.642014	+	2.14192i	0.101511	+	0.338667i
$41$			1.45541i			0.227297i	0.993521	+	0.113649i	$0.0362538\pi$
$41$			1.45541i			0.227297i	−0.993521	+	0.113649i	$0.963746\pi$
$42$		0			0
$43$	1.90794	−	1.90794i	0.290959	−	0.290959i	−0.546500	−	0.837459i	$-0.684040\pi$
$43$	1.90794	−	1.90794i	0.290959	−	0.290959i	0.837459	+	0.546500i	$0.184040\pi$
$44$		−	0.804733i		−	0.121318i
$45$		0			0
$46$		−	8.77487i		−	1.29378i
$47$	−0.499434	−	0.499434i	−0.0728500	−	0.0728500i	0.669743	−	0.742593i	$-0.266404\pi$
$47$	−0.499434	−	0.499434i	−0.0728500	−	0.0728500i	−0.742593	+	0.669743i	$0.766404\pi$
$48$		0			0
$49$		−	1.50057i		−	0.214367i
$50$	−4.89736	−	1.00788i	−0.692592	−	0.142535i
$51$		0			0
$52$	−3.05219	+	3.05219i	−0.423263	+	0.423263i
$53$	−3.40535	−	3.40535i	−0.467760	−	0.467760i	0.433428	−	0.901188i	$-0.357304\pi$
$53$	−3.40535	−	3.40535i	−0.467760	−	0.467760i	−0.901188	+	0.433428i	$0.857304\pi$
$54$		0			0
$55$	1.58415	+	0.853494i	0.213606	+	0.115085i
$56$			2.34509i			0.313375i
$57$		0			0
$58$	−3.99153	+	3.99153i	−0.524113	+	0.524113i
$59$	−2.77684			−0.361514			−0.180757	−	0.983528i	$-0.557855\pi$
$59$	−2.77684			−0.361514			−0.180757	+	0.983528i	$0.557855\pi$
$60$		0			0
$61$	6.17945			0.791197			0.395599	−	0.918423i	$-0.370537\pi$
$61$	6.17945			0.791197			0.395599	+	0.918423i	$0.370537\pi$
$62$	−2.21324	−	2.21324i	−0.281082	−	0.281082i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−2.77122	−	9.24550i	−0.343728	−	1.14676i
$66$		0			0
$67$	0.345265	−	0.345265i	0.0421808	−	0.0421808i	−0.685702	−	0.727883i	$-0.740505\pi$
$67$	0.345265	−	0.345265i	0.0421808	−	0.0421808i	0.727883	+	0.685702i	$0.240505\pi$
$68$	4.37090	−	4.37090i	0.530050	−	0.530050i
$69$		0			0
$70$	−4.61639	−	2.48718i	−0.551765	−	0.297275i
$71$			6.68211i			0.793020i	0.918030	+	0.396510i	$0.129779\pi$
$71$			6.68211i			0.793020i	−0.918030	+	0.396510i	$0.870221\pi$
$72$		0			0
$73$	1.05445	−	1.05445i	0.123414	−	0.123414i	−0.642702	−	0.766116i	$-0.722187\pi$
$73$	1.05445	−	1.05445i	0.123414	−	0.123414i	0.766116	+	0.642702i	$0.222187\pi$
$74$			0.741809i			0.0862335i
$75$		0			0
$76$	−2.62062	−	3.48315i	−0.300606	−	0.399545i
$77$	1.33443	+	1.33443i	0.152072	+	0.152072i
$78$		0			0
$79$	7.16924			0.806603			0.403301	−	0.915067i	$-0.367863\pi$
$79$	7.16924			0.806603			0.403301	+	0.915067i	$0.367863\pi$
$80$	−1.96854	−	1.06059i	−0.220089	−	0.118578i
$81$		0			0
$82$	−1.02913	−	1.02913i	−0.113649	−	0.113649i
$83$	4.12119	−	4.12119i	0.452359	−	0.452359i	−0.443778	−	0.896137i	$-0.646362\pi$
$83$	4.12119	−	4.12119i	0.452359	−	0.452359i	0.896137	+	0.443778i	$0.146362\pi$
$84$		0			0
$85$	3.96854	+	13.2400i	0.430448	+	1.43608i
$86$			2.69824i			0.290959i
$87$		0			0
$88$	0.569032	+	0.569032i	0.0606590	+	0.0606590i
$89$	−16.7356			−1.77397			−0.886986	−	0.461797i	$-0.847205\pi$
$89$	−16.7356			−1.77397			−0.886986	+	0.461797i	$0.847205\pi$
$90$		0			0
$91$		−	10.1225i		−	1.06112i
$92$	6.20477	+	6.20477i	0.646892	+	0.646892i
$93$		0			0
$94$	0.706307			0.0728500
$95$	9.63613	−	1.46458i	0.988646	−	0.150263i
$96$		0			0
$97$	−8.25033	+	8.25033i	−0.837694	+	0.837694i	−0.988555	−	0.150861i	$-0.951795\pi$
$97$	−8.25033	+	8.25033i	−0.837694	+	0.837694i	0.150861	+	0.988555i	$0.451795\pi$
$98$	1.06106	+	1.06106i	0.107183	+	0.107183i
$99$		0			0
$100$	4.17564	−	2.75028i	0.417564	−	0.275028i
$101$	1.75296			0.174426			0.0872132	−	0.996190i	$-0.472204\pi$
$101$	1.75296			0.174426			0.0872132	+	0.996190i	$0.472204\pi$
$102$		0			0
$103$	5.55918	+	5.55918i	0.547762	+	0.547762i	0.925793	−	0.378031i	$-0.123399\pi$
$103$	5.55918	+	5.55918i	0.547762	+	0.547762i	−0.378031	+	0.925793i	$0.623399\pi$
$104$		−	4.31645i		−	0.423263i
$105$		0			0
$106$	4.81589			0.467760
$107$	−2.01985	+	2.01985i	−0.195266	+	0.195266i	−0.797967	−	0.602701i	$-0.794091\pi$
$107$	−2.01985	+	2.01985i	−0.195266	+	0.195266i	0.602701	+	0.797967i	$0.294091\pi$
$108$		0			0
$109$	13.3175			1.27558			0.637792	−	0.770209i	$-0.279848\pi$
$109$	13.3175			1.27558			0.637792	+	0.770209i	$0.279848\pi$
$110$	−1.72367	+	0.516649i	−0.164346	+	0.0492606i
$111$		0			0
$112$	−1.65823	−	1.65823i	−0.156688	−	0.156688i
$113$	10.8883	+	10.8883i	1.02429	+	1.02429i	0.999698	+	0.0245874i	$0.00782719\pi$
$113$	10.8883	+	10.8883i	1.02429	+	1.02429i	0.0245874	+	0.999698i	$0.492173\pi$
$114$		0			0
$115$	−18.7951	+	5.63358i	−1.75265	+	0.525334i
$116$		−	5.64487i		−	0.524113i
$117$		0			0
$118$	1.96353	−	1.96353i	0.180757	−	0.180757i
$119$			14.4959i			1.32884i
$120$		0			0
$121$	−10.3524			−0.941128
$122$	−4.36953	+	4.36953i	−0.395599	+	0.395599i
$123$		0			0
$124$	3.13000			0.281082
$125$	0.985382	+	11.1368i	0.0881353	+	0.996109i
$126$		0			0
$127$	−10.4120	+	10.4120i	−0.923920	+	0.923920i	−0.997304	−	0.0733839i	$-0.976620\pi$
$127$	−10.4120	+	10.4120i	−0.923920	+	0.923920i	0.0733839	+	0.997304i	$0.476620\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	8.49710	+	4.57800i	0.745245	+	0.401517i
$131$	15.4836			1.35281			0.676405	−	0.736530i	$-0.263537\pi$
$131$	15.4836			1.35281			0.676405	+	0.736530i	$0.263537\pi$
$132$		0			0
$133$	10.1214	+	1.43027i	0.877640	+	0.124020i
$134$			0.488279i			0.0421808i
$135$		0			0
$136$			6.18139i			0.530050i
$137$	3.37204	+	3.37204i	0.288092	+	0.288092i	0.836326	−	0.548233i	$-0.184699\pi$
$137$	3.37204	+	3.37204i	0.288092	+	0.288092i	−0.548233	+	0.836326i	$0.684699\pi$
$138$		0			0
$139$			2.05826i			0.174580i	0.996183	+	0.0872898i	$0.0278206\pi$
$139$			2.05826i			0.174580i	−0.996183	+	0.0872898i	$0.972179\pi$
$140$	5.02299	−	1.50558i	0.424520	−	0.127245i
$141$		0			0
$142$	−4.72496	−	4.72496i	−0.396510	−	0.396510i
$143$	−2.45620	−	2.45620i	−0.205398	−	0.205398i
$144$		0			0
$145$	11.1121	+	5.98691i	0.922813	+	0.497186i
$146$			1.49122i			0.123414i
$147$		0			0
$148$	−0.524538	−	0.524538i	−0.0431167	−	0.0431167i
$149$		−	19.5419i		−	1.60093i	−0.599377	−	0.800467i	$-0.704585\pi$
$149$		−	19.5419i		−	1.60093i	0.599377	−	0.800467i	$-0.295415\pi$
$150$		0			0
$151$			0.641287i			0.0521872i	0.999660	+	0.0260936i	$0.00830680\pi$
$151$			0.641287i			0.0521872i	−0.999660	+	0.0260936i	$0.991693\pi$
$152$	4.31602	+	0.609901i	0.350075	+	0.0494695i
$153$		0			0
$154$	−1.88717			−0.152072
$155$	−3.31966	+	6.16152i	−0.266641	+	0.494905i
$156$		0			0
$157$	12.6689	+	12.6689i	1.01109	+	1.01109i	0.999938	+	0.0111472i	$0.00354833\pi$
$157$	12.6689	+	12.6689i	1.01109	+	1.01109i	0.0111472	+	0.999938i	$0.496452\pi$
$158$	−5.06942	+	5.06942i	−0.403301	+	0.403301i
$159$		0			0
$160$	2.14192	−	0.642014i	0.169334	−	0.0507556i
$161$	−20.5778			−1.62176
$162$		0			0
$163$	−3.47143	+	3.47143i	−0.271904	+	0.271904i	−0.829866	−	0.557962i	$-0.811583\pi$
$163$	−3.47143	+	3.47143i	−0.271904	+	0.271904i	0.557962	+	0.829866i	$0.311583\pi$
$164$	1.45541			0.113649
$165$		0			0
$166$			5.82824i			0.452359i
$167$	−13.1032	+	13.1032i	−1.01396	+	1.01396i	−0.0140549	+	0.999901i	$0.504474\pi$
$167$	−13.1032	+	13.1032i	−1.01396	+	1.01396i	−0.999901	+	0.0140549i	$0.995526\pi$
$168$		0			0
$169$			5.63178i			0.433214i
$170$	−12.1683	−	6.55594i	−0.933266	−	0.502818i
$171$		0			0
$172$	−1.90794	−	1.90794i	−0.145479	−	0.145479i
$173$	7.50662	+	7.50662i	0.570718	+	0.570718i	0.932329	−	0.361611i	$-0.117773\pi$
$173$	7.50662	+	7.50662i	0.570718	+	0.570718i	−0.361611	+	0.932329i	$0.617773\pi$
$174$		0			0
$175$	−2.36356	+	11.4847i	−0.178668	+	0.868165i
$176$	−0.804733			−0.0606590
$177$		0			0
$178$	11.8339	−	11.8339i	0.886986	−	0.886986i
$179$	−19.4273			−1.45206			−0.726031	−	0.687662i	$-0.758637\pi$
$179$	−19.4273			−1.45206			−0.726031	+	0.687662i	$0.758637\pi$
$180$		0			0
$181$		−	4.58541i		−	0.340831i	−0.985372	−	0.170415i	$-0.945489\pi$
$181$		−	4.58541i		−	0.340831i	0.985372	−	0.170415i	$-0.0545110\pi$
$182$	7.15766	+	7.15766i	0.530561	+	0.530561i
$183$		0			0
$184$	−8.77487			−0.646892
$185$	1.58889	−	0.476251i	0.116818	−	0.0350147i
$186$		0			0
$187$	3.51741	+	3.51741i	0.257218	+	0.257218i
$188$	−0.499434	+	0.499434i	−0.0364250	+	0.0364250i
$189$		0			0
$190$	−5.77815	+	7.84939i	−0.419191	+	0.569455i
$191$	−4.86413			−0.351956			−0.175978	−	0.984394i	$-0.556309\pi$
$191$	−4.86413			−0.351956			−0.175978	+	0.984394i	$0.556309\pi$
$192$		0			0
$193$	−10.3313	−	10.3313i	−0.743660	−	0.743660i	0.229620	−	0.973280i	$-0.426252\pi$
$193$	−10.3313	−	10.3313i	−0.743660	−	0.743660i	−0.973280	+	0.229620i	$0.926252\pi$
$194$		−	11.6677i		−	0.837694i
$195$		0			0
$196$	−1.50057			−0.107183
$197$	−8.32327	−	8.32327i	−0.593009	−	0.593009i	0.345434	−	0.938443i	$-0.387732\pi$
$197$	−8.32327	−	8.32327i	−0.593009	−	0.593009i	−0.938443	+	0.345434i	$0.887732\pi$
$198$		0			0
$199$		−	23.1042i		−	1.63782i	−0.573925	−	0.818908i	$-0.694580\pi$
$199$		−	23.1042i		−	1.63782i	0.573925	−	0.818908i	$-0.305420\pi$
$200$	−1.00788	+	4.89736i	−0.0712677	+	0.346296i
$201$		0			0
$202$	−1.23953	+	1.23953i	−0.0872132	+	0.0872132i
$203$	9.36048	+	9.36048i	0.656977	+	0.656977i
$204$		0			0
$205$	−1.54360	+	2.86503i	−0.107810	+	0.200103i
$206$	−7.86186			−0.547762
$207$		0			0
$208$	3.05219	+	3.05219i	0.211632	+	0.211632i
$209$	2.80301	−	2.10890i	0.193888	−	0.145876i
$210$		0			0
$211$		−	15.3492i		−	1.05668i	−0.849033	−	0.528340i	$-0.822815\pi$
$211$		−	15.3492i		−	1.05668i	0.849033	−	0.528340i	$-0.177185\pi$
$212$	−3.40535	+	3.40535i	−0.233880	+	0.233880i
$213$		0			0
$214$		−	2.85650i		−	0.195266i
$215$	5.77941	−	1.73231i	0.394153	−	0.118142i
$216$		0			0
$217$	−5.19025	+	5.19025i	−0.352337	+	0.352337i
$218$	−9.41688	+	9.41688i	−0.637792	+	0.637792i
$219$		0			0
$220$	0.853494	−	1.58415i	0.0575426	−	0.106803i
$221$		−	26.6817i		−	1.79481i
$222$		0			0
$223$	18.5974	+	18.5974i	1.24537	+	1.24537i	0.957742	+	0.287629i	$0.0928672\pi$
$223$	18.5974	+	18.5974i	1.24537	+	1.24537i	0.287629	+	0.957742i	$0.407133\pi$
$224$	2.34509			0.156688
$225$		0			0
$226$	−15.3984			−1.02429
$227$	5.51878	−	5.51878i	0.366294	−	0.366294i	−0.499830	−	0.866124i	$-0.666604\pi$
$227$	5.51878	−	5.51878i	0.366294	−	0.366294i	0.866124	+	0.499830i	$0.166604\pi$
$228$		0			0
$229$		−	9.94379i		−	0.657104i	−0.944486	−	0.328552i	$-0.893439\pi$
$229$		−	9.94379i		−	0.657104i	0.944486	−	0.328552i	$-0.106561\pi$
$230$	9.30657	−	17.2737i	0.613657	−	1.13899i
$231$		0			0
$232$	3.99153	+	3.99153i	0.262057	+	0.262057i
$233$	5.11116	−	5.11116i	0.334843	−	0.334843i	−0.519579	−	0.854422i	$-0.673911\pi$
$233$	5.11116	−	5.11116i	0.334843	−	0.334843i	0.854422	+	0.519579i	$0.173911\pi$
$234$		0			0
$235$	−0.453459	−	1.51285i	−0.0295804	−	0.0986876i
$236$			2.77684i			0.180757i
$237$		0			0
$238$	−10.2502	−	10.2502i	−0.664419	−	0.664419i
$239$			9.30530i			0.601910i	0.953638	+	0.300955i	$0.0973053\pi$
$239$			9.30530i			0.601910i	−0.953638	+	0.300955i	$0.902695\pi$
$240$		0			0
$241$		−	8.31390i		−	0.535545i	−0.963482	−	0.267773i	$-0.913712\pi$
$241$		−	8.31390i		−	0.535545i	0.963482	−	0.267773i	$-0.0862876\pi$
$242$	7.32026	−	7.32026i	0.470564	−	0.470564i
$243$		0			0
$244$		−	6.17945i		−	0.395599i
$245$	1.59149	−	2.95392i	0.101677	−	0.188719i
$246$		0			0
$247$	−18.6299	−	2.63261i	−1.18539	−	0.167509i
$248$	−2.21324	+	2.21324i	−0.140541	+	0.140541i
$249$		0			0
$250$	−8.57170	−	7.17816i	−0.542122	−	0.453987i
$251$	−10.7710			−0.679862			−0.339931	−	0.940450i	$-0.610404\pi$
$251$	−10.7710			−0.679862			−0.339931	+	0.940450i	$0.610404\pi$
$252$		0			0
$253$	−4.99318	+	4.99318i	−0.313919	+	0.313919i
$254$		−	14.7249i		−	0.923920i
$255$		0			0
$256$	1.00000			0.0625000
$257$	19.8607	−	19.8607i	1.23888	−	1.23888i	0.278417	−	0.960460i	$-0.410190\pi$
$257$	19.8607	−	19.8607i	1.23888	−	1.23888i	0.960460	−	0.278417i	$-0.0898097\pi$
$258$		0			0
$259$	1.73961			0.108094
$260$	−9.24550	+	2.77122i	−0.573381	+	0.171864i
$261$		0			0
$262$	−10.9486	+	10.9486i	−0.676405	+	0.676405i
$263$	−13.1964	+	13.1964i	−0.813725	+	0.813725i	−0.985190	−	0.171465i	$-0.945150\pi$
$263$	−13.1964	+	13.1964i	−0.813725	+	0.813725i	0.171465	+	0.985190i	$0.445150\pi$
$264$		0			0
$265$	−3.09187	−	10.3152i	−0.189932	−	0.633660i
$266$	−8.16829	+	6.14559i	−0.500830	+	0.376810i
$267$		0			0
$268$	−0.345265	−	0.345265i	−0.0210904	−	0.0210904i
$269$	18.1260			1.10516			0.552581	−	0.833459i	$-0.313643\pi$
$269$	18.1260			1.10516			0.552581	+	0.833459i	$0.313643\pi$
$270$		0			0
$271$	−7.62288			−0.463057			−0.231529	−	0.972828i	$-0.574373\pi$
$271$	−7.62288			−0.463057			−0.231529	+	0.972828i	$0.574373\pi$
$272$	−4.37090	−	4.37090i	−0.265025	−	0.265025i
$273$		0			0
$274$	−4.76878			−0.288092
$275$	2.21324	+	3.36027i	0.133464	+	0.202632i
$276$		0			0
$277$	−1.94710	−	1.94710i	−0.116990	−	0.116990i	0.646188	−	0.763178i	$-0.276362\pi$
$277$	−1.94710	−	1.94710i	−0.116990	−	0.116990i	−0.763178	+	0.646188i	$0.776362\pi$
$278$	−1.45541	−	1.45541i	−0.0872898	−	0.0872898i
$279$		0			0
$280$	−2.48718	+	4.61639i	−0.148638	+	0.275882i
$281$		−	5.77885i		−	0.344737i	−0.985033	−	0.172369i	$-0.944858\pi$
$281$		−	5.77885i		−	0.344737i	0.985033	−	0.172369i	$-0.0551420\pi$
$282$		0			0
$283$	−21.2948	+	21.2948i	−1.26585	+	1.26585i	−0.317634	+	0.948214i	$0.602888\pi$
$283$	−21.2948	+	21.2948i	−1.26585	+	1.26585i	−0.948214	+	0.317634i	$0.897112\pi$
$284$	6.68211			0.396510
$285$		0			0
$286$	3.47359			0.205398
$287$	−2.41340	+	2.41340i	−0.142459	+	0.142459i
$288$		0			0
$289$			21.2096i			1.24762i
$290$	−12.0909	+	3.62408i	−0.710000	+	0.212813i
$291$		0			0
$292$	−1.05445	−	1.05445i	−0.0617070	−	0.0617070i
$293$	5.94185	+	5.94185i	0.347126	+	0.347126i	0.859038	−	0.511912i	$-0.171062\pi$
$293$	5.94185	+	5.94185i	0.347126	+	0.347126i	−0.511912	+	0.859038i	$0.671062\pi$
$294$		0			0
$295$	−5.46632	−	2.94510i	−0.318262	−	0.171471i
$296$	0.741809			0.0431167
$297$		0			0
$298$	13.8182	+	13.8182i	0.800467	+	0.800467i
$299$	37.8763			2.19044
$300$		0			0
$301$	6.32761			0.364717
$302$	−0.453459	−	0.453459i	−0.0260936	−	0.0260936i
$303$		0			0
$304$	−3.48315	+	2.62062i	−0.199772	+	0.150303i
$305$	12.1645	+	6.55388i	0.696536	+	0.375274i
$306$		0			0
$307$	2.67442	−	2.67442i	0.152637	−	0.152637i	−0.626658	−	0.779295i	$-0.715578\pi$
$307$	2.67442	−	2.67442i	0.152637	−	0.152637i	0.779295	+	0.626658i	$0.215578\pi$
$308$	1.33443	−	1.33443i	0.0760362	−	0.0760362i
$309$		0			0
$310$	−2.00950	−	6.70420i	−0.114132	−	0.380773i
$311$	−18.8112			−1.06669			−0.533343	−	0.845899i	$-0.679065\pi$
$311$	−18.8112			−1.06669			−0.533343	+	0.845899i	$0.679065\pi$
$312$		0			0
$313$	14.6481	−	14.6481i	0.827959	−	0.827959i	−0.159275	−	0.987234i	$-0.550916\pi$
$313$	14.6481	−	14.6481i	0.827959	−	0.827959i	0.987234	+	0.159275i	$0.0509156\pi$
$314$	−17.9165			−1.01109
$315$		0			0
$316$		−	7.16924i		−	0.403301i
$317$	0.943658	−	0.943658i	0.0530011	−	0.0530011i	−0.680109	−	0.733111i	$-0.738068\pi$
$317$	0.943658	−	0.943658i	0.0530011	−	0.0530011i	0.733111	+	0.680109i	$0.238068\pi$
$318$		0			0
$319$	4.54261			0.254337
$320$	−1.06059	+	1.96854i	−0.0592890	+	0.110045i
$321$		0			0
$322$	14.5507	−	14.5507i	0.810880	−	0.810880i
$323$	26.6790	+	3.77004i	1.48446	+	0.209770i
$324$		0			0
$325$	4.35046	−	21.1393i	0.241320	−	1.17259i
$326$		−	4.90935i		−	0.271904i
$327$		0			0
$328$	−1.02913	+	1.02913i	−0.0568243	+	0.0568243i
$329$		−	1.65635i		−	0.0913176i
$330$		0			0
$331$			14.9698i			0.822817i	0.911451	+	0.411409i	$0.134963\pi$
$331$			14.9698i			0.822817i	−0.911451	+	0.411409i	$0.865037\pi$
$332$	−4.12119	−	4.12119i	−0.226180	−	0.226180i
$333$		0			0
$334$		−	18.5307i		−	1.01396i
$335$	1.04585	−	0.313481i	0.0571411	−	0.0171273i
$336$		0			0
$337$	18.4481	−	18.4481i	1.00493	−	1.00493i	0.00494423	−	0.999988i	$-0.498426\pi$
$337$	18.4481	−	18.4481i	1.00493	−	1.00493i	0.999988	−	0.00494423i	$-0.00157380\pi$
$338$	−3.98227	−	3.98227i	−0.216607	−	0.216607i
$339$		0			0
$340$	13.2400	−	3.96854i	0.718042	−	0.215224i
$341$			2.51881i			0.136401i
$342$		0			0
$343$	14.0959	−	14.0959i	0.761105	−	0.761105i
$344$	2.69824			0.145479
$345$		0			0
$346$	−10.6160			−0.570718
$347$	−13.3578	−	13.3578i	−0.717083	−	0.717083i	0.250924	−	0.968007i	$-0.419266\pi$
$347$	−13.3578	−	13.3578i	−0.717083	−	0.717083i	−0.968007	+	0.250924i	$0.919266\pi$
$348$		0			0
$349$		−	7.74830i		−	0.414757i	−0.978261	−	0.207379i	$-0.933507\pi$
$349$		−	7.74830i		−	0.414757i	0.978261	−	0.207379i	$-0.0664932\pi$
$350$	−6.44965	−	9.79223i	−0.344748	−	0.523417i
$351$		0			0
$352$	0.569032	−	0.569032i	0.0303295	−	0.0303295i
$353$	24.2462	−	24.2462i	1.29049	−	1.29049i	0.356014	−	0.934481i	$-0.384136\pi$
$353$	24.2462	−	24.2462i	1.29049	−	1.29049i	0.934481	−	0.356014i	$-0.115864\pi$
$354$		0			0
$355$	−7.08700	+	13.1540i	−0.376139	+	0.698141i
$356$			16.7356i			0.886986i
$357$		0			0
$358$	13.7371	−	13.7371i	0.726031	−	0.726031i
$359$		−	0.430016i		−	0.0226954i	−0.999936	−	0.0113477i	$-0.996388\pi$
$359$		−	0.430016i		−	0.0226954i	0.999936	−	0.0113477i	$-0.00361216\pi$
$360$		0			0
$361$	5.26469	−	18.2560i	0.277089	−	0.960844i
$362$	3.24237	+	3.24237i	0.170415	+	0.170415i
$363$		0			0
$364$	−10.1225			−0.530561
$365$	3.19407	−	0.957382i	0.167185	−	0.0501117i
$366$		0			0
$367$	−7.94174	−	7.94174i	−0.414555	−	0.414555i	0.468767	−	0.883322i	$-0.344698\pi$
$367$	−7.94174	−	7.94174i	−0.414555	−	0.414555i	−0.883322	+	0.468767i	$0.844698\pi$
$368$	6.20477	−	6.20477i	0.323446	−	0.323446i
$369$		0			0
$370$	−0.786757	+	1.46028i	−0.0409016	+	0.0759162i
$371$		−	11.2937i		−	0.586339i
$372$		0			0
$373$	−5.72661	−	5.72661i	−0.296513	−	0.296513i	0.543134	−	0.839646i	$-0.317238\pi$
$373$	−5.72661	−	5.72661i	−0.296513	−	0.296513i	−0.839646	+	0.543134i	$0.817238\pi$
$374$	−4.97437			−0.257218
$375$		0			0
$376$		−	0.706307i		−	0.0364250i
$377$	−17.2292	−	17.2292i	−0.887351	−	0.887351i
$378$		0			0
$379$	1.74355			0.0895599			0.0447800	−	0.998997i	$-0.485741\pi$
$379$	1.74355			0.0895599			0.0447800	+	0.998997i	$0.485741\pi$
$380$	−1.46458	−	9.63613i	−0.0751316	−	0.494323i
$381$		0			0
$382$	3.43946	−	3.43946i	0.175978	−	0.175978i
$383$	−14.9492	−	14.9492i	−0.763867	−	0.763867i	0.213152	−	0.977019i	$-0.431627\pi$
$383$	−14.9492	−	14.9492i	−0.763867	−	0.763867i	−0.977019	+	0.213152i	$0.931627\pi$
$384$		0			0
$385$	1.21159	+	4.04216i	0.0617482	+	0.206008i
$386$	14.6106			0.743660
$387$		0			0
$388$	8.25033	+	8.25033i	0.418847	+	0.418847i
$389$		−	9.21427i		−	0.467182i	−0.972335	−	0.233591i	$-0.924952\pi$
$389$		−	9.21427i		−	0.467182i	0.972335	−	0.233591i	$-0.0750477\pi$
$390$		0			0
$391$	−54.2409			−2.74308
$392$	1.06106	−	1.06106i	0.0535916	−	0.0535916i
$393$		0			0
$394$	11.7709			0.593009
$395$	14.1129	+	7.60365i	0.710098	+	0.382581i
$396$		0			0
$397$	−9.28722	−	9.28722i	−0.466112	−	0.466112i	0.434540	−	0.900652i	$-0.356911\pi$
$397$	−9.28722	−	9.28722i	−0.466112	−	0.466112i	−0.900652	+	0.434540i	$0.856911\pi$
$398$	16.3372	+	16.3372i	0.818908	+	0.818908i
$399$		0			0
$400$	−2.75028	−	4.17564i	−0.137514	−	0.208782i
$401$		−	38.6944i		−	1.93231i	−0.257971	−	0.966153i	$-0.583054\pi$
$401$		−	38.6944i		−	1.93231i	0.257971	−	0.966153i	$-0.416946\pi$
$402$		0			0
$403$	9.55336	−	9.55336i	0.475887	−	0.475887i
$404$		−	1.75296i		−	0.0872132i
$405$		0			0
$406$	−13.2377			−0.656977
$407$	0.422113	−	0.422113i	0.0209234	−	0.0209234i
$408$		0			0
$409$	−14.6817			−0.725964			−0.362982	−	0.931796i	$-0.618241\pi$
$409$	−14.6817			−0.725964			−0.362982	+	0.931796i	$0.618241\pi$
$410$	−0.934394	−	3.11737i	−0.0461464	−	0.153956i
$411$		0			0
$412$	5.55918	−	5.55918i	0.273881	−	0.273881i
$413$	−4.60464	−	4.60464i	−0.226579	−	0.226579i
$414$		0			0
$415$	12.4836	−	3.74181i	0.612797	−	0.183678i
$416$	−4.31645			−0.211632
$417$		0			0
$418$	−0.490807	+	3.47324i	−0.0240062	+	0.169882i
$419$			1.27584i			0.0623290i	0.999514	+	0.0311645i	$0.00992157\pi$
$419$			1.27584i			0.0623290i	−0.999514	+	0.0311645i	$0.990078\pi$
$420$		0			0
$421$		−	6.74319i		−	0.328643i	−0.986407	−	0.164321i	$-0.947457\pi$
$421$		−	6.74319i		−	0.328643i	0.986407	−	0.164321i	$-0.0525434\pi$
$422$	10.8535	+	10.8535i	0.528340	+	0.528340i
$423$		0			0
$424$		−	4.81589i		−	0.233880i
$425$	−6.23009	+	30.2725i	−0.302204	+	1.46843i
$426$		0			0
$427$	10.2469	+	10.2469i	0.495884	+	0.495884i
$428$	2.01985	+	2.01985i	0.0976332	+	0.0976332i
$429$		0			0
$430$	−2.86174	+	5.31159i	−0.138005	+	0.256148i
$431$			11.0055i			0.530118i	0.964232	+	0.265059i	$0.0853915\pi$
$431$			11.0055i			0.530118i	−0.964232	+	0.265059i	$0.914608\pi$
$432$		0			0
$433$	−3.70282	−	3.70282i	−0.177946	−	0.177946i	0.612514	−	0.790460i	$-0.290158\pi$
$433$	−3.70282	−	3.70282i	−0.177946	−	0.177946i	−0.790460	+	0.612514i	$0.790158\pi$
$434$		−	7.34012i		−	0.352337i
$435$		0			0
$436$		−	13.3175i		−	0.637792i
$437$	−5.35180	+	37.8725i	−0.256011	+	1.81169i
$438$		0			0
$439$	32.4807			1.55022			0.775110	−	0.631826i	$-0.217694\pi$
$439$	32.4807			1.55022			0.775110	+	0.631826i	$0.217694\pi$
$440$	0.516649	+	1.72367i	0.0246303	+	0.0821729i
$441$		0			0
$442$	18.8668	+	18.8668i	0.897403	+	0.897403i
$443$	−9.15145	+	9.15145i	−0.434798	+	0.434798i	−0.890257	−	0.455459i	$-0.849475\pi$
$443$	−9.15145	+	9.15145i	−0.434798	+	0.434798i	0.455459	+	0.890257i	$0.349475\pi$
$444$		0			0
$445$	−32.9447	−	17.7497i	−1.56173	−	0.841416i
$446$	−26.3006			−1.24537
$447$		0			0
$448$	−1.65823	+	1.65823i	−0.0783439	+	0.0783439i
$449$	0.503369			0.0237554			0.0118777	−	0.999929i	$-0.496219\pi$
$449$	0.503369			0.0237554			0.0118777	+	0.999929i	$0.496219\pi$
$450$		0			0
$451$			1.17122i			0.0551505i
$452$	10.8883	−	10.8883i	0.512143	−	0.512143i
$453$		0			0
$454$			7.80473i			0.366294i
$455$	10.7358	−	19.9265i	0.503303	−	0.934166i
$456$		0			0
$457$	8.26087	+	8.26087i	0.386427	+	0.386427i	0.873411	−	0.486984i	$-0.161903\pi$
$457$	8.26087	+	8.26087i	0.386427	+	0.386427i	−0.486984	+	0.873411i	$0.661903\pi$
$458$	7.03132	+	7.03132i	0.328552	+	0.328552i
$459$		0			0
$460$	5.63358	+	18.7951i	0.262667	+	0.876324i
$461$	−18.1189			−0.843882			−0.421941	−	0.906623i	$-0.638651\pi$
$461$	−18.1189			−0.843882			−0.421941	+	0.906623i	$0.638651\pi$
$462$		0			0
$463$	20.7494	−	20.7494i	0.964308	−	0.964308i	−0.0350766	−	0.999385i	$-0.511168\pi$
$463$	20.7494	−	20.7494i	0.964308	−	0.964308i	0.999385	+	0.0350766i	$0.0111675\pi$
$464$	−5.64487			−0.262057
$465$		0			0
$466$			7.22827i			0.334843i
$467$	−18.0874	−	18.0874i	−0.836985	−	0.836985i	0.151476	−	0.988461i	$-0.451597\pi$
$467$	−18.0874	−	18.0874i	−0.836985	−	0.836985i	−0.988461	+	0.151476i	$0.951597\pi$
$468$		0			0
$469$	1.14506			0.0528738
$470$	1.39039	+	0.749105i	0.0641340	+	0.0345536i
$471$		0			0
$472$	−1.96353	−	1.96353i	−0.0903786	−	0.0903786i
$473$	1.53539	−	1.53539i	0.0705971	−	0.0705971i
$474$		0			0
$475$	20.5224	+	7.33693i	0.941633	+	0.336641i
$476$	14.4959			0.664419
$477$		0			0
$478$	−6.57984	−	6.57984i	−0.300955	−	0.300955i
$479$		−	1.97995i		−	0.0904662i	−0.998976	−	0.0452331i	$-0.985597\pi$
$479$		−	1.97995i		−	0.0904662i	0.998976	−	0.0452331i	$-0.0144031\pi$
$480$		0			0
$481$	−3.20198			−0.145998
$482$	5.87881	+	5.87881i	0.267773	+	0.267773i
$483$		0			0
$484$			10.3524i			0.470564i
$485$	−24.9913	+	7.49084i	−1.13480	+	0.340142i
$486$		0			0
$487$	−1.84597	+	1.84597i	−0.0836489	+	0.0836489i	−0.747693	−	0.664044i	$-0.768839\pi$
$487$	−1.84597	+	1.84597i	−0.0836489	+	0.0836489i	0.664044	+	0.747693i	$0.268839\pi$
$488$	4.36953	+	4.36953i	0.197799	+	0.197799i
$489$		0			0
$490$	0.963384	+	3.21409i	0.0435212	+	0.145198i
$491$	5.60811			0.253091			0.126545	−	0.991961i	$-0.459611\pi$
$491$	5.60811			0.253091			0.126545	+	0.991961i	$0.459611\pi$
$492$		0			0
$493$	24.6732	+	24.6732i	1.11122	+	1.11122i
$494$	15.0349	−	11.3118i	0.676450	−	0.508942i
$495$		0			0
$496$		−	3.13000i		−	0.140541i
$497$	−11.0805	+	11.0805i	−0.497026	+	0.497026i
$498$		0			0
$499$			18.8853i			0.845422i	0.906264	+	0.422711i	$0.138922\pi$
$499$			18.8853i			0.845422i	−0.906264	+	0.422711i	$0.861078\pi$
$500$	11.1368	−	0.985382i	0.498054	−	0.0440676i
$501$		0			0
$502$	7.61628	−	7.61628i	0.339931	−	0.339931i
$503$	26.9767	−	26.9767i	1.20283	−	1.20283i	0.229532	−	0.973301i	$-0.426280\pi$
$503$	26.9767	−	26.9767i	1.20283	−	1.20283i	0.973301	−	0.229532i	$-0.0737196\pi$
$504$		0			0
$505$	3.45078	+	1.85918i	0.153558	+	0.0827325i
$506$		−	7.06142i		−	0.313919i
$507$		0			0
$508$	10.4120	+	10.4120i	0.461960	+	0.461960i
$509$	−30.3840			−1.34675			−0.673374	−	0.739302i	$-0.735156\pi$
$509$	−30.3840			−1.34675			−0.673374	+	0.739302i	$0.735156\pi$
$510$		0			0
$511$	3.49704			0.154700
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			28.0873i			1.23888i
$515$	5.04742	+	16.8395i	0.222416	+	0.742036i
$516$		0			0
$517$	−0.401911	−	0.401911i	−0.0176760	−	0.0176760i
$518$	−1.23009	+	1.23009i	−0.0540469	+	0.0540469i
$519$		0			0
$520$	4.57800	−	8.49710i	0.200759	−	0.372623i
$521$		−	41.3468i		−	1.81143i	−0.423882	−	0.905717i	$-0.639333\pi$
$521$		−	41.3468i		−	1.81143i	0.423882	−	0.905717i	$-0.360667\pi$
$522$		0			0
$523$	−10.9169	−	10.9169i	−0.477361	−	0.477361i	0.426926	−	0.904287i	$-0.359597\pi$
$523$	−10.9169	−	10.9169i	−0.477361	−	0.477361i	−0.904287	+	0.426926i	$0.859597\pi$
$524$		−	15.4836i		−	0.676405i
$525$		0			0
$526$		−	18.6625i		−	0.813725i
$527$	−13.6809	+	13.6809i	−0.595950	+	0.595950i
$528$		0			0
$529$		−	53.9983i		−	2.34775i
$530$	9.48026	+	5.10770i	0.411796	+	0.221864i
$531$		0			0
$532$	1.43027	−	10.1214i	0.0620101	−	0.438820i
$533$	4.44220	−	4.44220i	0.192413	−	0.192413i
$534$		0			0
$535$	−6.11839	+	1.83391i	−0.264521	+	0.0792870i
$536$	0.488279			0.0210904
$537$		0			0
$538$	−12.8170	+	12.8170i	−0.552581	+	0.552581i
$539$		−	1.20755i		−	0.0520130i
$540$		0			0
$541$	41.7436			1.79470			0.897350	−	0.441320i	$-0.145490\pi$
$541$	41.7436			1.79470			0.897350	+	0.441320i	$0.145490\pi$
$542$	5.39019	−	5.39019i	0.231529	−	0.231529i
$543$		0			0
$544$	6.18139			0.265025
$545$	26.2160	+	14.1244i	1.12297	+	0.605024i
$546$		0			0
$547$	16.6189	−	16.6189i	0.710571	−	0.710571i	−0.256083	−	0.966655i	$-0.582432\pi$
$547$	16.6189	−	16.6189i	0.710571	−	0.710571i	0.966655	+	0.256083i	$0.0824322\pi$
$548$	3.37204	−	3.37204i	0.144046	−	0.144046i
$549$		0			0
$550$	−3.94107	−	0.811072i	−0.168048	−	0.0345842i
$551$	19.6619	−	14.7931i	0.837627	−	0.630206i
$552$		0			0
$553$	11.8882	+	11.8882i	0.505539	+	0.505539i
$554$	2.75362			0.116990
$555$		0			0
$556$	2.05826			0.0872898
$557$	−14.9213	−	14.9213i	−0.632234	−	0.632234i	0.316394	−	0.948628i	$-0.397528\pi$
$557$	−14.9213	−	14.9213i	−0.632234	−	0.632234i	−0.948628	+	0.316394i	$0.897528\pi$
$558$		0			0
$559$	−11.6468			−0.492609
$560$	−1.50558	−	5.02299i	−0.0636223	−	0.212260i
$561$		0			0
$562$	4.08626	+	4.08626i	0.172369	+	0.172369i
$563$	−24.7032	−	24.7032i	−1.04112	−	1.04112i	−0.999118	−	0.0419980i	$-0.986628\pi$
$563$	−24.7032	−	24.7032i	−1.04112	−	1.04112i	−0.0419980	−	0.999118i	$-0.513372\pi$
$564$		0			0
$565$	9.88597	+	32.9821i	0.415906	+	1.38757i
$566$		−	30.1155i		−	1.26585i
$567$		0			0
$568$	−4.72496	+	4.72496i	−0.198255	+	0.198255i
$569$	19.1003			0.800725			0.400362	−	0.916357i	$-0.368884\pi$
$569$	19.1003			0.800725			0.400362	+	0.916357i	$0.368884\pi$
$570$		0			0
$571$	−33.3161			−1.39424			−0.697118	−	0.716957i	$-0.745535\pi$
$571$	−33.3161			−1.39424			−0.697118	+	0.716957i	$0.745535\pi$
$572$	−2.45620	+	2.45620i	−0.102699	+	0.102699i
$573$		0			0
$574$		−	3.41307i		−	0.142459i
$575$	−42.9737	−	8.84399i	−1.79213	−	0.368820i
$576$		0			0
$577$	15.5550	+	15.5550i	0.647564	+	0.647564i	0.952404	−	0.304840i	$-0.0986029\pi$
$577$	15.5550	+	15.5550i	0.647564	+	0.647564i	−0.304840	+	0.952404i	$0.598603\pi$
$578$	−14.9975	−	14.9975i	−0.623812	−	0.623812i
$579$		0			0
$580$	5.98691	−	11.1121i	0.248593	−	0.461407i
$581$	13.6677			0.567033
$582$		0			0
$583$	−2.74039	−	2.74039i	−0.113496	−	0.113496i
$584$	1.49122			0.0617070
$585$		0			0
$586$	−8.40304			−0.347126
$587$	12.0651	+	12.0651i	0.497979	+	0.497979i	0.910808	−	0.412829i	$-0.135459\pi$
$587$	12.0651	+	12.0651i	0.497979	+	0.497979i	−0.412829	+	0.910808i	$0.635459\pi$
$588$		0			0
$589$	8.20254	+	10.9023i	0.337980	+	0.449220i
$590$	5.94778	−	1.78277i	0.244866	−	0.0733956i
$591$		0			0
$592$	−0.524538	+	0.524538i	−0.0215584	+	0.0215584i
$593$	−11.1513	+	11.1513i	−0.457931	+	0.457931i	−0.897976	−	0.440045i	$-0.854963\pi$
$593$	−11.1513	+	11.1513i	−0.457931	+	0.457931i	0.440045	+	0.897976i	$0.354963\pi$
$594$		0			0
$595$	−15.3743	+	28.5357i	−0.630283	+	1.16985i
$596$	−19.5419			−0.800467
$597$		0			0
$598$	−26.7826	+	26.7826i	−1.09522	+	1.09522i
$599$	9.96626			0.407210			0.203605	−	0.979053i	$-0.434734\pi$
$599$	9.96626			0.407210			0.203605	+	0.979053i	$0.434734\pi$
$600$		0			0
$601$		−	13.6021i		−	0.554840i	−0.960749	−	0.277420i	$-0.910521\pi$
$601$		−	13.6021i		−	0.554840i	0.960749	−	0.277420i	$-0.0894794\pi$
$602$	−4.47430	+	4.47430i	−0.182359	+	0.182359i
$603$		0			0
$604$	0.641287			0.0260936
$605$	−20.3791	−	10.9797i	−0.828528	−	0.446388i
$606$		0			0
$607$	−11.0390	+	11.0390i	−0.448060	+	0.448060i	−0.894709	−	0.446649i	$-0.852617\pi$
$607$	−11.0390	+	11.0390i	−0.448060	+	0.448060i	0.446649	+	0.894709i	$0.352617\pi$
$608$	0.609901	−	4.31602i	0.0247347	−	0.175038i
$609$		0			0
$610$	−13.2359	+	3.96729i	−0.535905	+	0.160631i
$611$			3.04874i			0.123339i
$612$		0			0
$613$	11.0338	−	11.0338i	0.445651	−	0.445651i	−0.448255	−	0.893906i	$-0.647954\pi$
$613$	11.0338	−	11.0338i	0.445651	−	0.445651i	0.893906	+	0.448255i	$0.147954\pi$
$614$			3.78220i			0.152637i
$615$		0			0
$616$			1.88717i			0.0760362i
$617$	−4.29188	−	4.29188i	−0.172785	−	0.172785i	0.615417	−	0.788202i	$-0.288988\pi$
$617$	−4.29188	−	4.29188i	−0.172785	−	0.172785i	−0.788202	+	0.615417i	$0.788988\pi$
$618$		0			0
$619$		−	34.2230i		−	1.37554i	−0.725929	−	0.687770i	$-0.758590\pi$
$619$		−	34.2230i		−	1.37554i	0.725929	−	0.687770i	$-0.241410\pi$
$620$	6.16152	+	3.31966i	0.247453	+	0.133321i
$621$		0			0
$622$	13.3015	−	13.3015i	0.533343	−	0.533343i
$623$	−27.7514	−	27.7514i	−1.11184	−	1.11184i
$624$		0			0
$625$	−9.87189	+	22.9684i	−0.394876	+	0.918735i
$626$			20.7155i			0.827959i
$627$		0			0
$628$	12.6689	−	12.6689i	0.505543	−	0.505543i
$629$	4.58541			0.182832
$630$		0			0
$631$	−14.1221			−0.562192			−0.281096	−	0.959680i	$-0.590698\pi$
$631$	−14.1221			−0.562192			−0.281096	+	0.959680i	$0.590698\pi$
$632$	5.06942	+	5.06942i	0.201651	+	0.201651i
$633$		0			0
$634$			1.33453i			0.0530011i
$635$	−31.5395	+	9.45356i	−1.25161	+	0.375153i
$636$		0			0
$637$	−4.58002	+	4.58002i	−0.181467	+	0.181467i
$638$	−3.21211	+	3.21211i	−0.127169	+	0.127169i
$639$		0			0
$640$	−0.642014	−	2.14192i	−0.0253778	−	0.0846668i
$641$			18.1482i			0.716812i	0.933566	+	0.358406i	$0.116680\pi$
$641$			18.1482i			0.716812i	−0.933566	+	0.358406i	$0.883320\pi$
$642$		0			0
$643$	−7.69230	+	7.69230i	−0.303355	+	0.303355i	−0.842325	−	0.538970i	$-0.818814\pi$
$643$	−7.69230	+	7.69230i	−0.303355	+	0.303355i	0.538970	+	0.842325i	$0.318814\pi$
$644$			20.5778i			0.810880i
$645$		0			0
$646$	−21.5307	+	16.1991i	−0.847115	+	0.637345i
$647$	−18.0736	−	18.0736i	−0.710545	−	0.710545i	0.256104	−	0.966649i	$-0.417561\pi$
$647$	−18.0736	−	18.0736i	−0.710545	−	0.710545i	−0.966649	+	0.256104i	$0.917561\pi$
$648$		0			0
$649$	−2.23462			−0.0877164
$650$	11.8715	+	18.0239i	0.465637	+	0.706957i
$651$		0			0
$652$	3.47143	+	3.47143i	0.135952	+	0.135952i
$653$	−14.3290	+	14.3290i	−0.560736	+	0.560736i	−0.929516	−	0.368781i	$-0.879775\pi$
$653$	−14.3290	+	14.3290i	−0.560736	+	0.560736i	0.368781	+	0.929516i	$0.379775\pi$
$654$		0			0
$655$	30.4801	+	16.4218i	1.19096	+	0.641654i
$656$		−	1.45541i		−	0.0568243i
$657$		0			0
$658$	1.17122	+	1.17122i	0.0456588	+	0.0456588i
$659$	15.0999			0.588208			0.294104	−	0.955773i	$-0.404979\pi$
$659$	15.0999			0.588208			0.294104	+	0.955773i	$0.404979\pi$
$660$		0			0
$661$		−	37.7035i		−	1.46650i	−0.679962	−	0.733248i	$-0.738004\pi$
$661$		−	37.7035i		−	1.46650i	0.679962	−	0.733248i	$-0.261996\pi$
$662$	−10.5853	−	10.5853i	−0.411409	−	0.411409i
$663$		0			0
$664$	5.82824			0.226180
$665$	18.4075	+	13.5503i	0.713812	+	0.525457i
$666$		0			0
$667$	−35.0251	+	35.0251i	−1.35618	+	1.35618i
$668$	13.1032	+	13.1032i	0.506978	+	0.506978i
$669$		0			0
$670$	−0.517865	+	0.961195i	−0.0200069	+	0.0371342i
$671$	4.97281			0.191973
$672$		0			0
$673$	−20.8241	−	20.8241i	−0.802710	−	0.802710i	0.180808	−	0.983518i	$-0.442129\pi$
$673$	−20.8241	−	20.8241i	−0.802710	−	0.802710i	−0.983518	+	0.180808i	$0.942129\pi$
$674$			26.0896i			1.00493i
$675$		0			0
$676$	5.63178			0.216607
$677$	−22.3987	+	22.3987i	−0.860850	+	0.860850i	−0.991437	−	0.130587i	$-0.958314\pi$
$677$	−22.3987	+	22.3987i	−0.860850	+	0.860850i	0.130587	+	0.991437i	$0.458314\pi$
$678$		0			0
$679$	−27.3618			−1.05005
$680$	−6.55594	+	12.1683i	−0.251409	+	0.466633i
$681$		0			0
$682$	−1.78107	−	1.78107i	−0.0682007	−	0.0682007i
$683$	−3.33340	−	3.33340i	−0.127549	−	0.127549i	0.640451	−	0.767999i	$-0.278748\pi$
$683$	−3.33340	−	3.33340i	−0.127549	−	0.127549i	−0.767999	+	0.640451i	$0.778748\pi$
$684$		0			0
$685$	3.06162	+	10.2143i	0.116979	+	0.390270i
$686$			19.9346i			0.761105i
$687$		0			0
$688$	−1.90794	+	1.90794i	−0.0727397	+	0.0727397i
$689$			20.7876i			0.791943i
$690$		0			0
$691$	−0.218008			−0.00829342			−0.00414671	−	0.999991i	$-0.501320\pi$
$691$	−0.218008			−0.00829342			−0.00414671	+	0.999991i	$0.501320\pi$
$692$	7.50662	−	7.50662i	0.285359	−	0.285359i
$693$		0			0
$694$	18.8907			0.717083
$695$	−2.18298	+	4.05177i	−0.0828052	+	0.153692i
$696$		0			0
$697$	−6.36146	+	6.36146i	−0.240958	+	0.240958i
$698$	5.47888	+	5.47888i	0.207379	+	0.207379i
$699$		0			0
$700$	11.4847	+	2.36356i	0.434083	+	0.0893342i
$701$	4.66660			0.176255			0.0881275	−	0.996109i	$-0.471912\pi$
$701$	4.66660			0.176255			0.0881275	+	0.996109i	$0.471912\pi$
$702$		0			0
$703$	0.452430	−	3.20166i	0.0170637	−	0.120753i
$704$			0.804733i			0.0303295i
$705$		0			0
$706$			34.2893i			1.29049i
$707$	2.90681	+	2.90681i	0.109322	+	0.109322i
$708$		0			0
$709$			0.424223i			0.0159320i	0.999968	+	0.00796602i	$0.00253569\pi$
$709$			0.424223i			0.0159320i	−0.999968	+	0.00796602i	$0.997464\pi$
$710$	−4.29000	−	14.3125i	−0.161001	−	0.537140i
$711$		0			0
$712$	−11.8339	−	11.8339i	−0.443493	−	0.443493i
$713$	−19.4209	−	19.4209i	−0.727319	−	0.727319i
$714$		0			0
$715$	−2.23009	−	7.44015i	−0.0834008	−	0.278246i
$716$			19.4273i			0.726031i
$717$		0			0
$718$	0.304067	+	0.304067i	0.0113477	+	0.0113477i
$719$			9.56441i			0.356692i	0.983968	+	0.178346i	$0.0570747\pi$
$719$			9.56441i			0.356692i	−0.983968	+	0.178346i	$0.942925\pi$
$720$		0			0
$721$			18.4368i			0.686621i
$722$	9.18628	+	16.6317i	0.341878	+	0.618967i
$723$		0			0
$724$	−4.58541			−0.170415
$725$	15.5250	+	23.5709i	0.576584	+	0.875402i
$726$		0			0
$727$	2.48083	+	2.48083i	0.0920089	+	0.0920089i	0.751613	−	0.659604i	$-0.229276\pi$
$727$	2.48083	+	2.48083i	0.0920089	+	0.0920089i	−0.659604	+	0.751613i	$0.729276\pi$
$728$	7.15766	−	7.15766i	0.265281	−	0.265281i
$729$		0			0
$730$	−1.58158	+	2.93552i	−0.0585367	+	0.108648i
$731$	16.6789			0.616891
$732$		0			0
$733$	−16.0819	+	16.0819i	−0.594000	+	0.594000i	−0.938709	−	0.344710i	$-0.887977\pi$
$733$	−16.0819	+	16.0819i	−0.594000	+	0.594000i	0.344710	+	0.938709i	$0.387977\pi$
$734$	11.2313			0.414555
$735$		0			0
$736$			8.77487i			0.323446i
$737$	0.277846	−	0.277846i	0.0102346	−	0.0102346i
$738$		0			0
$739$		−	35.9583i		−	1.32275i	−0.750056	−	0.661374i	$-0.769973\pi$
$739$		−	35.9583i		−	1.32275i	0.750056	−	0.661374i	$-0.230027\pi$
$740$	−0.476251	−	1.58889i	−0.0175073	−	0.0584089i
$741$		0			0
$742$	7.98584	+	7.98584i	0.293169	+	0.293169i
$743$	−24.1408	−	24.1408i	−0.885639	−	0.885639i	0.108462	−	0.994101i	$-0.465407\pi$
$743$	−24.1408	−	24.1408i	−0.885639	−	0.885639i	−0.994101	+	0.108462i	$0.965407\pi$
$744$		0			0
$745$	20.7260	−	38.4689i	0.759342	−	1.40939i
$746$	8.09865			0.296513
$747$		0			0
$748$	3.51741	−	3.51741i	0.128609	−	0.128609i
$749$	−6.69874			−0.244767
$750$		0			0
$751$			1.42885i			0.0521395i	0.999660	+	0.0260697i	$0.00829920\pi$
$751$			1.42885i			0.0521395i	−0.999660	+	0.0260697i	$0.991701\pi$
$752$	0.499434	+	0.499434i	0.0182125	+	0.0182125i
$753$		0			0
$754$	24.3658			0.887351
$755$	−0.680145	+	1.26240i	−0.0247530	+	0.0459434i
$756$		0			0
$757$	−17.6271	−	17.6271i	−0.640668	−	0.640668i	0.310051	−	0.950720i	$-0.399654\pi$
$757$	−17.6271	−	17.6271i	−0.640668	−	0.640668i	−0.950720	+	0.310051i	$0.899654\pi$
$758$	−1.23287	+	1.23287i	−0.0447800	+	0.0447800i
$759$		0			0
$760$	7.84939	+	5.77815i	0.284727	+	0.209596i
$761$	33.0942			1.19966			0.599832	−	0.800126i	$-0.295234\pi$
$761$	33.0942			1.19966			0.599832	+	0.800126i	$0.295234\pi$
$762$		0			0
$763$	22.0834	+	22.0834i	0.799473	+	0.799473i
$764$			4.86413i			0.175978i
$765$		0			0
$766$	21.1413			0.763867
$767$	8.47547	+	8.47547i	0.306031	+	0.306031i
$768$		0			0
$769$		−	2.61399i		−	0.0942629i	−0.998889	−	0.0471314i	$-0.984992\pi$
$769$		−	2.61399i		−	0.0942629i	0.998889	−	0.0471314i	$-0.0150080\pi$
$770$	−3.71496	−	2.00152i	−0.133878	−	0.0721297i
$771$		0			0
$772$	−10.3313	+	10.3313i	−0.371830	+	0.371830i
$773$	14.4070	+	14.4070i	0.518182	+	0.518182i	0.917021	−	0.398839i	$-0.130587\pi$
$773$	14.4070	+	14.4070i	0.518182	+	0.518182i	−0.398839	+	0.917021i	$0.630587\pi$
$774$		0			0
$775$	−13.0697	+	8.60838i	−0.469479	+	0.309222i
$776$	−11.6677			−0.418847
$777$		0			0
$778$	6.51547	+	6.51547i	0.233591	+	0.233591i
$779$	3.81408	+	5.06942i	0.136654	+	0.181631i
$780$		0			0
$781$			5.37731i			0.192415i
$782$	38.3541	−	38.3541i	1.37154	−	1.37154i
$783$		0			0
$784$			1.50057i			0.0535916i
$785$	11.5026	+	38.3756i	0.410546	+	1.36969i
$786$		0			0
$787$	28.5405	−	28.5405i	1.01736	−	1.01736i	0.0175140	−	0.999847i	$-0.494425\pi$
$787$	28.5405	−	28.5405i	1.01736	−	1.01736i	0.999847	−	0.0175140i	$-0.00557518\pi$
$788$	−8.32327	+	8.32327i	−0.296504	+	0.296504i
$789$		0			0
$790$	−15.3559	+	4.60275i	−0.546340	+	0.163759i
$791$			36.1105i			1.28394i
$792$		0			0
$793$	−18.8609	−	18.8609i	−0.669769	−	0.669769i
$794$	13.1341			0.466112
$795$		0			0
$796$	−23.1042			−0.818908
$797$	19.4519	−	19.4519i	0.689021	−	0.689021i	−0.272995	−	0.962016i	$-0.588014\pi$
$797$	19.4519	−	19.4519i	0.689021	−	0.689021i	0.962016	+	0.272995i	$0.0880141\pi$
$798$		0			0
$799$		−	4.36596i		−	0.154457i
$800$	4.89736	+	1.00788i	0.173148	+	0.0356339i
$801$		0			0
$802$	27.3611	+	27.3611i	0.966153	+	0.966153i
$803$	0.848550	−	0.848550i	0.0299447	−	0.0299447i
$804$		0			0
$805$	−40.5082	−	21.8247i	−1.42773	−	0.769220i
$806$			13.5105i			0.475887i
$807$		0			0
$808$	1.23953	+	1.23953i	0.0436066	+	0.0436066i
$809$		−	1.15579i		−	0.0406353i	−0.999794	−	0.0203176i	$-0.993532\pi$
$809$		−	1.15579i		−	0.0406353i	0.999794	−	0.0203176i	$-0.00646775\pi$
$810$		0			0
$811$			39.4268i			1.38446i	0.721675	+	0.692232i	$0.243372\pi$
$811$			39.4268i			1.38446i	−0.721675	+	0.692232i	$0.756628\pi$
$812$	9.36048	−	9.36048i	0.328488	−	0.328488i
$813$		0			0
$814$			0.596958i			0.0209234i
$815$	−10.5154	+	3.15187i	−0.368339	+	0.110405i
$816$		0			0
$817$	1.64566	−	11.6457i	0.0575743	−	0.407430i
$818$	10.3815	−	10.3815i	0.362982	−	0.362982i
$819$		0			0
$820$	2.86503	+	1.54360i	0.100051	+	0.0539049i
$821$	−12.3926			−0.432504			−0.216252	−	0.976338i	$-0.569383\pi$
$821$	−12.3926			−0.432504			−0.216252	+	0.976338i	$0.569383\pi$
$822$		0			0
$823$	15.3766	−	15.3766i	0.535994	−	0.535994i	−0.386356	−	0.922350i	$-0.626266\pi$
$823$	15.3766	−	15.3766i	0.535994	−	0.535994i	0.922350	+	0.386356i	$0.126266\pi$
$824$			7.86186i			0.273881i
$825$		0			0
$826$	6.51194			0.226579
$827$	−26.9516	+	26.9516i	−0.937197	+	0.937197i	−0.998141	−	0.0609437i	$-0.980589\pi$
$827$	−26.9516	+	26.9516i	−0.937197	+	0.937197i	0.0609437	+	0.998141i	$0.480589\pi$
$828$		0			0
$829$	12.4871			0.433696			0.216848	−	0.976205i	$-0.430422\pi$
$829$	12.4871			0.433696			0.216848	+	0.976205i	$0.430422\pi$
$830$	−6.18139	+	11.4731i	−0.214559	+	0.398237i
$831$		0			0
$832$	3.05219	−	3.05219i	0.105816	−	0.105816i
$833$	6.55883	−	6.55883i	0.227250	−	0.227250i
$834$		0			0
$835$	−39.6913	+	11.8970i	−1.37357	+	0.411712i
$836$	−2.10890	−	2.80301i	−0.0729378	−	0.0969440i
$837$		0			0
$838$	−0.902156	−	0.902156i	−0.0311645	−	0.0311645i
$839$	−6.90128			−0.238259			−0.119129	−	0.992879i	$-0.538010\pi$
$839$	−6.90128			−0.238259			−0.119129	+	0.992879i	$0.538010\pi$
$840$		0			0
$841$	2.86456			0.0987778
$842$	4.76815	+	4.76815i	0.164321	+	0.164321i
$843$		0			0
$844$	−15.3492			−0.528340
$845$	−5.97303	+	11.0864i	−0.205478	+	0.381383i
$846$		0			0
$847$	−17.1666	−	17.1666i	−0.589853	−	0.589853i
$848$	3.40535	+	3.40535i	0.116940	+	0.116940i
$849$		0			0
$850$	−17.0006	−	25.8112i	−0.583115	−	0.885319i
$851$			6.50927i			0.223135i
$852$		0			0
$853$	−19.4959	+	19.4959i	−0.667527	+	0.667527i	−0.957143	−	0.289616i	$-0.906472\pi$
$853$	−19.4959	+	19.4959i	−0.667527	+	0.667527i	0.289616	+	0.957143i	$0.406472\pi$
$854$	−14.4913			−0.495884
$855$		0			0
$856$	−2.85650			−0.0976332
$857$	−31.0425	+	31.0425i	−1.06039	+	1.06039i	−0.0623378	+	0.998055i	$0.519856\pi$
$857$	−31.0425	+	31.0425i	−1.06039	+	1.06039i	−0.998055	+	0.0623378i	$0.980144\pi$
$858$		0			0
$859$			33.3721i			1.13864i	0.822115	+	0.569321i	$0.192794\pi$
$859$			33.3721i			1.13864i	−0.822115	+	0.569321i	$0.807206\pi$
$860$	−1.73231	−	5.77941i	−0.0590712	−	0.197076i
$861$		0			0
$862$	−7.78210	−	7.78210i	−0.265059	−	0.265059i
$863$	−10.3810	−	10.3810i	−0.353373	−	0.353373i	0.507990	−	0.861363i	$-0.330389\pi$
$863$	−10.3810	−	10.3810i	−0.353373	−	0.353373i	−0.861363	+	0.507990i	$0.830389\pi$
$864$		0			0
$865$	6.81559	+	22.7385i	0.231737	+	0.773133i
$866$	5.23658			0.177946
$867$		0			0
$868$	5.19025	+	5.19025i	0.176168	+	0.176168i
$869$	5.76932			0.195711
$870$		0			0
$871$	−2.10763			−0.0714144
$872$	9.41688	+	9.41688i	0.318896	+	0.318896i
$873$		0			0
$874$	−22.9956	−	30.5642i	−0.777838	−	1.03385i
$875$	−16.8334	+	20.1014i	−0.569073	+	0.679551i
$876$		0			0
$877$	−1.64017	+	1.64017i	−0.0553847	+	0.0553847i	−0.734257	−	0.678872i	$-0.762469\pi$
$877$	−1.64017	+	1.64017i	−0.0553847	+	0.0553847i	0.678872	+	0.734257i	$0.262469\pi$
$878$	−22.9673	+	22.9673i	−0.775110	+	0.775110i
$879$		0			0
$880$	−1.58415	−	0.853494i	−0.0534016	−	0.0287713i
$881$	44.0880			1.48536			0.742681	−	0.669645i	$-0.233554\pi$
$881$	44.0880			1.48536			0.742681	+	0.669645i	$0.233554\pi$
$882$		0			0
$883$	15.3555	−	15.3555i	0.516754	−	0.516754i	−0.399834	−	0.916588i	$-0.630932\pi$
$883$	15.3555	−	15.3555i	0.516754	−	0.516754i	0.916588	+	0.399834i	$0.130932\pi$
$884$	−26.6817			−0.897403
$885$		0			0
$886$		−	12.9421i		−	0.434798i
$887$	20.5729	−	20.5729i	0.690769	−	0.690769i	−0.271632	−	0.962401i	$-0.587563\pi$
$887$	20.5729	−	20.5729i	0.690769	−	0.690769i	0.962401	+	0.271632i	$0.0875633\pi$
$888$		0			0
$889$	−34.5311			−1.15814
$890$	35.8463	−	10.7445i	1.20157	−	0.360156i
$891$		0			0
$892$	18.5974	−	18.5974i	0.622686	−	0.622686i
$893$	−3.04843	−	0.430777i	−0.102012	−	0.0144154i
$894$		0			0
$895$	−38.2433	−	20.6044i	−1.27833	−	0.688730i
$896$		−	2.34509i		−	0.0783439i
$897$		0			0
$898$	−0.355936	+	0.355936i	−0.0118777	+	0.0118777i
$899$			17.6684i			0.589275i
$900$		0			0
$901$		−	29.7689i		−	0.991746i
$902$	−0.828176	−	0.828176i	−0.0275752	−	0.0275752i
$903$		0			0
$904$			15.3984i			0.512143i
$905$	4.86326	−	9.02655i	0.161660	−	0.300053i
$906$		0			0
$907$	−34.7376	+	34.7376i	−1.15344	+	1.15344i	−0.167584	+	0.985858i	$0.553597\pi$
$907$	−34.7376	+	34.7376i	−1.15344	+	1.15344i	−0.985858	+	0.167584i	$0.946403\pi$
$908$	−5.51878	−	5.51878i	−0.183147	−	0.183147i
$909$		0			0
$910$	6.49876	+	21.6815i	0.215432	+	0.718735i
$911$			30.8489i			1.02207i	0.859560	+	0.511035i	$0.170738\pi$
$911$			30.8489i			1.02207i	−0.859560	+	0.511035i	$0.829262\pi$
$912$		0			0
$913$	3.31645	−	3.31645i	0.109759	−	0.109759i
$914$	−11.6826			−0.386427
$915$		0			0
$916$	−9.94379			−0.328552
$917$	25.6754	+	25.6754i	0.847875	+	0.847875i
$918$		0			0
$919$			31.7256i			1.04653i	0.852170	+	0.523265i	$0.175286\pi$
$919$			31.7256i			1.04653i	−0.852170	+	0.523265i	$0.824714\pi$
$920$	−17.2737	−	9.30657i	−0.569496	−	0.306828i
$921$		0			0
$922$	12.8120	−	12.8120i	0.421941	−	0.421941i
$923$	20.3951	−	20.3951i	0.671313	−	0.671313i
$924$		0			0
$925$	3.63291	+	0.747652i	0.119449	+	0.0245827i
$926$			29.3441i			0.964308i
$927$		0			0
$928$	3.99153	−	3.99153i	0.131028	−	0.131028i
$929$		−	5.78107i		−	0.189671i	−0.995493	−	0.0948354i	$-0.969768\pi$
$929$		−	5.78107i		−	0.189671i	0.995493	−	0.0948354i	$-0.0302325\pi$
$930$		0			0
$931$	−3.93241	−	5.22670i	−0.128880	−	0.171298i
$932$	−5.11116	−	5.11116i	−0.167422	−	0.167422i
$933$		0			0
$934$	25.5794			0.836985
$935$	3.19361	+	10.6547i	0.104442	+	0.348446i
$936$		0			0
$937$	12.5571	+	12.5571i	0.410222	+	0.410222i	0.881816	−	0.471594i	$-0.156321\pi$
$937$	12.5571	+	12.5571i	0.410222	+	0.410222i	−0.471594	+	0.881816i	$0.656321\pi$
$938$	−0.809677	+	0.809677i	−0.0264369	+	0.0264369i
$939$		0			0
$940$	−1.51285	+	0.453459i	−0.0493438	+	0.0147902i
$941$		−	26.4197i		−	0.861258i	−0.902529	−	0.430629i	$-0.858292\pi$
$941$		−	26.4197i		−	0.861258i	0.902529	−	0.430629i	$-0.141708\pi$
$942$		0			0
$943$	−9.03049	−	9.03049i	−0.294073	−	0.294073i
$944$	2.77684			0.0903786
$945$		0			0
$946$			2.17136i			0.0705971i
$947$	−0.351274	−	0.351274i	−0.0114149	−	0.0114149i	0.701376	−	0.712791i	$-0.252569\pi$
$947$	−0.351274	−	0.351274i	−0.0114149	−	0.0114149i	−0.712791	+	0.701376i	$0.752569\pi$
$948$		0			0
$949$	−6.43677			−0.208946
$950$	−19.6995	+	9.32355i	−0.639137	+	0.302496i
$951$		0			0
$952$	−10.2502	+	10.2502i	−0.332209	+	0.332209i
$953$	37.8897	+	37.8897i	1.22737	+	1.22737i	0.964956	+	0.262411i	$0.0845176\pi$
$953$	37.8897	+	37.8897i	1.22737	+	1.22737i	0.262411	+	0.964956i	$0.415482\pi$
$954$		0			0
$955$	−9.57522	−	5.15886i	−0.309847	−	0.166937i
$956$	9.30530			0.300955
$957$		0			0
$958$	1.40004	+	1.40004i	0.0452331	+	0.0452331i
$959$			11.1832i			0.361124i
$960$		0			0
$961$	21.2031			0.683971
$962$	2.26414	−	2.26414i	0.0729989	−	0.0729989i
$963$		0			0
$964$	−8.31390			−0.267773
$965$	−9.38020	−	31.2947i	−0.301959	−	1.00741i
$966$		0			0
$967$	29.9302	+	29.9302i	0.962489	+	0.962489i	0.999321	−	0.0368326i	$-0.0117268\pi$
$967$	29.9302	+	29.9302i	0.962489	+	0.962489i	−0.0368326	+	0.999321i	$0.511727\pi$
$968$	−7.32026	−	7.32026i	−0.235282	−	0.235282i
$969$		0			0
$970$	12.3747	−	22.9684i	0.397328	−	0.737470i
$971$			20.7610i			0.666252i	0.942882	+	0.333126i	$0.108103\pi$
$971$			20.7610i			0.666252i	−0.942882	+	0.333126i	$0.891897\pi$
$972$		0			0
$973$	−3.41307	+	3.41307i	−0.109418	+	0.109418i
$974$		−	2.61060i		−	0.0836489i
$975$		0			0
$976$	−6.17945			−0.197799
$977$	−3.40331	+	3.40331i	−0.108882	+	0.108882i	−0.759449	−	0.650567i	$-0.774531\pi$
$977$	−3.40331	+	3.40331i	−0.108882	+	0.108882i	0.650567	+	0.759449i	$0.274531\pi$
$978$		0			0
$979$	−13.4677			−0.430429
$980$	−2.95392	−	1.59149i	−0.0943595	−	0.0508383i
$981$		0			0
$982$	−3.96554	+	3.96554i	−0.126545	+	0.126545i
$983$	29.7757	+	29.7757i	0.949699	+	0.949699i	0.998794	−	0.0490954i	$-0.0156339\pi$
$983$	29.7757	+	29.7757i	0.949699	+	0.949699i	−0.0490954	+	0.998794i	$0.515634\pi$
$984$		0			0
$985$	−7.55707	−	25.2123i	−0.240788	−	0.803330i
$986$	−34.8932			−1.11122
$987$		0			0
$988$	−2.63261	+	18.6299i	−0.0837544	+	0.592696i
$989$			23.6767i			0.752875i
$990$		0			0
$991$			45.0530i			1.43116i	0.698532	+	0.715578i	$0.253837\pi$
$991$			45.0530i			1.43116i	−0.698532	+	0.715578i	$0.746163\pi$
$992$	2.21324	+	2.21324i	0.0702705	+	0.0702705i
$993$		0			0
$994$		−	15.6701i		−	0.497026i
$995$	24.5042	−	45.4816i	0.776836	−	1.44186i
$996$		0			0
$997$	−0.131537	−	0.131537i	−0.00416581	−	0.00416581i	0.705021	−	0.709187i	$-0.250938\pi$
$997$	−0.131537	−	0.131537i	−0.00416581	−	0.00416581i	−0.709187	+	0.705021i	$0.750938\pi$
$998$	−13.3539	−	13.3539i	−0.422711	−	0.422711i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.p.b.37.4		16
3.2	odd	2		190.2.f.b.37.5	yes	16
5.3	odd	4	inner	1710.2.p.b.1063.8		16
15.2	even	4		950.2.f.c.493.5		16
15.8	even	4		190.2.f.b.113.4	yes	16
15.14	odd	2		950.2.f.c.607.4		16
19.18	odd	2	inner	1710.2.p.b.37.8		16
57.56	even	2		190.2.f.b.37.4	✓	16
95.18	even	4	inner	1710.2.p.b.1063.4		16
285.113	odd	4		190.2.f.b.113.5	yes	16
285.227	odd	4		950.2.f.c.493.4		16
285.284	even	2		950.2.f.c.607.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.f.b.37.4	✓	16	57.56	even	2
190.2.f.b.37.5	yes	16	3.2	odd	2
190.2.f.b.113.4	yes	16	15.8	even	4
190.2.f.b.113.5	yes	16	285.113	odd	4
950.2.f.c.493.4		16	285.227	odd	4
950.2.f.c.493.5		16	15.2	even	4
950.2.f.c.607.4		16	15.14	odd	2
950.2.f.c.607.5		16	285.284	even	2
1710.2.p.b.37.4		16	1.1	even	1	trivial
1710.2.p.b.37.8		16	19.18	odd	2	inner
1710.2.p.b.1063.4		16	95.18	even	4	inner
1710.2.p.b.1063.8		16	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.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(1.96854 + 1.06059i) q^{5} +(1.65823 + 1.65823i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(1.96854 + 1.06059i) q^{5} +(1.65823 + 1.65823i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.14192 + 0.642014i) q^{10} +0.804733 q^{11} +(-3.05219 - 3.05219i) q^{13} -2.34509 q^{14} -1.00000 q^{16} +(4.37090 + 4.37090i) q^{17} +(3.48315 - 2.62062i) q^{19} +(1.06059 - 1.96854i) q^{20} +(-0.569032 + 0.569032i) q^{22} +(-6.20477 + 6.20477i) q^{23} +(2.75028 + 4.17564i) q^{25} +4.31645 q^{26} +(1.65823 - 1.65823i) q^{28} +5.64487 q^{29} +3.13000i q^{31} +(0.707107 - 0.707107i) q^{32} -6.18139 q^{34} +(1.50558 + 5.02299i) q^{35} +(0.524538 - 0.524538i) q^{37} +(-0.609901 + 4.31602i) q^{38} +(0.642014 + 2.14192i) q^{40} +1.45541i q^{41} +(1.90794 - 1.90794i) q^{43} -0.804733i q^{44} -8.77487i q^{46} +(-0.499434 - 0.499434i) q^{47} -1.50057i q^{49} +(-4.89736 - 1.00788i) q^{50} +(-3.05219 + 3.05219i) q^{52} +(-3.40535 - 3.40535i) q^{53} +(1.58415 + 0.853494i) q^{55} +2.34509i q^{56} +(-3.99153 + 3.99153i) q^{58} -2.77684 q^{59} +6.17945 q^{61} +(-2.21324 - 2.21324i) q^{62} +1.00000i q^{64} +(-2.77122 - 9.24550i) q^{65} +(0.345265 - 0.345265i) q^{67} +(4.37090 - 4.37090i) q^{68} +(-4.61639 - 2.48718i) q^{70} +6.68211i q^{71} +(1.05445 - 1.05445i) q^{73} +0.741809i q^{74} +(-2.62062 - 3.48315i) q^{76} +(1.33443 + 1.33443i) q^{77} +7.16924 q^{79} +(-1.96854 - 1.06059i) q^{80} +(-1.02913 - 1.02913i) q^{82} +(4.12119 - 4.12119i) q^{83} +(3.96854 + 13.2400i) q^{85} +2.69824i q^{86} +(0.569032 + 0.569032i) q^{88} -16.7356 q^{89} -10.1225i q^{91} +(6.20477 + 6.20477i) q^{92} +0.706307 q^{94} +(9.63613 - 1.46458i) q^{95} +(-8.25033 + 8.25033i) q^{97} +(1.06106 + 1.06106i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} - 16 q^{16} + 32 q^{17} - 8 q^{20} + 8 q^{23} + 32 q^{25} + 32 q^{26} + 8 q^{28} + 24 q^{35} - 8 q^{38} + 24 q^{43} - 32 q^{47} - 56 q^{55} - 64 q^{61} + 8 q^{62} + 32 q^{68} + 16 q^{73} - 16 q^{76} - 72 q^{77} + 40 q^{82} + 16 q^{83} + 32 q^{85} - 8 q^{92} - 24 q^{95}+O(q^{100}) \) 16 * q + 8 * q^7 - 16 * q^16 + 32 * q^17 - 8 * q^20 + 8 * q^23 + 32 * q^25 + 32 * q^26 + 8 * q^28 + 24 * q^35 - 8 * q^38 + 24 * q^43 - 32 * q^47 - 56 * q^55 - 64 * q^61 + 8 * q^62 + 32 * q^68 + 16 * q^73 - 16 * q^76 - 72 * q^77 + 40 * q^82 + 16 * q^83 + 32 * q^85 - 8 * q^92 - 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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